id	sid	tid	token	lemma	pos
ejpam-5003	1	1	european	european	PROPN
ejpam-5003	1	2	journal	journal	PROPN
ejpam-5003	1	3	of	of	ADP
ejpam-5003	1	4	pure	pure	ADJ
ejpam-5003	1	5	and	and	CCONJ
ejpam-5003	1	6	applied	apply	VERB
ejpam-5003	1	7	mathematics	mathematic	NOUN
ejpam-5003	1	8	vol	vol	NOUN
ejpam-5003	1	9	.	.	PROPN
ejpam-5003	2	1	17	17	NUM
ejpam-5003	2	2	,	,	PUNCT
ejpam-5003	2	3	no	no	INTJ
ejpam-5003	2	4	.	.	NOUN
ejpam-5003	2	5	1	1	NUM
ejpam-5003	2	6	,	,	PUNCT
ejpam-5003	2	7	2024	2024	NUM
ejpam-5003	2	8	,	,	PUNCT
ejpam-5003	2	9	222	222	NUM
ejpam-5003	2	10	-	-	SYM
ejpam-5003	2	11	242	242	NUM
ejpam-5003	2	12	issn	issn	PROPN
ejpam-5003	2	13	1307	1307	NUM
ejpam-5003	2	14	-	-	SYM
ejpam-5003	2	15	5543	5543	NUM
ejpam-5003	2	16	–	–	PUNCT
ejpam-5003	2	17	ejpam.com	ejpam.com	X
ejpam-5003	2	18	published	publish	VERB
ejpam-5003	2	19	by	by	ADP
ejpam-5003	3	1	new	new	PROPN
ejpam-5003	3	2	york	york	PROPN
ejpam-5003	3	3	business	business	PROPN
ejpam-5003	3	4	global	global	PROPN
ejpam-5003	3	5	looking	look	VERB
ejpam-5003	3	6	at	at	ADP
ejpam-5003	3	7	two	two	NUM
ejpam-5003	3	8	ways	way	NOUN
ejpam-5003	3	9	of	of	ADP
ejpam-5003	3	10	constructing	construct	VERB
ejpam-5003	3	11	quotient	quotient	NOUN
ejpam-5003	3	12	hyper	hyper	NOUN
ejpam-5003	3	13	bn	bn	NOUN
ejpam-5003	3	14	-	-	PUNCT
ejpam-5003	3	15	algebras	algebras	PROPN
ejpam-5003	3	16	and	and	CCONJ
ejpam-5003	3	17	some	some	DET
ejpam-5003	3	18	notes	note	NOUN
ejpam-5003	3	19	on	on	ADP
ejpam-5003	3	20	hyper	hyper	ADJ
ejpam-5003	3	21	bn	bn	NOUN
ejpam-5003	3	22	-	-	PUNCT
ejpam-5003	3	23	ideals	ideal	NOUN
ejpam-5003	3	24	lyster	lyster	PROPN
ejpam-5003	3	25	rey	rey	PROPN
ejpam-5003	3	26	b.	b.	PROPN
ejpam-5003	4	1	cabardo1,2,∗	cabardo1,2,∗	PROPN
ejpam-5003	4	2	,	,	PUNCT
ejpam-5003	4	3	gaudencio	gaudencio	PROPN
ejpam-5003	4	4	c.	c.	PROPN
ejpam-5003	4	5	petalcorin	petalcorin	PROPN
ejpam-5003	4	6	,	,	PUNCT
ejpam-5003	4	7	jr.1,2	jr.1,2	PROPN
ejpam-5003	4	8	1	1	NUM
ejpam-5003	4	9	department	department	NOUN
ejpam-5003	4	10	of	of	ADP
ejpam-5003	4	11	mathematics	mathematic	NOUN
ejpam-5003	4	12	and	and	CCONJ
ejpam-5003	4	13	statistics	statistic	NOUN
ejpam-5003	4	14	,	,	PUNCT
ejpam-5003	4	15	college	college	NOUN
ejpam-5003	4	16	of	of	ADP
ejpam-5003	4	17	science	science	NOUN
ejpam-5003	4	18	and	and	CCONJ
ejpam-5003	4	19	mathematics	mathematic	NOUN
ejpam-5003	4	20	,	,	PUNCT
ejpam-5003	4	21	mindanao	mindanao	PROPN
ejpam-5003	4	22	state	state	PROPN
ejpam-5003	4	23	university	university	PROPN
ejpam-5003	4	24	iligan	iligan	PROPN
ejpam-5003	4	25	institute	institute	PROPN
ejpam-5003	4	26	of	of	ADP
ejpam-5003	4	27	technology	technology	PROPN
ejpam-5003	4	28	,	,	PUNCT
ejpam-5003	4	29	iligan	iligan	PROPN
ejpam-5003	4	30	city	city	PROPN
ejpam-5003	4	31	,	,	PUNCT
ejpam-5003	4	32	lanao	lanao	PROPN
ejpam-5003	4	33	del	del	PROPN
ejpam-5003	4	34	norte	norte	PROPN
ejpam-5003	4	35	,	,	PUNCT
ejpam-5003	4	36	philippines	philippine	NOUN
ejpam-5003	4	37	2	2	NUM
ejpam-5003	4	38	center	center	NOUN
ejpam-5003	4	39	for	for	ADP
ejpam-5003	4	40	graph	graph	NOUN
ejpam-5003	4	41	theory	theory	NOUN
ejpam-5003	4	42	,	,	PUNCT
ejpam-5003	4	43	algebra	algebra	NOUN
ejpam-5003	4	44	,	,	PUNCT
ejpam-5003	4	45	and	and	CCONJ
ejpam-5003	4	46	analysis	analysis	NOUN
ejpam-5003	4	47	,	,	PUNCT
ejpam-5003	4	48	premier	premier	PROPN
ejpam-5003	4	49	research	research	PROPN
ejpam-5003	4	50	institute	institute	PROPN
ejpam-5003	4	51	of	of	ADP
ejpam-5003	4	52	science	science	NOUN
ejpam-5003	4	53	and	and	CCONJ
ejpam-5003	4	54	mathematics	mathematic	NOUN
ejpam-5003	4	55	,	,	PUNCT
ejpam-5003	4	56	mindanao	mindanao	PROPN
ejpam-5003	4	57	state	state	PROPN
ejpam-5003	4	58	university	university	PROPN
ejpam-5003	4	59	iligan	iligan	PROPN
ejpam-5003	4	60	institute	institute	PROPN
ejpam-5003	4	61	of	of	ADP
ejpam-5003	4	62	technology	technology	PROPN
ejpam-5003	4	63	,	,	PUNCT
ejpam-5003	4	64	iligan	iligan	PROPN
ejpam-5003	4	65	city	city	PROPN
ejpam-5003	4	66	,	,	PUNCT
ejpam-5003	4	67	lanao	lanao	PROPN
ejpam-5003	4	68	del	del	PROPN
ejpam-5003	4	69	norte	norte	PROPN
ejpam-5003	4	70	,	,	PUNCT
ejpam-5003	4	71	philippines	philippine	NOUN
ejpam-5003	4	72	abstract	abstract	ADJ
ejpam-5003	4	73	.	.	PUNCT
ejpam-5003	5	1	a	a	DET
ejpam-5003	5	2	hyper	hyper	ADJ
ejpam-5003	5	3	bn	bn	NOUN
ejpam-5003	5	4	-algebra	-algebra	NOUN
ejpam-5003	5	5	is	be	AUX
ejpam-5003	5	6	a	a	DET
ejpam-5003	5	7	nonempty	nonempty	ADV
ejpam-5003	5	8	set	set	VERB
ejpam-5003	5	9	h	h	NOUN
ejpam-5003	5	10	together	together	ADV
ejpam-5003	5	11	with	with	ADP
ejpam-5003	5	12	a	a	DET
ejpam-5003	5	13	hyperoperation	hyperoperation	NOUN
ejpam-5003	5	14	“	"	PUNCT
ejpam-5003	5	15	⊛	⊛	NUM
ejpam-5003	5	16	”	"	PUNCT
ejpam-5003	5	17	and	and	CCONJ
ejpam-5003	5	18	a	a	DET
ejpam-5003	5	19	constant	constant	ADJ
ejpam-5003	5	20	0	0	NUM
ejpam-5003	5	21	such	such	ADJ
ejpam-5003	5	22	that	that	DET
ejpam-5003	5	23	for	for	ADP
ejpam-5003	5	24	all	all	DET
ejpam-5003	5	25	x	x	NOUN
ejpam-5003	5	26	,	,	PUNCT
ejpam-5003	5	27	y	y	PROPN
ejpam-5003	5	28	,	,	PUNCT
ejpam-5003	5	29	z	z	PROPN
ejpam-5003	5	30	∈	∈	PROPN
ejpam-5003	5	31	h	h	NOUN
ejpam-5003	5	32	:	:	PUNCT
ejpam-5003	5	33	x	x	SYM
ejpam-5003	5	34	≪	≪	X
ejpam-5003	5	35	x	x	X
ejpam-5003	5	36	,	,	PUNCT
ejpam-5003	5	37	x⊛0	x⊛0	PROPN
ejpam-5003	5	38	=	=	PUNCT
ejpam-5003	5	39	{	{	PUNCT
ejpam-5003	5	40	x	x	NOUN
ejpam-5003	5	41	}	}	PUNCT
ejpam-5003	5	42	,	,	PUNCT
ejpam-5003	5	43	and	and	CCONJ
ejpam-5003	5	44	(	(	PUNCT
ejpam-5003	5	45	x⊛y)⊛z	x⊛y)⊛z	PROPN
ejpam-5003	5	46	=	=	SYM
ejpam-5003	5	47	(	(	PUNCT
ejpam-5003	5	48	0⊛z)⊛(y⊛x	0⊛z)⊛(y⊛x	PROPN
ejpam-5003	5	49	)	)	PUNCT
ejpam-5003	5	50	,	,	PUNCT
ejpam-5003	5	51	where	where	SCONJ
ejpam-5003	5	52	x	x	X
ejpam-5003	5	53	≪	≪	VERB
ejpam-5003	5	54	y	y	PROPN
ejpam-5003	5	55	if	if	SCONJ
ejpam-5003	5	56	and	and	CCONJ
ejpam-5003	5	57	only	only	ADV
ejpam-5003	5	58	if	if	SCONJ
ejpam-5003	5	59	0	0	NUM
ejpam-5003	5	60	∈	∈	PROPN
ejpam-5003	6	1	x⊛	x⊛	VERB
ejpam-5003	7	1	y.	y.	NOUN
ejpam-5003	7	2	we	we	PRON
ejpam-5003	7	3	investigated	investigate	VERB
ejpam-5003	7	4	the	the	DET
ejpam-5003	7	5	structures	structure	NOUN
ejpam-5003	7	6	of	of	ADP
ejpam-5003	7	7	ideals	ideal	NOUN
ejpam-5003	7	8	in	in	ADP
ejpam-5003	7	9	the	the	DET
ejpam-5003	7	10	hyper	hyper	ADJ
ejpam-5003	7	11	bn	bn	NOUN
ejpam-5003	7	12	-algebra	-algebra	PROPN
ejpam-5003	7	13	setting	setting	NOUN
ejpam-5003	7	14	.	.	PUNCT
ejpam-5003	8	1	we	we	PRON
ejpam-5003	8	2	established	establish	VERB
ejpam-5003	8	3	equivalency	equivalency	NOUN
ejpam-5003	8	4	of	of	ADP
ejpam-5003	8	5	weak	weak	ADJ
ejpam-5003	8	6	hyper	hyper	ADJ
ejpam-5003	8	7	bn	bn	ADJ
ejpam-5003	8	8	-ideals	-ideal	NOUN
ejpam-5003	8	9	and	and	CCONJ
ejpam-5003	8	10	hyper	hyper	ADJ
ejpam-5003	8	11	subbn	subbn	NOUN
ejpam-5003	8	12	-algebras	-algebras	PROPN
ejpam-5003	8	13	.	.	PUNCT
ejpam-5003	9	1	also	also	ADV
ejpam-5003	9	2	,	,	PUNCT
ejpam-5003	9	3	we	we	PRON
ejpam-5003	9	4	found	find	VERB
ejpam-5003	9	5	a	a	DET
ejpam-5003	9	6	condition	condition	NOUN
ejpam-5003	9	7	when	when	SCONJ
ejpam-5003	9	8	a	a	DET
ejpam-5003	9	9	strong	strong	ADJ
ejpam-5003	9	10	hyper	hyper	ADJ
ejpam-5003	9	11	bn	bn	NOUN
ejpam-5003	9	12	-ideal	-ideal	NOUN
ejpam-5003	9	13	become	become	VERB
ejpam-5003	9	14	a	a	DET
ejpam-5003	9	15	hyper	hyper	NOUN
ejpam-5003	9	16	bn	bn	NOUN
ejpam-5003	9	17	-ideal	-ideal	NOUN
ejpam-5003	9	18	.	.	PUNCT
ejpam-5003	10	1	finally	finally	ADV
ejpam-5003	10	2	,	,	PUNCT
ejpam-5003	10	3	we	we	PRON
ejpam-5003	10	4	looked	look	VERB
ejpam-5003	10	5	at	at	ADP
ejpam-5003	10	6	two	two	NUM
ejpam-5003	10	7	ways	way	NOUN
ejpam-5003	10	8	in	in	ADP
ejpam-5003	10	9	constructing	construct	VERB
ejpam-5003	10	10	the	the	DET
ejpam-5003	10	11	quotient	quotient	NOUN
ejpam-5003	10	12	hyper	hyper	NOUN
ejpam-5003	10	13	bn	bn	NOUN
ejpam-5003	10	14	-algebras	-algebra	NOUN
ejpam-5003	10	15	and	and	CCONJ
ejpam-5003	10	16	investigated	investigate	VERB
ejpam-5003	10	17	the	the	DET
ejpam-5003	10	18	relationship	relationship	NOUN
ejpam-5003	10	19	between	between	ADP
ejpam-5003	10	20	the	the	DET
ejpam-5003	10	21	two	two	NUM
ejpam-5003	10	22	constructions	construction	NOUN
ejpam-5003	10	23	.	.	PUNCT
ejpam-5003	11	1	2020	2020	NUM
ejpam-5003	11	2	mathematics	mathematic	NOUN
ejpam-5003	11	3	subject	subject	NOUN
ejpam-5003	11	4	classifications	classification	NOUN
ejpam-5003	11	5	:	:	PUNCT
ejpam-5003	11	6	08a05	08a05	NUM
ejpam-5003	11	7	,	,	PUNCT
ejpam-5003	11	8	08a30	08a30	VERB
ejpam-5003	11	9	key	key	ADJ
ejpam-5003	11	10	words	word	NOUN
ejpam-5003	11	11	and	and	CCONJ
ejpam-5003	11	12	phrases	phrase	NOUN
ejpam-5003	11	13	:	:	PUNCT
ejpam-5003	11	14	hyper	hyper	ADJ
ejpam-5003	11	15	bn	bn	PROPN
ejpam-5003	11	16	-algebra	-algebra	PROPN
ejpam-5003	11	17	,	,	PUNCT
ejpam-5003	11	18	hyper	hyper	ADJ
ejpam-5003	11	19	bn	bn	NOUN
ejpam-5003	11	20	-ideal	-ideal	NOUN
ejpam-5003	11	21	,	,	PUNCT
ejpam-5003	11	22	quotient	quotient	VERB
ejpam-5003	11	23	hyper	hyper	PROPN
ejpam-5003	11	24	bn	bn	PROPN
ejpam-5003	11	25	-algebra	-algebra	PROPN
ejpam-5003	11	26	,	,	PUNCT
ejpam-5003	11	27	congruence	congruence	PROPN
ejpam-5003	11	28	relation	relation	NOUN
ejpam-5003	11	29	,	,	PUNCT
ejpam-5003	11	30	reflexive	reflexive	VERB
ejpam-5003	11	31	normal	normal	ADJ
ejpam-5003	11	32	hyper	hyper	ADJ
ejpam-5003	11	33	bn	bn	NOUN
ejpam-5003	11	34	-algebra	-algebra	NOUN
ejpam-5003	11	35	1	1	NUM
ejpam-5003	11	36	.	.	PUNCT
ejpam-5003	12	1	introduction	introduction	NOUN
ejpam-5003	12	2	in	in	ADP
ejpam-5003	12	3	classical	classical	ADJ
ejpam-5003	12	4	algebraic	algebraic	ADJ
ejpam-5003	12	5	theory	theory	NOUN
ejpam-5003	12	6	,	,	PUNCT
ejpam-5003	12	7	groups	group	NOUN
ejpam-5003	12	8	are	be	AUX
ejpam-5003	12	9	sets	set	NOUN
ejpam-5003	12	10	equipped	equip	VERB
ejpam-5003	12	11	with	with	ADP
ejpam-5003	12	12	an	an	DET
ejpam-5003	12	13	operation	operation	NOUN
ejpam-5003	12	14	that	that	PRON
ejpam-5003	12	15	combines	combine	VERB
ejpam-5003	12	16	any	any	DET
ejpam-5003	12	17	two	two	NUM
ejpam-5003	12	18	elements	element	NOUN
ejpam-5003	12	19	to	to	PART
ejpam-5003	12	20	produce	produce	VERB
ejpam-5003	12	21	a	a	DET
ejpam-5003	12	22	third	third	ADJ
ejpam-5003	12	23	element	element	NOUN
ejpam-5003	12	24	.	.	PUNCT
ejpam-5003	13	1	they	they	PRON
ejpam-5003	13	2	are	be	AUX
ejpam-5003	13	3	often	often	ADV
ejpam-5003	13	4	used	use	VERB
ejpam-5003	13	5	to	to	PART
ejpam-5003	13	6	study	study	VERB
ejpam-5003	13	7	symmetry	symmetry	NOUN
ejpam-5003	13	8	and	and	CCONJ
ejpam-5003	13	9	transformations	transformation	NOUN
ejpam-5003	13	10	.	.	PUNCT
ejpam-5003	14	1	rings	ring	NOUN
ejpam-5003	14	2	,	,	PUNCT
ejpam-5003	14	3	on	on	ADP
ejpam-5003	14	4	the	the	DET
ejpam-5003	14	5	other	other	ADJ
ejpam-5003	14	6	hand	hand	NOUN
ejpam-5003	14	7	,	,	PUNCT
ejpam-5003	14	8	are	be	AUX
ejpam-5003	14	9	sets	set	NOUN
ejpam-5003	14	10	with	with	ADP
ejpam-5003	14	11	two	two	NUM
ejpam-5003	14	12	operations	operation	NOUN
ejpam-5003	14	13	,	,	PUNCT
ejpam-5003	14	14	usually	usually	ADV
ejpam-5003	14	15	addition	addition	NOUN
ejpam-5003	14	16	and	and	CCONJ
ejpam-5003	14	17	multiplication	multiplication	NOUN
ejpam-5003	14	18	,	,	PUNCT
ejpam-5003	14	19	and	and	CCONJ
ejpam-5003	14	20	they	they	PRON
ejpam-5003	14	21	are	be	AUX
ejpam-5003	14	22	used	use	VERB
ejpam-5003	14	23	to	to	PART
ejpam-5003	14	24	study	study	VERB
ejpam-5003	14	25	arithmetic	arithmetic	ADJ
ejpam-5003	14	26	properties	property	NOUN
ejpam-5003	14	27	.	.	PUNCT
ejpam-5003	15	1	fields	field	NOUN
ejpam-5003	15	2	are	be	AUX
ejpam-5003	15	3	algebraic	algebraic	ADJ
ejpam-5003	15	4	structures	structure	NOUN
ejpam-5003	15	5	that	that	PRON
ejpam-5003	15	6	have	have	VERB
ejpam-5003	15	7	both	both	CCONJ
ejpam-5003	15	8	addition	addition	NOUN
ejpam-5003	15	9	and	and	CCONJ
ejpam-5003	15	10	multiplication	multiplication	NOUN
ejpam-5003	15	11	operations	operation	NOUN
ejpam-5003	15	12	,	,	PUNCT
ejpam-5003	15	13	and	and	CCONJ
ejpam-5003	15	14	they	they	PRON
ejpam-5003	15	15	are	be	AUX
ejpam-5003	15	16	fundamental	fundamental	ADJ
ejpam-5003	15	17	in	in	ADP
ejpam-5003	15	18	areas	area	NOUN
ejpam-5003	15	19	like	like	ADP
ejpam-5003	15	20	number	number	NOUN
ejpam-5003	15	21	theory	theory	NOUN
ejpam-5003	15	22	and	and	CCONJ
ejpam-5003	15	23	geometry	geometry	NOUN
ejpam-5003	15	24	.	.	PUNCT
ejpam-5003	16	1	the	the	DET
ejpam-5003	16	2	concept	concept	NOUN
ejpam-5003	16	3	of	of	ADP
ejpam-5003	16	4	the	the	DET
ejpam-5003	16	5	algebraic	algebraic	ADJ
ejpam-5003	16	6	hyperstructure	hyperstructure	NOUN
ejpam-5003	16	7	theory	theory	NOUN
ejpam-5003	16	8	was	be	AUX
ejpam-5003	16	9	brought	bring	VERB
ejpam-5003	16	10	by	by	ADP
ejpam-5003	16	11	f.	f.	PROPN
ejpam-5003	16	12	marty	marty	PROPN
ejpam-5003	17	1	[	[	X
ejpam-5003	17	2	9	9	X
ejpam-5003	17	3	]	]	PUNCT
ejpam-5003	17	4	at	at	ADP
ejpam-5003	17	5	the	the	DET
ejpam-5003	17	6	8th	8th	ADJ
ejpam-5003	17	7	congress	congress	PROPN
ejpam-5003	17	8	of	of	ADP
ejpam-5003	17	9	scandinavian	scandinavian	ADJ
ejpam-5003	17	10	mathematicians	mathematician	NOUN
ejpam-5003	17	11	in	in	ADP
ejpam-5003	17	12	1934	1934	NUM
ejpam-5003	17	13	.	.	PUNCT
ejpam-5003	18	1	one	one	NUM
ejpam-5003	18	2	of	of	ADP
ejpam-5003	18	3	the	the	DET
ejpam-5003	18	4	main	main	ADJ
ejpam-5003	18	5	point	point	NOUN
ejpam-5003	18	6	of	of	ADP
ejpam-5003	18	7	this	this	DET
ejpam-5003	18	8	∗corresponding	∗corresponde	VERB
ejpam-5003	18	9	author	author	NOUN
ejpam-5003	18	10	.	.	PUNCT
ejpam-5003	19	1	doi	doi	NOUN
ejpam-5003	19	2	:	:	PUNCT
ejpam-5003	19	3	https://doi.org/10.29020/nybg.ejpam.v17i1.5003	https://doi.org/10.29020/nybg.ejpam.v17i1.5003	ADJ
ejpam-5003	19	4	email	email	NOUN
ejpam-5003	19	5	addresses	address	VERB
ejpam-5003	19	6	:	:	PUNCT
ejpam-5003	19	7	lysterrey.cabardo@g.msuiit.edu.ph	lysterrey.cabardo@g.msuiit.edu.ph	PROPN
ejpam-5003	19	8	(	(	PUNCT
ejpam-5003	19	9	l.r	l.r	PROPN
ejpam-5003	19	10	.	.	PROPN
ejpam-5003	19	11	cabardo	cabardo	PROPN
ejpam-5003	19	12	)	)	PUNCT
ejpam-5003	19	13	,	,	PUNCT
ejpam-5003	19	14	gaudencio.petalcorin@g.msuiit.edu.ph	gaudencio.petalcorin@g.msuiit.edu.ph	PROPN
ejpam-5003	19	15	(	(	PUNCT
ejpam-5003	19	16	g.	g.	PROPN
ejpam-5003	19	17	petalcorin	petalcorin	PROPN
ejpam-5003	19	18	)	)	PUNCT
ejpam-5003	19	19	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5003	20	1	222	222	NUM
ejpam-5003	20	2	©	©	ADP
ejpam-5003	20	3	2024	2024	NUM
ejpam-5003	20	4	ejpam	ejpam	NOUN
ejpam-5003	20	5	all	all	DET
ejpam-5003	20	6	rights	right	NOUN
ejpam-5003	20	7	reserved	reserve	VERB
ejpam-5003	20	8	.	.	PUNCT
ejpam-5003	21	1	l.r	l.r	PROPN
ejpam-5003	21	2	.	.	PROPN
ejpam-5003	21	3	cabardo	cabardo	PROPN
ejpam-5003	21	4	,	,	PUNCT
ejpam-5003	21	5	g.	g.	PROPN
ejpam-5003	21	6	petalcorin	petalcorin	PROPN
ejpam-5003	21	7	/	/	SYM
ejpam-5003	21	8	eur	eur	PROPN
ejpam-5003	21	9	.	.	PUNCT
ejpam-5003	22	1	j.	j.	PROPN
ejpam-5003	22	2	pure	pure	PROPN
ejpam-5003	22	3	appl	appl	PROPN
ejpam-5003	22	4	.	.	PROPN
ejpam-5003	22	5	math	math	PROPN
ejpam-5003	22	6	,	,	PUNCT
ejpam-5003	22	7	17	17	NUM
ejpam-5003	22	8	(	(	PUNCT
ejpam-5003	22	9	1	1	NUM
ejpam-5003	22	10	)	)	PUNCT
ejpam-5003	22	11	(	(	PUNCT
ejpam-5003	22	12	2024	2024	NUM
ejpam-5003	22	13	)	)	PUNCT
ejpam-5003	22	14	,	,	PUNCT
ejpam-5003	22	15	222	222	NUM
ejpam-5003	22	16	-	-	SYM
ejpam-5003	22	17	242	242	NUM
ejpam-5003	22	18	223	223	NUM
ejpam-5003	22	19	introduction	introduction	NOUN
ejpam-5003	22	20	is	be	AUX
ejpam-5003	22	21	to	to	ADP
ejpam-5003	22	22	generalized	generalized	ADJ
ejpam-5003	22	23	groups	group	NOUN
ejpam-5003	22	24	.	.	PUNCT
ejpam-5003	23	1	a	a	DET
ejpam-5003	23	2	binary	binary	ADJ
ejpam-5003	23	3	operation	operation	NOUN
ejpam-5003	23	4	was	be	AUX
ejpam-5003	23	5	generalized	generalize	VERB
ejpam-5003	23	6	using	use	VERB
ejpam-5003	23	7	hyperoperation	hyperoperation	NOUN
ejpam-5003	23	8	in	in	ADP
ejpam-5003	23	9	this	this	DET
ejpam-5003	23	10	setting	setting	NOUN
ejpam-5003	23	11	.	.	PUNCT
ejpam-5003	24	1	if	if	SCONJ
ejpam-5003	24	2	we	we	PRON
ejpam-5003	24	3	have	have	VERB
ejpam-5003	24	4	a	a	DET
ejpam-5003	24	5	set	set	ADJ
ejpam-5003	24	6	h	h	NOUN
ejpam-5003	24	7	,	,	PUNCT
ejpam-5003	24	8	then	then	ADV
ejpam-5003	24	9	a	a	DET
ejpam-5003	24	10	hyperoperation	hyperoperation	NOUN
ejpam-5003	24	11	is	be	AUX
ejpam-5003	24	12	a	a	DET
ejpam-5003	24	13	mapping	mapping	NOUN
ejpam-5003	24	14	from	from	ADP
ejpam-5003	24	15	h	h	NOUN
ejpam-5003	24	16	×h	×h	PROPN
ejpam-5003	24	17	to	to	ADP
ejpam-5003	24	18	the	the	DET
ejpam-5003	24	19	set	set	NOUN
ejpam-5003	24	20	of	of	ADP
ejpam-5003	24	21	nonempty	nonempty	ADJ
ejpam-5003	24	22	subsets	subset	NOUN
ejpam-5003	24	23	of	of	ADP
ejpam-5003	24	24	h.	h.	PROPN
ejpam-5003	24	25	after	after	ADP
ejpam-5003	24	26	quite	quite	DET
ejpam-5003	24	27	some	some	DET
ejpam-5003	24	28	time	time	NOUN
ejpam-5003	24	29	,	,	PUNCT
ejpam-5003	24	30	researchers	researcher	NOUN
ejpam-5003	24	31	explore	explore	VERB
ejpam-5003	24	32	this	this	DET
ejpam-5003	24	33	concept	concept	NOUN
ejpam-5003	24	34	and	and	CCONJ
ejpam-5003	24	35	formulated	formulated	ADJ
ejpam-5003	24	36	counterparts	counterpart	NOUN
ejpam-5003	24	37	of	of	ADP
ejpam-5003	24	38	some	some	DET
ejpam-5003	24	39	classical	classical	ADJ
ejpam-5003	24	40	algebraic	algebraic	ADJ
ejpam-5003	24	41	structures	structure	NOUN
ejpam-5003	24	42	.	.	PUNCT
ejpam-5003	25	1	this	this	PRON
ejpam-5003	25	2	led	lead	VERB
ejpam-5003	25	3	to	to	ADP
ejpam-5003	25	4	various	various	ADJ
ejpam-5003	25	5	introduction	introduction	NOUN
ejpam-5003	25	6	of	of	ADP
ejpam-5003	25	7	algebraic	algebraic	ADJ
ejpam-5003	25	8	hyperstructures	hyperstructure	NOUN
ejpam-5003	25	9	:	:	PUNCT
ejpam-5003	25	10	hyper	hyper	ADJ
ejpam-5003	25	11	bci	bci	NOUN
ejpam-5003	25	12	-	-	PUNCT
ejpam-5003	25	13	algebras	algebras	X
ejpam-5003	26	1	[	[	X
ejpam-5003	26	2	10	10	NUM
ejpam-5003	26	3	]	]	PUNCT
ejpam-5003	26	4	,	,	PUNCT
ejpam-5003	26	5	hyper	hyper	ADJ
ejpam-5003	26	6	bcc	bcc	PROPN
ejpam-5003	26	7	-	-	PUNCT
ejpam-5003	26	8	algebras	algebras	X
ejpam-5003	27	1	[	[	X
ejpam-5003	27	2	1	1	NUM
ejpam-5003	27	3	]	]	PUNCT
ejpam-5003	27	4	,	,	PUNCT
ejpam-5003	27	5	hyper	hyper	ADJ
ejpam-5003	27	6	gr	gr	NOUN
ejpam-5003	27	7	-	-	PUNCT
ejpam-5003	27	8	algebras	algebras	NOUN
ejpam-5003	27	9	[	[	X
ejpam-5003	27	10	7	7	NUM
ejpam-5003	27	11	]	]	PUNCT
ejpam-5003	27	12	,	,	PUNCT
ejpam-5003	27	13	hyper	hyper	PROPN
ejpam-5003	27	14	b	b	NOUN
ejpam-5003	27	15	-	-	PUNCT
ejpam-5003	27	16	algebras	algebras	X
ejpam-5003	28	1	[	[	X
ejpam-5003	28	2	5	5	NUM
ejpam-5003	28	3	]	]	PUNCT
ejpam-5003	28	4	,	,	PUNCT
ejpam-5003	28	5	etc	etc	X
ejpam-5003	28	6	.	.	X
ejpam-5003	28	7	in	in	ADP
ejpam-5003	28	8	2022	2022	NUM
ejpam-5003	28	9	,	,	PUNCT
ejpam-5003	28	10	we	we	PRON
ejpam-5003	28	11	applied	apply	VERB
ejpam-5003	28	12	this	this	DET
ejpam-5003	28	13	concept	concept	NOUN
ejpam-5003	28	14	to	to	ADP
ejpam-5003	28	15	bn	bn	NUM
ejpam-5003	28	16	-algebras	-algebra	NOUN
ejpam-5003	28	17	[	[	NOUN
ejpam-5003	28	18	8	8	NUM
ejpam-5003	28	19	]	]	PUNCT
ejpam-5003	28	20	.	.	PUNCT
ejpam-5003	29	1	we	we	PRON
ejpam-5003	29	2	called	call	VERB
ejpam-5003	29	3	them	they	PRON
ejpam-5003	29	4	hyper	hyper	ADJ
ejpam-5003	29	5	bn	bn	ADP
ejpam-5003	29	6	-algebras	-algebras	X
ejpam-5003	29	7	[	[	X
ejpam-5003	29	8	3	3	NUM
ejpam-5003	29	9	]	]	PUNCT
ejpam-5003	29	10	.	.	PUNCT
ejpam-5003	30	1	in	in	ADP
ejpam-5003	30	2	mathematics	mathematics	PROPN
ejpam-5003	30	3	,	,	PUNCT
ejpam-5003	30	4	an	an	DET
ejpam-5003	30	5	ideal	ideal	NOUN
ejpam-5003	30	6	is	be	AUX
ejpam-5003	30	7	a	a	DET
ejpam-5003	30	8	fundamental	fundamental	ADJ
ejpam-5003	30	9	concept	concept	NOUN
ejpam-5003	30	10	in	in	ADP
ejpam-5003	30	11	the	the	DET
ejpam-5003	30	12	study	study	NOUN
ejpam-5003	30	13	of	of	ADP
ejpam-5003	30	14	algebraic	algebraic	ADJ
ejpam-5003	30	15	structures	structure	NOUN
ejpam-5003	30	16	,	,	PUNCT
ejpam-5003	30	17	particularly	particularly	ADV
ejpam-5003	30	18	in	in	ADP
ejpam-5003	30	19	the	the	DET
ejpam-5003	30	20	field	field	NOUN
ejpam-5003	30	21	of	of	ADP
ejpam-5003	30	22	abstract	abstract	ADJ
ejpam-5003	30	23	algebra	algebra	NOUN
ejpam-5003	30	24	.	.	PUNCT
ejpam-5003	31	1	ideals	ideal	NOUN
ejpam-5003	31	2	are	be	AUX
ejpam-5003	31	3	subsets	subset	NOUN
ejpam-5003	31	4	of	of	ADP
ejpam-5003	31	5	algebraic	algebraic	ADJ
ejpam-5003	31	6	structures	structure	NOUN
ejpam-5003	31	7	that	that	PRON
ejpam-5003	31	8	possess	possess	VERB
ejpam-5003	31	9	special	special	ADJ
ejpam-5003	31	10	properties	property	NOUN
ejpam-5003	31	11	.	.	PUNCT
ejpam-5003	32	1	they	they	PRON
ejpam-5003	32	2	are	be	AUX
ejpam-5003	32	3	a	a	DET
ejpam-5003	32	4	powerful	powerful	ADJ
ejpam-5003	32	5	tool	tool	NOUN
ejpam-5003	32	6	in	in	ADP
ejpam-5003	32	7	abstract	abstract	ADJ
ejpam-5003	32	8	algebra	algebra	NOUN
ejpam-5003	32	9	,	,	PUNCT
ejpam-5003	32	10	allowing	allow	VERB
ejpam-5003	32	11	mathematicians	mathematician	NOUN
ejpam-5003	32	12	to	to	PART
ejpam-5003	32	13	study	study	VERB
ejpam-5003	32	14	the	the	DET
ejpam-5003	32	15	structure	structure	NOUN
ejpam-5003	32	16	and	and	CCONJ
ejpam-5003	32	17	properties	property	NOUN
ejpam-5003	32	18	of	of	ADP
ejpam-5003	32	19	algebraic	algebraic	ADJ
ejpam-5003	32	20	structures	structure	NOUN
ejpam-5003	32	21	in	in	ADP
ejpam-5003	32	22	a	a	DET
ejpam-5003	32	23	more	more	ADV
ejpam-5003	32	24	general	general	ADJ
ejpam-5003	32	25	and	and	CCONJ
ejpam-5003	32	26	systematic	systematic	ADJ
ejpam-5003	32	27	way	way	NOUN
ejpam-5003	32	28	.	.	PUNCT
ejpam-5003	33	1	in	in	ADP
ejpam-5003	33	2	[	[	X
ejpam-5003	33	3	10	10	NUM
ejpam-5003	33	4	]	]	PUNCT
ejpam-5003	33	5	,	,	PUNCT
ejpam-5003	33	6	various	various	ADJ
ejpam-5003	33	7	ideals	ideal	NOUN
ejpam-5003	33	8	of	of	ADP
ejpam-5003	33	9	a	a	DET
ejpam-5003	33	10	hyper	hyper	ADJ
ejpam-5003	33	11	bci	bci	NOUN
ejpam-5003	33	12	-	-	PUNCT
ejpam-5003	33	13	algebra	algebra	NOUN
ejpam-5003	33	14	was	be	AUX
ejpam-5003	33	15	introduced	introduce	VERB
ejpam-5003	33	16	and	and	CCONJ
ejpam-5003	33	17	some	some	DET
ejpam-5003	33	18	relationship	relationship	NOUN
ejpam-5003	33	19	were	be	AUX
ejpam-5003	33	20	established	establish	VERB
ejpam-5003	33	21	from	from	ADP
ejpam-5003	33	22	among	among	ADP
ejpam-5003	33	23	these	these	DET
ejpam-5003	33	24	ideals	ideal	NOUN
ejpam-5003	33	25	.	.	PUNCT
ejpam-5003	34	1	a	a	DET
ejpam-5003	34	2	more	more	ADV
ejpam-5003	34	3	specific	specific	ADJ
ejpam-5003	34	4	properties	property	NOUN
ejpam-5003	34	5	involving	involve	VERB
ejpam-5003	34	6	weak	weak	ADJ
ejpam-5003	34	7	and	and	CCONJ
ejpam-5003	34	8	strong	strong	ADJ
ejpam-5003	34	9	hyper	hyper	ADJ
ejpam-5003	34	10	bci	bci	NOUN
ejpam-5003	34	11	-	-	PUNCT
ejpam-5003	34	12	ideals	ideal	NOUN
ejpam-5003	34	13	was	be	AUX
ejpam-5003	34	14	dealt	deal	VERB
ejpam-5003	34	15	in	in	ADP
ejpam-5003	34	16	[	[	X
ejpam-5003	34	17	2	2	NUM
ejpam-5003	34	18	]	]	PUNCT
ejpam-5003	34	19	.	.	PUNCT
ejpam-5003	35	1	ideals	ideal	NOUN
ejpam-5003	35	2	were	be	AUX
ejpam-5003	35	3	also	also	ADV
ejpam-5003	35	4	investigated	investigate	VERB
ejpam-5003	35	5	in	in	ADP
ejpam-5003	35	6	other	other	ADJ
ejpam-5003	35	7	hyper	hyper	ADJ
ejpam-5003	35	8	algebras	algebra	NOUN
ejpam-5003	35	9	.	.	PUNCT
ejpam-5003	36	1	on	on	ADP
ejpam-5003	36	2	the	the	DET
ejpam-5003	36	3	other	other	ADJ
ejpam-5003	36	4	hand	hand	NOUN
ejpam-5003	36	5	,	,	PUNCT
ejpam-5003	36	6	quotient	quotient	VERB
ejpam-5003	36	7	structures	structure	NOUN
ejpam-5003	36	8	of	of	ADP
ejpam-5003	36	9	algebras	algebra	NOUN
ejpam-5003	36	10	are	be	AUX
ejpam-5003	36	11	a	a	DET
ejpam-5003	36	12	concept	concept	NOUN
ejpam-5003	36	13	in	in	ADP
ejpam-5003	36	14	abstract	abstract	ADJ
ejpam-5003	36	15	algebra	algebra	NOUN
ejpam-5003	36	16	that	that	PRON
ejpam-5003	36	17	allow	allow	VERB
ejpam-5003	36	18	us	we	PRON
ejpam-5003	36	19	to	to	PART
ejpam-5003	36	20	create	create	VERB
ejpam-5003	36	21	new	new	ADJ
ejpam-5003	36	22	algebraic	algebraic	ADJ
ejpam-5003	36	23	structures	structure	NOUN
ejpam-5003	36	24	by	by	ADP
ejpam-5003	36	25	“	"	PUNCT
ejpam-5003	36	26	modding	modde	VERB
ejpam-5003	36	27	out	out	ADP
ejpam-5003	36	28	”	"	PUNCT
ejpam-5003	36	29	or	or	CCONJ
ejpam-5003	36	30	“	"	PUNCT
ejpam-5003	36	31	factoring	factor	VERB
ejpam-5003	36	32	out	out	ADP
ejpam-5003	36	33	”	"	PUNCT
ejpam-5003	36	34	certain	certain	ADJ
ejpam-5003	36	35	elements	element	NOUN
ejpam-5003	36	36	or	or	CCONJ
ejpam-5003	36	37	subsets	subset	NOUN
ejpam-5003	36	38	of	of	ADP
ejpam-5003	36	39	an	an	DET
ejpam-5003	36	40	existing	exist	VERB
ejpam-5003	36	41	algebraic	algebraic	ADJ
ejpam-5003	36	42	structure	structure	NOUN
ejpam-5003	36	43	.	.	PUNCT
ejpam-5003	37	1	this	this	DET
ejpam-5003	37	2	process	process	NOUN
ejpam-5003	37	3	involves	involve	VERB
ejpam-5003	37	4	defining	define	VERB
ejpam-5003	37	5	an	an	DET
ejpam-5003	37	6	equivalence	equivalence	NOUN
ejpam-5003	37	7	relation	relation	NOUN
ejpam-5003	37	8	on	on	ADP
ejpam-5003	37	9	the	the	DET
ejpam-5003	37	10	original	original	ADJ
ejpam-5003	37	11	structure	structure	NOUN
ejpam-5003	37	12	and	and	CCONJ
ejpam-5003	37	13	then	then	ADV
ejpam-5003	37	14	forming	form	VERB
ejpam-5003	37	15	equivalence	equivalence	NOUN
ejpam-5003	37	16	classes	class	NOUN
ejpam-5003	37	17	based	base	VERB
ejpam-5003	37	18	on	on	ADP
ejpam-5003	37	19	this	this	DET
ejpam-5003	37	20	relation	relation	NOUN
ejpam-5003	37	21	.	.	PUNCT
ejpam-5003	38	1	the	the	DET
ejpam-5003	38	2	significance	significance	NOUN
ejpam-5003	38	3	of	of	ADP
ejpam-5003	38	4	quotient	quotient	NOUN
ejpam-5003	38	5	structures	structure	NOUN
ejpam-5003	38	6	lies	lie	VERB
ejpam-5003	38	7	in	in	ADP
ejpam-5003	38	8	their	their	PRON
ejpam-5003	38	9	ability	ability	NOUN
ejpam-5003	38	10	to	to	PART
ejpam-5003	38	11	simplify	simplify	VERB
ejpam-5003	38	12	the	the	DET
ejpam-5003	38	13	study	study	NOUN
ejpam-5003	38	14	of	of	ADP
ejpam-5003	38	15	algebraic	algebraic	ADJ
ejpam-5003	38	16	structures	structure	NOUN
ejpam-5003	38	17	by	by	ADP
ejpam-5003	38	18	focusing	focus	VERB
ejpam-5003	38	19	on	on	ADP
ejpam-5003	38	20	the	the	DET
ejpam-5003	38	21	essential	essential	ADJ
ejpam-5003	38	22	properties	property	NOUN
ejpam-5003	38	23	and	and	CCONJ
ejpam-5003	38	24	relationships	relationship	NOUN
ejpam-5003	38	25	.	.	PUNCT
ejpam-5003	39	1	they	they	PRON
ejpam-5003	39	2	provide	provide	VERB
ejpam-5003	39	3	a	a	DET
ejpam-5003	39	4	way	way	NOUN
ejpam-5003	39	5	to	to	PART
ejpam-5003	39	6	abstract	abstract	VERB
ejpam-5003	39	7	away	away	ADV
ejpam-5003	39	8	certain	certain	ADJ
ejpam-5003	39	9	elements	element	NOUN
ejpam-5003	39	10	or	or	CCONJ
ejpam-5003	39	11	subsets	subset	NOUN
ejpam-5003	39	12	that	that	PRON
ejpam-5003	39	13	may	may	AUX
ejpam-5003	39	14	not	not	PART
ejpam-5003	39	15	be	be	AUX
ejpam-5003	39	16	of	of	ADP
ejpam-5003	39	17	immediate	immediate	ADJ
ejpam-5003	39	18	interest	interest	NOUN
ejpam-5003	39	19	,	,	PUNCT
ejpam-5003	39	20	allowing	allow	VERB
ejpam-5003	39	21	mathematicians	mathematician	NOUN
ejpam-5003	39	22	to	to	PART
ejpam-5003	39	23	analyze	analyze	VERB
ejpam-5003	39	24	the	the	DET
ejpam-5003	39	25	structure	structure	NOUN
ejpam-5003	39	26	in	in	ADP
ejpam-5003	39	27	a	a	DET
ejpam-5003	39	28	more	more	ADV
ejpam-5003	39	29	manageable	manageable	ADJ
ejpam-5003	39	30	and	and	CCONJ
ejpam-5003	39	31	structured	structured	ADJ
ejpam-5003	39	32	manner	manner	NOUN
ejpam-5003	39	33	.	.	PUNCT
ejpam-5003	40	1	in	in	ADP
ejpam-5003	40	2	this	this	DET
ejpam-5003	40	3	paper	paper	NOUN
ejpam-5003	40	4	,	,	PUNCT
ejpam-5003	40	5	we	we	PRON
ejpam-5003	40	6	will	will	AUX
ejpam-5003	40	7	introduce	introduce	VERB
ejpam-5003	40	8	the	the	DET
ejpam-5003	40	9	notion	notion	NOUN
ejpam-5003	40	10	of	of	ADP
ejpam-5003	40	11	ideals	ideal	NOUN
ejpam-5003	40	12	on	on	ADP
ejpam-5003	40	13	hyper	hyper	ADJ
ejpam-5003	40	14	bn	bn	ADJ
ejpam-5003	40	15	-algebras	-algebra	NOUN
ejpam-5003	40	16	and	and	CCONJ
ejpam-5003	40	17	look	look	VERB
ejpam-5003	40	18	at	at	ADP
ejpam-5003	40	19	two	two	NUM
ejpam-5003	40	20	ways	way	NOUN
ejpam-5003	40	21	of	of	ADP
ejpam-5003	40	22	constructing	construct	VERB
ejpam-5003	40	23	quotient	quotient	NOUN
ejpam-5003	40	24	hyper	hyper	ADJ
ejpam-5003	40	25	bn	bn	ADP
ejpam-5003	40	26	-algebras	-algebra	NOUN
ejpam-5003	40	27	.	.	NOUN
ejpam-5003	41	1	2	2	NUM
ejpam-5003	41	2	.	.	X
ejpam-5003	41	3	preliminaries	preliminary	NOUN
ejpam-5003	41	4	this	this	DET
ejpam-5003	41	5	section	section	NOUN
ejpam-5003	41	6	provides	provide	VERB
ejpam-5003	41	7	some	some	DET
ejpam-5003	41	8	preliminary	preliminary	ADJ
ejpam-5003	41	9	concepts	concept	NOUN
ejpam-5003	41	10	and	and	CCONJ
ejpam-5003	41	11	results	result	NOUN
ejpam-5003	41	12	needed	need	VERB
ejpam-5003	41	13	for	for	ADP
ejpam-5003	41	14	this	this	DET
ejpam-5003	41	15	paper	paper	NOUN
ejpam-5003	41	16	.	.	PUNCT
ejpam-5003	42	1	definition	definition	NOUN
ejpam-5003	42	2	1	1	NUM
ejpam-5003	42	3	.	.	PUNCT
ejpam-5003	43	1	[	[	X
ejpam-5003	43	2	6	6	NUM
ejpam-5003	43	3	]	]	PUNCT
ejpam-5003	43	4	a	a	DET
ejpam-5003	43	5	binary	binary	ADJ
ejpam-5003	43	6	relation	relation	NOUN
ejpam-5003	43	7	or	or	CCONJ
ejpam-5003	43	8	simply	simply	ADV
ejpam-5003	43	9	a	a	DET
ejpam-5003	43	10	relation	relation	NOUN
ejpam-5003	43	11	∼	∼	NOUN
ejpam-5003	43	12	from	from	ADP
ejpam-5003	43	13	a	a	DET
ejpam-5003	43	14	set	set	NOUN
ejpam-5003	43	15	a	a	PRON
ejpam-5003	43	16	into	into	ADP
ejpam-5003	43	17	a	a	DET
ejpam-5003	43	18	set	set	NOUN
ejpam-5003	43	19	b	b	NOUN
ejpam-5003	43	20	is	be	AUX
ejpam-5003	43	21	a	a	DET
ejpam-5003	43	22	subset	subset	NOUN
ejpam-5003	43	23	of	of	ADP
ejpam-5003	43	24	a×b	a×b	PROPN
ejpam-5003	43	25	.	.	PROPN
ejpam-5003	44	1	if	if	SCONJ
ejpam-5003	44	2	∼	∼	NOUN
ejpam-5003	44	3	is	be	AUX
ejpam-5003	44	4	a	a	DET
ejpam-5003	44	5	relation	relation	NOUN
ejpam-5003	44	6	from	from	ADP
ejpam-5003	44	7	a	a	DET
ejpam-5003	44	8	to	to	PART
ejpam-5003	44	9	b	b	NOUN
ejpam-5003	44	10	,	,	PUNCT
ejpam-5003	44	11	we	we	PRON
ejpam-5003	44	12	denote	denote	VERB
ejpam-5003	44	13	(	(	PUNCT
ejpam-5003	44	14	a	a	PRON
ejpam-5003	44	15	,	,	PUNCT
ejpam-5003	44	16	b	b	NOUN
ejpam-5003	44	17	)	)	PUNCT
ejpam-5003	44	18	∈	∈	NOUN
ejpam-5003	44	19	∼	∼	NOUN
ejpam-5003	44	20	as	as	ADP
ejpam-5003	44	21	a	a	DET
ejpam-5003	44	22	∼	∼	NOUN
ejpam-5003	44	23	b.	b.	NOUN
ejpam-5003	44	24	if	if	SCONJ
ejpam-5003	44	25	a	a	DET
ejpam-5003	44	26	=	=	SYM
ejpam-5003	44	27	b	b	NOUN
ejpam-5003	44	28	,	,	PUNCT
ejpam-5003	44	29	we	we	PRON
ejpam-5003	44	30	say	say	VERB
ejpam-5003	44	31	that	that	SCONJ
ejpam-5003	44	32	∼	∼	NOUN
ejpam-5003	44	33	is	be	AUX
ejpam-5003	44	34	a	a	DET
ejpam-5003	44	35	relation	relation	NOUN
ejpam-5003	44	36	on	on	ADP
ejpam-5003	44	37	a.	a.	NOUN
ejpam-5003	44	38	definition	definition	NOUN
ejpam-5003	44	39	2	2	NUM
ejpam-5003	44	40	.	.	PUNCT
ejpam-5003	45	1	[	[	X
ejpam-5003	45	2	6	6	NUM
ejpam-5003	45	3	]	]	PUNCT
ejpam-5003	45	4	let	let	VERB
ejpam-5003	45	5	∼	∼	NOUN
ejpam-5003	45	6	be	be	AUX
ejpam-5003	45	7	a	a	DET
ejpam-5003	45	8	binary	binary	ADJ
ejpam-5003	45	9	relation	relation	NOUN
ejpam-5003	45	10	on	on	ADP
ejpam-5003	45	11	a	a	DET
ejpam-5003	45	12	set	set	NOUN
ejpam-5003	45	13	a.	a.	NOUN
ejpam-5003	45	14	then	then	ADV
ejpam-5003	45	15	∼	∼	NOUN
ejpam-5003	45	16	is	be	AUX
ejpam-5003	45	17	called	call	VERB
ejpam-5003	45	18	(	(	PUNCT
ejpam-5003	45	19	i	i	NOUN
ejpam-5003	45	20	)	)	PUNCT
ejpam-5003	45	21	reflexive	reflexive	VERB
ejpam-5003	45	22	if	if	SCONJ
ejpam-5003	45	23	for	for	ADP
ejpam-5003	45	24	all	all	DET
ejpam-5003	45	25	x	x	SYM
ejpam-5003	45	26	∈	∈	PROPN
ejpam-5003	45	27	a	a	PRON
ejpam-5003	45	28	,	,	PUNCT
ejpam-5003	45	29	x	x	SYM
ejpam-5003	45	30	∼	∼	NOUN
ejpam-5003	45	31	x	x	SYM
ejpam-5003	45	32	;	;	PUNCT
ejpam-5003	45	33	(	(	PUNCT
ejpam-5003	45	34	ii	ii	NOUN
ejpam-5003	45	35	)	)	PUNCT
ejpam-5003	45	36	symmetric	symmetric	NOUN
ejpam-5003	45	37	if	if	SCONJ
ejpam-5003	45	38	for	for	ADP
ejpam-5003	45	39	all	all	DET
ejpam-5003	45	40	x	x	NOUN
ejpam-5003	45	41	,	,	PUNCT
ejpam-5003	45	42	y	y	PROPN
ejpam-5003	45	43	∈	∈	PROPN
ejpam-5003	45	44	a	a	PRON
ejpam-5003	45	45	,	,	PUNCT
ejpam-5003	45	46	x	x	SYM
ejpam-5003	45	47	∼	∼	NOUN
ejpam-5003	45	48	y	y	PROPN
ejpam-5003	45	49	implies	imply	VERB
ejpam-5003	45	50	y	y	PROPN
ejpam-5003	45	51	∼	∼	NOUN
ejpam-5003	45	52	x	x	ADP
ejpam-5003	45	53	;	;	PUNCT
ejpam-5003	45	54	and	and	CCONJ
ejpam-5003	45	55	(	(	PUNCT
ejpam-5003	45	56	iii	iii	X
ejpam-5003	45	57	)	)	PUNCT
ejpam-5003	45	58	transitive	transitive	ADJ
ejpam-5003	45	59	if	if	SCONJ
ejpam-5003	45	60	for	for	ADP
ejpam-5003	45	61	all	all	DET
ejpam-5003	45	62	x	x	NOUN
ejpam-5003	45	63	,	,	PUNCT
ejpam-5003	45	64	y	y	PROPN
ejpam-5003	45	65	,	,	PUNCT
ejpam-5003	45	66	z	z	PROPN
ejpam-5003	45	67	∈	∈	PROPN
ejpam-5003	46	1	a	a	PRON
ejpam-5003	46	2	,	,	PUNCT
ejpam-5003	46	3	x	x	SYM
ejpam-5003	46	4	∼	∼	NOUN
ejpam-5003	46	5	y	y	NOUN
ejpam-5003	46	6	and	and	CCONJ
ejpam-5003	46	7	y	y	PROPN
ejpam-5003	46	8	∼	∼	NOUN
ejpam-5003	47	1	z	z	NOUN
ejpam-5003	47	2	imply	imply	VERB
ejpam-5003	47	3	x	x	PUNCT
ejpam-5003	47	4	∼	∼	NOUN
ejpam-5003	47	5	z.	z.	NOUN
ejpam-5003	47	6	if	if	SCONJ
ejpam-5003	47	7	∼	∼	NOUN
ejpam-5003	47	8	is	be	AUX
ejpam-5003	47	9	reflexive	reflexive	ADJ
ejpam-5003	47	10	,	,	PUNCT
ejpam-5003	47	11	symmetric	symmetric	ADJ
ejpam-5003	47	12	,	,	PUNCT
ejpam-5003	47	13	and	and	CCONJ
ejpam-5003	47	14	transitive	transitive	ADJ
ejpam-5003	47	15	,	,	PUNCT
ejpam-5003	47	16	then	then	ADV
ejpam-5003	47	17	∼	∼	NOUN
ejpam-5003	47	18	is	be	AUX
ejpam-5003	47	19	called	call	VERB
ejpam-5003	47	20	an	an	DET
ejpam-5003	47	21	equivalence	equivalence	NOUN
ejpam-5003	47	22	relation	relation	NOUN
ejpam-5003	47	23	on	on	ADP
ejpam-5003	47	24	a.	a.	PROPN
ejpam-5003	47	25	l.r	l.r	PROPN
ejpam-5003	47	26	.	.	PROPN
ejpam-5003	47	27	cabardo	cabardo	PROPN
ejpam-5003	47	28	,	,	PUNCT
ejpam-5003	47	29	g.	g.	PROPN
ejpam-5003	47	30	petalcorin	petalcorin	PROPN
ejpam-5003	47	31	/	/	SYM
ejpam-5003	47	32	eur	eur	PROPN
ejpam-5003	47	33	.	.	PUNCT
ejpam-5003	48	1	j.	j.	PROPN
ejpam-5003	48	2	pure	pure	PROPN
ejpam-5003	48	3	appl	appl	PROPN
ejpam-5003	48	4	.	.	PROPN
ejpam-5003	48	5	math	math	PROPN
ejpam-5003	48	6	,	,	PUNCT
ejpam-5003	48	7	17	17	NUM
ejpam-5003	48	8	(	(	PUNCT
ejpam-5003	48	9	1	1	NUM
ejpam-5003	48	10	)	)	PUNCT
ejpam-5003	48	11	(	(	PUNCT
ejpam-5003	48	12	2024	2024	NUM
ejpam-5003	48	13	)	)	PUNCT
ejpam-5003	48	14	,	,	PUNCT
ejpam-5003	48	15	222	222	NUM
ejpam-5003	48	16	-	-	SYM
ejpam-5003	48	17	242	242	NUM
ejpam-5003	48	18	224	224	NUM
ejpam-5003	48	19	definition	definition	NOUN
ejpam-5003	48	20	3	3	NUM
ejpam-5003	48	21	.	.	PUNCT
ejpam-5003	49	1	[	[	X
ejpam-5003	49	2	6	6	NUM
ejpam-5003	49	3	]	]	PUNCT
ejpam-5003	49	4	let	let	VERB
ejpam-5003	49	5	∼	∼	NOUN
ejpam-5003	49	6	be	be	AUX
ejpam-5003	49	7	an	an	DET
ejpam-5003	49	8	equivalence	equivalence	NOUN
ejpam-5003	49	9	relation	relation	NOUN
ejpam-5003	49	10	on	on	ADP
ejpam-5003	49	11	a	a	DET
ejpam-5003	49	12	set	set	NOUN
ejpam-5003	49	13	a.	a.	NOUN
ejpam-5003	49	14	for	for	ADP
ejpam-5003	49	15	all	all	DET
ejpam-5003	49	16	x	x	SYM
ejpam-5003	49	17	∈	∈	PROPN
ejpam-5003	49	18	a	a	PRON
ejpam-5003	49	19	,	,	PUNCT
ejpam-5003	49	20	the	the	DET
ejpam-5003	49	21	set	set	NOUN
ejpam-5003	49	22	{	{	PUNCT
ejpam-5003	49	23	y	y	PROPN
ejpam-5003	49	24	∈	∈	PROPN
ejpam-5003	49	25	a	a	DET
ejpam-5003	49	26	:	:	PUNCT
ejpam-5003	49	27	y	y	PROPN
ejpam-5003	49	28	∼	∼	NOUN
ejpam-5003	49	29	x	x	VERB
ejpam-5003	49	30	}	}	PUNCT
ejpam-5003	49	31	is	be	AUX
ejpam-5003	49	32	called	call	VERB
ejpam-5003	49	33	the	the	DET
ejpam-5003	49	34	equivalence	equivalence	NOUN
ejpam-5003	49	35	class	class	NOUN
ejpam-5003	49	36	determined	determine	VERB
ejpam-5003	49	37	by	by	ADP
ejpam-5003	49	38	x	x	PRON
ejpam-5003	49	39	,	,	PUNCT
ejpam-5003	49	40	denoted	denote	VERB
ejpam-5003	49	41	by	by	ADP
ejpam-5003	49	42	[	[	PUNCT
ejpam-5003	49	43	x]∼.	x]∼.	PROPN
ejpam-5003	49	44	definition	definition	NOUN
ejpam-5003	49	45	4	4	NUM
ejpam-5003	49	46	.	.	PUNCT
ejpam-5003	50	1	[	[	X
ejpam-5003	50	2	4	4	X
ejpam-5003	50	3	]	]	PUNCT
ejpam-5003	50	4	define	define	VERB
ejpam-5003	50	5	p(h	p(h	NOUN
ejpam-5003	50	6	)	)	PUNCT
ejpam-5003	50	7	to	to	PART
ejpam-5003	50	8	be	be	AUX
ejpam-5003	50	9	the	the	DET
ejpam-5003	50	10	power	power	NOUN
ejpam-5003	50	11	set	set	NOUN
ejpam-5003	50	12	of	of	ADP
ejpam-5003	50	13	h	h	NOUN
ejpam-5003	50	14	and	and	CCONJ
ejpam-5003	50	15	p∗(h	p∗(h	PROPN
ejpam-5003	50	16	)	)	PUNCT
ejpam-5003	51	1	=	=	SYM
ejpam-5003	51	2	p(h	p(h	PROPN
ejpam-5003	51	3	)	)	PUNCT
ejpam-5003	51	4	\	\	NOUN
ejpam-5003	51	5	{	{	PUNCT
ejpam-5003	51	6	∅	∅	NOUN
ejpam-5003	51	7	}	}	PUNCT
ejpam-5003	51	8	.	.	PUNCT
ejpam-5003	52	1	a	a	DET
ejpam-5003	52	2	hyperoperation	hyperoperation	NOUN
ejpam-5003	52	3	on	on	ADP
ejpam-5003	52	4	a	a	DET
ejpam-5003	52	5	nonempty	nonempty	ADV
ejpam-5003	52	6	set	set	VERB
ejpam-5003	52	7	h	h	NOUN
ejpam-5003	52	8	is	be	AUX
ejpam-5003	52	9	a	a	DET
ejpam-5003	52	10	function	function	NOUN
ejpam-5003	52	11	⊛	⊛	NUM
ejpam-5003	52	12	:	:	PUNCT
ejpam-5003	52	13	h	h	PROPN
ejpam-5003	52	14	×	×	NOUN
ejpam-5003	52	15	h	h	NOUN
ejpam-5003	52	16	→	→	SYM
ejpam-5003	52	17	p∗(h	p∗(h	PROPN
ejpam-5003	52	18	)	)	PUNCT
ejpam-5003	52	19	.	.	PUNCT
ejpam-5003	53	1	the	the	DET
ejpam-5003	53	2	value	value	NOUN
ejpam-5003	53	3	(	(	PUNCT
ejpam-5003	53	4	x	x	NOUN
ejpam-5003	53	5	,	,	PUNCT
ejpam-5003	53	6	y	y	NOUN
ejpam-5003	53	7	)	)	PUNCT
ejpam-5003	53	8	∈	∈	PROPN
ejpam-5003	53	9	h	h	NOUN
ejpam-5003	53	10	×h	×h	PROPN
ejpam-5003	53	11	under	under	ADP
ejpam-5003	53	12	⊛	⊛	NUM
ejpam-5003	53	13	is	be	AUX
ejpam-5003	53	14	defined	define	VERB
ejpam-5003	53	15	by	by	ADP
ejpam-5003	53	16	x⊛	x⊛	PROPN
ejpam-5003	53	17	y.	y.	PROPN
ejpam-5003	54	1	if	if	SCONJ
ejpam-5003	54	2	x	x	SYM
ejpam-5003	54	3	∈	∈	PROPN
ejpam-5003	54	4	h	h	NOUN
ejpam-5003	54	5	and	and	CCONJ
ejpam-5003	54	6	∅	∅	NOUN
ejpam-5003	54	7	̸=	̸=	PROPN
ejpam-5003	54	8	a	a	PRON
ejpam-5003	54	9	,	,	PUNCT
ejpam-5003	54	10	b	b	PROPN
ejpam-5003	54	11	⊆	⊆	NUM
ejpam-5003	54	12	h	h	NOUN
ejpam-5003	54	13	,	,	PUNCT
ejpam-5003	54	14	then	then	ADV
ejpam-5003	54	15	(	(	PUNCT
ejpam-5003	54	16	i	i	NOUN
ejpam-5003	54	17	)	)	PUNCT
ejpam-5003	54	18	a⊛b	a⊛b	PROPN
ejpam-5003	54	19	=	=	PUNCT
ejpam-5003	54	20	⋃	⋃	NOUN
ejpam-5003	54	21	a∈a	a∈a	ADJ
ejpam-5003	54	22	,	,	PUNCT
ejpam-5003	54	23	b∈b	b∈b	VERB
ejpam-5003	54	24	a⊛	a⊛	PROPN
ejpam-5003	54	25	b	b	PROPN
ejpam-5003	54	26	;	;	PUNCT
ejpam-5003	54	27	and	and	CCONJ
ejpam-5003	54	28	(	(	PUNCT
ejpam-5003	54	29	ii	ii	NOUN
ejpam-5003	54	30	)	)	PUNCT
ejpam-5003	54	31	a⊛	a⊛	NOUN
ejpam-5003	54	32	x	x	X
ejpam-5003	54	33	=	=	SYM
ejpam-5003	54	34	a⊛	a⊛	X
ejpam-5003	54	35	{	{	PUNCT
ejpam-5003	54	36	x	x	NOUN
ejpam-5003	54	37	}	}	PUNCT
ejpam-5003	54	38	and	and	CCONJ
ejpam-5003	54	39	x⊛b	x⊛b	PROPN
ejpam-5003	54	40	=	=	PRON
ejpam-5003	54	41	{	{	PUNCT
ejpam-5003	54	42	x}⊛b	x}⊛b	PROPN
ejpam-5003	54	43	.	.	PROPN
ejpam-5003	55	1	in	in	ADP
ejpam-5003	55	2	what	what	PRON
ejpam-5003	55	3	follows	follow	VERB
ejpam-5003	55	4	,	,	PUNCT
ejpam-5003	55	5	the	the	DET
ejpam-5003	55	6	concepts	concept	NOUN
ejpam-5003	55	7	and	and	CCONJ
ejpam-5003	55	8	results	result	NOUN
ejpam-5003	55	9	are	be	AUX
ejpam-5003	55	10	taken	take	VERB
ejpam-5003	55	11	from	from	ADP
ejpam-5003	55	12	[	[	X
ejpam-5003	55	13	3	3	NUM
ejpam-5003	55	14	]	]	PUNCT
ejpam-5003	55	15	as	as	SCONJ
ejpam-5003	55	16	this	this	PRON
ejpam-5003	55	17	is	be	AUX
ejpam-5003	55	18	the	the	DET
ejpam-5003	55	19	main	main	ADJ
ejpam-5003	55	20	reference	reference	NOUN
ejpam-5003	55	21	of	of	ADP
ejpam-5003	55	22	this	this	DET
ejpam-5003	55	23	paper	paper	NOUN
ejpam-5003	55	24	.	.	PUNCT
ejpam-5003	56	1	definition	definition	NOUN
ejpam-5003	56	2	5	5	NUM
ejpam-5003	56	3	.	.	PUNCT
ejpam-5003	57	1	let	let	VERB
ejpam-5003	57	2	h	h	PRON
ejpam-5003	57	3	be	be	AUX
ejpam-5003	57	4	a	a	DET
ejpam-5003	57	5	nonempty	nonempty	ADV
ejpam-5003	57	6	set	set	VERB
ejpam-5003	57	7	and	and	CCONJ
ejpam-5003	57	8	⊛	⊛	NUM
ejpam-5003	57	9	be	be	VERB
ejpam-5003	57	10	a	a	DET
ejpam-5003	57	11	hyperoperation	hyperoperation	NOUN
ejpam-5003	57	12	on	on	ADP
ejpam-5003	57	13	h.	h.	PROPN
ejpam-5003	57	14	then	then	ADV
ejpam-5003	57	15	(	(	PUNCT
ejpam-5003	57	16	h,⊛	h,⊛	PROPN
ejpam-5003	57	17	,	,	PUNCT
ejpam-5003	57	18	0	0	NUM
ejpam-5003	57	19	)	)	PUNCT
ejpam-5003	57	20	is	be	AUX
ejpam-5003	57	21	called	call	VERB
ejpam-5003	57	22	a	a	DET
ejpam-5003	57	23	hyper	hyper	ADJ
ejpam-5003	57	24	bn	bn	ADJ
ejpam-5003	57	25	-algebra	-algebra	NOUN
ejpam-5003	57	26	,	,	PUNCT
ejpam-5003	57	27	if	if	SCONJ
ejpam-5003	57	28	0	0	NUM
ejpam-5003	57	29	∈	∈	PROPN
ejpam-5003	57	30	h	h	NOUN
ejpam-5003	57	31	and	and	CCONJ
ejpam-5003	57	32	the	the	DET
ejpam-5003	57	33	following	follow	VERB
ejpam-5003	57	34	conditions	condition	NOUN
ejpam-5003	57	35	hold	hold	VERB
ejpam-5003	57	36	:	:	PUNCT
ejpam-5003	57	37	for	for	ADP
ejpam-5003	57	38	all	all	DET
ejpam-5003	57	39	x	x	NOUN
ejpam-5003	57	40	,	,	PUNCT
ejpam-5003	57	41	y	y	PROPN
ejpam-5003	57	42	,	,	PUNCT
ejpam-5003	57	43	z	z	PROPN
ejpam-5003	57	44	∈	∈	PROPN
ejpam-5003	57	45	h	h	NOUN
ejpam-5003	57	46	,	,	PUNCT
ejpam-5003	57	47	(	(	PUNCT
ejpam-5003	57	48	i	i	NOUN
ejpam-5003	57	49	)	)	PUNCT
ejpam-5003	57	50	x	x	SYM
ejpam-5003	57	51	≪	≪	PUNCT
ejpam-5003	57	52	x	x	X
ejpam-5003	57	53	;	;	PUNCT
ejpam-5003	57	54	(	(	PUNCT
ejpam-5003	57	55	ii	ii	NOUN
ejpam-5003	57	56	)	)	PUNCT
ejpam-5003	57	57	x⊛	x⊛	PROPN
ejpam-5003	57	58	0	0	PUNCT
ejpam-5003	58	1	=	=	SYM
ejpam-5003	58	2	{	{	PUNCT
ejpam-5003	58	3	x	x	NOUN
ejpam-5003	58	4	}	}	PUNCT
ejpam-5003	58	5	;	;	PUNCT
ejpam-5003	58	6	and	and	CCONJ
ejpam-5003	58	7	(	(	PUNCT
ejpam-5003	58	8	iii	iii	NOUN
ejpam-5003	58	9	)	)	PUNCT
ejpam-5003	58	10	(	(	PUNCT
ejpam-5003	58	11	x⊛	x⊛	PROPN
ejpam-5003	59	1	y)⊛	y)⊛	NOUN
ejpam-5003	59	2	z	z	NOUN
ejpam-5003	59	3	=	=	SYM
ejpam-5003	59	4	(	(	PUNCT
ejpam-5003	59	5	0⊛	0⊛	NUM
ejpam-5003	59	6	z)⊛	z)⊛	PROPN
ejpam-5003	59	7	(	(	PUNCT
ejpam-5003	59	8	y	y	PROPN
ejpam-5003	59	9	⊛	⊛	NUM
ejpam-5003	59	10	x	x	NOUN
ejpam-5003	59	11	)	)	PUNCT
ejpam-5003	59	12	,	,	PUNCT
ejpam-5003	59	13	where	where	SCONJ
ejpam-5003	59	14	x	x	X
ejpam-5003	59	15	≪	≪	VERB
ejpam-5003	59	16	y	y	PROPN
ejpam-5003	59	17	if	if	SCONJ
ejpam-5003	59	18	and	and	CCONJ
ejpam-5003	59	19	only	only	ADV
ejpam-5003	60	1	if	if	SCONJ
ejpam-5003	60	2	0	0	NUM
ejpam-5003	60	3	∈	∈	PROPN
ejpam-5003	60	4	x⊛	x⊛	PROPN
ejpam-5003	61	1	y.	y.	PROPN
ejpam-5003	61	2	example	example	NOUN
ejpam-5003	62	1	1	1	X
ejpam-5003	62	2	.	.	PUNCT
ejpam-5003	62	3	let	let	VERB
ejpam-5003	62	4	h	h	NOUN
ejpam-5003	62	5	=	=	PRON
ejpam-5003	62	6	{	{	PUNCT
ejpam-5003	62	7	0	0	NUM
ejpam-5003	62	8	,	,	PUNCT
ejpam-5003	62	9	a	a	PRON
ejpam-5003	62	10	,	,	PUNCT
ejpam-5003	62	11	b	b	AUX
ejpam-5003	62	12	}	}	PUNCT
ejpam-5003	62	13	be	be	AUX
ejpam-5003	62	14	a	a	DET
ejpam-5003	62	15	set	set	NOUN
ejpam-5003	62	16	.	.	PUNCT
ejpam-5003	63	1	if	if	SCONJ
ejpam-5003	63	2	we	we	PRON
ejpam-5003	63	3	define	define	VERB
ejpam-5003	63	4	a	a	DET
ejpam-5003	63	5	hyperoperation	hyperoperation	NOUN
ejpam-5003	63	6	“	"	PUNCT
ejpam-5003	63	7	⊛	⊛	NUM
ejpam-5003	63	8	”	"	PUNCT
ejpam-5003	63	9	on	on	ADP
ejpam-5003	63	10	h	h	NOUN
ejpam-5003	63	11	as	as	SCONJ
ejpam-5003	63	12	follows	follow	VERB
ejpam-5003	63	13	:	:	PUNCT
ejpam-5003	63	14	⊛	⊛	NUM
ejpam-5003	63	15	0	0	NUM
ejpam-5003	63	16	a	a	DET
ejpam-5003	63	17	b	b	PROPN
ejpam-5003	63	18	0	0	NUM
ejpam-5003	63	19	{	{	PUNCT
ejpam-5003	63	20	0	0	NUM
ejpam-5003	63	21	}	}	PUNCT
ejpam-5003	63	22	{	{	PUNCT
ejpam-5003	63	23	a	a	NOUN
ejpam-5003	63	24	}	}	PUNCT
ejpam-5003	63	25	{	{	PUNCT
ejpam-5003	63	26	b	b	NOUN
ejpam-5003	63	27	}	}	PUNCT
ejpam-5003	63	28	a	a	DET
ejpam-5003	63	29	{	{	PUNCT
ejpam-5003	63	30	a	a	NOUN
ejpam-5003	63	31	}	}	PUNCT
ejpam-5003	63	32	{	{	PUNCT
ejpam-5003	63	33	0	0	NUM
ejpam-5003	63	34	,	,	PUNCT
ejpam-5003	63	35	a	a	PRON
ejpam-5003	63	36	}	}	PUNCT
ejpam-5003	63	37	{	{	PUNCT
ejpam-5003	63	38	b	b	NOUN
ejpam-5003	63	39	}	}	PUNCT
ejpam-5003	63	40	b	b	PROPN
ejpam-5003	63	41	{	{	PUNCT
ejpam-5003	63	42	b	b	NOUN
ejpam-5003	63	43	}	}	PUNCT
ejpam-5003	63	44	{	{	PUNCT
ejpam-5003	63	45	b	b	NOUN
ejpam-5003	63	46	}	}	PUNCT
ejpam-5003	63	47	{	{	PUNCT
ejpam-5003	63	48	0	0	NUM
ejpam-5003	63	49	,	,	PUNCT
ejpam-5003	63	50	b	b	NOUN
ejpam-5003	63	51	}	}	PUNCT
ejpam-5003	63	52	then	then	ADV
ejpam-5003	63	53	by	by	ADP
ejpam-5003	63	54	routinary	routinary	ADJ
ejpam-5003	63	55	calculations	calculation	NOUN
ejpam-5003	63	56	(	(	PUNCT
ejpam-5003	63	57	h,⊛	h,⊛	PROPN
ejpam-5003	63	58	,	,	PUNCT
ejpam-5003	63	59	0	0	NUM
ejpam-5003	63	60	)	)	PUNCT
ejpam-5003	63	61	is	be	AUX
ejpam-5003	63	62	a	a	DET
ejpam-5003	63	63	hyper	hyper	ADJ
ejpam-5003	63	64	bn	bn	NOUN
ejpam-5003	63	65	-algebra	-algebra	PROPN
ejpam-5003	63	66	.	.	PUNCT
ejpam-5003	63	67	example	example	NOUN
ejpam-5003	64	1	2	2	NUM
ejpam-5003	64	2	.	.	PUNCT
ejpam-5003	65	1	let	let	VERB
ejpam-5003	65	2	h	h	NOUN
ejpam-5003	65	3	=	=	PRON
ejpam-5003	65	4	{	{	PUNCT
ejpam-5003	65	5	0	0	NUM
ejpam-5003	65	6	,	,	PUNCT
ejpam-5003	65	7	1	1	NUM
ejpam-5003	65	8	,	,	PUNCT
ejpam-5003	65	9	2	2	NUM
ejpam-5003	65	10	}	}	PUNCT
ejpam-5003	65	11	be	be	AUX
ejpam-5003	65	12	a	a	DET
ejpam-5003	65	13	set	set	NOUN
ejpam-5003	65	14	.	.	PUNCT
ejpam-5003	66	1	if	if	SCONJ
ejpam-5003	66	2	we	we	PRON
ejpam-5003	66	3	define	define	VERB
ejpam-5003	66	4	a	a	DET
ejpam-5003	66	5	hyperoperation	hyperoperation	NOUN
ejpam-5003	66	6	“	"	PUNCT
ejpam-5003	66	7	⊛	⊛	NUM
ejpam-5003	66	8	”	"	PUNCT
ejpam-5003	66	9	on	on	ADP
ejpam-5003	66	10	h	h	NOUN
ejpam-5003	66	11	as	as	SCONJ
ejpam-5003	66	12	follows	follow	VERB
ejpam-5003	66	13	:	:	PUNCT
ejpam-5003	66	14	⊛	⊛	NUM
ejpam-5003	66	15	0	0	NUM
ejpam-5003	66	16	1	1	NUM
ejpam-5003	66	17	2	2	NUM
ejpam-5003	66	18	0	0	NUM
ejpam-5003	66	19	{	{	PUNCT
ejpam-5003	66	20	0	0	NUM
ejpam-5003	66	21	}	}	PUNCT
ejpam-5003	66	22	{	{	PUNCT
ejpam-5003	66	23	1	1	NUM
ejpam-5003	66	24	}	}	PUNCT
ejpam-5003	66	25	{	{	PUNCT
ejpam-5003	66	26	2	2	NUM
ejpam-5003	66	27	}	}	SYM
ejpam-5003	66	28	1	1	NUM
ejpam-5003	66	29	{	{	PUNCT
ejpam-5003	66	30	1	1	NUM
ejpam-5003	66	31	}	}	PUNCT
ejpam-5003	66	32	{	{	PUNCT
ejpam-5003	66	33	0	0	NUM
ejpam-5003	66	34	,	,	PUNCT
ejpam-5003	66	35	2	2	NUM
ejpam-5003	66	36	}	}	PUNCT
ejpam-5003	66	37	{	{	PUNCT
ejpam-5003	66	38	0	0	NUM
ejpam-5003	66	39	,	,	PUNCT
ejpam-5003	66	40	1	1	NUM
ejpam-5003	66	41	}	}	SYM
ejpam-5003	66	42	2	2	NUM
ejpam-5003	66	43	{	{	PUNCT
ejpam-5003	66	44	2	2	NUM
ejpam-5003	66	45	}	}	PUNCT
ejpam-5003	66	46	{	{	PUNCT
ejpam-5003	66	47	0	0	NUM
ejpam-5003	66	48	,	,	PUNCT
ejpam-5003	66	49	1	1	NUM
ejpam-5003	66	50	}	}	PUNCT
ejpam-5003	66	51	{	{	PUNCT
ejpam-5003	66	52	0	0	NUM
ejpam-5003	66	53	,	,	PUNCT
ejpam-5003	66	54	1	1	NUM
ejpam-5003	66	55	}	}	PUNCT
ejpam-5003	66	56	then	then	ADV
ejpam-5003	66	57	by	by	ADP
ejpam-5003	66	58	routinary	routinary	ADJ
ejpam-5003	66	59	calculations	calculation	NOUN
ejpam-5003	66	60	(	(	PUNCT
ejpam-5003	66	61	h,⊛	h,⊛	PROPN
ejpam-5003	66	62	,	,	PUNCT
ejpam-5003	66	63	0	0	NUM
ejpam-5003	66	64	)	)	PUNCT
ejpam-5003	66	65	is	be	AUX
ejpam-5003	66	66	a	a	DET
ejpam-5003	66	67	hyper	hyper	ADJ
ejpam-5003	66	68	bn	bn	NOUN
ejpam-5003	66	69	-algebra	-algebra	PROPN
ejpam-5003	66	70	.	.	PUNCT
ejpam-5003	66	71	example	example	NOUN
ejpam-5003	67	1	3	3	X
ejpam-5003	67	2	.	.	PUNCT
ejpam-5003	67	3	let	let	VERB
ejpam-5003	67	4	h	h	NOUN
ejpam-5003	67	5	=	=	PUNCT
ejpam-5003	67	6	{	{	PUNCT
ejpam-5003	67	7	0	0	NUM
ejpam-5003	67	8	,	,	PUNCT
ejpam-5003	67	9	1	1	NUM
ejpam-5003	67	10	,	,	PUNCT
ejpam-5003	67	11	2	2	NUM
ejpam-5003	67	12	,	,	PUNCT
ejpam-5003	67	13	3	3	NUM
ejpam-5003	67	14	}	}	PUNCT
ejpam-5003	67	15	be	be	AUX
ejpam-5003	67	16	a	a	DET
ejpam-5003	67	17	set	set	NOUN
ejpam-5003	67	18	.	.	PUNCT
ejpam-5003	68	1	if	if	SCONJ
ejpam-5003	68	2	we	we	PRON
ejpam-5003	68	3	define	define	VERB
ejpam-5003	68	4	a	a	DET
ejpam-5003	68	5	hyperoperation	hyperoperation	NOUN
ejpam-5003	68	6	“	"	PUNCT
ejpam-5003	68	7	⊛	⊛	NUM
ejpam-5003	68	8	”	"	PUNCT
ejpam-5003	68	9	on	on	ADP
ejpam-5003	68	10	h	h	NOUN
ejpam-5003	68	11	as	as	SCONJ
ejpam-5003	68	12	follows	follow	VERB
ejpam-5003	68	13	:	:	PUNCT
ejpam-5003	68	14	l.r	l.r	PROPN
ejpam-5003	68	15	.	.	PROPN
ejpam-5003	68	16	cabardo	cabardo	PROPN
ejpam-5003	68	17	,	,	PUNCT
ejpam-5003	68	18	g.	g.	PROPN
ejpam-5003	68	19	petalcorin	petalcorin	PROPN
ejpam-5003	68	20	/	/	SYM
ejpam-5003	68	21	eur	eur	PROPN
ejpam-5003	68	22	.	.	PUNCT
ejpam-5003	69	1	j.	j.	PROPN
ejpam-5003	69	2	pure	pure	PROPN
ejpam-5003	69	3	appl	appl	PROPN
ejpam-5003	69	4	.	.	PROPN
ejpam-5003	69	5	math	math	PROPN
ejpam-5003	69	6	,	,	PUNCT
ejpam-5003	69	7	17	17	NUM
ejpam-5003	69	8	(	(	PUNCT
ejpam-5003	69	9	1	1	NUM
ejpam-5003	69	10	)	)	PUNCT
ejpam-5003	69	11	(	(	PUNCT
ejpam-5003	69	12	2024	2024	NUM
ejpam-5003	69	13	)	)	PUNCT
ejpam-5003	69	14	,	,	PUNCT
ejpam-5003	69	15	222	222	NUM
ejpam-5003	69	16	-	-	SYM
ejpam-5003	69	17	242	242	NUM
ejpam-5003	69	18	225	225	NUM
ejpam-5003	69	19	⊛	⊛	NUM
ejpam-5003	69	20	0	0	NUM
ejpam-5003	69	21	1	1	NUM
ejpam-5003	69	22	2	2	NUM
ejpam-5003	69	23	3	3	NUM
ejpam-5003	69	24	0	0	NUM
ejpam-5003	69	25	{	{	PUNCT
ejpam-5003	69	26	0	0	NUM
ejpam-5003	69	27	}	}	PUNCT
ejpam-5003	69	28	{	{	PUNCT
ejpam-5003	69	29	1	1	NUM
ejpam-5003	69	30	}	}	PUNCT
ejpam-5003	69	31	{	{	PUNCT
ejpam-5003	69	32	3	3	NUM
ejpam-5003	69	33	}	}	PUNCT
ejpam-5003	69	34	{	{	PUNCT
ejpam-5003	69	35	2	2	NUM
ejpam-5003	69	36	}	}	SYM
ejpam-5003	69	37	1	1	NUM
ejpam-5003	69	38	{	{	PUNCT
ejpam-5003	69	39	1	1	NUM
ejpam-5003	69	40	}	}	PUNCT
ejpam-5003	69	41	{	{	PUNCT
ejpam-5003	69	42	0	0	NUM
ejpam-5003	69	43	,	,	PUNCT
ejpam-5003	69	44	1	1	NUM
ejpam-5003	69	45	}	}	PUNCT
ejpam-5003	69	46	{	{	PUNCT
ejpam-5003	69	47	0	0	NUM
ejpam-5003	69	48	,	,	PUNCT
ejpam-5003	69	49	1	1	NUM
ejpam-5003	69	50	,	,	PUNCT
ejpam-5003	69	51	2	2	NUM
ejpam-5003	69	52	}	}	PUNCT
ejpam-5003	69	53	{	{	PUNCT
ejpam-5003	69	54	0	0	NUM
ejpam-5003	69	55	,	,	PUNCT
ejpam-5003	69	56	1	1	NUM
ejpam-5003	69	57	,	,	PUNCT
ejpam-5003	69	58	3	3	NUM
ejpam-5003	69	59	}	}	SYM
ejpam-5003	69	60	2	2	NUM
ejpam-5003	69	61	{	{	PUNCT
ejpam-5003	69	62	2	2	NUM
ejpam-5003	69	63	}	}	PUNCT
ejpam-5003	69	64	{	{	PUNCT
ejpam-5003	69	65	0	0	NUM
ejpam-5003	69	66	,	,	PUNCT
ejpam-5003	69	67	1	1	NUM
ejpam-5003	69	68	,	,	PUNCT
ejpam-5003	69	69	3	3	NUM
ejpam-5003	69	70	}	}	PUNCT
ejpam-5003	69	71	{	{	PUNCT
ejpam-5003	69	72	0	0	NUM
ejpam-5003	69	73	,	,	PUNCT
ejpam-5003	69	74	1	1	NUM
ejpam-5003	69	75	,	,	PUNCT
ejpam-5003	69	76	2	2	NUM
ejpam-5003	69	77	,	,	PUNCT
ejpam-5003	69	78	3	3	NUM
ejpam-5003	69	79	}	}	PUNCT
ejpam-5003	69	80	{	{	PUNCT
ejpam-5003	69	81	0	0	NUM
ejpam-5003	69	82	,	,	PUNCT
ejpam-5003	69	83	2	2	NUM
ejpam-5003	69	84	}	}	SYM
ejpam-5003	69	85	3	3	NUM
ejpam-5003	69	86	{	{	PUNCT
ejpam-5003	69	87	3	3	NUM
ejpam-5003	69	88	}	}	PUNCT
ejpam-5003	69	89	{	{	PUNCT
ejpam-5003	69	90	0	0	NUM
ejpam-5003	69	91	,	,	PUNCT
ejpam-5003	69	92	1	1	NUM
ejpam-5003	69	93	,	,	PUNCT
ejpam-5003	69	94	2	2	NUM
ejpam-5003	69	95	}	}	PUNCT
ejpam-5003	69	96	{	{	PUNCT
ejpam-5003	69	97	0	0	NUM
ejpam-5003	69	98	,	,	PUNCT
ejpam-5003	69	99	3	3	NUM
ejpam-5003	69	100	}	}	PUNCT
ejpam-5003	69	101	{	{	PUNCT
ejpam-5003	69	102	0	0	NUM
ejpam-5003	69	103	,	,	PUNCT
ejpam-5003	69	104	1	1	NUM
ejpam-5003	69	105	,	,	PUNCT
ejpam-5003	69	106	2	2	NUM
ejpam-5003	69	107	,	,	PUNCT
ejpam-5003	69	108	3	3	NUM
ejpam-5003	69	109	}	}	PUNCT
ejpam-5003	69	110	then	then	ADV
ejpam-5003	69	111	by	by	ADP
ejpam-5003	69	112	routinary	routinary	ADJ
ejpam-5003	69	113	calculations	calculation	NOUN
ejpam-5003	69	114	(	(	PUNCT
ejpam-5003	69	115	h,⊛	h,⊛	PROPN
ejpam-5003	69	116	,	,	PUNCT
ejpam-5003	69	117	0	0	NUM
ejpam-5003	69	118	)	)	PUNCT
ejpam-5003	69	119	is	be	AUX
ejpam-5003	69	120	a	a	DET
ejpam-5003	69	121	hyper	hyper	ADJ
ejpam-5003	69	122	bn	bn	NOUN
ejpam-5003	69	123	-algebra	-algebra	PROPN
ejpam-5003	69	124	.	.	PUNCT
ejpam-5003	69	125	example	example	NOUN
ejpam-5003	70	1	4	4	NUM
ejpam-5003	70	2	.	.	PUNCT
ejpam-5003	70	3	let	let	VERB
ejpam-5003	70	4	z	z	NOUN
ejpam-5003	70	5	be	be	AUX
ejpam-5003	70	6	the	the	DET
ejpam-5003	70	7	set	set	NOUN
ejpam-5003	70	8	of	of	ADP
ejpam-5003	70	9	integers	integer	NOUN
ejpam-5003	70	10	.	.	PUNCT
ejpam-5003	71	1	define	define	VERB
ejpam-5003	71	2	a	a	DET
ejpam-5003	71	3	hyperoperation	hyperoperation	NOUN
ejpam-5003	71	4	“	"	PUNCT
ejpam-5003	71	5	⊛	⊛	NUM
ejpam-5003	71	6	”	"	PUNCT
ejpam-5003	71	7	on	on	ADP
ejpam-5003	71	8	z	z	PROPN
ejpam-5003	71	9	by	by	ADP
ejpam-5003	71	10	:	:	PUNCT
ejpam-5003	71	11	x⊛	x⊛	PROPN
ejpam-5003	71	12	y	y	NOUN
ejpam-5003	71	13	=	=	PUNCT
ejpam-5003	71	14			PUNCT
ejpam-5003	71	15	{	{	PUNCT
ejpam-5003	71	16	x	x	NOUN
ejpam-5003	71	17	}	}	PUNCT
ejpam-5003	71	18	,	,	PUNCT
ejpam-5003	71	19	if	if	SCONJ
ejpam-5003	71	20	y	y	PROPN
ejpam-5003	71	21	=	=	SYM
ejpam-5003	71	22	0	0	PUNCT
ejpam-5003	71	23	{	{	PUNCT
ejpam-5003	71	24	y	y	NOUN
ejpam-5003	71	25	}	}	PUNCT
ejpam-5003	71	26	,	,	PUNCT
ejpam-5003	71	27	if	if	SCONJ
ejpam-5003	71	28	x	x	ADP
ejpam-5003	71	29	=	=	SYM
ejpam-5003	71	30	0	0	NUM
ejpam-5003	71	31	{	{	PUNCT
ejpam-5003	71	32	x−	x−	PROPN
ejpam-5003	71	33	y	y	PROPN
ejpam-5003	71	34	,	,	PUNCT
ejpam-5003	71	35	y	y	PROPN
ejpam-5003	71	36	−	−	PROPN
ejpam-5003	71	37	x	x	SYM
ejpam-5003	71	38	,	,	PUNCT
ejpam-5003	71	39	x+	x+	ADJ
ejpam-5003	71	40	y	y	NOUN
ejpam-5003	71	41	}	}	PUNCT
ejpam-5003	71	42	,	,	PUNCT
ejpam-5003	71	43	otherwise	otherwise	ADV
ejpam-5003	71	44	.	.	PUNCT
ejpam-5003	72	1	then	then	ADV
ejpam-5003	72	2	,	,	PUNCT
ejpam-5003	72	3	we	we	PRON
ejpam-5003	72	4	can	can	AUX
ejpam-5003	72	5	show	show	VERB
ejpam-5003	72	6	that	that	SCONJ
ejpam-5003	72	7	(	(	PUNCT
ejpam-5003	72	8	z,⊛	z,⊛	NUM
ejpam-5003	72	9	,	,	PUNCT
ejpam-5003	72	10	0	0	NUM
ejpam-5003	72	11	)	)	PUNCT
ejpam-5003	72	12	is	be	AUX
ejpam-5003	72	13	a	a	DET
ejpam-5003	72	14	hyper	hyper	ADJ
ejpam-5003	72	15	bn	bn	NOUN
ejpam-5003	72	16	-algebra	-algebra	NOUN
ejpam-5003	72	17	.	.	PUNCT
ejpam-5003	73	1	note	note	VERB
ejpam-5003	73	2	that	that	SCONJ
ejpam-5003	73	3	,	,	PUNCT
ejpam-5003	73	4	the	the	DET
ejpam-5003	73	5	same	same	ADJ
ejpam-5003	73	6	holds	hold	VERB
ejpam-5003	73	7	when	when	SCONJ
ejpam-5003	73	8	z	z	NOUN
ejpam-5003	73	9	is	be	AUX
ejpam-5003	73	10	replaced	replace	VERB
ejpam-5003	73	11	by	by	ADP
ejpam-5003	73	12	q	q	PROPN
ejpam-5003	73	13	,	,	PUNCT
ejpam-5003	73	14	r	r	NOUN
ejpam-5003	73	15	or	or	CCONJ
ejpam-5003	73	16	c.	c.	NOUN
ejpam-5003	73	17	theorem	theorem	NOUN
ejpam-5003	73	18	1	1	NUM
ejpam-5003	73	19	.	.	PUNCT
ejpam-5003	74	1	in	in	ADP
ejpam-5003	74	2	any	any	DET
ejpam-5003	74	3	hyper	hyper	ADJ
ejpam-5003	74	4	bn	bn	NOUN
ejpam-5003	74	5	-algebra	-algebra	PROPN
ejpam-5003	74	6	h	h	NOUN
ejpam-5003	74	7	,	,	PUNCT
ejpam-5003	74	8	the	the	DET
ejpam-5003	74	9	following	follow	VERB
ejpam-5003	74	10	hold	hold	NOUN
ejpam-5003	74	11	:	:	PUNCT
ejpam-5003	74	12	for	for	ADP
ejpam-5003	74	13	any	any	DET
ejpam-5003	74	14	x	x	NOUN
ejpam-5003	74	15	,	,	PUNCT
ejpam-5003	74	16	y	y	PROPN
ejpam-5003	74	17	,	,	PUNCT
ejpam-5003	74	18	z	z	PROPN
ejpam-5003	74	19	∈	∈	PROPN
ejpam-5003	74	20	h	h	NOUN
ejpam-5003	74	21	and	and	CCONJ
ejpam-5003	74	22	∅	∅	NOUN
ejpam-5003	74	23	̸=	̸=	PROPN
ejpam-5003	74	24	a	a	DET
ejpam-5003	74	25	,	,	PUNCT
ejpam-5003	74	26	b	b	NOUN
ejpam-5003	74	27	,	,	PUNCT
ejpam-5003	74	28	c	c	PROPN
ejpam-5003	74	29	⊆	⊆	NUM
ejpam-5003	74	30	h	h	NOUN
ejpam-5003	74	31	,	,	PUNCT
ejpam-5003	74	32	(	(	PUNCT
ejpam-5003	74	33	i	i	NOUN
ejpam-5003	74	34	)	)	PUNCT
ejpam-5003	74	35	x⊛	x⊛	PROPN
ejpam-5003	75	1	x	x	X
ejpam-5003	75	2	=	=	PRON
ejpam-5003	75	3	{	{	PUNCT
ejpam-5003	75	4	x	x	NOUN
ejpam-5003	75	5	}	}	PUNCT
ejpam-5003	75	6	⇔	⇔	NOUN
ejpam-5003	75	7	x	x	PUNCT
ejpam-5003	75	8	=	=	SYM
ejpam-5003	75	9	0	0	NUM
ejpam-5003	75	10	;	;	PUNCT
ejpam-5003	75	11	(	(	PUNCT
ejpam-5003	75	12	ii	ii	NOUN
ejpam-5003	75	13	)	)	PUNCT
ejpam-5003	75	14	x	x	PUNCT
ejpam-5003	75	15	≪	≪	ADJ
ejpam-5003	75	16	0	0	NUM
ejpam-5003	75	17	⇒	⇒	NOUN
ejpam-5003	75	18	x	x	PUNCT
ejpam-5003	76	1	=	=	SYM
ejpam-5003	76	2	0	0	NUM
ejpam-5003	76	3	;	;	PUNCT
ejpam-5003	76	4	(	(	PUNCT
ejpam-5003	76	5	iii	iii	X
ejpam-5003	76	6	)	)	PUNCT
ejpam-5003	76	7	0⊛	0⊛	NUM
ejpam-5003	76	8	(	(	PUNCT
ejpam-5003	76	9	0⊛	0⊛	NUM
ejpam-5003	76	10	x	x	X
ejpam-5003	76	11	)	)	PUNCT
ejpam-5003	76	12	=	=	SYM
ejpam-5003	76	13	{	{	PUNCT
ejpam-5003	76	14	x	x	NOUN
ejpam-5003	76	15	}	}	PUNCT
ejpam-5003	76	16	;	;	PUNCT
ejpam-5003	76	17	(	(	PUNCT
ejpam-5003	76	18	iv	iv	X
ejpam-5003	76	19	)	)	PUNCT
ejpam-5003	76	20	0⊛	0⊛	NUM
ejpam-5003	76	21	(	(	PUNCT
ejpam-5003	76	22	x⊛	x⊛	PROPN
ejpam-5003	76	23	y	y	NOUN
ejpam-5003	76	24	)	)	PUNCT
ejpam-5003	77	1	=	=	SYM
ejpam-5003	77	2	y	y	PROPN
ejpam-5003	77	3	⊛	⊛	NUM
ejpam-5003	77	4	x	x	NOUN
ejpam-5003	77	5	;	;	PUNCT
ejpam-5003	77	6	(	(	PUNCT
ejpam-5003	77	7	v	v	NOUN
ejpam-5003	77	8	)	)	PUNCT
ejpam-5003	77	9	x⊛	x⊛	PROPN
ejpam-5003	78	1	y	y	NOUN
ejpam-5003	78	2	=	=	PUNCT
ejpam-5003	78	3	(	(	PUNCT
ejpam-5003	78	4	0⊛	0⊛	NUM
ejpam-5003	78	5	y)⊛	y)⊛	NOUN
ejpam-5003	78	6	(	(	PUNCT
ejpam-5003	78	7	0⊛	0⊛	NUM
ejpam-5003	78	8	x	x	NOUN
ejpam-5003	78	9	)	)	PUNCT
ejpam-5003	78	10	;	;	PUNCT
ejpam-5003	78	11	(	(	PUNCT
ejpam-5003	78	12	vi	vi	X
ejpam-5003	78	13	)	)	PUNCT
ejpam-5003	78	14	(	(	PUNCT
ejpam-5003	78	15	0⊛	0⊛	NUM
ejpam-5003	78	16	x)⊛	x)⊛	PROPN
ejpam-5003	79	1	y	y	SYM
ejpam-5003	79	2	=	=	PUNCT
ejpam-5003	79	3	(	(	PUNCT
ejpam-5003	79	4	0⊛	0⊛	NUM
ejpam-5003	79	5	y)⊛	y)⊛	NOUN
ejpam-5003	79	6	x	x	SYM
ejpam-5003	79	7	;	;	PUNCT
ejpam-5003	79	8	(	(	PUNCT
ejpam-5003	79	9	vii	vii	PROPN
ejpam-5003	79	10	)	)	PUNCT
ejpam-5003	79	11	x	x	PUNCT
ejpam-5003	79	12	≪	≪	PUNCT
ejpam-5003	79	13	y	y	PROPN
ejpam-5003	79	14	⇒	⇒	NOUN
ejpam-5003	79	15	y	y	PROPN
ejpam-5003	79	16	≪	≪	PROPN
ejpam-5003	79	17	x	x	PRON
ejpam-5003	79	18	;	;	PUNCT
ejpam-5003	79	19	(	(	PUNCT
ejpam-5003	79	20	viii	viii	NOUN
ejpam-5003	79	21	)	)	PUNCT
ejpam-5003	79	22	0⊛	0⊛	NUM
ejpam-5003	79	23	x	x	X
ejpam-5003	79	24	=	=	SYM
ejpam-5003	79	25	0⊛	0⊛	NUM
ejpam-5003	79	26	y	y	PROPN
ejpam-5003	79	27	⇒	⇒	NOUN
ejpam-5003	79	28	x	x	PUNCT
ejpam-5003	79	29	=	=	SYM
ejpam-5003	79	30	y	y	PROPN
ejpam-5003	79	31	;	;	PUNCT
ejpam-5003	79	32	(	(	PUNCT
ejpam-5003	79	33	ix	ix	X
ejpam-5003	79	34	)	)	PUNCT
ejpam-5003	79	35	(	(	PUNCT
ejpam-5003	79	36	x⊛	x⊛	PROPN
ejpam-5003	79	37	z)⊛	z)⊛	PROPN
ejpam-5003	79	38	(	(	PUNCT
ejpam-5003	79	39	y	y	PROPN
ejpam-5003	79	40	⊛	⊛	PROPN
ejpam-5003	79	41	z	z	PROPN
ejpam-5003	79	42	)	)	PUNCT
ejpam-5003	79	43	=	=	SYM
ejpam-5003	79	44	(	(	PUNCT
ejpam-5003	79	45	z	z	NOUN
ejpam-5003	79	46	⊛	⊛	NUM
ejpam-5003	79	47	y)⊛	y)⊛	NOUN
ejpam-5003	79	48	(	(	PUNCT
ejpam-5003	79	49	z	z	NOUN
ejpam-5003	79	50	⊛	⊛	NUM
ejpam-5003	79	51	x	x	NOUN
ejpam-5003	79	52	)	)	PUNCT
ejpam-5003	79	53	;	;	PUNCT
ejpam-5003	79	54	(	(	PUNCT
ejpam-5003	79	55	x	x	X
ejpam-5003	79	56	)	)	PUNCT
ejpam-5003	79	57	a	a	DET
ejpam-5003	79	58	≪	≪	ADJ
ejpam-5003	79	59	a	a	DET
ejpam-5003	79	60	;	;	PUNCT
ejpam-5003	79	61	(	(	PUNCT
ejpam-5003	79	62	xi	xi	X
ejpam-5003	79	63	)	)	PUNCT
ejpam-5003	79	64	a	a	DET
ejpam-5003	79	65	⊆	⊆	NUM
ejpam-5003	79	66	b	b	NOUN
ejpam-5003	79	67	⇒	⇒	NOUN
ejpam-5003	79	68	a	a	DET
ejpam-5003	79	69	≪	≪	ADJ
ejpam-5003	79	70	b	b	NOUN
ejpam-5003	79	71	;	;	PUNCT
ejpam-5003	79	72	(	(	PUNCT
ejpam-5003	79	73	xii	xii	NOUN
ejpam-5003	79	74	)	)	PUNCT
ejpam-5003	79	75	a	a	DET
ejpam-5003	79	76	⊆	⊆	NUM
ejpam-5003	79	77	b	b	NOUN
ejpam-5003	79	78	and	and	CCONJ
ejpam-5003	79	79	b	b	PROPN
ejpam-5003	79	80	≪	≪	PUNCT
ejpam-5003	79	81	c	c	PUNCT
ejpam-5003	79	82	imply	imply	VERB
ejpam-5003	79	83	a	a	DET
ejpam-5003	79	84	≪	≪	ADJ
ejpam-5003	79	85	c	c	NOUN
ejpam-5003	79	86	;	;	PUNCT
ejpam-5003	79	87	(	(	PUNCT
ejpam-5003	79	88	xiii	xiii	X
ejpam-5003	79	89	)	)	PUNCT
ejpam-5003	79	90	a	a	DET
ejpam-5003	79	91	≪	≪	PUNCT
ejpam-5003	79	92	{	{	PUNCT
ejpam-5003	79	93	0	0	NUM
ejpam-5003	79	94	}	}	PUNCT
ejpam-5003	79	95	⇒	⇒	VERB
ejpam-5003	79	96	a	a	DET
ejpam-5003	79	97	=	=	X
ejpam-5003	79	98	{	{	PUNCT
ejpam-5003	79	99	0	0	NUM
ejpam-5003	79	100	}	}	PUNCT
ejpam-5003	79	101	;	;	PUNCT
ejpam-5003	79	102	(	(	PUNCT
ejpam-5003	79	103	xiv	xiv	NOUN
ejpam-5003	79	104	)	)	PUNCT
ejpam-5003	79	105	a⊛	a⊛	NOUN
ejpam-5003	79	106	{	{	PUNCT
ejpam-5003	79	107	0	0	NUM
ejpam-5003	79	108	}	}	PUNCT
ejpam-5003	79	109	=	=	SYM
ejpam-5003	79	110	{	{	PUNCT
ejpam-5003	79	111	0	0	NUM
ejpam-5003	79	112	}	}	PUNCT
ejpam-5003	79	113	⇒	⇒	VERB
ejpam-5003	79	114	a	a	DET
ejpam-5003	79	115	=	=	X
ejpam-5003	79	116	{	{	PUNCT
ejpam-5003	79	117	0	0	NUM
ejpam-5003	79	118	}	}	PUNCT
ejpam-5003	79	119	;	;	PUNCT
ejpam-5003	79	120	and	and	CCONJ
ejpam-5003	79	121	(	(	PUNCT
ejpam-5003	79	122	xv	xv	PROPN
ejpam-5003	79	123	)	)	PUNCT
ejpam-5003	79	124	(	(	PUNCT
ejpam-5003	80	1	a⊛b)⊛	a⊛b)⊛	PROPN
ejpam-5003	80	2	c	c	NOUN
ejpam-5003	80	3	=	=	PUNCT
ejpam-5003	80	4	(	(	PUNCT
ejpam-5003	80	5	0⊛	0⊛	NUM
ejpam-5003	80	6	c)⊛	c)⊛	PROPN
ejpam-5003	80	7	(	(	PUNCT
ejpam-5003	80	8	b	b	NOUN
ejpam-5003	80	9	⊛a	⊛a	PROPN
ejpam-5003	80	10	)	)	PUNCT
ejpam-5003	80	11	.	.	PUNCT
ejpam-5003	81	1	definition	definition	NOUN
ejpam-5003	81	2	6	6	NUM
ejpam-5003	81	3	.	.	PUNCT
ejpam-5003	82	1	a	a	DET
ejpam-5003	82	2	hyper	hyper	ADJ
ejpam-5003	82	3	bn	bn	NOUN
ejpam-5003	82	4	-algebra	-algebra	NOUN
ejpam-5003	82	5	h	h	NOUN
ejpam-5003	82	6	is	be	AUX
ejpam-5003	82	7	said	say	VERB
ejpam-5003	82	8	to	to	PART
ejpam-5003	82	9	be	be	AUX
ejpam-5003	82	10	commutative	commutative	ADJ
ejpam-5003	82	11	if	if	SCONJ
ejpam-5003	82	12	for	for	ADP
ejpam-5003	82	13	all	all	DET
ejpam-5003	82	14	x	x	NOUN
ejpam-5003	82	15	,	,	PUNCT
ejpam-5003	82	16	y	y	PROPN
ejpam-5003	82	17	∈	∈	PROPN
ejpam-5003	82	18	h	h	NOUN
ejpam-5003	82	19	,	,	PUNCT
ejpam-5003	82	20	x⊛	x⊛	PROPN
ejpam-5003	82	21	y	y	NOUN
ejpam-5003	82	22	=	=	SYM
ejpam-5003	82	23	y	y	PROPN
ejpam-5003	82	24	⊛	⊛	NUM
ejpam-5003	82	25	x.	x.	NOUN
ejpam-5003	82	26	example	example	NOUN
ejpam-5003	82	27	5	5	NUM
ejpam-5003	82	28	.	.	PUNCT
ejpam-5003	83	1	the	the	DET
ejpam-5003	83	2	hyper	hyper	ADJ
ejpam-5003	83	3	bn	bn	ADJ
ejpam-5003	83	4	-algebras	-algebra	NOUN
ejpam-5003	83	5	in	in	ADP
ejpam-5003	83	6	example	example	NOUN
ejpam-5003	83	7	1	1	NUM
ejpam-5003	83	8	and	and	CCONJ
ejpam-5003	83	9	example	example	NOUN
ejpam-5003	83	10	2	2	NUM
ejpam-5003	83	11	are	be	AUX
ejpam-5003	83	12	commutative	commutative	ADJ
ejpam-5003	83	13	while	while	SCONJ
ejpam-5003	83	14	the	the	DET
ejpam-5003	83	15	hyper	hyper	ADJ
ejpam-5003	83	16	bn	bn	NOUN
ejpam-5003	83	17	-algebra	-algebra	PROPN
ejpam-5003	83	18	in	in	ADP
ejpam-5003	83	19	example	example	NOUN
ejpam-5003	83	20	3	3	NUM
ejpam-5003	83	21	is	be	AUX
ejpam-5003	83	22	not	not	PART
ejpam-5003	83	23	because	because	SCONJ
ejpam-5003	83	24	2⊛	2⊛	NUM
ejpam-5003	83	25	0	0	NUM
ejpam-5003	83	26	=	=	SYM
ejpam-5003	83	27	{	{	PUNCT
ejpam-5003	83	28	2	2	NUM
ejpam-5003	83	29	}	}	PUNCT
ejpam-5003	83	30	=	=	NOUN
ejpam-5003	83	31	̸	̸	NUM
ejpam-5003	83	32	{	{	PUNCT
ejpam-5003	83	33	3	3	NUM
ejpam-5003	83	34	}	}	PUNCT
ejpam-5003	83	35	=	=	NOUN
ejpam-5003	83	36	0⊛	0⊛	NUM
ejpam-5003	83	37	2	2	NUM
ejpam-5003	83	38	.	.	PUNCT
ejpam-5003	83	39	theorem	theorem	NOUN
ejpam-5003	83	40	2	2	NUM
ejpam-5003	83	41	.	.	PUNCT
ejpam-5003	84	1	let	let	VERB
ejpam-5003	84	2	h	h	PRON
ejpam-5003	84	3	be	be	AUX
ejpam-5003	84	4	a	a	DET
ejpam-5003	84	5	hyper	hyper	ADJ
ejpam-5003	84	6	bn	bn	NOUN
ejpam-5003	84	7	-algebra	-algebra	NOUN
ejpam-5003	84	8	.	.	PUNCT
ejpam-5003	85	1	then	then	ADV
ejpam-5003	85	2	h	h	PROPN
ejpam-5003	85	3	is	be	AUX
ejpam-5003	85	4	commutative	commutative	ADJ
ejpam-5003	85	5	if	if	SCONJ
ejpam-5003	85	6	and	and	CCONJ
ejpam-5003	85	7	only	only	ADV
ejpam-5003	85	8	if	if	SCONJ
ejpam-5003	85	9	0⊛	0⊛	NUM
ejpam-5003	85	10	x	x	X
ejpam-5003	85	11	=	=	SYM
ejpam-5003	85	12	{	{	PUNCT
ejpam-5003	85	13	x	x	NOUN
ejpam-5003	85	14	}	}	PUNCT
ejpam-5003	85	15	for	for	ADP
ejpam-5003	85	16	all	all	DET
ejpam-5003	85	17	x	x	SYM
ejpam-5003	85	18	∈	∈	PROPN
ejpam-5003	85	19	h.	h.	NOUN
ejpam-5003	85	20	we	we	PRON
ejpam-5003	85	21	will	will	AUX
ejpam-5003	85	22	provide	provide	VERB
ejpam-5003	85	23	some	some	DET
ejpam-5003	85	24	basic	basic	ADJ
ejpam-5003	85	25	concepts	concept	NOUN
ejpam-5003	85	26	and	and	CCONJ
ejpam-5003	85	27	results	result	NOUN
ejpam-5003	85	28	related	relate	VERB
ejpam-5003	85	29	to	to	ADP
ejpam-5003	85	30	hyper	hyper	ADJ
ejpam-5003	85	31	bn	bn	ADJ
ejpam-5003	85	32	-algebras	-algebra	NOUN
ejpam-5003	85	33	.	.	PUNCT
ejpam-5003	86	1	these	these	PRON
ejpam-5003	86	2	are	be	AUX
ejpam-5003	86	3	taken	take	VERB
ejpam-5003	86	4	again	again	ADV
ejpam-5003	86	5	from	from	ADP
ejpam-5003	86	6	[	[	X
ejpam-5003	86	7	3	3	NUM
ejpam-5003	86	8	]	]	PUNCT
ejpam-5003	86	9	.	.	PUNCT
ejpam-5003	87	1	l.r	l.r	PROPN
ejpam-5003	87	2	.	.	PROPN
ejpam-5003	87	3	cabardo	cabardo	PROPN
ejpam-5003	87	4	,	,	PUNCT
ejpam-5003	87	5	g.	g.	PROPN
ejpam-5003	87	6	petalcorin	petalcorin	PROPN
ejpam-5003	87	7	/	/	SYM
ejpam-5003	87	8	eur	eur	PROPN
ejpam-5003	87	9	.	.	PUNCT
ejpam-5003	88	1	j.	j.	PROPN
ejpam-5003	88	2	pure	pure	PROPN
ejpam-5003	88	3	appl	appl	PROPN
ejpam-5003	88	4	.	.	PROPN
ejpam-5003	88	5	math	math	PROPN
ejpam-5003	88	6	,	,	PUNCT
ejpam-5003	88	7	17	17	NUM
ejpam-5003	88	8	(	(	PUNCT
ejpam-5003	88	9	1	1	NUM
ejpam-5003	88	10	)	)	PUNCT
ejpam-5003	88	11	(	(	PUNCT
ejpam-5003	88	12	2024	2024	NUM
ejpam-5003	88	13	)	)	PUNCT
ejpam-5003	88	14	,	,	PUNCT
ejpam-5003	88	15	222	222	NUM
ejpam-5003	88	16	-	-	SYM
ejpam-5003	88	17	242	242	NUM
ejpam-5003	88	18	226	226	NUM
ejpam-5003	88	19	definition	definition	NOUN
ejpam-5003	88	20	7	7	NUM
ejpam-5003	88	21	.	.	PUNCT
ejpam-5003	89	1	let	let	AUX
ejpam-5003	89	2	(	(	PUNCT
ejpam-5003	89	3	h,⊛	h,⊛	ADV
ejpam-5003	89	4	,	,	PUNCT
ejpam-5003	89	5	0	0	NUM
ejpam-5003	89	6	)	)	PUNCT
ejpam-5003	89	7	be	be	AUX
ejpam-5003	89	8	a	a	DET
ejpam-5003	89	9	hyper	hyper	ADJ
ejpam-5003	89	10	bn	bn	NOUN
ejpam-5003	89	11	-algebra	-algebra	NOUN
ejpam-5003	89	12	and	and	CCONJ
ejpam-5003	89	13	let	let	VERB
ejpam-5003	89	14	s	s	PRON
ejpam-5003	89	15	be	be	AUX
ejpam-5003	89	16	a	a	DET
ejpam-5003	89	17	subset	subset	NOUN
ejpam-5003	89	18	of	of	ADP
ejpam-5003	89	19	h	h	NOUN
ejpam-5003	89	20	containing	contain	VERB
ejpam-5003	89	21	0	0	NUM
ejpam-5003	89	22	.	.	PUNCT
ejpam-5003	90	1	if	if	SCONJ
ejpam-5003	90	2	s	s	PROPN
ejpam-5003	90	3	is	be	AUX
ejpam-5003	90	4	a	a	DET
ejpam-5003	90	5	hyper	hyper	ADJ
ejpam-5003	90	6	bn	bn	NOUN
ejpam-5003	90	7	-algebra	-algebra	NOUN
ejpam-5003	90	8	with	with	ADP
ejpam-5003	90	9	respect	respect	NOUN
ejpam-5003	90	10	to	to	ADP
ejpam-5003	90	11	the	the	DET
ejpam-5003	90	12	hyperoperation	hyperoperation	NOUN
ejpam-5003	90	13	“	"	PUNCT
ejpam-5003	90	14	⊛	⊛	NUM
ejpam-5003	90	15	”	"	PUNCT
ejpam-5003	90	16	on	on	ADP
ejpam-5003	90	17	h	h	NOUN
ejpam-5003	90	18	,	,	PUNCT
ejpam-5003	90	19	we	we	PRON
ejpam-5003	90	20	say	say	VERB
ejpam-5003	90	21	that	that	SCONJ
ejpam-5003	90	22	s	s	VERB
ejpam-5003	90	23	is	be	AUX
ejpam-5003	90	24	a	a	DET
ejpam-5003	90	25	hyper	hyper	ADJ
ejpam-5003	90	26	subbn	subbn	NOUN
ejpam-5003	90	27	-algebra	-algebra	NOUN
ejpam-5003	90	28	of	of	ADP
ejpam-5003	90	29	h.	h.	PROPN
ejpam-5003	90	30	example	example	PROPN
ejpam-5003	90	31	6	6	X
ejpam-5003	90	32	.	.	PUNCT
ejpam-5003	90	33	consider	consider	VERB
ejpam-5003	90	34	the	the	DET
ejpam-5003	90	35	hyper	hyper	ADJ
ejpam-5003	90	36	bn	bn	ADJ
ejpam-5003	90	37	-algebra	-algebra	PROPN
ejpam-5003	90	38	h	h	NOUN
ejpam-5003	90	39	in	in	ADP
ejpam-5003	90	40	example	example	NOUN
ejpam-5003	91	1	1	1	X
ejpam-5003	91	2	.	.	PUNCT
ejpam-5003	92	1	let	let	VERB
ejpam-5003	92	2	s	s	VERB
ejpam-5003	92	3	=	=	X
ejpam-5003	92	4	{	{	PUNCT
ejpam-5003	92	5	0	0	NUM
ejpam-5003	92	6	,	,	PUNCT
ejpam-5003	92	7	a	a	PRON
ejpam-5003	92	8	}	}	PUNCT
ejpam-5003	92	9	and	and	CCONJ
ejpam-5003	92	10	t	t	NOUN
ejpam-5003	92	11	=	=	SYM
ejpam-5003	92	12	{	{	PUNCT
ejpam-5003	92	13	0	0	NUM
ejpam-5003	92	14	,	,	PUNCT
ejpam-5003	92	15	b	b	NOUN
ejpam-5003	92	16	}	}	PUNCT
ejpam-5003	92	17	.	.	PUNCT
ejpam-5003	93	1	by	by	ADP
ejpam-5003	93	2	routine	routine	ADJ
ejpam-5003	93	3	calculations	calculation	NOUN
ejpam-5003	93	4	,	,	PUNCT
ejpam-5003	93	5	both	both	PRON
ejpam-5003	93	6	s	s	NOUN
ejpam-5003	93	7	and	and	CCONJ
ejpam-5003	93	8	t	t	PROPN
ejpam-5003	93	9	are	be	AUX
ejpam-5003	93	10	hyper	hyper	ADJ
ejpam-5003	93	11	subbn	subbn	NOUN
ejpam-5003	93	12	-algebra	-algebra	PROPN
ejpam-5003	93	13	of	of	ADP
ejpam-5003	93	14	h.	h.	NOUN
ejpam-5003	93	15	if	if	SCONJ
ejpam-5003	93	16	we	we	PRON
ejpam-5003	93	17	consider	consider	VERB
ejpam-5003	93	18	the	the	DET
ejpam-5003	93	19	hyper	hyper	ADJ
ejpam-5003	93	20	bn	bn	ADJ
ejpam-5003	93	21	-algebra	-algebra	PROPN
ejpam-5003	93	22	h	h	NOUN
ejpam-5003	93	23	in	in	ADP
ejpam-5003	93	24	example	example	NOUN
ejpam-5003	93	25	2	2	NUM
ejpam-5003	93	26	,	,	PUNCT
ejpam-5003	93	27	then	then	ADV
ejpam-5003	93	28	the	the	DET
ejpam-5003	93	29	sets	set	NOUN
ejpam-5003	93	30	l	l	NOUN
ejpam-5003	93	31	=	=	SYM
ejpam-5003	93	32	{	{	PUNCT
ejpam-5003	93	33	0	0	NUM
ejpam-5003	93	34	,	,	PUNCT
ejpam-5003	93	35	1	1	NUM
ejpam-5003	93	36	}	}	PUNCT
ejpam-5003	93	37	and	and	CCONJ
ejpam-5003	93	38	m	m	VERB
ejpam-5003	93	39	=	=	SYM
ejpam-5003	93	40	{	{	PUNCT
ejpam-5003	93	41	0	0	NUM
ejpam-5003	93	42	,	,	PUNCT
ejpam-5003	93	43	2	2	NUM
ejpam-5003	93	44	}	}	PUNCT
ejpam-5003	93	45	are	be	AUX
ejpam-5003	93	46	not	not	PART
ejpam-5003	93	47	hyper	hyper	ADJ
ejpam-5003	93	48	subbn	subbn	NOUN
ejpam-5003	93	49	-algebra	-algebra	PROPN
ejpam-5003	93	50	of	of	ADP
ejpam-5003	93	51	h.	h.	PROPN
ejpam-5003	93	52	theorem	theorem	PROPN
ejpam-5003	93	53	3	3	X
ejpam-5003	93	54	.	.	PUNCT
ejpam-5003	94	1	let	let	VERB
ejpam-5003	94	2	s	s	PRON
ejpam-5003	94	3	be	be	AUX
ejpam-5003	94	4	a	a	DET
ejpam-5003	94	5	nonempty	nonempty	ADJ
ejpam-5003	94	6	subset	subset	NOUN
ejpam-5003	94	7	of	of	ADP
ejpam-5003	94	8	a	a	DET
ejpam-5003	94	9	hyper	hyper	ADJ
ejpam-5003	94	10	bn	bn	NOUN
ejpam-5003	94	11	algebra	algebra	NOUN
ejpam-5003	94	12	.	.	PUNCT
ejpam-5003	95	1	then	then	ADV
ejpam-5003	95	2	s	s	VERB
ejpam-5003	95	3	is	be	AUX
ejpam-5003	95	4	a	a	DET
ejpam-5003	95	5	hyper	hyper	ADJ
ejpam-5003	95	6	subbn	subbn	NOUN
ejpam-5003	95	7	-algebra	-algebra	PROPN
ejpam-5003	95	8	if	if	SCONJ
ejpam-5003	95	9	and	and	CCONJ
ejpam-5003	95	10	only	only	ADV
ejpam-5003	95	11	if	if	SCONJ
ejpam-5003	95	12	x⊛	x⊛	PROPN
ejpam-5003	95	13	y	y	PROPN
ejpam-5003	95	14	⊆	⊆	NUM
ejpam-5003	95	15	s	s	NOUN
ejpam-5003	95	16	,	,	PUNCT
ejpam-5003	95	17	for	for	ADP
ejpam-5003	95	18	all	all	DET
ejpam-5003	95	19	x	x	NOUN
ejpam-5003	95	20	,	,	PUNCT
ejpam-5003	95	21	y	y	PROPN
ejpam-5003	95	22	∈	∈	PROPN
ejpam-5003	95	23	s.	s.	PROPN
ejpam-5003	95	24	definition	definition	NOUN
ejpam-5003	95	25	8	8	NUM
ejpam-5003	95	26	.	.	PUNCT
ejpam-5003	96	1	let	let	VERB
ejpam-5003	96	2	n	n	PRON
ejpam-5003	96	3	be	be	AUX
ejpam-5003	96	4	a	a	DET
ejpam-5003	96	5	nonempty	nonempty	ADJ
ejpam-5003	96	6	subset	subset	NOUN
ejpam-5003	96	7	of	of	ADP
ejpam-5003	96	8	a	a	DET
ejpam-5003	96	9	hyper	hyper	ADJ
ejpam-5003	96	10	bn	bn	NOUN
ejpam-5003	96	11	-algebra	-algebra	NOUN
ejpam-5003	96	12	.	.	PUNCT
ejpam-5003	97	1	then	then	ADV
ejpam-5003	97	2	n	n	VERB
ejpam-5003	97	3	is	be	AUX
ejpam-5003	97	4	called	call	VERB
ejpam-5003	97	5	normal	normal	ADJ
ejpam-5003	97	6	if	if	SCONJ
ejpam-5003	97	7	(	(	PUNCT
ejpam-5003	97	8	x⊛	x⊛	PROPN
ejpam-5003	97	9	a)⊛	a)⊛	INTJ
ejpam-5003	97	10	(	(	PUNCT
ejpam-5003	97	11	y	y	PROPN
ejpam-5003	97	12	⊛	⊛	NUM
ejpam-5003	97	13	b	b	NUM
ejpam-5003	97	14	)	)	PUNCT
ejpam-5003	97	15	⊆	⊆	NUM
ejpam-5003	97	16	n	n	NUM
ejpam-5003	97	17	whenever	whenever	SCONJ
ejpam-5003	97	18	x⊛	x⊛	PROPN
ejpam-5003	97	19	y	y	PROPN
ejpam-5003	97	20	,	,	PUNCT
ejpam-5003	97	21	a⊛	a⊛	PROPN
ejpam-5003	97	22	b	b	PROPN
ejpam-5003	97	23	⊆	⊆	NUM
ejpam-5003	97	24	n	n	NOUN
ejpam-5003	97	25	.	.	PUNCT
ejpam-5003	97	26	example	example	NOUN
ejpam-5003	97	27	7	7	NUM
ejpam-5003	97	28	.	.	X
ejpam-5003	97	29	consider	consider	VERB
ejpam-5003	97	30	the	the	DET
ejpam-5003	97	31	hyper	hyper	ADJ
ejpam-5003	97	32	bn	bn	NOUN
ejpam-5003	97	33	-algebra	-algebra	PROPN
ejpam-5003	97	34	h	h	NOUN
ejpam-5003	97	35	=	=	SYM
ejpam-5003	97	36	{	{	PUNCT
ejpam-5003	97	37	0	0	NUM
ejpam-5003	97	38	,	,	PUNCT
ejpam-5003	97	39	a	a	DET
ejpam-5003	97	40	,	,	PUNCT
ejpam-5003	97	41	b	b	NOUN
ejpam-5003	97	42	}	}	PUNCT
ejpam-5003	97	43	in	in	ADP
ejpam-5003	97	44	example	example	NOUN
ejpam-5003	98	1	1	1	X
ejpam-5003	98	2	.	.	PUNCT
ejpam-5003	98	3	let	let	VERB
ejpam-5003	98	4	n1	n1	PROPN
ejpam-5003	98	5	=	=	SYM
ejpam-5003	98	6	{	{	PUNCT
ejpam-5003	98	7	0	0	NUM
ejpam-5003	98	8	,	,	PUNCT
ejpam-5003	98	9	a	a	PRON
ejpam-5003	98	10	}	}	PUNCT
ejpam-5003	98	11	and	and	CCONJ
ejpam-5003	98	12	n2	n2	ADJ
ejpam-5003	98	13	=	=	PUNCT
ejpam-5003	98	14	{	{	PUNCT
ejpam-5003	98	15	0	0	NUM
ejpam-5003	98	16	,	,	PUNCT
ejpam-5003	98	17	b	b	NOUN
ejpam-5003	98	18	}	}	PUNCT
ejpam-5003	98	19	.	.	PUNCT
ejpam-5003	99	1	then	then	ADV
ejpam-5003	99	2	it	it	PRON
ejpam-5003	99	3	can	can	AUX
ejpam-5003	99	4	be	be	AUX
ejpam-5003	99	5	shown	show	VERB
ejpam-5003	99	6	that	that	SCONJ
ejpam-5003	99	7	n1	n1	NOUN
ejpam-5003	99	8	is	be	AUX
ejpam-5003	99	9	normal	normal	ADJ
ejpam-5003	99	10	.	.	PUNCT
ejpam-5003	100	1	however	however	ADV
ejpam-5003	100	2	,	,	PUNCT
ejpam-5003	100	3	n2	n2	PROPN
ejpam-5003	100	4	is	be	AUX
ejpam-5003	100	5	not	not	PART
ejpam-5003	100	6	normal	normal	ADJ
ejpam-5003	100	7	because	because	SCONJ
ejpam-5003	100	8	0⊛	0⊛	NUM
ejpam-5003	100	9	b	b	X
ejpam-5003	100	10	=	=	PRON
ejpam-5003	100	11	{	{	PUNCT
ejpam-5003	100	12	b	b	NOUN
ejpam-5003	100	13	}	}	PUNCT
ejpam-5003	100	14	⊆	⊆	NUM
ejpam-5003	100	15	n2	n2	NOUN
ejpam-5003	100	16	and	and	CCONJ
ejpam-5003	100	17	a⊛	a⊛	NOUN
ejpam-5003	100	18	b	b	PROPN
ejpam-5003	100	19	=	=	PUNCT
ejpam-5003	100	20	{	{	PUNCT
ejpam-5003	100	21	b	b	NOUN
ejpam-5003	100	22	}	}	PUNCT
ejpam-5003	100	23	⊆	⊆	NUM
ejpam-5003	100	24	n2	n2	NOUN
ejpam-5003	100	25	but	but	CCONJ
ejpam-5003	100	26	(	(	PUNCT
ejpam-5003	100	27	0⊛	0⊛	NUM
ejpam-5003	100	28	a)⊛	a)⊛	NOUN
ejpam-5003	100	29	(	(	PUNCT
ejpam-5003	100	30	b⊛	b⊛	PROPN
ejpam-5003	100	31	b	b	NOUN
ejpam-5003	100	32	)	)	PUNCT
ejpam-5003	100	33	=	=	NOUN
ejpam-5003	100	34	{	{	PUNCT
ejpam-5003	100	35	a	a	PRON
ejpam-5003	100	36	,	,	PUNCT
ejpam-5003	100	37	b	b	NOUN
ejpam-5003	100	38	}	}	PUNCT
ejpam-5003	100	39	̸⊆	̸⊆	NOUN
ejpam-5003	100	40	n2	n2	NOUN
ejpam-5003	100	41	.	.	PUNCT
ejpam-5003	101	1	definition	definition	NOUN
ejpam-5003	101	2	9	9	NUM
ejpam-5003	101	3	.	.	PUNCT
ejpam-5003	102	1	a	a	DET
ejpam-5003	102	2	nonempty	nonempty	NOUN
ejpam-5003	102	3	subset	subset	VERB
ejpam-5003	102	4	i	i	PRON
ejpam-5003	102	5	of	of	ADP
ejpam-5003	102	6	a	a	DET
ejpam-5003	102	7	hyper	hyper	ADJ
ejpam-5003	102	8	bn	bn	NOUN
ejpam-5003	102	9	-algebra	-algebra	NOUN
ejpam-5003	102	10	h	h	NOUN
ejpam-5003	102	11	is	be	AUX
ejpam-5003	102	12	said	say	VERB
ejpam-5003	102	13	to	to	PART
ejpam-5003	102	14	be	be	AUX
ejpam-5003	102	15	reflexive	reflexive	ADJ
ejpam-5003	102	16	if	if	SCONJ
ejpam-5003	102	17	x⊛	x⊛	PROPN
ejpam-5003	102	18	x	x	VERB
ejpam-5003	102	19	⊆	⊆	NUM
ejpam-5003	102	20	i	i	PRON
ejpam-5003	102	21	for	for	ADP
ejpam-5003	102	22	all	all	DET
ejpam-5003	102	23	x	x	SYM
ejpam-5003	102	24	∈	∈	PROPN
ejpam-5003	102	25	h.	h.	PROPN
ejpam-5003	102	26	example	example	NOUN
ejpam-5003	102	27	8	8	X
ejpam-5003	102	28	.	.	PUNCT
ejpam-5003	103	1	let	let	VERB
ejpam-5003	103	2	h	h	NOUN
ejpam-5003	103	3	=	=	PRON
ejpam-5003	103	4	{	{	PUNCT
ejpam-5003	103	5	0	0	NUM
ejpam-5003	103	6	,	,	PUNCT
ejpam-5003	103	7	1	1	NUM
ejpam-5003	103	8	,	,	PUNCT
ejpam-5003	103	9	2	2	NUM
ejpam-5003	103	10	}	}	PUNCT
ejpam-5003	103	11	with	with	ADP
ejpam-5003	103	12	hyperoperation	hyperoperation	NOUN
ejpam-5003	103	13	⊛	⊛	NUM
ejpam-5003	103	14	defined	define	VERB
ejpam-5003	103	15	by	by	ADP
ejpam-5003	103	16	the	the	DET
ejpam-5003	103	17	following	following	ADJ
ejpam-5003	103	18	cayley	cayley	ADJ
ejpam-5003	103	19	table	table	NOUN
ejpam-5003	103	20	:	:	PUNCT
ejpam-5003	103	21	⊛	⊛	NUM
ejpam-5003	103	22	0	0	NUM
ejpam-5003	103	23	1	1	NUM
ejpam-5003	103	24	2	2	NUM
ejpam-5003	103	25	0	0	NUM
ejpam-5003	103	26	{	{	PUNCT
ejpam-5003	103	27	0	0	NUM
ejpam-5003	103	28	}	}	PUNCT
ejpam-5003	103	29	{	{	PUNCT
ejpam-5003	103	30	1	1	NUM
ejpam-5003	103	31	}	}	PUNCT
ejpam-5003	103	32	{	{	PUNCT
ejpam-5003	103	33	2	2	NUM
ejpam-5003	103	34	}	}	SYM
ejpam-5003	103	35	1	1	NUM
ejpam-5003	103	36	{	{	PUNCT
ejpam-5003	103	37	1	1	NUM
ejpam-5003	103	38	}	}	PUNCT
ejpam-5003	103	39	{	{	PUNCT
ejpam-5003	103	40	0	0	NUM
ejpam-5003	103	41	,	,	PUNCT
ejpam-5003	103	42	1	1	NUM
ejpam-5003	103	43	}	}	PUNCT
ejpam-5003	103	44	{	{	PUNCT
ejpam-5003	103	45	2	2	NUM
ejpam-5003	103	46	}	}	SYM
ejpam-5003	103	47	2	2	NUM
ejpam-5003	103	48	{	{	PUNCT
ejpam-5003	103	49	2	2	NUM
ejpam-5003	103	50	}	}	PUNCT
ejpam-5003	103	51	{	{	PUNCT
ejpam-5003	103	52	2	2	NUM
ejpam-5003	103	53	}	}	PUNCT
ejpam-5003	103	54	{	{	PUNCT
ejpam-5003	103	55	0	0	NUM
ejpam-5003	103	56	,	,	PUNCT
ejpam-5003	103	57	1	1	NUM
ejpam-5003	103	58	}	}	PUNCT
ejpam-5003	103	59	h	h	NOUN
ejpam-5003	103	60	is	be	AUX
ejpam-5003	103	61	a	a	DET
ejpam-5003	103	62	hyper	hyper	ADJ
ejpam-5003	103	63	bn	bn	NOUN
ejpam-5003	103	64	-algebra	-algebra	NOUN
ejpam-5003	103	65	by	by	ADP
ejpam-5003	103	66	routine	routine	ADJ
ejpam-5003	103	67	calculations	calculation	NOUN
ejpam-5003	103	68	.	.	PUNCT
ejpam-5003	104	1	let	let	VERB
ejpam-5003	104	2	i	i	PRON
ejpam-5003	104	3	=	=	PUNCT
ejpam-5003	104	4	{	{	PUNCT
ejpam-5003	104	5	0	0	NUM
ejpam-5003	104	6	,	,	PUNCT
ejpam-5003	104	7	1	1	NUM
ejpam-5003	104	8	}	}	PUNCT
ejpam-5003	104	9	.	.	PUNCT
ejpam-5003	105	1	then	then	ADV
ejpam-5003	105	2	it	it	PRON
ejpam-5003	105	3	is	be	AUX
ejpam-5003	105	4	reflexive	reflexive	ADJ
ejpam-5003	105	5	because	because	SCONJ
ejpam-5003	105	6	x	x	PROPN
ejpam-5003	105	7	⊛	⊛	NUM
ejpam-5003	105	8	x	x	SYM
ejpam-5003	105	9	⊆	⊆	NUM
ejpam-5003	105	10	i	i	PRON
ejpam-5003	105	11	for	for	ADP
ejpam-5003	105	12	x	x	X
ejpam-5003	105	13	=	=	SYM
ejpam-5003	105	14	0	0	NUM
ejpam-5003	105	15	,	,	PUNCT
ejpam-5003	105	16	1	1	NUM
ejpam-5003	105	17	,	,	PUNCT
ejpam-5003	105	18	2	2	NUM
ejpam-5003	105	19	.	.	PUNCT
ejpam-5003	106	1	let	let	VERB
ejpam-5003	106	2	j	j	PROPN
ejpam-5003	106	3	=	=	PUNCT
ejpam-5003	106	4	{	{	PUNCT
ejpam-5003	106	5	0	0	NUM
ejpam-5003	106	6	,	,	PUNCT
ejpam-5003	106	7	2	2	NUM
ejpam-5003	106	8	}	}	PUNCT
ejpam-5003	106	9	.	.	PUNCT
ejpam-5003	107	1	then	then	ADV
ejpam-5003	107	2	j	j	PROPN
ejpam-5003	107	3	is	be	AUX
ejpam-5003	107	4	not	not	PART
ejpam-5003	107	5	reflexive	reflexive	ADJ
ejpam-5003	107	6	because	because	SCONJ
ejpam-5003	107	7	1⊛	1⊛	NUM
ejpam-5003	107	8	1	1	NUM
ejpam-5003	107	9	̸⊆	̸⊆	PROPN
ejpam-5003	107	10	j	j	PROPN
ejpam-5003	107	11	.	.	PUNCT
ejpam-5003	108	1	theorem	theorem	VERB
ejpam-5003	108	2	4	4	NUM
ejpam-5003	108	3	.	.	PUNCT
ejpam-5003	109	1	every	every	DET
ejpam-5003	109	2	normal	normal	ADJ
ejpam-5003	109	3	subset	subset	NOUN
ejpam-5003	109	4	n	n	PROPN
ejpam-5003	109	5	of	of	ADP
ejpam-5003	109	6	a	a	DET
ejpam-5003	109	7	hyper	hyper	ADJ
ejpam-5003	109	8	bn	bn	NOUN
ejpam-5003	109	9	-algebra	-algebra	NOUN
ejpam-5003	109	10	h	h	NOUN
ejpam-5003	109	11	is	be	AUX
ejpam-5003	109	12	a	a	DET
ejpam-5003	109	13	hyper	hyper	ADJ
ejpam-5003	109	14	subbn	subbn	NOUN
ejpam-5003	109	15	-algebra	-algebra	NOUN
ejpam-5003	109	16	of	of	ADP
ejpam-5003	109	17	h.	h.	PROPN
ejpam-5003	109	18	definition	definition	NOUN
ejpam-5003	109	19	10	10	NUM
ejpam-5003	109	20	.	.	PUNCT
ejpam-5003	110	1	a	a	DET
ejpam-5003	110	2	hyper	hyper	ADJ
ejpam-5003	110	3	subbn	subbn	NOUN
ejpam-5003	110	4	-algebra	-algebra	PROPN
ejpam-5003	110	5	s	s	PART
ejpam-5003	110	6	of	of	ADP
ejpam-5003	110	7	a	a	DET
ejpam-5003	110	8	hyper	hyper	ADJ
ejpam-5003	110	9	bn	bn	NOUN
ejpam-5003	110	10	-algebra	-algebra	NOUN
ejpam-5003	110	11	h	h	NOUN
ejpam-5003	110	12	is	be	AUX
ejpam-5003	110	13	called	call	VERB
ejpam-5003	110	14	reflexive	reflexive	ADJ
ejpam-5003	110	15	(	(	PUNCT
ejpam-5003	110	16	resp	resp	NOUN
ejpam-5003	110	17	.	.	PUNCT
ejpam-5003	111	1	normal	normal	ADJ
ejpam-5003	111	2	)	)	PUNCT
ejpam-5003	111	3	hyper	hyper	ADJ
ejpam-5003	111	4	subbn	subbn	NOUN
ejpam-5003	111	5	-algebra	-algebra	PROPN
ejpam-5003	111	6	if	if	SCONJ
ejpam-5003	111	7	it	it	PRON
ejpam-5003	111	8	is	be	AUX
ejpam-5003	111	9	reflexive	reflexive	ADJ
ejpam-5003	111	10	(	(	PUNCT
ejpam-5003	111	11	resp	resp	NOUN
ejpam-5003	111	12	.	.	PUNCT
ejpam-5003	112	1	normal	normal	ADJ
ejpam-5003	112	2	)	)	PUNCT
ejpam-5003	112	3	.	.	PUNCT
ejpam-5003	113	1	s	s	PART
ejpam-5003	113	2	is	be	AUX
ejpam-5003	113	3	called	call	VERB
ejpam-5003	113	4	a	a	DET
ejpam-5003	113	5	reflexive	reflexive	ADJ
ejpam-5003	113	6	normal	normal	ADJ
ejpam-5003	113	7	hyper	hyper	ADJ
ejpam-5003	113	8	subbn	subbn	NOUN
ejpam-5003	113	9	-algebra	-algebra	PROPN
ejpam-5003	113	10	if	if	SCONJ
ejpam-5003	113	11	it	it	PRON
ejpam-5003	113	12	is	be	AUX
ejpam-5003	113	13	both	both	CCONJ
ejpam-5003	113	14	reflexive	reflexive	ADJ
ejpam-5003	113	15	and	and	CCONJ
ejpam-5003	113	16	normal	normal	ADJ
ejpam-5003	113	17	.	.	PUNCT
ejpam-5003	113	18	example	example	NOUN
ejpam-5003	114	1	9	9	NUM
ejpam-5003	114	2	.	.	X
ejpam-5003	114	3	consider	consider	VERB
ejpam-5003	114	4	the	the	DET
ejpam-5003	114	5	set	set	NOUN
ejpam-5003	114	6	h	h	NOUN
ejpam-5003	114	7	=	=	SYM
ejpam-5003	114	8	{	{	PUNCT
ejpam-5003	114	9	0	0	NUM
ejpam-5003	114	10	,	,	PUNCT
ejpam-5003	114	11	1	1	NUM
ejpam-5003	114	12	,	,	PUNCT
ejpam-5003	114	13	2	2	NUM
ejpam-5003	114	14	,	,	PUNCT
ejpam-5003	114	15	3	3	NUM
ejpam-5003	114	16	,	,	PUNCT
ejpam-5003	114	17	4	4	NUM
ejpam-5003	114	18	}	}	PUNCT
ejpam-5003	114	19	.	.	PUNCT
ejpam-5003	115	1	define	define	VERB
ejpam-5003	115	2	the	the	DET
ejpam-5003	115	3	hyperoperation	hyperoperation	NOUN
ejpam-5003	115	4	“	"	PUNCT
ejpam-5003	115	5	⊛	⊛	NUM
ejpam-5003	115	6	”	"	PUNCT
ejpam-5003	115	7	by	by	ADP
ejpam-5003	115	8	the	the	DET
ejpam-5003	115	9	following	following	ADJ
ejpam-5003	115	10	cayley	cayley	ADJ
ejpam-5003	115	11	table	table	NOUN
ejpam-5003	115	12	:	:	PUNCT
ejpam-5003	115	13	⊛	⊛	NUM
ejpam-5003	115	14	0	0	NUM
ejpam-5003	115	15	1	1	NUM
ejpam-5003	115	16	2	2	NUM
ejpam-5003	115	17	3	3	NUM
ejpam-5003	115	18	4	4	NUM
ejpam-5003	115	19	0	0	NUM
ejpam-5003	115	20	{	{	PUNCT
ejpam-5003	115	21	0	0	NUM
ejpam-5003	115	22	}	}	PUNCT
ejpam-5003	115	23	{	{	PUNCT
ejpam-5003	115	24	1	1	NUM
ejpam-5003	115	25	}	}	PUNCT
ejpam-5003	115	26	{	{	PUNCT
ejpam-5003	115	27	2	2	NUM
ejpam-5003	115	28	}	}	PUNCT
ejpam-5003	115	29	{	{	PUNCT
ejpam-5003	115	30	3	3	NUM
ejpam-5003	115	31	}	}	PUNCT
ejpam-5003	115	32	{	{	PUNCT
ejpam-5003	115	33	4	4	NUM
ejpam-5003	115	34	}	}	SYM
ejpam-5003	115	35	1	1	NUM
ejpam-5003	115	36	{	{	PUNCT
ejpam-5003	115	37	1	1	NUM
ejpam-5003	115	38	}	}	PUNCT
ejpam-5003	115	39	{	{	PUNCT
ejpam-5003	115	40	0	0	NUM
ejpam-5003	115	41	,	,	PUNCT
ejpam-5003	115	42	3	3	NUM
ejpam-5003	115	43	}	}	PUNCT
ejpam-5003	115	44	{	{	PUNCT
ejpam-5003	115	45	3	3	NUM
ejpam-5003	115	46	}	}	PUNCT
ejpam-5003	115	47	{	{	PUNCT
ejpam-5003	115	48	1	1	NUM
ejpam-5003	115	49	}	}	PUNCT
ejpam-5003	115	50	{	{	PUNCT
ejpam-5003	115	51	4	4	NUM
ejpam-5003	115	52	}	}	SYM
ejpam-5003	115	53	2	2	NUM
ejpam-5003	115	54	{	{	PUNCT
ejpam-5003	115	55	2	2	NUM
ejpam-5003	115	56	}	}	PUNCT
ejpam-5003	115	57	{	{	PUNCT
ejpam-5003	115	58	3	3	NUM
ejpam-5003	115	59	}	}	PUNCT
ejpam-5003	115	60	{	{	PUNCT
ejpam-5003	115	61	0	0	NUM
ejpam-5003	115	62	,	,	PUNCT
ejpam-5003	115	63	3	3	NUM
ejpam-5003	115	64	}	}	PUNCT
ejpam-5003	115	65	{	{	PUNCT
ejpam-5003	115	66	3	3	NUM
ejpam-5003	115	67	}	}	PUNCT
ejpam-5003	115	68	{	{	PUNCT
ejpam-5003	115	69	4	4	NUM
ejpam-5003	115	70	}	}	SYM
ejpam-5003	115	71	3	3	NUM
ejpam-5003	115	72	{	{	PUNCT
ejpam-5003	115	73	3	3	NUM
ejpam-5003	115	74	}	}	PUNCT
ejpam-5003	115	75	{	{	PUNCT
ejpam-5003	115	76	1	1	NUM
ejpam-5003	115	77	}	}	PUNCT
ejpam-5003	115	78	{	{	PUNCT
ejpam-5003	115	79	3	3	NUM
ejpam-5003	115	80	}	}	PUNCT
ejpam-5003	115	81	{	{	PUNCT
ejpam-5003	115	82	0	0	NUM
ejpam-5003	115	83	,	,	PUNCT
ejpam-5003	115	84	3	3	NUM
ejpam-5003	115	85	}	}	PUNCT
ejpam-5003	115	86	{	{	PUNCT
ejpam-5003	115	87	4	4	NUM
ejpam-5003	115	88	}	}	SYM
ejpam-5003	115	89	4	4	NUM
ejpam-5003	115	90	{	{	PUNCT
ejpam-5003	115	91	4	4	NUM
ejpam-5003	115	92	}	}	PUNCT
ejpam-5003	115	93	{	{	PUNCT
ejpam-5003	115	94	4	4	NUM
ejpam-5003	115	95	}	}	PUNCT
ejpam-5003	115	96	{	{	PUNCT
ejpam-5003	115	97	4	4	NUM
ejpam-5003	115	98	}	}	PUNCT
ejpam-5003	115	99	{	{	PUNCT
ejpam-5003	115	100	4	4	NUM
ejpam-5003	115	101	}	}	PUNCT
ejpam-5003	115	102	{	{	PUNCT
ejpam-5003	115	103	0	0	NUM
ejpam-5003	115	104	,	,	PUNCT
ejpam-5003	115	105	3	3	NUM
ejpam-5003	115	106	}	}	PUNCT
ejpam-5003	115	107	l.r	l.r	PROPN
ejpam-5003	115	108	.	.	PROPN
ejpam-5003	115	109	cabardo	cabardo	PROPN
ejpam-5003	115	110	,	,	PUNCT
ejpam-5003	115	111	g.	g.	PROPN
ejpam-5003	115	112	petalcorin	petalcorin	PROPN
ejpam-5003	115	113	/	/	SYM
ejpam-5003	115	114	eur	eur	PROPN
ejpam-5003	115	115	.	.	PUNCT
ejpam-5003	116	1	j.	j.	PROPN
ejpam-5003	116	2	pure	pure	PROPN
ejpam-5003	116	3	appl	appl	PROPN
ejpam-5003	116	4	.	.	PROPN
ejpam-5003	116	5	math	math	PROPN
ejpam-5003	116	6	,	,	PUNCT
ejpam-5003	116	7	17	17	NUM
ejpam-5003	116	8	(	(	PUNCT
ejpam-5003	116	9	1	1	NUM
ejpam-5003	116	10	)	)	PUNCT
ejpam-5003	116	11	(	(	PUNCT
ejpam-5003	116	12	2024	2024	NUM
ejpam-5003	116	13	)	)	PUNCT
ejpam-5003	116	14	,	,	PUNCT
ejpam-5003	116	15	222	222	NUM
ejpam-5003	116	16	-	-	SYM
ejpam-5003	116	17	242	242	NUM
ejpam-5003	116	18	227	227	NUM
ejpam-5003	116	19	by	by	ADP
ejpam-5003	116	20	routine	routine	ADJ
ejpam-5003	116	21	calculations	calculation	NOUN
ejpam-5003	116	22	,	,	PUNCT
ejpam-5003	116	23	h	h	NOUN
ejpam-5003	116	24	is	be	AUX
ejpam-5003	116	25	a	a	DET
ejpam-5003	116	26	hyper	hyper	ADJ
ejpam-5003	116	27	bn	bn	NOUN
ejpam-5003	116	28	-algebra	-algebra	NOUN
ejpam-5003	116	29	.	.	PUNCT
ejpam-5003	117	1	let	let	VERB
ejpam-5003	117	2	i	i	PRON
ejpam-5003	117	3	=	=	PUNCT
ejpam-5003	117	4	{	{	PUNCT
ejpam-5003	117	5	0	0	NUM
ejpam-5003	117	6	,	,	PUNCT
ejpam-5003	117	7	3	3	NUM
ejpam-5003	117	8	}	}	PUNCT
ejpam-5003	117	9	.	.	PUNCT
ejpam-5003	118	1	then	then	ADV
ejpam-5003	118	2	i	i	PRON
ejpam-5003	118	3	is	be	AUX
ejpam-5003	118	4	a	a	DET
ejpam-5003	118	5	reflexive	reflexive	ADJ
ejpam-5003	118	6	normal	normal	ADJ
ejpam-5003	118	7	hyper	hyper	ADJ
ejpam-5003	118	8	subbn	subbn	NOUN
ejpam-5003	118	9	-algebra	-algebra	PROPN
ejpam-5003	118	10	of	of	ADP
ejpam-5003	118	11	h.	h.	PROPN
ejpam-5003	118	12	theorem	theorem	PROPN
ejpam-5003	118	13	5	5	NUM
ejpam-5003	118	14	.	.	PUNCT
ejpam-5003	119	1	the	the	DET
ejpam-5003	119	2	intersection	intersection	NOUN
ejpam-5003	119	3	of	of	ADP
ejpam-5003	119	4	family	family	NOUN
ejpam-5003	119	5	of	of	ADP
ejpam-5003	119	6	reflexive	reflexive	ADJ
ejpam-5003	119	7	normal	normal	ADJ
ejpam-5003	119	8	hyper	hyper	ADJ
ejpam-5003	119	9	subbn	subbn	NOUN
ejpam-5003	119	10	-algebras	-algebras	PROPN
ejpam-5003	119	11	of	of	ADP
ejpam-5003	119	12	a	a	DET
ejpam-5003	119	13	hyper	hyper	ADJ
ejpam-5003	119	14	bn	bn	NOUN
ejpam-5003	119	15	-algebra	-algebra	NOUN
ejpam-5003	119	16	h	h	NOUN
ejpam-5003	119	17	is	be	AUX
ejpam-5003	119	18	a	a	DET
ejpam-5003	119	19	reflexive	reflexive	ADJ
ejpam-5003	119	20	normal	normal	ADJ
ejpam-5003	119	21	hyper	hyper	ADJ
ejpam-5003	119	22	subbn	subbn	NOUN
ejpam-5003	119	23	-algebra	-algebra	PROPN
ejpam-5003	119	24	of	of	ADP
ejpam-5003	119	25	h.	h.	PROPN
ejpam-5003	119	26	3	3	NUM
ejpam-5003	119	27	.	.	PUNCT
ejpam-5003	119	28	hyper	hyper	PROPN
ejpam-5003	119	29	bn	bn	NOUN
ejpam-5003	119	30	-	-	PUNCT
ejpam-5003	119	31	ideals	ideal	NOUN
ejpam-5003	119	32	in	in	ADP
ejpam-5003	119	33	this	this	DET
ejpam-5003	119	34	section	section	NOUN
ejpam-5003	119	35	,	,	PUNCT
ejpam-5003	119	36	we	we	PRON
ejpam-5003	119	37	introduce	introduce	VERB
ejpam-5003	119	38	hyper	hyper	ADJ
ejpam-5003	119	39	bn	bn	ADJ
ejpam-5003	119	40	-ideals	-ideal	NOUN
ejpam-5003	119	41	and	and	CCONJ
ejpam-5003	119	42	reflexive	reflexive	VERB
ejpam-5003	119	43	normal	normal	ADJ
ejpam-5003	119	44	hyper	hyper	ADJ
ejpam-5003	119	45	bn	bn	ADJ
ejpam-5003	119	46	-ideals	-ideal	NOUN
ejpam-5003	119	47	.	.	PUNCT
ejpam-5003	120	1	we	we	PRON
ejpam-5003	120	2	also	also	ADV
ejpam-5003	120	3	give	give	VERB
ejpam-5003	120	4	a	a	DET
ejpam-5003	120	5	weaker	weak	ADJ
ejpam-5003	120	6	and	and	CCONJ
ejpam-5003	120	7	stronger	strong	ADJ
ejpam-5003	120	8	version	version	NOUN
ejpam-5003	120	9	of	of	ADP
ejpam-5003	120	10	this	this	DET
ejpam-5003	120	11	concept	concept	NOUN
ejpam-5003	120	12	.	.	PUNCT
ejpam-5003	121	1	we	we	PRON
ejpam-5003	121	2	will	will	AUX
ejpam-5003	121	3	investigate	investigate	VERB
ejpam-5003	121	4	the	the	DET
ejpam-5003	121	5	nature	nature	NOUN
ejpam-5003	121	6	of	of	ADP
ejpam-5003	121	7	relationships	relationship	NOUN
ejpam-5003	121	8	between	between	ADP
ejpam-5003	121	9	these	these	DET
ejpam-5003	121	10	ideals	ideal	NOUN
ejpam-5003	121	11	and	and	CCONJ
ejpam-5003	121	12	also	also	ADV
ejpam-5003	121	13	gave	give	VERB
ejpam-5003	121	14	some	some	DET
ejpam-5003	121	15	conditions	condition	NOUN
ejpam-5003	121	16	where	where	SCONJ
ejpam-5003	121	17	equivalency	equivalency	NOUN
ejpam-5003	121	18	of	of	ADP
ejpam-5003	121	19	some	some	PRON
ejpam-5003	121	20	of	of	ADP
ejpam-5003	121	21	these	these	DET
ejpam-5003	121	22	ideals	ideal	NOUN
ejpam-5003	121	23	are	be	AUX
ejpam-5003	121	24	achieved	achieve	VERB
ejpam-5003	121	25	.	.	PUNCT
ejpam-5003	122	1	3.1	3.1	NUM
ejpam-5003	122	2	.	.	PUNCT
ejpam-5003	123	1	(	(	PUNCT
ejpam-5003	123	2	weak	weak	ADJ
ejpam-5003	123	3	,	,	PUNCT
ejpam-5003	123	4	strong	strong	ADJ
ejpam-5003	123	5	)	)	PUNCT
ejpam-5003	123	6	hyper	hyper	ADJ
ejpam-5003	123	7	bn	bn	NOUN
ejpam-5003	123	8	-	-	PUNCT
ejpam-5003	123	9	ideals	ideal	NOUN
ejpam-5003	123	10	in	in	ADP
ejpam-5003	123	11	what	what	PRON
ejpam-5003	123	12	follows	follow	VERB
ejpam-5003	123	13	,	,	PUNCT
ejpam-5003	123	14	we	we	PRON
ejpam-5003	123	15	will	will	AUX
ejpam-5003	123	16	introduce	introduce	VERB
ejpam-5003	123	17	the	the	DET
ejpam-5003	123	18	concepts	concept	NOUN
ejpam-5003	123	19	of	of	ADP
ejpam-5003	123	20	hyper	hyper	ADJ
ejpam-5003	123	21	bn	bn	ADJ
ejpam-5003	123	22	-ideals	-ideal	NOUN
ejpam-5003	123	23	,	,	PUNCT
ejpam-5003	123	24	weak	weak	ADJ
ejpam-5003	123	25	hyper	hyper	ADJ
ejpam-5003	123	26	bn	bn	NOUN
ejpam-5003	123	27	ideals	ideal	NOUN
ejpam-5003	123	28	,	,	PUNCT
ejpam-5003	123	29	and	and	CCONJ
ejpam-5003	123	30	strong	strong	ADJ
ejpam-5003	123	31	hyper	hyper	ADJ
ejpam-5003	123	32	bn	bn	ADJ
ejpam-5003	123	33	-ideals	-ideal	NOUN
ejpam-5003	123	34	.	.	PUNCT
ejpam-5003	124	1	we	we	PRON
ejpam-5003	124	2	will	will	AUX
ejpam-5003	124	3	also	also	ADV
ejpam-5003	124	4	investigate	investigate	VERB
ejpam-5003	124	5	their	their	PRON
ejpam-5003	124	6	general	general	ADJ
ejpam-5003	124	7	relationship	relationship	NOUN
ejpam-5003	124	8	.	.	PUNCT
ejpam-5003	125	1	finally	finally	ADV
ejpam-5003	125	2	,	,	PUNCT
ejpam-5003	125	3	we	we	PRON
ejpam-5003	125	4	will	will	AUX
ejpam-5003	125	5	investigate	investigate	VERB
ejpam-5003	125	6	the	the	DET
ejpam-5003	125	7	relationship	relationship	NOUN
ejpam-5003	125	8	between	between	ADP
ejpam-5003	125	9	hyper	hyper	NOUN
ejpam-5003	125	10	bn	bn	ADJ
ejpam-5003	125	11	-ideals	-ideal	NOUN
ejpam-5003	125	12	and	and	CCONJ
ejpam-5003	125	13	hyper	hyper	ADJ
ejpam-5003	125	14	subbn	subbn	NOUN
ejpam-5003	125	15	algebras	algebras	PROPN
ejpam-5003	125	16	.	.	PUNCT
ejpam-5003	126	1	definition	definition	NOUN
ejpam-5003	126	2	11	11	NUM
ejpam-5003	126	3	.	.	PUNCT
ejpam-5003	127	1	let	let	VERB
ejpam-5003	127	2	i	i	PRON
ejpam-5003	127	3	be	be	AUX
ejpam-5003	127	4	a	a	DET
ejpam-5003	127	5	nonempty	nonempty	ADJ
ejpam-5003	127	6	subset	subset	NOUN
ejpam-5003	127	7	of	of	ADP
ejpam-5003	127	8	a	a	DET
ejpam-5003	127	9	hyper	hyper	ADJ
ejpam-5003	127	10	bn	bn	NOUN
ejpam-5003	127	11	-algebra	-algebra	NOUN
ejpam-5003	127	12	h	h	NOUN
ejpam-5003	127	13	such	such	ADJ
ejpam-5003	127	14	that	that	DET
ejpam-5003	127	15	0	0	NUM
ejpam-5003	127	16	∈	∈	PROPN
ejpam-5003	127	17	i.	i.	NOUN
ejpam-5003	127	18	(	(	PUNCT
ejpam-5003	127	19	i	i	NOUN
ejpam-5003	127	20	)	)	PUNCT
ejpam-5003	128	1	i	i	PRON
ejpam-5003	128	2	is	be	AUX
ejpam-5003	128	3	a	a	DET
ejpam-5003	128	4	hyper	hyper	ADJ
ejpam-5003	128	5	bn	bn	NOUN
ejpam-5003	128	6	-ideal	-ideal	ADJ
ejpam-5003	128	7	if	if	SCONJ
ejpam-5003	128	8	for	for	ADP
ejpam-5003	128	9	all	all	DET
ejpam-5003	128	10	x	x	NOUN
ejpam-5003	128	11	,	,	PUNCT
ejpam-5003	128	12	y	y	PROPN
ejpam-5003	128	13	∈	∈	PROPN
ejpam-5003	128	14	h	h	NOUN
ejpam-5003	128	15	,	,	PUNCT
ejpam-5003	128	16	x⊛	x⊛	PROPN
ejpam-5003	128	17	y	y	PROPN
ejpam-5003	128	18	≪	≪	ADJ
ejpam-5003	128	19	i	i	PRON
ejpam-5003	128	20	and	and	CCONJ
ejpam-5003	128	21	y	y	PROPN
ejpam-5003	128	22	∈	∈	PROPN
ejpam-5003	129	1	i	i	PRON
ejpam-5003	129	2	imply	imply	VERB
ejpam-5003	129	3	that	that	SCONJ
ejpam-5003	129	4	x	x	SYM
ejpam-5003	129	5	∈	∈	PROPN
ejpam-5003	129	6	i.	i.	NOUN
ejpam-5003	129	7	(	(	PUNCT
ejpam-5003	129	8	ii	ii	PROPN
ejpam-5003	129	9	)	)	PUNCT
ejpam-5003	129	10	i	i	PRON
ejpam-5003	129	11	is	be	AUX
ejpam-5003	129	12	a	a	DET
ejpam-5003	129	13	weak	weak	ADJ
ejpam-5003	129	14	hyper	hyper	ADJ
ejpam-5003	129	15	bn	bn	NOUN
ejpam-5003	129	16	-ideal	-ideal	ADJ
ejpam-5003	129	17	if	if	SCONJ
ejpam-5003	129	18	for	for	ADP
ejpam-5003	129	19	all	all	DET
ejpam-5003	129	20	x	x	NOUN
ejpam-5003	129	21	,	,	PUNCT
ejpam-5003	129	22	y	y	PROPN
ejpam-5003	129	23	∈	∈	PROPN
ejpam-5003	129	24	h	h	NOUN
ejpam-5003	129	25	,	,	PUNCT
ejpam-5003	129	26	x⊛	x⊛	PROPN
ejpam-5003	129	27	y	y	PROPN
ejpam-5003	129	28	⊆	⊆	NUM
ejpam-5003	129	29	i	i	PROPN
ejpam-5003	129	30	and	and	CCONJ
ejpam-5003	129	31	y	y	PROPN
ejpam-5003	129	32	∈	∈	PROPN
ejpam-5003	130	1	i	i	PRON
ejpam-5003	130	2	imply	imply	VERB
ejpam-5003	130	3	that	that	SCONJ
ejpam-5003	130	4	x	x	SYM
ejpam-5003	130	5	∈	∈	PROPN
ejpam-5003	130	6	i.	i.	NOUN
ejpam-5003	130	7	(	(	PUNCT
ejpam-5003	130	8	iii	iii	X
ejpam-5003	130	9	)	)	PUNCT
ejpam-5003	130	10	i	i	PRON
ejpam-5003	130	11	is	be	AUX
ejpam-5003	130	12	a	a	DET
ejpam-5003	130	13	strong	strong	ADJ
ejpam-5003	130	14	hyper	hyper	ADJ
ejpam-5003	130	15	bn	bn	NOUN
ejpam-5003	130	16	-ideal	-ideal	NOUN
ejpam-5003	130	17	if	if	SCONJ
ejpam-5003	130	18	for	for	ADP
ejpam-5003	130	19	all	all	DET
ejpam-5003	130	20	x	x	NOUN
ejpam-5003	130	21	,	,	PUNCT
ejpam-5003	130	22	y	y	PROPN
ejpam-5003	130	23	∈	∈	PROPN
ejpam-5003	130	24	h	h	NOUN
ejpam-5003	130	25	,	,	PUNCT
ejpam-5003	130	26	(	(	PUNCT
ejpam-5003	130	27	x	x	PROPN
ejpam-5003	130	28	⊛	⊛	NUM
ejpam-5003	130	29	y	y	NUM
ejpam-5003	130	30	)	)	PUNCT
ejpam-5003	130	31	∩	∩	NOUN
ejpam-5003	130	32	i	i	PRON
ejpam-5003	130	33	̸=	̸=	PROPN
ejpam-5003	130	34	∅	∅	NOUN
ejpam-5003	130	35	and	and	CCONJ
ejpam-5003	130	36	y	y	PROPN
ejpam-5003	130	37	∈	∈	PROPN
ejpam-5003	130	38	i	i	PRON
ejpam-5003	130	39	imply	imply	VERB
ejpam-5003	130	40	that	that	SCONJ
ejpam-5003	130	41	x	x	X
ejpam-5003	130	42	∈	∈	PROPN
ejpam-5003	130	43	i.	i.	NOUN
ejpam-5003	130	44	example	example	NOUN
ejpam-5003	130	45	10	10	NUM
ejpam-5003	130	46	.	.	PUNCT
ejpam-5003	131	1	consider	consider	VERB
ejpam-5003	131	2	the	the	DET
ejpam-5003	131	3	hyper	hyper	ADJ
ejpam-5003	131	4	bn	bn	ADJ
ejpam-5003	131	5	-algebra	-algebra	PROPN
ejpam-5003	131	6	h	h	NOUN
ejpam-5003	131	7	in	in	ADP
ejpam-5003	131	8	example	example	NOUN
ejpam-5003	131	9	1	1	X
ejpam-5003	131	10	.	.	PUNCT
ejpam-5003	132	1	let	let	VERB
ejpam-5003	132	2	i	i	PRON
ejpam-5003	132	3	=	=	PUNCT
ejpam-5003	132	4	{	{	PUNCT
ejpam-5003	132	5	0	0	NUM
ejpam-5003	132	6	}	}	PUNCT
ejpam-5003	132	7	and	and	CCONJ
ejpam-5003	132	8	i1	i1	PROPN
ejpam-5003	132	9	=	=	PUNCT
ejpam-5003	132	10	{	{	PUNCT
ejpam-5003	132	11	0	0	NUM
ejpam-5003	132	12	,	,	PUNCT
ejpam-5003	132	13	a	a	PRON
ejpam-5003	132	14	}	}	PUNCT
ejpam-5003	132	15	.	.	PUNCT
ejpam-5003	133	1	by	by	ADP
ejpam-5003	133	2	routine	routine	ADJ
ejpam-5003	133	3	calculations	calculation	NOUN
ejpam-5003	133	4	,	,	PUNCT
ejpam-5003	133	5	i	i	PRON
ejpam-5003	133	6	,	,	PUNCT
ejpam-5003	133	7	and	and	CCONJ
ejpam-5003	133	8	i1	i1	PROPN
ejpam-5003	133	9	,	,	PUNCT
ejpam-5003	133	10	are	be	AUX
ejpam-5003	133	11	hyper	hyper	ADJ
ejpam-5003	133	12	bn	bn	ADP
ejpam-5003	133	13	-ideals	-ideal	NOUN
ejpam-5003	133	14	of	of	ADP
ejpam-5003	133	15	h.	h.	NOUN
ejpam-5003	133	16	if	if	SCONJ
ejpam-5003	133	17	we	we	PRON
ejpam-5003	133	18	consider	consider	VERB
ejpam-5003	133	19	the	the	DET
ejpam-5003	133	20	hyper	hyper	ADJ
ejpam-5003	133	21	bn	bn	ADJ
ejpam-5003	133	22	-algebra	-algebra	PROPN
ejpam-5003	133	23	h	h	NOUN
ejpam-5003	133	24	in	in	ADP
ejpam-5003	133	25	example	example	NOUN
ejpam-5003	133	26	2	2	NUM
ejpam-5003	133	27	,	,	PUNCT
ejpam-5003	133	28	then	then	ADV
ejpam-5003	133	29	the	the	DET
ejpam-5003	133	30	set	set	NOUN
ejpam-5003	133	31	j	j	PROPN
ejpam-5003	133	32	=	=	PUNCT
ejpam-5003	133	33	{	{	PUNCT
ejpam-5003	133	34	0	0	NUM
ejpam-5003	133	35	}	}	PUNCT
ejpam-5003	133	36	is	be	AUX
ejpam-5003	133	37	a	a	DET
ejpam-5003	133	38	hyper	hyper	ADJ
ejpam-5003	133	39	bn	bn	ADP
ejpam-5003	133	40	-ideal	-ideal	NOUN
ejpam-5003	133	41	of	of	ADP
ejpam-5003	133	42	h.	h.	PROPN
ejpam-5003	133	43	however	however	ADV
ejpam-5003	133	44	,	,	PUNCT
ejpam-5003	133	45	j1	j1	PROPN
ejpam-5003	133	46	=	=	PUNCT
ejpam-5003	133	47	{	{	PUNCT
ejpam-5003	133	48	0	0	NUM
ejpam-5003	133	49	,	,	PUNCT
ejpam-5003	133	50	1	1	NUM
ejpam-5003	133	51	}	}	PUNCT
ejpam-5003	133	52	is	be	AUX
ejpam-5003	133	53	not	not	PART
ejpam-5003	133	54	a	a	DET
ejpam-5003	133	55	hyper	hyper	ADJ
ejpam-5003	133	56	bn	bn	ADP
ejpam-5003	133	57	-ideal	-ideal	NOUN
ejpam-5003	133	58	of	of	ADP
ejpam-5003	133	59	h	h	NOUN
ejpam-5003	133	60	because	because	SCONJ
ejpam-5003	133	61	2⊛1	2⊛1	NUM
ejpam-5003	133	62	=	=	SYM
ejpam-5003	133	63	{	{	PUNCT
ejpam-5003	133	64	0	0	NUM
ejpam-5003	133	65	,	,	PUNCT
ejpam-5003	133	66	1	1	NUM
ejpam-5003	133	67	}	}	PUNCT
ejpam-5003	133	68	≪	≪	PUNCT
ejpam-5003	133	69	j1	j1	NOUN
ejpam-5003	133	70	and	and	CCONJ
ejpam-5003	133	71	1	1	NUM
ejpam-5003	133	72	∈	∈	NOUN
ejpam-5003	133	73	j1	j1	NOUN
ejpam-5003	133	74	but	but	CCONJ
ejpam-5003	133	75	2	2	NUM
ejpam-5003	133	76	/∈	/∈	NOUN
ejpam-5003	133	77	j1	j1	PROPN
ejpam-5003	133	78	.	.	PUNCT
ejpam-5003	134	1	also	also	ADV
ejpam-5003	134	2	,	,	PUNCT
ejpam-5003	134	3	j2	j2	PROPN
ejpam-5003	134	4	=	=	SYM
ejpam-5003	134	5	{	{	PUNCT
ejpam-5003	134	6	0	0	NUM
ejpam-5003	134	7	,	,	PUNCT
ejpam-5003	134	8	2	2	NUM
ejpam-5003	134	9	}	}	PUNCT
ejpam-5003	134	10	is	be	AUX
ejpam-5003	134	11	not	not	PART
ejpam-5003	134	12	a	a	DET
ejpam-5003	134	13	hyper	hyper	ADJ
ejpam-5003	134	14	bn	bn	ADP
ejpam-5003	134	15	-ideal	-ideal	NOUN
ejpam-5003	134	16	of	of	ADP
ejpam-5003	134	17	h	h	NOUN
ejpam-5003	134	18	because	because	SCONJ
ejpam-5003	134	19	1	1	NUM
ejpam-5003	134	20	⊛	⊛	NUM
ejpam-5003	134	21	2	2	NUM
ejpam-5003	134	22	=	=	SYM
ejpam-5003	134	23	{	{	PUNCT
ejpam-5003	134	24	0	0	NUM
ejpam-5003	134	25	,	,	PUNCT
ejpam-5003	134	26	1	1	NUM
ejpam-5003	134	27	}	}	PUNCT
ejpam-5003	134	28	≪	≪	PUNCT
ejpam-5003	134	29	j2	j2	NOUN
ejpam-5003	134	30	and	and	CCONJ
ejpam-5003	134	31	2	2	NUM
ejpam-5003	134	32	∈	∈	PROPN
ejpam-5003	134	33	j2	j2	NOUN
ejpam-5003	134	34	but	but	CCONJ
ejpam-5003	134	35	1	1	NUM
ejpam-5003	134	36	/∈	/∈	NOUN
ejpam-5003	134	37	j2	j2	PROPN
ejpam-5003	134	38	.	.	PROPN
ejpam-5003	134	39	example	example	NOUN
ejpam-5003	135	1	11	11	NUM
ejpam-5003	135	2	.	.	PUNCT
ejpam-5003	136	1	consider	consider	VERB
ejpam-5003	136	2	the	the	DET
ejpam-5003	136	3	hyper	hyper	ADJ
ejpam-5003	136	4	bn	bn	ADJ
ejpam-5003	136	5	-algebra	-algebra	PROPN
ejpam-5003	136	6	(	(	PUNCT
ejpam-5003	136	7	z,⊛	z,⊛	NUM
ejpam-5003	136	8	,	,	PUNCT
ejpam-5003	136	9	0	0	NUM
ejpam-5003	136	10	)	)	PUNCT
ejpam-5003	136	11	in	in	ADP
ejpam-5003	136	12	example	example	NOUN
ejpam-5003	136	13	4	4	X
ejpam-5003	136	14	.	.	PUNCT
ejpam-5003	137	1	let	let	VERB
ejpam-5003	137	2	ix	ix	VERB
ejpam-5003	137	3	=	=	PUNCT
ejpam-5003	137	4	{	{	PUNCT
ejpam-5003	137	5	0	0	NUM
ejpam-5003	137	6	,	,	PUNCT
ejpam-5003	137	7	x	x	NOUN
ejpam-5003	137	8	}	}	PUNCT
ejpam-5003	137	9	.	.	PUNCT
ejpam-5003	138	1	by	by	ADP
ejpam-5003	138	2	routine	routine	ADJ
ejpam-5003	138	3	calculations	calculation	NOUN
ejpam-5003	138	4	,	,	PUNCT
ejpam-5003	138	5	ix	ix	ADV
ejpam-5003	138	6	is	be	AUX
ejpam-5003	138	7	a	a	DET
ejpam-5003	138	8	hyper	hyper	ADJ
ejpam-5003	138	9	bn	bn	ADP
ejpam-5003	138	10	-ideal	-ideal	NOUN
ejpam-5003	138	11	of	of	ADP
ejpam-5003	138	12	h	h	NOUN
ejpam-5003	138	13	for	for	ADP
ejpam-5003	138	14	all	all	DET
ejpam-5003	138	15	x	x	SYM
ejpam-5003	138	16	∈	∈	PROPN
ejpam-5003	138	17	z.	z.	PROPN
ejpam-5003	138	18	example	example	NOUN
ejpam-5003	138	19	12	12	NUM
ejpam-5003	138	20	.	.	PUNCT
ejpam-5003	139	1	consider	consider	VERB
ejpam-5003	139	2	the	the	DET
ejpam-5003	139	3	hyper	hyper	ADJ
ejpam-5003	139	4	bn	bn	NOUN
ejpam-5003	139	5	-algebra	-algebra	PROPN
ejpam-5003	139	6	h	h	NOUN
ejpam-5003	139	7	=	=	SYM
ejpam-5003	139	8	{	{	PUNCT
ejpam-5003	139	9	0	0	NUM
ejpam-5003	139	10	,	,	PUNCT
ejpam-5003	139	11	a	a	DET
ejpam-5003	139	12	,	,	PUNCT
ejpam-5003	139	13	b	b	NOUN
ejpam-5003	139	14	}	}	PUNCT
ejpam-5003	139	15	in	in	ADP
ejpam-5003	139	16	example	example	NOUN
ejpam-5003	139	17	1	1	X
ejpam-5003	139	18	.	.	PUNCT
ejpam-5003	140	1	let	let	VERB
ejpam-5003	140	2	i	i	PRON
ejpam-5003	140	3	=	=	PUNCT
ejpam-5003	140	4	{	{	PUNCT
ejpam-5003	140	5	0	0	NUM
ejpam-5003	140	6	}	}	PUNCT
ejpam-5003	140	7	and	and	CCONJ
ejpam-5003	140	8	i1	i1	PROPN
ejpam-5003	140	9	=	=	PUNCT
ejpam-5003	140	10	{	{	PUNCT
ejpam-5003	140	11	0	0	NUM
ejpam-5003	140	12	,	,	PUNCT
ejpam-5003	140	13	a	a	PRON
ejpam-5003	140	14	}	}	PUNCT
ejpam-5003	140	15	.	.	PUNCT
ejpam-5003	141	1	by	by	ADP
ejpam-5003	141	2	routine	routine	ADJ
ejpam-5003	141	3	calculations	calculation	NOUN
ejpam-5003	141	4	,	,	PUNCT
ejpam-5003	141	5	i	i	PRON
ejpam-5003	141	6	and	and	CCONJ
ejpam-5003	141	7	i1	i1	PROPN
ejpam-5003	141	8	are	be	AUX
ejpam-5003	141	9	strong	strong	ADJ
ejpam-5003	141	10	hyper	hyper	ADJ
ejpam-5003	141	11	bn	bn	ADJ
ejpam-5003	141	12	-ideals	-ideal	NOUN
ejpam-5003	141	13	of	of	ADP
ejpam-5003	141	14	h.	h.	NOUN
ejpam-5003	141	15	furthermore	furthermore	ADV
ejpam-5003	141	16	,	,	PUNCT
ejpam-5003	141	17	i	i	PRON
ejpam-5003	141	18	and	and	CCONJ
ejpam-5003	141	19	i1	i1	PROPN
ejpam-5003	141	20	are	be	AUX
ejpam-5003	141	21	weak	weak	ADJ
ejpam-5003	141	22	hyper	hyper	ADJ
ejpam-5003	141	23	bn	bn	ADJ
ejpam-5003	141	24	-ideals	-ideal	NOUN
ejpam-5003	141	25	of	of	ADP
ejpam-5003	141	26	h.	h.	PROPN
ejpam-5003	141	27	example	example	PROPN
ejpam-5003	141	28	13	13	NUM
ejpam-5003	141	29	.	.	PUNCT
ejpam-5003	142	1	consider	consider	VERB
ejpam-5003	142	2	the	the	DET
ejpam-5003	142	3	hyper	hyper	ADJ
ejpam-5003	142	4	bn	bn	NOUN
ejpam-5003	142	5	-algebra	-algebra	PROPN
ejpam-5003	142	6	h	h	NOUN
ejpam-5003	142	7	=	=	SYM
ejpam-5003	142	8	{	{	PUNCT
ejpam-5003	142	9	0	0	NUM
ejpam-5003	142	10	,	,	PUNCT
ejpam-5003	142	11	1	1	NUM
ejpam-5003	142	12	,	,	PUNCT
ejpam-5003	142	13	2	2	NUM
ejpam-5003	142	14	}	}	PUNCT
ejpam-5003	142	15	in	in	ADP
ejpam-5003	142	16	example	example	NOUN
ejpam-5003	142	17	2	2	X
ejpam-5003	142	18	.	.	PUNCT
ejpam-5003	143	1	let	let	VERB
ejpam-5003	143	2	i1	i1	PROPN
ejpam-5003	143	3	=	=	PUNCT
ejpam-5003	143	4	{	{	PUNCT
ejpam-5003	143	5	0	0	NUM
ejpam-5003	143	6	,	,	PUNCT
ejpam-5003	143	7	1	1	NUM
ejpam-5003	143	8	}	}	PUNCT
ejpam-5003	143	9	.	.	PUNCT
ejpam-5003	144	1	i1	i1	PROPN
ejpam-5003	144	2	is	be	AUX
ejpam-5003	144	3	not	not	PART
ejpam-5003	144	4	a	a	DET
ejpam-5003	144	5	strong	strong	ADJ
ejpam-5003	144	6	hyper	hyper	NOUN
ejpam-5003	144	7	bn	bn	NOUN
ejpam-5003	144	8	-ideal	-ideal	NOUN
ejpam-5003	144	9	of	of	ADP
ejpam-5003	144	10	h	h	NOUN
ejpam-5003	144	11	because	because	SCONJ
ejpam-5003	144	12	(	(	PUNCT
ejpam-5003	144	13	2	2	NUM
ejpam-5003	144	14	⊛	⊛	NUM
ejpam-5003	144	15	1	1	NUM
ejpam-5003	144	16	)	)	PUNCT
ejpam-5003	144	17	∩	∩	PROPN
ejpam-5003	144	18	i1	i1	PROPN
ejpam-5003	144	19	̸=	̸=	PROPN
ejpam-5003	144	20	∅	∅	NOUN
ejpam-5003	144	21	and	and	CCONJ
ejpam-5003	144	22	1	1	NUM
ejpam-5003	144	23	∈	∈	PROPN
ejpam-5003	144	24	i1	i1	NOUN
ejpam-5003	144	25	but	but	CCONJ
ejpam-5003	144	26	2	2	NUM
ejpam-5003	144	27	/∈	/∈	NOUN
ejpam-5003	144	28	i1	i1	PROPN
ejpam-5003	144	29	.	.	PUNCT
ejpam-5003	145	1	it	it	PRON
ejpam-5003	145	2	is	be	AUX
ejpam-5003	145	3	not	not	PART
ejpam-5003	145	4	also	also	ADV
ejpam-5003	145	5	a	a	DET
ejpam-5003	145	6	weak	weak	ADJ
ejpam-5003	145	7	hyper	hyper	ADJ
ejpam-5003	145	8	bn	bn	ADJ
ejpam-5003	145	9	-ideal	-ideal	NOUN
ejpam-5003	145	10	of	of	ADP
ejpam-5003	145	11	h	h	NOUN
ejpam-5003	145	12	because	because	SCONJ
ejpam-5003	145	13	2	2	NUM
ejpam-5003	145	14	⊛	⊛	NUM
ejpam-5003	145	15	1	1	NUM
ejpam-5003	145	16	⊆	⊆	NUM
ejpam-5003	145	17	i1	i1	NOUN
ejpam-5003	145	18	and	and	CCONJ
ejpam-5003	145	19	1	1	NUM
ejpam-5003	145	20	∈	∈	PROPN
ejpam-5003	145	21	i1	i1	NOUN
ejpam-5003	145	22	but	but	CCONJ
ejpam-5003	145	23	2	2	NUM
ejpam-5003	145	24	/∈	/∈	NOUN
ejpam-5003	145	25	i1	i1	PROPN
ejpam-5003	145	26	.	.	PUNCT
ejpam-5003	146	1	l.r	l.r	PROPN
ejpam-5003	146	2	.	.	PROPN
ejpam-5003	146	3	cabardo	cabardo	PROPN
ejpam-5003	146	4	,	,	PUNCT
ejpam-5003	146	5	g.	g.	PROPN
ejpam-5003	146	6	petalcorin	petalcorin	PROPN
ejpam-5003	146	7	/	/	SYM
ejpam-5003	146	8	eur	eur	PROPN
ejpam-5003	146	9	.	.	PUNCT
ejpam-5003	147	1	j.	j.	PROPN
ejpam-5003	147	2	pure	pure	PROPN
ejpam-5003	147	3	appl	appl	PROPN
ejpam-5003	147	4	.	.	PROPN
ejpam-5003	147	5	math	math	PROPN
ejpam-5003	147	6	,	,	PUNCT
ejpam-5003	147	7	17	17	NUM
ejpam-5003	147	8	(	(	PUNCT
ejpam-5003	147	9	1	1	NUM
ejpam-5003	147	10	)	)	PUNCT
ejpam-5003	147	11	(	(	PUNCT
ejpam-5003	147	12	2024	2024	NUM
ejpam-5003	147	13	)	)	PUNCT
ejpam-5003	147	14	,	,	PUNCT
ejpam-5003	147	15	222	222	NUM
ejpam-5003	147	16	-	-	SYM
ejpam-5003	147	17	242	242	NUM
ejpam-5003	147	18	228	228	NUM
ejpam-5003	147	19	proposition	proposition	NOUN
ejpam-5003	147	20	1	1	NUM
ejpam-5003	147	21	.	.	PUNCT
ejpam-5003	148	1	let	let	VERB
ejpam-5003	148	2	h	h	PRON
ejpam-5003	148	3	be	be	AUX
ejpam-5003	148	4	a	a	DET
ejpam-5003	148	5	hyper	hyper	ADJ
ejpam-5003	148	6	bn	bn	NOUN
ejpam-5003	148	7	-algebra	-algebra	NOUN
ejpam-5003	148	8	.	.	PUNCT
ejpam-5003	149	1	then	then	ADV
ejpam-5003	149	2	(	(	PUNCT
ejpam-5003	149	3	i	i	NOUN
ejpam-5003	149	4	)	)	PUNCT
ejpam-5003	150	1	every	every	DET
ejpam-5003	150	2	hyper	hyper	ADJ
ejpam-5003	150	3	bn	bn	ADP
ejpam-5003	150	4	-ideal	-ideal	NOUN
ejpam-5003	150	5	of	of	ADP
ejpam-5003	150	6	h	h	NOUN
ejpam-5003	150	7	is	be	AUX
ejpam-5003	150	8	a	a	DET
ejpam-5003	150	9	weak	weak	ADJ
ejpam-5003	150	10	hyper	hyper	NOUN
ejpam-5003	150	11	bn	bn	ADJ
ejpam-5003	150	12	-ideal	-ideal	NOUN
ejpam-5003	150	13	of	of	ADP
ejpam-5003	150	14	h	h	NOUN
ejpam-5003	150	15	;	;	PUNCT
ejpam-5003	150	16	and	and	CCONJ
ejpam-5003	150	17	(	(	PUNCT
ejpam-5003	150	18	ii	ii	NOUN
ejpam-5003	150	19	)	)	PUNCT
ejpam-5003	150	20	every	every	DET
ejpam-5003	150	21	strong	strong	ADJ
ejpam-5003	150	22	hyper	hyper	ADJ
ejpam-5003	150	23	bn	bn	NOUN
ejpam-5003	150	24	-ideal	-ideal	NOUN
ejpam-5003	150	25	of	of	ADP
ejpam-5003	150	26	h	h	NOUN
ejpam-5003	150	27	is	be	AUX
ejpam-5003	150	28	a	a	DET
ejpam-5003	150	29	hyper	hyper	ADJ
ejpam-5003	150	30	bn	bn	ADP
ejpam-5003	150	31	-ideal	-ideal	NOUN
ejpam-5003	150	32	of	of	ADP
ejpam-5003	150	33	h.	h.	NOUN
ejpam-5003	150	34	proof	proof	NOUN
ejpam-5003	150	35	.	.	PUNCT
ejpam-5003	151	1	let	let	VERB
ejpam-5003	151	2	h	h	PRON
ejpam-5003	151	3	be	be	AUX
ejpam-5003	151	4	a	a	DET
ejpam-5003	151	5	hyper	hyper	ADJ
ejpam-5003	151	6	bn	bn	NOUN
ejpam-5003	151	7	-algebra	-algebra	NOUN
ejpam-5003	151	8	.	.	PUNCT
ejpam-5003	152	1	(	(	PUNCT
ejpam-5003	152	2	i	i	NOUN
ejpam-5003	152	3	)	)	PUNCT
ejpam-5003	152	4	let	let	VERB
ejpam-5003	152	5	i	i	PRON
ejpam-5003	152	6	be	be	AUX
ejpam-5003	152	7	a	a	DET
ejpam-5003	152	8	hyper	hyper	ADJ
ejpam-5003	152	9	bn	bn	ADP
ejpam-5003	152	10	-ideal	-ideal	NOUN
ejpam-5003	152	11	of	of	ADP
ejpam-5003	152	12	h.	h.	NOUN
ejpam-5003	152	13	thus	thus	ADV
ejpam-5003	152	14	,	,	PUNCT
ejpam-5003	152	15	0	0	NUM
ejpam-5003	152	16	∈	∈	PROPN
ejpam-5003	152	17	i.	i.	NOUN
ejpam-5003	152	18	suppose	suppose	VERB
ejpam-5003	152	19	that	that	SCONJ
ejpam-5003	152	20	x	x	X
ejpam-5003	152	21	,	,	PUNCT
ejpam-5003	152	22	y	y	PROPN
ejpam-5003	152	23	∈	∈	PROPN
ejpam-5003	152	24	h	h	NOUN
ejpam-5003	152	25	such	such	ADJ
ejpam-5003	152	26	that	that	PRON
ejpam-5003	152	27	x⊛	x⊛	PROPN
ejpam-5003	152	28	y	y	PROPN
ejpam-5003	152	29	⊆	⊆	NUM
ejpam-5003	152	30	i	i	PROPN
ejpam-5003	152	31	and	and	CCONJ
ejpam-5003	152	32	y	y	PROPN
ejpam-5003	152	33	∈	∈	PROPN
ejpam-5003	152	34	i.	i.	NOUN
ejpam-5003	152	35	by	by	ADP
ejpam-5003	152	36	theorem	theorem	PROPN
ejpam-5003	152	37	1(xi	1(xi	PROPN
ejpam-5003	152	38	)	)	PUNCT
ejpam-5003	152	39	,	,	PUNCT
ejpam-5003	152	40	x⊛	x⊛	PROPN
ejpam-5003	152	41	y	y	PROPN
ejpam-5003	152	42	≪	≪	PUNCT
ejpam-5003	152	43	i.	i.	NOUN
ejpam-5003	152	44	since	since	SCONJ
ejpam-5003	152	45	i	i	PRON
ejpam-5003	152	46	is	be	AUX
ejpam-5003	152	47	a	a	DET
ejpam-5003	152	48	hyper	hyper	ADJ
ejpam-5003	152	49	bn	bn	ADP
ejpam-5003	152	50	-ideal	-ideal	NOUN
ejpam-5003	152	51	of	of	ADP
ejpam-5003	152	52	h	h	NOUN
ejpam-5003	152	53	,	,	PUNCT
ejpam-5003	152	54	it	it	PRON
ejpam-5003	152	55	follows	follow	VERB
ejpam-5003	152	56	that	that	SCONJ
ejpam-5003	152	57	x	x	SYM
ejpam-5003	152	58	∈	∈	PROPN
ejpam-5003	152	59	i.	i.	NOUN
ejpam-5003	152	60	thus	thus	ADV
ejpam-5003	152	61	,	,	PUNCT
ejpam-5003	152	62	i	i	PRON
ejpam-5003	152	63	is	be	AUX
ejpam-5003	152	64	a	a	DET
ejpam-5003	152	65	weak	weak	ADJ
ejpam-5003	152	66	hyper	hyper	NOUN
ejpam-5003	152	67	bn	bn	ADJ
ejpam-5003	152	68	-ideal	-ideal	NOUN
ejpam-5003	152	69	of	of	ADP
ejpam-5003	152	70	h.	h.	PROPN
ejpam-5003	152	71	(	(	PUNCT
ejpam-5003	152	72	ii	ii	NOUN
ejpam-5003	152	73	)	)	PUNCT
ejpam-5003	152	74	let	let	VERB
ejpam-5003	152	75	i	i	PRON
ejpam-5003	152	76	be	be	AUX
ejpam-5003	152	77	a	a	DET
ejpam-5003	152	78	strong	strong	ADJ
ejpam-5003	152	79	hyper	hyper	NOUN
ejpam-5003	152	80	bn	bn	NOUN
ejpam-5003	152	81	-ideal	-ideal	NOUN
ejpam-5003	152	82	of	of	ADP
ejpam-5003	152	83	h.	h.	NOUN
ejpam-5003	152	84	thus	thus	ADV
ejpam-5003	152	85	,	,	PUNCT
ejpam-5003	152	86	0	0	NUM
ejpam-5003	152	87	∈	∈	PROPN
ejpam-5003	152	88	i.	i.	NOUN
ejpam-5003	152	89	suppose	suppose	VERB
ejpam-5003	152	90	that	that	SCONJ
ejpam-5003	152	91	x	x	X
ejpam-5003	152	92	,	,	PUNCT
ejpam-5003	152	93	y	y	PROPN
ejpam-5003	152	94	∈	∈	PROPN
ejpam-5003	152	95	h	h	NOUN
ejpam-5003	152	96	such	such	ADJ
ejpam-5003	152	97	that	that	SCONJ
ejpam-5003	152	98	x	x	PROPN
ejpam-5003	152	99	⊛	⊛	NUM
ejpam-5003	152	100	y	y	PROPN
ejpam-5003	152	101	≪	≪	PROPN
ejpam-5003	152	102	i	i	PRON
ejpam-5003	152	103	and	and	CCONJ
ejpam-5003	152	104	y	y	PROPN
ejpam-5003	152	105	∈	∈	PROPN
ejpam-5003	152	106	i.	i.	NOUN
ejpam-5003	152	107	then	then	ADV
ejpam-5003	152	108	for	for	ADP
ejpam-5003	152	109	each	each	PRON
ejpam-5003	152	110	a	a	DET
ejpam-5003	152	111	∈	∈	NOUN
ejpam-5003	152	112	x	x	SYM
ejpam-5003	152	113	⊛	⊛	NUM
ejpam-5003	152	114	y	y	PROPN
ejpam-5003	152	115	,	,	PUNCT
ejpam-5003	152	116	there	there	PRON
ejpam-5003	152	117	exists	exist	VERB
ejpam-5003	152	118	b	b	PROPN
ejpam-5003	152	119	∈	∈	PROPN
ejpam-5003	152	120	i	i	PRON
ejpam-5003	152	121	such	such	ADJ
ejpam-5003	152	122	that	that	SCONJ
ejpam-5003	152	123	a	a	DET
ejpam-5003	152	124	≪	≪	ADJ
ejpam-5003	152	125	b	b	NOUN
ejpam-5003	152	126	,	,	PUNCT
ejpam-5003	152	127	that	that	ADV
ejpam-5003	152	128	is	is	ADV
ejpam-5003	152	129	,	,	PUNCT
ejpam-5003	152	130	0	0	NUM
ejpam-5003	152	131	∈	∈	PROPN
ejpam-5003	152	132	a⊛	a⊛	PROPN
ejpam-5003	152	133	b.	b.	PROPN
ejpam-5003	152	134	since	since	SCONJ
ejpam-5003	152	135	0	0	NUM
ejpam-5003	152	136	∈	∈	PROPN
ejpam-5003	152	137	i	i	PRON
ejpam-5003	152	138	,	,	PUNCT
ejpam-5003	152	139	(	(	PUNCT
ejpam-5003	152	140	a⊛	a⊛	NOUN
ejpam-5003	152	141	b	b	NOUN
ejpam-5003	152	142	)	)	PUNCT
ejpam-5003	152	143	∩	∩	NOUN
ejpam-5003	152	144	i	i	PRON
ejpam-5003	152	145	̸=	̸=	PROPN
ejpam-5003	152	146	∅.	∅.	VERB
ejpam-5003	152	147	i	i	PRON
ejpam-5003	152	148	is	be	AUX
ejpam-5003	152	149	a	a	DET
ejpam-5003	152	150	strong	strong	ADJ
ejpam-5003	152	151	ideal	ideal	NOUN
ejpam-5003	152	152	with	with	ADP
ejpam-5003	152	153	b	b	PROPN
ejpam-5003	152	154	∈	∈	PROPN
ejpam-5003	152	155	i	i	PRON
ejpam-5003	152	156	implies	imply	VERB
ejpam-5003	152	157	that	that	SCONJ
ejpam-5003	152	158	a	a	DET
ejpam-5003	152	159	∈	∈	PROPN
ejpam-5003	152	160	i.	i.	NOUN
ejpam-5003	152	161	thus	thus	ADV
ejpam-5003	152	162	,	,	PUNCT
ejpam-5003	152	163	x⊛	x⊛	PROPN
ejpam-5003	152	164	y	y	PROPN
ejpam-5003	152	165	⊆	⊆	NUM
ejpam-5003	152	166	i.	i.	NOUN
ejpam-5003	152	167	hence	hence	ADV
ejpam-5003	152	168	,	,	PUNCT
ejpam-5003	152	169	(	(	PUNCT
ejpam-5003	152	170	x⊛	x⊛	PROPN
ejpam-5003	152	171	y	y	NOUN
ejpam-5003	152	172	)	)	PUNCT
ejpam-5003	152	173	∩	∩	NOUN
ejpam-5003	152	174	i	i	PRON
ejpam-5003	152	175	̸=	̸=	PROPN
ejpam-5003	152	176	∅	∅	NOUN
ejpam-5003	153	1	and	and	CCONJ
ejpam-5003	153	2	so	so	ADV
ejpam-5003	153	3	we	we	PRON
ejpam-5003	153	4	have	have	VERB
ejpam-5003	153	5	x	x	X
ejpam-5003	153	6	∈	∈	PROPN
ejpam-5003	153	7	i.	i.	NOUN
ejpam-5003	153	8	therefore	therefore	ADV
ejpam-5003	153	9	,	,	PUNCT
ejpam-5003	153	10	i	i	PRON
ejpam-5003	153	11	is	be	AUX
ejpam-5003	153	12	a	a	DET
ejpam-5003	153	13	hyper	hyper	ADJ
ejpam-5003	153	14	bn	bn	ADP
ejpam-5003	153	15	-ideal	-ideal	NOUN
ejpam-5003	153	16	of	of	ADP
ejpam-5003	153	17	h.	h.	NOUN
ejpam-5003	153	18	the	the	DET
ejpam-5003	153	19	following	follow	VERB
ejpam-5003	153	20	example	example	NOUN
ejpam-5003	153	21	will	will	AUX
ejpam-5003	153	22	show	show	VERB
ejpam-5003	153	23	that	that	SCONJ
ejpam-5003	153	24	the	the	DET
ejpam-5003	153	25	converse	converse	NOUN
ejpam-5003	153	26	of	of	ADP
ejpam-5003	153	27	proposition	proposition	NOUN
ejpam-5003	153	28	1(i	1(i	NUM
ejpam-5003	153	29	)	)	PUNCT
ejpam-5003	153	30	is	be	AUX
ejpam-5003	153	31	not	not	PART
ejpam-5003	153	32	necessarily	necessarily	ADV
ejpam-5003	153	33	true	true	ADJ
ejpam-5003	153	34	.	.	PUNCT
ejpam-5003	154	1	example	example	NOUN
ejpam-5003	154	2	14	14	NUM
ejpam-5003	154	3	.	.	PUNCT
ejpam-5003	155	1	consider	consider	VERB
ejpam-5003	155	2	the	the	DET
ejpam-5003	155	3	hyper	hyper	ADJ
ejpam-5003	155	4	bn	bn	ADJ
ejpam-5003	155	5	-algebra	-algebra	PROPN
ejpam-5003	155	6	h	h	NOUN
ejpam-5003	155	7	in	in	ADP
ejpam-5003	155	8	example	example	NOUN
ejpam-5003	155	9	2	2	NUM
ejpam-5003	155	10	and	and	CCONJ
ejpam-5003	155	11	let	let	VERB
ejpam-5003	155	12	j2	j2	PROPN
ejpam-5003	155	13	=	=	SYM
ejpam-5003	155	14	{	{	PUNCT
ejpam-5003	155	15	0	0	NUM
ejpam-5003	155	16	,	,	PUNCT
ejpam-5003	155	17	2	2	NUM
ejpam-5003	155	18	}	}	PUNCT
ejpam-5003	155	19	.	.	PUNCT
ejpam-5003	156	1	j2	j2	PROPN
ejpam-5003	156	2	is	be	AUX
ejpam-5003	156	3	a	a	DET
ejpam-5003	156	4	weak	weak	ADJ
ejpam-5003	156	5	hyper	hyper	NOUN
ejpam-5003	156	6	bn	bn	ADJ
ejpam-5003	156	7	-ideal	-ideal	NOUN
ejpam-5003	156	8	of	of	ADP
ejpam-5003	156	9	h	h	NOUN
ejpam-5003	156	10	by	by	ADP
ejpam-5003	156	11	routine	routine	ADJ
ejpam-5003	156	12	calculations	calculation	NOUN
ejpam-5003	156	13	.	.	PUNCT
ejpam-5003	157	1	however	however	ADV
ejpam-5003	157	2	,	,	PUNCT
ejpam-5003	157	3	it	it	PRON
ejpam-5003	157	4	is	be	AUX
ejpam-5003	157	5	not	not	PART
ejpam-5003	157	6	a	a	DET
ejpam-5003	157	7	hyper	hyper	ADJ
ejpam-5003	157	8	bn	bn	ADP
ejpam-5003	157	9	-ideal	-ideal	NOUN
ejpam-5003	157	10	of	of	ADP
ejpam-5003	157	11	h	h	NOUN
ejpam-5003	157	12	as	as	SCONJ
ejpam-5003	157	13	shown	show	VERB
ejpam-5003	157	14	in	in	ADP
ejpam-5003	157	15	example	example	NOUN
ejpam-5003	157	16	10	10	NUM
ejpam-5003	157	17	.	.	PUNCT
ejpam-5003	158	1	the	the	DET
ejpam-5003	158	2	following	follow	VERB
ejpam-5003	158	3	example	example	NOUN
ejpam-5003	158	4	will	will	AUX
ejpam-5003	158	5	show	show	VERB
ejpam-5003	158	6	that	that	SCONJ
ejpam-5003	158	7	the	the	DET
ejpam-5003	158	8	converse	converse	NOUN
ejpam-5003	158	9	of	of	ADP
ejpam-5003	158	10	proposition	proposition	NOUN
ejpam-5003	158	11	1(ii	1(ii	NUM
ejpam-5003	158	12	)	)	PUNCT
ejpam-5003	158	13	is	be	AUX
ejpam-5003	158	14	not	not	PART
ejpam-5003	158	15	necessarily	necessarily	ADV
ejpam-5003	158	16	true	true	ADJ
ejpam-5003	158	17	.	.	PUNCT
ejpam-5003	159	1	example	example	NOUN
ejpam-5003	160	1	15	15	NUM
ejpam-5003	160	2	.	.	PUNCT
ejpam-5003	161	1	let	let	VERB
ejpam-5003	161	2	h	h	NOUN
ejpam-5003	161	3	=	=	PRON
ejpam-5003	161	4	{	{	PUNCT
ejpam-5003	161	5	0	0	NUM
ejpam-5003	161	6	,	,	PUNCT
ejpam-5003	161	7	1	1	NUM
ejpam-5003	161	8	,	,	PUNCT
ejpam-5003	161	9	2	2	NUM
ejpam-5003	161	10	,	,	PUNCT
ejpam-5003	161	11	3	3	NUM
ejpam-5003	161	12	}	}	PUNCT
ejpam-5003	161	13	be	be	AUX
ejpam-5003	161	14	a	a	DET
ejpam-5003	161	15	set	set	NOUN
ejpam-5003	161	16	with	with	ADP
ejpam-5003	161	17	hyperoperation	hyperoperation	NOUN
ejpam-5003	161	18	⊛	⊛	NUM
ejpam-5003	161	19	defined	define	VERB
ejpam-5003	161	20	by	by	ADP
ejpam-5003	161	21	the	the	DET
ejpam-5003	161	22	following	following	ADJ
ejpam-5003	161	23	cayley	cayley	ADJ
ejpam-5003	161	24	table	table	NOUN
ejpam-5003	161	25	:	:	PUNCT
ejpam-5003	162	1	⊛	⊛	NUM
ejpam-5003	162	2	0	0	NUM
ejpam-5003	162	3	1	1	NUM
ejpam-5003	162	4	2	2	NUM
ejpam-5003	162	5	3	3	NUM
ejpam-5003	162	6	0	0	NUM
ejpam-5003	162	7	{	{	PUNCT
ejpam-5003	162	8	0	0	NUM
ejpam-5003	162	9	}	}	PUNCT
ejpam-5003	162	10	{	{	PUNCT
ejpam-5003	162	11	1	1	NUM
ejpam-5003	162	12	}	}	PUNCT
ejpam-5003	162	13	{	{	PUNCT
ejpam-5003	162	14	2	2	NUM
ejpam-5003	162	15	}	}	PUNCT
ejpam-5003	162	16	{	{	PUNCT
ejpam-5003	162	17	3	3	NUM
ejpam-5003	162	18	}	}	SYM
ejpam-5003	162	19	1	1	NUM
ejpam-5003	162	20	{	{	PUNCT
ejpam-5003	162	21	1	1	NUM
ejpam-5003	162	22	}	}	PUNCT
ejpam-5003	162	23	{	{	PUNCT
ejpam-5003	162	24	0	0	NUM
ejpam-5003	162	25	,	,	PUNCT
ejpam-5003	162	26	1	1	NUM
ejpam-5003	162	27	}	}	PUNCT
ejpam-5003	162	28	{	{	PUNCT
ejpam-5003	162	29	1	1	NUM
ejpam-5003	162	30	,	,	PUNCT
ejpam-5003	162	31	2	2	NUM
ejpam-5003	162	32	}	}	PUNCT
ejpam-5003	162	33	{	{	PUNCT
ejpam-5003	162	34	1	1	NUM
ejpam-5003	162	35	,	,	PUNCT
ejpam-5003	162	36	3	3	NUM
ejpam-5003	162	37	}	}	SYM
ejpam-5003	162	38	2	2	NUM
ejpam-5003	162	39	{	{	PUNCT
ejpam-5003	162	40	2	2	NUM
ejpam-5003	162	41	}	}	PUNCT
ejpam-5003	162	42	{	{	PUNCT
ejpam-5003	162	43	1	1	NUM
ejpam-5003	162	44	,	,	PUNCT
ejpam-5003	162	45	2	2	NUM
ejpam-5003	162	46	}	}	PUNCT
ejpam-5003	162	47	{	{	PUNCT
ejpam-5003	162	48	0	0	NUM
ejpam-5003	162	49	,	,	PUNCT
ejpam-5003	162	50	2	2	NUM
ejpam-5003	162	51	}	}	PUNCT
ejpam-5003	162	52	{	{	PUNCT
ejpam-5003	162	53	2	2	NUM
ejpam-5003	162	54	,	,	PUNCT
ejpam-5003	162	55	3	3	NUM
ejpam-5003	162	56	}	}	SYM
ejpam-5003	162	57	3	3	NUM
ejpam-5003	162	58	{	{	PUNCT
ejpam-5003	162	59	3	3	NUM
ejpam-5003	162	60	}	}	PUNCT
ejpam-5003	162	61	{	{	PUNCT
ejpam-5003	162	62	1	1	NUM
ejpam-5003	162	63	,	,	PUNCT
ejpam-5003	162	64	3	3	NUM
ejpam-5003	162	65	}	}	PUNCT
ejpam-5003	162	66	{	{	PUNCT
ejpam-5003	162	67	2	2	NUM
ejpam-5003	162	68	,	,	PUNCT
ejpam-5003	162	69	3	3	NUM
ejpam-5003	162	70	}	}	PUNCT
ejpam-5003	162	71	{	{	PUNCT
ejpam-5003	162	72	0	0	NUM
ejpam-5003	162	73	,	,	PUNCT
ejpam-5003	162	74	3	3	NUM
ejpam-5003	162	75	}	}	PUNCT
ejpam-5003	162	76	by	by	ADP
ejpam-5003	162	77	routine	routine	ADJ
ejpam-5003	162	78	calculations	calculation	NOUN
ejpam-5003	162	79	,	,	PUNCT
ejpam-5003	162	80	h	h	NOUN
ejpam-5003	162	81	is	be	AUX
ejpam-5003	162	82	a	a	DET
ejpam-5003	162	83	hyper	hyper	ADJ
ejpam-5003	162	84	bn	bn	NOUN
ejpam-5003	162	85	-algebra	-algebra	NOUN
ejpam-5003	162	86	.	.	PUNCT
ejpam-5003	163	1	let	let	VERB
ejpam-5003	163	2	i	i	PRON
ejpam-5003	163	3	=	=	PUNCT
ejpam-5003	163	4	{	{	PUNCT
ejpam-5003	163	5	0	0	NUM
ejpam-5003	163	6	,	,	PUNCT
ejpam-5003	163	7	1	1	NUM
ejpam-5003	163	8	}	}	PUNCT
ejpam-5003	163	9	.	.	PUNCT
ejpam-5003	164	1	then	then	ADV
ejpam-5003	164	2	i	i	PRON
ejpam-5003	164	3	is	be	AUX
ejpam-5003	164	4	a	a	DET
ejpam-5003	164	5	hyper	hyper	ADJ
ejpam-5003	164	6	bn	bn	NOUN
ejpam-5003	164	7	ideal	ideal	NOUN
ejpam-5003	164	8	of	of	ADP
ejpam-5003	164	9	h.	h.	PROPN
ejpam-5003	164	10	however	however	ADV
ejpam-5003	164	11	,	,	PUNCT
ejpam-5003	164	12	i	i	PRON
ejpam-5003	164	13	is	be	AUX
ejpam-5003	164	14	not	not	PART
ejpam-5003	164	15	a	a	DET
ejpam-5003	164	16	strong	strong	ADJ
ejpam-5003	164	17	hyper	hyper	NOUN
ejpam-5003	164	18	bn	bn	NOUN
ejpam-5003	164	19	-ideal	-ideal	NOUN
ejpam-5003	164	20	of	of	ADP
ejpam-5003	164	21	h	h	NOUN
ejpam-5003	164	22	because	because	SCONJ
ejpam-5003	164	23	(	(	PUNCT
ejpam-5003	164	24	2⊛1)∩	2⊛1)∩	NUM
ejpam-5003	164	25	i	i	NOUN
ejpam-5003	164	26	=	=	PUNCT
ejpam-5003	164	27	{	{	PUNCT
ejpam-5003	164	28	1	1	NUM
ejpam-5003	164	29	}	}	PUNCT
ejpam-5003	164	30	=	=	NOUN
ejpam-5003	164	31	̸	̸	ADJ
ejpam-5003	164	32	∅	∅	NOUN
ejpam-5003	164	33	and	and	CCONJ
ejpam-5003	164	34	1	1	NUM
ejpam-5003	164	35	∈	∈	NOUN
ejpam-5003	164	36	i	i	PRON
ejpam-5003	164	37	but	but	CCONJ
ejpam-5003	164	38	2	2	NUM
ejpam-5003	164	39	/∈	/∈	NOUN
ejpam-5003	164	40	i.	i.	NOUN
ejpam-5003	164	41	theorem	theorem	VERB
ejpam-5003	164	42	6	6	NUM
ejpam-5003	164	43	.	.	PUNCT
ejpam-5003	165	1	if	if	SCONJ
ejpam-5003	165	2	h	h	NOUN
ejpam-5003	165	3	is	be	AUX
ejpam-5003	165	4	a	a	DET
ejpam-5003	165	5	hyper	hyper	ADJ
ejpam-5003	165	6	bn	bn	ADJ
ejpam-5003	165	7	-algebra	-algebra	NOUN
ejpam-5003	165	8	,	,	PUNCT
ejpam-5003	165	9	then	then	ADV
ejpam-5003	165	10	{	{	PUNCT
ejpam-5003	165	11	0	0	NUM
ejpam-5003	165	12	}	}	PUNCT
ejpam-5003	165	13	is	be	AUX
ejpam-5003	165	14	a	a	DET
ejpam-5003	165	15	strong	strong	ADJ
ejpam-5003	165	16	hyper	hyper	NOUN
ejpam-5003	165	17	bn	bn	NOUN
ejpam-5003	165	18	-ideal	-ideal	NOUN
ejpam-5003	165	19	.	.	PUNCT
ejpam-5003	166	1	moreover	moreover	ADV
ejpam-5003	166	2	,	,	PUNCT
ejpam-5003	166	3	it	it	PRON
ejpam-5003	166	4	is	be	AUX
ejpam-5003	166	5	a	a	DET
ejpam-5003	166	6	hyper	hyper	ADJ
ejpam-5003	166	7	bn	bn	ADP
ejpam-5003	166	8	-ideal	-ideal	NOUN
ejpam-5003	166	9	and	and	CCONJ
ejpam-5003	166	10	a	a	DET
ejpam-5003	166	11	weak	weak	ADJ
ejpam-5003	166	12	hyper	hyper	NOUN
ejpam-5003	166	13	bn	bn	NOUN
ejpam-5003	166	14	-ideal	-ideal	NOUN
ejpam-5003	166	15	.	.	PUNCT
ejpam-5003	167	1	proof	proof	NOUN
ejpam-5003	167	2	.	.	PUNCT
ejpam-5003	168	1	let	let	VERB
ejpam-5003	168	2	x	x	PRON
ejpam-5003	168	3	,	,	PUNCT
ejpam-5003	168	4	y	y	PROPN
ejpam-5003	168	5	∈	∈	PROPN
ejpam-5003	168	6	h	h	NOUN
ejpam-5003	168	7	and	and	CCONJ
ejpam-5003	168	8	suppose	suppose	VERB
ejpam-5003	168	9	that	that	SCONJ
ejpam-5003	168	10	(	(	PUNCT
ejpam-5003	168	11	x⊛	x⊛	PROPN
ejpam-5003	168	12	y)∩	y)∩	PROPN
ejpam-5003	168	13	{	{	PUNCT
ejpam-5003	168	14	0	0	NUM
ejpam-5003	168	15	}	}	PUNCT
ejpam-5003	168	16	=	=	NOUN
ejpam-5003	168	17	̸	̸	ADJ
ejpam-5003	168	18	∅	∅	NOUN
ejpam-5003	168	19	and	and	CCONJ
ejpam-5003	168	20	y	y	PROPN
ejpam-5003	168	21	∈	∈	PROPN
ejpam-5003	168	22	{	{	PUNCT
ejpam-5003	168	23	0	0	NUM
ejpam-5003	168	24	}	}	PUNCT
ejpam-5003	168	25	.	.	PUNCT
ejpam-5003	169	1	then	then	ADV
ejpam-5003	169	2	y	y	PROPN
ejpam-5003	169	3	=	=	PUNCT
ejpam-5003	169	4	0	0	PROPN
ejpam-5003	170	1	and	and	CCONJ
ejpam-5003	170	2	(	(	PUNCT
ejpam-5003	170	3	x⊛	x⊛	NOUN
ejpam-5003	170	4	0	0	NUM
ejpam-5003	170	5	)	)	PUNCT
ejpam-5003	170	6	∩	∩	NOUN
ejpam-5003	170	7	{	{	PUNCT
ejpam-5003	170	8	0	0	NUM
ejpam-5003	170	9	}	}	PUNCT
ejpam-5003	170	10	=	=	NOUN
ejpam-5003	170	11	̸	̸	X
ejpam-5003	170	12	∅.	∅.	ADP
ejpam-5003	170	13	this	this	PRON
ejpam-5003	170	14	implies	imply	VERB
ejpam-5003	170	15	that	that	SCONJ
ejpam-5003	170	16	0	0	NUM
ejpam-5003	170	17	∈	∈	ADJ
ejpam-5003	170	18	x⊛	x⊛	NOUN
ejpam-5003	170	19	0	0	NUM
ejpam-5003	170	20	,	,	PUNCT
ejpam-5003	170	21	that	that	ADV
ejpam-5003	170	22	is	is	ADV
ejpam-5003	170	23	,	,	PUNCT
ejpam-5003	170	24	x	x	SYM
ejpam-5003	170	25	≪	≪	ADJ
ejpam-5003	170	26	0	0	X
ejpam-5003	170	27	.	.	PUNCT
ejpam-5003	170	28	by	by	ADP
ejpam-5003	170	29	theorem	theorem	NOUN
ejpam-5003	170	30	1(ii	1(ii	NUM
ejpam-5003	170	31	)	)	PUNCT
ejpam-5003	170	32	,	,	PUNCT
ejpam-5003	170	33	x	x	PUNCT
ejpam-5003	170	34	=	=	SYM
ejpam-5003	170	35	0	0	NUM
ejpam-5003	170	36	and	and	CCONJ
ejpam-5003	170	37	so	so	ADV
ejpam-5003	170	38	x	x	SYM
ejpam-5003	170	39	∈	∈	NOUN
ejpam-5003	170	40	{	{	PUNCT
ejpam-5003	170	41	0	0	NUM
ejpam-5003	170	42	}	}	PUNCT
ejpam-5003	170	43	.	.	PUNCT
ejpam-5003	171	1	thus	thus	ADV
ejpam-5003	171	2	,	,	PUNCT
ejpam-5003	171	3	{	{	PUNCT
ejpam-5003	171	4	0	0	X
ejpam-5003	171	5	}	}	PUNCT
ejpam-5003	171	6	is	be	AUX
ejpam-5003	171	7	a	a	DET
ejpam-5003	171	8	strong	strong	ADJ
ejpam-5003	171	9	hyper	hyper	NOUN
ejpam-5003	171	10	bn	bn	NOUN
ejpam-5003	171	11	-ideal	-ideal	NOUN
ejpam-5003	171	12	of	of	ADP
ejpam-5003	171	13	h.	h.	NOUN
ejpam-5003	171	14	by	by	ADP
ejpam-5003	171	15	propositions	proposition	NOUN
ejpam-5003	171	16	1(ii	1(ii	NUM
ejpam-5003	171	17	)	)	PUNCT
ejpam-5003	171	18	and	and	CCONJ
ejpam-5003	171	19	(	(	PUNCT
ejpam-5003	171	20	i	i	NOUN
ejpam-5003	171	21	)	)	PUNCT
ejpam-5003	171	22	,	,	PUNCT
ejpam-5003	171	23	{	{	PUNCT
ejpam-5003	171	24	0	0	X
ejpam-5003	171	25	}	}	PUNCT
ejpam-5003	171	26	is	be	AUX
ejpam-5003	171	27	also	also	ADV
ejpam-5003	171	28	a	a	DET
ejpam-5003	171	29	hyper	hyper	ADJ
ejpam-5003	171	30	bn	bn	ADP
ejpam-5003	171	31	-ideal	-ideal	NOUN
ejpam-5003	171	32	and	and	CCONJ
ejpam-5003	171	33	a	a	DET
ejpam-5003	171	34	weak	weak	ADJ
ejpam-5003	171	35	hyper	hyper	ADJ
ejpam-5003	171	36	bn	bn	ADJ
ejpam-5003	171	37	-ideal	-ideal	NOUN
ejpam-5003	171	38	of	of	ADP
ejpam-5003	171	39	h.	h.	PROPN
ejpam-5003	171	40	l.r	l.r	PROPN
ejpam-5003	171	41	.	.	PROPN
ejpam-5003	171	42	cabardo	cabardo	PROPN
ejpam-5003	171	43	,	,	PUNCT
ejpam-5003	171	44	g.	g.	PROPN
ejpam-5003	171	45	petalcorin	petalcorin	PROPN
ejpam-5003	171	46	/	/	SYM
ejpam-5003	171	47	eur	eur	PROPN
ejpam-5003	171	48	.	.	PUNCT
ejpam-5003	172	1	j.	j.	PROPN
ejpam-5003	172	2	pure	pure	PROPN
ejpam-5003	172	3	appl	appl	PROPN
ejpam-5003	172	4	.	.	PROPN
ejpam-5003	172	5	math	math	PROPN
ejpam-5003	172	6	,	,	PUNCT
ejpam-5003	172	7	17	17	NUM
ejpam-5003	172	8	(	(	PUNCT
ejpam-5003	172	9	1	1	NUM
ejpam-5003	172	10	)	)	PUNCT
ejpam-5003	172	11	(	(	PUNCT
ejpam-5003	172	12	2024	2024	NUM
ejpam-5003	172	13	)	)	PUNCT
ejpam-5003	172	14	,	,	PUNCT
ejpam-5003	172	15	222	222	NUM
ejpam-5003	172	16	-	-	SYM
ejpam-5003	172	17	242	242	NUM
ejpam-5003	172	18	229	229	NUM
ejpam-5003	172	19	lemma	lemma	PROPN
ejpam-5003	172	20	1	1	NUM
ejpam-5003	172	21	.	.	PUNCT
ejpam-5003	173	1	let	let	VERB
ejpam-5003	173	2	a	a	DET
ejpam-5003	173	3	,	,	PUNCT
ejpam-5003	173	4	b	b	NOUN
ejpam-5003	173	5	,	,	PUNCT
ejpam-5003	173	6	and	and	CCONJ
ejpam-5003	173	7	c	c	PROPN
ejpam-5003	173	8	be	be	AUX
ejpam-5003	173	9	nonempty	nonempty	X
ejpam-5003	173	10	subsets	subset	NOUN
ejpam-5003	173	11	of	of	ADP
ejpam-5003	173	12	a	a	DET
ejpam-5003	173	13	hyper	hyper	ADJ
ejpam-5003	173	14	bn	bn	NOUN
ejpam-5003	173	15	-algebra	-algebra	NOUN
ejpam-5003	173	16	.	.	PUNCT
ejpam-5003	174	1	if	if	SCONJ
ejpam-5003	174	2	a	a	DET
ejpam-5003	174	3	≪	≪	ADJ
ejpam-5003	174	4	b	b	NOUN
ejpam-5003	174	5	and	and	CCONJ
ejpam-5003	174	6	b	b	NOUN
ejpam-5003	174	7	⊆	⊆	NUM
ejpam-5003	174	8	c	c	NOUN
ejpam-5003	174	9	,	,	PUNCT
ejpam-5003	174	10	then	then	ADV
ejpam-5003	174	11	a	a	DET
ejpam-5003	174	12	≪	≪	ADJ
ejpam-5003	174	13	c.	c.	NOUN
ejpam-5003	174	14	proof	proof	NOUN
ejpam-5003	174	15	.	.	PUNCT
ejpam-5003	175	1	let	let	VERB
ejpam-5003	175	2	a	a	DET
ejpam-5003	175	3	∈	∈	NOUN
ejpam-5003	175	4	a.	a.	NOUN
ejpam-5003	175	5	since	since	SCONJ
ejpam-5003	175	6	a	a	DET
ejpam-5003	175	7	≪	≪	ADJ
ejpam-5003	175	8	b	b	NOUN
ejpam-5003	175	9	,	,	PUNCT
ejpam-5003	175	10	there	there	PRON
ejpam-5003	175	11	exists	exist	VERB
ejpam-5003	175	12	b	b	PROPN
ejpam-5003	175	13	∈	∈	PROPN
ejpam-5003	175	14	b	b	NOUN
ejpam-5003	175	15	such	such	ADJ
ejpam-5003	175	16	that	that	SCONJ
ejpam-5003	175	17	a	a	DET
ejpam-5003	175	18	≪	≪	ADJ
ejpam-5003	175	19	b.	b.	NOUN
ejpam-5003	175	20	since	since	SCONJ
ejpam-5003	175	21	b	b	PROPN
ejpam-5003	175	22	⊆	⊆	NUM
ejpam-5003	175	23	c	c	NOUN
ejpam-5003	175	24	,	,	PUNCT
ejpam-5003	175	25	b	b	X
ejpam-5003	175	26	∈	∈	PROPN
ejpam-5003	175	27	c	c	NOUN
ejpam-5003	175	28	with	with	ADP
ejpam-5003	175	29	a	a	DET
ejpam-5003	175	30	≪	≪	ADJ
ejpam-5003	175	31	b.	b.	NOUN
ejpam-5003	175	32	therefore	therefore	ADV
ejpam-5003	175	33	,	,	PUNCT
ejpam-5003	175	34	a	a	DET
ejpam-5003	175	35	≪	≪	ADJ
ejpam-5003	175	36	c.	c.	NOUN
ejpam-5003	175	37	theorem	theorem	VERB
ejpam-5003	175	38	7	7	NUM
ejpam-5003	175	39	.	.	PUNCT
ejpam-5003	176	1	let	let	VERB
ejpam-5003	176	2	{	{	PUNCT
ejpam-5003	176	3	ai	ai	VERB
ejpam-5003	176	4	:	:	PUNCT
ejpam-5003	176	5	i	i	PRON
ejpam-5003	176	6	∈	∈	PROPN
ejpam-5003	177	1	i	i	PRON
ejpam-5003	177	2	}	}	PUNCT
ejpam-5003	177	3	be	be	AUX
ejpam-5003	177	4	a	a	DET
ejpam-5003	177	5	nonempty	nonempty	ADJ
ejpam-5003	177	6	collection	collection	NOUN
ejpam-5003	177	7	of	of	ADP
ejpam-5003	177	8	subsets	subset	NOUN
ejpam-5003	177	9	of	of	ADP
ejpam-5003	177	10	a	a	DET
ejpam-5003	177	11	hyper	hyper	ADJ
ejpam-5003	177	12	bn	bn	NOUN
ejpam-5003	177	13	-algebra	-algebra	PROPN
ejpam-5003	177	14	h.	h.	PROPN
ejpam-5003	177	15	(	(	PUNCT
ejpam-5003	177	16	i	i	NOUN
ejpam-5003	177	17	)	)	PUNCT
ejpam-5003	177	18	if	if	SCONJ
ejpam-5003	177	19	ai	ai	ADV
ejpam-5003	177	20	is	be	AUX
ejpam-5003	177	21	a	a	DET
ejpam-5003	177	22	hyper	hyper	ADJ
ejpam-5003	177	23	bn	bn	ADP
ejpam-5003	177	24	-ideal	-ideal	NOUN
ejpam-5003	177	25	of	of	ADP
ejpam-5003	177	26	h	h	NOUN
ejpam-5003	177	27	for	for	ADP
ejpam-5003	177	28	all	all	PRON
ejpam-5003	177	29	i	i	PRON
ejpam-5003	177	30	∈	∈	PROPN
ejpam-5003	178	1	i	i	PRON
ejpam-5003	178	2	,	,	PUNCT
ejpam-5003	178	3	then	then	ADV
ejpam-5003	178	4	so	so	ADV
ejpam-5003	178	5	is	be	AUX
ejpam-5003	178	6	⋂	⋂	PROPN
ejpam-5003	178	7	i∈i	i∈i	ADJ
ejpam-5003	178	8	ai	ai	NOUN
ejpam-5003	178	9	.	.	PUNCT
ejpam-5003	179	1	(	(	PUNCT
ejpam-5003	179	2	ii	ii	NOUN
ejpam-5003	179	3	)	)	PUNCT
ejpam-5003	179	4	if	if	SCONJ
ejpam-5003	179	5	ai	ai	ADV
ejpam-5003	179	6	is	be	AUX
ejpam-5003	179	7	a	a	DET
ejpam-5003	179	8	weak	weak	ADJ
ejpam-5003	179	9	hyper	hyper	NOUN
ejpam-5003	179	10	bn	bn	ADJ
ejpam-5003	179	11	-ideal	-ideal	NOUN
ejpam-5003	179	12	of	of	ADP
ejpam-5003	179	13	h	h	NOUN
ejpam-5003	179	14	for	for	ADP
ejpam-5003	179	15	all	all	PRON
ejpam-5003	179	16	i	i	PRON
ejpam-5003	179	17	∈	∈	PROPN
ejpam-5003	180	1	i	i	PRON
ejpam-5003	180	2	,	,	PUNCT
ejpam-5003	180	3	then	then	ADV
ejpam-5003	180	4	so	so	ADV
ejpam-5003	180	5	is	be	AUX
ejpam-5003	180	6	⋂	⋂	PROPN
ejpam-5003	180	7	i∈i	i∈i	ADJ
ejpam-5003	180	8	ai	ai	VERB
ejpam-5003	180	9	.	.	PUNCT
ejpam-5003	181	1	(	(	PUNCT
ejpam-5003	181	2	iii	iii	X
ejpam-5003	181	3	)	)	PUNCT
ejpam-5003	181	4	if	if	SCONJ
ejpam-5003	181	5	ai	ai	NOUN
ejpam-5003	181	6	is	be	AUX
ejpam-5003	181	7	a	a	DET
ejpam-5003	181	8	strong	strong	ADJ
ejpam-5003	181	9	hyper	hyper	NOUN
ejpam-5003	181	10	bn	bn	NOUN
ejpam-5003	181	11	-ideal	-ideal	NOUN
ejpam-5003	181	12	of	of	ADP
ejpam-5003	181	13	h	h	NOUN
ejpam-5003	181	14	for	for	ADP
ejpam-5003	181	15	all	all	PRON
ejpam-5003	181	16	i	i	PRON
ejpam-5003	181	17	∈	∈	PROPN
ejpam-5003	182	1	i	i	PRON
ejpam-5003	182	2	,	,	PUNCT
ejpam-5003	182	3	then	then	ADV
ejpam-5003	182	4	so	so	ADV
ejpam-5003	182	5	is	be	AUX
ejpam-5003	182	6	⋂	⋂	PROPN
ejpam-5003	182	7	i∈i	i∈i	ADJ
ejpam-5003	182	8	ai	ai	PROPN
ejpam-5003	182	9	.	.	PUNCT
ejpam-5003	183	1	proof	proof	NOUN
ejpam-5003	183	2	.	.	PUNCT
ejpam-5003	184	1	let	let	VERB
ejpam-5003	184	2	{	{	PUNCT
ejpam-5003	184	3	ai	ai	VERB
ejpam-5003	184	4	:	:	PUNCT
ejpam-5003	184	5	i	i	PRON
ejpam-5003	184	6	∈	∈	PROPN
ejpam-5003	184	7	i	i	PRON
ejpam-5003	184	8	}	}	PUNCT
ejpam-5003	184	9	be	be	AUX
ejpam-5003	184	10	a	a	DET
ejpam-5003	184	11	nonempty	nonempty	ADJ
ejpam-5003	184	12	collection	collection	NOUN
ejpam-5003	184	13	of	of	ADP
ejpam-5003	184	14	subsets	subset	NOUN
ejpam-5003	184	15	of	of	ADP
ejpam-5003	184	16	a	a	DET
ejpam-5003	184	17	hyper	hyper	ADJ
ejpam-5003	184	18	bn	bn	NOUN
ejpam-5003	184	19	-algebra	-algebra	PROPN
ejpam-5003	184	20	h.	h.	PROPN
ejpam-5003	184	21	(	(	PUNCT
ejpam-5003	184	22	i	i	NOUN
ejpam-5003	184	23	)	)	PUNCT
ejpam-5003	184	24	suppose	suppose	VERB
ejpam-5003	184	25	that	that	SCONJ
ejpam-5003	184	26	ai	ai	VERB
ejpam-5003	184	27	is	be	AUX
ejpam-5003	184	28	a	a	DET
ejpam-5003	184	29	hyper	hyper	ADJ
ejpam-5003	184	30	bn	bn	ADP
ejpam-5003	184	31	-ideal	-ideal	NOUN
ejpam-5003	184	32	of	of	ADP
ejpam-5003	184	33	h	h	NOUN
ejpam-5003	184	34	for	for	ADP
ejpam-5003	184	35	all	all	DET
ejpam-5003	184	36	i	i	PRON
ejpam-5003	184	37	∈	∈	PROPN
ejpam-5003	184	38	i.	i.	NOUN
ejpam-5003	184	39	thus	thus	ADV
ejpam-5003	184	40	,	,	PUNCT
ejpam-5003	184	41	0	0	NUM
ejpam-5003	184	42	∈	∈	NOUN
ejpam-5003	184	43	ai	ai	VERB
ejpam-5003	184	44	for	for	ADP
ejpam-5003	184	45	all	all	PRON
ejpam-5003	184	46	i	i	PRON
ejpam-5003	184	47	∈	∈	PROPN
ejpam-5003	184	48	i.	i.	NOUN
ejpam-5003	184	49	and	and	CCONJ
ejpam-5003	184	50	so	so	ADV
ejpam-5003	184	51	,	,	PUNCT
ejpam-5003	184	52	0	0	NUM
ejpam-5003	184	53	∈	∈	PROPN
ejpam-5003	184	54	⋂	⋂	PROPN
ejpam-5003	184	55	i∈i	i∈i	ADJ
ejpam-5003	184	56	ai	ai	PROPN
ejpam-5003	184	57	.	.	PUNCT
ejpam-5003	185	1	assume	assume	VERB
ejpam-5003	185	2	x	x	X
ejpam-5003	185	3	,	,	PUNCT
ejpam-5003	185	4	y	y	PROPN
ejpam-5003	185	5	∈	∈	PROPN
ejpam-5003	185	6	h	h	NOUN
ejpam-5003	185	7	such	such	ADJ
ejpam-5003	185	8	that	that	SCONJ
ejpam-5003	185	9	x⊛	x⊛	PROPN
ejpam-5003	186	1	y	y	PROPN
ejpam-5003	186	2	≪	≪	VERB
ejpam-5003	186	3	⋂	⋂	PROPN
ejpam-5003	186	4	i∈i	i∈i	ADJ
ejpam-5003	186	5	ai	ai	VERB
ejpam-5003	186	6	and	and	CCONJ
ejpam-5003	186	7	y	y	PROPN
ejpam-5003	186	8	∈	∈	PROPN
ejpam-5003	186	9	⋂	⋂	PROPN
ejpam-5003	186	10	i∈i	i∈i	ADJ
ejpam-5003	186	11	ai	ai	VERB
ejpam-5003	186	12	.	.	PUNCT
ejpam-5003	187	1	since⋂	since⋂	PROPN
ejpam-5003	187	2	i∈i	i∈i	NOUN
ejpam-5003	187	3	ai	ai	VERB
ejpam-5003	187	4	⊆	⊆	NUM
ejpam-5003	187	5	ai	ai	NOUN
ejpam-5003	187	6	for	for	ADP
ejpam-5003	187	7	all	all	PRON
ejpam-5003	187	8	i	i	PRON
ejpam-5003	187	9	∈	∈	PROPN
ejpam-5003	188	1	i	i	PRON
ejpam-5003	188	2	,	,	PUNCT
ejpam-5003	188	3	it	it	PRON
ejpam-5003	188	4	follows	follow	VERB
ejpam-5003	188	5	from	from	ADP
ejpam-5003	188	6	lemma	lemma	PROPN
ejpam-5003	188	7	1	1	NUM
ejpam-5003	188	8	that	that	PRON
ejpam-5003	188	9	x⊛y	x⊛y	PROPN
ejpam-5003	188	10	≪	≪	AUX
ejpam-5003	188	11	ai	ai	VERB
ejpam-5003	188	12	for	for	ADP
ejpam-5003	188	13	all	all	PRON
ejpam-5003	188	14	i	i	PRON
ejpam-5003	188	15	∈	∈	PROPN
ejpam-5003	188	16	i.	i.	NOUN
ejpam-5003	188	17	also	also	ADV
ejpam-5003	188	18	,	,	PUNCT
ejpam-5003	188	19	y	y	PROPN
ejpam-5003	188	20	∈	∈	PROPN
ejpam-5003	188	21	ai	ai	VERB
ejpam-5003	188	22	for	for	ADP
ejpam-5003	188	23	all	all	PRON
ejpam-5003	188	24	i	i	PRON
ejpam-5003	188	25	∈	∈	PROPN
ejpam-5003	188	26	i.	i.	NOUN
ejpam-5003	188	27	since	since	SCONJ
ejpam-5003	188	28	ai	ai	PROPN
ejpam-5003	188	29	is	be	AUX
ejpam-5003	188	30	a	a	DET
ejpam-5003	188	31	hyper	hyper	ADJ
ejpam-5003	189	1	bn	bn	ADP
ejpam-5003	189	2	-ideal	-ideal	NOUN
ejpam-5003	189	3	of	of	ADP
ejpam-5003	189	4	h	h	NOUN
ejpam-5003	189	5	for	for	ADP
ejpam-5003	189	6	all	all	PRON
ejpam-5003	189	7	i	i	PRON
ejpam-5003	189	8	∈	∈	PROPN
ejpam-5003	190	1	i	i	PRON
ejpam-5003	190	2	,	,	PUNCT
ejpam-5003	190	3	we	we	PRON
ejpam-5003	190	4	have	have	VERB
ejpam-5003	190	5	x	x	PART
ejpam-5003	190	6	∈	∈	PROPN
ejpam-5003	190	7	ai	ai	VERB
ejpam-5003	190	8	for	for	ADP
ejpam-5003	190	9	all	all	PRON
ejpam-5003	190	10	i	i	PRON
ejpam-5003	190	11	∈	∈	PROPN
ejpam-5003	190	12	i.	i.	NOUN
ejpam-5003	190	13	therefore	therefore	ADV
ejpam-5003	190	14	,	,	PUNCT
ejpam-5003	190	15	x	x	PROPN
ejpam-5003	190	16	∈	∈	PROPN
ejpam-5003	190	17	⋂	⋂	PROPN
ejpam-5003	190	18	i∈i	i∈i	ADJ
ejpam-5003	190	19	ai	ai	VERB
ejpam-5003	190	20	,	,	PUNCT
ejpam-5003	190	21	and	and	CCONJ
ejpam-5003	190	22	so	so	ADV
ejpam-5003	190	23	⋂	⋂	PROPN
ejpam-5003	190	24	i∈i	i∈i	NOUN
ejpam-5003	190	25	ai	ai	VERB
ejpam-5003	190	26	is	be	AUX
ejpam-5003	190	27	a	a	DET
ejpam-5003	190	28	hyper	hyper	ADJ
ejpam-5003	190	29	bn	bn	ADP
ejpam-5003	190	30	-ideal	-ideal	NOUN
ejpam-5003	190	31	of	of	ADP
ejpam-5003	190	32	h.	h.	PROPN
ejpam-5003	190	33	(	(	PUNCT
ejpam-5003	190	34	ii	ii	PROPN
ejpam-5003	190	35	)	)	PUNCT
ejpam-5003	190	36	suppose	suppose	VERB
ejpam-5003	190	37	that	that	SCONJ
ejpam-5003	190	38	ai	ai	VERB
ejpam-5003	190	39	is	be	AUX
ejpam-5003	190	40	a	a	DET
ejpam-5003	190	41	weak	weak	ADJ
ejpam-5003	190	42	hyper	hyper	NOUN
ejpam-5003	190	43	bn	bn	ADJ
ejpam-5003	190	44	-ideal	-ideal	NOUN
ejpam-5003	190	45	of	of	ADP
ejpam-5003	190	46	h	h	NOUN
ejpam-5003	190	47	for	for	ADP
ejpam-5003	190	48	all	all	DET
ejpam-5003	190	49	i	i	PRON
ejpam-5003	190	50	∈	∈	PROPN
ejpam-5003	190	51	i.	i.	NOUN
ejpam-5003	190	52	thus	thus	ADV
ejpam-5003	190	53	,	,	PUNCT
ejpam-5003	190	54	0	0	NUM
ejpam-5003	190	55	∈	∈	NOUN
ejpam-5003	190	56	ai	ai	VERB
ejpam-5003	190	57	for	for	ADP
ejpam-5003	190	58	all	all	PRON
ejpam-5003	190	59	i	i	PRON
ejpam-5003	190	60	∈	∈	PROPN
ejpam-5003	190	61	i.	i.	NOUN
ejpam-5003	190	62	and	and	CCONJ
ejpam-5003	190	63	so	so	ADV
ejpam-5003	190	64	,	,	PUNCT
ejpam-5003	190	65	0	0	NUM
ejpam-5003	190	66	∈	∈	PROPN
ejpam-5003	190	67	⋂	⋂	PROPN
ejpam-5003	190	68	i∈i	i∈i	ADJ
ejpam-5003	190	69	ai	ai	PROPN
ejpam-5003	190	70	.	.	PUNCT
ejpam-5003	191	1	assume	assume	VERB
ejpam-5003	191	2	x	x	X
ejpam-5003	191	3	,	,	PUNCT
ejpam-5003	191	4	y	y	PROPN
ejpam-5003	191	5	∈	∈	PROPN
ejpam-5003	191	6	h	h	NOUN
ejpam-5003	191	7	such	such	ADJ
ejpam-5003	191	8	that	that	SCONJ
ejpam-5003	191	9	x⊛	x⊛	PROPN
ejpam-5003	192	1	y	y	PROPN
ejpam-5003	192	2	⊆	⊆	NUM
ejpam-5003	192	3	⋂	⋂	PROPN
ejpam-5003	192	4	i∈i	i∈i	ADJ
ejpam-5003	192	5	ai	ai	VERB
ejpam-5003	192	6	and	and	CCONJ
ejpam-5003	192	7	y	y	PROPN
ejpam-5003	192	8	∈	∈	PROPN
ejpam-5003	192	9	⋂	⋂	PROPN
ejpam-5003	192	10	i∈i	i∈i	ADJ
ejpam-5003	192	11	ai	ai	VERB
ejpam-5003	192	12	.	.	PUNCT
ejpam-5003	193	1	since	since	SCONJ
ejpam-5003	193	2	⋂	⋂	PROPN
ejpam-5003	193	3	i∈i	i∈i	ADJ
ejpam-5003	193	4	ai	ai	VERB
ejpam-5003	193	5	⊆	⊆	NUM
ejpam-5003	193	6	ai	ai	NOUN
ejpam-5003	193	7	for	for	ADP
ejpam-5003	193	8	all	all	PRON
ejpam-5003	193	9	i	i	PRON
ejpam-5003	193	10	∈	∈	PROPN
ejpam-5003	194	1	i	i	PRON
ejpam-5003	194	2	,	,	PUNCT
ejpam-5003	194	3	it	it	PRON
ejpam-5003	194	4	follows	follow	VERB
ejpam-5003	194	5	that	that	PRON
ejpam-5003	194	6	x⊛	x⊛	PROPN
ejpam-5003	194	7	y	y	PROPN
ejpam-5003	194	8	⊆	⊆	NUM
ejpam-5003	194	9	ai	ai	VERB
ejpam-5003	194	10	for	for	ADP
ejpam-5003	194	11	all	all	DET
ejpam-5003	194	12	i	i	PRON
ejpam-5003	194	13	∈	∈	PROPN
ejpam-5003	194	14	i.	i.	NOUN
ejpam-5003	194	15	also	also	ADV
ejpam-5003	194	16	,	,	PUNCT
ejpam-5003	194	17	y	y	PROPN
ejpam-5003	194	18	∈	∈	PROPN
ejpam-5003	194	19	ai	ai	VERB
ejpam-5003	194	20	for	for	ADP
ejpam-5003	194	21	all	all	PRON
ejpam-5003	194	22	i	i	PRON
ejpam-5003	194	23	∈	∈	PROPN
ejpam-5003	194	24	i.	i.	NOUN
ejpam-5003	194	25	since	since	SCONJ
ejpam-5003	194	26	ai	ai	VERB
ejpam-5003	194	27	is	be	AUX
ejpam-5003	194	28	a	a	DET
ejpam-5003	194	29	weak	weak	ADJ
ejpam-5003	194	30	hyper	hyper	NOUN
ejpam-5003	194	31	bn	bn	ADJ
ejpam-5003	194	32	-ideal	-ideal	NOUN
ejpam-5003	194	33	of	of	ADP
ejpam-5003	194	34	h	h	NOUN
ejpam-5003	194	35	for	for	ADP
ejpam-5003	194	36	all	all	PRON
ejpam-5003	194	37	i	i	PRON
ejpam-5003	194	38	∈	∈	PROPN
ejpam-5003	195	1	i	i	PRON
ejpam-5003	195	2	,	,	PUNCT
ejpam-5003	195	3	we	we	PRON
ejpam-5003	195	4	have	have	VERB
ejpam-5003	195	5	x	x	PART
ejpam-5003	195	6	∈	∈	PROPN
ejpam-5003	195	7	ai	ai	VERB
ejpam-5003	195	8	for	for	ADP
ejpam-5003	195	9	all	all	PRON
ejpam-5003	195	10	i	i	PRON
ejpam-5003	195	11	∈	∈	PROPN
ejpam-5003	195	12	i.	i.	NOUN
ejpam-5003	195	13	therefore	therefore	ADV
ejpam-5003	195	14	,	,	PUNCT
ejpam-5003	195	15	x	x	PROPN
ejpam-5003	195	16	∈	∈	PROPN
ejpam-5003	195	17	⋂	⋂	PROPN
ejpam-5003	195	18	i∈i	i∈i	ADJ
ejpam-5003	195	19	ai	ai	VERB
ejpam-5003	195	20	,	,	PUNCT
ejpam-5003	195	21	and	and	CCONJ
ejpam-5003	195	22	so	so	ADV
ejpam-5003	195	23	⋂	⋂	PROPN
ejpam-5003	195	24	i∈i	i∈i	NOUN
ejpam-5003	195	25	ai	ai	VERB
ejpam-5003	195	26	is	be	AUX
ejpam-5003	195	27	a	a	DET
ejpam-5003	195	28	weak	weak	ADJ
ejpam-5003	195	29	hyper	hyper	NOUN
ejpam-5003	195	30	bn	bn	ADJ
ejpam-5003	195	31	-ideal	-ideal	NOUN
ejpam-5003	195	32	of	of	ADP
ejpam-5003	195	33	h.	h.	PROPN
ejpam-5003	195	34	(	(	PUNCT
ejpam-5003	195	35	iii	iii	NOUN
ejpam-5003	195	36	)	)	PUNCT
ejpam-5003	195	37	suppose	suppose	VERB
ejpam-5003	195	38	that	that	SCONJ
ejpam-5003	195	39	ai	ai	VERB
ejpam-5003	195	40	is	be	AUX
ejpam-5003	195	41	a	a	DET
ejpam-5003	195	42	strong	strong	ADJ
ejpam-5003	195	43	hyper	hyper	NOUN
ejpam-5003	195	44	bn	bn	NOUN
ejpam-5003	195	45	-ideal	-ideal	NOUN
ejpam-5003	195	46	of	of	ADP
ejpam-5003	195	47	h	h	NOUN
ejpam-5003	195	48	for	for	ADP
ejpam-5003	195	49	all	all	DET
ejpam-5003	195	50	i	i	PRON
ejpam-5003	195	51	∈	∈	PROPN
ejpam-5003	195	52	i.	i.	NOUN
ejpam-5003	195	53	thus	thus	ADV
ejpam-5003	195	54	,	,	PUNCT
ejpam-5003	195	55	0	0	NUM
ejpam-5003	195	56	∈	∈	NOUN
ejpam-5003	195	57	ai	ai	VERB
ejpam-5003	195	58	for	for	ADP
ejpam-5003	195	59	all	all	PRON
ejpam-5003	195	60	i	i	PRON
ejpam-5003	195	61	∈	∈	PROPN
ejpam-5003	195	62	i.	i.	NOUN
ejpam-5003	195	63	and	and	CCONJ
ejpam-5003	195	64	so	so	ADV
ejpam-5003	195	65	,	,	PUNCT
ejpam-5003	195	66	0	0	NUM
ejpam-5003	195	67	∈	∈	PROPN
ejpam-5003	195	68	⋂	⋂	PROPN
ejpam-5003	195	69	i∈i	i∈i	ADJ
ejpam-5003	195	70	ai	ai	PROPN
ejpam-5003	195	71	.	.	PUNCT
ejpam-5003	196	1	assume	assume	VERB
ejpam-5003	196	2	x	x	X
ejpam-5003	196	3	,	,	PUNCT
ejpam-5003	196	4	y	y	PROPN
ejpam-5003	196	5	∈	∈	PROPN
ejpam-5003	196	6	h	h	NOUN
ejpam-5003	196	7	such	such	ADJ
ejpam-5003	196	8	that	that	SCONJ
ejpam-5003	196	9	(	(	PUNCT
ejpam-5003	196	10	x	x	PROPN
ejpam-5003	196	11	⊛	⊛	NUM
ejpam-5003	196	12	y	y	NOUN
ejpam-5003	196	13	)	)	PUNCT
ejpam-5003	196	14	∩	∩	NOUN
ejpam-5003	196	15	(	(	PUNCT
ejpam-5003	196	16	⋂	⋂	PROPN
ejpam-5003	196	17	i∈i	i∈i	ADJ
ejpam-5003	196	18	ai	ai	VERB
ejpam-5003	196	19	)	)	PUNCT
ejpam-5003	196	20	̸=	̸=	PROPN
ejpam-5003	196	21	∅	∅	NOUN
ejpam-5003	196	22	and	and	CCONJ
ejpam-5003	196	23	y	y	PROPN
ejpam-5003	196	24	∈	∈	PROPN
ejpam-5003	196	25	⋂	⋂	PROPN
ejpam-5003	196	26	i∈i	i∈i	ADJ
ejpam-5003	196	27	ai	ai	VERB
ejpam-5003	196	28	.	.	PUNCT
ejpam-5003	197	1	since	since	SCONJ
ejpam-5003	197	2	⋂	⋂	PROPN
ejpam-5003	197	3	i∈i	i∈i	ADJ
ejpam-5003	197	4	ai	ai	VERB
ejpam-5003	197	5	⊆	⊆	NUM
ejpam-5003	197	6	ai	ai	NOUN
ejpam-5003	197	7	for	for	ADP
ejpam-5003	197	8	all	all	PRON
ejpam-5003	197	9	i	i	PRON
ejpam-5003	197	10	∈	∈	PROPN
ejpam-5003	198	1	i	i	PRON
ejpam-5003	198	2	,	,	PUNCT
ejpam-5003	198	3	it	it	PRON
ejpam-5003	198	4	follows	follow	VERB
ejpam-5003	198	5	that	that	SCONJ
ejpam-5003	198	6	(	(	PUNCT
ejpam-5003	198	7	x	x	PROPN
ejpam-5003	198	8	⊛	⊛	NUM
ejpam-5003	198	9	y	y	NUM
ejpam-5003	198	10	)	)	PUNCT
ejpam-5003	198	11	∩	∩	NOUN
ejpam-5003	198	12	ai	ai	VERB
ejpam-5003	198	13	̸=	̸=	PROPN
ejpam-5003	198	14	∅	∅	NOUN
ejpam-5003	198	15	for	for	ADP
ejpam-5003	198	16	all	all	PRON
ejpam-5003	198	17	i	i	PRON
ejpam-5003	198	18	∈	∈	PROPN
ejpam-5003	198	19	i.	i.	NOUN
ejpam-5003	198	20	also	also	ADV
ejpam-5003	198	21	,	,	PUNCT
ejpam-5003	198	22	y	y	PROPN
ejpam-5003	198	23	∈	∈	PROPN
ejpam-5003	198	24	ai	ai	VERB
ejpam-5003	198	25	for	for	ADP
ejpam-5003	198	26	all	all	PRON
ejpam-5003	198	27	i	i	PRON
ejpam-5003	198	28	∈	∈	PROPN
ejpam-5003	198	29	i.	i.	NOUN
ejpam-5003	198	30	since	since	SCONJ
ejpam-5003	198	31	ai	ai	NOUN
ejpam-5003	198	32	is	be	AUX
ejpam-5003	198	33	a	a	DET
ejpam-5003	198	34	strong	strong	ADJ
ejpam-5003	198	35	hyper	hyper	NOUN
ejpam-5003	198	36	bn	bn	NOUN
ejpam-5003	198	37	-ideal	-ideal	NOUN
ejpam-5003	198	38	of	of	ADP
ejpam-5003	198	39	h	h	NOUN
ejpam-5003	198	40	for	for	ADP
ejpam-5003	198	41	all	all	PRON
ejpam-5003	198	42	i	i	PRON
ejpam-5003	198	43	∈	∈	PROPN
ejpam-5003	199	1	i	i	PRON
ejpam-5003	199	2	,	,	PUNCT
ejpam-5003	199	3	we	we	PRON
ejpam-5003	199	4	have	have	VERB
ejpam-5003	199	5	x	x	PART
ejpam-5003	199	6	∈	∈	PROPN
ejpam-5003	199	7	ai	ai	VERB
ejpam-5003	199	8	for	for	ADP
ejpam-5003	199	9	all	all	PRON
ejpam-5003	199	10	i	i	PRON
ejpam-5003	199	11	∈	∈	PROPN
ejpam-5003	199	12	i.	i.	NOUN
ejpam-5003	199	13	therefore	therefore	ADV
ejpam-5003	199	14	,	,	PUNCT
ejpam-5003	199	15	x	x	PROPN
ejpam-5003	199	16	∈	∈	PROPN
ejpam-5003	199	17	⋂	⋂	PROPN
ejpam-5003	199	18	i∈i	i∈i	ADJ
ejpam-5003	199	19	ai	ai	VERB
ejpam-5003	199	20	,	,	PUNCT
ejpam-5003	199	21	and	and	CCONJ
ejpam-5003	199	22	so	so	ADV
ejpam-5003	199	23	⋂	⋂	PROPN
ejpam-5003	199	24	i∈i	i∈i	NOUN
ejpam-5003	199	25	ai	ai	VERB
ejpam-5003	199	26	is	be	AUX
ejpam-5003	199	27	a	a	DET
ejpam-5003	199	28	strong	strong	ADJ
ejpam-5003	199	29	hyper	hyper	NOUN
ejpam-5003	199	30	bn	bn	NOUN
ejpam-5003	199	31	-ideal	-ideal	NOUN
ejpam-5003	199	32	of	of	ADP
ejpam-5003	199	33	h.	h.	PROPN
ejpam-5003	199	34	l.r	l.r	PROPN
ejpam-5003	199	35	.	.	PROPN
ejpam-5003	199	36	cabardo	cabardo	PROPN
ejpam-5003	199	37	,	,	PUNCT
ejpam-5003	199	38	g.	g.	PROPN
ejpam-5003	199	39	petalcorin	petalcorin	PROPN
ejpam-5003	199	40	/	/	SYM
ejpam-5003	199	41	eur	eur	PROPN
ejpam-5003	199	42	.	.	PUNCT
ejpam-5003	200	1	j.	j.	PROPN
ejpam-5003	200	2	pure	pure	PROPN
ejpam-5003	200	3	appl	appl	PROPN
ejpam-5003	200	4	.	.	PROPN
ejpam-5003	200	5	math	math	PROPN
ejpam-5003	200	6	,	,	PUNCT
ejpam-5003	200	7	17	17	NUM
ejpam-5003	200	8	(	(	PUNCT
ejpam-5003	200	9	1	1	NUM
ejpam-5003	200	10	)	)	PUNCT
ejpam-5003	200	11	(	(	PUNCT
ejpam-5003	200	12	2024	2024	NUM
ejpam-5003	200	13	)	)	PUNCT
ejpam-5003	200	14	,	,	PUNCT
ejpam-5003	200	15	222	222	NUM
ejpam-5003	200	16	-	-	SYM
ejpam-5003	200	17	242	242	NUM
ejpam-5003	200	18	230	230	NUM
ejpam-5003	200	19	the	the	DET
ejpam-5003	200	20	following	follow	VERB
ejpam-5003	200	21	examples	example	NOUN
ejpam-5003	200	22	will	will	AUX
ejpam-5003	200	23	show	show	VERB
ejpam-5003	200	24	the	the	DET
ejpam-5003	200	25	relationship	relationship	NOUN
ejpam-5003	200	26	between	between	ADP
ejpam-5003	200	27	hyper	hyper	ADJ
ejpam-5003	200	28	subbn	subbn	NOUN
ejpam-5003	200	29	-algebras	-algebras	PROPN
ejpam-5003	200	30	and	and	CCONJ
ejpam-5003	200	31	hyper	hyper	ADJ
ejpam-5003	200	32	bn	bn	ADJ
ejpam-5003	200	33	-ideals	-ideal	NOUN
ejpam-5003	200	34	of	of	ADP
ejpam-5003	200	35	hyper	hyper	ADJ
ejpam-5003	200	36	bn	bn	ADJ
ejpam-5003	200	37	-algebras	-algebras	PROPN
ejpam-5003	200	38	.	.	PUNCT
ejpam-5003	200	39	example	example	NOUN
ejpam-5003	201	1	16	16	NUM
ejpam-5003	201	2	.	.	PUNCT
ejpam-5003	202	1	consider	consider	VERB
ejpam-5003	202	2	the	the	DET
ejpam-5003	202	3	set	set	NOUN
ejpam-5003	202	4	h	h	NOUN
ejpam-5003	202	5	=	=	SYM
ejpam-5003	202	6	{	{	PUNCT
ejpam-5003	202	7	0	0	NUM
ejpam-5003	202	8	,	,	PUNCT
ejpam-5003	202	9	1	1	NUM
ejpam-5003	202	10	,	,	PUNCT
ejpam-5003	202	11	2	2	NUM
ejpam-5003	202	12	,	,	PUNCT
ejpam-5003	202	13	3	3	NUM
ejpam-5003	202	14	}	}	PUNCT
ejpam-5003	202	15	with	with	ADP
ejpam-5003	202	16	hyperoperation	hyperoperation	NOUN
ejpam-5003	202	17	⊛	⊛	NUM
ejpam-5003	202	18	defined	define	VERB
ejpam-5003	202	19	by	by	ADP
ejpam-5003	202	20	the	the	DET
ejpam-5003	202	21	following	following	ADJ
ejpam-5003	202	22	cayley	cayley	ADJ
ejpam-5003	202	23	table	table	NOUN
ejpam-5003	202	24	:	:	PUNCT
ejpam-5003	203	1	⊛	⊛	NUM
ejpam-5003	203	2	0	0	NUM
ejpam-5003	203	3	1	1	NUM
ejpam-5003	203	4	2	2	NUM
ejpam-5003	203	5	3	3	NUM
ejpam-5003	203	6	0	0	NUM
ejpam-5003	203	7	{	{	PUNCT
ejpam-5003	203	8	0	0	NUM
ejpam-5003	203	9	}	}	PUNCT
ejpam-5003	203	10	{	{	PUNCT
ejpam-5003	203	11	1	1	NUM
ejpam-5003	203	12	}	}	PUNCT
ejpam-5003	203	13	{	{	PUNCT
ejpam-5003	203	14	2	2	NUM
ejpam-5003	203	15	}	}	PUNCT
ejpam-5003	203	16	{	{	PUNCT
ejpam-5003	203	17	3	3	NUM
ejpam-5003	203	18	}	}	SYM
ejpam-5003	203	19	1	1	NUM
ejpam-5003	203	20	{	{	PUNCT
ejpam-5003	203	21	1	1	NUM
ejpam-5003	203	22	}	}	PUNCT
ejpam-5003	203	23	{	{	PUNCT
ejpam-5003	203	24	0	0	NUM
ejpam-5003	203	25	}	}	PUNCT
ejpam-5003	203	26	{	{	PUNCT
ejpam-5003	203	27	1	1	NUM
ejpam-5003	203	28	}	}	PUNCT
ejpam-5003	203	29	{	{	PUNCT
ejpam-5003	203	30	1	1	NUM
ejpam-5003	203	31	,	,	PUNCT
ejpam-5003	203	32	3	3	NUM
ejpam-5003	203	33	}	}	SYM
ejpam-5003	203	34	2	2	NUM
ejpam-5003	203	35	{	{	PUNCT
ejpam-5003	203	36	2	2	NUM
ejpam-5003	203	37	}	}	PUNCT
ejpam-5003	203	38	{	{	PUNCT
ejpam-5003	203	39	1	1	NUM
ejpam-5003	203	40	}	}	PUNCT
ejpam-5003	203	41	{	{	PUNCT
ejpam-5003	203	42	0	0	NUM
ejpam-5003	203	43	}	}	PUNCT
ejpam-5003	203	44	{	{	PUNCT
ejpam-5003	203	45	2	2	NUM
ejpam-5003	203	46	,	,	PUNCT
ejpam-5003	203	47	3	3	NUM
ejpam-5003	203	48	}	}	SYM
ejpam-5003	203	49	3	3	NUM
ejpam-5003	203	50	{	{	PUNCT
ejpam-5003	203	51	3	3	NUM
ejpam-5003	203	52	}	}	PUNCT
ejpam-5003	203	53	{	{	PUNCT
ejpam-5003	203	54	1	1	NUM
ejpam-5003	203	55	,	,	PUNCT
ejpam-5003	203	56	3	3	NUM
ejpam-5003	203	57	}	}	PUNCT
ejpam-5003	203	58	{	{	PUNCT
ejpam-5003	203	59	2	2	NUM
ejpam-5003	203	60	,	,	PUNCT
ejpam-5003	203	61	3	3	NUM
ejpam-5003	203	62	}	}	PUNCT
ejpam-5003	203	63	{	{	PUNCT
ejpam-5003	203	64	0	0	NUM
ejpam-5003	203	65	,	,	PUNCT
ejpam-5003	203	66	3	3	NUM
ejpam-5003	203	67	}	}	PUNCT
ejpam-5003	203	68	by	by	ADP
ejpam-5003	203	69	routine	routine	ADJ
ejpam-5003	203	70	calculations	calculation	NOUN
ejpam-5003	203	71	,	,	PUNCT
ejpam-5003	203	72	we	we	PRON
ejpam-5003	203	73	can	can	AUX
ejpam-5003	203	74	show	show	VERB
ejpam-5003	203	75	that	that	SCONJ
ejpam-5003	203	76	h	h	NOUN
ejpam-5003	203	77	is	be	AUX
ejpam-5003	203	78	a	a	DET
ejpam-5003	203	79	hyper	hyper	ADJ
ejpam-5003	203	80	bn	bn	NOUN
ejpam-5003	203	81	-algebra	-algebra	NOUN
ejpam-5003	203	82	.	.	PUNCT
ejpam-5003	204	1	let	let	VERB
ejpam-5003	204	2	s	s	PRON
ejpam-5003	204	3	=	=	X
ejpam-5003	204	4	{	{	PUNCT
ejpam-5003	204	5	0	0	NUM
ejpam-5003	204	6	,	,	PUNCT
ejpam-5003	204	7	1	1	NUM
ejpam-5003	204	8	}	}	PUNCT
ejpam-5003	204	9	.	.	PUNCT
ejpam-5003	205	1	in	in	ADP
ejpam-5003	205	2	view	view	NOUN
ejpam-5003	205	3	of	of	ADP
ejpam-5003	205	4	theorem	theorem	ADJ
ejpam-5003	205	5	3	3	NUM
ejpam-5003	205	6	,	,	PUNCT
ejpam-5003	205	7	s	s	VERB
ejpam-5003	205	8	is	be	AUX
ejpam-5003	205	9	a	a	DET
ejpam-5003	205	10	hyper	hyper	ADJ
ejpam-5003	205	11	subbn	subbn	NOUN
ejpam-5003	205	12	-algebra	-algebra	NOUN
ejpam-5003	205	13	of	of	ADP
ejpam-5003	205	14	h.	h.	PROPN
ejpam-5003	205	15	however	however	ADV
ejpam-5003	205	16	,	,	PUNCT
ejpam-5003	205	17	it	it	PRON
ejpam-5003	205	18	is	be	AUX
ejpam-5003	205	19	not	not	PART
ejpam-5003	205	20	a	a	DET
ejpam-5003	205	21	hyper	hyper	ADJ
ejpam-5003	205	22	bn	bn	NOUN
ejpam-5003	205	23	-ideal	-ideal	NOUN
ejpam-5003	205	24	because	because	SCONJ
ejpam-5003	205	25	2⊛	2⊛	NUM
ejpam-5003	205	26	1	1	NUM
ejpam-5003	205	27	≪	≪	NOUN
ejpam-5003	205	28	s	s	X
ejpam-5003	205	29	and	and	CCONJ
ejpam-5003	205	30	1	1	NUM
ejpam-5003	205	31	∈	∈	NOUN
ejpam-5003	205	32	s	s	NOUN
ejpam-5003	205	33	but	but	CCONJ
ejpam-5003	205	34	2	2	NUM
ejpam-5003	205	35	/∈	/∈	PUNCT
ejpam-5003	205	36	s.	s.	PROPN
ejpam-5003	205	37	a	a	DET
ejpam-5003	205	38	hyper	hyper	ADJ
ejpam-5003	205	39	subbn	subbn	NOUN
ejpam-5003	205	40	-algebra	-algebra	NOUN
ejpam-5003	205	41	of	of	ADP
ejpam-5003	205	42	a	a	DET
ejpam-5003	205	43	hyper	hyper	ADJ
ejpam-5003	205	44	bn	bn	NOUN
ejpam-5003	205	45	-algebra	-algebra	NOUN
ejpam-5003	205	46	h	h	NOUN
ejpam-5003	205	47	may	may	AUX
ejpam-5003	205	48	not	not	PART
ejpam-5003	205	49	be	be	AUX
ejpam-5003	205	50	a	a	DET
ejpam-5003	205	51	hyper	hyper	ADJ
ejpam-5003	205	52	bn	bn	ADP
ejpam-5003	205	53	-ideal	-ideal	NOUN
ejpam-5003	205	54	of	of	ADP
ejpam-5003	205	55	h	h	NOUN
ejpam-5003	205	56	and	and	CCONJ
ejpam-5003	205	57	a	a	DET
ejpam-5003	205	58	hyper	hyper	NOUN
ejpam-5003	205	59	bn	bn	ADP
ejpam-5003	205	60	-ideal	-ideal	NOUN
ejpam-5003	205	61	of	of	ADP
ejpam-5003	205	62	h	h	NOUN
ejpam-5003	205	63	may	may	AUX
ejpam-5003	205	64	not	not	PART
ejpam-5003	205	65	be	be	AUX
ejpam-5003	205	66	a	a	DET
ejpam-5003	205	67	hyper	hyper	ADJ
ejpam-5003	205	68	subbn	subbn	NOUN
ejpam-5003	205	69	-algebra	-algebra	PROPN
ejpam-5003	205	70	as	as	SCONJ
ejpam-5003	205	71	shown	show	VERB
ejpam-5003	205	72	in	in	ADP
ejpam-5003	205	73	the	the	DET
ejpam-5003	205	74	next	next	ADJ
ejpam-5003	205	75	example	example	NOUN
ejpam-5003	205	76	example	example	NOUN
ejpam-5003	205	77	17	17	NUM
ejpam-5003	205	78	.	.	PUNCT
ejpam-5003	206	1	consider	consider	VERB
ejpam-5003	206	2	the	the	DET
ejpam-5003	206	3	set	set	NOUN
ejpam-5003	206	4	h	h	NOUN
ejpam-5003	206	5	=	=	SYM
ejpam-5003	206	6	{	{	PUNCT
ejpam-5003	206	7	0	0	NUM
ejpam-5003	206	8	,	,	PUNCT
ejpam-5003	206	9	a	a	DET
ejpam-5003	206	10	,	,	PUNCT
ejpam-5003	206	11	b	b	NOUN
ejpam-5003	206	12	}	}	PUNCT
ejpam-5003	206	13	with	with	ADP
ejpam-5003	206	14	hyperoperation	hyperoperation	NOUN
ejpam-5003	206	15	⊛	⊛	NUM
ejpam-5003	206	16	defined	define	VERB
ejpam-5003	206	17	by	by	ADP
ejpam-5003	206	18	the	the	DET
ejpam-5003	206	19	following	following	ADJ
ejpam-5003	206	20	cayley	cayley	ADJ
ejpam-5003	206	21	table	table	NOUN
ejpam-5003	206	22	:	:	PUNCT
ejpam-5003	206	23	⊛	⊛	NUM
ejpam-5003	206	24	0	0	NUM
ejpam-5003	206	25	a	a	DET
ejpam-5003	206	26	b	b	PROPN
ejpam-5003	206	27	0	0	NUM
ejpam-5003	206	28	{	{	PUNCT
ejpam-5003	206	29	0	0	NUM
ejpam-5003	206	30	}	}	PUNCT
ejpam-5003	206	31	{	{	PUNCT
ejpam-5003	206	32	b	b	NOUN
ejpam-5003	206	33	}	}	PUNCT
ejpam-5003	206	34	{	{	PUNCT
ejpam-5003	206	35	a	a	PROPN
ejpam-5003	206	36	}	}	PUNCT
ejpam-5003	206	37	a	a	DET
ejpam-5003	206	38	{	{	PUNCT
ejpam-5003	206	39	a	a	NOUN
ejpam-5003	206	40	}	}	PUNCT
ejpam-5003	206	41	{	{	PUNCT
ejpam-5003	206	42	0	0	NUM
ejpam-5003	206	43	,	,	PUNCT
ejpam-5003	206	44	a	a	DET
ejpam-5003	206	45	,	,	PUNCT
ejpam-5003	206	46	b	b	NOUN
ejpam-5003	206	47	}	}	PUNCT
ejpam-5003	206	48	{	{	PUNCT
ejpam-5003	206	49	a	a	PRON
ejpam-5003	206	50	,	,	PUNCT
ejpam-5003	206	51	b	b	NOUN
ejpam-5003	206	52	}	}	PUNCT
ejpam-5003	206	53	b	b	PROPN
ejpam-5003	206	54	{	{	PUNCT
ejpam-5003	206	55	b	b	NOUN
ejpam-5003	206	56	}	}	PUNCT
ejpam-5003	206	57	{	{	PUNCT
ejpam-5003	206	58	a	a	DET
ejpam-5003	206	59	,	,	PUNCT
ejpam-5003	206	60	b	b	NOUN
ejpam-5003	206	61	}	}	PUNCT
ejpam-5003	206	62	{	{	PUNCT
ejpam-5003	206	63	0	0	NUM
ejpam-5003	206	64	,	,	PUNCT
ejpam-5003	206	65	a	a	DET
ejpam-5003	206	66	,	,	PUNCT
ejpam-5003	206	67	b	b	NOUN
ejpam-5003	206	68	}	}	PUNCT
ejpam-5003	206	69	by	by	ADP
ejpam-5003	206	70	routine	routine	ADJ
ejpam-5003	206	71	calculations	calculation	NOUN
ejpam-5003	206	72	,	,	PUNCT
ejpam-5003	206	73	we	we	PRON
ejpam-5003	206	74	can	can	AUX
ejpam-5003	206	75	show	show	VERB
ejpam-5003	206	76	that	that	SCONJ
ejpam-5003	206	77	h	h	NOUN
ejpam-5003	206	78	is	be	AUX
ejpam-5003	206	79	a	a	DET
ejpam-5003	206	80	hyper	hyper	ADJ
ejpam-5003	206	81	bn	bn	NOUN
ejpam-5003	206	82	-algebra	-algebra	NOUN
ejpam-5003	206	83	.	.	PUNCT
ejpam-5003	207	1	let	let	VERB
ejpam-5003	207	2	i	i	PRON
ejpam-5003	207	3	=	=	PUNCT
ejpam-5003	207	4	{	{	PUNCT
ejpam-5003	207	5	0	0	NUM
ejpam-5003	207	6	,	,	PUNCT
ejpam-5003	207	7	a	a	PRON
ejpam-5003	207	8	}	}	PUNCT
ejpam-5003	207	9	.	.	PUNCT
ejpam-5003	208	1	it	it	PRON
ejpam-5003	208	2	can	can	AUX
ejpam-5003	208	3	be	be	AUX
ejpam-5003	208	4	shown	show	VERB
ejpam-5003	208	5	that	that	SCONJ
ejpam-5003	208	6	i	i	PRON
ejpam-5003	208	7	is	be	AUX
ejpam-5003	208	8	a	a	DET
ejpam-5003	208	9	hyper	hyper	ADJ
ejpam-5003	208	10	bn	bn	ADP
ejpam-5003	208	11	-ideal	-ideal	NOUN
ejpam-5003	208	12	of	of	ADP
ejpam-5003	208	13	h.	h.	NOUN
ejpam-5003	208	14	however	however	ADV
ejpam-5003	208	15	,	,	PUNCT
ejpam-5003	208	16	in	in	ADP
ejpam-5003	208	17	view	view	NOUN
ejpam-5003	208	18	of	of	ADP
ejpam-5003	208	19	theorem	theorem	NOUN
ejpam-5003	208	20	3	3	NUM
ejpam-5003	208	21	,	,	PUNCT
ejpam-5003	208	22	i	i	PRON
ejpam-5003	208	23	is	be	AUX
ejpam-5003	208	24	not	not	PART
ejpam-5003	208	25	a	a	DET
ejpam-5003	208	26	hyper	hyper	ADJ
ejpam-5003	208	27	subbn	subbn	NOUN
ejpam-5003	208	28	-algebra	-algebra	NOUN
ejpam-5003	208	29	because	because	SCONJ
ejpam-5003	208	30	0	0	NUM
ejpam-5003	208	31	,	,	PUNCT
ejpam-5003	208	32	a	a	DET
ejpam-5003	208	33	∈	∈	NOUN
ejpam-5003	208	34	i	i	PRON
ejpam-5003	208	35	but	but	CCONJ
ejpam-5003	208	36	0⊛	0⊛	NUM
ejpam-5003	208	37	a	a	PRON
ejpam-5003	208	38	=	=	X
ejpam-5003	208	39	{	{	PUNCT
ejpam-5003	208	40	b	b	NOUN
ejpam-5003	208	41	}	}	PUNCT
ejpam-5003	208	42	̸⊆	̸⊆	PROPN
ejpam-5003	208	43	i.	i.	PROPN
ejpam-5003	208	44	3.2	3.2	NUM
ejpam-5003	208	45	.	.	PUNCT
ejpam-5003	209	1	reflexive	reflexive	VERB
ejpam-5003	209	2	normal	normal	ADJ
ejpam-5003	209	3	hyper	hyper	ADJ
ejpam-5003	209	4	bn	bn	NOUN
ejpam-5003	209	5	-	-	PUNCT
ejpam-5003	209	6	ideals	ideal	NOUN
ejpam-5003	209	7	at	at	ADP
ejpam-5003	209	8	this	this	DET
ejpam-5003	209	9	point	point	NOUN
ejpam-5003	209	10	,	,	PUNCT
ejpam-5003	209	11	we	we	PRON
ejpam-5003	209	12	will	will	AUX
ejpam-5003	209	13	give	give	VERB
ejpam-5003	209	14	additional	additional	ADJ
ejpam-5003	209	15	conditions	condition	NOUN
ejpam-5003	209	16	to	to	ADP
ejpam-5003	209	17	the	the	DET
ejpam-5003	209	18	underlying	underlie	VERB
ejpam-5003	209	19	set	set	NOUN
ejpam-5003	209	20	of	of	ADP
ejpam-5003	209	21	a	a	DET
ejpam-5003	209	22	hyper	hyper	ADJ
ejpam-5003	209	23	bn	bn	NOUN
ejpam-5003	209	24	ideals	ideal	NOUN
ejpam-5003	209	25	.	.	PUNCT
ejpam-5003	210	1	with	with	ADP
ejpam-5003	210	2	regards	regard	NOUN
ejpam-5003	210	3	to	to	ADP
ejpam-5003	210	4	this	this	PRON
ejpam-5003	210	5	,	,	PUNCT
ejpam-5003	210	6	we	we	PRON
ejpam-5003	210	7	will	will	AUX
ejpam-5003	210	8	establish	establish	VERB
ejpam-5003	210	9	the	the	DET
ejpam-5003	210	10	equivalency	equivalency	NOUN
ejpam-5003	210	11	of	of	ADP
ejpam-5003	210	12	weak	weak	ADJ
ejpam-5003	210	13	hyper	hyper	ADJ
ejpam-5003	210	14	bn	bn	ADJ
ejpam-5003	210	15	-ideals	-ideal	NOUN
ejpam-5003	210	16	and	and	CCONJ
ejpam-5003	210	17	hyper	hyper	ADJ
ejpam-5003	210	18	subbn	subbn	NOUN
ejpam-5003	210	19	-algebras	-algebras	PROPN
ejpam-5003	210	20	.	.	PUNCT
ejpam-5003	211	1	also	also	ADV
ejpam-5003	211	2	,	,	PUNCT
ejpam-5003	211	3	these	these	DET
ejpam-5003	211	4	conditions	condition	NOUN
ejpam-5003	211	5	will	will	AUX
ejpam-5003	211	6	be	be	AUX
ejpam-5003	211	7	the	the	DET
ejpam-5003	211	8	key	key	NOUN
ejpam-5003	211	9	to	to	ADP
ejpam-5003	211	10	the	the	DET
ejpam-5003	211	11	equivalency	equivalency	NOUN
ejpam-5003	211	12	of	of	ADP
ejpam-5003	211	13	strong	strong	ADJ
ejpam-5003	211	14	hyper	hyper	ADJ
ejpam-5003	211	15	bn	bn	ADJ
ejpam-5003	211	16	-ideals	-ideal	NOUN
ejpam-5003	211	17	and	and	CCONJ
ejpam-5003	211	18	hyper	hyper	ADJ
ejpam-5003	211	19	bn	bn	ADJ
ejpam-5003	211	20	-ideals	-ideal	NOUN
ejpam-5003	211	21	.	.	PUNCT
ejpam-5003	212	1	definition	definition	NOUN
ejpam-5003	212	2	12	12	NUM
ejpam-5003	212	3	.	.	PUNCT
ejpam-5003	213	1	a	a	DET
ejpam-5003	213	2	hyper	hyper	ADJ
ejpam-5003	213	3	bn	bn	ADP
ejpam-5003	213	4	-ideal	-ideal	ADJ
ejpam-5003	213	5	i	i	PRON
ejpam-5003	213	6	of	of	ADP
ejpam-5003	213	7	a	a	DET
ejpam-5003	213	8	hyper	hyper	ADJ
ejpam-5003	213	9	bn	bn	NOUN
ejpam-5003	213	10	-algebra	-algebra	NOUN
ejpam-5003	213	11	h	h	NOUN
ejpam-5003	213	12	is	be	AUX
ejpam-5003	213	13	called	call	VERB
ejpam-5003	213	14	reflexive	reflexive	ADJ
ejpam-5003	213	15	(	(	PUNCT
ejpam-5003	213	16	resp	resp	NOUN
ejpam-5003	213	17	.	.	PUNCT
ejpam-5003	214	1	normal	normal	ADJ
ejpam-5003	214	2	)	)	PUNCT
ejpam-5003	214	3	hyper	hyper	ADJ
ejpam-5003	214	4	bn	bn	ADP
ejpam-5003	214	5	-ideal	-ideal	ADJ
ejpam-5003	214	6	if	if	SCONJ
ejpam-5003	214	7	it	it	PRON
ejpam-5003	214	8	is	be	AUX
ejpam-5003	214	9	reflexive	reflexive	ADJ
ejpam-5003	214	10	(	(	PUNCT
ejpam-5003	214	11	resp	resp	NOUN
ejpam-5003	214	12	.	.	PUNCT
ejpam-5003	215	1	normal	normal	ADJ
ejpam-5003	215	2	)	)	PUNCT
ejpam-5003	215	3	.	.	PUNCT
ejpam-5003	216	1	i	i	PRON
ejpam-5003	216	2	is	be	AUX
ejpam-5003	216	3	called	call	VERB
ejpam-5003	216	4	a	a	DET
ejpam-5003	216	5	reflexive	reflexive	ADJ
ejpam-5003	216	6	normal	normal	ADJ
ejpam-5003	216	7	hyper	hyper	NOUN
ejpam-5003	216	8	bn	bn	NOUN
ejpam-5003	216	9	-ideal	-ideal	NOUN
ejpam-5003	216	10	if	if	SCONJ
ejpam-5003	216	11	it	it	PRON
ejpam-5003	216	12	is	be	AUX
ejpam-5003	216	13	both	both	CCONJ
ejpam-5003	216	14	reflexive	reflexive	ADJ
ejpam-5003	216	15	and	and	CCONJ
ejpam-5003	216	16	normal	normal	ADJ
ejpam-5003	216	17	.	.	PUNCT
ejpam-5003	217	1	in	in	ADP
ejpam-5003	217	2	the	the	DET
ejpam-5003	217	3	definition	definition	NOUN
ejpam-5003	217	4	above	above	ADV
ejpam-5003	217	5	,	,	PUNCT
ejpam-5003	217	6	we	we	PRON
ejpam-5003	217	7	can	can	AUX
ejpam-5003	217	8	replace	replace	VERB
ejpam-5003	217	9	a	a	DET
ejpam-5003	217	10	hyper	hyper	NOUN
ejpam-5003	217	11	bn	bn	ADP
ejpam-5003	217	12	-ideal	-ideal	ADJ
ejpam-5003	217	13	to	to	ADP
ejpam-5003	217	14	a	a	DET
ejpam-5003	217	15	weak	weak	ADJ
ejpam-5003	217	16	or	or	CCONJ
ejpam-5003	217	17	strong	strong	ADJ
ejpam-5003	217	18	hyper	hyper	ADJ
ejpam-5003	217	19	bn	bn	NOUN
ejpam-5003	217	20	-ideal	-ideal	NOUN
ejpam-5003	217	21	.	.	PUNCT
ejpam-5003	218	1	l.r	l.r	PROPN
ejpam-5003	218	2	.	.	PROPN
ejpam-5003	218	3	cabardo	cabardo	PROPN
ejpam-5003	218	4	,	,	PUNCT
ejpam-5003	218	5	g.	g.	PROPN
ejpam-5003	218	6	petalcorin	petalcorin	PROPN
ejpam-5003	218	7	/	/	SYM
ejpam-5003	218	8	eur	eur	PROPN
ejpam-5003	218	9	.	.	PUNCT
ejpam-5003	219	1	j.	j.	PROPN
ejpam-5003	219	2	pure	pure	PROPN
ejpam-5003	219	3	appl	appl	PROPN
ejpam-5003	219	4	.	.	PROPN
ejpam-5003	219	5	math	math	PROPN
ejpam-5003	219	6	,	,	PUNCT
ejpam-5003	219	7	17	17	NUM
ejpam-5003	219	8	(	(	PUNCT
ejpam-5003	219	9	1	1	NUM
ejpam-5003	219	10	)	)	PUNCT
ejpam-5003	219	11	(	(	PUNCT
ejpam-5003	219	12	2024	2024	NUM
ejpam-5003	219	13	)	)	PUNCT
ejpam-5003	219	14	,	,	PUNCT
ejpam-5003	219	15	222	222	NUM
ejpam-5003	219	16	-	-	SYM
ejpam-5003	219	17	242	242	NUM
ejpam-5003	219	18	231	231	NUM
ejpam-5003	219	19	example	example	NOUN
ejpam-5003	219	20	18	18	NUM
ejpam-5003	219	21	.	.	PUNCT
ejpam-5003	220	1	in	in	ADP
ejpam-5003	220	2	example	example	NOUN
ejpam-5003	220	3	8	8	NUM
ejpam-5003	220	4	,	,	PUNCT
ejpam-5003	220	5	we	we	PRON
ejpam-5003	220	6	can	can	AUX
ejpam-5003	220	7	show	show	VERB
ejpam-5003	220	8	that	that	SCONJ
ejpam-5003	220	9	i	i	PRON
ejpam-5003	220	10	and	and	CCONJ
ejpam-5003	220	11	j	j	PROPN
ejpam-5003	220	12	are	be	AUX
ejpam-5003	220	13	hyper	hyper	ADJ
ejpam-5003	220	14	bn	bn	ADJ
ejpam-5003	220	15	-ideals	-ideal	NOUN
ejpam-5003	220	16	.	.	PUNCT
ejpam-5003	221	1	since	since	SCONJ
ejpam-5003	221	2	i	i	PRON
ejpam-5003	221	3	is	be	AUX
ejpam-5003	221	4	reflexive	reflexive	ADJ
ejpam-5003	221	5	,	,	PUNCT
ejpam-5003	221	6	i	i	PRON
ejpam-5003	221	7	is	be	AUX
ejpam-5003	221	8	a	a	DET
ejpam-5003	221	9	reflexive	reflexive	ADJ
ejpam-5003	221	10	hyper	hyper	NOUN
ejpam-5003	221	11	bn	bn	ADP
ejpam-5003	221	12	-ideal	-ideal	NOUN
ejpam-5003	221	13	of	of	ADP
ejpam-5003	221	14	h.	h.	NOUN
ejpam-5003	221	15	furthermore	furthermore	ADV
ejpam-5003	221	16	,	,	PUNCT
ejpam-5003	221	17	we	we	PRON
ejpam-5003	221	18	can	can	AUX
ejpam-5003	221	19	show	show	VERB
ejpam-5003	221	20	that	that	SCONJ
ejpam-5003	221	21	i	i	PRON
ejpam-5003	221	22	is	be	AUX
ejpam-5003	221	23	normal	normal	ADJ
ejpam-5003	221	24	.	.	PUNCT
ejpam-5003	222	1	then	then	ADV
ejpam-5003	222	2	i	i	PRON
ejpam-5003	222	3	is	be	AUX
ejpam-5003	222	4	a	a	DET
ejpam-5003	222	5	normal	normal	ADJ
ejpam-5003	222	6	hyper	hyper	NOUN
ejpam-5003	222	7	bn	bn	NOUN
ejpam-5003	222	8	-ideal	-ideal	NOUN
ejpam-5003	222	9	.	.	PUNCT
ejpam-5003	223	1	thus	thus	ADV
ejpam-5003	223	2	,	,	PUNCT
ejpam-5003	223	3	i	i	PRON
ejpam-5003	223	4	is	be	AUX
ejpam-5003	223	5	a	a	DET
ejpam-5003	223	6	reflexive	reflexive	ADJ
ejpam-5003	223	7	normal	normal	ADJ
ejpam-5003	223	8	hyper	hyper	NOUN
ejpam-5003	223	9	bn	bn	NOUN
ejpam-5003	223	10	-ideal	-ideal	NOUN
ejpam-5003	223	11	of	of	ADP
ejpam-5003	223	12	h.	h.	PROPN
ejpam-5003	223	13	j	j	PROPN
ejpam-5003	223	14	is	be	AUX
ejpam-5003	223	15	not	not	PART
ejpam-5003	223	16	a	a	DET
ejpam-5003	223	17	reflexive	reflexive	ADJ
ejpam-5003	223	18	hyper	hyper	NOUN
ejpam-5003	223	19	bn	bn	NOUN
ejpam-5003	223	20	-ideal	-ideal	ADJ
ejpam-5003	223	21	because	because	SCONJ
ejpam-5003	223	22	j	j	PROPN
ejpam-5003	223	23	is	be	AUX
ejpam-5003	223	24	not	not	PART
ejpam-5003	223	25	reflexive	reflexive	ADJ
ejpam-5003	223	26	since	since	SCONJ
ejpam-5003	223	27	2	2	NUM
ejpam-5003	223	28	⊛	⊛	NUM
ejpam-5003	223	29	2	2	NUM
ejpam-5003	223	30	=	=	SYM
ejpam-5003	223	31	{	{	PUNCT
ejpam-5003	223	32	0	0	NUM
ejpam-5003	223	33	,	,	PUNCT
ejpam-5003	223	34	1	1	NUM
ejpam-5003	223	35	}	}	PUNCT
ejpam-5003	223	36	̸⊆	̸⊆	NOUN
ejpam-5003	223	37	j	j	PROPN
ejpam-5003	223	38	.	.	PUNCT
ejpam-5003	224	1	further	far	ADV
ejpam-5003	224	2	,	,	PUNCT
ejpam-5003	224	3	j	j	PROPN
ejpam-5003	224	4	is	be	AUX
ejpam-5003	224	5	not	not	PART
ejpam-5003	224	6	a	a	DET
ejpam-5003	224	7	normal	normal	ADJ
ejpam-5003	224	8	hyper	hyper	NOUN
ejpam-5003	224	9	bn	bn	NOUN
ejpam-5003	224	10	-ideal	-ideal	NOUN
ejpam-5003	224	11	because	because	SCONJ
ejpam-5003	224	12	j	j	PROPN
ejpam-5003	224	13	is	be	AUX
ejpam-5003	224	14	not	not	PART
ejpam-5003	224	15	normal	normal	ADJ
ejpam-5003	224	16	since	since	SCONJ
ejpam-5003	224	17	1	1	NUM
ejpam-5003	224	18	⊛	⊛	NUM
ejpam-5003	224	19	2	2	NUM
ejpam-5003	224	20	⊆	⊆	NUM
ejpam-5003	224	21	j	j	NOUN
ejpam-5003	224	22	and	and	CCONJ
ejpam-5003	224	23	2	2	NUM
ejpam-5003	224	24	⊛	⊛	NUM
ejpam-5003	224	25	1	1	NUM
ejpam-5003	224	26	⊆	⊆	NUM
ejpam-5003	224	27	j	j	PROPN
ejpam-5003	224	28	but	but	CCONJ
ejpam-5003	224	29	(	(	PUNCT
ejpam-5003	224	30	1	1	NUM
ejpam-5003	224	31	⊛	⊛	NUM
ejpam-5003	224	32	2	2	NUM
ejpam-5003	224	33	)	)	PUNCT
ejpam-5003	224	34	⊛	⊛	NUM
ejpam-5003	224	35	(	(	PUNCT
ejpam-5003	224	36	2	2	NUM
ejpam-5003	224	37	⊛	⊛	NUM
ejpam-5003	224	38	1	1	NUM
ejpam-5003	224	39	)	)	PUNCT
ejpam-5003	224	40	=	=	PRON
ejpam-5003	224	41	{	{	PUNCT
ejpam-5003	224	42	0	0	NUM
ejpam-5003	224	43	,	,	PUNCT
ejpam-5003	224	44	1	1	NUM
ejpam-5003	224	45	}	}	PUNCT
ejpam-5003	224	46	̸⊆	̸⊆	NOUN
ejpam-5003	224	47	j	j	PROPN
ejpam-5003	224	48	.	.	PUNCT
ejpam-5003	225	1	also	also	ADV
ejpam-5003	225	2	,	,	PUNCT
ejpam-5003	225	3	i	i	PRON
ejpam-5003	225	4	and	and	CCONJ
ejpam-5003	225	5	j	j	PROPN
ejpam-5003	225	6	are	be	AUX
ejpam-5003	225	7	weak	weak	ADJ
ejpam-5003	225	8	hyper	hyper	ADJ
ejpam-5003	225	9	bn	bn	ADJ
ejpam-5003	225	10	-ideals	-ideal	NOUN
ejpam-5003	225	11	of	of	ADP
ejpam-5003	225	12	h.	h.	NOUN
ejpam-5003	225	13	thus	thus	ADV
ejpam-5003	225	14	,	,	PUNCT
ejpam-5003	225	15	i	i	PRON
ejpam-5003	225	16	is	be	AUX
ejpam-5003	225	17	a	a	DET
ejpam-5003	225	18	reflexive	reflexive	ADJ
ejpam-5003	225	19	normal	normal	ADJ
ejpam-5003	225	20	weak	weak	ADJ
ejpam-5003	225	21	hyper	hyper	ADJ
ejpam-5003	225	22	bn	bn	ADJ
ejpam-5003	225	23	-ideal	-ideal	NOUN
ejpam-5003	225	24	of	of	ADP
ejpam-5003	225	25	h	h	NOUN
ejpam-5003	225	26	while	while	SCONJ
ejpam-5003	225	27	j	j	PROPN
ejpam-5003	225	28	is	be	AUX
ejpam-5003	225	29	not	not	PART
ejpam-5003	225	30	because	because	SCONJ
ejpam-5003	225	31	it	it	PRON
ejpam-5003	225	32	is	be	AUX
ejpam-5003	225	33	not	not	PART
ejpam-5003	225	34	reflexive	reflexive	ADJ
ejpam-5003	225	35	nor	nor	CCONJ
ejpam-5003	225	36	normal	normal	ADJ
ejpam-5003	225	37	as	as	SCONJ
ejpam-5003	225	38	shown	show	VERB
ejpam-5003	225	39	above	above	ADV
ejpam-5003	225	40	.	.	PUNCT
ejpam-5003	226	1	furthermore	furthermore	ADV
ejpam-5003	226	2	,	,	PUNCT
ejpam-5003	226	3	i	i	PRON
ejpam-5003	226	4	is	be	AUX
ejpam-5003	226	5	a	a	DET
ejpam-5003	226	6	strong	strong	ADJ
ejpam-5003	226	7	hyper	hyper	NOUN
ejpam-5003	226	8	bn	bn	NOUN
ejpam-5003	226	9	-ideal	-ideal	NOUN
ejpam-5003	226	10	of	of	ADP
ejpam-5003	226	11	h.	h.	NOUN
ejpam-5003	226	12	hence	hence	ADV
ejpam-5003	226	13	,	,	PUNCT
ejpam-5003	226	14	i	i	PRON
ejpam-5003	226	15	is	be	AUX
ejpam-5003	226	16	a	a	DET
ejpam-5003	226	17	reflexive	reflexive	ADJ
ejpam-5003	226	18	normal	normal	ADJ
ejpam-5003	226	19	strong	strong	ADJ
ejpam-5003	226	20	hyper	hyper	ADJ
ejpam-5003	226	21	bn	bn	NOUN
ejpam-5003	226	22	-ideal	-ideal	NOUN
ejpam-5003	226	23	of	of	ADP
ejpam-5003	226	24	h	h	NOUN
ejpam-5003	226	25	while	while	SCONJ
ejpam-5003	226	26	j	j	PROPN
ejpam-5003	226	27	is	be	AUX
ejpam-5003	226	28	not	not	PART
ejpam-5003	226	29	because	because	SCONJ
ejpam-5003	226	30	it	it	PRON
ejpam-5003	226	31	is	be	AUX
ejpam-5003	226	32	not	not	PART
ejpam-5003	226	33	even	even	ADV
ejpam-5003	226	34	a	a	DET
ejpam-5003	226	35	strong	strong	ADJ
ejpam-5003	226	36	hyper	hyper	NOUN
ejpam-5003	226	37	bn	bn	NOUN
ejpam-5003	226	38	-ideal	-ideal	NOUN
ejpam-5003	226	39	of	of	ADP
ejpam-5003	226	40	h	h	NOUN
ejpam-5003	226	41	since	since	SCONJ
ejpam-5003	226	42	(	(	PUNCT
ejpam-5003	226	43	1⊛	1⊛	NUM
ejpam-5003	226	44	2	2	NUM
ejpam-5003	226	45	)	)	PUNCT
ejpam-5003	226	46	∩	∩	NOUN
ejpam-5003	226	47	j	j	PROPN
ejpam-5003	226	48	̸=	̸=	PROPN
ejpam-5003	226	49	∅	∅	NOUN
ejpam-5003	226	50	and	and	CCONJ
ejpam-5003	226	51	2	2	NUM
ejpam-5003	226	52	∈	∈	PROPN
ejpam-5003	226	53	j	j	NOUN
ejpam-5003	226	54	but	but	CCONJ
ejpam-5003	226	55	1	1	NUM
ejpam-5003	226	56	/∈	/∈	NUM
ejpam-5003	226	57	j	j	PROPN
ejpam-5003	226	58	.	.	PUNCT
ejpam-5003	227	1	the	the	DET
ejpam-5003	227	2	next	next	ADJ
ejpam-5003	227	3	result	result	NOUN
ejpam-5003	227	4	is	be	AUX
ejpam-5003	227	5	a	a	DET
ejpam-5003	227	6	special	special	ADJ
ejpam-5003	227	7	case	case	NOUN
ejpam-5003	227	8	of	of	ADP
ejpam-5003	227	9	theorem	theorem	ADJ
ejpam-5003	227	10	4	4	NUM
ejpam-5003	227	11	.	.	PUNCT
ejpam-5003	227	12	corollary	corollary	ADJ
ejpam-5003	227	13	1	1	NUM
ejpam-5003	227	14	.	.	PUNCT
ejpam-5003	228	1	if	if	SCONJ
ejpam-5003	228	2	i	i	PRON
ejpam-5003	228	3	is	be	AUX
ejpam-5003	228	4	a	a	DET
ejpam-5003	228	5	normal	normal	ADJ
ejpam-5003	228	6	weak	weak	ADJ
ejpam-5003	228	7	hyper	hyper	NOUN
ejpam-5003	228	8	bn	bn	ADJ
ejpam-5003	228	9	-ideal	-ideal	NOUN
ejpam-5003	228	10	of	of	ADP
ejpam-5003	228	11	a	a	DET
ejpam-5003	228	12	hyper	hyper	ADJ
ejpam-5003	228	13	bn	bn	NOUN
ejpam-5003	228	14	-algebra	-algebra	PROPN
ejpam-5003	228	15	h	h	NOUN
ejpam-5003	228	16	,	,	PUNCT
ejpam-5003	228	17	then	then	ADV
ejpam-5003	228	18	i	i	PRON
ejpam-5003	228	19	is	be	AUX
ejpam-5003	228	20	a	a	DET
ejpam-5003	228	21	hyper	hyper	ADJ
ejpam-5003	228	22	subbn	subbn	NOUN
ejpam-5003	228	23	-algebra	-algebra	NOUN
ejpam-5003	228	24	of	of	ADP
ejpam-5003	228	25	h.	h.	NOUN
ejpam-5003	228	26	proposition	proposition	PROPN
ejpam-5003	228	27	2	2	X
ejpam-5003	228	28	.	.	PUNCT
ejpam-5003	229	1	let	let	VERB
ejpam-5003	229	2	h	h	PRON
ejpam-5003	229	3	be	be	AUX
ejpam-5003	229	4	a	a	DET
ejpam-5003	229	5	hyper	hyper	ADJ
ejpam-5003	229	6	bn	bn	NOUN
ejpam-5003	229	7	-algebra	-algebra	NOUN
ejpam-5003	229	8	and	and	CCONJ
ejpam-5003	229	9	let	let	VERB
ejpam-5003	229	10	s	s	PRON
ejpam-5003	229	11	⊆	⊆	NUM
ejpam-5003	229	12	h.	h.	NOUN
ejpam-5003	229	13	then	then	ADV
ejpam-5003	229	14	s	s	VERB
ejpam-5003	229	15	is	be	AUX
ejpam-5003	229	16	a	a	DET
ejpam-5003	229	17	normal	normal	ADJ
ejpam-5003	229	18	hyper	hyper	ADJ
ejpam-5003	229	19	subbn	subbn	NOUN
ejpam-5003	229	20	-algebra	-algebra	NOUN
ejpam-5003	229	21	of	of	ADP
ejpam-5003	229	22	h	h	NOUN
ejpam-5003	229	23	if	if	SCONJ
ejpam-5003	230	1	and	and	CCONJ
ejpam-5003	230	2	only	only	ADV
ejpam-5003	230	3	if	if	SCONJ
ejpam-5003	230	4	s	s	NOUN
ejpam-5003	230	5	is	be	AUX
ejpam-5003	230	6	a	a	DET
ejpam-5003	230	7	normal	normal	ADJ
ejpam-5003	230	8	weak	weak	ADJ
ejpam-5003	230	9	hyper	hyper	NOUN
ejpam-5003	230	10	bn	bn	ADJ
ejpam-5003	230	11	-ideal	-ideal	NOUN
ejpam-5003	230	12	of	of	ADP
ejpam-5003	230	13	h.	h.	NOUN
ejpam-5003	230	14	proof	proof	NOUN
ejpam-5003	230	15	.	.	PUNCT
ejpam-5003	231	1	let	let	VERB
ejpam-5003	231	2	s	s	PRON
ejpam-5003	231	3	be	be	AUX
ejpam-5003	231	4	a	a	DET
ejpam-5003	231	5	normal	normal	ADJ
ejpam-5003	231	6	hyper	hyper	ADJ
ejpam-5003	231	7	subbn	subbn	NOUN
ejpam-5003	231	8	-algebra	-algebra	NOUN
ejpam-5003	231	9	of	of	ADP
ejpam-5003	231	10	a	a	DET
ejpam-5003	231	11	hyper	hyper	ADJ
ejpam-5003	231	12	bn	bn	NOUN
ejpam-5003	231	13	-algebra	-algebra	PROPN
ejpam-5003	231	14	h.	h.	PROPN
ejpam-5003	231	15	thus	thus	ADV
ejpam-5003	231	16	,	,	PUNCT
ejpam-5003	231	17	0	0	NUM
ejpam-5003	231	18	∈	∈	PROPN
ejpam-5003	231	19	s.	s.	PROPN
ejpam-5003	231	20	now	now	ADV
ejpam-5003	231	21	,	,	PUNCT
ejpam-5003	231	22	let	let	VERB
ejpam-5003	231	23	x	x	PUNCT
ejpam-5003	231	24	⊛	⊛	ADV
ejpam-5003	231	25	y	y	PROPN
ejpam-5003	231	26	⊆	⊆	NUM
ejpam-5003	231	27	s	s	NOUN
ejpam-5003	231	28	and	and	CCONJ
ejpam-5003	231	29	y	y	PROPN
ejpam-5003	231	30	∈	∈	PROPN
ejpam-5003	231	31	s.	s.	PROPN
ejpam-5003	231	32	since	since	SCONJ
ejpam-5003	231	33	s	s	PROPN
ejpam-5003	231	34	is	be	AUX
ejpam-5003	231	35	a	a	DET
ejpam-5003	231	36	hyper	hyper	ADJ
ejpam-5003	231	37	subbn	subbn	NOUN
ejpam-5003	231	38	-algebra	-algebra	NOUN
ejpam-5003	231	39	,	,	PUNCT
ejpam-5003	231	40	we	we	PRON
ejpam-5003	231	41	have	have	VERB
ejpam-5003	231	42	0⊛	0⊛	NUM
ejpam-5003	231	43	y	y	PROPN
ejpam-5003	231	44	⊆	⊆	NUM
ejpam-5003	231	45	s.	s.	PROPN
ejpam-5003	231	46	by	by	ADP
ejpam-5003	231	47	normality	normality	NOUN
ejpam-5003	231	48	of	of	ADP
ejpam-5003	231	49	s	s	PROPN
ejpam-5003	231	50	,	,	PUNCT
ejpam-5003	231	51	we	we	PRON
ejpam-5003	231	52	have	have	VERB
ejpam-5003	231	53	{	{	PUNCT
ejpam-5003	231	54	x	x	NOUN
ejpam-5003	231	55	}	}	PUNCT
ejpam-5003	231	56	=	=	PUNCT
ejpam-5003	231	57	x⊛	x⊛	PROPN
ejpam-5003	231	58	0	0	PUNCT
ejpam-5003	231	59	=	=	SYM
ejpam-5003	231	60	(	(	PUNCT
ejpam-5003	231	61	x⊛	x⊛	PROPN
ejpam-5003	231	62	0)⊛	0)⊛	NOUN
ejpam-5003	231	63	0	0	SYM
ejpam-5003	232	1	⊆	⊆	NUM
ejpam-5003	232	2	(	(	PUNCT
ejpam-5003	232	3	x⊛	x⊛	PROPN
ejpam-5003	232	4	0)⊛	0)⊛	PROPN
ejpam-5003	232	5	(	(	PUNCT
ejpam-5003	232	6	y⊛	y⊛	PROPN
ejpam-5003	232	7	y	y	PROPN
ejpam-5003	232	8	)	)	PUNCT
ejpam-5003	232	9	⊆	⊆	NUM
ejpam-5003	232	10	s.	s.	PROPN
ejpam-5003	232	11	thus	thus	ADV
ejpam-5003	232	12	,	,	PUNCT
ejpam-5003	232	13	x	x	PROPN
ejpam-5003	232	14	∈	∈	PROPN
ejpam-5003	232	15	s.	s.	PROPN
ejpam-5003	232	16	hence	hence	ADV
ejpam-5003	232	17	,	,	PUNCT
ejpam-5003	232	18	s	s	VERB
ejpam-5003	232	19	is	be	AUX
ejpam-5003	232	20	a	a	DET
ejpam-5003	232	21	normal	normal	ADJ
ejpam-5003	232	22	weak	weak	ADJ
ejpam-5003	232	23	hyper	hyper	NOUN
ejpam-5003	232	24	bn	bn	ADJ
ejpam-5003	232	25	-ideal	-ideal	NOUN
ejpam-5003	232	26	of	of	ADP
ejpam-5003	232	27	h.	h.	NOUN
ejpam-5003	232	28	the	the	DET
ejpam-5003	232	29	converse	converse	NOUN
ejpam-5003	232	30	follows	follow	VERB
ejpam-5003	232	31	from	from	ADP
ejpam-5003	232	32	corollary	corollary	ADJ
ejpam-5003	232	33	1	1	NUM
ejpam-5003	232	34	.	.	PUNCT
ejpam-5003	232	35	corollary	corollary	ADJ
ejpam-5003	232	36	2	2	NUM
ejpam-5003	232	37	.	.	PUNCT
ejpam-5003	233	1	let	let	VERB
ejpam-5003	233	2	h	h	PRON
ejpam-5003	233	3	be	be	AUX
ejpam-5003	233	4	a	a	DET
ejpam-5003	233	5	hyper	hyper	ADJ
ejpam-5003	233	6	bn	bn	NOUN
ejpam-5003	233	7	-algebra	-algebra	NOUN
ejpam-5003	233	8	and	and	CCONJ
ejpam-5003	233	9	let	let	VERB
ejpam-5003	233	10	s	s	PRON
ejpam-5003	233	11	⊆	⊆	NUM
ejpam-5003	233	12	h.	h.	NOUN
ejpam-5003	234	1	then	then	ADV
ejpam-5003	234	2	s	s	VERB
ejpam-5003	234	3	is	be	AUX
ejpam-5003	234	4	a	a	DET
ejpam-5003	234	5	reflexive	reflexive	ADJ
ejpam-5003	234	6	normal	normal	ADJ
ejpam-5003	234	7	hyper	hyper	ADJ
ejpam-5003	234	8	subbn	subbn	NOUN
ejpam-5003	234	9	-algebra	-algebra	NOUN
ejpam-5003	234	10	of	of	ADP
ejpam-5003	234	11	h	h	NOUN
ejpam-5003	234	12	if	if	SCONJ
ejpam-5003	235	1	and	and	CCONJ
ejpam-5003	235	2	only	only	ADV
ejpam-5003	235	3	if	if	SCONJ
ejpam-5003	235	4	s	s	NOUN
ejpam-5003	235	5	is	be	AUX
ejpam-5003	235	6	a	a	DET
ejpam-5003	235	7	reflexive	reflexive	ADJ
ejpam-5003	235	8	normal	normal	ADJ
ejpam-5003	235	9	weak	weak	ADJ
ejpam-5003	235	10	hyper	hyper	ADJ
ejpam-5003	235	11	bn	bn	ADJ
ejpam-5003	235	12	-ideal	-ideal	NOUN
ejpam-5003	235	13	of	of	ADP
ejpam-5003	235	14	h.	h.	PROPN
ejpam-5003	235	15	theorem	theorem	PROPN
ejpam-5003	235	16	8	8	NUM
ejpam-5003	235	17	.	.	PUNCT
ejpam-5003	236	1	let	let	VERB
ejpam-5003	236	2	{	{	PUNCT
ejpam-5003	236	3	ai|i	ai|i	NOUN
ejpam-5003	236	4	∈	∈	PROPN
ejpam-5003	237	1	i	i	PRON
ejpam-5003	237	2	}	}	PUNCT
ejpam-5003	237	3	be	be	VERB
ejpam-5003	237	4	a	a	DET
ejpam-5003	237	5	family	family	NOUN
ejpam-5003	237	6	of	of	ADP
ejpam-5003	237	7	reflexive	reflexive	ADJ
ejpam-5003	237	8	normal	normal	ADJ
ejpam-5003	237	9	weak	weak	ADJ
ejpam-5003	237	10	hyper	hyper	ADJ
ejpam-5003	237	11	bn	bn	ADJ
ejpam-5003	237	12	-ideals	-ideal	NOUN
ejpam-5003	237	13	of	of	ADP
ejpam-5003	237	14	a	a	DET
ejpam-5003	237	15	hyper	hyper	ADJ
ejpam-5003	237	16	bn	bn	PROPN
ejpam-5003	237	17	-algebra	-algebra	PROPN
ejpam-5003	237	18	h.	h.	NOUN
ejpam-5003	237	19	then	then	ADV
ejpam-5003	237	20	⋂	⋂	PROPN
ejpam-5003	237	21	i∈i	i∈i	NOUN
ejpam-5003	237	22	ai	ai	VERB
ejpam-5003	237	23	is	be	AUX
ejpam-5003	237	24	also	also	ADV
ejpam-5003	237	25	a	a	DET
ejpam-5003	237	26	reflexive	reflexive	ADJ
ejpam-5003	237	27	normal	normal	ADJ
ejpam-5003	237	28	weak	weak	ADJ
ejpam-5003	237	29	hyper	hyper	ADJ
ejpam-5003	237	30	bn	bn	ADJ
ejpam-5003	237	31	-ideal	-ideal	NOUN
ejpam-5003	237	32	of	of	ADP
ejpam-5003	237	33	h.	h.	NOUN
ejpam-5003	237	34	proof	proof	NOUN
ejpam-5003	237	35	.	.	PUNCT
ejpam-5003	238	1	since	since	SCONJ
ejpam-5003	238	2	reflexive	reflexive	ADJ
ejpam-5003	238	3	normal	normal	ADJ
ejpam-5003	238	4	weak	weak	ADJ
ejpam-5003	238	5	hyper	hyper	ADJ
ejpam-5003	238	6	bn	bn	ADJ
ejpam-5003	238	7	-ideals	-ideal	NOUN
ejpam-5003	238	8	are	be	AUX
ejpam-5003	238	9	reflexive	reflexive	ADJ
ejpam-5003	238	10	normal	normal	ADJ
ejpam-5003	238	11	hyper	hyper	ADJ
ejpam-5003	238	12	subbn	subbn	NOUN
ejpam-5003	238	13	algebra	algebra	NOUN
ejpam-5003	238	14	by	by	ADP
ejpam-5003	238	15	corollary	corollary	ADJ
ejpam-5003	238	16	2	2	NUM
ejpam-5003	238	17	,	,	PUNCT
ejpam-5003	238	18	the	the	DET
ejpam-5003	238	19	conclusion	conclusion	NOUN
ejpam-5003	238	20	follows	follow	VERB
ejpam-5003	238	21	from	from	ADP
ejpam-5003	238	22	theorem	theorem	ADJ
ejpam-5003	238	23	5	5	NUM
ejpam-5003	238	24	.	.	PUNCT
ejpam-5003	239	1	lemma	lemma	PROPN
ejpam-5003	239	2	2	2	X
ejpam-5003	239	3	.	.	PUNCT
ejpam-5003	239	4	let	let	VERB
ejpam-5003	239	5	a	a	DET
ejpam-5003	239	6	,	,	PUNCT
ejpam-5003	239	7	b	b	NOUN
ejpam-5003	239	8	,	,	PUNCT
ejpam-5003	239	9	c	c	NOUN
ejpam-5003	240	1	and	and	CCONJ
ejpam-5003	240	2	i	i	PRON
ejpam-5003	240	3	be	be	VERB
ejpam-5003	240	4	subsets	subset	NOUN
ejpam-5003	240	5	of	of	ADP
ejpam-5003	240	6	a	a	DET
ejpam-5003	240	7	hyper	hyper	ADJ
ejpam-5003	240	8	bn	bn	NOUN
ejpam-5003	240	9	-algebra	-algebra	PROPN
ejpam-5003	241	1	h.	h.	PROPN
ejpam-5003	241	2	(	(	PUNCT
ejpam-5003	241	3	i	i	NOUN
ejpam-5003	241	4	)	)	PUNCT
ejpam-5003	241	5	if	if	SCONJ
ejpam-5003	241	6	a⊛	a⊛	NOUN
ejpam-5003	241	7	x	x	PUNCT
ejpam-5003	241	8	≪	≪	VERB
ejpam-5003	241	9	i	i	PRON
ejpam-5003	241	10	for	for	ADP
ejpam-5003	241	11	all	all	DET
ejpam-5003	241	12	x	x	SYM
ejpam-5003	241	13	∈	∈	PROPN
ejpam-5003	241	14	h	h	NOUN
ejpam-5003	241	15	,	,	PUNCT
ejpam-5003	241	16	then	then	ADV
ejpam-5003	241	17	a⊛	a⊛	NOUN
ejpam-5003	241	18	x	x	PUNCT
ejpam-5003	241	19	≪	≪	PROPN
ejpam-5003	241	20	i	i	PRON
ejpam-5003	241	21	for	for	ADP
ejpam-5003	241	22	all	all	DET
ejpam-5003	241	23	a	a	DET
ejpam-5003	241	24	∈	∈	PROPN
ejpam-5003	241	25	a.	a.	NOUN
ejpam-5003	241	26	(	(	PUNCT
ejpam-5003	241	27	ii	ii	NOUN
ejpam-5003	241	28	)	)	PUNCT
ejpam-5003	241	29	if	if	SCONJ
ejpam-5003	241	30	i	i	PRON
ejpam-5003	241	31	is	be	AUX
ejpam-5003	241	32	a	a	DET
ejpam-5003	241	33	hyper	hyper	ADJ
ejpam-5003	241	34	bn	bn	ADP
ejpam-5003	241	35	-ideal	-ideal	NOUN
ejpam-5003	241	36	of	of	ADP
ejpam-5003	241	37	h	h	NOUN
ejpam-5003	241	38	and	and	CCONJ
ejpam-5003	241	39	if	if	SCONJ
ejpam-5003	241	40	a⊛	a⊛	NOUN
ejpam-5003	241	41	x	x	PUNCT
ejpam-5003	241	42	≪	≪	VERB
ejpam-5003	241	43	i	i	PRON
ejpam-5003	241	44	for	for	ADP
ejpam-5003	241	45	all	all	DET
ejpam-5003	241	46	x	x	SYM
ejpam-5003	241	47	∈	∈	PROPN
ejpam-5003	241	48	i	i	PRON
ejpam-5003	241	49	,	,	PUNCT
ejpam-5003	241	50	then	then	ADV
ejpam-5003	241	51	a	a	DET
ejpam-5003	241	52	≪	≪	ADJ
ejpam-5003	241	53	i.	i.	NOUN
ejpam-5003	241	54	proof	proof	NOUN
ejpam-5003	241	55	.	.	PUNCT
ejpam-5003	242	1	let	let	VERB
ejpam-5003	242	2	a	a	DET
ejpam-5003	242	3	,	,	PUNCT
ejpam-5003	242	4	b	b	NOUN
ejpam-5003	242	5	,	,	PUNCT
ejpam-5003	242	6	c	c	NOUN
ejpam-5003	243	1	and	and	CCONJ
ejpam-5003	243	2	i	i	PRON
ejpam-5003	243	3	be	be	VERB
ejpam-5003	243	4	subsets	subset	NOUN
ejpam-5003	243	5	of	of	ADP
ejpam-5003	243	6	a	a	DET
ejpam-5003	243	7	hyper	hyper	ADJ
ejpam-5003	243	8	bn	bn	NOUN
ejpam-5003	243	9	-algebra	-algebra	PROPN
ejpam-5003	243	10	h.	h.	PROPN
ejpam-5003	243	11	(	(	PUNCT
ejpam-5003	243	12	i	i	NOUN
ejpam-5003	243	13	)	)	PUNCT
ejpam-5003	243	14	suppose	suppose	VERB
ejpam-5003	243	15	that	that	SCONJ
ejpam-5003	243	16	a	a	DET
ejpam-5003	243	17	⊛	⊛	NUM
ejpam-5003	243	18	x	x	PUNCT
ejpam-5003	243	19	≪	≪	PROPN
ejpam-5003	243	20	i	i	PRON
ejpam-5003	243	21	for	for	ADP
ejpam-5003	243	22	all	all	PRON
ejpam-5003	243	23	x	x	SYM
ejpam-5003	243	24	∈	∈	PROPN
ejpam-5003	243	25	h.	h.	PROPN
ejpam-5003	243	26	assume	assume	VERB
ejpam-5003	243	27	that	that	SCONJ
ejpam-5003	243	28	there	there	PRON
ejpam-5003	243	29	exists	exist	VERB
ejpam-5003	243	30	a′	a′	PROPN
ejpam-5003	243	31	∈	∈	PROPN
ejpam-5003	243	32	a	a	PRON
ejpam-5003	243	33	with	with	ADP
ejpam-5003	243	34	a′	a′	PROPN
ejpam-5003	243	35	⊛	⊛	NUM
ejpam-5003	243	36	x	x	NOUN
ejpam-5003	243	37	̸≪	̸≪	X
ejpam-5003	243	38	i.	i.	PROPN
ejpam-5003	243	39	then	then	ADV
ejpam-5003	243	40	there	there	PRON
ejpam-5003	243	41	is	be	VERB
ejpam-5003	243	42	an	an	DET
ejpam-5003	243	43	element	element	NOUN
ejpam-5003	243	44	d	d	PROPN
ejpam-5003	243	45	∈	∈	PROPN
ejpam-5003	243	46	a′	a′	PROPN
ejpam-5003	243	47	⊛	⊛	NUM
ejpam-5003	243	48	x	x	SYM
ejpam-5003	243	49	⊆	⊆	X
ejpam-5003	243	50	⋃	⋃	ADP
ejpam-5003	243	51	a∈a	a∈a	ADJ
ejpam-5003	243	52	a⊛	a⊛	NOUN
ejpam-5003	243	53	x	x	NOUN
ejpam-5003	243	54	=	=	PUNCT
ejpam-5003	243	55	a	a	DET
ejpam-5003	243	56	⊛	⊛	NUM
ejpam-5003	243	57	x	x	PUNCT
ejpam-5003	243	58	such	such	ADJ
ejpam-5003	243	59	that	that	SCONJ
ejpam-5003	243	60	d	d	NOUN
ejpam-5003	243	61	̸≪	̸≪	X
ejpam-5003	243	62	k	k	NOUN
ejpam-5003	243	63	for	for	ADP
ejpam-5003	243	64	all	all	DET
ejpam-5003	243	65	k	k	PROPN
ejpam-5003	243	66	∈	∈	PROPN
ejpam-5003	243	67	i	i	PRON
ejpam-5003	243	68	,	,	PUNCT
ejpam-5003	243	69	which	which	PRON
ejpam-5003	243	70	is	be	AUX
ejpam-5003	243	71	a	a	DET
ejpam-5003	243	72	contradiction	contradiction	NOUN
ejpam-5003	243	73	.	.	PUNCT
ejpam-5003	244	1	thus	thus	ADV
ejpam-5003	244	2	,	,	PUNCT
ejpam-5003	244	3	a⊛	a⊛	NOUN
ejpam-5003	244	4	x	x	PUNCT
ejpam-5003	244	5	≪	≪	VERB
ejpam-5003	244	6	i	i	PRON
ejpam-5003	244	7	for	for	ADP
ejpam-5003	244	8	all	all	DET
ejpam-5003	244	9	a	a	DET
ejpam-5003	244	10	∈	∈	PROPN
ejpam-5003	244	11	a.	a.	NOUN
ejpam-5003	244	12	l.r	l.r	PROPN
ejpam-5003	244	13	.	.	PROPN
ejpam-5003	244	14	cabardo	cabardo	PROPN
ejpam-5003	244	15	,	,	PUNCT
ejpam-5003	244	16	g.	g.	PROPN
ejpam-5003	244	17	petalcorin	petalcorin	PROPN
ejpam-5003	244	18	/	/	SYM
ejpam-5003	244	19	eur	eur	PROPN
ejpam-5003	244	20	.	.	PUNCT
ejpam-5003	245	1	j.	j.	PROPN
ejpam-5003	245	2	pure	pure	PROPN
ejpam-5003	245	3	appl	appl	PROPN
ejpam-5003	245	4	.	.	PROPN
ejpam-5003	245	5	math	math	PROPN
ejpam-5003	245	6	,	,	PUNCT
ejpam-5003	245	7	17	17	NUM
ejpam-5003	245	8	(	(	PUNCT
ejpam-5003	245	9	1	1	NUM
ejpam-5003	245	10	)	)	PUNCT
ejpam-5003	245	11	(	(	PUNCT
ejpam-5003	245	12	2024	2024	NUM
ejpam-5003	245	13	)	)	PUNCT
ejpam-5003	245	14	,	,	PUNCT
ejpam-5003	245	15	222	222	NUM
ejpam-5003	245	16	-	-	SYM
ejpam-5003	245	17	242	242	NUM
ejpam-5003	245	18	232	232	NUM
ejpam-5003	245	19	(	(	PUNCT
ejpam-5003	245	20	ii	ii	NOUN
ejpam-5003	245	21	)	)	PUNCT
ejpam-5003	245	22	assume	assume	VERB
ejpam-5003	245	23	that	that	SCONJ
ejpam-5003	245	24	i	i	PRON
ejpam-5003	245	25	is	be	AUX
ejpam-5003	245	26	a	a	DET
ejpam-5003	245	27	hyper	hyper	ADJ
ejpam-5003	245	28	bn	bn	ADP
ejpam-5003	245	29	-ideal	-ideal	NOUN
ejpam-5003	245	30	of	of	ADP
ejpam-5003	245	31	h	h	NOUN
ejpam-5003	245	32	and	and	CCONJ
ejpam-5003	245	33	a⊛	a⊛	NOUN
ejpam-5003	245	34	x	x	PUNCT
ejpam-5003	245	35	≪	≪	PROPN
ejpam-5003	245	36	i	i	PRON
ejpam-5003	245	37	for	for	ADP
ejpam-5003	245	38	all	all	DET
ejpam-5003	245	39	x	x	SYM
ejpam-5003	245	40	∈	∈	PROPN
ejpam-5003	245	41	i.	i.	NOUN
ejpam-5003	245	42	then	then	ADV
ejpam-5003	245	43	by	by	ADP
ejpam-5003	245	44	(	(	PUNCT
ejpam-5003	245	45	i	i	NOUN
ejpam-5003	245	46	)	)	PUNCT
ejpam-5003	245	47	,	,	PUNCT
ejpam-5003	245	48	a	a	DET
ejpam-5003	245	49	⊛	⊛	NUM
ejpam-5003	245	50	x	x	PUNCT
ejpam-5003	245	51	≪	≪	PROPN
ejpam-5003	245	52	i	i	PRON
ejpam-5003	245	53	for	for	ADP
ejpam-5003	245	54	all	all	DET
ejpam-5003	245	55	a	a	DET
ejpam-5003	245	56	∈	∈	NOUN
ejpam-5003	245	57	a.	a.	NOUN
ejpam-5003	245	58	since	since	SCONJ
ejpam-5003	245	59	i	i	PRON
ejpam-5003	245	60	is	be	AUX
ejpam-5003	245	61	a	a	DET
ejpam-5003	245	62	hyper	hyper	ADJ
ejpam-5003	245	63	bn	bn	ADP
ejpam-5003	245	64	-ideal	-ideal	NOUN
ejpam-5003	245	65	of	of	ADP
ejpam-5003	245	66	h	h	NOUN
ejpam-5003	245	67	,	,	PUNCT
ejpam-5003	245	68	a	a	DET
ejpam-5003	245	69	⊛	⊛	ADJ
ejpam-5003	245	70	x	x	PUNCT
ejpam-5003	245	71	≪	≪	ADJ
ejpam-5003	245	72	i	i	PRON
ejpam-5003	245	73	and	and	CCONJ
ejpam-5003	245	74	x	x	SYM
ejpam-5003	245	75	∈	∈	NOUN
ejpam-5003	245	76	i	i	PRON
ejpam-5003	245	77	imply	imply	VERB
ejpam-5003	245	78	that	that	SCONJ
ejpam-5003	245	79	a	a	DET
ejpam-5003	245	80	∈	∈	PROPN
ejpam-5003	245	81	i.	i.	NOUN
ejpam-5003	245	82	thus	thus	ADV
ejpam-5003	245	83	,	,	PUNCT
ejpam-5003	245	84	a	a	DET
ejpam-5003	245	85	⊆	⊆	NUM
ejpam-5003	245	86	i.	i.	NOUN
ejpam-5003	245	87	by	by	ADP
ejpam-5003	245	88	theorem	theorem	PROPN
ejpam-5003	245	89	1(xi	1(xi	PROPN
ejpam-5003	245	90	)	)	PUNCT
ejpam-5003	245	91	,	,	PUNCT
ejpam-5003	245	92	a	a	DET
ejpam-5003	245	93	≪	≪	VERB
ejpam-5003	245	94	i.	i.	NOUN
ejpam-5003	245	95	theorem	theorem	NOUN
ejpam-5003	245	96	9	9	NUM
ejpam-5003	245	97	.	.	PUNCT
ejpam-5003	246	1	let	let	VERB
ejpam-5003	246	2	i	i	PRON
ejpam-5003	246	3	be	be	AUX
ejpam-5003	246	4	a	a	DET
ejpam-5003	246	5	reflexive	reflexive	ADJ
ejpam-5003	246	6	normal	normal	ADJ
ejpam-5003	246	7	hyper	hyper	NOUN
ejpam-5003	246	8	bn	bn	NOUN
ejpam-5003	246	9	-ideal	-ideal	NOUN
ejpam-5003	246	10	of	of	ADP
ejpam-5003	246	11	a	a	DET
ejpam-5003	246	12	hyper	hyper	ADJ
ejpam-5003	246	13	bn	bn	NOUN
ejpam-5003	246	14	-algebra	-algebra	PROPN
ejpam-5003	246	15	h.	h.	NOUN
ejpam-5003	246	16	then	then	ADV
ejpam-5003	246	17	(	(	PUNCT
ejpam-5003	246	18	x⊛	x⊛	PROPN
ejpam-5003	246	19	y	y	NOUN
ejpam-5003	246	20	)	)	PUNCT
ejpam-5003	246	21	∩	∩	NOUN
ejpam-5003	246	22	i	i	PRON
ejpam-5003	246	23	̸=	̸=	PROPN
ejpam-5003	246	24	∅	∅	NOUN
ejpam-5003	246	25	implies	imply	VERB
ejpam-5003	246	26	x⊛	x⊛	PROPN
ejpam-5003	247	1	y	y	PROPN
ejpam-5003	247	2	≪	≪	VERB
ejpam-5003	247	3	i	i	PRON
ejpam-5003	247	4	for	for	ADP
ejpam-5003	247	5	all	all	DET
ejpam-5003	247	6	x	x	NOUN
ejpam-5003	247	7	,	,	PUNCT
ejpam-5003	247	8	y	y	PROPN
ejpam-5003	247	9	∈	∈	PROPN
ejpam-5003	247	10	h.	h.	NOUN
ejpam-5003	247	11	proof	proof	NOUN
ejpam-5003	247	12	.	.	PUNCT
ejpam-5003	248	1	let	let	VERB
ejpam-5003	248	2	x	x	PRON
ejpam-5003	248	3	,	,	PUNCT
ejpam-5003	248	4	y	y	PROPN
ejpam-5003	248	5	∈	∈	PROPN
ejpam-5003	248	6	h	h	NOUN
ejpam-5003	248	7	such	such	ADJ
ejpam-5003	248	8	that	that	SCONJ
ejpam-5003	248	9	(	(	PUNCT
ejpam-5003	248	10	x	x	PROPN
ejpam-5003	248	11	⊛	⊛	NUM
ejpam-5003	248	12	y	y	NUM
ejpam-5003	248	13	)	)	PUNCT
ejpam-5003	248	14	∩	∩	NOUN
ejpam-5003	248	15	i	i	PRON
ejpam-5003	248	16	̸=	̸=	PROPN
ejpam-5003	248	17	∅	∅	NOUN
ejpam-5003	248	18	where	where	SCONJ
ejpam-5003	248	19	i	i	PRON
ejpam-5003	248	20	is	be	AUX
ejpam-5003	248	21	a	a	DET
ejpam-5003	248	22	reflexive	reflexive	ADJ
ejpam-5003	248	23	normal	normal	ADJ
ejpam-5003	248	24	hyper	hyper	NOUN
ejpam-5003	248	25	bn	bn	NOUN
ejpam-5003	248	26	-ideal	-ideal	NOUN
ejpam-5003	248	27	of	of	ADP
ejpam-5003	248	28	h.	h.	NOUN
ejpam-5003	248	29	since	since	SCONJ
ejpam-5003	248	30	i	i	PRON
ejpam-5003	248	31	is	be	AUX
ejpam-5003	248	32	reflexive	reflexive	ADJ
ejpam-5003	248	33	,	,	PUNCT
ejpam-5003	248	34	x	x	X
ejpam-5003	248	35	⊛	⊛	NUM
ejpam-5003	248	36	x	x	SYM
ejpam-5003	248	37	⊆	⊆	NUM
ejpam-5003	248	38	i	i	NOUN
ejpam-5003	248	39	and	and	CCONJ
ejpam-5003	248	40	y	y	PROPN
ejpam-5003	248	41	⊛	⊛	NUM
ejpam-5003	248	42	y	y	PROPN
ejpam-5003	248	43	⊆	⊆	NUM
ejpam-5003	248	44	i.	i.	NOUN
ejpam-5003	248	45	by	by	ADP
ejpam-5003	248	46	normality	normality	NOUN
ejpam-5003	248	47	of	of	ADP
ejpam-5003	248	48	i	i	PRON
ejpam-5003	248	49	,	,	PUNCT
ejpam-5003	248	50	(	(	PUNCT
ejpam-5003	248	51	x	x	PROPN
ejpam-5003	248	52	⊛	⊛	NUM
ejpam-5003	248	53	y	y	NOUN
ejpam-5003	248	54	)	)	PUNCT
ejpam-5003	248	55	⊛	⊛	NOUN
ejpam-5003	248	56	(	(	PUNCT
ejpam-5003	248	57	x	x	PROPN
ejpam-5003	248	58	⊛	⊛	NUM
ejpam-5003	248	59	y	y	PROPN
ejpam-5003	248	60	)	)	PUNCT
ejpam-5003	248	61	⊆	⊆	NUM
ejpam-5003	248	62	i.	i.	NOUN
ejpam-5003	248	63	since	since	SCONJ
ejpam-5003	248	64	(	(	PUNCT
ejpam-5003	248	65	x	x	PROPN
ejpam-5003	248	66	⊛	⊛	NUM
ejpam-5003	248	67	y	y	NUM
ejpam-5003	248	68	)	)	PUNCT
ejpam-5003	248	69	∩	∩	NOUN
ejpam-5003	248	70	i	i	PRON
ejpam-5003	248	71	̸=	̸=	PROPN
ejpam-5003	248	72	∅	∅	NOUN
ejpam-5003	248	73	,	,	PUNCT
ejpam-5003	248	74	there	there	PRON
ejpam-5003	248	75	exists	exist	VERB
ejpam-5003	248	76	a	a	DET
ejpam-5003	248	77	∈	∈	NOUN
ejpam-5003	248	78	(	(	PUNCT
ejpam-5003	248	79	x	x	PROPN
ejpam-5003	248	80	⊛	⊛	NUM
ejpam-5003	248	81	y	y	NOUN
ejpam-5003	248	82	)	)	PUNCT
ejpam-5003	248	83	∩	∩	PROPN
ejpam-5003	248	84	i.	i.	NOUN
ejpam-5003	248	85	now	now	ADV
ejpam-5003	248	86	,	,	PUNCT
ejpam-5003	248	87	(	(	PUNCT
ejpam-5003	248	88	x⊛	x⊛	PROPN
ejpam-5003	248	89	y)⊛	y)⊛	NOUN
ejpam-5003	248	90	a	a	DET
ejpam-5003	248	91	⊆	⊆	NUM
ejpam-5003	248	92	(	(	PUNCT
ejpam-5003	248	93	x⊛	x⊛	NOUN
ejpam-5003	248	94	y)⊛	y)⊛	PROPN
ejpam-5003	248	95	(	(	PUNCT
ejpam-5003	248	96	x⊛	x⊛	PROPN
ejpam-5003	248	97	y	y	NOUN
ejpam-5003	248	98	)	)	PUNCT
ejpam-5003	248	99	⊆	⊆	NUM
ejpam-5003	248	100	i.	i.	NOUN
ejpam-5003	248	101	by	by	ADP
ejpam-5003	248	102	theorem	theorem	PROPN
ejpam-5003	248	103	1(xi	1(xi	PROPN
ejpam-5003	248	104	)	)	PUNCT
ejpam-5003	248	105	,	,	PUNCT
ejpam-5003	248	106	(	(	PUNCT
ejpam-5003	248	107	x⊛	x⊛	PROPN
ejpam-5003	248	108	y)⊛	y)⊛	PROPN
ejpam-5003	248	109	a	a	DET
ejpam-5003	248	110	≪	≪	ADJ
ejpam-5003	248	111	i.	i.	NOUN
ejpam-5003	248	112	note	note	NOUN
ejpam-5003	248	113	that	that	SCONJ
ejpam-5003	248	114	a	a	DET
ejpam-5003	248	115	∈	∈	NOUN
ejpam-5003	248	116	i	i	PRON
ejpam-5003	248	117	and	and	CCONJ
ejpam-5003	248	118	so	so	ADV
ejpam-5003	248	119	,	,	PUNCT
ejpam-5003	248	120	by	by	ADP
ejpam-5003	248	121	lemma	lemma	PROPN
ejpam-5003	248	122	2(ii	2(ii	NUM
ejpam-5003	248	123	)	)	PUNCT
ejpam-5003	248	124	,	,	PUNCT
ejpam-5003	248	125	x⊛	x⊛	PROPN
ejpam-5003	249	1	y	y	PROPN
ejpam-5003	249	2	≪	≪	PUNCT
ejpam-5003	249	3	i.	i.	NOUN
ejpam-5003	249	4	theorem	theorem	VERB
ejpam-5003	249	5	10	10	NUM
ejpam-5003	249	6	.	.	PUNCT
ejpam-5003	250	1	let	let	VERB
ejpam-5003	250	2	i	i	PRON
ejpam-5003	250	3	be	be	AUX
ejpam-5003	250	4	a	a	DET
ejpam-5003	250	5	reflexive	reflexive	ADJ
ejpam-5003	250	6	normal	normal	ADJ
ejpam-5003	250	7	hyper	hyper	NOUN
ejpam-5003	250	8	bn	bn	NOUN
ejpam-5003	250	9	-ideal	-ideal	NOUN
ejpam-5003	250	10	of	of	ADP
ejpam-5003	250	11	a	a	DET
ejpam-5003	250	12	hyper	hyper	ADJ
ejpam-5003	250	13	bn	bn	NOUN
ejpam-5003	250	14	-algebra	-algebra	NOUN
ejpam-5003	250	15	h	h	NOUN
ejpam-5003	250	16	and	and	CCONJ
ejpam-5003	250	17	let	let	VERB
ejpam-5003	250	18	a	a	PRON
ejpam-5003	250	19	be	be	AUX
ejpam-5003	250	20	a	a	DET
ejpam-5003	250	21	subset	subset	NOUN
ejpam-5003	250	22	of	of	ADP
ejpam-5003	250	23	h.	h.	PROPN
ejpam-5003	250	24	if	if	SCONJ
ejpam-5003	250	25	a	a	DET
ejpam-5003	250	26	≪	≪	ADJ
ejpam-5003	250	27	i	i	PRON
ejpam-5003	250	28	,	,	PUNCT
ejpam-5003	250	29	then	then	ADV
ejpam-5003	250	30	a	a	DET
ejpam-5003	250	31	⊆	⊆	NUM
ejpam-5003	250	32	i.	i.	NOUN
ejpam-5003	250	33	proof	proof	NOUN
ejpam-5003	250	34	.	.	PUNCT
ejpam-5003	251	1	assume	assume	VERB
ejpam-5003	251	2	that	that	SCONJ
ejpam-5003	251	3	a	a	DET
ejpam-5003	251	4	≪	≪	ADJ
ejpam-5003	251	5	i	i	PRON
ejpam-5003	251	6	and	and	CCONJ
ejpam-5003	251	7	let	let	VERB
ejpam-5003	251	8	a	a	DET
ejpam-5003	251	9	∈	∈	NOUN
ejpam-5003	251	10	a.	a.	NOUN
ejpam-5003	251	11	then	then	ADV
ejpam-5003	251	12	there	there	PRON
ejpam-5003	251	13	exists	exist	VERB
ejpam-5003	251	14	x	x	X
ejpam-5003	251	15	∈	∈	PROPN
ejpam-5003	251	16	i	i	PRON
ejpam-5003	251	17	such	such	ADJ
ejpam-5003	251	18	that	that	SCONJ
ejpam-5003	251	19	a	a	DET
ejpam-5003	251	20	≪	≪	ADJ
ejpam-5003	251	21	x	x	NOUN
ejpam-5003	251	22	,	,	PUNCT
ejpam-5003	251	23	that	that	ADV
ejpam-5003	251	24	is	is	ADV
ejpam-5003	251	25	,	,	PUNCT
ejpam-5003	251	26	0	0	X
ejpam-5003	251	27	∈	∈	PROPN
ejpam-5003	251	28	a	a	DET
ejpam-5003	251	29	⊛	⊛	NUM
ejpam-5003	251	30	x.	x.	NOUN
ejpam-5003	251	31	hence	hence	ADV
ejpam-5003	251	32	,	,	PUNCT
ejpam-5003	251	33	0	0	X
ejpam-5003	251	34	∈	∈	PROPN
ejpam-5003	251	35	(	(	PUNCT
ejpam-5003	251	36	a	a	DET
ejpam-5003	251	37	⊛	⊛	NUM
ejpam-5003	251	38	x	x	NOUN
ejpam-5003	251	39	)	)	PUNCT
ejpam-5003	251	40	∩	∩	PROPN
ejpam-5003	251	41	i	i	PRON
ejpam-5003	251	42	,	,	PUNCT
ejpam-5003	251	43	and	and	CCONJ
ejpam-5003	251	44	so	so	ADV
ejpam-5003	251	45	,	,	PUNCT
ejpam-5003	251	46	(	(	PUNCT
ejpam-5003	251	47	a	a	DET
ejpam-5003	251	48	⊛	⊛	NUM
ejpam-5003	251	49	x	x	NOUN
ejpam-5003	251	50	)	)	PUNCT
ejpam-5003	251	51	∩	∩	NOUN
ejpam-5003	251	52	i	i	PRON
ejpam-5003	251	53	̸=	̸=	PROPN
ejpam-5003	251	54	∅.	∅.	ADV
ejpam-5003	251	55	by	by	ADP
ejpam-5003	251	56	theorem	theorem	NOUN
ejpam-5003	251	57	9	9	NUM
ejpam-5003	251	58	,	,	PUNCT
ejpam-5003	251	59	a⊛	a⊛	NOUN
ejpam-5003	251	60	x	x	PUNCT
ejpam-5003	251	61	≪	≪	NOUN
ejpam-5003	251	62	i.	i.	NOUN
ejpam-5003	251	63	since	since	SCONJ
ejpam-5003	251	64	i	i	PRON
ejpam-5003	251	65	is	be	AUX
ejpam-5003	251	66	a	a	DET
ejpam-5003	251	67	hyper	hyper	ADJ
ejpam-5003	251	68	bn	bn	ADP
ejpam-5003	251	69	-ideal	-ideal	NOUN
ejpam-5003	251	70	of	of	ADP
ejpam-5003	251	71	h	h	NOUN
ejpam-5003	251	72	,	,	PUNCT
ejpam-5003	251	73	we	we	PRON
ejpam-5003	251	74	have	have	VERB
ejpam-5003	251	75	a	a	DET
ejpam-5003	251	76	∈	∈	NOUN
ejpam-5003	251	77	i	i	PRON
ejpam-5003	251	78	so	so	SCONJ
ejpam-5003	251	79	that	that	SCONJ
ejpam-5003	251	80	a	a	DET
ejpam-5003	251	81	⊆	⊆	NUM
ejpam-5003	251	82	i.	i.	NOUN
ejpam-5003	251	83	the	the	DET
ejpam-5003	251	84	next	next	ADJ
ejpam-5003	251	85	result	result	NOUN
ejpam-5003	251	86	follows	follow	VERB
ejpam-5003	251	87	from	from	ADP
ejpam-5003	251	88	theorem	theorem	ADJ
ejpam-5003	251	89	9	9	NUM
ejpam-5003	251	90	and	and	CCONJ
ejpam-5003	251	91	theorem	theorem	VERB
ejpam-5003	251	92	10	10	NUM
ejpam-5003	251	93	.	.	PUNCT
ejpam-5003	252	1	corollary	corollary	ADJ
ejpam-5003	252	2	3	3	X
ejpam-5003	252	3	.	.	PUNCT
ejpam-5003	253	1	let	let	VERB
ejpam-5003	253	2	i	i	PRON
ejpam-5003	253	3	be	be	AUX
ejpam-5003	253	4	a	a	DET
ejpam-5003	253	5	reflexive	reflexive	ADJ
ejpam-5003	253	6	normal	normal	ADJ
ejpam-5003	253	7	hyper	hyper	NOUN
ejpam-5003	253	8	bn	bn	NOUN
ejpam-5003	253	9	-ideal	-ideal	NOUN
ejpam-5003	253	10	of	of	ADP
ejpam-5003	253	11	a	a	DET
ejpam-5003	253	12	hyper	hyper	ADJ
ejpam-5003	253	13	bn	bn	NOUN
ejpam-5003	253	14	-algebra	-algebra	PROPN
ejpam-5003	253	15	h.	h.	NOUN
ejpam-5003	253	16	then	then	ADV
ejpam-5003	253	17	(	(	PUNCT
ejpam-5003	253	18	x⊛	x⊛	PROPN
ejpam-5003	253	19	y	y	NOUN
ejpam-5003	253	20	)	)	PUNCT
ejpam-5003	253	21	∩	∩	NOUN
ejpam-5003	253	22	i	i	PRON
ejpam-5003	253	23	̸=	̸=	PROPN
ejpam-5003	253	24	∅	∅	NOUN
ejpam-5003	253	25	implies	imply	VERB
ejpam-5003	253	26	x⊛	x⊛	PROPN
ejpam-5003	253	27	y	y	PROPN
ejpam-5003	253	28	⊆	⊆	NUM
ejpam-5003	253	29	i	i	PRON
ejpam-5003	253	30	for	for	ADP
ejpam-5003	253	31	all	all	DET
ejpam-5003	253	32	x	x	NOUN
ejpam-5003	253	33	,	,	PUNCT
ejpam-5003	253	34	y	y	PROPN
ejpam-5003	253	35	∈	∈	PROPN
ejpam-5003	253	36	h.	h.	PROPN
ejpam-5003	253	37	theorem	theorem	VERB
ejpam-5003	253	38	11	11	NUM
ejpam-5003	253	39	.	.	PUNCT
ejpam-5003	254	1	every	every	DET
ejpam-5003	254	2	reflexive	reflexive	ADJ
ejpam-5003	254	3	normal	normal	ADJ
ejpam-5003	254	4	hyper	hyper	NOUN
ejpam-5003	254	5	bn	bn	NOUN
ejpam-5003	254	6	-ideal	-ideal	NOUN
ejpam-5003	254	7	of	of	ADP
ejpam-5003	254	8	a	a	DET
ejpam-5003	254	9	hyper	hyper	ADJ
ejpam-5003	254	10	bn	bn	NOUN
ejpam-5003	254	11	-algebra	-algebra	NOUN
ejpam-5003	254	12	h	h	NOUN
ejpam-5003	254	13	is	be	AUX
ejpam-5003	254	14	a	a	DET
ejpam-5003	254	15	strong	strong	ADJ
ejpam-5003	254	16	hyper	hyper	NOUN
ejpam-5003	254	17	bn	bn	NOUN
ejpam-5003	254	18	-ideal	-ideal	NOUN
ejpam-5003	254	19	of	of	ADP
ejpam-5003	254	20	h.	h.	NOUN
ejpam-5003	254	21	proof	proof	NOUN
ejpam-5003	254	22	.	.	PUNCT
ejpam-5003	255	1	let	let	VERB
ejpam-5003	255	2	i	i	PRON
ejpam-5003	255	3	be	be	AUX
ejpam-5003	255	4	a	a	DET
ejpam-5003	255	5	reflexive	reflexive	ADJ
ejpam-5003	255	6	normal	normal	ADJ
ejpam-5003	255	7	hyper	hyper	NOUN
ejpam-5003	255	8	bn	bn	NOUN
ejpam-5003	255	9	-ideal	-ideal	NOUN
ejpam-5003	255	10	of	of	ADP
ejpam-5003	255	11	a	a	DET
ejpam-5003	255	12	hyper	hyper	ADJ
ejpam-5003	255	13	bn	bn	NOUN
ejpam-5003	255	14	-algebra	-algebra	NOUN
ejpam-5003	255	15	h	h	NOUN
ejpam-5003	255	16	and	and	CCONJ
ejpam-5003	255	17	let	let	VERB
ejpam-5003	255	18	x	x	PRON
ejpam-5003	255	19	,	,	PUNCT
ejpam-5003	255	20	y	y	PROPN
ejpam-5003	255	21	∈	∈	PROPN
ejpam-5003	255	22	h	h	NOUN
ejpam-5003	255	23	such	such	ADJ
ejpam-5003	255	24	that	that	SCONJ
ejpam-5003	255	25	(	(	PUNCT
ejpam-5003	255	26	x⊛	x⊛	NOUN
ejpam-5003	255	27	y	y	NOUN
ejpam-5003	255	28	)	)	PUNCT
ejpam-5003	255	29	∩	∩	NOUN
ejpam-5003	255	30	i	i	PRON
ejpam-5003	255	31	̸=	̸=	PROPN
ejpam-5003	255	32	∅	∅	NOUN
ejpam-5003	255	33	and	and	CCONJ
ejpam-5003	255	34	y	y	PROPN
ejpam-5003	255	35	∈	∈	PROPN
ejpam-5003	255	36	i.	i.	NOUN
ejpam-5003	255	37	then	then	ADV
ejpam-5003	255	38	x⊛	x⊛	PROPN
ejpam-5003	256	1	y	y	PROPN
ejpam-5003	256	2	≪	≪	VERB
ejpam-5003	256	3	i	i	PRON
ejpam-5003	256	4	by	by	ADP
ejpam-5003	256	5	theorem	theorem	NOUN
ejpam-5003	256	6	9	9	NUM
ejpam-5003	256	7	.	.	PUNCT
ejpam-5003	257	1	i	i	PRON
ejpam-5003	257	2	being	be	AUX
ejpam-5003	257	3	a	a	DET
ejpam-5003	257	4	hyper	hyper	ADJ
ejpam-5003	257	5	bn	bn	ADJ
ejpam-5003	257	6	-ideal	-ideal	NOUN
ejpam-5003	257	7	means	mean	VERB
ejpam-5003	257	8	that	that	SCONJ
ejpam-5003	257	9	x	x	PROPN
ejpam-5003	257	10	∈	∈	PROPN
ejpam-5003	257	11	i.	i.	NOUN
ejpam-5003	257	12	hence	hence	ADV
ejpam-5003	257	13	,	,	PUNCT
ejpam-5003	257	14	i	i	PRON
ejpam-5003	257	15	is	be	AUX
ejpam-5003	257	16	a	a	DET
ejpam-5003	257	17	strong	strong	ADJ
ejpam-5003	257	18	hyper	hyper	NOUN
ejpam-5003	257	19	bn	bn	NOUN
ejpam-5003	257	20	-ideal	-ideal	NOUN
ejpam-5003	257	21	of	of	ADP
ejpam-5003	257	22	h.	h.	NOUN
ejpam-5003	257	23	the	the	DET
ejpam-5003	257	24	converse	converse	NOUN
ejpam-5003	257	25	of	of	ADP
ejpam-5003	257	26	theorem	theorem	NOUN
ejpam-5003	257	27	11	11	NUM
ejpam-5003	257	28	is	be	AUX
ejpam-5003	257	29	not	not	PART
ejpam-5003	257	30	true	true	ADJ
ejpam-5003	257	31	as	as	SCONJ
ejpam-5003	257	32	shown	show	VERB
ejpam-5003	257	33	in	in	ADP
ejpam-5003	257	34	the	the	DET
ejpam-5003	257	35	next	next	ADJ
ejpam-5003	257	36	example	example	NOUN
ejpam-5003	257	37	.	.	PUNCT
ejpam-5003	258	1	example	example	NOUN
ejpam-5003	258	2	19	19	NUM
ejpam-5003	258	3	.	.	PUNCT
ejpam-5003	259	1	consider	consider	VERB
ejpam-5003	259	2	the	the	DET
ejpam-5003	259	3	hyper	hyper	ADJ
ejpam-5003	259	4	bn	bn	NOUN
ejpam-5003	259	5	-algebra	-algebra	PROPN
ejpam-5003	259	6	h	h	NOUN
ejpam-5003	259	7	=	=	SYM
ejpam-5003	259	8	{	{	PUNCT
ejpam-5003	259	9	0	0	NUM
ejpam-5003	259	10	,	,	PUNCT
ejpam-5003	259	11	a	a	DET
ejpam-5003	259	12	,	,	PUNCT
ejpam-5003	259	13	b	b	NOUN
ejpam-5003	259	14	}	}	PUNCT
ejpam-5003	259	15	in	in	ADP
ejpam-5003	259	16	example	example	NOUN
ejpam-5003	259	17	1	1	X
ejpam-5003	259	18	.	.	PUNCT
ejpam-5003	260	1	the	the	DET
ejpam-5003	260	2	sets	set	NOUN
ejpam-5003	260	3	i1	i1	PROPN
ejpam-5003	260	4	=	=	PUNCT
ejpam-5003	260	5	{	{	PUNCT
ejpam-5003	260	6	0	0	NUM
ejpam-5003	260	7	,	,	PUNCT
ejpam-5003	260	8	a	a	PRON
ejpam-5003	260	9	}	}	PUNCT
ejpam-5003	260	10	and	and	CCONJ
ejpam-5003	260	11	i2	i2	PROPN
ejpam-5003	260	12	=	=	PUNCT
ejpam-5003	260	13	{	{	PUNCT
ejpam-5003	260	14	0	0	NUM
ejpam-5003	260	15	,	,	PUNCT
ejpam-5003	260	16	b	b	NOUN
ejpam-5003	260	17	}	}	PUNCT
ejpam-5003	260	18	are	be	AUX
ejpam-5003	260	19	strong	strong	ADJ
ejpam-5003	260	20	hyper	hyper	ADJ
ejpam-5003	260	21	bn	bn	ADJ
ejpam-5003	260	22	-ideals	-ideal	NOUN
ejpam-5003	260	23	in	in	ADP
ejpam-5003	260	24	example	example	NOUN
ejpam-5003	260	25	12	12	NUM
ejpam-5003	260	26	.	.	PUNCT
ejpam-5003	261	1	i1	i1	PROPN
ejpam-5003	261	2	is	be	AUX
ejpam-5003	261	3	normal	normal	ADJ
ejpam-5003	261	4	as	as	SCONJ
ejpam-5003	261	5	shown	show	VERB
ejpam-5003	261	6	in	in	ADP
ejpam-5003	261	7	example	example	NOUN
ejpam-5003	261	8	7	7	NUM
ejpam-5003	261	9	but	but	CCONJ
ejpam-5003	261	10	not	not	PART
ejpam-5003	261	11	reflexive	reflexive	VERB
ejpam-5003	261	12	since	since	SCONJ
ejpam-5003	261	13	b	b	NOUN
ejpam-5003	261	14	⊛	⊛	NUM
ejpam-5003	261	15	b	b	NOUN
ejpam-5003	261	16	=	=	SYM
ejpam-5003	261	17	{	{	PUNCT
ejpam-5003	261	18	0	0	NUM
ejpam-5003	261	19	,	,	PUNCT
ejpam-5003	261	20	b	b	NOUN
ejpam-5003	261	21	}	}	PUNCT
ejpam-5003	261	22	̸⊆	̸⊆	PROPN
ejpam-5003	261	23	i1	i1	PROPN
ejpam-5003	261	24	.	.	PUNCT
ejpam-5003	262	1	on	on	ADP
ejpam-5003	262	2	the	the	DET
ejpam-5003	262	3	other	other	ADJ
ejpam-5003	262	4	hand	hand	NOUN
ejpam-5003	262	5	,	,	PUNCT
ejpam-5003	262	6	i2	i2	PROPN
ejpam-5003	262	7	is	be	AUX
ejpam-5003	262	8	not	not	PART
ejpam-5003	262	9	normal	normal	ADJ
ejpam-5003	262	10	as	as	SCONJ
ejpam-5003	262	11	shown	show	VERB
ejpam-5003	262	12	in	in	ADP
ejpam-5003	262	13	example	example	NOUN
ejpam-5003	262	14	7	7	NUM
ejpam-5003	262	15	and	and	CCONJ
ejpam-5003	262	16	is	be	AUX
ejpam-5003	262	17	not	not	PART
ejpam-5003	262	18	reflexive	reflexive	ADJ
ejpam-5003	262	19	because	because	SCONJ
ejpam-5003	262	20	a	a	DET
ejpam-5003	262	21	⊛	⊛	ADJ
ejpam-5003	262	22	a	a	DET
ejpam-5003	262	23	=	=	SYM
ejpam-5003	262	24	{	{	PUNCT
ejpam-5003	262	25	0	0	NUM
ejpam-5003	262	26	,	,	PUNCT
ejpam-5003	262	27	a	a	DET
ejpam-5003	262	28	}	}	PUNCT
ejpam-5003	262	29	̸⊆	̸⊆	NOUN
ejpam-5003	262	30	i2	i2	PROPN
ejpam-5003	262	31	.	.	PUNCT
ejpam-5003	263	1	hence	hence	ADV
ejpam-5003	263	2	,	,	PUNCT
ejpam-5003	263	3	both	both	PRON
ejpam-5003	263	4	i1	i1	PROPN
ejpam-5003	263	5	and	and	CCONJ
ejpam-5003	263	6	i2	i2	PROPN
ejpam-5003	263	7	are	be	AUX
ejpam-5003	263	8	not	not	PART
ejpam-5003	263	9	reflexive	reflexive	ADJ
ejpam-5003	263	10	normal	normal	ADJ
ejpam-5003	263	11	hyper	hyper	ADJ
ejpam-5003	263	12	bn	bn	ADJ
ejpam-5003	263	13	-ideals	-ideal	NOUN
ejpam-5003	263	14	of	of	ADP
ejpam-5003	263	15	h.	h.	NOUN
ejpam-5003	263	16	since	since	SCONJ
ejpam-5003	263	17	reflexivity	reflexivity	NOUN
ejpam-5003	263	18	and	and	CCONJ
ejpam-5003	263	19	normality	normality	NOUN
ejpam-5003	263	20	are	be	AUX
ejpam-5003	263	21	innate	innate	ADJ
ejpam-5003	263	22	in	in	ADP
ejpam-5003	263	23	a	a	DET
ejpam-5003	263	24	set	set	NOUN
ejpam-5003	263	25	,	,	PUNCT
ejpam-5003	263	26	we	we	PRON
ejpam-5003	263	27	can	can	AUX
ejpam-5003	263	28	conclude	conclude	VERB
ejpam-5003	263	29	that	that	SCONJ
ejpam-5003	263	30	the	the	DET
ejpam-5003	263	31	strong	strong	ADJ
ejpam-5003	263	32	hyper	hyper	NOUN
ejpam-5003	263	33	bn	bn	NOUN
ejpam-5003	263	34	-ideal	-ideal	NOUN
ejpam-5003	263	35	in	in	ADP
ejpam-5003	263	36	theorem	theorem	ADJ
ejpam-5003	263	37	11	11	NUM
ejpam-5003	263	38	is	be	AUX
ejpam-5003	263	39	not	not	PART
ejpam-5003	263	40	a	a	DET
ejpam-5003	263	41	reflexive	reflexive	ADJ
ejpam-5003	263	42	normal	normal	ADJ
ejpam-5003	263	43	hyper	hyper	NOUN
ejpam-5003	263	44	bn	bn	NOUN
ejpam-5003	263	45	-ideal	-ideal	NOUN
ejpam-5003	263	46	.	.	PUNCT
ejpam-5003	264	1	and	and	CCONJ
ejpam-5003	264	2	so	so	ADV
ejpam-5003	264	3	,	,	PUNCT
ejpam-5003	264	4	together	together	ADV
ejpam-5003	264	5	with	with	ADP
ejpam-5003	264	6	proposition	proposition	NOUN
ejpam-5003	264	7	1(ii	1(ii	NUM
ejpam-5003	264	8	)	)	PUNCT
ejpam-5003	264	9	,	,	PUNCT
ejpam-5003	264	10	we	we	PRON
ejpam-5003	264	11	have	have	VERB
ejpam-5003	264	12	the	the	DET
ejpam-5003	264	13	following	follow	VERB
ejpam-5003	264	14	result	result	NOUN
ejpam-5003	264	15	.	.	PUNCT
ejpam-5003	265	1	corollary	corollary	ADJ
ejpam-5003	265	2	4	4	NUM
ejpam-5003	265	3	.	.	PUNCT
ejpam-5003	266	1	let	let	VERB
ejpam-5003	266	2	i	i	PRON
ejpam-5003	266	3	be	be	AUX
ejpam-5003	266	4	a	a	DET
ejpam-5003	266	5	reflexive	reflexive	ADJ
ejpam-5003	266	6	normal	normal	ADJ
ejpam-5003	266	7	set	set	NOUN
ejpam-5003	266	8	of	of	ADP
ejpam-5003	266	9	a	a	DET
ejpam-5003	266	10	hyper	hyper	ADJ
ejpam-5003	266	11	bn	bn	NOUN
ejpam-5003	266	12	-algebra	-algebra	PROPN
ejpam-5003	266	13	h.	h.	NOUN
ejpam-5003	267	1	i	i	PRON
ejpam-5003	267	2	is	be	AUX
ejpam-5003	267	3	a	a	DET
ejpam-5003	267	4	strong	strong	ADJ
ejpam-5003	267	5	hyper	hyper	NOUN
ejpam-5003	267	6	bn	bn	NOUN
ejpam-5003	267	7	-ideal	-ideal	NOUN
ejpam-5003	267	8	of	of	ADP
ejpam-5003	267	9	h	h	NOUN
ejpam-5003	267	10	if	if	SCONJ
ejpam-5003	268	1	and	and	CCONJ
ejpam-5003	268	2	only	only	ADV
ejpam-5003	268	3	if	if	SCONJ
ejpam-5003	268	4	i	i	PRON
ejpam-5003	268	5	is	be	AUX
ejpam-5003	268	6	a	a	DET
ejpam-5003	268	7	hyper	hyper	ADJ
ejpam-5003	268	8	bn	bn	ADP
ejpam-5003	268	9	-ideal	-ideal	NOUN
ejpam-5003	268	10	of	of	ADP
ejpam-5003	268	11	h.	h.	PROPN
ejpam-5003	268	12	l.r	l.r	PROPN
ejpam-5003	268	13	.	.	PROPN
ejpam-5003	268	14	cabardo	cabardo	PROPN
ejpam-5003	268	15	,	,	PUNCT
ejpam-5003	268	16	g.	g.	PROPN
ejpam-5003	268	17	petalcorin	petalcorin	PROPN
ejpam-5003	268	18	/	/	SYM
ejpam-5003	268	19	eur	eur	PROPN
ejpam-5003	268	20	.	.	PUNCT
ejpam-5003	269	1	j.	j.	PROPN
ejpam-5003	269	2	pure	pure	PROPN
ejpam-5003	269	3	appl	appl	PROPN
ejpam-5003	269	4	.	.	PROPN
ejpam-5003	269	5	math	math	PROPN
ejpam-5003	269	6	,	,	PUNCT
ejpam-5003	269	7	17	17	NUM
ejpam-5003	269	8	(	(	PUNCT
ejpam-5003	269	9	1	1	NUM
ejpam-5003	269	10	)	)	PUNCT
ejpam-5003	269	11	(	(	PUNCT
ejpam-5003	269	12	2024	2024	NUM
ejpam-5003	269	13	)	)	PUNCT
ejpam-5003	269	14	,	,	PUNCT
ejpam-5003	269	15	222	222	NUM
ejpam-5003	269	16	-	-	SYM
ejpam-5003	269	17	242	242	NUM
ejpam-5003	269	18	233	233	NUM
ejpam-5003	269	19	4	4	NUM
ejpam-5003	269	20	.	.	PUNCT
ejpam-5003	270	1	quotient	quotient	NOUN
ejpam-5003	270	2	structure	structure	NOUN
ejpam-5003	270	3	of	of	ADP
ejpam-5003	270	4	hyper	hyper	ADJ
ejpam-5003	270	5	bn	bn	NOUN
ejpam-5003	270	6	-	-	PUNCT
ejpam-5003	270	7	algebras	algebras	NOUN
ejpam-5003	270	8	in	in	ADP
ejpam-5003	270	9	this	this	DET
ejpam-5003	270	10	section	section	NOUN
ejpam-5003	270	11	,	,	PUNCT
ejpam-5003	270	12	we	we	PRON
ejpam-5003	270	13	will	will	AUX
ejpam-5003	270	14	be	be	AUX
ejpam-5003	270	15	looking	look	VERB
ejpam-5003	270	16	at	at	ADP
ejpam-5003	270	17	two	two	NUM
ejpam-5003	270	18	ways	way	NOUN
ejpam-5003	270	19	of	of	ADP
ejpam-5003	270	20	constructing	construct	VERB
ejpam-5003	270	21	the	the	DET
ejpam-5003	270	22	quotient	quotient	NOUN
ejpam-5003	270	23	structures	structure	NOUN
ejpam-5003	270	24	of	of	ADP
ejpam-5003	270	25	hyper	hyper	ADJ
ejpam-5003	270	26	bn	bn	ADJ
ejpam-5003	270	27	-algebras	-algebra	NOUN
ejpam-5003	270	28	.	.	PUNCT
ejpam-5003	271	1	4.1	4.1	NUM
ejpam-5003	271	2	.	.	PUNCT
ejpam-5003	272	1	quotient	quotient	VERB
ejpam-5003	272	2	hyper	hyper	PROPN
ejpam-5003	272	3	bn	bn	NOUN
ejpam-5003	272	4	-	-	PUNCT
ejpam-5003	272	5	algebra	algebra	NOUN
ejpam-5003	272	6	via	via	ADP
ejpam-5003	272	7	reflexive	reflexive	ADJ
ejpam-5003	272	8	normal	normal	ADJ
ejpam-5003	272	9	hyper	hyper	NOUN
ejpam-5003	272	10	subbnalgebra	subbnalgebra	NOUN
ejpam-5003	272	11	we	we	PRON
ejpam-5003	272	12	now	now	ADV
ejpam-5003	272	13	begin	begin	VERB
ejpam-5003	272	14	constructing	construct	VERB
ejpam-5003	272	15	the	the	DET
ejpam-5003	272	16	quotient	quotient	NOUN
ejpam-5003	272	17	structure	structure	NOUN
ejpam-5003	272	18	of	of	ADP
ejpam-5003	272	19	hyper	hyper	ADJ
ejpam-5003	272	20	bn	bn	PROPN
ejpam-5003	272	21	-algebra	-algebra	NOUN
ejpam-5003	272	22	via	via	ADP
ejpam-5003	272	23	reflexive	reflexive	ADJ
ejpam-5003	272	24	normal	normal	ADJ
ejpam-5003	272	25	hyper	hyper	ADJ
ejpam-5003	272	26	subbn	subbn	NOUN
ejpam-5003	272	27	-algebra	-algebra	PROPN
ejpam-5003	272	28	.	.	PUNCT
ejpam-5003	273	1	lemma	lemma	PROPN
ejpam-5003	273	2	3	3	X
ejpam-5003	273	3	.	.	PUNCT
ejpam-5003	274	1	let	let	VERB
ejpam-5003	274	2	i	i	PRON
ejpam-5003	274	3	be	be	AUX
ejpam-5003	274	4	a	a	DET
ejpam-5003	274	5	normal	normal	ADJ
ejpam-5003	274	6	subset	subset	NOUN
ejpam-5003	274	7	of	of	ADP
ejpam-5003	274	8	a	a	DET
ejpam-5003	274	9	hyper	hyper	ADJ
ejpam-5003	274	10	bn	bn	NOUN
ejpam-5003	274	11	-algebra	-algebra	PROPN
ejpam-5003	274	12	h	h	NOUN
ejpam-5003	274	13	and	and	CCONJ
ejpam-5003	274	14	x	x	NOUN
ejpam-5003	275	1	,	,	PUNCT
ejpam-5003	275	2	y	y	PROPN
ejpam-5003	275	3	∈	∈	PROPN
ejpam-5003	275	4	h.	h.	NOUN
ejpam-5003	275	5	then	then	ADV
ejpam-5003	275	6	(	(	PUNCT
ejpam-5003	275	7	i	i	NOUN
ejpam-5003	275	8	)	)	PUNCT
ejpam-5003	276	1	x	x	SYM
ejpam-5003	276	2	∈	∈	NOUN
ejpam-5003	276	3	i	i	PRON
ejpam-5003	276	4	⇒	⇒	VERB
ejpam-5003	276	5	0⊛	0⊛	NUM
ejpam-5003	276	6	x	x	SYM
ejpam-5003	276	7	⊆	⊆	NUM
ejpam-5003	276	8	i	i	PRON
ejpam-5003	276	9	,	,	PUNCT
ejpam-5003	276	10	and	and	CCONJ
ejpam-5003	276	11	(	(	PUNCT
ejpam-5003	276	12	ii	ii	NOUN
ejpam-5003	276	13	)	)	PUNCT
ejpam-5003	276	14	x⊛	x⊛	PROPN
ejpam-5003	277	1	y	y	PROPN
ejpam-5003	277	2	⊆	⊆	NUM
ejpam-5003	277	3	i	i	PRON
ejpam-5003	277	4	⇒	⇒	VERB
ejpam-5003	277	5	y	y	PROPN
ejpam-5003	277	6	⊛	⊛	NUM
ejpam-5003	277	7	x	x	SYM
ejpam-5003	277	8	⊆	⊆	NUM
ejpam-5003	277	9	i.	i.	NOUN
ejpam-5003	277	10	proof	proof	NOUN
ejpam-5003	277	11	.	.	PUNCT
ejpam-5003	278	1	let	let	VERB
ejpam-5003	278	2	i	i	PRON
ejpam-5003	278	3	be	be	AUX
ejpam-5003	278	4	a	a	DET
ejpam-5003	278	5	normal	normal	ADJ
ejpam-5003	278	6	subset	subset	NOUN
ejpam-5003	278	7	of	of	ADP
ejpam-5003	278	8	a	a	DET
ejpam-5003	278	9	hyper	hyper	ADJ
ejpam-5003	278	10	bn	bn	NOUN
ejpam-5003	278	11	-algebra	-algebra	NOUN
ejpam-5003	278	12	h	h	NOUN
ejpam-5003	278	13	and	and	CCONJ
ejpam-5003	278	14	let	let	VERB
ejpam-5003	278	15	x	x	PRON
ejpam-5003	278	16	,	,	PUNCT
ejpam-5003	278	17	y	y	PROPN
ejpam-5003	278	18	∈	∈	PROPN
ejpam-5003	278	19	h.	h.	PROPN
ejpam-5003	278	20	(	(	PUNCT
ejpam-5003	278	21	i	i	NOUN
ejpam-5003	278	22	)	)	PUNCT
ejpam-5003	278	23	let	let	VERB
ejpam-5003	278	24	x	x	X
ejpam-5003	278	25	∈	∈	PROPN
ejpam-5003	278	26	i.	i.	NOUN
ejpam-5003	278	27	then	then	ADV
ejpam-5003	278	28	x	x	X
ejpam-5003	278	29	⊛	⊛	NUM
ejpam-5003	278	30	0	0	NUM
ejpam-5003	278	31	=	=	SYM
ejpam-5003	278	32	{	{	PUNCT
ejpam-5003	278	33	x	x	NOUN
ejpam-5003	278	34	}	}	PUNCT
ejpam-5003	278	35	⊆	⊆	NUM
ejpam-5003	278	36	i	i	PRON
ejpam-5003	278	37	by	by	ADP
ejpam-5003	278	38	theorem	theorem	NOUN
ejpam-5003	278	39	1(ii	1(ii	NUM
ejpam-5003	278	40	)	)	PUNCT
ejpam-5003	278	41	.	.	PUNCT
ejpam-5003	279	1	since	since	SCONJ
ejpam-5003	279	2	i	i	PRON
ejpam-5003	279	3	is	be	AUX
ejpam-5003	279	4	normal	normal	ADJ
ejpam-5003	279	5	,	,	PUNCT
ejpam-5003	279	6	we	we	PRON
ejpam-5003	279	7	have	have	VERB
ejpam-5003	279	8	0	0	NUM
ejpam-5003	279	9	∈	∈	NOUN
ejpam-5003	279	10	i	i	PRON
ejpam-5003	279	11	and	and	CCONJ
ejpam-5003	280	1	so	so	ADV
ejpam-5003	280	2	0	0	NUM
ejpam-5003	280	3	⊛	⊛	ADJ
ejpam-5003	280	4	0	0	NUM
ejpam-5003	280	5	=	=	SYM
ejpam-5003	280	6	{	{	PUNCT
ejpam-5003	280	7	0	0	NUM
ejpam-5003	280	8	}	}	SYM
ejpam-5003	280	9	⊆	⊆	NUM
ejpam-5003	280	10	i.	i.	NOUN
ejpam-5003	280	11	by	by	ADP
ejpam-5003	280	12	normality	normality	NOUN
ejpam-5003	280	13	of	of	ADP
ejpam-5003	280	14	i	i	PRON
ejpam-5003	280	15	,	,	PUNCT
ejpam-5003	280	16	we	we	PRON
ejpam-5003	280	17	have	have	VERB
ejpam-5003	280	18	0	0	NUM
ejpam-5003	280	19	⊛	⊛	NUM
ejpam-5003	280	20	x	x	NOUN
ejpam-5003	280	21	=	=	SYM
ejpam-5003	280	22	(	(	PUNCT
ejpam-5003	280	23	0	0	NUM
ejpam-5003	280	24	⊛	⊛	NUM
ejpam-5003	280	25	x	x	NOUN
ejpam-5003	280	26	)	)	PUNCT
ejpam-5003	280	27	⊛	⊛	NUM
ejpam-5003	280	28	0	0	NUM
ejpam-5003	281	1	=	=	SYM
ejpam-5003	281	2	(	(	PUNCT
ejpam-5003	281	3	0⊛	0⊛	NUM
ejpam-5003	281	4	x)⊛	x)⊛	PROPN
ejpam-5003	281	5	(	(	PUNCT
ejpam-5003	281	6	0⊛	0⊛	NUM
ejpam-5003	281	7	0	0	NUM
ejpam-5003	281	8	)	)	PUNCT
ejpam-5003	281	9	⊆	⊆	NUM
ejpam-5003	281	10	i.	i.	NOUN
ejpam-5003	281	11	thus	thus	ADV
ejpam-5003	281	12	,	,	PUNCT
ejpam-5003	281	13	0⊛	0⊛	NUM
ejpam-5003	281	14	x	x	SYM
ejpam-5003	281	15	⊆	⊆	NUM
ejpam-5003	281	16	i.	i.	NOUN
ejpam-5003	281	17	(	(	PUNCT
ejpam-5003	281	18	ii	ii	NOUN
ejpam-5003	281	19	)	)	PUNCT
ejpam-5003	281	20	let	let	VERB
ejpam-5003	281	21	x	x	SYM
ejpam-5003	281	22	⊛	⊛	NUM
ejpam-5003	281	23	y	y	PROPN
ejpam-5003	281	24	⊆	⊆	NUM
ejpam-5003	281	25	i.	i.	NOUN
ejpam-5003	281	26	then	then	ADV
ejpam-5003	281	27	for	for	ADP
ejpam-5003	281	28	all	all	DET
ejpam-5003	281	29	a	a	DET
ejpam-5003	281	30	∈	∈	NOUN
ejpam-5003	281	31	x	x	SYM
ejpam-5003	281	32	⊛	⊛	NUM
ejpam-5003	281	33	y	y	PROPN
ejpam-5003	281	34	,	,	PUNCT
ejpam-5003	281	35	a	a	DET
ejpam-5003	281	36	∈	∈	PROPN
ejpam-5003	281	37	i.	i.	NOUN
ejpam-5003	281	38	by	by	ADP
ejpam-5003	281	39	(	(	PUNCT
ejpam-5003	281	40	i	i	NOUN
ejpam-5003	281	41	)	)	PUNCT
ejpam-5003	281	42	,	,	PUNCT
ejpam-5003	281	43	we	we	PRON
ejpam-5003	281	44	have	have	VERB
ejpam-5003	281	45	0	0	NUM
ejpam-5003	281	46	⊛	⊛	NUM
ejpam-5003	281	47	a	a	DET
ejpam-5003	281	48	⊆	⊆	NUM
ejpam-5003	281	49	i	i	PRON
ejpam-5003	281	50	for	for	ADP
ejpam-5003	281	51	all	all	DET
ejpam-5003	281	52	a	a	DET
ejpam-5003	281	53	∈	∈	NOUN
ejpam-5003	281	54	x	x	PUNCT
ejpam-5003	281	55	⊛	⊛	NUM
ejpam-5003	281	56	y.	y.	PROPN
ejpam-5003	281	57	thus	thus	ADV
ejpam-5003	281	58	,	,	PUNCT
ejpam-5003	281	59	0	0	NUM
ejpam-5003	281	60	⊛	⊛	NUM
ejpam-5003	281	61	(	(	PUNCT
ejpam-5003	281	62	x	x	PROPN
ejpam-5003	281	63	⊛	⊛	NUM
ejpam-5003	281	64	y	y	PROPN
ejpam-5003	281	65	)	)	PUNCT
ejpam-5003	281	66	⊆	⊆	NUM
ejpam-5003	281	67	i.	i.	NOUN
ejpam-5003	281	68	but	but	CCONJ
ejpam-5003	281	69	0	0	NUM
ejpam-5003	281	70	⊛	⊛	NUM
ejpam-5003	281	71	(	(	PUNCT
ejpam-5003	281	72	x	x	PROPN
ejpam-5003	281	73	⊛	⊛	NUM
ejpam-5003	281	74	y	y	NOUN
ejpam-5003	281	75	)	)	PUNCT
ejpam-5003	281	76	=	=	SYM
ejpam-5003	282	1	y	y	PROPN
ejpam-5003	282	2	⊛	⊛	NUM
ejpam-5003	282	3	x	x	PUNCT
ejpam-5003	282	4	by	by	ADP
ejpam-5003	282	5	theorem	theorem	NOUN
ejpam-5003	282	6	1(iv	1(iv	NUM
ejpam-5003	282	7	)	)	PUNCT
ejpam-5003	282	8	.	.	PUNCT
ejpam-5003	283	1	therefore	therefore	ADV
ejpam-5003	283	2	,	,	PUNCT
ejpam-5003	283	3	y	y	PROPN
ejpam-5003	283	4	⊛	⊛	NUM
ejpam-5003	283	5	x	x	SYM
ejpam-5003	283	6	⊆	⊆	NUM
ejpam-5003	283	7	i.	i.	NOUN
ejpam-5003	283	8	definition	definition	NOUN
ejpam-5003	283	9	13	13	NUM
ejpam-5003	283	10	.	.	PUNCT
ejpam-5003	284	1	let	let	AUX
ejpam-5003	284	2	(	(	PUNCT
ejpam-5003	284	3	h,⊛	h,⊛	ADV
ejpam-5003	284	4	,	,	PUNCT
ejpam-5003	284	5	0	0	NUM
ejpam-5003	284	6	)	)	PUNCT
ejpam-5003	284	7	be	be	AUX
ejpam-5003	284	8	a	a	DET
ejpam-5003	284	9	hyper	hyper	ADJ
ejpam-5003	284	10	bn	bn	NOUN
ejpam-5003	284	11	-algebra	-algebra	NOUN
ejpam-5003	284	12	and	and	CCONJ
ejpam-5003	284	13	s	s	AUX
ejpam-5003	284	14	be	be	AUX
ejpam-5003	284	15	a	a	DET
ejpam-5003	284	16	reflexive	reflexive	ADJ
ejpam-5003	284	17	normal	normal	ADJ
ejpam-5003	284	18	hyper	hyper	ADJ
ejpam-5003	284	19	subbn	subbn	NOUN
ejpam-5003	284	20	-algebra	-algebra	PROPN
ejpam-5003	284	21	of	of	ADP
ejpam-5003	284	22	h.	h.	NOUN
ejpam-5003	284	23	we	we	PRON
ejpam-5003	284	24	define	define	VERB
ejpam-5003	284	25	a	a	DET
ejpam-5003	284	26	relation	relation	NOUN
ejpam-5003	284	27	∼s	∼s	PROPN
ejpam-5003	284	28	on	on	ADP
ejpam-5003	284	29	h	h	NOUN
ejpam-5003	284	30	by	by	ADP
ejpam-5003	284	31	x	x	PROPN
ejpam-5003	284	32	∼s	∼s	PROPN
ejpam-5003	284	33	y	y	PROPN
ejpam-5003	285	1	if	if	SCONJ
ejpam-5003	286	1	and	and	CCONJ
ejpam-5003	286	2	only	only	ADV
ejpam-5003	286	3	if	if	SCONJ
ejpam-5003	286	4	x	x	PROPN
ejpam-5003	286	5	⊛	⊛	ADV
ejpam-5003	286	6	y	y	PROPN
ejpam-5003	286	7	⊆	⊆	NUM
ejpam-5003	286	8	s	s	NOUN
ejpam-5003	286	9	,	,	PUNCT
ejpam-5003	286	10	where	where	SCONJ
ejpam-5003	286	11	x	x	X
ejpam-5003	286	12	,	,	PUNCT
ejpam-5003	286	13	y	y	PROPN
ejpam-5003	286	14	∈	∈	PROPN
ejpam-5003	286	15	h.	h.	PROPN
ejpam-5003	286	16	lemma	lemma	PROPN
ejpam-5003	286	17	4	4	X
ejpam-5003	286	18	.	.	X
ejpam-5003	286	19	∼s	∼s	PROPN
ejpam-5003	286	20	is	be	AUX
ejpam-5003	286	21	an	an	DET
ejpam-5003	286	22	equivalence	equivalence	NOUN
ejpam-5003	286	23	relation	relation	NOUN
ejpam-5003	286	24	.	.	PUNCT
ejpam-5003	287	1	proof	proof	NOUN
ejpam-5003	287	2	.	.	PUNCT
ejpam-5003	288	1	let	let	VERB
ejpam-5003	288	2	h	h	PRON
ejpam-5003	288	3	be	be	AUX
ejpam-5003	288	4	a	a	DET
ejpam-5003	288	5	hyper	hyper	ADJ
ejpam-5003	288	6	bn	bn	NOUN
ejpam-5003	288	7	-algebra	-algebra	NOUN
ejpam-5003	288	8	and	and	CCONJ
ejpam-5003	288	9	s	s	AUX
ejpam-5003	288	10	be	be	AUX
ejpam-5003	288	11	a	a	DET
ejpam-5003	288	12	reflexive	reflexive	ADJ
ejpam-5003	288	13	normal	normal	ADJ
ejpam-5003	288	14	hyper	hyper	ADJ
ejpam-5003	288	15	subbn	subbn	NOUN
ejpam-5003	288	16	algebra	algebra	PROPN
ejpam-5003	288	17	of	of	ADP
ejpam-5003	288	18	h.	h.	PROPN
ejpam-5003	288	19	since	since	SCONJ
ejpam-5003	288	20	s	s	PROPN
ejpam-5003	288	21	is	be	AUX
ejpam-5003	288	22	reflexive	reflexive	ADJ
ejpam-5003	288	23	,	,	PUNCT
ejpam-5003	288	24	for	for	ADP
ejpam-5003	288	25	all	all	DET
ejpam-5003	288	26	x	x	SYM
ejpam-5003	288	27	∈	∈	PROPN
ejpam-5003	288	28	h	h	NOUN
ejpam-5003	288	29	,	,	PUNCT
ejpam-5003	288	30	x⊛x	x⊛x	PROPN
ejpam-5003	289	1	⊆	⊆	NUM
ejpam-5003	289	2	s.	s.	PROPN
ejpam-5003	289	3	thus	thus	ADV
ejpam-5003	289	4	,	,	PUNCT
ejpam-5003	289	5	x	x	PROPN
ejpam-5003	289	6	∼s	∼s	PROPN
ejpam-5003	289	7	x.	x.	NOUN
ejpam-5003	289	8	whence	whence	NOUN
ejpam-5003	289	9	,	,	PUNCT
ejpam-5003	289	10	∼s	∼s	PROPN
ejpam-5003	289	11	is	be	AUX
ejpam-5003	289	12	reflexive	reflexive	ADJ
ejpam-5003	289	13	.	.	PUNCT
ejpam-5003	290	1	let	let	VERB
ejpam-5003	290	2	x	x	X
ejpam-5003	290	3	∼s	∼s	PROPN
ejpam-5003	291	1	y.	y.	NOUN
ejpam-5003	291	2	then	then	ADV
ejpam-5003	291	3	x⊛y	x⊛y	PROPN
ejpam-5003	292	1	⊆	⊆	NUM
ejpam-5003	292	2	s.	s.	PROPN
ejpam-5003	292	3	by	by	ADP
ejpam-5003	292	4	lemma	lemma	PROPN
ejpam-5003	292	5	3(ii	3(ii	NUM
ejpam-5003	292	6	)	)	PUNCT
ejpam-5003	292	7	,	,	PUNCT
ejpam-5003	292	8	y⊛x	y⊛x	PROPN
ejpam-5003	292	9	⊆	⊆	NUM
ejpam-5003	292	10	s.	s.	PROPN
ejpam-5003	292	11	thus	thus	ADV
ejpam-5003	292	12	,	,	PUNCT
ejpam-5003	292	13	y	y	PROPN
ejpam-5003	292	14	∼s	∼s	PROPN
ejpam-5003	292	15	x.	x.	NOUN
ejpam-5003	292	16	hence	hence	ADV
ejpam-5003	292	17	,	,	PUNCT
ejpam-5003	292	18	∼s	∼s	PROPN
ejpam-5003	292	19	is	be	AUX
ejpam-5003	292	20	symmetric	symmetric	ADJ
ejpam-5003	292	21	.	.	PUNCT
ejpam-5003	293	1	let	let	VERB
ejpam-5003	293	2	x	x	PRON
ejpam-5003	293	3	,	,	PUNCT
ejpam-5003	293	4	y	y	PROPN
ejpam-5003	293	5	,	,	PUNCT
ejpam-5003	293	6	z	z	PROPN
ejpam-5003	293	7	∈	∈	PROPN
ejpam-5003	293	8	h	h	NOUN
ejpam-5003	293	9	such	such	ADJ
ejpam-5003	293	10	that	that	SCONJ
ejpam-5003	293	11	x	x	SYM
ejpam-5003	293	12	∼s	∼s	PROPN
ejpam-5003	293	13	y	y	PROPN
ejpam-5003	293	14	and	and	CCONJ
ejpam-5003	293	15	y	y	PROPN
ejpam-5003	293	16	∼s	∼s	PROPN
ejpam-5003	293	17	z.	z.	PROPN
ejpam-5003	293	18	then	then	ADV
ejpam-5003	293	19	x	x	PROPN
ejpam-5003	293	20	⊛	⊛	NUM
ejpam-5003	293	21	y	y	PROPN
ejpam-5003	293	22	⊆	⊆	NUM
ejpam-5003	293	23	s	s	NOUN
ejpam-5003	293	24	and	and	CCONJ
ejpam-5003	293	25	y	y	PROPN
ejpam-5003	293	26	⊛	⊛	NUM
ejpam-5003	293	27	z	z	NOUN
ejpam-5003	293	28	⊆	⊆	NUM
ejpam-5003	293	29	s.	s.	PROPN
ejpam-5003	293	30	by	by	ADP
ejpam-5003	293	31	applying	apply	VERB
ejpam-5003	293	32	lemma	lemma	PROPN
ejpam-5003	293	33	3(ii	3(ii	NUM
ejpam-5003	293	34	)	)	PUNCT
ejpam-5003	293	35	again	again	ADV
ejpam-5003	293	36	,	,	PUNCT
ejpam-5003	293	37	we	we	PRON
ejpam-5003	293	38	have	have	VERB
ejpam-5003	293	39	z	z	NOUN
ejpam-5003	293	40	⊛	⊛	NUM
ejpam-5003	293	41	y	y	PROPN
ejpam-5003	293	42	⊆	⊆	NUM
ejpam-5003	293	43	s.	s.	PROPN
ejpam-5003	293	44	now	now	ADV
ejpam-5003	293	45	,	,	PUNCT
ejpam-5003	293	46	by	by	ADP
ejpam-5003	293	47	normality	normality	NOUN
ejpam-5003	293	48	of	of	ADP
ejpam-5003	293	49	s	s	AUX
ejpam-5003	293	50	using	use	VERB
ejpam-5003	293	51	x⊛	x⊛	PROPN
ejpam-5003	293	52	y	y	PROPN
ejpam-5003	293	53	⊆	⊆	NUM
ejpam-5003	293	54	s	s	NOUN
ejpam-5003	293	55	and	and	CCONJ
ejpam-5003	293	56	z⊛	z⊛	PROPN
ejpam-5003	293	57	y	y	PROPN
ejpam-5003	293	58	⊆	⊆	NUM
ejpam-5003	293	59	s	s	NOUN
ejpam-5003	293	60	,	,	PUNCT
ejpam-5003	293	61	we	we	PRON
ejpam-5003	293	62	have	have	VERB
ejpam-5003	293	63	x⊛	x⊛	PROPN
ejpam-5003	293	64	z	z	NOUN
ejpam-5003	293	65	=	=	SYM
ejpam-5003	293	66	(	(	PUNCT
ejpam-5003	293	67	x⊛	x⊛	PROPN
ejpam-5003	293	68	z)⊛	z)⊛	INTJ
ejpam-5003	293	69	0	0	NUM
ejpam-5003	294	1	⊆	⊆	NUM
ejpam-5003	294	2	(	(	PUNCT
ejpam-5003	294	3	x⊛	x⊛	PROPN
ejpam-5003	294	4	z)⊛	z)⊛	PROPN
ejpam-5003	294	5	(	(	PUNCT
ejpam-5003	294	6	y⊛	y⊛	PROPN
ejpam-5003	294	7	y	y	PROPN
ejpam-5003	294	8	)	)	PUNCT
ejpam-5003	294	9	⊆	⊆	NUM
ejpam-5003	294	10	s.	s.	PROPN
ejpam-5003	294	11	thus	thus	ADV
ejpam-5003	294	12	,	,	PUNCT
ejpam-5003	294	13	x⊛	x⊛	PROPN
ejpam-5003	294	14	z	z	PROPN
ejpam-5003	294	15	⊆	⊆	NUM
ejpam-5003	294	16	s	s	AUX
ejpam-5003	294	17	implying	imply	VERB
ejpam-5003	294	18	that	that	SCONJ
ejpam-5003	294	19	x	x	SYM
ejpam-5003	294	20	∼s	∼s	PROPN
ejpam-5003	294	21	z.	z.	PROPN
ejpam-5003	294	22	thus	thus	ADV
ejpam-5003	294	23	,	,	PUNCT
ejpam-5003	294	24	∼s	∼s	PROPN
ejpam-5003	294	25	is	be	AUX
ejpam-5003	294	26	transitive	transitive	ADJ
ejpam-5003	294	27	.	.	PUNCT
ejpam-5003	295	1	therefore	therefore	ADV
ejpam-5003	295	2	,	,	PUNCT
ejpam-5003	295	3	∼s	∼s	PROPN
ejpam-5003	295	4	is	be	AUX
ejpam-5003	295	5	an	an	DET
ejpam-5003	295	6	equivalence	equivalence	NOUN
ejpam-5003	295	7	relation	relation	NOUN
ejpam-5003	295	8	.	.	PUNCT
ejpam-5003	296	1	definition	definition	NOUN
ejpam-5003	296	2	14	14	NUM
ejpam-5003	296	3	.	.	PUNCT
ejpam-5003	297	1	let	let	AUX
ejpam-5003	297	2	(	(	PUNCT
ejpam-5003	297	3	h,⊛	h,⊛	ADV
ejpam-5003	297	4	,	,	PUNCT
ejpam-5003	297	5	0	0	NUM
ejpam-5003	297	6	)	)	PUNCT
ejpam-5003	297	7	be	be	AUX
ejpam-5003	297	8	a	a	DET
ejpam-5003	297	9	hyper	hyper	ADJ
ejpam-5003	297	10	bn	bn	ADJ
ejpam-5003	297	11	-algebra	-algebra	NOUN
ejpam-5003	297	12	,	,	PUNCT
ejpam-5003	297	13	s	s	AUX
ejpam-5003	297	14	be	be	AUX
ejpam-5003	297	15	a	a	DET
ejpam-5003	297	16	reflexive	reflexive	ADJ
ejpam-5003	297	17	normal	normal	ADJ
ejpam-5003	297	18	hyper	hyper	ADJ
ejpam-5003	297	19	subbn	subbn	NOUN
ejpam-5003	297	20	-algebra	-algebra	NOUN
ejpam-5003	297	21	of	of	ADP
ejpam-5003	297	22	h	h	NOUN
ejpam-5003	297	23	,	,	PUNCT
ejpam-5003	297	24	and	and	CCONJ
ejpam-5003	297	25	∅	∅	NOUN
ejpam-5003	297	26	̸=	̸=	PROPN
ejpam-5003	297	27	a	a	PRON
ejpam-5003	297	28	,	,	PUNCT
ejpam-5003	297	29	b	b	PROPN
ejpam-5003	297	30	⊆	⊆	NUM
ejpam-5003	297	31	h.	h.	NOUN
ejpam-5003	297	32	then	then	ADV
ejpam-5003	297	33	a	a	DET
ejpam-5003	297	34	∼s	∼s	PROPN
ejpam-5003	297	35	b	b	NOUN
ejpam-5003	297	36	if	if	SCONJ
ejpam-5003	297	37	for	for	ADP
ejpam-5003	297	38	all	all	DET
ejpam-5003	297	39	a	a	DET
ejpam-5003	297	40	∈	∈	PROPN
ejpam-5003	297	41	a	a	PRON
ejpam-5003	297	42	and	and	CCONJ
ejpam-5003	297	43	b	b	PROPN
ejpam-5003	297	44	∈	∈	PROPN
ejpam-5003	297	45	b	b	PROPN
ejpam-5003	297	46	,	,	PUNCT
ejpam-5003	297	47	a	a	DET
ejpam-5003	297	48	∼s	∼s	PROPN
ejpam-5003	297	49	b.	b.	PROPN
ejpam-5003	297	50	l.r	l.r	PROPN
ejpam-5003	297	51	.	.	PROPN
ejpam-5003	297	52	cabardo	cabardo	PROPN
ejpam-5003	297	53	,	,	PUNCT
ejpam-5003	297	54	g.	g.	PROPN
ejpam-5003	297	55	petalcorin	petalcorin	PROPN
ejpam-5003	297	56	/	/	SYM
ejpam-5003	297	57	eur	eur	PROPN
ejpam-5003	297	58	.	.	PUNCT
ejpam-5003	298	1	j.	j.	PROPN
ejpam-5003	298	2	pure	pure	PROPN
ejpam-5003	298	3	appl	appl	PROPN
ejpam-5003	298	4	.	.	PROPN
ejpam-5003	298	5	math	math	PROPN
ejpam-5003	298	6	,	,	PUNCT
ejpam-5003	298	7	17	17	NUM
ejpam-5003	298	8	(	(	PUNCT
ejpam-5003	298	9	1	1	NUM
ejpam-5003	298	10	)	)	PUNCT
ejpam-5003	298	11	(	(	PUNCT
ejpam-5003	298	12	2024	2024	NUM
ejpam-5003	298	13	)	)	PUNCT
ejpam-5003	298	14	,	,	PUNCT
ejpam-5003	298	15	222	222	NUM
ejpam-5003	298	16	-	-	SYM
ejpam-5003	298	17	242	242	NUM
ejpam-5003	298	18	234	234	NUM
ejpam-5003	298	19	lemma	lemma	PROPN
ejpam-5003	298	20	5	5	NUM
ejpam-5003	298	21	.	.	PUNCT
ejpam-5003	299	1	let	let	AUX
ejpam-5003	299	2	(	(	PUNCT
ejpam-5003	299	3	h,⊛	h,⊛	ADV
ejpam-5003	299	4	,	,	PUNCT
ejpam-5003	299	5	0	0	NUM
ejpam-5003	299	6	)	)	PUNCT
ejpam-5003	299	7	be	be	AUX
ejpam-5003	299	8	a	a	DET
ejpam-5003	299	9	hyper	hyper	ADJ
ejpam-5003	299	10	bn	bn	ADJ
ejpam-5003	299	11	-algebra	-algebra	NOUN
ejpam-5003	299	12	,	,	PUNCT
ejpam-5003	299	13	s	s	AUX
ejpam-5003	299	14	be	be	AUX
ejpam-5003	299	15	a	a	DET
ejpam-5003	299	16	reflexive	reflexive	ADJ
ejpam-5003	299	17	normal	normal	ADJ
ejpam-5003	299	18	hyper	hyper	ADJ
ejpam-5003	299	19	subbn	subbn	NOUN
ejpam-5003	299	20	algebra	algebra	NOUN
ejpam-5003	299	21	of	of	ADP
ejpam-5003	299	22	h	h	NOUN
ejpam-5003	299	23	,	,	PUNCT
ejpam-5003	299	24	and	and	CCONJ
ejpam-5003	299	25	∅	∅	NOUN
ejpam-5003	299	26	̸=	̸=	PROPN
ejpam-5003	299	27	a	a	PRON
ejpam-5003	299	28	,	,	PUNCT
ejpam-5003	299	29	b	b	PROPN
ejpam-5003	299	30	⊆	⊆	NUM
ejpam-5003	299	31	h.	h.	NOUN
ejpam-5003	299	32	a	a	DET
ejpam-5003	299	33	∼s	∼s	PROPN
ejpam-5003	299	34	b	b	NOUN
ejpam-5003	299	35	if	if	SCONJ
ejpam-5003	300	1	and	and	CCONJ
ejpam-5003	300	2	only	only	ADV
ejpam-5003	300	3	if	if	SCONJ
ejpam-5003	300	4	a⊛b	a⊛b	PROPN
ejpam-5003	300	5	⊆	⊆	NUM
ejpam-5003	300	6	s.	s.	PROPN
ejpam-5003	300	7	proof	proof	NOUN
ejpam-5003	300	8	.	.	PUNCT
ejpam-5003	301	1	let	let	VERB
ejpam-5003	301	2	a	a	DET
ejpam-5003	301	3	∼s	∼s	PROPN
ejpam-5003	301	4	b.	b.	NOUN
ejpam-5003	301	5	then	then	ADV
ejpam-5003	301	6	for	for	ADP
ejpam-5003	301	7	all	all	DET
ejpam-5003	301	8	a	a	DET
ejpam-5003	301	9	∈	∈	PROPN
ejpam-5003	301	10	a	a	PRON
ejpam-5003	301	11	and	and	CCONJ
ejpam-5003	301	12	b	b	PROPN
ejpam-5003	301	13	∈	∈	PROPN
ejpam-5003	301	14	b	b	PROPN
ejpam-5003	301	15	,	,	PUNCT
ejpam-5003	301	16	a	a	DET
ejpam-5003	301	17	⊛	⊛	NUM
ejpam-5003	301	18	b	b	NOUN
ejpam-5003	301	19	⊆	⊆	NUM
ejpam-5003	301	20	s.	s.	PROPN
ejpam-5003	301	21	thus	thus	ADV
ejpam-5003	301	22	,	,	PUNCT
ejpam-5003	301	23	a	a	DET
ejpam-5003	301	24	⊛	⊛	NUM
ejpam-5003	301	25	b	b	NOUN
ejpam-5003	301	26	=	=	NOUN
ejpam-5003	301	27	⋃	⋃	NOUN
ejpam-5003	301	28	a∈a	a∈a	ADJ
ejpam-5003	301	29	,	,	PUNCT
ejpam-5003	301	30	b∈b	b∈b	NOUN
ejpam-5003	301	31	(	(	PUNCT
ejpam-5003	301	32	a	a	DET
ejpam-5003	301	33	⊛	⊛	NUM
ejpam-5003	301	34	b	b	NUM
ejpam-5003	301	35	)	)	PUNCT
ejpam-5003	301	36	⊆	⊆	NUM
ejpam-5003	301	37	s.	s.	PROPN
ejpam-5003	301	38	for	for	ADP
ejpam-5003	301	39	the	the	DET
ejpam-5003	301	40	converse	converse	NOUN
ejpam-5003	301	41	,	,	PUNCT
ejpam-5003	301	42	suppose	suppose	VERB
ejpam-5003	301	43	a	a	DET
ejpam-5003	301	44	⊛	⊛	NUM
ejpam-5003	301	45	b	b	NOUN
ejpam-5003	301	46	⊆	⊆	NUM
ejpam-5003	301	47	s.	s.	PROPN
ejpam-5003	301	48	let	let	VERB
ejpam-5003	301	49	a	a	DET
ejpam-5003	301	50	∈	∈	PROPN
ejpam-5003	301	51	a	a	PRON
ejpam-5003	301	52	and	and	CCONJ
ejpam-5003	301	53	b	b	PROPN
ejpam-5003	301	54	∈	∈	PROPN
ejpam-5003	301	55	b.	b.	PROPN
ejpam-5003	301	56	then	then	ADV
ejpam-5003	301	57	a⊛	a⊛	PROPN
ejpam-5003	301	58	b	b	PROPN
ejpam-5003	301	59	⊆	⊆	NUM
ejpam-5003	301	60	a⊛b	a⊛b	PROPN
ejpam-5003	301	61	⊆	⊆	NUM
ejpam-5003	301	62	s.	s.	PROPN
ejpam-5003	301	63	hence	hence	PROPN
ejpam-5003	301	64	,	,	PUNCT
ejpam-5003	301	65	a	a	DET
ejpam-5003	301	66	∼s	∼s	PROPN
ejpam-5003	301	67	b.	b.	NOUN
ejpam-5003	301	68	lemma	lemma	PROPN
ejpam-5003	301	69	6	6	X
ejpam-5003	301	70	.	.	PUNCT
ejpam-5003	302	1	let	let	AUX
ejpam-5003	302	2	(	(	PUNCT
ejpam-5003	302	3	h,⊛	h,⊛	ADV
ejpam-5003	302	4	,	,	PUNCT
ejpam-5003	302	5	0	0	NUM
ejpam-5003	302	6	)	)	PUNCT
ejpam-5003	302	7	be	be	AUX
ejpam-5003	302	8	a	a	DET
ejpam-5003	302	9	hyper	hyper	ADJ
ejpam-5003	302	10	bn	bn	ADJ
ejpam-5003	302	11	-algebra	-algebra	NOUN
ejpam-5003	302	12	,	,	PUNCT
ejpam-5003	302	13	s	s	AUX
ejpam-5003	302	14	be	be	AUX
ejpam-5003	302	15	a	a	DET
ejpam-5003	302	16	reflexive	reflexive	ADJ
ejpam-5003	302	17	normal	normal	ADJ
ejpam-5003	302	18	hyper	hyper	ADJ
ejpam-5003	302	19	subbn	subbn	NOUN
ejpam-5003	302	20	algebra	algebra	NOUN
ejpam-5003	302	21	of	of	ADP
ejpam-5003	302	22	h	h	NOUN
ejpam-5003	302	23	,	,	PUNCT
ejpam-5003	302	24	and	and	CCONJ
ejpam-5003	302	25	∅	∅	NOUN
ejpam-5003	302	26	̸=	̸=	PROPN
ejpam-5003	302	27	a	a	PRON
ejpam-5003	302	28	,	,	PUNCT
ejpam-5003	302	29	b	b	PROPN
ejpam-5003	302	30	⊆	⊆	NUM
ejpam-5003	302	31	h.	h.	NOUN
ejpam-5003	302	32	then	then	ADV
ejpam-5003	302	33	the	the	DET
ejpam-5003	302	34	equivalence	equivalence	NOUN
ejpam-5003	302	35	class	class	NOUN
ejpam-5003	302	36	containing	contain	VERB
ejpam-5003	302	37	0	0	NUM
ejpam-5003	302	38	is	be	AUX
ejpam-5003	302	39	s.	s.	PROPN
ejpam-5003	302	40	in	in	ADP
ejpam-5003	302	41	other	other	ADJ
ejpam-5003	302	42	words	word	NOUN
ejpam-5003	302	43	,	,	PUNCT
ejpam-5003	302	44	[	[	X
ejpam-5003	302	45	0]∼s	0]∼s	PUNCT
ejpam-5003	302	46	=	=	PUNCT
ejpam-5003	302	47	s.	s.	PROPN
ejpam-5003	302	48	proof	proof	NOUN
ejpam-5003	302	49	.	.	PUNCT
ejpam-5003	303	1	let	let	VERB
ejpam-5003	303	2	x	x	PUNCT
ejpam-5003	303	3	∈	∈	PROPN
ejpam-5003	304	1	[	[	X
ejpam-5003	304	2	0]∼s	0]∼s	NUM
ejpam-5003	304	3	.	.	PUNCT
ejpam-5003	305	1	then	then	ADV
ejpam-5003	305	2	{	{	PUNCT
ejpam-5003	305	3	x	x	X
ejpam-5003	305	4	}	}	PUNCT
ejpam-5003	305	5	=	=	PUNCT
ejpam-5003	305	6	x	x	SYM
ejpam-5003	305	7	⊛	⊛	NUM
ejpam-5003	305	8	0	0	NUM
ejpam-5003	305	9	⊆	⊆	NUM
ejpam-5003	305	10	s.	s.	PROPN
ejpam-5003	305	11	thus	thus	ADV
ejpam-5003	305	12	,	,	PUNCT
ejpam-5003	305	13	x	x	PUNCT
ejpam-5003	305	14	∈	∈	NOUN
ejpam-5003	305	15	s	s	X
ejpam-5003	305	16	and	and	CCONJ
ejpam-5003	305	17	hence	hence	ADV
ejpam-5003	306	1	[	[	X
ejpam-5003	306	2	0]∼s	0]∼s	NOUN
ejpam-5003	306	3	⊆	⊆	NUM
ejpam-5003	306	4	s.	s.	PROPN
ejpam-5003	306	5	for	for	ADP
ejpam-5003	306	6	the	the	DET
ejpam-5003	306	7	other	other	ADJ
ejpam-5003	306	8	inclusion	inclusion	NOUN
ejpam-5003	306	9	,	,	PUNCT
ejpam-5003	306	10	let	let	VERB
ejpam-5003	306	11	x	x	PROPN
ejpam-5003	306	12	∈	∈	PROPN
ejpam-5003	306	13	s.	s.	PROPN
ejpam-5003	306	14	note	note	VERB
ejpam-5003	306	15	that	that	SCONJ
ejpam-5003	306	16	0	0	NUM
ejpam-5003	306	17	∈	∈	PROPN
ejpam-5003	306	18	s.	s.	PROPN
ejpam-5003	306	19	since	since	SCONJ
ejpam-5003	306	20	s	s	PROPN
ejpam-5003	306	21	is	be	AUX
ejpam-5003	306	22	a	a	DET
ejpam-5003	306	23	hyper	hyper	ADJ
ejpam-5003	306	24	subbn	subbn	NOUN
ejpam-5003	306	25	-algebra	-algebra	PROPN
ejpam-5003	306	26	,	,	PUNCT
ejpam-5003	306	27	x⊛	x⊛	PROPN
ejpam-5003	306	28	0	0	PROPN
ejpam-5003	307	1	⊆	⊆	NUM
ejpam-5003	307	2	s.	s.	PROPN
ejpam-5003	307	3	thus	thus	ADV
ejpam-5003	307	4	,	,	PUNCT
ejpam-5003	307	5	x	x	PROPN
ejpam-5003	307	6	∼s	∼s	PROPN
ejpam-5003	307	7	0	0	NUM
ejpam-5003	307	8	and	and	CCONJ
ejpam-5003	307	9	x	x	PUNCT
ejpam-5003	307	10	∈	∈	PROPN
ejpam-5003	308	1	[	[	X
ejpam-5003	308	2	0]∼s	0]∼s	NUM
ejpam-5003	308	3	.	.	PUNCT
ejpam-5003	309	1	hence	hence	ADV
ejpam-5003	309	2	,	,	PUNCT
ejpam-5003	309	3	s	s	VERB
ejpam-5003	309	4	⊆	⊆	NUM
ejpam-5003	309	5	[	[	X
ejpam-5003	309	6	0]∼s	0]∼s	NUM
ejpam-5003	309	7	.	.	PUNCT
ejpam-5003	310	1	therefore	therefore	ADV
ejpam-5003	310	2	,	,	PUNCT
ejpam-5003	310	3	[	[	X
ejpam-5003	310	4	0]∼s	0]∼s	PUNCT
ejpam-5003	310	5	=	=	SYM
ejpam-5003	310	6	s.	s.	PROPN
ejpam-5003	310	7	in	in	ADP
ejpam-5003	310	8	the	the	DET
ejpam-5003	310	9	following	follow	VERB
ejpam-5003	310	10	result	result	NOUN
ejpam-5003	310	11	,	,	PUNCT
ejpam-5003	310	12	we	we	PRON
ejpam-5003	310	13	define	define	VERB
ejpam-5003	310	14	h	h	PROPN
ejpam-5003	310	15	/	/	SYM
ejpam-5003	310	16	s	s	NOUN
ejpam-5003	310	17	=	=	PUNCT
ejpam-5003	310	18	{	{	PUNCT
ejpam-5003	310	19	[	[	X
ejpam-5003	310	20	x]∼s	x]∼s	X
ejpam-5003	310	21	|x	|x	PROPN
ejpam-5003	310	22	∈	∈	PROPN
ejpam-5003	310	23	h	h	NOUN
ejpam-5003	310	24	}	}	PUNCT
ejpam-5003	310	25	.	.	PUNCT
ejpam-5003	311	1	theorem	theorem	NOUN
ejpam-5003	311	2	12	12	NUM
ejpam-5003	311	3	.	.	PUNCT
ejpam-5003	312	1	let	let	VERB
ejpam-5003	312	2	s	s	PRON
ejpam-5003	312	3	be	be	AUX
ejpam-5003	312	4	a	a	DET
ejpam-5003	312	5	reflexive	reflexive	ADJ
ejpam-5003	312	6	normal	normal	ADJ
ejpam-5003	312	7	hyper	hyper	ADJ
ejpam-5003	312	8	subbn	subbn	NOUN
ejpam-5003	312	9	-algebra	-algebra	NOUN
ejpam-5003	312	10	of	of	ADP
ejpam-5003	312	11	a	a	DET
ejpam-5003	312	12	hyper	hyper	ADJ
ejpam-5003	312	13	bn	bn	ADJ
ejpam-5003	312	14	-algebra	-algebra	NOUN
ejpam-5003	312	15	(	(	PUNCT
ejpam-5003	312	16	h,⊛	h,⊛	PROPN
ejpam-5003	312	17	,	,	PUNCT
ejpam-5003	312	18	0	0	NUM
ejpam-5003	312	19	)	)	PUNCT
ejpam-5003	312	20	.	.	PUNCT
ejpam-5003	313	1	then	then	ADV
ejpam-5003	313	2	h	h	PROPN
ejpam-5003	313	3	/	/	SYM
ejpam-5003	313	4	s	s	PART
ejpam-5003	313	5	is	be	AUX
ejpam-5003	313	6	a	a	DET
ejpam-5003	313	7	hyper	hyper	ADJ
ejpam-5003	313	8	bn	bn	ADJ
ejpam-5003	313	9	-algebra	-algebra	NOUN
ejpam-5003	313	10	with	with	ADP
ejpam-5003	313	11	hyperoperation	hyperoperation	NOUN
ejpam-5003	313	12	⊙	⊙	PROPN
ejpam-5003	313	13	defined	define	VERB
ejpam-5003	313	14	by	by	ADP
ejpam-5003	313	15	[	[	X
ejpam-5003	313	16	x]∼s	x]∼s	PROPN
ejpam-5003	313	17	⊙	⊙	PROPN
ejpam-5003	314	1	[	[	X
ejpam-5003	314	2	y]∼s	y]∼s	NOUN
ejpam-5003	314	3	=	=	SYM
ejpam-5003	314	4	{	{	PUNCT
ejpam-5003	314	5	[	[	X
ejpam-5003	314	6	z]∼s	z]∼s	X
ejpam-5003	314	7	|z	|z	X
ejpam-5003	314	8	∈	∈	PROPN
ejpam-5003	314	9	x⊛	x⊛	PROPN
ejpam-5003	315	1	y	y	NOUN
ejpam-5003	315	2	}	}	PUNCT
ejpam-5003	315	3	and	and	CCONJ
ejpam-5003	316	1	[	[	X
ejpam-5003	316	2	x]∼s	x]∼s	ADP
ejpam-5003	316	3	≪∼s	≪∼s	X
ejpam-5003	316	4	[	[	X
ejpam-5003	316	5	y]∼s	y]∼s	PROPN
ejpam-5003	316	6	if	if	SCONJ
ejpam-5003	316	7	and	and	CCONJ
ejpam-5003	316	8	only	only	ADV
ejpam-5003	316	9	if	if	SCONJ
ejpam-5003	316	10	[	[	X
ejpam-5003	316	11	0]∼s	0]∼s	X
ejpam-5003	316	12	∈	∈	PROPN
ejpam-5003	316	13	[	[	X
ejpam-5003	316	14	x]∼s	x]∼s	X
ejpam-5003	316	15	⊙	⊙	PROPN
ejpam-5003	317	1	[	[	X
ejpam-5003	317	2	y]∼s	y]∼s	PROPN
ejpam-5003	317	3	.	.	PUNCT
ejpam-5003	318	1	proof	proof	NOUN
ejpam-5003	318	2	.	.	PUNCT
ejpam-5003	319	1	if	if	SCONJ
ejpam-5003	319	2	x	x	PROPN
ejpam-5003	319	3	∼s	∼s	PROPN
ejpam-5003	319	4	p	p	NOUN
ejpam-5003	319	5	and	and	CCONJ
ejpam-5003	319	6	y	y	PROPN
ejpam-5003	319	7	∼s	∼s	PROPN
ejpam-5003	319	8	q	q	NOUN
ejpam-5003	319	9	,	,	PUNCT
ejpam-5003	319	10	then	then	ADV
ejpam-5003	319	11	we	we	PRON
ejpam-5003	319	12	have	have	VERB
ejpam-5003	319	13	x⊛	x⊛	PROPN
ejpam-5003	319	14	p	p	NOUN
ejpam-5003	319	15	⊆	⊆	NUM
ejpam-5003	319	16	s	s	NOUN
ejpam-5003	319	17	and	and	CCONJ
ejpam-5003	319	18	y	y	PROPN
ejpam-5003	319	19	⊛	⊛	NUM
ejpam-5003	319	20	q	q	NOUN
ejpam-5003	319	21	⊆	⊆	NUM
ejpam-5003	319	22	s.	s.	NOUN
ejpam-5003	319	23	by	by	ADP
ejpam-5003	319	24	normality	normality	NOUN
ejpam-5003	319	25	of	of	ADP
ejpam-5003	319	26	s	s	PROPN
ejpam-5003	319	27	,	,	PUNCT
ejpam-5003	319	28	(	(	PUNCT
ejpam-5003	319	29	x⊛	x⊛	INTJ
ejpam-5003	319	30	y)⊛	y)⊛	PROPN
ejpam-5003	319	31	(	(	PUNCT
ejpam-5003	319	32	p⊛	p⊛	ADP
ejpam-5003	319	33	q	q	NOUN
ejpam-5003	319	34	)	)	PUNCT
ejpam-5003	319	35	⊆	⊆	NUM
ejpam-5003	319	36	s.	s.	PROPN
ejpam-5003	319	37	thus	thus	ADV
ejpam-5003	319	38	,	,	PUNCT
ejpam-5003	319	39	by	by	ADP
ejpam-5003	319	40	lemma	lemma	PROPN
ejpam-5003	319	41	5	5	NUM
ejpam-5003	319	42	,	,	PUNCT
ejpam-5003	319	43	x⊛	x⊛	PROPN
ejpam-5003	319	44	y	y	PROPN
ejpam-5003	319	45	∼s	∼s	PROPN
ejpam-5003	319	46	p⊛	p⊛	ADP
ejpam-5003	319	47	q	q	NOUN
ejpam-5003	320	1	and	and	CCONJ
ejpam-5003	320	2	so	so	ADV
ejpam-5003	321	1	[	[	X
ejpam-5003	321	2	x⊛	x⊛	X
ejpam-5003	321	3	y]∼s	y]∼s	PROPN
ejpam-5003	321	4	=	=	PUNCT
ejpam-5003	322	1	[	[	X
ejpam-5003	322	2	p⊛	p⊛	X
ejpam-5003	322	3	q]∼s	q]∼s	NOUN
ejpam-5003	322	4	.	.	PUNCT
ejpam-5003	323	1	hence	hence	ADV
ejpam-5003	323	2	,	,	PUNCT
ejpam-5003	323	3	the	the	DET
ejpam-5003	323	4	hyperoperation	hyperoperation	NOUN
ejpam-5003	323	5	⊙	⊙	PROPN
ejpam-5003	323	6	is	be	AUX
ejpam-5003	323	7	well	well	ADV
ejpam-5003	323	8	-	-	PUNCT
ejpam-5003	323	9	defined	define	VERB
ejpam-5003	323	10	.	.	PUNCT
ejpam-5003	324	1	now	now	ADV
ejpam-5003	324	2	,	,	PUNCT
ejpam-5003	324	3	let	let	VERB
ejpam-5003	324	4	x	x	X
ejpam-5003	324	5	∈	∈	PROPN
ejpam-5003	324	6	h.	h.	PROPN
ejpam-5003	324	7	by	by	ADP
ejpam-5003	324	8	(	(	PUNCT
ejpam-5003	324	9	hbn1	hbn1	PROPN
ejpam-5003	324	10	)	)	PUNCT
ejpam-5003	324	11	,	,	PUNCT
ejpam-5003	324	12	x	x	SYM
ejpam-5003	324	13	≪	≪	PUNCT
ejpam-5003	324	14	x	x	X
ejpam-5003	324	15	,	,	PUNCT
ejpam-5003	324	16	that	that	ADV
ejpam-5003	324	17	is	is	ADV
ejpam-5003	324	18	,	,	PUNCT
ejpam-5003	324	19	0	0	NUM
ejpam-5003	324	20	∈	∈	PROPN
ejpam-5003	324	21	x	x	SYM
ejpam-5003	324	22	⊛	⊛	NUM
ejpam-5003	324	23	x.	x.	NOUN
ejpam-5003	324	24	thus	thus	ADV
ejpam-5003	324	25	,	,	PUNCT
ejpam-5003	324	26	[	[	X
ejpam-5003	324	27	0]∼s	0]∼s	X
ejpam-5003	324	28	∈	∈	NOUN
ejpam-5003	324	29	{	{	PUNCT
ejpam-5003	324	30	[	[	X
ejpam-5003	324	31	z]∼s	z]∼s	X
ejpam-5003	324	32	|z	|z	X
ejpam-5003	324	33	∈	∈	PROPN
ejpam-5003	324	34	x	x	SYM
ejpam-5003	324	35	⊛	⊛	NUM
ejpam-5003	324	36	x	x	X
ejpam-5003	324	37	}	}	PUNCT
ejpam-5003	324	38	=	=	SYM
ejpam-5003	325	1	[	[	X
ejpam-5003	325	2	x]∼s	x]∼s	X
ejpam-5003	325	3	⊙	⊙	PROPN
ejpam-5003	326	1	[	[	X
ejpam-5003	326	2	x]∼s	x]∼s	X
ejpam-5003	326	3	which	which	PRON
ejpam-5003	326	4	implies	imply	VERB
ejpam-5003	326	5	[	[	X
ejpam-5003	326	6	x]∼s	x]∼s	ADP
ejpam-5003	326	7	≪∼s	≪∼s	PART
ejpam-5003	326	8	[	[	X
ejpam-5003	326	9	x]∼s	x]∼s	X
ejpam-5003	326	10	.	.	PUNCT
ejpam-5003	327	1	hence	hence	ADV
ejpam-5003	327	2	,	,	PUNCT
ejpam-5003	327	3	(	(	PUNCT
ejpam-5003	327	4	hbn1	hbn1	ADJ
ejpam-5003	327	5	)	)	PUNCT
ejpam-5003	327	6	holds	hold	VERB
ejpam-5003	327	7	for	for	ADP
ejpam-5003	327	8	h	h	NOUN
ejpam-5003	327	9	/	/	SYM
ejpam-5003	327	10	s.	s.	PROPN
ejpam-5003	327	11	for	for	ADP
ejpam-5003	327	12	(	(	PUNCT
ejpam-5003	327	13	hbn2	hbn2	NOUN
ejpam-5003	327	14	)	)	PUNCT
ejpam-5003	327	15	,	,	PUNCT
ejpam-5003	327	16	let	let	VERB
ejpam-5003	327	17	[	[	PUNCT
ejpam-5003	327	18	x]∼s	x]∼s	X
ejpam-5003	327	19	∈	∈	PROPN
ejpam-5003	327	20	h	h	PROPN
ejpam-5003	327	21	/	/	SYM
ejpam-5003	327	22	s.	s.	PROPN
ejpam-5003	327	23	then	then	ADV
ejpam-5003	327	24	,	,	PUNCT
ejpam-5003	327	25	[	[	X
ejpam-5003	327	26	x]∼s	x]∼s	X
ejpam-5003	327	27	⊙	⊙	PROPN
ejpam-5003	328	1	[	[	X
ejpam-5003	328	2	0]∼s	0]∼s	PUNCT
ejpam-5003	328	3	=	=	SYM
ejpam-5003	328	4	{	{	PUNCT
ejpam-5003	328	5	[	[	X
ejpam-5003	328	6	z]∼s	z]∼s	X
ejpam-5003	328	7	|z	|z	X
ejpam-5003	328	8	∈	∈	PROPN
ejpam-5003	328	9	x⊛	x⊛	PROPN
ejpam-5003	328	10	0	0	NUM
ejpam-5003	328	11	}	}	PUNCT
ejpam-5003	328	12	=	=	SYM
ejpam-5003	328	13	{	{	PUNCT
ejpam-5003	329	1	[	[	X
ejpam-5003	329	2	z]∼s	z]∼s	X
ejpam-5003	329	3	|z	|z	X
ejpam-5003	330	1	=	=	PUNCT
ejpam-5003	330	2	x	x	X
ejpam-5003	330	3	}	}	PUNCT
ejpam-5003	330	4	=	=	SYM
ejpam-5003	330	5	{	{	PUNCT
ejpam-5003	330	6	[	[	X
ejpam-5003	330	7	x]∼s	x]∼s	X
ejpam-5003	330	8	}	}	PUNCT
ejpam-5003	330	9	.	.	PUNCT
ejpam-5003	331	1	finally	finally	ADV
ejpam-5003	331	2	,	,	PUNCT
ejpam-5003	331	3	let	let	VERB
ejpam-5003	331	4	[	[	X
ejpam-5003	331	5	w]∼s	w]∼s	X
ejpam-5003	331	6	∈	∈	NOUN
ejpam-5003	331	7	(	(	PUNCT
ejpam-5003	331	8	[	[	X
ejpam-5003	331	9	x]∼s	x]∼s	X
ejpam-5003	331	10	⊙	⊙	PROPN
ejpam-5003	332	1	[	[	X
ejpam-5003	332	2	y]∼s	y]∼s	PROPN
ejpam-5003	332	3	)	)	PUNCT
ejpam-5003	332	4	⊙	⊙	NOUN
ejpam-5003	333	1	[	[	X
ejpam-5003	333	2	z]∼s	z]∼s	X
ejpam-5003	333	3	where	where	SCONJ
ejpam-5003	333	4	[	[	X
ejpam-5003	333	5	x]∼s	x]∼s	X
ejpam-5003	333	6	,	,	PUNCT
ejpam-5003	333	7	[	[	X
ejpam-5003	333	8	y]∼s	y]∼	NOUN
ejpam-5003	333	9	,	,	PUNCT
ejpam-5003	333	10	[	[	X
ejpam-5003	333	11	z]∼s	z]∼s	X
ejpam-5003	333	12	∈	∈	PROPN
ejpam-5003	333	13	h	h	PROPN
ejpam-5003	333	14	/	/	SYM
ejpam-5003	333	15	s.	s.	PROPN
ejpam-5003	333	16	then	then	ADV
ejpam-5003	333	17	there	there	PRON
ejpam-5003	333	18	exists	exist	VERB
ejpam-5003	333	19	u	u	PROPN
ejpam-5003	333	20	∈	∈	PROPN
ejpam-5003	333	21	x⊛y	x⊛y	PROPN
ejpam-5003	334	1	such	such	ADJ
ejpam-5003	334	2	that	that	SCONJ
ejpam-5003	334	3	[	[	X
ejpam-5003	334	4	w]∼s	w]∼s	X
ejpam-5003	334	5	∈	∈	NOUN
ejpam-5003	334	6	[	[	X
ejpam-5003	334	7	u]∼s	u]∼s	PROPN
ejpam-5003	334	8	⊙	⊙	VERB
ejpam-5003	335	1	[	[	X
ejpam-5003	335	2	z]∼s	z]∼s	X
ejpam-5003	335	3	.	.	PUNCT
ejpam-5003	336	1	consequently	consequently	ADV
ejpam-5003	336	2	,	,	PUNCT
ejpam-5003	336	3	there	there	PRON
ejpam-5003	336	4	exists	exist	VERB
ejpam-5003	336	5	w	w	NOUN
ejpam-5003	336	6	′	′	NUM
ejpam-5003	336	7	∈	∈	PROPN
ejpam-5003	336	8	u⊛z	u⊛z	VERB
ejpam-5003	336	9	such	such	ADJ
ejpam-5003	336	10	that	that	SCONJ
ejpam-5003	337	1	[	[	X
ejpam-5003	337	2	w]∼s	w]∼s	X
ejpam-5003	337	3	=	=	PUNCT
ejpam-5003	338	1	[	[	X
ejpam-5003	338	2	w′]∼s	w′]∼s	X
ejpam-5003	338	3	.	.	PUNCT
ejpam-5003	339	1	now	now	ADV
ejpam-5003	339	2	,	,	PUNCT
ejpam-5003	339	3	observe	observe	VERB
ejpam-5003	339	4	that	that	SCONJ
ejpam-5003	339	5	by	by	ADP
ejpam-5003	339	6	(	(	PUNCT
ejpam-5003	339	7	hbn3	hbn3	PROPN
ejpam-5003	339	8	)	)	PUNCT
ejpam-5003	339	9	for	for	ADP
ejpam-5003	339	10	h	h	NOUN
ejpam-5003	339	11	,	,	PUNCT
ejpam-5003	339	12	we	we	PRON
ejpam-5003	339	13	have	have	VERB
ejpam-5003	339	14	w′	w′	PROPN
ejpam-5003	339	15	∈	∈	PROPN
ejpam-5003	339	16	u⊛z	u⊛z	NOUN
ejpam-5003	339	17	⊆	⊆	NUM
ejpam-5003	339	18	(	(	PUNCT
ejpam-5003	340	1	x⊛y)⊛	x⊛y)⊛	NOUN
ejpam-5003	340	2	z	z	NOUN
ejpam-5003	340	3	=	=	SYM
ejpam-5003	340	4	(	(	PUNCT
ejpam-5003	340	5	0	0	NUM
ejpam-5003	340	6	⊛	⊛	NUM
ejpam-5003	340	7	z	z	NOUN
ejpam-5003	340	8	)	)	PUNCT
ejpam-5003	340	9	⊛	⊛	NUM
ejpam-5003	340	10	(	(	PUNCT
ejpam-5003	340	11	y	y	PROPN
ejpam-5003	340	12	⊛	⊛	NUM
ejpam-5003	340	13	x	x	NOUN
ejpam-5003	340	14	)	)	PUNCT
ejpam-5003	340	15	.	.	PUNCT
ejpam-5003	341	1	now	now	ADV
ejpam-5003	341	2	,	,	PUNCT
ejpam-5003	341	3	w′	w′	PROPN
ejpam-5003	341	4	∈	∈	PROPN
ejpam-5003	341	5	a	a	DET
ejpam-5003	341	6	⊛	⊛	NUM
ejpam-5003	341	7	b	b	NUM
ejpam-5003	341	8	where	where	SCONJ
ejpam-5003	341	9	a	a	DET
ejpam-5003	341	10	∈	∈	NOUN
ejpam-5003	341	11	0	0	NUM
ejpam-5003	341	12	⊛	⊛	NUM
ejpam-5003	341	13	z	z	PROPN
ejpam-5003	341	14	and	and	CCONJ
ejpam-5003	341	15	b	b	PROPN
ejpam-5003	341	16	∈	∈	PROPN
ejpam-5003	341	17	y	y	PROPN
ejpam-5003	341	18	⊛	⊛	NUM
ejpam-5003	341	19	x.	x.	NOUN
ejpam-5003	341	20	this	this	PRON
ejpam-5003	341	21	means	mean	VERB
ejpam-5003	341	22	that	that	SCONJ
ejpam-5003	341	23	[	[	X
ejpam-5003	341	24	w′]∼s	w′]∼s	X
ejpam-5003	341	25	∈	∈	PROPN
ejpam-5003	341	26	{	{	PUNCT
ejpam-5003	341	27	[	[	X
ejpam-5003	341	28	k]∼s	k]∼s	X
ejpam-5003	341	29	|k	|k	VERB
ejpam-5003	341	30	∈	∈	PROPN
ejpam-5003	341	31	a	a	DET
ejpam-5003	341	32	⊛	⊛	NUM
ejpam-5003	341	33	b	b	NOUN
ejpam-5003	341	34	}	}	PUNCT
ejpam-5003	341	35	=	=	NOUN
ejpam-5003	342	1	[	[	X
ejpam-5003	342	2	a]∼s	a]∼s	X
ejpam-5003	342	3	⊙	⊙	NOUN
ejpam-5003	343	1	[	[	X
ejpam-5003	343	2	b]∼s	b]∼s	PROPN
ejpam-5003	343	3	.	.	PUNCT
ejpam-5003	344	1	notice	notice	VERB
ejpam-5003	344	2	that	that	SCONJ
ejpam-5003	344	3	a	a	DET
ejpam-5003	344	4	∈	∈	PROPN
ejpam-5003	344	5	0	0	NUM
ejpam-5003	344	6	⊛	⊛	NUM
ejpam-5003	344	7	z	z	PROPN
ejpam-5003	344	8	and	and	CCONJ
ejpam-5003	344	9	b	b	PROPN
ejpam-5003	344	10	∈	∈	PROPN
ejpam-5003	344	11	y	y	PROPN
ejpam-5003	344	12	⊛	⊛	NUM
ejpam-5003	344	13	x	x	AUX
ejpam-5003	344	14	mean	mean	VERB
ejpam-5003	344	15	[	[	X
ejpam-5003	344	16	a]∼s	a]∼s	X
ejpam-5003	344	17	∈	∈	NOUN
ejpam-5003	344	18	{	{	PUNCT
ejpam-5003	345	1	[	[	X
ejpam-5003	345	2	l]∼s	l]∼s	X
ejpam-5003	345	3	|l	|l	PROPN
ejpam-5003	345	4	∈	∈	PROPN
ejpam-5003	345	5	0	0	PUNCT
ejpam-5003	345	6	⊛	⊛	PROPN
ejpam-5003	345	7	z	z	PROPN
ejpam-5003	345	8	}	}	PUNCT
ejpam-5003	345	9	=	=	SYM
ejpam-5003	346	1	[	[	X
ejpam-5003	346	2	0]∼s	0]∼s	NUM
ejpam-5003	346	3	⊙	⊙	NOUN
ejpam-5003	347	1	[	[	X
ejpam-5003	347	2	z]∼s	z]∼s	X
ejpam-5003	347	3	and	and	CCONJ
ejpam-5003	347	4	[	[	X
ejpam-5003	347	5	b]∼s	b]∼s	X
ejpam-5003	347	6	∈	∈	X
ejpam-5003	347	7	{	{	PUNCT
ejpam-5003	347	8	[	[	X
ejpam-5003	347	9	m]∼s	m]∼s	NOUN
ejpam-5003	347	10	|m	|m	NOUN
ejpam-5003	347	11	∈	∈	PROPN
ejpam-5003	347	12	y	y	PROPN
ejpam-5003	347	13	⊛	⊛	NUM
ejpam-5003	347	14	x	x	X
ejpam-5003	347	15	}	}	PUNCT
ejpam-5003	347	16	=	=	SYM
ejpam-5003	348	1	[	[	X
ejpam-5003	348	2	y]∼s	y]∼s	X
ejpam-5003	348	3	⊙	⊙	NOUN
ejpam-5003	349	1	[	[	X
ejpam-5003	349	2	x]∼s	x]∼s	X
ejpam-5003	349	3	,	,	PUNCT
ejpam-5003	349	4	respectively	respectively	ADV
ejpam-5003	349	5	.	.	PUNCT
ejpam-5003	350	1	thus	thus	ADV
ejpam-5003	350	2	,	,	PUNCT
ejpam-5003	350	3	[	[	X
ejpam-5003	350	4	w]∼s	w]∼s	X
ejpam-5003	350	5	=	=	PUNCT
ejpam-5003	351	1	[	[	X
ejpam-5003	351	2	w′]∼s	w′]∼s	X
ejpam-5003	351	3	∈	∈	PROPN
ejpam-5003	352	1	[	[	X
ejpam-5003	352	2	a]∼s	a]∼s	X
ejpam-5003	352	3	⊙	⊙	NOUN
ejpam-5003	353	1	[	[	X
ejpam-5003	353	2	b]∼s	b]∼s	PROPN
ejpam-5003	353	3	⊆	⊆	NUM
ejpam-5003	353	4	(	(	PUNCT
ejpam-5003	353	5	[	[	X
ejpam-5003	353	6	0]∼s	0]∼s	NUM
ejpam-5003	353	7	⊙	⊙	NOUN
ejpam-5003	354	1	[	[	X
ejpam-5003	354	2	z]∼s	z]∼s	X
ejpam-5003	354	3	)	)	PUNCT
ejpam-5003	354	4	⊙	⊙	NOUN
ejpam-5003	354	5	(	(	PUNCT
ejpam-5003	354	6	[	[	X
ejpam-5003	354	7	y]∼s	y]∼s	X
ejpam-5003	354	8	⊙	⊙	NOUN
ejpam-5003	355	1	[	[	X
ejpam-5003	355	2	x]∼s	x]∼s	PROPN
ejpam-5003	355	3	)	)	PUNCT
ejpam-5003	355	4	.	.	PUNCT
ejpam-5003	356	1	since	since	SCONJ
ejpam-5003	356	2	[	[	X
ejpam-5003	356	3	w]∼s	w]∼s	NOUN
ejpam-5003	356	4	is	be	AUX
ejpam-5003	356	5	arbitrary	arbitrary	ADJ
ejpam-5003	356	6	,	,	PUNCT
ejpam-5003	356	7	it	it	PRON
ejpam-5003	356	8	follows	follow	VERB
ejpam-5003	356	9	that	that	SCONJ
ejpam-5003	356	10	(	(	PUNCT
ejpam-5003	356	11	[	[	X
ejpam-5003	356	12	x]∼s	x]∼s	X
ejpam-5003	356	13	⊙	⊙	PROPN
ejpam-5003	357	1	[	[	X
ejpam-5003	357	2	y]∼s	y]∼s	PROPN
ejpam-5003	357	3	)	)	PUNCT
ejpam-5003	357	4	⊙	⊙	NOUN
ejpam-5003	358	1	[	[	X
ejpam-5003	358	2	z]∼s	z]∼s	NOUN
ejpam-5003	358	3	⊆	⊆	NUM
ejpam-5003	358	4	(	(	PUNCT
ejpam-5003	358	5	[	[	X
ejpam-5003	358	6	0]∼s	0]∼s	NUM
ejpam-5003	358	7	⊙	⊙	NOUN
ejpam-5003	359	1	[	[	X
ejpam-5003	359	2	z]∼s	z]∼s	X
ejpam-5003	359	3	)	)	PUNCT
ejpam-5003	359	4	⊙	⊙	NOUN
ejpam-5003	359	5	(	(	PUNCT
ejpam-5003	359	6	[	[	X
ejpam-5003	359	7	y]∼s	y]∼s	X
ejpam-5003	359	8	⊙	⊙	NOUN
ejpam-5003	360	1	[	[	X
ejpam-5003	360	2	x]∼s	x]∼s	PROPN
ejpam-5003	360	3	)	)	PUNCT
ejpam-5003	360	4	.	.	PUNCT
ejpam-5003	361	1	next	next	ADV
ejpam-5003	361	2	,	,	PUNCT
ejpam-5003	361	3	let	let	VERB
ejpam-5003	361	4	[	[	X
ejpam-5003	361	5	v]∼s	v]∼s	ADJ
ejpam-5003	361	6	∈	∈	NOUN
ejpam-5003	361	7	(	(	PUNCT
ejpam-5003	361	8	[	[	X
ejpam-5003	361	9	0]∼s	0]∼s	X
ejpam-5003	361	10	⊙	⊙	NOUN
ejpam-5003	362	1	[	[	X
ejpam-5003	362	2	z]∼s	z]∼s	X
ejpam-5003	362	3	)	)	PUNCT
ejpam-5003	362	4	⊙	⊙	NOUN
ejpam-5003	362	5	(	(	PUNCT
ejpam-5003	362	6	[	[	X
ejpam-5003	362	7	y]∼s	y]∼s	X
ejpam-5003	362	8	⊙	⊙	NOUN
ejpam-5003	363	1	[	[	X
ejpam-5003	363	2	x]∼s	x]∼s	X
ejpam-5003	363	3	)	)	PUNCT
ejpam-5003	363	4	where	where	SCONJ
ejpam-5003	363	5	[	[	X
ejpam-5003	363	6	x]∼s	x]∼s	X
ejpam-5003	363	7	,	,	PUNCT
ejpam-5003	363	8	[	[	X
ejpam-5003	363	9	y]∼s	y]∼	NOUN
ejpam-5003	363	10	,	,	PUNCT
ejpam-5003	363	11	[	[	X
ejpam-5003	363	12	z]∼s	z]∼s	X
ejpam-5003	363	13	∈	∈	PROPN
ejpam-5003	363	14	h	h	PROPN
ejpam-5003	363	15	/	/	SYM
ejpam-5003	363	16	s.	s.	PROPN
ejpam-5003	363	17	then	then	ADV
ejpam-5003	363	18	there	there	PRON
ejpam-5003	363	19	exist	exist	VERB
ejpam-5003	363	20	a	a	DET
ejpam-5003	363	21	∈	∈	NOUN
ejpam-5003	363	22	0	0	NUM
ejpam-5003	363	23	⊛	⊛	NUM
ejpam-5003	363	24	z	z	PROPN
ejpam-5003	363	25	and	and	CCONJ
ejpam-5003	363	26	b	b	PROPN
ejpam-5003	363	27	∈	∈	PROPN
ejpam-5003	363	28	y⊛x	y⊛x	NUM
ejpam-5003	364	1	such	such	ADJ
ejpam-5003	364	2	that	that	SCONJ
ejpam-5003	364	3	[	[	X
ejpam-5003	364	4	v]∼s	v]∼s	NOUN
ejpam-5003	364	5	∈	∈	PROPN
ejpam-5003	365	1	[	[	X
ejpam-5003	365	2	a]∼s	a]∼s	X
ejpam-5003	365	3	⊙	⊙	NOUN
ejpam-5003	366	1	[	[	X
ejpam-5003	366	2	b]∼s	b]∼s	PROPN
ejpam-5003	366	3	.	.	PUNCT
ejpam-5003	367	1	this	this	PRON
ejpam-5003	367	2	implies	imply	VERB
ejpam-5003	367	3	that	that	SCONJ
ejpam-5003	367	4	there	there	PRON
ejpam-5003	367	5	exists	exist	VERB
ejpam-5003	367	6	v′	v′	NOUN
ejpam-5003	367	7	∈	∈	PROPN
ejpam-5003	367	8	a⊛b	a⊛b	VERB
ejpam-5003	367	9	such	such	ADJ
ejpam-5003	367	10	that	that	SCONJ
ejpam-5003	368	1	[	[	X
ejpam-5003	368	2	v]∼s	v]∼s	NOUN
ejpam-5003	368	3	=	=	PUNCT
ejpam-5003	369	1	[	[	X
ejpam-5003	369	2	v′]∼s	v′]∼s	PROPN
ejpam-5003	369	3	.	.	PUNCT
ejpam-5003	370	1	now	now	ADV
ejpam-5003	370	2	,	,	PUNCT
ejpam-5003	370	3	using	use	VERB
ejpam-5003	370	4	(	(	PUNCT
ejpam-5003	370	5	hbn3	hbn3	PROPN
ejpam-5003	370	6	)	)	PUNCT
ejpam-5003	370	7	forh	forh	NOUN
ejpam-5003	370	8	,	,	PUNCT
ejpam-5003	370	9	we	we	PRON
ejpam-5003	370	10	have	have	VERB
ejpam-5003	370	11	v′	v′	NOUN
ejpam-5003	370	12	∈	∈	PRON
ejpam-5003	370	13	a⊛b	a⊛b	PROPN
ejpam-5003	370	14	⊆	⊆	NUM
ejpam-5003	370	15	(	(	PUNCT
ejpam-5003	370	16	0⊛z)⊛(y⊛x	0⊛z)⊛(y⊛x	PROPN
ejpam-5003	370	17	)	)	PUNCT
ejpam-5003	370	18	=	=	SYM
ejpam-5003	370	19	(	(	PUNCT
ejpam-5003	370	20	x⊛y)⊛z	x⊛y)⊛z	PROPN
ejpam-5003	370	21	.	.	PUNCT
ejpam-5003	371	1	this	this	PRON
ejpam-5003	371	2	means	mean	VERB
ejpam-5003	371	3	that	that	SCONJ
ejpam-5003	371	4	v′	v′	PROPN
ejpam-5003	371	5	∈	∈	PROPN
ejpam-5003	371	6	d⊛z	d⊛z	PROPN
ejpam-5003	371	7	where	where	SCONJ
ejpam-5003	371	8	d	d	PROPN
ejpam-5003	371	9	∈	∈	PROPN
ejpam-5003	371	10	x⊛y	x⊛y	PROPN
ejpam-5003	371	11	.	.	PUNCT
ejpam-5003	372	1	thus	thus	ADV
ejpam-5003	372	2	,	,	PUNCT
ejpam-5003	372	3	[	[	X
ejpam-5003	372	4	v′]∼s	v′]∼s	PROPN
ejpam-5003	372	5	∈	∈	PROPN
ejpam-5003	372	6	{	{	PUNCT
ejpam-5003	372	7	[	[	X
ejpam-5003	372	8	n]∼s	n]∼s	X
ejpam-5003	372	9	|n	|n	X
ejpam-5003	372	10	∈	∈	PROPN
ejpam-5003	372	11	d⊛z	d⊛z	PROPN
ejpam-5003	372	12	}	}	PUNCT
ejpam-5003	372	13	=	=	PUNCT
ejpam-5003	373	1	[	[	X
ejpam-5003	373	2	d]∼s⊙[z]∼s	d]∼s⊙[z]∼s	X
ejpam-5003	373	3	.	.	PUNCT
ejpam-5003	374	1	but	but	CCONJ
ejpam-5003	374	2	d	d	X
ejpam-5003	374	3	∈	∈	PROPN
ejpam-5003	374	4	x	x	SYM
ejpam-5003	374	5	⊛	⊛	NUM
ejpam-5003	374	6	y	y	PROPN
ejpam-5003	374	7	means	mean	VERB
ejpam-5003	374	8	that	that	SCONJ
ejpam-5003	375	1	[	[	X
ejpam-5003	375	2	d]∼s	d]∼s	ADP
ejpam-5003	375	3	∈	∈	NOUN
ejpam-5003	375	4	{	{	PUNCT
ejpam-5003	375	5	[	[	X
ejpam-5003	375	6	t]∼s	t]∼s	NUM
ejpam-5003	375	7	|t	|t	NOUN
ejpam-5003	375	8	∈	∈	PROPN
ejpam-5003	375	9	x	x	SYM
ejpam-5003	375	10	⊛	⊛	NUM
ejpam-5003	375	11	y	y	NOUN
ejpam-5003	375	12	}	}	PUNCT
ejpam-5003	375	13	=	=	SYM
ejpam-5003	376	1	[	[	X
ejpam-5003	376	2	x]∼s	x]∼s	X
ejpam-5003	376	3	⊙	⊙	PROPN
ejpam-5003	377	1	[	[	X
ejpam-5003	377	2	y]∼s	y]∼s	PROPN
ejpam-5003	377	3	.	.	PUNCT
ejpam-5003	378	1	hence	hence	ADV
ejpam-5003	378	2	,	,	PUNCT
ejpam-5003	378	3	[	[	X
ejpam-5003	378	4	v]∼s	v]∼s	NOUN
ejpam-5003	378	5	=	=	PUNCT
ejpam-5003	379	1	[	[	X
ejpam-5003	379	2	v′]∼s	v′]∼s	PROPN
ejpam-5003	379	3	∈	∈	PROPN
ejpam-5003	380	1	[	[	X
ejpam-5003	380	2	d]∼s	d]∼s	PRON
ejpam-5003	380	3	⊙	⊙	NOUN
ejpam-5003	381	1	[	[	X
ejpam-5003	381	2	z]∼s	z]∼s	NOUN
ejpam-5003	381	3	⊆	⊆	NUM
ejpam-5003	381	4	(	(	PUNCT
ejpam-5003	381	5	[	[	X
ejpam-5003	381	6	x]∼s	x]∼s	X
ejpam-5003	381	7	⊙	⊙	PROPN
ejpam-5003	382	1	[	[	X
ejpam-5003	382	2	y]∼s	y]∼s	PROPN
ejpam-5003	382	3	)	)	PUNCT
ejpam-5003	382	4	⊙	⊙	NOUN
ejpam-5003	383	1	[	[	X
ejpam-5003	383	2	z]∼s	z]∼s	X
ejpam-5003	383	3	.	.	PUNCT
ejpam-5003	384	1	thus	thus	ADV
ejpam-5003	384	2	,	,	PUNCT
ejpam-5003	384	3	(	(	PUNCT
ejpam-5003	384	4	[	[	X
ejpam-5003	384	5	0]∼s	0]∼s	X
ejpam-5003	384	6	⊙	⊙	NOUN
ejpam-5003	385	1	[	[	X
ejpam-5003	385	2	z]∼s	z]∼s	X
ejpam-5003	385	3	)	)	PUNCT
ejpam-5003	385	4	⊙	⊙	NOUN
ejpam-5003	385	5	(	(	PUNCT
ejpam-5003	385	6	[	[	X
ejpam-5003	385	7	y]∼s	y]∼s	X
ejpam-5003	385	8	⊙	⊙	NOUN
ejpam-5003	386	1	[	[	X
ejpam-5003	386	2	x]∼s	x]∼s	X
ejpam-5003	386	3	)	)	PUNCT
ejpam-5003	387	1	⊆	⊆	NUM
ejpam-5003	387	2	l.r	l.r	PROPN
ejpam-5003	387	3	.	.	PROPN
ejpam-5003	387	4	cabardo	cabardo	PROPN
ejpam-5003	387	5	,	,	PUNCT
ejpam-5003	387	6	g.	g.	PROPN
ejpam-5003	387	7	petalcorin	petalcorin	PROPN
ejpam-5003	387	8	/	/	SYM
ejpam-5003	387	9	eur	eur	PROPN
ejpam-5003	387	10	.	.	PUNCT
ejpam-5003	388	1	j.	j.	PROPN
ejpam-5003	388	2	pure	pure	PROPN
ejpam-5003	388	3	appl	appl	PROPN
ejpam-5003	388	4	.	.	PROPN
ejpam-5003	388	5	math	math	PROPN
ejpam-5003	388	6	,	,	PUNCT
ejpam-5003	388	7	17	17	NUM
ejpam-5003	388	8	(	(	PUNCT
ejpam-5003	388	9	1	1	NUM
ejpam-5003	388	10	)	)	PUNCT
ejpam-5003	388	11	(	(	PUNCT
ejpam-5003	388	12	2024	2024	NUM
ejpam-5003	388	13	)	)	PUNCT
ejpam-5003	388	14	,	,	PUNCT
ejpam-5003	388	15	222	222	NUM
ejpam-5003	388	16	-	-	SYM
ejpam-5003	388	17	242	242	NUM
ejpam-5003	388	18	235	235	NUM
ejpam-5003	388	19	(	(	PUNCT
ejpam-5003	388	20	[	[	X
ejpam-5003	388	21	x]∼s	x]∼s	X
ejpam-5003	388	22	⊙	⊙	PROPN
ejpam-5003	389	1	[	[	X
ejpam-5003	389	2	y]∼s	y]∼s	PROPN
ejpam-5003	389	3	)	)	PUNCT
ejpam-5003	389	4	⊙	⊙	NOUN
ejpam-5003	390	1	[	[	X
ejpam-5003	390	2	z]∼s	z]∼s	X
ejpam-5003	390	3	.	.	PUNCT
ejpam-5003	391	1	hence	hence	ADV
ejpam-5003	391	2	,	,	PUNCT
ejpam-5003	391	3	(	(	PUNCT
ejpam-5003	391	4	[	[	X
ejpam-5003	391	5	x]∼s	x]∼s	X
ejpam-5003	391	6	⊙	⊙	PROPN
ejpam-5003	392	1	[	[	X
ejpam-5003	392	2	y]∼s	y]∼s	PROPN
ejpam-5003	392	3	)	)	PUNCT
ejpam-5003	392	4	⊙	⊙	NOUN
ejpam-5003	393	1	[	[	X
ejpam-5003	393	2	z]∼s	z]∼s	X
ejpam-5003	393	3	=	=	SYM
ejpam-5003	393	4	(	(	PUNCT
ejpam-5003	393	5	[	[	X
ejpam-5003	393	6	0]∼s	0]∼s	X
ejpam-5003	393	7	⊙	⊙	NOUN
ejpam-5003	394	1	[	[	X
ejpam-5003	394	2	z]∼s	z]∼s	X
ejpam-5003	394	3	)	)	PUNCT
ejpam-5003	394	4	⊙	⊙	NOUN
ejpam-5003	394	5	(	(	PUNCT
ejpam-5003	394	6	[	[	X
ejpam-5003	394	7	y]∼s	y]∼s	X
ejpam-5003	394	8	⊙	⊙	NOUN
ejpam-5003	395	1	[	[	X
ejpam-5003	395	2	x]∼s	x]∼s	X
ejpam-5003	395	3	)	)	PUNCT
ejpam-5003	395	4	for	for	ADP
ejpam-5003	395	5	all	all	PRON
ejpam-5003	395	6	[	[	X
ejpam-5003	395	7	x]∼s	x]∼s	X
ejpam-5003	395	8	,	,	PUNCT
ejpam-5003	395	9	[	[	X
ejpam-5003	395	10	y]∼s	y]∼	NOUN
ejpam-5003	395	11	,	,	PUNCT
ejpam-5003	395	12	[	[	X
ejpam-5003	395	13	z]∼s	z]∼s	X
ejpam-5003	395	14	∈	∈	PROPN
ejpam-5003	395	15	h	h	PROPN
ejpam-5003	395	16	/	/	SYM
ejpam-5003	395	17	s	s	AUX
ejpam-5003	395	18	holding	hold	VERB
ejpam-5003	395	19	(	(	PUNCT
ejpam-5003	395	20	hbn3	hbn3	PROPN
ejpam-5003	395	21	)	)	PUNCT
ejpam-5003	395	22	.	.	PUNCT
ejpam-5003	396	1	therefore	therefore	ADV
ejpam-5003	396	2	,	,	PUNCT
ejpam-5003	396	3	(	(	PUNCT
ejpam-5003	396	4	h	h	X
ejpam-5003	396	5	/	/	SYM
ejpam-5003	396	6	s,⊙	s,⊙	PROPN
ejpam-5003	396	7	,	,	PUNCT
ejpam-5003	396	8	[	[	X
ejpam-5003	396	9	0]∼s	0]∼s	NUM
ejpam-5003	396	10	)	)	PUNCT
ejpam-5003	396	11	is	be	AUX
ejpam-5003	396	12	a	a	DET
ejpam-5003	396	13	hyper	hyper	ADJ
ejpam-5003	396	14	bn	bn	NOUN
ejpam-5003	396	15	-algebra	-algebra	NOUN
ejpam-5003	396	16	.	.	PUNCT
ejpam-5003	397	1	let	let	VERB
ejpam-5003	397	2	us	we	PRON
ejpam-5003	397	3	illustrate	illustrate	VERB
ejpam-5003	397	4	the	the	DET
ejpam-5003	397	5	construction	construction	NOUN
ejpam-5003	397	6	of	of	ADP
ejpam-5003	397	7	the	the	DET
ejpam-5003	397	8	quotient	quotient	NOUN
ejpam-5003	397	9	structure	structure	NOUN
ejpam-5003	397	10	of	of	ADP
ejpam-5003	397	11	a	a	DET
ejpam-5003	397	12	hyper	hyper	ADJ
ejpam-5003	397	13	bn	bn	ADJ
ejpam-5003	397	14	-algebra	-algebra	NOUN
ejpam-5003	397	15	via	via	ADP
ejpam-5003	397	16	reflexive	reflexive	ADJ
ejpam-5003	397	17	normal	normal	ADJ
ejpam-5003	397	18	hyper	hyper	ADJ
ejpam-5003	397	19	subbn	subbn	NOUN
ejpam-5003	397	20	-algebra	-algebra	PROPN
ejpam-5003	397	21	.	.	PUNCT
ejpam-5003	398	1	example	example	NOUN
ejpam-5003	398	2	20	20	NUM
ejpam-5003	398	3	.	.	PUNCT
ejpam-5003	399	1	let	let	VERB
ejpam-5003	399	2	h	h	NOUN
ejpam-5003	399	3	=	=	PUNCT
ejpam-5003	399	4	{	{	PUNCT
ejpam-5003	399	5	0	0	NUM
ejpam-5003	399	6	,	,	PUNCT
ejpam-5003	399	7	1	1	NUM
ejpam-5003	399	8	,	,	PUNCT
ejpam-5003	399	9	2	2	NUM
ejpam-5003	399	10	,	,	PUNCT
ejpam-5003	399	11	3	3	NUM
ejpam-5003	399	12	,	,	PUNCT
ejpam-5003	399	13	4	4	NUM
ejpam-5003	399	14	}	}	PUNCT
ejpam-5003	399	15	be	be	AUX
ejpam-5003	399	16	the	the	DET
ejpam-5003	399	17	hyper	hyper	ADJ
ejpam-5003	399	18	bn	bn	ADJ
ejpam-5003	399	19	-algebra	-algebra	NOUN
ejpam-5003	399	20	in	in	ADP
ejpam-5003	399	21	example	example	NOUN
ejpam-5003	399	22	9	9	NUM
ejpam-5003	399	23	.	.	PUNCT
ejpam-5003	400	1	let	let	VERB
ejpam-5003	400	2	s	s	VERB
ejpam-5003	400	3	=	=	X
ejpam-5003	400	4	{	{	PUNCT
ejpam-5003	400	5	0	0	NUM
ejpam-5003	400	6	,	,	PUNCT
ejpam-5003	400	7	3	3	NUM
ejpam-5003	400	8	}	}	PUNCT
ejpam-5003	400	9	.	.	PUNCT
ejpam-5003	401	1	then	then	ADV
ejpam-5003	401	2	it	it	PRON
ejpam-5003	401	3	has	have	AUX
ejpam-5003	401	4	been	be	AUX
ejpam-5003	401	5	shown	show	VERB
ejpam-5003	401	6	that	that	SCONJ
ejpam-5003	401	7	s	s	VERB
ejpam-5003	401	8	is	be	AUX
ejpam-5003	401	9	a	a	DET
ejpam-5003	401	10	reflexive	reflexive	ADJ
ejpam-5003	401	11	normal	normal	ADJ
ejpam-5003	401	12	hyper	hyper	ADJ
ejpam-5003	401	13	subbn	subbn	NOUN
ejpam-5003	401	14	-algebra	-algebra	PROPN
ejpam-5003	401	15	of	of	ADP
ejpam-5003	401	16	h.	h.	PROPN
ejpam-5003	401	17	now	now	ADV
ejpam-5003	401	18	,	,	PUNCT
ejpam-5003	401	19	[	[	X
ejpam-5003	401	20	0]∼s	0]∼s	PUNCT
ejpam-5003	401	21	=	=	SYM
ejpam-5003	401	22	{	{	PUNCT
ejpam-5003	401	23	0	0	NUM
ejpam-5003	401	24	,	,	PUNCT
ejpam-5003	401	25	3	3	NUM
ejpam-5003	401	26	}	}	PUNCT
ejpam-5003	401	27	=	=	PUNCT
ejpam-5003	402	1	[	[	X
ejpam-5003	402	2	3]∼s	3]∼s	NUM
ejpam-5003	402	3	,	,	PUNCT
ejpam-5003	402	4	[	[	X
ejpam-5003	402	5	1]∼s	1]∼s	NUM
ejpam-5003	402	6	=	=	SYM
ejpam-5003	402	7	{	{	PUNCT
ejpam-5003	402	8	1	1	NUM
ejpam-5003	402	9	,	,	PUNCT
ejpam-5003	402	10	2	2	NUM
ejpam-5003	402	11	}	}	PUNCT
ejpam-5003	402	12	=	=	PUNCT
ejpam-5003	403	1	[	[	X
ejpam-5003	403	2	2]∼s	2]∼s	NUM
ejpam-5003	403	3	,	,	PUNCT
ejpam-5003	403	4	and	and	CCONJ
ejpam-5003	404	1	[	[	X
ejpam-5003	404	2	4]∼s	4]∼s	PUNCT
ejpam-5003	404	3	=	=	SYM
ejpam-5003	404	4	{	{	PUNCT
ejpam-5003	404	5	4	4	NUM
ejpam-5003	404	6	}	}	PUNCT
ejpam-5003	404	7	.	.	PUNCT
ejpam-5003	405	1	hence	hence	ADV
ejpam-5003	405	2	,	,	PUNCT
ejpam-5003	405	3	h	h	PROPN
ejpam-5003	405	4	/	/	SYM
ejpam-5003	405	5	s	s	NOUN
ejpam-5003	405	6	=	=	PUNCT
ejpam-5003	405	7	{	{	PUNCT
ejpam-5003	406	1	[	[	X
ejpam-5003	406	2	0]∼s	0]∼s	NUM
ejpam-5003	406	3	,	,	PUNCT
ejpam-5003	407	1	[	[	X
ejpam-5003	407	2	1]∼s	1]∼s	NUM
ejpam-5003	407	3	,	,	PUNCT
ejpam-5003	407	4	[	[	X
ejpam-5003	407	5	4]∼s	4]∼s	X
ejpam-5003	407	6	}	}	PUNCT
ejpam-5003	407	7	and	and	CCONJ
ejpam-5003	407	8	the	the	DET
ejpam-5003	407	9	hyperoperation	hyperoperation	NOUN
ejpam-5003	407	10	⊙	⊙	PROPN
ejpam-5003	407	11	is	be	AUX
ejpam-5003	407	12	defined	define	VERB
ejpam-5003	407	13	by	by	ADP
ejpam-5003	407	14	the	the	DET
ejpam-5003	407	15	following	following	ADJ
ejpam-5003	407	16	cayley	cayley	ADJ
ejpam-5003	407	17	table	table	NOUN
ejpam-5003	407	18	:	:	PUNCT
ejpam-5003	407	19	⊙	⊙	NOUN
ejpam-5003	408	1	[	[	X
ejpam-5003	408	2	0]∼s	0]∼s	PUNCT
ejpam-5003	409	1	[	[	X
ejpam-5003	409	2	1]∼s	1]∼s	NUM
ejpam-5003	410	1	[	[	X
ejpam-5003	410	2	4]∼s	4]∼s	PUNCT
ejpam-5003	411	1	[	[	X
ejpam-5003	411	2	0]∼s	0]∼s	PUNCT
ejpam-5003	411	3	{	{	PUNCT
ejpam-5003	411	4	[	[	X
ejpam-5003	411	5	0]∼s	0]∼s	NUM
ejpam-5003	411	6	}	}	PUNCT
ejpam-5003	411	7	{	{	PUNCT
ejpam-5003	411	8	[	[	NOUN
ejpam-5003	411	9	1]∼s	1]∼s	NUM
ejpam-5003	411	10	}	}	PUNCT
ejpam-5003	411	11	{	{	PUNCT
ejpam-5003	411	12	[	[	X
ejpam-5003	411	13	4]∼s	4]∼s	PRON
ejpam-5003	411	14	}	}	PUNCT
ejpam-5003	411	15	[	[	X
ejpam-5003	411	16	1]∼s	1]∼s	NUM
ejpam-5003	411	17	{	{	PUNCT
ejpam-5003	411	18	[	[	NOUN
ejpam-5003	411	19	1]∼s	1]∼s	NUM
ejpam-5003	411	20	}	}	PUNCT
ejpam-5003	411	21	{	{	PUNCT
ejpam-5003	411	22	[	[	NOUN
ejpam-5003	411	23	0]∼s	0]∼s	NUM
ejpam-5003	411	24	}	}	PUNCT
ejpam-5003	411	25	{	{	PUNCT
ejpam-5003	411	26	[	[	X
ejpam-5003	411	27	4]∼s	4]∼s	PRON
ejpam-5003	411	28	}	}	PUNCT
ejpam-5003	411	29	[	[	X
ejpam-5003	411	30	4]∼s	4]∼s	NUM
ejpam-5003	411	31	{	{	PUNCT
ejpam-5003	411	32	[	[	X
ejpam-5003	411	33	4]∼s	4]∼s	NOUN
ejpam-5003	411	34	}	}	PUNCT
ejpam-5003	411	35	{	{	PUNCT
ejpam-5003	411	36	[	[	X
ejpam-5003	411	37	4]∼s	4]∼s	NOUN
ejpam-5003	411	38	}	}	PUNCT
ejpam-5003	411	39	{	{	PUNCT
ejpam-5003	411	40	[	[	NOUN
ejpam-5003	411	41	0]∼s	0]∼s	NUM
ejpam-5003	411	42	}	}	PUNCT
ejpam-5003	411	43	by	by	ADP
ejpam-5003	411	44	routine	routine	ADJ
ejpam-5003	411	45	calculations	calculation	NOUN
ejpam-5003	411	46	,	,	PUNCT
ejpam-5003	411	47	(	(	PUNCT
ejpam-5003	411	48	h	h	X
ejpam-5003	411	49	/	/	SYM
ejpam-5003	411	50	s,⊙	s,⊙	PROPN
ejpam-5003	411	51	,	,	PUNCT
ejpam-5003	411	52	[	[	X
ejpam-5003	411	53	0]∼s	0]∼s	NUM
ejpam-5003	411	54	)	)	PUNCT
ejpam-5003	411	55	is	be	AUX
ejpam-5003	411	56	a	a	DET
ejpam-5003	411	57	hyper	hyper	ADJ
ejpam-5003	411	58	bn	bn	NOUN
ejpam-5003	411	59	-algebra	-algebra	NOUN
ejpam-5003	411	60	.	.	PUNCT
ejpam-5003	412	1	4.2	4.2	NUM
ejpam-5003	412	2	.	.	PUNCT
ejpam-5003	413	1	quotient	quotient	VERB
ejpam-5003	413	2	hyper	hyper	PROPN
ejpam-5003	413	3	bn	bn	NOUN
ejpam-5003	413	4	-	-	PUNCT
ejpam-5003	413	5	algebra	algebra	NOUN
ejpam-5003	413	6	via	via	ADP
ejpam-5003	413	7	congruence	congruence	PROPN
ejpam-5003	413	8	relation	relation	NOUN
ejpam-5003	413	9	now	now	ADV
ejpam-5003	413	10	,	,	PUNCT
ejpam-5003	413	11	we	we	PRON
ejpam-5003	413	12	will	will	AUX
ejpam-5003	413	13	construct	construct	VERB
ejpam-5003	413	14	the	the	DET
ejpam-5003	413	15	quotient	quotient	NOUN
ejpam-5003	413	16	hyper	hyper	PROPN
ejpam-5003	413	17	bn	bn	PROPN
ejpam-5003	413	18	-algebra	-algebra	NOUN
ejpam-5003	413	19	via	via	ADP
ejpam-5003	413	20	congruence	congruence	PROPN
ejpam-5003	413	21	relation	relation	NOUN
ejpam-5003	413	22	.	.	PUNCT
ejpam-5003	414	1	also	also	ADV
ejpam-5003	414	2	,	,	PUNCT
ejpam-5003	414	3	we	we	PRON
ejpam-5003	414	4	will	will	AUX
ejpam-5003	414	5	show	show	VERB
ejpam-5003	414	6	the	the	DET
ejpam-5003	414	7	relationship	relationship	NOUN
ejpam-5003	414	8	between	between	ADP
ejpam-5003	414	9	the	the	DET
ejpam-5003	414	10	construction	construction	NOUN
ejpam-5003	414	11	of	of	ADP
ejpam-5003	414	12	quotient	quotient	NOUN
ejpam-5003	414	13	hyper	hyper	PROPN
ejpam-5003	414	14	bn	bn	PROPN
ejpam-5003	414	15	-algebra	-algebra	PROPN
ejpam-5003	414	16	in	in	ADP
ejpam-5003	414	17	4.1	4.1	NUM
ejpam-5003	414	18	and	and	CCONJ
ejpam-5003	414	19	the	the	DET
ejpam-5003	414	20	construction	construction	NOUN
ejpam-5003	414	21	here	here	ADV
ejpam-5003	414	22	.	.	PUNCT
ejpam-5003	415	1	definition	definition	NOUN
ejpam-5003	415	2	15	15	NUM
ejpam-5003	415	3	.	.	PUNCT
ejpam-5003	416	1	let	let	VERB
ejpam-5003	416	2	θ	θ	NOUN
ejpam-5003	416	3	be	be	AUX
ejpam-5003	416	4	an	an	DET
ejpam-5003	416	5	equivalence	equivalence	NOUN
ejpam-5003	416	6	relation	relation	NOUN
ejpam-5003	416	7	on	on	ADP
ejpam-5003	416	8	a	a	DET
ejpam-5003	416	9	hyper	hyper	ADJ
ejpam-5003	416	10	bn	bn	NOUN
ejpam-5003	416	11	-algebra	-algebra	PROPN
ejpam-5003	416	12	h	h	NOUN
ejpam-5003	416	13	and	and	CCONJ
ejpam-5003	416	14	∅	∅	NOUN
ejpam-5003	416	15	̸=	̸=	PROPN
ejpam-5003	416	16	a	a	PRON
ejpam-5003	416	17	,	,	PUNCT
ejpam-5003	416	18	b	b	PROPN
ejpam-5003	416	19	⊆	⊆	NUM
ejpam-5003	416	20	h.	h.	NOUN
ejpam-5003	416	21	then	then	ADV
ejpam-5003	416	22	(	(	PUNCT
ejpam-5003	416	23	i	i	NOUN
ejpam-5003	416	24	)	)	PUNCT
ejpam-5003	416	25	aθb	aθb	NOUN
ejpam-5003	416	26	if	if	SCONJ
ejpam-5003	416	27	there	there	PRON
ejpam-5003	416	28	exist	exist	VERB
ejpam-5003	416	29	a	a	DET
ejpam-5003	416	30	∈	∈	PROPN
ejpam-5003	416	31	a	a	DET
ejpam-5003	416	32	and	and	CCONJ
ejpam-5003	416	33	b	b	NOUN
ejpam-5003	416	34	∈	∈	PROPN
ejpam-5003	416	35	b	b	NOUN
ejpam-5003	416	36	such	such	ADJ
ejpam-5003	416	37	that	that	DET
ejpam-5003	416	38	aθb	aθb	NOUN
ejpam-5003	416	39	;	;	PUNCT
ejpam-5003	416	40	(	(	PUNCT
ejpam-5003	416	41	ii	ii	NOUN
ejpam-5003	416	42	)	)	PUNCT
ejpam-5003	416	43	aθb	aθb	NOUN
ejpam-5003	416	44	if	if	SCONJ
ejpam-5003	416	45	for	for	ADP
ejpam-5003	416	46	every	every	DET
ejpam-5003	416	47	a	a	DET
ejpam-5003	416	48	∈	∈	PROPN
ejpam-5003	416	49	a	a	PRON
ejpam-5003	416	50	,	,	PUNCT
ejpam-5003	416	51	there	there	PRON
ejpam-5003	416	52	exists	exist	VERB
ejpam-5003	416	53	b	b	PROPN
ejpam-5003	416	54	∈	∈	PROPN
ejpam-5003	416	55	b	b	NOUN
ejpam-5003	416	56	such	such	ADJ
ejpam-5003	416	57	that	that	DET
ejpam-5003	416	58	aθb	aθb	NOUN
ejpam-5003	416	59	and	and	CCONJ
ejpam-5003	416	60	for	for	ADP
ejpam-5003	416	61	every	every	DET
ejpam-5003	416	62	b	b	PROPN
ejpam-5003	416	63	∈	∈	PROPN
ejpam-5003	416	64	b	b	NOUN
ejpam-5003	416	65	,	,	PUNCT
ejpam-5003	416	66	there	there	PRON
ejpam-5003	416	67	exists	exist	VERB
ejpam-5003	416	68	a	a	DET
ejpam-5003	416	69	∈	∈	NOUN
ejpam-5003	416	70	a	a	DET
ejpam-5003	416	71	such	such	ADJ
ejpam-5003	416	72	that	that	DET
ejpam-5003	416	73	aθb	aθb	NOUN
ejpam-5003	416	74	;	;	PUNCT
ejpam-5003	416	75	(	(	PUNCT
ejpam-5003	416	76	iii	iii	X
ejpam-5003	416	77	)	)	PUNCT
ejpam-5003	416	78	θ	θ	PROPN
ejpam-5003	416	79	is	be	AUX
ejpam-5003	416	80	called	call	VERB
ejpam-5003	416	81	a	a	DET
ejpam-5003	416	82	congruence	congruence	NOUN
ejpam-5003	416	83	relation	relation	NOUN
ejpam-5003	416	84	onh	onh	PROPN
ejpam-5003	416	85	,	,	PUNCT
ejpam-5003	416	86	if	if	SCONJ
ejpam-5003	416	87	whenever	whenever	SCONJ
ejpam-5003	416	88	xθy	xθy	PROPN
ejpam-5003	416	89	and	and	CCONJ
ejpam-5003	416	90	x′θy′	x′θy′	NUM
ejpam-5003	416	91	,	,	PUNCT
ejpam-5003	416	92	then	then	ADV
ejpam-5003	416	93	(	(	PUNCT
ejpam-5003	416	94	x⊛x′)θ(y⊛y′	x⊛x′)θ(y⊛y′	PROPN
ejpam-5003	416	95	)	)	PUNCT
ejpam-5003	416	96	for	for	ADP
ejpam-5003	416	97	all	all	DET
ejpam-5003	416	98	x	x	PROPN
ejpam-5003	416	99	,	,	PUNCT
ejpam-5003	416	100	y	y	PROPN
ejpam-5003	416	101	,	,	PUNCT
ejpam-5003	416	102	x′	x′	NUM
ejpam-5003	416	103	,	,	PUNCT
ejpam-5003	416	104	y′	y′	NOUN
ejpam-5003	416	105	∈	∈	PROPN
ejpam-5003	416	106	h.	h.	NOUN
ejpam-5003	416	107	not	not	PART
ejpam-5003	416	108	all	all	DET
ejpam-5003	416	109	equivalence	equivalence	NOUN
ejpam-5003	416	110	relations	relation	NOUN
ejpam-5003	416	111	are	be	AUX
ejpam-5003	416	112	congruence	congruence	NOUN
ejpam-5003	416	113	relations	relation	NOUN
ejpam-5003	416	114	as	as	SCONJ
ejpam-5003	416	115	shown	show	VERB
ejpam-5003	416	116	in	in	ADP
ejpam-5003	416	117	the	the	DET
ejpam-5003	416	118	following	follow	VERB
ejpam-5003	416	119	example	example	NOUN
ejpam-5003	416	120	.	.	PUNCT
ejpam-5003	417	1	example	example	NOUN
ejpam-5003	417	2	21	21	NUM
ejpam-5003	417	3	.	.	PUNCT
ejpam-5003	418	1	consider	consider	VERB
ejpam-5003	418	2	h	h	NOUN
ejpam-5003	418	3	=	=	PRON
ejpam-5003	418	4	{	{	PUNCT
ejpam-5003	418	5	0	0	NUM
ejpam-5003	418	6	,	,	PUNCT
ejpam-5003	418	7	1	1	NUM
ejpam-5003	418	8	,	,	PUNCT
ejpam-5003	418	9	2	2	NUM
ejpam-5003	418	10	,	,	PUNCT
ejpam-5003	418	11	3	3	NUM
ejpam-5003	418	12	,	,	PUNCT
ejpam-5003	418	13	4	4	NUM
ejpam-5003	418	14	}	}	PUNCT
ejpam-5003	418	15	and	and	CCONJ
ejpam-5003	418	16	its	its	PRON
ejpam-5003	418	17	hyperoperation	hyperoperation	NOUN
ejpam-5003	418	18	given	give	VERB
ejpam-5003	418	19	by	by	ADP
ejpam-5003	418	20	the	the	DET
ejpam-5003	418	21	following	follow	VERB
ejpam-5003	418	22	cayley	cayley	ADJ
ejpam-5003	418	23	table	table	NOUN
ejpam-5003	418	24	:	:	PUNCT
ejpam-5003	419	1	⊛	⊛	NUM
ejpam-5003	419	2	0	0	NUM
ejpam-5003	419	3	1	1	NUM
ejpam-5003	419	4	2	2	NUM
ejpam-5003	419	5	3	3	NUM
ejpam-5003	419	6	4	4	NUM
ejpam-5003	419	7	0	0	NUM
ejpam-5003	419	8	{	{	PUNCT
ejpam-5003	419	9	0	0	NUM
ejpam-5003	419	10	}	}	PUNCT
ejpam-5003	419	11	{	{	PUNCT
ejpam-5003	419	12	1	1	NUM
ejpam-5003	419	13	}	}	PUNCT
ejpam-5003	419	14	{	{	PUNCT
ejpam-5003	419	15	2	2	NUM
ejpam-5003	419	16	}	}	PUNCT
ejpam-5003	419	17	{	{	PUNCT
ejpam-5003	419	18	3	3	NUM
ejpam-5003	419	19	}	}	PUNCT
ejpam-5003	419	20	{	{	PUNCT
ejpam-5003	419	21	4	4	NUM
ejpam-5003	419	22	}	}	SYM
ejpam-5003	419	23	1	1	NUM
ejpam-5003	419	24	{	{	PUNCT
ejpam-5003	419	25	1	1	NUM
ejpam-5003	419	26	}	}	PUNCT
ejpam-5003	419	27	{	{	PUNCT
ejpam-5003	419	28	0	0	NUM
ejpam-5003	419	29	,	,	PUNCT
ejpam-5003	419	30	1	1	NUM
ejpam-5003	419	31	}	}	PUNCT
ejpam-5003	419	32	{	{	PUNCT
ejpam-5003	419	33	2	2	NUM
ejpam-5003	419	34	}	}	PUNCT
ejpam-5003	419	35	{	{	PUNCT
ejpam-5003	419	36	3	3	NUM
ejpam-5003	419	37	}	}	PUNCT
ejpam-5003	419	38	{	{	PUNCT
ejpam-5003	419	39	4	4	NUM
ejpam-5003	419	40	}	}	SYM
ejpam-5003	419	41	2	2	NUM
ejpam-5003	419	42	{	{	PUNCT
ejpam-5003	419	43	2	2	NUM
ejpam-5003	419	44	}	}	PUNCT
ejpam-5003	419	45	{	{	PUNCT
ejpam-5003	419	46	2	2	NUM
ejpam-5003	419	47	}	}	PUNCT
ejpam-5003	419	48	{	{	PUNCT
ejpam-5003	419	49	0	0	NUM
ejpam-5003	419	50	,	,	PUNCT
ejpam-5003	419	51	2	2	NUM
ejpam-5003	419	52	}	}	PUNCT
ejpam-5003	419	53	{	{	PUNCT
ejpam-5003	419	54	0	0	NUM
ejpam-5003	419	55	,	,	PUNCT
ejpam-5003	419	56	2	2	NUM
ejpam-5003	419	57	,	,	PUNCT
ejpam-5003	419	58	3	3	NUM
ejpam-5003	419	59	}	}	PUNCT
ejpam-5003	419	60	{	{	PUNCT
ejpam-5003	419	61	2	2	NUM
ejpam-5003	419	62	,	,	PUNCT
ejpam-5003	419	63	4	4	NUM
ejpam-5003	419	64	}	}	SYM
ejpam-5003	419	65	3	3	NUM
ejpam-5003	419	66	{	{	PUNCT
ejpam-5003	419	67	3	3	NUM
ejpam-5003	419	68	}	}	PUNCT
ejpam-5003	419	69	{	{	PUNCT
ejpam-5003	419	70	3	3	NUM
ejpam-5003	419	71	}	}	PUNCT
ejpam-5003	419	72	{	{	PUNCT
ejpam-5003	419	73	0	0	NUM
ejpam-5003	419	74	,	,	PUNCT
ejpam-5003	419	75	2	2	NUM
ejpam-5003	419	76	,	,	PUNCT
ejpam-5003	419	77	3	3	NUM
ejpam-5003	419	78	}	}	PUNCT
ejpam-5003	419	79	{	{	PUNCT
ejpam-5003	419	80	0	0	NUM
ejpam-5003	419	81	,	,	PUNCT
ejpam-5003	419	82	3	3	NUM
ejpam-5003	419	83	}	}	PUNCT
ejpam-5003	419	84	{	{	PUNCT
ejpam-5003	419	85	3	3	NUM
ejpam-5003	419	86	,	,	PUNCT
ejpam-5003	419	87	4	4	NUM
ejpam-5003	419	88	}	}	SYM
ejpam-5003	419	89	4	4	NUM
ejpam-5003	419	90	{	{	PUNCT
ejpam-5003	419	91	4	4	NUM
ejpam-5003	419	92	}	}	PUNCT
ejpam-5003	419	93	{	{	PUNCT
ejpam-5003	419	94	4	4	NUM
ejpam-5003	419	95	}	}	PUNCT
ejpam-5003	419	96	{	{	PUNCT
ejpam-5003	419	97	2	2	NUM
ejpam-5003	419	98	,	,	PUNCT
ejpam-5003	419	99	4	4	NUM
ejpam-5003	419	100	}	}	PUNCT
ejpam-5003	419	101	{	{	PUNCT
ejpam-5003	419	102	3	3	NUM
ejpam-5003	419	103	,	,	PUNCT
ejpam-5003	419	104	4	4	NUM
ejpam-5003	419	105	}	}	PUNCT
ejpam-5003	419	106	{	{	PUNCT
ejpam-5003	419	107	0	0	NUM
ejpam-5003	419	108	,	,	PUNCT
ejpam-5003	419	109	4	4	NUM
ejpam-5003	419	110	}	}	PUNCT
ejpam-5003	419	111	l.r	l.r	PROPN
ejpam-5003	419	112	.	.	PROPN
ejpam-5003	419	113	cabardo	cabardo	PROPN
ejpam-5003	419	114	,	,	PUNCT
ejpam-5003	419	115	g.	g.	PROPN
ejpam-5003	419	116	petalcorin	petalcorin	PROPN
ejpam-5003	419	117	/	/	SYM
ejpam-5003	419	118	eur	eur	PROPN
ejpam-5003	419	119	.	.	PUNCT
ejpam-5003	420	1	j.	j.	PROPN
ejpam-5003	420	2	pure	pure	PROPN
ejpam-5003	420	3	appl	appl	PROPN
ejpam-5003	420	4	.	.	PROPN
ejpam-5003	420	5	math	math	PROPN
ejpam-5003	420	6	,	,	PUNCT
ejpam-5003	420	7	17	17	NUM
ejpam-5003	420	8	(	(	PUNCT
ejpam-5003	420	9	1	1	NUM
ejpam-5003	420	10	)	)	PUNCT
ejpam-5003	420	11	(	(	PUNCT
ejpam-5003	420	12	2024	2024	NUM
ejpam-5003	420	13	)	)	PUNCT
ejpam-5003	420	14	,	,	PUNCT
ejpam-5003	420	15	222	222	NUM
ejpam-5003	420	16	-	-	SYM
ejpam-5003	420	17	242	242	NUM
ejpam-5003	420	18	236	236	NUM
ejpam-5003	420	19	by	by	ADP
ejpam-5003	420	20	routine	routine	ADJ
ejpam-5003	420	21	calculations	calculation	NOUN
ejpam-5003	420	22	,	,	PUNCT
ejpam-5003	420	23	h	h	NOUN
ejpam-5003	420	24	is	be	AUX
ejpam-5003	420	25	a	a	DET
ejpam-5003	420	26	hyper	hyper	ADJ
ejpam-5003	420	27	bn	bn	NOUN
ejpam-5003	420	28	-algebra	-algebra	NOUN
ejpam-5003	420	29	.	.	PUNCT
ejpam-5003	421	1	define	define	VERB
ejpam-5003	421	2	a	a	DET
ejpam-5003	421	3	relation	relation	NOUN
ejpam-5003	421	4	θ	θ	PROPN
ejpam-5003	421	5	on	on	ADP
ejpam-5003	421	6	h	h	NOUN
ejpam-5003	421	7	by	by	ADP
ejpam-5003	421	8	θ	θ	PROPN
ejpam-5003	421	9	=	=	SYM
ejpam-5003	421	10	{	{	PUNCT
ejpam-5003	421	11	(	(	PUNCT
ejpam-5003	421	12	0	0	NUM
ejpam-5003	421	13	,	,	PUNCT
ejpam-5003	421	14	0	0	NUM
ejpam-5003	421	15	)	)	PUNCT
ejpam-5003	421	16	,	,	PUNCT
ejpam-5003	421	17	(	(	PUNCT
ejpam-5003	421	18	0	0	NUM
ejpam-5003	421	19	,	,	PUNCT
ejpam-5003	421	20	2	2	NUM
ejpam-5003	421	21	)	)	PUNCT
ejpam-5003	421	22	,	,	PUNCT
ejpam-5003	421	23	(	(	PUNCT
ejpam-5003	421	24	1	1	NUM
ejpam-5003	421	25	,	,	PUNCT
ejpam-5003	421	26	1	1	NUM
ejpam-5003	421	27	)	)	PUNCT
ejpam-5003	421	28	,	,	PUNCT
ejpam-5003	421	29	(	(	PUNCT
ejpam-5003	421	30	1	1	NUM
ejpam-5003	421	31	,	,	PUNCT
ejpam-5003	421	32	3	3	NUM
ejpam-5003	421	33	)	)	PUNCT
ejpam-5003	421	34	,	,	PUNCT
ejpam-5003	421	35	(	(	PUNCT
ejpam-5003	421	36	2	2	NUM
ejpam-5003	421	37	,	,	PUNCT
ejpam-5003	421	38	0	0	NUM
ejpam-5003	421	39	)	)	PUNCT
ejpam-5003	421	40	,	,	PUNCT
ejpam-5003	421	41	(	(	PUNCT
ejpam-5003	421	42	2	2	NUM
ejpam-5003	421	43	,	,	PUNCT
ejpam-5003	421	44	2	2	NUM
ejpam-5003	421	45	)	)	PUNCT
ejpam-5003	421	46	,	,	PUNCT
ejpam-5003	421	47	(	(	PUNCT
ejpam-5003	421	48	3	3	NUM
ejpam-5003	421	49	,	,	PUNCT
ejpam-5003	421	50	1	1	NUM
ejpam-5003	421	51	)	)	PUNCT
ejpam-5003	421	52	,	,	PUNCT
ejpam-5003	421	53	(	(	PUNCT
ejpam-5003	421	54	3	3	NUM
ejpam-5003	421	55	,	,	PUNCT
ejpam-5003	421	56	3	3	NUM
ejpam-5003	421	57	)	)	PUNCT
ejpam-5003	421	58	,	,	PUNCT
ejpam-5003	421	59	(	(	PUNCT
ejpam-5003	421	60	4	4	NUM
ejpam-5003	421	61	,	,	PUNCT
ejpam-5003	421	62	4	4	NUM
ejpam-5003	421	63	)	)	PUNCT
ejpam-5003	421	64	}	}	PUNCT
ejpam-5003	421	65	.	.	PUNCT
ejpam-5003	422	1	by	by	ADP
ejpam-5003	422	2	inspection	inspection	NOUN
ejpam-5003	422	3	,	,	PUNCT
ejpam-5003	422	4	θ	θ	PROPN
ejpam-5003	422	5	is	be	AUX
ejpam-5003	422	6	an	an	DET
ejpam-5003	422	7	equivalence	equivalence	NOUN
ejpam-5003	422	8	relation	relation	NOUN
ejpam-5003	422	9	on	on	ADP
ejpam-5003	422	10	h.	h.	PROPN
ejpam-5003	422	11	now	now	ADV
ejpam-5003	422	12	,	,	PUNCT
ejpam-5003	422	13	observe	observe	VERB
ejpam-5003	422	14	that	that	SCONJ
ejpam-5003	422	15	1θ3	1θ3	NUM
ejpam-5003	422	16	and	and	CCONJ
ejpam-5003	422	17	2θ0	2θ0	NUM
ejpam-5003	422	18	but	but	CCONJ
ejpam-5003	422	19	1⊛	1⊛	NUM
ejpam-5003	422	20	2	2	NUM
ejpam-5003	422	21	=	=	SYM
ejpam-5003	422	22	{	{	PUNCT
ejpam-5003	422	23	2}̸	2}̸	PROPN
ejpam-5003	422	24	θ{3	θ{3	PROPN
ejpam-5003	422	25	}	}	PUNCT
ejpam-5003	422	26	=	=	PUNCT
ejpam-5003	423	1	3⊛	3⊛	NUM
ejpam-5003	423	2	0	0	PUNCT
ejpam-5003	424	1	because	because	SCONJ
ejpam-5003	424	2	(	(	PUNCT
ejpam-5003	424	3	2	2	NUM
ejpam-5003	424	4	,	,	PUNCT
ejpam-5003	424	5	3	3	NUM
ejpam-5003	424	6	)	)	PUNCT
ejpam-5003	424	7	/∈	/∈	PUNCT
ejpam-5003	424	8	θ	θ	X
ejpam-5003	424	9	.	.	PUNCT
ejpam-5003	424	10	thus	thus	ADV
ejpam-5003	424	11	,	,	PUNCT
ejpam-5003	424	12	θ	θ	PROPN
ejpam-5003	424	13	is	be	AUX
ejpam-5003	424	14	not	not	PART
ejpam-5003	424	15	a	a	DET
ejpam-5003	424	16	congruence	congruence	NOUN
ejpam-5003	424	17	relation	relation	NOUN
ejpam-5003	424	18	on	on	ADP
ejpam-5003	424	19	h.	h.	PROPN
ejpam-5003	424	20	hence	hence	ADV
ejpam-5003	424	21	,	,	PUNCT
ejpam-5003	424	22	if	if	SCONJ
ejpam-5003	424	23	θ	θ	PROPN
ejpam-5003	424	24	is	be	AUX
ejpam-5003	424	25	an	an	DET
ejpam-5003	424	26	equivalence	equivalence	NOUN
ejpam-5003	424	27	relation	relation	NOUN
ejpam-5003	424	28	on	on	ADP
ejpam-5003	424	29	h	h	NOUN
ejpam-5003	424	30	,	,	PUNCT
ejpam-5003	424	31	then	then	ADV
ejpam-5003	424	32	θ	θ	PROPN
ejpam-5003	424	33	need	need	AUX
ejpam-5003	424	34	not	not	PART
ejpam-5003	424	35	be	be	AUX
ejpam-5003	424	36	a	a	DET
ejpam-5003	424	37	congruence	congruence	NOUN
ejpam-5003	424	38	relation	relation	NOUN
ejpam-5003	424	39	on	on	ADP
ejpam-5003	424	40	h.	h.	PROPN
ejpam-5003	424	41	the	the	DET
ejpam-5003	424	42	following	follow	VERB
ejpam-5003	424	43	lemma	lemma	PROPN
ejpam-5003	424	44	shows	show	VERB
ejpam-5003	424	45	that	that	SCONJ
ejpam-5003	424	46	θ	θ	PROPN
ejpam-5003	424	47	is	be	AUX
ejpam-5003	424	48	transitive	transitive	ADJ
ejpam-5003	424	49	on	on	ADP
ejpam-5003	424	50	p∗(h	p∗(h	PROPN
ejpam-5003	424	51	)	)	PUNCT
ejpam-5003	424	52	.	.	PUNCT
ejpam-5003	425	1	lemma	lemma	PROPN
ejpam-5003	425	2	7	7	X
ejpam-5003	425	3	.	.	PUNCT
ejpam-5003	426	1	let	let	VERB
ejpam-5003	426	2	θ	θ	NOUN
ejpam-5003	426	3	be	be	AUX
ejpam-5003	426	4	an	an	DET
ejpam-5003	426	5	equivalence	equivalence	NOUN
ejpam-5003	426	6	relation	relation	NOUN
ejpam-5003	426	7	on	on	ADP
ejpam-5003	426	8	h	h	NOUN
ejpam-5003	426	9	and	and	CCONJ
ejpam-5003	426	10	∅	∅	NOUN
ejpam-5003	426	11	̸=	̸=	PROPN
ejpam-5003	426	12	a	a	DET
ejpam-5003	426	13	,	,	PUNCT
ejpam-5003	426	14	b	b	NOUN
ejpam-5003	426	15	,	,	PUNCT
ejpam-5003	426	16	c	c	PROPN
ejpam-5003	426	17	⊆	⊆	NUM
ejpam-5003	426	18	h.	h.	NOUN
ejpam-5003	426	19	if	if	SCONJ
ejpam-5003	426	20	aθb	aθb	PRON
ejpam-5003	426	21	and	and	CCONJ
ejpam-5003	426	22	bθc	bθc	NOUN
ejpam-5003	426	23	,	,	PUNCT
ejpam-5003	426	24	then	then	ADV
ejpam-5003	426	25	aθc	aθc	NOUN
ejpam-5003	426	26	.	.	PUNCT
ejpam-5003	427	1	proof	proof	NOUN
ejpam-5003	427	2	.	.	PUNCT
ejpam-5003	428	1	let	let	VERB
ejpam-5003	428	2	θ	θ	NOUN
ejpam-5003	428	3	be	be	AUX
ejpam-5003	428	4	an	an	DET
ejpam-5003	428	5	equivalence	equivalence	NOUN
ejpam-5003	428	6	relation	relation	NOUN
ejpam-5003	428	7	on	on	ADP
ejpam-5003	428	8	h	h	NOUN
ejpam-5003	428	9	and	and	CCONJ
ejpam-5003	428	10	∅	∅	NOUN
ejpam-5003	428	11	̸=	̸=	PROPN
ejpam-5003	428	12	a	a	DET
ejpam-5003	428	13	,	,	PUNCT
ejpam-5003	428	14	b	b	NOUN
ejpam-5003	428	15	,	,	PUNCT
ejpam-5003	428	16	c	c	PROPN
ejpam-5003	428	17	⊆	⊆	NUM
ejpam-5003	428	18	h.	h.	PROPN
ejpam-5003	428	19	assume	assume	VERB
ejpam-5003	428	20	that	that	SCONJ
ejpam-5003	428	21	aθb	aθb	NOUN
ejpam-5003	428	22	and	and	CCONJ
ejpam-5003	428	23	bθc	bθc	NOUN
ejpam-5003	428	24	.	.	PUNCT
ejpam-5003	429	1	by	by	ADP
ejpam-5003	429	2	definition	definition	NOUN
ejpam-5003	429	3	15(ii	15(ii	NUM
ejpam-5003	429	4	)	)	PUNCT
ejpam-5003	429	5	,	,	PUNCT
ejpam-5003	429	6	for	for	ADP
ejpam-5003	429	7	each	each	DET
ejpam-5003	429	8	a	a	DET
ejpam-5003	429	9	∈	∈	PROPN
ejpam-5003	429	10	a	a	DET
ejpam-5003	429	11	(	(	PUNCT
ejpam-5003	429	12	resp	resp	NOUN
ejpam-5003	429	13	.	.	PUNCT
ejpam-5003	430	1	b	b	X
ejpam-5003	430	2	∈	∈	PROPN
ejpam-5003	430	3	b	b	X
ejpam-5003	430	4	)	)	PUNCT
ejpam-5003	430	5	,	,	PUNCT
ejpam-5003	430	6	there	there	PRON
ejpam-5003	430	7	exists	exist	VERB
ejpam-5003	430	8	b	b	PROPN
ejpam-5003	430	9	∈	∈	PROPN
ejpam-5003	430	10	b	b	PROPN
ejpam-5003	430	11	(	(	PUNCT
ejpam-5003	430	12	resp	resp	NOUN
ejpam-5003	430	13	.	.	PUNCT
ejpam-5003	431	1	a	a	DET
ejpam-5003	431	2	∈	∈	PROPN
ejpam-5003	431	3	a	a	NOUN
ejpam-5003	431	4	)	)	PUNCT
ejpam-5003	431	5	such	such	ADJ
ejpam-5003	431	6	that	that	DET
ejpam-5003	431	7	aθb	aθb	NOUN
ejpam-5003	431	8	(	(	PUNCT
ejpam-5003	431	9	resp	resp	NOUN
ejpam-5003	431	10	.	.	PUNCT
ejpam-5003	432	1	bθa	bθa	ADJ
ejpam-5003	432	2	)	)	PUNCT
ejpam-5003	432	3	and	and	CCONJ
ejpam-5003	432	4	for	for	ADP
ejpam-5003	432	5	all	all	DET
ejpam-5003	432	6	b	b	NOUN
ejpam-5003	432	7	∈	∈	ADP
ejpam-5003	432	8	b	b	PROPN
ejpam-5003	432	9	(	(	PUNCT
ejpam-5003	432	10	resp	resp	NOUN
ejpam-5003	432	11	.	.	PUNCT
ejpam-5003	433	1	c	c	PROPN
ejpam-5003	433	2	∈	∈	PROPN
ejpam-5003	433	3	c	c	X
ejpam-5003	433	4	)	)	PUNCT
ejpam-5003	433	5	,	,	PUNCT
ejpam-5003	433	6	there	there	PRON
ejpam-5003	433	7	exists	exist	VERB
ejpam-5003	433	8	c	c	PROPN
ejpam-5003	433	9	∈	∈	PROPN
ejpam-5003	433	10	c	c	PROPN
ejpam-5003	433	11	(	(	PUNCT
ejpam-5003	433	12	resp	resp	NOUN
ejpam-5003	433	13	.	.	PUNCT
ejpam-5003	434	1	b	b	X
ejpam-5003	434	2	∈	∈	PROPN
ejpam-5003	434	3	b	b	NOUN
ejpam-5003	434	4	)	)	PUNCT
ejpam-5003	434	5	such	such	ADJ
ejpam-5003	434	6	that	that	DET
ejpam-5003	434	7	bθc	bθc	NOUN
ejpam-5003	434	8	(	(	PUNCT
ejpam-5003	434	9	resp	resp	NOUN
ejpam-5003	434	10	.	.	PUNCT
ejpam-5003	435	1	cθb	cθb	PROPN
ejpam-5003	435	2	)	)	PUNCT
ejpam-5003	435	3	.	.	PUNCT
ejpam-5003	436	1	since	since	SCONJ
ejpam-5003	436	2	θ	θ	PROPN
ejpam-5003	436	3	is	be	AUX
ejpam-5003	436	4	an	an	DET
ejpam-5003	436	5	equivalence	equivalence	NOUN
ejpam-5003	436	6	relation	relation	NOUN
ejpam-5003	436	7	,	,	PUNCT
ejpam-5003	436	8	aθc	aθc	NOUN
ejpam-5003	436	9	(	(	PUNCT
ejpam-5003	436	10	resp	resp	NOUN
ejpam-5003	436	11	.	.	PUNCT
ejpam-5003	436	12	cθa	cθa	ADJ
ejpam-5003	436	13	)	)	PUNCT
ejpam-5003	436	14	.	.	PUNCT
ejpam-5003	437	1	therefore	therefore	ADV
ejpam-5003	437	2	,	,	PUNCT
ejpam-5003	437	3	aθc	aθc	PROPN
ejpam-5003	437	4	.	.	PUNCT
ejpam-5003	438	1	lemma	lemma	PROPN
ejpam-5003	438	2	8	8	NUM
ejpam-5003	438	3	.	.	PUNCT
ejpam-5003	439	1	let	let	VERB
ejpam-5003	439	2	θ	θ	NOUN
ejpam-5003	439	3	be	be	AUX
ejpam-5003	439	4	an	an	DET
ejpam-5003	439	5	equivalence	equivalence	NOUN
ejpam-5003	439	6	relation	relation	NOUN
ejpam-5003	439	7	on	on	ADP
ejpam-5003	439	8	h.	h.	PROPN
ejpam-5003	439	9	the	the	DET
ejpam-5003	439	10	following	follow	VERB
ejpam-5003	439	11	statements	statement	NOUN
ejpam-5003	439	12	are	be	AUX
ejpam-5003	439	13	equivalent	equivalent	ADJ
ejpam-5003	439	14	:	:	PUNCT
ejpam-5003	439	15	(	(	PUNCT
ejpam-5003	439	16	i	i	NOUN
ejpam-5003	439	17	)	)	PUNCT
ejpam-5003	439	18	θ	θ	PROPN
ejpam-5003	439	19	is	be	AUX
ejpam-5003	439	20	a	a	DET
ejpam-5003	439	21	congruence	congruence	NOUN
ejpam-5003	439	22	relation	relation	NOUN
ejpam-5003	439	23	on	on	ADP
ejpam-5003	439	24	h.	h.	PROPN
ejpam-5003	439	25	(	(	PUNCT
ejpam-5003	439	26	ii	ii	PROPN
ejpam-5003	439	27	)	)	PUNCT
ejpam-5003	439	28	if	if	SCONJ
ejpam-5003	439	29	x	x	X
ejpam-5003	439	30	,	,	PUNCT
ejpam-5003	439	31	y	y	PROPN
ejpam-5003	439	32	∈	∈	PROPN
ejpam-5003	439	33	h	h	NOUN
ejpam-5003	439	34	such	such	ADJ
ejpam-5003	439	35	that	that	SCONJ
ejpam-5003	439	36	xθy	xθy	PROPN
ejpam-5003	439	37	,	,	PUNCT
ejpam-5003	439	38	then	then	ADV
ejpam-5003	439	39	(	(	PUNCT
ejpam-5003	439	40	x⊛	x⊛	PROPN
ejpam-5003	439	41	a)θ(y	a)θ(y	PROPN
ejpam-5003	439	42	⊛	⊛	ADJ
ejpam-5003	439	43	a	a	NOUN
ejpam-5003	439	44	)	)	PUNCT
ejpam-5003	439	45	and	and	CCONJ
ejpam-5003	439	46	(	(	PUNCT
ejpam-5003	439	47	a⊛	a⊛	PROPN
ejpam-5003	439	48	x)θ(a⊛	x)θ(a⊛	PROPN
ejpam-5003	439	49	y	y	PROPN
ejpam-5003	439	50	)	)	PUNCT
ejpam-5003	439	51	for	for	ADP
ejpam-5003	439	52	all	all	DET
ejpam-5003	439	53	a	a	DET
ejpam-5003	439	54	∈	∈	PROPN
ejpam-5003	439	55	h.	h.	NOUN
ejpam-5003	439	56	proof	proof	NOUN
ejpam-5003	439	57	.	.	PUNCT
ejpam-5003	440	1	let	let	VERB
ejpam-5003	440	2	θ	θ	NOUN
ejpam-5003	440	3	be	be	AUX
ejpam-5003	440	4	an	an	DET
ejpam-5003	440	5	equivalence	equivalence	NOUN
ejpam-5003	440	6	relation	relation	NOUN
ejpam-5003	440	7	on	on	ADP
ejpam-5003	440	8	h.	h.	PROPN
ejpam-5003	440	9	(	(	PUNCT
ejpam-5003	440	10	i	i	NOUN
ejpam-5003	440	11	)	)	PUNCT
ejpam-5003	440	12	⇒	⇒	PROPN
ejpam-5003	440	13	(	(	PUNCT
ejpam-5003	440	14	ii	ii	NOUN
ejpam-5003	440	15	)	)	PUNCT
ejpam-5003	440	16	let	let	VERB
ejpam-5003	440	17	θ	θ	NOUN
ejpam-5003	440	18	be	be	AUX
ejpam-5003	440	19	a	a	DET
ejpam-5003	440	20	congruence	congruence	NOUN
ejpam-5003	440	21	relation	relation	NOUN
ejpam-5003	440	22	on	on	ADP
ejpam-5003	440	23	h	h	NOUN
ejpam-5003	440	24	and	and	CCONJ
ejpam-5003	440	25	a	a	DET
ejpam-5003	440	26	,	,	PUNCT
ejpam-5003	440	27	x	x	X
ejpam-5003	440	28	,	,	PUNCT
ejpam-5003	440	29	y	y	PROPN
ejpam-5003	440	30	∈	∈	PROPN
ejpam-5003	440	31	h	h	NOUN
ejpam-5003	440	32	such	such	ADJ
ejpam-5003	440	33	that	that	DET
ejpam-5003	440	34	xθy	xθy	PROPN
ejpam-5003	440	35	.	.	PUNCT
ejpam-5003	441	1	since	since	SCONJ
ejpam-5003	441	2	aθa	aθa	PROPN
ejpam-5003	441	3	,	,	PUNCT
ejpam-5003	441	4	(	(	PUNCT
ejpam-5003	441	5	x⊛	x⊛	PROPN
ejpam-5003	441	6	a)θ(y	a)θ(y	PROPN
ejpam-5003	441	7	⊛	⊛	ADJ
ejpam-5003	441	8	a	a	NOUN
ejpam-5003	441	9	)	)	PUNCT
ejpam-5003	441	10	and	and	CCONJ
ejpam-5003	441	11	(	(	PUNCT
ejpam-5003	441	12	a⊛	a⊛	PROPN
ejpam-5003	441	13	x)θ(a⊛	x)θ(a⊛	PROPN
ejpam-5003	441	14	y	y	PROPN
ejpam-5003	441	15	)	)	PUNCT
ejpam-5003	441	16	,	,	PUNCT
ejpam-5003	441	17	by	by	ADP
ejpam-5003	441	18	definition	definition	NOUN
ejpam-5003	441	19	15(iii	15(iii	NUM
ejpam-5003	441	20	)	)	PUNCT
ejpam-5003	441	21	.	.	PUNCT
ejpam-5003	442	1	(	(	PUNCT
ejpam-5003	442	2	ii	ii	NOUN
ejpam-5003	442	3	)	)	PUNCT
ejpam-5003	442	4	⇒	⇒	NOUN
ejpam-5003	442	5	(	(	PUNCT
ejpam-5003	442	6	i	i	NOUN
ejpam-5003	442	7	)	)	PUNCT
ejpam-5003	442	8	assume	assume	VERB
ejpam-5003	442	9	that	that	SCONJ
ejpam-5003	442	10	if	if	SCONJ
ejpam-5003	442	11	xθy	xθy	PROPN
ejpam-5003	442	12	,	,	PUNCT
ejpam-5003	442	13	then	then	ADV
ejpam-5003	442	14	(	(	PUNCT
ejpam-5003	442	15	x⊛	x⊛	PROPN
ejpam-5003	442	16	a)θ(y⊛	a)θ(y⊛	PROPN
ejpam-5003	442	17	a	a	NOUN
ejpam-5003	442	18	)	)	PUNCT
ejpam-5003	442	19	and	and	CCONJ
ejpam-5003	442	20	(	(	PUNCT
ejpam-5003	442	21	a⊛	a⊛	PROPN
ejpam-5003	442	22	x)θ(a⊛	x)θ(a⊛	PROPN
ejpam-5003	442	23	y	y	PROPN
ejpam-5003	442	24	)	)	PUNCT
ejpam-5003	442	25	for	for	ADP
ejpam-5003	442	26	all	all	DET
ejpam-5003	442	27	a	a	PRON
ejpam-5003	442	28	,	,	PUNCT
ejpam-5003	442	29	x	x	NOUN
ejpam-5003	442	30	,	,	PUNCT
ejpam-5003	442	31	y	y	PROPN
ejpam-5003	442	32	∈	∈	PROPN
ejpam-5003	442	33	h.	h.	PROPN
ejpam-5003	442	34	let	let	VERB
ejpam-5003	442	35	x	x	PRON
ejpam-5003	442	36	,	,	PUNCT
ejpam-5003	442	37	y	y	PROPN
ejpam-5003	442	38	,	,	PUNCT
ejpam-5003	442	39	x′	x′	NUM
ejpam-5003	442	40	,	,	PUNCT
ejpam-5003	442	41	y′	y′	NOUN
ejpam-5003	442	42	∈	∈	PROPN
ejpam-5003	442	43	h	h	NOUN
ejpam-5003	442	44	such	such	ADJ
ejpam-5003	442	45	that	that	SCONJ
ejpam-5003	442	46	xθy	xθy	PROPN
ejpam-5003	442	47	and	and	CCONJ
ejpam-5003	442	48	x′θy′.	x′θy′.	NUM
ejpam-5003	442	49	then	then	ADV
ejpam-5003	442	50	,	,	PUNCT
ejpam-5003	442	51	(	(	PUNCT
ejpam-5003	442	52	x⊛x′)θ(y⊛x′	x⊛x′)θ(y⊛x′	ADV
ejpam-5003	442	53	)	)	PUNCT
ejpam-5003	442	54	and	and	CCONJ
ejpam-5003	442	55	(	(	PUNCT
ejpam-5003	442	56	y⊛x′)θ(y⊛y′	y⊛x′)θ(y⊛y′	PROPN
ejpam-5003	442	57	)	)	PUNCT
ejpam-5003	442	58	.	.	PUNCT
ejpam-5003	443	1	by	by	ADP
ejpam-5003	443	2	lemma	lemma	PROPN
ejpam-5003	443	3	7	7	NUM
ejpam-5003	443	4	,	,	PUNCT
ejpam-5003	443	5	(	(	PUNCT
ejpam-5003	443	6	x⊛x′)θ(y⊛	x⊛x′)θ(y⊛	NUM
ejpam-5003	443	7	y′	y′	NUM
ejpam-5003	443	8	)	)	PUNCT
ejpam-5003	443	9	.	.	PUNCT
ejpam-5003	444	1	by	by	ADP
ejpam-5003	444	2	definition	definition	NOUN
ejpam-5003	444	3	15(iii	15(iii	NUM
ejpam-5003	444	4	)	)	PUNCT
ejpam-5003	444	5	,	,	PUNCT
ejpam-5003	444	6	θ	θ	PROPN
ejpam-5003	444	7	is	be	AUX
ejpam-5003	444	8	a	a	DET
ejpam-5003	444	9	congruence	congruence	NOUN
ejpam-5003	444	10	relation	relation	NOUN
ejpam-5003	444	11	.	.	PUNCT
ejpam-5003	445	1	the	the	DET
ejpam-5003	445	2	following	follow	VERB
ejpam-5003	445	3	proposition	proposition	NOUN
ejpam-5003	445	4	tells	tell	VERB
ejpam-5003	445	5	us	we	PRON
ejpam-5003	445	6	that	that	DET
ejpam-5003	445	7	∼s	∼s	NOUN
ejpam-5003	445	8	in	in	ADP
ejpam-5003	445	9	definition	definition	NOUN
ejpam-5003	445	10	13	13	NUM
ejpam-5003	445	11	is	be	AUX
ejpam-5003	445	12	a	a	DET
ejpam-5003	445	13	congruence	congruence	NOUN
ejpam-5003	445	14	relation	relation	NOUN
ejpam-5003	445	15	.	.	PUNCT
ejpam-5003	446	1	proposition	proposition	NOUN
ejpam-5003	446	2	3	3	X
ejpam-5003	446	3	.	.	PUNCT
ejpam-5003	447	1	let	let	VERB
ejpam-5003	447	2	s	s	PRON
ejpam-5003	447	3	be	be	AUX
ejpam-5003	447	4	a	a	DET
ejpam-5003	447	5	reflexive	reflexive	ADJ
ejpam-5003	447	6	normal	normal	ADJ
ejpam-5003	447	7	hyper	hyper	ADJ
ejpam-5003	447	8	subbn	subbn	NOUN
ejpam-5003	447	9	-algebra	-algebra	NOUN
ejpam-5003	447	10	of	of	ADP
ejpam-5003	447	11	a	a	DET
ejpam-5003	447	12	hyper	hyper	ADJ
ejpam-5003	447	13	bn	bn	NOUN
ejpam-5003	447	14	-algebra	-algebra	PROPN
ejpam-5003	447	15	h.	h.	NOUN
ejpam-5003	447	16	then	then	ADV
ejpam-5003	447	17	∼s	∼s	PROPN
ejpam-5003	447	18	is	be	AUX
ejpam-5003	447	19	a	a	DET
ejpam-5003	447	20	congruence	congruence	NOUN
ejpam-5003	447	21	relation	relation	NOUN
ejpam-5003	447	22	on	on	ADP
ejpam-5003	447	23	h.	h.	PROPN
ejpam-5003	447	24	proof	proof	NOUN
ejpam-5003	447	25	.	.	PUNCT
ejpam-5003	448	1	by	by	ADP
ejpam-5003	448	2	lemma	lemma	PROPN
ejpam-5003	448	3	4	4	NUM
ejpam-5003	448	4	,	,	PUNCT
ejpam-5003	448	5	∼s	∼s	PROPN
ejpam-5003	448	6	is	be	AUX
ejpam-5003	448	7	an	an	DET
ejpam-5003	448	8	equivalence	equivalence	NOUN
ejpam-5003	448	9	relation	relation	NOUN
ejpam-5003	448	10	.	.	PUNCT
ejpam-5003	449	1	we	we	PRON
ejpam-5003	449	2	will	will	AUX
ejpam-5003	449	3	show	show	VERB
ejpam-5003	449	4	that	that	SCONJ
ejpam-5003	449	5	∼s	∼s	PROPN
ejpam-5003	449	6	is	be	AUX
ejpam-5003	449	7	a	a	DET
ejpam-5003	449	8	congruence	congruence	NOUN
ejpam-5003	449	9	relation	relation	NOUN
ejpam-5003	449	10	using	use	VERB
ejpam-5003	449	11	lemma	lemma	PROPN
ejpam-5003	449	12	8	8	NUM
ejpam-5003	449	13	.	.	PUNCT
ejpam-5003	450	1	let	let	VERB
ejpam-5003	450	2	x	x	PRON
ejpam-5003	450	3	,	,	PUNCT
ejpam-5003	450	4	y	y	PROPN
ejpam-5003	450	5	∈	∈	PROPN
ejpam-5003	450	6	h	h	NOUN
ejpam-5003	450	7	with	with	ADP
ejpam-5003	450	8	x	x	PROPN
ejpam-5003	450	9	∼s	∼s	PROPN
ejpam-5003	450	10	y	y	NOUN
ejpam-5003	450	11	and	and	CCONJ
ejpam-5003	450	12	let	let	VERB
ejpam-5003	450	13	a	a	DET
ejpam-5003	450	14	∈	∈	PROPN
ejpam-5003	450	15	h.	h.	NOUN
ejpam-5003	451	1	then	then	ADV
ejpam-5003	451	2	x⊛	x⊛	PROPN
ejpam-5003	451	3	y	y	PROPN
ejpam-5003	451	4	⊆	⊆	NUM
ejpam-5003	451	5	s.	s.	PROPN
ejpam-5003	451	6	also	also	ADV
ejpam-5003	451	7	,	,	PUNCT
ejpam-5003	451	8	since	since	SCONJ
ejpam-5003	451	9	s	s	NOUN
ejpam-5003	451	10	is	be	AUX
ejpam-5003	451	11	reflexive	reflexive	ADJ
ejpam-5003	451	12	,	,	PUNCT
ejpam-5003	451	13	a	a	DET
ejpam-5003	451	14	⊛	⊛	NUM
ejpam-5003	451	15	a	a	DET
ejpam-5003	451	16	⊆	⊆	NUM
ejpam-5003	451	17	s.	s.	NOUN
ejpam-5003	451	18	by	by	ADP
ejpam-5003	451	19	normality	normality	NOUN
ejpam-5003	451	20	of	of	ADP
ejpam-5003	451	21	s	s	PROPN
ejpam-5003	451	22	,	,	PUNCT
ejpam-5003	451	23	(	(	PUNCT
ejpam-5003	451	24	x	x	PROPN
ejpam-5003	451	25	⊛	⊛	NUM
ejpam-5003	451	26	a	a	PRON
ejpam-5003	451	27	)	)	PUNCT
ejpam-5003	451	28	⊛	⊛	NUM
ejpam-5003	451	29	(	(	PUNCT
ejpam-5003	451	30	y	y	PROPN
ejpam-5003	451	31	⊛	⊛	NUM
ejpam-5003	451	32	a	a	X
ejpam-5003	451	33	)	)	PUNCT
ejpam-5003	451	34	⊆	⊆	NUM
ejpam-5003	451	35	s	s	NOUN
ejpam-5003	451	36	and	and	CCONJ
ejpam-5003	451	37	(	(	PUNCT
ejpam-5003	451	38	a	a	DET
ejpam-5003	451	39	⊛	⊛	NUM
ejpam-5003	451	40	x	x	NOUN
ejpam-5003	451	41	)	)	PUNCT
ejpam-5003	451	42	⊛	⊛	NUM
ejpam-5003	451	43	(	(	PUNCT
ejpam-5003	451	44	a	a	DET
ejpam-5003	451	45	⊛	⊛	NUM
ejpam-5003	451	46	y	y	NOUN
ejpam-5003	451	47	)	)	PUNCT
ejpam-5003	451	48	⊆	⊆	NUM
ejpam-5003	451	49	s.	s.	PROPN
ejpam-5003	451	50	also	also	ADV
ejpam-5003	451	51	,	,	PUNCT
ejpam-5003	451	52	by	by	ADP
ejpam-5003	451	53	lemma	lemma	PROPN
ejpam-5003	451	54	3(ii	3(ii	NUM
ejpam-5003	451	55	)	)	PUNCT
ejpam-5003	451	56	,	,	PUNCT
ejpam-5003	451	57	we	we	PRON
ejpam-5003	451	58	have	have	VERB
ejpam-5003	451	59	y	y	NOUN
ejpam-5003	451	60	⊛	⊛	NUM
ejpam-5003	451	61	x	x	X
ejpam-5003	451	62	⊆	⊆	NUM
ejpam-5003	451	63	s.	s.	PROPN
ejpam-5003	451	64	now	now	ADV
ejpam-5003	451	65	,	,	PUNCT
ejpam-5003	451	66	y	y	PROPN
ejpam-5003	451	67	⊛	⊛	NUM
ejpam-5003	451	68	x	x	X
ejpam-5003	451	69	⊆	⊆	NUM
ejpam-5003	451	70	s	s	NOUN
ejpam-5003	451	71	and	and	CCONJ
ejpam-5003	451	72	a⊛a	a⊛a	X
ejpam-5003	451	73	⊆	⊆	NUM
ejpam-5003	451	74	s	s	X
ejpam-5003	451	75	imply	imply	X
ejpam-5003	451	76	(	(	PUNCT
ejpam-5003	451	77	y⊛a)⊛	y⊛a)⊛	X
ejpam-5003	451	78	(	(	PUNCT
ejpam-5003	451	79	x⊛a	x⊛a	PROPN
ejpam-5003	451	80	)	)	PUNCT
ejpam-5003	451	81	⊆	⊆	NUM
ejpam-5003	451	82	s	s	NOUN
ejpam-5003	451	83	and	and	CCONJ
ejpam-5003	451	84	(	(	PUNCT
ejpam-5003	451	85	a⊛y)⊛	a⊛y)⊛	X
ejpam-5003	451	86	(	(	PUNCT
ejpam-5003	451	87	a⊛x	a⊛x	X
ejpam-5003	451	88	)	)	PUNCT
ejpam-5003	451	89	⊆	⊆	NUM
ejpam-5003	451	90	s.	s.	PROPN
ejpam-5003	451	91	now	now	ADV
ejpam-5003	451	92	,	,	PUNCT
ejpam-5003	451	93	(	(	PUNCT
ejpam-5003	451	94	x⊛a)⊛	x⊛a)⊛	X
ejpam-5003	451	95	(	(	PUNCT
ejpam-5003	451	96	y⊛a	y⊛a	PROPN
ejpam-5003	451	97	)	)	PUNCT
ejpam-5003	451	98	⊆	⊆	NUM
ejpam-5003	451	99	s	s	NOUN
ejpam-5003	451	100	implies	imply	VERB
ejpam-5003	451	101	that	that	SCONJ
ejpam-5003	451	102	u	u	PROPN
ejpam-5003	451	103	⊛	⊛	ADV
ejpam-5003	451	104	v	v	NUM
ejpam-5003	451	105	⊆	⊆	NUM
ejpam-5003	451	106	s	s	NOUN
ejpam-5003	451	107	for	for	ADP
ejpam-5003	451	108	all	all	DET
ejpam-5003	451	109	u	u	NOUN
ejpam-5003	451	110	∈	∈	PROPN
ejpam-5003	451	111	x	x	X
ejpam-5003	451	112	⊛	⊛	NUM
ejpam-5003	451	113	a	a	PRON
ejpam-5003	451	114	and	and	CCONJ
ejpam-5003	451	115	v	v	NOUN
ejpam-5003	451	116	∈	∈	PROPN
ejpam-5003	451	117	y	y	PROPN
ejpam-5003	451	118	⊛	⊛	ADJ
ejpam-5003	451	119	a.	a.	NOUN
ejpam-5003	451	120	similarly	similarly	ADV
ejpam-5003	451	121	,	,	PUNCT
ejpam-5003	451	122	(	(	PUNCT
ejpam-5003	451	123	y	y	PROPN
ejpam-5003	451	124	⊛	⊛	NUM
ejpam-5003	451	125	a	a	X
ejpam-5003	451	126	)	)	PUNCT
ejpam-5003	451	127	⊛	⊛	NOUN
ejpam-5003	451	128	(	(	PUNCT
ejpam-5003	451	129	x	x	PROPN
ejpam-5003	451	130	⊛	⊛	NUM
ejpam-5003	451	131	a	a	X
ejpam-5003	451	132	)	)	PUNCT
ejpam-5003	451	133	⊆	⊆	NUM
ejpam-5003	451	134	s	s	NOUN
ejpam-5003	451	135	implies	imply	VERB
ejpam-5003	451	136	that	that	SCONJ
ejpam-5003	451	137	v	v	ADP
ejpam-5003	451	138	⊛	⊛	NUM
ejpam-5003	451	139	u	u	NOUN
ejpam-5003	451	140	⊆	⊆	NUM
ejpam-5003	451	141	s	s	NOUN
ejpam-5003	451	142	for	for	ADP
ejpam-5003	451	143	all	all	DET
ejpam-5003	451	144	u	u	NOUN
ejpam-5003	451	145	∈	∈	PROPN
ejpam-5003	451	146	x	x	X
ejpam-5003	451	147	⊛	⊛	NUM
ejpam-5003	451	148	a	a	PRON
ejpam-5003	451	149	and	and	CCONJ
ejpam-5003	451	150	v	v	NOUN
ejpam-5003	451	151	∈	∈	PROPN
ejpam-5003	451	152	y	y	PROPN
ejpam-5003	451	153	⊛	⊛	NUM
ejpam-5003	451	154	a.	a.	NOUN
ejpam-5003	451	155	thus	thus	ADV
ejpam-5003	451	156	,	,	PUNCT
ejpam-5003	451	157	for	for	ADP
ejpam-5003	451	158	all	all	DET
ejpam-5003	451	159	u	u	NOUN
ejpam-5003	451	160	∈	∈	PROPN
ejpam-5003	451	161	x	x	X
ejpam-5003	451	162	⊛	⊛	NUM
ejpam-5003	451	163	a	a	PRON
ejpam-5003	451	164	and	and	CCONJ
ejpam-5003	451	165	v	v	NOUN
ejpam-5003	451	166	∈	∈	PROPN
ejpam-5003	451	167	y	y	PROPN
ejpam-5003	451	168	⊛	⊛	NUM
ejpam-5003	451	169	a	a	X
ejpam-5003	451	170	,	,	PUNCT
ejpam-5003	451	171	u	u	PROPN
ejpam-5003	451	172	∼s	∼s	PROPN
ejpam-5003	451	173	v	v	NOUN
ejpam-5003	452	1	and	and	CCONJ
ejpam-5003	452	2	this	this	PRON
ejpam-5003	452	3	means	mean	VERB
ejpam-5003	452	4	that	that	SCONJ
ejpam-5003	452	5	(	(	PUNCT
ejpam-5003	452	6	x⊛	x⊛	X
ejpam-5003	452	7	a)∼s(y	a)∼s(y	NOUN
ejpam-5003	452	8	⊛	⊛	ADJ
ejpam-5003	452	9	a	a	X
ejpam-5003	452	10	)	)	PUNCT
ejpam-5003	452	11	for	for	ADP
ejpam-5003	452	12	all	all	DET
ejpam-5003	452	13	a	a	DET
ejpam-5003	452	14	∈	∈	PROPN
ejpam-5003	452	15	h	h	NOUN
ejpam-5003	452	16	since	since	SCONJ
ejpam-5003	452	17	a	a	PRON
ejpam-5003	452	18	is	be	AUX
ejpam-5003	452	19	arbitrary	arbitrary	ADJ
ejpam-5003	452	20	.	.	PUNCT
ejpam-5003	453	1	in	in	ADP
ejpam-5003	453	2	similar	similar	ADJ
ejpam-5003	453	3	fashion	fashion	NOUN
ejpam-5003	453	4	,	,	PUNCT
ejpam-5003	453	5	using	use	VERB
ejpam-5003	453	6	(	(	PUNCT
ejpam-5003	453	7	a⊛	a⊛	PROPN
ejpam-5003	453	8	x)⊛	x)⊛	PROPN
ejpam-5003	453	9	(	(	PUNCT
ejpam-5003	453	10	a⊛	a⊛	PROPN
ejpam-5003	453	11	y	y	PROPN
ejpam-5003	453	12	)	)	PUNCT
ejpam-5003	453	13	⊆	⊆	NUM
ejpam-5003	453	14	s	s	NOUN
ejpam-5003	453	15	and	and	CCONJ
ejpam-5003	453	16	(	(	PUNCT
ejpam-5003	453	17	a⊛	a⊛	NOUN
ejpam-5003	453	18	y)⊛	y)⊛	NOUN
ejpam-5003	453	19	(	(	PUNCT
ejpam-5003	453	20	a⊛	a⊛	NOUN
ejpam-5003	453	21	x	x	NOUN
ejpam-5003	453	22	)	)	PUNCT
ejpam-5003	453	23	⊆	⊆	NUM
ejpam-5003	453	24	s	s	NOUN
ejpam-5003	453	25	,	,	PUNCT
ejpam-5003	453	26	we	we	PRON
ejpam-5003	453	27	will	will	AUX
ejpam-5003	453	28	obtain	obtain	VERB
ejpam-5003	453	29	(	(	PUNCT
ejpam-5003	453	30	a⊛	a⊛	PROPN
ejpam-5003	453	31	x)∼s(a⊛	x)∼s(a⊛	PROPN
ejpam-5003	453	32	y	y	PROPN
ejpam-5003	453	33	)	)	PUNCT
ejpam-5003	453	34	for	for	ADP
ejpam-5003	453	35	all	all	DET
ejpam-5003	453	36	a	a	DET
ejpam-5003	453	37	∈	∈	PROPN
ejpam-5003	453	38	h.	h.	NOUN
ejpam-5003	453	39	therefore	therefore	ADV
ejpam-5003	453	40	,	,	PUNCT
ejpam-5003	453	41	∼s	∼s	PROPN
ejpam-5003	453	42	is	be	AUX
ejpam-5003	453	43	a	a	DET
ejpam-5003	453	44	congruence	congruence	NOUN
ejpam-5003	453	45	relation	relation	NOUN
ejpam-5003	453	46	on	on	ADP
ejpam-5003	453	47	h.	h.	PROPN
ejpam-5003	453	48	the	the	DET
ejpam-5003	453	49	converse	converse	NOUN
ejpam-5003	453	50	of	of	ADP
ejpam-5003	453	51	proposition	proposition	NOUN
ejpam-5003	453	52	3	3	NUM
ejpam-5003	453	53	is	be	AUX
ejpam-5003	453	54	not	not	PART
ejpam-5003	453	55	true	true	ADJ
ejpam-5003	453	56	in	in	ADP
ejpam-5003	453	57	general	general	ADJ
ejpam-5003	453	58	as	as	SCONJ
ejpam-5003	453	59	shown	show	VERB
ejpam-5003	453	60	in	in	ADP
ejpam-5003	453	61	the	the	DET
ejpam-5003	453	62	following	follow	VERB
ejpam-5003	453	63	example	example	NOUN
ejpam-5003	453	64	:	:	PUNCT
ejpam-5003	453	65	l.r	l.r	PROPN
ejpam-5003	453	66	.	.	PROPN
ejpam-5003	453	67	cabardo	cabardo	PROPN
ejpam-5003	453	68	,	,	PUNCT
ejpam-5003	453	69	g.	g.	PROPN
ejpam-5003	453	70	petalcorin	petalcorin	PROPN
ejpam-5003	453	71	/	/	SYM
ejpam-5003	453	72	eur	eur	PROPN
ejpam-5003	453	73	.	.	PUNCT
ejpam-5003	454	1	j.	j.	PROPN
ejpam-5003	454	2	pure	pure	PROPN
ejpam-5003	454	3	appl	appl	PROPN
ejpam-5003	454	4	.	.	PROPN
ejpam-5003	454	5	math	math	PROPN
ejpam-5003	454	6	,	,	PUNCT
ejpam-5003	454	7	17	17	NUM
ejpam-5003	454	8	(	(	PUNCT
ejpam-5003	454	9	1	1	NUM
ejpam-5003	454	10	)	)	PUNCT
ejpam-5003	454	11	(	(	PUNCT
ejpam-5003	454	12	2024	2024	NUM
ejpam-5003	454	13	)	)	PUNCT
ejpam-5003	454	14	,	,	PUNCT
ejpam-5003	454	15	222	222	NUM
ejpam-5003	454	16	-	-	SYM
ejpam-5003	454	17	242	242	NUM
ejpam-5003	454	18	237	237	NUM
ejpam-5003	454	19	example	example	NOUN
ejpam-5003	454	20	22	22	NUM
ejpam-5003	454	21	.	.	PUNCT
ejpam-5003	455	1	let	let	VERB
ejpam-5003	455	2	h	h	NOUN
ejpam-5003	455	3	=	=	PUNCT
ejpam-5003	455	4	{	{	PUNCT
ejpam-5003	455	5	0	0	NUM
ejpam-5003	455	6	,	,	PUNCT
ejpam-5003	455	7	1	1	NUM
ejpam-5003	455	8	,	,	PUNCT
ejpam-5003	455	9	2	2	NUM
ejpam-5003	455	10	,	,	PUNCT
ejpam-5003	455	11	3	3	NUM
ejpam-5003	455	12	,	,	PUNCT
ejpam-5003	455	13	4	4	NUM
ejpam-5003	455	14	,	,	PUNCT
ejpam-5003	455	15	5	5	NUM
ejpam-5003	455	16	}	}	PUNCT
ejpam-5003	455	17	be	be	AUX
ejpam-5003	455	18	a	a	DET
ejpam-5003	455	19	set	set	NOUN
ejpam-5003	455	20	.	.	PUNCT
ejpam-5003	456	1	define	define	VERB
ejpam-5003	456	2	a	a	DET
ejpam-5003	456	3	hyperoperation	hyperoperation	NOUN
ejpam-5003	456	4	⊛	⊛	ADJ
ejpam-5003	456	5	on	on	ADP
ejpam-5003	456	6	h	h	NOUN
ejpam-5003	456	7	by	by	ADP
ejpam-5003	456	8	the	the	DET
ejpam-5003	456	9	following	following	ADJ
ejpam-5003	456	10	cayley	cayley	ADJ
ejpam-5003	456	11	table	table	NOUN
ejpam-5003	456	12	:	:	PUNCT
ejpam-5003	456	13	⊛	⊛	NUM
ejpam-5003	456	14	0	0	NUM
ejpam-5003	456	15	1	1	NUM
ejpam-5003	456	16	2	2	NUM
ejpam-5003	456	17	3	3	NUM
ejpam-5003	456	18	4	4	NUM
ejpam-5003	456	19	5	5	NUM
ejpam-5003	456	20	0	0	NUM
ejpam-5003	456	21	{	{	PUNCT
ejpam-5003	456	22	0	0	NUM
ejpam-5003	456	23	}	}	PUNCT
ejpam-5003	456	24	{	{	PUNCT
ejpam-5003	456	25	1	1	NUM
ejpam-5003	456	26	}	}	PUNCT
ejpam-5003	456	27	{	{	PUNCT
ejpam-5003	456	28	2	2	NUM
ejpam-5003	456	29	}	}	PUNCT
ejpam-5003	456	30	{	{	PUNCT
ejpam-5003	456	31	3	3	NUM
ejpam-5003	456	32	}	}	PUNCT
ejpam-5003	456	33	{	{	PUNCT
ejpam-5003	456	34	4	4	NUM
ejpam-5003	456	35	}	}	PUNCT
ejpam-5003	456	36	{	{	PUNCT
ejpam-5003	456	37	5	5	NUM
ejpam-5003	456	38	}	}	SYM
ejpam-5003	456	39	1	1	NUM
ejpam-5003	456	40	{	{	PUNCT
ejpam-5003	456	41	1	1	NUM
ejpam-5003	456	42	}	}	PUNCT
ejpam-5003	456	43	{	{	PUNCT
ejpam-5003	456	44	0	0	NUM
ejpam-5003	456	45	,	,	PUNCT
ejpam-5003	456	46	1	1	NUM
ejpam-5003	456	47	}	}	PUNCT
ejpam-5003	456	48	{	{	PUNCT
ejpam-5003	456	49	2	2	NUM
ejpam-5003	456	50	}	}	PUNCT
ejpam-5003	456	51	{	{	PUNCT
ejpam-5003	456	52	3	3	NUM
ejpam-5003	456	53	}	}	PUNCT
ejpam-5003	456	54	{	{	PUNCT
ejpam-5003	456	55	4	4	NUM
ejpam-5003	456	56	}	}	PUNCT
ejpam-5003	456	57	{	{	PUNCT
ejpam-5003	456	58	5	5	NUM
ejpam-5003	456	59	}	}	SYM
ejpam-5003	456	60	2	2	NUM
ejpam-5003	456	61	{	{	PUNCT
ejpam-5003	456	62	2	2	NUM
ejpam-5003	456	63	}	}	PUNCT
ejpam-5003	456	64	{	{	PUNCT
ejpam-5003	456	65	2	2	NUM
ejpam-5003	456	66	}	}	PUNCT
ejpam-5003	456	67	{	{	PUNCT
ejpam-5003	456	68	0	0	NUM
ejpam-5003	456	69	,	,	PUNCT
ejpam-5003	456	70	1	1	NUM
ejpam-5003	456	71	}	}	PUNCT
ejpam-5003	456	72	{	{	PUNCT
ejpam-5003	456	73	0	0	NUM
ejpam-5003	456	74	,	,	PUNCT
ejpam-5003	456	75	1	1	NUM
ejpam-5003	456	76	}	}	PUNCT
ejpam-5003	456	77	{	{	PUNCT
ejpam-5003	456	78	0	0	NUM
ejpam-5003	456	79	,	,	PUNCT
ejpam-5003	456	80	4	4	NUM
ejpam-5003	456	81	}	}	PUNCT
ejpam-5003	456	82	{	{	PUNCT
ejpam-5003	456	83	0	0	NUM
ejpam-5003	456	84	,	,	PUNCT
ejpam-5003	456	85	5	5	NUM
ejpam-5003	456	86	}	}	SYM
ejpam-5003	456	87	3	3	NUM
ejpam-5003	456	88	{	{	PUNCT
ejpam-5003	456	89	3	3	NUM
ejpam-5003	456	90	}	}	PUNCT
ejpam-5003	456	91	{	{	PUNCT
ejpam-5003	456	92	3	3	NUM
ejpam-5003	456	93	}	}	PUNCT
ejpam-5003	456	94	{	{	PUNCT
ejpam-5003	456	95	0	0	NUM
ejpam-5003	456	96	,	,	PUNCT
ejpam-5003	456	97	1	1	NUM
ejpam-5003	456	98	}	}	PUNCT
ejpam-5003	456	99	{	{	PUNCT
ejpam-5003	456	100	0	0	NUM
ejpam-5003	456	101	,	,	PUNCT
ejpam-5003	456	102	1	1	NUM
ejpam-5003	456	103	}	}	PUNCT
ejpam-5003	456	104	{	{	PUNCT
ejpam-5003	456	105	0	0	NUM
ejpam-5003	456	106	,	,	PUNCT
ejpam-5003	456	107	4	4	NUM
ejpam-5003	456	108	}	}	PUNCT
ejpam-5003	456	109	{	{	PUNCT
ejpam-5003	456	110	0	0	NUM
ejpam-5003	456	111	,	,	PUNCT
ejpam-5003	456	112	5	5	NUM
ejpam-5003	456	113	}	}	SYM
ejpam-5003	456	114	4	4	NUM
ejpam-5003	456	115	{	{	PUNCT
ejpam-5003	456	116	4	4	NUM
ejpam-5003	456	117	}	}	PUNCT
ejpam-5003	456	118	{	{	PUNCT
ejpam-5003	456	119	4	4	NUM
ejpam-5003	456	120	}	}	PUNCT
ejpam-5003	456	121	{	{	PUNCT
ejpam-5003	456	122	0	0	NUM
ejpam-5003	456	123	,	,	PUNCT
ejpam-5003	456	124	4	4	NUM
ejpam-5003	456	125	}	}	PUNCT
ejpam-5003	456	126	{	{	PUNCT
ejpam-5003	456	127	0	0	NUM
ejpam-5003	456	128	,	,	PUNCT
ejpam-5003	456	129	4	4	NUM
ejpam-5003	456	130	}	}	PUNCT
ejpam-5003	456	131	{	{	PUNCT
ejpam-5003	456	132	0	0	NUM
ejpam-5003	456	133	,	,	PUNCT
ejpam-5003	456	134	1	1	NUM
ejpam-5003	456	135	}	}	PUNCT
ejpam-5003	456	136	{	{	PUNCT
ejpam-5003	456	137	0	0	NUM
ejpam-5003	456	138	,	,	PUNCT
ejpam-5003	456	139	1	1	NUM
ejpam-5003	456	140	}	}	SYM
ejpam-5003	456	141	5	5	NUM
ejpam-5003	456	142	{	{	PUNCT
ejpam-5003	456	143	5	5	NUM
ejpam-5003	456	144	}	}	PUNCT
ejpam-5003	456	145	{	{	PUNCT
ejpam-5003	456	146	5	5	NUM
ejpam-5003	456	147	}	}	PUNCT
ejpam-5003	456	148	{	{	PUNCT
ejpam-5003	456	149	0	0	NUM
ejpam-5003	456	150	,	,	PUNCT
ejpam-5003	456	151	5	5	NUM
ejpam-5003	456	152	}	}	PUNCT
ejpam-5003	456	153	{	{	PUNCT
ejpam-5003	456	154	0	0	NUM
ejpam-5003	456	155	,	,	PUNCT
ejpam-5003	456	156	5	5	NUM
ejpam-5003	456	157	}	}	PUNCT
ejpam-5003	456	158	{	{	PUNCT
ejpam-5003	456	159	0	0	NUM
ejpam-5003	456	160	,	,	PUNCT
ejpam-5003	456	161	1	1	NUM
ejpam-5003	456	162	}	}	PUNCT
ejpam-5003	456	163	{	{	PUNCT
ejpam-5003	456	164	0	0	NUM
ejpam-5003	456	165	,	,	PUNCT
ejpam-5003	456	166	1	1	NUM
ejpam-5003	456	167	}	}	PUNCT
ejpam-5003	456	168	by	by	ADP
ejpam-5003	456	169	routine	routine	ADJ
ejpam-5003	456	170	calculations	calculation	NOUN
ejpam-5003	456	171	,	,	PUNCT
ejpam-5003	456	172	h	h	NOUN
ejpam-5003	456	173	is	be	AUX
ejpam-5003	456	174	a	a	DET
ejpam-5003	456	175	hyper	hyper	ADJ
ejpam-5003	456	176	bn	bn	NOUN
ejpam-5003	456	177	-algebra	-algebra	NOUN
ejpam-5003	456	178	.	.	PUNCT
ejpam-5003	457	1	let	let	VERB
ejpam-5003	457	2	s	s	PRON
ejpam-5003	457	3	=	=	X
ejpam-5003	457	4	{	{	PUNCT
ejpam-5003	457	5	0	0	NUM
ejpam-5003	457	6	,	,	PUNCT
ejpam-5003	457	7	1	1	NUM
ejpam-5003	457	8	}	}	PUNCT
ejpam-5003	457	9	and	and	CCONJ
ejpam-5003	457	10	∼s	∼s	NUM
ejpam-5003	457	11	be	be	AUX
ejpam-5003	457	12	a	a	DET
ejpam-5003	457	13	relation	relation	NOUN
ejpam-5003	457	14	on	on	ADP
ejpam-5003	457	15	h	h	NOUN
ejpam-5003	457	16	defined	define	VERB
ejpam-5003	457	17	by	by	ADP
ejpam-5003	457	18	x	x	PROPN
ejpam-5003	457	19	∼s	∼s	PROPN
ejpam-5003	457	20	y	y	PROPN
ejpam-5003	457	21	if	if	SCONJ
ejpam-5003	457	22	and	and	CCONJ
ejpam-5003	458	1	only	only	ADV
ejpam-5003	458	2	if	if	SCONJ
ejpam-5003	458	3	x	x	PROPN
ejpam-5003	458	4	⊛	⊛	ADV
ejpam-5003	458	5	y	y	PROPN
ejpam-5003	458	6	⊆	⊆	NUM
ejpam-5003	458	7	s	s	NOUN
ejpam-5003	458	8	for	for	ADP
ejpam-5003	458	9	all	all	DET
ejpam-5003	458	10	x	x	NOUN
ejpam-5003	458	11	,	,	PUNCT
ejpam-5003	458	12	y	y	PROPN
ejpam-5003	458	13	∈	∈	PROPN
ejpam-5003	458	14	h.	h.	PROPN
ejpam-5003	458	15	then	then	ADV
ejpam-5003	458	16	∼s=	∼s=	PUNCT
ejpam-5003	458	17	{	{	PUNCT
ejpam-5003	458	18	(	(	PUNCT
ejpam-5003	458	19	0	0	NUM
ejpam-5003	458	20	,	,	PUNCT
ejpam-5003	458	21	0	0	NUM
ejpam-5003	458	22	)	)	PUNCT
ejpam-5003	458	23	,	,	PUNCT
ejpam-5003	458	24	(	(	PUNCT
ejpam-5003	458	25	0	0	NUM
ejpam-5003	458	26	,	,	PUNCT
ejpam-5003	458	27	1	1	NUM
ejpam-5003	458	28	)	)	PUNCT
ejpam-5003	458	29	,	,	PUNCT
ejpam-5003	458	30	(	(	PUNCT
ejpam-5003	458	31	1	1	NUM
ejpam-5003	458	32	,	,	PUNCT
ejpam-5003	458	33	0	0	NUM
ejpam-5003	458	34	)	)	PUNCT
ejpam-5003	458	35	,	,	PUNCT
ejpam-5003	458	36	(	(	PUNCT
ejpam-5003	458	37	1	1	NUM
ejpam-5003	458	38	,	,	PUNCT
ejpam-5003	458	39	1	1	NUM
ejpam-5003	458	40	)	)	PUNCT
ejpam-5003	458	41	,	,	PUNCT
ejpam-5003	458	42	(	(	PUNCT
ejpam-5003	458	43	2	2	NUM
ejpam-5003	458	44	,	,	PUNCT
ejpam-5003	458	45	2	2	NUM
ejpam-5003	458	46	)	)	PUNCT
ejpam-5003	458	47	,	,	PUNCT
ejpam-5003	458	48	(	(	PUNCT
ejpam-5003	458	49	2	2	NUM
ejpam-5003	458	50	,	,	PUNCT
ejpam-5003	458	51	3	3	NUM
ejpam-5003	458	52	)	)	PUNCT
ejpam-5003	458	53	,	,	PUNCT
ejpam-5003	458	54	(	(	PUNCT
ejpam-5003	458	55	3	3	NUM
ejpam-5003	458	56	,	,	PUNCT
ejpam-5003	458	57	2	2	NUM
ejpam-5003	458	58	)	)	PUNCT
ejpam-5003	458	59	,	,	PUNCT
ejpam-5003	458	60	(	(	PUNCT
ejpam-5003	458	61	3	3	NUM
ejpam-5003	458	62	,	,	PUNCT
ejpam-5003	458	63	3	3	NUM
ejpam-5003	458	64	)	)	PUNCT
ejpam-5003	458	65	,	,	PUNCT
ejpam-5003	458	66	(	(	PUNCT
ejpam-5003	458	67	4	4	NUM
ejpam-5003	458	68	,	,	PUNCT
ejpam-5003	458	69	4	4	NUM
ejpam-5003	458	70	)	)	PUNCT
ejpam-5003	458	71	,	,	PUNCT
ejpam-5003	458	72	(	(	PUNCT
ejpam-5003	458	73	4	4	NUM
ejpam-5003	458	74	,	,	PUNCT
ejpam-5003	458	75	5	5	NUM
ejpam-5003	458	76	)	)	PUNCT
ejpam-5003	458	77	,	,	PUNCT
ejpam-5003	458	78	(	(	PUNCT
ejpam-5003	458	79	5	5	NUM
ejpam-5003	458	80	,	,	PUNCT
ejpam-5003	458	81	4	4	NUM
ejpam-5003	458	82	)	)	PUNCT
ejpam-5003	458	83	,	,	PUNCT
ejpam-5003	458	84	(	(	PUNCT
ejpam-5003	458	85	5	5	NUM
ejpam-5003	458	86	,	,	PUNCT
ejpam-5003	458	87	5	5	NUM
ejpam-5003	458	88	)	)	PUNCT
ejpam-5003	458	89	}	}	PUNCT
ejpam-5003	458	90	.	.	PUNCT
ejpam-5003	459	1	by	by	ADP
ejpam-5003	459	2	inspection	inspection	NOUN
ejpam-5003	459	3	,	,	PUNCT
ejpam-5003	459	4	∼s	∼s	PROPN
ejpam-5003	459	5	is	be	AUX
ejpam-5003	459	6	an	an	DET
ejpam-5003	459	7	equivalence	equivalence	NOUN
ejpam-5003	459	8	relation	relation	NOUN
ejpam-5003	459	9	.	.	PUNCT
ejpam-5003	460	1	now	now	ADV
ejpam-5003	460	2	,	,	PUNCT
ejpam-5003	460	3	we	we	PRON
ejpam-5003	460	4	can	can	AUX
ejpam-5003	460	5	verify	verify	VERB
ejpam-5003	460	6	that	that	SCONJ
ejpam-5003	460	7	∼s	∼s	PROPN
ejpam-5003	460	8	is	be	AUX
ejpam-5003	460	9	a	a	DET
ejpam-5003	460	10	congruence	congruence	NOUN
ejpam-5003	460	11	relation	relation	NOUN
ejpam-5003	460	12	using	use	VERB
ejpam-5003	460	13	lemma	lemma	PROPN
ejpam-5003	460	14	8	8	NUM
ejpam-5003	460	15	.	.	PUNCT
ejpam-5003	461	1	note	note	VERB
ejpam-5003	461	2	that	that	SCONJ
ejpam-5003	461	3	s	s	VERB
ejpam-5003	461	4	is	be	AUX
ejpam-5003	461	5	a	a	DET
ejpam-5003	461	6	hyper	hyper	ADJ
ejpam-5003	461	7	subbn	subbn	NOUN
ejpam-5003	461	8	-algebra	-algebra	NOUN
ejpam-5003	461	9	of	of	ADP
ejpam-5003	461	10	h.	h.	PROPN
ejpam-5003	461	11	also	also	ADV
ejpam-5003	461	12	,	,	PUNCT
ejpam-5003	461	13	it	it	PRON
ejpam-5003	461	14	is	be	AUX
ejpam-5003	461	15	reflexive	reflexive	ADJ
ejpam-5003	461	16	because	because	SCONJ
ejpam-5003	461	17	for	for	ADP
ejpam-5003	461	18	all	all	DET
ejpam-5003	461	19	a	a	DET
ejpam-5003	461	20	∈	∈	PROPN
ejpam-5003	461	21	h	h	NOUN
ejpam-5003	461	22	a	a	DET
ejpam-5003	461	23	⊛	⊛	NUM
ejpam-5003	461	24	a	a	DET
ejpam-5003	461	25	⊆	⊆	NUM
ejpam-5003	461	26	s.	s.	PROPN
ejpam-5003	461	27	however	however	ADV
ejpam-5003	461	28	,	,	PUNCT
ejpam-5003	461	29	it	it	PRON
ejpam-5003	461	30	is	be	AUX
ejpam-5003	461	31	not	not	PART
ejpam-5003	461	32	normal	normal	ADJ
ejpam-5003	461	33	because	because	SCONJ
ejpam-5003	461	34	2	2	NUM
ejpam-5003	461	35	⊛	⊛	NUM
ejpam-5003	461	36	3	3	NUM
ejpam-5003	461	37	⊆	⊆	NUM
ejpam-5003	461	38	s	s	NOUN
ejpam-5003	461	39	and	and	CCONJ
ejpam-5003	461	40	4	4	NUM
ejpam-5003	461	41	⊛	⊛	NUM
ejpam-5003	461	42	4	4	NUM
ejpam-5003	461	43	⊆	⊆	NUM
ejpam-5003	461	44	s	s	NOUN
ejpam-5003	461	45	but	but	CCONJ
ejpam-5003	461	46	(	(	PUNCT
ejpam-5003	461	47	2	2	NUM
ejpam-5003	461	48	⊛	⊛	NUM
ejpam-5003	461	49	4	4	NUM
ejpam-5003	461	50	)	)	PUNCT
ejpam-5003	461	51	⊛	⊛	NUM
ejpam-5003	461	52	(	(	PUNCT
ejpam-5003	461	53	3	3	NUM
ejpam-5003	461	54	⊛	⊛	NUM
ejpam-5003	461	55	4	4	NUM
ejpam-5003	461	56	)	)	PUNCT
ejpam-5003	461	57	=	=	PRON
ejpam-5003	461	58	{	{	PUNCT
ejpam-5003	461	59	0	0	NUM
ejpam-5003	461	60	,	,	PUNCT
ejpam-5003	461	61	1	1	NUM
ejpam-5003	461	62	,	,	PUNCT
ejpam-5003	461	63	4	4	NUM
ejpam-5003	461	64	}	}	PUNCT
ejpam-5003	461	65	̸⊆	̸⊆	NOUN
ejpam-5003	461	66	s.	s.	PROPN
ejpam-5003	461	67	therefore	therefore	ADV
ejpam-5003	461	68	,	,	PUNCT
ejpam-5003	461	69	s	s	VERB
ejpam-5003	461	70	is	be	AUX
ejpam-5003	461	71	not	not	PART
ejpam-5003	461	72	a	a	DET
ejpam-5003	461	73	reflexive	reflexive	ADJ
ejpam-5003	461	74	normal	normal	ADJ
ejpam-5003	461	75	hyper	hyper	ADJ
ejpam-5003	461	76	subbn	subbn	NOUN
ejpam-5003	461	77	-algebra	-algebra	PROPN
ejpam-5003	461	78	of	of	ADP
ejpam-5003	461	79	h.	h.	NOUN
ejpam-5003	461	80	the	the	DET
ejpam-5003	461	81	following	follow	VERB
ejpam-5003	461	82	example	example	NOUN
ejpam-5003	461	83	will	will	AUX
ejpam-5003	461	84	illustrate	illustrate	VERB
ejpam-5003	461	85	that	that	SCONJ
ejpam-5003	461	86	the	the	DET
ejpam-5003	461	87	congruence	congruence	NOUN
ejpam-5003	461	88	class	class	NOUN
ejpam-5003	461	89	containing	contain	VERB
ejpam-5003	461	90	0	0	NUM
ejpam-5003	461	91	is	be	AUX
ejpam-5003	461	92	not	not	PART
ejpam-5003	461	93	necessarily	necessarily	ADV
ejpam-5003	461	94	reflexive	reflexive	ADJ
ejpam-5003	461	95	.	.	PUNCT
ejpam-5003	462	1	this	this	PRON
ejpam-5003	462	2	will	will	AUX
ejpam-5003	462	3	mean	mean	VERB
ejpam-5003	462	4	that	that	SCONJ
ejpam-5003	462	5	the	the	DET
ejpam-5003	462	6	construction	construction	NOUN
ejpam-5003	462	7	of	of	ADP
ejpam-5003	462	8	the	the	DET
ejpam-5003	462	9	quotient	quotient	NOUN
ejpam-5003	462	10	structure	structure	NOUN
ejpam-5003	462	11	via	via	ADP
ejpam-5003	462	12	reflexive	reflexive	ADJ
ejpam-5003	462	13	normal	normal	ADJ
ejpam-5003	462	14	hyper	hyper	ADJ
ejpam-5003	462	15	subbn	subbn	NOUN
ejpam-5003	462	16	-algebra	-algebra	PROPN
ejpam-5003	462	17	is	be	AUX
ejpam-5003	462	18	just	just	ADV
ejpam-5003	462	19	a	a	DET
ejpam-5003	462	20	special	special	ADJ
ejpam-5003	462	21	case	case	NOUN
ejpam-5003	462	22	of	of	ADP
ejpam-5003	462	23	the	the	DET
ejpam-5003	462	24	construction	construction	NOUN
ejpam-5003	462	25	of	of	ADP
ejpam-5003	462	26	the	the	DET
ejpam-5003	462	27	quotient	quotient	NOUN
ejpam-5003	462	28	structure	structure	NOUN
ejpam-5003	462	29	via	via	ADP
ejpam-5003	462	30	congruence	congruence	PROPN
ejpam-5003	462	31	relation	relation	PROPN
ejpam-5003	462	32	.	.	PUNCT
ejpam-5003	463	1	example	example	NOUN
ejpam-5003	463	2	23	23	NUM
ejpam-5003	463	3	.	.	PUNCT
ejpam-5003	464	1	let	let	VERB
ejpam-5003	464	2	h	h	NOUN
ejpam-5003	464	3	=	=	PUNCT
ejpam-5003	464	4	{	{	PUNCT
ejpam-5003	464	5	0	0	NUM
ejpam-5003	464	6	,	,	PUNCT
ejpam-5003	464	7	1	1	NUM
ejpam-5003	464	8	,	,	PUNCT
ejpam-5003	464	9	2	2	NUM
ejpam-5003	464	10	,	,	PUNCT
ejpam-5003	464	11	3	3	NUM
ejpam-5003	464	12	,	,	PUNCT
ejpam-5003	464	13	4	4	NUM
ejpam-5003	464	14	}	}	PUNCT
ejpam-5003	464	15	be	be	AUX
ejpam-5003	464	16	a	a	DET
ejpam-5003	464	17	set	set	NOUN
ejpam-5003	464	18	.	.	PUNCT
ejpam-5003	465	1	define	define	VERB
ejpam-5003	465	2	a	a	DET
ejpam-5003	465	3	hyperoperation	hyperoperation	NOUN
ejpam-5003	465	4	⊛	⊛	ADJ
ejpam-5003	465	5	on	on	ADP
ejpam-5003	465	6	h	h	NOUN
ejpam-5003	465	7	by	by	ADP
ejpam-5003	465	8	the	the	DET
ejpam-5003	465	9	following	following	ADJ
ejpam-5003	465	10	cayley	cayley	ADJ
ejpam-5003	465	11	table	table	NOUN
ejpam-5003	465	12	:	:	PUNCT
ejpam-5003	465	13	⊛	⊛	NUM
ejpam-5003	465	14	0	0	NUM
ejpam-5003	465	15	1	1	NUM
ejpam-5003	465	16	2	2	NUM
ejpam-5003	465	17	3	3	NUM
ejpam-5003	465	18	4	4	NUM
ejpam-5003	465	19	0	0	NUM
ejpam-5003	465	20	{	{	PUNCT
ejpam-5003	465	21	0	0	NUM
ejpam-5003	465	22	}	}	PUNCT
ejpam-5003	465	23	{	{	PUNCT
ejpam-5003	465	24	1	1	NUM
ejpam-5003	465	25	}	}	PUNCT
ejpam-5003	465	26	{	{	PUNCT
ejpam-5003	465	27	3	3	NUM
ejpam-5003	465	28	}	}	PUNCT
ejpam-5003	465	29	{	{	PUNCT
ejpam-5003	465	30	2	2	NUM
ejpam-5003	465	31	}	}	PUNCT
ejpam-5003	465	32	{	{	PUNCT
ejpam-5003	465	33	4	4	NUM
ejpam-5003	465	34	}	}	SYM
ejpam-5003	465	35	1	1	NUM
ejpam-5003	465	36	{	{	PUNCT
ejpam-5003	465	37	1	1	NUM
ejpam-5003	465	38	}	}	PUNCT
ejpam-5003	465	39	{	{	PUNCT
ejpam-5003	465	40	0	0	NUM
ejpam-5003	465	41	,	,	PUNCT
ejpam-5003	465	42	1	1	NUM
ejpam-5003	465	43	}	}	PUNCT
ejpam-5003	465	44	{	{	PUNCT
ejpam-5003	465	45	2	2	NUM
ejpam-5003	465	46	}	}	PUNCT
ejpam-5003	465	47	{	{	PUNCT
ejpam-5003	465	48	3	3	NUM
ejpam-5003	465	49	}	}	PUNCT
ejpam-5003	465	50	{	{	PUNCT
ejpam-5003	465	51	4	4	NUM
ejpam-5003	465	52	}	}	SYM
ejpam-5003	465	53	2	2	NUM
ejpam-5003	465	54	{	{	PUNCT
ejpam-5003	465	55	2	2	NUM
ejpam-5003	465	56	}	}	PUNCT
ejpam-5003	465	57	{	{	PUNCT
ejpam-5003	465	58	3	3	NUM
ejpam-5003	465	59	}	}	PUNCT
ejpam-5003	465	60	{	{	PUNCT
ejpam-5003	465	61	0	0	NUM
ejpam-5003	465	62	,	,	PUNCT
ejpam-5003	465	63	2	2	NUM
ejpam-5003	465	64	,	,	PUNCT
ejpam-5003	465	65	3	3	NUM
ejpam-5003	465	66	}	}	PUNCT
ejpam-5003	465	67	{	{	PUNCT
ejpam-5003	465	68	1	1	NUM
ejpam-5003	465	69	,	,	PUNCT
ejpam-5003	465	70	2	2	NUM
ejpam-5003	465	71	,	,	PUNCT
ejpam-5003	465	72	3	3	NUM
ejpam-5003	465	73	}	}	PUNCT
ejpam-5003	465	74	{	{	PUNCT
ejpam-5003	465	75	0	0	NUM
ejpam-5003	465	76	,	,	PUNCT
ejpam-5003	465	77	1	1	NUM
ejpam-5003	465	78	}	}	SYM
ejpam-5003	465	79	3	3	NUM
ejpam-5003	465	80	{	{	PUNCT
ejpam-5003	465	81	3	3	NUM
ejpam-5003	465	82	}	}	PUNCT
ejpam-5003	465	83	{	{	PUNCT
ejpam-5003	465	84	2	2	NUM
ejpam-5003	465	85	}	}	PUNCT
ejpam-5003	465	86	{	{	PUNCT
ejpam-5003	465	87	1	1	NUM
ejpam-5003	465	88	,	,	PUNCT
ejpam-5003	465	89	2	2	NUM
ejpam-5003	465	90	,	,	PUNCT
ejpam-5003	465	91	3	3	NUM
ejpam-5003	465	92	}	}	PUNCT
ejpam-5003	465	93	{	{	PUNCT
ejpam-5003	465	94	0	0	NUM
ejpam-5003	465	95	,	,	PUNCT
ejpam-5003	465	96	2	2	NUM
ejpam-5003	465	97	,	,	PUNCT
ejpam-5003	465	98	3	3	NUM
ejpam-5003	465	99	}	}	PUNCT
ejpam-5003	465	100	{	{	PUNCT
ejpam-5003	465	101	0	0	NUM
ejpam-5003	465	102	,	,	PUNCT
ejpam-5003	465	103	1	1	NUM
ejpam-5003	465	104	}	}	SYM
ejpam-5003	465	105	4	4	NUM
ejpam-5003	465	106	{	{	PUNCT
ejpam-5003	465	107	4	4	NUM
ejpam-5003	465	108	}	}	PUNCT
ejpam-5003	465	109	{	{	PUNCT
ejpam-5003	465	110	4	4	NUM
ejpam-5003	465	111	}	}	PUNCT
ejpam-5003	465	112	{	{	PUNCT
ejpam-5003	465	113	0	0	NUM
ejpam-5003	465	114	,	,	PUNCT
ejpam-5003	465	115	1	1	NUM
ejpam-5003	465	116	}	}	PUNCT
ejpam-5003	465	117	{	{	PUNCT
ejpam-5003	465	118	0	0	NUM
ejpam-5003	465	119	,	,	PUNCT
ejpam-5003	465	120	1	1	NUM
ejpam-5003	465	121	}	}	PUNCT
ejpam-5003	465	122	{	{	PUNCT
ejpam-5003	465	123	0	0	NUM
ejpam-5003	465	124	,	,	PUNCT
ejpam-5003	465	125	4	4	NUM
ejpam-5003	465	126	}	}	PUNCT
ejpam-5003	465	127	by	by	ADP
ejpam-5003	465	128	routine	routine	ADJ
ejpam-5003	465	129	calculations	calculation	NOUN
ejpam-5003	465	130	,	,	PUNCT
ejpam-5003	465	131	h	h	NOUN
ejpam-5003	465	132	is	be	AUX
ejpam-5003	465	133	a	a	DET
ejpam-5003	465	134	hyper	hyper	ADJ
ejpam-5003	465	135	bn	bn	NOUN
ejpam-5003	465	136	-algebra	-algebra	NOUN
ejpam-5003	465	137	.	.	PUNCT
ejpam-5003	466	1	let	let	VERB
ejpam-5003	466	2	θ	θ	NOUN
ejpam-5003	466	3	=	=	PRON
ejpam-5003	466	4	{	{	PUNCT
ejpam-5003	466	5	(	(	PUNCT
ejpam-5003	466	6	0	0	NUM
ejpam-5003	466	7	,	,	PUNCT
ejpam-5003	466	8	0	0	NUM
ejpam-5003	466	9	)	)	PUNCT
ejpam-5003	466	10	,	,	PUNCT
ejpam-5003	466	11	(	(	PUNCT
ejpam-5003	466	12	0	0	NUM
ejpam-5003	466	13	,	,	PUNCT
ejpam-5003	466	14	1	1	NUM
ejpam-5003	466	15	)	)	PUNCT
ejpam-5003	466	16	,	,	PUNCT
ejpam-5003	466	17	(	(	PUNCT
ejpam-5003	466	18	1	1	NUM
ejpam-5003	466	19	,	,	PUNCT
ejpam-5003	466	20	0	0	NUM
ejpam-5003	466	21	)	)	PUNCT
ejpam-5003	466	22	,	,	PUNCT
ejpam-5003	466	23	(	(	PUNCT
ejpam-5003	466	24	1	1	NUM
ejpam-5003	466	25	,	,	PUNCT
ejpam-5003	466	26	1	1	NUM
ejpam-5003	466	27	)	)	PUNCT
ejpam-5003	466	28	,	,	PUNCT
ejpam-5003	466	29	(	(	PUNCT
ejpam-5003	466	30	2	2	NUM
ejpam-5003	466	31	,	,	PUNCT
ejpam-5003	466	32	2	2	NUM
ejpam-5003	466	33	)	)	PUNCT
ejpam-5003	466	34	,	,	PUNCT
ejpam-5003	466	35	(	(	PUNCT
ejpam-5003	466	36	2	2	NUM
ejpam-5003	466	37	,	,	PUNCT
ejpam-5003	466	38	3	3	NUM
ejpam-5003	466	39	)	)	PUNCT
ejpam-5003	466	40	,	,	PUNCT
ejpam-5003	466	41	(	(	PUNCT
ejpam-5003	466	42	3	3	NUM
ejpam-5003	466	43	,	,	PUNCT
ejpam-5003	466	44	2	2	NUM
ejpam-5003	466	45	)	)	PUNCT
ejpam-5003	466	46	,	,	PUNCT
ejpam-5003	466	47	(	(	PUNCT
ejpam-5003	466	48	3	3	NUM
ejpam-5003	466	49	,	,	PUNCT
ejpam-5003	466	50	3	3	NUM
ejpam-5003	466	51	)	)	PUNCT
ejpam-5003	466	52	,	,	PUNCT
ejpam-5003	466	53	(	(	PUNCT
ejpam-5003	466	54	4	4	NUM
ejpam-5003	466	55	,	,	PUNCT
ejpam-5003	466	56	4	4	NUM
ejpam-5003	466	57	)	)	PUNCT
ejpam-5003	466	58	}	}	PUNCT
ejpam-5003	466	59	.	.	PUNCT
ejpam-5003	467	1	by	by	ADP
ejpam-5003	467	2	inspection	inspection	NOUN
ejpam-5003	467	3	,	,	PUNCT
ejpam-5003	467	4	θ	θ	PROPN
ejpam-5003	467	5	is	be	AUX
ejpam-5003	467	6	an	an	DET
ejpam-5003	467	7	equivalence	equivalence	NOUN
ejpam-5003	467	8	relation	relation	NOUN
ejpam-5003	467	9	.	.	PUNCT
ejpam-5003	468	1	verify	verify	VERB
ejpam-5003	468	2	that	that	SCONJ
ejpam-5003	468	3	θ	θ	PROPN
ejpam-5003	468	4	is	be	AUX
ejpam-5003	468	5	a	a	DET
ejpam-5003	468	6	congruence	congruence	NOUN
ejpam-5003	468	7	relation	relation	NOUN
ejpam-5003	468	8	using	use	VERB
ejpam-5003	468	9	lemma	lemma	PROPN
ejpam-5003	468	10	8	8	NUM
ejpam-5003	468	11	.	.	PUNCT
ejpam-5003	469	1	note	note	VERB
ejpam-5003	469	2	that	that	SCONJ
ejpam-5003	469	3	[	[	X
ejpam-5003	469	4	0]θ	0]θ	X
ejpam-5003	469	5	=	=	SYM
ejpam-5003	469	6	{	{	PUNCT
ejpam-5003	469	7	0	0	NUM
ejpam-5003	469	8	,	,	PUNCT
ejpam-5003	469	9	1	1	NUM
ejpam-5003	469	10	}	}	PUNCT
ejpam-5003	469	11	is	be	AUX
ejpam-5003	469	12	a	a	DET
ejpam-5003	469	13	hyper	hyper	ADJ
ejpam-5003	469	14	subbn	subbn	NOUN
ejpam-5003	469	15	-algebra	-algebra	NOUN
ejpam-5003	469	16	of	of	ADP
ejpam-5003	469	17	h.	h.	PROPN
ejpam-5003	469	18	however	however	ADV
ejpam-5003	469	19	,	,	PUNCT
ejpam-5003	469	20	it	it	PRON
ejpam-5003	469	21	is	be	AUX
ejpam-5003	469	22	not	not	PART
ejpam-5003	469	23	reflexive	reflexive	ADJ
ejpam-5003	469	24	because	because	SCONJ
ejpam-5003	469	25	2⊛	2⊛	NUM
ejpam-5003	469	26	2	2	NUM
ejpam-5003	469	27	=	=	SYM
ejpam-5003	469	28	{	{	PUNCT
ejpam-5003	469	29	0	0	NUM
ejpam-5003	469	30	,	,	PUNCT
ejpam-5003	469	31	2	2	NUM
ejpam-5003	469	32	,	,	PUNCT
ejpam-5003	469	33	3	3	NUM
ejpam-5003	469	34	}	}	PUNCT
ejpam-5003	469	35	̸⊆	̸⊆	NOUN
ejpam-5003	470	1	[	[	X
ejpam-5003	470	2	0]θ	0]θ	NUM
ejpam-5003	470	3	.	.	PUNCT
ejpam-5003	471	1	also	also	ADV
ejpam-5003	471	2	,	,	PUNCT
ejpam-5003	471	3	it	it	PRON
ejpam-5003	471	4	is	be	AUX
ejpam-5003	471	5	not	not	PART
ejpam-5003	471	6	normal	normal	ADJ
ejpam-5003	471	7	because	because	SCONJ
ejpam-5003	471	8	4⊛	4⊛	NUM
ejpam-5003	471	9	3	3	NUM
ejpam-5003	471	10	⊆	⊆	NUM
ejpam-5003	472	1	[	[	X
ejpam-5003	472	2	0]θ	0]θ	X
ejpam-5003	472	3	but	but	CCONJ
ejpam-5003	472	4	(	(	PUNCT
ejpam-5003	472	5	4⊛	4⊛	NUM
ejpam-5003	472	6	4)⊛	4)⊛	X
ejpam-5003	472	7	(	(	PUNCT
ejpam-5003	472	8	3⊛	3⊛	NUM
ejpam-5003	472	9	3	3	NUM
ejpam-5003	472	10	)	)	PUNCT
ejpam-5003	472	11	=	=	PRON
ejpam-5003	472	12	{	{	PUNCT
ejpam-5003	472	13	0	0	NUM
ejpam-5003	472	14	,	,	PUNCT
ejpam-5003	472	15	1	1	NUM
ejpam-5003	472	16	,	,	PUNCT
ejpam-5003	472	17	2	2	NUM
ejpam-5003	472	18	,	,	PUNCT
ejpam-5003	472	19	3	3	NUM
ejpam-5003	472	20	,	,	PUNCT
ejpam-5003	472	21	4	4	NUM
ejpam-5003	472	22	}	}	PUNCT
ejpam-5003	472	23	̸⊆	̸⊆	NOUN
ejpam-5003	473	1	[	[	X
ejpam-5003	473	2	0]θ	0]θ	NUM
ejpam-5003	473	3	.	.	PUNCT
ejpam-5003	474	1	therefore	therefore	ADV
ejpam-5003	474	2	,	,	PUNCT
ejpam-5003	474	3	[	[	X
ejpam-5003	474	4	0]θ	0]θ	X
ejpam-5003	474	5	is	be	AUX
ejpam-5003	474	6	not	not	PART
ejpam-5003	474	7	a	a	DET
ejpam-5003	474	8	reflexive	reflexive	ADJ
ejpam-5003	474	9	normal	normal	ADJ
ejpam-5003	474	10	hyper	hyper	ADJ
ejpam-5003	474	11	subbn	subbn	NOUN
ejpam-5003	474	12	-algebra	-algebra	PROPN
ejpam-5003	474	13	of	of	ADP
ejpam-5003	474	14	h.	h.	PROPN
ejpam-5003	474	15	in	in	ADP
ejpam-5003	474	16	lemma	lemma	PROPN
ejpam-5003	474	17	6	6	NUM
ejpam-5003	474	18	,	,	PUNCT
ejpam-5003	474	19	[	[	X
ejpam-5003	474	20	0]∼s	0]∼s	PUNCT
ejpam-5003	474	21	=	=	SYM
ejpam-5003	474	22	s	s	VERB
ejpam-5003	474	23	where	where	SCONJ
ejpam-5003	474	24	s	s	NOUN
ejpam-5003	474	25	is	be	AUX
ejpam-5003	474	26	a	a	DET
ejpam-5003	474	27	hyper	hyper	ADJ
ejpam-5003	474	28	subbn	subbn	NOUN
ejpam-5003	474	29	-algebra	-algebra	PROPN
ejpam-5003	474	30	.	.	PUNCT
ejpam-5003	475	1	the	the	DET
ejpam-5003	475	2	next	next	ADJ
ejpam-5003	475	3	result	result	NOUN
ejpam-5003	475	4	will	will	AUX
ejpam-5003	475	5	tell	tell	VERB
ejpam-5003	475	6	us	we	PRON
ejpam-5003	475	7	that	that	SCONJ
ejpam-5003	475	8	in	in	ADP
ejpam-5003	475	9	general	general	ADJ
ejpam-5003	475	10	,	,	PUNCT
ejpam-5003	475	11	the	the	DET
ejpam-5003	475	12	congruence	congruence	NOUN
ejpam-5003	475	13	class	class	NOUN
ejpam-5003	475	14	containing	contain	VERB
ejpam-5003	475	15	0	0	NUM
ejpam-5003	475	16	is	be	AUX
ejpam-5003	475	17	a	a	DET
ejpam-5003	475	18	hyper	hyper	ADJ
ejpam-5003	475	19	subbn	subbn	NOUN
ejpam-5003	475	20	-algebra	-algebra	PROPN
ejpam-5003	475	21	.	.	PUNCT
ejpam-5003	475	22	theorem	theorem	VERB
ejpam-5003	475	23	13	13	NUM
ejpam-5003	475	24	.	.	PUNCT
ejpam-5003	476	1	let	let	VERB
ejpam-5003	476	2	θ	θ	NOUN
ejpam-5003	476	3	be	be	AUX
ejpam-5003	476	4	a	a	DET
ejpam-5003	476	5	congruence	congruence	NOUN
ejpam-5003	476	6	relation	relation	NOUN
ejpam-5003	476	7	on	on	ADP
ejpam-5003	476	8	a	a	DET
ejpam-5003	476	9	hyper	hyper	ADJ
ejpam-5003	476	10	bn	bn	NOUN
ejpam-5003	476	11	-algebra	-algebra	PROPN
ejpam-5003	476	12	h.	h.	NOUN
ejpam-5003	477	1	then	then	ADV
ejpam-5003	477	2	[	[	X
ejpam-5003	477	3	0]θ	0]θ	X
ejpam-5003	477	4	is	be	AUX
ejpam-5003	477	5	a	a	DET
ejpam-5003	477	6	hyper	hyper	ADJ
ejpam-5003	477	7	subbn	subbn	NOUN
ejpam-5003	477	8	-algebra	-algebra	NOUN
ejpam-5003	477	9	of	of	ADP
ejpam-5003	477	10	h.	h.	PROPN
ejpam-5003	477	11	l.r	l.r	PROPN
ejpam-5003	477	12	.	.	PROPN
ejpam-5003	477	13	cabardo	cabardo	PROPN
ejpam-5003	477	14	,	,	PUNCT
ejpam-5003	477	15	g.	g.	PROPN
ejpam-5003	477	16	petalcorin	petalcorin	PROPN
ejpam-5003	477	17	/	/	SYM
ejpam-5003	477	18	eur	eur	PROPN
ejpam-5003	477	19	.	.	PUNCT
ejpam-5003	478	1	j.	j.	PROPN
ejpam-5003	478	2	pure	pure	PROPN
ejpam-5003	478	3	appl	appl	PROPN
ejpam-5003	478	4	.	.	PROPN
ejpam-5003	478	5	math	math	PROPN
ejpam-5003	478	6	,	,	PUNCT
ejpam-5003	478	7	17	17	NUM
ejpam-5003	478	8	(	(	PUNCT
ejpam-5003	478	9	1	1	NUM
ejpam-5003	478	10	)	)	PUNCT
ejpam-5003	478	11	(	(	PUNCT
ejpam-5003	478	12	2024	2024	NUM
ejpam-5003	478	13	)	)	PUNCT
ejpam-5003	478	14	,	,	PUNCT
ejpam-5003	478	15	222	222	NUM
ejpam-5003	478	16	-	-	SYM
ejpam-5003	478	17	242	242	NUM
ejpam-5003	478	18	238	238	NUM
ejpam-5003	478	19	proof	proof	NOUN
ejpam-5003	478	20	.	.	PUNCT
ejpam-5003	479	1	clearly	clearly	ADV
ejpam-5003	479	2	,	,	PUNCT
ejpam-5003	479	3	0	0	NUM
ejpam-5003	479	4	∈	∈	PROPN
ejpam-5003	480	1	[	[	X
ejpam-5003	480	2	0]θ	0]θ	NOUN
ejpam-5003	480	3	.	.	PUNCT
ejpam-5003	481	1	now	now	ADV
ejpam-5003	481	2	,	,	PUNCT
ejpam-5003	481	3	let	let	VERB
ejpam-5003	481	4	x	x	PRON
ejpam-5003	481	5	,	,	PUNCT
ejpam-5003	481	6	y	y	PROPN
ejpam-5003	481	7	∈	∈	PROPN
ejpam-5003	482	1	[	[	X
ejpam-5003	482	2	0]θ	0]θ	NOUN
ejpam-5003	482	3	.	.	PUNCT
ejpam-5003	483	1	then	then	ADV
ejpam-5003	483	2	xθ0	xθ0	PROPN
ejpam-5003	483	3	and	and	CCONJ
ejpam-5003	483	4	yθ0	yθ0	PROPN
ejpam-5003	483	5	which	which	PRON
ejpam-5003	483	6	imply	imply	VERB
ejpam-5003	483	7	that	that	SCONJ
ejpam-5003	483	8	yθx	yθx	NOUN
ejpam-5003	483	9	by	by	ADP
ejpam-5003	483	10	symmetric	symmetric	ADJ
ejpam-5003	483	11	and	and	CCONJ
ejpam-5003	483	12	transitive	transitive	ADJ
ejpam-5003	483	13	properties	property	NOUN
ejpam-5003	483	14	of	of	ADP
ejpam-5003	483	15	θ	θ	PROPN
ejpam-5003	483	16	.	.	PUNCT
ejpam-5003	484	1	since	since	SCONJ
ejpam-5003	484	2	yθx	yθx	NOUN
ejpam-5003	484	3	and	and	CCONJ
ejpam-5003	484	4	0θy	0θy	NOUN
ejpam-5003	484	5	,	,	PUNCT
ejpam-5003	484	6	and	and	CCONJ
ejpam-5003	484	7	θ	θ	PROPN
ejpam-5003	484	8	is	be	AUX
ejpam-5003	484	9	a	a	DET
ejpam-5003	484	10	congruence	congruence	NOUN
ejpam-5003	484	11	relation	relation	NOUN
ejpam-5003	484	12	,	,	PUNCT
ejpam-5003	484	13	we	we	PRON
ejpam-5003	484	14	have	have	VERB
ejpam-5003	484	15	by	by	ADP
ejpam-5003	484	16	lemma	lemma	PROPN
ejpam-5003	484	17	8	8	NUM
ejpam-5003	484	18	,	,	PUNCT
ejpam-5003	484	19	{	{	PUNCT
ejpam-5003	484	20	y	y	NOUN
ejpam-5003	484	21	}	}	PUNCT
ejpam-5003	484	22	=	=	SYM
ejpam-5003	484	23	(	(	PUNCT
ejpam-5003	484	24	y⊛0)θ(x⊛y	y⊛0)θ(x⊛y	NOUN
ejpam-5003	484	25	)	)	PUNCT
ejpam-5003	484	26	.	.	PUNCT
ejpam-5003	485	1	this	this	PRON
ejpam-5003	485	2	means	mean	VERB
ejpam-5003	485	3	that	that	SCONJ
ejpam-5003	485	4	for	for	ADP
ejpam-5003	485	5	all	all	DET
ejpam-5003	485	6	a	a	DET
ejpam-5003	485	7	∈	∈	PROPN
ejpam-5003	485	8	x⊛y	x⊛y	PROPN
ejpam-5003	485	9	,	,	PUNCT
ejpam-5003	485	10	aθy	aθy	PROPN
ejpam-5003	485	11	.	.	PUNCT
ejpam-5003	485	12	by	by	ADP
ejpam-5003	485	13	transitive	transitive	ADJ
ejpam-5003	485	14	property	property	NOUN
ejpam-5003	485	15	of	of	ADP
ejpam-5003	485	16	θ	θ	PROPN
ejpam-5003	485	17	,	,	PUNCT
ejpam-5003	485	18	aθy	aθy	PROPN
ejpam-5003	485	19	and	and	CCONJ
ejpam-5003	485	20	yθ0	yθ0	PROPN
ejpam-5003	485	21	imply	imply	VERB
ejpam-5003	485	22	aθ0	aθ0	NOUN
ejpam-5003	485	23	for	for	ADP
ejpam-5003	485	24	all	all	DET
ejpam-5003	485	25	a	a	DET
ejpam-5003	485	26	∈	∈	NOUN
ejpam-5003	485	27	x⊛	x⊛	PROPN
ejpam-5003	486	1	y.	y.	PROPN
ejpam-5003	486	2	hence	hence	ADV
ejpam-5003	486	3	,	,	PUNCT
ejpam-5003	486	4	x⊛	x⊛	PROPN
ejpam-5003	486	5	y	y	PROPN
ejpam-5003	486	6	⊆	⊆	NUM
ejpam-5003	487	1	[	[	X
ejpam-5003	487	2	0]θ	0]θ	NOUN
ejpam-5003	487	3	.	.	PUNCT
ejpam-5003	487	4	by	by	ADP
ejpam-5003	487	5	theorem	theorem	NOUN
ejpam-5003	487	6	3	3	NUM
ejpam-5003	487	7	,	,	PUNCT
ejpam-5003	487	8	[	[	X
ejpam-5003	487	9	0]θ	0]θ	X
ejpam-5003	487	10	is	be	AUX
ejpam-5003	487	11	a	a	DET
ejpam-5003	487	12	hyper	hyper	ADJ
ejpam-5003	487	13	subbn	subbn	NOUN
ejpam-5003	487	14	-algebra	-algebra	PROPN
ejpam-5003	487	15	of	of	ADP
ejpam-5003	487	16	h.	h.	PROPN
ejpam-5003	487	17	theorem	theorem	PROPN
ejpam-5003	487	18	14	14	NUM
ejpam-5003	487	19	.	.	PUNCT
ejpam-5003	488	1	let	let	VERB
ejpam-5003	488	2	θ	θ	NOUN
ejpam-5003	488	3	be	be	AUX
ejpam-5003	488	4	a	a	DET
ejpam-5003	488	5	congruence	congruence	NOUN
ejpam-5003	488	6	relation	relation	NOUN
ejpam-5003	488	7	on	on	ADP
ejpam-5003	488	8	a	a	DET
ejpam-5003	488	9	hyper	hyper	ADJ
ejpam-5003	488	10	bn	bn	NOUN
ejpam-5003	488	11	-algebra	-algebra	PROPN
ejpam-5003	488	12	h.	h.	NOUN
ejpam-5003	489	1	then	then	ADV
ejpam-5003	489	2	[	[	X
ejpam-5003	489	3	0]θ	0]θ	X
ejpam-5003	489	4	is	be	AUX
ejpam-5003	489	5	a	a	DET
ejpam-5003	489	6	strong	strong	ADJ
ejpam-5003	489	7	hyper	hyper	NOUN
ejpam-5003	489	8	bn	bn	NOUN
ejpam-5003	489	9	-ideal	-ideal	NOUN
ejpam-5003	489	10	of	of	ADP
ejpam-5003	489	11	h.	h.	NOUN
ejpam-5003	489	12	consequently	consequently	ADV
ejpam-5003	489	13	,	,	PUNCT
ejpam-5003	489	14	it	it	PRON
ejpam-5003	489	15	is	be	AUX
ejpam-5003	489	16	a	a	DET
ejpam-5003	489	17	hyper	hyper	ADJ
ejpam-5003	489	18	bn	bn	ADP
ejpam-5003	489	19	-ideal	-ideal	NOUN
ejpam-5003	489	20	and	and	CCONJ
ejpam-5003	489	21	a	a	DET
ejpam-5003	489	22	weak	weak	ADJ
ejpam-5003	489	23	hyper	hyper	ADJ
ejpam-5003	489	24	bn	bn	ADJ
ejpam-5003	489	25	-ideal	-ideal	NOUN
ejpam-5003	489	26	of	of	ADP
ejpam-5003	489	27	h.	h.	NOUN
ejpam-5003	489	28	proof	proof	NOUN
ejpam-5003	489	29	.	.	PUNCT
ejpam-5003	490	1	clearly	clearly	ADV
ejpam-5003	490	2	,	,	PUNCT
ejpam-5003	490	3	0	0	NUM
ejpam-5003	490	4	∈	∈	PROPN
ejpam-5003	491	1	[	[	X
ejpam-5003	491	2	0]θ	0]θ	NOUN
ejpam-5003	491	3	.	.	PUNCT
ejpam-5003	492	1	now	now	ADV
ejpam-5003	492	2	,	,	PUNCT
ejpam-5003	492	3	let	let	VERB
ejpam-5003	492	4	x	x	PRON
ejpam-5003	492	5	,	,	PUNCT
ejpam-5003	492	6	y	y	PROPN
ejpam-5003	492	7	∈	∈	PROPN
ejpam-5003	492	8	h	h	NOUN
ejpam-5003	492	9	such	such	ADJ
ejpam-5003	492	10	that	that	SCONJ
ejpam-5003	492	11	(	(	PUNCT
ejpam-5003	492	12	x⊛	x⊛	NOUN
ejpam-5003	492	13	y	y	NOUN
ejpam-5003	492	14	)	)	PUNCT
ejpam-5003	492	15	∩	∩	NOUN
ejpam-5003	493	1	[	[	X
ejpam-5003	493	2	0]θ	0]θ	NOUN
ejpam-5003	493	3	and	and	CCONJ
ejpam-5003	493	4	y	y	PROPN
ejpam-5003	493	5	∈	∈	PROPN
ejpam-5003	494	1	[	[	X
ejpam-5003	494	2	0]θ	0]θ	NOUN
ejpam-5003	494	3	.	.	PUNCT
ejpam-5003	495	1	then	then	ADV
ejpam-5003	495	2	there	there	PRON
ejpam-5003	495	3	exists	exist	VERB
ejpam-5003	495	4	a	a	DET
ejpam-5003	495	5	∈	∈	NOUN
ejpam-5003	495	6	x	x	PUNCT
ejpam-5003	495	7	⊛	⊛	NUM
ejpam-5003	495	8	y	y	PRON
ejpam-5003	495	9	such	such	ADJ
ejpam-5003	495	10	that	that	SCONJ
ejpam-5003	495	11	a	a	DET
ejpam-5003	495	12	∈	∈	PROPN
ejpam-5003	496	1	[	[	X
ejpam-5003	496	2	0]θ	0]θ	X
ejpam-5003	496	3	and	and	CCONJ
ejpam-5003	496	4	so	so	ADV
ejpam-5003	496	5	aθ0	aθ0	PROPN
ejpam-5003	496	6	.	.	PUNCT
ejpam-5003	497	1	hence	hence	ADV
ejpam-5003	497	2	,	,	PUNCT
ejpam-5003	497	3	(	(	PUNCT
ejpam-5003	497	4	x	x	PROPN
ejpam-5003	497	5	⊛	⊛	ADP
ejpam-5003	497	6	y)θ0	y)θ0	PROPN
ejpam-5003	497	7	.	.	PUNCT
ejpam-5003	498	1	moreover	moreover	ADV
ejpam-5003	498	2	,	,	PUNCT
ejpam-5003	498	3	yθ0	yθ0	PROPN
ejpam-5003	498	4	implies	imply	VERB
ejpam-5003	498	5	0θy	0θy	NOUN
ejpam-5003	498	6	because	because	SCONJ
ejpam-5003	498	7	θ	θ	PROPN
ejpam-5003	498	8	is	be	AUX
ejpam-5003	498	9	symmetric	symmetric	ADJ
ejpam-5003	498	10	.	.	PUNCT
ejpam-5003	499	1	since	since	SCONJ
ejpam-5003	499	2	0θy	0θy	NOUN
ejpam-5003	499	3	and	and	CCONJ
ejpam-5003	499	4	θ	θ	PROPN
ejpam-5003	499	5	is	be	AUX
ejpam-5003	499	6	a	a	DET
ejpam-5003	499	7	congruence	congruence	NOUN
ejpam-5003	499	8	relation	relation	NOUN
ejpam-5003	499	9	on	on	ADP
ejpam-5003	499	10	h	h	NOUN
ejpam-5003	499	11	,	,	PUNCT
ejpam-5003	499	12	by	by	ADP
ejpam-5003	499	13	lemma	lemma	PROPN
ejpam-5003	499	14	8	8	NUM
ejpam-5003	499	15	,	,	PUNCT
ejpam-5003	499	16	{	{	PUNCT
ejpam-5003	499	17	x	x	NOUN
ejpam-5003	499	18	}	}	PUNCT
ejpam-5003	499	19	=	=	SYM
ejpam-5003	499	20	(	(	PUNCT
ejpam-5003	499	21	x⊛	x⊛	PROPN
ejpam-5003	499	22	0)θ(x⊛	0)θ(x⊛	NUM
ejpam-5003	499	23	y	y	PROPN
ejpam-5003	499	24	)	)	PUNCT
ejpam-5003	499	25	.	.	PUNCT
ejpam-5003	500	1	this	this	PRON
ejpam-5003	500	2	means	mean	VERB
ejpam-5003	500	3	that	that	SCONJ
ejpam-5003	500	4	for	for	ADP
ejpam-5003	500	5	all	all	DET
ejpam-5003	500	6	b	b	PROPN
ejpam-5003	500	7	∈	∈	PROPN
ejpam-5003	500	8	x⊛	x⊛	PROPN
ejpam-5003	500	9	y	y	PROPN
ejpam-5003	500	10	,	,	PUNCT
ejpam-5003	500	11	xθb	xθb	PROPN
ejpam-5003	500	12	.	.	PUNCT
ejpam-5003	501	1	also	also	ADV
ejpam-5003	501	2	,	,	PUNCT
ejpam-5003	501	3	(	(	PUNCT
ejpam-5003	501	4	x⊛	x⊛	INTJ
ejpam-5003	501	5	y)θ{0	y)θ{0	CCONJ
ejpam-5003	501	6	}	}	PUNCT
ejpam-5003	501	7	means	mean	VERB
ejpam-5003	501	8	that	that	SCONJ
ejpam-5003	501	9	there	there	PRON
ejpam-5003	501	10	is	be	VERB
ejpam-5003	501	11	an	an	DET
ejpam-5003	501	12	element	element	ADJ
ejpam-5003	501	13	b′	b′	NOUN
ejpam-5003	501	14	∈	∈	PROPN
ejpam-5003	501	15	x	x	PUNCT
ejpam-5003	501	16	⊛	⊛	NUM
ejpam-5003	501	17	y	y	PRON
ejpam-5003	501	18	such	such	ADJ
ejpam-5003	501	19	that	that	SCONJ
ejpam-5003	501	20	b′θ0	b′θ0	PROPN
ejpam-5003	501	21	.	.	PUNCT
ejpam-5003	502	1	since	since	SCONJ
ejpam-5003	502	2	b′	b′	ADJ
ejpam-5003	502	3	∈	∈	PROPN
ejpam-5003	502	4	x	x	SYM
ejpam-5003	502	5	⊛	⊛	NUM
ejpam-5003	502	6	y	y	PROPN
ejpam-5003	502	7	,	,	PUNCT
ejpam-5003	502	8	we	we	PRON
ejpam-5003	502	9	have	have	VERB
ejpam-5003	502	10	xθb′.	xθb′.	PROPN
ejpam-5003	502	11	by	by	ADP
ejpam-5003	502	12	transitive	transitive	ADJ
ejpam-5003	502	13	property	property	NOUN
ejpam-5003	502	14	of	of	ADP
ejpam-5003	502	15	θ	θ	PROPN
ejpam-5003	502	16	,	,	PUNCT
ejpam-5003	502	17	xθ0	xθ0	NOUN
ejpam-5003	503	1	and	and	CCONJ
ejpam-5003	503	2	x	x	PUNCT
ejpam-5003	503	3	∈	∈	PROPN
ejpam-5003	504	1	[	[	X
ejpam-5003	504	2	0]θ	0]θ	NOUN
ejpam-5003	504	3	.	.	PUNCT
ejpam-5003	505	1	therefore	therefore	ADV
ejpam-5003	505	2	,	,	PUNCT
ejpam-5003	505	3	[	[	X
ejpam-5003	505	4	0]θ	0]θ	X
ejpam-5003	505	5	is	be	AUX
ejpam-5003	505	6	a	a	DET
ejpam-5003	505	7	strong	strong	ADJ
ejpam-5003	505	8	hyper	hyper	NOUN
ejpam-5003	505	9	bn	bn	NOUN
ejpam-5003	505	10	-ideal	-ideal	NOUN
ejpam-5003	505	11	of	of	ADP
ejpam-5003	505	12	h.	h.	NOUN
ejpam-5003	505	13	by	by	ADP
ejpam-5003	505	14	propositions	proposition	NOUN
ejpam-5003	505	15	1(ii	1(ii	NUM
ejpam-5003	505	16	)	)	PUNCT
ejpam-5003	505	17	and	and	CCONJ
ejpam-5003	505	18	(	(	PUNCT
ejpam-5003	505	19	i	i	NOUN
ejpam-5003	505	20	)	)	PUNCT
ejpam-5003	505	21	,	,	PUNCT
ejpam-5003	506	1	[	[	X
ejpam-5003	506	2	0]θ	0]θ	X
ejpam-5003	506	3	is	be	AUX
ejpam-5003	506	4	a	a	DET
ejpam-5003	506	5	also	also	ADV
ejpam-5003	506	6	a	a	DET
ejpam-5003	506	7	hyper	hyper	ADJ
ejpam-5003	506	8	bn	bn	ADP
ejpam-5003	506	9	-ideal	-ideal	NOUN
ejpam-5003	506	10	and	and	CCONJ
ejpam-5003	506	11	a	a	DET
ejpam-5003	506	12	weak	weak	ADJ
ejpam-5003	506	13	hyper	hyper	ADJ
ejpam-5003	506	14	bn	bn	ADJ
ejpam-5003	506	15	-ideal	-ideal	NOUN
ejpam-5003	506	16	of	of	ADP
ejpam-5003	506	17	h.	h.	NOUN
ejpam-5003	506	18	the	the	DET
ejpam-5003	506	19	following	follow	VERB
ejpam-5003	506	20	example	example	NOUN
ejpam-5003	506	21	serves	serve	VERB
ejpam-5003	506	22	as	as	ADP
ejpam-5003	506	23	our	our	PRON
ejpam-5003	506	24	motivation	motivation	NOUN
ejpam-5003	506	25	in	in	ADP
ejpam-5003	506	26	the	the	DET
ejpam-5003	506	27	construction	construction	NOUN
ejpam-5003	506	28	of	of	ADP
ejpam-5003	506	29	quotient	quotient	NOUN
ejpam-5003	506	30	structure	structure	NOUN
ejpam-5003	506	31	via	via	ADP
ejpam-5003	506	32	congruence	congruence	PROPN
ejpam-5003	506	33	relation	relation	PROPN
ejpam-5003	506	34	.	.	PUNCT
ejpam-5003	507	1	example	example	NOUN
ejpam-5003	507	2	24	24	NUM
ejpam-5003	507	3	.	.	PUNCT
ejpam-5003	508	1	consider	consider	VERB
ejpam-5003	508	2	the	the	DET
ejpam-5003	508	3	hyper	hyper	ADJ
ejpam-5003	508	4	bn	bn	NOUN
ejpam-5003	508	5	-algebra	-algebra	PROPN
ejpam-5003	508	6	h	h	NOUN
ejpam-5003	508	7	=	=	SYM
ejpam-5003	508	8	{	{	PUNCT
ejpam-5003	508	9	0	0	NUM
ejpam-5003	508	10	,	,	PUNCT
ejpam-5003	508	11	1	1	NUM
ejpam-5003	508	12	,	,	PUNCT
ejpam-5003	508	13	2	2	NUM
ejpam-5003	508	14	,	,	PUNCT
ejpam-5003	508	15	3	3	NUM
ejpam-5003	508	16	,	,	PUNCT
ejpam-5003	508	17	4	4	NUM
ejpam-5003	508	18	}	}	PUNCT
ejpam-5003	508	19	in	in	ADP
ejpam-5003	508	20	example	example	NOUN
ejpam-5003	508	21	23	23	NUM
ejpam-5003	508	22	.	.	PUNCT
ejpam-5003	509	1	the	the	DET
ejpam-5003	509	2	relation	relation	NOUN
ejpam-5003	509	3	θ	θ	PROPN
ejpam-5003	509	4	defined	define	VERB
ejpam-5003	509	5	on	on	ADP
ejpam-5003	509	6	h	h	NOUN
ejpam-5003	509	7	is	be	AUX
ejpam-5003	509	8	a	a	DET
ejpam-5003	509	9	congruence	congruence	NOUN
ejpam-5003	509	10	relation	relation	NOUN
ejpam-5003	509	11	as	as	SCONJ
ejpam-5003	509	12	shown	show	VERB
ejpam-5003	509	13	.	.	PUNCT
ejpam-5003	510	1	we	we	PRON
ejpam-5003	510	2	have	have	VERB
ejpam-5003	510	3	i	i	PRON
ejpam-5003	510	4	=	=	PUNCT
ejpam-5003	511	1	[	[	X
ejpam-5003	511	2	0]θ	0]θ	X
ejpam-5003	511	3	=	=	SYM
ejpam-5003	511	4	{	{	PUNCT
ejpam-5003	511	5	0	0	NUM
ejpam-5003	511	6	,	,	PUNCT
ejpam-5003	511	7	1	1	NUM
ejpam-5003	511	8	}	}	PUNCT
ejpam-5003	511	9	,	,	PUNCT
ejpam-5003	511	10	i2	i2	PROPN
ejpam-5003	511	11	=	=	PUNCT
ejpam-5003	511	12	{	{	PUNCT
ejpam-5003	511	13	2	2	NUM
ejpam-5003	511	14	,	,	PUNCT
ejpam-5003	511	15	3	3	NUM
ejpam-5003	511	16	}	}	PUNCT
ejpam-5003	511	17	=	=	SYM
ejpam-5003	511	18	i3	i3	NOUN
ejpam-5003	511	19	,	,	PUNCT
ejpam-5003	511	20	and	and	CCONJ
ejpam-5003	511	21	i4	i4	PROPN
ejpam-5003	511	22	=	=	SYM
ejpam-5003	511	23	{	{	PUNCT
ejpam-5003	511	24	4	4	NUM
ejpam-5003	511	25	}	}	PUNCT
ejpam-5003	511	26	.	.	PUNCT
ejpam-5003	512	1	let	let	VERB
ejpam-5003	512	2	h	h	NOUN
ejpam-5003	512	3	/	/	SYM
ejpam-5003	512	4	i	i	PRON
ejpam-5003	512	5	=	=	PUNCT
ejpam-5003	512	6	{	{	PUNCT
ejpam-5003	512	7	ix	ix	X
ejpam-5003	512	8	:	:	PUNCT
ejpam-5003	512	9	x	x	X
ejpam-5003	512	10	∈	∈	NOUN
ejpam-5003	512	11	h	h	NOUN
ejpam-5003	512	12	}	}	PUNCT
ejpam-5003	512	13	=	=	SYM
ejpam-5003	512	14	{	{	PUNCT
ejpam-5003	512	15	i	i	PROPN
ejpam-5003	512	16	,	,	PUNCT
ejpam-5003	512	17	i2	i2	PROPN
ejpam-5003	512	18	,	,	PUNCT
ejpam-5003	512	19	i4	i4	PROPN
ejpam-5003	512	20	}	}	PUNCT
ejpam-5003	512	21	.	.	PUNCT
ejpam-5003	513	1	define	define	VERB
ejpam-5003	513	2	a	a	DET
ejpam-5003	513	3	hyperoperation	hyperoperation	NOUN
ejpam-5003	513	4	⊗	⊗	ADJ
ejpam-5003	513	5	on	on	ADP
ejpam-5003	513	6	h	h	PROPN
ejpam-5003	513	7	/	/	SYM
ejpam-5003	513	8	i	i	PRON
ejpam-5003	513	9	by	by	ADP
ejpam-5003	513	10	ix⊗iy	ix⊗iy	NOUN
ejpam-5003	513	11	=	=	PUNCT
ejpam-5003	513	12	{	{	PUNCT
ejpam-5003	513	13	iz	iz	INTJ
ejpam-5003	513	14	:	:	PUNCT
ejpam-5003	513	15	z	z	PROPN
ejpam-5003	513	16	∈	∈	PROPN
ejpam-5003	513	17	x⊛y	x⊛y	PROPN
ejpam-5003	513	18	}	}	PUNCT
ejpam-5003	513	19	and	and	CCONJ
ejpam-5003	513	20	the	the	DET
ejpam-5003	513	21	hyperoder	hyperoder	NOUN
ejpam-5003	513	22	≪i	≪i	X
ejpam-5003	513	23	by	by	ADP
ejpam-5003	513	24	ix	ix	ADV
ejpam-5003	513	25	≪i	≪i	X
ejpam-5003	513	26	iy	iy	X
ejpam-5003	513	27	if	if	SCONJ
ejpam-5003	513	28	and	and	CCONJ
ejpam-5003	513	29	only	only	ADV
ejpam-5003	513	30	if	if	SCONJ
ejpam-5003	513	31	i	i	PRON
ejpam-5003	513	32	∈	∈	VERB
ejpam-5003	513	33	ix	ix	ADP
ejpam-5003	513	34	⊗	⊗	PROPN
ejpam-5003	513	35	iy	iy	PROPN
ejpam-5003	513	36	.	.	PUNCT
ejpam-5003	514	1	thus	thus	ADV
ejpam-5003	514	2	,	,	PUNCT
ejpam-5003	514	3	our	our	PRON
ejpam-5003	514	4	cayley	cayley	ADJ
ejpam-5003	514	5	table	table	NOUN
ejpam-5003	514	6	is	be	AUX
ejpam-5003	514	7	as	as	SCONJ
ejpam-5003	514	8	follows	follow	VERB
ejpam-5003	514	9	:	:	PUNCT
ejpam-5003	514	10	⊗	⊗	PROPN
ejpam-5003	514	11	i	i	PROPN
ejpam-5003	514	12	i2	i2	PROPN
ejpam-5003	514	13	i4	i4	PROPN
ejpam-5003	514	14	i	i	PRON
ejpam-5003	514	15	{	{	PUNCT
ejpam-5003	514	16	i	i	PRON
ejpam-5003	514	17	}	}	PUNCT
ejpam-5003	514	18	{	{	PUNCT
ejpam-5003	514	19	i2	i2	PROPN
ejpam-5003	514	20	}	}	PUNCT
ejpam-5003	514	21	{	{	PUNCT
ejpam-5003	514	22	i4	i4	PROPN
ejpam-5003	514	23	}	}	PUNCT
ejpam-5003	514	24	i2	i2	PROPN
ejpam-5003	514	25	{	{	PUNCT
ejpam-5003	514	26	i2	i2	PROPN
ejpam-5003	514	27	}	}	PUNCT
ejpam-5003	514	28	{	{	PUNCT
ejpam-5003	514	29	i	i	PROPN
ejpam-5003	514	30	,	,	PUNCT
ejpam-5003	514	31	i2	i2	PROPN
ejpam-5003	514	32	}	}	PUNCT
ejpam-5003	514	33	{	{	PUNCT
ejpam-5003	514	34	i	i	PROPN
ejpam-5003	514	35	}	}	PUNCT
ejpam-5003	514	36	i4	i4	PROPN
ejpam-5003	514	37	{	{	PUNCT
ejpam-5003	514	38	i4	i4	PROPN
ejpam-5003	514	39	}	}	PUNCT
ejpam-5003	514	40	{	{	PUNCT
ejpam-5003	514	41	i	i	NOUN
ejpam-5003	514	42	}	}	PUNCT
ejpam-5003	514	43	{	{	PUNCT
ejpam-5003	514	44	i	i	PROPN
ejpam-5003	514	45	,	,	PUNCT
ejpam-5003	514	46	i4	i4	PROPN
ejpam-5003	514	47	}	}	PUNCT
ejpam-5003	514	48	using	use	VERB
ejpam-5003	514	49	routine	routine	ADJ
ejpam-5003	514	50	calculations	calculation	NOUN
ejpam-5003	514	51	,	,	PUNCT
ejpam-5003	514	52	we	we	PRON
ejpam-5003	514	53	can	can	AUX
ejpam-5003	514	54	show	show	VERB
ejpam-5003	514	55	that	that	SCONJ
ejpam-5003	514	56	(	(	PUNCT
ejpam-5003	514	57	h	h	NOUN
ejpam-5003	514	58	/	/	SYM
ejpam-5003	514	59	i,⊗	i,⊗	PROPN
ejpam-5003	514	60	,	,	PUNCT
ejpam-5003	514	61	i	i	PRON
ejpam-5003	514	62	)	)	PUNCT
ejpam-5003	514	63	is	be	AUX
ejpam-5003	514	64	a	a	DET
ejpam-5003	514	65	hyper	hyper	ADJ
ejpam-5003	514	66	bn	bn	NOUN
ejpam-5003	514	67	-algebra	-algebra	NOUN
ejpam-5003	514	68	.	.	PUNCT
ejpam-5003	515	1	we	we	PRON
ejpam-5003	515	2	will	will	AUX
ejpam-5003	515	3	now	now	ADV
ejpam-5003	515	4	show	show	VERB
ejpam-5003	515	5	that	that	SCONJ
ejpam-5003	515	6	using	use	VERB
ejpam-5003	515	7	congruence	congruence	NOUN
ejpam-5003	515	8	relation	relation	NOUN
ejpam-5003	515	9	,	,	PUNCT
ejpam-5003	515	10	the	the	DET
ejpam-5003	515	11	quotient	quotient	NOUN
ejpam-5003	515	12	structure	structure	NOUN
ejpam-5003	515	13	obtained	obtain	VERB
ejpam-5003	515	14	is	be	AUX
ejpam-5003	515	15	a	a	DET
ejpam-5003	515	16	hyper	hyper	ADJ
ejpam-5003	515	17	bn	bn	ADJ
ejpam-5003	515	18	-algebra	-algebra	NOUN
ejpam-5003	515	19	.	.	PUNCT
ejpam-5003	516	1	theorem	theorem	NOUN
ejpam-5003	516	2	15	15	NUM
ejpam-5003	516	3	.	.	PUNCT
ejpam-5003	517	1	let	let	VERB
ejpam-5003	517	2	θ	θ	NOUN
ejpam-5003	517	3	be	be	AUX
ejpam-5003	517	4	a	a	DET
ejpam-5003	517	5	congruence	congruence	NOUN
ejpam-5003	517	6	relation	relation	NOUN
ejpam-5003	517	7	on	on	ADP
ejpam-5003	517	8	a	a	DET
ejpam-5003	517	9	hyper	hyper	ADJ
ejpam-5003	517	10	bn	bn	NOUN
ejpam-5003	517	11	-algebra	-algebra	NOUN
ejpam-5003	517	12	h	h	NOUN
ejpam-5003	518	1	such	such	ADJ
ejpam-5003	518	2	that	that	SCONJ
ejpam-5003	518	3	i	i	PRON
ejpam-5003	518	4	=	=	PUNCT
ejpam-5003	519	1	[	[	X
ejpam-5003	519	2	0]θ	0]θ	X
ejpam-5003	519	3	and	and	CCONJ
ejpam-5003	519	4	h	h	NOUN
ejpam-5003	519	5	/	/	SYM
ejpam-5003	519	6	i	i	PRON
ejpam-5003	519	7	=	=	PUNCT
ejpam-5003	519	8	{	{	PUNCT
ejpam-5003	519	9	ix	ix	X
ejpam-5003	519	10	:	:	PUNCT
ejpam-5003	519	11	x	x	SYM
ejpam-5003	519	12	∈	∈	PROPN
ejpam-5003	519	13	h	h	NOUN
ejpam-5003	519	14	}	}	PUNCT
ejpam-5003	519	15	,	,	PUNCT
ejpam-5003	519	16	where	where	SCONJ
ejpam-5003	519	17	ix	ix	ADV
ejpam-5003	519	18	=	=	PUNCT
ejpam-5003	520	1	[	[	X
ejpam-5003	520	2	x]θ	x]θ	ADV
ejpam-5003	520	3	for	for	ADP
ejpam-5003	520	4	all	all	DET
ejpam-5003	520	5	x	x	SYM
ejpam-5003	520	6	∈	∈	PROPN
ejpam-5003	520	7	h.	h.	NOUN
ejpam-5003	520	8	then	then	ADV
ejpam-5003	520	9	h	h	X
ejpam-5003	520	10	/	/	SYM
ejpam-5003	520	11	i	i	PRON
ejpam-5003	520	12	with	with	ADP
ejpam-5003	520	13	the	the	DET
ejpam-5003	520	14	hyperoperation	hyperoperation	NOUN
ejpam-5003	520	15	⊗	⊗	PROPN
ejpam-5003	520	16	and	and	CCONJ
ejpam-5003	520	17	hyperorder	hyperorder	PROPN
ejpam-5003	520	18	≪i	≪i	NOUN
ejpam-5003	520	19	which	which	PRON
ejpam-5003	520	20	are	be	AUX
ejpam-5003	520	21	defined	define	VERB
ejpam-5003	520	22	as	as	SCONJ
ejpam-5003	520	23	follows	follow	VERB
ejpam-5003	520	24	:	:	PUNCT
ejpam-5003	520	25	ix	ix	PROPN
ejpam-5003	521	1	⊗	⊗	PROPN
ejpam-5003	521	2	iy	iy	PROPN
ejpam-5003	522	1	=	=	PUNCT
ejpam-5003	522	2	{	{	PUNCT
ejpam-5003	522	3	iz	iz	INTJ
ejpam-5003	522	4	:	:	PUNCT
ejpam-5003	522	5	z	z	PROPN
ejpam-5003	522	6	∈	∈	PROPN
ejpam-5003	522	7	x⊛	x⊛	PROPN
ejpam-5003	522	8	y	y	NOUN
ejpam-5003	522	9	}	}	PUNCT
ejpam-5003	522	10	and	and	CCONJ
ejpam-5003	522	11	ix	ix	ADV
ejpam-5003	522	12	≪i	≪i	PRON
ejpam-5003	522	13	iy	iy	X
ejpam-5003	522	14	if	if	SCONJ
ejpam-5003	523	1	and	and	CCONJ
ejpam-5003	523	2	only	only	ADV
ejpam-5003	523	3	if	if	SCONJ
ejpam-5003	523	4	i	i	PRON
ejpam-5003	523	5	∈	∈	VERB
ejpam-5003	523	6	ix	ix	ADP
ejpam-5003	523	7	⊗	⊗	PROPN
ejpam-5003	523	8	iy	iy	PROPN
ejpam-5003	523	9	is	be	AUX
ejpam-5003	523	10	a	a	DET
ejpam-5003	523	11	hyper	hyper	ADJ
ejpam-5003	523	12	bn	bn	NOUN
ejpam-5003	523	13	-algebra	-algebra	NOUN
ejpam-5003	523	14	which	which	PRON
ejpam-5003	523	15	we	we	PRON
ejpam-5003	523	16	call	call	VERB
ejpam-5003	523	17	the	the	DET
ejpam-5003	523	18	quotient	quotient	NOUN
ejpam-5003	523	19	hyper	hyper	PROPN
ejpam-5003	523	20	bn	bn	PROPN
ejpam-5003	523	21	-algebra	-algebra	PROPN
ejpam-5003	523	22	.	.	PUNCT
ejpam-5003	524	1	l.r	l.r	PROPN
ejpam-5003	524	2	.	.	PROPN
ejpam-5003	524	3	cabardo	cabardo	PROPN
ejpam-5003	524	4	,	,	PUNCT
ejpam-5003	524	5	g.	g.	PROPN
ejpam-5003	524	6	petalcorin	petalcorin	PROPN
ejpam-5003	524	7	/	/	SYM
ejpam-5003	524	8	eur	eur	PROPN
ejpam-5003	524	9	.	.	PUNCT
ejpam-5003	525	1	j.	j.	PROPN
ejpam-5003	525	2	pure	pure	PROPN
ejpam-5003	525	3	appl	appl	PROPN
ejpam-5003	525	4	.	.	PROPN
ejpam-5003	525	5	math	math	PROPN
ejpam-5003	525	6	,	,	PUNCT
ejpam-5003	525	7	17	17	NUM
ejpam-5003	525	8	(	(	PUNCT
ejpam-5003	525	9	1	1	NUM
ejpam-5003	525	10	)	)	PUNCT
ejpam-5003	525	11	(	(	PUNCT
ejpam-5003	525	12	2024	2024	NUM
ejpam-5003	525	13	)	)	PUNCT
ejpam-5003	525	14	,	,	PUNCT
ejpam-5003	525	15	222	222	NUM
ejpam-5003	525	16	-	-	SYM
ejpam-5003	525	17	242	242	NUM
ejpam-5003	525	18	239	239	NUM
ejpam-5003	525	19	proof	proof	NOUN
ejpam-5003	525	20	.	.	PUNCT
ejpam-5003	526	1	let	let	VERB
ejpam-5003	526	2	us	we	PRON
ejpam-5003	526	3	show	show	VERB
ejpam-5003	526	4	first	first	ADV
ejpam-5003	526	5	that	that	SCONJ
ejpam-5003	526	6	the	the	DET
ejpam-5003	526	7	hyperoperation	hyperoperation	NOUN
ejpam-5003	526	8	⊗	⊗	PROPN
ejpam-5003	526	9	is	be	AUX
ejpam-5003	526	10	well	well	ADV
ejpam-5003	526	11	-	-	PUNCT
ejpam-5003	526	12	defined	define	VERB
ejpam-5003	526	13	on	on	ADP
ejpam-5003	526	14	h	h	PROPN
ejpam-5003	526	15	/	/	SYM
ejpam-5003	526	16	i.	i.	NOUN
ejpam-5003	526	17	assume	assume	VERB
ejpam-5003	526	18	x	x	X
ejpam-5003	526	19	,	,	PUNCT
ejpam-5003	526	20	y	y	PROPN
ejpam-5003	526	21	,	,	PUNCT
ejpam-5003	526	22	x′	x′	NUM
ejpam-5003	526	23	,	,	PUNCT
ejpam-5003	526	24	y′	y′	NOUN
ejpam-5003	526	25	∈	∈	PROPN
ejpam-5003	526	26	h	h	NOUN
ejpam-5003	526	27	with	with	ADP
ejpam-5003	526	28	ix	ix	PROPN
ejpam-5003	526	29	=	=	PUNCT
ejpam-5003	526	30	ix′	ix′	PROPN
ejpam-5003	526	31	and	and	CCONJ
ejpam-5003	526	32	iy	iy	NOUN
ejpam-5003	526	33	=	=	PUNCT
ejpam-5003	526	34	iy′	iy′	NOUN
ejpam-5003	526	35	.	.	PUNCT
ejpam-5003	527	1	let	let	VERB
ejpam-5003	527	2	j	j	PROPN
ejpam-5003	527	3	∈	∈	PROPN
ejpam-5003	527	4	ix	ix	ADP
ejpam-5003	527	5	⊗	⊗	PROPN
ejpam-5003	527	6	iy	iy	PROPN
ejpam-5003	527	7	.	.	PUNCT
ejpam-5003	528	1	then	then	ADV
ejpam-5003	528	2	there	there	PRON
ejpam-5003	528	3	exists	exist	VERB
ejpam-5003	528	4	u	u	NOUN
ejpam-5003	528	5	∈	∈	PROPN
ejpam-5003	528	6	x	x	X
ejpam-5003	528	7	⊛	⊛	ADP
ejpam-5003	528	8	y	y	NUM
ejpam-5003	528	9	such	such	ADJ
ejpam-5003	528	10	that	that	PRON
ejpam-5003	528	11	j	j	PROPN
ejpam-5003	528	12	=	=	PUNCT
ejpam-5003	528	13	iu	iu	PROPN
ejpam-5003	528	14	.	.	PROPN
ejpam-5003	528	15	note	note	VERB
ejpam-5003	528	16	that	that	SCONJ
ejpam-5003	528	17	xθx′	xθx′	PROPN
ejpam-5003	528	18	and	and	CCONJ
ejpam-5003	528	19	yθy′.	yθy′.	PROPN
ejpam-5003	528	20	since	since	SCONJ
ejpam-5003	528	21	θ	θ	PROPN
ejpam-5003	528	22	is	be	AUX
ejpam-5003	528	23	a	a	DET
ejpam-5003	528	24	congruence	congruence	NOUN
ejpam-5003	528	25	relation	relation	NOUN
ejpam-5003	528	26	on	on	ADP
ejpam-5003	528	27	h	h	NOUN
ejpam-5003	528	28	,	,	PUNCT
ejpam-5003	528	29	it	it	PRON
ejpam-5003	528	30	follows	follow	VERB
ejpam-5003	528	31	that	that	SCONJ
ejpam-5003	528	32	(	(	PUNCT
ejpam-5003	528	33	x⊛	x⊛	PROPN
ejpam-5003	528	34	y)θ(x′	y)θ(x′	X
ejpam-5003	528	35	⊛	⊛	ADJ
ejpam-5003	528	36	y′	y′	NUM
ejpam-5003	528	37	)	)	PUNCT
ejpam-5003	528	38	.	.	PUNCT
ejpam-5003	529	1	hence	hence	ADV
ejpam-5003	529	2	,	,	PUNCT
ejpam-5003	529	3	there	there	PRON
ejpam-5003	529	4	is	be	VERB
ejpam-5003	529	5	an	an	DET
ejpam-5003	529	6	element	element	NOUN
ejpam-5003	529	7	z′	z′	NUM
ejpam-5003	529	8	∈	∈	PROPN
ejpam-5003	529	9	x′	x′	PROPN
ejpam-5003	529	10	⊛	⊛	NUM
ejpam-5003	529	11	y′	y′	NOUN
ejpam-5003	529	12	such	such	ADJ
ejpam-5003	529	13	that	that	SCONJ
ejpam-5003	529	14	uθz′	uθz′	NOUN
ejpam-5003	529	15	,	,	PUNCT
ejpam-5003	529	16	and	and	CCONJ
ejpam-5003	529	17	so	so	ADV
ejpam-5003	529	18	j	j	PROPN
ejpam-5003	529	19	=	=	PRON
ejpam-5003	529	20	iu	iu	PROPN
ejpam-5003	529	21	=	=	PUNCT
ejpam-5003	529	22	iz′	iz′	PROPN
ejpam-5003	529	23	.	.	PUNCT
ejpam-5003	530	1	thus	thus	ADV
ejpam-5003	530	2	,	,	PUNCT
ejpam-5003	530	3	j	j	PROPN
ejpam-5003	530	4	∈	∈	PROPN
ejpam-5003	530	5	ix′	ix′	X
ejpam-5003	530	6	⊗	⊗	ADJ
ejpam-5003	530	7	iy′	iy′	NOUN
ejpam-5003	530	8	.	.	PUNCT
ejpam-5003	531	1	so	so	ADV
ejpam-5003	531	2	,	,	PUNCT
ejpam-5003	531	3	ix	ix	PROPN
ejpam-5003	531	4	⊗	⊗	PROPN
ejpam-5003	531	5	iy	iy	PROPN
ejpam-5003	531	6	⊆	⊆	NUM
ejpam-5003	531	7	ix′	ix′	X
ejpam-5003	531	8	⊗	⊗	ADJ
ejpam-5003	531	9	iy′	iy′	NOUN
ejpam-5003	531	10	.	.	PUNCT
ejpam-5003	532	1	conversely	conversely	ADV
ejpam-5003	532	2	,	,	PUNCT
ejpam-5003	532	3	let	let	VERB
ejpam-5003	532	4	l	l	PROPN
ejpam-5003	532	5	∈	∈	PROPN
ejpam-5003	532	6	ix′	ix′	X
ejpam-5003	532	7	⊗	⊗	ADJ
ejpam-5003	532	8	iy′	iy′	NOUN
ejpam-5003	532	9	.	.	PUNCT
ejpam-5003	533	1	then	then	ADV
ejpam-5003	533	2	there	there	PRON
ejpam-5003	533	3	is	be	VERB
ejpam-5003	533	4	an	an	DET
ejpam-5003	533	5	element	element	NOUN
ejpam-5003	533	6	v′	v′	NOUN
ejpam-5003	533	7	∈	∈	PROPN
ejpam-5003	533	8	x′	x′	PROPN
ejpam-5003	533	9	⊛	⊛	NUM
ejpam-5003	533	10	y′	y′	NOUN
ejpam-5003	533	11	such	such	ADJ
ejpam-5003	533	12	that	that	SCONJ
ejpam-5003	533	13	l	l	NOUN
ejpam-5003	534	1	=	=	PUNCT
ejpam-5003	534	2	iv′	iv′	NOUN
ejpam-5003	534	3	.	.	PUNCT
ejpam-5003	535	1	note	note	VERB
ejpam-5003	535	2	that	that	SCONJ
ejpam-5003	535	3	x′θx	x′θx	PROPN
ejpam-5003	535	4	and	and	CCONJ
ejpam-5003	535	5	y′θy	y′θy	PROPN
ejpam-5003	535	6	.	.	PUNCT
ejpam-5003	536	1	hence	hence	ADV
ejpam-5003	536	2	,	,	PUNCT
ejpam-5003	536	3	(	(	PUNCT
ejpam-5003	536	4	x′	x′	PROPN
ejpam-5003	536	5	⊛	⊛	NUM
ejpam-5003	536	6	y′)θ(x	y′)θ(x	PROPN
ejpam-5003	536	7	⊛	⊛	NUM
ejpam-5003	536	8	y	y	NOUN
ejpam-5003	536	9	)	)	PUNCT
ejpam-5003	536	10	.	.	PUNCT
ejpam-5003	537	1	thus	thus	ADV
ejpam-5003	537	2	,	,	PUNCT
ejpam-5003	537	3	there	there	PRON
ejpam-5003	537	4	exists	exist	VERB
ejpam-5003	537	5	z	z	NOUN
ejpam-5003	537	6	∈	∈	PROPN
ejpam-5003	537	7	x	x	X
ejpam-5003	537	8	⊛	⊛	NUM
ejpam-5003	537	9	y	y	PRON
ejpam-5003	537	10	such	such	ADJ
ejpam-5003	537	11	that	that	DET
ejpam-5003	537	12	v′θz	v′θz	NOUN
ejpam-5003	537	13	,	,	PUNCT
ejpam-5003	537	14	so	so	SCONJ
ejpam-5003	537	15	that	that	SCONJ
ejpam-5003	537	16	l	l	NOUN
ejpam-5003	537	17	=	=	PUNCT
ejpam-5003	538	1	iv′	iv′	NOUN
ejpam-5003	538	2	=	=	NOUN
ejpam-5003	539	1	iz	iz	INTJ
ejpam-5003	539	2	.	.	PUNCT
ejpam-5003	540	1	it	it	PRON
ejpam-5003	540	2	means	mean	VERB
ejpam-5003	540	3	that	that	SCONJ
ejpam-5003	540	4	l	l	PROPN
ejpam-5003	540	5	∈	∈	PROPN
ejpam-5003	540	6	ix	ix	ADP
ejpam-5003	540	7	⊗	⊗	PROPN
ejpam-5003	540	8	iy	iy	PROPN
ejpam-5003	540	9	and	and	CCONJ
ejpam-5003	540	10	ix′	ix′	X
ejpam-5003	540	11	⊗	⊗	PROPN
ejpam-5003	540	12	iy′	iy′	NOUN
ejpam-5003	540	13	⊆	⊆	NUM
ejpam-5003	540	14	ix	ix	ADP
ejpam-5003	540	15	⊗	⊗	PROPN
ejpam-5003	540	16	iy	iy	PROPN
ejpam-5003	540	17	.	.	PUNCT
ejpam-5003	541	1	therefore	therefore	ADV
ejpam-5003	541	2	,	,	PUNCT
ejpam-5003	541	3	ix	ix	ADP
ejpam-5003	541	4	⊗	⊗	PROPN
ejpam-5003	541	5	iy	iy	PROPN
ejpam-5003	542	1	=	=	PUNCT
ejpam-5003	542	2	ix′	ix′	PROPN
ejpam-5003	542	3	⊗	⊗	ADJ
ejpam-5003	542	4	iy′	iy′	NOUN
ejpam-5003	542	5	and	and	CCONJ
ejpam-5003	542	6	⊗	⊗	PROPN
ejpam-5003	542	7	is	be	AUX
ejpam-5003	542	8	a	a	DET
ejpam-5003	542	9	well	well	ADV
ejpam-5003	542	10	-	-	PUNCT
ejpam-5003	542	11	defined	define	VERB
ejpam-5003	542	12	hyperoperation	hyperoperation	NOUN
ejpam-5003	542	13	on	on	ADP
ejpam-5003	542	14	h	h	PROPN
ejpam-5003	542	15	/	/	SYM
ejpam-5003	542	16	i.	i.	NOUN
ejpam-5003	542	17	now	now	ADV
ejpam-5003	542	18	,	,	PUNCT
ejpam-5003	542	19	we	we	PRON
ejpam-5003	542	20	will	will	AUX
ejpam-5003	542	21	show	show	VERB
ejpam-5003	542	22	that	that	SCONJ
ejpam-5003	542	23	(	(	PUNCT
ejpam-5003	542	24	i	i	NOUN
ejpam-5003	542	25	)	)	PUNCT
ejpam-5003	542	26	of	of	ADP
ejpam-5003	542	27	definition	definition	NOUN
ejpam-5003	542	28	5	5	NUM
ejpam-5003	542	29	holds	hold	VERB
ejpam-5003	542	30	for	for	ADP
ejpam-5003	542	31	h	h	NOUN
ejpam-5003	542	32	/	/	SYM
ejpam-5003	542	33	i	i	PROPN
ejpam-5003	542	34	,	,	PUNCT
ejpam-5003	542	35	that	that	ADV
ejpam-5003	542	36	is	is	ADV
ejpam-5003	542	37	,	,	PUNCT
ejpam-5003	542	38	ix	ix	ADP
ejpam-5003	542	39	≪i	≪i	NOUN
ejpam-5003	542	40	ix	ix	ADV
ejpam-5003	542	41	for	for	ADP
ejpam-5003	542	42	all	all	DET
ejpam-5003	542	43	ix	ix	ADP
ejpam-5003	542	44	∈	∈	PROPN
ejpam-5003	542	45	h	h	PROPN
ejpam-5003	542	46	/	/	SYM
ejpam-5003	542	47	i.	i.	NOUN
ejpam-5003	542	48	since	since	SCONJ
ejpam-5003	542	49	h	h	PROPN
ejpam-5003	542	50	is	be	AUX
ejpam-5003	542	51	a	a	DET
ejpam-5003	542	52	hyper	hyper	ADJ
ejpam-5003	542	53	bn	bn	ADJ
ejpam-5003	542	54	-algebra	-algebra	NOUN
ejpam-5003	542	55	,	,	PUNCT
ejpam-5003	542	56	x	x	SYM
ejpam-5003	542	57	≪	≪	ADJ
ejpam-5003	542	58	x	x	X
ejpam-5003	542	59	,	,	PUNCT
ejpam-5003	542	60	that	that	ADV
ejpam-5003	542	61	is	is	ADV
ejpam-5003	542	62	,	,	PUNCT
ejpam-5003	542	63	0	0	NUM
ejpam-5003	542	64	∈	∈	PROPN
ejpam-5003	542	65	x	x	SYM
ejpam-5003	542	66	⊛	⊛	NUM
ejpam-5003	542	67	x.	x.	PUNCT
ejpam-5003	542	68	thus	thus	ADV
ejpam-5003	542	69	,	,	PUNCT
ejpam-5003	542	70	we	we	PRON
ejpam-5003	542	71	have	have	VERB
ejpam-5003	542	72	i	i	PRON
ejpam-5003	542	73	∈	∈	PROPN
ejpam-5003	542	74	ix	ix	ADP
ejpam-5003	542	75	⊗	⊗	PROPN
ejpam-5003	542	76	ix	ix	PROPN
ejpam-5003	542	77	.	.	PUNCT
ejpam-5003	543	1	for	for	ADP
ejpam-5003	543	2	definition	definition	NOUN
ejpam-5003	543	3	5(ii	5(ii	NUM
ejpam-5003	543	4	)	)	PUNCT
ejpam-5003	543	5	,	,	PUNCT
ejpam-5003	543	6	we	we	PRON
ejpam-5003	543	7	will	will	AUX
ejpam-5003	543	8	show	show	VERB
ejpam-5003	543	9	that	that	SCONJ
ejpam-5003	543	10	ix⊗	ix⊗	NOUN
ejpam-5003	544	1	i	i	PRON
ejpam-5003	544	2	=	=	PUNCT
ejpam-5003	544	3	{	{	PUNCT
ejpam-5003	544	4	ix	ix	ADP
ejpam-5003	544	5	}	}	PUNCT
ejpam-5003	544	6	for	for	ADP
ejpam-5003	544	7	all	all	DET
ejpam-5003	544	8	ix	ix	ADP
ejpam-5003	544	9	∈	∈	PROPN
ejpam-5003	544	10	h	h	PROPN
ejpam-5003	544	11	/	/	SYM
ejpam-5003	544	12	i.	i.	PROPN
ejpam-5003	544	13	h	h	PROPN
ejpam-5003	544	14	being	be	AUX
ejpam-5003	544	15	a	a	DET
ejpam-5003	544	16	hyper	hyper	ADJ
ejpam-5003	544	17	bn	bn	NOUN
ejpam-5003	544	18	-algebra	-algebra	NOUN
ejpam-5003	544	19	means	mean	VERB
ejpam-5003	544	20	that	that	SCONJ
ejpam-5003	544	21	x⊛	x⊛	PROPN
ejpam-5003	544	22	0	0	PUNCT
ejpam-5003	544	23	=	=	SYM
ejpam-5003	544	24	{	{	PUNCT
ejpam-5003	544	25	x	x	NOUN
ejpam-5003	544	26	}	}	PUNCT
ejpam-5003	544	27	.	.	PUNCT
ejpam-5003	545	1	thus	thus	ADV
ejpam-5003	545	2	,	,	PUNCT
ejpam-5003	545	3	definition	definition	NOUN
ejpam-5003	545	4	5(ii	5(ii	NUM
ejpam-5003	545	5	)	)	PUNCT
ejpam-5003	545	6	follows	follow	VERB
ejpam-5003	545	7	for	for	ADP
ejpam-5003	545	8	h	h	NOUN
ejpam-5003	545	9	/	/	SYM
ejpam-5003	545	10	i.	i.	NOUN
ejpam-5003	545	11	let	let	VERB
ejpam-5003	545	12	iw	iw	PRON
ejpam-5003	545	13	∈	∈	PROPN
ejpam-5003	545	14	(	(	PUNCT
ejpam-5003	545	15	ix	ix	PROPN
ejpam-5003	545	16	⊗	⊗	PROPN
ejpam-5003	545	17	iy	iy	PROPN
ejpam-5003	545	18	)	)	PUNCT
ejpam-5003	546	1	⊗	⊗	PROPN
ejpam-5003	546	2	iz	iz	INTJ
ejpam-5003	546	3	where	where	SCONJ
ejpam-5003	546	4	ix	ix	INTJ
ejpam-5003	546	5	,	,	PUNCT
ejpam-5003	546	6	iy	iy	INTJ
ejpam-5003	546	7	,	,	PUNCT
ejpam-5003	546	8	iz	iz	INTJ
ejpam-5003	546	9	∈	∈	PROPN
ejpam-5003	546	10	h	h	PROPN
ejpam-5003	546	11	/	/	SYM
ejpam-5003	546	12	i.	i.	NOUN
ejpam-5003	546	13	then	then	ADV
ejpam-5003	546	14	there	there	PRON
ejpam-5003	546	15	exists	exist	VERB
ejpam-5003	546	16	u	u	NOUN
ejpam-5003	546	17	∈	∈	PROPN
ejpam-5003	546	18	x	x	X
ejpam-5003	546	19	⊛	⊛	ADP
ejpam-5003	546	20	y	y	NUM
ejpam-5003	546	21	such	such	ADJ
ejpam-5003	546	22	that	that	SCONJ
ejpam-5003	546	23	iw	iw	PROPN
ejpam-5003	546	24	∈	∈	PROPN
ejpam-5003	546	25	iu	iu	ADP
ejpam-5003	546	26	⊗	⊗	PROPN
ejpam-5003	546	27	iz	iz	INTJ
ejpam-5003	546	28	.	.	PUNCT
ejpam-5003	547	1	since	since	SCONJ
ejpam-5003	547	2	h	h	PROPN
ejpam-5003	547	3	is	be	AUX
ejpam-5003	547	4	a	a	DET
ejpam-5003	547	5	hyper	hyper	ADJ
ejpam-5003	547	6	bn	bn	ADJ
ejpam-5003	547	7	-algebra	-algebra	NOUN
ejpam-5003	547	8	,	,	PUNCT
ejpam-5003	547	9	we	we	PRON
ejpam-5003	547	10	have	have	VERB
ejpam-5003	547	11	w′	w′	PROPN
ejpam-5003	547	12	∈	∈	PROPN
ejpam-5003	547	13	u	u	PROPN
ejpam-5003	547	14	⊛	⊛	ADP
ejpam-5003	547	15	z	z	NOUN
ejpam-5003	547	16	⊆	⊆	NUM
ejpam-5003	547	17	(	(	PUNCT
ejpam-5003	547	18	x	x	PROPN
ejpam-5003	547	19	⊛	⊛	NUM
ejpam-5003	547	20	y	y	NOUN
ejpam-5003	547	21	)	)	PUNCT
ejpam-5003	547	22	⊛	⊛	NUM
ejpam-5003	547	23	z	z	NOUN
ejpam-5003	547	24	=	=	PUNCT
ejpam-5003	547	25	(	(	PUNCT
ejpam-5003	547	26	0⊛	0⊛	NUM
ejpam-5003	547	27	z)⊛	z)⊛	PROPN
ejpam-5003	547	28	(	(	PUNCT
ejpam-5003	547	29	y	y	PROPN
ejpam-5003	547	30	⊛	⊛	NUM
ejpam-5003	547	31	x	x	NOUN
ejpam-5003	547	32	)	)	PUNCT
ejpam-5003	547	33	which	which	PRON
ejpam-5003	547	34	implies	imply	VERB
ejpam-5003	547	35	that	that	SCONJ
ejpam-5003	547	36	iw	iw	INTJ
ejpam-5003	547	37	=	=	SYM
ejpam-5003	547	38	iw′	iw′	X
ejpam-5003	547	39	∈	∈	PROPN
ejpam-5003	547	40	(	(	PUNCT
ejpam-5003	547	41	i	i	NOUN
ejpam-5003	547	42	⊗	⊗	PROPN
ejpam-5003	547	43	iz)⊗	iz)⊗	PROPN
ejpam-5003	547	44	(	(	PUNCT
ejpam-5003	547	45	iy	iy	PROPN
ejpam-5003	547	46	⊗	⊗	PROPN
ejpam-5003	547	47	ix	ix	PROPN
ejpam-5003	547	48	)	)	PUNCT
ejpam-5003	547	49	.	.	PUNCT
ejpam-5003	548	1	since	since	SCONJ
ejpam-5003	548	2	iw	iw	PROPN
ejpam-5003	548	3	is	be	AUX
ejpam-5003	548	4	arbitrary	arbitrary	ADJ
ejpam-5003	548	5	,	,	PUNCT
ejpam-5003	548	6	we	we	PRON
ejpam-5003	548	7	have	have	VERB
ejpam-5003	548	8	(	(	PUNCT
ejpam-5003	548	9	ix	ix	PROPN
ejpam-5003	548	10	⊗	⊗	PROPN
ejpam-5003	548	11	iy	iy	PROPN
ejpam-5003	548	12	)	)	PUNCT
ejpam-5003	549	1	⊗	⊗	PROPN
ejpam-5003	549	2	iz	iz	INTJ
ejpam-5003	550	1	⊆	⊆	NUM
ejpam-5003	550	2	(	(	PUNCT
ejpam-5003	550	3	i	i	PRON
ejpam-5003	550	4	⊗	⊗	PROPN
ejpam-5003	550	5	iz	iz	INTJ
ejpam-5003	550	6	)	)	PUNCT
ejpam-5003	550	7	⊗	⊗	PROPN
ejpam-5003	550	8	(	(	PUNCT
ejpam-5003	550	9	iy	iy	PROPN
ejpam-5003	550	10	⊗	⊗	PROPN
ejpam-5003	550	11	ix	ix	PROPN
ejpam-5003	550	12	)	)	PUNCT
ejpam-5003	550	13	.	.	PUNCT
ejpam-5003	551	1	conversely	conversely	ADV
ejpam-5003	551	2	,	,	PUNCT
ejpam-5003	551	3	pick	pick	VERB
ejpam-5003	551	4	an	an	DET
ejpam-5003	551	5	arbitrary	arbitrary	ADJ
ejpam-5003	551	6	element	element	NOUN
ejpam-5003	551	7	iv	iv	X
ejpam-5003	551	8	∈	∈	PROPN
ejpam-5003	551	9	(	(	PUNCT
ejpam-5003	551	10	i⊗	i⊗	PROPN
ejpam-5003	551	11	iz)⊗	iz)⊗	NOUN
ejpam-5003	551	12	(	(	PUNCT
ejpam-5003	551	13	iy⊗	iy⊗	PROPN
ejpam-5003	551	14	ix	ix	PROPN
ejpam-5003	551	15	)	)	PUNCT
ejpam-5003	551	16	.	.	PUNCT
ejpam-5003	552	1	then	then	ADV
ejpam-5003	552	2	there	there	PRON
ejpam-5003	552	3	exist	exist	VERB
ejpam-5003	552	4	s	s	X
ejpam-5003	552	5	∈	∈	NOUN
ejpam-5003	552	6	0⊛	0⊛	NUM
ejpam-5003	552	7	z	z	NOUN
ejpam-5003	552	8	and	and	CCONJ
ejpam-5003	552	9	t	t	PROPN
ejpam-5003	552	10	∈	∈	PROPN
ejpam-5003	552	11	y⊛x	y⊛x	NUM
ejpam-5003	552	12	such	such	ADJ
ejpam-5003	552	13	that	that	PRON
ejpam-5003	552	14	is	be	AUX
ejpam-5003	552	15	∈	∈	PROPN
ejpam-5003	552	16	i⊗	i⊗	NOUN
ejpam-5003	553	1	iz	iz	INTJ
ejpam-5003	554	1	and	and	CCONJ
ejpam-5003	554	2	it	it	PRON
ejpam-5003	554	3	∈	∈	PROPN
ejpam-5003	554	4	iy	iy	INTJ
ejpam-5003	555	1	⊗	⊗	X
ejpam-5003	555	2	ix	ix	PROPN
ejpam-5003	555	3	.	.	PUNCT
ejpam-5003	556	1	and	and	CCONJ
ejpam-5003	556	2	so	so	ADV
ejpam-5003	556	3	,	,	PUNCT
ejpam-5003	556	4	iv	iv	NUM
ejpam-5003	556	5	∈	∈	PROPN
ejpam-5003	556	6	is⊗	is⊗	VERB
ejpam-5003	556	7	it	it	PRON
ejpam-5003	556	8	.	.	PUNCT
ejpam-5003	557	1	this	this	PRON
ejpam-5003	557	2	means	mean	VERB
ejpam-5003	557	3	that	that	SCONJ
ejpam-5003	557	4	there	there	PRON
ejpam-5003	557	5	is	be	VERB
ejpam-5003	557	6	an	an	DET
ejpam-5003	557	7	element	element	NOUN
ejpam-5003	557	8	v′	v′	NOUN
ejpam-5003	557	9	∈	∈	PROPN
ejpam-5003	558	1	s⊛	s⊛	PRON
ejpam-5003	558	2	t	t	VERB
ejpam-5003	558	3	such	such	ADJ
ejpam-5003	558	4	that	that	SCONJ
ejpam-5003	558	5	iv	iv	ADP
ejpam-5003	558	6	=	=	SYM
ejpam-5003	558	7	iv′	iv′	PROPN
ejpam-5003	558	8	.	.	PUNCT
ejpam-5003	559	1	since	since	SCONJ
ejpam-5003	559	2	h	h	NOUN
ejpam-5003	559	3	is	be	AUX
ejpam-5003	559	4	a	a	DET
ejpam-5003	559	5	hyper	hyper	ADJ
ejpam-5003	559	6	bn	bn	ADJ
ejpam-5003	559	7	-algebra	-algebra	NOUN
ejpam-5003	559	8	,	,	PUNCT
ejpam-5003	559	9	v′	v′	PROPN
ejpam-5003	559	10	∈	∈	PROPN
ejpam-5003	560	1	s⊛	s⊛	X
ejpam-5003	560	2	t	t	VERB
ejpam-5003	560	3	⊆	⊆	NUM
ejpam-5003	560	4	(	(	PUNCT
ejpam-5003	560	5	0⊛z)⊛	0⊛z)⊛	NUM
ejpam-5003	560	6	(	(	PUNCT
ejpam-5003	560	7	y⊛x	y⊛x	PROPN
ejpam-5003	560	8	)	)	PUNCT
ejpam-5003	560	9	=	=	NOUN
ejpam-5003	560	10	(	(	PUNCT
ejpam-5003	560	11	x⊛y)⊛z	x⊛y)⊛z	PROPN
ejpam-5003	560	12	.	.	PUNCT
ejpam-5003	561	1	thus	thus	ADV
ejpam-5003	561	2	,	,	PUNCT
ejpam-5003	561	3	iv	iv	X
ejpam-5003	561	4	=	=	PUNCT
ejpam-5003	561	5	iv′	iv′	PROPN
ejpam-5003	561	6	∈	∈	PROPN
ejpam-5003	561	7	(	(	PUNCT
ejpam-5003	561	8	ix⊗	ix⊗	X
ejpam-5003	561	9	iy)⊗	iy)⊗	X
ejpam-5003	561	10	iz	iz	INTJ
ejpam-5003	561	11	.	.	PUNCT
ejpam-5003	562	1	since	since	SCONJ
ejpam-5003	562	2	iv	iv	NUM
ejpam-5003	562	3	is	be	AUX
ejpam-5003	562	4	arbitrary	arbitrary	ADJ
ejpam-5003	562	5	,	,	PUNCT
ejpam-5003	562	6	we	we	PRON
ejpam-5003	562	7	have	have	VERB
ejpam-5003	562	8	(	(	PUNCT
ejpam-5003	562	9	i⊗	i⊗	PROPN
ejpam-5003	562	10	iz)⊛	iz)⊛	PROPN
ejpam-5003	562	11	(	(	PUNCT
ejpam-5003	562	12	iy	iy	PROPN
ejpam-5003	562	13	⊗	⊗	PROPN
ejpam-5003	562	14	ix	ix	PROPN
ejpam-5003	562	15	)	)	PUNCT
ejpam-5003	562	16	⊆	⊆	NUM
ejpam-5003	562	17	(	(	PUNCT
ejpam-5003	562	18	ix⊗	ix⊗	X
ejpam-5003	562	19	iy)⊗	iy)⊗	X
ejpam-5003	562	20	iz	iz	INTJ
ejpam-5003	562	21	.	.	PUNCT
ejpam-5003	563	1	hence	hence	ADV
ejpam-5003	563	2	,	,	PUNCT
ejpam-5003	563	3	(	(	PUNCT
ejpam-5003	563	4	ix	ix	PROPN
ejpam-5003	563	5	⊗	⊗	PROPN
ejpam-5003	563	6	iy)⊗	iy)⊗	PROPN
ejpam-5003	563	7	iz	iz	INTJ
ejpam-5003	564	1	=	=	PUNCT
ejpam-5003	564	2	(	(	PUNCT
ejpam-5003	564	3	i	i	NOUN
ejpam-5003	564	4	⊗	⊗	PROPN
ejpam-5003	564	5	iz)⊗	iz)⊗	PROPN
ejpam-5003	564	6	(	(	PUNCT
ejpam-5003	564	7	iy	iy	PROPN
ejpam-5003	564	8	⊗	⊗	PROPN
ejpam-5003	564	9	ix	ix	PROPN
ejpam-5003	564	10	)	)	PUNCT
ejpam-5003	564	11	and	and	CCONJ
ejpam-5003	564	12	definition	definition	NOUN
ejpam-5003	564	13	5(iii	5(iii	NUM
ejpam-5003	564	14	)	)	PUNCT
ejpam-5003	564	15	holds	hold	VERB
ejpam-5003	564	16	for	for	ADP
ejpam-5003	564	17	h	h	NOUN
ejpam-5003	564	18	/	/	SYM
ejpam-5003	564	19	i.	i.	NOUN
ejpam-5003	564	20	therefore	therefore	ADV
ejpam-5003	564	21	,	,	PUNCT
ejpam-5003	564	22	(	(	PUNCT
ejpam-5003	564	23	h	h	X
ejpam-5003	564	24	/	/	SYM
ejpam-5003	564	25	i,⊗	i,⊗	PROPN
ejpam-5003	564	26	,	,	PUNCT
ejpam-5003	564	27	i	i	PRON
ejpam-5003	564	28	)	)	PUNCT
ejpam-5003	564	29	is	be	AUX
ejpam-5003	564	30	a	a	DET
ejpam-5003	564	31	hyper	hyper	ADJ
ejpam-5003	564	32	bn	bn	ADJ
ejpam-5003	564	33	-algebra	-algebra	NOUN
ejpam-5003	564	34	.	.	PUNCT
ejpam-5003	565	1	theorem	theorem	NOUN
ejpam-5003	565	2	16	16	NUM
ejpam-5003	565	3	.	.	PUNCT
ejpam-5003	566	1	let	let	VERB
ejpam-5003	566	2	θ	θ	NOUN
ejpam-5003	566	3	be	be	AUX
ejpam-5003	566	4	a	a	DET
ejpam-5003	566	5	congruence	congruence	NOUN
ejpam-5003	566	6	relation	relation	NOUN
ejpam-5003	566	7	on	on	ADP
ejpam-5003	566	8	a	a	DET
ejpam-5003	566	9	hyper	hyper	ADJ
ejpam-5003	566	10	bn	bn	NOUN
ejpam-5003	566	11	-algebra	-algebra	NOUN
ejpam-5003	566	12	h	h	NOUN
ejpam-5003	567	1	such	such	ADJ
ejpam-5003	567	2	that	that	SCONJ
ejpam-5003	567	3	i	i	PRON
ejpam-5003	567	4	=	=	PUNCT
ejpam-5003	568	1	[	[	X
ejpam-5003	568	2	0]θ	0]θ	X
ejpam-5003	568	3	and	and	CCONJ
ejpam-5003	568	4	h	h	NOUN
ejpam-5003	568	5	/	/	SYM
ejpam-5003	568	6	i	i	PRON
ejpam-5003	568	7	=	=	PUNCT
ejpam-5003	568	8	{	{	PUNCT
ejpam-5003	568	9	ix	ix	X
ejpam-5003	568	10	:	:	PUNCT
ejpam-5003	568	11	x	x	SYM
ejpam-5003	568	12	∈	∈	PROPN
ejpam-5003	568	13	h	h	NOUN
ejpam-5003	568	14	}	}	PUNCT
ejpam-5003	568	15	,	,	PUNCT
ejpam-5003	568	16	where	where	SCONJ
ejpam-5003	568	17	ix	ix	ADV
ejpam-5003	568	18	=	=	PUNCT
ejpam-5003	569	1	[	[	X
ejpam-5003	569	2	x]θ	x]θ	ADV
ejpam-5003	569	3	for	for	ADP
ejpam-5003	569	4	all	all	DET
ejpam-5003	569	5	x	x	SYM
ejpam-5003	569	6	∈	∈	PROPN
ejpam-5003	569	7	h.	h.	NOUN
ejpam-5003	569	8	if	if	SCONJ
ejpam-5003	569	9	h	h	NOUN
ejpam-5003	569	10	is	be	AUX
ejpam-5003	569	11	commutative	commutative	ADJ
ejpam-5003	569	12	,	,	PUNCT
ejpam-5003	569	13	then	then	ADV
ejpam-5003	569	14	so	so	ADV
ejpam-5003	569	15	is	be	AUX
ejpam-5003	569	16	h	h	NOUN
ejpam-5003	569	17	/	/	SYM
ejpam-5003	569	18	i.	i.	NOUN
ejpam-5003	569	19	proof	proof	NOUN
ejpam-5003	569	20	.	.	PUNCT
ejpam-5003	570	1	suppose	suppose	VERB
ejpam-5003	570	2	h	h	NOUN
ejpam-5003	570	3	is	be	AUX
ejpam-5003	570	4	commutative	commutative	ADJ
ejpam-5003	570	5	.	.	PUNCT
ejpam-5003	571	1	then	then	ADV
ejpam-5003	571	2	for	for	ADP
ejpam-5003	571	3	all	all	DET
ejpam-5003	571	4	x	x	NOUN
ejpam-5003	571	5	,	,	PUNCT
ejpam-5003	571	6	y	y	PROPN
ejpam-5003	571	7	∈	∈	PROPN
ejpam-5003	571	8	h	h	NOUN
ejpam-5003	571	9	,	,	PUNCT
ejpam-5003	571	10	x	x	PROPN
ejpam-5003	571	11	⊛	⊛	NUM
ejpam-5003	571	12	y	y	PROPN
ejpam-5003	571	13	=	=	SYM
ejpam-5003	571	14	y	y	PROPN
ejpam-5003	571	15	⊛	⊛	NUM
ejpam-5003	571	16	x.	x.	NOUN
ejpam-5003	571	17	let	let	VERB
ejpam-5003	571	18	ix	ix	ADV
ejpam-5003	571	19	,	,	PUNCT
ejpam-5003	571	20	iy	iy	PROPN
ejpam-5003	571	21	∈	∈	PROPN
ejpam-5003	571	22	h	h	PROPN
ejpam-5003	571	23	/	/	SYM
ejpam-5003	571	24	i.	i.	NOUN
ejpam-5003	571	25	then	then	ADV
ejpam-5003	571	26	ix	ix	PROPN
ejpam-5003	571	27	⊗	⊗	PROPN
ejpam-5003	571	28	iy	iy	PROPN
ejpam-5003	572	1	=	=	PUNCT
ejpam-5003	572	2	{	{	PUNCT
ejpam-5003	572	3	iz	iz	INTJ
ejpam-5003	572	4	:	:	PUNCT
ejpam-5003	572	5	z	z	NOUN
ejpam-5003	572	6	∈	∈	PROPN
ejpam-5003	572	7	x	x	X
ejpam-5003	572	8	⊛	⊛	PROPN
ejpam-5003	572	9	y	y	PROPN
ejpam-5003	572	10	=	=	SYM
ejpam-5003	572	11	y	y	PROPN
ejpam-5003	572	12	⊛	⊛	NUM
ejpam-5003	572	13	x	x	X
ejpam-5003	572	14	}	}	PUNCT
ejpam-5003	572	15	=	=	SYM
ejpam-5003	572	16	iy	iy	PROPN
ejpam-5003	572	17	⊗	⊗	PROPN
ejpam-5003	572	18	ix	ix	PROPN
ejpam-5003	572	19	.	.	PUNCT
ejpam-5003	573	1	hence	hence	ADV
ejpam-5003	573	2	,	,	PUNCT
ejpam-5003	573	3	h	h	NOUN
ejpam-5003	573	4	/	/	SYM
ejpam-5003	573	5	i	i	PRON
ejpam-5003	573	6	is	be	AUX
ejpam-5003	573	7	commutative	commutative	ADJ
ejpam-5003	573	8	.	.	PUNCT
ejpam-5003	574	1	the	the	DET
ejpam-5003	574	2	converse	converse	NOUN
ejpam-5003	574	3	of	of	ADP
ejpam-5003	574	4	theorem	theorem	NOUN
ejpam-5003	574	5	16	16	NUM
ejpam-5003	574	6	is	be	AUX
ejpam-5003	574	7	not	not	PART
ejpam-5003	574	8	necessarily	necessarily	ADV
ejpam-5003	574	9	true	true	ADJ
ejpam-5003	574	10	.	.	PUNCT
ejpam-5003	575	1	h	h	X
ejpam-5003	575	2	/	/	SYM
ejpam-5003	576	1	i	i	PRON
ejpam-5003	576	2	in	in	ADP
ejpam-5003	576	3	example	example	NOUN
ejpam-5003	576	4	24	24	NUM
ejpam-5003	576	5	is	be	AUX
ejpam-5003	576	6	commutative	commutative	ADJ
ejpam-5003	576	7	but	but	CCONJ
ejpam-5003	576	8	h	h	NOUN
ejpam-5003	576	9	is	be	AUX
ejpam-5003	576	10	not	not	PART
ejpam-5003	576	11	because	because	SCONJ
ejpam-5003	576	12	0⊛	0⊛	NUM
ejpam-5003	576	13	3	3	NUM
ejpam-5003	576	14	=	=	SYM
ejpam-5003	576	15	{	{	PUNCT
ejpam-5003	576	16	2	2	NUM
ejpam-5003	576	17	}	}	PUNCT
ejpam-5003	576	18	=	=	NOUN
ejpam-5003	576	19	̸	̸	NUM
ejpam-5003	576	20	{	{	PUNCT
ejpam-5003	576	21	3	3	NUM
ejpam-5003	576	22	}	}	PUNCT
ejpam-5003	576	23	=	=	PUNCT
ejpam-5003	576	24	3⊛	3⊛	NUM
ejpam-5003	577	1	0	0	X
ejpam-5003	577	2	.	.	PUNCT
ejpam-5003	578	1	lemma	lemma	PROPN
ejpam-5003	578	2	9	9	NUM
ejpam-5003	578	3	.	.	PUNCT
ejpam-5003	579	1	let	let	VERB
ejpam-5003	579	2	h	h	PRON
ejpam-5003	579	3	be	be	AUX
ejpam-5003	579	4	a	a	DET
ejpam-5003	579	5	hyper	hyper	ADJ
ejpam-5003	579	6	bn	bn	ADJ
ejpam-5003	579	7	-algebra	-algebra	NOUN
ejpam-5003	579	8	,	,	PUNCT
ejpam-5003	579	9	θ	θ	PROPN
ejpam-5003	579	10	be	be	VERB
ejpam-5003	579	11	a	a	DET
ejpam-5003	579	12	congruence	congruence	NOUN
ejpam-5003	579	13	relation	relation	NOUN
ejpam-5003	579	14	on	on	ADP
ejpam-5003	579	15	h	h	PROPN
ejpam-5003	579	16	and	and	CCONJ
ejpam-5003	579	17	x	x	X
ejpam-5003	579	18	,	,	PUNCT
ejpam-5003	579	19	y	y	PROPN
ejpam-5003	579	20	∈	∈	PROPN
ejpam-5003	579	21	h.	h.	NOUN
ejpam-5003	580	1	if	if	SCONJ
ejpam-5003	580	2	(	(	PUNCT
ejpam-5003	580	3	x⊛	x⊛	INTJ
ejpam-5003	580	4	y)θ{0	y)θ{0	ADP
ejpam-5003	580	5	}	}	PUNCT
ejpam-5003	580	6	,	,	PUNCT
ejpam-5003	580	7	then	then	ADV
ejpam-5003	580	8	(	(	PUNCT
ejpam-5003	580	9	y	y	PROPN
ejpam-5003	580	10	⊛	⊛	NUM
ejpam-5003	580	11	x)θ{0	x)θ{0	NUM
ejpam-5003	580	12	}	}	PUNCT
ejpam-5003	580	13	.	.	PUNCT
ejpam-5003	581	1	proof	proof	NOUN
ejpam-5003	581	2	.	.	PUNCT
ejpam-5003	582	1	let	let	VERB
ejpam-5003	582	2	h	h	PRON
ejpam-5003	582	3	be	be	AUX
ejpam-5003	582	4	a	a	DET
ejpam-5003	582	5	hyper	hyper	ADJ
ejpam-5003	582	6	bn	bn	NOUN
ejpam-5003	582	7	-algebra	-algebra	NOUN
ejpam-5003	582	8	and	and	CCONJ
ejpam-5003	582	9	θ	θ	PROPN
ejpam-5003	582	10	be	be	VERB
ejpam-5003	582	11	a	a	DET
ejpam-5003	582	12	congruence	congruence	NOUN
ejpam-5003	582	13	relation	relation	NOUN
ejpam-5003	582	14	on	on	ADP
ejpam-5003	582	15	h.	h.	PROPN
ejpam-5003	582	16	let	let	VERB
ejpam-5003	582	17	x	x	PRON
ejpam-5003	582	18	,	,	PUNCT
ejpam-5003	582	19	y	y	PROPN
ejpam-5003	582	20	∈	∈	PROPN
ejpam-5003	582	21	h	h	NOUN
ejpam-5003	582	22	such	such	ADJ
ejpam-5003	582	23	that	that	PRON
ejpam-5003	582	24	(	(	PUNCT
ejpam-5003	582	25	x⊛	x⊛	INTJ
ejpam-5003	582	26	y)θ{0	y)θ{0	ADJ
ejpam-5003	582	27	}	}	PUNCT
ejpam-5003	582	28	.	.	PUNCT
ejpam-5003	583	1	then	then	ADV
ejpam-5003	583	2	there	there	PRON
ejpam-5003	583	3	exists	exist	VERB
ejpam-5003	583	4	a	a	DET
ejpam-5003	583	5	∈	∈	NOUN
ejpam-5003	583	6	x⊛	x⊛	PUNCT
ejpam-5003	584	1	y	y	PROPN
ejpam-5003	584	2	such	such	ADJ
ejpam-5003	584	3	that	that	DET
ejpam-5003	584	4	aθ0	aθ0	PROPN
ejpam-5003	584	5	.	.	PUNCT
ejpam-5003	585	1	since	since	SCONJ
ejpam-5003	585	2	0	0	NUM
ejpam-5003	585	3	∈	∈	PROPN
ejpam-5003	585	4	h	h	NOUN
ejpam-5003	585	5	and	and	CCONJ
ejpam-5003	585	6	θ	θ	PROPN
ejpam-5003	585	7	is	be	AUX
ejpam-5003	585	8	a	a	DET
ejpam-5003	585	9	congruence	congruence	NOUN
ejpam-5003	585	10	relation	relation	NOUN
ejpam-5003	585	11	,	,	PUNCT
ejpam-5003	585	12	we	we	PRON
ejpam-5003	585	13	have	have	VERB
ejpam-5003	585	14	(	(	PUNCT
ejpam-5003	585	15	0	0	NUM
ejpam-5003	585	16	⊛	⊛	NUM
ejpam-5003	585	17	a)θ(0	a)θ(0	PROPN
ejpam-5003	585	18	⊛	⊛	NUM
ejpam-5003	585	19	0	0	NUM
ejpam-5003	585	20	)	)	PUNCT
ejpam-5003	585	21	=	=	PRON
ejpam-5003	585	22	{	{	PUNCT
ejpam-5003	585	23	0	0	NUM
ejpam-5003	585	24	}	}	PUNCT
ejpam-5003	585	25	.	.	PUNCT
ejpam-5003	586	1	this	this	PRON
ejpam-5003	586	2	means	mean	VERB
ejpam-5003	586	3	that	that	SCONJ
ejpam-5003	586	4	for	for	ADP
ejpam-5003	586	5	all	all	PRON
ejpam-5003	586	6	s	s	PART
ejpam-5003	586	7	∈	∈	NOUN
ejpam-5003	586	8	0	0	NUM
ejpam-5003	586	9	⊛	⊛	NUM
ejpam-5003	586	10	a	a	DET
ejpam-5003	586	11	,	,	PUNCT
ejpam-5003	586	12	sθ0	sθ0	NOUN
ejpam-5003	586	13	.	.	PUNCT
ejpam-5003	587	1	but	but	CCONJ
ejpam-5003	587	2	s	s	X
ejpam-5003	587	3	∈	∈	NOUN
ejpam-5003	587	4	0	0	NUM
ejpam-5003	587	5	⊛	⊛	NUM
ejpam-5003	587	6	a	a	DET
ejpam-5003	587	7	⊆	⊆	NUM
ejpam-5003	587	8	0	0	NUM
ejpam-5003	587	9	⊛	⊛	NUM
ejpam-5003	587	10	(	(	PUNCT
ejpam-5003	587	11	x	x	PROPN
ejpam-5003	587	12	⊛	⊛	NUM
ejpam-5003	587	13	y	y	NOUN
ejpam-5003	587	14	)	)	PUNCT
ejpam-5003	587	15	=	=	SYM
ejpam-5003	588	1	y	y	PROPN
ejpam-5003	588	2	⊛	⊛	NUM
ejpam-5003	588	3	x	x	PUNCT
ejpam-5003	588	4	by	by	ADP
ejpam-5003	588	5	theorem	theorem	NOUN
ejpam-5003	588	6	1(iii	1(iii	NUM
ejpam-5003	588	7	)	)	PUNCT
ejpam-5003	588	8	.	.	PUNCT
ejpam-5003	589	1	thus	thus	ADV
ejpam-5003	589	2	,	,	PUNCT
ejpam-5003	589	3	s	s	VERB
ejpam-5003	589	4	∈	∈	PROPN
ejpam-5003	589	5	y	y	PROPN
ejpam-5003	589	6	⊛	⊛	NUM
ejpam-5003	589	7	x	x	PUNCT
ejpam-5003	589	8	with	with	ADP
ejpam-5003	589	9	sθ0	sθ0	NUM
ejpam-5003	589	10	.	.	PUNCT
ejpam-5003	590	1	therefore	therefore	ADV
ejpam-5003	590	2	,	,	PUNCT
ejpam-5003	590	3	(	(	PUNCT
ejpam-5003	590	4	y	y	PROPN
ejpam-5003	590	5	⊛	⊛	NUM
ejpam-5003	590	6	x)θ{0	x)θ{0	NUM
ejpam-5003	590	7	}	}	PUNCT
ejpam-5003	590	8	.	.	PUNCT
ejpam-5003	591	1	l.r	l.r	PROPN
ejpam-5003	591	2	.	.	PROPN
ejpam-5003	591	3	cabardo	cabardo	PROPN
ejpam-5003	591	4	,	,	PUNCT
ejpam-5003	591	5	g.	g.	PROPN
ejpam-5003	591	6	petalcorin	petalcorin	PROPN
ejpam-5003	591	7	/	/	SYM
ejpam-5003	591	8	eur	eur	PROPN
ejpam-5003	591	9	.	.	PUNCT
ejpam-5003	592	1	j.	j.	PROPN
ejpam-5003	592	2	pure	pure	PROPN
ejpam-5003	592	3	appl	appl	PROPN
ejpam-5003	592	4	.	.	PROPN
ejpam-5003	592	5	math	math	PROPN
ejpam-5003	592	6	,	,	PUNCT
ejpam-5003	592	7	17	17	NUM
ejpam-5003	592	8	(	(	PUNCT
ejpam-5003	592	9	1	1	NUM
ejpam-5003	592	10	)	)	PUNCT
ejpam-5003	592	11	(	(	PUNCT
ejpam-5003	592	12	2024	2024	NUM
ejpam-5003	592	13	)	)	PUNCT
ejpam-5003	592	14	,	,	PUNCT
ejpam-5003	592	15	222	222	NUM
ejpam-5003	592	16	-	-	SYM
ejpam-5003	592	17	242	242	NUM
ejpam-5003	592	18	240	240	NUM
ejpam-5003	592	19	lemma	lemma	PROPN
ejpam-5003	592	20	9	9	NUM
ejpam-5003	592	21	serves	serve	VERB
ejpam-5003	592	22	as	as	ADP
ejpam-5003	592	23	our	our	PRON
ejpam-5003	592	24	motivation	motivation	NOUN
ejpam-5003	592	25	in	in	ADP
ejpam-5003	592	26	defining	define	VERB
ejpam-5003	592	27	regularity	regularity	NOUN
ejpam-5003	592	28	of	of	ADP
ejpam-5003	592	29	an	an	DET
ejpam-5003	592	30	equivalence	equivalence	NOUN
ejpam-5003	592	31	relation	relation	NOUN
ejpam-5003	592	32	on	on	ADP
ejpam-5003	592	33	a	a	DET
ejpam-5003	592	34	hyper	hyper	ADJ
ejpam-5003	592	35	bn	bn	NOUN
ejpam-5003	592	36	-algebra	-algebra	NOUN
ejpam-5003	592	37	.	.	PUNCT
ejpam-5003	593	1	definition	definition	NOUN
ejpam-5003	593	2	16	16	NUM
ejpam-5003	593	3	.	.	PUNCT
ejpam-5003	594	1	let	let	VERB
ejpam-5003	594	2	h	h	PRON
ejpam-5003	594	3	be	be	AUX
ejpam-5003	594	4	a	a	DET
ejpam-5003	594	5	hyper	hyper	ADJ
ejpam-5003	594	6	bn	bn	NOUN
ejpam-5003	594	7	-algebra	-algebra	NOUN
ejpam-5003	594	8	and	and	CCONJ
ejpam-5003	594	9	θ	θ	PROPN
ejpam-5003	594	10	be	be	VERB
ejpam-5003	594	11	an	an	DET
ejpam-5003	594	12	equivalence	equivalence	NOUN
ejpam-5003	594	13	relation	relation	NOUN
ejpam-5003	594	14	on	on	ADP
ejpam-5003	594	15	h.	h.	PROPN
ejpam-5003	594	16	then	then	ADV
ejpam-5003	594	17	θ	θ	PROPN
ejpam-5003	594	18	is	be	AUX
ejpam-5003	594	19	called	call	VERB
ejpam-5003	594	20	a	a	DET
ejpam-5003	594	21	regular	regular	ADJ
ejpam-5003	594	22	congruence	congruence	NOUN
ejpam-5003	594	23	relation	relation	NOUN
ejpam-5003	594	24	on	on	ADP
ejpam-5003	594	25	h	h	NOUN
ejpam-5003	594	26	,	,	PUNCT
ejpam-5003	594	27	if	if	SCONJ
ejpam-5003	594	28	θ	θ	PROPN
ejpam-5003	594	29	is	be	AUX
ejpam-5003	594	30	a	a	DET
ejpam-5003	594	31	congruence	congruence	NOUN
ejpam-5003	594	32	relation	relation	NOUN
ejpam-5003	594	33	on	on	ADP
ejpam-5003	594	34	h	h	NOUN
ejpam-5003	594	35	and	and	CCONJ
ejpam-5003	594	36	whenever	whenever	SCONJ
ejpam-5003	594	37	(	(	PUNCT
ejpam-5003	594	38	x⊛	x⊛	INTJ
ejpam-5003	594	39	y)θ{0	y)θ{0	ADP
ejpam-5003	594	40	}	}	PUNCT
ejpam-5003	594	41	,	,	PUNCT
ejpam-5003	594	42	then	then	ADV
ejpam-5003	594	43	xθy	xθy	VERB
ejpam-5003	594	44	for	for	ADP
ejpam-5003	594	45	all	all	DET
ejpam-5003	594	46	x	x	NOUN
ejpam-5003	594	47	,	,	PUNCT
ejpam-5003	594	48	y	y	PROPN
ejpam-5003	594	49	∈	∈	PROPN
ejpam-5003	594	50	h.	h.	PROPN
ejpam-5003	594	51	theorem	theorem	VERB
ejpam-5003	594	52	17	17	NUM
ejpam-5003	594	53	.	.	PUNCT
ejpam-5003	595	1	let	let	VERB
ejpam-5003	595	2	θ	θ	NOUN
ejpam-5003	595	3	and	and	CCONJ
ejpam-5003	595	4	θ′	θ′	NOUN
ejpam-5003	595	5	be	be	AUX
ejpam-5003	595	6	regular	regular	ADJ
ejpam-5003	595	7	congruence	congruence	NOUN
ejpam-5003	595	8	relations	relation	NOUN
ejpam-5003	595	9	on	on	ADP
ejpam-5003	595	10	h	h	NOUN
ejpam-5003	595	11	with	with	ADP
ejpam-5003	595	12	[	[	X
ejpam-5003	595	13	0]θ	0]θ	X
ejpam-5003	595	14	=	=	PUNCT
ejpam-5003	596	1	[	[	X
ejpam-5003	596	2	0]θ′.	0]θ′.	X
ejpam-5003	596	3	then	then	ADV
ejpam-5003	596	4	θ	θ	NOUN
ejpam-5003	596	5	=	=	SYM
ejpam-5003	596	6	θ′.	θ′.	ADP
ejpam-5003	596	7	proof	proof	NOUN
ejpam-5003	596	8	.	.	PUNCT
ejpam-5003	597	1	let	let	VERB
ejpam-5003	597	2	θ	θ	NOUN
ejpam-5003	597	3	and	and	CCONJ
ejpam-5003	597	4	θ′	θ′	NOUN
ejpam-5003	597	5	be	be	AUX
ejpam-5003	597	6	regular	regular	ADJ
ejpam-5003	597	7	congruence	congruence	NOUN
ejpam-5003	597	8	relations	relation	NOUN
ejpam-5003	597	9	onh	onh	PROPN
ejpam-5003	597	10	with	with	ADP
ejpam-5003	597	11	[	[	X
ejpam-5003	597	12	0]θ	0]θ	X
ejpam-5003	597	13	=	=	PUNCT
ejpam-5003	598	1	[	[	X
ejpam-5003	598	2	0]θ′	0]θ′	X
ejpam-5003	598	3	.	.	PUNCT
ejpam-5003	599	1	since	since	SCONJ
ejpam-5003	599	2	θ	θ	PROPN
ejpam-5003	599	3	and	and	CCONJ
ejpam-5003	599	4	θ′	θ′	NOUN
ejpam-5003	599	5	are	be	AUX
ejpam-5003	599	6	both	both	DET
ejpam-5003	599	7	relations	relation	NOUN
ejpam-5003	599	8	on	on	ADP
ejpam-5003	599	9	h	h	NOUN
ejpam-5003	599	10	,	,	PUNCT
ejpam-5003	599	11	we	we	PRON
ejpam-5003	599	12	just	just	ADV
ejpam-5003	599	13	need	need	VERB
ejpam-5003	599	14	to	to	PART
ejpam-5003	599	15	show	show	VERB
ejpam-5003	599	16	that	that	DET
ejpam-5003	599	17	xθy	xθy	PROPN
ejpam-5003	600	1	if	if	SCONJ
ejpam-5003	600	2	and	and	CCONJ
ejpam-5003	600	3	only	only	ADV
ejpam-5003	600	4	if	if	SCONJ
ejpam-5003	600	5	xθ′y	xθ′y	PROPN
ejpam-5003	600	6	for	for	ADP
ejpam-5003	600	7	all	all	DET
ejpam-5003	600	8	x	x	NOUN
ejpam-5003	600	9	,	,	PUNCT
ejpam-5003	600	10	y	y	PROPN
ejpam-5003	600	11	∈	∈	PROPN
ejpam-5003	600	12	h.	h.	PROPN
ejpam-5003	600	13	let	let	VERB
ejpam-5003	600	14	xθy	xθy	NOUN
ejpam-5003	600	15	.	.	PUNCT
ejpam-5003	601	1	since	since	SCONJ
ejpam-5003	601	2	θ	θ	PROPN
ejpam-5003	601	3	is	be	AUX
ejpam-5003	601	4	a	a	DET
ejpam-5003	601	5	congruence	congruence	NOUN
ejpam-5003	601	6	relation	relation	NOUN
ejpam-5003	601	7	on	on	ADP
ejpam-5003	601	8	h	h	NOUN
ejpam-5003	601	9	,	,	PUNCT
ejpam-5003	601	10	by	by	ADP
ejpam-5003	601	11	lemma	lemma	PROPN
ejpam-5003	601	12	8	8	NUM
ejpam-5003	601	13	,	,	PUNCT
ejpam-5003	601	14	(	(	PUNCT
ejpam-5003	601	15	x	x	PROPN
ejpam-5003	601	16	⊛	⊛	NUM
ejpam-5003	601	17	x)θ(x	x)θ(x	PROPN
ejpam-5003	601	18	⊛	⊛	NUM
ejpam-5003	601	19	y	y	NOUN
ejpam-5003	601	20	)	)	PUNCT
ejpam-5003	601	21	.	.	PUNCT
ejpam-5003	602	1	since	since	SCONJ
ejpam-5003	602	2	0	0	NUM
ejpam-5003	602	3	∈	∈	NOUN
ejpam-5003	602	4	x⊛	x⊛	NOUN
ejpam-5003	602	5	x	x	NOUN
ejpam-5003	602	6	,	,	PUNCT
ejpam-5003	602	7	there	there	PRON
ejpam-5003	602	8	exists	exist	VERB
ejpam-5003	602	9	an	an	DET
ejpam-5003	602	10	element	element	NOUN
ejpam-5003	602	11	s	s	PART
ejpam-5003	602	12	∈	∈	NOUN
ejpam-5003	602	13	x⊛	x⊛	PUNCT
ejpam-5003	603	1	y	y	PROPN
ejpam-5003	603	2	such	such	ADJ
ejpam-5003	603	3	that	that	DET
ejpam-5003	603	4	0θs	0θs	NOUN
ejpam-5003	603	5	.	.	PUNCT
ejpam-5003	604	1	it	it	PRON
ejpam-5003	604	2	follows	follow	VERB
ejpam-5003	604	3	that	that	PRON
ejpam-5003	604	4	s	s	VERB
ejpam-5003	604	5	∈	∈	PROPN
ejpam-5003	605	1	[	[	X
ejpam-5003	605	2	0]θ	0]θ	X
ejpam-5003	605	3	=	=	PUNCT
ejpam-5003	606	1	[	[	X
ejpam-5003	606	2	0]θ′	0]θ′	NUM
ejpam-5003	606	3	.	.	PUNCT
ejpam-5003	607	1	thus	thus	ADV
ejpam-5003	607	2	,	,	PUNCT
ejpam-5003	607	3	(	(	PUNCT
ejpam-5003	607	4	x	x	X
ejpam-5003	607	5	⊛	⊛	NUM
ejpam-5003	607	6	y)θ′{0	y)θ′{0	PROPN
ejpam-5003	607	7	}	}	PUNCT
ejpam-5003	607	8	.	.	PUNCT
ejpam-5003	608	1	now	now	ADV
ejpam-5003	608	2	,	,	PUNCT
ejpam-5003	608	3	since	since	SCONJ
ejpam-5003	608	4	θ′	θ′	NOUN
ejpam-5003	608	5	is	be	AUX
ejpam-5003	608	6	a	a	DET
ejpam-5003	608	7	regular	regular	ADJ
ejpam-5003	608	8	congruence	congruence	NOUN
ejpam-5003	608	9	relation	relation	NOUN
ejpam-5003	608	10	on	on	ADP
ejpam-5003	608	11	h	h	NOUN
ejpam-5003	608	12	,	,	PUNCT
ejpam-5003	608	13	we	we	PRON
ejpam-5003	608	14	have	have	VERB
ejpam-5003	608	15	xθ′y	xθ′y	PROPN
ejpam-5003	608	16	.	.	PUNCT
ejpam-5003	609	1	conversely	conversely	ADV
ejpam-5003	609	2	,	,	PUNCT
ejpam-5003	609	3	let	let	VERB
ejpam-5003	609	4	xθ′y	xθ′y	PROPN
ejpam-5003	609	5	.	.	PUNCT
ejpam-5003	610	1	then	then	ADV
ejpam-5003	610	2	(	(	PUNCT
ejpam-5003	610	3	x	x	PROPN
ejpam-5003	610	4	⊛	⊛	NUM
ejpam-5003	610	5	x)θ′(x	x)θ′(x	PROPN
ejpam-5003	610	6	⊛	⊛	NUM
ejpam-5003	610	7	y	y	NOUN
ejpam-5003	610	8	)	)	PUNCT
ejpam-5003	610	9	.	.	PUNCT
ejpam-5003	611	1	since	since	SCONJ
ejpam-5003	611	2	0	0	NUM
ejpam-5003	611	3	∈	∈	PROPN
ejpam-5003	611	4	x	x	SYM
ejpam-5003	611	5	⊛	⊛	NUM
ejpam-5003	611	6	x	x	X
ejpam-5003	611	7	,	,	PUNCT
ejpam-5003	611	8	there	there	PRON
ejpam-5003	611	9	exists	exist	VERB
ejpam-5003	611	10	an	an	DET
ejpam-5003	611	11	element	element	NOUN
ejpam-5003	611	12	s	s	PART
ejpam-5003	611	13	∈	∈	NOUN
ejpam-5003	611	14	x	x	X
ejpam-5003	611	15	⊛	⊛	NUM
ejpam-5003	611	16	y	y	PRON
ejpam-5003	611	17	such	such	ADJ
ejpam-5003	611	18	that	that	SCONJ
ejpam-5003	611	19	0θ′s	0θ′s	X
ejpam-5003	611	20	.	.	PUNCT
ejpam-5003	612	1	it	it	PRON
ejpam-5003	612	2	follows	follow	VERB
ejpam-5003	612	3	that	that	PRON
ejpam-5003	612	4	s	s	VERB
ejpam-5003	612	5	∈	∈	PROPN
ejpam-5003	613	1	[	[	X
ejpam-5003	613	2	0]θ′	0]θ′	NOUN
ejpam-5003	613	3	=	=	PUNCT
ejpam-5003	614	1	[	[	X
ejpam-5003	614	2	0]θ	0]θ	NOUN
ejpam-5003	614	3	.	.	PUNCT
ejpam-5003	615	1	thus	thus	ADV
ejpam-5003	615	2	,	,	PUNCT
ejpam-5003	615	3	(	(	PUNCT
ejpam-5003	615	4	x	x	X
ejpam-5003	615	5	⊛	⊛	NUM
ejpam-5003	615	6	y)θ{0	y)θ{0	NOUN
ejpam-5003	615	7	}	}	PUNCT
ejpam-5003	615	8	.	.	PUNCT
ejpam-5003	616	1	since	since	SCONJ
ejpam-5003	616	2	θ	θ	PROPN
ejpam-5003	616	3	is	be	AUX
ejpam-5003	616	4	a	a	DET
ejpam-5003	616	5	regular	regular	ADJ
ejpam-5003	616	6	congruence	congruence	NOUN
ejpam-5003	616	7	relation	relation	NOUN
ejpam-5003	616	8	on	on	ADP
ejpam-5003	616	9	h	h	NOUN
ejpam-5003	616	10	,	,	PUNCT
ejpam-5003	616	11	we	we	PRON
ejpam-5003	616	12	have	have	VERB
ejpam-5003	616	13	xθy	xθy	NOUN
ejpam-5003	616	14	.	.	PUNCT
ejpam-5003	617	1	definition	definition	NOUN
ejpam-5003	617	2	17	17	NUM
ejpam-5003	617	3	.	.	PUNCT
ejpam-5003	618	1	a	a	DET
ejpam-5003	618	2	hyper	hyper	ADJ
ejpam-5003	618	3	bn	bn	NOUN
ejpam-5003	618	4	-algebra	-algebra	NOUN
ejpam-5003	618	5	h	h	NOUN
ejpam-5003	618	6	that	that	PRON
ejpam-5003	618	7	satisfies	satisfy	VERB
ejpam-5003	618	8	the	the	DET
ejpam-5003	618	9	condition	condition	NOUN
ejpam-5003	618	10	:	:	PUNCT
ejpam-5003	618	11	if	if	SCONJ
ejpam-5003	618	12	x	x	PRON
ejpam-5003	618	13	≪	≪	VERB
ejpam-5003	618	14	y	y	NOUN
ejpam-5003	618	15	,	,	PUNCT
ejpam-5003	618	16	then	then	ADV
ejpam-5003	618	17	x	x	X
ejpam-5003	618	18	=	=	PUNCT
ejpam-5003	618	19	y	y	PROPN
ejpam-5003	618	20	for	for	ADP
ejpam-5003	618	21	all	all	DET
ejpam-5003	618	22	x	x	NOUN
ejpam-5003	618	23	,	,	PUNCT
ejpam-5003	618	24	y	y	PROPN
ejpam-5003	618	25	∈	∈	PROPN
ejpam-5003	618	26	h	h	NOUN
ejpam-5003	618	27	,	,	PUNCT
ejpam-5003	618	28	is	be	AUX
ejpam-5003	618	29	called	call	VERB
ejpam-5003	618	30	a	a	DET
ejpam-5003	618	31	hyper	hyper	ADJ
ejpam-5003	618	32	bn1	bn1	PROPN
ejpam-5003	618	33	-	-	PUNCT
ejpam-5003	618	34	algebra	algebra	PROPN
ejpam-5003	618	35	.	.	PUNCT
ejpam-5003	619	1	example	example	NOUN
ejpam-5003	619	2	25	25	NUM
ejpam-5003	619	3	.	.	PUNCT
ejpam-5003	620	1	consider	consider	VERB
ejpam-5003	620	2	the	the	DET
ejpam-5003	620	3	hyper	hyper	ADJ
ejpam-5003	620	4	bn	bn	NOUN
ejpam-5003	620	5	-algebra	-algebra	PROPN
ejpam-5003	620	6	h	h	NOUN
ejpam-5003	620	7	=	=	SYM
ejpam-5003	620	8	{	{	PUNCT
ejpam-5003	620	9	0	0	NUM
ejpam-5003	620	10	,	,	PUNCT
ejpam-5003	620	11	a	a	DET
ejpam-5003	620	12	,	,	PUNCT
ejpam-5003	620	13	b	b	NOUN
ejpam-5003	620	14	}	}	PUNCT
ejpam-5003	620	15	in	in	ADP
ejpam-5003	620	16	example	example	NOUN
ejpam-5003	620	17	1	1	X
ejpam-5003	620	18	.	.	PUNCT
ejpam-5003	621	1	then	then	ADV
ejpam-5003	621	2	h	h	PROPN
ejpam-5003	621	3	is	be	AUX
ejpam-5003	621	4	a	a	DET
ejpam-5003	621	5	hyper	hyper	ADJ
ejpam-5003	621	6	bn1	bn1	PROPN
ejpam-5003	621	7	-	-	PUNCT
ejpam-5003	621	8	algebra	algebra	PROPN
ejpam-5003	621	9	.	.	PUNCT
ejpam-5003	622	1	also	also	ADV
ejpam-5003	622	2	,	,	PUNCT
ejpam-5003	622	3	the	the	DET
ejpam-5003	622	4	hyper	hyper	ADJ
ejpam-5003	622	5	bn	bn	NOUN
ejpam-5003	622	6	-algebra	-algebra	PROPN
ejpam-5003	622	7	h	h	NOUN
ejpam-5003	622	8	=	=	SYM
ejpam-5003	622	9	{	{	PUNCT
ejpam-5003	622	10	0	0	NUM
ejpam-5003	622	11	,	,	PUNCT
ejpam-5003	622	12	1	1	NUM
ejpam-5003	622	13	,	,	PUNCT
ejpam-5003	622	14	2	2	NUM
ejpam-5003	622	15	,	,	PUNCT
ejpam-5003	622	16	3	3	NUM
ejpam-5003	622	17	}	}	PUNCT
ejpam-5003	622	18	in	in	ADP
ejpam-5003	622	19	example	example	NOUN
ejpam-5003	622	20	15	15	NUM
ejpam-5003	622	21	is	be	AUX
ejpam-5003	622	22	a	a	DET
ejpam-5003	622	23	hyper	hyper	ADJ
ejpam-5003	622	24	bn1	bn1	PROPN
ejpam-5003	622	25	-	-	PUNCT
ejpam-5003	622	26	algebra	algebra	PROPN
ejpam-5003	622	27	.	.	PUNCT
ejpam-5003	622	28	example	example	NOUN
ejpam-5003	623	1	26	26	NUM
ejpam-5003	623	2	.	.	PUNCT
ejpam-5003	624	1	the	the	DET
ejpam-5003	624	2	hyper	hyper	ADJ
ejpam-5003	624	3	bn	bn	NOUN
ejpam-5003	624	4	-algebra	-algebra	PROPN
ejpam-5003	624	5	h	h	NOUN
ejpam-5003	624	6	′	′	NUM
ejpam-5003	624	7	=	=	PUNCT
ejpam-5003	624	8	{	{	PUNCT
ejpam-5003	624	9	0	0	NUM
ejpam-5003	624	10	,	,	PUNCT
ejpam-5003	624	11	1	1	NUM
ejpam-5003	624	12	,	,	PUNCT
ejpam-5003	624	13	2	2	NUM
ejpam-5003	624	14	}	}	PUNCT
ejpam-5003	624	15	in	in	ADP
ejpam-5003	624	16	example	example	NOUN
ejpam-5003	624	17	2	2	NUM
ejpam-5003	624	18	is	be	AUX
ejpam-5003	624	19	not	not	PART
ejpam-5003	624	20	a	a	DET
ejpam-5003	624	21	hyper	hyper	ADJ
ejpam-5003	624	22	bn1algebra	bn1algebra	NOUN
ejpam-5003	624	23	because	because	SCONJ
ejpam-5003	624	24	1	1	NUM
ejpam-5003	624	25	≪	≪	SYM
ejpam-5003	624	26	2	2	NUM
ejpam-5003	624	27	but	but	CCONJ
ejpam-5003	624	28	1	1	NUM
ejpam-5003	624	29	̸=	̸=	PROPN
ejpam-5003	624	30	2	2	NUM
ejpam-5003	624	31	.	.	PUNCT
ejpam-5003	625	1	also	also	ADV
ejpam-5003	625	2	,	,	PUNCT
ejpam-5003	625	3	the	the	DET
ejpam-5003	625	4	hyper	hyper	ADJ
ejpam-5003	625	5	bn	bn	NOUN
ejpam-5003	625	6	-algebra	-algebra	PROPN
ejpam-5003	625	7	h	h	NOUN
ejpam-5003	625	8	′	′	NUM
ejpam-5003	625	9	=	=	PUNCT
ejpam-5003	625	10	{	{	PUNCT
ejpam-5003	625	11	0	0	NUM
ejpam-5003	625	12	,	,	PUNCT
ejpam-5003	625	13	1	1	NUM
ejpam-5003	625	14	,	,	PUNCT
ejpam-5003	625	15	2	2	NUM
ejpam-5003	625	16	,	,	PUNCT
ejpam-5003	625	17	3	3	NUM
ejpam-5003	625	18	}	}	PUNCT
ejpam-5003	625	19	in	in	ADP
ejpam-5003	625	20	example	example	NOUN
ejpam-5003	625	21	3	3	NUM
ejpam-5003	625	22	is	be	AUX
ejpam-5003	625	23	not	not	PART
ejpam-5003	625	24	a	a	DET
ejpam-5003	625	25	hyper	hyper	ADJ
ejpam-5003	625	26	bn1	bn1	NOUN
ejpam-5003	625	27	-	-	NOUN
ejpam-5003	625	28	algebra	algebra	PROPN
ejpam-5003	625	29	because	because	SCONJ
ejpam-5003	625	30	2	2	NUM
ejpam-5003	625	31	≪	≪	X
ejpam-5003	625	32	3	3	NUM
ejpam-5003	625	33	but	but	CCONJ
ejpam-5003	625	34	2	2	NUM
ejpam-5003	625	35	̸=	̸=	PROPN
ejpam-5003	625	36	3	3	NUM
ejpam-5003	625	37	.	.	PUNCT
ejpam-5003	625	38	notice	notice	VERB
ejpam-5003	625	39	that	that	SCONJ
ejpam-5003	625	40	θ	θ	PROPN
ejpam-5003	625	41	in	in	ADP
ejpam-5003	625	42	example	example	NOUN
ejpam-5003	625	43	23	23	NUM
ejpam-5003	625	44	is	be	AUX
ejpam-5003	625	45	not	not	PART
ejpam-5003	625	46	regular	regular	ADJ
ejpam-5003	625	47	since	since	SCONJ
ejpam-5003	625	48	(	(	PUNCT
ejpam-5003	625	49	2	2	NUM
ejpam-5003	625	50	⊛	⊛	NUM
ejpam-5003	625	51	4)θ{0	4)θ{0	NUM
ejpam-5003	625	52	}	}	PUNCT
ejpam-5003	625	53	but	but	CCONJ
ejpam-5003	625	54	(	(	PUNCT
ejpam-5003	625	55	2	2	NUM
ejpam-5003	625	56	,	,	PUNCT
ejpam-5003	625	57	4	4	NUM
ejpam-5003	625	58	)	)	PUNCT
ejpam-5003	625	59	/∈	/∈	PUNCT
ejpam-5003	626	1	θ	θ	X
ejpam-5003	626	2	.	.	PUNCT
ejpam-5003	627	1	the	the	DET
ejpam-5003	627	2	resulting	result	VERB
ejpam-5003	627	3	quotient	quotient	NOUN
ejpam-5003	627	4	structure	structure	NOUN
ejpam-5003	627	5	which	which	PRON
ejpam-5003	627	6	is	be	AUX
ejpam-5003	627	7	given	give	VERB
ejpam-5003	627	8	in	in	ADP
ejpam-5003	627	9	example	example	NOUN
ejpam-5003	627	10	24	24	NUM
ejpam-5003	627	11	is	be	AUX
ejpam-5003	627	12	not	not	PART
ejpam-5003	627	13	a	a	DET
ejpam-5003	627	14	hyper	hyper	ADJ
ejpam-5003	627	15	bn1	bn1	NOUN
ejpam-5003	627	16	-	-	PUNCT
ejpam-5003	627	17	algebra	algebra	PROPN
ejpam-5003	627	18	.	.	PUNCT
ejpam-5003	628	1	to	to	PART
ejpam-5003	628	2	support	support	VERB
ejpam-5003	628	3	it	it	PRON
ejpam-5003	628	4	further	far	ADV
ejpam-5003	628	5	,	,	PUNCT
ejpam-5003	628	6	i4	i4	PROPN
ejpam-5003	628	7	≪i	≪i	PRON
ejpam-5003	628	8	i2	i2	PROPN
ejpam-5003	628	9	but	but	CCONJ
ejpam-5003	628	10	i4	i4	PROPN
ejpam-5003	628	11	̸=	̸=	PROPN
ejpam-5003	628	12	i2	i2	PROPN
ejpam-5003	628	13	.	.	PROPN
ejpam-5003	628	14	example	example	NOUN
ejpam-5003	629	1	27	27	NUM
ejpam-5003	629	2	.	.	PUNCT
ejpam-5003	630	1	if	if	SCONJ
ejpam-5003	630	2	we	we	PRON
ejpam-5003	630	3	consider	consider	VERB
ejpam-5003	630	4	θ	θ	X
ejpam-5003	630	5	=	=	PRON
ejpam-5003	630	6	{	{	PUNCT
ejpam-5003	630	7	(	(	PUNCT
ejpam-5003	630	8	0	0	NUM
ejpam-5003	630	9	,	,	PUNCT
ejpam-5003	630	10	0	0	NUM
ejpam-5003	630	11	)	)	PUNCT
ejpam-5003	630	12	,	,	PUNCT
ejpam-5003	630	13	(	(	PUNCT
ejpam-5003	630	14	0	0	NUM
ejpam-5003	630	15	,	,	PUNCT
ejpam-5003	630	16	1	1	NUM
ejpam-5003	630	17	)	)	PUNCT
ejpam-5003	630	18	,	,	PUNCT
ejpam-5003	630	19	(	(	PUNCT
ejpam-5003	630	20	1	1	NUM
ejpam-5003	630	21	,	,	PUNCT
ejpam-5003	630	22	0	0	NUM
ejpam-5003	630	23	)	)	PUNCT
ejpam-5003	630	24	,	,	PUNCT
ejpam-5003	630	25	(	(	PUNCT
ejpam-5003	630	26	1	1	NUM
ejpam-5003	630	27	,	,	PUNCT
ejpam-5003	630	28	1	1	NUM
ejpam-5003	630	29	)	)	PUNCT
ejpam-5003	630	30	,	,	PUNCT
ejpam-5003	630	31	(	(	PUNCT
ejpam-5003	630	32	2	2	NUM
ejpam-5003	630	33	,	,	PUNCT
ejpam-5003	630	34	2	2	NUM
ejpam-5003	630	35	)	)	PUNCT
ejpam-5003	630	36	,	,	PUNCT
ejpam-5003	630	37	(	(	PUNCT
ejpam-5003	630	38	2	2	NUM
ejpam-5003	630	39	,	,	PUNCT
ejpam-5003	630	40	3	3	NUM
ejpam-5003	630	41	)	)	PUNCT
ejpam-5003	630	42	,	,	PUNCT
ejpam-5003	630	43	(	(	PUNCT
ejpam-5003	630	44	2	2	NUM
ejpam-5003	630	45	,	,	PUNCT
ejpam-5003	630	46	4	4	NUM
ejpam-5003	630	47	)	)	PUNCT
ejpam-5003	630	48	,	,	PUNCT
ejpam-5003	630	49	(	(	PUNCT
ejpam-5003	630	50	3	3	NUM
ejpam-5003	630	51	,	,	PUNCT
ejpam-5003	630	52	2	2	NUM
ejpam-5003	630	53	)	)	PUNCT
ejpam-5003	630	54	,	,	PUNCT
ejpam-5003	630	55	(	(	PUNCT
ejpam-5003	630	56	3	3	NUM
ejpam-5003	630	57	,	,	PUNCT
ejpam-5003	630	58	3	3	NUM
ejpam-5003	630	59	)	)	PUNCT
ejpam-5003	630	60	,	,	PUNCT
ejpam-5003	630	61	(	(	PUNCT
ejpam-5003	630	62	3	3	NUM
ejpam-5003	630	63	,	,	PUNCT
ejpam-5003	630	64	4	4	NUM
ejpam-5003	630	65	)	)	PUNCT
ejpam-5003	630	66	,	,	PUNCT
ejpam-5003	630	67	(	(	PUNCT
ejpam-5003	630	68	4	4	NUM
ejpam-5003	630	69	,	,	PUNCT
ejpam-5003	630	70	2	2	NUM
ejpam-5003	630	71	)	)	PUNCT
ejpam-5003	630	72	,	,	PUNCT
ejpam-5003	630	73	(	(	PUNCT
ejpam-5003	630	74	4	4	NUM
ejpam-5003	630	75	,	,	PUNCT
ejpam-5003	630	76	3	3	NUM
ejpam-5003	630	77	)	)	PUNCT
ejpam-5003	630	78	,	,	PUNCT
ejpam-5003	630	79	(	(	PUNCT
ejpam-5003	630	80	4	4	NUM
ejpam-5003	630	81	,	,	PUNCT
ejpam-5003	630	82	4	4	NUM
ejpam-5003	630	83	)	)	PUNCT
ejpam-5003	630	84	}	}	PUNCT
ejpam-5003	630	85	in	in	ADP
ejpam-5003	630	86	example	example	NOUN
ejpam-5003	630	87	23	23	NUM
ejpam-5003	630	88	.	.	PUNCT
ejpam-5003	631	1	we	we	PRON
ejpam-5003	631	2	can	can	AUX
ejpam-5003	631	3	show	show	VERB
ejpam-5003	631	4	that	that	SCONJ
ejpam-5003	631	5	θ	θ	PROPN
ejpam-5003	631	6	is	be	AUX
ejpam-5003	631	7	a	a	DET
ejpam-5003	631	8	regular	regular	ADJ
ejpam-5003	631	9	congruence	congruence	NOUN
ejpam-5003	631	10	relation	relation	NOUN
ejpam-5003	631	11	.	.	PUNCT
ejpam-5003	632	1	now	now	ADV
ejpam-5003	632	2	,	,	PUNCT
ejpam-5003	632	3	i	i	PRON
ejpam-5003	632	4	=	=	PUNCT
ejpam-5003	633	1	[	[	X
ejpam-5003	633	2	0]θ	0]θ	X
ejpam-5003	633	3	=	=	SYM
ejpam-5003	633	4	{	{	PUNCT
ejpam-5003	633	5	0	0	NUM
ejpam-5003	633	6	,	,	PUNCT
ejpam-5003	633	7	1	1	NUM
ejpam-5003	633	8	}	}	PUNCT
ejpam-5003	633	9	=	=	SYM
ejpam-5003	633	10	i1	i1	PROPN
ejpam-5003	633	11	and	and	CCONJ
ejpam-5003	633	12	i2	i2	PROPN
ejpam-5003	633	13	=	=	PUNCT
ejpam-5003	634	1	[	[	X
ejpam-5003	634	2	2]θ	2]θ	NUM
ejpam-5003	634	3	=	=	SYM
ejpam-5003	634	4	{	{	PUNCT
ejpam-5003	634	5	2	2	NUM
ejpam-5003	634	6	,	,	PUNCT
ejpam-5003	634	7	3	3	NUM
ejpam-5003	634	8	,	,	PUNCT
ejpam-5003	634	9	4	4	NUM
ejpam-5003	634	10	}	}	PUNCT
ejpam-5003	634	11	=	=	SYM
ejpam-5003	634	12	i3	i3	NOUN
ejpam-5003	634	13	=	=	SYM
ejpam-5003	634	14	i4	i4	PROPN
ejpam-5003	634	15	.	.	PUNCT
ejpam-5003	635	1	thus	thus	ADV
ejpam-5003	635	2	,	,	PUNCT
ejpam-5003	635	3	h	h	NOUN
ejpam-5003	635	4	/	/	SYM
ejpam-5003	635	5	i	i	PRON
ejpam-5003	635	6	=	=	PUNCT
ejpam-5003	635	7	{	{	PUNCT
ejpam-5003	635	8	i	i	PROPN
ejpam-5003	635	9	,	,	PUNCT
ejpam-5003	635	10	i2	i2	PROPN
ejpam-5003	635	11	}	}	PUNCT
ejpam-5003	635	12	and	and	CCONJ
ejpam-5003	635	13	the	the	DET
ejpam-5003	635	14	hyperoperation	hyperoperation	NOUN
ejpam-5003	635	15	⊗	⊗	PROPN
ejpam-5003	635	16	is	be	AUX
ejpam-5003	635	17	defined	define	VERB
ejpam-5003	635	18	by	by	ADP
ejpam-5003	635	19	the	the	DET
ejpam-5003	635	20	following	following	ADJ
ejpam-5003	635	21	cayley	cayley	ADJ
ejpam-5003	635	22	table	table	NOUN
ejpam-5003	635	23	:	:	PUNCT
ejpam-5003	636	1	⊗	⊗	PROPN
ejpam-5003	636	2	i	i	PROPN
ejpam-5003	636	3	i2	i2	PROPN
ejpam-5003	636	4	i	i	PRON
ejpam-5003	636	5	{	{	PUNCT
ejpam-5003	636	6	i	i	NOUN
ejpam-5003	636	7	}	}	PUNCT
ejpam-5003	636	8	{	{	PUNCT
ejpam-5003	636	9	i2	i2	PROPN
ejpam-5003	636	10	}	}	PUNCT
ejpam-5003	636	11	i2	i2	PROPN
ejpam-5003	636	12	{	{	PUNCT
ejpam-5003	636	13	i2	i2	PROPN
ejpam-5003	636	14	}	}	PUNCT
ejpam-5003	636	15	{	{	PUNCT
ejpam-5003	636	16	i	i	PROPN
ejpam-5003	636	17	,	,	PUNCT
ejpam-5003	636	18	i2	i2	PROPN
ejpam-5003	636	19	}	}	PUNCT
ejpam-5003	636	20	using	use	VERB
ejpam-5003	636	21	routine	routine	ADJ
ejpam-5003	636	22	calculations	calculation	NOUN
ejpam-5003	636	23	,	,	PUNCT
ejpam-5003	636	24	we	we	PRON
ejpam-5003	636	25	can	can	AUX
ejpam-5003	636	26	show	show	VERB
ejpam-5003	636	27	that	that	SCONJ
ejpam-5003	636	28	(	(	PUNCT
ejpam-5003	636	29	h	h	NOUN
ejpam-5003	636	30	/	/	SYM
ejpam-5003	636	31	i,⊗	i,⊗	PROPN
ejpam-5003	636	32	,	,	PUNCT
ejpam-5003	636	33	i	i	PRON
ejpam-5003	636	34	)	)	PUNCT
ejpam-5003	636	35	is	be	AUX
ejpam-5003	636	36	a	a	DET
ejpam-5003	636	37	hyper	hyper	ADJ
ejpam-5003	636	38	bn1	bn1	PROPN
ejpam-5003	636	39	-	-	PUNCT
ejpam-5003	636	40	algebra	algebra	PROPN
ejpam-5003	636	41	.	.	PUNCT
ejpam-5003	637	1	we	we	PRON
ejpam-5003	637	2	can	can	AUX
ejpam-5003	637	3	deduce	deduce	VERB
ejpam-5003	637	4	from	from	ADP
ejpam-5003	637	5	example	example	NOUN
ejpam-5003	637	6	27	27	NUM
ejpam-5003	637	7	that	that	SCONJ
ejpam-5003	637	8	if	if	SCONJ
ejpam-5003	637	9	θ	θ	PROPN
ejpam-5003	637	10	is	be	AUX
ejpam-5003	637	11	a	a	DET
ejpam-5003	637	12	regular	regular	ADJ
ejpam-5003	637	13	congruence	congruence	NOUN
ejpam-5003	637	14	relation	relation	NOUN
ejpam-5003	637	15	on	on	ADP
ejpam-5003	637	16	a	a	DET
ejpam-5003	637	17	hyper	hyper	ADJ
ejpam-5003	637	18	bn	bn	NOUN
ejpam-5003	637	19	-algebra	-algebra	PROPN
ejpam-5003	637	20	h	h	NOUN
ejpam-5003	637	21	,	,	PUNCT
ejpam-5003	637	22	then	then	ADV
ejpam-5003	637	23	the	the	DET
ejpam-5003	637	24	resulting	result	VERB
ejpam-5003	637	25	structure	structure	NOUN
ejpam-5003	637	26	would	would	AUX
ejpam-5003	637	27	be	be	AUX
ejpam-5003	637	28	a	a	DET
ejpam-5003	637	29	hyper	hyper	ADJ
ejpam-5003	637	30	bn1	bn1	NOUN
ejpam-5003	637	31	-	-	PUNCT
ejpam-5003	637	32	algebra	algebra	PROPN
ejpam-5003	637	33	.	.	PUNCT
ejpam-5003	638	1	the	the	DET
ejpam-5003	638	2	following	follow	VERB
ejpam-5003	638	3	result	result	NOUN
ejpam-5003	638	4	generalizes	generalize	VERB
ejpam-5003	638	5	this	this	DET
ejpam-5003	638	6	observation	observation	NOUN
ejpam-5003	638	7	.	.	PUNCT
ejpam-5003	639	1	references	reference	NOUN
ejpam-5003	639	2	241	241	NUM
ejpam-5003	639	3	theorem	theorem	VERB
ejpam-5003	639	4	18	18	NUM
ejpam-5003	639	5	.	.	PUNCT
ejpam-5003	640	1	let	let	VERB
ejpam-5003	640	2	h	h	PRON
ejpam-5003	640	3	be	be	AUX
ejpam-5003	640	4	a	a	DET
ejpam-5003	640	5	hyper	hyper	ADJ
ejpam-5003	640	6	bn	bn	ADJ
ejpam-5003	640	7	-algebra	-algebra	NOUN
ejpam-5003	640	8	,	,	PUNCT
ejpam-5003	640	9	θ	θ	PROPN
ejpam-5003	640	10	be	be	VERB
ejpam-5003	640	11	a	a	DET
ejpam-5003	640	12	regular	regular	ADJ
ejpam-5003	640	13	congruence	congruence	NOUN
ejpam-5003	640	14	relation	relation	NOUN
ejpam-5003	640	15	on	on	ADP
ejpam-5003	640	16	h	h	NOUN
ejpam-5003	641	1	and	and	CCONJ
ejpam-5003	641	2	i	i	PRON
ejpam-5003	641	3	=	=	PUNCT
ejpam-5003	642	1	[	[	X
ejpam-5003	642	2	0]θ	0]θ	NOUN
ejpam-5003	642	3	.	.	PUNCT
ejpam-5003	643	1	then	then	ADV
ejpam-5003	643	2	h	h	X
ejpam-5003	643	3	/	/	SYM
ejpam-5003	643	4	i	i	PRON
ejpam-5003	643	5	is	be	AUX
ejpam-5003	643	6	a	a	DET
ejpam-5003	643	7	hyper	hyper	ADJ
ejpam-5003	643	8	bn1	bn1	PROPN
ejpam-5003	643	9	-	-	PUNCT
ejpam-5003	643	10	algebra	algebra	NOUN
ejpam-5003	643	11	.	.	PUNCT
ejpam-5003	644	1	proof	proof	NOUN
ejpam-5003	644	2	.	.	PUNCT
ejpam-5003	645	1	by	by	ADP
ejpam-5003	645	2	theorem	theorem	NOUN
ejpam-5003	645	3	15	15	NUM
ejpam-5003	645	4	,	,	PUNCT
ejpam-5003	645	5	h	h	NOUN
ejpam-5003	645	6	/	/	SYM
ejpam-5003	645	7	i	i	PRON
ejpam-5003	645	8	is	be	AUX
ejpam-5003	645	9	a	a	DET
ejpam-5003	645	10	hyper	hyper	ADJ
ejpam-5003	645	11	bn	bn	NOUN
ejpam-5003	645	12	-algebra	-algebra	NOUN
ejpam-5003	645	13	.	.	PUNCT
ejpam-5003	646	1	now	now	ADV
ejpam-5003	646	2	,	,	PUNCT
ejpam-5003	646	3	let	let	VERB
ejpam-5003	646	4	ix	ix	ADV
ejpam-5003	646	5	≪	≪	VERB
ejpam-5003	646	6	iy	iy	PROPN
ejpam-5003	646	7	where	where	SCONJ
ejpam-5003	646	8	ix	ix	ADV
ejpam-5003	646	9	,	,	PUNCT
ejpam-5003	646	10	iy	iy	PROPN
ejpam-5003	646	11	∈	∈	PROPN
ejpam-5003	646	12	h	h	PROPN
ejpam-5003	646	13	/	/	SYM
ejpam-5003	646	14	i.	i.	NOUN
ejpam-5003	647	1	then	then	ADV
ejpam-5003	647	2	i	i	PRON
ejpam-5003	647	3	∈	∈	PROPN
ejpam-5003	647	4	ix	ix	ADP
ejpam-5003	647	5	⊗	⊗	PROPN
ejpam-5003	647	6	iy	iy	PROPN
ejpam-5003	647	7	.	.	PUNCT
ejpam-5003	648	1	hence	hence	ADV
ejpam-5003	648	2	,	,	PUNCT
ejpam-5003	648	3	there	there	PRON
ejpam-5003	648	4	exists	exist	VERB
ejpam-5003	648	5	u	u	PROPN
ejpam-5003	648	6	∈	∈	PROPN
ejpam-5003	648	7	x	x	X
ejpam-5003	648	8	⊛	⊛	ADP
ejpam-5003	648	9	y	y	NUM
ejpam-5003	648	10	such	such	ADJ
ejpam-5003	648	11	that	that	SCONJ
ejpam-5003	648	12	iu	iu	ADP
ejpam-5003	648	13	=	=	PUNCT
ejpam-5003	648	14	i	i	PRON
ejpam-5003	648	15	and	and	CCONJ
ejpam-5003	648	16	so	so	ADV
ejpam-5003	648	17	,	,	PUNCT
ejpam-5003	648	18	uθ0	uθ0	PROPN
ejpam-5003	648	19	.	.	PUNCT
ejpam-5003	649	1	hence	hence	ADV
ejpam-5003	649	2	,	,	PUNCT
ejpam-5003	649	3	(	(	PUNCT
ejpam-5003	649	4	x	x	X
ejpam-5003	649	5	⊛	⊛	NUM
ejpam-5003	649	6	y)θ{0	y)θ{0	NOUN
ejpam-5003	649	7	}	}	PUNCT
ejpam-5003	649	8	.	.	PUNCT
ejpam-5003	650	1	since	since	SCONJ
ejpam-5003	650	2	θ	θ	PROPN
ejpam-5003	650	3	is	be	AUX
ejpam-5003	650	4	regular	regular	ADJ
ejpam-5003	650	5	,	,	PUNCT
ejpam-5003	650	6	xθy	xθy	PROPN
ejpam-5003	650	7	.	.	PUNCT
ejpam-5003	651	1	thus	thus	ADV
ejpam-5003	651	2	,	,	PUNCT
ejpam-5003	651	3	ix	ix	ADP
ejpam-5003	651	4	=	=	PROPN
ejpam-5003	651	5	iy	iy	PROPN
ejpam-5003	651	6	.	.	PUNCT
ejpam-5003	652	1	therefore	therefore	ADV
ejpam-5003	652	2	,	,	PUNCT
ejpam-5003	652	3	h	h	PROPN
ejpam-5003	652	4	/	/	SYM
ejpam-5003	652	5	i	i	PRON
ejpam-5003	652	6	is	be	AUX
ejpam-5003	652	7	a	a	DET
ejpam-5003	652	8	hyper	hyper	ADJ
ejpam-5003	652	9	bn1	bn1	PROPN
ejpam-5003	652	10	-	-	PUNCT
ejpam-5003	652	11	algebra	algebra	NOUN
ejpam-5003	652	12	.	.	PUNCT
ejpam-5003	653	1	5	5	X
ejpam-5003	653	2	.	.	X
ejpam-5003	653	3	conclusion	conclusion	NOUN
ejpam-5003	653	4	we	we	PRON
ejpam-5003	653	5	have	have	AUX
ejpam-5003	653	6	defined	define	VERB
ejpam-5003	653	7	various	various	ADJ
ejpam-5003	653	8	types	type	NOUN
ejpam-5003	653	9	of	of	ADP
ejpam-5003	653	10	ideals	ideal	NOUN
ejpam-5003	653	11	for	for	ADP
ejpam-5003	653	12	hyper	hyper	ADJ
ejpam-5003	653	13	bn	bn	ADJ
ejpam-5003	653	14	-algebras	-algebra	NOUN
ejpam-5003	653	15	.	.	PUNCT
ejpam-5003	654	1	we	we	PRON
ejpam-5003	654	2	also	also	ADV
ejpam-5003	654	3	obtained	obtain	VERB
ejpam-5003	654	4	some	some	DET
ejpam-5003	654	5	properties	property	NOUN
ejpam-5003	654	6	.	.	PUNCT
ejpam-5003	655	1	we	we	PRON
ejpam-5003	655	2	showed	show	VERB
ejpam-5003	655	3	the	the	DET
ejpam-5003	655	4	general	general	ADJ
ejpam-5003	655	5	relationship	relationship	NOUN
ejpam-5003	655	6	among	among	ADP
ejpam-5003	655	7	various	various	ADJ
ejpam-5003	655	8	types	type	NOUN
ejpam-5003	655	9	of	of	ADP
ejpam-5003	655	10	ideals	ideal	NOUN
ejpam-5003	655	11	and	and	CCONJ
ejpam-5003	655	12	hyper	hyper	ADJ
ejpam-5003	655	13	subbn	subbn	NOUN
ejpam-5003	655	14	-algebras	-algebras	PROPN
ejpam-5003	655	15	.	.	PUNCT
ejpam-5003	656	1	we	we	PRON
ejpam-5003	656	2	established	establish	VERB
ejpam-5003	656	3	the	the	DET
ejpam-5003	656	4	equivalency	equivalency	NOUN
ejpam-5003	656	5	of	of	ADP
ejpam-5003	656	6	weak	weak	ADJ
ejpam-5003	656	7	hyper	hyper	ADJ
ejpam-5003	656	8	bn	bn	ADJ
ejpam-5003	656	9	-ideals	-ideal	NOUN
ejpam-5003	656	10	and	and	CCONJ
ejpam-5003	656	11	hyper	hyper	ADJ
ejpam-5003	656	12	sub	sub	NOUN
ejpam-5003	656	13	bn	bn	X
ejpam-5003	656	14	-algebras	-algebra	NOUN
ejpam-5003	656	15	.	.	PUNCT
ejpam-5003	657	1	we	we	PRON
ejpam-5003	657	2	also	also	ADV
ejpam-5003	657	3	found	find	VERB
ejpam-5003	657	4	a	a	DET
ejpam-5003	657	5	condition	condition	NOUN
ejpam-5003	657	6	such	such	ADJ
ejpam-5003	657	7	that	that	SCONJ
ejpam-5003	657	8	a	a	DET
ejpam-5003	657	9	strong	strong	ADJ
ejpam-5003	657	10	hyper	hyper	ADJ
ejpam-5003	657	11	bn	bn	NOUN
ejpam-5003	657	12	-ideal	-ideal	NOUN
ejpam-5003	657	13	become	become	VERB
ejpam-5003	657	14	a	a	DET
ejpam-5003	657	15	hyper	hyper	NOUN
ejpam-5003	657	16	bn	bn	NOUN
ejpam-5003	657	17	-ideal	-ideal	NOUN
ejpam-5003	657	18	.	.	PUNCT
ejpam-5003	658	1	finally	finally	ADV
ejpam-5003	658	2	,	,	PUNCT
ejpam-5003	658	3	we	we	PRON
ejpam-5003	658	4	were	be	AUX
ejpam-5003	658	5	able	able	ADJ
ejpam-5003	658	6	to	to	PART
ejpam-5003	658	7	construct	construct	VERB
ejpam-5003	658	8	quotient	quotient	NOUN
ejpam-5003	658	9	hyper	hyper	PROPN
ejpam-5003	658	10	bn	bn	ADP
ejpam-5003	658	11	-algebras	-algebras	PROPN
ejpam-5003	658	12	via	via	ADP
ejpam-5003	658	13	reflexive	reflexive	ADJ
ejpam-5003	658	14	normal	normal	ADJ
ejpam-5003	658	15	hyper	hyper	ADJ
ejpam-5003	658	16	subbn	subbn	NOUN
ejpam-5003	658	17	-algebra	-algebra	NOUN
ejpam-5003	658	18	and	and	CCONJ
ejpam-5003	658	19	via	via	ADP
ejpam-5003	658	20	congruence	congruence	PROPN
ejpam-5003	658	21	relation	relation	NOUN
ejpam-5003	658	22	.	.	PUNCT
ejpam-5003	659	1	we	we	PRON
ejpam-5003	659	2	likewise	likewise	ADV
ejpam-5003	659	3	showed	show	VERB
ejpam-5003	659	4	that	that	SCONJ
ejpam-5003	659	5	the	the	DET
ejpam-5003	659	6	construction	construction	NOUN
ejpam-5003	659	7	via	via	ADP
ejpam-5003	659	8	reflexive	reflexive	ADJ
ejpam-5003	659	9	normal	normal	ADJ
ejpam-5003	659	10	hyper	hyper	ADJ
ejpam-5003	659	11	subbn	subbn	NOUN
ejpam-5003	659	12	-algebra	-algebra	PROPN
ejpam-5003	659	13	is	be	AUX
ejpam-5003	659	14	just	just	ADV
ejpam-5003	659	15	a	a	DET
ejpam-5003	659	16	special	special	ADJ
ejpam-5003	659	17	case	case	NOUN
ejpam-5003	659	18	of	of	ADP
ejpam-5003	659	19	the	the	DET
ejpam-5003	659	20	construction	construction	NOUN
ejpam-5003	659	21	via	via	ADP
ejpam-5003	659	22	congruence	congruence	PROPN
ejpam-5003	659	23	relation	relation	NOUN
ejpam-5003	659	24	.	.	PUNCT
ejpam-5003	660	1	furthermore	furthermore	ADV
ejpam-5003	660	2	,	,	PUNCT
ejpam-5003	660	3	we	we	PRON
ejpam-5003	660	4	have	have	AUX
ejpam-5003	660	5	introduced	introduce	VERB
ejpam-5003	660	6	the	the	DET
ejpam-5003	660	7	notion	notion	NOUN
ejpam-5003	660	8	of	of	ADP
ejpam-5003	660	9	hyper	hyper	PROPN
ejpam-5003	660	10	bn1	bn1	PROPN
ejpam-5003	660	11	-	-	PUNCT
ejpam-5003	660	12	algebra	algebra	NOUN
ejpam-5003	660	13	by	by	ADP
ejpam-5003	660	14	giving	give	VERB
ejpam-5003	660	15	additional	additional	ADJ
ejpam-5003	660	16	axiom	axiom	NOUN
ejpam-5003	660	17	on	on	ADP
ejpam-5003	660	18	the	the	DET
ejpam-5003	660	19	definition	definition	NOUN
ejpam-5003	660	20	of	of	ADP
ejpam-5003	660	21	hyper	hyper	ADJ
ejpam-5003	660	22	bn	bn	PROPN
ejpam-5003	660	23	-algebra	-algebra	PROPN
ejpam-5003	660	24	.	.	PUNCT
ejpam-5003	661	1	construction	construction	NOUN
ejpam-5003	661	2	of	of	ADP
ejpam-5003	661	3	quotient	quotient	NOUN
ejpam-5003	661	4	hyper	hyper	ADJ
ejpam-5003	661	5	bn	bn	PROPN
ejpam-5003	661	6	-algebras	-algebras	PROPN
ejpam-5003	661	7	will	will	AUX
ejpam-5003	661	8	result	result	VERB
ejpam-5003	661	9	to	to	ADP
ejpam-5003	661	10	hyper	hyper	PROPN
ejpam-5003	661	11	bn1	bn1	PROPN
ejpam-5003	661	12	-	-	PUNCT
ejpam-5003	661	13	algebras	algebra	VERB
ejpam-5003	661	14	if	if	SCONJ
ejpam-5003	661	15	the	the	DET
ejpam-5003	661	16	congruence	congruence	PROPN
ejpam-5003	661	17	relation	relation	NOUN
ejpam-5003	661	18	is	be	AUX
ejpam-5003	661	19	regular	regular	ADJ
ejpam-5003	661	20	.	.	PUNCT
ejpam-5003	662	1	for	for	ADP
ejpam-5003	662	2	future	future	ADJ
ejpam-5003	662	3	work	work	NOUN
ejpam-5003	662	4	,	,	PUNCT
ejpam-5003	662	5	we	we	PRON
ejpam-5003	662	6	have	have	AUX
ejpam-5003	662	7	currently	currently	ADV
ejpam-5003	662	8	looked	look	VERB
ejpam-5003	662	9	at	at	ADP
ejpam-5003	662	10	homomorphisms	homomorphism	NOUN
ejpam-5003	662	11	and	and	CCONJ
ejpam-5003	662	12	isomorphisms	isomorphism	NOUN
ejpam-5003	662	13	on	on	ADP
ejpam-5003	662	14	hyper	hyper	ADJ
ejpam-5003	662	15	bn	bn	ADJ
ejpam-5003	662	16	-algebras	-algebra	NOUN
ejpam-5003	662	17	.	.	PUNCT
ejpam-5003	663	1	acknowledgements	acknowledgement	NOUN
ejpam-5003	663	2	the	the	DET
ejpam-5003	663	3	authors	author	NOUN
ejpam-5003	663	4	thank	thank	VERB
ejpam-5003	663	5	the	the	DET
ejpam-5003	663	6	department	department	PROPN
ejpam-5003	663	7	of	of	ADP
ejpam-5003	663	8	science	science	NOUN
ejpam-5003	663	9	and	and	CCONJ
ejpam-5003	663	10	technology	technology	NOUN
ejpam-5003	663	11	(	(	PUNCT
ejpam-5003	663	12	dost	dost	NOUN
ejpam-5003	663	13	)	)	PUNCT
ejpam-5003	663	14	of	of	ADP
ejpam-5003	663	15	the	the	DET
ejpam-5003	663	16	philippines	philippine	NOUN
ejpam-5003	663	17	through	through	ADP
ejpam-5003	663	18	the	the	DET
ejpam-5003	663	19	accelerated	accelerated	ADJ
ejpam-5003	663	20	science	science	NOUN
ejpam-5003	663	21	and	and	CCONJ
ejpam-5003	663	22	technology	technology	NOUN
ejpam-5003	663	23	human	human	ADJ
ejpam-5003	663	24	resource	resource	NOUN
ejpam-5003	663	25	development	development	NOUN
ejpam-5003	663	26	program	program	NOUN
ejpam-5003	663	27	(	(	PUNCT
ejpam-5003	663	28	asthrdp	asthrdp	PROPN
ejpam-5003	663	29	)	)	PUNCT
ejpam-5003	663	30	for	for	ADP
ejpam-5003	663	31	the	the	DET
ejpam-5003	663	32	financial	financial	ADJ
ejpam-5003	663	33	support	support	NOUN
ejpam-5003	663	34	.	.	PUNCT
ejpam-5003	664	1	also	also	ADV
ejpam-5003	664	2	,	,	PUNCT
ejpam-5003	664	3	the	the	DET
ejpam-5003	664	4	authors	author	NOUN
ejpam-5003	664	5	would	would	AUX
ejpam-5003	664	6	like	like	VERB
ejpam-5003	664	7	to	to	PART
ejpam-5003	664	8	extend	extend	VERB
ejpam-5003	664	9	their	their	PRON
ejpam-5003	664	10	gratitude	gratitude	NOUN
ejpam-5003	664	11	to	to	ADP
ejpam-5003	664	12	the	the	DET
ejpam-5003	664	13	anonymous	anonymous	ADJ
ejpam-5003	664	14	referees	referee	NOUN
ejpam-5003	664	15	for	for	ADP
ejpam-5003	664	16	giving	give	VERB
ejpam-5003	664	17	some	some	DET
ejpam-5003	664	18	comments	comment	NOUN
ejpam-5003	664	19	for	for	ADP
ejpam-5003	664	20	the	the	DET
ejpam-5003	664	21	improvement	improvement	NOUN
ejpam-5003	664	22	of	of	ADP
ejpam-5003	664	23	this	this	DET
ejpam-5003	664	24	paper	paper	NOUN
ejpam-5003	664	25	.	.	PUNCT
ejpam-5003	665	1	references	reference	NOUN
ejpam-5003	665	2	[	[	X
ejpam-5003	665	3	1	1	NUM
ejpam-5003	665	4	]	]	X
ejpam-5003	665	5	r.a	r.a	PROPN
ejpam-5003	665	6	.	.	PROPN
ejpam-5003	665	7	borzooei	borzooei	PROPN
ejpam-5003	665	8	,	,	PUNCT
ejpam-5003	665	9	w.a	w.a	PROPN
ejpam-5003	665	10	.	.	PROPN
ejpam-5003	665	11	dudek	dudek	PROPN
ejpam-5003	665	12	,	,	PUNCT
ejpam-5003	665	13	and	and	CCONJ
ejpam-5003	665	14	n.	n.	PROPN
ejpam-5003	665	15	koohestani	koohestani	PROPN
ejpam-5003	665	16	.	.	PUNCT
ejpam-5003	666	1	on	on	ADP
ejpam-5003	666	2	hyper	hyper	ADJ
ejpam-5003	666	3	bcc	bcc	PROPN
ejpam-5003	666	4	-	-	PUNCT
ejpam-5003	666	5	algebras	algebras	PROPN
ejpam-5003	666	6	.	.	PUNCT
ejpam-5003	667	1	international	international	ADJ
ejpam-5003	667	2	journal	journal	PROPN
ejpam-5003	667	3	of	of	ADP
ejpam-5003	667	4	mathematics	mathematics	PROPN
ejpam-5003	667	5	and	and	CCONJ
ejpam-5003	667	6	mathematical	mathematical	ADJ
ejpam-5003	667	7	sciences	science	NOUN
ejpam-5003	667	8	,	,	PUNCT
ejpam-5003	667	9	2006	2006	NUM
ejpam-5003	667	10	.	.	PUNCT
ejpam-5003	668	1	[	[	X
ejpam-5003	668	2	2	2	NUM
ejpam-5003	668	3	]	]	X
ejpam-5003	668	4	l.r	l.r	PROPN
ejpam-5003	668	5	.	.	PROPN
ejpam-5003	668	6	cabardo	cabardo	PROPN
ejpam-5003	668	7	and	and	CCONJ
ejpam-5003	668	8	g.	g.	PROPN
ejpam-5003	668	9	petalcorin	petalcorin	PROPN
ejpam-5003	668	10	.	.	PUNCT
ejpam-5003	669	1	on	on	ADP
ejpam-5003	669	2	weak	weak	ADJ
ejpam-5003	669	3	decomposable	decomposable	ADJ
ejpam-5003	669	4	hyper	hyper	ADJ
ejpam-5003	669	5	bci	bci	NOUN
ejpam-5003	669	6	-	-	PUNCT
ejpam-5003	669	7	algebras	algebra	NOUN
ejpam-5003	669	8	and	and	CCONJ
ejpam-5003	669	9	some	some	DET
ejpam-5003	669	10	notes	note	NOUN
ejpam-5003	669	11	on	on	ADP
ejpam-5003	669	12	weak	weak	ADJ
ejpam-5003	669	13	and	and	CCONJ
ejpam-5003	669	14	strong	strong	ADJ
ejpam-5003	669	15	hyper	hyper	ADJ
ejpam-5003	669	16	bci	bci	NOUN
ejpam-5003	669	17	-	-	NOUN
ejpam-5003	669	18	ideals	ideal	NOUN
ejpam-5003	669	19	.	.	PUNCT
ejpam-5003	670	1	journal	journal	NOUN
ejpam-5003	670	2	of	of	ADP
ejpam-5003	670	3	algebra	algebra	PROPN
ejpam-5003	670	4	and	and	CCONJ
ejpam-5003	670	5	applied	apply	VERB
ejpam-5003	670	6	mathematics	mathematic	NOUN
ejpam-5003	670	7	,	,	PUNCT
ejpam-5003	670	8	16:45–62	16:45–62	NUM
ejpam-5003	670	9	,	,	PUNCT
ejpam-5003	670	10	2018	2018	NUM
ejpam-5003	670	11	.	.	PUNCT
ejpam-5003	671	1	[	[	X
ejpam-5003	671	2	3	3	X
ejpam-5003	671	3	]	]	X
ejpam-5003	671	4	l.r	l.r	PROPN
ejpam-5003	671	5	.	.	PROPN
ejpam-5003	671	6	cabardo	cabardo	PROPN
ejpam-5003	671	7	and	and	CCONJ
ejpam-5003	671	8	g.	g.	PROPN
ejpam-5003	671	9	petalcorin	petalcorin	PROPN
ejpam-5003	671	10	.	.	PUNCT
ejpam-5003	672	1	hyper	hyper	ADJ
ejpam-5003	672	2	bn	bn	ADP
ejpam-5003	672	3	-algebras	-algebras	PROPN
ejpam-5003	672	4	:	:	PUNCT
ejpam-5003	672	5	hyperstructure	hyperstructure	PROPN
ejpam-5003	672	6	theory	theory	NOUN
ejpam-5003	672	7	applied	apply	VERB
ejpam-5003	672	8	to	to	ADP
ejpam-5003	672	9	bn	bn	NOUN
ejpam-5003	672	10	-algebras	-algebra	NOUN
ejpam-5003	672	11	.	.	PUNCT
ejpam-5003	673	1	italian	italian	ADJ
ejpam-5003	673	2	journal	journal	NOUN
ejpam-5003	673	3	of	of	ADP
ejpam-5003	673	4	pure	pure	ADJ
ejpam-5003	673	5	and	and	CCONJ
ejpam-5003	673	6	applied	applied	ADJ
ejpam-5003	673	7	mathematics	mathematic	NOUN
ejpam-5003	673	8	,	,	PUNCT
ejpam-5003	673	9	48:406–422	48:406–422	NUM
ejpam-5003	673	10	,	,	PUNCT
ejpam-5003	673	11	2022	2022	NUM
ejpam-5003	673	12	.	.	PUNCT
ejpam-5003	674	1	references	reference	NOUN
ejpam-5003	674	2	242	242	NUM
ejpam-5003	674	3	[	[	X
ejpam-5003	674	4	4	4	NUM
ejpam-5003	674	5	]	]	X
ejpam-5003	674	6	b.	b.	PROPN
ejpam-5003	674	7	davvaz	davvaz	PROPN
ejpam-5003	674	8	and	and	CCONJ
ejpam-5003	674	9	s.	s.	PROPN
ejpam-5003	674	10	omidi	omidi	PROPN
ejpam-5003	674	11	.	.	PUNCT
ejpam-5003	675	1	ordered	order	VERB
ejpam-5003	675	2	krasner	krasner	PROPN
ejpam-5003	675	3	hyperrings	hyperring	NOUN
ejpam-5003	675	4	.	.	PUNCT
ejpam-5003	676	1	iranian	iranian	ADJ
ejpam-5003	676	2	journal	journal	PROPN
ejpam-5003	676	3	of	of	ADP
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ejpam-5003	686	4	.	.	PUNCT
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ejpam-5003	686	8	,	,	PUNCT
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