id	sid	tid	token	lemma	pos
ejpam-4479	1	1	european	european	PROPN
ejpam-4479	1	2	journal	journal	PROPN
ejpam-4479	1	3	of	of	ADP
ejpam-4479	1	4	pure	pure	ADJ
ejpam-4479	1	5	and	and	CCONJ
ejpam-4479	1	6	applied	apply	VERB
ejpam-4479	1	7	mathematics	mathematic	NOUN
ejpam-4479	1	8	vol	vol	NOUN
ejpam-4479	1	9	.	.	PROPN
ejpam-4479	2	1	15	15	NUM
ejpam-4479	2	2	,	,	PUNCT
ejpam-4479	2	3	no	no	INTJ
ejpam-4479	2	4	.	.	NOUN
ejpam-4479	2	5	4	4	NUM
ejpam-4479	2	6	,	,	PUNCT
ejpam-4479	2	7	2022	2022	NUM
ejpam-4479	2	8	,	,	PUNCT
ejpam-4479	2	9	1482	1482	NUM
ejpam-4479	2	10	-	-	SYM
ejpam-4479	2	11	1497	1497	NUM
ejpam-4479	2	12	issn	issn	PROPN
ejpam-4479	2	13	1307	1307	NUM
ejpam-4479	2	14	-	-	SYM
ejpam-4479	2	15	5543	5543	NUM
ejpam-4479	2	16	–	–	PUNCT
ejpam-4479	3	1	ejpam.com	ejpam.com	X
ejpam-4479	3	2	published	publish	VERB
ejpam-4479	3	3	by	by	ADP
ejpam-4479	3	4	new	new	PROPN
ejpam-4479	3	5	york	york	PROPN
ejpam-4479	3	6	business	business	PROPN
ejpam-4479	3	7	global	global	ADJ
ejpam-4479	3	8	soft	soft	ADJ
ejpam-4479	3	9	hyper	hyper	ADJ
ejpam-4479	3	10	gr	gr	NOUN
ejpam-4479	3	11	-	-	PUNCT
ejpam-4479	3	12	algebra	algebra	NOUN
ejpam-4479	3	13	mark	mark	PROPN
ejpam-4479	3	14	kenneth	kenneth	PROPN
ejpam-4479	3	15	c.	c.	PROPN
ejpam-4479	3	16	engcot1,∗	engcot1,∗	PROPN
ejpam-4479	3	17	,	,	PUNCT
ejpam-4479	3	18	gaudencio	gaudencio	PROPN
ejpam-4479	3	19	c.	c.	PROPN
ejpam-4479	3	20	petalcorin	petalcorin	PROPN
ejpam-4479	3	21	,	,	PUNCT
ejpam-4479	3	22	jr.2	jr.2	PROPN
ejpam-4479	3	23	1	1	NUM
ejpam-4479	3	24	department	department	NOUN
ejpam-4479	3	25	of	of	ADP
ejpam-4479	3	26	computer	computer	NOUN
ejpam-4479	3	27	,	,	PUNCT
ejpam-4479	3	28	information	information	NOUN
ejpam-4479	3	29	sciences	science	NOUN
ejpam-4479	3	30	and	and	CCONJ
ejpam-4479	3	31	mathematics	mathematic	NOUN
ejpam-4479	3	32	,	,	PUNCT
ejpam-4479	3	33	school	school	NOUN
ejpam-4479	3	34	of	of	ADP
ejpam-4479	3	35	arts	art	NOUN
ejpam-4479	3	36	and	and	CCONJ
ejpam-4479	3	37	sciences	science	NOUN
ejpam-4479	3	38	,	,	PUNCT
ejpam-4479	3	39	university	university	NOUN
ejpam-4479	3	40	of	of	ADP
ejpam-4479	3	41	san	san	PROPN
ejpam-4479	3	42	carlos	carlos	PROPN
ejpam-4479	3	43	,	,	PUNCT
ejpam-4479	3	44	6000	6000	NUM
ejpam-4479	3	45	cebu	cebu	NOUN
ejpam-4479	3	46	city	city	NOUN
ejpam-4479	3	47	,	,	PUNCT
ejpam-4479	3	48	philippines	philippines	PROPN
ejpam-4479	3	49	2	2	NUM
ejpam-4479	3	50	department	department	NOUN
ejpam-4479	3	51	of	of	ADP
ejpam-4479	3	52	mathematics	mathematic	NOUN
ejpam-4479	3	53	and	and	CCONJ
ejpam-4479	3	54	statistics	statistic	NOUN
ejpam-4479	3	55	,	,	PUNCT
ejpam-4479	3	56	college	college	NOUN
ejpam-4479	3	57	of	of	ADP
ejpam-4479	3	58	science	science	NOUN
ejpam-4479	3	59	and	and	CCONJ
ejpam-4479	3	60	mathematics	mathematic	NOUN
ejpam-4479	3	61	,	,	PUNCT
ejpam-4479	3	62	center	center	NOUN
ejpam-4479	3	63	of	of	ADP
ejpam-4479	3	64	graph	graph	NOUN
ejpam-4479	3	65	theory	theory	NOUN
ejpam-4479	3	66	,	,	PUNCT
ejpam-4479	3	67	algebra	algebra	NOUN
ejpam-4479	3	68	and	and	CCONJ
ejpam-4479	3	69	analysis	analysis	NOUN
ejpam-4479	3	70	,	,	PUNCT
ejpam-4479	3	71	premier	premier	PROPN
ejpam-4479	3	72	research	research	PROPN
ejpam-4479	3	73	institute	institute	PROPN
ejpam-4479	3	74	of	of	ADP
ejpam-4479	3	75	science	science	NOUN
ejpam-4479	3	76	and	and	CCONJ
ejpam-4479	3	77	mathematics	mathematic	NOUN
ejpam-4479	3	78	,	,	PUNCT
ejpam-4479	3	79	mindanao	mindanao	PROPN
ejpam-4479	3	80	state	state	PROPN
ejpam-4479	3	81	university	university	PROPN
ejpam-4479	3	82	-	-	PUNCT
ejpam-4479	3	83	iligan	iligan	PROPN
ejpam-4479	3	84	institute	institute	PROPN
ejpam-4479	3	85	of	of	ADP
ejpam-4479	3	86	technology	technology	PROPN
ejpam-4479	3	87	,	,	PUNCT
ejpam-4479	3	88	9200	9200	NUM
ejpam-4479	3	89	iligan	iligan	ADJ
ejpam-4479	3	90	city	city	NOUN
ejpam-4479	3	91	,	,	PUNCT
ejpam-4479	3	92	philippines	philippine	NOUN
ejpam-4479	3	93	abstract	abstract	ADJ
ejpam-4479	3	94	.	.	PUNCT
ejpam-4479	4	1	in	in	ADP
ejpam-4479	4	2	this	this	DET
ejpam-4479	4	3	paper	paper	NOUN
ejpam-4479	4	4	,	,	PUNCT
ejpam-4479	4	5	we	we	PRON
ejpam-4479	4	6	apply	apply	VERB
ejpam-4479	4	7	the	the	DET
ejpam-4479	4	8	notion	notion	NOUN
ejpam-4479	4	9	of	of	ADP
ejpam-4479	4	10	soft	soft	ADJ
ejpam-4479	4	11	sets	set	NOUN
ejpam-4479	4	12	to	to	ADP
ejpam-4479	4	13	the	the	DET
ejpam-4479	4	14	theory	theory	NOUN
ejpam-4479	4	15	of	of	ADP
ejpam-4479	4	16	hyper	hyper	ADJ
ejpam-4479	4	17	gr	gr	NOUN
ejpam-4479	4	18	-	-	NOUN
ejpam-4479	4	19	algebra	algebra	NOUN
ejpam-4479	4	20	.	.	PUNCT
ejpam-4479	5	1	also	also	ADV
ejpam-4479	5	2	,	,	PUNCT
ejpam-4479	5	3	we	we	PRON
ejpam-4479	5	4	introduce	introduce	VERB
ejpam-4479	5	5	the	the	DET
ejpam-4479	5	6	concept	concept	NOUN
ejpam-4479	5	7	of	of	ADP
ejpam-4479	5	8	soft	soft	ADJ
ejpam-4479	5	9	hyper	hyper	ADJ
ejpam-4479	5	10	gr	gr	NOUN
ejpam-4479	5	11	-	-	PUNCT
ejpam-4479	5	12	algebras	algebra	NOUN
ejpam-4479	5	13	and	and	CCONJ
ejpam-4479	5	14	some	some	DET
ejpam-4479	5	15	properties	property	NOUN
ejpam-4479	5	16	of	of	ADP
ejpam-4479	5	17	soft	soft	ADJ
ejpam-4479	5	18	hyper	hyper	ADJ
ejpam-4479	5	19	gr	gr	NOUN
ejpam-4479	5	20	-	-	PUNCT
ejpam-4479	5	21	ideals	ideal	NOUN
ejpam-4479	5	22	.	.	PUNCT
ejpam-4479	6	1	2020	2020	NUM
ejpam-4479	6	2	mathematics	mathematic	NOUN
ejpam-4479	6	3	subject	subject	NOUN
ejpam-4479	6	4	classifications	classification	NOUN
ejpam-4479	6	5	:	:	PUNCT
ejpam-4479	6	6	06d72	06d72	NUM
ejpam-4479	6	7	,	,	PUNCT
ejpam-4479	6	8	14l17	14l17	NUM
ejpam-4479	6	9	key	key	ADJ
ejpam-4479	6	10	words	word	NOUN
ejpam-4479	6	11	and	and	CCONJ
ejpam-4479	6	12	phrases	phrase	NOUN
ejpam-4479	6	13	:	:	PUNCT
ejpam-4479	6	14	hyper	hyper	ADJ
ejpam-4479	6	15	gr	gr	NOUN
ejpam-4479	6	16	-	-	PUNCT
ejpam-4479	6	17	algebra	algebra	NOUN
ejpam-4479	6	18	,	,	PUNCT
ejpam-4479	6	19	soft	soft	ADJ
ejpam-4479	6	20	hyper	hyper	ADJ
ejpam-4479	6	21	gr	gr	NOUN
ejpam-4479	6	22	-	-	PUNCT
ejpam-4479	6	23	algebra	algebra	NOUN
ejpam-4479	6	24	,	,	PUNCT
ejpam-4479	6	25	soft	soft	ADJ
ejpam-4479	6	26	set	set	NOUN
ejpam-4479	6	27	1	1	NUM
ejpam-4479	6	28	.	.	PUNCT
ejpam-4479	7	1	introduction	introduction	NOUN
ejpam-4479	7	2	during	during	ADP
ejpam-4479	7	3	the	the	DET
ejpam-4479	7	4	congress	congress	PROPN
ejpam-4479	7	5	of	of	ADP
ejpam-4479	7	6	scandinavian	scandinavian	ADJ
ejpam-4479	7	7	mathematics	mathematic	NOUN
ejpam-4479	7	8	in	in	ADP
ejpam-4479	7	9	1954	1954	NUM
ejpam-4479	7	10	,	,	PUNCT
ejpam-4479	7	11	marty	marty	PROPN
ejpam-4479	8	1	[	[	X
ejpam-4479	8	2	9	9	NUM
ejpam-4479	8	3	]	]	PUNCT
ejpam-4479	8	4	introduced	introduce	VERB
ejpam-4479	8	5	the	the	DET
ejpam-4479	8	6	concept	concept	NOUN
ejpam-4479	8	7	of	of	ADP
ejpam-4479	8	8	hyperstructure	hyperstructure	PROPN
ejpam-4479	8	9	theory	theory	NOUN
ejpam-4479	8	10	(	(	PUNCT
ejpam-4479	8	11	also	also	ADV
ejpam-4479	8	12	known	know	VERB
ejpam-4479	8	13	as	as	ADP
ejpam-4479	8	14	multialgebra	multialgebra	NOUN
ejpam-4479	8	15	)	)	PUNCT
ejpam-4479	8	16	and	and	CCONJ
ejpam-4479	8	17	defined	define	VERB
ejpam-4479	8	18	groups	group	NOUN
ejpam-4479	8	19	based	base	VERB
ejpam-4479	8	20	on	on	ADP
ejpam-4479	8	21	the	the	DET
ejpam-4479	8	22	concept	concept	NOUN
ejpam-4479	8	23	of	of	ADP
ejpam-4479	8	24	hyperoperation	hyperoperation	NOUN
ejpam-4479	8	25	,	,	PUNCT
ejpam-4479	8	26	which	which	PRON
ejpam-4479	8	27	is	be	AUX
ejpam-4479	8	28	a	a	DET
ejpam-4479	8	29	generalization	generalization	NOUN
ejpam-4479	8	30	of	of	ADP
ejpam-4479	8	31	a	a	DET
ejpam-4479	8	32	binary	binary	ADJ
ejpam-4479	8	33	operation	operation	NOUN
ejpam-4479	8	34	in	in	ADP
ejpam-4479	8	35	algebra	algebra	NOUN
ejpam-4479	8	36	,	,	PUNCT
ejpam-4479	8	37	and	and	CCONJ
ejpam-4479	8	38	did	do	VERB
ejpam-4479	8	39	an	an	DET
ejpam-4479	8	40	analysis	analysis	NOUN
ejpam-4479	8	41	on	on	ADP
ejpam-4479	8	42	the	the	DET
ejpam-4479	8	43	application	application	NOUN
ejpam-4479	8	44	of	of	ADP
ejpam-4479	8	45	its	its	PRON
ejpam-4479	8	46	properties	property	NOUN
ejpam-4479	8	47	to	to	ADP
ejpam-4479	8	48	groups	group	NOUN
ejpam-4479	8	49	.	.	PUNCT
ejpam-4479	9	1	the	the	DET
ejpam-4479	9	2	notion	notion	NOUN
ejpam-4479	9	3	of	of	ADP
ejpam-4479	9	4	hyper	hyper	ADJ
ejpam-4479	9	5	gr	gr	NOUN
ejpam-4479	9	6	-	-	PUNCT
ejpam-4479	9	7	algebra	algebra	NOUN
ejpam-4479	9	8	was	be	AUX
ejpam-4479	9	9	first	first	ADV
ejpam-4479	9	10	initiated	initiate	VERB
ejpam-4479	9	11	by	by	ADP
ejpam-4479	9	12	indangan	indangan	NOUN
ejpam-4479	9	13	and	and	CCONJ
ejpam-4479	9	14	petalcorin	petalcorin	NOUN
ejpam-4479	10	1	[	[	X
ejpam-4479	10	2	3	3	X
ejpam-4479	10	3	]	]	PUNCT
ejpam-4479	10	4	in	in	ADP
ejpam-4479	10	5	2016	2016	NUM
ejpam-4479	10	6	.	.	PUNCT
ejpam-4479	11	1	from	from	ADP
ejpam-4479	11	2	then	then	ADV
ejpam-4479	11	3	,	,	PUNCT
ejpam-4479	11	4	some	some	DET
ejpam-4479	11	5	studies	study	NOUN
ejpam-4479	11	6	have	have	AUX
ejpam-4479	11	7	been	be	AUX
ejpam-4479	11	8	developed	develop	VERB
ejpam-4479	11	9	to	to	PART
ejpam-4479	11	10	establish	establish	VERB
ejpam-4479	11	11	some	some	PRON
ejpam-4479	11	12	of	of	ADP
ejpam-4479	11	13	its	its	PRON
ejpam-4479	11	14	properties	property	NOUN
ejpam-4479	11	15	.	.	PUNCT
ejpam-4479	12	1	on	on	ADP
ejpam-4479	12	2	the	the	DET
ejpam-4479	12	3	other	other	ADJ
ejpam-4479	12	4	hand	hand	NOUN
ejpam-4479	12	5	,	,	PUNCT
ejpam-4479	12	6	the	the	DET
ejpam-4479	12	7	concept	concept	NOUN
ejpam-4479	12	8	of	of	ADP
ejpam-4479	12	9	soft	soft	ADJ
ejpam-4479	12	10	sets	set	NOUN
ejpam-4479	12	11	was	be	AUX
ejpam-4479	12	12	initiated	initiate	VERB
ejpam-4479	12	13	by	by	ADP
ejpam-4479	12	14	molodtsov	molodtsov	NOUN
ejpam-4479	12	15	[	[	X
ejpam-4479	12	16	10	10	NUM
ejpam-4479	12	17	]	]	PUNCT
ejpam-4479	12	18	in	in	ADP
ejpam-4479	12	19	1999	1999	NUM
ejpam-4479	12	20	as	as	ADP
ejpam-4479	12	21	a	a	DET
ejpam-4479	12	22	new	new	ADJ
ejpam-4479	12	23	mathematical	mathematical	ADJ
ejpam-4479	12	24	tool	tool	NOUN
ejpam-4479	12	25	for	for	ADP
ejpam-4479	12	26	dealing	deal	VERB
ejpam-4479	12	27	with	with	ADP
ejpam-4479	12	28	uncertainties	uncertainty	NOUN
ejpam-4479	12	29	.	.	PUNCT
ejpam-4479	13	1	it	it	PRON
ejpam-4479	13	2	is	be	AUX
ejpam-4479	13	3	free	free	ADJ
ejpam-4479	13	4	from	from	ADP
ejpam-4479	13	5	difficulties	difficulty	NOUN
ejpam-4479	13	6	that	that	PRON
ejpam-4479	13	7	have	have	AUX
ejpam-4479	13	8	troubled	trouble	VERB
ejpam-4479	13	9	the	the	DET
ejpam-4479	13	10	usual	usual	ADJ
ejpam-4479	13	11	theoretical	theoretical	ADJ
ejpam-4479	13	12	approaches	approach	NOUN
ejpam-4479	13	13	.	.	PUNCT
ejpam-4479	14	1	since	since	SCONJ
ejpam-4479	14	2	then	then	ADV
ejpam-4479	14	3	,	,	PUNCT
ejpam-4479	14	4	there	there	PRON
ejpam-4479	14	5	are	be	VERB
ejpam-4479	14	6	various	various	ADJ
ejpam-4479	14	7	studies	study	NOUN
ejpam-4479	14	8	on	on	ADP
ejpam-4479	14	9	soft	soft	ADJ
ejpam-4479	14	10	sets	set	NOUN
ejpam-4479	14	11	.	.	PUNCT
ejpam-4479	15	1	in	in	ADP
ejpam-4479	15	2	2003	2003	NUM
ejpam-4479	15	3	,	,	PUNCT
ejpam-4479	15	4	maji	maji	PROPN
ejpam-4479	15	5	[	[	X
ejpam-4479	15	6	8	8	NUM
ejpam-4479	15	7	]	]	PUNCT
ejpam-4479	15	8	proposed	propose	VERB
ejpam-4479	15	9	some	some	DET
ejpam-4479	15	10	basic	basic	ADJ
ejpam-4479	15	11	operations	operation	NOUN
ejpam-4479	15	12	on	on	ADP
ejpam-4479	15	13	soft	soft	ADJ
ejpam-4479	15	14	sets	set	NOUN
ejpam-4479	15	15	.	.	PUNCT
ejpam-4479	16	1	moreover	moreover	ADV
ejpam-4479	16	2	,	,	PUNCT
ejpam-4479	16	3	ali	ali	PROPN
ejpam-4479	17	1	[	[	X
ejpam-4479	17	2	2	2	NUM
ejpam-4479	17	3	]	]	PUNCT
ejpam-4479	17	4	in	in	ADP
ejpam-4479	17	5	2009	2009	NUM
ejpam-4479	17	6	revised	revise	VERB
ejpam-4479	17	7	some	some	PRON
ejpam-4479	17	8	of	of	ADP
ejpam-4479	17	9	these	these	DET
ejpam-4479	17	10	operations	operation	NOUN
ejpam-4479	17	11	and	and	CCONJ
ejpam-4479	17	12	alcantud	alcantud	X
ejpam-4479	18	1	[	[	X
ejpam-4479	18	2	1	1	NUM
ejpam-4479	18	3	]	]	PUNCT
ejpam-4479	18	4	in	in	ADP
ejpam-4479	18	5	2015	2015	NUM
ejpam-4479	18	6	extended	extend	VERB
ejpam-4479	18	7	some	some	PRON
ejpam-4479	18	8	of	of	ADP
ejpam-4479	18	9	the	the	DET
ejpam-4479	18	10	theories	theory	NOUN
ejpam-4479	18	11	on	on	ADP
ejpam-4479	18	12	soft	soft	ADJ
ejpam-4479	18	13	sets	set	NOUN
ejpam-4479	18	14	.	.	PUNCT
ejpam-4479	19	1	in	in	ADP
ejpam-4479	19	2	this	this	DET
ejpam-4479	19	3	paper	paper	NOUN
ejpam-4479	19	4	we	we	PRON
ejpam-4479	19	5	apply	apply	VERB
ejpam-4479	19	6	the	the	DET
ejpam-4479	19	7	soft	soft	ADJ
ejpam-4479	19	8	set	set	NOUN
ejpam-4479	19	9	theory	theory	NOUN
ejpam-4479	19	10	to	to	AUX
ejpam-4479	19	11	hyper	hyper	VERB
ejpam-4479	19	12	gr	gr	NOUN
ejpam-4479	19	13	-	-	PUNCT
ejpam-4479	19	14	algebras	algebra	NOUN
ejpam-4479	19	15	.	.	PUNCT
ejpam-4479	20	1	∗corresponding	∗corresponde	VERB
ejpam-4479	20	2	author	author	NOUN
ejpam-4479	20	3	.	.	PUNCT
ejpam-4479	21	1	doi	doi	NOUN
ejpam-4479	21	2	:	:	PUNCT
ejpam-4479	21	3	https://doi.org/10.29020/nybg.ejpam.v15i4.4479	https://doi.org/10.29020/nybg.ejpam.v15i4.4479	ADJ
ejpam-4479	21	4	email	email	NOUN
ejpam-4479	21	5	addresses	address	NOUN
ejpam-4479	21	6	:	:	PUNCT
ejpam-4479	21	7	mkcengcot@usc	mkcengcot@usc	NUM
ejpam-4479	21	8	,	,	PUNCT
ejpam-4479	21	9	edu.ph	edu.ph	PROPN
ejpam-4479	21	10	(	(	PUNCT
ejpam-4479	21	11	m.k	m.k	PROPN
ejpam-4479	21	12	.	.	PROPN
ejpam-4479	21	13	engcot	engcot	PROPN
ejpam-4479	21	14	)	)	PUNCT
ejpam-4479	21	15	,	,	PUNCT
ejpam-4479	21	16	gaudencio.petalcorin@g.msuiit.edu.ph	gaudencio.petalcorin@g.msuiit.edu.ph	PROPN
ejpam-4479	21	17	(	(	PUNCT
ejpam-4479	21	18	g.	g.	PROPN
ejpam-4479	21	19	petalcorin	petalcorin	PROPN
ejpam-4479	21	20	)	)	PUNCT
ejpam-4479	21	21	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4479	21	22	1482	1482	NUM
ejpam-4479	22	1	©	©	PROPN
ejpam-4479	22	2	2022	2022	NUM
ejpam-4479	22	3	ejpam	ejpam	VERB
ejpam-4479	22	4	all	all	DET
ejpam-4479	22	5	rights	right	NOUN
ejpam-4479	22	6	reserved	reserve	VERB
ejpam-4479	22	7	.	.	PUNCT
ejpam-4479	23	1	m.k	m.k	X
ejpam-4479	23	2	.	.	PUNCT
ejpam-4479	23	3	engcot	engcot	PROPN
ejpam-4479	23	4	,	,	PUNCT
ejpam-4479	23	5	g.	g.	PROPN
ejpam-4479	23	6	petalcorin	petalcorin	PROPN
ejpam-4479	23	7	/	/	SYM
ejpam-4479	23	8	eur	eur	PROPN
ejpam-4479	23	9	.	.	PUNCT
ejpam-4479	24	1	j.	j.	PROPN
ejpam-4479	24	2	pure	pure	PROPN
ejpam-4479	24	3	appl	appl	PROPN
ejpam-4479	24	4	.	.	PROPN
ejpam-4479	24	5	math	math	PROPN
ejpam-4479	24	6	,	,	PUNCT
ejpam-4479	24	7	15	15	NUM
ejpam-4479	24	8	(	(	PUNCT
ejpam-4479	24	9	4	4	NUM
ejpam-4479	24	10	)	)	PUNCT
ejpam-4479	24	11	(	(	PUNCT
ejpam-4479	24	12	2022	2022	NUM
ejpam-4479	24	13	)	)	PUNCT
ejpam-4479	24	14	,	,	PUNCT
ejpam-4479	24	15	1482	1482	NUM
ejpam-4479	24	16	-	-	SYM
ejpam-4479	24	17	1497	1497	NUM
ejpam-4479	24	18	1483	1483	NUM
ejpam-4479	24	19	2	2	NUM
ejpam-4479	24	20	.	.	PUNCT
ejpam-4479	24	21	preliminaries	preliminary	NOUN
ejpam-4479	24	22	an	an	DET
ejpam-4479	24	23	algebra	algebra	NOUN
ejpam-4479	24	24	of	of	ADP
ejpam-4479	24	25	type	type	NOUN
ejpam-4479	24	26	(	(	PUNCT
ejpam-4479	24	27	2,0	2,0	NOUN
ejpam-4479	24	28	)	)	PUNCT
ejpam-4479	24	29	is	be	AUX
ejpam-4479	24	30	an	an	DET
ejpam-4479	24	31	algebra	algebra	NOUN
ejpam-4479	24	32	with	with	ADP
ejpam-4479	24	33	a	a	DET
ejpam-4479	24	34	binary	binary	ADJ
ejpam-4479	24	35	operation	operation	NOUN
ejpam-4479	24	36	and	and	CCONJ
ejpam-4479	24	37	a	a	DET
ejpam-4479	24	38	constant	constant	ADJ
ejpam-4479	24	39	element	element	NOUN
ejpam-4479	24	40	.	.	PUNCT
ejpam-4479	25	1	definition	definition	NOUN
ejpam-4479	25	2	1	1	NUM
ejpam-4479	25	3	.	.	PUNCT
ejpam-4479	26	1	[	[	X
ejpam-4479	26	2	3	3	X
ejpam-4479	26	3	]	]	PUNCT
ejpam-4479	26	4	let	let	VERB
ejpam-4479	26	5	h	h	NOUN
ejpam-4479	26	6	be	be	AUX
ejpam-4479	26	7	a	a	DET
ejpam-4479	26	8	nonempty	nonempty	ADV
ejpam-4479	26	9	set	set	VERB
ejpam-4479	26	10	and	and	CCONJ
ejpam-4479	26	11	⊛	⊛	NUM
ejpam-4479	26	12	be	be	VERB
ejpam-4479	26	13	a	a	DET
ejpam-4479	26	14	hyperoperation	hyperoperation	NOUN
ejpam-4479	26	15	on	on	ADP
ejpam-4479	26	16	h.	h.	PROPN
ejpam-4479	26	17	then	then	ADV
ejpam-4479	26	18	(	(	PUNCT
ejpam-4479	26	19	h;⊛	h;⊛	NUM
ejpam-4479	26	20	,	,	PUNCT
ejpam-4479	26	21	0	0	NUM
ejpam-4479	26	22	)	)	PUNCT
ejpam-4479	26	23	is	be	AUX
ejpam-4479	26	24	a	a	DET
ejpam-4479	26	25	called	call	VERB
ejpam-4479	26	26	a	a	DET
ejpam-4479	26	27	hyper	hyper	ADJ
ejpam-4479	26	28	gr	gr	NOUN
ejpam-4479	26	29	-	-	PUNCT
ejpam-4479	26	30	algebra	algebra	NOUN
ejpam-4479	26	31	if	if	SCONJ
ejpam-4479	26	32	it	it	PRON
ejpam-4479	26	33	satisfies	satisfy	VERB
ejpam-4479	26	34	the	the	DET
ejpam-4479	26	35	following	follow	VERB
ejpam-4479	26	36	conditions	condition	NOUN
ejpam-4479	26	37	,	,	PUNCT
ejpam-4479	26	38	for	for	ADP
ejpam-4479	26	39	all	all	DET
ejpam-4479	26	40	x	x	NOUN
ejpam-4479	26	41	,	,	PUNCT
ejpam-4479	26	42	y	y	PROPN
ejpam-4479	26	43	,	,	PUNCT
ejpam-4479	26	44	z	z	PROPN
ejpam-4479	26	45	∈	∈	PROPN
ejpam-4479	26	46	h	h	NOUN
ejpam-4479	26	47	:	:	PUNCT
ejpam-4479	26	48	(	(	PUNCT
ejpam-4479	26	49	i	i	NOUN
ejpam-4479	26	50	)	)	PUNCT
ejpam-4479	26	51	(	(	PUNCT
ejpam-4479	26	52	hgr1	hgr1	PROPN
ejpam-4479	26	53	)	)	PUNCT
ejpam-4479	26	54	(	(	PUNCT
ejpam-4479	26	55	x⊛	x⊛	PROPN
ejpam-4479	26	56	z)⊛	z)⊛	PROPN
ejpam-4479	26	57	(	(	PUNCT
ejpam-4479	26	58	y	y	PROPN
ejpam-4479	26	59	⊛	⊛	PROPN
ejpam-4479	26	60	z	z	PROPN
ejpam-4479	26	61	)	)	PUNCT
ejpam-4479	26	62	≪	≪	PUNCT
ejpam-4479	26	63	x⊛	x⊛	PROPN
ejpam-4479	26	64	y	y	PROPN
ejpam-4479	26	65	;	;	PUNCT
ejpam-4479	26	66	(	(	PUNCT
ejpam-4479	26	67	ii	ii	NOUN
ejpam-4479	26	68	)	)	PUNCT
ejpam-4479	26	69	(	(	PUNCT
ejpam-4479	26	70	hgr2	hgr2	NOUN
ejpam-4479	26	71	)	)	PUNCT
ejpam-4479	26	72	(	(	PUNCT
ejpam-4479	26	73	x⊛	x⊛	PROPN
ejpam-4479	27	1	y)⊛	y)⊛	NOUN
ejpam-4479	27	2	z	z	NOUN
ejpam-4479	27	3	=	=	SYM
ejpam-4479	27	4	(	(	PUNCT
ejpam-4479	27	5	x⊛	x⊛	PROPN
ejpam-4479	27	6	z)⊛	z)⊛	PROPN
ejpam-4479	27	7	y	y	NOUN
ejpam-4479	27	8	;	;	PUNCT
ejpam-4479	27	9	(	(	PUNCT
ejpam-4479	27	10	iii	iii	X
ejpam-4479	27	11	)	)	PUNCT
ejpam-4479	27	12	(	(	PUNCT
ejpam-4479	27	13	hgr3	hgr3	PROPN
ejpam-4479	27	14	)	)	PUNCT
ejpam-4479	27	15	x	x	PUNCT
ejpam-4479	27	16	≪	≪	VERB
ejpam-4479	27	17	x	x	X
ejpam-4479	27	18	;	;	PUNCT
ejpam-4479	27	19	(	(	PUNCT
ejpam-4479	27	20	iv	iv	X
ejpam-4479	27	21	)	)	PUNCT
ejpam-4479	27	22	(	(	PUNCT
ejpam-4479	27	23	hgr4	hgr4	NOUN
ejpam-4479	27	24	)	)	PUNCT
ejpam-4479	27	25	0⊛	0⊛	NUM
ejpam-4479	27	26	(	(	PUNCT
ejpam-4479	27	27	0⊛	0⊛	NUM
ejpam-4479	27	28	x	x	NOUN
ejpam-4479	27	29	)	)	PUNCT
ejpam-4479	27	30	≪	≪	PUNCT
ejpam-4479	27	31	x	x	X
ejpam-4479	27	32	,	,	PUNCT
ejpam-4479	27	33	x	x	PUNCT
ejpam-4479	27	34	̸=	̸=	PROPN
ejpam-4479	27	35	0	0	NUM
ejpam-4479	27	36	;	;	PUNCT
ejpam-4479	27	37	and	and	CCONJ
ejpam-4479	27	38	(	(	PUNCT
ejpam-4479	27	39	v	v	NOUN
ejpam-4479	27	40	)	)	PUNCT
ejpam-4479	27	41	(	(	PUNCT
ejpam-4479	27	42	hgr5	hgr5	PROPN
ejpam-4479	27	43	)	)	PUNCT
ejpam-4479	27	44	(	(	PUNCT
ejpam-4479	27	45	x⊛	x⊛	PROPN
ejpam-4479	28	1	y)⊛	y)⊛	NOUN
ejpam-4479	28	2	z	z	NOUN
ejpam-4479	28	3	≪	≪	VERB
ejpam-4479	28	4	y	y	PROPN
ejpam-4479	28	5	⊛	⊛	NUM
ejpam-4479	28	6	z.	z.	PROPN
ejpam-4479	28	7	example	example	NOUN
ejpam-4479	28	8	1	1	NUM
ejpam-4479	28	9	.	.	PUNCT
ejpam-4479	29	1	[	[	X
ejpam-4479	29	2	3	3	X
ejpam-4479	29	3	]	]	X
ejpam-4479	29	4	let	let	NOUN
ejpam-4479	29	5	h	h	NOUN
ejpam-4479	29	6	=	=	PRON
ejpam-4479	29	7	{	{	PUNCT
ejpam-4479	29	8	0	0	NUM
ejpam-4479	29	9	,	,	PUNCT
ejpam-4479	29	10	1	1	NUM
ejpam-4479	29	11	,	,	PUNCT
ejpam-4479	29	12	2	2	NUM
ejpam-4479	29	13	}	}	PUNCT
ejpam-4479	29	14	with	with	ADP
ejpam-4479	29	15	hyperoperation	hyperoperation	NOUN
ejpam-4479	29	16	⊛	⊛	NUM
ejpam-4479	29	17	defined	define	VERB
ejpam-4479	29	18	by	by	ADP
ejpam-4479	29	19	the	the	DET
ejpam-4479	29	20	cayley	cayley	ADJ
ejpam-4479	29	21	table	table	NOUN
ejpam-4479	29	22	below	below	ADV
ejpam-4479	29	23	.	.	PUNCT
ejpam-4479	30	1	⊛	⊛	NUM
ejpam-4479	30	2	0	0	NUM
ejpam-4479	30	3	1	1	NUM
ejpam-4479	30	4	2	2	NUM
ejpam-4479	30	5	0	0	NUM
ejpam-4479	30	6	{	{	PUNCT
ejpam-4479	30	7	0	0	NUM
ejpam-4479	30	8	}	}	PUNCT
ejpam-4479	30	9	{	{	PUNCT
ejpam-4479	30	10	0	0	NUM
ejpam-4479	30	11	}	}	PUNCT
ejpam-4479	30	12	{	{	PUNCT
ejpam-4479	30	13	0	0	NUM
ejpam-4479	30	14	}	}	SYM
ejpam-4479	30	15	1	1	NUM
ejpam-4479	30	16	{	{	PUNCT
ejpam-4479	30	17	0	0	NUM
ejpam-4479	30	18	,	,	PUNCT
ejpam-4479	30	19	1	1	NUM
ejpam-4479	30	20	,	,	PUNCT
ejpam-4479	30	21	2	2	NUM
ejpam-4479	30	22	}	}	PUNCT
ejpam-4479	30	23	{	{	PUNCT
ejpam-4479	30	24	0	0	NUM
ejpam-4479	30	25	,	,	PUNCT
ejpam-4479	30	26	1	1	NUM
ejpam-4479	30	27	}	}	PUNCT
ejpam-4479	30	28	{	{	PUNCT
ejpam-4479	30	29	0	0	NUM
ejpam-4479	30	30	,	,	PUNCT
ejpam-4479	30	31	1	1	NUM
ejpam-4479	30	32	}	}	SYM
ejpam-4479	30	33	2	2	NUM
ejpam-4479	30	34	{	{	PUNCT
ejpam-4479	30	35	0	0	NUM
ejpam-4479	30	36	,	,	PUNCT
ejpam-4479	30	37	2	2	NUM
ejpam-4479	30	38	}	}	PUNCT
ejpam-4479	30	39	{	{	PUNCT
ejpam-4479	30	40	0	0	NUM
ejpam-4479	30	41	,	,	PUNCT
ejpam-4479	30	42	1	1	NUM
ejpam-4479	30	43	,	,	PUNCT
ejpam-4479	30	44	2	2	NUM
ejpam-4479	30	45	}	}	PUNCT
ejpam-4479	30	46	{	{	PUNCT
ejpam-4479	30	47	0	0	NUM
ejpam-4479	30	48	,	,	PUNCT
ejpam-4479	30	49	2	2	NUM
ejpam-4479	30	50	}	}	PUNCT
ejpam-4479	30	51	by	by	ADP
ejpam-4479	30	52	routine	routine	ADJ
ejpam-4479	30	53	calculation	calculation	NOUN
ejpam-4479	30	54	,	,	PUNCT
ejpam-4479	30	55	we	we	PRON
ejpam-4479	30	56	see	see	VERB
ejpam-4479	30	57	that	that	SCONJ
ejpam-4479	30	58	(	(	PUNCT
ejpam-4479	30	59	h;⊛	h;⊛	NUM
ejpam-4479	30	60	,	,	PUNCT
ejpam-4479	30	61	0	0	NUM
ejpam-4479	30	62	)	)	PUNCT
ejpam-4479	30	63	is	be	AUX
ejpam-4479	30	64	a	a	DET
ejpam-4479	30	65	hyper	hyper	ADJ
ejpam-4479	30	66	gr	gr	NOUN
ejpam-4479	30	67	-	-	PUNCT
ejpam-4479	30	68	algebra	algebra	NOUN
ejpam-4479	30	69	.	.	PUNCT
ejpam-4479	31	1	example	example	NOUN
ejpam-4479	32	1	2	2	NUM
ejpam-4479	32	2	.	.	PUNCT
ejpam-4479	33	1	[	[	X
ejpam-4479	33	2	3	3	X
ejpam-4479	33	3	]	]	X
ejpam-4479	33	4	let	let	NOUN
ejpam-4479	33	5	h	h	NOUN
ejpam-4479	34	1	=	=	SYM
ejpam-4479	34	2	z	z	NOUN
ejpam-4479	34	3	,	,	PUNCT
ejpam-4479	34	4	where	where	SCONJ
ejpam-4479	34	5	z	z	NOUN
ejpam-4479	34	6	is	be	AUX
ejpam-4479	34	7	the	the	DET
ejpam-4479	34	8	set	set	NOUN
ejpam-4479	34	9	of	of	ADP
ejpam-4479	34	10	integers	integer	NOUN
ejpam-4479	34	11	such	such	ADJ
ejpam-4479	34	12	that	that	PRON
ejpam-4479	34	13	for	for	ADP
ejpam-4479	34	14	all	all	DET
ejpam-4479	34	15	x	x	NOUN
ejpam-4479	34	16	,	,	PUNCT
ejpam-4479	34	17	y,∈	y,∈	NOUN
ejpam-4479	34	18	h	h	NOUN
ejpam-4479	34	19	,	,	PUNCT
ejpam-4479	34	20	x⊛	x⊛	PROPN
ejpam-4479	34	21	y	y	NOUN
ejpam-4479	34	22	=	=	PUNCT
ejpam-4479	34	23	{	{	PUNCT
ejpam-4479	34	24	0	0	NUM
ejpam-4479	34	25	,	,	PUNCT
ejpam-4479	34	26	x	x	NOUN
ejpam-4479	34	27	,	,	PUNCT
ejpam-4479	34	28	y	y	PROPN
ejpam-4479	34	29	}	}	PUNCT
ejpam-4479	34	30	.	.	PUNCT
ejpam-4479	35	1	then	then	ADV
ejpam-4479	35	2	h	h	PROPN
ejpam-4479	35	3	is	be	AUX
ejpam-4479	35	4	a	a	DET
ejpam-4479	35	5	hyper	hyper	ADJ
ejpam-4479	35	6	gr	gr	NOUN
ejpam-4479	35	7	-	-	NOUN
ejpam-4479	35	8	algebra	algebra	NOUN
ejpam-4479	35	9	.	.	PUNCT
ejpam-4479	36	1	definition	definition	NOUN
ejpam-4479	36	2	2	2	NUM
ejpam-4479	36	3	.	.	PUNCT
ejpam-4479	37	1	[	[	X
ejpam-4479	37	2	3	3	X
ejpam-4479	37	3	]	]	X
ejpam-4479	37	4	a	a	DET
ejpam-4479	37	5	hyper	hyper	ADJ
ejpam-4479	37	6	gr	gr	NOUN
ejpam-4479	37	7	-	-	PUNCT
ejpam-4479	37	8	algebra	algebra	NOUN
ejpam-4479	37	9	h	h	NOUN
ejpam-4479	37	10	is	be	AUX
ejpam-4479	37	11	faithful	faithful	ADJ
ejpam-4479	37	12	if	if	SCONJ
ejpam-4479	37	13	for	for	ADP
ejpam-4479	37	14	all	all	DET
ejpam-4479	37	15	a	a	DET
ejpam-4479	37	16	,	,	PUNCT
ejpam-4479	37	17	b	b	PROPN
ejpam-4479	37	18	⊆	⊆	NUM
ejpam-4479	37	19	h	h	NOUN
ejpam-4479	37	20	,	,	PUNCT
ejpam-4479	37	21	0	0	NUM
ejpam-4479	37	22	∈	∈	PROPN
ejpam-4479	37	23	a⊛b	a⊛b	PROPN
ejpam-4479	37	24	implies	imply	VERB
ejpam-4479	37	25	a	a	DET
ejpam-4479	37	26	≪	≪	ADJ
ejpam-4479	37	27	b.	b.	NOUN
ejpam-4479	37	28	example	example	NOUN
ejpam-4479	37	29	3	3	X
ejpam-4479	37	30	.	.	PUNCT
ejpam-4479	38	1	the	the	DET
ejpam-4479	38	2	hyper	hyper	ADJ
ejpam-4479	38	3	gr	gr	NOUN
ejpam-4479	38	4	-	-	PUNCT
ejpam-4479	38	5	algebra	algebra	NOUN
ejpam-4479	38	6	h	h	NOUN
ejpam-4479	38	7	=	=	SYM
ejpam-4479	38	8	{	{	PUNCT
ejpam-4479	38	9	0	0	NUM
ejpam-4479	38	10	,	,	PUNCT
ejpam-4479	38	11	1	1	NUM
ejpam-4479	38	12	,	,	PUNCT
ejpam-4479	38	13	2	2	NUM
ejpam-4479	38	14	}	}	PUNCT
ejpam-4479	38	15	in	in	ADP
ejpam-4479	38	16	example	example	NOUN
ejpam-4479	38	17	1	1	NUM
ejpam-4479	38	18	is	be	AUX
ejpam-4479	38	19	faithful	faithful	ADJ
ejpam-4479	38	20	.	.	PUNCT
ejpam-4479	39	1	definition	definition	NOUN
ejpam-4479	39	2	3	3	NUM
ejpam-4479	39	3	.	.	PUNCT
ejpam-4479	40	1	[	[	X
ejpam-4479	40	2	4	4	X
ejpam-4479	40	3	]	]	PUNCT
ejpam-4479	40	4	let	let	VERB
ejpam-4479	40	5	h1	h1	NOUN
ejpam-4479	40	6	and	and	CCONJ
ejpam-4479	40	7	h2	h2	NOUN
ejpam-4479	40	8	be	be	AUX
ejpam-4479	40	9	hyper	hyper	ADJ
ejpam-4479	40	10	gr	gr	NOUN
ejpam-4479	40	11	-	-	PUNCT
ejpam-4479	40	12	algebras	algebra	NOUN
ejpam-4479	40	13	where	where	SCONJ
ejpam-4479	40	14	⊛1	⊛1	NOUN
ejpam-4479	40	15	and	and	CCONJ
ejpam-4479	40	16	⊛2	⊛2	NUM
ejpam-4479	40	17	are	be	AUX
ejpam-4479	40	18	the	the	DET
ejpam-4479	40	19	hyperoperations	hyperoperation	NOUN
ejpam-4479	40	20	of	of	ADP
ejpam-4479	40	21	h1	h1	NOUN
ejpam-4479	40	22	and	and	CCONJ
ejpam-4479	40	23	h2	h2	NOUN
ejpam-4479	40	24	,	,	PUNCT
ejpam-4479	40	25	respectively	respectively	ADV
ejpam-4479	40	26	,	,	PUNCT
ejpam-4479	40	27	and	and	CCONJ
ejpam-4479	40	28	f	f	NOUN
ejpam-4479	40	29	:	:	PUNCT
ejpam-4479	40	30	h1	h1	PROPN
ejpam-4479	40	31	→	→	SYM
ejpam-4479	40	32	h2	h2	PROPN
ejpam-4479	40	33	be	be	AUX
ejpam-4479	40	34	function	function	NOUN
ejpam-4479	40	35	.	.	PUNCT
ejpam-4479	41	1	then	then	ADV
ejpam-4479	41	2	f	f	PROPN
ejpam-4479	41	3	is	be	AUX
ejpam-4479	41	4	called	call	VERB
ejpam-4479	41	5	a	a	DET
ejpam-4479	41	6	hyper	hyper	ADJ
ejpam-4479	41	7	gr	gr	NOUN
ejpam-4479	41	8	-	-	PUNCT
ejpam-4479	41	9	algebra	algebra	NOUN
ejpam-4479	41	10	hyper	hyper	ADJ
ejpam-4479	41	11	homomorphism	homomorphism	NOUN
ejpam-4479	41	12	if	if	SCONJ
ejpam-4479	41	13	(	(	PUNCT
ejpam-4479	41	14	i	i	NOUN
ejpam-4479	41	15	)	)	PUNCT
ejpam-4479	41	16	f(01	f(01	NOUN
ejpam-4479	41	17	)	)	PUNCT
ejpam-4479	41	18	=	=	SYM
ejpam-4479	41	19	02	02	NUM
ejpam-4479	41	20	;	;	PUNCT
ejpam-4479	41	21	and	and	CCONJ
ejpam-4479	41	22	ii	ii	X
ejpam-4479	41	23	)	)	PUNCT
ejpam-4479	41	24	f(x⊛1	f(x⊛1	PROPN
ejpam-4479	41	25	y	y	NOUN
ejpam-4479	41	26	)	)	PUNCT
ejpam-4479	42	1	=	=	SYM
ejpam-4479	42	2	f(x)⊛2	f(x)⊛2	ADJ
ejpam-4479	42	3	f(y	f(y	NOUN
ejpam-4479	42	4	)	)	PUNCT
ejpam-4479	42	5	.	.	PUNCT
ejpam-4479	43	1	a	a	DET
ejpam-4479	43	2	hyper	hyper	ADJ
ejpam-4479	43	3	homomorphism	homomorphism	NOUN
ejpam-4479	43	4	f	f	PROPN
ejpam-4479	43	5	is	be	AUX
ejpam-4479	43	6	a	a	DET
ejpam-4479	43	7	hyper	hyper	ADJ
ejpam-4479	43	8	monorphism	monorphism	NOUN
ejpam-4479	43	9	if	if	SCONJ
ejpam-4479	43	10	f	f	PROPN
ejpam-4479	43	11	is	be	AUX
ejpam-4479	43	12	one	one	NUM
ejpam-4479	43	13	-	-	PUNCT
ejpam-4479	43	14	to	to	ADP
ejpam-4479	43	15	-	-	PUNCT
ejpam-4479	43	16	one	one	NUM
ejpam-4479	43	17	and	and	CCONJ
ejpam-4479	43	18	f	f	PROPN
ejpam-4479	43	19	is	be	AUX
ejpam-4479	43	20	a	a	DET
ejpam-4479	43	21	hyper	hyper	ADJ
ejpam-4479	43	22	epimorphism	epimorphism	NOUN
ejpam-4479	43	23	if	if	SCONJ
ejpam-4479	43	24	f	f	PROPN
ejpam-4479	43	25	is	be	AUX
ejpam-4479	43	26	onto	onto	ADP
ejpam-4479	43	27	;	;	PUNCT
ejpam-4479	43	28	f	f	PROPN
ejpam-4479	43	29	is	be	AUX
ejpam-4479	43	30	called	call	VERB
ejpam-4479	43	31	a	a	DET
ejpam-4479	43	32	hyper	hyper	ADJ
ejpam-4479	43	33	isomorphism	isomorphism	NOUN
ejpam-4479	43	34	if	if	SCONJ
ejpam-4479	43	35	f	f	PROPN
ejpam-4479	43	36	is	be	AUX
ejpam-4479	43	37	a	a	DET
ejpam-4479	43	38	hyper	hyper	ADJ
ejpam-4479	43	39	monorphism	monorphism	NOUN
ejpam-4479	43	40	and	and	CCONJ
ejpam-4479	43	41	hyper	hyper	NOUN
ejpam-4479	43	42	epimorphism	epimorphism	NOUN
ejpam-4479	43	43	(	(	PUNCT
ejpam-4479	43	44	denoted	denote	VERB
ejpam-4479	43	45	by	by	ADP
ejpam-4479	43	46	∼=h	∼=h	NOUN
ejpam-4479	43	47	)	)	PUNCT
ejpam-4479	43	48	.	.	PUNCT
ejpam-4479	44	1	m.k	m.k	PROPN
ejpam-4479	44	2	.	.	PUNCT
ejpam-4479	44	3	engcot	engcot	PROPN
ejpam-4479	44	4	,	,	PUNCT
ejpam-4479	44	5	g.	g.	PROPN
ejpam-4479	44	6	petalcorin	petalcorin	PROPN
ejpam-4479	44	7	/	/	SYM
ejpam-4479	44	8	eur	eur	PROPN
ejpam-4479	44	9	.	.	PUNCT
ejpam-4479	45	1	j.	j.	PROPN
ejpam-4479	45	2	pure	pure	PROPN
ejpam-4479	45	3	appl	appl	PROPN
ejpam-4479	45	4	.	.	PROPN
ejpam-4479	45	5	math	math	PROPN
ejpam-4479	45	6	,	,	PUNCT
ejpam-4479	45	7	15	15	NUM
ejpam-4479	45	8	(	(	PUNCT
ejpam-4479	45	9	4	4	NUM
ejpam-4479	45	10	)	)	PUNCT
ejpam-4479	45	11	(	(	PUNCT
ejpam-4479	45	12	2022	2022	NUM
ejpam-4479	45	13	)	)	PUNCT
ejpam-4479	45	14	,	,	PUNCT
ejpam-4479	45	15	1482	1482	NUM
ejpam-4479	45	16	-	-	SYM
ejpam-4479	45	17	1497	1497	NUM
ejpam-4479	45	18	1484	1484	NUM
ejpam-4479	45	19	definition	definition	NOUN
ejpam-4479	45	20	4	4	NUM
ejpam-4479	45	21	.	.	PUNCT
ejpam-4479	46	1	[	[	X
ejpam-4479	46	2	3	3	X
ejpam-4479	46	3	]	]	PUNCT
ejpam-4479	46	4	let	let	VERB
ejpam-4479	46	5	h	h	PRON
ejpam-4479	46	6	be	be	AUX
ejpam-4479	46	7	a	a	DET
ejpam-4479	46	8	hyper	hyper	ADJ
ejpam-4479	46	9	gr	gr	NOUN
ejpam-4479	46	10	-	-	PUNCT
ejpam-4479	46	11	algebra	algebra	NOUN
ejpam-4479	46	12	and	and	CCONJ
ejpam-4479	46	13	s	s	AUX
ejpam-4479	46	14	be	be	AUX
ejpam-4479	46	15	a	a	DET
ejpam-4479	46	16	subset	subset	NOUN
ejpam-4479	46	17	of	of	ADP
ejpam-4479	46	18	h	h	NOUN
ejpam-4479	46	19	containing	contain	VERB
ejpam-4479	46	20	0	0	NUM
ejpam-4479	46	21	.	.	PUNCT
ejpam-4479	47	1	if	if	SCONJ
ejpam-4479	47	2	s	s	PROPN
ejpam-4479	47	3	is	be	AUX
ejpam-4479	47	4	a	a	DET
ejpam-4479	47	5	hyper	hyper	ADJ
ejpam-4479	47	6	gr	gr	NOUN
ejpam-4479	47	7	-	-	NOUN
ejpam-4479	47	8	algebra	algebra	NOUN
ejpam-4479	47	9	with	with	ADP
ejpam-4479	47	10	respect	respect	NOUN
ejpam-4479	47	11	to	to	ADP
ejpam-4479	47	12	the	the	DET
ejpam-4479	47	13	hyperoperation	hyperoperation	NOUN
ejpam-4479	47	14	⊛	⊛	ADJ
ejpam-4479	47	15	on	on	ADP
ejpam-4479	47	16	h	h	NOUN
ejpam-4479	47	17	,	,	PUNCT
ejpam-4479	47	18	then	then	ADV
ejpam-4479	47	19	we	we	PRON
ejpam-4479	47	20	say	say	VERB
ejpam-4479	47	21	that	that	SCONJ
ejpam-4479	47	22	h	h	NOUN
ejpam-4479	47	23	is	be	AUX
ejpam-4479	47	24	a	a	DET
ejpam-4479	47	25	hyper	hyper	ADJ
ejpam-4479	47	26	subgr	subgr	NOUN
ejpam-4479	47	27	-	-	PUNCT
ejpam-4479	47	28	algebra	algebra	NOUN
ejpam-4479	47	29	of	of	ADP
ejpam-4479	47	30	h.	h.	PROPN
ejpam-4479	47	31	lemma	lemma	PROPN
ejpam-4479	48	1	1	1	X
ejpam-4479	48	2	.	.	PUNCT
ejpam-4479	49	1	[	[	X
ejpam-4479	49	2	4	4	X
ejpam-4479	49	3	]	]	PUNCT
ejpam-4479	49	4	let	let	VERB
ejpam-4479	49	5	f	f	PRON
ejpam-4479	49	6	:	:	PUNCT
ejpam-4479	49	7	h	h	PROPN
ejpam-4479	49	8	→	→	SYM
ejpam-4479	49	9	y	y	PROPN
ejpam-4479	49	10	be	be	AUX
ejpam-4479	49	11	homomorphism	homomorphism	NOUN
ejpam-4479	49	12	of	of	ADP
ejpam-4479	49	13	hyper	hyper	ADJ
ejpam-4479	49	14	gr	gr	NOUN
ejpam-4479	49	15	-	-	PUNCT
ejpam-4479	49	16	algebras	algebras	NOUN
ejpam-4479	49	17	.	.	PUNCT
ejpam-4479	50	1	if	if	SCONJ
ejpam-4479	50	2	s	s	PROPN
ejpam-4479	50	3	is	be	AUX
ejpam-4479	50	4	a	a	DET
ejpam-4479	50	5	hyper	hyper	ADJ
ejpam-4479	50	6	subgr	subgr	NOUN
ejpam-4479	50	7	-	-	PUNCT
ejpam-4479	50	8	algebra	algebra	NOUN
ejpam-4479	50	9	of	of	ADP
ejpam-4479	50	10	h	h	NOUN
ejpam-4479	50	11	,	,	PUNCT
ejpam-4479	50	12	then	then	ADV
ejpam-4479	50	13	f(s	f(	VERB
ejpam-4479	50	14	)	)	PUNCT
ejpam-4479	50	15	is	be	AUX
ejpam-4479	50	16	a	a	DET
ejpam-4479	50	17	hyper	hyper	ADJ
ejpam-4479	50	18	subgr	subgr	NOUN
ejpam-4479	50	19	-	-	PUNCT
ejpam-4479	50	20	algebra	algebra	NOUN
ejpam-4479	50	21	.	.	PUNCT
ejpam-4479	51	1	theorem	theorem	NOUN
ejpam-4479	51	2	1	1	NUM
ejpam-4479	51	3	.	.	PUNCT
ejpam-4479	52	1	[	[	X
ejpam-4479	52	2	3	3	NUM
ejpam-4479	52	3	]	]	X
ejpam-4479	52	4	(	(	PUNCT
ejpam-4479	52	5	hyper	hyper	ADJ
ejpam-4479	52	6	subgr	subgr	NOUN
ejpam-4479	52	7	-	-	PUNCT
ejpam-4479	52	8	algebra	algebra	NOUN
ejpam-4479	52	9	criterion	criterion	NOUN
ejpam-4479	52	10	)	)	PUNCT
ejpam-4479	52	11	let	let	VERB
ejpam-4479	52	12	h	h	NOUN
ejpam-4479	52	13	be	be	AUX
ejpam-4479	52	14	a	a	DET
ejpam-4479	52	15	hyper	hyper	ADJ
ejpam-4479	52	16	gr	gr	NOUN
ejpam-4479	52	17	-	-	PUNCT
ejpam-4479	52	18	algebra	algebra	NOUN
ejpam-4479	52	19	and	and	CCONJ
ejpam-4479	52	20	s	s	AUX
ejpam-4479	52	21	be	be	AUX
ejpam-4479	52	22	a	a	DET
ejpam-4479	52	23	nonempty	nonempty	ADJ
ejpam-4479	52	24	subset	subset	NOUN
ejpam-4479	52	25	of	of	ADP
ejpam-4479	52	26	h.	h.	PROPN
ejpam-4479	53	1	then	then	ADV
ejpam-4479	53	2	s	s	VERB
ejpam-4479	53	3	is	be	AUX
ejpam-4479	53	4	a	a	DET
ejpam-4479	53	5	hyper	hyper	ADJ
ejpam-4479	53	6	subgr	subgr	NOUN
ejpam-4479	53	7	-	-	PUNCT
ejpam-4479	53	8	algebra	algebra	NOUN
ejpam-4479	53	9	of	of	ADP
ejpam-4479	53	10	h	h	NOUN
ejpam-4479	53	11	if	if	SCONJ
ejpam-4479	54	1	and	and	CCONJ
ejpam-4479	54	2	only	only	ADV
ejpam-4479	54	3	if	if	SCONJ
ejpam-4479	54	4	x⊛	x⊛	PROPN
ejpam-4479	54	5	y	y	PROPN
ejpam-4479	54	6	⊆	⊆	NUM
ejpam-4479	54	7	s	s	NOUN
ejpam-4479	54	8	,	,	PUNCT
ejpam-4479	54	9	for	for	ADP
ejpam-4479	54	10	all	all	DET
ejpam-4479	54	11	x	x	NOUN
ejpam-4479	54	12	,	,	PUNCT
ejpam-4479	54	13	y	y	PROPN
ejpam-4479	54	14	∈	∈	PROPN
ejpam-4479	54	15	s.	s.	PROPN
ejpam-4479	54	16	theorem	theorem	VERB
ejpam-4479	54	17	2	2	NUM
ejpam-4479	54	18	.	.	PUNCT
ejpam-4479	55	1	[	[	X
ejpam-4479	55	2	3	3	X
ejpam-4479	55	3	]	]	X
ejpam-4479	55	4	if	if	SCONJ
ejpam-4479	55	5	{	{	PUNCT
ejpam-4479	55	6	ii|i	ii|i	NOUN
ejpam-4479	55	7	∈	∈	NOUN
ejpam-4479	55	8	v	v	NOUN
ejpam-4479	55	9	}	}	PUNCT
ejpam-4479	55	10	is	be	AUX
ejpam-4479	55	11	a	a	DET
ejpam-4479	55	12	nonempty	nonempty	ADJ
ejpam-4479	55	13	collection	collection	NOUN
ejpam-4479	55	14	of	of	ADP
ejpam-4479	55	15	hyper	hyper	ADJ
ejpam-4479	55	16	gr	gr	NOUN
ejpam-4479	55	17	-	-	PUNCT
ejpam-4479	55	18	ideals	ideal	NOUN
ejpam-4479	55	19	of	of	ADP
ejpam-4479	55	20	a	a	DET
ejpam-4479	55	21	hyper	hyper	ADJ
ejpam-4479	55	22	gr	gr	NOUN
ejpam-4479	55	23	-	-	PUNCT
ejpam-4479	55	24	algebra	algebra	NOUN
ejpam-4479	55	25	h	h	NOUN
ejpam-4479	55	26	,	,	PUNCT
ejpam-4479	55	27	then	then	ADV
ejpam-4479	55	28	so	so	ADV
ejpam-4479	55	29	is	be	AUX
ejpam-4479	55	30	⋂	⋂	PROPN
ejpam-4479	55	31	i∈	i∈	ADP
ejpam-4479	55	32	vii	vii	PROPN
ejpam-4479	55	33	.	.	PROPN
ejpam-4479	56	1	definition	definition	NOUN
ejpam-4479	56	2	5	5	NUM
ejpam-4479	56	3	.	.	PUNCT
ejpam-4479	57	1	[	[	X
ejpam-4479	57	2	6	6	NUM
ejpam-4479	57	3	]	]	PUNCT
ejpam-4479	57	4	let	let	VERB
ejpam-4479	57	5	u	u	PRON
ejpam-4479	57	6	be	be	AUX
ejpam-4479	57	7	an	an	DET
ejpam-4479	57	8	initial	initial	ADJ
ejpam-4479	57	9	universal	universal	ADJ
ejpam-4479	57	10	set	set	NOUN
ejpam-4479	57	11	and	and	CCONJ
ejpam-4479	57	12	e	e	X
ejpam-4479	57	13	a	a	DET
ejpam-4479	57	14	set	set	NOUN
ejpam-4479	57	15	of	of	ADP
ejpam-4479	57	16	all	all	DET
ejpam-4479	57	17	possible	possible	ADJ
ejpam-4479	57	18	parameters	parameter	NOUN
ejpam-4479	57	19	under	under	ADP
ejpam-4479	57	20	consideration	consideration	NOUN
ejpam-4479	57	21	.	.	PUNCT
ejpam-4479	58	1	if	if	SCONJ
ejpam-4479	58	2	a	a	DET
ejpam-4479	58	3	⊂	⊂	X
ejpam-4479	58	4	e	e	NOUN
ejpam-4479	58	5	,	,	PUNCT
ejpam-4479	58	6	then	then	ADV
ejpam-4479	58	7	a	a	DET
ejpam-4479	58	8	soft	soft	ADJ
ejpam-4479	58	9	set	set	NOUN
ejpam-4479	58	10	(	(	PUNCT
ejpam-4479	58	11	f	f	X
ejpam-4479	58	12	,	,	PUNCT
ejpam-4479	58	13	a	a	PRON
ejpam-4479	58	14	)	)	PUNCT
ejpam-4479	58	15	over	over	ADP
ejpam-4479	58	16	u	u	NOUN
ejpam-4479	58	17	is	be	AUX
ejpam-4479	58	18	defined	define	VERB
ejpam-4479	58	19	to	to	PART
ejpam-4479	58	20	be	be	AUX
ejpam-4479	58	21	the	the	DET
ejpam-4479	58	22	set	set	NOUN
ejpam-4479	58	23	of	of	ADP
ejpam-4479	58	24	ordered	order	VERB
ejpam-4479	58	25	pairs	pair	NOUN
ejpam-4479	58	26	(	(	PUNCT
ejpam-4479	58	27	f	f	X
ejpam-4479	58	28	,	,	PUNCT
ejpam-4479	58	29	a	a	PRON
ejpam-4479	58	30	)	)	PUNCT
ejpam-4479	58	31	=	=	SYM
ejpam-4479	58	32	{	{	PUNCT
ejpam-4479	58	33	(	(	PUNCT
ejpam-4479	58	34	x	x	X
ejpam-4479	58	35	,	,	PUNCT
ejpam-4479	58	36	fa(x	fa(x	NOUN
ejpam-4479	58	37	)	)	PUNCT
ejpam-4479	58	38	)	)	PUNCT
ejpam-4479	58	39	:	:	PUNCT
ejpam-4479	59	1	x	x	X
ejpam-4479	59	2	∈	∈	PROPN
ejpam-4479	59	3	e	e	NOUN
ejpam-4479	59	4	,	,	PUNCT
ejpam-4479	59	5	fa(x	fa(x	NOUN
ejpam-4479	59	6	)	)	PUNCT
ejpam-4479	59	7	∈	∈	PROPN
ejpam-4479	59	8	p	p	X
ejpam-4479	59	9	(	(	PUNCT
ejpam-4479	59	10	u	u	NOUN
ejpam-4479	59	11	)	)	PUNCT
ejpam-4479	59	12	}	}	PUNCT
ejpam-4479	59	13	,	,	PUNCT
ejpam-4479	59	14	where	where	SCONJ
ejpam-4479	59	15	fa	fa	INTJ
ejpam-4479	59	16	:	:	PUNCT
ejpam-4479	59	17	e	e	X
ejpam-4479	59	18	→	→	SYM
ejpam-4479	59	19	p	p	X
ejpam-4479	59	20	(	(	PUNCT
ejpam-4479	59	21	u	u	NOUN
ejpam-4479	59	22	)	)	PUNCT
ejpam-4479	59	23	such	such	ADJ
ejpam-4479	59	24	that	that	SCONJ
ejpam-4479	59	25	fa(x	fa(x	NOUN
ejpam-4479	59	26	)	)	PUNCT
ejpam-4479	59	27	=	=	PUNCT
ejpam-4479	59	28	∅	∅	NOUN
ejpam-4479	59	29	if	if	SCONJ
ejpam-4479	59	30	x	x	X
ejpam-4479	59	31	/∈	/∈	PUNCT
ejpam-4479	59	32	a.	a.	NOUN
ejpam-4479	60	1	the	the	DET
ejpam-4479	60	2	function	function	NOUN
ejpam-4479	60	3	fa	fa	PROPN
ejpam-4479	60	4	is	be	AUX
ejpam-4479	60	5	called	call	VERB
ejpam-4479	60	6	the	the	DET
ejpam-4479	60	7	approximation	approximation	NOUN
ejpam-4479	60	8	function	function	NOUN
ejpam-4479	60	9	of	of	ADP
ejpam-4479	60	10	the	the	DET
ejpam-4479	60	11	soft	soft	ADJ
ejpam-4479	60	12	set	set	NOUN
ejpam-4479	60	13	(	(	PUNCT
ejpam-4479	60	14	f	f	X
ejpam-4479	60	15	,	,	PUNCT
ejpam-4479	60	16	a	a	PRON
ejpam-4479	60	17	)	)	PUNCT
ejpam-4479	60	18	.	.	PUNCT
ejpam-4479	61	1	the	the	DET
ejpam-4479	61	2	subscript	subscript	NOUN
ejpam-4479	61	3	a	a	PRON
ejpam-4479	61	4	in	in	ADP
ejpam-4479	61	5	the	the	DET
ejpam-4479	61	6	notion	notion	NOUN
ejpam-4479	61	7	fa	fa	PROPN
ejpam-4479	61	8	indicates	indicate	VERB
ejpam-4479	61	9	that	that	SCONJ
ejpam-4479	61	10	fa	fa	PROPN
ejpam-4479	61	11	is	be	AUX
ejpam-4479	61	12	the	the	DET
ejpam-4479	61	13	approximate	approximate	ADJ
ejpam-4479	61	14	function	function	NOUN
ejpam-4479	61	15	of	of	ADP
ejpam-4479	61	16	(	(	PUNCT
ejpam-4479	61	17	f	f	X
ejpam-4479	61	18	,	,	PUNCT
ejpam-4479	61	19	a	a	PRON
ejpam-4479	61	20	)	)	PUNCT
ejpam-4479	61	21	.	.	PUNCT
ejpam-4479	62	1	in	in	ADP
ejpam-4479	62	2	what	what	PRON
ejpam-4479	62	3	follows	follow	VERB
ejpam-4479	62	4	,	,	PUNCT
ejpam-4479	62	5	let	let	VERB
ejpam-4479	62	6	s(u	s(u	PROPN
ejpam-4479	62	7	)	)	PUNCT
ejpam-4479	62	8	denote	denote	VERB
ejpam-4479	62	9	the	the	DET
ejpam-4479	62	10	set	set	NOUN
ejpam-4479	62	11	of	of	ADP
ejpam-4479	62	12	all	all	DET
ejpam-4479	62	13	soft	soft	ADJ
ejpam-4479	62	14	sets	set	NOUN
ejpam-4479	62	15	over	over	ADP
ejpam-4479	62	16	u	u	NOUN
ejpam-4479	62	17	by	by	ADP
ejpam-4479	62	18	cagman	cagman	PROPN
ejpam-4479	62	19	et	et	PROPN
ejpam-4479	62	20	al	al	PROPN
ejpam-4479	62	21	.	.	PUNCT
ejpam-4479	63	1	[	[	X
ejpam-4479	63	2	7	7	NUM
ejpam-4479	63	3	]	]	PUNCT
ejpam-4479	63	4	.	.	PUNCT
ejpam-4479	64	1	definition	definition	NOUN
ejpam-4479	64	2	6	6	NUM
ejpam-4479	64	3	.	.	PUNCT
ejpam-4479	65	1	[	[	X
ejpam-4479	65	2	5	5	NUM
ejpam-4479	65	3	]	]	X
ejpam-4479	65	4	let	let	VERB
ejpam-4479	65	5	(	(	PUNCT
ejpam-4479	65	6	f	f	X
ejpam-4479	65	7	,	,	PUNCT
ejpam-4479	65	8	a	a	PRON
ejpam-4479	65	9	)	)	PUNCT
ejpam-4479	65	10	and	and	CCONJ
ejpam-4479	65	11	(	(	PUNCT
ejpam-4479	65	12	g	g	NOUN
ejpam-4479	65	13	,	,	PUNCT
ejpam-4479	65	14	b	b	NOUN
ejpam-4479	65	15	)	)	PUNCT
ejpam-4479	65	16	be	be	AUX
ejpam-4479	65	17	two	two	NUM
ejpam-4479	65	18	soft	soft	ADJ
ejpam-4479	65	19	sets	set	NOUN
ejpam-4479	65	20	over	over	ADP
ejpam-4479	65	21	u	u	NOUN
ejpam-4479	65	22	.	.	PUNCT
ejpam-4479	66	1	the	the	DET
ejpam-4479	66	2	intersection	intersection	NOUN
ejpam-4479	66	3	of	of	ADP
ejpam-4479	66	4	(	(	PUNCT
ejpam-4479	66	5	f	f	X
ejpam-4479	66	6	,	,	PUNCT
ejpam-4479	66	7	a	a	PRON
ejpam-4479	66	8	)	)	PUNCT
ejpam-4479	66	9	and	and	CCONJ
ejpam-4479	66	10	(	(	PUNCT
ejpam-4479	66	11	g	g	NOUN
ejpam-4479	66	12	,	,	PUNCT
ejpam-4479	66	13	b	b	NOUN
ejpam-4479	66	14	)	)	PUNCT
ejpam-4479	66	15	is	be	AUX
ejpam-4479	66	16	defined	define	VERB
ejpam-4479	66	17	to	to	PART
ejpam-4479	66	18	be	be	AUX
ejpam-4479	66	19	the	the	DET
ejpam-4479	66	20	soft	soft	ADJ
ejpam-4479	66	21	set	set	NOUN
ejpam-4479	66	22	(	(	PUNCT
ejpam-4479	66	23	h	h	NOUN
ejpam-4479	66	24	,	,	PUNCT
ejpam-4479	66	25	c	c	NOUN
ejpam-4479	66	26	)	)	PUNCT
ejpam-4479	66	27	satisfying	satisfy	VERB
ejpam-4479	66	28	the	the	DET
ejpam-4479	66	29	following	follow	VERB
ejpam-4479	66	30	conditions	condition	NOUN
ejpam-4479	66	31	:	:	PUNCT
ejpam-4479	66	32	(	(	PUNCT
ejpam-4479	66	33	i	i	NOUN
ejpam-4479	66	34	)	)	PUNCT
ejpam-4479	67	1	c	c	NOUN
ejpam-4479	67	2	=	=	PUNCT
ejpam-4479	67	3	a	a	DET
ejpam-4479	67	4	∩b	∩b	NOUN
ejpam-4479	67	5	̸=	̸=	PROPN
ejpam-4479	67	6	∅	∅	NOUN
ejpam-4479	67	7	(	(	PUNCT
ejpam-4479	67	8	ii	ii	NOUN
ejpam-4479	67	9	)	)	PUNCT
ejpam-4479	67	10	h(e	h(e	PROPN
ejpam-4479	67	11	)	)	PUNCT
ejpam-4479	68	1	=	=	SYM
ejpam-4479	68	2	f	f	X
ejpam-4479	68	3	(	(	PUNCT
ejpam-4479	68	4	e	e	NOUN
ejpam-4479	68	5	)	)	PUNCT
ejpam-4479	68	6	∩g(e	∩g(e	PROPN
ejpam-4479	68	7	)	)	PUNCT
ejpam-4479	68	8	,	,	PUNCT
ejpam-4479	68	9	for	for	ADP
ejpam-4479	68	10	all	all	DET
ejpam-4479	68	11	e	e	PROPN
ejpam-4479	68	12	∈	∈	PROPN
ejpam-4479	68	13	c.	c.	NOUN
ejpam-4479	68	14	in	in	ADP
ejpam-4479	68	15	this	this	DET
ejpam-4479	68	16	case	case	NOUN
ejpam-4479	68	17	,	,	PUNCT
ejpam-4479	68	18	we	we	PRON
ejpam-4479	68	19	write	write	VERB
ejpam-4479	68	20	(	(	PUNCT
ejpam-4479	68	21	f	f	X
ejpam-4479	68	22	,	,	PUNCT
ejpam-4479	68	23	a	a	PRON
ejpam-4479	68	24	)	)	PUNCT
ejpam-4479	68	25	∼	∼	NOUN
ejpam-4479	68	26	∩	∩	NOUN
ejpam-4479	68	27	(	(	PUNCT
ejpam-4479	68	28	g	g	PROPN
ejpam-4479	68	29	,	,	PUNCT
ejpam-4479	68	30	b	b	NOUN
ejpam-4479	68	31	)	)	PUNCT
ejpam-4479	68	32	=	=	SYM
ejpam-4479	68	33	(	(	PUNCT
ejpam-4479	68	34	h	h	NOUN
ejpam-4479	68	35	,	,	PUNCT
ejpam-4479	68	36	c	c	NOUN
ejpam-4479	68	37	)	)	PUNCT
ejpam-4479	68	38	.	.	PUNCT
ejpam-4479	69	1	definition	definition	NOUN
ejpam-4479	69	2	7	7	NUM
ejpam-4479	69	3	.	.	PUNCT
ejpam-4479	70	1	[	[	X
ejpam-4479	70	2	5	5	NUM
ejpam-4479	70	3	]	]	X
ejpam-4479	70	4	let	let	VERB
ejpam-4479	70	5	(	(	PUNCT
ejpam-4479	70	6	f	f	X
ejpam-4479	70	7	,	,	PUNCT
ejpam-4479	70	8	a	a	PRON
ejpam-4479	70	9	)	)	PUNCT
ejpam-4479	70	10	and	and	CCONJ
ejpam-4479	70	11	(	(	PUNCT
ejpam-4479	70	12	g	g	NOUN
ejpam-4479	70	13	,	,	PUNCT
ejpam-4479	70	14	b	b	NOUN
ejpam-4479	70	15	)	)	PUNCT
ejpam-4479	70	16	be	be	AUX
ejpam-4479	70	17	two	two	NUM
ejpam-4479	70	18	soft	soft	ADJ
ejpam-4479	70	19	sets	set	NOUN
ejpam-4479	70	20	over	over	ADP
ejpam-4479	70	21	a	a	DET
ejpam-4479	70	22	common	common	ADJ
ejpam-4479	70	23	universe	universe	NOUN
ejpam-4479	70	24	u	u	NOUN
ejpam-4479	70	25	.	.	PUNCT
ejpam-4479	71	1	then	then	ADV
ejpam-4479	71	2	the	the	DET
ejpam-4479	71	3	union	union	NOUN
ejpam-4479	71	4	of	of	ADP
ejpam-4479	71	5	(	(	PUNCT
ejpam-4479	71	6	f	f	X
ejpam-4479	71	7	,	,	PUNCT
ejpam-4479	71	8	a	a	PRON
ejpam-4479	71	9	)	)	PUNCT
ejpam-4479	71	10	and	and	CCONJ
ejpam-4479	71	11	(	(	PUNCT
ejpam-4479	71	12	g	g	NOUN
ejpam-4479	71	13	,	,	PUNCT
ejpam-4479	71	14	b	b	NOUN
ejpam-4479	71	15	)	)	PUNCT
ejpam-4479	71	16	is	be	AUX
ejpam-4479	71	17	defined	define	VERB
ejpam-4479	71	18	to	to	PART
ejpam-4479	71	19	be	be	AUX
ejpam-4479	71	20	a	a	DET
ejpam-4479	71	21	soft	soft	ADJ
ejpam-4479	71	22	set	set	NOUN
ejpam-4479	71	23	(	(	PUNCT
ejpam-4479	71	24	h	h	NOUN
ejpam-4479	71	25	,	,	PUNCT
ejpam-4479	71	26	c	c	NOUN
ejpam-4479	71	27	)	)	PUNCT
ejpam-4479	71	28	satisfying	satisfy	VERB
ejpam-4479	71	29	the	the	DET
ejpam-4479	71	30	following	follow	VERB
ejpam-4479	71	31	conditions	condition	NOUN
ejpam-4479	71	32	:	:	PUNCT
ejpam-4479	71	33	(	(	PUNCT
ejpam-4479	71	34	i	i	NOUN
ejpam-4479	71	35	)	)	PUNCT
ejpam-4479	71	36	c	c	PROPN
ejpam-4479	72	1	=	=	PUNCT
ejpam-4479	72	2	a	a	PRON
ejpam-4479	72	3	∪b	∪b	NOUN
ejpam-4479	72	4	;	;	PUNCT
ejpam-4479	72	5	(	(	PUNCT
ejpam-4479	72	6	ii	ii	NOUN
ejpam-4479	72	7	)	)	PUNCT
ejpam-4479	72	8	for	for	ADP
ejpam-4479	72	9	all	all	DET
ejpam-4479	72	10	e	e	PROPN
ejpam-4479	72	11	∈	∈	PROPN
ejpam-4479	72	12	c	c	X
ejpam-4479	72	13	,	,	PUNCT
ejpam-4479	72	14	h(e	h(e	PROPN
ejpam-4479	72	15	)	)	PUNCT
ejpam-4479	73	1	=	=	PUNCT
ejpam-4479	74	1			ADJ
ejpam-4479	74	2	f	f	X
ejpam-4479	74	3	(	(	PUNCT
ejpam-4479	74	4	e	e	NOUN
ejpam-4479	74	5	)	)	PUNCT
ejpam-4479	74	6	,	,	PUNCT
ejpam-4479	74	7	if	if	SCONJ
ejpam-4479	74	8	e	e	PROPN
ejpam-4479	74	9	∈	∈	PROPN
ejpam-4479	74	10	a	a	DET
ejpam-4479	74	11	\b	\b	ADJ
ejpam-4479	74	12	g(e	g(e	PROPN
ejpam-4479	74	13	)	)	PUNCT
ejpam-4479	74	14	,	,	PUNCT
ejpam-4479	74	15	if	if	SCONJ
ejpam-4479	74	16	e	e	PROPN
ejpam-4479	74	17	∈	∈	PROPN
ejpam-4479	74	18	b	b	PROPN
ejpam-4479	74	19	\a	\a	VERB
ejpam-4479	74	20	f	f	NOUN
ejpam-4479	74	21	(	(	PUNCT
ejpam-4479	74	22	e	e	NOUN
ejpam-4479	74	23	)	)	PUNCT
ejpam-4479	74	24	∪g(e	∪g(e	NOUN
ejpam-4479	74	25	)	)	PUNCT
ejpam-4479	74	26	,	,	PUNCT
ejpam-4479	74	27	if	if	SCONJ
ejpam-4479	74	28	e	e	PROPN
ejpam-4479	74	29	∈	∈	VERB
ejpam-4479	74	30	a	a	DET
ejpam-4479	74	31	∩b	∩b	NOUN
ejpam-4479	74	32	.	.	PUNCT
ejpam-4479	75	1	in	in	ADP
ejpam-4479	75	2	this	this	DET
ejpam-4479	75	3	case	case	NOUN
ejpam-4479	75	4	,	,	PUNCT
ejpam-4479	75	5	we	we	PRON
ejpam-4479	75	6	write	write	VERB
ejpam-4479	75	7	(	(	PUNCT
ejpam-4479	75	8	f	f	X
ejpam-4479	75	9	,	,	PUNCT
ejpam-4479	75	10	a	a	PRON
ejpam-4479	75	11	)	)	PUNCT
ejpam-4479	75	12	∼	∼	NOUN
ejpam-4479	75	13	∪	∪	NOUN
ejpam-4479	75	14	(	(	PUNCT
ejpam-4479	75	15	g	g	NOUN
ejpam-4479	75	16	,	,	PUNCT
ejpam-4479	75	17	b	b	NOUN
ejpam-4479	75	18	)	)	PUNCT
ejpam-4479	75	19	=	=	SYM
ejpam-4479	75	20	(	(	PUNCT
ejpam-4479	75	21	h	h	NOUN
ejpam-4479	75	22	,	,	PUNCT
ejpam-4479	75	23	c	c	NOUN
ejpam-4479	75	24	)	)	PUNCT
ejpam-4479	75	25	.	.	PUNCT
ejpam-4479	76	1	m.k	m.k	PROPN
ejpam-4479	76	2	.	.	PUNCT
ejpam-4479	76	3	engcot	engcot	PROPN
ejpam-4479	76	4	,	,	PUNCT
ejpam-4479	76	5	g.	g.	PROPN
ejpam-4479	76	6	petalcorin	petalcorin	PROPN
ejpam-4479	76	7	/	/	SYM
ejpam-4479	76	8	eur	eur	PROPN
ejpam-4479	76	9	.	.	PUNCT
ejpam-4479	77	1	j.	j.	PROPN
ejpam-4479	77	2	pure	pure	PROPN
ejpam-4479	77	3	appl	appl	PROPN
ejpam-4479	77	4	.	.	PROPN
ejpam-4479	77	5	math	math	PROPN
ejpam-4479	77	6	,	,	PUNCT
ejpam-4479	77	7	15	15	NUM
ejpam-4479	77	8	(	(	PUNCT
ejpam-4479	77	9	4	4	NUM
ejpam-4479	77	10	)	)	PUNCT
ejpam-4479	77	11	(	(	PUNCT
ejpam-4479	77	12	2022	2022	NUM
ejpam-4479	77	13	)	)	PUNCT
ejpam-4479	77	14	,	,	PUNCT
ejpam-4479	77	15	1482	1482	NUM
ejpam-4479	77	16	-	-	SYM
ejpam-4479	77	17	1497	1497	NUM
ejpam-4479	77	18	1485	1485	NUM
ejpam-4479	77	19	definition	definition	NOUN
ejpam-4479	77	20	8	8	NUM
ejpam-4479	77	21	.	.	PUNCT
ejpam-4479	78	1	[	[	X
ejpam-4479	78	2	5	5	X
ejpam-4479	78	3	]	]	PUNCT
ejpam-4479	78	4	if	if	SCONJ
ejpam-4479	78	5	(	(	PUNCT
ejpam-4479	78	6	f	f	X
ejpam-4479	78	7	,	,	PUNCT
ejpam-4479	78	8	a	a	PRON
ejpam-4479	78	9	)	)	PUNCT
ejpam-4479	78	10	and	and	CCONJ
ejpam-4479	78	11	(	(	PUNCT
ejpam-4479	78	12	g	g	NOUN
ejpam-4479	78	13	,	,	PUNCT
ejpam-4479	78	14	b	b	NOUN
ejpam-4479	78	15	)	)	PUNCT
ejpam-4479	78	16	are	be	AUX
ejpam-4479	78	17	two	two	NUM
ejpam-4479	78	18	sets	set	NOUN
ejpam-4479	78	19	over	over	ADP
ejpam-4479	78	20	u	u	NOUN
ejpam-4479	78	21	,	,	PUNCT
ejpam-4479	78	22	then	then	ADV
ejpam-4479	78	23	“	"	PUNCT
ejpam-4479	78	24	(	(	PUNCT
ejpam-4479	78	25	f	f	X
ejpam-4479	78	26	,	,	PUNCT
ejpam-4479	78	27	a	a	PRON
ejpam-4479	78	28	)	)	PUNCT
ejpam-4479	78	29	and	and	CCONJ
ejpam-4479	78	30	(	(	PUNCT
ejpam-4479	78	31	g	g	NOUN
ejpam-4479	78	32	,	,	PUNCT
ejpam-4479	78	33	b	b	NOUN
ejpam-4479	78	34	)	)	PUNCT
ejpam-4479	78	35	”	"	PUNCT
ejpam-4479	78	36	denoted	denote	VERB
ejpam-4479	78	37	by	by	ADP
ejpam-4479	78	38	(	(	PUNCT
ejpam-4479	78	39	f	f	X
ejpam-4479	78	40	,	,	PUNCT
ejpam-4479	78	41	a	a	PRON
ejpam-4479	78	42	)	)	PUNCT
ejpam-4479	78	43	∼	∼	NOUN
ejpam-4479	78	44	∧	∧	NOUN
ejpam-4479	78	45	(	(	PUNCT
ejpam-4479	78	46	g	g	PROPN
ejpam-4479	78	47	,	,	PUNCT
ejpam-4479	78	48	b	b	NOUN
ejpam-4479	78	49	)	)	PUNCT
ejpam-4479	78	50	is	be	AUX
ejpam-4479	78	51	defined	define	VERB
ejpam-4479	78	52	by	by	ADP
ejpam-4479	78	53	(	(	PUNCT
ejpam-4479	78	54	f	f	X
ejpam-4479	78	55	,	,	PUNCT
ejpam-4479	78	56	a	a	PRON
ejpam-4479	78	57	)	)	PUNCT
ejpam-4479	78	58	∼	∼	NOUN
ejpam-4479	78	59	∧	∧	NOUN
ejpam-4479	78	60	(	(	PUNCT
ejpam-4479	78	61	g	g	PROPN
ejpam-4479	78	62	,	,	PUNCT
ejpam-4479	78	63	b	b	NOUN
ejpam-4479	78	64	)	)	PUNCT
ejpam-4479	78	65	=	=	SYM
ejpam-4479	78	66	(	(	PUNCT
ejpam-4479	78	67	h	h	NOUN
ejpam-4479	78	68	,	,	PUNCT
ejpam-4479	78	69	a	a	DET
ejpam-4479	78	70	×	×	PROPN
ejpam-4479	78	71	b	b	NOUN
ejpam-4479	78	72	)	)	PUNCT
ejpam-4479	78	73	where	where	SCONJ
ejpam-4479	78	74	h(α	h(α	ADV
ejpam-4479	78	75	,	,	PUNCT
ejpam-4479	78	76	β	β	X
ejpam-4479	78	77	)	)	PUNCT
ejpam-4479	78	78	=	=	SYM
ejpam-4479	78	79	f	f	PROPN
ejpam-4479	78	80	(	(	PUNCT
ejpam-4479	78	81	α	α	NOUN
ejpam-4479	78	82	)	)	PUNCT
ejpam-4479	78	83	∩g(β	∩g(β	NOUN
ejpam-4479	78	84	)	)	PUNCT
ejpam-4479	78	85	for	for	ADP
ejpam-4479	78	86	all	all	PRON
ejpam-4479	78	87	(	(	PUNCT
ejpam-4479	78	88	α	α	NOUN
ejpam-4479	78	89	,	,	PUNCT
ejpam-4479	78	90	β	β	NOUN
ejpam-4479	78	91	)	)	PUNCT
ejpam-4479	78	92	∈	∈	PROPN
ejpam-4479	78	93	a×b	a×b	PROPN
ejpam-4479	78	94	.	.	PUNCT
ejpam-4479	79	1	definition	definition	NOUN
ejpam-4479	79	2	9	9	NUM
ejpam-4479	79	3	.	.	PUNCT
ejpam-4479	80	1	[	[	X
ejpam-4479	80	2	5	5	NUM
ejpam-4479	80	3	]	]	PUNCT
ejpam-4479	80	4	for	for	ADP
ejpam-4479	80	5	two	two	NUM
ejpam-4479	80	6	soft	soft	ADJ
ejpam-4479	80	7	sets	set	NOUN
ejpam-4479	80	8	(	(	PUNCT
ejpam-4479	80	9	f	f	X
ejpam-4479	80	10	,	,	PUNCT
ejpam-4479	80	11	a	a	PRON
ejpam-4479	80	12	)	)	PUNCT
ejpam-4479	80	13	and	and	CCONJ
ejpam-4479	80	14	(	(	PUNCT
ejpam-4479	80	15	g	g	NOUN
ejpam-4479	80	16	,	,	PUNCT
ejpam-4479	80	17	b	b	NOUN
ejpam-4479	80	18	)	)	PUNCT
ejpam-4479	80	19	over	over	ADP
ejpam-4479	80	20	u	u	PROPN
ejpam-4479	80	21	,	,	PUNCT
ejpam-4479	80	22	then	then	ADV
ejpam-4479	80	23	“	"	PUNCT
ejpam-4479	80	24	(	(	PUNCT
ejpam-4479	80	25	f	f	X
ejpam-4479	80	26	,	,	PUNCT
ejpam-4479	80	27	a	a	NOUN
ejpam-4479	80	28	)	)	PUNCT
ejpam-4479	80	29	or	or	CCONJ
ejpam-4479	80	30	(	(	PUNCT
ejpam-4479	80	31	g	g	NOUN
ejpam-4479	80	32	,	,	PUNCT
ejpam-4479	80	33	b	b	NOUN
ejpam-4479	80	34	)	)	PUNCT
ejpam-4479	80	35	”	"	PUNCT
ejpam-4479	80	36	denoted	denote	VERB
ejpam-4479	80	37	by	by	ADP
ejpam-4479	80	38	(	(	PUNCT
ejpam-4479	80	39	f	f	X
ejpam-4479	80	40	,	,	PUNCT
ejpam-4479	80	41	a	a	PRON
ejpam-4479	80	42	)	)	PUNCT
ejpam-4479	80	43	∼	∼	NOUN
ejpam-4479	80	44	∨	∨	NOUN
ejpam-4479	80	45	(	(	PUNCT
ejpam-4479	80	46	g	g	PROPN
ejpam-4479	80	47	,	,	PUNCT
ejpam-4479	80	48	b	b	NOUN
ejpam-4479	80	49	)	)	PUNCT
ejpam-4479	80	50	is	be	AUX
ejpam-4479	80	51	defined	define	VERB
ejpam-4479	80	52	by	by	ADP
ejpam-4479	80	53	(	(	PUNCT
ejpam-4479	80	54	f	f	X
ejpam-4479	80	55	,	,	PUNCT
ejpam-4479	80	56	a	a	PRON
ejpam-4479	80	57	)	)	PUNCT
ejpam-4479	80	58	∼	∼	NOUN
ejpam-4479	80	59	∨	∨	NOUN
ejpam-4479	80	60	(	(	PUNCT
ejpam-4479	80	61	g	g	PROPN
ejpam-4479	80	62	,	,	PUNCT
ejpam-4479	80	63	b	b	NOUN
ejpam-4479	80	64	)	)	PUNCT
ejpam-4479	80	65	=	=	SYM
ejpam-4479	80	66	(	(	PUNCT
ejpam-4479	80	67	h	h	NOUN
ejpam-4479	80	68	,	,	PUNCT
ejpam-4479	80	69	a	a	DET
ejpam-4479	80	70	×	×	PROPN
ejpam-4479	80	71	b	b	NOUN
ejpam-4479	80	72	)	)	PUNCT
ejpam-4479	80	73	where	where	SCONJ
ejpam-4479	80	74	h(α	h(α	ADV
ejpam-4479	80	75	,	,	PUNCT
ejpam-4479	80	76	β	β	X
ejpam-4479	80	77	)	)	PUNCT
ejpam-4479	80	78	=	=	SYM
ejpam-4479	80	79	f	f	PROPN
ejpam-4479	80	80	(	(	PUNCT
ejpam-4479	80	81	α	α	NOUN
ejpam-4479	80	82	)	)	PUNCT
ejpam-4479	80	83	∪g(β	∪g(β	NOUN
ejpam-4479	80	84	)	)	PUNCT
ejpam-4479	80	85	for	for	ADP
ejpam-4479	80	86	all	all	PRON
ejpam-4479	80	87	(	(	PUNCT
ejpam-4479	80	88	α	α	NOUN
ejpam-4479	80	89	,	,	PUNCT
ejpam-4479	80	90	β	β	NOUN
ejpam-4479	80	91	)	)	PUNCT
ejpam-4479	80	92	∈	∈	PROPN
ejpam-4479	80	93	a×b	a×b	PROPN
ejpam-4479	80	94	.	.	PUNCT
ejpam-4479	81	1	definition	definition	NOUN
ejpam-4479	81	2	10	10	NUM
ejpam-4479	81	3	.	.	PUNCT
ejpam-4479	82	1	[	[	X
ejpam-4479	82	2	5	5	NUM
ejpam-4479	82	3	]	]	PUNCT
ejpam-4479	82	4	for	for	ADP
ejpam-4479	82	5	two	two	NUM
ejpam-4479	82	6	soft	soft	ADJ
ejpam-4479	82	7	sets	set	NOUN
ejpam-4479	82	8	(	(	PUNCT
ejpam-4479	82	9	f	f	X
ejpam-4479	82	10	,	,	PUNCT
ejpam-4479	82	11	a	a	PRON
ejpam-4479	82	12	)	)	PUNCT
ejpam-4479	82	13	and	and	CCONJ
ejpam-4479	82	14	(	(	PUNCT
ejpam-4479	82	15	g	g	NOUN
ejpam-4479	82	16	,	,	PUNCT
ejpam-4479	82	17	b	b	NOUN
ejpam-4479	82	18	)	)	PUNCT
ejpam-4479	82	19	over	over	ADP
ejpam-4479	82	20	u	u	PROPN
ejpam-4479	82	21	,	,	PUNCT
ejpam-4479	82	22	we	we	PRON
ejpam-4479	82	23	say	say	VERB
ejpam-4479	82	24	that	that	SCONJ
ejpam-4479	82	25	(	(	PUNCT
ejpam-4479	82	26	f	f	X
ejpam-4479	82	27	,	,	PUNCT
ejpam-4479	82	28	a	a	PRON
ejpam-4479	82	29	)	)	PUNCT
ejpam-4479	82	30	is	be	AUX
ejpam-4479	82	31	a	a	DET
ejpam-4479	82	32	soft	soft	ADJ
ejpam-4479	82	33	subset	subset	NOUN
ejpam-4479	82	34	of	of	ADP
ejpam-4479	82	35	(	(	PUNCT
ejpam-4479	82	36	g	g	PROPN
ejpam-4479	82	37	,	,	PUNCT
ejpam-4479	82	38	b	b	NOUN
ejpam-4479	82	39	)	)	PUNCT
ejpam-4479	82	40	,	,	PUNCT
ejpam-4479	82	41	denoted	denote	VERB
ejpam-4479	82	42	by	by	ADP
ejpam-4479	82	43	(	(	PUNCT
ejpam-4479	82	44	f	f	X
ejpam-4479	82	45	,	,	PUNCT
ejpam-4479	82	46	a	a	PRON
ejpam-4479	82	47	)	)	PUNCT
ejpam-4479	82	48	∼	∼	NOUN
ejpam-4479	82	49	⊂	⊂	PROPN
ejpam-4479	82	50	(	(	PUNCT
ejpam-4479	82	51	g	g	PROPN
ejpam-4479	82	52	,	,	PUNCT
ejpam-4479	82	53	b	b	NOUN
ejpam-4479	82	54	)	)	PUNCT
ejpam-4479	82	55	,	,	PUNCT
ejpam-4479	82	56	if	if	SCONJ
ejpam-4479	82	57	it	it	PRON
ejpam-4479	82	58	satisfies	satisfy	VERB
ejpam-4479	82	59	:	:	PUNCT
ejpam-4479	82	60	(	(	PUNCT
ejpam-4479	82	61	i	i	NOUN
ejpam-4479	82	62	)	)	PUNCT
ejpam-4479	82	63	a	a	DET
ejpam-4479	82	64	⊆	⊆	NUM
ejpam-4479	82	65	b	b	PROPN
ejpam-4479	82	66	(	(	PUNCT
ejpam-4479	82	67	ii	ii	NOUN
ejpam-4479	82	68	)	)	PUNCT
ejpam-4479	82	69	for	for	ADP
ejpam-4479	82	70	every	every	DET
ejpam-4479	82	71	ϵ	ϵ	PROPN
ejpam-4479	82	72	∈	∈	PROPN
ejpam-4479	82	73	a	a	PRON
ejpam-4479	82	74	,	,	PUNCT
ejpam-4479	82	75	f	f	PROPN
ejpam-4479	82	76	(	(	PUNCT
ejpam-4479	82	77	ϵ	ϵ	X
ejpam-4479	82	78	)	)	PUNCT
ejpam-4479	82	79	=	=	SYM
ejpam-4479	82	80	g(ϵ	g(ϵ	PROPN
ejpam-4479	82	81	)	)	PUNCT
ejpam-4479	82	82	.	.	PUNCT
ejpam-4479	83	1	definition	definition	NOUN
ejpam-4479	83	2	11	11	NUM
ejpam-4479	83	3	.	.	PUNCT
ejpam-4479	84	1	[	[	X
ejpam-4479	84	2	6	6	NUM
ejpam-4479	84	3	]	]	PUNCT
ejpam-4479	84	4	let	let	VERB
ejpam-4479	84	5	(	(	PUNCT
ejpam-4479	84	6	f	f	X
ejpam-4479	84	7	,	,	PUNCT
ejpam-4479	84	8	a	a	PRON
ejpam-4479	84	9	)	)	PUNCT
ejpam-4479	84	10	∈	∈	PROPN
ejpam-4479	84	11	s(u	s(u	PROPN
ejpam-4479	84	12	)	)	PUNCT
ejpam-4479	84	13	and	and	CCONJ
ejpam-4479	84	14	τ	τ	PROPN
ejpam-4479	84	15	⊆	⊆	NUM
ejpam-4479	84	16	u	u	NOUN
ejpam-4479	84	17	.	.	PUNCT
ejpam-4479	85	1	then	then	ADV
ejpam-4479	85	2	the	the	DET
ejpam-4479	85	3	τ	τ	PROPN
ejpam-4479	85	4	-exclusive	-exclusive	ADJ
ejpam-4479	85	5	set	set	NOUN
ejpam-4479	85	6	of	of	ADP
ejpam-4479	85	7	(	(	PUNCT
ejpam-4479	85	8	f	f	X
ejpam-4479	85	9	,	,	PUNCT
ejpam-4479	85	10	a	a	PRON
ejpam-4479	85	11	)	)	PUNCT
ejpam-4479	85	12	is	be	AUX
ejpam-4479	85	13	defined	define	VERB
ejpam-4479	85	14	to	to	PART
ejpam-4479	85	15	be	be	AUX
ejpam-4479	85	16	the	the	DET
ejpam-4479	85	17	set	set	NOUN
ejpam-4479	85	18	e((f	e((f	NOUN
ejpam-4479	85	19	,	,	PUNCT
ejpam-4479	85	20	a	a	PRON
ejpam-4479	85	21	)	)	PUNCT
ejpam-4479	85	22	,	,	PUNCT
ejpam-4479	85	23	τ	τ	PROPN
ejpam-4479	85	24	)	)	PUNCT
ejpam-4479	85	25	=	=	PRON
ejpam-4479	86	1	{	{	PUNCT
ejpam-4479	86	2	x	x	PUNCT
ejpam-4479	86	3	∈	∈	PROPN
ejpam-4479	86	4	a	a	PRON
ejpam-4479	86	5	:	:	PUNCT
ejpam-4479	86	6	fa(x	fa(x	NOUN
ejpam-4479	86	7	)	)	PUNCT
ejpam-4479	86	8	⊆	⊆	NUM
ejpam-4479	86	9	τ	τ	X
ejpam-4479	86	10	}	}	PUNCT
ejpam-4479	86	11	.	.	PUNCT
ejpam-4479	87	1	from	from	ADP
ejpam-4479	87	2	definition	definition	NOUN
ejpam-4479	87	3	11	11	NUM
ejpam-4479	87	4	,	,	PUNCT
ejpam-4479	87	5	we	we	PRON
ejpam-4479	87	6	have	have	VERB
ejpam-4479	87	7	the	the	DET
ejpam-4479	87	8	following	follow	VERB
ejpam-4479	87	9	properties	property	NOUN
ejpam-4479	87	10	[	[	X
ejpam-4479	87	11	6	6	NUM
ejpam-4479	87	12	]	]	SYM
ejpam-4479	87	13	:	:	PUNCT
ejpam-4479	87	14	1	1	X
ejpam-4479	87	15	.	.	X
ejpam-4479	88	1	e((f	e((f	NOUN
ejpam-4479	88	2	,	,	PUNCT
ejpam-4479	88	3	a	a	PRON
ejpam-4479	88	4	)	)	PUNCT
ejpam-4479	88	5	,	,	PUNCT
ejpam-4479	88	6	u	u	NOUN
ejpam-4479	88	7	)	)	PUNCT
ejpam-4479	88	8	=	=	SYM
ejpam-4479	88	9	a	a	PRON
ejpam-4479	88	10	,	,	PUNCT
ejpam-4479	88	11	2	2	NUM
ejpam-4479	88	12	.	.	NUM
ejpam-4479	88	13	fa(x	fa(x	PROPN
ejpam-4479	88	14	)	)	PUNCT
ejpam-4479	88	15	=	=	SYM
ejpam-4479	88	16	∩{τ	∩{τ	NOUN
ejpam-4479	88	17	⊆	⊆	NUM
ejpam-4479	88	18	u	u	NOUN
ejpam-4479	88	19	:	:	PUNCT
ejpam-4479	88	20	x	x	SYM
ejpam-4479	88	21	∈	∈	PROPN
ejpam-4479	88	22	e((f	e((f	NOUN
ejpam-4479	88	23	,	,	PUNCT
ejpam-4479	88	24	a	a	PRON
ejpam-4479	88	25	)	)	PUNCT
ejpam-4479	88	26	,	,	PUNCT
ejpam-4479	88	27	τ	τ	PROPN
ejpam-4479	88	28	)	)	PUNCT
ejpam-4479	88	29	}	}	PUNCT
ejpam-4479	88	30	,	,	PUNCT
ejpam-4479	88	31	∀x	∀x	VERB
ejpam-4479	88	32	∈	∈	PROPN
ejpam-4479	88	33	a	a	PRON
ejpam-4479	88	34	,	,	PUNCT
ejpam-4479	88	35	and	and	CCONJ
ejpam-4479	88	36	3	3	X
ejpam-4479	88	37	.	.	NOUN
ejpam-4479	88	38	τ1	τ1	ADP
ejpam-4479	88	39	⊆	⊆	NUM
ejpam-4479	88	40	τ2	τ2	NOUN
ejpam-4479	88	41	implies	imply	VERB
ejpam-4479	88	42	e((f	e((f	NOUN
ejpam-4479	88	43	,	,	PUNCT
ejpam-4479	88	44	a	a	PRON
ejpam-4479	88	45	)	)	PUNCT
ejpam-4479	88	46	,	,	PUNCT
ejpam-4479	88	47	τ1	τ1	NOUN
ejpam-4479	88	48	)	)	PUNCT
ejpam-4479	88	49	⊆	⊆	NUM
ejpam-4479	88	50	e((f	e((f	NOUN
ejpam-4479	88	51	,	,	PUNCT
ejpam-4479	88	52	a	a	PRON
ejpam-4479	88	53	)	)	PUNCT
ejpam-4479	88	54	,	,	PUNCT
ejpam-4479	88	55	τ2	τ2	NOUN
ejpam-4479	88	56	)	)	PUNCT
ejpam-4479	88	57	,	,	PUNCT
ejpam-4479	88	58	∀τ1	∀τ1	PUNCT
ejpam-4479	88	59	,	,	PUNCT
ejpam-4479	88	60	τ2	τ2	VERB
ejpam-4479	88	61	⊆	⊆	NUM
ejpam-4479	88	62	u	u	NOUN
ejpam-4479	88	63	.	.	PUNCT
ejpam-4479	89	1	3	3	X
ejpam-4479	89	2	.	.	X
ejpam-4479	89	3	soft	soft	ADJ
ejpam-4479	89	4	hyper	hyper	ADJ
ejpam-4479	89	5	gr	gr	NOUN
ejpam-4479	89	6	-	-	PUNCT
ejpam-4479	89	7	algebra	algebra	NOUN
ejpam-4479	89	8	let	let	VERB
ejpam-4479	89	9	h	h	NOUN
ejpam-4479	89	10	be	be	AUX
ejpam-4479	89	11	a	a	DET
ejpam-4479	89	12	hyper	hyper	ADJ
ejpam-4479	89	13	gr	gr	NOUN
ejpam-4479	89	14	-	-	PUNCT
ejpam-4479	89	15	algebra	algebra	NOUN
ejpam-4479	89	16	,	,	PUNCT
ejpam-4479	89	17	a	a	DET
ejpam-4479	89	18	a	a	DET
ejpam-4479	89	19	nonempty	nonempty	ADJ
ejpam-4479	89	20	set	set	NOUN
ejpam-4479	89	21	,	,	PUNCT
ejpam-4479	89	22	and	and	CCONJ
ejpam-4479	89	23	r̊	r̊	PRON
ejpam-4479	89	24	an	an	DET
ejpam-4479	89	25	arbitrary	arbitrary	ADJ
ejpam-4479	89	26	binary	binary	ADJ
ejpam-4479	89	27	relation	relation	NOUN
ejpam-4479	89	28	between	between	ADP
ejpam-4479	89	29	an	an	DET
ejpam-4479	89	30	element	element	NOUN
ejpam-4479	89	31	of	of	ADP
ejpam-4479	89	32	a	a	PRON
ejpam-4479	89	33	and	and	CCONJ
ejpam-4479	89	34	an	an	DET
ejpam-4479	89	35	element	element	NOUN
ejpam-4479	89	36	of	of	ADP
ejpam-4479	89	37	p	p	NOUN
ejpam-4479	89	38	(	(	PUNCT
ejpam-4479	89	39	h	h	NOUN
ejpam-4479	89	40	)	)	PUNCT
ejpam-4479	89	41	,	,	PUNCT
ejpam-4479	89	42	that	that	ADV
ejpam-4479	89	43	is	be	AUX
ejpam-4479	89	44	,	,	PUNCT
ejpam-4479	89	45	r̊	r̊	PROPN
ejpam-4479	89	46	⊆	⊆	NUM
ejpam-4479	89	47	a	a	DET
ejpam-4479	89	48	×	×	NOUN
ejpam-4479	89	49	p	p	NOUN
ejpam-4479	89	50	(	(	PUNCT
ejpam-4479	89	51	h	h	NOUN
ejpam-4479	89	52	)	)	PUNCT
ejpam-4479	89	53	.	.	PUNCT
ejpam-4479	90	1	a	a	DET
ejpam-4479	90	2	set	set	NOUN
ejpam-4479	90	3	-	-	PUNCT
ejpam-4479	90	4	valued	value	VERB
ejpam-4479	90	5	function	function	NOUN
ejpam-4479	90	6	f	f	NOUN
ejpam-4479	90	7	:	:	PUNCT
ejpam-4479	90	8	a	a	DET
ejpam-4479	90	9	→	→	SYM
ejpam-4479	90	10	p	p	X
ejpam-4479	90	11	(	(	PUNCT
ejpam-4479	90	12	h	h	NOUN
ejpam-4479	90	13	)	)	PUNCT
ejpam-4479	90	14	can	can	AUX
ejpam-4479	90	15	be	be	AUX
ejpam-4479	90	16	defined	define	VERB
ejpam-4479	90	17	as	as	ADP
ejpam-4479	90	18	f	f	PROPN
ejpam-4479	90	19	(	(	PUNCT
ejpam-4479	90	20	a	a	NOUN
ejpam-4479	90	21	)	)	PUNCT
ejpam-4479	90	22	=	=	PUNCT
ejpam-4479	91	1	⋃	⋃	PROPN
ejpam-4479	91	2	b	b	NOUN
ejpam-4479	91	3	where	where	SCONJ
ejpam-4479	91	4	b	b	X
ejpam-4479	91	5	⊂	⊂	PROPN
ejpam-4479	91	6	h	h	PROPN
ejpam-4479	91	7	and	and	CCONJ
ejpam-4479	91	8	ar̊b	ar̊b	PROPN
ejpam-4479	91	9	,	,	PUNCT
ejpam-4479	91	10	for	for	ADP
ejpam-4479	91	11	all	all	DET
ejpam-4479	91	12	a	a	DET
ejpam-4479	91	13	∈	∈	NOUN
ejpam-4479	91	14	a.	a.	NOUN
ejpam-4479	91	15	then	then	ADV
ejpam-4479	91	16	(	(	PUNCT
ejpam-4479	91	17	f	f	X
ejpam-4479	91	18	,	,	PUNCT
ejpam-4479	91	19	a	a	PRON
ejpam-4479	91	20	)	)	PUNCT
ejpam-4479	91	21	is	be	AUX
ejpam-4479	91	22	then	then	ADV
ejpam-4479	91	23	a	a	DET
ejpam-4479	91	24	soft	soft	ADJ
ejpam-4479	91	25	set	set	NOUN
ejpam-4479	91	26	over	over	ADP
ejpam-4479	91	27	h.	h.	NOUN
ejpam-4479	91	28	definition	definition	NOUN
ejpam-4479	91	29	12	12	NUM
ejpam-4479	91	30	.	.	PUNCT
ejpam-4479	92	1	let	let	AUX
ejpam-4479	92	2	(	(	PUNCT
ejpam-4479	92	3	f	f	X
ejpam-4479	92	4	,	,	PUNCT
ejpam-4479	92	5	a	a	PRON
ejpam-4479	92	6	)	)	PUNCT
ejpam-4479	92	7	be	be	AUX
ejpam-4479	92	8	a	a	DET
ejpam-4479	92	9	soft	soft	ADJ
ejpam-4479	92	10	set	set	NOUN
ejpam-4479	92	11	over	over	ADP
ejpam-4479	92	12	a	a	DET
ejpam-4479	92	13	hyper	hyper	ADJ
ejpam-4479	92	14	gr	gr	NOUN
ejpam-4479	92	15	-	-	PUNCT
ejpam-4479	92	16	algebra	algebra	NOUN
ejpam-4479	92	17	h.	h.	NOUN
ejpam-4479	92	18	then	then	ADV
ejpam-4479	92	19	(	(	PUNCT
ejpam-4479	92	20	f	f	X
ejpam-4479	92	21	,	,	PUNCT
ejpam-4479	92	22	a	a	PRON
ejpam-4479	92	23	)	)	PUNCT
ejpam-4479	92	24	is	be	AUX
ejpam-4479	92	25	called	call	VERB
ejpam-4479	92	26	a	a	DET
ejpam-4479	92	27	soft	soft	ADJ
ejpam-4479	92	28	hyper	hyper	ADJ
ejpam-4479	92	29	gr	gr	NOUN
ejpam-4479	92	30	-	-	NOUN
ejpam-4479	92	31	algebra	algebra	NOUN
ejpam-4479	92	32	over	over	ADP
ejpam-4479	92	33	h	h	NOUN
ejpam-4479	92	34	if	if	SCONJ
ejpam-4479	92	35	f	f	PROPN
ejpam-4479	92	36	(	(	PUNCT
ejpam-4479	92	37	a	a	NOUN
ejpam-4479	92	38	)	)	PUNCT
ejpam-4479	92	39	=	=	SYM
ejpam-4479	92	40	⋃	⋃	NOUN
ejpam-4479	92	41	b⊂h	b⊂h	NOUN
ejpam-4479	92	42	,	,	PUNCT
ejpam-4479	92	43	ar̊b	ar̊b	PROPN
ejpam-4479	92	44	b	b	PROPN
ejpam-4479	92	45	is	be	AUX
ejpam-4479	92	46	a	a	DET
ejpam-4479	92	47	hyper	hyper	ADJ
ejpam-4479	92	48	gr	gr	NOUN
ejpam-4479	92	49	-	-	NOUN
ejpam-4479	92	50	algebra	algebra	NOUN
ejpam-4479	92	51	of	of	ADP
ejpam-4479	92	52	h	h	NOUN
ejpam-4479	92	53	,	,	PUNCT
ejpam-4479	92	54	for	for	ADP
ejpam-4479	92	55	all	all	DET
ejpam-4479	92	56	a	a	DET
ejpam-4479	92	57	∈	∈	PROPN
ejpam-4479	92	58	a.	a.	NOUN
ejpam-4479	92	59	example	example	NOUN
ejpam-4479	92	60	4	4	X
ejpam-4479	92	61	.	.	X
ejpam-4479	93	1	consider	consider	VERB
ejpam-4479	93	2	h	h	NOUN
ejpam-4479	93	3	=	=	PRON
ejpam-4479	93	4	{	{	PUNCT
ejpam-4479	93	5	0	0	NUM
ejpam-4479	93	6	,	,	PUNCT
ejpam-4479	93	7	1	1	NUM
ejpam-4479	93	8	,	,	PUNCT
ejpam-4479	93	9	2	2	NUM
ejpam-4479	93	10	,	,	PUNCT
ejpam-4479	93	11	3	3	NUM
ejpam-4479	93	12	}	}	PUNCT
ejpam-4479	93	13	defined	define	VERB
ejpam-4479	93	14	by	by	ADP
ejpam-4479	93	15	the	the	DET
ejpam-4479	93	16	cayley	cayley	ADJ
ejpam-4479	93	17	table	table	NOUN
ejpam-4479	93	18	below	below	ADV
ejpam-4479	93	19	.	.	PUNCT
ejpam-4479	94	1	⊛	⊛	NUM
ejpam-4479	95	1	0	0	NUM
ejpam-4479	95	2	1	1	NUM
ejpam-4479	95	3	2	2	NUM
ejpam-4479	95	4	3	3	NUM
ejpam-4479	95	5	0	0	NUM
ejpam-4479	95	6	{	{	PUNCT
ejpam-4479	95	7	0,1	0,1	NUM
ejpam-4479	95	8	}	}	PUNCT
ejpam-4479	95	9	{	{	PUNCT
ejpam-4479	95	10	0,1	0,1	NOUN
ejpam-4479	95	11	}	}	PUNCT
ejpam-4479	95	12	{	{	PUNCT
ejpam-4479	95	13	0,1	0,1	NOUN
ejpam-4479	95	14	}	}	PUNCT
ejpam-4479	95	15	{	{	PUNCT
ejpam-4479	95	16	0,1	0,1	NOUN
ejpam-4479	95	17	}	}	SYM
ejpam-4479	95	18	1	1	NUM
ejpam-4479	95	19	{	{	PUNCT
ejpam-4479	95	20	1	1	NUM
ejpam-4479	95	21	}	}	PUNCT
ejpam-4479	95	22	{	{	PUNCT
ejpam-4479	95	23	0,1	0,1	NOUN
ejpam-4479	95	24	}	}	PUNCT
ejpam-4479	95	25	{	{	PUNCT
ejpam-4479	95	26	0,1	0,1	NOUN
ejpam-4479	95	27	}	}	PUNCT
ejpam-4479	95	28	{	{	PUNCT
ejpam-4479	95	29	0,1	0,1	NOUN
ejpam-4479	95	30	}	}	SYM
ejpam-4479	95	31	2	2	NUM
ejpam-4479	95	32	{	{	PUNCT
ejpam-4479	95	33	0,2	0,2	NUM
ejpam-4479	95	34	}	}	PUNCT
ejpam-4479	95	35	{	{	PUNCT
ejpam-4479	95	36	0,2	0,2	NUM
ejpam-4479	95	37	}	}	PUNCT
ejpam-4479	95	38	{	{	PUNCT
ejpam-4479	95	39	0,1,2	0,1,2	NOUN
ejpam-4479	95	40	}	}	PUNCT
ejpam-4479	95	41	{	{	PUNCT
ejpam-4479	95	42	0,1,2	0,1,2	NOUN
ejpam-4479	95	43	}	}	SYM
ejpam-4479	95	44	3	3	NUM
ejpam-4479	95	45	{	{	PUNCT
ejpam-4479	95	46	3	3	NUM
ejpam-4479	95	47	}	}	PUNCT
ejpam-4479	95	48	{	{	PUNCT
ejpam-4479	95	49	0,1,3	0,1,3	NOUN
ejpam-4479	95	50	}	}	PUNCT
ejpam-4479	95	51	{	{	PUNCT
ejpam-4479	95	52	0,1,3	0,1,3	NOUN
ejpam-4479	95	53	}	}	PUNCT
ejpam-4479	95	54	{	{	PUNCT
ejpam-4479	95	55	0,1,3	0,1,3	NOUN
ejpam-4479	95	56	}	}	PUNCT
ejpam-4479	95	57	.	.	PUNCT
ejpam-4479	96	1	m.k	m.k	PROPN
ejpam-4479	96	2	.	.	PUNCT
ejpam-4479	96	3	engcot	engcot	PROPN
ejpam-4479	96	4	,	,	PUNCT
ejpam-4479	96	5	g.	g.	PROPN
ejpam-4479	96	6	petalcorin	petalcorin	PROPN
ejpam-4479	96	7	/	/	SYM
ejpam-4479	96	8	eur	eur	PROPN
ejpam-4479	96	9	.	.	PUNCT
ejpam-4479	97	1	j.	j.	PROPN
ejpam-4479	97	2	pure	pure	PROPN
ejpam-4479	97	3	appl	appl	PROPN
ejpam-4479	97	4	.	.	PROPN
ejpam-4479	97	5	math	math	PROPN
ejpam-4479	97	6	,	,	PUNCT
ejpam-4479	97	7	15	15	NUM
ejpam-4479	97	8	(	(	PUNCT
ejpam-4479	97	9	4	4	NUM
ejpam-4479	97	10	)	)	PUNCT
ejpam-4479	97	11	(	(	PUNCT
ejpam-4479	97	12	2022	2022	NUM
ejpam-4479	97	13	)	)	PUNCT
ejpam-4479	97	14	,	,	PUNCT
ejpam-4479	97	15	1482	1482	NUM
ejpam-4479	97	16	-	-	SYM
ejpam-4479	97	17	1497	1497	NUM
ejpam-4479	97	18	1486	1486	NUM
ejpam-4479	97	19	by	by	ADP
ejpam-4479	97	20	definition	definition	NOUN
ejpam-4479	97	21	1	1	NUM
ejpam-4479	97	22	(	(	PUNCT
ejpam-4479	97	23	h;⊛	h;⊛	NUM
ejpam-4479	97	24	,	,	PUNCT
ejpam-4479	97	25	0	0	NUM
ejpam-4479	97	26	)	)	PUNCT
ejpam-4479	97	27	is	be	AUX
ejpam-4479	97	28	a	a	DET
ejpam-4479	97	29	hyper	hyper	ADJ
ejpam-4479	97	30	gr	gr	NOUN
ejpam-4479	97	31	-	-	NOUN
ejpam-4479	97	32	algebra	algebra	NOUN
ejpam-4479	97	33	.	.	PUNCT
ejpam-4479	98	1	we	we	PRON
ejpam-4479	98	2	will	will	AUX
ejpam-4479	98	3	verify	verify	VERB
ejpam-4479	98	4	if	if	SCONJ
ejpam-4479	98	5	(	(	PUNCT
ejpam-4479	98	6	h;⊛	h;⊛	NUM
ejpam-4479	98	7	,	,	PUNCT
ejpam-4479	98	8	0	0	NUM
ejpam-4479	98	9	)	)	PUNCT
ejpam-4479	98	10	is	be	AUX
ejpam-4479	98	11	a	a	DET
ejpam-4479	98	12	soft	soft	ADJ
ejpam-4479	98	13	hyper	hyper	ADJ
ejpam-4479	98	14	gr	gr	NOUN
ejpam-4479	98	15	-	-	NOUN
ejpam-4479	98	16	algebra	algebra	NOUN
ejpam-4479	98	17	.	.	PUNCT
ejpam-4479	99	1	let	let	VERB
ejpam-4479	99	2	a	a	DET
ejpam-4479	99	3	=	=	NOUN
ejpam-4479	99	4	h	h	NOUN
ejpam-4479	99	5	and	and	CCONJ
ejpam-4479	99	6	define	define	VERB
ejpam-4479	99	7	a	a	DET
ejpam-4479	99	8	relation	relation	NOUN
ejpam-4479	99	9	r̊	r̊	PRON
ejpam-4479	99	10	such	such	ADJ
ejpam-4479	99	11	that	that	SCONJ
ejpam-4479	99	12	ar̊b	ar̊b	PROPN
ejpam-4479	99	13	if	if	SCONJ
ejpam-4479	99	14	and	and	CCONJ
ejpam-4479	99	15	only	only	ADV
ejpam-4479	99	16	if	if	SCONJ
ejpam-4479	99	17	b	b	X
ejpam-4479	99	18	=	=	SYM
ejpam-4479	99	19	an	an	PROPN
ejpam-4479	99	20	,	,	PUNCT
ejpam-4479	99	21	where	where	SCONJ
ejpam-4479	99	22	b	b	X
ejpam-4479	99	23	⊂	⊂	PROPN
ejpam-4479	99	24	h	h	PROPN
ejpam-4479	99	25	and	and	CCONJ
ejpam-4479	99	26	a	a	DET
ejpam-4479	99	27	∈	∈	PROPN
ejpam-4479	99	28	a	a	PRON
ejpam-4479	99	29	,	,	PUNCT
ejpam-4479	99	30	let	let	VERB
ejpam-4479	99	31	f	f	PRON
ejpam-4479	99	32	:	:	PUNCT
ejpam-4479	99	33	a	a	DET
ejpam-4479	99	34	→	→	SYM
ejpam-4479	99	35	p	p	X
ejpam-4479	99	36	(	(	PUNCT
ejpam-4479	99	37	h	h	NOUN
ejpam-4479	99	38	)	)	PUNCT
ejpam-4479	99	39	be	be	AUX
ejpam-4479	99	40	a	a	DET
ejpam-4479	99	41	set	set	NOUN
ejpam-4479	99	42	-	-	PUNCT
ejpam-4479	99	43	valued	value	VERB
ejpam-4479	99	44	function	function	NOUN
ejpam-4479	99	45	defined	define	VERB
ejpam-4479	99	46	as	as	SCONJ
ejpam-4479	99	47	follows	follow	VERB
ejpam-4479	99	48	:	:	PUNCT
ejpam-4479	99	49	f	f	X
ejpam-4479	99	50	(	(	PUNCT
ejpam-4479	99	51	a	a	NOUN
ejpam-4479	99	52	)	)	PUNCT
ejpam-4479	99	53	=	=	SYM
ejpam-4479	99	54	⋃	⋃	NOUN
ejpam-4479	99	55	b⊂h	b⊂h	NOUN
ejpam-4479	99	56	,	,	PUNCT
ejpam-4479	99	57	arb⇔b	arb⇔b	NOUN
ejpam-4479	99	58	=	=	NOUN
ejpam-4479	99	59	an	an	DET
ejpam-4479	99	60	b	b	NOUN
ejpam-4479	99	61	,	,	PUNCT
ejpam-4479	99	62	for	for	ADP
ejpam-4479	99	63	all	all	DET
ejpam-4479	99	64	a	a	DET
ejpam-4479	99	65	∈	∈	PROPN
ejpam-4479	99	66	a	a	PRON
ejpam-4479	99	67	,	,	PUNCT
ejpam-4479	99	68	where	where	SCONJ
ejpam-4479	99	69	an	an	PRON
ejpam-4479	99	70	=	=	X
ejpam-4479	99	71	(	(	PUNCT
ejpam-4479	99	72	(	(	PUNCT
ejpam-4479	99	73	(	(	PUNCT
ejpam-4479	99	74	(	(	PUNCT
ejpam-4479	99	75	a	a	DET
ejpam-4479	99	76	⊛	⊛	NUM
ejpam-4479	99	77	a	a	X
ejpam-4479	99	78	)	)	PUNCT
ejpam-4479	99	79	⊛	⊛	NUM
ejpam-4479	99	80	a	a	DET
ejpam-4479	99	81	)	)	PUNCT
ejpam-4479	99	82	⊛	⊛	NUM
ejpam-4479	99	83	a	a	PRON
ejpam-4479	99	84	)	)	PUNCT
ejpam-4479	99	85	⊛	⊛	NUM
ejpam-4479	99	86	...	...	PUNCT
ejpam-4479	99	87	⊛	⊛	NUM
ejpam-4479	99	88	a	a	PRON
ejpam-4479	99	89	)	)	PUNCT
ejpam-4479	99	90	.	.	PUNCT
ejpam-4479	100	1	then	then	ADV
ejpam-4479	100	2	f	f	X
ejpam-4479	100	3	(	(	PUNCT
ejpam-4479	100	4	0	0	NUM
ejpam-4479	100	5	)	)	PUNCT
ejpam-4479	100	6	=	=	PRON
ejpam-4479	100	7	{	{	PUNCT
ejpam-4479	100	8	0	0	NUM
ejpam-4479	100	9	,	,	PUNCT
ejpam-4479	100	10	1	1	NUM
ejpam-4479	100	11	}	}	PUNCT
ejpam-4479	100	12	,	,	PUNCT
ejpam-4479	100	13	f	f	PROPN
ejpam-4479	100	14	(	(	PUNCT
ejpam-4479	100	15	1	1	NUM
ejpam-4479	100	16	)	)	PUNCT
ejpam-4479	100	17	=	=	PRON
ejpam-4479	100	18	{	{	PUNCT
ejpam-4479	100	19	0	0	NUM
ejpam-4479	100	20	,	,	PUNCT
ejpam-4479	100	21	1	1	NUM
ejpam-4479	100	22	}	}	PUNCT
ejpam-4479	100	23	,	,	PUNCT
ejpam-4479	100	24	f	f	PROPN
ejpam-4479	100	25	(	(	PUNCT
ejpam-4479	100	26	2	2	NUM
ejpam-4479	100	27	)	)	PUNCT
ejpam-4479	100	28	=	=	NOUN
ejpam-4479	100	29	{	{	PUNCT
ejpam-4479	100	30	0	0	NUM
ejpam-4479	100	31	,	,	PUNCT
ejpam-4479	100	32	1	1	NUM
ejpam-4479	100	33	,	,	PUNCT
ejpam-4479	100	34	2	2	NUM
ejpam-4479	100	35	}	}	PUNCT
ejpam-4479	100	36	and	and	CCONJ
ejpam-4479	100	37	f	f	PROPN
ejpam-4479	100	38	(	(	PUNCT
ejpam-4479	100	39	3	3	X
ejpam-4479	100	40	)	)	PUNCT
ejpam-4479	100	41	=	=	PRON
ejpam-4479	100	42	{	{	PUNCT
ejpam-4479	100	43	0	0	NUM
ejpam-4479	100	44	,	,	PUNCT
ejpam-4479	100	45	1	1	NUM
ejpam-4479	100	46	,	,	PUNCT
ejpam-4479	100	47	3	3	NUM
ejpam-4479	100	48	}	}	PUNCT
ejpam-4479	100	49	.	.	PUNCT
ejpam-4479	101	1	note	note	VERB
ejpam-4479	101	2	that	that	SCONJ
ejpam-4479	101	3	s	s	VERB
ejpam-4479	101	4	is	be	AUX
ejpam-4479	101	5	nonempty	nonempty	ADJ
ejpam-4479	101	6	.	.	PUNCT
ejpam-4479	102	1	let	let	VERB
ejpam-4479	102	2	s	s	PRON
ejpam-4479	102	3	=	=	ADJ
ejpam-4479	102	4	f	f	X
ejpam-4479	102	5	(	(	PUNCT
ejpam-4479	102	6	0	0	NUM
ejpam-4479	102	7	)	)	PUNCT
ejpam-4479	102	8	=	=	SYM
ejpam-4479	102	9	f	f	X
ejpam-4479	102	10	(	(	PUNCT
ejpam-4479	102	11	1	1	NUM
ejpam-4479	102	12	)	)	PUNCT
ejpam-4479	102	13	=	=	PRON
ejpam-4479	102	14	{	{	PUNCT
ejpam-4479	102	15	0	0	NUM
ejpam-4479	102	16	,	,	PUNCT
ejpam-4479	102	17	1	1	NUM
ejpam-4479	102	18	}	}	PUNCT
ejpam-4479	102	19	.	.	PUNCT
ejpam-4479	103	1	then	then	ADV
ejpam-4479	103	2	0	0	NUM
ejpam-4479	103	3	⊛	⊛	ADJ
ejpam-4479	103	4	0	0	NUM
ejpam-4479	104	1	=	=	SYM
ejpam-4479	104	2	0	0	SYM
ejpam-4479	104	3	⊛	⊛	NUM
ejpam-4479	104	4	1	1	NUM
ejpam-4479	104	5	=	=	SYM
ejpam-4479	104	6	1	1	NUM
ejpam-4479	104	7	⊛	⊛	NUM
ejpam-4479	104	8	1	1	NUM
ejpam-4479	104	9	=	=	SYM
ejpam-4479	104	10	{	{	PUNCT
ejpam-4479	104	11	0	0	NUM
ejpam-4479	104	12	,	,	PUNCT
ejpam-4479	104	13	1	1	NUM
ejpam-4479	104	14	}	}	PUNCT
ejpam-4479	104	15	∈	∈	PROPN
ejpam-4479	104	16	s	s	NOUN
ejpam-4479	104	17	and	and	CCONJ
ejpam-4479	104	18	1⊛	1⊛	NUM
ejpam-4479	104	19	0	0	SYM
ejpam-4479	105	1	=	=	SYM
ejpam-4479	105	2	{	{	PUNCT
ejpam-4479	105	3	1	1	NUM
ejpam-4479	105	4	}	}	PUNCT
ejpam-4479	105	5	∈	∈	PROPN
ejpam-4479	105	6	s.	s.	PROPN
ejpam-4479	105	7	thus	thus	ADV
ejpam-4479	105	8	,	,	PUNCT
ejpam-4479	105	9	by	by	ADP
ejpam-4479	105	10	theorem	theorem	NOUN
ejpam-4479	105	11	1	1	NUM
ejpam-4479	105	12	,	,	PUNCT
ejpam-4479	105	13	f	f	PROPN
ejpam-4479	105	14	(	(	PUNCT
ejpam-4479	105	15	0	0	NUM
ejpam-4479	105	16	)	)	PUNCT
ejpam-4479	105	17	=	=	SYM
ejpam-4479	105	18	f	f	X
ejpam-4479	105	19	(	(	PUNCT
ejpam-4479	105	20	1	1	NUM
ejpam-4479	105	21	)	)	PUNCT
ejpam-4479	105	22	is	be	AUX
ejpam-4479	105	23	a	a	DET
ejpam-4479	105	24	hyper	hyper	ADJ
ejpam-4479	105	25	subgr	subgr	NOUN
ejpam-4479	105	26	-	-	PUNCT
ejpam-4479	105	27	algebra	algebra	NOUN
ejpam-4479	105	28	.	.	PUNCT
ejpam-4479	106	1	similarly	similarly	ADV
ejpam-4479	106	2	,	,	PUNCT
ejpam-4479	106	3	f	f	PROPN
ejpam-4479	106	4	(	(	PUNCT
ejpam-4479	106	5	2	2	NUM
ejpam-4479	106	6	)	)	PUNCT
ejpam-4479	106	7	and	and	CCONJ
ejpam-4479	106	8	f	f	PROPN
ejpam-4479	106	9	(	(	PUNCT
ejpam-4479	106	10	3	3	X
ejpam-4479	106	11	)	)	PUNCT
ejpam-4479	106	12	are	be	AUX
ejpam-4479	106	13	hyper	hyper	ADJ
ejpam-4479	106	14	subgr	subgr	NOUN
ejpam-4479	106	15	-	-	PUNCT
ejpam-4479	106	16	algebras	algebra	NOUN
ejpam-4479	106	17	.	.	PUNCT
ejpam-4479	107	1	hence	hence	ADV
ejpam-4479	107	2	,	,	PUNCT
ejpam-4479	107	3	f	f	PROPN
ejpam-4479	107	4	(	(	PUNCT
ejpam-4479	107	5	a	a	NOUN
ejpam-4479	107	6	)	)	PUNCT
ejpam-4479	107	7	is	be	AUX
ejpam-4479	107	8	a	a	DET
ejpam-4479	107	9	hyper	hyper	ADJ
ejpam-4479	107	10	gr	gr	NOUN
ejpam-4479	107	11	-	-	NOUN
ejpam-4479	107	12	algebra	algebra	NOUN
ejpam-4479	107	13	over	over	ADP
ejpam-4479	107	14	h	h	NOUN
ejpam-4479	107	15	,	,	PUNCT
ejpam-4479	107	16	for	for	ADP
ejpam-4479	107	17	all	all	DET
ejpam-4479	107	18	a	a	DET
ejpam-4479	107	19	∈	∈	PROPN
ejpam-4479	107	20	a.	a.	NOUN
ejpam-4479	107	21	therefore	therefore	ADV
ejpam-4479	107	22	,	,	PUNCT
ejpam-4479	107	23	(	(	PUNCT
ejpam-4479	107	24	f	f	X
ejpam-4479	107	25	,	,	PUNCT
ejpam-4479	107	26	a	a	PRON
ejpam-4479	107	27	)	)	PUNCT
ejpam-4479	107	28	is	be	AUX
ejpam-4479	107	29	a	a	DET
ejpam-4479	107	30	soft	soft	ADJ
ejpam-4479	107	31	hyper	hyper	ADJ
ejpam-4479	107	32	gr	gr	NOUN
ejpam-4479	107	33	-	-	PUNCT
ejpam-4479	107	34	algebra	algebra	NOUN
ejpam-4479	107	35	.	.	PUNCT
ejpam-4479	108	1	example	example	NOUN
ejpam-4479	108	2	5	5	NUM
ejpam-4479	108	3	.	.	PUNCT
ejpam-4479	109	1	consider	consider	VERB
ejpam-4479	109	2	the	the	DET
ejpam-4479	109	3	same	same	ADJ
ejpam-4479	109	4	hyper	hyper	ADJ
ejpam-4479	109	5	gr	gr	NOUN
ejpam-4479	109	6	-	-	PUNCT
ejpam-4479	109	7	algebra	algebra	NOUN
ejpam-4479	109	8	h	h	NOUN
ejpam-4479	109	9	=	=	SYM
ejpam-4479	109	10	{	{	PUNCT
ejpam-4479	109	11	0	0	NUM
ejpam-4479	109	12	,	,	PUNCT
ejpam-4479	109	13	1	1	NUM
ejpam-4479	109	14	,	,	PUNCT
ejpam-4479	109	15	2	2	NUM
ejpam-4479	109	16	,	,	PUNCT
ejpam-4479	109	17	3	3	NUM
ejpam-4479	109	18	}	}	PUNCT
ejpam-4479	109	19	in	in	ADP
ejpam-4479	109	20	example	example	NOUN
ejpam-4479	109	21	4	4	X
ejpam-4479	109	22	.	.	PUNCT
ejpam-4479	110	1	let	let	VERB
ejpam-4479	110	2	a	a	PRON
ejpam-4479	110	3	=	=	X
ejpam-4479	110	4	{	{	PUNCT
ejpam-4479	110	5	a	a	PROPN
ejpam-4479	110	6	,	,	PUNCT
ejpam-4479	110	7	b	b	NOUN
ejpam-4479	110	8	}	}	PUNCT
ejpam-4479	110	9	and	and	CCONJ
ejpam-4479	110	10	r̊	r̊	PRON
ejpam-4479	110	11	=	=	SYM
ejpam-4479	110	12	{	{	PUNCT
ejpam-4479	110	13	(	(	PUNCT
ejpam-4479	110	14	a	a	PRON
ejpam-4479	110	15	,	,	PUNCT
ejpam-4479	110	16	{	{	PUNCT
ejpam-4479	110	17	0	0	NUM
ejpam-4479	110	18	,	,	PUNCT
ejpam-4479	110	19	1	1	NUM
ejpam-4479	110	20	}	}	PUNCT
ejpam-4479	110	21	)	)	PUNCT
ejpam-4479	110	22	,	,	PUNCT
ejpam-4479	110	23	(	(	PUNCT
ejpam-4479	110	24	a	a	X
ejpam-4479	110	25	,	,	PUNCT
ejpam-4479	110	26	{	{	PUNCT
ejpam-4479	110	27	0	0	NUM
ejpam-4479	110	28	,	,	PUNCT
ejpam-4479	110	29	1	1	NUM
ejpam-4479	110	30	,	,	PUNCT
ejpam-4479	110	31	2	2	NUM
ejpam-4479	110	32	}	}	PUNCT
ejpam-4479	110	33	)	)	PUNCT
ejpam-4479	110	34	,	,	PUNCT
ejpam-4479	110	35	(	(	PUNCT
ejpam-4479	110	36	b	b	X
ejpam-4479	110	37	,	,	PUNCT
ejpam-4479	110	38	{	{	PUNCT
ejpam-4479	110	39	0	0	NUM
ejpam-4479	110	40	,	,	PUNCT
ejpam-4479	110	41	1	1	NUM
ejpam-4479	110	42	}	}	PUNCT
ejpam-4479	110	43	)	)	PUNCT
ejpam-4479	110	44	,	,	PUNCT
ejpam-4479	110	45	(	(	PUNCT
ejpam-4479	110	46	b	b	X
ejpam-4479	110	47	,	,	PUNCT
ejpam-4479	110	48	{	{	PUNCT
ejpam-4479	110	49	0	0	NUM
ejpam-4479	110	50	,	,	PUNCT
ejpam-4479	110	51	1	1	NUM
ejpam-4479	110	52	,	,	PUNCT
ejpam-4479	110	53	3	3	NUM
ejpam-4479	110	54	}	}	PUNCT
ejpam-4479	110	55	)	)	PUNCT
ejpam-4479	110	56	}	}	PUNCT
ejpam-4479	110	57	.	.	PUNCT
ejpam-4479	111	1	then	then	ADV
ejpam-4479	111	2	f	f	X
ejpam-4479	111	3	(	(	PUNCT
ejpam-4479	111	4	a	a	NOUN
ejpam-4479	111	5	)	)	PUNCT
ejpam-4479	111	6	=	=	SYM
ejpam-4479	111	7	⋃	⋃	NOUN
ejpam-4479	111	8	b⊂h	b⊂h	NOUN
ejpam-4479	111	9	,	,	PUNCT
ejpam-4479	111	10	ar̊b	ar̊b	PROPN
ejpam-4479	111	11	b	b	NOUN
ejpam-4479	111	12	=	=	PUNCT
ejpam-4479	111	13	{	{	PUNCT
ejpam-4479	111	14	0	0	NUM
ejpam-4479	111	15	,	,	PUNCT
ejpam-4479	111	16	1	1	NUM
ejpam-4479	111	17	,	,	PUNCT
ejpam-4479	111	18	2	2	NUM
ejpam-4479	111	19	}	}	PUNCT
ejpam-4479	111	20	and	and	CCONJ
ejpam-4479	111	21	f	f	PROPN
ejpam-4479	111	22	(	(	PUNCT
ejpam-4479	111	23	b	b	NOUN
ejpam-4479	111	24	)	)	PUNCT
ejpam-4479	111	25	=	=	SYM
ejpam-4479	111	26	⋃	⋃	NOUN
ejpam-4479	111	27	b⊂h	b⊂h	NOUN
ejpam-4479	111	28	,	,	PUNCT
ejpam-4479	111	29	br̊b	br̊b	PROPN
ejpam-4479	111	30	b	b	X
ejpam-4479	111	31	=	=	PUNCT
ejpam-4479	111	32	{	{	PUNCT
ejpam-4479	111	33	0	0	NUM
ejpam-4479	111	34	,	,	PUNCT
ejpam-4479	111	35	1	1	NUM
ejpam-4479	111	36	,	,	PUNCT
ejpam-4479	111	37	3	3	NUM
ejpam-4479	111	38	}	}	PUNCT
ejpam-4479	111	39	which	which	PRON
ejpam-4479	111	40	are	be	AUX
ejpam-4479	111	41	both	both	PRON
ejpam-4479	111	42	hyper	hyper	ADJ
ejpam-4479	111	43	subgr	subgr	NOUN
ejpam-4479	111	44	-	-	PUNCT
ejpam-4479	111	45	algebra	algebra	NOUN
ejpam-4479	111	46	of	of	ADP
ejpam-4479	111	47	h.	h.	PROPN
ejpam-4479	111	48	hence	hence	ADV
ejpam-4479	111	49	,	,	PUNCT
ejpam-4479	111	50	(	(	PUNCT
ejpam-4479	111	51	f	f	X
ejpam-4479	111	52	,	,	PUNCT
ejpam-4479	111	53	a	a	PRON
ejpam-4479	111	54	)	)	PUNCT
ejpam-4479	111	55	is	be	AUX
ejpam-4479	111	56	a	a	DET
ejpam-4479	111	57	soft	soft	ADJ
ejpam-4479	111	58	hyper	hyper	ADJ
ejpam-4479	111	59	gr	gr	NOUN
ejpam-4479	111	60	-	-	NOUN
ejpam-4479	111	61	algebra	algebra	NOUN
ejpam-4479	111	62	with	with	ADP
ejpam-4479	111	63	respect	respect	NOUN
ejpam-4479	111	64	to	to	ADP
ejpam-4479	111	65	r̊.	r̊.	PROPN
ejpam-4479	111	66	example	example	NOUN
ejpam-4479	111	67	6	6	NUM
ejpam-4479	111	68	.	.	PUNCT
ejpam-4479	112	1	consider	consider	VERB
ejpam-4479	112	2	the	the	DET
ejpam-4479	112	3	same	same	ADJ
ejpam-4479	112	4	hyper	hyper	ADJ
ejpam-4479	112	5	gr	gr	NOUN
ejpam-4479	112	6	-	-	PUNCT
ejpam-4479	112	7	algebra	algebra	NOUN
ejpam-4479	112	8	h	h	NOUN
ejpam-4479	112	9	=	=	SYM
ejpam-4479	112	10	{	{	PUNCT
ejpam-4479	112	11	0	0	NUM
ejpam-4479	112	12	,	,	PUNCT
ejpam-4479	112	13	1	1	NUM
ejpam-4479	112	14	,	,	PUNCT
ejpam-4479	112	15	2	2	NUM
ejpam-4479	112	16	,	,	PUNCT
ejpam-4479	112	17	3	3	NUM
ejpam-4479	112	18	}	}	PUNCT
ejpam-4479	112	19	in	in	ADP
ejpam-4479	112	20	example	example	NOUN
ejpam-4479	112	21	4	4	X
ejpam-4479	112	22	.	.	PUNCT
ejpam-4479	113	1	let	let	VERB
ejpam-4479	113	2	a	a	PRON
ejpam-4479	113	3	=	=	X
ejpam-4479	113	4	{	{	PUNCT
ejpam-4479	113	5	a	a	PROPN
ejpam-4479	113	6	,	,	PUNCT
ejpam-4479	113	7	b	b	NOUN
ejpam-4479	113	8	}	}	PUNCT
ejpam-4479	113	9	and	and	CCONJ
ejpam-4479	113	10	r̊	r̊	PRON
ejpam-4479	113	11	=	=	SYM
ejpam-4479	113	12	{	{	PUNCT
ejpam-4479	113	13	(	(	PUNCT
ejpam-4479	113	14	a	a	X
ejpam-4479	113	15	,	,	PUNCT
ejpam-4479	113	16	{	{	PUNCT
ejpam-4479	113	17	1	1	NUM
ejpam-4479	113	18	,	,	PUNCT
ejpam-4479	113	19	3	3	NUM
ejpam-4479	113	20	}	}	PUNCT
ejpam-4479	113	21	)	)	PUNCT
ejpam-4479	113	22	,	,	PUNCT
ejpam-4479	113	23	(	(	PUNCT
ejpam-4479	113	24	a	a	X
ejpam-4479	113	25	,	,	PUNCT
ejpam-4479	113	26	{	{	PUNCT
ejpam-4479	113	27	0	0	NUM
ejpam-4479	113	28	}	}	PUNCT
ejpam-4479	113	29	)	)	PUNCT
ejpam-4479	113	30	,	,	PUNCT
ejpam-4479	113	31	(	(	PUNCT
ejpam-4479	113	32	b	b	X
ejpam-4479	113	33	,	,	PUNCT
ejpam-4479	113	34	{	{	PUNCT
ejpam-4479	113	35	0	0	NUM
ejpam-4479	113	36	}	}	PUNCT
ejpam-4479	113	37	)	)	PUNCT
ejpam-4479	113	38	,	,	PUNCT
ejpam-4479	113	39	(	(	PUNCT
ejpam-4479	113	40	b	b	X
ejpam-4479	113	41	,	,	PUNCT
ejpam-4479	113	42	{	{	PUNCT
ejpam-4479	113	43	2	2	NUM
ejpam-4479	113	44	}	}	PUNCT
ejpam-4479	113	45	)	)	PUNCT
ejpam-4479	113	46	}	}	PUNCT
ejpam-4479	113	47	.	.	PUNCT
ejpam-4479	114	1	then	then	ADV
ejpam-4479	114	2	f	f	X
ejpam-4479	114	3	(	(	PUNCT
ejpam-4479	114	4	a	a	NOUN
ejpam-4479	114	5	)	)	PUNCT
ejpam-4479	114	6	=	=	SYM
ejpam-4479	114	7	⋃	⋃	NOUN
ejpam-4479	114	8	b⊂h	b⊂h	NOUN
ejpam-4479	114	9	,	,	PUNCT
ejpam-4479	114	10	ar̊b	ar̊b	PROPN
ejpam-4479	114	11	b	b	NOUN
ejpam-4479	114	12	=	=	PUNCT
ejpam-4479	114	13	{	{	PUNCT
ejpam-4479	114	14	0	0	NUM
ejpam-4479	114	15	,	,	PUNCT
ejpam-4479	114	16	1	1	NUM
ejpam-4479	114	17	,	,	PUNCT
ejpam-4479	114	18	3	3	NUM
ejpam-4479	114	19	}	}	PUNCT
ejpam-4479	114	20	which	which	PRON
ejpam-4479	114	21	is	be	AUX
ejpam-4479	114	22	a	a	DET
ejpam-4479	114	23	hyper	hyper	ADJ
ejpam-4479	114	24	subgr	subgr	NOUN
ejpam-4479	114	25	-	-	PUNCT
ejpam-4479	114	26	algebra	algebra	NOUN
ejpam-4479	114	27	.	.	PUNCT
ejpam-4479	115	1	now	now	ADV
ejpam-4479	115	2	,	,	PUNCT
ejpam-4479	115	3	f	f	PROPN
ejpam-4479	115	4	(	(	PUNCT
ejpam-4479	115	5	b	b	NOUN
ejpam-4479	115	6	)	)	PUNCT
ejpam-4479	115	7	=	=	SYM
ejpam-4479	115	8	⋃	⋃	NOUN
ejpam-4479	115	9	b⊂h	b⊂h	NOUN
ejpam-4479	115	10	,	,	PUNCT
ejpam-4479	115	11	ar̊b	ar̊b	PROPN
ejpam-4479	115	12	b	b	NOUN
ejpam-4479	115	13	=	=	PUNCT
ejpam-4479	115	14	{	{	PUNCT
ejpam-4479	115	15	0	0	NUM
ejpam-4479	115	16	,	,	PUNCT
ejpam-4479	115	17	2	2	NUM
ejpam-4479	115	18	}	}	PUNCT
ejpam-4479	115	19	.	.	PUNCT
ejpam-4479	116	1	however	however	ADV
ejpam-4479	116	2	,	,	PUNCT
ejpam-4479	116	3	0⊛	0⊛	NUM
ejpam-4479	116	4	0	0	NUM
ejpam-4479	117	1	=	=	SYM
ejpam-4479	117	2	{	{	PUNCT
ejpam-4479	117	3	0	0	NUM
ejpam-4479	117	4	,	,	PUNCT
ejpam-4479	117	5	1	1	NUM
ejpam-4479	117	6	}	}	PUNCT
ejpam-4479	117	7	⊈	⊈	PROPN
ejpam-4479	117	8	f	f	X
ejpam-4479	117	9	(	(	PUNCT
ejpam-4479	117	10	b	b	NOUN
ejpam-4479	117	11	)	)	PUNCT
ejpam-4479	117	12	.	.	PUNCT
ejpam-4479	118	1	thus	thus	ADV
ejpam-4479	118	2	,	,	PUNCT
ejpam-4479	118	3	f	f	PROPN
ejpam-4479	118	4	(	(	PUNCT
ejpam-4479	118	5	b	b	NOUN
ejpam-4479	118	6	)	)	PUNCT
ejpam-4479	118	7	is	be	AUX
ejpam-4479	118	8	not	not	PART
ejpam-4479	118	9	a	a	DET
ejpam-4479	118	10	hyper	hyper	ADJ
ejpam-4479	118	11	subgr	subgr	NOUN
ejpam-4479	118	12	-	-	PUNCT
ejpam-4479	118	13	algebra	algebra	NOUN
ejpam-4479	118	14	.	.	PUNCT
ejpam-4479	119	1	hence	hence	ADV
ejpam-4479	119	2	,	,	PUNCT
ejpam-4479	119	3	(	(	PUNCT
ejpam-4479	119	4	f	f	X
ejpam-4479	119	5	,	,	PUNCT
ejpam-4479	119	6	a	a	PRON
ejpam-4479	119	7	)	)	PUNCT
ejpam-4479	119	8	is	be	AUX
ejpam-4479	119	9	not	not	PART
ejpam-4479	119	10	a	a	DET
ejpam-4479	119	11	soft	soft	ADJ
ejpam-4479	119	12	hyper	hyper	ADJ
ejpam-4479	119	13	gr	gr	NOUN
ejpam-4479	119	14	-	-	PUNCT
ejpam-4479	119	15	algebra	algebra	NOUN
ejpam-4479	119	16	.	.	PUNCT
ejpam-4479	120	1	theorem	theorem	NOUN
ejpam-4479	120	2	3	3	X
ejpam-4479	120	3	.	.	PUNCT
ejpam-4479	121	1	let	let	AUX
ejpam-4479	121	2	(	(	PUNCT
ejpam-4479	121	3	f	f	X
ejpam-4479	121	4	,	,	PUNCT
ejpam-4479	121	5	a	a	PRON
ejpam-4479	121	6	)	)	PUNCT
ejpam-4479	121	7	be	be	AUX
ejpam-4479	121	8	a	a	DET
ejpam-4479	121	9	soft	soft	ADJ
ejpam-4479	121	10	hyper	hyper	ADJ
ejpam-4479	121	11	gr	gr	NOUN
ejpam-4479	121	12	-	-	NOUN
ejpam-4479	121	13	algebra	algebra	NOUN
ejpam-4479	121	14	over	over	ADP
ejpam-4479	121	15	h.	h.	PROPN
ejpam-4479	121	16	if	if	SCONJ
ejpam-4479	121	17	b	b	PROPN
ejpam-4479	121	18	⊆	⊆	SYM
ejpam-4479	121	19	a	a	PRON
ejpam-4479	121	20	,	,	PUNCT
ejpam-4479	121	21	then	then	ADV
ejpam-4479	121	22	(	(	PUNCT
ejpam-4479	121	23	f	f	X
ejpam-4479	121	24	,	,	PUNCT
ejpam-4479	121	25	b	b	NOUN
ejpam-4479	121	26	)	)	PUNCT
ejpam-4479	121	27	is	be	AUX
ejpam-4479	121	28	a	a	DET
ejpam-4479	121	29	soft	soft	ADJ
ejpam-4479	121	30	hyper	hyper	ADJ
ejpam-4479	121	31	gr	gr	NOUN
ejpam-4479	121	32	-	-	NOUN
ejpam-4479	121	33	algebra	algebra	NOUN
ejpam-4479	121	34	over	over	ADP
ejpam-4479	121	35	h.	h.	PROPN
ejpam-4479	121	36	proof	proof	NOUN
ejpam-4479	121	37	:	:	PUNCT
ejpam-4479	121	38	since	since	SCONJ
ejpam-4479	121	39	(	(	PUNCT
ejpam-4479	121	40	f	f	X
ejpam-4479	121	41	,	,	PUNCT
ejpam-4479	121	42	a	a	PRON
ejpam-4479	121	43	)	)	PUNCT
ejpam-4479	121	44	is	be	AUX
ejpam-4479	121	45	a	a	DET
ejpam-4479	121	46	soft	soft	ADJ
ejpam-4479	121	47	hyper	hyper	ADJ
ejpam-4479	121	48	gr	gr	NOUN
ejpam-4479	121	49	-	-	PUNCT
ejpam-4479	121	50	algebra	algebra	NOUN
ejpam-4479	121	51	it	it	PRON
ejpam-4479	121	52	follows	follow	VERB
ejpam-4479	121	53	that	that	SCONJ
ejpam-4479	121	54	f	f	PROPN
ejpam-4479	121	55	(	(	PUNCT
ejpam-4479	121	56	a	a	NOUN
ejpam-4479	121	57	)	)	PUNCT
ejpam-4479	121	58	is	be	AUX
ejpam-4479	121	59	a	a	DET
ejpam-4479	121	60	hyper	hyper	ADJ
ejpam-4479	121	61	gralgebra	gralgebra	NOUN
ejpam-4479	121	62	for	for	ADP
ejpam-4479	121	63	all	all	DET
ejpam-4479	121	64	a	a	DET
ejpam-4479	121	65	∈	∈	NOUN
ejpam-4479	121	66	a.	a.	NOUN
ejpam-4479	121	67	since	since	SCONJ
ejpam-4479	121	68	b	b	PROPN
ejpam-4479	121	69	⊆	⊆	NUM
ejpam-4479	121	70	a	a	NOUN
ejpam-4479	121	71	,	,	PUNCT
ejpam-4479	121	72	f	f	PROPN
ejpam-4479	121	73	(	(	PUNCT
ejpam-4479	121	74	a	a	NOUN
ejpam-4479	121	75	)	)	PUNCT
ejpam-4479	121	76	is	be	AUX
ejpam-4479	121	77	a	a	DET
ejpam-4479	121	78	hyper	hyper	ADJ
ejpam-4479	121	79	gr	gr	NOUN
ejpam-4479	121	80	-	-	NOUN
ejpam-4479	121	81	algebra	algebra	NOUN
ejpam-4479	121	82	over	over	ADP
ejpam-4479	121	83	h	h	NOUN
ejpam-4479	121	84	for	for	ADP
ejpam-4479	121	85	all	all	DET
ejpam-4479	121	86	a	a	DET
ejpam-4479	121	87	∈	∈	PROPN
ejpam-4479	121	88	b.	b.	NOUN
ejpam-4479	121	89	hence	hence	ADV
ejpam-4479	121	90	,	,	PUNCT
ejpam-4479	121	91	(	(	PUNCT
ejpam-4479	121	92	f	f	X
ejpam-4479	121	93	,	,	PUNCT
ejpam-4479	121	94	b	b	NOUN
ejpam-4479	121	95	)	)	PUNCT
ejpam-4479	121	96	is	be	AUX
ejpam-4479	121	97	a	a	DET
ejpam-4479	121	98	soft	soft	ADJ
ejpam-4479	121	99	hyper	hyper	ADJ
ejpam-4479	121	100	gr	gr	NOUN
ejpam-4479	121	101	-	-	NOUN
ejpam-4479	121	102	algebra	algebra	NOUN
ejpam-4479	121	103	over	over	ADP
ejpam-4479	121	104	h.	h.	PROPN
ejpam-4479	121	105	theorem	theorem	PROPN
ejpam-4479	121	106	4	4	X
ejpam-4479	121	107	.	.	PUNCT
ejpam-4479	122	1	let	let	VERB
ejpam-4479	122	2	(	(	PUNCT
ejpam-4479	122	3	f	f	X
ejpam-4479	122	4	,	,	PUNCT
ejpam-4479	122	5	a	a	PRON
ejpam-4479	122	6	)	)	PUNCT
ejpam-4479	122	7	and	and	CCONJ
ejpam-4479	122	8	(	(	PUNCT
ejpam-4479	122	9	g	g	NOUN
ejpam-4479	122	10	,	,	PUNCT
ejpam-4479	122	11	b	b	NOUN
ejpam-4479	122	12	)	)	PUNCT
ejpam-4479	122	13	be	be	AUX
ejpam-4479	122	14	two	two	NUM
ejpam-4479	122	15	soft	soft	ADJ
ejpam-4479	122	16	hyper	hyper	ADJ
ejpam-4479	122	17	gr	gr	NOUN
ejpam-4479	122	18	-	-	PUNCT
ejpam-4479	122	19	algebras	algebras	NOUN
ejpam-4479	122	20	over	over	ADP
ejpam-4479	122	21	h.	h.	PROPN
ejpam-4479	122	22	if	if	SCONJ
ejpam-4479	122	23	a∩b	a∩b	PROPN
ejpam-4479	122	24	̸=	̸=	PROPN
ejpam-4479	122	25	∅	∅	NOUN
ejpam-4479	122	26	,	,	PUNCT
ejpam-4479	122	27	then	then	ADV
ejpam-4479	122	28	the	the	DET
ejpam-4479	122	29	intersection	intersection	NOUN
ejpam-4479	122	30	(	(	PUNCT
ejpam-4479	122	31	f	f	X
ejpam-4479	122	32	,	,	PUNCT
ejpam-4479	122	33	a	a	PRON
ejpam-4479	122	34	)	)	PUNCT
ejpam-4479	122	35	∼	∼	NOUN
ejpam-4479	122	36	∩	∩	NOUN
ejpam-4479	122	37	(	(	PUNCT
ejpam-4479	122	38	g	g	PROPN
ejpam-4479	122	39	,	,	PUNCT
ejpam-4479	122	40	b	b	NOUN
ejpam-4479	122	41	)	)	PUNCT
ejpam-4479	122	42	is	be	AUX
ejpam-4479	122	43	a	a	DET
ejpam-4479	122	44	soft	soft	ADJ
ejpam-4479	122	45	hyper	hyper	ADJ
ejpam-4479	122	46	gr	gr	NOUN
ejpam-4479	122	47	-	-	NOUN
ejpam-4479	122	48	algebra	algebra	NOUN
ejpam-4479	122	49	over	over	ADP
ejpam-4479	122	50	h.	h.	PROPN
ejpam-4479	122	51	m.k	m.k	PROPN
ejpam-4479	122	52	.	.	PROPN
ejpam-4479	122	53	engcot	engcot	PROPN
ejpam-4479	122	54	,	,	PUNCT
ejpam-4479	122	55	g.	g.	PROPN
ejpam-4479	122	56	petalcorin	petalcorin	PROPN
ejpam-4479	122	57	/	/	SYM
ejpam-4479	122	58	eur	eur	PROPN
ejpam-4479	122	59	.	.	PUNCT
ejpam-4479	123	1	j.	j.	PROPN
ejpam-4479	123	2	pure	pure	PROPN
ejpam-4479	123	3	appl	appl	PROPN
ejpam-4479	123	4	.	.	PROPN
ejpam-4479	123	5	math	math	PROPN
ejpam-4479	123	6	,	,	PUNCT
ejpam-4479	123	7	15	15	NUM
ejpam-4479	123	8	(	(	PUNCT
ejpam-4479	123	9	4	4	NUM
ejpam-4479	123	10	)	)	PUNCT
ejpam-4479	123	11	(	(	PUNCT
ejpam-4479	123	12	2022	2022	NUM
ejpam-4479	123	13	)	)	PUNCT
ejpam-4479	123	14	,	,	PUNCT
ejpam-4479	123	15	1482	1482	NUM
ejpam-4479	123	16	-	-	SYM
ejpam-4479	123	17	1497	1497	NUM
ejpam-4479	123	18	1487	1487	NUM
ejpam-4479	123	19	proof	proof	NOUN
ejpam-4479	123	20	:	:	PUNCT
ejpam-4479	123	21	using	use	VERB
ejpam-4479	123	22	definition	definition	NOUN
ejpam-4479	123	23	6	6	NUM
ejpam-4479	123	24	,	,	PUNCT
ejpam-4479	123	25	we	we	PRON
ejpam-4479	123	26	can	can	AUX
ejpam-4479	123	27	write	write	VERB
ejpam-4479	123	28	(	(	PUNCT
ejpam-4479	123	29	f	f	X
ejpam-4479	123	30	,	,	PUNCT
ejpam-4479	123	31	a	a	PRON
ejpam-4479	123	32	)	)	PUNCT
ejpam-4479	123	33	∼	∼	NOUN
ejpam-4479	123	34	∩(g	∩(g	PROPN
ejpam-4479	123	35	,	,	PUNCT
ejpam-4479	123	36	b	b	NOUN
ejpam-4479	123	37	)	)	PUNCT
ejpam-4479	123	38	=	=	SYM
ejpam-4479	124	1	(	(	PUNCT
ejpam-4479	124	2	d	d	NOUN
ejpam-4479	124	3	,	,	PUNCT
ejpam-4479	124	4	c	c	NOUN
ejpam-4479	124	5	)	)	PUNCT
ejpam-4479	124	6	,	,	PUNCT
ejpam-4479	124	7	where	where	SCONJ
ejpam-4479	124	8	a∩b	a∩b	PROPN
ejpam-4479	124	9	=	=	PUNCT
ejpam-4479	124	10	c	c	X
ejpam-4479	124	11	̸=	̸=	PROPN
ejpam-4479	124	12	∅	∅	NOUN
ejpam-4479	124	13	and	and	CCONJ
ejpam-4479	124	14	d(x	d(x	NOUN
ejpam-4479	124	15	)	)	PUNCT
ejpam-4479	125	1	=	=	SYM
ejpam-4479	125	2	f	f	X
ejpam-4479	125	3	(	(	PUNCT
ejpam-4479	125	4	x	x	NOUN
ejpam-4479	125	5	)	)	PUNCT
ejpam-4479	125	6	∩	∩	ADJ
ejpam-4479	125	7	g(x	g(x	NOUN
ejpam-4479	125	8	)	)	PUNCT
ejpam-4479	125	9	for	for	ADP
ejpam-4479	125	10	all	all	PRON
ejpam-4479	125	11	x	x	SYM
ejpam-4479	125	12	∈	∈	PROPN
ejpam-4479	125	13	g.	g.	NOUN
ejpam-4479	125	14	note	note	VERB
ejpam-4479	125	15	that	that	SCONJ
ejpam-4479	125	16	d	d	X
ejpam-4479	125	17	:	:	PUNCT
ejpam-4479	125	18	c	c	X
ejpam-4479	125	19	→	→	SYM
ejpam-4479	125	20	p	p	X
ejpam-4479	125	21	(	(	PUNCT
ejpam-4479	125	22	h	h	NOUN
ejpam-4479	125	23	)	)	PUNCT
ejpam-4479	125	24	is	be	AUX
ejpam-4479	125	25	a	a	DET
ejpam-4479	125	26	mapping	mapping	NOUN
ejpam-4479	125	27	since	since	SCONJ
ejpam-4479	125	28	the	the	DET
ejpam-4479	125	29	intersection	intersection	NOUN
ejpam-4479	125	30	of	of	ADP
ejpam-4479	125	31	two	two	NUM
ejpam-4479	125	32	hyper	hyper	ADJ
ejpam-4479	125	33	gr	gr	NOUN
ejpam-4479	125	34	-	-	PUNCT
ejpam-4479	125	35	algebra	algebra	NOUN
ejpam-4479	125	36	is	be	AUX
ejpam-4479	125	37	a	a	DET
ejpam-4479	125	38	hyper	hyper	ADJ
ejpam-4479	125	39	gr	gr	NOUN
ejpam-4479	125	40	-	-	PUNCT
ejpam-4479	125	41	algebra	algebra	NOUN
ejpam-4479	125	42	,	,	PUNCT
ejpam-4479	125	43	thus	thus	ADV
ejpam-4479	125	44	,	,	PUNCT
ejpam-4479	125	45	(	(	PUNCT
ejpam-4479	125	46	d	d	X
ejpam-4479	125	47	,	,	PUNCT
ejpam-4479	125	48	c	c	NOUN
ejpam-4479	125	49	)	)	PUNCT
ejpam-4479	125	50	is	be	AUX
ejpam-4479	125	51	a	a	DET
ejpam-4479	125	52	soft	soft	ADJ
ejpam-4479	125	53	set	set	NOUN
ejpam-4479	125	54	over	over	ADP
ejpam-4479	125	55	h.	h.	PROPN
ejpam-4479	125	56	since	since	SCONJ
ejpam-4479	125	57	(	(	PUNCT
ejpam-4479	125	58	f	f	X
ejpam-4479	125	59	,	,	PUNCT
ejpam-4479	125	60	a	a	PRON
ejpam-4479	125	61	)	)	PUNCT
ejpam-4479	125	62	and	and	CCONJ
ejpam-4479	125	63	(	(	PUNCT
ejpam-4479	125	64	g	g	NOUN
ejpam-4479	125	65	,	,	PUNCT
ejpam-4479	125	66	b	b	NOUN
ejpam-4479	125	67	)	)	PUNCT
ejpam-4479	125	68	are	be	AUX
ejpam-4479	125	69	soft	soft	ADJ
ejpam-4479	125	70	hyper	hyper	ADJ
ejpam-4479	125	71	gr	gr	NOUN
ejpam-4479	125	72	-	-	PUNCT
ejpam-4479	125	73	algebras	algebras	NOUN
ejpam-4479	125	74	over	over	ADP
ejpam-4479	125	75	h	h	NOUN
ejpam-4479	125	76	,	,	PUNCT
ejpam-4479	125	77	it	it	PRON
ejpam-4479	125	78	follows	follow	VERB
ejpam-4479	125	79	that	that	SCONJ
ejpam-4479	125	80	d(x	d(x	NOUN
ejpam-4479	125	81	)	)	PUNCT
ejpam-4479	126	1	=	=	SYM
ejpam-4479	126	2	f	f	X
ejpam-4479	126	3	(	(	PUNCT
ejpam-4479	126	4	x	x	NOUN
ejpam-4479	126	5	)	)	PUNCT
ejpam-4479	126	6	or	or	CCONJ
ejpam-4479	126	7	d(x	d(x	NOUN
ejpam-4479	126	8	)	)	PUNCT
ejpam-4479	126	9	=	=	SYM
ejpam-4479	127	1	g(x	g(x	NOUN
ejpam-4479	127	2	)	)	PUNCT
ejpam-4479	127	3	for	for	ADP
ejpam-4479	127	4	all	all	DET
ejpam-4479	127	5	x	x	SYM
ejpam-4479	127	6	∈	∈	PROPN
ejpam-4479	127	7	c.	c.	NOUN
ejpam-4479	127	8	thus	thus	ADV
ejpam-4479	127	9	,	,	PUNCT
ejpam-4479	127	10	(	(	PUNCT
ejpam-4479	127	11	d	d	X
ejpam-4479	127	12	,	,	PUNCT
ejpam-4479	127	13	c	c	NOUN
ejpam-4479	127	14	)	)	PUNCT
ejpam-4479	127	15	is	be	AUX
ejpam-4479	127	16	a	a	DET
ejpam-4479	127	17	soft	soft	ADJ
ejpam-4479	127	18	hyper	hyper	ADJ
ejpam-4479	127	19	gr	gr	NOUN
ejpam-4479	127	20	-	-	NOUN
ejpam-4479	127	21	algebra	algebra	NOUN
ejpam-4479	127	22	over	over	ADP
ejpam-4479	127	23	h.	h.	PROPN
ejpam-4479	127	24	hence	hence	ADV
ejpam-4479	127	25	,	,	PUNCT
ejpam-4479	127	26	(	(	PUNCT
ejpam-4479	127	27	d	d	X
ejpam-4479	127	28	,	,	PUNCT
ejpam-4479	127	29	c	c	NOUN
ejpam-4479	127	30	)	)	PUNCT
ejpam-4479	127	31	=	=	SYM
ejpam-4479	127	32	(	(	PUNCT
ejpam-4479	127	33	f	f	X
ejpam-4479	127	34	,	,	PUNCT
ejpam-4479	127	35	a	a	PRON
ejpam-4479	127	36	)	)	PUNCT
ejpam-4479	127	37	∼	∼	NOUN
ejpam-4479	127	38	∩	∩	NOUN
ejpam-4479	127	39	(	(	PUNCT
ejpam-4479	127	40	g	g	PROPN
ejpam-4479	127	41	,	,	PUNCT
ejpam-4479	127	42	b	b	NOUN
ejpam-4479	127	43	)	)	PUNCT
ejpam-4479	127	44	is	be	AUX
ejpam-4479	127	45	a	a	DET
ejpam-4479	127	46	soft	soft	ADJ
ejpam-4479	127	47	hyper	hyper	ADJ
ejpam-4479	127	48	gr	gr	NOUN
ejpam-4479	127	49	-	-	NOUN
ejpam-4479	127	50	algebra	algebra	NOUN
ejpam-4479	127	51	over	over	ADP
ejpam-4479	127	52	h.	h.	PROPN
ejpam-4479	127	53	theorem	theorem	PROPN
ejpam-4479	127	54	5	5	X
ejpam-4479	127	55	.	.	PUNCT
ejpam-4479	128	1	let	let	VERB
ejpam-4479	128	2	(	(	PUNCT
ejpam-4479	128	3	f	f	X
ejpam-4479	128	4	,	,	PUNCT
ejpam-4479	128	5	a	a	PRON
ejpam-4479	128	6	)	)	PUNCT
ejpam-4479	128	7	and	and	CCONJ
ejpam-4479	128	8	(	(	PUNCT
ejpam-4479	128	9	g	g	NOUN
ejpam-4479	128	10	,	,	PUNCT
ejpam-4479	128	11	b	b	NOUN
ejpam-4479	128	12	)	)	PUNCT
ejpam-4479	128	13	be	be	AUX
ejpam-4479	128	14	two	two	NUM
ejpam-4479	128	15	soft	soft	ADJ
ejpam-4479	128	16	hyper	hyper	ADJ
ejpam-4479	128	17	gr	gr	NOUN
ejpam-4479	128	18	-	-	PUNCT
ejpam-4479	128	19	algebras	algebras	NOUN
ejpam-4479	128	20	over	over	ADP
ejpam-4479	128	21	h.	h.	PROPN
ejpam-4479	128	22	if	if	SCONJ
ejpam-4479	128	23	a∩b	a∩b	PROPN
ejpam-4479	128	24	=	=	SYM
ejpam-4479	128	25	∅	∅	NOUN
ejpam-4479	128	26	,	,	PUNCT
ejpam-4479	128	27	then	then	ADV
ejpam-4479	128	28	the	the	DET
ejpam-4479	128	29	union	union	NOUN
ejpam-4479	128	30	(	(	PUNCT
ejpam-4479	128	31	f	f	X
ejpam-4479	128	32	,	,	PUNCT
ejpam-4479	128	33	a	a	PRON
ejpam-4479	128	34	)	)	PUNCT
ejpam-4479	128	35	∼	∼	NOUN
ejpam-4479	128	36	∪	∪	NOUN
ejpam-4479	128	37	(	(	PUNCT
ejpam-4479	128	38	g	g	NOUN
ejpam-4479	128	39	,	,	PUNCT
ejpam-4479	128	40	b	b	NOUN
ejpam-4479	128	41	)	)	PUNCT
ejpam-4479	128	42	is	be	AUX
ejpam-4479	128	43	a	a	DET
ejpam-4479	128	44	soft	soft	ADJ
ejpam-4479	128	45	hyper	hyper	ADJ
ejpam-4479	128	46	gr	gr	NOUN
ejpam-4479	128	47	-	-	NOUN
ejpam-4479	128	48	algebra	algebra	NOUN
ejpam-4479	128	49	over	over	ADP
ejpam-4479	128	50	h.	h.	PROPN
ejpam-4479	128	51	proof	proof	NOUN
ejpam-4479	128	52	:	:	PUNCT
ejpam-4479	128	53	using	use	VERB
ejpam-4479	128	54	definition	definition	NOUN
ejpam-4479	128	55	7	7	NUM
ejpam-4479	128	56	,	,	PUNCT
ejpam-4479	128	57	we	we	PRON
ejpam-4479	128	58	can	can	AUX
ejpam-4479	128	59	write	write	VERB
ejpam-4479	128	60	(	(	PUNCT
ejpam-4479	128	61	f	f	X
ejpam-4479	128	62	,	,	PUNCT
ejpam-4479	128	63	a	a	PRON
ejpam-4479	128	64	)	)	PUNCT
ejpam-4479	128	65	∼	∼	NOUN
ejpam-4479	128	66	∪	∪	NOUN
ejpam-4479	128	67	(	(	PUNCT
ejpam-4479	128	68	g	g	NOUN
ejpam-4479	128	69	,	,	PUNCT
ejpam-4479	128	70	b	b	NOUN
ejpam-4479	128	71	)	)	PUNCT
ejpam-4479	128	72	=	=	SYM
ejpam-4479	128	73	(	(	PUNCT
ejpam-4479	128	74	j	j	NOUN
ejpam-4479	128	75	,	,	PUNCT
ejpam-4479	128	76	c	c	NOUN
ejpam-4479	128	77	)	)	PUNCT
ejpam-4479	128	78	,	,	PUNCT
ejpam-4479	129	1	where	where	SCONJ
ejpam-4479	129	2	c	c	NOUN
ejpam-4479	129	3	=	=	PUNCT
ejpam-4479	129	4	a	a	DET
ejpam-4479	129	5	∪	∪	X
ejpam-4479	129	6	b	b	NOUN
ejpam-4479	129	7	,	,	PUNCT
ejpam-4479	129	8	and	and	CCONJ
ejpam-4479	129	9	for	for	ADP
ejpam-4479	129	10	all	all	DET
ejpam-4479	129	11	x	x	SYM
ejpam-4479	129	12	∈	∈	PROPN
ejpam-4479	129	13	c	c	X
ejpam-4479	129	14	,	,	PUNCT
ejpam-4479	129	15	j(x	j(x	PROPN
ejpam-4479	129	16	)	)	PUNCT
ejpam-4479	129	17	=	=	PUNCT
ejpam-4479	130	1			ADJ
ejpam-4479	130	2	f	f	X
ejpam-4479	130	3	(	(	PUNCT
ejpam-4479	130	4	x	x	NOUN
ejpam-4479	130	5	)	)	PUNCT
ejpam-4479	130	6	,	,	PUNCT
ejpam-4479	130	7	if	if	SCONJ
ejpam-4479	130	8	x	x	SYM
ejpam-4479	130	9	∈	∈	PROPN
ejpam-4479	130	10	a	a	DET
ejpam-4479	130	11	\b	\b	ADJ
ejpam-4479	130	12	g(x	g(x	NOUN
ejpam-4479	130	13	)	)	PUNCT
ejpam-4479	130	14	,	,	PUNCT
ejpam-4479	130	15	if	if	SCONJ
ejpam-4479	130	16	x	x	PROPN
ejpam-4479	130	17	∈	∈	PROPN
ejpam-4479	130	18	b	b	PROPN
ejpam-4479	130	19	\a	\a	VERB
ejpam-4479	130	20	f	f	NOUN
ejpam-4479	130	21	(	(	PUNCT
ejpam-4479	130	22	x	x	X
ejpam-4479	130	23	)	)	PUNCT
ejpam-4479	130	24	∪g(x	∪g(x	ADV
ejpam-4479	130	25	)	)	PUNCT
ejpam-4479	130	26	,	,	PUNCT
ejpam-4479	130	27	if	if	SCONJ
ejpam-4479	130	28	x	x	SYM
ejpam-4479	130	29	∈	∈	PROPN
ejpam-4479	130	30	a	a	DET
ejpam-4479	130	31	∩b	∩b	NOUN
ejpam-4479	130	32	.	.	PUNCT
ejpam-4479	131	1	since	since	SCONJ
ejpam-4479	131	2	a∩b	a∩b	PROPN
ejpam-4479	131	3	=	=	SYM
ejpam-4479	131	4	∅	∅	NOUN
ejpam-4479	131	5	,	,	PUNCT
ejpam-4479	131	6	this	this	PRON
ejpam-4479	131	7	implies	imply	VERB
ejpam-4479	131	8	that	that	SCONJ
ejpam-4479	131	9	either	either	CCONJ
ejpam-4479	131	10	x	x	SYM
ejpam-4479	131	11	∈	∈	PROPN
ejpam-4479	131	12	a\b	a\b	ADP
ejpam-4479	131	13	or	or	CCONJ
ejpam-4479	131	14	x	x	PROPN
ejpam-4479	131	15	∈	∈	PROPN
ejpam-4479	131	16	b	b	PROPN
ejpam-4479	131	17	\a	\a	VERB
ejpam-4479	131	18	for	for	ADP
ejpam-4479	131	19	all	all	PRON
ejpam-4479	131	20	x	x	SYM
ejpam-4479	131	21	∈	∈	PROPN
ejpam-4479	131	22	c.	c.	NOUN
ejpam-4479	131	23	if	if	SCONJ
ejpam-4479	131	24	x	x	PROPN
ejpam-4479	131	25	∈	∈	PROPN
ejpam-4479	131	26	a\b	a\b	NOUN
ejpam-4479	131	27	,	,	PUNCT
ejpam-4479	131	28	j(x	j(x	PROPN
ejpam-4479	131	29	)	)	PUNCT
ejpam-4479	131	30	=	=	SYM
ejpam-4479	131	31	f	f	PROPN
ejpam-4479	131	32	(	(	PUNCT
ejpam-4479	131	33	x	x	NOUN
ejpam-4479	131	34	)	)	PUNCT
ejpam-4479	131	35	.	.	PUNCT
ejpam-4479	132	1	thus	thus	ADV
ejpam-4479	132	2	,	,	PUNCT
ejpam-4479	132	3	(	(	PUNCT
ejpam-4479	132	4	j	j	NOUN
ejpam-4479	132	5	,	,	PUNCT
ejpam-4479	132	6	c	c	NOUN
ejpam-4479	132	7	)	)	PUNCT
ejpam-4479	132	8	is	be	AUX
ejpam-4479	132	9	a	a	DET
ejpam-4479	132	10	soft	soft	ADJ
ejpam-4479	132	11	hyper	hyper	ADJ
ejpam-4479	132	12	gr	gr	NOUN
ejpam-4479	132	13	-	-	NOUN
ejpam-4479	132	14	algebra	algebra	NOUN
ejpam-4479	132	15	over	over	ADP
ejpam-4479	132	16	h.	h.	NOUN
ejpam-4479	132	17	if	if	SCONJ
ejpam-4479	132	18	x	x	PROPN
ejpam-4479	132	19	∈	∈	PROPN
ejpam-4479	132	20	b	b	NOUN
ejpam-4479	132	21	\a	\a	ADJ
ejpam-4479	132	22	,	,	PUNCT
ejpam-4479	132	23	j(x	j(x	PROPN
ejpam-4479	132	24	)	)	PUNCT
ejpam-4479	132	25	=	=	PUNCT
ejpam-4479	132	26	g(x	g(x	NOUN
ejpam-4479	132	27	)	)	PUNCT
ejpam-4479	132	28	.	.	PUNCT
ejpam-4479	133	1	thus	thus	ADV
ejpam-4479	133	2	,	,	PUNCT
ejpam-4479	133	3	(	(	PUNCT
ejpam-4479	133	4	j	j	NOUN
ejpam-4479	133	5	,	,	PUNCT
ejpam-4479	133	6	c	c	NOUN
ejpam-4479	133	7	)	)	PUNCT
ejpam-4479	133	8	is	be	AUX
ejpam-4479	133	9	a	a	DET
ejpam-4479	133	10	soft	soft	ADJ
ejpam-4479	133	11	hyper	hyper	ADJ
ejpam-4479	133	12	gr	gr	NOUN
ejpam-4479	133	13	-	-	NOUN
ejpam-4479	133	14	algebra	algebra	NOUN
ejpam-4479	133	15	over	over	ADP
ejpam-4479	133	16	h.	h.	PROPN
ejpam-4479	133	17	hence	hence	ADV
ejpam-4479	133	18	,	,	PUNCT
ejpam-4479	133	19	(	(	PUNCT
ejpam-4479	133	20	j	j	NOUN
ejpam-4479	133	21	,	,	PUNCT
ejpam-4479	133	22	c	c	NOUN
ejpam-4479	133	23	)	)	PUNCT
ejpam-4479	133	24	=	=	SYM
ejpam-4479	133	25	(	(	PUNCT
ejpam-4479	133	26	f	f	X
ejpam-4479	133	27	,	,	PUNCT
ejpam-4479	133	28	a	a	PRON
ejpam-4479	133	29	)	)	PUNCT
ejpam-4479	133	30	∼	∼	NOUN
ejpam-4479	133	31	∪	∪	NOUN
ejpam-4479	133	32	(	(	PUNCT
ejpam-4479	133	33	g	g	NOUN
ejpam-4479	133	34	,	,	PUNCT
ejpam-4479	133	35	b	b	NOUN
ejpam-4479	133	36	)	)	PUNCT
ejpam-4479	133	37	is	be	AUX
ejpam-4479	133	38	a	a	DET
ejpam-4479	133	39	soft	soft	ADJ
ejpam-4479	133	40	hyper	hyper	ADJ
ejpam-4479	133	41	gr	gr	NOUN
ejpam-4479	133	42	-	-	NOUN
ejpam-4479	133	43	algebra	algebra	NOUN
ejpam-4479	133	44	over	over	ADP
ejpam-4479	133	45	h.	h.	PROPN
ejpam-4479	133	46	theorem	theorem	PROPN
ejpam-4479	133	47	6	6	NUM
ejpam-4479	133	48	.	.	PUNCT
ejpam-4479	134	1	if	if	SCONJ
ejpam-4479	134	2	(	(	PUNCT
ejpam-4479	134	3	f	f	X
ejpam-4479	134	4	,	,	PUNCT
ejpam-4479	134	5	a	a	PRON
ejpam-4479	134	6	)	)	PUNCT
ejpam-4479	134	7	and	and	CCONJ
ejpam-4479	134	8	(	(	PUNCT
ejpam-4479	134	9	g	g	NOUN
ejpam-4479	134	10	,	,	PUNCT
ejpam-4479	134	11	b	b	NOUN
ejpam-4479	134	12	)	)	PUNCT
ejpam-4479	134	13	are	be	AUX
ejpam-4479	134	14	soft	soft	ADJ
ejpam-4479	134	15	hyper	hyper	ADJ
ejpam-4479	134	16	gr	gr	ADJ
ejpam-4479	134	17	-	-	PUNCT
ejpam-4479	134	18	algebras	algebras	PROPN
ejpam-4479	134	19	overh	overh	PROPN
ejpam-4479	134	20	.	.	PUNCT
ejpam-4479	135	1	then	then	ADV
ejpam-4479	135	2	(	(	PUNCT
ejpam-4479	135	3	f	f	X
ejpam-4479	135	4	,	,	PUNCT
ejpam-4479	135	5	a	a	PRON
ejpam-4479	135	6	)	)	PUNCT
ejpam-4479	135	7	∼	∼	NOUN
ejpam-4479	135	8	∧(g	∧(g	NOUN
ejpam-4479	135	9	,	,	PUNCT
ejpam-4479	135	10	b	b	NOUN
ejpam-4479	135	11	)	)	PUNCT
ejpam-4479	135	12	is	be	AUX
ejpam-4479	135	13	a	a	DET
ejpam-4479	135	14	soft	soft	ADJ
ejpam-4479	135	15	hyper	hyper	ADJ
ejpam-4479	135	16	gr	gr	NOUN
ejpam-4479	135	17	-	-	NOUN
ejpam-4479	135	18	algebra	algebra	NOUN
ejpam-4479	135	19	over	over	ADP
ejpam-4479	135	20	h.	h.	PROPN
ejpam-4479	135	21	proof	proof	NOUN
ejpam-4479	135	22	:	:	PUNCT
ejpam-4479	135	23	by	by	ADP
ejpam-4479	135	24	definition	definition	NOUN
ejpam-4479	135	25	8	8	NUM
ejpam-4479	135	26	,	,	PUNCT
ejpam-4479	135	27	(	(	PUNCT
ejpam-4479	135	28	f	f	X
ejpam-4479	135	29	,	,	PUNCT
ejpam-4479	135	30	a	a	PRON
ejpam-4479	135	31	)	)	PUNCT
ejpam-4479	135	32	∼	∼	NOUN
ejpam-4479	135	33	∧	∧	NOUN
ejpam-4479	135	34	(	(	PUNCT
ejpam-4479	135	35	g	g	PROPN
ejpam-4479	135	36	,	,	PUNCT
ejpam-4479	135	37	b	b	NOUN
ejpam-4479	135	38	)	)	PUNCT
ejpam-4479	135	39	=	=	SYM
ejpam-4479	135	40	(	(	PUNCT
ejpam-4479	135	41	j	j	PROPN
ejpam-4479	135	42	,	,	PUNCT
ejpam-4479	135	43	a×	a×	PROPN
ejpam-4479	135	44	b	b	NOUN
ejpam-4479	135	45	)	)	PUNCT
ejpam-4479	135	46	.	.	PUNCT
ejpam-4479	136	1	since	since	SCONJ
ejpam-4479	136	2	f	f	PROPN
ejpam-4479	136	3	(	(	PUNCT
ejpam-4479	136	4	x	x	NOUN
ejpam-4479	136	5	)	)	PUNCT
ejpam-4479	136	6	and	and	CCONJ
ejpam-4479	136	7	g(y	g(y	NOUN
ejpam-4479	136	8	)	)	PUNCT
ejpam-4479	136	9	are	be	AUX
ejpam-4479	136	10	hyper	hyper	ADJ
ejpam-4479	136	11	gr	gr	NOUN
ejpam-4479	136	12	-	-	PUNCT
ejpam-4479	136	13	algebras	algebra	NOUN
ejpam-4479	136	14	of	of	ADP
ejpam-4479	136	15	h	h	NOUN
ejpam-4479	136	16	,	,	PUNCT
ejpam-4479	136	17	it	it	PRON
ejpam-4479	136	18	follows	follow	VERB
ejpam-4479	136	19	that	that	SCONJ
ejpam-4479	136	20	the	the	DET
ejpam-4479	136	21	intersection	intersection	NOUN
ejpam-4479	136	22	(	(	PUNCT
ejpam-4479	136	23	f	f	PROPN
ejpam-4479	136	24	∩	∩	PROPN
ejpam-4479	136	25	g)(x	g)(x	PROPN
ejpam-4479	136	26	,	,	PUNCT
ejpam-4479	136	27	y	y	PROPN
ejpam-4479	136	28	)	)	PUNCT
ejpam-4479	136	29	,	,	PUNCT
ejpam-4479	136	30	is	be	AUX
ejpam-4479	136	31	also	also	ADV
ejpam-4479	136	32	a	a	DET
ejpam-4479	136	33	hyper	hyper	ADJ
ejpam-4479	136	34	subgralgebra	subgralgebra	NOUN
ejpam-4479	136	35	of	of	ADP
ejpam-4479	136	36	h.	h.	PROPN
ejpam-4479	136	37	hence	hence	PROPN
ejpam-4479	136	38	,	,	PUNCT
ejpam-4479	136	39	j(x	j(x	PROPN
ejpam-4479	136	40	,	,	PUNCT
ejpam-4479	136	41	y	y	PROPN
ejpam-4479	136	42	)	)	PUNCT
ejpam-4479	136	43	is	be	AUX
ejpam-4479	136	44	a	a	DET
ejpam-4479	136	45	hyper	hyper	ADJ
ejpam-4479	136	46	subgr	subgr	NOUN
ejpam-4479	136	47	-	-	PUNCT
ejpam-4479	136	48	algebra	algebra	NOUN
ejpam-4479	136	49	of	of	ADP
ejpam-4479	136	50	h	h	NOUN
ejpam-4479	136	51	for	for	ADP
ejpam-4479	136	52	all	all	DET
ejpam-4479	136	53	(	(	PUNCT
ejpam-4479	136	54	x	x	NOUN
ejpam-4479	136	55	,	,	PUNCT
ejpam-4479	136	56	y	y	NOUN
ejpam-4479	136	57	)	)	PUNCT
ejpam-4479	136	58	∈	∈	PROPN
ejpam-4479	136	59	a×b	a×b	PROPN
ejpam-4479	136	60	,	,	PUNCT
ejpam-4479	136	61	and	and	CCONJ
ejpam-4479	136	62	so	so	ADV
ejpam-4479	136	63	(	(	PUNCT
ejpam-4479	136	64	f	f	X
ejpam-4479	136	65	,	,	PUNCT
ejpam-4479	136	66	a	a	PRON
ejpam-4479	136	67	)	)	PUNCT
ejpam-4479	136	68	∼	∼	NOUN
ejpam-4479	136	69	∧	∧	NOUN
ejpam-4479	136	70	(	(	PUNCT
ejpam-4479	136	71	g	g	PROPN
ejpam-4479	136	72	,	,	PUNCT
ejpam-4479	136	73	b	b	NOUN
ejpam-4479	136	74	)	)	PUNCT
ejpam-4479	136	75	=	=	SYM
ejpam-4479	136	76	(	(	PUNCT
ejpam-4479	136	77	j	j	PROPN
ejpam-4479	136	78	,	,	PUNCT
ejpam-4479	136	79	a×b	a×b	PROPN
ejpam-4479	136	80	)	)	PUNCT
ejpam-4479	136	81	is	be	AUX
ejpam-4479	136	82	a	a	DET
ejpam-4479	136	83	soft	soft	ADJ
ejpam-4479	136	84	hyper	hyper	ADJ
ejpam-4479	136	85	gr	gr	NOUN
ejpam-4479	136	86	-	-	NOUN
ejpam-4479	136	87	algebra	algebra	NOUN
ejpam-4479	136	88	over	over	ADP
ejpam-4479	136	89	h.	h.	PROPN
ejpam-4479	136	90	definition	definition	NOUN
ejpam-4479	136	91	13	13	NUM
ejpam-4479	136	92	.	.	PUNCT
ejpam-4479	137	1	a	a	DET
ejpam-4479	137	2	soft	soft	ADJ
ejpam-4479	137	3	hyper	hyper	ADJ
ejpam-4479	137	4	gr	gr	NOUN
ejpam-4479	137	5	-	-	PUNCT
ejpam-4479	137	6	algebra	algebra	NOUN
ejpam-4479	137	7	(	(	PUNCT
ejpam-4479	137	8	f	f	X
ejpam-4479	137	9	,	,	PUNCT
ejpam-4479	137	10	a	a	PRON
ejpam-4479	137	11	)	)	PUNCT
ejpam-4479	137	12	over	over	ADP
ejpam-4479	137	13	h	h	NOUN
ejpam-4479	137	14	is	be	AUX
ejpam-4479	137	15	said	say	VERB
ejpam-4479	137	16	to	to	PART
ejpam-4479	137	17	be	be	AUX
ejpam-4479	137	18	trivial	trivial	ADJ
ejpam-4479	137	19	(	(	PUNCT
ejpam-4479	137	20	respectively	respectively	ADV
ejpam-4479	137	21	,	,	PUNCT
ejpam-4479	137	22	whole	whole	ADJ
ejpam-4479	137	23	)	)	PUNCT
ejpam-4479	138	1	if	if	SCONJ
ejpam-4479	138	2	f	f	PROPN
ejpam-4479	138	3	(	(	PUNCT
ejpam-4479	138	4	a	a	X
ejpam-4479	138	5	)	)	PUNCT
ejpam-4479	138	6	=	=	SYM
ejpam-4479	138	7	{	{	PUNCT
ejpam-4479	138	8	0	0	NUM
ejpam-4479	138	9	}	}	PUNCT
ejpam-4479	138	10	(	(	PUNCT
ejpam-4479	138	11	respectively	respectively	ADV
ejpam-4479	138	12	,	,	PUNCT
ejpam-4479	138	13	f	f	PROPN
ejpam-4479	138	14	(	(	PUNCT
ejpam-4479	138	15	a	a	NOUN
ejpam-4479	138	16	)	)	PUNCT
ejpam-4479	138	17	=	=	SYM
ejpam-4479	138	18	x	x	X
ejpam-4479	138	19	)	)	PUNCT
ejpam-4479	138	20	for	for	ADP
ejpam-4479	138	21	all	all	DET
ejpam-4479	138	22	a	a	DET
ejpam-4479	138	23	∈	∈	PROPN
ejpam-4479	138	24	a.	a.	NOUN
ejpam-4479	138	25	example	example	NOUN
ejpam-4479	138	26	7	7	X
ejpam-4479	138	27	.	.	PUNCT
ejpam-4479	139	1	let	let	VERB
ejpam-4479	139	2	h	h	NOUN
ejpam-4479	139	3	=	=	PRON
ejpam-4479	139	4	{	{	PUNCT
ejpam-4479	139	5	0	0	NUM
ejpam-4479	139	6	,	,	PUNCT
ejpam-4479	139	7	1	1	NUM
ejpam-4479	139	8	}	}	PUNCT
ejpam-4479	139	9	.	.	PUNCT
ejpam-4479	140	1	define	define	VERB
ejpam-4479	140	2	⊛	⊛	NOUN
ejpam-4479	140	3	as	as	SCONJ
ejpam-4479	140	4	shown	show	VERB
ejpam-4479	140	5	in	in	ADP
ejpam-4479	140	6	the	the	DET
ejpam-4479	140	7	table	table	NOUN
ejpam-4479	140	8	below	below	ADV
ejpam-4479	140	9	.	.	PUNCT
ejpam-4479	141	1	⊛	⊛	NUM
ejpam-4479	141	2	0	0	NUM
ejpam-4479	141	3	1	1	NUM
ejpam-4479	141	4	0	0	NUM
ejpam-4479	141	5	{	{	PUNCT
ejpam-4479	141	6	0	0	NUM
ejpam-4479	141	7	}	}	PUNCT
ejpam-4479	141	8	{	{	PUNCT
ejpam-4479	141	9	0	0	NUM
ejpam-4479	141	10	}	}	SYM
ejpam-4479	141	11	1	1	NUM
ejpam-4479	141	12	{	{	PUNCT
ejpam-4479	141	13	0	0	NUM
ejpam-4479	141	14	}	}	PUNCT
ejpam-4479	141	15	{	{	PUNCT
ejpam-4479	141	16	0	0	NUM
ejpam-4479	141	17	}	}	PUNCT
ejpam-4479	141	18	.	.	PUNCT
ejpam-4479	142	1	by	by	ADP
ejpam-4479	142	2	routine	routine	ADJ
ejpam-4479	142	3	calculations	calculation	NOUN
ejpam-4479	142	4	,	,	PUNCT
ejpam-4479	142	5	(	(	PUNCT
ejpam-4479	142	6	h;⊛	h;⊛	X
ejpam-4479	142	7	,	,	PUNCT
ejpam-4479	142	8	0	0	NUM
ejpam-4479	142	9	)	)	PUNCT
ejpam-4479	142	10	is	be	AUX
ejpam-4479	142	11	a	a	DET
ejpam-4479	142	12	hyper	hyper	ADJ
ejpam-4479	142	13	gr	gr	NOUN
ejpam-4479	142	14	-	-	NOUN
ejpam-4479	142	15	algebra	algebra	NOUN
ejpam-4479	142	16	.	.	PUNCT
ejpam-4479	143	1	let	let	VERB
ejpam-4479	143	2	a	a	DET
ejpam-4479	143	3	=	=	NOUN
ejpam-4479	143	4	h	h	NOUN
ejpam-4479	143	5	and	and	CCONJ
ejpam-4479	143	6	let	let	VERB
ejpam-4479	143	7	f	f	NOUN
ejpam-4479	143	8	:	:	PUNCT
ejpam-4479	143	9	a	a	DET
ejpam-4479	143	10	→	→	SYM
ejpam-4479	143	11	p	p	X
ejpam-4479	143	12	(	(	PUNCT
ejpam-4479	143	13	h	h	NOUN
ejpam-4479	143	14	)	)	PUNCT
ejpam-4479	143	15	be	be	VERB
ejpam-4479	143	16	the	the	DET
ejpam-4479	143	17	set	set	NOUN
ejpam-4479	143	18	-	-	PUNCT
ejpam-4479	143	19	valued	value	VERB
ejpam-4479	143	20	function	function	NOUN
ejpam-4479	143	21	defined	define	VERB
ejpam-4479	143	22	as	as	SCONJ
ejpam-4479	143	23	follows	follow	VERB
ejpam-4479	143	24	:	:	PUNCT
ejpam-4479	143	25	f	f	X
ejpam-4479	143	26	(	(	PUNCT
ejpam-4479	143	27	a	a	NOUN
ejpam-4479	143	28	)	)	PUNCT
ejpam-4479	143	29	=	=	SYM
ejpam-4479	143	30	⋃	⋃	NOUN
ejpam-4479	143	31	b⊂h	b⊂h	NOUN
ejpam-4479	143	32	,	,	PUNCT
ejpam-4479	143	33	ar̊b⇔0⊛x≪b	ar̊b⇔0⊛x≪b	NOUN
ejpam-4479	143	34	b.	b.	PROPN
ejpam-4479	144	1	then	then	ADV
ejpam-4479	144	2	,	,	PUNCT
ejpam-4479	144	3	f	f	PROPN
ejpam-4479	144	4	(	(	PUNCT
ejpam-4479	144	5	0	0	NUM
ejpam-4479	144	6	)	)	PUNCT
ejpam-4479	144	7	=	=	SYM
ejpam-4479	144	8	f	f	X
ejpam-4479	144	9	(	(	PUNCT
ejpam-4479	144	10	1	1	NUM
ejpam-4479	144	11	)	)	PUNCT
ejpam-4479	144	12	=	=	SYM
ejpam-4479	144	13	f	f	PROPN
ejpam-4479	144	14	(	(	PUNCT
ejpam-4479	144	15	2	2	NUM
ejpam-4479	144	16	)	)	PUNCT
ejpam-4479	144	17	=	=	NOUN
ejpam-4479	144	18	{	{	PUNCT
ejpam-4479	144	19	0	0	NUM
ejpam-4479	144	20	}	}	PUNCT
ejpam-4479	144	21	.	.	PUNCT
ejpam-4479	145	1	since	since	SCONJ
ejpam-4479	145	2	{	{	PUNCT
ejpam-4479	145	3	0	0	NUM
ejpam-4479	145	4	}	}	PUNCT
ejpam-4479	145	5	is	be	AUX
ejpam-4479	145	6	a	a	DET
ejpam-4479	145	7	hyper	hyper	ADJ
ejpam-4479	145	8	subgr	subgr	NOUN
ejpam-4479	145	9	-	-	PUNCT
ejpam-4479	145	10	algebra	algebra	NOUN
ejpam-4479	145	11	of	of	ADP
ejpam-4479	145	12	h	h	NOUN
ejpam-4479	145	13	,	,	PUNCT
ejpam-4479	145	14	(	(	PUNCT
ejpam-4479	145	15	f	f	X
ejpam-4479	145	16	,	,	PUNCT
ejpam-4479	145	17	a	a	PRON
ejpam-4479	145	18	)	)	PUNCT
ejpam-4479	145	19	is	be	AUX
ejpam-4479	145	20	a	a	DET
ejpam-4479	145	21	trivial	trivial	ADJ
ejpam-4479	145	22	soft	soft	ADJ
ejpam-4479	145	23	hyper	hyper	ADJ
ejpam-4479	145	24	gr	gr	NOUN
ejpam-4479	145	25	-	-	PUNCT
ejpam-4479	145	26	algebra	algebra	NOUN
ejpam-4479	145	27	of	of	ADP
ejpam-4479	145	28	h.	h.	PROPN
ejpam-4479	145	29	m.k	m.k	PROPN
ejpam-4479	145	30	.	.	PROPN
ejpam-4479	145	31	engcot	engcot	PROPN
ejpam-4479	145	32	,	,	PUNCT
ejpam-4479	145	33	g.	g.	PROPN
ejpam-4479	145	34	petalcorin	petalcorin	PROPN
ejpam-4479	145	35	/	/	SYM
ejpam-4479	145	36	eur	eur	PROPN
ejpam-4479	145	37	.	.	PUNCT
ejpam-4479	146	1	j.	j.	PROPN
ejpam-4479	146	2	pure	pure	PROPN
ejpam-4479	146	3	appl	appl	PROPN
ejpam-4479	146	4	.	.	PROPN
ejpam-4479	146	5	math	math	PROPN
ejpam-4479	146	6	,	,	PUNCT
ejpam-4479	146	7	15	15	NUM
ejpam-4479	146	8	(	(	PUNCT
ejpam-4479	146	9	4	4	NUM
ejpam-4479	146	10	)	)	PUNCT
ejpam-4479	146	11	(	(	PUNCT
ejpam-4479	146	12	2022	2022	NUM
ejpam-4479	146	13	)	)	PUNCT
ejpam-4479	146	14	,	,	PUNCT
ejpam-4479	146	15	1482	1482	NUM
ejpam-4479	146	16	-	-	SYM
ejpam-4479	146	17	1497	1497	NUM
ejpam-4479	146	18	1488	1488	NUM
ejpam-4479	146	19	example	example	NOUN
ejpam-4479	146	20	8	8	NUM
ejpam-4479	146	21	.	.	PUNCT
ejpam-4479	147	1	let	let	VERB
ejpam-4479	147	2	h	h	NOUN
ejpam-4479	147	3	=	=	PRON
ejpam-4479	147	4	{	{	PUNCT
ejpam-4479	147	5	0	0	NUM
ejpam-4479	147	6	,	,	PUNCT
ejpam-4479	147	7	1	1	NUM
ejpam-4479	147	8	,	,	PUNCT
ejpam-4479	147	9	2	2	NUM
ejpam-4479	147	10	}	}	PUNCT
ejpam-4479	147	11	.	.	PUNCT
ejpam-4479	148	1	define	define	VERB
ejpam-4479	148	2	⊛	⊛	NOUN
ejpam-4479	148	3	as	as	SCONJ
ejpam-4479	148	4	shown	show	VERB
ejpam-4479	148	5	in	in	ADP
ejpam-4479	148	6	the	the	DET
ejpam-4479	148	7	table	table	NOUN
ejpam-4479	148	8	below	below	ADV
ejpam-4479	148	9	:	:	PUNCT
ejpam-4479	148	10	⊛	⊛	NUM
ejpam-4479	148	11	0	0	NUM
ejpam-4479	148	12	1	1	NUM
ejpam-4479	148	13	2	2	NUM
ejpam-4479	148	14	0	0	NUM
ejpam-4479	148	15	{	{	PUNCT
ejpam-4479	148	16	0	0	NUM
ejpam-4479	148	17	}	}	PUNCT
ejpam-4479	148	18	{	{	PUNCT
ejpam-4479	148	19	0	0	NUM
ejpam-4479	148	20	}	}	PUNCT
ejpam-4479	148	21	{	{	PUNCT
ejpam-4479	148	22	0	0	NUM
ejpam-4479	148	23	}	}	SYM
ejpam-4479	148	24	1	1	NUM
ejpam-4479	148	25	{	{	PUNCT
ejpam-4479	148	26	0,1,2	0,1,2	NOUN
ejpam-4479	148	27	}	}	PUNCT
ejpam-4479	148	28	{	{	PUNCT
ejpam-4479	148	29	0,1	0,1	NOUN
ejpam-4479	148	30	}	}	PUNCT
ejpam-4479	148	31	{	{	PUNCT
ejpam-4479	148	32	0,1	0,1	NOUN
ejpam-4479	148	33	}	}	SYM
ejpam-4479	148	34	2	2	NUM
ejpam-4479	148	35	{	{	PUNCT
ejpam-4479	148	36	0,2	0,2	NUM
ejpam-4479	148	37	}	}	PUNCT
ejpam-4479	148	38	{	{	PUNCT
ejpam-4479	148	39	0,1,2	0,1,2	NOUN
ejpam-4479	148	40	}	}	PUNCT
ejpam-4479	148	41	{	{	PUNCT
ejpam-4479	148	42	0,1,2	0,1,2	NOUN
ejpam-4479	148	43	}	}	PUNCT
ejpam-4479	148	44	.	.	PUNCT
ejpam-4479	149	1	by	by	ADP
ejpam-4479	149	2	routine	routine	ADJ
ejpam-4479	149	3	calculations	calculation	NOUN
ejpam-4479	149	4	,	,	PUNCT
ejpam-4479	149	5	(	(	PUNCT
ejpam-4479	149	6	h;⊛	h;⊛	X
ejpam-4479	149	7	,	,	PUNCT
ejpam-4479	149	8	0	0	NUM
ejpam-4479	149	9	)	)	PUNCT
ejpam-4479	149	10	is	be	AUX
ejpam-4479	149	11	a	a	DET
ejpam-4479	149	12	hyper	hyper	ADJ
ejpam-4479	149	13	gr	gr	NOUN
ejpam-4479	149	14	-	-	NOUN
ejpam-4479	149	15	algebra	algebra	NOUN
ejpam-4479	149	16	.	.	PUNCT
ejpam-4479	150	1	let	let	VERB
ejpam-4479	150	2	a	a	DET
ejpam-4479	150	3	=	=	NOUN
ejpam-4479	150	4	h	h	NOUN
ejpam-4479	150	5	and	and	CCONJ
ejpam-4479	150	6	let	let	VERB
ejpam-4479	150	7	f	f	NOUN
ejpam-4479	150	8	:	:	PUNCT
ejpam-4479	150	9	a	a	DET
ejpam-4479	150	10	→	→	SYM
ejpam-4479	150	11	p	p	X
ejpam-4479	150	12	(	(	PUNCT
ejpam-4479	150	13	h	h	NOUN
ejpam-4479	150	14	)	)	PUNCT
ejpam-4479	150	15	be	be	VERB
ejpam-4479	150	16	the	the	DET
ejpam-4479	150	17	set	set	NOUN
ejpam-4479	150	18	-	-	PUNCT
ejpam-4479	150	19	valued	value	VERB
ejpam-4479	150	20	function	function	NOUN
ejpam-4479	150	21	defined	define	VERB
ejpam-4479	150	22	as	as	SCONJ
ejpam-4479	150	23	follows	follow	VERB
ejpam-4479	150	24	:	:	PUNCT
ejpam-4479	150	25	f	f	X
ejpam-4479	150	26	(	(	PUNCT
ejpam-4479	150	27	a	a	NOUN
ejpam-4479	150	28	)	)	PUNCT
ejpam-4479	150	29	=	=	SYM
ejpam-4479	150	30	⋃	⋃	NOUN
ejpam-4479	150	31	b⊂h	b⊂h	NOUN
ejpam-4479	150	32	,	,	PUNCT
ejpam-4479	150	33	ar̊b⇔x⊛0≪b	ar̊b⇔x⊛0≪b	PROPN
ejpam-4479	150	34	b	b	PROPN
ejpam-4479	150	35	,	,	PUNCT
ejpam-4479	150	36	where	where	SCONJ
ejpam-4479	150	37	b	b	X
ejpam-4479	150	38	⊂	⊂	PROPN
ejpam-4479	150	39	h	h	NOUN
ejpam-4479	150	40	and	and	CCONJ
ejpam-4479	150	41	define	define	VERB
ejpam-4479	150	42	a	a	DET
ejpam-4479	150	43	relation	relation	NOUN
ejpam-4479	150	44	r̊	r̊	PRON
ejpam-4479	150	45	such	such	ADJ
ejpam-4479	150	46	that	that	SCONJ
ejpam-4479	150	47	ar̊b	ar̊b	PROPN
ejpam-4479	150	48	if	if	SCONJ
ejpam-4479	150	49	and	and	CCONJ
ejpam-4479	150	50	only	only	ADV
ejpam-4479	150	51	if	if	SCONJ
ejpam-4479	150	52	x⊛	x⊛	PROPN
ejpam-4479	150	53	0	0	NUM
ejpam-4479	150	54	≪	≪	NOUN
ejpam-4479	150	55	b	b	NOUN
ejpam-4479	150	56	and	and	CCONJ
ejpam-4479	150	57	a	a	DET
ejpam-4479	150	58	∈	∈	NOUN
ejpam-4479	150	59	a.	a.	NOUN
ejpam-4479	151	1	then	then	ADV
ejpam-4479	151	2	f	f	X
ejpam-4479	151	3	(	(	PUNCT
ejpam-4479	151	4	0	0	NUM
ejpam-4479	151	5	)	)	PUNCT
ejpam-4479	151	6	=	=	SYM
ejpam-4479	151	7	f	f	X
ejpam-4479	151	8	(	(	PUNCT
ejpam-4479	151	9	1	1	NUM
ejpam-4479	151	10	)	)	PUNCT
ejpam-4479	151	11	=	=	SYM
ejpam-4479	151	12	f	f	PROPN
ejpam-4479	151	13	(	(	PUNCT
ejpam-4479	151	14	2	2	NUM
ejpam-4479	151	15	)	)	PUNCT
ejpam-4479	151	16	=	=	NOUN
ejpam-4479	151	17	{	{	PUNCT
ejpam-4479	151	18	0	0	NUM
ejpam-4479	151	19	,	,	PUNCT
ejpam-4479	151	20	1	1	NUM
ejpam-4479	151	21	,	,	PUNCT
ejpam-4479	151	22	2	2	NUM
ejpam-4479	151	23	}	}	PUNCT
ejpam-4479	151	24	=	=	SYM
ejpam-4479	151	25	h.	h.	NOUN
ejpam-4479	151	26	since	since	SCONJ
ejpam-4479	151	27	h	h	PROPN
ejpam-4479	151	28	is	be	AUX
ejpam-4479	151	29	a	a	DET
ejpam-4479	151	30	hyper	hyper	ADJ
ejpam-4479	151	31	gr	gr	NOUN
ejpam-4479	151	32	-	-	NOUN
ejpam-4479	151	33	algebra	algebra	NOUN
ejpam-4479	151	34	of	of	ADP
ejpam-4479	151	35	h	h	NOUN
ejpam-4479	151	36	,	,	PUNCT
ejpam-4479	151	37	(	(	PUNCT
ejpam-4479	151	38	f	f	X
ejpam-4479	151	39	,	,	PUNCT
ejpam-4479	151	40	a	a	PRON
ejpam-4479	151	41	)	)	PUNCT
ejpam-4479	151	42	is	be	AUX
ejpam-4479	151	43	whole	whole	ADJ
ejpam-4479	151	44	soft	soft	ADJ
ejpam-4479	151	45	hyper	hyper	ADJ
ejpam-4479	151	46	gr	gr	NOUN
ejpam-4479	151	47	-	-	PUNCT
ejpam-4479	151	48	algebra	algebra	NOUN
ejpam-4479	151	49	of	of	ADP
ejpam-4479	151	50	h.	h.	PROPN
ejpam-4479	151	51	lemma	lemma	PROPN
ejpam-4479	152	1	2	2	X
ejpam-4479	152	2	.	.	PUNCT
ejpam-4479	152	3	let	let	VERB
ejpam-4479	152	4	f	f	NOUN
ejpam-4479	152	5	:	:	PUNCT
ejpam-4479	152	6	h	h	PROPN
ejpam-4479	152	7	→	→	SYM
ejpam-4479	152	8	y	y	PROPN
ejpam-4479	152	9	be	be	AUX
ejpam-4479	152	10	a	a	DET
ejpam-4479	152	11	homomorphism	homomorphism	NOUN
ejpam-4479	152	12	of	of	ADP
ejpam-4479	152	13	hyper	hyper	ADJ
ejpam-4479	152	14	gr	gr	NOUN
ejpam-4479	152	15	-	-	PUNCT
ejpam-4479	152	16	algebras	algebras	NOUN
ejpam-4479	152	17	.	.	PUNCT
ejpam-4479	153	1	if	if	SCONJ
ejpam-4479	153	2	(	(	PUNCT
ejpam-4479	153	3	f	f	X
ejpam-4479	153	4	,	,	PUNCT
ejpam-4479	153	5	a	a	PRON
ejpam-4479	153	6	)	)	PUNCT
ejpam-4479	153	7	is	be	AUX
ejpam-4479	153	8	a	a	DET
ejpam-4479	153	9	soft	soft	ADJ
ejpam-4479	153	10	hyper	hyper	ADJ
ejpam-4479	153	11	gr	gr	NOUN
ejpam-4479	153	12	-	-	NOUN
ejpam-4479	153	13	algebra	algebra	NOUN
ejpam-4479	153	14	over	over	ADP
ejpam-4479	153	15	h	h	NOUN
ejpam-4479	153	16	,	,	PUNCT
ejpam-4479	153	17	then	then	ADV
ejpam-4479	153	18	(	(	PUNCT
ejpam-4479	153	19	f(f	f(f	PROPN
ejpam-4479	153	20	)	)	PUNCT
ejpam-4479	153	21	,	,	PUNCT
ejpam-4479	153	22	a	a	PRON
ejpam-4479	153	23	)	)	PUNCT
ejpam-4479	153	24	is	be	AUX
ejpam-4479	153	25	a	a	DET
ejpam-4479	153	26	soft	soft	ADJ
ejpam-4479	153	27	hyper	hyper	ADJ
ejpam-4479	153	28	gr	gr	NOUN
ejpam-4479	153	29	-	-	NOUN
ejpam-4479	153	30	algebra	algebra	NOUN
ejpam-4479	153	31	over	over	ADP
ejpam-4479	153	32	y	y	PROPN
ejpam-4479	153	33	.	.	PUNCT
ejpam-4479	154	1	proof	proof	NOUN
ejpam-4479	154	2	:	:	PUNCT
ejpam-4479	154	3	let	let	VERB
ejpam-4479	154	4	a	a	DET
ejpam-4479	154	5	∈	∈	NOUN
ejpam-4479	154	6	a.	a.	NOUN
ejpam-4479	154	7	since	since	SCONJ
ejpam-4479	154	8	f	f	PROPN
ejpam-4479	154	9	(	(	PUNCT
ejpam-4479	154	10	a	a	NOUN
ejpam-4479	154	11	)	)	PUNCT
ejpam-4479	154	12	is	be	AUX
ejpam-4479	154	13	a	a	DET
ejpam-4479	154	14	hyper	hyper	ADJ
ejpam-4479	154	15	subgr	subgr	NOUN
ejpam-4479	154	16	-	-	PUNCT
ejpam-4479	154	17	algebra	algebra	NOUN
ejpam-4479	154	18	on	on	ADP
ejpam-4479	154	19	h	h	NOUN
ejpam-4479	154	20	and	and	CCONJ
ejpam-4479	154	21	f	f	PROPN
ejpam-4479	154	22	is	be	AUX
ejpam-4479	154	23	a	a	DET
ejpam-4479	154	24	homomorphism	homomorphism	NOUN
ejpam-4479	154	25	,	,	PUNCT
ejpam-4479	154	26	it	it	PRON
ejpam-4479	154	27	follows	follow	VERB
ejpam-4479	154	28	that	that	SCONJ
ejpam-4479	154	29	f(f	f(f	PROPN
ejpam-4479	154	30	)	)	PUNCT
ejpam-4479	154	31	(	(	PUNCT
ejpam-4479	154	32	a	a	X
ejpam-4479	154	33	)	)	PUNCT
ejpam-4479	154	34	=	=	SYM
ejpam-4479	154	35	f(f	f(f	X
ejpam-4479	154	36	(	(	PUNCT
ejpam-4479	154	37	a	a	NOUN
ejpam-4479	154	38	)	)	PUNCT
ejpam-4479	154	39	)	)	PUNCT
ejpam-4479	154	40	is	be	AUX
ejpam-4479	154	41	a	a	DET
ejpam-4479	154	42	hyper	hyper	ADJ
ejpam-4479	154	43	subgr	subgr	NOUN
ejpam-4479	154	44	-	-	PUNCT
ejpam-4479	154	45	algebra	algebra	NOUN
ejpam-4479	154	46	on	on	ADP
ejpam-4479	154	47	y	y	PROPN
ejpam-4479	154	48	by	by	ADP
ejpam-4479	154	49	lemma	lemma	PROPN
ejpam-4479	154	50	1	1	NUM
ejpam-4479	154	51	.	.	PUNCT
ejpam-4479	155	1	hence	hence	ADV
ejpam-4479	155	2	,	,	PUNCT
ejpam-4479	155	3	(	(	PUNCT
ejpam-4479	155	4	f(f	f(f	PROPN
ejpam-4479	155	5	)	)	PUNCT
ejpam-4479	155	6	,	,	PUNCT
ejpam-4479	155	7	a	a	PRON
ejpam-4479	155	8	)	)	PUNCT
ejpam-4479	155	9	is	be	AUX
ejpam-4479	155	10	a	a	DET
ejpam-4479	155	11	soft	soft	ADJ
ejpam-4479	155	12	hyper	hyper	ADJ
ejpam-4479	155	13	gr	gr	NOUN
ejpam-4479	155	14	-	-	NOUN
ejpam-4479	155	15	algebra	algebra	NOUN
ejpam-4479	155	16	on	on	ADP
ejpam-4479	155	17	y	y	PROPN
ejpam-4479	155	18	.	.	PUNCT
ejpam-4479	156	1	theorem	theorem	ADJ
ejpam-4479	156	2	7	7	NUM
ejpam-4479	156	3	.	.	PUNCT
ejpam-4479	157	1	let	let	VERB
ejpam-4479	157	2	f	f	NOUN
ejpam-4479	157	3	:	:	PUNCT
ejpam-4479	157	4	h	h	PROPN
ejpam-4479	157	5	→	→	SYM
ejpam-4479	157	6	y	y	PROPN
ejpam-4479	157	7	be	be	AUX
ejpam-4479	157	8	a	a	DET
ejpam-4479	157	9	homomorphism	homomorphism	NOUN
ejpam-4479	157	10	of	of	ADP
ejpam-4479	157	11	hyper	hyper	ADJ
ejpam-4479	157	12	gr	gr	NOUN
ejpam-4479	157	13	-	-	PUNCT
ejpam-4479	157	14	algebras	algebras	NOUN
ejpam-4479	157	15	and	and	CCONJ
ejpam-4479	157	16	let	let	VERB
ejpam-4479	157	17	(	(	PUNCT
ejpam-4479	157	18	f	f	X
ejpam-4479	157	19	,	,	PUNCT
ejpam-4479	157	20	a	a	PRON
ejpam-4479	157	21	)	)	PUNCT
ejpam-4479	157	22	be	be	AUX
ejpam-4479	157	23	a	a	DET
ejpam-4479	157	24	soft	soft	ADJ
ejpam-4479	157	25	hyper	hyper	ADJ
ejpam-4479	157	26	gr	gr	NOUN
ejpam-4479	157	27	-	-	NOUN
ejpam-4479	157	28	algebra	algebra	NOUN
ejpam-4479	157	29	over	over	ADP
ejpam-4479	157	30	h.	h.	PROPN
ejpam-4479	157	31	(	(	PUNCT
ejpam-4479	157	32	i	i	NOUN
ejpam-4479	157	33	)	)	PUNCT
ejpam-4479	157	34	(	(	PUNCT
ejpam-4479	157	35	f(f	f(f	PROPN
ejpam-4479	157	36	)	)	PUNCT
ejpam-4479	157	37	,	,	PUNCT
ejpam-4479	157	38	a	a	PRON
ejpam-4479	157	39	)	)	PUNCT
ejpam-4479	157	40	is	be	AUX
ejpam-4479	157	41	trivial	trivial	ADJ
ejpam-4479	157	42	soft	soft	ADJ
ejpam-4479	157	43	hyper	hyper	ADJ
ejpam-4479	157	44	gr	gr	NOUN
ejpam-4479	157	45	-	-	NOUN
ejpam-4479	157	46	algebra	algebra	NOUN
ejpam-4479	157	47	over	over	ADP
ejpam-4479	157	48	y	y	PROPN
ejpam-4479	157	49	if	if	SCONJ
ejpam-4479	158	1	and	and	CCONJ
ejpam-4479	158	2	only	only	ADV
ejpam-4479	158	3	if	if	SCONJ
ejpam-4479	158	4	f	f	PROPN
ejpam-4479	158	5	(	(	PUNCT
ejpam-4479	158	6	x	x	X
ejpam-4479	158	7	)	)	PUNCT
ejpam-4479	158	8	⊆	⊆	NUM
ejpam-4479	158	9	ker	ker	NOUN
ejpam-4479	158	10	f	f	PROPN
ejpam-4479	158	11	for	for	ADP
ejpam-4479	158	12	all	all	DET
ejpam-4479	158	13	x	x	SYM
ejpam-4479	158	14	∈	∈	PROPN
ejpam-4479	158	15	a.	a.	NOUN
ejpam-4479	158	16	(	(	PUNCT
ejpam-4479	158	17	ii	ii	NOUN
ejpam-4479	158	18	)	)	PUNCT
ejpam-4479	158	19	if	if	SCONJ
ejpam-4479	158	20	f	f	PROPN
ejpam-4479	158	21	is	be	AUX
ejpam-4479	158	22	onto	onto	ADP
ejpam-4479	158	23	and	and	CCONJ
ejpam-4479	158	24	(	(	PUNCT
ejpam-4479	158	25	f	f	X
ejpam-4479	158	26	,	,	PUNCT
ejpam-4479	158	27	a	a	PRON
ejpam-4479	158	28	)	)	PUNCT
ejpam-4479	158	29	is	be	AUX
ejpam-4479	158	30	whole	whole	ADJ
ejpam-4479	158	31	,	,	PUNCT
ejpam-4479	158	32	then	then	ADV
ejpam-4479	158	33	(	(	PUNCT
ejpam-4479	158	34	f(f	f(f	PROPN
ejpam-4479	158	35	)	)	PUNCT
ejpam-4479	158	36	,	,	PUNCT
ejpam-4479	158	37	a	a	PRON
ejpam-4479	158	38	)	)	PUNCT
ejpam-4479	158	39	is	be	AUX
ejpam-4479	158	40	a	a	DET
ejpam-4479	158	41	whole	whole	ADJ
ejpam-4479	158	42	soft	soft	ADJ
ejpam-4479	158	43	hyper	hyper	ADJ
ejpam-4479	158	44	gr	gr	NOUN
ejpam-4479	158	45	-	-	NOUN
ejpam-4479	158	46	algebra	algebra	NOUN
ejpam-4479	158	47	over	over	ADP
ejpam-4479	158	48	y	y	PROPN
ejpam-4479	158	49	.	.	PUNCT
ejpam-4479	159	1	(	(	PUNCT
ejpam-4479	159	2	iii	iii	X
ejpam-4479	159	3	)	)	PUNCT
ejpam-4479	159	4	if	if	SCONJ
ejpam-4479	159	5	(	(	PUNCT
ejpam-4479	159	6	f(f	f(f	PROPN
ejpam-4479	159	7	)	)	PUNCT
ejpam-4479	159	8	,	,	PUNCT
ejpam-4479	159	9	a	a	PRON
ejpam-4479	159	10	)	)	PUNCT
ejpam-4479	159	11	is	be	AUX
ejpam-4479	159	12	whole	whole	ADJ
ejpam-4479	159	13	and	and	CCONJ
ejpam-4479	159	14	f	f	PROPN
ejpam-4479	159	15	is	be	AUX
ejpam-4479	159	16	one	one	NUM
ejpam-4479	159	17	-	-	PUNCT
ejpam-4479	159	18	to	to	ADP
ejpam-4479	159	19	-	-	PUNCT
ejpam-4479	159	20	one	one	NUM
ejpam-4479	159	21	,	,	PUNCT
ejpam-4479	159	22	then	then	ADV
ejpam-4479	159	23	f	f	PROPN
ejpam-4479	159	24	is	be	AUX
ejpam-4479	159	25	onto	onto	ADP
ejpam-4479	159	26	and	and	CCONJ
ejpam-4479	159	27	(	(	PUNCT
ejpam-4479	159	28	f	f	X
ejpam-4479	159	29	,	,	PUNCT
ejpam-4479	159	30	a	a	PRON
ejpam-4479	159	31	)	)	PUNCT
ejpam-4479	159	32	is	be	AUX
ejpam-4479	159	33	a	a	DET
ejpam-4479	159	34	whole	whole	ADJ
ejpam-4479	159	35	soft	soft	ADJ
ejpam-4479	159	36	hyper	hyper	ADJ
ejpam-4479	159	37	gr	gr	NOUN
ejpam-4479	159	38	-	-	NOUN
ejpam-4479	159	39	algebra	algebra	NOUN
ejpam-4479	159	40	over	over	ADP
ejpam-4479	159	41	y	y	PROPN
ejpam-4479	159	42	.	.	PUNCT
ejpam-4479	160	1	(	(	PUNCT
ejpam-4479	160	2	iv	iv	X
ejpam-4479	160	3	)	)	PUNCT
ejpam-4479	160	4	if	if	SCONJ
ejpam-4479	160	5	f	f	PROPN
ejpam-4479	160	6	is	be	AUX
ejpam-4479	160	7	bijective	bijective	ADJ
ejpam-4479	160	8	,	,	PUNCT
ejpam-4479	160	9	then	then	ADV
ejpam-4479	160	10	(	(	PUNCT
ejpam-4479	160	11	f	f	X
ejpam-4479	160	12	,	,	PUNCT
ejpam-4479	160	13	a	a	PRON
ejpam-4479	160	14	)	)	PUNCT
ejpam-4479	160	15	is	be	AUX
ejpam-4479	160	16	whole	whole	ADJ
ejpam-4479	160	17	over	over	ADP
ejpam-4479	160	18	h	h	NOUN
ejpam-4479	160	19	if	if	SCONJ
ejpam-4479	161	1	and	and	CCONJ
ejpam-4479	161	2	only	only	ADV
ejpam-4479	161	3	if	if	SCONJ
ejpam-4479	161	4	(	(	PUNCT
ejpam-4479	161	5	f(f	f(f	PROPN
ejpam-4479	161	6	)	)	PUNCT
ejpam-4479	161	7	,	,	PUNCT
ejpam-4479	161	8	a	a	PRON
ejpam-4479	161	9	)	)	PUNCT
ejpam-4479	161	10	is	be	AUX
ejpam-4479	161	11	whole	whole	ADJ
ejpam-4479	161	12	over	over	ADP
ejpam-4479	161	13	h.	h.	PROPN
ejpam-4479	161	14	proof	proof	NOUN
ejpam-4479	161	15	:	:	PUNCT
ejpam-4479	161	16	(	(	PUNCT
ejpam-4479	161	17	i	i	NOUN
ejpam-4479	161	18	)	)	PUNCT
ejpam-4479	161	19	suppose	suppose	VERB
ejpam-4479	162	1	f	f	X
ejpam-4479	162	2	(	(	PUNCT
ejpam-4479	162	3	a	a	NOUN
ejpam-4479	162	4	)	)	PUNCT
ejpam-4479	162	5	⊆	⊆	NUM
ejpam-4479	162	6	kerf	kerf	NOUN
ejpam-4479	162	7	for	for	ADP
ejpam-4479	162	8	all	all	DET
ejpam-4479	162	9	a	a	DET
ejpam-4479	162	10	∈	∈	NOUN
ejpam-4479	162	11	a.	a.	NOUN
ejpam-4479	162	12	then	then	ADV
ejpam-4479	162	13	f(f	f(f	PROPN
ejpam-4479	162	14	)	)	PUNCT
ejpam-4479	162	15	(	(	PUNCT
ejpam-4479	162	16	a	a	X
ejpam-4479	162	17	)	)	PUNCT
ejpam-4479	162	18	=	=	SYM
ejpam-4479	162	19	f(f	f(f	X
ejpam-4479	162	20	(	(	PUNCT
ejpam-4479	162	21	a	a	NOUN
ejpam-4479	162	22	)	)	PUNCT
ejpam-4479	162	23	)	)	PUNCT
ejpam-4479	162	24	=	=	PRON
ejpam-4479	162	25	{	{	PUNCT
ejpam-4479	162	26	0y	0y	NOUN
ejpam-4479	162	27	}	}	PUNCT
ejpam-4479	162	28	for	for	ADP
ejpam-4479	162	29	all	all	DET
ejpam-4479	162	30	a	a	DET
ejpam-4479	162	31	∈	∈	NOUN
ejpam-4479	162	32	a.	a.	NOUN
ejpam-4479	162	33	hence	hence	ADV
ejpam-4479	162	34	,	,	PUNCT
ejpam-4479	162	35	(	(	PUNCT
ejpam-4479	162	36	f(f	f(f	PROPN
ejpam-4479	162	37	)	)	PUNCT
ejpam-4479	162	38	,	,	PUNCT
ejpam-4479	162	39	a	a	PRON
ejpam-4479	162	40	)	)	PUNCT
ejpam-4479	162	41	is	be	AUX
ejpam-4479	162	42	a	a	DET
ejpam-4479	162	43	trivial	trivial	ADJ
ejpam-4479	162	44	soft	soft	ADJ
ejpam-4479	162	45	hyper	hyper	ADJ
ejpam-4479	162	46	gr	gr	NOUN
ejpam-4479	162	47	-	-	NOUN
ejpam-4479	162	48	algebra	algebra	NOUN
ejpam-4479	162	49	over	over	ADP
ejpam-4479	162	50	y	y	NOUN
ejpam-4479	162	51	by	by	ADP
ejpam-4479	162	52	definition	definition	NOUN
ejpam-4479	162	53	13	13	NUM
ejpam-4479	162	54	and	and	CCONJ
ejpam-4479	162	55	lemma	lemma	PROPN
ejpam-4479	162	56	2	2	NUM
ejpam-4479	162	57	.	.	PUNCT
ejpam-4479	162	58	conversely	conversely	ADV
ejpam-4479	162	59	,	,	PUNCT
ejpam-4479	162	60	suppose	suppose	VERB
ejpam-4479	162	61	that	that	SCONJ
ejpam-4479	162	62	(	(	PUNCT
ejpam-4479	162	63	f(f	f(f	PROPN
ejpam-4479	162	64	)	)	PUNCT
ejpam-4479	162	65	,	,	PUNCT
ejpam-4479	162	66	a	a	PRON
ejpam-4479	162	67	)	)	PUNCT
ejpam-4479	162	68	is	be	AUX
ejpam-4479	162	69	a	a	DET
ejpam-4479	162	70	trivial	trivial	ADJ
ejpam-4479	162	71	soft	soft	ADJ
ejpam-4479	162	72	hyper	hyper	ADJ
ejpam-4479	162	73	gr	gr	NOUN
ejpam-4479	162	74	-	-	NOUN
ejpam-4479	162	75	algebra	algebra	NOUN
ejpam-4479	162	76	over	over	ADP
ejpam-4479	162	77	y	y	PROPN
ejpam-4479	162	78	.	.	PUNCT
ejpam-4479	163	1	then	then	ADV
ejpam-4479	163	2	f(f	f(f	PROPN
ejpam-4479	163	3	)	)	PUNCT
ejpam-4479	163	4	(	(	PUNCT
ejpam-4479	163	5	a	a	X
ejpam-4479	163	6	)	)	PUNCT
ejpam-4479	163	7	=	=	SYM
ejpam-4479	163	8	f(f	f(f	X
ejpam-4479	163	9	(	(	PUNCT
ejpam-4479	163	10	a	a	NOUN
ejpam-4479	163	11	)	)	PUNCT
ejpam-4479	163	12	)	)	PUNCT
ejpam-4479	163	13	=	=	PRON
ejpam-4479	163	14	{	{	PUNCT
ejpam-4479	163	15	0y	0y	NOUN
ejpam-4479	163	16	}	}	PUNCT
ejpam-4479	163	17	for	for	ADP
ejpam-4479	163	18	all	all	DET
ejpam-4479	163	19	a	a	DET
ejpam-4479	163	20	∈	∈	NOUN
ejpam-4479	163	21	a.	a.	NOUN
ejpam-4479	163	22	this	this	PRON
ejpam-4479	163	23	means	mean	VERB
ejpam-4479	163	24	that	that	SCONJ
ejpam-4479	163	25	f	f	PROPN
ejpam-4479	163	26	(	(	PUNCT
ejpam-4479	163	27	a	a	NOUN
ejpam-4479	163	28	)	)	PUNCT
ejpam-4479	163	29	⊆	⊆	NUM
ejpam-4479	163	30	ker	ker	NOUN
ejpam-4479	163	31	f	f	X
ejpam-4479	163	32	,	,	PUNCT
ejpam-4479	163	33	for	for	ADP
ejpam-4479	163	34	all	all	DET
ejpam-4479	163	35	a	a	DET
ejpam-4479	163	36	∈	∈	PROPN
ejpam-4479	163	37	a.	a.	NOUN
ejpam-4479	163	38	(	(	PUNCT
ejpam-4479	163	39	ii	ii	NOUN
ejpam-4479	163	40	)	)	PUNCT
ejpam-4479	163	41	assume	assume	VERB
ejpam-4479	163	42	that	that	SCONJ
ejpam-4479	163	43	f	f	PROPN
ejpam-4479	163	44	is	be	AUX
ejpam-4479	163	45	onto	onto	ADP
ejpam-4479	163	46	and	and	CCONJ
ejpam-4479	163	47	(	(	PUNCT
ejpam-4479	163	48	f	f	X
ejpam-4479	163	49	,	,	PUNCT
ejpam-4479	163	50	a	a	PRON
ejpam-4479	163	51	)	)	PUNCT
ejpam-4479	163	52	is	be	AUX
ejpam-4479	163	53	whole	whole	ADJ
ejpam-4479	163	54	.	.	PUNCT
ejpam-4479	164	1	then	then	ADV
ejpam-4479	164	2	f	f	X
ejpam-4479	164	3	(	(	PUNCT
ejpam-4479	164	4	a	a	X
ejpam-4479	164	5	)	)	PUNCT
ejpam-4479	164	6	=	=	SYM
ejpam-4479	164	7	h	h	NOUN
ejpam-4479	164	8	for	for	ADP
ejpam-4479	164	9	all	all	DET
ejpam-4479	164	10	a	a	DET
ejpam-4479	164	11	∈	∈	PROPN
ejpam-4479	164	12	a	a	PRON
ejpam-4479	164	13	,	,	PUNCT
ejpam-4479	164	14	and	and	CCONJ
ejpam-4479	164	15	so	so	ADV
ejpam-4479	164	16	f(f	f(f	PROPN
ejpam-4479	164	17	)	)	PUNCT
ejpam-4479	164	18	(	(	PUNCT
ejpam-4479	164	19	a	a	X
ejpam-4479	164	20	)	)	PUNCT
ejpam-4479	164	21	=	=	SYM
ejpam-4479	164	22	f(f	f(f	X
ejpam-4479	164	23	(	(	PUNCT
ejpam-4479	164	24	a	a	NOUN
ejpam-4479	164	25	)	)	PUNCT
ejpam-4479	164	26	)	)	PUNCT
ejpam-4479	165	1	=	=	SYM
ejpam-4479	165	2	h	h	NOUN
ejpam-4479	165	3	for	for	ADP
ejpam-4479	165	4	all	all	DET
ejpam-4479	165	5	a	a	DET
ejpam-4479	165	6	∈	∈	NOUN
ejpam-4479	165	7	a.	a.	NOUN
ejpam-4479	165	8	it	it	PRON
ejpam-4479	165	9	follows	follow	VERB
ejpam-4479	165	10	from	from	ADP
ejpam-4479	165	11	definition	definition	NOUN
ejpam-4479	165	12	13	13	NUM
ejpam-4479	165	13	and	and	CCONJ
ejpam-4479	165	14	lemma	lemma	PROPN
ejpam-4479	165	15	2	2	NUM
ejpam-4479	165	16	that	that	PRON
ejpam-4479	165	17	(	(	PUNCT
ejpam-4479	165	18	f(f	f(f	PROPN
ejpam-4479	165	19	)	)	PUNCT
ejpam-4479	165	20	,	,	PUNCT
ejpam-4479	165	21	a	a	PRON
ejpam-4479	165	22	)	)	PUNCT
ejpam-4479	165	23	is	be	AUX
ejpam-4479	165	24	a	a	DET
ejpam-4479	165	25	whole	whole	ADJ
ejpam-4479	165	26	soft	soft	ADJ
ejpam-4479	165	27	hyper	hyper	ADJ
ejpam-4479	165	28	gr	gr	NOUN
ejpam-4479	165	29	-	-	NOUN
ejpam-4479	165	30	algebra	algebra	NOUN
ejpam-4479	165	31	.	.	PUNCT
ejpam-4479	166	1	m.k	m.k	PROPN
ejpam-4479	166	2	.	.	PUNCT
ejpam-4479	166	3	engcot	engcot	PROPN
ejpam-4479	166	4	,	,	PUNCT
ejpam-4479	166	5	g.	g.	PROPN
ejpam-4479	166	6	petalcorin	petalcorin	PROPN
ejpam-4479	166	7	/	/	SYM
ejpam-4479	166	8	eur	eur	PROPN
ejpam-4479	166	9	.	.	PUNCT
ejpam-4479	167	1	j.	j.	PROPN
ejpam-4479	167	2	pure	pure	PROPN
ejpam-4479	167	3	appl	appl	PROPN
ejpam-4479	167	4	.	.	PROPN
ejpam-4479	167	5	math	math	PROPN
ejpam-4479	167	6	,	,	PUNCT
ejpam-4479	167	7	15	15	NUM
ejpam-4479	167	8	(	(	PUNCT
ejpam-4479	167	9	4	4	NUM
ejpam-4479	167	10	)	)	PUNCT
ejpam-4479	167	11	(	(	PUNCT
ejpam-4479	167	12	2022	2022	NUM
ejpam-4479	167	13	)	)	PUNCT
ejpam-4479	167	14	,	,	PUNCT
ejpam-4479	167	15	1482	1482	NUM
ejpam-4479	167	16	-	-	SYM
ejpam-4479	167	17	1497	1497	NUM
ejpam-4479	167	18	1489	1489	NUM
ejpam-4479	167	19	(	(	PUNCT
ejpam-4479	167	20	iii	iii	NOUN
ejpam-4479	167	21	)	)	PUNCT
ejpam-4479	167	22	suppose	suppose	VERB
ejpam-4479	167	23	(	(	PUNCT
ejpam-4479	167	24	f(f	f(f	PROPN
ejpam-4479	167	25	)	)	PUNCT
ejpam-4479	167	26	,	,	PUNCT
ejpam-4479	167	27	a	a	PRON
ejpam-4479	167	28	)	)	PUNCT
ejpam-4479	167	29	is	be	AUX
ejpam-4479	167	30	whole	whole	ADJ
ejpam-4479	167	31	.	.	PUNCT
ejpam-4479	168	1	then	then	ADV
ejpam-4479	168	2	f(f	f(f	PROPN
ejpam-4479	168	3	)	)	PUNCT
ejpam-4479	168	4	(	(	PUNCT
ejpam-4479	168	5	a	a	X
ejpam-4479	168	6	)	)	PUNCT
ejpam-4479	168	7	=	=	SYM
ejpam-4479	168	8	f(f	f(f	X
ejpam-4479	168	9	(	(	PUNCT
ejpam-4479	168	10	a	a	NOUN
ejpam-4479	168	11	)	)	PUNCT
ejpam-4479	168	12	)	)	PUNCT
ejpam-4479	169	1	=	=	SYM
ejpam-4479	169	2	h	h	NOUN
ejpam-4479	169	3	for	for	ADP
ejpam-4479	169	4	all	all	DET
ejpam-4479	169	5	a	a	DET
ejpam-4479	169	6	∈	∈	PROPN
ejpam-4479	169	7	a.	a.	NOUN
ejpam-4479	169	8	thus	thus	ADV
ejpam-4479	169	9	,	,	PUNCT
ejpam-4479	169	10	f(h	f(h	PROPN
ejpam-4479	169	11	)	)	PUNCT
ejpam-4479	170	1	=	=	SYM
ejpam-4479	170	2	y	y	PROPN
ejpam-4479	170	3	since	since	SCONJ
ejpam-4479	170	4	f	f	PROPN
ejpam-4479	170	5	(	(	PUNCT
ejpam-4479	170	6	a	a	NOUN
ejpam-4479	170	7	)	)	PUNCT
ejpam-4479	170	8	⊆	⊆	NUM
ejpam-4479	170	9	h	h	NOUN
ejpam-4479	170	10	for	for	ADP
ejpam-4479	170	11	all	all	DET
ejpam-4479	170	12	a	a	DET
ejpam-4479	170	13	∈	∈	NOUN
ejpam-4479	170	14	a.	a.	NOUN
ejpam-4479	170	15	hence	hence	ADV
ejpam-4479	170	16	,	,	PUNCT
ejpam-4479	170	17	f	f	PROPN
ejpam-4479	170	18	is	be	AUX
ejpam-4479	170	19	onto	onto	ADP
ejpam-4479	170	20	.	.	PUNCT
ejpam-4479	171	1	now	now	ADV
ejpam-4479	171	2	,	,	PUNCT
ejpam-4479	171	3	let	let	VERB
ejpam-4479	171	4	a	a	DET
ejpam-4479	171	5	∈	∈	PROPN
ejpam-4479	171	6	a	a	DET
ejpam-4479	171	7	and	and	CCONJ
ejpam-4479	171	8	z	z	PROPN
ejpam-4479	171	9	∈	∈	PROPN
ejpam-4479	171	10	h.	h.	PROPN
ejpam-4479	171	11	since	since	SCONJ
ejpam-4479	171	12	f(z	f(z	PROPN
ejpam-4479	171	13	)	)	PUNCT
ejpam-4479	171	14	∈	∈	PROPN
ejpam-4479	171	15	y	y	PROPN
ejpam-4479	171	16	=	=	SYM
ejpam-4479	171	17	f(f	f(f	PROPN
ejpam-4479	171	18	(	(	PUNCT
ejpam-4479	171	19	a	a	NOUN
ejpam-4479	171	20	)	)	PUNCT
ejpam-4479	171	21	)	)	PUNCT
ejpam-4479	171	22	,	,	PUNCT
ejpam-4479	171	23	there	there	PRON
ejpam-4479	171	24	exists	exist	VERB
ejpam-4479	171	25	x	x	X
ejpam-4479	171	26	∈	∈	PROPN
ejpam-4479	171	27	f	f	X
ejpam-4479	171	28	(	(	PUNCT
ejpam-4479	171	29	a	a	NOUN
ejpam-4479	171	30	)	)	PUNCT
ejpam-4479	171	31	such	such	ADJ
ejpam-4479	171	32	that	that	SCONJ
ejpam-4479	171	33	f(x	f(x	NOUN
ejpam-4479	171	34	)	)	PUNCT
ejpam-4479	171	35	=	=	SYM
ejpam-4479	172	1	f(z	f(z	PROPN
ejpam-4479	172	2	)	)	PUNCT
ejpam-4479	172	3	.	.	PUNCT
ejpam-4479	173	1	since	since	SCONJ
ejpam-4479	173	2	f	f	PROPN
ejpam-4479	173	3	is	be	AUX
ejpam-4479	173	4	one	one	NUM
ejpam-4479	173	5	-	-	PUNCT
ejpam-4479	173	6	to	to	ADP
ejpam-4479	173	7	-	-	PUNCT
ejpam-4479	173	8	one	one	NUM
ejpam-4479	173	9	,	,	PUNCT
ejpam-4479	173	10	it	it	PRON
ejpam-4479	173	11	follows	follow	VERB
ejpam-4479	173	12	that	that	SCONJ
ejpam-4479	173	13	x	x	PUNCT
ejpam-4479	174	1	=	=	PUNCT
ejpam-4479	174	2	z	z	SYM
ejpam-4479	174	3	∈	∈	PROPN
ejpam-4479	174	4	f	f	X
ejpam-4479	174	5	(	(	PUNCT
ejpam-4479	174	6	a	a	NOUN
ejpam-4479	174	7	)	)	PUNCT
ejpam-4479	174	8	.	.	PUNCT
ejpam-4479	175	1	therefore	therefore	ADV
ejpam-4479	175	2	,	,	PUNCT
ejpam-4479	175	3	f	f	PROPN
ejpam-4479	175	4	(	(	PUNCT
ejpam-4479	175	5	a	a	X
ejpam-4479	175	6	)	)	PUNCT
ejpam-4479	175	7	=	=	SYM
ejpam-4479	175	8	h	h	NOUN
ejpam-4479	175	9	implying	imply	VERB
ejpam-4479	175	10	that	that	SCONJ
ejpam-4479	175	11	(	(	PUNCT
ejpam-4479	175	12	f	f	X
ejpam-4479	175	13	,	,	PUNCT
ejpam-4479	175	14	a	a	PRON
ejpam-4479	175	15	)	)	PUNCT
ejpam-4479	175	16	is	be	AUX
ejpam-4479	175	17	whole	whole	ADJ
ejpam-4479	175	18	.	.	PUNCT
ejpam-4479	176	1	(	(	PUNCT
ejpam-4479	176	2	iv	iv	X
ejpam-4479	176	3	)	)	PUNCT
ejpam-4479	176	4	the	the	DET
ejpam-4479	176	5	proof	proof	NOUN
ejpam-4479	176	6	follows	follow	VERB
ejpam-4479	176	7	from	from	ADP
ejpam-4479	176	8	(	(	PUNCT
ejpam-4479	176	9	ii	ii	NOUN
ejpam-4479	176	10	)	)	PUNCT
ejpam-4479	176	11	and	and	CCONJ
ejpam-4479	176	12	(	(	PUNCT
ejpam-4479	176	13	iii	iii	NOUN
ejpam-4479	176	14	)	)	PUNCT
ejpam-4479	176	15	.	.	PUNCT
ejpam-4479	177	1	definition	definition	NOUN
ejpam-4479	177	2	14	14	NUM
ejpam-4479	177	3	.	.	PUNCT
ejpam-4479	178	1	let	let	VERB
ejpam-4479	178	2	(	(	PUNCT
ejpam-4479	178	3	f	f	X
ejpam-4479	178	4	,	,	PUNCT
ejpam-4479	178	5	a	a	PRON
ejpam-4479	178	6	)	)	PUNCT
ejpam-4479	178	7	and	and	CCONJ
ejpam-4479	178	8	(	(	PUNCT
ejpam-4479	178	9	g	g	NOUN
ejpam-4479	178	10	,	,	PUNCT
ejpam-4479	178	11	c	c	NOUN
ejpam-4479	178	12	)	)	PUNCT
ejpam-4479	178	13	be	be	VERB
ejpam-4479	178	14	two	two	NUM
ejpam-4479	178	15	soft	soft	ADJ
ejpam-4479	178	16	hyper	hyper	ADJ
ejpam-4479	178	17	gr	gr	NOUN
ejpam-4479	178	18	-	-	PUNCT
ejpam-4479	178	19	algebras	algebras	NOUN
ejpam-4479	178	20	over	over	ADP
ejpam-4479	178	21	h.	h.	PROPN
ejpam-4479	179	1	then	then	ADV
ejpam-4479	179	2	(	(	PUNCT
ejpam-4479	179	3	f	f	X
ejpam-4479	179	4	,	,	PUNCT
ejpam-4479	179	5	a	a	PRON
ejpam-4479	179	6	)	)	PUNCT
ejpam-4479	179	7	is	be	AUX
ejpam-4479	179	8	called	call	VERB
ejpam-4479	179	9	a	a	DET
ejpam-4479	179	10	soft	soft	ADJ
ejpam-4479	179	11	hyper	hyper	ADJ
ejpam-4479	179	12	subgr	subgr	NOUN
ejpam-4479	179	13	-	-	PUNCT
ejpam-4479	179	14	algebra	algebra	NOUN
ejpam-4479	179	15	of	of	ADP
ejpam-4479	179	16	(	(	PUNCT
ejpam-4479	179	17	g	g	PROPN
ejpam-4479	179	18	,	,	PUNCT
ejpam-4479	179	19	c	c	NOUN
ejpam-4479	179	20	)	)	PUNCT
ejpam-4479	179	21	,	,	PUNCT
ejpam-4479	179	22	written	write	VERB
ejpam-4479	179	23	as	as	ADP
ejpam-4479	179	24	(	(	PUNCT
ejpam-4479	179	25	f	f	X
ejpam-4479	179	26	,	,	PUNCT
ejpam-4479	179	27	a	a	PRON
ejpam-4479	179	28	)	)	PUNCT
ejpam-4479	179	29	∼	∼	NOUN
ejpam-4479	179	30	<	<	X
ejpam-4479	179	31	(	(	PUNCT
ejpam-4479	179	32	g	g	NOUN
ejpam-4479	179	33	,	,	PUNCT
ejpam-4479	179	34	c	c	NOUN
ejpam-4479	179	35	)	)	PUNCT
ejpam-4479	179	36	,	,	PUNCT
ejpam-4479	179	37	if	if	SCONJ
ejpam-4479	179	38	it	it	PRON
ejpam-4479	179	39	satisfies	satisfy	VERB
ejpam-4479	179	40	the	the	DET
ejpam-4479	179	41	following	following	NOUN
ejpam-4479	179	42	:	:	PUNCT
ejpam-4479	179	43	(	(	PUNCT
ejpam-4479	179	44	i	i	NOUN
ejpam-4479	179	45	)	)	PUNCT
ejpam-4479	179	46	a	a	DET
ejpam-4479	179	47	⊆	⊆	NUM
ejpam-4479	179	48	c	c	PROPN
ejpam-4479	179	49	(	(	PUNCT
ejpam-4479	179	50	ii	ii	PROPN
ejpam-4479	179	51	)	)	PUNCT
ejpam-4479	179	52	f	f	PROPN
ejpam-4479	179	53	(	(	PUNCT
ejpam-4479	179	54	a	a	NOUN
ejpam-4479	179	55	)	)	PUNCT
ejpam-4479	179	56	is	be	AUX
ejpam-4479	179	57	a	a	DET
ejpam-4479	179	58	hyper	hyper	ADJ
ejpam-4479	179	59	subgr	subgr	NOUN
ejpam-4479	179	60	-	-	PUNCT
ejpam-4479	179	61	algebra	algebra	NOUN
ejpam-4479	179	62	of	of	ADP
ejpam-4479	179	63	g(a	g(a	PROPN
ejpam-4479	179	64	)	)	PUNCT
ejpam-4479	179	65	for	for	ADP
ejpam-4479	179	66	all	all	DET
ejpam-4479	179	67	a	a	DET
ejpam-4479	179	68	∈	∈	PROPN
ejpam-4479	179	69	a.	a.	NOUN
ejpam-4479	179	70	example	example	NOUN
ejpam-4479	179	71	9	9	NUM
ejpam-4479	179	72	.	.	X
ejpam-4479	180	1	consider	consider	VERB
ejpam-4479	180	2	the	the	DET
ejpam-4479	180	3	hyper	hyper	ADJ
ejpam-4479	180	4	gr	gr	NOUN
ejpam-4479	180	5	-	-	NOUN
ejpam-4479	180	6	algebra	algebra	NOUN
ejpam-4479	180	7	in	in	ADP
ejpam-4479	180	8	example	example	NOUN
ejpam-4479	180	9	8	8	NUM
ejpam-4479	180	10	.	.	PUNCT
ejpam-4479	181	1	for	for	ADP
ejpam-4479	181	2	c	c	NOUN
ejpam-4479	181	3	=	=	SYM
ejpam-4479	181	4	h	h	NOUN
ejpam-4479	181	5	,	,	PUNCT
ejpam-4479	181	6	let	let	VERB
ejpam-4479	181	7	g	g	NOUN
ejpam-4479	181	8	:	:	PUNCT
ejpam-4479	181	9	c	c	X
ejpam-4479	181	10	→	→	SYM
ejpam-4479	181	11	p	p	X
ejpam-4479	181	12	(	(	PUNCT
ejpam-4479	181	13	h	h	NOUN
ejpam-4479	181	14	)	)	PUNCT
ejpam-4479	181	15	be	be	VERB
ejpam-4479	181	16	the	the	DET
ejpam-4479	181	17	set	set	NOUN
ejpam-4479	181	18	-	-	PUNCT
ejpam-4479	181	19	valued	value	VERB
ejpam-4479	181	20	function	function	NOUN
ejpam-4479	181	21	defined	define	VERB
ejpam-4479	181	22	by	by	ADP
ejpam-4479	181	23	g(a	g(a	PROPN
ejpam-4479	181	24	)	)	PUNCT
ejpam-4479	182	1	=	=	SYM
ejpam-4479	182	2	⋃	⋃	NOUN
ejpam-4479	182	3	b⊂h	b⊂h	NOUN
ejpam-4479	182	4	,	,	PUNCT
ejpam-4479	182	5	ar̊b⇔b≪a	ar̊b⇔b≪a	ADJ
ejpam-4479	182	6	b	b	NOUN
ejpam-4479	182	7	,	,	PUNCT
ejpam-4479	182	8	for	for	ADP
ejpam-4479	182	9	all	all	DET
ejpam-4479	182	10	a	a	DET
ejpam-4479	182	11	∈	∈	PROPN
ejpam-4479	182	12	c.	c.	NOUN
ejpam-4479	182	13	then	then	ADV
ejpam-4479	182	14	g(0	g(0	PROPN
ejpam-4479	182	15	)	)	PUNCT
ejpam-4479	182	16	=	=	PUNCT
ejpam-4479	183	1	⋃	⋃	NOUN
ejpam-4479	183	2	b⊂h,0r̊b⇔b≪0	b⊂h,0r̊b⇔b≪0	X
ejpam-4479	183	3	b	b	X
ejpam-4479	183	4	=	=	PRON
ejpam-4479	183	5	{	{	PUNCT
ejpam-4479	183	6	0	0	NUM
ejpam-4479	183	7	}	}	PUNCT
ejpam-4479	183	8	,	,	PUNCT
ejpam-4479	183	9	g(1	g(1	NOUN
ejpam-4479	183	10	)	)	PUNCT
ejpam-4479	183	11	=	=	SYM
ejpam-4479	183	12	⋃	⋃	NOUN
ejpam-4479	183	13	b⊂h,1r̊b⇔b≪1	b⊂h,1r̊b⇔b≪1	NOUN
ejpam-4479	183	14	b	b	X
ejpam-4479	183	15	=	=	SYM
ejpam-4479	183	16	{	{	PUNCT
ejpam-4479	183	17	0	0	NUM
ejpam-4479	183	18	,	,	PUNCT
ejpam-4479	183	19	1	1	NUM
ejpam-4479	183	20	,	,	PUNCT
ejpam-4479	183	21	2	2	NUM
ejpam-4479	183	22	}	}	PUNCT
ejpam-4479	183	23	and	and	CCONJ
ejpam-4479	183	24	g(2	g(2	PROPN
ejpam-4479	183	25	)	)	PUNCT
ejpam-4479	183	26	=	=	PUNCT
ejpam-4479	183	27	⋃	⋃	ADP
ejpam-4479	183	28	b⊂h,2r̊b⇔b≪2	b⊂h,2r̊b⇔b≪2	NOUN
ejpam-4479	183	29	b	b	X
ejpam-4479	183	30	=	=	PUNCT
ejpam-4479	183	31	{	{	PUNCT
ejpam-4479	183	32	0	0	NUM
ejpam-4479	183	33	,	,	PUNCT
ejpam-4479	183	34	1	1	NUM
ejpam-4479	183	35	,	,	PUNCT
ejpam-4479	183	36	2	2	NUM
ejpam-4479	183	37	}	}	PUNCT
ejpam-4479	183	38	.	.	PUNCT
ejpam-4479	184	1	let	let	VERB
ejpam-4479	184	2	a	a	DET
ejpam-4479	184	3	=	=	PUNCT
ejpam-4479	184	4	{	{	PUNCT
ejpam-4479	184	5	0	0	NUM
ejpam-4479	184	6	,	,	PUNCT
ejpam-4479	184	7	1	1	NUM
ejpam-4479	184	8	,	,	PUNCT
ejpam-4479	184	9	2	2	NUM
ejpam-4479	184	10	}	}	PUNCT
ejpam-4479	184	11	and	and	CCONJ
ejpam-4479	184	12	f	f	X
ejpam-4479	184	13	:	:	PUNCT
ejpam-4479	184	14	a	a	DET
ejpam-4479	184	15	→	→	SYM
ejpam-4479	184	16	p	p	X
ejpam-4479	184	17	(	(	PUNCT
ejpam-4479	184	18	h	h	NOUN
ejpam-4479	184	19	)	)	PUNCT
ejpam-4479	184	20	be	be	VERB
ejpam-4479	184	21	the	the	DET
ejpam-4479	184	22	set	set	NOUN
ejpam-4479	184	23	-	-	PUNCT
ejpam-4479	184	24	valued	value	VERB
ejpam-4479	184	25	function	function	NOUN
ejpam-4479	184	26	defined	define	VERB
ejpam-4479	184	27	by	by	ADP
ejpam-4479	184	28	f	f	PROPN
ejpam-4479	184	29	(	(	PUNCT
ejpam-4479	184	30	a	a	NOUN
ejpam-4479	184	31	)	)	PUNCT
ejpam-4479	184	32	=	=	SYM
ejpam-4479	184	33	⋃	⋃	NOUN
ejpam-4479	184	34	b⊂h	b⊂h	NOUN
ejpam-4479	184	35	,	,	PUNCT
ejpam-4479	184	36	ar̊b⇔b	ar̊b⇔b	NOUN
ejpam-4479	184	37	=	=	SYM
ejpam-4479	184	38	an	an	DET
ejpam-4479	184	39	b	b	NOUN
ejpam-4479	184	40	,	,	PUNCT
ejpam-4479	184	41	where	where	SCONJ
ejpam-4479	184	42	an	an	DET
ejpam-4479	184	43	=	=	X
ejpam-4479	184	44	(	(	PUNCT
ejpam-4479	184	45	(	(	PUNCT
ejpam-4479	184	46	(	(	PUNCT
ejpam-4479	184	47	(	(	PUNCT
ejpam-4479	184	48	a⊛	a⊛	PROPN
ejpam-4479	184	49	a)⊛	a)⊛	NOUN
ejpam-4479	184	50	a)⊛	a)⊛	NOUN
ejpam-4479	184	51	a)⊛	a)⊛	NOUN
ejpam-4479	184	52	...	...	PUNCT
ejpam-4479	184	53	⊛	⊛	ADV
ejpam-4479	184	54	a	a	X
ejpam-4479	184	55	)	)	PUNCT
ejpam-4479	184	56	for	for	ADP
ejpam-4479	184	57	all	all	DET
ejpam-4479	184	58	a	a	DET
ejpam-4479	184	59	∈	∈	NOUN
ejpam-4479	184	60	a.	a.	NOUN
ejpam-4479	185	1	then	then	ADV
ejpam-4479	185	2	f	f	X
ejpam-4479	185	3	(	(	PUNCT
ejpam-4479	185	4	0	0	NUM
ejpam-4479	185	5	)	)	PUNCT
ejpam-4479	185	6	=	=	NOUN
ejpam-4479	185	7	⋃	⋃	ADP
ejpam-4479	185	8	b⊂h,0r̊b⇔b=0n	b⊂h,0r̊b⇔b=0n	X
ejpam-4479	185	9	b	b	X
ejpam-4479	185	10	=	=	SYM
ejpam-4479	185	11	{	{	PUNCT
ejpam-4479	185	12	0	0	NUM
ejpam-4479	185	13	}	}	PUNCT
ejpam-4479	185	14	,	,	PUNCT
ejpam-4479	185	15	f	f	PROPN
ejpam-4479	185	16	(	(	PUNCT
ejpam-4479	185	17	1	1	NUM
ejpam-4479	185	18	)	)	PUNCT
ejpam-4479	185	19	=	=	PUNCT
ejpam-4479	185	20	⋃	⋃	PROPN
ejpam-4479	185	21	b⊂h,1r̊b⇔b=1n	b⊂h,1r̊b⇔b=1n	PROPN
ejpam-4479	185	22	b	b	X
ejpam-4479	185	23	=	=	SYM
ejpam-4479	185	24	{	{	PUNCT
ejpam-4479	185	25	0	0	NUM
ejpam-4479	185	26	,	,	PUNCT
ejpam-4479	185	27	1	1	NUM
ejpam-4479	185	28	}	}	PUNCT
ejpam-4479	185	29	and	and	CCONJ
ejpam-4479	185	30	f	f	X
ejpam-4479	185	31	(	(	PUNCT
ejpam-4479	185	32	2	2	NUM
ejpam-4479	185	33	)	)	PUNCT
ejpam-4479	185	34	=	=	PUNCT
ejpam-4479	185	35	⋃	⋃	ADP
ejpam-4479	185	36	b⊂h,2r̊b⇔b=2n	b⊂h,2r̊b⇔b=2n	NOUN
ejpam-4479	185	37	b	b	X
ejpam-4479	185	38	=	=	SYM
ejpam-4479	185	39	{	{	PUNCT
ejpam-4479	185	40	0	0	NUM
ejpam-4479	185	41	,	,	PUNCT
ejpam-4479	185	42	1	1	NUM
ejpam-4479	185	43	,	,	PUNCT
ejpam-4479	185	44	2	2	NUM
ejpam-4479	185	45	}	}	PUNCT
ejpam-4479	185	46	.	.	PUNCT
ejpam-4479	186	1	hence	hence	ADV
ejpam-4479	186	2	,	,	PUNCT
ejpam-4479	186	3	f	f	PROPN
ejpam-4479	186	4	(	(	PUNCT
ejpam-4479	186	5	0	0	NUM
ejpam-4479	186	6	)	)	PUNCT
ejpam-4479	186	7	,	,	PUNCT
ejpam-4479	186	8	f	f	PROPN
ejpam-4479	186	9	(	(	PUNCT
ejpam-4479	186	10	1	1	NUM
ejpam-4479	186	11	)	)	PUNCT
ejpam-4479	186	12	and	and	CCONJ
ejpam-4479	186	13	f	f	PROPN
ejpam-4479	186	14	(	(	PUNCT
ejpam-4479	186	15	2	2	NUM
ejpam-4479	186	16	)	)	PUNCT
ejpam-4479	186	17	are	be	AUX
ejpam-4479	186	18	soft	soft	ADJ
ejpam-4479	186	19	hyper	hyper	ADJ
ejpam-4479	186	20	subgr	subgr	NOUN
ejpam-4479	186	21	-	-	PUNCT
ejpam-4479	186	22	algebras	algebras	PROPN
ejpam-4479	186	23	on	on	ADP
ejpam-4479	186	24	g(0	g(0	NOUN
ejpam-4479	186	25	)	)	PUNCT
ejpam-4479	186	26	,	,	PUNCT
ejpam-4479	186	27	g(1	g(1	PROPN
ejpam-4479	186	28	)	)	PUNCT
ejpam-4479	186	29	and	and	CCONJ
ejpam-4479	186	30	g(2	g(2	PROPN
ejpam-4479	186	31	)	)	PUNCT
ejpam-4479	186	32	,	,	PUNCT
ejpam-4479	186	33	respectively	respectively	ADV
ejpam-4479	186	34	.	.	PUNCT
ejpam-4479	187	1	therefore	therefore	ADV
ejpam-4479	187	2	,	,	PUNCT
ejpam-4479	187	3	(	(	PUNCT
ejpam-4479	187	4	f	f	X
ejpam-4479	187	5	,	,	PUNCT
ejpam-4479	187	6	a	a	PRON
ejpam-4479	187	7	)	)	PUNCT
ejpam-4479	187	8	∼	∼	NOUN
ejpam-4479	187	9	<	<	X
ejpam-4479	187	10	(	(	PUNCT
ejpam-4479	187	11	g	g	NOUN
ejpam-4479	187	12	,	,	PUNCT
ejpam-4479	187	13	c	c	NOUN
ejpam-4479	187	14	)	)	PUNCT
ejpam-4479	187	15	.	.	PUNCT
ejpam-4479	188	1	m.k	m.k	PROPN
ejpam-4479	188	2	.	.	PUNCT
ejpam-4479	188	3	engcot	engcot	PROPN
ejpam-4479	188	4	,	,	PUNCT
ejpam-4479	188	5	g.	g.	PROPN
ejpam-4479	188	6	petalcorin	petalcorin	PROPN
ejpam-4479	188	7	/	/	SYM
ejpam-4479	188	8	eur	eur	PROPN
ejpam-4479	188	9	.	.	PUNCT
ejpam-4479	189	1	j.	j.	PROPN
ejpam-4479	189	2	pure	pure	PROPN
ejpam-4479	189	3	appl	appl	PROPN
ejpam-4479	189	4	.	.	PROPN
ejpam-4479	189	5	math	math	PROPN
ejpam-4479	189	6	,	,	PUNCT
ejpam-4479	189	7	15	15	NUM
ejpam-4479	189	8	(	(	PUNCT
ejpam-4479	189	9	4	4	NUM
ejpam-4479	189	10	)	)	PUNCT
ejpam-4479	189	11	(	(	PUNCT
ejpam-4479	189	12	2022	2022	NUM
ejpam-4479	189	13	)	)	PUNCT
ejpam-4479	189	14	,	,	PUNCT
ejpam-4479	189	15	1482	1482	NUM
ejpam-4479	189	16	-	-	SYM
ejpam-4479	189	17	1497	1497	NUM
ejpam-4479	189	18	1490	1490	NUM
ejpam-4479	189	19	theorem	theorem	NOUN
ejpam-4479	189	20	8	8	NUM
ejpam-4479	189	21	.	.	PUNCT
ejpam-4479	190	1	let	let	VERB
ejpam-4479	190	2	(	(	PUNCT
ejpam-4479	190	3	f	f	X
ejpam-4479	190	4	,	,	PUNCT
ejpam-4479	190	5	a	a	PRON
ejpam-4479	190	6	)	)	PUNCT
ejpam-4479	190	7	and	and	CCONJ
ejpam-4479	190	8	(	(	PUNCT
ejpam-4479	190	9	g	g	NOUN
ejpam-4479	190	10	,	,	PUNCT
ejpam-4479	190	11	a	a	PRON
ejpam-4479	190	12	)	)	PUNCT
ejpam-4479	190	13	be	be	AUX
ejpam-4479	190	14	two	two	NUM
ejpam-4479	190	15	soft	soft	ADJ
ejpam-4479	190	16	hyper	hyper	ADJ
ejpam-4479	190	17	gr	gr	NOUN
ejpam-4479	190	18	-	-	PUNCT
ejpam-4479	190	19	algebras	algebras	NOUN
ejpam-4479	190	20	over	over	ADP
ejpam-4479	190	21	h.	h.	PROPN
ejpam-4479	191	1	then	then	ADV
ejpam-4479	191	2	(	(	PUNCT
ejpam-4479	191	3	f	f	X
ejpam-4479	191	4	,	,	PUNCT
ejpam-4479	191	5	a	a	PRON
ejpam-4479	191	6	)	)	PUNCT
ejpam-4479	191	7	∼	∼	NOUN
ejpam-4479	191	8	<	<	X
ejpam-4479	191	9	(	(	PUNCT
ejpam-4479	191	10	g	g	NOUN
ejpam-4479	191	11	,	,	PUNCT
ejpam-4479	191	12	a	a	PRON
ejpam-4479	191	13	)	)	PUNCT
ejpam-4479	191	14	if	if	SCONJ
ejpam-4479	192	1	and	and	CCONJ
ejpam-4479	192	2	only	only	ADV
ejpam-4479	192	3	if	if	SCONJ
ejpam-4479	192	4	f	f	PROPN
ejpam-4479	192	5	(	(	PUNCT
ejpam-4479	192	6	a	a	NOUN
ejpam-4479	192	7	)	)	PUNCT
ejpam-4479	192	8	⊆	⊆	PROPN
ejpam-4479	192	9	g(a	g(a	PROPN
ejpam-4479	192	10	)	)	PUNCT
ejpam-4479	192	11	for	for	ADP
ejpam-4479	192	12	all	all	DET
ejpam-4479	192	13	a	a	DET
ejpam-4479	192	14	∈	∈	NOUN
ejpam-4479	192	15	a.	a.	NOUN
ejpam-4479	192	16	proof	proof	NOUN
ejpam-4479	192	17	:	:	PUNCT
ejpam-4479	192	18	let	let	VERB
ejpam-4479	192	19	(	(	PUNCT
ejpam-4479	192	20	f	f	X
ejpam-4479	192	21	,	,	PUNCT
ejpam-4479	192	22	a	a	PRON
ejpam-4479	192	23	)	)	PUNCT
ejpam-4479	192	24	∼	∼	NOUN
ejpam-4479	192	25	<	<	X
ejpam-4479	192	26	(	(	PUNCT
ejpam-4479	192	27	g	g	NOUN
ejpam-4479	192	28	,	,	PUNCT
ejpam-4479	192	29	a	a	PRON
ejpam-4479	192	30	)	)	PUNCT
ejpam-4479	192	31	.	.	PUNCT
ejpam-4479	193	1	by	by	ADP
ejpam-4479	193	2	definition	definition	NOUN
ejpam-4479	193	3	14	14	NUM
ejpam-4479	193	4	,	,	PUNCT
ejpam-4479	193	5	f	f	PROPN
ejpam-4479	193	6	(	(	PUNCT
ejpam-4479	193	7	a	a	NOUN
ejpam-4479	193	8	)	)	PUNCT
ejpam-4479	193	9	is	be	AUX
ejpam-4479	193	10	a	a	DET
ejpam-4479	193	11	hyper	hyper	ADJ
ejpam-4479	193	12	subgr	subgr	NOUN
ejpam-4479	193	13	-	-	PUNCT
ejpam-4479	193	14	algebra	algebra	NOUN
ejpam-4479	193	15	of	of	ADP
ejpam-4479	193	16	g(a	g(a	PROPN
ejpam-4479	193	17	)	)	PUNCT
ejpam-4479	193	18	for	for	ADP
ejpam-4479	193	19	all	all	DET
ejpam-4479	193	20	a	a	DET
ejpam-4479	193	21	∈	∈	NOUN
ejpam-4479	193	22	a.	a.	NOUN
ejpam-4479	193	23	this	this	PRON
ejpam-4479	193	24	implies	imply	VERB
ejpam-4479	193	25	that	that	SCONJ
ejpam-4479	194	1	f	f	PROPN
ejpam-4479	194	2	(	(	PUNCT
ejpam-4479	194	3	a	a	NOUN
ejpam-4479	194	4	)	)	PUNCT
ejpam-4479	194	5	⊆	⊆	PROPN
ejpam-4479	194	6	g(a	g(a	PROPN
ejpam-4479	194	7	)	)	PUNCT
ejpam-4479	194	8	for	for	ADP
ejpam-4479	194	9	all	all	DET
ejpam-4479	194	10	a	a	DET
ejpam-4479	194	11	∈	∈	NOUN
ejpam-4479	194	12	a.	a.	NOUN
ejpam-4479	194	13	conversely	conversely	ADV
ejpam-4479	194	14	,	,	PUNCT
ejpam-4479	194	15	let	let	VERB
ejpam-4479	194	16	f	f	PROPN
ejpam-4479	194	17	(	(	PUNCT
ejpam-4479	194	18	a	a	NOUN
ejpam-4479	194	19	)	)	PUNCT
ejpam-4479	194	20	⊆	⊆	PROPN
ejpam-4479	194	21	g(a	g(a	PROPN
ejpam-4479	194	22	)	)	PUNCT
ejpam-4479	194	23	for	for	ADP
ejpam-4479	194	24	all	all	DET
ejpam-4479	194	25	a	a	DET
ejpam-4479	194	26	∈	∈	PROPN
ejpam-4479	194	27	a.	a.	NOUN
ejpam-4479	194	28	since	since	SCONJ
ejpam-4479	194	29	(	(	PUNCT
ejpam-4479	194	30	f	f	X
ejpam-4479	194	31	,	,	PUNCT
ejpam-4479	194	32	a	a	PRON
ejpam-4479	194	33	)	)	PUNCT
ejpam-4479	194	34	and	and	CCONJ
ejpam-4479	194	35	(	(	PUNCT
ejpam-4479	194	36	g	g	NOUN
ejpam-4479	194	37	,	,	PUNCT
ejpam-4479	194	38	a	a	PRON
ejpam-4479	194	39	)	)	PUNCT
ejpam-4479	194	40	are	be	AUX
ejpam-4479	194	41	soft	soft	ADJ
ejpam-4479	194	42	hyper	hyper	ADJ
ejpam-4479	194	43	gr	gr	NOUN
ejpam-4479	194	44	-	-	PUNCT
ejpam-4479	194	45	algebras	algebras	NOUN
ejpam-4479	194	46	over	over	ADP
ejpam-4479	194	47	h	h	PROPN
ejpam-4479	194	48	and	and	CCONJ
ejpam-4479	194	49	f	f	PROPN
ejpam-4479	194	50	(	(	PUNCT
ejpam-4479	194	51	a	a	NOUN
ejpam-4479	194	52	)	)	PUNCT
ejpam-4479	194	53	⊆	⊆	PROPN
ejpam-4479	194	54	g(a	g(a	PROPN
ejpam-4479	194	55	)	)	PUNCT
ejpam-4479	194	56	for	for	ADP
ejpam-4479	194	57	all	all	DET
ejpam-4479	194	58	a	a	DET
ejpam-4479	194	59	∈	∈	PROPN
ejpam-4479	194	60	a	a	PRON
ejpam-4479	194	61	,	,	PUNCT
ejpam-4479	194	62	it	it	PRON
ejpam-4479	194	63	follows	follow	VERB
ejpam-4479	194	64	that	that	SCONJ
ejpam-4479	194	65	f	f	PROPN
ejpam-4479	194	66	(	(	PUNCT
ejpam-4479	194	67	a	a	NOUN
ejpam-4479	194	68	)	)	PUNCT
ejpam-4479	194	69	is	be	AUX
ejpam-4479	194	70	a	a	DET
ejpam-4479	194	71	hyper	hyper	ADJ
ejpam-4479	194	72	subgr	subgr	NOUN
ejpam-4479	194	73	-	-	PUNCT
ejpam-4479	194	74	algebra	algebra	NOUN
ejpam-4479	194	75	of	of	ADP
ejpam-4479	194	76	g(a	g(a	PROPN
ejpam-4479	194	77	)	)	PUNCT
ejpam-4479	194	78	for	for	ADP
ejpam-4479	194	79	all	all	DET
ejpam-4479	194	80	a	a	DET
ejpam-4479	194	81	∈	∈	NOUN
ejpam-4479	194	82	a.	a.	NOUN
ejpam-4479	194	83	hence	hence	ADV
ejpam-4479	194	84	,	,	PUNCT
ejpam-4479	194	85	(	(	PUNCT
ejpam-4479	194	86	f	f	X
ejpam-4479	194	87	,	,	PUNCT
ejpam-4479	194	88	a	a	PRON
ejpam-4479	194	89	)	)	PUNCT
ejpam-4479	194	90	∼	∼	NOUN
ejpam-4479	194	91	<	<	X
ejpam-4479	194	92	(	(	PUNCT
ejpam-4479	194	93	g	g	NOUN
ejpam-4479	194	94	,	,	PUNCT
ejpam-4479	194	95	a	a	PRON
ejpam-4479	194	96	)	)	PUNCT
ejpam-4479	194	97	.	.	PUNCT
ejpam-4479	195	1	theorem	theorem	NOUN
ejpam-4479	195	2	9	9	NUM
ejpam-4479	195	3	.	.	PUNCT
ejpam-4479	196	1	let	let	AUX
ejpam-4479	196	2	(	(	PUNCT
ejpam-4479	196	3	f	f	X
ejpam-4479	196	4	,	,	PUNCT
ejpam-4479	196	5	a	a	PRON
ejpam-4479	196	6	)	)	PUNCT
ejpam-4479	196	7	be	be	AUX
ejpam-4479	196	8	soft	soft	ADJ
ejpam-4479	196	9	hyper	hyper	ADJ
ejpam-4479	196	10	gr	gr	NOUN
ejpam-4479	196	11	-	-	NOUN
ejpam-4479	196	12	algebra	algebra	NOUN
ejpam-4479	196	13	over	over	ADP
ejpam-4479	196	14	h	h	NOUN
ejpam-4479	196	15	and	and	CCONJ
ejpam-4479	196	16	let	let	VERB
ejpam-4479	196	17	(	(	PUNCT
ejpam-4479	196	18	g1	g1	X
ejpam-4479	196	19	,	,	PUNCT
ejpam-4479	196	20	c1	c1	PROPN
ejpam-4479	196	21	)	)	PUNCT
ejpam-4479	196	22	and	and	CCONJ
ejpam-4479	196	23	(	(	PUNCT
ejpam-4479	196	24	g2	g2	PROPN
ejpam-4479	196	25	,	,	PUNCT
ejpam-4479	196	26	c2	c2	PROPN
ejpam-4479	196	27	)	)	PUNCT
ejpam-4479	196	28	be	be	VERB
ejpam-4479	196	29	two	two	NUM
ejpam-4479	196	30	soft	soft	ADJ
ejpam-4479	196	31	hyper	hyper	ADJ
ejpam-4479	196	32	subgr	subgr	NOUN
ejpam-4479	196	33	-	-	PUNCT
ejpam-4479	196	34	algebras	algebra	NOUN
ejpam-4479	196	35	of	of	ADP
ejpam-4479	196	36	(	(	PUNCT
ejpam-4479	196	37	f	f	PROPN
ejpam-4479	196	38	,	,	PUNCT
ejpam-4479	196	39	a	a	PRON
ejpam-4479	196	40	)	)	PUNCT
ejpam-4479	196	41	.	.	PUNCT
ejpam-4479	197	1	then	then	ADV
ejpam-4479	197	2	(	(	PUNCT
ejpam-4479	197	3	i	i	NOUN
ejpam-4479	197	4	)	)	PUNCT
ejpam-4479	197	5	(	(	PUNCT
ejpam-4479	197	6	g1	g1	PROPN
ejpam-4479	197	7	,	,	PUNCT
ejpam-4479	197	8	c1	c1	NOUN
ejpam-4479	197	9	)	)	PUNCT
ejpam-4479	197	10	∼	∼	NOUN
ejpam-4479	197	11	∩	∩	NOUN
ejpam-4479	197	12	(	(	PUNCT
ejpam-4479	197	13	g2	g2	PROPN
ejpam-4479	197	14	,	,	PUNCT
ejpam-4479	197	15	c2	c2	PROPN
ejpam-4479	197	16	)	)	PUNCT
ejpam-4479	197	17	∼	∼	NOUN
ejpam-4479	197	18	<	<	X
ejpam-4479	197	19	(	(	PUNCT
ejpam-4479	197	20	f	f	X
ejpam-4479	197	21	,	,	PUNCT
ejpam-4479	197	22	a	a	NOUN
ejpam-4479	197	23	)	)	PUNCT
ejpam-4479	197	24	(	(	PUNCT
ejpam-4479	197	25	ii	ii	NOUN
ejpam-4479	197	26	)	)	PUNCT
ejpam-4479	197	27	c1	c1	PROPN
ejpam-4479	197	28	∩	∩	PROPN
ejpam-4479	197	29	c2	c2	PROPN
ejpam-4479	197	30	=	=	SYM
ejpam-4479	197	31	∅	∅	NOUN
ejpam-4479	197	32	=	=	NOUN
ejpam-4479	197	33	⇒	⇒	NOUN
ejpam-4479	197	34	(	(	PUNCT
ejpam-4479	197	35	g1	g1	PROPN
ejpam-4479	197	36	,	,	PUNCT
ejpam-4479	197	37	c1	c1	NOUN
ejpam-4479	197	38	)	)	PUNCT
ejpam-4479	197	39	∼	∼	NOUN
ejpam-4479	197	40	∪	∪	ADJ
ejpam-4479	197	41	(	(	PUNCT
ejpam-4479	197	42	g2	g2	PROPN
ejpam-4479	197	43	,	,	PUNCT
ejpam-4479	197	44	c2	c2	PROPN
ejpam-4479	197	45	)	)	PUNCT
ejpam-4479	197	46	∼	∼	NOUN
ejpam-4479	197	47	<	<	X
ejpam-4479	197	48	(	(	PUNCT
ejpam-4479	197	49	f	f	X
ejpam-4479	197	50	,	,	PUNCT
ejpam-4479	197	51	a	a	PRON
ejpam-4479	197	52	)	)	PUNCT
ejpam-4479	197	53	.	.	PUNCT
ejpam-4479	198	1	proof	proof	NOUN
ejpam-4479	198	2	:	:	PUNCT
ejpam-4479	198	3	(	(	PUNCT
ejpam-4479	198	4	i	i	NOUN
ejpam-4479	198	5	)	)	PUNCT
ejpam-4479	198	6	by	by	ADP
ejpam-4479	198	7	definition	definition	NOUN
ejpam-4479	198	8	6	6	NUM
ejpam-4479	198	9	,	,	PUNCT
ejpam-4479	198	10	we	we	PRON
ejpam-4479	198	11	can	can	AUX
ejpam-4479	198	12	write	write	VERB
ejpam-4479	198	13	(	(	PUNCT
ejpam-4479	198	14	g1	g1	PROPN
ejpam-4479	198	15	,	,	PUNCT
ejpam-4479	198	16	c1	c1	NOUN
ejpam-4479	198	17	)	)	PUNCT
ejpam-4479	198	18	∼	∼	NOUN
ejpam-4479	198	19	∩(g2	∩(g2	NOUN
ejpam-4479	198	20	,	,	PUNCT
ejpam-4479	198	21	c2	c2	PROPN
ejpam-4479	198	22	)	)	PUNCT
ejpam-4479	198	23	=	=	PUNCT
ejpam-4479	199	1	(	(	PUNCT
ejpam-4479	199	2	g	g	NOUN
ejpam-4479	199	3	,	,	PUNCT
ejpam-4479	199	4	c	c	NOUN
ejpam-4479	199	5	)	)	PUNCT
ejpam-4479	199	6	,	,	PUNCT
ejpam-4479	199	7	where	where	SCONJ
ejpam-4479	199	8	c	c	NOUN
ejpam-4479	199	9	=	=	SYM
ejpam-4479	199	10	c1∩c2	c1∩c2	PROPN
ejpam-4479	199	11	and	and	CCONJ
ejpam-4479	199	12	g(a	g(a	PROPN
ejpam-4479	199	13	)	)	PUNCT
ejpam-4479	199	14	=	=	SYM
ejpam-4479	199	15	g1(a)∩g2(a	g1(a)∩g2(a	NOUN
ejpam-4479	199	16	)	)	PUNCT
ejpam-4479	199	17	for	for	ADP
ejpam-4479	199	18	all	all	DET
ejpam-4479	199	19	a	a	DET
ejpam-4479	199	20	∈	∈	PROPN
ejpam-4479	199	21	c.	c.	NOUN
ejpam-4479	199	22	since	since	SCONJ
ejpam-4479	199	23	g1(a	g1(a	PROPN
ejpam-4479	199	24	)	)	PUNCT
ejpam-4479	199	25	,	,	PUNCT
ejpam-4479	199	26	g2(a	g2(a	NOUN
ejpam-4479	199	27	)	)	PUNCT
ejpam-4479	199	28	⊆	⊆	NUM
ejpam-4479	199	29	f	f	X
ejpam-4479	199	30	(	(	PUNCT
ejpam-4479	199	31	a	a	NOUN
ejpam-4479	199	32	)	)	PUNCT
ejpam-4479	199	33	,	,	PUNCT
ejpam-4479	199	34	g1(a)∩g2(a	g1(a)∩g2(a	NOUN
ejpam-4479	199	35	)	)	PUNCT
ejpam-4479	199	36	⊆	⊆	NUM
ejpam-4479	199	37	f	f	X
ejpam-4479	199	38	(	(	PUNCT
ejpam-4479	199	39	a	a	NOUN
ejpam-4479	199	40	)	)	PUNCT
ejpam-4479	199	41	for	for	ADP
ejpam-4479	199	42	all	all	DET
ejpam-4479	199	43	a	a	DET
ejpam-4479	199	44	∈	∈	PROPN
ejpam-4479	199	45	c.	c.	NOUN
ejpam-4479	199	46	thus	thus	ADV
ejpam-4479	199	47	,	,	PUNCT
ejpam-4479	199	48	g(a	g(a	PROPN
ejpam-4479	199	49	)	)	PUNCT
ejpam-4479	199	50	=	=	SYM
ejpam-4479	199	51	g1(a)∩g2(a	g1(a)∩g2(a	NOUN
ejpam-4479	199	52	)	)	PUNCT
ejpam-4479	199	53	is	be	AUX
ejpam-4479	199	54	a	a	DET
ejpam-4479	199	55	hyper	hyper	ADJ
ejpam-4479	199	56	subgr	subgr	NOUN
ejpam-4479	199	57	-	-	PUNCT
ejpam-4479	199	58	algebra	algebra	NOUN
ejpam-4479	199	59	of	of	ADP
ejpam-4479	199	60	f	f	PROPN
ejpam-4479	199	61	(	(	PUNCT
ejpam-4479	199	62	a	a	NOUN
ejpam-4479	199	63	)	)	PUNCT
ejpam-4479	199	64	for	for	ADP
ejpam-4479	199	65	all	all	DET
ejpam-4479	199	66	a	a	DET
ejpam-4479	199	67	∈	∈	PROPN
ejpam-4479	199	68	c.	c.	NOUN
ejpam-4479	199	69	(	(	PUNCT
ejpam-4479	199	70	ii	ii	NOUN
ejpam-4479	199	71	)	)	PUNCT
ejpam-4479	199	72	assume	assume	VERB
ejpam-4479	199	73	that	that	SCONJ
ejpam-4479	199	74	c1∩c2	c1∩c2	PROPN
ejpam-4479	199	75	=	=	PUNCT
ejpam-4479	199	76	∅.	∅.	NOUN
ejpam-4479	199	77	by	by	ADP
ejpam-4479	199	78	definition	definition	NOUN
ejpam-4479	199	79	7	7	NUM
ejpam-4479	199	80	,	,	PUNCT
ejpam-4479	199	81	we	we	PRON
ejpam-4479	199	82	can	can	AUX
ejpam-4479	199	83	write	write	VERB
ejpam-4479	199	84	(	(	PUNCT
ejpam-4479	199	85	g1	g1	PROPN
ejpam-4479	199	86	,	,	PUNCT
ejpam-4479	199	87	c1	c1	NOUN
ejpam-4479	199	88	)	)	PUNCT
ejpam-4479	199	89	∼	∼	NOUN
ejpam-4479	199	90	∪	∪	ADJ
ejpam-4479	199	91	(	(	PUNCT
ejpam-4479	199	92	g2	g2	PROPN
ejpam-4479	199	93	,	,	PUNCT
ejpam-4479	199	94	c2	c2	PROPN
ejpam-4479	199	95	)	)	PUNCT
ejpam-4479	200	1	=	=	PUNCT
ejpam-4479	200	2	(	(	PUNCT
ejpam-4479	200	3	g	g	NOUN
ejpam-4479	200	4	,	,	PUNCT
ejpam-4479	200	5	c	c	NOUN
ejpam-4479	200	6	)	)	PUNCT
ejpam-4479	200	7	,	,	PUNCT
ejpam-4479	200	8	where	where	SCONJ
ejpam-4479	200	9	c	c	PROPN
ejpam-4479	200	10	=	=	PROPN
ejpam-4479	200	11	c1	c1	PROPN
ejpam-4479	200	12	∪	∪	PROPN
ejpam-4479	200	13	c2	c2	PROPN
ejpam-4479	200	14	and	and	CCONJ
ejpam-4479	200	15	g(x	g(x	NOUN
ejpam-4479	200	16	)	)	PUNCT
ejpam-4479	201	1	=	=	PUNCT
ejpam-4479	201	2			PRON
ejpam-4479	201	3	g1(a	g1(a	PROPN
ejpam-4479	201	4	)	)	PUNCT
ejpam-4479	201	5	,	,	PUNCT
ejpam-4479	201	6	if	if	SCONJ
ejpam-4479	201	7	a	a	DET
ejpam-4479	201	8	∈	∈	PROPN
ejpam-4479	201	9	c1	c1	NOUN
ejpam-4479	201	10	\	\	PROPN
ejpam-4479	201	11	c2	c2	PROPN
ejpam-4479	201	12	g2(a	g2(a	PROPN
ejpam-4479	201	13	)	)	PUNCT
ejpam-4479	201	14	,	,	PUNCT
ejpam-4479	201	15	if	if	SCONJ
ejpam-4479	201	16	a	a	DET
ejpam-4479	201	17	∈	∈	PROPN
ejpam-4479	201	18	c2	c2	PROPN
ejpam-4479	201	19	\	\	PROPN
ejpam-4479	201	20	c1	c1	PROPN
ejpam-4479	201	21	g1(a	g1(a	PROPN
ejpam-4479	201	22	)	)	PUNCT
ejpam-4479	201	23	∪g2(a	∪g2(a	NOUN
ejpam-4479	201	24	)	)	PUNCT
ejpam-4479	201	25	,	,	PUNCT
ejpam-4479	201	26	if	if	SCONJ
ejpam-4479	201	27	a	a	DET
ejpam-4479	201	28	∈	∈	PROPN
ejpam-4479	201	29	c1	c1	NOUN
ejpam-4479	201	30	∩	∩	PROPN
ejpam-4479	201	31	c2	c2	PROPN
ejpam-4479	201	32	for	for	ADP
ejpam-4479	201	33	all	all	DET
ejpam-4479	201	34	a	a	DET
ejpam-4479	201	35	∈	∈	PROPN
ejpam-4479	201	36	c.	c.	NOUN
ejpam-4479	201	37	by	by	ADP
ejpam-4479	201	38	the	the	DET
ejpam-4479	201	39	hypothesis	hypothesis	NOUN
ejpam-4479	201	40	,	,	PUNCT
ejpam-4479	201	41	c1	c1	PROPN
ejpam-4479	201	42	,	,	PUNCT
ejpam-4479	201	43	c2	c2	PROPN
ejpam-4479	201	44	⊆	⊆	NUM
ejpam-4479	201	45	a.	a.	NOUN
ejpam-4479	201	46	this	this	PRON
ejpam-4479	201	47	implies	imply	VERB
ejpam-4479	201	48	that	that	SCONJ
ejpam-4479	201	49	c	c	PROPN
ejpam-4479	201	50	=	=	PROPN
ejpam-4479	201	51	c1	c1	PROPN
ejpam-4479	201	52	∪	∪	ADP
ejpam-4479	201	53	c2	c2	PROPN
ejpam-4479	201	54	⊆	⊆	NUM
ejpam-4479	201	55	a.	a.	NOUN
ejpam-4479	201	56	also	also	ADV
ejpam-4479	201	57	,	,	PUNCT
ejpam-4479	201	58	gi(a	gi(a	X
ejpam-4479	201	59	)	)	PUNCT
ejpam-4479	201	60	is	be	AUX
ejpam-4479	201	61	a	a	DET
ejpam-4479	201	62	hyper	hyper	ADJ
ejpam-4479	201	63	subgr	subgr	NOUN
ejpam-4479	201	64	-	-	PUNCT
ejpam-4479	201	65	algebra	algebra	NOUN
ejpam-4479	201	66	of	of	ADP
ejpam-4479	201	67	f	f	PROPN
ejpam-4479	201	68	(	(	PUNCT
ejpam-4479	201	69	a	a	NOUN
ejpam-4479	201	70	)	)	PUNCT
ejpam-4479	201	71	for	for	ADP
ejpam-4479	201	72	all	all	DET
ejpam-4479	201	73	a	a	DET
ejpam-4479	201	74	∈	∈	PROPN
ejpam-4479	201	75	ci	ci	NOUN
ejpam-4479	201	76	,	,	PUNCT
ejpam-4479	201	77	i	i	NOUN
ejpam-4479	201	78	=	=	NOUN
ejpam-4479	201	79	1	1	NUM
ejpam-4479	201	80	,	,	PUNCT
ejpam-4479	201	81	2	2	NUM
ejpam-4479	201	82	.	.	PUNCT
ejpam-4479	201	83	since	since	SCONJ
ejpam-4479	201	84	c1	c1	PROPN
ejpam-4479	201	85	∩	∩	PROPN
ejpam-4479	201	86	c2	c2	PROPN
ejpam-4479	201	87	=	=	PUNCT
ejpam-4479	201	88	∅	∅	NOUN
ejpam-4479	201	89	,	,	PUNCT
ejpam-4479	201	90	by	by	ADP
ejpam-4479	201	91	theorem	theorem	NOUN
ejpam-4479	201	92	5	5	NUM
ejpam-4479	201	93	,	,	PUNCT
ejpam-4479	201	94	g(a	g(a	PROPN
ejpam-4479	201	95	)	)	PUNCT
ejpam-4479	201	96	is	be	AUX
ejpam-4479	201	97	a	a	DET
ejpam-4479	201	98	hyper	hyper	ADJ
ejpam-4479	201	99	subgr	subgr	NOUN
ejpam-4479	201	100	-	-	PUNCT
ejpam-4479	201	101	algebra	algebra	NOUN
ejpam-4479	201	102	of	of	ADP
ejpam-4479	201	103	f	f	PROPN
ejpam-4479	201	104	(	(	PUNCT
ejpam-4479	201	105	a	a	NOUN
ejpam-4479	201	106	)	)	PUNCT
ejpam-4479	201	107	for	for	ADP
ejpam-4479	201	108	all	all	DET
ejpam-4479	201	109	a	a	DET
ejpam-4479	201	110	∈	∈	PROPN
ejpam-4479	201	111	c.	c.	NOUN
ejpam-4479	201	112	therefore	therefore	ADV
ejpam-4479	201	113	,	,	PUNCT
ejpam-4479	201	114	(	(	PUNCT
ejpam-4479	201	115	g1	g1	PROPN
ejpam-4479	201	116	,	,	PUNCT
ejpam-4479	201	117	c1	c1	NOUN
ejpam-4479	201	118	)	)	PUNCT
ejpam-4479	201	119	∼	∼	NOUN
ejpam-4479	201	120	∪	∪	ADJ
ejpam-4479	201	121	(	(	PUNCT
ejpam-4479	201	122	g2	g2	PROPN
ejpam-4479	201	123	,	,	PUNCT
ejpam-4479	201	124	c2	c2	PROPN
ejpam-4479	201	125	)	)	PUNCT
ejpam-4479	201	126	∼	∼	NOUN
ejpam-4479	201	127	<	<	X
ejpam-4479	201	128	(	(	PUNCT
ejpam-4479	201	129	f	f	X
ejpam-4479	201	130	,	,	PUNCT
ejpam-4479	201	131	a	a	PRON
ejpam-4479	201	132	)	)	PUNCT
ejpam-4479	201	133	.	.	PUNCT
ejpam-4479	202	1	definition	definition	NOUN
ejpam-4479	202	2	15	15	NUM
ejpam-4479	202	3	.	.	PUNCT
ejpam-4479	203	1	let	let	AUX
ejpam-4479	203	2	(	(	PUNCT
ejpam-4479	203	3	f	f	X
ejpam-4479	203	4	,	,	PUNCT
ejpam-4479	203	5	a	a	PRON
ejpam-4479	203	6	)	)	PUNCT
ejpam-4479	203	7	be	be	AUX
ejpam-4479	203	8	a	a	DET
ejpam-4479	203	9	soft	soft	ADJ
ejpam-4479	203	10	set	set	NOUN
ejpam-4479	203	11	over	over	ADP
ejpam-4479	203	12	hyper	hyper	ADJ
ejpam-4479	203	13	gr	gr	PROPN
ejpam-4479	203	14	-	-	PUNCT
ejpam-4479	203	15	algebra	algebra	NOUN
ejpam-4479	203	16	h.	h.	NOUN
ejpam-4479	203	17	a	a	DET
ejpam-4479	203	18	soft	soft	ADJ
ejpam-4479	203	19	set	set	NOUN
ejpam-4479	203	20	(	(	PUNCT
ejpam-4479	203	21	g	g	NOUN
ejpam-4479	203	22	,	,	PUNCT
ejpam-4479	203	23	i	i	NOUN
ejpam-4479	203	24	)	)	PUNCT
ejpam-4479	203	25	over	over	ADP
ejpam-4479	203	26	h	h	NOUN
ejpam-4479	203	27	is	be	AUX
ejpam-4479	203	28	called	call	VERB
ejpam-4479	203	29	a	a	DET
ejpam-4479	203	30	soft	soft	ADJ
ejpam-4479	203	31	hyper	hyper	ADJ
ejpam-4479	203	32	gr	gr	NOUN
ejpam-4479	203	33	-	-	PUNCT
ejpam-4479	203	34	ideal	ideal	NOUN
ejpam-4479	203	35	of	of	ADP
ejpam-4479	203	36	(	(	PUNCT
ejpam-4479	203	37	f	f	X
ejpam-4479	203	38	,	,	PUNCT
ejpam-4479	203	39	a	a	PRON
ejpam-4479	203	40	)	)	PUNCT
ejpam-4479	203	41	,	,	PUNCT
ejpam-4479	203	42	written	write	VERB
ejpam-4479	203	43	as	as	ADP
ejpam-4479	203	44	(	(	PUNCT
ejpam-4479	203	45	g	g	PROPN
ejpam-4479	203	46	,	,	PUNCT
ejpam-4479	203	47	m	m	NOUN
ejpam-4479	203	48	)	)	PUNCT
ejpam-4479	203	49	∼⋄	∼⋄	PROPN
ejpam-4479	203	50	(	(	PUNCT
ejpam-4479	203	51	f	f	X
ejpam-4479	203	52	,	,	PUNCT
ejpam-4479	203	53	a	a	PRON
ejpam-4479	203	54	)	)	PUNCT
ejpam-4479	203	55	if	if	SCONJ
ejpam-4479	203	56	the	the	DET
ejpam-4479	203	57	following	following	NOUN
ejpam-4479	203	58	are	be	AUX
ejpam-4479	203	59	satisfied	satisfied	ADJ
ejpam-4479	203	60	:	:	PUNCT
ejpam-4479	203	61	(	(	PUNCT
ejpam-4479	203	62	i	i	NOUN
ejpam-4479	203	63	)	)	PUNCT
ejpam-4479	204	1	i	i	PRON
ejpam-4479	204	2	⊂	⊂	PROPN
ejpam-4479	204	3	a	a	PRON
ejpam-4479	204	4	with	with	ADP
ejpam-4479	204	5	i	i	PRON
ejpam-4479	204	6	̸=	̸=	PROPN
ejpam-4479	204	7	∅	∅	NOUN
ejpam-4479	204	8	(	(	PUNCT
ejpam-4479	204	9	ii	ii	NOUN
ejpam-4479	204	10	)	)	PUNCT
ejpam-4479	204	11	for	for	ADP
ejpam-4479	204	12	all	all	DET
ejpam-4479	204	13	a	a	DET
ejpam-4479	204	14	∈	∈	PROPN
ejpam-4479	204	15	i	i	NOUN
ejpam-4479	204	16	,	,	PUNCT
ejpam-4479	204	17	g(a	g(a	PROPN
ejpam-4479	204	18	)	)	PUNCT
ejpam-4479	204	19	is	be	AUX
ejpam-4479	204	20	a	a	DET
ejpam-4479	204	21	hyper	hyper	ADJ
ejpam-4479	204	22	gr	gr	NOUN
ejpam-4479	204	23	-	-	PUNCT
ejpam-4479	204	24	ideal	ideal	NOUN
ejpam-4479	204	25	on	on	ADP
ejpam-4479	204	26	f	f	PROPN
ejpam-4479	204	27	(	(	PUNCT
ejpam-4479	204	28	a	a	NOUN
ejpam-4479	204	29	)	)	PUNCT
ejpam-4479	204	30	.	.	PUNCT
ejpam-4479	205	1	example	example	NOUN
ejpam-4479	206	1	10	10	NUM
ejpam-4479	206	2	.	.	PUNCT
ejpam-4479	207	1	consider	consider	VERB
ejpam-4479	207	2	the	the	DET
ejpam-4479	207	3	same	same	ADJ
ejpam-4479	207	4	hyper	hyper	ADJ
ejpam-4479	207	5	gr	gr	NOUN
ejpam-4479	207	6	-	-	PUNCT
ejpam-4479	207	7	algebra	algebra	NOUN
ejpam-4479	207	8	h	h	NOUN
ejpam-4479	207	9	=	=	SYM
ejpam-4479	207	10	{	{	PUNCT
ejpam-4479	207	11	0	0	NUM
ejpam-4479	207	12	,	,	PUNCT
ejpam-4479	207	13	1	1	NUM
ejpam-4479	207	14	,	,	PUNCT
ejpam-4479	207	15	2	2	NUM
ejpam-4479	207	16	,	,	PUNCT
ejpam-4479	207	17	3	3	NUM
ejpam-4479	207	18	}	}	PUNCT
ejpam-4479	207	19	in	in	ADP
ejpam-4479	207	20	example	example	NOUN
ejpam-4479	207	21	4	4	X
ejpam-4479	207	22	.	.	PUNCT
ejpam-4479	208	1	let	let	VERB
ejpam-4479	208	2	a	a	DET
ejpam-4479	208	3	=	=	NOUN
ejpam-4479	208	4	h	h	NOUN
ejpam-4479	209	1	and	and	CCONJ
ejpam-4479	209	2	i	i	PRON
ejpam-4479	209	3	=	=	PUNCT
ejpam-4479	209	4	{	{	PUNCT
ejpam-4479	209	5	0	0	NUM
ejpam-4479	209	6	,	,	PUNCT
ejpam-4479	209	7	1	1	NUM
ejpam-4479	209	8	}	}	PUNCT
ejpam-4479	209	9	.	.	PUNCT
ejpam-4479	210	1	suppose	suppose	VERB
ejpam-4479	210	2	f	f	X
ejpam-4479	210	3	:	:	PUNCT
ejpam-4479	210	4	a	a	DET
ejpam-4479	210	5	→	→	SYM
ejpam-4479	210	6	p	p	X
ejpam-4479	210	7	(	(	PUNCT
ejpam-4479	210	8	h	h	NOUN
ejpam-4479	210	9	)	)	PUNCT
ejpam-4479	210	10	is	be	AUX
ejpam-4479	210	11	defined	define	VERB
ejpam-4479	210	12	by	by	ADP
ejpam-4479	210	13	f	f	PROPN
ejpam-4479	210	14	(	(	PUNCT
ejpam-4479	210	15	a	a	NOUN
ejpam-4479	210	16	)	)	PUNCT
ejpam-4479	210	17	=	=	SYM
ejpam-4479	210	18	⋃	⋃	NOUN
ejpam-4479	210	19	b⊂h	b⊂h	NOUN
ejpam-4479	210	20	,	,	PUNCT
ejpam-4479	210	21	ar̊b	ar̊b	PROPN
ejpam-4479	210	22	b	b	PROPN
ejpam-4479	210	23	with	with	ADP
ejpam-4479	210	24	r̊	r̊	PRON
ejpam-4479	210	25	=	=	SYM
ejpam-4479	210	26	{	{	PUNCT
ejpam-4479	210	27	(	(	PUNCT
ejpam-4479	210	28	0	0	NUM
ejpam-4479	210	29	,	,	PUNCT
ejpam-4479	210	30	{	{	PUNCT
ejpam-4479	210	31	1	1	NUM
ejpam-4479	210	32	}	}	PUNCT
ejpam-4479	210	33	)	)	PUNCT
ejpam-4479	210	34	,	,	PUNCT
ejpam-4479	210	35	(	(	PUNCT
ejpam-4479	210	36	0	0	NUM
ejpam-4479	210	37	,	,	PUNCT
ejpam-4479	210	38	{	{	PUNCT
ejpam-4479	210	39	0	0	NUM
ejpam-4479	210	40	,	,	PUNCT
ejpam-4479	210	41	2	2	NUM
ejpam-4479	210	42	}	}	PUNCT
ejpam-4479	210	43	)	)	PUNCT
ejpam-4479	210	44	,	,	PUNCT
ejpam-4479	210	45	(	(	PUNCT
ejpam-4479	210	46	1	1	NUM
ejpam-4479	210	47	,	,	PUNCT
ejpam-4479	210	48	{	{	PUNCT
ejpam-4479	210	49	0	0	NUM
ejpam-4479	210	50	,	,	PUNCT
ejpam-4479	210	51	2	2	NUM
ejpam-4479	210	52	}	}	PUNCT
ejpam-4479	210	53	)	)	PUNCT
ejpam-4479	210	54	,	,	PUNCT
ejpam-4479	210	55	(	(	PUNCT
ejpam-4479	210	56	1	1	NUM
ejpam-4479	210	57	,	,	PUNCT
ejpam-4479	210	58	{	{	PUNCT
ejpam-4479	210	59	0	0	NUM
ejpam-4479	210	60	,	,	PUNCT
ejpam-4479	210	61	1	1	NUM
ejpam-4479	210	62	,	,	PUNCT
ejpam-4479	210	63	3	3	NUM
ejpam-4479	210	64	}	}	PUNCT
ejpam-4479	210	65	)	)	PUNCT
ejpam-4479	210	66	}	}	PUNCT
ejpam-4479	210	67	.	.	PUNCT
ejpam-4479	211	1	then	then	ADV
ejpam-4479	211	2	f	f	X
ejpam-4479	211	3	(	(	PUNCT
ejpam-4479	211	4	0	0	NUM
ejpam-4479	211	5	)	)	PUNCT
ejpam-4479	211	6	=	=	NOUN
ejpam-4479	211	7	⋃	⋃	NOUN
ejpam-4479	211	8	b⊂h,0r̊b	b⊂h,0r̊b	NOUN
ejpam-4479	211	9	b	b	X
ejpam-4479	211	10	=	=	SYM
ejpam-4479	211	11	{	{	PUNCT
ejpam-4479	211	12	0	0	NUM
ejpam-4479	211	13	,	,	PUNCT
ejpam-4479	211	14	1	1	NUM
ejpam-4479	211	15	,	,	PUNCT
ejpam-4479	211	16	2	2	NUM
ejpam-4479	211	17	}	}	PUNCT
ejpam-4479	211	18	m.k	m.k	PROPN
ejpam-4479	211	19	.	.	PUNCT
ejpam-4479	211	20	engcot	engcot	PROPN
ejpam-4479	211	21	,	,	PUNCT
ejpam-4479	211	22	g.	g.	PROPN
ejpam-4479	211	23	petalcorin	petalcorin	PROPN
ejpam-4479	211	24	/	/	SYM
ejpam-4479	211	25	eur	eur	PROPN
ejpam-4479	211	26	.	.	PUNCT
ejpam-4479	212	1	j.	j.	PROPN
ejpam-4479	212	2	pure	pure	PROPN
ejpam-4479	212	3	appl	appl	PROPN
ejpam-4479	212	4	.	.	PROPN
ejpam-4479	212	5	math	math	PROPN
ejpam-4479	212	6	,	,	PUNCT
ejpam-4479	212	7	15	15	NUM
ejpam-4479	212	8	(	(	PUNCT
ejpam-4479	212	9	4	4	NUM
ejpam-4479	212	10	)	)	PUNCT
ejpam-4479	212	11	(	(	PUNCT
ejpam-4479	212	12	2022	2022	NUM
ejpam-4479	212	13	)	)	PUNCT
ejpam-4479	212	14	,	,	PUNCT
ejpam-4479	212	15	1482	1482	NUM
ejpam-4479	212	16	-	-	SYM
ejpam-4479	212	17	1497	1497	NUM
ejpam-4479	212	18	1491	1491	NUM
ejpam-4479	212	19	and	and	CCONJ
ejpam-4479	212	20	f	f	PROPN
ejpam-4479	212	21	(	(	PUNCT
ejpam-4479	212	22	1	1	NUM
ejpam-4479	212	23	)	)	PUNCT
ejpam-4479	212	24	=	=	NOUN
ejpam-4479	212	25	⋃	⋃	ADP
ejpam-4479	212	26	b⊂h,1r̊b	b⊂h,1r̊b	NOUN
ejpam-4479	212	27	b	b	X
ejpam-4479	212	28	=	=	SYM
ejpam-4479	212	29	{	{	PUNCT
ejpam-4479	212	30	0	0	NUM
ejpam-4479	212	31	,	,	PUNCT
ejpam-4479	212	32	1	1	NUM
ejpam-4479	212	33	,	,	PUNCT
ejpam-4479	212	34	2	2	NUM
ejpam-4479	212	35	,	,	PUNCT
ejpam-4479	212	36	3	3	NUM
ejpam-4479	212	37	}	}	PUNCT
ejpam-4479	212	38	.	.	PUNCT
ejpam-4479	213	1	defineg(a	defineg(a	NOUN
ejpam-4479	213	2	)	)	PUNCT
ejpam-4479	213	3	=	=	SYM
ejpam-4479	213	4	⋃	⋃	NOUN
ejpam-4479	213	5	b⊂h	b⊂h	NOUN
ejpam-4479	213	6	,	,	PUNCT
ejpam-4479	213	7	ar̊b⇔b	ar̊b⇔b	NOUN
ejpam-4479	213	8	=	=	SYM
ejpam-4479	213	9	an	an	DET
ejpam-4479	213	10	b	b	NOUN
ejpam-4479	213	11	for	for	ADP
ejpam-4479	213	12	some	some	DET
ejpam-4479	213	13	n	n	PRON
ejpam-4479	213	14	∈	∈	NOUN
ejpam-4479	213	15	n.	n.	NOUN
ejpam-4479	213	16	theng(0	theng(0	NOUN
ejpam-4479	213	17	)	)	PUNCT
ejpam-4479	213	18	=	=	PUNCT
ejpam-4479	213	19	{	{	PUNCT
ejpam-4479	213	20	0	0	NUM
ejpam-4479	213	21	,	,	PUNCT
ejpam-4479	213	22	1	1	NUM
ejpam-4479	213	23	}	}	PUNCT
ejpam-4479	213	24	,	,	PUNCT
ejpam-4479	213	25	g(1	g(1	NOUN
ejpam-4479	213	26	)	)	PUNCT
ejpam-4479	213	27	=	=	PUNCT
ejpam-4479	213	28	{	{	PUNCT
ejpam-4479	213	29	0	0	NUM
ejpam-4479	213	30	,	,	PUNCT
ejpam-4479	213	31	1	1	NUM
ejpam-4479	213	32	}	}	PUNCT
ejpam-4479	213	33	,	,	PUNCT
ejpam-4479	213	34	g(2	g(2	PROPN
ejpam-4479	213	35	)	)	PUNCT
ejpam-4479	213	36	=	=	PRON
ejpam-4479	213	37	{	{	PUNCT
ejpam-4479	213	38	0	0	NUM
ejpam-4479	213	39	,	,	PUNCT
ejpam-4479	213	40	1	1	NUM
ejpam-4479	213	41	,	,	PUNCT
ejpam-4479	213	42	2	2	NUM
ejpam-4479	213	43	}	}	PUNCT
ejpam-4479	213	44	and	and	CCONJ
ejpam-4479	213	45	g(3	g(3	PROPN
ejpam-4479	213	46	)	)	PUNCT
ejpam-4479	213	47	=	=	PRON
ejpam-4479	213	48	{	{	PUNCT
ejpam-4479	213	49	0	0	NUM
ejpam-4479	213	50	,	,	PUNCT
ejpam-4479	213	51	1	1	NUM
ejpam-4479	213	52	,	,	PUNCT
ejpam-4479	213	53	3	3	NUM
ejpam-4479	213	54	}	}	PUNCT
ejpam-4479	213	55	.	.	PUNCT
ejpam-4479	214	1	a	a	DET
ejpam-4479	214	2	b	b	NOUN
ejpam-4479	214	3	a	a	DET
ejpam-4479	214	4	⊛	⊛	NUM
ejpam-4479	214	5	b	b	NOUN
ejpam-4479	214	6	≪	≪	PUNCT
ejpam-4479	214	7	i	i	PRON
ejpam-4479	214	8	a	a	DET
ejpam-4479	214	9	∈	∈	X
ejpam-4479	215	1	i	i	X
ejpam-4479	215	2	0	0	NUM
ejpam-4479	215	3	0	0	NUM
ejpam-4479	215	4	{	{	PUNCT
ejpam-4479	215	5	0,1	0,1	NUM
ejpam-4479	215	6	}	}	PUNCT
ejpam-4479	215	7	✓	✓	ADJ
ejpam-4479	215	8	✓	✓	ADJ
ejpam-4479	215	9	0	0	NUM
ejpam-4479	215	10	1	1	NUM
ejpam-4479	215	11	{	{	PUNCT
ejpam-4479	215	12	0,1	0,1	NUM
ejpam-4479	215	13	}	}	PUNCT
ejpam-4479	215	14	✓	✓	ADJ
ejpam-4479	215	15	✓	✓	ADJ
ejpam-4479	215	16	1	1	NUM
ejpam-4479	215	17	0	0	NUM
ejpam-4479	215	18	{	{	PUNCT
ejpam-4479	215	19	1	1	NUM
ejpam-4479	215	20	}	}	PUNCT
ejpam-4479	215	21	✓	✓	ADJ
ejpam-4479	215	22	✓	✓	ADJ
ejpam-4479	215	23	2	2	NUM
ejpam-4479	215	24	0	0	NUM
ejpam-4479	215	25	{	{	PUNCT
ejpam-4479	215	26	0,2	0,2	NUM
ejpam-4479	215	27	}	}	PUNCT
ejpam-4479	215	28	×	×	NOUN
ejpam-4479	215	29	2	2	NUM
ejpam-4479	215	30	1	1	NUM
ejpam-4479	215	31	{	{	PUNCT
ejpam-4479	215	32	0,2	0,2	NUM
ejpam-4479	215	33	}	}	PUNCT
ejpam-4479	215	34	×	×	NOUN
ejpam-4479	215	35	table	table	NOUN
ejpam-4479	215	36	3.1	3.1	NUM
ejpam-4479	215	37	a	a	DET
ejpam-4479	215	38	b	b	NOUN
ejpam-4479	215	39	a	a	DET
ejpam-4479	215	40	⊛	⊛	NUM
ejpam-4479	215	41	b	b	NOUN
ejpam-4479	215	42	≪	≪	ADJ
ejpam-4479	215	43	g(1	g(1	NOUN
ejpam-4479	215	44	)	)	PUNCT
ejpam-4479	215	45	=	=	PUNCT
ejpam-4479	215	46	{	{	PUNCT
ejpam-4479	215	47	0	0	NUM
ejpam-4479	215	48	,	,	PUNCT
ejpam-4479	215	49	1	1	NUM
ejpam-4479	215	50	}	}	PUNCT
ejpam-4479	215	51	a	a	DET
ejpam-4479	215	52	∈	∈	PROPN
ejpam-4479	215	53	g(1	g(1	NOUN
ejpam-4479	215	54	)	)	PUNCT
ejpam-4479	215	55	=	=	PRON
ejpam-4479	215	56	{	{	PUNCT
ejpam-4479	215	57	0	0	NUM
ejpam-4479	215	58	,	,	PUNCT
ejpam-4479	215	59	1	1	NUM
ejpam-4479	215	60	}	}	SYM
ejpam-4479	215	61	0	0	NUM
ejpam-4479	215	62	0	0	NUM
ejpam-4479	215	63	{	{	PUNCT
ejpam-4479	215	64	0,1	0,1	NUM
ejpam-4479	215	65	}	}	PUNCT
ejpam-4479	215	66	✓	✓	ADJ
ejpam-4479	215	67	✓	✓	ADJ
ejpam-4479	215	68	1	1	NUM
ejpam-4479	215	69	0	0	NUM
ejpam-4479	215	70	{	{	PUNCT
ejpam-4479	215	71	1	1	NUM
ejpam-4479	215	72	}	}	PUNCT
ejpam-4479	215	73	✓	✓	ADJ
ejpam-4479	215	74	✓	✓	ADJ
ejpam-4479	215	75	1	1	NUM
ejpam-4479	215	76	1	1	NUM
ejpam-4479	215	77	{	{	PUNCT
ejpam-4479	215	78	0,1	0,1	NUM
ejpam-4479	215	79	}	}	PUNCT
ejpam-4479	215	80	✓	✓	ADJ
ejpam-4479	215	81	✓	✓	ADJ
ejpam-4479	215	82	.	.	NOUN
ejpam-4479	215	83	2	2	NUM
ejpam-4479	215	84	0	0	NUM
ejpam-4479	215	85	{	{	PUNCT
ejpam-4479	215	86	0,2	0,2	NUM
ejpam-4479	215	87	}	}	PUNCT
ejpam-4479	215	88	×	×	NOUN
ejpam-4479	215	89	2	2	NUM
ejpam-4479	215	90	1	1	NUM
ejpam-4479	215	91	{	{	PUNCT
ejpam-4479	215	92	0,2	0,2	NUM
ejpam-4479	215	93	}	}	PUNCT
ejpam-4479	215	94	×	×	NOUN
ejpam-4479	215	95	3	3	NUM
ejpam-4479	215	96	0	0	NUM
ejpam-4479	215	97	{	{	PUNCT
ejpam-4479	215	98	3	3	NUM
ejpam-4479	215	99	}	}	PUNCT
ejpam-4479	215	100	×	×	NOUN
ejpam-4479	215	101	3	3	NUM
ejpam-4479	215	102	1	1	NUM
ejpam-4479	215	103	{	{	PUNCT
ejpam-4479	215	104	0,1,3	0,1,3	PROPN
ejpam-4479	215	105	}	}	PUNCT
ejpam-4479	215	106	×	×	NOUN
ejpam-4479	215	107	table	table	NOUN
ejpam-4479	215	108	3.2	3.2	NUM
ejpam-4479	215	109	note	note	NOUN
ejpam-4479	215	110	that	that	SCONJ
ejpam-4479	215	111	g(0	g(0	NOUN
ejpam-4479	215	112	)	)	PUNCT
ejpam-4479	215	113	is	be	AUX
ejpam-4479	215	114	a	a	DET
ejpam-4479	215	115	hyper	hyper	ADJ
ejpam-4479	215	116	gr	gr	NOUN
ejpam-4479	215	117	-	-	PUNCT
ejpam-4479	215	118	ideal	ideal	NOUN
ejpam-4479	215	119	of	of	ADP
ejpam-4479	215	120	f	f	PROPN
ejpam-4479	215	121	(	(	PUNCT
ejpam-4479	215	122	0	0	NUM
ejpam-4479	215	123	)	)	PUNCT
ejpam-4479	215	124	(	(	PUNCT
ejpam-4479	215	125	see	see	VERB
ejpam-4479	215	126	table	table	NOUN
ejpam-4479	215	127	3.1	3.1	NUM
ejpam-4479	215	128	)	)	PUNCT
ejpam-4479	215	129	and	and	CCONJ
ejpam-4479	215	130	g(1	g(1	NOUN
ejpam-4479	215	131	)	)	PUNCT
ejpam-4479	215	132	is	be	AUX
ejpam-4479	215	133	a	a	DET
ejpam-4479	215	134	hyper	hyper	ADJ
ejpam-4479	215	135	gr	gr	NOUN
ejpam-4479	215	136	-	-	PUNCT
ejpam-4479	215	137	ideal	ideal	NOUN
ejpam-4479	215	138	of	of	ADP
ejpam-4479	215	139	f	f	PROPN
ejpam-4479	215	140	(	(	PUNCT
ejpam-4479	215	141	1	1	NUM
ejpam-4479	215	142	)	)	PUNCT
ejpam-4479	215	143	is	be	AUX
ejpam-4479	215	144	a	a	DET
ejpam-4479	215	145	hyper	hyper	ADJ
ejpam-4479	215	146	gr	gr	NOUN
ejpam-4479	215	147	-	-	PUNCT
ejpam-4479	215	148	ideal	ideal	NOUN
ejpam-4479	215	149	(	(	PUNCT
ejpam-4479	215	150	see	see	VERB
ejpam-4479	215	151	table	table	NOUN
ejpam-4479	215	152	3.2	3.2	NUM
ejpam-4479	215	153	)	)	PUNCT
ejpam-4479	215	154	.	.	PUNCT
ejpam-4479	216	1	hence	hence	ADV
ejpam-4479	216	2	,	,	PUNCT
ejpam-4479	216	3	for	for	ADP
ejpam-4479	216	4	all	all	DET
ejpam-4479	216	5	a	a	DET
ejpam-4479	216	6	∈	∈	NOUN
ejpam-4479	216	7	i	i	NOUN
ejpam-4479	216	8	,	,	PUNCT
ejpam-4479	216	9	g(a	g(a	PROPN
ejpam-4479	216	10	)	)	PUNCT
ejpam-4479	216	11	is	be	AUX
ejpam-4479	216	12	a	a	DET
ejpam-4479	216	13	hyper	hyper	ADJ
ejpam-4479	216	14	gr	gr	NOUN
ejpam-4479	216	15	-	-	PUNCT
ejpam-4479	216	16	ideal	ideal	NOUN
ejpam-4479	216	17	of	of	ADP
ejpam-4479	216	18	f	f	PROPN
ejpam-4479	216	19	(	(	PUNCT
ejpam-4479	216	20	a	a	NOUN
ejpam-4479	216	21	)	)	PUNCT
ejpam-4479	216	22	.	.	PUNCT
ejpam-4479	217	1	therefore	therefore	ADV
ejpam-4479	217	2	,	,	PUNCT
ejpam-4479	217	3	(	(	PUNCT
ejpam-4479	217	4	g	g	NOUN
ejpam-4479	217	5	,	,	PUNCT
ejpam-4479	217	6	i	i	NOUN
ejpam-4479	217	7	)	)	PUNCT
ejpam-4479	217	8	is	be	AUX
ejpam-4479	217	9	a	a	DET
ejpam-4479	217	10	soft	soft	ADJ
ejpam-4479	217	11	hyper	hyper	ADJ
ejpam-4479	217	12	gr	gr	NOUN
ejpam-4479	217	13	-	-	PUNCT
ejpam-4479	217	14	ideal	ideal	NOUN
ejpam-4479	217	15	of	of	ADP
ejpam-4479	217	16	(	(	PUNCT
ejpam-4479	217	17	f	f	X
ejpam-4479	217	18	,	,	PUNCT
ejpam-4479	217	19	a	a	PRON
ejpam-4479	217	20	)	)	PUNCT
ejpam-4479	217	21	.	.	PUNCT
ejpam-4479	218	1	theorem	theorem	ADJ
ejpam-4479	218	2	10	10	NUM
ejpam-4479	218	3	.	.	PUNCT
ejpam-4479	219	1	let	let	AUX
ejpam-4479	219	2	(	(	PUNCT
ejpam-4479	219	3	f	f	X
ejpam-4479	219	4	,	,	PUNCT
ejpam-4479	219	5	a	a	PRON
ejpam-4479	219	6	)	)	PUNCT
ejpam-4479	219	7	be	be	AUX
ejpam-4479	219	8	a	a	DET
ejpam-4479	219	9	soft	soft	ADJ
ejpam-4479	219	10	hyper	hyper	ADJ
ejpam-4479	219	11	gr	gr	NOUN
ejpam-4479	219	12	-	-	PUNCT
ejpam-4479	219	13	algebra	algebra	NOUN
ejpam-4479	219	14	overh	overh	NOUN
ejpam-4479	219	15	.	.	PUNCT
ejpam-4479	220	1	suppose	suppose	VERB
ejpam-4479	220	2	(	(	PUNCT
ejpam-4479	220	3	g	g	NOUN
ejpam-4479	220	4	,	,	PUNCT
ejpam-4479	220	5	m1	m1	NOUN
ejpam-4479	220	6	)	)	PUNCT
ejpam-4479	220	7	and	and	CCONJ
ejpam-4479	220	8	(	(	PUNCT
ejpam-4479	220	9	j	j	PROPN
ejpam-4479	220	10	,	,	PUNCT
ejpam-4479	220	11	m2	m2	PROPN
ejpam-4479	220	12	)	)	PUNCT
ejpam-4479	220	13	are	be	AUX
ejpam-4479	220	14	two	two	NUM
ejpam-4479	220	15	soft	soft	ADJ
ejpam-4479	220	16	hyper	hyper	ADJ
ejpam-4479	220	17	gr	gr	NOUN
ejpam-4479	220	18	-	-	PUNCT
ejpam-4479	220	19	ideals	ideal	NOUN
ejpam-4479	220	20	of	of	ADP
ejpam-4479	220	21	(	(	PUNCT
ejpam-4479	220	22	f	f	X
ejpam-4479	220	23	,	,	PUNCT
ejpam-4479	220	24	a	a	PRON
ejpam-4479	220	25	)	)	PUNCT
ejpam-4479	220	26	such	such	ADJ
ejpam-4479	220	27	that	that	DET
ejpam-4479	220	28	m1	m1	PROPN
ejpam-4479	220	29	∩m2	∩m2	PROPN
ejpam-4479	220	30	̸=	̸=	PROPN
ejpam-4479	220	31	∅.	∅.	ADV
ejpam-4479	220	32	then	then	ADV
ejpam-4479	220	33	(	(	PUNCT
ejpam-4479	220	34	g	g	NOUN
ejpam-4479	220	35	,	,	PUNCT
ejpam-4479	220	36	m1	m1	NOUN
ejpam-4479	220	37	)	)	PUNCT
ejpam-4479	220	38	∼	∼	NOUN
ejpam-4479	220	39	∩	∩	NOUN
ejpam-4479	220	40	(	(	PUNCT
ejpam-4479	220	41	j	j	PROPN
ejpam-4479	220	42	,	,	PUNCT
ejpam-4479	220	43	m2	m2	PROPN
ejpam-4479	220	44	)	)	PUNCT
ejpam-4479	220	45	is	be	AUX
ejpam-4479	220	46	a	a	DET
ejpam-4479	220	47	soft	soft	ADJ
ejpam-4479	220	48	hyper	hyper	ADJ
ejpam-4479	220	49	gr	gr	NOUN
ejpam-4479	220	50	-	-	PUNCT
ejpam-4479	220	51	ideal	ideal	NOUN
ejpam-4479	220	52	of	of	ADP
ejpam-4479	220	53	(	(	PUNCT
ejpam-4479	220	54	f	f	X
ejpam-4479	220	55	,	,	PUNCT
ejpam-4479	220	56	a	a	PRON
ejpam-4479	220	57	)	)	PUNCT
ejpam-4479	220	58	.	.	PUNCT
ejpam-4479	221	1	proof	proof	NOUN
ejpam-4479	221	2	:	:	PUNCT
ejpam-4479	221	3	suppose	suppose	VERB
ejpam-4479	221	4	(	(	PUNCT
ejpam-4479	221	5	g	g	NOUN
ejpam-4479	221	6	,	,	PUNCT
ejpam-4479	221	7	m1	m1	NOUN
ejpam-4479	221	8	)	)	PUNCT
ejpam-4479	221	9	and	and	CCONJ
ejpam-4479	221	10	(	(	PUNCT
ejpam-4479	221	11	j	j	PROPN
ejpam-4479	221	12	,	,	PUNCT
ejpam-4479	221	13	m2	m2	PROPN
ejpam-4479	221	14	)	)	PUNCT
ejpam-4479	221	15	are	be	AUX
ejpam-4479	221	16	two	two	NUM
ejpam-4479	221	17	soft	soft	ADJ
ejpam-4479	221	18	hyper	hyper	ADJ
ejpam-4479	221	19	gr	gr	NOUN
ejpam-4479	221	20	-	-	PUNCT
ejpam-4479	221	21	ideals	ideal	NOUN
ejpam-4479	221	22	such	such	ADJ
ejpam-4479	221	23	that	that	SCONJ
ejpam-4479	221	24	m1∩m2	m1∩m2	AUX
ejpam-4479	221	25	̸=	̸=	PROPN
ejpam-4479	221	26	∅.	∅.	ADV
ejpam-4479	221	27	take	take	VERB
ejpam-4479	221	28	m	m	NOUN
ejpam-4479	221	29	=	=	PUNCT
ejpam-4479	221	30	m1	m1	PROPN
ejpam-4479	221	31	∩m2	∩m2	PROPN
ejpam-4479	221	32	.	.	PUNCT
ejpam-4479	222	1	clearly	clearly	ADV
ejpam-4479	222	2	,	,	PUNCT
ejpam-4479	222	3	m	m	VERB
ejpam-4479	222	4	⊆	⊆	NUM
ejpam-4479	222	5	a	a	PRON
ejpam-4479	222	6	and	and	CCONJ
ejpam-4479	222	7	by	by	ADP
ejpam-4479	222	8	hypothesis	hypothesis	NOUN
ejpam-4479	222	9	m	m	NOUN
ejpam-4479	222	10	̸=	̸=	PROPN
ejpam-4479	222	11	∅.	∅.	ADV
ejpam-4479	222	12	by	by	ADP
ejpam-4479	222	13	theorem	theorem	ADJ
ejpam-4479	222	14	2,m	2,m	NOUN
ejpam-4479	222	15	is	be	AUX
ejpam-4479	222	16	a	a	DET
ejpam-4479	222	17	hyper	hyper	ADJ
ejpam-4479	222	18	gr	gr	NOUN
ejpam-4479	222	19	-	-	PUNCT
ejpam-4479	222	20	ideal	ideal	NOUN
ejpam-4479	222	21	.	.	PUNCT
ejpam-4479	223	1	let	let	VERB
ejpam-4479	223	2	m	m	PRON
ejpam-4479	223	3	∈	∈	VERB
ejpam-4479	223	4	m	m	NOUN
ejpam-4479	223	5	.	.	PUNCT
ejpam-4479	224	1	then	then	ADV
ejpam-4479	224	2	this	this	PRON
ejpam-4479	224	3	implies	imply	VERB
ejpam-4479	224	4	that	that	SCONJ
ejpam-4479	224	5	m	m	PROPN
ejpam-4479	224	6	∈	∈	PROPN
ejpam-4479	224	7	m1	m1	PROPN
ejpam-4479	224	8	and	and	CCONJ
ejpam-4479	224	9	m	m	PROPN
ejpam-4479	224	10	∈	∈	PROPN
ejpam-4479	224	11	m2	m2	PROPN
ejpam-4479	224	12	.	.	PUNCT
ejpam-4479	225	1	also	also	ADV
ejpam-4479	225	2	,	,	PUNCT
ejpam-4479	225	3	g(m	g(m	PROPN
ejpam-4479	225	4	)	)	PUNCT
ejpam-4479	226	1	⋄	⋄	PROPN
ejpam-4479	226	2	f	f	PROPN
ejpam-4479	226	3	(	(	PUNCT
ejpam-4479	226	4	m	m	NOUN
ejpam-4479	226	5	)	)	PUNCT
ejpam-4479	226	6	and	and	CCONJ
ejpam-4479	226	7	j(m	j(m	PROPN
ejpam-4479	226	8	)	)	PUNCT
ejpam-4479	227	1	⋄	⋄	PROPN
ejpam-4479	227	2	f	f	PROPN
ejpam-4479	227	3	(	(	PUNCT
ejpam-4479	227	4	m	m	PROPN
ejpam-4479	227	5	)	)	PUNCT
ejpam-4479	227	6	.	.	PUNCT
ejpam-4479	228	1	thus	thus	ADV
ejpam-4479	228	2	,	,	PUNCT
ejpam-4479	228	3	[	[	X
ejpam-4479	228	4	g(m	g(m	ADJ
ejpam-4479	228	5	)	)	PUNCT
ejpam-4479	228	6	∩	∩	NOUN
ejpam-4479	228	7	j(m	j(m	PROPN
ejpam-4479	228	8	)	)	PUNCT
ejpam-4479	228	9	]	]	PUNCT
ejpam-4479	229	1	⋄	⋄	PROPN
ejpam-4479	229	2	f	f	X
ejpam-4479	229	3	(	(	PUNCT
ejpam-4479	229	4	m	m	PROPN
ejpam-4479	229	5	)	)	PUNCT
ejpam-4479	229	6	.	.	PUNCT
ejpam-4479	230	1	hence	hence	ADV
ejpam-4479	230	2	,	,	PUNCT
ejpam-4479	230	3	(	(	PUNCT
ejpam-4479	230	4	g	g	NOUN
ejpam-4479	230	5	,	,	PUNCT
ejpam-4479	230	6	m1	m1	NOUN
ejpam-4479	230	7	)	)	PUNCT
ejpam-4479	230	8	∼	∼	NOUN
ejpam-4479	230	9	∩	∩	NOUN
ejpam-4479	230	10	(	(	PUNCT
ejpam-4479	230	11	j	j	PROPN
ejpam-4479	230	12	,	,	PUNCT
ejpam-4479	230	13	m2	m2	PROPN
ejpam-4479	230	14	)	)	PUNCT
ejpam-4479	230	15	is	be	AUX
ejpam-4479	230	16	a	a	DET
ejpam-4479	230	17	soft	soft	ADJ
ejpam-4479	230	18	hyper	hyper	ADJ
ejpam-4479	230	19	gr	gr	NOUN
ejpam-4479	230	20	-	-	PUNCT
ejpam-4479	230	21	ideal	ideal	NOUN
ejpam-4479	230	22	of	of	ADP
ejpam-4479	230	23	(	(	PUNCT
ejpam-4479	230	24	f	f	X
ejpam-4479	230	25	,	,	PUNCT
ejpam-4479	230	26	a	a	PRON
ejpam-4479	230	27	)	)	PUNCT
ejpam-4479	230	28	.	.	PUNCT
ejpam-4479	231	1	if	if	SCONJ
ejpam-4479	231	2	m	m	NOUN
ejpam-4479	231	3	=	=	VERB
ejpam-4479	231	4	m1	m1	PROPN
ejpam-4479	231	5	=	=	SYM
ejpam-4479	231	6	m2	m2	PROPN
ejpam-4479	231	7	,	,	PUNCT
ejpam-4479	231	8	then	then	ADV
ejpam-4479	231	9	we	we	PRON
ejpam-4479	231	10	have	have	VERB
ejpam-4479	231	11	the	the	DET
ejpam-4479	231	12	following	follow	VERB
ejpam-4479	231	13	corollary	corollary	NOUN
ejpam-4479	231	14	.	.	PUNCT
ejpam-4479	232	1	corollary	corollary	ADJ
ejpam-4479	232	2	1	1	NUM
ejpam-4479	232	3	.	.	PUNCT
ejpam-4479	233	1	let	let	AUX
ejpam-4479	233	2	(	(	PUNCT
ejpam-4479	233	3	f	f	X
ejpam-4479	233	4	,	,	PUNCT
ejpam-4479	233	5	a	a	PRON
ejpam-4479	233	6	)	)	PUNCT
ejpam-4479	233	7	be	be	AUX
ejpam-4479	233	8	a	a	DET
ejpam-4479	233	9	soft	soft	ADJ
ejpam-4479	233	10	hyper	hyper	ADJ
ejpam-4479	233	11	gr	gr	NOUN
ejpam-4479	233	12	-	-	NOUN
ejpam-4479	233	13	algebra	algebra	NOUN
ejpam-4479	233	14	over	over	ADP
ejpam-4479	233	15	h.	h.	NOUN
ejpam-4479	233	16	for	for	ADP
ejpam-4479	233	17	any	any	DET
ejpam-4479	233	18	soft	soft	ADJ
ejpam-4479	233	19	sets	set	NOUN
ejpam-4479	233	20	(	(	PUNCT
ejpam-4479	233	21	g	g	NOUN
ejpam-4479	233	22	,	,	PUNCT
ejpam-4479	233	23	m	m	PROPN
ejpam-4479	233	24	)	)	PUNCT
ejpam-4479	233	25	and	and	CCONJ
ejpam-4479	233	26	(	(	PUNCT
ejpam-4479	233	27	j	j	PROPN
ejpam-4479	233	28	,	,	PUNCT
ejpam-4479	233	29	m	m	PROPN
ejpam-4479	233	30	)	)	PUNCT
ejpam-4479	233	31	over	over	ADP
ejpam-4479	233	32	h	h	NOUN
ejpam-4479	233	33	,	,	PUNCT
ejpam-4479	233	34	we	we	PRON
ejpam-4479	233	35	have	have	VERB
ejpam-4479	233	36	(	(	PUNCT
ejpam-4479	233	37	g	g	PROPN
ejpam-4479	233	38	,	,	PUNCT
ejpam-4479	233	39	m	m	NOUN
ejpam-4479	233	40	)	)	PUNCT
ejpam-4479	233	41	∼⋄	∼⋄	PROPN
ejpam-4479	233	42	(	(	PUNCT
ejpam-4479	233	43	f	f	X
ejpam-4479	233	44	,	,	PUNCT
ejpam-4479	233	45	a	a	PRON
ejpam-4479	233	46	)	)	PUNCT
ejpam-4479	233	47	=	=	NOUN
ejpam-4479	233	48	⇒	⇒	NOUN
ejpam-4479	233	49	(	(	PUNCT
ejpam-4479	233	50	g	g	PROPN
ejpam-4479	233	51	,	,	PUNCT
ejpam-4479	233	52	m	m	NOUN
ejpam-4479	233	53	)	)	PUNCT
ejpam-4479	233	54	∼	∼	NOUN
ejpam-4479	233	55	∩	∩	NOUN
ejpam-4479	233	56	(	(	PUNCT
ejpam-4479	233	57	j	j	PROPN
ejpam-4479	233	58	,	,	PUNCT
ejpam-4479	233	59	m	m	NOUN
ejpam-4479	233	60	)	)	PUNCT
ejpam-4479	233	61	∼⋄	∼⋄	PROPN
ejpam-4479	233	62	(	(	PUNCT
ejpam-4479	233	63	f	f	X
ejpam-4479	233	64	,	,	PUNCT
ejpam-4479	233	65	a	a	PRON
ejpam-4479	233	66	)	)	PUNCT
ejpam-4479	233	67	.	.	PUNCT
ejpam-4479	234	1	theorem	theorem	NOUN
ejpam-4479	234	2	11	11	NUM
ejpam-4479	234	3	.	.	PUNCT
ejpam-4479	235	1	let	let	AUX
ejpam-4479	235	2	(	(	PUNCT
ejpam-4479	235	3	f	f	X
ejpam-4479	235	4	,	,	PUNCT
ejpam-4479	235	5	a	a	PRON
ejpam-4479	235	6	)	)	PUNCT
ejpam-4479	235	7	be	be	AUX
ejpam-4479	235	8	a	a	DET
ejpam-4479	235	9	soft	soft	ADJ
ejpam-4479	235	10	hyper	hyper	ADJ
ejpam-4479	235	11	gr	gr	NOUN
ejpam-4479	235	12	-	-	NOUN
ejpam-4479	235	13	algebra	algebra	NOUN
ejpam-4479	235	14	over	over	ADP
ejpam-4479	235	15	h.	h.	NOUN
ejpam-4479	235	16	for	for	ADP
ejpam-4479	235	17	any	any	DET
ejpam-4479	235	18	soft	soft	ADJ
ejpam-4479	235	19	sets	set	NOUN
ejpam-4479	235	20	(	(	PUNCT
ejpam-4479	235	21	g	g	NOUN
ejpam-4479	235	22	,	,	PUNCT
ejpam-4479	235	23	i	i	PROPN
ejpam-4479	235	24	)	)	PUNCT
ejpam-4479	235	25	and	and	CCONJ
ejpam-4479	235	26	(	(	PUNCT
ejpam-4479	235	27	j	j	PROPN
ejpam-4479	235	28	,	,	PUNCT
ejpam-4479	235	29	k	k	NOUN
ejpam-4479	235	30	)	)	PUNCT
ejpam-4479	235	31	with	with	ADP
ejpam-4479	235	32	i	i	PRON
ejpam-4479	235	33	∩k	∩k	NOUN
ejpam-4479	235	34	=	=	SYM
ejpam-4479	236	1	∅	∅	NOUN
ejpam-4479	236	2	,	,	PUNCT
ejpam-4479	236	3	we	we	PRON
ejpam-4479	236	4	have	have	VERB
ejpam-4479	236	5	(	(	PUNCT
ejpam-4479	236	6	g	g	NOUN
ejpam-4479	236	7	,	,	PUNCT
ejpam-4479	236	8	i	i	NOUN
ejpam-4479	236	9	)	)	PUNCT
ejpam-4479	236	10	∼⋄	∼⋄	PROPN
ejpam-4479	236	11	(	(	PUNCT
ejpam-4479	236	12	f	f	X
ejpam-4479	236	13	,	,	PUNCT
ejpam-4479	236	14	a	a	PRON
ejpam-4479	236	15	)	)	PUNCT
ejpam-4479	236	16	,	,	PUNCT
ejpam-4479	236	17	(	(	PUNCT
ejpam-4479	236	18	j	j	PROPN
ejpam-4479	236	19	,	,	PUNCT
ejpam-4479	236	20	k	k	NOUN
ejpam-4479	236	21	)	)	PUNCT
ejpam-4479	236	22	∼⋄	∼⋄	PROPN
ejpam-4479	236	23	(	(	PUNCT
ejpam-4479	236	24	f	f	X
ejpam-4479	236	25	,	,	PUNCT
ejpam-4479	236	26	a	a	PRON
ejpam-4479	236	27	)	)	PUNCT
ejpam-4479	237	1	=	=	NOUN
ejpam-4479	237	2	⇒	⇒	NOUN
ejpam-4479	237	3	(	(	PUNCT
ejpam-4479	237	4	g	g	NOUN
ejpam-4479	237	5	,	,	PUNCT
ejpam-4479	237	6	i	i	NOUN
ejpam-4479	237	7	)	)	PUNCT
ejpam-4479	237	8	∼	∼	NOUN
ejpam-4479	237	9	∪	∪	ADJ
ejpam-4479	237	10	(	(	PUNCT
ejpam-4479	237	11	j	j	PROPN
ejpam-4479	237	12	,	,	PUNCT
ejpam-4479	237	13	k	k	NOUN
ejpam-4479	237	14	)	)	PUNCT
ejpam-4479	237	15	∼⋄	∼⋄	PROPN
ejpam-4479	237	16	(	(	PUNCT
ejpam-4479	237	17	f	f	X
ejpam-4479	237	18	,	,	PUNCT
ejpam-4479	237	19	a	a	PRON
ejpam-4479	237	20	)	)	PUNCT
ejpam-4479	237	21	.	.	PUNCT
ejpam-4479	238	1	m.k	m.k	PROPN
ejpam-4479	238	2	.	.	PUNCT
ejpam-4479	238	3	engcot	engcot	PROPN
ejpam-4479	238	4	,	,	PUNCT
ejpam-4479	238	5	g.	g.	PROPN
ejpam-4479	238	6	petalcorin	petalcorin	PROPN
ejpam-4479	238	7	/	/	SYM
ejpam-4479	238	8	eur	eur	PROPN
ejpam-4479	238	9	.	.	PUNCT
ejpam-4479	239	1	j.	j.	PROPN
ejpam-4479	239	2	pure	pure	PROPN
ejpam-4479	239	3	appl	appl	PROPN
ejpam-4479	239	4	.	.	PROPN
ejpam-4479	239	5	math	math	PROPN
ejpam-4479	239	6	,	,	PUNCT
ejpam-4479	239	7	15	15	NUM
ejpam-4479	239	8	(	(	PUNCT
ejpam-4479	239	9	4	4	NUM
ejpam-4479	239	10	)	)	PUNCT
ejpam-4479	239	11	(	(	PUNCT
ejpam-4479	239	12	2022	2022	NUM
ejpam-4479	239	13	)	)	PUNCT
ejpam-4479	239	14	,	,	PUNCT
ejpam-4479	239	15	1482	1482	NUM
ejpam-4479	239	16	-	-	SYM
ejpam-4479	239	17	1497	1497	NUM
ejpam-4479	239	18	1492	1492	NUM
ejpam-4479	239	19	proof	proof	NOUN
ejpam-4479	239	20	:	:	PUNCT
ejpam-4479	239	21	using	use	VERB
ejpam-4479	239	22	definition	definition	NOUN
ejpam-4479	239	23	7	7	NUM
ejpam-4479	239	24	,	,	PUNCT
ejpam-4479	239	25	we	we	PRON
ejpam-4479	239	26	can	can	AUX
ejpam-4479	239	27	write	write	VERB
ejpam-4479	239	28	(	(	PUNCT
ejpam-4479	239	29	g	g	PROPN
ejpam-4479	239	30	,	,	PUNCT
ejpam-4479	239	31	i	i	NOUN
ejpam-4479	239	32	)	)	PUNCT
ejpam-4479	239	33	∼	∼	NOUN
ejpam-4479	239	34	∪	∪	ADJ
ejpam-4479	239	35	(	(	PUNCT
ejpam-4479	239	36	j	j	NOUN
ejpam-4479	239	37	,	,	PUNCT
ejpam-4479	239	38	k	k	NOUN
ejpam-4479	239	39	)	)	PUNCT
ejpam-4479	239	40	=	=	SYM
ejpam-4479	240	1	(	(	PUNCT
ejpam-4479	240	2	r	r	NOUN
ejpam-4479	240	3	,	,	PUNCT
ejpam-4479	240	4	u	u	NOUN
ejpam-4479	240	5	)	)	PUNCT
ejpam-4479	240	6	,	,	PUNCT
ejpam-4479	240	7	where	where	SCONJ
ejpam-4479	240	8	u	u	NOUN
ejpam-4479	241	1	=	=	NOUN
ejpam-4479	241	2	i	i	PRON
ejpam-4479	241	3	∪	∪	VERB
ejpam-4479	241	4	k	k	NOUN
ejpam-4479	241	5	,	,	PUNCT
ejpam-4479	241	6	and	and	CCONJ
ejpam-4479	241	7	for	for	ADP
ejpam-4479	241	8	all	all	DET
ejpam-4479	241	9	x	x	SYM
ejpam-4479	241	10	∈	∈	PROPN
ejpam-4479	241	11	u	u	NOUN
ejpam-4479	241	12	,	,	PUNCT
ejpam-4479	241	13	r(x	r(x	PROPN
ejpam-4479	241	14	)	)	PUNCT
ejpam-4479	241	15	=	=	PUNCT
ejpam-4479	242	1			PROPN
ejpam-4479	242	2	g(x	g(x	NOUN
ejpam-4479	242	3	)	)	PUNCT
ejpam-4479	242	4	,	,	PUNCT
ejpam-4479	242	5	if	if	SCONJ
ejpam-4479	242	6	x	x	SYM
ejpam-4479	242	7	∈	∈	PROPN
ejpam-4479	242	8	i	i	PRON
ejpam-4479	242	9	\k	\k	VERB
ejpam-4479	242	10	j(x	j(x	NOUN
ejpam-4479	242	11	)	)	PUNCT
ejpam-4479	242	12	,	,	PUNCT
ejpam-4479	242	13	if	if	SCONJ
ejpam-4479	242	14	x	x	PROPN
ejpam-4479	242	15	∈	∈	PROPN
ejpam-4479	242	16	k	k	X
ejpam-4479	242	17	\	\	PROPN
ejpam-4479	243	1	i	i	PRON
ejpam-4479	243	2	g(x	g(x	NOUN
ejpam-4479	243	3	)	)	PUNCT
ejpam-4479	243	4	∪	∪	ADP
ejpam-4479	243	5	j(x	j(x	PROPN
ejpam-4479	243	6	)	)	PUNCT
ejpam-4479	243	7	,	,	PUNCT
ejpam-4479	243	8	if	if	SCONJ
ejpam-4479	243	9	x	x	SYM
ejpam-4479	243	10	∈	∈	PROPN
ejpam-4479	243	11	i	i	PRON
ejpam-4479	243	12	∩k	∩k	PROPN
ejpam-4479	243	13	.	.	PUNCT
ejpam-4479	244	1	now	now	ADV
ejpam-4479	244	2	,	,	PUNCT
ejpam-4479	244	3	i	i	PRON
ejpam-4479	244	4	∩k	∩k	NOUN
ejpam-4479	244	5	=	=	PUNCT
ejpam-4479	244	6	∅	∅	NOUN
ejpam-4479	244	7	implies	imply	VERB
ejpam-4479	244	8	either	either	CCONJ
ejpam-4479	244	9	x	x	SYM
ejpam-4479	244	10	∈	∈	PROPN
ejpam-4479	244	11	i	i	PRON
ejpam-4479	244	12	\k	\k	NOUN
ejpam-4479	244	13	or	or	CCONJ
ejpam-4479	244	14	x	x	ADP
ejpam-4479	244	15	∈	∈	PROPN
ejpam-4479	244	16	k	k	X
ejpam-4479	244	17	\	\	PROPN
ejpam-4479	244	18	i	i	PRON
ejpam-4479	244	19	for	for	ADP
ejpam-4479	244	20	all	all	DET
ejpam-4479	244	21	x	x	SYM
ejpam-4479	244	22	∈	∈	PROPN
ejpam-4479	244	23	u	u	NOUN
ejpam-4479	244	24	.	.	PUNCT
ejpam-4479	245	1	if	if	SCONJ
ejpam-4479	245	2	x	x	SYM
ejpam-4479	245	3	∈	∈	PROPN
ejpam-4479	245	4	i	i	PRON
ejpam-4479	245	5	\k	\k	NOUN
ejpam-4479	245	6	,	,	PUNCT
ejpam-4479	245	7	then	then	ADV
ejpam-4479	245	8	r(x	r(x	NOUN
ejpam-4479	245	9	)	)	PUNCT
ejpam-4479	245	10	=	=	SYM
ejpam-4479	245	11	g(x	g(x	NOUN
ejpam-4479	245	12	)	)	PUNCT
ejpam-4479	246	1	⋄	⋄	NOUN
ejpam-4479	246	2	f	f	X
ejpam-4479	246	3	(	(	PUNCT
ejpam-4479	246	4	x	x	NOUN
ejpam-4479	246	5	)	)	PUNCT
ejpam-4479	246	6	.	.	PUNCT
ejpam-4479	247	1	if	if	SCONJ
ejpam-4479	247	2	x	x	SYM
ejpam-4479	247	3	∈	∈	PROPN
ejpam-4479	247	4	k	k	X
ejpam-4479	247	5	\	\	PROPN
ejpam-4479	247	6	i	i	PRON
ejpam-4479	247	7	,	,	PUNCT
ejpam-4479	247	8	then	then	ADV
ejpam-4479	247	9	r(x	r(x	PROPN
ejpam-4479	247	10	)	)	PUNCT
ejpam-4479	247	11	=	=	SYM
ejpam-4479	247	12	j(x	j(x	PROPN
ejpam-4479	247	13	)	)	PUNCT
ejpam-4479	247	14	⋄	⋄	PROPN
ejpam-4479	247	15	f	f	PROPN
ejpam-4479	247	16	(	(	PUNCT
ejpam-4479	247	17	x	x	NOUN
ejpam-4479	247	18	)	)	PUNCT
ejpam-4479	247	19	.	.	PUNCT
ejpam-4479	248	1	thus	thus	ADV
ejpam-4479	248	2	,	,	PUNCT
ejpam-4479	248	3	r(x	r(x	PROPN
ejpam-4479	248	4	)	)	PUNCT
ejpam-4479	248	5	⋄	⋄	PROPN
ejpam-4479	248	6	f	f	PROPN
ejpam-4479	248	7	(	(	PUNCT
ejpam-4479	248	8	x	x	X
ejpam-4479	248	9	)	)	PUNCT
ejpam-4479	248	10	for	for	ADP
ejpam-4479	248	11	all	all	DET
ejpam-4479	248	12	x	x	SYM
ejpam-4479	248	13	∈	∈	PROPN
ejpam-4479	248	14	u	u	NOUN
ejpam-4479	248	15	.	.	PUNCT
ejpam-4479	249	1	hence	hence	ADV
ejpam-4479	249	2	,	,	PUNCT
ejpam-4479	249	3	(	(	PUNCT
ejpam-4479	249	4	g	g	NOUN
ejpam-4479	249	5	,	,	PUNCT
ejpam-4479	249	6	i	i	NOUN
ejpam-4479	249	7	)	)	PUNCT
ejpam-4479	249	8	∼	∼	NOUN
ejpam-4479	249	9	∪	∪	ADJ
ejpam-4479	249	10	(	(	PUNCT
ejpam-4479	249	11	j	j	NOUN
ejpam-4479	249	12	,	,	PUNCT
ejpam-4479	249	13	k	k	NOUN
ejpam-4479	249	14	)	)	PUNCT
ejpam-4479	249	15	=	=	SYM
ejpam-4479	249	16	(	(	PUNCT
ejpam-4479	249	17	r	r	NOUN
ejpam-4479	249	18	,	,	PUNCT
ejpam-4479	249	19	u	u	NOUN
ejpam-4479	249	20	)	)	PUNCT
ejpam-4479	249	21	∼⋄	∼⋄	PROPN
ejpam-4479	249	22	(	(	PUNCT
ejpam-4479	249	23	f	f	X
ejpam-4479	249	24	,	,	PUNCT
ejpam-4479	249	25	a	a	PRON
ejpam-4479	249	26	)	)	PUNCT
ejpam-4479	249	27	.	.	PUNCT
ejpam-4479	250	1	theorem	theorem	NOUN
ejpam-4479	250	2	12	12	NUM
ejpam-4479	250	3	.	.	PUNCT
ejpam-4479	251	1	let	let	AUX
ejpam-4479	251	2	(	(	PUNCT
ejpam-4479	251	3	f	f	X
ejpam-4479	251	4	,	,	PUNCT
ejpam-4479	251	5	a	a	PRON
ejpam-4479	251	6	)	)	PUNCT
ejpam-4479	251	7	be	be	AUX
ejpam-4479	251	8	a	a	DET
ejpam-4479	251	9	soft	soft	ADJ
ejpam-4479	251	10	hyper	hyper	ADJ
ejpam-4479	251	11	gr	gr	NOUN
ejpam-4479	251	12	-	-	NOUN
ejpam-4479	251	13	algebra	algebra	NOUN
ejpam-4479	251	14	over	over	ADP
ejpam-4479	251	15	h.	h.	PROPN
ejpam-4479	252	1	if	if	SCONJ
ejpam-4479	252	2	(	(	PUNCT
ejpam-4479	252	3	g	g	NOUN
ejpam-4479	252	4	,	,	PUNCT
ejpam-4479	252	5	m	m	PROPN
ejpam-4479	252	6	)	)	PUNCT
ejpam-4479	252	7	and	and	CCONJ
ejpam-4479	252	8	(	(	PUNCT
ejpam-4479	252	9	j	j	PROPN
ejpam-4479	252	10	,	,	PUNCT
ejpam-4479	252	11	k	k	NOUN
ejpam-4479	252	12	)	)	PUNCT
ejpam-4479	252	13	are	be	AUX
ejpam-4479	252	14	soft	soft	ADJ
ejpam-4479	252	15	hyper	hyper	ADJ
ejpam-4479	252	16	gr	gr	NOUN
ejpam-4479	252	17	-	-	PUNCT
ejpam-4479	252	18	ideals	ideal	NOUN
ejpam-4479	252	19	of	of	ADP
ejpam-4479	252	20	(	(	PUNCT
ejpam-4479	252	21	f	f	X
ejpam-4479	252	22	,	,	PUNCT
ejpam-4479	252	23	a	a	PRON
ejpam-4479	252	24	)	)	PUNCT
ejpam-4479	252	25	,	,	PUNCT
ejpam-4479	252	26	then	then	ADV
ejpam-4479	252	27	(	(	PUNCT
ejpam-4479	252	28	g	g	NOUN
ejpam-4479	252	29	,	,	PUNCT
ejpam-4479	252	30	m	m	NOUN
ejpam-4479	252	31	)	)	PUNCT
ejpam-4479	252	32	∼	∼	NOUN
ejpam-4479	252	33	∧	∧	PROPN
ejpam-4479	252	34	(	(	PUNCT
ejpam-4479	252	35	j	j	PROPN
ejpam-4479	252	36	,	,	PUNCT
ejpam-4479	252	37	k	k	NOUN
ejpam-4479	252	38	)	)	PUNCT
ejpam-4479	252	39	is	be	AUX
ejpam-4479	252	40	a	a	DET
ejpam-4479	252	41	soft	soft	ADJ
ejpam-4479	252	42	hyper	hyper	ADJ
ejpam-4479	252	43	gr	gr	NOUN
ejpam-4479	252	44	-	-	PUNCT
ejpam-4479	252	45	ideal	ideal	NOUN
ejpam-4479	252	46	of	of	ADP
ejpam-4479	252	47	(	(	PUNCT
ejpam-4479	252	48	f	f	X
ejpam-4479	252	49	,	,	PUNCT
ejpam-4479	252	50	a	a	PRON
ejpam-4479	252	51	)	)	PUNCT
ejpam-4479	252	52	.	.	PUNCT
ejpam-4479	253	1	proof	proof	NOUN
ejpam-4479	253	2	:	:	PUNCT
ejpam-4479	253	3	using	use	VERB
ejpam-4479	253	4	definition	definition	NOUN
ejpam-4479	253	5	8	8	NUM
ejpam-4479	253	6	,	,	PUNCT
ejpam-4479	253	7	we	we	PRON
ejpam-4479	253	8	can	can	AUX
ejpam-4479	253	9	write	write	VERB
ejpam-4479	253	10	(	(	PUNCT
ejpam-4479	253	11	g	g	PROPN
ejpam-4479	253	12	,	,	PUNCT
ejpam-4479	253	13	m	m	NOUN
ejpam-4479	253	14	)	)	PUNCT
ejpam-4479	253	15	∼	∼	NOUN
ejpam-4479	253	16	∧(j	∧(j	PROPN
ejpam-4479	253	17	,	,	PUNCT
ejpam-4479	253	18	k	k	NOUN
ejpam-4479	253	19	)	)	PUNCT
ejpam-4479	253	20	=	=	SYM
ejpam-4479	254	1	(	(	PUNCT
ejpam-4479	254	2	r	r	NOUN
ejpam-4479	254	3	,	,	PUNCT
ejpam-4479	254	4	m×k	m×k	PROPN
ejpam-4479	254	5	)	)	PUNCT
ejpam-4479	254	6	,	,	PUNCT
ejpam-4479	254	7	where	where	SCONJ
ejpam-4479	254	8	r(x	r(x	PROPN
ejpam-4479	254	9	,	,	PUNCT
ejpam-4479	254	10	y	y	NOUN
ejpam-4479	254	11	)	)	PUNCT
ejpam-4479	254	12	=	=	SYM
ejpam-4479	254	13	g(x	g(x	NOUN
ejpam-4479	254	14	)	)	PUNCT
ejpam-4479	254	15	∩	∩	NOUN
ejpam-4479	254	16	j(y	j(y	PROPN
ejpam-4479	254	17	)	)	PUNCT
ejpam-4479	254	18	for	for	ADP
ejpam-4479	254	19	all	all	DET
ejpam-4479	254	20	(	(	PUNCT
ejpam-4479	254	21	x	x	NOUN
ejpam-4479	254	22	,	,	PUNCT
ejpam-4479	254	23	y	y	NOUN
ejpam-4479	254	24	)	)	PUNCT
ejpam-4479	254	25	∈	∈	PROPN
ejpam-4479	254	26	m	m	NOUN
ejpam-4479	254	27	×k	×k	NOUN
ejpam-4479	254	28	.	.	PUNCT
ejpam-4479	255	1	by	by	ADP
ejpam-4479	255	2	theorem	theorem	ADJ
ejpam-4479	255	3	10	10	NUM
ejpam-4479	255	4	,	,	PUNCT
ejpam-4479	255	5	g(x	g(x	NOUN
ejpam-4479	255	6	)	)	PUNCT
ejpam-4479	256	1	⋄	⋄	NOUN
ejpam-4479	256	2	f	f	X
ejpam-4479	256	3	(	(	PUNCT
ejpam-4479	256	4	x	x	NOUN
ejpam-4479	256	5	)	)	PUNCT
ejpam-4479	256	6	,	,	PUNCT
ejpam-4479	256	7	j(y	j(y	PROPN
ejpam-4479	256	8	)	)	PUNCT
ejpam-4479	256	9	⋄	⋄	PROPN
ejpam-4479	256	10	f	f	X
ejpam-4479	256	11	(	(	PUNCT
ejpam-4479	256	12	x	x	X
ejpam-4479	256	13	)	)	PUNCT
ejpam-4479	256	14	=	=	VERB
ejpam-4479	256	15	⇒	⇒	X
ejpam-4479	256	16	g(x	g(x	NOUN
ejpam-4479	256	17	)	)	PUNCT
ejpam-4479	256	18	∩	∩	NOUN
ejpam-4479	256	19	j(y	j(y	PROPN
ejpam-4479	256	20	)	)	PUNCT
ejpam-4479	257	1	⋄	⋄	PROPN
ejpam-4479	257	2	f	f	X
ejpam-4479	257	3	(	(	PUNCT
ejpam-4479	257	4	x	x	X
ejpam-4479	257	5	)	)	PUNCT
ejpam-4479	257	6	=	=	NOUN
ejpam-4479	257	7	⇒	⇒	PRON
ejpam-4479	257	8	r(x	r(x	PROPN
ejpam-4479	257	9	,	,	PUNCT
ejpam-4479	257	10	y	y	PROPN
ejpam-4479	257	11	)	)	PUNCT
ejpam-4479	257	12	⋄	⋄	PROPN
ejpam-4479	257	13	f	f	PROPN
ejpam-4479	257	14	(	(	PUNCT
ejpam-4479	257	15	x	x	X
ejpam-4479	257	16	)	)	PUNCT
ejpam-4479	257	17	for	for	ADP
ejpam-4479	257	18	all	all	DET
ejpam-4479	257	19	(	(	PUNCT
ejpam-4479	257	20	x	x	NOUN
ejpam-4479	257	21	,	,	PUNCT
ejpam-4479	257	22	y	y	NOUN
ejpam-4479	257	23	)	)	PUNCT
ejpam-4479	257	24	∈	∈	PROPN
ejpam-4479	257	25	m	m	NOUN
ejpam-4479	257	26	×k	×k	NOUN
ejpam-4479	257	27	.	.	PUNCT
ejpam-4479	258	1	therefore	therefore	ADV
ejpam-4479	258	2	,	,	PUNCT
ejpam-4479	258	3	(	(	PUNCT
ejpam-4479	258	4	g	g	NOUN
ejpam-4479	258	5	,	,	PUNCT
ejpam-4479	258	6	m	m	NOUN
ejpam-4479	258	7	)	)	PUNCT
ejpam-4479	258	8	∼	∼	NOUN
ejpam-4479	258	9	∧	∧	PROPN
ejpam-4479	258	10	(	(	PUNCT
ejpam-4479	258	11	j	j	PROPN
ejpam-4479	258	12	,	,	PUNCT
ejpam-4479	258	13	k	k	NOUN
ejpam-4479	258	14	)	)	PUNCT
ejpam-4479	258	15	=	=	SYM
ejpam-4479	258	16	(	(	PUNCT
ejpam-4479	258	17	r	r	NOUN
ejpam-4479	258	18	,	,	PUNCT
ejpam-4479	258	19	m	m	NOUN
ejpam-4479	258	20	×k	×k	NOUN
ejpam-4479	258	21	)	)	PUNCT
ejpam-4479	258	22	is	be	AUX
ejpam-4479	258	23	a	a	DET
ejpam-4479	258	24	soft	soft	ADJ
ejpam-4479	258	25	hyper	hyper	ADJ
ejpam-4479	258	26	gr	gr	NOUN
ejpam-4479	258	27	-	-	PUNCT
ejpam-4479	258	28	ideal	ideal	NOUN
ejpam-4479	258	29	of	of	ADP
ejpam-4479	258	30	(	(	PUNCT
ejpam-4479	258	31	f	f	X
ejpam-4479	258	32	,	,	PUNCT
ejpam-4479	258	33	a	a	PRON
ejpam-4479	258	34	)	)	PUNCT
ejpam-4479	258	35	.	.	PUNCT
ejpam-4479	259	1	definition	definition	NOUN
ejpam-4479	259	2	16	16	NUM
ejpam-4479	259	3	.	.	PUNCT
ejpam-4479	260	1	let	let	VERB
ejpam-4479	260	2	s	s	PRON
ejpam-4479	260	3	be	be	AUX
ejpam-4479	260	4	a	a	DET
ejpam-4479	260	5	hyper	hyper	ADJ
ejpam-4479	260	6	subgr	subgr	NOUN
ejpam-4479	260	7	-	-	PUNCT
ejpam-4479	260	8	algebra	algebra	NOUN
ejpam-4479	260	9	on	on	ADP
ejpam-4479	260	10	h.	h.	PROPN
ejpam-4479	260	11	a	a	DET
ejpam-4479	260	12	subset	subset	NOUN
ejpam-4479	260	13	m	m	NOUN
ejpam-4479	260	14	of	of	ADP
ejpam-4479	260	15	h	h	NOUN
ejpam-4479	260	16	is	be	AUX
ejpam-4479	260	17	a	a	DET
ejpam-4479	260	18	hyper	hyper	ADJ
ejpam-4479	260	19	gr	gr	ADJ
ejpam-4479	260	20	-	-	PUNCT
ejpam-4479	260	21	commutative	commutative	ADJ
ejpam-4479	260	22	ideal	ideal	NOUN
ejpam-4479	260	23	of	of	ADP
ejpam-4479	260	24	h	h	NOUN
ejpam-4479	260	25	related	relate	VERB
ejpam-4479	260	26	to	to	ADP
ejpam-4479	260	27	s	s	PRON
ejpam-4479	260	28	denoted	denote	VERB
ejpam-4479	260	29	by	by	ADP
ejpam-4479	260	30	m	m	PROPN
ejpam-4479	260	31	⋄hgrc	⋄hgrc	NOUN
ejpam-4479	260	32	s	s	PRON
ejpam-4479	260	33	if	if	SCONJ
ejpam-4479	260	34	it	it	PRON
ejpam-4479	260	35	satisfies	satisfy	VERB
ejpam-4479	260	36	the	the	DET
ejpam-4479	260	37	following	following	NOUN
ejpam-4479	260	38	:	:	PUNCT
ejpam-4479	260	39	(	(	PUNCT
ejpam-4479	260	40	i	i	NOUN
ejpam-4479	260	41	)	)	PUNCT
ejpam-4479	260	42	0	0	PUNCT
ejpam-4479	261	1	∈	∈	NOUN
ejpam-4479	261	2	m	m	NOUN
ejpam-4479	261	3	;	;	PUNCT
ejpam-4479	261	4	(	(	PUNCT
ejpam-4479	261	5	ii	ii	NOUN
ejpam-4479	261	6	)	)	PUNCT
ejpam-4479	261	7	(	(	PUNCT
ejpam-4479	261	8	x⊛	x⊛	PROPN
ejpam-4479	262	1	y)⊛	y)⊛	NOUN
ejpam-4479	262	2	z	z	PROPN
ejpam-4479	262	3	⊆	⊆	NUM
ejpam-4479	262	4	m	m	NOUN
ejpam-4479	262	5	and	and	CCONJ
ejpam-4479	262	6	z	z	PROPN
ejpam-4479	262	7	∈	∈	PROPN
ejpam-4479	262	8	m	m	VERB
ejpam-4479	262	9	imply	imply	VERB
ejpam-4479	262	10	that	that	SCONJ
ejpam-4479	263	1	x⊛	x⊛	PROPN
ejpam-4479	263	2	(	(	PUNCT
ejpam-4479	263	3	y	y	PROPN
ejpam-4479	263	4	⊛	⊛	NUM
ejpam-4479	263	5	(	(	PUNCT
ejpam-4479	263	6	y	y	PROPN
ejpam-4479	263	7	⊛	⊛	NUM
ejpam-4479	263	8	x	x	NOUN
ejpam-4479	263	9	)	)	PUNCT
ejpam-4479	263	10	)	)	PUNCT
ejpam-4479	264	1	⊆	⊆	NUM
ejpam-4479	264	2	m	m	NOUN
ejpam-4479	264	3	for	for	ADP
ejpam-4479	264	4	all	all	DET
ejpam-4479	264	5	x	x	NOUN
ejpam-4479	264	6	,	,	PUNCT
ejpam-4479	264	7	y	y	PROPN
ejpam-4479	264	8	∈	∈	PROPN
ejpam-4479	264	9	s.	s.	PROPN
ejpam-4479	264	10	example	example	NOUN
ejpam-4479	264	11	11	11	NUM
ejpam-4479	264	12	.	.	PUNCT
ejpam-4479	265	1	consider	consider	VERB
ejpam-4479	265	2	the	the	DET
ejpam-4479	265	3	same	same	ADJ
ejpam-4479	265	4	hyper	hyper	ADJ
ejpam-4479	265	5	gr	gr	NOUN
ejpam-4479	265	6	-	-	PUNCT
ejpam-4479	265	7	algebra	algebra	NOUN
ejpam-4479	265	8	h	h	NOUN
ejpam-4479	265	9	=	=	SYM
ejpam-4479	265	10	{	{	PUNCT
ejpam-4479	265	11	0	0	NUM
ejpam-4479	265	12	,	,	PUNCT
ejpam-4479	265	13	1	1	NUM
ejpam-4479	265	14	,	,	PUNCT
ejpam-4479	265	15	2	2	NUM
ejpam-4479	265	16	,	,	PUNCT
ejpam-4479	265	17	3	3	NUM
ejpam-4479	265	18	}	}	PUNCT
ejpam-4479	265	19	in	in	ADP
ejpam-4479	265	20	example	example	NOUN
ejpam-4479	266	1	4	4	X
ejpam-4479	266	2	.	.	PUNCT
ejpam-4479	266	3	then	then	ADV
ejpam-4479	266	4	s	s	VERB
ejpam-4479	266	5	=	=	PUNCT
ejpam-4479	266	6	{	{	PUNCT
ejpam-4479	266	7	0	0	NUM
ejpam-4479	266	8	,	,	PUNCT
ejpam-4479	266	9	1	1	NUM
ejpam-4479	266	10	,	,	PUNCT
ejpam-4479	266	11	3	3	NUM
ejpam-4479	266	12	}	}	PUNCT
ejpam-4479	266	13	is	be	AUX
ejpam-4479	266	14	a	a	DET
ejpam-4479	266	15	hyper	hyper	ADJ
ejpam-4479	266	16	subgr	subgr	NOUN
ejpam-4479	266	17	-	-	PUNCT
ejpam-4479	266	18	algebra	algebra	NOUN
ejpam-4479	266	19	of	of	ADP
ejpam-4479	266	20	h	h	NOUN
ejpam-4479	266	21	and	and	CCONJ
ejpam-4479	266	22	m	m	PROPN
ejpam-4479	266	23	=	=	X
ejpam-4479	266	24	{	{	PUNCT
ejpam-4479	266	25	0	0	NUM
ejpam-4479	266	26	,	,	PUNCT
ejpam-4479	266	27	1	1	NUM
ejpam-4479	266	28	,	,	PUNCT
ejpam-4479	266	29	2	2	NUM
ejpam-4479	266	30	}	}	PUNCT
ejpam-4479	266	31	is	be	AUX
ejpam-4479	266	32	a	a	DET
ejpam-4479	266	33	hyper	hyper	ADJ
ejpam-4479	266	34	gr	gr	ADJ
ejpam-4479	266	35	-	-	PUNCT
ejpam-4479	266	36	commutative	commutative	ADJ
ejpam-4479	266	37	ideal	ideal	NOUN
ejpam-4479	266	38	of	of	ADP
ejpam-4479	266	39	s.	s.	PROPN
ejpam-4479	266	40	definition	definition	PROPN
ejpam-4479	266	41	17	17	NUM
ejpam-4479	266	42	.	.	PUNCT
ejpam-4479	267	1	let	let	AUX
ejpam-4479	267	2	(	(	PUNCT
ejpam-4479	267	3	f	f	X
ejpam-4479	267	4	,	,	PUNCT
ejpam-4479	267	5	a	a	PRON
ejpam-4479	267	6	)	)	PUNCT
ejpam-4479	267	7	be	be	AUX
ejpam-4479	267	8	a	a	DET
ejpam-4479	267	9	soft	soft	ADJ
ejpam-4479	267	10	set	set	NOUN
ejpam-4479	267	11	over	over	ADP
ejpam-4479	267	12	a	a	DET
ejpam-4479	267	13	hyper	hyper	ADJ
ejpam-4479	267	14	gr	gr	NOUN
ejpam-4479	267	15	-	-	PUNCT
ejpam-4479	267	16	algebra	algebra	NOUN
ejpam-4479	267	17	h.	h.	NOUN
ejpam-4479	267	18	a	a	DET
ejpam-4479	267	19	soft	soft	ADJ
ejpam-4479	267	20	set	set	NOUN
ejpam-4479	267	21	(	(	PUNCT
ejpam-4479	267	22	g	g	NOUN
ejpam-4479	267	23	,	,	PUNCT
ejpam-4479	267	24	m	m	NOUN
ejpam-4479	267	25	)	)	PUNCT
ejpam-4479	267	26	over	over	ADP
ejpam-4479	267	27	h	h	NOUN
ejpam-4479	267	28	is	be	AUX
ejpam-4479	267	29	called	call	VERB
ejpam-4479	267	30	a	a	DET
ejpam-4479	267	31	soft	soft	ADJ
ejpam-4479	267	32	hyper	hyper	ADJ
ejpam-4479	267	33	gr	gr	ADJ
ejpam-4479	267	34	-	-	PUNCT
ejpam-4479	267	35	commutative	commutative	ADJ
ejpam-4479	267	36	ideal	ideal	NOUN
ejpam-4479	267	37	of	of	ADP
ejpam-4479	267	38	(	(	PUNCT
ejpam-4479	267	39	f	f	X
ejpam-4479	267	40	,	,	PUNCT
ejpam-4479	267	41	a	a	PRON
ejpam-4479	267	42	)	)	PUNCT
ejpam-4479	267	43	denoted	denote	VERB
ejpam-4479	267	44	by	by	ADP
ejpam-4479	267	45	(	(	PUNCT
ejpam-4479	267	46	g	g	PROPN
ejpam-4479	267	47	,	,	PUNCT
ejpam-4479	267	48	m	m	NOUN
ejpam-4479	267	49	)	)	PUNCT
ejpam-4479	267	50	∼⋄hgrc	∼⋄hgrc	PROPN
ejpam-4479	267	51	(	(	PUNCT
ejpam-4479	267	52	f	f	PROPN
ejpam-4479	267	53	,	,	PUNCT
ejpam-4479	267	54	a	a	NOUN
ejpam-4479	267	55	)	)	PUNCT
ejpam-4479	267	56	,	,	PUNCT
ejpam-4479	267	57	if	if	SCONJ
ejpam-4479	267	58	the	the	DET
ejpam-4479	267	59	following	following	NOUN
ejpam-4479	267	60	are	be	AUX
ejpam-4479	267	61	satisfied	satisfied	ADJ
ejpam-4479	267	62	:	:	PUNCT
ejpam-4479	267	63	(	(	PUNCT
ejpam-4479	267	64	i	i	NOUN
ejpam-4479	267	65	)	)	PUNCT
ejpam-4479	267	66	m	m	VERB
ejpam-4479	267	67	⊂	⊂	PROPN
ejpam-4479	267	68	a	a	PRON
ejpam-4479	267	69	with	with	ADP
ejpam-4479	267	70	m	m	PROPN
ejpam-4479	267	71	̸=	̸=	PROPN
ejpam-4479	267	72	∅	∅	NOUN
ejpam-4479	267	73	;	;	PUNCT
ejpam-4479	267	74	(	(	PUNCT
ejpam-4479	267	75	ii	ii	NOUN
ejpam-4479	267	76	)	)	PUNCT
ejpam-4479	267	77	for	for	ADP
ejpam-4479	267	78	all	all	DET
ejpam-4479	267	79	a	a	DET
ejpam-4479	267	80	∈	∈	NOUN
ejpam-4479	267	81	m	m	NOUN
ejpam-4479	267	82	,	,	PUNCT
ejpam-4479	267	83	g(a	g(a	PROPN
ejpam-4479	268	1	)	)	PUNCT
ejpam-4479	268	2	⋄hgrc	⋄hgrc	PROPN
ejpam-4479	268	3	f	f	PROPN
ejpam-4479	268	4	(	(	PUNCT
ejpam-4479	268	5	a	a	NOUN
ejpam-4479	268	6	)	)	PUNCT
ejpam-4479	268	7	.	.	PUNCT
ejpam-4479	269	1	example	example	NOUN
ejpam-4479	269	2	12	12	NUM
ejpam-4479	269	3	.	.	PUNCT
ejpam-4479	270	1	consider	consider	VERB
ejpam-4479	270	2	the	the	DET
ejpam-4479	270	3	same	same	ADJ
ejpam-4479	270	4	hyper	hyper	ADJ
ejpam-4479	270	5	gr	gr	NOUN
ejpam-4479	270	6	-	-	PUNCT
ejpam-4479	270	7	algebra	algebra	NOUN
ejpam-4479	270	8	h	h	NOUN
ejpam-4479	270	9	=	=	SYM
ejpam-4479	270	10	{	{	PUNCT
ejpam-4479	270	11	0	0	NUM
ejpam-4479	270	12	,	,	PUNCT
ejpam-4479	270	13	1	1	NUM
ejpam-4479	270	14	,	,	PUNCT
ejpam-4479	270	15	2	2	NUM
ejpam-4479	270	16	,	,	PUNCT
ejpam-4479	270	17	3	3	NUM
ejpam-4479	270	18	}	}	PUNCT
ejpam-4479	270	19	in	in	ADP
ejpam-4479	270	20	example	example	NOUN
ejpam-4479	271	1	4	4	X
ejpam-4479	271	2	.	.	PUNCT
ejpam-4479	272	1	let	let	VERB
ejpam-4479	272	2	m	m	VERB
ejpam-4479	272	3	=	=	PUNCT
ejpam-4479	272	4	{	{	PUNCT
ejpam-4479	272	5	0	0	NUM
ejpam-4479	272	6	,	,	PUNCT
ejpam-4479	272	7	1	1	NUM
ejpam-4479	272	8	,	,	PUNCT
ejpam-4479	272	9	2	2	NUM
ejpam-4479	272	10	}	}	PUNCT
ejpam-4479	272	11	and	and	CCONJ
ejpam-4479	272	12	(	(	PUNCT
ejpam-4479	272	13	f	f	X
ejpam-4479	272	14	,	,	PUNCT
ejpam-4479	272	15	a	a	PRON
ejpam-4479	272	16	)	)	PUNCT
ejpam-4479	272	17	be	be	AUX
ejpam-4479	272	18	a	a	DET
ejpam-4479	272	19	soft	soft	ADJ
ejpam-4479	272	20	set	set	NOUN
ejpam-4479	272	21	over	over	ADP
ejpam-4479	272	22	h	h	NOUN
ejpam-4479	272	23	,	,	PUNCT
ejpam-4479	272	24	where	where	SCONJ
ejpam-4479	272	25	a	a	PRON
ejpam-4479	272	26	=	=	X
ejpam-4479	272	27	h.	h.	NOUN
ejpam-4479	272	28	let	let	VERB
ejpam-4479	272	29	f	f	NOUN
ejpam-4479	272	30	:	:	PUNCT
ejpam-4479	272	31	a	a	DET
ejpam-4479	272	32	→	→	SYM
ejpam-4479	272	33	p	p	X
ejpam-4479	272	34	(	(	PUNCT
ejpam-4479	272	35	h	h	NOUN
ejpam-4479	272	36	)	)	PUNCT
ejpam-4479	272	37	be	be	AUX
ejpam-4479	272	38	defined	define	VERB
ejpam-4479	272	39	by	by	ADP
ejpam-4479	272	40	f	f	PROPN
ejpam-4479	272	41	(	(	PUNCT
ejpam-4479	272	42	a	a	NOUN
ejpam-4479	272	43	)	)	PUNCT
ejpam-4479	272	44	=	=	SYM
ejpam-4479	272	45	⋃	⋃	NOUN
ejpam-4479	272	46	b⊂h	b⊂h	NOUN
ejpam-4479	272	47	,	,	PUNCT
ejpam-4479	272	48	ar̊b	ar̊b	PROPN
ejpam-4479	272	49	b	b	PROPN
ejpam-4479	272	50	m.k	m.k	PROPN
ejpam-4479	272	51	.	.	PROPN
ejpam-4479	272	52	engcot	engcot	PROPN
ejpam-4479	272	53	,	,	PUNCT
ejpam-4479	272	54	g.	g.	PROPN
ejpam-4479	272	55	petalcorin	petalcorin	PROPN
ejpam-4479	272	56	/	/	SYM
ejpam-4479	272	57	eur	eur	PROPN
ejpam-4479	272	58	.	.	PUNCT
ejpam-4479	273	1	j.	j.	PROPN
ejpam-4479	273	2	pure	pure	PROPN
ejpam-4479	273	3	appl	appl	PROPN
ejpam-4479	273	4	.	.	PROPN
ejpam-4479	273	5	math	math	PROPN
ejpam-4479	273	6	,	,	PUNCT
ejpam-4479	273	7	15	15	NUM
ejpam-4479	273	8	(	(	PUNCT
ejpam-4479	273	9	4	4	NUM
ejpam-4479	273	10	)	)	PUNCT
ejpam-4479	273	11	(	(	PUNCT
ejpam-4479	273	12	2022	2022	NUM
ejpam-4479	273	13	)	)	PUNCT
ejpam-4479	273	14	,	,	PUNCT
ejpam-4479	273	15	1482	1482	NUM
ejpam-4479	273	16	-	-	SYM
ejpam-4479	273	17	1497	1497	NUM
ejpam-4479	273	18	1493	1493	NUM
ejpam-4479	273	19	with	with	ADP
ejpam-4479	273	20	r̊	r̊	PRON
ejpam-4479	273	21	=	=	SYM
ejpam-4479	273	22	{	{	PUNCT
ejpam-4479	273	23	(	(	PUNCT
ejpam-4479	273	24	0	0	NUM
ejpam-4479	273	25	,	,	PUNCT
ejpam-4479	273	26	0	0	NUM
ejpam-4479	273	27	)	)	PUNCT
ejpam-4479	273	28	,	,	PUNCT
ejpam-4479	273	29	(	(	PUNCT
ejpam-4479	273	30	0	0	NUM
ejpam-4479	273	31	,	,	PUNCT
ejpam-4479	273	32	{	{	PUNCT
ejpam-4479	273	33	1	1	NUM
ejpam-4479	273	34	,	,	PUNCT
ejpam-4479	273	35	2	2	NUM
ejpam-4479	273	36	}	}	PUNCT
ejpam-4479	273	37	)	)	PUNCT
ejpam-4479	273	38	,	,	PUNCT
ejpam-4479	273	39	(	(	PUNCT
ejpam-4479	273	40	1	1	NUM
ejpam-4479	273	41	,	,	PUNCT
ejpam-4479	273	42	{	{	PUNCT
ejpam-4479	273	43	0	0	NUM
ejpam-4479	273	44	,	,	PUNCT
ejpam-4479	273	45	1	1	NUM
ejpam-4479	273	46	}	}	PUNCT
ejpam-4479	273	47	)	)	PUNCT
ejpam-4479	273	48	,	,	PUNCT
ejpam-4479	273	49	(	(	PUNCT
ejpam-4479	273	50	1	1	NUM
ejpam-4479	273	51	,	,	PUNCT
ejpam-4479	273	52	{	{	PUNCT
ejpam-4479	273	53	1	1	NUM
ejpam-4479	273	54	}	}	PUNCT
ejpam-4479	273	55	)	)	PUNCT
ejpam-4479	273	56	,	,	PUNCT
ejpam-4479	273	57	(	(	PUNCT
ejpam-4479	273	58	2	2	NUM
ejpam-4479	273	59	,	,	PUNCT
ejpam-4479	273	60	{	{	PUNCT
ejpam-4479	273	61	0	0	NUM
ejpam-4479	273	62	,	,	PUNCT
ejpam-4479	273	63	1	1	NUM
ejpam-4479	273	64	}	}	PUNCT
ejpam-4479	273	65	)	)	PUNCT
ejpam-4479	273	66	,	,	PUNCT
ejpam-4479	273	67	(	(	PUNCT
ejpam-4479	273	68	2	2	NUM
ejpam-4479	273	69	,	,	PUNCT
ejpam-4479	273	70	{	{	PUNCT
ejpam-4479	273	71	0	0	NUM
ejpam-4479	273	72	,	,	PUNCT
ejpam-4479	273	73	3	3	NUM
ejpam-4479	273	74	}	}	PUNCT
ejpam-4479	273	75	)	)	PUNCT
ejpam-4479	273	76	}	}	PUNCT
ejpam-4479	273	77	.	.	PUNCT
ejpam-4479	274	1	then	then	ADV
ejpam-4479	274	2	f	f	X
ejpam-4479	274	3	(	(	PUNCT
ejpam-4479	274	4	0	0	NUM
ejpam-4479	274	5	)	)	PUNCT
ejpam-4479	274	6	=	=	NOUN
ejpam-4479	274	7	⋃	⋃	NOUN
ejpam-4479	274	8	b⊂h,0r̊b	b⊂h,0r̊b	NOUN
ejpam-4479	274	9	b	b	X
ejpam-4479	274	10	=	=	SYM
ejpam-4479	274	11	{	{	PUNCT
ejpam-4479	274	12	0	0	NUM
ejpam-4479	274	13	,	,	PUNCT
ejpam-4479	274	14	1	1	NUM
ejpam-4479	274	15	,	,	PUNCT
ejpam-4479	274	16	2	2	NUM
ejpam-4479	274	17	}	}	SYM
ejpam-4479	274	18	f	f	NOUN
ejpam-4479	274	19	(	(	PUNCT
ejpam-4479	274	20	1	1	NUM
ejpam-4479	274	21	)	)	PUNCT
ejpam-4479	274	22	=	=	NOUN
ejpam-4479	274	23	⋃	⋃	ADP
ejpam-4479	274	24	b⊂h,1r̊b	b⊂h,1r̊b	NOUN
ejpam-4479	274	25	b	b	X
ejpam-4479	274	26	=	=	SYM
ejpam-4479	274	27	{	{	PUNCT
ejpam-4479	274	28	0	0	NUM
ejpam-4479	274	29	,	,	PUNCT
ejpam-4479	274	30	1	1	NUM
ejpam-4479	274	31	}	}	PUNCT
ejpam-4479	274	32	and	and	CCONJ
ejpam-4479	274	33	f	f	X
ejpam-4479	274	34	(	(	PUNCT
ejpam-4479	274	35	2	2	NUM
ejpam-4479	274	36	)	)	PUNCT
ejpam-4479	274	37	=	=	NOUN
ejpam-4479	274	38	⋃	⋃	NOUN
ejpam-4479	274	39	b⊂h,2r̊b	b⊂h,2r̊b	NOUN
ejpam-4479	274	40	b	b	X
ejpam-4479	274	41	=	=	PUNCT
ejpam-4479	274	42	{	{	PUNCT
ejpam-4479	274	43	0	0	NUM
ejpam-4479	274	44	,	,	PUNCT
ejpam-4479	274	45	1	1	NUM
ejpam-4479	274	46	,	,	PUNCT
ejpam-4479	274	47	3	3	NUM
ejpam-4479	274	48	}	}	PUNCT
ejpam-4479	274	49	.	.	PUNCT
ejpam-4479	275	1	also	also	ADV
ejpam-4479	275	2	,	,	PUNCT
ejpam-4479	275	3	let	let	VERB
ejpam-4479	275	4	g	g	NOUN
ejpam-4479	275	5	:	:	PUNCT
ejpam-4479	275	6	a	a	DET
ejpam-4479	275	7	→	→	SYM
ejpam-4479	275	8	p	p	X
ejpam-4479	275	9	(	(	PUNCT
ejpam-4479	275	10	h	h	NOUN
ejpam-4479	275	11	)	)	PUNCT
ejpam-4479	275	12	be	be	AUX
ejpam-4479	275	13	a	a	DET
ejpam-4479	275	14	set	set	NOUN
ejpam-4479	275	15	-	-	PUNCT
ejpam-4479	275	16	valued	value	VERB
ejpam-4479	275	17	function	function	NOUN
ejpam-4479	275	18	defined	define	VERB
ejpam-4479	275	19	by	by	ADP
ejpam-4479	275	20	g(a	g(a	PROPN
ejpam-4479	275	21	)	)	PUNCT
ejpam-4479	276	1	=	=	SYM
ejpam-4479	276	2	⋃	⋃	NOUN
ejpam-4479	276	3	b⊂h	b⊂h	NOUN
ejpam-4479	276	4	,	,	PUNCT
ejpam-4479	276	5	ar̊b⇔b	ar̊b⇔b	NOUN
ejpam-4479	276	6	=	=	SYM
ejpam-4479	276	7	an	an	DET
ejpam-4479	276	8	b	b	NOUN
ejpam-4479	276	9	,	,	PUNCT
ejpam-4479	276	10	where	where	SCONJ
ejpam-4479	276	11	an	an	DET
ejpam-4479	276	12	=	=	X
ejpam-4479	276	13	(	(	PUNCT
ejpam-4479	276	14	(	(	PUNCT
ejpam-4479	276	15	(	(	PUNCT
ejpam-4479	276	16	(	(	PUNCT
ejpam-4479	276	17	a	a	DET
ejpam-4479	276	18	⊛	⊛	NUM
ejpam-4479	276	19	a	a	X
ejpam-4479	276	20	)	)	PUNCT
ejpam-4479	276	21	⊛	⊛	NUM
ejpam-4479	276	22	a	a	PRON
ejpam-4479	276	23	)	)	PUNCT
ejpam-4479	276	24	⊛	⊛	NUM
ejpam-4479	276	25	a	a	PRON
ejpam-4479	276	26	)	)	PUNCT
ejpam-4479	276	27	⊛	⊛	NUM
ejpam-4479	276	28	...	...	PUNCT
ejpam-4479	276	29	⊛	⊛	NUM
ejpam-4479	276	30	a	a	PRON
ejpam-4479	276	31	)	)	PUNCT
ejpam-4479	276	32	.	.	PUNCT
ejpam-4479	277	1	then	then	ADV
ejpam-4479	277	2	g(0	g(0	PROPN
ejpam-4479	277	3	)	)	PUNCT
ejpam-4479	277	4	=	=	SYM
ejpam-4479	277	5	g(1	g(1	NOUN
ejpam-4479	277	6	)	)	PUNCT
ejpam-4479	277	7	=	=	PRON
ejpam-4479	277	8	{	{	PUNCT
ejpam-4479	277	9	0	0	NUM
ejpam-4479	277	10	,	,	PUNCT
ejpam-4479	277	11	1	1	NUM
ejpam-4479	277	12	}	}	PUNCT
ejpam-4479	277	13	,	,	PUNCT
ejpam-4479	277	14	g(2	g(2	PROPN
ejpam-4479	277	15	)	)	PUNCT
ejpam-4479	277	16	=	=	PRON
ejpam-4479	277	17	{	{	PUNCT
ejpam-4479	277	18	0	0	NUM
ejpam-4479	277	19	,	,	PUNCT
ejpam-4479	277	20	1	1	NUM
ejpam-4479	277	21	,	,	PUNCT
ejpam-4479	277	22	2	2	NUM
ejpam-4479	277	23	}	}	PUNCT
ejpam-4479	277	24	and	and	CCONJ
ejpam-4479	277	25	g(3	g(3	PROPN
ejpam-4479	277	26	)	)	PUNCT
ejpam-4479	277	27	=	=	PRON
ejpam-4479	277	28	{	{	PUNCT
ejpam-4479	277	29	0	0	NUM
ejpam-4479	277	30	,	,	PUNCT
ejpam-4479	277	31	1	1	NUM
ejpam-4479	277	32	,	,	PUNCT
ejpam-4479	277	33	3	3	NUM
ejpam-4479	277	34	}	}	PUNCT
ejpam-4479	277	35	.	.	PUNCT
ejpam-4479	278	1	then	then	ADV
ejpam-4479	278	2	g(0	g(0	PROPN
ejpam-4479	278	3	)	)	PUNCT
ejpam-4479	278	4	=	=	PUNCT
ejpam-4479	278	5	{	{	PUNCT
ejpam-4479	278	6	0	0	NUM
ejpam-4479	278	7	,	,	PUNCT
ejpam-4479	278	8	1	1	NUM
ejpam-4479	278	9	}	}	PUNCT
ejpam-4479	278	10	⋄hgrc	⋄hgrc	NOUN
ejpam-4479	278	11	f	f	PROPN
ejpam-4479	278	12	(	(	PUNCT
ejpam-4479	278	13	0	0	NUM
ejpam-4479	278	14	)	)	PUNCT
ejpam-4479	278	15	=	=	PRON
ejpam-4479	278	16	{	{	PUNCT
ejpam-4479	278	17	0	0	NUM
ejpam-4479	278	18	,	,	PUNCT
ejpam-4479	278	19	1	1	NUM
ejpam-4479	278	20	,	,	PUNCT
ejpam-4479	278	21	2	2	NUM
ejpam-4479	278	22	}	}	PUNCT
ejpam-4479	278	23	,	,	PUNCT
ejpam-4479	278	24	g(1	g(1	NOUN
ejpam-4479	278	25	)	)	PUNCT
ejpam-4479	278	26	=	=	PUNCT
ejpam-4479	278	27	{	{	PUNCT
ejpam-4479	278	28	0	0	NUM
ejpam-4479	278	29	,	,	PUNCT
ejpam-4479	278	30	1	1	NUM
ejpam-4479	278	31	}	}	PUNCT
ejpam-4479	278	32	⋄hgrc	⋄hgrc	NOUN
ejpam-4479	278	33	f	f	NOUN
ejpam-4479	278	34	(	(	PUNCT
ejpam-4479	278	35	1	1	X
ejpam-4479	278	36	)	)	PUNCT
ejpam-4479	278	37	=	=	PRON
ejpam-4479	278	38	{	{	PUNCT
ejpam-4479	278	39	0	0	NUM
ejpam-4479	278	40	,	,	PUNCT
ejpam-4479	278	41	1	1	NUM
ejpam-4479	278	42	}	}	PUNCT
ejpam-4479	278	43	since	since	SCONJ
ejpam-4479	278	44	they	they	PRON
ejpam-4479	278	45	are	be	AUX
ejpam-4479	278	46	equal	equal	ADJ
ejpam-4479	278	47	,	,	PUNCT
ejpam-4479	278	48	and	and	CCONJ
ejpam-4479	278	49	g(2	g(2	PROPN
ejpam-4479	278	50	)	)	PUNCT
ejpam-4479	278	51	=	=	PRON
ejpam-4479	278	52	{	{	PUNCT
ejpam-4479	278	53	0	0	NUM
ejpam-4479	278	54	,	,	PUNCT
ejpam-4479	278	55	1	1	NUM
ejpam-4479	278	56	,	,	PUNCT
ejpam-4479	278	57	2	2	NUM
ejpam-4479	278	58	}	}	PUNCT
ejpam-4479	278	59	⋄hgrc	⋄hgrc	NOUN
ejpam-4479	278	60	f	f	NOUN
ejpam-4479	278	61	(	(	PUNCT
ejpam-4479	278	62	2	2	NUM
ejpam-4479	278	63	)	)	PUNCT
ejpam-4479	278	64	=	=	NOUN
ejpam-4479	278	65	{	{	PUNCT
ejpam-4479	278	66	0	0	NUM
ejpam-4479	278	67	,	,	PUNCT
ejpam-4479	278	68	1	1	NUM
ejpam-4479	278	69	,	,	PUNCT
ejpam-4479	278	70	3	3	NUM
ejpam-4479	278	71	}	}	PUNCT
ejpam-4479	278	72	.	.	PUNCT
ejpam-4479	279	1	hence	hence	ADV
ejpam-4479	279	2	,	,	PUNCT
ejpam-4479	279	3	for	for	ADP
ejpam-4479	279	4	all	all	DET
ejpam-4479	279	5	a	a	DET
ejpam-4479	279	6	∈	∈	PROPN
ejpam-4479	279	7	m	m	NOUN
ejpam-4479	279	8	,	,	PUNCT
ejpam-4479	279	9	g(a	g(a	PROPN
ejpam-4479	279	10	)	)	PUNCT
ejpam-4479	279	11	∼⋄hgrc	∼⋄hgrc	PROPN
ejpam-4479	279	12	f	f	PROPN
ejpam-4479	279	13	(	(	PUNCT
ejpam-4479	279	14	a	a	NOUN
ejpam-4479	279	15	)	)	PUNCT
ejpam-4479	279	16	.	.	PUNCT
ejpam-4479	279	17	theorem	theorem	NOUN
ejpam-4479	279	18	13	13	NUM
ejpam-4479	279	19	.	.	PUNCT
ejpam-4479	280	1	let	let	VERB
ejpam-4479	280	2	s	s	PRON
ejpam-4479	280	3	be	be	AUX
ejpam-4479	280	4	a	a	DET
ejpam-4479	280	5	hyper	hyper	ADJ
ejpam-4479	280	6	subgr	subgr	NOUN
ejpam-4479	280	7	-	-	PUNCT
ejpam-4479	280	8	algebra	algebra	NOUN
ejpam-4479	280	9	of	of	ADP
ejpam-4479	280	10	a	a	DET
ejpam-4479	280	11	hyper	hyper	ADJ
ejpam-4479	280	12	gr	gr	NOUN
ejpam-4479	280	13	-	-	PUNCT
ejpam-4479	280	14	algebra	algebra	NOUN
ejpam-4479	280	15	h.	h.	NOUN
ejpam-4479	281	1	if	if	SCONJ
ejpam-4479	281	2	i1	i1	PROPN
ejpam-4479	281	3	⋄hgrc	⋄hgrc	PROPN
ejpam-4479	281	4	s	s	PROPN
ejpam-4479	281	5	and	and	CCONJ
ejpam-4479	281	6	i2	i2	PROPN
ejpam-4479	281	7	⋄hgrc	⋄hgrc	PROPN
ejpam-4479	281	8	s	s	PROPN
ejpam-4479	281	9	,	,	PUNCT
ejpam-4479	281	10	then	then	ADV
ejpam-4479	281	11	i1	i1	PROPN
ejpam-4479	281	12	∩	∩	PROPN
ejpam-4479	281	13	i2	i2	PROPN
ejpam-4479	281	14	⋄hgrc	⋄hgrc	PROPN
ejpam-4479	281	15	s.	s.	PROPN
ejpam-4479	281	16	proof	proof	NOUN
ejpam-4479	281	17	:	:	PUNCT
ejpam-4479	281	18	since	since	SCONJ
ejpam-4479	281	19	0	0	NUM
ejpam-4479	281	20	∈	∈	PROPN
ejpam-4479	281	21	i1	i1	PROPN
ejpam-4479	281	22	and	and	CCONJ
ejpam-4479	281	23	0	0	NUM
ejpam-4479	281	24	∈	∈	PROPN
ejpam-4479	281	25	i2	i2	NOUN
ejpam-4479	281	26	,	,	PUNCT
ejpam-4479	281	27	0	0	NUM
ejpam-4479	281	28	∈	∈	PROPN
ejpam-4479	281	29	i1	i1	PROPN
ejpam-4479	281	30	∩	∩	PROPN
ejpam-4479	281	31	i2	i2	PROPN
ejpam-4479	281	32	.	.	PUNCT
ejpam-4479	281	33	suppose	suppose	VERB
ejpam-4479	281	34	x	x	X
ejpam-4479	281	35	,	,	PUNCT
ejpam-4479	281	36	y	y	PROPN
ejpam-4479	281	37	∈	∈	PROPN
ejpam-4479	281	38	s	s	X
ejpam-4479	281	39	and	and	CCONJ
ejpam-4479	281	40	(	(	PUNCT
ejpam-4479	281	41	x⊛	x⊛	PROPN
ejpam-4479	281	42	y)⊛	y)⊛	NOUN
ejpam-4479	281	43	z	z	PROPN
ejpam-4479	281	44	⊆	⊆	NUM
ejpam-4479	281	45	m	m	NOUN
ejpam-4479	281	46	=	=	PROPN
ejpam-4479	281	47	i1	i1	PROPN
ejpam-4479	281	48	∩	∩	PROPN
ejpam-4479	281	49	i2	i2	PROPN
ejpam-4479	281	50	with	with	ADP
ejpam-4479	281	51	z	z	PROPN
ejpam-4479	281	52	∈	∈	PROPN
ejpam-4479	281	53	i1	i1	PROPN
ejpam-4479	281	54	∩	∩	PROPN
ejpam-4479	281	55	i2	i2	PROPN
ejpam-4479	281	56	.	.	PUNCT
ejpam-4479	282	1	since	since	SCONJ
ejpam-4479	282	2	i1	i1	PROPN
ejpam-4479	282	3	⋄hgrc	⋄hgrc	PROPN
ejpam-4479	282	4	s	s	PROPN
ejpam-4479	282	5	and	and	CCONJ
ejpam-4479	282	6	i2	i2	PROPN
ejpam-4479	282	7	⋄hgrc	⋄hgrc	PROPN
ejpam-4479	282	8	s	s	PROPN
ejpam-4479	282	9	,	,	PUNCT
ejpam-4479	282	10	it	it	PRON
ejpam-4479	282	11	follows	follow	VERB
ejpam-4479	282	12	that	that	SCONJ
ejpam-4479	282	13	(	(	PUNCT
ejpam-4479	282	14	x1	x1	PROPN
ejpam-4479	282	15	⊛	⊛	NUM
ejpam-4479	282	16	y1)⊛	y1)⊛	PROPN
ejpam-4479	282	17	z1	z1	PROPN
ejpam-4479	282	18	⊆	⊆	NUM
ejpam-4479	282	19	m	m	NOUN
ejpam-4479	282	20	and	and	CCONJ
ejpam-4479	282	21	(	(	PUNCT
ejpam-4479	282	22	x2⊛	x2⊛	PROPN
ejpam-4479	282	23	y2)⊛	y2)⊛	PROPN
ejpam-4479	282	24	z2	z2	PROPN
ejpam-4479	282	25	⊆	⊆	NUM
ejpam-4479	282	26	m	m	VERB
ejpam-4479	282	27	implying	imply	VERB
ejpam-4479	282	28	that	that	SCONJ
ejpam-4479	282	29	x1⊛	x1⊛	PROPN
ejpam-4479	282	30	(	(	PUNCT
ejpam-4479	282	31	y1⊛	y1⊛	PROPN
ejpam-4479	282	32	(	(	PUNCT
ejpam-4479	282	33	y1⊛x1	y1⊛x1	NUM
ejpam-4479	282	34	)	)	PUNCT
ejpam-4479	282	35	)	)	PUNCT
ejpam-4479	283	1	⊆	⊆	NUM
ejpam-4479	283	2	m	m	NOUN
ejpam-4479	283	3	and	and	CCONJ
ejpam-4479	283	4	x2⊛	x2⊛	PROPN
ejpam-4479	283	5	(	(	PUNCT
ejpam-4479	283	6	y2⊛	y2⊛	NOUN
ejpam-4479	283	7	(	(	PUNCT
ejpam-4479	283	8	y2⊛x2	y2⊛x2	NOUN
ejpam-4479	283	9	)	)	PUNCT
ejpam-4479	283	10	)	)	PUNCT
ejpam-4479	283	11	,	,	PUNCT
ejpam-4479	283	12	respectively	respectively	ADV
ejpam-4479	283	13	,	,	PUNCT
ejpam-4479	283	14	for	for	ADP
ejpam-4479	283	15	all	all	DET
ejpam-4479	283	16	x1	x1	PROPN
ejpam-4479	283	17	,	,	PUNCT
ejpam-4479	283	18	x2	x2	PROPN
ejpam-4479	283	19	,	,	PUNCT
ejpam-4479	283	20	y1	y1	NOUN
ejpam-4479	283	21	,	,	PUNCT
ejpam-4479	283	22	y2	y2	PROPN
ejpam-4479	283	23	∈	∈	PROPN
ejpam-4479	283	24	s	s	X
ejpam-4479	283	25	and	and	CCONJ
ejpam-4479	283	26	for	for	ADP
ejpam-4479	283	27	all	all	DET
ejpam-4479	283	28	z1	z1	VERB
ejpam-4479	283	29	,	,	PUNCT
ejpam-4479	283	30	z2	z2	PROPN
ejpam-4479	283	31	∈	∈	PROPN
ejpam-4479	283	32	m	m	VERB
ejpam-4479	283	33	.	.	PUNCT
ejpam-4479	284	1	let	let	VERB
ejpam-4479	284	2	x	x	SYM
ejpam-4479	284	3	⊆	⊆	NUM
ejpam-4479	284	4	i1	i1	NOUN
ejpam-4479	284	5	,	,	PUNCT
ejpam-4479	284	6	y	y	PROPN
ejpam-4479	284	7	⊆	⊆	NUM
ejpam-4479	284	8	i2	i2	PROPN
ejpam-4479	284	9	and	and	CCONJ
ejpam-4479	284	10	z	z	PROPN
ejpam-4479	284	11	⊆	⊆	NUM
ejpam-4479	284	12	m	m	NOUN
ejpam-4479	284	13	.	.	PUNCT
ejpam-4479	285	1	consider	consider	VERB
ejpam-4479	285	2	that	that	SCONJ
ejpam-4479	285	3	x1	x1	PROPN
ejpam-4479	285	4	,	,	PUNCT
ejpam-4479	285	5	x2	x2	PROPN
ejpam-4479	285	6	,	,	PUNCT
ejpam-4479	285	7	y1	y1	NOUN
ejpam-4479	285	8	,	,	PUNCT
ejpam-4479	285	9	y2	y2	PROPN
ejpam-4479	285	10	⊆	⊆	NUM
ejpam-4479	285	11	s	s	NOUN
ejpam-4479	285	12	and	and	CCONJ
ejpam-4479	285	13	for	for	ADP
ejpam-4479	285	14	all	all	DET
ejpam-4479	285	15	z1	z1	VERB
ejpam-4479	285	16	,	,	PUNCT
ejpam-4479	285	17	z2	z2	PROPN
ejpam-4479	285	18	⊆	⊆	NUM
ejpam-4479	285	19	m	m	NOUN
ejpam-4479	285	20	such	such	ADJ
ejpam-4479	285	21	that	that	SCONJ
ejpam-4479	285	22	x	x	X
ejpam-4479	285	23	=	=	SYM
ejpam-4479	285	24	x1	x1	PROPN
ejpam-4479	285	25	∩	∩	ADJ
ejpam-4479	285	26	x2	x2	PROPN
ejpam-4479	285	27	,	,	PUNCT
ejpam-4479	285	28	y	y	PROPN
ejpam-4479	285	29	=	=	SYM
ejpam-4479	285	30	y1	y1	NOUN
ejpam-4479	285	31	∩	∩	X
ejpam-4479	285	32	y2	y2	PROPN
ejpam-4479	285	33	and	and	CCONJ
ejpam-4479	285	34	z	z	NOUN
ejpam-4479	285	35	=	=	SYM
ejpam-4479	285	36	z1	z1	PROPN
ejpam-4479	285	37	∩	∩	ADJ
ejpam-4479	285	38	z2	z2	PROPN
ejpam-4479	285	39	.	.	PUNCT
ejpam-4479	286	1	then	then	ADV
ejpam-4479	286	2	(	(	PUNCT
ejpam-4479	286	3	x⊛	x⊛	PROPN
ejpam-4479	286	4	y)⊛	y)⊛	NOUN
ejpam-4479	286	5	z	z	NOUN
ejpam-4479	286	6	=	=	SYM
ejpam-4479	287	1	[	[	X
ejpam-4479	287	2	(	(	PUNCT
ejpam-4479	287	3	x1	x1	PROPN
ejpam-4479	287	4	∩	∩	NOUN
ejpam-4479	287	5	x2)⊛	x2)⊛	PUNCT
ejpam-4479	288	1	(	(	PUNCT
ejpam-4479	288	2	y1	y1	NOUN
ejpam-4479	288	3	∩	∩	X
ejpam-4479	288	4	y2)]⊛	y2)]⊛	PROPN
ejpam-4479	288	5	(	(	PUNCT
ejpam-4479	288	6	z1	z1	PROPN
ejpam-4479	288	7	∩	∩	ADJ
ejpam-4479	288	8	z2	z2	NOUN
ejpam-4479	288	9	)	)	PUNCT
ejpam-4479	288	10	=	=	PUNCT
ejpam-4479	289	1	[	[	X
ejpam-4479	289	2	(	(	PUNCT
ejpam-4479	289	3	x1	x1	PROPN
ejpam-4479	289	4	⊛	⊛	NUM
ejpam-4479	289	5	y1	y1	NOUN
ejpam-4479	289	6	)	)	PUNCT
ejpam-4479	289	7	∩	∩	NOUN
ejpam-4479	289	8	(	(	PUNCT
ejpam-4479	289	9	x2	x2	PROPN
ejpam-4479	289	10	⊛	⊛	NUM
ejpam-4479	289	11	y2)]⊛	y2)]⊛	PROPN
ejpam-4479	289	12	(	(	PUNCT
ejpam-4479	289	13	z1	z1	PROPN
ejpam-4479	289	14	∩	∩	ADJ
ejpam-4479	289	15	z2	z2	NOUN
ejpam-4479	289	16	)	)	PUNCT
ejpam-4479	289	17	=	=	PUNCT
ejpam-4479	290	1	[	[	X
ejpam-4479	290	2	(	(	PUNCT
ejpam-4479	290	3	x1	x1	PROPN
ejpam-4479	290	4	⊛	⊛	NUM
ejpam-4479	290	5	y1)⊛	y1)⊛	PROPN
ejpam-4479	290	6	(	(	PUNCT
ejpam-4479	290	7	z1	z1	VERB
ejpam-4479	290	8	∩	∩	X
ejpam-4479	290	9	z2	z2	NOUN
ejpam-4479	290	10	)	)	PUNCT
ejpam-4479	290	11	]	]	PUNCT
ejpam-4479	290	12	∩	∩	NOUN
ejpam-4479	290	13	[	[	X
ejpam-4479	290	14	(	(	PUNCT
ejpam-4479	290	15	x2	x2	PROPN
ejpam-4479	290	16	⊛	⊛	ADV
ejpam-4479	290	17	y2)⊛	y2)⊛	PROPN
ejpam-4479	290	18	(	(	PUNCT
ejpam-4479	290	19	z1	z1	VERB
ejpam-4479	290	20	∩	∩	X
ejpam-4479	290	21	z2	z2	NOUN
ejpam-4479	290	22	)	)	PUNCT
ejpam-4479	290	23	]	]	PUNCT
ejpam-4479	291	1	=	=	PUNCT
ejpam-4479	291	2	[	[	PUNCT
ejpam-4479	291	3	(	(	PUNCT
ejpam-4479	291	4	x′1	x′1	PROPN
ejpam-4479	291	5	⊛	⊛	PROPN
ejpam-4479	291	6	y′1)⊛	y′1)⊛	PROPN
ejpam-4479	291	7	z′1	z′1	NOUN
ejpam-4479	291	8	]	]	PUNCT
ejpam-4479	291	9	∩	∩	NOUN
ejpam-4479	291	10	[	[	PUNCT
ejpam-4479	291	11	(	(	PUNCT
ejpam-4479	291	12	x′2	x′2	NOUN
ejpam-4479	291	13	⊛	⊛	NUM
ejpam-4479	291	14	y′2)⊛	y′2)⊛	NOUN
ejpam-4479	291	15	z′2	z′2	X
ejpam-4479	291	16	]	]	PUNCT
ejpam-4479	292	1	⊆	⊆	NUM
ejpam-4479	292	2	i1	i1	PROPN
ejpam-4479	292	3	∩	∩	PROPN
ejpam-4479	292	4	i2	i2	PROPN
ejpam-4479	292	5	=	=	PUNCT
ejpam-4479	292	6	m.	m.	NOUN
ejpam-4479	292	7	by	by	ADP
ejpam-4479	292	8	definition	definition	NOUN
ejpam-4479	292	9	16	16	NUM
ejpam-4479	292	10	,	,	PUNCT
ejpam-4479	292	11	x⊛	x⊛	PROPN
ejpam-4479	292	12	(	(	PUNCT
ejpam-4479	292	13	y	y	PROPN
ejpam-4479	292	14	⊛	⊛	NUM
ejpam-4479	292	15	(	(	PUNCT
ejpam-4479	292	16	y	y	PROPN
ejpam-4479	292	17	⊛	⊛	NUM
ejpam-4479	292	18	x	x	NOUN
ejpam-4479	292	19	)	)	PUNCT
ejpam-4479	292	20	)	)	PUNCT
ejpam-4479	293	1	⊆	⊆	NUM
ejpam-4479	293	2	m	m	NOUN
ejpam-4479	293	3	.	.	PUNCT
ejpam-4479	294	1	hence	hence	ADV
ejpam-4479	294	2	,	,	PUNCT
ejpam-4479	294	3	m	m	PROPN
ejpam-4479	294	4	=	=	PROPN
ejpam-4479	294	5	i1	i1	PROPN
ejpam-4479	294	6	∩	∩	PROPN
ejpam-4479	294	7	i2	i2	PROPN
ejpam-4479	294	8	⋄hgrc	⋄hgrc	PROPN
ejpam-4479	294	9	s.	s.	PROPN
ejpam-4479	294	10	theorem	theorem	VERB
ejpam-4479	294	11	14	14	NUM
ejpam-4479	294	12	.	.	PUNCT
ejpam-4479	295	1	let	let	AUX
ejpam-4479	295	2	(	(	PUNCT
ejpam-4479	295	3	f	f	X
ejpam-4479	295	4	,	,	PUNCT
ejpam-4479	295	5	a	a	PRON
ejpam-4479	295	6	)	)	PUNCT
ejpam-4479	295	7	be	be	AUX
ejpam-4479	295	8	a	a	DET
ejpam-4479	295	9	soft	soft	ADJ
ejpam-4479	295	10	hyper	hyper	ADJ
ejpam-4479	295	11	gr	gr	NOUN
ejpam-4479	295	12	-	-	NOUN
ejpam-4479	295	13	algebra	algebra	NOUN
ejpam-4479	295	14	over	over	ADP
ejpam-4479	295	15	h.	h.	NOUN
ejpam-4479	295	16	for	for	ADP
ejpam-4479	295	17	any	any	DET
ejpam-4479	295	18	soft	soft	ADJ
ejpam-4479	295	19	sets	set	NOUN
ejpam-4479	295	20	(	(	PUNCT
ejpam-4479	295	21	g1,m1	g1,m1	PROPN
ejpam-4479	295	22	)	)	PUNCT
ejpam-4479	295	23	and	and	CCONJ
ejpam-4479	295	24	(	(	PUNCT
ejpam-4479	295	25	g2,m2	g2,m2	PROPN
ejpam-4479	295	26	)	)	PUNCT
ejpam-4479	295	27	over	over	ADP
ejpam-4479	295	28	h	h	NOUN
ejpam-4479	295	29	,	,	PUNCT
ejpam-4479	295	30	where	where	SCONJ
ejpam-4479	295	31	m1	m1	PROPN
ejpam-4479	295	32	∩m2	∩m2	PROPN
ejpam-4479	295	33	̸=	̸=	PROPN
ejpam-4479	295	34	∅	∅	NOUN
ejpam-4479	295	35	we	we	PRON
ejpam-4479	295	36	have	have	VERB
ejpam-4479	295	37	(	(	PUNCT
ejpam-4479	295	38	g1,m1	g1,m1	PROPN
ejpam-4479	295	39	)	)	PUNCT
ejpam-4479	295	40	∼⋄hgrc	∼⋄hgrc	PROPN
ejpam-4479	295	41	(	(	PUNCT
ejpam-4479	295	42	f	f	PROPN
ejpam-4479	295	43	,	,	PUNCT
ejpam-4479	295	44	a	a	PRON
ejpam-4479	295	45	)	)	PUNCT
ejpam-4479	295	46	,	,	PUNCT
ejpam-4479	295	47	(	(	PUNCT
ejpam-4479	295	48	g2,m2	g2,m2	PROPN
ejpam-4479	295	49	)	)	PUNCT
ejpam-4479	295	50	∼⋄hgrc	∼⋄hgrc	PROPN
ejpam-4479	295	51	(	(	PUNCT
ejpam-4479	295	52	f	f	PROPN
ejpam-4479	295	53	,	,	PUNCT
ejpam-4479	295	54	a	a	PRON
ejpam-4479	295	55	)	)	PUNCT
ejpam-4479	296	1	=	=	NOUN
ejpam-4479	296	2	⇒	⇒	NOUN
ejpam-4479	296	3	(	(	PUNCT
ejpam-4479	296	4	g1,m1	g1,m1	PROPN
ejpam-4479	296	5	)	)	PUNCT
ejpam-4479	296	6	∼	∼	NOUN
ejpam-4479	296	7	∩	∩	NOUN
ejpam-4479	296	8	(	(	PUNCT
ejpam-4479	296	9	g2,m2	g2,m2	PROPN
ejpam-4479	296	10	)	)	PUNCT
ejpam-4479	296	11	∼⋄hgrc	∼⋄hgrc	PROPN
ejpam-4479	296	12	(	(	PUNCT
ejpam-4479	296	13	f	f	PROPN
ejpam-4479	296	14	,	,	PUNCT
ejpam-4479	296	15	a	a	PRON
ejpam-4479	296	16	)	)	PUNCT
ejpam-4479	296	17	.	.	PUNCT
ejpam-4479	297	1	proof	proof	NOUN
ejpam-4479	297	2	:	:	PUNCT
ejpam-4479	297	3	by	by	ADP
ejpam-4479	297	4	definition	definition	NOUN
ejpam-4479	297	5	6	6	NUM
ejpam-4479	297	6	,	,	PUNCT
ejpam-4479	297	7	we	we	PRON
ejpam-4479	297	8	write	write	VERB
ejpam-4479	297	9	(	(	PUNCT
ejpam-4479	297	10	g1,m1	g1,m1	PROPN
ejpam-4479	297	11	)	)	PUNCT
ejpam-4479	297	12	∼	∼	NOUN
ejpam-4479	297	13	∩	∩	NOUN
ejpam-4479	297	14	(	(	PUNCT
ejpam-4479	297	15	g2,m2	g2,m2	PROPN
ejpam-4479	297	16	)	)	PUNCT
ejpam-4479	297	17	=	=	PUNCT
ejpam-4479	297	18	(	(	PUNCT
ejpam-4479	297	19	g	g	PROPN
ejpam-4479	297	20	,	,	PUNCT
ejpam-4479	297	21	m	m	NOUN
ejpam-4479	297	22	)	)	PUNCT
ejpam-4479	297	23	where	where	SCONJ
ejpam-4479	297	24	m	m	VERB
ejpam-4479	297	25	=	=	VERB
ejpam-4479	297	26	m1	m1	PROPN
ejpam-4479	297	27	∩m2	∩m2	PROPN
ejpam-4479	297	28	and	and	CCONJ
ejpam-4479	297	29	g(a	g(a	PROPN
ejpam-4479	297	30	)	)	PUNCT
ejpam-4479	297	31	=	=	SYM
ejpam-4479	297	32	g1(a	g1(a	NOUN
ejpam-4479	297	33	)	)	PUNCT
ejpam-4479	297	34	∩	∩	ADJ
ejpam-4479	297	35	g2(a	g2(a	NOUN
ejpam-4479	297	36	)	)	PUNCT
ejpam-4479	297	37	for	for	ADP
ejpam-4479	297	38	all	all	DET
ejpam-4479	297	39	a	a	DET
ejpam-4479	297	40	∈	∈	NOUN
ejpam-4479	297	41	m	m	NOUN
ejpam-4479	297	42	.	.	PUNCT
ejpam-4479	298	1	clearly	clearly	ADV
ejpam-4479	298	2	,	,	PUNCT
ejpam-4479	298	3	m	m	PROPN
ejpam-4479	298	4	⊆	⊆	NUM
ejpam-4479	298	5	a.	a.	NOUN
ejpam-4479	298	6	by	by	ADP
ejpam-4479	298	7	theorem	theorem	ADJ
ejpam-4479	298	8	13	13	NUM
ejpam-4479	298	9	,	,	PUNCT
ejpam-4479	298	10	g1(a	g1(a	NOUN
ejpam-4479	298	11	)	)	PUNCT
ejpam-4479	298	12	∩	∩	ADJ
ejpam-4479	298	13	g2(a	g2(a	NOUN
ejpam-4479	298	14	)	)	PUNCT
ejpam-4479	298	15	⋄hgrc	⋄hgrc	NOUN
ejpam-4479	298	16	f	f	PROPN
ejpam-4479	298	17	(	(	PUNCT
ejpam-4479	298	18	a	a	NOUN
ejpam-4479	298	19	)	)	PUNCT
ejpam-4479	298	20	.	.	PUNCT
ejpam-4479	299	1	hence	hence	ADV
ejpam-4479	299	2	,	,	PUNCT
ejpam-4479	299	3	(	(	PUNCT
ejpam-4479	299	4	g1,m1	g1,m1	PROPN
ejpam-4479	299	5	)	)	PUNCT
ejpam-4479	299	6	∼	∼	NOUN
ejpam-4479	299	7	∩	∩	NOUN
ejpam-4479	299	8	(	(	PUNCT
ejpam-4479	299	9	g2,m2	g2,m2	PROPN
ejpam-4479	299	10	)	)	PUNCT
ejpam-4479	299	11	=	=	PUNCT
ejpam-4479	299	12	(	(	PUNCT
ejpam-4479	299	13	g	g	PROPN
ejpam-4479	299	14	,	,	PUNCT
ejpam-4479	299	15	m	m	NOUN
ejpam-4479	299	16	)	)	PUNCT
ejpam-4479	299	17	∼⋄hgrc	∼⋄hgrc	PROPN
ejpam-4479	299	18	(	(	PUNCT
ejpam-4479	299	19	f	f	PROPN
ejpam-4479	299	20	,	,	PUNCT
ejpam-4479	299	21	a	a	PRON
ejpam-4479	299	22	)	)	PUNCT
ejpam-4479	299	23	.	.	PUNCT
ejpam-4479	300	1	if	if	SCONJ
ejpam-4479	300	2	m	m	NOUN
ejpam-4479	300	3	=	=	VERB
ejpam-4479	300	4	m1	m1	PROPN
ejpam-4479	300	5	=	=	SYM
ejpam-4479	300	6	m2	m2	PROPN
ejpam-4479	300	7	,	,	PUNCT
ejpam-4479	300	8	then	then	ADV
ejpam-4479	300	9	we	we	PRON
ejpam-4479	300	10	have	have	VERB
ejpam-4479	300	11	the	the	DET
ejpam-4479	300	12	following	follow	VERB
ejpam-4479	300	13	corollary	corollary	NOUN
ejpam-4479	300	14	.	.	PUNCT
ejpam-4479	301	1	m.k	m.k	PROPN
ejpam-4479	301	2	.	.	PUNCT
ejpam-4479	301	3	engcot	engcot	PROPN
ejpam-4479	301	4	,	,	PUNCT
ejpam-4479	301	5	g.	g.	PROPN
ejpam-4479	301	6	petalcorin	petalcorin	PROPN
ejpam-4479	301	7	/	/	SYM
ejpam-4479	301	8	eur	eur	PROPN
ejpam-4479	301	9	.	.	PUNCT
ejpam-4479	302	1	j.	j.	PROPN
ejpam-4479	302	2	pure	pure	PROPN
ejpam-4479	302	3	appl	appl	PROPN
ejpam-4479	302	4	.	.	PROPN
ejpam-4479	302	5	math	math	PROPN
ejpam-4479	302	6	,	,	PUNCT
ejpam-4479	302	7	15	15	NUM
ejpam-4479	302	8	(	(	PUNCT
ejpam-4479	302	9	4	4	NUM
ejpam-4479	302	10	)	)	PUNCT
ejpam-4479	302	11	(	(	PUNCT
ejpam-4479	302	12	2022	2022	NUM
ejpam-4479	302	13	)	)	PUNCT
ejpam-4479	302	14	,	,	PUNCT
ejpam-4479	302	15	1482	1482	NUM
ejpam-4479	302	16	-	-	SYM
ejpam-4479	302	17	1497	1497	NUM
ejpam-4479	302	18	1494	1494	NUM
ejpam-4479	302	19	corollary	corollary	NOUN
ejpam-4479	302	20	2	2	NUM
ejpam-4479	302	21	.	.	PUNCT
ejpam-4479	303	1	let	let	AUX
ejpam-4479	303	2	(	(	PUNCT
ejpam-4479	303	3	f	f	X
ejpam-4479	303	4	,	,	PUNCT
ejpam-4479	303	5	a	a	PRON
ejpam-4479	303	6	)	)	PUNCT
ejpam-4479	303	7	be	be	AUX
ejpam-4479	303	8	a	a	DET
ejpam-4479	303	9	soft	soft	ADJ
ejpam-4479	303	10	hyper	hyper	ADJ
ejpam-4479	303	11	gr	gr	NOUN
ejpam-4479	303	12	-	-	NOUN
ejpam-4479	303	13	algebra	algebra	NOUN
ejpam-4479	303	14	over	over	ADP
ejpam-4479	303	15	h.	h.	NOUN
ejpam-4479	303	16	for	for	ADP
ejpam-4479	303	17	any	any	DET
ejpam-4479	303	18	soft	soft	ADJ
ejpam-4479	303	19	sets	set	NOUN
ejpam-4479	303	20	(	(	PUNCT
ejpam-4479	303	21	g	g	NOUN
ejpam-4479	303	22	,	,	PUNCT
ejpam-4479	303	23	m	m	PROPN
ejpam-4479	303	24	)	)	PUNCT
ejpam-4479	303	25	and	and	CCONJ
ejpam-4479	303	26	(	(	PUNCT
ejpam-4479	303	27	j	j	PROPN
ejpam-4479	303	28	,	,	PUNCT
ejpam-4479	303	29	m	m	PROPN
ejpam-4479	303	30	)	)	PUNCT
ejpam-4479	303	31	over	over	ADP
ejpam-4479	303	32	h	h	NOUN
ejpam-4479	303	33	,	,	PUNCT
ejpam-4479	303	34	we	we	PRON
ejpam-4479	303	35	have	have	VERB
ejpam-4479	303	36	(	(	PUNCT
ejpam-4479	303	37	g	g	PROPN
ejpam-4479	303	38	,	,	PUNCT
ejpam-4479	303	39	m	m	NOUN
ejpam-4479	303	40	)	)	PUNCT
ejpam-4479	303	41	∼⋄hgrc	∼⋄hgrc	PROPN
ejpam-4479	303	42	(	(	PUNCT
ejpam-4479	303	43	f	f	PROPN
ejpam-4479	303	44	,	,	PUNCT
ejpam-4479	303	45	a	a	PRON
ejpam-4479	303	46	)	)	PUNCT
ejpam-4479	303	47	,	,	PUNCT
ejpam-4479	303	48	(	(	PUNCT
ejpam-4479	303	49	j	j	PROPN
ejpam-4479	303	50	,	,	PUNCT
ejpam-4479	303	51	m	m	NOUN
ejpam-4479	303	52	)	)	PUNCT
ejpam-4479	303	53	∼⋄hgrc	∼⋄hgrc	PROPN
ejpam-4479	303	54	(	(	PUNCT
ejpam-4479	303	55	f	f	PROPN
ejpam-4479	303	56	,	,	PUNCT
ejpam-4479	303	57	a	a	PRON
ejpam-4479	303	58	)	)	PUNCT
ejpam-4479	303	59	=	=	NOUN
ejpam-4479	303	60	⇒	⇒	NOUN
ejpam-4479	303	61	(	(	PUNCT
ejpam-4479	303	62	g	g	PROPN
ejpam-4479	303	63	,	,	PUNCT
ejpam-4479	303	64	m	m	NOUN
ejpam-4479	303	65	)	)	PUNCT
ejpam-4479	303	66	∼	∼	NOUN
ejpam-4479	303	67	∩	∩	NOUN
ejpam-4479	303	68	(	(	PUNCT
ejpam-4479	303	69	j	j	PROPN
ejpam-4479	303	70	,	,	PUNCT
ejpam-4479	303	71	m	m	NOUN
ejpam-4479	303	72	)	)	PUNCT
ejpam-4479	303	73	∼⋄hgrc	∼⋄hgrc	PROPN
ejpam-4479	303	74	(	(	PUNCT
ejpam-4479	303	75	f	f	PROPN
ejpam-4479	303	76	,	,	PUNCT
ejpam-4479	303	77	a	a	PRON
ejpam-4479	303	78	)	)	PUNCT
ejpam-4479	303	79	.	.	PUNCT
ejpam-4479	304	1	theorem	theorem	NOUN
ejpam-4479	304	2	15	15	NUM
ejpam-4479	304	3	.	.	PUNCT
ejpam-4479	305	1	let	let	AUX
ejpam-4479	305	2	(	(	PUNCT
ejpam-4479	305	3	f	f	X
ejpam-4479	305	4	,	,	PUNCT
ejpam-4479	305	5	a	a	PRON
ejpam-4479	305	6	)	)	PUNCT
ejpam-4479	305	7	be	be	AUX
ejpam-4479	305	8	a	a	DET
ejpam-4479	305	9	soft	soft	ADJ
ejpam-4479	305	10	hyper	hyper	ADJ
ejpam-4479	305	11	gr	gr	NOUN
ejpam-4479	305	12	-	-	NOUN
ejpam-4479	305	13	algebra	algebra	NOUN
ejpam-4479	305	14	over	over	ADP
ejpam-4479	305	15	h.	h.	NOUN
ejpam-4479	305	16	for	for	ADP
ejpam-4479	305	17	any	any	DET
ejpam-4479	305	18	soft	soft	ADJ
ejpam-4479	305	19	sets	set	NOUN
ejpam-4479	305	20	(	(	PUNCT
ejpam-4479	305	21	g	g	NOUN
ejpam-4479	305	22	,	,	PUNCT
ejpam-4479	305	23	m	m	PROPN
ejpam-4479	305	24	)	)	PUNCT
ejpam-4479	305	25	and	and	CCONJ
ejpam-4479	305	26	(	(	PUNCT
ejpam-4479	305	27	j	j	PROPN
ejpam-4479	305	28	,	,	PUNCT
ejpam-4479	305	29	n	n	CCONJ
ejpam-4479	305	30	)	)	PUNCT
ejpam-4479	305	31	,	,	PUNCT
ejpam-4479	305	32	with	with	ADP
ejpam-4479	305	33	m	m	PROPN
ejpam-4479	305	34	∩n	∩n	NOUN
ejpam-4479	305	35	=	=	SYM
ejpam-4479	305	36	∅	∅	NOUN
ejpam-4479	305	37	,	,	PUNCT
ejpam-4479	305	38	we	we	PRON
ejpam-4479	305	39	have	have	VERB
ejpam-4479	305	40	(	(	PUNCT
ejpam-4479	305	41	g	g	PROPN
ejpam-4479	305	42	,	,	PUNCT
ejpam-4479	305	43	m	m	NOUN
ejpam-4479	305	44	)	)	PUNCT
ejpam-4479	305	45	∼⋄hgrc	∼⋄hgrc	PROPN
ejpam-4479	305	46	(	(	PUNCT
ejpam-4479	305	47	f	f	PROPN
ejpam-4479	305	48	,	,	PUNCT
ejpam-4479	305	49	a	a	PRON
ejpam-4479	305	50	)	)	PUNCT
ejpam-4479	305	51	,	,	PUNCT
ejpam-4479	305	52	(	(	PUNCT
ejpam-4479	305	53	j	j	NOUN
ejpam-4479	305	54	,	,	PUNCT
ejpam-4479	305	55	n	n	CCONJ
ejpam-4479	305	56	)	)	PUNCT
ejpam-4479	305	57	∼⋄hgrc	∼⋄hgrc	PROPN
ejpam-4479	305	58	(	(	PUNCT
ejpam-4479	305	59	f	f	PROPN
ejpam-4479	305	60	,	,	PUNCT
ejpam-4479	305	61	a	a	PRON
ejpam-4479	305	62	)	)	PUNCT
ejpam-4479	306	1	=	=	NOUN
ejpam-4479	306	2	⇒	⇒	NOUN
ejpam-4479	306	3	(	(	PUNCT
ejpam-4479	306	4	g	g	PROPN
ejpam-4479	306	5	,	,	PUNCT
ejpam-4479	306	6	m	m	NOUN
ejpam-4479	306	7	)	)	PUNCT
ejpam-4479	306	8	∼	∼	NOUN
ejpam-4479	306	9	∪	∪	NOUN
ejpam-4479	306	10	(	(	PUNCT
ejpam-4479	306	11	j	j	NOUN
ejpam-4479	306	12	,	,	PUNCT
ejpam-4479	306	13	n	n	CCONJ
ejpam-4479	306	14	)	)	PUNCT
ejpam-4479	306	15	∼⋄hgrc	∼⋄hgrc	PROPN
ejpam-4479	306	16	(	(	PUNCT
ejpam-4479	306	17	f	f	PROPN
ejpam-4479	306	18	,	,	PUNCT
ejpam-4479	306	19	a	a	PRON
ejpam-4479	306	20	)	)	PUNCT
ejpam-4479	306	21	.	.	PUNCT
ejpam-4479	307	1	proof	proof	NOUN
ejpam-4479	307	2	:	:	PUNCT
ejpam-4479	307	3	using	use	VERB
ejpam-4479	307	4	definition	definition	NOUN
ejpam-4479	307	5	7	7	NUM
ejpam-4479	307	6	,	,	PUNCT
ejpam-4479	307	7	we	we	PRON
ejpam-4479	307	8	can	can	AUX
ejpam-4479	307	9	write	write	VERB
ejpam-4479	307	10	(	(	PUNCT
ejpam-4479	307	11	g	g	PROPN
ejpam-4479	307	12	,	,	PUNCT
ejpam-4479	307	13	m	m	NOUN
ejpam-4479	307	14	)	)	PUNCT
ejpam-4479	307	15	∼	∼	NOUN
ejpam-4479	307	16	∪	∪	NOUN
ejpam-4479	307	17	(	(	PUNCT
ejpam-4479	307	18	j	j	NOUN
ejpam-4479	307	19	,	,	PUNCT
ejpam-4479	307	20	n	n	CCONJ
ejpam-4479	307	21	)	)	PUNCT
ejpam-4479	307	22	=	=	SYM
ejpam-4479	308	1	(	(	PUNCT
ejpam-4479	308	2	r	r	NOUN
ejpam-4479	308	3	,	,	PUNCT
ejpam-4479	308	4	u	u	NOUN
ejpam-4479	308	5	)	)	PUNCT
ejpam-4479	308	6	,	,	PUNCT
ejpam-4479	308	7	where	where	SCONJ
ejpam-4479	308	8	u	u	NOUN
ejpam-4479	308	9	=	=	NOUN
ejpam-4479	308	10	m	m	VERB
ejpam-4479	308	11	∪n	∪n	X
ejpam-4479	308	12	,	,	PUNCT
ejpam-4479	308	13	and	and	CCONJ
ejpam-4479	308	14	for	for	ADP
ejpam-4479	308	15	all	all	DET
ejpam-4479	308	16	x	x	SYM
ejpam-4479	308	17	∈	∈	PROPN
ejpam-4479	308	18	u	u	NOUN
ejpam-4479	308	19	,	,	PUNCT
ejpam-4479	308	20	r(x	r(x	PROPN
ejpam-4479	308	21	)	)	PUNCT
ejpam-4479	308	22	=	=	PUNCT
ejpam-4479	309	1			PROPN
ejpam-4479	309	2	g(x	g(x	NOUN
ejpam-4479	309	3	)	)	PUNCT
ejpam-4479	309	4	,	,	PUNCT
ejpam-4479	309	5	if	if	SCONJ
ejpam-4479	309	6	x	x	PROPN
ejpam-4479	309	7	∈	∈	PROPN
ejpam-4479	309	8	m	m	NOUN
ejpam-4479	309	9	\n	\n	PUNCT
ejpam-4479	309	10	j(x	j(x	PROPN
ejpam-4479	309	11	)	)	PUNCT
ejpam-4479	309	12	,	,	PUNCT
ejpam-4479	309	13	if	if	SCONJ
ejpam-4479	309	14	x	x	SYM
ejpam-4479	309	15	∈	∈	NOUN
ejpam-4479	309	16	n	n	PRON
ejpam-4479	309	17	\m	\m	NOUN
ejpam-4479	309	18	g(x	g(x	NOUN
ejpam-4479	309	19	)	)	PUNCT
ejpam-4479	309	20	∪	∪	ADP
ejpam-4479	309	21	j(x	j(x	PROPN
ejpam-4479	309	22	)	)	PUNCT
ejpam-4479	309	23	,	,	PUNCT
ejpam-4479	309	24	if	if	SCONJ
ejpam-4479	309	25	x	x	PROPN
ejpam-4479	309	26	∈	∈	PROPN
ejpam-4479	309	27	m	m	VERB
ejpam-4479	309	28	∩n	∩n	NOUN
ejpam-4479	309	29	.	.	PUNCT
ejpam-4479	310	1	since	since	SCONJ
ejpam-4479	310	2	m	m	NOUN
ejpam-4479	310	3	∩	∩	ADJ
ejpam-4479	310	4	n	n	NOUN
ejpam-4479	310	5	=	=	SYM
ejpam-4479	310	6	∅	∅	NOUN
ejpam-4479	310	7	,	,	PUNCT
ejpam-4479	310	8	it	it	PRON
ejpam-4479	310	9	implies	imply	VERB
ejpam-4479	310	10	that	that	SCONJ
ejpam-4479	310	11	either	either	CCONJ
ejpam-4479	310	12	x	x	SYM
ejpam-4479	310	13	∈	∈	PROPN
ejpam-4479	310	14	m	m	VERB
ejpam-4479	310	15	\	\	NOUN
ejpam-4479	310	16	n	n	CCONJ
ejpam-4479	310	17	or	or	CCONJ
ejpam-4479	310	18	x	x	SYM
ejpam-4479	310	19	∈	∈	PROPN
ejpam-4479	310	20	n	n	CCONJ
ejpam-4479	310	21	\	\	NOUN
ejpam-4479	310	22	m	m	PROPN
ejpam-4479	310	23	,	,	PUNCT
ejpam-4479	310	24	for	for	ADP
ejpam-4479	310	25	all	all	DET
ejpam-4479	310	26	x	x	SYM
ejpam-4479	310	27	∈	∈	PROPN
ejpam-4479	310	28	u	u	NOUN
ejpam-4479	310	29	.	.	PUNCT
ejpam-4479	311	1	if	if	SCONJ
ejpam-4479	311	2	x	x	SYM
ejpam-4479	311	3	∈	∈	PROPN
ejpam-4479	311	4	m	m	VERB
ejpam-4479	311	5	\	\	PROPN
ejpam-4479	311	6	n	n	PROPN
ejpam-4479	311	7	,	,	PUNCT
ejpam-4479	311	8	r(x	r(x	PROPN
ejpam-4479	311	9	)	)	PUNCT
ejpam-4479	311	10	=	=	SYM
ejpam-4479	311	11	g(x	g(x	NOUN
ejpam-4479	311	12	)	)	PUNCT
ejpam-4479	311	13	⋄hgrc	⋄hgrc	NOUN
ejpam-4479	311	14	f	f	X
ejpam-4479	311	15	(	(	PUNCT
ejpam-4479	311	16	x	x	NOUN
ejpam-4479	311	17	)	)	PUNCT
ejpam-4479	311	18	.	.	PUNCT
ejpam-4479	312	1	if	if	SCONJ
ejpam-4479	312	2	x	x	SYM
ejpam-4479	312	3	∈	∈	PROPN
ejpam-4479	312	4	n	n	CCONJ
ejpam-4479	312	5	\	\	NOUN
ejpam-4479	312	6	m	m	PROPN
ejpam-4479	312	7	,	,	PUNCT
ejpam-4479	312	8	r(x	r(x	PROPN
ejpam-4479	312	9	)	)	PUNCT
ejpam-4479	312	10	=	=	SYM
ejpam-4479	312	11	j(x	j(x	PROPN
ejpam-4479	312	12	)	)	PUNCT
ejpam-4479	312	13	⋄hgrc	⋄hgrc	PROPN
ejpam-4479	312	14	f	f	PROPN
ejpam-4479	312	15	(	(	PUNCT
ejpam-4479	312	16	x	x	NOUN
ejpam-4479	312	17	)	)	PUNCT
ejpam-4479	312	18	.	.	PUNCT
ejpam-4479	313	1	thus	thus	ADV
ejpam-4479	313	2	,	,	PUNCT
ejpam-4479	313	3	r(x	r(x	NOUN
ejpam-4479	313	4	)	)	PUNCT
ejpam-4479	313	5	⋄hgrc	⋄hgrc	PROPN
ejpam-4479	313	6	f	f	PROPN
ejpam-4479	313	7	(	(	PUNCT
ejpam-4479	313	8	x	x	NOUN
ejpam-4479	313	9	)	)	PUNCT
ejpam-4479	313	10	for	for	ADP
ejpam-4479	313	11	all	all	DET
ejpam-4479	313	12	x	x	SYM
ejpam-4479	313	13	∈	∈	PROPN
ejpam-4479	313	14	u	u	NOUN
ejpam-4479	313	15	.	.	PUNCT
ejpam-4479	314	1	hence	hence	ADV
ejpam-4479	314	2	,	,	PUNCT
ejpam-4479	314	3	(	(	PUNCT
ejpam-4479	314	4	g	g	NOUN
ejpam-4479	314	5	,	,	PUNCT
ejpam-4479	314	6	m	m	NOUN
ejpam-4479	314	7	)	)	PUNCT
ejpam-4479	314	8	∼	∼	NOUN
ejpam-4479	314	9	∪	∪	NOUN
ejpam-4479	314	10	(	(	PUNCT
ejpam-4479	314	11	j	j	NOUN
ejpam-4479	314	12	,	,	PUNCT
ejpam-4479	314	13	n	n	CCONJ
ejpam-4479	314	14	)	)	PUNCT
ejpam-4479	314	15	=	=	SYM
ejpam-4479	314	16	(	(	PUNCT
ejpam-4479	314	17	r	r	NOUN
ejpam-4479	314	18	,	,	PUNCT
ejpam-4479	314	19	u	u	NOUN
ejpam-4479	314	20	)	)	PUNCT
ejpam-4479	314	21	∼⋄hgrc	∼⋄hgrc	PROPN
ejpam-4479	314	22	(	(	PUNCT
ejpam-4479	314	23	f	f	PROPN
ejpam-4479	314	24	,	,	PUNCT
ejpam-4479	314	25	a	a	PRON
ejpam-4479	314	26	)	)	PUNCT
ejpam-4479	314	27	.	.	PUNCT
ejpam-4479	315	1	definition	definition	NOUN
ejpam-4479	315	2	18	18	NUM
ejpam-4479	315	3	.	.	PUNCT
ejpam-4479	316	1	let	let	VERB
ejpam-4479	316	2	e	e	PRON
ejpam-4479	316	3	be	be	AUX
ejpam-4479	316	4	a	a	DET
ejpam-4479	316	5	hyper	hyper	ADJ
ejpam-4479	316	6	gr	gr	NOUN
ejpam-4479	316	7	-	-	NOUN
ejpam-4479	316	8	algebra	algebra	NOUN
ejpam-4479	316	9	.	.	PUNCT
ejpam-4479	317	1	given	give	VERB
ejpam-4479	317	2	a	a	DET
ejpam-4479	317	3	hyper	hyper	ADJ
ejpam-4479	317	4	subgr	subgr	NOUN
ejpam-4479	317	5	-	-	PUNCT
ejpam-4479	317	6	algebra	algebra	NOUN
ejpam-4479	317	7	a	a	PRON
ejpam-4479	317	8	of	of	ADP
ejpam-4479	317	9	e	e	NOUN
ejpam-4479	317	10	,	,	PUNCT
ejpam-4479	317	11	let	let	VERB
ejpam-4479	317	12	(	(	PUNCT
ejpam-4479	317	13	f	f	X
ejpam-4479	317	14	,	,	PUNCT
ejpam-4479	317	15	a	a	PRON
ejpam-4479	317	16	)	)	PUNCT
ejpam-4479	317	17	∈	∈	PROPN
ejpam-4479	317	18	s(u	s(u	PROPN
ejpam-4479	317	19	)	)	PUNCT
ejpam-4479	317	20	.	.	PUNCT
ejpam-4479	318	1	then	then	ADV
ejpam-4479	318	2	(	(	PUNCT
ejpam-4479	318	3	f	f	X
ejpam-4479	318	4	,	,	PUNCT
ejpam-4479	318	5	a	a	PRON
ejpam-4479	318	6	)	)	PUNCT
ejpam-4479	318	7	is	be	AUX
ejpam-4479	318	8	called	call	VERB
ejpam-4479	318	9	a	a	DET
ejpam-4479	318	10	union	union	NOUN
ejpam-4479	318	11	-	-	PUNCT
ejpam-4479	318	12	soft	soft	ADJ
ejpam-4479	318	13	hyper	hyper	ADJ
ejpam-4479	318	14	gr	gr	NOUN
ejpam-4479	318	15	-	-	NOUN
ejpam-4479	318	16	algebra	algebra	NOUN
ejpam-4479	318	17	over	over	ADP
ejpam-4479	318	18	u	u	NOUN
ejpam-4479	318	19	if	if	SCONJ
ejpam-4479	318	20	fa	fa	PROPN
ejpam-4479	318	21	satisfies	satisfy	VERB
ejpam-4479	318	22	fa(x⊛	fa(x⊛	NUM
ejpam-4479	318	23	y	y	NOUN
ejpam-4479	318	24	)	)	PUNCT
ejpam-4479	318	25	⊆	⊆	NUM
ejpam-4479	318	26	fa(x	fa(x	NOUN
ejpam-4479	318	27	)	)	PUNCT
ejpam-4479	318	28	∪	∪	ADP
ejpam-4479	318	29	fa(y),∀x	fa(y),∀x	PROPN
ejpam-4479	318	30	,	,	PUNCT
ejpam-4479	318	31	y	y	PROPN
ejpam-4479	318	32	∈	∈	PROPN
ejpam-4479	318	33	a.	a.	NOUN
ejpam-4479	318	34	example	example	NOUN
ejpam-4479	318	35	13	13	NUM
ejpam-4479	318	36	.	.	PUNCT
ejpam-4479	318	37	consider	consider	VERB
ejpam-4479	318	38	the	the	DET
ejpam-4479	318	39	hyper	hyper	ADJ
ejpam-4479	318	40	gr	gr	NOUN
ejpam-4479	318	41	-	-	PUNCT
ejpam-4479	318	42	algebra	algebra	NOUN
ejpam-4479	318	43	h	h	NOUN
ejpam-4479	318	44	=	=	SYM
ejpam-4479	318	45	{	{	PUNCT
ejpam-4479	318	46	0	0	NUM
ejpam-4479	318	47	,	,	PUNCT
ejpam-4479	318	48	1	1	NUM
ejpam-4479	318	49	,	,	PUNCT
ejpam-4479	318	50	2	2	NUM
ejpam-4479	318	51	,	,	PUNCT
ejpam-4479	318	52	3	3	NUM
ejpam-4479	318	53	}	}	PUNCT
ejpam-4479	318	54	defined	define	VERB
ejpam-4479	318	55	in	in	ADP
ejpam-4479	318	56	example	example	NOUN
ejpam-4479	318	57	4	4	NUM
ejpam-4479	318	58	.	.	PUNCT
ejpam-4479	319	1	let	let	VERB
ejpam-4479	319	2	τ1	τ1	NOUN
ejpam-4479	319	3	,	,	PUNCT
ejpam-4479	319	4	τ2	τ2	PROPN
ejpam-4479	319	5	,	,	PUNCT
ejpam-4479	319	6	τ3	τ3	NOUN
ejpam-4479	319	7	be	be	VERB
ejpam-4479	319	8	subsets	subset	NOUN
ejpam-4479	319	9	of	of	ADP
ejpam-4479	319	10	h	h	NOUN
ejpam-4479	319	11	such	such	ADJ
ejpam-4479	319	12	that	that	PRON
ejpam-4479	319	13	τ1	τ1	NOUN
ejpam-4479	319	14	⊆	⊆	NUM
ejpam-4479	319	15	τ2	τ2	NOUN
ejpam-4479	319	16	⊆	⊆	NUM
ejpam-4479	319	17	τ3	τ3	NOUN
ejpam-4479	319	18	.	.	PUNCT
ejpam-4479	320	1	define	define	VERB
ejpam-4479	320	2	a	a	DET
ejpam-4479	320	3	soft	soft	ADJ
ejpam-4479	320	4	set	set	NOUN
ejpam-4479	320	5	(	(	PUNCT
ejpam-4479	320	6	f	f	X
ejpam-4479	320	7	,	,	PUNCT
ejpam-4479	320	8	a	a	PRON
ejpam-4479	320	9	)	)	PUNCT
ejpam-4479	320	10	as	as	SCONJ
ejpam-4479	320	11	follows	follow	VERB
ejpam-4479	320	12	:	:	PUNCT
ejpam-4479	320	13	(	(	PUNCT
ejpam-4479	320	14	f	f	X
ejpam-4479	320	15	,	,	PUNCT
ejpam-4479	320	16	a	a	PRON
ejpam-4479	320	17	)	)	PUNCT
ejpam-4479	320	18	=	=	SYM
ejpam-4479	320	19	{	{	PUNCT
ejpam-4479	320	20	(	(	PUNCT
ejpam-4479	320	21	0	0	NUM
ejpam-4479	320	22	,	,	PUNCT
ejpam-4479	320	23	τ1	τ1	NOUN
ejpam-4479	320	24	)	)	PUNCT
ejpam-4479	320	25	,	,	PUNCT
ejpam-4479	320	26	(	(	PUNCT
ejpam-4479	320	27	1	1	NUM
ejpam-4479	320	28	,	,	PUNCT
ejpam-4479	320	29	τ1	τ1	NOUN
ejpam-4479	320	30	)	)	PUNCT
ejpam-4479	320	31	,	,	PUNCT
ejpam-4479	320	32	(	(	PUNCT
ejpam-4479	320	33	2	2	NUM
ejpam-4479	320	34	,	,	PUNCT
ejpam-4479	320	35	τ2	τ2	NOUN
ejpam-4479	320	36	)	)	PUNCT
ejpam-4479	320	37	,	,	PUNCT
ejpam-4479	320	38	(	(	PUNCT
ejpam-4479	320	39	3	3	NUM
ejpam-4479	320	40	,	,	PUNCT
ejpam-4479	320	41	τ3	τ3	NOUN
ejpam-4479	320	42	)	)	PUNCT
ejpam-4479	320	43	}	}	PUNCT
ejpam-4479	320	44	.	.	PUNCT
ejpam-4479	321	1	by	by	ADP
ejpam-4479	321	2	routine	routine	ADJ
ejpam-4479	321	3	calculations	calculation	NOUN
ejpam-4479	321	4	,	,	PUNCT
ejpam-4479	321	5	(	(	PUNCT
ejpam-4479	321	6	f	f	X
ejpam-4479	321	7	,	,	PUNCT
ejpam-4479	321	8	a	a	PRON
ejpam-4479	321	9	)	)	PUNCT
ejpam-4479	321	10	is	be	AUX
ejpam-4479	321	11	a	a	DET
ejpam-4479	321	12	union	union	NOUN
ejpam-4479	321	13	-	-	PUNCT
ejpam-4479	321	14	soft	soft	ADJ
ejpam-4479	321	15	hyper	hyper	ADJ
ejpam-4479	321	16	gr	gr	NOUN
ejpam-4479	321	17	-	-	PUNCT
ejpam-4479	321	18	algebra	algebra	NOUN
ejpam-4479	321	19	.	.	PUNCT
ejpam-4479	321	20	example	example	NOUN
ejpam-4479	321	21	14	14	NUM
ejpam-4479	321	22	.	.	PUNCT
ejpam-4479	322	1	consider	consider	VERB
ejpam-4479	322	2	the	the	DET
ejpam-4479	322	3	hyper	hyper	ADJ
ejpam-4479	322	4	gr	gr	NOUN
ejpam-4479	322	5	-	-	PUNCT
ejpam-4479	322	6	algebra	algebra	NOUN
ejpam-4479	322	7	h	h	NOUN
ejpam-4479	322	8	=	=	SYM
ejpam-4479	322	9	{	{	PUNCT
ejpam-4479	322	10	0	0	NUM
ejpam-4479	322	11	,	,	PUNCT
ejpam-4479	322	12	1	1	NUM
ejpam-4479	322	13	,	,	PUNCT
ejpam-4479	322	14	2	2	NUM
ejpam-4479	322	15	,	,	PUNCT
ejpam-4479	322	16	3	3	NUM
ejpam-4479	322	17	}	}	PUNCT
ejpam-4479	322	18	defined	define	VERB
ejpam-4479	322	19	in	in	ADP
ejpam-4479	322	20	example	example	NOUN
ejpam-4479	322	21	4	4	NUM
ejpam-4479	322	22	.	.	PUNCT
ejpam-4479	323	1	let	let	VERB
ejpam-4479	323	2	τ1	τ1	NOUN
ejpam-4479	323	3	,	,	PUNCT
ejpam-4479	323	4	τ2	τ2	PROPN
ejpam-4479	323	5	,	,	PUNCT
ejpam-4479	323	6	τ3	τ3	NOUN
ejpam-4479	323	7	,	,	PUNCT
ejpam-4479	323	8	τ4	τ4	PROPN
ejpam-4479	323	9	be	be	AUX
ejpam-4479	323	10	subsets	subset	NOUN
ejpam-4479	323	11	of	of	ADP
ejpam-4479	323	12	h	h	NOUN
ejpam-4479	324	1	such	such	ADJ
ejpam-4479	324	2	that	that	DET
ejpam-4479	324	3	τ1	τ1	NOUN
ejpam-4479	324	4	⊊	⊊	VERB
ejpam-4479	324	5	τ2	τ2	NOUN
ejpam-4479	324	6	⊊	⊊	NOUN
ejpam-4479	324	7	τ3	τ3	NOUN
ejpam-4479	324	8	⊊	⊊	AUX
ejpam-4479	324	9	τ4	τ4	PROPN
ejpam-4479	324	10	.	.	PUNCT
ejpam-4479	325	1	define	define	VERB
ejpam-4479	325	2	a	a	DET
ejpam-4479	325	3	soft	soft	ADJ
ejpam-4479	325	4	set	set	NOUN
ejpam-4479	325	5	(	(	PUNCT
ejpam-4479	325	6	f	f	X
ejpam-4479	325	7	,	,	PUNCT
ejpam-4479	325	8	a	a	PRON
ejpam-4479	325	9	)	)	PUNCT
ejpam-4479	325	10	as	as	SCONJ
ejpam-4479	325	11	follows	follow	VERB
ejpam-4479	325	12	:	:	PUNCT
ejpam-4479	325	13	(	(	PUNCT
ejpam-4479	325	14	f	f	X
ejpam-4479	325	15	,	,	PUNCT
ejpam-4479	325	16	a	a	PRON
ejpam-4479	325	17	)	)	PUNCT
ejpam-4479	325	18	=	=	SYM
ejpam-4479	325	19	{	{	PUNCT
ejpam-4479	325	20	(	(	PUNCT
ejpam-4479	325	21	0	0	NUM
ejpam-4479	325	22	,	,	PUNCT
ejpam-4479	325	23	τ1	τ1	NOUN
ejpam-4479	325	24	)	)	PUNCT
ejpam-4479	325	25	,	,	PUNCT
ejpam-4479	325	26	(	(	PUNCT
ejpam-4479	325	27	1	1	NUM
ejpam-4479	325	28	,	,	PUNCT
ejpam-4479	325	29	τ2	τ2	NOUN
ejpam-4479	325	30	)	)	PUNCT
ejpam-4479	325	31	,	,	PUNCT
ejpam-4479	325	32	)	)	PUNCT
ejpam-4479	325	33	(	(	PUNCT
ejpam-4479	325	34	2	2	NUM
ejpam-4479	325	35	,	,	PUNCT
ejpam-4479	325	36	τ3	τ3	NOUN
ejpam-4479	325	37	)	)	PUNCT
ejpam-4479	325	38	,	,	PUNCT
ejpam-4479	325	39	(	(	PUNCT
ejpam-4479	325	40	3	3	NUM
ejpam-4479	325	41	,	,	PUNCT
ejpam-4479	325	42	τ4	τ4	NOUN
ejpam-4479	325	43	)	)	PUNCT
ejpam-4479	325	44	}	}	PUNCT
ejpam-4479	325	45	.	.	PUNCT
ejpam-4479	326	1	by	by	ADP
ejpam-4479	326	2	routine	routine	ADJ
ejpam-4479	326	3	calculations	calculation	NOUN
ejpam-4479	326	4	,	,	PUNCT
ejpam-4479	326	5	(	(	PUNCT
ejpam-4479	326	6	f	f	X
ejpam-4479	326	7	,	,	PUNCT
ejpam-4479	326	8	a	a	PRON
ejpam-4479	326	9	)	)	PUNCT
ejpam-4479	326	10	is	be	AUX
ejpam-4479	326	11	not	not	PART
ejpam-4479	326	12	a	a	DET
ejpam-4479	326	13	union	union	NOUN
ejpam-4479	326	14	-	-	PUNCT
ejpam-4479	326	15	soft	soft	ADJ
ejpam-4479	326	16	hyper	hyper	ADJ
ejpam-4479	326	17	gr	gr	NOUN
ejpam-4479	326	18	-	-	NOUN
ejpam-4479	326	19	algebra	algebra	NOUN
ejpam-4479	326	20	since	since	SCONJ
ejpam-4479	326	21	fa(0	fa(0	ADJ
ejpam-4479	326	22	⊛	⊛	NUM
ejpam-4479	326	23	0	0	NUM
ejpam-4479	326	24	)	)	PUNCT
ejpam-4479	326	25	=	=	SYM
ejpam-4479	326	26	τ2	τ2	VERB
ejpam-4479	326	27	⊈	⊈	NUM
ejpam-4479	326	28	fa(0	fa(0	NOUN
ejpam-4479	326	29	)	)	PUNCT
ejpam-4479	326	30	∪	∪	ADP
ejpam-4479	326	31	fa(0	fa(0	NOUN
ejpam-4479	326	32	)	)	PUNCT
ejpam-4479	326	33	=	=	SYM
ejpam-4479	326	34	τ1	τ1	NOUN
ejpam-4479	326	35	.	.	PUNCT
ejpam-4479	327	1	theorem	theorem	VERB
ejpam-4479	327	2	16	16	NUM
ejpam-4479	327	3	.	.	PUNCT
ejpam-4479	328	1	let	let	VERB
ejpam-4479	328	2	e	e	PRON
ejpam-4479	328	3	be	be	AUX
ejpam-4479	328	4	a	a	DET
ejpam-4479	328	5	hyper	hyper	ADJ
ejpam-4479	328	6	gr	gr	NOUN
ejpam-4479	328	7	-	-	NOUN
ejpam-4479	328	8	algebra	algebra	NOUN
ejpam-4479	328	9	.	.	PUNCT
ejpam-4479	329	1	given	give	VERB
ejpam-4479	329	2	a	a	DET
ejpam-4479	329	3	hyper	hyper	ADJ
ejpam-4479	329	4	subgr	subgr	NOUN
ejpam-4479	329	5	-	-	PUNCT
ejpam-4479	329	6	algebra	algebra	NOUN
ejpam-4479	329	7	a	a	PRON
ejpam-4479	329	8	of	of	ADP
ejpam-4479	329	9	e	e	NOUN
ejpam-4479	329	10	,	,	PUNCT
ejpam-4479	329	11	let	let	VERB
ejpam-4479	329	12	(	(	PUNCT
ejpam-4479	329	13	f	f	X
ejpam-4479	329	14	,	,	PUNCT
ejpam-4479	329	15	a	a	PRON
ejpam-4479	329	16	)	)	PUNCT
ejpam-4479	329	17	∈	∈	PROPN
ejpam-4479	329	18	s(u	s(u	PROPN
ejpam-4479	329	19	)	)	PUNCT
ejpam-4479	329	20	.	.	PUNCT
ejpam-4479	330	1	then	then	ADV
ejpam-4479	330	2	(	(	PUNCT
ejpam-4479	330	3	f	f	X
ejpam-4479	330	4	,	,	PUNCT
ejpam-4479	330	5	a	a	PRON
ejpam-4479	330	6	)	)	PUNCT
ejpam-4479	330	7	is	be	AUX
ejpam-4479	330	8	a	a	DET
ejpam-4479	330	9	union	union	NOUN
ejpam-4479	330	10	-	-	PUNCT
ejpam-4479	330	11	soft	soft	ADJ
ejpam-4479	330	12	hyper	hyper	ADJ
ejpam-4479	330	13	gr	gr	NOUN
ejpam-4479	330	14	-	-	NOUN
ejpam-4479	330	15	algebra	algebra	NOUN
ejpam-4479	330	16	over	over	ADP
ejpam-4479	330	17	u	u	NOUN
ejpam-4479	330	18	if	if	SCONJ
ejpam-4479	331	1	and	and	CCONJ
ejpam-4479	331	2	only	only	ADV
ejpam-4479	331	3	if	if	SCONJ
ejpam-4479	331	4	the	the	DET
ejpam-4479	331	5	nonempty	nonempty	ADJ
ejpam-4479	331	6	τ	τ	X
ejpam-4479	331	7	-exclusive	-exclusive	ADJ
ejpam-4479	331	8	set	set	NOUN
ejpam-4479	331	9	of	of	ADP
ejpam-4479	331	10	(	(	PUNCT
ejpam-4479	331	11	f	f	X
ejpam-4479	331	12	,	,	PUNCT
ejpam-4479	331	13	a	a	PRON
ejpam-4479	331	14	)	)	PUNCT
ejpam-4479	331	15	is	be	AUX
ejpam-4479	331	16	a	a	DET
ejpam-4479	331	17	hyper	hyper	ADJ
ejpam-4479	331	18	subgr	subgr	NOUN
ejpam-4479	331	19	-	-	PUNCT
ejpam-4479	331	20	algebra	algebra	NOUN
ejpam-4479	331	21	of	of	ADP
ejpam-4479	331	22	a	a	PRON
ejpam-4479	331	23	for	for	ADP
ejpam-4479	331	24	all	all	DET
ejpam-4479	331	25	τ	τ	PROPN
ejpam-4479	331	26	⊆	⊆	NUM
ejpam-4479	331	27	u	u	NOUN
ejpam-4479	331	28	.	.	PUNCT
ejpam-4479	332	1	m.k	m.k	PROPN
ejpam-4479	332	2	.	.	PUNCT
ejpam-4479	332	3	engcot	engcot	PROPN
ejpam-4479	332	4	,	,	PUNCT
ejpam-4479	332	5	g.	g.	PROPN
ejpam-4479	332	6	petalcorin	petalcorin	PROPN
ejpam-4479	332	7	/	/	SYM
ejpam-4479	332	8	eur	eur	PROPN
ejpam-4479	332	9	.	.	PUNCT
ejpam-4479	333	1	j.	j.	PROPN
ejpam-4479	333	2	pure	pure	PROPN
ejpam-4479	333	3	appl	appl	PROPN
ejpam-4479	333	4	.	.	PROPN
ejpam-4479	333	5	math	math	PROPN
ejpam-4479	333	6	,	,	PUNCT
ejpam-4479	333	7	15	15	NUM
ejpam-4479	333	8	(	(	PUNCT
ejpam-4479	333	9	4	4	NUM
ejpam-4479	333	10	)	)	PUNCT
ejpam-4479	333	11	(	(	PUNCT
ejpam-4479	333	12	2022	2022	NUM
ejpam-4479	333	13	)	)	PUNCT
ejpam-4479	333	14	,	,	PUNCT
ejpam-4479	333	15	1482	1482	NUM
ejpam-4479	333	16	-	-	SYM
ejpam-4479	333	17	1497	1497	NUM
ejpam-4479	333	18	1495	1495	NUM
ejpam-4479	333	19	proof	proof	NOUN
ejpam-4479	333	20	:	:	PUNCT
ejpam-4479	333	21	assume	assume	VERB
ejpam-4479	333	22	(	(	PUNCT
ejpam-4479	333	23	f	f	X
ejpam-4479	333	24	,	,	PUNCT
ejpam-4479	333	25	a	a	PRON
ejpam-4479	333	26	)	)	PUNCT
ejpam-4479	333	27	is	be	AUX
ejpam-4479	333	28	the	the	DET
ejpam-4479	333	29	union	union	NOUN
ejpam-4479	333	30	-	-	PUNCT
ejpam-4479	333	31	soft	soft	ADJ
ejpam-4479	333	32	hyper	hyper	ADJ
ejpam-4479	333	33	gr	gr	NOUN
ejpam-4479	333	34	-	-	NOUN
ejpam-4479	333	35	algebra	algebra	NOUN
ejpam-4479	333	36	over	over	ADP
ejpam-4479	333	37	u	u	PROPN
ejpam-4479	333	38	.	.	PUNCT
ejpam-4479	334	1	let	let	VERB
ejpam-4479	334	2	τ	τ	PROPN
ejpam-4479	334	3	⊆	⊆	NUM
ejpam-4479	334	4	u	u	NOUN
ejpam-4479	334	5	and	and	CCONJ
ejpam-4479	334	6	x	x	NOUN
ejpam-4479	334	7	,	,	PUNCT
ejpam-4479	334	8	y	y	PROPN
ejpam-4479	334	9	∈	∈	PROPN
ejpam-4479	334	10	e((f	e((f	NOUN
ejpam-4479	334	11	,	,	PUNCT
ejpam-4479	334	12	a	a	PRON
ejpam-4479	334	13	)	)	PUNCT
ejpam-4479	334	14	;	;	PUNCT
ejpam-4479	334	15	τ	τ	PROPN
ejpam-4479	334	16	)	)	PUNCT
ejpam-4479	334	17	.	.	PUNCT
ejpam-4479	335	1	then	then	ADV
ejpam-4479	335	2	fa(x	fa(x	NOUN
ejpam-4479	335	3	)	)	PUNCT
ejpam-4479	335	4	⊆	⊆	NUM
ejpam-4479	335	5	τ	τ	X
ejpam-4479	335	6	and	and	CCONJ
ejpam-4479	335	7	fa(y	fa(y	PROPN
ejpam-4479	335	8	)	)	PUNCT
ejpam-4479	335	9	⊆	⊆	NUM
ejpam-4479	335	10	τ	τ	X
ejpam-4479	335	11	.	.	PUNCT
ejpam-4479	336	1	it	it	PRON
ejpam-4479	336	2	follows	follow	VERB
ejpam-4479	336	3	from	from	ADP
ejpam-4479	336	4	the	the	DET
ejpam-4479	336	5	definition	definition	NOUN
ejpam-4479	336	6	that	that	PRON
ejpam-4479	336	7	fa(x	fa(x	VERB
ejpam-4479	336	8	⊛	⊛	NUM
ejpam-4479	336	9	y	y	NOUN
ejpam-4479	336	10	)	)	PUNCT
ejpam-4479	336	11	⊆	⊆	NUM
ejpam-4479	336	12	fa(x	fa(x	NOUN
ejpam-4479	336	13	)	)	PUNCT
ejpam-4479	336	14	∪	∪	ADP
ejpam-4479	336	15	fa(y	fa(y	PROPN
ejpam-4479	336	16	)	)	PUNCT
ejpam-4479	336	17	⊆	⊆	NUM
ejpam-4479	336	18	τ	τ	X
ejpam-4479	336	19	.	.	PUNCT
ejpam-4479	337	1	hence	hence	ADV
ejpam-4479	337	2	,	,	PUNCT
ejpam-4479	337	3	x	x	PROPN
ejpam-4479	337	4	⊛	⊛	ADV
ejpam-4479	337	5	y	y	PROPN
ejpam-4479	337	6	⊆	⊆	NUM
ejpam-4479	337	7	e((f	e((f	NOUN
ejpam-4479	337	8	,	,	PUNCT
ejpam-4479	337	9	a	a	PRON
ejpam-4479	337	10	)	)	PUNCT
ejpam-4479	337	11	;	;	PUNCT
ejpam-4479	337	12	τ	τ	X
ejpam-4479	337	13	)	)	PUNCT
ejpam-4479	337	14	and	and	CCONJ
ejpam-4479	337	15	so	so	ADV
ejpam-4479	337	16	e((f	e((f	NOUN
ejpam-4479	337	17	,	,	PUNCT
ejpam-4479	337	18	a	a	PRON
ejpam-4479	337	19	)	)	PUNCT
ejpam-4479	337	20	;	;	PUNCT
ejpam-4479	337	21	τ	τ	X
ejpam-4479	337	22	)	)	PUNCT
ejpam-4479	337	23	is	be	AUX
ejpam-4479	337	24	a	a	DET
ejpam-4479	337	25	hyper	hyper	ADJ
ejpam-4479	337	26	subgr	subgr	NOUN
ejpam-4479	337	27	-	-	PUNCT
ejpam-4479	337	28	algebra	algebra	NOUN
ejpam-4479	337	29	.	.	PUNCT
ejpam-4479	338	1	conversely	conversely	ADV
ejpam-4479	338	2	,	,	PUNCT
ejpam-4479	338	3	suppose	suppose	VERB
ejpam-4479	338	4	that	that	SCONJ
ejpam-4479	338	5	the	the	DET
ejpam-4479	338	6	nonempty	nonempty	ADJ
ejpam-4479	338	7	τ	τ	X
ejpam-4479	338	8	-exclusive	-exclusive	ADJ
ejpam-4479	338	9	set	set	NOUN
ejpam-4479	338	10	of	of	ADP
ejpam-4479	338	11	(	(	PUNCT
ejpam-4479	338	12	f	f	X
ejpam-4479	338	13	,	,	PUNCT
ejpam-4479	338	14	a	a	PRON
ejpam-4479	338	15	)	)	PUNCT
ejpam-4479	338	16	is	be	AUX
ejpam-4479	338	17	a	a	DET
ejpam-4479	338	18	hyper	hyper	ADJ
ejpam-4479	338	19	subgr	subgr	NOUN
ejpam-4479	338	20	-	-	PUNCT
ejpam-4479	338	21	algebra	algebra	NOUN
ejpam-4479	338	22	of	of	ADP
ejpam-4479	338	23	a	a	PRON
ejpam-4479	338	24	for	for	ADP
ejpam-4479	338	25	all	all	PRON
ejpam-4479	338	26	τ	τ	PROPN
ejpam-4479	338	27	⊆	⊆	NUM
ejpam-4479	338	28	u	u	NOUN
ejpam-4479	338	29	.	.	PUNCT
ejpam-4479	339	1	let	let	VERB
ejpam-4479	339	2	x	x	PRON
ejpam-4479	339	3	,	,	PUNCT
ejpam-4479	339	4	y	y	PROPN
ejpam-4479	339	5	∈	∈	PROPN
ejpam-4479	339	6	a	a	DET
ejpam-4479	339	7	such	such	ADJ
ejpam-4479	339	8	that	that	PRON
ejpam-4479	339	9	fa(x	fa(x	NOUN
ejpam-4479	339	10	)	)	PUNCT
ejpam-4479	339	11	=	=	SYM
ejpam-4479	339	12	τ1	τ1	NOUN
ejpam-4479	339	13	and	and	CCONJ
ejpam-4479	339	14	fa(y	fa(y	NOUN
ejpam-4479	339	15	)	)	PUNCT
ejpam-4479	340	1	=	=	SYM
ejpam-4479	340	2	τ2	τ2	NOUN
ejpam-4479	340	3	.	.	PUNCT
ejpam-4479	341	1	take	take	VERB
ejpam-4479	341	2	τ	τ	PROPN
ejpam-4479	341	3	=	=	SYM
ejpam-4479	341	4	τ1	τ1	PROPN
ejpam-4479	341	5	∪	∪	X
ejpam-4479	341	6	τ2	τ2	NOUN
ejpam-4479	341	7	.	.	PUNCT
ejpam-4479	342	1	then	then	ADV
ejpam-4479	342	2	x	x	X
ejpam-4479	342	3	,	,	PUNCT
ejpam-4479	342	4	y	y	PROPN
ejpam-4479	342	5	∈	∈	PROPN
ejpam-4479	342	6	e((f	e((f	NOUN
ejpam-4479	342	7	,	,	PUNCT
ejpam-4479	342	8	a	a	PRON
ejpam-4479	342	9	)	)	PUNCT
ejpam-4479	342	10	;	;	PUNCT
ejpam-4479	342	11	τ	τ	X
ejpam-4479	342	12	)	)	PUNCT
ejpam-4479	342	13	and	and	CCONJ
ejpam-4479	342	14	so	so	ADV
ejpam-4479	342	15	x	x	SYM
ejpam-4479	342	16	⊛	⊛	ADJ
ejpam-4479	342	17	y	y	PROPN
ejpam-4479	342	18	⊆	⊆	NUM
ejpam-4479	342	19	e((f	e((f	NOUN
ejpam-4479	342	20	,	,	PUNCT
ejpam-4479	342	21	a	a	PRON
ejpam-4479	342	22	)	)	PUNCT
ejpam-4479	342	23	;	;	PUNCT
ejpam-4479	342	24	τ	τ	PROPN
ejpam-4479	342	25	)	)	PUNCT
ejpam-4479	342	26	.	.	PUNCT
ejpam-4479	343	1	thus	thus	ADV
ejpam-4479	343	2	,	,	PUNCT
ejpam-4479	343	3	fa(x	fa(x	VERB
ejpam-4479	343	4	⊛	⊛	NUM
ejpam-4479	343	5	y	y	NOUN
ejpam-4479	343	6	)	)	PUNCT
ejpam-4479	343	7	⊆	⊆	NUM
ejpam-4479	343	8	τ	τ	X
ejpam-4479	343	9	=	=	PUNCT
ejpam-4479	343	10	τ1	τ1	PROPN
ejpam-4479	343	11	∪	∪	NOUN
ejpam-4479	343	12	τ2	τ2	NOUN
ejpam-4479	343	13	=	=	SYM
ejpam-4479	343	14	fa(x	fa(x	NOUN
ejpam-4479	343	15	)	)	PUNCT
ejpam-4479	343	16	∪	∪	ADP
ejpam-4479	343	17	fa(y	fa(y	PROPN
ejpam-4479	343	18	)	)	PUNCT
ejpam-4479	343	19	.	.	PUNCT
ejpam-4479	344	1	hence	hence	ADV
ejpam-4479	344	2	,	,	PUNCT
ejpam-4479	344	3	(	(	PUNCT
ejpam-4479	344	4	f	f	X
ejpam-4479	344	5	,	,	PUNCT
ejpam-4479	344	6	a	a	PRON
ejpam-4479	344	7	)	)	PUNCT
ejpam-4479	344	8	is	be	AUX
ejpam-4479	344	9	a	a	DET
ejpam-4479	344	10	union	union	NOUN
ejpam-4479	344	11	-	-	PUNCT
ejpam-4479	344	12	soft	soft	ADJ
ejpam-4479	344	13	hyper	hyper	ADJ
ejpam-4479	344	14	gr	gr	NOUN
ejpam-4479	344	15	-	-	PUNCT
ejpam-4479	344	16	algebra	algebra	NOUN
ejpam-4479	344	17	.	.	PUNCT
ejpam-4479	345	1	theorem	theorem	NOUN
ejpam-4479	345	2	17	17	NUM
ejpam-4479	345	3	.	.	PUNCT
ejpam-4479	346	1	let	let	VERB
ejpam-4479	346	2	e	e	PRON
ejpam-4479	346	3	be	be	AUX
ejpam-4479	346	4	a	a	DET
ejpam-4479	346	5	hyper	hyper	ADJ
ejpam-4479	346	6	gr	gr	NOUN
ejpam-4479	346	7	-	-	NOUN
ejpam-4479	346	8	algebra	algebra	NOUN
ejpam-4479	346	9	.	.	PUNCT
ejpam-4479	347	1	given	give	VERB
ejpam-4479	347	2	a	a	DET
ejpam-4479	347	3	hyper	hyper	ADJ
ejpam-4479	347	4	subgr	subgr	NOUN
ejpam-4479	347	5	-	-	PUNCT
ejpam-4479	347	6	algebra	algebra	NOUN
ejpam-4479	347	7	a	a	PRON
ejpam-4479	347	8	of	of	ADP
ejpam-4479	347	9	e	e	NOUN
ejpam-4479	347	10	,	,	PUNCT
ejpam-4479	347	11	let	let	VERB
ejpam-4479	347	12	(	(	PUNCT
ejpam-4479	347	13	f	f	X
ejpam-4479	347	14	,	,	PUNCT
ejpam-4479	347	15	a	a	PRON
ejpam-4479	347	16	)	)	PUNCT
ejpam-4479	347	17	∈	∈	PROPN
ejpam-4479	347	18	s(u	s(u	PROPN
ejpam-4479	347	19	)	)	PUNCT
ejpam-4479	347	20	.	.	PUNCT
ejpam-4479	348	1	suppose	suppose	VERB
ejpam-4479	348	2	(	(	PUNCT
ejpam-4479	348	3	f	f	X
ejpam-4479	348	4	,	,	PUNCT
ejpam-4479	348	5	a)∗	a)∗	PROPN
ejpam-4479	348	6	∈	∈	PROPN
ejpam-4479	348	7	s(u	s(u	PROPN
ejpam-4479	348	8	)	)	PUNCT
ejpam-4479	348	9	with	with	ADP
ejpam-4479	348	10	approximation	approximation	NOUN
ejpam-4479	348	11	function	function	NOUN
ejpam-4479	348	12	f∗	f∗	NOUN
ejpam-4479	349	1	a	a	PRON
ejpam-4479	349	2	defined	define	VERB
ejpam-4479	349	3	by	by	ADP
ejpam-4479	349	4	f∗	f∗	NOUN
ejpam-4479	349	5	a	a	DET
ejpam-4479	349	6	:	:	PUNCT
ejpam-4479	349	7	e	e	X
ejpam-4479	349	8	→	→	SYM
ejpam-4479	349	9	p	p	X
ejpam-4479	349	10	(	(	PUNCT
ejpam-4479	349	11	u	u	NOUN
ejpam-4479	349	12	)	)	PUNCT
ejpam-4479	349	13	,	,	PUNCT
ejpam-4479	349	14	x	x	X
ejpam-4479	349	15	7−→	7−→	NOUN
ejpam-4479	349	16	{	{	PUNCT
ejpam-4479	349	17	fa(x	fa(x	NOUN
ejpam-4479	349	18	)	)	PUNCT
ejpam-4479	349	19	,	,	PUNCT
ejpam-4479	349	20	if	if	SCONJ
ejpam-4479	349	21	x	x	PROPN
ejpam-4479	349	22	∈	∈	PROPN
ejpam-4479	349	23	e((f	e((f	NOUN
ejpam-4479	349	24	,	,	PUNCT
ejpam-4479	349	25	a	a	PRON
ejpam-4479	349	26	)	)	PUNCT
ejpam-4479	349	27	;	;	PUNCT
ejpam-4479	349	28	τ	τ	X
ejpam-4479	349	29	)	)	PUNCT
ejpam-4479	349	30	u	u	NOUN
ejpam-4479	349	31	,	,	PUNCT
ejpam-4479	349	32	otherwise	otherwise	ADV
ejpam-4479	349	33	.	.	PUNCT
ejpam-4479	350	1	if	if	SCONJ
ejpam-4479	350	2	(	(	PUNCT
ejpam-4479	350	3	f	f	X
ejpam-4479	350	4	,	,	PUNCT
ejpam-4479	350	5	a	a	PRON
ejpam-4479	350	6	)	)	PUNCT
ejpam-4479	350	7	is	be	AUX
ejpam-4479	350	8	a	a	DET
ejpam-4479	350	9	union	union	NOUN
ejpam-4479	350	10	-	-	PUNCT
ejpam-4479	350	11	soft	soft	ADJ
ejpam-4479	350	12	hyper	hyper	ADJ
ejpam-4479	350	13	gr	gr	NOUN
ejpam-4479	350	14	-	-	NOUN
ejpam-4479	350	15	algebra	algebra	NOUN
ejpam-4479	350	16	over	over	ADP
ejpam-4479	350	17	u	u	PROPN
ejpam-4479	350	18	,	,	PUNCT
ejpam-4479	350	19	then	then	ADV
ejpam-4479	350	20	so	so	ADV
ejpam-4479	350	21	is	be	AUX
ejpam-4479	350	22	(	(	PUNCT
ejpam-4479	350	23	f	f	X
ejpam-4479	350	24	,	,	PUNCT
ejpam-4479	350	25	a)∗.	a)∗.	NOUN
ejpam-4479	350	26	proof	proof	NOUN
ejpam-4479	350	27	:	:	PUNCT
ejpam-4479	350	28	since	since	SCONJ
ejpam-4479	350	29	(	(	PUNCT
ejpam-4479	350	30	f	f	X
ejpam-4479	350	31	,	,	PUNCT
ejpam-4479	350	32	a	a	PRON
ejpam-4479	350	33	)	)	PUNCT
ejpam-4479	350	34	is	be	AUX
ejpam-4479	350	35	a	a	DET
ejpam-4479	350	36	union	union	NOUN
ejpam-4479	350	37	-	-	PUNCT
ejpam-4479	350	38	soft	soft	ADJ
ejpam-4479	350	39	hyper	hyper	ADJ
ejpam-4479	350	40	gr	gr	NOUN
ejpam-4479	350	41	-	-	NOUN
ejpam-4479	350	42	algebra	algebra	NOUN
ejpam-4479	350	43	over	over	ADP
ejpam-4479	350	44	u	u	PROPN
ejpam-4479	350	45	,	,	PUNCT
ejpam-4479	350	46	it	it	PRON
ejpam-4479	350	47	follows	follow	VERB
ejpam-4479	350	48	from	from	ADP
ejpam-4479	350	49	theorem	theorem	ADJ
ejpam-4479	350	50	16	16	NUM
ejpam-4479	350	51	that	that	SCONJ
ejpam-4479	350	52	e((f	e((f	ADV
ejpam-4479	350	53	,	,	PUNCT
ejpam-4479	350	54	a	a	PRON
ejpam-4479	350	55	)	)	PUNCT
ejpam-4479	350	56	;	;	PUNCT
ejpam-4479	350	57	τ	τ	X
ejpam-4479	350	58	)	)	PUNCT
ejpam-4479	350	59	is	be	AUX
ejpam-4479	350	60	a	a	DET
ejpam-4479	350	61	hyper	hyper	ADJ
ejpam-4479	350	62	subgr	subgr	NOUN
ejpam-4479	350	63	-	-	PUNCT
ejpam-4479	350	64	algebra	algebra	NOUN
ejpam-4479	350	65	of	of	ADP
ejpam-4479	350	66	a	a	PRON
ejpam-4479	350	67	for	for	ADP
ejpam-4479	350	68	all	all	PRON
ejpam-4479	350	69	τ	τ	PROPN
ejpam-4479	350	70	⊆	⊆	NUM
ejpam-4479	350	71	u	u	NOUN
ejpam-4479	350	72	.	.	PUNCT
ejpam-4479	351	1	let	let	VERB
ejpam-4479	351	2	x	x	PRON
ejpam-4479	351	3	,	,	PUNCT
ejpam-4479	351	4	y	y	PROPN
ejpam-4479	351	5	∈	∈	PROPN
ejpam-4479	351	6	a.	a.	NOUN
ejpam-4479	351	7	if	if	SCONJ
ejpam-4479	351	8	x	x	PROPN
ejpam-4479	351	9	,	,	PUNCT
ejpam-4479	351	10	y	y	PROPN
ejpam-4479	351	11	∈	∈	PROPN
ejpam-4479	351	12	e((f	e((f	NOUN
ejpam-4479	351	13	,	,	PUNCT
ejpam-4479	351	14	a	a	PRON
ejpam-4479	351	15	)	)	PUNCT
ejpam-4479	351	16	;	;	PUNCT
ejpam-4479	351	17	τ	τ	X
ejpam-4479	351	18	)	)	PUNCT
ejpam-4479	351	19	,	,	PUNCT
ejpam-4479	351	20	then	then	ADV
ejpam-4479	351	21	x⊛y	x⊛y	PROPN
ejpam-4479	351	22	⊆	⊆	NUM
ejpam-4479	351	23	e((f	e((f	NOUN
ejpam-4479	351	24	,	,	PUNCT
ejpam-4479	351	25	a	a	PRON
ejpam-4479	351	26	)	)	PUNCT
ejpam-4479	351	27	;	;	PUNCT
ejpam-4479	351	28	τ	τ	X
ejpam-4479	351	29	)	)	PUNCT
ejpam-4479	351	30	and	and	CCONJ
ejpam-4479	351	31	so	so	ADV
ejpam-4479	351	32	f∗	f∗	PROPN
ejpam-4479	351	33	a(x⊛y	a(x⊛y	PROPN
ejpam-4479	351	34	)	)	PUNCT
ejpam-4479	351	35	=	=	SYM
ejpam-4479	352	1	fa(x⊛y	fa(x⊛y	NUM
ejpam-4479	352	2	)	)	PUNCT
ejpam-4479	352	3	⊆	⊆	NUM
ejpam-4479	352	4	fa(x)∪fa(y	fa(x)∪fa(y	PROPN
ejpam-4479	352	5	)	)	PUNCT
ejpam-4479	352	6	=	=	X
ejpam-4479	352	7	f∗	f∗	NOUN
ejpam-4479	352	8	a(x	a(x	NOUN
ejpam-4479	352	9	)	)	PUNCT
ejpam-4479	352	10	∪	∪	NOUN
ejpam-4479	352	11	f∗	f∗	X
ejpam-4479	352	12	a(y	a(y	PROPN
ejpam-4479	352	13	)	)	PUNCT
ejpam-4479	352	14	.	.	PUNCT
ejpam-4479	353	1	x	x	X
ejpam-4479	353	2	/∈	/∈	PUNCT
ejpam-4479	354	1	e((f	e((f	ADJ
ejpam-4479	354	2	,	,	PUNCT
ejpam-4479	354	3	a	a	PRON
ejpam-4479	354	4	)	)	PUNCT
ejpam-4479	354	5	;	;	PUNCT
ejpam-4479	354	6	τ	τ	X
ejpam-4479	354	7	)	)	PUNCT
ejpam-4479	354	8	or	or	CCONJ
ejpam-4479	354	9	y	y	PROPN
ejpam-4479	354	10	/∈	/∈	PUNCT
ejpam-4479	355	1	e((f	e((f	PROPN
ejpam-4479	355	2	,	,	PUNCT
ejpam-4479	355	3	a	a	PRON
ejpam-4479	355	4	)	)	PUNCT
ejpam-4479	355	5	;	;	PUNCT
ejpam-4479	355	6	τ	τ	X
ejpam-4479	355	7	)	)	PUNCT
ejpam-4479	355	8	,	,	PUNCT
ejpam-4479	355	9	then	then	ADV
ejpam-4479	355	10	f∗	f∗	NOUN
ejpam-4479	355	11	a(x	a(x	NOUN
ejpam-4479	355	12	)	)	PUNCT
ejpam-4479	355	13	=	=	SYM
ejpam-4479	355	14	u	u	NOUN
ejpam-4479	355	15	or	or	CCONJ
ejpam-4479	355	16	f∗	f∗	NOUN
ejpam-4479	355	17	a(y	a(y	PROPN
ejpam-4479	355	18	)	)	PUNCT
ejpam-4479	355	19	=	=	SYM
ejpam-4479	355	20	u	u	NOUN
ejpam-4479	355	21	.	.	PUNCT
ejpam-4479	356	1	hence	hence	ADV
ejpam-4479	356	2	,	,	PUNCT
ejpam-4479	356	3	fa(x⊛	fa(x⊛	PROPN
ejpam-4479	356	4	y	y	NOUN
ejpam-4479	356	5	)	)	PUNCT
ejpam-4479	357	1	⊂	⊂	PROPN
ejpam-4479	357	2	u	u	X
ejpam-4479	357	3	=	=	X
ejpam-4479	357	4	f∗	f∗	NOUN
ejpam-4479	357	5	a(x	a(x	NOUN
ejpam-4479	357	6	)	)	PUNCT
ejpam-4479	357	7	∪	∪	NOUN
ejpam-4479	357	8	f∗	f∗	X
ejpam-4479	357	9	a(y	a(y	PROPN
ejpam-4479	357	10	)	)	PUNCT
ejpam-4479	357	11	.	.	PUNCT
ejpam-4479	358	1	therefore	therefore	ADV
ejpam-4479	358	2	,	,	PUNCT
ejpam-4479	358	3	(	(	PUNCT
ejpam-4479	358	4	f	f	X
ejpam-4479	358	5	,	,	PUNCT
ejpam-4479	358	6	a)∗	a)∗	PROPN
ejpam-4479	358	7	is	be	AUX
ejpam-4479	358	8	a	a	DET
ejpam-4479	358	9	union	union	NOUN
ejpam-4479	358	10	-	-	PUNCT
ejpam-4479	358	11	soft	soft	ADJ
ejpam-4479	358	12	hyper	hyper	ADJ
ejpam-4479	358	13	gr	gr	NOUN
ejpam-4479	358	14	-	-	NOUN
ejpam-4479	358	15	algebra	algebra	NOUN
ejpam-4479	358	16	over	over	ADP
ejpam-4479	358	17	u	u	PROPN
ejpam-4479	358	18	.	.	PUNCT
ejpam-4479	359	1	definition	definition	NOUN
ejpam-4479	359	2	19	19	NUM
ejpam-4479	359	3	.	.	PUNCT
ejpam-4479	360	1	let	let	VERB
ejpam-4479	360	2	e	e	PRON
ejpam-4479	360	3	be	be	AUX
ejpam-4479	360	4	a	a	DET
ejpam-4479	360	5	hyper	hyper	ADJ
ejpam-4479	360	6	gr	gr	NOUN
ejpam-4479	360	7	-	-	NOUN
ejpam-4479	360	8	algebra	algebra	NOUN
ejpam-4479	360	9	.	.	PUNCT
ejpam-4479	361	1	given	give	VERB
ejpam-4479	361	2	a	a	DET
ejpam-4479	361	3	hyper	hyper	ADJ
ejpam-4479	361	4	subgr	subgr	NOUN
ejpam-4479	361	5	-	-	PUNCT
ejpam-4479	361	6	algebra	algebra	NOUN
ejpam-4479	361	7	a	a	PRON
ejpam-4479	361	8	of	of	ADP
ejpam-4479	361	9	e	e	NOUN
ejpam-4479	361	10	,	,	PUNCT
ejpam-4479	361	11	let	let	VERB
ejpam-4479	361	12	(	(	PUNCT
ejpam-4479	361	13	f	f	X
ejpam-4479	361	14	,	,	PUNCT
ejpam-4479	361	15	a	a	PRON
ejpam-4479	361	16	)	)	PUNCT
ejpam-4479	361	17	∈	∈	PROPN
ejpam-4479	361	18	s(u	s(u	PROPN
ejpam-4479	361	19	)	)	PUNCT
ejpam-4479	361	20	.	.	PUNCT
ejpam-4479	362	1	then	then	ADV
ejpam-4479	362	2	(	(	PUNCT
ejpam-4479	362	3	f	f	X
ejpam-4479	362	4	,	,	PUNCT
ejpam-4479	362	5	a	a	PRON
ejpam-4479	362	6	)	)	PUNCT
ejpam-4479	362	7	is	be	AUX
ejpam-4479	362	8	called	call	VERB
ejpam-4479	362	9	a	a	DET
ejpam-4479	362	10	union	union	NOUN
ejpam-4479	362	11	-	-	PUNCT
ejpam-4479	362	12	soft	soft	ADJ
ejpam-4479	362	13	hyper	hyper	ADJ
ejpam-4479	362	14	gr	gr	NOUN
ejpam-4479	362	15	-	-	PUNCT
ejpam-4479	362	16	ideal	ideal	NOUN
ejpam-4479	362	17	over	over	ADP
ejpam-4479	362	18	u	u	NOUN
ejpam-4479	362	19	if	if	SCONJ
ejpam-4479	362	20	fa(x	fa(x	NOUN
ejpam-4479	362	21	)	)	PUNCT
ejpam-4479	362	22	satisfies	satisfy	VERB
ejpam-4479	362	23	the	the	DET
ejpam-4479	362	24	following	following	NOUN
ejpam-4479	362	25	:	:	PUNCT
ejpam-4479	362	26	(	(	PUNCT
ejpam-4479	362	27	i	i	NOUN
ejpam-4479	362	28	)	)	PUNCT
ejpam-4479	362	29	fa(0	fa(0	NOUN
ejpam-4479	362	30	)	)	PUNCT
ejpam-4479	362	31	⊆	⊆	NUM
ejpam-4479	362	32	fa(x	fa(x	NOUN
ejpam-4479	362	33	)	)	PUNCT
ejpam-4479	362	34	,	,	PUNCT
ejpam-4479	362	35	∀x	∀x	VERB
ejpam-4479	362	36	∈	∈	PROPN
ejpam-4479	362	37	a	a	DET
ejpam-4479	362	38	(	(	PUNCT
ejpam-4479	362	39	ii	ii	NOUN
ejpam-4479	362	40	)	)	PUNCT
ejpam-4479	362	41	fa(x	fa(x	PROPN
ejpam-4479	362	42	)	)	PUNCT
ejpam-4479	362	43	⊆	⊆	NUM
ejpam-4479	362	44	fa(x⊛	fa(x⊛	NUM
ejpam-4479	362	45	y	y	NOUN
ejpam-4479	362	46	)	)	PUNCT
ejpam-4479	362	47	∪	∪	ADP
ejpam-4479	362	48	fa(y),∀x	fa(y),∀x	PROPN
ejpam-4479	362	49	,	,	PUNCT
ejpam-4479	362	50	y	y	PROPN
ejpam-4479	362	51	∈	∈	PROPN
ejpam-4479	362	52	a.	a.	NOUN
ejpam-4479	362	53	example	example	NOUN
ejpam-4479	362	54	15	15	NUM
ejpam-4479	362	55	.	.	PUNCT
ejpam-4479	362	56	consider	consider	VERB
ejpam-4479	362	57	the	the	DET
ejpam-4479	362	58	hyper	hyper	ADJ
ejpam-4479	362	59	gr	gr	NOUN
ejpam-4479	362	60	-	-	PUNCT
ejpam-4479	362	61	algebra	algebra	NOUN
ejpam-4479	362	62	h	h	NOUN
ejpam-4479	362	63	=	=	SYM
ejpam-4479	362	64	{	{	PUNCT
ejpam-4479	362	65	0	0	NUM
ejpam-4479	362	66	,	,	PUNCT
ejpam-4479	362	67	1	1	NUM
ejpam-4479	362	68	,	,	PUNCT
ejpam-4479	362	69	2	2	NUM
ejpam-4479	362	70	,	,	PUNCT
ejpam-4479	362	71	3	3	NUM
ejpam-4479	362	72	}	}	PUNCT
ejpam-4479	362	73	defined	define	VERB
ejpam-4479	362	74	in	in	ADP
ejpam-4479	362	75	example	example	NOUN
ejpam-4479	362	76	4	4	NUM
ejpam-4479	362	77	.	.	PUNCT
ejpam-4479	363	1	let	let	VERB
ejpam-4479	363	2	τ1	τ1	NOUN
ejpam-4479	363	3	,	,	PUNCT
ejpam-4479	363	4	τ2	τ2	PROPN
ejpam-4479	363	5	,	,	PUNCT
ejpam-4479	363	6	τ3	τ3	NOUN
ejpam-4479	363	7	,	,	PUNCT
ejpam-4479	363	8	τ4	τ4	PROPN
ejpam-4479	363	9	be	be	AUX
ejpam-4479	363	10	subsets	subset	NOUN
ejpam-4479	363	11	of	of	ADP
ejpam-4479	363	12	h	h	NOUN
ejpam-4479	364	1	such	such	ADJ
ejpam-4479	364	2	that	that	PRON
ejpam-4479	364	3	τ1	τ1	NOUN
ejpam-4479	364	4	⊆	⊆	NUM
ejpam-4479	364	5	τ2	τ2	PROPN
ejpam-4479	364	6	⊆	⊆	NUM
ejpam-4479	364	7	τ3	τ3	NOUN
ejpam-4479	364	8	⊆	⊆	NUM
ejpam-4479	364	9	τ4	τ4	NOUN
ejpam-4479	364	10	.	.	PUNCT
ejpam-4479	365	1	define	define	VERB
ejpam-4479	365	2	a	a	DET
ejpam-4479	365	3	soft	soft	ADJ
ejpam-4479	365	4	set	set	NOUN
ejpam-4479	365	5	(	(	PUNCT
ejpam-4479	365	6	f	f	X
ejpam-4479	365	7	,	,	PUNCT
ejpam-4479	365	8	a	a	PRON
ejpam-4479	365	9	)	)	PUNCT
ejpam-4479	365	10	as	as	SCONJ
ejpam-4479	365	11	follows	follow	VERB
ejpam-4479	365	12	:	:	PUNCT
ejpam-4479	365	13	(	(	PUNCT
ejpam-4479	365	14	f	f	X
ejpam-4479	365	15	,	,	PUNCT
ejpam-4479	365	16	a	a	PRON
ejpam-4479	365	17	)	)	PUNCT
ejpam-4479	365	18	=	=	SYM
ejpam-4479	365	19	{	{	PUNCT
ejpam-4479	365	20	(	(	PUNCT
ejpam-4479	365	21	0	0	NUM
ejpam-4479	365	22	,	,	PUNCT
ejpam-4479	365	23	τ1	τ1	NOUN
ejpam-4479	365	24	)	)	PUNCT
ejpam-4479	365	25	,	,	PUNCT
ejpam-4479	365	26	(	(	PUNCT
ejpam-4479	365	27	1	1	NUM
ejpam-4479	365	28	,	,	PUNCT
ejpam-4479	365	29	τ2	τ2	NOUN
ejpam-4479	365	30	)	)	PUNCT
ejpam-4479	365	31	,	,	PUNCT
ejpam-4479	365	32	(	(	PUNCT
ejpam-4479	365	33	3	3	NUM
ejpam-4479	365	34	,	,	PUNCT
ejpam-4479	365	35	τ3	τ3	PROPN
ejpam-4479	365	36	)	)	PUNCT
ejpam-4479	365	37	,	,	PUNCT
ejpam-4479	365	38	(	(	PUNCT
ejpam-4479	365	39	4	4	NUM
ejpam-4479	365	40	,	,	PUNCT
ejpam-4479	365	41	τ4	τ4	NOUN
ejpam-4479	365	42	)	)	PUNCT
ejpam-4479	365	43	}	}	PUNCT
ejpam-4479	365	44	.	.	PUNCT
ejpam-4479	366	1	by	by	ADP
ejpam-4479	366	2	routine	routine	ADJ
ejpam-4479	366	3	calculations	calculation	NOUN
ejpam-4479	366	4	,	,	PUNCT
ejpam-4479	366	5	(	(	PUNCT
ejpam-4479	366	6	f	f	X
ejpam-4479	366	7	,	,	PUNCT
ejpam-4479	366	8	a	a	PRON
ejpam-4479	366	9	)	)	PUNCT
ejpam-4479	366	10	is	be	AUX
ejpam-4479	366	11	a	a	DET
ejpam-4479	366	12	union	union	NOUN
ejpam-4479	366	13	-	-	PUNCT
ejpam-4479	366	14	soft	soft	ADJ
ejpam-4479	366	15	hyper	hyper	ADJ
ejpam-4479	366	16	gr	gr	NOUN
ejpam-4479	366	17	-	-	PUNCT
ejpam-4479	366	18	ideal	ideal	NOUN
ejpam-4479	366	19	.	.	PUNCT
ejpam-4479	366	20	example	example	NOUN
ejpam-4479	367	1	16	16	NUM
ejpam-4479	367	2	.	.	PUNCT
ejpam-4479	368	1	consider	consider	VERB
ejpam-4479	368	2	the	the	DET
ejpam-4479	368	3	h	h	NOUN
ejpam-4479	368	4	=	=	PUNCT
ejpam-4479	368	5	{	{	PUNCT
ejpam-4479	368	6	0	0	NUM
ejpam-4479	368	7	,	,	PUNCT
ejpam-4479	368	8	1	1	NUM
ejpam-4479	368	9	,	,	PUNCT
ejpam-4479	368	10	2	2	NUM
ejpam-4479	368	11	}	}	PUNCT
ejpam-4479	368	12	defined	define	VERB
ejpam-4479	368	13	in	in	ADP
ejpam-4479	368	14	the	the	DET
ejpam-4479	368	15	cayley	cayley	ADJ
ejpam-4479	368	16	table	table	NOUN
ejpam-4479	368	17	below	below	ADV
ejpam-4479	368	18	.	.	PUNCT
ejpam-4479	369	1	⊛	⊛	NUM
ejpam-4479	369	2	0	0	NUM
ejpam-4479	369	3	1	1	NUM
ejpam-4479	369	4	2	2	NUM
ejpam-4479	369	5	0	0	NUM
ejpam-4479	369	6	{	{	PUNCT
ejpam-4479	369	7	0	0	NUM
ejpam-4479	369	8	}	}	PUNCT
ejpam-4479	369	9	{	{	PUNCT
ejpam-4479	369	10	0	0	NUM
ejpam-4479	369	11	}	}	PUNCT
ejpam-4479	369	12	{	{	PUNCT
ejpam-4479	369	13	0	0	NUM
ejpam-4479	369	14	}	}	SYM
ejpam-4479	369	15	1	1	NUM
ejpam-4479	369	16	{	{	PUNCT
ejpam-4479	369	17	0,1	0,1	NUM
ejpam-4479	369	18	}	}	PUNCT
ejpam-4479	369	19	{	{	PUNCT
ejpam-4479	369	20	0,1	0,1	NOUN
ejpam-4479	369	21	}	}	PUNCT
ejpam-4479	369	22	{	{	PUNCT
ejpam-4479	369	23	0,1	0,1	NOUN
ejpam-4479	369	24	}	}	SYM
ejpam-4479	369	25	2	2	NUM
ejpam-4479	369	26	{	{	PUNCT
ejpam-4479	369	27	0,2	0,2	NUM
ejpam-4479	369	28	}	}	PUNCT
ejpam-4479	369	29	{	{	PUNCT
ejpam-4479	369	30	0,1	0,1	NOUN
ejpam-4479	369	31	}	}	PUNCT
ejpam-4479	369	32	{	{	PUNCT
ejpam-4479	369	33	0,1,2	0,1,2	NOUN
ejpam-4479	369	34	}	}	PUNCT
ejpam-4479	369	35	.	.	PUNCT
ejpam-4479	370	1	references	reference	NOUN
ejpam-4479	370	2	1496	1496	NUM
ejpam-4479	370	3	by	by	ADP
ejpam-4479	370	4	routine	routine	ADJ
ejpam-4479	370	5	calculations	calculation	NOUN
ejpam-4479	370	6	,	,	PUNCT
ejpam-4479	370	7	(	(	PUNCT
ejpam-4479	370	8	h;⊛	h;⊛	X
ejpam-4479	370	9	,	,	PUNCT
ejpam-4479	370	10	0	0	NUM
ejpam-4479	370	11	)	)	PUNCT
ejpam-4479	370	12	is	be	AUX
ejpam-4479	370	13	hyper	hyper	ADJ
ejpam-4479	370	14	gr	gr	NOUN
ejpam-4479	370	15	-	-	PUNCT
ejpam-4479	370	16	algebra	algebra	NOUN
ejpam-4479	370	17	.	.	PUNCT
ejpam-4479	371	1	let	let	VERB
ejpam-4479	371	2	τ1	τ1	NOUN
ejpam-4479	371	3	,	,	PUNCT
ejpam-4479	371	4	τ2	τ2	PROPN
ejpam-4479	371	5	,	,	PUNCT
ejpam-4479	371	6	τ3	τ3	NOUN
ejpam-4479	371	7	be	be	VERB
ejpam-4479	371	8	subsets	subset	NOUN
ejpam-4479	371	9	of	of	ADP
ejpam-4479	371	10	h	h	NOUN
ejpam-4479	371	11	such	such	ADJ
ejpam-4479	371	12	that	that	DET
ejpam-4479	371	13	τ1	τ1	NOUN
ejpam-4479	371	14	⊊	⊊	VERB
ejpam-4479	371	15	τ2	τ2	NOUN
ejpam-4479	371	16	⊊	⊊	NOUN
ejpam-4479	371	17	τ3	τ3	NOUN
ejpam-4479	371	18	.	.	PUNCT
ejpam-4479	372	1	define	define	VERB
ejpam-4479	372	2	a	a	DET
ejpam-4479	372	3	soft	soft	ADJ
ejpam-4479	372	4	set	set	NOUN
ejpam-4479	372	5	(	(	PUNCT
ejpam-4479	372	6	f	f	X
ejpam-4479	372	7	,	,	PUNCT
ejpam-4479	372	8	a	a	PRON
ejpam-4479	372	9	)	)	PUNCT
ejpam-4479	372	10	as	as	SCONJ
ejpam-4479	372	11	follows	follow	VERB
ejpam-4479	372	12	:	:	PUNCT
ejpam-4479	372	13	(	(	PUNCT
ejpam-4479	372	14	f	f	X
ejpam-4479	372	15	,	,	PUNCT
ejpam-4479	372	16	a	a	PRON
ejpam-4479	372	17	)	)	PUNCT
ejpam-4479	372	18	=	=	SYM
ejpam-4479	372	19	{	{	PUNCT
ejpam-4479	372	20	(	(	PUNCT
ejpam-4479	372	21	0	0	NUM
ejpam-4479	372	22	,	,	PUNCT
ejpam-4479	372	23	τ1	τ1	NOUN
ejpam-4479	372	24	)	)	PUNCT
ejpam-4479	372	25	,	,	PUNCT
ejpam-4479	372	26	(	(	PUNCT
ejpam-4479	372	27	1	1	NUM
ejpam-4479	372	28	,	,	PUNCT
ejpam-4479	372	29	τ2	τ2	NOUN
ejpam-4479	372	30	)	)	PUNCT
ejpam-4479	372	31	,	,	PUNCT
ejpam-4479	372	32	(	(	PUNCT
ejpam-4479	372	33	2	2	NUM
ejpam-4479	372	34	,	,	PUNCT
ejpam-4479	372	35	τ3	τ3	NOUN
ejpam-4479	372	36	)	)	PUNCT
ejpam-4479	372	37	}	}	PUNCT
ejpam-4479	372	38	.	.	PUNCT
ejpam-4479	373	1	by	by	ADP
ejpam-4479	373	2	routine	routine	ADJ
ejpam-4479	373	3	calculations	calculation	NOUN
ejpam-4479	373	4	,	,	PUNCT
ejpam-4479	373	5	(	(	PUNCT
ejpam-4479	373	6	f	f	X
ejpam-4479	373	7	,	,	PUNCT
ejpam-4479	373	8	a	a	PRON
ejpam-4479	373	9	)	)	PUNCT
ejpam-4479	373	10	is	be	AUX
ejpam-4479	373	11	not	not	PART
ejpam-4479	373	12	a	a	DET
ejpam-4479	373	13	union	union	NOUN
ejpam-4479	373	14	-	-	PUNCT
ejpam-4479	373	15	soft	soft	ADJ
ejpam-4479	373	16	hyper	hyper	ADJ
ejpam-4479	373	17	gr	gr	NOUN
ejpam-4479	373	18	-	-	PUNCT
ejpam-4479	373	19	ideal	ideal	NOUN
ejpam-4479	373	20	since	since	SCONJ
ejpam-4479	373	21	f	f	PROPN
ejpam-4479	373	22	(	(	PUNCT
ejpam-4479	373	23	2	2	NUM
ejpam-4479	373	24	)	)	PUNCT
ejpam-4479	373	25	=	=	VERB
ejpam-4479	373	26	τ3	τ3	NOUN
ejpam-4479	373	27	⊈	⊈	PROPN
ejpam-4479	373	28	f	f	X
ejpam-4479	373	29	(	(	PUNCT
ejpam-4479	373	30	2⊛	2⊛	NUM
ejpam-4479	373	31	1	1	NUM
ejpam-4479	373	32	)	)	PUNCT
ejpam-4479	373	33	∪	∪	PROPN
ejpam-4479	373	34	f	f	X
ejpam-4479	373	35	(	(	PUNCT
ejpam-4479	373	36	1	1	NUM
ejpam-4479	373	37	)	)	PUNCT
ejpam-4479	373	38	=	=	SYM
ejpam-4479	373	39	τ2	τ2	PROPN
ejpam-4479	373	40	.	.	PUNCT
ejpam-4479	374	1	theorem	theorem	VERB
ejpam-4479	374	2	18	18	NUM
ejpam-4479	374	3	.	.	PUNCT
ejpam-4479	375	1	let	let	VERB
ejpam-4479	375	2	e	e	PRON
ejpam-4479	375	3	be	be	AUX
ejpam-4479	375	4	a	a	DET
ejpam-4479	375	5	hyper	hyper	ADJ
ejpam-4479	375	6	gr	gr	NOUN
ejpam-4479	375	7	-	-	NOUN
ejpam-4479	375	8	algebra	algebra	NOUN
ejpam-4479	375	9	.	.	PUNCT
ejpam-4479	376	1	given	give	VERB
ejpam-4479	376	2	a	a	DET
ejpam-4479	376	3	hyper	hyper	ADJ
ejpam-4479	376	4	subgr	subgr	NOUN
ejpam-4479	376	5	-	-	PUNCT
ejpam-4479	376	6	algebra	algebra	NOUN
ejpam-4479	376	7	a	a	PRON
ejpam-4479	376	8	of	of	ADP
ejpam-4479	376	9	e	e	NOUN
ejpam-4479	376	10	,	,	PUNCT
ejpam-4479	376	11	suppose	suppose	VERB
ejpam-4479	376	12	(	(	PUNCT
ejpam-4479	376	13	f	f	X
ejpam-4479	376	14	,	,	PUNCT
ejpam-4479	376	15	a	a	PRON
ejpam-4479	376	16	)	)	PUNCT
ejpam-4479	376	17	⊆	⊆	NUM
ejpam-4479	376	18	s(u	s(u	PROPN
ejpam-4479	376	19	)	)	PUNCT
ejpam-4479	376	20	.	.	PUNCT
ejpam-4479	377	1	if	if	SCONJ
ejpam-4479	377	2	(	(	PUNCT
ejpam-4479	377	3	f	f	X
ejpam-4479	377	4	,	,	PUNCT
ejpam-4479	377	5	a	a	PRON
ejpam-4479	377	6	)	)	PUNCT
ejpam-4479	377	7	is	be	AUX
ejpam-4479	377	8	a	a	DET
ejpam-4479	377	9	union	union	NOUN
ejpam-4479	377	10	-	-	PUNCT
ejpam-4479	377	11	soft	soft	ADJ
ejpam-4479	377	12	hyper	hyper	ADJ
ejpam-4479	377	13	gr	gr	NOUN
ejpam-4479	377	14	-	-	PUNCT
ejpam-4479	377	15	ideal	ideal	NOUN
ejpam-4479	377	16	over	over	ADP
ejpam-4479	377	17	u	u	PROPN
ejpam-4479	377	18	,	,	PUNCT
ejpam-4479	377	19	then	then	ADV
ejpam-4479	377	20	for	for	ADP
ejpam-4479	377	21	all	all	DET
ejpam-4479	377	22	x	x	NOUN
ejpam-4479	377	23	,	,	PUNCT
ejpam-4479	377	24	y	y	PROPN
ejpam-4479	377	25	∈	∈	PROPN
ejpam-4479	377	26	a	a	PRON
ejpam-4479	377	27	,	,	PUNCT
ejpam-4479	377	28	fa(x	fa(x	NOUN
ejpam-4479	377	29	)	)	PUNCT
ejpam-4479	377	30	⊆	⊆	NUM
ejpam-4479	378	1	[	[	X
ejpam-4479	378	2	fa(x⊛	fa(x⊛	NUM
ejpam-4479	378	3	y	y	NOUN
ejpam-4479	378	4	)	)	PUNCT
ejpam-4479	378	5	∩	∩	NOUN
ejpam-4479	378	6	fa(x	fa(x	NOUN
ejpam-4479	378	7	)	)	PUNCT
ejpam-4479	378	8	]	]	PUNCT
ejpam-4479	378	9	∪	∪	ADP
ejpam-4479	378	10	[	[	PUNCT
ejpam-4479	378	11	fa(x⊛	fa(x⊛	NUM
ejpam-4479	378	12	y	y	NOUN
ejpam-4479	378	13	)	)	PUNCT
ejpam-4479	378	14	∩	∩	NOUN
ejpam-4479	378	15	fa(y	fa(y	PROPN
ejpam-4479	378	16	)	)	PUNCT
ejpam-4479	378	17	]	]	PUNCT
ejpam-4479	378	18	∪	∪	ADP
ejpam-4479	378	19	[	[	X
ejpam-4479	378	20	fa(x	fa(x	NOUN
ejpam-4479	378	21	)	)	PUNCT
ejpam-4479	378	22	∩	∩	NOUN
ejpam-4479	378	23	fa(y	fa(y	PROPN
ejpam-4479	378	24	)	)	PUNCT
ejpam-4479	378	25	]	]	PUNCT
ejpam-4479	378	26	∪	∪	ADP
ejpam-4479	378	27	fa(y	fa(y	PROPN
ejpam-4479	378	28	)	)	PUNCT
ejpam-4479	378	29	.	.	PUNCT
ejpam-4479	379	1	proof	proof	NOUN
ejpam-4479	379	2	:	:	PUNCT
ejpam-4479	379	3	note	note	VERB
ejpam-4479	379	4	that	that	SCONJ
ejpam-4479	379	5	fa(x	fa(x	NOUN
ejpam-4479	379	6	)	)	PUNCT
ejpam-4479	379	7	⊆	⊆	NUM
ejpam-4479	379	8	fa(x	fa(x	NOUN
ejpam-4479	379	9	)	)	PUNCT
ejpam-4479	379	10	∪	∪	ADP
ejpam-4479	379	11	fa(y	fa(y	PROPN
ejpam-4479	379	12	)	)	PUNCT
ejpam-4479	379	13	and	and	CCONJ
ejpam-4479	379	14	fa(x	fa(x	NOUN
ejpam-4479	379	15	)	)	PUNCT
ejpam-4479	379	16	⊆	⊆	NUM
ejpam-4479	379	17	fa(x⊛	fa(x⊛	NUM
ejpam-4479	379	18	y	y	NOUN
ejpam-4479	379	19	)	)	PUNCT
ejpam-4479	379	20	∪	∪	ADP
ejpam-4479	379	21	fa(y	fa(y	PROPN
ejpam-4479	379	22	)	)	PUNCT
ejpam-4479	379	23	.	.	PUNCT
ejpam-4479	380	1	this	this	PRON
ejpam-4479	380	2	implies	imply	VERB
ejpam-4479	380	3	that	that	SCONJ
ejpam-4479	380	4	fa(x	fa(x	NOUN
ejpam-4479	380	5	)	)	PUNCT
ejpam-4479	380	6	=	=	PUNCT
ejpam-4479	381	1	[	[	X
ejpam-4479	381	2	fa(x⊛	fa(x⊛	NUM
ejpam-4479	381	3	y	y	NOUN
ejpam-4479	381	4	)	)	PUNCT
ejpam-4479	381	5	∪	∪	ADP
ejpam-4479	381	6	fa(y	fa(y	PROPN
ejpam-4479	381	7	)	)	PUNCT
ejpam-4479	381	8	]	]	PUNCT
ejpam-4479	381	9	∩	∩	NOUN
ejpam-4479	381	10	[	[	X
ejpam-4479	381	11	fa(x	fa(x	NOUN
ejpam-4479	381	12	)	)	PUNCT
ejpam-4479	381	13	∪	∪	ADP
ejpam-4479	381	14	fa(y	fa(y	PROPN
ejpam-4479	381	15	)	)	PUNCT
ejpam-4479	381	16	]	]	PUNCT
ejpam-4479	381	17	.	.	PUNCT
ejpam-4479	382	1	hence	hence	ADV
ejpam-4479	382	2	,	,	PUNCT
ejpam-4479	382	3	fa(x	fa(x	NOUN
ejpam-4479	382	4	)	)	PUNCT
ejpam-4479	382	5	⊆	⊆	NUM
ejpam-4479	383	1	[	[	X
ejpam-4479	383	2	fa(x⊛	fa(x⊛	NUM
ejpam-4479	383	3	y	y	NOUN
ejpam-4479	383	4	)	)	PUNCT
ejpam-4479	383	5	∩	∩	NOUN
ejpam-4479	383	6	fa(x	fa(x	NOUN
ejpam-4479	383	7	)	)	PUNCT
ejpam-4479	383	8	]	]	PUNCT
ejpam-4479	383	9	∪	∪	ADP
ejpam-4479	383	10	[	[	PUNCT
ejpam-4479	383	11	fa(x⊛	fa(x⊛	NUM
ejpam-4479	383	12	y	y	NOUN
ejpam-4479	383	13	)	)	PUNCT
ejpam-4479	383	14	∩	∩	NOUN
ejpam-4479	383	15	fa(y	fa(y	PROPN
ejpam-4479	383	16	)	)	PUNCT
ejpam-4479	383	17	]	]	PUNCT
ejpam-4479	383	18	∪	∪	ADP
ejpam-4479	383	19	[	[	X
ejpam-4479	383	20	fa(x	fa(x	NOUN
ejpam-4479	383	21	)	)	PUNCT
ejpam-4479	383	22	∩	∩	NOUN
ejpam-4479	383	23	fa(y	fa(y	PROPN
ejpam-4479	383	24	)	)	PUNCT
ejpam-4479	383	25	]	]	PUNCT
ejpam-4479	383	26	∪	∪	ADP
ejpam-4479	383	27	fa(y	fa(y	PROPN
ejpam-4479	383	28	)	)	PUNCT
ejpam-4479	383	29	.	.	PUNCT
ejpam-4479	384	1	theorem	theorem	NOUN
ejpam-4479	384	2	19	19	NUM
ejpam-4479	384	3	.	.	PUNCT
ejpam-4479	385	1	let	let	VERB
ejpam-4479	385	2	e	e	PRON
ejpam-4479	385	3	be	be	AUX
ejpam-4479	385	4	a	a	DET
ejpam-4479	385	5	hyper	hyper	ADJ
ejpam-4479	385	6	gr	gr	NOUN
ejpam-4479	385	7	-	-	NOUN
ejpam-4479	385	8	algebra	algebra	NOUN
ejpam-4479	385	9	.	.	PUNCT
ejpam-4479	386	1	given	give	VERB
ejpam-4479	386	2	a	a	DET
ejpam-4479	386	3	hyper	hyper	ADJ
ejpam-4479	386	4	subgr	subgr	NOUN
ejpam-4479	386	5	-	-	PUNCT
ejpam-4479	386	6	algebra	algebra	NOUN
ejpam-4479	386	7	a	a	PRON
ejpam-4479	386	8	of	of	ADP
ejpam-4479	386	9	e	e	NOUN
ejpam-4479	386	10	,	,	PUNCT
ejpam-4479	386	11	suppose	suppose	VERB
ejpam-4479	386	12	(	(	PUNCT
ejpam-4479	386	13	f	f	X
ejpam-4479	386	14	,	,	PUNCT
ejpam-4479	386	15	a	a	PRON
ejpam-4479	386	16	)	)	PUNCT
ejpam-4479	386	17	⊆	⊆	NUM
ejpam-4479	386	18	s(u	s(u	PROPN
ejpam-4479	386	19	)	)	PUNCT
ejpam-4479	386	20	.	.	PUNCT
ejpam-4479	387	1	if	if	SCONJ
ejpam-4479	387	2	(	(	PUNCT
ejpam-4479	387	3	f	f	X
ejpam-4479	387	4	,	,	PUNCT
ejpam-4479	387	5	a	a	PRON
ejpam-4479	387	6	)	)	PUNCT
ejpam-4479	387	7	is	be	AUX
ejpam-4479	387	8	a	a	DET
ejpam-4479	387	9	union	union	NOUN
ejpam-4479	387	10	-	-	PUNCT
ejpam-4479	387	11	soft	soft	ADJ
ejpam-4479	387	12	hyper	hyper	ADJ
ejpam-4479	387	13	gr	gr	NOUN
ejpam-4479	387	14	-	-	PUNCT
ejpam-4479	387	15	ideal	ideal	NOUN
ejpam-4479	387	16	over	over	ADP
ejpam-4479	387	17	u	u	PROPN
ejpam-4479	387	18	,	,	PUNCT
ejpam-4479	387	19	then	then	ADV
ejpam-4479	387	20	the	the	DET
ejpam-4479	387	21	nonempty	nonempty	ADJ
ejpam-4479	387	22	τ	τ	X
ejpam-4479	387	23	-exclusive	-exclusive	ADJ
ejpam-4479	387	24	set	set	NOUN
ejpam-4479	387	25	of	of	ADP
ejpam-4479	387	26	(	(	PUNCT
ejpam-4479	387	27	f	f	X
ejpam-4479	387	28	,	,	PUNCT
ejpam-4479	387	29	a	a	PRON
ejpam-4479	387	30	)	)	PUNCT
ejpam-4479	387	31	is	be	AUX
ejpam-4479	387	32	an	an	DET
ejpam-4479	387	33	ideal	ideal	NOUN
ejpam-4479	387	34	of	of	ADP
ejpam-4479	387	35	a	a	PRON
ejpam-4479	387	36	for	for	ADP
ejpam-4479	387	37	all	all	PRON
ejpam-4479	387	38	τ	τ	PROPN
ejpam-4479	387	39	⊆	⊆	NUM
ejpam-4479	387	40	u	u	NOUN
ejpam-4479	387	41	.	.	PUNCT
ejpam-4479	388	1	proof	proof	NOUN
ejpam-4479	388	2	:	:	PUNCT
ejpam-4479	388	3	let	let	VERB
ejpam-4479	388	4	(	(	PUNCT
ejpam-4479	388	5	f	f	X
ejpam-4479	388	6	,	,	PUNCT
ejpam-4479	388	7	a	a	PRON
ejpam-4479	388	8	)	)	PUNCT
ejpam-4479	388	9	be	be	AUX
ejpam-4479	388	10	a	a	DET
ejpam-4479	388	11	union	union	NOUN
ejpam-4479	388	12	-	-	PUNCT
ejpam-4479	388	13	soft	soft	ADJ
ejpam-4479	388	14	hyper	hyper	ADJ
ejpam-4479	388	15	gr	gr	NOUN
ejpam-4479	388	16	-	-	PUNCT
ejpam-4479	388	17	ideal	ideal	NOUN
ejpam-4479	388	18	over	over	ADP
ejpam-4479	388	19	u	u	PROPN
ejpam-4479	388	20	.	.	PUNCT
ejpam-4479	389	1	let	let	VERB
ejpam-4479	389	2	τ	τ	PROPN
ejpam-4479	389	3	⊂	⊂	PROPN
ejpam-4479	389	4	u	u	PROPN
ejpam-4479	389	5	such	such	ADJ
ejpam-4479	389	6	that	that	SCONJ
ejpam-4479	389	7	e((f	e((f	NOUN
ejpam-4479	389	8	,	,	PUNCT
ejpam-4479	389	9	a	a	PRON
ejpam-4479	389	10	)	)	PUNCT
ejpam-4479	389	11	;	;	PUNCT
ejpam-4479	389	12	τ	τ	X
ejpam-4479	389	13	)	)	PUNCT
ejpam-4479	389	14	̸=	̸=	PROPN
ejpam-4479	389	15	∅.	∅.	VERB
ejpam-4479	389	16	then	then	ADV
ejpam-4479	389	17	for	for	ADP
ejpam-4479	389	18	some	some	DET
ejpam-4479	389	19	x	x	SYM
ejpam-4479	389	20	∈	∈	PROPN
ejpam-4479	389	21	a	a	PRON
ejpam-4479	389	22	,	,	PUNCT
ejpam-4479	389	23	fa(x	fa(x	NOUN
ejpam-4479	389	24	)	)	PUNCT
ejpam-4479	389	25	⊆	⊆	NUM
ejpam-4479	389	26	τ	τ	X
ejpam-4479	389	27	.	.	PUNCT
ejpam-4479	390	1	it	it	PRON
ejpam-4479	390	2	follows	follow	VERB
ejpam-4479	390	3	from	from	ADP
ejpam-4479	390	4	definition	definition	NOUN
ejpam-4479	390	5	19	19	NUM
ejpam-4479	390	6	(	(	PUNCT
ejpam-4479	390	7	i	i	NOUN
ejpam-4479	390	8	)	)	PUNCT
ejpam-4479	390	9	that	that	PRON
ejpam-4479	390	10	fa(0	fa(0	X
ejpam-4479	390	11	)	)	PUNCT
ejpam-4479	390	12	⊆	⊆	NUM
ejpam-4479	390	13	fa(x	fa(x	NOUN
ejpam-4479	390	14	)	)	PUNCT
ejpam-4479	390	15	⊆	⊆	NUM
ejpam-4479	390	16	τ	τ	X
ejpam-4479	390	17	.	.	PUNCT
ejpam-4479	391	1	thus	thus	ADV
ejpam-4479	391	2	,	,	PUNCT
ejpam-4479	391	3	0	0	X
ejpam-4479	391	4	∈	∈	PROPN
ejpam-4479	391	5	e((f	e((f	NOUN
ejpam-4479	391	6	,	,	PUNCT
ejpam-4479	391	7	a	a	PRON
ejpam-4479	391	8	)	)	PUNCT
ejpam-4479	391	9	;	;	PUNCT
ejpam-4479	391	10	τ	τ	X
ejpam-4479	391	11	)	)	PUNCT
ejpam-4479	391	12	.	.	PUNCT
ejpam-4479	392	1	now	now	ADV
ejpam-4479	392	2	let	let	VERB
ejpam-4479	392	3	x	x	PRON
ejpam-4479	392	4	,	,	PUNCT
ejpam-4479	392	5	y	y	PROPN
ejpam-4479	392	6	∈	∈	PROPN
ejpam-4479	392	7	a	a	DET
ejpam-4479	392	8	such	such	ADJ
ejpam-4479	392	9	that	that	PRON
ejpam-4479	392	10	x⊛y	x⊛y	PROPN
ejpam-4479	392	11	⊆	⊆	NUM
ejpam-4479	392	12	e((f	e((f	NOUN
ejpam-4479	392	13	,	,	PUNCT
ejpam-4479	392	14	a	a	PRON
ejpam-4479	392	15	)	)	PUNCT
ejpam-4479	392	16	;	;	PUNCT
ejpam-4479	392	17	τ	τ	X
ejpam-4479	392	18	)	)	PUNCT
ejpam-4479	392	19	and	and	CCONJ
ejpam-4479	392	20	y	y	PROPN
ejpam-4479	392	21	⊆	⊆	NUM
ejpam-4479	392	22	e((f	e((f	NOUN
ejpam-4479	392	23	,	,	PUNCT
ejpam-4479	392	24	a	a	PRON
ejpam-4479	392	25	)	)	PUNCT
ejpam-4479	392	26	;	;	PUNCT
ejpam-4479	392	27	τ	τ	X
ejpam-4479	392	28	)	)	PUNCT
ejpam-4479	392	29	.	.	PUNCT
ejpam-4479	393	1	hence	hence	ADV
ejpam-4479	393	2	,	,	PUNCT
ejpam-4479	393	3	fa(x	fa(x	PUNCT
ejpam-4479	393	4	⊛	⊛	NUM
ejpam-4479	393	5	y	y	NOUN
ejpam-4479	393	6	)	)	PUNCT
ejpam-4479	393	7	⊆	⊆	NUM
ejpam-4479	393	8	τ	τ	X
ejpam-4479	393	9	and	and	CCONJ
ejpam-4479	393	10	fa(y	fa(y	PROPN
ejpam-4479	393	11	)	)	PUNCT
ejpam-4479	393	12	⊆	⊆	NUM
ejpam-4479	393	13	τ	τ	X
ejpam-4479	393	14	.	.	PUNCT
ejpam-4479	394	1	by	by	ADP
ejpam-4479	394	2	definition	definition	NOUN
ejpam-4479	394	3	19(ii	19(ii	NUM
ejpam-4479	394	4	)	)	PUNCT
ejpam-4479	394	5	fa(x	fa(x	PROPN
ejpam-4479	394	6	)	)	PUNCT
ejpam-4479	394	7	⊆	⊆	NUM
ejpam-4479	394	8	fa(x⊛	fa(x⊛	NUM
ejpam-4479	394	9	y	y	NOUN
ejpam-4479	394	10	)	)	PUNCT
ejpam-4479	394	11	∪	∪	ADP
ejpam-4479	394	12	fa(y	fa(y	PROPN
ejpam-4479	394	13	)	)	PUNCT
ejpam-4479	394	14	⊆	⊆	NUM
ejpam-4479	394	15	τ	τ	X
ejpam-4479	394	16	.	.	PUNCT
ejpam-4479	395	1	hence	hence	ADV
ejpam-4479	395	2	,	,	PUNCT
ejpam-4479	395	3	x	x	PROPN
ejpam-4479	395	4	∈	∈	PROPN
ejpam-4479	395	5	e((f	e((f	NOUN
ejpam-4479	395	6	,	,	PUNCT
ejpam-4479	395	7	a	a	PRON
ejpam-4479	395	8	)	)	PUNCT
ejpam-4479	395	9	;	;	PUNCT
ejpam-4479	395	10	τ	τ	X
ejpam-4479	395	11	)	)	PUNCT
ejpam-4479	395	12	and	and	CCONJ
ejpam-4479	395	13	so	so	ADV
ejpam-4479	395	14	e((f	e((f	NOUN
ejpam-4479	395	15	,	,	PUNCT
ejpam-4479	395	16	a	a	PRON
ejpam-4479	395	17	)	)	PUNCT
ejpam-4479	395	18	;	;	PUNCT
ejpam-4479	395	19	τ	τ	X
ejpam-4479	395	20	)	)	PUNCT
ejpam-4479	395	21	is	be	AUX
ejpam-4479	395	22	an	an	DET
ejpam-4479	395	23	ideal	ideal	NOUN
ejpam-4479	395	24	of	of	ADP
ejpam-4479	395	25	a.	a.	NOUN
ejpam-4479	395	26	4	4	NUM
ejpam-4479	395	27	.	.	PUNCT
ejpam-4479	395	28	conclusion	conclusion	NOUN
ejpam-4479	395	29	in	in	ADP
ejpam-4479	395	30	this	this	DET
ejpam-4479	395	31	paper	paper	NOUN
ejpam-4479	395	32	,	,	PUNCT
ejpam-4479	395	33	the	the	DET
ejpam-4479	395	34	notion	notion	NOUN
ejpam-4479	395	35	of	of	ADP
ejpam-4479	395	36	soft	soft	ADJ
ejpam-4479	395	37	hyper	hyper	ADJ
ejpam-4479	395	38	gr	gr	NOUN
ejpam-4479	395	39	-	-	PUNCT
ejpam-4479	395	40	algebra	algebra	NOUN
ejpam-4479	395	41	is	be	AUX
ejpam-4479	395	42	presented	present	VERB
ejpam-4479	395	43	.	.	PUNCT
ejpam-4479	396	1	some	some	PRON
ejpam-4479	396	2	of	of	ADP
ejpam-4479	396	3	its	its	PRON
ejpam-4479	396	4	properties	property	NOUN
ejpam-4479	396	5	and	and	CCONJ
ejpam-4479	396	6	characterization	characterization	NOUN
ejpam-4479	396	7	are	be	AUX
ejpam-4479	396	8	also	also	ADV
ejpam-4479	396	9	presented	present	VERB
ejpam-4479	396	10	such	such	ADJ
ejpam-4479	396	11	as	as	ADP
ejpam-4479	396	12	the	the	DET
ejpam-4479	396	13	soft	soft	ADJ
ejpam-4479	396	14	hyper	hyper	ADJ
ejpam-4479	396	15	subgr	subgr	NOUN
ejpam-4479	396	16	-	-	PUNCT
ejpam-4479	396	17	algebra	algebra	NOUN
ejpam-4479	396	18	,	,	PUNCT
ejpam-4479	396	19	the	the	DET
ejpam-4479	396	20	soft	soft	ADJ
ejpam-4479	396	21	hyper	hyper	ADJ
ejpam-4479	396	22	gr	gr	NOUN
ejpam-4479	396	23	-	-	PUNCT
ejpam-4479	396	24	ideal	ideal	NOUN
ejpam-4479	396	25	,	,	PUNCT
ejpam-4479	396	26	the	the	DET
ejpam-4479	396	27	soft	soft	ADJ
ejpam-4479	396	28	hyper	hyper	ADJ
ejpam-4479	396	29	gr	gr	ADJ
ejpam-4479	396	30	-	-	PUNCT
ejpam-4479	396	31	commutative	commutative	ADJ
ejpam-4479	396	32	ideal	ideal	NOUN
ejpam-4479	396	33	and	and	CCONJ
ejpam-4479	396	34	the	the	DET
ejpam-4479	396	35	union	union	NOUN
ejpam-4479	396	36	-	-	PUNCT
ejpam-4479	396	37	soft	soft	ADJ
ejpam-4479	396	38	hyper	hyper	ADJ
ejpam-4479	396	39	gr	gr	NOUN
ejpam-4479	396	40	-	-	PUNCT
ejpam-4479	396	41	ideal	ideal	NOUN
ejpam-4479	396	42	.	.	PUNCT
ejpam-4479	397	1	acknowledgements	acknowledgement	NOUN
ejpam-4479	397	2	this	this	DET
ejpam-4479	397	3	research	research	NOUN
ejpam-4479	397	4	is	be	AUX
ejpam-4479	397	5	funded	fund	VERB
ejpam-4479	397	6	by	by	ADP
ejpam-4479	397	7	the	the	DET
ejpam-4479	397	8	commission	commission	NOUN
ejpam-4479	397	9	on	on	ADP
ejpam-4479	397	10	higher	high	ADJ
ejpam-4479	397	11	education	education	NOUN
ejpam-4479	397	12	(	(	PUNCT
ejpam-4479	397	13	ched	che	VERB
ejpam-4479	397	14	)	)	PUNCT
ejpam-4479	397	15	,	,	PUNCT
ejpam-4479	397	16	university	university	NOUN
ejpam-4479	397	17	of	of	ADP
ejpam-4479	397	18	san	san	PROPN
ejpam-4479	397	19	carlos	carlos	PROPN
ejpam-4479	397	20	,	,	PUNCT
ejpam-4479	397	21	philippines	philippine	NOUN
ejpam-4479	397	22	and	and	CCONJ
ejpam-4479	397	23	mindanao	mindanao	PROPN
ejpam-4479	397	24	state	state	PROPN
ejpam-4479	397	25	university	university	PROPN
ejpam-4479	397	26	-	-	PUNCT
ejpam-4479	397	27	iligan	iligan	PROPN
ejpam-4479	397	28	institute	institute	PROPN
ejpam-4479	397	29	of	of	ADP
ejpam-4479	397	30	technology	technology	PROPN
ejpam-4479	397	31	,	,	PUNCT
ejpam-4479	397	32	philippines	philippine	NOUN
ejpam-4479	397	33	.	.	PUNCT
ejpam-4479	398	1	references	reference	NOUN
ejpam-4479	398	2	[	[	X
ejpam-4479	398	3	1	1	NUM
ejpam-4479	398	4	]	]	X
ejpam-4479	398	5	j.c	j.c	PROPN
ejpam-4479	398	6	.	.	PROPN
ejpam-4479	398	7	alcantud	alcantud	PROPN
ejpam-4479	398	8	.	.	PUNCT
ejpam-4479	399	1	some	some	DET
ejpam-4479	399	2	formal	formal	ADJ
ejpam-4479	399	3	relationships	relationship	NOUN
ejpam-4479	399	4	among	among	ADP
ejpam-4479	399	5	soft	soft	ADJ
ejpam-4479	399	6	sets	set	NOUN
ejpam-4479	399	7	,	,	PUNCT
ejpam-4479	399	8	fuzzy	fuzzy	ADJ
ejpam-4479	399	9	sets	set	NOUN
ejpam-4479	399	10	,	,	PUNCT
ejpam-4479	399	11	and	and	CCONJ
ejpam-4479	399	12	their	their	PRON
ejpam-4479	399	13	extensions	extension	NOUN
ejpam-4479	399	14	.	.	PUNCT
ejpam-4479	400	1	international	international	ADJ
ejpam-4479	400	2	journal	journal	PROPN
ejpam-4479	400	3	of	of	ADP
ejpam-4479	400	4	approximate	approximate	ADJ
ejpam-4479	400	5	reasoning	reasoning	NOUN
ejpam-4479	400	6	,	,	PUNCT
ejpam-4479	400	7	68:45–53	68:45–53	NUM
ejpam-4479	400	8	,	,	PUNCT
ejpam-4479	400	9	2016	2016	NUM
ejpam-4479	400	10	.	.	PUNCT
ejpam-4479	401	1	[	[	X
ejpam-4479	401	2	2	2	NUM
ejpam-4479	401	3	]	]	PUNCT
ejpam-4479	401	4	m.	m.	PROPN
ejpam-4479	401	5	ali	ali	PROPN
ejpam-4479	401	6	,	,	PUNCT
ejpam-4479	401	7	f.	f.	PROPN
ejpam-4479	401	8	feng	feng	PROPN
ejpam-4479	401	9	,	,	PUNCT
ejpam-4479	401	10	x.	x.	PROPN
ejpam-4479	401	11	liu	liu	PROPN
ejpam-4479	401	12	,	,	PUNCT
ejpam-4479	401	13	w.	w.	PROPN
ejpam-4479	401	14	min	min	PROPN
ejpam-4479	401	15	,	,	PUNCT
ejpam-4479	401	16	and	and	CCONJ
ejpam-4479	401	17	m.	m.	NOUN
ejpam-4479	401	18	shabir	shabir	PROPN
ejpam-4479	401	19	.	.	PUNCT
ejpam-4479	402	1	on	on	ADP
ejpam-4479	402	2	some	some	DET
ejpam-4479	402	3	new	new	ADJ
ejpam-4479	402	4	operations	operation	NOUN
ejpam-4479	402	5	in	in	ADP
ejpam-4479	402	6	soft	soft	ADJ
ejpam-4479	402	7	set	set	NOUN
ejpam-4479	402	8	theory	theory	NOUN
ejpam-4479	402	9	.	.	PUNCT
ejpam-4479	403	1	comput	comput	NOUN
ejpam-4479	403	2	.	.	PUNCT
ejpam-4479	404	1	math	math	NOUN
ejpam-4479	404	2	.	.	PUNCT
ejpam-4479	405	1	appl	appl	PROPN
ejpam-4479	405	2	.	.	PROPN
ejpam-4479	405	3	,	,	PUNCT
ejpam-4479	405	4	59(9):1547–1553	59(9):1547–1553	NUM
ejpam-4479	405	5	,	,	PUNCT
ejpam-4479	405	6	2009	2009	NUM
ejpam-4479	405	7	.	.	PUNCT
ejpam-4479	406	1	references	reference	NOUN
ejpam-4479	406	2	1497	1497	NUM
ejpam-4479	407	1	[	[	X
ejpam-4479	407	2	3	3	NUM
ejpam-4479	407	3	]	]	X
ejpam-4479	407	4	r.	r.	NOUN
ejpam-4479	407	5	indangan	indangan	PROPN
ejpam-4479	407	6	and	and	CCONJ
ejpam-4479	407	7	g.	g.	PROPN
ejpam-4479	407	8	petalcorin	petalcorin	PROPN
ejpam-4479	407	9	.	.	PUNCT
ejpam-4479	408	1	some	some	DET
ejpam-4479	408	2	results	result	NOUN
ejpam-4479	408	3	on	on	ADP
ejpam-4479	408	4	hyper	hyper	ADJ
ejpam-4479	408	5	gr	gr	NOUN
ejpam-4479	408	6	-	-	PUNCT
ejpam-4479	408	7	ideals	ideal	NOUN
ejpam-4479	408	8	of	of	ADP
ejpam-4479	408	9	a	a	DET
ejpam-4479	408	10	hyper	hyper	ADJ
ejpam-4479	408	11	gralgebra	gralgebra	NOUN
ejpam-4479	408	12	.	.	PUNCT
ejpam-4479	409	1	journal	journal	NOUN
ejpam-4479	409	2	of	of	ADP
ejpam-4479	409	3	algebra	algebra	PROPN
ejpam-4479	409	4	and	and	CCONJ
ejpam-4479	409	5	applied	apply	VERB
ejpam-4479	409	6	mathematics	mathematic	NOUN
ejpam-4479	409	7	.	.	PUNCT
ejpam-4479	409	8	,	,	PUNCT
ejpam-4479	409	9	14:101–119	14:101–119	NUM
ejpam-4479	409	10	,	,	PUNCT
ejpam-4479	409	11	2016	2016	NUM
ejpam-4479	409	12	.	.	PUNCT
ejpam-4479	410	1	[	[	X
ejpam-4479	410	2	4	4	NUM
ejpam-4479	410	3	]	]	X
ejpam-4479	410	4	r.	r.	X
ejpam-4479	410	5	indangan	indangan	PROPN
ejpam-4479	410	6	and	and	CCONJ
ejpam-4479	410	7	g.	g.	PROPN
ejpam-4479	410	8	petalcorin	petalcorin	PROPN
ejpam-4479	410	9	.	.	PUNCT
ejpam-4479	411	1	some	some	DET
ejpam-4479	411	2	hyper	hyper	ADJ
ejpam-4479	411	3	homomorphic	homomorphic	ADJ
ejpam-4479	411	4	properties	property	NOUN
ejpam-4479	411	5	on	on	ADP
ejpam-4479	411	6	hyper	hyper	ADJ
ejpam-4479	411	7	gr	gr	NOUN
ejpam-4479	411	8	-	-	PUNCT
ejpam-4479	411	9	algebras	algebra	NOUN
ejpam-4479	411	10	.	.	PUNCT
ejpam-4479	411	11	journal	journal	PROPN
ejpam-4479	411	12	of	of	ADP
ejpam-4479	411	13	algebra	algebra	PROPN
ejpam-4479	411	14	and	and	CCONJ
ejpam-4479	411	15	applied	apply	VERB
ejpam-4479	411	16	mathematics	mathematic	NOUN
ejpam-4479	411	17	,	,	PUNCT
ejpam-4479	411	18	15:100–121	15:100–121	PROPN
ejpam-4479	411	19	,	,	PUNCT
ejpam-4479	411	20	2017	2017	NUM
ejpam-4479	411	21	.	.	PUNCT
ejpam-4479	412	1	[	[	X
ejpam-4479	412	2	5	5	NUM
ejpam-4479	412	3	]	]	X
ejpam-4479	412	4	y.b	y.b	PROPN
ejpam-4479	412	5	.	.	PROPN
ejpam-4479	412	6	jun	jun	PROPN
ejpam-4479	412	7	.	.	PROPN
ejpam-4479	412	8	soft	soft	ADJ
ejpam-4479	412	9	bck	bck	PROPN
ejpam-4479	412	10	/	/	SYM
ejpam-4479	412	11	bci	bci	NOUN
ejpam-4479	412	12	-	-	PUNCT
ejpam-4479	412	13	algebras	algebra	NOUN
ejpam-4479	412	14	.	.	PUNCT
ejpam-4479	413	1	comput	comput	NOUN
ejpam-4479	413	2	.	.	PUNCT
ejpam-4479	414	1	math	math	PROPN
ejpam-4479	414	2	appl	appl	PROPN
ejpam-4479	414	3	.	.	PROPN
ejpam-4479	414	4	,	,	PUNCT
ejpam-4479	414	5	8:127–136	8:127–136	NUM
ejpam-4479	414	6	,	,	PUNCT
ejpam-4479	414	7	2000	2000	NUM
ejpam-4479	414	8	.	.	PUNCT
ejpam-4479	415	1	[	[	X
ejpam-4479	415	2	6	6	NUM
ejpam-4479	415	3	]	]	X
ejpam-4479	415	4	y.b	y.b	PROPN
ejpam-4479	415	5	.	.	PROPN
ejpam-4479	415	6	jun	jun	PROPN
ejpam-4479	415	7	.	.	PUNCT
ejpam-4479	415	8	union	union	NOUN
ejpam-4479	415	9	-	-	PUNCT
ejpam-4479	415	10	soft	soft	ADJ
ejpam-4479	415	11	sets	set	NOUN
ejpam-4479	415	12	with	with	ADP
ejpam-4479	415	13	application	application	NOUN
ejpam-4479	415	14	in	in	ADP
ejpam-4479	415	15	bck	bck	PROPN
ejpam-4479	415	16	/	/	SYM
ejpam-4479	415	17	bci	bci	NOUN
ejpam-4479	415	18	-	-	PUNCT
ejpam-4479	415	19	algebras	algebra	NOUN
ejpam-4479	415	20	.	.	PUNCT
ejpam-4479	416	1	bull	bull	NOUN
ejpam-4479	416	2	.	.	PUNCT
ejpam-4479	417	1	korean	korean	ADJ
ejpam-4479	417	2	math	math	PROPN
ejpam-4479	417	3	soc	soc	PROPN
ejpam-4479	417	4	.	.	PUNCT
ejpam-4479	417	5	,	,	PUNCT
ejpam-4479	417	6	50:1937–1956	50:1937–1956	NUM
ejpam-4479	417	7	,	,	PUNCT
ejpam-4479	417	8	2013	2013	NUM
ejpam-4479	417	9	.	.	PUNCT
ejpam-4479	418	1	[	[	X
ejpam-4479	418	2	7	7	X
ejpam-4479	418	3	]	]	X
ejpam-4479	418	4	y.b	y.b	PROPN
ejpam-4479	418	5	.	.	PROPN
ejpam-4479	418	6	jun	jun	PROPN
ejpam-4479	418	7	,	,	PUNCT
ejpam-4479	418	8	m.m	m.m	PROPN
ejpam-4479	418	9	.	.	PROPN
ejpam-4479	418	10	zahedi	zahedi	PROPN
ejpam-4479	418	11	,	,	PUNCT
ejpam-4479	418	12	x.l	x.l	PROPN
ejpam-4479	418	13	.	.	PUNCT
ejpam-4479	418	14	xin	xin	PROPN
ejpam-4479	418	15	,	,	PUNCT
ejpam-4479	418	16	and	and	CCONJ
ejpam-4479	418	17	r.a	r.a	PROPN
ejpam-4479	418	18	.	.	PROPN
ejpam-4479	418	19	borzooei	borzooei	PROPN
ejpam-4479	418	20	.	.	PUNCT
ejpam-4479	419	1	on	on	ADP
ejpam-4479	419	2	hyper	hyper	ADJ
ejpam-4479	419	3	bck	bck	NOUN
ejpam-4479	419	4	-	-	PUNCT
ejpam-4479	419	5	algebras	algebras	PROPN
ejpam-4479	419	6	.	.	PUNCT
ejpam-4479	420	1	italian	italian	ADJ
ejpam-4479	420	2	journal	journal	NOUN
ejpam-4479	420	3	of	of	ADP
ejpam-4479	420	4	pure	pure	ADJ
ejpam-4479	420	5	and	and	CCONJ
ejpam-4479	420	6	applied	applied	ADJ
ejpam-4479	420	7	mathematics	mathematic	NOUN
ejpam-4479	420	8	,	,	PUNCT
ejpam-4479	420	9	8:127–136	8:127–136	NUM
ejpam-4479	420	10	,	,	PUNCT
ejpam-4479	420	11	2000	2000	NUM
ejpam-4479	420	12	.	.	PUNCT
ejpam-4479	421	1	[	[	X
ejpam-4479	421	2	8	8	NUM
ejpam-4479	421	3	]	]	X
ejpam-4479	421	4	p.k	p.k	PROPN
ejpam-4479	421	5	.	.	PROPN
ejpam-4479	421	6	maji	maji	PROPN
ejpam-4479	421	7	,	,	PUNCT
ejpam-4479	421	8	a.r	a.r	PROPN
ejpam-4479	421	9	.	.	PROPN
ejpam-4479	421	10	roy	roy	PROPN
ejpam-4479	421	11	,	,	PUNCT
ejpam-4479	421	12	and	and	CCONJ
ejpam-4479	421	13	r.	r.	PROPN
ejpam-4479	421	14	biswas	biswas	PROPN
ejpam-4479	421	15	.	.	PUNCT
ejpam-4479	421	16	soft	soft	ADJ
ejpam-4479	421	17	set	set	VERB
ejpam-4479	421	18	theory	theory	NOUN
ejpam-4479	421	19	.	.	PUNCT
ejpam-4479	422	1	comput	comput	NOUN
ejpam-4479	422	2	.	.	PUNCT
ejpam-4479	423	1	math	math	NOUN
ejpam-4479	423	2	.	.	PUNCT
ejpam-4479	424	1	appl	appl	PROPN
ejpam-4479	424	2	.	.	PROPN
ejpam-4479	424	3	,	,	PUNCT
ejpam-4479	424	4	45:555	45:555	NUM
ejpam-4479	424	5	–	–	PUNCT
ejpam-4479	424	6	562	562	NUM
ejpam-4479	424	7	,	,	PUNCT
ejpam-4479	424	8	2003	2003	NUM
ejpam-4479	424	9	.	.	PUNCT
ejpam-4479	425	1	[	[	X
ejpam-4479	425	2	9	9	NUM
ejpam-4479	425	3	]	]	X
ejpam-4479	425	4	f.	f.	PROPN
ejpam-4479	425	5	marty	marty	PROPN
ejpam-4479	425	6	.	.	PUNCT
ejpam-4479	426	1	sur	sur	PROPN
ejpam-4479	426	2	une	une	PROPN
ejpam-4479	426	3	generalization	generalization	PROPN
ejpam-4479	426	4	de	de	X
ejpam-4479	426	5	la	la	PROPN
ejpam-4479	426	6	notion	notion	PROPN
ejpam-4479	426	7	de	de	X
ejpam-4479	426	8	groupe	groupe	PROPN
ejpam-4479	426	9	.	.	PUNCT
ejpam-4479	427	1	8th	8th	ADJ
ejpam-4479	427	2	congress	congress	PROPN
ejpam-4479	427	3	math	math	NOUN
ejpam-4479	427	4	.	.	PUNCT
ejpam-4479	428	1	scandinaves	scandinave	NOUN
ejpam-4479	428	2	,	,	PUNCT
ejpam-4479	428	3	stockholm	stockholm	PROPN
ejpam-4479	428	4	,	,	PUNCT
ejpam-4479	428	5	pages	page	NOUN
ejpam-4479	428	6	45–49	45–49	NUM
ejpam-4479	428	7	,	,	PUNCT
ejpam-4479	428	8	1934	1934	NUM
ejpam-4479	428	9	.	.	PUNCT
ejpam-4479	429	1	[	[	X
ejpam-4479	429	2	10	10	NUM
ejpam-4479	429	3	]	]	X
ejpam-4479	429	4	d.	d.	PROPN
ejpam-4479	429	5	molodtsov	molodtsov	PROPN
ejpam-4479	429	6	.	.	PUNCT
ejpam-4479	430	1	soft	soft	ADJ
ejpam-4479	430	2	set	set	VERB
ejpam-4479	430	3	theoryfirst	theoryfirst	NOUN
ejpam-4479	430	4	results	result	NOUN
ejpam-4479	430	5	.	.	PUNCT
ejpam-4479	431	1	comput	comput	NOUN
ejpam-4479	431	2	.	.	PUNCT
ejpam-4479	432	1	math	math	PROPN
ejpam-4479	432	2	appl	appl	PROPN
ejpam-4479	432	3	.	.	PROPN
ejpam-4479	432	4	,	,	PUNCT
ejpam-4479	432	5	37:19–31	37:19–31	PROPN
ejpam-4479	432	6	,	,	PUNCT
ejpam-4479	432	7	1999	1999	NUM
ejpam-4479	432	8	.	.	PUNCT