id	sid	tid	token	lemma	pos
ejpam-3431	1	1	european	european	PROPN
ejpam-3431	1	2	journal	journal	PROPN
ejpam-3431	1	3	of	of	ADP
ejpam-3431	1	4	pure	pure	ADJ
ejpam-3431	1	5	and	and	CCONJ
ejpam-3431	1	6	applied	apply	VERB
ejpam-3431	1	7	mathematics	mathematic	NOUN
ejpam-3431	1	8	vol	vol	NOUN
ejpam-3431	1	9	.	.	PROPN
ejpam-3431	2	1	12	12	NUM
ejpam-3431	2	2	,	,	PUNCT
ejpam-3431	2	3	no	no	INTJ
ejpam-3431	2	4	.	.	NOUN
ejpam-3431	2	5	3	3	NUM
ejpam-3431	2	6	,	,	PUNCT
ejpam-3431	2	7	2019	2019	NUM
ejpam-3431	2	8	,	,	PUNCT
ejpam-3431	2	9	821	821	NUM
ejpam-3431	2	10	-	-	SYM
ejpam-3431	2	11	833	833	NUM
ejpam-3431	2	12	issn	issn	PROPN
ejpam-3431	2	13	1307	1307	NUM
ejpam-3431	2	14	-	-	SYM
ejpam-3431	2	15	5543	5543	NUM
ejpam-3431	2	16	–	–	PUNCT
ejpam-3431	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3431	2	18	published	publish	VERB
ejpam-3431	2	19	by	by	ADP
ejpam-3431	2	20	new	new	PROPN
ejpam-3431	2	21	york	york	PROPN
ejpam-3431	2	22	business	business	PROPN
ejpam-3431	2	23	global	global	ADJ
ejpam-3431	2	24	on	on	ADP
ejpam-3431	2	25	varieties	variety	NOUN
ejpam-3431	2	26	of	of	ADP
ejpam-3431	2	27	pseudo	pseudo	NOUN
ejpam-3431	2	28	hyper	hyper	ADJ
ejpam-3431	2	29	gr	gr	NOUN
ejpam-3431	2	30	-	-	PUNCT
ejpam-3431	2	31	ideals	ideal	NOUN
ejpam-3431	2	32	of	of	ADP
ejpam-3431	2	33	pseudo	pseudo	NOUN
ejpam-3431	2	34	hyper	hyper	ADJ
ejpam-3431	2	35	gr	gr	ADJ
ejpam-3431	2	36	-	-	PUNCT
ejpam-3431	2	37	algebras	algebras	PROPN
ejpam-3431	2	38	ramises	ramise	NOUN
ejpam-3431	2	39	g.	g.	PROPN
ejpam-3431	2	40	manzano	manzano	PROPN
ejpam-3431	2	41	,	,	PUNCT
ejpam-3431	2	42	jr.1	jr.1	PROPN
ejpam-3431	2	43	,	,	PUNCT
ejpam-3431	2	44	gaudencio	gaudencio	PROPN
ejpam-3431	2	45	c.	c.	PROPN
ejpam-3431	2	46	petalcorin	petalcorin	PROPN
ejpam-3431	2	47	,	,	PUNCT
ejpam-3431	2	48	jr.2,∗	jr.2,∗	PROPN
ejpam-3431	2	49	1	1	NUM
ejpam-3431	2	50	mathematics	mathematics	PROPN
ejpam-3431	2	51	department	department	NOUN
ejpam-3431	2	52	,	,	PUNCT
ejpam-3431	2	53	college	college	NOUN
ejpam-3431	2	54	of	of	ADP
ejpam-3431	2	55	science	science	NOUN
ejpam-3431	2	56	,	,	PUNCT
ejpam-3431	2	57	university	university	NOUN
ejpam-3431	2	58	of	of	ADP
ejpam-3431	2	59	the	the	DET
ejpam-3431	2	60	philippines	philippine	NOUN
ejpam-3431	2	61	cebu	cebu	NOUN
ejpam-3431	2	62	,	,	PUNCT
ejpam-3431	2	63	6000	6000	NUM
ejpam-3431	2	64	cebu	cebu	NOUN
ejpam-3431	2	65	city	city	NOUN
ejpam-3431	2	66	,	,	PUNCT
ejpam-3431	2	67	philippines	philippines	PROPN
ejpam-3431	2	68	2	2	NUM
ejpam-3431	2	69	department	department	NOUN
ejpam-3431	2	70	of	of	ADP
ejpam-3431	2	71	mathematics	mathematic	NOUN
ejpam-3431	2	72	and	and	CCONJ
ejpam-3431	2	73	statistics	statistic	NOUN
ejpam-3431	2	74	,	,	PUNCT
ejpam-3431	2	75	college	college	NOUN
ejpam-3431	2	76	of	of	ADP
ejpam-3431	2	77	science	science	NOUN
ejpam-3431	2	78	and	and	CCONJ
ejpam-3431	2	79	mathematics	mathematic	NOUN
ejpam-3431	2	80	,	,	PUNCT
ejpam-3431	2	81	mindanao	mindanao	PROPN
ejpam-3431	2	82	state	state	PROPN
ejpam-3431	2	83	university	university	PROPN
ejpam-3431	2	84	-	-	PUNCT
ejpam-3431	2	85	iligan	iligan	PROPN
ejpam-3431	2	86	institute	institute	PROPN
ejpam-3431	2	87	of	of	ADP
ejpam-3431	2	88	technology	technology	PROPN
ejpam-3431	2	89	,	,	PUNCT
ejpam-3431	2	90	9200	9200	NUM
ejpam-3431	2	91	iligan	iligan	ADJ
ejpam-3431	2	92	city	city	NOUN
ejpam-3431	2	93	,	,	PUNCT
ejpam-3431	2	94	philippines	philippine	NOUN
ejpam-3431	2	95	abstract	abstract	ADJ
ejpam-3431	2	96	.	.	PUNCT
ejpam-3431	3	1	this	this	DET
ejpam-3431	3	2	study	study	NOUN
ejpam-3431	3	3	is	be	AUX
ejpam-3431	3	4	based	base	VERB
ejpam-3431	3	5	on	on	ADP
ejpam-3431	3	6	the	the	DET
ejpam-3431	3	7	structure	structure	NOUN
ejpam-3431	3	8	of	of	ADP
ejpam-3431	3	9	hyper	hyper	ADJ
ejpam-3431	3	10	gr	gr	NOUN
ejpam-3431	3	11	-	-	PUNCT
ejpam-3431	3	12	algebras	algebra	NOUN
ejpam-3431	3	13	,	,	PUNCT
ejpam-3431	3	14	an	an	DET
ejpam-3431	3	15	algebra	algebra	NOUN
ejpam-3431	3	16	that	that	PRON
ejpam-3431	3	17	is	be	AUX
ejpam-3431	3	18	partially	partially	ADV
ejpam-3431	3	19	related	relate	VERB
ejpam-3431	3	20	on	on	ADP
ejpam-3431	3	21	some	some	DET
ejpam-3431	3	22	class	class	NOUN
ejpam-3431	3	23	of	of	ADP
ejpam-3431	3	24	hyper	hyper	ADJ
ejpam-3431	3	25	bci	bci	NOUN
ejpam-3431	3	26	-	-	PUNCT
ejpam-3431	3	27	algebras	algebras	X
ejpam-3431	3	28	.	.	PUNCT
ejpam-3431	4	1	this	this	PRON
ejpam-3431	4	2	allows	allow	VERB
ejpam-3431	4	3	us	we	PRON
ejpam-3431	4	4	to	to	PART
ejpam-3431	4	5	create	create	VERB
ejpam-3431	4	6	a	a	DET
ejpam-3431	4	7	new	new	ADJ
ejpam-3431	4	8	structure	structure	NOUN
ejpam-3431	4	9	and	and	CCONJ
ejpam-3431	4	10	investigate	investigate	VERB
ejpam-3431	4	11	how	how	SCONJ
ejpam-3431	4	12	this	this	DET
ejpam-3431	4	13	two	two	NUM
ejpam-3431	4	14	algebras	algebra	NOUN
ejpam-3431	4	15	are	be	AUX
ejpam-3431	4	16	related	relate	VERB
ejpam-3431	4	17	to	to	ADP
ejpam-3431	4	18	each	each	DET
ejpam-3431	4	19	other	other	ADJ
ejpam-3431	4	20	.	.	PUNCT
ejpam-3431	5	1	a	a	DET
ejpam-3431	5	2	pseudo	pseudo	NOUN
ejpam-3431	5	3	hyper	hyper	ADJ
ejpam-3431	5	4	gr	gr	NOUN
ejpam-3431	5	5	-	-	PUNCT
ejpam-3431	5	6	algebra	algebra	NOUN
ejpam-3431	5	7	involves	involve	VERB
ejpam-3431	5	8	two	two	NUM
ejpam-3431	5	9	hyper	hyper	ADJ
ejpam-3431	5	10	operations	operation	NOUN
ejpam-3431	5	11	and	and	CCONJ
ejpam-3431	5	12	a	a	DET
ejpam-3431	5	13	set	set	NOUN
ejpam-3431	5	14	of	of	ADP
ejpam-3431	5	15	axioms	axiom	NOUN
ejpam-3431	5	16	that	that	PRON
ejpam-3431	5	17	come	come	VERB
ejpam-3431	5	18	in	in	ADP
ejpam-3431	5	19	pairs	pair	NOUN
ejpam-3431	5	20	or	or	CCONJ
ejpam-3431	5	21	a	a	DET
ejpam-3431	5	22	combination	combination	NOUN
ejpam-3431	5	23	of	of	ADP
ejpam-3431	5	24	both	both	PRON
ejpam-3431	5	25	making	make	VERB
ejpam-3431	5	26	it	it	PRON
ejpam-3431	5	27	interesting	interesting	ADJ
ejpam-3431	5	28	like	like	SCONJ
ejpam-3431	5	29	some	some	DET
ejpam-3431	5	30	algebras	algebra	NOUN
ejpam-3431	5	31	established	establish	VERB
ejpam-3431	5	32	.	.	PUNCT
ejpam-3431	6	1	this	this	DET
ejpam-3431	6	2	paper	paper	NOUN
ejpam-3431	6	3	focuses	focus	VERB
ejpam-3431	6	4	on	on	ADP
ejpam-3431	6	5	some	some	DET
ejpam-3431	6	6	properties	property	NOUN
ejpam-3431	6	7	of	of	ADP
ejpam-3431	6	8	pseudo	pseudo	NOUN
ejpam-3431	6	9	hyper	hyper	ADJ
ejpam-3431	6	10	gr	gr	NOUN
ejpam-3431	6	11	-	-	PUNCT
ejpam-3431	6	12	algebras	algebra	NOUN
ejpam-3431	6	13	and	and	CCONJ
ejpam-3431	6	14	its	its	PRON
ejpam-3431	6	15	ideals	ideal	NOUN
ejpam-3431	6	16	.	.	PUNCT
ejpam-3431	7	1	moreover	moreover	ADV
ejpam-3431	7	2	,	,	PUNCT
ejpam-3431	7	3	pseudo	pseudo	NOUN
ejpam-3431	7	4	hyper	hyper	ADJ
ejpam-3431	7	5	gr	gr	NOUN
ejpam-3431	7	6	-	-	PUNCT
ejpam-3431	7	7	ideals	ideal	NOUN
ejpam-3431	7	8	were	be	AUX
ejpam-3431	7	9	defined	define	VERB
ejpam-3431	7	10	and	and	CCONJ
ejpam-3431	7	11	classified	classify	VERB
ejpam-3431	7	12	to	to	PART
ejpam-3431	7	13	determine	determine	VERB
ejpam-3431	7	14	their	their	PRON
ejpam-3431	7	15	relationship	relationship	NOUN
ejpam-3431	7	16	to	to	ADP
ejpam-3431	7	17	each	each	DET
ejpam-3431	7	18	other	other	ADJ
ejpam-3431	7	19	.	.	PUNCT
ejpam-3431	8	1	2010	2010	NUM
ejpam-3431	8	2	mathematics	mathematic	NOUN
ejpam-3431	8	3	subject	subject	NOUN
ejpam-3431	8	4	classifications	classification	NOUN
ejpam-3431	8	5	:	:	PUNCT
ejpam-3431	8	6	14l17	14l17	NUM
ejpam-3431	8	7	,	,	PUNCT
ejpam-3431	8	8	20n20	20n20	NUM
ejpam-3431	8	9	,	,	PUNCT
ejpam-3431	8	10	03g25	03g25	NOUN
ejpam-3431	8	11	key	key	ADJ
ejpam-3431	8	12	words	word	NOUN
ejpam-3431	8	13	and	and	CCONJ
ejpam-3431	8	14	phrases	phrase	NOUN
ejpam-3431	8	15	:	:	PUNCT
ejpam-3431	8	16	pseudo	pseudo	NOUN
ejpam-3431	8	17	hyper	hyper	ADJ
ejpam-3431	8	18	gr	gr	NOUN
ejpam-3431	8	19	-	-	PUNCT
ejpam-3431	8	20	algebras	algebra	NOUN
ejpam-3431	8	21	,	,	PUNCT
ejpam-3431	8	22	pseudo	pseudo	NOUN
ejpam-3431	8	23	hyper	hyper	ADJ
ejpam-3431	8	24	gr	gr	NOUN
ejpam-3431	8	25	-	-	PUNCT
ejpam-3431	8	26	ideals	ideal	NOUN
ejpam-3431	8	27	1	1	NUM
ejpam-3431	8	28	.	.	PUNCT
ejpam-3431	9	1	introduction	introduction	NOUN
ejpam-3431	9	2	algebraic	algebraic	PROPN
ejpam-3431	9	3	hyperstructures	hyperstructure	NOUN
ejpam-3431	9	4	were	be	AUX
ejpam-3431	9	5	introduced	introduce	VERB
ejpam-3431	9	6	by	by	ADP
ejpam-3431	9	7	a	a	DET
ejpam-3431	9	8	french	french	ADJ
ejpam-3431	9	9	mathematician	mathematician	NOUN
ejpam-3431	9	10	,	,	PUNCT
ejpam-3431	9	11	marty	marty	PROPN
ejpam-3431	10	1	[	[	X
ejpam-3431	10	2	7	7	NUM
ejpam-3431	10	3	]	]	PUNCT
ejpam-3431	10	4	,	,	PUNCT
ejpam-3431	10	5	in	in	ADP
ejpam-3431	10	6	1934	1934	NUM
ejpam-3431	10	7	.	.	PUNCT
ejpam-3431	11	1	they	they	PRON
ejpam-3431	11	2	represent	represent	VERB
ejpam-3431	11	3	a	a	DET
ejpam-3431	11	4	natural	natural	ADJ
ejpam-3431	11	5	extension	extension	NOUN
ejpam-3431	11	6	of	of	ADP
ejpam-3431	11	7	classical	classical	ADJ
ejpam-3431	11	8	hyperstructures	hyperstructure	NOUN
ejpam-3431	11	9	in	in	ADP
ejpam-3431	11	10	which	which	PRON
ejpam-3431	11	11	the	the	DET
ejpam-3431	11	12	composition	composition	NOUN
ejpam-3431	11	13	of	of	ADP
ejpam-3431	11	14	two	two	NUM
ejpam-3431	11	15	elements	element	NOUN
ejpam-3431	11	16	of	of	ADP
ejpam-3431	11	17	a	a	DET
ejpam-3431	11	18	given	give	VERB
ejpam-3431	11	19	set	set	NOUN
ejpam-3431	11	20	is	be	AUX
ejpam-3431	11	21	a	a	DET
ejpam-3431	11	22	set	set	NOUN
ejpam-3431	11	23	,	,	PUNCT
ejpam-3431	11	24	instead	instead	ADV
ejpam-3431	11	25	of	of	ADP
ejpam-3431	11	26	an	an	DET
ejpam-3431	11	27	element	element	NOUN
ejpam-3431	11	28	.	.	PUNCT
ejpam-3431	12	1	afterwards	afterwards	ADV
ejpam-3431	12	2	,	,	PUNCT
ejpam-3431	12	3	this	this	DET
ejpam-3431	12	4	new	new	ADJ
ejpam-3431	12	5	idea	idea	NOUN
ejpam-3431	12	6	was	be	AUX
ejpam-3431	12	7	expanded	expand	VERB
ejpam-3431	12	8	rapidly	rapidly	ADV
ejpam-3431	12	9	and	and	CCONJ
ejpam-3431	12	10	showed	show	VERB
ejpam-3431	12	11	itself	itself	PRON
ejpam-3431	12	12	as	as	ADP
ejpam-3431	12	13	a	a	DET
ejpam-3431	12	14	new	new	ADJ
ejpam-3431	12	15	view	view	NOUN
ejpam-3431	12	16	of	of	ADP
ejpam-3431	12	17	sets	set	NOUN
ejpam-3431	12	18	.	.	PUNCT
ejpam-3431	13	1	the	the	DET
ejpam-3431	13	2	introduction	introduction	NOUN
ejpam-3431	13	3	of	of	ADP
ejpam-3431	13	4	hyperstructure	hyperstructure	PROPN
ejpam-3431	13	5	theory	theory	NOUN
ejpam-3431	13	6	led	lead	VERB
ejpam-3431	13	7	to	to	ADP
ejpam-3431	13	8	the	the	DET
ejpam-3431	13	9	study	study	NOUN
ejpam-3431	13	10	of	of	ADP
ejpam-3431	13	11	several	several	ADJ
ejpam-3431	13	12	problems	problem	NOUN
ejpam-3431	13	13	of	of	ADP
ejpam-3431	13	14	noncommutative	noncommutative	ADJ
ejpam-3431	13	15	algebra	algebra	NOUN
ejpam-3431	13	16	.	.	PUNCT
ejpam-3431	14	1	algebraic	algebraic	PROPN
ejpam-3431	14	2	hyperstructure	hyperstructure	PROPN
ejpam-3431	14	3	theory	theory	NOUN
ejpam-3431	14	4	has	have	VERB
ejpam-3431	14	5	multiple	multiple	ADJ
ejpam-3431	14	6	applications	application	NOUN
ejpam-3431	14	7	to	to	ADP
ejpam-3431	14	8	other	other	ADJ
ejpam-3431	14	9	fields	field	NOUN
ejpam-3431	14	10	such	such	ADJ
ejpam-3431	14	11	as	as	ADP
ejpam-3431	14	12	:	:	PUNCT
ejpam-3431	14	13	geometry	geometry	NOUN
ejpam-3431	14	14	,	,	PUNCT
ejpam-3431	14	15	graphs	graph	NOUN
ejpam-3431	14	16	and	and	CCONJ
ejpam-3431	14	17	hypergraphs	hypergraph	NOUN
ejpam-3431	14	18	,	,	PUNCT
ejpam-3431	14	19	binary	binary	ADJ
ejpam-3431	14	20	relations	relation	NOUN
ejpam-3431	14	21	,	,	PUNCT
ejpam-3431	14	22	lattices	lattice	NOUN
ejpam-3431	14	23	,	,	PUNCT
ejpam-3431	14	24	groups	group	NOUN
ejpam-3431	14	25	,	,	PUNCT
ejpam-3431	14	26	relation	relation	NOUN
ejpam-3431	14	27	algebras	algebra	NOUN
ejpam-3431	14	28	,	,	PUNCT
ejpam-3431	14	29	artificial	artificial	ADJ
ejpam-3431	14	30	intelligence	intelligence	NOUN
ejpam-3431	14	31	,	,	PUNCT
ejpam-3431	14	32	probabilities	probability	NOUN
ejpam-3431	14	33	,	,	PUNCT
ejpam-3431	14	34	and	and	CCONJ
ejpam-3431	14	35	so	so	ADV
ejpam-3431	14	36	on	on	ADV
ejpam-3431	14	37	.	.	PUNCT
ejpam-3431	15	1	in	in	ADP
ejpam-3431	15	2	1966	1966	NUM
ejpam-3431	15	3	,	,	PUNCT
ejpam-3431	15	4	y.	y.	PROPN
ejpam-3431	15	5	imai	imai	PROPN
ejpam-3431	15	6	and	and	CCONJ
ejpam-3431	15	7	k.	k.	PROPN
ejpam-3431	15	8	iséki	iséki	PROPN
ejpam-3431	15	9	[	[	X
ejpam-3431	15	10	4	4	X
ejpam-3431	15	11	]	]	PUNCT
ejpam-3431	15	12	initiated	initiate	VERB
ejpam-3431	15	13	the	the	DET
ejpam-3431	15	14	notion	notion	NOUN
ejpam-3431	15	15	of	of	ADP
ejpam-3431	15	16	bck	bck	NOUN
ejpam-3431	15	17	-	-	PUNCT
ejpam-3431	15	18	algebra	algebra	NOUN
ejpam-3431	15	19	as	as	ADP
ejpam-3431	15	20	a	a	DET
ejpam-3431	15	21	generalization	generalization	NOUN
ejpam-3431	15	22	of	of	ADP
ejpam-3431	15	23	the	the	DET
ejpam-3431	15	24	concept	concept	NOUN
ejpam-3431	15	25	of	of	ADP
ejpam-3431	15	26	set	set	NOUN
ejpam-3431	15	27	-	-	PUNCT
ejpam-3431	15	28	theoretic	theoretic	NOUN
ejpam-3431	15	29	difference	difference	NOUN
ejpam-3431	15	30	and	and	CCONJ
ejpam-3431	15	31	propositional	propositional	ADJ
ejpam-3431	15	32	calculi	calculi	NOUN
ejpam-3431	15	33	.	.	PUNCT
ejpam-3431	16	1	furthermore	furthermore	ADV
ejpam-3431	16	2	,	,	PUNCT
ejpam-3431	16	3	y.b	y.b	PROPN
ejpam-3431	16	4	.	.	PROPN
ejpam-3431	16	5	jun	jun	PROPN
ejpam-3431	16	6	et	et	PROPN
ejpam-3431	16	7	al	al	PROPN
ejpam-3431	16	8	.	.	PUNCT
ejpam-3431	17	1	[	[	X
ejpam-3431	17	2	6	6	NUM
ejpam-3431	17	3	]	]	PUNCT
ejpam-3431	17	4	applied	apply	VERB
ejpam-3431	17	5	hyperstructure	hyperstructure	NOUN
ejpam-3431	17	6	theory	theory	NOUN
ejpam-3431	17	7	to	to	PART
ejpam-3431	17	8	bck	bck	VERB
ejpam-3431	17	9	-	-	PUNCT
ejpam-3431	17	10	algebras	algebras	PROPN
ejpam-3431	17	11	and	and	CCONJ
ejpam-3431	17	12	introduced	introduce	VERB
ejpam-3431	17	13	the	the	DET
ejpam-3431	17	14	notion	notion	NOUN
ejpam-3431	17	15	of	of	ADP
ejpam-3431	17	16	hyper	hyper	ADJ
ejpam-3431	17	17	bck	bck	NOUN
ejpam-3431	17	18	-	-	PUNCT
ejpam-3431	17	19	algebras	algebras	PROPN
ejpam-3431	17	20	as	as	ADP
ejpam-3431	17	21	a	a	DET
ejpam-3431	17	22	generalization	generalization	NOUN
ejpam-3431	17	23	of	of	ADP
ejpam-3431	17	24	bck	bck	NOUN
ejpam-3431	17	25	-	-	PUNCT
ejpam-3431	17	26	algebra	algebra	NOUN
ejpam-3431	17	27	.	.	PUNCT
ejpam-3431	18	1	∗corresponding	∗corresponde	VERB
ejpam-3431	18	2	author	author	NOUN
ejpam-3431	18	3	.	.	PUNCT
ejpam-3431	19	1	doi	doi	NOUN
ejpam-3431	19	2	:	:	PUNCT
ejpam-3431	19	3	https://doi.org/10.29020/nybg.ejpam.v12i3.3431	https://doi.org/10.29020/nybg.ejpam.v12i3.3431	NOUN
ejpam-3431	19	4	email	email	NOUN
ejpam-3431	19	5	addresses	address	NOUN
ejpam-3431	19	6	:	:	PUNCT
ejpam-3431	19	7	rgmanzano@up.edu.ph	rgmanzano@up.edu.ph	PROPN
ejpam-3431	19	8	(	(	PUNCT
ejpam-3431	19	9	r.	r.	PROPN
ejpam-3431	19	10	manzano	manzano	PROPN
ejpam-3431	19	11	,	,	PUNCT
ejpam-3431	19	12	jr	jr	PROPN
ejpam-3431	19	13	.	.	PROPN
ejpam-3431	19	14	)	)	PUNCT
ejpam-3431	19	15	,	,	PUNCT
ejpam-3431	19	16	gaudencio.petalcorin@g.msuiit.edu.ph	gaudencio.petalcorin@g.msuiit.edu.ph	PROPN
ejpam-3431	19	17	(	(	PUNCT
ejpam-3431	19	18	g.	g.	PROPN
ejpam-3431	19	19	petalcorin	petalcorin	PROPN
ejpam-3431	19	20	,	,	PUNCT
ejpam-3431	19	21	jr	jr	PROPN
ejpam-3431	19	22	.	.	PUNCT
ejpam-3431	19	23	)	)	PUNCT
ejpam-3431	19	24	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3431	20	1	821	821	NUM
ejpam-3431	20	2	c	c	NOUN
ejpam-3431	20	3	©	©	PROPN
ejpam-3431	20	4	2019	2019	NUM
ejpam-3431	20	5	ejpam	ejpam	NOUN
ejpam-3431	20	6	all	all	DET
ejpam-3431	20	7	rights	right	NOUN
ejpam-3431	20	8	reserved	reserve	VERB
ejpam-3431	20	9	.	.	PUNCT
ejpam-3431	21	1	r.	r.	PROPN
ejpam-3431	21	2	manzano	manzano	PROPN
ejpam-3431	21	3	,	,	PUNCT
ejpam-3431	21	4	jr	jr	PROPN
ejpam-3431	21	5	.	.	PROPN
ejpam-3431	21	6	,	,	PUNCT
ejpam-3431	21	7	g.	g.	PROPN
ejpam-3431	21	8	petalcorin	petalcorin	PROPN
ejpam-3431	21	9	,	,	PUNCT
ejpam-3431	21	10	jr	jr	PROPN
ejpam-3431	21	11	.	.	PROPN
ejpam-3431	21	12	/	/	SYM
ejpam-3431	21	13	eur	eur	PROPN
ejpam-3431	21	14	.	.	PUNCT
ejpam-3431	22	1	j.	j.	PROPN
ejpam-3431	22	2	pure	pure	PROPN
ejpam-3431	22	3	appl	appl	PROPN
ejpam-3431	22	4	.	.	PROPN
ejpam-3431	22	5	math	math	PROPN
ejpam-3431	22	6	,	,	PUNCT
ejpam-3431	22	7	12	12	NUM
ejpam-3431	22	8	(	(	PUNCT
ejpam-3431	22	9	3	3	NUM
ejpam-3431	22	10	)	)	PUNCT
ejpam-3431	22	11	(	(	PUNCT
ejpam-3431	22	12	2019	2019	NUM
ejpam-3431	22	13	)	)	PUNCT
ejpam-3431	22	14	,	,	PUNCT
ejpam-3431	22	15	821	821	NUM
ejpam-3431	22	16	-	-	SYM
ejpam-3431	22	17	833	833	NUM
ejpam-3431	22	18	822	822	NUM
ejpam-3431	22	19	in	in	ADP
ejpam-3431	22	20	order	order	NOUN
ejpam-3431	22	21	to	to	PART
ejpam-3431	22	22	extend	extend	VERB
ejpam-3431	22	23	bck	bck	NOUN
ejpam-3431	22	24	-	-	PUNCT
ejpam-3431	22	25	algebra	algebra	NOUN
ejpam-3431	22	26	to	to	ADP
ejpam-3431	22	27	a	a	DET
ejpam-3431	22	28	noncommutative	noncommutative	ADJ
ejpam-3431	22	29	form	form	NOUN
ejpam-3431	22	30	,	,	PUNCT
ejpam-3431	22	31	g.	g.	PROPN
ejpam-3431	22	32	georgescu	georgescu	PROPN
ejpam-3431	22	33	and	and	CCONJ
ejpam-3431	22	34	a.	a.	NOUN
ejpam-3431	22	35	iorgulescu	iorgulescu	NOUN
ejpam-3431	23	1	[	[	X
ejpam-3431	23	2	3	3	X
ejpam-3431	23	3	]	]	PUNCT
ejpam-3431	23	4	introduced	introduce	VERB
ejpam-3431	23	5	the	the	DET
ejpam-3431	23	6	notion	notion	NOUN
ejpam-3431	23	7	of	of	ADP
ejpam-3431	23	8	pseudo	pseudo	NOUN
ejpam-3431	23	9	bck	bck	NOUN
ejpam-3431	23	10	-	-	PUNCT
ejpam-3431	23	11	algebras	algebras	PROPN
ejpam-3431	23	12	and	and	CCONJ
ejpam-3431	23	13	studied	study	VERB
ejpam-3431	23	14	their	their	PRON
ejpam-3431	23	15	properties	property	NOUN
ejpam-3431	23	16	.	.	PUNCT
ejpam-3431	24	1	on	on	ADP
ejpam-3431	24	2	the	the	DET
ejpam-3431	24	3	other	other	ADJ
ejpam-3431	24	4	hand	hand	NOUN
ejpam-3431	24	5	,	,	PUNCT
ejpam-3431	24	6	r.	r.	PROPN
ejpam-3431	24	7	a.	a.	PROPN
ejpam-3431	24	8	borzooei	borzooei	PROPN
ejpam-3431	24	9	,	,	PUNCT
ejpam-3431	24	10	a.	a.	NOUN
ejpam-3431	24	11	rezazadeh	rezazadeh	PROPN
ejpam-3431	24	12	and	and	CCONJ
ejpam-3431	24	13	r.	r.	PROPN
ejpam-3431	24	14	ameri	ameri	PROPN
ejpam-3431	25	1	[	[	X
ejpam-3431	25	2	1	1	X
ejpam-3431	25	3	]	]	PUNCT
ejpam-3431	25	4	introduced	introduce	VERB
ejpam-3431	25	5	the	the	DET
ejpam-3431	25	6	concept	concept	NOUN
ejpam-3431	25	7	of	of	ADP
ejpam-3431	25	8	hyper	hyper	ADJ
ejpam-3431	25	9	pseudo	pseudo	NOUN
ejpam-3431	25	10	bck	bck	NOUN
ejpam-3431	25	11	-	-	PUNCT
ejpam-3431	25	12	algebra	algebra	NOUN
ejpam-3431	25	13	which	which	PRON
ejpam-3431	25	14	is	be	AUX
ejpam-3431	25	15	a	a	DET
ejpam-3431	25	16	generalization	generalization	NOUN
ejpam-3431	25	17	of	of	ADP
ejpam-3431	25	18	pseudo	pseudo	NOUN
ejpam-3431	25	19	bck	bck	NOUN
ejpam-3431	25	20	-	-	PUNCT
ejpam-3431	25	21	algebra	algebra	NOUN
ejpam-3431	25	22	.	.	PUNCT
ejpam-3431	26	1	r.a	r.a	PROPN
ejpam-3431	26	2	.	.	PROPN
ejpam-3431	26	3	indangan	indangan	PROPN
ejpam-3431	26	4	and	and	CCONJ
ejpam-3431	26	5	g.c	g.c	PROPN
ejpam-3431	26	6	.	.	PROPN
ejpam-3431	26	7	petalcorin	petalcorin	PROPN
ejpam-3431	27	1	[	[	X
ejpam-3431	27	2	5	5	NUM
ejpam-3431	27	3	]	]	PUNCT
ejpam-3431	27	4	defined	define	VERB
ejpam-3431	27	5	a	a	DET
ejpam-3431	27	6	new	new	ADJ
ejpam-3431	27	7	class	class	NOUN
ejpam-3431	27	8	of	of	ADP
ejpam-3431	27	9	algebraic	algebraic	PROPN
ejpam-3431	27	10	hyperstructure	hyperstructure	NOUN
ejpam-3431	27	11	called	call	VERB
ejpam-3431	27	12	hyper	hyper	ADJ
ejpam-3431	27	13	gr	gr	NOUN
ejpam-3431	27	14	-	-	NOUN
ejpam-3431	27	15	algebra	algebra	NOUN
ejpam-3431	27	16	.	.	PUNCT
ejpam-3431	28	1	in	in	ADP
ejpam-3431	28	2	this	this	DET
ejpam-3431	28	3	algebra	algebra	NOUN
ejpam-3431	28	4	,	,	PUNCT
ejpam-3431	28	5	they	they	PRON
ejpam-3431	28	6	presented	present	VERB
ejpam-3431	28	7	a	a	DET
ejpam-3431	28	8	helpful	helpful	ADJ
ejpam-3431	28	9	understanding	understanding	NOUN
ejpam-3431	28	10	on	on	ADP
ejpam-3431	28	11	how	how	SCONJ
ejpam-3431	28	12	this	this	DET
ejpam-3431	28	13	hyper	hyper	ADJ
ejpam-3431	28	14	algebra	algebra	NOUN
ejpam-3431	28	15	differs	differ	VERB
ejpam-3431	28	16	from	from	ADP
ejpam-3431	28	17	the	the	DET
ejpam-3431	28	18	rest	rest	NOUN
ejpam-3431	28	19	.	.	PUNCT
ejpam-3431	29	1	in	in	ADP
ejpam-3431	29	2	this	this	DET
ejpam-3431	29	3	paper	paper	NOUN
ejpam-3431	29	4	we	we	PRON
ejpam-3431	29	5	define	define	VERB
ejpam-3431	29	6	a	a	DET
ejpam-3431	29	7	pseudo	pseudo	NOUN
ejpam-3431	29	8	hyper	hyper	ADJ
ejpam-3431	29	9	gr	gr	NOUN
ejpam-3431	29	10	-	-	PUNCT
ejpam-3431	29	11	algebra	algebra	NOUN
ejpam-3431	29	12	analogous	analogous	ADJ
ejpam-3431	29	13	to	to	ADP
ejpam-3431	29	14	that	that	PRON
ejpam-3431	29	15	of	of	ADP
ejpam-3431	29	16	a	a	DET
ejpam-3431	29	17	hyper	hyper	ADJ
ejpam-3431	29	18	gralgebra	gralgebra	NOUN
ejpam-3431	29	19	and	and	CCONJ
ejpam-3431	29	20	its	its	PRON
ejpam-3431	29	21	pseudo	pseudo	NOUN
ejpam-3431	29	22	hyper	hyper	ADJ
ejpam-3431	29	23	gr	gr	NOUN
ejpam-3431	29	24	-	-	PUNCT
ejpam-3431	29	25	ideals	ideal	NOUN
ejpam-3431	29	26	and	and	CCONJ
ejpam-3431	29	27	their	their	PRON
ejpam-3431	29	28	relationships	relationship	NOUN
ejpam-3431	29	29	.	.	PUNCT
ejpam-3431	30	1	2	2	X
ejpam-3431	30	2	.	.	X
ejpam-3431	30	3	preliminaries	preliminary	NOUN
ejpam-3431	30	4	let	let	VERB
ejpam-3431	30	5	h	h	NOUN
ejpam-3431	30	6	be	be	AUX
ejpam-3431	30	7	a	a	DET
ejpam-3431	30	8	nonempty	nonempty	ADJ
ejpam-3431	30	9	set	set	VERB
ejpam-3431	30	10	endowed	endow	VERB
ejpam-3431	30	11	with	with	ADP
ejpam-3431	30	12	a	a	DET
ejpam-3431	30	13	hyperoperation	hyperoperation	NOUN
ejpam-3431	30	14	“	"	PUNCT
ejpam-3431	30	15	∗	∗	NOUN
ejpam-3431	30	16	”	"	PUNCT
ejpam-3431	30	17	,	,	PUNCT
ejpam-3431	30	18	that	that	ADV
ejpam-3431	30	19	is	is	ADV
ejpam-3431	30	20	,	,	PUNCT
ejpam-3431	30	21	“	"	PUNCT
ejpam-3431	30	22	∗	∗	NOUN
ejpam-3431	30	23	”	"	PUNCT
ejpam-3431	30	24	is	be	AUX
ejpam-3431	30	25	a	a	DET
ejpam-3431	30	26	function	function	NOUN
ejpam-3431	30	27	from	from	ADP
ejpam-3431	30	28	h	h	PROPN
ejpam-3431	30	29	×	×	PROPN
ejpam-3431	30	30	h	h	NOUN
ejpam-3431	30	31	to	to	ADP
ejpam-3431	30	32	p	p	PROPN
ejpam-3431	30	33	∗(h	∗(h	PROPN
ejpam-3431	30	34	)	)	PUNCT
ejpam-3431	31	1	=	=	SYM
ejpam-3431	31	2	p	p	X
ejpam-3431	31	3	(	(	PUNCT
ejpam-3431	31	4	h	h	NOUN
ejpam-3431	31	5	)	)	PUNCT
ejpam-3431	31	6	\	\	NOUN
ejpam-3431	31	7	{	{	PUNCT
ejpam-3431	31	8	∅	∅	NOUN
ejpam-3431	31	9	}	}	PUNCT
ejpam-3431	31	10	.	.	PUNCT
ejpam-3431	32	1	for	for	ADP
ejpam-3431	32	2	two	two	NUM
ejpam-3431	32	3	nonempty	nonempty	ADJ
ejpam-3431	32	4	subsets	subset	NOUN
ejpam-3431	32	5	a	a	PRON
ejpam-3431	32	6	and	and	CCONJ
ejpam-3431	32	7	b	b	NOUN
ejpam-3431	32	8	of	of	ADP
ejpam-3431	32	9	h	h	NOUN
ejpam-3431	32	10	,	,	PUNCT
ejpam-3431	32	11	a	a	DET
ejpam-3431	32	12	∗	∗	NOUN
ejpam-3431	32	13	b	b	NOUN
ejpam-3431	32	14	=	=	PUNCT
ejpam-3431	32	15	⋃	⋃	NOUN
ejpam-3431	32	16	a∈a	a∈a	ADJ
ejpam-3431	32	17	,	,	PUNCT
ejpam-3431	32	18	b∈b	b∈b	VERB
ejpam-3431	32	19	a	a	DET
ejpam-3431	32	20	∗	∗	NOUN
ejpam-3431	32	21	b.	b.	NOUN
ejpam-3431	33	1	we	we	PRON
ejpam-3431	33	2	shall	shall	AUX
ejpam-3431	33	3	use	use	VERB
ejpam-3431	33	4	x	x	PUNCT
ejpam-3431	33	5	∗	∗	NOUN
ejpam-3431	33	6	y	y	PROPN
ejpam-3431	33	7	instead	instead	ADV
ejpam-3431	33	8	of	of	ADP
ejpam-3431	33	9	x	x	VERB
ejpam-3431	33	10	∗	∗	X
ejpam-3431	33	11	{	{	PUNCT
ejpam-3431	33	12	y	y	NOUN
ejpam-3431	33	13	}	}	PUNCT
ejpam-3431	33	14	,	,	PUNCT
ejpam-3431	33	15	{	{	PUNCT
ejpam-3431	33	16	x	x	NOUN
ejpam-3431	33	17	}	}	PUNCT
ejpam-3431	33	18	∗	∗	NOUN
ejpam-3431	33	19	y	y	NOUN
ejpam-3431	33	20	or	or	CCONJ
ejpam-3431	33	21	{	{	PUNCT
ejpam-3431	33	22	x	x	NOUN
ejpam-3431	33	23	}	}	PUNCT
ejpam-3431	33	24	∗	∗	NOUN
ejpam-3431	33	25	{	{	PUNCT
ejpam-3431	33	26	y	y	NOUN
ejpam-3431	33	27	}	}	PUNCT
ejpam-3431	33	28	.	.	PUNCT
ejpam-3431	34	1	when	when	SCONJ
ejpam-3431	34	2	a	a	PRON
ejpam-3431	34	3	is	be	AUX
ejpam-3431	34	4	a	a	DET
ejpam-3431	34	5	nonempty	nonempty	ADJ
ejpam-3431	34	6	subset	subset	NOUN
ejpam-3431	34	7	of	of	ADP
ejpam-3431	34	8	h	h	NOUN
ejpam-3431	34	9	and	and	CCONJ
ejpam-3431	34	10	x	x	PUNCT
ejpam-3431	34	11	∈	∈	PROPN
ejpam-3431	34	12	h	h	NOUN
ejpam-3431	34	13	,	,	PUNCT
ejpam-3431	34	14	we	we	PRON
ejpam-3431	34	15	agree	agree	VERB
ejpam-3431	34	16	to	to	PART
ejpam-3431	34	17	write	write	VERB
ejpam-3431	34	18	a	a	DET
ejpam-3431	34	19	∗x	∗x	PROPN
ejpam-3431	34	20	instead	instead	ADV
ejpam-3431	34	21	of	of	ADP
ejpam-3431	34	22	a	a	DET
ejpam-3431	34	23	∗	∗	NOUN
ejpam-3431	34	24	{	{	PUNCT
ejpam-3431	34	25	x	x	NOUN
ejpam-3431	34	26	}	}	PUNCT
ejpam-3431	34	27	.	.	PUNCT
ejpam-3431	35	1	similarly	similarly	ADV
ejpam-3431	35	2	,	,	PUNCT
ejpam-3431	35	3	we	we	PRON
ejpam-3431	35	4	write	write	VERB
ejpam-3431	35	5	x	x	PUNCT
ejpam-3431	35	6	∗a	∗a	ADJ
ejpam-3431	35	7	for	for	ADP
ejpam-3431	35	8	{	{	PUNCT
ejpam-3431	35	9	x	x	NOUN
ejpam-3431	35	10	}	}	PUNCT
ejpam-3431	35	11	∗a	∗a	ADJ
ejpam-3431	35	12	.	.	PUNCT
ejpam-3431	36	1	in	in	ADP
ejpam-3431	36	2	effect	effect	NOUN
ejpam-3431	36	3	,	,	PUNCT
ejpam-3431	36	4	a	a	DET
ejpam-3431	36	5	∗x	∗x	PROPN
ejpam-3431	36	6	=	=	SYM
ejpam-3431	36	7	⋃	⋃	NOUN
ejpam-3431	36	8	a∈a	a∈a	ADJ
ejpam-3431	36	9	a	a	DET
ejpam-3431	36	10	∗	∗	NOUN
ejpam-3431	36	11	x	x	PUNCT
ejpam-3431	36	12	and	and	CCONJ
ejpam-3431	36	13	x	x	ADJ
ejpam-3431	36	14	∗a	∗a	PROPN
ejpam-3431	36	15	=	=	SYM
ejpam-3431	36	16	⋃	⋃	NOUN
ejpam-3431	36	17	a∈a	a∈a	ADJ
ejpam-3431	36	18	x	x	NOUN
ejpam-3431	36	19	∗	∗	NOUN
ejpam-3431	36	20	a.	a.	NOUN
ejpam-3431	36	21	a	a	DET
ejpam-3431	36	22	set	set	NOUN
ejpam-3431	36	23	h	h	NOUN
ejpam-3431	36	24	endowed	endow	VERB
ejpam-3431	36	25	with	with	ADP
ejpam-3431	36	26	a	a	DET
ejpam-3431	36	27	family	family	NOUN
ejpam-3431	36	28	γ	γ	NOUN
ejpam-3431	36	29	of	of	ADP
ejpam-3431	36	30	hyperoperations	hyperoperation	NOUN
ejpam-3431	36	31	is	be	AUX
ejpam-3431	36	32	called	call	VERB
ejpam-3431	36	33	a	a	DET
ejpam-3431	36	34	hyperstructure	hyperstructure	NOUN
ejpam-3431	36	35	.	.	PUNCT
ejpam-3431	37	1	if	if	SCONJ
ejpam-3431	37	2	γ	γ	PROPN
ejpam-3431	37	3	is	be	AUX
ejpam-3431	37	4	singleton	singleton	NOUN
ejpam-3431	37	5	,	,	PUNCT
ejpam-3431	37	6	that	that	ADV
ejpam-3431	37	7	is	is	ADV
ejpam-3431	37	8	,	,	PUNCT
ejpam-3431	37	9	γ	γ	X
ejpam-3431	37	10	=	=	X
ejpam-3431	37	11	{	{	PUNCT
ejpam-3431	37	12	f	f	NOUN
ejpam-3431	37	13	}	}	PUNCT
ejpam-3431	37	14	,	,	PUNCT
ejpam-3431	37	15	then	then	ADV
ejpam-3431	37	16	the	the	DET
ejpam-3431	37	17	hyperstructure	hyperstructure	NOUN
ejpam-3431	37	18	is	be	AUX
ejpam-3431	37	19	called	call	VERB
ejpam-3431	37	20	a	a	DET
ejpam-3431	37	21	hypergroupoid	hypergroupoid	NOUN
ejpam-3431	37	22	.	.	PUNCT
ejpam-3431	38	1	definition	definition	NOUN
ejpam-3431	38	2	2.1	2.1	NUM
ejpam-3431	38	3	.	.	PUNCT
ejpam-3431	39	1	[	[	X
ejpam-3431	39	2	2	2	X
ejpam-3431	39	3	]	]	X
ejpam-3431	39	4	let	let	VERB
ejpam-3431	39	5	x	x	PRON
ejpam-3431	39	6	,	,	PUNCT
ejpam-3431	39	7	y	y	PROPN
ejpam-3431	39	8	∈	∈	PROPN
ejpam-3431	39	9	h	h	NOUN
ejpam-3431	39	10	and	and	CCONJ
ejpam-3431	39	11	a	a	PRON
ejpam-3431	39	12	,	,	PUNCT
ejpam-3431	39	13	b	b	PROPN
ejpam-3431	39	14	⊆	⊆	NUM
ejpam-3431	39	15	h.	h.	NOUN
ejpam-3431	39	16	then	then	ADV
ejpam-3431	39	17	(	(	PUNCT
ejpam-3431	39	18	i	i	NOUN
ejpam-3431	39	19	)	)	PUNCT
ejpam-3431	39	20	x	x	NOUN
ejpam-3431	39	21	�	�	PROPN
ejpam-3431	39	22	y	y	PROPN
ejpam-3431	39	23	if	if	SCONJ
ejpam-3431	39	24	and	and	CCONJ
ejpam-3431	39	25	only	only	ADV
ejpam-3431	40	1	if	if	SCONJ
ejpam-3431	40	2	0	0	NUM
ejpam-3431	40	3	∈	∈	PROPN
ejpam-3431	40	4	x~	x~	NUM
ejpam-3431	40	5	y	y	PROPN
ejpam-3431	40	6	;	;	PUNCT
ejpam-3431	40	7	and	and	CCONJ
ejpam-3431	40	8	(	(	PUNCT
ejpam-3431	40	9	ii	ii	NOUN
ejpam-3431	40	10	)	)	PUNCT
ejpam-3431	40	11	a	a	DET
ejpam-3431	40	12	�	�	PROPN
ejpam-3431	40	13	b	b	PROPN
ejpam-3431	40	14	if	if	SCONJ
ejpam-3431	40	15	and	and	CCONJ
ejpam-3431	40	16	only	only	ADV
ejpam-3431	40	17	if	if	SCONJ
ejpam-3431	40	18	for	for	ADP
ejpam-3431	40	19	any	any	DET
ejpam-3431	40	20	a	a	DET
ejpam-3431	40	21	∈	∈	PROPN
ejpam-3431	40	22	a	a	PRON
ejpam-3431	40	23	,	,	PUNCT
ejpam-3431	40	24	there	there	PRON
ejpam-3431	40	25	exists	exist	VERB
ejpam-3431	40	26	b	b	PROPN
ejpam-3431	40	27	∈	∈	PROPN
ejpam-3431	40	28	b	b	NOUN
ejpam-3431	40	29	such	such	ADJ
ejpam-3431	40	30	that	that	SCONJ
ejpam-3431	40	31	a	a	DET
ejpam-3431	40	32	�	�	PROPN
ejpam-3431	40	33	b.	b.	PROPN
ejpam-3431	40	34	we	we	PRON
ejpam-3431	40	35	call	call	VERB
ejpam-3431	40	36	�	�	PROPN
ejpam-3431	40	37	a	a	DET
ejpam-3431	40	38	hyperorder	hyperorder	NOUN
ejpam-3431	40	39	on	on	ADP
ejpam-3431	40	40	h.	h.	PROPN
ejpam-3431	40	41	remark	remark	PROPN
ejpam-3431	40	42	2.2	2.2	NUM
ejpam-3431	40	43	.	.	PUNCT
ejpam-3431	41	1	[	[	X
ejpam-3431	41	2	2	2	X
ejpam-3431	41	3	]	]	PUNCT
ejpam-3431	41	4	for	for	ADP
ejpam-3431	41	5	all	all	DET
ejpam-3431	41	6	a	a	DET
ejpam-3431	41	7	,	,	PUNCT
ejpam-3431	41	8	b	b	PROPN
ejpam-3431	41	9	⊆	⊆	NUM
ejpam-3431	41	10	h	h	NOUN
ejpam-3431	41	11	,	,	PUNCT
ejpam-3431	41	12	a	a	DET
ejpam-3431	41	13	�	�	PROPN
ejpam-3431	41	14	b	b	PROPN
ejpam-3431	41	15	implies	imply	VERB
ejpam-3431	41	16	0	0	NUM
ejpam-3431	41	17	∈	∈	PROPN
ejpam-3431	41	18	a	a	DET
ejpam-3431	41	19	~	~	PROPN
ejpam-3431	41	20	b.	b.	NOUN
ejpam-3431	41	21	definition	definition	NOUN
ejpam-3431	41	22	2.3	2.3	NUM
ejpam-3431	41	23	.	.	PUNCT
ejpam-3431	42	1	[	[	X
ejpam-3431	42	2	5	5	X
ejpam-3431	42	3	]	]	PUNCT
ejpam-3431	42	4	let	let	VERB
ejpam-3431	42	5	h	h	NOUN
ejpam-3431	42	6	be	be	AUX
ejpam-3431	42	7	a	a	DET
ejpam-3431	42	8	nonempty	nonempty	NOUN
ejpam-3431	42	9	set	set	VERB
ejpam-3431	42	10	with	with	ADP
ejpam-3431	42	11	a	a	DET
ejpam-3431	42	12	hyperoperation“~	hyperoperation“~	PROPN
ejpam-3431	42	13	”	"	PUNCT
ejpam-3431	42	14	on	on	ADP
ejpam-3431	42	15	h.	h.	PROPN
ejpam-3431	42	16	then	then	ADV
ejpam-3431	42	17	(	(	PUNCT
ejpam-3431	42	18	h;~	h;~	NOUN
ejpam-3431	42	19	,	,	PUNCT
ejpam-3431	42	20	0	0	NUM
ejpam-3431	42	21	)	)	PUNCT
ejpam-3431	42	22	is	be	AUX
ejpam-3431	42	23	called	call	VERB
ejpam-3431	42	24	a	a	DET
ejpam-3431	42	25	hyper	hyper	ADJ
ejpam-3431	42	26	gr	gr	NOUN
ejpam-3431	42	27	-	-	PUNCT
ejpam-3431	42	28	algebra	algebra	NOUN
ejpam-3431	42	29	if	if	SCONJ
ejpam-3431	42	30	it	it	PRON
ejpam-3431	42	31	contains	contain	VERB
ejpam-3431	42	32	a	a	DET
ejpam-3431	42	33	constant	constant	ADJ
ejpam-3431	42	34	0	0	NUM
ejpam-3431	42	35	∈	∈	PROPN
ejpam-3431	42	36	h	h	NOUN
ejpam-3431	42	37	and	and	CCONJ
ejpam-3431	42	38	for	for	ADP
ejpam-3431	42	39	all	all	DET
ejpam-3431	42	40	x	x	NOUN
ejpam-3431	42	41	,	,	PUNCT
ejpam-3431	42	42	y	y	PROPN
ejpam-3431	42	43	,	,	PUNCT
ejpam-3431	42	44	z	z	PROPN
ejpam-3431	42	45	∈	∈	PROPN
ejpam-3431	42	46	h	h	NOUN
ejpam-3431	42	47	,	,	PUNCT
ejpam-3431	42	48	the	the	DET
ejpam-3431	42	49	following	follow	VERB
ejpam-3431	42	50	conditions	condition	NOUN
ejpam-3431	42	51	are	be	AUX
ejpam-3431	42	52	satisfied	satisfied	ADJ
ejpam-3431	42	53	:	:	PUNCT
ejpam-3431	42	54	[	[	X
ejpam-3431	42	55	hgr1	hgr1	X
ejpam-3431	42	56	]	]	X
ejpam-3431	42	57	(	(	PUNCT
ejpam-3431	42	58	x~	x~	PROPN
ejpam-3431	42	59	z)~	z)~	PROPN
ejpam-3431	42	60	(	(	PUNCT
ejpam-3431	42	61	y	y	PROPN
ejpam-3431	42	62	~	~	PUNCT
ejpam-3431	42	63	z	z	X
ejpam-3431	42	64	)	)	PUNCT
ejpam-3431	42	65	�	�	PROPN
ejpam-3431	42	66	x~	x~	NUM
ejpam-3431	42	67	y	y	PROPN
ejpam-3431	42	68	;	;	PUNCT
ejpam-3431	42	69	[	[	X
ejpam-3431	42	70	hgr2	hgr2	NOUN
ejpam-3431	42	71	]	]	PUNCT
ejpam-3431	42	72	(	(	PUNCT
ejpam-3431	42	73	x~	x~	PROPN
ejpam-3431	42	74	y)~	y)~	PROPN
ejpam-3431	42	75	z	z	NOUN
ejpam-3431	42	76	=	=	SYM
ejpam-3431	42	77	(	(	PUNCT
ejpam-3431	42	78	x~	x~	PROPN
ejpam-3431	42	79	z)~	z)~	PROPN
ejpam-3431	42	80	y	y	NOUN
ejpam-3431	42	81	;	;	PUNCT
ejpam-3431	43	1	[	[	X
ejpam-3431	43	2	hgr3	hgr3	X
ejpam-3431	43	3	]	]	X
ejpam-3431	43	4	x	x	X
ejpam-3431	43	5	�	�	PROPN
ejpam-3431	43	6	x	x	SYM
ejpam-3431	43	7	;	;	PUNCT
ejpam-3431	43	8	[	[	X
ejpam-3431	43	9	hgr4	hgr4	X
ejpam-3431	43	10	]	]	X
ejpam-3431	43	11	0~	0~	NOUN
ejpam-3431	43	12	(	(	PUNCT
ejpam-3431	43	13	0~	0~	NOUN
ejpam-3431	43	14	x	x	SYM
ejpam-3431	43	15	)	)	PUNCT
ejpam-3431	43	16	�	�	PROPN
ejpam-3431	43	17	x	x	SYM
ejpam-3431	43	18	,	,	PUNCT
ejpam-3431	43	19	for	for	ADP
ejpam-3431	43	20	all	all	DET
ejpam-3431	43	21	x	x	PUNCT
ejpam-3431	43	22	6=	6=	ADP
ejpam-3431	43	23	0	0	NUM
ejpam-3431	43	24	;	;	PUNCT
ejpam-3431	43	25	and	and	CCONJ
ejpam-3431	43	26	[	[	X
ejpam-3431	43	27	hgr5	hgr5	X
ejpam-3431	43	28	]	]	X
ejpam-3431	43	29	(	(	PUNCT
ejpam-3431	43	30	x~	x~	PROPN
ejpam-3431	43	31	y)~	y)~	PROPN
ejpam-3431	43	32	z	z	PROPN
ejpam-3431	43	33	�	�	PROPN
ejpam-3431	43	34	y	y	PROPN
ejpam-3431	43	35	~	~	PUNCT
ejpam-3431	43	36	z.	z.	PROPN
ejpam-3431	43	37	example	example	NOUN
ejpam-3431	43	38	2.4	2.4	NUM
ejpam-3431	43	39	.	.	PUNCT
ejpam-3431	44	1	[	[	X
ejpam-3431	44	2	5	5	NUM
ejpam-3431	44	3	]	]	PUNCT
ejpam-3431	44	4	let	let	NOUN
ejpam-3431	44	5	h	h	NOUN
ejpam-3431	44	6	=	=	PRON
ejpam-3431	44	7	{	{	PUNCT
ejpam-3431	44	8	0	0	NUM
ejpam-3431	44	9	,	,	PUNCT
ejpam-3431	44	10	1	1	NUM
ejpam-3431	44	11	,	,	PUNCT
ejpam-3431	44	12	2	2	NUM
ejpam-3431	44	13	}	}	PUNCT
ejpam-3431	44	14	.	.	PUNCT
ejpam-3431	45	1	define	define	VERB
ejpam-3431	45	2	the	the	DET
ejpam-3431	45	3	operation	operation	NOUN
ejpam-3431	45	4	“	"	PUNCT
ejpam-3431	45	5	~	~	PROPN
ejpam-3431	45	6	”	"	PUNCT
ejpam-3431	45	7	by	by	ADP
ejpam-3431	45	8	the	the	DET
ejpam-3431	45	9	cayley	cayley	ADJ
ejpam-3431	45	10	table	table	NOUN
ejpam-3431	45	11	shown	show	VERB
ejpam-3431	45	12	below	below	ADP
ejpam-3431	45	13	.	.	PUNCT
ejpam-3431	46	1	r.	r.	PROPN
ejpam-3431	46	2	manzano	manzano	PROPN
ejpam-3431	46	3	,	,	PUNCT
ejpam-3431	46	4	jr	jr	PROPN
ejpam-3431	46	5	.	.	PROPN
ejpam-3431	46	6	,	,	PUNCT
ejpam-3431	46	7	g.	g.	PROPN
ejpam-3431	46	8	petalcorin	petalcorin	PROPN
ejpam-3431	46	9	,	,	PUNCT
ejpam-3431	46	10	jr	jr	PROPN
ejpam-3431	46	11	.	.	PROPN
ejpam-3431	46	12	/	/	SYM
ejpam-3431	46	13	eur	eur	PROPN
ejpam-3431	46	14	.	.	PUNCT
ejpam-3431	47	1	j.	j.	PROPN
ejpam-3431	47	2	pure	pure	PROPN
ejpam-3431	47	3	appl	appl	PROPN
ejpam-3431	47	4	.	.	PROPN
ejpam-3431	47	5	math	math	PROPN
ejpam-3431	47	6	,	,	PUNCT
ejpam-3431	47	7	12	12	NUM
ejpam-3431	47	8	(	(	PUNCT
ejpam-3431	47	9	3	3	NUM
ejpam-3431	47	10	)	)	PUNCT
ejpam-3431	47	11	(	(	PUNCT
ejpam-3431	47	12	2019	2019	NUM
ejpam-3431	47	13	)	)	PUNCT
ejpam-3431	47	14	,	,	PUNCT
ejpam-3431	47	15	821	821	NUM
ejpam-3431	47	16	-	-	SYM
ejpam-3431	47	17	833	833	NUM
ejpam-3431	47	18	823	823	NUM
ejpam-3431	47	19	~	~	SYM
ejpam-3431	47	20	0	0	NUM
ejpam-3431	48	1	1	1	NUM
ejpam-3431	48	2	2	2	NUM
ejpam-3431	48	3	0	0	NUM
ejpam-3431	48	4	{	{	PUNCT
ejpam-3431	48	5	0	0	NUM
ejpam-3431	48	6	}	}	PUNCT
ejpam-3431	48	7	{	{	PUNCT
ejpam-3431	48	8	0	0	NUM
ejpam-3431	48	9	}	}	PUNCT
ejpam-3431	48	10	{	{	PUNCT
ejpam-3431	48	11	0	0	NUM
ejpam-3431	48	12	}	}	SYM
ejpam-3431	48	13	1	1	NUM
ejpam-3431	48	14	{	{	PUNCT
ejpam-3431	48	15	0	0	NUM
ejpam-3431	48	16	,	,	PUNCT
ejpam-3431	48	17	1	1	NUM
ejpam-3431	48	18	,	,	PUNCT
ejpam-3431	48	19	2	2	NUM
ejpam-3431	48	20	}	}	PUNCT
ejpam-3431	48	21	{	{	PUNCT
ejpam-3431	48	22	0	0	NUM
ejpam-3431	48	23	,	,	PUNCT
ejpam-3431	48	24	1	1	NUM
ejpam-3431	48	25	}	}	PUNCT
ejpam-3431	48	26	{	{	PUNCT
ejpam-3431	48	27	0	0	NUM
ejpam-3431	48	28	,	,	PUNCT
ejpam-3431	48	29	1	1	NUM
ejpam-3431	48	30	}	}	SYM
ejpam-3431	48	31	2	2	NUM
ejpam-3431	48	32	{	{	PUNCT
ejpam-3431	48	33	0	0	NUM
ejpam-3431	48	34	,	,	PUNCT
ejpam-3431	48	35	2	2	NUM
ejpam-3431	48	36	}	}	PUNCT
ejpam-3431	48	37	{	{	PUNCT
ejpam-3431	48	38	0	0	NUM
ejpam-3431	48	39	,	,	PUNCT
ejpam-3431	48	40	1	1	NUM
ejpam-3431	48	41	,	,	PUNCT
ejpam-3431	48	42	2	2	NUM
ejpam-3431	48	43	}	}	PUNCT
ejpam-3431	48	44	{	{	PUNCT
ejpam-3431	48	45	0	0	NUM
ejpam-3431	48	46	,	,	PUNCT
ejpam-3431	48	47	2	2	NUM
ejpam-3431	48	48	}	}	PUNCT
ejpam-3431	48	49	by	by	ADP
ejpam-3431	48	50	routine	routine	ADJ
ejpam-3431	48	51	calculations	calculation	NOUN
ejpam-3431	48	52	,	,	PUNCT
ejpam-3431	48	53	(	(	PUNCT
ejpam-3431	48	54	h;~	h;~	NOUN
ejpam-3431	48	55	,	,	PUNCT
ejpam-3431	48	56	0	0	NUM
ejpam-3431	48	57	)	)	PUNCT
ejpam-3431	48	58	is	be	AUX
ejpam-3431	48	59	a	a	DET
ejpam-3431	48	60	hyper	hyper	ADJ
ejpam-3431	48	61	gr	gr	NOUN
ejpam-3431	48	62	-	-	NOUN
ejpam-3431	48	63	algebra	algebra	NOUN
ejpam-3431	48	64	.	.	PUNCT
ejpam-3431	49	1	definition	definition	NOUN
ejpam-3431	49	2	2.5	2.5	NUM
ejpam-3431	49	3	.	.	PUNCT
ejpam-3431	50	1	[	[	X
ejpam-3431	50	2	5	5	NUM
ejpam-3431	50	3	]	]	PUNCT
ejpam-3431	50	4	a	a	DET
ejpam-3431	50	5	hyper	hyper	ADJ
ejpam-3431	50	6	gr	gr	NOUN
ejpam-3431	50	7	-	-	PUNCT
ejpam-3431	50	8	algebra	algebra	NOUN
ejpam-3431	50	9	h	h	NOUN
ejpam-3431	50	10	is	be	AUX
ejpam-3431	50	11	faithful	faithful	ADJ
ejpam-3431	50	12	if	if	SCONJ
ejpam-3431	50	13	for	for	ADP
ejpam-3431	50	14	all	all	DET
ejpam-3431	50	15	a	a	DET
ejpam-3431	50	16	,	,	PUNCT
ejpam-3431	50	17	b	b	PROPN
ejpam-3431	50	18	⊆	⊆	NUM
ejpam-3431	50	19	h	h	NOUN
ejpam-3431	50	20	,	,	PUNCT
ejpam-3431	50	21	0	0	NUM
ejpam-3431	50	22	∈	∈	PROPN
ejpam-3431	50	23	a	a	DET
ejpam-3431	50	24	~	~	PUNCT
ejpam-3431	50	25	b	b	NOUN
ejpam-3431	50	26	implies	imply	VERB
ejpam-3431	50	27	a	a	DET
ejpam-3431	50	28	�	�	PROPN
ejpam-3431	50	29	b.	b.	PROPN
ejpam-3431	50	30	definition	definition	NOUN
ejpam-3431	50	31	2.6	2.6	NUM
ejpam-3431	50	32	.	.	PUNCT
ejpam-3431	51	1	[	[	X
ejpam-3431	51	2	5	5	X
ejpam-3431	51	3	]	]	PUNCT
ejpam-3431	51	4	let	let	VERB
ejpam-3431	51	5	h	h	PRON
ejpam-3431	51	6	be	be	AUX
ejpam-3431	51	7	a	a	DET
ejpam-3431	51	8	hyper	hyper	ADJ
ejpam-3431	51	9	gr	gr	NOUN
ejpam-3431	51	10	-	-	PUNCT
ejpam-3431	51	11	algebra	algebra	NOUN
ejpam-3431	51	12	and	and	CCONJ
ejpam-3431	51	13	s	s	AUX
ejpam-3431	51	14	be	be	AUX
ejpam-3431	51	15	a	a	DET
ejpam-3431	51	16	subset	subset	NOUN
ejpam-3431	51	17	of	of	ADP
ejpam-3431	51	18	h	h	NOUN
ejpam-3431	51	19	containing	contain	VERB
ejpam-3431	51	20	0	0	NUM
ejpam-3431	51	21	.	.	PUNCT
ejpam-3431	52	1	if	if	SCONJ
ejpam-3431	52	2	s	s	PROPN
ejpam-3431	52	3	is	be	AUX
ejpam-3431	52	4	a	a	DET
ejpam-3431	52	5	hyper	hyper	ADJ
ejpam-3431	52	6	gr	gr	NOUN
ejpam-3431	52	7	-	-	NOUN
ejpam-3431	52	8	algebra	algebra	NOUN
ejpam-3431	52	9	with	with	ADP
ejpam-3431	52	10	respect	respect	NOUN
ejpam-3431	52	11	to	to	ADP
ejpam-3431	52	12	the	the	DET
ejpam-3431	52	13	hyperoperation	hyperoperation	NOUN
ejpam-3431	52	14	~	~	PUNCT
ejpam-3431	52	15	on	on	ADP
ejpam-3431	52	16	h	h	NOUN
ejpam-3431	52	17	,	,	PUNCT
ejpam-3431	52	18	then	then	ADV
ejpam-3431	52	19	we	we	PRON
ejpam-3431	52	20	say	say	VERB
ejpam-3431	52	21	that	that	PRON
ejpam-3431	52	22	s	s	VERB
ejpam-3431	52	23	is	be	AUX
ejpam-3431	52	24	a	a	DET
ejpam-3431	52	25	hyper	hyper	ADJ
ejpam-3431	52	26	subgr	subgr	NOUN
ejpam-3431	52	27	-	-	PUNCT
ejpam-3431	52	28	algebra	algebra	NOUN
ejpam-3431	52	29	of	of	ADP
ejpam-3431	52	30	h.	h.	PROPN
ejpam-3431	52	31	theorem	theorem	PROPN
ejpam-3431	52	32	2.7	2.7	NUM
ejpam-3431	52	33	.	.	PUNCT
ejpam-3431	53	1	[	[	X
ejpam-3431	53	2	5	5	NUM
ejpam-3431	53	3	]	]	PUNCT
ejpam-3431	53	4	(	(	PUNCT
ejpam-3431	53	5	hyper	hyper	ADJ
ejpam-3431	53	6	subgr	subgr	NOUN
ejpam-3431	53	7	-	-	PUNCT
ejpam-3431	53	8	algebra	algebra	NOUN
ejpam-3431	53	9	criterion	criterion	NOUN
ejpam-3431	53	10	)	)	PUNCT
ejpam-3431	53	11	let	let	VERB
ejpam-3431	53	12	h	h	NOUN
ejpam-3431	53	13	be	be	AUX
ejpam-3431	53	14	a	a	DET
ejpam-3431	53	15	hyper	hyper	ADJ
ejpam-3431	53	16	gr	gr	NOUN
ejpam-3431	53	17	-	-	PUNCT
ejpam-3431	53	18	algebra	algebra	NOUN
ejpam-3431	53	19	and	and	CCONJ
ejpam-3431	53	20	s	s	AUX
ejpam-3431	53	21	be	be	AUX
ejpam-3431	53	22	a	a	DET
ejpam-3431	53	23	nonempty	nonempty	ADJ
ejpam-3431	53	24	subset	subset	NOUN
ejpam-3431	53	25	of	of	ADP
ejpam-3431	53	26	h.	h.	PROPN
ejpam-3431	54	1	then	then	ADV
ejpam-3431	54	2	s	s	VERB
ejpam-3431	54	3	is	be	AUX
ejpam-3431	54	4	a	a	DET
ejpam-3431	54	5	hyper	hyper	ADJ
ejpam-3431	54	6	subgr	subgr	NOUN
ejpam-3431	54	7	-	-	PUNCT
ejpam-3431	54	8	algebra	algebra	NOUN
ejpam-3431	54	9	of	of	ADP
ejpam-3431	54	10	h	h	NOUN
ejpam-3431	54	11	if	if	SCONJ
ejpam-3431	55	1	and	and	CCONJ
ejpam-3431	55	2	only	only	ADV
ejpam-3431	55	3	if	if	SCONJ
ejpam-3431	55	4	x~	x~	PROPN
ejpam-3431	55	5	y	y	PROPN
ejpam-3431	55	6	⊆	⊆	NUM
ejpam-3431	55	7	s	s	NOUN
ejpam-3431	55	8	,	,	PUNCT
ejpam-3431	55	9	for	for	ADP
ejpam-3431	55	10	all	all	DET
ejpam-3431	55	11	x	x	NOUN
ejpam-3431	55	12	,	,	PUNCT
ejpam-3431	55	13	y	y	PROPN
ejpam-3431	55	14	∈	∈	PROPN
ejpam-3431	55	15	s.	s.	PROPN
ejpam-3431	55	16	definition	definition	NOUN
ejpam-3431	55	17	2.8	2.8	NUM
ejpam-3431	55	18	.	.	PUNCT
ejpam-3431	56	1	[	[	X
ejpam-3431	56	2	5	5	X
ejpam-3431	56	3	]	]	PUNCT
ejpam-3431	56	4	let	let	VERB
ejpam-3431	56	5	i	i	PRON
ejpam-3431	56	6	be	be	AUX
ejpam-3431	56	7	a	a	DET
ejpam-3431	56	8	subset	subset	NOUN
ejpam-3431	56	9	of	of	ADP
ejpam-3431	56	10	a	a	DET
ejpam-3431	56	11	hyper	hyper	ADJ
ejpam-3431	56	12	gr	gr	NOUN
ejpam-3431	56	13	-	-	PUNCT
ejpam-3431	56	14	algebra	algebra	NOUN
ejpam-3431	56	15	h	h	NOUN
ejpam-3431	56	16	such	such	ADJ
ejpam-3431	56	17	that	that	DET
ejpam-3431	56	18	0	0	NUM
ejpam-3431	56	19	∈	∈	PROPN
ejpam-3431	56	20	i.	i.	NOUN
ejpam-3431	56	21	then	then	ADV
ejpam-3431	56	22	(	(	PUNCT
ejpam-3431	56	23	i	i	NOUN
ejpam-3431	56	24	)	)	PUNCT
ejpam-3431	57	1	i	i	PRON
ejpam-3431	57	2	is	be	AUX
ejpam-3431	57	3	a	a	DET
ejpam-3431	57	4	hyper	hyper	ADJ
ejpam-3431	57	5	gr	gr	NOUN
ejpam-3431	57	6	-	-	PUNCT
ejpam-3431	57	7	ideal	ideal	NOUN
ejpam-3431	57	8	of	of	ADP
ejpam-3431	57	9	h	h	NOUN
ejpam-3431	57	10	if	if	SCONJ
ejpam-3431	57	11	for	for	ADP
ejpam-3431	57	12	all	all	DET
ejpam-3431	57	13	x	x	NOUN
ejpam-3431	57	14	,	,	PUNCT
ejpam-3431	57	15	y	y	PROPN
ejpam-3431	57	16	∈	∈	PROPN
ejpam-3431	57	17	h	h	NOUN
ejpam-3431	57	18	,	,	PUNCT
ejpam-3431	57	19	x~	x~	PROPN
ejpam-3431	57	20	y	y	PROPN
ejpam-3431	57	21	⊆	⊆	NUM
ejpam-3431	57	22	i	i	PROPN
ejpam-3431	57	23	and	and	CCONJ
ejpam-3431	57	24	y	y	PROPN
ejpam-3431	57	25	∈	∈	PROPN
ejpam-3431	58	1	i	i	PRON
ejpam-3431	58	2	imply	imply	VERB
ejpam-3431	58	3	that	that	SCONJ
ejpam-3431	58	4	x	x	X
ejpam-3431	58	5	∈	∈	PROPN
ejpam-3431	58	6	i	i	PRON
ejpam-3431	58	7	;	;	PUNCT
ejpam-3431	58	8	(	(	PUNCT
ejpam-3431	58	9	ii	ii	NOUN
ejpam-3431	58	10	)	)	PUNCT
ejpam-3431	58	11	if	if	SCONJ
ejpam-3431	58	12	h	h	NOUN
ejpam-3431	58	13	is	be	AUX
ejpam-3431	58	14	faithful	faithful	ADJ
ejpam-3431	58	15	such	such	ADJ
ejpam-3431	58	16	that	that	SCONJ
ejpam-3431	58	17	x~	x~	PROPN
ejpam-3431	58	18	x	x	SYM
ejpam-3431	58	19	�	�	PROPN
ejpam-3431	58	20	i	i	PRON
ejpam-3431	58	21	for	for	ADP
ejpam-3431	58	22	all	all	DET
ejpam-3431	58	23	x	x	SYM
ejpam-3431	58	24	∈	∈	PROPN
ejpam-3431	58	25	h	h	NOUN
ejpam-3431	58	26	,	,	PUNCT
ejpam-3431	58	27	then	then	ADV
ejpam-3431	58	28	i	i	PRON
ejpam-3431	58	29	is	be	AUX
ejpam-3431	58	30	gr	gr	ADV
ejpam-3431	58	31	-	-	PUNCT
ejpam-3431	58	32	reflexive	reflexive	ADJ
ejpam-3431	58	33	in	in	ADP
ejpam-3431	58	34	h	h	NOUN
ejpam-3431	58	35	;	;	PUNCT
ejpam-3431	58	36	(	(	PUNCT
ejpam-3431	58	37	iii	iii	X
ejpam-3431	58	38	)	)	PUNCT
ejpam-3431	58	39	i	i	PRON
ejpam-3431	58	40	is	be	AUX
ejpam-3431	58	41	hyper	hyper	ADJ
ejpam-3431	58	42	left	left	NOUN
ejpam-3431	58	43	(	(	PUNCT
ejpam-3431	58	44	resp	resp	NOUN
ejpam-3431	58	45	.	.	PUNCT
ejpam-3431	59	1	hyper	hyper	ADJ
ejpam-3431	59	2	right	right	NOUN
ejpam-3431	59	3	)	)	PUNCT
ejpam-3431	59	4	stable	stable	ADJ
ejpam-3431	59	5	in	in	ADP
ejpam-3431	59	6	h	h	NOUN
ejpam-3431	60	1	if	if	SCONJ
ejpam-3431	60	2	x~	x~	PROPN
ejpam-3431	60	3	a	a	DET
ejpam-3431	60	4	�	�	PROPN
ejpam-3431	60	5	i	i	PRON
ejpam-3431	60	6	(	(	PUNCT
ejpam-3431	60	7	resp	resp	NOUN
ejpam-3431	60	8	.	.	PUNCT
ejpam-3431	61	1	a~	a~	PROPN
ejpam-3431	61	2	x	x	SYM
ejpam-3431	61	3	�	�	PROPN
ejpam-3431	61	4	i	i	PROPN
ejpam-3431	61	5	)	)	PUNCT
ejpam-3431	61	6	for	for	ADP
ejpam-3431	61	7	all	all	DET
ejpam-3431	61	8	x	x	SYM
ejpam-3431	61	9	∈	∈	PROPN
ejpam-3431	61	10	h	h	NOUN
ejpam-3431	61	11	and	and	CCONJ
ejpam-3431	61	12	for	for	ADP
ejpam-3431	61	13	all	all	DET
ejpam-3431	61	14	a	a	DET
ejpam-3431	61	15	∈	∈	NOUN
ejpam-3431	62	1	i	i	PRON
ejpam-3431	62	2	;	;	PUNCT
ejpam-3431	62	3	(	(	PUNCT
ejpam-3431	62	4	iv	iv	X
ejpam-3431	62	5	)	)	PUNCT
ejpam-3431	62	6	i	i	PRON
ejpam-3431	62	7	is	be	AUX
ejpam-3431	62	8	hyper	hyper	ADJ
ejpam-3431	62	9	stable	stable	ADJ
ejpam-3431	62	10	in	in	ADP
ejpam-3431	62	11	h	h	NOUN
ejpam-3431	62	12	if	if	SCONJ
ejpam-3431	62	13	i	i	PRON
ejpam-3431	62	14	is	be	AUX
ejpam-3431	62	15	both	both	PRON
ejpam-3431	62	16	hyper	hyper	ADJ
ejpam-3431	62	17	left	left	ADJ
ejpam-3431	62	18	and	and	CCONJ
ejpam-3431	62	19	hyper	hyper	ADJ
ejpam-3431	62	20	right	right	ADJ
ejpam-3431	62	21	stable	stable	ADJ
ejpam-3431	62	22	in	in	ADP
ejpam-3431	62	23	h	h	NOUN
ejpam-3431	62	24	;	;	PUNCT
ejpam-3431	62	25	(	(	PUNCT
ejpam-3431	62	26	v	v	X
ejpam-3431	62	27	)	)	PUNCT
ejpam-3431	62	28	i	i	PRON
ejpam-3431	62	29	is	be	AUX
ejpam-3431	62	30	hyper	hyper	ADJ
ejpam-3431	62	31	left	left	NOUN
ejpam-3431	62	32	(	(	PUNCT
ejpam-3431	62	33	resp	resp	NOUN
ejpam-3431	62	34	.	.	PUNCT
ejpam-3431	63	1	hyper	hyper	ADJ
ejpam-3431	63	2	right	right	NOUN
ejpam-3431	63	3	)	)	PUNCT
ejpam-3431	63	4	stable	stable	ADJ
ejpam-3431	63	5	gr	gr	NOUN
ejpam-3431	63	6	-	-	PUNCT
ejpam-3431	63	7	ideal	ideal	NOUN
ejpam-3431	63	8	of	of	ADP
ejpam-3431	63	9	h	h	NOUN
ejpam-3431	63	10	if	if	SCONJ
ejpam-3431	63	11	(	(	PUNCT
ejpam-3431	63	12	a	a	X
ejpam-3431	63	13	)	)	PUNCT
ejpam-3431	63	14	i	i	PRON
ejpam-3431	63	15	is	be	AUX
ejpam-3431	63	16	hyper	hyper	ADJ
ejpam-3431	63	17	left	left	NOUN
ejpam-3431	63	18	(	(	PUNCT
ejpam-3431	63	19	resp	resp	NOUN
ejpam-3431	63	20	.	.	PUNCT
ejpam-3431	64	1	hyper	hyper	ADJ
ejpam-3431	64	2	right	right	NOUN
ejpam-3431	64	3	)	)	PUNCT
ejpam-3431	64	4	stable	stable	ADJ
ejpam-3431	64	5	in	in	ADP
ejpam-3431	64	6	h	h	NOUN
ejpam-3431	64	7	;	;	PUNCT
ejpam-3431	64	8	and	and	CCONJ
ejpam-3431	64	9	(	(	PUNCT
ejpam-3431	64	10	b	b	X
ejpam-3431	64	11	)	)	PUNCT
ejpam-3431	65	1	i	i	PRON
ejpam-3431	65	2	is	be	AUX
ejpam-3431	65	3	a	a	DET
ejpam-3431	65	4	hyper	hyper	ADJ
ejpam-3431	65	5	gr	gr	NOUN
ejpam-3431	65	6	-	-	PUNCT
ejpam-3431	65	7	ideal	ideal	NOUN
ejpam-3431	65	8	of	of	ADP
ejpam-3431	65	9	h.	h.	PROPN
ejpam-3431	65	10	(	(	PUNCT
ejpam-3431	65	11	vi	vi	PROPN
ejpam-3431	65	12	)	)	PUNCT
ejpam-3431	65	13	i	i	PRON
ejpam-3431	65	14	is	be	AUX
ejpam-3431	65	15	a	a	DET
ejpam-3431	65	16	hyper	hyper	ADJ
ejpam-3431	65	17	stable	stable	ADJ
ejpam-3431	65	18	gr	gr	NOUN
ejpam-3431	65	19	-	-	PUNCT
ejpam-3431	65	20	ideal	ideal	NOUN
ejpam-3431	65	21	of	of	ADP
ejpam-3431	65	22	h	h	NOUN
ejpam-3431	65	23	if	if	SCONJ
ejpam-3431	65	24	i	i	PRON
ejpam-3431	65	25	is	be	AUX
ejpam-3431	65	26	both	both	PRON
ejpam-3431	65	27	hyper	hyper	ADJ
ejpam-3431	65	28	left	left	ADJ
ejpam-3431	65	29	and	and	CCONJ
ejpam-3431	65	30	hyper	hyper	ADJ
ejpam-3431	65	31	right	right	ADJ
ejpam-3431	65	32	stable	stable	ADJ
ejpam-3431	65	33	gr	gr	NOUN
ejpam-3431	65	34	-	-	PUNCT
ejpam-3431	65	35	ideal	ideal	NOUN
ejpam-3431	65	36	of	of	ADP
ejpam-3431	65	37	h.	h.	PROPN
ejpam-3431	65	38	theorem	theorem	PROPN
ejpam-3431	65	39	2.9	2.9	NUM
ejpam-3431	65	40	.	.	PUNCT
ejpam-3431	66	1	[	[	X
ejpam-3431	66	2	5	5	X
ejpam-3431	66	3	]	]	PUNCT
ejpam-3431	66	4	if	if	SCONJ
ejpam-3431	66	5	{	{	PUNCT
ejpam-3431	66	6	ii|i	ii|i	NOUN
ejpam-3431	66	7	∈	∈	PROPN
ejpam-3431	66	8	λ	λ	PROPN
ejpam-3431	66	9	}	}	PUNCT
ejpam-3431	66	10	is	be	AUX
ejpam-3431	66	11	a	a	DET
ejpam-3431	66	12	nonempty	nonempty	ADJ
ejpam-3431	66	13	collection	collection	NOUN
ejpam-3431	66	14	of	of	ADP
ejpam-3431	66	15	hyper	hyper	ADJ
ejpam-3431	66	16	gr	gr	NOUN
ejpam-3431	66	17	-	-	PUNCT
ejpam-3431	66	18	ideals	ideal	NOUN
ejpam-3431	66	19	of	of	ADP
ejpam-3431	66	20	a	a	DET
ejpam-3431	66	21	hyper	hyper	ADJ
ejpam-3431	66	22	gr	gr	NOUN
ejpam-3431	66	23	-	-	PUNCT
ejpam-3431	66	24	algebra	algebra	NOUN
ejpam-3431	66	25	h	h	NOUN
ejpam-3431	66	26	,	,	PUNCT
ejpam-3431	66	27	then	then	ADV
ejpam-3431	66	28	so	so	ADV
ejpam-3431	66	29	is	be	AUX
ejpam-3431	66	30	⋂	⋂	PROPN
ejpam-3431	66	31	i∈λ	i∈λ	PROPN
ejpam-3431	66	32	ii	ii	PROPN
ejpam-3431	66	33	.	.	PUNCT
ejpam-3431	67	1	definition	definition	NOUN
ejpam-3431	67	2	2.10	2.10	NUM
ejpam-3431	67	3	.	.	PUNCT
ejpam-3431	68	1	[	[	X
ejpam-3431	68	2	5	5	X
ejpam-3431	68	3	]	]	PUNCT
ejpam-3431	68	4	let	let	VERB
ejpam-3431	68	5	h	h	PRON
ejpam-3431	68	6	be	be	AUX
ejpam-3431	68	7	a	a	DET
ejpam-3431	68	8	hyper	hyper	ADJ
ejpam-3431	68	9	gr	gr	NOUN
ejpam-3431	68	10	-	-	PUNCT
ejpam-3431	68	11	algebra	algebra	NOUN
ejpam-3431	68	12	,	,	PUNCT
ejpam-3431	68	13	x	x	PUNCT
ejpam-3431	68	14	a	a	DET
ejpam-3431	68	15	nonempty	nonempty	ADV
ejpam-3431	68	16	proper	proper	ADJ
ejpam-3431	68	17	subset	subset	NOUN
ejpam-3431	68	18	of	of	ADP
ejpam-3431	68	19	h	h	NOUN
ejpam-3431	68	20	,	,	PUNCT
ejpam-3431	68	21	and	and	CCONJ
ejpam-3431	68	22	i	i	PRON
ejpam-3431	68	23	a	a	DET
ejpam-3431	68	24	subset	subset	NOUN
ejpam-3431	68	25	of	of	ADP
ejpam-3431	68	26	h	h	NOUN
ejpam-3431	68	27	such	such	ADJ
ejpam-3431	68	28	that	that	DET
ejpam-3431	68	29	0	0	NUM
ejpam-3431	68	30	∈	∈	PROPN
ejpam-3431	68	31	i.	i.	NOUN
ejpam-3431	68	32	then	then	ADV
ejpam-3431	68	33	(	(	PUNCT
ejpam-3431	68	34	i	i	NOUN
ejpam-3431	68	35	)	)	PUNCT
ejpam-3431	69	1	i	i	PRON
ejpam-3431	69	2	is	be	AUX
ejpam-3431	69	3	a	a	DET
ejpam-3431	69	4	hyper	hyper	ADJ
ejpam-3431	69	5	gr	gr	NOUN
ejpam-3431	69	6	-	-	PUNCT
ejpam-3431	69	7	ideal	ideal	NOUN
ejpam-3431	69	8	of	of	ADP
ejpam-3431	69	9	h	h	NOUN
ejpam-3431	69	10	related	relate	VERB
ejpam-3431	69	11	to	to	ADP
ejpam-3431	69	12	x	x	PRON
ejpam-3431	69	13	if	if	SCONJ
ejpam-3431	69	14	for	for	ADP
ejpam-3431	69	15	all	all	DET
ejpam-3431	69	16	x	x	NOUN
ejpam-3431	69	17	,	,	PUNCT
ejpam-3431	69	18	y	y	PROPN
ejpam-3431	69	19	∈	∈	PROPN
ejpam-3431	69	20	x	x	X
ejpam-3431	69	21	,	,	PUNCT
ejpam-3431	69	22	x	x	X
ejpam-3431	69	23	~	~	PUNCT
ejpam-3431	69	24	y	y	PROPN
ejpam-3431	69	25	⊆	⊆	NUM
ejpam-3431	69	26	i	i	PROPN
ejpam-3431	69	27	and	and	CCONJ
ejpam-3431	69	28	y	y	PROPN
ejpam-3431	69	29	∈	∈	PROPN
ejpam-3431	69	30	i	i	PRON
ejpam-3431	69	31	imply	imply	VERB
ejpam-3431	69	32	that	that	SCONJ
ejpam-3431	69	33	x	x	X
ejpam-3431	69	34	∈	∈	PROPN
ejpam-3431	70	1	i	i	PRON
ejpam-3431	70	2	;	;	PUNCT
ejpam-3431	70	3	(	(	PUNCT
ejpam-3431	70	4	ii	ii	X
ejpam-3431	70	5	)	)	PUNCT
ejpam-3431	71	1	i	i	PRON
ejpam-3431	71	2	is	be	AUX
ejpam-3431	71	3	hyper	hyper	ADJ
ejpam-3431	71	4	left	left	NOUN
ejpam-3431	71	5	(	(	PUNCT
ejpam-3431	71	6	resp	resp	NOUN
ejpam-3431	71	7	.	.	PUNCT
ejpam-3431	72	1	hyper	hyper	ADJ
ejpam-3431	72	2	right	right	NOUN
ejpam-3431	72	3	)	)	PUNCT
ejpam-3431	72	4	stable	stable	ADJ
ejpam-3431	72	5	in	in	ADP
ejpam-3431	72	6	h	h	NOUN
ejpam-3431	72	7	related	relate	VERB
ejpam-3431	72	8	to	to	ADP
ejpam-3431	72	9	x	x	PUNCT
ejpam-3431	72	10	if	if	SCONJ
ejpam-3431	72	11	x	x	X
ejpam-3431	72	12	~	~	PUNCT
ejpam-3431	72	13	a	a	DET
ejpam-3431	72	14	�	�	PROPN
ejpam-3431	72	15	i	i	PRON
ejpam-3431	72	16	(	(	PUNCT
ejpam-3431	72	17	resp	resp	NOUN
ejpam-3431	72	18	.	.	PUNCT
ejpam-3431	73	1	a~	a~	PROPN
ejpam-3431	73	2	x	x	SYM
ejpam-3431	73	3	�	�	PROPN
ejpam-3431	73	4	i	i	PROPN
ejpam-3431	73	5	)	)	PUNCT
ejpam-3431	73	6	for	for	ADP
ejpam-3431	73	7	all	all	DET
ejpam-3431	73	8	x	x	SYM
ejpam-3431	73	9	∈	∈	PROPN
ejpam-3431	73	10	x	x	X
ejpam-3431	73	11	and	and	CCONJ
ejpam-3431	73	12	for	for	ADP
ejpam-3431	73	13	all	all	DET
ejpam-3431	73	14	a	a	DET
ejpam-3431	73	15	∈	∈	NOUN
ejpam-3431	73	16	i	i	PRON
ejpam-3431	73	17	;	;	PUNCT
ejpam-3431	73	18	r.	r.	PROPN
ejpam-3431	73	19	manzano	manzano	PROPN
ejpam-3431	73	20	,	,	PUNCT
ejpam-3431	73	21	jr	jr	PROPN
ejpam-3431	73	22	.	.	PROPN
ejpam-3431	73	23	,	,	PUNCT
ejpam-3431	73	24	g.	g.	PROPN
ejpam-3431	73	25	petalcorin	petalcorin	PROPN
ejpam-3431	73	26	,	,	PUNCT
ejpam-3431	73	27	jr	jr	PROPN
ejpam-3431	73	28	.	.	PROPN
ejpam-3431	73	29	/	/	SYM
ejpam-3431	73	30	eur	eur	PROPN
ejpam-3431	73	31	.	.	PUNCT
ejpam-3431	74	1	j.	j.	PROPN
ejpam-3431	74	2	pure	pure	PROPN
ejpam-3431	74	3	appl	appl	PROPN
ejpam-3431	74	4	.	.	PROPN
ejpam-3431	74	5	math	math	PROPN
ejpam-3431	74	6	,	,	PUNCT
ejpam-3431	74	7	12	12	NUM
ejpam-3431	74	8	(	(	PUNCT
ejpam-3431	74	9	3	3	NUM
ejpam-3431	74	10	)	)	PUNCT
ejpam-3431	74	11	(	(	PUNCT
ejpam-3431	74	12	2019	2019	NUM
ejpam-3431	74	13	)	)	PUNCT
ejpam-3431	74	14	,	,	PUNCT
ejpam-3431	74	15	821	821	NUM
ejpam-3431	74	16	-	-	SYM
ejpam-3431	74	17	833	833	NUM
ejpam-3431	74	18	824	824	NUM
ejpam-3431	74	19	(	(	PUNCT
ejpam-3431	74	20	iii	iii	X
ejpam-3431	74	21	)	)	PUNCT
ejpam-3431	74	22	i	i	PRON
ejpam-3431	74	23	is	be	AUX
ejpam-3431	74	24	hyper	hyper	ADJ
ejpam-3431	74	25	stable	stable	ADJ
ejpam-3431	74	26	in	in	ADP
ejpam-3431	74	27	h	h	NOUN
ejpam-3431	74	28	related	relate	VERB
ejpam-3431	74	29	to	to	ADP
ejpam-3431	74	30	x	x	PRON
ejpam-3431	74	31	if	if	SCONJ
ejpam-3431	74	32	i	i	PRON
ejpam-3431	74	33	is	be	AUX
ejpam-3431	74	34	both	both	PRON
ejpam-3431	74	35	hyper	hyper	ADJ
ejpam-3431	74	36	left	left	ADJ
ejpam-3431	74	37	and	and	CCONJ
ejpam-3431	74	38	hyper	hyper	ADJ
ejpam-3431	74	39	right	right	ADJ
ejpam-3431	74	40	stable	stable	ADJ
ejpam-3431	74	41	in	in	ADP
ejpam-3431	74	42	h	h	NOUN
ejpam-3431	74	43	related	relate	VERB
ejpam-3431	74	44	to	to	ADP
ejpam-3431	74	45	x	x	PRON
ejpam-3431	74	46	;	;	PUNCT
ejpam-3431	74	47	(	(	PUNCT
ejpam-3431	74	48	iv	iv	X
ejpam-3431	74	49	)	)	PUNCT
ejpam-3431	74	50	i	i	PRON
ejpam-3431	74	51	is	be	AUX
ejpam-3431	74	52	hyper	hyper	ADJ
ejpam-3431	74	53	left	left	NOUN
ejpam-3431	74	54	(	(	PUNCT
ejpam-3431	74	55	resp	resp	NOUN
ejpam-3431	74	56	.	.	PUNCT
ejpam-3431	75	1	hyper	hyper	ADJ
ejpam-3431	75	2	right	right	NOUN
ejpam-3431	75	3	)	)	PUNCT
ejpam-3431	75	4	stable	stable	ADJ
ejpam-3431	75	5	gr	gr	NOUN
ejpam-3431	75	6	-	-	PUNCT
ejpam-3431	75	7	ideal	ideal	NOUN
ejpam-3431	75	8	of	of	ADP
ejpam-3431	75	9	h	h	NOUN
ejpam-3431	75	10	related	relate	VERB
ejpam-3431	75	11	to	to	ADP
ejpam-3431	75	12	x	x	PRON
ejpam-3431	75	13	if	if	SCONJ
ejpam-3431	75	14	(	(	PUNCT
ejpam-3431	75	15	a	a	X
ejpam-3431	75	16	)	)	PUNCT
ejpam-3431	75	17	i	i	PRON
ejpam-3431	75	18	is	be	AUX
ejpam-3431	75	19	hyper	hyper	ADJ
ejpam-3431	75	20	left	left	NOUN
ejpam-3431	75	21	(	(	PUNCT
ejpam-3431	75	22	resp	resp	NOUN
ejpam-3431	75	23	.	.	PUNCT
ejpam-3431	76	1	hyper	hyper	ADJ
ejpam-3431	76	2	right	right	NOUN
ejpam-3431	76	3	)	)	PUNCT
ejpam-3431	76	4	stable	stable	ADJ
ejpam-3431	76	5	in	in	ADP
ejpam-3431	76	6	h	h	NOUN
ejpam-3431	76	7	related	relate	VERB
ejpam-3431	76	8	to	to	ADP
ejpam-3431	76	9	x	x	PRON
ejpam-3431	76	10	;	;	PUNCT
ejpam-3431	76	11	and	and	CCONJ
ejpam-3431	76	12	(	(	PUNCT
ejpam-3431	76	13	b	b	X
ejpam-3431	76	14	)	)	PUNCT
ejpam-3431	77	1	i	i	PRON
ejpam-3431	77	2	is	be	AUX
ejpam-3431	77	3	a	a	DET
ejpam-3431	77	4	hyper	hyper	ADJ
ejpam-3431	77	5	gr	gr	NOUN
ejpam-3431	77	6	-	-	PUNCT
ejpam-3431	77	7	ideal	ideal	NOUN
ejpam-3431	77	8	of	of	ADP
ejpam-3431	77	9	h	h	NOUN
ejpam-3431	77	10	related	relate	VERB
ejpam-3431	77	11	to	to	ADP
ejpam-3431	77	12	x.	x.	NOUN
ejpam-3431	77	13	(	(	PUNCT
ejpam-3431	77	14	v	v	NOUN
ejpam-3431	77	15	)	)	PUNCT
ejpam-3431	78	1	i	i	PRON
ejpam-3431	78	2	is	be	AUX
ejpam-3431	78	3	a	a	DET
ejpam-3431	78	4	hyper	hyper	ADJ
ejpam-3431	78	5	stable	stable	ADJ
ejpam-3431	78	6	gr	gr	NOUN
ejpam-3431	78	7	-	-	PUNCT
ejpam-3431	78	8	ideal	ideal	NOUN
ejpam-3431	78	9	of	of	ADP
ejpam-3431	78	10	h	h	NOUN
ejpam-3431	78	11	related	relate	VERB
ejpam-3431	78	12	to	to	ADP
ejpam-3431	78	13	x	x	PRON
ejpam-3431	78	14	if	if	SCONJ
ejpam-3431	78	15	i	i	PRON
ejpam-3431	78	16	is	be	AUX
ejpam-3431	78	17	both	both	PRON
ejpam-3431	78	18	hyper	hyper	ADJ
ejpam-3431	78	19	left	left	ADJ
ejpam-3431	78	20	and	and	CCONJ
ejpam-3431	78	21	hyper	hyper	ADJ
ejpam-3431	78	22	right	right	ADJ
ejpam-3431	78	23	stable	stable	ADJ
ejpam-3431	78	24	gr	gr	NOUN
ejpam-3431	78	25	-	-	PUNCT
ejpam-3431	78	26	ideal	ideal	NOUN
ejpam-3431	78	27	of	of	ADP
ejpam-3431	78	28	h	h	NOUN
ejpam-3431	78	29	related	relate	VERB
ejpam-3431	78	30	to	to	ADP
ejpam-3431	78	31	x.	x.	NOUN
ejpam-3431	78	32	3	3	NUM
ejpam-3431	78	33	.	.	X
ejpam-3431	78	34	pseudo	pseudo	NOUN
ejpam-3431	78	35	hyper	hyper	ADJ
ejpam-3431	78	36	gr	gr	NOUN
ejpam-3431	78	37	-	-	PUNCT
ejpam-3431	78	38	ideals	ideal	NOUN
ejpam-3431	78	39	in	in	ADP
ejpam-3431	78	40	this	this	DET
ejpam-3431	78	41	section	section	NOUN
ejpam-3431	78	42	we	we	PRON
ejpam-3431	78	43	will	will	AUX
ejpam-3431	78	44	define	define	VERB
ejpam-3431	78	45	a	a	DET
ejpam-3431	78	46	pseudo	pseudo	NOUN
ejpam-3431	78	47	hyper	hyper	ADJ
ejpam-3431	78	48	gr	gr	NOUN
ejpam-3431	78	49	-	-	PUNCT
ejpam-3431	78	50	algebra	algebra	NOUN
ejpam-3431	78	51	and	and	CCONJ
ejpam-3431	78	52	the	the	DET
ejpam-3431	78	53	different	different	ADJ
ejpam-3431	78	54	types	type	NOUN
ejpam-3431	78	55	of	of	ADP
ejpam-3431	78	56	pseudo	pseudo	NOUN
ejpam-3431	78	57	hyper	hyper	ADJ
ejpam-3431	78	58	gr	gr	NOUN
ejpam-3431	78	59	-	-	PUNCT
ejpam-3431	78	60	ideals	ideal	NOUN
ejpam-3431	78	61	.	.	PUNCT
ejpam-3431	79	1	also	also	ADV
ejpam-3431	79	2	,	,	PUNCT
ejpam-3431	79	3	relationship	relationship	NOUN
ejpam-3431	79	4	among	among	ADP
ejpam-3431	79	5	the	the	DET
ejpam-3431	79	6	twelve	twelve	NUM
ejpam-3431	79	7	types	type	NOUN
ejpam-3431	79	8	of	of	ADP
ejpam-3431	79	9	these	these	DET
ejpam-3431	79	10	ideals	ideal	NOUN
ejpam-3431	79	11	are	be	AUX
ejpam-3431	79	12	discussed	discuss	VERB
ejpam-3431	79	13	.	.	PUNCT
ejpam-3431	80	1	definition	definition	NOUN
ejpam-3431	80	2	3.1	3.1	NUM
ejpam-3431	80	3	.	.	PUNCT
ejpam-3431	81	1	let	let	AUX
ejpam-3431	81	2	h	h	PRON
ejpam-3431	81	3	be	be	AUX
ejpam-3431	81	4	a	a	DET
ejpam-3431	81	5	nonempty	nonempty	ADV
ejpam-3431	81	6	set	set	VERB
ejpam-3431	81	7	with	with	ADP
ejpam-3431	81	8	“	"	PUNCT
ejpam-3431	81	9	~	~	NOUN
ejpam-3431	81	10	”	"	PUNCT
ejpam-3431	81	11	and	and	CCONJ
ejpam-3431	81	12	“	"	PUNCT
ejpam-3431	81	13	◦	◦	NOUN
ejpam-3431	81	14	”	"	PUNCT
ejpam-3431	81	15	be	be	AUX
ejpam-3431	81	16	the	the	DET
ejpam-3431	81	17	two	two	NUM
ejpam-3431	81	18	hyperoperations	hyperoperation	NOUN
ejpam-3431	81	19	on	on	ADP
ejpam-3431	81	20	h.	h.	PROPN
ejpam-3431	81	21	then	then	ADV
ejpam-3431	81	22	(	(	PUNCT
ejpam-3431	81	23	h;~	h;~	NOUN
ejpam-3431	81	24	,	,	PUNCT
ejpam-3431	81	25	◦	◦	NOUN
ejpam-3431	81	26	,	,	PUNCT
ejpam-3431	81	27	0	0	NUM
ejpam-3431	81	28	)	)	PUNCT
ejpam-3431	81	29	is	be	AUX
ejpam-3431	81	30	called	call	VERB
ejpam-3431	81	31	a	a	DET
ejpam-3431	81	32	pseudo	pseudo	NOUN
ejpam-3431	81	33	hyper	hyper	ADJ
ejpam-3431	81	34	gr	gr	NOUN
ejpam-3431	81	35	-	-	PUNCT
ejpam-3431	81	36	algebra	algebra	NOUN
ejpam-3431	81	37	,	,	PUNCT
ejpam-3431	81	38	if	if	SCONJ
ejpam-3431	81	39	it	it	PRON
ejpam-3431	81	40	contains	contain	VERB
ejpam-3431	81	41	a	a	DET
ejpam-3431	81	42	constant	constant	ADJ
ejpam-3431	81	43	0	0	NUM
ejpam-3431	81	44	∈	∈	PROPN
ejpam-3431	81	45	h	h	NOUN
ejpam-3431	81	46	and	and	CCONJ
ejpam-3431	81	47	for	for	ADP
ejpam-3431	81	48	all	all	DET
ejpam-3431	81	49	x	x	NOUN
ejpam-3431	81	50	,	,	PUNCT
ejpam-3431	81	51	y	y	PROPN
ejpam-3431	81	52	,	,	PUNCT
ejpam-3431	81	53	z	z	PROPN
ejpam-3431	81	54	∈	∈	PROPN
ejpam-3431	81	55	h	h	NOUN
ejpam-3431	81	56	,	,	PUNCT
ejpam-3431	81	57	the	the	DET
ejpam-3431	81	58	following	follow	VERB
ejpam-3431	81	59	conditions	condition	NOUN
ejpam-3431	81	60	are	be	AUX
ejpam-3431	81	61	satisfied	satisfied	ADJ
ejpam-3431	81	62	:	:	PUNCT
ejpam-3431	82	1	[	[	X
ejpam-3431	82	2	phgr1	phgr1	X
ejpam-3431	82	3	]	]	X
ejpam-3431	82	4	(	(	PUNCT
ejpam-3431	82	5	x	x	SYM
ejpam-3431	82	6	◦	◦	NOUN
ejpam-3431	82	7	z	z	NOUN
ejpam-3431	82	8	)	)	PUNCT
ejpam-3431	82	9	◦	◦	NOUN
ejpam-3431	82	10	(	(	PUNCT
ejpam-3431	82	11	y	y	PROPN
ejpam-3431	82	12	◦	◦	PROPN
ejpam-3431	82	13	z	z	PROPN
ejpam-3431	82	14	)	)	PUNCT
ejpam-3431	82	15	�	�	PROPN
ejpam-3431	82	16	x	x	SYM
ejpam-3431	82	17	◦	◦	NOUN
ejpam-3431	82	18	y	y	PROPN
ejpam-3431	82	19	and	and	CCONJ
ejpam-3431	82	20	(	(	PUNCT
ejpam-3431	82	21	x~	x~	PROPN
ejpam-3431	82	22	z)~	z)~	PROPN
ejpam-3431	82	23	(	(	PUNCT
ejpam-3431	82	24	y	y	PROPN
ejpam-3431	82	25	~	~	PUNCT
ejpam-3431	82	26	z	z	X
ejpam-3431	82	27	)	)	PUNCT
ejpam-3431	82	28	�	�	PROPN
ejpam-3431	82	29	x~	x~	NUM
ejpam-3431	82	30	y	y	PROPN
ejpam-3431	82	31	;	;	PUNCT
ejpam-3431	82	32	[	[	X
ejpam-3431	82	33	phgr2	phgr2	NOUN
ejpam-3431	82	34	]	]	X
ejpam-3431	82	35	(	(	PUNCT
ejpam-3431	82	36	x	x	X
ejpam-3431	82	37	◦	◦	NOUN
ejpam-3431	82	38	y)~	y)~	NOUN
ejpam-3431	82	39	z	z	NOUN
ejpam-3431	83	1	=	=	SYM
ejpam-3431	83	2	(	(	PUNCT
ejpam-3431	83	3	x~	x~	PROPN
ejpam-3431	83	4	z	z	X
ejpam-3431	83	5	)	)	PUNCT
ejpam-3431	83	6	◦	◦	NOUN
ejpam-3431	83	7	y	y	NOUN
ejpam-3431	83	8	;	;	PUNCT
ejpam-3431	83	9	[	[	X
ejpam-3431	83	10	phgr3	phgr3	X
ejpam-3431	83	11	]	]	PUNCT
ejpam-3431	83	12	0	0	PUNCT
ejpam-3431	84	1	∈	∈	PROPN
ejpam-3431	84	2	x~	x~	PUNCT
ejpam-3431	84	3	x	x	PUNCT
ejpam-3431	84	4	and	and	CCONJ
ejpam-3431	84	5	0	0	NUM
ejpam-3431	84	6	∈	∈	NOUN
ejpam-3431	84	7	x	x	PUNCT
ejpam-3431	84	8	◦	◦	NOUN
ejpam-3431	84	9	x	x	SYM
ejpam-3431	84	10	;	;	PUNCT
ejpam-3431	84	11	[	[	X
ejpam-3431	84	12	phgr4	phgr4	X
ejpam-3431	84	13	]	]	X
ejpam-3431	84	14	0	0	PUNCT
ejpam-3431	85	1	◦	◦	NOUN
ejpam-3431	85	2	(	(	PUNCT
ejpam-3431	85	3	0~	0~	NOUN
ejpam-3431	85	4	x	x	SYM
ejpam-3431	85	5	)	)	PUNCT
ejpam-3431	85	6	�	�	PROPN
ejpam-3431	85	7	x	x	SYM
ejpam-3431	85	8	,	,	PUNCT
ejpam-3431	85	9	for	for	ADP
ejpam-3431	85	10	all	all	DET
ejpam-3431	85	11	x	x	PUNCT
ejpam-3431	85	12	6=	6=	ADP
ejpam-3431	85	13	0	0	NUM
ejpam-3431	85	14	;	;	PUNCT
ejpam-3431	85	15	and	and	CCONJ
ejpam-3431	85	16	[	[	X
ejpam-3431	85	17	phgr5	phgr5	X
ejpam-3431	85	18	]	]	X
ejpam-3431	85	19	(	(	PUNCT
ejpam-3431	85	20	x~	x~	PROPN
ejpam-3431	85	21	y)~	y)~	PROPN
ejpam-3431	85	22	z	z	PROPN
ejpam-3431	85	23	�	�	PROPN
ejpam-3431	85	24	y	y	PROPN
ejpam-3431	85	25	◦	◦	PROPN
ejpam-3431	85	26	z.	z.	PROPN
ejpam-3431	85	27	where	where	SCONJ
ejpam-3431	85	28	x	x	X
ejpam-3431	85	29	�	�	PROPN
ejpam-3431	85	30	y	y	PROPN
ejpam-3431	85	31	if	if	SCONJ
ejpam-3431	85	32	and	and	CCONJ
ejpam-3431	85	33	only	only	ADV
ejpam-3431	85	34	if	if	SCONJ
ejpam-3431	85	35	0	0	NUM
ejpam-3431	85	36	∈	∈	NOUN
ejpam-3431	85	37	x	x	VERB
ejpam-3431	85	38	◦	◦	NOUN
ejpam-3431	85	39	y	y	NOUN
ejpam-3431	85	40	and	and	CCONJ
ejpam-3431	85	41	0	0	NUM
ejpam-3431	85	42	∈	∈	PROPN
ejpam-3431	85	43	x~	x~	NUM
ejpam-3431	85	44	y	y	PROPN
ejpam-3431	85	45	,	,	PUNCT
ejpam-3431	85	46	and	and	CCONJ
ejpam-3431	85	47	for	for	ADP
ejpam-3431	85	48	every	every	DET
ejpam-3431	85	49	a	a	PROPN
ejpam-3431	85	50	,	,	PUNCT
ejpam-3431	85	51	b	b	PROPN
ejpam-3431	85	52	⊆	⊆	NUM
ejpam-3431	85	53	h	h	NOUN
ejpam-3431	85	54	,	,	PUNCT
ejpam-3431	85	55	a	a	DET
ejpam-3431	85	56	�	�	PROPN
ejpam-3431	85	57	b	b	PROPN
ejpam-3431	85	58	means	mean	VERB
ejpam-3431	85	59	that	that	SCONJ
ejpam-3431	85	60	for	for	ADP
ejpam-3431	85	61	every	every	DET
ejpam-3431	85	62	a	a	DET
ejpam-3431	85	63	∈	∈	PROPN
ejpam-3431	85	64	a	a	PRON
ejpam-3431	85	65	,	,	PUNCT
ejpam-3431	85	66	there	there	PRON
ejpam-3431	85	67	exists	exist	VERB
ejpam-3431	85	68	b	b	PROPN
ejpam-3431	85	69	∈	∈	PROPN
ejpam-3431	85	70	b	b	NOUN
ejpam-3431	85	71	such	such	ADJ
ejpam-3431	85	72	that	that	SCONJ
ejpam-3431	85	73	a	a	DET
ejpam-3431	85	74	�	�	PROPN
ejpam-3431	85	75	b.	b.	PROPN
ejpam-3431	85	76	throughout	throughout	ADP
ejpam-3431	85	77	this	this	DET
ejpam-3431	85	78	chapter	chapter	NOUN
ejpam-3431	85	79	,	,	PUNCT
ejpam-3431	85	80	we	we	PRON
ejpam-3431	85	81	denote	denote	VERB
ejpam-3431	85	82	a	a	DET
ejpam-3431	85	83	pseudo	pseudo	NOUN
ejpam-3431	85	84	hyper	hyper	ADJ
ejpam-3431	85	85	gr	gr	NOUN
ejpam-3431	85	86	-	-	PUNCT
ejpam-3431	85	87	algebra	algebra	NOUN
ejpam-3431	85	88	(	(	PUNCT
ejpam-3431	85	89	h,~	h,~	NOUN
ejpam-3431	85	90	,	,	PUNCT
ejpam-3431	85	91	◦	◦	NOUN
ejpam-3431	85	92	,	,	PUNCT
ejpam-3431	85	93	0	0	NUM
ejpam-3431	85	94	)	)	PUNCT
ejpam-3431	85	95	simply	simply	ADV
ejpam-3431	85	96	by	by	ADP
ejpam-3431	85	97	h	h	NOUN
ejpam-3431	85	98	,	,	PUNCT
ejpam-3431	85	99	unless	unless	SCONJ
ejpam-3431	85	100	otherwise	otherwise	ADV
ejpam-3431	85	101	stated	state	VERB
ejpam-3431	85	102	.	.	PUNCT
ejpam-3431	86	1	example	example	NOUN
ejpam-3431	86	2	3.2	3.2	NUM
ejpam-3431	86	3	.	.	PUNCT
ejpam-3431	87	1	let	let	VERB
ejpam-3431	87	2	h	h	NOUN
ejpam-3431	87	3	=	=	PRON
ejpam-3431	87	4	{	{	PUNCT
ejpam-3431	87	5	0	0	NUM
ejpam-3431	87	6	,	,	PUNCT
ejpam-3431	87	7	1	1	NUM
ejpam-3431	87	8	,	,	PUNCT
ejpam-3431	87	9	2	2	NUM
ejpam-3431	87	10	,	,	PUNCT
ejpam-3431	87	11	3	3	NUM
ejpam-3431	87	12	}	}	PUNCT
ejpam-3431	87	13	and	and	CCONJ
ejpam-3431	87	14	consider	consider	VERB
ejpam-3431	87	15	the	the	DET
ejpam-3431	87	16	following	follow	VERB
ejpam-3431	87	17	cayley	cayley	ADJ
ejpam-3431	87	18	tables	table	NOUN
ejpam-3431	87	19	below	below	ADV
ejpam-3431	87	20	.	.	PUNCT
ejpam-3431	88	1	~	~	PUNCT
ejpam-3431	88	2	0	0	NUM
ejpam-3431	89	1	1	1	NUM
ejpam-3431	89	2	2	2	NUM
ejpam-3431	89	3	3	3	NUM
ejpam-3431	89	4	0	0	NUM
ejpam-3431	89	5	{	{	PUNCT
ejpam-3431	89	6	0	0	NUM
ejpam-3431	89	7	,	,	PUNCT
ejpam-3431	89	8	1	1	NUM
ejpam-3431	89	9	}	}	PUNCT
ejpam-3431	89	10	{	{	PUNCT
ejpam-3431	89	11	0	0	NUM
ejpam-3431	89	12	,	,	PUNCT
ejpam-3431	89	13	1	1	NUM
ejpam-3431	89	14	}	}	PUNCT
ejpam-3431	89	15	{	{	PUNCT
ejpam-3431	89	16	0	0	NUM
ejpam-3431	89	17	,	,	PUNCT
ejpam-3431	89	18	1	1	NUM
ejpam-3431	89	19	}	}	PUNCT
ejpam-3431	89	20	{	{	PUNCT
ejpam-3431	89	21	0	0	NUM
ejpam-3431	89	22	,	,	PUNCT
ejpam-3431	89	23	1	1	NUM
ejpam-3431	89	24	}	}	SYM
ejpam-3431	89	25	1	1	NUM
ejpam-3431	89	26	{	{	PUNCT
ejpam-3431	89	27	0	0	NUM
ejpam-3431	89	28	,	,	PUNCT
ejpam-3431	89	29	1	1	NUM
ejpam-3431	89	30	}	}	PUNCT
ejpam-3431	89	31	{	{	PUNCT
ejpam-3431	89	32	0	0	NUM
ejpam-3431	89	33	,	,	PUNCT
ejpam-3431	89	34	1	1	NUM
ejpam-3431	89	35	}	}	PUNCT
ejpam-3431	89	36	{	{	PUNCT
ejpam-3431	89	37	0	0	NUM
ejpam-3431	89	38	,	,	PUNCT
ejpam-3431	89	39	1	1	NUM
ejpam-3431	89	40	}	}	PUNCT
ejpam-3431	89	41	{	{	PUNCT
ejpam-3431	89	42	0	0	NUM
ejpam-3431	89	43	,	,	PUNCT
ejpam-3431	89	44	1	1	NUM
ejpam-3431	89	45	}	}	SYM
ejpam-3431	89	46	2	2	NUM
ejpam-3431	89	47	{	{	PUNCT
ejpam-3431	89	48	0	0	NUM
ejpam-3431	89	49	,	,	PUNCT
ejpam-3431	89	50	2	2	NUM
ejpam-3431	89	51	}	}	PUNCT
ejpam-3431	89	52	{	{	PUNCT
ejpam-3431	89	53	0	0	NUM
ejpam-3431	89	54	,	,	PUNCT
ejpam-3431	89	55	1	1	NUM
ejpam-3431	89	56	,	,	PUNCT
ejpam-3431	89	57	2	2	NUM
ejpam-3431	89	58	}	}	PUNCT
ejpam-3431	89	59	{	{	PUNCT
ejpam-3431	89	60	0	0	NUM
ejpam-3431	89	61	,	,	PUNCT
ejpam-3431	89	62	2	2	NUM
ejpam-3431	89	63	}	}	PUNCT
ejpam-3431	89	64	{	{	PUNCT
ejpam-3431	89	65	0	0	NUM
ejpam-3431	89	66	,	,	PUNCT
ejpam-3431	89	67	1	1	NUM
ejpam-3431	89	68	,	,	PUNCT
ejpam-3431	89	69	2	2	NUM
ejpam-3431	89	70	}	}	SYM
ejpam-3431	89	71	3	3	NUM
ejpam-3431	89	72	{	{	PUNCT
ejpam-3431	89	73	0	0	NUM
ejpam-3431	89	74	,	,	PUNCT
ejpam-3431	89	75	1	1	NUM
ejpam-3431	89	76	,	,	PUNCT
ejpam-3431	89	77	2	2	NUM
ejpam-3431	89	78	}	}	PUNCT
ejpam-3431	89	79	{	{	PUNCT
ejpam-3431	89	80	0	0	NUM
ejpam-3431	89	81	,	,	PUNCT
ejpam-3431	89	82	3	3	NUM
ejpam-3431	89	83	}	}	PUNCT
ejpam-3431	89	84	{	{	PUNCT
ejpam-3431	89	85	0	0	NUM
ejpam-3431	89	86	,	,	PUNCT
ejpam-3431	89	87	1	1	NUM
ejpam-3431	89	88	,	,	PUNCT
ejpam-3431	89	89	3	3	NUM
ejpam-3431	89	90	}	}	PUNCT
ejpam-3431	89	91	{	{	PUNCT
ejpam-3431	89	92	0	0	NUM
ejpam-3431	89	93	,	,	PUNCT
ejpam-3431	89	94	3	3	NUM
ejpam-3431	89	95	}	}	PUNCT
ejpam-3431	89	96	r.	r.	PROPN
ejpam-3431	89	97	manzano	manzano	PROPN
ejpam-3431	89	98	,	,	PUNCT
ejpam-3431	89	99	jr	jr	PROPN
ejpam-3431	89	100	.	.	PROPN
ejpam-3431	89	101	,	,	PUNCT
ejpam-3431	89	102	g.	g.	PROPN
ejpam-3431	89	103	petalcorin	petalcorin	PROPN
ejpam-3431	89	104	,	,	PUNCT
ejpam-3431	89	105	jr	jr	PROPN
ejpam-3431	89	106	.	.	PROPN
ejpam-3431	89	107	/	/	SYM
ejpam-3431	89	108	eur	eur	PROPN
ejpam-3431	89	109	.	.	PUNCT
ejpam-3431	90	1	j.	j.	PROPN
ejpam-3431	90	2	pure	pure	PROPN
ejpam-3431	90	3	appl	appl	PROPN
ejpam-3431	90	4	.	.	PROPN
ejpam-3431	90	5	math	math	PROPN
ejpam-3431	90	6	,	,	PUNCT
ejpam-3431	90	7	12	12	NUM
ejpam-3431	90	8	(	(	PUNCT
ejpam-3431	90	9	3	3	NUM
ejpam-3431	90	10	)	)	PUNCT
ejpam-3431	90	11	(	(	PUNCT
ejpam-3431	90	12	2019	2019	NUM
ejpam-3431	90	13	)	)	PUNCT
ejpam-3431	90	14	,	,	PUNCT
ejpam-3431	90	15	821	821	NUM
ejpam-3431	90	16	-	-	SYM
ejpam-3431	90	17	833	833	NUM
ejpam-3431	90	18	825	825	NUM
ejpam-3431	90	19	◦	◦	NOUN
ejpam-3431	90	20	0	0	NUM
ejpam-3431	90	21	1	1	NUM
ejpam-3431	90	22	2	2	NUM
ejpam-3431	90	23	3	3	NUM
ejpam-3431	90	24	0	0	NUM
ejpam-3431	90	25	{	{	PUNCT
ejpam-3431	90	26	0	0	NUM
ejpam-3431	90	27	,	,	PUNCT
ejpam-3431	90	28	1	1	NUM
ejpam-3431	90	29	}	}	PUNCT
ejpam-3431	90	30	{	{	PUNCT
ejpam-3431	90	31	0	0	NUM
ejpam-3431	90	32	,	,	PUNCT
ejpam-3431	90	33	1	1	NUM
ejpam-3431	90	34	}	}	PUNCT
ejpam-3431	90	35	{	{	PUNCT
ejpam-3431	90	36	0	0	NUM
ejpam-3431	90	37	,	,	PUNCT
ejpam-3431	90	38	1	1	NUM
ejpam-3431	90	39	}	}	PUNCT
ejpam-3431	90	40	{	{	PUNCT
ejpam-3431	90	41	0	0	NUM
ejpam-3431	90	42	,	,	PUNCT
ejpam-3431	90	43	1	1	NUM
ejpam-3431	90	44	}	}	SYM
ejpam-3431	90	45	1	1	NUM
ejpam-3431	90	46	{	{	PUNCT
ejpam-3431	90	47	1	1	NUM
ejpam-3431	90	48	}	}	PUNCT
ejpam-3431	90	49	{	{	PUNCT
ejpam-3431	90	50	0	0	NUM
ejpam-3431	90	51	,	,	PUNCT
ejpam-3431	90	52	1	1	NUM
ejpam-3431	90	53	}	}	PUNCT
ejpam-3431	90	54	{	{	PUNCT
ejpam-3431	90	55	0	0	NUM
ejpam-3431	90	56	,	,	PUNCT
ejpam-3431	90	57	1	1	NUM
ejpam-3431	90	58	}	}	PUNCT
ejpam-3431	90	59	{	{	PUNCT
ejpam-3431	90	60	0	0	NUM
ejpam-3431	90	61	,	,	PUNCT
ejpam-3431	90	62	1	1	NUM
ejpam-3431	90	63	}	}	SYM
ejpam-3431	90	64	2	2	NUM
ejpam-3431	90	65	{	{	PUNCT
ejpam-3431	90	66	0	0	NUM
ejpam-3431	90	67	,	,	PUNCT
ejpam-3431	90	68	2	2	NUM
ejpam-3431	90	69	}	}	PUNCT
ejpam-3431	90	70	{	{	PUNCT
ejpam-3431	90	71	0	0	NUM
ejpam-3431	90	72	,	,	PUNCT
ejpam-3431	90	73	2	2	NUM
ejpam-3431	90	74	}	}	PUNCT
ejpam-3431	90	75	{	{	PUNCT
ejpam-3431	90	76	0	0	NUM
ejpam-3431	90	77	,	,	PUNCT
ejpam-3431	90	78	1	1	NUM
ejpam-3431	90	79	,	,	PUNCT
ejpam-3431	90	80	2	2	NUM
ejpam-3431	90	81	}	}	PUNCT
ejpam-3431	90	82	{	{	PUNCT
ejpam-3431	90	83	0	0	NUM
ejpam-3431	90	84	,	,	PUNCT
ejpam-3431	90	85	1	1	NUM
ejpam-3431	90	86	,	,	PUNCT
ejpam-3431	90	87	2	2	NUM
ejpam-3431	90	88	}	}	SYM
ejpam-3431	90	89	3	3	NUM
ejpam-3431	90	90	{	{	PUNCT
ejpam-3431	90	91	0	0	NUM
ejpam-3431	90	92	,	,	PUNCT
ejpam-3431	90	93	3	3	NUM
ejpam-3431	90	94	}	}	PUNCT
ejpam-3431	90	95	{	{	PUNCT
ejpam-3431	90	96	0	0	NUM
ejpam-3431	90	97	,	,	PUNCT
ejpam-3431	90	98	1	1	NUM
ejpam-3431	90	99	,	,	PUNCT
ejpam-3431	90	100	3	3	NUM
ejpam-3431	90	101	}	}	PUNCT
ejpam-3431	90	102	{	{	PUNCT
ejpam-3431	90	103	0	0	NUM
ejpam-3431	90	104	,	,	PUNCT
ejpam-3431	90	105	1	1	NUM
ejpam-3431	90	106	,	,	PUNCT
ejpam-3431	90	107	3	3	NUM
ejpam-3431	90	108	}	}	PUNCT
ejpam-3431	90	109	{	{	PUNCT
ejpam-3431	90	110	0	0	NUM
ejpam-3431	90	111	,	,	PUNCT
ejpam-3431	90	112	1	1	NUM
ejpam-3431	90	113	,	,	PUNCT
ejpam-3431	90	114	3	3	NUM
ejpam-3431	90	115	}	}	PUNCT
ejpam-3431	90	116	by	by	ADP
ejpam-3431	90	117	routine	routine	ADJ
ejpam-3431	90	118	calculations	calculation	NOUN
ejpam-3431	90	119	,	,	PUNCT
ejpam-3431	90	120	we	we	PRON
ejpam-3431	90	121	see	see	VERB
ejpam-3431	90	122	that	that	PRON
ejpam-3431	90	123	(	(	PUNCT
ejpam-3431	90	124	h;~	h;~	NOUN
ejpam-3431	90	125	,	,	PUNCT
ejpam-3431	90	126	◦	◦	NOUN
ejpam-3431	90	127	,	,	PUNCT
ejpam-3431	90	128	0	0	NUM
ejpam-3431	90	129	)	)	PUNCT
ejpam-3431	90	130	is	be	AUX
ejpam-3431	90	131	a	a	DET
ejpam-3431	90	132	pseudo	pseudo	NOUN
ejpam-3431	90	133	hyper	hyper	ADJ
ejpam-3431	90	134	gr	gr	NOUN
ejpam-3431	90	135	-	-	PUNCT
ejpam-3431	90	136	algebra	algebra	NOUN
ejpam-3431	90	137	.	.	PUNCT
ejpam-3431	91	1	remark	remark	NOUN
ejpam-3431	91	2	3.3	3.3	NUM
ejpam-3431	91	3	.	.	PUNCT
ejpam-3431	92	1	in	in	ADP
ejpam-3431	92	2	a	a	DET
ejpam-3431	92	3	pseudo	pseudo	NOUN
ejpam-3431	92	4	hyper	hyper	ADJ
ejpam-3431	92	5	gr	gr	NOUN
ejpam-3431	92	6	-	-	PUNCT
ejpam-3431	92	7	algebra	algebra	NOUN
ejpam-3431	92	8	h	h	NOUN
ejpam-3431	92	9	,	,	PUNCT
ejpam-3431	92	10	the	the	DET
ejpam-3431	92	11	following	follow	VERB
ejpam-3431	92	12	are	be	AUX
ejpam-3431	92	13	evident	evident	ADJ
ejpam-3431	92	14	:	:	PUNCT
ejpam-3431	92	15	(	(	PUNCT
ejpam-3431	92	16	i	i	NOUN
ejpam-3431	92	17	)	)	PUNCT
ejpam-3431	93	1	x	x	PROPN
ejpam-3431	93	2	�	�	PROPN
ejpam-3431	93	3	x	x	SYM
ejpam-3431	93	4	;	;	PUNCT
ejpam-3431	93	5	(	(	PUNCT
ejpam-3431	93	6	ii	ii	NOUN
ejpam-3431	93	7	)	)	PUNCT
ejpam-3431	93	8	(	(	PUNCT
ejpam-3431	93	9	x	x	X
ejpam-3431	93	10	◦	◦	NOUN
ejpam-3431	93	11	y)~	y)~	PROPN
ejpam-3431	93	12	z	z	PROPN
ejpam-3431	93	13	�	�	PROPN
ejpam-3431	93	14	(	(	PUNCT
ejpam-3431	93	15	x~	x~	PROPN
ejpam-3431	93	16	z	z	X
ejpam-3431	93	17	)	)	PUNCT
ejpam-3431	93	18	◦	◦	NOUN
ejpam-3431	93	19	y	y	PROPN
ejpam-3431	93	20	;	;	PUNCT
ejpam-3431	93	21	(	(	PUNCT
ejpam-3431	93	22	iii	iii	X
ejpam-3431	93	23	)	)	PUNCT
ejpam-3431	93	24	(	(	PUNCT
ejpam-3431	93	25	a	a	DET
ejpam-3431	93	26	◦	◦	NOUN
ejpam-3431	93	27	b)~	b)~	VERB
ejpam-3431	93	28	c	c	NOUN
ejpam-3431	93	29	=	=	SYM
ejpam-3431	93	30	(	(	PUNCT
ejpam-3431	93	31	a~	a~	PROPN
ejpam-3431	93	32	c	c	NOUN
ejpam-3431	93	33	)	)	PUNCT
ejpam-3431	93	34	◦	◦	NOUN
ejpam-3431	93	35	b	b	NOUN
ejpam-3431	93	36	;	;	PUNCT
ejpam-3431	93	37	and	and	CCONJ
ejpam-3431	93	38	(	(	PUNCT
ejpam-3431	93	39	iv	iv	X
ejpam-3431	93	40	)	)	PUNCT
ejpam-3431	93	41	a	a	DET
ejpam-3431	93	42	⊆	⊆	NUM
ejpam-3431	93	43	b	b	NOUN
ejpam-3431	93	44	implies	imply	VERB
ejpam-3431	93	45	a	a	DET
ejpam-3431	93	46	�	�	PROPN
ejpam-3431	93	47	b.	b.	PROPN
ejpam-3431	93	48	example	example	NOUN
ejpam-3431	93	49	3.4	3.4	NUM
ejpam-3431	93	50	.	.	PUNCT
ejpam-3431	94	1	let	let	VERB
ejpam-3431	94	2	h	h	NOUN
ejpam-3431	94	3	=	=	NOUN
ejpam-3431	94	4	n	n	CCONJ
ejpam-3431	94	5	∪	∪	X
ejpam-3431	94	6	{	{	PUNCT
ejpam-3431	94	7	0	0	NUM
ejpam-3431	94	8	}	}	PUNCT
ejpam-3431	94	9	be	be	AUX
ejpam-3431	94	10	the	the	DET
ejpam-3431	94	11	set	set	NOUN
ejpam-3431	94	12	of	of	ADP
ejpam-3431	94	13	all	all	DET
ejpam-3431	94	14	nonnegative	nonnegative	ADJ
ejpam-3431	94	15	integers	integer	NOUN
ejpam-3431	94	16	and	and	CCONJ
ejpam-3431	94	17	let	let	VERB
ejpam-3431	94	18	the	the	DET
ejpam-3431	94	19	hyperoperations	hyperoperation	NOUN
ejpam-3431	94	20	“	"	PUNCT
ejpam-3431	94	21	~	~	PUNCT
ejpam-3431	94	22	”	"	PUNCT
ejpam-3431	94	23	and	and	CCONJ
ejpam-3431	94	24	“	"	PUNCT
ejpam-3431	94	25	◦	◦	NOUN
ejpam-3431	94	26	”	"	PUNCT
ejpam-3431	94	27	be	be	AUX
ejpam-3431	94	28	defined	define	VERB
ejpam-3431	94	29	on	on	ADP
ejpam-3431	94	30	h	h	NOUN
ejpam-3431	94	31	as	as	SCONJ
ejpam-3431	94	32	follows	follow	VERB
ejpam-3431	94	33	:	:	PUNCT
ejpam-3431	95	1	x~	x~	NUM
ejpam-3431	95	2	y	y	X
ejpam-3431	95	3	=	=	PUNCT
ejpam-3431	95	4	{	{	PUNCT
ejpam-3431	95	5	0	0	NUM
ejpam-3431	95	6	,	,	PUNCT
ejpam-3431	95	7	x	x	NOUN
ejpam-3431	95	8	}	}	PUNCT
ejpam-3431	95	9	and	and	CCONJ
ejpam-3431	95	10	x	x	PUNCT
ejpam-3431	95	11	◦	◦	NOUN
ejpam-3431	95	12	y	y	NOUN
ejpam-3431	95	13	=	=	PUNCT
ejpam-3431	95	14	{	{	PUNCT
ejpam-3431	95	15	0	0	NUM
ejpam-3431	95	16	,	,	PUNCT
ejpam-3431	95	17	x	x	NOUN
ejpam-3431	95	18	,	,	PUNCT
ejpam-3431	95	19	y	y	PROPN
ejpam-3431	95	20	}	}	PUNCT
ejpam-3431	95	21	.	.	PUNCT
ejpam-3431	96	1	then	then	ADV
ejpam-3431	96	2	h	h	PROPN
ejpam-3431	96	3	is	be	AUX
ejpam-3431	96	4	a	a	DET
ejpam-3431	96	5	pseudo	pseudo	NOUN
ejpam-3431	96	6	hyper	hyper	ADJ
ejpam-3431	96	7	gr	gr	NOUN
ejpam-3431	96	8	-	-	NOUN
ejpam-3431	96	9	algebra	algebra	NOUN
ejpam-3431	96	10	.	.	PUNCT
ejpam-3431	97	1	to	to	PART
ejpam-3431	97	2	verify	verify	VERB
ejpam-3431	97	3	this	this	PRON
ejpam-3431	97	4	,	,	PUNCT
ejpam-3431	97	5	we	we	PRON
ejpam-3431	97	6	need	need	VERB
ejpam-3431	97	7	to	to	PART
ejpam-3431	97	8	check	check	VERB
ejpam-3431	97	9	that	that	SCONJ
ejpam-3431	97	10	the	the	DET
ejpam-3431	97	11	five	five	NUM
ejpam-3431	97	12	conditions	condition	NOUN
ejpam-3431	97	13	are	be	AUX
ejpam-3431	97	14	satisfied	satisfied	ADJ
ejpam-3431	97	15	.	.	PUNCT
ejpam-3431	98	1	note	note	VERB
ejpam-3431	98	2	that	that	SCONJ
ejpam-3431	98	3	{	{	PUNCT
ejpam-3431	98	4	0	0	NUM
ejpam-3431	98	5	,	,	PUNCT
ejpam-3431	98	6	x	x	X
ejpam-3431	98	7	,	,	PUNCT
ejpam-3431	98	8	z	z	NOUN
ejpam-3431	98	9	}	}	PUNCT
ejpam-3431	98	10	◦	◦	VERB
ejpam-3431	98	11	{	{	PUNCT
ejpam-3431	98	12	0	0	NUM
ejpam-3431	98	13	,	,	PUNCT
ejpam-3431	98	14	y	y	PROPN
ejpam-3431	98	15	,	,	PUNCT
ejpam-3431	98	16	z	z	NOUN
ejpam-3431	98	17	}	}	PUNCT
ejpam-3431	98	18	=	=	SYM
ejpam-3431	98	19	{	{	PUNCT
ejpam-3431	98	20	0	0	NUM
ejpam-3431	98	21	,	,	PUNCT
ejpam-3431	98	22	x	x	NOUN
ejpam-3431	98	23	,	,	PUNCT
ejpam-3431	98	24	y	y	PROPN
ejpam-3431	98	25	,	,	PUNCT
ejpam-3431	98	26	z	z	PROPN
ejpam-3431	98	27	}	}	PUNCT
ejpam-3431	98	28	�	�	PROPN
ejpam-3431	98	29	{	{	PUNCT
ejpam-3431	98	30	0	0	NUM
ejpam-3431	98	31	,	,	PUNCT
ejpam-3431	98	32	x	x	NOUN
ejpam-3431	98	33	,	,	PUNCT
ejpam-3431	98	34	y	y	PROPN
ejpam-3431	98	35	}	}	PUNCT
ejpam-3431	98	36	.	.	PUNCT
ejpam-3431	99	1	this	this	PRON
ejpam-3431	99	2	means	mean	VERB
ejpam-3431	99	3	that	that	SCONJ
ejpam-3431	99	4	(	(	PUNCT
ejpam-3431	99	5	x	x	SYM
ejpam-3431	99	6	◦	◦	NOUN
ejpam-3431	99	7	z	z	NOUN
ejpam-3431	99	8	)	)	PUNCT
ejpam-3431	99	9	◦	◦	NOUN
ejpam-3431	99	10	(	(	PUNCT
ejpam-3431	99	11	y	y	PROPN
ejpam-3431	99	12	◦	◦	PROPN
ejpam-3431	99	13	z	z	PROPN
ejpam-3431	99	14	)	)	PUNCT
ejpam-3431	99	15	�	�	PROPN
ejpam-3431	99	16	x	x	PUNCT
ejpam-3431	99	17	◦	◦	NOUN
ejpam-3431	99	18	y	y	PROPN
ejpam-3431	99	19	.	.	PUNCT
ejpam-3431	100	1	on	on	ADP
ejpam-3431	100	2	the	the	DET
ejpam-3431	100	3	other	other	ADJ
ejpam-3431	100	4	hand	hand	NOUN
ejpam-3431	100	5	,	,	PUNCT
ejpam-3431	100	6	{	{	PUNCT
ejpam-3431	100	7	0	0	NUM
ejpam-3431	100	8	,	,	PUNCT
ejpam-3431	100	9	x	x	NOUN
ejpam-3431	100	10	}	}	PUNCT
ejpam-3431	100	11	~	~	PUNCT
ejpam-3431	100	12	{	{	PUNCT
ejpam-3431	100	13	0	0	NUM
ejpam-3431	100	14	,	,	PUNCT
ejpam-3431	100	15	y	y	NOUN
ejpam-3431	100	16	}	}	PUNCT
ejpam-3431	100	17	=	=	PUNCT
ejpam-3431	100	18	{	{	PUNCT
ejpam-3431	100	19	0	0	NUM
ejpam-3431	100	20	,	,	PUNCT
ejpam-3431	100	21	x	x	ADJ
ejpam-3431	100	22	}	}	PUNCT
ejpam-3431	100	23	�	�	PROPN
ejpam-3431	100	24	{	{	PUNCT
ejpam-3431	100	25	0	0	NUM
ejpam-3431	100	26	,	,	PUNCT
ejpam-3431	100	27	x	x	PRON
ejpam-3431	100	28	}	}	PUNCT
ejpam-3431	100	29	means	mean	VERB
ejpam-3431	100	30	that	that	SCONJ
ejpam-3431	100	31	(	(	PUNCT
ejpam-3431	100	32	x	x	X
ejpam-3431	100	33	~	~	PUNCT
ejpam-3431	100	34	z	z	X
ejpam-3431	100	35	)	)	PUNCT
ejpam-3431	100	36	~	~	PUNCT
ejpam-3431	100	37	(	(	PUNCT
ejpam-3431	100	38	y	y	X
ejpam-3431	100	39	~	~	PUNCT
ejpam-3431	100	40	z	z	X
ejpam-3431	100	41	)	)	PUNCT
ejpam-3431	100	42	�	�	PROPN
ejpam-3431	100	43	x	x	PUNCT
ejpam-3431	100	44	~	~	PUNCT
ejpam-3431	100	45	y.	y.	PROPN
ejpam-3431	100	46	thus	thus	ADV
ejpam-3431	100	47	,	,	PUNCT
ejpam-3431	100	48	[	[	X
ejpam-3431	100	49	phgr1	phgr1	X
ejpam-3431	100	50	]	]	X
ejpam-3431	100	51	holds	hold	VERB
ejpam-3431	100	52	.	.	PUNCT
ejpam-3431	101	1	now	now	ADV
ejpam-3431	101	2	,	,	PUNCT
ejpam-3431	101	3	(	(	PUNCT
ejpam-3431	101	4	x	x	X
ejpam-3431	101	5	◦	◦	VERB
ejpam-3431	101	6	y	y	NOUN
ejpam-3431	101	7	)	)	PUNCT
ejpam-3431	101	8	~	~	PUNCT
ejpam-3431	102	1	z	z	X
ejpam-3431	102	2	=	=	SYM
ejpam-3431	102	3	{	{	PUNCT
ejpam-3431	102	4	0	0	NUM
ejpam-3431	102	5	,	,	PUNCT
ejpam-3431	102	6	x	x	NOUN
ejpam-3431	102	7	,	,	PUNCT
ejpam-3431	102	8	y	y	PROPN
ejpam-3431	102	9	}	}	PUNCT
ejpam-3431	102	10	~	~	PUNCT
ejpam-3431	102	11	z	z	X
ejpam-3431	102	12	=	=	SYM
ejpam-3431	102	13	{	{	PUNCT
ejpam-3431	102	14	0	0	NUM
ejpam-3431	102	15	,	,	PUNCT
ejpam-3431	102	16	x	x	NOUN
ejpam-3431	102	17	,	,	PUNCT
ejpam-3431	102	18	y	y	PROPN
ejpam-3431	102	19	}	}	PUNCT
ejpam-3431	102	20	,	,	PUNCT
ejpam-3431	102	21	also	also	ADV
ejpam-3431	102	22	(	(	PUNCT
ejpam-3431	102	23	x	x	SYM
ejpam-3431	102	24	~	~	PUNCT
ejpam-3431	102	25	z	z	X
ejpam-3431	102	26	)	)	PUNCT
ejpam-3431	102	27	◦	◦	NOUN
ejpam-3431	102	28	y	y	NOUN
ejpam-3431	102	29	=	=	PUNCT
ejpam-3431	102	30	{	{	PUNCT
ejpam-3431	102	31	0	0	NUM
ejpam-3431	102	32	,	,	PUNCT
ejpam-3431	102	33	x}	x}	PROPN
ejpam-3431	102	34	◦	◦	NOUN
ejpam-3431	102	35	y	y	NOUN
ejpam-3431	102	36	=	=	PUNCT
ejpam-3431	102	37	{	{	PUNCT
ejpam-3431	102	38	0	0	NUM
ejpam-3431	102	39	,	,	PUNCT
ejpam-3431	102	40	x	x	NOUN
ejpam-3431	102	41	,	,	PUNCT
ejpam-3431	102	42	y	y	PROPN
ejpam-3431	102	43	}	}	PUNCT
ejpam-3431	102	44	and	and	CCONJ
ejpam-3431	102	45	so	so	ADV
ejpam-3431	102	46	(	(	PUNCT
ejpam-3431	102	47	x	x	SYM
ejpam-3431	102	48	◦	◦	NOUN
ejpam-3431	102	49	y)~z	y)~z	ADJ
ejpam-3431	102	50	=	=	SYM
ejpam-3431	102	51	(	(	PUNCT
ejpam-3431	102	52	x	x	X
ejpam-3431	102	53	~	~	X
ejpam-3431	102	54	z)	z)	NUM
ejpam-3431	102	55	◦	◦	NOUN
ejpam-3431	102	56	y	y	NOUN
ejpam-3431	102	57	,	,	PUNCT
ejpam-3431	102	58	that	that	ADV
ejpam-3431	102	59	is	is	ADV
ejpam-3431	102	60	,	,	PUNCT
ejpam-3431	102	61	[	[	X
ejpam-3431	102	62	phgr2	phgr2	NOUN
ejpam-3431	102	63	]	]	PUNCT
ejpam-3431	102	64	is	be	AUX
ejpam-3431	102	65	satisfied	satisfied	ADJ
ejpam-3431	102	66	.	.	PUNCT
ejpam-3431	103	1	[	[	X
ejpam-3431	103	2	phgr3	phgr3	X
ejpam-3431	103	3	]	]	PUNCT
ejpam-3431	103	4	follows	follow	VERB
ejpam-3431	103	5	immediately	immediately	ADV
ejpam-3431	103	6	from	from	ADP
ejpam-3431	103	7	the	the	DET
ejpam-3431	103	8	defined	define	VERB
ejpam-3431	103	9	operations	operation	NOUN
ejpam-3431	103	10	◦	◦	NOUN
ejpam-3431	103	11	and	and	CCONJ
ejpam-3431	103	12	~	~	PUNCT
ejpam-3431	103	13	on	on	ADP
ejpam-3431	103	14	h	h	NOUN
ejpam-3431	103	15	,	,	PUNCT
ejpam-3431	103	16	that	that	ADV
ejpam-3431	103	17	is	is	ADV
ejpam-3431	103	18	,	,	PUNCT
ejpam-3431	103	19	x	x	SYM
ejpam-3431	103	20	◦	◦	NOUN
ejpam-3431	103	21	x	x	SYM
ejpam-3431	103	22	=	=	X
ejpam-3431	103	23	{	{	PUNCT
ejpam-3431	103	24	0	0	NUM
ejpam-3431	103	25	,	,	PUNCT
ejpam-3431	103	26	x	x	NOUN
ejpam-3431	103	27	}	}	PUNCT
ejpam-3431	103	28	and	and	CCONJ
ejpam-3431	103	29	x~	x~	NUM
ejpam-3431	103	30	x	x	SYM
ejpam-3431	103	31	=	=	PUNCT
ejpam-3431	103	32	{	{	PUNCT
ejpam-3431	103	33	0	0	NUM
ejpam-3431	103	34	,	,	PUNCT
ejpam-3431	103	35	x	x	NOUN
ejpam-3431	103	36	}	}	PUNCT
ejpam-3431	103	37	for	for	ADP
ejpam-3431	103	38	all	all	PRON
ejpam-3431	103	39	x	x	SYM
ejpam-3431	103	40	∈	∈	PROPN
ejpam-3431	103	41	h.	h.	NOUN
ejpam-3431	103	42	let	let	VERB
ejpam-3431	103	43	x	x	PRON
ejpam-3431	103	44	6=	6=	ADP
ejpam-3431	103	45	0	0	NUM
ejpam-3431	103	46	,	,	PUNCT
ejpam-3431	103	47	then	then	ADV
ejpam-3431	103	48	0	0	NUM
ejpam-3431	103	49	◦	◦	NOUN
ejpam-3431	103	50	(	(	PUNCT
ejpam-3431	103	51	0~	0~	NOUN
ejpam-3431	103	52	x	x	NOUN
ejpam-3431	103	53	)	)	PUNCT
ejpam-3431	104	1	=	=	SYM
ejpam-3431	104	2	0	0	NUM
ejpam-3431	104	3	◦	◦	NOUN
ejpam-3431	104	4	{	{	PUNCT
ejpam-3431	104	5	0	0	NUM
ejpam-3431	104	6	}	}	PUNCT
ejpam-3431	104	7	=	=	SYM
ejpam-3431	104	8	{	{	PUNCT
ejpam-3431	104	9	0	0	NUM
ejpam-3431	104	10	}	}	PUNCT
ejpam-3431	104	11	�	�	PROPN
ejpam-3431	104	12	x	x	PROPN
ejpam-3431	104	13	,	,	PUNCT
ejpam-3431	104	14	and	and	CCONJ
ejpam-3431	104	15	thus	thus	ADV
ejpam-3431	104	16	,	,	PUNCT
ejpam-3431	104	17	[	[	X
ejpam-3431	104	18	phgr4	phgr4	X
ejpam-3431	104	19	]	]	PUNCT
ejpam-3431	104	20	holds	hold	VERB
ejpam-3431	104	21	.	.	PUNCT
ejpam-3431	105	1	finally	finally	ADV
ejpam-3431	105	2	,	,	PUNCT
ejpam-3431	105	3	{	{	PUNCT
ejpam-3431	105	4	0	0	NUM
ejpam-3431	105	5	,	,	PUNCT
ejpam-3431	105	6	x}~z	x}~z	PUNCT
ejpam-3431	105	7	=	=	PUNCT
ejpam-3431	105	8	{	{	PUNCT
ejpam-3431	105	9	0	0	NUM
ejpam-3431	105	10	,	,	PUNCT
ejpam-3431	105	11	x	x	ADJ
ejpam-3431	105	12	}	}	PUNCT
ejpam-3431	105	13	�	�	PROPN
ejpam-3431	105	14	{	{	PUNCT
ejpam-3431	105	15	0	0	NUM
ejpam-3431	105	16	,	,	PUNCT
ejpam-3431	105	17	y	y	PROPN
ejpam-3431	105	18	,	,	PUNCT
ejpam-3431	105	19	z	z	NOUN
ejpam-3431	105	20	}	}	PUNCT
ejpam-3431	105	21	=	=	SYM
ejpam-3431	105	22	y	y	PROPN
ejpam-3431	105	23	◦	◦	PROPN
ejpam-3431	105	24	z.	z.	PROPN
ejpam-3431	105	25	hence	hence	ADV
ejpam-3431	105	26	,	,	PUNCT
ejpam-3431	105	27	(	(	PUNCT
ejpam-3431	105	28	x	x	SYM
ejpam-3431	105	29	~	~	PROPN
ejpam-3431	105	30	y)~z	y)~z	ADJ
ejpam-3431	105	31	�	�	PROPN
ejpam-3431	105	32	y	y	PROPN
ejpam-3431	105	33	◦	◦	PROPN
ejpam-3431	105	34	z	z	PROPN
ejpam-3431	105	35	,	,	PUNCT
ejpam-3431	105	36	that	that	ADV
ejpam-3431	105	37	is	is	ADV
ejpam-3431	105	38	,	,	PUNCT
ejpam-3431	105	39	[	[	X
ejpam-3431	105	40	phgr5	phgr5	X
ejpam-3431	105	41	]	]	PUNCT
ejpam-3431	105	42	holds	hold	VERB
ejpam-3431	105	43	.	.	PUNCT
ejpam-3431	106	1	therefore	therefore	ADV
ejpam-3431	106	2	,	,	PUNCT
ejpam-3431	106	3	h	h	NOUN
ejpam-3431	106	4	is	be	AUX
ejpam-3431	106	5	a	a	DET
ejpam-3431	106	6	pseudo	pseudo	NOUN
ejpam-3431	106	7	hyper	hyper	ADJ
ejpam-3431	106	8	gr	gr	NOUN
ejpam-3431	106	9	-	-	PUNCT
ejpam-3431	106	10	algebra	algebra	NOUN
ejpam-3431	106	11	.	.	PUNCT
ejpam-3431	107	1	remark	remark	NOUN
ejpam-3431	107	2	3.5	3.5	NUM
ejpam-3431	107	3	.	.	PUNCT
ejpam-3431	108	1	note	note	VERB
ejpam-3431	108	2	that	that	SCONJ
ejpam-3431	108	3	if	if	SCONJ
ejpam-3431	108	4	the	the	DET
ejpam-3431	108	5	two	two	NUM
ejpam-3431	108	6	hyperoperations	hyperoperation	NOUN
ejpam-3431	108	7	are	be	AUX
ejpam-3431	108	8	equal	equal	ADJ
ejpam-3431	108	9	,	,	PUNCT
ejpam-3431	108	10	that	that	ADV
ejpam-3431	108	11	is	be	AUX
ejpam-3431	108	12	,	,	PUNCT
ejpam-3431	108	13	~	~	PUNCT
ejpam-3431	108	14	=	=	SYM
ejpam-3431	108	15	◦	◦	NOUN
ejpam-3431	108	16	,	,	PUNCT
ejpam-3431	108	17	then	then	ADV
ejpam-3431	108	18	a	a	DET
ejpam-3431	108	19	pseudo	pseudo	NOUN
ejpam-3431	108	20	hyper	hyper	ADJ
ejpam-3431	108	21	-	-	ADJ
ejpam-3431	108	22	gr	gr	ADJ
ejpam-3431	108	23	algebra	algebra	NOUN
ejpam-3431	108	24	h	h	NOUN
ejpam-3431	108	25	becomes	become	VERB
ejpam-3431	108	26	a	a	DET
ejpam-3431	108	27	hyper	hyper	ADJ
ejpam-3431	108	28	gr	gr	NOUN
ejpam-3431	108	29	-	-	NOUN
ejpam-3431	108	30	algebra	algebra	NOUN
ejpam-3431	108	31	.	.	PUNCT
ejpam-3431	109	1	definition	definition	NOUN
ejpam-3431	109	2	3.6	3.6	NUM
ejpam-3431	109	3	.	.	PUNCT
ejpam-3431	110	1	let	let	VERB
ejpam-3431	110	2	h	h	PRON
ejpam-3431	110	3	be	be	AUX
ejpam-3431	110	4	a	a	DET
ejpam-3431	110	5	pseudo	pseudo	NOUN
ejpam-3431	110	6	hyper	hyper	ADJ
ejpam-3431	110	7	gr	gr	NOUN
ejpam-3431	110	8	-	-	PUNCT
ejpam-3431	110	9	algebra	algebra	NOUN
ejpam-3431	110	10	and	and	CCONJ
ejpam-3431	110	11	s	s	AUX
ejpam-3431	110	12	be	be	AUX
ejpam-3431	110	13	a	a	DET
ejpam-3431	110	14	subset	subset	NOUN
ejpam-3431	110	15	of	of	ADP
ejpam-3431	110	16	h	h	NOUN
ejpam-3431	110	17	containing	contain	VERB
ejpam-3431	110	18	0	0	NUM
ejpam-3431	110	19	.	.	PUNCT
ejpam-3431	111	1	if	if	SCONJ
ejpam-3431	111	2	s	s	PRON
ejpam-3431	111	3	itself	itself	PRON
ejpam-3431	111	4	is	be	AUX
ejpam-3431	111	5	a	a	DET
ejpam-3431	111	6	pseudo	pseudo	NOUN
ejpam-3431	111	7	hyper	hyper	ADJ
ejpam-3431	111	8	gr	gr	NOUN
ejpam-3431	111	9	-	-	NOUN
ejpam-3431	111	10	algebra	algebra	NOUN
ejpam-3431	111	11	with	with	ADP
ejpam-3431	111	12	respect	respect	NOUN
ejpam-3431	111	13	to	to	ADP
ejpam-3431	111	14	the	the	DET
ejpam-3431	111	15	hyperoperations	hyperoperation	NOUN
ejpam-3431	111	16	~	~	PUNCT
ejpam-3431	111	17	and	and	CCONJ
ejpam-3431	111	18	◦	◦	VERB
ejpam-3431	111	19	on	on	ADP
ejpam-3431	111	20	h	h	NOUN
ejpam-3431	111	21	,	,	PUNCT
ejpam-3431	111	22	then	then	ADV
ejpam-3431	111	23	s	s	VERB
ejpam-3431	111	24	is	be	AUX
ejpam-3431	111	25	called	call	VERB
ejpam-3431	111	26	a	a	DET
ejpam-3431	111	27	pseudo	pseudo	NOUN
ejpam-3431	111	28	hyper	hyper	ADJ
ejpam-3431	111	29	subgr	subgr	NOUN
ejpam-3431	111	30	-	-	PUNCT
ejpam-3431	111	31	algebra	algebra	NOUN
ejpam-3431	111	32	of	of	ADP
ejpam-3431	111	33	h.	h.	PROPN
ejpam-3431	111	34	theorem	theorem	PROPN
ejpam-3431	111	35	3.7	3.7	NUM
ejpam-3431	111	36	.	.	PUNCT
ejpam-3431	112	1	(	(	PUNCT
ejpam-3431	112	2	pseudo	pseudo	NOUN
ejpam-3431	112	3	hyper	hyper	ADJ
ejpam-3431	112	4	subgr	subgr	NOUN
ejpam-3431	112	5	-	-	PUNCT
ejpam-3431	112	6	algebra	algebra	NOUN
ejpam-3431	112	7	criterion	criterion	NOUN
ejpam-3431	112	8	)	)	PUNCT
ejpam-3431	112	9	let	let	VERB
ejpam-3431	112	10	s	s	PRON
ejpam-3431	112	11	be	be	AUX
ejpam-3431	112	12	a	a	DET
ejpam-3431	112	13	nonempty	nonempty	ADJ
ejpam-3431	112	14	subset	subset	NOUN
ejpam-3431	112	15	of	of	ADP
ejpam-3431	112	16	a	a	DET
ejpam-3431	112	17	pseudo	pseudo	NOUN
ejpam-3431	112	18	hyper	hyper	ADJ
ejpam-3431	112	19	gr	gr	NOUN
ejpam-3431	112	20	-	-	PUNCT
ejpam-3431	112	21	algebra	algebra	NOUN
ejpam-3431	112	22	h.	h.	NOUN
ejpam-3431	113	1	then	then	ADV
ejpam-3431	113	2	s	s	VERB
ejpam-3431	113	3	is	be	AUX
ejpam-3431	113	4	a	a	DET
ejpam-3431	113	5	pseudo	pseudo	NOUN
ejpam-3431	113	6	hyper	hyper	ADJ
ejpam-3431	113	7	subgr	subgr	NOUN
ejpam-3431	113	8	-	-	PUNCT
ejpam-3431	113	9	algebra	algebra	NOUN
ejpam-3431	113	10	if	if	SCONJ
ejpam-3431	113	11	and	and	CCONJ
ejpam-3431	113	12	only	only	ADV
ejpam-3431	113	13	if	if	SCONJ
ejpam-3431	113	14	both	both	PRON
ejpam-3431	113	15	x~	x~	PROPN
ejpam-3431	113	16	y	y	PROPN
ejpam-3431	113	17	⊆	⊆	NUM
ejpam-3431	113	18	s	s	PART
ejpam-3431	113	19	and	and	CCONJ
ejpam-3431	113	20	x	x	PUNCT
ejpam-3431	113	21	◦	◦	NOUN
ejpam-3431	113	22	y	y	NUM
ejpam-3431	113	23	⊆	⊆	NUM
ejpam-3431	113	24	s	s	NOUN
ejpam-3431	113	25	for	for	ADP
ejpam-3431	113	26	all	all	DET
ejpam-3431	113	27	x	x	NOUN
ejpam-3431	113	28	,	,	PUNCT
ejpam-3431	113	29	y	y	PROPN
ejpam-3431	113	30	∈	∈	PROPN
ejpam-3431	113	31	s.	s.	PROPN
ejpam-3431	113	32	r.	r.	PROPN
ejpam-3431	113	33	manzano	manzano	PROPN
ejpam-3431	113	34	,	,	PUNCT
ejpam-3431	113	35	jr	jr	PROPN
ejpam-3431	113	36	.	.	PROPN
ejpam-3431	113	37	,	,	PUNCT
ejpam-3431	113	38	g.	g.	PROPN
ejpam-3431	113	39	petalcorin	petalcorin	PROPN
ejpam-3431	113	40	,	,	PUNCT
ejpam-3431	113	41	jr	jr	PROPN
ejpam-3431	113	42	.	.	PROPN
ejpam-3431	113	43	/	/	SYM
ejpam-3431	113	44	eur	eur	PROPN
ejpam-3431	113	45	.	.	PUNCT
ejpam-3431	114	1	j.	j.	PROPN
ejpam-3431	114	2	pure	pure	PROPN
ejpam-3431	114	3	appl	appl	PROPN
ejpam-3431	114	4	.	.	PROPN
ejpam-3431	114	5	math	math	PROPN
ejpam-3431	114	6	,	,	PUNCT
ejpam-3431	114	7	12	12	NUM
ejpam-3431	114	8	(	(	PUNCT
ejpam-3431	114	9	3	3	NUM
ejpam-3431	114	10	)	)	PUNCT
ejpam-3431	114	11	(	(	PUNCT
ejpam-3431	114	12	2019	2019	NUM
ejpam-3431	114	13	)	)	PUNCT
ejpam-3431	114	14	,	,	PUNCT
ejpam-3431	114	15	821	821	NUM
ejpam-3431	114	16	-	-	SYM
ejpam-3431	114	17	833	833	NUM
ejpam-3431	114	18	826	826	NUM
ejpam-3431	114	19	proof	proof	NOUN
ejpam-3431	114	20	.	.	PUNCT
ejpam-3431	114	21	suppose	suppose	VERB
ejpam-3431	114	22	that	that	SCONJ
ejpam-3431	114	23	s	s	VERB
ejpam-3431	114	24	is	be	AUX
ejpam-3431	114	25	a	a	DET
ejpam-3431	114	26	pseudo	pseudo	NOUN
ejpam-3431	114	27	hyper	hyper	ADJ
ejpam-3431	114	28	subgr	subgr	NOUN
ejpam-3431	114	29	-	-	PUNCT
ejpam-3431	114	30	algebra	algebra	NOUN
ejpam-3431	114	31	of	of	ADP
ejpam-3431	114	32	h.	h.	NOUN
ejpam-3431	114	33	by	by	ADP
ejpam-3431	114	34	definition	definition	NOUN
ejpam-3431	114	35	3.6	3.6	NUM
ejpam-3431	114	36	,	,	PUNCT
ejpam-3431	114	37	s	s	PART
ejpam-3431	114	38	is	be	AUX
ejpam-3431	114	39	closed	close	VERB
ejpam-3431	114	40	under	under	ADP
ejpam-3431	114	41	the	the	DET
ejpam-3431	114	42	hyperoperations	hyperoperation	NOUN
ejpam-3431	114	43	~	~	PUNCT
ejpam-3431	114	44	and	and	CCONJ
ejpam-3431	114	45	◦	◦	VERB
ejpam-3431	114	46	so	so	SCONJ
ejpam-3431	114	47	that	that	SCONJ
ejpam-3431	114	48	x~	x~	NUM
ejpam-3431	114	49	y	y	PROPN
ejpam-3431	114	50	⊆	⊆	NUM
ejpam-3431	114	51	s	s	PART
ejpam-3431	114	52	and	and	CCONJ
ejpam-3431	114	53	x	x	PUNCT
ejpam-3431	114	54	◦	◦	NOUN
ejpam-3431	114	55	y	y	NUM
ejpam-3431	114	56	⊆	⊆	NUM
ejpam-3431	114	57	s	s	NOUN
ejpam-3431	114	58	for	for	ADP
ejpam-3431	114	59	all	all	DET
ejpam-3431	114	60	x	x	NOUN
ejpam-3431	114	61	,	,	PUNCT
ejpam-3431	114	62	y	y	PROPN
ejpam-3431	114	63	∈	∈	PROPN
ejpam-3431	114	64	s.	s.	PROPN
ejpam-3431	114	65	conversely	conversely	ADV
ejpam-3431	114	66	,	,	PUNCT
ejpam-3431	114	67	suppose	suppose	VERB
ejpam-3431	114	68	that	that	SCONJ
ejpam-3431	114	69	s	s	VERB
ejpam-3431	114	70	has	have	VERB
ejpam-3431	114	71	the	the	DET
ejpam-3431	114	72	property	property	NOUN
ejpam-3431	114	73	x~	x~	PROPN
ejpam-3431	114	74	y	y	PROPN
ejpam-3431	114	75	⊆	⊆	NUM
ejpam-3431	114	76	s	s	PART
ejpam-3431	114	77	and	and	CCONJ
ejpam-3431	114	78	x	x	PUNCT
ejpam-3431	114	79	◦	◦	NOUN
ejpam-3431	114	80	y	y	NUM
ejpam-3431	114	81	⊆	⊆	NUM
ejpam-3431	114	82	s	s	NOUN
ejpam-3431	114	83	for	for	ADP
ejpam-3431	114	84	all	all	DET
ejpam-3431	114	85	x	x	NOUN
ejpam-3431	114	86	,	,	PUNCT
ejpam-3431	114	87	y	y	PROPN
ejpam-3431	114	88	∈	∈	PROPN
ejpam-3431	114	89	s.	s.	PROPN
ejpam-3431	114	90	since	since	SCONJ
ejpam-3431	114	91	s	s	PROPN
ejpam-3431	114	92	⊆	⊆	NUM
ejpam-3431	114	93	h	h	NOUN
ejpam-3431	114	94	,	,	PUNCT
ejpam-3431	114	95	all	all	DET
ejpam-3431	114	96	the	the	DET
ejpam-3431	114	97	axioms	axiom	NOUN
ejpam-3431	114	98	[	[	X
ejpam-3431	114	99	phgr1	phgr1	X
ejpam-3431	114	100	]	]	X
ejpam-3431	114	101	to	to	ADP
ejpam-3431	114	102	[	[	X
ejpam-3431	114	103	phgr5	phgr5	X
ejpam-3431	114	104	]	]	PUNCT
ejpam-3431	114	105	of	of	ADP
ejpam-3431	114	106	definition	definition	NOUN
ejpam-3431	114	107	3.1	3.1	NUM
ejpam-3431	114	108	are	be	AUX
ejpam-3431	114	109	all	all	ADV
ejpam-3431	114	110	satisfied	satisfied	ADJ
ejpam-3431	114	111	.	.	PUNCT
ejpam-3431	115	1	it	it	PRON
ejpam-3431	115	2	remains	remain	VERB
ejpam-3431	115	3	to	to	PART
ejpam-3431	115	4	show	show	VERB
ejpam-3431	115	5	that	that	SCONJ
ejpam-3431	115	6	s	s	PART
ejpam-3431	115	7	contains	contain	VERB
ejpam-3431	115	8	the	the	DET
ejpam-3431	115	9	element	element	NOUN
ejpam-3431	115	10	0	0	NUM
ejpam-3431	115	11	.	.	PUNCT
ejpam-3431	116	1	from	from	ADP
ejpam-3431	116	2	the	the	DET
ejpam-3431	116	3	above	above	ADJ
ejpam-3431	116	4	hypothesis	hypothesis	NOUN
ejpam-3431	116	5	,	,	PUNCT
ejpam-3431	116	6	s	s	PART
ejpam-3431	116	7	is	be	AUX
ejpam-3431	116	8	nonempty	nonempty	ADJ
ejpam-3431	116	9	and	and	CCONJ
ejpam-3431	116	10	thus	thus	ADV
ejpam-3431	116	11	,	,	PUNCT
ejpam-3431	116	12	must	must	AUX
ejpam-3431	116	13	contain	contain	VERB
ejpam-3431	116	14	an	an	DET
ejpam-3431	116	15	element	element	NOUN
ejpam-3431	116	16	,	,	PUNCT
ejpam-3431	116	17	say	say	VERB
ejpam-3431	116	18	c.	c.	PROPN
ejpam-3431	116	19	then	then	ADV
ejpam-3431	116	20	by	by	ADP
ejpam-3431	116	21	definition	definition	NOUN
ejpam-3431	116	22	3.1	3.1	NUM
ejpam-3431	117	1	[	[	X
ejpam-3431	117	2	phgr3	phgr3	X
ejpam-3431	117	3	]	]	PUNCT
ejpam-3431	117	4	,	,	PUNCT
ejpam-3431	117	5	0	0	X
ejpam-3431	117	6	∈	∈	PROPN
ejpam-3431	117	7	c~	c~	PROPN
ejpam-3431	117	8	c	c	PROPN
ejpam-3431	117	9	and	and	CCONJ
ejpam-3431	117	10	0	0	NUM
ejpam-3431	117	11	∈	∈	PROPN
ejpam-3431	117	12	c	c	PROPN
ejpam-3431	117	13	◦	◦	PROPN
ejpam-3431	117	14	c.	c.	NOUN
ejpam-3431	117	15	note	note	VERB
ejpam-3431	117	16	that	that	SCONJ
ejpam-3431	117	17	c~	c~	PROPN
ejpam-3431	117	18	c	c	VERB
ejpam-3431	117	19	⊆	⊆	NUM
ejpam-3431	117	20	s	s	NOUN
ejpam-3431	117	21	and	and	CCONJ
ejpam-3431	117	22	c	c	NOUN
ejpam-3431	117	23	◦	◦	NOUN
ejpam-3431	117	24	c	c	NOUN
ejpam-3431	117	25	⊆	⊆	NUM
ejpam-3431	117	26	s.	s.	PROPN
ejpam-3431	117	27	thus	thus	ADV
ejpam-3431	117	28	,	,	PUNCT
ejpam-3431	117	29	0	0	NUM
ejpam-3431	117	30	∈	∈	PROPN
ejpam-3431	117	31	s.	s.	PROPN
ejpam-3431	117	32	�	�	PROPN
ejpam-3431	117	33	example	example	VERB
ejpam-3431	117	34	3.8	3.8	NUM
ejpam-3431	117	35	.	.	PUNCT
ejpam-3431	118	1	for	for	ADP
ejpam-3431	118	2	any	any	DET
ejpam-3431	118	3	pseudo	pseudo	NOUN
ejpam-3431	118	4	hyper	hyper	ADJ
ejpam-3431	118	5	gr	gr	NOUN
ejpam-3431	118	6	-	-	PUNCT
ejpam-3431	118	7	algebra	algebra	NOUN
ejpam-3431	118	8	h	h	NOUN
ejpam-3431	118	9	,	,	PUNCT
ejpam-3431	118	10	the	the	DET
ejpam-3431	118	11	set	set	NOUN
ejpam-3431	118	12	s	s	PART
ejpam-3431	118	13	=	=	X
ejpam-3431	118	14	{	{	PUNCT
ejpam-3431	118	15	0	0	NUM
ejpam-3431	118	16	}	}	PUNCT
ejpam-3431	118	17	is	be	AUX
ejpam-3431	118	18	a	a	DET
ejpam-3431	118	19	pseudo	pseudo	NOUN
ejpam-3431	118	20	hyper	hyper	ADJ
ejpam-3431	118	21	subgr	subgr	NOUN
ejpam-3431	118	22	-	-	PUNCT
ejpam-3431	118	23	algebra	algebra	NOUN
ejpam-3431	118	24	of	of	ADP
ejpam-3431	118	25	h.	h.	NOUN
ejpam-3431	118	26	for	for	ADP
ejpam-3431	118	27	any	any	DET
ejpam-3431	118	28	nonempty	nonempty	NOUN
ejpam-3431	118	29	subset	subset	VERB
ejpam-3431	118	30	i	i	PRON
ejpam-3431	118	31	of	of	ADP
ejpam-3431	118	32	a	a	DET
ejpam-3431	118	33	pseudo	pseudo	NOUN
ejpam-3431	118	34	hyper	hyper	ADJ
ejpam-3431	118	35	gr	gr	NOUN
ejpam-3431	118	36	-	-	PUNCT
ejpam-3431	118	37	algebra	algebra	NOUN
ejpam-3431	118	38	h	h	NOUN
ejpam-3431	118	39	and	and	CCONJ
ejpam-3431	118	40	any	any	DET
ejpam-3431	118	41	element	element	NOUN
ejpam-3431	118	42	y	y	PROPN
ejpam-3431	118	43	of	of	ADP
ejpam-3431	118	44	h	h	NOUN
ejpam-3431	118	45	,	,	PUNCT
ejpam-3431	118	46	we	we	PRON
ejpam-3431	118	47	introduce	introduce	VERB
ejpam-3431	118	48	the	the	DET
ejpam-3431	118	49	following	following	ADJ
ejpam-3431	118	50	notations	notation	NOUN
ejpam-3431	118	51	and	and	CCONJ
ejpam-3431	118	52	their	their	PRON
ejpam-3431	118	53	meanings	meaning	NOUN
ejpam-3431	118	54	:	:	PUNCT
ejpam-3431	118	55	i	i	PRON
ejpam-3431	118	56	�	�	VERB
ejpam-3431	118	57	~,y	~,y	PUNCT
ejpam-3431	118	58	=	=	SYM
ejpam-3431	118	59	{	{	PUNCT
ejpam-3431	118	60	x	x	SYM
ejpam-3431	118	61	∈	∈	PROPN
ejpam-3431	118	62	h	h	NOUN
ejpam-3431	118	63	|x~	|x~	PROPN
ejpam-3431	118	64	y	y	PROPN
ejpam-3431	118	65	�	�	PROPN
ejpam-3431	118	66	i	i	NOUN
ejpam-3431	118	67	}	}	PUNCT
ejpam-3431	118	68	.	.	PUNCT
ejpam-3431	119	1	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	119	2	=	=	SYM
ejpam-3431	120	1	{	{	PUNCT
ejpam-3431	120	2	x	x	PUNCT
ejpam-3431	120	3	∈	∈	PROPN
ejpam-3431	120	4	h	h	NOUN
ejpam-3431	120	5	|x~	|x~	NOUN
ejpam-3431	120	6	y	y	PROPN
ejpam-3431	120	7	⊆	⊆	NUM
ejpam-3431	120	8	i	i	PROPN
ejpam-3431	120	9	}	}	PUNCT
ejpam-3431	120	10	.	.	PUNCT
ejpam-3431	121	1	i	i	PRON
ejpam-3431	121	2	�	�	PROPN
ejpam-3431	121	3	◦	◦	NOUN
ejpam-3431	121	4	,y	,y	PUNCT
ejpam-3431	121	5	=	=	PRON
ejpam-3431	121	6	{	{	PUNCT
ejpam-3431	121	7	x	x	PUNCT
ejpam-3431	121	8	∈	∈	PROPN
ejpam-3431	121	9	h	h	NOUN
ejpam-3431	121	10	|x	|x	NOUN
ejpam-3431	121	11	◦	◦	VERB
ejpam-3431	121	12	y	y	PROPN
ejpam-3431	121	13	�	�	PROPN
ejpam-3431	121	14	i	i	NOUN
ejpam-3431	121	15	}	}	PUNCT
ejpam-3431	121	16	.	.	PUNCT
ejpam-3431	122	1	i⊆	i⊆	NOUN
ejpam-3431	122	2	◦	◦	NOUN
ejpam-3431	122	3	,y	,y	PUNCT
ejpam-3431	122	4	=	=	SYM
ejpam-3431	122	5	{	{	PUNCT
ejpam-3431	122	6	x	x	PUNCT
ejpam-3431	122	7	∈	∈	PROPN
ejpam-3431	122	8	h	h	NOUN
ejpam-3431	122	9	|x	|x	NOUN
ejpam-3431	122	10	◦	◦	VERB
ejpam-3431	122	11	y	y	PROPN
ejpam-3431	122	12	⊆	⊆	NUM
ejpam-3431	122	13	i	i	PROPN
ejpam-3431	122	14	}	}	PUNCT
ejpam-3431	122	15	.	.	PUNCT
ejpam-3431	123	1	definition	definition	NOUN
ejpam-3431	123	2	3.9	3.9	NUM
ejpam-3431	123	3	.	.	PUNCT
ejpam-3431	124	1	let	let	VERB
ejpam-3431	124	2	i	i	PRON
ejpam-3431	124	3	be	be	AUX
ejpam-3431	124	4	a	a	DET
ejpam-3431	124	5	nonempty	nonempty	ADJ
ejpam-3431	124	6	subset	subset	NOUN
ejpam-3431	124	7	of	of	ADP
ejpam-3431	124	8	a	a	DET
ejpam-3431	124	9	pseudo	pseudo	NOUN
ejpam-3431	124	10	hyper	hyper	ADJ
ejpam-3431	124	11	gr	gr	NOUN
ejpam-3431	124	12	-	-	PUNCT
ejpam-3431	124	13	algebra	algebra	NOUN
ejpam-3431	124	14	h	h	NOUN
ejpam-3431	124	15	such	such	ADJ
ejpam-3431	124	16	that	that	DET
ejpam-3431	124	17	0	0	NUM
ejpam-3431	124	18	∈	∈	PROPN
ejpam-3431	124	19	i.	i.	NOUN
ejpam-3431	125	1	then	then	ADV
ejpam-3431	125	2	i	i	PRON
ejpam-3431	125	3	is	be	AUX
ejpam-3431	125	4	said	say	VERB
ejpam-3431	125	5	to	to	PART
ejpam-3431	125	6	be	be	AUX
ejpam-3431	125	7	a	a	DET
ejpam-3431	125	8	pseudo	pseudo	NOUN
ejpam-3431	125	9	hyper	hyper	ADJ
ejpam-3431	125	10	-	-	ADJ
ejpam-3431	125	11	gr	gr	ADJ
ejpam-3431	125	12	ideal	ideal	NOUN
ejpam-3431	125	13	of	of	ADP
ejpam-3431	125	14	h	h	NOUN
ejpam-3431	125	15	if	if	SCONJ
ejpam-3431	125	16	for	for	ADP
ejpam-3431	125	17	any	any	DET
ejpam-3431	125	18	y	y	PROPN
ejpam-3431	125	19	∈	∈	PROPN
ejpam-3431	126	1	i	i	PRON
ejpam-3431	126	2	,	,	PUNCT
ejpam-3431	126	3	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	126	4	⊆	⊆	NUM
ejpam-3431	126	5	i	i	PROPN
ejpam-3431	126	6	and	and	CCONJ
ejpam-3431	126	7	i⊆	i⊆	PROPN
ejpam-3431	126	8	◦	◦	NOUN
ejpam-3431	126	9	,y	,y	PUNCT
ejpam-3431	126	10	⊆	⊆	NUM
ejpam-3431	126	11	i.	i.	NOUN
ejpam-3431	126	12	example	example	NOUN
ejpam-3431	126	13	3.10	3.10	NUM
ejpam-3431	126	14	.	.	PUNCT
ejpam-3431	127	1	consider	consider	VERB
ejpam-3431	127	2	the	the	DET
ejpam-3431	127	3	pseudo	pseudo	NOUN
ejpam-3431	127	4	hyper	hyper	ADJ
ejpam-3431	127	5	gr	gr	NOUN
ejpam-3431	127	6	-	-	PUNCT
ejpam-3431	127	7	algebra	algebra	NOUN
ejpam-3431	127	8	h	h	NOUN
ejpam-3431	127	9	in	in	ADP
ejpam-3431	127	10	example	example	NOUN
ejpam-3431	127	11	3.2	3.2	NUM
ejpam-3431	127	12	.	.	PUNCT
ejpam-3431	128	1	let	let	VERB
ejpam-3431	128	2	i	i	PRON
ejpam-3431	128	3	=	=	PUNCT
ejpam-3431	128	4	{	{	PUNCT
ejpam-3431	128	5	0	0	NUM
ejpam-3431	128	6	,	,	PUNCT
ejpam-3431	128	7	2	2	NUM
ejpam-3431	128	8	}	}	PUNCT
ejpam-3431	128	9	.	.	PUNCT
ejpam-3431	129	1	observe	observe	VERB
ejpam-3431	129	2	that	that	DET
ejpam-3431	129	3	i⊆~,0	i⊆~,0	NOUN
ejpam-3431	129	4	=	=	PRON
ejpam-3431	129	5	{	{	PUNCT
ejpam-3431	129	6	x	x	PUNCT
ejpam-3431	129	7	∈	∈	PROPN
ejpam-3431	129	8	h	h	NOUN
ejpam-3431	129	9	|x~	|x~	ADP
ejpam-3431	129	10	0	0	NUM
ejpam-3431	130	1	⊆	⊆	NUM
ejpam-3431	130	2	i	i	NOUN
ejpam-3431	130	3	}	}	PUNCT
ejpam-3431	130	4	=	=	PUNCT
ejpam-3431	130	5	{	{	PUNCT
ejpam-3431	130	6	2	2	NUM
ejpam-3431	130	7	}	}	SYM
ejpam-3431	130	8	⊆	⊆	NUM
ejpam-3431	130	9	i	i	PRON
ejpam-3431	130	10	i⊆~,2	i⊆~,2	VERB
ejpam-3431	131	1	=	=	PUNCT
ejpam-3431	132	1	{	{	PUNCT
ejpam-3431	132	2	x	x	PUNCT
ejpam-3431	132	3	∈	∈	PROPN
ejpam-3431	132	4	h	h	NOUN
ejpam-3431	132	5	|x~	|x~	ADP
ejpam-3431	132	6	2	2	NUM
ejpam-3431	132	7	⊆	⊆	NUM
ejpam-3431	132	8	i	i	NOUN
ejpam-3431	132	9	}	}	PUNCT
ejpam-3431	132	10	=	=	PUNCT
ejpam-3431	132	11	{	{	PUNCT
ejpam-3431	132	12	2	2	NUM
ejpam-3431	132	13	}	}	SYM
ejpam-3431	132	14	⊆	⊆	NUM
ejpam-3431	132	15	i	i	PROPN
ejpam-3431	132	16	i⊆	i⊆	VERB
ejpam-3431	132	17	◦	◦	NOUN
ejpam-3431	132	18	,0	,0	PUNCT
ejpam-3431	132	19	=	=	SYM
ejpam-3431	132	20	{	{	PUNCT
ejpam-3431	132	21	x	x	PUNCT
ejpam-3431	132	22	∈	∈	PROPN
ejpam-3431	132	23	h	h	NOUN
ejpam-3431	132	24	|x	|x	NOUN
ejpam-3431	132	25	◦	◦	NOUN
ejpam-3431	132	26	0	0	NUM
ejpam-3431	132	27	⊆	⊆	NUM
ejpam-3431	132	28	i	i	NOUN
ejpam-3431	132	29	}	}	PUNCT
ejpam-3431	132	30	=	=	PUNCT
ejpam-3431	132	31	{	{	PUNCT
ejpam-3431	132	32	2	2	NUM
ejpam-3431	132	33	}	}	SYM
ejpam-3431	132	34	⊆	⊆	NUM
ejpam-3431	132	35	i	i	PROPN
ejpam-3431	132	36	i⊆	i⊆	VERB
ejpam-3431	132	37	◦	◦	NOUN
ejpam-3431	132	38	,2	,2	PUNCT
ejpam-3431	132	39	=	=	SYM
ejpam-3431	132	40	{	{	PUNCT
ejpam-3431	132	41	x	x	PUNCT
ejpam-3431	132	42	∈	∈	PROPN
ejpam-3431	132	43	h	h	NOUN
ejpam-3431	132	44	|x	|x	NOUN
ejpam-3431	132	45	◦	◦	VERB
ejpam-3431	132	46	2	2	NUM
ejpam-3431	132	47	⊆	⊆	NUM
ejpam-3431	132	48	i	i	NOUN
ejpam-3431	132	49	}	}	PUNCT
ejpam-3431	132	50	=	=	PUNCT
ejpam-3431	132	51	∅	∅	NOUN
ejpam-3431	132	52	⊆	⊆	NUM
ejpam-3431	132	53	i.	i.	NOUN
ejpam-3431	132	54	thus	thus	ADV
ejpam-3431	132	55	,	,	PUNCT
ejpam-3431	132	56	i	i	PRON
ejpam-3431	132	57	is	be	AUX
ejpam-3431	132	58	indeed	indeed	ADV
ejpam-3431	132	59	a	a	DET
ejpam-3431	132	60	pseudo	pseudo	NOUN
ejpam-3431	132	61	hyper	hyper	ADJ
ejpam-3431	132	62	gr	gr	NOUN
ejpam-3431	132	63	-	-	PUNCT
ejpam-3431	132	64	ideal	ideal	NOUN
ejpam-3431	132	65	.	.	PUNCT
ejpam-3431	133	1	from	from	ADP
ejpam-3431	133	2	now	now	ADV
ejpam-3431	133	3	on	on	ADV
ejpam-3431	133	4	,	,	PUNCT
ejpam-3431	133	5	we	we	PRON
ejpam-3431	133	6	shall	shall	AUX
ejpam-3431	133	7	call	call	VERB
ejpam-3431	133	8	the	the	DET
ejpam-3431	133	9	ideal	ideal	NOUN
ejpam-3431	133	10	in	in	ADP
ejpam-3431	133	11	definition	definition	NOUN
ejpam-3431	133	12	3.9	3.9	NUM
ejpam-3431	133	13	as	as	ADP
ejpam-3431	133	14	pseudo	pseudo	NOUN
ejpam-3431	133	15	hyper	hyper	ADJ
ejpam-3431	133	16	gr	gr	NOUN
ejpam-3431	133	17	-	-	PUNCT
ejpam-3431	133	18	ideal	ideal	NOUN
ejpam-3431	133	19	of	of	ADP
ejpam-3431	133	20	type	type	NOUN
ejpam-3431	133	21	1	1	NUM
ejpam-3431	133	22	for	for	SCONJ
ejpam-3431	133	23	we	we	PRON
ejpam-3431	133	24	will	will	AUX
ejpam-3431	133	25	be	be	AUX
ejpam-3431	133	26	considering	consider	VERB
ejpam-3431	133	27	some	some	DET
ejpam-3431	133	28	forms	form	NOUN
ejpam-3431	133	29	of	of	ADP
ejpam-3431	133	30	pseudo	pseudo	NOUN
ejpam-3431	133	31	hyper	hyper	ADJ
ejpam-3431	133	32	gr	gr	NOUN
ejpam-3431	133	33	-	-	PUNCT
ejpam-3431	133	34	ideals	ideal	NOUN
ejpam-3431	133	35	which	which	PRON
ejpam-3431	133	36	will	will	AUX
ejpam-3431	133	37	be	be	AUX
ejpam-3431	133	38	defined	define	VERB
ejpam-3431	133	39	analogously	analogously	ADV
ejpam-3431	133	40	as	as	ADP
ejpam-3431	133	41	in	in	ADP
ejpam-3431	133	42	definition	definition	NOUN
ejpam-3431	133	43	3.9	3.9	NUM
ejpam-3431	133	44	.	.	PUNCT
ejpam-3431	134	1	r.	r.	PROPN
ejpam-3431	134	2	manzano	manzano	PROPN
ejpam-3431	134	3	,	,	PUNCT
ejpam-3431	134	4	jr	jr	PROPN
ejpam-3431	134	5	.	.	PROPN
ejpam-3431	134	6	,	,	PUNCT
ejpam-3431	134	7	g.	g.	PROPN
ejpam-3431	134	8	petalcorin	petalcorin	PROPN
ejpam-3431	134	9	,	,	PUNCT
ejpam-3431	134	10	jr	jr	PROPN
ejpam-3431	134	11	.	.	PROPN
ejpam-3431	134	12	/	/	SYM
ejpam-3431	134	13	eur	eur	PROPN
ejpam-3431	134	14	.	.	PUNCT
ejpam-3431	135	1	j.	j.	PROPN
ejpam-3431	135	2	pure	pure	PROPN
ejpam-3431	135	3	appl	appl	PROPN
ejpam-3431	135	4	.	.	PROPN
ejpam-3431	135	5	math	math	PROPN
ejpam-3431	135	6	,	,	PUNCT
ejpam-3431	135	7	12	12	NUM
ejpam-3431	135	8	(	(	PUNCT
ejpam-3431	135	9	3	3	NUM
ejpam-3431	135	10	)	)	PUNCT
ejpam-3431	135	11	(	(	PUNCT
ejpam-3431	135	12	2019	2019	NUM
ejpam-3431	135	13	)	)	PUNCT
ejpam-3431	135	14	,	,	PUNCT
ejpam-3431	135	15	821	821	NUM
ejpam-3431	135	16	-	-	SYM
ejpam-3431	135	17	833	833	NUM
ejpam-3431	135	18	827	827	NUM
ejpam-3431	135	19	definition	definition	NOUN
ejpam-3431	135	20	3.11	3.11	NUM
ejpam-3431	135	21	.	.	PUNCT
ejpam-3431	136	1	let	let	VERB
ejpam-3431	136	2	i	i	PRON
ejpam-3431	136	3	be	be	AUX
ejpam-3431	136	4	a	a	DET
ejpam-3431	136	5	nonempty	nonempty	ADJ
ejpam-3431	136	6	subset	subset	NOUN
ejpam-3431	136	7	of	of	ADP
ejpam-3431	136	8	a	a	DET
ejpam-3431	136	9	pseudo	pseudo	NOUN
ejpam-3431	136	10	hyper	hyper	ADJ
ejpam-3431	136	11	gr	gr	NOUN
ejpam-3431	136	12	-	-	PUNCT
ejpam-3431	136	13	algebra	algebra	NOUN
ejpam-3431	136	14	h	h	NOUN
ejpam-3431	136	15	such	such	ADJ
ejpam-3431	136	16	that	that	DET
ejpam-3431	136	17	0	0	NUM
ejpam-3431	136	18	∈	∈	PROPN
ejpam-3431	136	19	i.	i.	NOUN
ejpam-3431	137	1	then	then	ADV
ejpam-3431	137	2	i	i	PRON
ejpam-3431	137	3	is	be	AUX
ejpam-3431	137	4	said	say	VERB
ejpam-3431	137	5	to	to	PART
ejpam-3431	137	6	be	be	AUX
ejpam-3431	137	7	a	a	DET
ejpam-3431	137	8	pseudo	pseudo	NOUN
ejpam-3431	137	9	hyper	hyper	ADJ
ejpam-3431	137	10	-	-	ADJ
ejpam-3431	137	11	gr	gr	ADJ
ejpam-3431	137	12	ideal	ideal	NOUN
ejpam-3431	137	13	of	of	ADP
ejpam-3431	137	14	h	h	NOUN
ejpam-3431	137	15	of	of	ADP
ejpam-3431	137	16	:	:	PUNCT
ejpam-3431	137	17	type	type	NOUN
ejpam-3431	137	18	2	2	NUM
ejpam-3431	137	19	,	,	PUNCT
ejpam-3431	137	20	if	if	SCONJ
ejpam-3431	137	21	for	for	ADP
ejpam-3431	137	22	any	any	DET
ejpam-3431	137	23	y	y	PROPN
ejpam-3431	137	24	∈	∈	PROPN
ejpam-3431	138	1	i	i	PRON
ejpam-3431	138	2	,	,	PUNCT
ejpam-3431	138	3	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	138	4	⊆	⊆	NUM
ejpam-3431	138	5	i	i	PROPN
ejpam-3431	138	6	and	and	CCONJ
ejpam-3431	138	7	i	i	PROPN
ejpam-3431	138	8	�	�	PROPN
ejpam-3431	138	9	◦	◦	NOUN
ejpam-3431	138	10	,y	,y	PUNCT
ejpam-3431	138	11	⊆	⊆	NUM
ejpam-3431	138	12	i.	i.	NOUN
ejpam-3431	138	13	type	type	NOUN
ejpam-3431	138	14	3	3	NUM
ejpam-3431	138	15	,	,	PUNCT
ejpam-3431	138	16	if	if	SCONJ
ejpam-3431	138	17	for	for	ADP
ejpam-3431	138	18	any	any	DET
ejpam-3431	138	19	y	y	PROPN
ejpam-3431	138	20	∈	∈	PROPN
ejpam-3431	139	1	i	i	PRON
ejpam-3431	139	2	,	,	PUNCT
ejpam-3431	139	3	i	i	PRON
ejpam-3431	139	4	�	�	VERB
ejpam-3431	139	5	~,y	~,y	VERB
ejpam-3431	139	6	⊆	⊆	NUM
ejpam-3431	139	7	i	i	NOUN
ejpam-3431	139	8	and	and	CCONJ
ejpam-3431	139	9	i⊆	i⊆	PROPN
ejpam-3431	139	10	◦	◦	NOUN
ejpam-3431	139	11	,y	,y	PUNCT
ejpam-3431	139	12	⊆	⊆	NUM
ejpam-3431	139	13	i.	i.	NOUN
ejpam-3431	139	14	type	type	NOUN
ejpam-3431	139	15	4	4	NUM
ejpam-3431	139	16	,	,	PUNCT
ejpam-3431	139	17	if	if	SCONJ
ejpam-3431	139	18	for	for	ADP
ejpam-3431	139	19	any	any	DET
ejpam-3431	139	20	y	y	PROPN
ejpam-3431	139	21	∈	∈	PROPN
ejpam-3431	140	1	i	i	PRON
ejpam-3431	140	2	,	,	PUNCT
ejpam-3431	140	3	i	i	PRON
ejpam-3431	140	4	�	�	VERB
ejpam-3431	140	5	~,y	~,y	VERB
ejpam-3431	140	6	⊆	⊆	NUM
ejpam-3431	141	1	i	i	PRON
ejpam-3431	141	2	and	and	CCONJ
ejpam-3431	141	3	i	i	PROPN
ejpam-3431	141	4	�	�	PROPN
ejpam-3431	141	5	◦	◦	NOUN
ejpam-3431	141	6	,y	,y	PUNCT
ejpam-3431	141	7	⊆	⊆	NUM
ejpam-3431	141	8	i.	i.	NOUN
ejpam-3431	141	9	type	type	NOUN
ejpam-3431	141	10	5	5	NUM
ejpam-3431	141	11	,	,	PUNCT
ejpam-3431	141	12	if	if	SCONJ
ejpam-3431	141	13	for	for	ADP
ejpam-3431	141	14	any	any	DET
ejpam-3431	141	15	y	y	PROPN
ejpam-3431	141	16	∈	∈	PROPN
ejpam-3431	142	1	i	i	PRON
ejpam-3431	142	2	,	,	PUNCT
ejpam-3431	142	3	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	142	4	⊆	⊆	NUM
ejpam-3431	142	5	i	i	NOUN
ejpam-3431	142	6	or	or	CCONJ
ejpam-3431	142	7	i⊆	i⊆	NOUN
ejpam-3431	142	8	◦	◦	NOUN
ejpam-3431	142	9	,y	,y	PUNCT
ejpam-3431	142	10	⊆	⊆	NUM
ejpam-3431	142	11	i.	i.	NOUN
ejpam-3431	142	12	type	type	NOUN
ejpam-3431	142	13	6	6	NUM
ejpam-3431	142	14	,	,	PUNCT
ejpam-3431	142	15	if	if	SCONJ
ejpam-3431	142	16	for	for	ADP
ejpam-3431	142	17	any	any	DET
ejpam-3431	142	18	y	y	PROPN
ejpam-3431	142	19	∈	∈	PROPN
ejpam-3431	143	1	i	i	PRON
ejpam-3431	143	2	,	,	PUNCT
ejpam-3431	143	3	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	143	4	⊆	⊆	NUM
ejpam-3431	143	5	i	i	PROPN
ejpam-3431	143	6	or	or	CCONJ
ejpam-3431	143	7	i	i	PRON
ejpam-3431	143	8	�	�	PROPN
ejpam-3431	143	9	◦	◦	NOUN
ejpam-3431	143	10	,y	,y	PUNCT
ejpam-3431	143	11	⊆	⊆	NUM
ejpam-3431	143	12	i.	i.	NOUN
ejpam-3431	143	13	type	type	NOUN
ejpam-3431	143	14	7	7	NUM
ejpam-3431	143	15	,	,	PUNCT
ejpam-3431	143	16	if	if	SCONJ
ejpam-3431	143	17	for	for	ADP
ejpam-3431	143	18	any	any	DET
ejpam-3431	143	19	y	y	PROPN
ejpam-3431	143	20	∈	∈	PROPN
ejpam-3431	144	1	i	i	PRON
ejpam-3431	144	2	,	,	PUNCT
ejpam-3431	144	3	i	i	PRON
ejpam-3431	144	4	�	�	VERB
ejpam-3431	144	5	~,y	~,y	VERB
ejpam-3431	144	6	⊆	⊆	NUM
ejpam-3431	144	7	i	i	NOUN
ejpam-3431	144	8	or	or	CCONJ
ejpam-3431	144	9	i⊆	i⊆	NOUN
ejpam-3431	144	10	◦	◦	NOUN
ejpam-3431	144	11	,y	,y	PUNCT
ejpam-3431	144	12	⊆	⊆	NUM
ejpam-3431	144	13	i.	i.	NOUN
ejpam-3431	144	14	type	type	NOUN
ejpam-3431	144	15	8	8	NUM
ejpam-3431	144	16	,	,	PUNCT
ejpam-3431	144	17	if	if	SCONJ
ejpam-3431	144	18	for	for	ADP
ejpam-3431	144	19	any	any	DET
ejpam-3431	144	20	y	y	PROPN
ejpam-3431	144	21	∈	∈	PROPN
ejpam-3431	145	1	i	i	PRON
ejpam-3431	145	2	,	,	PUNCT
ejpam-3431	145	3	i	i	PRON
ejpam-3431	145	4	�	�	VERB
ejpam-3431	145	5	~,y	~,y	VERB
ejpam-3431	145	6	⊆	⊆	NUM
ejpam-3431	146	1	i	i	NOUN
ejpam-3431	146	2	or	or	CCONJ
ejpam-3431	146	3	i	i	PRON
ejpam-3431	146	4	�	�	PROPN
ejpam-3431	146	5	◦	◦	NOUN
ejpam-3431	146	6	,y	,y	PUNCT
ejpam-3431	146	7	⊆	⊆	NUM
ejpam-3431	146	8	i.	i.	NOUN
ejpam-3431	146	9	type	type	NOUN
ejpam-3431	146	10	9	9	NUM
ejpam-3431	146	11	,	,	PUNCT
ejpam-3431	146	12	if	if	SCONJ
ejpam-3431	146	13	for	for	ADP
ejpam-3431	146	14	any	any	DET
ejpam-3431	146	15	y	y	PROPN
ejpam-3431	146	16	∈	∈	PROPN
ejpam-3431	147	1	i	i	PRON
ejpam-3431	147	2	,	,	PUNCT
ejpam-3431	147	3	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	147	4	∩	∩	NOUN
ejpam-3431	147	5	i⊆	i⊆	NOUN
ejpam-3431	147	6	◦	◦	NOUN
ejpam-3431	147	7	,y	,y	PUNCT
ejpam-3431	147	8	⊆	⊆	NUM
ejpam-3431	147	9	i.	i.	NOUN
ejpam-3431	147	10	type	type	NOUN
ejpam-3431	147	11	10	10	NUM
ejpam-3431	147	12	,	,	PUNCT
ejpam-3431	147	13	if	if	SCONJ
ejpam-3431	147	14	for	for	ADP
ejpam-3431	147	15	any	any	DET
ejpam-3431	147	16	y	y	PROPN
ejpam-3431	147	17	∈	∈	PROPN
ejpam-3431	148	1	i	i	PRON
ejpam-3431	148	2	,	,	PUNCT
ejpam-3431	148	3	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	148	4	∩	∩	X
ejpam-3431	148	5	i	i	PRON
ejpam-3431	148	6	�	�	PROPN
ejpam-3431	148	7	◦	◦	NOUN
ejpam-3431	148	8	,y	,y	PUNCT
ejpam-3431	148	9	⊆	⊆	NUM
ejpam-3431	148	10	i.	i.	NOUN
ejpam-3431	148	11	type	type	NOUN
ejpam-3431	148	12	11	11	NUM
ejpam-3431	148	13	,	,	PUNCT
ejpam-3431	148	14	if	if	SCONJ
ejpam-3431	148	15	for	for	ADP
ejpam-3431	148	16	any	any	PRON
ejpam-3431	148	17	y	y	PROPN
ejpam-3431	148	18	∈	∈	PROPN
ejpam-3431	149	1	i	i	PRON
ejpam-3431	149	2	,	,	PUNCT
ejpam-3431	149	3	i	i	PROPN
ejpam-3431	149	4	�	�	VERB
ejpam-3431	149	5	~,y	~,y	NOUN
ejpam-3431	149	6	∩	∩	ADJ
ejpam-3431	149	7	i⊆	i⊆	NOUN
ejpam-3431	149	8	◦	◦	NOUN
ejpam-3431	149	9	,y	,y	PUNCT
ejpam-3431	149	10	⊆	⊆	NUM
ejpam-3431	149	11	i.	i.	NOUN
ejpam-3431	149	12	type	type	NOUN
ejpam-3431	149	13	12	12	NUM
ejpam-3431	149	14	,	,	PUNCT
ejpam-3431	149	15	if	if	SCONJ
ejpam-3431	149	16	for	for	ADP
ejpam-3431	149	17	any	any	DET
ejpam-3431	149	18	y	y	PROPN
ejpam-3431	149	19	∈	∈	PROPN
ejpam-3431	150	1	i	i	PRON
ejpam-3431	150	2	,	,	PUNCT
ejpam-3431	150	3	i	i	PROPN
ejpam-3431	150	4	�	�	VERB
ejpam-3431	150	5	~,y	~,y	PROPN
ejpam-3431	150	6	∩	∩	ADJ
ejpam-3431	150	7	i	i	PRON
ejpam-3431	150	8	�	�	PROPN
ejpam-3431	150	9	◦	◦	NOUN
ejpam-3431	150	10	,y	,y	PUNCT
ejpam-3431	150	11	⊆	⊆	NUM
ejpam-3431	150	12	i.	i.	NOUN
ejpam-3431	150	13	example	example	NOUN
ejpam-3431	150	14	3.12	3.12	NUM
ejpam-3431	150	15	.	.	PUNCT
ejpam-3431	151	1	let	let	VERB
ejpam-3431	151	2	h	h	NOUN
ejpam-3431	151	3	=	=	PRON
ejpam-3431	151	4	{	{	PUNCT
ejpam-3431	151	5	0	0	NUM
ejpam-3431	151	6	,	,	PUNCT
ejpam-3431	151	7	1	1	NUM
ejpam-3431	151	8	,	,	PUNCT
ejpam-3431	151	9	2	2	NUM
ejpam-3431	151	10	}	}	PUNCT
ejpam-3431	151	11	with	with	ADP
ejpam-3431	151	12	the	the	DET
ejpam-3431	151	13	hyperoperations	hyperoperation	NOUN
ejpam-3431	151	14	~	~	PUNCT
ejpam-3431	151	15	and	and	CCONJ
ejpam-3431	151	16	◦	◦	NOUN
ejpam-3431	151	17	on	on	ADP
ejpam-3431	151	18	h	h	NOUN
ejpam-3431	151	19	given	give	VERB
ejpam-3431	151	20	by	by	ADP
ejpam-3431	151	21	the	the	DET
ejpam-3431	151	22	cayley	cayley	ADJ
ejpam-3431	151	23	table	table	NOUN
ejpam-3431	151	24	below	below	ADP
ejpam-3431	151	25	~	~	PUNCT
ejpam-3431	151	26	0	0	NUM
ejpam-3431	152	1	1	1	NUM
ejpam-3431	152	2	2	2	NUM
ejpam-3431	152	3	0	0	NUM
ejpam-3431	152	4	{	{	PUNCT
ejpam-3431	152	5	0	0	NUM
ejpam-3431	152	6	}	}	PUNCT
ejpam-3431	152	7	{	{	PUNCT
ejpam-3431	152	8	0	0	NUM
ejpam-3431	152	9	}	}	PUNCT
ejpam-3431	152	10	{	{	PUNCT
ejpam-3431	152	11	0	0	NUM
ejpam-3431	152	12	}	}	SYM
ejpam-3431	152	13	1	1	NUM
ejpam-3431	152	14	{	{	PUNCT
ejpam-3431	152	15	1	1	NUM
ejpam-3431	152	16	}	}	PUNCT
ejpam-3431	152	17	{	{	PUNCT
ejpam-3431	152	18	0	0	NUM
ejpam-3431	152	19	}	}	PUNCT
ejpam-3431	152	20	{	{	PUNCT
ejpam-3431	152	21	0	0	NUM
ejpam-3431	152	22	}	}	SYM
ejpam-3431	152	23	2	2	NUM
ejpam-3431	152	24	{	{	PUNCT
ejpam-3431	152	25	2	2	NUM
ejpam-3431	152	26	}	}	PUNCT
ejpam-3431	152	27	{	{	PUNCT
ejpam-3431	152	28	0	0	NUM
ejpam-3431	152	29	,	,	PUNCT
ejpam-3431	152	30	2	2	NUM
ejpam-3431	152	31	}	}	PUNCT
ejpam-3431	152	32	{	{	PUNCT
ejpam-3431	152	33	0	0	NOUN
ejpam-3431	152	34	}	}	PUNCT
ejpam-3431	152	35	◦	◦	NOUN
ejpam-3431	152	36	0	0	NUM
ejpam-3431	152	37	1	1	NUM
ejpam-3431	152	38	2	2	NUM
ejpam-3431	152	39	0	0	NUM
ejpam-3431	152	40	{	{	PUNCT
ejpam-3431	152	41	0	0	NUM
ejpam-3431	152	42	}	}	PUNCT
ejpam-3431	152	43	{	{	PUNCT
ejpam-3431	152	44	0	0	NUM
ejpam-3431	152	45	}	}	PUNCT
ejpam-3431	152	46	{	{	PUNCT
ejpam-3431	152	47	0	0	NUM
ejpam-3431	152	48	}	}	SYM
ejpam-3431	152	49	1	1	NUM
ejpam-3431	152	50	{	{	PUNCT
ejpam-3431	152	51	1	1	NUM
ejpam-3431	152	52	}	}	PUNCT
ejpam-3431	152	53	{	{	PUNCT
ejpam-3431	152	54	0	0	NUM
ejpam-3431	152	55	}	}	PUNCT
ejpam-3431	152	56	{	{	PUNCT
ejpam-3431	152	57	0	0	NUM
ejpam-3431	152	58	}	}	SYM
ejpam-3431	152	59	2	2	NUM
ejpam-3431	152	60	{	{	PUNCT
ejpam-3431	152	61	0	0	NUM
ejpam-3431	152	62	,	,	PUNCT
ejpam-3431	152	63	2	2	NUM
ejpam-3431	152	64	}	}	PUNCT
ejpam-3431	152	65	{	{	PUNCT
ejpam-3431	152	66	2	2	NUM
ejpam-3431	152	67	}	}	PUNCT
ejpam-3431	152	68	{	{	PUNCT
ejpam-3431	152	69	0	0	NUM
ejpam-3431	152	70	,	,	PUNCT
ejpam-3431	152	71	2	2	NUM
ejpam-3431	152	72	}	}	PUNCT
ejpam-3431	152	73	by	by	ADP
ejpam-3431	152	74	routine	routine	ADJ
ejpam-3431	152	75	calculations	calculation	NOUN
ejpam-3431	152	76	,	,	PUNCT
ejpam-3431	152	77	h	h	NOUN
ejpam-3431	152	78	is	be	AUX
ejpam-3431	152	79	a	a	DET
ejpam-3431	152	80	pseudo	pseudo	NOUN
ejpam-3431	152	81	hyper	hyper	ADJ
ejpam-3431	152	82	gr	gr	NOUN
ejpam-3431	152	83	-	-	NOUN
ejpam-3431	152	84	algebra	algebra	NOUN
ejpam-3431	152	85	.	.	PUNCT
ejpam-3431	153	1	let	let	VERB
ejpam-3431	153	2	i	i	PRON
ejpam-3431	153	3	=	=	PUNCT
ejpam-3431	153	4	{	{	PUNCT
ejpam-3431	153	5	0	0	NUM
ejpam-3431	153	6	,	,	PUNCT
ejpam-3431	153	7	1	1	NUM
ejpam-3431	153	8	}	}	PUNCT
ejpam-3431	153	9	.	.	PUNCT
ejpam-3431	154	1	note	note	VERB
ejpam-3431	154	2	that	that	SCONJ
ejpam-3431	154	3	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	154	4	=	=	SYM
ejpam-3431	154	5	{	{	PUNCT
ejpam-3431	154	6	0	0	NUM
ejpam-3431	154	7	,	,	PUNCT
ejpam-3431	154	8	1	1	NUM
ejpam-3431	154	9	}	}	SYM
ejpam-3431	154	10	⊆	⊆	NUM
ejpam-3431	155	1	i	i	PROPN
ejpam-3431	155	2	and	and	CCONJ
ejpam-3431	155	3	i	i	PROPN
ejpam-3431	155	4	�	�	PROPN
ejpam-3431	155	5	◦	◦	NOUN
ejpam-3431	155	6	,y	,y	PUNCT
ejpam-3431	155	7	=	=	SYM
ejpam-3431	155	8	{	{	PUNCT
ejpam-3431	155	9	0	0	NUM
ejpam-3431	155	10	,	,	PUNCT
ejpam-3431	155	11	1	1	NUM
ejpam-3431	155	12	}	}	SYM
ejpam-3431	155	13	⊆	⊆	NUM
ejpam-3431	155	14	i.	i.	NOUN
ejpam-3431	155	15	thus	thus	ADV
ejpam-3431	155	16	,	,	PUNCT
ejpam-3431	155	17	i	i	PRON
ejpam-3431	155	18	is	be	AUX
ejpam-3431	155	19	pseudo	pseudo	NOUN
ejpam-3431	155	20	hyper	hyper	ADJ
ejpam-3431	155	21	gr	gr	NOUN
ejpam-3431	155	22	-	-	PUNCT
ejpam-3431	155	23	ideal	ideal	NOUN
ejpam-3431	155	24	of	of	ADP
ejpam-3431	155	25	type	type	NOUN
ejpam-3431	155	26	2	2	NUM
ejpam-3431	155	27	.	.	PUNCT
ejpam-3431	155	28	note	note	NOUN
ejpam-3431	155	29	also	also	ADV
ejpam-3431	155	30	that	that	SCONJ
ejpam-3431	155	31	i	i	PRON
ejpam-3431	155	32	�	�	VERB
ejpam-3431	155	33	~,y	~,y	NOUN
ejpam-3431	155	34	=	=	SYM
ejpam-3431	155	35	{	{	PUNCT
ejpam-3431	155	36	0	0	NUM
ejpam-3431	155	37	,	,	PUNCT
ejpam-3431	155	38	1	1	NUM
ejpam-3431	155	39	}	}	SYM
ejpam-3431	155	40	⊆	⊆	NUM
ejpam-3431	155	41	i	i	PROPN
ejpam-3431	155	42	and	and	CCONJ
ejpam-3431	155	43	i⊆	i⊆	PROPN
ejpam-3431	155	44	◦	◦	NOUN
ejpam-3431	155	45	,y	,y	PUNCT
ejpam-3431	155	46	=	=	SYM
ejpam-3431	155	47	{	{	PUNCT
ejpam-3431	155	48	0	0	NUM
ejpam-3431	155	49	,	,	PUNCT
ejpam-3431	155	50	1	1	NUM
ejpam-3431	155	51	}	}	SYM
ejpam-3431	155	52	⊆	⊆	NUM
ejpam-3431	155	53	i.	i.	NOUN
ejpam-3431	155	54	thus	thus	ADV
ejpam-3431	155	55	,	,	PUNCT
ejpam-3431	155	56	i	i	PRON
ejpam-3431	155	57	is	be	AUX
ejpam-3431	155	58	pseudo	pseudo	NOUN
ejpam-3431	155	59	hyper	hyper	ADJ
ejpam-3431	155	60	gr	gr	NOUN
ejpam-3431	155	61	-	-	PUNCT
ejpam-3431	155	62	ideal	ideal	NOUN
ejpam-3431	155	63	of	of	ADP
ejpam-3431	155	64	type	type	NOUN
ejpam-3431	155	65	3	3	NUM
ejpam-3431	155	66	.	.	PUNCT
ejpam-3431	156	1	moreover	moreover	ADV
ejpam-3431	156	2	,	,	PUNCT
ejpam-3431	156	3	r.	r.	PROPN
ejpam-3431	156	4	manzano	manzano	PROPN
ejpam-3431	156	5	,	,	PUNCT
ejpam-3431	156	6	jr	jr	PROPN
ejpam-3431	156	7	.	.	PROPN
ejpam-3431	156	8	,	,	PUNCT
ejpam-3431	156	9	g.	g.	PROPN
ejpam-3431	156	10	petalcorin	petalcorin	PROPN
ejpam-3431	156	11	,	,	PUNCT
ejpam-3431	156	12	jr	jr	PROPN
ejpam-3431	156	13	.	.	PROPN
ejpam-3431	156	14	/	/	SYM
ejpam-3431	156	15	eur	eur	PROPN
ejpam-3431	156	16	.	.	PUNCT
ejpam-3431	157	1	j.	j.	PROPN
ejpam-3431	157	2	pure	pure	PROPN
ejpam-3431	157	3	appl	appl	PROPN
ejpam-3431	157	4	.	.	PROPN
ejpam-3431	157	5	math	math	PROPN
ejpam-3431	157	6	,	,	PUNCT
ejpam-3431	157	7	12	12	NUM
ejpam-3431	157	8	(	(	PUNCT
ejpam-3431	157	9	3	3	NUM
ejpam-3431	157	10	)	)	PUNCT
ejpam-3431	157	11	(	(	PUNCT
ejpam-3431	157	12	2019	2019	NUM
ejpam-3431	157	13	)	)	PUNCT
ejpam-3431	157	14	,	,	PUNCT
ejpam-3431	157	15	821	821	NUM
ejpam-3431	157	16	-	-	SYM
ejpam-3431	157	17	833	833	NUM
ejpam-3431	157	18	828	828	NUM
ejpam-3431	157	19	i	i	PRON
ejpam-3431	157	20	�	�	VERB
ejpam-3431	157	21	~,y	~,y	NOUN
ejpam-3431	157	22	=	=	SYM
ejpam-3431	157	23	{	{	PUNCT
ejpam-3431	157	24	0	0	NUM
ejpam-3431	157	25	,	,	PUNCT
ejpam-3431	157	26	1	1	NUM
ejpam-3431	157	27	}	}	SYM
ejpam-3431	157	28	⊆	⊆	NUM
ejpam-3431	157	29	i	i	PROPN
ejpam-3431	157	30	and	and	CCONJ
ejpam-3431	157	31	i	i	PROPN
ejpam-3431	157	32	�	�	PROPN
ejpam-3431	157	33	◦	◦	NOUN
ejpam-3431	157	34	,y	,y	PUNCT
ejpam-3431	157	35	=	=	SYM
ejpam-3431	157	36	{	{	PUNCT
ejpam-3431	157	37	0	0	NUM
ejpam-3431	157	38	,	,	PUNCT
ejpam-3431	157	39	1	1	NUM
ejpam-3431	157	40	}	}	SYM
ejpam-3431	157	41	⊆	⊆	NUM
ejpam-3431	157	42	i	i	PRON
ejpam-3431	157	43	,	,	PUNCT
ejpam-3431	157	44	i	i	PRON
ejpam-3431	157	45	�	�	VERB
ejpam-3431	157	46	~,y	~,y	VERB
ejpam-3431	157	47	=	=	SYM
ejpam-3431	157	48	{	{	PUNCT
ejpam-3431	157	49	0	0	NUM
ejpam-3431	157	50	,	,	PUNCT
ejpam-3431	157	51	1	1	NUM
ejpam-3431	157	52	}	}	SYM
ejpam-3431	157	53	⊆	⊆	NUM
ejpam-3431	157	54	i	i	NOUN
ejpam-3431	157	55	or	or	CCONJ
ejpam-3431	157	56	i	i	PRON
ejpam-3431	157	57	�	�	PROPN
ejpam-3431	157	58	◦	◦	NOUN
ejpam-3431	157	59	,y	,y	PUNCT
ejpam-3431	157	60	=	=	SYM
ejpam-3431	157	61	{	{	PUNCT
ejpam-3431	157	62	0	0	NUM
ejpam-3431	157	63	,	,	PUNCT
ejpam-3431	157	64	1	1	NUM
ejpam-3431	157	65	}	}	SYM
ejpam-3431	157	66	⊆	⊆	NUM
ejpam-3431	157	67	i	i	PROPN
ejpam-3431	157	68	and	and	CCONJ
ejpam-3431	157	69	i	i	PRON
ejpam-3431	157	70	�	�	NOUN
ejpam-3431	157	71	~,y	~,y	PROPN
ejpam-3431	157	72	∩	∩	ADJ
ejpam-3431	157	73	i	i	PRON
ejpam-3431	157	74	�	�	PROPN
ejpam-3431	157	75	◦	◦	NOUN
ejpam-3431	157	76	,y	,y	PUNCT
ejpam-3431	157	77	=	=	SYM
ejpam-3431	157	78	{	{	PUNCT
ejpam-3431	157	79	0	0	NUM
ejpam-3431	157	80	,	,	PUNCT
ejpam-3431	157	81	1	1	NUM
ejpam-3431	157	82	}	}	SYM
ejpam-3431	157	83	⊆	⊆	NUM
ejpam-3431	157	84	i.	i.	NOUN
ejpam-3431	157	85	therefore	therefore	ADV
ejpam-3431	157	86	,	,	PUNCT
ejpam-3431	157	87	i	i	PRON
ejpam-3431	157	88	is	be	AUX
ejpam-3431	157	89	pseudo	pseudo	NOUN
ejpam-3431	157	90	hyper	hyper	ADJ
ejpam-3431	157	91	gr	gr	NOUN
ejpam-3431	157	92	-	-	PUNCT
ejpam-3431	157	93	ideal	ideal	NOUN
ejpam-3431	157	94	of	of	ADP
ejpam-3431	157	95	type	type	NOUN
ejpam-3431	157	96	4	4	NUM
ejpam-3431	157	97	,	,	PUNCT
ejpam-3431	157	98	8	8	NUM
ejpam-3431	157	99	and	and	CCONJ
ejpam-3431	157	100	12	12	NUM
ejpam-3431	157	101	respectively	respectively	ADV
ejpam-3431	157	102	.	.	PUNCT
ejpam-3431	157	103	example	example	NOUN
ejpam-3431	157	104	3.13	3.13	NUM
ejpam-3431	157	105	.	.	PUNCT
ejpam-3431	158	1	consider	consider	VERB
ejpam-3431	158	2	the	the	DET
ejpam-3431	158	3	pseudo	pseudo	NOUN
ejpam-3431	158	4	hyper	hyper	ADJ
ejpam-3431	158	5	gr	gr	NOUN
ejpam-3431	158	6	-	-	PUNCT
ejpam-3431	158	7	algebra	algebra	NOUN
ejpam-3431	158	8	h	h	NOUN
ejpam-3431	158	9	in	in	ADP
ejpam-3431	158	10	example	example	NOUN
ejpam-3431	158	11	3.2	3.2	NUM
ejpam-3431	158	12	.	.	PUNCT
ejpam-3431	159	1	let	let	VERB
ejpam-3431	159	2	i	i	PRON
ejpam-3431	159	3	=	=	PUNCT
ejpam-3431	159	4	{	{	PUNCT
ejpam-3431	159	5	0	0	NUM
ejpam-3431	159	6	,	,	PUNCT
ejpam-3431	159	7	3	3	NUM
ejpam-3431	159	8	}	}	PUNCT
ejpam-3431	159	9	.	.	PUNCT
ejpam-3431	160	1	note	note	VERB
ejpam-3431	160	2	that	that	SCONJ
ejpam-3431	160	3	for	for	ADP
ejpam-3431	160	4	any	any	DET
ejpam-3431	160	5	y	y	PROPN
ejpam-3431	160	6	∈	∈	PROPN
ejpam-3431	161	1	i	i	PRON
ejpam-3431	161	2	,	,	PUNCT
ejpam-3431	161	3	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	161	4	=	=	SYM
ejpam-3431	161	5	{	{	PUNCT
ejpam-3431	161	6	3	3	NUM
ejpam-3431	161	7	}	}	SYM
ejpam-3431	161	8	⊆	⊆	NUM
ejpam-3431	161	9	i.	i.	NOUN
ejpam-3431	161	10	this	this	PRON
ejpam-3431	161	11	is	be	AUX
ejpam-3431	161	12	enough	enough	ADJ
ejpam-3431	161	13	to	to	PART
ejpam-3431	161	14	categorize	categorize	VERB
ejpam-3431	161	15	i	i	PRON
ejpam-3431	161	16	as	as	ADP
ejpam-3431	161	17	a	a	DET
ejpam-3431	161	18	pseudo	pseudo	NOUN
ejpam-3431	161	19	hyper	hyper	ADJ
ejpam-3431	161	20	gr	gr	NOUN
ejpam-3431	161	21	-	-	PUNCT
ejpam-3431	161	22	ideal	ideal	NOUN
ejpam-3431	161	23	of	of	ADP
ejpam-3431	161	24	type	type	NOUN
ejpam-3431	161	25	6	6	NUM
ejpam-3431	161	26	.	.	PUNCT
ejpam-3431	162	1	also	also	ADV
ejpam-3431	162	2	for	for	ADP
ejpam-3431	162	3	any	any	PRON
ejpam-3431	162	4	y	y	PROPN
ejpam-3431	162	5	∈	∈	PROPN
ejpam-3431	163	1	i	i	PRON
ejpam-3431	163	2	,	,	PUNCT
ejpam-3431	163	3	i	i	PRON
ejpam-3431	163	4	�	�	PROPN
ejpam-3431	163	5	◦	◦	NOUN
ejpam-3431	163	6	,y	,y	PUNCT
ejpam-3431	163	7	=	=	SYM
ejpam-3431	163	8	{	{	PUNCT
ejpam-3431	163	9	0	0	NUM
ejpam-3431	163	10	,	,	PUNCT
ejpam-3431	163	11	1	1	NUM
ejpam-3431	163	12	,	,	PUNCT
ejpam-3431	163	13	2	2	NUM
ejpam-3431	163	14	,	,	PUNCT
ejpam-3431	163	15	3	3	NUM
ejpam-3431	163	16	}	}	PUNCT
ejpam-3431	163	17	.	.	PUNCT
ejpam-3431	164	1	even	even	ADV
ejpam-3431	164	2	if	if	SCONJ
ejpam-3431	164	3	i	i	PRON
ejpam-3431	164	4	�	�	VERB
ejpam-3431	164	5	◦	◦	NOUN
ejpam-3431	164	6	,y	,y	PUNCT
ejpam-3431	164	7	6⊆	6⊆	NUM
ejpam-3431	164	8	i	i	PROPN
ejpam-3431	164	9	,	,	PUNCT
ejpam-3431	164	10	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	164	11	∩	∩	X
ejpam-3431	164	12	i	i	PRON
ejpam-3431	164	13	�	�	PROPN
ejpam-3431	164	14	◦	◦	NOUN
ejpam-3431	164	15	,y	,y	PUNCT
ejpam-3431	164	16	=	=	SYM
ejpam-3431	164	17	{	{	PUNCT
ejpam-3431	164	18	3	3	NUM
ejpam-3431	164	19	}	}	SYM
ejpam-3431	164	20	⊆	⊆	NUM
ejpam-3431	164	21	i.	i.	NOUN
ejpam-3431	164	22	thus	thus	ADV
ejpam-3431	164	23	,	,	PUNCT
ejpam-3431	164	24	i	i	PRON
ejpam-3431	164	25	must	must	AUX
ejpam-3431	164	26	be	be	AUX
ejpam-3431	164	27	a	a	DET
ejpam-3431	164	28	pseudo	pseudo	NOUN
ejpam-3431	164	29	hyper	hyper	ADJ
ejpam-3431	164	30	gr	gr	NOUN
ejpam-3431	164	31	-	-	PUNCT
ejpam-3431	164	32	ideal	ideal	NOUN
ejpam-3431	164	33	of	of	ADP
ejpam-3431	164	34	type	type	NOUN
ejpam-3431	164	35	10	10	NUM
ejpam-3431	164	36	.	.	PUNCT
ejpam-3431	165	1	hence	hence	ADV
ejpam-3431	165	2	,	,	PUNCT
ejpam-3431	165	3	i	i	PRON
ejpam-3431	165	4	is	be	AUX
ejpam-3431	165	5	an	an	DET
ejpam-3431	165	6	example	example	NOUN
ejpam-3431	165	7	of	of	ADP
ejpam-3431	165	8	pseudo	pseudo	NOUN
ejpam-3431	165	9	hyper	hyper	ADJ
ejpam-3431	165	10	gr	gr	NOUN
ejpam-3431	165	11	-	-	PUNCT
ejpam-3431	165	12	ideal	ideal	NOUN
ejpam-3431	165	13	of	of	ADP
ejpam-3431	165	14	type	type	NOUN
ejpam-3431	165	15	6	6	NUM
ejpam-3431	165	16	and	and	CCONJ
ejpam-3431	165	17	10	10	NUM
ejpam-3431	165	18	but	but	CCONJ
ejpam-3431	165	19	not	not	PART
ejpam-3431	165	20	type	type	VERB
ejpam-3431	165	21	2	2	NUM
ejpam-3431	165	22	since	since	SCONJ
ejpam-3431	165	23	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	165	24	⊆	⊆	NUM
ejpam-3431	165	25	i	i	NOUN
ejpam-3431	166	1	but	but	CCONJ
ejpam-3431	166	2	i	i	PROPN
ejpam-3431	166	3	�	�	PROPN
ejpam-3431	166	4	◦	◦	NOUN
ejpam-3431	166	5	,y	,y	PUNCT
ejpam-3431	166	6	6⊆	6⊆	PROPN
ejpam-3431	166	7	i.	i.	PROPN
ejpam-3431	166	8	example	example	NOUN
ejpam-3431	166	9	3.14	3.14	NUM
ejpam-3431	166	10	.	.	PUNCT
ejpam-3431	167	1	consider	consider	VERB
ejpam-3431	167	2	the	the	DET
ejpam-3431	167	3	pseudo	pseudo	NOUN
ejpam-3431	167	4	hyper	hyper	ADJ
ejpam-3431	167	5	gr	gr	NOUN
ejpam-3431	167	6	-	-	PUNCT
ejpam-3431	167	7	algebra	algebra	NOUN
ejpam-3431	167	8	h	h	NOUN
ejpam-3431	167	9	in	in	ADP
ejpam-3431	167	10	example	example	NOUN
ejpam-3431	167	11	3.2	3.2	NUM
ejpam-3431	167	12	.	.	PUNCT
ejpam-3431	168	1	let	let	VERB
ejpam-3431	168	2	i	i	PRON
ejpam-3431	168	3	=	=	PUNCT
ejpam-3431	168	4	{	{	PUNCT
ejpam-3431	168	5	0	0	NUM
ejpam-3431	168	6	,	,	PUNCT
ejpam-3431	168	7	1	1	NUM
ejpam-3431	168	8	}	}	PUNCT
ejpam-3431	168	9	.	.	PUNCT
ejpam-3431	169	1	by	by	ADP
ejpam-3431	169	2	routine	routine	ADJ
ejpam-3431	169	3	calculations	calculation	NOUN
ejpam-3431	169	4	,	,	PUNCT
ejpam-3431	169	5	i	i	PRON
ejpam-3431	169	6	is	be	AUX
ejpam-3431	169	7	a	a	DET
ejpam-3431	169	8	pseudo	pseudo	NOUN
ejpam-3431	169	9	hyper	hyper	ADJ
ejpam-3431	169	10	gr	gr	NOUN
ejpam-3431	169	11	-	-	PUNCT
ejpam-3431	169	12	ideal	ideal	NOUN
ejpam-3431	169	13	of	of	ADP
ejpam-3431	169	14	type	type	NOUN
ejpam-3431	169	15	5	5	NUM
ejpam-3431	169	16	.	.	NOUN
ejpam-3431	169	17	example	example	NOUN
ejpam-3431	170	1	3.15	3.15	NUM
ejpam-3431	170	2	.	.	PUNCT
ejpam-3431	171	1	consider	consider	VERB
ejpam-3431	171	2	the	the	DET
ejpam-3431	171	3	pseudo	pseudo	NOUN
ejpam-3431	171	4	hyper	hyper	ADJ
ejpam-3431	171	5	gr	gr	NOUN
ejpam-3431	171	6	-	-	PUNCT
ejpam-3431	171	7	algebra	algebra	NOUN
ejpam-3431	171	8	h	h	NOUN
ejpam-3431	171	9	in	in	ADP
ejpam-3431	171	10	example	example	NOUN
ejpam-3431	171	11	3.2	3.2	NUM
ejpam-3431	171	12	.	.	PUNCT
ejpam-3431	172	1	let	let	VERB
ejpam-3431	172	2	i	i	PRON
ejpam-3431	172	3	=	=	PUNCT
ejpam-3431	172	4	{	{	PUNCT
ejpam-3431	172	5	0	0	NUM
ejpam-3431	172	6	,	,	PUNCT
ejpam-3431	172	7	1	1	NUM
ejpam-3431	172	8	,	,	PUNCT
ejpam-3431	172	9	3	3	NUM
ejpam-3431	172	10	}	}	PUNCT
ejpam-3431	172	11	.	.	PUNCT
ejpam-3431	173	1	by	by	ADP
ejpam-3431	173	2	routine	routine	ADJ
ejpam-3431	173	3	calculations	calculation	NOUN
ejpam-3431	173	4	,	,	PUNCT
ejpam-3431	173	5	i	i	PRON
ejpam-3431	173	6	is	be	AUX
ejpam-3431	173	7	a	a	DET
ejpam-3431	173	8	pseudo	pseudo	NOUN
ejpam-3431	173	9	hyper	hyper	ADJ
ejpam-3431	173	10	gr	gr	NOUN
ejpam-3431	173	11	-	-	PUNCT
ejpam-3431	173	12	ideal	ideal	NOUN
ejpam-3431	173	13	of	of	ADP
ejpam-3431	173	14	type	type	NOUN
ejpam-3431	173	15	6	6	NUM
ejpam-3431	173	16	.	.	PUNCT
ejpam-3431	173	17	example	example	NOUN
ejpam-3431	174	1	3.16	3.16	NUM
ejpam-3431	174	2	.	.	PUNCT
ejpam-3431	175	1	consider	consider	VERB
ejpam-3431	175	2	the	the	DET
ejpam-3431	175	3	pseudo	pseudo	NOUN
ejpam-3431	175	4	hyper	hyper	ADJ
ejpam-3431	175	5	gr	gr	NOUN
ejpam-3431	175	6	-	-	PUNCT
ejpam-3431	175	7	algebra	algebra	NOUN
ejpam-3431	175	8	h	h	NOUN
ejpam-3431	175	9	in	in	ADP
ejpam-3431	175	10	example	example	NOUN
ejpam-3431	175	11	3.2	3.2	NUM
ejpam-3431	175	12	.	.	PUNCT
ejpam-3431	176	1	let	let	VERB
ejpam-3431	176	2	i	i	PRON
ejpam-3431	176	3	=	=	PUNCT
ejpam-3431	176	4	{	{	PUNCT
ejpam-3431	176	5	0	0	NUM
ejpam-3431	176	6	,	,	PUNCT
ejpam-3431	176	7	2	2	NUM
ejpam-3431	176	8	}	}	PUNCT
ejpam-3431	176	9	.	.	PUNCT
ejpam-3431	177	1	by	by	ADP
ejpam-3431	177	2	routine	routine	ADJ
ejpam-3431	177	3	calculations	calculation	NOUN
ejpam-3431	177	4	,	,	PUNCT
ejpam-3431	177	5	i	i	PRON
ejpam-3431	177	6	is	be	AUX
ejpam-3431	177	7	a	a	DET
ejpam-3431	177	8	pseudo	pseudo	NOUN
ejpam-3431	177	9	hyper	hyper	ADJ
ejpam-3431	177	10	gr	gr	NOUN
ejpam-3431	177	11	-	-	PUNCT
ejpam-3431	177	12	ideal	ideal	NOUN
ejpam-3431	177	13	of	of	ADP
ejpam-3431	177	14	type	type	NOUN
ejpam-3431	177	15	7	7	NUM
ejpam-3431	177	16	.	.	NOUN
ejpam-3431	177	17	example	example	NOUN
ejpam-3431	177	18	3.17	3.17	NUM
ejpam-3431	177	19	.	.	PUNCT
ejpam-3431	178	1	consider	consider	VERB
ejpam-3431	178	2	the	the	DET
ejpam-3431	178	3	pseudo	pseudo	NOUN
ejpam-3431	178	4	hyper	hyper	ADJ
ejpam-3431	178	5	gr	gr	NOUN
ejpam-3431	178	6	-	-	PUNCT
ejpam-3431	178	7	algebra	algebra	NOUN
ejpam-3431	178	8	h	h	NOUN
ejpam-3431	178	9	in	in	ADP
ejpam-3431	178	10	example	example	NOUN
ejpam-3431	178	11	3.4	3.4	NUM
ejpam-3431	178	12	.	.	PUNCT
ejpam-3431	179	1	let	let	VERB
ejpam-3431	179	2	h	h	NOUN
ejpam-3431	179	3	′	′	NUM
ejpam-3431	179	4	=	=	PUNCT
ejpam-3431	180	1	{	{	PUNCT
ejpam-3431	180	2	0	0	NUM
ejpam-3431	180	3	,	,	PUNCT
ejpam-3431	180	4	1	1	NUM
ejpam-3431	180	5	,	,	PUNCT
ejpam-3431	180	6	2	2	NUM
ejpam-3431	180	7	,	,	PUNCT
ejpam-3431	180	8	3	3	NUM
ejpam-3431	180	9	}	}	PUNCT
ejpam-3431	180	10	.	.	PUNCT
ejpam-3431	181	1	then	then	ADV
ejpam-3431	181	2	h	h	NOUN
ejpam-3431	181	3	′	′	VERB
ejpam-3431	181	4	together	together	ADV
ejpam-3431	181	5	with	with	ADP
ejpam-3431	181	6	the	the	DET
ejpam-3431	181	7	hyperoperations	hyperoperation	NOUN
ejpam-3431	181	8	~	~	PUNCT
ejpam-3431	181	9	and	and	CCONJ
ejpam-3431	181	10	◦	◦	NOUN
ejpam-3431	181	11	given	give	VERB
ejpam-3431	181	12	by	by	ADP
ejpam-3431	181	13	the	the	DET
ejpam-3431	181	14	cayley	cayley	ADJ
ejpam-3431	181	15	table	table	NOUN
ejpam-3431	181	16	below	below	ADV
ejpam-3431	181	17	is	be	AUX
ejpam-3431	181	18	a	a	DET
ejpam-3431	181	19	pseudo	pseudo	NOUN
ejpam-3431	181	20	hyper	hyper	ADJ
ejpam-3431	181	21	subgr	subgr	NOUN
ejpam-3431	181	22	-	-	PUNCT
ejpam-3431	181	23	algebra	algebra	NOUN
ejpam-3431	181	24	of	of	ADP
ejpam-3431	181	25	h.	h.	PROPN
ejpam-3431	182	1	~	~	PUNCT
ejpam-3431	182	2	0	0	NUM
ejpam-3431	182	3	1	1	NUM
ejpam-3431	182	4	2	2	NUM
ejpam-3431	182	5	3	3	NUM
ejpam-3431	182	6	0	0	NUM
ejpam-3431	182	7	{	{	PUNCT
ejpam-3431	182	8	0	0	NUM
ejpam-3431	182	9	}	}	PUNCT
ejpam-3431	182	10	{	{	PUNCT
ejpam-3431	182	11	0	0	NUM
ejpam-3431	182	12	}	}	PUNCT
ejpam-3431	182	13	{	{	PUNCT
ejpam-3431	182	14	0	0	NUM
ejpam-3431	182	15	}	}	PUNCT
ejpam-3431	182	16	{	{	PUNCT
ejpam-3431	182	17	0	0	NUM
ejpam-3431	182	18	}	}	SYM
ejpam-3431	182	19	1	1	NUM
ejpam-3431	182	20	{	{	PUNCT
ejpam-3431	182	21	0	0	NUM
ejpam-3431	182	22	,	,	PUNCT
ejpam-3431	182	23	1	1	NUM
ejpam-3431	182	24	}	}	PUNCT
ejpam-3431	182	25	{	{	PUNCT
ejpam-3431	182	26	0	0	NUM
ejpam-3431	182	27	,	,	PUNCT
ejpam-3431	182	28	1	1	NUM
ejpam-3431	182	29	}	}	PUNCT
ejpam-3431	182	30	{	{	PUNCT
ejpam-3431	182	31	0	0	NUM
ejpam-3431	182	32	,	,	PUNCT
ejpam-3431	182	33	1	1	NUM
ejpam-3431	182	34	}	}	PUNCT
ejpam-3431	182	35	{	{	PUNCT
ejpam-3431	182	36	0	0	NUM
ejpam-3431	182	37	,	,	PUNCT
ejpam-3431	182	38	1	1	NUM
ejpam-3431	182	39	}	}	SYM
ejpam-3431	182	40	2	2	NUM
ejpam-3431	182	41	{	{	PUNCT
ejpam-3431	182	42	0	0	NUM
ejpam-3431	182	43	,	,	PUNCT
ejpam-3431	182	44	2	2	NUM
ejpam-3431	182	45	}	}	PUNCT
ejpam-3431	182	46	{	{	PUNCT
ejpam-3431	182	47	0	0	NUM
ejpam-3431	182	48	,	,	PUNCT
ejpam-3431	182	49	2	2	NUM
ejpam-3431	182	50	}	}	PUNCT
ejpam-3431	182	51	{	{	PUNCT
ejpam-3431	182	52	0	0	NUM
ejpam-3431	182	53	,	,	PUNCT
ejpam-3431	182	54	2	2	NUM
ejpam-3431	182	55	}	}	PUNCT
ejpam-3431	182	56	{	{	PUNCT
ejpam-3431	182	57	0	0	NUM
ejpam-3431	182	58	,	,	PUNCT
ejpam-3431	182	59	2	2	NUM
ejpam-3431	182	60	}	}	SYM
ejpam-3431	182	61	3	3	NUM
ejpam-3431	182	62	{	{	PUNCT
ejpam-3431	182	63	0	0	NUM
ejpam-3431	182	64	,	,	PUNCT
ejpam-3431	182	65	3	3	NUM
ejpam-3431	182	66	}	}	PUNCT
ejpam-3431	182	67	{	{	PUNCT
ejpam-3431	182	68	0	0	NUM
ejpam-3431	182	69	,	,	PUNCT
ejpam-3431	182	70	3	3	NUM
ejpam-3431	182	71	}	}	PUNCT
ejpam-3431	182	72	{	{	PUNCT
ejpam-3431	182	73	0	0	NUM
ejpam-3431	182	74	,	,	PUNCT
ejpam-3431	182	75	3	3	NUM
ejpam-3431	182	76	}	}	PUNCT
ejpam-3431	182	77	{	{	PUNCT
ejpam-3431	182	78	0	0	NUM
ejpam-3431	182	79	,	,	PUNCT
ejpam-3431	182	80	3	3	X
ejpam-3431	182	81	}	}	PUNCT
ejpam-3431	182	82	◦	◦	NOUN
ejpam-3431	182	83	0	0	NUM
ejpam-3431	182	84	1	1	NUM
ejpam-3431	182	85	2	2	NUM
ejpam-3431	182	86	3	3	NUM
ejpam-3431	182	87	0	0	NUM
ejpam-3431	182	88	{	{	PUNCT
ejpam-3431	182	89	0	0	NUM
ejpam-3431	182	90	}	}	PUNCT
ejpam-3431	182	91	{	{	PUNCT
ejpam-3431	182	92	0	0	NUM
ejpam-3431	182	93	,	,	PUNCT
ejpam-3431	182	94	1	1	NUM
ejpam-3431	182	95	}	}	PUNCT
ejpam-3431	182	96	{	{	PUNCT
ejpam-3431	182	97	0	0	NUM
ejpam-3431	182	98	,	,	PUNCT
ejpam-3431	182	99	2	2	NUM
ejpam-3431	182	100	}	}	PUNCT
ejpam-3431	182	101	{	{	PUNCT
ejpam-3431	182	102	0	0	NUM
ejpam-3431	182	103	,	,	PUNCT
ejpam-3431	182	104	3	3	NUM
ejpam-3431	182	105	}	}	SYM
ejpam-3431	182	106	1	1	NUM
ejpam-3431	182	107	{	{	PUNCT
ejpam-3431	182	108	0	0	NUM
ejpam-3431	182	109	,	,	PUNCT
ejpam-3431	182	110	1	1	NUM
ejpam-3431	182	111	}	}	PUNCT
ejpam-3431	182	112	{	{	PUNCT
ejpam-3431	182	113	0	0	NUM
ejpam-3431	182	114	,	,	PUNCT
ejpam-3431	182	115	1	1	NUM
ejpam-3431	182	116	}	}	PUNCT
ejpam-3431	182	117	{	{	PUNCT
ejpam-3431	182	118	0	0	NUM
ejpam-3431	182	119	,	,	PUNCT
ejpam-3431	182	120	1	1	NUM
ejpam-3431	182	121	,	,	PUNCT
ejpam-3431	182	122	2	2	NUM
ejpam-3431	182	123	}	}	PUNCT
ejpam-3431	182	124	{	{	PUNCT
ejpam-3431	182	125	0	0	NUM
ejpam-3431	182	126	,	,	PUNCT
ejpam-3431	182	127	1	1	NUM
ejpam-3431	182	128	,	,	PUNCT
ejpam-3431	182	129	3	3	NUM
ejpam-3431	182	130	}	}	SYM
ejpam-3431	182	131	2	2	NUM
ejpam-3431	182	132	{	{	PUNCT
ejpam-3431	182	133	0	0	NUM
ejpam-3431	182	134	,	,	PUNCT
ejpam-3431	182	135	2	2	NUM
ejpam-3431	182	136	}	}	PUNCT
ejpam-3431	182	137	{	{	PUNCT
ejpam-3431	182	138	0	0	NUM
ejpam-3431	182	139	,	,	PUNCT
ejpam-3431	182	140	1	1	NUM
ejpam-3431	182	141	,	,	PUNCT
ejpam-3431	182	142	2	2	NUM
ejpam-3431	182	143	}	}	PUNCT
ejpam-3431	182	144	{	{	PUNCT
ejpam-3431	182	145	0	0	NUM
ejpam-3431	182	146	,	,	PUNCT
ejpam-3431	182	147	2	2	NUM
ejpam-3431	182	148	}	}	PUNCT
ejpam-3431	182	149	{	{	PUNCT
ejpam-3431	182	150	0	0	NUM
ejpam-3431	182	151	,	,	PUNCT
ejpam-3431	182	152	2	2	NUM
ejpam-3431	182	153	,	,	PUNCT
ejpam-3431	182	154	3	3	NUM
ejpam-3431	182	155	}	}	SYM
ejpam-3431	182	156	3	3	NUM
ejpam-3431	182	157	{	{	PUNCT
ejpam-3431	182	158	0	0	NUM
ejpam-3431	182	159	,	,	PUNCT
ejpam-3431	182	160	3	3	NUM
ejpam-3431	182	161	}	}	PUNCT
ejpam-3431	182	162	{	{	PUNCT
ejpam-3431	182	163	0	0	NUM
ejpam-3431	182	164	,	,	PUNCT
ejpam-3431	182	165	1	1	NUM
ejpam-3431	182	166	,	,	PUNCT
ejpam-3431	182	167	3	3	NUM
ejpam-3431	182	168	}	}	PUNCT
ejpam-3431	182	169	{	{	PUNCT
ejpam-3431	182	170	0	0	NUM
ejpam-3431	182	171	,	,	PUNCT
ejpam-3431	182	172	2	2	NUM
ejpam-3431	182	173	,	,	PUNCT
ejpam-3431	182	174	3	3	NUM
ejpam-3431	182	175	}	}	PUNCT
ejpam-3431	182	176	{	{	PUNCT
ejpam-3431	182	177	0	0	NUM
ejpam-3431	182	178	,	,	PUNCT
ejpam-3431	182	179	3	3	NUM
ejpam-3431	182	180	}	}	PUNCT
ejpam-3431	182	181	consider	consider	VERB
ejpam-3431	182	182	i	i	PRON
ejpam-3431	182	183	=	=	PUNCT
ejpam-3431	182	184	{	{	PUNCT
ejpam-3431	182	185	0	0	NUM
ejpam-3431	182	186	,	,	PUNCT
ejpam-3431	182	187	2	2	NUM
ejpam-3431	182	188	,	,	PUNCT
ejpam-3431	182	189	3	3	NUM
ejpam-3431	182	190	}	}	PUNCT
ejpam-3431	182	191	.	.	PUNCT
ejpam-3431	183	1	observe	observe	VERB
ejpam-3431	183	2	that	that	SCONJ
ejpam-3431	183	3	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	183	4	=	=	SYM
ejpam-3431	183	5	{	{	PUNCT
ejpam-3431	183	6	0	0	NUM
ejpam-3431	183	7	,	,	PUNCT
ejpam-3431	183	8	2	2	NUM
ejpam-3431	183	9	,	,	PUNCT
ejpam-3431	183	10	3	3	NUM
ejpam-3431	183	11	}	}	PUNCT
ejpam-3431	183	12	=	=	PUNCT
ejpam-3431	183	13	i⊆	i⊆	NOUN
ejpam-3431	183	14	◦	◦	NOUN
ejpam-3431	183	15	,y	,y	PUNCT
ejpam-3431	183	16	.	.	PUNCT
ejpam-3431	184	1	this	this	PRON
ejpam-3431	184	2	means	mean	VERB
ejpam-3431	184	3	that	that	SCONJ
ejpam-3431	184	4	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	184	5	∩	∩	NOUN
ejpam-3431	184	6	i⊆	i⊆	NOUN
ejpam-3431	184	7	◦	◦	NOUN
ejpam-3431	184	8	,y	,y	PUNCT
ejpam-3431	184	9	=	=	SYM
ejpam-3431	184	10	{	{	PUNCT
ejpam-3431	184	11	0	0	NUM
ejpam-3431	184	12	,	,	PUNCT
ejpam-3431	184	13	2	2	NUM
ejpam-3431	184	14	,	,	PUNCT
ejpam-3431	184	15	3	3	NUM
ejpam-3431	184	16	}	}	SYM
ejpam-3431	184	17	⊆	⊆	NUM
ejpam-3431	184	18	i.	i.	NOUN
ejpam-3431	184	19	thus	thus	ADV
ejpam-3431	184	20	,	,	PUNCT
ejpam-3431	184	21	i	i	PRON
ejpam-3431	184	22	is	be	AUX
ejpam-3431	184	23	a	a	DET
ejpam-3431	184	24	pseudo	pseudo	NOUN
ejpam-3431	184	25	hyper	hyper	ADJ
ejpam-3431	184	26	gr	gr	NOUN
ejpam-3431	184	27	-	-	PUNCT
ejpam-3431	184	28	ideal	ideal	NOUN
ejpam-3431	184	29	of	of	ADP
ejpam-3431	184	30	type	type	NOUN
ejpam-3431	184	31	9	9	NUM
ejpam-3431	184	32	.	.	PUNCT
ejpam-3431	185	1	let	let	VERB
ejpam-3431	185	2	i	i	PRON
ejpam-3431	185	3	=	=	PUNCT
ejpam-3431	185	4	{	{	PUNCT
ejpam-3431	185	5	0	0	NUM
ejpam-3431	185	6	,	,	PUNCT
ejpam-3431	185	7	1	1	NUM
ejpam-3431	185	8	,	,	PUNCT
ejpam-3431	185	9	2	2	NUM
ejpam-3431	185	10	}	}	PUNCT
ejpam-3431	185	11	.	.	PUNCT
ejpam-3431	186	1	o	o	NOUN
ejpam-3431	186	2	bservier	bservier	NOUN
ejpam-3431	186	3	that	that	PRON
ejpam-3431	186	4	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	186	5	=	=	SYM
ejpam-3431	186	6	{	{	PUNCT
ejpam-3431	186	7	0	0	NUM
ejpam-3431	186	8	,	,	PUNCT
ejpam-3431	186	9	1	1	NUM
ejpam-3431	186	10	,	,	PUNCT
ejpam-3431	186	11	2	2	NUM
ejpam-3431	186	12	}	}	PUNCT
ejpam-3431	186	13	and	and	CCONJ
ejpam-3431	186	14	i	i	PRON
ejpam-3431	186	15	�	�	PROPN
ejpam-3431	186	16	◦	◦	NOUN
ejpam-3431	186	17	,y	,y	PUNCT
ejpam-3431	186	18	=	=	SYM
ejpam-3431	186	19	{	{	PUNCT
ejpam-3431	186	20	0	0	NUM
ejpam-3431	186	21	,	,	PUNCT
ejpam-3431	186	22	1	1	NUM
ejpam-3431	186	23	,	,	PUNCT
ejpam-3431	186	24	2	2	NUM
ejpam-3431	186	25	,	,	PUNCT
ejpam-3431	186	26	3	3	NUM
ejpam-3431	186	27	}	}	PUNCT
ejpam-3431	186	28	.	.	PUNCT
ejpam-3431	187	1	thus	thus	ADV
ejpam-3431	187	2	,	,	PUNCT
ejpam-3431	187	3	we	we	PRON
ejpam-3431	187	4	have	have	VERB
ejpam-3431	187	5	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	187	6	∩	∩	NOUN
ejpam-3431	187	7	i	i	PRON
ejpam-3431	187	8	�	�	PROPN
ejpam-3431	187	9	◦	◦	NOUN
ejpam-3431	187	10	,y	,y	PUNCT
ejpam-3431	187	11	=	=	SYM
ejpam-3431	187	12	{	{	PUNCT
ejpam-3431	187	13	0	0	NUM
ejpam-3431	187	14	,	,	PUNCT
ejpam-3431	187	15	1	1	NUM
ejpam-3431	187	16	,	,	PUNCT
ejpam-3431	187	17	2	2	NUM
ejpam-3431	187	18	}	}	SYM
ejpam-3431	187	19	⊆	⊆	NUM
ejpam-3431	187	20	i.	i.	NOUN
ejpam-3431	187	21	therefore	therefore	ADV
ejpam-3431	187	22	,	,	PUNCT
ejpam-3431	187	23	i	i	PRON
ejpam-3431	187	24	is	be	AUX
ejpam-3431	187	25	a	a	DET
ejpam-3431	187	26	pseudo	pseudo	NOUN
ejpam-3431	187	27	hyper	hyper	ADJ
ejpam-3431	187	28	gr	gr	NOUN
ejpam-3431	187	29	-	-	PUNCT
ejpam-3431	187	30	ideal	ideal	NOUN
ejpam-3431	187	31	of	of	ADP
ejpam-3431	187	32	type	type	NOUN
ejpam-3431	187	33	10	10	NUM
ejpam-3431	187	34	.	.	PUNCT
ejpam-3431	188	1	let	let	VERB
ejpam-3431	188	2	i	i	PRON
ejpam-3431	188	3	=	=	PUNCT
ejpam-3431	188	4	{	{	PUNCT
ejpam-3431	188	5	0	0	NUM
ejpam-3431	188	6	,	,	PUNCT
ejpam-3431	188	7	1	1	NUM
ejpam-3431	188	8	,	,	PUNCT
ejpam-3431	188	9	3	3	NUM
ejpam-3431	188	10	}	}	PUNCT
ejpam-3431	188	11	.	.	PUNCT
ejpam-3431	189	1	observe	observe	VERB
ejpam-3431	189	2	that	that	SCONJ
ejpam-3431	189	3	i	i	PRON
ejpam-3431	189	4	�	�	VERB
ejpam-3431	189	5	~,y	~,y	NOUN
ejpam-3431	189	6	=	=	SYM
ejpam-3431	189	7	{	{	PUNCT
ejpam-3431	189	8	0	0	NUM
ejpam-3431	189	9	,	,	PUNCT
ejpam-3431	189	10	1	1	NUM
ejpam-3431	189	11	,	,	PUNCT
ejpam-3431	189	12	2	2	NUM
ejpam-3431	189	13	,	,	PUNCT
ejpam-3431	189	14	3	3	NUM
ejpam-3431	189	15	}	}	PUNCT
ejpam-3431	189	16	and	and	CCONJ
ejpam-3431	189	17	i⊆	i⊆	NOUN
ejpam-3431	189	18	◦	◦	NOUN
ejpam-3431	189	19	,y	,y	PUNCT
ejpam-3431	189	20	=	=	SYM
ejpam-3431	189	21	{	{	PUNCT
ejpam-3431	189	22	0	0	NUM
ejpam-3431	189	23	,	,	PUNCT
ejpam-3431	189	24	1	1	NUM
ejpam-3431	189	25	,	,	PUNCT
ejpam-3431	189	26	3	3	NUM
ejpam-3431	189	27	}	}	PUNCT
ejpam-3431	189	28	.	.	PUNCT
ejpam-3431	190	1	thus	thus	ADV
ejpam-3431	190	2	,	,	PUNCT
ejpam-3431	190	3	we	we	PRON
ejpam-3431	190	4	have	have	VERB
ejpam-3431	190	5	i	i	PRON
ejpam-3431	190	6	�	�	NOUN
ejpam-3431	190	7	~,y	~,y	NOUN
ejpam-3431	190	8	∩	∩	ADJ
ejpam-3431	190	9	i⊆	i⊆	NOUN
ejpam-3431	190	10	◦	◦	NOUN
ejpam-3431	190	11	,y	,y	PUNCT
ejpam-3431	190	12	=	=	SYM
ejpam-3431	190	13	{	{	PUNCT
ejpam-3431	190	14	0	0	NUM
ejpam-3431	190	15	,	,	PUNCT
ejpam-3431	190	16	1	1	NUM
ejpam-3431	190	17	,	,	PUNCT
ejpam-3431	190	18	3	3	NUM
ejpam-3431	190	19	}	}	SYM
ejpam-3431	190	20	⊆	⊆	NUM
ejpam-3431	190	21	i.	i.	NOUN
ejpam-3431	190	22	therefore	therefore	ADV
ejpam-3431	190	23	,	,	PUNCT
ejpam-3431	190	24	i	i	PRON
ejpam-3431	190	25	is	be	AUX
ejpam-3431	190	26	a	a	DET
ejpam-3431	190	27	pseudo	pseudo	NOUN
ejpam-3431	190	28	hyper	hyper	ADJ
ejpam-3431	190	29	gr	gr	NOUN
ejpam-3431	190	30	-	-	PUNCT
ejpam-3431	190	31	ideal	ideal	NOUN
ejpam-3431	190	32	of	of	ADP
ejpam-3431	190	33	type	type	NOUN
ejpam-3431	190	34	11	11	NUM
ejpam-3431	190	35	.	.	PUNCT
ejpam-3431	191	1	r.	r.	PROPN
ejpam-3431	191	2	manzano	manzano	PROPN
ejpam-3431	191	3	,	,	PUNCT
ejpam-3431	191	4	jr	jr	PROPN
ejpam-3431	191	5	.	.	PROPN
ejpam-3431	191	6	,	,	PUNCT
ejpam-3431	191	7	g.	g.	PROPN
ejpam-3431	191	8	petalcorin	petalcorin	PROPN
ejpam-3431	191	9	,	,	PUNCT
ejpam-3431	191	10	jr	jr	PROPN
ejpam-3431	191	11	.	.	PROPN
ejpam-3431	191	12	/	/	SYM
ejpam-3431	191	13	eur	eur	PROPN
ejpam-3431	191	14	.	.	PUNCT
ejpam-3431	192	1	j.	j.	PROPN
ejpam-3431	192	2	pure	pure	PROPN
ejpam-3431	192	3	appl	appl	PROPN
ejpam-3431	192	4	.	.	PROPN
ejpam-3431	192	5	math	math	PROPN
ejpam-3431	192	6	,	,	PUNCT
ejpam-3431	192	7	12	12	NUM
ejpam-3431	192	8	(	(	PUNCT
ejpam-3431	192	9	3	3	NUM
ejpam-3431	192	10	)	)	PUNCT
ejpam-3431	192	11	(	(	PUNCT
ejpam-3431	192	12	2019	2019	NUM
ejpam-3431	192	13	)	)	PUNCT
ejpam-3431	192	14	,	,	PUNCT
ejpam-3431	192	15	821	821	NUM
ejpam-3431	192	16	-	-	SYM
ejpam-3431	192	17	833	833	NUM
ejpam-3431	192	18	829	829	NUM
ejpam-3431	192	19	theorem	theorem	VERB
ejpam-3431	192	20	3.18	3.18	NUM
ejpam-3431	192	21	.	.	PUNCT
ejpam-3431	193	1	every	every	DET
ejpam-3431	193	2	pseudo	pseudo	NOUN
ejpam-3431	193	3	hyper	hyper	ADJ
ejpam-3431	193	4	gr	gr	NOUN
ejpam-3431	193	5	-	-	PUNCT
ejpam-3431	193	6	ideal	ideal	NOUN
ejpam-3431	193	7	in	in	ADP
ejpam-3431	193	8	h	h	NOUN
ejpam-3431	193	9	of	of	ADP
ejpam-3431	193	10	type	type	NOUN
ejpam-3431	193	11	2	2	NUM
ejpam-3431	193	12	is	be	AUX
ejpam-3431	193	13	a	a	DET
ejpam-3431	193	14	pseudo	pseudo	NOUN
ejpam-3431	193	15	hyper	hyper	ADJ
ejpam-3431	193	16	gr	gr	NOUN
ejpam-3431	193	17	-	-	PUNCT
ejpam-3431	193	18	ideal	ideal	NOUN
ejpam-3431	193	19	in	in	ADP
ejpam-3431	193	20	h	h	NOUN
ejpam-3431	193	21	of	of	ADP
ejpam-3431	193	22	type	type	NOUN
ejpam-3431	193	23	1	1	NUM
ejpam-3431	193	24	.	.	PUNCT
ejpam-3431	194	1	proof	proof	NOUN
ejpam-3431	194	2	.	.	PUNCT
ejpam-3431	195	1	let	let	VERB
ejpam-3431	195	2	i	i	PRON
ejpam-3431	195	3	be	be	AUX
ejpam-3431	195	4	a	a	DET
ejpam-3431	195	5	pseudo	pseudo	NOUN
ejpam-3431	195	6	hyper	hyper	ADJ
ejpam-3431	195	7	gr	gr	NOUN
ejpam-3431	195	8	-	-	PUNCT
ejpam-3431	195	9	ideal	ideal	NOUN
ejpam-3431	195	10	of	of	ADP
ejpam-3431	195	11	type	type	NOUN
ejpam-3431	195	12	2	2	NUM
ejpam-3431	195	13	.	.	PUNCT
ejpam-3431	196	1	now	now	ADV
ejpam-3431	196	2	,	,	PUNCT
ejpam-3431	196	3	we	we	PRON
ejpam-3431	196	4	will	will	AUX
ejpam-3431	196	5	show	show	VERB
ejpam-3431	196	6	that	that	SCONJ
ejpam-3431	196	7	i	i	PRON
ejpam-3431	196	8	is	be	AUX
ejpam-3431	196	9	a	a	DET
ejpam-3431	196	10	pseudo	pseudo	NOUN
ejpam-3431	196	11	hyper	hyper	ADJ
ejpam-3431	196	12	gr	gr	NOUN
ejpam-3431	196	13	-	-	PUNCT
ejpam-3431	196	14	ideal	ideal	NOUN
ejpam-3431	196	15	of	of	ADP
ejpam-3431	196	16	type	type	NOUN
ejpam-3431	196	17	1	1	NUM
ejpam-3431	196	18	.	.	PUNCT
ejpam-3431	197	1	it	it	PRON
ejpam-3431	197	2	is	be	AUX
ejpam-3431	197	3	enough	enough	ADJ
ejpam-3431	197	4	to	to	PART
ejpam-3431	197	5	show	show	VERB
ejpam-3431	197	6	that	that	SCONJ
ejpam-3431	197	7	for	for	ADP
ejpam-3431	197	8	any	any	DET
ejpam-3431	197	9	y	y	PROPN
ejpam-3431	197	10	∈	∈	PROPN
ejpam-3431	197	11	i	i	PROPN
ejpam-3431	197	12	,	,	PUNCT
ejpam-3431	197	13	i⊆	i⊆	PROPN
ejpam-3431	197	14	◦	◦	NOUN
ejpam-3431	197	15	,y	,y	PUNCT
ejpam-3431	197	16	⊆	⊆	NUM
ejpam-3431	197	17	i.	i.	NOUN
ejpam-3431	197	18	let	let	VERB
ejpam-3431	197	19	y	y	PROPN
ejpam-3431	197	20	∈	∈	PROPN
ejpam-3431	198	1	i	i	PRON
ejpam-3431	198	2	and	and	CCONJ
ejpam-3431	198	3	x	x	PROPN
ejpam-3431	198	4	∈	∈	PROPN
ejpam-3431	198	5	i⊆	i⊆	PROPN
ejpam-3431	198	6	◦	◦	NOUN
ejpam-3431	198	7	,y	,y	PUNCT
ejpam-3431	198	8	.	.	PUNCT
ejpam-3431	199	1	then	then	ADV
ejpam-3431	199	2	,	,	PUNCT
ejpam-3431	199	3	x	x	PUNCT
ejpam-3431	199	4	◦	◦	VERB
ejpam-3431	199	5	y	y	NUM
ejpam-3431	199	6	⊆	⊆	NUM
ejpam-3431	199	7	i	i	PROPN
ejpam-3431	199	8	and	and	CCONJ
ejpam-3431	199	9	by	by	ADP
ejpam-3431	199	10	remark	remark	NOUN
ejpam-3431	199	11	3.3	3.3	NUM
ejpam-3431	199	12	(	(	PUNCT
ejpam-3431	199	13	iv	iv	NUM
ejpam-3431	199	14	)	)	PUNCT
ejpam-3431	199	15	,	,	PUNCT
ejpam-3431	199	16	x	x	PUNCT
ejpam-3431	199	17	◦	◦	NOUN
ejpam-3431	199	18	y	y	PROPN
ejpam-3431	199	19	�	�	PROPN
ejpam-3431	199	20	i.	i.	PROPN
ejpam-3431	199	21	hence	hence	ADV
ejpam-3431	199	22	x	x	PROPN
ejpam-3431	199	23	∈	∈	PROPN
ejpam-3431	199	24	i	i	PRON
ejpam-3431	199	25	�	�	PROPN
ejpam-3431	199	26	◦	◦	NOUN
ejpam-3431	199	27	,y	,y	NOUN
ejpam-3431	199	28	.	.	PUNCT
ejpam-3431	200	1	since	since	SCONJ
ejpam-3431	200	2	i	i	PRON
ejpam-3431	200	3	is	be	AUX
ejpam-3431	200	4	a	a	DET
ejpam-3431	200	5	pseudo	pseudo	NOUN
ejpam-3431	200	6	hyper	hyper	ADJ
ejpam-3431	200	7	gr	gr	NOUN
ejpam-3431	200	8	-	-	PUNCT
ejpam-3431	200	9	ideal	ideal	NOUN
ejpam-3431	200	10	of	of	ADP
ejpam-3431	200	11	type	type	NOUN
ejpam-3431	200	12	2	2	NUM
ejpam-3431	200	13	,	,	PUNCT
ejpam-3431	200	14	i	i	PRON
ejpam-3431	200	15	�	�	PROPN
ejpam-3431	200	16	◦	◦	NOUN
ejpam-3431	200	17	,y	,y	PUNCT
ejpam-3431	200	18	⊆	⊆	NUM
ejpam-3431	200	19	i	i	PROPN
ejpam-3431	200	20	and	and	CCONJ
ejpam-3431	200	21	so	so	ADV
ejpam-3431	200	22	x	x	SYM
ejpam-3431	200	23	∈	∈	PROPN
ejpam-3431	200	24	i.	i.	NOUN
ejpam-3431	200	25	therefore	therefore	ADV
ejpam-3431	200	26	,	,	PUNCT
ejpam-3431	200	27	i⊆	i⊆	PROPN
ejpam-3431	200	28	◦	◦	NOUN
ejpam-3431	200	29	,y	,y	PUNCT
ejpam-3431	200	30	⊆	⊆	NUM
ejpam-3431	200	31	i.	i.	PROPN
ejpam-3431	200	32	�	�	PROPN
ejpam-3431	200	33	theorem	theorem	VERB
ejpam-3431	200	34	3.19	3.19	NUM
ejpam-3431	200	35	.	.	PUNCT
ejpam-3431	201	1	every	every	DET
ejpam-3431	201	2	pseudo	pseudo	NOUN
ejpam-3431	201	3	hyper	hyper	ADJ
ejpam-3431	201	4	gr	gr	NOUN
ejpam-3431	201	5	-	-	PUNCT
ejpam-3431	201	6	ideal	ideal	NOUN
ejpam-3431	201	7	in	in	ADP
ejpam-3431	201	8	h	h	NOUN
ejpam-3431	201	9	of	of	ADP
ejpam-3431	201	10	type	type	NOUN
ejpam-3431	201	11	4	4	NUM
ejpam-3431	201	12	is	be	AUX
ejpam-3431	201	13	a	a	DET
ejpam-3431	201	14	pseudo	pseudo	NOUN
ejpam-3431	201	15	hyper	hyper	ADJ
ejpam-3431	201	16	gr	gr	NOUN
ejpam-3431	201	17	-	-	PUNCT
ejpam-3431	201	18	ideal	ideal	NOUN
ejpam-3431	201	19	in	in	ADP
ejpam-3431	201	20	h	h	NOUN
ejpam-3431	201	21	of	of	ADP
ejpam-3431	201	22	types	type	NOUN
ejpam-3431	201	23	1	1	NUM
ejpam-3431	201	24	,	,	PUNCT
ejpam-3431	201	25	2	2	NUM
ejpam-3431	201	26	and	and	CCONJ
ejpam-3431	201	27	8	8	NUM
ejpam-3431	201	28	.	.	PUNCT
ejpam-3431	202	1	proof	proof	NOUN
ejpam-3431	202	2	.	.	PUNCT
ejpam-3431	203	1	let	let	VERB
ejpam-3431	203	2	i	i	PRON
ejpam-3431	203	3	be	be	AUX
ejpam-3431	203	4	a	a	DET
ejpam-3431	203	5	pseudo	pseudo	NOUN
ejpam-3431	203	6	hyper	hyper	ADJ
ejpam-3431	203	7	gr	gr	NOUN
ejpam-3431	203	8	-	-	PUNCT
ejpam-3431	203	9	ideal	ideal	NOUN
ejpam-3431	203	10	in	in	ADP
ejpam-3431	203	11	h	h	NOUN
ejpam-3431	203	12	of	of	ADP
ejpam-3431	203	13	type	type	NOUN
ejpam-3431	203	14	4	4	NUM
ejpam-3431	203	15	.	.	PUNCT
ejpam-3431	204	1	we	we	PRON
ejpam-3431	204	2	will	will	AUX
ejpam-3431	204	3	show	show	VERB
ejpam-3431	204	4	that	that	SCONJ
ejpam-3431	204	5	i	i	PRON
ejpam-3431	204	6	is	be	AUX
ejpam-3431	204	7	a	a	DET
ejpam-3431	204	8	pseudo	pseudo	NOUN
ejpam-3431	204	9	hyper	hyper	ADJ
ejpam-3431	204	10	gr	gr	NOUN
ejpam-3431	204	11	-	-	PUNCT
ejpam-3431	204	12	ideal	ideal	NOUN
ejpam-3431	204	13	of	of	ADP
ejpam-3431	204	14	type	type	NOUN
ejpam-3431	204	15	2	2	NUM
ejpam-3431	204	16	.	.	PUNCT
ejpam-3431	205	1	it	it	PRON
ejpam-3431	205	2	is	be	AUX
ejpam-3431	205	3	enough	enough	ADJ
ejpam-3431	205	4	to	to	PART
ejpam-3431	205	5	show	show	VERB
ejpam-3431	205	6	that	that	SCONJ
ejpam-3431	205	7	for	for	ADP
ejpam-3431	205	8	any	any	DET
ejpam-3431	205	9	y	y	PROPN
ejpam-3431	205	10	∈	∈	PROPN
ejpam-3431	205	11	i	i	PRON
ejpam-3431	205	12	,	,	PUNCT
ejpam-3431	205	13	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	205	14	⊆	⊆	NUM
ejpam-3431	205	15	i.	i.	NOUN
ejpam-3431	205	16	let	let	VERB
ejpam-3431	205	17	y	y	PROPN
ejpam-3431	205	18	∈	∈	PROPN
ejpam-3431	206	1	i	i	PRON
ejpam-3431	206	2	and	and	CCONJ
ejpam-3431	206	3	x	x	PROPN
ejpam-3431	206	4	∈	∈	PROPN
ejpam-3431	206	5	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	206	6	.	.	PUNCT
ejpam-3431	207	1	then	then	ADV
ejpam-3431	207	2	,	,	PUNCT
ejpam-3431	207	3	x	x	X
ejpam-3431	207	4	~	~	PUNCT
ejpam-3431	207	5	y	y	PROPN
ejpam-3431	207	6	⊆	⊆	NUM
ejpam-3431	207	7	i	i	PROPN
ejpam-3431	207	8	and	and	CCONJ
ejpam-3431	207	9	by	by	ADP
ejpam-3431	207	10	remark	remark	NOUN
ejpam-3431	207	11	3.3	3.3	NUM
ejpam-3431	207	12	(	(	PUNCT
ejpam-3431	207	13	iv	iv	NUM
ejpam-3431	207	14	)	)	PUNCT
ejpam-3431	207	15	,	,	PUNCT
ejpam-3431	207	16	x	x	X
ejpam-3431	207	17	~	~	PUNCT
ejpam-3431	207	18	y	y	PROPN
ejpam-3431	207	19	�	�	PROPN
ejpam-3431	207	20	i.	i.	PROPN
ejpam-3431	207	21	hence	hence	ADV
ejpam-3431	207	22	,	,	PUNCT
ejpam-3431	207	23	x	x	PROPN
ejpam-3431	207	24	∈	∈	PROPN
ejpam-3431	207	25	i	i	PRON
ejpam-3431	207	26	�	�	PROPN
ejpam-3431	207	27	~,y	~,y	PROPN
ejpam-3431	207	28	.	.	PUNCT
ejpam-3431	208	1	since	since	SCONJ
ejpam-3431	208	2	i	i	PRON
ejpam-3431	208	3	is	be	AUX
ejpam-3431	208	4	a	a	DET
ejpam-3431	208	5	pseudo	pseudo	NOUN
ejpam-3431	208	6	hyper	hyper	ADJ
ejpam-3431	208	7	gr	gr	NOUN
ejpam-3431	208	8	-	-	PUNCT
ejpam-3431	208	9	ideal	ideal	NOUN
ejpam-3431	208	10	of	of	ADP
ejpam-3431	208	11	type	type	NOUN
ejpam-3431	208	12	4	4	NUM
ejpam-3431	208	13	,	,	PUNCT
ejpam-3431	208	14	i	i	PRON
ejpam-3431	208	15	�	�	VERB
ejpam-3431	208	16	~,y	~,y	VERB
ejpam-3431	208	17	⊆	⊆	NUM
ejpam-3431	208	18	i	i	PRON
ejpam-3431	208	19	and	and	CCONJ
ejpam-3431	208	20	so	so	ADV
ejpam-3431	208	21	x	x	SYM
ejpam-3431	208	22	∈	∈	PROPN
ejpam-3431	208	23	i.	i.	NOUN
ejpam-3431	208	24	thus	thus	ADV
ejpam-3431	208	25	,	,	PUNCT
ejpam-3431	208	26	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	208	27	⊆	⊆	NUM
ejpam-3431	208	28	i.	i.	NOUN
ejpam-3431	208	29	hence	hence	ADV
ejpam-3431	208	30	,	,	PUNCT
ejpam-3431	208	31	i	i	PRON
ejpam-3431	208	32	is	be	AUX
ejpam-3431	208	33	a	a	DET
ejpam-3431	208	34	pseudo	pseudo	NOUN
ejpam-3431	208	35	hyper	hyper	ADJ
ejpam-3431	208	36	gr	gr	NOUN
ejpam-3431	208	37	-	-	PUNCT
ejpam-3431	208	38	ideal	ideal	NOUN
ejpam-3431	208	39	of	of	ADP
ejpam-3431	208	40	type	type	NOUN
ejpam-3431	208	41	2	2	NUM
ejpam-3431	208	42	and	and	CCONJ
ejpam-3431	208	43	by	by	ADP
ejpam-3431	208	44	theorem	theorem	NOUN
ejpam-3431	208	45	3.18	3.18	NUM
ejpam-3431	208	46	,	,	PUNCT
ejpam-3431	208	47	i	i	PRON
ejpam-3431	208	48	is	be	AUX
ejpam-3431	208	49	a	a	DET
ejpam-3431	208	50	pseudo	pseudo	NOUN
ejpam-3431	208	51	hyper	hyper	ADJ
ejpam-3431	208	52	gr	gr	NOUN
ejpam-3431	208	53	-	-	PUNCT
ejpam-3431	208	54	ideal	ideal	NOUN
ejpam-3431	208	55	of	of	ADP
ejpam-3431	208	56	type	type	NOUN
ejpam-3431	208	57	1	1	NUM
ejpam-3431	208	58	.	.	PUNCT
ejpam-3431	209	1	furthermore	furthermore	ADV
ejpam-3431	209	2	,	,	PUNCT
ejpam-3431	209	3	we	we	PRON
ejpam-3431	209	4	will	will	AUX
ejpam-3431	209	5	show	show	VERB
ejpam-3431	209	6	that	that	SCONJ
ejpam-3431	209	7	i	i	PRON
ejpam-3431	209	8	is	be	AUX
ejpam-3431	209	9	a	a	DET
ejpam-3431	209	10	pseudo	pseudo	NOUN
ejpam-3431	209	11	hyper	hyper	ADJ
ejpam-3431	209	12	gr	gr	NOUN
ejpam-3431	209	13	-	-	PUNCT
ejpam-3431	209	14	ideal	ideal	NOUN
ejpam-3431	209	15	of	of	ADP
ejpam-3431	209	16	type	type	NOUN
ejpam-3431	209	17	8	8	NUM
ejpam-3431	209	18	.	.	PUNCT
ejpam-3431	210	1	that	that	PRON
ejpam-3431	210	2	is	is	ADV
ejpam-3431	210	3	,	,	PUNCT
ejpam-3431	210	4	to	to	PART
ejpam-3431	210	5	show	show	VERB
ejpam-3431	210	6	that	that	SCONJ
ejpam-3431	210	7	for	for	ADP
ejpam-3431	210	8	any	any	DET
ejpam-3431	210	9	y	y	PROPN
ejpam-3431	210	10	∈	∈	PROPN
ejpam-3431	211	1	i	i	PRON
ejpam-3431	211	2	,	,	PUNCT
ejpam-3431	211	3	i	i	PRON
ejpam-3431	211	4	�	�	VERB
ejpam-3431	211	5	~,y	~,y	VERB
ejpam-3431	211	6	⊆	⊆	NUM
ejpam-3431	211	7	i	i	NOUN
ejpam-3431	211	8	or	or	CCONJ
ejpam-3431	211	9	i	i	PRON
ejpam-3431	211	10	�	�	PROPN
ejpam-3431	211	11	◦	◦	NOUN
ejpam-3431	211	12	,y	,y	PUNCT
ejpam-3431	211	13	⊆	⊆	NUM
ejpam-3431	211	14	i.	i.	NOUN
ejpam-3431	211	15	let	let	VERB
ejpam-3431	211	16	y	y	PROPN
ejpam-3431	211	17	∈	∈	PROPN
ejpam-3431	212	1	i	i	PRON
ejpam-3431	212	2	and	and	CCONJ
ejpam-3431	212	3	x	x	SYM
ejpam-3431	212	4	∈	∈	PROPN
ejpam-3431	212	5	i	i	PRON
ejpam-3431	212	6	�	�	PROPN
ejpam-3431	212	7	~,y	~,y	PROPN
ejpam-3431	212	8	.	.	PUNCT
ejpam-3431	213	1	since	since	SCONJ
ejpam-3431	213	2	i	i	PRON
ejpam-3431	213	3	is	be	AUX
ejpam-3431	213	4	a	a	DET
ejpam-3431	213	5	pseudo	pseudo	NOUN
ejpam-3431	213	6	hyper	hyper	ADJ
ejpam-3431	213	7	gr	gr	NOUN
ejpam-3431	213	8	-	-	PUNCT
ejpam-3431	213	9	ideal	ideal	NOUN
ejpam-3431	213	10	of	of	ADP
ejpam-3431	213	11	type	type	NOUN
ejpam-3431	213	12	4	4	NUM
ejpam-3431	213	13	,	,	PUNCT
ejpam-3431	213	14	i	i	PRON
ejpam-3431	213	15	�	�	VERB
ejpam-3431	213	16	~,y	~,y	VERB
ejpam-3431	213	17	⊆	⊆	NUM
ejpam-3431	213	18	i	i	PRON
ejpam-3431	213	19	and	and	CCONJ
ejpam-3431	213	20	so	so	ADV
ejpam-3431	213	21	,	,	PUNCT
ejpam-3431	213	22	x	x	PROPN
ejpam-3431	213	23	∈	∈	PROPN
ejpam-3431	213	24	i.	i.	NOUN
ejpam-3431	213	25	therefore	therefore	ADV
ejpam-3431	213	26	,	,	PUNCT
ejpam-3431	213	27	i	i	PRON
ejpam-3431	213	28	�	�	VERB
ejpam-3431	213	29	~,y	~,y	NUM
ejpam-3431	213	30	⊆	⊆	NUM
ejpam-3431	213	31	i.	i.	NOUN
ejpam-3431	213	32	similarly	similarly	ADV
ejpam-3431	213	33	,	,	PUNCT
ejpam-3431	213	34	we	we	PRON
ejpam-3431	213	35	can	can	AUX
ejpam-3431	213	36	show	show	VERB
ejpam-3431	213	37	for	for	ADP
ejpam-3431	213	38	the	the	DET
ejpam-3431	213	39	other	other	ADJ
ejpam-3431	213	40	case	case	NOUN
ejpam-3431	213	41	that	that	SCONJ
ejpam-3431	213	42	i	i	PRON
ejpam-3431	213	43	�	�	VERB
ejpam-3431	213	44	◦	◦	NOUN
ejpam-3431	213	45	,y	,y	PUNCT
ejpam-3431	213	46	⊆	⊆	NUM
ejpam-3431	213	47	i.	i.	PROPN
ejpam-3431	213	48	�	�	PROPN
ejpam-3431	213	49	theorem	theorem	VERB
ejpam-3431	213	50	3.20	3.20	NUM
ejpam-3431	213	51	.	.	PUNCT
ejpam-3431	214	1	every	every	DET
ejpam-3431	214	2	pseudo	pseudo	NOUN
ejpam-3431	214	3	hyper	hyper	ADJ
ejpam-3431	214	4	gr	gr	NOUN
ejpam-3431	214	5	-	-	PUNCT
ejpam-3431	214	6	ideal	ideal	NOUN
ejpam-3431	214	7	in	in	ADP
ejpam-3431	214	8	h	h	NOUN
ejpam-3431	214	9	of	of	ADP
ejpam-3431	214	10	type	type	NOUN
ejpam-3431	214	11	8	8	NUM
ejpam-3431	214	12	is	be	AUX
ejpam-3431	214	13	a	a	DET
ejpam-3431	214	14	pseudo	pseudo	NOUN
ejpam-3431	214	15	hyper	hyper	ADJ
ejpam-3431	214	16	gr	gr	NOUN
ejpam-3431	214	17	-	-	PUNCT
ejpam-3431	214	18	ideal	ideal	NOUN
ejpam-3431	214	19	in	in	ADP
ejpam-3431	214	20	h	h	NOUN
ejpam-3431	214	21	of	of	ADP
ejpam-3431	214	22	types	type	NOUN
ejpam-3431	214	23	5	5	NUM
ejpam-3431	214	24	,	,	PUNCT
ejpam-3431	214	25	6	6	NUM
ejpam-3431	214	26	,	,	PUNCT
ejpam-3431	214	27	7	7	NUM
ejpam-3431	214	28	and	and	CCONJ
ejpam-3431	214	29	12	12	NUM
ejpam-3431	214	30	.	.	PUNCT
ejpam-3431	215	1	proof	proof	NOUN
ejpam-3431	215	2	.	.	PUNCT
ejpam-3431	216	1	let	let	VERB
ejpam-3431	216	2	i	i	PRON
ejpam-3431	216	3	be	be	AUX
ejpam-3431	216	4	a	a	DET
ejpam-3431	216	5	pseudo	pseudo	NOUN
ejpam-3431	216	6	hyper	hyper	ADJ
ejpam-3431	216	7	gr	gr	NOUN
ejpam-3431	216	8	-	-	PUNCT
ejpam-3431	216	9	ideal	ideal	NOUN
ejpam-3431	216	10	of	of	ADP
ejpam-3431	216	11	type	type	NOUN
ejpam-3431	216	12	8	8	NUM
ejpam-3431	216	13	.	.	PUNCT
ejpam-3431	217	1	we	we	PRON
ejpam-3431	217	2	will	will	AUX
ejpam-3431	217	3	show	show	VERB
ejpam-3431	217	4	that	that	SCONJ
ejpam-3431	217	5	i	i	PRON
ejpam-3431	217	6	is	be	AUX
ejpam-3431	217	7	a	a	DET
ejpam-3431	217	8	pseudo	pseudo	NOUN
ejpam-3431	217	9	hyper	hyper	ADJ
ejpam-3431	217	10	gr	gr	NOUN
ejpam-3431	217	11	-	-	PUNCT
ejpam-3431	217	12	ideal	ideal	NOUN
ejpam-3431	217	13	of	of	ADP
ejpam-3431	217	14	type	type	NOUN
ejpam-3431	217	15	5	5	NUM
ejpam-3431	217	16	.	.	PUNCT
ejpam-3431	218	1	we	we	PRON
ejpam-3431	218	2	will	will	AUX
ejpam-3431	218	3	consider	consider	VERB
ejpam-3431	218	4	two	two	NUM
ejpam-3431	218	5	cases	case	NOUN
ejpam-3431	218	6	:	:	PUNCT
ejpam-3431	218	7	when	when	SCONJ
ejpam-3431	218	8	i⊆	i⊆	PROPN
ejpam-3431	218	9	◦	◦	NOUN
ejpam-3431	218	10	,y	,y	PUNCT
ejpam-3431	218	11	⊆	⊆	NUM
ejpam-3431	218	12	i	i	NOUN
ejpam-3431	218	13	and	and	CCONJ
ejpam-3431	218	14	when	when	SCONJ
ejpam-3431	218	15	i⊆	i⊆	NOUN
ejpam-3431	218	16	◦	◦	NOUN
ejpam-3431	218	17	,y	,y	PUNCT
ejpam-3431	218	18	6⊆	6⊆	NUM
ejpam-3431	218	19	i.	i.	NOUN
ejpam-3431	218	20	if	if	SCONJ
ejpam-3431	218	21	i⊆	i⊆	NOUN
ejpam-3431	218	22	◦	◦	NOUN
ejpam-3431	218	23	,y	,y	PUNCT
ejpam-3431	218	24	⊆	⊆	NUM
ejpam-3431	218	25	i	i	PRON
ejpam-3431	218	26	,	,	PUNCT
ejpam-3431	218	27	then	then	ADV
ejpam-3431	218	28	we	we	PRON
ejpam-3431	218	29	are	be	AUX
ejpam-3431	218	30	done	do	VERB
ejpam-3431	218	31	.	.	PUNCT
ejpam-3431	219	1	suppose	suppose	VERB
ejpam-3431	219	2	that	that	SCONJ
ejpam-3431	219	3	i⊆	i⊆	NOUN
ejpam-3431	219	4	◦	◦	NOUN
ejpam-3431	219	5	,y	,y	PUNCT
ejpam-3431	219	6	6⊆	6⊆	PROPN
ejpam-3431	219	7	i.	i.	NOUN
ejpam-3431	219	8	let	let	VERB
ejpam-3431	219	9	x	x	SYM
ejpam-3431	219	10	∈	∈	PROPN
ejpam-3431	219	11	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	219	12	,	,	PUNCT
ejpam-3431	219	13	where	where	SCONJ
ejpam-3431	219	14	y	y	PROPN
ejpam-3431	219	15	∈	∈	PROPN
ejpam-3431	219	16	i.	i.	NOUN
ejpam-3431	219	17	then	then	ADV
ejpam-3431	219	18	,	,	PUNCT
ejpam-3431	219	19	x~	x~	PROPN
ejpam-3431	219	20	y	y	PROPN
ejpam-3431	219	21	⊆	⊆	NUM
ejpam-3431	219	22	i	i	PRON
ejpam-3431	219	23	,	,	PUNCT
ejpam-3431	219	24	thus	thus	ADV
ejpam-3431	219	25	by	by	ADP
ejpam-3431	219	26	remark	remark	NOUN
ejpam-3431	219	27	3.3	3.3	NUM
ejpam-3431	219	28	(	(	PUNCT
ejpam-3431	219	29	iv	iv	NUM
ejpam-3431	219	30	)	)	PUNCT
ejpam-3431	219	31	,	,	PUNCT
ejpam-3431	219	32	x~	x~	PROPN
ejpam-3431	219	33	y	y	PROPN
ejpam-3431	219	34	�	�	PROPN
ejpam-3431	219	35	i.	i.	PROPN
ejpam-3431	219	36	hence	hence	ADV
ejpam-3431	219	37	,	,	PUNCT
ejpam-3431	219	38	x	x	PROPN
ejpam-3431	219	39	∈	∈	PROPN
ejpam-3431	219	40	i	i	PRON
ejpam-3431	219	41	�	�	PROPN
ejpam-3431	219	42	~,y	~,y	PROPN
ejpam-3431	219	43	.	.	PUNCT
ejpam-3431	220	1	since	since	SCONJ
ejpam-3431	220	2	i	i	PRON
ejpam-3431	220	3	is	be	AUX
ejpam-3431	220	4	a	a	DET
ejpam-3431	220	5	pseudo	pseudo	NOUN
ejpam-3431	220	6	hyper	hyper	ADJ
ejpam-3431	220	7	gr	gr	NOUN
ejpam-3431	220	8	-	-	PUNCT
ejpam-3431	220	9	ideal	ideal	NOUN
ejpam-3431	220	10	of	of	ADP
ejpam-3431	220	11	type	type	NOUN
ejpam-3431	220	12	8	8	NUM
ejpam-3431	220	13	,	,	PUNCT
ejpam-3431	220	14	i	i	PRON
ejpam-3431	220	15	�	�	PROPN
ejpam-3431	220	16	◦	◦	NOUN
ejpam-3431	220	17	,y	,y	PUNCT
ejpam-3431	220	18	⊆	⊆	NUM
ejpam-3431	220	19	i	i	NOUN
ejpam-3431	220	20	or	or	CCONJ
ejpam-3431	220	21	i	i	PRON
ejpam-3431	220	22	�	�	VERB
ejpam-3431	220	23	~,y	~,y	VERB
ejpam-3431	220	24	⊆	⊆	NUM
ejpam-3431	220	25	i.	i.	NOUN
ejpam-3431	220	26	suppose	suppose	VERB
ejpam-3431	220	27	that	that	SCONJ
ejpam-3431	220	28	i	i	PRON
ejpam-3431	220	29	�	�	PROPN
ejpam-3431	220	30	◦	◦	NOUN
ejpam-3431	220	31	,y	,y	PUNCT
ejpam-3431	220	32	⊆	⊆	NUM
ejpam-3431	220	33	i.	i.	NOUN
ejpam-3431	220	34	the	the	DET
ejpam-3431	220	35	hypothesis	hypothesis	NOUN
ejpam-3431	220	36	i⊆	i⊆	NOUN
ejpam-3431	220	37	◦	◦	NOUN
ejpam-3431	220	38	,y	,y	PUNCT
ejpam-3431	220	39	6⊆	6⊆	NUM
ejpam-3431	220	40	i	i	PRON
ejpam-3431	220	41	implies	imply	VERB
ejpam-3431	220	42	that	that	SCONJ
ejpam-3431	220	43	there	there	PRON
ejpam-3431	220	44	exists	exist	VERB
ejpam-3431	220	45	z	z	PROPN
ejpam-3431	220	46	∈	∈	PROPN
ejpam-3431	220	47	i⊆	i⊆	PROPN
ejpam-3431	220	48	◦	◦	NOUN
ejpam-3431	220	49	,y	,y	PUNCT
ejpam-3431	220	50	such	such	ADJ
ejpam-3431	220	51	that	that	SCONJ
ejpam-3431	220	52	z	z	PROPN
ejpam-3431	220	53	6∈	6∈	PROPN
ejpam-3431	220	54	i.	i.	NOUN
ejpam-3431	220	55	moreover	moreover	ADV
ejpam-3431	220	56	,	,	PUNCT
ejpam-3431	220	57	z	z	NOUN
ejpam-3431	220	58	◦	◦	NOUN
ejpam-3431	220	59	y	y	PROPN
ejpam-3431	221	1	⊆	⊆	NUM
ejpam-3431	221	2	i	i	PROPN
ejpam-3431	221	3	and	and	CCONJ
ejpam-3431	221	4	by	by	ADP
ejpam-3431	221	5	remark	remark	NOUN
ejpam-3431	221	6	3.3	3.3	NUM
ejpam-3431	221	7	(	(	PUNCT
ejpam-3431	221	8	iv	iv	NUM
ejpam-3431	221	9	)	)	PUNCT
ejpam-3431	221	10	,	,	PUNCT
ejpam-3431	221	11	z	z	X
ejpam-3431	221	12	◦	◦	NOUN
ejpam-3431	221	13	y	y	PROPN
ejpam-3431	221	14	�	�	PROPN
ejpam-3431	221	15	i.	i.	PROPN
ejpam-3431	221	16	hence	hence	ADV
ejpam-3431	221	17	,	,	PUNCT
ejpam-3431	221	18	z	z	PROPN
ejpam-3431	221	19	∈	∈	PROPN
ejpam-3431	221	20	i	i	PRON
ejpam-3431	221	21	�	�	NOUN
ejpam-3431	221	22	◦	◦	NOUN
ejpam-3431	221	23	,y	,y	PUNCT
ejpam-3431	221	24	and	and	CCONJ
ejpam-3431	221	25	so	so	ADV
ejpam-3431	221	26	z	z	PROPN
ejpam-3431	221	27	∈	∈	PROPN
ejpam-3431	221	28	i.	i.	NOUN
ejpam-3431	221	29	a	a	DET
ejpam-3431	221	30	contradiction	contradiction	NOUN
ejpam-3431	221	31	.	.	PUNCT
ejpam-3431	222	1	thus	thus	ADV
ejpam-3431	222	2	,	,	PUNCT
ejpam-3431	222	3	i	i	PRON
ejpam-3431	222	4	�	�	PROPN
ejpam-3431	222	5	◦	◦	NOUN
ejpam-3431	222	6	,y	,y	PUNCT
ejpam-3431	222	7	6⊆	6⊆	NUM
ejpam-3431	222	8	i.	i.	PROPN
ejpam-3431	222	9	thus	thus	ADV
ejpam-3431	222	10	,	,	PUNCT
ejpam-3431	222	11	i	i	PRON
ejpam-3431	222	12	�	�	VERB
ejpam-3431	222	13	~,y	~,y	VERB
ejpam-3431	222	14	⊆	⊆	NUM
ejpam-3431	222	15	i	i	PRON
ejpam-3431	222	16	and	and	CCONJ
ejpam-3431	222	17	so	so	ADV
ejpam-3431	222	18	x	x	SYM
ejpam-3431	222	19	∈	∈	PROPN
ejpam-3431	222	20	i.	i.	NOUN
ejpam-3431	222	21	therefore	therefore	ADV
ejpam-3431	222	22	,	,	PUNCT
ejpam-3431	222	23	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	222	24	⊆	⊆	NUM
ejpam-3431	222	25	i.	i.	NOUN
ejpam-3431	222	26	next	next	ADV
ejpam-3431	222	27	,	,	PUNCT
ejpam-3431	222	28	we	we	PRON
ejpam-3431	222	29	will	will	AUX
ejpam-3431	222	30	prove	prove	VERB
ejpam-3431	222	31	that	that	SCONJ
ejpam-3431	222	32	i	i	PRON
ejpam-3431	222	33	is	be	AUX
ejpam-3431	222	34	a	a	DET
ejpam-3431	222	35	pseudo	pseudo	NOUN
ejpam-3431	222	36	hyper	hyper	ADJ
ejpam-3431	222	37	gr	gr	NOUN
ejpam-3431	222	38	-	-	PUNCT
ejpam-3431	222	39	ideal	ideal	NOUN
ejpam-3431	222	40	of	of	ADP
ejpam-3431	222	41	type	type	NOUN
ejpam-3431	222	42	6	6	NUM
ejpam-3431	222	43	.	.	PUNCT
ejpam-3431	223	1	if	if	SCONJ
ejpam-3431	223	2	i	i	PRON
ejpam-3431	223	3	�	�	VERB
ejpam-3431	223	4	◦	◦	NOUN
ejpam-3431	223	5	,y	,y	PUNCT
ejpam-3431	223	6	⊆	⊆	NUM
ejpam-3431	223	7	i	i	PRON
ejpam-3431	223	8	,	,	PUNCT
ejpam-3431	223	9	then	then	ADV
ejpam-3431	223	10	we	we	PRON
ejpam-3431	223	11	are	be	AUX
ejpam-3431	223	12	done	do	VERB
ejpam-3431	223	13	.	.	PUNCT
ejpam-3431	224	1	suppose	suppose	VERB
ejpam-3431	224	2	i	i	PRON
ejpam-3431	224	3	�	�	PROPN
ejpam-3431	224	4	◦	◦	NOUN
ejpam-3431	224	5	,y	,y	PUNCT
ejpam-3431	224	6	6⊆	6⊆	PROPN
ejpam-3431	224	7	i.	i.	NOUN
ejpam-3431	224	8	let	let	VERB
ejpam-3431	224	9	x	x	SYM
ejpam-3431	224	10	∈	∈	PROPN
ejpam-3431	224	11	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	224	12	,	,	PUNCT
ejpam-3431	224	13	where	where	SCONJ
ejpam-3431	224	14	y	y	PROPN
ejpam-3431	224	15	∈	∈	PROPN
ejpam-3431	224	16	i.	i.	NOUN
ejpam-3431	224	17	then	then	ADV
ejpam-3431	224	18	,	,	PUNCT
ejpam-3431	224	19	x~	x~	PROPN
ejpam-3431	224	20	y	y	PROPN
ejpam-3431	224	21	⊆	⊆	NUM
ejpam-3431	224	22	i	i	PRON
ejpam-3431	224	23	,	,	PUNCT
ejpam-3431	224	24	thus	thus	ADV
ejpam-3431	224	25	by	by	ADP
ejpam-3431	224	26	remark	remark	NOUN
ejpam-3431	224	27	3.3	3.3	NUM
ejpam-3431	224	28	(	(	PUNCT
ejpam-3431	224	29	iv	iv	NUM
ejpam-3431	224	30	)	)	PUNCT
ejpam-3431	224	31	,	,	PUNCT
ejpam-3431	224	32	x	x	X
ejpam-3431	224	33	~	~	PUNCT
ejpam-3431	224	34	y	y	PROPN
ejpam-3431	224	35	�	�	PROPN
ejpam-3431	224	36	i.	i.	PROPN
ejpam-3431	224	37	hence	hence	ADV
ejpam-3431	224	38	,	,	PUNCT
ejpam-3431	224	39	x	x	PROPN
ejpam-3431	224	40	∈	∈	PROPN
ejpam-3431	224	41	i	i	PRON
ejpam-3431	224	42	�	�	PROPN
ejpam-3431	224	43	~,y	~,y	PROPN
ejpam-3431	224	44	.	.	PUNCT
ejpam-3431	225	1	since	since	SCONJ
ejpam-3431	225	2	i	i	PRON
ejpam-3431	225	3	is	be	AUX
ejpam-3431	225	4	a	a	DET
ejpam-3431	225	5	pseudo	pseudo	NOUN
ejpam-3431	225	6	hyper	hyper	ADJ
ejpam-3431	225	7	gr	gr	NOUN
ejpam-3431	225	8	-	-	PUNCT
ejpam-3431	225	9	ideal	ideal	NOUN
ejpam-3431	225	10	of	of	ADP
ejpam-3431	225	11	type	type	NOUN
ejpam-3431	225	12	8	8	NUM
ejpam-3431	225	13	and	and	CCONJ
ejpam-3431	225	14	i	i	PRON
ejpam-3431	225	15	�	�	PROPN
ejpam-3431	225	16	◦	◦	NOUN
ejpam-3431	225	17	,y	,y	PUNCT
ejpam-3431	225	18	6⊆	6⊆	NUM
ejpam-3431	225	19	i	i	PRON
ejpam-3431	225	20	,	,	PUNCT
ejpam-3431	225	21	then	then	ADV
ejpam-3431	225	22	i	i	PRON
ejpam-3431	225	23	�	�	VERB
ejpam-3431	225	24	~,y	~,y	VERB
ejpam-3431	225	25	⊆	⊆	NUM
ejpam-3431	225	26	i	i	PRON
ejpam-3431	225	27	and	and	CCONJ
ejpam-3431	225	28	so	so	ADV
ejpam-3431	225	29	x	x	SYM
ejpam-3431	225	30	∈	∈	PROPN
ejpam-3431	225	31	i.	i.	NOUN
ejpam-3431	225	32	therefore	therefore	ADV
ejpam-3431	225	33	,	,	PUNCT
ejpam-3431	225	34	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	225	35	⊆	⊆	NUM
ejpam-3431	225	36	i.	i.	NOUN
ejpam-3431	225	37	the	the	DET
ejpam-3431	225	38	proof	proof	NOUN
ejpam-3431	225	39	for	for	ADP
ejpam-3431	225	40	type	type	NOUN
ejpam-3431	225	41	7	7	NUM
ejpam-3431	225	42	follows	follow	VERB
ejpam-3431	225	43	similarly	similarly	ADV
ejpam-3431	225	44	as	as	ADP
ejpam-3431	225	45	in	in	ADP
ejpam-3431	225	46	the	the	DET
ejpam-3431	225	47	case	case	NOUN
ejpam-3431	225	48	of	of	ADP
ejpam-3431	225	49	type	type	NOUN
ejpam-3431	225	50	6	6	NUM
ejpam-3431	225	51	.	.	PUNCT
ejpam-3431	226	1	furthermore	furthermore	ADV
ejpam-3431	226	2	,	,	PUNCT
ejpam-3431	226	3	we	we	PRON
ejpam-3431	226	4	will	will	AUX
ejpam-3431	226	5	prove	prove	VERB
ejpam-3431	226	6	that	that	SCONJ
ejpam-3431	226	7	i	i	PRON
ejpam-3431	226	8	is	be	AUX
ejpam-3431	226	9	a	a	DET
ejpam-3431	226	10	pseudo	pseudo	NOUN
ejpam-3431	226	11	hyper	hyper	ADJ
ejpam-3431	226	12	gr	gr	NOUN
ejpam-3431	226	13	-	-	PUNCT
ejpam-3431	226	14	ideal	ideal	NOUN
ejpam-3431	226	15	of	of	ADP
ejpam-3431	226	16	type	type	NOUN
ejpam-3431	226	17	12	12	NUM
ejpam-3431	226	18	.	.	PUNCT
ejpam-3431	227	1	let	let	VERB
ejpam-3431	227	2	y	y	PRON
ejpam-3431	227	3	∈	∈	PROPN
ejpam-3431	228	1	i	i	PRON
ejpam-3431	228	2	and	and	CCONJ
ejpam-3431	228	3	x	x	SYM
ejpam-3431	228	4	∈	∈	PROPN
ejpam-3431	228	5	i	i	NOUN
ejpam-3431	228	6	�	�	NOUN
ejpam-3431	228	7	~,y	~,y	PROPN
ejpam-3431	228	8	∩	∩	ADJ
ejpam-3431	228	9	i	i	PRON
ejpam-3431	228	10	�	�	PROPN
ejpam-3431	228	11	◦	◦	NOUN
ejpam-3431	228	12	,y	,y	PROPN
ejpam-3431	228	13	.	.	PUNCT
ejpam-3431	229	1	then	then	ADV
ejpam-3431	229	2	x	x	SYM
ejpam-3431	229	3	∈	∈	PROPN
ejpam-3431	229	4	i	i	PRON
ejpam-3431	229	5	�	�	VERB
ejpam-3431	229	6	~,y	~,y	PROPN
ejpam-3431	229	7	and	and	CCONJ
ejpam-3431	229	8	i	i	PROPN
ejpam-3431	229	9	�	�	PROPN
ejpam-3431	229	10	◦	◦	NOUN
ejpam-3431	229	11	,y	,y	NOUN
ejpam-3431	229	12	.	.	PUNCT
ejpam-3431	230	1	since	since	SCONJ
ejpam-3431	230	2	i	i	PRON
ejpam-3431	230	3	is	be	AUX
ejpam-3431	230	4	a	a	DET
ejpam-3431	230	5	pseudo	pseudo	NOUN
ejpam-3431	230	6	hyper	hyper	ADJ
ejpam-3431	230	7	gr	gr	NOUN
ejpam-3431	230	8	-	-	PUNCT
ejpam-3431	230	9	ideal	ideal	NOUN
ejpam-3431	230	10	of	of	ADP
ejpam-3431	230	11	type	type	NOUN
ejpam-3431	230	12	8	8	NUM
ejpam-3431	230	13	,	,	PUNCT
ejpam-3431	230	14	we	we	PRON
ejpam-3431	230	15	have	have	VERB
ejpam-3431	230	16	i	i	PRON
ejpam-3431	230	17	�	�	X
ejpam-3431	230	18	~,y	~,y	NUM
ejpam-3431	230	19	⊆	⊆	NUM
ejpam-3431	230	20	i	i	NOUN
ejpam-3431	230	21	or	or	CCONJ
ejpam-3431	230	22	i	i	PRON
ejpam-3431	230	23	�	�	PROPN
ejpam-3431	230	24	◦	◦	NOUN
ejpam-3431	230	25	,y	,y	PUNCT
ejpam-3431	230	26	⊆	⊆	NUM
ejpam-3431	230	27	i	i	PROPN
ejpam-3431	230	28	and	and	CCONJ
ejpam-3431	230	29	so	so	ADV
ejpam-3431	230	30	x	x	SYM
ejpam-3431	230	31	∈	∈	PROPN
ejpam-3431	230	32	i.	i.	NOUN
ejpam-3431	230	33	hence	hence	ADV
ejpam-3431	230	34	,	,	PUNCT
ejpam-3431	230	35	i	i	PRON
ejpam-3431	230	36	�	�	VERB
ejpam-3431	230	37	~,y	~,y	PROPN
ejpam-3431	230	38	∩	∩	ADJ
ejpam-3431	230	39	i	i	PRON
ejpam-3431	230	40	�	�	PROPN
ejpam-3431	230	41	◦	◦	NOUN
ejpam-3431	230	42	,y	,y	PUNCT
ejpam-3431	230	43	⊆	⊆	NUM
ejpam-3431	230	44	i.	i.	PROPN
ejpam-3431	230	45	�	�	PROPN
ejpam-3431	230	46	r.	r.	PROPN
ejpam-3431	230	47	manzano	manzano	PROPN
ejpam-3431	230	48	,	,	PUNCT
ejpam-3431	230	49	jr	jr	PROPN
ejpam-3431	230	50	.	.	PROPN
ejpam-3431	230	51	,	,	PUNCT
ejpam-3431	230	52	g.	g.	PROPN
ejpam-3431	230	53	petalcorin	petalcorin	PROPN
ejpam-3431	230	54	,	,	PUNCT
ejpam-3431	230	55	jr	jr	PROPN
ejpam-3431	230	56	.	.	PROPN
ejpam-3431	230	57	/	/	SYM
ejpam-3431	230	58	eur	eur	PROPN
ejpam-3431	230	59	.	.	PUNCT
ejpam-3431	231	1	j.	j.	PROPN
ejpam-3431	231	2	pure	pure	PROPN
ejpam-3431	231	3	appl	appl	PROPN
ejpam-3431	231	4	.	.	PROPN
ejpam-3431	231	5	math	math	PROPN
ejpam-3431	231	6	,	,	PUNCT
ejpam-3431	231	7	12	12	NUM
ejpam-3431	231	8	(	(	PUNCT
ejpam-3431	231	9	3	3	NUM
ejpam-3431	231	10	)	)	PUNCT
ejpam-3431	231	11	(	(	PUNCT
ejpam-3431	231	12	2019	2019	NUM
ejpam-3431	231	13	)	)	PUNCT
ejpam-3431	231	14	,	,	PUNCT
ejpam-3431	231	15	821	821	NUM
ejpam-3431	231	16	-	-	SYM
ejpam-3431	231	17	833	833	NUM
ejpam-3431	231	18	830	830	NUM
ejpam-3431	231	19	theorem	theorem	VERB
ejpam-3431	231	20	3.21	3.21	NUM
ejpam-3431	231	21	.	.	PUNCT
ejpam-3431	232	1	every	every	DET
ejpam-3431	232	2	pseudo	pseudo	NOUN
ejpam-3431	232	3	hyper	hyper	ADJ
ejpam-3431	232	4	gr	gr	NOUN
ejpam-3431	232	5	-	-	PUNCT
ejpam-3431	232	6	ideal	ideal	NOUN
ejpam-3431	232	7	in	in	ADP
ejpam-3431	232	8	h	h	NOUN
ejpam-3431	232	9	of	of	ADP
ejpam-3431	232	10	type	type	NOUN
ejpam-3431	232	11	6	6	NUM
ejpam-3431	232	12	is	be	AUX
ejpam-3431	232	13	a	a	DET
ejpam-3431	232	14	pseudo	pseudo	NOUN
ejpam-3431	232	15	hyper	hyper	ADJ
ejpam-3431	232	16	gr	gr	NOUN
ejpam-3431	232	17	-	-	PUNCT
ejpam-3431	232	18	ideal	ideal	NOUN
ejpam-3431	232	19	in	in	ADP
ejpam-3431	232	20	h	h	NOUN
ejpam-3431	232	21	of	of	ADP
ejpam-3431	232	22	types	type	NOUN
ejpam-3431	232	23	5	5	NUM
ejpam-3431	232	24	and	and	CCONJ
ejpam-3431	232	25	10	10	NUM
ejpam-3431	232	26	.	.	PUNCT
ejpam-3431	233	1	proof	proof	NOUN
ejpam-3431	233	2	.	.	PUNCT
ejpam-3431	234	1	let	let	VERB
ejpam-3431	234	2	i	i	PRON
ejpam-3431	234	3	be	be	AUX
ejpam-3431	234	4	a	a	DET
ejpam-3431	234	5	pseudo	pseudo	NOUN
ejpam-3431	234	6	hyper	hyper	ADJ
ejpam-3431	234	7	gr	gr	NOUN
ejpam-3431	234	8	-	-	PUNCT
ejpam-3431	234	9	ideal	ideal	NOUN
ejpam-3431	234	10	of	of	ADP
ejpam-3431	234	11	type	type	NOUN
ejpam-3431	234	12	6	6	NUM
ejpam-3431	234	13	.	.	PUNCT
ejpam-3431	235	1	now	now	ADV
ejpam-3431	235	2	,	,	PUNCT
ejpam-3431	235	3	we	we	PRON
ejpam-3431	235	4	will	will	AUX
ejpam-3431	235	5	show	show	VERB
ejpam-3431	235	6	that	that	SCONJ
ejpam-3431	235	7	i	i	PRON
ejpam-3431	235	8	is	be	AUX
ejpam-3431	235	9	a	a	DET
ejpam-3431	235	10	pseudo	pseudo	NOUN
ejpam-3431	235	11	hyper	hyper	ADJ
ejpam-3431	235	12	gr	gr	NOUN
ejpam-3431	235	13	-	-	PUNCT
ejpam-3431	235	14	ideal	ideal	NOUN
ejpam-3431	235	15	of	of	ADP
ejpam-3431	235	16	type	type	NOUN
ejpam-3431	235	17	5	5	NUM
ejpam-3431	235	18	.	.	PUNCT
ejpam-3431	236	1	if	if	SCONJ
ejpam-3431	236	2	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	236	3	⊆	⊆	NUM
ejpam-3431	236	4	i	i	PRON
ejpam-3431	236	5	,	,	PUNCT
ejpam-3431	236	6	then	then	ADV
ejpam-3431	236	7	we	we	PRON
ejpam-3431	236	8	are	be	AUX
ejpam-3431	236	9	done	do	VERB
ejpam-3431	236	10	.	.	PUNCT
ejpam-3431	237	1	suppose	suppose	VERB
ejpam-3431	237	2	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	237	3	6⊆	6⊆	PROPN
ejpam-3431	237	4	i.	i.	PROPN
ejpam-3431	237	5	let	let	VERB
ejpam-3431	237	6	x	x	X
ejpam-3431	237	7	∈	∈	VERB
ejpam-3431	237	8	i⊆	i⊆	NOUN
ejpam-3431	237	9	◦	◦	NOUN
ejpam-3431	237	10	,y	,y	PUNCT
ejpam-3431	237	11	for	for	ADP
ejpam-3431	237	12	any	any	DET
ejpam-3431	237	13	y	y	PROPN
ejpam-3431	237	14	∈	∈	PROPN
ejpam-3431	237	15	i.	i.	NOUN
ejpam-3431	237	16	then	then	ADV
ejpam-3431	237	17	x	x	SYM
ejpam-3431	237	18	◦	◦	NOUN
ejpam-3431	237	19	y	y	PROPN
ejpam-3431	238	1	⊆	⊆	NUM
ejpam-3431	238	2	i	i	PROPN
ejpam-3431	238	3	and	and	CCONJ
ejpam-3431	238	4	so	so	ADV
ejpam-3431	238	5	by	by	ADP
ejpam-3431	238	6	remark	remark	NOUN
ejpam-3431	238	7	3.3	3.3	NUM
ejpam-3431	238	8	(	(	PUNCT
ejpam-3431	238	9	iv	iv	NUM
ejpam-3431	238	10	)	)	PUNCT
ejpam-3431	238	11	,	,	PUNCT
ejpam-3431	238	12	x	x	PUNCT
ejpam-3431	238	13	◦	◦	NOUN
ejpam-3431	238	14	y	y	PROPN
ejpam-3431	238	15	�	�	PROPN
ejpam-3431	238	16	i.	i.	PROPN
ejpam-3431	238	17	hence	hence	ADV
ejpam-3431	238	18	,	,	PUNCT
ejpam-3431	238	19	x	x	PROPN
ejpam-3431	238	20	∈	∈	PROPN
ejpam-3431	238	21	i	i	NOUN
ejpam-3431	238	22	�	�	PROPN
ejpam-3431	238	23	◦	◦	NOUN
ejpam-3431	238	24	,y	,y	NOUN
ejpam-3431	238	25	.	.	PUNCT
ejpam-3431	239	1	since	since	SCONJ
ejpam-3431	239	2	i	i	PRON
ejpam-3431	239	3	is	be	AUX
ejpam-3431	239	4	a	a	DET
ejpam-3431	239	5	pseudo	pseudo	NOUN
ejpam-3431	239	6	hyper	hyper	ADJ
ejpam-3431	239	7	gr	gr	NOUN
ejpam-3431	239	8	-	-	PUNCT
ejpam-3431	239	9	ideal	ideal	NOUN
ejpam-3431	239	10	of	of	ADP
ejpam-3431	239	11	type	type	NOUN
ejpam-3431	239	12	6	6	NUM
ejpam-3431	239	13	and	and	CCONJ
ejpam-3431	239	14	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	239	15	6⊆	6⊆	NUM
ejpam-3431	239	16	i	i	PRON
ejpam-3431	239	17	,	,	PUNCT
ejpam-3431	239	18	i	i	PRON
ejpam-3431	239	19	�	�	PROPN
ejpam-3431	239	20	◦	◦	NOUN
ejpam-3431	239	21	,y	,y	PUNCT
ejpam-3431	240	1	⊆	⊆	NUM
ejpam-3431	240	2	i	i	PROPN
ejpam-3431	240	3	and	and	CCONJ
ejpam-3431	240	4	thus	thus	ADV
ejpam-3431	240	5	,	,	PUNCT
ejpam-3431	240	6	x	x	PROPN
ejpam-3431	240	7	∈	∈	PROPN
ejpam-3431	240	8	i.	i.	NOUN
ejpam-3431	240	9	hence	hence	ADV
ejpam-3431	240	10	,	,	PUNCT
ejpam-3431	240	11	i⊆	i⊆	NOUN
ejpam-3431	240	12	◦	◦	NOUN
ejpam-3431	240	13	,y	,y	PUNCT
ejpam-3431	240	14	⊆	⊆	NUM
ejpam-3431	240	15	i.	i.	NOUN
ejpam-3431	240	16	next	next	ADV
ejpam-3431	240	17	,	,	PUNCT
ejpam-3431	240	18	we	we	PRON
ejpam-3431	240	19	will	will	AUX
ejpam-3431	240	20	show	show	VERB
ejpam-3431	240	21	that	that	SCONJ
ejpam-3431	240	22	i	i	PRON
ejpam-3431	240	23	is	be	AUX
ejpam-3431	240	24	a	a	DET
ejpam-3431	240	25	pseudo	pseudo	NOUN
ejpam-3431	240	26	hyper	hyper	ADJ
ejpam-3431	240	27	gr	gr	NOUN
ejpam-3431	240	28	-	-	PUNCT
ejpam-3431	240	29	ideal	ideal	NOUN
ejpam-3431	240	30	of	of	ADP
ejpam-3431	240	31	type	type	NOUN
ejpam-3431	240	32	10	10	NUM
ejpam-3431	240	33	.	.	PUNCT
ejpam-3431	241	1	let	let	VERB
ejpam-3431	241	2	y	y	PRON
ejpam-3431	241	3	∈	∈	PROPN
ejpam-3431	242	1	i	i	PRON
ejpam-3431	242	2	and	and	CCONJ
ejpam-3431	242	3	x	x	PROPN
ejpam-3431	242	4	∈	∈	PROPN
ejpam-3431	242	5	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	242	6	∩	∩	X
ejpam-3431	242	7	i	i	PRON
ejpam-3431	242	8	�	�	PROPN
ejpam-3431	242	9	◦	◦	NOUN
ejpam-3431	242	10	,y	,y	PROPN
ejpam-3431	242	11	.	.	PUNCT
ejpam-3431	243	1	then	then	ADV
ejpam-3431	243	2	,	,	PUNCT
ejpam-3431	243	3	x	x	PROPN
ejpam-3431	243	4	∈	∈	PROPN
ejpam-3431	243	5	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	243	6	and	and	CCONJ
ejpam-3431	243	7	x	x	PUNCT
ejpam-3431	243	8	∈	∈	PROPN
ejpam-3431	243	9	i	i	PRON
ejpam-3431	243	10	�	�	PROPN
ejpam-3431	243	11	◦	◦	NOUN
ejpam-3431	243	12	,y	,y	NOUN
ejpam-3431	243	13	.	.	PUNCT
ejpam-3431	244	1	since	since	SCONJ
ejpam-3431	244	2	i	i	PRON
ejpam-3431	244	3	is	be	AUX
ejpam-3431	244	4	a	a	DET
ejpam-3431	244	5	pseudo	pseudo	NOUN
ejpam-3431	244	6	hyper	hyper	ADJ
ejpam-3431	244	7	gr	gr	NOUN
ejpam-3431	244	8	-	-	PUNCT
ejpam-3431	244	9	ideal	ideal	NOUN
ejpam-3431	244	10	of	of	ADP
ejpam-3431	244	11	type	type	NOUN
ejpam-3431	244	12	6	6	NUM
ejpam-3431	244	13	,	,	PUNCT
ejpam-3431	244	14	we	we	PRON
ejpam-3431	244	15	have	have	AUX
ejpam-3431	244	16	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	244	17	⊆	⊆	NUM
ejpam-3431	244	18	i	i	PROPN
ejpam-3431	244	19	or	or	CCONJ
ejpam-3431	244	20	i	i	PRON
ejpam-3431	244	21	�	�	PROPN
ejpam-3431	244	22	◦	◦	NOUN
ejpam-3431	244	23	,y	,y	PUNCT
ejpam-3431	244	24	⊆	⊆	NUM
ejpam-3431	244	25	i	i	PROPN
ejpam-3431	244	26	and	and	CCONJ
ejpam-3431	244	27	so	so	ADV
ejpam-3431	244	28	x	x	SYM
ejpam-3431	244	29	∈	∈	PROPN
ejpam-3431	244	30	i.	i.	NOUN
ejpam-3431	244	31	hence	hence	ADV
ejpam-3431	244	32	,	,	PUNCT
ejpam-3431	244	33	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	244	34	∩	∩	X
ejpam-3431	244	35	i	i	PRON
ejpam-3431	244	36	�	�	PROPN
ejpam-3431	244	37	◦	◦	NOUN
ejpam-3431	244	38	,y	,y	PUNCT
ejpam-3431	244	39	⊆	⊆	NUM
ejpam-3431	244	40	i.	i.	PROPN
ejpam-3431	244	41	�	�	PROPN
ejpam-3431	244	42	theorem	theorem	VERB
ejpam-3431	244	43	3.22	3.22	NUM
ejpam-3431	244	44	.	.	PUNCT
ejpam-3431	245	1	every	every	DET
ejpam-3431	245	2	pseudo	pseudo	NOUN
ejpam-3431	245	3	hyper	hyper	ADJ
ejpam-3431	245	4	gr	gr	NOUN
ejpam-3431	245	5	-	-	PUNCT
ejpam-3431	245	6	ideal	ideal	NOUN
ejpam-3431	245	7	in	in	ADP
ejpam-3431	245	8	h	h	NOUN
ejpam-3431	245	9	of	of	ADP
ejpam-3431	245	10	type	type	NOUN
ejpam-3431	245	11	7	7	NUM
ejpam-3431	245	12	is	be	AUX
ejpam-3431	245	13	a	a	DET
ejpam-3431	245	14	pseudo	pseudo	NOUN
ejpam-3431	245	15	hyper	hyper	ADJ
ejpam-3431	245	16	gr	gr	NOUN
ejpam-3431	245	17	-	-	PUNCT
ejpam-3431	245	18	ideal	ideal	NOUN
ejpam-3431	245	19	in	in	ADP
ejpam-3431	245	20	h	h	NOUN
ejpam-3431	245	21	of	of	ADP
ejpam-3431	245	22	types	type	NOUN
ejpam-3431	245	23	5	5	NUM
ejpam-3431	245	24	and	and	CCONJ
ejpam-3431	245	25	11	11	NUM
ejpam-3431	245	26	.	.	PUNCT
ejpam-3431	246	1	proof	proof	NOUN
ejpam-3431	246	2	.	.	PUNCT
ejpam-3431	247	1	let	let	VERB
ejpam-3431	247	2	i	i	PRON
ejpam-3431	247	3	be	be	AUX
ejpam-3431	247	4	a	a	DET
ejpam-3431	247	5	pseudo	pseudo	NOUN
ejpam-3431	247	6	hyper	hyper	ADJ
ejpam-3431	247	7	gr	gr	NOUN
ejpam-3431	247	8	-	-	PUNCT
ejpam-3431	247	9	ideal	ideal	NOUN
ejpam-3431	247	10	of	of	ADP
ejpam-3431	247	11	type	type	NOUN
ejpam-3431	247	12	7	7	NUM
ejpam-3431	247	13	.	.	PUNCT
ejpam-3431	248	1	now	now	ADV
ejpam-3431	248	2	,	,	PUNCT
ejpam-3431	248	3	we	we	PRON
ejpam-3431	248	4	will	will	AUX
ejpam-3431	248	5	show	show	VERB
ejpam-3431	248	6	that	that	SCONJ
ejpam-3431	248	7	i	i	PRON
ejpam-3431	248	8	is	be	AUX
ejpam-3431	248	9	a	a	DET
ejpam-3431	248	10	pseudo	pseudo	NOUN
ejpam-3431	248	11	hyper	hyper	ADJ
ejpam-3431	248	12	gr	gr	NOUN
ejpam-3431	248	13	-	-	PUNCT
ejpam-3431	248	14	ideal	ideal	NOUN
ejpam-3431	248	15	of	of	ADP
ejpam-3431	248	16	type	type	NOUN
ejpam-3431	248	17	5	5	NUM
ejpam-3431	248	18	.	.	PUNCT
ejpam-3431	249	1	if	if	SCONJ
ejpam-3431	249	2	i⊆	i⊆	NOUN
ejpam-3431	249	3	◦	◦	NOUN
ejpam-3431	249	4	,y	,y	PUNCT
ejpam-3431	249	5	⊆	⊆	NUM
ejpam-3431	249	6	i	i	PRON
ejpam-3431	249	7	,	,	PUNCT
ejpam-3431	249	8	then	then	ADV
ejpam-3431	249	9	we	we	PRON
ejpam-3431	249	10	are	be	AUX
ejpam-3431	249	11	done	do	VERB
ejpam-3431	249	12	.	.	PUNCT
ejpam-3431	250	1	suppose	suppose	VERB
ejpam-3431	250	2	i⊆	i⊆	PROPN
ejpam-3431	250	3	◦	◦	NOUN
ejpam-3431	250	4	,y	,y	PUNCT
ejpam-3431	250	5	6⊆	6⊆	PROPN
ejpam-3431	250	6	i.	i.	NOUN
ejpam-3431	250	7	let	let	VERB
ejpam-3431	250	8	x	x	X
ejpam-3431	250	9	∈	∈	PROPN
ejpam-3431	250	10	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	250	11	for	for	ADP
ejpam-3431	250	12	any	any	DET
ejpam-3431	250	13	y	y	PROPN
ejpam-3431	250	14	∈	∈	PROPN
ejpam-3431	250	15	i.	i.	NOUN
ejpam-3431	250	16	then	then	ADV
ejpam-3431	250	17	x	x	X
ejpam-3431	250	18	~	~	PUNCT
ejpam-3431	250	19	y	y	PROPN
ejpam-3431	250	20	⊆	⊆	NUM
ejpam-3431	250	21	i	i	PROPN
ejpam-3431	250	22	and	and	CCONJ
ejpam-3431	250	23	so	so	ADV
ejpam-3431	250	24	by	by	ADP
ejpam-3431	250	25	remark	remark	NOUN
ejpam-3431	250	26	3.3	3.3	NUM
ejpam-3431	250	27	(	(	PUNCT
ejpam-3431	250	28	iv	iv	NUM
ejpam-3431	250	29	)	)	PUNCT
ejpam-3431	250	30	,	,	PUNCT
ejpam-3431	250	31	x	x	X
ejpam-3431	250	32	~	~	PUNCT
ejpam-3431	250	33	y	y	PROPN
ejpam-3431	250	34	�	�	PROPN
ejpam-3431	250	35	i.	i.	PROPN
ejpam-3431	250	36	hence	hence	ADV
ejpam-3431	250	37	,	,	PUNCT
ejpam-3431	250	38	x	x	PROPN
ejpam-3431	250	39	∈	∈	PROPN
ejpam-3431	250	40	i	i	PRON
ejpam-3431	250	41	�	�	PROPN
ejpam-3431	250	42	~,y	~,y	PROPN
ejpam-3431	250	43	.	.	PUNCT
ejpam-3431	251	1	since	since	SCONJ
ejpam-3431	251	2	i	i	PRON
ejpam-3431	251	3	is	be	AUX
ejpam-3431	251	4	a	a	DET
ejpam-3431	251	5	pseudo	pseudo	NOUN
ejpam-3431	251	6	hyper	hyper	ADJ
ejpam-3431	251	7	gr	gr	NOUN
ejpam-3431	251	8	-	-	PUNCT
ejpam-3431	251	9	ideal	ideal	NOUN
ejpam-3431	251	10	of	of	ADP
ejpam-3431	251	11	type	type	NOUN
ejpam-3431	251	12	7	7	NUM
ejpam-3431	251	13	and	and	CCONJ
ejpam-3431	251	14	i⊆	i⊆	NOUN
ejpam-3431	251	15	◦	◦	NOUN
ejpam-3431	251	16	,y	,y	PUNCT
ejpam-3431	251	17	6⊆	6⊆	NUM
ejpam-3431	251	18	i	i	PRON
ejpam-3431	251	19	,	,	PUNCT
ejpam-3431	251	20	i	i	PRON
ejpam-3431	251	21	�	�	VERB
ejpam-3431	251	22	~,y	~,y	VERB
ejpam-3431	251	23	⊆	⊆	NUM
ejpam-3431	251	24	i	i	PRON
ejpam-3431	251	25	and	and	CCONJ
ejpam-3431	251	26	thus	thus	ADV
ejpam-3431	251	27	,	,	PUNCT
ejpam-3431	251	28	x	x	PROPN
ejpam-3431	251	29	∈	∈	PROPN
ejpam-3431	251	30	i.	i.	NOUN
ejpam-3431	251	31	hence	hence	ADV
ejpam-3431	251	32	,	,	PUNCT
ejpam-3431	251	33	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	251	34	⊆	⊆	NUM
ejpam-3431	251	35	i.	i.	NOUN
ejpam-3431	251	36	next	next	ADV
ejpam-3431	251	37	,	,	PUNCT
ejpam-3431	251	38	we	we	PRON
ejpam-3431	251	39	will	will	AUX
ejpam-3431	251	40	show	show	VERB
ejpam-3431	251	41	that	that	SCONJ
ejpam-3431	251	42	i	i	PRON
ejpam-3431	251	43	is	be	AUX
ejpam-3431	251	44	a	a	DET
ejpam-3431	251	45	pseudo	pseudo	NOUN
ejpam-3431	251	46	hyper	hyper	ADJ
ejpam-3431	251	47	gr	gr	NOUN
ejpam-3431	251	48	-	-	PUNCT
ejpam-3431	251	49	ideal	ideal	NOUN
ejpam-3431	251	50	of	of	ADP
ejpam-3431	251	51	type	type	NOUN
ejpam-3431	251	52	11	11	NUM
ejpam-3431	251	53	.	.	PUNCT
ejpam-3431	252	1	let	let	VERB
ejpam-3431	252	2	y	y	PRON
ejpam-3431	252	3	∈	∈	PROPN
ejpam-3431	253	1	i	i	PRON
ejpam-3431	253	2	and	and	CCONJ
ejpam-3431	253	3	x	x	SYM
ejpam-3431	253	4	∈	∈	PROPN
ejpam-3431	253	5	i	i	NOUN
ejpam-3431	253	6	�	�	NOUN
ejpam-3431	253	7	~,y	~,y	NOUN
ejpam-3431	253	8	∩	∩	ADJ
ejpam-3431	253	9	i⊆	i⊆	NOUN
ejpam-3431	253	10	◦	◦	NOUN
ejpam-3431	253	11	,y	,y	PUNCT
ejpam-3431	253	12	.	.	PUNCT
ejpam-3431	254	1	then	then	ADV
ejpam-3431	254	2	,	,	PUNCT
ejpam-3431	254	3	x	x	PUNCT
ejpam-3431	254	4	∈	∈	PROPN
ejpam-3431	254	5	i	i	NOUN
ejpam-3431	254	6	�	�	VERB
ejpam-3431	254	7	~,y	~,y	PROPN
ejpam-3431	254	8	and	and	CCONJ
ejpam-3431	254	9	x	x	PART
ejpam-3431	254	10	∈	∈	PROPN
ejpam-3431	254	11	i⊆	i⊆	PROPN
ejpam-3431	254	12	◦	◦	NOUN
ejpam-3431	254	13	,y	,y	PUNCT
ejpam-3431	254	14	.	.	PUNCT
ejpam-3431	255	1	since	since	SCONJ
ejpam-3431	255	2	i	i	PRON
ejpam-3431	255	3	is	be	AUX
ejpam-3431	255	4	a	a	DET
ejpam-3431	255	5	pseudo	pseudo	NOUN
ejpam-3431	255	6	hyper	hyper	ADJ
ejpam-3431	255	7	gr	gr	NOUN
ejpam-3431	255	8	-	-	PUNCT
ejpam-3431	255	9	ideal	ideal	NOUN
ejpam-3431	255	10	of	of	ADP
ejpam-3431	255	11	type	type	NOUN
ejpam-3431	255	12	7	7	NUM
ejpam-3431	255	13	,	,	PUNCT
ejpam-3431	255	14	we	we	PRON
ejpam-3431	255	15	have	have	VERB
ejpam-3431	255	16	i	i	PRON
ejpam-3431	255	17	�	�	X
ejpam-3431	255	18	~,y	~,y	NUM
ejpam-3431	255	19	⊆	⊆	NUM
ejpam-3431	255	20	i	i	NOUN
ejpam-3431	255	21	or	or	CCONJ
ejpam-3431	255	22	i⊆	i⊆	NOUN
ejpam-3431	255	23	◦	◦	NOUN
ejpam-3431	255	24	,y	,y	PUNCT
ejpam-3431	255	25	⊆	⊆	NUM
ejpam-3431	256	1	i	i	PROPN
ejpam-3431	257	1	and	and	CCONJ
ejpam-3431	257	2	so	so	ADV
ejpam-3431	257	3	x	x	SYM
ejpam-3431	257	4	∈	∈	PROPN
ejpam-3431	257	5	i.	i.	NOUN
ejpam-3431	257	6	hence	hence	ADV
ejpam-3431	257	7	,	,	PUNCT
ejpam-3431	257	8	i	i	PRON
ejpam-3431	257	9	�	�	VERB
ejpam-3431	257	10	~,y	~,y	NOUN
ejpam-3431	257	11	∩	∩	ADJ
ejpam-3431	257	12	i⊆	i⊆	NOUN
ejpam-3431	257	13	◦	◦	NOUN
ejpam-3431	257	14	,y	,y	PUNCT
ejpam-3431	257	15	⊆	⊆	NUM
ejpam-3431	257	16	i.	i.	PROPN
ejpam-3431	257	17	�	�	PROPN
ejpam-3431	257	18	theorem	theorem	VERB
ejpam-3431	257	19	3.23	3.23	NUM
ejpam-3431	257	20	.	.	PUNCT
ejpam-3431	258	1	every	every	DET
ejpam-3431	258	2	pseudo	pseudo	NOUN
ejpam-3431	258	3	hyper	hyper	ADJ
ejpam-3431	258	4	gr	gr	NOUN
ejpam-3431	258	5	-	-	PUNCT
ejpam-3431	258	6	ideal	ideal	NOUN
ejpam-3431	258	7	in	in	ADP
ejpam-3431	258	8	h	h	NOUN
ejpam-3431	258	9	of	of	ADP
ejpam-3431	258	10	type	type	NOUN
ejpam-3431	258	11	5	5	NUM
ejpam-3431	258	12	is	be	AUX
ejpam-3431	258	13	a	a	DET
ejpam-3431	258	14	pseudo	pseudo	NOUN
ejpam-3431	258	15	hyper	hyper	ADJ
ejpam-3431	258	16	gr	gr	NOUN
ejpam-3431	258	17	-	-	PUNCT
ejpam-3431	258	18	ideal	ideal	NOUN
ejpam-3431	258	19	in	in	ADP
ejpam-3431	258	20	h	h	NOUN
ejpam-3431	258	21	of	of	ADP
ejpam-3431	258	22	type	type	NOUN
ejpam-3431	258	23	9	9	NUM
ejpam-3431	258	24	.	.	PUNCT
ejpam-3431	259	1	proof	proof	NOUN
ejpam-3431	259	2	.	.	PUNCT
ejpam-3431	260	1	suppose	suppose	VERB
ejpam-3431	260	2	that	that	SCONJ
ejpam-3431	260	3	i	i	PRON
ejpam-3431	260	4	be	be	VERB
ejpam-3431	260	5	a	a	DET
ejpam-3431	260	6	pseudo	pseudo	NOUN
ejpam-3431	260	7	hyper	hyper	ADJ
ejpam-3431	260	8	gr	gr	NOUN
ejpam-3431	260	9	-	-	PUNCT
ejpam-3431	260	10	ideal	ideal	NOUN
ejpam-3431	260	11	of	of	ADP
ejpam-3431	260	12	type	type	NOUN
ejpam-3431	260	13	5	5	NUM
ejpam-3431	260	14	.	.	PUNCT
ejpam-3431	261	1	now	now	ADV
ejpam-3431	261	2	,	,	PUNCT
ejpam-3431	261	3	we	we	PRON
ejpam-3431	261	4	will	will	AUX
ejpam-3431	261	5	show	show	VERB
ejpam-3431	261	6	that	that	SCONJ
ejpam-3431	261	7	i	i	PRON
ejpam-3431	261	8	is	be	AUX
ejpam-3431	261	9	a	a	DET
ejpam-3431	261	10	pseudo	pseudo	NOUN
ejpam-3431	261	11	hyper	hyper	ADJ
ejpam-3431	261	12	gr	gr	NOUN
ejpam-3431	261	13	-	-	PUNCT
ejpam-3431	261	14	ideal	ideal	NOUN
ejpam-3431	261	15	of	of	ADP
ejpam-3431	261	16	type	type	NOUN
ejpam-3431	261	17	9	9	NUM
ejpam-3431	261	18	.	.	PUNCT
ejpam-3431	262	1	let	let	VERB
ejpam-3431	262	2	y	y	PROPN
ejpam-3431	262	3	∈	∈	PROPN
ejpam-3431	263	1	i	i	PRON
ejpam-3431	263	2	and	and	CCONJ
ejpam-3431	263	3	x	x	PROPN
ejpam-3431	263	4	∈	∈	PROPN
ejpam-3431	263	5	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	263	6	∩	∩	NOUN
ejpam-3431	263	7	i	i	PROPN
ejpam-3431	263	8	⊆	⊆	NUM
ejpam-3431	263	9	◦	◦	NOUN
ejpam-3431	263	10	,	,	PUNCT
ejpam-3431	263	11	y.	y.	PROPN
ejpam-3431	263	12	then	then	ADV
ejpam-3431	263	13	,	,	PUNCT
ejpam-3431	263	14	x	x	PROPN
ejpam-3431	263	15	∈	∈	PROPN
ejpam-3431	263	16	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	263	17	and	and	CCONJ
ejpam-3431	263	18	x	x	PART
ejpam-3431	263	19	∈	∈	PROPN
ejpam-3431	263	20	i⊆	i⊆	PROPN
ejpam-3431	263	21	◦	◦	NOUN
ejpam-3431	263	22	,y	,y	PUNCT
ejpam-3431	263	23	.	.	PUNCT
ejpam-3431	264	1	since	since	SCONJ
ejpam-3431	264	2	i	i	PRON
ejpam-3431	264	3	is	be	AUX
ejpam-3431	264	4	a	a	DET
ejpam-3431	264	5	pseudo	pseudo	NOUN
ejpam-3431	264	6	hyper	hyper	ADJ
ejpam-3431	264	7	gr	gr	NOUN
ejpam-3431	264	8	-	-	PUNCT
ejpam-3431	264	9	ideal	ideal	NOUN
ejpam-3431	264	10	of	of	ADP
ejpam-3431	264	11	type	type	NOUN
ejpam-3431	264	12	5	5	NUM
ejpam-3431	264	13	,	,	PUNCT
ejpam-3431	264	14	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	264	15	⊆	⊆	NUM
ejpam-3431	264	16	i	i	NOUN
ejpam-3431	264	17	or	or	CCONJ
ejpam-3431	264	18	i⊆	i⊆	NOUN
ejpam-3431	264	19	◦	◦	NOUN
ejpam-3431	264	20	,y	,y	PUNCT
ejpam-3431	264	21	⊆	⊆	NUM
ejpam-3431	264	22	i	i	PROPN
ejpam-3431	264	23	and	and	CCONJ
ejpam-3431	264	24	so	so	ADV
ejpam-3431	264	25	x	x	SYM
ejpam-3431	264	26	∈	∈	PROPN
ejpam-3431	264	27	i.	i.	NOUN
ejpam-3431	264	28	hence	hence	ADV
ejpam-3431	264	29	,	,	PUNCT
ejpam-3431	264	30	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	264	31	∩	∩	NOUN
ejpam-3431	264	32	i⊆	i⊆	NOUN
ejpam-3431	264	33	◦	◦	NOUN
ejpam-3431	264	34	,y	,y	PUNCT
ejpam-3431	264	35	⊆	⊆	NUM
ejpam-3431	264	36	i.	i.	PROPN
ejpam-3431	264	37	�	�	PROPN
ejpam-3431	264	38	theorem	theorem	VERB
ejpam-3431	264	39	3.24	3.24	NUM
ejpam-3431	264	40	.	.	PUNCT
ejpam-3431	265	1	every	every	DET
ejpam-3431	265	2	pseudo	pseudo	NOUN
ejpam-3431	265	3	hyper	hyper	ADJ
ejpam-3431	265	4	gr	gr	NOUN
ejpam-3431	265	5	-	-	PUNCT
ejpam-3431	265	6	ideal	ideal	NOUN
ejpam-3431	265	7	in	in	ADP
ejpam-3431	265	8	h	h	NOUN
ejpam-3431	265	9	of	of	ADP
ejpam-3431	265	10	type	type	NOUN
ejpam-3431	265	11	12	12	NUM
ejpam-3431	265	12	is	be	AUX
ejpam-3431	265	13	a	a	DET
ejpam-3431	265	14	pseudo	pseudo	NOUN
ejpam-3431	265	15	hyper	hyper	ADJ
ejpam-3431	265	16	gr	gr	NOUN
ejpam-3431	265	17	-	-	PUNCT
ejpam-3431	265	18	ideal	ideal	NOUN
ejpam-3431	265	19	in	in	ADP
ejpam-3431	265	20	h	h	NOUN
ejpam-3431	265	21	of	of	ADP
ejpam-3431	265	22	types	type	NOUN
ejpam-3431	265	23	9	9	NUM
ejpam-3431	265	24	,	,	PUNCT
ejpam-3431	265	25	10	10	NUM
ejpam-3431	265	26	and	and	CCONJ
ejpam-3431	265	27	11	11	NUM
ejpam-3431	265	28	.	.	PUNCT
ejpam-3431	266	1	proof	proof	NOUN
ejpam-3431	266	2	.	.	PUNCT
ejpam-3431	267	1	suppose	suppose	VERB
ejpam-3431	267	2	that	that	SCONJ
ejpam-3431	267	3	i	i	PRON
ejpam-3431	267	4	be	be	VERB
ejpam-3431	267	5	a	a	DET
ejpam-3431	267	6	pseudo	pseudo	NOUN
ejpam-3431	267	7	hyper	hyper	ADJ
ejpam-3431	267	8	gr	gr	NOUN
ejpam-3431	267	9	-	-	PUNCT
ejpam-3431	267	10	ideal	ideal	NOUN
ejpam-3431	267	11	of	of	ADP
ejpam-3431	267	12	type	type	NOUN
ejpam-3431	267	13	12	12	NUM
ejpam-3431	267	14	.	.	PUNCT
ejpam-3431	268	1	now	now	ADV
ejpam-3431	268	2	,	,	PUNCT
ejpam-3431	268	3	we	we	PRON
ejpam-3431	268	4	will	will	AUX
ejpam-3431	268	5	show	show	VERB
ejpam-3431	268	6	that	that	SCONJ
ejpam-3431	268	7	i	i	PRON
ejpam-3431	268	8	is	be	AUX
ejpam-3431	268	9	a	a	DET
ejpam-3431	268	10	pseudo	pseudo	NOUN
ejpam-3431	268	11	hyper	hyper	ADJ
ejpam-3431	268	12	gr	gr	NOUN
ejpam-3431	268	13	-	-	PUNCT
ejpam-3431	268	14	ideal	ideal	NOUN
ejpam-3431	268	15	of	of	ADP
ejpam-3431	268	16	type	type	NOUN
ejpam-3431	268	17	9	9	NUM
ejpam-3431	268	18	.	.	PUNCT
ejpam-3431	269	1	let	let	VERB
ejpam-3431	269	2	y	y	PROPN
ejpam-3431	269	3	∈	∈	PROPN
ejpam-3431	270	1	i	i	PRON
ejpam-3431	270	2	and	and	CCONJ
ejpam-3431	270	3	x	x	PROPN
ejpam-3431	270	4	∈	∈	PROPN
ejpam-3431	270	5	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	270	6	∩	∩	ADJ
ejpam-3431	270	7	i⊆	i⊆	NOUN
ejpam-3431	270	8	◦	◦	NOUN
ejpam-3431	270	9	,y	,y	PUNCT
ejpam-3431	270	10	.	.	PUNCT
ejpam-3431	271	1	then	then	ADV
ejpam-3431	271	2	,	,	PUNCT
ejpam-3431	271	3	x	x	PROPN
ejpam-3431	271	4	∈	∈	PROPN
ejpam-3431	271	5	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	271	6	and	and	CCONJ
ejpam-3431	271	7	x	x	PART
ejpam-3431	271	8	∈	∈	PROPN
ejpam-3431	271	9	i⊆	i⊆	PROPN
ejpam-3431	271	10	◦	◦	NOUN
ejpam-3431	271	11	,y	,y	PUNCT
ejpam-3431	271	12	.	.	PUNCT
ejpam-3431	272	1	thus	thus	ADV
ejpam-3431	272	2	,	,	PUNCT
ejpam-3431	272	3	x	x	X
ejpam-3431	272	4	~	~	PUNCT
ejpam-3431	272	5	y	y	PROPN
ejpam-3431	272	6	⊆	⊆	NUM
ejpam-3431	272	7	i	i	PROPN
ejpam-3431	272	8	and	and	CCONJ
ejpam-3431	272	9	x	x	VERB
ejpam-3431	272	10	◦	◦	NOUN
ejpam-3431	272	11	y	y	PROPN
ejpam-3431	272	12	⊆	⊆	NUM
ejpam-3431	272	13	i	i	PROPN
ejpam-3431	272	14	and	and	CCONJ
ejpam-3431	272	15	and	and	CCONJ
ejpam-3431	272	16	by	by	ADP
ejpam-3431	272	17	remark	remark	NOUN
ejpam-3431	272	18	3.3	3.3	NUM
ejpam-3431	272	19	(	(	PUNCT
ejpam-3431	272	20	iv	iv	NUM
ejpam-3431	272	21	)	)	PUNCT
ejpam-3431	272	22	,	,	PUNCT
ejpam-3431	272	23	x	x	X
ejpam-3431	272	24	~	~	PUNCT
ejpam-3431	272	25	y	y	X
ejpam-3431	272	26	�	�	PROPN
ejpam-3431	272	27	i	i	PRON
ejpam-3431	272	28	and	and	CCONJ
ejpam-3431	272	29	x	x	AUX
ejpam-3431	272	30	◦	◦	NOUN
ejpam-3431	272	31	y	y	PROPN
ejpam-3431	272	32	�	�	PROPN
ejpam-3431	272	33	i.	i.	PROPN
ejpam-3431	272	34	this	this	PRON
ejpam-3431	272	35	means	mean	VERB
ejpam-3431	272	36	that	that	SCONJ
ejpam-3431	272	37	x	x	PUNCT
ejpam-3431	272	38	∈	∈	PROPN
ejpam-3431	272	39	i	i	PRON
ejpam-3431	272	40	�	�	VERB
ejpam-3431	272	41	~,y	~,y	PROPN
ejpam-3431	272	42	and	and	CCONJ
ejpam-3431	272	43	x	x	SYM
ejpam-3431	272	44	∈	∈	PROPN
ejpam-3431	272	45	i	i	PRON
ejpam-3431	272	46	�	�	NOUN
ejpam-3431	272	47	◦	◦	NOUN
ejpam-3431	272	48	,y	,y	PUNCT
ejpam-3431	272	49	or	or	CCONJ
ejpam-3431	272	50	equivalently	equivalently	ADV
ejpam-3431	272	51	x	x	AUX
ejpam-3431	272	52	∈	∈	PROPN
ejpam-3431	272	53	i	i	NOUN
ejpam-3431	272	54	�	�	NOUN
ejpam-3431	272	55	~,y	~,y	PROPN
ejpam-3431	272	56	∩	∩	ADJ
ejpam-3431	272	57	i	i	PRON
ejpam-3431	272	58	�	�	PROPN
ejpam-3431	272	59	◦	◦	NOUN
ejpam-3431	272	60	,y	,y	PUNCT
ejpam-3431	272	61	.	.	PUNCT
ejpam-3431	273	1	since	since	SCONJ
ejpam-3431	273	2	i	i	PRON
ejpam-3431	273	3	is	be	AUX
ejpam-3431	273	4	a	a	DET
ejpam-3431	273	5	pseudo	pseudo	NOUN
ejpam-3431	273	6	hyper	hyper	ADJ
ejpam-3431	273	7	gr	gr	NOUN
ejpam-3431	273	8	-	-	PUNCT
ejpam-3431	273	9	ideal	ideal	NOUN
ejpam-3431	273	10	of	of	ADP
ejpam-3431	273	11	type	type	NOUN
ejpam-3431	273	12	12	12	NUM
ejpam-3431	273	13	,	,	PUNCT
ejpam-3431	273	14	i	i	PRON
ejpam-3431	273	15	�	�	VERB
ejpam-3431	273	16	~,y	~,y	PROPN
ejpam-3431	273	17	∩	∩	ADJ
ejpam-3431	273	18	i	i	PRON
ejpam-3431	273	19	�	�	PROPN
ejpam-3431	273	20	◦	◦	NOUN
ejpam-3431	273	21	,y	,y	PUNCT
ejpam-3431	273	22	⊆	⊆	NUM
ejpam-3431	273	23	i	i	PRON
ejpam-3431	273	24	,	,	PUNCT
ejpam-3431	273	25	and	and	CCONJ
ejpam-3431	273	26	so	so	ADV
ejpam-3431	273	27	x	x	SYM
ejpam-3431	273	28	∈	∈	PROPN
ejpam-3431	273	29	i.	i.	NOUN
ejpam-3431	273	30	therefore	therefore	ADV
ejpam-3431	273	31	,	,	PUNCT
ejpam-3431	273	32	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	273	33	∩	∩	NOUN
ejpam-3431	273	34	i⊆	i⊆	NOUN
ejpam-3431	273	35	◦	◦	NOUN
ejpam-3431	273	36	,y	,y	PUNCT
ejpam-3431	273	37	⊆	⊆	NUM
ejpam-3431	273	38	i.	i.	NOUN
ejpam-3431	273	39	next	next	ADV
ejpam-3431	273	40	,	,	PUNCT
ejpam-3431	273	41	we	we	PRON
ejpam-3431	273	42	will	will	AUX
ejpam-3431	273	43	show	show	VERB
ejpam-3431	273	44	that	that	SCONJ
ejpam-3431	273	45	i	i	PRON
ejpam-3431	273	46	is	be	AUX
ejpam-3431	273	47	a	a	DET
ejpam-3431	273	48	pseudo	pseudo	NOUN
ejpam-3431	273	49	hyper	hyper	ADJ
ejpam-3431	273	50	gr	gr	NOUN
ejpam-3431	273	51	-	-	PUNCT
ejpam-3431	273	52	ideal	ideal	NOUN
ejpam-3431	273	53	of	of	ADP
ejpam-3431	273	54	type	type	NOUN
ejpam-3431	273	55	10	10	NUM
ejpam-3431	273	56	.	.	PUNCT
ejpam-3431	274	1	let	let	VERB
ejpam-3431	274	2	y	y	PRON
ejpam-3431	274	3	∈	∈	PROPN
ejpam-3431	275	1	i	i	PRON
ejpam-3431	275	2	and	and	CCONJ
ejpam-3431	275	3	x	x	PROPN
ejpam-3431	275	4	∈	∈	PROPN
ejpam-3431	275	5	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	275	6	∩	∩	X
ejpam-3431	275	7	i	i	PRON
ejpam-3431	275	8	�	�	PROPN
ejpam-3431	275	9	◦	◦	NOUN
ejpam-3431	275	10	,y	,y	PROPN
ejpam-3431	275	11	.	.	PUNCT
ejpam-3431	276	1	then	then	ADV
ejpam-3431	276	2	,	,	PUNCT
ejpam-3431	276	3	x	x	PROPN
ejpam-3431	276	4	∈	∈	PROPN
ejpam-3431	276	5	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	276	6	and	and	CCONJ
ejpam-3431	276	7	x	x	PUNCT
ejpam-3431	276	8	∈	∈	PROPN
ejpam-3431	276	9	i	i	PRON
ejpam-3431	276	10	�	�	PROPN
ejpam-3431	276	11	◦	◦	NOUN
ejpam-3431	276	12	,y	,y	PUNCT
ejpam-3431	276	13	.	.	PUNCT
ejpam-3431	277	1	thus	thus	ADV
ejpam-3431	277	2	,	,	PUNCT
ejpam-3431	277	3	x	x	X
ejpam-3431	277	4	~	~	PUNCT
ejpam-3431	277	5	y	y	PROPN
ejpam-3431	277	6	⊆	⊆	NUM
ejpam-3431	277	7	i	i	PROPN
ejpam-3431	277	8	and	and	CCONJ
ejpam-3431	277	9	x	x	PART
ejpam-3431	277	10	◦	◦	NOUN
ejpam-3431	277	11	y	y	PROPN
ejpam-3431	277	12	�	�	PROPN
ejpam-3431	277	13	i	i	PRON
ejpam-3431	277	14	and	and	CCONJ
ejpam-3431	277	15	and	and	CCONJ
ejpam-3431	277	16	r.	r.	PROPN
ejpam-3431	277	17	manzano	manzano	PROPN
ejpam-3431	277	18	,	,	PUNCT
ejpam-3431	277	19	jr	jr	PROPN
ejpam-3431	277	20	.	.	PROPN
ejpam-3431	277	21	,	,	PUNCT
ejpam-3431	277	22	g.	g.	PROPN
ejpam-3431	277	23	petalcorin	petalcorin	PROPN
ejpam-3431	277	24	,	,	PUNCT
ejpam-3431	277	25	jr	jr	PROPN
ejpam-3431	277	26	.	.	PROPN
ejpam-3431	277	27	/	/	SYM
ejpam-3431	277	28	eur	eur	PROPN
ejpam-3431	277	29	.	.	PUNCT
ejpam-3431	278	1	j.	j.	PROPN
ejpam-3431	278	2	pure	pure	PROPN
ejpam-3431	278	3	appl	appl	PROPN
ejpam-3431	278	4	.	.	PROPN
ejpam-3431	278	5	math	math	PROPN
ejpam-3431	278	6	,	,	PUNCT
ejpam-3431	278	7	12	12	NUM
ejpam-3431	278	8	(	(	PUNCT
ejpam-3431	278	9	3	3	NUM
ejpam-3431	278	10	)	)	PUNCT
ejpam-3431	278	11	(	(	PUNCT
ejpam-3431	278	12	2019	2019	NUM
ejpam-3431	278	13	)	)	PUNCT
ejpam-3431	278	14	,	,	PUNCT
ejpam-3431	278	15	821	821	NUM
ejpam-3431	278	16	-	-	SYM
ejpam-3431	278	17	833	833	NUM
ejpam-3431	278	18	831	831	NUM
ejpam-3431	278	19	by	by	ADP
ejpam-3431	278	20	remark	remark	NOUN
ejpam-3431	278	21	3.3	3.3	NUM
ejpam-3431	278	22	(	(	PUNCT
ejpam-3431	278	23	iv	iv	NUM
ejpam-3431	278	24	)	)	PUNCT
ejpam-3431	278	25	,	,	PUNCT
ejpam-3431	278	26	x	x	X
ejpam-3431	278	27	~	~	PUNCT
ejpam-3431	278	28	y	y	PROPN
ejpam-3431	278	29	�	�	PROPN
ejpam-3431	278	30	i.	i.	PROPN
ejpam-3431	278	31	this	this	PRON
ejpam-3431	278	32	means	mean	VERB
ejpam-3431	278	33	that	that	SCONJ
ejpam-3431	278	34	x	x	PUNCT
ejpam-3431	278	35	∈	∈	PROPN
ejpam-3431	278	36	i	i	PRON
ejpam-3431	278	37	�	�	VERB
ejpam-3431	278	38	~,y	~,y	PROPN
ejpam-3431	278	39	and	and	CCONJ
ejpam-3431	278	40	x	x	SYM
ejpam-3431	278	41	∈	∈	PROPN
ejpam-3431	278	42	i	i	PRON
ejpam-3431	278	43	�	�	NOUN
ejpam-3431	278	44	◦	◦	NOUN
ejpam-3431	278	45	,y	,y	PUNCT
ejpam-3431	278	46	or	or	CCONJ
ejpam-3431	278	47	equivalently	equivalently	ADV
ejpam-3431	278	48	x	x	AUX
ejpam-3431	278	49	∈	∈	PROPN
ejpam-3431	278	50	i	i	NOUN
ejpam-3431	278	51	�	�	NOUN
ejpam-3431	278	52	~,y	~,y	PROPN
ejpam-3431	278	53	∩	∩	ADJ
ejpam-3431	278	54	i	i	PRON
ejpam-3431	278	55	�	�	PROPN
ejpam-3431	278	56	◦	◦	NOUN
ejpam-3431	278	57	,y	,y	PUNCT
ejpam-3431	278	58	.	.	PUNCT
ejpam-3431	279	1	since	since	SCONJ
ejpam-3431	279	2	i	i	PRON
ejpam-3431	279	3	is	be	AUX
ejpam-3431	279	4	a	a	DET
ejpam-3431	279	5	pseudo	pseudo	NOUN
ejpam-3431	279	6	hyper	hyper	ADJ
ejpam-3431	279	7	gr	gr	NOUN
ejpam-3431	279	8	-	-	PUNCT
ejpam-3431	279	9	ideal	ideal	NOUN
ejpam-3431	279	10	of	of	ADP
ejpam-3431	279	11	type	type	NOUN
ejpam-3431	279	12	12	12	NUM
ejpam-3431	279	13	,	,	PUNCT
ejpam-3431	279	14	i	i	PRON
ejpam-3431	279	15	�	�	VERB
ejpam-3431	279	16	~,y	~,y	PROPN
ejpam-3431	279	17	∩	∩	ADJ
ejpam-3431	279	18	i	i	PRON
ejpam-3431	279	19	�	�	PROPN
ejpam-3431	279	20	◦	◦	NOUN
ejpam-3431	279	21	,y	,y	PUNCT
ejpam-3431	279	22	⊆	⊆	NUM
ejpam-3431	279	23	i	i	PRON
ejpam-3431	279	24	,	,	PUNCT
ejpam-3431	279	25	and	and	CCONJ
ejpam-3431	279	26	so	so	ADV
ejpam-3431	279	27	x	x	SYM
ejpam-3431	279	28	∈	∈	PROPN
ejpam-3431	279	29	i.	i.	NOUN
ejpam-3431	279	30	therefore	therefore	ADV
ejpam-3431	279	31	,	,	PUNCT
ejpam-3431	279	32	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	279	33	∩	∩	X
ejpam-3431	279	34	i	i	PRON
ejpam-3431	279	35	�	�	PROPN
ejpam-3431	279	36	◦	◦	NOUN
ejpam-3431	279	37	,y	,y	PUNCT
ejpam-3431	279	38	⊆	⊆	NUM
ejpam-3431	279	39	i.	i.	NOUN
ejpam-3431	279	40	the	the	DET
ejpam-3431	279	41	proof	proof	NOUN
ejpam-3431	279	42	for	for	ADP
ejpam-3431	279	43	type	type	NOUN
ejpam-3431	279	44	11	11	NUM
ejpam-3431	279	45	follows	follow	VERB
ejpam-3431	279	46	similarly	similarly	ADV
ejpam-3431	279	47	as	as	ADP
ejpam-3431	279	48	of	of	ADP
ejpam-3431	279	49	type	type	NOUN
ejpam-3431	279	50	10	10	NUM
ejpam-3431	279	51	with	with	ADP
ejpam-3431	279	52	some	some	DET
ejpam-3431	279	53	modifications	modification	NOUN
ejpam-3431	279	54	.	.	PUNCT
ejpam-3431	280	1	�	�	PROPN
ejpam-3431	280	2	theorem	theorem	VERB
ejpam-3431	280	3	3.25	3.25	NUM
ejpam-3431	280	4	.	.	PUNCT
ejpam-3431	281	1	every	every	DET
ejpam-3431	281	2	pseudo	pseudo	NOUN
ejpam-3431	281	3	hyper	hyper	ADJ
ejpam-3431	281	4	gr	gr	NOUN
ejpam-3431	281	5	-	-	PUNCT
ejpam-3431	281	6	ideal	ideal	NOUN
ejpam-3431	281	7	in	in	ADP
ejpam-3431	281	8	h	h	NOUN
ejpam-3431	281	9	of	of	ADP
ejpam-3431	281	10	type	type	NOUN
ejpam-3431	281	11	10	10	NUM
ejpam-3431	281	12	is	be	AUX
ejpam-3431	281	13	a	a	DET
ejpam-3431	281	14	pseudo	pseudo	NOUN
ejpam-3431	281	15	hyper	hyper	ADJ
ejpam-3431	281	16	gr	gr	NOUN
ejpam-3431	281	17	-	-	PUNCT
ejpam-3431	281	18	ideal	ideal	NOUN
ejpam-3431	281	19	in	in	ADP
ejpam-3431	281	20	h	h	NOUN
ejpam-3431	281	21	of	of	ADP
ejpam-3431	281	22	type	type	NOUN
ejpam-3431	281	23	9	9	NUM
ejpam-3431	281	24	.	.	PUNCT
ejpam-3431	282	1	proof	proof	NOUN
ejpam-3431	282	2	.	.	PUNCT
ejpam-3431	283	1	suppose	suppose	VERB
ejpam-3431	283	2	that	that	SCONJ
ejpam-3431	283	3	i	i	PRON
ejpam-3431	283	4	be	be	VERB
ejpam-3431	283	5	a	a	DET
ejpam-3431	283	6	pseudo	pseudo	NOUN
ejpam-3431	283	7	hyper	hyper	ADJ
ejpam-3431	283	8	gr	gr	NOUN
ejpam-3431	283	9	-	-	PUNCT
ejpam-3431	283	10	ideal	ideal	NOUN
ejpam-3431	283	11	of	of	ADP
ejpam-3431	283	12	type	type	NOUN
ejpam-3431	283	13	10	10	NUM
ejpam-3431	283	14	.	.	PUNCT
ejpam-3431	284	1	now	now	ADV
ejpam-3431	284	2	,	,	PUNCT
ejpam-3431	284	3	we	we	PRON
ejpam-3431	284	4	will	will	AUX
ejpam-3431	284	5	show	show	VERB
ejpam-3431	284	6	that	that	SCONJ
ejpam-3431	284	7	i	i	PRON
ejpam-3431	284	8	is	be	AUX
ejpam-3431	284	9	a	a	DET
ejpam-3431	284	10	pseudo	pseudo	NOUN
ejpam-3431	284	11	hyper	hyper	ADJ
ejpam-3431	284	12	gr	gr	NOUN
ejpam-3431	284	13	-	-	PUNCT
ejpam-3431	284	14	ideal	ideal	NOUN
ejpam-3431	284	15	of	of	ADP
ejpam-3431	284	16	type	type	NOUN
ejpam-3431	284	17	9	9	NUM
ejpam-3431	284	18	.	.	PUNCT
ejpam-3431	285	1	let	let	VERB
ejpam-3431	285	2	y	y	PROPN
ejpam-3431	285	3	∈	∈	PROPN
ejpam-3431	286	1	i	i	PRON
ejpam-3431	286	2	and	and	CCONJ
ejpam-3431	286	3	x	x	PROPN
ejpam-3431	286	4	∈	∈	PROPN
ejpam-3431	286	5	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	286	6	∩	∩	ADJ
ejpam-3431	286	7	i⊆	i⊆	NOUN
ejpam-3431	286	8	◦	◦	NOUN
ejpam-3431	286	9	,y	,y	PUNCT
ejpam-3431	286	10	.	.	PUNCT
ejpam-3431	287	1	then	then	ADV
ejpam-3431	287	2	,	,	PUNCT
ejpam-3431	287	3	x	x	PROPN
ejpam-3431	287	4	∈	∈	PROPN
ejpam-3431	287	5	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	287	6	and	and	CCONJ
ejpam-3431	287	7	x	x	PART
ejpam-3431	287	8	∈	∈	PROPN
ejpam-3431	287	9	i⊆	i⊆	PROPN
ejpam-3431	287	10	◦	◦	NOUN
ejpam-3431	287	11	,y	,y	PUNCT
ejpam-3431	287	12	.	.	PUNCT
ejpam-3431	288	1	thus	thus	ADV
ejpam-3431	288	2	,	,	PUNCT
ejpam-3431	288	3	x	x	PUNCT
ejpam-3431	288	4	◦	◦	VERB
ejpam-3431	288	5	y	y	PROPN
ejpam-3431	288	6	⊆	⊆	NUM
ejpam-3431	288	7	i	i	PROPN
ejpam-3431	288	8	and	and	CCONJ
ejpam-3431	288	9	and	and	CCONJ
ejpam-3431	288	10	by	by	ADP
ejpam-3431	288	11	remark	remark	NOUN
ejpam-3431	288	12	3.3	3.3	NUM
ejpam-3431	288	13	(	(	PUNCT
ejpam-3431	288	14	iv	iv	NUM
ejpam-3431	288	15	)	)	PUNCT
ejpam-3431	288	16	,	,	PUNCT
ejpam-3431	288	17	x	x	PUNCT
ejpam-3431	288	18	◦	◦	VERB
ejpam-3431	288	19	y	y	PROPN
ejpam-3431	288	20	�	�	PROPN
ejpam-3431	288	21	i	i	PRON
ejpam-3431	288	22	which	which	PRON
ejpam-3431	288	23	means	mean	VERB
ejpam-3431	288	24	that	that	SCONJ
ejpam-3431	288	25	x	x	PUNCT
ejpam-3431	288	26	∈	∈	PROPN
ejpam-3431	288	27	i	i	NOUN
ejpam-3431	288	28	�	�	PROPN
ejpam-3431	288	29	◦	◦	NOUN
ejpam-3431	288	30	,y	,y	PUNCT
ejpam-3431	288	31	.	.	PUNCT
ejpam-3431	289	1	thus	thus	ADV
ejpam-3431	289	2	,	,	PUNCT
ejpam-3431	289	3	x	x	PROPN
ejpam-3431	289	4	∈	∈	PROPN
ejpam-3431	289	5	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	289	6	∩	∩	X
ejpam-3431	289	7	i	i	PRON
ejpam-3431	289	8	�	�	PROPN
ejpam-3431	289	9	◦	◦	NOUN
ejpam-3431	289	10	,y	,y	NOUN
ejpam-3431	289	11	.	.	PUNCT
ejpam-3431	290	1	since	since	SCONJ
ejpam-3431	290	2	i	i	PRON
ejpam-3431	290	3	is	be	AUX
ejpam-3431	290	4	a	a	DET
ejpam-3431	290	5	pseudo	pseudo	NOUN
ejpam-3431	290	6	hyper	hyper	ADJ
ejpam-3431	290	7	gr	gr	NOUN
ejpam-3431	290	8	-	-	PUNCT
ejpam-3431	290	9	ideal	ideal	NOUN
ejpam-3431	290	10	of	of	ADP
ejpam-3431	290	11	type	type	NOUN
ejpam-3431	290	12	10	10	NUM
ejpam-3431	290	13	,	,	PUNCT
ejpam-3431	290	14	we	we	PRON
ejpam-3431	290	15	have	have	VERB
ejpam-3431	290	16	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	290	17	∩	∩	NOUN
ejpam-3431	290	18	i	i	PRON
ejpam-3431	290	19	�	�	PROPN
ejpam-3431	290	20	◦	◦	NOUN
ejpam-3431	290	21	,y	,y	PUNCT
ejpam-3431	290	22	⊆	⊆	NUM
ejpam-3431	290	23	i	i	PROPN
ejpam-3431	290	24	and	and	CCONJ
ejpam-3431	290	25	so	so	ADV
ejpam-3431	290	26	x	x	SYM
ejpam-3431	290	27	∈	∈	PROPN
ejpam-3431	290	28	i.	i.	NOUN
ejpam-3431	290	29	hence	hence	ADV
ejpam-3431	290	30	,	,	PUNCT
ejpam-3431	290	31	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	290	32	∩	∩	NOUN
ejpam-3431	290	33	i⊆	i⊆	NOUN
ejpam-3431	290	34	◦	◦	NOUN
ejpam-3431	290	35	,y	,y	PUNCT
ejpam-3431	290	36	⊆	⊆	NUM
ejpam-3431	290	37	i.	i.	PROPN
ejpam-3431	290	38	�	�	PROPN
ejpam-3431	290	39	theorem	theorem	VERB
ejpam-3431	290	40	3.26	3.26	NUM
ejpam-3431	290	41	.	.	PUNCT
ejpam-3431	291	1	every	every	DET
ejpam-3431	291	2	pseudo	pseudo	NOUN
ejpam-3431	291	3	hyper	hyper	ADJ
ejpam-3431	291	4	gr	gr	NOUN
ejpam-3431	291	5	-	-	PUNCT
ejpam-3431	291	6	ideal	ideal	NOUN
ejpam-3431	291	7	in	in	ADP
ejpam-3431	291	8	h	h	NOUN
ejpam-3431	291	9	of	of	ADP
ejpam-3431	291	10	type	type	NOUN
ejpam-3431	291	11	11	11	NUM
ejpam-3431	291	12	is	be	AUX
ejpam-3431	291	13	a	a	DET
ejpam-3431	291	14	pseudo	pseudo	NOUN
ejpam-3431	291	15	hyper	hyper	ADJ
ejpam-3431	291	16	gr	gr	NOUN
ejpam-3431	291	17	-	-	PUNCT
ejpam-3431	291	18	ideal	ideal	NOUN
ejpam-3431	291	19	in	in	ADP
ejpam-3431	291	20	h	h	NOUN
ejpam-3431	291	21	of	of	ADP
ejpam-3431	291	22	type	type	NOUN
ejpam-3431	291	23	9	9	NUM
ejpam-3431	291	24	.	.	PUNCT
ejpam-3431	292	1	proof	proof	NOUN
ejpam-3431	292	2	.	.	PUNCT
ejpam-3431	293	1	suppose	suppose	VERB
ejpam-3431	293	2	that	that	SCONJ
ejpam-3431	293	3	i	i	PRON
ejpam-3431	293	4	be	be	VERB
ejpam-3431	293	5	a	a	DET
ejpam-3431	293	6	pseudo	pseudo	NOUN
ejpam-3431	293	7	hyper	hyper	ADJ
ejpam-3431	293	8	gr	gr	NOUN
ejpam-3431	293	9	-	-	PUNCT
ejpam-3431	293	10	ideal	ideal	NOUN
ejpam-3431	293	11	of	of	ADP
ejpam-3431	293	12	type	type	NOUN
ejpam-3431	293	13	11	11	NUM
ejpam-3431	293	14	.	.	PUNCT
ejpam-3431	294	1	now	now	ADV
ejpam-3431	294	2	,	,	PUNCT
ejpam-3431	294	3	we	we	PRON
ejpam-3431	294	4	will	will	AUX
ejpam-3431	294	5	show	show	VERB
ejpam-3431	294	6	that	that	SCONJ
ejpam-3431	294	7	i	i	PRON
ejpam-3431	294	8	is	be	AUX
ejpam-3431	294	9	a	a	DET
ejpam-3431	294	10	pseudo	pseudo	NOUN
ejpam-3431	294	11	hyper	hyper	ADJ
ejpam-3431	294	12	gr	gr	NOUN
ejpam-3431	294	13	-	-	PUNCT
ejpam-3431	294	14	ideal	ideal	NOUN
ejpam-3431	294	15	of	of	ADP
ejpam-3431	294	16	type	type	NOUN
ejpam-3431	294	17	9	9	NUM
ejpam-3431	294	18	.	.	PUNCT
ejpam-3431	295	1	let	let	VERB
ejpam-3431	295	2	y	y	PROPN
ejpam-3431	295	3	∈	∈	PROPN
ejpam-3431	296	1	i	i	PRON
ejpam-3431	296	2	and	and	CCONJ
ejpam-3431	296	3	x	x	PROPN
ejpam-3431	296	4	∈	∈	PROPN
ejpam-3431	296	5	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	296	6	∩	∩	ADJ
ejpam-3431	296	7	i⊆	i⊆	NOUN
ejpam-3431	296	8	◦	◦	NOUN
ejpam-3431	296	9	,y	,y	PUNCT
ejpam-3431	296	10	.	.	PUNCT
ejpam-3431	297	1	then	then	ADV
ejpam-3431	297	2	x	x	PROPN
ejpam-3431	297	3	∈	∈	PROPN
ejpam-3431	297	4	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	297	5	and	and	CCONJ
ejpam-3431	297	6	x	x	PART
ejpam-3431	297	7	∈	∈	PROPN
ejpam-3431	297	8	i⊆	i⊆	PROPN
ejpam-3431	297	9	◦	◦	NOUN
ejpam-3431	297	10	,y	,y	PUNCT
ejpam-3431	297	11	.	.	PUNCT
ejpam-3431	298	1	thus	thus	ADV
ejpam-3431	298	2	,	,	PUNCT
ejpam-3431	298	3	x~	x~	PROPN
ejpam-3431	298	4	y	y	PROPN
ejpam-3431	298	5	⊆	⊆	NUM
ejpam-3431	298	6	i	i	PROPN
ejpam-3431	298	7	and	and	CCONJ
ejpam-3431	298	8	and	and	CCONJ
ejpam-3431	298	9	by	by	ADP
ejpam-3431	298	10	remark	remark	NOUN
ejpam-3431	298	11	3.3	3.3	NUM
ejpam-3431	298	12	(	(	PUNCT
ejpam-3431	298	13	iv	iv	NUM
ejpam-3431	298	14	)	)	PUNCT
ejpam-3431	298	15	,	,	PUNCT
ejpam-3431	298	16	x~	x~	PROPN
ejpam-3431	298	17	y	y	PROPN
ejpam-3431	298	18	�	�	PROPN
ejpam-3431	298	19	i	i	PRON
ejpam-3431	298	20	which	which	PRON
ejpam-3431	298	21	means	mean	VERB
ejpam-3431	298	22	that	that	SCONJ
ejpam-3431	298	23	x	x	PUNCT
ejpam-3431	298	24	∈	∈	PROPN
ejpam-3431	298	25	i	i	PRON
ejpam-3431	298	26	�	�	PROPN
ejpam-3431	298	27	~,y	~,y	PROPN
ejpam-3431	298	28	.	.	PUNCT
ejpam-3431	299	1	thus	thus	ADV
ejpam-3431	299	2	,	,	PUNCT
ejpam-3431	299	3	x	x	PROPN
ejpam-3431	299	4	∈	∈	PROPN
ejpam-3431	299	5	i	i	NOUN
ejpam-3431	299	6	�	�	NOUN
ejpam-3431	299	7	~,y	~,y	NOUN
ejpam-3431	299	8	∩	∩	ADJ
ejpam-3431	299	9	i⊆	i⊆	NOUN
ejpam-3431	299	10	◦	◦	NOUN
ejpam-3431	299	11	,y	,y	NOUN
ejpam-3431	299	12	.	.	PUNCT
ejpam-3431	300	1	since	since	SCONJ
ejpam-3431	300	2	i	i	PRON
ejpam-3431	300	3	is	be	AUX
ejpam-3431	300	4	a	a	DET
ejpam-3431	300	5	pseudo	pseudo	NOUN
ejpam-3431	300	6	hyper	hyper	ADJ
ejpam-3431	300	7	gr	gr	NOUN
ejpam-3431	300	8	-	-	PUNCT
ejpam-3431	300	9	ideal	ideal	NOUN
ejpam-3431	300	10	of	of	ADP
ejpam-3431	300	11	type	type	NOUN
ejpam-3431	300	12	11	11	NUM
ejpam-3431	300	13	,	,	PUNCT
ejpam-3431	300	14	we	we	PRON
ejpam-3431	300	15	have	have	VERB
ejpam-3431	300	16	i	i	PRON
ejpam-3431	300	17	�	�	NOUN
ejpam-3431	300	18	~,y	~,y	NOUN
ejpam-3431	300	19	∩	∩	ADJ
ejpam-3431	300	20	i⊆	i⊆	NOUN
ejpam-3431	300	21	◦	◦	NOUN
ejpam-3431	300	22	,y	,y	PUNCT
ejpam-3431	300	23	⊆	⊆	NUM
ejpam-3431	300	24	i	i	PROPN
ejpam-3431	300	25	and	and	CCONJ
ejpam-3431	300	26	so	so	ADV
ejpam-3431	300	27	,	,	PUNCT
ejpam-3431	300	28	x	x	PROPN
ejpam-3431	300	29	∈	∈	PROPN
ejpam-3431	300	30	i.	i.	NOUN
ejpam-3431	300	31	hence	hence	ADV
ejpam-3431	300	32	,	,	PUNCT
ejpam-3431	300	33	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	300	34	∩	∩	NOUN
ejpam-3431	300	35	i⊆	i⊆	NOUN
ejpam-3431	300	36	◦	◦	NOUN
ejpam-3431	300	37	,y	,y	PUNCT
ejpam-3431	300	38	⊆	⊆	NUM
ejpam-3431	300	39	i.	i.	PROPN
ejpam-3431	300	40	�	�	PROPN
ejpam-3431	300	41	theorem	theorem	VERB
ejpam-3431	300	42	3.27	3.27	NUM
ejpam-3431	300	43	.	.	PUNCT
ejpam-3431	301	1	let	let	VERB
ejpam-3431	301	2	{	{	PUNCT
ejpam-3431	301	3	iω|ω	iω|ω	NOUN
ejpam-3431	301	4	∈	∈	PROPN
ejpam-3431	301	5	ω	ω	PROPN
ejpam-3431	301	6	}	}	PUNCT
ejpam-3431	301	7	be	be	AUX
ejpam-3431	301	8	a	a	DET
ejpam-3431	301	9	family	family	NOUN
ejpam-3431	301	10	of	of	ADP
ejpam-3431	301	11	pseudo	pseudo	NOUN
ejpam-3431	301	12	hyper	hyper	ADJ
ejpam-3431	301	13	gr	gr	NOUN
ejpam-3431	301	14	-	-	PUNCT
ejpam-3431	301	15	ideals	ideal	NOUN
ejpam-3431	301	16	of	of	ADP
ejpam-3431	301	17	type	type	NOUN
ejpam-3431	301	18	i	i	PRON
ejpam-3431	301	19	,	,	PUNCT
ejpam-3431	301	20	1	1	NUM
ejpam-3431	301	21	≤	≤	NUM
ejpam-3431	301	22	i	i	PRON
ejpam-3431	301	23	≤	≤	NOUN
ejpam-3431	301	24	12	12	NUM
ejpam-3431	301	25	,	,	PUNCT
ejpam-3431	301	26	in	in	ADP
ejpam-3431	301	27	h.	h.	PROPN
ejpam-3431	301	28	then	then	ADV
ejpam-3431	301	29	⋂	⋂	PROPN
ejpam-3431	301	30	ω∈ω	ω∈ω	X
ejpam-3431	301	31	iω	iω	NOUN
ejpam-3431	301	32	is	be	AUX
ejpam-3431	301	33	also	also	ADV
ejpam-3431	301	34	a	a	DET
ejpam-3431	301	35	pseudo	pseudo	NOUN
ejpam-3431	301	36	hyper	hyper	ADJ
ejpam-3431	301	37	gr	gr	NOUN
ejpam-3431	301	38	-	-	PUNCT
ejpam-3431	301	39	ideal	ideal	NOUN
ejpam-3431	301	40	of	of	ADP
ejpam-3431	301	41	type	type	NOUN
ejpam-3431	301	42	i	i	PRON
ejpam-3431	301	43	,	,	PUNCT
ejpam-3431	301	44	1	1	NUM
ejpam-3431	301	45	≤	≤	NUM
ejpam-3431	301	46	i	i	PRON
ejpam-3431	301	47	≤	≤	ADV
ejpam-3431	301	48	12	12	NUM
ejpam-3431	301	49	in	in	ADP
ejpam-3431	301	50	h.	h.	PROPN
ejpam-3431	301	51	proof	proof	NOUN
ejpam-3431	301	52	.	.	PUNCT
ejpam-3431	302	1	assume	assume	VERB
ejpam-3431	302	2	that	that	SCONJ
ejpam-3431	302	3	i	i	PRON
ejpam-3431	302	4	=	=	SYM
ejpam-3431	302	5	⋂	⋂	PROPN
ejpam-3431	302	6	ω∈ω	ω∈ω	X
ejpam-3431	302	7	iω	iω	PROPN
ejpam-3431	302	8	.	.	PUNCT
ejpam-3431	303	1	let	let	VERB
ejpam-3431	303	2	iω	iω	PRON
ejpam-3431	303	3	be	be	AUX
ejpam-3431	303	4	a	a	DET
ejpam-3431	303	5	pseudo	pseudo	NOUN
ejpam-3431	303	6	hyper	hyper	ADJ
ejpam-3431	303	7	gr	gr	NOUN
ejpam-3431	303	8	-	-	PUNCT
ejpam-3431	303	9	ideal	ideal	NOUN
ejpam-3431	303	10	of	of	ADP
ejpam-3431	303	11	specific	specific	ADJ
ejpam-3431	303	12	type	type	NOUN
ejpam-3431	303	13	,	,	PUNCT
ejpam-3431	303	14	say	say	VERB
ejpam-3431	303	15	type	type	NOUN
ejpam-3431	303	16	1	1	NUM
ejpam-3431	303	17	,	,	PUNCT
ejpam-3431	303	18	for	for	ADP
ejpam-3431	303	19	any	any	DET
ejpam-3431	303	20	ω	ω	PROPN
ejpam-3431	303	21	∈	∈	PROPN
ejpam-3431	303	22	ω	ω	NOUN
ejpam-3431	303	23	.	.	PUNCT
ejpam-3431	304	1	we	we	PRON
ejpam-3431	304	2	will	will	AUX
ejpam-3431	304	3	prove	prove	VERB
ejpam-3431	304	4	that	that	SCONJ
ejpam-3431	304	5	i	i	PRON
ejpam-3431	304	6	is	be	AUX
ejpam-3431	304	7	a	a	DET
ejpam-3431	304	8	pseudo	pseudo	NOUN
ejpam-3431	304	9	hyper	hyper	ADJ
ejpam-3431	304	10	gr	gr	NOUN
ejpam-3431	304	11	-	-	PUNCT
ejpam-3431	304	12	ideal	ideal	NOUN
ejpam-3431	304	13	of	of	ADP
ejpam-3431	304	14	type	type	NOUN
ejpam-3431	304	15	1	1	NUM
ejpam-3431	304	16	.	.	PUNCT
ejpam-3431	305	1	since	since	SCONJ
ejpam-3431	305	2	every	every	DET
ejpam-3431	305	3	iω	iω	NOUN
ejpam-3431	305	4	is	be	AUX
ejpam-3431	305	5	a	a	DET
ejpam-3431	305	6	pseudo	pseudo	NOUN
ejpam-3431	305	7	hyper	hyper	ADJ
ejpam-3431	305	8	gr	gr	NOUN
ejpam-3431	305	9	-	-	PUNCT
ejpam-3431	305	10	ideal	ideal	NOUN
ejpam-3431	305	11	for	for	ADP
ejpam-3431	305	12	each	each	DET
ejpam-3431	305	13	ω	ω	NOUN
ejpam-3431	305	14	,	,	PUNCT
ejpam-3431	305	15	0	0	NUM
ejpam-3431	305	16	∈	∈	PROPN
ejpam-3431	305	17	iω	iω	NOUN
ejpam-3431	305	18	,	,	PUNCT
ejpam-3431	305	19	for	for	ADP
ejpam-3431	305	20	all	all	DET
ejpam-3431	305	21	ω	ω	NUM
ejpam-3431	305	22	∈	∈	PROPN
ejpam-3431	305	23	ω	ω	NOUN
ejpam-3431	305	24	and	and	CCONJ
ejpam-3431	305	25	thus	thus	ADV
ejpam-3431	305	26	,	,	PUNCT
ejpam-3431	305	27	0	0	NUM
ejpam-3431	305	28	∈	∈	PROPN
ejpam-3431	305	29	⋂	⋂	PROPN
ejpam-3431	305	30	ω∈ω	ω∈ω	X
ejpam-3431	305	31	iω	iω	PROPN
ejpam-3431	305	32	=	=	PUNCT
ejpam-3431	305	33	i.	i.	NOUN
ejpam-3431	305	34	let	let	VERB
ejpam-3431	305	35	y	y	PROPN
ejpam-3431	305	36	∈	∈	PROPN
ejpam-3431	306	1	i	i	PRON
ejpam-3431	306	2	,	,	PUNCT
ejpam-3431	306	3	x	x	PROPN
ejpam-3431	306	4	∈	∈	PROPN
ejpam-3431	306	5	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	306	6	and	and	CCONJ
ejpam-3431	306	7	z	z	NOUN
ejpam-3431	306	8	∈	∈	PROPN
ejpam-3431	306	9	i⊆	i⊆	PROPN
ejpam-3431	306	10	◦	◦	NOUN
ejpam-3431	306	11	,y	,y	PUNCT
ejpam-3431	306	12	.	.	PUNCT
ejpam-3431	307	1	then	then	ADV
ejpam-3431	307	2	x	x	X
ejpam-3431	307	3	~	~	PUNCT
ejpam-3431	307	4	y	y	PROPN
ejpam-3431	307	5	⊆	⊆	NUM
ejpam-3431	307	6	i	i	PROPN
ejpam-3431	307	7	and	and	CCONJ
ejpam-3431	307	8	z	z	NOUN
ejpam-3431	307	9	◦	◦	NOUN
ejpam-3431	307	10	y	y	PROPN
ejpam-3431	307	11	⊆	⊆	NUM
ejpam-3431	307	12	i.	i.	NOUN
ejpam-3431	307	13	this	this	PRON
ejpam-3431	307	14	means	mean	VERB
ejpam-3431	307	15	that	that	SCONJ
ejpam-3431	307	16	for	for	SCONJ
ejpam-3431	307	17	any	any	DET
ejpam-3431	307	18	u	u	NOUN
ejpam-3431	307	19	∈	∈	PROPN
ejpam-3431	307	20	x	x	PUNCT
ejpam-3431	307	21	~	~	PUNCT
ejpam-3431	307	22	y	y	X
ejpam-3431	307	23	,	,	PUNCT
ejpam-3431	307	24	u	u	PROPN
ejpam-3431	307	25	∈	∈	PROPN
ejpam-3431	307	26	i.	i.	NOUN
ejpam-3431	307	27	thus	thus	ADV
ejpam-3431	307	28	,	,	PUNCT
ejpam-3431	307	29	u	u	PROPN
ejpam-3431	307	30	∈	∈	PROPN
ejpam-3431	307	31	iω	iω	X
ejpam-3431	307	32	for	for	ADP
ejpam-3431	307	33	any	any	DET
ejpam-3431	307	34	ω	ω	PROPN
ejpam-3431	307	35	∈	∈	PROPN
ejpam-3431	307	36	ω	ω	NOUN
ejpam-3431	307	37	and	and	CCONJ
ejpam-3431	307	38	so	so	ADV
ejpam-3431	307	39	,	,	PUNCT
ejpam-3431	307	40	x	x	X
ejpam-3431	307	41	~	~	PUNCT
ejpam-3431	307	42	y	y	PROPN
ejpam-3431	307	43	⊆	⊆	NUM
ejpam-3431	307	44	iω	iω	NOUN
ejpam-3431	307	45	.	.	PUNCT
ejpam-3431	308	1	hence	hence	ADV
ejpam-3431	308	2	,	,	PUNCT
ejpam-3431	308	3	x	x	PUNCT
ejpam-3431	308	4	∈	∈	PROPN
ejpam-3431	308	5	i⊆ω,~,y	i⊆ω,~,y	PROPN
ejpam-3431	308	6	and	and	CCONJ
ejpam-3431	308	7	y	y	PROPN
ejpam-3431	308	8	∈	∈	PROPN
ejpam-3431	309	1	iω	iω	VERB
ejpam-3431	309	2	,	,	PUNCT
ejpam-3431	309	3	for	for	ADP
ejpam-3431	309	4	any	any	DET
ejpam-3431	309	5	ω	ω	PROPN
ejpam-3431	309	6	∈	∈	PROPN
ejpam-3431	309	7	ω	ω	PROPN
ejpam-3431	309	8	.	.	PUNCT
ejpam-3431	310	1	since	since	SCONJ
ejpam-3431	310	2	iω	iω	PRON
ejpam-3431	310	3	is	be	AUX
ejpam-3431	310	4	a	a	DET
ejpam-3431	310	5	pseudo	pseudo	NOUN
ejpam-3431	310	6	hyper	hyper	ADJ
ejpam-3431	310	7	gr	gr	NOUN
ejpam-3431	310	8	-	-	PUNCT
ejpam-3431	310	9	ideal	ideal	NOUN
ejpam-3431	310	10	of	of	ADP
ejpam-3431	310	11	type	type	NOUN
ejpam-3431	310	12	1	1	NUM
ejpam-3431	310	13	,	,	PUNCT
ejpam-3431	310	14	i⊆ω,~,y	i⊆ω,~,y	VERB
ejpam-3431	310	15	⊆	⊆	NUM
ejpam-3431	310	16	iω	iω	NOUN
ejpam-3431	310	17	so	so	SCONJ
ejpam-3431	310	18	that	that	SCONJ
ejpam-3431	310	19	x	x	X
ejpam-3431	310	20	∈	∈	NOUN
ejpam-3431	310	21	iω	iω	X
ejpam-3431	310	22	for	for	ADP
ejpam-3431	310	23	any	any	DET
ejpam-3431	310	24	ω	ω	PROPN
ejpam-3431	310	25	∈	∈	PROPN
ejpam-3431	310	26	ω	ω	PROPN
ejpam-3431	310	27	.	.	PUNCT
ejpam-3431	311	1	hence	hence	ADV
ejpam-3431	311	2	,	,	PUNCT
ejpam-3431	311	3	x	x	PUNCT
ejpam-3431	311	4	∈	∈	PROPN
ejpam-3431	311	5	i	i	PRON
ejpam-3431	311	6	and	and	CCONJ
ejpam-3431	311	7	thus	thus	ADV
ejpam-3431	311	8	,	,	PUNCT
ejpam-3431	311	9	i⊆~,y	i⊆~,y	PROPN
ejpam-3431	311	10	⊆	⊆	NUM
ejpam-3431	311	11	i.	i.	NOUN
ejpam-3431	311	12	in	in	ADP
ejpam-3431	311	13	a	a	DET
ejpam-3431	311	14	similar	similar	ADJ
ejpam-3431	311	15	manner	manner	NOUN
ejpam-3431	311	16	,	,	PUNCT
ejpam-3431	311	17	we	we	PRON
ejpam-3431	311	18	can	can	AUX
ejpam-3431	311	19	also	also	ADV
ejpam-3431	311	20	prove	prove	VERB
ejpam-3431	311	21	that	that	SCONJ
ejpam-3431	311	22	z	z	NOUN
ejpam-3431	311	23	∈	∈	PROPN
ejpam-3431	312	1	i	i	PRON
ejpam-3431	312	2	so	so	SCONJ
ejpam-3431	312	3	that	that	SCONJ
ejpam-3431	312	4	i⊆	i⊆	NOUN
ejpam-3431	312	5	◦	◦	NOUN
ejpam-3431	312	6	,y	,y	PUNCT
ejpam-3431	312	7	⊆	⊆	NUM
ejpam-3431	312	8	i.	i.	NOUN
ejpam-3431	312	9	the	the	DET
ejpam-3431	312	10	proof	proof	NOUN
ejpam-3431	312	11	for	for	ADP
ejpam-3431	312	12	the	the	DET
ejpam-3431	312	13	remaining	remain	VERB
ejpam-3431	312	14	cases	case	NOUN
ejpam-3431	312	15	(	(	PUNCT
ejpam-3431	312	16	i	i	NOUN
ejpam-3431	312	17	=	=	NOUN
ejpam-3431	312	18	2	2	NUM
ejpam-3431	312	19	,	,	PUNCT
ejpam-3431	312	20	3	3	NUM
ejpam-3431	312	21	,	,	PUNCT
ejpam-3431	312	22	.	.	PUNCT
ejpam-3431	312	23	.	.	PUNCT
ejpam-3431	312	24	.	.	PUNCT
ejpam-3431	313	1	,	,	PUNCT
ejpam-3431	313	2	12	12	NUM
ejpam-3431	313	3	)	)	PUNCT
ejpam-3431	313	4	follows	follow	VERB
ejpam-3431	313	5	the	the	DET
ejpam-3431	313	6	same	same	ADJ
ejpam-3431	313	7	argument	argument	NOUN
ejpam-3431	313	8	with	with	ADP
ejpam-3431	313	9	some	some	DET
ejpam-3431	313	10	modifications	modification	NOUN
ejpam-3431	313	11	.	.	PUNCT
ejpam-3431	314	1	�	�	PROPN
ejpam-3431	314	2	theorem	theorem	VERB
ejpam-3431	314	3	3.28	3.28	NUM
ejpam-3431	314	4	.	.	PUNCT
ejpam-3431	315	1	let	let	AUX
ejpam-3431	315	2	d	d	PRON
ejpam-3431	315	3	be	be	AUX
ejpam-3431	315	4	a	a	DET
ejpam-3431	315	5	nonempty	nonempty	ADJ
ejpam-3431	315	6	subset	subset	NOUN
ejpam-3431	315	7	of	of	ADP
ejpam-3431	315	8	h.	h.	PROPN
ejpam-3431	315	9	let	let	VERB
ejpam-3431	315	10	[	[	PUNCT
ejpam-3431	315	11	d]i	d]i	X
ejpam-3431	315	12	denote	denote	VERB
ejpam-3431	315	13	the	the	DET
ejpam-3431	315	14	intersection	intersection	NOUN
ejpam-3431	315	15	of	of	ADP
ejpam-3431	315	16	all	all	DET
ejpam-3431	315	17	pseudo	pseudo	NOUN
ejpam-3431	315	18	hyper	hyper	ADJ
ejpam-3431	315	19	gr	gr	NOUN
ejpam-3431	315	20	-	-	PUNCT
ejpam-3431	315	21	ideals	ideal	NOUN
ejpam-3431	315	22	of	of	ADP
ejpam-3431	315	23	type	type	NOUN
ejpam-3431	315	24	i	i	PRON
ejpam-3431	315	25	,	,	PUNCT
ejpam-3431	315	26	1	1	NUM
ejpam-3431	315	27	≤	≤	NUM
ejpam-3431	315	28	i	i	PRON
ejpam-3431	315	29	≤	≤	NOUN
ejpam-3431	315	30	4	4	NUM
ejpam-3431	315	31	containing	contain	VERB
ejpam-3431	315	32	d.	d.	NOUN
ejpam-3431	315	33	then	then	ADV
ejpam-3431	315	34	{	{	PUNCT
ejpam-3431	315	35	x	x	PROPN
ejpam-3431	315	36	∈	∈	NOUN
ejpam-3431	315	37	h|(	h|(	PRON
ejpam-3431	315	38	...	...	PUNCT
ejpam-3431	316	1	((x~	((x~	PROPN
ejpam-3431	316	2	d1)~	d1)~	PROPN
ejpam-3431	316	3	d2)~	d2)~	NOUN
ejpam-3431	316	4	...	...	PUNCT
ejpam-3431	316	5	)	)	PUNCT
ejpam-3431	317	1	~	~	PUNCT
ejpam-3431	317	2	dn	dn	X
ejpam-3431	317	3	=	=	PUNCT
ejpam-3431	317	4	{	{	PUNCT
ejpam-3431	317	5	0	0	NUM
ejpam-3431	317	6	}	}	PUNCT
ejpam-3431	317	7	,	,	PUNCT
ejpam-3431	317	8	di	di	X
ejpam-3431	317	9	∈	∈	PROPN
ejpam-3431	317	10	d	d	NOUN
ejpam-3431	317	11	}	}	PUNCT
ejpam-3431	317	12	⊆	⊆	NUM
ejpam-3431	317	13	[	[	X
ejpam-3431	317	14	d]i	d]i	NOUN
ejpam-3431	317	15	.	.	PUNCT
ejpam-3431	318	1	references	reference	NOUN
ejpam-3431	318	2	832	832	NUM
ejpam-3431	318	3	proof	proof	NOUN
ejpam-3431	318	4	.	.	PUNCT
ejpam-3431	319	1	we	we	PRON
ejpam-3431	319	2	will	will	AUX
ejpam-3431	319	3	prove	prove	VERB
ejpam-3431	319	4	only	only	ADV
ejpam-3431	319	5	the	the	DET
ejpam-3431	319	6	case	case	NOUN
ejpam-3431	319	7	for	for	ADP
ejpam-3431	319	8	i	i	PRON
ejpam-3431	319	9	=	=	NOUN
ejpam-3431	319	10	1	1	NUM
ejpam-3431	319	11	,	,	PUNCT
ejpam-3431	319	12	that	that	PRON
ejpam-3431	319	13	is	be	AUX
ejpam-3431	319	14	for	for	ADP
ejpam-3431	319	15	the	the	DET
ejpam-3431	319	16	case	case	NOUN
ejpam-3431	319	17	of	of	ADP
ejpam-3431	319	18	pseudo	pseudo	NOUN
ejpam-3431	319	19	hyper	hyper	ADJ
ejpam-3431	319	20	gr	gr	NOUN
ejpam-3431	319	21	-	-	PUNCT
ejpam-3431	319	22	ideals	ideal	NOUN
ejpam-3431	319	23	of	of	ADP
ejpam-3431	319	24	type	type	NOUN
ejpam-3431	319	25	1	1	NUM
ejpam-3431	319	26	.	.	PUNCT
ejpam-3431	320	1	let	let	VERB
ejpam-3431	320	2	x	x	SYM
ejpam-3431	320	3	∈	∈	PROPN
ejpam-3431	320	4	h	h	NOUN
ejpam-3431	320	5	and	and	CCONJ
ejpam-3431	320	6	suppose	suppose	VERB
ejpam-3431	320	7	that	that	SCONJ
ejpam-3431	320	8	the	the	DET
ejpam-3431	320	9	condition	condition	NOUN
ejpam-3431	320	10	(	(	PUNCT
ejpam-3431	320	11	...	...	PUNCT
ejpam-3431	320	12	(	(	PUNCT
ejpam-3431	320	13	(	(	PUNCT
ejpam-3431	320	14	x~	x~	PROPN
ejpam-3431	320	15	d1)~	d1)~	PROPN
ejpam-3431	320	16	d2)~	d2)~	NOUN
ejpam-3431	320	17	...	...	PUNCT
ejpam-3431	320	18	)	)	PUNCT
ejpam-3431	321	1	~	~	PUNCT
ejpam-3431	321	2	dn	dn	X
ejpam-3431	321	3	=	=	PUNCT
ejpam-3431	321	4	{	{	PUNCT
ejpam-3431	321	5	0	0	NUM
ejpam-3431	321	6	}	}	PUNCT
ejpam-3431	321	7	is	be	AUX
ejpam-3431	321	8	satisfied	satisfied	ADJ
ejpam-3431	321	9	for	for	ADP
ejpam-3431	321	10	some	some	DET
ejpam-3431	321	11	d1	d1	NOUN
ejpam-3431	321	12	,	,	PUNCT
ejpam-3431	321	13	d2	d2	PROPN
ejpam-3431	321	14	,	,	PUNCT
ejpam-3431	321	15	...	...	PUNCT
ejpam-3431	321	16	,	,	PUNCT
ejpam-3431	321	17	dn	dn	PROPN
ejpam-3431	321	18	∈	∈	PROPN
ejpam-3431	321	19	d.	d.	PROPN
ejpam-3431	321	20	note	note	VERB
ejpam-3431	321	21	that	that	SCONJ
ejpam-3431	321	22	0	0	NUM
ejpam-3431	321	23	∈	∈	PROPN
ejpam-3431	321	24	[	[	X
ejpam-3431	321	25	d]1	d]1	NOUN
ejpam-3431	321	26	,	,	PUNCT
ejpam-3431	321	27	hence	hence	ADV
ejpam-3431	321	28	(	(	PUNCT
ejpam-3431	321	29	...	...	PUNCT
ejpam-3431	321	30	(	(	PUNCT
ejpam-3431	321	31	(	(	PUNCT
ejpam-3431	321	32	x~	x~	PROPN
ejpam-3431	321	33	d1)~	d1)~	PROPN
ejpam-3431	321	34	d2)~	d2)~	NOUN
ejpam-3431	321	35	...	...	PUNCT
ejpam-3431	321	36	)	)	PUNCT
ejpam-3431	322	1	~	~	PUNCT
ejpam-3431	322	2	dn	dn	X
ejpam-3431	322	3	=	=	PUNCT
ejpam-3431	322	4	{	{	PUNCT
ejpam-3431	322	5	0	0	NUM
ejpam-3431	322	6	}	}	PUNCT
ejpam-3431	322	7	⊆	⊆	NUM
ejpam-3431	322	8	[	[	X
ejpam-3431	322	9	d]1	d]1	NOUN
ejpam-3431	322	10	thus	thus	ADV
ejpam-3431	322	11	,	,	PUNCT
ejpam-3431	322	12	for	for	SCONJ
ejpam-3431	322	13	each	each	DET
ejpam-3431	322	14	d	d	PROPN
ejpam-3431	322	15	∈	∈	PROPN
ejpam-3431	322	16	(	(	PUNCT
ejpam-3431	322	17	...	...	PUNCT
ejpam-3431	322	18	(	(	PUNCT
ejpam-3431	322	19	(	(	PUNCT
ejpam-3431	322	20	x~	x~	PROPN
ejpam-3431	322	21	d1)~	d1)~	PROPN
ejpam-3431	322	22	d2)~	d2)~	NOUN
ejpam-3431	322	23	...	...	PUNCT
ejpam-3431	322	24	)	)	PUNCT
ejpam-3431	323	1	~	~	PUNCT
ejpam-3431	323	2	dn−1	dn−1	NOUN
ejpam-3431	323	3	,	,	PUNCT
ejpam-3431	323	4	we	we	PRON
ejpam-3431	323	5	have	have	VERB
ejpam-3431	323	6	d~	d~	NUM
ejpam-3431	323	7	dn	dn	PROPN
ejpam-3431	323	8	⊆	⊆	NUM
ejpam-3431	323	9	[	[	X
ejpam-3431	323	10	d]1	d]1	PROPN
ejpam-3431	323	11	,	,	PUNCT
ejpam-3431	323	12	or	or	CCONJ
ejpam-3431	323	13	equivalently	equivalently	ADV
ejpam-3431	323	14	,	,	PUNCT
ejpam-3431	323	15	d	d	PROPN
ejpam-3431	323	16	∈	∈	PROPN
ejpam-3431	323	17	(	(	PUNCT
ejpam-3431	323	18	[	[	X
ejpam-3431	323	19	d]1)⊆~,dn	d]1)⊆~,dn	X
ejpam-3431	323	20	.	.	PUNCT
ejpam-3431	324	1	since	since	SCONJ
ejpam-3431	324	2	[	[	X
ejpam-3431	324	3	d]1	d]1	PROPN
ejpam-3431	324	4	is	be	AUX
ejpam-3431	324	5	a	a	DET
ejpam-3431	324	6	pseudo	pseudo	NOUN
ejpam-3431	324	7	hyper	hyper	ADJ
ejpam-3431	324	8	gr	gr	NOUN
ejpam-3431	324	9	-	-	PUNCT
ejpam-3431	324	10	ideal	ideal	NOUN
ejpam-3431	324	11	of	of	ADP
ejpam-3431	324	12	type	type	NOUN
ejpam-3431	324	13	1	1	NUM
ejpam-3431	324	14	,	,	PUNCT
ejpam-3431	324	15	(	(	PUNCT
ejpam-3431	324	16	[	[	X
ejpam-3431	324	17	d]1)⊆~,dn	d]1)⊆~,dn	VERB
ejpam-3431	324	18	⊆	⊆	NUM
ejpam-3431	324	19	[	[	X
ejpam-3431	324	20	d]1	d]1	PROPN
ejpam-3431	324	21	,	,	PUNCT
ejpam-3431	324	22	and	and	CCONJ
ejpam-3431	324	23	so	so	ADV
ejpam-3431	324	24	,	,	PUNCT
ejpam-3431	324	25	d	d	PROPN
ejpam-3431	324	26	∈	∈	PROPN
ejpam-3431	325	1	[	[	X
ejpam-3431	325	2	d]1	d]1	PROPN
ejpam-3431	325	3	.	.	PUNCT
ejpam-3431	326	1	thus	thus	ADV
ejpam-3431	326	2	,	,	PUNCT
ejpam-3431	326	3	(	(	PUNCT
ejpam-3431	326	4	...	...	PUNCT
ejpam-3431	326	5	(	(	PUNCT
ejpam-3431	326	6	(	(	PUNCT
ejpam-3431	326	7	x~	x~	PROPN
ejpam-3431	326	8	d1)~	d1)~	PROPN
ejpam-3431	326	9	d2)~	d2)~	NOUN
ejpam-3431	326	10	...	...	PUNCT
ejpam-3431	326	11	)	)	PUNCT
ejpam-3431	327	1	~	~	PUNCT
ejpam-3431	327	2	dn−1	dn−1	NOUN
ejpam-3431	327	3	⊆	⊆	NUM
ejpam-3431	327	4	[	[	X
ejpam-3431	327	5	d]1	d]1	NOUN
ejpam-3431	327	6	continuing	continue	VERB
ejpam-3431	327	7	this	this	DET
ejpam-3431	327	8	process	process	NOUN
ejpam-3431	327	9	,	,	PUNCT
ejpam-3431	327	10	we	we	PRON
ejpam-3431	327	11	obtain	obtain	VERB
ejpam-3431	327	12	{	{	PUNCT
ejpam-3431	327	13	x	x	NOUN
ejpam-3431	327	14	}	}	PUNCT
ejpam-3431	327	15	∈	∈	PROPN
ejpam-3431	328	1	[	[	X
ejpam-3431	328	2	d]1	d]1	NOUN
ejpam-3431	328	3	and	and	CCONJ
ejpam-3431	328	4	so	so	ADV
ejpam-3431	328	5	,	,	PUNCT
ejpam-3431	328	6	x	x	SYM
ejpam-3431	328	7	∈	∈	NOUN
ejpam-3431	328	8	[	[	X
ejpam-3431	328	9	d]1	d]1	PROPN
ejpam-3431	328	10	.	.	PUNCT
ejpam-3431	329	1	therefore	therefore	ADV
ejpam-3431	329	2	,	,	PUNCT
ejpam-3431	329	3	{	{	PUNCT
ejpam-3431	329	4	x	x	SYM
ejpam-3431	329	5	∈	∈	NOUN
ejpam-3431	329	6	h|(	h|(	PRON
ejpam-3431	329	7	...	...	PUNCT
ejpam-3431	330	1	((x~	((x~	PROPN
ejpam-3431	330	2	d1)~	d1)~	PROPN
ejpam-3431	330	3	d2)~	d2)~	NOUN
ejpam-3431	330	4	...	...	PUNCT
ejpam-3431	330	5	)	)	PUNCT
ejpam-3431	331	1	~	~	PUNCT
ejpam-3431	331	2	dn	dn	X
ejpam-3431	331	3	=	=	PUNCT
ejpam-3431	331	4	{	{	PUNCT
ejpam-3431	331	5	0	0	NUM
ejpam-3431	331	6	}	}	PUNCT
ejpam-3431	331	7	,	,	PUNCT
ejpam-3431	331	8	di	di	X
ejpam-3431	331	9	∈	∈	PROPN
ejpam-3431	331	10	d	d	NOUN
ejpam-3431	331	11	}	}	PUNCT
ejpam-3431	331	12	⊆	⊆	NUM
ejpam-3431	331	13	[	[	X
ejpam-3431	331	14	d]1	d]1	PROPN
ejpam-3431	331	15	.	.	PUNCT
ejpam-3431	332	1	�	�	PROPN
ejpam-3431	332	2	the	the	DET
ejpam-3431	332	3	ideal	ideal	NOUN
ejpam-3431	333	1	[	[	X
ejpam-3431	333	2	d]i	d]i	X
ejpam-3431	333	3	in	in	ADP
ejpam-3431	333	4	theorem	theorem	ADJ
ejpam-3431	333	5	3.28	3.28	NUM
ejpam-3431	333	6	is	be	AUX
ejpam-3431	333	7	called	call	VERB
ejpam-3431	333	8	the	the	DET
ejpam-3431	333	9	pseudo	pseudo	NOUN
ejpam-3431	333	10	hyper	hyper	ADJ
ejpam-3431	333	11	gr	gr	ADJ
ejpam-3431	333	12	-	-	PUNCT
ejpam-3431	333	13	ideal	ideal	NOUN
ejpam-3431	333	14	generated	generate	VERB
ejpam-3431	333	15	by	by	ADP
ejpam-3431	333	16	d.	d.	PROPN
ejpam-3431	333	17	acknowledgements	acknowledgement	NOUN
ejpam-3431	333	18	the	the	DET
ejpam-3431	333	19	first	first	ADJ
ejpam-3431	333	20	author	author	NOUN
ejpam-3431	333	21	would	would	AUX
ejpam-3431	333	22	like	like	VERB
ejpam-3431	333	23	to	to	PART
ejpam-3431	333	24	thank	thank	VERB
ejpam-3431	333	25	the	the	DET
ejpam-3431	333	26	philippine	philippine	ADJ
ejpam-3431	333	27	department	department	PROPN
ejpam-3431	333	28	of	of	ADP
ejpam-3431	333	29	science	science	NOUN
ejpam-3431	333	30	and	and	CCONJ
ejpam-3431	333	31	technologyaccelerated	technologyaccelerated	ADJ
ejpam-3431	333	32	science	science	NOUN
ejpam-3431	333	33	and	and	CCONJ
ejpam-3431	333	34	technology	technology	NOUN
ejpam-3431	333	35	human	human	ADJ
ejpam-3431	333	36	resource	resource	NOUN
ejpam-3431	333	37	development	development	NOUN
ejpam-3431	333	38	program	program	NOUN
ejpam-3431	333	39	(	(	PUNCT
ejpam-3431	333	40	dostasthrdp	dostasthrdp	PROPN
ejpam-3431	333	41	)	)	PUNCT
ejpam-3431	333	42	for	for	ADP
ejpam-3431	333	43	the	the	DET
ejpam-3431	333	44	financial	financial	ADJ
ejpam-3431	333	45	support	support	NOUN
ejpam-3431	333	46	for	for	ADP
ejpam-3431	333	47	this	this	DET
ejpam-3431	333	48	publication	publication	NOUN
ejpam-3431	333	49	and	and	CCONJ
ejpam-3431	333	50	for	for	ADP
ejpam-3431	333	51	the	the	DET
ejpam-3431	333	52	three	three	NUM
ejpam-3431	333	53	-	-	PUNCT
ejpam-3431	333	54	year	year	NOUN
ejpam-3431	333	55	phd	phd	NOUN
ejpam-3431	333	56	scholarship	scholarship	NOUN
ejpam-3431	333	57	grant	grant	NOUN
ejpam-3431	333	58	in	in	ADP
ejpam-3431	333	59	mindanao	mindanao	PROPN
ejpam-3431	333	60	state	state	PROPN
ejpam-3431	333	61	university	university	PROPN
ejpam-3431	333	62	-	-	PUNCT
ejpam-3431	333	63	iligan	iligan	PROPN
ejpam-3431	333	64	institute	institute	PROPN
ejpam-3431	333	65	of	of	ADP
ejpam-3431	333	66	technology	technology	PROPN
ejpam-3431	333	67	.	.	PUNCT
ejpam-3431	334	1	lastly	lastly	ADV
ejpam-3431	334	2	,	,	PUNCT
ejpam-3431	334	3	the	the	DET
ejpam-3431	334	4	authors	author	NOUN
ejpam-3431	334	5	would	would	AUX
ejpam-3431	334	6	like	like	VERB
ejpam-3431	334	7	to	to	PART
ejpam-3431	334	8	thank	thank	VERB
ejpam-3431	334	9	the	the	DET
ejpam-3431	334	10	referees	referee	NOUN
ejpam-3431	334	11	who	who	PRON
ejpam-3431	334	12	gave	give	VERB
ejpam-3431	334	13	their	their	PRON
ejpam-3431	334	14	brilliant	brilliant	ADJ
ejpam-3431	334	15	suggestions	suggestion	NOUN
ejpam-3431	334	16	in	in	ADP
ejpam-3431	334	17	refining	refine	VERB
ejpam-3431	334	18	this	this	DET
ejpam-3431	334	19	paper	paper	NOUN
ejpam-3431	334	20	before	before	ADP
ejpam-3431	334	21	publication	publication	NOUN
ejpam-3431	334	22	to	to	ADP
ejpam-3431	334	23	the	the	DET
ejpam-3431	334	24	european	european	PROPN
ejpam-3431	334	25	journal	journal	PROPN
ejpam-3431	334	26	of	of	ADP
ejpam-3431	334	27	pure	pure	ADJ
ejpam-3431	334	28	and	and	CCONJ
ejpam-3431	334	29	applied	applied	ADJ
ejpam-3431	334	30	mathematics	mathematic	NOUN
ejpam-3431	334	31	.	.	PUNCT
ejpam-3431	335	1	references	reference	NOUN
ejpam-3431	335	2	[	[	X
ejpam-3431	335	3	1	1	NUM
ejpam-3431	335	4	]	]	PUNCT
ejpam-3431	335	5	a.	a.	NOUN
ejpam-3431	335	6	borzooei	borzooei	PROPN
ejpam-3431	335	7	,	,	PUNCT
ejpam-3431	335	8	a.	a.	NOUN
ejpam-3431	335	9	rezazadeh	rezazadeh	PROPN
ejpam-3431	335	10	,	,	PUNCT
ejpam-3431	335	11	and	and	CCONJ
ejpam-3431	335	12	r.	r.	PROPN
ejpam-3431	335	13	ameri	ameri	PROPN
ejpam-3431	335	14	.	.	PUNCT
ejpam-3431	336	1	on	on	ADP
ejpam-3431	336	2	hyper	hyper	ADJ
ejpam-3431	336	3	pseudo	pseudo	NOUN
ejpam-3431	336	4	bck	bck	NOUN
ejpam-3431	336	5	-	-	PUNCT
ejpam-3431	336	6	algebras	algebras	PROPN
ejpam-3431	336	7	.	.	PUNCT
ejpam-3431	337	1	iranian	iranian	PROPN
ejpam-3431	337	2	journal	journal	PROPN
ejpam-3431	337	3	of	of	ADP
ejpam-3431	337	4	mathematical	mathematical	ADJ
ejpam-3431	337	5	sciences	sciences	PROPN
ejpam-3431	337	6	and	and	CCONJ
ejpam-3431	337	7	informatics	informatic	NOUN
ejpam-3431	337	8	,	,	PUNCT
ejpam-3431	337	9	9(1):13–29	9(1):13–29	NUM
ejpam-3431	337	10	,	,	PUNCT
ejpam-3431	337	11	2014	2014	NUM
ejpam-3431	337	12	.	.	PUNCT
ejpam-3431	338	1	[	[	X
ejpam-3431	338	2	2	2	X
ejpam-3431	338	3	]	]	PUNCT
ejpam-3431	338	4	k.	k.	PROPN
ejpam-3431	338	5	hila	hila	PROPN
ejpam-3431	338	6	et	et	PROPN
ejpam-3431	338	7	.	.	PUNCT
ejpam-3431	339	1	al	al	PROPN
ejpam-3431	339	2	.	.	PUNCT
ejpam-3431	340	1	algebraic	algebraic	PROPN
ejpam-3431	340	2	hyperstructure	hyperstructure	NOUN
ejpam-3431	340	3	of	of	ADP
ejpam-3431	340	4	soft	soft	ADJ
ejpam-3431	340	5	sets	set	NOUN
ejpam-3431	340	6	associated	associate	VERB
ejpam-3431	340	7	with	with	ADP
ejpam-3431	340	8	ternary	ternary	ADJ
ejpam-3431	340	9	semihypergroups	semihypergroup	NOUN
ejpam-3431	340	10	.	.	PUNCT
ejpam-3431	341	1	italian	italian	ADJ
ejpam-3431	341	2	journal	journal	NOUN
ejpam-3431	341	3	of	of	ADP
ejpam-3431	341	4	pure	pure	ADJ
ejpam-3431	341	5	and	and	CCONJ
ejpam-3431	341	6	applied	applied	ADJ
ejpam-3431	341	7	mathematics	mathematic	NOUN
ejpam-3431	341	8	,	,	PUNCT
ejpam-3431	341	9	30:349–372	30:349–372	PROPN
ejpam-3431	341	10	,	,	PUNCT
ejpam-3431	341	11	2013	2013	NUM
ejpam-3431	341	12	.	.	PUNCT
ejpam-3431	342	1	[	[	X
ejpam-3431	342	2	3	3	X
ejpam-3431	342	3	]	]	X
ejpam-3431	342	4	g.	g.	PROPN
ejpam-3431	342	5	georgescu	georgescu	PROPN
ejpam-3431	342	6	and	and	CCONJ
ejpam-3431	342	7	iorgulescu	iorgulescu	NOUN
ejpam-3431	342	8	.	.	PUNCT
ejpam-3431	343	1	pseudo	pseudo	NOUN
ejpam-3431	343	2	bck	bck	NOUN
ejpam-3431	343	3	-	-	PUNCT
ejpam-3431	343	4	algebras	algebra	NOUN
ejpam-3431	343	5	:	:	PUNCT
ejpam-3431	343	6	an	an	DET
ejpam-3431	343	7	extension	extension	NOUN
ejpam-3431	343	8	of	of	ADP
ejpam-3431	343	9	bck	bck	NOUN
ejpam-3431	343	10	-	-	PUNCT
ejpam-3431	343	11	algebras	algebras	PROPN
ejpam-3431	343	12	.	.	PUNCT
ejpam-3431	344	1	in	in	ADP
ejpam-3431	344	2	springer	springer	NOUN
ejpam-3431	344	3	,	,	PUNCT
ejpam-3431	344	4	editor	editor	NOUN
ejpam-3431	344	5	,	,	PUNCT
ejpam-3431	344	6	combinatorics	combinatoric	NOUN
ejpam-3431	344	7	,	,	PUNCT
ejpam-3431	344	8	computability	computability	NOUN
ejpam-3431	344	9	and	and	CCONJ
ejpam-3431	344	10	logic	logic	NOUN
ejpam-3431	344	11	,	,	PUNCT
ejpam-3431	344	12	pages	page	NOUN
ejpam-3431	344	13	97–114	97–114	NUM
ejpam-3431	344	14	,	,	PUNCT
ejpam-3431	344	15	london	london	PROPN
ejpam-3431	344	16	,	,	PUNCT
ejpam-3431	344	17	2001	2001	NUM
ejpam-3431	344	18	.	.	PUNCT
ejpam-3431	345	1	proceedings	proceeding	NOUN
ejpam-3431	345	2	of	of	ADP
ejpam-3431	345	3	dmtsc	dmtsc	NOUN
ejpam-3431	345	4	01	01	NUM
ejpam-3431	345	5	.	.	PUNCT
ejpam-3431	346	1	[	[	X
ejpam-3431	346	2	4	4	X
ejpam-3431	346	3	]	]	X
ejpam-3431	346	4	y.	y.	PROPN
ejpam-3431	346	5	imai	imai	PROPN
ejpam-3431	346	6	and	and	CCONJ
ejpam-3431	346	7	k.	k.	PROPN
ejpam-3431	346	8	iseki	iseki	PROPN
ejpam-3431	346	9	.	.	PUNCT
ejpam-3431	347	1	on	on	ADP
ejpam-3431	347	2	axiom	axiom	NOUN
ejpam-3431	347	3	systems	system	NOUN
ejpam-3431	347	4	of	of	ADP
ejpam-3431	347	5	propositional	propositional	ADJ
ejpam-3431	347	6	calculi	calculi	PROPN
ejpam-3431	347	7	xiv	xiv	PROPN
ejpam-3431	347	8	.	.	PUNCT
ejpam-3431	348	1	pages	page	NOUN
ejpam-3431	348	2	19–22	19–22	NUM
ejpam-3431	348	3	,	,	PUNCT
ejpam-3431	348	4	japan	japan	PROPN
ejpam-3431	348	5	,	,	PUNCT
ejpam-3431	348	6	1966	1966	NUM
ejpam-3431	348	7	.	.	PUNCT
ejpam-3431	349	1	proceedings	proceeding	NOUN
ejpam-3431	349	2	of	of	ADP
ejpam-3431	349	3	japan	japan	PROPN
ejpam-3431	349	4	acedemy	acedemy	PROPN
ejpam-3431	349	5	.	.	PUNCT
ejpam-3431	350	1	[	[	X
ejpam-3431	350	2	5	5	NUM
ejpam-3431	350	3	]	]	X
ejpam-3431	350	4	r.	r.	NOUN
ejpam-3431	350	5	indangan	indangan	PROPN
ejpam-3431	350	6	and	and	CCONJ
ejpam-3431	350	7	g.	g.	PROPN
ejpam-3431	350	8	petalcorin	petalcorin	PROPN
ejpam-3431	350	9	.	.	PUNCT
ejpam-3431	351	1	some	some	DET
ejpam-3431	351	2	results	result	NOUN
ejpam-3431	351	3	on	on	ADP
ejpam-3431	351	4	hyper	hyper	ADJ
ejpam-3431	351	5	gr	gr	NOUN
ejpam-3431	351	6	-	-	PUNCT
ejpam-3431	351	7	ideals	ideal	NOUN
ejpam-3431	351	8	of	of	ADP
ejpam-3431	351	9	a	a	DET
ejpam-3431	351	10	hyper	hyper	ADJ
ejpam-3431	351	11	gralgebra	gralgebra	NOUN
ejpam-3431	351	12	.	.	PUNCT
ejpam-3431	352	1	journal	journal	NOUN
ejpam-3431	352	2	of	of	ADP
ejpam-3431	352	3	algebra	algebra	PROPN
ejpam-3431	352	4	and	and	CCONJ
ejpam-3431	352	5	applied	apply	VERB
ejpam-3431	352	6	mathematics	mathematic	NOUN
ejpam-3431	352	7	,	,	PUNCT
ejpam-3431	352	8	14:101–119	14:101–119	NUM
ejpam-3431	352	9	,	,	PUNCT
ejpam-3431	352	10	2016	2016	NUM
ejpam-3431	352	11	.	.	PUNCT
ejpam-3431	353	1	references	reference	NOUN
ejpam-3431	353	2	833	833	NUM
ejpam-3431	354	1	[	[	X
ejpam-3431	354	2	6	6	NUM
ejpam-3431	354	3	]	]	X
ejpam-3431	354	4	y.	y.	PROPN
ejpam-3431	354	5	jun	jun	PROPN
ejpam-3431	354	6	,	,	PUNCT
ejpam-3431	354	7	m.	m.	PROPN
ejpam-3431	354	8	zahedi	zahedi	PROPN
ejpam-3431	354	9	,	,	PUNCT
ejpam-3431	354	10	x.	x.	PROPN
ejpam-3431	354	11	xin	xin	PROPN
ejpam-3431	354	12	,	,	PUNCT
ejpam-3431	354	13	and	and	CCONJ
ejpam-3431	354	14	r.	r.	PROPN
ejpam-3431	354	15	borzooei	borzooei	PROPN
ejpam-3431	354	16	.	.	PUNCT
ejpam-3431	355	1	on	on	ADP
ejpam-3431	355	2	hyper	hyper	ADJ
ejpam-3431	355	3	bck	bck	NOUN
ejpam-3431	355	4	-	-	PUNCT
ejpam-3431	355	5	algebras	algebras	PROPN
ejpam-3431	355	6	.	.	PUNCT
ejpam-3431	356	1	journal	journal	PROPN
ejpam-3431	356	2	of	of	ADP
ejpam-3431	356	3	algebra	algebra	PROPN
ejpam-3431	356	4	and	and	CCONJ
ejpam-3431	356	5	applied	apply	VERB
ejpam-3431	356	6	mathematics	mathematic	NOUN
ejpam-3431	356	7	,	,	PUNCT
ejpam-3431	356	8	8:127–136	8:127–136	NUM
ejpam-3431	356	9	,	,	PUNCT
ejpam-3431	356	10	2000	2000	NUM
ejpam-3431	356	11	.	.	PUNCT
ejpam-3431	357	1	[	[	X
ejpam-3431	357	2	7	7	X
ejpam-3431	357	3	]	]	X
ejpam-3431	357	4	f.	f.	PROPN
ejpam-3431	357	5	marty	marty	PROPN
ejpam-3431	357	6	.	.	PUNCT
ejpam-3431	358	1	sur	sur	PROPN
ejpam-3431	358	2	une	une	PROPN
ejpam-3431	358	3	generalization	generalization	PROPN
ejpam-3431	358	4	de	de	X
ejpam-3431	358	5	la	la	PROPN
ejpam-3431	358	6	notion	notion	PROPN
ejpam-3431	358	7	de	de	X
ejpam-3431	358	8	groupe	groupe	PROPN
ejpam-3431	358	9	.	.	PUNCT
ejpam-3431	359	1	in	in	ADP
ejpam-3431	359	2	proceedings	proceeding	NOUN
ejpam-3431	359	3	of	of	ADP
ejpam-3431	359	4	the	the	DET
ejpam-3431	359	5	8th	8th	ADJ
ejpam-3431	359	6	congress	congress	PROPN
ejpam-3431	359	7	math	math	NOUN
ejpam-3431	359	8	.	.	PUNCT
ejpam-3431	360	1	scandinaves	scandinave	NOUN
ejpam-3431	360	2	,	,	PUNCT
ejpam-3431	360	3	pages	page	NOUN
ejpam-3431	360	4	45–49	45–49	PROPN
ejpam-3431	360	5	.	.	PUNCT
ejpam-3431	361	1	stockholm	stockholm	PROPN
ejpam-3431	361	2	,	,	PUNCT
ejpam-3431	361	3	1934	1934	NUM
ejpam-3431	361	4	.	.	PUNCT