id	sid	tid	token	lemma	pos
ejpam-6679	1	1	european	european	PROPN
ejpam-6679	1	2	journal	journal	PROPN
ejpam-6679	1	3	of	of	ADP
ejpam-6679	1	4	pure	pure	ADJ
ejpam-6679	1	5	and	and	CCONJ
ejpam-6679	1	6	applied	applied	ADJ
ejpam-6679	1	7	mathematics	mathematic	NOUN
ejpam-6679	1	8	2025	2025	NUM
ejpam-6679	1	9	,	,	PUNCT
ejpam-6679	1	10	vol	vol	NOUN
ejpam-6679	1	11	.	.	PROPN
ejpam-6679	1	12	18	18	NUM
ejpam-6679	1	13	,	,	PUNCT
ejpam-6679	1	14	issue	issue	NOUN
ejpam-6679	1	15	4	4	NUM
ejpam-6679	1	16	,	,	PUNCT
ejpam-6679	1	17	article	article	NOUN
ejpam-6679	1	18	number	number	NOUN
ejpam-6679	1	19	6679	6679	NUM
ejpam-6679	1	20	issn	issn	PROPN
ejpam-6679	1	21	1307	1307	NUM
ejpam-6679	1	22	-	-	SYM
ejpam-6679	1	23	5543	5543	NUM
ejpam-6679	1	24	–	–	PUNCT
ejpam-6679	1	25	ejpam.com	ejpam.com	X
ejpam-6679	1	26	published	publish	VERB
ejpam-6679	1	27	by	by	ADP
ejpam-6679	1	28	new	new	PROPN
ejpam-6679	1	29	york	york	PROPN
ejpam-6679	1	30	business	business	PROPN
ejpam-6679	1	31	global	global	PROPN
ejpam-6679	1	32	menger	menger	PROPN
ejpam-6679	1	33	algebras	algebras	PROPN
ejpam-6679	1	34	of	of	ADP
ejpam-6679	1	35	alternating	alternate	VERB
ejpam-6679	1	36	terms	term	NOUN
ejpam-6679	2	1	thawhat	thawhat	PROPN
ejpam-6679	2	2	changphas	changphas	PROPN
ejpam-6679	2	3	department	department	PROPN
ejpam-6679	2	4	of	of	ADP
ejpam-6679	2	5	mathematics	mathematic	NOUN
ejpam-6679	2	6	,	,	PUNCT
ejpam-6679	2	7	faculty	faculty	NOUN
ejpam-6679	2	8	of	of	ADP
ejpam-6679	2	9	science	science	NOUN
ejpam-6679	2	10	,	,	PUNCT
ejpam-6679	2	11	khon	khon	PROPN
ejpam-6679	2	12	kaen	kaen	PROPN
ejpam-6679	2	13	university	university	PROPN
ejpam-6679	2	14	,	,	PUNCT
ejpam-6679	2	15	khon	khon	PROPN
ejpam-6679	2	16	kaen	kaen	PROPN
ejpam-6679	2	17	40002	40002	NUM
ejpam-6679	2	18	,	,	PUNCT
ejpam-6679	2	19	thailand	thailand	PROPN
ejpam-6679	2	20	abstract	abstract	PROPN
ejpam-6679	2	21	.	.	PUNCT
ejpam-6679	3	1	let	let	VERB
ejpam-6679	3	2	τn	τn	VERB
ejpam-6679	3	3	=	=	PUNCT
ejpam-6679	3	4	(	(	PUNCT
ejpam-6679	3	5	ni)i∈i	ni)i∈i	NUM
ejpam-6679	3	6	be	be	VERB
ejpam-6679	3	7	a	a	DET
ejpam-6679	3	8	particular	particular	ADJ
ejpam-6679	3	9	language	language	NOUN
ejpam-6679	3	10	(	(	PUNCT
ejpam-6679	3	11	type	type	NOUN
ejpam-6679	3	12	)	)	PUNCT
ejpam-6679	3	13	of	of	ADP
ejpam-6679	3	14	algebras	algebra	NOUN
ejpam-6679	3	15	such	such	ADJ
ejpam-6679	3	16	that	that	SCONJ
ejpam-6679	3	17	ni	ni	PROPN
ejpam-6679	3	18	=	=	PROPN
ejpam-6679	3	19	n	n	PROPN
ejpam-6679	3	20	for	for	ADP
ejpam-6679	3	21	all	all	DET
ejpam-6679	3	22	i	i	PRON
ejpam-6679	3	23	in	in	ADP
ejpam-6679	3	24	i	i	PRON
ejpam-6679	3	25	;	;	PUNCT
ejpam-6679	3	26	n	n	PRON
ejpam-6679	3	27	is	be	AUX
ejpam-6679	3	28	a	a	DET
ejpam-6679	3	29	positive	positive	ADJ
ejpam-6679	3	30	integer	integer	NOUN
ejpam-6679	3	31	.	.	PUNCT
ejpam-6679	4	1	this	this	DET
ejpam-6679	4	2	paper	paper	NOUN
ejpam-6679	4	3	aims	aim	VERB
ejpam-6679	4	4	to	to	PART
ejpam-6679	4	5	introduce	introduce	VERB
ejpam-6679	4	6	n	n	CCONJ
ejpam-6679	4	7	-	-	PUNCT
ejpam-6679	4	8	ary	ary	NOUN
ejpam-6679	4	9	alternating	alternate	VERB
ejpam-6679	4	10	terms	term	NOUN
ejpam-6679	4	11	(	(	PUNCT
ejpam-6679	4	12	alt	alt	VERB
ejpam-6679	4	13	-	-	PUNCT
ejpam-6679	4	14	terms	term	NOUN
ejpam-6679	4	15	)	)	PUNCT
ejpam-6679	4	16	of	of	ADP
ejpam-6679	4	17	type	type	NOUN
ejpam-6679	4	18	τn	τn	PROPN
ejpam-6679	4	19	,	,	PUNCT
ejpam-6679	4	20	based	base	VERB
ejpam-6679	4	21	on	on	ADP
ejpam-6679	4	22	the	the	DET
ejpam-6679	4	23	alternating	alternate	VERB
ejpam-6679	4	24	group	group	NOUN
ejpam-6679	4	25	alt(n	alt(n	PROPN
ejpam-6679	4	26	)	)	PUNCT
ejpam-6679	4	27	of	of	ADP
ejpam-6679	4	28	degree	degree	NOUN
ejpam-6679	4	29	n.	n.	NOUN
ejpam-6679	4	30	we	we	PRON
ejpam-6679	4	31	demonstrate	demonstrate	VERB
ejpam-6679	4	32	that	that	SCONJ
ejpam-6679	4	33	the	the	DET
ejpam-6679	4	34	set	set	NOUN
ejpam-6679	4	35	of	of	ADP
ejpam-6679	4	36	all	all	DET
ejpam-6679	4	37	n	n	CCONJ
ejpam-6679	4	38	-	-	PUNCT
ejpam-6679	4	39	ary	ary	NOUN
ejpam-6679	4	40	alternating	alternate	VERB
ejpam-6679	4	41	terms	term	NOUN
ejpam-6679	4	42	of	of	ADP
ejpam-6679	4	43	type	type	NOUN
ejpam-6679	4	44	τn	τn	ADP
ejpam-6679	4	45	forms	form	VERB
ejpam-6679	4	46	a	a	DET
ejpam-6679	4	47	menger	menger	PROPN
ejpam-6679	4	48	algebra	algebra	PROPN
ejpam-6679	4	49	of	of	ADP
ejpam-6679	4	50	rank	rank	NOUN
ejpam-6679	4	51	n	n	NUM
ejpam-6679	4	52	;	;	PUNCT
ejpam-6679	4	53	such	such	ADJ
ejpam-6679	4	54	algebra	algebra	NOUN
ejpam-6679	4	55	is	be	AUX
ejpam-6679	4	56	denoted	denote	VERB
ejpam-6679	4	57	by	by	ADP
ejpam-6679	4	58	walt(n	walt(n	PROPN
ejpam-6679	4	59	)	)	PUNCT
ejpam-6679	4	60	τn	τn	X
ejpam-6679	4	61	(	(	PUNCT
ejpam-6679	4	62	ωn	ωn	NUM
ejpam-6679	4	63	)	)	PUNCT
ejpam-6679	4	64	.	.	PUNCT
ejpam-6679	5	1	we	we	PRON
ejpam-6679	5	2	prove	prove	VERB
ejpam-6679	5	3	that	that	SCONJ
ejpam-6679	5	4	the	the	DET
ejpam-6679	5	5	algebra	algebra	PROPN
ejpam-6679	5	6	walt(n	walt(n	NOUN
ejpam-6679	5	7	)	)	PUNCT
ejpam-6679	5	8	τn	τn	X
ejpam-6679	5	9	(	(	PUNCT
ejpam-6679	5	10	ωn	ωn	X
ejpam-6679	5	11	)	)	PUNCT
ejpam-6679	5	12	is	be	AUX
ejpam-6679	5	13	free	free	ADJ
ejpam-6679	5	14	with	with	ADP
ejpam-6679	5	15	respect	respect	NOUN
ejpam-6679	5	16	to	to	ADP
ejpam-6679	5	17	the	the	DET
ejpam-6679	5	18	variety	variety	NOUN
ejpam-6679	5	19	vmenger	vmenger	NOUN
ejpam-6679	5	20	of	of	ADP
ejpam-6679	5	21	menger	menger	PROPN
ejpam-6679	5	22	algebras	algebras	PROPN
ejpam-6679	5	23	of	of	ADP
ejpam-6679	5	24	rank	rank	PROPN
ejpam-6679	5	25	n	n	CCONJ
ejpam-6679	5	26	,	,	PUNCT
ejpam-6679	5	27	and	and	CCONJ
ejpam-6679	5	28	it	it	PRON
ejpam-6679	5	29	is	be	AUX
ejpam-6679	5	30	freely	freely	ADV
ejpam-6679	5	31	generated	generate	VERB
ejpam-6679	5	32	by	by	ADP
ejpam-6679	5	33	the	the	DET
ejpam-6679	5	34	set	set	NOUN
ejpam-6679	5	35	{	{	PUNCT
ejpam-6679	5	36	ω(i	ω(i	PROPN
ejpam-6679	5	37	,	,	PUNCT
ejpam-6679	5	38	σ	σ	PROPN
ejpam-6679	5	39	)	)	PUNCT
ejpam-6679	5	40	:	:	PUNCT
ejpam-6679	6	1	i	i	PRON
ejpam-6679	6	2	∈	∈	VERB
ejpam-6679	6	3	i	i	PRON
ejpam-6679	6	4	,	,	PUNCT
ejpam-6679	6	5	σ	σ	PROPN
ejpam-6679	6	6	∈	∈	PROPN
ejpam-6679	6	7	alt(n	alt(n	PROPN
ejpam-6679	6	8	)	)	PUNCT
ejpam-6679	6	9	}	}	PUNCT
ejpam-6679	6	10	.	.	PUNCT
ejpam-6679	7	1	we	we	PRON
ejpam-6679	7	2	introduce	introduce	VERB
ejpam-6679	7	3	alternating	alternate	VERB
ejpam-6679	7	4	hypersubstitutions	hypersubstitution	NOUN
ejpam-6679	7	5	of	of	ADP
ejpam-6679	7	6	type	type	NOUN
ejpam-6679	7	7	τn	τn	ADP
ejpam-6679	7	8	and	and	CCONJ
ejpam-6679	7	9	prove	prove	VERB
ejpam-6679	7	10	that	that	SCONJ
ejpam-6679	7	11	the	the	DET
ejpam-6679	7	12	extension	extension	NOUN
ejpam-6679	7	13	of	of	ADP
ejpam-6679	7	14	an	an	DET
ejpam-6679	7	15	alternating	alternate	VERB
ejpam-6679	7	16	hypersubstitution	hypersubstitution	NOUN
ejpam-6679	7	17	of	of	ADP
ejpam-6679	7	18	type	type	NOUN
ejpam-6679	7	19	τn	τn	ADP
ejpam-6679	7	20	acts	act	NOUN
ejpam-6679	7	21	as	as	ADP
ejpam-6679	7	22	an	an	DET
ejpam-6679	7	23	endomorphism	endomorphism	NOUN
ejpam-6679	7	24	on	on	ADP
ejpam-6679	7	25	the	the	DET
ejpam-6679	7	26	algebra	algebra	PROPN
ejpam-6679	7	27	walt(n	walt(n	NOUN
ejpam-6679	7	28	)	)	PUNCT
ejpam-6679	7	29	τn	τn	ADP
ejpam-6679	7	30	(	(	PUNCT
ejpam-6679	7	31	ωn	ωn	NOUN
ejpam-6679	7	32	)	)	PUNCT
ejpam-6679	7	33	.	.	PUNCT
ejpam-6679	8	1	furthermore	furthermore	ADV
ejpam-6679	8	2	,	,	PUNCT
ejpam-6679	8	3	we	we	PRON
ejpam-6679	8	4	have	have	VERB
ejpam-6679	8	5	that	that	SCONJ
ejpam-6679	8	6	the	the	DET
ejpam-6679	8	7	set	set	NOUN
ejpam-6679	8	8	of	of	ADP
ejpam-6679	8	9	all	all	PRON
ejpam-6679	8	10	alternating	alternate	VERB
ejpam-6679	8	11	hypersubstitutions	hypersubstitution	NOUN
ejpam-6679	8	12	of	of	ADP
ejpam-6679	8	13	type	type	NOUN
ejpam-6679	8	14	τn	τn	ADP
ejpam-6679	8	15	forms	form	NOUN
ejpam-6679	8	16	a	a	DET
ejpam-6679	8	17	monoid	monoid	NOUN
ejpam-6679	8	18	,	,	PUNCT
ejpam-6679	8	19	denoted	denote	VERB
ejpam-6679	8	20	by	by	ADP
ejpam-6679	8	21	hypalt(n)(τn	hypalt(n)(τn	PROPN
ejpam-6679	8	22	)	)	PUNCT
ejpam-6679	8	23	.	.	PUNCT
ejpam-6679	9	1	finally	finally	ADV
ejpam-6679	9	2	,	,	PUNCT
ejpam-6679	9	3	we	we	PRON
ejpam-6679	9	4	establish	establish	VERB
ejpam-6679	9	5	that	that	SCONJ
ejpam-6679	9	6	the	the	DET
ejpam-6679	9	7	set	set	NOUN
ejpam-6679	9	8	of	of	ADP
ejpam-6679	9	9	all	all	DET
ejpam-6679	9	10	identities	identity	NOUN
ejpam-6679	9	11	s	s	PROPN
ejpam-6679	9	12	≈	≈	PROPN
ejpam-6679	9	13	t	t	PROPN
ejpam-6679	9	14	of	of	ADP
ejpam-6679	9	15	a	a	DET
ejpam-6679	9	16	variety	variety	NOUN
ejpam-6679	9	17	v	v	NOUN
ejpam-6679	9	18	of	of	ADP
ejpam-6679	9	19	type	type	NOUN
ejpam-6679	9	20	τn	τn	NOUN
ejpam-6679	9	21	,	,	PUNCT
ejpam-6679	9	22	where	where	SCONJ
ejpam-6679	9	23	s	s	PRON
ejpam-6679	9	24	and	and	CCONJ
ejpam-6679	9	25	t	t	PROPN
ejpam-6679	9	26	are	be	AUX
ejpam-6679	9	27	n	n	PRON
ejpam-6679	9	28	-	-	PUNCT
ejpam-6679	9	29	ary	ary	NOUN
ejpam-6679	9	30	alternating	alternate	VERB
ejpam-6679	9	31	terms	term	NOUN
ejpam-6679	9	32	of	of	ADP
ejpam-6679	9	33	type	type	NOUN
ejpam-6679	9	34	τn	τn	PROPN
ejpam-6679	9	35	,	,	PUNCT
ejpam-6679	9	36	constitutes	constitute	VERB
ejpam-6679	9	37	a	a	DET
ejpam-6679	9	38	congruence	congruence	NOUN
ejpam-6679	9	39	on	on	ADP
ejpam-6679	9	40	the	the	DET
ejpam-6679	9	41	algebra	algebra	PROPN
ejpam-6679	9	42	walt(n	walt(n	NOUN
ejpam-6679	9	43	)	)	PUNCT
ejpam-6679	9	44	τn	τn	ADP
ejpam-6679	9	45	(	(	PUNCT
ejpam-6679	9	46	ωn	ωn	NOUN
ejpam-6679	9	47	)	)	PUNCT
ejpam-6679	9	48	.	.	PUNCT
ejpam-6679	10	1	according	accord	VERB
ejpam-6679	10	2	to	to	ADP
ejpam-6679	10	3	the	the	DET
ejpam-6679	10	4	monoid	monoid	NOUN
ejpam-6679	10	5	hypalt(n)(τn	hypalt(n)(τn	PROPN
ejpam-6679	10	6	)	)	PUNCT
ejpam-6679	10	7	,	,	PUNCT
ejpam-6679	10	8	we	we	PRON
ejpam-6679	10	9	investigate	investigate	VERB
ejpam-6679	10	10	alternating	alternate	VERB
ejpam-6679	10	11	hyperidentities	hyperidentitie	NOUN
ejpam-6679	10	12	and	and	CCONJ
ejpam-6679	10	13	alternating	alternate	VERB
ejpam-6679	10	14	closed	closed	ADJ
ejpam-6679	10	15	varieties	variety	NOUN
ejpam-6679	10	16	.	.	PUNCT
ejpam-6679	11	1	2020	2020	NUM
ejpam-6679	11	2	mathematics	mathematic	NOUN
ejpam-6679	11	3	subject	subject	NOUN
ejpam-6679	11	4	classifications	classification	NOUN
ejpam-6679	11	5	:	:	PUNCT
ejpam-6679	11	6	20m35	20m35	NUM
ejpam-6679	11	7	,	,	PUNCT
ejpam-6679	11	8	20n15	20n15	NUM
ejpam-6679	11	9	,	,	PUNCT
ejpam-6679	11	10	08a40	08a40	NOUN
ejpam-6679	11	11	,	,	PUNCT
ejpam-6679	11	12	08a60	08a60	NUM
ejpam-6679	11	13	,	,	PUNCT
ejpam-6679	11	14	08a02	08a02	NUM
ejpam-6679	11	15	key	key	ADJ
ejpam-6679	11	16	words	word	NOUN
ejpam-6679	11	17	and	and	CCONJ
ejpam-6679	11	18	phrases	phrase	NOUN
ejpam-6679	11	19	:	:	PUNCT
ejpam-6679	11	20	alternating	alternate	VERB
ejpam-6679	11	21	group	group	NOUN
ejpam-6679	11	22	,	,	PUNCT
ejpam-6679	11	23	n	n	CCONJ
ejpam-6679	11	24	-	-	PUNCT
ejpam-6679	11	25	ary	ary	NOUN
ejpam-6679	11	26	alternating	alternate	VERB
ejpam-6679	11	27	term	term	NOUN
ejpam-6679	11	28	,	,	PUNCT
ejpam-6679	11	29	menger	menger	PROPN
ejpam-6679	11	30	algebra	algebra	PROPN
ejpam-6679	11	31	,	,	PUNCT
ejpam-6679	11	32	alternating	alternate	VERB
ejpam-6679	11	33	hypersubstitution	hypersubstitution	NOUN
ejpam-6679	11	34	,	,	PUNCT
ejpam-6679	11	35	alternating	alternate	VERB
ejpam-6679	11	36	hyperidentity	hyperidentity	NOUN
ejpam-6679	11	37	,	,	PUNCT
ejpam-6679	11	38	alternating	alternate	VERB
ejpam-6679	11	39	closed	closed	ADJ
ejpam-6679	11	40	variety	variety	NOUN
ejpam-6679	11	41	1	1	NUM
ejpam-6679	11	42	.	.	PUNCT
ejpam-6679	11	43	introduction	introduction	NOUN
ejpam-6679	11	44	and	and	CCONJ
ejpam-6679	11	45	preliminaries	preliminary	NOUN
ejpam-6679	11	46	karl	karl	PROPN
ejpam-6679	11	47	menger	menger	PROPN
ejpam-6679	11	48	(	(	PUNCT
ejpam-6679	11	49	cf	cf	NOUN
ejpam-6679	11	50	.	.	PUNCT
ejpam-6679	12	1	[	[	X
ejpam-6679	12	2	1	1	NUM
ejpam-6679	12	3	]	]	PUNCT
ejpam-6679	12	4	,	,	PUNCT
ejpam-6679	12	5	pp	pp	ADJ
ejpam-6679	12	6	.	.	PUNCT
ejpam-6679	12	7	21	21	NUM
ejpam-6679	12	8	-	-	SYM
ejpam-6679	12	9	24	24	NUM
ejpam-6679	12	10	)	)	PUNCT
ejpam-6679	12	11	introduced	introduce	VERB
ejpam-6679	12	12	the	the	DET
ejpam-6679	12	13	notion	notion	NOUN
ejpam-6679	12	14	of	of	ADP
ejpam-6679	12	15	menger	menger	PROPN
ejpam-6679	12	16	algebra	algebra	PROPN
ejpam-6679	12	17	as	as	ADP
ejpam-6679	12	18	a	a	DET
ejpam-6679	12	19	generalization	generalization	NOUN
ejpam-6679	12	20	of	of	ADP
ejpam-6679	12	21	the	the	DET
ejpam-6679	12	22	notion	notion	NOUN
ejpam-6679	12	23	of	of	ADP
ejpam-6679	12	24	semigroup	semigroup	PROPN
ejpam-6679	12	25	;	;	PUNCT
ejpam-6679	12	26	such	such	ADJ
ejpam-6679	12	27	algebras	algebras	PROPN
ejpam-6679	12	28	satisfy	satisfy	VERB
ejpam-6679	12	29	superassociative	superassociative	ADJ
ejpam-6679	12	30	law	law	NOUN
ejpam-6679	12	31	,	,	PUNCT
ejpam-6679	12	32	this	this	PRON
ejpam-6679	12	33	is	be	AUX
ejpam-6679	12	34	a	a	DET
ejpam-6679	12	35	generalization	generalization	NOUN
ejpam-6679	12	36	of	of	ADP
ejpam-6679	12	37	associative	associative	ADJ
ejpam-6679	12	38	law	law	NOUN
ejpam-6679	12	39	.	.	PUNCT
ejpam-6679	13	1	throughout	throughout	ADP
ejpam-6679	13	2	,	,	PUNCT
ejpam-6679	13	3	n	n	PRON
ejpam-6679	13	4	stands	stand	VERB
ejpam-6679	13	5	for	for	ADP
ejpam-6679	13	6	a	a	DET
ejpam-6679	13	7	positive	positive	ADJ
ejpam-6679	13	8	integer	integer	NOUN
ejpam-6679	13	9	.	.	PUNCT
ejpam-6679	14	1	for	for	ADP
ejpam-6679	14	2	a	a	DET
ejpam-6679	14	3	nonempty	nonempty	ADJ
ejpam-6679	14	4	set	set	VERB
ejpam-6679	14	5	m	m	PROPN
ejpam-6679	14	6	,	,	PUNCT
ejpam-6679	14	7	an	an	DET
ejpam-6679	14	8	n	n	CCONJ
ejpam-6679	14	9	-	-	PUNCT
ejpam-6679	14	10	ary	ary	NOUN
ejpam-6679	14	11	operation	operation	NOUN
ejpam-6679	14	12	(	(	PUNCT
ejpam-6679	14	13	n	n	CCONJ
ejpam-6679	14	14	-	-	PUNCT
ejpam-6679	14	15	ary	ary	NOUN
ejpam-6679	14	16	function	function	NOUN
ejpam-6679	14	17	)	)	PUNCT
ejpam-6679	14	18	on	on	ADP
ejpam-6679	14	19	m	m	PROPN
ejpam-6679	14	20	is	be	AUX
ejpam-6679	14	21	f	f	X
ejpam-6679	14	22	:	:	PUNCT
ejpam-6679	14	23	mn	mn	PROPN
ejpam-6679	14	24	→m	→m	PUNCT
ejpam-6679	14	25	.	.	PUNCT
ejpam-6679	15	1	definition	definition	NOUN
ejpam-6679	15	2	1	1	NUM
ejpam-6679	15	3	.	.	PUNCT
ejpam-6679	16	1	a	a	DET
ejpam-6679	16	2	pair	pair	NOUN
ejpam-6679	16	3	(	(	PUNCT
ejpam-6679	16	4	m	m	PROPN
ejpam-6679	16	5	,	,	PUNCT
ejpam-6679	16	6	f	f	X
ejpam-6679	16	7	)	)	PUNCT
ejpam-6679	16	8	consists	consist	VERB
ejpam-6679	16	9	of	of	ADP
ejpam-6679	16	10	a	a	DET
ejpam-6679	16	11	nonempty	nonempty	ADV
ejpam-6679	16	12	set	set	VERB
ejpam-6679	16	13	m	m	PROPN
ejpam-6679	16	14	and	and	CCONJ
ejpam-6679	16	15	an	an	DET
ejpam-6679	16	16	n	n	CCONJ
ejpam-6679	16	17	-	-	PUNCT
ejpam-6679	16	18	ary	ary	PROPN
ejpam-6679	16	19	operation	operation	NOUN
ejpam-6679	16	20	f	f	PROPN
ejpam-6679	16	21	on	on	ADP
ejpam-6679	16	22	m	m	PROPN
ejpam-6679	16	23	is	be	AUX
ejpam-6679	16	24	a	a	DET
ejpam-6679	16	25	menger	menger	PROPN
ejpam-6679	16	26	algebra	algebra	NOUN
ejpam-6679	16	27	of	of	ADP
ejpam-6679	16	28	rank	rank	NOUN
ejpam-6679	16	29	n	n	PROPN
ejpam-6679	16	30	if	if	SCONJ
ejpam-6679	16	31	f(f(µ	f(f(µ	PROPN
ejpam-6679	16	32	,	,	PUNCT
ejpam-6679	16	33	ν1	ν1	NOUN
ejpam-6679	16	34	,	,	PUNCT
ejpam-6679	16	35	.	.	PUNCT
ejpam-6679	16	36	.	.	PUNCT
ejpam-6679	17	1	.	.	PUNCT
ejpam-6679	18	1	,	,	PUNCT
ejpam-6679	18	2	νn	νn	NOUN
ejpam-6679	18	3	)	)	PUNCT
ejpam-6679	18	4	,	,	PUNCT
ejpam-6679	18	5	o1	o1	NOUN
ejpam-6679	18	6	,	,	PUNCT
ejpam-6679	18	7	.	.	PUNCT
ejpam-6679	18	8	.	.	PUNCT
ejpam-6679	19	1	.	.	PUNCT
ejpam-6679	20	1	,	,	PUNCT
ejpam-6679	20	2	on	on	ADP
ejpam-6679	20	3	)	)	PUNCT
ejpam-6679	20	4	=	=	SYM
ejpam-6679	20	5	f(µ	f(µ	NOUN
ejpam-6679	20	6	,	,	PUNCT
ejpam-6679	20	7	f(ν1	f(ν1	NOUN
ejpam-6679	20	8	,	,	PUNCT
ejpam-6679	20	9	o1	o1	NOUN
ejpam-6679	20	10	,	,	PUNCT
ejpam-6679	20	11	.	.	PUNCT
ejpam-6679	20	12	.	.	PUNCT
ejpam-6679	20	13	.	.	PUNCT
ejpam-6679	21	1	,	,	PUNCT
ejpam-6679	21	2	on	on	ADP
ejpam-6679	21	3	)	)	PUNCT
ejpam-6679	21	4	,	,	PUNCT
ejpam-6679	21	5	.	.	PUNCT
ejpam-6679	21	6	.	.	PUNCT
ejpam-6679	22	1	.	.	PUNCT
ejpam-6679	23	1	,	,	PUNCT
ejpam-6679	23	2	f(νn	f(νn	PROPN
ejpam-6679	23	3	,	,	PUNCT
ejpam-6679	23	4	o1	o1	NOUN
ejpam-6679	23	5	,	,	PUNCT
ejpam-6679	23	6	.	.	PUNCT
ejpam-6679	23	7	.	.	PUNCT
ejpam-6679	24	1	.	.	PUNCT
ejpam-6679	25	1	,	,	PUNCT
ejpam-6679	25	2	on	on	ADP
ejpam-6679	25	3	)	)	PUNCT
ejpam-6679	25	4	)	)	PUNCT
ejpam-6679	25	5	for	for	ADP
ejpam-6679	25	6	any	any	DET
ejpam-6679	25	7	µ	µ	NOUN
ejpam-6679	25	8	,	,	PUNCT
ejpam-6679	25	9	ν1	ν1	NOUN
ejpam-6679	25	10	,	,	PUNCT
ejpam-6679	25	11	.	.	PUNCT
ejpam-6679	25	12	.	.	PUNCT
ejpam-6679	25	13	.	.	PUNCT
ejpam-6679	26	1	,	,	PUNCT
ejpam-6679	26	2	νn	νn	NOUN
ejpam-6679	26	3	,	,	PUNCT
ejpam-6679	26	4	o1	o1	NOUN
ejpam-6679	26	5	,	,	PUNCT
ejpam-6679	26	6	.	.	PUNCT
ejpam-6679	26	7	.	.	PUNCT
ejpam-6679	27	1	.	.	PUNCT
ejpam-6679	28	1	,	,	PUNCT
ejpam-6679	28	2	on	on	ADP
ejpam-6679	28	3	∈m	∈m	NOUN
ejpam-6679	28	4	.	.	PUNCT
ejpam-6679	29	1	doi	doi	NOUN
ejpam-6679	29	2	:	:	PUNCT
ejpam-6679	29	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6679	https://doi.org/10.29020/nybg.ejpam.v18i4.6679	PRON
ejpam-6679	29	4	email	email	NOUN
ejpam-6679	29	5	address	address	NOUN
ejpam-6679	29	6	:	:	PUNCT
ejpam-6679	29	7	thacha@kku.ac.th	thacha@kku.ac.th	NOUN
ejpam-6679	29	8	(	(	PUNCT
ejpam-6679	29	9	t.	t.	NOUN
ejpam-6679	29	10	changphas	changphas	PROPN
ejpam-6679	29	11	)	)	PUNCT
ejpam-6679	29	12	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6679	30	1	1	1	NUM
ejpam-6679	30	2	copyright	copyright	NOUN
ejpam-6679	30	3	:	:	PUNCT
ejpam-6679	30	4	©	©	PROPN
ejpam-6679	30	5	2025	2025	NUM
ejpam-6679	30	6	the	the	DET
ejpam-6679	30	7	author(s	author(s	NOUN
ejpam-6679	30	8	)	)	PUNCT
ejpam-6679	30	9	.	.	PUNCT
ejpam-6679	31	1	(	(	PUNCT
ejpam-6679	31	2	cc	cc	NOUN
ejpam-6679	31	3	by	by	ADP
ejpam-6679	31	4	-	-	PUNCT
ejpam-6679	31	5	nc	nc	PROPN
ejpam-6679	31	6	4.0	4.0	NUM
ejpam-6679	31	7	)	)	PUNCT
ejpam-6679	31	8	t.	t.	NOUN
ejpam-6679	31	9	changphas	changphas	PROPN
ejpam-6679	31	10	/	/	SYM
ejpam-6679	31	11	eur	eur	PROPN
ejpam-6679	31	12	.	.	PUNCT
ejpam-6679	32	1	j.	j.	PROPN
ejpam-6679	32	2	pure	pure	PROPN
ejpam-6679	32	3	appl	appl	PROPN
ejpam-6679	32	4	.	.	PROPN
ejpam-6679	32	5	math	math	PROPN
ejpam-6679	32	6	,	,	PUNCT
ejpam-6679	32	7	18	18	NUM
ejpam-6679	32	8	(	(	PUNCT
ejpam-6679	32	9	4	4	NUM
ejpam-6679	32	10	)	)	PUNCT
ejpam-6679	32	11	(	(	PUNCT
ejpam-6679	32	12	2025	2025	NUM
ejpam-6679	32	13	)	)	PUNCT
ejpam-6679	32	14	,	,	PUNCT
ejpam-6679	32	15	6679	6679	NUM
ejpam-6679	32	16	2	2	NUM
ejpam-6679	32	17	of	of	ADP
ejpam-6679	32	18	15	15	NUM
ejpam-6679	32	19	menger	menger	NOUN
ejpam-6679	32	20	algebras	algebra	NOUN
ejpam-6679	32	21	of	of	ADP
ejpam-6679	32	22	rank	rank	PROPN
ejpam-6679	32	23	1	1	NUM
ejpam-6679	32	24	are	be	AUX
ejpam-6679	32	25	semigroups	semigroup	NOUN
ejpam-6679	32	26	.	.	PUNCT
ejpam-6679	33	1	menger	menger	PROPN
ejpam-6679	33	2	algebras	algebras	PROPN
ejpam-6679	33	3	of	of	ADP
ejpam-6679	33	4	rank	rank	PROPN
ejpam-6679	33	5	n	n	X
ejpam-6679	33	6	are	be	AUX
ejpam-6679	33	7	a	a	DET
ejpam-6679	33	8	significant	significant	ADJ
ejpam-6679	33	9	extension	extension	NOUN
ejpam-6679	33	10	of	of	ADP
ejpam-6679	33	11	the	the	DET
ejpam-6679	33	12	classical	classical	ADJ
ejpam-6679	33	13	menger	menger	NOUN
ejpam-6679	33	14	algebras	algebras	PROPN
ejpam-6679	33	15	,	,	PUNCT
ejpam-6679	33	16	providing	provide	VERB
ejpam-6679	33	17	a	a	DET
ejpam-6679	33	18	powerful	powerful	ADJ
ejpam-6679	33	19	tool	tool	NOUN
ejpam-6679	33	20	for	for	ADP
ejpam-6679	33	21	modeling	modeling	NOUN
ejpam-6679	33	22	and	and	CCONJ
ejpam-6679	33	23	analyzing	analyze	VERB
ejpam-6679	33	24	multi	multi	ADJ
ejpam-6679	33	25	-	-	ADJ
ejpam-6679	33	26	level	level	ADJ
ejpam-6679	33	27	and	and	CCONJ
ejpam-6679	33	28	hierarchical	hierarchical	ADJ
ejpam-6679	33	29	systems	system	NOUN
ejpam-6679	33	30	.	.	PUNCT
ejpam-6679	34	1	their	their	PRON
ejpam-6679	34	2	applications	application	NOUN
ejpam-6679	34	3	in	in	ADP
ejpam-6679	34	4	fuzzy	fuzzy	ADJ
ejpam-6679	34	5	logic	logic	NOUN
ejpam-6679	34	6	,	,	PUNCT
ejpam-6679	34	7	probability	probability	NOUN
ejpam-6679	34	8	,	,	PUNCT
ejpam-6679	34	9	and	and	CCONJ
ejpam-6679	34	10	artificial	artificial	ADJ
ejpam-6679	34	11	intelligence	intelligence	NOUN
ejpam-6679	34	12	make	make	VERB
ejpam-6679	34	13	them	they	PRON
ejpam-6679	34	14	relevant	relevant	ADJ
ejpam-6679	34	15	in	in	ADP
ejpam-6679	34	16	both	both	CCONJ
ejpam-6679	34	17	theoretical	theoretical	ADJ
ejpam-6679	34	18	and	and	CCONJ
ejpam-6679	34	19	applied	applied	ADJ
ejpam-6679	34	20	mathematics	mathematic	NOUN
ejpam-6679	34	21	.	.	PUNCT
ejpam-6679	35	1	however	however	ADV
ejpam-6679	35	2	,	,	PUNCT
ejpam-6679	35	3	their	their	PRON
ejpam-6679	35	4	increasing	increase	VERB
ejpam-6679	35	5	complexity	complexity	NOUN
ejpam-6679	35	6	with	with	ADP
ejpam-6679	35	7	higher	high	ADJ
ejpam-6679	35	8	ranks	rank	NOUN
ejpam-6679	35	9	necessitates	necessitate	VERB
ejpam-6679	35	10	a	a	DET
ejpam-6679	35	11	careful	careful	ADJ
ejpam-6679	35	12	balance	balance	NOUN
ejpam-6679	35	13	between	between	ADP
ejpam-6679	35	14	theoretical	theoretical	ADJ
ejpam-6679	35	15	exploration	exploration	NOUN
ejpam-6679	35	16	and	and	CCONJ
ejpam-6679	35	17	practical	practical	ADJ
ejpam-6679	35	18	applicability	applicability	NOUN
ejpam-6679	35	19	.	.	PUNCT
ejpam-6679	36	1	in	in	ADP
ejpam-6679	36	2	theoretical	theoretical	ADJ
ejpam-6679	36	3	mathematics	mathematic	NOUN
ejpam-6679	36	4	,	,	PUNCT
ejpam-6679	36	5	dicker	dicker	PROPN
ejpam-6679	36	6	demonstrated	demonstrate	VERB
ejpam-6679	36	7	in	in	ADP
ejpam-6679	36	8	1963	1963	NUM
ejpam-6679	36	9	that	that	PRON
ejpam-6679	36	10	every	every	DET
ejpam-6679	36	11	menger	menger	PROPN
ejpam-6679	36	12	algebra	algebra	PROPN
ejpam-6679	36	13	of	of	ADP
ejpam-6679	36	14	rank	rank	NOUN
ejpam-6679	36	15	n	n	X
ejpam-6679	36	16	is	be	AUX
ejpam-6679	36	17	isomorphic	isomorphic	ADJ
ejpam-6679	36	18	to	to	ADP
ejpam-6679	36	19	a	a	DET
ejpam-6679	36	20	menger	menger	NOUN
ejpam-6679	36	21	algebra	algebra	NOUN
ejpam-6679	36	22	of	of	ADP
ejpam-6679	36	23	n	n	CCONJ
ejpam-6679	36	24	-	-	PUNCT
ejpam-6679	36	25	ary	ary	PROPN
ejpam-6679	36	26	operations	operation	NOUN
ejpam-6679	36	27	defined	define	VERB
ejpam-6679	36	28	on	on	ADP
ejpam-6679	36	29	some	some	DET
ejpam-6679	36	30	set	set	NOUN
ejpam-6679	36	31	;	;	PUNCT
ejpam-6679	36	32	the	the	DET
ejpam-6679	36	33	result	result	NOUN
ejpam-6679	36	34	is	be	AUX
ejpam-6679	36	35	similar	similar	ADJ
ejpam-6679	36	36	to	to	ADP
ejpam-6679	36	37	cayley	cayley	PROPN
ejpam-6679	36	38	’s	’s	PART
ejpam-6679	36	39	theorem	theorem	NOUN
ejpam-6679	36	40	for	for	ADP
ejpam-6679	36	41	semigroups	semigroup	NOUN
ejpam-6679	36	42	:	:	PUNCT
ejpam-6679	36	43	any	any	DET
ejpam-6679	36	44	semigroup	semigroup	NOUN
ejpam-6679	36	45	is	be	AUX
ejpam-6679	36	46	isomorphic	isomorphic	ADJ
ejpam-6679	36	47	to	to	ADP
ejpam-6679	36	48	a	a	DET
ejpam-6679	36	49	transformation	transformation	NOUN
ejpam-6679	36	50	semigroup	semigroup	NOUN
ejpam-6679	36	51	.	.	PUNCT
ejpam-6679	37	1	based	base	VERB
ejpam-6679	37	2	on	on	ADP
ejpam-6679	37	3	permutations	permutation	NOUN
ejpam-6679	37	4	and	and	CCONJ
ejpam-6679	37	5	transformations	transformation	NOUN
ejpam-6679	37	6	(	(	PUNCT
ejpam-6679	37	7	for	for	ADP
ejpam-6679	37	8	example	example	NOUN
ejpam-6679	37	9	,	,	PUNCT
ejpam-6679	37	10	full	full	ADJ
ejpam-6679	37	11	transformations	transformation	NOUN
ejpam-6679	37	12	,	,	PUNCT
ejpam-6679	37	13	orderpreserving	orderpreserve	VERB
ejpam-6679	37	14	transformations	transformation	NOUN
ejpam-6679	37	15	,	,	PUNCT
ejpam-6679	37	16	order	order	NOUN
ejpam-6679	37	17	-	-	PUNCT
ejpam-6679	37	18	decreasing	decrease	VERB
ejpam-6679	37	19	transformations	transformation	NOUN
ejpam-6679	37	20	)	)	PUNCT
ejpam-6679	37	21	,	,	PUNCT
ejpam-6679	37	22	several	several	ADJ
ejpam-6679	37	23	kinds	kind	NOUN
ejpam-6679	37	24	of	of	ADP
ejpam-6679	37	25	terms	term	NOUN
ejpam-6679	37	26	and	and	CCONJ
ejpam-6679	37	27	of	of	ADP
ejpam-6679	37	28	generalized	generalized	ADJ
ejpam-6679	37	29	terms	term	NOUN
ejpam-6679	37	30	(	(	PUNCT
ejpam-6679	37	31	such	such	ADJ
ejpam-6679	37	32	as	as	ADP
ejpam-6679	37	33	strongly	strongly	ADV
ejpam-6679	37	34	full	full	ADJ
ejpam-6679	37	35	terms	term	NOUN
ejpam-6679	37	36	,	,	PUNCT
ejpam-6679	37	37	full	full	ADJ
ejpam-6679	37	38	terms	term	NOUN
ejpam-6679	37	39	,	,	PUNCT
ejpam-6679	37	40	order	order	NOUN
ejpam-6679	37	41	-	-	PUNCT
ejpam-6679	37	42	preserving	preserve	VERB
ejpam-6679	37	43	full	full	ADJ
ejpam-6679	37	44	terms	term	NOUN
ejpam-6679	37	45	,	,	PUNCT
ejpam-6679	37	46	order	order	NOUN
ejpam-6679	37	47	-	-	PUNCT
ejpam-6679	37	48	decreasing	decrease	VERB
ejpam-6679	37	49	full	full	ADJ
ejpam-6679	37	50	terms	term	NOUN
ejpam-6679	37	51	,	,	PUNCT
ejpam-6679	37	52	and	and	CCONJ
ejpam-6679	37	53	generalized	generalize	VERB
ejpam-6679	37	54	full	full	ADJ
ejpam-6679	37	55	terms	term	NOUN
ejpam-6679	37	56	)	)	PUNCT
ejpam-6679	37	57	are	be	AUX
ejpam-6679	37	58	introduced	introduce	VERB
ejpam-6679	37	59	and	and	CCONJ
ejpam-6679	37	60	studied	study	VERB
ejpam-6679	37	61	.	.	PUNCT
ejpam-6679	38	1	menger	menger	PROPN
ejpam-6679	38	2	algebras	algebras	PROPN
ejpam-6679	38	3	and	and	CCONJ
ejpam-6679	38	4	unitary	unitary	ADJ
ejpam-6679	38	5	menger	menger	NOUN
ejpam-6679	38	6	algebras	algebra	NOUN
ejpam-6679	38	7	of	of	ADP
ejpam-6679	38	8	particular	particular	ADJ
ejpam-6679	38	9	terms	term	NOUN
ejpam-6679	38	10	have	have	AUX
ejpam-6679	38	11	been	be	AUX
ejpam-6679	38	12	extensively	extensively	ADV
ejpam-6679	38	13	studied	study	VERB
ejpam-6679	38	14	.	.	PUNCT
ejpam-6679	39	1	according	accord	VERB
ejpam-6679	39	2	to	to	ADP
ejpam-6679	39	3	the	the	DET
ejpam-6679	39	4	account	account	NOUN
ejpam-6679	39	5	provided	provide	VERB
ejpam-6679	39	6	in	in	ADP
ejpam-6679	39	7	the	the	DET
ejpam-6679	39	8	reference	reference	NOUN
ejpam-6679	39	9	,	,	PUNCT
ejpam-6679	39	10	denecke	denecke	NOUN
ejpam-6679	40	1	[	[	X
ejpam-6679	40	2	2	2	NUM
ejpam-6679	40	3	]	]	PUNCT
ejpam-6679	40	4	studied	study	VERB
ejpam-6679	40	5	menger	menger	PROPN
ejpam-6679	40	6	algebras	algebras	PROPN
ejpam-6679	40	7	and	and	CCONJ
ejpam-6679	40	8	clone	clone	NOUN
ejpam-6679	40	9	of	of	ADP
ejpam-6679	40	10	terms	term	NOUN
ejpam-6679	40	11	of	of	ADP
ejpam-6679	40	12	an	an	DET
ejpam-6679	40	13	arbitrary	arbitrary	ADJ
ejpam-6679	40	14	type	type	NOUN
ejpam-6679	40	15	.	.	PUNCT
ejpam-6679	41	1	since	since	SCONJ
ejpam-6679	41	2	then	then	ADV
ejpam-6679	41	3	several	several	ADJ
ejpam-6679	41	4	kinds	kind	NOUN
ejpam-6679	41	5	of	of	ADP
ejpam-6679	41	6	menger	menger	PROPN
ejpam-6679	41	7	algebras	algebras	PROPN
ejpam-6679	41	8	of	of	ADP
ejpam-6679	41	9	particular	particular	ADJ
ejpam-6679	41	10	terms	term	NOUN
ejpam-6679	41	11	have	have	AUX
ejpam-6679	41	12	been	be	AUX
ejpam-6679	41	13	investigated	investigate	VERB
ejpam-6679	41	14	.	.	PUNCT
ejpam-6679	42	1	denecke	denecke	NOUN
ejpam-6679	42	2	and	and	CCONJ
ejpam-6679	42	3	freiberg	freiberg	PROPN
ejpam-6679	42	4	[	[	X
ejpam-6679	42	5	3	3	NUM
ejpam-6679	42	6	]	]	PUNCT
ejpam-6679	42	7	examined	examine	VERB
ejpam-6679	42	8	menger	menger	PROPN
ejpam-6679	42	9	algebras	algebras	PROPN
ejpam-6679	42	10	of	of	ADP
ejpam-6679	42	11	strongly	strongly	ADV
ejpam-6679	42	12	full	full	ADJ
ejpam-6679	42	13	terms	term	NOUN
ejpam-6679	42	14	defined	define	VERB
ejpam-6679	42	15	using	use	VERB
ejpam-6679	42	16	permutations	permutation	NOUN
ejpam-6679	42	17	.	.	PUNCT
ejpam-6679	43	1	denecke	denecke	NOUN
ejpam-6679	43	2	and	and	CCONJ
ejpam-6679	43	3	jampachon	jampachon	ADJ
ejpam-6679	44	1	[	[	X
ejpam-6679	44	2	4	4	NUM
ejpam-6679	44	3	]	]	PUNCT
ejpam-6679	44	4	introduced	introduce	VERB
ejpam-6679	44	5	and	and	CCONJ
ejpam-6679	44	6	studied	study	VERB
ejpam-6679	44	7	menger	menger	PROPN
ejpam-6679	44	8	algebras	algebra	NOUN
ejpam-6679	44	9	of	of	ADP
ejpam-6679	44	10	full	full	ADJ
ejpam-6679	44	11	terms	term	NOUN
ejpam-6679	44	12	,	,	PUNCT
ejpam-6679	44	13	such	such	ADJ
ejpam-6679	44	14	terms	term	NOUN
ejpam-6679	44	15	are	be	AUX
ejpam-6679	44	16	defined	define	VERB
ejpam-6679	44	17	by	by	ADP
ejpam-6679	44	18	full	full	ADJ
ejpam-6679	44	19	transformations	transformation	NOUN
ejpam-6679	44	20	.	.	PUNCT
ejpam-6679	45	1	by	by	ADP
ejpam-6679	45	2	order	order	NOUN
ejpam-6679	45	3	-	-	PUNCT
ejpam-6679	45	4	decreasing	decrease	VERB
ejpam-6679	45	5	transformations	transformation	NOUN
ejpam-6679	45	6	,	,	PUNCT
ejpam-6679	45	7	wattanatripop	wattanatripop	NOUN
ejpam-6679	45	8	and	and	CCONJ
ejpam-6679	45	9	changphas	changphas	ADJ
ejpam-6679	45	10	[	[	X
ejpam-6679	45	11	5	5	NUM
ejpam-6679	45	12	,	,	PUNCT
ejpam-6679	45	13	6	6	NUM
ejpam-6679	45	14	]	]	PUNCT
ejpam-6679	45	15	introduced	introduce	VERB
ejpam-6679	45	16	and	and	CCONJ
ejpam-6679	45	17	investigated	investigate	VERB
ejpam-6679	45	18	menger	menger	PROPN
ejpam-6679	45	19	algebras	algebras	PROPN
ejpam-6679	45	20	of	of	ADP
ejpam-6679	45	21	order	order	NOUN
ejpam-6679	45	22	-	-	PUNCT
ejpam-6679	45	23	decresing	decrese	VERB
ejpam-6679	45	24	full	full	ADJ
ejpam-6679	45	25	terms	term	NOUN
ejpam-6679	45	26	.	.	PUNCT
ejpam-6679	46	1	puapong	puapong	PROPN
ejpam-6679	46	2	and	and	CCONJ
ejpam-6679	46	3	leeratanawalee	leeratanawalee	VERB
ejpam-6679	47	1	[	[	X
ejpam-6679	47	2	7	7	X
ejpam-6679	47	3	]	]	PUNCT
ejpam-6679	47	4	explored	explore	VERB
ejpam-6679	47	5	menger	menger	PROPN
ejpam-6679	47	6	algebras	algebras	PROPN
ejpam-6679	47	7	of	of	ADP
ejpam-6679	47	8	generalized	generalized	ADJ
ejpam-6679	47	9	full	full	ADJ
ejpam-6679	47	10	terms	term	NOUN
ejpam-6679	47	11	.	.	PUNCT
ejpam-6679	48	1	denecke	denecke	NOUN
ejpam-6679	48	2	and	and	CCONJ
ejpam-6679	48	3	hounnon	hounnon	NOUN
ejpam-6679	48	4	[	[	X
ejpam-6679	48	5	8	8	NUM
ejpam-6679	48	6	]	]	PUNCT
ejpam-6679	48	7	(	(	PUNCT
ejpam-6679	48	8	also	also	ADV
ejpam-6679	48	9	lekkoksung	lekkoksung	PROPN
ejpam-6679	48	10	and	and	CCONJ
ejpam-6679	48	11	lekkoksung	lekkoksung	ADJ
ejpam-6679	49	1	[	[	X
ejpam-6679	49	2	9	9	NUM
ejpam-6679	49	3	]	]	PUNCT
ejpam-6679	49	4	)	)	PUNCT
ejpam-6679	49	5	studied	study	VERB
ejpam-6679	49	6	partial	partial	ADJ
ejpam-6679	49	7	menger	menger	PROPN
ejpam-6679	49	8	algebras	algebras	PROPN
ejpam-6679	49	9	of	of	ADP
ejpam-6679	49	10	linear	linear	PROPN
ejpam-6679	49	11	terms	term	NOUN
ejpam-6679	49	12	and	and	CCONJ
ejpam-6679	49	13	of	of	ADP
ejpam-6679	49	14	r	r	NOUN
ejpam-6679	49	15	-	-	PUNCT
ejpam-6679	49	16	terms	term	NOUN
ejpam-6679	49	17	;	;	PUNCT
ejpam-6679	49	18	some	some	DET
ejpam-6679	49	19	algebraic	algebraic	ADJ
ejpam-6679	49	20	properties	property	NOUN
ejpam-6679	49	21	such	such	ADJ
ejpam-6679	49	22	as	as	ADP
ejpam-6679	49	23	generating	generating	NOUN
ejpam-6679	49	24	systems	system	NOUN
ejpam-6679	49	25	,	,	PUNCT
ejpam-6679	49	26	homomorphic	homomorphic	ADJ
ejpam-6679	49	27	images	image	NOUN
ejpam-6679	49	28	and	and	CCONJ
ejpam-6679	49	29	freeness	freeness	NOUN
ejpam-6679	49	30	are	be	AUX
ejpam-6679	49	31	investigated	investigate	VERB
ejpam-6679	49	32	.	.	PUNCT
ejpam-6679	50	1	recently	recently	ADV
ejpam-6679	50	2	,	,	PUNCT
ejpam-6679	50	3	punigool	punigool	NOUN
ejpam-6679	50	4	,	,	PUNCT
ejpam-6679	50	5	phuapong	phuapong	NOUN
ejpam-6679	50	6	and	and	CCONJ
ejpam-6679	50	7	chansuriya	chansuriya	VERB
ejpam-6679	51	1	[	[	X
ejpam-6679	51	2	10	10	NUM
ejpam-6679	51	3	]	]	PUNCT
ejpam-6679	51	4	introduced	introduce	VERB
ejpam-6679	51	5	and	and	CCONJ
ejpam-6679	51	6	studied	study	VERB
ejpam-6679	51	7	menger	menger	PROPN
ejpam-6679	51	8	algebras	algebra	NOUN
ejpam-6679	51	9	of	of	ADP
ejpam-6679	51	10	terms	term	NOUN
ejpam-6679	51	11	defined	define	VERB
ejpam-6679	51	12	based	base	VERB
ejpam-6679	51	13	on	on	ADP
ejpam-6679	51	14	transformations	transformation	NOUN
ejpam-6679	51	15	with	with	ADP
ejpam-6679	51	16	restricted	restricted	ADJ
ejpam-6679	51	17	range	range	NOUN
ejpam-6679	51	18	.	.	PUNCT
ejpam-6679	52	1	definition	definition	NOUN
ejpam-6679	52	2	2	2	NUM
ejpam-6679	52	3	.	.	PUNCT
ejpam-6679	52	4	a	a	DET
ejpam-6679	52	5	type	type	NOUN
ejpam-6679	52	6	(	(	PUNCT
ejpam-6679	52	7	or	or	CCONJ
ejpam-6679	52	8	language	language	NOUN
ejpam-6679	52	9	)	)	PUNCT
ejpam-6679	52	10	of	of	ADP
ejpam-6679	52	11	algebras	algebras	PROPN
ejpam-6679	52	12	is	be	AUX
ejpam-6679	52	13	a	a	DET
ejpam-6679	52	14	nonempty	nonempty	ADV
ejpam-6679	52	15	indexed	index	VERB
ejpam-6679	52	16	sequence	sequence	NOUN
ejpam-6679	52	17	τ	τ	X
ejpam-6679	52	18	=	=	SYM
ejpam-6679	52	19	(	(	PUNCT
ejpam-6679	52	20	ni)i∈i	ni)i∈i	NUM
ejpam-6679	52	21	of	of	ADP
ejpam-6679	52	22	nonnegative	nonnegative	ADJ
ejpam-6679	52	23	integers	integer	NOUN
ejpam-6679	52	24	ni	ni	NOUN
ejpam-6679	52	25	such	such	ADJ
ejpam-6679	52	26	that	that	PRON
ejpam-6679	52	27	for	for	ADP
ejpam-6679	52	28	each	each	DET
ejpam-6679	52	29	ni	ni	PROPN
ejpam-6679	52	30	is	be	AUX
ejpam-6679	52	31	assigned	assign	VERB
ejpam-6679	52	32	to	to	ADP
ejpam-6679	52	33	a	a	DET
ejpam-6679	52	34	symbol	symbol	NOUN
ejpam-6679	52	35	fi	fi	NOUN
ejpam-6679	52	36	.	.	PUNCT
ejpam-6679	53	1	this	this	DET
ejpam-6679	53	2	integer	integer	NOUN
ejpam-6679	53	3	is	be	AUX
ejpam-6679	53	4	called	call	VERB
ejpam-6679	53	5	the	the	DET
ejpam-6679	53	6	arity	arity	NOUN
ejpam-6679	53	7	(	(	PUNCT
ejpam-6679	53	8	or	or	CCONJ
ejpam-6679	53	9	rank	rank	NOUN
ejpam-6679	53	10	)	)	PUNCT
ejpam-6679	53	11	of	of	ADP
ejpam-6679	53	12	fi	fi	NOUN
ejpam-6679	53	13	,	,	PUNCT
ejpam-6679	53	14	and	and	CCONJ
ejpam-6679	53	15	fi	fi	NOUN
ejpam-6679	53	16	is	be	AUX
ejpam-6679	53	17	called	call	VERB
ejpam-6679	53	18	an	an	DET
ejpam-6679	53	19	ni	ni	PROPN
ejpam-6679	53	20	-	-	PROPN
ejpam-6679	53	21	ary	ary	PROPN
ejpam-6679	53	22	operation	operation	NOUN
ejpam-6679	53	23	(	(	PUNCT
ejpam-6679	53	24	or	or	CCONJ
ejpam-6679	53	25	function	function	NOUN
ejpam-6679	53	26	)	)	PUNCT
ejpam-6679	53	27	symbol	symbol	NOUN
ejpam-6679	53	28	.	.	PUNCT
ejpam-6679	54	1	in	in	ADP
ejpam-6679	54	2	particular	particular	ADJ
ejpam-6679	54	3	,	,	PUNCT
ejpam-6679	54	4	let	let	VERB
ejpam-6679	54	5	τn	τn	VERB
ejpam-6679	54	6	=	=	PUNCT
ejpam-6679	54	7	(	(	PUNCT
ejpam-6679	54	8	ni)i∈i	ni)i∈i	NUM
ejpam-6679	54	9	denote	denote	VERB
ejpam-6679	54	10	a	a	DET
ejpam-6679	54	11	type	type	NOUN
ejpam-6679	54	12	of	of	ADP
ejpam-6679	54	13	algebras	algebra	NOUN
ejpam-6679	54	14	such	such	ADJ
ejpam-6679	54	15	that	that	SCONJ
ejpam-6679	54	16	ni	ni	PROPN
ejpam-6679	54	17	=	=	PROPN
ejpam-6679	54	18	n	n	PROPN
ejpam-6679	54	19	for	for	ADP
ejpam-6679	54	20	all	all	PRON
ejpam-6679	54	21	i	i	PRON
ejpam-6679	54	22	∈	∈	PROPN
ejpam-6679	54	23	i.	i.	NOUN
ejpam-6679	54	24	drawing	drawing	NOUN
ejpam-6679	54	25	inspiration	inspiration	NOUN
ejpam-6679	54	26	from	from	ADP
ejpam-6679	54	27	research	research	NOUN
ejpam-6679	54	28	results	result	NOUN
ejpam-6679	54	29	mentioned	mention	VERB
ejpam-6679	54	30	above	above	ADV
ejpam-6679	54	31	,	,	PUNCT
ejpam-6679	54	32	this	this	DET
ejpam-6679	54	33	paper	paper	NOUN
ejpam-6679	54	34	aims	aim	VERB
ejpam-6679	54	35	to	to	PART
ejpam-6679	54	36	introduce	introduce	VERB
ejpam-6679	54	37	n	n	CCONJ
ejpam-6679	54	38	-	-	PUNCT
ejpam-6679	54	39	ary	ary	NOUN
ejpam-6679	54	40	alternating	alternate	VERB
ejpam-6679	54	41	terms	term	NOUN
ejpam-6679	54	42	of	of	ADP
ejpam-6679	54	43	type	type	NOUN
ejpam-6679	54	44	τn	τn	PROPN
ejpam-6679	54	45	,	,	PUNCT
ejpam-6679	54	46	based	base	VERB
ejpam-6679	54	47	on	on	ADP
ejpam-6679	54	48	the	the	DET
ejpam-6679	54	49	alternating	alternate	VERB
ejpam-6679	54	50	group	group	NOUN
ejpam-6679	54	51	alt(n	alt(n	PROPN
ejpam-6679	54	52	)	)	PUNCT
ejpam-6679	54	53	of	of	ADP
ejpam-6679	54	54	degree	degree	NOUN
ejpam-6679	54	55	n.	n.	NOUN
ejpam-6679	54	56	firstly	firstly	ADV
ejpam-6679	54	57	,	,	PUNCT
ejpam-6679	54	58	we	we	PRON
ejpam-6679	54	59	demonstrate	demonstrate	VERB
ejpam-6679	54	60	that	that	SCONJ
ejpam-6679	54	61	the	the	DET
ejpam-6679	54	62	set	set	NOUN
ejpam-6679	54	63	of	of	ADP
ejpam-6679	54	64	all	all	DET
ejpam-6679	54	65	n	n	CCONJ
ejpam-6679	54	66	-	-	PUNCT
ejpam-6679	54	67	ary	ary	NOUN
ejpam-6679	54	68	alternating	alternate	VERB
ejpam-6679	54	69	terms	term	NOUN
ejpam-6679	54	70	of	of	ADP
ejpam-6679	54	71	type	type	NOUN
ejpam-6679	54	72	τn	τn	ADP
ejpam-6679	54	73	forms	form	VERB
ejpam-6679	54	74	a	a	DET
ejpam-6679	54	75	menger	menger	PROPN
ejpam-6679	54	76	algebra	algebra	PROPN
ejpam-6679	54	77	of	of	ADP
ejpam-6679	54	78	rank	rank	NOUN
ejpam-6679	54	79	n	n	CCONJ
ejpam-6679	54	80	;	;	PUNCT
ejpam-6679	54	81	we	we	PRON
ejpam-6679	54	82	denote	denote	VERB
ejpam-6679	54	83	this	this	DET
ejpam-6679	54	84	algebra	algebra	NOUN
ejpam-6679	54	85	by	by	ADP
ejpam-6679	54	86	walt(n	walt(n	PROPN
ejpam-6679	54	87	)	)	PUNCT
ejpam-6679	54	88	τn	τn	X
ejpam-6679	54	89	(	(	PUNCT
ejpam-6679	54	90	ωn	ωn	NUM
ejpam-6679	54	91	)	)	PUNCT
ejpam-6679	54	92	.	.	PUNCT
ejpam-6679	55	1	we	we	PRON
ejpam-6679	55	2	prove	prove	VERB
ejpam-6679	55	3	that	that	SCONJ
ejpam-6679	55	4	the	the	DET
ejpam-6679	55	5	algebra	algebra	PROPN
ejpam-6679	55	6	walt(n	walt(n	NOUN
ejpam-6679	55	7	)	)	PUNCT
ejpam-6679	55	8	τn	τn	X
ejpam-6679	55	9	(	(	PUNCT
ejpam-6679	55	10	ωn	ωn	X
ejpam-6679	55	11	)	)	PUNCT
ejpam-6679	55	12	is	be	AUX
ejpam-6679	55	13	free	free	ADJ
ejpam-6679	55	14	with	with	ADP
ejpam-6679	55	15	respect	respect	NOUN
ejpam-6679	55	16	to	to	ADP
ejpam-6679	55	17	the	the	DET
ejpam-6679	55	18	variety	variety	NOUN
ejpam-6679	55	19	vmenger	vmenger	NOUN
ejpam-6679	55	20	of	of	ADP
ejpam-6679	55	21	menger	menger	PROPN
ejpam-6679	55	22	algebras	algebras	PROPN
ejpam-6679	55	23	of	of	ADP
ejpam-6679	55	24	rank	rank	PROPN
ejpam-6679	55	25	n	n	CCONJ
ejpam-6679	55	26	,	,	PUNCT
ejpam-6679	55	27	and	and	CCONJ
ejpam-6679	55	28	it	it	PRON
ejpam-6679	55	29	is	be	AUX
ejpam-6679	55	30	freely	freely	ADV
ejpam-6679	55	31	generated	generate	VERB
ejpam-6679	55	32	by	by	ADP
ejpam-6679	55	33	the	the	DET
ejpam-6679	55	34	set	set	NOUN
ejpam-6679	55	35	{	{	PUNCT
ejpam-6679	55	36	ω(i	ω(i	PROPN
ejpam-6679	55	37	,	,	PUNCT
ejpam-6679	55	38	σ	σ	PROPN
ejpam-6679	55	39	)	)	PUNCT
ejpam-6679	55	40	:	:	PUNCT
ejpam-6679	56	1	i	i	PRON
ejpam-6679	56	2	∈	∈	VERB
ejpam-6679	56	3	i	i	PRON
ejpam-6679	56	4	,	,	PUNCT
ejpam-6679	56	5	σ	σ	PROPN
ejpam-6679	56	6	∈	∈	PROPN
ejpam-6679	56	7	alt(n	alt(n	PROPN
ejpam-6679	56	8	)	)	PUNCT
ejpam-6679	56	9	}	}	PUNCT
ejpam-6679	56	10	.	.	PUNCT
ejpam-6679	57	1	secondly	secondly	ADV
ejpam-6679	57	2	,	,	PUNCT
ejpam-6679	57	3	we	we	PRON
ejpam-6679	57	4	introduce	introduce	VERB
ejpam-6679	57	5	alternating	alternate	VERB
ejpam-6679	57	6	hypersubstitutions	hypersubstitution	NOUN
ejpam-6679	57	7	of	of	ADP
ejpam-6679	57	8	type	type	NOUN
ejpam-6679	57	9	τn	τn	ADP
ejpam-6679	57	10	and	and	CCONJ
ejpam-6679	57	11	prove	prove	VERB
ejpam-6679	57	12	that	that	SCONJ
ejpam-6679	57	13	the	the	DET
ejpam-6679	57	14	extension	extension	NOUN
ejpam-6679	57	15	of	of	ADP
ejpam-6679	57	16	an	an	DET
ejpam-6679	57	17	alternating	alternate	VERB
ejpam-6679	57	18	hypersubstitution	hypersubstitution	NOUN
ejpam-6679	57	19	of	of	ADP
ejpam-6679	57	20	type	type	NOUN
ejpam-6679	57	21	τn	τn	ADP
ejpam-6679	57	22	acts	act	NOUN
ejpam-6679	57	23	as	as	ADP
ejpam-6679	57	24	an	an	DET
ejpam-6679	57	25	endomorphism	endomorphism	NOUN
ejpam-6679	57	26	on	on	ADP
ejpam-6679	57	27	walt(n	walt(n	PROPN
ejpam-6679	57	28	)	)	PUNCT
ejpam-6679	57	29	τn	τn	X
ejpam-6679	57	30	(	(	PUNCT
ejpam-6679	57	31	ωn	ωn	NOUN
ejpam-6679	57	32	)	)	PUNCT
ejpam-6679	57	33	.	.	PUNCT
ejpam-6679	58	1	furthermore	furthermore	ADV
ejpam-6679	58	2	,	,	PUNCT
ejpam-6679	58	3	we	we	PRON
ejpam-6679	58	4	have	have	VERB
ejpam-6679	58	5	that	that	SCONJ
ejpam-6679	58	6	the	the	DET
ejpam-6679	58	7	set	set	NOUN
ejpam-6679	58	8	of	of	ADP
ejpam-6679	58	9	all	all	PRON
ejpam-6679	58	10	alternating	alternate	VERB
ejpam-6679	58	11	hypersubstitutions	hypersubstitution	NOUN
ejpam-6679	58	12	of	of	ADP
ejpam-6679	58	13	type	type	NOUN
ejpam-6679	58	14	τn	τn	ADP
ejpam-6679	58	15	forms	form	NOUN
ejpam-6679	58	16	a	a	DET
ejpam-6679	58	17	monoid	monoid	NOUN
ejpam-6679	58	18	,	,	PUNCT
ejpam-6679	58	19	denoted	denote	VERB
ejpam-6679	58	20	by	by	ADP
ejpam-6679	58	21	hypalt(n)(τn	hypalt(n)(τn	PROPN
ejpam-6679	58	22	)	)	PUNCT
ejpam-6679	58	23	.	.	PUNCT
ejpam-6679	59	1	finally	finally	ADV
ejpam-6679	59	2	,	,	PUNCT
ejpam-6679	59	3	we	we	PRON
ejpam-6679	59	4	establish	establish	VERB
ejpam-6679	59	5	that	that	SCONJ
ejpam-6679	59	6	the	the	DET
ejpam-6679	59	7	set	set	NOUN
ejpam-6679	59	8	of	of	ADP
ejpam-6679	59	9	all	all	DET
ejpam-6679	59	10	identities	identity	NOUN
ejpam-6679	59	11	s	s	PROPN
ejpam-6679	59	12	≈	≈	PROPN
ejpam-6679	59	13	t	t	PROPN
ejpam-6679	59	14	of	of	ADP
ejpam-6679	59	15	a	a	DET
ejpam-6679	59	16	variety	variety	NOUN
ejpam-6679	59	17	v	v	ADP
ejpam-6679	59	18	t.	t.	PROPN
ejpam-6679	59	19	changphas	changphas	PROPN
ejpam-6679	59	20	/	/	SYM
ejpam-6679	59	21	eur	eur	PROPN
ejpam-6679	59	22	.	.	PUNCT
ejpam-6679	60	1	j.	j.	PROPN
ejpam-6679	60	2	pure	pure	PROPN
ejpam-6679	60	3	appl	appl	PROPN
ejpam-6679	60	4	.	.	PROPN
ejpam-6679	60	5	math	math	PROPN
ejpam-6679	60	6	,	,	PUNCT
ejpam-6679	60	7	18	18	NUM
ejpam-6679	60	8	(	(	PUNCT
ejpam-6679	60	9	4	4	NUM
ejpam-6679	60	10	)	)	PUNCT
ejpam-6679	60	11	(	(	PUNCT
ejpam-6679	60	12	2025	2025	NUM
ejpam-6679	60	13	)	)	PUNCT
ejpam-6679	60	14	,	,	PUNCT
ejpam-6679	60	15	6679	6679	NUM
ejpam-6679	60	16	3	3	NUM
ejpam-6679	60	17	of	of	ADP
ejpam-6679	60	18	15	15	NUM
ejpam-6679	60	19	of	of	ADP
ejpam-6679	60	20	type	type	NOUN
ejpam-6679	60	21	τn	τn	NOUN
ejpam-6679	60	22	,	,	PUNCT
ejpam-6679	60	23	where	where	SCONJ
ejpam-6679	60	24	s	s	PRON
ejpam-6679	60	25	and	and	CCONJ
ejpam-6679	60	26	t	t	PROPN
ejpam-6679	60	27	are	be	AUX
ejpam-6679	60	28	n	n	PRON
ejpam-6679	60	29	-	-	PUNCT
ejpam-6679	60	30	ary	ary	NOUN
ejpam-6679	60	31	alternating	alternate	VERB
ejpam-6679	60	32	terms	term	NOUN
ejpam-6679	60	33	of	of	ADP
ejpam-6679	60	34	type	type	NOUN
ejpam-6679	60	35	τn	τn	PROPN
ejpam-6679	60	36	,	,	PUNCT
ejpam-6679	60	37	constitutes	constitute	VERB
ejpam-6679	60	38	a	a	DET
ejpam-6679	60	39	congruence	congruence	NOUN
ejpam-6679	60	40	on	on	ADP
ejpam-6679	60	41	walt(n	walt(n	PROPN
ejpam-6679	60	42	)	)	PUNCT
ejpam-6679	60	43	τn	τn	X
ejpam-6679	60	44	(	(	PUNCT
ejpam-6679	60	45	ωn	ωn	NOUN
ejpam-6679	60	46	)	)	PUNCT
ejpam-6679	60	47	.	.	PUNCT
ejpam-6679	61	1	according	accord	VERB
ejpam-6679	61	2	to	to	ADP
ejpam-6679	61	3	the	the	DET
ejpam-6679	61	4	monoid	monoid	NOUN
ejpam-6679	61	5	hypalt(n)(τn	hypalt(n)(τn	PROPN
ejpam-6679	61	6	)	)	PUNCT
ejpam-6679	61	7	,	,	PUNCT
ejpam-6679	61	8	we	we	PRON
ejpam-6679	61	9	investigate	investigate	VERB
ejpam-6679	61	10	alternating	alternate	VERB
ejpam-6679	61	11	hyperidentities	hyperidentitie	NOUN
ejpam-6679	61	12	and	and	CCONJ
ejpam-6679	61	13	alternating	alternate	VERB
ejpam-6679	61	14	closed	closed	ADJ
ejpam-6679	61	15	vareities	vareitie	NOUN
ejpam-6679	61	16	.	.	PUNCT
ejpam-6679	62	1	2	2	X
ejpam-6679	62	2	.	.	X
ejpam-6679	62	3	alternating	alternate	VERB
ejpam-6679	62	4	terms	term	NOUN
ejpam-6679	62	5	using	use	VERB
ejpam-6679	62	6	alt(n	alt(n	PROPN
ejpam-6679	62	7	)	)	PUNCT
ejpam-6679	62	8	the	the	DET
ejpam-6679	62	9	alternating	alternate	VERB
ejpam-6679	62	10	group	group	NOUN
ejpam-6679	62	11	of	of	ADP
ejpam-6679	62	12	degree	degree	NOUN
ejpam-6679	62	13	n	n	CCONJ
ejpam-6679	62	14	(	(	PUNCT
ejpam-6679	62	15	see	see	VERB
ejpam-6679	62	16	[	[	X
ejpam-6679	62	17	11	11	NUM
ejpam-6679	62	18	]	]	NUM
ejpam-6679	62	19	)	)	PUNCT
ejpam-6679	62	20	,	,	PUNCT
ejpam-6679	62	21	which	which	PRON
ejpam-6679	62	22	is	be	AUX
ejpam-6679	62	23	a	a	DET
ejpam-6679	62	24	subgroup	subgroup	NOUN
ejpam-6679	62	25	of	of	ADP
ejpam-6679	62	26	the	the	DET
ejpam-6679	62	27	symmetric	symmetric	ADJ
ejpam-6679	62	28	group	group	NOUN
ejpam-6679	62	29	sn	sn	PROPN
ejpam-6679	62	30	on	on	ADP
ejpam-6679	62	31	the	the	DET
ejpam-6679	62	32	set	set	NOUN
ejpam-6679	62	33	{	{	PUNCT
ejpam-6679	62	34	1	1	NUM
ejpam-6679	62	35	,	,	PUNCT
ejpam-6679	62	36	2	2	NUM
ejpam-6679	62	37	,	,	PUNCT
ejpam-6679	62	38	.	.	PUNCT
ejpam-6679	62	39	.	.	PUNCT
ejpam-6679	63	1	.	.	PUNCT
ejpam-6679	63	2	,	,	PUNCT
ejpam-6679	64	1	n	n	CCONJ
ejpam-6679	64	2	}	}	PUNCT
ejpam-6679	64	3	,	,	PUNCT
ejpam-6679	64	4	n	n	CCONJ
ejpam-6679	64	5	-	-	PUNCT
ejpam-6679	64	6	ary	ary	NOUN
ejpam-6679	64	7	alternating	alternate	VERB
ejpam-6679	64	8	terms	term	NOUN
ejpam-6679	64	9	(	(	PUNCT
ejpam-6679	64	10	alt	alt	VERB
ejpam-6679	64	11	-	-	PUNCT
ejpam-6679	64	12	terms	term	NOUN
ejpam-6679	64	13	)	)	PUNCT
ejpam-6679	64	14	of	of	ADP
ejpam-6679	64	15	type	type	NOUN
ejpam-6679	64	16	τn	τn	PART
ejpam-6679	64	17	are	be	AUX
ejpam-6679	64	18	defined	define	VERB
ejpam-6679	64	19	as	as	SCONJ
ejpam-6679	64	20	follows	follow	VERB
ejpam-6679	64	21	:	:	PUNCT
ejpam-6679	64	22	definition	definition	NOUN
ejpam-6679	64	23	3	3	NUM
ejpam-6679	64	24	.	.	PUNCT
ejpam-6679	65	1	let	let	VERB
ejpam-6679	65	2	ωn	ωn	VERB
ejpam-6679	65	3	=	=	SYM
ejpam-6679	65	4	{	{	PUNCT
ejpam-6679	65	5	ω1	ω1	PROPN
ejpam-6679	65	6	,	,	PUNCT
ejpam-6679	65	7	ω2	ω2	ADJ
ejpam-6679	65	8	,	,	PUNCT
ejpam-6679	65	9	.	.	PUNCT
ejpam-6679	65	10	.	.	PUNCT
ejpam-6679	66	1	.	.	PUNCT
ejpam-6679	67	1	,	,	PUNCT
ejpam-6679	67	2	ωn	ωn	X
ejpam-6679	67	3	}	}	PUNCT
ejpam-6679	67	4	denote	denote	VERB
ejpam-6679	67	5	a	a	DET
ejpam-6679	67	6	set	set	NOUN
ejpam-6679	67	7	of	of	ADP
ejpam-6679	67	8	finite	finite	PROPN
ejpam-6679	67	9	alphabet	alphabet	PROPN
ejpam-6679	67	10	ω1	ω1	PROPN
ejpam-6679	67	11	,	,	PUNCT
ejpam-6679	67	12	ω2	ω2	ADJ
ejpam-6679	67	13	,	,	PUNCT
ejpam-6679	67	14	.	.	PUNCT
ejpam-6679	67	15	.	.	PUNCT
ejpam-6679	68	1	.	.	PUNCT
ejpam-6679	69	1	,	,	PUNCT
ejpam-6679	69	2	ωn	ωn	X
ejpam-6679	69	3	,	,	PUNCT
ejpam-6679	69	4	called	call	VERB
ejpam-6679	69	5	variables	variable	NOUN
ejpam-6679	69	6	.	.	PUNCT
ejpam-6679	70	1	let	let	VERB
ejpam-6679	70	2	(	(	PUNCT
ejpam-6679	70	3	fi)i∈i	fi)i∈i	NOUN
ejpam-6679	70	4	be	be	AUX
ejpam-6679	70	5	an	an	DET
ejpam-6679	70	6	indexed	indexed	ADJ
ejpam-6679	70	7	sequence	sequence	NOUN
ejpam-6679	70	8	of	of	ADP
ejpam-6679	70	9	n	n	CCONJ
ejpam-6679	70	10	-	-	PUNCT
ejpam-6679	70	11	ary	ary	PROPN
ejpam-6679	70	12	operation	operation	NOUN
ejpam-6679	70	13	symbols	symbol	NOUN
ejpam-6679	70	14	according	accord	VERB
ejpam-6679	70	15	to	to	ADP
ejpam-6679	70	16	a	a	DET
ejpam-6679	70	17	type	type	NOUN
ejpam-6679	70	18	τn	τn	ADP
ejpam-6679	70	19	=	=	PUNCT
ejpam-6679	70	20	(	(	PUNCT
ejpam-6679	70	21	ni)i∈i	ni)i∈i	NUM
ejpam-6679	70	22	;	;	PUNCT
ejpam-6679	70	23	this	this	DET
ejpam-6679	70	24	set	set	NOUN
ejpam-6679	70	25	is	be	AUX
ejpam-6679	70	26	disjoint	disjoint	NOUN
ejpam-6679	70	27	to	to	ADP
ejpam-6679	70	28	the	the	DET
ejpam-6679	70	29	set	set	NOUN
ejpam-6679	70	30	ωn	ωn	NOUN
ejpam-6679	70	31	.	.	PUNCT
ejpam-6679	71	1	for	for	ADP
ejpam-6679	71	2	any	any	DET
ejpam-6679	71	3	i	i	PRON
ejpam-6679	71	4	∈	∈	PROPN
ejpam-6679	72	1	i	i	PRON
ejpam-6679	72	2	and	and	CCONJ
ejpam-6679	72	3	σ	σ	PROPN
ejpam-6679	72	4	∈	∈	PROPN
ejpam-6679	72	5	alt(n	alt(n	PROPN
ejpam-6679	72	6	)	)	PUNCT
ejpam-6679	72	7	,	,	PUNCT
ejpam-6679	72	8	(	(	PUNCT
ejpam-6679	72	9	1	1	X
ejpam-6679	72	10	)	)	PUNCT
ejpam-6679	72	11	fi(ωσ(1	fi(ωσ(1	NOUN
ejpam-6679	72	12	)	)	PUNCT
ejpam-6679	72	13	,	,	PUNCT
ejpam-6679	72	14	ωσ(2	ωσ(2	NOUN
ejpam-6679	72	15	)	)	PUNCT
ejpam-6679	72	16	,	,	PUNCT
ejpam-6679	72	17	.	.	PUNCT
ejpam-6679	72	18	.	.	PUNCT
ejpam-6679	72	19	.	.	PUNCT
ejpam-6679	73	1	,	,	PUNCT
ejpam-6679	73	2	ωσ(n	ωσ(n	NOUN
ejpam-6679	73	3	)	)	PUNCT
ejpam-6679	73	4	)	)	PUNCT
ejpam-6679	73	5	is	be	AUX
ejpam-6679	73	6	an	an	DET
ejpam-6679	73	7	n	n	CCONJ
ejpam-6679	73	8	-	-	PUNCT
ejpam-6679	73	9	ary	ary	ADJ
ejpam-6679	73	10	alt	alt	ADJ
ejpam-6679	73	11	-	-	PUNCT
ejpam-6679	73	12	term	term	NOUN
ejpam-6679	73	13	;	;	PUNCT
ejpam-6679	73	14	(	(	PUNCT
ejpam-6679	73	15	2	2	X
ejpam-6679	73	16	)	)	PUNCT
ejpam-6679	73	17	if	if	SCONJ
ejpam-6679	73	18	θ1	θ1	NOUN
ejpam-6679	73	19	,	,	PUNCT
ejpam-6679	73	20	θ2	θ2	PROPN
ejpam-6679	73	21	,	,	PUNCT
ejpam-6679	73	22	.	.	PUNCT
ejpam-6679	73	23	.	.	PUNCT
ejpam-6679	74	1	.	.	PUNCT
ejpam-6679	75	1	,	,	PUNCT
ejpam-6679	75	2	θn	θn	PRON
ejpam-6679	75	3	are	be	AUX
ejpam-6679	75	4	n	n	PRON
ejpam-6679	75	5	-	-	PUNCT
ejpam-6679	75	6	ary	ary	ADJ
ejpam-6679	75	7	alt	alt	ADJ
ejpam-6679	75	8	-	-	PUNCT
ejpam-6679	75	9	terms	term	NOUN
ejpam-6679	75	10	,	,	PUNCT
ejpam-6679	75	11	then	then	ADV
ejpam-6679	75	12	fi(θ1	fi(θ1	PROPN
ejpam-6679	75	13	,	,	PUNCT
ejpam-6679	75	14	θ2	θ2	PROPN
ejpam-6679	75	15	,	,	PUNCT
ejpam-6679	75	16	.	.	PUNCT
ejpam-6679	75	17	.	.	PUNCT
ejpam-6679	76	1	.	.	PUNCT
ejpam-6679	77	1	,	,	PUNCT
ejpam-6679	77	2	θn	θn	X
ejpam-6679	77	3	)	)	PUNCT
ejpam-6679	77	4	is	be	AUX
ejpam-6679	77	5	an	an	DET
ejpam-6679	77	6	n	n	CCONJ
ejpam-6679	77	7	-	-	PUNCT
ejpam-6679	77	8	ary	ary	ADJ
ejpam-6679	77	9	alt	alt	ADJ
ejpam-6679	77	10	-	-	PUNCT
ejpam-6679	77	11	term	term	NOUN
ejpam-6679	77	12	.	.	PUNCT
ejpam-6679	78	1	let	let	VERB
ejpam-6679	78	2	walt(n	walt(n	NOUN
ejpam-6679	78	3	)	)	PUNCT
ejpam-6679	78	4	τn	τn	AUX
ejpam-6679	78	5	(	(	PUNCT
ejpam-6679	78	6	ωn	ωn	X
ejpam-6679	78	7	)	)	PUNCT
ejpam-6679	78	8	represent	represent	VERB
ejpam-6679	78	9	the	the	DET
ejpam-6679	78	10	smallest	small	ADJ
ejpam-6679	78	11	set	set	NOUN
ejpam-6679	78	12	of	of	ADP
ejpam-6679	78	13	n	n	CCONJ
ejpam-6679	78	14	-	-	PUNCT
ejpam-6679	78	15	ary	ary	ADJ
ejpam-6679	78	16	alt	alt	ADJ
ejpam-6679	78	17	-	-	PUNCT
ejpam-6679	78	18	terms	term	NOUN
ejpam-6679	78	19	of	of	ADP
ejpam-6679	78	20	type	type	NOUN
ejpam-6679	78	21	τn	τn	ADP
ejpam-6679	78	22	which	which	PRON
ejpam-6679	78	23	is	be	AUX
ejpam-6679	78	24	closed	close	VERB
ejpam-6679	78	25	under	under	ADP
ejpam-6679	78	26	finite	finite	ADJ
ejpam-6679	78	27	application	application	NOUN
ejpam-6679	78	28	of	of	ADP
ejpam-6679	78	29	(	(	PUNCT
ejpam-6679	78	30	2	2	NUM
ejpam-6679	78	31	)	)	PUNCT
ejpam-6679	78	32	.	.	PUNCT
ejpam-6679	79	1	example	example	NOUN
ejpam-6679	80	1	1	1	NUM
ejpam-6679	80	2	.	.	X
ejpam-6679	80	3	for	for	ADP
ejpam-6679	80	4	the	the	DET
ejpam-6679	80	5	symmetric	symmetric	ADJ
ejpam-6679	80	6	group	group	NOUN
ejpam-6679	80	7	s3	s3	PROPN
ejpam-6679	80	8	=	=	SYM
ejpam-6679	80	9	{	{	PUNCT
ejpam-6679	80	10	(	(	PUNCT
ejpam-6679	80	11	1	1	NUM
ejpam-6679	80	12	)	)	PUNCT
ejpam-6679	80	13	,	,	PUNCT
ejpam-6679	80	14	(	(	PUNCT
ejpam-6679	80	15	12	12	NUM
ejpam-6679	80	16	)	)	PUNCT
ejpam-6679	80	17	,	,	PUNCT
ejpam-6679	80	18	(	(	PUNCT
ejpam-6679	80	19	13	13	NUM
ejpam-6679	80	20	)	)	PUNCT
ejpam-6679	80	21	,	,	PUNCT
ejpam-6679	80	22	(	(	PUNCT
ejpam-6679	80	23	23	23	NUM
ejpam-6679	80	24	)	)	PUNCT
ejpam-6679	80	25	,	,	PUNCT
ejpam-6679	80	26	(	(	PUNCT
ejpam-6679	80	27	123	123	NUM
ejpam-6679	80	28	)	)	PUNCT
ejpam-6679	80	29	,	,	PUNCT
ejpam-6679	80	30	(	(	PUNCT
ejpam-6679	80	31	132	132	NUM
ejpam-6679	80	32	)	)	PUNCT
ejpam-6679	80	33	}	}	PUNCT
ejpam-6679	80	34	,	,	PUNCT
ejpam-6679	80	35	the	the	DET
ejpam-6679	80	36	alternating	alternate	VERB
ejpam-6679	80	37	group	group	NOUN
ejpam-6679	80	38	alt(3	alt(3	NOUN
ejpam-6679	80	39	)	)	PUNCT
ejpam-6679	81	1	=	=	PRON
ejpam-6679	81	2	{	{	PUNCT
ejpam-6679	81	3	(	(	PUNCT
ejpam-6679	81	4	1	1	NUM
ejpam-6679	81	5	)	)	PUNCT
ejpam-6679	81	6	,	,	PUNCT
ejpam-6679	81	7	(	(	PUNCT
ejpam-6679	81	8	123	123	NUM
ejpam-6679	81	9	)	)	PUNCT
ejpam-6679	81	10	,	,	PUNCT
ejpam-6679	81	11	(	(	PUNCT
ejpam-6679	81	12	132	132	NUM
ejpam-6679	81	13	)	)	PUNCT
ejpam-6679	81	14	}	}	PUNCT
ejpam-6679	81	15	.	.	PUNCT
ejpam-6679	82	1	consider	consider	VERB
ejpam-6679	82	2	τ3	τ3	NOUN
ejpam-6679	82	3	=	=	SYM
ejpam-6679	82	4	(	(	PUNCT
ejpam-6679	82	5	3	3	NUM
ejpam-6679	82	6	)	)	PUNCT
ejpam-6679	82	7	with	with	ADP
ejpam-6679	82	8	3	3	NUM
ejpam-6679	82	9	-	-	PUNCT
ejpam-6679	82	10	ary	ary	NOUN
ejpam-6679	82	11	operation	operation	NOUN
ejpam-6679	82	12	symbol	symbol	NOUN
ejpam-6679	82	13	g.	g.	PROPN
ejpam-6679	82	14	then	then	ADV
ejpam-6679	82	15	g(ω1	g(ω1	ADV
ejpam-6679	82	16	,	,	PUNCT
ejpam-6679	82	17	ω2	ω2	ADJ
ejpam-6679	82	18	,	,	PUNCT
ejpam-6679	82	19	ω3	ω3	NOUN
ejpam-6679	82	20	)	)	PUNCT
ejpam-6679	82	21	,	,	PUNCT
ejpam-6679	82	22	g(ω2	g(ω2	NOUN
ejpam-6679	82	23	,	,	PUNCT
ejpam-6679	82	24	ω3	ω3	NOUN
ejpam-6679	82	25	,	,	PUNCT
ejpam-6679	82	26	ω1	ω1	PROPN
ejpam-6679	82	27	)	)	PUNCT
ejpam-6679	82	28	,	,	PUNCT
ejpam-6679	82	29	g(ω3	g(ω3	NOUN
ejpam-6679	82	30	,	,	PUNCT
ejpam-6679	82	31	ω1	ω1	PROPN
ejpam-6679	82	32	,	,	PUNCT
ejpam-6679	82	33	ω2	ω2	NUM
ejpam-6679	82	34	)	)	PUNCT
ejpam-6679	82	35	,	,	PUNCT
ejpam-6679	82	36	g(g(ω1	g(g(ω1	NOUN
ejpam-6679	82	37	,	,	PUNCT
ejpam-6679	82	38	ω2	ω2	ADJ
ejpam-6679	82	39	,	,	PUNCT
ejpam-6679	82	40	ω3	ω3	NOUN
ejpam-6679	82	41	)	)	PUNCT
ejpam-6679	82	42	,	,	PUNCT
ejpam-6679	82	43	g(ω2	g(ω2	NOUN
ejpam-6679	82	44	,	,	PUNCT
ejpam-6679	82	45	ω3	ω3	NOUN
ejpam-6679	82	46	,	,	PUNCT
ejpam-6679	82	47	ω1	ω1	PROPN
ejpam-6679	82	48	)	)	PUNCT
ejpam-6679	82	49	,	,	PUNCT
ejpam-6679	82	50	g(ω3	g(ω3	NOUN
ejpam-6679	82	51	,	,	PUNCT
ejpam-6679	82	52	ω1	ω1	PROPN
ejpam-6679	82	53	,	,	PUNCT
ejpam-6679	82	54	ω2	ω2	NUM
ejpam-6679	82	55	)	)	PUNCT
ejpam-6679	82	56	)	)	PUNCT
ejpam-6679	82	57	are	be	AUX
ejpam-6679	82	58	3	3	NUM
ejpam-6679	82	59	-	-	PUNCT
ejpam-6679	82	60	ary	ary	ADJ
ejpam-6679	82	61	alt	alt	ADJ
ejpam-6679	82	62	-	-	PUNCT
ejpam-6679	82	63	terms	term	NOUN
ejpam-6679	82	64	,	,	PUNCT
ejpam-6679	82	65	where	where	SCONJ
ejpam-6679	82	66	as	as	ADP
ejpam-6679	82	67	ω1	ω1	PROPN
ejpam-6679	82	68	,	,	PUNCT
ejpam-6679	82	69	ω2	ω2	ADJ
ejpam-6679	82	70	,	,	PUNCT
ejpam-6679	82	71	ω3	ω3	NOUN
ejpam-6679	82	72	,	,	PUNCT
ejpam-6679	82	73	g(ω2	g(ω2	NOUN
ejpam-6679	82	74	,	,	PUNCT
ejpam-6679	82	75	ω1	ω1	PROPN
ejpam-6679	82	76	,	,	PUNCT
ejpam-6679	82	77	ω3	ω3	PROPN
ejpam-6679	82	78	)	)	PUNCT
ejpam-6679	82	79	,	,	PUNCT
ejpam-6679	82	80	g(ω3	g(ω3	NOUN
ejpam-6679	82	81	,	,	PUNCT
ejpam-6679	82	82	ω2	ω2	ADJ
ejpam-6679	82	83	,	,	PUNCT
ejpam-6679	82	84	ω1	ω1	PROPN
ejpam-6679	82	85	)	)	PUNCT
ejpam-6679	82	86	,	,	PUNCT
ejpam-6679	82	87	g(ω1	g(ω1	ADJ
ejpam-6679	82	88	,	,	PUNCT
ejpam-6679	82	89	ω3	ω3	NOUN
ejpam-6679	82	90	,	,	PUNCT
ejpam-6679	82	91	ω2	ω2	NUM
ejpam-6679	82	92	)	)	PUNCT
ejpam-6679	82	93	,	,	PUNCT
ejpam-6679	82	94	g(ω1	g(ω1	ADJ
ejpam-6679	82	95	,	,	PUNCT
ejpam-6679	82	96	ω2	ω2	ADJ
ejpam-6679	82	97	,	,	PUNCT
ejpam-6679	82	98	g(ω3	g(ω3	NOUN
ejpam-6679	82	99	,	,	PUNCT
ejpam-6679	82	100	ω1	ω1	PROPN
ejpam-6679	82	101	,	,	PUNCT
ejpam-6679	82	102	ω2	ω2	NUM
ejpam-6679	82	103	)	)	PUNCT
ejpam-6679	82	104	)	)	PUNCT
ejpam-6679	82	105	are	be	AUX
ejpam-6679	82	106	not	not	PART
ejpam-6679	82	107	3	3	NUM
ejpam-6679	82	108	-	-	PUNCT
ejpam-6679	82	109	ary	ary	ADJ
ejpam-6679	82	110	alt	alt	NOUN
ejpam-6679	82	111	-	-	PUNCT
ejpam-6679	82	112	terms	term	NOUN
ejpam-6679	82	113	.	.	PUNCT
ejpam-6679	83	1	example	example	NOUN
ejpam-6679	83	2	2	2	NUM
ejpam-6679	83	3	.	.	X
ejpam-6679	84	1	consider	consider	VERB
ejpam-6679	84	2	the	the	DET
ejpam-6679	84	3	symmetric	symmetric	ADJ
ejpam-6679	84	4	group	group	NOUN
ejpam-6679	84	5	s4	s4	PROPN
ejpam-6679	84	6	.	.	PUNCT
ejpam-6679	85	1	for	for	ADP
ejpam-6679	85	2	τ4	τ4	PROPN
ejpam-6679	85	3	=	=	PUNCT
ejpam-6679	85	4	(	(	PUNCT
ejpam-6679	85	5	4	4	NUM
ejpam-6679	85	6	)	)	PUNCT
ejpam-6679	85	7	with	with	ADP
ejpam-6679	85	8	4	4	NUM
ejpam-6679	85	9	-	-	PUNCT
ejpam-6679	85	10	ary	ary	NOUN
ejpam-6679	85	11	operation	operation	NOUN
ejpam-6679	85	12	symbol	symbol	NOUN
ejpam-6679	85	13	f	f	PROPN
ejpam-6679	85	14	,	,	PUNCT
ejpam-6679	85	15	f(ω1	f(ω1	ADJ
ejpam-6679	85	16	,	,	PUNCT
ejpam-6679	85	17	ω2	ω2	ADJ
ejpam-6679	85	18	,	,	PUNCT
ejpam-6679	85	19	ω3	ω3	NOUN
ejpam-6679	85	20	,	,	PUNCT
ejpam-6679	85	21	ω4	ω4	NUM
ejpam-6679	85	22	)	)	PUNCT
ejpam-6679	85	23	,	,	PUNCT
ejpam-6679	85	24	f(ω2	f(ω2	X
ejpam-6679	85	25	,	,	PUNCT
ejpam-6679	85	26	ω1	ω1	PROPN
ejpam-6679	85	27	,	,	PUNCT
ejpam-6679	85	28	ω4	ω4	NUM
ejpam-6679	85	29	,	,	PUNCT
ejpam-6679	85	30	ω3	ω3	PROPN
ejpam-6679	85	31	)	)	PUNCT
ejpam-6679	85	32	,	,	PUNCT
ejpam-6679	85	33	f(ω3	f(ω3	ADJ
ejpam-6679	85	34	,	,	PUNCT
ejpam-6679	85	35	ω4	ω4	NUM
ejpam-6679	85	36	,	,	PUNCT
ejpam-6679	85	37	ω1	ω1	PROPN
ejpam-6679	85	38	,	,	PUNCT
ejpam-6679	85	39	ω2	ω2	NUM
ejpam-6679	85	40	)	)	PUNCT
ejpam-6679	85	41	,	,	PUNCT
ejpam-6679	85	42	f(ω4	f(ω4	PROPN
ejpam-6679	85	43	,	,	PUNCT
ejpam-6679	85	44	ω3	ω3	PROPN
ejpam-6679	85	45	,	,	PUNCT
ejpam-6679	85	46	ω2	ω2	ADJ
ejpam-6679	85	47	,	,	PUNCT
ejpam-6679	85	48	ω1	ω1	PROPN
ejpam-6679	85	49	)	)	PUNCT
ejpam-6679	85	50	,	,	PUNCT
ejpam-6679	85	51	f(ω2	f(ω2	X
ejpam-6679	85	52	,	,	PUNCT
ejpam-6679	85	53	ω3	ω3	NOUN
ejpam-6679	85	54	,	,	PUNCT
ejpam-6679	85	55	ω1	ω1	PROPN
ejpam-6679	85	56	,	,	PUNCT
ejpam-6679	85	57	ω4	ω4	NUM
ejpam-6679	85	58	)	)	PUNCT
ejpam-6679	85	59	,	,	PUNCT
ejpam-6679	85	60	f(ω1	f(ω1	ADV
ejpam-6679	85	61	,	,	PUNCT
ejpam-6679	85	62	ω4	ω4	NUM
ejpam-6679	85	63	,	,	PUNCT
ejpam-6679	85	64	ω2	ω2	ADJ
ejpam-6679	85	65	,	,	PUNCT
ejpam-6679	85	66	ω3	ω3	NOUN
ejpam-6679	85	67	)	)	PUNCT
ejpam-6679	85	68	,	,	PUNCT
ejpam-6679	85	69	f(ω1	f(ω1	ADJ
ejpam-6679	85	70	,	,	PUNCT
ejpam-6679	85	71	ω1	ω1	PROPN
ejpam-6679	85	72	,	,	PUNCT
ejpam-6679	85	73	ω3	ω3	NOUN
ejpam-6679	85	74	,	,	PUNCT
ejpam-6679	85	75	ω2	ω2	NUM
ejpam-6679	85	76	)	)	PUNCT
ejpam-6679	85	77	,	,	PUNCT
ejpam-6679	85	78	f(ω3	f(ω3	ADJ
ejpam-6679	85	79	,	,	PUNCT
ejpam-6679	85	80	ω2	ω2	ADJ
ejpam-6679	85	81	,	,	PUNCT
ejpam-6679	85	82	ω4	ω4	NUM
ejpam-6679	85	83	,	,	PUNCT
ejpam-6679	85	84	ω1	ω1	PROPN
ejpam-6679	85	85	)	)	PUNCT
ejpam-6679	85	86	,	,	PUNCT
ejpam-6679	85	87	f(ω3	f(ω3	ADJ
ejpam-6679	85	88	,	,	PUNCT
ejpam-6679	85	89	ω1	ω1	PROPN
ejpam-6679	85	90	,	,	PUNCT
ejpam-6679	85	91	ω2	ω2	ADJ
ejpam-6679	85	92	,	,	PUNCT
ejpam-6679	85	93	ω4	ω4	NUM
ejpam-6679	85	94	)	)	PUNCT
ejpam-6679	85	95	,	,	PUNCT
ejpam-6679	85	96	f(ω4	f(ω4	X
ejpam-6679	85	97	,	,	PUNCT
ejpam-6679	85	98	ω2	ω2	ADJ
ejpam-6679	85	99	,	,	PUNCT
ejpam-6679	85	100	ω1	ω1	PROPN
ejpam-6679	85	101	,	,	PUNCT
ejpam-6679	85	102	ω3	ω3	PROPN
ejpam-6679	85	103	)	)	PUNCT
ejpam-6679	85	104	,	,	PUNCT
ejpam-6679	85	105	f(ω1	f(ω1	ADJ
ejpam-6679	85	106	,	,	PUNCT
ejpam-6679	85	107	ω3	ω3	ADJ
ejpam-6679	85	108	,	,	PUNCT
ejpam-6679	85	109	ω4	ω4	NUM
ejpam-6679	85	110	,	,	PUNCT
ejpam-6679	85	111	ω2	ω2	NUM
ejpam-6679	85	112	)	)	PUNCT
ejpam-6679	85	113	,	,	PUNCT
ejpam-6679	85	114	f(ω2	f(ω2	X
ejpam-6679	85	115	,	,	PUNCT
ejpam-6679	85	116	ω4	ω4	NUM
ejpam-6679	85	117	,	,	PUNCT
ejpam-6679	85	118	ω3	ω3	PROPN
ejpam-6679	85	119	,	,	PUNCT
ejpam-6679	85	120	ω1	ω1	PROPN
ejpam-6679	85	121	)	)	PUNCT
ejpam-6679	85	122	∈	∈	PROPN
ejpam-6679	85	123	w	w	NOUN
ejpam-6679	85	124	alt(4	alt(4	NOUN
ejpam-6679	85	125	)	)	PUNCT
ejpam-6679	85	126	τ4	τ4	PROPN
ejpam-6679	85	127	(	(	PUNCT
ejpam-6679	85	128	ω4	ω4	NUM
ejpam-6679	85	129	)	)	PUNCT
ejpam-6679	85	130	.	.	PUNCT
ejpam-6679	86	1	clearly	clearly	ADV
ejpam-6679	86	2	,	,	PUNCT
ejpam-6679	86	3	ω1	ω1	PROPN
ejpam-6679	86	4	,	,	PUNCT
ejpam-6679	86	5	ω2	ω2	ADJ
ejpam-6679	86	6	,	,	PUNCT
ejpam-6679	86	7	ω3	ω3	NOUN
ejpam-6679	86	8	,	,	PUNCT
ejpam-6679	86	9	ω4	ω4	NUM
ejpam-6679	86	10	/∈	/∈	PUNCT
ejpam-6679	87	1	w	w	NOUN
ejpam-6679	87	2	alt(4	alt(4	NOUN
ejpam-6679	87	3	)	)	PUNCT
ejpam-6679	87	4	τ4	τ4	PROPN
ejpam-6679	87	5	(	(	PUNCT
ejpam-6679	87	6	ω4	ω4	NUM
ejpam-6679	87	7	)	)	PUNCT
ejpam-6679	87	8	;	;	PUNCT
ejpam-6679	87	9	hence	hence	ADV
ejpam-6679	87	10	f(ω1	f(ω1	ADJ
ejpam-6679	87	11	,	,	PUNCT
ejpam-6679	87	12	ω2	ω2	ADJ
ejpam-6679	87	13	,	,	PUNCT
ejpam-6679	87	14	ω3	ω3	ADJ
ejpam-6679	87	15	,	,	PUNCT
ejpam-6679	87	16	f(ω1	f(ω1	ADJ
ejpam-6679	87	17	,	,	PUNCT
ejpam-6679	87	18	ω2	ω2	ADJ
ejpam-6679	87	19	,	,	PUNCT
ejpam-6679	87	20	ω3	ω3	NOUN
ejpam-6679	87	21	,	,	PUNCT
ejpam-6679	87	22	ω4	ω4	NUM
ejpam-6679	87	23	)	)	PUNCT
ejpam-6679	87	24	)	)	PUNCT
ejpam-6679	87	25	,	,	PUNCT
ejpam-6679	87	26	f(ω1	f(ω1	ADV
ejpam-6679	87	27	,	,	PUNCT
ejpam-6679	87	28	f(ω2	f(ω2	NOUN
ejpam-6679	87	29	,	,	PUNCT
ejpam-6679	87	30	ω4	ω4	NUM
ejpam-6679	87	31	,	,	PUNCT
ejpam-6679	87	32	ω3	ω3	PROPN
ejpam-6679	87	33	,	,	PUNCT
ejpam-6679	87	34	ω1	ω1	PROPN
ejpam-6679	87	35	)	)	PUNCT
ejpam-6679	87	36	,	,	PUNCT
ejpam-6679	87	37	ω3	ω3	PROPN
ejpam-6679	87	38	,	,	PUNCT
ejpam-6679	87	39	f(ω1	f(ω1	ADJ
ejpam-6679	87	40	,	,	PUNCT
ejpam-6679	87	41	ω2	ω2	ADJ
ejpam-6679	87	42	,	,	PUNCT
ejpam-6679	87	43	ω3	ω3	NOUN
ejpam-6679	87	44	,	,	PUNCT
ejpam-6679	87	45	ω4	ω4	NUM
ejpam-6679	87	46	)	)	PUNCT
ejpam-6679	87	47	)	)	PUNCT
ejpam-6679	87	48	/∈	/∈	PUNCT
ejpam-6679	88	1	w	w	NOUN
ejpam-6679	88	2	alt(4	alt(4	NOUN
ejpam-6679	88	3	)	)	PUNCT
ejpam-6679	88	4	τ4	τ4	PROPN
ejpam-6679	88	5	(	(	PUNCT
ejpam-6679	88	6	ω4	ω4	NUM
ejpam-6679	88	7	)	)	PUNCT
ejpam-6679	88	8	,	,	PUNCT
ejpam-6679	88	9	as	as	ADV
ejpam-6679	88	10	well	well	ADV
ejpam-6679	88	11	.	.	PUNCT
ejpam-6679	89	1	example	example	NOUN
ejpam-6679	90	1	3	3	X
ejpam-6679	90	2	.	.	PUNCT
ejpam-6679	90	3	let	let	VERB
ejpam-6679	90	4	us	we	PRON
ejpam-6679	90	5	consider	consider	VERB
ejpam-6679	90	6	the	the	DET
ejpam-6679	90	7	symmetric	symmetric	ADJ
ejpam-6679	90	8	group	group	NOUN
ejpam-6679	90	9	s4	s4	VERB
ejpam-6679	90	10	again	again	ADV
ejpam-6679	90	11	,	,	PUNCT
ejpam-6679	90	12	but	but	CCONJ
ejpam-6679	90	13	τ4	τ4	NOUN
ejpam-6679	90	14	=	=	PUNCT
ejpam-6679	90	15	(	(	PUNCT
ejpam-6679	90	16	4	4	NUM
ejpam-6679	90	17	,	,	PUNCT
ejpam-6679	90	18	4	4	NUM
ejpam-6679	90	19	,	,	PUNCT
ejpam-6679	90	20	4	4	NUM
ejpam-6679	90	21	)	)	PUNCT
ejpam-6679	90	22	with	with	ADP
ejpam-6679	90	23	4	4	NUM
ejpam-6679	90	24	-	-	PUNCT
ejpam-6679	90	25	ary	ary	NOUN
ejpam-6679	90	26	operation	operation	NOUN
ejpam-6679	90	27	symbols	symbol	NOUN
ejpam-6679	90	28	f	f	PROPN
ejpam-6679	90	29	,	,	PUNCT
ejpam-6679	90	30	g	g	PROPN
ejpam-6679	90	31	and	and	CCONJ
ejpam-6679	90	32	h.	h.	PROPN
ejpam-6679	90	33	we	we	PRON
ejpam-6679	90	34	have	have	VERB
ejpam-6679	90	35	f(ω1	f(ω1	VERB
ejpam-6679	90	36	,	,	PUNCT
ejpam-6679	90	37	ω2	ω2	ADJ
ejpam-6679	90	38	,	,	PUNCT
ejpam-6679	90	39	ω3	ω3	NOUN
ejpam-6679	90	40	,	,	PUNCT
ejpam-6679	90	41	ω4	ω4	NUM
ejpam-6679	90	42	)	)	PUNCT
ejpam-6679	90	43	,	,	PUNCT
ejpam-6679	90	44	g(ω2	g(ω2	NOUN
ejpam-6679	90	45	,	,	PUNCT
ejpam-6679	90	46	ω1	ω1	PROPN
ejpam-6679	90	47	,	,	PUNCT
ejpam-6679	90	48	ω4	ω4	NUM
ejpam-6679	90	49	,	,	PUNCT
ejpam-6679	90	50	ω3	ω3	PROPN
ejpam-6679	90	51	)	)	PUNCT
ejpam-6679	90	52	,	,	PUNCT
ejpam-6679	90	53	f(ω3	f(ω3	ADJ
ejpam-6679	90	54	,	,	PUNCT
ejpam-6679	90	55	ω4	ω4	NUM
ejpam-6679	90	56	,	,	PUNCT
ejpam-6679	90	57	ω1	ω1	PROPN
ejpam-6679	90	58	,	,	PUNCT
ejpam-6679	90	59	ω2	ω2	NUM
ejpam-6679	90	60	)	)	PUNCT
ejpam-6679	90	61	,	,	PUNCT
ejpam-6679	90	62	h(ω4	h(ω4	PROPN
ejpam-6679	90	63	,	,	PUNCT
ejpam-6679	90	64	ω3	ω3	PROPN
ejpam-6679	90	65	,	,	PUNCT
ejpam-6679	90	66	ω2	ω2	ADJ
ejpam-6679	90	67	,	,	PUNCT
ejpam-6679	90	68	ω1	ω1	PROPN
ejpam-6679	90	69	)	)	PUNCT
ejpam-6679	90	70	are	be	AUX
ejpam-6679	90	71	4	4	NUM
ejpam-6679	90	72	-	-	PUNCT
ejpam-6679	90	73	ary	ary	NOUN
ejpam-6679	90	74	alternating	alternate	VERB
ejpam-6679	90	75	terms	term	NOUN
ejpam-6679	90	76	of	of	ADP
ejpam-6679	90	77	type	type	NOUN
ejpam-6679	90	78	τ4	τ4	PROPN
ejpam-6679	90	79	;	;	PUNCT
ejpam-6679	90	80	then	then	ADV
ejpam-6679	90	81	g(f(ω1	g(f(ω1	ADJ
ejpam-6679	90	82	,	,	PUNCT
ejpam-6679	90	83	ω2	ω2	ADJ
ejpam-6679	90	84	,	,	PUNCT
ejpam-6679	90	85	ω3	ω3	NOUN
ejpam-6679	90	86	,	,	PUNCT
ejpam-6679	90	87	ω4	ω4	NUM
ejpam-6679	90	88	)	)	PUNCT
ejpam-6679	90	89	,	,	PUNCT
ejpam-6679	90	90	g(ω2	g(ω2	NOUN
ejpam-6679	90	91	,	,	PUNCT
ejpam-6679	90	92	ω1	ω1	PROPN
ejpam-6679	90	93	,	,	PUNCT
ejpam-6679	90	94	ω4	ω4	NUM
ejpam-6679	90	95	,	,	PUNCT
ejpam-6679	90	96	ω3	ω3	PROPN
ejpam-6679	90	97	)	)	PUNCT
ejpam-6679	90	98	,	,	PUNCT
ejpam-6679	90	99	f(ω3	f(ω3	ADJ
ejpam-6679	90	100	,	,	PUNCT
ejpam-6679	90	101	ω4	ω4	NUM
ejpam-6679	90	102	,	,	PUNCT
ejpam-6679	90	103	ω1	ω1	PROPN
ejpam-6679	90	104	,	,	PUNCT
ejpam-6679	90	105	ω2	ω2	NUM
ejpam-6679	90	106	)	)	PUNCT
ejpam-6679	90	107	,	,	PUNCT
ejpam-6679	90	108	h(ω4	h(ω4	PROPN
ejpam-6679	90	109	,	,	PUNCT
ejpam-6679	90	110	ω3	ω3	PROPN
ejpam-6679	90	111	,	,	PUNCT
ejpam-6679	90	112	ω2	ω2	ADJ
ejpam-6679	90	113	,	,	PUNCT
ejpam-6679	90	114	ω1	ω1	PROPN
ejpam-6679	90	115	)	)	PUNCT
ejpam-6679	90	116	)	)	PUNCT
ejpam-6679	90	117	and	and	CCONJ
ejpam-6679	90	118	h(h(ω4	h(h(ω4	ADV
ejpam-6679	90	119	,	,	PUNCT
ejpam-6679	90	120	ω3	ω3	PROPN
ejpam-6679	90	121	,	,	PUNCT
ejpam-6679	90	122	ω2	ω2	ADJ
ejpam-6679	90	123	,	,	PUNCT
ejpam-6679	90	124	ω1	ω1	PROPN
ejpam-6679	90	125	)	)	PUNCT
ejpam-6679	90	126	,	,	PUNCT
ejpam-6679	90	127	g(ω2	g(ω2	NOUN
ejpam-6679	90	128	,	,	PUNCT
ejpam-6679	90	129	ω1	ω1	PROPN
ejpam-6679	90	130	,	,	PUNCT
ejpam-6679	90	131	ω4	ω4	NUM
ejpam-6679	90	132	,	,	PUNCT
ejpam-6679	90	133	ω3	ω3	PROPN
ejpam-6679	90	134	)	)	PUNCT
ejpam-6679	90	135	,	,	PUNCT
ejpam-6679	90	136	f(ω3	f(ω3	ADJ
ejpam-6679	90	137	,	,	PUNCT
ejpam-6679	90	138	ω4	ω4	NUM
ejpam-6679	90	139	,	,	PUNCT
ejpam-6679	90	140	ω1	ω1	PROPN
ejpam-6679	90	141	,	,	PUNCT
ejpam-6679	90	142	ω2	ω2	NUM
ejpam-6679	90	143	)	)	PUNCT
ejpam-6679	90	144	,	,	PUNCT
ejpam-6679	90	145	f(ω1	f(ω1	ADJ
ejpam-6679	90	146	,	,	PUNCT
ejpam-6679	90	147	ω2	ω2	ADJ
ejpam-6679	90	148	,	,	PUNCT
ejpam-6679	90	149	ω3	ω3	NOUN
ejpam-6679	90	150	,	,	PUNCT
ejpam-6679	90	151	ω4	ω4	NUM
ejpam-6679	90	152	)	)	PUNCT
ejpam-6679	90	153	)	)	PUNCT
ejpam-6679	90	154	are	be	AUX
ejpam-6679	90	155	4	4	NUM
ejpam-6679	90	156	-	-	PUNCT
ejpam-6679	90	157	ary	ary	NOUN
ejpam-6679	90	158	alternating	alternate	VERB
ejpam-6679	90	159	terms	term	NOUN
ejpam-6679	90	160	of	of	ADP
ejpam-6679	90	161	type	type	NOUN
ejpam-6679	90	162	τ4	τ4	PROPN
ejpam-6679	90	163	.	.	PUNCT
ejpam-6679	91	1	t.	t.	PROPN
ejpam-6679	91	2	changphas	changphas	PROPN
ejpam-6679	91	3	/	/	SYM
ejpam-6679	91	4	eur	eur	PROPN
ejpam-6679	91	5	.	.	PUNCT
ejpam-6679	92	1	j.	j.	PROPN
ejpam-6679	92	2	pure	pure	PROPN
ejpam-6679	92	3	appl	appl	PROPN
ejpam-6679	92	4	.	.	PROPN
ejpam-6679	92	5	math	math	PROPN
ejpam-6679	92	6	,	,	PUNCT
ejpam-6679	92	7	18	18	NUM
ejpam-6679	92	8	(	(	PUNCT
ejpam-6679	92	9	4	4	NUM
ejpam-6679	92	10	)	)	PUNCT
ejpam-6679	92	11	(	(	PUNCT
ejpam-6679	92	12	2025	2025	NUM
ejpam-6679	92	13	)	)	PUNCT
ejpam-6679	92	14	,	,	PUNCT
ejpam-6679	92	15	6679	6679	NUM
ejpam-6679	92	16	4	4	NUM
ejpam-6679	92	17	of	of	ADP
ejpam-6679	92	18	15	15	NUM
ejpam-6679	92	19	on	on	ADP
ejpam-6679	92	20	w	w	PROPN
ejpam-6679	92	21	alt(n	alt(n	PROPN
ejpam-6679	92	22	)	)	PUNCT
ejpam-6679	92	23	τn	τn	X
ejpam-6679	92	24	(	(	PUNCT
ejpam-6679	92	25	ωn	ωn	NUM
ejpam-6679	92	26	)	)	PUNCT
ejpam-6679	92	27	,	,	PUNCT
ejpam-6679	92	28	define	define	VERB
ejpam-6679	92	29	sn	sn	PROPN
ejpam-6679	92	30	:	:	PUNCT
ejpam-6679	92	31	(	(	PUNCT
ejpam-6679	92	32	walt(n	walt(n	NOUN
ejpam-6679	92	33	)	)	PUNCT
ejpam-6679	92	34	τn	τn	X
ejpam-6679	92	35	(	(	PUNCT
ejpam-6679	92	36	ωn	ωn	NOUN
ejpam-6679	92	37	)	)	PUNCT
ejpam-6679	92	38	)	)	PUNCT
ejpam-6679	93	1	n+1	n+1	NUM
ejpam-6679	93	2	→walt(n	→walt(n	ADV
ejpam-6679	93	3	)	)	PUNCT
ejpam-6679	93	4	τn	τn	ADP
ejpam-6679	93	5	(	(	PUNCT
ejpam-6679	93	6	ωn	ωn	X
ejpam-6679	93	7	)	)	PUNCT
ejpam-6679	93	8	to	to	PART
ejpam-6679	93	9	be	be	AUX
ejpam-6679	93	10	(	(	PUNCT
ejpam-6679	93	11	n+	n+	NUM
ejpam-6679	93	12	1)-ary	1)-ary	ADJ
ejpam-6679	93	13	operation	operation	NOUN
ejpam-6679	93	14	by	by	ADP
ejpam-6679	93	15	:	:	PUNCT
ejpam-6679	93	16	(	(	PUNCT
ejpam-6679	93	17	1	1	X
ejpam-6679	93	18	)	)	PUNCT
ejpam-6679	93	19	sn(fi(ωσ(1	sn(fi(ωσ(1	NOUN
ejpam-6679	93	20	)	)	PUNCT
ejpam-6679	93	21	,	,	PUNCT
ejpam-6679	93	22	ωσ(2	ωσ(2	NOUN
ejpam-6679	93	23	)	)	PUNCT
ejpam-6679	93	24	,	,	PUNCT
ejpam-6679	93	25	.	.	PUNCT
ejpam-6679	93	26	.	.	PUNCT
ejpam-6679	94	1	.	.	PUNCT
ejpam-6679	95	1	,	,	PUNCT
ejpam-6679	95	2	ωσ(n	ωσ(n	NOUN
ejpam-6679	95	3	)	)	PUNCT
ejpam-6679	95	4	)	)	PUNCT
ejpam-6679	95	5	,	,	PUNCT
ejpam-6679	95	6	ϑ1	ϑ1	NOUN
ejpam-6679	95	7	,	,	PUNCT
ejpam-6679	95	8	.	.	PUNCT
ejpam-6679	95	9	.	.	PUNCT
ejpam-6679	96	1	.	.	PUNCT
ejpam-6679	97	1	,	,	PUNCT
ejpam-6679	97	2	ϑn	ϑn	NOUN
ejpam-6679	97	3	)	)	PUNCT
ejpam-6679	97	4	=	=	SYM
ejpam-6679	98	1	fi(ϑσ(1	fi(ϑσ(1	NUM
ejpam-6679	98	2	)	)	PUNCT
ejpam-6679	98	3	,	,	PUNCT
ejpam-6679	98	4	ϑσ(2	ϑσ(2	PROPN
ejpam-6679	98	5	)	)	PUNCT
ejpam-6679	98	6	,	,	PUNCT
ejpam-6679	98	7	.	.	PUNCT
ejpam-6679	98	8	.	.	PUNCT
ejpam-6679	99	1	.	.	PUNCT
ejpam-6679	100	1	,	,	PUNCT
ejpam-6679	100	2	ϑσ(n	ϑσ(n	NOUN
ejpam-6679	100	3	)	)	PUNCT
ejpam-6679	100	4	)	)	PUNCT
ejpam-6679	100	5	;	;	PUNCT
ejpam-6679	100	6	(	(	PUNCT
ejpam-6679	100	7	2	2	X
ejpam-6679	100	8	)	)	PUNCT
ejpam-6679	100	9	sn(fi(θ1	sn(fi(θ1	NOUN
ejpam-6679	100	10	,	,	PUNCT
ejpam-6679	100	11	.	.	PUNCT
ejpam-6679	100	12	.	.	PUNCT
ejpam-6679	101	1	.	.	PUNCT
ejpam-6679	102	1	,	,	PUNCT
ejpam-6679	102	2	θn	θn	NOUN
ejpam-6679	102	3	)	)	PUNCT
ejpam-6679	102	4	,	,	PUNCT
ejpam-6679	102	5	ϑ1	ϑ1	NOUN
ejpam-6679	102	6	,	,	PUNCT
ejpam-6679	102	7	.	.	PUNCT
ejpam-6679	102	8	.	.	PUNCT
ejpam-6679	103	1	.	.	PUNCT
ejpam-6679	104	1	,	,	PUNCT
ejpam-6679	104	2	ϑn	ϑn	NOUN
ejpam-6679	104	3	)	)	PUNCT
ejpam-6679	104	4	=	=	SYM
ejpam-6679	104	5	fi(s	fi(s	X
ejpam-6679	104	6	n(θ1	n(θ1	ADJ
ejpam-6679	104	7	,	,	PUNCT
ejpam-6679	104	8	ϑ1	ϑ1	PROPN
ejpam-6679	104	9	,	,	PUNCT
ejpam-6679	104	10	.	.	PUNCT
ejpam-6679	104	11	.	.	PUNCT
ejpam-6679	105	1	.	.	PUNCT
ejpam-6679	106	1	,	,	PUNCT
ejpam-6679	106	2	ϑn	ϑn	NOUN
ejpam-6679	106	3	)	)	PUNCT
ejpam-6679	106	4	,	,	PUNCT
ejpam-6679	106	5	.	.	PUNCT
ejpam-6679	106	6	.	.	PUNCT
ejpam-6679	107	1	.	.	PUNCT
ejpam-6679	108	1	,	,	PUNCT
ejpam-6679	108	2	s	s	PROPN
ejpam-6679	108	3	n(θn	n(θn	PROPN
ejpam-6679	108	4	,	,	PUNCT
ejpam-6679	108	5	ϑ1	ϑ1	NOUN
ejpam-6679	108	6	,	,	PUNCT
ejpam-6679	108	7	.	.	PUNCT
ejpam-6679	108	8	.	.	PUNCT
ejpam-6679	109	1	.	.	PUNCT
ejpam-6679	110	1	,	,	PUNCT
ejpam-6679	110	2	ϑn	ϑn	NOUN
ejpam-6679	110	3	)	)	PUNCT
ejpam-6679	110	4	)	)	PUNCT
ejpam-6679	111	1	for	for	ADP
ejpam-6679	111	2	any	any	DET
ejpam-6679	111	3	fi	fi	NOUN
ejpam-6679	111	4	,	,	PUNCT
ejpam-6679	111	5	σ	σ	PROPN
ejpam-6679	111	6	∈	∈	PROPN
ejpam-6679	111	7	alt(n	alt(n	PROPN
ejpam-6679	111	8	)	)	PUNCT
ejpam-6679	111	9	,	,	PUNCT
ejpam-6679	111	10	θ1	θ1	NOUN
ejpam-6679	111	11	,	,	PUNCT
ejpam-6679	111	12	.	.	PUNCT
ejpam-6679	111	13	.	.	PUNCT
ejpam-6679	112	1	.	.	PUNCT
ejpam-6679	113	1	,	,	PUNCT
ejpam-6679	113	2	θn	θn	NOUN
ejpam-6679	113	3	,	,	PUNCT
ejpam-6679	113	4	ϑ1	ϑ1	PROPN
ejpam-6679	113	5	,	,	PUNCT
ejpam-6679	113	6	.	.	PUNCT
ejpam-6679	113	7	.	.	PUNCT
ejpam-6679	113	8	.	.	PUNCT
ejpam-6679	114	1	,	,	PUNCT
ejpam-6679	114	2	ϑn	ϑn	PROPN
ejpam-6679	114	3	∈w	∈w	PROPN
ejpam-6679	114	4	alt(n	alt(n	NOUN
ejpam-6679	114	5	)	)	PUNCT
ejpam-6679	114	6	τn	τn	X
ejpam-6679	114	7	(	(	PUNCT
ejpam-6679	114	8	ωn	ωn	NOUN
ejpam-6679	114	9	)	)	PUNCT
ejpam-6679	114	10	.	.	PUNCT
ejpam-6679	115	1	theorem	theorem	NOUN
ejpam-6679	115	2	1	1	NUM
ejpam-6679	115	3	.	.	PUNCT
ejpam-6679	116	1	walt(n	walt(n	NOUN
ejpam-6679	116	2	)	)	PUNCT
ejpam-6679	116	3	τn	τn	X
ejpam-6679	116	4	(	(	PUNCT
ejpam-6679	116	5	ωn	ωn	X
ejpam-6679	116	6	)	)	PUNCT
ejpam-6679	116	7	=	=	SYM
ejpam-6679	116	8	(	(	PUNCT
ejpam-6679	116	9	walt(n	walt(n	NOUN
ejpam-6679	116	10	)	)	PUNCT
ejpam-6679	116	11	τn	τn	X
ejpam-6679	116	12	(	(	PUNCT
ejpam-6679	116	13	ωn	ωn	NUM
ejpam-6679	116	14	)	)	PUNCT
ejpam-6679	116	15	,	,	PUNCT
ejpam-6679	116	16	s	s	NOUN
ejpam-6679	116	17	n	n	CCONJ
ejpam-6679	116	18	)	)	PUNCT
ejpam-6679	116	19	is	be	AUX
ejpam-6679	116	20	an	an	DET
ejpam-6679	116	21	algebra	algebra	NOUN
ejpam-6679	116	22	of	of	ADP
ejpam-6679	116	23	type	type	NOUN
ejpam-6679	116	24	(	(	PUNCT
ejpam-6679	116	25	n+	n+	NOUN
ejpam-6679	116	26	1	1	NUM
ejpam-6679	116	27	)	)	PUNCT
ejpam-6679	116	28	.	.	PUNCT
ejpam-6679	117	1	proof	proof	NOUN
ejpam-6679	117	2	.	.	PUNCT
ejpam-6679	118	1	we	we	PRON
ejpam-6679	118	2	claim	claim	VERB
ejpam-6679	118	3	that	that	SCONJ
ejpam-6679	118	4	for	for	ADP
ejpam-6679	118	5	any	any	DET
ejpam-6679	118	6	θ	θ	PROPN
ejpam-6679	118	7	,	,	PUNCT
ejpam-6679	118	8	θ1	θ1	NOUN
ejpam-6679	118	9	,	,	PUNCT
ejpam-6679	118	10	θ2	θ2	PROPN
ejpam-6679	118	11	,	,	PUNCT
ejpam-6679	118	12	.	.	PUNCT
ejpam-6679	118	13	.	.	PUNCT
ejpam-6679	118	14	.	.	PUNCT
ejpam-6679	119	1	,	,	PUNCT
ejpam-6679	119	2	θn	θn	PROPN
ejpam-6679	119	3	∈	∈	PROPN
ejpam-6679	119	4	w	w	PROPN
ejpam-6679	119	5	alt(n	alt(n	PROPN
ejpam-6679	119	6	)	)	PUNCT
ejpam-6679	119	7	τn	τn	X
ejpam-6679	119	8	(	(	PUNCT
ejpam-6679	119	9	ωn	ωn	NOUN
ejpam-6679	119	10	)	)	PUNCT
ejpam-6679	119	11	,	,	PUNCT
ejpam-6679	119	12	sn(θ	sn(θ	NOUN
ejpam-6679	119	13	,	,	PUNCT
ejpam-6679	119	14	θ1	θ1	NOUN
ejpam-6679	119	15	,	,	PUNCT
ejpam-6679	119	16	θ2	θ2	PROPN
ejpam-6679	119	17	,	,	PUNCT
ejpam-6679	119	18	.	.	PUNCT
ejpam-6679	119	19	.	.	PUNCT
ejpam-6679	120	1	.	.	PUNCT
ejpam-6679	121	1	,	,	PUNCT
ejpam-6679	121	2	θn	θn	X
ejpam-6679	121	3	)	)	PUNCT
ejpam-6679	121	4	∈	∈	PROPN
ejpam-6679	121	5	w	w	PROPN
ejpam-6679	121	6	alt(n	alt(n	PROPN
ejpam-6679	121	7	)	)	PUNCT
ejpam-6679	122	1	τn	τn	X
ejpam-6679	122	2	(	(	PUNCT
ejpam-6679	122	3	ωn	ωn	NUM
ejpam-6679	122	4	)	)	PUNCT
ejpam-6679	122	5	,	,	PUNCT
ejpam-6679	122	6	which	which	PRON
ejpam-6679	122	7	can	can	AUX
ejpam-6679	122	8	be	be	AUX
ejpam-6679	122	9	proved	prove	VERB
ejpam-6679	122	10	by	by	ADP
ejpam-6679	122	11	induction	induction	NOUN
ejpam-6679	122	12	on	on	ADP
ejpam-6679	122	13	the	the	DET
ejpam-6679	122	14	number	number	NOUN
ejpam-6679	122	15	of	of	ADP
ejpam-6679	122	16	occurrence	occurrence	NOUN
ejpam-6679	122	17	of	of	ADP
ejpam-6679	122	18	operation	operation	NOUN
ejpam-6679	122	19	symbols	symbol	NOUN
ejpam-6679	122	20	in	in	ADP
ejpam-6679	122	21	θ	θ	PROPN
ejpam-6679	122	22	.	.	PUNCT
ejpam-6679	123	1	assume	assume	VERB
ejpam-6679	123	2	θ	θ	X
ejpam-6679	123	3	=	=	SYM
ejpam-6679	123	4	fi(ωσ(1	fi(ωσ(1	NOUN
ejpam-6679	123	5	)	)	PUNCT
ejpam-6679	123	6	,	,	PUNCT
ejpam-6679	123	7	ωσ(2	ωσ(2	NOUN
ejpam-6679	123	8	)	)	PUNCT
ejpam-6679	123	9	,	,	PUNCT
ejpam-6679	123	10	.	.	PUNCT
ejpam-6679	123	11	.	.	PUNCT
ejpam-6679	124	1	.	.	PUNCT
ejpam-6679	125	1	,	,	PUNCT
ejpam-6679	125	2	ωσ(n	ωσ(n	NOUN
ejpam-6679	125	3	)	)	PUNCT
ejpam-6679	125	4	)	)	PUNCT
ejpam-6679	126	1	for	for	ADP
ejpam-6679	126	2	some	some	DET
ejpam-6679	126	3	σ	σ	NUM
ejpam-6679	126	4	∈	∈	PROPN
ejpam-6679	126	5	alt(n	alt(n	PROPN
ejpam-6679	126	6	)	)	PUNCT
ejpam-6679	126	7	.	.	PUNCT
ejpam-6679	127	1	by	by	ADP
ejpam-6679	127	2	θ1	θ1	PROPN
ejpam-6679	127	3	,	,	PUNCT
ejpam-6679	127	4	θ2	θ2	PROPN
ejpam-6679	127	5	,	,	PUNCT
ejpam-6679	127	6	.	.	PUNCT
ejpam-6679	127	7	.	.	PUNCT
ejpam-6679	127	8	.	.	PUNCT
ejpam-6679	128	1	,	,	PUNCT
ejpam-6679	128	2	θn	θn	PRON
ejpam-6679	128	3	∈w	∈w	NOUN
ejpam-6679	128	4	alt(n	alt(n	NOUN
ejpam-6679	128	5	)	)	PUNCT
ejpam-6679	128	6	τn	τn	X
ejpam-6679	128	7	(	(	PUNCT
ejpam-6679	128	8	ωn	ωn	NOUN
ejpam-6679	128	9	)	)	PUNCT
ejpam-6679	128	10	,	,	PUNCT
ejpam-6679	128	11	sn(θ	sn(θ	NOUN
ejpam-6679	128	12	,	,	PUNCT
ejpam-6679	128	13	θ1	θ1	NOUN
ejpam-6679	128	14	,	,	PUNCT
ejpam-6679	128	15	θ2	θ2	PROPN
ejpam-6679	128	16	,	,	PUNCT
ejpam-6679	128	17	.	.	PUNCT
ejpam-6679	128	18	.	.	PUNCT
ejpam-6679	129	1	.	.	PUNCT
ejpam-6679	130	1	,	,	PUNCT
ejpam-6679	130	2	θn	θn	NOUN
ejpam-6679	130	3	)	)	PUNCT
ejpam-6679	130	4	=	=	SYM
ejpam-6679	130	5	sn(fi(ωσ(1	sn(fi(ωσ(1	NOUN
ejpam-6679	130	6	)	)	PUNCT
ejpam-6679	130	7	,	,	PUNCT
ejpam-6679	130	8	ωσ(2	ωσ(2	NOUN
ejpam-6679	130	9	)	)	PUNCT
ejpam-6679	130	10	,	,	PUNCT
ejpam-6679	130	11	.	.	PUNCT
ejpam-6679	130	12	.	.	PUNCT
ejpam-6679	130	13	.	.	PUNCT
ejpam-6679	131	1	,	,	PUNCT
ejpam-6679	131	2	ωσ(n	ωσ(n	NOUN
ejpam-6679	131	3	)	)	PUNCT
ejpam-6679	131	4	)	)	PUNCT
ejpam-6679	132	1	,	,	PUNCT
ejpam-6679	132	2	θ1	θ1	NOUN
ejpam-6679	132	3	,	,	PUNCT
ejpam-6679	132	4	θ2	θ2	PROPN
ejpam-6679	132	5	,	,	PUNCT
ejpam-6679	132	6	.	.	PUNCT
ejpam-6679	132	7	.	.	PUNCT
ejpam-6679	132	8	.	.	PUNCT
ejpam-6679	133	1	,	,	PUNCT
ejpam-6679	133	2	θn	θn	NOUN
ejpam-6679	133	3	)	)	PUNCT
ejpam-6679	133	4	=	=	SYM
ejpam-6679	133	5	fi(θσ(1	fi(θσ(1	NOUN
ejpam-6679	133	6	)	)	PUNCT
ejpam-6679	133	7	,	,	PUNCT
ejpam-6679	133	8	θσ(2	θσ(2	NOUN
ejpam-6679	133	9	)	)	PUNCT
ejpam-6679	133	10	,	,	PUNCT
ejpam-6679	133	11	.	.	PUNCT
ejpam-6679	133	12	.	.	PUNCT
ejpam-6679	134	1	.	.	PUNCT
ejpam-6679	135	1	,	,	PUNCT
ejpam-6679	135	2	θσ(n	θσ(n	NOUN
ejpam-6679	135	3	)	)	PUNCT
ejpam-6679	135	4	)	)	PUNCT
ejpam-6679	136	1	∈walt(n	∈walt(n	X
ejpam-6679	136	2	)	)	PUNCT
ejpam-6679	136	3	τn	τn	X
ejpam-6679	136	4	(	(	PUNCT
ejpam-6679	136	5	ωn	ωn	NOUN
ejpam-6679	136	6	)	)	PUNCT
ejpam-6679	136	7	.	.	PUNCT
ejpam-6679	137	1	assume	assume	VERB
ejpam-6679	137	2	θ	θ	NOUN
ejpam-6679	137	3	=	=	SYM
ejpam-6679	137	4	fi(ϑ1	fi(ϑ1	NOUN
ejpam-6679	137	5	,	,	PUNCT
ejpam-6679	137	6	ϑ2	ϑ2	NOUN
ejpam-6679	137	7	,	,	PUNCT
ejpam-6679	137	8	.	.	PUNCT
ejpam-6679	137	9	.	.	PUNCT
ejpam-6679	138	1	.	.	PUNCT
ejpam-6679	139	1	,	,	PUNCT
ejpam-6679	139	2	ϑn	ϑn	NOUN
ejpam-6679	139	3	)	)	PUNCT
ejpam-6679	139	4	and	and	CCONJ
ejpam-6679	139	5	sn(ϑ1	sn(ϑ1	ADJ
ejpam-6679	139	6	,	,	PUNCT
ejpam-6679	139	7	θ1	θ1	NOUN
ejpam-6679	139	8	,	,	PUNCT
ejpam-6679	139	9	θ2	θ2	PROPN
ejpam-6679	139	10	,	,	PUNCT
ejpam-6679	139	11	.	.	PUNCT
ejpam-6679	139	12	.	.	PUNCT
ejpam-6679	140	1	.	.	PUNCT
ejpam-6679	141	1	,	,	PUNCT
ejpam-6679	141	2	θn	θn	NOUN
ejpam-6679	141	3	)	)	PUNCT
ejpam-6679	141	4	,	,	PUNCT
ejpam-6679	141	5	s	s	VERB
ejpam-6679	141	6	n(ϑ2	n(ϑ2	NOUN
ejpam-6679	141	7	,	,	PUNCT
ejpam-6679	141	8	θ1	θ1	NOUN
ejpam-6679	141	9	,	,	PUNCT
ejpam-6679	141	10	θ2	θ2	PROPN
ejpam-6679	141	11	,	,	PUNCT
ejpam-6679	141	12	.	.	PUNCT
ejpam-6679	141	13	.	.	PUNCT
ejpam-6679	142	1	.	.	PUNCT
ejpam-6679	143	1	,	,	PUNCT
ejpam-6679	143	2	θn	θn	NOUN
ejpam-6679	143	3	)	)	PUNCT
ejpam-6679	143	4	,	,	PUNCT
ejpam-6679	143	5	.	.	PUNCT
ejpam-6679	143	6	.	.	PUNCT
ejpam-6679	144	1	.	.	PUNCT
ejpam-6679	145	1	,	,	PUNCT
ejpam-6679	145	2	s	s	VERB
ejpam-6679	145	3	n(ϑn	n(ϑn	PROPN
ejpam-6679	145	4	,	,	PUNCT
ejpam-6679	145	5	θ1	θ1	NOUN
ejpam-6679	145	6	,	,	PUNCT
ejpam-6679	145	7	θ2	θ2	PROPN
ejpam-6679	145	8	,	,	PUNCT
ejpam-6679	145	9	.	.	PUNCT
ejpam-6679	145	10	.	.	PUNCT
ejpam-6679	146	1	.	.	PUNCT
ejpam-6679	147	1	,	,	PUNCT
ejpam-6679	147	2	θn	θn	NOUN
ejpam-6679	147	3	)	)	PUNCT
ejpam-6679	147	4	∈w	∈w	PROPN
ejpam-6679	147	5	alt(n	alt(n	NOUN
ejpam-6679	147	6	)	)	PUNCT
ejpam-6679	147	7	τn	τn	X
ejpam-6679	147	8	(	(	PUNCT
ejpam-6679	147	9	ωn	ωn	NOUN
ejpam-6679	147	10	)	)	PUNCT
ejpam-6679	147	11	.	.	PUNCT
ejpam-6679	148	1	then	then	ADV
ejpam-6679	148	2	sn(θ	sn(θ	NOUN
ejpam-6679	148	3	,	,	PUNCT
ejpam-6679	148	4	θ1	θ1	NOUN
ejpam-6679	148	5	,	,	PUNCT
ejpam-6679	148	6	θ2	θ2	PROPN
ejpam-6679	148	7	,	,	PUNCT
ejpam-6679	148	8	.	.	PUNCT
ejpam-6679	148	9	.	.	PUNCT
ejpam-6679	148	10	.	.	PUNCT
ejpam-6679	149	1	,	,	PUNCT
ejpam-6679	149	2	θn	θn	NOUN
ejpam-6679	149	3	)	)	PUNCT
ejpam-6679	149	4	=	=	NOUN
ejpam-6679	149	5	sn(fi(ϑ1	sn(fi(ϑ1	NOUN
ejpam-6679	149	6	,	,	PUNCT
ejpam-6679	149	7	ϑ2	ϑ2	NOUN
ejpam-6679	149	8	,	,	PUNCT
ejpam-6679	149	9	.	.	PUNCT
ejpam-6679	149	10	.	.	PUNCT
ejpam-6679	150	1	.	.	PUNCT
ejpam-6679	151	1	,	,	PUNCT
ejpam-6679	151	2	ϑn	ϑn	NOUN
ejpam-6679	151	3	)	)	PUNCT
ejpam-6679	151	4	,	,	PUNCT
ejpam-6679	151	5	θ1	θ1	NOUN
ejpam-6679	151	6	,	,	PUNCT
ejpam-6679	151	7	θ2	θ2	PROPN
ejpam-6679	151	8	,	,	PUNCT
ejpam-6679	151	9	.	.	PUNCT
ejpam-6679	151	10	.	.	PUNCT
ejpam-6679	152	1	.	.	PUNCT
ejpam-6679	153	1	,	,	PUNCT
ejpam-6679	153	2	θn	θn	NOUN
ejpam-6679	153	3	)	)	PUNCT
ejpam-6679	153	4	=	=	SYM
ejpam-6679	153	5	fi(s	fi(s	NOUN
ejpam-6679	153	6	n(ϑ1	n(ϑ1	VERB
ejpam-6679	153	7	,	,	PUNCT
ejpam-6679	153	8	θ1	θ1	NOUN
ejpam-6679	153	9	,	,	PUNCT
ejpam-6679	153	10	θ2	θ2	PROPN
ejpam-6679	153	11	,	,	PUNCT
ejpam-6679	153	12	.	.	PUNCT
ejpam-6679	153	13	.	.	PUNCT
ejpam-6679	154	1	.	.	PUNCT
ejpam-6679	155	1	,	,	PUNCT
ejpam-6679	155	2	θn	θn	NOUN
ejpam-6679	155	3	)	)	PUNCT
ejpam-6679	155	4	,	,	PUNCT
ejpam-6679	155	5	s	s	VERB
ejpam-6679	155	6	n(ϑ2	n(ϑ2	NOUN
ejpam-6679	155	7	,	,	PUNCT
ejpam-6679	155	8	θ1	θ1	NOUN
ejpam-6679	155	9	,	,	PUNCT
ejpam-6679	155	10	θ2	θ2	PROPN
ejpam-6679	155	11	,	,	PUNCT
ejpam-6679	155	12	.	.	PUNCT
ejpam-6679	155	13	.	.	PUNCT
ejpam-6679	156	1	.	.	PUNCT
ejpam-6679	157	1	,	,	PUNCT
ejpam-6679	157	2	θn	θn	NOUN
ejpam-6679	157	3	)	)	PUNCT
ejpam-6679	157	4	,	,	PUNCT
ejpam-6679	157	5	.	.	PUNCT
ejpam-6679	157	6	.	.	PUNCT
ejpam-6679	158	1	.	.	PUNCT
ejpam-6679	159	1	,	,	PUNCT
ejpam-6679	159	2	s	s	VERB
ejpam-6679	159	3	n(ϑn	n(ϑn	PROPN
ejpam-6679	159	4	,	,	PUNCT
ejpam-6679	159	5	θ1	θ1	NOUN
ejpam-6679	159	6	,	,	PUNCT
ejpam-6679	159	7	θ2	θ2	PROPN
ejpam-6679	159	8	,	,	PUNCT
ejpam-6679	159	9	.	.	PUNCT
ejpam-6679	159	10	.	.	PUNCT
ejpam-6679	160	1	.	.	PUNCT
ejpam-6679	161	1	,	,	PUNCT
ejpam-6679	161	2	θn	θn	NOUN
ejpam-6679	161	3	)	)	PUNCT
ejpam-6679	161	4	)	)	PUNCT
ejpam-6679	162	1	∈walt(n	∈walt(n	X
ejpam-6679	162	2	)	)	PUNCT
ejpam-6679	162	3	τn	τn	X
ejpam-6679	162	4	(	(	PUNCT
ejpam-6679	162	5	ωn	ωn	NOUN
ejpam-6679	162	6	)	)	PUNCT
ejpam-6679	162	7	.	.	PUNCT
ejpam-6679	163	1	so	so	ADV
ejpam-6679	163	2	we	we	PRON
ejpam-6679	163	3	have	have	VERB
ejpam-6679	163	4	the	the	DET
ejpam-6679	163	5	claim	claim	NOUN
ejpam-6679	163	6	.	.	PUNCT
ejpam-6679	164	1	furthermore	furthermore	ADV
ejpam-6679	164	2	,	,	PUNCT
ejpam-6679	164	3	we	we	PRON
ejpam-6679	164	4	have	have	AUX
ejpam-6679	164	5	theorem	theorem	VERB
ejpam-6679	164	6	2	2	NUM
ejpam-6679	164	7	.	.	PUNCT
ejpam-6679	165	1	the	the	DET
ejpam-6679	165	2	algebra	algebra	PROPN
ejpam-6679	165	3	walt(n	walt(n	PROPN
ejpam-6679	165	4	)	)	PUNCT
ejpam-6679	165	5	τn	τn	ADP
ejpam-6679	165	6	(	(	PUNCT
ejpam-6679	165	7	xn	xn	X
ejpam-6679	165	8	)	)	PUNCT
ejpam-6679	165	9	is	be	AUX
ejpam-6679	165	10	a	a	DET
ejpam-6679	165	11	menger	menger	PROPN
ejpam-6679	165	12	algebra	algebra	NOUN
ejpam-6679	165	13	of	of	ADP
ejpam-6679	165	14	rank	rank	PROPN
ejpam-6679	165	15	n.	n.	PROPN
ejpam-6679	165	16	proof	proof	NOUN
ejpam-6679	165	17	.	.	PUNCT
ejpam-6679	166	1	let	let	VERB
ejpam-6679	166	2	θ	θ	NOUN
ejpam-6679	166	3	,	,	PUNCT
ejpam-6679	166	4	θ1	θ1	NOUN
ejpam-6679	166	5	,	,	PUNCT
ejpam-6679	166	6	.	.	PUNCT
ejpam-6679	166	7	.	.	PUNCT
ejpam-6679	167	1	.	.	PUNCT
ejpam-6679	168	1	,	,	PUNCT
ejpam-6679	168	2	θn	θn	NOUN
ejpam-6679	168	3	,	,	PUNCT
ejpam-6679	168	4	ϑ1	ϑ1	PROPN
ejpam-6679	168	5	,	,	PUNCT
ejpam-6679	168	6	.	.	PUNCT
ejpam-6679	168	7	.	.	PUNCT
ejpam-6679	168	8	.	.	PUNCT
ejpam-6679	169	1	,	,	PUNCT
ejpam-6679	169	2	ϑn	ϑn	PROPN
ejpam-6679	169	3	∈w	∈w	PROPN
ejpam-6679	169	4	alt(n	alt(n	NOUN
ejpam-6679	169	5	)	)	PUNCT
ejpam-6679	169	6	τn	τn	X
ejpam-6679	169	7	(	(	PUNCT
ejpam-6679	169	8	ωn	ωn	NUM
ejpam-6679	169	9	)	)	PUNCT
ejpam-6679	169	10	.	.	PUNCT
ejpam-6679	170	1	suppose	suppose	VERB
ejpam-6679	170	2	θ	θ	PROPN
ejpam-6679	170	3	=	=	SYM
ejpam-6679	170	4	fi(ωσ(1	fi(ωσ(1	NOUN
ejpam-6679	170	5	)	)	PUNCT
ejpam-6679	170	6	,	,	PUNCT
ejpam-6679	170	7	.	.	PUNCT
ejpam-6679	170	8	.	.	PUNCT
ejpam-6679	171	1	.	.	PUNCT
ejpam-6679	172	1	,	,	PUNCT
ejpam-6679	172	2	ωσ(n	ωσ(n	NOUN
ejpam-6679	172	3	)	)	PUNCT
ejpam-6679	172	4	)	)	PUNCT
ejpam-6679	173	1	for	for	ADP
ejpam-6679	173	2	some	some	DET
ejpam-6679	173	3	σ	σ	NUM
ejpam-6679	173	4	∈	∈	PROPN
ejpam-6679	173	5	alt(n	alt(n	PROPN
ejpam-6679	173	6	)	)	PUNCT
ejpam-6679	173	7	.	.	PUNCT
ejpam-6679	174	1	then	then	ADV
ejpam-6679	174	2	sn(sn(θ	sn(sn(θ	NUM
ejpam-6679	174	3	,	,	PUNCT
ejpam-6679	174	4	θ1	θ1	NOUN
ejpam-6679	174	5	,	,	PUNCT
ejpam-6679	174	6	.	.	PUNCT
ejpam-6679	174	7	.	.	PUNCT
ejpam-6679	174	8	.	.	PUNCT
ejpam-6679	175	1	,	,	PUNCT
ejpam-6679	175	2	θn	θn	NOUN
ejpam-6679	175	3	)	)	PUNCT
ejpam-6679	175	4	,	,	PUNCT
ejpam-6679	175	5	ϑ1	ϑ1	NOUN
ejpam-6679	175	6	,	,	PUNCT
ejpam-6679	175	7	.	.	PUNCT
ejpam-6679	175	8	.	.	PUNCT
ejpam-6679	176	1	.	.	PUNCT
ejpam-6679	177	1	,	,	PUNCT
ejpam-6679	177	2	ϑn	ϑn	NOUN
ejpam-6679	177	3	)	)	PUNCT
ejpam-6679	177	4	t.	t.	NOUN
ejpam-6679	177	5	changphas	changphas	PROPN
ejpam-6679	177	6	/	/	SYM
ejpam-6679	177	7	eur	eur	PROPN
ejpam-6679	177	8	.	.	PUNCT
ejpam-6679	178	1	j.	j.	PROPN
ejpam-6679	178	2	pure	pure	PROPN
ejpam-6679	178	3	appl	appl	PROPN
ejpam-6679	178	4	.	.	PROPN
ejpam-6679	178	5	math	math	PROPN
ejpam-6679	178	6	,	,	PUNCT
ejpam-6679	178	7	18	18	NUM
ejpam-6679	178	8	(	(	PUNCT
ejpam-6679	178	9	4	4	NUM
ejpam-6679	178	10	)	)	PUNCT
ejpam-6679	178	11	(	(	PUNCT
ejpam-6679	178	12	2025	2025	NUM
ejpam-6679	178	13	)	)	PUNCT
ejpam-6679	178	14	,	,	PUNCT
ejpam-6679	178	15	6679	6679	NUM
ejpam-6679	178	16	5	5	NUM
ejpam-6679	178	17	of	of	ADP
ejpam-6679	178	18	15	15	NUM
ejpam-6679	178	19	=	=	SYM
ejpam-6679	178	20	sn(sn(fi(ωσ(1	sn(sn(fi(ωσ(1	NOUN
ejpam-6679	178	21	)	)	PUNCT
ejpam-6679	178	22	,	,	PUNCT
ejpam-6679	178	23	.	.	PUNCT
ejpam-6679	178	24	.	.	PUNCT
ejpam-6679	178	25	.	.	PUNCT
ejpam-6679	179	1	,	,	PUNCT
ejpam-6679	179	2	ωσ(n	ωσ(n	NOUN
ejpam-6679	179	3	)	)	PUNCT
ejpam-6679	179	4	)	)	PUNCT
ejpam-6679	179	5	,	,	PUNCT
ejpam-6679	179	6	θ1	θ1	NOUN
ejpam-6679	179	7	,	,	PUNCT
ejpam-6679	179	8	.	.	PUNCT
ejpam-6679	179	9	.	.	PUNCT
ejpam-6679	179	10	.	.	PUNCT
ejpam-6679	180	1	,	,	PUNCT
ejpam-6679	180	2	θn	θn	NOUN
ejpam-6679	180	3	)	)	PUNCT
ejpam-6679	180	4	,	,	PUNCT
ejpam-6679	180	5	ϑ1	ϑ1	NOUN
ejpam-6679	180	6	,	,	PUNCT
ejpam-6679	180	7	.	.	PUNCT
ejpam-6679	180	8	.	.	PUNCT
ejpam-6679	181	1	.	.	PUNCT
ejpam-6679	182	1	,	,	PUNCT
ejpam-6679	182	2	ϑn	ϑn	NOUN
ejpam-6679	182	3	)	)	PUNCT
ejpam-6679	182	4	=	=	SYM
ejpam-6679	182	5	sn(fi(θσ(1	sn(fi(θσ(1	NOUN
ejpam-6679	182	6	)	)	PUNCT
ejpam-6679	182	7	,	,	PUNCT
ejpam-6679	182	8	θσ(2	θσ(2	NOUN
ejpam-6679	182	9	)	)	PUNCT
ejpam-6679	182	10	,	,	PUNCT
ejpam-6679	182	11	.	.	PUNCT
ejpam-6679	182	12	.	.	PUNCT
ejpam-6679	183	1	.	.	PUNCT
ejpam-6679	184	1	,	,	PUNCT
ejpam-6679	184	2	θσ(n	θσ(n	NOUN
ejpam-6679	184	3	)	)	PUNCT
ejpam-6679	184	4	)	)	PUNCT
ejpam-6679	184	5	,	,	PUNCT
ejpam-6679	185	1	ϑ1	ϑ1	NOUN
ejpam-6679	185	2	,	,	PUNCT
ejpam-6679	185	3	.	.	PUNCT
ejpam-6679	185	4	.	.	PUNCT
ejpam-6679	185	5	.	.	PUNCT
ejpam-6679	186	1	,	,	PUNCT
ejpam-6679	186	2	ϑn	ϑn	NOUN
ejpam-6679	186	3	)	)	PUNCT
ejpam-6679	186	4	=	=	SYM
ejpam-6679	186	5	fi(s	fi(s	X
ejpam-6679	186	6	n(θσ(1	n(θσ(1	NOUN
ejpam-6679	186	7	)	)	PUNCT
ejpam-6679	186	8	,	,	PUNCT
ejpam-6679	186	9	ϑ1	ϑ1	PROPN
ejpam-6679	186	10	,	,	PUNCT
ejpam-6679	186	11	.	.	PUNCT
ejpam-6679	186	12	.	.	PUNCT
ejpam-6679	187	1	.	.	PUNCT
ejpam-6679	188	1	,	,	PUNCT
ejpam-6679	188	2	ϑn	ϑn	NOUN
ejpam-6679	188	3	)	)	PUNCT
ejpam-6679	188	4	,	,	PUNCT
ejpam-6679	188	5	.	.	PUNCT
ejpam-6679	188	6	.	.	PUNCT
ejpam-6679	189	1	.	.	PUNCT
ejpam-6679	190	1	,	,	PUNCT
ejpam-6679	190	2	s	s	NOUN
ejpam-6679	190	3	n(θσ(n	n(θσ(n	PROPN
ejpam-6679	190	4	)	)	PUNCT
ejpam-6679	190	5	,	,	PUNCT
ejpam-6679	190	6	ϑ1	ϑ1	NOUN
ejpam-6679	190	7	,	,	PUNCT
ejpam-6679	190	8	.	.	PUNCT
ejpam-6679	190	9	.	.	PUNCT
ejpam-6679	191	1	.	.	PUNCT
ejpam-6679	192	1	,	,	PUNCT
ejpam-6679	192	2	ϑn	ϑn	NOUN
ejpam-6679	192	3	)	)	PUNCT
ejpam-6679	192	4	)	)	PUNCT
ejpam-6679	193	1	=	=	SYM
ejpam-6679	193	2	sn(fi(ωσ(1	sn(fi(ωσ(1	NOUN
ejpam-6679	193	3	)	)	PUNCT
ejpam-6679	193	4	,	,	PUNCT
ejpam-6679	193	5	.	.	PUNCT
ejpam-6679	193	6	.	.	PUNCT
ejpam-6679	193	7	.	.	PUNCT
ejpam-6679	194	1	,	,	PUNCT
ejpam-6679	194	2	ωσ(n	ωσ(n	NOUN
ejpam-6679	194	3	)	)	PUNCT
ejpam-6679	194	4	)	)	PUNCT
ejpam-6679	194	5	,	,	PUNCT
ejpam-6679	194	6	s	s	NOUN
ejpam-6679	194	7	n(θ1	n(θ1	NOUN
ejpam-6679	194	8	,	,	PUNCT
ejpam-6679	194	9	ϑ1	ϑ1	PROPN
ejpam-6679	194	10	,	,	PUNCT
ejpam-6679	194	11	.	.	PUNCT
ejpam-6679	194	12	.	.	PUNCT
ejpam-6679	195	1	.	.	PUNCT
ejpam-6679	196	1	,	,	PUNCT
ejpam-6679	196	2	ϑn	ϑn	NOUN
ejpam-6679	196	3	)	)	PUNCT
ejpam-6679	196	4	,	,	PUNCT
ejpam-6679	196	5	.	.	PUNCT
ejpam-6679	196	6	.	.	PUNCT
ejpam-6679	197	1	.	.	PUNCT
ejpam-6679	198	1	,	,	PUNCT
ejpam-6679	198	2	s	s	PROPN
ejpam-6679	198	3	n(θn	n(θn	PROPN
ejpam-6679	198	4	,	,	PUNCT
ejpam-6679	198	5	ϑ1	ϑ1	NOUN
ejpam-6679	198	6	,	,	PUNCT
ejpam-6679	198	7	.	.	PUNCT
ejpam-6679	198	8	.	.	PUNCT
ejpam-6679	199	1	.	.	PUNCT
ejpam-6679	200	1	,	,	PUNCT
ejpam-6679	200	2	ϑn	ϑn	NOUN
ejpam-6679	200	3	)	)	PUNCT
ejpam-6679	200	4	)	)	PUNCT
ejpam-6679	201	1	=	=	SYM
ejpam-6679	201	2	sn(θ	sn(θ	X
ejpam-6679	201	3	,	,	PUNCT
ejpam-6679	201	4	sn(θ1	sn(θ1	NOUN
ejpam-6679	201	5	,	,	PUNCT
ejpam-6679	201	6	ϑ1	ϑ1	PROPN
ejpam-6679	201	7	,	,	PUNCT
ejpam-6679	201	8	.	.	PUNCT
ejpam-6679	201	9	.	.	PUNCT
ejpam-6679	201	10	.	.	PUNCT
ejpam-6679	202	1	,	,	PUNCT
ejpam-6679	202	2	ϑn	ϑn	NOUN
ejpam-6679	202	3	)	)	PUNCT
ejpam-6679	202	4	,	,	PUNCT
ejpam-6679	202	5	.	.	PUNCT
ejpam-6679	202	6	.	.	PUNCT
ejpam-6679	203	1	.	.	PUNCT
ejpam-6679	204	1	,	,	PUNCT
ejpam-6679	204	2	s	s	PROPN
ejpam-6679	204	3	n(θn	n(θn	PROPN
ejpam-6679	204	4	,	,	PUNCT
ejpam-6679	204	5	ϑ1	ϑ1	NOUN
ejpam-6679	204	6	,	,	PUNCT
ejpam-6679	204	7	.	.	PUNCT
ejpam-6679	204	8	.	.	PUNCT
ejpam-6679	205	1	.	.	PUNCT
ejpam-6679	206	1	,	,	PUNCT
ejpam-6679	206	2	ϑn	ϑn	NOUN
ejpam-6679	206	3	)	)	PUNCT
ejpam-6679	206	4	)	)	PUNCT
ejpam-6679	206	5	.	.	PUNCT
ejpam-6679	207	1	let	let	VERB
ejpam-6679	207	2	θ	θ	NOUN
ejpam-6679	207	3	=	=	SYM
ejpam-6679	207	4	fi(θ	fi(θ	NOUN
ejpam-6679	207	5	′	′	NUM
ejpam-6679	207	6	1	1	NUM
ejpam-6679	207	7	,	,	PUNCT
ejpam-6679	207	8	.	.	PUNCT
ejpam-6679	207	9	.	.	PUNCT
ejpam-6679	208	1	.	.	PUNCT
ejpam-6679	209	1	,	,	PUNCT
ejpam-6679	209	2	θ	θ	NOUN
ejpam-6679	209	3	′	′	NUM
ejpam-6679	209	4	n	n	CCONJ
ejpam-6679	209	5	)	)	PUNCT
ejpam-6679	209	6	be	be	AUX
ejpam-6679	209	7	such	such	ADJ
ejpam-6679	209	8	that	that	SCONJ
ejpam-6679	209	9	sn(sn(θ′j	sn(sn(θ′j	PROPN
ejpam-6679	209	10	,	,	PUNCT
ejpam-6679	209	11	θ1	θ1	NOUN
ejpam-6679	209	12	,	,	PUNCT
ejpam-6679	209	13	.	.	PUNCT
ejpam-6679	209	14	.	.	PUNCT
ejpam-6679	210	1	.	.	PUNCT
ejpam-6679	211	1	,	,	PUNCT
ejpam-6679	211	2	θn	θn	NOUN
ejpam-6679	211	3	)	)	PUNCT
ejpam-6679	211	4	,	,	PUNCT
ejpam-6679	211	5	ϑ1	ϑ1	NOUN
ejpam-6679	211	6	,	,	PUNCT
ejpam-6679	211	7	.	.	PUNCT
ejpam-6679	211	8	.	.	PUNCT
ejpam-6679	212	1	.	.	PUNCT
ejpam-6679	213	1	,	,	PUNCT
ejpam-6679	213	2	ϑn	ϑn	NOUN
ejpam-6679	213	3	)	)	PUNCT
ejpam-6679	214	1	=	=	SYM
ejpam-6679	214	2	sn(θ′j	sn(θ′j	PROPN
ejpam-6679	214	3	,	,	PUNCT
ejpam-6679	214	4	s	s	NOUN
ejpam-6679	214	5	n(θ1	n(θ1	ADJ
ejpam-6679	214	6	,	,	PUNCT
ejpam-6679	214	7	ϑ1	ϑ1	PROPN
ejpam-6679	214	8	,	,	PUNCT
ejpam-6679	214	9	.	.	PUNCT
ejpam-6679	214	10	.	.	PUNCT
ejpam-6679	214	11	.	.	PUNCT
ejpam-6679	215	1	,	,	PUNCT
ejpam-6679	215	2	ϑn	ϑn	NOUN
ejpam-6679	215	3	)	)	PUNCT
ejpam-6679	215	4	,	,	PUNCT
ejpam-6679	215	5	.	.	PUNCT
ejpam-6679	215	6	.	.	PUNCT
ejpam-6679	216	1	.	.	PUNCT
ejpam-6679	217	1	,	,	PUNCT
ejpam-6679	217	2	s	s	PROPN
ejpam-6679	217	3	n(θn	n(θn	PROPN
ejpam-6679	217	4	,	,	PUNCT
ejpam-6679	217	5	ϑ1	ϑ1	NOUN
ejpam-6679	217	6	,	,	PUNCT
ejpam-6679	217	7	.	.	PUNCT
ejpam-6679	217	8	.	.	PUNCT
ejpam-6679	218	1	.	.	PUNCT
ejpam-6679	219	1	,	,	PUNCT
ejpam-6679	219	2	ϑn	ϑn	NOUN
ejpam-6679	219	3	)	)	PUNCT
ejpam-6679	219	4	)	)	PUNCT
ejpam-6679	220	1	for	for	ADP
ejpam-6679	220	2	any	any	DET
ejpam-6679	220	3	1	1	NUM
ejpam-6679	220	4	≤	≤	NUM
ejpam-6679	220	5	j	j	PROPN
ejpam-6679	220	6	≤	≤	PROPN
ejpam-6679	220	7	n.	n.	NOUN
ejpam-6679	220	8	then	then	ADV
ejpam-6679	220	9	,	,	PUNCT
ejpam-6679	220	10	by	by	ADP
ejpam-6679	220	11	induction	induction	NOUN
ejpam-6679	220	12	hypothesis	hypothesis	NOUN
ejpam-6679	220	13	,	,	PUNCT
ejpam-6679	220	14	we	we	PRON
ejpam-6679	220	15	have	have	VERB
ejpam-6679	220	16	sn(sn(θ	sn(sn(θ	NOUN
ejpam-6679	220	17	,	,	PUNCT
ejpam-6679	220	18	θ1	θ1	NOUN
ejpam-6679	220	19	,	,	PUNCT
ejpam-6679	220	20	.	.	PUNCT
ejpam-6679	220	21	.	.	PUNCT
ejpam-6679	221	1	.	.	PUNCT
ejpam-6679	222	1	,	,	PUNCT
ejpam-6679	222	2	θn	θn	NOUN
ejpam-6679	222	3	)	)	PUNCT
ejpam-6679	222	4	,	,	PUNCT
ejpam-6679	222	5	ϑ1	ϑ1	NOUN
ejpam-6679	222	6	,	,	PUNCT
ejpam-6679	222	7	.	.	PUNCT
ejpam-6679	222	8	.	.	PUNCT
ejpam-6679	223	1	.	.	PUNCT
ejpam-6679	224	1	,	,	PUNCT
ejpam-6679	224	2	ϑn	ϑn	NOUN
ejpam-6679	224	3	)	)	PUNCT
ejpam-6679	225	1	=	=	VERB
ejpam-6679	225	2	sn(sn(fi(θ	sn(sn(fi(θ	NOUN
ejpam-6679	225	3	′	′	NOUN
ejpam-6679	225	4	1	1	NUM
ejpam-6679	225	5	,	,	PUNCT
ejpam-6679	225	6	.	.	PUNCT
ejpam-6679	225	7	.	.	PUNCT
ejpam-6679	226	1	.	.	PUNCT
ejpam-6679	227	1	,	,	PUNCT
ejpam-6679	227	2	θ	θ	NOUN
ejpam-6679	227	3	′	′	NUM
ejpam-6679	227	4	n	n	CCONJ
ejpam-6679	227	5	)	)	PUNCT
ejpam-6679	227	6	,	,	PUNCT
ejpam-6679	227	7	θ1	θ1	NOUN
ejpam-6679	227	8	,	,	PUNCT
ejpam-6679	227	9	.	.	PUNCT
ejpam-6679	227	10	.	.	PUNCT
ejpam-6679	228	1	.	.	PUNCT
ejpam-6679	229	1	,	,	PUNCT
ejpam-6679	229	2	θn	θn	NOUN
ejpam-6679	229	3	)	)	PUNCT
ejpam-6679	229	4	,	,	PUNCT
ejpam-6679	229	5	ϑ1	ϑ1	NOUN
ejpam-6679	229	6	,	,	PUNCT
ejpam-6679	229	7	.	.	PUNCT
ejpam-6679	229	8	.	.	PUNCT
ejpam-6679	230	1	.	.	PUNCT
ejpam-6679	231	1	,	,	PUNCT
ejpam-6679	231	2	ϑn	ϑn	NOUN
ejpam-6679	231	3	)	)	PUNCT
ejpam-6679	231	4	=	=	SYM
ejpam-6679	232	1	sn(fi(s	sn(fi(s	NOUN
ejpam-6679	232	2	n(θ′1	n(θ′1	NUM
ejpam-6679	232	3	,	,	PUNCT
ejpam-6679	232	4	θ1	θ1	NOUN
ejpam-6679	232	5	,	,	PUNCT
ejpam-6679	232	6	.	.	PUNCT
ejpam-6679	232	7	.	.	PUNCT
ejpam-6679	233	1	.	.	PUNCT
ejpam-6679	234	1	,	,	PUNCT
ejpam-6679	234	2	θn	θn	NOUN
ejpam-6679	234	3	)	)	PUNCT
ejpam-6679	234	4	,	,	PUNCT
ejpam-6679	234	5	.	.	PUNCT
ejpam-6679	234	6	.	.	PUNCT
ejpam-6679	235	1	.	.	PUNCT
ejpam-6679	236	1	,	,	PUNCT
ejpam-6679	236	2	s	s	VERB
ejpam-6679	236	3	n(θ′n	n(θ′n	ADJ
ejpam-6679	236	4	,	,	PUNCT
ejpam-6679	236	5	θ1	θ1	NOUN
ejpam-6679	236	6	,	,	PUNCT
ejpam-6679	236	7	.	.	PUNCT
ejpam-6679	236	8	.	.	PUNCT
ejpam-6679	237	1	.	.	PUNCT
ejpam-6679	238	1	,	,	PUNCT
ejpam-6679	238	2	θn	θn	NOUN
ejpam-6679	238	3	)	)	PUNCT
ejpam-6679	238	4	)	)	PUNCT
ejpam-6679	238	5	,	,	PUNCT
ejpam-6679	238	6	ϑ1	ϑ1	NOUN
ejpam-6679	238	7	,	,	PUNCT
ejpam-6679	238	8	.	.	PUNCT
ejpam-6679	238	9	.	.	PUNCT
ejpam-6679	239	1	.	.	PUNCT
ejpam-6679	240	1	,	,	PUNCT
ejpam-6679	240	2	ϑn	ϑn	NOUN
ejpam-6679	240	3	)	)	PUNCT
ejpam-6679	240	4	=	=	SYM
ejpam-6679	240	5	fi(s	fi(s	X
ejpam-6679	240	6	n(sn(θ′1	n(sn(θ′1	PROPN
ejpam-6679	240	7	,	,	PUNCT
ejpam-6679	240	8	θ1	θ1	NOUN
ejpam-6679	240	9	,	,	PUNCT
ejpam-6679	240	10	.	.	PUNCT
ejpam-6679	240	11	.	.	PUNCT
ejpam-6679	241	1	.	.	PUNCT
ejpam-6679	242	1	,	,	PUNCT
ejpam-6679	242	2	θn	θn	NOUN
ejpam-6679	242	3	)	)	PUNCT
ejpam-6679	242	4	,	,	PUNCT
ejpam-6679	242	5	ϑ1	ϑ1	NOUN
ejpam-6679	242	6	,	,	PUNCT
ejpam-6679	242	7	.	.	PUNCT
ejpam-6679	242	8	.	.	PUNCT
ejpam-6679	243	1	.	.	PUNCT
ejpam-6679	244	1	,	,	PUNCT
ejpam-6679	244	2	ϑn	ϑn	NOUN
ejpam-6679	244	3	)	)	PUNCT
ejpam-6679	244	4	,	,	PUNCT
ejpam-6679	244	5	.	.	PUNCT
ejpam-6679	244	6	.	.	PUNCT
ejpam-6679	245	1	.	.	PUNCT
ejpam-6679	246	1	,	,	PUNCT
ejpam-6679	246	2	s	s	VERB
ejpam-6679	246	3	n(sn(θ′n	n(sn(θ′n	NOUN
ejpam-6679	246	4	,	,	PUNCT
ejpam-6679	246	5	θ1	θ1	NOUN
ejpam-6679	246	6	,	,	PUNCT
ejpam-6679	246	7	.	.	PUNCT
ejpam-6679	246	8	.	.	PUNCT
ejpam-6679	247	1	.	.	PUNCT
ejpam-6679	248	1	,	,	PUNCT
ejpam-6679	248	2	θn	θn	NOUN
ejpam-6679	248	3	)	)	PUNCT
ejpam-6679	248	4	,	,	PUNCT
ejpam-6679	248	5	ϑ1	ϑ1	NOUN
ejpam-6679	248	6	,	,	PUNCT
ejpam-6679	248	7	.	.	PUNCT
ejpam-6679	248	8	.	.	PUNCT
ejpam-6679	249	1	.	.	PUNCT
ejpam-6679	250	1	,	,	PUNCT
ejpam-6679	250	2	ϑn	ϑn	NOUN
ejpam-6679	250	3	)	)	PUNCT
ejpam-6679	250	4	)	)	PUNCT
ejpam-6679	251	1	=	=	PRON
ejpam-6679	251	2	fi(s	fi(s	X
ejpam-6679	251	3	n(θ′1	n(θ′1	VERB
ejpam-6679	251	4	,	,	PUNCT
ejpam-6679	251	5	s	s	PART
ejpam-6679	251	6	n(θ1	n(θ1	ADJ
ejpam-6679	251	7	,	,	PUNCT
ejpam-6679	251	8	ϑ1	ϑ1	PROPN
ejpam-6679	251	9	,	,	PUNCT
ejpam-6679	251	10	.	.	PUNCT
ejpam-6679	251	11	.	.	PUNCT
ejpam-6679	251	12	.	.	PUNCT
ejpam-6679	252	1	,	,	PUNCT
ejpam-6679	252	2	ϑn	ϑn	NOUN
ejpam-6679	252	3	)	)	PUNCT
ejpam-6679	252	4	,	,	PUNCT
ejpam-6679	252	5	.	.	PUNCT
ejpam-6679	252	6	.	.	PUNCT
ejpam-6679	253	1	.	.	PUNCT
ejpam-6679	254	1	,	,	PUNCT
ejpam-6679	254	2	s	s	PROPN
ejpam-6679	254	3	n(θn	n(θn	PROPN
ejpam-6679	254	4	,	,	PUNCT
ejpam-6679	254	5	ϑ1	ϑ1	NOUN
ejpam-6679	254	6	,	,	PUNCT
ejpam-6679	254	7	.	.	PUNCT
ejpam-6679	254	8	.	.	PUNCT
ejpam-6679	255	1	.	.	PUNCT
ejpam-6679	256	1	,	,	PUNCT
ejpam-6679	256	2	ϑn	ϑn	NOUN
ejpam-6679	256	3	)	)	PUNCT
ejpam-6679	256	4	)	)	PUNCT
ejpam-6679	256	5	,	,	PUNCT
ejpam-6679	256	6	.	.	PUNCT
ejpam-6679	256	7	.	.	PUNCT
ejpam-6679	257	1	.	.	PUNCT
ejpam-6679	258	1	,	,	PUNCT
ejpam-6679	258	2	sn(θ′n	sn(θ′n	NOUN
ejpam-6679	258	3	,	,	PUNCT
ejpam-6679	258	4	s	s	PART
ejpam-6679	258	5	n(θ1	n(θ1	NOUN
ejpam-6679	258	6	,	,	PUNCT
ejpam-6679	258	7	ϑ1	ϑ1	PROPN
ejpam-6679	258	8	,	,	PUNCT
ejpam-6679	258	9	.	.	PUNCT
ejpam-6679	258	10	.	.	PUNCT
ejpam-6679	259	1	.	.	PUNCT
ejpam-6679	260	1	,	,	PUNCT
ejpam-6679	260	2	ϑn	ϑn	NOUN
ejpam-6679	260	3	)	)	PUNCT
ejpam-6679	260	4	,	,	PUNCT
ejpam-6679	260	5	.	.	PUNCT
ejpam-6679	260	6	.	.	PUNCT
ejpam-6679	261	1	.	.	PUNCT
ejpam-6679	262	1	,	,	PUNCT
ejpam-6679	262	2	s	s	PROPN
ejpam-6679	262	3	n(θn	n(θn	PROPN
ejpam-6679	262	4	,	,	PUNCT
ejpam-6679	262	5	ϑ1	ϑ1	NOUN
ejpam-6679	262	6	,	,	PUNCT
ejpam-6679	262	7	.	.	PUNCT
ejpam-6679	262	8	.	.	PUNCT
ejpam-6679	263	1	.	.	PUNCT
ejpam-6679	264	1	,	,	PUNCT
ejpam-6679	264	2	ϑn	ϑn	NOUN
ejpam-6679	264	3	)	)	PUNCT
ejpam-6679	264	4	)	)	PUNCT
ejpam-6679	264	5	)	)	PUNCT
ejpam-6679	265	1	=	=	PRON
ejpam-6679	265	2	sn(fi(θ	sn(fi(θ	NOUN
ejpam-6679	265	3	′	′	NOUN
ejpam-6679	265	4	1	1	NUM
ejpam-6679	265	5	,	,	PUNCT
ejpam-6679	265	6	.	.	PUNCT
ejpam-6679	265	7	.	.	PUNCT
ejpam-6679	265	8	.	.	PUNCT
ejpam-6679	266	1	,	,	PUNCT
ejpam-6679	266	2	θ	θ	NOUN
ejpam-6679	266	3	′	′	NUM
ejpam-6679	266	4	n	n	CCONJ
ejpam-6679	266	5	)	)	PUNCT
ejpam-6679	266	6	,	,	PUNCT
ejpam-6679	266	7	s	s	NOUN
ejpam-6679	266	8	n(θ1	n(θ1	NOUN
ejpam-6679	266	9	,	,	PUNCT
ejpam-6679	266	10	ϑ1	ϑ1	PROPN
ejpam-6679	266	11	,	,	PUNCT
ejpam-6679	266	12	.	.	PUNCT
ejpam-6679	266	13	.	.	PUNCT
ejpam-6679	267	1	.	.	PUNCT
ejpam-6679	268	1	,	,	PUNCT
ejpam-6679	268	2	ϑn	ϑn	NOUN
ejpam-6679	268	3	)	)	PUNCT
ejpam-6679	268	4	,	,	PUNCT
ejpam-6679	268	5	.	.	PUNCT
ejpam-6679	268	6	.	.	PUNCT
ejpam-6679	269	1	.	.	PUNCT
ejpam-6679	270	1	,	,	PUNCT
ejpam-6679	270	2	s	s	PROPN
ejpam-6679	270	3	n(θn	n(θn	PROPN
ejpam-6679	270	4	,	,	PUNCT
ejpam-6679	270	5	ϑ1	ϑ1	NOUN
ejpam-6679	270	6	,	,	PUNCT
ejpam-6679	270	7	.	.	PUNCT
ejpam-6679	270	8	.	.	PUNCT
ejpam-6679	271	1	.	.	PUNCT
ejpam-6679	272	1	,	,	PUNCT
ejpam-6679	272	2	ϑn	ϑn	NOUN
ejpam-6679	272	3	)	)	PUNCT
ejpam-6679	272	4	)	)	PUNCT
ejpam-6679	273	1	=	=	SYM
ejpam-6679	273	2	sn(θ	sn(θ	X
ejpam-6679	273	3	,	,	PUNCT
ejpam-6679	273	4	sn(θ1	sn(θ1	NOUN
ejpam-6679	273	5	,	,	PUNCT
ejpam-6679	273	6	ϑ1	ϑ1	PROPN
ejpam-6679	273	7	,	,	PUNCT
ejpam-6679	273	8	.	.	PUNCT
ejpam-6679	273	9	.	.	PUNCT
ejpam-6679	273	10	.	.	PUNCT
ejpam-6679	274	1	,	,	PUNCT
ejpam-6679	274	2	ϑn	ϑn	NOUN
ejpam-6679	274	3	)	)	PUNCT
ejpam-6679	274	4	,	,	PUNCT
ejpam-6679	274	5	.	.	PUNCT
ejpam-6679	274	6	.	.	PUNCT
ejpam-6679	275	1	.	.	PUNCT
ejpam-6679	276	1	,	,	PUNCT
ejpam-6679	276	2	s	s	PROPN
ejpam-6679	276	3	n(θn	n(θn	PROPN
ejpam-6679	276	4	,	,	PUNCT
ejpam-6679	276	5	ϑ1	ϑ1	NOUN
ejpam-6679	276	6	,	,	PUNCT
ejpam-6679	276	7	.	.	PUNCT
ejpam-6679	276	8	.	.	PUNCT
ejpam-6679	277	1	.	.	PUNCT
ejpam-6679	278	1	,	,	PUNCT
ejpam-6679	278	2	ϑn	ϑn	NOUN
ejpam-6679	278	3	)	)	PUNCT
ejpam-6679	278	4	)	)	PUNCT
ejpam-6679	278	5	.	.	PUNCT
ejpam-6679	279	1	the	the	DET
ejpam-6679	279	2	proof	proof	NOUN
ejpam-6679	279	3	is	be	AUX
ejpam-6679	279	4	complete	complete	ADJ
ejpam-6679	279	5	.	.	PUNCT
ejpam-6679	280	1	3	3	X
ejpam-6679	280	2	.	.	X
ejpam-6679	280	3	freeness	freeness	PROPN
ejpam-6679	280	4	let	let	VERB
ejpam-6679	280	5	vmenger	vmenger	NOUN
ejpam-6679	280	6	denote	denote	VERB
ejpam-6679	280	7	the	the	DET
ejpam-6679	280	8	variety	variety	NOUN
ejpam-6679	280	9	of	of	ADP
ejpam-6679	280	10	all	all	DET
ejpam-6679	280	11	menger	menger	PROPN
ejpam-6679	280	12	algebras	algebras	PROPN
ejpam-6679	280	13	of	of	ADP
ejpam-6679	280	14	rank	rank	PROPN
ejpam-6679	280	15	n+	n+	PUNCT
ejpam-6679	280	16	1	1	NUM
ejpam-6679	280	17	,	,	PUNCT
ejpam-6679	280	18	and	and	CCONJ
ejpam-6679	280	19	let	let	VERB
ejpam-6679	280	20	fvmenger	fvmenger	NOUN
ejpam-6679	280	21	(	(	PUNCT
ejpam-6679	280	22	ξ	ξ	X
ejpam-6679	280	23	)	)	PUNCT
ejpam-6679	280	24	=	=	SYM
ejpam-6679	280	25	(	(	PUNCT
ejpam-6679	280	26	fvmenger	fvmenger	X
ejpam-6679	280	27	(	(	PUNCT
ejpam-6679	280	28	ξ	ξ	NOUN
ejpam-6679	280	29	)	)	PUNCT
ejpam-6679	280	30	,	,	PUNCT
ejpam-6679	280	31	s̃n	s̃n	PROPN
ejpam-6679	280	32	)	)	PUNCT
ejpam-6679	280	33	be	be	AUX
ejpam-6679	280	34	the	the	DET
ejpam-6679	280	35	free	free	ADJ
ejpam-6679	280	36	algebra	algebra	NOUN
ejpam-6679	280	37	with	with	ADP
ejpam-6679	280	38	respect	respect	NOUN
ejpam-6679	280	39	to	to	ADP
ejpam-6679	280	40	vmenger	vmenger	NOUN
ejpam-6679	280	41	,	,	PUNCT
ejpam-6679	280	42	freely	freely	ADV
ejpam-6679	280	43	generated	generate	VERB
ejpam-6679	280	44	by	by	ADP
ejpam-6679	280	45	an	an	DET
ejpam-6679	280	46	indexed	indexed	ADJ
ejpam-6679	280	47	set	set	NOUN
ejpam-6679	280	48	of	of	ADP
ejpam-6679	280	49	alphabet	alphabet	NOUN
ejpam-6679	280	50	of	of	ADP
ejpam-6679	280	51	variables	variable	NOUN
ejpam-6679	281	1	ξ	ξ	PROPN
ejpam-6679	281	2	=	=	SYM
ejpam-6679	281	3	{	{	PUNCT
ejpam-6679	281	4	ω(i	ω(i	PROPN
ejpam-6679	281	5	,	,	PUNCT
ejpam-6679	281	6	σ	σ	NOUN
ejpam-6679	281	7	)	)	PUNCT
ejpam-6679	281	8	:	:	PUNCT
ejpam-6679	281	9	(	(	PUNCT
ejpam-6679	281	10	i	i	PRON
ejpam-6679	281	11	,	,	PUNCT
ejpam-6679	281	12	σ	σ	PROPN
ejpam-6679	281	13	)	)	PUNCT
ejpam-6679	281	14	∈	∈	PROPN
ejpam-6679	281	15	i	i	PRON
ejpam-6679	281	16	×alt(n	×alt(n	PROPN
ejpam-6679	281	17	)	)	PUNCT
ejpam-6679	281	18	}	}	PUNCT
ejpam-6679	281	19	.	.	PUNCT
ejpam-6679	282	1	theorem	theorem	NOUN
ejpam-6679	282	2	3	3	NUM
ejpam-6679	282	3	.	.	PUNCT
ejpam-6679	283	1	the	the	DET
ejpam-6679	283	2	menger	menger	PROPN
ejpam-6679	283	3	algebra	algebra	PROPN
ejpam-6679	283	4	walt(n	walt(n	PROPN
ejpam-6679	283	5	)	)	PUNCT
ejpam-6679	283	6	τn	τn	X
ejpam-6679	283	7	(	(	PUNCT
ejpam-6679	283	8	ωn	ωn	X
ejpam-6679	283	9	)	)	PUNCT
ejpam-6679	283	10	is	be	AUX
ejpam-6679	283	11	free	free	ADJ
ejpam-6679	283	12	with	with	ADP
ejpam-6679	283	13	respect	respect	NOUN
ejpam-6679	283	14	to	to	ADP
ejpam-6679	283	15	the	the	DET
ejpam-6679	283	16	variety	variety	NOUN
ejpam-6679	283	17	vmenger	vmenger	NOUN
ejpam-6679	283	18	,	,	PUNCT
ejpam-6679	283	19	freely	freely	ADV
ejpam-6679	283	20	generated	generate	VERB
ejpam-6679	283	21	by	by	ADP
ejpam-6679	283	22	ξ	ξ	PROPN
ejpam-6679	283	23	.	.	PUNCT
ejpam-6679	283	24	proof	proof	NOUN
ejpam-6679	283	25	.	.	PUNCT
ejpam-6679	284	1	to	to	PART
ejpam-6679	284	2	prove	prove	VERB
ejpam-6679	284	3	the	the	DET
ejpam-6679	284	4	assertion	assertion	NOUN
ejpam-6679	284	5	we	we	PRON
ejpam-6679	284	6	show	show	VERB
ejpam-6679	284	7	that	that	SCONJ
ejpam-6679	284	8	walt(n	walt(n	NOUN
ejpam-6679	284	9	)	)	PUNCT
ejpam-6679	284	10	τn	τn	X
ejpam-6679	284	11	(	(	PUNCT
ejpam-6679	284	12	ωn	ωn	X
ejpam-6679	284	13	)	)	PUNCT
ejpam-6679	284	14	is	be	AUX
ejpam-6679	284	15	isomorphic	isomorphic	ADJ
ejpam-6679	284	16	to	to	ADP
ejpam-6679	284	17	the	the	DET
ejpam-6679	284	18	algebra	algebra	NOUN
ejpam-6679	284	19	fvmenger	fvmenger	NOUN
ejpam-6679	284	20	(	(	PUNCT
ejpam-6679	284	21	ξ	ξ	NOUN
ejpam-6679	284	22	)	)	PUNCT
ejpam-6679	284	23	.	.	PUNCT
ejpam-6679	285	1	define	define	VERB
ejpam-6679	285	2	a	a	DET
ejpam-6679	285	3	mapping	mapping	NOUN
ejpam-6679	285	4	φ	φ	PROPN
ejpam-6679	285	5	:	:	PUNCT
ejpam-6679	285	6	walt(n	walt(n	NOUN
ejpam-6679	285	7	)	)	PUNCT
ejpam-6679	285	8	τn	τn	X
ejpam-6679	285	9	(	(	PUNCT
ejpam-6679	285	10	ωn	ωn	NOUN
ejpam-6679	285	11	)	)	PUNCT
ejpam-6679	285	12	→	→	SYM
ejpam-6679	285	13	fvmenger	fvmenger	X
ejpam-6679	285	14	(	(	PUNCT
ejpam-6679	285	15	ξ	ξ	NOUN
ejpam-6679	285	16	)	)	PUNCT
ejpam-6679	285	17	by	by	ADP
ejpam-6679	285	18	:	:	PUNCT
ejpam-6679	285	19	t.	t.	PROPN
ejpam-6679	285	20	changphas	changphas	PROPN
ejpam-6679	285	21	/	/	SYM
ejpam-6679	285	22	eur	eur	PROPN
ejpam-6679	285	23	.	.	PUNCT
ejpam-6679	286	1	j.	j.	PROPN
ejpam-6679	286	2	pure	pure	PROPN
ejpam-6679	286	3	appl	appl	PROPN
ejpam-6679	286	4	.	.	PROPN
ejpam-6679	286	5	math	math	PROPN
ejpam-6679	286	6	,	,	PUNCT
ejpam-6679	286	7	18	18	NUM
ejpam-6679	286	8	(	(	PUNCT
ejpam-6679	286	9	4	4	NUM
ejpam-6679	286	10	)	)	PUNCT
ejpam-6679	286	11	(	(	PUNCT
ejpam-6679	286	12	2025	2025	NUM
ejpam-6679	286	13	)	)	PUNCT
ejpam-6679	286	14	,	,	PUNCT
ejpam-6679	286	15	6679	6679	NUM
ejpam-6679	286	16	6	6	NUM
ejpam-6679	286	17	of	of	ADP
ejpam-6679	286	18	15	15	NUM
ejpam-6679	286	19	(	(	PUNCT
ejpam-6679	286	20	1	1	NUM
ejpam-6679	286	21	)	)	PUNCT
ejpam-6679	286	22	φ(fi(ωσ(1	φ(fi(ωσ(1	PROPN
ejpam-6679	286	23	)	)	PUNCT
ejpam-6679	286	24	,	,	PUNCT
ejpam-6679	286	25	.	.	PUNCT
ejpam-6679	286	26	.	.	PUNCT
ejpam-6679	286	27	.	.	PUNCT
ejpam-6679	287	1	,	,	PUNCT
ejpam-6679	287	2	ωσ(n	ωσ(n	NOUN
ejpam-6679	287	3	)	)	PUNCT
ejpam-6679	287	4	)	)	PUNCT
ejpam-6679	287	5	)	)	PUNCT
ejpam-6679	288	1	=	=	PUNCT
ejpam-6679	288	2	ω(i	ω(i	PROPN
ejpam-6679	288	3	,	,	PUNCT
ejpam-6679	288	4	σ	σ	NOUN
ejpam-6679	288	5	)	)	PUNCT
ejpam-6679	288	6	;	;	PUNCT
ejpam-6679	288	7	(	(	PUNCT
ejpam-6679	288	8	2	2	X
ejpam-6679	288	9	)	)	PUNCT
ejpam-6679	288	10	φ(sn(fi(ωσ(1	φ(sn(fi(ωσ(1	NUM
ejpam-6679	288	11	)	)	PUNCT
ejpam-6679	288	12	,	,	PUNCT
ejpam-6679	288	13	.	.	PUNCT
ejpam-6679	288	14	.	.	PUNCT
ejpam-6679	288	15	.	.	PUNCT
ejpam-6679	288	16	,	,	PUNCT
ejpam-6679	288	17	ωσ(n	ωσ(n	NOUN
ejpam-6679	288	18	)	)	PUNCT
ejpam-6679	288	19	)	)	PUNCT
ejpam-6679	288	20	,	,	PUNCT
ejpam-6679	288	21	θ1	θ1	NOUN
ejpam-6679	288	22	,	,	PUNCT
ejpam-6679	288	23	.	.	PUNCT
ejpam-6679	288	24	.	.	PUNCT
ejpam-6679	288	25	.	.	PUNCT
ejpam-6679	288	26	,	,	PUNCT
ejpam-6679	288	27	θn	θn	NOUN
ejpam-6679	288	28	)	)	PUNCT
ejpam-6679	288	29	)	)	PUNCT
ejpam-6679	288	30	=	=	SYM
ejpam-6679	288	31	s̃n(ω(i	s̃n(ω(i	ADJ
ejpam-6679	288	32	,	,	PUNCT
ejpam-6679	288	33	σ),φ(θ1	σ),φ(θ1	PROPN
ejpam-6679	288	34	)	)	PUNCT
ejpam-6679	288	35	,	,	PUNCT
ejpam-6679	288	36	.	.	PUNCT
ejpam-6679	288	37	.	.	PUNCT
ejpam-6679	288	38	.	.	PUNCT
ejpam-6679	289	1	,	,	PUNCT
ejpam-6679	289	2	φ(θn	φ(θn	PROPN
ejpam-6679	289	3	)	)	PUNCT
ejpam-6679	289	4	)	)	PUNCT
ejpam-6679	289	5	for	for	ADP
ejpam-6679	289	6	any	any	PRON
ejpam-6679	289	7	(	(	PUNCT
ejpam-6679	289	8	i	i	PROPN
ejpam-6679	289	9	,	,	PUNCT
ejpam-6679	289	10	σ	σ	PROPN
ejpam-6679	289	11	)	)	PUNCT
ejpam-6679	289	12	∈	∈	PROPN
ejpam-6679	290	1	i	i	PRON
ejpam-6679	290	2	×alt(n	×alt(n	PROPN
ejpam-6679	290	3	)	)	PUNCT
ejpam-6679	290	4	and	and	CCONJ
ejpam-6679	290	5	θ1	θ1	NOUN
ejpam-6679	290	6	,	,	PUNCT
ejpam-6679	290	7	.	.	PUNCT
ejpam-6679	290	8	.	.	PUNCT
ejpam-6679	290	9	.	.	PUNCT
ejpam-6679	291	1	,	,	PUNCT
ejpam-6679	291	2	θn	θn	PRON
ejpam-6679	291	3	∈w	∈w	NOUN
ejpam-6679	291	4	alt(n	alt(n	NOUN
ejpam-6679	291	5	)	)	PUNCT
ejpam-6679	291	6	τn	τn	X
ejpam-6679	291	7	(	(	PUNCT
ejpam-6679	291	8	ωn	ωn	NUM
ejpam-6679	291	9	)	)	PUNCT
ejpam-6679	291	10	.	.	PUNCT
ejpam-6679	292	1	the	the	DET
ejpam-6679	292	2	mapping	mapping	NOUN
ejpam-6679	292	3	φ	φ	PROPN
ejpam-6679	292	4	is	be	AUX
ejpam-6679	292	5	a	a	DET
ejpam-6679	292	6	homomorphism	homomorphism	NOUN
ejpam-6679	292	7	,	,	PUNCT
ejpam-6679	292	8	i.e.	i.e.	X
ejpam-6679	292	9	,	,	PUNCT
ejpam-6679	292	10	φ(sn(θ	φ(sn(θ	NOUN
ejpam-6679	292	11	,	,	PUNCT
ejpam-6679	292	12	θ1	θ1	NOUN
ejpam-6679	292	13	,	,	PUNCT
ejpam-6679	292	14	.	.	PUNCT
ejpam-6679	292	15	.	.	PUNCT
ejpam-6679	293	1	.	.	PUNCT
ejpam-6679	294	1	,	,	PUNCT
ejpam-6679	294	2	θn	θn	NOUN
ejpam-6679	294	3	)	)	PUNCT
ejpam-6679	294	4	)	)	PUNCT
ejpam-6679	295	1	=	=	PUNCT
ejpam-6679	295	2	s̃n(φ(θ),φ(θ1	s̃n(φ(θ),φ(θ1	PROPN
ejpam-6679	295	3	)	)	PUNCT
ejpam-6679	295	4	,	,	PUNCT
ejpam-6679	295	5	.	.	PUNCT
ejpam-6679	295	6	.	.	PUNCT
ejpam-6679	295	7	.	.	PUNCT
ejpam-6679	296	1	,	,	PUNCT
ejpam-6679	296	2	φ(θn	φ(θn	PROPN
ejpam-6679	296	3	)	)	PUNCT
ejpam-6679	296	4	)	)	PUNCT
ejpam-6679	297	1	for	for	ADP
ejpam-6679	297	2	all	all	DET
ejpam-6679	297	3	θ	θ	PROPN
ejpam-6679	297	4	,	,	PUNCT
ejpam-6679	297	5	θ1	θ1	NOUN
ejpam-6679	297	6	,	,	PUNCT
ejpam-6679	297	7	.	.	PUNCT
ejpam-6679	297	8	.	.	PUNCT
ejpam-6679	297	9	.	.	PUNCT
ejpam-6679	298	1	,	,	PUNCT
ejpam-6679	298	2	θn	θn	PROPN
ejpam-6679	298	3	∈	∈	PROPN
ejpam-6679	298	4	w	w	PROPN
ejpam-6679	298	5	alt(n	alt(n	PROPN
ejpam-6679	298	6	)	)	PUNCT
ejpam-6679	298	7	τn	τn	X
ejpam-6679	298	8	(	(	PUNCT
ejpam-6679	298	9	ωn	ωn	NUM
ejpam-6679	298	10	)	)	PUNCT
ejpam-6679	298	11	.	.	PUNCT
ejpam-6679	299	1	suppose	suppose	VERB
ejpam-6679	299	2	θ	θ	PROPN
ejpam-6679	299	3	=	=	SYM
ejpam-6679	299	4	fi(ωσ(1	fi(ωσ(1	NOUN
ejpam-6679	299	5	)	)	PUNCT
ejpam-6679	299	6	,	,	PUNCT
ejpam-6679	299	7	.	.	PUNCT
ejpam-6679	299	8	.	.	PUNCT
ejpam-6679	300	1	.	.	PUNCT
ejpam-6679	301	1	,	,	PUNCT
ejpam-6679	301	2	ωσ(n	ωσ(n	NOUN
ejpam-6679	301	3	)	)	PUNCT
ejpam-6679	301	4	)	)	PUNCT
ejpam-6679	302	1	for	for	ADP
ejpam-6679	302	2	some	some	PRON
ejpam-6679	302	3	i	i	PRON
ejpam-6679	302	4	∈	∈	PROPN
ejpam-6679	303	1	i	i	PRON
ejpam-6679	303	2	and	and	CCONJ
ejpam-6679	303	3	σ	σ	PROPN
ejpam-6679	303	4	∈	∈	PROPN
ejpam-6679	303	5	alt(n	alt(n	PROPN
ejpam-6679	303	6	)	)	PUNCT
ejpam-6679	303	7	.	.	PUNCT
ejpam-6679	304	1	then	then	ADV
ejpam-6679	304	2	φ(sn(θ	φ(sn(θ	NOUN
ejpam-6679	304	3	,	,	PUNCT
ejpam-6679	304	4	θ1	θ1	NOUN
ejpam-6679	304	5	,	,	PUNCT
ejpam-6679	304	6	.	.	PUNCT
ejpam-6679	304	7	.	.	PUNCT
ejpam-6679	304	8	.	.	PUNCT
ejpam-6679	305	1	,	,	PUNCT
ejpam-6679	305	2	θn	θn	NOUN
ejpam-6679	305	3	)	)	PUNCT
ejpam-6679	305	4	)	)	PUNCT
ejpam-6679	306	1	=	=	PUNCT
ejpam-6679	306	2	φ(sn(fi(ωσ(1	φ(sn(fi(ωσ(1	NOUN
ejpam-6679	306	3	)	)	PUNCT
ejpam-6679	306	4	,	,	PUNCT
ejpam-6679	306	5	.	.	PUNCT
ejpam-6679	306	6	.	.	PUNCT
ejpam-6679	306	7	.	.	PUNCT
ejpam-6679	307	1	,	,	PUNCT
ejpam-6679	307	2	ωσ(n	ωσ(n	NOUN
ejpam-6679	307	3	)	)	PUNCT
ejpam-6679	307	4	)	)	PUNCT
ejpam-6679	307	5	,	,	PUNCT
ejpam-6679	307	6	θ1	θ1	NOUN
ejpam-6679	307	7	,	,	PUNCT
ejpam-6679	307	8	.	.	PUNCT
ejpam-6679	307	9	.	.	PUNCT
ejpam-6679	307	10	.	.	PUNCT
ejpam-6679	308	1	,	,	PUNCT
ejpam-6679	308	2	θn	θn	NOUN
ejpam-6679	308	3	)	)	PUNCT
ejpam-6679	308	4	)	)	PUNCT
ejpam-6679	309	1	=	=	SYM
ejpam-6679	309	2	s̃n(ω(i	s̃n(ω(i	ADJ
ejpam-6679	309	3	,	,	PUNCT
ejpam-6679	309	4	σ),φ(θ1	σ),φ(θ1	PROPN
ejpam-6679	309	5	)	)	PUNCT
ejpam-6679	309	6	,	,	PUNCT
ejpam-6679	309	7	.	.	PUNCT
ejpam-6679	309	8	.	.	PUNCT
ejpam-6679	309	9	.	.	PUNCT
ejpam-6679	310	1	,	,	PUNCT
ejpam-6679	310	2	φ(θn	φ(θn	PROPN
ejpam-6679	310	3	)	)	PUNCT
ejpam-6679	310	4	)	)	PUNCT
ejpam-6679	311	1	=	=	SYM
ejpam-6679	311	2	s̃n(φ(fi(ωσ(1	s̃n(φ(fi(ωσ(1	PROPN
ejpam-6679	311	3	)	)	PUNCT
ejpam-6679	311	4	,	,	PUNCT
ejpam-6679	311	5	.	.	PUNCT
ejpam-6679	311	6	.	.	PUNCT
ejpam-6679	312	1	.	.	PUNCT
ejpam-6679	313	1	,	,	PUNCT
ejpam-6679	313	2	ωσ(n))),φ(θ1	ωσ(n))),φ(θ1	PROPN
ejpam-6679	313	3	)	)	PUNCT
ejpam-6679	313	4	,	,	PUNCT
ejpam-6679	313	5	.	.	PUNCT
ejpam-6679	313	6	.	.	PUNCT
ejpam-6679	314	1	.	.	PUNCT
ejpam-6679	315	1	,	,	PUNCT
ejpam-6679	315	2	φ(θn	φ(θn	PROPN
ejpam-6679	315	3	)	)	PUNCT
ejpam-6679	315	4	)	)	PUNCT
ejpam-6679	316	1	=	=	PUNCT
ejpam-6679	316	2	s̃n(φ(θ),φ(θ1	s̃n(φ(θ),φ(θ1	PROPN
ejpam-6679	316	3	)	)	PUNCT
ejpam-6679	316	4	,	,	PUNCT
ejpam-6679	316	5	.	.	PUNCT
ejpam-6679	316	6	.	.	PUNCT
ejpam-6679	316	7	.	.	PUNCT
ejpam-6679	317	1	,	,	PUNCT
ejpam-6679	317	2	φ(θn	φ(θn	PROPN
ejpam-6679	317	3	)	)	PUNCT
ejpam-6679	317	4	)	)	PUNCT
ejpam-6679	317	5	.	.	PUNCT
ejpam-6679	318	1	let	let	VERB
ejpam-6679	318	2	θ	θ	NOUN
ejpam-6679	318	3	=	=	SYM
ejpam-6679	318	4	fi(θ	fi(θ	NOUN
ejpam-6679	318	5	′	′	NUM
ejpam-6679	318	6	1	1	NUM
ejpam-6679	318	7	,	,	PUNCT
ejpam-6679	318	8	.	.	PUNCT
ejpam-6679	318	9	.	.	PUNCT
ejpam-6679	319	1	.	.	PUNCT
ejpam-6679	320	1	,	,	PUNCT
ejpam-6679	320	2	θ	θ	NOUN
ejpam-6679	320	3	′	′	NUM
ejpam-6679	320	4	n	n	CCONJ
ejpam-6679	320	5	)	)	PUNCT
ejpam-6679	320	6	such	such	ADJ
ejpam-6679	320	7	that	that	SCONJ
ejpam-6679	320	8	,	,	PUNCT
ejpam-6679	320	9	for	for	ADP
ejpam-6679	320	10	1	1	NUM
ejpam-6679	320	11	≤	≤	NUM
ejpam-6679	320	12	k	k	NOUN
ejpam-6679	320	13	≤	≤	PROPN
ejpam-6679	320	14	n	n	CCONJ
ejpam-6679	320	15	,	,	PUNCT
ejpam-6679	320	16	φ(sn(θ′k	φ(sn(θ′k	NOUN
ejpam-6679	320	17	,	,	PUNCT
ejpam-6679	320	18	θ1	θ1	NOUN
ejpam-6679	320	19	,	,	PUNCT
ejpam-6679	320	20	.	.	PUNCT
ejpam-6679	320	21	.	.	PUNCT
ejpam-6679	321	1	.	.	PUNCT
ejpam-6679	322	1	,	,	PUNCT
ejpam-6679	322	2	θn	θn	NOUN
ejpam-6679	322	3	)	)	PUNCT
ejpam-6679	322	4	)	)	PUNCT
ejpam-6679	323	1	=	=	SYM
ejpam-6679	323	2	sn(φ(θ′k),φ(θ1	sn(φ(θ′k),φ(θ1	X
ejpam-6679	323	3	)	)	PUNCT
ejpam-6679	323	4	,	,	PUNCT
ejpam-6679	323	5	.	.	PUNCT
ejpam-6679	323	6	.	.	PUNCT
ejpam-6679	323	7	.	.	PUNCT
ejpam-6679	324	1	,	,	PUNCT
ejpam-6679	324	2	φ(θn	φ(θn	PROPN
ejpam-6679	324	3	)	)	PUNCT
ejpam-6679	324	4	)	)	PUNCT
ejpam-6679	324	5	.	.	PUNCT
ejpam-6679	325	1	from	from	ADP
ejpam-6679	325	2	φ(fi(θ	φ(fi(θ	ADP
ejpam-6679	325	3	′	′	NUM
ejpam-6679	325	4	1	1	NUM
ejpam-6679	325	5	,	,	PUNCT
ejpam-6679	325	6	.	.	PUNCT
ejpam-6679	325	7	.	.	PUNCT
ejpam-6679	325	8	.	.	PUNCT
ejpam-6679	326	1	,	,	PUNCT
ejpam-6679	326	2	θ	θ	NOUN
ejpam-6679	326	3	′	′	NUM
ejpam-6679	326	4	n	n	CCONJ
ejpam-6679	326	5	)	)	PUNCT
ejpam-6679	326	6	)	)	PUNCT
ejpam-6679	327	1	=	=	SYM
ejpam-6679	327	2	s̃n(ω(i	s̃n(ω(i	ADJ
ejpam-6679	327	3	,	,	PUNCT
ejpam-6679	327	4	idn),φ(θ	idn),φ(θ	ADJ
ejpam-6679	327	5	′	′	NOUN
ejpam-6679	327	6	1	1	NUM
ejpam-6679	327	7	)	)	PUNCT
ejpam-6679	327	8	,	,	PUNCT
ejpam-6679	327	9	.	.	PUNCT
ejpam-6679	327	10	.	.	PUNCT
ejpam-6679	327	11	.	.	PUNCT
ejpam-6679	328	1	,	,	PUNCT
ejpam-6679	328	2	φ(θ	φ(θ	PROPN
ejpam-6679	328	3	′	′	NUM
ejpam-6679	328	4	n	n	CCONJ
ejpam-6679	328	5	)	)	PUNCT
ejpam-6679	328	6	)	)	PUNCT
ejpam-6679	328	7	for	for	ADP
ejpam-6679	328	8	all	all	DET
ejpam-6679	328	9	θ′1	θ′1	ADJ
ejpam-6679	328	10	,	,	PUNCT
ejpam-6679	328	11	.	.	PUNCT
ejpam-6679	328	12	.	.	PUNCT
ejpam-6679	329	1	.	.	PUNCT
ejpam-6679	330	1	,	,	PUNCT
ejpam-6679	330	2	θ′n	θ′n	PROPN
ejpam-6679	330	3	∈w	∈w	VERB
ejpam-6679	330	4	alt(n	alt(n	NOUN
ejpam-6679	330	5	)	)	PUNCT
ejpam-6679	330	6	τn	τn	X
ejpam-6679	330	7	(	(	PUNCT
ejpam-6679	330	8	ωn	ωn	NOUN
ejpam-6679	330	9	)	)	PUNCT
ejpam-6679	330	10	where	where	SCONJ
ejpam-6679	330	11	idn	idn	PROPN
ejpam-6679	330	12	is	be	AUX
ejpam-6679	330	13	the	the	DET
ejpam-6679	330	14	identity	identity	NOUN
ejpam-6679	330	15	map	map	NOUN
ejpam-6679	330	16	in	in	ADP
ejpam-6679	330	17	alt(n	alt(n	PROPN
ejpam-6679	330	18	)	)	PUNCT
ejpam-6679	330	19	,	,	PUNCT
ejpam-6679	330	20	we	we	PRON
ejpam-6679	330	21	then	then	ADV
ejpam-6679	330	22	have	have	VERB
ejpam-6679	330	23	that	that	DET
ejpam-6679	330	24	φ(sn(θ	φ(sn(θ	NOUN
ejpam-6679	330	25	,	,	PUNCT
ejpam-6679	330	26	θ1	θ1	NOUN
ejpam-6679	330	27	,	,	PUNCT
ejpam-6679	330	28	.	.	PUNCT
ejpam-6679	330	29	.	.	PUNCT
ejpam-6679	330	30	.	.	PUNCT
ejpam-6679	331	1	,	,	PUNCT
ejpam-6679	331	2	θn	θn	NOUN
ejpam-6679	331	3	)	)	PUNCT
ejpam-6679	331	4	)	)	PUNCT
ejpam-6679	332	1	=	=	PUNCT
ejpam-6679	332	2	φ(sn(fi(θ	φ(sn(fi(θ	NOUN
ejpam-6679	332	3	′	′	NOUN
ejpam-6679	332	4	1	1	NUM
ejpam-6679	332	5	,	,	PUNCT
ejpam-6679	332	6	.	.	PUNCT
ejpam-6679	332	7	.	.	PUNCT
ejpam-6679	333	1	.	.	PUNCT
ejpam-6679	334	1	,	,	PUNCT
ejpam-6679	334	2	θ	θ	NOUN
ejpam-6679	334	3	′	′	NUM
ejpam-6679	334	4	n	n	CCONJ
ejpam-6679	334	5	)	)	PUNCT
ejpam-6679	334	6	,	,	PUNCT
ejpam-6679	334	7	θ1	θ1	NOUN
ejpam-6679	334	8	,	,	PUNCT
ejpam-6679	334	9	.	.	PUNCT
ejpam-6679	334	10	.	.	PUNCT
ejpam-6679	335	1	.	.	PUNCT
ejpam-6679	336	1	,	,	PUNCT
ejpam-6679	336	2	θn	θn	NOUN
ejpam-6679	336	3	)	)	PUNCT
ejpam-6679	336	4	)	)	PUNCT
ejpam-6679	337	1	=	=	PUNCT
ejpam-6679	337	2	φ(fi(s	φ(fi(s	NOUN
ejpam-6679	337	3	n(θ′1	n(θ′1	NOUN
ejpam-6679	337	4	,	,	PUNCT
ejpam-6679	337	5	θ1	θ1	NOUN
ejpam-6679	337	6	,	,	PUNCT
ejpam-6679	337	7	.	.	PUNCT
ejpam-6679	337	8	.	.	PUNCT
ejpam-6679	338	1	.	.	PUNCT
ejpam-6679	339	1	,	,	PUNCT
ejpam-6679	339	2	θn	θn	NOUN
ejpam-6679	339	3	)	)	PUNCT
ejpam-6679	339	4	,	,	PUNCT
ejpam-6679	339	5	.	.	PUNCT
ejpam-6679	339	6	.	.	PUNCT
ejpam-6679	340	1	.	.	PUNCT
ejpam-6679	341	1	,	,	PUNCT
ejpam-6679	341	2	s	s	VERB
ejpam-6679	341	3	n(θ′n	n(θ′n	ADJ
ejpam-6679	341	4	,	,	PUNCT
ejpam-6679	341	5	θ1	θ1	NOUN
ejpam-6679	341	6	,	,	PUNCT
ejpam-6679	341	7	.	.	PUNCT
ejpam-6679	341	8	.	.	PUNCT
ejpam-6679	342	1	.	.	PUNCT
ejpam-6679	343	1	,	,	PUNCT
ejpam-6679	343	2	θn	θn	NOUN
ejpam-6679	343	3	)	)	PUNCT
ejpam-6679	343	4	)	)	PUNCT
ejpam-6679	343	5	)	)	PUNCT
ejpam-6679	344	1	=	=	SYM
ejpam-6679	344	2	s̃n(ω(i	s̃n(ω(i	ADJ
ejpam-6679	344	3	,	,	PUNCT
ejpam-6679	344	4	idn),φ(s	idn),φ(s	PROPN
ejpam-6679	344	5	n(θ′1	n(θ′1	NOUN
ejpam-6679	344	6	,	,	PUNCT
ejpam-6679	344	7	θ1	θ1	NOUN
ejpam-6679	344	8	,	,	PUNCT
ejpam-6679	344	9	.	.	PUNCT
ejpam-6679	344	10	.	.	PUNCT
ejpam-6679	344	11	.	.	PUNCT
ejpam-6679	344	12	,	,	PUNCT
ejpam-6679	344	13	θn	θn	NOUN
ejpam-6679	344	14	)	)	PUNCT
ejpam-6679	344	15	)	)	PUNCT
ejpam-6679	344	16	,	,	PUNCT
ejpam-6679	344	17	.	.	PUNCT
ejpam-6679	344	18	.	.	PUNCT
ejpam-6679	344	19	.	.	PUNCT
ejpam-6679	345	1	,	,	PUNCT
ejpam-6679	345	2	φ(s	φ(s	PROPN
ejpam-6679	345	3	n(θ′n	n(θ′n	PROPN
ejpam-6679	345	4	,	,	PUNCT
ejpam-6679	345	5	θ1	θ1	NOUN
ejpam-6679	345	6	,	,	PUNCT
ejpam-6679	345	7	.	.	PUNCT
ejpam-6679	345	8	.	.	PUNCT
ejpam-6679	345	9	.	.	PUNCT
ejpam-6679	346	1	,	,	PUNCT
ejpam-6679	346	2	θn	θn	NOUN
ejpam-6679	346	3	)	)	PUNCT
ejpam-6679	346	4	)	)	PUNCT
ejpam-6679	346	5	)	)	PUNCT
ejpam-6679	347	1	=	=	SYM
ejpam-6679	347	2	s̃n(ω(i	s̃n(ω(i	PROPN
ejpam-6679	347	3	,	,	PUNCT
ejpam-6679	347	4	idn	idn	PROPN
ejpam-6679	347	5	)	)	PUNCT
ejpam-6679	347	6	,	,	PUNCT
ejpam-6679	347	7	s̃	s̃	PROPN
ejpam-6679	347	8	n(φ(θ′1),φ(θ1	n(φ(θ′1),φ(θ1	NUM
ejpam-6679	347	9	)	)	PUNCT
ejpam-6679	347	10	,	,	PUNCT
ejpam-6679	347	11	.	.	PUNCT
ejpam-6679	347	12	.	.	PUNCT
ejpam-6679	347	13	.	.	PUNCT
ejpam-6679	348	1	,	,	PUNCT
ejpam-6679	348	2	φ(θn	φ(θn	PROPN
ejpam-6679	348	3	)	)	PUNCT
ejpam-6679	348	4	)	)	PUNCT
ejpam-6679	348	5	,	,	PUNCT
ejpam-6679	348	6	.	.	PUNCT
ejpam-6679	348	7	.	.	PUNCT
ejpam-6679	349	1	.	.	PUNCT
ejpam-6679	350	1	,	,	PUNCT
ejpam-6679	350	2	s̃	s̃	PROPN
ejpam-6679	350	3	n(φ(θ′n),φ(θ1	n(φ(θ′n),φ(θ1	NUM
ejpam-6679	350	4	)	)	PUNCT
ejpam-6679	350	5	,	,	PUNCT
ejpam-6679	350	6	.	.	PUNCT
ejpam-6679	350	7	.	.	PUNCT
ejpam-6679	351	1	.	.	PUNCT
ejpam-6679	352	1	,	,	PUNCT
ejpam-6679	352	2	φ(θn	φ(θn	PROPN
ejpam-6679	352	3	)	)	PUNCT
ejpam-6679	352	4	)	)	PUNCT
ejpam-6679	352	5	)	)	PUNCT
ejpam-6679	353	1	=	=	SYM
ejpam-6679	353	2	s̃n(s̃n(y(i	s̃n(s̃n(y(i	PROPN
ejpam-6679	353	3	,	,	PUNCT
ejpam-6679	353	4	idn),φ(θ	idn),φ(θ	PROPN
ejpam-6679	353	5	′	′	NUM
ejpam-6679	353	6	1	1	NUM
ejpam-6679	353	7	)	)	PUNCT
ejpam-6679	353	8	,	,	PUNCT
ejpam-6679	353	9	.	.	PUNCT
ejpam-6679	353	10	.	.	PUNCT
ejpam-6679	353	11	.	.	PUNCT
ejpam-6679	354	1	,	,	PUNCT
ejpam-6679	354	2	φ(θ	φ(θ	PROPN
ejpam-6679	354	3	′	′	NUM
ejpam-6679	354	4	n)),φ(θ1	n)),φ(θ1	PROPN
ejpam-6679	354	5	)	)	PUNCT
ejpam-6679	354	6	,	,	PUNCT
ejpam-6679	354	7	.	.	PUNCT
ejpam-6679	354	8	.	.	PUNCT
ejpam-6679	354	9	.	.	PUNCT
ejpam-6679	355	1	,	,	PUNCT
ejpam-6679	355	2	φ(θn	φ(θn	PROPN
ejpam-6679	355	3	)	)	PUNCT
ejpam-6679	355	4	)	)	PUNCT
ejpam-6679	356	1	=	=	PUNCT
ejpam-6679	356	2	s̃n(φ(θ),φ(θ1	s̃n(φ(θ),φ(θ1	PROPN
ejpam-6679	356	3	)	)	PUNCT
ejpam-6679	356	4	,	,	PUNCT
ejpam-6679	356	5	.	.	PUNCT
ejpam-6679	356	6	.	.	PUNCT
ejpam-6679	356	7	.	.	PUNCT
ejpam-6679	357	1	,	,	PUNCT
ejpam-6679	357	2	φ(θn	φ(θn	PROPN
ejpam-6679	357	3	)	)	PUNCT
ejpam-6679	357	4	)	)	PUNCT
ejpam-6679	357	5	.	.	PUNCT
ejpam-6679	358	1	the	the	DET
ejpam-6679	358	2	mapping	mapping	NOUN
ejpam-6679	358	3	φ	φ	PROPN
ejpam-6679	358	4	is	be	AUX
ejpam-6679	358	5	bijective	bijective	ADJ
ejpam-6679	358	6	:	:	PUNCT
ejpam-6679	358	7	assume	assume	VERB
ejpam-6679	358	8	φ(fi(ωσ(1	φ(fi(ωσ(1	PROPN
ejpam-6679	358	9	)	)	PUNCT
ejpam-6679	358	10	,	,	PUNCT
ejpam-6679	358	11	.	.	PUNCT
ejpam-6679	358	12	.	.	PUNCT
ejpam-6679	359	1	.	.	PUNCT
ejpam-6679	360	1	,	,	PUNCT
ejpam-6679	360	2	ωσ(n	ωσ(n	NOUN
ejpam-6679	360	3	)	)	PUNCT
ejpam-6679	360	4	)	)	PUNCT
ejpam-6679	360	5	)	)	PUNCT
ejpam-6679	361	1	=	=	SYM
ejpam-6679	361	2	φ(fj(ωρ(1	φ(fj(ωρ(1	NOUN
ejpam-6679	361	3	)	)	PUNCT
ejpam-6679	361	4	,	,	PUNCT
ejpam-6679	361	5	.	.	PUNCT
ejpam-6679	361	6	.	.	PUNCT
ejpam-6679	361	7	.	.	PUNCT
ejpam-6679	362	1	,	,	PUNCT
ejpam-6679	362	2	ωρ(n	ωρ(n	NUM
ejpam-6679	362	3	)	)	PUNCT
ejpam-6679	362	4	)	)	PUNCT
ejpam-6679	362	5	)	)	PUNCT
ejpam-6679	363	1	for	for	ADP
ejpam-6679	363	2	some	some	DET
ejpam-6679	363	3	σ	σ	PROPN
ejpam-6679	363	4	,	,	PUNCT
ejpam-6679	363	5	ρ	ρ	PROPN
ejpam-6679	363	6	∈	∈	PROPN
ejpam-6679	363	7	alt(n	alt(n	PROPN
ejpam-6679	363	8	)	)	PUNCT
ejpam-6679	363	9	.	.	PUNCT
ejpam-6679	364	1	then	then	ADV
ejpam-6679	364	2	ω(i	ω(i	PROPN
ejpam-6679	364	3	,	,	PUNCT
ejpam-6679	364	4	σ	σ	X
ejpam-6679	364	5	)	)	PUNCT
ejpam-6679	364	6	=	=	SYM
ejpam-6679	364	7	ω(j	ω(j	PROPN
ejpam-6679	364	8	,	,	PUNCT
ejpam-6679	364	9	ρ	ρ	NOUN
ejpam-6679	364	10	)	)	PUNCT
ejpam-6679	364	11	.	.	PUNCT
ejpam-6679	365	1	this	this	PRON
ejpam-6679	365	2	means	mean	VERB
ejpam-6679	365	3	(	(	PUNCT
ejpam-6679	365	4	i	i	PROPN
ejpam-6679	365	5	,	,	PUNCT
ejpam-6679	365	6	σ	σ	PROPN
ejpam-6679	365	7	)	)	PUNCT
ejpam-6679	365	8	=	=	PUNCT
ejpam-6679	365	9	(	(	PUNCT
ejpam-6679	365	10	j	j	PROPN
ejpam-6679	365	11	,	,	PUNCT
ejpam-6679	365	12	ρ	ρ	PROPN
ejpam-6679	365	13	)	)	PUNCT
ejpam-6679	365	14	.	.	PUNCT
ejpam-6679	366	1	t.	t.	PROPN
ejpam-6679	366	2	changphas	changphas	PROPN
ejpam-6679	366	3	/	/	SYM
ejpam-6679	366	4	eur	eur	PROPN
ejpam-6679	366	5	.	.	PUNCT
ejpam-6679	367	1	j.	j.	PROPN
ejpam-6679	367	2	pure	pure	PROPN
ejpam-6679	367	3	appl	appl	PROPN
ejpam-6679	367	4	.	.	PROPN
ejpam-6679	367	5	math	math	PROPN
ejpam-6679	367	6	,	,	PUNCT
ejpam-6679	367	7	18	18	NUM
ejpam-6679	367	8	(	(	PUNCT
ejpam-6679	367	9	4	4	NUM
ejpam-6679	367	10	)	)	PUNCT
ejpam-6679	367	11	(	(	PUNCT
ejpam-6679	367	12	2025	2025	NUM
ejpam-6679	367	13	)	)	PUNCT
ejpam-6679	367	14	,	,	PUNCT
ejpam-6679	367	15	6679	6679	NUM
ejpam-6679	367	16	7	7	NUM
ejpam-6679	367	17	of	of	ADP
ejpam-6679	367	18	15	15	NUM
ejpam-6679	367	19	so	so	ADV
ejpam-6679	367	20	fi(ωσ(1	fi(ωσ(1	NOUN
ejpam-6679	367	21	)	)	PUNCT
ejpam-6679	367	22	,	,	PUNCT
ejpam-6679	367	23	.	.	PUNCT
ejpam-6679	367	24	.	.	PUNCT
ejpam-6679	367	25	.	.	PUNCT
ejpam-6679	368	1	,	,	PUNCT
ejpam-6679	368	2	ωσ(n	ωσ(n	NOUN
ejpam-6679	368	3	)	)	PUNCT
ejpam-6679	368	4	)	)	PUNCT
ejpam-6679	369	1	=	=	SYM
ejpam-6679	369	2	fj(ωρ(1	fj(ωρ(1	PROPN
ejpam-6679	369	3	)	)	PUNCT
ejpam-6679	369	4	,	,	PUNCT
ejpam-6679	369	5	.	.	PUNCT
ejpam-6679	369	6	.	.	PUNCT
ejpam-6679	370	1	.	.	PUNCT
ejpam-6679	371	1	,	,	PUNCT
ejpam-6679	371	2	ωρ(n	ωρ(n	NUM
ejpam-6679	371	3	)	)	PUNCT
ejpam-6679	371	4	)	)	PUNCT
ejpam-6679	371	5	.	.	PUNCT
ejpam-6679	372	1	if	if	SCONJ
ejpam-6679	372	2	ω(i	ω(i	PROPN
ejpam-6679	372	3	,	,	PUNCT
ejpam-6679	372	4	σ	σ	NOUN
ejpam-6679	372	5	)	)	PUNCT
ejpam-6679	372	6	∈	∈	PROPN
ejpam-6679	372	7	ξ	ξ	PROPN
ejpam-6679	372	8	,	,	PUNCT
ejpam-6679	372	9	then	then	ADV
ejpam-6679	372	10	φ(fi(ωσ(1	φ(fi(ωσ(1	PROPN
ejpam-6679	372	11	)	)	PUNCT
ejpam-6679	372	12	,	,	PUNCT
ejpam-6679	372	13	.	.	PUNCT
ejpam-6679	372	14	.	.	PUNCT
ejpam-6679	372	15	.	.	PUNCT
ejpam-6679	373	1	,	,	PUNCT
ejpam-6679	373	2	ωσ(n	ωσ(n	NOUN
ejpam-6679	373	3	)	)	PUNCT
ejpam-6679	373	4	)	)	PUNCT
ejpam-6679	373	5	)	)	PUNCT
ejpam-6679	374	1	=	=	PUNCT
ejpam-6679	374	2	ω(i	ω(i	PROPN
ejpam-6679	374	3	,	,	PUNCT
ejpam-6679	374	4	σ	σ	NOUN
ejpam-6679	374	5	)	)	PUNCT
ejpam-6679	374	6	.	.	PUNCT
ejpam-6679	375	1	hence	hence	ADV
ejpam-6679	375	2	φ	φ	PROPN
ejpam-6679	375	3	is	be	AUX
ejpam-6679	375	4	an	an	DET
ejpam-6679	375	5	isomorphism	isomorphism	NOUN
ejpam-6679	375	6	,	,	PUNCT
ejpam-6679	375	7	and	and	CCONJ
ejpam-6679	375	8	the	the	DET
ejpam-6679	375	9	proof	proof	NOUN
ejpam-6679	375	10	is	be	AUX
ejpam-6679	375	11	completed	complete	VERB
ejpam-6679	375	12	.	.	PUNCT
ejpam-6679	376	1	4	4	X
ejpam-6679	376	2	.	.	X
ejpam-6679	376	3	alternating	alternate	VERB
ejpam-6679	376	4	hypersubstitutions	hypersubstitution	NOUN
ejpam-6679	376	5	we	we	PRON
ejpam-6679	376	6	begin	begin	VERB
ejpam-6679	376	7	this	this	DET
ejpam-6679	376	8	section	section	NOUN
ejpam-6679	376	9	with	with	ADP
ejpam-6679	376	10	introducing	introduce	VERB
ejpam-6679	376	11	alternating	alternate	VERB
ejpam-6679	376	12	hypersubstitutions	hypersubstitution	NOUN
ejpam-6679	376	13	;	;	PUNCT
ejpam-6679	376	14	hypersubstitutions	hypersubstitution	NOUN
ejpam-6679	376	15	are	be	AUX
ejpam-6679	376	16	important	important	ADJ
ejpam-6679	376	17	notion	notion	NOUN
ejpam-6679	376	18	for	for	ADP
ejpam-6679	376	19	studying	study	VERB
ejpam-6679	376	20	hyperidentities	hyperidentitie	NOUN
ejpam-6679	376	21	and	and	CCONJ
ejpam-6679	376	22	solid	solid	ADJ
ejpam-6679	376	23	vareities	vareitie	NOUN
ejpam-6679	376	24	(	(	PUNCT
ejpam-6679	376	25	see	see	VERB
ejpam-6679	376	26	[	[	X
ejpam-6679	376	27	12	12	NUM
ejpam-6679	376	28	]	]	NUM
ejpam-6679	376	29	)	)	PUNCT
ejpam-6679	376	30	.	.	PUNCT
ejpam-6679	377	1	definition	definition	NOUN
ejpam-6679	377	2	4	4	NUM
ejpam-6679	377	3	.	.	PUNCT
ejpam-6679	378	1	a	a	DET
ejpam-6679	378	2	mapping	mapping	NOUN
ejpam-6679	378	3	α	α	NOUN
ejpam-6679	378	4	:	:	PUNCT
ejpam-6679	378	5	{	{	PUNCT
ejpam-6679	378	6	fi	fi	NOUN
ejpam-6679	378	7	:	:	PUNCT
ejpam-6679	378	8	i	i	PRON
ejpam-6679	378	9	∈	∈	VERB
ejpam-6679	378	10	i	i	PRON
ejpam-6679	378	11	}	}	PUNCT
ejpam-6679	378	12	→walt(n	→walt(n	ADV
ejpam-6679	378	13	)	)	PUNCT
ejpam-6679	378	14	τn	τn	ADP
ejpam-6679	378	15	(	(	PUNCT
ejpam-6679	378	16	ωn	ωn	X
ejpam-6679	378	17	)	)	PUNCT
ejpam-6679	378	18	is	be	AUX
ejpam-6679	378	19	called	call	VERB
ejpam-6679	378	20	an	an	DET
ejpam-6679	378	21	alternating	alternate	VERB
ejpam-6679	378	22	hypersubstitution	hypersubstitution	NOUN
ejpam-6679	378	23	(	(	PUNCT
ejpam-6679	378	24	or	or	CCONJ
ejpam-6679	378	25	alt	alt	ADJ
ejpam-6679	378	26	-	-	PUNCT
ejpam-6679	378	27	hypersubstitution	hypersubstitution	NOUN
ejpam-6679	378	28	)	)	PUNCT
ejpam-6679	378	29	of	of	ADP
ejpam-6679	378	30	type	type	NOUN
ejpam-6679	378	31	τn	τn	PROPN
ejpam-6679	378	32	.	.	PUNCT
ejpam-6679	378	33	to	to	PART
ejpam-6679	378	34	define	define	VERB
ejpam-6679	378	35	the	the	DET
ejpam-6679	378	36	extension	extension	NOUN
ejpam-6679	378	37	of	of	ADP
ejpam-6679	378	38	an	an	DET
ejpam-6679	378	39	alternating	alternate	VERB
ejpam-6679	378	40	hypersubstitution	hypersubstitution	NOUN
ejpam-6679	378	41	of	of	ADP
ejpam-6679	378	42	type	type	NOUN
ejpam-6679	378	43	τn	τn	ADP
ejpam-6679	378	44	to	to	ADP
ejpam-6679	378	45	the	the	DET
ejpam-6679	378	46	set	set	NOUN
ejpam-6679	378	47	w	w	PROPN
ejpam-6679	378	48	alt(n	alt(n	PROPN
ejpam-6679	378	49	)	)	PUNCT
ejpam-6679	378	50	τn	τn	X
ejpam-6679	378	51	(	(	PUNCT
ejpam-6679	378	52	ωn	ωn	NUM
ejpam-6679	378	53	)	)	PUNCT
ejpam-6679	378	54	,	,	PUNCT
ejpam-6679	378	55	for	for	ADP
ejpam-6679	378	56	any	any	DET
ejpam-6679	378	57	θ	θ	PROPN
ejpam-6679	378	58	∈w	∈w	PROPN
ejpam-6679	378	59	alt(n	alt(n	NOUN
ejpam-6679	378	60	)	)	PUNCT
ejpam-6679	378	61	τn	τn	X
ejpam-6679	378	62	(	(	PUNCT
ejpam-6679	378	63	ωn	ωn	X
ejpam-6679	378	64	)	)	PUNCT
ejpam-6679	378	65	and	and	CCONJ
ejpam-6679	378	66	ρ	ρ	PROPN
ejpam-6679	378	67	∈	∈	PROPN
ejpam-6679	378	68	alt(n	alt(n	PROPN
ejpam-6679	378	69	)	)	PUNCT
ejpam-6679	378	70	,	,	PUNCT
ejpam-6679	378	71	let	let	VERB
ejpam-6679	378	72	(	(	PUNCT
ejpam-6679	378	73	1	1	NUM
ejpam-6679	378	74	)	)	PUNCT
ejpam-6679	378	75	(	(	PUNCT
ejpam-6679	378	76	θ)ρ	θ)ρ	X
ejpam-6679	378	77	=	=	SYM
ejpam-6679	378	78	fi(ωρ(σ(1	fi(ωρ(σ(1	NUM
ejpam-6679	378	79	)	)	PUNCT
ejpam-6679	378	80	)	)	PUNCT
ejpam-6679	378	81	,	,	PUNCT
ejpam-6679	378	82	ωρ(σ(2	ωρ(σ(2	NUM
ejpam-6679	378	83	)	)	PUNCT
ejpam-6679	378	84	)	)	PUNCT
ejpam-6679	378	85	,	,	PUNCT
ejpam-6679	378	86	.	.	PUNCT
ejpam-6679	378	87	.	.	PUNCT
ejpam-6679	379	1	.	.	PUNCT
ejpam-6679	380	1	,	,	PUNCT
ejpam-6679	380	2	ωρ(σ(n	ωρ(σ(n	NOUN
ejpam-6679	380	3	)	)	PUNCT
ejpam-6679	380	4	)	)	PUNCT
ejpam-6679	380	5	)	)	PUNCT
ejpam-6679	381	1	if	if	SCONJ
ejpam-6679	381	2	θ	θ	PROPN
ejpam-6679	381	3	=	=	SYM
ejpam-6679	381	4	fi(ωσ(1	fi(ωσ(1	NOUN
ejpam-6679	381	5	)	)	PUNCT
ejpam-6679	381	6	,	,	PUNCT
ejpam-6679	381	7	ωσ(2	ωσ(2	NOUN
ejpam-6679	381	8	)	)	PUNCT
ejpam-6679	381	9	,	,	PUNCT
ejpam-6679	381	10	.	.	PUNCT
ejpam-6679	381	11	.	.	PUNCT
ejpam-6679	381	12	.	.	PUNCT
ejpam-6679	382	1	,	,	PUNCT
ejpam-6679	382	2	ωσ(n	ωσ(n	NOUN
ejpam-6679	382	3	)	)	PUNCT
ejpam-6679	382	4	)	)	PUNCT
ejpam-6679	383	1	for	for	ADP
ejpam-6679	383	2	some	some	PRON
ejpam-6679	383	3	i	i	PRON
ejpam-6679	383	4	∈	∈	PROPN
ejpam-6679	384	1	i	i	PRON
ejpam-6679	384	2	,	,	PUNCT
ejpam-6679	384	3	σ	σ	PROPN
ejpam-6679	384	4	∈	∈	PROPN
ejpam-6679	384	5	alt(n	alt(n	PROPN
ejpam-6679	384	6	)	)	PUNCT
ejpam-6679	384	7	;	;	PUNCT
ejpam-6679	384	8	(	(	PUNCT
ejpam-6679	384	9	2	2	X
ejpam-6679	384	10	)	)	PUNCT
ejpam-6679	384	11	(	(	PUNCT
ejpam-6679	384	12	θ)ρ	θ)ρ	X
ejpam-6679	384	13	=	=	SYM
ejpam-6679	384	14	fi((θ1)ρ	fi((θ1)ρ	PROPN
ejpam-6679	384	15	,	,	PUNCT
ejpam-6679	384	16	(	(	PUNCT
ejpam-6679	384	17	θ2)ρ	θ2)ρ	NOUN
ejpam-6679	384	18	,	,	PUNCT
ejpam-6679	384	19	.	.	PUNCT
ejpam-6679	384	20	.	.	PUNCT
ejpam-6679	384	21	.	.	PUNCT
ejpam-6679	385	1	,	,	PUNCT
ejpam-6679	385	2	(	(	PUNCT
ejpam-6679	385	3	θn)ρ	θn)ρ	PROPN
ejpam-6679	385	4	)	)	PUNCT
ejpam-6679	385	5	if	if	SCONJ
ejpam-6679	385	6	θ	θ	PROPN
ejpam-6679	385	7	=	=	SYM
ejpam-6679	385	8	fi(θ1	fi(θ1	PROPN
ejpam-6679	385	9	,	,	PUNCT
ejpam-6679	385	10	θ2	θ2	PROPN
ejpam-6679	385	11	,	,	PUNCT
ejpam-6679	385	12	.	.	PUNCT
ejpam-6679	385	13	.	.	PUNCT
ejpam-6679	385	14	.	.	PUNCT
ejpam-6679	386	1	,	,	PUNCT
ejpam-6679	386	2	θn	θn	NOUN
ejpam-6679	386	3	)	)	PUNCT
ejpam-6679	386	4	for	for	ADP
ejpam-6679	386	5	some	some	PRON
ejpam-6679	386	6	i	i	PRON
ejpam-6679	386	7	∈	∈	PROPN
ejpam-6679	387	1	i	i	PRON
ejpam-6679	387	2	,	,	PUNCT
ejpam-6679	387	3	θ1	θ1	PROPN
ejpam-6679	387	4	,	,	PUNCT
ejpam-6679	387	5	θ2	θ2	PROPN
ejpam-6679	387	6	,	,	PUNCT
ejpam-6679	387	7	.	.	PUNCT
ejpam-6679	387	8	.	.	PUNCT
ejpam-6679	387	9	.	.	PUNCT
ejpam-6679	388	1	,	,	PUNCT
ejpam-6679	388	2	θn	θn	PROPN
ejpam-6679	388	3	∈	∈	PROPN
ejpam-6679	388	4	w	w	PROPN
ejpam-6679	388	5	alt(n	alt(n	PROPN
ejpam-6679	388	6	)	)	PUNCT
ejpam-6679	389	1	τn	τn	X
ejpam-6679	389	2	(	(	PUNCT
ejpam-6679	389	3	ωn	ωn	NUM
ejpam-6679	389	4	)	)	PUNCT
ejpam-6679	389	5	.	.	PUNCT
ejpam-6679	390	1	it	it	PRON
ejpam-6679	390	2	is	be	AUX
ejpam-6679	390	3	observed	observe	VERB
ejpam-6679	390	4	that	that	SCONJ
ejpam-6679	390	5	(	(	PUNCT
ejpam-6679	390	6	θ)ρ	θ)ρ	X
ejpam-6679	390	7	∈w	∈w	NOUN
ejpam-6679	390	8	alt(n	alt(n	NOUN
ejpam-6679	390	9	)	)	PUNCT
ejpam-6679	390	10	τn	τn	X
ejpam-6679	390	11	(	(	PUNCT
ejpam-6679	390	12	ωn	ωn	X
ejpam-6679	390	13	)	)	PUNCT
ejpam-6679	390	14	for	for	ADP
ejpam-6679	390	15	any	any	DET
ejpam-6679	390	16	ρ	ρ	PROPN
ejpam-6679	390	17	∈	∈	PROPN
ejpam-6679	390	18	alt(n	alt(n	PROPN
ejpam-6679	390	19	)	)	PUNCT
ejpam-6679	390	20	and	and	CCONJ
ejpam-6679	390	21	θ	θ	PROPN
ejpam-6679	390	22	∈w	∈w	VERB
ejpam-6679	390	23	alt(n	alt(n	NOUN
ejpam-6679	390	24	)	)	PUNCT
ejpam-6679	390	25	τn	τn	X
ejpam-6679	390	26	(	(	PUNCT
ejpam-6679	390	27	ωn	ωn	NOUN
ejpam-6679	390	28	)	)	PUNCT
ejpam-6679	390	29	.	.	PUNCT
ejpam-6679	391	1	moreover	moreover	ADV
ejpam-6679	391	2	,	,	PUNCT
ejpam-6679	391	3	(	(	PUNCT
ejpam-6679	391	4	(	(	PUNCT
ejpam-6679	391	5	θ)ρ)σ	θ)ρ)σ	NOUN
ejpam-6679	391	6	=	=	SYM
ejpam-6679	391	7	(	(	PUNCT
ejpam-6679	391	8	θ)σρ	θ)σρ	PROPN
ejpam-6679	391	9	and	and	CCONJ
ejpam-6679	391	10	sn(θ	sn(θ	NOUN
ejpam-6679	391	11	,	,	PUNCT
ejpam-6679	391	12	(	(	PUNCT
ejpam-6679	391	13	θ1)σ	θ1)σ	VERB
ejpam-6679	391	14	,	,	PUNCT
ejpam-6679	391	15	.	.	PUNCT
ejpam-6679	391	16	.	.	PUNCT
ejpam-6679	391	17	.	.	PUNCT
ejpam-6679	392	1	,	,	PUNCT
ejpam-6679	392	2	(	(	PUNCT
ejpam-6679	392	3	θn)σ	θn)σ	NOUN
ejpam-6679	392	4	)	)	PUNCT
ejpam-6679	392	5	)	)	PUNCT
ejpam-6679	393	1	=	=	SYM
ejpam-6679	393	2	(	(	PUNCT
ejpam-6679	393	3	sn(θ	sn(θ	X
ejpam-6679	393	4	,	,	PUNCT
ejpam-6679	393	5	θ1	θ1	NOUN
ejpam-6679	393	6	,	,	PUNCT
ejpam-6679	393	7	.	.	PUNCT
ejpam-6679	393	8	.	.	PUNCT
ejpam-6679	393	9	.	.	PUNCT
ejpam-6679	394	1	,	,	PUNCT
ejpam-6679	394	2	θn))σ	θn))σ	NOUN
ejpam-6679	394	3	for	for	ADP
ejpam-6679	394	4	any	any	DET
ejpam-6679	394	5	θ	θ	NOUN
ejpam-6679	394	6	,	,	PUNCT
ejpam-6679	394	7	θ1	θ1	NOUN
ejpam-6679	394	8	,	,	PUNCT
ejpam-6679	394	9	.	.	PUNCT
ejpam-6679	394	10	.	.	PUNCT
ejpam-6679	394	11	.	.	PUNCT
ejpam-6679	395	1	,	,	PUNCT
ejpam-6679	395	2	θn	θn	PRON
ejpam-6679	395	3	∈w	∈w	NOUN
ejpam-6679	395	4	alt(n	alt(n	NOUN
ejpam-6679	395	5	)	)	PUNCT
ejpam-6679	395	6	τn	τn	X
ejpam-6679	395	7	(	(	PUNCT
ejpam-6679	395	8	ωn	ωn	X
ejpam-6679	395	9	)	)	PUNCT
ejpam-6679	395	10	and	and	CCONJ
ejpam-6679	395	11	σ	σ	PROPN
ejpam-6679	395	12	,	,	PUNCT
ejpam-6679	395	13	ρ	ρ	PROPN
ejpam-6679	395	14	∈	∈	PROPN
ejpam-6679	395	15	alt(n	alt(n	PROPN
ejpam-6679	395	16	)	)	PUNCT
ejpam-6679	395	17	.	.	PUNCT
ejpam-6679	396	1	using	use	VERB
ejpam-6679	396	2	notation	notation	NOUN
ejpam-6679	396	3	introduced	introduce	VERB
ejpam-6679	396	4	above	above	ADV
ejpam-6679	396	5	,	,	PUNCT
ejpam-6679	396	6	an	an	DET
ejpam-6679	396	7	alternating	alternate	VERB
ejpam-6679	396	8	hypersubstitution	hypersubstitution	NOUN
ejpam-6679	396	9	α	α	NOUN
ejpam-6679	396	10	:	:	PUNCT
ejpam-6679	396	11	{	{	PUNCT
ejpam-6679	396	12	fi	fi	NOUN
ejpam-6679	396	13	:	:	PUNCT
ejpam-6679	396	14	i	i	PRON
ejpam-6679	396	15	∈	∈	VERB
ejpam-6679	396	16	i	i	PRON
ejpam-6679	396	17	}	}	PUNCT
ejpam-6679	396	18	→	→	SYM
ejpam-6679	396	19	w	w	PROPN
ejpam-6679	396	20	alt(n	alt(n	PROPN
ejpam-6679	396	21	)	)	PUNCT
ejpam-6679	396	22	τn	τn	X
ejpam-6679	396	23	(	(	PUNCT
ejpam-6679	396	24	ωn	ωn	NOUN
ejpam-6679	396	25	)	)	PUNCT
ejpam-6679	396	26	of	of	ADP
ejpam-6679	396	27	type	type	NOUN
ejpam-6679	396	28	τn	τn	VERB
ejpam-6679	396	29	can	can	AUX
ejpam-6679	396	30	be	be	AUX
ejpam-6679	396	31	extended	extend	VERB
ejpam-6679	396	32	to	to	ADP
ejpam-6679	396	33	a	a	DET
ejpam-6679	396	34	mapping	mapping	NOUN
ejpam-6679	396	35	α̂	α̂	NUM
ejpam-6679	396	36	:	:	PUNCT
ejpam-6679	396	37	walt(n	walt(n	NOUN
ejpam-6679	396	38	)	)	PUNCT
ejpam-6679	396	39	τn	τn	X
ejpam-6679	396	40	(	(	PUNCT
ejpam-6679	396	41	ωn	ωn	NOUN
ejpam-6679	396	42	)	)	PUNCT
ejpam-6679	396	43	→walt(n	→walt(n	ADV
ejpam-6679	396	44	)	)	PUNCT
ejpam-6679	396	45	τn	τn	ADP
ejpam-6679	396	46	(	(	PUNCT
ejpam-6679	396	47	ωn	ωn	X
ejpam-6679	396	48	)	)	PUNCT
ejpam-6679	396	49	by	by	ADP
ejpam-6679	396	50	:	:	PUNCT
ejpam-6679	396	51	(	(	PUNCT
ejpam-6679	396	52	1	1	X
ejpam-6679	396	53	)	)	PUNCT
ejpam-6679	396	54	α̂[fi(ωσ(1	α̂[fi(ωσ(1	NOUN
ejpam-6679	396	55	)	)	PUNCT
ejpam-6679	396	56	,	,	PUNCT
ejpam-6679	396	57	ωσ(2	ωσ(2	NOUN
ejpam-6679	396	58	)	)	PUNCT
ejpam-6679	396	59	,	,	PUNCT
ejpam-6679	396	60	.	.	PUNCT
ejpam-6679	396	61	.	.	PUNCT
ejpam-6679	396	62	.	.	PUNCT
ejpam-6679	397	1	,	,	PUNCT
ejpam-6679	397	2	ωσ(n	ωσ(n	NOUN
ejpam-6679	397	3	)	)	PUNCT
ejpam-6679	397	4	)	)	PUNCT
ejpam-6679	397	5	]	]	PUNCT
ejpam-6679	398	1	=	=	SYM
ejpam-6679	398	2	(	(	PUNCT
ejpam-6679	398	3	α(fi))σ	α(fi))σ	NOUN
ejpam-6679	398	4	;	;	PUNCT
ejpam-6679	398	5	t.	t.	PROPN
ejpam-6679	398	6	changphas	changphas	PROPN
ejpam-6679	398	7	/	/	SYM
ejpam-6679	398	8	eur	eur	PROPN
ejpam-6679	398	9	.	.	PUNCT
ejpam-6679	399	1	j.	j.	PROPN
ejpam-6679	399	2	pure	pure	PROPN
ejpam-6679	399	3	appl	appl	PROPN
ejpam-6679	399	4	.	.	PROPN
ejpam-6679	399	5	math	math	PROPN
ejpam-6679	399	6	,	,	PUNCT
ejpam-6679	399	7	18	18	NUM
ejpam-6679	399	8	(	(	PUNCT
ejpam-6679	399	9	4	4	NUM
ejpam-6679	399	10	)	)	PUNCT
ejpam-6679	399	11	(	(	PUNCT
ejpam-6679	399	12	2025	2025	NUM
ejpam-6679	399	13	)	)	PUNCT
ejpam-6679	399	14	,	,	PUNCT
ejpam-6679	399	15	6679	6679	NUM
ejpam-6679	399	16	8	8	NUM
ejpam-6679	399	17	of	of	ADP
ejpam-6679	399	18	15	15	NUM
ejpam-6679	399	19	(	(	PUNCT
ejpam-6679	399	20	2	2	NUM
ejpam-6679	399	21	)	)	PUNCT
ejpam-6679	399	22	α̂[fi(θ1	α̂[fi(θ1	NOUN
ejpam-6679	399	23	,	,	PUNCT
ejpam-6679	399	24	θ2	θ2	PROPN
ejpam-6679	399	25	,	,	PUNCT
ejpam-6679	399	26	.	.	PUNCT
ejpam-6679	399	27	.	.	PUNCT
ejpam-6679	399	28	.	.	PUNCT
ejpam-6679	400	1	,	,	PUNCT
ejpam-6679	400	2	θn	θn	NOUN
ejpam-6679	400	3	)	)	PUNCT
ejpam-6679	400	4	]	]	PUNCT
ejpam-6679	401	1	=	=	PUNCT
ejpam-6679	401	2	sn(α(fi	sn(α(fi	NOUN
ejpam-6679	401	3	)	)	PUNCT
ejpam-6679	401	4	,	,	PUNCT
ejpam-6679	401	5	α̂[θ1	α̂[θ1	NOUN
ejpam-6679	401	6	]	]	X
ejpam-6679	401	7	,	,	PUNCT
ejpam-6679	401	8	α̂[θ2	α̂[θ2	PUNCT
ejpam-6679	401	9	]	]	PUNCT
ejpam-6679	401	10	,	,	PUNCT
ejpam-6679	401	11	.	.	PUNCT
ejpam-6679	401	12	.	.	PUNCT
ejpam-6679	402	1	.	.	PUNCT
ejpam-6679	403	1	,	,	PUNCT
ejpam-6679	403	2	α̂[θn	α̂[θn	NOUN
ejpam-6679	403	3	]	]	PUNCT
ejpam-6679	403	4	)	)	PUNCT
ejpam-6679	403	5	.	.	PUNCT
ejpam-6679	404	1	lemma	lemma	PROPN
ejpam-6679	404	2	1	1	X
ejpam-6679	404	3	.	.	PUNCT
ejpam-6679	405	1	let	let	VERB
ejpam-6679	405	2	α	α	PRON
ejpam-6679	405	3	be	be	AUX
ejpam-6679	405	4	an	an	DET
ejpam-6679	405	5	alt	alt	ADJ
ejpam-6679	405	6	-	-	PUNCT
ejpam-6679	405	7	hypersubstitution	hypersubstitution	NOUN
ejpam-6679	405	8	of	of	ADP
ejpam-6679	405	9	type	type	NOUN
ejpam-6679	405	10	τn	τn	PROPN
ejpam-6679	405	11	.	.	PUNCT
ejpam-6679	406	1	for	for	ADP
ejpam-6679	406	2	θ	θ	PROPN
ejpam-6679	406	3	,	,	PUNCT
ejpam-6679	406	4	θ1	θ1	NOUN
ejpam-6679	406	5	,	,	PUNCT
ejpam-6679	406	6	θ2	θ2	PROPN
ejpam-6679	406	7	,	,	PUNCT
ejpam-6679	406	8	.	.	PUNCT
ejpam-6679	406	9	.	.	PUNCT
ejpam-6679	407	1	.	.	PUNCT
ejpam-6679	408	1	,	,	PUNCT
ejpam-6679	408	2	θn	θn	PRON
ejpam-6679	408	3	∈w	∈w	NOUN
ejpam-6679	408	4	alt(n	alt(n	NOUN
ejpam-6679	408	5	)	)	PUNCT
ejpam-6679	408	6	τn	τn	X
ejpam-6679	408	7	(	(	PUNCT
ejpam-6679	408	8	ωn	ωn	X
ejpam-6679	408	9	)	)	PUNCT
ejpam-6679	408	10	and	and	CCONJ
ejpam-6679	408	11	ρ	ρ	PROPN
ejpam-6679	408	12	∈	∈	PROPN
ejpam-6679	408	13	alt(n	alt(n	PROPN
ejpam-6679	408	14	)	)	PUNCT
ejpam-6679	408	15	,	,	PUNCT
ejpam-6679	408	16	sn(θ	sn(θ	X
ejpam-6679	408	17	,	,	PUNCT
ejpam-6679	408	18	α̂[θρ(1	α̂[θρ(1	ADJ
ejpam-6679	408	19	)	)	PUNCT
ejpam-6679	408	20	]	]	PUNCT
ejpam-6679	408	21	,	,	PUNCT
ejpam-6679	408	22	.	.	PUNCT
ejpam-6679	408	23	.	.	PUNCT
ejpam-6679	409	1	.	.	PUNCT
ejpam-6679	410	1	,	,	PUNCT
ejpam-6679	410	2	α̂[θρ(n	α̂[θρ(n	NUM
ejpam-6679	410	3	)	)	PUNCT
ejpam-6679	410	4	]	]	PUNCT
ejpam-6679	410	5	)	)	PUNCT
ejpam-6679	411	1	=	=	SYM
ejpam-6679	411	2	sn((θ)ρ	sn((θ)ρ	NOUN
ejpam-6679	411	3	,	,	PUNCT
ejpam-6679	411	4	α̂[θ1	α̂[θ1	NOUN
ejpam-6679	411	5	]	]	X
ejpam-6679	411	6	,	,	PUNCT
ejpam-6679	411	7	.	.	PUNCT
ejpam-6679	411	8	.	.	PUNCT
ejpam-6679	411	9	.	.	PUNCT
ejpam-6679	412	1	,	,	PUNCT
ejpam-6679	412	2	α̂[θn	α̂[θn	NOUN
ejpam-6679	412	3	]	]	PUNCT
ejpam-6679	412	4	)	)	PUNCT
ejpam-6679	412	5	.	.	PUNCT
ejpam-6679	413	1	proof	proof	NOUN
ejpam-6679	413	2	.	.	PUNCT
ejpam-6679	414	1	let	let	VERB
ejpam-6679	414	2	θ	θ	NOUN
ejpam-6679	414	3	,	,	PUNCT
ejpam-6679	414	4	θ1	θ1	NOUN
ejpam-6679	414	5	,	,	PUNCT
ejpam-6679	414	6	.	.	PUNCT
ejpam-6679	414	7	.	.	PUNCT
ejpam-6679	415	1	.	.	PUNCT
ejpam-6679	416	1	,	,	PUNCT
ejpam-6679	416	2	θn	θn	DET
ejpam-6679	416	3	∈w	∈w	NOUN
ejpam-6679	416	4	alt(n	alt(n	NOUN
ejpam-6679	416	5	)	)	PUNCT
ejpam-6679	416	6	τn	τn	ADP
ejpam-6679	416	7	(	(	PUNCT
ejpam-6679	416	8	xn	xn	PROPN
ejpam-6679	416	9	)	)	PUNCT
ejpam-6679	416	10	and	and	CCONJ
ejpam-6679	416	11	ρ	ρ	PROPN
ejpam-6679	416	12	∈	∈	PROPN
ejpam-6679	416	13	alt(n	alt(n	PROPN
ejpam-6679	416	14	)	)	PUNCT
ejpam-6679	416	15	.	.	PUNCT
ejpam-6679	417	1	suppose	suppose	VERB
ejpam-6679	417	2	θ	θ	PROPN
ejpam-6679	417	3	=	=	SYM
ejpam-6679	417	4	fi(ωσ(1	fi(ωσ(1	NOUN
ejpam-6679	417	5	)	)	PUNCT
ejpam-6679	417	6	,	,	PUNCT
ejpam-6679	417	7	.	.	PUNCT
ejpam-6679	417	8	.	.	PUNCT
ejpam-6679	418	1	.	.	PUNCT
ejpam-6679	419	1	,	,	PUNCT
ejpam-6679	419	2	ωσ(n	ωσ(n	NOUN
ejpam-6679	419	3	)	)	PUNCT
ejpam-6679	419	4	)	)	PUNCT
ejpam-6679	420	1	for	for	ADP
ejpam-6679	420	2	some	some	DET
ejpam-6679	420	3	σ	σ	NUM
ejpam-6679	420	4	∈	∈	PROPN
ejpam-6679	420	5	alt(n	alt(n	PROPN
ejpam-6679	420	6	)	)	PUNCT
ejpam-6679	420	7	.	.	PUNCT
ejpam-6679	421	1	then	then	ADV
ejpam-6679	421	2	sn(θ	sn(θ	VERB
ejpam-6679	421	3	,	,	PUNCT
ejpam-6679	421	4	α̂[θρ(1	α̂[θρ(1	ADJ
ejpam-6679	421	5	)	)	PUNCT
ejpam-6679	421	6	]	]	PUNCT
ejpam-6679	421	7	,	,	PUNCT
ejpam-6679	421	8	.	.	PUNCT
ejpam-6679	421	9	.	.	PUNCT
ejpam-6679	422	1	.	.	PUNCT
ejpam-6679	423	1	,	,	PUNCT
ejpam-6679	423	2	α̂[θρ(n	α̂[θρ(n	NUM
ejpam-6679	423	3	)	)	PUNCT
ejpam-6679	423	4	]	]	PUNCT
ejpam-6679	423	5	)	)	PUNCT
ejpam-6679	424	1	=	=	SYM
ejpam-6679	424	2	sn(fi(ωσ(1	sn(fi(ωσ(1	NOUN
ejpam-6679	424	3	)	)	PUNCT
ejpam-6679	424	4	,	,	PUNCT
ejpam-6679	424	5	.	.	PUNCT
ejpam-6679	424	6	.	.	PUNCT
ejpam-6679	424	7	.	.	PUNCT
ejpam-6679	425	1	,	,	PUNCT
ejpam-6679	425	2	ωσ(n	ωσ(n	NOUN
ejpam-6679	425	3	)	)	PUNCT
ejpam-6679	425	4	)	)	PUNCT
ejpam-6679	425	5	,	,	PUNCT
ejpam-6679	425	6	α̂[θρ(1	α̂[θρ(1	ADJ
ejpam-6679	425	7	)	)	PUNCT
ejpam-6679	425	8	]	]	PUNCT
ejpam-6679	425	9	,	,	PUNCT
ejpam-6679	425	10	.	.	PUNCT
ejpam-6679	425	11	.	.	PUNCT
ejpam-6679	426	1	.	.	PUNCT
ejpam-6679	427	1	,	,	PUNCT
ejpam-6679	427	2	α̂[θρ(n	α̂[θρ(n	NUM
ejpam-6679	427	3	)	)	PUNCT
ejpam-6679	427	4	]	]	PUNCT
ejpam-6679	427	5	)	)	PUNCT
ejpam-6679	428	1	=	=	SYM
ejpam-6679	428	2	fi(α̂[θρ(σ(1	fi(α̂[θρ(σ(1	PROPN
ejpam-6679	428	3	)	)	PUNCT
ejpam-6679	428	4	)	)	PUNCT
ejpam-6679	429	1	]	]	PUNCT
ejpam-6679	429	2	,	,	PUNCT
ejpam-6679	429	3	.	.	PUNCT
ejpam-6679	429	4	.	.	PUNCT
ejpam-6679	430	1	.	.	PUNCT
ejpam-6679	431	1	,	,	PUNCT
ejpam-6679	431	2	α̂[θρ(σ(n	α̂[θρ(σ(n	PROPN
ejpam-6679	431	3	)	)	PUNCT
ejpam-6679	431	4	)	)	PUNCT
ejpam-6679	431	5	]	]	PUNCT
ejpam-6679	431	6	)	)	PUNCT
ejpam-6679	432	1	=	=	SYM
ejpam-6679	432	2	sn(fi(ωρ(σ(1	sn(fi(ωρ(σ(1	NOUN
ejpam-6679	432	3	)	)	PUNCT
ejpam-6679	432	4	)	)	PUNCT
ejpam-6679	432	5	,	,	PUNCT
ejpam-6679	432	6	.	.	PUNCT
ejpam-6679	432	7	.	.	PUNCT
ejpam-6679	432	8	.	.	PUNCT
ejpam-6679	433	1	,	,	PUNCT
ejpam-6679	433	2	ωρ(σ(n	ωρ(σ(n	NOUN
ejpam-6679	433	3	)	)	PUNCT
ejpam-6679	433	4	)	)	PUNCT
ejpam-6679	433	5	)	)	PUNCT
ejpam-6679	433	6	,	,	PUNCT
ejpam-6679	434	1	α̂[θ1	α̂[θ1	X
ejpam-6679	434	2	]	]	X
ejpam-6679	434	3	,	,	PUNCT
ejpam-6679	434	4	.	.	PUNCT
ejpam-6679	434	5	.	.	PUNCT
ejpam-6679	435	1	.	.	PUNCT
ejpam-6679	436	1	,	,	PUNCT
ejpam-6679	436	2	α̂[θn	α̂[θn	NUM
ejpam-6679	436	3	]	]	PUNCT
ejpam-6679	436	4	)	)	PUNCT
ejpam-6679	436	5	=	=	SYM
ejpam-6679	436	6	sn((θ)ρ	sn((θ)ρ	NOUN
ejpam-6679	436	7	,	,	PUNCT
ejpam-6679	436	8	α̂[θ1	α̂[θ1	NOUN
ejpam-6679	436	9	]	]	X
ejpam-6679	436	10	,	,	PUNCT
ejpam-6679	436	11	.	.	PUNCT
ejpam-6679	436	12	.	.	PUNCT
ejpam-6679	437	1	.	.	PUNCT
ejpam-6679	438	1	,	,	PUNCT
ejpam-6679	438	2	α̂[θn	α̂[θn	NOUN
ejpam-6679	438	3	]	]	PUNCT
ejpam-6679	438	4	)	)	PUNCT
ejpam-6679	438	5	.	.	PUNCT
ejpam-6679	439	1	let	let	VERB
ejpam-6679	439	2	θ	θ	NOUN
ejpam-6679	439	3	=	=	SYM
ejpam-6679	439	4	fi(θ	fi(θ	NOUN
ejpam-6679	439	5	′	′	NUM
ejpam-6679	439	6	1	1	NUM
ejpam-6679	439	7	,	,	PUNCT
ejpam-6679	439	8	.	.	PUNCT
ejpam-6679	439	9	.	.	PUNCT
ejpam-6679	440	1	.	.	PUNCT
ejpam-6679	441	1	,	,	PUNCT
ejpam-6679	441	2	θ	θ	NOUN
ejpam-6679	441	3	′	′	NUM
ejpam-6679	441	4	n	n	CCONJ
ejpam-6679	441	5	)	)	PUNCT
ejpam-6679	441	6	and	and	CCONJ
ejpam-6679	441	7	assume	assume	VERB
ejpam-6679	441	8	that	that	SCONJ
ejpam-6679	441	9	,	,	PUNCT
ejpam-6679	441	10	for	for	ADP
ejpam-6679	441	11	1	1	NUM
ejpam-6679	441	12	≤	≤	NUM
ejpam-6679	441	13	k	k	NOUN
ejpam-6679	441	14	≤	≤	PROPN
ejpam-6679	441	15	n	n	CCONJ
ejpam-6679	441	16	,	,	PUNCT
ejpam-6679	441	17	sn(θ′k	sn(θ′k	NOUN
ejpam-6679	441	18	,	,	PUNCT
ejpam-6679	441	19	α̂[θρ(1	α̂[θρ(1	ADJ
ejpam-6679	441	20	)	)	PUNCT
ejpam-6679	441	21	]	]	PUNCT
ejpam-6679	441	22	,	,	PUNCT
ejpam-6679	441	23	.	.	PUNCT
ejpam-6679	441	24	.	.	PUNCT
ejpam-6679	441	25	.	.	PUNCT
ejpam-6679	441	26	,	,	PUNCT
ejpam-6679	441	27	α̂[θρ(n	α̂[θρ(n	NUM
ejpam-6679	441	28	)	)	PUNCT
ejpam-6679	441	29	]	]	PUNCT
ejpam-6679	441	30	)	)	PUNCT
ejpam-6679	441	31	=	=	SYM
ejpam-6679	441	32	sn((θ′k)ρ	sn((θ′k)ρ	X
ejpam-6679	441	33	,	,	PUNCT
ejpam-6679	441	34	α̂[θ1	α̂[θ1	X
ejpam-6679	441	35	]	]	X
ejpam-6679	441	36	,	,	PUNCT
ejpam-6679	441	37	.	.	PUNCT
ejpam-6679	441	38	.	.	PUNCT
ejpam-6679	442	1	.	.	PUNCT
ejpam-6679	443	1	,	,	PUNCT
ejpam-6679	443	2	α̂[θn	α̂[θn	NOUN
ejpam-6679	443	3	]	]	PUNCT
ejpam-6679	443	4	)	)	PUNCT
ejpam-6679	443	5	.	.	PUNCT
ejpam-6679	444	1	then	then	ADV
ejpam-6679	444	2	sn(θ	sn(θ	VERB
ejpam-6679	444	3	,	,	PUNCT
ejpam-6679	444	4	α̂[θρ(1	α̂[θρ(1	ADJ
ejpam-6679	444	5	)	)	PUNCT
ejpam-6679	444	6	]	]	PUNCT
ejpam-6679	444	7	,	,	PUNCT
ejpam-6679	444	8	.	.	PUNCT
ejpam-6679	444	9	.	.	PUNCT
ejpam-6679	445	1	.	.	PUNCT
ejpam-6679	446	1	,	,	PUNCT
ejpam-6679	446	2	α̂[θρ(n	α̂[θρ(n	NUM
ejpam-6679	446	3	)	)	PUNCT
ejpam-6679	446	4	]	]	PUNCT
ejpam-6679	446	5	)	)	PUNCT
ejpam-6679	447	1	=	=	SYM
ejpam-6679	447	2	sn(fi(θ	sn(fi(θ	NOUN
ejpam-6679	447	3	′	′	NOUN
ejpam-6679	447	4	1	1	NUM
ejpam-6679	447	5	,	,	PUNCT
ejpam-6679	447	6	.	.	PUNCT
ejpam-6679	447	7	.	.	PUNCT
ejpam-6679	447	8	.	.	PUNCT
ejpam-6679	448	1	,	,	PUNCT
ejpam-6679	448	2	θ	θ	NOUN
ejpam-6679	448	3	′	′	NUM
ejpam-6679	448	4	n	n	CCONJ
ejpam-6679	448	5	)	)	PUNCT
ejpam-6679	448	6	,	,	PUNCT
ejpam-6679	448	7	α̂[θρ(1	α̂[θρ(1	ADJ
ejpam-6679	448	8	)	)	PUNCT
ejpam-6679	448	9	]	]	PUNCT
ejpam-6679	448	10	,	,	PUNCT
ejpam-6679	448	11	.	.	PUNCT
ejpam-6679	448	12	.	.	PUNCT
ejpam-6679	449	1	.	.	PUNCT
ejpam-6679	450	1	,	,	PUNCT
ejpam-6679	450	2	α̂[θρ(n	α̂[θρ(n	NUM
ejpam-6679	450	3	)	)	PUNCT
ejpam-6679	450	4	]	]	PUNCT
ejpam-6679	450	5	)	)	PUNCT
ejpam-6679	451	1	=	=	SYM
ejpam-6679	451	2	fi(s	fi(s	X
ejpam-6679	451	3	n(θ′1	n(θ′1	NUM
ejpam-6679	451	4	,	,	PUNCT
ejpam-6679	451	5	α̂[θρ(1	α̂[θρ(1	ADJ
ejpam-6679	451	6	)	)	PUNCT
ejpam-6679	451	7	]	]	PUNCT
ejpam-6679	451	8	,	,	PUNCT
ejpam-6679	451	9	.	.	PUNCT
ejpam-6679	451	10	.	.	PUNCT
ejpam-6679	451	11	.	.	PUNCT
ejpam-6679	452	1	,	,	PUNCT
ejpam-6679	452	2	α̂[θρ(n	α̂[θρ(n	NUM
ejpam-6679	452	3	)	)	PUNCT
ejpam-6679	452	4	]	]	PUNCT
ejpam-6679	452	5	)	)	PUNCT
ejpam-6679	452	6	,	,	PUNCT
ejpam-6679	452	7	.	.	PUNCT
ejpam-6679	452	8	.	.	PUNCT
ejpam-6679	453	1	.	.	PUNCT
ejpam-6679	454	1	,	,	PUNCT
ejpam-6679	454	2	s	s	VERB
ejpam-6679	454	3	n(θ′n	n(θ′n	PROPN
ejpam-6679	454	4	,	,	PUNCT
ejpam-6679	454	5	α̂[θρ(1	α̂[θρ(1	ADJ
ejpam-6679	454	6	)	)	PUNCT
ejpam-6679	454	7	]	]	PUNCT
ejpam-6679	454	8	,	,	PUNCT
ejpam-6679	454	9	.	.	PUNCT
ejpam-6679	454	10	.	.	PUNCT
ejpam-6679	455	1	.	.	PUNCT
ejpam-6679	456	1	,	,	PUNCT
ejpam-6679	456	2	α̂[θρ(n	α̂[θρ(n	NUM
ejpam-6679	456	3	)	)	PUNCT
ejpam-6679	456	4	]	]	PUNCT
ejpam-6679	456	5	)	)	PUNCT
ejpam-6679	456	6	)	)	PUNCT
ejpam-6679	457	1	=	=	PRON
ejpam-6679	457	2	fi(s	fi(s	NUM
ejpam-6679	457	3	n((θ′1)ρ	n((θ′1)ρ	NOUN
ejpam-6679	457	4	,	,	PUNCT
ejpam-6679	457	5	α̂[θ1	α̂[θ1	NOUN
ejpam-6679	457	6	]	]	X
ejpam-6679	457	7	,	,	PUNCT
ejpam-6679	457	8	.	.	PUNCT
ejpam-6679	457	9	.	.	PUNCT
ejpam-6679	458	1	.	.	PUNCT
ejpam-6679	459	1	,	,	PUNCT
ejpam-6679	459	2	α̂[θn	α̂[θn	NUM
ejpam-6679	459	3	]	]	PUNCT
ejpam-6679	459	4	)	)	PUNCT
ejpam-6679	459	5	,	,	PUNCT
ejpam-6679	459	6	.	.	PUNCT
ejpam-6679	459	7	.	.	PUNCT
ejpam-6679	460	1	.	.	PUNCT
ejpam-6679	461	1	,	,	PUNCT
ejpam-6679	461	2	s	s	VERB
ejpam-6679	461	3	n((θ′n)ρ	n((θ′n)ρ	NOUN
ejpam-6679	461	4	,	,	PUNCT
ejpam-6679	461	5	α̂[θ1	α̂[θ1	NOUN
ejpam-6679	461	6	]	]	X
ejpam-6679	461	7	,	,	PUNCT
ejpam-6679	461	8	.	.	PUNCT
ejpam-6679	461	9	.	.	PUNCT
ejpam-6679	462	1	.	.	PUNCT
ejpam-6679	463	1	,	,	PUNCT
ejpam-6679	463	2	α̂[θn	α̂[θn	NOUN
ejpam-6679	463	3	]	]	PUNCT
ejpam-6679	463	4	)	)	PUNCT
ejpam-6679	463	5	)	)	PUNCT
ejpam-6679	464	1	=	=	PUNCT
ejpam-6679	464	2	sn(fi((θ	sn(fi((θ	NOUN
ejpam-6679	464	3	′	′	NUM
ejpam-6679	464	4	1)ρ	1)ρ	NOUN
ejpam-6679	464	5	,	,	PUNCT
ejpam-6679	464	6	.	.	PUNCT
ejpam-6679	464	7	.	.	PUNCT
ejpam-6679	464	8	.	.	PUNCT
ejpam-6679	465	1	,	,	PUNCT
ejpam-6679	465	2	(	(	PUNCT
ejpam-6679	465	3	θ	θ	NOUN
ejpam-6679	465	4	′	′	NOUN
ejpam-6679	465	5	n)ρ	n)ρ	NUM
ejpam-6679	465	6	)	)	PUNCT
ejpam-6679	465	7	,	,	PUNCT
ejpam-6679	465	8	α̂[θ1	α̂[θ1	X
ejpam-6679	465	9	]	]	X
ejpam-6679	465	10	,	,	PUNCT
ejpam-6679	465	11	.	.	PUNCT
ejpam-6679	465	12	.	.	PUNCT
ejpam-6679	466	1	.	.	PUNCT
ejpam-6679	467	1	,	,	PUNCT
ejpam-6679	467	2	α̂[θn	α̂[θn	NUM
ejpam-6679	467	3	]	]	PUNCT
ejpam-6679	467	4	)	)	PUNCT
ejpam-6679	467	5	=	=	SYM
ejpam-6679	467	6	sn((θ)ρ	sn((θ)ρ	NOUN
ejpam-6679	467	7	,	,	PUNCT
ejpam-6679	467	8	α̂[θ1	α̂[θ1	NOUN
ejpam-6679	467	9	]	]	X
ejpam-6679	467	10	,	,	PUNCT
ejpam-6679	467	11	.	.	PUNCT
ejpam-6679	467	12	.	.	PUNCT
ejpam-6679	468	1	.	.	PUNCT
ejpam-6679	469	1	,	,	PUNCT
ejpam-6679	469	2	α̂[θn	α̂[θn	NOUN
ejpam-6679	469	3	]	]	PUNCT
ejpam-6679	469	4	)	)	PUNCT
ejpam-6679	469	5	.	.	PUNCT
ejpam-6679	470	1	hence	hence	ADV
ejpam-6679	470	2	,	,	PUNCT
ejpam-6679	470	3	the	the	DET
ejpam-6679	470	4	proof	proof	NOUN
ejpam-6679	470	5	is	be	AUX
ejpam-6679	470	6	complete	complete	ADJ
ejpam-6679	470	7	.	.	PUNCT
ejpam-6679	471	1	theorem	theorem	ADJ
ejpam-6679	471	2	4	4	NUM
ejpam-6679	471	3	.	.	X
ejpam-6679	472	1	for	for	ADP
ejpam-6679	472	2	any	any	DET
ejpam-6679	472	3	α	α	NOUN
ejpam-6679	472	4	∈	∈	NOUN
ejpam-6679	472	5	hypalt(n)(τn	hypalt(n)(τn	PROPN
ejpam-6679	472	6	)	)	PUNCT
ejpam-6679	472	7	,	,	PUNCT
ejpam-6679	472	8	the	the	DET
ejpam-6679	472	9	extension	extension	NOUN
ejpam-6679	472	10	α̂	α̂	NUM
ejpam-6679	472	11	:	:	PUNCT
ejpam-6679	472	12	w	w	X
ejpam-6679	472	13	alt(n	alt(n	PROPN
ejpam-6679	472	14	)	)	PUNCT
ejpam-6679	472	15	τn	τn	X
ejpam-6679	472	16	(	(	PUNCT
ejpam-6679	472	17	ωn	ωn	NOUN
ejpam-6679	472	18	)	)	PUNCT
ejpam-6679	472	19	→	→	PUNCT
ejpam-6679	472	20	w	w	PROPN
ejpam-6679	472	21	alt(n	alt(n	PROPN
ejpam-6679	472	22	)	)	PUNCT
ejpam-6679	472	23	τn	τn	X
ejpam-6679	472	24	(	(	PUNCT
ejpam-6679	472	25	ωn	ωn	X
ejpam-6679	472	26	)	)	PUNCT
ejpam-6679	472	27	is	be	AUX
ejpam-6679	472	28	an	an	DET
ejpam-6679	472	29	endomorphism	endomorphism	NOUN
ejpam-6679	472	30	on	on	ADP
ejpam-6679	472	31	the	the	DET
ejpam-6679	472	32	menger	menger	PROPN
ejpam-6679	472	33	algebra	algebra	PROPN
ejpam-6679	472	34	walt(n	walt(n	PROPN
ejpam-6679	472	35	)	)	PUNCT
ejpam-6679	472	36	τn	τn	ADP
ejpam-6679	472	37	(	(	PUNCT
ejpam-6679	472	38	ωn	ωn	NOUN
ejpam-6679	472	39	)	)	PUNCT
ejpam-6679	472	40	.	.	PUNCT
ejpam-6679	473	1	proof	proof	NOUN
ejpam-6679	473	2	.	.	PUNCT
ejpam-6679	474	1	let	let	VERB
ejpam-6679	474	2	α	α	PRON
ejpam-6679	474	3	∈	∈	PROPN
ejpam-6679	474	4	hypalt(n)(τn	hypalt(n)(τn	PROPN
ejpam-6679	474	5	)	)	PUNCT
ejpam-6679	474	6	.	.	PUNCT
ejpam-6679	475	1	we	we	PRON
ejpam-6679	475	2	have	have	VERB
ejpam-6679	475	3	to	to	PART
ejpam-6679	475	4	show	show	VERB
ejpam-6679	475	5	that	that	SCONJ
ejpam-6679	475	6	,	,	PUNCT
ejpam-6679	475	7	for	for	ADP
ejpam-6679	475	8	any	any	DET
ejpam-6679	475	9	θ0	θ0	NOUN
ejpam-6679	475	10	,	,	PUNCT
ejpam-6679	475	11	θ1	θ1	NOUN
ejpam-6679	475	12	,	,	PUNCT
ejpam-6679	475	13	.	.	PUNCT
ejpam-6679	475	14	.	.	PUNCT
ejpam-6679	475	15	.	.	PUNCT
ejpam-6679	476	1	,	,	PUNCT
ejpam-6679	476	2	θn	θn	PRON
ejpam-6679	476	3	∈w	∈w	NOUN
ejpam-6679	476	4	alt(n	alt(n	NOUN
ejpam-6679	476	5	)	)	PUNCT
ejpam-6679	476	6	τn	τn	X
ejpam-6679	476	7	(	(	PUNCT
ejpam-6679	476	8	ωn	ωn	NUM
ejpam-6679	476	9	)	)	PUNCT
ejpam-6679	476	10	,	,	PUNCT
ejpam-6679	476	11	α̂[sn(θ0	α̂[sn(θ0	PROPN
ejpam-6679	476	12	,	,	PUNCT
ejpam-6679	476	13	θ1	θ1	NOUN
ejpam-6679	476	14	,	,	PUNCT
ejpam-6679	476	15	.	.	PUNCT
ejpam-6679	476	16	.	.	PUNCT
ejpam-6679	477	1	.	.	PUNCT
ejpam-6679	478	1	,	,	PUNCT
ejpam-6679	478	2	θn	θn	NOUN
ejpam-6679	478	3	)	)	PUNCT
ejpam-6679	478	4	]	]	PUNCT
ejpam-6679	479	1	=	=	PUNCT
ejpam-6679	479	2	sn(α̂[θ0	sn(α̂[θ0	X
ejpam-6679	479	3	]	]	X
ejpam-6679	479	4	,	,	PUNCT
ejpam-6679	479	5	α̂[θ1	α̂[θ1	X
ejpam-6679	479	6	]	]	X
ejpam-6679	479	7	,	,	PUNCT
ejpam-6679	479	8	.	.	PUNCT
ejpam-6679	479	9	.	.	PUNCT
ejpam-6679	480	1	.	.	PUNCT
ejpam-6679	481	1	,	,	PUNCT
ejpam-6679	481	2	α̂[θn	α̂[θn	NOUN
ejpam-6679	481	3	]	]	PUNCT
ejpam-6679	481	4	)	)	PUNCT
ejpam-6679	481	5	.	.	PUNCT
ejpam-6679	482	1	let	let	VERB
ejpam-6679	482	2	θ0	θ0	NOUN
ejpam-6679	482	3	,	,	PUNCT
ejpam-6679	482	4	θ1	θ1	NOUN
ejpam-6679	482	5	,	,	PUNCT
ejpam-6679	482	6	.	.	PUNCT
ejpam-6679	482	7	.	.	PUNCT
ejpam-6679	483	1	.	.	PUNCT
ejpam-6679	484	1	,	,	PUNCT
ejpam-6679	484	2	θn	θn	PROPN
ejpam-6679	484	3	∈	∈	PROPN
ejpam-6679	484	4	w	w	PROPN
ejpam-6679	484	5	alt(n	alt(n	PROPN
ejpam-6679	484	6	)	)	PUNCT
ejpam-6679	484	7	τn	τn	X
ejpam-6679	484	8	(	(	PUNCT
ejpam-6679	484	9	ωn	ωn	NUM
ejpam-6679	484	10	)	)	PUNCT
ejpam-6679	484	11	.	.	PUNCT
ejpam-6679	485	1	suppose	suppose	VERB
ejpam-6679	485	2	θ0	θ0	PROPN
ejpam-6679	485	3	=	=	SYM
ejpam-6679	485	4	fi(ωσ(1	fi(ωσ(1	PROPN
ejpam-6679	485	5	)	)	PUNCT
ejpam-6679	485	6	,	,	PUNCT
ejpam-6679	485	7	.	.	PUNCT
ejpam-6679	485	8	.	.	PUNCT
ejpam-6679	486	1	.	.	PUNCT
ejpam-6679	487	1	,	,	PUNCT
ejpam-6679	487	2	ωσ(n	ωσ(n	NOUN
ejpam-6679	487	3	)	)	PUNCT
ejpam-6679	487	4	)	)	PUNCT
ejpam-6679	488	1	for	for	ADP
ejpam-6679	488	2	some	some	PRON
ejpam-6679	488	3	i	i	PRON
ejpam-6679	488	4	∈	∈	PROPN
ejpam-6679	489	1	i	i	PRON
ejpam-6679	489	2	,	,	PUNCT
ejpam-6679	489	3	σ	σ	PROPN
ejpam-6679	489	4	∈	∈	PROPN
ejpam-6679	489	5	alt(n	alt(n	PROPN
ejpam-6679	489	6	)	)	PUNCT
ejpam-6679	489	7	.	.	PUNCT
ejpam-6679	490	1	by	by	ADP
ejpam-6679	490	2	lemma	lemma	PROPN
ejpam-6679	490	3	1	1	NUM
ejpam-6679	490	4	,	,	PUNCT
ejpam-6679	490	5	α̂[sn(θ0	α̂[sn(θ0	PROPN
ejpam-6679	490	6	,	,	PUNCT
ejpam-6679	490	7	θ1	θ1	NOUN
ejpam-6679	490	8	,	,	PUNCT
ejpam-6679	490	9	.	.	PUNCT
ejpam-6679	490	10	.	.	PUNCT
ejpam-6679	490	11	.	.	PUNCT
ejpam-6679	491	1	,	,	PUNCT
ejpam-6679	491	2	θn	θn	NOUN
ejpam-6679	491	3	)	)	PUNCT
ejpam-6679	491	4	]	]	PUNCT
ejpam-6679	492	1	=	=	PUNCT
ejpam-6679	492	2	α̂[sn(fi(ωσ(1	α̂[sn(fi(ωσ(1	PROPN
ejpam-6679	492	3	)	)	PUNCT
ejpam-6679	492	4	,	,	PUNCT
ejpam-6679	492	5	.	.	PUNCT
ejpam-6679	492	6	.	.	PUNCT
ejpam-6679	492	7	.	.	PUNCT
ejpam-6679	493	1	,	,	PUNCT
ejpam-6679	493	2	ωσ(n	ωσ(n	NOUN
ejpam-6679	493	3	)	)	PUNCT
ejpam-6679	493	4	)	)	PUNCT
ejpam-6679	493	5	,	,	PUNCT
ejpam-6679	493	6	θ1	θ1	NOUN
ejpam-6679	493	7	,	,	PUNCT
ejpam-6679	493	8	.	.	PUNCT
ejpam-6679	493	9	.	.	PUNCT
ejpam-6679	493	10	.	.	PUNCT
ejpam-6679	494	1	,	,	PUNCT
ejpam-6679	494	2	θn	θn	NOUN
ejpam-6679	494	3	)	)	PUNCT
ejpam-6679	494	4	]	]	PUNCT
ejpam-6679	495	1	=	=	PUNCT
ejpam-6679	495	2	α̂[fi(θσ(1	α̂[fi(θσ(1	PROPN
ejpam-6679	495	3	)	)	PUNCT
ejpam-6679	495	4	,	,	PUNCT
ejpam-6679	495	5	.	.	PUNCT
ejpam-6679	495	6	.	.	PUNCT
ejpam-6679	496	1	.	.	PUNCT
ejpam-6679	497	1	,	,	PUNCT
ejpam-6679	497	2	θσ(n	θσ(n	NOUN
ejpam-6679	497	3	)	)	PUNCT
ejpam-6679	497	4	)	)	PUNCT
ejpam-6679	497	5	]	]	PUNCT
ejpam-6679	498	1	=	=	PUNCT
ejpam-6679	498	2	sn(α(fi	sn(α(fi	NOUN
ejpam-6679	498	3	)	)	PUNCT
ejpam-6679	498	4	,	,	PUNCT
ejpam-6679	498	5	α̂[θσ(1	α̂[θσ(1	NOUN
ejpam-6679	498	6	)	)	PUNCT
ejpam-6679	498	7	]	]	PUNCT
ejpam-6679	498	8	,	,	PUNCT
ejpam-6679	498	9	.	.	PUNCT
ejpam-6679	498	10	.	.	PUNCT
ejpam-6679	499	1	.	.	PUNCT
ejpam-6679	500	1	,	,	PUNCT
ejpam-6679	500	2	α̂[θσ(n	α̂[θσ(n	NOUN
ejpam-6679	500	3	)	)	PUNCT
ejpam-6679	500	4	]	]	PUNCT
ejpam-6679	500	5	)	)	PUNCT
ejpam-6679	501	1	t.	t.	PROPN
ejpam-6679	501	2	changphas	changphas	PROPN
ejpam-6679	501	3	/	/	SYM
ejpam-6679	501	4	eur	eur	PROPN
ejpam-6679	501	5	.	.	PUNCT
ejpam-6679	502	1	j.	j.	PROPN
ejpam-6679	502	2	pure	pure	PROPN
ejpam-6679	502	3	appl	appl	PROPN
ejpam-6679	502	4	.	.	PROPN
ejpam-6679	502	5	math	math	PROPN
ejpam-6679	502	6	,	,	PUNCT
ejpam-6679	502	7	18	18	NUM
ejpam-6679	502	8	(	(	PUNCT
ejpam-6679	502	9	4	4	NUM
ejpam-6679	502	10	)	)	PUNCT
ejpam-6679	502	11	(	(	PUNCT
ejpam-6679	502	12	2025	2025	NUM
ejpam-6679	502	13	)	)	PUNCT
ejpam-6679	502	14	,	,	PUNCT
ejpam-6679	502	15	6679	6679	NUM
ejpam-6679	502	16	9	9	NUM
ejpam-6679	502	17	of	of	ADP
ejpam-6679	502	18	15	15	NUM
ejpam-6679	502	19	=	=	NOUN
ejpam-6679	502	20	sn((α(fi))σ	sn((α(fi))σ	NOUN
ejpam-6679	502	21	,	,	PUNCT
ejpam-6679	502	22	α̂[θ1	α̂[θ1	NOUN
ejpam-6679	502	23	]	]	X
ejpam-6679	502	24	,	,	PUNCT
ejpam-6679	502	25	.	.	PUNCT
ejpam-6679	502	26	.	.	PUNCT
ejpam-6679	503	1	.	.	PUNCT
ejpam-6679	504	1	,	,	PUNCT
ejpam-6679	504	2	α̂[θn	α̂[θn	NUM
ejpam-6679	504	3	]	]	PUNCT
ejpam-6679	504	4	)	)	PUNCT
ejpam-6679	504	5	=	=	SYM
ejpam-6679	504	6	sn(α̂[fi(ωσ(1	sn(α̂[fi(ωσ(1	NOUN
ejpam-6679	504	7	)	)	PUNCT
ejpam-6679	504	8	,	,	PUNCT
ejpam-6679	504	9	.	.	PUNCT
ejpam-6679	504	10	.	.	PUNCT
ejpam-6679	504	11	.	.	PUNCT
ejpam-6679	505	1	,	,	PUNCT
ejpam-6679	505	2	ωσ(n	ωσ(n	NOUN
ejpam-6679	505	3	)	)	PUNCT
ejpam-6679	505	4	)	)	PUNCT
ejpam-6679	506	1	]	]	PUNCT
ejpam-6679	506	2	,	,	PUNCT
ejpam-6679	506	3	α̂[θ1	α̂[θ1	X
ejpam-6679	506	4	]	]	X
ejpam-6679	506	5	,	,	PUNCT
ejpam-6679	506	6	.	.	PUNCT
ejpam-6679	506	7	.	.	PUNCT
ejpam-6679	507	1	.	.	PUNCT
ejpam-6679	508	1	,	,	PUNCT
ejpam-6679	508	2	α̂[θn	α̂[θn	NUM
ejpam-6679	508	3	]	]	PUNCT
ejpam-6679	508	4	)	)	PUNCT
ejpam-6679	508	5	=	=	PUNCT
ejpam-6679	508	6	sn(α̂[θ0	sn(α̂[θ0	X
ejpam-6679	508	7	]	]	X
ejpam-6679	508	8	,	,	PUNCT
ejpam-6679	508	9	α̂[θ1	α̂[θ1	X
ejpam-6679	508	10	]	]	X
ejpam-6679	508	11	,	,	PUNCT
ejpam-6679	508	12	.	.	PUNCT
ejpam-6679	508	13	.	.	PUNCT
ejpam-6679	509	1	.	.	PUNCT
ejpam-6679	510	1	,	,	PUNCT
ejpam-6679	510	2	α̂[θn	α̂[θn	NOUN
ejpam-6679	510	3	]	]	PUNCT
ejpam-6679	510	4	)	)	PUNCT
ejpam-6679	510	5	.	.	PUNCT
ejpam-6679	511	1	let	let	VERB
ejpam-6679	511	2	θ0	θ0	PROPN
ejpam-6679	511	3	=	=	SYM
ejpam-6679	511	4	fi(θ	fi(θ	NOUN
ejpam-6679	511	5	′	′	NUM
ejpam-6679	511	6	1	1	NUM
ejpam-6679	511	7	,	,	PUNCT
ejpam-6679	511	8	.	.	PUNCT
ejpam-6679	511	9	.	.	PUNCT
ejpam-6679	512	1	.	.	PUNCT
ejpam-6679	513	1	,	,	PUNCT
ejpam-6679	513	2	θ	θ	NOUN
ejpam-6679	513	3	′	′	NUM
ejpam-6679	513	4	n	n	CCONJ
ejpam-6679	513	5	)	)	PUNCT
ejpam-6679	513	6	,	,	PUNCT
ejpam-6679	513	7	and	and	CCONJ
ejpam-6679	513	8	assume	assume	VERB
ejpam-6679	513	9	,	,	PUNCT
ejpam-6679	513	10	for	for	ADP
ejpam-6679	513	11	1	1	NUM
ejpam-6679	513	12	≤	≤	NUM
ejpam-6679	513	13	k	k	NOUN
ejpam-6679	513	14	≤	≤	PROPN
ejpam-6679	513	15	n	n	CCONJ
ejpam-6679	513	16	,	,	PUNCT
ejpam-6679	513	17	that	that	DET
ejpam-6679	513	18	α̂[sn(θ′k	α̂[sn(θ′k	NOUN
ejpam-6679	513	19	,	,	PUNCT
ejpam-6679	513	20	θ1	θ1	NOUN
ejpam-6679	513	21	,	,	PUNCT
ejpam-6679	513	22	.	.	PUNCT
ejpam-6679	513	23	.	.	PUNCT
ejpam-6679	514	1	.	.	PUNCT
ejpam-6679	515	1	,	,	PUNCT
ejpam-6679	515	2	θn	θn	NOUN
ejpam-6679	515	3	)	)	PUNCT
ejpam-6679	515	4	]	]	PUNCT
ejpam-6679	516	1	=	=	PUNCT
ejpam-6679	516	2	sn(α̂[θ′k	sn(α̂[θ′k	PROPN
ejpam-6679	516	3	]	]	PUNCT
ejpam-6679	516	4	,	,	PUNCT
ejpam-6679	516	5	α̂[θ1	α̂[θ1	X
ejpam-6679	516	6	]	]	X
ejpam-6679	516	7	,	,	PUNCT
ejpam-6679	516	8	.	.	PUNCT
ejpam-6679	516	9	.	.	PUNCT
ejpam-6679	516	10	.	.	PUNCT
ejpam-6679	517	1	,	,	PUNCT
ejpam-6679	517	2	α̂[θn	α̂[θn	NOUN
ejpam-6679	517	3	]	]	PUNCT
ejpam-6679	517	4	)	)	PUNCT
ejpam-6679	517	5	.	.	PUNCT
ejpam-6679	518	1	from	from	ADP
ejpam-6679	518	2	theorem	theorem	ADJ
ejpam-6679	518	3	3	3	NUM
ejpam-6679	518	4	,	,	PUNCT
ejpam-6679	518	5	α̂[sn(θ0	α̂[sn(θ0	PROPN
ejpam-6679	518	6	,	,	PUNCT
ejpam-6679	518	7	θ1	θ1	NOUN
ejpam-6679	518	8	,	,	PUNCT
ejpam-6679	518	9	.	.	PUNCT
ejpam-6679	518	10	.	.	PUNCT
ejpam-6679	518	11	.	.	PUNCT
ejpam-6679	519	1	,	,	PUNCT
ejpam-6679	519	2	θn	θn	NOUN
ejpam-6679	519	3	)	)	PUNCT
ejpam-6679	519	4	]	]	PUNCT
ejpam-6679	520	1	=	=	PUNCT
ejpam-6679	520	2	α̂[sn(fi(θ	α̂[sn(fi(θ	NOUN
ejpam-6679	520	3	′	′	NOUN
ejpam-6679	520	4	1	1	NUM
ejpam-6679	520	5	,	,	PUNCT
ejpam-6679	520	6	.	.	PUNCT
ejpam-6679	520	7	.	.	PUNCT
ejpam-6679	520	8	.	.	PUNCT
ejpam-6679	521	1	,	,	PUNCT
ejpam-6679	521	2	θ	θ	NOUN
ejpam-6679	521	3	′	′	NUM
ejpam-6679	521	4	n	n	CCONJ
ejpam-6679	521	5	)	)	PUNCT
ejpam-6679	521	6	,	,	PUNCT
ejpam-6679	521	7	θ1	θ1	NOUN
ejpam-6679	521	8	,	,	PUNCT
ejpam-6679	521	9	.	.	PUNCT
ejpam-6679	521	10	.	.	PUNCT
ejpam-6679	522	1	.	.	PUNCT
ejpam-6679	523	1	,	,	PUNCT
ejpam-6679	523	2	θn	θn	NOUN
ejpam-6679	523	3	)	)	PUNCT
ejpam-6679	523	4	]	]	PUNCT
ejpam-6679	524	1	=	=	SYM
ejpam-6679	524	2	α̂[fi(s	α̂[fi(s	NOUN
ejpam-6679	524	3	n(θ′1	n(θ′1	NOUN
ejpam-6679	524	4	,	,	PUNCT
ejpam-6679	524	5	θ1	θ1	NOUN
ejpam-6679	524	6	,	,	PUNCT
ejpam-6679	524	7	.	.	PUNCT
ejpam-6679	524	8	.	.	PUNCT
ejpam-6679	524	9	.	.	PUNCT
ejpam-6679	525	1	,	,	PUNCT
ejpam-6679	525	2	θn	θn	NOUN
ejpam-6679	525	3	)	)	PUNCT
ejpam-6679	525	4	,	,	PUNCT
ejpam-6679	525	5	.	.	PUNCT
ejpam-6679	525	6	.	.	PUNCT
ejpam-6679	526	1	.	.	PUNCT
ejpam-6679	527	1	,	,	PUNCT
ejpam-6679	527	2	s	s	VERB
ejpam-6679	527	3	n(θ′n	n(θ′n	ADJ
ejpam-6679	527	4	,	,	PUNCT
ejpam-6679	527	5	θ1	θ1	NOUN
ejpam-6679	527	6	,	,	PUNCT
ejpam-6679	527	7	.	.	PUNCT
ejpam-6679	527	8	.	.	PUNCT
ejpam-6679	528	1	.	.	PUNCT
ejpam-6679	529	1	,	,	PUNCT
ejpam-6679	529	2	θn	θn	NOUN
ejpam-6679	529	3	)	)	PUNCT
ejpam-6679	529	4	)	)	PUNCT
ejpam-6679	529	5	]	]	PUNCT
ejpam-6679	530	1	=	=	PUNCT
ejpam-6679	530	2	sn(α(fi	sn(α(fi	NOUN
ejpam-6679	530	3	)	)	PUNCT
ejpam-6679	530	4	,	,	PUNCT
ejpam-6679	530	5	α̂[s	α̂[s	PROPN
ejpam-6679	530	6	n(θ′1	n(θ′1	NOUN
ejpam-6679	530	7	,	,	PUNCT
ejpam-6679	530	8	θ1	θ1	NOUN
ejpam-6679	530	9	,	,	PUNCT
ejpam-6679	530	10	.	.	PUNCT
ejpam-6679	530	11	.	.	PUNCT
ejpam-6679	530	12	.	.	PUNCT
ejpam-6679	531	1	,	,	PUNCT
ejpam-6679	531	2	θn	θn	NOUN
ejpam-6679	531	3	)	)	PUNCT
ejpam-6679	531	4	]	]	PUNCT
ejpam-6679	531	5	,	,	PUNCT
ejpam-6679	531	6	.	.	PUNCT
ejpam-6679	531	7	.	.	PUNCT
ejpam-6679	532	1	.	.	PUNCT
ejpam-6679	533	1	,	,	PUNCT
ejpam-6679	533	2	α̂[s	α̂[s	PROPN
ejpam-6679	533	3	n(θ′n	n(θ′n	NOUN
ejpam-6679	533	4	,	,	PUNCT
ejpam-6679	533	5	θ1	θ1	NOUN
ejpam-6679	533	6	,	,	PUNCT
ejpam-6679	533	7	.	.	PUNCT
ejpam-6679	533	8	.	.	PUNCT
ejpam-6679	533	9	.	.	PUNCT
ejpam-6679	534	1	,	,	PUNCT
ejpam-6679	534	2	θn	θn	NOUN
ejpam-6679	534	3	)	)	PUNCT
ejpam-6679	534	4	]	]	PUNCT
ejpam-6679	534	5	)	)	PUNCT
ejpam-6679	535	1	=	=	SYM
ejpam-6679	535	2	sn(α(fi	sn(α(fi	PROPN
ejpam-6679	535	3	)	)	PUNCT
ejpam-6679	535	4	,	,	PUNCT
ejpam-6679	535	5	s	s	VERB
ejpam-6679	535	6	n(α̂[θ′1	n(α̂[θ′1	VERB
ejpam-6679	535	7	]	]	X
ejpam-6679	535	8	,	,	PUNCT
ejpam-6679	535	9	α̂[θ1	α̂[θ1	NOUN
ejpam-6679	535	10	]	]	X
ejpam-6679	535	11	,	,	PUNCT
ejpam-6679	535	12	.	.	PUNCT
ejpam-6679	535	13	.	.	PUNCT
ejpam-6679	536	1	.	.	PUNCT
ejpam-6679	537	1	,	,	PUNCT
ejpam-6679	537	2	α̂[θn	α̂[θn	NUM
ejpam-6679	537	3	]	]	PUNCT
ejpam-6679	537	4	)	)	PUNCT
ejpam-6679	537	5	,	,	PUNCT
ejpam-6679	537	6	.	.	PUNCT
ejpam-6679	537	7	.	.	PUNCT
ejpam-6679	538	1	.	.	PUNCT
ejpam-6679	539	1	,	,	PUNCT
ejpam-6679	539	2	s	s	VERB
ejpam-6679	539	3	n(α̂[θ′n	n(α̂[θ′n	NOUN
ejpam-6679	539	4	]	]	X
ejpam-6679	539	5	,	,	PUNCT
ejpam-6679	539	6	α̂[θ1	α̂[θ1	X
ejpam-6679	539	7	]	]	X
ejpam-6679	539	8	,	,	PUNCT
ejpam-6679	539	9	.	.	PUNCT
ejpam-6679	539	10	.	.	PUNCT
ejpam-6679	540	1	.	.	PUNCT
ejpam-6679	541	1	,	,	PUNCT
ejpam-6679	541	2	α̂[θn	α̂[θn	NOUN
ejpam-6679	541	3	]	]	PUNCT
ejpam-6679	541	4	)	)	PUNCT
ejpam-6679	541	5	)	)	PUNCT
ejpam-6679	542	1	=	=	SYM
ejpam-6679	542	2	sn(sn(α(fi	sn(sn(α(fi	PROPN
ejpam-6679	542	3	)	)	PUNCT
ejpam-6679	542	4	,	,	PUNCT
ejpam-6679	542	5	α̂[θ	α̂[θ	PROPN
ejpam-6679	542	6	′	′	NOUN
ejpam-6679	542	7	1	1	NUM
ejpam-6679	542	8	]	]	PUNCT
ejpam-6679	542	9	,	,	PUNCT
ejpam-6679	542	10	.	.	PUNCT
ejpam-6679	542	11	.	.	PUNCT
ejpam-6679	542	12	.	.	PUNCT
ejpam-6679	543	1	,	,	PUNCT
ejpam-6679	543	2	α̂[θ	α̂[θ	PROPN
ejpam-6679	543	3	′	′	NUM
ejpam-6679	543	4	n	n	CCONJ
ejpam-6679	543	5	]	]	PUNCT
ejpam-6679	543	6	)	)	PUNCT
ejpam-6679	543	7	,	,	PUNCT
ejpam-6679	543	8	α̂[θ1	α̂[θ1	X
ejpam-6679	543	9	]	]	X
ejpam-6679	543	10	,	,	PUNCT
ejpam-6679	543	11	.	.	PUNCT
ejpam-6679	543	12	.	.	PUNCT
ejpam-6679	544	1	.	.	PUNCT
ejpam-6679	545	1	,	,	PUNCT
ejpam-6679	545	2	α̂[θn	α̂[θn	NUM
ejpam-6679	545	3	]	]	PUNCT
ejpam-6679	545	4	)	)	PUNCT
ejpam-6679	546	1	=	=	PUNCT
ejpam-6679	546	2	sn(α̂[fi(θ	sn(α̂[fi(θ	PROPN
ejpam-6679	546	3	′	′	NUM
ejpam-6679	546	4	1	1	NUM
ejpam-6679	546	5	,	,	PUNCT
ejpam-6679	546	6	.	.	PUNCT
ejpam-6679	546	7	.	.	PUNCT
ejpam-6679	546	8	.	.	PUNCT
ejpam-6679	547	1	,	,	PUNCT
ejpam-6679	547	2	θ	θ	NOUN
ejpam-6679	547	3	′	′	NUM
ejpam-6679	547	4	n	n	CCONJ
ejpam-6679	547	5	)	)	PUNCT
ejpam-6679	547	6	]	]	PUNCT
ejpam-6679	547	7	,	,	PUNCT
ejpam-6679	547	8	α̂[θ1	α̂[θ1	X
ejpam-6679	547	9	]	]	X
ejpam-6679	547	10	,	,	PUNCT
ejpam-6679	547	11	.	.	PUNCT
ejpam-6679	547	12	.	.	PUNCT
ejpam-6679	548	1	.	.	PUNCT
ejpam-6679	549	1	,	,	PUNCT
ejpam-6679	549	2	α̂[θn	α̂[θn	NUM
ejpam-6679	549	3	]	]	PUNCT
ejpam-6679	549	4	)	)	PUNCT
ejpam-6679	549	5	=	=	PUNCT
ejpam-6679	549	6	sn(α̂[θ0	sn(α̂[θ0	X
ejpam-6679	549	7	]	]	X
ejpam-6679	549	8	,	,	PUNCT
ejpam-6679	549	9	α̂[θ1	α̂[θ1	X
ejpam-6679	549	10	]	]	X
ejpam-6679	549	11	,	,	PUNCT
ejpam-6679	549	12	.	.	PUNCT
ejpam-6679	549	13	.	.	PUNCT
ejpam-6679	550	1	.	.	PUNCT
ejpam-6679	551	1	,	,	PUNCT
ejpam-6679	551	2	α̂[θn	α̂[θn	NOUN
ejpam-6679	551	3	]	]	PUNCT
ejpam-6679	551	4	)	)	PUNCT
ejpam-6679	551	5	.	.	PUNCT
ejpam-6679	552	1	hence	hence	ADV
ejpam-6679	552	2	α̂[sn(θ0	α̂[sn(θ0	PROPN
ejpam-6679	552	3	,	,	PUNCT
ejpam-6679	552	4	θ1	θ1	NOUN
ejpam-6679	552	5	,	,	PUNCT
ejpam-6679	552	6	.	.	PUNCT
ejpam-6679	552	7	.	.	PUNCT
ejpam-6679	552	8	.	.	PUNCT
ejpam-6679	553	1	,	,	PUNCT
ejpam-6679	553	2	θn	θn	NOUN
ejpam-6679	553	3	)	)	PUNCT
ejpam-6679	553	4	]	]	PUNCT
ejpam-6679	554	1	=	=	PUNCT
ejpam-6679	554	2	sn(α̂[θ0	sn(α̂[θ0	X
ejpam-6679	554	3	]	]	X
ejpam-6679	554	4	,	,	PUNCT
ejpam-6679	554	5	α̂[θ1	α̂[θ1	X
ejpam-6679	554	6	]	]	X
ejpam-6679	554	7	,	,	PUNCT
ejpam-6679	554	8	.	.	PUNCT
ejpam-6679	554	9	.	.	PUNCT
ejpam-6679	555	1	.	.	PUNCT
ejpam-6679	556	1	,	,	PUNCT
ejpam-6679	556	2	α̂[θn	α̂[θn	NOUN
ejpam-6679	556	3	]	]	PUNCT
ejpam-6679	556	4	)	)	PUNCT
ejpam-6679	556	5	.	.	PUNCT
ejpam-6679	557	1	define	define	VERB
ejpam-6679	557	2	an	an	DET
ejpam-6679	557	3	operation	operation	NOUN
ejpam-6679	557	4	◦	◦	NOUN
ejpam-6679	557	5	h	h	NOUN
ejpam-6679	557	6	on	on	ADP
ejpam-6679	557	7	hypalt(n)(τn	hypalt(n)(τn	PROPN
ejpam-6679	557	8	)	)	PUNCT
ejpam-6679	557	9	by	by	ADP
ejpam-6679	557	10	,	,	PUNCT
ejpam-6679	557	11	for	for	ADP
ejpam-6679	557	12	any	any	DET
ejpam-6679	557	13	α1	α1	NOUN
ejpam-6679	557	14	,	,	PUNCT
ejpam-6679	557	15	α2	α2	PROPN
ejpam-6679	557	16	∈	∈	PROPN
ejpam-6679	557	17	hypalt(n)(τn	hypalt(n)(τn	PROPN
ejpam-6679	557	18	)	)	PUNCT
ejpam-6679	557	19	,	,	PUNCT
ejpam-6679	557	20	(	(	PUNCT
ejpam-6679	557	21	α1	α1	PROPN
ejpam-6679	557	22	◦	◦	NOUN
ejpam-6679	557	23	h	h	NOUN
ejpam-6679	557	24	α2)(fi	α2)(fi	PROPN
ejpam-6679	557	25	)	)	PUNCT
ejpam-6679	558	1	=	=	SYM
ejpam-6679	558	2	α̂1[α2(fi	α̂1[α2(fi	NOUN
ejpam-6679	558	3	)	)	PUNCT
ejpam-6679	558	4	]	]	PUNCT
ejpam-6679	558	5	for	for	ADP
ejpam-6679	558	6	all	all	PRON
ejpam-6679	558	7	i	i	PRON
ejpam-6679	558	8	∈	∈	PROPN
ejpam-6679	558	9	i.	i.	NOUN
ejpam-6679	558	10	lemma	lemma	PROPN
ejpam-6679	559	1	2	2	NUM
ejpam-6679	559	2	.	.	X
ejpam-6679	559	3	for	for	ADP
ejpam-6679	559	4	any	any	DET
ejpam-6679	559	5	α1	α1	NOUN
ejpam-6679	559	6	,	,	PUNCT
ejpam-6679	559	7	α2	α2	PROPN
ejpam-6679	559	8	∈	∈	PROPN
ejpam-6679	559	9	hypalt(n)(τn	hypalt(n)(τn	PROPN
ejpam-6679	559	10	)	)	PUNCT
ejpam-6679	559	11	,	,	PUNCT
ejpam-6679	559	12	(	(	PUNCT
ejpam-6679	559	13	α1	α1	PROPN
ejpam-6679	559	14	◦	◦	NOUN
ejpam-6679	559	15	h	h	NOUN
ejpam-6679	559	16	α2)̂	α2)̂	NOUN
ejpam-6679	559	17	=	=	PUNCT
ejpam-6679	559	18	α̂1	α̂1	PRON
ejpam-6679	559	19	◦	◦	VERB
ejpam-6679	559	20	α̂2	α̂2	ADJ
ejpam-6679	559	21	.	.	PUNCT
ejpam-6679	560	1	proof	proof	NOUN
ejpam-6679	560	2	.	.	PUNCT
ejpam-6679	561	1	at	at	ADP
ejpam-6679	561	2	first	first	ADV
ejpam-6679	561	3	,	,	PUNCT
ejpam-6679	561	4	we	we	PRON
ejpam-6679	561	5	prove	prove	VERB
ejpam-6679	561	6	that	that	SCONJ
ejpam-6679	561	7	for	for	ADP
ejpam-6679	561	8	any	any	DET
ejpam-6679	561	9	α	α	NOUN
ejpam-6679	561	10	∈	∈	NOUN
ejpam-6679	561	11	hypalt(n)(τn	hypalt(n)(τn	PROPN
ejpam-6679	561	12	)	)	PUNCT
ejpam-6679	561	13	,	,	PUNCT
ejpam-6679	561	14	α̂[(θ)σ	α̂[(θ)σ	NUM
ejpam-6679	561	15	]	]	PUNCT
ejpam-6679	561	16	=	=	SYM
ejpam-6679	561	17	(	(	PUNCT
ejpam-6679	561	18	α̂[θ])σ	α̂[θ])σ	VERB
ejpam-6679	561	19	for	for	ADP
ejpam-6679	561	20	any	any	DET
ejpam-6679	561	21	θ	θ	PROPN
ejpam-6679	561	22	∈	∈	PROPN
ejpam-6679	561	23	w	w	PROPN
ejpam-6679	561	24	alt(n	alt(n	PROPN
ejpam-6679	561	25	)	)	PUNCT
ejpam-6679	561	26	τn	τn	X
ejpam-6679	561	27	(	(	PUNCT
ejpam-6679	561	28	ωn	ωn	X
ejpam-6679	561	29	)	)	PUNCT
ejpam-6679	561	30	and	and	CCONJ
ejpam-6679	561	31	σ	σ	PROPN
ejpam-6679	561	32	∈	∈	PROPN
ejpam-6679	561	33	alt(n	alt(n	PROPN
ejpam-6679	561	34	)	)	PUNCT
ejpam-6679	561	35	.	.	PUNCT
ejpam-6679	562	1	suppose	suppose	VERB
ejpam-6679	562	2	θ	θ	PROPN
ejpam-6679	562	3	=	=	SYM
ejpam-6679	562	4	fi(ωρ(1	fi(ωρ(1	NUM
ejpam-6679	562	5	)	)	PUNCT
ejpam-6679	562	6	,	,	PUNCT
ejpam-6679	562	7	.	.	PUNCT
ejpam-6679	562	8	.	.	PUNCT
ejpam-6679	563	1	.	.	PUNCT
ejpam-6679	564	1	,	,	PUNCT
ejpam-6679	564	2	ωρ(n	ωρ(n	NUM
ejpam-6679	564	3	)	)	PUNCT
ejpam-6679	564	4	)	)	PUNCT
ejpam-6679	565	1	for	for	ADP
ejpam-6679	565	2	some	some	PRON
ejpam-6679	565	3	i	i	PRON
ejpam-6679	565	4	∈	∈	PROPN
ejpam-6679	566	1	i	i	PRON
ejpam-6679	566	2	,	,	PUNCT
ejpam-6679	566	3	ρ	ρ	PROPN
ejpam-6679	566	4	∈	∈	PROPN
ejpam-6679	566	5	alt(n	alt(n	PROPN
ejpam-6679	566	6	)	)	PUNCT
ejpam-6679	566	7	.	.	PUNCT
ejpam-6679	567	1	then	then	ADV
ejpam-6679	567	2	(	(	PUNCT
ejpam-6679	567	3	θ)σ	θ)σ	X
ejpam-6679	567	4	=	=	SYM
ejpam-6679	567	5	fi(ωσ(ρ(1	fi(ωσ(ρ(1	NOUN
ejpam-6679	567	6	)	)	PUNCT
ejpam-6679	567	7	)	)	PUNCT
ejpam-6679	567	8	,	,	PUNCT
ejpam-6679	567	9	.	.	PUNCT
ejpam-6679	567	10	.	.	PUNCT
ejpam-6679	567	11	.	.	PUNCT
ejpam-6679	568	1	,	,	PUNCT
ejpam-6679	568	2	xσ(ρ(n	xσ(ρ(n	NUM
ejpam-6679	568	3	)	)	PUNCT
ejpam-6679	568	4	)	)	PUNCT
ejpam-6679	568	5	)	)	PUNCT
ejpam-6679	569	1	;	;	PUNCT
ejpam-6679	569	2	so	so	ADV
ejpam-6679	569	3	α̂[(θ)σ	α̂[(θ)σ	ADV
ejpam-6679	569	4	]	]	PUNCT
ejpam-6679	569	5	=	=	PUNCT
ejpam-6679	569	6	sn(α(fi	sn(α(fi	PROPN
ejpam-6679	569	7	)	)	PUNCT
ejpam-6679	569	8	,	,	PUNCT
ejpam-6679	569	9	ωσ(ρ(1	ωσ(ρ(1	NUM
ejpam-6679	569	10	)	)	PUNCT
ejpam-6679	569	11	)	)	PUNCT
ejpam-6679	569	12	,	,	PUNCT
ejpam-6679	569	13	.	.	PUNCT
ejpam-6679	569	14	.	.	PUNCT
ejpam-6679	570	1	.	.	PUNCT
ejpam-6679	571	1	,	,	PUNCT
ejpam-6679	571	2	ωσ(ρ(n	ωσ(ρ(n	NUM
ejpam-6679	571	3	)	)	PUNCT
ejpam-6679	571	4	)	)	PUNCT
ejpam-6679	571	5	)	)	PUNCT
ejpam-6679	572	1	=	=	SYM
ejpam-6679	572	2	sn((α(fi))σρ	sn((α(fi))σρ	PROPN
ejpam-6679	572	3	,	,	PUNCT
ejpam-6679	572	4	ω1	ω1	PROPN
ejpam-6679	572	5	,	,	PUNCT
ejpam-6679	572	6	.	.	PUNCT
ejpam-6679	572	7	.	.	PUNCT
ejpam-6679	572	8	.	.	PUNCT
ejpam-6679	572	9	,	,	PUNCT
ejpam-6679	572	10	ωn	ωn	X
ejpam-6679	572	11	)	)	PUNCT
ejpam-6679	572	12	)	)	PUNCT
ejpam-6679	573	1	=	=	SYM
ejpam-6679	573	2	(	(	PUNCT
ejpam-6679	573	3	α(fi))σρ	α(fi))σρ	PROPN
ejpam-6679	573	4	.	.	PUNCT
ejpam-6679	574	1	also	also	ADV
ejpam-6679	574	2	,	,	PUNCT
ejpam-6679	574	3	(	(	PUNCT
ejpam-6679	574	4	α̂[θ])σ	α̂[θ])σ	PROPN
ejpam-6679	574	5	=	=	SYM
ejpam-6679	574	6	(	(	PUNCT
ejpam-6679	574	7	(	(	PUNCT
ejpam-6679	574	8	α(fi))rho)σ	α(fi))rho)σ	NOUN
ejpam-6679	574	9	=	=	SYM
ejpam-6679	574	10	(	(	PUNCT
ejpam-6679	574	11	α(fi))σρ	α(fi))σρ	PROPN
ejpam-6679	574	12	.	.	PUNCT
ejpam-6679	575	1	let	let	VERB
ejpam-6679	575	2	θ	θ	NOUN
ejpam-6679	575	3	=	=	SYM
ejpam-6679	575	4	fi(θ1	fi(θ1	PROPN
ejpam-6679	575	5	,	,	PUNCT
ejpam-6679	575	6	.	.	PUNCT
ejpam-6679	575	7	.	.	PUNCT
ejpam-6679	576	1	.	.	PUNCT
ejpam-6679	577	1	,	,	PUNCT
ejpam-6679	577	2	θn	θn	NOUN
ejpam-6679	577	3	)	)	PUNCT
ejpam-6679	577	4	and	and	CCONJ
ejpam-6679	577	5	assume	assume	VERB
ejpam-6679	577	6	α̂[(θk)σ	α̂[(θk)σ	NUM
ejpam-6679	577	7	]	]	X
ejpam-6679	578	1	=	=	SYM
ejpam-6679	578	2	(	(	PUNCT
ejpam-6679	578	3	α̂[θk])σ	α̂[θk])σ	PROPN
ejpam-6679	578	4	for	for	ADP
ejpam-6679	578	5	any	any	DET
ejpam-6679	578	6	1	1	NUM
ejpam-6679	578	7	≤	≤	NUM
ejpam-6679	578	8	k	k	PROPN
ejpam-6679	578	9	≤	≤	PROPN
ejpam-6679	578	10	n.	n.	NOUN
ejpam-6679	578	11	so	so	ADV
ejpam-6679	578	12	(	(	PUNCT
ejpam-6679	578	13	θ)σ	θ)σ	X
ejpam-6679	578	14	=	=	SYM
ejpam-6679	578	15	fi((θ1)σ	fi((θ1)σ	PROPN
ejpam-6679	578	16	,	,	PUNCT
ejpam-6679	578	17	.	.	PUNCT
ejpam-6679	578	18	.	.	PUNCT
ejpam-6679	578	19	.	.	PUNCT
ejpam-6679	579	1	,	,	PUNCT
ejpam-6679	579	2	(	(	PUNCT
ejpam-6679	579	3	θn)σ	θn)σ	NOUN
ejpam-6679	579	4	)	)	PUNCT
ejpam-6679	579	5	.	.	PUNCT
ejpam-6679	580	1	t.	t.	PROPN
ejpam-6679	580	2	changphas	changphas	PROPN
ejpam-6679	580	3	/	/	SYM
ejpam-6679	580	4	eur	eur	PROPN
ejpam-6679	580	5	.	.	PUNCT
ejpam-6679	581	1	j.	j.	PROPN
ejpam-6679	581	2	pure	pure	PROPN
ejpam-6679	581	3	appl	appl	PROPN
ejpam-6679	581	4	.	.	PROPN
ejpam-6679	581	5	math	math	PROPN
ejpam-6679	581	6	,	,	PUNCT
ejpam-6679	581	7	18	18	NUM
ejpam-6679	581	8	(	(	PUNCT
ejpam-6679	581	9	4	4	NUM
ejpam-6679	581	10	)	)	PUNCT
ejpam-6679	581	11	(	(	PUNCT
ejpam-6679	581	12	2025	2025	NUM
ejpam-6679	581	13	)	)	PUNCT
ejpam-6679	581	14	,	,	PUNCT
ejpam-6679	581	15	6679	6679	NUM
ejpam-6679	581	16	10	10	NUM
ejpam-6679	581	17	of	of	ADP
ejpam-6679	581	18	15	15	NUM
ejpam-6679	581	19	thus	thus	ADV
ejpam-6679	581	20	α̂[(θ)σ	α̂[(θ)σ	NUM
ejpam-6679	581	21	]	]	PUNCT
ejpam-6679	581	22	=	=	PUNCT
ejpam-6679	581	23	sn(α(fi	sn(α(fi	PROPN
ejpam-6679	581	24	)	)	PUNCT
ejpam-6679	581	25	,	,	PUNCT
ejpam-6679	581	26	α̂[(θ1)σ	α̂[(θ1)σ	PROPN
ejpam-6679	581	27	]	]	PUNCT
ejpam-6679	581	28	,	,	PUNCT
ejpam-6679	581	29	.	.	PUNCT
ejpam-6679	581	30	.	.	PUNCT
ejpam-6679	582	1	.	.	PUNCT
ejpam-6679	583	1	,	,	PUNCT
ejpam-6679	583	2	α̂[(θn)σ	α̂[(θn)σ	ADV
ejpam-6679	583	3	]	]	X
ejpam-6679	583	4	)	)	PUNCT
ejpam-6679	583	5	=	=	SYM
ejpam-6679	583	6	sn(α(fi	sn(α(fi	PROPN
ejpam-6679	583	7	)	)	PUNCT
ejpam-6679	583	8	,	,	PUNCT
ejpam-6679	583	9	(	(	PUNCT
ejpam-6679	583	10	α̂[t1])σ	α̂[t1])σ	NOUN
ejpam-6679	583	11	,	,	PUNCT
ejpam-6679	583	12	.	.	PUNCT
ejpam-6679	583	13	.	.	PUNCT
ejpam-6679	583	14	.	.	PUNCT
ejpam-6679	584	1	,	,	PUNCT
ejpam-6679	584	2	(	(	PUNCT
ejpam-6679	584	3	α̂[θn])σ	α̂[θn])σ	NOUN
ejpam-6679	584	4	)	)	PUNCT
ejpam-6679	584	5	)	)	PUNCT
ejpam-6679	585	1	=	=	SYM
ejpam-6679	585	2	(	(	PUNCT
ejpam-6679	585	3	sn(α(fi	sn(α(fi	NOUN
ejpam-6679	585	4	)	)	PUNCT
ejpam-6679	585	5	,	,	PUNCT
ejpam-6679	585	6	α̂[θ1	α̂[θ1	X
ejpam-6679	585	7	]	]	X
ejpam-6679	585	8	,	,	PUNCT
ejpam-6679	585	9	.	.	PUNCT
ejpam-6679	585	10	.	.	PUNCT
ejpam-6679	585	11	.	.	PUNCT
ejpam-6679	586	1	,	,	PUNCT
ejpam-6679	586	2	α̂[θn]))σ	α̂[θn]))σ	NOUN
ejpam-6679	586	3	=	=	SYM
ejpam-6679	586	4	(	(	PUNCT
ejpam-6679	586	5	α̂[θ])σ	α̂[θ])σ	PROPN
ejpam-6679	586	6	.	.	PUNCT
ejpam-6679	587	1	now	now	ADV
ejpam-6679	587	2	,	,	PUNCT
ejpam-6679	587	3	let	let	VERB
ejpam-6679	587	4	α1	α1	PROPN
ejpam-6679	587	5	,	,	PUNCT
ejpam-6679	587	6	α2	α2	PROPN
ejpam-6679	587	7	∈	∈	PROPN
ejpam-6679	587	8	hypalt(n)(τn	hypalt(n)(τn	PROPN
ejpam-6679	587	9	)	)	PUNCT
ejpam-6679	587	10	,	,	PUNCT
ejpam-6679	587	11	and	and	CCONJ
ejpam-6679	587	12	let	let	VERB
ejpam-6679	587	13	θ	θ	PROPN
ejpam-6679	587	14	∈	∈	PROPN
ejpam-6679	587	15	w	w	PROPN
ejpam-6679	587	16	alt(n	alt(n	PROPN
ejpam-6679	587	17	)	)	PUNCT
ejpam-6679	587	18	τn	τn	X
ejpam-6679	587	19	(	(	PUNCT
ejpam-6679	587	20	ωn	ωn	NOUN
ejpam-6679	587	21	)	)	PUNCT
ejpam-6679	587	22	.	.	PUNCT
ejpam-6679	588	1	if	if	SCONJ
ejpam-6679	588	2	θ	θ	PROPN
ejpam-6679	588	3	=	=	SYM
ejpam-6679	588	4	fi(ωσ(1	fi(ωσ(1	NOUN
ejpam-6679	588	5	)	)	PUNCT
ejpam-6679	588	6	,	,	PUNCT
ejpam-6679	588	7	.	.	PUNCT
ejpam-6679	588	8	.	.	PUNCT
ejpam-6679	588	9	.	.	PUNCT
ejpam-6679	589	1	,	,	PUNCT
ejpam-6679	589	2	ωσ(n	ωσ(n	NOUN
ejpam-6679	589	3	)	)	PUNCT
ejpam-6679	589	4	)	)	PUNCT
ejpam-6679	590	1	for	for	ADP
ejpam-6679	590	2	some	some	PRON
ejpam-6679	590	3	i	i	PRON
ejpam-6679	590	4	∈	∈	PROPN
ejpam-6679	591	1	i	i	PRON
ejpam-6679	591	2	,	,	PUNCT
ejpam-6679	591	3	σ	σ	PROPN
ejpam-6679	591	4	∈	∈	PROPN
ejpam-6679	591	5	alt(n	alt(n	PROPN
ejpam-6679	591	6	)	)	PUNCT
ejpam-6679	591	7	,	,	PUNCT
ejpam-6679	591	8	then	then	ADV
ejpam-6679	591	9	(	(	PUNCT
ejpam-6679	591	10	α1	α1	PROPN
ejpam-6679	591	11	◦	◦	NOUN
ejpam-6679	591	12	h	h	NOUN
ejpam-6679	591	13	α2)̂[θ	α2)̂[θ	NOUN
ejpam-6679	591	14	]	]	X
ejpam-6679	591	15	=	=	SYM
ejpam-6679	591	16	(	(	PUNCT
ejpam-6679	591	17	α1	α1	PROPN
ejpam-6679	591	18	◦	◦	NOUN
ejpam-6679	591	19	h	h	NOUN
ejpam-6679	591	20	α2)̂[fi(ωσ(1	α2)̂[fi(ωσ(1	NOUN
ejpam-6679	591	21	)	)	PUNCT
ejpam-6679	591	22	,	,	PUNCT
ejpam-6679	591	23	.	.	PUNCT
ejpam-6679	591	24	.	.	PUNCT
ejpam-6679	591	25	.	.	PUNCT
ejpam-6679	592	1	,	,	PUNCT
ejpam-6679	592	2	ωσ(n	ωσ(n	NOUN
ejpam-6679	592	3	)	)	PUNCT
ejpam-6679	592	4	)	)	PUNCT
ejpam-6679	592	5	]	]	PUNCT
ejpam-6679	593	1	=	=	PUNCT
ejpam-6679	593	2	(	(	PUNCT
ejpam-6679	593	3	(	(	PUNCT
ejpam-6679	593	4	α1	α1	PROPN
ejpam-6679	593	5	◦	◦	NOUN
ejpam-6679	593	6	h	h	NOUN
ejpam-6679	593	7	α2)(fi))σ	α2)(fi))σ	NOUN
ejpam-6679	593	8	=	=	SYM
ejpam-6679	593	9	(	(	PUNCT
ejpam-6679	593	10	(	(	PUNCT
ejpam-6679	593	11	α̂1[α2(fi)])σ	α̂1[α2(fi)])σ	NUM
ejpam-6679	593	12	and	and	CCONJ
ejpam-6679	593	13	(	(	PUNCT
ejpam-6679	593	14	α̂1	α̂1	PRON
ejpam-6679	593	15	◦	◦	VERB
ejpam-6679	593	16	α̂2)[θ	α̂2)[θ	NOUN
ejpam-6679	593	17	]	]	X
ejpam-6679	593	18	=	=	SYM
ejpam-6679	593	19	(	(	PUNCT
ejpam-6679	593	20	α̂1	α̂1	PRON
ejpam-6679	593	21	◦	◦	NOUN
ejpam-6679	593	22	α̂2)[fi(ωσ(1	α̂2)[fi(ωσ(1	NOUN
ejpam-6679	593	23	)	)	PUNCT
ejpam-6679	593	24	,	,	PUNCT
ejpam-6679	593	25	.	.	PUNCT
ejpam-6679	593	26	.	.	PUNCT
ejpam-6679	593	27	.	.	PUNCT
ejpam-6679	594	1	,	,	PUNCT
ejpam-6679	594	2	ωσ(n	ωσ(n	NOUN
ejpam-6679	594	3	)	)	PUNCT
ejpam-6679	594	4	)	)	PUNCT
ejpam-6679	594	5	]	]	PUNCT
ejpam-6679	595	1	=	=	PUNCT
ejpam-6679	595	2	α̂1(α̂2[fi(ωσ(1	α̂1(α̂2[fi(ωσ(1	NUM
ejpam-6679	595	3	)	)	PUNCT
ejpam-6679	595	4	,	,	PUNCT
ejpam-6679	595	5	.	.	PUNCT
ejpam-6679	595	6	.	.	PUNCT
ejpam-6679	595	7	.	.	PUNCT
ejpam-6679	596	1	,	,	PUNCT
ejpam-6679	596	2	ωσ(n	ωσ(n	NOUN
ejpam-6679	596	3	)	)	PUNCT
ejpam-6679	596	4	)	)	PUNCT
ejpam-6679	597	1	]	]	PUNCT
ejpam-6679	597	2	)	)	PUNCT
ejpam-6679	598	1	=	=	SYM
ejpam-6679	598	2	α̂1((α2(fi))σ	α̂1((α2(fi))σ	NOUN
ejpam-6679	598	3	)	)	PUNCT
ejpam-6679	598	4	.	.	PUNCT
ejpam-6679	599	1	thus	thus	ADV
ejpam-6679	599	2	(	(	PUNCT
ejpam-6679	599	3	α1	α1	PROPN
ejpam-6679	599	4	◦	◦	NOUN
ejpam-6679	599	5	h	h	NOUN
ejpam-6679	599	6	α2)̂[θ	α2)̂[θ	NOUN
ejpam-6679	599	7	]	]	PUNCT
ejpam-6679	599	8	=	=	SYM
ejpam-6679	599	9	α̂1	α̂1	PRON
ejpam-6679	599	10	◦	◦	VERB
ejpam-6679	599	11	α̂2[θ	α̂2[θ	PROPN
ejpam-6679	599	12	]	]	PUNCT
ejpam-6679	599	13	.	.	PUNCT
ejpam-6679	600	1	let	let	VERB
ejpam-6679	600	2	θ	θ	NOUN
ejpam-6679	600	3	=	=	SYM
ejpam-6679	600	4	fi(θ1	fi(θ1	PROPN
ejpam-6679	600	5	,	,	PUNCT
ejpam-6679	600	6	.	.	PUNCT
ejpam-6679	600	7	.	.	PUNCT
ejpam-6679	601	1	.	.	PUNCT
ejpam-6679	602	1	,	,	PUNCT
ejpam-6679	602	2	θn	θn	NOUN
ejpam-6679	602	3	)	)	PUNCT
ejpam-6679	602	4	,	,	PUNCT
ejpam-6679	602	5	and	and	CCONJ
ejpam-6679	602	6	assume	assume	VERB
ejpam-6679	602	7	(	(	PUNCT
ejpam-6679	602	8	α1	α1	PROPN
ejpam-6679	602	9	◦	◦	NOUN
ejpam-6679	602	10	h	h	NOUN
ejpam-6679	602	11	α2)̂[θk	α2)̂[θk	NOUN
ejpam-6679	602	12	]	]	X
ejpam-6679	603	1	=	=	SYM
ejpam-6679	603	2	(	(	PUNCT
ejpam-6679	603	3	α̂1	α̂1	PRON
ejpam-6679	603	4	◦	◦	VERB
ejpam-6679	603	5	α̂2)[θk	α̂2)[θk	ADP
ejpam-6679	603	6	]	]	X
ejpam-6679	603	7	for	for	ADP
ejpam-6679	603	8	any	any	DET
ejpam-6679	603	9	1	1	NUM
ejpam-6679	603	10	≤	≤	NUM
ejpam-6679	603	11	k	k	PROPN
ejpam-6679	603	12	≤	≤	PROPN
ejpam-6679	603	13	n.	n.	NOUN
ejpam-6679	603	14	then	then	ADV
ejpam-6679	603	15	(	(	PUNCT
ejpam-6679	603	16	α1	α1	PROPN
ejpam-6679	603	17	◦	◦	NOUN
ejpam-6679	603	18	h	h	NOUN
ejpam-6679	603	19	α2)̂[θ	α2)̂[θ	NOUN
ejpam-6679	603	20	]	]	X
ejpam-6679	603	21	=	=	SYM
ejpam-6679	603	22	(	(	PUNCT
ejpam-6679	603	23	α1	α1	PROPN
ejpam-6679	603	24	◦	◦	NOUN
ejpam-6679	603	25	h	h	NOUN
ejpam-6679	603	26	α2)̂[fi(θ1	α2)̂[fi(θ1	NUM
ejpam-6679	603	27	,	,	PUNCT
ejpam-6679	603	28	.	.	PUNCT
ejpam-6679	603	29	.	.	PUNCT
ejpam-6679	604	1	.	.	PUNCT
ejpam-6679	605	1	,	,	PUNCT
ejpam-6679	605	2	θn	θn	NOUN
ejpam-6679	605	3	)	)	PUNCT
ejpam-6679	605	4	]	]	PUNCT
ejpam-6679	606	1	=	=	SYM
ejpam-6679	606	2	sn((α1	sn((α1	ADP
ejpam-6679	606	3	◦	◦	NOUN
ejpam-6679	606	4	h	h	NOUN
ejpam-6679	606	5	α2)(fi	α2)(fi	PROPN
ejpam-6679	606	6	)	)	PUNCT
ejpam-6679	606	7	,	,	PUNCT
ejpam-6679	606	8	(	(	PUNCT
ejpam-6679	606	9	α1	α1	PROPN
ejpam-6679	606	10	◦	◦	NOUN
ejpam-6679	606	11	h	h	NOUN
ejpam-6679	606	12	α2)̂[θ1	α2)̂[θ1	NOUN
ejpam-6679	606	13	]	]	PUNCT
ejpam-6679	606	14	,	,	PUNCT
ejpam-6679	606	15	.	.	PUNCT
ejpam-6679	606	16	.	.	PUNCT
ejpam-6679	606	17	.	.	PUNCT
ejpam-6679	607	1	,	,	PUNCT
ejpam-6679	607	2	(	(	PUNCT
ejpam-6679	607	3	α1	α1	PROPN
ejpam-6679	607	4	◦	◦	NOUN
ejpam-6679	607	5	h	h	NOUN
ejpam-6679	607	6	α2)̂[θn	α2)̂[θn	NOUN
ejpam-6679	607	7	]	]	PUNCT
ejpam-6679	607	8	)	)	PUNCT
ejpam-6679	607	9	=	=	SYM
ejpam-6679	607	10	sn((α̂1[α2(fi	sn((α̂1[α2(fi	PROPN
ejpam-6679	607	11	)	)	PUNCT
ejpam-6679	607	12	]	]	X
ejpam-6679	607	13	,	,	PUNCT
ejpam-6679	607	14	α̂1[α̂2[θ1	α̂1[α̂2[θ1	NOUN
ejpam-6679	607	15	]	]	X
ejpam-6679	607	16	]	]	PUNCT
ejpam-6679	607	17	,	,	PUNCT
ejpam-6679	607	18	.	.	PUNCT
ejpam-6679	607	19	.	.	PUNCT
ejpam-6679	608	1	.	.	PUNCT
ejpam-6679	609	1	,	,	PUNCT
ejpam-6679	609	2	α̂1[α̂2[θn	α̂1[α̂2[θn	PROPN
ejpam-6679	609	3	]	]	X
ejpam-6679	609	4	]	]	PUNCT
ejpam-6679	609	5	)	)	PUNCT
ejpam-6679	610	1	=	=	SYM
ejpam-6679	610	2	α̂1(s	α̂1(s	PROPN
ejpam-6679	610	3	n(α2(fi	n(α2(fi	PROPN
ejpam-6679	610	4	)	)	PUNCT
ejpam-6679	610	5	,	,	PUNCT
ejpam-6679	610	6	α̂2[θ1	α̂2[θ1	NUM
ejpam-6679	610	7	]	]	PUNCT
ejpam-6679	610	8	,	,	PUNCT
ejpam-6679	610	9	.	.	PUNCT
ejpam-6679	610	10	.	.	PUNCT
ejpam-6679	610	11	.	.	PUNCT
ejpam-6679	611	1	,	,	PUNCT
ejpam-6679	611	2	α̂2[θn	α̂2[θn	NOUN
ejpam-6679	611	3	]	]	PUNCT
ejpam-6679	611	4	)	)	PUNCT
ejpam-6679	611	5	)	)	PUNCT
ejpam-6679	612	1	=	=	PUNCT
ejpam-6679	612	2	α̂1[α̂2[fi(θ1	α̂1[α̂2[fi(θ1	NOUN
ejpam-6679	612	3	,	,	PUNCT
ejpam-6679	612	4	.	.	PUNCT
ejpam-6679	612	5	.	.	PUNCT
ejpam-6679	612	6	.	.	PUNCT
ejpam-6679	613	1	,	,	PUNCT
ejpam-6679	613	2	θn	θn	NOUN
ejpam-6679	613	3	)	)	PUNCT
ejpam-6679	613	4	]	]	X
ejpam-6679	613	5	]	]	X
ejpam-6679	614	1	=	=	SYM
ejpam-6679	614	2	(	(	PUNCT
ejpam-6679	614	3	α̂1	α̂1	PRON
ejpam-6679	614	4	◦	◦	VERB
ejpam-6679	614	5	α̂2)[θ	α̂2)[θ	NUM
ejpam-6679	614	6	]	]	PUNCT
ejpam-6679	614	7	.	.	PUNCT
ejpam-6679	615	1	therefore	therefore	ADV
ejpam-6679	615	2	the	the	DET
ejpam-6679	615	3	assertion	assertion	NOUN
ejpam-6679	615	4	holds	hold	VERB
ejpam-6679	615	5	.	.	PUNCT
ejpam-6679	616	1	the	the	DET
ejpam-6679	616	2	mapping	mapping	NOUN
ejpam-6679	616	3	αid	αid	NOUN
ejpam-6679	616	4	:	:	PUNCT
ejpam-6679	616	5	{	{	PUNCT
ejpam-6679	616	6	fi	fi	NOUN
ejpam-6679	616	7	:	:	PUNCT
ejpam-6679	616	8	i	i	PRON
ejpam-6679	616	9	∈	∈	VERB
ejpam-6679	616	10	i	i	PRON
ejpam-6679	616	11	}	}	PUNCT
ejpam-6679	616	12	→w	→w	NUM
ejpam-6679	616	13	alt(n	alt(n	PROPN
ejpam-6679	616	14	)	)	PUNCT
ejpam-6679	616	15	τn	τn	X
ejpam-6679	616	16	(	(	PUNCT
ejpam-6679	616	17	ωn	ωn	NOUN
ejpam-6679	616	18	)	)	PUNCT
ejpam-6679	616	19	which	which	PRON
ejpam-6679	616	20	is	be	AUX
ejpam-6679	616	21	defined	define	VERB
ejpam-6679	616	22	by	by	ADP
ejpam-6679	616	23	,	,	PUNCT
ejpam-6679	616	24	for	for	ADP
ejpam-6679	616	25	all	all	PRON
ejpam-6679	616	26	i	i	PRON
ejpam-6679	616	27	∈	∈	PROPN
ejpam-6679	616	28	i	i	PRON
ejpam-6679	616	29	,	,	PUNCT
ejpam-6679	616	30	αid(fi	αid(fi	NUM
ejpam-6679	616	31	)	)	PUNCT
ejpam-6679	616	32	=	=	SYM
ejpam-6679	616	33	fi(ω1	fi(ω1	NOUN
ejpam-6679	616	34	,	,	PUNCT
ejpam-6679	616	35	.	.	PUNCT
ejpam-6679	616	36	.	.	PUNCT
ejpam-6679	616	37	.	.	PUNCT
ejpam-6679	617	1	,	,	PUNCT
ejpam-6679	617	2	ωn	ωn	X
ejpam-6679	617	3	)	)	PUNCT
ejpam-6679	617	4	is	be	AUX
ejpam-6679	617	5	an	an	DET
ejpam-6679	617	6	alt	alt	ADJ
ejpam-6679	617	7	-	-	PUNCT
ejpam-6679	617	8	hypersubstitution	hypersubstitution	NOUN
ejpam-6679	617	9	of	of	ADP
ejpam-6679	617	10	type	type	NOUN
ejpam-6679	617	11	τn	τn	PROPN
ejpam-6679	617	12	.	.	PUNCT
ejpam-6679	618	1	theorem	theorem	NOUN
ejpam-6679	618	2	5	5	NUM
ejpam-6679	618	3	.	.	PUNCT
ejpam-6679	619	1	hypalt(n)(τn	hypalt(n)(τn	PROPN
ejpam-6679	619	2	)	)	PUNCT
ejpam-6679	619	3	=	=	NOUN
ejpam-6679	619	4	(	(	PUNCT
ejpam-6679	619	5	hypalt(n)(τn	hypalt(n)(τn	PROPN
ejpam-6679	619	6	)	)	PUNCT
ejpam-6679	619	7	,	,	PUNCT
ejpam-6679	619	8	◦	◦	NOUN
ejpam-6679	619	9	h	h	NOUN
ejpam-6679	619	10	,	,	PUNCT
ejpam-6679	619	11	αid	αid	NOUN
ejpam-6679	619	12	)	)	PUNCT
ejpam-6679	619	13	forms	form	VERB
ejpam-6679	619	14	a	a	DET
ejpam-6679	619	15	monoid	monoid	NOUN
ejpam-6679	619	16	.	.	PUNCT
ejpam-6679	620	1	proof	proof	NOUN
ejpam-6679	620	2	.	.	PUNCT
ejpam-6679	621	1	let	let	VERB
ejpam-6679	621	2	α1	α1	PROPN
ejpam-6679	621	3	,	,	PUNCT
ejpam-6679	621	4	α2	α2	PROPN
ejpam-6679	621	5	∈	∈	PROPN
ejpam-6679	621	6	hypalt(n)(τn	hypalt(n)(τn	PROPN
ejpam-6679	621	7	)	)	PUNCT
ejpam-6679	621	8	.	.	PUNCT
ejpam-6679	622	1	then	then	ADV
ejpam-6679	622	2	,	,	PUNCT
ejpam-6679	622	3	for	for	ADP
ejpam-6679	622	4	any	any	DET
ejpam-6679	622	5	fi	fi	NOUN
ejpam-6679	622	6	,	,	PUNCT
ejpam-6679	622	7	we	we	PRON
ejpam-6679	622	8	have	have	VERB
ejpam-6679	622	9	(	(	PUNCT
ejpam-6679	622	10	α1	α1	PROPN
ejpam-6679	622	11	◦	◦	NOUN
ejpam-6679	622	12	hα2)(fi	hα2)(fi	NOUN
ejpam-6679	622	13	)	)	PUNCT
ejpam-6679	622	14	=	=	SYM
ejpam-6679	622	15	α̂1[α2(fi	α̂1[α2(fi	NOUN
ejpam-6679	622	16	)	)	PUNCT
ejpam-6679	622	17	]	]	PUNCT
ejpam-6679	622	18	.	.	PUNCT
ejpam-6679	623	1	since	since	SCONJ
ejpam-6679	623	2	α2	α2	PROPN
ejpam-6679	623	3	∈	∈	PROPN
ejpam-6679	623	4	hypalt(n)(τn	hypalt(n)(τn	PROPN
ejpam-6679	623	5	)	)	PUNCT
ejpam-6679	623	6	,	,	PUNCT
ejpam-6679	623	7	α2(fi	α2(fi	NUM
ejpam-6679	623	8	)	)	PUNCT
ejpam-6679	623	9	∈	∈	PROPN
ejpam-6679	623	10	w	w	NOUN
ejpam-6679	623	11	alt(n	alt(n	PROPN
ejpam-6679	623	12	)	)	PUNCT
ejpam-6679	623	13	τn	τn	X
ejpam-6679	623	14	(	(	PUNCT
ejpam-6679	623	15	ωn	ωn	NOUN
ejpam-6679	623	16	)	)	PUNCT
ejpam-6679	623	17	.	.	PUNCT
ejpam-6679	624	1	if	if	SCONJ
ejpam-6679	624	2	α2(fi	α2(fi	NUM
ejpam-6679	624	3	)	)	PUNCT
ejpam-6679	624	4	=	=	SYM
ejpam-6679	624	5	fi(ωσ(1	fi(ωσ(1	NOUN
ejpam-6679	624	6	)	)	PUNCT
ejpam-6679	624	7	,	,	PUNCT
ejpam-6679	624	8	.	.	PUNCT
ejpam-6679	624	9	.	.	PUNCT
ejpam-6679	624	10	.	.	PUNCT
ejpam-6679	625	1	,	,	PUNCT
ejpam-6679	625	2	ωσ(n	ωσ(n	NOUN
ejpam-6679	625	3	)	)	PUNCT
ejpam-6679	625	4	)	)	PUNCT
ejpam-6679	626	1	for	for	ADP
ejpam-6679	626	2	some	some	DET
ejpam-6679	626	3	σ	σ	NUM
ejpam-6679	626	4	∈	∈	PROPN
ejpam-6679	626	5	alt(n	alt(n	PROPN
ejpam-6679	626	6	)	)	PUNCT
ejpam-6679	626	7	,	,	PUNCT
ejpam-6679	626	8	then	then	ADV
ejpam-6679	626	9	by	by	ADP
ejpam-6679	626	10	α1(fi	α1(fi	PROPN
ejpam-6679	626	11	)	)	PUNCT
ejpam-6679	626	12	∈w	∈w	VERB
ejpam-6679	626	13	alt(n	alt(n	NOUN
ejpam-6679	626	14	)	)	PUNCT
ejpam-6679	626	15	τn	τn	X
ejpam-6679	626	16	(	(	PUNCT
ejpam-6679	626	17	ωn	ωn	NUM
ejpam-6679	626	18	)	)	PUNCT
ejpam-6679	626	19	,	,	PUNCT
ejpam-6679	626	20	we	we	PRON
ejpam-6679	626	21	have	have	VERB
ejpam-6679	626	22	(	(	PUNCT
ejpam-6679	626	23	α1	α1	PROPN
ejpam-6679	626	24	◦	◦	NOUN
ejpam-6679	626	25	h	h	NOUN
ejpam-6679	626	26	α2)(fi	α2)(fi	PROPN
ejpam-6679	626	27	)	)	PUNCT
ejpam-6679	627	1	=	=	SYM
ejpam-6679	627	2	α̂1[α2(fi	α̂1[α2(fi	NOUN
ejpam-6679	627	3	)	)	PUNCT
ejpam-6679	627	4	]	]	PUNCT
ejpam-6679	628	1	=	=	PUNCT
ejpam-6679	628	2	(	(	PUNCT
ejpam-6679	628	3	α1(fi))σ	α1(fi))σ	NOUN
ejpam-6679	628	4	∈w	∈w	PROPN
ejpam-6679	628	5	alt(n	alt(n	NOUN
ejpam-6679	628	6	)	)	PUNCT
ejpam-6679	628	7	τn	τn	X
ejpam-6679	628	8	(	(	PUNCT
ejpam-6679	628	9	ωn	ωn	NOUN
ejpam-6679	628	10	)	)	PUNCT
ejpam-6679	628	11	.	.	PUNCT
ejpam-6679	629	1	t.	t.	PROPN
ejpam-6679	629	2	changphas	changphas	PROPN
ejpam-6679	629	3	/	/	SYM
ejpam-6679	629	4	eur	eur	PROPN
ejpam-6679	629	5	.	.	PUNCT
ejpam-6679	630	1	j.	j.	PROPN
ejpam-6679	630	2	pure	pure	PROPN
ejpam-6679	630	3	appl	appl	PROPN
ejpam-6679	630	4	.	.	PROPN
ejpam-6679	630	5	math	math	PROPN
ejpam-6679	630	6	,	,	PUNCT
ejpam-6679	630	7	18	18	NUM
ejpam-6679	630	8	(	(	PUNCT
ejpam-6679	630	9	4	4	NUM
ejpam-6679	630	10	)	)	PUNCT
ejpam-6679	630	11	(	(	PUNCT
ejpam-6679	630	12	2025	2025	NUM
ejpam-6679	630	13	)	)	PUNCT
ejpam-6679	630	14	,	,	PUNCT
ejpam-6679	630	15	6679	6679	NUM
ejpam-6679	630	16	11	11	NUM
ejpam-6679	630	17	of	of	ADP
ejpam-6679	630	18	15	15	NUM
ejpam-6679	630	19	let	let	VERB
ejpam-6679	630	20	α2(fi	α2(fi	NUM
ejpam-6679	630	21	)	)	PUNCT
ejpam-6679	630	22	=	=	SYM
ejpam-6679	630	23	fi(θ1	fi(θ1	NOUN
ejpam-6679	630	24	,	,	PUNCT
ejpam-6679	630	25	.	.	PUNCT
ejpam-6679	630	26	.	.	PUNCT
ejpam-6679	630	27	.	.	PUNCT
ejpam-6679	631	1	,	,	PUNCT
ejpam-6679	631	2	θn	θn	NOUN
ejpam-6679	631	3	)	)	PUNCT
ejpam-6679	631	4	and	and	CCONJ
ejpam-6679	631	5	assume	assume	VERB
ejpam-6679	631	6	α̂1[θ1	α̂1[θ1	PROPN
ejpam-6679	631	7	]	]	PUNCT
ejpam-6679	631	8	,	,	PUNCT
ejpam-6679	631	9	.	.	PUNCT
ejpam-6679	631	10	.	.	PUNCT
ejpam-6679	632	1	.	.	PUNCT
ejpam-6679	633	1	,	,	PUNCT
ejpam-6679	633	2	α̂1[θn	α̂1[θn	PROPN
ejpam-6679	633	3	]	]	PUNCT
ejpam-6679	633	4	∈w	∈w	VERB
ejpam-6679	633	5	alt(n	alt(n	NOUN
ejpam-6679	633	6	)	)	PUNCT
ejpam-6679	633	7	τn	τn	X
ejpam-6679	633	8	(	(	PUNCT
ejpam-6679	633	9	ωn	ωn	NOUN
ejpam-6679	633	10	)	)	PUNCT
ejpam-6679	633	11	.	.	PUNCT
ejpam-6679	634	1	by	by	ADP
ejpam-6679	634	2	α̂1[fi(θ1	α̂1[fi(θ1	PROPN
ejpam-6679	634	3	,	,	PUNCT
ejpam-6679	634	4	.	.	PUNCT
ejpam-6679	634	5	.	.	PUNCT
ejpam-6679	634	6	.	.	PUNCT
ejpam-6679	635	1	,	,	PUNCT
ejpam-6679	635	2	θn	θn	NOUN
ejpam-6679	635	3	)	)	PUNCT
ejpam-6679	635	4	]	]	PUNCT
ejpam-6679	636	1	=	=	SYM
ejpam-6679	636	2	sn(α1(fi	sn(α1(fi	PROPN
ejpam-6679	636	3	)	)	PUNCT
ejpam-6679	636	4	,	,	PUNCT
ejpam-6679	636	5	α̂1[θ1	α̂1[θ1	PROPN
ejpam-6679	636	6	]	]	PUNCT
ejpam-6679	636	7	,	,	PUNCT
ejpam-6679	636	8	.	.	PUNCT
ejpam-6679	636	9	.	.	PUNCT
ejpam-6679	637	1	.	.	PUNCT
ejpam-6679	638	1	,	,	PUNCT
ejpam-6679	638	2	α̂1[θn	α̂1[θn	PROPN
ejpam-6679	638	3	]	]	PUNCT
ejpam-6679	638	4	)	)	PUNCT
ejpam-6679	638	5	and	and	CCONJ
ejpam-6679	638	6	α1(fi	α1(fi	PROPN
ejpam-6679	638	7	)	)	PUNCT
ejpam-6679	638	8	∈	∈	PROPN
ejpam-6679	638	9	w	w	PROPN
ejpam-6679	638	10	alt(n	alt(n	PROPN
ejpam-6679	638	11	)	)	PUNCT
ejpam-6679	638	12	τn	τn	X
ejpam-6679	638	13	(	(	PUNCT
ejpam-6679	638	14	ωn	ωn	NUM
ejpam-6679	638	15	)	)	PUNCT
ejpam-6679	638	16	,	,	PUNCT
ejpam-6679	638	17	it	it	PRON
ejpam-6679	638	18	follows	follow	VERB
ejpam-6679	638	19	that	that	PRON
ejpam-6679	638	20	α̂1[α2(fi	α̂1[α2(fi	NOUN
ejpam-6679	638	21	)	)	PUNCT
ejpam-6679	638	22	]	]	PUNCT
ejpam-6679	639	1	∈	∈	PROPN
ejpam-6679	639	2	w	w	PROPN
ejpam-6679	639	3	alt(n	alt(n	PROPN
ejpam-6679	639	4	)	)	PUNCT
ejpam-6679	639	5	τn	τn	X
ejpam-6679	639	6	(	(	PUNCT
ejpam-6679	639	7	ωn	ωn	NUM
ejpam-6679	639	8	)	)	PUNCT
ejpam-6679	639	9	.	.	PUNCT
ejpam-6679	640	1	the	the	DET
ejpam-6679	640	2	associativity	associativity	NOUN
ejpam-6679	640	3	of	of	ADP
ejpam-6679	640	4	◦	◦	NOUN
ejpam-6679	640	5	h	h	NOUN
ejpam-6679	640	6	follows	follow	VERB
ejpam-6679	640	7	by	by	ADP
ejpam-6679	640	8	lemma	lemma	PROPN
ejpam-6679	640	9	2	2	PROPN
ejpam-6679	640	10	.	.	PUNCT
ejpam-6679	641	1	lemma	lemma	PROPN
ejpam-6679	641	2	3	3	NUM
ejpam-6679	641	3	.	.	PUNCT
ejpam-6679	642	1	the	the	DET
ejpam-6679	642	2	menger	menger	PROPN
ejpam-6679	642	3	algebra	algebra	PROPN
ejpam-6679	642	4	walt(n	walt(n	PROPN
ejpam-6679	642	5	)	)	PUNCT
ejpam-6679	642	6	τn	τn	X
ejpam-6679	642	7	(	(	PUNCT
ejpam-6679	642	8	ωn	ωn	X
ejpam-6679	642	9	)	)	PUNCT
ejpam-6679	642	10	of	of	ADP
ejpam-6679	642	11	rank	rank	NOUN
ejpam-6679	642	12	n	n	VERB
ejpam-6679	642	13	is	be	AUX
ejpam-6679	642	14	generated	generate	VERB
ejpam-6679	642	15	by	by	ADP
ejpam-6679	642	16	f	f	PROPN
ejpam-6679	642	17	w	w	PROPN
ejpam-6679	642	18	alt(n	alt(n	PROPN
ejpam-6679	642	19	)	)	PUNCT
ejpam-6679	642	20	τn	τn	X
ejpam-6679	642	21	(	(	PUNCT
ejpam-6679	642	22	ωn	ωn	X
ejpam-6679	642	23	)	)	PUNCT
ejpam-6679	642	24	=	=	PRON
ejpam-6679	642	25	{	{	PUNCT
ejpam-6679	642	26	fi(ωσ(1	fi(ωσ(1	NOUN
ejpam-6679	642	27	)	)	PUNCT
ejpam-6679	642	28	,	,	PUNCT
ejpam-6679	642	29	.	.	PUNCT
ejpam-6679	642	30	.	.	PUNCT
ejpam-6679	642	31	.	.	PUNCT
ejpam-6679	643	1	,	,	PUNCT
ejpam-6679	643	2	ωσ(n	ωσ(n	NOUN
ejpam-6679	643	3	)	)	PUNCT
ejpam-6679	643	4	)	)	PUNCT
ejpam-6679	644	1	:	:	PUNCT
ejpam-6679	644	2	i	i	PRON
ejpam-6679	644	3	∈	∈	VERB
ejpam-6679	645	1	i	i	PRON
ejpam-6679	645	2	,	,	PUNCT
ejpam-6679	645	3	σ	σ	PROPN
ejpam-6679	645	4	∈	∈	PROPN
ejpam-6679	645	5	alt(n	alt(n	PROPN
ejpam-6679	645	6	)	)	PUNCT
ejpam-6679	645	7	}	}	PUNCT
ejpam-6679	645	8	.	.	PUNCT
ejpam-6679	646	1	proof	proof	NOUN
ejpam-6679	646	2	.	.	PUNCT
ejpam-6679	647	1	clearly	clearly	ADV
ejpam-6679	647	2	,	,	PUNCT
ejpam-6679	647	3	fi(ωσ(1	fi(ωσ(1	NOUN
ejpam-6679	647	4	)	)	PUNCT
ejpam-6679	647	5	,	,	PUNCT
ejpam-6679	647	6	.	.	PUNCT
ejpam-6679	647	7	.	.	PUNCT
ejpam-6679	647	8	.	.	PUNCT
ejpam-6679	648	1	,	,	PUNCT
ejpam-6679	648	2	ωσ(n	ωσ(n	NOUN
ejpam-6679	648	3	)	)	PUNCT
ejpam-6679	648	4	)	)	PUNCT
ejpam-6679	649	1	∈	∈	PROPN
ejpam-6679	649	2	w	w	NOUN
ejpam-6679	649	3	alt(n	alt(n	PROPN
ejpam-6679	649	4	)	)	PUNCT
ejpam-6679	649	5	τn	τn	X
ejpam-6679	649	6	(	(	PUNCT
ejpam-6679	649	7	ωn	ωn	X
ejpam-6679	649	8	)	)	PUNCT
ejpam-6679	649	9	for	for	ADP
ejpam-6679	649	10	any	any	DET
ejpam-6679	649	11	i	i	PRON
ejpam-6679	649	12	∈	∈	PROPN
ejpam-6679	649	13	i	i	PRON
ejpam-6679	649	14	,	,	PUNCT
ejpam-6679	649	15	σ	σ	PROPN
ejpam-6679	649	16	∈	∈	PROPN
ejpam-6679	649	17	alt(n	alt(n	PROPN
ejpam-6679	649	18	)	)	PUNCT
ejpam-6679	649	19	.	.	PUNCT
ejpam-6679	650	1	let	let	VERB
ejpam-6679	650	2	θ	θ	NOUN
ejpam-6679	650	3	=	=	SYM
ejpam-6679	650	4	fi(θ1	fi(θ1	PROPN
ejpam-6679	650	5	,	,	PUNCT
ejpam-6679	650	6	θ2	θ2	PROPN
ejpam-6679	650	7	,	,	PUNCT
ejpam-6679	650	8	.	.	PUNCT
ejpam-6679	650	9	.	.	PUNCT
ejpam-6679	651	1	.	.	PUNCT
ejpam-6679	652	1	,	,	PUNCT
ejpam-6679	652	2	θn	θn	X
ejpam-6679	652	3	)	)	PUNCT
ejpam-6679	652	4	∈	∈	PROPN
ejpam-6679	652	5	w	w	PROPN
ejpam-6679	652	6	alt(n	alt(n	PROPN
ejpam-6679	652	7	)	)	PUNCT
ejpam-6679	652	8	τn	τn	X
ejpam-6679	652	9	(	(	PUNCT
ejpam-6679	652	10	ωn	ωn	X
ejpam-6679	652	11	)	)	PUNCT
ejpam-6679	652	12	such	such	ADJ
ejpam-6679	652	13	that	that	SCONJ
ejpam-6679	652	14	f	f	PROPN
ejpam-6679	652	15	w	w	PROPN
ejpam-6679	652	16	alt(n	alt(n	PROPN
ejpam-6679	652	17	)	)	PUNCT
ejpam-6679	652	18	τn	τn	X
ejpam-6679	652	19	(	(	PUNCT
ejpam-6679	652	20	ωn	ωn	X
ejpam-6679	652	21	)	)	PUNCT
ejpam-6679	652	22	generates	generate	VERB
ejpam-6679	652	23	θ1	θ1	NOUN
ejpam-6679	652	24	,	,	PUNCT
ejpam-6679	652	25	θ2	θ2	PROPN
ejpam-6679	652	26	,	,	PUNCT
ejpam-6679	652	27	.	.	PUNCT
ejpam-6679	652	28	.	.	PUNCT
ejpam-6679	653	1	.	.	PUNCT
ejpam-6679	654	1	,	,	PUNCT
ejpam-6679	654	2	θn	θn	X
ejpam-6679	654	3	.	.	PROPN
ejpam-6679	655	1	we	we	PRON
ejpam-6679	655	2	have	have	VERB
ejpam-6679	655	3	sn(fi(ω1	sn(fi(ω1	NOUN
ejpam-6679	655	4	,	,	PUNCT
ejpam-6679	655	5	.	.	PUNCT
ejpam-6679	655	6	.	.	PUNCT
ejpam-6679	656	1	.	.	PUNCT
ejpam-6679	657	1	,	,	PUNCT
ejpam-6679	657	2	ωn	ωn	X
ejpam-6679	657	3	)	)	PUNCT
ejpam-6679	657	4	,	,	PUNCT
ejpam-6679	657	5	θ1	θ1	NOUN
ejpam-6679	657	6	,	,	PUNCT
ejpam-6679	657	7	.	.	PUNCT
ejpam-6679	657	8	.	.	PUNCT
ejpam-6679	657	9	.	.	PUNCT
ejpam-6679	658	1	,	,	PUNCT
ejpam-6679	658	2	θn	θn	NOUN
ejpam-6679	658	3	)	)	PUNCT
ejpam-6679	658	4	=	=	SYM
ejpam-6679	658	5	fi(θ1	fi(θ1	PROPN
ejpam-6679	658	6	,	,	PUNCT
ejpam-6679	658	7	.	.	PUNCT
ejpam-6679	658	8	.	.	PUNCT
ejpam-6679	659	1	.	.	PUNCT
ejpam-6679	660	1	,	,	PUNCT
ejpam-6679	660	2	θn	θn	NOUN
ejpam-6679	660	3	)	)	PUNCT
ejpam-6679	660	4	=	=	SYM
ejpam-6679	660	5	θ	θ	PROPN
ejpam-6679	660	6	.	.	PUNCT
ejpam-6679	661	1	since	since	SCONJ
ejpam-6679	661	2	the	the	DET
ejpam-6679	661	3	menger	menger	PROPN
ejpam-6679	661	4	algebra	algebra	PROPN
ejpam-6679	661	5	walt(n	walt(n	PROPN
ejpam-6679	661	6	)	)	PUNCT
ejpam-6679	661	7	τn	τn	X
ejpam-6679	661	8	(	(	PUNCT
ejpam-6679	661	9	ωn	ωn	X
ejpam-6679	661	10	)	)	PUNCT
ejpam-6679	661	11	is	be	AUX
ejpam-6679	661	12	generated	generate	VERB
ejpam-6679	661	13	by	by	ADP
ejpam-6679	661	14	the	the	DET
ejpam-6679	661	15	set	set	NOUN
ejpam-6679	661	16	f	f	PROPN
ejpam-6679	661	17	w	w	PROPN
ejpam-6679	661	18	alt(n	alt(n	PROPN
ejpam-6679	661	19	)	)	PUNCT
ejpam-6679	661	20	τn	τn	X
ejpam-6679	661	21	(	(	PUNCT
ejpam-6679	661	22	ωn	ωn	X
ejpam-6679	661	23	)	)	PUNCT
ejpam-6679	661	24	=	=	PRON
ejpam-6679	661	25	{	{	PUNCT
ejpam-6679	661	26	fi(ωσ(1	fi(ωσ(1	NOUN
ejpam-6679	661	27	)	)	PUNCT
ejpam-6679	661	28	,	,	PUNCT
ejpam-6679	661	29	.	.	PUNCT
ejpam-6679	661	30	.	.	PUNCT
ejpam-6679	662	1	.	.	PUNCT
ejpam-6679	663	1	,	,	PUNCT
ejpam-6679	663	2	ωσ(n	ωσ(n	NOUN
ejpam-6679	663	3	)	)	PUNCT
ejpam-6679	663	4	)	)	PUNCT
ejpam-6679	664	1	:	:	PUNCT
ejpam-6679	664	2	i	i	PRON
ejpam-6679	664	3	∈	∈	VERB
ejpam-6679	665	1	i	i	PRON
ejpam-6679	665	2	,	,	PUNCT
ejpam-6679	665	3	σ	σ	PROPN
ejpam-6679	665	4	∈	∈	PROPN
ejpam-6679	665	5	alt(n	alt(n	PROPN
ejpam-6679	665	6	)	)	PUNCT
ejpam-6679	665	7	}	}	PUNCT
ejpam-6679	666	1	so	so	SCONJ
ejpam-6679	666	2	any	any	DET
ejpam-6679	666	3	mapping	mapping	NOUN
ejpam-6679	666	4	η	η	NOUN
ejpam-6679	666	5	:	:	PUNCT
ejpam-6679	666	6	f	f	PROPN
ejpam-6679	666	7	w	w	PROPN
ejpam-6679	666	8	alt(n	alt(n	PROPN
ejpam-6679	666	9	)	)	PUNCT
ejpam-6679	666	10	τn	τn	X
ejpam-6679	666	11	(	(	PUNCT
ejpam-6679	666	12	ωn	ωn	NOUN
ejpam-6679	666	13	)	)	PUNCT
ejpam-6679	666	14	→walt(n	→walt(n	ADV
ejpam-6679	666	15	)	)	PUNCT
ejpam-6679	666	16	τn	τn	X
ejpam-6679	666	17	(	(	PUNCT
ejpam-6679	666	18	ωn	ωn	X
ejpam-6679	666	19	)	)	PUNCT
ejpam-6679	666	20	can	can	AUX
ejpam-6679	666	21	be	be	AUX
ejpam-6679	666	22	uniquely	uniquely	ADV
ejpam-6679	666	23	extended	extend	VERB
ejpam-6679	666	24	to	to	ADP
ejpam-6679	666	25	an	an	DET
ejpam-6679	666	26	endomorphism	endomorphism	NOUN
ejpam-6679	666	27	η̄	η̄	NOUN
ejpam-6679	666	28	:	:	PUNCT
ejpam-6679	666	29	walt(n	walt(n	NOUN
ejpam-6679	666	30	)	)	PUNCT
ejpam-6679	666	31	τn	τn	X
ejpam-6679	666	32	(	(	PUNCT
ejpam-6679	666	33	ωn	ωn	NOUN
ejpam-6679	666	34	)	)	PUNCT
ejpam-6679	666	35	→walt(n	→walt(n	ADV
ejpam-6679	666	36	)	)	PUNCT
ejpam-6679	666	37	τn	τn	ADP
ejpam-6679	666	38	(	(	PUNCT
ejpam-6679	666	39	ωn	ωn	NOUN
ejpam-6679	666	40	)	)	PUNCT
ejpam-6679	666	41	.	.	PUNCT
ejpam-6679	667	1	such	such	ADJ
ejpam-6679	667	2	mappings	mapping	NOUN
ejpam-6679	667	3	are	be	AUX
ejpam-6679	667	4	called	call	VERB
ejpam-6679	667	5	alternating	alternate	VERB
ejpam-6679	667	6	substitutions	substitution	NOUN
ejpam-6679	667	7	(	(	PUNCT
ejpam-6679	667	8	alt	alt	NOUN
ejpam-6679	667	9	-	-	PUNCT
ejpam-6679	667	10	substitutions	substitution	NOUN
ejpam-6679	667	11	)	)	PUNCT
ejpam-6679	667	12	.	.	PUNCT
ejpam-6679	668	1	the	the	DET
ejpam-6679	668	2	set	set	NOUN
ejpam-6679	668	3	of	of	ADP
ejpam-6679	668	4	all	all	DET
ejpam-6679	668	5	altsubstitutions	altsubstitution	NOUN
ejpam-6679	668	6	will	will	AUX
ejpam-6679	668	7	be	be	AUX
ejpam-6679	668	8	denoted	denote	VERB
ejpam-6679	668	9	by	by	ADP
ejpam-6679	668	10	substalt(n)(τn	substalt(n)(τn	PROPN
ejpam-6679	668	11	)	)	PUNCT
ejpam-6679	668	12	.	.	PUNCT
ejpam-6679	669	1	for	for	ADP
ejpam-6679	669	2	η1	η1	NOUN
ejpam-6679	669	3	,	,	PUNCT
ejpam-6679	669	4	η2	η2	PROPN
ejpam-6679	669	5	∈	∈	PROPN
ejpam-6679	669	6	substalt(n)(τn	substalt(n)(τn	PROPN
ejpam-6679	669	7	)	)	PUNCT
ejpam-6679	669	8	,	,	PUNCT
ejpam-6679	669	9	define	define	VERB
ejpam-6679	669	10	η1	η1	NOUN
ejpam-6679	669	11	�	�	NOUN
ejpam-6679	669	12	η2	η2	PROPN
ejpam-6679	669	13	=	=	PUNCT
ejpam-6679	669	14	η̄1	η̄1	PUNCT
ejpam-6679	669	15	◦	◦	NOUN
ejpam-6679	669	16	η2	η2	NOUN
ejpam-6679	669	17	where	where	SCONJ
ejpam-6679	669	18	◦	◦	NOUN
ejpam-6679	669	19	is	be	AUX
ejpam-6679	669	20	the	the	DET
ejpam-6679	669	21	usual	usual	ADJ
ejpam-6679	669	22	composition	composition	NOUN
ejpam-6679	669	23	.	.	PUNCT
ejpam-6679	670	1	the	the	DET
ejpam-6679	670	2	identity	identity	NOUN
ejpam-6679	670	3	map	map	NOUN
ejpam-6679	670	4	idf	idf	PROPN
ejpam-6679	670	5	w	w	PROPN
ejpam-6679	670	6	alt(n	alt(n	PROPN
ejpam-6679	670	7	)	)	PUNCT
ejpam-6679	670	8	τn	τn	X
ejpam-6679	670	9	(	(	PUNCT
ejpam-6679	670	10	ωn	ωn	X
ejpam-6679	670	11	)	)	PUNCT
ejpam-6679	670	12	is	be	AUX
ejpam-6679	670	13	an	an	DET
ejpam-6679	670	14	identity	identity	NOUN
ejpam-6679	670	15	element	element	NOUN
ejpam-6679	670	16	with	with	ADP
ejpam-6679	670	17	respect	respect	NOUN
ejpam-6679	670	18	to	to	ADP
ejpam-6679	670	19	�	�	PROPN
ejpam-6679	670	20	.	.	PUNCT
ejpam-6679	671	1	it	it	PRON
ejpam-6679	671	2	turns	turn	VERB
ejpam-6679	671	3	out	out	ADP
ejpam-6679	671	4	that	that	SCONJ
ejpam-6679	671	5	substalt(n)(τn	substalt(n)(τn	PROPN
ejpam-6679	671	6	)	)	PUNCT
ejpam-6679	671	7	=	=	SYM
ejpam-6679	671	8	(	(	PUNCT
ejpam-6679	671	9	substalt(n)(τn	substalt(n)(τn	PROPN
ejpam-6679	671	10	)	)	PUNCT
ejpam-6679	671	11	,	,	PUNCT
ejpam-6679	671	12	�	�	PROPN
ejpam-6679	671	13	,	,	PUNCT
ejpam-6679	671	14	idf	idf	PROPN
ejpam-6679	671	15	w	w	PROPN
ejpam-6679	671	16	alt(n	alt(n	PROPN
ejpam-6679	671	17	)	)	PUNCT
ejpam-6679	671	18	τn	τn	X
ejpam-6679	671	19	(	(	PUNCT
ejpam-6679	671	20	ωn	ωn	NOUN
ejpam-6679	671	21	)	)	PUNCT
ejpam-6679	671	22	)	)	PUNCT
ejpam-6679	671	23	forms	form	VERB
ejpam-6679	671	24	a	a	DET
ejpam-6679	671	25	monoid	monoid	NOUN
ejpam-6679	671	26	.	.	PUNCT
ejpam-6679	672	1	let	let	VERB
ejpam-6679	672	2	α	α	PRON
ejpam-6679	672	3	∈	∈	PROPN
ejpam-6679	672	4	hypalt(n)(τn	hypalt(n)(τn	PROPN
ejpam-6679	672	5	)	)	PUNCT
ejpam-6679	672	6	.	.	PUNCT
ejpam-6679	673	1	since	since	SCONJ
ejpam-6679	673	2	α̂	α̂	NUM
ejpam-6679	673	3	:	:	PUNCT
ejpam-6679	673	4	w	w	PROPN
ejpam-6679	673	5	alt(n	alt(n	PROPN
ejpam-6679	673	6	)	)	PUNCT
ejpam-6679	673	7	τn	τn	X
ejpam-6679	673	8	(	(	PUNCT
ejpam-6679	673	9	ωn	ωn	NOUN
ejpam-6679	673	10	)	)	PUNCT
ejpam-6679	673	11	→	→	PUNCT
ejpam-6679	673	12	w	w	PROPN
ejpam-6679	673	13	alt(n	alt(n	PROPN
ejpam-6679	673	14	)	)	PUNCT
ejpam-6679	673	15	τn	τn	X
ejpam-6679	673	16	(	(	PUNCT
ejpam-6679	673	17	ωn	ωn	X
ejpam-6679	673	18	)	)	PUNCT
ejpam-6679	673	19	is	be	AUX
ejpam-6679	673	20	an	an	DET
ejpam-6679	673	21	endomorphism	endomorphism	NOUN
ejpam-6679	673	22	and	and	CCONJ
ejpam-6679	673	23	f	f	PROPN
ejpam-6679	673	24	w	w	PROPN
ejpam-6679	673	25	alt(n	alt(n	PROPN
ejpam-6679	673	26	)	)	PUNCT
ejpam-6679	673	27	τn	τn	X
ejpam-6679	673	28	(	(	PUNCT
ejpam-6679	673	29	ωn	ωn	X
ejpam-6679	673	30	)	)	PUNCT
ejpam-6679	673	31	is	be	AUX
ejpam-6679	673	32	a	a	DET
ejpam-6679	673	33	generating	generate	VERB
ejpam-6679	673	34	system	system	NOUN
ejpam-6679	673	35	of	of	ADP
ejpam-6679	673	36	walt(n	walt(n	NOUN
ejpam-6679	673	37	)	)	PUNCT
ejpam-6679	673	38	τn	τn	X
ejpam-6679	673	39	(	(	PUNCT
ejpam-6679	673	40	ωn	ωn	NUM
ejpam-6679	673	41	)	)	PUNCT
ejpam-6679	673	42	,	,	PUNCT
ejpam-6679	673	43	so	so	ADV
ejpam-6679	673	44	α̂|f	α̂|f	PRON
ejpam-6679	673	45	w	w	ADJ
ejpam-6679	673	46	alt(n	alt(n	NOUN
ejpam-6679	673	47	)	)	PUNCT
ejpam-6679	673	48	τn	τn	X
ejpam-6679	673	49	(	(	PUNCT
ejpam-6679	673	50	ωn	ωn	X
ejpam-6679	673	51	)	)	PUNCT
ejpam-6679	673	52	is	be	AUX
ejpam-6679	673	53	an	an	DET
ejpam-6679	673	54	alt	alt	ADJ
ejpam-6679	673	55	-	-	PUNCT
ejpam-6679	673	56	substitution	substitution	NOUN
ejpam-6679	673	57	such	such	ADJ
ejpam-6679	673	58	that	that	SCONJ
ejpam-6679	673	59	σ̂|f	σ̂|f	PROPN
ejpam-6679	673	60	w	w	NOUN
ejpam-6679	673	61	alt(n	alt(n	PROPN
ejpam-6679	673	62	)	)	PUNCT
ejpam-6679	673	63	τn	τn	X
ejpam-6679	673	64	(	(	PUNCT
ejpam-6679	673	65	ωn	ωn	X
ejpam-6679	673	66	)	)	PUNCT
ejpam-6679	673	67	=	=	SYM
ejpam-6679	673	68	α̂.	α̂.	PROPN
ejpam-6679	673	69	t.	t.	PROPN
ejpam-6679	673	70	changphas	changphas	PROPN
ejpam-6679	673	71	/	/	SYM
ejpam-6679	673	72	eur	eur	PROPN
ejpam-6679	673	73	.	.	PUNCT
ejpam-6679	674	1	j.	j.	PROPN
ejpam-6679	674	2	pure	pure	PROPN
ejpam-6679	674	3	appl	appl	PROPN
ejpam-6679	674	4	.	.	PROPN
ejpam-6679	674	5	math	math	PROPN
ejpam-6679	674	6	,	,	PUNCT
ejpam-6679	674	7	18	18	NUM
ejpam-6679	674	8	(	(	PUNCT
ejpam-6679	674	9	4	4	NUM
ejpam-6679	674	10	)	)	PUNCT
ejpam-6679	674	11	(	(	PUNCT
ejpam-6679	674	12	2025	2025	NUM
ejpam-6679	674	13	)	)	PUNCT
ejpam-6679	674	14	,	,	PUNCT
ejpam-6679	674	15	6679	6679	NUM
ejpam-6679	674	16	12	12	NUM
ejpam-6679	674	17	of	of	ADP
ejpam-6679	674	18	15	15	NUM
ejpam-6679	674	19	define	define	NOUN
ejpam-6679	674	20	ψ	ψ	NOUN
ejpam-6679	674	21	:	:	PUNCT
ejpam-6679	674	22	hypalt(n)(τn	hypalt(n)(τn	PROPN
ejpam-6679	674	23	)	)	PUNCT
ejpam-6679	674	24	→	→	SYM
ejpam-6679	674	25	substalt(n)(τn	substalt(n)(τn	PROPN
ejpam-6679	674	26	)	)	PUNCT
ejpam-6679	674	27	by	by	ADP
ejpam-6679	674	28	ψ(α	ψ(α	NOUN
ejpam-6679	674	29	)	)	PUNCT
ejpam-6679	674	30	=	=	X
ejpam-6679	675	1	α̂|f	α̂|f	PUNCT
ejpam-6679	676	1	w	w	ADJ
ejpam-6679	676	2	alt(n	alt(n	NOUN
ejpam-6679	676	3	)	)	PUNCT
ejpam-6679	676	4	τn	τn	X
ejpam-6679	676	5	(	(	PUNCT
ejpam-6679	676	6	ωn	ωn	X
ejpam-6679	676	7	)	)	PUNCT
ejpam-6679	676	8	for	for	ADP
ejpam-6679	676	9	any	any	DET
ejpam-6679	676	10	α	α	NOUN
ejpam-6679	676	11	∈	∈	NOUN
ejpam-6679	676	12	hypalt(n)(τn	hypalt(n)(τn	PROPN
ejpam-6679	676	13	)	)	PUNCT
ejpam-6679	676	14	.	.	PUNCT
ejpam-6679	677	1	let	let	VERB
ejpam-6679	677	2	α1	α1	PROPN
ejpam-6679	677	3	,	,	PUNCT
ejpam-6679	677	4	α2	α2	PROPN
ejpam-6679	677	5	∈	∈	PROPN
ejpam-6679	677	6	hypalt(n)(τn	hypalt(n)(τn	PROPN
ejpam-6679	677	7	)	)	PUNCT
ejpam-6679	677	8	.	.	PUNCT
ejpam-6679	678	1	then	then	ADV
ejpam-6679	678	2	ψ(α1	ψ(α1	VERB
ejpam-6679	678	3	◦	◦	NOUN
ejpam-6679	678	4	h	h	NOUN
ejpam-6679	678	5	α2	α2	ADV
ejpam-6679	678	6	)	)	PUNCT
ejpam-6679	679	1	=	=	PRON
ejpam-6679	679	2	(	(	PUNCT
ejpam-6679	679	3	α1	α1	PROPN
ejpam-6679	679	4	◦	◦	NOUN
ejpam-6679	679	5	h	h	NOUN
ejpam-6679	679	6	α2	α2	VERB
ejpam-6679	679	7	)	)	PUNCT
ejpam-6679	679	8	ˆ|f	ˆ|f	VERB
ejpam-6679	679	9	w	w	PROPN
ejpam-6679	679	10	alt(n	alt(n	PROPN
ejpam-6679	679	11	)	)	PUNCT
ejpam-6679	679	12	τn	τn	X
ejpam-6679	679	13	(	(	PUNCT
ejpam-6679	679	14	ωn	ωn	X
ejpam-6679	679	15	)	)	PUNCT
ejpam-6679	679	16	=	=	SYM
ejpam-6679	680	1	(	(	PUNCT
ejpam-6679	680	2	α̂1	α̂1	PRON
ejpam-6679	680	3	◦	◦	VERB
ejpam-6679	680	4	α̂2)|f	α̂2)|f	NOUN
ejpam-6679	680	5	w	w	PROPN
ejpam-6679	680	6	alt(n	alt(n	PROPN
ejpam-6679	680	7	)	)	PUNCT
ejpam-6679	680	8	τn	τn	X
ejpam-6679	680	9	(	(	PUNCT
ejpam-6679	680	10	ωn	ωn	NOUN
ejpam-6679	680	11	)	)	PUNCT
ejpam-6679	680	12	=	=	NOUN
ejpam-6679	680	13	α̂1|f	α̂1|f	NOUN
ejpam-6679	680	14	w	w	PROPN
ejpam-6679	680	15	alt(n	alt(n	PROPN
ejpam-6679	680	16	)	)	PUNCT
ejpam-6679	680	17	τn	τn	X
ejpam-6679	680	18	(	(	PUNCT
ejpam-6679	680	19	ωn	ωn	NOUN
ejpam-6679	680	20	)	)	PUNCT
ejpam-6679	680	21	◦	◦	NOUN
ejpam-6679	680	22	α̂2|f	α̂2|f	PROPN
ejpam-6679	680	23	w	w	PROPN
ejpam-6679	680	24	alt(n	alt(n	PROPN
ejpam-6679	680	25	)	)	PUNCT
ejpam-6679	680	26	τn	τn	AUX
ejpam-6679	680	27	(	(	PUNCT
ejpam-6679	680	28	ωn	ωn	NOUN
ejpam-6679	680	29	)	)	PUNCT
ejpam-6679	680	30	=	=	NOUN
ejpam-6679	680	31	ψ(α1	ψ(α1	NOUN
ejpam-6679	680	32	)	)	PUNCT
ejpam-6679	680	33	◦	◦	NOUN
ejpam-6679	680	34	ψ(α2	ψ(α2	NOUN
ejpam-6679	680	35	)	)	PUNCT
ejpam-6679	680	36	=	=	SYM
ejpam-6679	680	37	ψ(α1	ψ(α1	NOUN
ejpam-6679	680	38	)	)	PUNCT
ejpam-6679	680	39	�	�	PROPN
ejpam-6679	680	40	ψ(α2	ψ(α2	NOUN
ejpam-6679	680	41	)	)	PUNCT
ejpam-6679	680	42	.	.	PUNCT
ejpam-6679	681	1	we	we	PRON
ejpam-6679	681	2	have	have	VERB
ejpam-6679	681	3	ψ	ψ	NOUN
ejpam-6679	681	4	is	be	AUX
ejpam-6679	681	5	a	a	DET
ejpam-6679	681	6	homomorphism	homomorphism	NOUN
ejpam-6679	681	7	.	.	PUNCT
ejpam-6679	682	1	clearly	clearly	ADV
ejpam-6679	682	2	,	,	PUNCT
ejpam-6679	682	3	ψ	ψ	NOUN
ejpam-6679	682	4	is	be	AUX
ejpam-6679	682	5	injective	injective	ADJ
ejpam-6679	682	6	.	.	PUNCT
ejpam-6679	683	1	we	we	PRON
ejpam-6679	683	2	conclude	conclude	VERB
ejpam-6679	683	3	the	the	DET
ejpam-6679	683	4	result	result	NOUN
ejpam-6679	683	5	as	as	SCONJ
ejpam-6679	683	6	follows	follow	VERB
ejpam-6679	683	7	.	.	PUNCT
ejpam-6679	684	1	theorem	theorem	ADJ
ejpam-6679	684	2	6	6	NUM
ejpam-6679	684	3	.	.	PUNCT
ejpam-6679	685	1	the	the	DET
ejpam-6679	685	2	monoid	monoid	NOUN
ejpam-6679	685	3	hypalt(n)(τn	hypalt(n)(τn	PROPN
ejpam-6679	685	4	)	)	PUNCT
ejpam-6679	685	5	can	can	AUX
ejpam-6679	685	6	be	be	AUX
ejpam-6679	685	7	embedded	embed	VERB
ejpam-6679	685	8	into	into	ADP
ejpam-6679	685	9	the	the	DET
ejpam-6679	685	10	monoid	monoid	NOUN
ejpam-6679	685	11	substalt(n)(τn	substalt(n)(τn	PROPN
ejpam-6679	685	12	)	)	PUNCT
ejpam-6679	685	13	.	.	PUNCT
ejpam-6679	686	1	5	5	X
ejpam-6679	686	2	.	.	X
ejpam-6679	686	3	alternating	alternate	VERB
ejpam-6679	686	4	hyperidentities	hyperidentitie	NOUN
ejpam-6679	686	5	in	in	ADP
ejpam-6679	686	6	this	this	DET
ejpam-6679	686	7	section	section	NOUN
ejpam-6679	686	8	let	let	VERB
ejpam-6679	686	9	v	v	PART
ejpam-6679	686	10	be	be	AUX
ejpam-6679	686	11	a	a	DET
ejpam-6679	686	12	variety	variety	NOUN
ejpam-6679	686	13	of	of	ADP
ejpam-6679	686	14	type	type	NOUN
ejpam-6679	686	15	τn	τn	PROPN
ejpam-6679	686	16	.	.	PUNCT
ejpam-6679	687	1	the	the	DET
ejpam-6679	687	2	set	set	NOUN
ejpam-6679	687	3	of	of	ADP
ejpam-6679	687	4	all	all	DET
ejpam-6679	687	5	identities	identity	NOUN
ejpam-6679	687	6	of	of	ADP
ejpam-6679	687	7	v	v	NOUN
ejpam-6679	687	8	will	will	AUX
ejpam-6679	687	9	be	be	AUX
ejpam-6679	687	10	represented	represent	VERB
ejpam-6679	687	11	by	by	ADP
ejpam-6679	687	12	id(v	id(v	PROPN
ejpam-6679	687	13	)	)	PUNCT
ejpam-6679	687	14	;	;	PUNCT
ejpam-6679	687	15	this	this	PRON
ejpam-6679	687	16	is	be	AUX
ejpam-6679	687	17	a	a	DET
ejpam-6679	687	18	congruence	congruence	NOUN
ejpam-6679	687	19	on	on	ADP
ejpam-6679	687	20	the	the	DET
ejpam-6679	687	21	free	free	ADJ
ejpam-6679	687	22	algebra	algebra	PROPN
ejpam-6679	687	23	fτn(ωn	fτn(ωn	NUM
ejpam-6679	687	24	)	)	PUNCT
ejpam-6679	687	25	(	(	PUNCT
ejpam-6679	687	26	see	see	VERB
ejpam-6679	687	27	[	[	X
ejpam-6679	687	28	13	13	NUM
ejpam-6679	687	29	]	]	NUM
ejpam-6679	687	30	)	)	PUNCT
ejpam-6679	687	31	.	.	PUNCT
ejpam-6679	688	1	let	let	VERB
ejpam-6679	688	2	idalt(n)(v	idalt(n)(v	X
ejpam-6679	688	3	)	)	PUNCT
ejpam-6679	688	4	denote	denote	VERB
ejpam-6679	688	5	the	the	DET
ejpam-6679	688	6	set	set	NOUN
ejpam-6679	688	7	of	of	ADP
ejpam-6679	688	8	all	all	DET
ejpam-6679	688	9	identities	identity	NOUN
ejpam-6679	688	10	θ	θ	PROPN
ejpam-6679	689	1	≈	≈	PROPN
ejpam-6679	689	2	ϑ	ϑ	PROPN
ejpam-6679	689	3	of	of	ADP
ejpam-6679	689	4	v	v	NOUN
ejpam-6679	689	5	such	such	ADJ
ejpam-6679	689	6	that	that	DET
ejpam-6679	689	7	θ	θ	NOUN
ejpam-6679	689	8	,	,	PUNCT
ejpam-6679	689	9	ϑ	ϑ	X
ejpam-6679	689	10	∈w	∈w	NOUN
ejpam-6679	689	11	alt(n	alt(n	NOUN
ejpam-6679	689	12	)	)	PUNCT
ejpam-6679	689	13	τn	τn	X
ejpam-6679	689	14	(	(	PUNCT
ejpam-6679	689	15	ωn	ωn	NOUN
ejpam-6679	689	16	)	)	PUNCT
ejpam-6679	689	17	,	,	PUNCT
ejpam-6679	689	18	i.e.	i.e.	X
ejpam-6679	689	19	,	,	PUNCT
ejpam-6679	689	20	idalt(n)(v	idalt(n)(v	ADJ
ejpam-6679	689	21	)	)	PUNCT
ejpam-6679	689	22	=	=	SYM
ejpam-6679	689	23	(	(	PUNCT
ejpam-6679	689	24	walt(n	walt(n	NOUN
ejpam-6679	689	25	)	)	PUNCT
ejpam-6679	689	26	τn	τn	X
ejpam-6679	689	27	(	(	PUNCT
ejpam-6679	689	28	ωn	ωn	NOUN
ejpam-6679	689	29	)	)	PUNCT
ejpam-6679	689	30	)	)	PUNCT
ejpam-6679	689	31	2	2	NUM
ejpam-6679	689	32	∩	∩	NOUN
ejpam-6679	689	33	id(v	id(v	NUM
ejpam-6679	689	34	)	)	PUNCT
ejpam-6679	689	35	.	.	PUNCT
ejpam-6679	690	1	lemma	lemma	PROPN
ejpam-6679	690	2	4	4	X
ejpam-6679	690	3	.	.	PUNCT
ejpam-6679	691	1	idalt(n)(v	idalt(n)(v	X
ejpam-6679	691	2	)	)	PUNCT
ejpam-6679	691	3	is	be	AUX
ejpam-6679	691	4	a	a	DET
ejpam-6679	691	5	congruence	congruence	NOUN
ejpam-6679	691	6	on	on	ADP
ejpam-6679	691	7	the	the	DET
ejpam-6679	691	8	menger	menger	PROPN
ejpam-6679	691	9	algebra	algebra	PROPN
ejpam-6679	691	10	walt(n	walt(n	PROPN
ejpam-6679	691	11	)	)	PUNCT
ejpam-6679	691	12	τn	τn	ADP
ejpam-6679	691	13	(	(	PUNCT
ejpam-6679	691	14	ωn	ωn	NOUN
ejpam-6679	691	15	)	)	PUNCT
ejpam-6679	691	16	.	.	PUNCT
ejpam-6679	692	1	proof	proof	NOUN
ejpam-6679	692	2	.	.	PUNCT
ejpam-6679	693	1	let	let	VERB
ejpam-6679	693	2	θ	θ	PROPN
ejpam-6679	693	3	≈	≈	PROPN
ejpam-6679	693	4	ϑ	ϑ	PROPN
ejpam-6679	693	5	,	,	PUNCT
ejpam-6679	693	6	θ1	θ1	PROPN
ejpam-6679	693	7	≈	≈	PROPN
ejpam-6679	693	8	ϑ1	ϑ1	PROPN
ejpam-6679	693	9	,	,	PUNCT
ejpam-6679	693	10	.	.	PUNCT
ejpam-6679	693	11	.	.	PUNCT
ejpam-6679	694	1	.	.	PUNCT
ejpam-6679	695	1	,	,	PUNCT
ejpam-6679	695	2	θn	θn	PROPN
ejpam-6679	695	3	≈	≈	PROPN
ejpam-6679	695	4	ϑn	ϑn	NOUN
ejpam-6679	695	5	∈	∈	PROPN
ejpam-6679	695	6	idalt(n)(v	idalt(n)(v	NOUN
ejpam-6679	695	7	)	)	PUNCT
ejpam-6679	695	8	.	.	PUNCT
ejpam-6679	696	1	at	at	ADP
ejpam-6679	696	2	first	first	ADV
ejpam-6679	696	3	,	,	PUNCT
ejpam-6679	696	4	we	we	PRON
ejpam-6679	696	5	have	have	VERB
ejpam-6679	696	6	sn(θ	sn(θ	NOUN
ejpam-6679	696	7	,	,	PUNCT
ejpam-6679	696	8	θ1	θ1	NOUN
ejpam-6679	696	9	,	,	PUNCT
ejpam-6679	696	10	.	.	PUNCT
ejpam-6679	696	11	.	.	PUNCT
ejpam-6679	696	12	.	.	PUNCT
ejpam-6679	697	1	,	,	PUNCT
ejpam-6679	697	2	θn	θn	NOUN
ejpam-6679	697	3	)	)	PUNCT
ejpam-6679	697	4	≈	≈	PROPN
ejpam-6679	697	5	sn(θ	sn(θ	NOUN
ejpam-6679	697	6	,	,	PUNCT
ejpam-6679	697	7	ϑ1	ϑ1	NOUN
ejpam-6679	697	8	,	,	PUNCT
ejpam-6679	697	9	.	.	PUNCT
ejpam-6679	697	10	.	.	PUNCT
ejpam-6679	697	11	.	.	PUNCT
ejpam-6679	698	1	,	,	PUNCT
ejpam-6679	698	2	ϑn	ϑn	NOUN
ejpam-6679	698	3	)	)	PUNCT
ejpam-6679	698	4	∈	∈	PROPN
ejpam-6679	698	5	idalt(n)(v	idalt(n)(v	NOUN
ejpam-6679	698	6	)	)	PUNCT
ejpam-6679	698	7	.	.	PUNCT
ejpam-6679	699	1	to	to	PART
ejpam-6679	699	2	see	see	VERB
ejpam-6679	699	3	this	this	PRON
ejpam-6679	699	4	,	,	PUNCT
ejpam-6679	699	5	suppose	suppose	VERB
ejpam-6679	699	6	θ	θ	PROPN
ejpam-6679	699	7	=	=	SYM
ejpam-6679	699	8	fi(ωσ(1	fi(ωσ(1	NOUN
ejpam-6679	699	9	)	)	PUNCT
ejpam-6679	699	10	,	,	PUNCT
ejpam-6679	699	11	.	.	PUNCT
ejpam-6679	699	12	.	.	PUNCT
ejpam-6679	700	1	.	.	PUNCT
ejpam-6679	701	1	,	,	PUNCT
ejpam-6679	701	2	ωσ(n	ωσ(n	NOUN
ejpam-6679	701	3	)	)	PUNCT
ejpam-6679	701	4	)	)	PUNCT
ejpam-6679	702	1	for	for	ADP
ejpam-6679	702	2	some	some	PRON
ejpam-6679	702	3	i	i	PRON
ejpam-6679	702	4	∈	∈	PROPN
ejpam-6679	703	1	i	i	PRON
ejpam-6679	703	2	,	,	PUNCT
ejpam-6679	703	3	σ	σ	PROPN
ejpam-6679	703	4	∈	∈	PROPN
ejpam-6679	703	5	alt(n	alt(n	PROPN
ejpam-6679	703	6	)	)	PUNCT
ejpam-6679	703	7	.	.	PUNCT
ejpam-6679	704	1	by	by	ADP
ejpam-6679	704	2	the	the	DET
ejpam-6679	704	3	compatibility	compatibility	NOUN
ejpam-6679	704	4	of	of	ADP
ejpam-6679	704	5	id(v	id(v	NOUN
ejpam-6679	704	6	)	)	PUNCT
ejpam-6679	704	7	with	with	ADP
ejpam-6679	704	8	the	the	DET
ejpam-6679	704	9	operations	operation	NOUN
ejpam-6679	704	10	f̄i	f̄i	NOUN
ejpam-6679	704	11	of	of	ADP
ejpam-6679	704	12	the	the	DET
ejpam-6679	704	13	absolutely	absolutely	ADV
ejpam-6679	704	14	free	free	ADJ
ejpam-6679	704	15	algebra	algebra	NOUN
ejpam-6679	704	16	fτn(ωn	fτn(ωn	NUM
ejpam-6679	704	17	)	)	PUNCT
ejpam-6679	704	18	,	,	PUNCT
ejpam-6679	704	19	fi(θσ(1	fi(θσ(1	NOUN
ejpam-6679	704	20	)	)	PUNCT
ejpam-6679	704	21	,	,	PUNCT
ejpam-6679	704	22	.	.	PUNCT
ejpam-6679	704	23	.	.	PUNCT
ejpam-6679	704	24	.	.	PUNCT
ejpam-6679	705	1	,	,	PUNCT
ejpam-6679	705	2	θσ(n	θσ(n	NOUN
ejpam-6679	705	3	)	)	PUNCT
ejpam-6679	705	4	)	)	PUNCT
ejpam-6679	706	1	≈	≈	PROPN
ejpam-6679	706	2	fi(ϑσ(1	fi(ϑσ(1	PROPN
ejpam-6679	706	3	)	)	PUNCT
ejpam-6679	706	4	,	,	PUNCT
ejpam-6679	706	5	.	.	PUNCT
ejpam-6679	706	6	.	.	PUNCT
ejpam-6679	707	1	.	.	PUNCT
ejpam-6679	708	1	,	,	PUNCT
ejpam-6679	708	2	ϑσ(n	ϑσ(n	ADJ
ejpam-6679	708	3	)	)	PUNCT
ejpam-6679	708	4	)	)	PUNCT
ejpam-6679	709	1	∈	∈	PROPN
ejpam-6679	709	2	idalt(n)(v	idalt(n)(v	NOUN
ejpam-6679	709	3	)	)	PUNCT
ejpam-6679	709	4	.	.	PUNCT
ejpam-6679	710	1	thus	thus	ADV
ejpam-6679	710	2	sn(fi(ωσ(1	sn(fi(ωσ(1	NOUN
ejpam-6679	710	3	)	)	PUNCT
ejpam-6679	710	4	,	,	PUNCT
ejpam-6679	710	5	.	.	PUNCT
ejpam-6679	710	6	.	.	PUNCT
ejpam-6679	710	7	.	.	PUNCT
ejpam-6679	711	1	,	,	PUNCT
ejpam-6679	711	2	ωσ(n	ωσ(n	NOUN
ejpam-6679	711	3	)	)	PUNCT
ejpam-6679	711	4	)	)	PUNCT
ejpam-6679	711	5	,	,	PUNCT
ejpam-6679	711	6	θ1	θ1	NOUN
ejpam-6679	711	7	,	,	PUNCT
ejpam-6679	711	8	.	.	PUNCT
ejpam-6679	711	9	.	.	PUNCT
ejpam-6679	711	10	.	.	PUNCT
ejpam-6679	712	1	,	,	PUNCT
ejpam-6679	712	2	θn	θn	NOUN
ejpam-6679	712	3	)	)	PUNCT
ejpam-6679	712	4	≈	≈	PROPN
ejpam-6679	712	5	sn(fi(ωσ(1	sn(fi(ωσ(1	NOUN
ejpam-6679	712	6	)	)	PUNCT
ejpam-6679	712	7	,	,	PUNCT
ejpam-6679	712	8	.	.	PUNCT
ejpam-6679	712	9	.	.	PUNCT
ejpam-6679	712	10	.	.	PUNCT
ejpam-6679	713	1	,	,	PUNCT
ejpam-6679	713	2	ωσ(n	ωσ(n	NOUN
ejpam-6679	713	3	)	)	PUNCT
ejpam-6679	713	4	)	)	PUNCT
ejpam-6679	713	5	,	,	PUNCT
ejpam-6679	713	6	ϑ1	ϑ1	NOUN
ejpam-6679	713	7	,	,	PUNCT
ejpam-6679	713	8	.	.	PUNCT
ejpam-6679	713	9	.	.	PUNCT
ejpam-6679	714	1	.	.	PUNCT
ejpam-6679	715	1	,	,	PUNCT
ejpam-6679	715	2	ϑn	ϑn	NOUN
ejpam-6679	715	3	)	)	PUNCT
ejpam-6679	715	4	∈	∈	PROPN
ejpam-6679	715	5	idalt(n)(v	idalt(n)(v	NOUN
ejpam-6679	715	6	)	)	PUNCT
ejpam-6679	715	7	.	.	PUNCT
ejpam-6679	716	1	hence	hence	ADV
ejpam-6679	716	2	sn(θ	sn(θ	VERB
ejpam-6679	716	3	,	,	PUNCT
ejpam-6679	716	4	θ1	θ1	NOUN
ejpam-6679	716	5	,	,	PUNCT
ejpam-6679	716	6	.	.	PUNCT
ejpam-6679	716	7	.	.	PUNCT
ejpam-6679	716	8	.	.	PUNCT
ejpam-6679	717	1	,	,	PUNCT
ejpam-6679	717	2	θn	θn	NOUN
ejpam-6679	717	3	)	)	PUNCT
ejpam-6679	717	4	≈	≈	PROPN
ejpam-6679	717	5	sn(θ	sn(θ	NOUN
ejpam-6679	717	6	,	,	PUNCT
ejpam-6679	717	7	ϑ1	ϑ1	NOUN
ejpam-6679	717	8	,	,	PUNCT
ejpam-6679	717	9	.	.	PUNCT
ejpam-6679	717	10	.	.	PUNCT
ejpam-6679	717	11	.	.	PUNCT
ejpam-6679	718	1	,	,	PUNCT
ejpam-6679	718	2	ϑn	ϑn	NOUN
ejpam-6679	718	3	)	)	PUNCT
ejpam-6679	718	4	∈	∈	PROPN
ejpam-6679	718	5	idalt(n)(v	idalt(n)(v	NOUN
ejpam-6679	718	6	)	)	PUNCT
ejpam-6679	718	7	.	.	PUNCT
ejpam-6679	719	1	let	let	VERB
ejpam-6679	719	2	θ	θ	NOUN
ejpam-6679	719	3	=	=	PRON
ejpam-6679	719	4	fi(ν1	fi(ν1	VERB
ejpam-6679	719	5	,	,	PUNCT
ejpam-6679	719	6	.	.	PUNCT
ejpam-6679	719	7	.	.	PUNCT
ejpam-6679	720	1	.	.	PUNCT
ejpam-6679	721	1	,	,	PUNCT
ejpam-6679	721	2	νn	νn	X
ejpam-6679	721	3	)	)	PUNCT
ejpam-6679	721	4	and	and	CCONJ
ejpam-6679	721	5	assume	assume	VERB
ejpam-6679	721	6	,	,	PUNCT
ejpam-6679	721	7	for	for	ADP
ejpam-6679	721	8	all	all	DET
ejpam-6679	721	9	1	1	NUM
ejpam-6679	721	10	≤	≤	NUM
ejpam-6679	721	11	k	k	NOUN
ejpam-6679	721	12	≤	≤	PROPN
ejpam-6679	721	13	n	n	CCONJ
ejpam-6679	721	14	,	,	PUNCT
ejpam-6679	721	15	sn(νk	sn(νk	PROPN
ejpam-6679	721	16	,	,	PUNCT
ejpam-6679	721	17	θ1	θ1	NOUN
ejpam-6679	721	18	,	,	PUNCT
ejpam-6679	721	19	.	.	PUNCT
ejpam-6679	721	20	.	.	PUNCT
ejpam-6679	722	1	.	.	PUNCT
ejpam-6679	723	1	,	,	PUNCT
ejpam-6679	723	2	θn	θn	NOUN
ejpam-6679	723	3	)	)	PUNCT
ejpam-6679	723	4	≈	≈	PROPN
ejpam-6679	723	5	sn(νk	sn(νk	PROPN
ejpam-6679	723	6	,	,	PUNCT
ejpam-6679	723	7	ϑ1	ϑ1	PROPN
ejpam-6679	723	8	,	,	PUNCT
ejpam-6679	723	9	.	.	PUNCT
ejpam-6679	723	10	.	.	PUNCT
ejpam-6679	723	11	.	.	PUNCT
ejpam-6679	724	1	,	,	PUNCT
ejpam-6679	724	2	ϑn	ϑn	NOUN
ejpam-6679	724	3	)	)	PUNCT
ejpam-6679	724	4	∈	∈	PROPN
ejpam-6679	724	5	idalt(n)(v	idalt(n)(v	NOUN
ejpam-6679	724	6	)	)	PUNCT
ejpam-6679	724	7	.	.	PUNCT
ejpam-6679	725	1	t.	t.	PROPN
ejpam-6679	725	2	changphas	changphas	PROPN
ejpam-6679	725	3	/	/	SYM
ejpam-6679	725	4	eur	eur	PROPN
ejpam-6679	725	5	.	.	PUNCT
ejpam-6679	726	1	j.	j.	PROPN
ejpam-6679	726	2	pure	pure	PROPN
ejpam-6679	726	3	appl	appl	PROPN
ejpam-6679	726	4	.	.	PROPN
ejpam-6679	726	5	math	math	PROPN
ejpam-6679	726	6	,	,	PUNCT
ejpam-6679	726	7	18	18	NUM
ejpam-6679	726	8	(	(	PUNCT
ejpam-6679	726	9	4	4	NUM
ejpam-6679	726	10	)	)	PUNCT
ejpam-6679	726	11	(	(	PUNCT
ejpam-6679	726	12	2025	2025	NUM
ejpam-6679	726	13	)	)	PUNCT
ejpam-6679	726	14	,	,	PUNCT
ejpam-6679	726	15	6679	6679	NUM
ejpam-6679	726	16	13	13	NUM
ejpam-6679	726	17	of	of	ADP
ejpam-6679	726	18	15	15	NUM
ejpam-6679	726	19	then	then	ADV
ejpam-6679	726	20	fi(s	fi(s	X
ejpam-6679	726	21	n(ν1	n(ν1	ADJ
ejpam-6679	726	22	,	,	PUNCT
ejpam-6679	726	23	θ1	θ1	NOUN
ejpam-6679	726	24	,	,	PUNCT
ejpam-6679	726	25	.	.	PUNCT
ejpam-6679	726	26	.	.	PUNCT
ejpam-6679	726	27	.	.	PUNCT
ejpam-6679	727	1	,	,	PUNCT
ejpam-6679	727	2	θn	θn	NOUN
ejpam-6679	727	3	)	)	PUNCT
ejpam-6679	727	4	,	,	PUNCT
ejpam-6679	727	5	.	.	PUNCT
ejpam-6679	727	6	.	.	PUNCT
ejpam-6679	728	1	.	.	PUNCT
ejpam-6679	729	1	,	,	PUNCT
ejpam-6679	729	2	s	s	VERB
ejpam-6679	729	3	n(νn	n(νn	NOUN
ejpam-6679	729	4	,	,	PUNCT
ejpam-6679	729	5	θ1	θ1	NOUN
ejpam-6679	729	6	,	,	PUNCT
ejpam-6679	729	7	.	.	PUNCT
ejpam-6679	729	8	.	.	PUNCT
ejpam-6679	730	1	.	.	PUNCT
ejpam-6679	731	1	,	,	PUNCT
ejpam-6679	731	2	θn	θn	NOUN
ejpam-6679	731	3	)	)	PUNCT
ejpam-6679	731	4	)	)	PUNCT
ejpam-6679	732	1	≈	≈	PROPN
ejpam-6679	732	2	fi(s	fi(s	X
ejpam-6679	732	3	n(ν1	n(ν1	NOUN
ejpam-6679	732	4	,	,	PUNCT
ejpam-6679	732	5	ϑ1	ϑ1	PROPN
ejpam-6679	732	6	,	,	PUNCT
ejpam-6679	732	7	.	.	PUNCT
ejpam-6679	732	8	.	.	PUNCT
ejpam-6679	732	9	.	.	PUNCT
ejpam-6679	733	1	,	,	PUNCT
ejpam-6679	733	2	ϑn	ϑn	NOUN
ejpam-6679	733	3	)	)	PUNCT
ejpam-6679	733	4	,	,	PUNCT
ejpam-6679	733	5	.	.	PUNCT
ejpam-6679	733	6	.	.	PUNCT
ejpam-6679	734	1	.	.	PUNCT
ejpam-6679	735	1	,	,	PUNCT
ejpam-6679	735	2	s	s	VERB
ejpam-6679	735	3	n(νn	n(νn	ADJ
ejpam-6679	735	4	,	,	PUNCT
ejpam-6679	735	5	ϑ1	ϑ1	PROPN
ejpam-6679	735	6	,	,	PUNCT
ejpam-6679	735	7	.	.	PUNCT
ejpam-6679	735	8	.	.	PUNCT
ejpam-6679	736	1	.	.	PUNCT
ejpam-6679	737	1	,	,	PUNCT
ejpam-6679	737	2	ϑn	ϑn	NOUN
ejpam-6679	737	3	)	)	PUNCT
ejpam-6679	737	4	)	)	PUNCT
ejpam-6679	738	1	∈	∈	PROPN
ejpam-6679	738	2	idalt(n)(v	idalt(n)(v	NOUN
ejpam-6679	738	3	)	)	PUNCT
ejpam-6679	738	4	.	.	PUNCT
ejpam-6679	739	1	so	so	ADV
ejpam-6679	739	2	sn(fi(ν1	sn(fi(ν1	NOUN
ejpam-6679	739	3	,	,	PUNCT
ejpam-6679	739	4	.	.	PUNCT
ejpam-6679	739	5	.	.	PUNCT
ejpam-6679	739	6	.	.	PUNCT
ejpam-6679	740	1	,	,	PUNCT
ejpam-6679	740	2	νn	νn	NOUN
ejpam-6679	740	3	)	)	PUNCT
ejpam-6679	740	4	,	,	PUNCT
ejpam-6679	740	5	θ1	θ1	NOUN
ejpam-6679	740	6	,	,	PUNCT
ejpam-6679	740	7	.	.	PUNCT
ejpam-6679	740	8	.	.	PUNCT
ejpam-6679	740	9	.	.	PUNCT
ejpam-6679	741	1	,	,	PUNCT
ejpam-6679	741	2	θn	θn	NOUN
ejpam-6679	741	3	)	)	PUNCT
ejpam-6679	741	4	≈	≈	PROPN
ejpam-6679	741	5	sn(fi(ν1	sn(fi(ν1	NOUN
ejpam-6679	741	6	,	,	PUNCT
ejpam-6679	741	7	.	.	PUNCT
ejpam-6679	741	8	.	.	PUNCT
ejpam-6679	742	1	.	.	PUNCT
ejpam-6679	743	1	,	,	PUNCT
ejpam-6679	743	2	νn	νn	NOUN
ejpam-6679	743	3	)	)	PUNCT
ejpam-6679	743	4	,	,	PUNCT
ejpam-6679	743	5	ϑ1	ϑ1	NOUN
ejpam-6679	743	6	,	,	PUNCT
ejpam-6679	743	7	.	.	PUNCT
ejpam-6679	743	8	.	.	PUNCT
ejpam-6679	744	1	.	.	PUNCT
ejpam-6679	745	1	,	,	PUNCT
ejpam-6679	745	2	ϑn	ϑn	NOUN
ejpam-6679	745	3	)	)	PUNCT
ejpam-6679	745	4	∈	∈	PROPN
ejpam-6679	745	5	idalt(n)(v	idalt(n)(v	NOUN
ejpam-6679	745	6	)	)	PUNCT
ejpam-6679	745	7	.	.	PUNCT
ejpam-6679	746	1	hence	hence	ADV
ejpam-6679	746	2	sn(θ	sn(θ	VERB
ejpam-6679	746	3	,	,	PUNCT
ejpam-6679	746	4	θ1	θ1	NOUN
ejpam-6679	746	5	,	,	PUNCT
ejpam-6679	746	6	.	.	PUNCT
ejpam-6679	746	7	.	.	PUNCT
ejpam-6679	746	8	.	.	PUNCT
ejpam-6679	747	1	,	,	PUNCT
ejpam-6679	747	2	θn	θn	NOUN
ejpam-6679	747	3	)	)	PUNCT
ejpam-6679	747	4	≈	≈	PROPN
ejpam-6679	747	5	sn(θ	sn(θ	NOUN
ejpam-6679	747	6	,	,	PUNCT
ejpam-6679	747	7	ϑ1	ϑ1	NOUN
ejpam-6679	747	8	,	,	PUNCT
ejpam-6679	747	9	.	.	PUNCT
ejpam-6679	747	10	.	.	PUNCT
ejpam-6679	747	11	.	.	PUNCT
ejpam-6679	748	1	,	,	PUNCT
ejpam-6679	748	2	ϑn	ϑn	NOUN
ejpam-6679	748	3	)	)	PUNCT
ejpam-6679	748	4	∈	∈	PROPN
ejpam-6679	748	5	idalt(n)(v	idalt(n)(v	NOUN
ejpam-6679	748	6	)	)	PUNCT
ejpam-6679	748	7	.	.	PUNCT
ejpam-6679	749	1	now	now	ADV
ejpam-6679	749	2	,	,	PUNCT
ejpam-6679	749	3	from	from	ADP
ejpam-6679	749	4	sn(θ	sn(θ	NUM
ejpam-6679	749	5	,	,	PUNCT
ejpam-6679	749	6	ϑ1	ϑ1	NOUN
ejpam-6679	749	7	,	,	PUNCT
ejpam-6679	749	8	.	.	PUNCT
ejpam-6679	749	9	.	.	PUNCT
ejpam-6679	749	10	.	.	PUNCT
ejpam-6679	750	1	,	,	PUNCT
ejpam-6679	750	2	ϑn	ϑn	NOUN
ejpam-6679	750	3	)	)	PUNCT
ejpam-6679	751	1	≈	≈	NUM
ejpam-6679	751	2	sn(ϑ	sn(ϑ	NOUN
ejpam-6679	751	3	,	,	PUNCT
ejpam-6679	751	4	ϑ1	ϑ1	PROPN
ejpam-6679	751	5	,	,	PUNCT
ejpam-6679	751	6	.	.	PUNCT
ejpam-6679	751	7	.	.	PUNCT
ejpam-6679	751	8	.	.	PUNCT
ejpam-6679	752	1	,	,	PUNCT
ejpam-6679	752	2	ϑn	ϑn	NOUN
ejpam-6679	752	3	)	)	PUNCT
ejpam-6679	752	4	∈	∈	PROPN
ejpam-6679	752	5	idalt(n)(v	idalt(n)(v	NOUN
ejpam-6679	752	6	)	)	PUNCT
ejpam-6679	752	7	,	,	PUNCT
ejpam-6679	752	8	it	it	PRON
ejpam-6679	752	9	follows	follow	VERB
ejpam-6679	752	10	that	that	SCONJ
ejpam-6679	752	11	sn(θ	sn(θ	NOUN
ejpam-6679	752	12	,	,	PUNCT
ejpam-6679	752	13	θ1	θ1	NOUN
ejpam-6679	752	14	,	,	PUNCT
ejpam-6679	752	15	.	.	PUNCT
ejpam-6679	752	16	.	.	PUNCT
ejpam-6679	753	1	.	.	PUNCT
ejpam-6679	754	1	,	,	PUNCT
ejpam-6679	754	2	θn	θn	NOUN
ejpam-6679	754	3	)	)	PUNCT
ejpam-6679	754	4	≈	≈	PROPN
ejpam-6679	754	5	sn(θ	sn(θ	NOUN
ejpam-6679	754	6	,	,	PUNCT
ejpam-6679	754	7	ϑ1	ϑ1	NOUN
ejpam-6679	754	8	,	,	PUNCT
ejpam-6679	754	9	.	.	PUNCT
ejpam-6679	754	10	.	.	PUNCT
ejpam-6679	754	11	.	.	PUNCT
ejpam-6679	755	1	,	,	PUNCT
ejpam-6679	755	2	ϑn	ϑn	NOUN
ejpam-6679	755	3	)	)	PUNCT
ejpam-6679	756	1	≈	≈	NUM
ejpam-6679	756	2	sn(ϑ	sn(ϑ	NOUN
ejpam-6679	756	3	,	,	PUNCT
ejpam-6679	756	4	ϑ1	ϑ1	PROPN
ejpam-6679	756	5	,	,	PUNCT
ejpam-6679	756	6	.	.	PUNCT
ejpam-6679	756	7	.	.	PUNCT
ejpam-6679	756	8	.	.	PUNCT
ejpam-6679	757	1	,	,	PUNCT
ejpam-6679	757	2	ϑn	ϑn	NOUN
ejpam-6679	757	3	)	)	PUNCT
ejpam-6679	757	4	∈	∈	PROPN
ejpam-6679	757	5	idalt(n)(v	idalt(n)(v	NOUN
ejpam-6679	757	6	)	)	PUNCT
ejpam-6679	757	7	.	.	PUNCT
ejpam-6679	758	1	therefore	therefore	ADV
ejpam-6679	758	2	the	the	DET
ejpam-6679	758	3	assertion	assertion	NOUN
ejpam-6679	758	4	holds	hold	VERB
ejpam-6679	758	5	.	.	PUNCT
ejpam-6679	759	1	definition	definition	NOUN
ejpam-6679	759	2	5	5	NUM
ejpam-6679	759	3	.	.	PUNCT
ejpam-6679	759	4	v	v	NOUN
ejpam-6679	759	5	is	be	AUX
ejpam-6679	759	6	said	say	VERB
ejpam-6679	759	7	to	to	PART
ejpam-6679	759	8	be	be	AUX
ejpam-6679	759	9	alternating	alternate	VERB
ejpam-6679	759	10	closed	closed	ADJ
ejpam-6679	759	11	(	(	PUNCT
ejpam-6679	759	12	alt	alt	ADV
ejpam-6679	759	13	-	-	PUNCT
ejpam-6679	759	14	closed	closed	ADJ
ejpam-6679	759	15	)	)	PUNCT
ejpam-6679	759	16	if	if	SCONJ
ejpam-6679	759	17	α̂[θ	α̂[θ	PROPN
ejpam-6679	759	18	]	]	PUNCT
ejpam-6679	760	1	≈	≈	PROPN
ejpam-6679	760	2	α̂[ϑ	α̂[ϑ	PROPN
ejpam-6679	760	3	]	]	X
ejpam-6679	760	4	∈	∈	PROPN
ejpam-6679	760	5	idalt(n)(v	idalt(n)(v	NOUN
ejpam-6679	760	6	)	)	PUNCT
ejpam-6679	760	7	for	for	ADP
ejpam-6679	760	8	all	all	PRON
ejpam-6679	760	9	θ	θ	PROPN
ejpam-6679	761	1	≈	≈	PROPN
ejpam-6679	761	2	ϑ	ϑ	X
ejpam-6679	761	3	∈	∈	ADJ
ejpam-6679	761	4	idalt(n)(v	idalt(n)(v	NOUN
ejpam-6679	761	5	)	)	PUNCT
ejpam-6679	761	6	and	and	CCONJ
ejpam-6679	761	7	for	for	ADP
ejpam-6679	761	8	all	all	DET
ejpam-6679	761	9	α	α	DET
ejpam-6679	761	10	∈	∈	NOUN
ejpam-6679	761	11	hypalt(n)(τn	hypalt(n)(τn	PROPN
ejpam-6679	761	12	)	)	PUNCT
ejpam-6679	761	13	.	.	PUNCT
ejpam-6679	762	1	definition	definition	NOUN
ejpam-6679	762	2	6	6	NUM
ejpam-6679	762	3	.	.	PUNCT
ejpam-6679	763	1	a	a	DET
ejpam-6679	763	2	congruence	congruence	NOUN
ejpam-6679	763	3	idalt(n)(v	idalt(n)(v	NOUN
ejpam-6679	763	4	)	)	PUNCT
ejpam-6679	763	5	on	on	ADP
ejpam-6679	763	6	the	the	DET
ejpam-6679	763	7	menger	menger	PROPN
ejpam-6679	763	8	algebra	algebra	PROPN
ejpam-6679	763	9	walt(n	walt(n	PROPN
ejpam-6679	763	10	)	)	PUNCT
ejpam-6679	763	11	τn	τn	X
ejpam-6679	763	12	(	(	PUNCT
ejpam-6679	763	13	ωn	ωn	X
ejpam-6679	763	14	)	)	PUNCT
ejpam-6679	763	15	is	be	AUX
ejpam-6679	763	16	said	say	VERB
ejpam-6679	763	17	to	to	PART
ejpam-6679	763	18	be	be	AUX
ejpam-6679	763	19	alternative	alternative	ADV
ejpam-6679	763	20	fully	fully	ADV
ejpam-6679	763	21	invariant	invariant	ADJ
ejpam-6679	763	22	(	(	PUNCT
ejpam-6679	763	23	alt	alt	ADV
ejpam-6679	763	24	-	-	PUNCT
ejpam-6679	763	25	fully	fully	ADV
ejpam-6679	763	26	invariant	invariant	ADJ
ejpam-6679	763	27	)	)	PUNCT
ejpam-6679	763	28	if	if	SCONJ
ejpam-6679	763	29	idalt(n)(v	idalt(n)(v	NOUN
ejpam-6679	763	30	)	)	PUNCT
ejpam-6679	763	31	is	be	AUX
ejpam-6679	763	32	compatible	compatible	ADJ
ejpam-6679	763	33	with	with	ADP
ejpam-6679	763	34	all	all	DET
ejpam-6679	763	35	endomorphisms	endomorphism	NOUN
ejpam-6679	763	36	α̂	α̂	X
ejpam-6679	763	37	on	on	ADP
ejpam-6679	763	38	walt(n	walt(n	NOUN
ejpam-6679	763	39	)	)	PUNCT
ejpam-6679	763	40	τn	τn	X
ejpam-6679	763	41	(	(	PUNCT
ejpam-6679	763	42	ωn	ωn	NOUN
ejpam-6679	763	43	)	)	PUNCT
ejpam-6679	763	44	.	.	PUNCT
ejpam-6679	764	1	theorem	theorem	VERB
ejpam-6679	764	2	7	7	NUM
ejpam-6679	764	3	.	.	PUNCT
ejpam-6679	765	1	if	if	SCONJ
ejpam-6679	765	2	idalt(n)(v	idalt(n)(v	NOUN
ejpam-6679	765	3	)	)	PUNCT
ejpam-6679	765	4	is	be	AUX
ejpam-6679	765	5	alt	alt	ADJ
ejpam-6679	765	6	-	-	PUNCT
ejpam-6679	765	7	fully	fully	ADV
ejpam-6679	765	8	invariant	invariant	ADJ
ejpam-6679	765	9	,	,	PUNCT
ejpam-6679	765	10	then	then	ADV
ejpam-6679	765	11	v	v	NOUN
ejpam-6679	765	12	is	be	AUX
ejpam-6679	765	13	alt	alt	ADV
ejpam-6679	765	14	-	-	PUNCT
ejpam-6679	765	15	closed	closed	ADJ
ejpam-6679	765	16	.	.	PUNCT
ejpam-6679	766	1	proof	proof	NOUN
ejpam-6679	766	2	.	.	PUNCT
ejpam-6679	767	1	assume	assume	VERB
ejpam-6679	767	2	idalt(n)(v	idalt(n)(v	X
ejpam-6679	767	3	)	)	PUNCT
ejpam-6679	767	4	is	be	AUX
ejpam-6679	767	5	alt	alt	ADJ
ejpam-6679	767	6	-	-	PUNCT
ejpam-6679	767	7	fully	fully	ADV
ejpam-6679	767	8	invariant	invariant	ADJ
ejpam-6679	767	9	.	.	PUNCT
ejpam-6679	768	1	let	let	VERB
ejpam-6679	768	2	θ	θ	PROPN
ejpam-6679	768	3	≈	≈	PROPN
ejpam-6679	768	4	ϑ	ϑ	X
ejpam-6679	768	5	∈	∈	ADJ
ejpam-6679	768	6	idalt(n)(v	idalt(n)(v	NOUN
ejpam-6679	768	7	)	)	PUNCT
ejpam-6679	768	8	and	and	CCONJ
ejpam-6679	768	9	α	α	PRON
ejpam-6679	768	10	∈	∈	PROPN
ejpam-6679	768	11	hypalt(n)(τn	hypalt(n)(τn	PROPN
ejpam-6679	768	12	)	)	PUNCT
ejpam-6679	768	13	.	.	PUNCT
ejpam-6679	769	1	by	by	ADP
ejpam-6679	769	2	theorem	theorem	NOUN
ejpam-6679	769	3	4	4	NUM
ejpam-6679	769	4	,	,	PUNCT
ejpam-6679	769	5	α̂	α̂	NUM
ejpam-6679	769	6	is	be	AUX
ejpam-6679	769	7	an	an	DET
ejpam-6679	769	8	endomorphism	endomorphism	NOUN
ejpam-6679	769	9	on	on	ADP
ejpam-6679	769	10	walt(n	walt(n	PROPN
ejpam-6679	769	11	)	)	PUNCT
ejpam-6679	769	12	τn	τn	X
ejpam-6679	769	13	(	(	PUNCT
ejpam-6679	769	14	ωn	ωn	NOUN
ejpam-6679	769	15	)	)	PUNCT
ejpam-6679	769	16	.	.	PUNCT
ejpam-6679	770	1	hence	hence	ADV
ejpam-6679	770	2	α̂[θ	α̂[θ	PROPN
ejpam-6679	770	3	]	]	PUNCT
ejpam-6679	771	1	≈	≈	PROPN
ejpam-6679	771	2	α̂[ϑ	α̂[ϑ	PROPN
ejpam-6679	771	3	]	]	PUNCT
ejpam-6679	771	4	∈	∈	PROPN
ejpam-6679	771	5	idalt(n)(τn	idalt(n)(τn	PROPN
ejpam-6679	771	6	)	)	PUNCT
ejpam-6679	771	7	,	,	PUNCT
ejpam-6679	771	8	so	so	SCONJ
ejpam-6679	771	9	v	v	NOUN
ejpam-6679	771	10	is	be	AUX
ejpam-6679	771	11	alt	alt	ADV
ejpam-6679	771	12	-	-	PUNCT
ejpam-6679	771	13	closed	closed	ADJ
ejpam-6679	771	14	.	.	PUNCT
ejpam-6679	772	1	we	we	PRON
ejpam-6679	772	2	have	have	AUX
ejpam-6679	772	3	shown	show	VERB
ejpam-6679	772	4	idalt(n)(v	idalt(n)(v	NOUN
ejpam-6679	772	5	)	)	PUNCT
ejpam-6679	772	6	is	be	AUX
ejpam-6679	772	7	a	a	DET
ejpam-6679	772	8	congruence	congruence	NOUN
ejpam-6679	772	9	on	on	ADP
ejpam-6679	772	10	walt(n	walt(n	PROPN
ejpam-6679	772	11	)	)	PUNCT
ejpam-6679	772	12	τn	τn	X
ejpam-6679	772	13	(	(	PUNCT
ejpam-6679	772	14	ωn	ωn	NOUN
ejpam-6679	772	15	)	)	PUNCT
ejpam-6679	772	16	.	.	PUNCT
ejpam-6679	773	1	consequently	consequently	ADV
ejpam-6679	773	2	,	,	PUNCT
ejpam-6679	773	3	quotient	quotient	NOUN
ejpam-6679	773	4	algebra	algebra	PROPN
ejpam-6679	773	5	walt(n	walt(n	PROPN
ejpam-6679	773	6	)	)	PUNCT
ejpam-6679	773	7	τn	τn	PROPN
ejpam-6679	773	8	(	(	PUNCT
ejpam-6679	773	9	ωn)/id	ωn)/id	PROPN
ejpam-6679	773	10	alt(n)(v	alt(n)(v	NUM
ejpam-6679	773	11	)	)	PUNCT
ejpam-6679	773	12	belongs	belong	VERB
ejpam-6679	773	13	to	to	ADP
ejpam-6679	773	14	vmenger	vmenger	NOUN
ejpam-6679	773	15	.	.	PUNCT
ejpam-6679	774	1	note	note	VERB
ejpam-6679	774	2	that	that	SCONJ
ejpam-6679	774	3	natidalt(n)(v	natidalt(n)(v	NOUN
ejpam-6679	774	4	)	)	PUNCT
ejpam-6679	774	5	:	:	PUNCT
ejpam-6679	774	6	w	w	PROPN
ejpam-6679	774	7	alt(n	alt(n	PROPN
ejpam-6679	774	8	)	)	PUNCT
ejpam-6679	774	9	τn	τn	X
ejpam-6679	774	10	(	(	PUNCT
ejpam-6679	774	11	ωn	ωn	NOUN
ejpam-6679	774	12	)	)	PUNCT
ejpam-6679	774	13	→walt(n	→walt(n	ADV
ejpam-6679	774	14	)	)	PUNCT
ejpam-6679	774	15	τn	τn	ADP
ejpam-6679	774	16	(	(	PUNCT
ejpam-6679	774	17	ωn)/id	ωn)/id	PROPN
ejpam-6679	774	18	alt(n)(v	alt(n)(v	NOUN
ejpam-6679	774	19	)	)	PUNCT
ejpam-6679	774	20	is	be	AUX
ejpam-6679	774	21	a	a	DET
ejpam-6679	774	22	homomorphism	homomorphism	NOUN
ejpam-6679	774	23	with	with	ADP
ejpam-6679	774	24	natidalt(n)(v	natidalt(n)(v	NOUN
ejpam-6679	774	25	)	)	PUNCT
ejpam-6679	774	26	(	(	PUNCT
ejpam-6679	774	27	θ	θ	NOUN
ejpam-6679	774	28	)	)	PUNCT
ejpam-6679	774	29	=	=	PUNCT
ejpam-6679	775	1	[	[	X
ejpam-6679	775	2	θ]idalt(n)(v	θ]idalt(n)(v	NUM
ejpam-6679	775	3	)	)	PUNCT
ejpam-6679	775	4	.	.	PUNCT
ejpam-6679	776	1	definition	definition	NOUN
ejpam-6679	776	2	7	7	NUM
ejpam-6679	776	3	.	.	PUNCT
ejpam-6679	777	1	an	an	DET
ejpam-6679	777	2	identity	identity	NOUN
ejpam-6679	777	3	θ	θ	PROPN
ejpam-6679	778	1	≈	≈	PROPN
ejpam-6679	778	2	ϑ	ϑ	X
ejpam-6679	778	3	∈	∈	PROPN
ejpam-6679	778	4	idalt(n)(v	idalt(n)(v	X
ejpam-6679	778	5	)	)	PUNCT
ejpam-6679	778	6	is	be	AUX
ejpam-6679	778	7	an	an	DET
ejpam-6679	778	8	alternative	alternative	ADJ
ejpam-6679	778	9	hyperidentity	hyperidentity	NOUN
ejpam-6679	778	10	(	(	PUNCT
ejpam-6679	778	11	althyperidentity	althyperidentity	PROPN
ejpam-6679	778	12	)	)	PUNCT
ejpam-6679	778	13	if	if	SCONJ
ejpam-6679	778	14	t.	t.	PROPN
ejpam-6679	778	15	changphas	changphas	PROPN
ejpam-6679	778	16	/	/	SYM
ejpam-6679	778	17	eur	eur	PROPN
ejpam-6679	778	18	.	.	PUNCT
ejpam-6679	779	1	j.	j.	PROPN
ejpam-6679	779	2	pure	pure	PROPN
ejpam-6679	779	3	appl	appl	PROPN
ejpam-6679	779	4	.	.	PROPN
ejpam-6679	779	5	math	math	PROPN
ejpam-6679	779	6	,	,	PUNCT
ejpam-6679	779	7	18	18	NUM
ejpam-6679	779	8	(	(	PUNCT
ejpam-6679	779	9	4	4	NUM
ejpam-6679	779	10	)	)	PUNCT
ejpam-6679	779	11	(	(	PUNCT
ejpam-6679	779	12	2025	2025	NUM
ejpam-6679	779	13	)	)	PUNCT
ejpam-6679	779	14	,	,	PUNCT
ejpam-6679	779	15	6679	6679	NUM
ejpam-6679	779	16	14	14	NUM
ejpam-6679	779	17	of	of	ADP
ejpam-6679	779	18	15	15	NUM
ejpam-6679	779	19	α̂[θ	α̂[θ	PROPN
ejpam-6679	779	20	]	]	PUNCT
ejpam-6679	780	1	≈	≈	PROPN
ejpam-6679	780	2	α̂[ϑ	α̂[ϑ	PROPN
ejpam-6679	780	3	]	]	X
ejpam-6679	780	4	∈	∈	PROPN
ejpam-6679	780	5	idalt(n)(v	idalt(n)(v	NOUN
ejpam-6679	780	6	)	)	PUNCT
ejpam-6679	780	7	for	for	ADP
ejpam-6679	780	8	all	all	DET
ejpam-6679	780	9	α	α	DET
ejpam-6679	780	10	∈	∈	NOUN
ejpam-6679	780	11	hypalt(n)(τn	hypalt(n)(τn	PROPN
ejpam-6679	780	12	)	)	PUNCT
ejpam-6679	780	13	.	.	PUNCT
ejpam-6679	781	1	theorem	theorem	VERB
ejpam-6679	781	2	8	8	NUM
ejpam-6679	781	3	.	.	PUNCT
ejpam-6679	782	1	let	let	VERB
ejpam-6679	782	2	θ	θ	PROPN
ejpam-6679	782	3	≈	≈	PROPN
ejpam-6679	782	4	ϑ	ϑ	X
ejpam-6679	782	5	∈	∈	X
ejpam-6679	782	6	idalt(n)(v	idalt(n)(v	NOUN
ejpam-6679	782	7	)	)	PUNCT
ejpam-6679	782	8	.	.	PUNCT
ejpam-6679	783	1	if	if	SCONJ
ejpam-6679	783	2	θ	θ	PROPN
ejpam-6679	783	3	≈	≈	PROPN
ejpam-6679	783	4	ϑ	ϑ	PROPN
ejpam-6679	783	5	is	be	AUX
ejpam-6679	783	6	an	an	DET
ejpam-6679	783	7	identity	identity	NOUN
ejpam-6679	783	8	in	in	ADP
ejpam-6679	783	9	walt(n	walt(n	NOUN
ejpam-6679	783	10	)	)	PUNCT
ejpam-6679	783	11	τn	τn	PROPN
ejpam-6679	783	12	(	(	PUNCT
ejpam-6679	783	13	ωn)/id	ωn)/id	PROPN
ejpam-6679	783	14	alt(n)(v	alt(n)(v	NUM
ejpam-6679	783	15	)	)	PUNCT
ejpam-6679	783	16	,	,	PUNCT
ejpam-6679	783	17	then	then	ADV
ejpam-6679	783	18	θ	θ	PROPN
ejpam-6679	784	1	≈	≈	PROPN
ejpam-6679	784	2	ϑ	ϑ	PROPN
ejpam-6679	784	3	is	be	AUX
ejpam-6679	784	4	an	an	DET
ejpam-6679	784	5	alt	alt	ADJ
ejpam-6679	784	6	-	-	PUNCT
ejpam-6679	784	7	hyperidentity	hyperidentity	NOUN
ejpam-6679	784	8	of	of	ADP
ejpam-6679	784	9	v	v	NOUN
ejpam-6679	784	10	.	.	PUNCT
ejpam-6679	785	1	proof	proof	NOUN
ejpam-6679	785	2	.	.	PUNCT
ejpam-6679	786	1	assume	assume	VERB
ejpam-6679	786	2	θ	θ	PROPN
ejpam-6679	787	1	≈	≈	PROPN
ejpam-6679	787	2	ϑ	ϑ	PROPN
ejpam-6679	787	3	is	be	AUX
ejpam-6679	787	4	an	an	DET
ejpam-6679	787	5	identity	identity	NOUN
ejpam-6679	787	6	inwalt(n	inwalt(n	NOUN
ejpam-6679	787	7	)	)	PUNCT
ejpam-6679	787	8	τn	τn	ADP
ejpam-6679	787	9	(	(	PUNCT
ejpam-6679	787	10	ωn)/id	ωn)/id	PROPN
ejpam-6679	787	11	alt(n)(v	alt(n)(v	NUM
ejpam-6679	787	12	)	)	PUNCT
ejpam-6679	787	13	,	,	PUNCT
ejpam-6679	787	14	and	and	CCONJ
ejpam-6679	787	15	let	let	VERB
ejpam-6679	787	16	α	α	PRON
ejpam-6679	787	17	∈	∈	PROPN
ejpam-6679	787	18	hypalt(n)(τn	hypalt(n)(τn	PROPN
ejpam-6679	787	19	)	)	PUNCT
ejpam-6679	787	20	.	.	PUNCT
ejpam-6679	788	1	by	by	ADP
ejpam-6679	788	2	α̂	α̂	NUM
ejpam-6679	788	3	:	:	PUNCT
ejpam-6679	788	4	walt(n	walt(n	NOUN
ejpam-6679	788	5	)	)	PUNCT
ejpam-6679	788	6	τn	τn	X
ejpam-6679	788	7	(	(	PUNCT
ejpam-6679	788	8	ωn	ωn	NOUN
ejpam-6679	788	9	)	)	PUNCT
ejpam-6679	788	10	→walt(n	→walt(n	ADV
ejpam-6679	788	11	)	)	PUNCT
ejpam-6679	788	12	τn	τn	X
ejpam-6679	788	13	(	(	PUNCT
ejpam-6679	788	14	ωn	ωn	X
ejpam-6679	788	15	)	)	PUNCT
ejpam-6679	788	16	is	be	AUX
ejpam-6679	788	17	an	an	DET
ejpam-6679	788	18	endomorphism	endomorphism	NOUN
ejpam-6679	788	19	,	,	PUNCT
ejpam-6679	788	20	we	we	PRON
ejpam-6679	788	21	have	have	VERB
ejpam-6679	788	22	κ	κ	X
ejpam-6679	788	23	:	:	PUNCT
ejpam-6679	788	24	walt(n	walt(n	NOUN
ejpam-6679	788	25	)	)	PUNCT
ejpam-6679	788	26	τn	τn	PROPN
ejpam-6679	788	27	(	(	PUNCT
ejpam-6679	788	28	ωn)/id	ωn)/id	PROPN
ejpam-6679	788	29	alt(n)(v	alt(n)(v	NUM
ejpam-6679	788	30	)	)	PUNCT
ejpam-6679	788	31	→walt(n	→walt(n	ADV
ejpam-6679	788	32	)	)	PUNCT
ejpam-6679	788	33	τn	τn	ADP
ejpam-6679	788	34	(	(	PUNCT
ejpam-6679	788	35	ωn)/id	ωn)/id	PROPN
ejpam-6679	788	36	alt(n)(v	alt(n)(v	VERB
ejpam-6679	788	37	)	)	PUNCT
ejpam-6679	788	38	defined	define	VERB
ejpam-6679	788	39	by	by	ADP
ejpam-6679	788	40	κ([θ]idalt(n)(v	κ([θ]idalt(n)(v	NOUN
ejpam-6679	788	41	)	)	PUNCT
ejpam-6679	788	42	)	)	PUNCT
ejpam-6679	789	1	=	=	PUNCT
ejpam-6679	790	1	[	[	X
ejpam-6679	790	2	α̂[θ]]idalt(n)(v	α̂[θ]]idalt(n)(v	X
ejpam-6679	790	3	)	)	PUNCT
ejpam-6679	790	4	for	for	ADP
ejpam-6679	790	5	all	all	PRON
ejpam-6679	790	6	[	[	X
ejpam-6679	790	7	θ]idalt(n)(v	θ]idalt(n)(v	ADJ
ejpam-6679	790	8	)	)	PUNCT
ejpam-6679	790	9	∈w	∈w	PROPN
ejpam-6679	790	10	alt(n	alt(n	NOUN
ejpam-6679	790	11	)	)	PUNCT
ejpam-6679	790	12	τn	τn	ADP
ejpam-6679	790	13	(	(	PUNCT
ejpam-6679	790	14	ωn)/id	ωn)/id	PROPN
ejpam-6679	790	15	alt(n)(v	alt(n)(v	NOUN
ejpam-6679	790	16	)	)	PUNCT
ejpam-6679	790	17	is	be	AUX
ejpam-6679	790	18	an	an	DET
ejpam-6679	790	19	endomorphism	endomorphism	NOUN
ejpam-6679	790	20	.	.	PUNCT
ejpam-6679	791	1	by	by	ADP
ejpam-6679	791	2	assumption	assumption	NOUN
ejpam-6679	791	3	,	,	PUNCT
ejpam-6679	791	4	[	[	X
ejpam-6679	791	5	θ]idalt(n)(v	θ]idalt(n)(v	X
ejpam-6679	791	6	)	)	PUNCT
ejpam-6679	791	7	=	=	PUNCT
ejpam-6679	792	1	[	[	X
ejpam-6679	792	2	ϑ]idalt(n)(v	ϑ]idalt(n)(v	ADV
ejpam-6679	792	3	)	)	PUNCT
ejpam-6679	792	4	.	.	PUNCT
ejpam-6679	793	1	then	then	ADV
ejpam-6679	793	2	κ([θ]idalt(n)(v	κ([θ]idalt(n)(v	NOUN
ejpam-6679	793	3	)	)	PUNCT
ejpam-6679	793	4	)	)	PUNCT
ejpam-6679	794	1	=	=	SYM
ejpam-6679	794	2	κ([ϑ]idalt(n)(v	κ([ϑ]idalt(n)(v	X
ejpam-6679	794	3	)	)	PUNCT
ejpam-6679	794	4	)	)	PUNCT
ejpam-6679	794	5	.	.	PUNCT
ejpam-6679	795	1	thus	thus	ADV
ejpam-6679	795	2	[	[	X
ejpam-6679	795	3	α̂[θ]]idalt(n)(v	α̂[θ]]idalt(n)(v	X
ejpam-6679	795	4	)	)	PUNCT
ejpam-6679	795	5	=	=	PUNCT
ejpam-6679	796	1	[	[	X
ejpam-6679	796	2	α̂[ϑ]]idalt(n)(v	α̂[ϑ]]idalt(n)(v	NOUN
ejpam-6679	796	3	)	)	PUNCT
ejpam-6679	796	4	.	.	PUNCT
ejpam-6679	797	1	therefore	therefore	ADV
ejpam-6679	797	2	α̂[θ	α̂[θ	PROPN
ejpam-6679	797	3	]	]	PUNCT
ejpam-6679	798	1	≈	≈	PROPN
ejpam-6679	798	2	α̂[ϑ	α̂[ϑ	PROPN
ejpam-6679	798	3	]	]	X
ejpam-6679	798	4	∈	∈	PROPN
ejpam-6679	798	5	idalt(n)(v	idalt(n)(v	NOUN
ejpam-6679	798	6	)	)	PUNCT
ejpam-6679	798	7	.	.	PUNCT
ejpam-6679	799	1	hence	hence	ADV
ejpam-6679	799	2	θ	θ	PROPN
ejpam-6679	800	1	≈	≈	PROPN
ejpam-6679	800	2	ϑ	ϑ	PROPN
ejpam-6679	800	3	is	be	AUX
ejpam-6679	800	4	an	an	DET
ejpam-6679	800	5	alt	alt	ADJ
ejpam-6679	800	6	-	-	PUNCT
ejpam-6679	800	7	hyperidentity	hyperidentity	NOUN
ejpam-6679	800	8	of	of	ADP
ejpam-6679	800	9	v	v	NOUN
ejpam-6679	800	10	.	.	PUNCT
ejpam-6679	801	1	acknowledgements	acknowledgement	VERB
ejpam-6679	801	2	the	the	DET
ejpam-6679	801	3	research	research	NOUN
ejpam-6679	801	4	on	on	ADP
ejpam-6679	801	5	”	"	PUNCT
ejpam-6679	801	6	menger	menger	PROPN
ejpam-6679	801	7	algebras	algebra	NOUN
ejpam-6679	801	8	of	of	ADP
ejpam-6679	801	9	alternating	alternate	VERB
ejpam-6679	801	10	terms	term	NOUN
ejpam-6679	801	11	”	"	PUNCT
ejpam-6679	801	12	by	by	ADP
ejpam-6679	801	13	khon	khon	PROPN
ejpam-6679	801	14	kaen	kaen	PROPN
ejpam-6679	801	15	university	university	PROPN
ejpam-6679	801	16	has	have	AUX
ejpam-6679	801	17	received	receive	VERB
ejpam-6679	801	18	funding	funding	NOUN
ejpam-6679	801	19	support	support	NOUN
ejpam-6679	801	20	from	from	ADP
ejpam-6679	801	21	the	the	DET
ejpam-6679	801	22	national	national	ADJ
ejpam-6679	801	23	science	science	NOUN
ejpam-6679	801	24	,	,	PUNCT
ejpam-6679	801	25	research	research	NOUN
ejpam-6679	801	26	and	and	CCONJ
ejpam-6679	801	27	innovation	innovation	NOUN
ejpam-6679	801	28	fund	fund	NOUN
ejpam-6679	801	29	(	(	PUNCT
ejpam-6679	801	30	nsrf	nsrf	NOUN
ejpam-6679	801	31	)	)	PUNCT
ejpam-6679	801	32	.	.	PUNCT
ejpam-6679	802	1	references	reference	NOUN
ejpam-6679	802	2	[	[	X
ejpam-6679	802	3	1	1	NUM
ejpam-6679	802	4	]	]	X
ejpam-6679	802	5	w.a	w.a	PROPN
ejpam-6679	802	6	.	.	PROPN
ejpam-6679	802	7	dudek	dudek	PROPN
ejpam-6679	802	8	and	and	CCONJ
ejpam-6679	802	9	s.v	s.v	PROPN
ejpam-6679	802	10	.	.	PROPN
ejpam-6679	802	11	trokhimenko	trokhimenko	PROPN
ejpam-6679	802	12	.	.	PUNCT
ejpam-6679	803	1	algebras	algebras	PROPN
ejpam-6679	803	2	of	of	ADP
ejpam-6679	803	3	multiplace	multiplace	NOUN
ejpam-6679	803	4	functions	function	NOUN
ejpam-6679	803	5	.	.	PUNCT
ejpam-6679	804	1	de	de	X
ejpam-6679	804	2	gruyter	gruyter	PROPN
ejpam-6679	804	3	berlin	berlin	PROPN
ejpam-6679	804	4	,	,	PUNCT
ejpam-6679	804	5	2012	2012	NUM
ejpam-6679	804	6	.	.	PUNCT
ejpam-6679	805	1	[	[	X
ejpam-6679	805	2	2	2	NUM
ejpam-6679	805	3	]	]	PUNCT
ejpam-6679	805	4	k.	k.	PROPN
ejpam-6679	805	5	denecke	denecke	PROPN
ejpam-6679	805	6	.	.	PUNCT
ejpam-6679	806	1	menger	menger	PROPN
ejpam-6679	806	2	algebra	algebra	PROPN
ejpam-6679	806	3	and	and	CCONJ
ejpam-6679	806	4	clones	clone	NOUN
ejpam-6679	806	5	of	of	ADP
ejpam-6679	806	6	terms	term	NOUN
ejpam-6679	806	7	.	.	PUNCT
ejpam-6679	807	1	east	east	PROPN
ejpam-6679	807	2	-	-	PUNCT
ejpam-6679	807	3	west	west	PROPN
ejpam-6679	807	4	j.	j.	PROPN
ejpam-6679	807	5	math	math	PROPN
ejpam-6679	807	6	.	.	PUNCT
ejpam-6679	807	7	,	,	PUNCT
ejpam-6679	807	8	5:179–193	5:179–193	NUM
ejpam-6679	807	9	,	,	PUNCT
ejpam-6679	807	10	2003	2003	NUM
ejpam-6679	807	11	.	.	PUNCT
ejpam-6679	808	1	[	[	X
ejpam-6679	808	2	3	3	X
ejpam-6679	808	3	]	]	PUNCT
ejpam-6679	808	4	k.	k.	NOUN
ejpam-6679	808	5	denecke	denecke	PROPN
ejpam-6679	808	6	and	and	CCONJ
ejpam-6679	808	7	l.	l.	PROPN
ejpam-6679	808	8	freiberg	freiberg	PROPN
ejpam-6679	808	9	.	.	PUNCT
ejpam-6679	809	1	the	the	DET
ejpam-6679	809	2	algebra	algebra	NOUN
ejpam-6679	809	3	of	of	ADP
ejpam-6679	809	4	strongly	strongly	ADV
ejpam-6679	809	5	full	full	ADJ
ejpam-6679	809	6	terms	term	NOUN
ejpam-6679	809	7	.	.	PUNCT
ejpam-6679	810	1	novi	novi	PROPN
ejpam-6679	810	2	sad	sad	PROPN
ejpam-6679	810	3	j.	j.	PROPN
ejpam-6679	810	4	math	math	PROPN
ejpam-6679	810	5	.	.	PUNCT
ejpam-6679	810	6	,	,	PUNCT
ejpam-6679	810	7	34:87–98	34:87–98	NUM
ejpam-6679	810	8	,	,	PUNCT
ejpam-6679	810	9	2004	2004	NUM
ejpam-6679	810	10	.	.	PUNCT
ejpam-6679	811	1	t.	t.	PROPN
ejpam-6679	811	2	changphas	changphas	PROPN
ejpam-6679	811	3	/	/	SYM
ejpam-6679	811	4	eur	eur	PROPN
ejpam-6679	811	5	.	.	PUNCT
ejpam-6679	812	1	j.	j.	PROPN
ejpam-6679	812	2	pure	pure	PROPN
ejpam-6679	812	3	appl	appl	PROPN
ejpam-6679	812	4	.	.	PROPN
ejpam-6679	812	5	math	math	PROPN
ejpam-6679	812	6	,	,	PUNCT
ejpam-6679	812	7	18	18	NUM
ejpam-6679	812	8	(	(	PUNCT
ejpam-6679	812	9	4	4	NUM
ejpam-6679	812	10	)	)	PUNCT
ejpam-6679	812	11	(	(	PUNCT
ejpam-6679	812	12	2025	2025	NUM
ejpam-6679	812	13	)	)	PUNCT
ejpam-6679	812	14	,	,	PUNCT
ejpam-6679	812	15	6679	6679	NUM
ejpam-6679	812	16	15	15	NUM
ejpam-6679	812	17	of	of	ADP
ejpam-6679	812	18	15	15	NUM
ejpam-6679	812	19	[	[	SYM
ejpam-6679	812	20	4	4	NUM
ejpam-6679	812	21	]	]	PUNCT
ejpam-6679	812	22	k.	k.	NOUN
ejpam-6679	812	23	denecke	denecke	PROPN
ejpam-6679	812	24	and	and	CCONJ
ejpam-6679	812	25	p.	p.	PROPN
ejpam-6679	812	26	jampachon	jampachon	PROPN
ejpam-6679	812	27	.	.	PUNCT
ejpam-6679	813	1	clones	clone	NOUN
ejpam-6679	813	2	of	of	ADP
ejpam-6679	813	3	full	full	ADJ
ejpam-6679	813	4	terms	term	NOUN
ejpam-6679	813	5	.	.	PUNCT
ejpam-6679	814	1	algebra	algebra	NOUN
ejpam-6679	814	2	discr	discr	PROPN
ejpam-6679	814	3	.	.	PUNCT
ejpam-6679	815	1	math	math	NOUN
ejpam-6679	815	2	.	.	PUNCT
ejpam-6679	815	3	,	,	PUNCT
ejpam-6679	815	4	4:1–11	4:1–11	NUM
ejpam-6679	815	5	,	,	PUNCT
ejpam-6679	815	6	2004	2004	NUM
ejpam-6679	815	7	.	.	PUNCT
ejpam-6679	816	1	[	[	X
ejpam-6679	816	2	5	5	X
ejpam-6679	816	3	]	]	PUNCT
ejpam-6679	816	4	k.	k.	NOUN
ejpam-6679	816	5	wattanatripop	wattanatripop	PROPN
ejpam-6679	816	6	and	and	CCONJ
ejpam-6679	816	7	t.	t.	PROPN
ejpam-6679	816	8	changphas	changphas	PROPN
ejpam-6679	816	9	.	.	PUNCT
ejpam-6679	817	1	the	the	DET
ejpam-6679	817	2	menger	menger	PROPN
ejpam-6679	817	3	algebra	algebra	PROPN
ejpam-6679	817	4	of	of	ADP
ejpam-6679	817	5	terms	term	NOUN
ejpam-6679	817	6	induced	induce	VERB
ejpam-6679	817	7	by	by	ADP
ejpam-6679	817	8	orderdecreasing	orderdecrease	VERB
ejpam-6679	817	9	transformations	transformation	NOUN
ejpam-6679	817	10	.	.	PUNCT
ejpam-6679	818	1	commun	commun	PROPN
ejpam-6679	818	2	.	.	PUNCT
ejpam-6679	819	1	algebra	algebra	PROPN
ejpam-6679	819	2	.	.	PUNCT
ejpam-6679	819	3	,	,	PUNCT
ejpam-6679	819	4	49:3114–3123	49:3114–3123	NUM
ejpam-6679	819	5	,	,	PUNCT
ejpam-6679	819	6	2021	2021	NUM
ejpam-6679	819	7	.	.	PUNCT
ejpam-6679	820	1	[	[	X
ejpam-6679	820	2	6	6	NUM
ejpam-6679	820	3	]	]	PUNCT
ejpam-6679	820	4	k.	k.	NOUN
ejpam-6679	820	5	wattanatripop	wattanatripop	PROPN
ejpam-6679	820	6	and	and	CCONJ
ejpam-6679	820	7	t.	t.	PROPN
ejpam-6679	820	8	changphas	changphas	PROPN
ejpam-6679	820	9	.	.	PUNCT
ejpam-6679	821	1	clone	clone	NOUN
ejpam-6679	821	2	of	of	ADP
ejpam-6679	821	3	terms	term	NOUN
ejpam-6679	821	4	of	of	ADP
ejpam-6679	821	5	a	a	DET
ejpam-6679	821	6	fixed	fix	VERB
ejpam-6679	821	7	variable	variable	NOUN
ejpam-6679	821	8	.	.	PUNCT
ejpam-6679	822	1	mathematics	mathematic	NOUN
ejpam-6679	822	2	,	,	PUNCT
ejpam-6679	822	3	8	8	NUM
ejpam-6679	822	4	,	,	PUNCT
ejpam-6679	822	5	2020	2020	NUM
ejpam-6679	822	6	.	.	PUNCT
ejpam-6679	823	1	[	[	X
ejpam-6679	823	2	7	7	X
ejpam-6679	823	3	]	]	X
ejpam-6679	823	4	s.	s.	PROPN
ejpam-6679	823	5	puapong	puapong	PROPN
ejpam-6679	823	6	and	and	CCONJ
ejpam-6679	823	7	s.	s.	PROPN
ejpam-6679	823	8	leeratanavalee	leeratanavalee	PROPN
ejpam-6679	823	9	.	.	PUNCT
ejpam-6679	824	1	the	the	DET
ejpam-6679	824	2	algebra	algebra	NOUN
ejpam-6679	824	3	of	of	ADP
ejpam-6679	824	4	generalized	generalized	ADJ
ejpam-6679	824	5	full	full	ADJ
ejpam-6679	824	6	terms	term	NOUN
ejpam-6679	824	7	.	.	PUNCT
ejpam-6679	825	1	international	international	ADJ
ejpam-6679	825	2	of	of	ADP
ejpam-6679	825	3	open	open	ADJ
ejpam-6679	825	4	problems	problem	NOUN
ejpam-6679	825	5	in	in	ADP
ejpam-6679	825	6	computer	computer	NOUN
ejpam-6679	825	7	science	science	NOUN
ejpam-6679	825	8	and	and	CCONJ
ejpam-6679	825	9	mathematics	mathematic	NOUN
ejpam-6679	825	10	,	,	PUNCT
ejpam-6679	825	11	4:54–65	4:54–65	NUM
ejpam-6679	825	12	,	,	PUNCT
ejpam-6679	825	13	2011	2011	NUM
ejpam-6679	825	14	.	.	PUNCT
ejpam-6679	826	1	[	[	X
ejpam-6679	826	2	8	8	NUM
ejpam-6679	826	3	]	]	PUNCT
ejpam-6679	826	4	k.	k.	NOUN
ejpam-6679	826	5	denecke	denecke	PROPN
ejpam-6679	826	6	and	and	CCONJ
ejpam-6679	826	7	h.	h.	PROPN
ejpam-6679	826	8	hounnon	hounnon	PROPN
ejpam-6679	826	9	.	.	PUNCT
ejpam-6679	827	1	partial	partial	ADJ
ejpam-6679	827	2	menger	menger	PROPN
ejpam-6679	827	3	algebras	algebras	PROPN
ejpam-6679	827	4	of	of	ADP
ejpam-6679	827	5	terms	term	NOUN
ejpam-6679	827	6	.	.	PUNCT
ejpam-6679	828	1	asian	asian	ADJ
ejpam-6679	828	2	-	-	PUNCT
ejpam-6679	828	3	european	european	ADJ
ejpam-6679	828	4	journal	journal	NOUN
ejpam-6679	828	5	of	of	ADP
ejpam-6679	828	6	mathematics	mathematic	NOUN
ejpam-6679	828	7	,	,	PUNCT
ejpam-6679	828	8	14(06):2150092	14(06):2150092	NUM
ejpam-6679	828	9	,	,	PUNCT
ejpam-6679	828	10	2021	2021	NUM
ejpam-6679	828	11	.	.	PUNCT
ejpam-6679	829	1	[	[	X
ejpam-6679	829	2	9	9	NUM
ejpam-6679	829	3	]	]	X
ejpam-6679	829	4	n.	n.	PROPN
ejpam-6679	829	5	lekkoksung	lekkoksung	PROPN
ejpam-6679	829	6	and	and	CCONJ
ejpam-6679	829	7	s.	s.	PROPN
ejpam-6679	829	8	lekkoksung	lekkoksung	PROPN
ejpam-6679	829	9	.	.	PUNCT
ejpam-6679	830	1	on	on	ADP
ejpam-6679	830	2	partial	partial	ADJ
ejpam-6679	830	3	clone	clone	NOUN
ejpam-6679	830	4	of	of	ADP
ejpam-6679	830	5	k	k	NOUN
ejpam-6679	830	6	-	-	NOUN
ejpam-6679	830	7	terms	term	NOUN
ejpam-6679	830	8	.	.	PUNCT
ejpam-6679	831	1	discussion	discussion	NOUN
ejpam-6679	831	2	mathematicae	mathematicae	PROPN
ejpam-6679	831	3	,	,	PUNCT
ejpam-6679	831	4	general	general	ADJ
ejpam-6679	831	5	algebra	algebra	NOUN
ejpam-6679	831	6	and	and	CCONJ
ejpam-6679	831	7	applications	application	NOUN
ejpam-6679	831	8	,	,	PUNCT
ejpam-6679	831	9	41:361–379	41:361–379	PROPN
ejpam-6679	831	10	,	,	PUNCT
ejpam-6679	831	11	2021	2021	NUM
ejpam-6679	831	12	.	.	PUNCT
ejpam-6679	832	1	[	[	X
ejpam-6679	832	2	10	10	NUM
ejpam-6679	832	3	]	]	X
ejpam-6679	832	4	w.	w.	NOUN
ejpam-6679	832	5	puninagool	puninagool	PROPN
ejpam-6679	832	6	and	and	CCONJ
ejpam-6679	832	7	et	et	NOUN
ejpam-6679	832	8	.	.	PUNCT
ejpam-6679	833	1	al	al	PROPN
ejpam-6679	833	2	.	.	PROPN
ejpam-6679	833	3	algebras	algebras	PROPN
ejpam-6679	833	4	of	of	ADP
ejpam-6679	833	5	generalized	generalized	ADJ
ejpam-6679	833	6	terms	term	NOUN
ejpam-6679	833	7	induced	induce	VERB
ejpam-6679	833	8	by	by	ADP
ejpam-6679	833	9	some	some	DET
ejpam-6679	833	10	classes	class	NOUN
ejpam-6679	833	11	of	of	ADP
ejpam-6679	833	12	transformations	transformation	NOUN
ejpam-6679	833	13	.	.	PUNCT
ejpam-6679	834	1	asia	asia	PROPN
ejpam-6679	834	2	pac	pac	PROPN
ejpam-6679	834	3	.	.	PUNCT
ejpam-6679	835	1	j.	j.	PROPN
ejpam-6679	835	2	math	math	PROPN
ejpam-6679	835	3	.	.	PUNCT
ejpam-6679	835	4	,	,	PUNCT
ejpam-6679	835	5	11	11	NUM
ejpam-6679	835	6	,	,	PUNCT
ejpam-6679	835	7	2024	2024	NUM
ejpam-6679	835	8	.	.	PUNCT
ejpam-6679	836	1	[	[	X
ejpam-6679	836	2	11	11	NUM
ejpam-6679	836	3	]	]	X
ejpam-6679	836	4	j.b	j.b	PROPN
ejpam-6679	836	5	.	.	PROPN
ejpam-6679	836	6	fraleigh	fraleigh	PROPN
ejpam-6679	836	7	.	.	PUNCT
ejpam-6679	837	1	a	a	DET
ejpam-6679	837	2	first	first	ADJ
ejpam-6679	837	3	course	course	NOUN
ejpam-6679	837	4	in	in	ADP
ejpam-6679	837	5	abstract	abstract	ADJ
ejpam-6679	837	6	algebra	algebra	NOUN
ejpam-6679	837	7	,	,	PUNCT
ejpam-6679	837	8	7th	7th	ADJ
ejpam-6679	837	9	edition	edition	NOUN
ejpam-6679	837	10	.	.	PUNCT
ejpam-6679	838	1	pearson	pearson	PROPN
ejpam-6679	838	2	,	,	PUNCT
ejpam-6679	838	3	2017	2017	NUM
ejpam-6679	838	4	.	.	PUNCT
ejpam-6679	839	1	[	[	X
ejpam-6679	839	2	12	12	NUM
ejpam-6679	839	3	]	]	PUNCT
ejpam-6679	839	4	k.	k.	PROPN
ejpam-6679	839	5	denecke	denecke	PROPN
ejpam-6679	839	6	and	and	CCONJ
ejpam-6679	839	7	s.l	s.l	PROPN
ejpam-6679	839	8	.	.	PROPN
ejpam-6679	839	9	wismath	wismath	PROPN
ejpam-6679	839	10	.	.	PUNCT
ejpam-6679	840	1	hyperidentities	hyperidentitie	NOUN
ejpam-6679	840	2	and	and	CCONJ
ejpam-6679	840	3	clones	clone	NOUN
ejpam-6679	840	4	.	.	PUNCT
ejpam-6679	841	1	gordon	gordon	PROPN
ejpam-6679	841	2	and	and	CCONJ
ejpam-6679	841	3	breach	breach	VERB
ejpam-6679	841	4	science	science	NOUN
ejpam-6679	841	5	publishers	publisher	NOUN
ejpam-6679	841	6	,	,	PUNCT
ejpam-6679	841	7	2000	2000	NUM
ejpam-6679	841	8	.	.	PUNCT
ejpam-6679	842	1	[	[	X
ejpam-6679	842	2	13	13	NUM
ejpam-6679	842	3	]	]	X
ejpam-6679	842	4	s.	s.	PROPN
ejpam-6679	842	5	burris	burris	PROPN
ejpam-6679	842	6	and	and	CCONJ
ejpam-6679	842	7	h.p	h.p	PROPN
ejpam-6679	842	8	.	.	PROPN
ejpam-6679	842	9	sankappanavar	sankappanavar	PROPN
ejpam-6679	842	10	.	.	PUNCT
ejpam-6679	843	1	a	a	DET
ejpam-6679	843	2	course	course	NOUN
ejpam-6679	843	3	in	in	ADP
ejpam-6679	843	4	universal	universal	ADJ
ejpam-6679	843	5	algebra	algebra	NOUN
ejpam-6679	843	6	.	.	PUNCT
ejpam-6679	844	1	springer	springer	NOUN
ejpam-6679	844	2	-	-	PUNCT
ejpam-6679	844	3	verlag	verlag	PROPN
ejpam-6679	844	4	.	.	PROPN
ejpam-6679	844	5	,	,	PUNCT
ejpam-6679	844	6	2000	2000	NUM
ejpam-6679	844	7	.	.	PUNCT