id	sid	tid	token	lemma	pos
ejpam-4637	1	1	european	european	PROPN
ejpam-4637	1	2	journal	journal	PROPN
ejpam-4637	1	3	of	of	ADP
ejpam-4637	1	4	pure	pure	ADJ
ejpam-4637	1	5	and	and	CCONJ
ejpam-4637	1	6	applied	apply	VERB
ejpam-4637	1	7	mathematics	mathematic	NOUN
ejpam-4637	1	8	vol	vol	NOUN
ejpam-4637	1	9	.	.	PUNCT
ejpam-4637	2	1	16	16	NUM
ejpam-4637	2	2	,	,	PUNCT
ejpam-4637	2	3	no	no	INTJ
ejpam-4637	2	4	.	.	NOUN
ejpam-4637	2	5	1	1	NUM
ejpam-4637	2	6	,	,	PUNCT
ejpam-4637	2	7	2023	2023	NUM
ejpam-4637	2	8	,	,	PUNCT
ejpam-4637	2	9	548	548	NUM
ejpam-4637	2	10	-	-	SYM
ejpam-4637	2	11	576	576	NUM
ejpam-4637	2	12	issn	issn	PROPN
ejpam-4637	2	13	1307	1307	NUM
ejpam-4637	2	14	-	-	SYM
ejpam-4637	2	15	5543	5543	NUM
ejpam-4637	2	16	–	–	PUNCT
ejpam-4637	2	17	ejpam.com	ejpam.com	X
ejpam-4637	2	18	published	publish	VERB
ejpam-4637	2	19	by	by	ADP
ejpam-4637	2	20	new	new	PROPN
ejpam-4637	2	21	york	york	PROPN
ejpam-4637	2	22	business	business	PROPN
ejpam-4637	2	23	global	global	ADJ
ejpam-4637	2	24	single	single	ADV
ejpam-4637	2	25	-	-	PUNCT
ejpam-4637	2	26	valued	value	VERB
ejpam-4637	2	27	neutrosophic	neutrosophic	ADJ
ejpam-4637	2	28	soft	soft	ADJ
ejpam-4637	2	29	sets	set	NOUN
ejpam-4637	2	30	in	in	ADP
ejpam-4637	2	31	hyper	hyper	ADJ
ejpam-4637	2	32	up	up	ADP
ejpam-4637	2	33	-	-	PUNCT
ejpam-4637	2	34	algebra	algebra	NOUN
ejpam-4637	2	35	allan	allan	PROPN
ejpam-4637	2	36	n.	n.	PROPN
ejpam-4637	2	37	cano1,∗	cano1,∗	PROPN
ejpam-4637	2	38	,	,	PUNCT
ejpam-4637	2	39	gaudencio	gaudencio	NOUN
ejpam-4637	2	40	c.	c.	PROPN
ejpam-4637	2	41	petalcorin	petalcorin	PROPN
ejpam-4637	2	42	,	,	PUNCT
ejpam-4637	2	43	jr.1	jr.1	PROPN
ejpam-4637	2	44	1	1	NUM
ejpam-4637	2	45	department	department	NOUN
ejpam-4637	2	46	of	of	ADP
ejpam-4637	2	47	mathematics	mathematic	NOUN
ejpam-4637	2	48	and	and	CCONJ
ejpam-4637	2	49	statistics	statistic	NOUN
ejpam-4637	2	50	,	,	PUNCT
ejpam-4637	2	51	college	college	NOUN
ejpam-4637	2	52	of	of	ADP
ejpam-4637	2	53	science	science	NOUN
ejpam-4637	2	54	and	and	CCONJ
ejpam-4637	2	55	mathematics	mathematic	NOUN
ejpam-4637	2	56	,	,	PUNCT
ejpam-4637	2	57	mindanao	mindanao	PROPN
ejpam-4637	2	58	state	state	PROPN
ejpam-4637	2	59	university	university	PROPN
ejpam-4637	2	60	-	-	PUNCT
ejpam-4637	2	61	iligan	iligan	PROPN
ejpam-4637	2	62	institute	institute	PROPN
ejpam-4637	2	63	of	of	ADP
ejpam-4637	2	64	technology	technology	PROPN
ejpam-4637	2	65	,	,	PUNCT
ejpam-4637	2	66	9200	9200	NUM
ejpam-4637	2	67	iligan	iligan	ADJ
ejpam-4637	2	68	city	city	NOUN
ejpam-4637	2	69	,	,	PUNCT
ejpam-4637	3	1	philippines	philippine	NOUN
ejpam-4637	3	2	abstract	abstract	ADJ
ejpam-4637	3	3	.	.	PUNCT
ejpam-4637	4	1	in	in	ADP
ejpam-4637	4	2	this	this	DET
ejpam-4637	4	3	paper	paper	NOUN
ejpam-4637	4	4	,	,	PUNCT
ejpam-4637	4	5	the	the	DET
ejpam-4637	4	6	notions	notion	NOUN
ejpam-4637	4	7	of	of	ADP
ejpam-4637	4	8	svn	svn	PROPN
ejpam-4637	4	9	hyper	hyper	PROPN
ejpam-4637	4	10	up	up	ADP
ejpam-4637	4	11	-algebra	-algebra	PROPN
ejpam-4637	4	12	and	and	CCONJ
ejpam-4637	4	13	svns	svn	NOUN
ejpam-4637	4	14	hyper	hyper	PROPN
ejpam-4637	4	15	up	up	ADP
ejpam-4637	4	16	-algebra	-algebra	PROPN
ejpam-4637	4	17	are	be	AUX
ejpam-4637	4	18	introduced	introduce	VERB
ejpam-4637	4	19	,	,	PUNCT
ejpam-4637	4	20	and	and	CCONJ
ejpam-4637	4	21	some	some	PRON
ejpam-4637	4	22	of	of	ADP
ejpam-4637	4	23	their	their	PRON
ejpam-4637	4	24	structural	structural	ADJ
ejpam-4637	4	25	properties	property	NOUN
ejpam-4637	4	26	are	be	AUX
ejpam-4637	4	27	investigated	investigate	VERB
ejpam-4637	4	28	.	.	PUNCT
ejpam-4637	5	1	moreover	moreover	ADV
ejpam-4637	5	2	,	,	PUNCT
ejpam-4637	5	3	the	the	DET
ejpam-4637	5	4	cartesian	cartesian	ADJ
ejpam-4637	5	5	product	product	NOUN
ejpam-4637	5	6	of	of	ADP
ejpam-4637	5	7	svns	svn	NOUN
ejpam-4637	5	8	hyper	hyper	ADJ
ejpam-4637	5	9	up	up	ADP
ejpam-4637	5	10	-algebra	-algebra	PROPN
ejpam-4637	5	11	is	be	AUX
ejpam-4637	5	12	discussed	discuss	VERB
ejpam-4637	5	13	and	and	CCONJ
ejpam-4637	5	14	proved	prove	VERB
ejpam-4637	5	15	to	to	PART
ejpam-4637	5	16	be	be	AUX
ejpam-4637	5	17	a	a	DET
ejpam-4637	5	18	svns	svns	NOUN
ejpam-4637	5	19	hyper	hyper	ADJ
ejpam-4637	5	20	up	up	ADP
ejpam-4637	5	21	algebra	algebra	PROPN
ejpam-4637	5	22	.	.	PUNCT
ejpam-4637	6	1	finally	finally	ADV
ejpam-4637	6	2	,	,	PUNCT
ejpam-4637	6	3	the	the	DET
ejpam-4637	6	4	homomorphic	homomorphic	ADJ
ejpam-4637	6	5	image	image	NOUN
ejpam-4637	6	6	and	and	CCONJ
ejpam-4637	6	7	preimage	preimage	NOUN
ejpam-4637	6	8	of	of	ADP
ejpam-4637	6	9	svns	svns	PROPN
ejpam-4637	6	10	hyper	hyper	ADJ
ejpam-4637	6	11	up	up	ADP
ejpam-4637	6	12	-algebra	-algebra	PROPN
ejpam-4637	6	13	under	under	ADP
ejpam-4637	6	14	svns	svns	NOUN
ejpam-4637	6	15	functions	function	NOUN
ejpam-4637	6	16	are	be	AUX
ejpam-4637	6	17	studied	study	VERB
ejpam-4637	6	18	and	and	CCONJ
ejpam-4637	6	19	showed	show	VERB
ejpam-4637	6	20	also	also	ADV
ejpam-4637	6	21	to	to	PART
ejpam-4637	6	22	be	be	AUX
ejpam-4637	6	23	svns	svns	NOUN
ejpam-4637	6	24	hyper	hyper	ADJ
ejpam-4637	6	25	up	up	ADP
ejpam-4637	6	26	-algebra	-algebra	NOUN
ejpam-4637	6	27	.	.	PUNCT
ejpam-4637	7	1	2020	2020	NUM
ejpam-4637	7	2	mathematics	mathematic	NOUN
ejpam-4637	7	3	subject	subject	NOUN
ejpam-4637	7	4	classifications	classification	NOUN
ejpam-4637	7	5	:	:	PUNCT
ejpam-4637	7	6	08a30	08a30	NOUN
ejpam-4637	7	7	key	key	ADJ
ejpam-4637	7	8	words	word	NOUN
ejpam-4637	7	9	and	and	CCONJ
ejpam-4637	7	10	phrases	phrase	NOUN
ejpam-4637	7	11	:	:	PUNCT
ejpam-4637	7	12	hyper	hyper	ADJ
ejpam-4637	7	13	up	up	ADP
ejpam-4637	7	14	-algebra	-algebra	PROPN
ejpam-4637	7	15	,	,	PUNCT
ejpam-4637	7	16	single	single	ADJ
ejpam-4637	7	17	-	-	PUNCT
ejpam-4637	7	18	valued	value	VERB
ejpam-4637	7	19	neutrosophic	neutrosophic	ADJ
ejpam-4637	7	20	set	set	NOUN
ejpam-4637	7	21	,	,	PUNCT
ejpam-4637	7	22	single	single	ADJ
ejpam-4637	7	23	-	-	PUNCT
ejpam-4637	7	24	valued	value	VERB
ejpam-4637	7	25	neutrosophic	neutrosophic	ADJ
ejpam-4637	7	26	soft	soft	ADJ
ejpam-4637	7	27	set	set	NOUN
ejpam-4637	7	28	1	1	NUM
ejpam-4637	7	29	.	.	PUNCT
ejpam-4637	7	30	introduction	introduction	NOUN
ejpam-4637	7	31	the	the	DET
ejpam-4637	7	32	concept	concept	NOUN
ejpam-4637	7	33	of	of	ADP
ejpam-4637	7	34	fuzzy	fuzzy	ADJ
ejpam-4637	7	35	sets	set	NOUN
ejpam-4637	7	36	and	and	CCONJ
ejpam-4637	7	37	fuzzy	fuzzy	ADJ
ejpam-4637	7	38	logic	logic	NOUN
ejpam-4637	7	39	has	have	AUX
ejpam-4637	7	40	been	be	AUX
ejpam-4637	7	41	used	use	VERB
ejpam-4637	7	42	widely	widely	ADV
ejpam-4637	7	43	in	in	ADP
ejpam-4637	7	44	many	many	ADJ
ejpam-4637	7	45	applications	application	NOUN
ejpam-4637	7	46	involving	involve	VERB
ejpam-4637	7	47	uncertainties	uncertainty	NOUN
ejpam-4637	7	48	.	.	PUNCT
ejpam-4637	8	1	such	such	ADJ
ejpam-4637	8	2	concept	concept	NOUN
ejpam-4637	8	3	was	be	AUX
ejpam-4637	8	4	initiated	initiate	VERB
ejpam-4637	8	5	by	by	ADP
ejpam-4637	8	6	l.	l.	PROPN
ejpam-4637	8	7	zadeh	zadeh	PROPN
ejpam-4637	9	1	[	[	X
ejpam-4637	9	2	10	10	NUM
ejpam-4637	9	3	]	]	PUNCT
ejpam-4637	9	4	.	.	PUNCT
ejpam-4637	10	1	resulting	result	VERB
ejpam-4637	10	2	from	from	ADP
ejpam-4637	10	3	vagueness	vagueness	NOUN
ejpam-4637	10	4	or	or	CCONJ
ejpam-4637	10	5	partial	partial	ADJ
ejpam-4637	10	6	belongingness	belongingness	NOUN
ejpam-4637	10	7	of	of	ADP
ejpam-4637	10	8	an	an	DET
ejpam-4637	10	9	element	element	NOUN
ejpam-4637	10	10	in	in	ADP
ejpam-4637	10	11	a	a	DET
ejpam-4637	10	12	set	set	NOUN
ejpam-4637	10	13	,	,	PUNCT
ejpam-4637	10	14	fuzzy	fuzzy	ADJ
ejpam-4637	10	15	set	set	NOUN
ejpam-4637	10	16	is	be	AUX
ejpam-4637	10	17	successful	successful	ADJ
ejpam-4637	10	18	in	in	ADP
ejpam-4637	10	19	handling	handle	VERB
ejpam-4637	10	20	uncertainties	uncertainty	NOUN
ejpam-4637	10	21	.	.	PUNCT
ejpam-4637	11	1	however	however	ADV
ejpam-4637	11	2	,	,	PUNCT
ejpam-4637	11	3	there	there	PRON
ejpam-4637	11	4	are	be	VERB
ejpam-4637	11	5	still	still	ADV
ejpam-4637	11	6	some	some	DET
ejpam-4637	11	7	situations	situation	NOUN
ejpam-4637	11	8	which	which	PRON
ejpam-4637	11	9	it	it	PRON
ejpam-4637	11	10	can	can	AUX
ejpam-4637	11	11	not	not	PART
ejpam-4637	11	12	cover	cover	VERB
ejpam-4637	11	13	like	like	ADP
ejpam-4637	11	14	problems	problem	NOUN
ejpam-4637	11	15	involving	involve	VERB
ejpam-4637	11	16	incomplete	incomplete	ADJ
ejpam-4637	11	17	information	information	NOUN
ejpam-4637	11	18	.	.	PUNCT
ejpam-4637	12	1	motivated	motivate	VERB
ejpam-4637	12	2	by	by	ADP
ejpam-4637	12	3	this	this	PRON
ejpam-4637	12	4	,	,	PUNCT
ejpam-4637	12	5	a	a	DET
ejpam-4637	12	6	lot	lot	NOUN
ejpam-4637	12	7	of	of	ADP
ejpam-4637	12	8	researchers	researcher	NOUN
ejpam-4637	12	9	extended	extend	VERB
ejpam-4637	12	10	this	this	DET
ejpam-4637	12	11	concept	concept	NOUN
ejpam-4637	12	12	and	and	CCONJ
ejpam-4637	12	13	presented	present	VERB
ejpam-4637	12	14	a	a	DET
ejpam-4637	12	15	different	different	ADJ
ejpam-4637	12	16	theories	theory	NOUN
ejpam-4637	12	17	regarding	regard	VERB
ejpam-4637	12	18	uncertainty	uncertainty	NOUN
ejpam-4637	12	19	which	which	PRON
ejpam-4637	12	20	include	include	VERB
ejpam-4637	12	21	intuitionistic	intuitionistic	ADJ
ejpam-4637	12	22	fuzzy	fuzzy	ADJ
ejpam-4637	12	23	set	set	NOUN
ejpam-4637	12	24	theory	theory	NOUN
ejpam-4637	12	25	[	[	X
ejpam-4637	12	26	3	3	NUM
ejpam-4637	12	27	]	]	PUNCT
ejpam-4637	12	28	,	,	PUNCT
ejpam-4637	12	29	interval	interval	NOUN
ejpam-4637	12	30	-	-	PUNCT
ejpam-4637	12	31	valued	value	VERB
ejpam-4637	12	32	intuitionistic	intuitionistic	ADJ
ejpam-4637	12	33	fuzzy	fuzzy	ADJ
ejpam-4637	12	34	set	set	NOUN
ejpam-4637	12	35	theory	theory	NOUN
ejpam-4637	12	36	[	[	X
ejpam-4637	12	37	9	9	NUM
ejpam-4637	12	38	]	]	PUNCT
ejpam-4637	12	39	and	and	CCONJ
ejpam-4637	12	40	so	so	ADV
ejpam-4637	12	41	on	on	ADV
ejpam-4637	12	42	.	.	PUNCT
ejpam-4637	13	1	later	later	ADV
ejpam-4637	13	2	on	on	ADV
ejpam-4637	13	3	,	,	PUNCT
ejpam-4637	13	4	smarandache	smarandache	X
ejpam-4637	13	5	[	[	X
ejpam-4637	13	6	18	18	NUM
ejpam-4637	13	7	]	]	X
ejpam-4637	13	8	generalized	generalized	ADJ
ejpam-4637	13	9	intuitionistic	intuitionistic	ADJ
ejpam-4637	13	10	fuzzy	fuzzy	ADJ
ejpam-4637	13	11	set	set	NOUN
ejpam-4637	13	12	theory	theory	NOUN
ejpam-4637	13	13	by	by	ADP
ejpam-4637	13	14	introducing	introduce	VERB
ejpam-4637	13	15	the	the	DET
ejpam-4637	13	16	concept	concept	NOUN
ejpam-4637	13	17	of	of	ADP
ejpam-4637	13	18	neutrosophic	neutrosophic	ADJ
ejpam-4637	13	19	set	set	NOUN
ejpam-4637	13	20	in	in	ADP
ejpam-4637	13	21	1998	1998	NUM
ejpam-4637	13	22	.	.	PUNCT
ejpam-4637	14	1	neutrosophic	neutrosophic	ADJ
ejpam-4637	14	2	set	set	NOUN
ejpam-4637	14	3	is	be	AUX
ejpam-4637	14	4	a	a	DET
ejpam-4637	14	5	part	part	NOUN
ejpam-4637	14	6	of	of	ADP
ejpam-4637	14	7	neutrosophy	neutrosophy	NOUN
ejpam-4637	14	8	which	which	PRON
ejpam-4637	14	9	studies	study	VERB
ejpam-4637	14	10	the	the	DET
ejpam-4637	14	11	origin	origin	NOUN
ejpam-4637	14	12	,	,	PUNCT
ejpam-4637	14	13	nature	nature	NOUN
ejpam-4637	14	14	,	,	PUNCT
ejpam-4637	14	15	and	and	CCONJ
ejpam-4637	14	16	scope	scope	NOUN
ejpam-4637	14	17	of	of	ADP
ejpam-4637	14	18	neutralities	neutrality	NOUN
ejpam-4637	14	19	,	,	PUNCT
ejpam-4637	14	20	as	as	ADV
ejpam-4637	14	21	well	well	ADV
ejpam-4637	14	22	as	as	ADP
ejpam-4637	14	23	their	their	PRON
ejpam-4637	14	24	interactions	interaction	NOUN
ejpam-4637	14	25	with	with	ADP
ejpam-4637	14	26	different	different	ADJ
ejpam-4637	14	27	ideational	ideational	ADJ
ejpam-4637	14	28	spectra	spectra	NOUN
ejpam-4637	14	29	.	.	PUNCT
ejpam-4637	15	1	it	it	PRON
ejpam-4637	15	2	is	be	AUX
ejpam-4637	15	3	a	a	DET
ejpam-4637	15	4	powerful	powerful	ADJ
ejpam-4637	15	5	general	general	ADJ
ejpam-4637	15	6	formal	formal	ADJ
ejpam-4637	15	7	framework	framework	NOUN
ejpam-4637	15	8	that	that	PRON
ejpam-4637	15	9	has	have	AUX
ejpam-4637	15	10	been	be	AUX
ejpam-4637	15	11	recently	recently	ADV
ejpam-4637	15	12	proposed	propose	VERB
ejpam-4637	15	13	.	.	PUNCT
ejpam-4637	16	1	to	to	PART
ejpam-4637	16	2	have	have	VERB
ejpam-4637	16	3	its	its	PRON
ejpam-4637	16	4	real	real	ADJ
ejpam-4637	16	5	life	life	NOUN
ejpam-4637	16	6	application	application	NOUN
ejpam-4637	16	7	in	in	ADP
ejpam-4637	16	8	engineering	engineering	NOUN
ejpam-4637	16	9	and	and	CCONJ
ejpam-4637	16	10	science	science	NOUN
ejpam-4637	16	11	,	,	PUNCT
ejpam-4637	16	12	neutrosophic	neutrosophic	PROPN
ejpam-4637	16	13	set	set	VERB
ejpam-4637	16	14	needs	need	NOUN
ejpam-4637	16	15	to	to	PART
ejpam-4637	16	16	be	be	AUX
ejpam-4637	16	17	specified	specify	VERB
ejpam-4637	16	18	from	from	ADP
ejpam-4637	16	19	a	a	DET
ejpam-4637	16	20	technical	technical	ADJ
ejpam-4637	16	21	point	point	NOUN
ejpam-4637	16	22	of	of	ADP
ejpam-4637	16	23	view	view	NOUN
ejpam-4637	16	24	.	.	PUNCT
ejpam-4637	17	1	that	that	PRON
ejpam-4637	17	2	is	be	AUX
ejpam-4637	17	3	why	why	SCONJ
ejpam-4637	17	4	single	single	ADJ
ejpam-4637	17	5	valued	value	VERB
ejpam-4637	17	6	neutrosophic	neutrosophic	ADJ
ejpam-4637	17	7	set	set	NOUN
ejpam-4637	17	8	was	be	AUX
ejpam-4637	17	9	introduced	introduce	VERB
ejpam-4637	17	10	by	by	ADP
ejpam-4637	17	11	wang	wang	PROPN
ejpam-4637	17	12	et	et	PROPN
ejpam-4637	17	13	al	al	PROPN
ejpam-4637	17	14	.	.	PUNCT
ejpam-4637	18	1	[	[	X
ejpam-4637	18	2	22	22	NUM
ejpam-4637	18	3	]	]	PUNCT
ejpam-4637	18	4	together	together	ADV
ejpam-4637	18	5	with	with	ADP
ejpam-4637	18	6	its	its	PRON
ejpam-4637	18	7	various	various	ADJ
ejpam-4637	18	8	properties	property	NOUN
ejpam-4637	18	9	.	.	PUNCT
ejpam-4637	19	1	single	single	ADJ
ejpam-4637	19	2	-	-	PUNCT
ejpam-4637	19	3	valued	value	VERB
ejpam-4637	19	4	neutrosophic	neutrosophic	ADJ
ejpam-4637	19	5	set	set	NOUN
ejpam-4637	19	6	has	have	AUX
ejpam-4637	19	7	been	be	AUX
ejpam-4637	19	8	developing	develop	VERB
ejpam-4637	19	9	rapidly	rapidly	ADV
ejpam-4637	19	10	due	due	ADP
ejpam-4637	19	11	to	to	ADP
ejpam-4637	19	12	its	its	PRON
ejpam-4637	19	13	wide	wide	ADJ
ejpam-4637	19	14	range	range	NOUN
ejpam-4637	19	15	of	of	ADP
ejpam-4637	19	16	∗corresponding	∗corresponde	VERB
ejpam-4637	19	17	author	author	NOUN
ejpam-4637	19	18	.	.	PUNCT
ejpam-4637	20	1	doi	doi	NOUN
ejpam-4637	20	2	:	:	PUNCT
ejpam-4637	20	3	https://doi.org/10.29020/nybg.ejpam.v16i1.4637	https://doi.org/10.29020/nybg.ejpam.v16i1.4637	ADJ
ejpam-4637	20	4	email	email	NOUN
ejpam-4637	20	5	addresses	address	NOUN
ejpam-4637	20	6	:	:	PUNCT
ejpam-4637	20	7	allan.cano@g.msuiit.edu.ph	allan.cano@g.msuiit.edu.ph	PROPN
ejpam-4637	20	8	(	(	PUNCT
ejpam-4637	20	9	a.	a.	PROPN
ejpam-4637	20	10	cano	cano	PROPN
ejpam-4637	20	11	)	)	PUNCT
ejpam-4637	20	12	,	,	PUNCT
ejpam-4637	20	13	gaudencio.petalcorin@g.msuiit.edu.ph	gaudencio.petalcorin@g.msuiit.edu.ph	PROPN
ejpam-4637	20	14	(	(	PUNCT
ejpam-4637	20	15	g.	g.	PROPN
ejpam-4637	20	16	petalcorin	petalcorin	PROPN
ejpam-4637	20	17	)	)	PUNCT
ejpam-4637	20	18	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4637	21	1	548	548	NUM
ejpam-4637	21	2	©	©	ADP
ejpam-4637	21	3	2023	2023	NUM
ejpam-4637	21	4	ejpam	ejpam	NOUN
ejpam-4637	21	5	all	all	DET
ejpam-4637	21	6	rights	right	NOUN
ejpam-4637	21	7	reserved	reserve	VERB
ejpam-4637	21	8	.	.	PUNCT
ejpam-4637	22	1	a.	a.	PROPN
ejpam-4637	22	2	cano	cano	PROPN
ejpam-4637	22	3	,	,	PUNCT
ejpam-4637	22	4	g.	g.	PROPN
ejpam-4637	22	5	petalcorin	petalcorin	PROPN
ejpam-4637	22	6	/	/	SYM
ejpam-4637	22	7	eur	eur	PROPN
ejpam-4637	22	8	.	.	PUNCT
ejpam-4637	23	1	j.	j.	PROPN
ejpam-4637	23	2	pure	pure	PROPN
ejpam-4637	23	3	appl	appl	PROPN
ejpam-4637	23	4	.	.	PROPN
ejpam-4637	23	5	math	math	PROPN
ejpam-4637	23	6	,	,	PUNCT
ejpam-4637	23	7	16	16	NUM
ejpam-4637	23	8	(	(	PUNCT
ejpam-4637	23	9	1	1	NUM
ejpam-4637	23	10	)	)	PUNCT
ejpam-4637	23	11	(	(	PUNCT
ejpam-4637	23	12	2023	2023	NUM
ejpam-4637	23	13	)	)	PUNCT
ejpam-4637	23	14	,	,	PUNCT
ejpam-4637	23	15	548	548	NUM
ejpam-4637	23	16	-	-	SYM
ejpam-4637	23	17	576	576	NUM
ejpam-4637	23	18	549	549	NUM
ejpam-4637	23	19	theoretical	theoretical	ADJ
ejpam-4637	23	20	elegance	elegance	NOUN
ejpam-4637	23	21	and	and	CCONJ
ejpam-4637	23	22	application	application	NOUN
ejpam-4637	23	23	areas	area	NOUN
ejpam-4637	23	24	.	.	PUNCT
ejpam-4637	24	1	the	the	DET
ejpam-4637	24	2	reader	reader	NOUN
ejpam-4637	24	3	may	may	AUX
ejpam-4637	24	4	refer	refer	VERB
ejpam-4637	24	5	to	to	ADP
ejpam-4637	24	6	the	the	DET
ejpam-4637	24	7	following	follow	VERB
ejpam-4637	24	8	articles	article	NOUN
ejpam-4637	24	9	[	[	X
ejpam-4637	24	10	7	7	NUM
ejpam-4637	24	11	,	,	PUNCT
ejpam-4637	24	12	8	8	NUM
ejpam-4637	24	13	,	,	PUNCT
ejpam-4637	24	14	16	16	NUM
ejpam-4637	24	15	,	,	PUNCT
ejpam-4637	24	16	17	17	NUM
ejpam-4637	24	17	,	,	PUNCT
ejpam-4637	24	18	19	19	NUM
ejpam-4637	24	19	,	,	PUNCT
ejpam-4637	24	20	20	20	NUM
ejpam-4637	24	21	]	]	PUNCT
ejpam-4637	24	22	as	as	ADP
ejpam-4637	24	23	references	reference	NOUN
ejpam-4637	24	24	.	.	PUNCT
ejpam-4637	25	1	in	in	ADP
ejpam-4637	25	2	1999	1999	NUM
ejpam-4637	25	3	,	,	PUNCT
ejpam-4637	25	4	molodtsov	molodtsov	NOUN
ejpam-4637	25	5	[	[	X
ejpam-4637	25	6	14	14	NUM
ejpam-4637	25	7	]	]	PUNCT
ejpam-4637	25	8	studied	study	VERB
ejpam-4637	25	9	another	another	DET
ejpam-4637	25	10	mathematical	mathematical	ADJ
ejpam-4637	25	11	theory	theory	NOUN
ejpam-4637	25	12	called	call	VERB
ejpam-4637	25	13	soft	soft	ADJ
ejpam-4637	25	14	set	set	NOUN
ejpam-4637	25	15	theory	theory	NOUN
ejpam-4637	25	16	by	by	ADP
ejpam-4637	25	17	giving	give	VERB
ejpam-4637	25	18	parameterized	parameterized	ADJ
ejpam-4637	25	19	approach	approach	NOUN
ejpam-4637	25	20	to	to	ADP
ejpam-4637	25	21	uncertainties	uncertainty	NOUN
ejpam-4637	25	22	.	.	PUNCT
ejpam-4637	26	1	on	on	ADP
ejpam-4637	26	2	the	the	DET
ejpam-4637	26	3	other	other	ADJ
ejpam-4637	26	4	hand	hand	NOUN
ejpam-4637	26	5	,	,	PUNCT
ejpam-4637	26	6	maji	maji	PROPN
ejpam-4637	27	1	[	[	X
ejpam-4637	27	2	12	12	NUM
ejpam-4637	27	3	]	]	PUNCT
ejpam-4637	27	4	unified	unify	VERB
ejpam-4637	27	5	the	the	DET
ejpam-4637	27	6	fundamental	fundamental	ADJ
ejpam-4637	27	7	theories	theory	NOUN
ejpam-4637	27	8	of	of	ADP
ejpam-4637	27	9	neutrosophic	neutrosophic	ADJ
ejpam-4637	27	10	set	set	VERB
ejpam-4637	27	11	and	and	CCONJ
ejpam-4637	27	12	soft	soft	ADJ
ejpam-4637	27	13	set	set	NOUN
ejpam-4637	27	14	,	,	PUNCT
ejpam-4637	27	15	and	and	CCONJ
ejpam-4637	27	16	came	come	VERB
ejpam-4637	27	17	up	up	ADP
ejpam-4637	27	18	with	with	ADP
ejpam-4637	27	19	the	the	DET
ejpam-4637	27	20	concept	concept	NOUN
ejpam-4637	27	21	of	of	ADP
ejpam-4637	27	22	neutrosophic	neutrosophic	ADJ
ejpam-4637	27	23	soft	soft	ADJ
ejpam-4637	27	24	set	set	NOUN
ejpam-4637	27	25	.	.	PUNCT
ejpam-4637	28	1	some	some	DET
ejpam-4637	28	2	theoretical	theoretical	ADJ
ejpam-4637	28	3	advancement	advancement	NOUN
ejpam-4637	28	4	and	and	CCONJ
ejpam-4637	28	5	applications	application	NOUN
ejpam-4637	28	6	have	have	AUX
ejpam-4637	28	7	been	be	AUX
ejpam-4637	28	8	reported	report	VERB
ejpam-4637	28	9	in	in	ADP
ejpam-4637	28	10	the	the	DET
ejpam-4637	28	11	following	follow	VERB
ejpam-4637	28	12	literatures	literature	NOUN
ejpam-4637	28	13	[	[	X
ejpam-4637	28	14	1	1	NUM
ejpam-4637	28	15	,	,	PUNCT
ejpam-4637	28	16	4	4	NUM
ejpam-4637	28	17	,	,	PUNCT
ejpam-4637	28	18	5	5	NUM
ejpam-4637	28	19	,	,	PUNCT
ejpam-4637	28	20	11	11	NUM
ejpam-4637	28	21	]	]	PUNCT
ejpam-4637	28	22	.	.	PUNCT
ejpam-4637	29	1	the	the	DET
ejpam-4637	29	2	hyper	hyper	ADJ
ejpam-4637	29	3	algebraic	algebraic	ADJ
ejpam-4637	29	4	structure	structure	NOUN
ejpam-4637	29	5	theory	theory	NOUN
ejpam-4637	29	6	was	be	AUX
ejpam-4637	29	7	introduced	introduce	VERB
ejpam-4637	29	8	in	in	ADP
ejpam-4637	29	9	1934	1934	NUM
ejpam-4637	29	10	by	by	ADP
ejpam-4637	29	11	f.	f.	PROPN
ejpam-4637	29	12	marty	marty	PROPN
ejpam-4637	30	1	[	[	X
ejpam-4637	30	2	13	13	NUM
ejpam-4637	30	3	]	]	PUNCT
ejpam-4637	30	4	at	at	ADP
ejpam-4637	30	5	the	the	DET
ejpam-4637	30	6	8th	8th	ADJ
ejpam-4637	30	7	congress	congress	PROPN
ejpam-4637	30	8	of	of	ADP
ejpam-4637	30	9	scandinavian	scandinavian	ADJ
ejpam-4637	30	10	mathematicians	mathematician	NOUN
ejpam-4637	30	11	.	.	PUNCT
ejpam-4637	31	1	this	this	DET
ejpam-4637	31	2	theory	theory	NOUN
ejpam-4637	31	3	is	be	AUX
ejpam-4637	31	4	then	then	ADV
ejpam-4637	31	5	applied	apply	VERB
ejpam-4637	31	6	by	by	ADP
ejpam-4637	31	7	y.	y.	PROPN
ejpam-4637	31	8	b.	b.	PROPN
ejpam-4637	31	9	jun	jun	PROPN
ejpam-4637	31	10	et	et	PROPN
ejpam-4637	31	11	al	al	PROPN
ejpam-4637	31	12	.	.	PUNCT
ejpam-4637	32	1	[	[	X
ejpam-4637	32	2	21	21	NUM
ejpam-4637	32	3	]	]	PUNCT
ejpam-4637	32	4	to	to	PART
ejpam-4637	32	5	bck	bck	VERB
ejpam-4637	32	6	-	-	PUNCT
ejpam-4637	32	7	algebras	algebras	PROPN
ejpam-4637	32	8	to	to	PART
ejpam-4637	32	9	produce	produce	VERB
ejpam-4637	32	10	the	the	DET
ejpam-4637	32	11	notion	notion	NOUN
ejpam-4637	32	12	of	of	ADP
ejpam-4637	32	13	hyper	hyper	ADJ
ejpam-4637	32	14	bck	bck	NOUN
ejpam-4637	32	15	-	-	PUNCT
ejpam-4637	32	16	algebras	algebras	PROPN
ejpam-4637	32	17	as	as	ADP
ejpam-4637	32	18	a	a	DET
ejpam-4637	32	19	generalization	generalization	NOUN
ejpam-4637	32	20	of	of	ADP
ejpam-4637	32	21	the	the	DET
ejpam-4637	32	22	bck	bck	NOUN
ejpam-4637	32	23	-	-	PUNCT
ejpam-4637	32	24	algebras	algebras	PROPN
ejpam-4637	32	25	.	.	PUNCT
ejpam-4637	33	1	after	after	ADP
ejpam-4637	33	2	that	that	PRON
ejpam-4637	33	3	,	,	PUNCT
ejpam-4637	33	4	many	many	ADJ
ejpam-4637	33	5	researchers	researcher	NOUN
ejpam-4637	33	6	have	have	AUX
ejpam-4637	33	7	been	be	AUX
ejpam-4637	33	8	inspired	inspire	VERB
ejpam-4637	33	9	to	to	PART
ejpam-4637	33	10	generalize	generalize	VERB
ejpam-4637	33	11	some	some	DET
ejpam-4637	33	12	existing	exist	VERB
ejpam-4637	33	13	algebras	algebra	NOUN
ejpam-4637	33	14	and	and	CCONJ
ejpam-4637	33	15	one	one	NUM
ejpam-4637	33	16	of	of	ADP
ejpam-4637	33	17	them	they	PRON
ejpam-4637	33	18	is	be	AUX
ejpam-4637	33	19	d.	d.	PROPN
ejpam-4637	33	20	romano	romano	VERB
ejpam-4637	34	1	[	[	X
ejpam-4637	34	2	15	15	NUM
ejpam-4637	34	3	]	]	PUNCT
ejpam-4637	34	4	.	.	PUNCT
ejpam-4637	35	1	he	he	PRON
ejpam-4637	35	2	has	have	AUX
ejpam-4637	35	3	come	come	VERB
ejpam-4637	35	4	up	up	ADP
ejpam-4637	35	5	with	with	ADP
ejpam-4637	35	6	the	the	DET
ejpam-4637	35	7	concept	concept	NOUN
ejpam-4637	35	8	of	of	ADP
ejpam-4637	35	9	hyper	hyper	ADJ
ejpam-4637	35	10	up	up	ADP
ejpam-4637	35	11	-algebras	-algebra	NOUN
ejpam-4637	35	12	to	to	PART
ejpam-4637	35	13	generalize	generalize	VERB
ejpam-4637	35	14	up	up	ADP
ejpam-4637	35	15	-algebras	-algebra	NOUN
ejpam-4637	35	16	.	.	PUNCT
ejpam-4637	36	1	in	in	ADP
ejpam-4637	36	2	this	this	DET
ejpam-4637	36	3	paper	paper	NOUN
ejpam-4637	36	4	,	,	PUNCT
ejpam-4637	36	5	we	we	PRON
ejpam-4637	36	6	utilize	utilize	VERB
ejpam-4637	36	7	the	the	DET
ejpam-4637	36	8	notions	notion	NOUN
ejpam-4637	36	9	of	of	ADP
ejpam-4637	36	10	single	single	ADV
ejpam-4637	36	11	-	-	PUNCT
ejpam-4637	36	12	valued	value	VERB
ejpam-4637	36	13	neutrosophic	neutrosophic	ADJ
ejpam-4637	36	14	sets	set	NOUN
ejpam-4637	36	15	and	and	CCONJ
ejpam-4637	36	16	single	single	ADV
ejpam-4637	36	17	-	-	PUNCT
ejpam-4637	36	18	valued	value	VERB
ejpam-4637	36	19	neutrosophic	neutrosophic	ADJ
ejpam-4637	36	20	soft	soft	ADJ
ejpam-4637	36	21	sets	set	NOUN
ejpam-4637	36	22	to	to	PART
ejpam-4637	36	23	hyper	hyper	VERB
ejpam-4637	36	24	up	up	ADP
ejpam-4637	36	25	-algebra	-algebra	NOUN
ejpam-4637	36	26	to	to	PART
ejpam-4637	36	27	generate	generate	VERB
ejpam-4637	36	28	svn	svn	PROPN
ejpam-4637	36	29	hyper	hyper	NOUN
ejpam-4637	36	30	up	up	ADP
ejpam-4637	36	31	-algebra	-algebra	PROPN
ejpam-4637	36	32	and	and	CCONJ
ejpam-4637	36	33	svns	svn	NOUN
ejpam-4637	36	34	hyper	hyper	PROPN
ejpam-4637	36	35	up	up	ADP
ejpam-4637	36	36	-algebra	-algebra	NOUN
ejpam-4637	36	37	.	.	PUNCT
ejpam-4637	37	1	several	several	ADJ
ejpam-4637	37	2	of	of	ADP
ejpam-4637	37	3	their	their	PRON
ejpam-4637	37	4	basic	basic	ADJ
ejpam-4637	37	5	properties	property	NOUN
ejpam-4637	37	6	are	be	AUX
ejpam-4637	37	7	studied	study	VERB
ejpam-4637	37	8	.	.	PUNCT
ejpam-4637	38	1	in	in	ADP
ejpam-4637	38	2	addition	addition	NOUN
ejpam-4637	38	3	,	,	PUNCT
ejpam-4637	38	4	we	we	PRON
ejpam-4637	38	5	define	define	VERB
ejpam-4637	38	6	the	the	DET
ejpam-4637	38	7	cartesian	cartesian	ADJ
ejpam-4637	38	8	product	product	NOUN
ejpam-4637	38	9	of	of	ADP
ejpam-4637	38	10	svns	svn	NOUN
ejpam-4637	38	11	hyper	hyper	ADJ
ejpam-4637	38	12	up	up	ADP
ejpam-4637	38	13	-algebra	-algebra	PROPN
ejpam-4637	38	14	,	,	PUNCT
ejpam-4637	38	15	and	and	CCONJ
ejpam-4637	38	16	image	image	NOUN
ejpam-4637	38	17	and	and	CCONJ
ejpam-4637	38	18	preimage	preimage	NOUN
ejpam-4637	38	19	of	of	ADP
ejpam-4637	38	20	svns	svns	PROPN
ejpam-4637	38	21	hyper	hyper	ADJ
ejpam-4637	38	22	up	up	ADP
ejpam-4637	38	23	-algebra	-algebra	PROPN
ejpam-4637	38	24	under	under	ADP
ejpam-4637	38	25	svns	svn	NOUN
ejpam-4637	38	26	function	function	NOUN
ejpam-4637	38	27	.	.	PUNCT
ejpam-4637	39	1	each	each	PRON
ejpam-4637	39	2	of	of	ADP
ejpam-4637	39	3	them	they	PRON
ejpam-4637	39	4	is	be	AUX
ejpam-4637	39	5	discussed	discuss	VERB
ejpam-4637	39	6	and	and	CCONJ
ejpam-4637	39	7	illustrated	illustrate	VERB
ejpam-4637	39	8	with	with	ADP
ejpam-4637	39	9	corresponding	correspond	VERB
ejpam-4637	39	10	examples	example	NOUN
ejpam-4637	39	11	.	.	PUNCT
ejpam-4637	40	1	2	2	X
ejpam-4637	40	2	.	.	X
ejpam-4637	40	3	preliminary	preliminary	ADJ
ejpam-4637	40	4	concepts	concept	NOUN
ejpam-4637	40	5	definition	definition	NOUN
ejpam-4637	40	6	1	1	NUM
ejpam-4637	40	7	.	.	PUNCT
ejpam-4637	41	1	[	[	X
ejpam-4637	41	2	15	15	NUM
ejpam-4637	41	3	]	]	PUNCT
ejpam-4637	41	4	let	let	VERB
ejpam-4637	41	5	p(h	p(h	NOUN
ejpam-4637	41	6	)	)	PUNCT
ejpam-4637	41	7	to	to	PART
ejpam-4637	41	8	be	be	AUX
ejpam-4637	41	9	the	the	DET
ejpam-4637	41	10	power	power	NOUN
ejpam-4637	41	11	set	set	NOUN
ejpam-4637	41	12	of	of	ADP
ejpam-4637	41	13	h.	h.	PROPN
ejpam-4637	41	14	consider	consider	VERB
ejpam-4637	41	15	p∗(h	p∗(h	NOUN
ejpam-4637	41	16	)	)	PUNCT
ejpam-4637	42	1	=	=	SYM
ejpam-4637	42	2	p(h	p(h	PROPN
ejpam-4637	42	3	)	)	PUNCT
ejpam-4637	42	4	\	\	NOUN
ejpam-4637	42	5	{	{	PUNCT
ejpam-4637	42	6	∅	∅	NOUN
ejpam-4637	42	7	}	}	PUNCT
ejpam-4637	42	8	.	.	PUNCT
ejpam-4637	43	1	a	a	DET
ejpam-4637	43	2	hyperoperation	hyperoperation	NOUN
ejpam-4637	43	3	on	on	ADP
ejpam-4637	43	4	a	a	DET
ejpam-4637	43	5	nonempty	nonempty	ADV
ejpam-4637	43	6	set	set	VERB
ejpam-4637	43	7	h	h	NOUN
ejpam-4637	43	8	is	be	AUX
ejpam-4637	43	9	a	a	DET
ejpam-4637	43	10	function	function	NOUN
ejpam-4637	43	11	◦	◦	NOUN
ejpam-4637	43	12	:	:	PUNCT
ejpam-4637	43	13	h	h	NOUN
ejpam-4637	43	14	×h	×h	PROPN
ejpam-4637	43	15	−→	−→	ADJ
ejpam-4637	43	16	p∗(h	p∗(h	PROPN
ejpam-4637	43	17	)	)	PUNCT
ejpam-4637	43	18	.	.	PUNCT
ejpam-4637	44	1	the	the	DET
ejpam-4637	44	2	image	image	NOUN
ejpam-4637	44	3	of	of	ADP
ejpam-4637	44	4	(	(	PUNCT
ejpam-4637	44	5	x	x	NOUN
ejpam-4637	44	6	,	,	PUNCT
ejpam-4637	44	7	y	y	NOUN
ejpam-4637	44	8	)	)	PUNCT
ejpam-4637	44	9	∈	∈	PROPN
ejpam-4637	44	10	h	h	NOUN
ejpam-4637	44	11	×h	×h	PROPN
ejpam-4637	44	12	under	under	ADP
ejpam-4637	44	13	◦	◦	NOUN
ejpam-4637	44	14	is	be	AUX
ejpam-4637	44	15	denoted	denote	VERB
ejpam-4637	44	16	by	by	ADP
ejpam-4637	44	17	x	x	X
ejpam-4637	44	18	◦	◦	NOUN
ejpam-4637	44	19	y.	y.	NOUN
ejpam-4637	44	20	if	if	SCONJ
ejpam-4637	44	21	x	x	SYM
ejpam-4637	44	22	∈	∈	PROPN
ejpam-4637	44	23	h	h	NOUN
ejpam-4637	44	24	and	and	CCONJ
ejpam-4637	44	25	a	a	DET
ejpam-4637	44	26	,	,	PUNCT
ejpam-4637	44	27	b	b	NOUN
ejpam-4637	44	28	are	be	AUX
ejpam-4637	44	29	nonempty	nonempty	ADJ
ejpam-4637	44	30	subsets	subset	NOUN
ejpam-4637	44	31	of	of	ADP
ejpam-4637	44	32	h	h	NOUN
ejpam-4637	44	33	,	,	PUNCT
ejpam-4637	44	34	then	then	ADV
ejpam-4637	44	35	we	we	PRON
ejpam-4637	44	36	define	define	VERB
ejpam-4637	44	37	(	(	PUNCT
ejpam-4637	44	38	i	i	NOUN
ejpam-4637	44	39	)	)	PUNCT
ejpam-4637	44	40	a	a	DET
ejpam-4637	44	41	◦	◦	NOUN
ejpam-4637	44	42	b	b	NOUN
ejpam-4637	44	43	=	=	PUNCT
ejpam-4637	44	44	⋃	⋃	NOUN
ejpam-4637	44	45	a∈a	a∈a	ADJ
ejpam-4637	44	46	,	,	PUNCT
ejpam-4637	44	47	b∈b	b∈b	VERB
ejpam-4637	44	48	a	a	DET
ejpam-4637	44	49	◦	◦	NOUN
ejpam-4637	44	50	b	b	NOUN
ejpam-4637	44	51	;	;	PUNCT
ejpam-4637	44	52	(	(	PUNCT
ejpam-4637	44	53	ii	ii	NOUN
ejpam-4637	44	54	)	)	PUNCT
ejpam-4637	44	55	a	a	DET
ejpam-4637	44	56	◦	◦	NOUN
ejpam-4637	44	57	x	x	X
ejpam-4637	44	58	=	=	PUNCT
ejpam-4637	44	59	a	a	DET
ejpam-4637	44	60	◦	◦	NOUN
ejpam-4637	44	61	{	{	PUNCT
ejpam-4637	44	62	x	x	NOUN
ejpam-4637	44	63	}	}	PUNCT
ejpam-4637	44	64	;	;	PUNCT
ejpam-4637	44	65	and	and	CCONJ
ejpam-4637	44	66	(	(	PUNCT
ejpam-4637	44	67	iii	iii	NOUN
ejpam-4637	44	68	)	)	PUNCT
ejpam-4637	44	69	x	x	PUNCT
ejpam-4637	44	70	◦	◦	NOUN
ejpam-4637	44	71	b	b	NOUN
ejpam-4637	44	72	=	=	SYM
ejpam-4637	44	73	{	{	PUNCT
ejpam-4637	44	74	x	x	NOUN
ejpam-4637	44	75	}	}	PUNCT
ejpam-4637	44	76	◦	◦	PROPN
ejpam-4637	44	77	b.	b.	NOUN
ejpam-4637	44	78	definition	definition	NOUN
ejpam-4637	44	79	2	2	NUM
ejpam-4637	44	80	.	.	PUNCT
ejpam-4637	45	1	[	[	X
ejpam-4637	45	2	15	15	NUM
ejpam-4637	45	3	]	]	X
ejpam-4637	45	4	let	let	VERB
ejpam-4637	45	5	x	x	PRON
ejpam-4637	45	6	,	,	PUNCT
ejpam-4637	45	7	y	y	PROPN
ejpam-4637	45	8	∈	∈	PROPN
ejpam-4637	45	9	h	h	NOUN
ejpam-4637	45	10	and	and	CCONJ
ejpam-4637	45	11	a	a	PRON
ejpam-4637	45	12	,	,	PUNCT
ejpam-4637	45	13	b	b	PROPN
ejpam-4637	45	14	⊆	⊆	NUM
ejpam-4637	45	15	h.	h.	NOUN
ejpam-4637	45	16	then	then	ADV
ejpam-4637	45	17	(	(	PUNCT
ejpam-4637	45	18	i	i	NOUN
ejpam-4637	45	19	)	)	PUNCT
ejpam-4637	45	20	x	x	PUNCT
ejpam-4637	45	21	≪	≪	VERB
ejpam-4637	45	22	y	y	PROPN
ejpam-4637	45	23	if	if	SCONJ
ejpam-4637	45	24	and	and	CCONJ
ejpam-4637	45	25	only	only	ADV
ejpam-4637	45	26	if	if	SCONJ
ejpam-4637	45	27	0	0	NUM
ejpam-4637	45	28	∈	∈	NOUN
ejpam-4637	45	29	x	x	PUNCT
ejpam-4637	45	30	◦	◦	NOUN
ejpam-4637	45	31	y	y	NOUN
ejpam-4637	45	32	;	;	PUNCT
ejpam-4637	45	33	and	and	CCONJ
ejpam-4637	45	34	(	(	PUNCT
ejpam-4637	45	35	ii	ii	NOUN
ejpam-4637	45	36	)	)	PUNCT
ejpam-4637	45	37	a	a	DET
ejpam-4637	45	38	≪	≪	ADJ
ejpam-4637	45	39	b	b	NOUN
ejpam-4637	45	40	if	if	SCONJ
ejpam-4637	45	41	and	and	CCONJ
ejpam-4637	45	42	only	only	ADV
ejpam-4637	45	43	if	if	SCONJ
ejpam-4637	45	44	for	for	ADP
ejpam-4637	45	45	any	any	DET
ejpam-4637	45	46	a	a	DET
ejpam-4637	45	47	∈	∈	PROPN
ejpam-4637	45	48	a	a	PRON
ejpam-4637	45	49	,	,	PUNCT
ejpam-4637	45	50	there	there	PRON
ejpam-4637	45	51	exists	exist	VERB
ejpam-4637	45	52	b	b	PROPN
ejpam-4637	45	53	∈	∈	PROPN
ejpam-4637	45	54	b	b	NOUN
ejpam-4637	45	55	such	such	ADJ
ejpam-4637	45	56	that	that	SCONJ
ejpam-4637	45	57	a	a	DET
ejpam-4637	45	58	≪	≪	ADJ
ejpam-4637	45	59	b.	b.	NOUN
ejpam-4637	45	60	we	we	PRON
ejpam-4637	45	61	call	call	VERB
ejpam-4637	45	62	≪	≪	PUNCT
ejpam-4637	45	63	a	a	DET
ejpam-4637	45	64	hyperorder	hyperorder	NOUN
ejpam-4637	45	65	on	on	ADP
ejpam-4637	45	66	h.	h.	PROPN
ejpam-4637	45	67	remark	remark	PROPN
ejpam-4637	45	68	1	1	NUM
ejpam-4637	45	69	.	.	PUNCT
ejpam-4637	46	1	[	[	X
ejpam-4637	46	2	15	15	NUM
ejpam-4637	46	3	]	]	PUNCT
ejpam-4637	46	4	for	for	ADP
ejpam-4637	46	5	all	all	DET
ejpam-4637	46	6	a	a	DET
ejpam-4637	46	7	,	,	PUNCT
ejpam-4637	46	8	b	b	PROPN
ejpam-4637	46	9	⊆	⊆	NUM
ejpam-4637	46	10	h	h	NOUN
ejpam-4637	46	11	,	,	PUNCT
ejpam-4637	46	12	a	a	DET
ejpam-4637	46	13	≪	≪	ADJ
ejpam-4637	46	14	b	b	NOUN
ejpam-4637	46	15	implies	imply	VERB
ejpam-4637	46	16	0	0	NUM
ejpam-4637	46	17	∈	∈	PROPN
ejpam-4637	46	18	a	a	DET
ejpam-4637	46	19	◦	◦	NOUN
ejpam-4637	46	20	b.	b.	NOUN
ejpam-4637	46	21	definition	definition	NOUN
ejpam-4637	46	22	3	3	NUM
ejpam-4637	46	23	.	.	PUNCT
ejpam-4637	47	1	[	[	X
ejpam-4637	47	2	15	15	NUM
ejpam-4637	47	3	]	]	PUNCT
ejpam-4637	47	4	let	let	VERB
ejpam-4637	47	5	x	x	PRON
ejpam-4637	47	6	be	be	AUX
ejpam-4637	47	7	a	a	DET
ejpam-4637	47	8	nonempty	nonempty	NOUN
ejpam-4637	47	9	set	set	VERB
ejpam-4637	47	10	such	such	ADJ
ejpam-4637	47	11	that	that	PRON
ejpam-4637	47	12	0	0	NUM
ejpam-4637	47	13	∈	∈	NOUN
ejpam-4637	47	14	x	x	X
ejpam-4637	47	15	and	and	CCONJ
ejpam-4637	47	16	(	(	PUNCT
ejpam-4637	47	17	x	x	NOUN
ejpam-4637	47	18	,	,	PUNCT
ejpam-4637	47	19	◦	◦	NOUN
ejpam-4637	47	20	,	,	PUNCT
ejpam-4637	47	21	≪	≪	ADJ
ejpam-4637	47	22	,	,	PUNCT
ejpam-4637	47	23	0	0	NUM
ejpam-4637	47	24	)	)	PUNCT
ejpam-4637	47	25	be	be	AUX
ejpam-4637	47	26	a	a	DET
ejpam-4637	47	27	hyperstructure	hyperstructure	NOUN
ejpam-4637	47	28	.	.	PUNCT
ejpam-4637	48	1	then	then	ADV
ejpam-4637	48	2	(	(	PUNCT
ejpam-4637	48	3	x	x	X
ejpam-4637	48	4	,	,	PUNCT
ejpam-4637	48	5	◦	◦	NOUN
ejpam-4637	48	6	,	,	PUNCT
ejpam-4637	48	7	≪	≪	ADJ
ejpam-4637	48	8	,	,	PUNCT
ejpam-4637	48	9	0	0	NUM
ejpam-4637	48	10	)	)	PUNCT
ejpam-4637	48	11	is	be	AUX
ejpam-4637	48	12	called	call	VERB
ejpam-4637	48	13	a	a	DET
ejpam-4637	48	14	hyper	hyper	ADJ
ejpam-4637	48	15	up	up	NOUN
ejpam-4637	48	16	-	-	PUNCT
ejpam-4637	48	17	algebra	algebra	NOUN
ejpam-4637	48	18	if	if	SCONJ
ejpam-4637	48	19	the	the	DET
ejpam-4637	48	20	following	follow	VERB
ejpam-4637	48	21	formulas	formula	NOUN
ejpam-4637	48	22	are	be	AUX
ejpam-4637	48	23	valid	valid	ADJ
ejpam-4637	48	24	:	:	PUNCT
ejpam-4637	48	25	∀x	∀x	NUM
ejpam-4637	48	26	,	,	PUNCT
ejpam-4637	48	27	y	y	PROPN
ejpam-4637	48	28	,	,	PUNCT
ejpam-4637	48	29	z	z	PROPN
ejpam-4637	48	30	∈	∈	PROPN
ejpam-4637	48	31	x	x	X
ejpam-4637	48	32	,	,	PUNCT
ejpam-4637	48	33	(	(	PUNCT
ejpam-4637	48	34	hup1	hup1	PROPN
ejpam-4637	48	35	)	)	PUNCT
ejpam-4637	48	36	y	y	PROPN
ejpam-4637	48	37	◦	◦	NOUN
ejpam-4637	48	38	z	z	NOUN
ejpam-4637	48	39	≪	≪	PUNCT
ejpam-4637	48	40	(	(	PUNCT
ejpam-4637	48	41	x	x	SYM
ejpam-4637	48	42	◦	◦	VERB
ejpam-4637	48	43	y	y	NOUN
ejpam-4637	48	44	)	)	PUNCT
ejpam-4637	48	45	◦	◦	NOUN
ejpam-4637	48	46	(	(	PUNCT
ejpam-4637	48	47	x	x	PART
ejpam-4637	48	48	◦	◦	NOUN
ejpam-4637	48	49	z	z	PROPN
ejpam-4637	48	50	)	)	PUNCT
ejpam-4637	48	51	,	,	PUNCT
ejpam-4637	48	52	a.	a.	PROPN
ejpam-4637	48	53	cano	cano	PROPN
ejpam-4637	48	54	,	,	PUNCT
ejpam-4637	48	55	g.	g.	PROPN
ejpam-4637	48	56	petalcorin	petalcorin	PROPN
ejpam-4637	48	57	/	/	SYM
ejpam-4637	48	58	eur	eur	PROPN
ejpam-4637	48	59	.	.	PUNCT
ejpam-4637	49	1	j.	j.	PROPN
ejpam-4637	49	2	pure	pure	PROPN
ejpam-4637	49	3	appl	appl	PROPN
ejpam-4637	49	4	.	.	PROPN
ejpam-4637	49	5	math	math	PROPN
ejpam-4637	49	6	,	,	PUNCT
ejpam-4637	49	7	16	16	NUM
ejpam-4637	49	8	(	(	PUNCT
ejpam-4637	49	9	1	1	NUM
ejpam-4637	49	10	)	)	PUNCT
ejpam-4637	49	11	(	(	PUNCT
ejpam-4637	49	12	2023	2023	NUM
ejpam-4637	49	13	)	)	PUNCT
ejpam-4637	49	14	,	,	PUNCT
ejpam-4637	49	15	548	548	NUM
ejpam-4637	49	16	-	-	SYM
ejpam-4637	49	17	576	576	NUM
ejpam-4637	49	18	550	550	NUM
ejpam-4637	49	19	(	(	PUNCT
ejpam-4637	49	20	hup2	hup2	PROPN
ejpam-4637	49	21	)	)	PUNCT
ejpam-4637	49	22	x	x	PUNCT
ejpam-4637	49	23	◦	◦	NOUN
ejpam-4637	49	24	0	0	NUM
ejpam-4637	50	1	=	=	SYM
ejpam-4637	50	2	{	{	PUNCT
ejpam-4637	50	3	0	0	NUM
ejpam-4637	50	4	}	}	PUNCT
ejpam-4637	50	5	,	,	PUNCT
ejpam-4637	50	6	(	(	PUNCT
ejpam-4637	50	7	hup3	hup3	PROPN
ejpam-4637	50	8	)	)	PUNCT
ejpam-4637	50	9	0	0	PUNCT
ejpam-4637	51	1	◦	◦	NOUN
ejpam-4637	51	2	x	x	SYM
ejpam-4637	51	3	=	=	SYM
ejpam-4637	51	4	{	{	PUNCT
ejpam-4637	51	5	x	x	NOUN
ejpam-4637	51	6	}	}	PUNCT
ejpam-4637	51	7	,	,	PUNCT
ejpam-4637	51	8	and	and	CCONJ
ejpam-4637	51	9	(	(	PUNCT
ejpam-4637	51	10	hup4	hup4	PROPN
ejpam-4637	51	11	)	)	PUNCT
ejpam-4637	51	12	x	x	SYM
ejpam-4637	51	13	≪	≪	PUNCT
ejpam-4637	51	14	y	y	PROPN
ejpam-4637	51	15	∧	∧	PROPN
ejpam-4637	51	16	y	y	PROPN
ejpam-4637	51	17	≪	≪	ADJ
ejpam-4637	51	18	x	x	PUNCT
ejpam-4637	52	1	=	=	NOUN
ejpam-4637	52	2	⇒	⇒	NOUN
ejpam-4637	52	3	x	x	PUNCT
ejpam-4637	53	1	=	=	PUNCT
ejpam-4637	53	2	y.	y.	NOUN
ejpam-4637	53	3	example	example	NOUN
ejpam-4637	53	4	1	1	X
ejpam-4637	53	5	.	.	PUNCT
ejpam-4637	54	1	let	let	VERB
ejpam-4637	54	2	x	x	PUNCT
ejpam-4637	54	3	=	=	PUNCT
ejpam-4637	54	4	{	{	PUNCT
ejpam-4637	54	5	0	0	NUM
ejpam-4637	54	6	,	,	PUNCT
ejpam-4637	54	7	r	r	NOUN
ejpam-4637	54	8	,	,	PUNCT
ejpam-4637	54	9	s	s	PROPN
ejpam-4637	54	10	,	,	PUNCT
ejpam-4637	54	11	t	t	PROPN
ejpam-4637	54	12	}	}	PUNCT
ejpam-4637	54	13	be	be	AUX
ejpam-4637	54	14	a	a	DET
ejpam-4637	54	15	set	set	NOUN
ejpam-4637	54	16	.	.	PUNCT
ejpam-4637	55	1	if	if	SCONJ
ejpam-4637	55	2	we	we	PRON
ejpam-4637	55	3	define	define	VERB
ejpam-4637	55	4	a	a	DET
ejpam-4637	55	5	hyper	hyper	ADJ
ejpam-4637	55	6	operation	operation	NOUN
ejpam-4637	55	7	“	"	PUNCT
ejpam-4637	55	8	◦	◦	NOUN
ejpam-4637	55	9	”	"	PUNCT
ejpam-4637	55	10	as	as	ADP
ejpam-4637	55	11	following	follow	VERB
ejpam-4637	55	12	:	:	PUNCT
ejpam-4637	55	13	◦	◦	NOUN
ejpam-4637	55	14	0	0	NUM
ejpam-4637	55	15	r	r	NOUN
ejpam-4637	55	16	s	s	PROPN
ejpam-4637	55	17	t	t	NOUN
ejpam-4637	55	18	0	0	NUM
ejpam-4637	55	19	{	{	PUNCT
ejpam-4637	55	20	0	0	NUM
ejpam-4637	55	21	}	}	PUNCT
ejpam-4637	55	22	{	{	PUNCT
ejpam-4637	55	23	r	r	AUX
ejpam-4637	55	24	}	}	PUNCT
ejpam-4637	55	25	{	{	PUNCT
ejpam-4637	55	26	s	s	NOUN
ejpam-4637	55	27	}	}	PUNCT
ejpam-4637	55	28	{	{	PUNCT
ejpam-4637	55	29	t	t	PROPN
ejpam-4637	55	30	}	}	PUNCT
ejpam-4637	55	31	r	r	NOUN
ejpam-4637	55	32	{	{	PUNCT
ejpam-4637	55	33	0	0	NUM
ejpam-4637	55	34	}	}	PUNCT
ejpam-4637	55	35	{	{	PUNCT
ejpam-4637	55	36	0	0	NUM
ejpam-4637	55	37	,	,	PUNCT
ejpam-4637	55	38	r	r	NOUN
ejpam-4637	55	39	}	}	PUNCT
ejpam-4637	55	40	{	{	PUNCT
ejpam-4637	55	41	0	0	NUM
ejpam-4637	55	42	,	,	PUNCT
ejpam-4637	55	43	s	s	AUX
ejpam-4637	55	44	}	}	PUNCT
ejpam-4637	55	45	{	{	PUNCT
ejpam-4637	55	46	r	r	NOUN
ejpam-4637	55	47	,	,	PUNCT
ejpam-4637	55	48	s	s	PART
ejpam-4637	55	49	}	}	PUNCT
ejpam-4637	55	50	s	s	PART
ejpam-4637	55	51	{	{	PUNCT
ejpam-4637	55	52	0	0	NUM
ejpam-4637	55	53	}	}	PUNCT
ejpam-4637	55	54	{	{	PUNCT
ejpam-4637	55	55	r	r	NOUN
ejpam-4637	55	56	,	,	PUNCT
ejpam-4637	55	57	s	s	NOUN
ejpam-4637	55	58	}	}	PUNCT
ejpam-4637	55	59	{	{	PUNCT
ejpam-4637	55	60	0	0	NUM
ejpam-4637	55	61	,	,	PUNCT
ejpam-4637	55	62	s	s	AUX
ejpam-4637	55	63	}	}	PUNCT
ejpam-4637	55	64	{	{	PUNCT
ejpam-4637	55	65	r	r	NOUN
ejpam-4637	55	66	}	}	PUNCT
ejpam-4637	55	67	t	t	NOUN
ejpam-4637	55	68	{	{	PUNCT
ejpam-4637	55	69	0	0	NUM
ejpam-4637	55	70	}	}	PUNCT
ejpam-4637	55	71	{	{	PUNCT
ejpam-4637	55	72	0	0	NUM
ejpam-4637	55	73	,	,	PUNCT
ejpam-4637	55	74	r	r	NOUN
ejpam-4637	55	75	,	,	PUNCT
ejpam-4637	55	76	s	s	PROPN
ejpam-4637	55	77	,	,	PUNCT
ejpam-4637	55	78	t	t	PROPN
ejpam-4637	55	79	}	}	PUNCT
ejpam-4637	55	80	{	{	PUNCT
ejpam-4637	55	81	s	s	PROPN
ejpam-4637	55	82	,	,	PUNCT
ejpam-4637	55	83	t	t	PROPN
ejpam-4637	55	84	}	}	PUNCT
ejpam-4637	55	85	{	{	PUNCT
ejpam-4637	55	86	0	0	NUM
ejpam-4637	55	87	}	}	PUNCT
ejpam-4637	55	88	,	,	PUNCT
ejpam-4637	55	89	then	then	ADV
ejpam-4637	55	90	the	the	DET
ejpam-4637	55	91	routine	routine	ADJ
ejpam-4637	55	92	calculation	calculation	NOUN
ejpam-4637	55	93	will	will	AUX
ejpam-4637	55	94	show	show	VERB
ejpam-4637	55	95	that	that	SCONJ
ejpam-4637	55	96	(	(	PUNCT
ejpam-4637	55	97	x	x	NOUN
ejpam-4637	55	98	,	,	PUNCT
ejpam-4637	55	99	◦	◦	NOUN
ejpam-4637	55	100	,	,	PUNCT
ejpam-4637	55	101	≪	≪	ADJ
ejpam-4637	55	102	,	,	PUNCT
ejpam-4637	55	103	0	0	NUM
ejpam-4637	55	104	)	)	PUNCT
ejpam-4637	55	105	is	be	AUX
ejpam-4637	55	106	a	a	DET
ejpam-4637	55	107	hyper	hyper	ADJ
ejpam-4637	55	108	up	up	ADP
ejpam-4637	55	109	-algebra	-algebra	PROPN
ejpam-4637	55	110	.	.	PUNCT
ejpam-4637	55	111	example	example	NOUN
ejpam-4637	56	1	2	2	NUM
ejpam-4637	56	2	.	.	PUNCT
ejpam-4637	57	1	let	let	VERB
ejpam-4637	57	2	x	x	PUNCT
ejpam-4637	57	3	=	=	PUNCT
ejpam-4637	57	4	{	{	PUNCT
ejpam-4637	57	5	0	0	NUM
ejpam-4637	57	6	,	,	PUNCT
ejpam-4637	57	7	u	u	NOUN
ejpam-4637	57	8	,	,	PUNCT
ejpam-4637	57	9	v	v	NOUN
ejpam-4637	57	10	}	}	PUNCT
ejpam-4637	57	11	.	.	PUNCT
ejpam-4637	58	1	define	define	VERB
ejpam-4637	58	2	a	a	DET
ejpam-4637	58	3	hyper	hyper	ADJ
ejpam-4637	58	4	operation	operation	NOUN
ejpam-4637	58	5	“	"	PUNCT
ejpam-4637	58	6	◦	◦	NOUN
ejpam-4637	58	7	”	"	PUNCT
ejpam-4637	58	8	as	as	SCONJ
ejpam-4637	58	9	follows	follow	VERB
ejpam-4637	58	10	:	:	PUNCT
ejpam-4637	58	11	◦	◦	NOUN
ejpam-4637	58	12	0	0	NUM
ejpam-4637	58	13	u	u	NOUN
ejpam-4637	58	14	v	v	ADP
ejpam-4637	58	15	0	0	NUM
ejpam-4637	58	16	{	{	PUNCT
ejpam-4637	58	17	0	0	NUM
ejpam-4637	58	18	}	}	PUNCT
ejpam-4637	58	19	{	{	PUNCT
ejpam-4637	58	20	u	u	NOUN
ejpam-4637	58	21	}	}	PUNCT
ejpam-4637	58	22	{	{	PUNCT
ejpam-4637	58	23	v	v	NOUN
ejpam-4637	58	24	}	}	PUNCT
ejpam-4637	58	25	u	u	NOUN
ejpam-4637	58	26	{	{	PUNCT
ejpam-4637	58	27	0	0	NUM
ejpam-4637	58	28	}	}	PUNCT
ejpam-4637	58	29	{	{	PUNCT
ejpam-4637	58	30	0	0	NUM
ejpam-4637	58	31	,	,	PUNCT
ejpam-4637	58	32	u	u	NOUN
ejpam-4637	58	33	}	}	PUNCT
ejpam-4637	58	34	{	{	PUNCT
ejpam-4637	58	35	0	0	NUM
ejpam-4637	58	36	,	,	PUNCT
ejpam-4637	58	37	v	v	NOUN
ejpam-4637	58	38	}	}	PUNCT
ejpam-4637	58	39	v	v	NOUN
ejpam-4637	58	40	{	{	PUNCT
ejpam-4637	58	41	0	0	NUM
ejpam-4637	58	42	}	}	PUNCT
ejpam-4637	58	43	{	{	PUNCT
ejpam-4637	58	44	u	u	NOUN
ejpam-4637	58	45	,	,	PUNCT
ejpam-4637	58	46	v	v	NOUN
ejpam-4637	58	47	}	}	PUNCT
ejpam-4637	58	48	{	{	PUNCT
ejpam-4637	58	49	0	0	NUM
ejpam-4637	58	50	,	,	PUNCT
ejpam-4637	58	51	v	v	NOUN
ejpam-4637	58	52	}	}	PUNCT
ejpam-4637	58	53	.	.	PUNCT
ejpam-4637	59	1	by	by	ADP
ejpam-4637	59	2	routine	routine	ADJ
ejpam-4637	59	3	calculation	calculation	NOUN
ejpam-4637	59	4	,	,	PUNCT
ejpam-4637	59	5	(	(	PUNCT
ejpam-4637	59	6	x	x	NOUN
ejpam-4637	59	7	,	,	PUNCT
ejpam-4637	59	8	◦	◦	NOUN
ejpam-4637	59	9	,	,	PUNCT
ejpam-4637	59	10	≪	≪	ADJ
ejpam-4637	59	11	,	,	PUNCT
ejpam-4637	59	12	0	0	NUM
ejpam-4637	59	13	)	)	PUNCT
ejpam-4637	59	14	is	be	AUX
ejpam-4637	59	15	a	a	DET
ejpam-4637	59	16	hyper	hyper	ADJ
ejpam-4637	59	17	up	up	ADP
ejpam-4637	59	18	-algebra	-algebra	PROPN
ejpam-4637	59	19	.	.	PUNCT
ejpam-4637	59	20	example	example	NOUN
ejpam-4637	60	1	3	3	X
ejpam-4637	60	2	.	.	PUNCT
ejpam-4637	60	3	let	let	VERB
ejpam-4637	60	4	x	x	PUNCT
ejpam-4637	60	5	=	=	PUNCT
ejpam-4637	60	6	{	{	PUNCT
ejpam-4637	60	7	0	0	NUM
ejpam-4637	60	8	,	,	PUNCT
ejpam-4637	60	9	a	a	DET
ejpam-4637	60	10	,	,	PUNCT
ejpam-4637	60	11	b	b	NOUN
ejpam-4637	60	12	}	}	PUNCT
ejpam-4637	60	13	.	.	PUNCT
ejpam-4637	61	1	define	define	VERB
ejpam-4637	61	2	a	a	DET
ejpam-4637	61	3	hyper	hyper	ADJ
ejpam-4637	61	4	operation	operation	NOUN
ejpam-4637	61	5	“	"	PUNCT
ejpam-4637	61	6	◦	◦	NOUN
ejpam-4637	61	7	”	"	PUNCT
ejpam-4637	61	8	as	as	SCONJ
ejpam-4637	61	9	follows	follow	VERB
ejpam-4637	61	10	:	:	PUNCT
ejpam-4637	61	11	◦	◦	NOUN
ejpam-4637	61	12	0	0	NUM
ejpam-4637	61	13	a	a	DET
ejpam-4637	61	14	b	b	PROPN
ejpam-4637	61	15	0	0	NUM
ejpam-4637	61	16	{	{	PUNCT
ejpam-4637	61	17	0	0	NUM
ejpam-4637	61	18	}	}	PUNCT
ejpam-4637	61	19	{	{	PUNCT
ejpam-4637	61	20	a	a	NOUN
ejpam-4637	61	21	}	}	PUNCT
ejpam-4637	61	22	{	{	PUNCT
ejpam-4637	61	23	b	b	NOUN
ejpam-4637	61	24	}	}	PUNCT
ejpam-4637	61	25	a	a	DET
ejpam-4637	61	26	{	{	PUNCT
ejpam-4637	61	27	0	0	NUM
ejpam-4637	61	28	}	}	PUNCT
ejpam-4637	61	29	{	{	PUNCT
ejpam-4637	61	30	0	0	NUM
ejpam-4637	61	31	,	,	PUNCT
ejpam-4637	61	32	a	a	DET
ejpam-4637	61	33	,	,	PUNCT
ejpam-4637	61	34	b	b	NOUN
ejpam-4637	61	35	}	}	PUNCT
ejpam-4637	61	36	{	{	PUNCT
ejpam-4637	61	37	0	0	NUM
ejpam-4637	61	38	,	,	PUNCT
ejpam-4637	61	39	b	b	NOUN
ejpam-4637	61	40	}	}	PUNCT
ejpam-4637	61	41	b	b	PROPN
ejpam-4637	61	42	{	{	PUNCT
ejpam-4637	61	43	0	0	NUM
ejpam-4637	61	44	}	}	PUNCT
ejpam-4637	61	45	{	{	PUNCT
ejpam-4637	61	46	0	0	NUM
ejpam-4637	61	47	,	,	PUNCT
ejpam-4637	61	48	a	a	DET
ejpam-4637	61	49	,	,	PUNCT
ejpam-4637	61	50	b	b	NOUN
ejpam-4637	61	51	}	}	PUNCT
ejpam-4637	61	52	{	{	PUNCT
ejpam-4637	61	53	0	0	NUM
ejpam-4637	61	54	}	}	PUNCT
ejpam-4637	61	55	.	.	PUNCT
ejpam-4637	62	1	observe	observe	VERB
ejpam-4637	62	2	that	that	SCONJ
ejpam-4637	62	3	a	a	DET
ejpam-4637	62	4	≪	≪	ADJ
ejpam-4637	62	5	b	b	NOUN
ejpam-4637	62	6	and	and	CCONJ
ejpam-4637	62	7	b	b	PROPN
ejpam-4637	62	8	≪	≪	VERB
ejpam-4637	62	9	a.	a.	NOUN
ejpam-4637	62	10	but	but	CCONJ
ejpam-4637	62	11	a	a	DET
ejpam-4637	62	12	̸=	̸=	PROPN
ejpam-4637	62	13	b.	b.	PROPN
ejpam-4637	62	14	thus	thus	ADV
ejpam-4637	62	15	,	,	PUNCT
ejpam-4637	62	16	(	(	PUNCT
ejpam-4637	62	17	x	x	NOUN
ejpam-4637	62	18	,	,	PUNCT
ejpam-4637	62	19	◦	◦	NOUN
ejpam-4637	62	20	,	,	PUNCT
ejpam-4637	62	21	≪	≪	ADJ
ejpam-4637	62	22	,	,	PUNCT
ejpam-4637	62	23	0	0	NUM
ejpam-4637	62	24	)	)	PUNCT
ejpam-4637	62	25	does	do	AUX
ejpam-4637	62	26	not	not	PART
ejpam-4637	62	27	satisfy	satisfy	VERB
ejpam-4637	62	28	(	(	PUNCT
ejpam-4637	62	29	hup4	hup4	PROPN
ejpam-4637	62	30	)	)	PUNCT
ejpam-4637	62	31	and	and	CCONJ
ejpam-4637	62	32	so	so	ADV
ejpam-4637	62	33	it	it	PRON
ejpam-4637	62	34	is	be	AUX
ejpam-4637	62	35	not	not	PART
ejpam-4637	62	36	a	a	DET
ejpam-4637	62	37	hyper	hyper	ADJ
ejpam-4637	62	38	up	up	ADP
ejpam-4637	62	39	-algebra	-algebra	NOUN
ejpam-4637	62	40	.	.	PUNCT
ejpam-4637	63	1	proposition	proposition	NOUN
ejpam-4637	63	2	1	1	NUM
ejpam-4637	63	3	.	.	PUNCT
ejpam-4637	64	1	[	[	X
ejpam-4637	64	2	15	15	NUM
ejpam-4637	64	3	]	]	X
ejpam-4637	64	4	let	let	NOUN
ejpam-4637	64	5	(	(	PUNCT
ejpam-4637	64	6	h	h	NOUN
ejpam-4637	64	7	,	,	PUNCT
ejpam-4637	64	8	◦	◦	NOUN
ejpam-4637	64	9	,	,	PUNCT
ejpam-4637	64	10	≪	≪	ADJ
ejpam-4637	64	11	,	,	PUNCT
ejpam-4637	64	12	0	0	NUM
ejpam-4637	64	13	)	)	PUNCT
ejpam-4637	64	14	be	be	AUX
ejpam-4637	64	15	a	a	DET
ejpam-4637	64	16	hyper	hyper	ADJ
ejpam-4637	64	17	up	up	NOUN
ejpam-4637	64	18	-	-	PUNCT
ejpam-4637	64	19	algebra	algebra	NOUN
ejpam-4637	64	20	.	.	PUNCT
ejpam-4637	65	1	then	then	ADV
ejpam-4637	65	2	the	the	DET
ejpam-4637	65	3	following	follow	VERB
ejpam-4637	65	4	hold	hold	NOUN
ejpam-4637	65	5	for	for	ADP
ejpam-4637	65	6	all	all	DET
ejpam-4637	65	7	x	x	NOUN
ejpam-4637	65	8	,	,	PUNCT
ejpam-4637	65	9	y	y	PROPN
ejpam-4637	65	10	,	,	PUNCT
ejpam-4637	65	11	z	z	PROPN
ejpam-4637	65	12	∈	∈	PROPN
ejpam-4637	65	13	h	h	NOUN
ejpam-4637	65	14	and	and	CCONJ
ejpam-4637	65	15	for	for	ADP
ejpam-4637	65	16	every	every	DET
ejpam-4637	65	17	nonempty	nonempty	NOUN
ejpam-4637	65	18	subsets	subset	NOUN
ejpam-4637	65	19	a	a	DET
ejpam-4637	65	20	,	,	PUNCT
ejpam-4637	65	21	b	b	NOUN
ejpam-4637	65	22	,	,	PUNCT
ejpam-4637	65	23	c	c	PROPN
ejpam-4637	65	24	⊆	⊆	NUM
ejpam-4637	65	25	h	h	NOUN
ejpam-4637	65	26	:	:	PUNCT
ejpam-4637	65	27	(	(	PUNCT
ejpam-4637	65	28	i	i	NOUN
ejpam-4637	65	29	)	)	PUNCT
ejpam-4637	65	30	a	a	DET
ejpam-4637	65	31	⊆	⊆	NUM
ejpam-4637	65	32	b	b	NOUN
ejpam-4637	65	33	implies	imply	VERB
ejpam-4637	65	34	a	a	DET
ejpam-4637	65	35	≪	≪	ADJ
ejpam-4637	65	36	b	b	X
ejpam-4637	65	37	(	(	PUNCT
ejpam-4637	65	38	v	v	NOUN
ejpam-4637	65	39	)	)	PUNCT
ejpam-4637	65	40	z	z	NOUN
ejpam-4637	65	41	≪	≪	NOUN
ejpam-4637	65	42	x	x	PUNCT
ejpam-4637	65	43	◦	◦	NOUN
ejpam-4637	65	44	z	z	X
ejpam-4637	65	45	(	(	PUNCT
ejpam-4637	65	46	ii	ii	NOUN
ejpam-4637	65	47	)	)	PUNCT
ejpam-4637	65	48	0	0	PUNCT
ejpam-4637	66	1	◦	◦	NOUN
ejpam-4637	66	2	0	0	NUM
ejpam-4637	66	3	=	=	SYM
ejpam-4637	66	4	{	{	PUNCT
ejpam-4637	66	5	0	0	NUM
ejpam-4637	66	6	}	}	PUNCT
ejpam-4637	66	7	(	(	PUNCT
ejpam-4637	66	8	vi	vi	NOUN
ejpam-4637	66	9	)	)	PUNCT
ejpam-4637	66	10	a	a	DET
ejpam-4637	66	11	◦	◦	NOUN
ejpam-4637	66	12	0	0	NUM
ejpam-4637	66	13	=	=	SYM
ejpam-4637	66	14	{	{	PUNCT
ejpam-4637	66	15	0	0	NUM
ejpam-4637	66	16	}	}	PUNCT
ejpam-4637	66	17	(	(	PUNCT
ejpam-4637	66	18	iii	iii	NOUN
ejpam-4637	66	19	)	)	PUNCT
ejpam-4637	66	20	x	x	PUNCT
ejpam-4637	66	21	≪	≪	ADJ
ejpam-4637	66	22	0	0	NUM
ejpam-4637	66	23	(	(	PUNCT
ejpam-4637	66	24	vii	vii	PROPN
ejpam-4637	66	25	)	)	PUNCT
ejpam-4637	66	26	0	0	PUNCT
ejpam-4637	67	1	◦	◦	NOUN
ejpam-4637	67	2	a	a	PRON
ejpam-4637	67	3	=	=	X
ejpam-4637	67	4	a	a	DET
ejpam-4637	67	5	(	(	PUNCT
ejpam-4637	67	6	iv	iv	NOUN
ejpam-4637	67	7	)	)	PUNCT
ejpam-4637	67	8	x	x	PUNCT
ejpam-4637	67	9	≪	≪	VERB
ejpam-4637	67	10	x	x	X
ejpam-4637	67	11	(	(	PUNCT
ejpam-4637	67	12	viii	viii	NOUN
ejpam-4637	67	13	)	)	PUNCT
ejpam-4637	67	14	(	(	PUNCT
ejpam-4637	67	15	0	0	NUM
ejpam-4637	67	16	◦	◦	NOUN
ejpam-4637	67	17	0	0	NUM
ejpam-4637	67	18	)	)	PUNCT
ejpam-4637	67	19	◦	◦	NOUN
ejpam-4637	67	20	x	x	SYM
ejpam-4637	68	1	=	=	SYM
ejpam-4637	68	2	{	{	PUNCT
ejpam-4637	68	3	x	x	NOUN
ejpam-4637	68	4	}	}	PUNCT
ejpam-4637	68	5	proposition	proposition	NOUN
ejpam-4637	68	6	2	2	NUM
ejpam-4637	68	7	.	.	PUNCT
ejpam-4637	69	1	[	[	X
ejpam-4637	69	2	15	15	NUM
ejpam-4637	69	3	]	]	X
ejpam-4637	69	4	let	let	VERB
ejpam-4637	69	5	s	s	PRON
ejpam-4637	69	6	be	be	AUX
ejpam-4637	69	7	a	a	DET
ejpam-4637	69	8	nonempty	nonempty	ADJ
ejpam-4637	69	9	subset	subset	NOUN
ejpam-4637	69	10	of	of	ADP
ejpam-4637	69	11	a	a	DET
ejpam-4637	69	12	hyper	hyper	ADJ
ejpam-4637	69	13	up	up	ADP
ejpam-4637	69	14	-	-	PUNCT
ejpam-4637	69	15	algebra	algebra	NOUN
ejpam-4637	69	16	(	(	PUNCT
ejpam-4637	69	17	x	x	NOUN
ejpam-4637	69	18	,	,	PUNCT
ejpam-4637	69	19	◦	◦	NOUN
ejpam-4637	69	20	,	,	PUNCT
ejpam-4637	69	21	≪	≪	ADJ
ejpam-4637	69	22	,	,	PUNCT
ejpam-4637	69	23	0	0	NUM
ejpam-4637	69	24	)	)	PUNCT
ejpam-4637	69	25	.	.	PUNCT
ejpam-4637	70	1	then	then	ADV
ejpam-4637	70	2	s	s	VERB
ejpam-4637	70	3	is	be	AUX
ejpam-4637	70	4	a	a	DET
ejpam-4637	70	5	hyper	hyper	ADJ
ejpam-4637	70	6	up	up	ADP
ejpam-4637	70	7	-	-	PUNCT
ejpam-4637	70	8	subalgebra	subalgebra	NOUN
ejpam-4637	70	9	of	of	ADP
ejpam-4637	70	10	x	x	PRON
ejpam-4637	70	11	if	if	SCONJ
ejpam-4637	70	12	and	and	CCONJ
ejpam-4637	70	13	only	only	ADV
ejpam-4637	70	14	if	if	SCONJ
ejpam-4637	70	15	∀x	∀x	NUM
ejpam-4637	70	16	,	,	PUNCT
ejpam-4637	70	17	y	y	PROPN
ejpam-4637	70	18	∈	∈	PROPN
ejpam-4637	70	19	s	s	PART
ejpam-4637	70	20	,	,	PUNCT
ejpam-4637	70	21	x	x	VERB
ejpam-4637	70	22	◦	◦	VERB
ejpam-4637	70	23	y	y	PROPN
ejpam-4637	70	24	⊆	⊆	NUM
ejpam-4637	70	25	s.	s.	PROPN
ejpam-4637	70	26	definition	definition	NOUN
ejpam-4637	70	27	4	4	NUM
ejpam-4637	70	28	.	.	PUNCT
ejpam-4637	71	1	[	[	X
ejpam-4637	71	2	15	15	NUM
ejpam-4637	71	3	]	]	X
ejpam-4637	71	4	let	let	NOUN
ejpam-4637	71	5	(	(	PUNCT
ejpam-4637	71	6	x1	x1	ADJ
ejpam-4637	71	7	,	,	PUNCT
ejpam-4637	71	8	◦	◦	NOUN
ejpam-4637	71	9	1,≪1	1,≪1	NUM
ejpam-4637	71	10	,	,	PUNCT
ejpam-4637	71	11	01	01	NUM
ejpam-4637	71	12	)	)	PUNCT
ejpam-4637	71	13	and	and	CCONJ
ejpam-4637	71	14	(	(	PUNCT
ejpam-4637	71	15	x2	x2	NOUN
ejpam-4637	71	16	,	,	PUNCT
ejpam-4637	71	17	◦	◦	NOUN
ejpam-4637	71	18	2,≪2	2,≪2	NUM
ejpam-4637	71	19	,	,	PUNCT
ejpam-4637	71	20	02	02	NUM
ejpam-4637	71	21	)	)	PUNCT
ejpam-4637	71	22	be	be	AUX
ejpam-4637	71	23	hyper	hyper	ADJ
ejpam-4637	71	24	up	up	ADP
ejpam-4637	71	25	-algebras	-algebra	NOUN
ejpam-4637	71	26	.	.	PUNCT
ejpam-4637	72	1	a	a	DET
ejpam-4637	72	2	mapping	mapping	NOUN
ejpam-4637	72	3	f	f	NOUN
ejpam-4637	72	4	:	:	PUNCT
ejpam-4637	73	1	x1	x1	NUM
ejpam-4637	73	2	−→	−→	NOUN
ejpam-4637	73	3	x2	x2	PRON
ejpam-4637	73	4	is	be	AUX
ejpam-4637	73	5	called	call	VERB
ejpam-4637	73	6	a	a	DET
ejpam-4637	73	7	hyper	hyper	ADJ
ejpam-4637	73	8	homomorphism	homomorphism	NOUN
ejpam-4637	73	9	if	if	SCONJ
ejpam-4637	73	10	for	for	ADP
ejpam-4637	73	11	all	all	DET
ejpam-4637	73	12	a	a	PRON
ejpam-4637	73	13	,	,	PUNCT
ejpam-4637	73	14	b	b	PROPN
ejpam-4637	73	15	∈	∈	PROPN
ejpam-4637	73	16	x1	x1	PROPN
ejpam-4637	73	17	,	,	PUNCT
ejpam-4637	73	18	(	(	PUNCT
ejpam-4637	73	19	i	i	NOUN
ejpam-4637	73	20	)	)	PUNCT
ejpam-4637	73	21	f(01	f(01	NOUN
ejpam-4637	73	22	)	)	PUNCT
ejpam-4637	73	23	=	=	SYM
ejpam-4637	73	24	02	02	NUM
ejpam-4637	73	25	and	and	CCONJ
ejpam-4637	73	26	a.	a.	PROPN
ejpam-4637	73	27	cano	cano	PROPN
ejpam-4637	73	28	,	,	PUNCT
ejpam-4637	73	29	g.	g.	PROPN
ejpam-4637	73	30	petalcorin	petalcorin	PROPN
ejpam-4637	73	31	/	/	SYM
ejpam-4637	73	32	eur	eur	PROPN
ejpam-4637	73	33	.	.	PUNCT
ejpam-4637	74	1	j.	j.	PROPN
ejpam-4637	74	2	pure	pure	PROPN
ejpam-4637	74	3	appl	appl	PROPN
ejpam-4637	74	4	.	.	PROPN
ejpam-4637	74	5	math	math	PROPN
ejpam-4637	74	6	,	,	PUNCT
ejpam-4637	74	7	16	16	NUM
ejpam-4637	74	8	(	(	PUNCT
ejpam-4637	74	9	1	1	NUM
ejpam-4637	74	10	)	)	PUNCT
ejpam-4637	74	11	(	(	PUNCT
ejpam-4637	74	12	2023	2023	NUM
ejpam-4637	74	13	)	)	PUNCT
ejpam-4637	74	14	,	,	PUNCT
ejpam-4637	74	15	548	548	NUM
ejpam-4637	74	16	-	-	SYM
ejpam-4637	74	17	576	576	NUM
ejpam-4637	74	18	551	551	NUM
ejpam-4637	74	19	(	(	PUNCT
ejpam-4637	74	20	ii	ii	NOUN
ejpam-4637	74	21	)	)	PUNCT
ejpam-4637	74	22	f(a	f(a	PROPN
ejpam-4637	74	23	◦	◦	NOUN
ejpam-4637	74	24	1	1	NUM
ejpam-4637	74	25	b	b	NOUN
ejpam-4637	74	26	)	)	PUNCT
ejpam-4637	74	27	=	=	SYM
ejpam-4637	74	28	f(a	f(a	NOUN
ejpam-4637	74	29	)	)	PUNCT
ejpam-4637	74	30	◦	◦	NOUN
ejpam-4637	74	31	2	2	NUM
ejpam-4637	74	32	f(b	f(b	NOUN
ejpam-4637	74	33	)	)	PUNCT
ejpam-4637	74	34	.	.	PUNCT
ejpam-4637	75	1	definition	definition	NOUN
ejpam-4637	75	2	5	5	NUM
ejpam-4637	75	3	.	.	PUNCT
ejpam-4637	76	1	[	[	X
ejpam-4637	76	2	2	2	X
ejpam-4637	76	3	]	]	PUNCT
ejpam-4637	76	4	let	let	VERB
ejpam-4637	76	5	f	f	X
ejpam-4637	76	6	:	:	PUNCT
ejpam-4637	76	7	(	(	PUNCT
ejpam-4637	76	8	x1	x1	ADJ
ejpam-4637	76	9	,	,	PUNCT
ejpam-4637	76	10	◦	◦	NOUN
ejpam-4637	76	11	1,≪1	1,≪1	NUM
ejpam-4637	76	12	,	,	PUNCT
ejpam-4637	76	13	01	01	NUM
ejpam-4637	76	14	)	)	PUNCT
ejpam-4637	76	15	−→	−→	NOUN
ejpam-4637	76	16	(	(	PUNCT
ejpam-4637	76	17	x2	x2	NOUN
ejpam-4637	76	18	,	,	PUNCT
ejpam-4637	76	19	◦	◦	NOUN
ejpam-4637	76	20	2,≪2	2,≪2	NUM
ejpam-4637	76	21	,	,	PUNCT
ejpam-4637	76	22	02	02	NUM
ejpam-4637	76	23	)	)	PUNCT
ejpam-4637	76	24	be	be	AUX
ejpam-4637	76	25	a	a	DET
ejpam-4637	76	26	hyper	hyper	ADJ
ejpam-4637	76	27	homomorphism	homomorphism	NOUN
ejpam-4637	76	28	.	.	PUNCT
ejpam-4637	77	1	we	we	PRON
ejpam-4637	77	2	say	say	VERB
ejpam-4637	77	3	that	that	SCONJ
ejpam-4637	77	4	f	f	PROPN
ejpam-4637	77	5	is	be	AUX
ejpam-4637	77	6	a	a	DET
ejpam-4637	77	7	hyper	hyper	ADJ
ejpam-4637	77	8	monomorphism	monomorphism	NOUN
ejpam-4637	77	9	if	if	SCONJ
ejpam-4637	77	10	f	f	PROPN
ejpam-4637	77	11	is	be	AUX
ejpam-4637	77	12	one	one	NUM
ejpam-4637	77	13	-	-	PUNCT
ejpam-4637	77	14	to	to	ADP
ejpam-4637	77	15	-	-	PUNCT
ejpam-4637	77	16	one	one	NUM
ejpam-4637	77	17	and	and	CCONJ
ejpam-4637	77	18	f	f	PROPN
ejpam-4637	77	19	is	be	AUX
ejpam-4637	77	20	a	a	DET
ejpam-4637	77	21	hyper	hyper	ADJ
ejpam-4637	77	22	epimorphism	epimorphism	NOUN
ejpam-4637	77	23	if	if	SCONJ
ejpam-4637	77	24	f	f	PROPN
ejpam-4637	77	25	is	be	AUX
ejpam-4637	77	26	onto	onto	ADP
ejpam-4637	77	27	.	.	PUNCT
ejpam-4637	78	1	we	we	PRON
ejpam-4637	78	2	also	also	ADV
ejpam-4637	78	3	say	say	VERB
ejpam-4637	78	4	that	that	SCONJ
ejpam-4637	78	5	f	f	PROPN
ejpam-4637	78	6	is	be	AUX
ejpam-4637	78	7	a	a	DET
ejpam-4637	78	8	hyper	hyper	ADJ
ejpam-4637	78	9	isomorphism	isomorphism	NOUN
ejpam-4637	78	10	if	if	SCONJ
ejpam-4637	78	11	f	f	PROPN
ejpam-4637	78	12	is	be	AUX
ejpam-4637	78	13	both	both	PRON
ejpam-4637	78	14	one	one	NUM
ejpam-4637	78	15	-	-	PUNCT
ejpam-4637	78	16	to	to	ADP
ejpam-4637	78	17	-	-	PUNCT
ejpam-4637	78	18	one	one	NUM
ejpam-4637	78	19	and	and	CCONJ
ejpam-4637	78	20	onto	onto	ADP
ejpam-4637	78	21	.	.	PUNCT
ejpam-4637	79	1	in	in	ADP
ejpam-4637	79	2	this	this	DET
ejpam-4637	79	3	case	case	NOUN
ejpam-4637	79	4	,	,	PUNCT
ejpam-4637	79	5	x1	x1	PROPN
ejpam-4637	79	6	and	and	CCONJ
ejpam-4637	79	7	x2	x2	PROPN
ejpam-4637	79	8	are	be	AUX
ejpam-4637	79	9	hyper	hyper	ADJ
ejpam-4637	79	10	isomorphic	isomorphic	ADJ
ejpam-4637	79	11	which	which	PRON
ejpam-4637	79	12	is	be	AUX
ejpam-4637	79	13	denoted	denote	VERB
ejpam-4637	79	14	as	as	ADP
ejpam-4637	79	15	x1	x1	PROPN
ejpam-4637	79	16	∼=h	∼=h	NOUN
ejpam-4637	79	17	x2	x2	PROPN
ejpam-4637	79	18	.	.	PUNCT
ejpam-4637	80	1	definition	definition	NOUN
ejpam-4637	80	2	6	6	NUM
ejpam-4637	80	3	.	.	PUNCT
ejpam-4637	81	1	[	[	X
ejpam-4637	81	2	2	2	NUM
ejpam-4637	81	3	]	]	X
ejpam-4637	81	4	let	let	VERB
ejpam-4637	81	5	(	(	PUNCT
ejpam-4637	81	6	x1	x1	ADJ
ejpam-4637	81	7	,	,	PUNCT
ejpam-4637	81	8	◦	◦	NOUN
ejpam-4637	81	9	1,≪1	1,≪1	NUM
ejpam-4637	81	10	,	,	PUNCT
ejpam-4637	81	11	01	01	NUM
ejpam-4637	81	12	)	)	PUNCT
ejpam-4637	81	13	and	and	CCONJ
ejpam-4637	81	14	(	(	PUNCT
ejpam-4637	81	15	x2	x2	NOUN
ejpam-4637	81	16	,	,	PUNCT
ejpam-4637	81	17	◦	◦	NOUN
ejpam-4637	81	18	2,≪2	2,≪2	NUM
ejpam-4637	81	19	,	,	PUNCT
ejpam-4637	81	20	02	02	NUM
ejpam-4637	81	21	)	)	PUNCT
ejpam-4637	81	22	be	be	AUX
ejpam-4637	81	23	hyper	hyper	ADJ
ejpam-4637	81	24	up	up	ADP
ejpam-4637	81	25	-algebras	-algebra	NOUN
ejpam-4637	81	26	.	.	PUNCT
ejpam-4637	82	1	define	define	VERB
ejpam-4637	82	2	a	a	DET
ejpam-4637	82	3	set	set	NOUN
ejpam-4637	82	4	x1	x1	NOUN
ejpam-4637	82	5	×x2	×x2	NOUN
ejpam-4637	82	6	by	by	ADP
ejpam-4637	82	7	x1	x1	PROPN
ejpam-4637	82	8	×x2	×x2	NOUN
ejpam-4637	82	9	=	=	SYM
ejpam-4637	82	10	{	{	PUNCT
ejpam-4637	82	11	(	(	PUNCT
ejpam-4637	82	12	a	a	DET
ejpam-4637	82	13	,	,	PUNCT
ejpam-4637	82	14	b	b	NOUN
ejpam-4637	82	15	)	)	PUNCT
ejpam-4637	82	16	:	:	PUNCT
ejpam-4637	82	17	a	a	DET
ejpam-4637	82	18	∈	∈	PROPN
ejpam-4637	82	19	x1	x1	PROPN
ejpam-4637	82	20	and	and	CCONJ
ejpam-4637	82	21	b	b	NOUN
ejpam-4637	82	22	∈	∈	PROPN
ejpam-4637	82	23	x2	x2	PROPN
ejpam-4637	82	24	}	}	PUNCT
ejpam-4637	82	25	.	.	PUNCT
ejpam-4637	83	1	with	with	ADP
ejpam-4637	83	2	a	a	DET
ejpam-4637	83	3	hyperoperation	hyperoperation	NOUN
ejpam-4637	83	4	“	"	PUNCT
ejpam-4637	83	5	◦	◦	NOUN
ejpam-4637	83	6	”	"	PUNCT
ejpam-4637	83	7	on	on	ADP
ejpam-4637	83	8	x1	x1	ADJ
ejpam-4637	83	9	×x2	×x2	NOUN
ejpam-4637	83	10	given	give	VERB
ejpam-4637	83	11	by	by	ADP
ejpam-4637	83	12	(	(	PUNCT
ejpam-4637	83	13	a	a	PRON
ejpam-4637	83	14	,	,	PUNCT
ejpam-4637	83	15	b	b	NOUN
ejpam-4637	83	16	)	)	PUNCT
ejpam-4637	83	17	◦	◦	NOUN
ejpam-4637	83	18	(	(	PUNCT
ejpam-4637	83	19	c	c	X
ejpam-4637	83	20	,	,	PUNCT
ejpam-4637	83	21	d	d	NOUN
ejpam-4637	83	22	)	)	PUNCT
ejpam-4637	83	23	=	=	SYM
ejpam-4637	83	24	(	(	PUNCT
ejpam-4637	83	25	a	a	DET
ejpam-4637	83	26	◦	◦	NOUN
ejpam-4637	83	27	1	1	NUM
ejpam-4637	83	28	c	c	NOUN
ejpam-4637	83	29	,	,	PUNCT
ejpam-4637	83	30	b	b	X
ejpam-4637	83	31	◦	◦	NOUN
ejpam-4637	83	32	2	2	NUM
ejpam-4637	83	33	d	d	NOUN
ejpam-4637	83	34	)	)	PUNCT
ejpam-4637	83	35	and	and	CCONJ
ejpam-4637	83	36	a	a	DET
ejpam-4637	83	37	hyperorder	hyperorder	NOUN
ejpam-4637	83	38	“	"	PUNCT
ejpam-4637	83	39	≪	≪	VERB
ejpam-4637	83	40	”	"	PUNCT
ejpam-4637	83	41	given	give	VERB
ejpam-4637	83	42	by	by	ADP
ejpam-4637	83	43	(	(	PUNCT
ejpam-4637	83	44	a	a	DET
ejpam-4637	83	45	,	,	PUNCT
ejpam-4637	83	46	b	b	NOUN
ejpam-4637	83	47	)	)	PUNCT
ejpam-4637	83	48	≪	≪	PUNCT
ejpam-4637	83	49	(	(	PUNCT
ejpam-4637	83	50	c	c	X
ejpam-4637	83	51	,	,	PUNCT
ejpam-4637	83	52	d	d	NOUN
ejpam-4637	83	53	)	)	PUNCT
ejpam-4637	83	54	⇐	⇐	ADJ
ejpam-4637	83	55	⇒	⇒	NOUN
ejpam-4637	83	56	a	a	DET
ejpam-4637	83	57	≪1	≪1	PUNCT
ejpam-4637	83	58	c	c	NOUN
ejpam-4637	83	59	and	and	CCONJ
ejpam-4637	83	60	b	b	NOUN
ejpam-4637	83	61	≪2	≪2	X
ejpam-4637	83	62	d	d	NOUN
ejpam-4637	83	63	for	for	ADP
ejpam-4637	83	64	all	all	PRON
ejpam-4637	83	65	(	(	PUNCT
ejpam-4637	83	66	a	a	DET
ejpam-4637	83	67	,	,	PUNCT
ejpam-4637	83	68	b	b	NOUN
ejpam-4637	83	69	)	)	PUNCT
ejpam-4637	83	70	,	,	PUNCT
ejpam-4637	83	71	(	(	PUNCT
ejpam-4637	83	72	c	c	X
ejpam-4637	83	73	,	,	PUNCT
ejpam-4637	83	74	d	d	NOUN
ejpam-4637	83	75	)	)	PUNCT
ejpam-4637	83	76	∈	∈	PROPN
ejpam-4637	83	77	x1	x1	PROPN
ejpam-4637	83	78	×x2	×x2	PROPN
ejpam-4637	83	79	..	..	PUNCT
ejpam-4637	83	80	then	then	ADV
ejpam-4637	83	81	(	(	PUNCT
ejpam-4637	83	82	x1	x1	ADJ
ejpam-4637	83	83	×x2	×x2	PROPN
ejpam-4637	83	84	,	,	PUNCT
ejpam-4637	83	85	◦	◦	NOUN
ejpam-4637	83	86	,	,	PUNCT
ejpam-4637	83	87	≪	≪	ADJ
ejpam-4637	83	88	,	,	PUNCT
ejpam-4637	83	89	(	(	PUNCT
ejpam-4637	83	90	01	01	NUM
ejpam-4637	83	91	,	,	PUNCT
ejpam-4637	83	92	02	02	NUM
ejpam-4637	83	93	)	)	PUNCT
ejpam-4637	83	94	)	)	PUNCT
ejpam-4637	83	95	is	be	AUX
ejpam-4637	83	96	called	call	VERB
ejpam-4637	83	97	the	the	DET
ejpam-4637	83	98	hyper	hyper	ADJ
ejpam-4637	83	99	product	product	NOUN
ejpam-4637	83	100	of	of	ADP
ejpam-4637	83	101	x1	x1	PROPN
ejpam-4637	83	102	and	and	CCONJ
ejpam-4637	83	103	x2	x2	PROPN
ejpam-4637	83	104	.	.	PUNCT
ejpam-4637	84	1	definition	definition	NOUN
ejpam-4637	84	2	7	7	NUM
ejpam-4637	84	3	.	.	PUNCT
ejpam-4637	85	1	[	[	X
ejpam-4637	85	2	18	18	NUM
ejpam-4637	85	3	]	]	PUNCT
ejpam-4637	85	4	let	let	VERB
ejpam-4637	85	5	u	u	PRON
ejpam-4637	85	6	be	be	AUX
ejpam-4637	85	7	the	the	DET
ejpam-4637	85	8	universe	universe	NOUN
ejpam-4637	85	9	.	.	PUNCT
ejpam-4637	86	1	a	a	DET
ejpam-4637	86	2	neutrosophic	neutrosophic	ADJ
ejpam-4637	86	3	set	set	NOUN
ejpam-4637	86	4	a	a	PRON
ejpam-4637	86	5	is	be	AUX
ejpam-4637	86	6	characterized	characterize	VERB
ejpam-4637	86	7	by	by	ADP
ejpam-4637	86	8	a	a	DET
ejpam-4637	86	9	truth	truth	NOUN
ejpam-4637	86	10	membership	membership	NOUN
ejpam-4637	86	11	function	function	NOUN
ejpam-4637	86	12	ta	ta	PROPN
ejpam-4637	86	13	,	,	PUNCT
ejpam-4637	86	14	an	an	DET
ejpam-4637	86	15	indeterminacy	indeterminacy	NOUN
ejpam-4637	86	16	membership	membership	NOUN
ejpam-4637	86	17	function	function	PROPN
ejpam-4637	86	18	ia	ia	PROPN
ejpam-4637	86	19	,	,	PUNCT
ejpam-4637	86	20	and	and	CCONJ
ejpam-4637	86	21	a	a	DET
ejpam-4637	86	22	falsity	falsity	NOUN
ejpam-4637	86	23	membership	membership	NOUN
ejpam-4637	86	24	function	function	NOUN
ejpam-4637	86	25	fa	fa	INTJ
ejpam-4637	86	26	where	where	SCONJ
ejpam-4637	86	27	ta	ta	PROPN
ejpam-4637	86	28	,	,	PUNCT
ejpam-4637	86	29	ia	ia	PROPN
ejpam-4637	86	30	,	,	PUNCT
ejpam-4637	86	31	fa	fa	PROPN
ejpam-4637	86	32	are	be	AUX
ejpam-4637	86	33	real	real	ADV
ejpam-4637	86	34	standard	standard	ADJ
ejpam-4637	86	35	or	or	CCONJ
ejpam-4637	86	36	non	non	ADJ
ejpam-4637	86	37	-	-	ADJ
ejpam-4637	86	38	standard	standard	ADJ
ejpam-4637	86	39	elements	element	NOUN
ejpam-4637	86	40	of	of	ADP
ejpam-4637	86	41	]	]	PUNCT
ejpam-4637	86	42	−0	−0	NOUN
ejpam-4637	86	43	,	,	PUNCT
ejpam-4637	86	44	1	1	NUM
ejpam-4637	86	45	+	+	NOUN
ejpam-4637	86	46	[	[	PUNCT
ejpam-4637	86	47	with	with	ADP
ejpam-4637	86	48	−0	−0	NOUN
ejpam-4637	86	49	=	=	SYM
ejpam-4637	87	1	0−	0−	NUM
ejpam-4637	87	2	ϵ	ϵ	X
ejpam-4637	87	3	and	and	CCONJ
ejpam-4637	87	4	1	1	NUM
ejpam-4637	87	5	+	+	NUM
ejpam-4637	87	6	=	=	SYM
ejpam-4637	87	7	1	1	NUM
ejpam-4637	87	8	+	+	CCONJ
ejpam-4637	87	9	ϵ	ϵ	X
ejpam-4637	87	10	for	for	ADP
ejpam-4637	87	11	any	any	DET
ejpam-4637	87	12	infinitesimal	infinitesimal	ADJ
ejpam-4637	87	13	number	number	NOUN
ejpam-4637	87	14	ϵ.	ϵ.	NOUN
ejpam-4637	87	15	it	it	PRON
ejpam-4637	87	16	can	can	AUX
ejpam-4637	87	17	be	be	AUX
ejpam-4637	87	18	written	write	VERB
ejpam-4637	87	19	as	as	ADP
ejpam-4637	87	20	a	a	DET
ejpam-4637	87	21	=	=	X
ejpam-4637	87	22	{	{	PUNCT
ejpam-4637	87	23	⟨x	⟨x	NUM
ejpam-4637	87	24	,	,	PUNCT
ejpam-4637	87	25	(	(	PUNCT
ejpam-4637	87	26	ta(x	ta(x	NOUN
ejpam-4637	87	27	)	)	PUNCT
ejpam-4637	87	28	,	,	PUNCT
ejpam-4637	87	29	ia(x),fa(x))⟩	ia(x),fa(x))⟩	VERB
ejpam-4637	87	30	|x	|x	NOUN
ejpam-4637	87	31	∈	∈	PROPN
ejpam-4637	87	32	u	u	NOUN
ejpam-4637	87	33	}	}	PUNCT
ejpam-4637	87	34	where	where	SCONJ
ejpam-4637	87	35	ta	ta	PROPN
ejpam-4637	87	36	,	,	PUNCT
ejpam-4637	87	37	ia	ia	PROPN
ejpam-4637	87	38	,	,	PUNCT
ejpam-4637	87	39	fa	fa	INTJ
ejpam-4637	87	40	:	:	PUNCT
ejpam-4637	87	41	u	u	PROPN
ejpam-4637	87	42	−→]−0	−→]−0	PROPN
ejpam-4637	87	43	,	,	PUNCT
ejpam-4637	87	44	1	1	NUM
ejpam-4637	87	45	+	+	NOUN
ejpam-4637	87	46	[	[	PUNCT
ejpam-4637	87	47	and	and	CCONJ
ejpam-4637	87	48	−0	−0	NOUN
ejpam-4637	87	49	≤	≤	NOUN
ejpam-4637	87	50	ta(x	ta(x	NOUN
ejpam-4637	87	51	)	)	PUNCT
ejpam-4637	87	52	+	+	NUM
ejpam-4637	87	53	ia(x	ia(x	NOUN
ejpam-4637	87	54	)	)	PUNCT
ejpam-4637	88	1	+	+	CCONJ
ejpam-4637	88	2	fa(x	fa(x	NOUN
ejpam-4637	88	3	)	)	PUNCT
ejpam-4637	88	4	≤	≤	NOUN
ejpam-4637	88	5	3	3	NUM
ejpam-4637	88	6	+	+	NOUN
ejpam-4637	88	7	.	.	PUNCT
ejpam-4637	89	1	however	however	ADV
ejpam-4637	89	2	,	,	PUNCT
ejpam-4637	89	3	it	it	PRON
ejpam-4637	89	4	is	be	AUX
ejpam-4637	89	5	difficult	difficult	ADJ
ejpam-4637	89	6	to	to	PART
ejpam-4637	89	7	use	use	VERB
ejpam-4637	89	8	a	a	DET
ejpam-4637	89	9	neutrosophic	neutrosophic	ADJ
ejpam-4637	89	10	set	set	VERB
ejpam-4637	89	11	with	with	ADP
ejpam-4637	89	12	values	value	NOUN
ejpam-4637	89	13	from	from	ADP
ejpam-4637	89	14	real	real	ADJ
ejpam-4637	89	15	standard	standard	ADJ
ejpam-4637	89	16	or	or	CCONJ
ejpam-4637	89	17	nonstandard	nonstandard	ADJ
ejpam-4637	89	18	subsets	subset	NOUN
ejpam-4637	89	19	of	of	ADP
ejpam-4637	89	20	]	]	PUNCT
ejpam-4637	89	21	−0	−0	NOUN
ejpam-4637	89	22	,	,	PUNCT
ejpam-4637	89	23	1	1	NUM
ejpam-4637	89	24	+	+	NOUN
ejpam-4637	89	25	[	[	PUNCT
ejpam-4637	89	26	in	in	ADP
ejpam-4637	89	27	real	real	ADJ
ejpam-4637	89	28	life	life	NOUN
ejpam-4637	89	29	application	application	NOUN
ejpam-4637	89	30	especially	especially	ADV
ejpam-4637	89	31	scientific	scientific	ADJ
ejpam-4637	89	32	and	and	CCONJ
ejpam-4637	89	33	engineering	engineering	NOUN
ejpam-4637	89	34	problem	problem	NOUN
ejpam-4637	89	35	[	[	X
ejpam-4637	89	36	22	22	NUM
ejpam-4637	89	37	]	]	PUNCT
ejpam-4637	89	38	.	.	PUNCT
ejpam-4637	90	1	so	so	ADV
ejpam-4637	90	2	,	,	PUNCT
ejpam-4637	90	3	this	this	DET
ejpam-4637	90	4	paper	paper	NOUN
ejpam-4637	90	5	considers	consider	VERB
ejpam-4637	90	6	the	the	DET
ejpam-4637	90	7	neutrosophic	neutrosophic	ADJ
ejpam-4637	90	8	set	set	NOUN
ejpam-4637	90	9	which	which	PRON
ejpam-4637	90	10	takes	take	VERB
ejpam-4637	90	11	values	value	NOUN
ejpam-4637	90	12	from	from	ADP
ejpam-4637	90	13	the	the	DET
ejpam-4637	90	14	interval	interval	NOUN
ejpam-4637	90	15	[	[	X
ejpam-4637	90	16	0	0	NUM
ejpam-4637	90	17	,	,	PUNCT
ejpam-4637	90	18	1	1	NUM
ejpam-4637	90	19	]	]	PUNCT
ejpam-4637	90	20	.	.	PUNCT
ejpam-4637	91	1	definition	definition	NOUN
ejpam-4637	91	2	8	8	NUM
ejpam-4637	91	3	.	.	PUNCT
ejpam-4637	92	1	[	[	X
ejpam-4637	92	2	22	22	NUM
ejpam-4637	92	3	]	]	PUNCT
ejpam-4637	92	4	let	let	VERB
ejpam-4637	92	5	x	x	PRON
ejpam-4637	92	6	be	be	AUX
ejpam-4637	92	7	a	a	DET
ejpam-4637	92	8	space	space	NOUN
ejpam-4637	92	9	of	of	ADP
ejpam-4637	92	10	points	point	NOUN
ejpam-4637	92	11	(	(	PUNCT
ejpam-4637	92	12	objects	object	NOUN
ejpam-4637	92	13	)	)	PUNCT
ejpam-4637	92	14	,	,	PUNCT
ejpam-4637	92	15	with	with	ADP
ejpam-4637	92	16	a	a	DET
ejpam-4637	92	17	generic	generic	ADJ
ejpam-4637	92	18	element	element	NOUN
ejpam-4637	92	19	in	in	ADP
ejpam-4637	92	20	x	x	PUNCT
ejpam-4637	92	21	denoted	denote	VERB
ejpam-4637	92	22	by	by	ADP
ejpam-4637	92	23	x.	x.	PROPN
ejpam-4637	92	24	a	a	DET
ejpam-4637	92	25	single	single	ADJ
ejpam-4637	92	26	valued	value	VERB
ejpam-4637	92	27	neutrosophic	neutrosophic	ADJ
ejpam-4637	92	28	set	set	NOUN
ejpam-4637	92	29	(	(	PUNCT
ejpam-4637	92	30	svns	svns	PROPN
ejpam-4637	92	31	)	)	PUNCT
ejpam-4637	92	32	a	a	PRON
ejpam-4637	92	33	in	in	NOUN
ejpam-4637	92	34	x	x	SYM
ejpam-4637	92	35	is	be	AUX
ejpam-4637	92	36	characterized	characterize	VERB
ejpam-4637	92	37	by	by	ADP
ejpam-4637	92	38	truthmembership	truthmembership	NOUN
ejpam-4637	92	39	function	function	NOUN
ejpam-4637	92	40	ta	ta	PROPN
ejpam-4637	92	41	,	,	PUNCT
ejpam-4637	92	42	indeterminacy	indeterminacy	NOUN
ejpam-4637	92	43	-	-	PUNCT
ejpam-4637	92	44	membership	membership	NOUN
ejpam-4637	92	45	function	function	NOUN
ejpam-4637	92	46	ia	ia	PROPN
ejpam-4637	92	47	and	and	CCONJ
ejpam-4637	92	48	falsity	falsity	NOUN
ejpam-4637	92	49	-	-	PUNCT
ejpam-4637	92	50	membership	membership	NOUN
ejpam-4637	92	51	function	function	NOUN
ejpam-4637	92	52	fa	fa	PROPN
ejpam-4637	92	53	.	.	PROPN
ejpam-4637	93	1	for	for	ADP
ejpam-4637	93	2	each	each	DET
ejpam-4637	93	3	point	point	NOUN
ejpam-4637	93	4	x	x	X
ejpam-4637	93	5	∈	∈	NOUN
ejpam-4637	93	6	x	x	NOUN
ejpam-4637	93	7	,	,	PUNCT
ejpam-4637	93	8	ta(x	ta(x	NOUN
ejpam-4637	93	9	)	)	PUNCT
ejpam-4637	93	10	,	,	PUNCT
ejpam-4637	93	11	ia(x),fa(x	ia(x),fa(x	PROPN
ejpam-4637	93	12	)	)	PUNCT
ejpam-4637	93	13	∈	∈	NOUN
ejpam-4637	94	1	[	[	X
ejpam-4637	94	2	0	0	NUM
ejpam-4637	94	3	,	,	PUNCT
ejpam-4637	94	4	1	1	NUM
ejpam-4637	94	5	]	]	PUNCT
ejpam-4637	94	6	.	.	PUNCT
ejpam-4637	95	1	definition	definition	NOUN
ejpam-4637	95	2	9	9	NUM
ejpam-4637	95	3	.	.	PUNCT
ejpam-4637	96	1	[	[	X
ejpam-4637	96	2	14	14	NUM
ejpam-4637	96	3	]	]	PUNCT
ejpam-4637	96	4	given	give	VERB
ejpam-4637	96	5	an	an	DET
ejpam-4637	96	6	initial	initial	ADJ
ejpam-4637	96	7	universe	universe	NOUN
ejpam-4637	96	8	set	set	VERB
ejpam-4637	96	9	u	u	NOUN
ejpam-4637	96	10	and	and	CCONJ
ejpam-4637	96	11	set	set	VERB
ejpam-4637	96	12	e	e	PROPN
ejpam-4637	96	13	of	of	ADP
ejpam-4637	96	14	parameters	parameter	NOUN
ejpam-4637	96	15	or	or	CCONJ
ejpam-4637	96	16	attributes	attribute	NOUN
ejpam-4637	96	17	with	with	ADP
ejpam-4637	96	18	respect	respect	NOUN
ejpam-4637	96	19	to	to	ADP
ejpam-4637	96	20	u	u	PRON
ejpam-4637	96	21	,	,	PUNCT
ejpam-4637	96	22	let	let	VERB
ejpam-4637	96	23	p(u	p(u	ADJ
ejpam-4637	96	24	)	)	PUNCT
ejpam-4637	96	25	denote	denote	VERB
ejpam-4637	96	26	the	the	DET
ejpam-4637	96	27	power	power	NOUN
ejpam-4637	96	28	set	set	NOUN
ejpam-4637	96	29	of	of	ADP
ejpam-4637	96	30	u	u	PROPN
ejpam-4637	96	31	and	and	CCONJ
ejpam-4637	96	32	a	a	DET
ejpam-4637	96	33	⊆	⊆	NUM
ejpam-4637	96	34	e.	e.	PROPN
ejpam-4637	96	35	a	a	DET
ejpam-4637	96	36	pair	pair	NOUN
ejpam-4637	96	37	(	(	PUNCT
ejpam-4637	96	38	f	f	X
ejpam-4637	96	39	,	,	PUNCT
ejpam-4637	96	40	a	a	PRON
ejpam-4637	96	41	)	)	PUNCT
ejpam-4637	96	42	is	be	AUX
ejpam-4637	96	43	called	call	VERB
ejpam-4637	96	44	a	a	DET
ejpam-4637	96	45	soft	soft	ADJ
ejpam-4637	96	46	set	set	NOUN
ejpam-4637	96	47	over	over	ADP
ejpam-4637	96	48	u	u	PROPN
ejpam-4637	96	49	,	,	PUNCT
ejpam-4637	96	50	where	where	SCONJ
ejpam-4637	96	51	f	f	PROPN
ejpam-4637	96	52	is	be	AUX
ejpam-4637	96	53	a	a	DET
ejpam-4637	96	54	mapping	mapping	NOUN
ejpam-4637	96	55	given	give	VERB
ejpam-4637	96	56	by	by	ADP
ejpam-4637	96	57	f	f	PROPN
ejpam-4637	96	58	:	:	PUNCT
ejpam-4637	96	59	a	a	DET
ejpam-4637	96	60	−→	−→	NOUN
ejpam-4637	96	61	p(u	p(u	NOUN
ejpam-4637	96	62	)	)	PUNCT
ejpam-4637	96	63	.	.	PUNCT
ejpam-4637	97	1	for	for	ADP
ejpam-4637	97	2	any	any	DET
ejpam-4637	97	3	ϵ	ϵ	PROPN
ejpam-4637	97	4	∈	∈	PROPN
ejpam-4637	97	5	a	a	PRON
ejpam-4637	97	6	,	,	PUNCT
ejpam-4637	97	7	f	f	PROPN
ejpam-4637	97	8	(	(	PUNCT
ejpam-4637	97	9	ϵ	ϵ	X
ejpam-4637	97	10	)	)	PUNCT
ejpam-4637	97	11	may	may	AUX
ejpam-4637	97	12	be	be	AUX
ejpam-4637	97	13	considered	consider	VERB
ejpam-4637	97	14	as	as	ADP
ejpam-4637	97	15	the	the	DET
ejpam-4637	97	16	set	set	NOUN
ejpam-4637	97	17	of	of	ADP
ejpam-4637	97	18	ϵ-approximate	ϵ-approximate	NOUN
ejpam-4637	97	19	elements	element	NOUN
ejpam-4637	97	20	of	of	ADP
ejpam-4637	97	21	the	the	DET
ejpam-4637	97	22	soft	soft	ADJ
ejpam-4637	97	23	set	set	NOUN
ejpam-4637	97	24	(	(	PUNCT
ejpam-4637	97	25	f	f	X
ejpam-4637	97	26	,	,	PUNCT
ejpam-4637	97	27	a	a	PRON
ejpam-4637	97	28	)	)	PUNCT
ejpam-4637	97	29	.	.	PUNCT
ejpam-4637	98	1	a.	a.	PROPN
ejpam-4637	98	2	cano	cano	PROPN
ejpam-4637	98	3	,	,	PUNCT
ejpam-4637	98	4	g.	g.	PROPN
ejpam-4637	98	5	petalcorin	petalcorin	PROPN
ejpam-4637	98	6	/	/	SYM
ejpam-4637	98	7	eur	eur	PROPN
ejpam-4637	98	8	.	.	PUNCT
ejpam-4637	99	1	j.	j.	PROPN
ejpam-4637	99	2	pure	pure	PROPN
ejpam-4637	99	3	appl	appl	PROPN
ejpam-4637	99	4	.	.	PROPN
ejpam-4637	99	5	math	math	PROPN
ejpam-4637	99	6	,	,	PUNCT
ejpam-4637	99	7	16	16	NUM
ejpam-4637	99	8	(	(	PUNCT
ejpam-4637	99	9	1	1	NUM
ejpam-4637	99	10	)	)	PUNCT
ejpam-4637	99	11	(	(	PUNCT
ejpam-4637	99	12	2023	2023	NUM
ejpam-4637	99	13	)	)	PUNCT
ejpam-4637	99	14	,	,	PUNCT
ejpam-4637	99	15	548	548	NUM
ejpam-4637	99	16	-	-	SYM
ejpam-4637	99	17	576	576	NUM
ejpam-4637	99	18	552	552	NUM
ejpam-4637	99	19	the	the	DET
ejpam-4637	99	20	concept	concept	NOUN
ejpam-4637	99	21	of	of	ADP
ejpam-4637	99	22	neutrosophic	neutrosophic	ADJ
ejpam-4637	99	23	soft	soft	ADJ
ejpam-4637	99	24	set	set	NOUN
ejpam-4637	99	25	was	be	AUX
ejpam-4637	99	26	first	first	ADV
ejpam-4637	99	27	defined	define	VERB
ejpam-4637	99	28	by	by	ADP
ejpam-4637	99	29	maji	maji	PROPN
ejpam-4637	99	30	[	[	X
ejpam-4637	99	31	12	12	NUM
ejpam-4637	99	32	]	]	PUNCT
ejpam-4637	99	33	and	and	CCONJ
ejpam-4637	99	34	later	later	ADV
ejpam-4637	99	35	on	on	ADV
ejpam-4637	99	36	,	,	PUNCT
ejpam-4637	99	37	it	it	PRON
ejpam-4637	99	38	was	be	AUX
ejpam-4637	99	39	modified	modify	VERB
ejpam-4637	99	40	by	by	ADP
ejpam-4637	99	41	deli	deli	NOUN
ejpam-4637	99	42	and	and	CCONJ
ejpam-4637	99	43	broumi	broumi	VERB
ejpam-4637	100	1	[	[	X
ejpam-4637	100	2	6	6	NUM
ejpam-4637	100	3	]	]	PUNCT
ejpam-4637	100	4	as	as	SCONJ
ejpam-4637	100	5	given	give	VERB
ejpam-4637	100	6	below	below	ADV
ejpam-4637	100	7	:	:	PUNCT
ejpam-4637	100	8	definition	definition	NOUN
ejpam-4637	100	9	10	10	NUM
ejpam-4637	100	10	.	.	PUNCT
ejpam-4637	101	1	let	let	VERB
ejpam-4637	101	2	u	u	PRON
ejpam-4637	101	3	be	be	AUX
ejpam-4637	101	4	an	an	DET
ejpam-4637	101	5	initial	initial	ADJ
ejpam-4637	101	6	universe	universe	NOUN
ejpam-4637	101	7	set	set	VERB
ejpam-4637	101	8	and	and	CCONJ
ejpam-4637	101	9	e	e	NOUN
ejpam-4637	101	10	be	be	AUX
ejpam-4637	101	11	a	a	DET
ejpam-4637	101	12	set	set	NOUN
ejpam-4637	101	13	of	of	ADP
ejpam-4637	101	14	parameters	parameter	NOUN
ejpam-4637	101	15	.	.	PUNCT
ejpam-4637	102	1	let	let	VERB
ejpam-4637	102	2	n	n	PROPN
ejpam-4637	102	3	(	(	PUNCT
ejpam-4637	102	4	u	u	NOUN
ejpam-4637	102	5	)	)	PUNCT
ejpam-4637	102	6	denote	denote	VERB
ejpam-4637	102	7	the	the	DET
ejpam-4637	102	8	set	set	NOUN
ejpam-4637	102	9	of	of	ADP
ejpam-4637	102	10	all	all	DET
ejpam-4637	102	11	neutrosophic	neutrosophic	ADJ
ejpam-4637	102	12	sets	set	NOUN
ejpam-4637	102	13	of	of	ADP
ejpam-4637	102	14	u	u	NOUN
ejpam-4637	102	15	.	.	PUNCT
ejpam-4637	103	1	then	then	ADV
ejpam-4637	103	2	a	a	DET
ejpam-4637	103	3	neutrosophic	neutrosophic	ADJ
ejpam-4637	103	4	soft	soft	ADJ
ejpam-4637	103	5	set	set	NOUN
ejpam-4637	103	6	(	(	PUNCT
ejpam-4637	103	7	f	f	X
ejpam-4637	103	8	,	,	PUNCT
ejpam-4637	103	9	e	e	NOUN
ejpam-4637	103	10	)	)	PUNCT
ejpam-4637	103	11	over	over	ADP
ejpam-4637	103	12	u	u	NOUN
ejpam-4637	103	13	is	be	AUX
ejpam-4637	103	14	a	a	DET
ejpam-4637	103	15	set	set	NOUN
ejpam-4637	103	16	defined	define	VERB
ejpam-4637	103	17	by	by	ADP
ejpam-4637	103	18	a	a	DET
ejpam-4637	103	19	set	set	NOUN
ejpam-4637	103	20	valued	value	VERB
ejpam-4637	103	21	function	function	NOUN
ejpam-4637	103	22	f	f	PROPN
ejpam-4637	103	23	representing	represent	VERB
ejpam-4637	103	24	a	a	DET
ejpam-4637	103	25	mapping	mapping	NOUN
ejpam-4637	103	26	f	f	NOUN
ejpam-4637	103	27	:	:	PUNCT
ejpam-4637	103	28	e	e	X
ejpam-4637	103	29	−→	−→	NOUN
ejpam-4637	103	30	n	n	PROPN
ejpam-4637	103	31	(	(	PUNCT
ejpam-4637	103	32	u	u	NOUN
ejpam-4637	103	33	)	)	PUNCT
ejpam-4637	103	34	where	where	SCONJ
ejpam-4637	103	35	f	f	PROPN
ejpam-4637	103	36	is	be	AUX
ejpam-4637	103	37	called	call	VERB
ejpam-4637	103	38	approximate	approximate	ADJ
ejpam-4637	103	39	function	function	NOUN
ejpam-4637	103	40	of	of	ADP
ejpam-4637	103	41	the	the	DET
ejpam-4637	103	42	neutrosophic	neutrosophic	ADJ
ejpam-4637	103	43	soft	soft	ADJ
ejpam-4637	103	44	set	set	NOUN
ejpam-4637	103	45	(	(	PUNCT
ejpam-4637	103	46	f	f	X
ejpam-4637	103	47	,	,	PUNCT
ejpam-4637	103	48	e	e	NOUN
ejpam-4637	103	49	)	)	PUNCT
ejpam-4637	103	50	.	.	PUNCT
ejpam-4637	104	1	in	in	ADP
ejpam-4637	104	2	other	other	ADJ
ejpam-4637	104	3	words	word	NOUN
ejpam-4637	104	4	,	,	PUNCT
ejpam-4637	104	5	the	the	DET
ejpam-4637	104	6	neutrosophic	neutrosophic	ADJ
ejpam-4637	104	7	soft	soft	ADJ
ejpam-4637	104	8	set	set	NOUN
ejpam-4637	104	9	is	be	AUX
ejpam-4637	104	10	a	a	DET
ejpam-4637	104	11	parameterized	parameterized	ADJ
ejpam-4637	104	12	family	family	NOUN
ejpam-4637	104	13	of	of	ADP
ejpam-4637	104	14	some	some	DET
ejpam-4637	104	15	elements	element	NOUN
ejpam-4637	104	16	of	of	ADP
ejpam-4637	104	17	the	the	DET
ejpam-4637	104	18	set	set	ADJ
ejpam-4637	104	19	n	n	PROPN
ejpam-4637	104	20	(	(	PUNCT
ejpam-4637	104	21	u	u	NOUN
ejpam-4637	104	22	)	)	PUNCT
ejpam-4637	104	23	and	and	CCONJ
ejpam-4637	104	24	therefore	therefore	ADV
ejpam-4637	104	25	it	it	PRON
ejpam-4637	104	26	can	can	AUX
ejpam-4637	104	27	be	be	AUX
ejpam-4637	104	28	written	write	VERB
ejpam-4637	104	29	as	as	ADP
ejpam-4637	104	30	a	a	DET
ejpam-4637	104	31	set	set	NOUN
ejpam-4637	104	32	of	of	ADP
ejpam-4637	104	33	ordered	order	VERB
ejpam-4637	104	34	pairs	pair	NOUN
ejpam-4637	104	35	(	(	PUNCT
ejpam-4637	104	36	f	f	X
ejpam-4637	104	37	,	,	PUNCT
ejpam-4637	104	38	e	e	NOUN
ejpam-4637	104	39	)	)	PUNCT
ejpam-4637	104	40	=	=	SYM
ejpam-4637	104	41	{	{	PUNCT
ejpam-4637	104	42	(	(	PUNCT
ejpam-4637	104	43	e	e	NOUN
ejpam-4637	104	44	,	,	PUNCT
ejpam-4637	104	45	{	{	PUNCT
ejpam-4637	104	46	〈	〈	NOUN
ejpam-4637	104	47	x	x	NOUN
ejpam-4637	104	48	,	,	PUNCT
ejpam-4637	104	49	(	(	PUNCT
ejpam-4637	104	50	tf	tf	INTJ
ejpam-4637	104	51	(	(	PUNCT
ejpam-4637	104	52	e)(x	e)(x	PROPN
ejpam-4637	104	53	)	)	PUNCT
ejpam-4637	104	54	,	,	PUNCT
ejpam-4637	104	55	if	if	SCONJ
ejpam-4637	104	56	(	(	PUNCT
ejpam-4637	104	57	e)(x),ff	e)(x),ff	INTJ
ejpam-4637	104	58	(	(	PUNCT
ejpam-4637	104	59	e)(x	e)(x	NOUN
ejpam-4637	104	60	)	)	PUNCT
ejpam-4637	104	61	)	)	PUNCT
ejpam-4637	104	62	〉	〉	NOUN
ejpam-4637	104	63	}	}	PUNCT
ejpam-4637	104	64	)	)	PUNCT
ejpam-4637	104	65	|x	|x	PROPN
ejpam-4637	104	66	∈	∈	PROPN
ejpam-4637	104	67	u	u	PROPN
ejpam-4637	104	68	,	,	PUNCT
ejpam-4637	104	69	e	e	PROPN
ejpam-4637	104	70	∈	∈	PROPN
ejpam-4637	104	71	e	e	X
ejpam-4637	104	72	}	}	PUNCT
ejpam-4637	104	73	where	where	SCONJ
ejpam-4637	104	74	tf	tf	INTJ
ejpam-4637	104	75	(	(	PUNCT
ejpam-4637	104	76	e)(x	e)(x	PROPN
ejpam-4637	104	77	)	)	PUNCT
ejpam-4637	104	78	,	,	PUNCT
ejpam-4637	104	79	if	if	SCONJ
ejpam-4637	104	80	(	(	PUNCT
ejpam-4637	104	81	e)(x),ff	e)(x),ff	INTJ
ejpam-4637	104	82	(	(	PUNCT
ejpam-4637	104	83	e)(x	e)(x	PROPN
ejpam-4637	104	84	)	)	PUNCT
ejpam-4637	104	85	∈	∈	PROPN
ejpam-4637	105	1	[	[	X
ejpam-4637	105	2	0	0	NUM
ejpam-4637	105	3	,	,	PUNCT
ejpam-4637	105	4	1	1	NUM
ejpam-4637	105	5	]	]	PUNCT
ejpam-4637	105	6	,	,	PUNCT
ejpam-4637	105	7	respectively	respectively	ADV
ejpam-4637	105	8	called	call	VERB
ejpam-4637	105	9	the	the	DET
ejpam-4637	105	10	truth	truth	NOUN
ejpam-4637	105	11	-	-	PUNCT
ejpam-4637	105	12	membership	membership	NOUN
ejpam-4637	105	13	,	,	PUNCT
ejpam-4637	105	14	indeterminacymembership	indeterminacymembership	NOUN
ejpam-4637	105	15	,	,	PUNCT
ejpam-4637	105	16	falsity	falsity	NOUN
ejpam-4637	105	17	-	-	PUNCT
ejpam-4637	105	18	membership	membership	NOUN
ejpam-4637	105	19	function	function	NOUN
ejpam-4637	105	20	of	of	ADP
ejpam-4637	105	21	f	f	PROPN
ejpam-4637	105	22	(	(	PUNCT
ejpam-4637	105	23	e	e	NOUN
ejpam-4637	105	24	)	)	PUNCT
ejpam-4637	105	25	.	.	PUNCT
ejpam-4637	106	1	since	since	SCONJ
ejpam-4637	106	2	supremum	supremum	ADJ
ejpam-4637	106	3	of	of	ADP
ejpam-4637	106	4	each	each	DET
ejpam-4637	106	5	t	t	NOUN
ejpam-4637	106	6	,	,	PUNCT
ejpam-4637	106	7	i	i	PRON
ejpam-4637	106	8	,	,	PUNCT
ejpam-4637	106	9	f	f	PROPN
ejpam-4637	106	10	is	be	AUX
ejpam-4637	106	11	1	1	NUM
ejpam-4637	106	12	so	so	SCONJ
ejpam-4637	106	13	the	the	DET
ejpam-4637	106	14	inequality	inequality	NOUN
ejpam-4637	106	15	0	0	NUM
ejpam-4637	106	16	≤	≤	NUM
ejpam-4637	106	17	tf	tf	INTJ
ejpam-4637	106	18	(	(	PUNCT
ejpam-4637	106	19	e)(x	e)(x	PROPN
ejpam-4637	106	20	)	)	PUNCT
ejpam-4637	106	21	+	+	CCONJ
ejpam-4637	106	22	if	if	SCONJ
ejpam-4637	106	23	(	(	PUNCT
ejpam-4637	106	24	e)(x	e)(x	PROPN
ejpam-4637	106	25	)	)	PUNCT
ejpam-4637	106	26	+	+	CCONJ
ejpam-4637	106	27	ff	ff	INTJ
ejpam-4637	106	28	(	(	PUNCT
ejpam-4637	106	29	e)(x	e)(x	NOUN
ejpam-4637	106	30	)	)	PUNCT
ejpam-4637	106	31	≤	≤	NOUN
ejpam-4637	106	32	3	3	NUM
ejpam-4637	106	33	is	be	AUX
ejpam-4637	106	34	obvious	obvious	ADJ
ejpam-4637	106	35	.	.	PUNCT
ejpam-4637	107	1	definition	definition	NOUN
ejpam-4637	107	2	11	11	NUM
ejpam-4637	107	3	.	.	PUNCT
ejpam-4637	108	1	[	[	X
ejpam-4637	108	2	6	6	NUM
ejpam-4637	108	3	]	]	PUNCT
ejpam-4637	108	4	the	the	DET
ejpam-4637	108	5	complement	complement	NOUN
ejpam-4637	108	6	of	of	ADP
ejpam-4637	108	7	a	a	DET
ejpam-4637	108	8	neutrosophic	neutrosophic	ADJ
ejpam-4637	108	9	soft	soft	ADJ
ejpam-4637	108	10	set	set	NOUN
ejpam-4637	108	11	(	(	PUNCT
ejpam-4637	108	12	f	f	X
ejpam-4637	108	13	,	,	PUNCT
ejpam-4637	108	14	e	e	NOUN
ejpam-4637	108	15	)	)	PUNCT
ejpam-4637	108	16	over	over	ADP
ejpam-4637	108	17	u	u	NOUN
ejpam-4637	108	18	is	be	AUX
ejpam-4637	108	19	denoted	denote	VERB
ejpam-4637	108	20	by	by	ADP
ejpam-4637	108	21	(	(	PUNCT
ejpam-4637	108	22	f	f	NOUN
ejpam-4637	108	23	,	,	PUNCT
ejpam-4637	108	24	e)c	e)c	PUNCT
ejpam-4637	108	25	and	and	CCONJ
ejpam-4637	108	26	is	be	AUX
ejpam-4637	108	27	defined	define	VERB
ejpam-4637	108	28	by	by	ADP
ejpam-4637	108	29	(	(	PUNCT
ejpam-4637	108	30	f	f	NOUN
ejpam-4637	108	31	,	,	PUNCT
ejpam-4637	108	32	e)c	e)c	X
ejpam-4637	108	33	=	=	PRON
ejpam-4637	108	34	{	{	PUNCT
ejpam-4637	108	35	(	(	PUNCT
ejpam-4637	108	36	e	e	NOUN
ejpam-4637	108	37	,	,	PUNCT
ejpam-4637	108	38	{	{	PUNCT
ejpam-4637	108	39	〈	〈	NOUN
ejpam-4637	108	40	x	x	NOUN
ejpam-4637	108	41	,	,	PUNCT
ejpam-4637	108	42	(	(	PUNCT
ejpam-4637	108	43	ff	ff	INTJ
ejpam-4637	108	44	(	(	PUNCT
ejpam-4637	108	45	e)(x	e)(x	PROPN
ejpam-4637	108	46	)	)	PUNCT
ejpam-4637	108	47	,	,	PUNCT
ejpam-4637	108	48	1−	1−	NUM
ejpam-4637	108	49	if	if	SCONJ
ejpam-4637	108	50	(	(	PUNCT
ejpam-4637	108	51	e)(x	e)(x	PROPN
ejpam-4637	108	52	)	)	PUNCT
ejpam-4637	108	53	,	,	PUNCT
ejpam-4637	108	54	tf	tf	INTJ
ejpam-4637	108	55	(	(	PUNCT
ejpam-4637	108	56	e)(x	e)(x	NOUN
ejpam-4637	108	57	)	)	PUNCT
ejpam-4637	108	58	)	)	PUNCT
ejpam-4637	108	59	〉	〉	NOUN
ejpam-4637	108	60	}	}	PUNCT
ejpam-4637	108	61	)	)	PUNCT
ejpam-4637	108	62	|x	|x	PROPN
ejpam-4637	108	63	∈	∈	PROPN
ejpam-4637	108	64	u	u	PROPN
ejpam-4637	108	65	,	,	PUNCT
ejpam-4637	108	66	e	e	PROPN
ejpam-4637	108	67	∈	∈	PROPN
ejpam-4637	108	68	e	e	NOUN
ejpam-4637	108	69	}	}	PUNCT
ejpam-4637	108	70	.	.	PUNCT
ejpam-4637	109	1	definition	definition	NOUN
ejpam-4637	109	2	12	12	NUM
ejpam-4637	109	3	.	.	PUNCT
ejpam-4637	110	1	[	[	X
ejpam-4637	110	2	6	6	NUM
ejpam-4637	110	3	]	]	PUNCT
ejpam-4637	110	4	let	let	VERB
ejpam-4637	110	5	(	(	PUNCT
ejpam-4637	110	6	h	h	NOUN
ejpam-4637	110	7	,	,	PUNCT
ejpam-4637	110	8	e	e	NOUN
ejpam-4637	110	9	)	)	PUNCT
ejpam-4637	110	10	and	and	CCONJ
ejpam-4637	110	11	(	(	PUNCT
ejpam-4637	110	12	g	g	NOUN
ejpam-4637	110	13	,	,	PUNCT
ejpam-4637	110	14	e	e	NOUN
ejpam-4637	110	15	)	)	PUNCT
ejpam-4637	110	16	be	be	AUX
ejpam-4637	110	17	two	two	NUM
ejpam-4637	110	18	neutrosophic	neutrosophic	ADJ
ejpam-4637	110	19	soft	soft	ADJ
ejpam-4637	110	20	sets	set	NOUN
ejpam-4637	110	21	over	over	ADP
ejpam-4637	110	22	the	the	DET
ejpam-4637	110	23	common	common	ADJ
ejpam-4637	110	24	universe	universe	NOUN
ejpam-4637	110	25	u	u	NOUN
ejpam-4637	110	26	.	.	PUNCT
ejpam-4637	111	1	then	then	ADV
ejpam-4637	111	2	(	(	PUNCT
ejpam-4637	111	3	h	h	NOUN
ejpam-4637	111	4	,	,	PUNCT
ejpam-4637	111	5	e	e	NOUN
ejpam-4637	111	6	)	)	PUNCT
ejpam-4637	111	7	is	be	AUX
ejpam-4637	111	8	said	say	VERB
ejpam-4637	111	9	to	to	PART
ejpam-4637	111	10	be	be	AUX
ejpam-4637	111	11	neutrosophic	neutrosophic	ADJ
ejpam-4637	111	12	soft	soft	ADJ
ejpam-4637	111	13	subset	subset	NOUN
ejpam-4637	111	14	of	of	ADP
ejpam-4637	111	15	(	(	PUNCT
ejpam-4637	111	16	g	g	PROPN
ejpam-4637	111	17	,	,	PUNCT
ejpam-4637	111	18	e	e	NOUN
ejpam-4637	111	19	)	)	PUNCT
ejpam-4637	111	20	if	if	SCONJ
ejpam-4637	111	21	∀e	∀e	PROPN
ejpam-4637	111	22	∈	∈	PROPN
ejpam-4637	111	23	e	e	X
ejpam-4637	111	24	and	and	CCONJ
ejpam-4637	111	25	∀x	∀x	NOUN
ejpam-4637	111	26	∈	∈	PROPN
ejpam-4637	111	27	u	u	NOUN
ejpam-4637	111	28	,	,	PUNCT
ejpam-4637	111	29	th(e)(x	th(e)(x	PROPN
ejpam-4637	111	30	)	)	PUNCT
ejpam-4637	111	31	≤	≤	NUM
ejpam-4637	111	32	tg(e)(x	tg(e)(x	NUM
ejpam-4637	111	33	)	)	PUNCT
ejpam-4637	111	34	,	,	PUNCT
ejpam-4637	111	35	ih(e)(x	ih(e)(x	NOUN
ejpam-4637	111	36	)	)	PUNCT
ejpam-4637	111	37	≥	≥	NOUN
ejpam-4637	111	38	ig(e)(x),fh(e)(x	ig(e)(x),fh(e)(x	PROPN
ejpam-4637	111	39	)	)	PUNCT
ejpam-4637	111	40	≥	≥	NOUN
ejpam-4637	111	41	fg(e)(x	fg(e)(x	PROPN
ejpam-4637	111	42	)	)	PUNCT
ejpam-4637	111	43	.	.	PUNCT
ejpam-4637	112	1	we	we	PRON
ejpam-4637	112	2	write	write	VERB
ejpam-4637	112	3	(	(	PUNCT
ejpam-4637	112	4	h	h	NOUN
ejpam-4637	112	5	,	,	PUNCT
ejpam-4637	112	6	e	e	NOUN
ejpam-4637	112	7	)	)	PUNCT
ejpam-4637	112	8	⊆	⊆	NUM
ejpam-4637	112	9	(	(	PUNCT
ejpam-4637	112	10	g	g	NOUN
ejpam-4637	112	11	,	,	PUNCT
ejpam-4637	112	12	e	e	NOUN
ejpam-4637	112	13	)	)	PUNCT
ejpam-4637	112	14	and	and	CCONJ
ejpam-4637	112	15	(	(	PUNCT
ejpam-4637	112	16	g	g	NOUN
ejpam-4637	112	17	,	,	PUNCT
ejpam-4637	112	18	e	e	NOUN
ejpam-4637	112	19	)	)	PUNCT
ejpam-4637	112	20	is	be	AUX
ejpam-4637	112	21	a	a	DET
ejpam-4637	112	22	neutrosophic	neutrosophic	ADJ
ejpam-4637	112	23	soft	soft	ADJ
ejpam-4637	112	24	superset	superset	NOUN
ejpam-4637	112	25	of	of	ADP
ejpam-4637	112	26	(	(	PUNCT
ejpam-4637	112	27	h	h	NOUN
ejpam-4637	112	28	,	,	PUNCT
ejpam-4637	112	29	e	e	NOUN
ejpam-4637	112	30	)	)	PUNCT
ejpam-4637	112	31	.	.	PUNCT
ejpam-4637	113	1	definition	definition	NOUN
ejpam-4637	113	2	13	13	NUM
ejpam-4637	113	3	.	.	PUNCT
ejpam-4637	114	1	[	[	X
ejpam-4637	114	2	5	5	NUM
ejpam-4637	114	3	]	]	PUNCT
ejpam-4637	114	4	a	a	DET
ejpam-4637	114	5	binary	binary	ADJ
ejpam-4637	114	6	operation	operation	NOUN
ejpam-4637	114	7	∗	∗	NOUN
ejpam-4637	114	8	:	:	PUNCT
ejpam-4637	115	1	[	[	X
ejpam-4637	115	2	0	0	NUM
ejpam-4637	115	3	,	,	PUNCT
ejpam-4637	115	4	1	1	NUM
ejpam-4637	115	5	]	]	SYM
ejpam-4637	115	6	×	×	NOUN
ejpam-4637	115	7	[	[	X
ejpam-4637	115	8	0	0	NUM
ejpam-4637	115	9	,	,	PUNCT
ejpam-4637	115	10	1	1	NUM
ejpam-4637	115	11	]	]	X
ejpam-4637	115	12	−→	−→	NOUN
ejpam-4637	115	13	[	[	X
ejpam-4637	115	14	0	0	NUM
ejpam-4637	115	15	,	,	PUNCT
ejpam-4637	115	16	1	1	NUM
ejpam-4637	115	17	]	]	PUNCT
ejpam-4637	115	18	is	be	AUX
ejpam-4637	115	19	continuous	continuous	ADJ
ejpam-4637	115	20	t	t	NOUN
ejpam-4637	115	21	-	-	PUNCT
ejpam-4637	115	22	norm	norm	NOUN
ejpam-4637	115	23	if	if	SCONJ
ejpam-4637	115	24	∗	∗	NOUN
ejpam-4637	115	25	satisfies	satisfy	VERB
ejpam-4637	115	26	the	the	DET
ejpam-4637	115	27	following	follow	VERB
ejpam-4637	115	28	conditions	condition	NOUN
ejpam-4637	115	29	:	:	PUNCT
ejpam-4637	115	30	(	(	PUNCT
ejpam-4637	115	31	i	i	NOUN
ejpam-4637	115	32	)	)	PUNCT
ejpam-4637	115	33	∗	∗	NOUN
ejpam-4637	115	34	is	be	AUX
ejpam-4637	115	35	commutative	commutative	ADJ
ejpam-4637	115	36	and	and	CCONJ
ejpam-4637	115	37	associative	associative	ADJ
ejpam-4637	115	38	.	.	PUNCT
ejpam-4637	116	1	(	(	PUNCT
ejpam-4637	116	2	ii	ii	NOUN
ejpam-4637	116	3	)	)	PUNCT
ejpam-4637	116	4	∗	∗	NOUN
ejpam-4637	116	5	is	be	AUX
ejpam-4637	116	6	continuous	continuous	ADJ
ejpam-4637	116	7	.	.	PUNCT
ejpam-4637	117	1	(	(	PUNCT
ejpam-4637	117	2	iii	iii	X
ejpam-4637	117	3	)	)	PUNCT
ejpam-4637	117	4	a	a	DET
ejpam-4637	117	5	∗	∗	NOUN
ejpam-4637	117	6	1	1	NUM
ejpam-4637	117	7	=	=	SYM
ejpam-4637	117	8	1	1	NUM
ejpam-4637	117	9	∗	∗	NOUN
ejpam-4637	117	10	a	a	DET
ejpam-4637	117	11	=	=	SYM
ejpam-4637	117	12	a	a	NOUN
ejpam-4637	117	13	,	,	PUNCT
ejpam-4637	117	14	∀a	∀a	NOUN
ejpam-4637	117	15	∈	∈	NOUN
ejpam-4637	118	1	[	[	X
ejpam-4637	118	2	0	0	NUM
ejpam-4637	118	3	,	,	PUNCT
ejpam-4637	118	4	1	1	NUM
ejpam-4637	118	5	]	]	PUNCT
ejpam-4637	118	6	.	.	PUNCT
ejpam-4637	119	1	(	(	PUNCT
ejpam-4637	119	2	iv	iv	X
ejpam-4637	119	3	)	)	PUNCT
ejpam-4637	119	4	a	a	DET
ejpam-4637	119	5	∗	∗	NOUN
ejpam-4637	119	6	b	b	NOUN
ejpam-4637	119	7	≤	≤	NOUN
ejpam-4637	119	8	c	c	NOUN
ejpam-4637	119	9	∗	∗	NOUN
ejpam-4637	119	10	d	d	NOUN
ejpam-4637	119	11	if	if	SCONJ
ejpam-4637	119	12	a	a	DET
ejpam-4637	119	13	≤	≤	NUM
ejpam-4637	119	14	c	c	NOUN
ejpam-4637	119	15	,	,	PUNCT
ejpam-4637	119	16	b	b	PROPN
ejpam-4637	119	17	≤	≤	NUM
ejpam-4637	119	18	d	d	NOUN
ejpam-4637	119	19	with	with	ADP
ejpam-4637	119	20	a	a	DET
ejpam-4637	119	21	,	,	PUNCT
ejpam-4637	119	22	b	b	NOUN
ejpam-4637	119	23	,	,	PUNCT
ejpam-4637	119	24	c	c	NOUN
ejpam-4637	119	25	,	,	PUNCT
ejpam-4637	119	26	d	d	PROPN
ejpam-4637	119	27	∈	∈	PROPN
ejpam-4637	120	1	[	[	X
ejpam-4637	120	2	0	0	NUM
ejpam-4637	120	3	,	,	PUNCT
ejpam-4637	120	4	1	1	NUM
ejpam-4637	120	5	]	]	PUNCT
ejpam-4637	120	6	.	.	PUNCT
ejpam-4637	121	1	a	a	DET
ejpam-4637	121	2	few	few	ADJ
ejpam-4637	121	3	examples	example	NOUN
ejpam-4637	121	4	of	of	ADP
ejpam-4637	121	5	continuous	continuous	ADJ
ejpam-4637	121	6	t	t	NOUN
ejpam-4637	121	7	-	-	PUNCT
ejpam-4637	121	8	norm	norm	NOUN
ejpam-4637	121	9	are	be	AUX
ejpam-4637	121	10	a	a	DET
ejpam-4637	121	11	∗	∗	NOUN
ejpam-4637	121	12	b	b	NOUN
ejpam-4637	121	13	=	=	SYM
ejpam-4637	121	14	ab	ab	PROPN
ejpam-4637	121	15	,	,	PUNCT
ejpam-4637	121	16	a	a	DET
ejpam-4637	121	17	∗	∗	NOUN
ejpam-4637	121	18	b	b	NOUN
ejpam-4637	121	19	=	=	SYM
ejpam-4637	121	20	min{a	min{a	NOUN
ejpam-4637	121	21	,	,	PUNCT
ejpam-4637	121	22	b	b	NOUN
ejpam-4637	121	23	}	}	PUNCT
ejpam-4637	121	24	,	,	PUNCT
ejpam-4637	121	25	a	a	DET
ejpam-4637	121	26	∗	∗	NOUN
ejpam-4637	121	27	b	b	X
ejpam-4637	121	28	=	=	X
ejpam-4637	121	29	max{a+	max{a+	NOUN
ejpam-4637	121	30	b−	b−	PROPN
ejpam-4637	121	31	1	1	NUM
ejpam-4637	121	32	,	,	PUNCT
ejpam-4637	121	33	0	0	NUM
ejpam-4637	121	34	}	}	PUNCT
ejpam-4637	121	35	.	.	PUNCT
ejpam-4637	122	1	definition	definition	NOUN
ejpam-4637	122	2	14	14	NUM
ejpam-4637	122	3	.	.	PUNCT
ejpam-4637	123	1	[	[	X
ejpam-4637	123	2	5	5	NUM
ejpam-4637	123	3	]	]	PUNCT
ejpam-4637	123	4	a	a	DET
ejpam-4637	123	5	binary	binary	ADJ
ejpam-4637	123	6	operation	operation	NOUN
ejpam-4637	123	7	⋄	⋄	NOUN
ejpam-4637	123	8	:	:	PUNCT
ejpam-4637	124	1	[	[	X
ejpam-4637	124	2	0	0	NUM
ejpam-4637	124	3	,	,	PUNCT
ejpam-4637	124	4	1	1	NUM
ejpam-4637	124	5	]	]	SYM
ejpam-4637	124	6	×	×	NOUN
ejpam-4637	124	7	[	[	X
ejpam-4637	124	8	0	0	NUM
ejpam-4637	124	9	,	,	PUNCT
ejpam-4637	124	10	1	1	NUM
ejpam-4637	124	11	]	]	X
ejpam-4637	124	12	−→	−→	NOUN
ejpam-4637	124	13	[	[	X
ejpam-4637	124	14	0	0	NUM
ejpam-4637	124	15	,	,	PUNCT
ejpam-4637	124	16	1	1	NUM
ejpam-4637	124	17	]	]	PUNCT
ejpam-4637	124	18	is	be	AUX
ejpam-4637	124	19	continuous	continuous	ADJ
ejpam-4637	124	20	t	t	NOUN
ejpam-4637	124	21	-	-	PUNCT
ejpam-4637	124	22	conorm	conorm	NOUN
ejpam-4637	124	23	(	(	PUNCT
ejpam-4637	124	24	s−	s−	PROPN
ejpam-4637	124	25	norm	norm	PROPN
ejpam-4637	124	26	)	)	PUNCT
ejpam-4637	124	27	if	if	SCONJ
ejpam-4637	124	28	⋄	⋄	NOUN
ejpam-4637	124	29	satisfies	satisfy	VERB
ejpam-4637	124	30	the	the	DET
ejpam-4637	124	31	following	follow	VERB
ejpam-4637	124	32	conditions	condition	NOUN
ejpam-4637	124	33	:	:	PUNCT
ejpam-4637	124	34	(	(	PUNCT
ejpam-4637	124	35	i	i	NOUN
ejpam-4637	124	36	)	)	PUNCT
ejpam-4637	124	37	⋄	⋄	PROPN
ejpam-4637	124	38	is	be	AUX
ejpam-4637	124	39	commutative	commutative	ADJ
ejpam-4637	124	40	and	and	CCONJ
ejpam-4637	124	41	associative	associative	ADJ
ejpam-4637	124	42	.	.	PUNCT
ejpam-4637	125	1	(	(	PUNCT
ejpam-4637	125	2	ii	ii	X
ejpam-4637	125	3	)	)	PUNCT
ejpam-4637	125	4	⋄	⋄	PROPN
ejpam-4637	125	5	is	be	AUX
ejpam-4637	125	6	continuous	continuous	ADJ
ejpam-4637	125	7	.	.	PUNCT
ejpam-4637	126	1	(	(	PUNCT
ejpam-4637	126	2	iii	iii	X
ejpam-4637	126	3	)	)	PUNCT
ejpam-4637	126	4	a	a	DET
ejpam-4637	126	5	⋄	⋄	NOUN
ejpam-4637	126	6	0	0	NUM
ejpam-4637	127	1	=	=	SYM
ejpam-4637	127	2	0	0	NUM
ejpam-4637	127	3	⋄	⋄	PROPN
ejpam-4637	127	4	a	a	DET
ejpam-4637	127	5	=	=	SYM
ejpam-4637	127	6	a	a	NOUN
ejpam-4637	127	7	,	,	PUNCT
ejpam-4637	127	8	∀a	∀a	NOUN
ejpam-4637	127	9	∈	∈	NOUN
ejpam-4637	128	1	[	[	X
ejpam-4637	128	2	0	0	NUM
ejpam-4637	128	3	,	,	PUNCT
ejpam-4637	128	4	1	1	NUM
ejpam-4637	128	5	]	]	PUNCT
ejpam-4637	128	6	.	.	PUNCT
ejpam-4637	129	1	a.	a.	PROPN
ejpam-4637	129	2	cano	cano	PROPN
ejpam-4637	129	3	,	,	PUNCT
ejpam-4637	129	4	g.	g.	PROPN
ejpam-4637	129	5	petalcorin	petalcorin	PROPN
ejpam-4637	129	6	/	/	SYM
ejpam-4637	129	7	eur	eur	PROPN
ejpam-4637	129	8	.	.	PUNCT
ejpam-4637	130	1	j.	j.	PROPN
ejpam-4637	130	2	pure	pure	PROPN
ejpam-4637	130	3	appl	appl	PROPN
ejpam-4637	130	4	.	.	PROPN
ejpam-4637	130	5	math	math	PROPN
ejpam-4637	130	6	,	,	PUNCT
ejpam-4637	130	7	16	16	NUM
ejpam-4637	130	8	(	(	PUNCT
ejpam-4637	130	9	1	1	NUM
ejpam-4637	130	10	)	)	PUNCT
ejpam-4637	130	11	(	(	PUNCT
ejpam-4637	130	12	2023	2023	NUM
ejpam-4637	130	13	)	)	PUNCT
ejpam-4637	130	14	,	,	PUNCT
ejpam-4637	131	1	548	548	NUM
ejpam-4637	131	2	-	-	SYM
ejpam-4637	131	3	576	576	NUM
ejpam-4637	131	4	553	553	NUM
ejpam-4637	131	5	(	(	PUNCT
ejpam-4637	131	6	iv	iv	X
ejpam-4637	131	7	)	)	PUNCT
ejpam-4637	131	8	a	a	DET
ejpam-4637	131	9	⋄	⋄	PROPN
ejpam-4637	131	10	b	b	PROPN
ejpam-4637	131	11	≤	≤	NUM
ejpam-4637	131	12	c	c	NOUN
ejpam-4637	131	13	⋄	⋄	PROPN
ejpam-4637	131	14	d	d	NOUN
ejpam-4637	131	15	if	if	SCONJ
ejpam-4637	131	16	a	a	DET
ejpam-4637	131	17	≤	≤	NUM
ejpam-4637	131	18	c	c	NOUN
ejpam-4637	131	19	,	,	PUNCT
ejpam-4637	131	20	b	b	PROPN
ejpam-4637	131	21	≤	≤	NUM
ejpam-4637	131	22	d	d	NOUN
ejpam-4637	131	23	with	with	ADP
ejpam-4637	131	24	a	a	DET
ejpam-4637	131	25	,	,	PUNCT
ejpam-4637	131	26	b	b	NOUN
ejpam-4637	131	27	,	,	PUNCT
ejpam-4637	131	28	c	c	NOUN
ejpam-4637	131	29	,	,	PUNCT
ejpam-4637	131	30	d	d	PROPN
ejpam-4637	131	31	∈	∈	PROPN
ejpam-4637	132	1	[	[	X
ejpam-4637	132	2	0	0	NUM
ejpam-4637	132	3	,	,	PUNCT
ejpam-4637	132	4	1	1	NUM
ejpam-4637	132	5	]	]	PUNCT
ejpam-4637	132	6	.	.	PUNCT
ejpam-4637	133	1	a	a	DET
ejpam-4637	133	2	few	few	ADJ
ejpam-4637	133	3	examples	example	NOUN
ejpam-4637	133	4	of	of	ADP
ejpam-4637	133	5	continuous	continuous	ADJ
ejpam-4637	133	6	s	s	NOUN
ejpam-4637	133	7	-	-	PUNCT
ejpam-4637	133	8	norm	norm	NOUN
ejpam-4637	133	9	are	be	AUX
ejpam-4637	133	10	a	a	DET
ejpam-4637	133	11	⋄	⋄	PROPN
ejpam-4637	133	12	b	b	NOUN
ejpam-4637	133	13	=	=	PUNCT
ejpam-4637	133	14	a	a	DET
ejpam-4637	133	15	+	+	NUM
ejpam-4637	133	16	b	b	NOUN
ejpam-4637	133	17	−	−	PROPN
ejpam-4637	133	18	ab	ab	PROPN
ejpam-4637	133	19	,	,	PUNCT
ejpam-4637	133	20	a	a	DET
ejpam-4637	133	21	⋄	⋄	PROPN
ejpam-4637	133	22	b	b	PROPN
ejpam-4637	133	23	=	=	SYM
ejpam-4637	133	24	max{a	max{a	PROPN
ejpam-4637	133	25	,	,	PUNCT
ejpam-4637	133	26	b	b	NOUN
ejpam-4637	133	27	}	}	PUNCT
ejpam-4637	133	28	,	,	PUNCT
ejpam-4637	133	29	a	a	DET
ejpam-4637	133	30	⋄	⋄	PROPN
ejpam-4637	133	31	b	b	X
ejpam-4637	133	32	=	=	X
ejpam-4637	133	33	min{a+	min{a+	PROPN
ejpam-4637	133	34	b	b	PROPN
ejpam-4637	133	35	,	,	PUNCT
ejpam-4637	133	36	1	1	NUM
ejpam-4637	133	37	}	}	PUNCT
ejpam-4637	133	38	.	.	PUNCT
ejpam-4637	134	1	definition	definition	NOUN
ejpam-4637	134	2	15	15	NUM
ejpam-4637	134	3	.	.	PUNCT
ejpam-4637	135	1	[	[	X
ejpam-4637	135	2	6	6	NUM
ejpam-4637	135	3	]	]	PUNCT
ejpam-4637	135	4	let	let	VERB
ejpam-4637	135	5	(	(	PUNCT
ejpam-4637	135	6	h	h	NOUN
ejpam-4637	135	7	,	,	PUNCT
ejpam-4637	135	8	e	e	NOUN
ejpam-4637	135	9	)	)	PUNCT
ejpam-4637	135	10	and	and	CCONJ
ejpam-4637	135	11	(	(	PUNCT
ejpam-4637	135	12	g	g	NOUN
ejpam-4637	135	13	,	,	PUNCT
ejpam-4637	135	14	e	e	NOUN
ejpam-4637	135	15	)	)	PUNCT
ejpam-4637	135	16	be	be	AUX
ejpam-4637	135	17	two	two	NUM
ejpam-4637	135	18	neutrosophic	neutrosophic	ADJ
ejpam-4637	135	19	soft	soft	ADJ
ejpam-4637	135	20	sets	set	NOUN
ejpam-4637	135	21	over	over	ADP
ejpam-4637	135	22	the	the	DET
ejpam-4637	135	23	common	common	ADJ
ejpam-4637	135	24	universe	universe	NOUN
ejpam-4637	135	25	u	u	NOUN
ejpam-4637	135	26	.	.	PUNCT
ejpam-4637	136	1	(	(	PUNCT
ejpam-4637	136	2	i	i	NOUN
ejpam-4637	136	3	)	)	PUNCT
ejpam-4637	136	4	then	then	ADV
ejpam-4637	136	5	the	the	DET
ejpam-4637	136	6	union	union	PROPN
ejpam-4637	136	7	of	of	ADP
ejpam-4637	136	8	(	(	PUNCT
ejpam-4637	136	9	h	h	NOUN
ejpam-4637	136	10	,	,	PUNCT
ejpam-4637	136	11	e	e	NOUN
ejpam-4637	136	12	)	)	PUNCT
ejpam-4637	136	13	and	and	CCONJ
ejpam-4637	136	14	(	(	PUNCT
ejpam-4637	136	15	g	g	NOUN
ejpam-4637	136	16	,	,	PUNCT
ejpam-4637	136	17	e	e	NOUN
ejpam-4637	136	18	)	)	PUNCT
ejpam-4637	136	19	is	be	AUX
ejpam-4637	136	20	denoted	denote	VERB
ejpam-4637	136	21	by	by	ADP
ejpam-4637	136	22	(	(	PUNCT
ejpam-4637	136	23	h	h	NOUN
ejpam-4637	136	24	,	,	PUNCT
ejpam-4637	136	25	e)∪	e)∪	PROPN
ejpam-4637	136	26	(	(	PUNCT
ejpam-4637	136	27	g	g	NOUN
ejpam-4637	136	28	,	,	PUNCT
ejpam-4637	136	29	e	e	NOUN
ejpam-4637	136	30	)	)	PUNCT
ejpam-4637	136	31	=	=	SYM
ejpam-4637	136	32	(	(	PUNCT
ejpam-4637	136	33	k	k	X
ejpam-4637	136	34	,	,	PUNCT
ejpam-4637	136	35	e	e	NOUN
ejpam-4637	136	36	)	)	PUNCT
ejpam-4637	136	37	and	and	CCONJ
ejpam-4637	136	38	is	be	AUX
ejpam-4637	136	39	defined	define	VERB
ejpam-4637	136	40	by	by	ADP
ejpam-4637	136	41	:	:	PUNCT
ejpam-4637	136	42	(	(	PUNCT
ejpam-4637	136	43	k	k	X
ejpam-4637	136	44	,	,	PUNCT
ejpam-4637	136	45	e	e	NOUN
ejpam-4637	136	46	)	)	PUNCT
ejpam-4637	136	47	=	=	SYM
ejpam-4637	136	48	{	{	PUNCT
ejpam-4637	136	49	(	(	PUNCT
ejpam-4637	136	50	e	e	NOUN
ejpam-4637	136	51	,	,	PUNCT
ejpam-4637	136	52	{	{	PUNCT
ejpam-4637	136	53	〈	〈	NOUN
ejpam-4637	136	54	x	x	SYM
ejpam-4637	136	55	,	,	PUNCT
ejpam-4637	136	56	(	(	PUNCT
ejpam-4637	136	57	tk(e)(x	tk(e)(x	NOUN
ejpam-4637	136	58	)	)	PUNCT
ejpam-4637	136	59	,	,	PUNCT
ejpam-4637	136	60	ik(e)(x),fk(e)(x	ik(e)(x),fk(e)(x	NOUN
ejpam-4637	136	61	)	)	PUNCT
ejpam-4637	136	62	)	)	PUNCT
ejpam-4637	136	63	〉	〉	NOUN
ejpam-4637	136	64	}	}	PUNCT
ejpam-4637	136	65	)	)	PUNCT
ejpam-4637	136	66	|x	|x	PROPN
ejpam-4637	136	67	∈	∈	PROPN
ejpam-4637	136	68	u	u	PROPN
ejpam-4637	136	69	,	,	PUNCT
ejpam-4637	136	70	e	e	PROPN
ejpam-4637	136	71	∈	∈	PROPN
ejpam-4637	136	72	e	e	NOUN
ejpam-4637	136	73	}	}	PUNCT
ejpam-4637	136	74	where	where	SCONJ
ejpam-4637	136	75	tk(e)(x	tk(e)(x	NOUN
ejpam-4637	136	76	)	)	PUNCT
ejpam-4637	136	77	=	=	SYM
ejpam-4637	136	78	th(e)(x	th(e)(x	NOUN
ejpam-4637	136	79	)	)	PUNCT
ejpam-4637	136	80	⋄	⋄	NOUN
ejpam-4637	136	81	tg(e)(x	tg(e)(x	NUM
ejpam-4637	136	82	)	)	PUNCT
ejpam-4637	136	83	ik(e)(x	ik(e)(x	NUM
ejpam-4637	136	84	)	)	PUNCT
ejpam-4637	136	85	=	=	SYM
ejpam-4637	136	86	ih(e)(x	ih(e)(x	NOUN
ejpam-4637	136	87	)	)	PUNCT
ejpam-4637	136	88	∗	∗	NOUN
ejpam-4637	136	89	ig(e)(x	ig(e)(x	PROPN
ejpam-4637	136	90	)	)	PUNCT
ejpam-4637	136	91	fk(e)(x	fk(e)(x	NUM
ejpam-4637	136	92	)	)	PUNCT
ejpam-4637	136	93	=	=	SYM
ejpam-4637	136	94	fh(e)(x	fh(e)(x	PROPN
ejpam-4637	136	95	)	)	PUNCT
ejpam-4637	136	96	∗	∗	NOUN
ejpam-4637	136	97	fg(e)(x	fg(e)(x	PROPN
ejpam-4637	136	98	)	)	PUNCT
ejpam-4637	136	99	.	.	PUNCT
ejpam-4637	137	1	(	(	PUNCT
ejpam-4637	137	2	ii	ii	NOUN
ejpam-4637	137	3	)	)	PUNCT
ejpam-4637	137	4	then	then	ADV
ejpam-4637	137	5	the	the	DET
ejpam-4637	137	6	intersection	intersection	NOUN
ejpam-4637	137	7	of	of	ADP
ejpam-4637	137	8	(	(	PUNCT
ejpam-4637	137	9	h	h	NOUN
ejpam-4637	137	10	,	,	PUNCT
ejpam-4637	137	11	e	e	NOUN
ejpam-4637	137	12	)	)	PUNCT
ejpam-4637	137	13	and	and	CCONJ
ejpam-4637	137	14	(	(	PUNCT
ejpam-4637	137	15	g	g	NOUN
ejpam-4637	137	16	,	,	PUNCT
ejpam-4637	137	17	e	e	NOUN
ejpam-4637	137	18	)	)	PUNCT
ejpam-4637	137	19	is	be	AUX
ejpam-4637	137	20	denoted	denote	VERB
ejpam-4637	137	21	by	by	ADP
ejpam-4637	137	22	(	(	PUNCT
ejpam-4637	137	23	h	h	NOUN
ejpam-4637	137	24	,	,	PUNCT
ejpam-4637	137	25	e	e	NOUN
ejpam-4637	137	26	)	)	PUNCT
ejpam-4637	137	27	∩	∩	NOUN
ejpam-4637	137	28	(	(	PUNCT
ejpam-4637	137	29	g	g	NOUN
ejpam-4637	137	30	,	,	PUNCT
ejpam-4637	137	31	e	e	NOUN
ejpam-4637	137	32	)	)	PUNCT
ejpam-4637	137	33	=	=	SYM
ejpam-4637	137	34	(	(	PUNCT
ejpam-4637	137	35	f	f	X
ejpam-4637	137	36	,	,	PUNCT
ejpam-4637	137	37	e	e	NOUN
ejpam-4637	137	38	)	)	PUNCT
ejpam-4637	137	39	and	and	CCONJ
ejpam-4637	137	40	is	be	AUX
ejpam-4637	137	41	defined	define	VERB
ejpam-4637	137	42	by	by	ADP
ejpam-4637	137	43	:	:	PUNCT
ejpam-4637	137	44	(	(	PUNCT
ejpam-4637	137	45	f	f	X
ejpam-4637	137	46	,	,	PUNCT
ejpam-4637	137	47	e	e	NOUN
ejpam-4637	137	48	)	)	PUNCT
ejpam-4637	137	49	=	=	SYM
ejpam-4637	137	50	{	{	PUNCT
ejpam-4637	137	51	(	(	PUNCT
ejpam-4637	137	52	e	e	NOUN
ejpam-4637	137	53	,	,	PUNCT
ejpam-4637	137	54	{	{	PUNCT
ejpam-4637	137	55	〈	〈	NOUN
ejpam-4637	137	56	x	x	NOUN
ejpam-4637	137	57	,	,	PUNCT
ejpam-4637	137	58	(	(	PUNCT
ejpam-4637	137	59	tf	tf	INTJ
ejpam-4637	137	60	(	(	PUNCT
ejpam-4637	137	61	e)(x	e)(x	PROPN
ejpam-4637	137	62	)	)	PUNCT
ejpam-4637	137	63	,	,	PUNCT
ejpam-4637	137	64	if	if	SCONJ
ejpam-4637	137	65	(	(	PUNCT
ejpam-4637	137	66	e)(x),ff	e)(x),ff	INTJ
ejpam-4637	137	67	(	(	PUNCT
ejpam-4637	137	68	e)(x	e)(x	NOUN
ejpam-4637	137	69	)	)	PUNCT
ejpam-4637	137	70	)	)	PUNCT
ejpam-4637	137	71	〉	〉	NOUN
ejpam-4637	137	72	}	}	PUNCT
ejpam-4637	137	73	)	)	PUNCT
ejpam-4637	137	74	|x	|x	PROPN
ejpam-4637	137	75	∈	∈	PROPN
ejpam-4637	137	76	u	u	PROPN
ejpam-4637	137	77	,	,	PUNCT
ejpam-4637	137	78	e	e	PROPN
ejpam-4637	137	79	∈	∈	PROPN
ejpam-4637	137	80	e	e	X
ejpam-4637	137	81	}	}	PUNCT
ejpam-4637	137	82	where	where	SCONJ
ejpam-4637	137	83	tf	tf	INTJ
ejpam-4637	137	84	(	(	PUNCT
ejpam-4637	137	85	e)(x	e)(x	PROPN
ejpam-4637	137	86	)	)	PUNCT
ejpam-4637	137	87	=	=	SYM
ejpam-4637	137	88	th(e)(x	th(e)(x	NOUN
ejpam-4637	137	89	)	)	PUNCT
ejpam-4637	137	90	∗	∗	NOUN
ejpam-4637	137	91	tg(e)(x	tg(e)(x	NUM
ejpam-4637	137	92	)	)	PUNCT
ejpam-4637	137	93	if	if	SCONJ
ejpam-4637	137	94	(	(	PUNCT
ejpam-4637	137	95	e)(x	e)(x	NOUN
ejpam-4637	137	96	)	)	PUNCT
ejpam-4637	137	97	=	=	SYM
ejpam-4637	137	98	ih(e)(x	ih(e)(x	NOUN
ejpam-4637	137	99	)	)	PUNCT
ejpam-4637	137	100	⋄	⋄	PROPN
ejpam-4637	137	101	ig(e)(x	ig(e)(x	PROPN
ejpam-4637	137	102	)	)	PUNCT
ejpam-4637	137	103	ff	ff	NOUN
ejpam-4637	137	104	(	(	PUNCT
ejpam-4637	137	105	e)(x	e)(x	PROPN
ejpam-4637	137	106	)	)	PUNCT
ejpam-4637	137	107	=	=	SYM
ejpam-4637	137	108	fh(e)(x	fh(e)(x	NUM
ejpam-4637	137	109	)	)	PUNCT
ejpam-4637	137	110	⋄	⋄	PROPN
ejpam-4637	137	111	fg(e)(x	fg(e)(x	PROPN
ejpam-4637	137	112	)	)	PUNCT
ejpam-4637	137	113	.	.	PUNCT
ejpam-4637	138	1	in	in	ADP
ejpam-4637	138	2	this	this	DET
ejpam-4637	138	3	paper	paper	NOUN
ejpam-4637	138	4	,	,	PUNCT
ejpam-4637	138	5	we	we	PRON
ejpam-4637	138	6	use	use	VERB
ejpam-4637	138	7	the	the	DET
ejpam-4637	138	8	minimality	minimality	NOUN
ejpam-4637	138	9	and	and	CCONJ
ejpam-4637	138	10	maximality	maximality	NOUN
ejpam-4637	138	11	as	as	ADP
ejpam-4637	138	12	binary	binary	ADJ
ejpam-4637	138	13	operations	operation	NOUN
ejpam-4637	138	14	∗	∗	NOUN
ejpam-4637	138	15	and	and	CCONJ
ejpam-4637	138	16	⋄	⋄	PROPN
ejpam-4637	138	17	respectively	respectively	ADV
ejpam-4637	138	18	to	to	PART
ejpam-4637	138	19	define	define	VERB
ejpam-4637	138	20	the	the	DET
ejpam-4637	138	21	union	union	NOUN
ejpam-4637	138	22	and	and	CCONJ
ejpam-4637	138	23	intersection	intersection	NOUN
ejpam-4637	138	24	of	of	ADP
ejpam-4637	138	25	two	two	NUM
ejpam-4637	138	26	nss	nss	NOUN
ejpam-4637	138	27	sets	set	NOUN
ejpam-4637	138	28	.	.	PUNCT
ejpam-4637	139	1	example	example	NOUN
ejpam-4637	139	2	4	4	NUM
ejpam-4637	139	3	.	.	PUNCT
ejpam-4637	140	1	consider	consider	VERB
ejpam-4637	140	2	u	u	PRON
ejpam-4637	140	3	=	=	X
ejpam-4637	140	4	{	{	PUNCT
ejpam-4637	140	5	s1	s1	NOUN
ejpam-4637	140	6	,	,	PUNCT
ejpam-4637	140	7	s2	s2	PROPN
ejpam-4637	140	8	,	,	PUNCT
ejpam-4637	140	9	s3	s3	PROPN
ejpam-4637	140	10	}	}	PUNCT
ejpam-4637	140	11	be	be	VERB
ejpam-4637	140	12	the	the	DET
ejpam-4637	140	13	set	set	NOUN
ejpam-4637	140	14	of	of	ADP
ejpam-4637	140	15	all	all	DET
ejpam-4637	140	16	students	student	NOUN
ejpam-4637	140	17	and	and	CCONJ
ejpam-4637	140	18	e	e	NOUN
ejpam-4637	140	19	=	=	NOUN
ejpam-4637	140	20	{	{	PUNCT
ejpam-4637	140	21	a1	a1	PROPN
ejpam-4637	140	22	,	,	PUNCT
ejpam-4637	140	23	a2	a2	PROPN
ejpam-4637	140	24	}	}	PUNCT
ejpam-4637	140	25	be	be	VERB
ejpam-4637	140	26	the	the	DET
ejpam-4637	140	27	set	set	NOUN
ejpam-4637	140	28	of	of	ADP
ejpam-4637	140	29	parameters	parameter	NOUN
ejpam-4637	140	30	where	where	SCONJ
ejpam-4637	140	31	a1	a1	NOUN
ejpam-4637	140	32	stands	stand	VERB
ejpam-4637	140	33	for	for	ADP
ejpam-4637	140	34	the	the	DET
ejpam-4637	140	35	parameter	parameter	NOUN
ejpam-4637	140	36	‘	'	PUNCT
ejpam-4637	140	37	brilliant	brilliant	ADJ
ejpam-4637	140	38	’	'	PUNCT
ejpam-4637	140	39	,	,	PUNCT
ejpam-4637	140	40	a2	a2	PROPN
ejpam-4637	140	41	stands	stand	VERB
ejpam-4637	140	42	for	for	ADP
ejpam-4637	140	43	the	the	DET
ejpam-4637	140	44	parameter	parameter	NOUN
ejpam-4637	140	45	‘	'	PUNCT
ejpam-4637	140	46	healthy	healthy	ADJ
ejpam-4637	140	47	’	'	PUNCT
ejpam-4637	140	48	.	.	PUNCT
ejpam-4637	141	1	define	define	VERB
ejpam-4637	141	2	a	a	DET
ejpam-4637	141	3	mapping	mapping	NOUN
ejpam-4637	141	4	h	h	NOUN
ejpam-4637	141	5	:	:	PUNCT
ejpam-4637	141	6	e	e	X
ejpam-4637	141	7	−→	−→	NOUN
ejpam-4637	141	8	n	n	PROPN
ejpam-4637	141	9	(	(	PUNCT
ejpam-4637	141	10	u	u	NOUN
ejpam-4637	141	11	)	)	PUNCT
ejpam-4637	141	12	by	by	ADP
ejpam-4637	141	13	h(a1	h(a1	NOUN
ejpam-4637	141	14	)	)	PUNCT
ejpam-4637	141	15	=	=	PRON
ejpam-4637	141	16	{	{	PUNCT
ejpam-4637	141	17	⟨s1	⟨s1	PROPN
ejpam-4637	141	18	,	,	PUNCT
ejpam-4637	141	19	(	(	PUNCT
ejpam-4637	141	20	0.1	0.1	NUM
ejpam-4637	141	21	,	,	PUNCT
ejpam-4637	141	22	0.5	0.5	NUM
ejpam-4637	141	23	,	,	PUNCT
ejpam-4637	141	24	0.4)⟩	0.4)⟩	NUM
ejpam-4637	141	25	,	,	PUNCT
ejpam-4637	141	26	⟨s2	⟨s2	PROPN
ejpam-4637	141	27	,	,	PUNCT
ejpam-4637	141	28	(	(	PUNCT
ejpam-4637	141	29	0.6	0.6	NUM
ejpam-4637	141	30	,	,	PUNCT
ejpam-4637	141	31	0.6	0.6	NUM
ejpam-4637	141	32	,	,	PUNCT
ejpam-4637	141	33	0.7)⟩	0.7)⟩	NUM
ejpam-4637	141	34	,	,	PUNCT
ejpam-4637	141	35	⟨s3	⟨s3	PROPN
ejpam-4637	141	36	,	,	PUNCT
ejpam-4637	141	37	(	(	PUNCT
ejpam-4637	141	38	0.5	0.5	NUM
ejpam-4637	141	39	,	,	PUNCT
ejpam-4637	141	40	0.6	0.6	NUM
ejpam-4637	141	41	,	,	PUNCT
ejpam-4637	141	42	0.4)⟩	0.4)⟩	NUM
ejpam-4637	141	43	}	}	PUNCT
ejpam-4637	141	44	h(a2	h(a2	NOUN
ejpam-4637	141	45	)	)	PUNCT
ejpam-4637	141	46	=	=	PRON
ejpam-4637	141	47	{	{	PUNCT
ejpam-4637	141	48	⟨s1	⟨s1	PROPN
ejpam-4637	141	49	,	,	PUNCT
ejpam-4637	141	50	(	(	PUNCT
ejpam-4637	141	51	0.8	0.8	NUM
ejpam-4637	141	52	,	,	PUNCT
ejpam-4637	141	53	0.4	0.4	NUM
ejpam-4637	141	54	,	,	PUNCT
ejpam-4637	141	55	0.5)⟩	0.5)⟩	NUM
ejpam-4637	141	56	,	,	PUNCT
ejpam-4637	141	57	⟨s2	⟨s2	PROPN
ejpam-4637	141	58	,	,	PUNCT
ejpam-4637	141	59	(	(	PUNCT
ejpam-4637	141	60	0.7	0.7	NUM
ejpam-4637	141	61	,	,	PUNCT
ejpam-4637	141	62	0.7	0.7	NUM
ejpam-4637	141	63	,	,	PUNCT
ejpam-4637	141	64	0.3)⟩	0.3)⟩	NUM
ejpam-4637	141	65	,	,	PUNCT
ejpam-4637	141	66	⟨s3	⟨s3	PROPN
ejpam-4637	141	67	,	,	PUNCT
ejpam-4637	141	68	(	(	PUNCT
ejpam-4637	141	69	0.7	0.7	NUM
ejpam-4637	141	70	,	,	PUNCT
ejpam-4637	141	71	0.5	0.5	NUM
ejpam-4637	141	72	,	,	PUNCT
ejpam-4637	141	73	0.6)⟩	0.6)⟩	NUM
ejpam-4637	141	74	}	}	PUNCT
ejpam-4637	141	75	.	.	PUNCT
ejpam-4637	142	1	and	and	CCONJ
ejpam-4637	142	2	a	a	DET
ejpam-4637	142	3	mapping	mapping	NOUN
ejpam-4637	142	4	g	g	NOUN
ejpam-4637	142	5	:	:	PUNCT
ejpam-4637	142	6	e	e	X
ejpam-4637	142	7	−→	−→	NOUN
ejpam-4637	142	8	n	n	PROPN
ejpam-4637	142	9	(	(	PUNCT
ejpam-4637	142	10	u	u	NOUN
ejpam-4637	142	11	)	)	PUNCT
ejpam-4637	142	12	by	by	ADP
ejpam-4637	142	13	g(a1	g(a1	NOUN
ejpam-4637	142	14	)	)	PUNCT
ejpam-4637	142	15	=	=	PRON
ejpam-4637	142	16	{	{	PUNCT
ejpam-4637	142	17	⟨s1	⟨s1	PROPN
ejpam-4637	142	18	,	,	PUNCT
ejpam-4637	142	19	(	(	PUNCT
ejpam-4637	142	20	0.8	0.8	NUM
ejpam-4637	142	21	,	,	PUNCT
ejpam-4637	142	22	0.5	0.5	NUM
ejpam-4637	142	23	,	,	PUNCT
ejpam-4637	142	24	0.6)⟩	0.6)⟩	NUM
ejpam-4637	142	25	,	,	PUNCT
ejpam-4637	142	26	⟨s2	⟨s2	PROPN
ejpam-4637	142	27	,	,	PUNCT
ejpam-4637	142	28	(	(	PUNCT
ejpam-4637	142	29	0.5	0.5	NUM
ejpam-4637	142	30	,	,	PUNCT
ejpam-4637	142	31	0.7	0.7	NUM
ejpam-4637	142	32	,	,	PUNCT
ejpam-4637	142	33	0.6)⟩	0.6)⟩	NUM
ejpam-4637	142	34	,	,	PUNCT
ejpam-4637	142	35	⟨s3	⟨s3	PROPN
ejpam-4637	142	36	,	,	PUNCT
ejpam-4637	142	37	(	(	PUNCT
ejpam-4637	142	38	0.4	0.4	NUM
ejpam-4637	142	39	,	,	PUNCT
ejpam-4637	142	40	0.7	0.7	NUM
ejpam-4637	142	41	,	,	PUNCT
ejpam-4637	142	42	0.5)⟩	0.5)⟩	NUM
ejpam-4637	142	43	}	}	PUNCT
ejpam-4637	142	44	,	,	PUNCT
ejpam-4637	142	45	a.	a.	PROPN
ejpam-4637	142	46	cano	cano	PROPN
ejpam-4637	142	47	,	,	PUNCT
ejpam-4637	142	48	g.	g.	PROPN
ejpam-4637	142	49	petalcorin	petalcorin	PROPN
ejpam-4637	142	50	/	/	SYM
ejpam-4637	142	51	eur	eur	PROPN
ejpam-4637	142	52	.	.	PUNCT
ejpam-4637	143	1	j.	j.	PROPN
ejpam-4637	143	2	pure	pure	PROPN
ejpam-4637	143	3	appl	appl	PROPN
ejpam-4637	143	4	.	.	PROPN
ejpam-4637	143	5	math	math	PROPN
ejpam-4637	143	6	,	,	PUNCT
ejpam-4637	143	7	16	16	NUM
ejpam-4637	143	8	(	(	PUNCT
ejpam-4637	143	9	1	1	NUM
ejpam-4637	143	10	)	)	PUNCT
ejpam-4637	143	11	(	(	PUNCT
ejpam-4637	143	12	2023	2023	NUM
ejpam-4637	143	13	)	)	PUNCT
ejpam-4637	143	14	,	,	PUNCT
ejpam-4637	143	15	548	548	NUM
ejpam-4637	143	16	-	-	SYM
ejpam-4637	143	17	576	576	NUM
ejpam-4637	143	18	554	554	NUM
ejpam-4637	143	19	g(a2	g(a2	NOUN
ejpam-4637	143	20	)	)	PUNCT
ejpam-4637	143	21	=	=	PRON
ejpam-4637	143	22	{	{	PUNCT
ejpam-4637	143	23	⟨s1	⟨s1	PROPN
ejpam-4637	143	24	,	,	PUNCT
ejpam-4637	143	25	(	(	PUNCT
ejpam-4637	143	26	0.7	0.7	NUM
ejpam-4637	143	27	,	,	PUNCT
ejpam-4637	143	28	0.6	0.6	NUM
ejpam-4637	143	29	,	,	PUNCT
ejpam-4637	143	30	0.5)⟩	0.5)⟩	NUM
ejpam-4637	143	31	,	,	PUNCT
ejpam-4637	143	32	⟨s2	⟨s2	PROPN
ejpam-4637	143	33	,	,	PUNCT
ejpam-4637	143	34	(	(	PUNCT
ejpam-4637	143	35	0.6	0.6	NUM
ejpam-4637	143	36	,	,	PUNCT
ejpam-4637	143	37	0.8	0.8	NUM
ejpam-4637	143	38	,	,	PUNCT
ejpam-4637	143	39	0.4)⟩	0.4)⟩	NUM
ejpam-4637	143	40	,	,	PUNCT
ejpam-4637	143	41	⟨s3	⟨s3	PROPN
ejpam-4637	143	42	,	,	PUNCT
ejpam-4637	143	43	(	(	PUNCT
ejpam-4637	143	44	0.5	0.5	NUM
ejpam-4637	143	45	,	,	PUNCT
ejpam-4637	143	46	0.8	0.8	NUM
ejpam-4637	143	47	,	,	PUNCT
ejpam-4637	143	48	0.6)⟩	0.6)⟩	NUM
ejpam-4637	143	49	}	}	PUNCT
ejpam-4637	143	50	.	.	PUNCT
ejpam-4637	144	1	then	then	ADV
ejpam-4637	144	2	the	the	DET
ejpam-4637	144	3	neutrosophic	neutrosophic	ADJ
ejpam-4637	144	4	soft	soft	ADJ
ejpam-4637	144	5	sets	set	NOUN
ejpam-4637	144	6	(	(	PUNCT
ejpam-4637	144	7	h	h	NOUN
ejpam-4637	144	8	,	,	PUNCT
ejpam-4637	144	9	e	e	NOUN
ejpam-4637	144	10	)	)	PUNCT
ejpam-4637	144	11	and	and	CCONJ
ejpam-4637	144	12	(	(	PUNCT
ejpam-4637	144	13	g	g	NOUN
ejpam-4637	144	14	,	,	PUNCT
ejpam-4637	144	15	e	e	NOUN
ejpam-4637	144	16	)	)	PUNCT
ejpam-4637	144	17	are	be	AUX
ejpam-4637	144	18	collections	collection	NOUN
ejpam-4637	144	19	of	of	ADP
ejpam-4637	144	20	approximations	approximation	NOUN
ejpam-4637	144	21	as	as	ADP
ejpam-4637	144	22	below	below	ADV
ejpam-4637	144	23	:	:	PUNCT
ejpam-4637	144	24	(	(	PUNCT
ejpam-4637	144	25	h	h	NOUN
ejpam-4637	144	26	,	,	PUNCT
ejpam-4637	144	27	e	e	NOUN
ejpam-4637	144	28	)	)	PUNCT
ejpam-4637	144	29	=	=	SYM
ejpam-4637	144	30	{	{	PUNCT
ejpam-4637	144	31	(	(	PUNCT
ejpam-4637	144	32	a1	a1	NOUN
ejpam-4637	144	33	,	,	PUNCT
ejpam-4637	144	34	{	{	PUNCT
ejpam-4637	144	35	⟨s1	⟨s1	NOUN
ejpam-4637	144	36	,	,	PUNCT
ejpam-4637	144	37	(	(	PUNCT
ejpam-4637	144	38	0.1	0.1	NUM
ejpam-4637	144	39	,	,	PUNCT
ejpam-4637	144	40	0.5	0.5	NUM
ejpam-4637	144	41	,	,	PUNCT
ejpam-4637	144	42	0.4)⟩	0.4)⟩	NUM
ejpam-4637	144	43	,	,	PUNCT
ejpam-4637	144	44	⟨s2	⟨s2	PROPN
ejpam-4637	144	45	,	,	PUNCT
ejpam-4637	144	46	(	(	PUNCT
ejpam-4637	144	47	0.6	0.6	NUM
ejpam-4637	144	48	,	,	PUNCT
ejpam-4637	144	49	0.6	0.6	NUM
ejpam-4637	144	50	,	,	PUNCT
ejpam-4637	144	51	0.7)⟩	0.7)⟩	NUM
ejpam-4637	144	52	,	,	PUNCT
ejpam-4637	144	53	⟨s3	⟨s3	PROPN
ejpam-4637	144	54	,	,	PUNCT
ejpam-4637	144	55	(	(	PUNCT
ejpam-4637	144	56	0.5	0.5	NUM
ejpam-4637	144	57	,	,	PUNCT
ejpam-4637	144	58	0.6	0.6	NUM
ejpam-4637	144	59	,	,	PUNCT
ejpam-4637	144	60	0.4)⟩	0.4)⟩	NUM
ejpam-4637	144	61	}	}	PUNCT
ejpam-4637	144	62	)	)	PUNCT
ejpam-4637	144	63	(	(	PUNCT
ejpam-4637	144	64	a2	a2	PROPN
ejpam-4637	144	65	,	,	PUNCT
ejpam-4637	144	66	{	{	PUNCT
ejpam-4637	144	67	⟨s1	⟨s1	PROPN
ejpam-4637	144	68	,	,	PUNCT
ejpam-4637	144	69	(	(	PUNCT
ejpam-4637	144	70	0.8	0.8	NUM
ejpam-4637	144	71	,	,	PUNCT
ejpam-4637	144	72	0.4	0.4	NUM
ejpam-4637	144	73	,	,	PUNCT
ejpam-4637	144	74	0.5)⟩	0.5)⟩	NUM
ejpam-4637	144	75	,	,	PUNCT
ejpam-4637	144	76	⟨s2	⟨s2	PROPN
ejpam-4637	144	77	,	,	PUNCT
ejpam-4637	144	78	(	(	PUNCT
ejpam-4637	144	79	0.7	0.7	NUM
ejpam-4637	144	80	,	,	PUNCT
ejpam-4637	144	81	0.7	0.7	NUM
ejpam-4637	144	82	,	,	PUNCT
ejpam-4637	144	83	0.3)⟩	0.3)⟩	NUM
ejpam-4637	144	84	,	,	PUNCT
ejpam-4637	144	85	⟨s3	⟨s3	PROPN
ejpam-4637	144	86	,	,	PUNCT
ejpam-4637	144	87	(	(	PUNCT
ejpam-4637	144	88	0.7	0.7	NUM
ejpam-4637	144	89	,	,	PUNCT
ejpam-4637	144	90	0.5	0.5	NUM
ejpam-4637	144	91	,	,	PUNCT
ejpam-4637	144	92	0.6)⟩	0.6)⟩	NUM
ejpam-4637	144	93	}	}	PUNCT
ejpam-4637	144	94	)	)	PUNCT
ejpam-4637	144	95	}	}	PUNCT
ejpam-4637	144	96	and	and	CCONJ
ejpam-4637	144	97	(	(	PUNCT
ejpam-4637	144	98	g	g	NOUN
ejpam-4637	144	99	,	,	PUNCT
ejpam-4637	144	100	e	e	NOUN
ejpam-4637	144	101	)	)	PUNCT
ejpam-4637	144	102	=	=	SYM
ejpam-4637	144	103	{	{	PUNCT
ejpam-4637	144	104	(	(	PUNCT
ejpam-4637	144	105	a1	a1	NOUN
ejpam-4637	144	106	,	,	PUNCT
ejpam-4637	144	107	{	{	PUNCT
ejpam-4637	144	108	⟨s1	⟨s1	NOUN
ejpam-4637	144	109	,	,	PUNCT
ejpam-4637	144	110	(	(	PUNCT
ejpam-4637	144	111	0.8	0.8	NUM
ejpam-4637	144	112	,	,	PUNCT
ejpam-4637	144	113	0.5	0.5	NUM
ejpam-4637	144	114	,	,	PUNCT
ejpam-4637	144	115	0.6)⟩	0.6)⟩	NUM
ejpam-4637	144	116	,	,	PUNCT
ejpam-4637	144	117	⟨s2	⟨s2	PROPN
ejpam-4637	144	118	,	,	PUNCT
ejpam-4637	144	119	(	(	PUNCT
ejpam-4637	144	120	0.5	0.5	NUM
ejpam-4637	144	121	,	,	PUNCT
ejpam-4637	144	122	0.7	0.7	NUM
ejpam-4637	144	123	,	,	PUNCT
ejpam-4637	144	124	0.6)⟩	0.6)⟩	NUM
ejpam-4637	144	125	,	,	PUNCT
ejpam-4637	144	126	⟨s3	⟨s3	PROPN
ejpam-4637	144	127	,	,	PUNCT
ejpam-4637	144	128	(	(	PUNCT
ejpam-4637	144	129	0.4	0.4	NUM
ejpam-4637	144	130	,	,	PUNCT
ejpam-4637	144	131	0.7	0.7	NUM
ejpam-4637	144	132	,	,	PUNCT
ejpam-4637	144	133	0.5)⟩	0.5)⟩	NUM
ejpam-4637	144	134	}	}	PUNCT
ejpam-4637	144	135	)	)	PUNCT
ejpam-4637	144	136	(	(	PUNCT
ejpam-4637	144	137	a2	a2	PROPN
ejpam-4637	144	138	,	,	PUNCT
ejpam-4637	144	139	{	{	PUNCT
ejpam-4637	144	140	⟨s1	⟨s1	PROPN
ejpam-4637	144	141	,	,	PUNCT
ejpam-4637	144	142	(	(	PUNCT
ejpam-4637	144	143	0.7	0.7	NUM
ejpam-4637	144	144	,	,	PUNCT
ejpam-4637	144	145	0.6	0.6	NUM
ejpam-4637	144	146	,	,	PUNCT
ejpam-4637	144	147	0.5)⟩	0.5)⟩	NUM
ejpam-4637	144	148	,	,	PUNCT
ejpam-4637	144	149	⟨s2	⟨s2	PROPN
ejpam-4637	144	150	,	,	PUNCT
ejpam-4637	144	151	(	(	PUNCT
ejpam-4637	144	152	0.6	0.6	NUM
ejpam-4637	144	153	,	,	PUNCT
ejpam-4637	144	154	0.8	0.8	NUM
ejpam-4637	144	155	,	,	PUNCT
ejpam-4637	144	156	0.4)⟩	0.4)⟩	NUM
ejpam-4637	144	157	,	,	PUNCT
ejpam-4637	144	158	⟨s3	⟨s3	PROPN
ejpam-4637	144	159	,	,	PUNCT
ejpam-4637	144	160	(	(	PUNCT
ejpam-4637	144	161	0.5	0.5	NUM
ejpam-4637	144	162	,	,	PUNCT
ejpam-4637	144	163	0.8	0.8	NUM
ejpam-4637	144	164	,	,	PUNCT
ejpam-4637	144	165	0.6)⟩	0.6)⟩	NUM
ejpam-4637	144	166	}	}	PUNCT
ejpam-4637	144	167	)	)	PUNCT
ejpam-4637	144	168	}	}	PUNCT
ejpam-4637	144	169	.	.	PUNCT
ejpam-4637	145	1	thus	thus	ADV
ejpam-4637	145	2	,	,	PUNCT
ejpam-4637	145	3	their	their	PRON
ejpam-4637	145	4	union	union	NOUN
ejpam-4637	145	5	and	and	CCONJ
ejpam-4637	145	6	intersection	intersection	NOUN
ejpam-4637	145	7	are	be	AUX
ejpam-4637	145	8	(	(	PUNCT
ejpam-4637	145	9	h	h	NOUN
ejpam-4637	145	10	,	,	PUNCT
ejpam-4637	145	11	e	e	NOUN
ejpam-4637	145	12	)	)	PUNCT
ejpam-4637	145	13	∪	∪	ADV
ejpam-4637	145	14	(	(	PUNCT
ejpam-4637	145	15	g	g	NOUN
ejpam-4637	145	16	,	,	PUNCT
ejpam-4637	145	17	e	e	NOUN
ejpam-4637	145	18	)	)	PUNCT
ejpam-4637	145	19	=	=	SYM
ejpam-4637	145	20	{	{	PUNCT
ejpam-4637	145	21	(	(	PUNCT
ejpam-4637	145	22	a1	a1	NOUN
ejpam-4637	145	23	,	,	PUNCT
ejpam-4637	145	24	{	{	PUNCT
ejpam-4637	145	25	⟨s1	⟨s1	NOUN
ejpam-4637	145	26	,	,	PUNCT
ejpam-4637	145	27	(	(	PUNCT
ejpam-4637	145	28	0.8	0.8	NUM
ejpam-4637	145	29	,	,	PUNCT
ejpam-4637	145	30	0.5	0.5	NUM
ejpam-4637	145	31	,	,	PUNCT
ejpam-4637	145	32	0.4)⟩	0.4)⟩	NUM
ejpam-4637	145	33	,	,	PUNCT
ejpam-4637	145	34	⟨s2	⟨s2	PROPN
ejpam-4637	145	35	,	,	PUNCT
ejpam-4637	145	36	(	(	PUNCT
ejpam-4637	145	37	0.6	0.6	NUM
ejpam-4637	145	38	,	,	PUNCT
ejpam-4637	145	39	0.6	0.6	NUM
ejpam-4637	145	40	,	,	PUNCT
ejpam-4637	145	41	0.6)⟩	0.6)⟩	NUM
ejpam-4637	145	42	,	,	PUNCT
ejpam-4637	145	43	⟨s3	⟨s3	PROPN
ejpam-4637	145	44	,	,	PUNCT
ejpam-4637	145	45	(	(	PUNCT
ejpam-4637	145	46	0.5	0.5	NUM
ejpam-4637	145	47	,	,	PUNCT
ejpam-4637	145	48	0.6	0.6	NUM
ejpam-4637	145	49	,	,	PUNCT
ejpam-4637	145	50	0.4)⟩	0.4)⟩	NUM
ejpam-4637	145	51	}	}	PUNCT
ejpam-4637	145	52	)	)	PUNCT
ejpam-4637	145	53	(	(	PUNCT
ejpam-4637	145	54	a2	a2	PROPN
ejpam-4637	145	55	,	,	PUNCT
ejpam-4637	145	56	{	{	PUNCT
ejpam-4637	145	57	⟨s1	⟨s1	PROPN
ejpam-4637	145	58	,	,	PUNCT
ejpam-4637	145	59	(	(	PUNCT
ejpam-4637	145	60	0.8	0.8	NUM
ejpam-4637	145	61	,	,	PUNCT
ejpam-4637	145	62	0.4	0.4	NUM
ejpam-4637	145	63	,	,	PUNCT
ejpam-4637	145	64	0.5)⟩	0.5)⟩	NUM
ejpam-4637	145	65	,	,	PUNCT
ejpam-4637	145	66	⟨s2	⟨s2	PROPN
ejpam-4637	145	67	,	,	PUNCT
ejpam-4637	145	68	(	(	PUNCT
ejpam-4637	145	69	0.7	0.7	NUM
ejpam-4637	145	70	,	,	PUNCT
ejpam-4637	145	71	0.7	0.7	NUM
ejpam-4637	145	72	,	,	PUNCT
ejpam-4637	145	73	0.3)⟩	0.3)⟩	NUM
ejpam-4637	145	74	,	,	PUNCT
ejpam-4637	145	75	⟨s3	⟨s3	PROPN
ejpam-4637	145	76	,	,	PUNCT
ejpam-4637	145	77	(	(	PUNCT
ejpam-4637	145	78	0.7	0.7	NUM
ejpam-4637	145	79	,	,	PUNCT
ejpam-4637	145	80	0.5	0.5	NUM
ejpam-4637	145	81	,	,	PUNCT
ejpam-4637	145	82	0.6)⟩	0.6)⟩	NUM
ejpam-4637	145	83	}	}	PUNCT
ejpam-4637	145	84	)	)	PUNCT
ejpam-4637	145	85	}	}	PUNCT
ejpam-4637	145	86	and	and	CCONJ
ejpam-4637	145	87	(	(	PUNCT
ejpam-4637	145	88	h	h	NOUN
ejpam-4637	145	89	,	,	PUNCT
ejpam-4637	145	90	e	e	NOUN
ejpam-4637	145	91	)	)	PUNCT
ejpam-4637	145	92	∩	∩	NOUN
ejpam-4637	145	93	(	(	PUNCT
ejpam-4637	145	94	g	g	NOUN
ejpam-4637	145	95	,	,	PUNCT
ejpam-4637	145	96	e	e	NOUN
ejpam-4637	145	97	)	)	PUNCT
ejpam-4637	145	98	=	=	SYM
ejpam-4637	145	99	{	{	PUNCT
ejpam-4637	145	100	(	(	PUNCT
ejpam-4637	145	101	a1	a1	NOUN
ejpam-4637	145	102	,	,	PUNCT
ejpam-4637	145	103	{	{	PUNCT
ejpam-4637	145	104	⟨s1	⟨s1	NOUN
ejpam-4637	145	105	,	,	PUNCT
ejpam-4637	145	106	(	(	PUNCT
ejpam-4637	145	107	0.1	0.1	NUM
ejpam-4637	145	108	,	,	PUNCT
ejpam-4637	145	109	0.5	0.5	NUM
ejpam-4637	145	110	,	,	PUNCT
ejpam-4637	145	111	0.6)⟩	0.6)⟩	NUM
ejpam-4637	145	112	,	,	PUNCT
ejpam-4637	145	113	⟨s2	⟨s2	PROPN
ejpam-4637	145	114	,	,	PUNCT
ejpam-4637	145	115	(	(	PUNCT
ejpam-4637	145	116	0.5	0.5	NUM
ejpam-4637	145	117	,	,	PUNCT
ejpam-4637	145	118	0.7	0.7	NUM
ejpam-4637	145	119	,	,	PUNCT
ejpam-4637	145	120	0.7)⟩	0.7)⟩	NUM
ejpam-4637	145	121	,	,	PUNCT
ejpam-4637	145	122	⟨s3	⟨s3	PROPN
ejpam-4637	145	123	,	,	PUNCT
ejpam-4637	145	124	(	(	PUNCT
ejpam-4637	145	125	0.4	0.4	NUM
ejpam-4637	145	126	,	,	PUNCT
ejpam-4637	145	127	0.7	0.7	NUM
ejpam-4637	145	128	,	,	PUNCT
ejpam-4637	145	129	0.5)⟩	0.5)⟩	NUM
ejpam-4637	145	130	}	}	PUNCT
ejpam-4637	145	131	)	)	PUNCT
ejpam-4637	145	132	(	(	PUNCT
ejpam-4637	145	133	a2	a2	PROPN
ejpam-4637	145	134	,	,	PUNCT
ejpam-4637	145	135	{	{	PUNCT
ejpam-4637	145	136	⟨s1	⟨s1	PROPN
ejpam-4637	145	137	,	,	PUNCT
ejpam-4637	145	138	(	(	PUNCT
ejpam-4637	145	139	0.7	0.7	NUM
ejpam-4637	145	140	,	,	PUNCT
ejpam-4637	145	141	0.6	0.6	NUM
ejpam-4637	145	142	,	,	PUNCT
ejpam-4637	145	143	0.5)⟩	0.5)⟩	NUM
ejpam-4637	145	144	,	,	PUNCT
ejpam-4637	145	145	⟨s2	⟨s2	PROPN
ejpam-4637	145	146	,	,	PUNCT
ejpam-4637	145	147	(	(	PUNCT
ejpam-4637	145	148	0.6	0.6	NUM
ejpam-4637	145	149	,	,	PUNCT
ejpam-4637	145	150	0.8	0.8	NUM
ejpam-4637	145	151	,	,	PUNCT
ejpam-4637	145	152	0.4)⟩	0.4)⟩	NUM
ejpam-4637	145	153	,	,	PUNCT
ejpam-4637	145	154	⟨s3	⟨s3	PROPN
ejpam-4637	145	155	,	,	PUNCT
ejpam-4637	145	156	(	(	PUNCT
ejpam-4637	145	157	0.5	0.5	NUM
ejpam-4637	145	158	,	,	PUNCT
ejpam-4637	145	159	0.8	0.8	NUM
ejpam-4637	145	160	,	,	PUNCT
ejpam-4637	145	161	0.6)⟩	0.6)⟩	NUM
ejpam-4637	145	162	}	}	PUNCT
ejpam-4637	145	163	)	)	PUNCT
ejpam-4637	145	164	}	}	PUNCT
ejpam-4637	145	165	,	,	PUNCT
ejpam-4637	145	166	respectively	respectively	ADV
ejpam-4637	145	167	.	.	PUNCT
ejpam-4637	146	1	3	3	X
ejpam-4637	146	2	.	.	X
ejpam-4637	146	3	main	main	ADJ
ejpam-4637	146	4	results	result	NOUN
ejpam-4637	146	5	3.1	3.1	NUM
ejpam-4637	146	6	.	.	PUNCT
ejpam-4637	146	7	single	single	ADV
ejpam-4637	146	8	-	-	PUNCT
ejpam-4637	146	9	valued	value	VERB
ejpam-4637	146	10	neutrosophic	neutrosophic	ADJ
ejpam-4637	146	11	hyper	hyper	ADJ
ejpam-4637	146	12	up	up	NOUN
ejpam-4637	146	13	-	-	PUNCT
ejpam-4637	146	14	subalgebra	subalgebra	NOUN
ejpam-4637	146	15	in	in	ADP
ejpam-4637	146	16	this	this	DET
ejpam-4637	146	17	section	section	NOUN
ejpam-4637	146	18	,	,	PUNCT
ejpam-4637	146	19	we	we	PRON
ejpam-4637	146	20	introduce	introduce	VERB
ejpam-4637	146	21	the	the	DET
ejpam-4637	146	22	concept	concept	NOUN
ejpam-4637	146	23	of	of	ADP
ejpam-4637	146	24	single	single	ADV
ejpam-4637	146	25	-	-	PUNCT
ejpam-4637	146	26	valued	value	VERB
ejpam-4637	146	27	neutrosophic	neutrosophic	ADJ
ejpam-4637	146	28	hyper	hyper	NOUN
ejpam-4637	146	29	up	up	ADP
ejpam-4637	146	30	subalgebra	subalgebra	NOUN
ejpam-4637	146	31	and	and	CCONJ
ejpam-4637	146	32	prove	prove	VERB
ejpam-4637	146	33	some	some	PRON
ejpam-4637	146	34	of	of	ADP
ejpam-4637	146	35	its	its	PRON
ejpam-4637	146	36	basic	basic	ADJ
ejpam-4637	146	37	properties	property	NOUN
ejpam-4637	146	38	.	.	PUNCT
ejpam-4637	147	1	from	from	ADP
ejpam-4637	147	2	here	here	ADV
ejpam-4637	147	3	onwards	onward	NOUN
ejpam-4637	147	4	,	,	PUNCT
ejpam-4637	147	5	we	we	PRON
ejpam-4637	147	6	simply	simply	ADV
ejpam-4637	147	7	denote	denote	VERB
ejpam-4637	147	8	a	a	DET
ejpam-4637	147	9	hyper	hyper	ADJ
ejpam-4637	147	10	up	up	ADP
ejpam-4637	147	11	-algebra	-algebra	PROPN
ejpam-4637	147	12	(	(	PUNCT
ejpam-4637	147	13	x	x	NOUN
ejpam-4637	147	14	,	,	PUNCT
ejpam-4637	147	15	◦	◦	NOUN
ejpam-4637	147	16	,	,	PUNCT
ejpam-4637	147	17	≪	≪	ADJ
ejpam-4637	147	18	,	,	PUNCT
ejpam-4637	147	19	0	0	NUM
ejpam-4637	147	20	)	)	PUNCT
ejpam-4637	147	21	by	by	ADP
ejpam-4637	147	22	x.	x.	NOUN
ejpam-4637	147	23	given	give	VERB
ejpam-4637	147	24	a	a	DET
ejpam-4637	147	25	single	single	ADV
ejpam-4637	147	26	-	-	PUNCT
ejpam-4637	147	27	valued	value	VERB
ejpam-4637	147	28	neutrosophic	neutrosophic	ADJ
ejpam-4637	147	29	set	set	VERB
ejpam-4637	147	30	a	a	DET
ejpam-4637	147	31	=	=	X
ejpam-4637	147	32	(	(	PUNCT
ejpam-4637	147	33	ta	ta	PROPN
ejpam-4637	147	34	,	,	PUNCT
ejpam-4637	147	35	ia	ia	PROPN
ejpam-4637	147	36	,	,	PUNCT
ejpam-4637	147	37	fa	fa	NOUN
ejpam-4637	147	38	)	)	PUNCT
ejpam-4637	147	39	in	in	ADP
ejpam-4637	147	40	a	a	DET
ejpam-4637	147	41	hyper	hyper	NOUN
ejpam-4637	147	42	up	up	ADP
ejpam-4637	147	43	-algebra	-algebra	PROPN
ejpam-4637	147	44	x	x	X
ejpam-4637	147	45	and	and	CCONJ
ejpam-4637	147	46	a	a	DET
ejpam-4637	147	47	subset	subset	NOUN
ejpam-4637	147	48	s	s	NOUN
ejpam-4637	147	49	of	of	ADP
ejpam-4637	147	50	x	x	PRON
ejpam-4637	147	51	,	,	PUNCT
ejpam-4637	147	52	we	we	PRON
ejpam-4637	147	53	denote	denote	VERB
ejpam-4637	147	54	the	the	DET
ejpam-4637	147	55	following	following	NOUN
ejpam-4637	147	56	:	:	PUNCT
ejpam-4637	147	57	∗ta(s	∗ta(s	NOUN
ejpam-4637	147	58	)	)	PUNCT
ejpam-4637	147	59	=	=	SYM
ejpam-4637	147	60	sup	sup	NOUN
ejpam-4637	147	61	y∈s	y∈s	NOUN
ejpam-4637	147	62	ta(y	ta(y	PUNCT
ejpam-4637	147	63	)	)	PUNCT
ejpam-4637	147	64	and	and	CCONJ
ejpam-4637	147	65	∗ta(s	∗ta(s	PROPN
ejpam-4637	147	66	)	)	PUNCT
ejpam-4637	147	67	=	=	SYM
ejpam-4637	147	68	inf	inf	PROPN
ejpam-4637	147	69	y∈s	y∈s	NOUN
ejpam-4637	147	70	ta(y	ta(y	PUNCT
ejpam-4637	147	71	)	)	PUNCT
ejpam-4637	147	72	;	;	PUNCT
ejpam-4637	147	73	∗ia(s	∗ia(s	PROPN
ejpam-4637	147	74	)	)	PUNCT
ejpam-4637	147	75	=	=	SYM
ejpam-4637	147	76	sup	sup	NOUN
ejpam-4637	147	77	y∈s	y∈s	NOUN
ejpam-4637	147	78	ia(y	ia(y	NOUN
ejpam-4637	147	79	)	)	PUNCT
ejpam-4637	147	80	and	and	CCONJ
ejpam-4637	147	81	∗ia(s	∗ia(s	PROPN
ejpam-4637	147	82	)	)	PUNCT
ejpam-4637	147	83	=	=	PROPN
ejpam-4637	147	84	inf	inf	PROPN
ejpam-4637	147	85	y∈s	y∈s	NOUN
ejpam-4637	147	86	ia(y	ia(y	NOUN
ejpam-4637	147	87	)	)	PUNCT
ejpam-4637	147	88	;	;	PUNCT
ejpam-4637	147	89	∗fa(s	∗fa(s	NUM
ejpam-4637	147	90	)	)	PUNCT
ejpam-4637	147	91	=	=	SYM
ejpam-4637	147	92	sup	sup	NOUN
ejpam-4637	147	93	y∈s	y∈s	NOUN
ejpam-4637	147	94	fa(y	fa(y	NOUN
ejpam-4637	147	95	)	)	PUNCT
ejpam-4637	147	96	and	and	CCONJ
ejpam-4637	147	97	∗fa(s	∗fa(	VERB
ejpam-4637	147	98	)	)	PUNCT
ejpam-4637	147	99	=	=	SYM
ejpam-4637	147	100	inf	inf	PROPN
ejpam-4637	147	101	y∈s	y∈s	NOUN
ejpam-4637	147	102	fa(y	fa(y	PROPN
ejpam-4637	147	103	)	)	PUNCT
ejpam-4637	147	104	.	.	PUNCT
ejpam-4637	148	1	definition	definition	NOUN
ejpam-4637	148	2	16	16	NUM
ejpam-4637	148	3	.	.	PUNCT
ejpam-4637	149	1	let	let	VERB
ejpam-4637	149	2	a	a	PRON
ejpam-4637	149	3	=	=	SYM
ejpam-4637	149	4	(	(	PUNCT
ejpam-4637	149	5	ta	ta	PROPN
ejpam-4637	149	6	,	,	PUNCT
ejpam-4637	149	7	ia	ia	PROPN
ejpam-4637	149	8	,	,	PUNCT
ejpam-4637	149	9	fa	fa	NOUN
ejpam-4637	149	10	)	)	PUNCT
ejpam-4637	149	11	be	be	AUX
ejpam-4637	149	12	a	a	DET
ejpam-4637	149	13	single	single	ADV
ejpam-4637	149	14	-	-	PUNCT
ejpam-4637	149	15	valued	value	VERB
ejpam-4637	149	16	neutrosophic	neutrosophic	ADJ
ejpam-4637	149	17	set	set	NOUN
ejpam-4637	149	18	in	in	ADP
ejpam-4637	149	19	a	a	DET
ejpam-4637	149	20	hyper	hyper	NOUN
ejpam-4637	149	21	up	up	ADP
ejpam-4637	149	22	algebra	algebra	PROPN
ejpam-4637	149	23	x.	x.	NOUN
ejpam-4637	150	1	then	then	ADV
ejpam-4637	150	2	a	a	PRON
ejpam-4637	150	3	is	be	AUX
ejpam-4637	150	4	said	say	VERB
ejpam-4637	150	5	to	to	PART
ejpam-4637	150	6	be	be	AUX
ejpam-4637	150	7	a	a	DET
ejpam-4637	150	8	single	single	ADV
ejpam-4637	150	9	-	-	PUNCT
ejpam-4637	150	10	valued	value	VERB
ejpam-4637	150	11	neutrosophic	neutrosophic	ADJ
ejpam-4637	150	12	(	(	PUNCT
ejpam-4637	150	13	svn	svn	NOUN
ejpam-4637	150	14	)	)	PUNCT
ejpam-4637	150	15	hyper	hyper	ADJ
ejpam-4637	150	16	up	up	ADP
ejpam-4637	150	17	-	-	PUNCT
ejpam-4637	150	18	subalgebra	subalgebra	NOUN
ejpam-4637	150	19	of	of	ADP
ejpam-4637	150	20	x	x	PRON
ejpam-4637	150	21	if	if	SCONJ
ejpam-4637	150	22	for	for	ADP
ejpam-4637	150	23	all	all	DET
ejpam-4637	150	24	x	x	NOUN
ejpam-4637	150	25	,	,	PUNCT
ejpam-4637	150	26	y	y	PROPN
ejpam-4637	150	27	∈	∈	PROPN
ejpam-4637	150	28	x	x	X
ejpam-4637	150	29	,	,	PUNCT
ejpam-4637	150	30	∗ta(x	∗ta(x	PROPN
ejpam-4637	150	31	◦	◦	NOUN
ejpam-4637	150	32	y	y	NOUN
ejpam-4637	150	33	)	)	PUNCT
ejpam-4637	150	34	≥	≥	NOUN
ejpam-4637	150	35	min{ta(x	min{ta(x	NOUN
ejpam-4637	150	36	)	)	PUNCT
ejpam-4637	150	37	,	,	PUNCT
ejpam-4637	150	38	ta(y	ta(y	NUM
ejpam-4637	150	39	)	)	PUNCT
ejpam-4637	150	40	}	}	PUNCT
ejpam-4637	150	41	,	,	PUNCT
ejpam-4637	150	42	a.	a.	PROPN
ejpam-4637	150	43	cano	cano	PROPN
ejpam-4637	150	44	,	,	PUNCT
ejpam-4637	150	45	g.	g.	PROPN
ejpam-4637	150	46	petalcorin	petalcorin	PROPN
ejpam-4637	150	47	/	/	SYM
ejpam-4637	150	48	eur	eur	PROPN
ejpam-4637	150	49	.	.	PUNCT
ejpam-4637	151	1	j.	j.	PROPN
ejpam-4637	151	2	pure	pure	PROPN
ejpam-4637	151	3	appl	appl	PROPN
ejpam-4637	151	4	.	.	PROPN
ejpam-4637	151	5	math	math	PROPN
ejpam-4637	151	6	,	,	PUNCT
ejpam-4637	151	7	16	16	NUM
ejpam-4637	151	8	(	(	PUNCT
ejpam-4637	151	9	1	1	NUM
ejpam-4637	151	10	)	)	PUNCT
ejpam-4637	151	11	(	(	PUNCT
ejpam-4637	151	12	2023	2023	NUM
ejpam-4637	151	13	)	)	PUNCT
ejpam-4637	151	14	,	,	PUNCT
ejpam-4637	151	15	548	548	NUM
ejpam-4637	151	16	-	-	SYM
ejpam-4637	151	17	576	576	NUM
ejpam-4637	151	18	555	555	NUM
ejpam-4637	151	19	∗ia(x	∗ia(x	NOUN
ejpam-4637	151	20	◦	◦	NOUN
ejpam-4637	151	21	y	y	NOUN
ejpam-4637	151	22	)	)	PUNCT
ejpam-4637	151	23	≤	≤	NUM
ejpam-4637	151	24	max{ia(x	max{ia(x	NOUN
ejpam-4637	151	25	)	)	PUNCT
ejpam-4637	151	26	,	,	PUNCT
ejpam-4637	151	27	ia(y	ia(y	NOUN
ejpam-4637	151	28	)	)	PUNCT
ejpam-4637	151	29	}	}	PUNCT
ejpam-4637	151	30	,	,	PUNCT
ejpam-4637	151	31	and	and	CCONJ
ejpam-4637	151	32	∗fa(x	∗fa(x	NOUN
ejpam-4637	151	33	◦	◦	VERB
ejpam-4637	151	34	y	y	NOUN
ejpam-4637	151	35	)	)	PUNCT
ejpam-4637	151	36	≤	≤	NOUN
ejpam-4637	151	37	max{fa(x),fa(y	max{fa(x),fa(y	PROPN
ejpam-4637	151	38	)	)	PUNCT
ejpam-4637	151	39	}	}	PUNCT
ejpam-4637	151	40	.	.	PUNCT
ejpam-4637	152	1	example	example	NOUN
ejpam-4637	152	2	5	5	NUM
ejpam-4637	152	3	.	.	X
ejpam-4637	153	1	consider	consider	VERB
ejpam-4637	153	2	a	a	DET
ejpam-4637	153	3	hyperup	hyperup	NOUN
ejpam-4637	153	4	-algebra	-algebra	NOUN
ejpam-4637	153	5	(	(	PUNCT
ejpam-4637	153	6	x	x	NOUN
ejpam-4637	153	7	,	,	PUNCT
ejpam-4637	153	8	◦	◦	NOUN
ejpam-4637	153	9	,	,	PUNCT
ejpam-4637	153	10	≪	≪	ADJ
ejpam-4637	153	11	,	,	PUNCT
ejpam-4637	153	12	0	0	NUM
ejpam-4637	153	13	)	)	PUNCT
ejpam-4637	153	14	of	of	ADP
ejpam-4637	153	15	example	example	NOUN
ejpam-4637	153	16	1	1	NUM
ejpam-4637	153	17	wherex	wherex	NOUN
ejpam-4637	153	18	=	=	SYM
ejpam-4637	153	19	{	{	PUNCT
ejpam-4637	153	20	0	0	NUM
ejpam-4637	153	21	,	,	PUNCT
ejpam-4637	153	22	r	r	NOUN
ejpam-4637	153	23	,	,	PUNCT
ejpam-4637	153	24	s	s	PROPN
ejpam-4637	153	25	,	,	PUNCT
ejpam-4637	153	26	t	t	PROPN
ejpam-4637	153	27	}	}	PUNCT
ejpam-4637	153	28	.	.	PUNCT
ejpam-4637	154	1	also	also	ADV
ejpam-4637	154	2	,	,	PUNCT
ejpam-4637	154	3	define	define	VERB
ejpam-4637	154	4	a	a	DET
ejpam-4637	154	5	single	single	ADV
ejpam-4637	154	6	-	-	PUNCT
ejpam-4637	154	7	valued	value	VERB
ejpam-4637	154	8	neutrosophic	neutrosophic	ADJ
ejpam-4637	154	9	set	set	VERB
ejpam-4637	154	10	a	a	PRON
ejpam-4637	154	11	=	=	X
ejpam-4637	154	12	(	(	PUNCT
ejpam-4637	154	13	ta	ta	PROPN
ejpam-4637	154	14	,	,	PUNCT
ejpam-4637	154	15	ia	ia	PROPN
ejpam-4637	154	16	,	,	PUNCT
ejpam-4637	154	17	fa	fa	NOUN
ejpam-4637	154	18	)	)	PUNCT
ejpam-4637	154	19	in	in	ADP
ejpam-4637	154	20	x	x	PUNCT
ejpam-4637	154	21	by	by	ADP
ejpam-4637	154	22	the	the	DET
ejpam-4637	154	23	following	following	NOUN
ejpam-4637	154	24	:	:	PUNCT
ejpam-4637	154	25	ta(x	ta(x	NOUN
ejpam-4637	154	26	)	)	PUNCT
ejpam-4637	154	27	=	=	SYM
ejpam-4637	155	1	(	(	PUNCT
ejpam-4637	155	2	0	0	NUM
ejpam-4637	155	3	r	r	NOUN
ejpam-4637	155	4	s	s	PROPN
ejpam-4637	155	5	t	t	NOUN
ejpam-4637	155	6	0.87	0.87	NUM
ejpam-4637	155	7	0.42	0.42	NUM
ejpam-4637	155	8	0.56	0.56	NUM
ejpam-4637	155	9	0.29	0.29	NUM
ejpam-4637	155	10	)	)	PUNCT
ejpam-4637	155	11	,	,	PUNCT
ejpam-4637	155	12	ia(x	ia(x	NOUN
ejpam-4637	155	13	)	)	PUNCT
ejpam-4637	155	14	=	=	PUNCT
ejpam-4637	156	1	(	(	PUNCT
ejpam-4637	156	2	0	0	NUM
ejpam-4637	156	3	r	r	NOUN
ejpam-4637	156	4	s	s	PROPN
ejpam-4637	156	5	t	t	NOUN
ejpam-4637	156	6	0.39	0.39	NUM
ejpam-4637	156	7	0.79	0.79	NUM
ejpam-4637	156	8	0.76	0.76	NUM
ejpam-4637	156	9	0.94	0.94	NUM
ejpam-4637	156	10	)	)	PUNCT
ejpam-4637	156	11	,	,	PUNCT
ejpam-4637	156	12	and	and	CCONJ
ejpam-4637	156	13	fa(x	fa(x	PROPN
ejpam-4637	156	14	)	)	PUNCT
ejpam-4637	156	15	=	=	SYM
ejpam-4637	157	1	(	(	PUNCT
ejpam-4637	157	2	0	0	NUM
ejpam-4637	157	3	r	r	NOUN
ejpam-4637	157	4	s	s	PROPN
ejpam-4637	157	5	t	t	NOUN
ejpam-4637	157	6	0.49	0.49	NUM
ejpam-4637	157	7	0.83	0.83	NUM
ejpam-4637	157	8	0.53	0.53	NUM
ejpam-4637	157	9	0.95	0.95	NUM
ejpam-4637	157	10	)	)	PUNCT
ejpam-4637	157	11	.	.	PUNCT
ejpam-4637	158	1	by	by	ADP
ejpam-4637	158	2	routine	routine	ADJ
ejpam-4637	158	3	calculation	calculation	NOUN
ejpam-4637	158	4	,	,	PUNCT
ejpam-4637	158	5	a	a	PRON
ejpam-4637	158	6	is	be	AUX
ejpam-4637	158	7	a	a	DET
ejpam-4637	158	8	svn	svn	NOUN
ejpam-4637	158	9	hyper	hyper	NOUN
ejpam-4637	158	10	up	up	ADP
ejpam-4637	158	11	-subalgebra	-subalgebra	NOUN
ejpam-4637	158	12	of	of	ADP
ejpam-4637	158	13	x.	x.	NOUN
ejpam-4637	158	14	example	example	NOUN
ejpam-4637	158	15	6	6	NUM
ejpam-4637	158	16	.	.	PUNCT
ejpam-4637	159	1	consider	consider	VERB
ejpam-4637	159	2	x	x	X
ejpam-4637	159	3	=	=	NOUN
ejpam-4637	159	4	n	n	NOUN
ejpam-4637	159	5	∪	∪	X
ejpam-4637	159	6	{	{	PUNCT
ejpam-4637	159	7	0	0	NUM
ejpam-4637	159	8	}	}	PUNCT
ejpam-4637	159	9	and	and	CCONJ
ejpam-4637	159	10	a	a	DET
ejpam-4637	159	11	hyperoperation	hyperoperation	NOUN
ejpam-4637	159	12	“	"	PUNCT
ejpam-4637	159	13	◦	◦	NOUN
ejpam-4637	159	14	”	"	PUNCT
ejpam-4637	159	15	on	on	ADP
ejpam-4637	159	16	x	x	PUNCT
ejpam-4637	159	17	defined	define	VERB
ejpam-4637	159	18	by	by	ADP
ejpam-4637	159	19	x	x	SYM
ejpam-4637	159	20	◦	◦	NOUN
ejpam-4637	159	21	y	y	NOUN
ejpam-4637	159	22	=	=	SYM
ejpam-4637	159	23			PROPN
ejpam-4637	159	24	{	{	PUNCT
ejpam-4637	159	25	0	0	NUM
ejpam-4637	159	26	}	}	PUNCT
ejpam-4637	159	27	if	if	SCONJ
ejpam-4637	159	28	y	y	PROPN
ejpam-4637	159	29	=	=	SYM
ejpam-4637	159	30	0	0	PROPN
ejpam-4637	159	31	,	,	PUNCT
ejpam-4637	159	32	{	{	PUNCT
ejpam-4637	159	33	0	0	NUM
ejpam-4637	159	34	,	,	PUNCT
ejpam-4637	159	35	y	y	PROPN
ejpam-4637	159	36	}	}	PUNCT
ejpam-4637	159	37	if	if	SCONJ
ejpam-4637	159	38	y	y	PROPN
ejpam-4637	159	39	=	=	SYM
ejpam-4637	159	40	x	x	PROPN
ejpam-4637	159	41	,	,	PUNCT
ejpam-4637	159	42	y	y	PROPN
ejpam-4637	159	43	̸=	̸=	PROPN
ejpam-4637	159	44	0	0	NUM
ejpam-4637	159	45	,	,	PUNCT
ejpam-4637	159	46	{	{	PUNCT
ejpam-4637	159	47	y	y	NOUN
ejpam-4637	159	48	}	}	PUNCT
ejpam-4637	159	49	otherwise	otherwise	ADV
ejpam-4637	159	50	.	.	PUNCT
ejpam-4637	160	1	by	by	ADP
ejpam-4637	160	2	thorough	thorough	ADJ
ejpam-4637	160	3	inspection	inspection	NOUN
ejpam-4637	160	4	,	,	PUNCT
ejpam-4637	160	5	x	x	X
ejpam-4637	160	6	is	be	AUX
ejpam-4637	160	7	a	a	DET
ejpam-4637	160	8	hyper	hyper	ADJ
ejpam-4637	160	9	up	up	ADP
ejpam-4637	160	10	-algebra	-algebra	PROPN
ejpam-4637	160	11	.	.	PUNCT
ejpam-4637	161	1	define	define	VERB
ejpam-4637	161	2	a	a	DET
ejpam-4637	161	3	single	single	ADV
ejpam-4637	161	4	-	-	PUNCT
ejpam-4637	161	5	valued	value	VERB
ejpam-4637	161	6	neutrosophic	neutrosophic	ADJ
ejpam-4637	161	7	set	set	VERB
ejpam-4637	161	8	a	a	PRON
ejpam-4637	161	9	=	=	X
ejpam-4637	161	10	(	(	PUNCT
ejpam-4637	161	11	ta	ta	PROPN
ejpam-4637	161	12	,	,	PUNCT
ejpam-4637	161	13	ia	ia	PROPN
ejpam-4637	161	14	,	,	PUNCT
ejpam-4637	161	15	fa	fa	NOUN
ejpam-4637	161	16	)	)	PUNCT
ejpam-4637	161	17	in	in	ADP
ejpam-4637	161	18	x	x	PUNCT
ejpam-4637	161	19	by	by	ADP
ejpam-4637	161	20	ta(x	ta(x	NOUN
ejpam-4637	161	21	)	)	PUNCT
ejpam-4637	161	22	=	=	PRON
ejpam-4637	161	23	{	{	PUNCT
ejpam-4637	161	24	1	1	NUM
ejpam-4637	161	25	if	if	SCONJ
ejpam-4637	161	26	x	x	PROPN
ejpam-4637	161	27	=	=	SYM
ejpam-4637	161	28	0	0	NUM
ejpam-4637	161	29	,	,	PUNCT
ejpam-4637	161	30	0.5	0.5	NUM
ejpam-4637	161	31	if	if	SCONJ
ejpam-4637	161	32	x	x	NUM
ejpam-4637	161	33	̸=	̸=	PROPN
ejpam-4637	161	34	0	0	NUM
ejpam-4637	161	35	.	.	PUNCT
ejpam-4637	161	36	ia(x	ia(x	PROPN
ejpam-4637	161	37	)	)	PUNCT
ejpam-4637	162	1	=	=	PRON
ejpam-4637	162	2	{	{	PUNCT
ejpam-4637	162	3	0	0	NUM
ejpam-4637	162	4	if	if	SCONJ
ejpam-4637	162	5	x	x	X
ejpam-4637	162	6	=	=	SYM
ejpam-4637	162	7	0	0	NUM
ejpam-4637	162	8	,	,	PUNCT
ejpam-4637	162	9	0.5	0.5	NUM
ejpam-4637	162	10	if	if	SCONJ
ejpam-4637	162	11	x	x	NUM
ejpam-4637	162	12	̸=	̸=	PROPN
ejpam-4637	162	13	0	0	NUM
ejpam-4637	162	14	.	.	PUNCT
ejpam-4637	163	1	fa(x	fa(x	PROPN
ejpam-4637	163	2	)	)	PUNCT
ejpam-4637	164	1	=	=	PRON
ejpam-4637	164	2	{	{	PUNCT
ejpam-4637	164	3	0	0	NUM
ejpam-4637	164	4	if	if	SCONJ
ejpam-4637	164	5	x	x	X
ejpam-4637	164	6	=	=	SYM
ejpam-4637	164	7	0	0	NUM
ejpam-4637	164	8	,	,	PUNCT
ejpam-4637	164	9	0.5	0.5	NUM
ejpam-4637	164	10	if	if	SCONJ
ejpam-4637	164	11	x	x	NUM
ejpam-4637	164	12	̸=	̸=	PROPN
ejpam-4637	164	13	0	0	NUM
ejpam-4637	164	14	.	.	PUNCT
ejpam-4637	165	1	again	again	ADV
ejpam-4637	165	2	,	,	PUNCT
ejpam-4637	165	3	by	by	ADP
ejpam-4637	165	4	thorough	thorough	ADJ
ejpam-4637	165	5	inspection	inspection	NOUN
ejpam-4637	165	6	,	,	PUNCT
ejpam-4637	165	7	a	a	PRON
ejpam-4637	165	8	is	be	AUX
ejpam-4637	165	9	a	a	DET
ejpam-4637	165	10	svn	svn	NOUN
ejpam-4637	165	11	hyper	hyper	NOUN
ejpam-4637	165	12	up	up	ADP
ejpam-4637	165	13	-subalgebra	-subalgebra	NOUN
ejpam-4637	165	14	of	of	ADP
ejpam-4637	165	15	x.	x.	NOUN
ejpam-4637	165	16	proposition	proposition	NOUN
ejpam-4637	165	17	3	3	NUM
ejpam-4637	165	18	.	.	PUNCT
ejpam-4637	166	1	let	let	VERB
ejpam-4637	166	2	a	a	PRON
ejpam-4637	166	3	=	=	SYM
ejpam-4637	166	4	(	(	PUNCT
ejpam-4637	166	5	ta	ta	PROPN
ejpam-4637	166	6	,	,	PUNCT
ejpam-4637	166	7	ia	ia	PROPN
ejpam-4637	166	8	,	,	PUNCT
ejpam-4637	166	9	fa	fa	NOUN
ejpam-4637	166	10	)	)	PUNCT
ejpam-4637	166	11	be	be	AUX
ejpam-4637	166	12	a	a	DET
ejpam-4637	166	13	svn	svn	NOUN
ejpam-4637	166	14	hyper	hyper	NOUN
ejpam-4637	166	15	up	up	ADP
ejpam-4637	166	16	-	-	PUNCT
ejpam-4637	166	17	subalgebra	subalgebra	NOUN
ejpam-4637	166	18	of	of	ADP
ejpam-4637	166	19	x.	x.	NOUN
ejpam-4637	166	20	then	then	ADV
ejpam-4637	166	21	for	for	ADP
ejpam-4637	166	22	all	all	DET
ejpam-4637	166	23	x	x	NOUN
ejpam-4637	166	24	,	,	PUNCT
ejpam-4637	166	25	y	y	PROPN
ejpam-4637	166	26	∈	∈	PROPN
ejpam-4637	166	27	x	x	X
ejpam-4637	166	28	,	,	PUNCT
ejpam-4637	166	29	(	(	PUNCT
ejpam-4637	166	30	i	i	NOUN
ejpam-4637	166	31	)	)	PUNCT
ejpam-4637	166	32	ta(0	ta(0	NOUN
ejpam-4637	166	33	)	)	PUNCT
ejpam-4637	166	34	≥	≥	NOUN
ejpam-4637	166	35	ta(x	ta(x	NOUN
ejpam-4637	166	36	)	)	PUNCT
ejpam-4637	166	37	ia(0	ia(0	NOUN
ejpam-4637	166	38	)	)	PUNCT
ejpam-4637	166	39	≤	≤	NOUN
ejpam-4637	166	40	ia(x	ia(x	NOUN
ejpam-4637	166	41	)	)	PUNCT
ejpam-4637	166	42	fa(0	fa(0	NOUN
ejpam-4637	166	43	)	)	PUNCT
ejpam-4637	166	44	≤	≤	NOUN
ejpam-4637	166	45	fa(x	fa(x	NOUN
ejpam-4637	166	46	)	)	PUNCT
ejpam-4637	166	47	.	.	PUNCT
ejpam-4637	167	1	(	(	PUNCT
ejpam-4637	167	2	ii	ii	NOUN
ejpam-4637	167	3	)	)	PUNCT
ejpam-4637	167	4	∗ta(0	∗ta(0	VERB
ejpam-4637	168	1	◦	◦	NOUN
ejpam-4637	168	2	x	x	SYM
ejpam-4637	168	3	)	)	PUNCT
ejpam-4637	168	4	=	=	SYM
ejpam-4637	168	5	ta(x	ta(x	NOUN
ejpam-4637	168	6	)	)	PUNCT
ejpam-4637	168	7	∗ia(0	∗ia(0	VERB
ejpam-4637	168	8	◦	◦	NOUN
ejpam-4637	168	9	x	x	SYM
ejpam-4637	168	10	)	)	PUNCT
ejpam-4637	168	11	=	=	SYM
ejpam-4637	168	12	ia(x	ia(x	NOUN
ejpam-4637	168	13	)	)	PUNCT
ejpam-4637	168	14	∗fa(0	∗fa(0	VERB
ejpam-4637	168	15	◦	◦	NOUN
ejpam-4637	168	16	x	x	NOUN
ejpam-4637	168	17	)	)	PUNCT
ejpam-4637	168	18	=	=	SYM
ejpam-4637	168	19	fa(x	fa(x	PROPN
ejpam-4637	169	1	)	)	PUNCT
ejpam-4637	169	2	a.	a.	NOUN
ejpam-4637	169	3	cano	cano	PROPN
ejpam-4637	169	4	,	,	PUNCT
ejpam-4637	169	5	g.	g.	PROPN
ejpam-4637	169	6	petalcorin	petalcorin	PROPN
ejpam-4637	169	7	/	/	SYM
ejpam-4637	169	8	eur	eur	PROPN
ejpam-4637	169	9	.	.	PUNCT
ejpam-4637	170	1	j.	j.	PROPN
ejpam-4637	170	2	pure	pure	PROPN
ejpam-4637	170	3	appl	appl	PROPN
ejpam-4637	170	4	.	.	PROPN
ejpam-4637	170	5	math	math	PROPN
ejpam-4637	170	6	,	,	PUNCT
ejpam-4637	170	7	16	16	NUM
ejpam-4637	170	8	(	(	PUNCT
ejpam-4637	170	9	1	1	NUM
ejpam-4637	170	10	)	)	PUNCT
ejpam-4637	170	11	(	(	PUNCT
ejpam-4637	170	12	2023	2023	NUM
ejpam-4637	170	13	)	)	PUNCT
ejpam-4637	170	14	,	,	PUNCT
ejpam-4637	170	15	548	548	NUM
ejpam-4637	170	16	-	-	SYM
ejpam-4637	170	17	576	576	NUM
ejpam-4637	170	18	556	556	NUM
ejpam-4637	170	19	(	(	PUNCT
ejpam-4637	170	20	iii	iii	NOUN
ejpam-4637	170	21	)	)	PUNCT
ejpam-4637	170	22	∗ta(x	∗ta(x	NOUN
ejpam-4637	170	23	◦	◦	NOUN
ejpam-4637	170	24	0	0	NUM
ejpam-4637	170	25	)	)	PUNCT
ejpam-4637	171	1	=	=	PUNCT
ejpam-4637	171	2	ta(0	ta(0	NOUN
ejpam-4637	171	3	)	)	PUNCT
ejpam-4637	171	4	∗ia(x	∗ia(x	NOUN
ejpam-4637	171	5	◦	◦	NOUN
ejpam-4637	171	6	0	0	NUM
ejpam-4637	171	7	)	)	PUNCT
ejpam-4637	172	1	=	=	SYM
ejpam-4637	172	2	ia(0	ia(0	NOUN
ejpam-4637	172	3	)	)	PUNCT
ejpam-4637	172	4	∗fa(x	∗fa(x	NOUN
ejpam-4637	172	5	◦	◦	NOUN
ejpam-4637	172	6	0	0	NUM
ejpam-4637	172	7	)	)	PUNCT
ejpam-4637	173	1	=	=	SYM
ejpam-4637	173	2	fa(0	fa(0	NOUN
ejpam-4637	173	3	)	)	PUNCT
ejpam-4637	173	4	(	(	PUNCT
ejpam-4637	173	5	iv	iv	X
ejpam-4637	173	6	)	)	PUNCT
ejpam-4637	173	7	if	if	SCONJ
ejpam-4637	173	8	ta(x	ta(x	NOUN
ejpam-4637	173	9	)	)	PUNCT
ejpam-4637	173	10	=	=	SYM
ejpam-4637	173	11	ta(0	ta(0	NOUN
ejpam-4637	173	12	)	)	PUNCT
ejpam-4637	173	13	ia(x	ia(x	NOUN
ejpam-4637	173	14	)	)	PUNCT
ejpam-4637	173	15	=	=	SYM
ejpam-4637	174	1	ia(0	ia(0	NOUN
ejpam-4637	174	2	)	)	PUNCT
ejpam-4637	174	3	fa(x	fa(x	PROPN
ejpam-4637	174	4	)	)	PUNCT
ejpam-4637	174	5	=	=	SYM
ejpam-4637	175	1	fa(0	fa(0	NOUN
ejpam-4637	175	2	)	)	PUNCT
ejpam-4637	175	3	,	,	PUNCT
ejpam-4637	175	4	then	then	ADV
ejpam-4637	175	5	∗ta(x	∗ta(x	PROPN
ejpam-4637	175	6	◦	◦	PROPN
ejpam-4637	175	7	y	y	PROPN
ejpam-4637	175	8	)	)	PUNCT
ejpam-4637	175	9	≥	≥	NOUN
ejpam-4637	175	10	ta(y	ta(y	PUNCT
ejpam-4637	175	11	)	)	PUNCT
ejpam-4637	175	12	∗ia(x	∗ia(x	VERB
ejpam-4637	175	13	◦	◦	NOUN
ejpam-4637	175	14	y	y	NOUN
ejpam-4637	175	15	)	)	PUNCT
ejpam-4637	175	16	≤	≤	NOUN
ejpam-4637	175	17	ia(y	ia(y	NOUN
ejpam-4637	175	18	)	)	PUNCT
ejpam-4637	175	19	∗fa(x	∗fa(x	NOUN
ejpam-4637	175	20	◦	◦	NOUN
ejpam-4637	175	21	y	y	NOUN
ejpam-4637	175	22	)	)	PUNCT
ejpam-4637	175	23	≤	≤	NOUN
ejpam-4637	175	24	fa(y	fa(y	NOUN
ejpam-4637	175	25	)	)	PUNCT
ejpam-4637	175	26	.	.	PUNCT
ejpam-4637	176	1	(	(	PUNCT
ejpam-4637	176	2	v	v	NOUN
ejpam-4637	176	3	)	)	PUNCT
ejpam-4637	176	4	if	if	SCONJ
ejpam-4637	176	5	ta(y	ta(y	PRON
ejpam-4637	176	6	)	)	PUNCT
ejpam-4637	176	7	=	=	PUNCT
ejpam-4637	176	8	ta(0	ta(0	NOUN
ejpam-4637	176	9	)	)	PUNCT
ejpam-4637	176	10	ia(y	ia(y	NOUN
ejpam-4637	176	11	)	)	PUNCT
ejpam-4637	177	1	=	=	PUNCT
ejpam-4637	177	2	ia(0	ia(0	ADJ
ejpam-4637	177	3	)	)	PUNCT
ejpam-4637	177	4	fa(y	fa(y	NOUN
ejpam-4637	177	5	)	)	PUNCT
ejpam-4637	177	6	=	=	SYM
ejpam-4637	178	1	fa(0	fa(0	NOUN
ejpam-4637	178	2	)	)	PUNCT
ejpam-4637	178	3	,	,	PUNCT
ejpam-4637	178	4	then	then	ADV
ejpam-4637	178	5	∗ta(x	∗ta(x	PROPN
ejpam-4637	178	6	◦	◦	PROPN
ejpam-4637	178	7	y	y	NOUN
ejpam-4637	178	8	)	)	PUNCT
ejpam-4637	178	9	≥	≥	NOUN
ejpam-4637	178	10	ta(x	ta(x	NOUN
ejpam-4637	178	11	)	)	PUNCT
ejpam-4637	178	12	∗ia(x	∗ia(x	NOUN
ejpam-4637	178	13	◦	◦	NOUN
ejpam-4637	178	14	y	y	NOUN
ejpam-4637	178	15	)	)	PUNCT
ejpam-4637	178	16	≤	≤	NOUN
ejpam-4637	178	17	ia(x	ia(x	NOUN
ejpam-4637	178	18	)	)	PUNCT
ejpam-4637	178	19	∗fa(x	∗fa(x	NOUN
ejpam-4637	178	20	◦	◦	NOUN
ejpam-4637	178	21	y	y	NOUN
ejpam-4637	178	22	)	)	PUNCT
ejpam-4637	178	23	≤	≤	NOUN
ejpam-4637	178	24	fa(x	fa(x	NOUN
ejpam-4637	178	25	)	)	PUNCT
ejpam-4637	178	26	.	.	PUNCT
ejpam-4637	179	1	(	(	PUNCT
ejpam-4637	179	2	vi	vi	X
ejpam-4637	179	3	)	)	PUNCT
ejpam-4637	179	4	if	if	SCONJ
ejpam-4637	179	5	∗ta(x	∗ta(x	NOUN
ejpam-4637	179	6	◦	◦	VERB
ejpam-4637	179	7	y	y	NOUN
ejpam-4637	179	8	)	)	PUNCT
ejpam-4637	179	9	=	=	SYM
ejpam-4637	179	10	ta(x	ta(x	NOUN
ejpam-4637	179	11	)	)	PUNCT
ejpam-4637	179	12	∗ia(x	∗ia(x	NOUN
ejpam-4637	179	13	◦	◦	NOUN
ejpam-4637	179	14	y	y	NOUN
ejpam-4637	179	15	)	)	PUNCT
ejpam-4637	179	16	=	=	PUNCT
ejpam-4637	179	17	ia(x	ia(x	NOUN
ejpam-4637	179	18	)	)	PUNCT
ejpam-4637	179	19	∗fa(x	∗fa(x	NOUN
ejpam-4637	179	20	◦	◦	NOUN
ejpam-4637	179	21	y	y	NOUN
ejpam-4637	179	22	)	)	PUNCT
ejpam-4637	179	23	=	=	SYM
ejpam-4637	179	24	fa(x	fa(x	PROPN
ejpam-4637	179	25	)	)	PUNCT
ejpam-4637	179	26	,	,	PUNCT
ejpam-4637	179	27	then	then	ADV
ejpam-4637	179	28	ta(x	ta(x	VERB
ejpam-4637	179	29	)	)	PUNCT
ejpam-4637	179	30	=	=	SYM
ejpam-4637	180	1	ta(0	ta(0	NOUN
ejpam-4637	180	2	)	)	PUNCT
ejpam-4637	180	3	ia(x	ia(x	NOUN
ejpam-4637	180	4	)	)	PUNCT
ejpam-4637	181	1	=	=	SYM
ejpam-4637	181	2	ia(0	ia(0	NOUN
ejpam-4637	181	3	)	)	PUNCT
ejpam-4637	181	4	fa(x	fa(x	PROPN
ejpam-4637	181	5	)	)	PUNCT
ejpam-4637	181	6	=	=	SYM
ejpam-4637	182	1	fa(0	fa(0	NOUN
ejpam-4637	182	2	)	)	PUNCT
ejpam-4637	182	3	and	and	CCONJ
ejpam-4637	182	4	ta(y	ta(y	PUNCT
ejpam-4637	182	5	)	)	PUNCT
ejpam-4637	183	1	=	=	PUNCT
ejpam-4637	183	2	ta(0	ta(0	NOUN
ejpam-4637	183	3	)	)	PUNCT
ejpam-4637	183	4	ia(y	ia(y	NOUN
ejpam-4637	183	5	)	)	PUNCT
ejpam-4637	183	6	=	=	PUNCT
ejpam-4637	184	1	ia(0	ia(0	ADJ
ejpam-4637	184	2	)	)	PUNCT
ejpam-4637	184	3	fa(y	fa(y	NOUN
ejpam-4637	184	4	)	)	PUNCT
ejpam-4637	184	5	=	=	SYM
ejpam-4637	185	1	fa(0	fa(0	NOUN
ejpam-4637	185	2	)	)	PUNCT
ejpam-4637	185	3	.	.	PUNCT
ejpam-4637	186	1	proof	proof	NOUN
ejpam-4637	186	2	.	.	PUNCT
ejpam-4637	187	1	let	let	VERB
ejpam-4637	187	2	a	a	PRON
ejpam-4637	187	3	=	=	SYM
ejpam-4637	187	4	(	(	PUNCT
ejpam-4637	187	5	ta	ta	PROPN
ejpam-4637	187	6	,	,	PUNCT
ejpam-4637	187	7	ia	ia	PROPN
ejpam-4637	187	8	,	,	PUNCT
ejpam-4637	187	9	fa	fa	NOUN
ejpam-4637	187	10	)	)	PUNCT
ejpam-4637	187	11	be	be	AUX
ejpam-4637	187	12	a	a	DET
ejpam-4637	187	13	svn	svn	NOUN
ejpam-4637	187	14	hyper	hyper	NOUN
ejpam-4637	187	15	up	up	ADP
ejpam-4637	187	16	-subalgebra	-subalgebra	NOUN
ejpam-4637	187	17	in	in	ADP
ejpam-4637	187	18	x	x	PUNCT
ejpam-4637	187	19	and	and	CCONJ
ejpam-4637	187	20	let	let	VERB
ejpam-4637	187	21	x	x	PRON
ejpam-4637	187	22	,	,	PUNCT
ejpam-4637	187	23	y	y	PROPN
ejpam-4637	187	24	∈	∈	PROPN
ejpam-4637	187	25	x	x	X
ejpam-4637	187	26	(	(	PUNCT
ejpam-4637	187	27	i	i	NOUN
ejpam-4637	187	28	)	)	PUNCT
ejpam-4637	187	29	note	note	VERB
ejpam-4637	187	30	that	that	SCONJ
ejpam-4637	187	31	x	x	PUNCT
ejpam-4637	187	32	≪	≪	X
ejpam-4637	187	33	x.	x.	NOUN
ejpam-4637	188	1	then	then	ADV
ejpam-4637	188	2	0	0	NUM
ejpam-4637	188	3	∈	∈	PROPN
ejpam-4637	188	4	x	x	PUNCT
ejpam-4637	188	5	◦	◦	NOUN
ejpam-4637	188	6	x.	x.	NOUN
ejpam-4637	188	7	by	by	ADP
ejpam-4637	188	8	hypothesis	hypothesis	NOUN
ejpam-4637	188	9	,	,	PUNCT
ejpam-4637	188	10	ta(0	ta(0	NOUN
ejpam-4637	188	11	)	)	PUNCT
ejpam-4637	188	12	≥	≥	NOUN
ejpam-4637	188	13	∗ta(x	∗ta(x	PROPN
ejpam-4637	188	14	◦	◦	NOUN
ejpam-4637	188	15	x	x	NOUN
ejpam-4637	188	16	)	)	PUNCT
ejpam-4637	188	17	≥	≥	NOUN
ejpam-4637	188	18	min{ta(x	min{ta(x	NOUN
ejpam-4637	188	19	)	)	PUNCT
ejpam-4637	188	20	,	,	PUNCT
ejpam-4637	188	21	ta(x	ta(x	NOUN
ejpam-4637	188	22	)	)	PUNCT
ejpam-4637	188	23	}	}	PUNCT
ejpam-4637	188	24	=	=	SYM
ejpam-4637	188	25	ta(x	ta(x	NOUN
ejpam-4637	188	26	)	)	PUNCT
ejpam-4637	188	27	,	,	PUNCT
ejpam-4637	188	28	ia(0	ia(0	X
ejpam-4637	188	29	)	)	PUNCT
ejpam-4637	188	30	≤	≤	NOUN
ejpam-4637	188	31	∗ia(x	∗ia(x	NOUN
ejpam-4637	188	32	◦	◦	NOUN
ejpam-4637	188	33	x	x	SYM
ejpam-4637	188	34	)	)	PUNCT
ejpam-4637	188	35	≤	≤	NUM
ejpam-4637	188	36	max{ia(x	max{ia(x	NOUN
ejpam-4637	188	37	)	)	PUNCT
ejpam-4637	188	38	,	,	PUNCT
ejpam-4637	188	39	ia(x	ia(x	NOUN
ejpam-4637	188	40	)	)	PUNCT
ejpam-4637	188	41	}	}	PUNCT
ejpam-4637	188	42	=	=	SYM
ejpam-4637	188	43	ia(x	ia(x	NOUN
ejpam-4637	188	44	)	)	PUNCT
ejpam-4637	188	45	,	,	PUNCT
ejpam-4637	188	46	and	and	CCONJ
ejpam-4637	188	47	fa(0	fa(0	NOUN
ejpam-4637	188	48	)	)	PUNCT
ejpam-4637	188	49	≤	≤	NUM
ejpam-4637	188	50	∗fa(x	∗fa(x	NOUN
ejpam-4637	188	51	◦	◦	NOUN
ejpam-4637	188	52	x	x	NOUN
ejpam-4637	188	53	)	)	PUNCT
ejpam-4637	188	54	≤	≤	NUM
ejpam-4637	188	55	max{fa(x),fa(x	max{fa(x),fa(x	NOUN
ejpam-4637	188	56	)	)	PUNCT
ejpam-4637	188	57	}	}	PUNCT
ejpam-4637	188	58	=	=	SYM
ejpam-4637	188	59	fa(x	fa(x	NOUN
ejpam-4637	188	60	)	)	PUNCT
ejpam-4637	188	61	.	.	PUNCT
ejpam-4637	189	1	(	(	PUNCT
ejpam-4637	189	2	ii	ii	NOUN
ejpam-4637	189	3	-	-	PUNCT
ejpam-4637	189	4	iii	iii	NOUN
ejpam-4637	189	5	)	)	PUNCT
ejpam-4637	189	6	the	the	DET
ejpam-4637	189	7	proofs	proof	NOUN
ejpam-4637	189	8	are	be	AUX
ejpam-4637	189	9	straightforward	straightforward	ADJ
ejpam-4637	189	10	since	since	SCONJ
ejpam-4637	189	11	0	0	NUM
ejpam-4637	189	12	◦	◦	NOUN
ejpam-4637	189	13	x	x	SYM
ejpam-4637	189	14	=	=	SYM
ejpam-4637	189	15	{	{	PUNCT
ejpam-4637	189	16	x	x	NOUN
ejpam-4637	189	17	}	}	PUNCT
ejpam-4637	189	18	and	and	CCONJ
ejpam-4637	189	19	x	x	PART
ejpam-4637	189	20	◦	◦	NOUN
ejpam-4637	189	21	0	0	NUM
ejpam-4637	189	22	=	=	SYM
ejpam-4637	189	23	{	{	PUNCT
ejpam-4637	189	24	0	0	NUM
ejpam-4637	189	25	}	}	PUNCT
ejpam-4637	189	26	.	.	PUNCT
ejpam-4637	190	1	(	(	PUNCT
ejpam-4637	190	2	iv	iv	X
ejpam-4637	190	3	)	)	PUNCT
ejpam-4637	190	4	assume	assume	VERB
ejpam-4637	190	5	that	that	SCONJ
ejpam-4637	190	6	ta(x	ta(x	VERB
ejpam-4637	190	7	)	)	PUNCT
ejpam-4637	190	8	=	=	SYM
ejpam-4637	190	9	ta(0	ta(0	NOUN
ejpam-4637	190	10	)	)	PUNCT
ejpam-4637	190	11	.	.	PUNCT
ejpam-4637	191	1	by	by	ADP
ejpam-4637	191	2	hypothesis	hypothesis	NOUN
ejpam-4637	191	3	and	and	CCONJ
ejpam-4637	191	4	by	by	ADP
ejpam-4637	191	5	(	(	PUNCT
ejpam-4637	191	6	i	i	NOUN
ejpam-4637	191	7	)	)	PUNCT
ejpam-4637	191	8	,	,	PUNCT
ejpam-4637	191	9	∗ta(x	∗ta(x	PROPN
ejpam-4637	191	10	◦	◦	NOUN
ejpam-4637	191	11	y	y	NOUN
ejpam-4637	191	12	)	)	PUNCT
ejpam-4637	191	13	≥	≥	NOUN
ejpam-4637	191	14	min{ta(0	min{ta(0	PROPN
ejpam-4637	191	15	)	)	PUNCT
ejpam-4637	191	16	,	,	PUNCT
ejpam-4637	191	17	ta(y	ta(y	NUM
ejpam-4637	191	18	)	)	PUNCT
ejpam-4637	191	19	}	}	PUNCT
ejpam-4637	191	20	=	=	SYM
ejpam-4637	191	21	ta(y	ta(y	NOUN
ejpam-4637	191	22	)	)	PUNCT
ejpam-4637	191	23	.	.	PUNCT
ejpam-4637	192	1	using	use	VERB
ejpam-4637	192	2	similar	similar	ADJ
ejpam-4637	192	3	routine	routine	NOUN
ejpam-4637	192	4	,	,	PUNCT
ejpam-4637	192	5	ia(x	ia(x	NOUN
ejpam-4637	192	6	)	)	PUNCT
ejpam-4637	192	7	=	=	SYM
ejpam-4637	192	8	ia(0	ia(0	NOUN
ejpam-4637	192	9	)	)	PUNCT
ejpam-4637	192	10	implies	imply	VERB
ejpam-4637	192	11	that	that	SCONJ
ejpam-4637	192	12	∗ia(x	∗ia(x	VERB
ejpam-4637	192	13	◦	◦	NOUN
ejpam-4637	192	14	y	y	NOUN
ejpam-4637	192	15	)	)	PUNCT
ejpam-4637	192	16	≤	≤	NOUN
ejpam-4637	192	17	ia(y	ia(y	NOUN
ejpam-4637	192	18	)	)	PUNCT
ejpam-4637	192	19	and	and	CCONJ
ejpam-4637	192	20	fa(x	fa(x	NOUN
ejpam-4637	192	21	)	)	PUNCT
ejpam-4637	192	22	=	=	SYM
ejpam-4637	192	23	fa(0	fa(0	NOUN
ejpam-4637	192	24	)	)	PUNCT
ejpam-4637	192	25	implies	imply	VERB
ejpam-4637	192	26	that	that	SCONJ
ejpam-4637	192	27	∗fa(x	∗fa(x	NOUN
ejpam-4637	192	28	◦	◦	NOUN
ejpam-4637	192	29	y	y	NOUN
ejpam-4637	192	30	)	)	PUNCT
ejpam-4637	192	31	≤	≤	NOUN
ejpam-4637	192	32	fa(y	fa(y	NOUN
ejpam-4637	192	33	)	)	PUNCT
ejpam-4637	192	34	.	.	PUNCT
ejpam-4637	193	1	(	(	PUNCT
ejpam-4637	193	2	v	v	NOUN
ejpam-4637	193	3	)	)	PUNCT
ejpam-4637	193	4	using	use	VERB
ejpam-4637	193	5	similar	similar	ADJ
ejpam-4637	193	6	arguments	argument	NOUN
ejpam-4637	193	7	from	from	ADP
ejpam-4637	193	8	(	(	PUNCT
ejpam-4637	193	9	iv	iv	X
ejpam-4637	193	10	)	)	PUNCT
ejpam-4637	193	11	,	,	PUNCT
ejpam-4637	193	12	the	the	DET
ejpam-4637	193	13	claim	claim	NOUN
ejpam-4637	193	14	is	be	AUX
ejpam-4637	193	15	true	true	ADJ
ejpam-4637	193	16	.	.	PUNCT
ejpam-4637	194	1	(	(	PUNCT
ejpam-4637	194	2	vi	vi	X
ejpam-4637	194	3	)	)	PUNCT
ejpam-4637	194	4	assume	assume	VERB
ejpam-4637	194	5	that	that	SCONJ
ejpam-4637	194	6	∗ta(x	∗ta(x	NOUN
ejpam-4637	194	7	◦	◦	NOUN
ejpam-4637	194	8	y	y	NOUN
ejpam-4637	194	9	)	)	PUNCT
ejpam-4637	194	10	=	=	SYM
ejpam-4637	194	11	ta(x	ta(x	NOUN
ejpam-4637	194	12	)	)	PUNCT
ejpam-4637	194	13	.	.	PUNCT
ejpam-4637	195	1	taking	take	VERB
ejpam-4637	195	2	x	x	PUNCT
ejpam-4637	195	3	=	=	SYM
ejpam-4637	195	4	0	0	NUM
ejpam-4637	195	5	,	,	PUNCT
ejpam-4637	195	6	we	we	PRON
ejpam-4637	195	7	have	have	AUX
ejpam-4637	195	8	∗ta(0	∗ta(0	VERB
ejpam-4637	195	9	◦	◦	NOUN
ejpam-4637	195	10	y	y	NOUN
ejpam-4637	195	11	)	)	PUNCT
ejpam-4637	196	1	=	=	PUNCT
ejpam-4637	196	2	ta(0	ta(0	NOUN
ejpam-4637	196	3	)	)	PUNCT
ejpam-4637	196	4	.	.	PUNCT
ejpam-4637	197	1	by	by	ADP
ejpam-4637	197	2	(	(	PUNCT
ejpam-4637	197	3	ii	ii	NOUN
ejpam-4637	197	4	)	)	PUNCT
ejpam-4637	197	5	,	,	PUNCT
ejpam-4637	197	6	ta(y	ta(y	PUNCT
ejpam-4637	197	7	)	)	PUNCT
ejpam-4637	197	8	=	=	NOUN
ejpam-4637	197	9	∗	∗	NOUN
ejpam-4637	197	10	ta(0	ta(0	NOUN
ejpam-4637	197	11	◦	◦	NOUN
ejpam-4637	197	12	y	y	NOUN
ejpam-4637	197	13	)	)	PUNCT
ejpam-4637	197	14	=	=	PUNCT
ejpam-4637	197	15	ta(0	ta(0	NOUN
ejpam-4637	197	16	)	)	PUNCT
ejpam-4637	197	17	.	.	PUNCT
ejpam-4637	198	1	similarly	similarly	ADV
ejpam-4637	198	2	,	,	PUNCT
ejpam-4637	198	3	∗ia(x	∗ia(x	NOUN
ejpam-4637	198	4	◦	◦	NOUN
ejpam-4637	198	5	y	y	NOUN
ejpam-4637	198	6	)	)	PUNCT
ejpam-4637	198	7	=	=	PUNCT
ejpam-4637	198	8	ia(x	ia(x	NOUN
ejpam-4637	198	9	)	)	PUNCT
ejpam-4637	198	10	implies	imply	VERB
ejpam-4637	198	11	that	that	SCONJ
ejpam-4637	198	12	ia(y	ia(y	VERB
ejpam-4637	198	13	)	)	PUNCT
ejpam-4637	198	14	=	=	PUNCT
ejpam-4637	199	1	ia(0	ia(0	NOUN
ejpam-4637	199	2	)	)	PUNCT
ejpam-4637	199	3	and	and	CCONJ
ejpam-4637	199	4	∗fa(x	∗fa(x	NOUN
ejpam-4637	199	5	◦	◦	VERB
ejpam-4637	199	6	y	y	NOUN
ejpam-4637	199	7	)	)	PUNCT
ejpam-4637	199	8	=	=	SYM
ejpam-4637	199	9	fa(x	fa(x	PROPN
ejpam-4637	199	10	)	)	PUNCT
ejpam-4637	199	11	implies	imply	VERB
ejpam-4637	199	12	that	that	SCONJ
ejpam-4637	199	13	fa(y	fa(y	PROPN
ejpam-4637	199	14	)	)	PUNCT
ejpam-4637	199	15	=	=	SYM
ejpam-4637	199	16	fa(0	fa(0	NOUN
ejpam-4637	199	17	)	)	PUNCT
ejpam-4637	199	18	.	.	PUNCT
ejpam-4637	200	1	on	on	ADP
ejpam-4637	200	2	the	the	DET
ejpam-4637	200	3	other	other	ADJ
ejpam-4637	200	4	hand	hand	NOUN
ejpam-4637	200	5	,	,	PUNCT
ejpam-4637	200	6	if	if	SCONJ
ejpam-4637	200	7	we	we	PRON
ejpam-4637	200	8	take	take	VERB
ejpam-4637	200	9	y	y	NOUN
ejpam-4637	200	10	=	=	SYM
ejpam-4637	200	11	0	0	PROPN
ejpam-4637	200	12	,	,	PUNCT
ejpam-4637	200	13	we	we	PRON
ejpam-4637	200	14	get	get	VERB
ejpam-4637	200	15	∗ta(x	∗ta(x	NOUN
ejpam-4637	200	16	◦	◦	NOUN
ejpam-4637	200	17	0	0	NUM
ejpam-4637	200	18	)	)	PUNCT
ejpam-4637	200	19	=	=	SYM
ejpam-4637	200	20	ta(x	ta(x	NOUN
ejpam-4637	200	21	)	)	PUNCT
ejpam-4637	200	22	.	.	PUNCT
ejpam-4637	201	1	by	by	ADP
ejpam-4637	201	2	(	(	PUNCT
ejpam-4637	201	3	iii	iii	NOUN
ejpam-4637	201	4	)	)	PUNCT
ejpam-4637	201	5	,	,	PUNCT
ejpam-4637	201	6	ta(0	ta(0	NOUN
ejpam-4637	201	7	)	)	PUNCT
ejpam-4637	201	8	=	=	NOUN
ejpam-4637	201	9	∗	∗	NOUN
ejpam-4637	201	10	ta(x	ta(x	NOUN
ejpam-4637	201	11	◦	◦	NOUN
ejpam-4637	201	12	0	0	NUM
ejpam-4637	201	13	)	)	PUNCT
ejpam-4637	201	14	=	=	SYM
ejpam-4637	201	15	ta(x	ta(x	NOUN
ejpam-4637	201	16	)	)	PUNCT
ejpam-4637	201	17	.	.	PUNCT
ejpam-4637	202	1	also	also	ADV
ejpam-4637	202	2	,	,	PUNCT
ejpam-4637	202	3	ia(x	ia(x	NOUN
ejpam-4637	202	4	)	)	PUNCT
ejpam-4637	202	5	=	=	SYM
ejpam-4637	203	1	ia(0	ia(0	NOUN
ejpam-4637	203	2	)	)	PUNCT
ejpam-4637	203	3	and	and	CCONJ
ejpam-4637	203	4	fa(x	fa(x	NOUN
ejpam-4637	203	5	)	)	PUNCT
ejpam-4637	203	6	=	=	SYM
ejpam-4637	204	1	fa(0	fa(0	X
ejpam-4637	204	2	)	)	PUNCT
ejpam-4637	204	3	will	will	AUX
ejpam-4637	204	4	follow	follow	VERB
ejpam-4637	204	5	.	.	PUNCT
ejpam-4637	205	1	proposition	proposition	NOUN
ejpam-4637	205	2	4	4	NUM
ejpam-4637	205	3	.	.	PUNCT
ejpam-4637	206	1	if	if	SCONJ
ejpam-4637	206	2	a	a	DET
ejpam-4637	206	3	=	=	X
ejpam-4637	206	4	(	(	PUNCT
ejpam-4637	206	5	ta	ta	PROPN
ejpam-4637	206	6	,	,	PUNCT
ejpam-4637	206	7	ia	ia	PROPN
ejpam-4637	206	8	,	,	PUNCT
ejpam-4637	206	9	fa	fa	NOUN
ejpam-4637	206	10	)	)	PUNCT
ejpam-4637	206	11	is	be	AUX
ejpam-4637	206	12	a	a	DET
ejpam-4637	206	13	svn	svn	NOUN
ejpam-4637	206	14	hyper	hyper	NOUN
ejpam-4637	206	15	up	up	ADP
ejpam-4637	206	16	-	-	PUNCT
ejpam-4637	206	17	subalgebra	subalgebra	NOUN
ejpam-4637	206	18	of	of	ADP
ejpam-4637	206	19	x	x	PRON
ejpam-4637	206	20	,	,	PUNCT
ejpam-4637	206	21	then	then	ADV
ejpam-4637	206	22	the	the	DET
ejpam-4637	206	23	set	set	NOUN
ejpam-4637	206	24	k	k	PROPN
ejpam-4637	206	25	=	=	PRON
ejpam-4637	206	26	{	{	PUNCT
ejpam-4637	206	27	x	x	PROPN
ejpam-4637	206	28	∈	∈	PROPN
ejpam-4637	206	29	x|ta(x	x|ta(x	PROPN
ejpam-4637	206	30	)	)	PUNCT
ejpam-4637	207	1	=	=	PUNCT
ejpam-4637	207	2	ta(0	ta(0	NOUN
ejpam-4637	207	3	)	)	PUNCT
ejpam-4637	207	4	,	,	PUNCT
ejpam-4637	207	5	ia(x	ia(x	X
ejpam-4637	207	6	)	)	PUNCT
ejpam-4637	207	7	=	=	SYM
ejpam-4637	207	8	ia(0),fa(x	ia(0),fa(x	NOUN
ejpam-4637	207	9	)	)	PUNCT
ejpam-4637	207	10	=	=	SYM
ejpam-4637	207	11	fa(0	fa(0	X
ejpam-4637	207	12	)	)	PUNCT
ejpam-4637	207	13	}	}	PUNCT
ejpam-4637	207	14	is	be	AUX
ejpam-4637	207	15	a	a	DET
ejpam-4637	207	16	hyper	hyper	ADJ
ejpam-4637	207	17	up	up	ADP
ejpam-4637	207	18	-	-	PUNCT
ejpam-4637	207	19	subalgebra	subalgebra	NOUN
ejpam-4637	207	20	of	of	ADP
ejpam-4637	207	21	x.	x.	NOUN
ejpam-4637	207	22	proof	proof	NOUN
ejpam-4637	207	23	.	.	PUNCT
ejpam-4637	208	1	let	let	VERB
ejpam-4637	208	2	a	a	PRON
ejpam-4637	208	3	=	=	SYM
ejpam-4637	208	4	(	(	PUNCT
ejpam-4637	208	5	ta	ta	PROPN
ejpam-4637	208	6	,	,	PUNCT
ejpam-4637	208	7	ia	ia	PROPN
ejpam-4637	208	8	,	,	PUNCT
ejpam-4637	208	9	fa	fa	NOUN
ejpam-4637	208	10	)	)	PUNCT
ejpam-4637	208	11	be	be	AUX
ejpam-4637	208	12	a	a	DET
ejpam-4637	208	13	svn	svn	NOUN
ejpam-4637	208	14	hyper	hyper	NOUN
ejpam-4637	208	15	up	up	ADP
ejpam-4637	208	16	-subalgebra	-subalgebra	NOUN
ejpam-4637	208	17	of	of	ADP
ejpam-4637	208	18	x	x	PUNCT
ejpam-4637	208	19	and	and	CCONJ
ejpam-4637	208	20	let	let	VERB
ejpam-4637	208	21	k	k	X
ejpam-4637	208	22	=	=	PRON
ejpam-4637	208	23	{	{	PUNCT
ejpam-4637	208	24	x	x	PROPN
ejpam-4637	208	25	∈	∈	PROPN
ejpam-4637	208	26	x|ta(x	x|ta(x	PROPN
ejpam-4637	208	27	)	)	PUNCT
ejpam-4637	209	1	=	=	PUNCT
ejpam-4637	209	2	ta(0	ta(0	NOUN
ejpam-4637	209	3	)	)	PUNCT
ejpam-4637	209	4	,	,	PUNCT
ejpam-4637	209	5	ia(x	ia(x	X
ejpam-4637	209	6	)	)	PUNCT
ejpam-4637	209	7	=	=	SYM
ejpam-4637	209	8	ia(0),fa(x	ia(0),fa(x	NOUN
ejpam-4637	209	9	)	)	PUNCT
ejpam-4637	209	10	=	=	SYM
ejpam-4637	209	11	fa(0	fa(0	NOUN
ejpam-4637	209	12	)	)	PUNCT
ejpam-4637	209	13	}	}	PUNCT
ejpam-4637	209	14	.	.	PUNCT
ejpam-4637	210	1	note	note	VERB
ejpam-4637	210	2	that	that	SCONJ
ejpam-4637	210	3	k	k	PROPN
ejpam-4637	210	4	̸=	̸=	PROPN
ejpam-4637	210	5	∅	∅	NOUN
ejpam-4637	210	6	since	since	SCONJ
ejpam-4637	210	7	0	0	NUM
ejpam-4637	210	8	∈	∈	PROPN
ejpam-4637	210	9	k.	k.	PROPN
ejpam-4637	210	10	a.	a.	PROPN
ejpam-4637	210	11	cano	cano	PROPN
ejpam-4637	210	12	,	,	PUNCT
ejpam-4637	210	13	g.	g.	PROPN
ejpam-4637	210	14	petalcorin	petalcorin	PROPN
ejpam-4637	210	15	/	/	SYM
ejpam-4637	210	16	eur	eur	PROPN
ejpam-4637	210	17	.	.	PUNCT
ejpam-4637	211	1	j.	j.	PROPN
ejpam-4637	211	2	pure	pure	PROPN
ejpam-4637	211	3	appl	appl	PROPN
ejpam-4637	211	4	.	.	PROPN
ejpam-4637	211	5	math	math	PROPN
ejpam-4637	211	6	,	,	PUNCT
ejpam-4637	211	7	16	16	NUM
ejpam-4637	211	8	(	(	PUNCT
ejpam-4637	211	9	1	1	NUM
ejpam-4637	211	10	)	)	PUNCT
ejpam-4637	211	11	(	(	PUNCT
ejpam-4637	211	12	2023	2023	NUM
ejpam-4637	211	13	)	)	PUNCT
ejpam-4637	211	14	,	,	PUNCT
ejpam-4637	211	15	548	548	NUM
ejpam-4637	211	16	-	-	SYM
ejpam-4637	211	17	576	576	NUM
ejpam-4637	211	18	557	557	NUM
ejpam-4637	211	19	now	now	ADV
ejpam-4637	211	20	,	,	PUNCT
ejpam-4637	211	21	suppose	suppose	VERB
ejpam-4637	211	22	x	x	PRON
ejpam-4637	211	23	,	,	PUNCT
ejpam-4637	211	24	y	y	PROPN
ejpam-4637	211	25	∈	∈	PROPN
ejpam-4637	211	26	k	k	PROPN
ejpam-4637	211	27	and	and	CCONJ
ejpam-4637	211	28	z	z	NOUN
ejpam-4637	211	29	∈	∈	PROPN
ejpam-4637	211	30	x	x	PUNCT
ejpam-4637	211	31	◦	◦	NOUN
ejpam-4637	211	32	y.	y.	NOUN
ejpam-4637	211	33	then	then	ADV
ejpam-4637	211	34	ta(x	ta(x	NOUN
ejpam-4637	211	35	)	)	PUNCT
ejpam-4637	211	36	=	=	SYM
ejpam-4637	211	37	ta(0	ta(0	NOUN
ejpam-4637	211	38	)	)	PUNCT
ejpam-4637	211	39	=	=	SYM
ejpam-4637	211	40	ta(y	ta(y	PROPN
ejpam-4637	211	41	)	)	PUNCT
ejpam-4637	211	42	,	,	PUNCT
ejpam-4637	211	43	ia(x	ia(x	X
ejpam-4637	211	44	)	)	PUNCT
ejpam-4637	211	45	=	=	SYM
ejpam-4637	212	1	ia(0	ia(0	X
ejpam-4637	212	2	)	)	PUNCT
ejpam-4637	212	3	=	=	SYM
ejpam-4637	212	4	ia(y),fa(x	ia(y),fa(x	X
ejpam-4637	212	5	)	)	PUNCT
ejpam-4637	212	6	=	=	SYM
ejpam-4637	212	7	fa(0	fa(0	X
ejpam-4637	212	8	)	)	PUNCT
ejpam-4637	212	9	=	=	SYM
ejpam-4637	212	10	fa(y	fa(y	NOUN
ejpam-4637	212	11	)	)	PUNCT
ejpam-4637	212	12	.	.	PUNCT
ejpam-4637	213	1	by	by	ADP
ejpam-4637	213	2	proposition	proposition	NOUN
ejpam-4637	213	3	3(i	3(i	NUM
ejpam-4637	213	4	)	)	PUNCT
ejpam-4637	213	5	and	and	CCONJ
ejpam-4637	213	6	by	by	ADP
ejpam-4637	213	7	hypothesis	hypothesis	NOUN
ejpam-4637	213	8	,	,	PUNCT
ejpam-4637	213	9	we	we	PRON
ejpam-4637	213	10	get	get	VERB
ejpam-4637	213	11	ta(z	ta(z	NOUN
ejpam-4637	213	12	)	)	PUNCT
ejpam-4637	213	13	≥	≥	NOUN
ejpam-4637	214	1	∗ta(x	∗ta(x	PROPN
ejpam-4637	214	2	◦	◦	VERB
ejpam-4637	214	3	y	y	NOUN
ejpam-4637	214	4	)	)	PUNCT
ejpam-4637	214	5	≥	≥	NOUN
ejpam-4637	214	6	min{ta(x	min{ta(x	NOUN
ejpam-4637	214	7	)	)	PUNCT
ejpam-4637	214	8	,	,	PUNCT
ejpam-4637	214	9	ta(y	ta(y	NUM
ejpam-4637	214	10	)	)	PUNCT
ejpam-4637	214	11	}	}	PUNCT
ejpam-4637	214	12	=	=	SYM
ejpam-4637	214	13	min{ta(0	min{ta(0	PROPN
ejpam-4637	214	14	)	)	PUNCT
ejpam-4637	214	15	,	,	PUNCT
ejpam-4637	214	16	ta(0	ta(0	NOUN
ejpam-4637	214	17	)	)	PUNCT
ejpam-4637	214	18	}	}	PUNCT
ejpam-4637	214	19	=	=	SYM
ejpam-4637	214	20	ta(0	ta(0	NOUN
ejpam-4637	214	21	)	)	PUNCT
ejpam-4637	214	22	,	,	PUNCT
ejpam-4637	214	23	ia(z	ia(z	NOUN
ejpam-4637	214	24	)	)	PUNCT
ejpam-4637	214	25	≤	≤	NUM
ejpam-4637	215	1	∗ia(x	∗ia(x	NOUN
ejpam-4637	215	2	◦	◦	NOUN
ejpam-4637	215	3	y	y	NOUN
ejpam-4637	215	4	)	)	PUNCT
ejpam-4637	215	5	≤	≤	NUM
ejpam-4637	215	6	max{ia(x	max{ia(x	NOUN
ejpam-4637	215	7	)	)	PUNCT
ejpam-4637	215	8	,	,	PUNCT
ejpam-4637	215	9	ia(y	ia(y	NOUN
ejpam-4637	215	10	)	)	PUNCT
ejpam-4637	215	11	}	}	PUNCT
ejpam-4637	215	12	=	=	SYM
ejpam-4637	215	13	max{ia(0	max{ia(0	PROPN
ejpam-4637	215	14	)	)	PUNCT
ejpam-4637	215	15	,	,	PUNCT
ejpam-4637	215	16	ia(0	ia(0	X
ejpam-4637	215	17	)	)	PUNCT
ejpam-4637	215	18	}	}	PUNCT
ejpam-4637	215	19	=	=	PUNCT
ejpam-4637	215	20	ia(0	ia(0	NOUN
ejpam-4637	215	21	)	)	PUNCT
ejpam-4637	215	22	,	,	PUNCT
ejpam-4637	215	23	and	and	CCONJ
ejpam-4637	215	24	similarly	similarly	ADV
ejpam-4637	215	25	,	,	PUNCT
ejpam-4637	215	26	fa(z	fa(z	PUNCT
ejpam-4637	215	27	)	)	PUNCT
ejpam-4637	215	28	≤	≤	NUM
ejpam-4637	215	29	fa(0	fa(0	NOUN
ejpam-4637	215	30	)	)	PUNCT
ejpam-4637	215	31	.	.	PUNCT
ejpam-4637	216	1	thus	thus	ADV
ejpam-4637	216	2	,	,	PUNCT
ejpam-4637	216	3	ta(z	ta(z	ADJ
ejpam-4637	216	4	)	)	PUNCT
ejpam-4637	216	5	=	=	PUNCT
ejpam-4637	216	6	ta(0	ta(0	NOUN
ejpam-4637	216	7	)	)	PUNCT
ejpam-4637	216	8	,	,	PUNCT
ejpam-4637	216	9	ia(z	ia(z	NOUN
ejpam-4637	216	10	)	)	PUNCT
ejpam-4637	216	11	=	=	SYM
ejpam-4637	217	1	ia(0	ia(0	NOUN
ejpam-4637	217	2	)	)	PUNCT
ejpam-4637	217	3	,	,	PUNCT
ejpam-4637	217	4	and	and	CCONJ
ejpam-4637	217	5	fa(z	fa(z	PUNCT
ejpam-4637	217	6	)	)	PUNCT
ejpam-4637	217	7	=	=	SYM
ejpam-4637	218	1	fa(0	fa(0	NOUN
ejpam-4637	218	2	)	)	PUNCT
ejpam-4637	218	3	.	.	PUNCT
ejpam-4637	219	1	that	that	PRON
ejpam-4637	219	2	is	be	AUX
ejpam-4637	219	3	,	,	PUNCT
ejpam-4637	220	1	z	z	PROPN
ejpam-4637	220	2	∈	∈	PROPN
ejpam-4637	220	3	k	k	NOUN
ejpam-4637	220	4	and	and	CCONJ
ejpam-4637	220	5	so	so	ADV
ejpam-4637	220	6	x	x	PUNCT
ejpam-4637	220	7	◦	◦	NOUN
ejpam-4637	220	8	y	y	PROPN
ejpam-4637	220	9	⊆	⊆	NUM
ejpam-4637	220	10	k.	k.	NOUN
ejpam-4637	220	11	by	by	ADP
ejpam-4637	220	12	proposition	proposition	NOUN
ejpam-4637	220	13	2	2	NUM
ejpam-4637	220	14	,	,	PUNCT
ejpam-4637	220	15	k	k	PROPN
ejpam-4637	220	16	is	be	AUX
ejpam-4637	220	17	a	a	DET
ejpam-4637	220	18	hyper	hyper	ADJ
ejpam-4637	220	19	up	up	ADP
ejpam-4637	220	20	-subalgebra	-subalgebra	NOUN
ejpam-4637	220	21	of	of	ADP
ejpam-4637	220	22	x.	x.	NOUN
ejpam-4637	220	23	we	we	PRON
ejpam-4637	220	24	define	define	VERB
ejpam-4637	220	25	the	the	DET
ejpam-4637	220	26	following	follow	VERB
ejpam-4637	220	27	α	α	PROPN
ejpam-4637	220	28	,	,	PUNCT
ejpam-4637	220	29	β	β	X
ejpam-4637	220	30	,	,	PUNCT
ejpam-4637	220	31	γ	γ	NOUN
ejpam-4637	220	32	-	-	PUNCT
ejpam-4637	220	33	level	level	NOUN
ejpam-4637	220	34	subsets	subset	NOUN
ejpam-4637	220	35	of	of	ADP
ejpam-4637	220	36	x	x	PUNCT
ejpam-4637	220	37	and	and	CCONJ
ejpam-4637	220	38	their	their	PRON
ejpam-4637	220	39	intersection	intersection	NOUN
ejpam-4637	220	40	:	:	PUNCT
ejpam-4637	220	41	tα	tα	VERB
ejpam-4637	220	42	a	a	DET
ejpam-4637	220	43	=	=	X
ejpam-4637	220	44	{	{	PUNCT
ejpam-4637	220	45	x	x	SYM
ejpam-4637	220	46	∈	∈	PROPN
ejpam-4637	220	47	x	x	X
ejpam-4637	220	48	:	:	PUNCT
ejpam-4637	220	49	ta(x	ta(x	PROPN
ejpam-4637	220	50	)	)	PUNCT
ejpam-4637	220	51	≥	≥	NOUN
ejpam-4637	220	52	α	α	NOUN
ejpam-4637	220	53	}	}	PUNCT
ejpam-4637	220	54	,	,	PUNCT
ejpam-4637	220	55	iβa	iβa	NOUN
ejpam-4637	220	56	=	=	SYM
ejpam-4637	220	57	{	{	PUNCT
ejpam-4637	220	58	x	x	SYM
ejpam-4637	220	59	∈	∈	PROPN
ejpam-4637	220	60	x	x	X
ejpam-4637	220	61	:	:	PUNCT
ejpam-4637	220	62	ia(x	ia(x	NOUN
ejpam-4637	220	63	)	)	PUNCT
ejpam-4637	220	64	≤	≤	NOUN
ejpam-4637	220	65	β	β	X
ejpam-4637	220	66	}	}	PUNCT
ejpam-4637	220	67	,	,	PUNCT
ejpam-4637	220	68	f	f	PROPN
ejpam-4637	220	69	γ	γ	X
ejpam-4637	220	70	a	a	PROPN
ejpam-4637	220	71	=	=	X
ejpam-4637	220	72	{	{	PUNCT
ejpam-4637	220	73	x	x	SYM
ejpam-4637	220	74	∈	∈	PROPN
ejpam-4637	220	75	x	x	X
ejpam-4637	220	76	:	:	PUNCT
ejpam-4637	220	77	fa(x	fa(x	NOUN
ejpam-4637	220	78	)	)	PUNCT
ejpam-4637	220	79	≤	≤	NUM
ejpam-4637	220	80	γ	γ	X
ejpam-4637	220	81	}	}	PUNCT
ejpam-4637	220	82	,	,	PUNCT
ejpam-4637	220	83	and	and	CCONJ
ejpam-4637	220	84	a(α	a(α	PROPN
ejpam-4637	220	85	,	,	PUNCT
ejpam-4637	220	86	β	β	X
ejpam-4637	220	87	,	,	PUNCT
ejpam-4637	220	88	γ	γ	NOUN
ejpam-4637	220	89	)	)	PUNCT
ejpam-4637	220	90	=	=	SYM
ejpam-4637	220	91	tα	tα	VERB
ejpam-4637	220	92	a	a	DET
ejpam-4637	220	93	∩	∩	NOUN
ejpam-4637	220	94	iβa	iβa	NOUN
ejpam-4637	220	95	∩	∩	NOUN
ejpam-4637	220	96	f	f	PROPN
ejpam-4637	220	97	γ	γ	X
ejpam-4637	220	98	a.	a.	VERB
ejpam-4637	220	99	where	where	SCONJ
ejpam-4637	220	100	a	a	DET
ejpam-4637	220	101	=	=	X
ejpam-4637	220	102	(	(	PUNCT
ejpam-4637	220	103	ta	ta	PROPN
ejpam-4637	220	104	,	,	PUNCT
ejpam-4637	220	105	ia	ia	PROPN
ejpam-4637	220	106	,	,	PUNCT
ejpam-4637	220	107	fa	fa	NOUN
ejpam-4637	220	108	)	)	PUNCT
ejpam-4637	220	109	is	be	AUX
ejpam-4637	220	110	a	a	DET
ejpam-4637	220	111	svn	svn	NOUN
ejpam-4637	220	112	set	set	NOUN
ejpam-4637	220	113	in	in	ADP
ejpam-4637	220	114	x	x	PUNCT
ejpam-4637	220	115	and	and	CCONJ
ejpam-4637	220	116	α	α	NOUN
ejpam-4637	220	117	,	,	PUNCT
ejpam-4637	220	118	β	β	X
ejpam-4637	220	119	,	,	PUNCT
ejpam-4637	220	120	γ	γ	PROPN
ejpam-4637	220	121	∈	∈	PROPN
ejpam-4637	221	1	[	[	X
ejpam-4637	221	2	0	0	NUM
ejpam-4637	221	3	,	,	PUNCT
ejpam-4637	221	4	1	1	NUM
ejpam-4637	221	5	]	]	PUNCT
ejpam-4637	221	6	.	.	PUNCT
ejpam-4637	222	1	theorem	theorem	NOUN
ejpam-4637	222	2	1	1	X
ejpam-4637	222	3	.	.	PUNCT
ejpam-4637	223	1	let	let	VERB
ejpam-4637	223	2	a	a	PRON
ejpam-4637	223	3	=	=	SYM
ejpam-4637	223	4	(	(	PUNCT
ejpam-4637	223	5	ta	ta	PROPN
ejpam-4637	223	6	,	,	PUNCT
ejpam-4637	223	7	ia	ia	PROPN
ejpam-4637	223	8	,	,	PUNCT
ejpam-4637	223	9	fa	fa	NOUN
ejpam-4637	223	10	)	)	PUNCT
ejpam-4637	223	11	be	be	AUX
ejpam-4637	223	12	a	a	DET
ejpam-4637	223	13	svn	svn	NOUN
ejpam-4637	223	14	set	set	NOUN
ejpam-4637	223	15	in	in	ADP
ejpam-4637	223	16	x.	x.	NOUN
ejpam-4637	223	17	then	then	ADV
ejpam-4637	223	18	a	a	PRON
ejpam-4637	223	19	is	be	AUX
ejpam-4637	223	20	a	a	DET
ejpam-4637	223	21	svn	svn	NOUN
ejpam-4637	223	22	hyper	hyper	ADJ
ejpam-4637	223	23	upsubalgebra	upsubalgebra	NOUN
ejpam-4637	223	24	of	of	ADP
ejpam-4637	223	25	x	x	PUNCT
ejpam-4637	223	26	if	if	SCONJ
ejpam-4637	223	27	and	and	CCONJ
ejpam-4637	223	28	only	only	ADV
ejpam-4637	223	29	if	if	SCONJ
ejpam-4637	223	30	a(α	a(α	NOUN
ejpam-4637	223	31	,	,	PUNCT
ejpam-4637	223	32	β	β	X
ejpam-4637	223	33	,	,	PUNCT
ejpam-4637	223	34	γ	γ	X
ejpam-4637	223	35	)	)	PUNCT
ejpam-4637	223	36	is	be	AUX
ejpam-4637	223	37	a	a	DET
ejpam-4637	223	38	hyper	hyper	ADJ
ejpam-4637	223	39	up	up	ADP
ejpam-4637	223	40	-	-	PUNCT
ejpam-4637	223	41	subalgebra	subalgebra	NOUN
ejpam-4637	223	42	of	of	ADP
ejpam-4637	223	43	x	x	PUNCT
ejpam-4637	223	44	for	for	ADP
ejpam-4637	223	45	all	all	DET
ejpam-4637	223	46	α	α	NOUN
ejpam-4637	223	47	,	,	PUNCT
ejpam-4637	223	48	β	β	X
ejpam-4637	223	49	,	,	PUNCT
ejpam-4637	223	50	γ	γ	PROPN
ejpam-4637	223	51	∈	∈	PROPN
ejpam-4637	224	1	[	[	X
ejpam-4637	224	2	0	0	NUM
ejpam-4637	224	3	,	,	PUNCT
ejpam-4637	224	4	1	1	NUM
ejpam-4637	224	5	]	]	PUNCT
ejpam-4637	224	6	.	.	PUNCT
ejpam-4637	225	1	proof	proof	NOUN
ejpam-4637	225	2	.	.	PUNCT
ejpam-4637	226	1	let	let	VERB
ejpam-4637	226	2	a	a	PRON
ejpam-4637	226	3	=	=	SYM
ejpam-4637	226	4	(	(	PUNCT
ejpam-4637	226	5	ta	ta	PROPN
ejpam-4637	226	6	,	,	PUNCT
ejpam-4637	226	7	ia	ia	PROPN
ejpam-4637	226	8	,	,	PUNCT
ejpam-4637	226	9	fa	fa	NOUN
ejpam-4637	226	10	)	)	PUNCT
ejpam-4637	226	11	be	be	AUX
ejpam-4637	226	12	a	a	DET
ejpam-4637	226	13	svn	svn	NOUN
ejpam-4637	226	14	set	set	NOUN
ejpam-4637	226	15	in	in	ADP
ejpam-4637	226	16	x.	x.	PROPN
ejpam-4637	226	17	(	(	PUNCT
ejpam-4637	226	18	⇒	⇒	PROPN
ejpam-4637	226	19	)	)	PUNCT
ejpam-4637	226	20	assume	assume	VERB
ejpam-4637	226	21	thata	thata	PROPN
ejpam-4637	226	22	is	be	AUX
ejpam-4637	226	23	a	a	DET
ejpam-4637	226	24	svn	svn	NOUN
ejpam-4637	226	25	hyperup	hyperup	NOUN
ejpam-4637	226	26	-subalgebra	-subalgebra	PROPN
ejpam-4637	226	27	ofx	ofx	PROPN
ejpam-4637	226	28	.	.	PUNCT
ejpam-4637	227	1	note	note	VERB
ejpam-4637	227	2	that	that	SCONJ
ejpam-4637	227	3	ta(x	ta(x	NOUN
ejpam-4637	227	4	)	)	PUNCT
ejpam-4637	227	5	,	,	PUNCT
ejpam-4637	227	6	ia(x),fa(x	ia(x),fa(x	PROPN
ejpam-4637	227	7	)	)	PUNCT
ejpam-4637	227	8	∈	∈	NOUN
ejpam-4637	228	1	[	[	X
ejpam-4637	228	2	0	0	NUM
ejpam-4637	228	3	,	,	PUNCT
ejpam-4637	228	4	1	1	NUM
ejpam-4637	228	5	]	]	PUNCT
ejpam-4637	228	6	∀x	∀x	X
ejpam-4637	228	7	∈	∈	PROPN
ejpam-4637	228	8	x.	x.	NOUN
ejpam-4637	228	9	then	then	ADV
ejpam-4637	228	10	take	take	VERB
ejpam-4637	228	11	α	α	NOUN
ejpam-4637	228	12	=	=	PUNCT
ejpam-4637	228	13	ta(x	ta(x	NOUN
ejpam-4637	228	14	)	)	PUNCT
ejpam-4637	228	15	,	,	PUNCT
ejpam-4637	228	16	β	β	X
ejpam-4637	228	17	=	=	PUNCT
ejpam-4637	228	18	ia(x	ia(x	NOUN
ejpam-4637	228	19	)	)	PUNCT
ejpam-4637	228	20	and	and	CCONJ
ejpam-4637	228	21	γ	γ	X
ejpam-4637	228	22	=	=	SYM
ejpam-4637	228	23	fa(x	fa(x	PROPN
ejpam-4637	228	24	)	)	PUNCT
ejpam-4637	228	25	.	.	PUNCT
ejpam-4637	229	1	by	by	ADP
ejpam-4637	229	2	proposition	proposition	NOUN
ejpam-4637	229	3	3(i	3(i	NUM
ejpam-4637	229	4	)	)	PUNCT
ejpam-4637	229	5	,	,	PUNCT
ejpam-4637	229	6	ta(0	ta(0	NOUN
ejpam-4637	229	7	)	)	PUNCT
ejpam-4637	229	8	≥	≥	NOUN
ejpam-4637	229	9	ta(x	ta(x	NOUN
ejpam-4637	229	10	)	)	PUNCT
ejpam-4637	229	11	=	=	SYM
ejpam-4637	229	12	α	α	PROPN
ejpam-4637	229	13	,	,	PUNCT
ejpam-4637	229	14	ia(0	ia(0	NOUN
ejpam-4637	229	15	)	)	PUNCT
ejpam-4637	229	16	≤	≤	NOUN
ejpam-4637	229	17	ia(x	ia(x	NOUN
ejpam-4637	229	18	)	)	PUNCT
ejpam-4637	229	19	=	=	SYM
ejpam-4637	230	1	β	β	NOUN
ejpam-4637	230	2	,	,	PUNCT
ejpam-4637	230	3	and	and	CCONJ
ejpam-4637	230	4	fa(0	fa(0	NOUN
ejpam-4637	230	5	)	)	PUNCT
ejpam-4637	230	6	≤	≤	NOUN
ejpam-4637	230	7	fa(x	fa(x	PROPN
ejpam-4637	230	8	)	)	PUNCT
ejpam-4637	230	9	=	=	SYM
ejpam-4637	231	1	γ	γ	X
ejpam-4637	231	2	.	.	PROPN
ejpam-4637	231	3	hence	hence	ADV
ejpam-4637	231	4	,	,	PUNCT
ejpam-4637	231	5	0	0	X
ejpam-4637	231	6	∈	∈	PROPN
ejpam-4637	231	7	tα	tα	VERB
ejpam-4637	231	8	a	a	DET
ejpam-4637	231	9	∩	∩	ADJ
ejpam-4637	231	10	iαa	iαa	NOUN
ejpam-4637	231	11	∩	∩	NOUN
ejpam-4637	231	12	fα	fα	ADP
ejpam-4637	231	13	a	a	DET
ejpam-4637	231	14	=	=	PUNCT
ejpam-4637	231	15	a(α	a(α	NOUN
ejpam-4637	231	16	,	,	PUNCT
ejpam-4637	231	17	β	β	X
ejpam-4637	231	18	,	,	PUNCT
ejpam-4637	231	19	γ	γ	NOUN
ejpam-4637	231	20	)	)	PUNCT
ejpam-4637	231	21	and	and	CCONJ
ejpam-4637	231	22	so	so	ADV
ejpam-4637	231	23	a(α	a(α	NOUN
ejpam-4637	231	24	,	,	PUNCT
ejpam-4637	231	25	β	β	X
ejpam-4637	231	26	,	,	PUNCT
ejpam-4637	231	27	γ	γ	NOUN
ejpam-4637	231	28	)	)	PUNCT
ejpam-4637	231	29	̸=	̸=	PROPN
ejpam-4637	231	30	∅.	∅.	ADP
ejpam-4637	231	31	now	now	ADV
ejpam-4637	231	32	,	,	PUNCT
ejpam-4637	231	33	we	we	PRON
ejpam-4637	231	34	let	let	VERB
ejpam-4637	231	35	x	x	PRON
ejpam-4637	231	36	,	,	PUNCT
ejpam-4637	231	37	y	y	PROPN
ejpam-4637	231	38	∈	∈	PROPN
ejpam-4637	231	39	a(α	a(α	NOUN
ejpam-4637	231	40	,	,	PUNCT
ejpam-4637	231	41	β	β	X
ejpam-4637	231	42	,	,	PUNCT
ejpam-4637	231	43	γ	γ	NOUN
ejpam-4637	231	44	)	)	PUNCT
ejpam-4637	231	45	for	for	ADP
ejpam-4637	231	46	all	all	DET
ejpam-4637	231	47	α	α	PROPN
ejpam-4637	231	48	,	,	PUNCT
ejpam-4637	231	49	β	β	X
ejpam-4637	231	50	,	,	PUNCT
ejpam-4637	231	51	γ	γ	PROPN
ejpam-4637	231	52	∈	∈	PROPN
ejpam-4637	232	1	[	[	X
ejpam-4637	232	2	0	0	NUM
ejpam-4637	232	3	,	,	PUNCT
ejpam-4637	232	4	1	1	NUM
ejpam-4637	232	5	]	]	PUNCT
ejpam-4637	232	6	.	.	PUNCT
ejpam-4637	233	1	dealing	deal	VERB
ejpam-4637	233	2	first	first	ADV
ejpam-4637	233	3	with	with	ADP
ejpam-4637	233	4	tα	tα	PROPN
ejpam-4637	233	5	a	a	DET
ejpam-4637	233	6	,	,	PUNCT
ejpam-4637	233	7	we	we	PRON
ejpam-4637	233	8	have	have	VERB
ejpam-4637	233	9	x	x	X
ejpam-4637	233	10	,	,	PUNCT
ejpam-4637	233	11	y	y	PROPN
ejpam-4637	233	12	∈	∈	PROPN
ejpam-4637	233	13	tα	tα	VERB
ejpam-4637	233	14	a	a	PRON
ejpam-4637	233	15	.	.	PUNCT
ejpam-4637	234	1	let	let	VERB
ejpam-4637	234	2	z	z	NOUN
ejpam-4637	234	3	∈	∈	PROPN
ejpam-4637	234	4	x	x	PUNCT
ejpam-4637	234	5	◦	◦	NOUN
ejpam-4637	234	6	y.	y.	NOUN
ejpam-4637	234	7	then	then	ADV
ejpam-4637	234	8	ta(x	ta(x	NOUN
ejpam-4637	234	9	)	)	PUNCT
ejpam-4637	234	10	≥	≥	NOUN
ejpam-4637	234	11	α	α	NOUN
ejpam-4637	234	12	,	,	PUNCT
ejpam-4637	234	13	ta(y	ta(y	PUNCT
ejpam-4637	234	14	)	)	PUNCT
ejpam-4637	234	15	≥	≥	NUM
ejpam-4637	234	16	α	α	NOUN
ejpam-4637	234	17	,	,	PUNCT
ejpam-4637	234	18	and	and	CCONJ
ejpam-4637	234	19	ta(z	ta(z	NOUN
ejpam-4637	234	20	)	)	PUNCT
ejpam-4637	234	21	≥∗	≥∗	NOUN
ejpam-4637	234	22	ta(x	ta(x	NOUN
ejpam-4637	234	23	◦	◦	VERB
ejpam-4637	234	24	y	y	NOUN
ejpam-4637	234	25	)	)	PUNCT
ejpam-4637	234	26	.	.	PUNCT
ejpam-4637	235	1	by	by	ADP
ejpam-4637	235	2	assumption	assumption	NOUN
ejpam-4637	235	3	,	,	PUNCT
ejpam-4637	235	4	ta(z	ta(z	NOUN
ejpam-4637	235	5	)	)	PUNCT
ejpam-4637	235	6	≥	≥	NOUN
ejpam-4637	235	7	∗ta(x	∗ta(x	PROPN
ejpam-4637	235	8	◦	◦	VERB
ejpam-4637	235	9	y	y	NOUN
ejpam-4637	235	10	)	)	PUNCT
ejpam-4637	235	11	≥	≥	NOUN
ejpam-4637	235	12	min{ta(x	min{ta(x	NOUN
ejpam-4637	235	13	)	)	PUNCT
ejpam-4637	235	14	,	,	PUNCT
ejpam-4637	235	15	ta(y	ta(y	NUM
ejpam-4637	235	16	)	)	PUNCT
ejpam-4637	235	17	}	}	PUNCT
ejpam-4637	236	1	=	=	SYM
ejpam-4637	236	2	α	α	X
ejpam-4637	236	3	.	.	PUNCT
ejpam-4637	236	4	a.	a.	PROPN
ejpam-4637	236	5	cano	cano	PROPN
ejpam-4637	236	6	,	,	PUNCT
ejpam-4637	236	7	g.	g.	PROPN
ejpam-4637	236	8	petalcorin	petalcorin	PROPN
ejpam-4637	236	9	/	/	SYM
ejpam-4637	236	10	eur	eur	PROPN
ejpam-4637	236	11	.	.	PUNCT
ejpam-4637	237	1	j.	j.	PROPN
ejpam-4637	237	2	pure	pure	PROPN
ejpam-4637	237	3	appl	appl	PROPN
ejpam-4637	237	4	.	.	PROPN
ejpam-4637	237	5	math	math	PROPN
ejpam-4637	237	6	,	,	PUNCT
ejpam-4637	237	7	16	16	NUM
ejpam-4637	237	8	(	(	PUNCT
ejpam-4637	237	9	1	1	NUM
ejpam-4637	237	10	)	)	PUNCT
ejpam-4637	237	11	(	(	PUNCT
ejpam-4637	237	12	2023	2023	NUM
ejpam-4637	237	13	)	)	PUNCT
ejpam-4637	237	14	,	,	PUNCT
ejpam-4637	237	15	548	548	NUM
ejpam-4637	237	16	-	-	SYM
ejpam-4637	237	17	576	576	NUM
ejpam-4637	237	18	558	558	NUM
ejpam-4637	237	19	thus	thus	ADV
ejpam-4637	237	20	,	,	PUNCT
ejpam-4637	237	21	z	z	PROPN
ejpam-4637	237	22	∈	∈	PROPN
ejpam-4637	237	23	tα	tα	VERB
ejpam-4637	237	24	a	a	PRON
ejpam-4637	237	25	and	and	CCONJ
ejpam-4637	237	26	so	so	ADV
ejpam-4637	237	27	x	x	VERB
ejpam-4637	237	28	◦	◦	NOUN
ejpam-4637	237	29	y	y	PROPN
ejpam-4637	237	30	⊆	⊆	NUM
ejpam-4637	237	31	tα	tα	ADP
ejpam-4637	237	32	a	a	PRON
ejpam-4637	237	33	.	.	PUNCT
ejpam-4637	238	1	for	for	SCONJ
ejpam-4637	238	2	i	i	PRON
ejpam-4637	238	3	β	β	PROPN
ejpam-4637	238	4	a	a	X
ejpam-4637	238	5	,	,	PUNCT
ejpam-4637	238	6	we	we	PRON
ejpam-4637	238	7	have	have	VERB
ejpam-4637	238	8	x	x	X
ejpam-4637	238	9	,	,	PUNCT
ejpam-4637	238	10	y	y	PROPN
ejpam-4637	238	11	∈	∈	PROPN
ejpam-4637	238	12	iβa	iβa	VERB
ejpam-4637	238	13	.	.	PUNCT
ejpam-4637	239	1	then	then	ADV
ejpam-4637	239	2	ia(x	ia(x	NOUN
ejpam-4637	239	3	)	)	PUNCT
ejpam-4637	239	4	≤	≤	NUM
ejpam-4637	239	5	β	β	NOUN
ejpam-4637	239	6	,	,	PUNCT
ejpam-4637	239	7	ia(y	ia(y	NOUN
ejpam-4637	239	8	)	)	PUNCT
ejpam-4637	239	9	≤	≤	NOUN
ejpam-4637	239	10	β	β	NOUN
ejpam-4637	239	11	,	,	PUNCT
ejpam-4637	239	12	and	and	CCONJ
ejpam-4637	239	13	ia(z	ia(z	NOUN
ejpam-4637	239	14	)	)	PUNCT
ejpam-4637	239	15	≤∗	≤∗	PROPN
ejpam-4637	239	16	ia(x	ia(x	VERB
ejpam-4637	239	17	◦	◦	VERB
ejpam-4637	239	18	y	y	NOUN
ejpam-4637	239	19	)	)	PUNCT
ejpam-4637	239	20	.	.	PUNCT
ejpam-4637	240	1	by	by	ADP
ejpam-4637	240	2	assumption	assumption	NOUN
ejpam-4637	240	3	,	,	PUNCT
ejpam-4637	240	4	ia(z	ia(z	NOUN
ejpam-4637	240	5	)	)	PUNCT
ejpam-4637	240	6	≤	≤	NUM
ejpam-4637	240	7	∗ia(x	∗ia(x	NOUN
ejpam-4637	240	8	◦	◦	NOUN
ejpam-4637	240	9	y	y	NOUN
ejpam-4637	240	10	)	)	PUNCT
ejpam-4637	240	11	≤	≤	NUM
ejpam-4637	240	12	max{ia(x	max{ia(x	NOUN
ejpam-4637	240	13	)	)	PUNCT
ejpam-4637	240	14	,	,	PUNCT
ejpam-4637	240	15	ia(y	ia(y	NOUN
ejpam-4637	240	16	)	)	PUNCT
ejpam-4637	240	17	}	}	PUNCT
ejpam-4637	240	18	=	=	SYM
ejpam-4637	240	19	β	β	X
ejpam-4637	240	20	.	.	PUNCT
ejpam-4637	241	1	thus	thus	ADV
ejpam-4637	241	2	,	,	PUNCT
ejpam-4637	241	3	z	z	PROPN
ejpam-4637	241	4	∈	∈	PROPN
ejpam-4637	241	5	iβa	iβa	NOUN
ejpam-4637	241	6	and	and	CCONJ
ejpam-4637	241	7	so	so	ADV
ejpam-4637	241	8	x	x	VERB
ejpam-4637	241	9	◦	◦	VERB
ejpam-4637	241	10	y	y	PROPN
ejpam-4637	241	11	⊆	⊆	NUM
ejpam-4637	241	12	iβa	iβa	NOUN
ejpam-4637	241	13	.	.	PUNCT
ejpam-4637	242	1	using	use	VERB
ejpam-4637	242	2	similar	similar	ADJ
ejpam-4637	242	3	arguments	argument	NOUN
ejpam-4637	242	4	,	,	PUNCT
ejpam-4637	242	5	x	x	PUNCT
ejpam-4637	242	6	◦	◦	VERB
ejpam-4637	242	7	y	y	PROPN
ejpam-4637	242	8	⊆	⊆	NUM
ejpam-4637	242	9	f	f	PROPN
ejpam-4637	242	10	γ	γ	X
ejpam-4637	242	11	a	a	PRON
ejpam-4637	242	12	for	for	ADP
ejpam-4637	242	13	x	x	PROPN
ejpam-4637	242	14	,	,	PUNCT
ejpam-4637	242	15	y	y	PROPN
ejpam-4637	242	16	∈	∈	PROPN
ejpam-4637	242	17	f	f	PROPN
ejpam-4637	242	18	γ	γ	X
ejpam-4637	242	19	a.	a.	NOUN
ejpam-4637	242	20	now	now	ADV
ejpam-4637	242	21	,	,	PUNCT
ejpam-4637	242	22	it	it	PRON
ejpam-4637	242	23	follows	follow	VERB
ejpam-4637	242	24	that	that	SCONJ
ejpam-4637	242	25	x	x	PUNCT
ejpam-4637	243	1	◦	◦	VERB
ejpam-4637	243	2	y	y	PROPN
ejpam-4637	243	3	⊆	⊆	NUM
ejpam-4637	243	4	tα	tα	ADP
ejpam-4637	243	5	a	a	DET
ejpam-4637	243	6	∩	∩	NOUN
ejpam-4637	243	7	iβa	iβa	NOUN
ejpam-4637	243	8	∩	∩	NOUN
ejpam-4637	243	9	f	f	PROPN
ejpam-4637	243	10	γ	γ	X
ejpam-4637	243	11	a	a	PRON
ejpam-4637	243	12	=	=	PUNCT
ejpam-4637	243	13	a(α	a(α	NOUN
ejpam-4637	243	14	,	,	PUNCT
ejpam-4637	243	15	β	β	X
ejpam-4637	243	16	,	,	PUNCT
ejpam-4637	243	17	γ	γ	NOUN
ejpam-4637	243	18	)	)	PUNCT
ejpam-4637	243	19	.	.	PUNCT
ejpam-4637	244	1	by	by	ADP
ejpam-4637	244	2	proposition	proposition	NOUN
ejpam-4637	244	3	2	2	NUM
ejpam-4637	244	4	,	,	PUNCT
ejpam-4637	244	5	a(α	a(α	VERB
ejpam-4637	244	6	,	,	PUNCT
ejpam-4637	244	7	β	β	X
ejpam-4637	244	8	,	,	PUNCT
ejpam-4637	244	9	γ	γ	X
ejpam-4637	244	10	)	)	PUNCT
ejpam-4637	244	11	is	be	AUX
ejpam-4637	244	12	a	a	DET
ejpam-4637	244	13	hyper	hyper	ADJ
ejpam-4637	244	14	up	up	ADP
ejpam-4637	244	15	-subalgebra	-subalgebra	NOUN
ejpam-4637	244	16	.	.	PUNCT
ejpam-4637	245	1	(	(	PUNCT
ejpam-4637	245	2	⇐	⇐	NOUN
ejpam-4637	245	3	)	)	PUNCT
ejpam-4637	245	4	assume	assume	VERB
ejpam-4637	245	5	that	that	SCONJ
ejpam-4637	245	6	a(α	a(α	NOUN
ejpam-4637	245	7	,	,	PUNCT
ejpam-4637	245	8	β	β	X
ejpam-4637	245	9	,	,	PUNCT
ejpam-4637	245	10	γ	γ	X
ejpam-4637	245	11	)	)	PUNCT
ejpam-4637	245	12	is	be	AUX
ejpam-4637	245	13	a	a	DET
ejpam-4637	245	14	hyper	hyper	ADJ
ejpam-4637	245	15	up	up	ADP
ejpam-4637	245	16	-subalgebra	-subalgebra	NOUN
ejpam-4637	245	17	of	of	ADP
ejpam-4637	245	18	x	x	PUNCT
ejpam-4637	245	19	for	for	ADP
ejpam-4637	245	20	all	all	DET
ejpam-4637	245	21	α	α	NOUN
ejpam-4637	245	22	,	,	PUNCT
ejpam-4637	245	23	β	β	X
ejpam-4637	245	24	,	,	PUNCT
ejpam-4637	245	25	γ	γ	PROPN
ejpam-4637	245	26	∈	∈	PROPN
ejpam-4637	246	1	[	[	X
ejpam-4637	246	2	0	0	NUM
ejpam-4637	246	3	,	,	PUNCT
ejpam-4637	246	4	1	1	NUM
ejpam-4637	246	5	]	]	PUNCT
ejpam-4637	246	6	and	and	CCONJ
ejpam-4637	246	7	let	let	VERB
ejpam-4637	246	8	x	x	PRON
ejpam-4637	246	9	,	,	PUNCT
ejpam-4637	246	10	y	y	PROPN
ejpam-4637	246	11	∈	∈	PROPN
ejpam-4637	246	12	x.	x.	NOUN
ejpam-4637	246	13	note	note	VERB
ejpam-4637	246	14	that	that	SCONJ
ejpam-4637	246	15	ta(x	ta(x	NOUN
ejpam-4637	246	16	)	)	PUNCT
ejpam-4637	246	17	,	,	PUNCT
ejpam-4637	246	18	ta(y	ta(y	NUM
ejpam-4637	246	19	)	)	PUNCT
ejpam-4637	246	20	,	,	PUNCT
ejpam-4637	246	21	ia(x	ia(x	NOUN
ejpam-4637	246	22	)	)	PUNCT
ejpam-4637	246	23	,	,	PUNCT
ejpam-4637	246	24	ia(y),fa(x),fa(y	ia(y),fa(x),fa(y	PROPN
ejpam-4637	246	25	)	)	PUNCT
ejpam-4637	246	26	∈	∈	PROPN
ejpam-4637	247	1	[	[	X
ejpam-4637	247	2	0	0	NUM
ejpam-4637	247	3	,	,	PUNCT
ejpam-4637	247	4	1	1	NUM
ejpam-4637	247	5	]	]	PUNCT
ejpam-4637	247	6	.	.	PUNCT
ejpam-4637	248	1	then	then	ADV
ejpam-4637	248	2	take	take	VERB
ejpam-4637	248	3	α	α	NOUN
ejpam-4637	248	4	=	=	PUNCT
ejpam-4637	248	5	min{ta(x	min{ta(x	NOUN
ejpam-4637	248	6	)	)	PUNCT
ejpam-4637	248	7	,	,	PUNCT
ejpam-4637	248	8	ta(y	ta(y	PUNCT
ejpam-4637	248	9	)	)	PUNCT
ejpam-4637	248	10	}	}	PUNCT
ejpam-4637	248	11	,	,	PUNCT
ejpam-4637	248	12	β	β	X
ejpam-4637	248	13	=	=	SYM
ejpam-4637	248	14	max{ia(x	max{ia(x	NOUN
ejpam-4637	248	15	)	)	PUNCT
ejpam-4637	248	16	,	,	PUNCT
ejpam-4637	248	17	ia(y	ia(y	NOUN
ejpam-4637	248	18	)	)	PUNCT
ejpam-4637	248	19	}	}	PUNCT
ejpam-4637	248	20	,	,	PUNCT
ejpam-4637	248	21	and	and	CCONJ
ejpam-4637	248	22	γ	γ	X
ejpam-4637	248	23	=	=	SYM
ejpam-4637	248	24	max{ta(x	max{ta(x	PROPN
ejpam-4637	248	25	)	)	PUNCT
ejpam-4637	248	26	,	,	PUNCT
ejpam-4637	248	27	ta(y	ta(y	NUM
ejpam-4637	248	28	)	)	PUNCT
ejpam-4637	248	29	}	}	PUNCT
ejpam-4637	248	30	and	and	CCONJ
ejpam-4637	248	31	so	so	ADV
ejpam-4637	248	32	we	we	PRON
ejpam-4637	248	33	have	have	VERB
ejpam-4637	248	34	ta(x	ta(x	NOUN
ejpam-4637	248	35	)	)	PUNCT
ejpam-4637	248	36	≥	≥	NOUN
ejpam-4637	248	37	α	α	NOUN
ejpam-4637	248	38	,	,	PUNCT
ejpam-4637	248	39	ta(y	ta(y	PUNCT
ejpam-4637	248	40	)	)	PUNCT
ejpam-4637	248	41	≥	≥	NUM
ejpam-4637	248	42	α	α	X
ejpam-4637	248	43	,	,	PUNCT
ejpam-4637	248	44	ia(x	ia(x	NOUN
ejpam-4637	248	45	)	)	PUNCT
ejpam-4637	248	46	≤	≤	NUM
ejpam-4637	248	47	β	β	NOUN
ejpam-4637	248	48	,	,	PUNCT
ejpam-4637	248	49	ia(y	ia(y	NOUN
ejpam-4637	248	50	)	)	PUNCT
ejpam-4637	248	51	≤	≤	NUM
ejpam-4637	248	52	β	β	NOUN
ejpam-4637	248	53	,	,	PUNCT
ejpam-4637	248	54	fa(x	fa(x	NOUN
ejpam-4637	248	55	)	)	PUNCT
ejpam-4637	248	56	≤	≤	NUM
ejpam-4637	248	57	γ	γ	X
ejpam-4637	248	58	,	,	PUNCT
ejpam-4637	248	59	and	and	CCONJ
ejpam-4637	248	60	fa(y	fa(y	NOUN
ejpam-4637	248	61	)	)	PUNCT
ejpam-4637	248	62	≤	≤	NUM
ejpam-4637	248	63	γ	γ	PROPN
ejpam-4637	248	64	.	.	PUNCT
ejpam-4637	249	1	thus	thus	ADV
ejpam-4637	249	2	,	,	PUNCT
ejpam-4637	249	3	x	x	PRON
ejpam-4637	249	4	,	,	PUNCT
ejpam-4637	249	5	y	y	PROPN
ejpam-4637	249	6	∈	∈	PROPN
ejpam-4637	249	7	tα	tα	VERB
ejpam-4637	249	8	a	a	DET
ejpam-4637	249	9	∩	∩	NOUN
ejpam-4637	249	10	iβa	iβa	NOUN
ejpam-4637	249	11	∩	∩	NOUN
ejpam-4637	249	12	f	f	PROPN
ejpam-4637	249	13	γ	γ	X
ejpam-4637	249	14	a	a	PRON
ejpam-4637	249	15	=	=	PUNCT
ejpam-4637	249	16	a(α	a(α	NOUN
ejpam-4637	249	17	,	,	PUNCT
ejpam-4637	249	18	β	β	X
ejpam-4637	249	19	,	,	PUNCT
ejpam-4637	249	20	γ	γ	NOUN
ejpam-4637	249	21	)	)	PUNCT
ejpam-4637	249	22	.	.	PUNCT
ejpam-4637	250	1	by	by	ADP
ejpam-4637	250	2	assumption	assumption	NOUN
ejpam-4637	250	3	,	,	PUNCT
ejpam-4637	250	4	x	x	PUNCT
ejpam-4637	250	5	◦	◦	VERB
ejpam-4637	250	6	y	y	PROPN
ejpam-4637	250	7	⊆	⊆	NUM
ejpam-4637	250	8	a(α	a(α	NOUN
ejpam-4637	250	9	,	,	PUNCT
ejpam-4637	250	10	β	β	X
ejpam-4637	250	11	,	,	PUNCT
ejpam-4637	250	12	γ	γ	NOUN
ejpam-4637	250	13	)	)	PUNCT
ejpam-4637	250	14	.	.	PUNCT
ejpam-4637	251	1	this	this	PRON
ejpam-4637	251	2	means	mean	VERB
ejpam-4637	251	3	that	that	SCONJ
ejpam-4637	251	4	∗ta(x	∗ta(x	NOUN
ejpam-4637	251	5	◦	◦	VERB
ejpam-4637	251	6	y	y	NOUN
ejpam-4637	251	7	)	)	PUNCT
ejpam-4637	251	8	≥	≥	NOUN
ejpam-4637	251	9	α	α	NOUN
ejpam-4637	251	10	=	=	PUNCT
ejpam-4637	251	11	min{ta(x	min{ta(x	NOUN
ejpam-4637	251	12	)	)	PUNCT
ejpam-4637	251	13	,	,	PUNCT
ejpam-4637	251	14	ta(y	ta(y	PUNCT
ejpam-4637	251	15	)	)	PUNCT
ejpam-4637	251	16	}	}	PUNCT
ejpam-4637	251	17	,	,	PUNCT
ejpam-4637	251	18	∗ia(x	∗ia(x	VERB
ejpam-4637	251	19	◦	◦	NOUN
ejpam-4637	251	20	y	y	NOUN
ejpam-4637	251	21	)	)	PUNCT
ejpam-4637	251	22	≤	≤	NOUN
ejpam-4637	251	23	β	β	X
ejpam-4637	251	24	=	=	SYM
ejpam-4637	251	25	max{ia(x	max{ia(x	NOUN
ejpam-4637	251	26	)	)	PUNCT
ejpam-4637	251	27	,	,	PUNCT
ejpam-4637	251	28	ia(y	ia(y	NOUN
ejpam-4637	251	29	)	)	PUNCT
ejpam-4637	251	30	}	}	PUNCT
ejpam-4637	251	31	,	,	PUNCT
ejpam-4637	251	32	and	and	CCONJ
ejpam-4637	251	33	∗fa(x	∗fa(x	NOUN
ejpam-4637	251	34	◦	◦	VERB
ejpam-4637	251	35	y	y	NOUN
ejpam-4637	251	36	)	)	PUNCT
ejpam-4637	251	37	≤	≤	NOUN
ejpam-4637	251	38	γ	γ	X
ejpam-4637	251	39	=	=	SYM
ejpam-4637	251	40	max{fa(x),fa(y	max{fa(x),fa(y	PROPN
ejpam-4637	251	41	)	)	PUNCT
ejpam-4637	251	42	}	}	PUNCT
ejpam-4637	251	43	.	.	PUNCT
ejpam-4637	252	1	hence	hence	ADV
ejpam-4637	252	2	,	,	PUNCT
ejpam-4637	252	3	a	a	PRON
ejpam-4637	252	4	is	be	AUX
ejpam-4637	252	5	a	a	DET
ejpam-4637	252	6	svn	svn	NOUN
ejpam-4637	252	7	hyper	hyper	NOUN
ejpam-4637	252	8	up	up	ADP
ejpam-4637	252	9	-subalgebra	-subalgebra	NOUN
ejpam-4637	252	10	of	of	ADP
ejpam-4637	252	11	x.	x.	NOUN
ejpam-4637	252	12	corollary	corollary	NOUN
ejpam-4637	252	13	1	1	X
ejpam-4637	252	14	.	.	PUNCT
ejpam-4637	253	1	let	let	VERB
ejpam-4637	253	2	a	a	PRON
ejpam-4637	253	3	=	=	SYM
ejpam-4637	253	4	(	(	PUNCT
ejpam-4637	253	5	ta	ta	PROPN
ejpam-4637	253	6	,	,	PUNCT
ejpam-4637	253	7	ia	ia	PROPN
ejpam-4637	253	8	,	,	PUNCT
ejpam-4637	253	9	fa	fa	NOUN
ejpam-4637	253	10	)	)	PUNCT
ejpam-4637	253	11	be	be	AUX
ejpam-4637	253	12	a	a	DET
ejpam-4637	253	13	svn	svn	NOUN
ejpam-4637	253	14	hyper	hyper	NOUN
ejpam-4637	253	15	up	up	ADP
ejpam-4637	253	16	-	-	PUNCT
ejpam-4637	253	17	subalgebra	subalgebra	NOUN
ejpam-4637	253	18	of	of	ADP
ejpam-4637	253	19	x.	x.	NOUN
ejpam-4637	253	20	if	if	SCONJ
ejpam-4637	253	21	0	0	NUM
ejpam-4637	253	22	≤	≤	NUM
ejpam-4637	253	23	α	α	NOUN
ejpam-4637	253	24	≤	≤	NUM
ejpam-4637	253	25	α	α	DET
ejpam-4637	253	26	′	′	NUM
ejpam-4637	253	27	≤	≤	NUM
ejpam-4637	253	28	1	1	NUM
ejpam-4637	253	29	,	,	PUNCT
ejpam-4637	253	30	0	0	NUM
ejpam-4637	253	31	≤	≤	NUM
ejpam-4637	253	32	β	β	NOUN
ejpam-4637	253	33	≤	≤	ADJ
ejpam-4637	253	34	β	β	X
ejpam-4637	253	35	′	′	NUM
ejpam-4637	253	36	≤	≤	NUM
ejpam-4637	253	37	1	1	NUM
ejpam-4637	253	38	,	,	PUNCT
ejpam-4637	253	39	and	and	CCONJ
ejpam-4637	253	40	0	0	NUM
ejpam-4637	253	41	≤	≤	NUM
ejpam-4637	253	42	γ	γ	PROPN
ejpam-4637	253	43	≤	≤	NUM
ejpam-4637	253	44	γ	γ	PROPN
ejpam-4637	253	45	′	′	NOUN
ejpam-4637	253	46	≤	≤	NUM
ejpam-4637	253	47	1	1	NUM
ejpam-4637	253	48	,	,	PUNCT
ejpam-4637	253	49	then	then	ADV
ejpam-4637	253	50	a(α	a(α	ADJ
ejpam-4637	253	51	′	′	NUM
ejpam-4637	253	52	,	,	PUNCT
ejpam-4637	253	53	β	β	X
ejpam-4637	253	54	,	,	PUNCT
ejpam-4637	253	55	γ	γ	X
ejpam-4637	253	56	)	)	PUNCT
ejpam-4637	253	57	is	be	AUX
ejpam-4637	253	58	a	a	DET
ejpam-4637	253	59	hyper	hyper	ADJ
ejpam-4637	253	60	up	up	ADP
ejpam-4637	253	61	-	-	PUNCT
ejpam-4637	253	62	subalgebra	subalgebra	NOUN
ejpam-4637	253	63	of	of	ADP
ejpam-4637	253	64	a(α	a(α	NOUN
ejpam-4637	253	65	,	,	PUNCT
ejpam-4637	253	66	β	β	X
ejpam-4637	253	67	′	′	NUM
ejpam-4637	253	68	,	,	PUNCT
ejpam-4637	253	69	γ	γ	X
ejpam-4637	253	70	′	′	NUM
ejpam-4637	253	71	)	)	PUNCT
ejpam-4637	253	72	.	.	PUNCT
ejpam-4637	254	1	proof	proof	NOUN
ejpam-4637	254	2	.	.	PUNCT
ejpam-4637	255	1	let	let	VERB
ejpam-4637	255	2	a	a	PRON
ejpam-4637	255	3	=	=	SYM
ejpam-4637	255	4	(	(	PUNCT
ejpam-4637	255	5	ta	ta	PROPN
ejpam-4637	255	6	,	,	PUNCT
ejpam-4637	255	7	ia	ia	PROPN
ejpam-4637	255	8	,	,	PUNCT
ejpam-4637	255	9	fa	fa	NOUN
ejpam-4637	255	10	)	)	PUNCT
ejpam-4637	255	11	be	be	AUX
ejpam-4637	255	12	a	a	DET
ejpam-4637	255	13	svn	svn	NOUN
ejpam-4637	255	14	hyper	hyper	NOUN
ejpam-4637	255	15	up	up	ADP
ejpam-4637	255	16	-subalgebra	-subalgebra	NOUN
ejpam-4637	255	17	of	of	ADP
ejpam-4637	255	18	x	x	PUNCT
ejpam-4637	255	19	and	and	CCONJ
ejpam-4637	255	20	let	let	VERB
ejpam-4637	255	21	0	0	NUM
ejpam-4637	255	22	≤	≤	NUM
ejpam-4637	255	23	α	α	NOUN
ejpam-4637	255	24	≤	≤	NUM
ejpam-4637	255	25	α	α	DET
ejpam-4637	255	26	′	′	NUM
ejpam-4637	255	27	≤	≤	NUM
ejpam-4637	255	28	1	1	NUM
ejpam-4637	255	29	,	,	PUNCT
ejpam-4637	255	30	0	0	NUM
ejpam-4637	255	31	≤	≤	NUM
ejpam-4637	255	32	β	β	NOUN
ejpam-4637	255	33	≤	≤	ADJ
ejpam-4637	255	34	β	β	X
ejpam-4637	255	35	′	′	NUM
ejpam-4637	255	36	≤	≤	NUM
ejpam-4637	255	37	1	1	NUM
ejpam-4637	255	38	,	,	PUNCT
ejpam-4637	255	39	and	and	CCONJ
ejpam-4637	255	40	0	0	NUM
ejpam-4637	255	41	≤	≤	NUM
ejpam-4637	255	42	γ	γ	PROPN
ejpam-4637	255	43	≤	≤	NUM
ejpam-4637	255	44	γ	γ	PROPN
ejpam-4637	255	45	′	′	NOUN
ejpam-4637	255	46	≤	≤	NUM
ejpam-4637	255	47	1	1	NUM
ejpam-4637	255	48	.	.	PUNCT
ejpam-4637	256	1	by	by	ADP
ejpam-4637	256	2	theorem	theorem	NOUN
ejpam-4637	256	3	1	1	NUM
ejpam-4637	256	4	,	,	PUNCT
ejpam-4637	256	5	a(α	a(α	NOUN
ejpam-4637	256	6	′	′	NUM
ejpam-4637	256	7	,	,	PUNCT
ejpam-4637	256	8	β	β	X
ejpam-4637	256	9	,	,	PUNCT
ejpam-4637	256	10	γ	γ	NOUN
ejpam-4637	256	11	)	)	PUNCT
ejpam-4637	256	12	and	and	CCONJ
ejpam-4637	256	13	a(α	a(α	NOUN
ejpam-4637	256	14	,	,	PUNCT
ejpam-4637	256	15	β	β	X
ejpam-4637	256	16	′	′	NUM
ejpam-4637	256	17	,	,	PUNCT
ejpam-4637	256	18	γ	γ	X
ejpam-4637	256	19	′	′	NUM
ejpam-4637	256	20	)	)	PUNCT
ejpam-4637	256	21	are	be	AUX
ejpam-4637	256	22	both	both	PRON
ejpam-4637	256	23	hyper	hyper	ADJ
ejpam-4637	256	24	up	up	ADP
ejpam-4637	256	25	-subalgebra	-subalgebra	NOUN
ejpam-4637	256	26	of	of	ADP
ejpam-4637	256	27	x.	x.	NOUN
ejpam-4637	256	28	we	we	PRON
ejpam-4637	256	29	are	be	AUX
ejpam-4637	256	30	left	leave	VERB
ejpam-4637	256	31	to	to	PART
ejpam-4637	256	32	show	show	VERB
ejpam-4637	256	33	that	that	SCONJ
ejpam-4637	256	34	a(α	a(α	ADJ
ejpam-4637	256	35	′	′	NUM
ejpam-4637	256	36	,	,	PUNCT
ejpam-4637	256	37	β	β	X
ejpam-4637	256	38	,	,	PUNCT
ejpam-4637	256	39	γ	γ	NOUN
ejpam-4637	256	40	)	)	PUNCT
ejpam-4637	256	41	⊆	⊆	NUM
ejpam-4637	256	42	a(α	a(α	NOUN
ejpam-4637	256	43	,	,	PUNCT
ejpam-4637	256	44	β	β	X
ejpam-4637	256	45	′	′	NUM
ejpam-4637	256	46	,	,	PUNCT
ejpam-4637	256	47	γ	γ	X
ejpam-4637	256	48	′	′	NUM
ejpam-4637	256	49	)	)	PUNCT
ejpam-4637	256	50	.	.	PUNCT
ejpam-4637	257	1	let	let	VERB
ejpam-4637	257	2	y	y	PROPN
ejpam-4637	257	3	∈	∈	PROPN
ejpam-4637	257	4	tα	tα	VERB
ejpam-4637	257	5	′	′	NUM
ejpam-4637	257	6	a	a	PRON
ejpam-4637	257	7	.	.	PUNCT
ejpam-4637	258	1	then	then	ADV
ejpam-4637	258	2	ta(y	ta(y	PUNCT
ejpam-4637	258	3	)	)	PUNCT
ejpam-4637	258	4	≥	≥	NUM
ejpam-4637	259	1	α	α	NOUN
ejpam-4637	259	2	′	′	NUM
ejpam-4637	259	3	≥	≥	NOUN
ejpam-4637	259	4	α	α	NOUN
ejpam-4637	259	5	.	.	PUNCT
ejpam-4637	260	1	thus	thus	ADV
ejpam-4637	260	2	,	,	PUNCT
ejpam-4637	260	3	y	y	PROPN
ejpam-4637	260	4	∈	∈	PROPN
ejpam-4637	260	5	tα	tα	VERB
ejpam-4637	260	6	a	a	PRON
ejpam-4637	260	7	and	and	CCONJ
ejpam-4637	260	8	so	so	ADV
ejpam-4637	260	9	tα	tα	INTJ
ejpam-4637	260	10	′	′	NUM
ejpam-4637	261	1	a	a	DET
ejpam-4637	261	2	⊆	⊆	NUM
ejpam-4637	261	3	tα	tα	ADP
ejpam-4637	261	4	a	a	PRON
ejpam-4637	261	5	.	.	PUNCT
ejpam-4637	262	1	next	next	ADV
ejpam-4637	262	2	,	,	PUNCT
ejpam-4637	262	3	let	let	VERB
ejpam-4637	262	4	z	z	NOUN
ejpam-4637	262	5	∈	∈	PROPN
ejpam-4637	262	6	iβa	iβa	VERB
ejpam-4637	262	7	.	.	PUNCT
ejpam-4637	263	1	then	then	ADV
ejpam-4637	263	2	ia(z	ia(z	NOUN
ejpam-4637	263	3	)	)	PUNCT
ejpam-4637	263	4	≤	≤	NOUN
ejpam-4637	263	5	β	β	X
ejpam-4637	263	6	≤	≤	NOUN
ejpam-4637	263	7	β	β	DET
ejpam-4637	263	8	′	′	NOUN
ejpam-4637	263	9	.	.	PUNCT
ejpam-4637	264	1	thus	thus	ADV
ejpam-4637	264	2	,	,	PUNCT
ejpam-4637	264	3	z	z	NOUN
ejpam-4637	264	4	∈	∈	PROPN
ejpam-4637	264	5	iβ	iβ	ADP
ejpam-4637	264	6	′	′	NUM
ejpam-4637	264	7	a	a	PRON
ejpam-4637	264	8	and	and	CCONJ
ejpam-4637	264	9	so	so	ADV
ejpam-4637	264	10	iβa	iβa	VERB
ejpam-4637	264	11	⊆	⊆	NUM
ejpam-4637	264	12	iβ	iβ	ADP
ejpam-4637	264	13	′	′	NUM
ejpam-4637	264	14	a	a	PRON
ejpam-4637	264	15	.	.	PUNCT
ejpam-4637	265	1	similarly	similarly	ADV
ejpam-4637	265	2	,	,	PUNCT
ejpam-4637	265	3	f	f	PROPN
ejpam-4637	265	4	γ	γ	PROPN
ejpam-4637	265	5	a	a	DET
ejpam-4637	265	6	⊆	⊆	NUM
ejpam-4637	265	7	f	f	SYM
ejpam-4637	265	8	γ	γ	X
ejpam-4637	265	9	′	′	NUM
ejpam-4637	265	10	a	a	PRON
ejpam-4637	265	11	.	.	PUNCT
ejpam-4637	266	1	hence	hence	ADV
ejpam-4637	266	2	,	,	PUNCT
ejpam-4637	266	3	a(α	a(α	ADJ
ejpam-4637	266	4	′	′	NUM
ejpam-4637	266	5	,	,	PUNCT
ejpam-4637	266	6	β	β	X
ejpam-4637	266	7	,	,	PUNCT
ejpam-4637	266	8	γ	γ	NOUN
ejpam-4637	266	9	)	)	PUNCT
ejpam-4637	266	10	=	=	PUNCT
ejpam-4637	266	11	tα	tα	PROPN
ejpam-4637	266	12	′	′	NUM
ejpam-4637	266	13	a	a	DET
ejpam-4637	266	14	∩	∩	NOUN
ejpam-4637	266	15	iβa	iβa	NOUN
ejpam-4637	266	16	∩	∩	NOUN
ejpam-4637	266	17	f	f	PROPN
ejpam-4637	266	18	γ	γ	PROPN
ejpam-4637	266	19	a	a	DET
ejpam-4637	266	20	⊆	⊆	NUM
ejpam-4637	266	21	tα	tα	ADP
ejpam-4637	266	22	a	a	DET
ejpam-4637	266	23	∩	∩	NOUN
ejpam-4637	266	24	iβ	iβ	ADP
ejpam-4637	266	25	′	′	NUM
ejpam-4637	266	26	a	a	DET
ejpam-4637	266	27	∩	∩	NOUN
ejpam-4637	266	28	f	f	PROPN
ejpam-4637	266	29	γ	γ	X
ejpam-4637	266	30	′	′	NUM
ejpam-4637	267	1	a	a	PRON
ejpam-4637	268	1	=	=	PUNCT
ejpam-4637	269	1	a(α	a(α	NOUN
ejpam-4637	269	2	,	,	PUNCT
ejpam-4637	269	3	β	β	X
ejpam-4637	269	4	′	′	NUM
ejpam-4637	269	5	,	,	PUNCT
ejpam-4637	269	6	γ	γ	X
ejpam-4637	269	7	′	′	NUM
ejpam-4637	269	8	)	)	PUNCT
ejpam-4637	269	9	.	.	PUNCT
ejpam-4637	270	1	consequently	consequently	ADV
ejpam-4637	270	2	,	,	PUNCT
ejpam-4637	270	3	a(α	a(α	NOUN
ejpam-4637	270	4	′	′	NUM
ejpam-4637	270	5	,	,	PUNCT
ejpam-4637	270	6	β	β	X
ejpam-4637	270	7	,	,	PUNCT
ejpam-4637	270	8	γ	γ	X
ejpam-4637	270	9	)	)	PUNCT
ejpam-4637	270	10	is	be	AUX
ejpam-4637	270	11	a	a	DET
ejpam-4637	270	12	hyper	hyper	ADJ
ejpam-4637	270	13	up	up	ADP
ejpam-4637	270	14	-subalgebra	-subalgebra	NOUN
ejpam-4637	270	15	of	of	ADP
ejpam-4637	270	16	a(α	a(α	NOUN
ejpam-4637	270	17	,	,	PUNCT
ejpam-4637	270	18	β	β	X
ejpam-4637	270	19	′	′	NUM
ejpam-4637	270	20	,	,	PUNCT
ejpam-4637	270	21	γ	γ	X
ejpam-4637	270	22	′	′	NUM
ejpam-4637	270	23	)	)	PUNCT
ejpam-4637	270	24	.	.	PUNCT
ejpam-4637	271	1	for	for	ADP
ejpam-4637	271	2	fixed	fix	VERB
ejpam-4637	271	3	numbers	number	NOUN
ejpam-4637	271	4	α1	α1	PROPN
ejpam-4637	271	5	,	,	PUNCT
ejpam-4637	271	6	α2	α2	ADJ
ejpam-4637	271	7	,	,	PUNCT
ejpam-4637	271	8	β1	β1	PROPN
ejpam-4637	271	9	,	,	PUNCT
ejpam-4637	271	10	β2	β2	NOUN
ejpam-4637	271	11	,	,	PUNCT
ejpam-4637	271	12	γ1	γ1	NOUN
ejpam-4637	271	13	,	,	PUNCT
ejpam-4637	271	14	γ2	γ2	PROPN
ejpam-4637	271	15	∈	∈	PROPN
ejpam-4637	272	1	[	[	X
ejpam-4637	272	2	0	0	NUM
ejpam-4637	272	3	,	,	PUNCT
ejpam-4637	272	4	1	1	NUM
ejpam-4637	272	5	]	]	PUNCT
ejpam-4637	272	6	such	such	ADJ
ejpam-4637	272	7	that	that	SCONJ
ejpam-4637	272	8	α1	α1	PROPN
ejpam-4637	272	9	≥	≥	NUM
ejpam-4637	272	10	α2	α2	PROPN
ejpam-4637	272	11	,	,	PUNCT
ejpam-4637	272	12	β1	β1	PROPN
ejpam-4637	272	13	≥	≥	NUM
ejpam-4637	272	14	β2,γ1	β2,γ1	PROPN
ejpam-4637	272	15	≥	≥	NOUN
ejpam-4637	272	16	γ2	γ2	NOUN
ejpam-4637	272	17	,	,	PUNCT
ejpam-4637	272	18	and	and	CCONJ
ejpam-4637	272	19	a	a	DET
ejpam-4637	272	20	nonempty	nonempty	NOUN
ejpam-4637	272	21	subset	subset	VERB
ejpam-4637	272	22	g	g	NOUN
ejpam-4637	272	23	of	of	ADP
ejpam-4637	272	24	x	x	SYM
ejpam-4637	272	25	,	,	PUNCT
ejpam-4637	272	26	we	we	PRON
ejpam-4637	272	27	define	define	VERB
ejpam-4637	272	28	a	a	DET
ejpam-4637	272	29	svn	svn	NOUN
ejpam-4637	272	30	set	set	NOUN
ejpam-4637	272	31	ag	ag	PROPN
ejpam-4637	272	32	[	[	PUNCT
ejpam-4637	272	33	α1	α1	PROPN
ejpam-4637	272	34	,	,	PUNCT
ejpam-4637	272	35	β2	β2	NOUN
ejpam-4637	272	36	,	,	PUNCT
ejpam-4637	272	37	γ2	γ2	PROPN
ejpam-4637	272	38	α2	α2	PROPN
ejpam-4637	272	39	,	,	PUNCT
ejpam-4637	272	40	β1	β1	PROPN
ejpam-4637	272	41	,	,	PUNCT
ejpam-4637	272	42	γ1	γ1	NOUN
ejpam-4637	272	43	]	]	PUNCT
ejpam-4637	272	44	=	=	PUNCT
ejpam-4637	272	45	(	(	PUNCT
ejpam-4637	272	46	tag	tag	NOUN
ejpam-4637	272	47	[	[	PUNCT
ejpam-4637	272	48	α1	α1	PROPN
ejpam-4637	272	49	α2	α2	PROPN
ejpam-4637	272	50	]	]	PUNCT
ejpam-4637	272	51	,	,	PUNCT
ejpam-4637	272	52	iag	iag	PROPN
ejpam-4637	272	53	[	[	PUNCT
ejpam-4637	272	54	β2	β2	NOUN
ejpam-4637	272	55	β1	β1	PROPN
ejpam-4637	272	56	]	]	PUNCT
ejpam-4637	272	57	,	,	PUNCT
ejpam-4637	272	58	fag	fag	X
ejpam-4637	272	59	[	[	PUNCT
ejpam-4637	272	60	γ2	γ2	PROPN
ejpam-4637	272	61	γ1	γ1	PROPN
ejpam-4637	272	62	]	]	PUNCT
ejpam-4637	272	63	)	)	PUNCT
ejpam-4637	272	64	where	where	SCONJ
ejpam-4637	272	65	tag	tag	NOUN
ejpam-4637	272	66	[	[	PUNCT
ejpam-4637	272	67	α1	α1	PROPN
ejpam-4637	272	68	α2	α2	PROPN
ejpam-4637	272	69	]	]	PUNCT
ejpam-4637	272	70	(	(	PUNCT
ejpam-4637	272	71	x	x	X
ejpam-4637	272	72	)	)	PUNCT
ejpam-4637	272	73	=	=	SYM
ejpam-4637	272	74	{	{	PUNCT
ejpam-4637	272	75	α1	α1	PROPN
ejpam-4637	272	76	if	if	SCONJ
ejpam-4637	272	77	x	x	PROPN
ejpam-4637	272	78	∈	∈	PROPN
ejpam-4637	272	79	g	g	NOUN
ejpam-4637	272	80	α2	α2	PROPN
ejpam-4637	272	81	otherwise	otherwise	ADV
ejpam-4637	272	82	,	,	PUNCT
ejpam-4637	272	83	a.	a.	PROPN
ejpam-4637	272	84	cano	cano	PROPN
ejpam-4637	272	85	,	,	PUNCT
ejpam-4637	272	86	g.	g.	PROPN
ejpam-4637	272	87	petalcorin	petalcorin	PROPN
ejpam-4637	272	88	/	/	SYM
ejpam-4637	272	89	eur	eur	PROPN
ejpam-4637	272	90	.	.	PUNCT
ejpam-4637	273	1	j.	j.	PROPN
ejpam-4637	273	2	pure	pure	PROPN
ejpam-4637	273	3	appl	appl	PROPN
ejpam-4637	273	4	.	.	PROPN
ejpam-4637	273	5	math	math	PROPN
ejpam-4637	273	6	,	,	PUNCT
ejpam-4637	273	7	16	16	NUM
ejpam-4637	273	8	(	(	PUNCT
ejpam-4637	273	9	1	1	NUM
ejpam-4637	273	10	)	)	PUNCT
ejpam-4637	273	11	(	(	PUNCT
ejpam-4637	273	12	2023	2023	NUM
ejpam-4637	273	13	)	)	PUNCT
ejpam-4637	273	14	,	,	PUNCT
ejpam-4637	273	15	548	548	NUM
ejpam-4637	273	16	-	-	SYM
ejpam-4637	273	17	576	576	NUM
ejpam-4637	273	18	559	559	NUM
ejpam-4637	273	19	iag	iag	PROPN
ejpam-4637	273	20	[	[	PUNCT
ejpam-4637	273	21	β2	β2	NOUN
ejpam-4637	273	22	β1	β1	PROPN
ejpam-4637	273	23	]	]	PUNCT
ejpam-4637	273	24	(	(	PUNCT
ejpam-4637	273	25	x	x	X
ejpam-4637	273	26	)	)	PUNCT
ejpam-4637	273	27	=	=	PRON
ejpam-4637	273	28	{	{	PUNCT
ejpam-4637	273	29	β2	β2	VERB
ejpam-4637	273	30	if	if	SCONJ
ejpam-4637	273	31	x	x	PROPN
ejpam-4637	273	32	∈	∈	PROPN
ejpam-4637	273	33	g	g	PROPN
ejpam-4637	273	34	β1	β1	PROPN
ejpam-4637	273	35	otherwise	otherwise	ADV
ejpam-4637	273	36	,	,	PUNCT
ejpam-4637	273	37	and	and	CCONJ
ejpam-4637	273	38	fag	fag	NOUN
ejpam-4637	273	39	[	[	PUNCT
ejpam-4637	273	40	γ2	γ2	PROPN
ejpam-4637	273	41	γ1	γ1	PROPN
ejpam-4637	273	42	]	]	PUNCT
ejpam-4637	273	43	(	(	PUNCT
ejpam-4637	273	44	x	x	X
ejpam-4637	273	45	)	)	PUNCT
ejpam-4637	273	46	=	=	SYM
ejpam-4637	273	47	{	{	PUNCT
ejpam-4637	273	48	γ2	γ2	VERB
ejpam-4637	273	49	if	if	SCONJ
ejpam-4637	273	50	x	x	PROPN
ejpam-4637	273	51	∈	∈	PROPN
ejpam-4637	273	52	g	g	PROPN
ejpam-4637	273	53	γ1	γ1	PROPN
ejpam-4637	273	54	otherwise	otherwise	ADV
ejpam-4637	273	55	.	.	PUNCT
ejpam-4637	274	1	theorem	theorem	NOUN
ejpam-4637	274	2	2	2	NUM
ejpam-4637	274	3	.	.	PUNCT
ejpam-4637	275	1	let	let	VERB
ejpam-4637	275	2	g	g	PRON
ejpam-4637	275	3	be	be	AUX
ejpam-4637	275	4	a	a	DET
ejpam-4637	275	5	nonempty	nonempty	ADJ
ejpam-4637	275	6	subset	subset	NOUN
ejpam-4637	275	7	of	of	ADP
ejpam-4637	275	8	x	x	X
ejpam-4637	275	9	and	and	CCONJ
ejpam-4637	275	10	ag	ag	PROPN
ejpam-4637	275	11	[	[	PUNCT
ejpam-4637	275	12	α1	α1	PROPN
ejpam-4637	275	13	,	,	PUNCT
ejpam-4637	275	14	β2	β2	NOUN
ejpam-4637	275	15	,	,	PUNCT
ejpam-4637	275	16	γ2	γ2	PROPN
ejpam-4637	275	17	α2	α2	PROPN
ejpam-4637	275	18	,	,	PUNCT
ejpam-4637	275	19	β1	β1	PROPN
ejpam-4637	275	20	,	,	PUNCT
ejpam-4637	275	21	γ1	γ1	PROPN
ejpam-4637	275	22	]	]	PUNCT
ejpam-4637	275	23	be	be	AUX
ejpam-4637	275	24	a	a	DET
ejpam-4637	275	25	svn	svn	NOUN
ejpam-4637	275	26	set	set	NOUN
ejpam-4637	275	27	in	in	ADP
ejpam-4637	275	28	x.	x.	PROPN
ejpam-4637	276	1	then	then	PROPN
ejpam-4637	276	2	ag	ag	PROPN
ejpam-4637	276	3	[	[	PUNCT
ejpam-4637	276	4	α1	α1	PROPN
ejpam-4637	276	5	,	,	PUNCT
ejpam-4637	276	6	β2	β2	NOUN
ejpam-4637	276	7	,	,	PUNCT
ejpam-4637	276	8	γ2	γ2	PROPN
ejpam-4637	276	9	α2	α2	PROPN
ejpam-4637	276	10	,	,	PUNCT
ejpam-4637	276	11	β1	β1	PROPN
ejpam-4637	276	12	,	,	PUNCT
ejpam-4637	276	13	γ1	γ1	PROPN
ejpam-4637	276	14	]	]	PUNCT
ejpam-4637	276	15	satisfies	satisfy	VERB
ejpam-4637	276	16	proposition	proposition	NOUN
ejpam-4637	276	17	3(i	3(i	NUM
ejpam-4637	276	18	)	)	PUNCT
ejpam-4637	276	19	if	if	SCONJ
ejpam-4637	276	20	and	and	CCONJ
ejpam-4637	276	21	only	only	ADV
ejpam-4637	276	22	if	if	SCONJ
ejpam-4637	276	23	0	0	NUM
ejpam-4637	276	24	∈	∈	PROPN
ejpam-4637	276	25	g.	g.	NOUN
ejpam-4637	276	26	proof	proof	NOUN
ejpam-4637	276	27	.	.	PUNCT
ejpam-4637	277	1	let	let	AUX
ejpam-4637	277	2	g	g	PRON
ejpam-4637	277	3	be	be	AUX
ejpam-4637	277	4	a	a	DET
ejpam-4637	277	5	nonempty	nonempty	ADJ
ejpam-4637	277	6	subset	subset	NOUN
ejpam-4637	277	7	of	of	ADP
ejpam-4637	277	8	x	x	X
ejpam-4637	277	9	and	and	CCONJ
ejpam-4637	277	10	ag	ag	PROPN
ejpam-4637	277	11	[	[	PUNCT
ejpam-4637	277	12	α1	α1	PROPN
ejpam-4637	277	13	,	,	PUNCT
ejpam-4637	277	14	β2	β2	NOUN
ejpam-4637	277	15	,	,	PUNCT
ejpam-4637	277	16	γ2	γ2	PROPN
ejpam-4637	277	17	α2	α2	PROPN
ejpam-4637	277	18	,	,	PUNCT
ejpam-4637	277	19	β1	β1	PROPN
ejpam-4637	277	20	,	,	PUNCT
ejpam-4637	277	21	γ1	γ1	PROPN
ejpam-4637	277	22	]	]	PUNCT
ejpam-4637	277	23	be	be	AUX
ejpam-4637	277	24	a	a	DET
ejpam-4637	277	25	svn	svn	NOUN
ejpam-4637	277	26	set	set	NOUN
ejpam-4637	277	27	in	in	ADP
ejpam-4637	277	28	x.	x.	PROPN
ejpam-4637	277	29	(	(	PUNCT
ejpam-4637	277	30	⇒	⇒	PROPN
ejpam-4637	277	31	)	)	PUNCT
ejpam-4637	277	32	assume	assume	VERB
ejpam-4637	277	33	that	that	SCONJ
ejpam-4637	277	34	ag	ag	PROPN
ejpam-4637	277	35	[	[	PUNCT
ejpam-4637	277	36	α1	α1	PROPN
ejpam-4637	277	37	,	,	PUNCT
ejpam-4637	277	38	β2	β2	NOUN
ejpam-4637	277	39	,	,	PUNCT
ejpam-4637	277	40	γ2	γ2	PROPN
ejpam-4637	277	41	α2	α2	PROPN
ejpam-4637	277	42	,	,	PUNCT
ejpam-4637	277	43	β1	β1	PROPN
ejpam-4637	277	44	,	,	PUNCT
ejpam-4637	277	45	γ1	γ1	PROPN
ejpam-4637	277	46	]	]	PUNCT
ejpam-4637	277	47	satisfies	satisfy	VERB
ejpam-4637	277	48	proposition	proposition	NOUN
ejpam-4637	277	49	3(i	3(i	NUM
ejpam-4637	277	50	)	)	PUNCT
ejpam-4637	277	51	.	.	PUNCT
ejpam-4637	278	1	since	since	SCONJ
ejpam-4637	278	2	g	g	PROPN
ejpam-4637	278	3	̸=	̸=	PROPN
ejpam-4637	278	4	∅	∅	NOUN
ejpam-4637	278	5	,	,	PUNCT
ejpam-4637	278	6	there	there	PRON
ejpam-4637	278	7	exists	exist	VERB
ejpam-4637	278	8	g	g	PROPN
ejpam-4637	278	9	∈	∈	PROPN
ejpam-4637	278	10	g.	g.	PROPN
ejpam-4637	278	11	thus	thus	ADV
ejpam-4637	278	12	,	,	PUNCT
ejpam-4637	278	13	tag	tag	NOUN
ejpam-4637	278	14	[	[	PUNCT
ejpam-4637	278	15	α1	α1	PROPN
ejpam-4637	278	16	α2	α2	PROPN
ejpam-4637	278	17	]	]	PUNCT
ejpam-4637	278	18	(	(	PUNCT
ejpam-4637	278	19	g	g	NOUN
ejpam-4637	278	20	)	)	PUNCT
ejpam-4637	278	21	=	=	SYM
ejpam-4637	278	22	α1	α1	PROPN
ejpam-4637	278	23	.	.	PUNCT
ejpam-4637	279	1	now	now	ADV
ejpam-4637	279	2	,	,	PUNCT
ejpam-4637	279	3	tag	tag	NOUN
ejpam-4637	279	4	[	[	PUNCT
ejpam-4637	279	5	α1	α1	PROPN
ejpam-4637	279	6	α2	α2	PROPN
ejpam-4637	279	7	]	]	PUNCT
ejpam-4637	279	8	(	(	PUNCT
ejpam-4637	279	9	0	0	NUM
ejpam-4637	279	10	)	)	PUNCT
ejpam-4637	279	11	≥	≥	NOUN
ejpam-4637	279	12	tag	tag	NOUN
ejpam-4637	279	13	[	[	PUNCT
ejpam-4637	279	14	α1	α1	PROPN
ejpam-4637	279	15	α2	α2	PROPN
ejpam-4637	279	16	]	]	PUNCT
ejpam-4637	279	17	(	(	PUNCT
ejpam-4637	279	18	g	g	NOUN
ejpam-4637	279	19	)	)	PUNCT
ejpam-4637	279	20	=	=	SYM
ejpam-4637	279	21	α1	α1	PROPN
ejpam-4637	279	22	≥	≥	NUM
ejpam-4637	279	23	tag	tag	NOUN
ejpam-4637	279	24	[	[	PUNCT
ejpam-4637	279	25	α1	α1	PROPN
ejpam-4637	279	26	α2	α2	PROPN
ejpam-4637	279	27	]	]	PUNCT
ejpam-4637	279	28	(	(	PUNCT
ejpam-4637	279	29	0	0	NUM
ejpam-4637	279	30	)	)	PUNCT
ejpam-4637	279	31	.	.	PUNCT
ejpam-4637	280	1	that	that	PRON
ejpam-4637	280	2	is	be	AUX
ejpam-4637	280	3	,	,	PUNCT
ejpam-4637	280	4	tag	tag	NOUN
ejpam-4637	280	5	[	[	PUNCT
ejpam-4637	280	6	α1	α1	PROPN
ejpam-4637	280	7	α2	α2	PROPN
ejpam-4637	280	8	]	]	PUNCT
ejpam-4637	280	9	(	(	PUNCT
ejpam-4637	280	10	0	0	NUM
ejpam-4637	280	11	)	)	PUNCT
ejpam-4637	280	12	=	=	SYM
ejpam-4637	280	13	α1	α1	PROPN
ejpam-4637	280	14	.	.	PUNCT
ejpam-4637	281	1	hence	hence	ADV
ejpam-4637	281	2	,	,	PUNCT
ejpam-4637	281	3	0	0	NUM
ejpam-4637	281	4	∈	∈	PROPN
ejpam-4637	281	5	g.	g.	NOUN
ejpam-4637	281	6	(	(	PUNCT
ejpam-4637	281	7	⇐	⇐	PROPN
ejpam-4637	281	8	)	)	PUNCT
ejpam-4637	281	9	assume	assume	VERB
ejpam-4637	281	10	that	that	SCONJ
ejpam-4637	281	11	0	0	NUM
ejpam-4637	281	12	∈	∈	PROPN
ejpam-4637	281	13	g.	g.	NOUN
ejpam-4637	281	14	then	then	ADV
ejpam-4637	281	15	tag	tag	VERB
ejpam-4637	281	16	[	[	PUNCT
ejpam-4637	281	17	α1	α1	PROPN
ejpam-4637	281	18	α2	α2	PROPN
ejpam-4637	281	19	]	]	PUNCT
ejpam-4637	281	20	(	(	PUNCT
ejpam-4637	281	21	0	0	NUM
ejpam-4637	281	22	)	)	PUNCT
ejpam-4637	281	23	=	=	SYM
ejpam-4637	281	24	α1	α1	PROPN
ejpam-4637	281	25	,	,	PUNCT
ejpam-4637	281	26	iag	iag	PROPN
ejpam-4637	281	27	[	[	PUNCT
ejpam-4637	281	28	β2	β2	NOUN
ejpam-4637	281	29	β1	β1	PROPN
ejpam-4637	281	30	]	]	PUNCT
ejpam-4637	281	31	(	(	PUNCT
ejpam-4637	281	32	0	0	NUM
ejpam-4637	281	33	)	)	PUNCT
ejpam-4637	282	1	=	=	VERB
ejpam-4637	282	2	β2	β2	NOUN
ejpam-4637	282	3	and	and	CCONJ
ejpam-4637	282	4	fag	fag	NOUN
ejpam-4637	282	5	[	[	PUNCT
ejpam-4637	282	6	γ2	γ2	PROPN
ejpam-4637	282	7	γ1	γ1	PROPN
ejpam-4637	282	8	]	]	PUNCT
ejpam-4637	282	9	(	(	PUNCT
ejpam-4637	282	10	0	0	NUM
ejpam-4637	282	11	)	)	PUNCT
ejpam-4637	282	12	=	=	SYM
ejpam-4637	282	13	γ2	γ2	NOUN
ejpam-4637	282	14	.	.	PUNCT
ejpam-4637	283	1	for	for	ADP
ejpam-4637	283	2	all	all	DET
ejpam-4637	283	3	x	x	SYM
ejpam-4637	283	4	∈	∈	PROPN
ejpam-4637	283	5	x	x	NOUN
ejpam-4637	283	6	,	,	PUNCT
ejpam-4637	283	7	tag	tag	NOUN
ejpam-4637	283	8	[	[	PUNCT
ejpam-4637	283	9	α1	α1	PROPN
ejpam-4637	283	10	α2	α2	PROPN
ejpam-4637	283	11	]	]	PUNCT
ejpam-4637	283	12	(	(	PUNCT
ejpam-4637	283	13	0	0	NUM
ejpam-4637	283	14	)	)	PUNCT
ejpam-4637	283	15	=	=	SYM
ejpam-4637	283	16	α1	α1	PROPN
ejpam-4637	283	17	≥	≥	NUM
ejpam-4637	283	18	tag	tag	NOUN
ejpam-4637	283	19	[	[	PUNCT
ejpam-4637	283	20	α1	α1	PROPN
ejpam-4637	283	21	α2	α2	PROPN
ejpam-4637	283	22	]	]	PUNCT
ejpam-4637	283	23	(	(	PUNCT
ejpam-4637	283	24	x	x	X
ejpam-4637	283	25	)	)	PUNCT
ejpam-4637	283	26	,	,	PUNCT
ejpam-4637	283	27	iag	iag	PROPN
ejpam-4637	283	28	[	[	PUNCT
ejpam-4637	283	29	β2	β2	NOUN
ejpam-4637	283	30	β1	β1	PROPN
ejpam-4637	283	31	]	]	PUNCT
ejpam-4637	283	32	(	(	PUNCT
ejpam-4637	283	33	0	0	NUM
ejpam-4637	283	34	)	)	PUNCT
ejpam-4637	283	35	=	=	VERB
ejpam-4637	283	36	β2	β2	VERB
ejpam-4637	283	37	≤	≤	PUNCT
ejpam-4637	283	38	iag	iag	PROPN
ejpam-4637	283	39	[	[	PUNCT
ejpam-4637	283	40	β2	β2	NOUN
ejpam-4637	283	41	β1	β1	PROPN
ejpam-4637	283	42	]	]	PUNCT
ejpam-4637	283	43	(	(	PUNCT
ejpam-4637	283	44	x	x	X
ejpam-4637	283	45	)	)	PUNCT
ejpam-4637	283	46	and	and	CCONJ
ejpam-4637	283	47	fag	fag	NOUN
ejpam-4637	283	48	[	[	PUNCT
ejpam-4637	283	49	γ2	γ2	PROPN
ejpam-4637	283	50	γ1	γ1	PROPN
ejpam-4637	283	51	]	]	PUNCT
ejpam-4637	283	52	(	(	PUNCT
ejpam-4637	283	53	0	0	NUM
ejpam-4637	283	54	)	)	PUNCT
ejpam-4637	283	55	=	=	SYM
ejpam-4637	284	1	γ2	γ2	ADJ
ejpam-4637	284	2	≤	≤	NUM
ejpam-4637	284	3	fag	fag	NOUN
ejpam-4637	284	4	[	[	PUNCT
ejpam-4637	284	5	γ2	γ2	PROPN
ejpam-4637	284	6	γ1	γ1	PROPN
ejpam-4637	284	7	]	]	PUNCT
ejpam-4637	284	8	(	(	PUNCT
ejpam-4637	284	9	x	x	NOUN
ejpam-4637	284	10	)	)	PUNCT
ejpam-4637	284	11	.	.	PUNCT
ejpam-4637	285	1	hence	hence	ADV
ejpam-4637	285	2	,	,	PUNCT
ejpam-4637	285	3	ag	ag	PROPN
ejpam-4637	285	4	[	[	PUNCT
ejpam-4637	285	5	α1	α1	PROPN
ejpam-4637	285	6	,	,	PUNCT
ejpam-4637	285	7	β2	β2	NOUN
ejpam-4637	285	8	,	,	PUNCT
ejpam-4637	285	9	γ2	γ2	PROPN
ejpam-4637	285	10	α2	α2	PROPN
ejpam-4637	285	11	,	,	PUNCT
ejpam-4637	285	12	β1	β1	PROPN
ejpam-4637	285	13	,	,	PUNCT
ejpam-4637	285	14	γ1	γ1	PROPN
ejpam-4637	285	15	]	]	PUNCT
ejpam-4637	285	16	satisfies	satisfy	VERB
ejpam-4637	285	17	proposition	proposition	NOUN
ejpam-4637	285	18	3(i	3(i	NUM
ejpam-4637	285	19	)	)	PUNCT
ejpam-4637	285	20	.	.	PUNCT
ejpam-4637	286	1	a.	a.	PROPN
ejpam-4637	286	2	cano	cano	PROPN
ejpam-4637	286	3	,	,	PUNCT
ejpam-4637	286	4	g.	g.	PROPN
ejpam-4637	286	5	petalcorin	petalcorin	PROPN
ejpam-4637	286	6	/	/	SYM
ejpam-4637	286	7	eur	eur	PROPN
ejpam-4637	286	8	.	.	PUNCT
ejpam-4637	287	1	j.	j.	PROPN
ejpam-4637	287	2	pure	pure	PROPN
ejpam-4637	287	3	appl	appl	PROPN
ejpam-4637	287	4	.	.	PROPN
ejpam-4637	287	5	math	math	PROPN
ejpam-4637	287	6	,	,	PUNCT
ejpam-4637	287	7	16	16	NUM
ejpam-4637	287	8	(	(	PUNCT
ejpam-4637	287	9	1	1	NUM
ejpam-4637	287	10	)	)	PUNCT
ejpam-4637	287	11	(	(	PUNCT
ejpam-4637	287	12	2023	2023	NUM
ejpam-4637	287	13	)	)	PUNCT
ejpam-4637	287	14	,	,	PUNCT
ejpam-4637	287	15	548	548	NUM
ejpam-4637	287	16	-	-	SYM
ejpam-4637	287	17	576	576	NUM
ejpam-4637	287	18	560	560	NUM
ejpam-4637	287	19	theorem	theorem	NOUN
ejpam-4637	287	20	3	3	X
ejpam-4637	287	21	.	.	PUNCT
ejpam-4637	288	1	let	let	VERB
ejpam-4637	288	2	ag	ag	PROPN
ejpam-4637	288	3	[	[	PUNCT
ejpam-4637	288	4	α1	α1	PROPN
ejpam-4637	288	5	,	,	PUNCT
ejpam-4637	288	6	β2	β2	NOUN
ejpam-4637	288	7	,	,	PUNCT
ejpam-4637	288	8	γ2	γ2	PROPN
ejpam-4637	288	9	α2	α2	PROPN
ejpam-4637	288	10	,	,	PUNCT
ejpam-4637	288	11	β1	β1	PROPN
ejpam-4637	288	12	,	,	PUNCT
ejpam-4637	288	13	γ1	γ1	PROPN
ejpam-4637	288	14	]	]	PUNCT
ejpam-4637	288	15	be	be	AUX
ejpam-4637	288	16	a	a	DET
ejpam-4637	288	17	svn	svn	NOUN
ejpam-4637	288	18	set	set	NOUN
ejpam-4637	288	19	in	in	ADP
ejpam-4637	288	20	x.	x.	PROPN
ejpam-4637	289	1	then	then	PROPN
ejpam-4637	289	2	ag	ag	PROPN
ejpam-4637	289	3	[	[	PUNCT
ejpam-4637	289	4	α1	α1	PROPN
ejpam-4637	289	5	,	,	PUNCT
ejpam-4637	289	6	β2	β2	NOUN
ejpam-4637	289	7	,	,	PUNCT
ejpam-4637	289	8	γ2	γ2	PROPN
ejpam-4637	289	9	α2	α2	PROPN
ejpam-4637	289	10	,	,	PUNCT
ejpam-4637	289	11	β1	β1	PROPN
ejpam-4637	289	12	,	,	PUNCT
ejpam-4637	289	13	γ1	γ1	PROPN
ejpam-4637	289	14	]	]	PUNCT
ejpam-4637	289	15	is	be	AUX
ejpam-4637	289	16	a	a	DET
ejpam-4637	289	17	svn	svn	NOUN
ejpam-4637	289	18	hyper	hyper	NOUN
ejpam-4637	289	19	up	up	ADP
ejpam-4637	289	20	-	-	PUNCT
ejpam-4637	289	21	subalgebra	subalgebra	NOUN
ejpam-4637	289	22	of	of	ADP
ejpam-4637	289	23	x	x	PRON
ejpam-4637	289	24	if	if	SCONJ
ejpam-4637	289	25	and	and	CCONJ
ejpam-4637	289	26	only	only	ADV
ejpam-4637	289	27	if	if	SCONJ
ejpam-4637	289	28	a	a	DET
ejpam-4637	289	29	nonempty	nonempty	NOUN
ejpam-4637	289	30	subset	subset	NOUN
ejpam-4637	289	31	of	of	ADP
ejpam-4637	289	32	g	g	PROPN
ejpam-4637	289	33	is	be	AUX
ejpam-4637	289	34	a	a	DET
ejpam-4637	289	35	hyper	hyper	ADJ
ejpam-4637	289	36	up	up	ADP
ejpam-4637	289	37	-	-	PUNCT
ejpam-4637	289	38	subalgebra	subalgebra	NOUN
ejpam-4637	289	39	of	of	ADP
ejpam-4637	289	40	x.	x.	NOUN
ejpam-4637	289	41	proof	proof	NOUN
ejpam-4637	289	42	.	.	PUNCT
ejpam-4637	290	1	let	let	VERB
ejpam-4637	290	2	ag	ag	PROPN
ejpam-4637	290	3	[	[	PUNCT
ejpam-4637	290	4	α1	α1	PROPN
ejpam-4637	290	5	,	,	PUNCT
ejpam-4637	290	6	β2	β2	NOUN
ejpam-4637	290	7	,	,	PUNCT
ejpam-4637	290	8	γ2	γ2	PROPN
ejpam-4637	290	9	α2	α2	PROPN
ejpam-4637	290	10	,	,	PUNCT
ejpam-4637	290	11	β1	β1	PROPN
ejpam-4637	290	12	,	,	PUNCT
ejpam-4637	290	13	γ1	γ1	PROPN
ejpam-4637	290	14	]	]	PUNCT
ejpam-4637	290	15	be	be	AUX
ejpam-4637	290	16	a	a	DET
ejpam-4637	290	17	svn	svn	NOUN
ejpam-4637	290	18	set	set	NOUN
ejpam-4637	290	19	in	in	ADP
ejpam-4637	290	20	x.	x.	PROPN
ejpam-4637	290	21	(	(	PUNCT
ejpam-4637	290	22	⇒	⇒	PROPN
ejpam-4637	290	23	)	)	PUNCT
ejpam-4637	290	24	assume	assume	VERB
ejpam-4637	290	25	that	that	SCONJ
ejpam-4637	290	26	ag	ag	PROPN
ejpam-4637	290	27	[	[	PUNCT
ejpam-4637	290	28	α1	α1	PROPN
ejpam-4637	290	29	,	,	PUNCT
ejpam-4637	290	30	β2	β2	NOUN
ejpam-4637	290	31	,	,	PUNCT
ejpam-4637	290	32	γ2	γ2	PROPN
ejpam-4637	290	33	α2	α2	PROPN
ejpam-4637	290	34	,	,	PUNCT
ejpam-4637	290	35	β1	β1	PROPN
ejpam-4637	290	36	,	,	PUNCT
ejpam-4637	290	37	γ1	γ1	PROPN
ejpam-4637	290	38	]	]	PUNCT
ejpam-4637	290	39	is	be	AUX
ejpam-4637	290	40	a	a	DET
ejpam-4637	290	41	svn	svn	NOUN
ejpam-4637	290	42	hyper	hyper	NOUN
ejpam-4637	290	43	up	up	ADP
ejpam-4637	290	44	-subalgebra	-subalgebra	NOUN
ejpam-4637	290	45	of	of	ADP
ejpam-4637	290	46	x.	x.	NOUN
ejpam-4637	290	47	since	since	SCONJ
ejpam-4637	290	48	g	g	PROPN
ejpam-4637	290	49	̸=	̸=	PROPN
ejpam-4637	290	50	∅	∅	NOUN
ejpam-4637	290	51	,	,	PUNCT
ejpam-4637	290	52	we	we	PRON
ejpam-4637	290	53	let	let	VERB
ejpam-4637	290	54	x	x	PRON
ejpam-4637	290	55	,	,	PUNCT
ejpam-4637	290	56	y	y	PROPN
ejpam-4637	290	57	∈	∈	PROPN
ejpam-4637	290	58	g	g	PROPN
ejpam-4637	290	59	and	and	CCONJ
ejpam-4637	290	60	z	z	NOUN
ejpam-4637	290	61	∈	∈	PROPN
ejpam-4637	290	62	x	x	PUNCT
ejpam-4637	291	1	◦	◦	NOUN
ejpam-4637	291	2	y.	y.	NOUN
ejpam-4637	291	3	then	then	ADV
ejpam-4637	291	4	tag	tag	VERB
ejpam-4637	291	5	[	[	PUNCT
ejpam-4637	291	6	α1	α1	PROPN
ejpam-4637	291	7	α2	α2	PROPN
ejpam-4637	291	8	]	]	PUNCT
ejpam-4637	291	9	(	(	PUNCT
ejpam-4637	291	10	x	x	X
ejpam-4637	291	11	)	)	PUNCT
ejpam-4637	291	12	=	=	SYM
ejpam-4637	291	13	α1	α1	PROPN
ejpam-4637	291	14	=	=	SYM
ejpam-4637	291	15	tag	tag	NOUN
ejpam-4637	291	16	[	[	PUNCT
ejpam-4637	291	17	α1	α1	PROPN
ejpam-4637	291	18	α2	α2	PROPN
ejpam-4637	291	19	]	]	PUNCT
ejpam-4637	291	20	(	(	PUNCT
ejpam-4637	291	21	y	y	NOUN
ejpam-4637	291	22	)	)	PUNCT
ejpam-4637	291	23	.	.	PUNCT
ejpam-4637	292	1	by	by	ADP
ejpam-4637	292	2	assumption	assumption	NOUN
ejpam-4637	292	3	,	,	PUNCT
ejpam-4637	292	4	tag	tag	NOUN
ejpam-4637	292	5	[	[	PUNCT
ejpam-4637	292	6	α1	α1	PROPN
ejpam-4637	292	7	α2	α2	PROPN
ejpam-4637	292	8	]	]	PUNCT
ejpam-4637	292	9	(	(	PUNCT
ejpam-4637	292	10	z	z	NOUN
ejpam-4637	292	11	)	)	PUNCT
ejpam-4637	292	12	≥	≥	NOUN
ejpam-4637	292	13	∗tag	∗tag	PROPN
ejpam-4637	292	14	[	[	PUNCT
ejpam-4637	292	15	α1	α1	PROPN
ejpam-4637	292	16	α2	α2	PROPN
ejpam-4637	292	17	]	]	PUNCT
ejpam-4637	292	18	(	(	PUNCT
ejpam-4637	292	19	x	x	PUNCT
ejpam-4637	292	20	◦	◦	VERB
ejpam-4637	292	21	y	y	PROPN
ejpam-4637	292	22	)	)	PUNCT
ejpam-4637	292	23	≥	≥	PROPN
ejpam-4637	292	24	min	min	NOUN
ejpam-4637	292	25	{	{	PUNCT
ejpam-4637	292	26	tag	tag	NOUN
ejpam-4637	292	27	[	[	PUNCT
ejpam-4637	292	28	α1	α1	PROPN
ejpam-4637	292	29	α2	α2	PROPN
ejpam-4637	292	30	]	]	PUNCT
ejpam-4637	292	31	(	(	PUNCT
ejpam-4637	292	32	x	x	X
ejpam-4637	292	33	)	)	PUNCT
ejpam-4637	292	34	,	,	PUNCT
ejpam-4637	292	35	tag	tag	NOUN
ejpam-4637	292	36	[	[	PUNCT
ejpam-4637	292	37	α1	α1	PROPN
ejpam-4637	292	38	α2	α2	PROPN
ejpam-4637	292	39	]	]	PUNCT
ejpam-4637	292	40	(	(	PUNCT
ejpam-4637	292	41	y	y	NOUN
ejpam-4637	292	42	)	)	PUNCT
ejpam-4637	292	43	}	}	PUNCT
ejpam-4637	293	1	=	=	SYM
ejpam-4637	293	2	α1	α1	PROPN
ejpam-4637	293	3	≥	≥	NUM
ejpam-4637	293	4	tag	tag	NOUN
ejpam-4637	293	5	[	[	PUNCT
ejpam-4637	293	6	α1	α1	PROPN
ejpam-4637	293	7	α2	α2	PROPN
ejpam-4637	293	8	]	]	PUNCT
ejpam-4637	293	9	(	(	PUNCT
ejpam-4637	293	10	z	z	NOUN
ejpam-4637	293	11	)	)	PUNCT
ejpam-4637	293	12	.	.	PUNCT
ejpam-4637	294	1	that	that	PRON
ejpam-4637	294	2	is	be	AUX
ejpam-4637	294	3	,	,	PUNCT
ejpam-4637	294	4	tag	tag	NOUN
ejpam-4637	294	5	[	[	PUNCT
ejpam-4637	294	6	α1	α1	PROPN
ejpam-4637	294	7	α2	α2	PROPN
ejpam-4637	294	8	]	]	PUNCT
ejpam-4637	294	9	(	(	PUNCT
ejpam-4637	294	10	z	z	NOUN
ejpam-4637	294	11	)	)	PUNCT
ejpam-4637	294	12	=	=	SYM
ejpam-4637	294	13	α1	α1	PROPN
ejpam-4637	294	14	.	.	PUNCT
ejpam-4637	295	1	thus	thus	ADV
ejpam-4637	295	2	,	,	PUNCT
ejpam-4637	295	3	z	z	PROPN
ejpam-4637	295	4	∈	∈	PROPN
ejpam-4637	295	5	g	g	NOUN
ejpam-4637	295	6	and	and	CCONJ
ejpam-4637	295	7	so	so	ADV
ejpam-4637	295	8	x	x	VERB
ejpam-4637	295	9	◦	◦	VERB
ejpam-4637	295	10	y	y	PROPN
ejpam-4637	295	11	⊆	⊆	NUM
ejpam-4637	295	12	g.	g.	NOUN
ejpam-4637	295	13	by	by	ADP
ejpam-4637	295	14	proposition	proposition	NOUN
ejpam-4637	295	15	2	2	NUM
ejpam-4637	295	16	,	,	PUNCT
ejpam-4637	295	17	g	g	PROPN
ejpam-4637	295	18	is	be	AUX
ejpam-4637	295	19	a	a	DET
ejpam-4637	295	20	hyper	hyper	ADJ
ejpam-4637	295	21	up	up	ADP
ejpam-4637	295	22	-subalgebra	-subalgebra	NOUN
ejpam-4637	295	23	of	of	ADP
ejpam-4637	295	24	x.	x.	NOUN
ejpam-4637	295	25	(	(	PUNCT
ejpam-4637	295	26	⇐	⇐	ADJ
ejpam-4637	295	27	)	)	PUNCT
ejpam-4637	295	28	assume	assume	VERB
ejpam-4637	295	29	that	that	SCONJ
ejpam-4637	295	30	g	g	PROPN
ejpam-4637	295	31	is	be	AUX
ejpam-4637	295	32	a	a	DET
ejpam-4637	295	33	hyper	hyper	ADJ
ejpam-4637	295	34	up	up	ADP
ejpam-4637	295	35	-subalgebra	-subalgebra	NOUN
ejpam-4637	295	36	of	of	ADP
ejpam-4637	295	37	x	x	PUNCT
ejpam-4637	295	38	and	and	CCONJ
ejpam-4637	295	39	suppose	suppose	VERB
ejpam-4637	295	40	x	x	PRON
ejpam-4637	295	41	,	,	PUNCT
ejpam-4637	295	42	y	y	PROPN
ejpam-4637	295	43	∈	∈	PROPN
ejpam-4637	295	44	x.	x.	NOUN
ejpam-4637	295	45	consider	consider	VERB
ejpam-4637	295	46	the	the	DET
ejpam-4637	295	47	following	follow	VERB
ejpam-4637	295	48	cases	case	NOUN
ejpam-4637	295	49	:	:	PUNCT
ejpam-4637	295	50	case	case	NOUN
ejpam-4637	295	51	1	1	NUM
ejpam-4637	295	52	.	.	NUM
ejpam-4637	295	53	x	x	X
ejpam-4637	295	54	,	,	PUNCT
ejpam-4637	295	55	y	y	PROPN
ejpam-4637	295	56	∈	∈	PROPN
ejpam-4637	295	57	g	g	PROPN
ejpam-4637	295	58	by	by	ADP
ejpam-4637	295	59	assumption	assumption	NOUN
ejpam-4637	295	60	,	,	PUNCT
ejpam-4637	295	61	x	x	PUNCT
ejpam-4637	295	62	◦	◦	VERB
ejpam-4637	295	63	y	y	PROPN
ejpam-4637	295	64	⊆	⊆	NUM
ejpam-4637	295	65	g.	g.	PROPN
ejpam-4637	295	66	thus	thus	ADV
ejpam-4637	295	67	,	,	PUNCT
ejpam-4637	295	68	∗tag	∗tag	PROPN
ejpam-4637	295	69	[	[	PUNCT
ejpam-4637	295	70	α1	α1	PROPN
ejpam-4637	295	71	α2	α2	PROPN
ejpam-4637	295	72	]	]	PUNCT
ejpam-4637	295	73	(	(	PUNCT
ejpam-4637	295	74	x	x	PUNCT
ejpam-4637	295	75	◦	◦	VERB
ejpam-4637	295	76	y	y	NOUN
ejpam-4637	295	77	)	)	PUNCT
ejpam-4637	295	78	=	=	SYM
ejpam-4637	295	79	α1	α1	PROPN
ejpam-4637	295	80	≥	≥	NUM
ejpam-4637	295	81	α1	α1	PROPN
ejpam-4637	295	82	=	=	SYM
ejpam-4637	295	83	min	min	NOUN
ejpam-4637	295	84	{	{	PUNCT
ejpam-4637	295	85	tag	tag	NOUN
ejpam-4637	295	86	[	[	PUNCT
ejpam-4637	295	87	α1	α1	PROPN
ejpam-4637	295	88	α2	α2	PROPN
ejpam-4637	295	89	]	]	PUNCT
ejpam-4637	295	90	(	(	PUNCT
ejpam-4637	295	91	x	x	X
ejpam-4637	295	92	)	)	PUNCT
ejpam-4637	295	93	,	,	PUNCT
ejpam-4637	295	94	tag	tag	NOUN
ejpam-4637	295	95	[	[	PUNCT
ejpam-4637	295	96	α1	α1	PROPN
ejpam-4637	295	97	α2	α2	PROPN
ejpam-4637	295	98	]	]	PUNCT
ejpam-4637	295	99	(	(	PUNCT
ejpam-4637	295	100	y	y	NOUN
ejpam-4637	295	101	)	)	PUNCT
ejpam-4637	295	102	}	}	PUNCT
ejpam-4637	295	103	,	,	PUNCT
ejpam-4637	295	104	∗iag	∗iag	PUNCT
ejpam-4637	295	105	[	[	PUNCT
ejpam-4637	295	106	β2	β2	NOUN
ejpam-4637	295	107	β1	β1	PROPN
ejpam-4637	295	108	]	]	PUNCT
ejpam-4637	295	109	(	(	PUNCT
ejpam-4637	295	110	x	x	SYM
ejpam-4637	295	111	◦	◦	VERB
ejpam-4637	295	112	y	y	NOUN
ejpam-4637	295	113	)	)	PUNCT
ejpam-4637	296	1	=	=	VERB
ejpam-4637	296	2	β2	β2	VERB
ejpam-4637	296	3	≤	≤	NUM
ejpam-4637	296	4	β2	β2	NOUN
ejpam-4637	296	5	=	=	SYM
ejpam-4637	296	6	max	max	PROPN
ejpam-4637	296	7	{	{	PUNCT
ejpam-4637	296	8	iag	iag	PROPN
ejpam-4637	296	9	[	[	PUNCT
ejpam-4637	296	10	β2	β2	NOUN
ejpam-4637	296	11	β1	β1	PROPN
ejpam-4637	296	12	]	]	PUNCT
ejpam-4637	296	13	(	(	PUNCT
ejpam-4637	296	14	x	x	X
ejpam-4637	296	15	)	)	PUNCT
ejpam-4637	296	16	,	,	PUNCT
ejpam-4637	296	17	iag	iag	PROPN
ejpam-4637	296	18	[	[	PUNCT
ejpam-4637	296	19	β2	β2	NOUN
ejpam-4637	296	20	β1	β1	PROPN
ejpam-4637	296	21	]	]	PUNCT
ejpam-4637	296	22	(	(	PUNCT
ejpam-4637	296	23	y	y	NOUN
ejpam-4637	296	24	)	)	PUNCT
ejpam-4637	296	25	}	}	PUNCT
ejpam-4637	296	26	,	,	PUNCT
ejpam-4637	296	27	and	and	CCONJ
ejpam-4637	296	28	∗fag	∗fag	NUM
ejpam-4637	296	29	[	[	PUNCT
ejpam-4637	296	30	γ2	γ2	PROPN
ejpam-4637	296	31	γ1	γ1	PROPN
ejpam-4637	296	32	]	]	PUNCT
ejpam-4637	296	33	(	(	PUNCT
ejpam-4637	296	34	x	x	SYM
ejpam-4637	296	35	◦	◦	VERB
ejpam-4637	296	36	y	y	NOUN
ejpam-4637	296	37	)	)	PUNCT
ejpam-4637	297	1	=	=	SYM
ejpam-4637	297	2	γ2	γ2	ADJ
ejpam-4637	297	3	≤	≤	PUNCT
ejpam-4637	297	4	γ2	γ2	NOUN
ejpam-4637	297	5	=	=	SYM
ejpam-4637	297	6	max	max	PROPN
ejpam-4637	297	7	{	{	PUNCT
ejpam-4637	297	8	fag	fag	NOUN
ejpam-4637	297	9	[	[	PUNCT
ejpam-4637	297	10	γ2	γ2	PROPN
ejpam-4637	297	11	γ1	γ1	PROPN
ejpam-4637	297	12	]	]	PUNCT
ejpam-4637	297	13	(	(	PUNCT
ejpam-4637	297	14	x),fag	x),fag	PUNCT
ejpam-4637	298	1	[	[	PUNCT
ejpam-4637	298	2	γ2	γ2	PROPN
ejpam-4637	298	3	γ1	γ1	PROPN
ejpam-4637	298	4	]	]	PUNCT
ejpam-4637	298	5	(	(	PUNCT
ejpam-4637	298	6	y	y	NOUN
ejpam-4637	298	7	)	)	PUNCT
ejpam-4637	298	8	}	}	PUNCT
ejpam-4637	298	9	.	.	PUNCT
ejpam-4637	299	1	case	case	NOUN
ejpam-4637	299	2	2	2	NUM
ejpam-4637	299	3	.	.	PUNCT
ejpam-4637	299	4	x	x	SYM
ejpam-4637	299	5	∈	∈	PROPN
ejpam-4637	299	6	g	g	PROPN
ejpam-4637	299	7	and	and	CCONJ
ejpam-4637	299	8	y	y	PROPN
ejpam-4637	299	9	/∈	/∈	PUNCT
ejpam-4637	300	1	g	g	PROPN
ejpam-4637	301	1	so	so	ADV
ejpam-4637	301	2	we	we	PRON
ejpam-4637	301	3	have	have	VERB
ejpam-4637	301	4	∗tag	∗tag	PROPN
ejpam-4637	301	5	[	[	PUNCT
ejpam-4637	301	6	α1	α1	PROPN
ejpam-4637	301	7	α2	α2	PROPN
ejpam-4637	301	8	]	]	PUNCT
ejpam-4637	301	9	(	(	PUNCT
ejpam-4637	301	10	x	x	PUNCT
ejpam-4637	301	11	◦	◦	VERB
ejpam-4637	301	12	y	y	NOUN
ejpam-4637	301	13	)	)	PUNCT
ejpam-4637	301	14	≥	≥	NOUN
ejpam-4637	301	15	α2	α2	PROPN
ejpam-4637	301	16	a.	a.	PROPN
ejpam-4637	301	17	cano	cano	PROPN
ejpam-4637	301	18	,	,	PUNCT
ejpam-4637	301	19	g.	g.	PROPN
ejpam-4637	301	20	petalcorin	petalcorin	PROPN
ejpam-4637	301	21	/	/	SYM
ejpam-4637	301	22	eur	eur	PROPN
ejpam-4637	301	23	.	.	PUNCT
ejpam-4637	302	1	j.	j.	PROPN
ejpam-4637	302	2	pure	pure	PROPN
ejpam-4637	302	3	appl	appl	PROPN
ejpam-4637	302	4	.	.	PROPN
ejpam-4637	302	5	math	math	PROPN
ejpam-4637	302	6	,	,	PUNCT
ejpam-4637	302	7	16	16	NUM
ejpam-4637	302	8	(	(	PUNCT
ejpam-4637	302	9	1	1	NUM
ejpam-4637	302	10	)	)	PUNCT
ejpam-4637	302	11	(	(	PUNCT
ejpam-4637	302	12	2023	2023	NUM
ejpam-4637	302	13	)	)	PUNCT
ejpam-4637	302	14	,	,	PUNCT
ejpam-4637	302	15	548	548	NUM
ejpam-4637	302	16	-	-	SYM
ejpam-4637	302	17	576	576	NUM
ejpam-4637	302	18	561	561	NUM
ejpam-4637	302	19	=	=	NOUN
ejpam-4637	302	20	min{α1	min{α1	PROPN
ejpam-4637	302	21	,	,	PUNCT
ejpam-4637	302	22	α2	α2	ADJ
ejpam-4637	302	23	}	}	PUNCT
ejpam-4637	302	24	=	=	SYM
ejpam-4637	302	25	min	min	NOUN
ejpam-4637	302	26	{	{	PUNCT
ejpam-4637	302	27	tag	tag	NOUN
ejpam-4637	302	28	[	[	PUNCT
ejpam-4637	302	29	α1	α1	PROPN
ejpam-4637	302	30	α2	α2	PROPN
ejpam-4637	302	31	]	]	PUNCT
ejpam-4637	302	32	(	(	PUNCT
ejpam-4637	302	33	x	x	X
ejpam-4637	302	34	)	)	PUNCT
ejpam-4637	302	35	,	,	PUNCT
ejpam-4637	302	36	tag	tag	NOUN
ejpam-4637	302	37	[	[	PUNCT
ejpam-4637	302	38	α1	α1	PROPN
ejpam-4637	302	39	α2	α2	PROPN
ejpam-4637	302	40	]	]	PUNCT
ejpam-4637	302	41	(	(	PUNCT
ejpam-4637	302	42	y	y	NOUN
ejpam-4637	302	43	)	)	PUNCT
ejpam-4637	302	44	}	}	PUNCT
ejpam-4637	302	45	,	,	PUNCT
ejpam-4637	302	46	∗iag	∗iag	PUNCT
ejpam-4637	302	47	[	[	PUNCT
ejpam-4637	302	48	β2	β2	NOUN
ejpam-4637	302	49	β1	β1	PROPN
ejpam-4637	302	50	]	]	PUNCT
ejpam-4637	302	51	(	(	PUNCT
ejpam-4637	302	52	x	x	SYM
ejpam-4637	302	53	◦	◦	VERB
ejpam-4637	302	54	y	y	NOUN
ejpam-4637	302	55	)	)	PUNCT
ejpam-4637	302	56	≤	≤	NOUN
ejpam-4637	302	57	β1	β1	NOUN
ejpam-4637	302	58	=	=	SYM
ejpam-4637	302	59	max{β2	max{β2	NOUN
ejpam-4637	302	60	,	,	PUNCT
ejpam-4637	302	61	β1	β1	NOUN
ejpam-4637	302	62	}	}	PUNCT
ejpam-4637	302	63	=	=	SYM
ejpam-4637	302	64	max	max	PROPN
ejpam-4637	302	65	{	{	PUNCT
ejpam-4637	302	66	iag	iag	PROPN
ejpam-4637	302	67	[	[	PUNCT
ejpam-4637	302	68	β2	β2	NOUN
ejpam-4637	302	69	β1	β1	PROPN
ejpam-4637	302	70	]	]	PUNCT
ejpam-4637	302	71	(	(	PUNCT
ejpam-4637	302	72	x	x	X
ejpam-4637	302	73	)	)	PUNCT
ejpam-4637	302	74	,	,	PUNCT
ejpam-4637	302	75	iag	iag	PROPN
ejpam-4637	302	76	[	[	PUNCT
ejpam-4637	302	77	β2	β2	NOUN
ejpam-4637	302	78	β1	β1	PROPN
ejpam-4637	302	79	]	]	PUNCT
ejpam-4637	302	80	(	(	PUNCT
ejpam-4637	302	81	y	y	NOUN
ejpam-4637	302	82	)	)	PUNCT
ejpam-4637	302	83	}	}	PUNCT
ejpam-4637	302	84	,	,	PUNCT
ejpam-4637	302	85	and	and	CCONJ
ejpam-4637	302	86	∗fag	∗fag	NUM
ejpam-4637	302	87	[	[	PUNCT
ejpam-4637	302	88	γ2	γ2	PROPN
ejpam-4637	302	89	γ1	γ1	PROPN
ejpam-4637	302	90	]	]	PUNCT
ejpam-4637	302	91	(	(	PUNCT
ejpam-4637	302	92	x	x	SYM
ejpam-4637	302	93	◦	◦	VERB
ejpam-4637	302	94	y	y	NOUN
ejpam-4637	302	95	)	)	PUNCT
ejpam-4637	302	96	≤	≤	NUM
ejpam-4637	302	97	γ1	γ1	NOUN
ejpam-4637	302	98	=	=	SYM
ejpam-4637	302	99	max{γ2	max{γ2	PROPN
ejpam-4637	302	100	,	,	PUNCT
ejpam-4637	302	101	γ1	γ1	NOUN
ejpam-4637	302	102	}	}	PUNCT
ejpam-4637	302	103	=	=	SYM
ejpam-4637	302	104	max	max	X
ejpam-4637	302	105	{	{	PUNCT
ejpam-4637	302	106	fag	fag	NOUN
ejpam-4637	302	107	[	[	PUNCT
ejpam-4637	302	108	γ2	γ2	PROPN
ejpam-4637	302	109	γ1	γ1	PROPN
ejpam-4637	302	110	]	]	PUNCT
ejpam-4637	302	111	(	(	PUNCT
ejpam-4637	302	112	x),fag	x),fag	PUNCT
ejpam-4637	303	1	[	[	PUNCT
ejpam-4637	303	2	γ2	γ2	PROPN
ejpam-4637	303	3	γ1	γ1	PROPN
ejpam-4637	303	4	]	]	PUNCT
ejpam-4637	303	5	(	(	PUNCT
ejpam-4637	303	6	y	y	NOUN
ejpam-4637	303	7	)	)	PUNCT
ejpam-4637	303	8	}	}	PUNCT
ejpam-4637	303	9	.	.	PUNCT
ejpam-4637	304	1	case	case	NOUN
ejpam-4637	304	2	3	3	NUM
ejpam-4637	304	3	.	.	NUM
ejpam-4637	304	4	x	x	X
ejpam-4637	304	5	/∈	/∈	PUNCT
ejpam-4637	305	1	g	g	NOUN
ejpam-4637	305	2	and	and	CCONJ
ejpam-4637	305	3	y	y	PROPN
ejpam-4637	305	4	∈	∈	PROPN
ejpam-4637	305	5	g	g	NOUN
ejpam-4637	305	6	using	use	VERB
ejpam-4637	305	7	similar	similar	ADJ
ejpam-4637	305	8	routine	routine	NOUN
ejpam-4637	305	9	done	do	VERB
ejpam-4637	305	10	in	in	ADP
ejpam-4637	305	11	case	case	NOUN
ejpam-4637	305	12	2	2	NUM
ejpam-4637	305	13	,	,	PUNCT
ejpam-4637	305	14	we	we	PRON
ejpam-4637	305	15	have	have	VERB
ejpam-4637	305	16	∗tag	∗tag	PROPN
ejpam-4637	305	17	[	[	PUNCT
ejpam-4637	305	18	α1	α1	PROPN
ejpam-4637	305	19	α2	α2	PROPN
ejpam-4637	305	20	]	]	PUNCT
ejpam-4637	305	21	(	(	PUNCT
ejpam-4637	305	22	x	x	PUNCT
ejpam-4637	305	23	◦	◦	VERB
ejpam-4637	305	24	y	y	PROPN
ejpam-4637	305	25	)	)	PUNCT
ejpam-4637	305	26	≥	≥	PROPN
ejpam-4637	305	27	min	min	NOUN
ejpam-4637	305	28	{	{	PUNCT
ejpam-4637	305	29	tag	tag	NOUN
ejpam-4637	305	30	[	[	PUNCT
ejpam-4637	305	31	α1	α1	PROPN
ejpam-4637	305	32	α2	α2	PROPN
ejpam-4637	305	33	]	]	PUNCT
ejpam-4637	305	34	(	(	PUNCT
ejpam-4637	305	35	x	x	X
ejpam-4637	305	36	)	)	PUNCT
ejpam-4637	305	37	,	,	PUNCT
ejpam-4637	305	38	tag	tag	NOUN
ejpam-4637	305	39	[	[	PUNCT
ejpam-4637	305	40	α1	α1	PROPN
ejpam-4637	305	41	α2	α2	PROPN
ejpam-4637	305	42	]	]	PUNCT
ejpam-4637	305	43	(	(	PUNCT
ejpam-4637	305	44	y	y	NOUN
ejpam-4637	305	45	)	)	PUNCT
ejpam-4637	305	46	}	}	PUNCT
ejpam-4637	305	47	,	,	PUNCT
ejpam-4637	305	48	∗iag	∗iag	PUNCT
ejpam-4637	305	49	[	[	PUNCT
ejpam-4637	305	50	β2	β2	NOUN
ejpam-4637	305	51	β1	β1	PROPN
ejpam-4637	305	52	]	]	PUNCT
ejpam-4637	305	53	(	(	PUNCT
ejpam-4637	305	54	x	x	SYM
ejpam-4637	305	55	◦	◦	VERB
ejpam-4637	305	56	y	y	NOUN
ejpam-4637	305	57	)	)	PUNCT
ejpam-4637	305	58	≤	≤	NOUN
ejpam-4637	305	59	max	max	PROPN
ejpam-4637	305	60	{	{	PUNCT
ejpam-4637	305	61	iag	iag	PROPN
ejpam-4637	305	62	[	[	PUNCT
ejpam-4637	305	63	β2	β2	NOUN
ejpam-4637	305	64	β1	β1	PROPN
ejpam-4637	305	65	]	]	PUNCT
ejpam-4637	305	66	(	(	PUNCT
ejpam-4637	305	67	x	x	X
ejpam-4637	305	68	)	)	PUNCT
ejpam-4637	305	69	,	,	PUNCT
ejpam-4637	305	70	iag	iag	PROPN
ejpam-4637	305	71	[	[	PUNCT
ejpam-4637	305	72	β1	β1	PROPN
ejpam-4637	305	73	β2	β2	PROPN
ejpam-4637	305	74	]	]	PUNCT
ejpam-4637	305	75	(	(	PUNCT
ejpam-4637	305	76	y	y	NOUN
ejpam-4637	305	77	)	)	PUNCT
ejpam-4637	305	78	}	}	PUNCT
ejpam-4637	305	79	,	,	PUNCT
ejpam-4637	305	80	and	and	CCONJ
ejpam-4637	305	81	∗fag	∗fag	NUM
ejpam-4637	305	82	[	[	PUNCT
ejpam-4637	305	83	γ2	γ2	PROPN
ejpam-4637	305	84	γ1	γ1	PROPN
ejpam-4637	305	85	]	]	PUNCT
ejpam-4637	305	86	(	(	PUNCT
ejpam-4637	305	87	x	x	SYM
ejpam-4637	305	88	◦	◦	VERB
ejpam-4637	305	89	y	y	NOUN
ejpam-4637	305	90	)	)	PUNCT
ejpam-4637	305	91	≤	≤	NUM
ejpam-4637	306	1	max	max	PROPN
ejpam-4637	306	2	{	{	PUNCT
ejpam-4637	306	3	fag	fag	PROPN
ejpam-4637	306	4	[	[	PUNCT
ejpam-4637	306	5	γ2	γ2	PROPN
ejpam-4637	306	6	γ1	γ1	PROPN
ejpam-4637	306	7	]	]	PUNCT
ejpam-4637	306	8	(	(	PUNCT
ejpam-4637	306	9	x),fag	x),fag	PUNCT
ejpam-4637	307	1	[	[	PUNCT
ejpam-4637	307	2	γ2	γ2	PROPN
ejpam-4637	307	3	γ1	γ1	PROPN
ejpam-4637	307	4	]	]	PUNCT
ejpam-4637	307	5	(	(	PUNCT
ejpam-4637	307	6	y	y	NOUN
ejpam-4637	307	7	)	)	PUNCT
ejpam-4637	307	8	}	}	PUNCT
ejpam-4637	307	9	.	.	PUNCT
ejpam-4637	308	1	case	case	NOUN
ejpam-4637	308	2	4	4	NUM
ejpam-4637	308	3	.	.	NUM
ejpam-4637	308	4	x	x	X
ejpam-4637	308	5	/∈	/∈	PUNCT
ejpam-4637	309	1	g	g	PROPN
ejpam-4637	309	2	and	and	CCONJ
ejpam-4637	309	3	y	y	PROPN
ejpam-4637	309	4	/∈	/∈	PUNCT
ejpam-4637	310	1	g	g	PROPN
ejpam-4637	310	2	now	now	ADV
ejpam-4637	310	3	,	,	PUNCT
ejpam-4637	310	4	∗tag	∗tag	PROPN
ejpam-4637	310	5	[	[	PUNCT
ejpam-4637	310	6	α1	α1	PROPN
ejpam-4637	310	7	α2	α2	PROPN
ejpam-4637	310	8	]	]	PUNCT
ejpam-4637	310	9	(	(	PUNCT
ejpam-4637	310	10	x	x	PUNCT
ejpam-4637	310	11	◦	◦	VERB
ejpam-4637	310	12	y	y	NOUN
ejpam-4637	310	13	)	)	PUNCT
ejpam-4637	310	14	≥	≥	NOUN
ejpam-4637	310	15	α2	α2	NOUN
ejpam-4637	310	16	=	=	SYM
ejpam-4637	310	17	min{α2	min{α2	NOUN
ejpam-4637	310	18	,	,	PUNCT
ejpam-4637	310	19	α2	α2	ADJ
ejpam-4637	310	20	}	}	PUNCT
ejpam-4637	310	21	=	=	SYM
ejpam-4637	310	22	min	min	NOUN
ejpam-4637	310	23	{	{	PUNCT
ejpam-4637	310	24	tag	tag	NOUN
ejpam-4637	310	25	[	[	PUNCT
ejpam-4637	310	26	α1	α1	PROPN
ejpam-4637	310	27	α2	α2	PROPN
ejpam-4637	310	28	]	]	PUNCT
ejpam-4637	310	29	(	(	PUNCT
ejpam-4637	310	30	x	x	X
ejpam-4637	310	31	)	)	PUNCT
ejpam-4637	310	32	,	,	PUNCT
ejpam-4637	310	33	tag	tag	NOUN
ejpam-4637	310	34	[	[	PUNCT
ejpam-4637	310	35	α1	α1	PROPN
ejpam-4637	310	36	α2	α2	PROPN
ejpam-4637	310	37	]	]	PUNCT
ejpam-4637	310	38	(	(	PUNCT
ejpam-4637	310	39	y	y	NOUN
ejpam-4637	310	40	)	)	PUNCT
ejpam-4637	310	41	}	}	PUNCT
ejpam-4637	310	42	,	,	PUNCT
ejpam-4637	310	43	∗iag	∗iag	PUNCT
ejpam-4637	310	44	[	[	PUNCT
ejpam-4637	310	45	β2	β2	NOUN
ejpam-4637	310	46	β1	β1	PROPN
ejpam-4637	310	47	]	]	PUNCT
ejpam-4637	310	48	(	(	PUNCT
ejpam-4637	310	49	x	x	SYM
ejpam-4637	310	50	◦	◦	VERB
ejpam-4637	310	51	y	y	NOUN
ejpam-4637	310	52	)	)	PUNCT
ejpam-4637	310	53	≤	≤	NOUN
ejpam-4637	310	54	β1	β1	NOUN
ejpam-4637	310	55	=	=	SYM
ejpam-4637	310	56	max{β1	max{β1	NOUN
ejpam-4637	310	57	,	,	PUNCT
ejpam-4637	310	58	β1	β1	PROPN
ejpam-4637	310	59	}	}	PUNCT
ejpam-4637	310	60	a.	a.	NOUN
ejpam-4637	310	61	cano	cano	PROPN
ejpam-4637	310	62	,	,	PUNCT
ejpam-4637	310	63	g.	g.	PROPN
ejpam-4637	310	64	petalcorin	petalcorin	PROPN
ejpam-4637	310	65	/	/	SYM
ejpam-4637	310	66	eur	eur	PROPN
ejpam-4637	310	67	.	.	PUNCT
ejpam-4637	311	1	j.	j.	PROPN
ejpam-4637	311	2	pure	pure	PROPN
ejpam-4637	311	3	appl	appl	PROPN
ejpam-4637	311	4	.	.	PROPN
ejpam-4637	311	5	math	math	PROPN
ejpam-4637	311	6	,	,	PUNCT
ejpam-4637	311	7	16	16	NUM
ejpam-4637	311	8	(	(	PUNCT
ejpam-4637	311	9	1	1	NUM
ejpam-4637	311	10	)	)	PUNCT
ejpam-4637	311	11	(	(	PUNCT
ejpam-4637	311	12	2023	2023	NUM
ejpam-4637	311	13	)	)	PUNCT
ejpam-4637	311	14	,	,	PUNCT
ejpam-4637	311	15	548	548	NUM
ejpam-4637	311	16	-	-	SYM
ejpam-4637	311	17	576	576	NUM
ejpam-4637	311	18	562	562	NUM
ejpam-4637	311	19	=	=	SYM
ejpam-4637	311	20	max	max	X
ejpam-4637	311	21	{	{	PUNCT
ejpam-4637	311	22	iag	iag	PROPN
ejpam-4637	311	23	[	[	PUNCT
ejpam-4637	311	24	β2	β2	NOUN
ejpam-4637	311	25	β1	β1	PROPN
ejpam-4637	311	26	]	]	PUNCT
ejpam-4637	311	27	(	(	PUNCT
ejpam-4637	311	28	x	x	X
ejpam-4637	311	29	)	)	PUNCT
ejpam-4637	311	30	,	,	PUNCT
ejpam-4637	311	31	iag	iag	PROPN
ejpam-4637	311	32	[	[	PUNCT
ejpam-4637	311	33	β2	β2	NOUN
ejpam-4637	311	34	β1	β1	PROPN
ejpam-4637	311	35	]	]	PUNCT
ejpam-4637	311	36	(	(	PUNCT
ejpam-4637	311	37	y	y	NOUN
ejpam-4637	311	38	)	)	PUNCT
ejpam-4637	311	39	}	}	PUNCT
ejpam-4637	311	40	,	,	PUNCT
ejpam-4637	311	41	and	and	CCONJ
ejpam-4637	311	42	∗fag	∗fag	NUM
ejpam-4637	311	43	[	[	PUNCT
ejpam-4637	311	44	γ2	γ2	PROPN
ejpam-4637	311	45	γ1	γ1	PROPN
ejpam-4637	311	46	]	]	PUNCT
ejpam-4637	311	47	(	(	PUNCT
ejpam-4637	311	48	x	x	SYM
ejpam-4637	311	49	◦	◦	VERB
ejpam-4637	311	50	y	y	NOUN
ejpam-4637	311	51	)	)	PUNCT
ejpam-4637	311	52	≤	≤	NUM
ejpam-4637	311	53	γ1	γ1	NOUN
ejpam-4637	311	54	=	=	PUNCT
ejpam-4637	311	55	max{γ1	max{γ1	NOUN
ejpam-4637	311	56	,	,	PUNCT
ejpam-4637	311	57	γ1	γ1	NOUN
ejpam-4637	311	58	}	}	PUNCT
ejpam-4637	311	59	=	=	SYM
ejpam-4637	311	60	max	max	X
ejpam-4637	311	61	{	{	PUNCT
ejpam-4637	311	62	fag	fag	NOUN
ejpam-4637	311	63	[	[	PUNCT
ejpam-4637	311	64	γ2	γ2	PROPN
ejpam-4637	311	65	γ1	γ1	PROPN
ejpam-4637	311	66	]	]	PUNCT
ejpam-4637	311	67	(	(	PUNCT
ejpam-4637	311	68	x),fag	x),fag	PUNCT
ejpam-4637	312	1	[	[	PUNCT
ejpam-4637	312	2	γ2	γ2	PROPN
ejpam-4637	312	3	γ1	γ1	PROPN
ejpam-4637	312	4	]	]	PUNCT
ejpam-4637	312	5	(	(	PUNCT
ejpam-4637	312	6	y	y	NOUN
ejpam-4637	312	7	)	)	PUNCT
ejpam-4637	312	8	}	}	PUNCT
ejpam-4637	312	9	.	.	PUNCT
ejpam-4637	313	1	hence	hence	ADV
ejpam-4637	313	2	,	,	PUNCT
ejpam-4637	313	3	ag	ag	PROPN
ejpam-4637	313	4	[	[	PUNCT
ejpam-4637	313	5	α1	α1	PROPN
ejpam-4637	313	6	,	,	PUNCT
ejpam-4637	313	7	β2	β2	NOUN
ejpam-4637	313	8	,	,	PUNCT
ejpam-4637	313	9	γ2	γ2	PROPN
ejpam-4637	313	10	α2	α2	PROPN
ejpam-4637	313	11	,	,	PUNCT
ejpam-4637	313	12	β1	β1	PROPN
ejpam-4637	313	13	,	,	PUNCT
ejpam-4637	313	14	γ1	γ1	PROPN
ejpam-4637	313	15	]	]	PUNCT
ejpam-4637	313	16	is	be	AUX
ejpam-4637	313	17	a	a	DET
ejpam-4637	313	18	svn	svn	NOUN
ejpam-4637	313	19	hyper	hyper	NOUN
ejpam-4637	313	20	up	up	ADP
ejpam-4637	313	21	-subalgebra	-subalgebra	NOUN
ejpam-4637	313	22	of	of	ADP
ejpam-4637	313	23	x.	x.	NOUN
ejpam-4637	313	24	theorem	theorem	VERB
ejpam-4637	313	25	4	4	NUM
ejpam-4637	313	26	.	.	PUNCT
ejpam-4637	314	1	let	let	VERB
ejpam-4637	314	2	g	g	PRON
ejpam-4637	314	3	be	be	AUX
ejpam-4637	314	4	a	a	DET
ejpam-4637	314	5	hyper	hyper	ADJ
ejpam-4637	314	6	up	up	ADP
ejpam-4637	314	7	-	-	PUNCT
ejpam-4637	314	8	subalgebra	subalgebra	NOUN
ejpam-4637	314	9	of	of	ADP
ejpam-4637	314	10	x.	x.	NOUN
ejpam-4637	314	11	then	then	ADV
ejpam-4637	314	12	there	there	PRON
ejpam-4637	314	13	exists	exist	VERB
ejpam-4637	314	14	a	a	DET
ejpam-4637	314	15	svn	svn	NOUN
ejpam-4637	314	16	hyper	hyper	NOUN
ejpam-4637	314	17	up	up	ADP
ejpam-4637	314	18	-	-	PUNCT
ejpam-4637	314	19	subalgebra	subalgebra	NOUN
ejpam-4637	314	20	a	a	PRON
ejpam-4637	314	21	=	=	SYM
ejpam-4637	314	22	(	(	PUNCT
ejpam-4637	314	23	ta	ta	PROPN
ejpam-4637	314	24	,	,	PUNCT
ejpam-4637	314	25	ia	ia	PROPN
ejpam-4637	314	26	,	,	PUNCT
ejpam-4637	314	27	fa	fa	NOUN
ejpam-4637	314	28	)	)	PUNCT
ejpam-4637	314	29	of	of	ADP
ejpam-4637	314	30	x	x	SYM
ejpam-4637	314	31	such	such	ADJ
ejpam-4637	314	32	that	that	SCONJ
ejpam-4637	314	33	a(α	a(α	NOUN
ejpam-4637	314	34	,	,	PUNCT
ejpam-4637	314	35	β	β	X
ejpam-4637	314	36	,	,	PUNCT
ejpam-4637	314	37	γ	γ	NOUN
ejpam-4637	314	38	)	)	PUNCT
ejpam-4637	314	39	=	=	SYM
ejpam-4637	314	40	g	g	NOUN
ejpam-4637	314	41	for	for	ADP
ejpam-4637	314	42	α	α	PROPN
ejpam-4637	314	43	,	,	PUNCT
ejpam-4637	314	44	β	β	X
ejpam-4637	314	45	,	,	PUNCT
ejpam-4637	314	46	γ	γ	PROPN
ejpam-4637	314	47	∈	∈	PROPN
ejpam-4637	315	1	[	[	X
ejpam-4637	315	2	0	0	NUM
ejpam-4637	315	3	,	,	PUNCT
ejpam-4637	315	4	1	1	NUM
ejpam-4637	315	5	]	]	PUNCT
ejpam-4637	315	6	.	.	PUNCT
ejpam-4637	316	1	proof	proof	NOUN
ejpam-4637	316	2	.	.	PUNCT
ejpam-4637	317	1	let	let	VERB
ejpam-4637	317	2	g	g	PRON
ejpam-4637	317	3	be	be	AUX
ejpam-4637	317	4	a	a	DET
ejpam-4637	317	5	hyper	hyper	ADJ
ejpam-4637	317	6	up	up	ADP
ejpam-4637	317	7	-subalgebra	-subalgebra	NOUN
ejpam-4637	317	8	of	of	ADP
ejpam-4637	317	9	x.	x.	NOUN
ejpam-4637	317	10	for	for	ADP
ejpam-4637	317	11	fixed	fixed	ADJ
ejpam-4637	317	12	α	α	PROPN
ejpam-4637	317	13	,	,	PUNCT
ejpam-4637	317	14	β	β	X
ejpam-4637	317	15	,	,	PUNCT
ejpam-4637	317	16	γ	γ	PROPN
ejpam-4637	317	17	∈	∈	PROPN
ejpam-4637	317	18	(	(	PUNCT
ejpam-4637	317	19	0	0	NUM
ejpam-4637	317	20	,	,	PUNCT
ejpam-4637	317	21	1	1	NUM
ejpam-4637	317	22	]	]	PUNCT
ejpam-4637	317	23	,	,	PUNCT
ejpam-4637	317	24	consider	consider	VERB
ejpam-4637	317	25	a	a	DET
ejpam-4637	317	26	=	=	SYM
ejpam-4637	317	27	ag	ag	PROPN
ejpam-4637	317	28	[	[	PUNCT
ejpam-4637	317	29	α	α	PROPN
ejpam-4637	317	30	,	,	PUNCT
ejpam-4637	317	31	0	0	NUM
ejpam-4637	317	32	,	,	PUNCT
ejpam-4637	317	33	0	0	NUM
ejpam-4637	317	34	0	0	NUM
ejpam-4637	317	35	,	,	PUNCT
ejpam-4637	317	36	β	β	X
ejpam-4637	317	37	,	,	PUNCT
ejpam-4637	317	38	γ	γ	X
ejpam-4637	317	39	]	]	PUNCT
ejpam-4637	317	40	.	.	PUNCT
ejpam-4637	318	1	since	since	SCONJ
ejpam-4637	318	2	g	g	PROPN
ejpam-4637	318	3	be	be	AUX
ejpam-4637	318	4	a	a	DET
ejpam-4637	318	5	hyper	hyper	ADJ
ejpam-4637	318	6	up	up	ADP
ejpam-4637	318	7	-subalgebra	-subalgebra	NOUN
ejpam-4637	318	8	of	of	ADP
ejpam-4637	318	9	x	x	PROPN
ejpam-4637	318	10	,	,	PUNCT
ejpam-4637	318	11	ag	ag	PROPN
ejpam-4637	318	12	[	[	PUNCT
ejpam-4637	318	13	α	α	PROPN
ejpam-4637	318	14	,	,	PUNCT
ejpam-4637	318	15	0	0	NUM
ejpam-4637	318	16	,	,	PUNCT
ejpam-4637	318	17	0	0	NUM
ejpam-4637	318	18	0	0	NUM
ejpam-4637	318	19	,	,	PUNCT
ejpam-4637	318	20	β	β	X
ejpam-4637	318	21	,	,	PUNCT
ejpam-4637	318	22	γ	γ	X
ejpam-4637	318	23	]	]	PUNCT
ejpam-4637	318	24	is	be	AUX
ejpam-4637	318	25	a	a	DET
ejpam-4637	318	26	svn	svn	NOUN
ejpam-4637	318	27	hyper	hyper	NOUN
ejpam-4637	318	28	up	up	ADP
ejpam-4637	318	29	-subalgebra	-subalgebra	NOUN
ejpam-4637	318	30	of	of	ADP
ejpam-4637	318	31	x	x	PUNCT
ejpam-4637	318	32	by	by	ADP
ejpam-4637	318	33	theorem	theorem	NOUN
ejpam-4637	318	34	3	3	NUM
ejpam-4637	318	35	.	.	PUNCT
ejpam-4637	319	1	now	now	ADV
ejpam-4637	319	2	,	,	PUNCT
ejpam-4637	319	3	let	let	VERB
ejpam-4637	319	4	x	x	X
ejpam-4637	319	5	∈	∈	PROPN
ejpam-4637	319	6	g.	g.	NOUN
ejpam-4637	319	7	then	then	ADV
ejpam-4637	319	8	ta(x	ta(x	VERB
ejpam-4637	319	9	)	)	PUNCT
ejpam-4637	320	1	=	=	SYM
ejpam-4637	320	2	tag	tag	NOUN
ejpam-4637	320	3	[	[	PUNCT
ejpam-4637	320	4	α	α	NOUN
ejpam-4637	320	5	0	0	NUM
ejpam-4637	320	6	]	]	PUNCT
ejpam-4637	320	7	(	(	PUNCT
ejpam-4637	320	8	x	x	X
ejpam-4637	320	9	)	)	PUNCT
ejpam-4637	320	10	=	=	SYM
ejpam-4637	320	11	α	α	PROPN
ejpam-4637	320	12	≥	≥	NUM
ejpam-4637	320	13	α	α	NOUN
ejpam-4637	320	14	,	,	PUNCT
ejpam-4637	320	15	ia(x	ia(x	NOUN
ejpam-4637	320	16	)	)	PUNCT
ejpam-4637	320	17	=	=	SYM
ejpam-4637	320	18	iag	iag	PROPN
ejpam-4637	320	19	[	[	PUNCT
ejpam-4637	320	20	0	0	NUM
ejpam-4637	320	21	β	β	X
ejpam-4637	320	22	]	]	PUNCT
ejpam-4637	320	23	(	(	PUNCT
ejpam-4637	320	24	x	x	X
ejpam-4637	320	25	)	)	PUNCT
ejpam-4637	320	26	=	=	SYM
ejpam-4637	320	27	0	0	NUM
ejpam-4637	320	28	≤	≤	NUM
ejpam-4637	320	29	β	β	NOUN
ejpam-4637	320	30	,	,	PUNCT
ejpam-4637	320	31	and	and	CCONJ
ejpam-4637	320	32	fa(x	fa(x	PROPN
ejpam-4637	320	33	)	)	PUNCT
ejpam-4637	320	34	=	=	SYM
ejpam-4637	320	35	fag	fag	NOUN
ejpam-4637	320	36	[	[	PUNCT
ejpam-4637	320	37	0	0	NUM
ejpam-4637	320	38	γ	γ	X
ejpam-4637	320	39	]	]	PUNCT
ejpam-4637	320	40	(	(	PUNCT
ejpam-4637	320	41	x	x	X
ejpam-4637	320	42	)	)	PUNCT
ejpam-4637	320	43	=	=	SYM
ejpam-4637	320	44	0	0	NUM
ejpam-4637	320	45	≤	≤	NUM
ejpam-4637	320	46	γ	γ	PROPN
ejpam-4637	320	47	.	.	PUNCT
ejpam-4637	321	1	thus	thus	ADV
ejpam-4637	321	2	,	,	PUNCT
ejpam-4637	321	3	x	x	SYM
ejpam-4637	321	4	∈	∈	PROPN
ejpam-4637	321	5	tα	tα	VERB
ejpam-4637	321	6	a	a	DET
ejpam-4637	321	7	∩	∩	NOUN
ejpam-4637	321	8	iβa	iβa	NOUN
ejpam-4637	321	9	∩	∩	NOUN
ejpam-4637	321	10	f	f	PROPN
ejpam-4637	321	11	γ	γ	X
ejpam-4637	321	12	a	a	PRON
ejpam-4637	321	13	=	=	PUNCT
ejpam-4637	321	14	a(α	a(α	NOUN
ejpam-4637	321	15	,	,	PUNCT
ejpam-4637	321	16	β	β	X
ejpam-4637	321	17	,	,	PUNCT
ejpam-4637	321	18	γ	γ	NOUN
ejpam-4637	321	19	)	)	PUNCT
ejpam-4637	321	20	and	and	CCONJ
ejpam-4637	321	21	so	so	ADV
ejpam-4637	321	22	g	g	PROPN
ejpam-4637	321	23	⊆	⊆	NUM
ejpam-4637	321	24	a(α	a(α	NOUN
ejpam-4637	321	25	,	,	PUNCT
ejpam-4637	321	26	β	β	X
ejpam-4637	321	27	,	,	PUNCT
ejpam-4637	321	28	γ	γ	NOUN
ejpam-4637	321	29	)	)	PUNCT
ejpam-4637	321	30	.	.	PUNCT
ejpam-4637	322	1	also	also	ADV
ejpam-4637	322	2	,	,	PUNCT
ejpam-4637	322	3	let	let	VERB
ejpam-4637	322	4	y	y	PROPN
ejpam-4637	322	5	∈	∈	PROPN
ejpam-4637	322	6	a(α	a(α	NOUN
ejpam-4637	322	7	,	,	PUNCT
ejpam-4637	322	8	β	β	X
ejpam-4637	322	9	,	,	PUNCT
ejpam-4637	322	10	γ	γ	NOUN
ejpam-4637	322	11	)	)	PUNCT
ejpam-4637	322	12	.	.	PUNCT
ejpam-4637	323	1	then	then	ADV
ejpam-4637	323	2	ta(y	ta(y	PUNCT
ejpam-4637	323	3	)	)	PUNCT
ejpam-4637	323	4	≥	≥	NUM
ejpam-4637	323	5	α	α	NOUN
ejpam-4637	323	6	,	,	PUNCT
ejpam-4637	323	7	ia(y	ia(y	ADJ
ejpam-4637	323	8	)	)	PUNCT
ejpam-4637	323	9	≤	≤	NOUN
ejpam-4637	323	10	β	β	NOUN
ejpam-4637	323	11	,	,	PUNCT
ejpam-4637	323	12	and	and	CCONJ
ejpam-4637	323	13	fa(y	fa(y	NOUN
ejpam-4637	323	14	)	)	PUNCT
ejpam-4637	323	15	≤	≤	NUM
ejpam-4637	324	1	γ	γ	PROPN
ejpam-4637	324	2	.	.	PROPN
ejpam-4637	324	3	suppose	suppose	VERB
ejpam-4637	325	1	that	that	SCONJ
ejpam-4637	325	2	y	y	PROPN
ejpam-4637	325	3	/∈	/∈	PUNCT
ejpam-4637	325	4	g.	g.	PROPN
ejpam-4637	326	1	then	then	ADV
ejpam-4637	326	2	0	0	NUM
ejpam-4637	326	3	=	=	SYM
ejpam-4637	326	4	tag	tag	NOUN
ejpam-4637	326	5	[	[	PUNCT
ejpam-4637	326	6	α	α	NOUN
ejpam-4637	326	7	0	0	NUM
ejpam-4637	326	8	]	]	PUNCT
ejpam-4637	326	9	(	(	PUNCT
ejpam-4637	326	10	y	y	NOUN
ejpam-4637	326	11	)	)	PUNCT
ejpam-4637	326	12	=	=	SYM
ejpam-4637	326	13	ta(y	ta(y	PROPN
ejpam-4637	326	14	)	)	PUNCT
ejpam-4637	326	15	≥	≥	NUM
ejpam-4637	326	16	α	α	NOUN
ejpam-4637	326	17	.	.	PUNCT
ejpam-4637	327	1	it	it	PRON
ejpam-4637	327	2	follows	follow	VERB
ejpam-4637	327	3	that	that	SCONJ
ejpam-4637	327	4	α	α	PRON
ejpam-4637	327	5	=	=	NOUN
ejpam-4637	327	6	0	0	PROPN
ejpam-4637	327	7	.	.	PUNCT
ejpam-4637	328	1	this	this	PRON
ejpam-4637	328	2	is	be	AUX
ejpam-4637	328	3	a	a	DET
ejpam-4637	328	4	contradiction	contradiction	NOUN
ejpam-4637	328	5	since	since	SCONJ
ejpam-4637	328	6	α	α	PROPN
ejpam-4637	328	7	∈	∈	PROPN
ejpam-4637	328	8	(	(	PUNCT
ejpam-4637	328	9	0	0	NUM
ejpam-4637	328	10	,	,	PUNCT
ejpam-4637	328	11	1	1	NUM
ejpam-4637	328	12	]	]	PUNCT
ejpam-4637	328	13	.	.	PUNCT
ejpam-4637	329	1	thus	thus	ADV
ejpam-4637	329	2	,	,	PUNCT
ejpam-4637	329	3	y	y	PROPN
ejpam-4637	329	4	∈	∈	PROPN
ejpam-4637	329	5	g	g	PROPN
ejpam-4637	329	6	and	and	CCONJ
ejpam-4637	329	7	so	so	ADV
ejpam-4637	329	8	a(α	a(α	NOUN
ejpam-4637	329	9	,	,	PUNCT
ejpam-4637	329	10	β	β	X
ejpam-4637	329	11	,	,	PUNCT
ejpam-4637	329	12	γ	γ	NOUN
ejpam-4637	329	13	)	)	PUNCT
ejpam-4637	329	14	⊆	⊆	NUM
ejpam-4637	329	15	g.	g.	NOUN
ejpam-4637	329	16	consequently	consequently	ADV
ejpam-4637	329	17	,	,	PUNCT
ejpam-4637	329	18	a(α	a(α	PROPN
ejpam-4637	329	19	,	,	PUNCT
ejpam-4637	329	20	β	β	X
ejpam-4637	329	21	,	,	PUNCT
ejpam-4637	329	22	γ	γ	NOUN
ejpam-4637	329	23	)	)	PUNCT
ejpam-4637	329	24	=	=	SYM
ejpam-4637	329	25	g.	g.	PROPN
ejpam-4637	329	26	theorem	theorem	VERB
ejpam-4637	329	27	5	5	NUM
ejpam-4637	329	28	.	.	PUNCT
ejpam-4637	329	29	given	give	VERB
ejpam-4637	329	30	a	a	DET
ejpam-4637	329	31	chain	chain	NOUN
ejpam-4637	329	32	of	of	ADP
ejpam-4637	329	33	hyper	hyper	ADJ
ejpam-4637	329	34	up	up	ADP
ejpam-4637	329	35	-	-	PUNCT
ejpam-4637	329	36	subalgebras	subalgebras	NOUN
ejpam-4637	329	37	of	of	ADP
ejpam-4637	329	38	x	x	PROPN
ejpam-4637	329	39	:	:	PUNCT
ejpam-4637	329	40	a0	a0	PROPN
ejpam-4637	329	41	⊂	⊂	PROPN
ejpam-4637	329	42	a1	a1	PROPN
ejpam-4637	329	43	⊂	⊂	PROPN
ejpam-4637	329	44	a2	a2	PROPN
ejpam-4637	329	45	⊂	⊂	PROPN
ejpam-4637	329	46	a3	a3	PROPN
ejpam-4637	329	47	⊂	⊂	PROPN
ejpam-4637	329	48	.	.	PUNCT
ejpam-4637	329	49	.	.	PUNCT
ejpam-4637	329	50	.	.	PUNCT
ejpam-4637	330	1	⊂	⊂	PROPN
ejpam-4637	331	1	an	an	PRON
ejpam-4637	332	1	=	=	X
ejpam-4637	332	2	x.	x.	NOUN
ejpam-4637	332	3	then	then	ADV
ejpam-4637	332	4	there	there	PRON
ejpam-4637	332	5	exists	exist	VERB
ejpam-4637	332	6	a	a	DET
ejpam-4637	332	7	svn	svn	NOUN
ejpam-4637	332	8	hyper	hyper	ADJ
ejpam-4637	332	9	upsubalgebra	upsubalgebra	NOUN
ejpam-4637	332	10	a	a	PRON
ejpam-4637	332	11	=	=	SYM
ejpam-4637	332	12	(	(	PUNCT
ejpam-4637	332	13	ta	ta	PROPN
ejpam-4637	332	14	,	,	PUNCT
ejpam-4637	332	15	ia	ia	PROPN
ejpam-4637	332	16	,	,	PUNCT
ejpam-4637	332	17	fa	fa	NOUN
ejpam-4637	332	18	)	)	PUNCT
ejpam-4637	332	19	of	of	ADP
ejpam-4637	332	20	x	x	SYM
ejpam-4637	332	21	such	such	ADJ
ejpam-4637	332	22	that	that	SCONJ
ejpam-4637	332	23	a(αk	a(αk	PROPN
ejpam-4637	332	24	,	,	PUNCT
ejpam-4637	332	25	βk	βk	NOUN
ejpam-4637	332	26	,	,	PUNCT
ejpam-4637	332	27	γk	γk	NOUN
ejpam-4637	332	28	)	)	PUNCT
ejpam-4637	332	29	=	=	SYM
ejpam-4637	332	30	ak	ak	PROPN
ejpam-4637	332	31	where	where	SCONJ
ejpam-4637	332	32	αk	αk	NOUN
ejpam-4637	332	33	,	,	PUNCT
ejpam-4637	332	34	βk	βk	NOUN
ejpam-4637	332	35	,	,	PUNCT
ejpam-4637	332	36	γk	γk	PROPN
ejpam-4637	332	37	∈	∈	PROPN
ejpam-4637	333	1	[	[	X
ejpam-4637	333	2	0	0	NUM
ejpam-4637	333	3	,	,	PUNCT
ejpam-4637	333	4	1	1	NUM
ejpam-4637	333	5	]	]	PUNCT
ejpam-4637	333	6	for	for	ADP
ejpam-4637	333	7	0	0	NUM
ejpam-4637	333	8	≤	≤	NUM
ejpam-4637	333	9	k	k	PROPN
ejpam-4637	333	10	≤	≤	PROPN
ejpam-4637	333	11	n.	n.	PROPN
ejpam-4637	333	12	a.	a.	PROPN
ejpam-4637	333	13	cano	cano	PROPN
ejpam-4637	333	14	,	,	PUNCT
ejpam-4637	333	15	g.	g.	PROPN
ejpam-4637	333	16	petalcorin	petalcorin	PROPN
ejpam-4637	333	17	/	/	SYM
ejpam-4637	333	18	eur	eur	PROPN
ejpam-4637	333	19	.	.	PUNCT
ejpam-4637	334	1	j.	j.	PROPN
ejpam-4637	334	2	pure	pure	PROPN
ejpam-4637	334	3	appl	appl	PROPN
ejpam-4637	334	4	.	.	PROPN
ejpam-4637	334	5	math	math	PROPN
ejpam-4637	334	6	,	,	PUNCT
ejpam-4637	334	7	16	16	NUM
ejpam-4637	334	8	(	(	PUNCT
ejpam-4637	334	9	1	1	NUM
ejpam-4637	334	10	)	)	PUNCT
ejpam-4637	334	11	(	(	PUNCT
ejpam-4637	334	12	2023	2023	NUM
ejpam-4637	334	13	)	)	PUNCT
ejpam-4637	334	14	,	,	PUNCT
ejpam-4637	334	15	548	548	NUM
ejpam-4637	334	16	-	-	SYM
ejpam-4637	334	17	576	576	NUM
ejpam-4637	334	18	563	563	NUM
ejpam-4637	334	19	proof	proof	NOUN
ejpam-4637	334	20	.	.	PUNCT
ejpam-4637	335	1	let	let	VERB
ejpam-4637	335	2	{	{	PUNCT
ejpam-4637	335	3	αk|k	αk|k	NOUN
ejpam-4637	335	4	=	=	SYM
ejpam-4637	335	5	0	0	NUM
ejpam-4637	335	6	,	,	PUNCT
ejpam-4637	335	7	1	1	NUM
ejpam-4637	335	8	,	,	PUNCT
ejpam-4637	335	9	.	.	PUNCT
ejpam-4637	335	10	.	.	PUNCT
ejpam-4637	336	1	.	.	PUNCT
ejpam-4637	337	1	,	,	PUNCT
ejpam-4637	337	2	n	n	CCONJ
ejpam-4637	337	3	}	}	PUNCT
ejpam-4637	337	4	be	be	AUX
ejpam-4637	337	5	a	a	DET
ejpam-4637	337	6	finite	finite	NOUN
ejpam-4637	337	7	decreasing	decrease	VERB
ejpam-4637	337	8	sequence	sequence	NOUN
ejpam-4637	337	9	and	and	CCONJ
ejpam-4637	337	10	{	{	PUNCT
ejpam-4637	337	11	βk|k	βk|k	PRON
ejpam-4637	338	1	=	=	SYM
ejpam-4637	338	2	0	0	NUM
ejpam-4637	338	3	,	,	PUNCT
ejpam-4637	338	4	1	1	NUM
ejpam-4637	338	5	,	,	PUNCT
ejpam-4637	338	6	.	.	PUNCT
ejpam-4637	338	7	.	.	PUNCT
ejpam-4637	339	1	.	.	PUNCT
ejpam-4637	340	1	,	,	PUNCT
ejpam-4637	340	2	n	n	CCONJ
ejpam-4637	340	3	}	}	PUNCT
ejpam-4637	340	4	,	,	PUNCT
ejpam-4637	340	5	{	{	PUNCT
ejpam-4637	340	6	γk|k	γk|k	ADJ
ejpam-4637	340	7	=	=	SYM
ejpam-4637	340	8	0	0	NUM
ejpam-4637	340	9	,	,	PUNCT
ejpam-4637	340	10	1	1	NUM
ejpam-4637	340	11	,	,	PUNCT
ejpam-4637	340	12	.	.	PUNCT
ejpam-4637	340	13	.	.	PUNCT
ejpam-4637	341	1	.	.	PUNCT
ejpam-4637	342	1	,	,	PUNCT
ejpam-4637	342	2	n	n	CCONJ
ejpam-4637	342	3	}	}	PUNCT
ejpam-4637	342	4	be	be	AUX
ejpam-4637	342	5	finite	finite	ADJ
ejpam-4637	342	6	increasing	increase	VERB
ejpam-4637	342	7	sequences	sequence	NOUN
ejpam-4637	342	8	such	such	ADJ
ejpam-4637	342	9	that	that	DET
ejpam-4637	342	10	αk	αk	NOUN
ejpam-4637	342	11	,	,	PUNCT
ejpam-4637	342	12	βk	βk	NOUN
ejpam-4637	342	13	,	,	PUNCT
ejpam-4637	342	14	γk	γk	PROPN
ejpam-4637	342	15	∈	∈	PROPN
ejpam-4637	343	1	[	[	X
ejpam-4637	343	2	0	0	NUM
ejpam-4637	343	3	,	,	PUNCT
ejpam-4637	343	4	1	1	NUM
ejpam-4637	343	5	]	]	PUNCT
ejpam-4637	343	6	for	for	ADP
ejpam-4637	343	7	1	1	NUM
ejpam-4637	343	8	≤	≤	NUM
ejpam-4637	343	9	k	k	PROPN
ejpam-4637	343	10	≤	≤	PROPN
ejpam-4637	343	11	n.	n.	NOUN
ejpam-4637	343	12	define	define	VERB
ejpam-4637	343	13	a	a	DET
ejpam-4637	343	14	svn	svn	NOUN
ejpam-4637	343	15	set	set	NOUN
ejpam-4637	343	16	a	a	PRON
ejpam-4637	343	17	=	=	X
ejpam-4637	343	18	(	(	PUNCT
ejpam-4637	343	19	ta	ta	PROPN
ejpam-4637	343	20	,	,	PUNCT
ejpam-4637	343	21	ia	ia	PROPN
ejpam-4637	343	22	,	,	PUNCT
ejpam-4637	343	23	fa	fa	NOUN
ejpam-4637	343	24	)	)	PUNCT
ejpam-4637	343	25	in	in	ADP
ejpam-4637	343	26	x	x	PUNCT
ejpam-4637	343	27	by	by	ADP
ejpam-4637	343	28	ta(a0	ta(a0	NOUN
ejpam-4637	343	29	)	)	PUNCT
ejpam-4637	343	30	=	=	SYM
ejpam-4637	344	1	α0	α0	VERB
ejpam-4637	344	2	,	,	PUNCT
ejpam-4637	344	3	ia(a0	ia(a0	NOUN
ejpam-4637	344	4	)	)	PUNCT
ejpam-4637	344	5	=	=	SYM
ejpam-4637	344	6	β0	β0	PROPN
ejpam-4637	344	7	,	,	PUNCT
ejpam-4637	344	8	fa(a0	fa(a0	X
ejpam-4637	344	9	)	)	PUNCT
ejpam-4637	344	10	=	=	VERB
ejpam-4637	345	1	γ0,ta(ak	γ0,ta(ak	NOUN
ejpam-4637	345	2	\	\	PROPN
ejpam-4637	345	3	ak−1	ak−1	PROPN
ejpam-4637	345	4	)	)	PUNCT
ejpam-4637	345	5	=	=	SYM
ejpam-4637	346	1	αk	αk	NOUN
ejpam-4637	346	2	,	,	PUNCT
ejpam-4637	346	3	ia(ak	ia(ak	PROPN
ejpam-4637	346	4	\	\	PROPN
ejpam-4637	346	5	ak−1	ak−1	PROPN
ejpam-4637	346	6	)	)	PUNCT
ejpam-4637	346	7	=	=	PUNCT
ejpam-4637	347	1	βk	βk	NOUN
ejpam-4637	347	2	,	,	PUNCT
ejpam-4637	347	3	and	and	CCONJ
ejpam-4637	347	4	fa(ak	fa(ak	VERB
ejpam-4637	347	5	\	\	PROPN
ejpam-4637	347	6	ak−1	ak−1	PROPN
ejpam-4637	347	7	)	)	PUNCT
ejpam-4637	347	8	=	=	SYM
ejpam-4637	347	9	γk	γk	NOUN
ejpam-4637	347	10	for	for	ADP
ejpam-4637	347	11	1	1	NUM
ejpam-4637	347	12	≤	≤	NUM
ejpam-4637	347	13	k	k	PROPN
ejpam-4637	347	14	≤	≤	PROPN
ejpam-4637	347	15	n.	n.	NOUN
ejpam-4637	347	16	we	we	PRON
ejpam-4637	347	17	will	will	AUX
ejpam-4637	347	18	show	show	VERB
ejpam-4637	347	19	that	that	SCONJ
ejpam-4637	347	20	a	a	PRON
ejpam-4637	347	21	is	be	AUX
ejpam-4637	347	22	a	a	DET
ejpam-4637	347	23	svn	svn	NOUN
ejpam-4637	347	24	hyper	hyper	NOUN
ejpam-4637	347	25	up	up	ADP
ejpam-4637	347	26	-subalgebra	-subalgebra	NOUN
ejpam-4637	347	27	of	of	ADP
ejpam-4637	347	28	x.	x.	NOUN
ejpam-4637	347	29	let	let	VERB
ejpam-4637	347	30	a	a	DET
ejpam-4637	347	31	,	,	PUNCT
ejpam-4637	347	32	b	b	X
ejpam-4637	347	33	∈	∈	PROPN
ejpam-4637	347	34	x.	x.	NOUN
ejpam-4637	347	35	consider	consider	VERB
ejpam-4637	347	36	the	the	DET
ejpam-4637	347	37	following	follow	VERB
ejpam-4637	347	38	cases	case	NOUN
ejpam-4637	347	39	:	:	PUNCT
ejpam-4637	347	40	case	case	NOUN
ejpam-4637	347	41	1	1	NUM
ejpam-4637	347	42	.	.	PUNCT
ejpam-4637	347	43	a	a	DET
ejpam-4637	347	44	,	,	PUNCT
ejpam-4637	347	45	b	b	PROPN
ejpam-4637	347	46	∈	∈	PROPN
ejpam-4637	347	47	ak	ak	PROPN
ejpam-4637	347	48	\ak−1	\ak−1	PROPN
ejpam-4637	347	49	then	then	ADV
ejpam-4637	347	50	ta(a	ta(a	NUM
ejpam-4637	347	51	)	)	PUNCT
ejpam-4637	348	1	=	=	SYM
ejpam-4637	348	2	αk	αk	NOUN
ejpam-4637	348	3	=	=	NOUN
ejpam-4637	348	4	ta(b	ta(b	NUM
ejpam-4637	348	5	)	)	PUNCT
ejpam-4637	348	6	,	,	PUNCT
ejpam-4637	348	7	ia(a	ia(a	NOUN
ejpam-4637	348	8	)	)	PUNCT
ejpam-4637	349	1	=	=	SYM
ejpam-4637	349	2	βk	βk	NOUN
ejpam-4637	349	3	=	=	SYM
ejpam-4637	349	4	ia(b	ia(b	NUM
ejpam-4637	349	5	)	)	PUNCT
ejpam-4637	349	6	,	,	PUNCT
ejpam-4637	349	7	and	and	CCONJ
ejpam-4637	349	8	fa(a	fa(a	NUM
ejpam-4637	349	9	)	)	PUNCT
ejpam-4637	349	10	=	=	SYM
ejpam-4637	349	11	γk	γk	NOUN
ejpam-4637	349	12	=	=	SYM
ejpam-4637	349	13	fa(b	fa(b	NUM
ejpam-4637	349	14	)	)	PUNCT
ejpam-4637	349	15	.	.	PUNCT
ejpam-4637	350	1	since	since	SCONJ
ejpam-4637	350	2	ak	ak	PROPN
ejpam-4637	350	3	is	be	AUX
ejpam-4637	350	4	a	a	DET
ejpam-4637	350	5	hyper	hyper	ADJ
ejpam-4637	350	6	up	up	ADP
ejpam-4637	350	7	-subalgebra	-subalgebra	NOUN
ejpam-4637	350	8	of	of	ADP
ejpam-4637	350	9	x	x	NOUN
ejpam-4637	350	10	,	,	PUNCT
ejpam-4637	350	11	a	a	DET
ejpam-4637	350	12	◦	◦	NOUN
ejpam-4637	350	13	b	b	NOUN
ejpam-4637	350	14	⊆	⊆	NUM
ejpam-4637	350	15	ak	ak	PROPN
ejpam-4637	350	16	.	.	PROPN
ejpam-4637	350	17	subcase	subcase	PROPN
ejpam-4637	350	18	1.1	1.1	NUM
ejpam-4637	350	19	.	.	PUNCT
ejpam-4637	351	1	a	a	DET
ejpam-4637	351	2	◦	◦	NOUN
ejpam-4637	351	3	b	b	NOUN
ejpam-4637	351	4	⊆	⊆	NUM
ejpam-4637	351	5	ak	ak	PROPN
ejpam-4637	351	6	\ak−1	\ak−1	PROPN
ejpam-4637	351	7	∗ta(a	∗ta(a	PROPN
ejpam-4637	351	8	◦	◦	NOUN
ejpam-4637	351	9	b	b	NOUN
ejpam-4637	351	10	)	)	PUNCT
ejpam-4637	352	1	=	=	PRON
ejpam-4637	352	2	αk	αk	CCONJ
ejpam-4637	352	3	≥	≥	NOUN
ejpam-4637	352	4	αk	αk	NOUN
ejpam-4637	352	5	=	=	SYM
ejpam-4637	352	6	min{ta(a	min{ta(a	PROPN
ejpam-4637	352	7	)	)	PUNCT
ejpam-4637	352	8	,	,	PUNCT
ejpam-4637	352	9	ta(b	ta(b	NUM
ejpam-4637	352	10	)	)	PUNCT
ejpam-4637	352	11	}	}	PUNCT
ejpam-4637	352	12	,	,	PUNCT
ejpam-4637	352	13	∗ia(a	∗ia(a	ADP
ejpam-4637	352	14	◦	◦	NOUN
ejpam-4637	352	15	b	b	X
ejpam-4637	352	16	)	)	PUNCT
ejpam-4637	352	17	=	=	VERB
ejpam-4637	352	18	βk	βk	VERB
ejpam-4637	352	19	≤	≤	NUM
ejpam-4637	352	20	βk	βk	ADP
ejpam-4637	352	21	=	=	PROPN
ejpam-4637	352	22	max{ia(a	max{ia(a	PROPN
ejpam-4637	352	23	)	)	PUNCT
ejpam-4637	352	24	,	,	PUNCT
ejpam-4637	352	25	ia(b	ia(b	NUM
ejpam-4637	352	26	)	)	PUNCT
ejpam-4637	352	27	}	}	PUNCT
ejpam-4637	352	28	,	,	PUNCT
ejpam-4637	352	29	and	and	CCONJ
ejpam-4637	352	30	∗fa(a	∗fa(a	PROPN
ejpam-4637	352	31	◦	◦	NOUN
ejpam-4637	352	32	b	b	X
ejpam-4637	352	33	)	)	PUNCT
ejpam-4637	352	34	=	=	SYM
ejpam-4637	352	35	γk	γk	PROPN
ejpam-4637	352	36	≤	≤	NUM
ejpam-4637	352	37	γk	γk	X
ejpam-4637	352	38	=	=	PUNCT
ejpam-4637	352	39	max{fa(a),fa(b	max{fa(a),fa(b	NOUN
ejpam-4637	352	40	)	)	PUNCT
ejpam-4637	352	41	}	}	PUNCT
ejpam-4637	352	42	.	.	PUNCT
ejpam-4637	353	1	subcase	subcase	PROPN
ejpam-4637	353	2	1.2	1.2	NUM
ejpam-4637	353	3	.	.	PUNCT
ejpam-4637	354	1	a	a	DET
ejpam-4637	354	2	◦	◦	NOUN
ejpam-4637	354	3	b	b	NUM
ejpam-4637	354	4	⊆	⊆	NUM
ejpam-4637	354	5	ak−1	ak−1	NOUN
ejpam-4637	354	6	for	for	ADP
ejpam-4637	354	7	some	some	DET
ejpam-4637	354	8	r	r	NOUN
ejpam-4637	354	9	∈	∈	NOUN
ejpam-4637	355	1	[	[	X
ejpam-4637	355	2	0	0	NUM
ejpam-4637	355	3	,	,	PUNCT
ejpam-4637	355	4	k	k	PROPN
ejpam-4637	355	5	−	−	PROPN
ejpam-4637	355	6	1	1	NUM
ejpam-4637	355	7	]	]	PUNCT
ejpam-4637	355	8	,	,	PUNCT
ejpam-4637	355	9	we	we	PRON
ejpam-4637	355	10	have	have	VERB
ejpam-4637	355	11	∗ta(a	∗ta(a	ADJ
ejpam-4637	355	12	◦	◦	NOUN
ejpam-4637	355	13	b	b	NOUN
ejpam-4637	355	14	)	)	PUNCT
ejpam-4637	355	15	=	=	SYM
ejpam-4637	355	16	αk−1−r	αk−1−r	NUM
ejpam-4637	355	17	≥	≥	NOUN
ejpam-4637	355	18	αk	αk	NOUN
ejpam-4637	355	19	=	=	SYM
ejpam-4637	355	20	min{ta(a	min{ta(a	PROPN
ejpam-4637	355	21	)	)	PUNCT
ejpam-4637	355	22	,	,	PUNCT
ejpam-4637	355	23	ta(b	ta(b	NUM
ejpam-4637	355	24	)	)	PUNCT
ejpam-4637	355	25	}	}	PUNCT
ejpam-4637	355	26	,	,	PUNCT
ejpam-4637	355	27	∗ia(a	∗ia(a	ADP
ejpam-4637	355	28	◦	◦	NOUN
ejpam-4637	355	29	b	b	X
ejpam-4637	355	30	)	)	PUNCT
ejpam-4637	355	31	=	=	NOUN
ejpam-4637	355	32	βk−1−r	βk−1−r	PUNCT
ejpam-4637	355	33	≤	≤	NUM
ejpam-4637	355	34	βk	βk	ADP
ejpam-4637	355	35	=	=	PROPN
ejpam-4637	355	36	max{ia(a	max{ia(a	PROPN
ejpam-4637	355	37	)	)	PUNCT
ejpam-4637	355	38	,	,	PUNCT
ejpam-4637	355	39	ia(b	ia(b	NUM
ejpam-4637	355	40	)	)	PUNCT
ejpam-4637	355	41	}	}	PUNCT
ejpam-4637	355	42	,	,	PUNCT
ejpam-4637	355	43	and	and	CCONJ
ejpam-4637	355	44	∗fa(a	∗fa(a	PROPN
ejpam-4637	355	45	◦	◦	NOUN
ejpam-4637	355	46	b	b	X
ejpam-4637	355	47	)	)	PUNCT
ejpam-4637	355	48	=	=	PRON
ejpam-4637	355	49	γk−1−r	γk−1−r	VERB
ejpam-4637	355	50	≤	≤	NUM
ejpam-4637	355	51	γk	γk	NOUN
ejpam-4637	355	52	=	=	PUNCT
ejpam-4637	355	53	max{fa(a),fa(b	max{fa(a),fa(b	NOUN
ejpam-4637	355	54	)	)	PUNCT
ejpam-4637	355	55	}	}	PUNCT
ejpam-4637	355	56	.	.	PUNCT
ejpam-4637	356	1	subcase	subcase	PROPN
ejpam-4637	356	2	1.3	1.3	NUM
ejpam-4637	356	3	.	.	PUNCT
ejpam-4637	357	1	a	a	DET
ejpam-4637	357	2	◦	◦	NOUN
ejpam-4637	357	3	b	b	NOUN
ejpam-4637	357	4	=	=	SYM
ejpam-4637	358	1	[	[	X
ejpam-4637	358	2	(	(	PUNCT
ejpam-4637	358	3	a	a	DET
ejpam-4637	358	4	◦	◦	NOUN
ejpam-4637	358	5	b)∩(ak\ak−1)]∪[(a	b)∩(ak\ak−1)]∪[(a	NOUN
ejpam-4637	358	6	◦	◦	NOUN
ejpam-4637	358	7	b)∩ak−1	b)∩ak−1	NOUN
ejpam-4637	358	8	]	]	PUNCT
ejpam-4637	358	9	where	where	SCONJ
ejpam-4637	358	10	(	(	PUNCT
ejpam-4637	358	11	a	a	DET
ejpam-4637	358	12	◦	◦	NOUN
ejpam-4637	358	13	b)∩(ak\ak−1	b)∩(ak\ak−1	ADJ
ejpam-4637	358	14	)	)	PUNCT
ejpam-4637	358	15	̸=	̸=	NOUN
ejpam-4637	358	16	∅	∅	NOUN
ejpam-4637	358	17	and	and	CCONJ
ejpam-4637	358	18	(	(	PUNCT
ejpam-4637	358	19	a	a	DET
ejpam-4637	358	20	◦	◦	NOUN
ejpam-4637	358	21	b	b	NOUN
ejpam-4637	358	22	)	)	PUNCT
ejpam-4637	358	23	∩ak−1	∩ak−1	PROPN
ejpam-4637	358	24	̸=	̸=	PROPN
ejpam-4637	358	25	∅	∅	VERB
ejpam-4637	358	26	∗ta(a	∗ta(a	ADJ
ejpam-4637	358	27	◦	◦	NOUN
ejpam-4637	358	28	b	b	X
ejpam-4637	358	29	)	)	PUNCT
ejpam-4637	358	30	=	=	PRON
ejpam-4637	359	1	αk	αk	CCONJ
ejpam-4637	359	2	≥	≥	NOUN
ejpam-4637	359	3	αk	αk	NOUN
ejpam-4637	359	4	=	=	SYM
ejpam-4637	359	5	min{ta(a	min{ta(a	PROPN
ejpam-4637	359	6	)	)	PUNCT
ejpam-4637	359	7	,	,	PUNCT
ejpam-4637	359	8	ta(b	ta(b	NUM
ejpam-4637	359	9	)	)	PUNCT
ejpam-4637	359	10	}	}	PUNCT
ejpam-4637	359	11	,	,	PUNCT
ejpam-4637	359	12	∗ia(a	∗ia(a	ADP
ejpam-4637	359	13	◦	◦	NOUN
ejpam-4637	359	14	b	b	X
ejpam-4637	359	15	)	)	PUNCT
ejpam-4637	359	16	=	=	VERB
ejpam-4637	359	17	βk	βk	VERB
ejpam-4637	359	18	≤	≤	NUM
ejpam-4637	359	19	βk	βk	ADP
ejpam-4637	359	20	=	=	PROPN
ejpam-4637	359	21	max{ia(a	max{ia(a	PROPN
ejpam-4637	359	22	)	)	PUNCT
ejpam-4637	359	23	,	,	PUNCT
ejpam-4637	359	24	ia(b	ia(b	NUM
ejpam-4637	359	25	)	)	PUNCT
ejpam-4637	359	26	}	}	PUNCT
ejpam-4637	359	27	,	,	PUNCT
ejpam-4637	359	28	and	and	CCONJ
ejpam-4637	359	29	∗fa(a	∗fa(a	PROPN
ejpam-4637	359	30	◦	◦	NOUN
ejpam-4637	359	31	b	b	X
ejpam-4637	359	32	)	)	PUNCT
ejpam-4637	359	33	=	=	SYM
ejpam-4637	359	34	γk	γk	PROPN
ejpam-4637	359	35	≤	≤	NUM
ejpam-4637	359	36	γk	γk	X
ejpam-4637	359	37	=	=	PUNCT
ejpam-4637	359	38	max{fa(a),fa(b	max{fa(a),fa(b	NOUN
ejpam-4637	359	39	)	)	PUNCT
ejpam-4637	359	40	}	}	PUNCT
ejpam-4637	359	41	.	.	PUNCT
ejpam-4637	360	1	case	case	NOUN
ejpam-4637	360	2	2	2	NUM
ejpam-4637	360	3	.	.	PUNCT
ejpam-4637	361	1	a	a	DET
ejpam-4637	361	2	∈	∈	NOUN
ejpam-4637	361	3	ai	ai	VERB
ejpam-4637	361	4	\ai−1	\ai−1	PROPN
ejpam-4637	361	5	and	and	CCONJ
ejpam-4637	361	6	b	b	PROPN
ejpam-4637	361	7	∈	∈	PROPN
ejpam-4637	361	8	aj	aj	PROPN
ejpam-4637	361	9	\aj−1	\aj−1	PROPN
ejpam-4637	361	10	for	for	ADP
ejpam-4637	361	11	i	i	PRON
ejpam-4637	361	12	>	>	X
ejpam-4637	361	13	j	j	PROPN
ejpam-4637	361	14	>	>	X
ejpam-4637	361	15	0	0	PUNCT
ejpam-4637	362	1	then	then	ADV
ejpam-4637	362	2	ta(a	ta(a	NUM
ejpam-4637	362	3	)	)	PUNCT
ejpam-4637	363	1	=	=	SYM
ejpam-4637	363	2	αi	αi	NOUN
ejpam-4637	363	3	,	,	PUNCT
ejpam-4637	363	4	ta(b	ta(b	NUM
ejpam-4637	363	5	)	)	PUNCT
ejpam-4637	363	6	=	=	SYM
ejpam-4637	363	7	αj	αj	PROPN
ejpam-4637	363	8	,	,	PUNCT
ejpam-4637	363	9	ia(a	ia(a	NOUN
ejpam-4637	363	10	)	)	PUNCT
ejpam-4637	363	11	=	=	SYM
ejpam-4637	363	12	βi	βi	PROPN
ejpam-4637	363	13	,	,	PUNCT
ejpam-4637	363	14	ia(b	ia(b	NUM
ejpam-4637	363	15	)	)	PUNCT
ejpam-4637	363	16	=	=	SYM
ejpam-4637	363	17	βj	βj	PROPN
ejpam-4637	363	18	,	,	PUNCT
ejpam-4637	363	19	fa(a	fa(a	PROPN
ejpam-4637	363	20	)	)	PUNCT
ejpam-4637	363	21	=	=	SYM
ejpam-4637	363	22	γi	γi	NOUN
ejpam-4637	363	23	,	,	PUNCT
ejpam-4637	363	24	and	and	CCONJ
ejpam-4637	363	25	fa(b	fa(b	NOUN
ejpam-4637	363	26	)	)	PUNCT
ejpam-4637	363	27	=	=	SYM
ejpam-4637	363	28	γj	γj	PROPN
ejpam-4637	363	29	.	.	PUNCT
ejpam-4637	364	1	since	since	SCONJ
ejpam-4637	364	2	ai	ai	NOUN
ejpam-4637	364	3	is	be	AUX
ejpam-4637	364	4	a	a	DET
ejpam-4637	364	5	hyper	hyper	ADJ
ejpam-4637	364	6	up	up	ADP
ejpam-4637	364	7	-subalgebra	-subalgebra	NOUN
ejpam-4637	364	8	of	of	ADP
ejpam-4637	364	9	x	x	PUNCT
ejpam-4637	364	10	and	and	CCONJ
ejpam-4637	364	11	aj	aj	PROPN
ejpam-4637	364	12	⊂	⊂	PROPN
ejpam-4637	364	13	ai	ai	VERB
ejpam-4637	364	14	,	,	PUNCT
ejpam-4637	364	15	we	we	PRON
ejpam-4637	364	16	have	have	VERB
ejpam-4637	364	17	a	a	DET
ejpam-4637	364	18	◦	◦	NOUN
ejpam-4637	364	19	b	b	NOUN
ejpam-4637	364	20	⊆	⊆	NUM
ejpam-4637	364	21	ai	ai	NOUN
ejpam-4637	364	22	.	.	PROPN
ejpam-4637	364	23	subcase	subcase	PROPN
ejpam-4637	364	24	2.1	2.1	NUM
ejpam-4637	364	25	.	.	PUNCT
ejpam-4637	365	1	a	a	DET
ejpam-4637	365	2	◦	◦	NOUN
ejpam-4637	365	3	b	b	SYM
ejpam-4637	365	4	⊆	⊆	NUM
ejpam-4637	365	5	ai	ai	ADJ
ejpam-4637	365	6	\aj	\aj	NOUN
ejpam-4637	365	7	for	for	ADP
ejpam-4637	365	8	some	some	DET
ejpam-4637	365	9	r	r	NOUN
ejpam-4637	365	10	∈	∈	NOUN
ejpam-4637	366	1	[	[	X
ejpam-4637	366	2	0	0	NUM
ejpam-4637	366	3	,	,	PUNCT
ejpam-4637	366	4	i−	i−	PROPN
ejpam-4637	366	5	j	j	PROPN
ejpam-4637	366	6	−	−	PROPN
ejpam-4637	366	7	1	1	NUM
ejpam-4637	366	8	]	]	PUNCT
ejpam-4637	366	9	,	,	PUNCT
ejpam-4637	366	10	we	we	PRON
ejpam-4637	366	11	have	have	VERB
ejpam-4637	366	12	∗ta(a	∗ta(a	ADJ
ejpam-4637	366	13	◦	◦	NOUN
ejpam-4637	366	14	b	b	NOUN
ejpam-4637	366	15	)	)	PUNCT
ejpam-4637	366	16	=	=	SYM
ejpam-4637	366	17	αi−r	αi−r	NOUN
ejpam-4637	366	18	≥	≥	NOUN
ejpam-4637	366	19	αi	αi	PART
ejpam-4637	366	20	=	=	SYM
ejpam-4637	366	21	min{ta(a	min{ta(a	PROPN
ejpam-4637	366	22	)	)	PUNCT
ejpam-4637	366	23	,	,	PUNCT
ejpam-4637	366	24	ta(b	ta(b	NUM
ejpam-4637	366	25	)	)	PUNCT
ejpam-4637	366	26	}	}	PUNCT
ejpam-4637	366	27	,	,	PUNCT
ejpam-4637	366	28	a.	a.	PROPN
ejpam-4637	366	29	cano	cano	PROPN
ejpam-4637	366	30	,	,	PUNCT
ejpam-4637	366	31	g.	g.	PROPN
ejpam-4637	366	32	petalcorin	petalcorin	PROPN
ejpam-4637	366	33	/	/	SYM
ejpam-4637	366	34	eur	eur	PROPN
ejpam-4637	366	35	.	.	PUNCT
ejpam-4637	367	1	j.	j.	PROPN
ejpam-4637	367	2	pure	pure	PROPN
ejpam-4637	367	3	appl	appl	PROPN
ejpam-4637	367	4	.	.	PROPN
ejpam-4637	367	5	math	math	PROPN
ejpam-4637	367	6	,	,	PUNCT
ejpam-4637	367	7	16	16	NUM
ejpam-4637	367	8	(	(	PUNCT
ejpam-4637	367	9	1	1	NUM
ejpam-4637	367	10	)	)	PUNCT
ejpam-4637	367	11	(	(	PUNCT
ejpam-4637	367	12	2023	2023	NUM
ejpam-4637	367	13	)	)	PUNCT
ejpam-4637	367	14	,	,	PUNCT
ejpam-4637	367	15	548	548	NUM
ejpam-4637	367	16	-	-	SYM
ejpam-4637	367	17	576	576	NUM
ejpam-4637	367	18	564	564	NUM
ejpam-4637	367	19	∗ia(a	∗ia(a	ADP
ejpam-4637	367	20	◦	◦	NOUN
ejpam-4637	367	21	b	b	NOUN
ejpam-4637	367	22	)	)	PUNCT
ejpam-4637	367	23	=	=	PUNCT
ejpam-4637	367	24	βi−r	βi−r	NOUN
ejpam-4637	367	25	≤	≤	NUM
ejpam-4637	367	26	βi	βi	X
ejpam-4637	367	27	=	=	SYM
ejpam-4637	367	28	max{ia(a	max{ia(a	PROPN
ejpam-4637	367	29	)	)	PUNCT
ejpam-4637	367	30	,	,	PUNCT
ejpam-4637	367	31	ia(b	ia(b	NUM
ejpam-4637	367	32	)	)	PUNCT
ejpam-4637	367	33	}	}	PUNCT
ejpam-4637	367	34	,	,	PUNCT
ejpam-4637	367	35	and	and	CCONJ
ejpam-4637	367	36	∗fa(a	∗fa(a	PROPN
ejpam-4637	367	37	◦	◦	NOUN
ejpam-4637	367	38	b	b	X
ejpam-4637	367	39	)	)	PUNCT
ejpam-4637	367	40	=	=	PUNCT
ejpam-4637	368	1	γi−r	γi−r	PROPN
ejpam-4637	368	2	≤	≤	NUM
ejpam-4637	368	3	γi	γi	NOUN
ejpam-4637	368	4	=	=	PUNCT
ejpam-4637	368	5	max{fa(a),fa(b	max{fa(a),fa(b	NOUN
ejpam-4637	368	6	)	)	PUNCT
ejpam-4637	368	7	}	}	PUNCT
ejpam-4637	368	8	.	.	PUNCT
ejpam-4637	369	1	subcase	subcase	PROPN
ejpam-4637	369	2	2.2	2.2	NUM
ejpam-4637	369	3	.	.	PUNCT
ejpam-4637	370	1	a	a	DET
ejpam-4637	370	2	◦	◦	NOUN
ejpam-4637	370	3	b	b	NOUN
ejpam-4637	370	4	⊆	⊆	NUM
ejpam-4637	370	5	aj	aj	PROPN
ejpam-4637	370	6	for	for	ADP
ejpam-4637	370	7	some	some	DET
ejpam-4637	370	8	r	r	NOUN
ejpam-4637	370	9	∈	∈	NOUN
ejpam-4637	370	10	[	[	X
ejpam-4637	370	11	0	0	NUM
ejpam-4637	370	12	,	,	PUNCT
ejpam-4637	370	13	j	j	PROPN
ejpam-4637	370	14	]	]	X
ejpam-4637	370	15	,	,	PUNCT
ejpam-4637	370	16	we	we	PRON
ejpam-4637	370	17	have	have	VERB
ejpam-4637	370	18	∗ta(a	∗ta(a	ADJ
ejpam-4637	370	19	◦	◦	NOUN
ejpam-4637	370	20	b	b	NOUN
ejpam-4637	370	21	)	)	PUNCT
ejpam-4637	370	22	=	=	SYM
ejpam-4637	370	23	αj−r	αj−r	PROPN
ejpam-4637	370	24	≥	≥	NOUN
ejpam-4637	370	25	αi	αi	NOUN
ejpam-4637	370	26	=	=	SYM
ejpam-4637	370	27	min{ta(a	min{ta(a	PROPN
ejpam-4637	370	28	)	)	PUNCT
ejpam-4637	370	29	,	,	PUNCT
ejpam-4637	370	30	ta(b	ta(b	NUM
ejpam-4637	370	31	)	)	PUNCT
ejpam-4637	370	32	}	}	PUNCT
ejpam-4637	370	33	,	,	PUNCT
ejpam-4637	370	34	∗ia(a	∗ia(a	ADP
ejpam-4637	370	35	◦	◦	NOUN
ejpam-4637	370	36	b	b	X
ejpam-4637	370	37	)	)	PUNCT
ejpam-4637	371	1	=	=	SYM
ejpam-4637	371	2	βj−r	βj−r	PROPN
ejpam-4637	371	3	≤	≤	X
ejpam-4637	371	4	βi	βi	PROPN
ejpam-4637	371	5	=	=	SYM
ejpam-4637	371	6	max{ia(a	max{ia(a	PROPN
ejpam-4637	371	7	)	)	PUNCT
ejpam-4637	371	8	,	,	PUNCT
ejpam-4637	371	9	ia(b	ia(b	NUM
ejpam-4637	371	10	)	)	PUNCT
ejpam-4637	371	11	}	}	PUNCT
ejpam-4637	371	12	,	,	PUNCT
ejpam-4637	371	13	and	and	CCONJ
ejpam-4637	371	14	∗fa(a	∗fa(a	PROPN
ejpam-4637	371	15	◦	◦	NOUN
ejpam-4637	371	16	b	b	NUM
ejpam-4637	371	17	)	)	PUNCT
ejpam-4637	371	18	=	=	SYM
ejpam-4637	371	19	γj−r	γj−r	NOUN
ejpam-4637	371	20	≤	≤	NOUN
ejpam-4637	372	1	γi	γi	NOUN
ejpam-4637	372	2	=	=	SYM
ejpam-4637	372	3	max{fa(a),fa(b	max{fa(a),fa(b	NOUN
ejpam-4637	372	4	)	)	PUNCT
ejpam-4637	372	5	}	}	PUNCT
ejpam-4637	372	6	.	.	PUNCT
ejpam-4637	373	1	subcase	subcase	PROPN
ejpam-4637	373	2	2.3	2.3	NUM
ejpam-4637	373	3	.	.	PUNCT
ejpam-4637	374	1	a	a	DET
ejpam-4637	374	2	◦	◦	NOUN
ejpam-4637	374	3	b	b	NOUN
ejpam-4637	374	4	=	=	SYM
ejpam-4637	375	1	[	[	X
ejpam-4637	375	2	(	(	PUNCT
ejpam-4637	375	3	a	a	DET
ejpam-4637	375	4	◦	◦	NOUN
ejpam-4637	375	5	b	b	NOUN
ejpam-4637	375	6	)	)	PUNCT
ejpam-4637	375	7	∩	∩	NOUN
ejpam-4637	375	8	(	(	PUNCT
ejpam-4637	375	9	ai	ai	PROPN
ejpam-4637	375	10	\aj	\aj	PROPN
ejpam-4637	375	11	)	)	PUNCT
ejpam-4637	375	12	]	]	PUNCT
ejpam-4637	375	13	∪	∪	X
ejpam-4637	375	14	[	[	X
ejpam-4637	375	15	(	(	PUNCT
ejpam-4637	375	16	a	a	DET
ejpam-4637	375	17	◦	◦	NOUN
ejpam-4637	375	18	b	b	NOUN
ejpam-4637	375	19	)	)	PUNCT
ejpam-4637	375	20	∩aj	∩aj	NOUN
ejpam-4637	375	21	]	]	PUNCT
ejpam-4637	375	22	where	where	SCONJ
ejpam-4637	375	23	(	(	PUNCT
ejpam-4637	375	24	a	a	DET
ejpam-4637	375	25	◦	◦	NOUN
ejpam-4637	375	26	b	b	NOUN
ejpam-4637	375	27	)	)	PUNCT
ejpam-4637	375	28	∩	∩	NOUN
ejpam-4637	375	29	(	(	PUNCT
ejpam-4637	375	30	ai	ai	PROPN
ejpam-4637	375	31	\aj	\aj	PROPN
ejpam-4637	375	32	)	)	PUNCT
ejpam-4637	375	33	̸=	̸=	PROPN
ejpam-4637	375	34	∅	∅	NOUN
ejpam-4637	375	35	and	and	CCONJ
ejpam-4637	375	36	(	(	PUNCT
ejpam-4637	375	37	a	a	DET
ejpam-4637	375	38	◦	◦	NOUN
ejpam-4637	375	39	b	b	NOUN
ejpam-4637	375	40	)	)	PUNCT
ejpam-4637	375	41	∩aj	∩aj	NOUN
ejpam-4637	375	42	̸=	̸=	PROPN
ejpam-4637	375	43	∅	∅	NOUN
ejpam-4637	375	44	for	for	ADP
ejpam-4637	375	45	some	some	DET
ejpam-4637	375	46	r	r	NOUN
ejpam-4637	375	47	∈	∈	NOUN
ejpam-4637	376	1	[	[	X
ejpam-4637	376	2	0	0	NUM
ejpam-4637	376	3	,	,	PUNCT
ejpam-4637	376	4	i−	i−	PROPN
ejpam-4637	376	5	j	j	PROPN
ejpam-4637	376	6	−	−	PROPN
ejpam-4637	376	7	1	1	NUM
ejpam-4637	376	8	]	]	PUNCT
ejpam-4637	376	9	,	,	PUNCT
ejpam-4637	376	10	we	we	PRON
ejpam-4637	376	11	have	have	VERB
ejpam-4637	376	12	∗ta(a	∗ta(a	ADJ
ejpam-4637	376	13	◦	◦	NOUN
ejpam-4637	376	14	b	b	NOUN
ejpam-4637	376	15	)	)	PUNCT
ejpam-4637	376	16	=	=	SYM
ejpam-4637	376	17	αi−r	αi−r	NOUN
ejpam-4637	376	18	≥	≥	NOUN
ejpam-4637	376	19	αi	αi	PART
ejpam-4637	376	20	=	=	SYM
ejpam-4637	376	21	min{ta(a	min{ta(a	PROPN
ejpam-4637	376	22	)	)	PUNCT
ejpam-4637	376	23	,	,	PUNCT
ejpam-4637	376	24	ta(b	ta(b	NUM
ejpam-4637	376	25	)	)	PUNCT
ejpam-4637	376	26	}	}	PUNCT
ejpam-4637	376	27	,	,	PUNCT
ejpam-4637	376	28	∗ia(a	∗ia(a	ADP
ejpam-4637	376	29	◦	◦	NOUN
ejpam-4637	376	30	b	b	X
ejpam-4637	376	31	)	)	PUNCT
ejpam-4637	376	32	=	=	PUNCT
ejpam-4637	376	33	βi−r	βi−r	NOUN
ejpam-4637	376	34	≤	≤	NUM
ejpam-4637	376	35	βi	βi	X
ejpam-4637	376	36	=	=	SYM
ejpam-4637	376	37	max{ia(a	max{ia(a	PROPN
ejpam-4637	376	38	)	)	PUNCT
ejpam-4637	376	39	,	,	PUNCT
ejpam-4637	376	40	ia(b	ia(b	NUM
ejpam-4637	376	41	)	)	PUNCT
ejpam-4637	376	42	}	}	PUNCT
ejpam-4637	376	43	,	,	PUNCT
ejpam-4637	376	44	and	and	CCONJ
ejpam-4637	376	45	∗fa(a	∗fa(a	PROPN
ejpam-4637	376	46	◦	◦	NOUN
ejpam-4637	376	47	b	b	X
ejpam-4637	376	48	)	)	PUNCT
ejpam-4637	376	49	=	=	PUNCT
ejpam-4637	377	1	γi−r	γi−r	PROPN
ejpam-4637	377	2	≤	≤	NUM
ejpam-4637	377	3	γi	γi	NOUN
ejpam-4637	377	4	=	=	PUNCT
ejpam-4637	377	5	max{fa(a),fa(b	max{fa(a),fa(b	NOUN
ejpam-4637	377	6	)	)	PUNCT
ejpam-4637	377	7	}	}	PUNCT
ejpam-4637	377	8	.	.	PUNCT
ejpam-4637	378	1	thus	thus	ADV
ejpam-4637	378	2	,	,	PUNCT
ejpam-4637	378	3	a	a	PRON
ejpam-4637	378	4	is	be	AUX
ejpam-4637	378	5	a	a	DET
ejpam-4637	378	6	svn	svn	NOUN
ejpam-4637	378	7	hyper	hyper	NOUN
ejpam-4637	378	8	up	up	ADP
ejpam-4637	378	9	-subalgebra	-subalgebra	NOUN
ejpam-4637	378	10	of	of	ADP
ejpam-4637	378	11	x.	x.	NOUN
ejpam-4637	378	12	furthermore	furthermore	ADV
ejpam-4637	378	13	,	,	PUNCT
ejpam-4637	378	14	note	note	VERB
ejpam-4637	378	15	that	that	SCONJ
ejpam-4637	378	16	tα0	tα0	VERB
ejpam-4637	378	17	a	a	PRON
ejpam-4637	378	18	=	=	X
ejpam-4637	378	19	{	{	PUNCT
ejpam-4637	378	20	s	s	NOUN
ejpam-4637	378	21	∈	∈	NOUN
ejpam-4637	378	22	x|ta(s	x|ta(s	NOUN
ejpam-4637	378	23	)	)	PUNCT
ejpam-4637	378	24	≥	≥	NOUN
ejpam-4637	378	25	α0	α0	VERB
ejpam-4637	378	26	}	}	PUNCT
ejpam-4637	378	27	=	=	SYM
ejpam-4637	378	28	a0	a0	NOUN
ejpam-4637	378	29	,	,	PUNCT
ejpam-4637	378	30	iβ0	iβ0	ADP
ejpam-4637	378	31	a	a	DET
ejpam-4637	378	32	=	=	X
ejpam-4637	378	33	{	{	PUNCT
ejpam-4637	378	34	s	s	NOUN
ejpam-4637	378	35	∈	∈	PROPN
ejpam-4637	378	36	x|ia(s	x|ia(s	NOUN
ejpam-4637	378	37	)	)	PUNCT
ejpam-4637	378	38	≤	≤	NUM
ejpam-4637	378	39	β0	β0	NOUN
ejpam-4637	378	40	}	}	PUNCT
ejpam-4637	378	41	=	=	SYM
ejpam-4637	378	42	a0	a0	PROPN
ejpam-4637	378	43	,	,	PUNCT
ejpam-4637	378	44	and	and	CCONJ
ejpam-4637	378	45	f	f	PROPN
ejpam-4637	378	46	γ0	γ0	NOUN
ejpam-4637	378	47	a	a	PRON
ejpam-4637	378	48	=	=	X
ejpam-4637	378	49	{	{	PUNCT
ejpam-4637	378	50	s	s	NOUN
ejpam-4637	378	51	∈	∈	NOUN
ejpam-4637	378	52	x|fa(s	x|fa(s	NOUN
ejpam-4637	378	53	)	)	PUNCT
ejpam-4637	378	54	≤	≤	NUM
ejpam-4637	378	55	γ0	γ0	PROPN
ejpam-4637	378	56	}	}	PUNCT
ejpam-4637	378	57	=	=	SYM
ejpam-4637	378	58	a0	a0	PROPN
ejpam-4637	378	59	.	.	PUNCT
ejpam-4637	379	1	thus	thus	ADV
ejpam-4637	379	2	,	,	PUNCT
ejpam-4637	379	3	a0	a0	PROPN
ejpam-4637	379	4	=	=	PUNCT
ejpam-4637	379	5	tα0	tα0	VERB
ejpam-4637	379	6	a	a	DET
ejpam-4637	379	7	∩	∩	NOUN
ejpam-4637	379	8	iβ0	iβ0	ADP
ejpam-4637	379	9	a	a	DET
ejpam-4637	379	10	∩	∩	ADJ
ejpam-4637	379	11	f	f	X
ejpam-4637	379	12	γ0	γ0	NOUN
ejpam-4637	379	13	a	a	DET
ejpam-4637	379	14	=	=	NOUN
ejpam-4637	379	15	a(α0,β0,γ0	a(α0,β0,γ0	NOUN
ejpam-4637	379	16	)	)	PUNCT
ejpam-4637	379	17	.	.	PUNCT
ejpam-4637	380	1	for	for	ADP
ejpam-4637	380	2	0	0	NUM
ejpam-4637	380	3	<	<	X
ejpam-4637	380	4	k	k	PROPN
ejpam-4637	380	5	≤	≤	PROPN
ejpam-4637	380	6	n	n	CCONJ
ejpam-4637	380	7	,	,	PUNCT
ejpam-4637	380	8	let	let	VERB
ejpam-4637	380	9	x	x	X
ejpam-4637	380	10	∈	∈	PROPN
ejpam-4637	380	11	ak	ak	PROPN
ejpam-4637	380	12	.	.	PROPN
ejpam-4637	381	1	then	then	ADV
ejpam-4637	381	2	x	x	SYM
ejpam-4637	381	3	∈	∈	NOUN
ejpam-4637	381	4	ak−i	ak−i	NOUN
ejpam-4637	381	5	\ak−i−1	\ak−i−1	PROPN
ejpam-4637	381	6	∃0	∃0	NOUN
ejpam-4637	381	7	≤	≤	NUM
ejpam-4637	381	8	i	i	NOUN
ejpam-4637	381	9	≤	≤	NOUN
ejpam-4637	382	1	k	k	PRON
ejpam-4637	383	1	−	−	NOUN
ejpam-4637	383	2	1	1	NUM
ejpam-4637	383	3	.	.	PUNCT
ejpam-4637	384	1	thus	thus	ADV
ejpam-4637	384	2	,	,	PUNCT
ejpam-4637	384	3	ta(x	ta(x	NOUN
ejpam-4637	384	4	)	)	PUNCT
ejpam-4637	384	5	=	=	SYM
ejpam-4637	384	6	αk−i	αk−i	NOUN
ejpam-4637	384	7	≥	≥	NUM
ejpam-4637	384	8	αk	αk	NOUN
ejpam-4637	384	9	,	,	PUNCT
ejpam-4637	384	10	ia(x	ia(x	X
ejpam-4637	384	11	)	)	PUNCT
ejpam-4637	384	12	=	=	SYM
ejpam-4637	385	1	βk−i	βk−i	NOUN
ejpam-4637	385	2	≤	≤	NOUN
ejpam-4637	385	3	βk	βk	ADP
ejpam-4637	385	4	and	and	CCONJ
ejpam-4637	385	5	fa(x	fa(x	NOUN
ejpam-4637	385	6	)	)	PUNCT
ejpam-4637	385	7	=	=	SYM
ejpam-4637	385	8	γk−i	γk−i	PROPN
ejpam-4637	385	9	≤	≤	X
ejpam-4637	385	10	γk	γk	X
ejpam-4637	385	11	∃0	∃0	PROPN
ejpam-4637	385	12	≤	≤	ADV
ejpam-4637	385	13	i	i	PRON
ejpam-4637	385	14	≤	≤	NOUN
ejpam-4637	386	1	k	k	PRON
ejpam-4637	387	1	−	−	NOUN
ejpam-4637	387	2	1	1	X
ejpam-4637	387	3	.	.	PUNCT
ejpam-4637	388	1	so	so	ADV
ejpam-4637	388	2	we	we	PRON
ejpam-4637	388	3	have	have	VERB
ejpam-4637	388	4	x	x	PART
ejpam-4637	388	5	∈	∈	PROPN
ejpam-4637	388	6	tαk	tαk	NOUN
ejpam-4637	388	7	a	a	DET
ejpam-4637	388	8	∩	∩	NOUN
ejpam-4637	388	9	iβk	iβk	VERB
ejpam-4637	388	10	a	a	DET
ejpam-4637	388	11	∩	∩	NOUN
ejpam-4637	388	12	f	f	PROPN
ejpam-4637	388	13	γk	γk	PROPN
ejpam-4637	388	14	a	a	DET
ejpam-4637	388	15	=	=	PUNCT
ejpam-4637	388	16	a(αk	a(αk	PROPN
ejpam-4637	388	17	,	,	PUNCT
ejpam-4637	388	18	βk	βk	NOUN
ejpam-4637	388	19	,	,	PUNCT
ejpam-4637	388	20	γk	γk	NOUN
ejpam-4637	388	21	)	)	PUNCT
ejpam-4637	388	22	and	and	CCONJ
ejpam-4637	388	23	ak	ak	PROPN
ejpam-4637	388	24	⊆	⊆	NUM
ejpam-4637	388	25	a(αk	a(αk	PROPN
ejpam-4637	388	26	,	,	PUNCT
ejpam-4637	388	27	βk	βk	NOUN
ejpam-4637	388	28	,	,	PUNCT
ejpam-4637	388	29	γk	γk	NOUN
ejpam-4637	388	30	)	)	PUNCT
ejpam-4637	388	31	.	.	PUNCT
ejpam-4637	389	1	also	also	ADV
ejpam-4637	389	2	,	,	PUNCT
ejpam-4637	389	3	let	let	VERB
ejpam-4637	389	4	y	y	PROPN
ejpam-4637	389	5	∈	∈	PROPN
ejpam-4637	389	6	a(αk	a(αk	PROPN
ejpam-4637	389	7	,	,	PUNCT
ejpam-4637	389	8	βk	βk	NOUN
ejpam-4637	389	9	,	,	PUNCT
ejpam-4637	389	10	γk	γk	NOUN
ejpam-4637	389	11	)	)	PUNCT
ejpam-4637	389	12	.	.	PUNCT
ejpam-4637	390	1	then	then	ADV
ejpam-4637	390	2	ta(y	ta(y	PUNCT
ejpam-4637	390	3	)	)	PUNCT
ejpam-4637	390	4	≥	≥	NOUN
ejpam-4637	390	5	αk	αk	NOUN
ejpam-4637	390	6	,	,	PUNCT
ejpam-4637	390	7	ia(y	ia(y	ADJ
ejpam-4637	390	8	)	)	PUNCT
ejpam-4637	390	9	≤	≤	NOUN
ejpam-4637	390	10	βk	βk	ADP
ejpam-4637	390	11	,	,	PUNCT
ejpam-4637	390	12	and	and	CCONJ
ejpam-4637	390	13	fa(y	fa(y	NOUN
ejpam-4637	390	14	)	)	PUNCT
ejpam-4637	390	15	≤	≤	NOUN
ejpam-4637	390	16	γk	γk	NOUN
ejpam-4637	390	17	.	.	PUNCT
ejpam-4637	391	1	the	the	DET
ejpam-4637	391	2	values	value	NOUN
ejpam-4637	391	3	of	of	ADP
ejpam-4637	391	4	ta(y	ta(y	PROPN
ejpam-4637	391	5	)	)	PUNCT
ejpam-4637	391	6	,	,	PUNCT
ejpam-4637	391	7	ia(y	ia(y	NOUN
ejpam-4637	391	8	)	)	PUNCT
ejpam-4637	391	9	,	,	PUNCT
ejpam-4637	391	10	and	and	CCONJ
ejpam-4637	391	11	fa(y	fa(y	NOUN
ejpam-4637	391	12	)	)	PUNCT
ejpam-4637	391	13	that	that	PRON
ejpam-4637	391	14	will	will	AUX
ejpam-4637	391	15	make	make	VERB
ejpam-4637	391	16	the	the	DET
ejpam-4637	391	17	three	three	NUM
ejpam-4637	391	18	inequalities	inequality	NOUN
ejpam-4637	391	19	true	true	ADJ
ejpam-4637	391	20	are	be	AUX
ejpam-4637	391	21	ta(y	ta(y	PUNCT
ejpam-4637	391	22	)	)	PUNCT
ejpam-4637	391	23	=	=	SYM
ejpam-4637	391	24	αt	αt	NOUN
ejpam-4637	391	25	,	,	PUNCT
ejpam-4637	391	26	ia(y	ia(y	PUNCT
ejpam-4637	391	27	)	)	PUNCT
ejpam-4637	391	28	=	=	SYM
ejpam-4637	391	29	βt	βt	PROPN
ejpam-4637	391	30	,	,	PUNCT
ejpam-4637	391	31	and	and	CCONJ
ejpam-4637	391	32	fa(y	fa(y	NOUN
ejpam-4637	391	33	)	)	PUNCT
ejpam-4637	391	34	=	=	PRON
ejpam-4637	391	35	γt	γt	NOUN
ejpam-4637	391	36	∃0	∃0	NOUN
ejpam-4637	391	37	<	<	X
ejpam-4637	391	38	t	t	PROPN
ejpam-4637	391	39	≤	≤	PROPN
ejpam-4637	391	40	k.	k.	PROPN
ejpam-4637	392	1	this	this	PRON
ejpam-4637	392	2	implies	imply	VERB
ejpam-4637	392	3	that	that	SCONJ
ejpam-4637	392	4	y	y	PROPN
ejpam-4637	392	5	∈	∈	PROPN
ejpam-4637	392	6	ak−i	ak−i	PROPN
ejpam-4637	392	7	\ak−i−1	\ak−i−1	PROPN
ejpam-4637	392	8	∃0	∃0	NOUN
ejpam-4637	392	9	≤	≤	NUM
ejpam-4637	392	10	i	i	NOUN
ejpam-4637	392	11	≤	≤	NOUN
ejpam-4637	393	1	k	k	PRON
ejpam-4637	394	1	−	−	NOUN
ejpam-4637	394	2	1	1	X
ejpam-4637	394	3	.	.	PUNCT
ejpam-4637	395	1	that	that	PRON
ejpam-4637	395	2	is	be	AUX
ejpam-4637	395	3	,	,	PUNCT
ejpam-4637	395	4	y	y	PROPN
ejpam-4637	395	5	∈	∈	PROPN
ejpam-4637	395	6	ak	ak	PROPN
ejpam-4637	395	7	since	since	SCONJ
ejpam-4637	395	8	(	(	PUNCT
ejpam-4637	395	9	ak−i	ak−i	NOUN
ejpam-4637	395	10	\ak−i−1	\ak−i−1	PROPN
ejpam-4637	395	11	)	)	PUNCT
ejpam-4637	395	12	⊆	⊆	NUM
ejpam-4637	395	13	ak	ak	PROPN
ejpam-4637	395	14	∃0	∃0	PROPN
ejpam-4637	395	15	≤	≤	NUM
ejpam-4637	395	16	i	i	PRON
ejpam-4637	395	17	≤	≤	PROPN
ejpam-4637	395	18	k−1	k−1	PROPN
ejpam-4637	395	19	.	.	PUNCT
ejpam-4637	396	1	hence	hence	ADV
ejpam-4637	396	2	,	,	PUNCT
ejpam-4637	396	3	a(αk	a(αk	PROPN
ejpam-4637	396	4	,	,	PUNCT
ejpam-4637	396	5	βk	βk	NOUN
ejpam-4637	396	6	,	,	PUNCT
ejpam-4637	396	7	γk	γk	NOUN
ejpam-4637	396	8	)	)	PUNCT
ejpam-4637	396	9	⊆	⊆	NUM
ejpam-4637	396	10	ak	ak	PROPN
ejpam-4637	396	11	.	.	PROPN
ejpam-4637	396	12	consequently	consequently	ADV
ejpam-4637	396	13	,	,	PUNCT
ejpam-4637	396	14	a(αk	a(αk	PROPN
ejpam-4637	396	15	,	,	PUNCT
ejpam-4637	396	16	βk	βk	NOUN
ejpam-4637	396	17	,	,	PUNCT
ejpam-4637	396	18	γk	γk	NOUN
ejpam-4637	396	19	)	)	PUNCT
ejpam-4637	396	20	=	=	SYM
ejpam-4637	396	21	ak	ak	PROPN
ejpam-4637	396	22	.	.	PROPN
ejpam-4637	396	23	a.	a.	PROPN
ejpam-4637	396	24	cano	cano	PROPN
ejpam-4637	396	25	,	,	PUNCT
ejpam-4637	396	26	g.	g.	PROPN
ejpam-4637	396	27	petalcorin	petalcorin	PROPN
ejpam-4637	396	28	/	/	SYM
ejpam-4637	396	29	eur	eur	PROPN
ejpam-4637	396	30	.	.	PUNCT
ejpam-4637	397	1	j.	j.	PROPN
ejpam-4637	397	2	pure	pure	PROPN
ejpam-4637	397	3	appl	appl	PROPN
ejpam-4637	397	4	.	.	PROPN
ejpam-4637	397	5	math	math	PROPN
ejpam-4637	397	6	,	,	PUNCT
ejpam-4637	397	7	16	16	NUM
ejpam-4637	397	8	(	(	PUNCT
ejpam-4637	397	9	1	1	NUM
ejpam-4637	397	10	)	)	PUNCT
ejpam-4637	397	11	(	(	PUNCT
ejpam-4637	397	12	2023	2023	NUM
ejpam-4637	397	13	)	)	PUNCT
ejpam-4637	397	14	,	,	PUNCT
ejpam-4637	397	15	548	548	NUM
ejpam-4637	397	16	-	-	SYM
ejpam-4637	397	17	576	576	NUM
ejpam-4637	397	18	565	565	NUM
ejpam-4637	397	19	3.2	3.2	NUM
ejpam-4637	397	20	.	.	PUNCT
ejpam-4637	398	1	single	single	ADV
ejpam-4637	398	2	-	-	PUNCT
ejpam-4637	398	3	valued	value	VERB
ejpam-4637	398	4	neutrosophic	neutrosophic	ADJ
ejpam-4637	398	5	soft	soft	ADJ
ejpam-4637	398	6	hyper	hyper	ADJ
ejpam-4637	398	7	up	up	ADP
ejpam-4637	398	8	-	-	PUNCT
ejpam-4637	398	9	subalgebra	subalgebra	NOUN
ejpam-4637	398	10	in	in	ADP
ejpam-4637	398	11	this	this	DET
ejpam-4637	398	12	section	section	NOUN
ejpam-4637	398	13	,	,	PUNCT
ejpam-4637	398	14	we	we	PRON
ejpam-4637	398	15	define	define	VERB
ejpam-4637	398	16	the	the	DET
ejpam-4637	398	17	single	single	ADV
ejpam-4637	398	18	-	-	PUNCT
ejpam-4637	398	19	valued	value	VERB
ejpam-4637	398	20	neutrosophic	neutrosophic	ADJ
ejpam-4637	398	21	soft	soft	ADJ
ejpam-4637	398	22	hyper	hyper	ADJ
ejpam-4637	398	23	up	up	ADP
ejpam-4637	398	24	-subalgebra	-subalgebra	NOUN
ejpam-4637	398	25	and	and	CCONJ
ejpam-4637	398	26	prove	prove	VERB
ejpam-4637	398	27	some	some	DET
ejpam-4637	398	28	related	related	ADJ
ejpam-4637	398	29	properties	property	NOUN
ejpam-4637	398	30	.	.	PUNCT
ejpam-4637	399	1	definition	definition	NOUN
ejpam-4637	399	2	17	17	NUM
ejpam-4637	399	3	.	.	PUNCT
ejpam-4637	400	1	let	let	VERB
ejpam-4637	400	2	(	(	PUNCT
ejpam-4637	400	3	∆	∆	X
ejpam-4637	400	4	,	,	PUNCT
ejpam-4637	400	5	e	e	X
ejpam-4637	400	6	)	)	PUNCT
ejpam-4637	400	7	be	be	AUX
ejpam-4637	400	8	a	a	DET
ejpam-4637	400	9	single	single	ADV
ejpam-4637	400	10	-	-	PUNCT
ejpam-4637	400	11	valued	value	VERB
ejpam-4637	400	12	neutrosophic	neutrosophic	ADJ
ejpam-4637	400	13	soft	soft	ADJ
ejpam-4637	400	14	set	set	NOUN
ejpam-4637	400	15	over	over	ADP
ejpam-4637	400	16	a	a	DET
ejpam-4637	400	17	hyper	hyper	NOUN
ejpam-4637	400	18	up	up	ADP
ejpam-4637	400	19	algebra	algebra	PROPN
ejpam-4637	400	20	x.	x.	NOUN
ejpam-4637	400	21	then	then	ADV
ejpam-4637	400	22	(	(	PUNCT
ejpam-4637	400	23	∆	∆	X
ejpam-4637	400	24	,	,	PUNCT
ejpam-4637	400	25	e	e	X
ejpam-4637	400	26	)	)	PUNCT
ejpam-4637	400	27	is	be	AUX
ejpam-4637	400	28	said	say	VERB
ejpam-4637	400	29	to	to	PART
ejpam-4637	400	30	be	be	AUX
ejpam-4637	400	31	single	single	ADV
ejpam-4637	400	32	-	-	PUNCT
ejpam-4637	400	33	valued	value	VERB
ejpam-4637	400	34	neutrosophic	neutrosophic	ADJ
ejpam-4637	400	35	soft	soft	ADJ
ejpam-4637	400	36	(	(	PUNCT
ejpam-4637	400	37	sv	sv	NOUN
ejpam-4637	400	38	ns	ns	NUM
ejpam-4637	400	39	)	)	PUNCT
ejpam-4637	400	40	hyper	hyper	ADJ
ejpam-4637	400	41	up	up	ADP
ejpam-4637	400	42	-	-	PUNCT
ejpam-4637	400	43	subalgebra	subalgebra	NOUN
ejpam-4637	400	44	of	of	ADP
ejpam-4637	400	45	x	x	PRON
ejpam-4637	400	46	if	if	SCONJ
ejpam-4637	400	47	for	for	ADP
ejpam-4637	400	48	all	all	DET
ejpam-4637	400	49	x	x	NOUN
ejpam-4637	400	50	,	,	PUNCT
ejpam-4637	400	51	y	y	PROPN
ejpam-4637	400	52	∈	∈	PROPN
ejpam-4637	400	53	x	x	X
ejpam-4637	400	54	and	and	CCONJ
ejpam-4637	400	55	e	e	PROPN
ejpam-4637	400	56	∈	∈	PROPN
ejpam-4637	400	57	e	e	NOUN
ejpam-4637	400	58	,	,	PUNCT
ejpam-4637	400	59	∗t∆(e)(x	∗t∆(e)(x	NOUN
ejpam-4637	400	60	◦	◦	NOUN
ejpam-4637	400	61	y	y	NOUN
ejpam-4637	400	62	)	)	PUNCT
ejpam-4637	400	63	≥	≥	NOUN
ejpam-4637	400	64	min{t∆(e)(x	min{t∆(e)(x	NOUN
ejpam-4637	400	65	)	)	PUNCT
ejpam-4637	400	66	,	,	PUNCT
ejpam-4637	400	67	t∆(e)(y	t∆(e)(y	PROPN
ejpam-4637	400	68	)	)	PUNCT
ejpam-4637	400	69	}	}	PUNCT
ejpam-4637	400	70	,	,	PUNCT
ejpam-4637	400	71	∗i∆(e)(x	∗i∆(e)(x	NUM
ejpam-4637	400	72	◦	◦	VERB
ejpam-4637	400	73	y	y	PROPN
ejpam-4637	400	74	)	)	PUNCT
ejpam-4637	400	75	≤	≤	NOUN
ejpam-4637	400	76	max{t∆(e)(x	max{t∆(e)(x	PROPN
ejpam-4637	400	77	)	)	PUNCT
ejpam-4637	400	78	,	,	PUNCT
ejpam-4637	400	79	t∆(e)(y	t∆(e)(y	PROPN
ejpam-4637	400	80	)	)	PUNCT
ejpam-4637	400	81	}	}	PUNCT
ejpam-4637	400	82	,	,	PUNCT
ejpam-4637	400	83	and	and	CCONJ
ejpam-4637	400	84	∗f∆(e)(x	∗f∆(e)(x	NUM
ejpam-4637	400	85	◦	◦	NOUN
ejpam-4637	400	86	y	y	NOUN
ejpam-4637	400	87	)	)	PUNCT
ejpam-4637	400	88	≤	≤	NOUN
ejpam-4637	400	89	max{t∆(e)(x	max{t∆(e)(x	PROPN
ejpam-4637	400	90	)	)	PUNCT
ejpam-4637	400	91	,	,	PUNCT
ejpam-4637	400	92	t∆(e)(y	t∆(e)(y	PROPN
ejpam-4637	400	93	)	)	PUNCT
ejpam-4637	400	94	}	}	PUNCT
ejpam-4637	400	95	;	;	PUNCT
ejpam-4637	400	96	that	that	PRON
ejpam-4637	400	97	is	is	ADV
ejpam-4637	400	98	,	,	PUNCT
ejpam-4637	400	99	∆(e	∆(e	NOUN
ejpam-4637	400	100	)	)	PUNCT
ejpam-4637	400	101	is	be	AUX
ejpam-4637	400	102	a	a	DET
ejpam-4637	400	103	svn	svn	NOUN
ejpam-4637	400	104	hyper	hyper	NOUN
ejpam-4637	400	105	up	up	ADP
ejpam-4637	400	106	-subalgebra	-subalgebra	NOUN
ejpam-4637	400	107	of	of	ADP
ejpam-4637	400	108	x.	x.	NOUN
ejpam-4637	400	109	example	example	NOUN
ejpam-4637	400	110	7	7	X
ejpam-4637	400	111	.	.	PUNCT
ejpam-4637	400	112	consider	consider	VERB
ejpam-4637	400	113	the	the	DET
ejpam-4637	400	114	hyper	hyper	ADJ
ejpam-4637	400	115	up	up	ADP
ejpam-4637	400	116	-algebra	-algebra	PROPN
ejpam-4637	400	117	(	(	PUNCT
ejpam-4637	400	118	x	x	NOUN
ejpam-4637	400	119	,	,	PUNCT
ejpam-4637	400	120	◦	◦	NOUN
ejpam-4637	400	121	,	,	PUNCT
ejpam-4637	400	122	≪	≪	ADJ
ejpam-4637	400	123	,	,	PUNCT
ejpam-4637	400	124	0	0	NUM
ejpam-4637	400	125	)	)	PUNCT
ejpam-4637	400	126	of	of	ADP
ejpam-4637	400	127	example	example	NOUN
ejpam-4637	400	128	2	2	NUM
ejpam-4637	400	129	where	where	SCONJ
ejpam-4637	400	130	x	x	X
ejpam-4637	400	131	=	=	PRON
ejpam-4637	400	132	{	{	PUNCT
ejpam-4637	400	133	0	0	NUM
ejpam-4637	400	134	,	,	PUNCT
ejpam-4637	400	135	u	u	NOUN
ejpam-4637	400	136	,	,	PUNCT
ejpam-4637	400	137	v	v	NOUN
ejpam-4637	400	138	}	}	PUNCT
ejpam-4637	400	139	.	.	PUNCT
ejpam-4637	401	1	let	let	VERB
ejpam-4637	401	2	e	e	NOUN
ejpam-4637	401	3	=	=	PRON
ejpam-4637	401	4	{	{	PUNCT
ejpam-4637	401	5	e1	e1	PROPN
ejpam-4637	401	6	,	,	PUNCT
ejpam-4637	401	7	e2	e2	PROPN
ejpam-4637	401	8	}	}	PUNCT
ejpam-4637	401	9	be	be	VERB
ejpam-4637	401	10	the	the	DET
ejpam-4637	401	11	set	set	NOUN
ejpam-4637	401	12	of	of	ADP
ejpam-4637	401	13	parameters	parameter	NOUN
ejpam-4637	401	14	and	and	CCONJ
ejpam-4637	401	15	let	let	VERB
ejpam-4637	401	16	∆	∆	PROPN
ejpam-4637	401	17	:	:	PUNCT
ejpam-4637	402	1	e	e	X
ejpam-4637	402	2	−→	−→	NOUN
ejpam-4637	402	3	n	n	PROPN
ejpam-4637	402	4	(	(	PUNCT
ejpam-4637	402	5	x	x	X
ejpam-4637	402	6	)	)	PUNCT
ejpam-4637	402	7	be	be	AUX
ejpam-4637	402	8	defined	define	VERB
ejpam-4637	402	9	by	by	ADP
ejpam-4637	402	10	∆(e1	∆(e1	NUM
ejpam-4637	402	11	)	)	PUNCT
ejpam-4637	402	12	=	=	PRON
ejpam-4637	402	13	{	{	PUNCT
ejpam-4637	402	14	⟨0	⟨0	PROPN
ejpam-4637	402	15	,	,	PUNCT
ejpam-4637	402	16	(	(	PUNCT
ejpam-4637	402	17	0.9	0.9	NUM
ejpam-4637	402	18	,	,	PUNCT
ejpam-4637	402	19	0.2	0.2	NUM
ejpam-4637	402	20	,	,	PUNCT
ejpam-4637	402	21	0.45)⟩	0.45)⟩	NUM
ejpam-4637	402	22	,	,	PUNCT
ejpam-4637	402	23	⟨u	⟨u	NOUN
ejpam-4637	402	24	,	,	PUNCT
ejpam-4637	402	25	(	(	PUNCT
ejpam-4637	402	26	0.74	0.74	NUM
ejpam-4637	402	27	,	,	PUNCT
ejpam-4637	402	28	0.57	0.57	NUM
ejpam-4637	402	29	,	,	PUNCT
ejpam-4637	402	30	0.7)⟩	0.7)⟩	NUM
ejpam-4637	402	31	,	,	PUNCT
ejpam-4637	402	32	⟨v	⟨v	CCONJ
ejpam-4637	402	33	,	,	PUNCT
ejpam-4637	402	34	(	(	PUNCT
ejpam-4637	402	35	0.8	0.8	NUM
ejpam-4637	402	36	,	,	PUNCT
ejpam-4637	402	37	0.42	0.42	NUM
ejpam-4637	402	38	,	,	PUNCT
ejpam-4637	402	39	0.52)⟩	0.52)⟩	NUM
ejpam-4637	402	40	}	}	PUNCT
ejpam-4637	402	41	and	and	CCONJ
ejpam-4637	402	42	∆(e2	∆(e2	PRON
ejpam-4637	402	43	)	)	PUNCT
ejpam-4637	402	44	=	=	PRON
ejpam-4637	402	45	{	{	PUNCT
ejpam-4637	402	46	⟨0	⟨0	PROPN
ejpam-4637	402	47	,	,	PUNCT
ejpam-4637	402	48	(	(	PUNCT
ejpam-4637	402	49	0.8	0.8	NUM
ejpam-4637	402	50	,	,	PUNCT
ejpam-4637	402	51	0.2	0.2	NUM
ejpam-4637	402	52	,	,	PUNCT
ejpam-4637	402	53	0.4)⟩	0.4)⟩	NUM
ejpam-4637	402	54	,	,	PUNCT
ejpam-4637	402	55	⟨u	⟨u	NOUN
ejpam-4637	402	56	,	,	PUNCT
ejpam-4637	402	57	(	(	PUNCT
ejpam-4637	402	58	0.4	0.4	NUM
ejpam-4637	402	59	,	,	PUNCT
ejpam-4637	402	60	0.45	0.45	NUM
ejpam-4637	402	61	,	,	PUNCT
ejpam-4637	402	62	0.5)⟩	0.5)⟩	NUM
ejpam-4637	402	63	,	,	PUNCT
ejpam-4637	402	64	⟨v	⟨v	PROPN
ejpam-4637	402	65	,	,	PUNCT
ejpam-4637	402	66	(	(	PUNCT
ejpam-4637	402	67	0.67	0.67	NUM
ejpam-4637	402	68	,	,	PUNCT
ejpam-4637	402	69	0.3	0.3	NUM
ejpam-4637	402	70	,	,	PUNCT
ejpam-4637	402	71	0.5)⟩	0.5)⟩	NUM
ejpam-4637	402	72	}	}	PUNCT
ejpam-4637	402	73	.	.	PUNCT
ejpam-4637	403	1	then	then	ADV
ejpam-4637	403	2	(	(	PUNCT
ejpam-4637	403	3	∆	∆	X
ejpam-4637	403	4	,	,	PUNCT
ejpam-4637	403	5	e	e	X
ejpam-4637	403	6	)	)	PUNCT
ejpam-4637	403	7	=	=	SYM
ejpam-4637	403	8	{	{	PUNCT
ejpam-4637	403	9	(	(	PUNCT
ejpam-4637	403	10	e1	e1	NOUN
ejpam-4637	403	11	,	,	PUNCT
ejpam-4637	403	12	{	{	PUNCT
ejpam-4637	403	13	⟨0	⟨0	PROPN
ejpam-4637	403	14	,	,	PUNCT
ejpam-4637	403	15	(	(	PUNCT
ejpam-4637	403	16	0.9	0.9	NUM
ejpam-4637	403	17	,	,	PUNCT
ejpam-4637	403	18	0.2	0.2	NUM
ejpam-4637	403	19	,	,	PUNCT
ejpam-4637	403	20	0.45)⟩	0.45)⟩	NUM
ejpam-4637	403	21	,	,	PUNCT
ejpam-4637	403	22	⟨u	⟨u	NOUN
ejpam-4637	403	23	,	,	PUNCT
ejpam-4637	403	24	(	(	PUNCT
ejpam-4637	403	25	0.74	0.74	NUM
ejpam-4637	403	26	,	,	PUNCT
ejpam-4637	403	27	0.57	0.57	NUM
ejpam-4637	403	28	,	,	PUNCT
ejpam-4637	403	29	0.7)⟩	0.7)⟩	NUM
ejpam-4637	403	30	,	,	PUNCT
ejpam-4637	403	31	⟨v	⟨v	CCONJ
ejpam-4637	403	32	,	,	PUNCT
ejpam-4637	403	33	(	(	PUNCT
ejpam-4637	403	34	0.8	0.8	NUM
ejpam-4637	403	35	,	,	PUNCT
ejpam-4637	403	36	0.42	0.42	NUM
ejpam-4637	403	37	,	,	PUNCT
ejpam-4637	403	38	0.52)⟩	0.52)⟩	NUM
ejpam-4637	403	39	}	}	PUNCT
ejpam-4637	403	40	)	)	PUNCT
ejpam-4637	403	41	,	,	PUNCT
ejpam-4637	403	42	(	(	PUNCT
ejpam-4637	403	43	e2	e2	PROPN
ejpam-4637	403	44	,	,	PUNCT
ejpam-4637	403	45	{	{	PUNCT
ejpam-4637	403	46	⟨0	⟨0	PROPN
ejpam-4637	403	47	,	,	PUNCT
ejpam-4637	403	48	(	(	PUNCT
ejpam-4637	403	49	0.8	0.8	NUM
ejpam-4637	403	50	,	,	PUNCT
ejpam-4637	403	51	0.2	0.2	NUM
ejpam-4637	403	52	,	,	PUNCT
ejpam-4637	403	53	0.4)⟩	0.4)⟩	NUM
ejpam-4637	403	54	,	,	PUNCT
ejpam-4637	403	55	⟨u	⟨u	NOUN
ejpam-4637	403	56	,	,	PUNCT
ejpam-4637	403	57	(	(	PUNCT
ejpam-4637	403	58	0.4	0.4	NUM
ejpam-4637	403	59	,	,	PUNCT
ejpam-4637	403	60	0.45	0.45	NUM
ejpam-4637	403	61	,	,	PUNCT
ejpam-4637	403	62	0.5)⟩	0.5)⟩	NUM
ejpam-4637	403	63	,	,	PUNCT
ejpam-4637	403	64	⟨v	⟨v	PROPN
ejpam-4637	403	65	,	,	PUNCT
ejpam-4637	403	66	(	(	PUNCT
ejpam-4637	403	67	0.67	0.67	NUM
ejpam-4637	403	68	,	,	PUNCT
ejpam-4637	403	69	0.3	0.3	NUM
ejpam-4637	403	70	,	,	PUNCT
ejpam-4637	403	71	0.5)⟩	0.5)⟩	NUM
ejpam-4637	403	72	}	}	PUNCT
ejpam-4637	403	73	)	)	PUNCT
ejpam-4637	403	74	}	}	PUNCT
ejpam-4637	403	75	.	.	PUNCT
ejpam-4637	404	1	is	be	AUX
ejpam-4637	404	2	a	a	DET
ejpam-4637	404	3	svns	svns	NOUN
ejpam-4637	404	4	set	set	VERB
ejpam-4637	404	5	over	over	ADP
ejpam-4637	404	6	x.	x.	NOUN
ejpam-4637	404	7	by	by	ADP
ejpam-4637	404	8	routine	routine	ADJ
ejpam-4637	404	9	calculation	calculation	NOUN
ejpam-4637	404	10	,	,	PUNCT
ejpam-4637	404	11	(	(	PUNCT
ejpam-4637	404	12	∆	∆	X
ejpam-4637	404	13	,	,	PUNCT
ejpam-4637	404	14	e	e	X
ejpam-4637	404	15	)	)	PUNCT
ejpam-4637	404	16	is	be	AUX
ejpam-4637	404	17	a	a	DET
ejpam-4637	404	18	svns	svns	NOUN
ejpam-4637	404	19	hyper	hyper	ADJ
ejpam-4637	404	20	up	up	ADP
ejpam-4637	404	21	-subalgebra	-subalgebra	NOUN
ejpam-4637	404	22	of	of	ADP
ejpam-4637	404	23	x.	x.	NOUN
ejpam-4637	404	24	proposition	proposition	NOUN
ejpam-4637	404	25	5	5	NUM
ejpam-4637	404	26	.	.	PUNCT
ejpam-4637	405	1	let	let	VERB
ejpam-4637	405	2	(	(	PUNCT
ejpam-4637	405	3	∆	∆	X
ejpam-4637	405	4	,	,	PUNCT
ejpam-4637	405	5	e	e	X
ejpam-4637	405	6	)	)	PUNCT
ejpam-4637	405	7	be	be	AUX
ejpam-4637	405	8	a	a	DET
ejpam-4637	405	9	svns	svns	NOUN
ejpam-4637	405	10	hyper	hyper	ADJ
ejpam-4637	405	11	up	up	ADP
ejpam-4637	405	12	-	-	PUNCT
ejpam-4637	405	13	subalgebra	subalgebra	NOUN
ejpam-4637	405	14	of	of	ADP
ejpam-4637	405	15	x.	x.	NOUN
ejpam-4637	405	16	then	then	ADV
ejpam-4637	405	17	for	for	ADP
ejpam-4637	405	18	all	all	DET
ejpam-4637	405	19	x	x	NOUN
ejpam-4637	405	20	,	,	PUNCT
ejpam-4637	405	21	y	y	PROPN
ejpam-4637	405	22	∈	∈	PROPN
ejpam-4637	405	23	x	x	X
ejpam-4637	405	24	and	and	CCONJ
ejpam-4637	405	25	e	e	PROPN
ejpam-4637	405	26	∈	∈	PROPN
ejpam-4637	405	27	e	e	PROPN
ejpam-4637	405	28	,	,	PUNCT
ejpam-4637	405	29	(	(	PUNCT
ejpam-4637	405	30	i	i	NOUN
ejpam-4637	405	31	)	)	PUNCT
ejpam-4637	405	32	t∆(e)(x	t∆(e)(x	PROPN
ejpam-4637	405	33	)	)	PUNCT
ejpam-4637	405	34	≤	≤	PUNCT
ejpam-4637	405	35	t∆(e)(0	t∆(e)(0	ADJ
ejpam-4637	405	36	)	)	PUNCT
ejpam-4637	405	37	i∆(e)(x	i∆(e)(x	PROPN
ejpam-4637	405	38	)	)	PUNCT
ejpam-4637	405	39	≥	≥	NOUN
ejpam-4637	405	40	i∆(e)(0	i∆(e)(0	NOUN
ejpam-4637	405	41	)	)	PUNCT
ejpam-4637	405	42	f∆(e)(x	f∆(e)(x	NOUN
ejpam-4637	405	43	)	)	PUNCT
ejpam-4637	405	44	≥	≥	NOUN
ejpam-4637	406	1	f∆(e)(0	f∆(e)(0	ADJ
ejpam-4637	406	2	)	)	PUNCT
ejpam-4637	406	3	,	,	PUNCT
ejpam-4637	406	4	(	(	PUNCT
ejpam-4637	406	5	ii	ii	NOUN
ejpam-4637	406	6	)	)	PUNCT
ejpam-4637	406	7	∗t∆(e)(0	∗t∆(e)(0	PUNCT
ejpam-4637	407	1	◦	◦	NOUN
ejpam-4637	407	2	x	x	NOUN
ejpam-4637	407	3	)	)	PUNCT
ejpam-4637	407	4	=	=	SYM
ejpam-4637	407	5	t∆(e)(x	t∆(e)(x	NOUN
ejpam-4637	407	6	)	)	PUNCT
ejpam-4637	407	7	.	.	PUNCT
ejpam-4637	408	1	∗i∆(e)(0	∗i∆(e)(0	ADP
ejpam-4637	408	2	◦	◦	NOUN
ejpam-4637	408	3	x	x	SYM
ejpam-4637	408	4	)	)	PUNCT
ejpam-4637	408	5	=	=	SYM
ejpam-4637	408	6	i∆(e)(x	i∆(e)(x	NOUN
ejpam-4637	408	7	)	)	PUNCT
ejpam-4637	408	8	∗f∆(e)(0	∗f∆(e)(0	VERB
ejpam-4637	408	9	◦	◦	NOUN
ejpam-4637	408	10	x	x	NOUN
ejpam-4637	408	11	)	)	PUNCT
ejpam-4637	408	12	=	=	SYM
ejpam-4637	408	13	f∆(e)(x	f∆(e)(x	NOUN
ejpam-4637	408	14	)	)	PUNCT
ejpam-4637	408	15	.	.	PUNCT
ejpam-4637	409	1	(	(	PUNCT
ejpam-4637	409	2	iii	iii	X
ejpam-4637	409	3	)	)	PUNCT
ejpam-4637	409	4	∗t∆(e)(x	∗t∆(e)(x	NOUN
ejpam-4637	409	5	◦	◦	NOUN
ejpam-4637	409	6	0	0	NUM
ejpam-4637	409	7	)	)	PUNCT
ejpam-4637	410	1	=	=	SYM
ejpam-4637	410	2	t∆(e)(0	t∆(e)(0	ADJ
ejpam-4637	410	3	)	)	PUNCT
ejpam-4637	410	4	∗i∆(e)(x	∗i∆(e)(x	NOUN
ejpam-4637	410	5	◦	◦	NOUN
ejpam-4637	410	6	0	0	NUM
ejpam-4637	410	7	)	)	PUNCT
ejpam-4637	410	8	=	=	SYM
ejpam-4637	410	9	i∆(e)(0	i∆(e)(0	ADJ
ejpam-4637	410	10	)	)	PUNCT
ejpam-4637	410	11	∗f∆(e)(x	∗f∆(e)(x	NUM
ejpam-4637	410	12	◦	◦	NOUN
ejpam-4637	410	13	0	0	NUM
ejpam-4637	410	14	)	)	PUNCT
ejpam-4637	411	1	=	=	SYM
ejpam-4637	411	2	f∆(e)(0	f∆(e)(0	ADJ
ejpam-4637	411	3	)	)	PUNCT
ejpam-4637	411	4	(	(	PUNCT
ejpam-4637	411	5	iv	iv	X
ejpam-4637	411	6	)	)	PUNCT
ejpam-4637	411	7	if	if	SCONJ
ejpam-4637	411	8	t∆(e)(x	t∆(e)(x	NOUN
ejpam-4637	411	9	)	)	PUNCT
ejpam-4637	411	10	=	=	SYM
ejpam-4637	411	11	t∆(e)(0	t∆(e)(0	ADJ
ejpam-4637	411	12	)	)	PUNCT
ejpam-4637	411	13	i∆(e)(x	i∆(e)(x	NOUN
ejpam-4637	411	14	)	)	PUNCT
ejpam-4637	411	15	=	=	SYM
ejpam-4637	411	16	i∆(e)(0	i∆(e)(0	ADJ
ejpam-4637	411	17	)	)	PUNCT
ejpam-4637	411	18	f∆(e)(x	f∆(e)(x	NOUN
ejpam-4637	411	19	)	)	PUNCT
ejpam-4637	412	1	=	=	SYM
ejpam-4637	412	2	f∆(e)(0	f∆(e)(0	ADJ
ejpam-4637	412	3	)	)	PUNCT
ejpam-4637	412	4	,	,	PUNCT
ejpam-4637	412	5	then	then	ADV
ejpam-4637	412	6	∗t∆(e)(x	∗t∆(e)(x	X
ejpam-4637	412	7	◦	◦	NOUN
ejpam-4637	412	8	y	y	PROPN
ejpam-4637	412	9	)	)	PUNCT
ejpam-4637	412	10	≥	≥	NOUN
ejpam-4637	412	11	t∆(e)(y	t∆(e)(y	NOUN
ejpam-4637	412	12	)	)	PUNCT
ejpam-4637	412	13	∗i∆(e)(x	∗i∆(e)(x	NOUN
ejpam-4637	413	1	◦	◦	PROPN
ejpam-4637	413	2	y	y	PROPN
ejpam-4637	413	3	)	)	PUNCT
ejpam-4637	413	4	≤	≤	NUM
ejpam-4637	413	5	i∆(e)(y	i∆(e)(y	PROPN
ejpam-4637	413	6	)	)	PUNCT
ejpam-4637	413	7	∗f∆(e)(x	∗f∆(e)(x	NUM
ejpam-4637	413	8	◦	◦	NOUN
ejpam-4637	413	9	y	y	NOUN
ejpam-4637	413	10	)	)	PUNCT
ejpam-4637	413	11	≤	≤	NUM
ejpam-4637	413	12	f∆(e)(y	f∆(e)(y	PROPN
ejpam-4637	413	13	)	)	PUNCT
ejpam-4637	413	14	.	.	PUNCT
ejpam-4637	414	1	a.	a.	PROPN
ejpam-4637	414	2	cano	cano	PROPN
ejpam-4637	414	3	,	,	PUNCT
ejpam-4637	414	4	g.	g.	PROPN
ejpam-4637	414	5	petalcorin	petalcorin	PROPN
ejpam-4637	414	6	/	/	SYM
ejpam-4637	414	7	eur	eur	PROPN
ejpam-4637	414	8	.	.	PUNCT
ejpam-4637	415	1	j.	j.	PROPN
ejpam-4637	415	2	pure	pure	PROPN
ejpam-4637	415	3	appl	appl	PROPN
ejpam-4637	415	4	.	.	PROPN
ejpam-4637	415	5	math	math	PROPN
ejpam-4637	415	6	,	,	PUNCT
ejpam-4637	415	7	16	16	NUM
ejpam-4637	415	8	(	(	PUNCT
ejpam-4637	415	9	1	1	NUM
ejpam-4637	415	10	)	)	PUNCT
ejpam-4637	415	11	(	(	PUNCT
ejpam-4637	415	12	2023	2023	NUM
ejpam-4637	415	13	)	)	PUNCT
ejpam-4637	415	14	,	,	PUNCT
ejpam-4637	415	15	548	548	NUM
ejpam-4637	415	16	-	-	SYM
ejpam-4637	415	17	576	576	NUM
ejpam-4637	415	18	566	566	NUM
ejpam-4637	415	19	(	(	PUNCT
ejpam-4637	415	20	v	v	NOUN
ejpam-4637	415	21	)	)	PUNCT
ejpam-4637	415	22	if	if	SCONJ
ejpam-4637	415	23	t∆(e)(y	t∆(e)(y	NOUN
ejpam-4637	415	24	)	)	PUNCT
ejpam-4637	416	1	=	=	SYM
ejpam-4637	416	2	t∆(e)(0	t∆(e)(0	X
ejpam-4637	416	3	)	)	PUNCT
ejpam-4637	416	4	i∆(e)(y	i∆(e)(y	PROPN
ejpam-4637	416	5	)	)	PUNCT
ejpam-4637	417	1	=	=	SYM
ejpam-4637	417	2	i∆(e)(0	i∆(e)(0	ADJ
ejpam-4637	417	3	)	)	PUNCT
ejpam-4637	417	4	f∆(e)(y	f∆(e)(y	PROPN
ejpam-4637	417	5	)	)	PUNCT
ejpam-4637	418	1	=	=	PUNCT
ejpam-4637	418	2	f∆(e)(0	f∆(e)(0	ADJ
ejpam-4637	418	3	)	)	PUNCT
ejpam-4637	418	4	,	,	PUNCT
ejpam-4637	418	5	then	then	ADV
ejpam-4637	418	6	∗t∆(e)(x	∗t∆(e)(x	X
ejpam-4637	418	7	◦	◦	NOUN
ejpam-4637	418	8	y	y	PROPN
ejpam-4637	418	9	)	)	PUNCT
ejpam-4637	418	10	≥	≥	NOUN
ejpam-4637	418	11	t∆(e)(x	t∆(e)(x	NOUN
ejpam-4637	418	12	)	)	PUNCT
ejpam-4637	418	13	∗i∆(e)(x	∗i∆(e)(x	NOUN
ejpam-4637	419	1	◦	◦	PROPN
ejpam-4637	419	2	y	y	PROPN
ejpam-4637	419	3	)	)	PUNCT
ejpam-4637	419	4	≤	≤	NUM
ejpam-4637	419	5	i∆(e)(x	i∆(e)(x	NOUN
ejpam-4637	419	6	)	)	PUNCT
ejpam-4637	419	7	∗f∆(e)(x	∗f∆(e)(x	NUM
ejpam-4637	419	8	◦	◦	NOUN
ejpam-4637	419	9	y	y	NOUN
ejpam-4637	419	10	)	)	PUNCT
ejpam-4637	419	11	≤	≤	NOUN
ejpam-4637	419	12	f∆(e)(x	f∆(e)(x	NOUN
ejpam-4637	419	13	)	)	PUNCT
ejpam-4637	419	14	.	.	PUNCT
ejpam-4637	420	1	(	(	PUNCT
ejpam-4637	420	2	vi	vi	X
ejpam-4637	420	3	)	)	PUNCT
ejpam-4637	420	4	if	if	SCONJ
ejpam-4637	420	5	∗t∆(e)(x	∗t∆(e)(x	NUM
ejpam-4637	420	6	◦	◦	VERB
ejpam-4637	420	7	y	y	NOUN
ejpam-4637	420	8	)	)	PUNCT
ejpam-4637	420	9	=	=	SYM
ejpam-4637	420	10	t∆(e)(x	t∆(e)(x	NOUN
ejpam-4637	420	11	)	)	PUNCT
ejpam-4637	420	12	∗i∆(e)(x	∗i∆(e)(x	NOUN
ejpam-4637	421	1	◦	◦	NOUN
ejpam-4637	421	2	y	y	NOUN
ejpam-4637	421	3	)	)	PUNCT
ejpam-4637	421	4	=	=	SYM
ejpam-4637	421	5	i∆(e)(x	i∆(e)(x	PROPN
ejpam-4637	421	6	)	)	PUNCT
ejpam-4637	421	7	∗f∆(e)(x	∗f∆(e)(x	NUM
ejpam-4637	421	8	◦	◦	NOUN
ejpam-4637	421	9	y	y	NOUN
ejpam-4637	421	10	)	)	PUNCT
ejpam-4637	421	11	=	=	PUNCT
ejpam-4637	421	12	f∆(e)(x	f∆(e)(x	NOUN
ejpam-4637	421	13	)	)	PUNCT
ejpam-4637	421	14	,	,	PUNCT
ejpam-4637	421	15	then	then	ADV
ejpam-4637	421	16	t∆(e)(x	t∆(e)(x	PROPN
ejpam-4637	421	17	)	)	PUNCT
ejpam-4637	422	1	=	=	SYM
ejpam-4637	422	2	t∆(e)(0	t∆(e)(0	ADJ
ejpam-4637	422	3	)	)	PUNCT
ejpam-4637	422	4	i∆(e)(x	i∆(e)(x	NOUN
ejpam-4637	422	5	)	)	PUNCT
ejpam-4637	423	1	=	=	SYM
ejpam-4637	423	2	i∆(e)(0	i∆(e)(0	ADJ
ejpam-4637	423	3	)	)	PUNCT
ejpam-4637	423	4	f∆(e)(x	f∆(e)(x	NOUN
ejpam-4637	423	5	)	)	PUNCT
ejpam-4637	424	1	=	=	SYM
ejpam-4637	424	2	f∆(e)(0	f∆(e)(0	ADJ
ejpam-4637	424	3	)	)	PUNCT
ejpam-4637	424	4	and	and	CCONJ
ejpam-4637	424	5	t∆(e)(y	t∆(e)(y	NUM
ejpam-4637	424	6	)	)	PUNCT
ejpam-4637	424	7	=	=	SYM
ejpam-4637	424	8	t∆(e)(0	t∆(e)(0	X
ejpam-4637	424	9	)	)	PUNCT
ejpam-4637	424	10	i∆(e)(y	i∆(e)(y	PROPN
ejpam-4637	424	11	)	)	PUNCT
ejpam-4637	425	1	=	=	SYM
ejpam-4637	425	2	i∆(e)(0	i∆(e)(0	ADJ
ejpam-4637	425	3	)	)	PUNCT
ejpam-4637	425	4	f∆(e)(y	f∆(e)(y	PROPN
ejpam-4637	425	5	)	)	PUNCT
ejpam-4637	426	1	=	=	PUNCT
ejpam-4637	426	2	f∆(e)(0	f∆(e)(0	ADJ
ejpam-4637	426	3	)	)	PUNCT
ejpam-4637	426	4	.	.	PUNCT
ejpam-4637	427	1	proof	proof	NOUN
ejpam-4637	427	2	.	.	PUNCT
ejpam-4637	428	1	using	use	VERB
ejpam-4637	428	2	similar	similar	ADJ
ejpam-4637	428	3	arguments	argument	NOUN
ejpam-4637	428	4	from	from	ADP
ejpam-4637	428	5	proposition	proposition	NOUN
ejpam-4637	428	6	3	3	NUM
ejpam-4637	428	7	,	,	PUNCT
ejpam-4637	428	8	this	this	DET
ejpam-4637	428	9	proposition	proposition	NOUN
ejpam-4637	428	10	is	be	AUX
ejpam-4637	428	11	valid	valid	ADJ
ejpam-4637	428	12	.	.	PUNCT
ejpam-4637	429	1	theorem	theorem	VERB
ejpam-4637	429	2	6	6	NUM
ejpam-4637	429	3	.	.	PUNCT
ejpam-4637	430	1	let	let	AUX
ejpam-4637	430	2	(	(	PUNCT
ejpam-4637	430	3	∆1	∆1	NOUN
ejpam-4637	430	4	,	,	PUNCT
ejpam-4637	430	5	e	e	NOUN
ejpam-4637	430	6	)	)	PUNCT
ejpam-4637	430	7	and	and	CCONJ
ejpam-4637	430	8	(	(	PUNCT
ejpam-4637	430	9	∆2	∆2	X
ejpam-4637	430	10	,	,	PUNCT
ejpam-4637	430	11	e	e	NOUN
ejpam-4637	430	12	)	)	PUNCT
ejpam-4637	430	13	be	be	VERB
ejpam-4637	430	14	two	two	NUM
ejpam-4637	430	15	svns	svns	NOUN
ejpam-4637	430	16	hyper	hyper	ADJ
ejpam-4637	430	17	up	up	ADP
ejpam-4637	430	18	-	-	PUNCT
ejpam-4637	430	19	subalgebras	subalgebras	NOUN
ejpam-4637	430	20	of	of	ADP
ejpam-4637	430	21	x.	x.	NOUN
ejpam-4637	430	22	then	then	ADV
ejpam-4637	430	23	(	(	PUNCT
ejpam-4637	430	24	i	i	NOUN
ejpam-4637	430	25	)	)	PUNCT
ejpam-4637	430	26	(	(	PUNCT
ejpam-4637	430	27	∆1	∆1	NOUN
ejpam-4637	430	28	,	,	PUNCT
ejpam-4637	430	29	e	e	NOUN
ejpam-4637	430	30	)	)	PUNCT
ejpam-4637	430	31	∩	∩	NOUN
ejpam-4637	430	32	(	(	PUNCT
ejpam-4637	430	33	∆2	∆2	X
ejpam-4637	430	34	,	,	PUNCT
ejpam-4637	430	35	e	e	NOUN
ejpam-4637	430	36	)	)	PUNCT
ejpam-4637	430	37	is	be	AUX
ejpam-4637	430	38	a	a	DET
ejpam-4637	430	39	svns	svns	NOUN
ejpam-4637	430	40	hyper	hyper	ADJ
ejpam-4637	430	41	up	up	ADP
ejpam-4637	430	42	-	-	PUNCT
ejpam-4637	430	43	subalgebra	subalgebra	NOUN
ejpam-4637	430	44	of	of	ADP
ejpam-4637	430	45	x.	x.	PROPN
ejpam-4637	430	46	(	(	PUNCT
ejpam-4637	430	47	ii	ii	PROPN
ejpam-4637	430	48	)	)	PUNCT
ejpam-4637	430	49	(	(	PUNCT
ejpam-4637	430	50	∆1	∆1	NOUN
ejpam-4637	430	51	,	,	PUNCT
ejpam-4637	430	52	e	e	NOUN
ejpam-4637	430	53	)	)	PUNCT
ejpam-4637	430	54	∪	∪	NOUN
ejpam-4637	430	55	(	(	PUNCT
ejpam-4637	430	56	∆2	∆2	X
ejpam-4637	430	57	,	,	PUNCT
ejpam-4637	430	58	e	e	NOUN
ejpam-4637	430	59	)	)	PUNCT
ejpam-4637	430	60	is	be	AUX
ejpam-4637	430	61	not	not	PART
ejpam-4637	430	62	generally	generally	ADV
ejpam-4637	430	63	a	a	DET
ejpam-4637	430	64	svns	svns	NOUN
ejpam-4637	430	65	hyper	hyper	ADJ
ejpam-4637	430	66	up	up	ADP
ejpam-4637	430	67	-	-	PUNCT
ejpam-4637	430	68	subalgebra	subalgebra	NOUN
ejpam-4637	430	69	of	of	ADP
ejpam-4637	430	70	x.	x.	NOUN
ejpam-4637	430	71	proof	proof	NOUN
ejpam-4637	430	72	.	.	PUNCT
ejpam-4637	431	1	let	let	VERB
ejpam-4637	431	2	(	(	PUNCT
ejpam-4637	431	3	∆1	∆1	NOUN
ejpam-4637	431	4	,	,	PUNCT
ejpam-4637	431	5	e	e	NOUN
ejpam-4637	431	6	)	)	PUNCT
ejpam-4637	431	7	and	and	CCONJ
ejpam-4637	431	8	(	(	PUNCT
ejpam-4637	431	9	∆2	∆2	X
ejpam-4637	431	10	,	,	PUNCT
ejpam-4637	431	11	e	e	NOUN
ejpam-4637	431	12	)	)	PUNCT
ejpam-4637	431	13	be	be	VERB
ejpam-4637	431	14	two	two	NUM
ejpam-4637	431	15	svns	svns	NOUN
ejpam-4637	431	16	hyper	hyper	ADJ
ejpam-4637	431	17	up	up	ADV
ejpam-4637	431	18	-subalgebras	-subalgebra	NOUN
ejpam-4637	431	19	of	of	ADP
ejpam-4637	431	20	x.	x.	NOUN
ejpam-4637	431	21	(	(	PUNCT
ejpam-4637	431	22	i	i	NOUN
ejpam-4637	431	23	)	)	PUNCT
ejpam-4637	431	24	let	let	VERB
ejpam-4637	431	25	(	(	PUNCT
ejpam-4637	431	26	∆	∆	X
ejpam-4637	431	27	,	,	PUNCT
ejpam-4637	431	28	e	e	NOUN
ejpam-4637	431	29	)	)	PUNCT
ejpam-4637	431	30	=	=	SYM
ejpam-4637	431	31	(	(	PUNCT
ejpam-4637	431	32	∆1	∆1	NOUN
ejpam-4637	431	33	,	,	PUNCT
ejpam-4637	431	34	e	e	NOUN
ejpam-4637	431	35	)	)	PUNCT
ejpam-4637	431	36	∩	∩	NOUN
ejpam-4637	431	37	(	(	PUNCT
ejpam-4637	431	38	∆2	∆2	X
ejpam-4637	431	39	,	,	PUNCT
ejpam-4637	431	40	e	e	NOUN
ejpam-4637	431	41	)	)	PUNCT
ejpam-4637	431	42	,	,	PUNCT
ejpam-4637	431	43	x	x	X
ejpam-4637	431	44	,	,	PUNCT
ejpam-4637	431	45	y	y	PROPN
ejpam-4637	431	46	∈	∈	PROPN
ejpam-4637	431	47	x	x	X
ejpam-4637	431	48	and	and	CCONJ
ejpam-4637	431	49	e	e	PROPN
ejpam-4637	431	50	∈	∈	PROPN
ejpam-4637	431	51	e.	e.	PROPN
ejpam-4637	431	52	then	then	ADV
ejpam-4637	431	53	we	we	PRON
ejpam-4637	431	54	have	have	VERB
ejpam-4637	431	55	∗t∆(e)(x	∗t∆(e)(x	NUM
ejpam-4637	431	56	◦	◦	NOUN
ejpam-4637	431	57	y	y	NOUN
ejpam-4637	431	58	)	)	PUNCT
ejpam-4637	432	1	=	=	SYM
ejpam-4637	432	2	inf	inf	NOUN
ejpam-4637	432	3	a∈x	a∈x	NOUN
ejpam-4637	432	4	◦	◦	NOUN
ejpam-4637	432	5	y	y	NOUN
ejpam-4637	432	6	t∆(e)(a	t∆(e)(a	NOUN
ejpam-4637	432	7	)	)	PUNCT
ejpam-4637	433	1	=	=	SYM
ejpam-4637	433	2	inf	inf	NOUN
ejpam-4637	433	3	a∈x	a∈x	NOUN
ejpam-4637	433	4	◦	◦	NOUN
ejpam-4637	433	5	y	y	PROPN
ejpam-4637	433	6	min{t∆1(e)(a	min{t∆1(e)(a	NOUN
ejpam-4637	433	7	)	)	PUNCT
ejpam-4637	433	8	,	,	PUNCT
ejpam-4637	433	9	t∆2(e)(a	t∆2(e)(a	PROPN
ejpam-4637	433	10	)	)	PUNCT
ejpam-4637	433	11	}	}	PUNCT
ejpam-4637	433	12	≥	≥	NOUN
ejpam-4637	433	13	min	min	PROPN
ejpam-4637	433	14	{	{	PUNCT
ejpam-4637	433	15	inf	inf	NOUN
ejpam-4637	433	16	a∈x	a∈x	PROPN
ejpam-4637	433	17	◦	◦	NOUN
ejpam-4637	433	18	y	y	NOUN
ejpam-4637	433	19	t∆1(e)(a	t∆1(e)(a	NOUN
ejpam-4637	433	20	)	)	PUNCT
ejpam-4637	433	21	,	,	PUNCT
ejpam-4637	433	22	inf	inf	PROPN
ejpam-4637	433	23	a∈x	a∈x	PROPN
ejpam-4637	433	24	◦	◦	NOUN
ejpam-4637	433	25	y	y	PROPN
ejpam-4637	433	26	t∆2(e)(a	t∆2(e)(a	NOUN
ejpam-4637	433	27	)	)	PUNCT
ejpam-4637	433	28	}	}	PUNCT
ejpam-4637	433	29	=	=	PUNCT
ejpam-4637	433	30	min{∗t∆1(e)(x	min{∗t∆1(e)(x	NOUN
ejpam-4637	433	31	◦	◦	NOUN
ejpam-4637	433	32	y),∗	y),∗	X
ejpam-4637	433	33	t∆2(e)(x	t∆2(e)(x	PROPN
ejpam-4637	433	34	◦	◦	PROPN
ejpam-4637	433	35	y	y	PROPN
ejpam-4637	433	36	)	)	PUNCT
ejpam-4637	433	37	}	}	PUNCT
ejpam-4637	433	38	≥	≥	NUM
ejpam-4637	433	39	min{min{t∆1(e)(x	min{min{t∆1(e)(x	NOUN
ejpam-4637	433	40	)	)	PUNCT
ejpam-4637	433	41	,	,	PUNCT
ejpam-4637	433	42	t∆1(e)(y)},min{t∆2(e)(x	t∆1(e)(y)},min{t∆2(e)(x	NUM
ejpam-4637	433	43	)	)	PUNCT
ejpam-4637	433	44	,	,	PUNCT
ejpam-4637	433	45	t∆2(e)(y	t∆2(e)(y	PROPN
ejpam-4637	433	46	)	)	PUNCT
ejpam-4637	433	47	}	}	PUNCT
ejpam-4637	433	48	}	}	PUNCT
ejpam-4637	433	49	=	=	SYM
ejpam-4637	433	50	min{min{t∆1(e)(x	min{min{t∆1(e)(x	PROPN
ejpam-4637	433	51	)	)	PUNCT
ejpam-4637	433	52	,	,	PUNCT
ejpam-4637	433	53	t∆2(e)(x)},min{t∆1(e)(y	t∆2(e)(x)},min{t∆1(e)(y	NUM
ejpam-4637	433	54	)	)	PUNCT
ejpam-4637	433	55	,	,	PUNCT
ejpam-4637	433	56	t∆2(e)(y	t∆2(e)(y	PROPN
ejpam-4637	433	57	)	)	PUNCT
ejpam-4637	433	58	}	}	PUNCT
ejpam-4637	433	59	}	}	PUNCT
ejpam-4637	433	60	=	=	SYM
ejpam-4637	433	61	min{t∆(e)(x	min{t∆(e)(x	NOUN
ejpam-4637	433	62	)	)	PUNCT
ejpam-4637	433	63	,	,	PUNCT
ejpam-4637	433	64	t∆(e)(y	t∆(e)(y	PROPN
ejpam-4637	433	65	)	)	PUNCT
ejpam-4637	433	66	}	}	PUNCT
ejpam-4637	433	67	.	.	PUNCT
ejpam-4637	434	1	also	also	ADV
ejpam-4637	434	2	,	,	PUNCT
ejpam-4637	434	3	∗i∆(e)(x	∗i∆(e)(x	NUM
ejpam-4637	434	4	◦	◦	NOUN
ejpam-4637	434	5	y	y	NOUN
ejpam-4637	434	6	)	)	PUNCT
ejpam-4637	434	7	=	=	NOUN
ejpam-4637	434	8	sup	sup	NOUN
ejpam-4637	434	9	a∈x	a∈x	NOUN
ejpam-4637	434	10	◦	◦	NOUN
ejpam-4637	434	11	y	y	NOUN
ejpam-4637	434	12	i∆(e)(a	i∆(e)(a	NUM
ejpam-4637	434	13	)	)	PUNCT
ejpam-4637	435	1	=	=	SYM
ejpam-4637	435	2	sup	sup	NOUN
ejpam-4637	435	3	a∈x	a∈x	NOUN
ejpam-4637	435	4	◦	◦	NOUN
ejpam-4637	435	5	y	y	PROPN
ejpam-4637	435	6	max{i∆1(e)(a	max{i∆1(e)(a	PROPN
ejpam-4637	435	7	)	)	PUNCT
ejpam-4637	435	8	,	,	PUNCT
ejpam-4637	435	9	i∆2(e)(a	i∆2(e)(a	PROPN
ejpam-4637	435	10	)	)	PUNCT
ejpam-4637	435	11	}	}	PUNCT
ejpam-4637	435	12	≤	≤	NUM
ejpam-4637	435	13	max	max	PROPN
ejpam-4637	435	14	{	{	PUNCT
ejpam-4637	435	15	sup	sup	NOUN
ejpam-4637	435	16	a∈x	a∈x	NOUN
ejpam-4637	435	17	◦	◦	NOUN
ejpam-4637	435	18	y	y	NOUN
ejpam-4637	435	19	i∆1(e)(a	i∆1(e)(a	NUM
ejpam-4637	435	20	)	)	PUNCT
ejpam-4637	435	21	,	,	PUNCT
ejpam-4637	435	22	sup	sup	NOUN
ejpam-4637	435	23	a∈x	a∈x	NOUN
ejpam-4637	435	24	◦	◦	NOUN
ejpam-4637	435	25	y	y	PROPN
ejpam-4637	435	26	i∆2(e)(a	i∆2(e)(a	PROPN
ejpam-4637	435	27	)	)	PUNCT
ejpam-4637	435	28	}	}	PUNCT
ejpam-4637	436	1	=	=	PUNCT
ejpam-4637	436	2	max{∗i∆1(e)(x	max{∗i∆1(e)(x	NOUN
ejpam-4637	436	3	◦	◦	NOUN
ejpam-4637	436	4	y),∗	y),∗	NOUN
ejpam-4637	436	5	i∆2(e)(x	i∆2(e)(x	PROPN
ejpam-4637	436	6	◦	◦	PROPN
ejpam-4637	436	7	y	y	PROPN
ejpam-4637	436	8	)	)	PUNCT
ejpam-4637	436	9	}	}	PUNCT
ejpam-4637	436	10	≤	≤	PROPN
ejpam-4637	436	11	max{max{i∆1(e)(x	max{max{i∆1(e)(x	PROPN
ejpam-4637	436	12	)	)	PUNCT
ejpam-4637	436	13	,	,	PUNCT
ejpam-4637	436	14	i∆1(e)(y)},max{i∆2(e)(x	i∆1(e)(y)},max{i∆2(e)(x	NUM
ejpam-4637	436	15	)	)	PUNCT
ejpam-4637	436	16	,	,	PUNCT
ejpam-4637	436	17	i∆2(e)(y	i∆2(e)(y	NOUN
ejpam-4637	436	18	)	)	PUNCT
ejpam-4637	436	19	}	}	PUNCT
ejpam-4637	436	20	}	}	PUNCT
ejpam-4637	436	21	=	=	SYM
ejpam-4637	436	22	max{max{i∆1(e)(x	max{max{i∆1(e)(x	PROPN
ejpam-4637	436	23	)	)	PUNCT
ejpam-4637	436	24	,	,	PUNCT
ejpam-4637	436	25	i∆2(e)(x)},max{i∆1(e)(y	i∆2(e)(x)},max{i∆1(e)(y	NUM
ejpam-4637	436	26	)	)	PUNCT
ejpam-4637	436	27	,	,	PUNCT
ejpam-4637	436	28	i∆2(e)(y	i∆2(e)(y	NOUN
ejpam-4637	436	29	)	)	PUNCT
ejpam-4637	436	30	}	}	PUNCT
ejpam-4637	436	31	}	}	PUNCT
ejpam-4637	436	32	=	=	SYM
ejpam-4637	436	33	max{i∆(e)(x	max{i∆(e)(x	NOUN
ejpam-4637	436	34	)	)	PUNCT
ejpam-4637	436	35	,	,	PUNCT
ejpam-4637	436	36	i∆(e)(y	i∆(e)(y	PROPN
ejpam-4637	436	37	)	)	PUNCT
ejpam-4637	436	38	}	}	PUNCT
ejpam-4637	436	39	.	.	PUNCT
ejpam-4637	437	1	similarly	similarly	ADV
ejpam-4637	437	2	,	,	PUNCT
ejpam-4637	437	3	∗f∆(e)(x	∗f∆(e)(x	PUNCT
ejpam-4637	437	4	◦	◦	NOUN
ejpam-4637	437	5	y	y	NOUN
ejpam-4637	437	6	)	)	PUNCT
ejpam-4637	437	7	≤	≤	NOUN
ejpam-4637	437	8	max{f∆(e)(x),f∆(e)(y	max{f∆(e)(x),f∆(e)(y	NUM
ejpam-4637	437	9	)	)	PUNCT
ejpam-4637	437	10	}	}	PUNCT
ejpam-4637	437	11	.	.	PUNCT
ejpam-4637	438	1	thus	thus	ADV
ejpam-4637	438	2	,	,	PUNCT
ejpam-4637	438	3	(	(	PUNCT
ejpam-4637	438	4	∆	∆	X
ejpam-4637	438	5	,	,	PUNCT
ejpam-4637	438	6	e	e	X
ejpam-4637	438	7	)	)	PUNCT
ejpam-4637	438	8	is	be	AUX
ejpam-4637	438	9	a	a	DET
ejpam-4637	438	10	svns	svns	NOUN
ejpam-4637	438	11	hyper	hyper	ADJ
ejpam-4637	438	12	up	up	ADP
ejpam-4637	438	13	-subalgebra	-subalgebra	NOUN
ejpam-4637	438	14	of	of	ADP
ejpam-4637	438	15	x.	x.	PROPN
ejpam-4637	438	16	a.	a.	PROPN
ejpam-4637	438	17	cano	cano	PROPN
ejpam-4637	438	18	,	,	PUNCT
ejpam-4637	438	19	g.	g.	PROPN
ejpam-4637	438	20	petalcorin	petalcorin	PROPN
ejpam-4637	438	21	/	/	SYM
ejpam-4637	438	22	eur	eur	PROPN
ejpam-4637	438	23	.	.	PUNCT
ejpam-4637	439	1	j.	j.	PROPN
ejpam-4637	439	2	pure	pure	PROPN
ejpam-4637	439	3	appl	appl	PROPN
ejpam-4637	439	4	.	.	PROPN
ejpam-4637	439	5	math	math	PROPN
ejpam-4637	439	6	,	,	PUNCT
ejpam-4637	439	7	16	16	NUM
ejpam-4637	439	8	(	(	PUNCT
ejpam-4637	439	9	1	1	NUM
ejpam-4637	439	10	)	)	PUNCT
ejpam-4637	439	11	(	(	PUNCT
ejpam-4637	439	12	2023	2023	NUM
ejpam-4637	439	13	)	)	PUNCT
ejpam-4637	439	14	,	,	PUNCT
ejpam-4637	439	15	548	548	NUM
ejpam-4637	439	16	-	-	SYM
ejpam-4637	439	17	576	576	NUM
ejpam-4637	439	18	567	567	NUM
ejpam-4637	439	19	(	(	PUNCT
ejpam-4637	439	20	ii	ii	NOUN
ejpam-4637	439	21	)	)	PUNCT
ejpam-4637	439	22	using	use	VERB
ejpam-4637	439	23	the	the	DET
ejpam-4637	439	24	hyper	hyper	ADJ
ejpam-4637	439	25	up	up	ADP
ejpam-4637	439	26	-algebra	-algebra	PROPN
ejpam-4637	439	27	(	(	PUNCT
ejpam-4637	439	28	x	x	NOUN
ejpam-4637	439	29	,	,	PUNCT
ejpam-4637	439	30	◦	◦	NOUN
ejpam-4637	439	31	,	,	PUNCT
ejpam-4637	439	32	≪	≪	ADJ
ejpam-4637	439	33	,	,	PUNCT
ejpam-4637	439	34	0	0	NUM
ejpam-4637	439	35	)	)	PUNCT
ejpam-4637	439	36	of	of	ADP
ejpam-4637	439	37	example	example	NOUN
ejpam-4637	439	38	1	1	NUM
ejpam-4637	439	39	where	where	SCONJ
ejpam-4637	439	40	x	x	X
ejpam-4637	439	41	=	=	PRON
ejpam-4637	439	42	{	{	PUNCT
ejpam-4637	439	43	0	0	NUM
ejpam-4637	439	44	,	,	PUNCT
ejpam-4637	439	45	r	r	NOUN
ejpam-4637	439	46	,	,	PUNCT
ejpam-4637	439	47	s	s	PROPN
ejpam-4637	439	48	,	,	PUNCT
ejpam-4637	439	49	t	t	PROPN
ejpam-4637	439	50	}	}	PUNCT
ejpam-4637	439	51	,	,	PUNCT
ejpam-4637	439	52	we	we	PRON
ejpam-4637	439	53	consider	consider	VERB
ejpam-4637	439	54	the	the	DET
ejpam-4637	439	55	two	two	NUM
ejpam-4637	439	56	svns	svns	NOUN
ejpam-4637	439	57	hyper	hyper	ADJ
ejpam-4637	439	58	up	up	ADV
ejpam-4637	439	59	-subalgebras	-subalgebra	NOUN
ejpam-4637	439	60	(	(	PUNCT
ejpam-4637	439	61	∆1	∆1	NOUN
ejpam-4637	439	62	,	,	PUNCT
ejpam-4637	439	63	e	e	NOUN
ejpam-4637	439	64	)	)	PUNCT
ejpam-4637	439	65	and	and	CCONJ
ejpam-4637	439	66	(	(	PUNCT
ejpam-4637	439	67	∆2	∆2	X
ejpam-4637	439	68	,	,	PUNCT
ejpam-4637	439	69	e	e	NOUN
ejpam-4637	439	70	)	)	PUNCT
ejpam-4637	439	71	of	of	ADP
ejpam-4637	439	72	x	x	PUNCT
ejpam-4637	439	73	given	give	VERB
ejpam-4637	439	74	by	by	ADP
ejpam-4637	439	75	:	:	PUNCT
ejpam-4637	439	76	for	for	ADP
ejpam-4637	439	77	e	e	PROPN
ejpam-4637	439	78	∈	∈	PROPN
ejpam-4637	439	79	e	e	PROPN
ejpam-4637	439	80	,	,	PUNCT
ejpam-4637	439	81	t∆1(e)(x	t∆1(e)(x	NOUN
ejpam-4637	439	82	)	)	PUNCT
ejpam-4637	439	83	=	=	PRON
ejpam-4637	439	84	{	{	PUNCT
ejpam-4637	439	85	0.5	0.5	NUM
ejpam-4637	439	86	if	if	SCONJ
ejpam-4637	439	87	x	x	SYM
ejpam-4637	439	88	∈	∈	PROPN
ejpam-4637	439	89	{	{	PUNCT
ejpam-4637	439	90	0	0	NUM
ejpam-4637	439	91	,	,	PUNCT
ejpam-4637	439	92	s	s	PART
ejpam-4637	439	93	}	}	PUNCT
ejpam-4637	439	94	,	,	PUNCT
ejpam-4637	439	95	0	0	NUM
ejpam-4637	439	96	otherwise	otherwise	ADV
ejpam-4637	439	97	.	.	PUNCT
ejpam-4637	440	1	i∆1(e)(x	i∆1(e)(x	PROPN
ejpam-4637	440	2	)	)	PUNCT
ejpam-4637	441	1	=	=	PRON
ejpam-4637	441	2	{	{	PUNCT
ejpam-4637	441	3	0	0	NUM
ejpam-4637	441	4	if	if	SCONJ
ejpam-4637	441	5	x	x	X
ejpam-4637	441	6	∈	∈	NOUN
ejpam-4637	441	7	{	{	PUNCT
ejpam-4637	441	8	0	0	NUM
ejpam-4637	441	9	,	,	PUNCT
ejpam-4637	441	10	s	s	PART
ejpam-4637	441	11	}	}	PUNCT
ejpam-4637	441	12	,	,	PUNCT
ejpam-4637	441	13	0.5	0.5	NUM
ejpam-4637	441	14	otherwise	otherwise	ADV
ejpam-4637	441	15	.	.	PUNCT
ejpam-4637	442	1	f∆1(e)(x	f∆1(e)(x	NOUN
ejpam-4637	442	2	)	)	PUNCT
ejpam-4637	442	3	=	=	PRON
ejpam-4637	442	4	{	{	PUNCT
ejpam-4637	442	5	0	0	NUM
ejpam-4637	442	6	if	if	SCONJ
ejpam-4637	442	7	x	x	X
ejpam-4637	442	8	∈	∈	NOUN
ejpam-4637	442	9	{	{	PUNCT
ejpam-4637	442	10	0	0	NUM
ejpam-4637	442	11	,	,	PUNCT
ejpam-4637	442	12	s	s	PART
ejpam-4637	442	13	}	}	PUNCT
ejpam-4637	442	14	,	,	PUNCT
ejpam-4637	442	15	0.5	0.5	NUM
ejpam-4637	442	16	otherwise	otherwise	ADV
ejpam-4637	442	17	.	.	PUNCT
ejpam-4637	443	1	and	and	CCONJ
ejpam-4637	443	2	t∆2(e)(x	t∆2(e)(x	NOUN
ejpam-4637	443	3	)	)	PUNCT
ejpam-4637	444	1	=	=	PRON
ejpam-4637	444	2	{	{	PUNCT
ejpam-4637	444	3	0.7	0.7	NUM
ejpam-4637	444	4	if	if	SCONJ
ejpam-4637	444	5	x	x	SYM
ejpam-4637	444	6	∈	∈	NOUN
ejpam-4637	444	7	{	{	PUNCT
ejpam-4637	444	8	0	0	NUM
ejpam-4637	444	9	,	,	PUNCT
ejpam-4637	444	10	t	t	PROPN
ejpam-4637	444	11	}	}	PUNCT
ejpam-4637	444	12	,	,	PUNCT
ejpam-4637	444	13	0	0	NUM
ejpam-4637	444	14	otherwise	otherwise	ADV
ejpam-4637	444	15	.	.	PUNCT
ejpam-4637	445	1	i∆2(e)(x	i∆2(e)(x	PROPN
ejpam-4637	445	2	)	)	PUNCT
ejpam-4637	446	1	=	=	PRON
ejpam-4637	446	2	{	{	PUNCT
ejpam-4637	446	3	0	0	NUM
ejpam-4637	446	4	if	if	SCONJ
ejpam-4637	446	5	x	x	X
ejpam-4637	446	6	∈	∈	PROPN
ejpam-4637	446	7	{	{	PUNCT
ejpam-4637	446	8	0	0	NUM
ejpam-4637	446	9	,	,	PUNCT
ejpam-4637	446	10	t	t	PROPN
ejpam-4637	446	11	}	}	PUNCT
ejpam-4637	446	12	,	,	PUNCT
ejpam-4637	446	13	0.7	0.7	NUM
ejpam-4637	446	14	otherwise	otherwise	ADV
ejpam-4637	446	15	.	.	PUNCT
ejpam-4637	447	1	f∆2(e)(x	f∆2(e)(x	NOUN
ejpam-4637	447	2	)	)	PUNCT
ejpam-4637	448	1	=	=	PRON
ejpam-4637	448	2	{	{	PUNCT
ejpam-4637	448	3	0	0	NUM
ejpam-4637	448	4	if	if	SCONJ
ejpam-4637	448	5	x	x	X
ejpam-4637	448	6	∈	∈	PROPN
ejpam-4637	448	7	{	{	PUNCT
ejpam-4637	448	8	0	0	NUM
ejpam-4637	448	9	,	,	PUNCT
ejpam-4637	448	10	t	t	PROPN
ejpam-4637	448	11	}	}	PUNCT
ejpam-4637	448	12	,	,	PUNCT
ejpam-4637	448	13	0.7	0.7	NUM
ejpam-4637	448	14	otherwise	otherwise	ADV
ejpam-4637	448	15	.	.	PUNCT
ejpam-4637	449	1	,	,	PUNCT
ejpam-4637	450	1	respectively	respectively	ADV
ejpam-4637	450	2	.	.	PUNCT
ejpam-4637	451	1	let	let	VERB
ejpam-4637	451	2	(	(	PUNCT
ejpam-4637	451	3	∆	∆	X
ejpam-4637	451	4	,	,	PUNCT
ejpam-4637	451	5	e	e	NOUN
ejpam-4637	451	6	)	)	PUNCT
ejpam-4637	451	7	=	=	SYM
ejpam-4637	451	8	(	(	PUNCT
ejpam-4637	451	9	∆1	∆1	NOUN
ejpam-4637	451	10	,	,	PUNCT
ejpam-4637	451	11	e	e	NOUN
ejpam-4637	451	12	)	)	PUNCT
ejpam-4637	451	13	∪	∪	NOUN
ejpam-4637	451	14	(	(	PUNCT
ejpam-4637	451	15	∆2	∆2	X
ejpam-4637	451	16	,	,	PUNCT
ejpam-4637	451	17	e	e	NOUN
ejpam-4637	451	18	)	)	PUNCT
ejpam-4637	451	19	.	.	PUNCT
ejpam-4637	452	1	for	for	ADP
ejpam-4637	452	2	all	all	DET
ejpam-4637	452	3	e	e	PROPN
ejpam-4637	452	4	∈	∈	PROPN
ejpam-4637	452	5	e	e	NOUN
ejpam-4637	452	6	,	,	PUNCT
ejpam-4637	452	7	taking	take	VERB
ejpam-4637	452	8	x	x	PUNCT
ejpam-4637	452	9	=	=	SYM
ejpam-4637	452	10	s	s	X
ejpam-4637	452	11	and	and	CCONJ
ejpam-4637	452	12	y	y	PROPN
ejpam-4637	452	13	=	=	SYM
ejpam-4637	452	14	t	t	PROPN
ejpam-4637	452	15	gives	give	VERB
ejpam-4637	452	16	∗t∆(e)(x	∗t∆(e)(x	NUM
ejpam-4637	452	17	◦	◦	NOUN
ejpam-4637	452	18	y	y	NOUN
ejpam-4637	452	19	)	)	PUNCT
ejpam-4637	453	1	=	=	NOUN
ejpam-4637	453	2	∗t∆(e)(s	∗t∆(e)(s	NOUN
ejpam-4637	453	3	◦	◦	NOUN
ejpam-4637	453	4	t	t	PROPN
ejpam-4637	453	5	)	)	PUNCT
ejpam-4637	453	6	=	=	PUNCT
ejpam-4637	453	7	∗t∆(e)({r	∗t∆(e)({r	NOUN
ejpam-4637	453	8	}	}	PUNCT
ejpam-4637	453	9	)	)	PUNCT
ejpam-4637	454	1	=	=	SYM
ejpam-4637	454	2	t∆(e)(r	t∆(e)(r	NUM
ejpam-4637	454	3	)	)	PUNCT
ejpam-4637	454	4	=	=	SYM
ejpam-4637	454	5	max{t∆1(e)(r	max{t∆1(e)(r	PROPN
ejpam-4637	454	6	)	)	PUNCT
ejpam-4637	454	7	,	,	PUNCT
ejpam-4637	454	8	t∆2(e)(r	t∆2(e)(r	NOUN
ejpam-4637	454	9	)	)	PUNCT
ejpam-4637	454	10	}	}	PUNCT
ejpam-4637	454	11	=	=	SYM
ejpam-4637	454	12	max{0	max{0	PROPN
ejpam-4637	454	13	,	,	PUNCT
ejpam-4637	454	14	0	0	NUM
ejpam-4637	454	15	}	}	PUNCT
ejpam-4637	454	16	=	=	SYM
ejpam-4637	454	17	0	0	NUM
ejpam-4637	454	18	and	and	CCONJ
ejpam-4637	454	19	min{t∆(e)(x	min{t∆(e)(x	NOUN
ejpam-4637	454	20	)	)	PUNCT
ejpam-4637	454	21	,	,	PUNCT
ejpam-4637	454	22	t∆(e)(y	t∆(e)(y	NOUN
ejpam-4637	454	23	)	)	PUNCT
ejpam-4637	454	24	}	}	PUNCT
ejpam-4637	454	25	=	=	SYM
ejpam-4637	454	26	min{t∆(e)(s	min{t∆(e)(s	PROPN
ejpam-4637	454	27	)	)	PUNCT
ejpam-4637	454	28	,	,	PUNCT
ejpam-4637	454	29	t∆(e)(t	t∆(e)(t	NOUN
ejpam-4637	454	30	)	)	PUNCT
ejpam-4637	454	31	}	}	PUNCT
ejpam-4637	454	32	=	=	SYM
ejpam-4637	454	33	min{max{t∆1(e)(s	min{max{t∆1(e)(s	NUM
ejpam-4637	454	34	)	)	PUNCT
ejpam-4637	454	35	,	,	PUNCT
ejpam-4637	454	36	t∆2(e)(s)},max{t∆1(e)(t	t∆2(e)(s)},max{t∆1(e)(t	NUM
ejpam-4637	454	37	)	)	PUNCT
ejpam-4637	454	38	,	,	PUNCT
ejpam-4637	454	39	t∆2(e)(t	t∆2(e)(t	PROPN
ejpam-4637	454	40	)	)	PUNCT
ejpam-4637	454	41	}	}	PUNCT
ejpam-4637	454	42	}	}	PUNCT
ejpam-4637	454	43	=	=	SYM
ejpam-4637	454	44	min{max{0.5	min{max{0.5	PROPN
ejpam-4637	454	45	,	,	PUNCT
ejpam-4637	454	46	0},max{0	0},max{0	NUM
ejpam-4637	454	47	,	,	PUNCT
ejpam-4637	454	48	0.7	0.7	NUM
ejpam-4637	454	49	}	}	PUNCT
ejpam-4637	454	50	}	}	PUNCT
ejpam-4637	454	51	=	=	SYM
ejpam-4637	454	52	min{0.5	min{0.5	PROPN
ejpam-4637	454	53	,	,	PUNCT
ejpam-4637	454	54	0.7	0.7	NUM
ejpam-4637	454	55	}	}	PUNCT
ejpam-4637	454	56	=	=	NUM
ejpam-4637	454	57	0.5	0.5	NUM
ejpam-4637	454	58	.	.	PUNCT
ejpam-4637	455	1	that	that	PRON
ejpam-4637	455	2	is	is	ADV
ejpam-4637	455	3	,	,	PUNCT
ejpam-4637	455	4	∗t∆(e)(x	∗t∆(e)(x	NOUN
ejpam-4637	455	5	◦	◦	NOUN
ejpam-4637	455	6	y	y	NOUN
ejpam-4637	455	7	)	)	PUNCT
ejpam-4637	456	1	=	=	PUNCT
ejpam-4637	456	2	0	0	NUM
ejpam-4637	456	3	<	<	X
ejpam-4637	456	4	0.5	0.5	NUM
ejpam-4637	456	5	=	=	SYM
ejpam-4637	456	6	min{t∆(e)(x	min{t∆(e)(x	NOUN
ejpam-4637	456	7	)	)	PUNCT
ejpam-4637	456	8	,	,	PUNCT
ejpam-4637	456	9	t∆(e)(y	t∆(e)(y	PROPN
ejpam-4637	456	10	)	)	PUNCT
ejpam-4637	456	11	}	}	PUNCT
ejpam-4637	456	12	.	.	PUNCT
ejpam-4637	457	1	thus	thus	ADV
ejpam-4637	457	2	,	,	PUNCT
ejpam-4637	457	3	(	(	PUNCT
ejpam-4637	457	4	∆	∆	X
ejpam-4637	457	5	,	,	PUNCT
ejpam-4637	457	6	e	e	X
ejpam-4637	457	7	)	)	PUNCT
ejpam-4637	457	8	is	be	AUX
ejpam-4637	457	9	not	not	PART
ejpam-4637	457	10	a	a	DET
ejpam-4637	457	11	svns	svns	NOUN
ejpam-4637	457	12	hyper	hyper	ADJ
ejpam-4637	457	13	up	up	ADP
ejpam-4637	457	14	-subalgebra	-subalgebra	NOUN
ejpam-4637	457	15	of	of	ADP
ejpam-4637	457	16	x.	x.	PROPN
ejpam-4637	457	17	a.	a.	PROPN
ejpam-4637	457	18	cano	cano	PROPN
ejpam-4637	457	19	,	,	PUNCT
ejpam-4637	457	20	g.	g.	PROPN
ejpam-4637	457	21	petalcorin	petalcorin	PROPN
ejpam-4637	457	22	/	/	SYM
ejpam-4637	457	23	eur	eur	PROPN
ejpam-4637	457	24	.	.	PUNCT
ejpam-4637	458	1	j.	j.	PROPN
ejpam-4637	458	2	pure	pure	PROPN
ejpam-4637	458	3	appl	appl	PROPN
ejpam-4637	458	4	.	.	PROPN
ejpam-4637	458	5	math	math	PROPN
ejpam-4637	458	6	,	,	PUNCT
ejpam-4637	458	7	16	16	NUM
ejpam-4637	458	8	(	(	PUNCT
ejpam-4637	458	9	1	1	NUM
ejpam-4637	458	10	)	)	PUNCT
ejpam-4637	458	11	(	(	PUNCT
ejpam-4637	458	12	2023	2023	NUM
ejpam-4637	458	13	)	)	PUNCT
ejpam-4637	458	14	,	,	PUNCT
ejpam-4637	458	15	548	548	NUM
ejpam-4637	458	16	-	-	SYM
ejpam-4637	458	17	576	576	NUM
ejpam-4637	458	18	568	568	NUM
ejpam-4637	458	19	3.3	3.3	NUM
ejpam-4637	458	20	.	.	PUNCT
ejpam-4637	459	1	cartesian	cartesian	ADJ
ejpam-4637	459	2	product	product	NOUN
ejpam-4637	459	3	of	of	ADP
ejpam-4637	459	4	svns	svns	PROPN
ejpam-4637	459	5	hyper	hyper	ADJ
ejpam-4637	459	6	up	up	ADP
ejpam-4637	459	7	-	-	PUNCT
ejpam-4637	459	8	subalgebra	subalgebra	NOUN
ejpam-4637	459	9	in	in	ADP
ejpam-4637	459	10	this	this	DET
ejpam-4637	459	11	section	section	NOUN
ejpam-4637	459	12	,	,	PUNCT
ejpam-4637	459	13	we	we	PRON
ejpam-4637	459	14	define	define	VERB
ejpam-4637	459	15	the	the	DET
ejpam-4637	459	16	cartesian	cartesian	ADJ
ejpam-4637	459	17	product	product	NOUN
ejpam-4637	459	18	of	of	ADP
ejpam-4637	459	19	svns	svns	PROPN
ejpam-4637	459	20	hyper	hyper	ADJ
ejpam-4637	459	21	up	up	ADP
ejpam-4637	459	22	-subalgebra	-subalgebra	NOUN
ejpam-4637	459	23	and	and	CCONJ
ejpam-4637	459	24	prove	prove	VERB
ejpam-4637	459	25	that	that	SCONJ
ejpam-4637	459	26	it	it	PRON
ejpam-4637	459	27	is	be	AUX
ejpam-4637	459	28	also	also	ADV
ejpam-4637	459	29	a	a	DET
ejpam-4637	459	30	svns	svns	NOUN
ejpam-4637	459	31	hyper	hyper	ADJ
ejpam-4637	459	32	up	up	ADP
ejpam-4637	459	33	-subalgebra	-subalgebra	NOUN
ejpam-4637	459	34	.	.	PUNCT
ejpam-4637	460	1	definition	definition	NOUN
ejpam-4637	460	2	18	18	NUM
ejpam-4637	460	3	.	.	PUNCT
ejpam-4637	461	1	let	let	AUX
ejpam-4637	461	2	(	(	PUNCT
ejpam-4637	461	3	∆1	∆1	NOUN
ejpam-4637	461	4	,	,	PUNCT
ejpam-4637	461	5	e	e	NOUN
ejpam-4637	461	6	)	)	PUNCT
ejpam-4637	461	7	and	and	CCONJ
ejpam-4637	461	8	(	(	PUNCT
ejpam-4637	461	9	∆2	∆2	X
ejpam-4637	461	10	,	,	PUNCT
ejpam-4637	461	11	e	e	NOUN
ejpam-4637	461	12	)	)	PUNCT
ejpam-4637	461	13	be	be	VERB
ejpam-4637	461	14	two	two	NUM
ejpam-4637	461	15	svns	svns	NOUN
ejpam-4637	461	16	hyper	hyper	ADJ
ejpam-4637	461	17	up	up	ADV
ejpam-4637	461	18	-subalgebras	-subalgebra	NOUN
ejpam-4637	461	19	of	of	ADP
ejpam-4637	461	20	x1	x1	PROPN
ejpam-4637	461	21	and	and	CCONJ
ejpam-4637	461	22	x2	x2	PROPN
ejpam-4637	461	23	,	,	PUNCT
ejpam-4637	461	24	respectively	respectively	ADV
ejpam-4637	461	25	.	.	PUNCT
ejpam-4637	462	1	then	then	ADV
ejpam-4637	462	2	their	their	PRON
ejpam-4637	462	3	cartesian	cartesian	ADJ
ejpam-4637	462	4	product	product	NOUN
ejpam-4637	462	5	is	be	AUX
ejpam-4637	462	6	(	(	PUNCT
ejpam-4637	462	7	∆	∆	PROPN
ejpam-4637	462	8	,	,	PUNCT
ejpam-4637	462	9	e	e	X
ejpam-4637	462	10	×e	×e	X
ejpam-4637	462	11	)	)	PUNCT
ejpam-4637	462	12	=	=	SYM
ejpam-4637	462	13	(	(	PUNCT
ejpam-4637	462	14	∆1	∆1	PROPN
ejpam-4637	462	15	,	,	PUNCT
ejpam-4637	462	16	e)×	e)×	NOUN
ejpam-4637	462	17	(	(	PUNCT
ejpam-4637	462	18	∆2	∆2	X
ejpam-4637	462	19	,	,	PUNCT
ejpam-4637	462	20	e	e	NOUN
ejpam-4637	462	21	)	)	PUNCT
ejpam-4637	462	22	,	,	PUNCT
ejpam-4637	462	23	where	where	SCONJ
ejpam-4637	462	24	∆(a	∆(a	NOUN
ejpam-4637	462	25	,	,	PUNCT
ejpam-4637	462	26	b	b	NOUN
ejpam-4637	462	27	)	)	PUNCT
ejpam-4637	462	28	=	=	SYM
ejpam-4637	462	29	∆1(a)×∆2(b	∆1(a)×∆2(b	NOUN
ejpam-4637	462	30	)	)	PUNCT
ejpam-4637	462	31	for	for	ADP
ejpam-4637	462	32	(	(	PUNCT
ejpam-4637	462	33	a	a	PRON
ejpam-4637	462	34	,	,	PUNCT
ejpam-4637	462	35	b	b	NOUN
ejpam-4637	462	36	)	)	PUNCT
ejpam-4637	462	37	∈	∈	PROPN
ejpam-4637	462	38	e	e	X
ejpam-4637	462	39	×	×	PROPN
ejpam-4637	462	40	e.	e.	PROPN
ejpam-4637	462	41	analytically	analytically	ADV
ejpam-4637	462	42	,	,	PUNCT
ejpam-4637	462	43	∆(a	∆(a	PROPN
ejpam-4637	462	44	,	,	PUNCT
ejpam-4637	462	45	b	b	NOUN
ejpam-4637	462	46	)	)	PUNCT
ejpam-4637	462	47	=	=	PRON
ejpam-4637	462	48	{	{	PUNCT
ejpam-4637	462	49	〈	〈	PROPN
ejpam-4637	462	50	(	(	PUNCT
ejpam-4637	462	51	x	x	PROPN
ejpam-4637	462	52	,	,	PUNCT
ejpam-4637	462	53	y	y	PROPN
ejpam-4637	462	54	)	)	PUNCT
ejpam-4637	462	55	,	,	PUNCT
ejpam-4637	462	56	(	(	PUNCT
ejpam-4637	462	57	t∆(a	t∆(a	NUM
ejpam-4637	462	58	,	,	PUNCT
ejpam-4637	462	59	b)(x	b)(x	PROPN
ejpam-4637	462	60	,	,	PUNCT
ejpam-4637	462	61	y	y	PROPN
ejpam-4637	462	62	)	)	PUNCT
ejpam-4637	462	63	,	,	PUNCT
ejpam-4637	462	64	i∆(a	i∆(a	ADP
ejpam-4637	462	65	,	,	PUNCT
ejpam-4637	462	66	b)(x	b)(x	PROPN
ejpam-4637	462	67	,	,	PUNCT
ejpam-4637	462	68	y),f∆(a	y),f∆(a	PROPN
ejpam-4637	462	69	,	,	PUNCT
ejpam-4637	462	70	b)(x	b)(x	PROPN
ejpam-4637	462	71	,	,	PUNCT
ejpam-4637	462	72	y	y	NOUN
ejpam-4637	462	73	)	)	PUNCT
ejpam-4637	462	74	)	)	PUNCT
ejpam-4637	462	75	〉	〉	NOUN
ejpam-4637	462	76	|(x	|(x	ADP
ejpam-4637	462	77	,	,	PUNCT
ejpam-4637	462	78	y	y	NOUN
ejpam-4637	462	79	)	)	PUNCT
ejpam-4637	462	80	∈	∈	PROPN
ejpam-4637	462	81	x1	x1	ADJ
ejpam-4637	462	82	×x2	×x2	NOUN
ejpam-4637	462	83	}	}	PUNCT
ejpam-4637	462	84	where	where	SCONJ
ejpam-4637	462	85	t∆(a	t∆(a	NOUN
ejpam-4637	462	86	,	,	PUNCT
ejpam-4637	462	87	b)(x	b)(x	PROPN
ejpam-4637	462	88	,	,	PUNCT
ejpam-4637	462	89	y	y	NOUN
ejpam-4637	462	90	)	)	PUNCT
ejpam-4637	462	91	=	=	SYM
ejpam-4637	462	92	min{t∆1(a)(x	min{t∆1(a)(x	PROPN
ejpam-4637	462	93	)	)	PUNCT
ejpam-4637	462	94	,	,	PUNCT
ejpam-4637	462	95	t∆2(b)(y	t∆2(b)(y	NUM
ejpam-4637	462	96	)	)	PUNCT
ejpam-4637	462	97	}	}	PUNCT
ejpam-4637	462	98	,	,	PUNCT
ejpam-4637	462	99	i∆(a	i∆(a	ADP
ejpam-4637	462	100	,	,	PUNCT
ejpam-4637	462	101	b)(x	b)(x	PROPN
ejpam-4637	462	102	,	,	PUNCT
ejpam-4637	462	103	y	y	NOUN
ejpam-4637	462	104	)	)	PUNCT
ejpam-4637	462	105	=	=	SYM
ejpam-4637	462	106	max{i∆1(a)(x	max{i∆1(a)(x	NOUN
ejpam-4637	462	107	)	)	PUNCT
ejpam-4637	462	108	,	,	PUNCT
ejpam-4637	462	109	i∆2(b)(y	i∆2(b)(y	NOUN
ejpam-4637	462	110	)	)	PUNCT
ejpam-4637	462	111	}	}	PUNCT
ejpam-4637	462	112	,	,	PUNCT
ejpam-4637	462	113	and	and	CCONJ
ejpam-4637	462	114	f∆(a	f∆(a	NOUN
ejpam-4637	462	115	,	,	PUNCT
ejpam-4637	462	116	b)(x	b)(x	PROPN
ejpam-4637	462	117	,	,	PUNCT
ejpam-4637	462	118	y	y	PROPN
ejpam-4637	462	119	)	)	PUNCT
ejpam-4637	462	120	=	=	SYM
ejpam-4637	462	121	max{f∆1(a)(x),f∆2(b)(y	max{f∆1(a)(x),f∆2(b)(y	X
ejpam-4637	462	122	)	)	PUNCT
ejpam-4637	462	123	}	}	PUNCT
ejpam-4637	462	124	.	.	PUNCT
ejpam-4637	463	1	for	for	ADP
ejpam-4637	463	2	(	(	PUNCT
ejpam-4637	463	3	a	a	PRON
ejpam-4637	463	4	,	,	PUNCT
ejpam-4637	463	5	b	b	NOUN
ejpam-4637	463	6	)	)	PUNCT
ejpam-4637	463	7	∈	∈	PROPN
ejpam-4637	463	8	e	e	PROPN
ejpam-4637	463	9	×	×	PROPN
ejpam-4637	463	10	e.	e.	PROPN
ejpam-4637	463	11	example	example	PROPN
ejpam-4637	463	12	8	8	NUM
ejpam-4637	463	13	.	.	PUNCT
ejpam-4637	463	14	using	use	VERB
ejpam-4637	463	15	e	e	NOUN
ejpam-4637	463	16	=	=	SYM
ejpam-4637	463	17	{	{	PUNCT
ejpam-4637	463	18	e1	e1	PROPN
ejpam-4637	463	19	,	,	PUNCT
ejpam-4637	463	20	e2	e2	PROPN
ejpam-4637	463	21	}	}	PUNCT
ejpam-4637	463	22	as	as	ADP
ejpam-4637	463	23	the	the	DET
ejpam-4637	463	24	set	set	NOUN
ejpam-4637	463	25	of	of	ADP
ejpam-4637	463	26	parameters	parameter	NOUN
ejpam-4637	463	27	,	,	PUNCT
ejpam-4637	463	28	consider	consider	VERB
ejpam-4637	463	29	the	the	DET
ejpam-4637	463	30	hyper	hyper	ADJ
ejpam-4637	463	31	up	up	ADP
ejpam-4637	463	32	-algebra	-algebra	PROPN
ejpam-4637	463	33	x	x	X
ejpam-4637	463	34	=	=	SYM
ejpam-4637	463	35	{	{	PUNCT
ejpam-4637	463	36	01	01	NUM
ejpam-4637	463	37	,	,	PUNCT
ejpam-4637	463	38	r	r	NOUN
ejpam-4637	463	39	,	,	PUNCT
ejpam-4637	463	40	s	s	PROPN
ejpam-4637	463	41	,	,	PUNCT
ejpam-4637	463	42	t	t	PROPN
ejpam-4637	463	43	}	}	PUNCT
ejpam-4637	463	44	of	of	ADP
ejpam-4637	463	45	example	example	NOUN
ejpam-4637	463	46	1	1	NUM
ejpam-4637	463	47	as	as	ADP
ejpam-4637	463	48	x1	x1	PROPN
ejpam-4637	463	49	with	with	ADP
ejpam-4637	463	50	its	its	PRON
ejpam-4637	463	51	hyperoperation	hyperoperation	NOUN
ejpam-4637	463	52	“	"	PUNCT
ejpam-4637	463	53	◦	◦	NOUN
ejpam-4637	463	54	1	1	NUM
ejpam-4637	463	55	”	"	PUNCT
ejpam-4637	463	56	and	and	CCONJ
ejpam-4637	463	57	its	its	PRON
ejpam-4637	463	58	svns	svns	NOUN
ejpam-4637	463	59	hyper	hyper	VERB
ejpam-4637	463	60	up	up	ADP
ejpam-4637	463	61	-subalgebra	-subalgebra	PROPN
ejpam-4637	463	62	(	(	PUNCT
ejpam-4637	463	63	∆1	∆1	NOUN
ejpam-4637	463	64	,	,	PUNCT
ejpam-4637	463	65	e	e	NOUN
ejpam-4637	463	66	)	)	PUNCT
ejpam-4637	463	67	given	give	VERB
ejpam-4637	463	68	by	by	ADP
ejpam-4637	463	69	t∆1(e)(x	t∆1(e)(x	NOUN
ejpam-4637	463	70	)	)	PUNCT
ejpam-4637	463	71	=	=	PRON
ejpam-4637	463	72	{	{	PUNCT
ejpam-4637	463	73	0.5	0.5	NUM
ejpam-4637	463	74	if	if	SCONJ
ejpam-4637	463	75	x	x	SYM
ejpam-4637	463	76	∈	∈	PROPN
ejpam-4637	463	77	{	{	PUNCT
ejpam-4637	463	78	01	01	NUM
ejpam-4637	463	79	,	,	PUNCT
ejpam-4637	463	80	s	s	PART
ejpam-4637	463	81	}	}	PUNCT
ejpam-4637	463	82	,	,	PUNCT
ejpam-4637	463	83	0	0	NUM
ejpam-4637	463	84	otherwise	otherwise	ADV
ejpam-4637	463	85	.	.	PUNCT
ejpam-4637	464	1	i∆1(e)(x	i∆1(e)(x	PROPN
ejpam-4637	464	2	)	)	PUNCT
ejpam-4637	465	1	=	=	PRON
ejpam-4637	465	2	{	{	PUNCT
ejpam-4637	465	3	0	0	NUM
ejpam-4637	465	4	if	if	SCONJ
ejpam-4637	465	5	x	x	X
ejpam-4637	465	6	∈	∈	PROPN
ejpam-4637	465	7	{	{	PUNCT
ejpam-4637	465	8	01	01	NUM
ejpam-4637	465	9	,	,	PUNCT
ejpam-4637	465	10	s	s	PART
ejpam-4637	465	11	}	}	PUNCT
ejpam-4637	465	12	,	,	PUNCT
ejpam-4637	465	13	0.5	0.5	NUM
ejpam-4637	465	14	otherwise	otherwise	ADV
ejpam-4637	465	15	.	.	PUNCT
ejpam-4637	466	1	f∆1(e)(x	f∆1(e)(x	NOUN
ejpam-4637	466	2	)	)	PUNCT
ejpam-4637	466	3	=	=	PRON
ejpam-4637	466	4	{	{	PUNCT
ejpam-4637	466	5	0	0	NUM
ejpam-4637	466	6	if	if	SCONJ
ejpam-4637	466	7	x	x	X
ejpam-4637	466	8	∈	∈	PROPN
ejpam-4637	466	9	{	{	PUNCT
ejpam-4637	466	10	01	01	NUM
ejpam-4637	466	11	,	,	PUNCT
ejpam-4637	466	12	s	s	PART
ejpam-4637	466	13	}	}	PUNCT
ejpam-4637	466	14	,	,	PUNCT
ejpam-4637	466	15	0.5	0.5	NUM
ejpam-4637	466	16	otherwise	otherwise	ADV
ejpam-4637	466	17	.	.	PUNCT
ejpam-4637	467	1	for	for	SCONJ
ejpam-4637	467	2	e	e	PROPN
ejpam-4637	467	3	∈	∈	PROPN
ejpam-4637	467	4	e.	e.	PROPN
ejpam-4637	467	5	consider	consider	VERB
ejpam-4637	467	6	also	also	ADV
ejpam-4637	467	7	hyper	hyper	VERB
ejpam-4637	467	8	up	up	ADP
ejpam-4637	467	9	-algebra	-algebra	PROPN
ejpam-4637	468	1	x	x	SYM
ejpam-4637	468	2	=	=	SYM
ejpam-4637	468	3	{	{	PUNCT
ejpam-4637	468	4	02	02	NUM
ejpam-4637	468	5	,	,	PUNCT
ejpam-4637	468	6	u	u	NOUN
ejpam-4637	468	7	,	,	PUNCT
ejpam-4637	468	8	v	v	NOUN
ejpam-4637	468	9	}	}	PUNCT
ejpam-4637	468	10	of	of	ADP
ejpam-4637	468	11	example	example	NOUN
ejpam-4637	468	12	2	2	NUM
ejpam-4637	468	13	as	as	ADP
ejpam-4637	468	14	x2	x2	PROPN
ejpam-4637	468	15	with	with	ADP
ejpam-4637	468	16	its	its	PRON
ejpam-4637	468	17	hyper	hyper	ADJ
ejpam-4637	468	18	operation	operation	NOUN
ejpam-4637	468	19	“	"	PUNCT
ejpam-4637	468	20	◦	◦	NOUN
ejpam-4637	468	21	2	2	NUM
ejpam-4637	468	22	”	"	PUNCT
ejpam-4637	468	23	and	and	CCONJ
ejpam-4637	468	24	its	its	PRON
ejpam-4637	468	25	svns	svns	NOUN
ejpam-4637	468	26	hyper	hyper	VERB
ejpam-4637	468	27	up	up	ADP
ejpam-4637	468	28	-subalgebra	-subalgebra	PROPN
ejpam-4637	468	29	(	(	PUNCT
ejpam-4637	468	30	∆2	∆2	X
ejpam-4637	468	31	,	,	PUNCT
ejpam-4637	468	32	e	e	NOUN
ejpam-4637	468	33	)	)	PUNCT
ejpam-4637	468	34	given	give	VERB
ejpam-4637	468	35	by	by	ADP
ejpam-4637	468	36	(	(	PUNCT
ejpam-4637	468	37	∆2	∆2	X
ejpam-4637	468	38	,	,	PUNCT
ejpam-4637	468	39	e	e	NOUN
ejpam-4637	468	40	)	)	PUNCT
ejpam-4637	468	41	=	=	SYM
ejpam-4637	468	42	{	{	PUNCT
ejpam-4637	468	43	(	(	PUNCT
ejpam-4637	468	44	e1	e1	NOUN
ejpam-4637	468	45	,	,	PUNCT
ejpam-4637	468	46	{	{	PUNCT
ejpam-4637	468	47	⟨02	⟨02	NOUN
ejpam-4637	468	48	,	,	PUNCT
ejpam-4637	468	49	(	(	PUNCT
ejpam-4637	468	50	0.9	0.9	NUM
ejpam-4637	468	51	,	,	PUNCT
ejpam-4637	468	52	0.2	0.2	NUM
ejpam-4637	468	53	,	,	PUNCT
ejpam-4637	468	54	0.45)⟩	0.45)⟩	NUM
ejpam-4637	468	55	,	,	PUNCT
ejpam-4637	468	56	⟨u	⟨u	NOUN
ejpam-4637	468	57	,	,	PUNCT
ejpam-4637	468	58	(	(	PUNCT
ejpam-4637	468	59	0.74	0.74	NUM
ejpam-4637	468	60	,	,	PUNCT
ejpam-4637	468	61	0.57	0.57	NUM
ejpam-4637	468	62	,	,	PUNCT
ejpam-4637	468	63	0.7)⟩	0.7)⟩	NUM
ejpam-4637	468	64	,	,	PUNCT
ejpam-4637	468	65	⟨v	⟨v	CCONJ
ejpam-4637	468	66	,	,	PUNCT
ejpam-4637	468	67	(	(	PUNCT
ejpam-4637	468	68	0.8	0.8	NUM
ejpam-4637	468	69	,	,	PUNCT
ejpam-4637	468	70	0.42	0.42	NUM
ejpam-4637	468	71	,	,	PUNCT
ejpam-4637	468	72	0.52)⟩	0.52)⟩	NUM
ejpam-4637	468	73	}	}	PUNCT
ejpam-4637	468	74	)	)	PUNCT
ejpam-4637	468	75	,	,	PUNCT
ejpam-4637	468	76	(	(	PUNCT
ejpam-4637	468	77	e2	e2	PROPN
ejpam-4637	468	78	,	,	PUNCT
ejpam-4637	468	79	{	{	PUNCT
ejpam-4637	468	80	⟨02	⟨02	NOUN
ejpam-4637	468	81	,	,	PUNCT
ejpam-4637	468	82	(	(	PUNCT
ejpam-4637	468	83	0.8	0.8	NUM
ejpam-4637	468	84	,	,	PUNCT
ejpam-4637	468	85	0.2	0.2	NUM
ejpam-4637	468	86	,	,	PUNCT
ejpam-4637	468	87	0.4)⟩	0.4)⟩	NUM
ejpam-4637	468	88	,	,	PUNCT
ejpam-4637	468	89	⟨u	⟨u	NOUN
ejpam-4637	468	90	,	,	PUNCT
ejpam-4637	468	91	(	(	PUNCT
ejpam-4637	468	92	0.4	0.4	NUM
ejpam-4637	468	93	,	,	PUNCT
ejpam-4637	468	94	0.45	0.45	NUM
ejpam-4637	468	95	,	,	PUNCT
ejpam-4637	468	96	0.5)⟩	0.5)⟩	NUM
ejpam-4637	468	97	,	,	PUNCT
ejpam-4637	468	98	⟨v	⟨v	PROPN
ejpam-4637	468	99	,	,	PUNCT
ejpam-4637	468	100	(	(	PUNCT
ejpam-4637	468	101	0.67	0.67	NUM
ejpam-4637	468	102	,	,	PUNCT
ejpam-4637	468	103	0.3	0.3	NUM
ejpam-4637	468	104	,	,	PUNCT
ejpam-4637	468	105	0.5)⟩	0.5)⟩	NUM
ejpam-4637	468	106	}	}	PUNCT
ejpam-4637	468	107	)	)	PUNCT
ejpam-4637	468	108	}	}	PUNCT
ejpam-4637	468	109	.	.	PUNCT
ejpam-4637	469	1	then	then	ADV
ejpam-4637	469	2	the	the	DET
ejpam-4637	469	3	cartesian	cartesian	ADJ
ejpam-4637	469	4	product	product	NOUN
ejpam-4637	469	5	of	of	ADP
ejpam-4637	469	6	(	(	PUNCT
ejpam-4637	469	7	∆1	∆1	NOUN
ejpam-4637	469	8	,	,	PUNCT
ejpam-4637	469	9	e	e	NOUN
ejpam-4637	469	10	)	)	PUNCT
ejpam-4637	469	11	and	and	CCONJ
ejpam-4637	469	12	(	(	PUNCT
ejpam-4637	469	13	∆2	∆2	X
ejpam-4637	469	14	,	,	PUNCT
ejpam-4637	469	15	e	e	NOUN
ejpam-4637	469	16	)	)	PUNCT
ejpam-4637	469	17	is	be	AUX
ejpam-4637	469	18	(	(	PUNCT
ejpam-4637	469	19	∆	∆	X
ejpam-4637	469	20	,	,	PUNCT
ejpam-4637	469	21	e	e	X
ejpam-4637	469	22	)	)	PUNCT
ejpam-4637	469	23	=	=	SYM
ejpam-4637	469	24	{	{	PUNCT
ejpam-4637	469	25	(	(	PUNCT
ejpam-4637	469	26	(	(	PUNCT
ejpam-4637	469	27	e1	e1	NOUN
ejpam-4637	469	28	,	,	PUNCT
ejpam-4637	469	29	e1	e1	NOUN
ejpam-4637	469	30	)	)	PUNCT
ejpam-4637	469	31	,	,	PUNCT
ejpam-4637	469	32	{	{	PUNCT
ejpam-4637	469	33	⟨(01	⟨(01	NOUN
ejpam-4637	469	34	,	,	PUNCT
ejpam-4637	469	35	02	02	NUM
ejpam-4637	469	36	)	)	PUNCT
ejpam-4637	469	37	,	,	PUNCT
ejpam-4637	469	38	(	(	PUNCT
ejpam-4637	469	39	0.5	0.5	NUM
ejpam-4637	469	40	,	,	PUNCT
ejpam-4637	469	41	0.2	0.2	NUM
ejpam-4637	469	42	,	,	PUNCT
ejpam-4637	469	43	0.45)⟩	0.45)⟩	NUM
ejpam-4637	469	44	,	,	PUNCT
ejpam-4637	469	45	⟨(01	⟨(01	PROPN
ejpam-4637	469	46	,	,	PUNCT
ejpam-4637	469	47	u	u	NOUN
ejpam-4637	469	48	)	)	PUNCT
ejpam-4637	469	49	,	,	PUNCT
ejpam-4637	469	50	(	(	PUNCT
ejpam-4637	469	51	0.5	0.5	NUM
ejpam-4637	469	52	,	,	PUNCT
ejpam-4637	469	53	0.57	0.57	NUM
ejpam-4637	469	54	,	,	PUNCT
ejpam-4637	469	55	0.7)⟩	0.7)⟩	NUM
ejpam-4637	469	56	,	,	PUNCT
ejpam-4637	469	57	⟨(01	⟨(01	PROPN
ejpam-4637	469	58	,	,	PUNCT
ejpam-4637	469	59	v	v	NOUN
ejpam-4637	469	60	)	)	PUNCT
ejpam-4637	469	61	,	,	PUNCT
ejpam-4637	469	62	(	(	PUNCT
ejpam-4637	469	63	0.5	0.5	NUM
ejpam-4637	469	64	,	,	PUNCT
ejpam-4637	469	65	0.42	0.42	NUM
ejpam-4637	469	66	,	,	PUNCT
ejpam-4637	469	67	0.52)⟩	0.52)⟩	NUM
ejpam-4637	469	68	,	,	PUNCT
ejpam-4637	469	69	⟨(r	⟨(r	NOUN
ejpam-4637	469	70	,	,	PUNCT
ejpam-4637	469	71	02	02	NUM
ejpam-4637	469	72	)	)	PUNCT
ejpam-4637	469	73	,	,	PUNCT
ejpam-4637	469	74	(	(	PUNCT
ejpam-4637	469	75	0	0	NUM
ejpam-4637	469	76	,	,	PUNCT
ejpam-4637	469	77	0.5	0.5	NUM
ejpam-4637	469	78	,	,	PUNCT
ejpam-4637	469	79	0.5)⟩	0.5)⟩	NUM
ejpam-4637	469	80	,	,	PUNCT
ejpam-4637	469	81	⟨(r	⟨(r	NOUN
ejpam-4637	469	82	,	,	PUNCT
ejpam-4637	469	83	u	u	NOUN
ejpam-4637	469	84	)	)	PUNCT
ejpam-4637	469	85	,	,	PUNCT
ejpam-4637	469	86	(	(	PUNCT
ejpam-4637	469	87	0	0	NUM
ejpam-4637	469	88	,	,	PUNCT
ejpam-4637	469	89	0.57	0.57	NUM
ejpam-4637	469	90	,	,	PUNCT
ejpam-4637	469	91	0.7)⟩	0.7)⟩	NUM
ejpam-4637	469	92	,	,	PUNCT
ejpam-4637	469	93	⟨(r	⟨(r	NOUN
ejpam-4637	469	94	,	,	PUNCT
ejpam-4637	469	95	v	v	NOUN
ejpam-4637	469	96	)	)	PUNCT
ejpam-4637	469	97	,	,	PUNCT
ejpam-4637	469	98	(	(	PUNCT
ejpam-4637	469	99	0	0	NUM
ejpam-4637	469	100	,	,	PUNCT
ejpam-4637	469	101	0.5	0.5	NUM
ejpam-4637	469	102	,	,	PUNCT
ejpam-4637	469	103	0.52)⟩	0.52)⟩	NUM
ejpam-4637	469	104	,	,	PUNCT
ejpam-4637	469	105	⟨(s	⟨(s	PROPN
ejpam-4637	469	106	,	,	PUNCT
ejpam-4637	469	107	02	02	NUM
ejpam-4637	469	108	)	)	PUNCT
ejpam-4637	469	109	,	,	PUNCT
ejpam-4637	469	110	(	(	PUNCT
ejpam-4637	469	111	0.5	0.5	NUM
ejpam-4637	469	112	,	,	PUNCT
ejpam-4637	469	113	0.2	0.2	NUM
ejpam-4637	469	114	,	,	PUNCT
ejpam-4637	469	115	0.45)⟩	0.45)⟩	NUM
ejpam-4637	469	116	,	,	PUNCT
ejpam-4637	469	117	⟨(s	⟨(s	PROPN
ejpam-4637	469	118	,	,	PUNCT
ejpam-4637	469	119	u	u	NOUN
ejpam-4637	469	120	)	)	PUNCT
ejpam-4637	469	121	,	,	PUNCT
ejpam-4637	469	122	(	(	PUNCT
ejpam-4637	469	123	0.5	0.5	NUM
ejpam-4637	469	124	,	,	PUNCT
ejpam-4637	469	125	0.57	0.57	NUM
ejpam-4637	469	126	,	,	PUNCT
ejpam-4637	469	127	0.7)⟩	0.7)⟩	NUM
ejpam-4637	469	128	,	,	PUNCT
ejpam-4637	469	129	⟨(s	⟨(s	PROPN
ejpam-4637	469	130	,	,	PUNCT
ejpam-4637	469	131	v	v	NOUN
ejpam-4637	469	132	)	)	PUNCT
ejpam-4637	469	133	,	,	PUNCT
ejpam-4637	469	134	(	(	PUNCT
ejpam-4637	469	135	0.5	0.5	NUM
ejpam-4637	469	136	,	,	PUNCT
ejpam-4637	469	137	0.42	0.42	NUM
ejpam-4637	469	138	,	,	PUNCT
ejpam-4637	469	139	0.52)⟩	0.52)⟩	NUM
ejpam-4637	469	140	,	,	PUNCT
ejpam-4637	469	141	⟨(t	⟨(t	PROPN
ejpam-4637	469	142	,	,	PUNCT
ejpam-4637	469	143	02	02	NUM
ejpam-4637	469	144	)	)	PUNCT
ejpam-4637	469	145	,	,	PUNCT
ejpam-4637	469	146	(	(	PUNCT
ejpam-4637	469	147	0	0	NUM
ejpam-4637	469	148	,	,	PUNCT
ejpam-4637	469	149	0.5	0.5	NUM
ejpam-4637	469	150	,	,	PUNCT
ejpam-4637	469	151	0.5)⟩	0.5)⟩	NUM
ejpam-4637	469	152	,	,	PUNCT
ejpam-4637	469	153	⟨(t	⟨(t	PROPN
ejpam-4637	469	154	,	,	PUNCT
ejpam-4637	469	155	u	u	NOUN
ejpam-4637	469	156	)	)	PUNCT
ejpam-4637	469	157	,	,	PUNCT
ejpam-4637	469	158	(	(	PUNCT
ejpam-4637	469	159	0	0	NUM
ejpam-4637	469	160	,	,	PUNCT
ejpam-4637	469	161	0.57	0.57	NUM
ejpam-4637	469	162	,	,	PUNCT
ejpam-4637	469	163	0.7)⟩	0.7)⟩	NUM
ejpam-4637	469	164	,	,	PUNCT
ejpam-4637	469	165	⟨(t	⟨(t	PROPN
ejpam-4637	469	166	,	,	PUNCT
ejpam-4637	469	167	v	v	NOUN
ejpam-4637	469	168	)	)	PUNCT
ejpam-4637	469	169	,	,	PUNCT
ejpam-4637	469	170	(	(	PUNCT
ejpam-4637	469	171	0	0	NUM
ejpam-4637	469	172	,	,	PUNCT
ejpam-4637	469	173	0.5	0.5	NUM
ejpam-4637	469	174	,	,	PUNCT
ejpam-4637	469	175	0.52)⟩	0.52)⟩	NUM
ejpam-4637	469	176	}	}	PUNCT
ejpam-4637	469	177	)	)	PUNCT
ejpam-4637	469	178	,	,	PUNCT
ejpam-4637	469	179	(	(	PUNCT
ejpam-4637	469	180	(	(	PUNCT
ejpam-4637	469	181	e1	e1	PROPN
ejpam-4637	469	182	,	,	PUNCT
ejpam-4637	469	183	e2	e2	PROPN
ejpam-4637	469	184	)	)	PUNCT
ejpam-4637	469	185	,	,	PUNCT
ejpam-4637	469	186	{	{	PUNCT
ejpam-4637	469	187	⟨(01	⟨(01	NOUN
ejpam-4637	469	188	,	,	PUNCT
ejpam-4637	469	189	02	02	NUM
ejpam-4637	469	190	)	)	PUNCT
ejpam-4637	469	191	,	,	PUNCT
ejpam-4637	469	192	(	(	PUNCT
ejpam-4637	469	193	0.5	0.5	NUM
ejpam-4637	469	194	,	,	PUNCT
ejpam-4637	469	195	0.2.0.4)⟩	0.2.0.4)⟩	NUM
ejpam-4637	469	196	,	,	PUNCT
ejpam-4637	469	197	a.	a.	PROPN
ejpam-4637	469	198	cano	cano	PROPN
ejpam-4637	469	199	,	,	PUNCT
ejpam-4637	469	200	g.	g.	PROPN
ejpam-4637	469	201	petalcorin	petalcorin	PROPN
ejpam-4637	469	202	/	/	SYM
ejpam-4637	469	203	eur	eur	PROPN
ejpam-4637	469	204	.	.	PUNCT
ejpam-4637	470	1	j.	j.	PROPN
ejpam-4637	470	2	pure	pure	PROPN
ejpam-4637	470	3	appl	appl	PROPN
ejpam-4637	470	4	.	.	PROPN
ejpam-4637	470	5	math	math	PROPN
ejpam-4637	470	6	,	,	PUNCT
ejpam-4637	470	7	16	16	NUM
ejpam-4637	470	8	(	(	PUNCT
ejpam-4637	470	9	1	1	NUM
ejpam-4637	470	10	)	)	PUNCT
ejpam-4637	470	11	(	(	PUNCT
ejpam-4637	470	12	2023	2023	NUM
ejpam-4637	470	13	)	)	PUNCT
ejpam-4637	470	14	,	,	PUNCT
ejpam-4637	470	15	548	548	NUM
ejpam-4637	470	16	-	-	SYM
ejpam-4637	470	17	576	576	NUM
ejpam-4637	470	18	569	569	NUM
ejpam-4637	470	19	⟨(01	⟨(01	PROPN
ejpam-4637	470	20	,	,	PUNCT
ejpam-4637	470	21	u	u	NOUN
ejpam-4637	470	22	)	)	PUNCT
ejpam-4637	470	23	,	,	PUNCT
ejpam-4637	470	24	(	(	PUNCT
ejpam-4637	470	25	0.4	0.4	NUM
ejpam-4637	470	26	,	,	PUNCT
ejpam-4637	470	27	0.45	0.45	NUM
ejpam-4637	470	28	,	,	PUNCT
ejpam-4637	470	29	0.5)⟩	0.5)⟩	NUM
ejpam-4637	470	30	,	,	PUNCT
ejpam-4637	470	31	⟨(01	⟨(01	PROPN
ejpam-4637	470	32	,	,	PUNCT
ejpam-4637	470	33	v	v	NOUN
ejpam-4637	470	34	)	)	PUNCT
ejpam-4637	470	35	,	,	PUNCT
ejpam-4637	470	36	(	(	PUNCT
ejpam-4637	470	37	0.5	0.5	NUM
ejpam-4637	470	38	,	,	PUNCT
ejpam-4637	470	39	0.3	0.3	NUM
ejpam-4637	470	40	,	,	PUNCT
ejpam-4637	470	41	0.5)⟩	0.5)⟩	NUM
ejpam-4637	470	42	,	,	PUNCT
ejpam-4637	470	43	⟨(r	⟨(r	NOUN
ejpam-4637	470	44	,	,	PUNCT
ejpam-4637	470	45	02	02	NUM
ejpam-4637	470	46	)	)	PUNCT
ejpam-4637	470	47	,	,	PUNCT
ejpam-4637	470	48	(	(	PUNCT
ejpam-4637	470	49	0	0	NUM
ejpam-4637	470	50	,	,	PUNCT
ejpam-4637	470	51	0.5	0.5	NUM
ejpam-4637	470	52	,	,	PUNCT
ejpam-4637	470	53	0.5)⟩	0.5)⟩	NUM
ejpam-4637	470	54	,	,	PUNCT
ejpam-4637	470	55	⟨(r	⟨(r	NOUN
ejpam-4637	470	56	,	,	PUNCT
ejpam-4637	470	57	u	u	NOUN
ejpam-4637	470	58	)	)	PUNCT
ejpam-4637	470	59	,	,	PUNCT
ejpam-4637	470	60	(	(	PUNCT
ejpam-4637	470	61	0	0	NUM
ejpam-4637	470	62	,	,	PUNCT
ejpam-4637	470	63	0.5	0.5	NUM
ejpam-4637	470	64	,	,	PUNCT
ejpam-4637	470	65	0.5)⟩	0.5)⟩	NUM
ejpam-4637	470	66	,	,	PUNCT
ejpam-4637	470	67	⟨(r	⟨(r	NOUN
ejpam-4637	470	68	,	,	PUNCT
ejpam-4637	470	69	v	v	NOUN
ejpam-4637	470	70	)	)	PUNCT
ejpam-4637	470	71	,	,	PUNCT
ejpam-4637	470	72	(	(	PUNCT
ejpam-4637	470	73	0	0	NUM
ejpam-4637	470	74	,	,	PUNCT
ejpam-4637	470	75	0.5	0.5	NUM
ejpam-4637	470	76	,	,	PUNCT
ejpam-4637	470	77	0.5)⟩	0.5)⟩	NUM
ejpam-4637	470	78	,	,	PUNCT
ejpam-4637	470	79	⟨(s	⟨(s	PROPN
ejpam-4637	470	80	,	,	PUNCT
ejpam-4637	470	81	02	02	NUM
ejpam-4637	470	82	)	)	PUNCT
ejpam-4637	470	83	,	,	PUNCT
ejpam-4637	470	84	(	(	PUNCT
ejpam-4637	470	85	0.5	0.5	NUM
ejpam-4637	470	86	,	,	PUNCT
ejpam-4637	470	87	0.2	0.2	NUM
ejpam-4637	470	88	,	,	PUNCT
ejpam-4637	470	89	0.4)⟩	0.4)⟩	NUM
ejpam-4637	470	90	,	,	PUNCT
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ejpam-4637	470	140	,	,	PUNCT
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ejpam-4637	470	147	0.5	0.5	NUM
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ejpam-4637	470	152	,	,	PUNCT
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ejpam-4637	470	161	⟨(01	⟨(01	NOUN
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ejpam-4637	470	163	02	02	NUM
ejpam-4637	470	164	)	)	PUNCT
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ejpam-4637	470	167	0.5	0.5	NUM
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ejpam-4637	470	170	,	,	PUNCT
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ejpam-4637	470	172	,	,	PUNCT
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ejpam-4637	470	174	,	,	PUNCT
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ejpam-4637	470	179	0.5	0.5	NUM
ejpam-4637	470	180	,	,	PUNCT
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ejpam-4637	470	182	,	,	PUNCT
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ejpam-4637	470	184	,	,	PUNCT
ejpam-4637	470	185	⟨(01	⟨(01	PROPN
ejpam-4637	470	186	,	,	PUNCT
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ejpam-4637	470	192	,	,	PUNCT
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ejpam-4637	470	194	,	,	PUNCT
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ejpam-4637	470	196	,	,	PUNCT
ejpam-4637	470	197	⟨(r	⟨(r	NOUN
ejpam-4637	470	198	,	,	PUNCT
ejpam-4637	470	199	02	02	NUM
ejpam-4637	470	200	)	)	PUNCT
ejpam-4637	470	201	,	,	PUNCT
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ejpam-4637	470	203	0	0	NUM
ejpam-4637	470	204	,	,	PUNCT
ejpam-4637	470	205	0.5	0.5	NUM
ejpam-4637	470	206	,	,	PUNCT
ejpam-4637	470	207	0.5)⟩	0.5)⟩	NUM
ejpam-4637	470	208	,	,	PUNCT
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ejpam-4637	470	210	,	,	PUNCT
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ejpam-4637	470	216	,	,	PUNCT
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ejpam-4637	470	218	,	,	PUNCT
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ejpam-4637	470	220	,	,	PUNCT
ejpam-4637	470	221	⟨(r	⟨(r	NOUN
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ejpam-4637	470	225	,	,	PUNCT
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ejpam-4637	470	228	,	,	PUNCT
ejpam-4637	470	229	0.5	0.5	NUM
ejpam-4637	470	230	,	,	PUNCT
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ejpam-4637	470	233	⟨(s	⟨(s	PROPN
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ejpam-4637	470	242	,	,	PUNCT
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ejpam-4637	470	244	,	,	PUNCT
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ejpam-4637	470	246	,	,	PUNCT
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ejpam-4637	470	249	,	,	PUNCT
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ejpam-4637	470	252	,	,	PUNCT
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ejpam-4637	470	254	,	,	PUNCT
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ejpam-4637	470	276	,	,	PUNCT
ejpam-4637	470	277	0.5	0.5	NUM
ejpam-4637	470	278	,	,	PUNCT
ejpam-4637	470	279	0.5)⟩	0.5)⟩	NUM
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ejpam-4637	470	282	,	,	PUNCT
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ejpam-4637	470	285	,	,	PUNCT
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ejpam-4637	470	288	,	,	PUNCT
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ejpam-4637	470	290	,	,	PUNCT
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ejpam-4637	470	293	⟨(t	⟨(t	PROPN
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ejpam-4637	470	300	,	,	PUNCT
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ejpam-4637	470	302	,	,	PUNCT
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ejpam-4637	470	304	}	}	PUNCT
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ejpam-4637	470	306	,	,	PUNCT
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ejpam-4637	470	308	(	(	PUNCT
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ejpam-4637	470	317	02	02	NUM
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ejpam-4637	470	319	,	,	PUNCT
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ejpam-4637	470	322	,	,	PUNCT
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ejpam-4637	470	326	,	,	PUNCT
ejpam-4637	470	327	u	u	NOUN
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ejpam-4637	470	338	,	,	PUNCT
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ejpam-4637	470	351	02	02	NUM
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ejpam-4637	470	392	,	,	PUNCT
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ejpam-4637	470	404	,	,	PUNCT
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ejpam-4637	470	416	,	,	PUNCT
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ejpam-4637	470	442	,	,	PUNCT
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ejpam-4637	470	448	)	)	PUNCT
ejpam-4637	470	449	,	,	PUNCT
ejpam-4637	470	450	(	(	PUNCT
ejpam-4637	470	451	0	0	NUM
ejpam-4637	470	452	,	,	PUNCT
ejpam-4637	470	453	0.5	0.5	NUM
ejpam-4637	470	454	,	,	PUNCT
ejpam-4637	470	455	0.5)⟩	0.5)⟩	NUM
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ejpam-4637	470	457	)	)	PUNCT
ejpam-4637	470	458	}	}	PUNCT
ejpam-4637	470	459	theorem	theorem	VERB
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ejpam-4637	470	461	.	.	PUNCT
ejpam-4637	471	1	let	let	AUX
ejpam-4637	471	2	(	(	PUNCT
ejpam-4637	471	3	∆1	∆1	NOUN
ejpam-4637	471	4	,	,	PUNCT
ejpam-4637	471	5	e	e	NOUN
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ejpam-4637	471	7	and	and	CCONJ
ejpam-4637	471	8	(	(	PUNCT
ejpam-4637	471	9	∆2	∆2	X
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ejpam-4637	471	12	)	)	PUNCT
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ejpam-4637	471	14	two	two	NUM
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ejpam-4637	471	16	hyper	hyper	ADJ
ejpam-4637	471	17	up	up	ADP
ejpam-4637	471	18	-	-	PUNCT
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ejpam-4637	471	23	,	,	PUNCT
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ejpam-4637	471	27	01	01	NUM
ejpam-4637	471	28	)	)	PUNCT
ejpam-4637	471	29	and	and	CCONJ
ejpam-4637	471	30	(	(	PUNCT
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ejpam-4637	471	32	,	,	PUNCT
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ejpam-4637	471	38	,	,	PUNCT
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ejpam-4637	471	40	.	.	PUNCT
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ejpam-4637	472	2	their	their	PRON
ejpam-4637	472	3	cartesian	cartesian	ADJ
ejpam-4637	472	4	product	product	NOUN
ejpam-4637	472	5	(	(	PUNCT
ejpam-4637	472	6	∆1	∆1	NOUN
ejpam-4637	472	7	,	,	PUNCT
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ejpam-4637	472	19	-	-	PUNCT
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ejpam-4637	472	22	(	(	PUNCT
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ejpam-4637	472	24	×x2	×x2	PROPN
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ejpam-4637	472	26	◦	◦	NOUN
ejpam-4637	472	27	,	,	PUNCT
ejpam-4637	472	28	≪	≪	ADJ
ejpam-4637	472	29	,	,	PUNCT
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ejpam-4637	472	31	01	01	NUM
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ejpam-4637	472	36	.	.	PUNCT
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ejpam-4637	474	17	up	up	ADV
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ejpam-4637	474	28	∆	∆	X
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ejpam-4637	474	30	e	e	X
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ejpam-4637	474	40	×	×	NOUN
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ejpam-4637	474	43	,	,	PUNCT
ejpam-4637	474	44	e	e	NOUN
ejpam-4637	474	45	)	)	PUNCT
ejpam-4637	474	46	,	,	PUNCT
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ejpam-4637	474	81	×x2	×x2	PROPN
ejpam-4637	474	82	,	,	PUNCT
ejpam-4637	474	83	we	we	PRON
ejpam-4637	474	84	have	have	VERB
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ejpam-4637	475	10	◦	◦	NOUN
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ejpam-4637	475	12	y	y	NOUN
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ejpam-4637	475	36	t)∈(u	t)∈(u	ADP
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ejpam-4637	475	38	1x)×(v	1x)×(v	NUM
ejpam-4637	475	39	◦	◦	NOUN
ejpam-4637	475	40	2y	2y	NUM
ejpam-4637	475	41	)	)	PUNCT
ejpam-4637	475	42	min{t∆1(a)(r	min{t∆1(a)(r	PROPN
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ejpam-4637	475	46	)	)	PUNCT
ejpam-4637	475	47	}	}	PUNCT
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ejpam-4637	475	50	{	{	PUNCT
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ejpam-4637	475	53	◦	◦	NOUN
ejpam-4637	475	54	1x	1x	NUM
ejpam-4637	475	55	t∆1(a)(r	t∆1(a)(r	NOUN
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ejpam-4637	475	60	◦	◦	NOUN
ejpam-4637	475	61	2y	2y	PROPN
ejpam-4637	475	62	t∆2(b)(t	t∆2(b)(t	VERB
ejpam-4637	475	63	)	)	PUNCT
ejpam-4637	475	64	}	}	PUNCT
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ejpam-4637	475	69	x),∗	x),∗	NOUN
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ejpam-4637	475	92	)	)	PUNCT
ejpam-4637	475	93	,	,	PUNCT
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ejpam-4637	477	86	}	}	PUNCT
ejpam-4637	477	87	=	=	SYM
ejpam-4637	477	88	max{max{i∆1(a)(u	max{max{i∆1(a)(u	NUM
ejpam-4637	477	89	)	)	PUNCT
ejpam-4637	477	90	,	,	PUNCT
ejpam-4637	477	91	i∆2(b)(v)},max{i∆1(a)(x	i∆2(b)(v)},max{i∆1(a)(x	NOUN
ejpam-4637	477	92	)	)	PUNCT
ejpam-4637	477	93	,	,	PUNCT
ejpam-4637	477	94	i∆2(b)(y	i∆2(b)(y	NOUN
ejpam-4637	477	95	)	)	PUNCT
ejpam-4637	477	96	}	}	PUNCT
ejpam-4637	477	97	}	}	PUNCT
ejpam-4637	477	98	a.	a.	NOUN
ejpam-4637	477	99	cano	cano	PROPN
ejpam-4637	477	100	,	,	PUNCT
ejpam-4637	477	101	g.	g.	PROPN
ejpam-4637	477	102	petalcorin	petalcorin	PROPN
ejpam-4637	477	103	/	/	SYM
ejpam-4637	477	104	eur	eur	PROPN
ejpam-4637	477	105	.	.	PUNCT
ejpam-4637	478	1	j.	j.	PROPN
ejpam-4637	478	2	pure	pure	PROPN
ejpam-4637	478	3	appl	appl	PROPN
ejpam-4637	478	4	.	.	PROPN
ejpam-4637	478	5	math	math	PROPN
ejpam-4637	478	6	,	,	PUNCT
ejpam-4637	478	7	16	16	NUM
ejpam-4637	478	8	(	(	PUNCT
ejpam-4637	478	9	1	1	NUM
ejpam-4637	478	10	)	)	PUNCT
ejpam-4637	478	11	(	(	PUNCT
ejpam-4637	478	12	2023	2023	NUM
ejpam-4637	478	13	)	)	PUNCT
ejpam-4637	478	14	,	,	PUNCT
ejpam-4637	478	15	548	548	NUM
ejpam-4637	478	16	-	-	SYM
ejpam-4637	478	17	576	576	NUM
ejpam-4637	478	18	570	570	NUM
ejpam-4637	478	19	=	=	SYM
ejpam-4637	478	20	max{i∆(a	max{i∆(a	NOUN
ejpam-4637	478	21	,	,	PUNCT
ejpam-4637	478	22	b)(u	b)(u	ADJ
ejpam-4637	478	23	,	,	PUNCT
ejpam-4637	478	24	v	v	NOUN
ejpam-4637	478	25	)	)	PUNCT
ejpam-4637	478	26	,	,	PUNCT
ejpam-4637	478	27	i∆(a	i∆(a	ADP
ejpam-4637	478	28	,	,	PUNCT
ejpam-4637	478	29	b)(x	b)(x	PROPN
ejpam-4637	478	30	,	,	PUNCT
ejpam-4637	478	31	y	y	NOUN
ejpam-4637	478	32	)	)	PUNCT
ejpam-4637	478	33	}	}	PUNCT
ejpam-4637	478	34	.	.	PUNCT
ejpam-4637	479	1	similarly	similarly	ADV
ejpam-4637	479	2	,	,	PUNCT
ejpam-4637	479	3	∗f∆(a	∗f∆(a	PROPN
ejpam-4637	479	4	,	,	PUNCT
ejpam-4637	479	5	b)((u	b)((u	NOUN
ejpam-4637	479	6	,	,	PUNCT
ejpam-4637	479	7	v	v	NOUN
ejpam-4637	479	8	)	)	PUNCT
ejpam-4637	479	9	◦	◦	NOUN
ejpam-4637	479	10	(	(	PUNCT
ejpam-4637	479	11	x	x	NOUN
ejpam-4637	479	12	,	,	PUNCT
ejpam-4637	479	13	y	y	NOUN
ejpam-4637	479	14	)	)	PUNCT
ejpam-4637	479	15	)	)	PUNCT
ejpam-4637	480	1	=	=	SYM
ejpam-4637	480	2	max{f∆(a	max{f∆(a	NOUN
ejpam-4637	480	3	,	,	PUNCT
ejpam-4637	480	4	b)(u	b)(u	ADJ
ejpam-4637	480	5	,	,	PUNCT
ejpam-4637	480	6	v),f∆(a	v),f∆(a	NUM
ejpam-4637	480	7	,	,	PUNCT
ejpam-4637	480	8	b)(x	b)(x	PROPN
ejpam-4637	480	9	,	,	PUNCT
ejpam-4637	480	10	y	y	NOUN
ejpam-4637	480	11	)	)	PUNCT
ejpam-4637	480	12	}	}	PUNCT
ejpam-4637	480	13	.	.	PUNCT
ejpam-4637	481	1	hence	hence	ADV
ejpam-4637	481	2	,	,	PUNCT
ejpam-4637	481	3	(	(	PUNCT
ejpam-4637	481	4	∆	∆	X
ejpam-4637	481	5	,	,	PUNCT
ejpam-4637	481	6	e	e	X
ejpam-4637	481	7	×	×	PROPN
ejpam-4637	481	8	e	e	NOUN
ejpam-4637	481	9	)	)	PUNCT
ejpam-4637	481	10	is	be	AUX
ejpam-4637	481	11	a	a	DET
ejpam-4637	481	12	svns	svns	NOUN
ejpam-4637	481	13	hyper	hyper	ADJ
ejpam-4637	481	14	up	up	ADP
ejpam-4637	481	15	-subalgebra	-subalgebra	NOUN
ejpam-4637	481	16	of	of	ADP
ejpam-4637	481	17	x1	x1	PROPN
ejpam-4637	481	18	×x2	×x2	NOUN
ejpam-4637	481	19	.	.	PUNCT
ejpam-4637	482	1	3.4	3.4	NUM
ejpam-4637	482	2	.	.	PUNCT
ejpam-4637	483	1	homomorphism	homomorphism	NOUN
ejpam-4637	483	2	of	of	ADP
ejpam-4637	483	3	svns	svns	PROPN
ejpam-4637	483	4	hyper	hyper	ADJ
ejpam-4637	483	5	up	up	ADP
ejpam-4637	483	6	-	-	PUNCT
ejpam-4637	483	7	subalgebra	subalgebra	NOUN
ejpam-4637	483	8	in	in	ADP
ejpam-4637	483	9	this	this	DET
ejpam-4637	483	10	section	section	NOUN
ejpam-4637	483	11	,	,	PUNCT
ejpam-4637	483	12	we	we	PRON
ejpam-4637	483	13	define	define	VERB
ejpam-4637	483	14	the	the	DET
ejpam-4637	483	15	image	image	NOUN
ejpam-4637	483	16	and	and	CCONJ
ejpam-4637	483	17	preimage	preimage	NOUN
ejpam-4637	483	18	of	of	ADP
ejpam-4637	483	19	svns	svns	PROPN
ejpam-4637	483	20	hyper	hyper	ADJ
ejpam-4637	483	21	up	up	ADP
ejpam-4637	483	22	-subalgebra	-subalgebra	NOUN
ejpam-4637	483	23	and	and	CCONJ
ejpam-4637	483	24	prove	prove	VERB
ejpam-4637	483	25	that	that	SCONJ
ejpam-4637	483	26	they	they	PRON
ejpam-4637	483	27	are	be	AUX
ejpam-4637	483	28	svns	svns	NOUN
ejpam-4637	483	29	hyper	hyper	ADJ
ejpam-4637	483	30	up	up	ADP
ejpam-4637	483	31	-subalgebra	-subalgebra	NOUN
ejpam-4637	483	32	under	under	ADP
ejpam-4637	483	33	svns	svns	NOUN
ejpam-4637	483	34	homomorphic	homomorphic	ADJ
ejpam-4637	483	35	function	function	NOUN
ejpam-4637	483	36	.	.	PUNCT
ejpam-4637	484	1	definition	definition	NOUN
ejpam-4637	484	2	19	19	NUM
ejpam-4637	484	3	.	.	PUNCT
ejpam-4637	485	1	let	let	AUX
ejpam-4637	485	2	(	(	PUNCT
ejpam-4637	485	3	x1	x1	ADJ
ejpam-4637	485	4	,	,	PUNCT
ejpam-4637	485	5	◦	◦	NOUN
ejpam-4637	485	6	1,≪1	1,≪1	NUM
ejpam-4637	485	7	,	,	PUNCT
ejpam-4637	485	8	01	01	NUM
ejpam-4637	485	9	)	)	PUNCT
ejpam-4637	485	10	and	and	CCONJ
ejpam-4637	485	11	(	(	PUNCT
ejpam-4637	485	12	x2	x2	NOUN
ejpam-4637	485	13	,	,	PUNCT
ejpam-4637	485	14	◦	◦	NOUN
ejpam-4637	485	15	2,≪2	2,≪2	NUM
ejpam-4637	485	16	,	,	PUNCT
ejpam-4637	485	17	02	02	NUM
ejpam-4637	485	18	)	)	PUNCT
ejpam-4637	485	19	be	be	VERB
ejpam-4637	485	20	two	two	NUM
ejpam-4637	485	21	hyper	hyper	ADJ
ejpam-4637	485	22	up	up	ADP
ejpam-4637	485	23	-algebras	-algebras	PROPN
ejpam-4637	485	24	and	and	CCONJ
ejpam-4637	485	25	(	(	PUNCT
ejpam-4637	485	26	∆1	∆1	NOUN
ejpam-4637	485	27	,	,	PUNCT
ejpam-4637	485	28	e	e	NOUN
ejpam-4637	485	29	)	)	PUNCT
ejpam-4637	485	30	,	,	PUNCT
ejpam-4637	485	31	(	(	PUNCT
ejpam-4637	485	32	∆2	∆2	X
ejpam-4637	485	33	,	,	PUNCT
ejpam-4637	485	34	e	e	NOUN
ejpam-4637	485	35	)	)	PUNCT
ejpam-4637	485	36	be	be	VERB
ejpam-4637	485	37	two	two	NUM
ejpam-4637	485	38	svns	svns	NOUN
ejpam-4637	485	39	hyper	hyper	ADJ
ejpam-4637	485	40	up	up	ADP
ejpam-4637	485	41	-subalgebra	-subalgebra	NOUN
ejpam-4637	485	42	of	of	ADP
ejpam-4637	485	43	x1	x1	PROPN
ejpam-4637	485	44	and	and	CCONJ
ejpam-4637	485	45	x2	x2	PROPN
ejpam-4637	485	46	,	,	PUNCT
ejpam-4637	485	47	respectively	respectively	ADV
ejpam-4637	485	48	.	.	PUNCT
ejpam-4637	486	1	then	then	ADV
ejpam-4637	486	2	the	the	DET
ejpam-4637	486	3	pair	pair	NOUN
ejpam-4637	486	4	(	(	PUNCT
ejpam-4637	486	5	φ	φ	PROPN
ejpam-4637	486	6	,	,	PUNCT
ejpam-4637	486	7	ρ	ρ	PROPN
ejpam-4637	486	8	)	)	PUNCT
ejpam-4637	486	9	is	be	AUX
ejpam-4637	486	10	called	call	VERB
ejpam-4637	486	11	a	a	DET
ejpam-4637	486	12	svns	svns	NOUN
ejpam-4637	486	13	function	function	NOUN
ejpam-4637	486	14	from	from	ADP
ejpam-4637	486	15	x1	x1	PROPN
ejpam-4637	486	16	to	to	ADP
ejpam-4637	486	17	x2	x2	PRON
ejpam-4637	486	18	where	where	SCONJ
ejpam-4637	486	19	φ	φ	PROPN
ejpam-4637	486	20	:	:	PUNCT
ejpam-4637	486	21	x1	x1	PROPN
ejpam-4637	486	22	−→	−→	NOUN
ejpam-4637	486	23	x2	x2	PROPN
ejpam-4637	486	24	and	and	CCONJ
ejpam-4637	486	25	ρ	ρ	NOUN
ejpam-4637	486	26	:	:	PUNCT
ejpam-4637	487	1	e	e	X
ejpam-4637	487	2	−→	−→	PROPN
ejpam-4637	487	3	e.	e.	PROPN
ejpam-4637	487	4	definition	definition	NOUN
ejpam-4637	487	5	20	20	NUM
ejpam-4637	487	6	.	.	PUNCT
ejpam-4637	488	1	under	under	ADP
ejpam-4637	488	2	the	the	DET
ejpam-4637	488	3	svns	svns	NOUN
ejpam-4637	488	4	function	function	NOUN
ejpam-4637	488	5	(	(	PUNCT
ejpam-4637	488	6	φ	φ	PROPN
ejpam-4637	488	7	,	,	PUNCT
ejpam-4637	488	8	ρ	ρ	PROPN
ejpam-4637	488	9	)	)	PUNCT
ejpam-4637	488	10	,	,	PUNCT
ejpam-4637	488	11	(	(	PUNCT
ejpam-4637	488	12	i	i	NOUN
ejpam-4637	488	13	)	)	PUNCT
ejpam-4637	488	14	the	the	DET
ejpam-4637	488	15	image	image	NOUN
ejpam-4637	488	16	of	of	ADP
ejpam-4637	488	17	(	(	PUNCT
ejpam-4637	488	18	∆1	∆1	NOUN
ejpam-4637	488	19	,	,	PUNCT
ejpam-4637	488	20	e	e	NOUN
ejpam-4637	488	21	)	)	PUNCT
ejpam-4637	488	22	is	be	AUX
ejpam-4637	488	23	denoted	denote	VERB
ejpam-4637	488	24	by	by	ADP
ejpam-4637	488	25	(	(	PUNCT
ejpam-4637	488	26	φ	φ	PROPN
ejpam-4637	488	27	,	,	PUNCT
ejpam-4637	488	28	ρ)(∆1	ρ)(∆1	PROPN
ejpam-4637	488	29	,	,	PUNCT
ejpam-4637	488	30	e	e	NOUN
ejpam-4637	488	31	)	)	PUNCT
ejpam-4637	488	32	and	and	CCONJ
ejpam-4637	488	33	is	be	AUX
ejpam-4637	488	34	defined	define	VERB
ejpam-4637	488	35	by	by	ADP
ejpam-4637	488	36	(	(	PUNCT
ejpam-4637	488	37	φ	φ	PROPN
ejpam-4637	488	38	,	,	PUNCT
ejpam-4637	488	39	ρ)(∆1	ρ)(∆1	PROPN
ejpam-4637	488	40	,	,	PUNCT
ejpam-4637	488	41	e	e	NOUN
ejpam-4637	488	42	)	)	PUNCT
ejpam-4637	489	1	=	=	SYM
ejpam-4637	489	2	(	(	PUNCT
ejpam-4637	489	3	φ(∆1	φ(∆1	PROPN
ejpam-4637	489	4	)	)	PUNCT
ejpam-4637	489	5	,	,	PUNCT
ejpam-4637	489	6	ρ(e	ρ(e	PROPN
ejpam-4637	489	7	)	)	PUNCT
ejpam-4637	489	8	)	)	PUNCT
ejpam-4637	490	1	=	=	PRON
ejpam-4637	490	2	{	{	PUNCT
ejpam-4637	490	3	(	(	PUNCT
ejpam-4637	490	4	b	b	NOUN
ejpam-4637	490	5	,	,	PUNCT
ejpam-4637	490	6	φ(∆1)(b))|b	φ(∆1)(b))|b	PROPN
ejpam-4637	490	7	∈	∈	PROPN
ejpam-4637	490	8	ρ(e	ρ(e	PROPN
ejpam-4637	490	9	)	)	PUNCT
ejpam-4637	490	10	}	}	PUNCT
ejpam-4637	490	11	where	where	SCONJ
ejpam-4637	490	12	for	for	ADP
ejpam-4637	490	13	all	all	DET
ejpam-4637	490	14	b	b	PROPN
ejpam-4637	490	15	∈	∈	PROPN
ejpam-4637	490	16	ρ(e	ρ(e	PROPN
ejpam-4637	490	17	)	)	PUNCT
ejpam-4637	490	18	and	and	CCONJ
ejpam-4637	490	19	y	y	PROPN
ejpam-4637	490	20	∈	∈	PROPN
ejpam-4637	490	21	x2	x2	PROPN
ejpam-4637	490	22	,	,	PUNCT
ejpam-4637	490	23	tφ(∆1)(b)(y	tφ(∆1)(b)(y	NOUN
ejpam-4637	490	24	)	)	PUNCT
ejpam-4637	490	25	=	=	PUNCT
ejpam-4637	491	1			PUNCT
ejpam-4637	491	2	max	max	PROPN
ejpam-4637	491	3	φ(x)=y	φ(x)=y	PROPN
ejpam-4637	491	4	max	max	PROPN
ejpam-4637	491	5	ρ(a)=b	ρ(a)=b	CCONJ
ejpam-4637	491	6	t∆1(a)(x	t∆1(a)(x	PROPN
ejpam-4637	491	7	)	)	PUNCT
ejpam-4637	491	8	if	if	SCONJ
ejpam-4637	491	9	x	x	PROPN
ejpam-4637	491	10	∈	∈	PROPN
ejpam-4637	491	11	φ−1(y	φ−1(y	PROPN
ejpam-4637	491	12	)	)	PUNCT
ejpam-4637	491	13	,	,	PUNCT
ejpam-4637	491	14	0	0	NUM
ejpam-4637	491	15	otherwise	otherwise	ADV
ejpam-4637	491	16	,	,	PUNCT
ejpam-4637	491	17	iφ(∆1)(b)(y	iφ(∆1)(b)(y	PROPN
ejpam-4637	491	18	)	)	PUNCT
ejpam-4637	491	19	=	=	PUNCT
ejpam-4637	492	1			PUNCT
ejpam-4637	492	2	min	min	PROPN
ejpam-4637	492	3	φ(x)=y	φ(x)=y	NOUN
ejpam-4637	492	4	min	min	NOUN
ejpam-4637	492	5	ρ(a)=b	ρ(a)=b	CCONJ
ejpam-4637	492	6	i∆1(a)(x	i∆1(a)(x	NOUN
ejpam-4637	492	7	)	)	PUNCT
ejpam-4637	492	8	if	if	SCONJ
ejpam-4637	492	9	x	x	PROPN
ejpam-4637	492	10	∈	∈	PROPN
ejpam-4637	492	11	φ−1(y	φ−1(y	PROPN
ejpam-4637	492	12	)	)	PUNCT
ejpam-4637	492	13	,	,	PUNCT
ejpam-4637	492	14	1	1	NUM
ejpam-4637	492	15	otherwise	otherwise	ADV
ejpam-4637	492	16	,	,	PUNCT
ejpam-4637	492	17	and	and	CCONJ
ejpam-4637	492	18	fφ(∆1)(b)(y	fφ(∆1)(b)(y	NOUN
ejpam-4637	492	19	)	)	PUNCT
ejpam-4637	492	20	=	=	PUNCT
ejpam-4637	493	1			PUNCT
ejpam-4637	493	2	min	min	PROPN
ejpam-4637	493	3	φ(x)=y	φ(x)=y	PROPN
ejpam-4637	493	4	min	min	NOUN
ejpam-4637	493	5	ρ(a)=b	ρ(a)=b	CCONJ
ejpam-4637	493	6	f∆1(a)(x	f∆1(a)(x	NOUN
ejpam-4637	493	7	)	)	PUNCT
ejpam-4637	493	8	if	if	SCONJ
ejpam-4637	493	9	x	x	PROPN
ejpam-4637	493	10	∈	∈	PROPN
ejpam-4637	493	11	φ−1(y	φ−1(y	PROPN
ejpam-4637	493	12	)	)	PUNCT
ejpam-4637	493	13	,	,	PUNCT
ejpam-4637	493	14	1	1	NUM
ejpam-4637	493	15	otherwise	otherwise	ADV
ejpam-4637	493	16	.	.	PUNCT
ejpam-4637	494	1	(	(	PUNCT
ejpam-4637	494	2	ii	ii	X
ejpam-4637	494	3	)	)	PUNCT
ejpam-4637	494	4	the	the	DET
ejpam-4637	494	5	preimage	preimage	NOUN
ejpam-4637	494	6	(	(	PUNCT
ejpam-4637	494	7	∆2	∆2	X
ejpam-4637	494	8	,	,	PUNCT
ejpam-4637	494	9	e	e	NOUN
ejpam-4637	494	10	)	)	PUNCT
ejpam-4637	494	11	is	be	AUX
ejpam-4637	494	12	denoted	denote	VERB
ejpam-4637	494	13	by	by	ADP
ejpam-4637	494	14	(	(	PUNCT
ejpam-4637	494	15	φ	φ	PROPN
ejpam-4637	494	16	,	,	PUNCT
ejpam-4637	494	17	ρ)−1(∆2	ρ)−1(∆2	ADJ
ejpam-4637	494	18	,	,	PUNCT
ejpam-4637	494	19	e	e	NOUN
ejpam-4637	494	20	)	)	PUNCT
ejpam-4637	494	21	and	and	CCONJ
ejpam-4637	494	22	defined	define	VERB
ejpam-4637	494	23	by	by	ADP
ejpam-4637	494	24	(	(	PUNCT
ejpam-4637	494	25	φ	φ	PROPN
ejpam-4637	494	26	,	,	PUNCT
ejpam-4637	494	27	ρ)−1(∆2	ρ)−1(∆2	ADJ
ejpam-4637	494	28	,	,	PUNCT
ejpam-4637	494	29	e	e	X
ejpam-4637	494	30	)	)	PUNCT
ejpam-4637	494	31	=	=	SYM
ejpam-4637	494	32	(	(	PUNCT
ejpam-4637	494	33	φ−1(∆2	φ−1(∆2	NOUN
ejpam-4637	494	34	)	)	PUNCT
ejpam-4637	494	35	,	,	PUNCT
ejpam-4637	494	36	ρ	ρ	PROPN
ejpam-4637	494	37	−1(e	−1(e	NOUN
ejpam-4637	494	38	)	)	PUNCT
ejpam-4637	494	39	)	)	PUNCT
ejpam-4637	495	1	=	=	PRON
ejpam-4637	495	2	{	{	PUNCT
ejpam-4637	495	3	(	(	PUNCT
ejpam-4637	495	4	a	a	PROPN
ejpam-4637	495	5	,	,	PUNCT
ejpam-4637	495	6	φ−1(∆2)(a))|a	φ−1(∆2)(a))|a	PROPN
ejpam-4637	495	7	∈	∈	PROPN
ejpam-4637	495	8	ρ−1(e	ρ−1(e	PROPN
ejpam-4637	495	9	)	)	PUNCT
ejpam-4637	495	10	}	}	PUNCT
ejpam-4637	495	11	where	where	SCONJ
ejpam-4637	495	12	for	for	ADP
ejpam-4637	495	13	all	all	DET
ejpam-4637	495	14	a	a	DET
ejpam-4637	495	15	∈	∈	NOUN
ejpam-4637	495	16	ρ−1(e	ρ−1(e	PROPN
ejpam-4637	495	17	)	)	PUNCT
ejpam-4637	495	18	and	and	CCONJ
ejpam-4637	495	19	x	x	PUNCT
ejpam-4637	495	20	∈	∈	PROPN
ejpam-4637	495	21	x1	x1	PROPN
ejpam-4637	495	22	,	,	PUNCT
ejpam-4637	495	23	tφ−1(∆2)(a)(x	tφ−1(∆2)(a)(x	NOUN
ejpam-4637	495	24	)	)	PUNCT
ejpam-4637	495	25	=	=	SYM
ejpam-4637	496	1	t∆2(ρ(a))(φ(x	t∆2(ρ(a))(φ(x	NOUN
ejpam-4637	496	2	)	)	PUNCT
ejpam-4637	496	3	)	)	PUNCT
ejpam-4637	496	4	,	,	PUNCT
ejpam-4637	496	5	iφ−1(∆2)(a)(x	iφ−1(∆2)(a)(x	PROPN
ejpam-4637	496	6	)	)	PUNCT
ejpam-4637	496	7	=	=	SYM
ejpam-4637	497	1	i∆2(ρ(a))(φ(x	i∆2(ρ(a))(φ(x	PROPN
ejpam-4637	497	2	)	)	PUNCT
ejpam-4637	497	3	)	)	PUNCT
ejpam-4637	497	4	,	,	PUNCT
ejpam-4637	497	5	and	and	CCONJ
ejpam-4637	497	6	fφ−1(∆2)(a)(x	fφ−1(∆2)(a)(x	PROPN
ejpam-4637	497	7	)	)	PUNCT
ejpam-4637	497	8	=	=	SYM
ejpam-4637	497	9	f∆2(ρ(a))(φ(x	f∆2(ρ(a))(φ(x	PROPN
ejpam-4637	497	10	)	)	PUNCT
ejpam-4637	497	11	)	)	PUNCT
ejpam-4637	497	12	.	.	PUNCT
ejpam-4637	498	1	a.	a.	PROPN
ejpam-4637	498	2	cano	cano	PROPN
ejpam-4637	498	3	,	,	PUNCT
ejpam-4637	498	4	g.	g.	PROPN
ejpam-4637	498	5	petalcorin	petalcorin	PROPN
ejpam-4637	498	6	/	/	SYM
ejpam-4637	498	7	eur	eur	PROPN
ejpam-4637	498	8	.	.	PUNCT
ejpam-4637	499	1	j.	j.	PROPN
ejpam-4637	499	2	pure	pure	PROPN
ejpam-4637	499	3	appl	appl	PROPN
ejpam-4637	499	4	.	.	PROPN
ejpam-4637	499	5	math	math	PROPN
ejpam-4637	499	6	,	,	PUNCT
ejpam-4637	499	7	16	16	NUM
ejpam-4637	499	8	(	(	PUNCT
ejpam-4637	499	9	1	1	NUM
ejpam-4637	499	10	)	)	PUNCT
ejpam-4637	499	11	(	(	PUNCT
ejpam-4637	499	12	2023	2023	NUM
ejpam-4637	499	13	)	)	PUNCT
ejpam-4637	499	14	,	,	PUNCT
ejpam-4637	499	15	548	548	NUM
ejpam-4637	499	16	-	-	SYM
ejpam-4637	499	17	576	576	NUM
ejpam-4637	499	18	571	571	NUM
ejpam-4637	499	19	definition	definition	NOUN
ejpam-4637	499	20	21	21	NUM
ejpam-4637	499	21	.	.	PUNCT
ejpam-4637	500	1	let	let	VERB
ejpam-4637	500	2	the	the	DET
ejpam-4637	500	3	pair	pair	NOUN
ejpam-4637	500	4	(	(	PUNCT
ejpam-4637	500	5	φ	φ	PROPN
ejpam-4637	500	6	,	,	PUNCT
ejpam-4637	500	7	ρ	ρ	PROPN
ejpam-4637	500	8	)	)	PUNCT
ejpam-4637	500	9	be	be	VERB
ejpam-4637	500	10	a	a	DET
ejpam-4637	500	11	svns	svns	NOUN
ejpam-4637	500	12	function	function	NOUN
ejpam-4637	500	13	from	from	ADP
ejpam-4637	500	14	x1	x1	PROPN
ejpam-4637	500	15	into	into	ADP
ejpam-4637	500	16	x2	x2	PROPN
ejpam-4637	500	17	,	,	PUNCT
ejpam-4637	500	18	then	then	ADV
ejpam-4637	500	19	(	(	PUNCT
ejpam-4637	500	20	φ	φ	PROPN
ejpam-4637	500	21	,	,	PUNCT
ejpam-4637	500	22	ρ	ρ	PROPN
ejpam-4637	500	23	)	)	PUNCT
ejpam-4637	500	24	is	be	AUX
ejpam-4637	500	25	called	call	VERB
ejpam-4637	500	26	a	a	DET
ejpam-4637	500	27	svns	svns	NOUN
ejpam-4637	500	28	homomorphism	homomorphism	NOUN
ejpam-4637	500	29	if	if	SCONJ
ejpam-4637	500	30	φ	φ	PROPN
ejpam-4637	500	31	is	be	AUX
ejpam-4637	500	32	a	a	DET
ejpam-4637	500	33	hyper	hyper	ADJ
ejpam-4637	500	34	homomorphism	homomorphism	NOUN
ejpam-4637	500	35	from	from	ADP
ejpam-4637	500	36	x1	x1	PROPN
ejpam-4637	500	37	to	to	ADP
ejpam-4637	500	38	x2	x2	PROPN
ejpam-4637	500	39	and	and	CCONJ
ejpam-4637	500	40	is	be	AUX
ejpam-4637	500	41	said	say	VERB
ejpam-4637	500	42	to	to	PART
ejpam-4637	500	43	be	be	AUX
ejpam-4637	500	44	a	a	DET
ejpam-4637	500	45	svns	svns	NOUN
ejpam-4637	500	46	isomorphism	isomorphism	NOUN
ejpam-4637	500	47	if	if	SCONJ
ejpam-4637	500	48	φ	φ	PROPN
ejpam-4637	500	49	is	be	AUX
ejpam-4637	500	50	a	a	DET
ejpam-4637	500	51	hyper	hyper	ADJ
ejpam-4637	500	52	isomorphism	isomorphism	NOUN
ejpam-4637	500	53	from	from	ADP
ejpam-4637	500	54	x1	x1	PROPN
ejpam-4637	500	55	to	to	ADP
ejpam-4637	500	56	x2	x2	PROPN
ejpam-4637	500	57	and	and	CCONJ
ejpam-4637	500	58	ρ	ρ	PROPN
ejpam-4637	500	59	is	be	AUX
ejpam-4637	500	60	an	an	DET
ejpam-4637	500	61	injective	injective	ADJ
ejpam-4637	500	62	map	map	NOUN
ejpam-4637	500	63	from	from	ADP
ejpam-4637	500	64	e	e	NOUN
ejpam-4637	500	65	to	to	ADP
ejpam-4637	500	66	e.	e.	PROPN
ejpam-4637	500	67	example	example	PROPN
ejpam-4637	501	1	9	9	NUM
ejpam-4637	501	2	.	.	PUNCT
ejpam-4637	502	1	let	let	VERB
ejpam-4637	502	2	x1	x1	PROPN
ejpam-4637	502	3	=	=	PUNCT
ejpam-4637	502	4	{	{	PUNCT
ejpam-4637	502	5	01	01	NUM
ejpam-4637	502	6	,	,	PUNCT
ejpam-4637	502	7	r	r	NOUN
ejpam-4637	502	8	,	,	PUNCT
ejpam-4637	502	9	s	s	PART
ejpam-4637	502	10	}	}	PUNCT
ejpam-4637	502	11	with	with	ADP
ejpam-4637	502	12	hyperoperation	hyperoperation	NOUN
ejpam-4637	502	13	given	give	VERB
ejpam-4637	502	14	by	by	ADP
ejpam-4637	502	15	◦	◦	NOUN
ejpam-4637	502	16	01	01	NUM
ejpam-4637	502	17	r	r	NOUN
ejpam-4637	502	18	s	s	VERB
ejpam-4637	502	19	01	01	NUM
ejpam-4637	502	20	{	{	PUNCT
ejpam-4637	502	21	01	01	NUM
ejpam-4637	502	22	}	}	PUNCT
ejpam-4637	502	23	{	{	PUNCT
ejpam-4637	502	24	r	r	NOUN
ejpam-4637	502	25	}	}	PUNCT
ejpam-4637	502	26	{	{	PUNCT
ejpam-4637	502	27	s	s	NOUN
ejpam-4637	502	28	}	}	PUNCT
ejpam-4637	502	29	r	r	NOUN
ejpam-4637	502	30	{	{	PUNCT
ejpam-4637	502	31	01	01	NUM
ejpam-4637	502	32	}	}	PUNCT
ejpam-4637	502	33	{	{	PUNCT
ejpam-4637	502	34	01	01	NUM
ejpam-4637	502	35	}	}	PUNCT
ejpam-4637	502	36	{	{	PUNCT
ejpam-4637	502	37	s	s	X
ejpam-4637	502	38	}	}	PUNCT
ejpam-4637	502	39	s	s	PART
ejpam-4637	502	40	{	{	PUNCT
ejpam-4637	502	41	01	01	NUM
ejpam-4637	502	42	}	}	PUNCT
ejpam-4637	502	43	{	{	PUNCT
ejpam-4637	502	44	r	r	NOUN
ejpam-4637	502	45	}	}	PUNCT
ejpam-4637	502	46	{	{	PUNCT
ejpam-4637	502	47	01	01	NUM
ejpam-4637	502	48	}	}	PUNCT
ejpam-4637	502	49	.	.	PUNCT
ejpam-4637	503	1	then	then	ADV
ejpam-4637	503	2	x1	x1	PROPN
ejpam-4637	503	3	is	be	AUX
ejpam-4637	503	4	hyper	hyper	ADJ
ejpam-4637	503	5	up	up	ADP
ejpam-4637	503	6	-algebra	-algebra	NOUN
ejpam-4637	503	7	by	by	ADP
ejpam-4637	503	8	thorough	thorough	ADJ
ejpam-4637	503	9	inspection	inspection	NOUN
ejpam-4637	503	10	.	.	PUNCT
ejpam-4637	504	1	considering	consider	VERB
ejpam-4637	504	2	x2	x2	PRON
ejpam-4637	505	1	=	=	PRON
ejpam-4637	505	2	{	{	PUNCT
ejpam-4637	505	3	02	02	NUM
ejpam-4637	505	4	,	,	PUNCT
ejpam-4637	505	5	u	u	NOUN
ejpam-4637	505	6	,	,	PUNCT
ejpam-4637	505	7	v	v	NOUN
ejpam-4637	505	8	}	}	PUNCT
ejpam-4637	505	9	as	as	ADP
ejpam-4637	505	10	the	the	DET
ejpam-4637	505	11	second	second	ADJ
ejpam-4637	505	12	hyper	hyper	NOUN
ejpam-4637	505	13	up	up	ADP
ejpam-4637	505	14	-algebra	-algebra	PROPN
ejpam-4637	505	15	of	of	ADP
ejpam-4637	505	16	example	example	NOUN
ejpam-4637	505	17	2	2	NUM
ejpam-4637	505	18	and	and	CCONJ
ejpam-4637	505	19	e	e	NOUN
ejpam-4637	505	20	=	=	SYM
ejpam-4637	505	21	n	n	PROPN
ejpam-4637	505	22	as	as	ADP
ejpam-4637	505	23	the	the	DET
ejpam-4637	505	24	set	set	NOUN
ejpam-4637	505	25	of	of	ADP
ejpam-4637	505	26	parameters	parameter	NOUN
ejpam-4637	505	27	,	,	PUNCT
ejpam-4637	505	28	we	we	PRON
ejpam-4637	505	29	define	define	VERB
ejpam-4637	505	30	mappings	mapping	NOUN
ejpam-4637	505	31	φ	φ	NOUN
ejpam-4637	505	32	:	:	PUNCT
ejpam-4637	505	33	x1	x1	NUM
ejpam-4637	505	34	−→	−→	NOUN
ejpam-4637	505	35	x2	x2	INTJ
ejpam-4637	505	36	by	by	ADP
ejpam-4637	505	37	φ(01	φ(01	ADJ
ejpam-4637	505	38	)	)	PUNCT
ejpam-4637	505	39	=	=	SYM
ejpam-4637	505	40	02	02	NUM
ejpam-4637	505	41	φ(r	φ(r	ADJ
ejpam-4637	505	42	)	)	PUNCT
ejpam-4637	505	43	=	=	SYM
ejpam-4637	505	44	v	v	ADP
ejpam-4637	505	45	φ(s	φ(s	NOUN
ejpam-4637	505	46	)	)	PUNCT
ejpam-4637	505	47	=	=	SYM
ejpam-4637	505	48	u	u	NOUN
ejpam-4637	505	49	;	;	PUNCT
ejpam-4637	505	50	and	and	CCONJ
ejpam-4637	505	51	ρ	ρ	NOUN
ejpam-4637	505	52	:	:	PUNCT
ejpam-4637	506	1	e	e	X
ejpam-4637	506	2	−→	−→	NOUN
ejpam-4637	506	3	e	e	NOUN
ejpam-4637	506	4	by	by	ADP
ejpam-4637	506	5	ρ(a	ρ(a	PROPN
ejpam-4637	506	6	)	)	PUNCT
ejpam-4637	506	7	=	=	SYM
ejpam-4637	506	8	2a	2a	NUM
ejpam-4637	506	9	.	.	PUNCT
ejpam-4637	507	1	let	let	VERB
ejpam-4637	507	2	(	(	PUNCT
ejpam-4637	507	3	∆1	∆1	NOUN
ejpam-4637	507	4	,	,	PUNCT
ejpam-4637	507	5	e	e	X
ejpam-4637	507	6	)	)	PUNCT
ejpam-4637	507	7	be	be	VERB
ejpam-4637	507	8	a	a	DET
ejpam-4637	507	9	svns	svns	NOUN
ejpam-4637	507	10	set	set	VERB
ejpam-4637	507	11	over	over	ADP
ejpam-4637	507	12	x1	x1	PROPN
ejpam-4637	507	13	given	give	VERB
ejpam-4637	507	14	by	by	ADP
ejpam-4637	507	15	t∆1(a)(x	t∆1(a)(x	PROPN
ejpam-4637	507	16	)	)	PUNCT
ejpam-4637	507	17	=	=	PRON
ejpam-4637	507	18	{	{	PUNCT
ejpam-4637	507	19	1	1	NUM
ejpam-4637	507	20	2a	2a	NUM
ejpam-4637	507	21	if	if	SCONJ
ejpam-4637	507	22	x	x	SYM
ejpam-4637	507	23	∈	∈	PROPN
ejpam-4637	507	24	{	{	PUNCT
ejpam-4637	507	25	01	01	NUM
ejpam-4637	507	26	,	,	PUNCT
ejpam-4637	507	27	s	s	PART
ejpam-4637	507	28	}	}	PUNCT
ejpam-4637	507	29	,	,	PUNCT
ejpam-4637	507	30	0	0	NUM
ejpam-4637	507	31	otherwise	otherwise	ADV
ejpam-4637	507	32	.	.	PUNCT
ejpam-4637	508	1	i∆1(a)(x	i∆1(a)(x	NOUN
ejpam-4637	508	2	)	)	PUNCT
ejpam-4637	508	3	=	=	PRON
ejpam-4637	508	4	{	{	PUNCT
ejpam-4637	508	5	0	0	NUM
ejpam-4637	508	6	if	if	SCONJ
ejpam-4637	508	7	x	x	X
ejpam-4637	508	8	∈	∈	PROPN
ejpam-4637	508	9	{	{	PUNCT
ejpam-4637	508	10	01	01	NUM
ejpam-4637	508	11	,	,	PUNCT
ejpam-4637	508	12	s	s	PART
ejpam-4637	508	13	}	}	PUNCT
ejpam-4637	508	14	,	,	PUNCT
ejpam-4637	508	15	1−	1−	NUM
ejpam-4637	508	16	1	1	NUM
ejpam-4637	509	1	a	a	DET
ejpam-4637	509	2	otherwise	otherwise	ADV
ejpam-4637	509	3	.	.	PUNCT
ejpam-4637	510	1	f∆1(a)(x	f∆1(a)(x	NOUN
ejpam-4637	510	2	)	)	PUNCT
ejpam-4637	511	1	=	=	PRON
ejpam-4637	511	2	{	{	PUNCT
ejpam-4637	511	3	0	0	NUM
ejpam-4637	511	4	if	if	SCONJ
ejpam-4637	511	5	x	x	X
ejpam-4637	511	6	∈	∈	PROPN
ejpam-4637	511	7	{	{	PUNCT
ejpam-4637	511	8	01	01	NUM
ejpam-4637	511	9	,	,	PUNCT
ejpam-4637	511	10	s	s	PART
ejpam-4637	511	11	}	}	PUNCT
ejpam-4637	511	12	,	,	PUNCT
ejpam-4637	511	13	1	1	NUM
ejpam-4637	511	14	2a+1	2a+1	PROPN
ejpam-4637	511	15	otherwise	otherwise	ADV
ejpam-4637	511	16	.	.	PUNCT
ejpam-4637	512	1	for	for	ADP
ejpam-4637	512	2	a	a	DET
ejpam-4637	512	3	∈	∈	PROPN
ejpam-4637	512	4	e.	e.	PROPN
ejpam-4637	512	5	by	by	ADP
ejpam-4637	512	6	inspection	inspection	NOUN
ejpam-4637	512	7	,	,	PUNCT
ejpam-4637	512	8	(	(	PUNCT
ejpam-4637	512	9	∆1	∆1	NOUN
ejpam-4637	512	10	,	,	PUNCT
ejpam-4637	512	11	e	e	NOUN
ejpam-4637	512	12	)	)	PUNCT
ejpam-4637	512	13	is	be	AUX
ejpam-4637	512	14	a	a	DET
ejpam-4637	512	15	svns	svns	NOUN
ejpam-4637	512	16	hyper	hyper	ADJ
ejpam-4637	512	17	up	up	ADP
ejpam-4637	512	18	-subalgebra	-subalgebra	NOUN
ejpam-4637	512	19	of	of	ADP
ejpam-4637	512	20	x1	x1	PROPN
ejpam-4637	512	21	.	.	PUNCT
ejpam-4637	513	1	thus	thus	ADV
ejpam-4637	513	2	,	,	PUNCT
ejpam-4637	513	3	the	the	DET
ejpam-4637	513	4	image	image	NOUN
ejpam-4637	513	5	of	of	ADP
ejpam-4637	513	6	(	(	PUNCT
ejpam-4637	513	7	∆1	∆1	NOUN
ejpam-4637	513	8	,	,	PUNCT
ejpam-4637	513	9	e	e	NOUN
ejpam-4637	513	10	)	)	PUNCT
ejpam-4637	513	11	under	under	ADP
ejpam-4637	513	12	(	(	PUNCT
ejpam-4637	513	13	φ	φ	PROPN
ejpam-4637	513	14	,	,	PUNCT
ejpam-4637	513	15	ρ	ρ	PROPN
ejpam-4637	513	16	)	)	PUNCT
ejpam-4637	513	17	is	be	AUX
ejpam-4637	513	18	tφ(∆1)(b)(y	tφ(∆1)(b)(y	VERB
ejpam-4637	513	19	)	)	PUNCT
ejpam-4637	514	1	=	=	PRON
ejpam-4637	514	2	{	{	PUNCT
ejpam-4637	514	3	0	0	NUM
ejpam-4637	514	4	if	if	SCONJ
ejpam-4637	514	5	y	y	PROPN
ejpam-4637	514	6	∈	∈	PROPN
ejpam-4637	514	7	{	{	PUNCT
ejpam-4637	514	8	v	v	NOUN
ejpam-4637	514	9	}	}	PUNCT
ejpam-4637	514	10	,	,	PUNCT
ejpam-4637	514	11	1	1	NUM
ejpam-4637	514	12	b	b	NOUN
ejpam-4637	514	13	otherwise	otherwise	ADV
ejpam-4637	514	14	.	.	PUNCT
ejpam-4637	515	1	iφ(∆1)(b)(y	iφ(∆1)(b)(y	NOUN
ejpam-4637	515	2	)	)	PUNCT
ejpam-4637	516	1	=	=	PRON
ejpam-4637	516	2	{	{	PUNCT
ejpam-4637	516	3	1−	1−	NUM
ejpam-4637	516	4	2	2	NUM
ejpam-4637	516	5	b	b	NOUN
ejpam-4637	516	6	if	if	SCONJ
ejpam-4637	516	7	y	y	PROPN
ejpam-4637	516	8	∈	∈	PROPN
ejpam-4637	516	9	{	{	PUNCT
ejpam-4637	516	10	v	v	NOUN
ejpam-4637	516	11	}	}	PUNCT
ejpam-4637	516	12	,	,	PUNCT
ejpam-4637	516	13	0	0	NUM
ejpam-4637	516	14	otherwise	otherwise	ADV
ejpam-4637	516	15	.	.	PUNCT
ejpam-4637	517	1	fφ(∆1)(b)(y	fφ(∆1)(b)(y	NOUN
ejpam-4637	517	2	)	)	PUNCT
ejpam-4637	518	1	=	=	PRON
ejpam-4637	518	2	{	{	PUNCT
ejpam-4637	518	3	1	1	NUM
ejpam-4637	518	4	b+1	b+1	NOUN
ejpam-4637	518	5	if	if	SCONJ
ejpam-4637	518	6	y	y	PROPN
ejpam-4637	518	7	∈	∈	PROPN
ejpam-4637	518	8	{	{	PUNCT
ejpam-4637	518	9	v	v	NOUN
ejpam-4637	518	10	}	}	PUNCT
ejpam-4637	518	11	,	,	PUNCT
ejpam-4637	518	12	0	0	NUM
ejpam-4637	518	13	otherwise	otherwise	ADV
ejpam-4637	518	14	.	.	PUNCT
ejpam-4637	519	1	for	for	ADP
ejpam-4637	519	2	b	b	PROPN
ejpam-4637	519	3	∈	∈	PROPN
ejpam-4637	519	4	2n	2n	NUM
ejpam-4637	519	5	and	and	CCONJ
ejpam-4637	519	6	y	y	PROPN
ejpam-4637	519	7	∈	∈	PROPN
ejpam-4637	519	8	x2	x2	PROPN
ejpam-4637	519	9	.	.	PUNCT
ejpam-4637	519	10	a.	a.	PROPN
ejpam-4637	519	11	cano	cano	PROPN
ejpam-4637	519	12	,	,	PUNCT
ejpam-4637	519	13	g.	g.	PROPN
ejpam-4637	519	14	petalcorin	petalcorin	PROPN
ejpam-4637	519	15	/	/	SYM
ejpam-4637	519	16	eur	eur	PROPN
ejpam-4637	519	17	.	.	PUNCT
ejpam-4637	520	1	j.	j.	PROPN
ejpam-4637	520	2	pure	pure	PROPN
ejpam-4637	520	3	appl	appl	PROPN
ejpam-4637	520	4	.	.	PROPN
ejpam-4637	520	5	math	math	PROPN
ejpam-4637	520	6	,	,	PUNCT
ejpam-4637	520	7	16	16	NUM
ejpam-4637	520	8	(	(	PUNCT
ejpam-4637	520	9	1	1	NUM
ejpam-4637	520	10	)	)	PUNCT
ejpam-4637	520	11	(	(	PUNCT
ejpam-4637	520	12	2023	2023	NUM
ejpam-4637	520	13	)	)	PUNCT
ejpam-4637	520	14	,	,	PUNCT
ejpam-4637	520	15	548	548	NUM
ejpam-4637	520	16	-	-	SYM
ejpam-4637	520	17	576	576	NUM
ejpam-4637	520	18	572	572	NUM
ejpam-4637	520	19	example	example	NOUN
ejpam-4637	520	20	10	10	NUM
ejpam-4637	520	21	.	.	PUNCT
ejpam-4637	520	22	consider	consider	VERB
ejpam-4637	520	23	the	the	DET
ejpam-4637	520	24	two	two	NUM
ejpam-4637	520	25	hyper	hyper	NOUN
ejpam-4637	520	26	up	up	ADP
ejpam-4637	520	27	-algebras	-algebras	PROPN
ejpam-4637	520	28	x1	x1	PROPN
ejpam-4637	520	29	and	and	CCONJ
ejpam-4637	520	30	x2	x2	PROPN
ejpam-4637	520	31	of	of	ADP
ejpam-4637	520	32	example	example	NOUN
ejpam-4637	520	33	9	9	NUM
ejpam-4637	520	34	.	.	PUNCT
ejpam-4637	520	35	define	define	VERB
ejpam-4637	520	36	e	e	NOUN
ejpam-4637	520	37	=	=	NOUN
ejpam-4637	520	38	{	{	PUNCT
ejpam-4637	520	39	e1	e1	PROPN
ejpam-4637	520	40	,	,	PUNCT
ejpam-4637	520	41	e2	e2	PROPN
ejpam-4637	520	42	}	}	PUNCT
ejpam-4637	520	43	as	as	ADP
ejpam-4637	520	44	set	set	NOUN
ejpam-4637	520	45	of	of	ADP
ejpam-4637	520	46	parameters	parameter	NOUN
ejpam-4637	520	47	and	and	CCONJ
ejpam-4637	520	48	mappings	mapping	NOUN
ejpam-4637	520	49	φ	φ	NOUN
ejpam-4637	520	50	:	:	PUNCT
ejpam-4637	521	1	x1	x1	NUM
ejpam-4637	521	2	−→	−→	NOUN
ejpam-4637	521	3	x2	x2	INTJ
ejpam-4637	521	4	by	by	ADP
ejpam-4637	521	5	φ(01	φ(01	ADJ
ejpam-4637	521	6	)	)	PUNCT
ejpam-4637	521	7	=	=	SYM
ejpam-4637	521	8	02	02	NUM
ejpam-4637	521	9	φ(r	φ(r	ADJ
ejpam-4637	521	10	)	)	PUNCT
ejpam-4637	521	11	=	=	SYM
ejpam-4637	521	12	v	v	ADP
ejpam-4637	521	13	φ(s	φ(s	NOUN
ejpam-4637	521	14	)	)	PUNCT
ejpam-4637	521	15	=	=	SYM
ejpam-4637	521	16	u	u	NOUN
ejpam-4637	521	17	;	;	PUNCT
ejpam-4637	521	18	and	and	CCONJ
ejpam-4637	521	19	ρ	ρ	NOUN
ejpam-4637	521	20	:	:	PUNCT
ejpam-4637	521	21	e	e	X
ejpam-4637	521	22	−→	−→	NOUN
ejpam-4637	521	23	e	e	X
ejpam-4637	521	24	by	by	ADP
ejpam-4637	521	25	ρ(e1	ρ(e1	NOUN
ejpam-4637	521	26	)	)	PUNCT
ejpam-4637	521	27	=	=	SYM
ejpam-4637	521	28	e2	e2	PROPN
ejpam-4637	521	29	ρ(e2	ρ(e2	NOUN
ejpam-4637	521	30	)	)	PUNCT
ejpam-4637	521	31	=	=	SYM
ejpam-4637	521	32	e1	e1	NOUN
ejpam-4637	521	33	.	.	PUNCT
ejpam-4637	522	1	also	also	ADV
ejpam-4637	522	2	,	,	PUNCT
ejpam-4637	522	3	consider	consider	VERB
ejpam-4637	522	4	the	the	DET
ejpam-4637	522	5	svns	svn	NOUN
ejpam-4637	522	6	hyper	hyper	VERB
ejpam-4637	522	7	up	up	ADP
ejpam-4637	522	8	-subalgebra	-subalgebra	PROPN
ejpam-4637	522	9	(	(	PUNCT
ejpam-4637	522	10	∆	∆	X
ejpam-4637	522	11	,	,	PUNCT
ejpam-4637	522	12	e	e	NOUN
ejpam-4637	522	13	)	)	PUNCT
ejpam-4637	522	14	of	of	ADP
ejpam-4637	522	15	x2	x2	PROPN
ejpam-4637	522	16	from	from	ADP
ejpam-4637	522	17	example	example	NOUN
ejpam-4637	522	18	7	7	NUM
ejpam-4637	522	19	which	which	PRON
ejpam-4637	522	20	is	be	AUX
ejpam-4637	522	21	given	give	VERB
ejpam-4637	522	22	by	by	ADP
ejpam-4637	522	23	∆(e1	∆(e1	NUM
ejpam-4637	522	24	)	)	PUNCT
ejpam-4637	522	25	=	=	PRON
ejpam-4637	522	26	{	{	PUNCT
ejpam-4637	522	27	⟨02	⟨02	NOUN
ejpam-4637	522	28	,	,	PUNCT
ejpam-4637	522	29	(	(	PUNCT
ejpam-4637	522	30	0.9	0.9	NUM
ejpam-4637	522	31	,	,	PUNCT
ejpam-4637	522	32	0.2	0.2	NUM
ejpam-4637	522	33	,	,	PUNCT
ejpam-4637	522	34	0.45)⟩	0.45)⟩	NUM
ejpam-4637	522	35	,	,	PUNCT
ejpam-4637	522	36	⟨u	⟨u	NOUN
ejpam-4637	522	37	,	,	PUNCT
ejpam-4637	522	38	(	(	PUNCT
ejpam-4637	522	39	0.74	0.74	NUM
ejpam-4637	522	40	,	,	PUNCT
ejpam-4637	522	41	0.57	0.57	NUM
ejpam-4637	522	42	,	,	PUNCT
ejpam-4637	522	43	0.7)⟩	0.7)⟩	NUM
ejpam-4637	522	44	,	,	PUNCT
ejpam-4637	522	45	⟨v	⟨v	CCONJ
ejpam-4637	522	46	,	,	PUNCT
ejpam-4637	522	47	(	(	PUNCT
ejpam-4637	522	48	0.8	0.8	NUM
ejpam-4637	522	49	,	,	PUNCT
ejpam-4637	522	50	0.42	0.42	NUM
ejpam-4637	522	51	,	,	PUNCT
ejpam-4637	522	52	0.52)⟩	0.52)⟩	NUM
ejpam-4637	522	53	}	}	PUNCT
ejpam-4637	522	54	and	and	CCONJ
ejpam-4637	522	55	∆(e2	∆(e2	PRON
ejpam-4637	522	56	)	)	PUNCT
ejpam-4637	522	57	=	=	PRON
ejpam-4637	522	58	{	{	PUNCT
ejpam-4637	522	59	⟨02	⟨02	NOUN
ejpam-4637	522	60	,	,	PUNCT
ejpam-4637	522	61	(	(	PUNCT
ejpam-4637	522	62	0.8	0.8	NUM
ejpam-4637	522	63	,	,	PUNCT
ejpam-4637	522	64	0.2	0.2	NUM
ejpam-4637	522	65	,	,	PUNCT
ejpam-4637	522	66	0.4)⟩	0.4)⟩	NUM
ejpam-4637	522	67	,	,	PUNCT
ejpam-4637	522	68	⟨u	⟨u	NOUN
ejpam-4637	522	69	,	,	PUNCT
ejpam-4637	522	70	(	(	PUNCT
ejpam-4637	522	71	0.4	0.4	NUM
ejpam-4637	522	72	,	,	PUNCT
ejpam-4637	522	73	0.45	0.45	NUM
ejpam-4637	522	74	,	,	PUNCT
ejpam-4637	522	75	0.5)⟩	0.5)⟩	NUM
ejpam-4637	522	76	,	,	PUNCT
ejpam-4637	522	77	⟨v	⟨v	PROPN
ejpam-4637	522	78	,	,	PUNCT
ejpam-4637	522	79	(	(	PUNCT
ejpam-4637	522	80	0.67	0.67	NUM
ejpam-4637	522	81	,	,	PUNCT
ejpam-4637	522	82	0.3	0.3	NUM
ejpam-4637	522	83	,	,	PUNCT
ejpam-4637	522	84	0.5)⟩	0.5)⟩	NUM
ejpam-4637	522	85	}	}	PUNCT
ejpam-4637	522	86	.	.	PUNCT
ejpam-4637	523	1	thus	thus	ADV
ejpam-4637	523	2	,	,	PUNCT
ejpam-4637	523	3	the	the	DET
ejpam-4637	523	4	preimage	preimage	NOUN
ejpam-4637	523	5	of	of	ADP
ejpam-4637	523	6	(	(	PUNCT
ejpam-4637	523	7	∆	∆	X
ejpam-4637	523	8	,	,	PUNCT
ejpam-4637	523	9	e	e	NOUN
ejpam-4637	523	10	)	)	PUNCT
ejpam-4637	523	11	under	under	ADP
ejpam-4637	523	12	(	(	PUNCT
ejpam-4637	523	13	φ	φ	PROPN
ejpam-4637	523	14	,	,	PUNCT
ejpam-4637	523	15	ρ	ρ	PROPN
ejpam-4637	523	16	)	)	PUNCT
ejpam-4637	523	17	is	be	AUX
ejpam-4637	523	18	given	give	VERB
ejpam-4637	523	19	by	by	ADP
ejpam-4637	523	20	tφ−1(∆)(e1)(01	tφ−1(∆)(e1)(01	NOUN
ejpam-4637	523	21	)	)	PUNCT
ejpam-4637	523	22	=	=	SYM
ejpam-4637	523	23	t∆(ρ(e1))(φ(01	t∆(ρ(e1))(φ(01	NUM
ejpam-4637	523	24	)	)	PUNCT
ejpam-4637	523	25	)	)	PUNCT
ejpam-4637	524	1	=	=	SYM
ejpam-4637	524	2	t∆(e2)(02	t∆(e2)(02	NOUN
ejpam-4637	524	3	)	)	PUNCT
ejpam-4637	524	4	=	=	NUM
ejpam-4637	524	5	0.8	0.8	NUM
ejpam-4637	524	6	iφ−1(∆)(e1)(01	iφ−1(∆)(e1)(01	NOUN
ejpam-4637	524	7	)	)	PUNCT
ejpam-4637	524	8	=	=	SYM
ejpam-4637	524	9	i∆(ρ(e1))(φ(01	i∆(ρ(e1))(φ(01	NOUN
ejpam-4637	524	10	)	)	PUNCT
ejpam-4637	524	11	)	)	PUNCT
ejpam-4637	525	1	=	=	SYM
ejpam-4637	525	2	i∆(e2)(02	i∆(e2)(02	NOUN
ejpam-4637	525	3	)	)	PUNCT
ejpam-4637	525	4	=	=	SYM
ejpam-4637	525	5	0.2	0.2	NUM
ejpam-4637	525	6	fφ−1(∆)(e1)(01	fφ−1(∆)(e1)(01	NOUN
ejpam-4637	525	7	)	)	PUNCT
ejpam-4637	525	8	=	=	SYM
ejpam-4637	525	9	f∆(ρ(e1))(φ(01	f∆(ρ(e1))(φ(01	X
ejpam-4637	525	10	)	)	PUNCT
ejpam-4637	525	11	)	)	PUNCT
ejpam-4637	526	1	=	=	SYM
ejpam-4637	526	2	f∆(e2)(02	f∆(e2)(02	NOUN
ejpam-4637	526	3	)	)	PUNCT
ejpam-4637	526	4	=	=	SYM
ejpam-4637	526	5	0.4	0.4	NUM
ejpam-4637	526	6	tφ−1(∆)(e1)(r	tφ−1(∆)(e1)(r	NOUN
ejpam-4637	526	7	)	)	PUNCT
ejpam-4637	526	8	=	=	SYM
ejpam-4637	526	9	t∆(ρ(e1))(φ(r	t∆(ρ(e1))(φ(r	NOUN
ejpam-4637	526	10	)	)	PUNCT
ejpam-4637	526	11	)	)	PUNCT
ejpam-4637	527	1	=	=	SYM
ejpam-4637	527	2	t∆(e2)(v	t∆(e2)(v	PROPN
ejpam-4637	527	3	)	)	PUNCT
ejpam-4637	527	4	=	=	NOUN
ejpam-4637	527	5	0.67	0.67	NUM
ejpam-4637	527	6	iφ−1(∆)(e1)(r	iφ−1(∆)(e1)(r	NOUN
ejpam-4637	527	7	)	)	PUNCT
ejpam-4637	527	8	=	=	SYM
ejpam-4637	528	1	i∆(ρ(e1))(φ(r	i∆(ρ(e1))(φ(r	PROPN
ejpam-4637	528	2	)	)	PUNCT
ejpam-4637	528	3	)	)	PUNCT
ejpam-4637	529	1	=	=	PUNCT
ejpam-4637	529	2	i∆(e2)(v	i∆(e2)(v	X
ejpam-4637	529	3	)	)	PUNCT
ejpam-4637	529	4	=	=	SYM
ejpam-4637	529	5	0.3	0.3	NUM
ejpam-4637	529	6	fφ−1(∆)(e1)(r	fφ−1(∆)(e1)(r	NOUN
ejpam-4637	529	7	)	)	PUNCT
ejpam-4637	529	8	=	=	SYM
ejpam-4637	529	9	f∆(ρ(e1))(φ(r	f∆(ρ(e1))(φ(r	NOUN
ejpam-4637	529	10	)	)	PUNCT
ejpam-4637	529	11	)	)	PUNCT
ejpam-4637	530	1	=	=	PUNCT
ejpam-4637	530	2	f∆(e2)(v	f∆(e2)(v	PROPN
ejpam-4637	530	3	)	)	PUNCT
ejpam-4637	530	4	=	=	SYM
ejpam-4637	530	5	0.5	0.5	NUM
ejpam-4637	530	6	tφ−1(∆)(e1)(s	tφ−1(∆)(e1)(s	NOUN
ejpam-4637	530	7	)	)	PUNCT
ejpam-4637	530	8	=	=	SYM
ejpam-4637	530	9	t∆(ρ(e1))(φ(s	t∆(ρ(e1))(φ(s	NOUN
ejpam-4637	530	10	)	)	PUNCT
ejpam-4637	530	11	)	)	PUNCT
ejpam-4637	531	1	=	=	SYM
ejpam-4637	531	2	t∆(e2)(u	t∆(e2)(u	PROPN
ejpam-4637	531	3	)	)	PUNCT
ejpam-4637	531	4	=	=	NOUN
ejpam-4637	531	5	0.4	0.4	NUM
ejpam-4637	531	6	iφ−1(∆)(e1)(s	iφ−1(∆)(e1)(s	NOUN
ejpam-4637	531	7	)	)	PUNCT
ejpam-4637	531	8	=	=	SYM
ejpam-4637	531	9	i∆(ρ(e1))(φ(s	i∆(ρ(e1))(φ(s	PROPN
ejpam-4637	531	10	)	)	PUNCT
ejpam-4637	531	11	)	)	PUNCT
ejpam-4637	532	1	=	=	PUNCT
ejpam-4637	532	2	i∆(e2)(u	i∆(e2)(u	ADJ
ejpam-4637	532	3	)	)	PUNCT
ejpam-4637	532	4	=	=	NOUN
ejpam-4637	532	5	0.45	0.45	NUM
ejpam-4637	532	6	fφ−1(∆)(e1)(s	fφ−1(∆)(e1)(s	NOUN
ejpam-4637	532	7	)	)	PUNCT
ejpam-4637	532	8	=	=	SYM
ejpam-4637	532	9	f∆(ρ(e1))(φ(s	f∆(ρ(e1))(φ(s	NOUN
ejpam-4637	532	10	)	)	PUNCT
ejpam-4637	532	11	)	)	PUNCT
ejpam-4637	533	1	=	=	PUNCT
ejpam-4637	533	2	f∆(e2)(u	f∆(e2)(u	PROPN
ejpam-4637	533	3	)	)	PUNCT
ejpam-4637	533	4	=	=	NUM
ejpam-4637	533	5	0.5	0.5	NUM
ejpam-4637	533	6	tφ−1(∆)(e2)(01	tφ−1(∆)(e2)(01	NOUN
ejpam-4637	533	7	)	)	PUNCT
ejpam-4637	533	8	=	=	SYM
ejpam-4637	533	9	t∆(ρ(e2))(φ(01	t∆(ρ(e2))(φ(01	NUM
ejpam-4637	533	10	)	)	PUNCT
ejpam-4637	533	11	)	)	PUNCT
ejpam-4637	534	1	=	=	SYM
ejpam-4637	534	2	t∆(e1)(02	t∆(e1)(02	X
ejpam-4637	534	3	)	)	PUNCT
ejpam-4637	534	4	=	=	SYM
ejpam-4637	534	5	0.9	0.9	NUM
ejpam-4637	534	6	iφ−1(∆)(e2)(01	iφ−1(∆)(e2)(01	NOUN
ejpam-4637	534	7	)	)	PUNCT
ejpam-4637	534	8	=	=	PUNCT
ejpam-4637	534	9	i∆(ρ(e2))(φ(01	i∆(ρ(e2))(φ(01	NUM
ejpam-4637	534	10	)	)	PUNCT
ejpam-4637	534	11	)	)	PUNCT
ejpam-4637	534	12	=	=	SYM
ejpam-4637	534	13	i∆(e1)(02	i∆(e1)(02	NOUN
ejpam-4637	534	14	)	)	PUNCT
ejpam-4637	534	15	=	=	SYM
ejpam-4637	534	16	0.2	0.2	NUM
ejpam-4637	534	17	fφ−1(∆)(e2)(01	fφ−1(∆)(e2)(01	NOUN
ejpam-4637	534	18	)	)	PUNCT
ejpam-4637	534	19	=	=	PUNCT
ejpam-4637	535	1	f∆(ρ(e2))(φ(01	f∆(ρ(e2))(φ(01	NOUN
ejpam-4637	535	2	)	)	PUNCT
ejpam-4637	535	3	)	)	PUNCT
ejpam-4637	536	1	=	=	SYM
ejpam-4637	536	2	f∆(e1)(02	f∆(e1)(02	PROPN
ejpam-4637	536	3	)	)	PUNCT
ejpam-4637	536	4	=	=	NUM
ejpam-4637	536	5	0.45	0.45	NUM
ejpam-4637	536	6	tφ−1(∆)(e2)(r	tφ−1(∆)(e2)(r	NUM
ejpam-4637	536	7	)	)	PUNCT
ejpam-4637	536	8	=	=	SYM
ejpam-4637	536	9	t∆(ρ(e2))(φ(r	t∆(ρ(e2))(φ(r	NOUN
ejpam-4637	536	10	)	)	PUNCT
ejpam-4637	536	11	)	)	PUNCT
ejpam-4637	537	1	=	=	PUNCT
ejpam-4637	537	2	t∆(e1)(v	t∆(e1)(v	X
ejpam-4637	537	3	)	)	PUNCT
ejpam-4637	537	4	=	=	SYM
ejpam-4637	537	5	0.8	0.8	NUM
ejpam-4637	537	6	iφ−1(∆)(e2)(r	iφ−1(∆)(e2)(r	NOUN
ejpam-4637	537	7	)	)	PUNCT
ejpam-4637	537	8	=	=	SYM
ejpam-4637	537	9	i∆(ρ(e2))(φ(r	i∆(ρ(e2))(φ(r	NOUN
ejpam-4637	537	10	)	)	PUNCT
ejpam-4637	537	11	)	)	PUNCT
ejpam-4637	538	1	=	=	SYM
ejpam-4637	538	2	i∆(e1)(v	i∆(e1)(v	NOUN
ejpam-4637	538	3	)	)	PUNCT
ejpam-4637	538	4	=	=	NOUN
ejpam-4637	538	5	0.42	0.42	NUM
ejpam-4637	538	6	fφ−1(∆)(e2)(r	fφ−1(∆)(e2)(r	NUM
ejpam-4637	538	7	)	)	PUNCT
ejpam-4637	538	8	=	=	SYM
ejpam-4637	538	9	f∆(ρ(e2))(φ(r	f∆(ρ(e2))(φ(r	NOUN
ejpam-4637	538	10	)	)	PUNCT
ejpam-4637	538	11	)	)	PUNCT
ejpam-4637	538	12	=	=	SYM
ejpam-4637	538	13	f∆(e1)(v	f∆(e1)(v	PROPN
ejpam-4637	538	14	)	)	PUNCT
ejpam-4637	538	15	=	=	SYM
ejpam-4637	538	16	0.52	0.52	NUM
ejpam-4637	538	17	tφ−1(∆)(e2)(s	tφ−1(∆)(e2)(s	NOUN
ejpam-4637	538	18	)	)	PUNCT
ejpam-4637	538	19	=	=	SYM
ejpam-4637	538	20	t∆(ρ(e2))(φ(s	t∆(ρ(e2))(φ(s	PROPN
ejpam-4637	538	21	)	)	PUNCT
ejpam-4637	538	22	)	)	PUNCT
ejpam-4637	539	1	=	=	SYM
ejpam-4637	539	2	t∆(e1)(u	t∆(e1)(u	PROPN
ejpam-4637	539	3	)	)	PUNCT
ejpam-4637	539	4	=	=	SYM
ejpam-4637	539	5	0.74	0.74	NUM
ejpam-4637	539	6	.	.	PUNCT
ejpam-4637	539	7	iφ−1(∆)(e2)(s	iφ−1(∆)(e2)(s	NOUN
ejpam-4637	539	8	)	)	PUNCT
ejpam-4637	539	9	=	=	SYM
ejpam-4637	539	10	i∆(ρ(e2))(φ(s	i∆(ρ(e2))(φ(s	PROPN
ejpam-4637	539	11	)	)	PUNCT
ejpam-4637	539	12	)	)	PUNCT
ejpam-4637	540	1	=	=	PUNCT
ejpam-4637	540	2	i∆(e1)(u	i∆(e1)(u	ADJ
ejpam-4637	540	3	)	)	PUNCT
ejpam-4637	540	4	=	=	SYM
ejpam-4637	540	5	0.57	0.57	NUM
ejpam-4637	540	6	.	.	PUNCT
ejpam-4637	540	7	fφ−1(∆)(e2)(s	fφ−1(∆)(e2)(s	NOUN
ejpam-4637	540	8	)	)	PUNCT
ejpam-4637	540	9	=	=	SYM
ejpam-4637	540	10	f∆(ρ(e2))(φ(s	f∆(ρ(e2))(φ(s	NUM
ejpam-4637	540	11	)	)	PUNCT
ejpam-4637	540	12	)	)	PUNCT
ejpam-4637	541	1	=	=	PUNCT
ejpam-4637	541	2	f∆(e1)(u	f∆(e1)(u	ADJ
ejpam-4637	541	3	)	)	PUNCT
ejpam-4637	541	4	=	=	SYM
ejpam-4637	541	5	0.7	0.7	NUM
ejpam-4637	541	6	.	.	PUNCT
ejpam-4637	541	7	theorem	theorem	VERB
ejpam-4637	541	8	8	8	NUM
ejpam-4637	541	9	.	.	PUNCT
ejpam-4637	542	1	let	let	AUX
ejpam-4637	542	2	(	(	PUNCT
ejpam-4637	542	3	φ	φ	PROPN
ejpam-4637	542	4	,	,	PUNCT
ejpam-4637	542	5	ρ	ρ	PROPN
ejpam-4637	542	6	)	)	PUNCT
ejpam-4637	542	7	be	be	VERB
ejpam-4637	542	8	a	a	DET
ejpam-4637	542	9	svns	svns	NOUN
ejpam-4637	542	10	homomorphism	homomorphism	NOUN
ejpam-4637	542	11	from	from	ADP
ejpam-4637	542	12	(	(	PUNCT
ejpam-4637	542	13	x1	x1	PROPN
ejpam-4637	542	14	,	,	PUNCT
ejpam-4637	542	15	◦	◦	NOUN
ejpam-4637	542	16	1,≪1	1,≪1	NUM
ejpam-4637	542	17	,	,	PUNCT
ejpam-4637	542	18	01	01	NUM
ejpam-4637	542	19	)	)	PUNCT
ejpam-4637	542	20	to	to	ADP
ejpam-4637	542	21	(	(	PUNCT
ejpam-4637	542	22	x2	x2	INTJ
ejpam-4637	542	23	,	,	PUNCT
ejpam-4637	542	24	◦	◦	NOUN
ejpam-4637	542	25	2,≪2	2,≪2	NUM
ejpam-4637	542	26	,	,	PUNCT
ejpam-4637	542	27	02	02	NUM
ejpam-4637	542	28	)	)	PUNCT
ejpam-4637	542	29	.	.	PUNCT
ejpam-4637	543	1	if	if	SCONJ
ejpam-4637	543	2	(	(	PUNCT
ejpam-4637	543	3	∆1	∆1	NOUN
ejpam-4637	543	4	,	,	PUNCT
ejpam-4637	543	5	e	e	NOUN
ejpam-4637	543	6	)	)	PUNCT
ejpam-4637	543	7	is	be	AUX
ejpam-4637	543	8	a	a	DET
ejpam-4637	543	9	svns	svns	NOUN
ejpam-4637	543	10	hyper	hyper	ADJ
ejpam-4637	543	11	up	up	ADP
ejpam-4637	543	12	-	-	PUNCT
ejpam-4637	543	13	subalgebra	subalgebra	NOUN
ejpam-4637	543	14	of	of	ADP
ejpam-4637	543	15	x1	x1	PROPN
ejpam-4637	543	16	,	,	PUNCT
ejpam-4637	543	17	then	then	ADV
ejpam-4637	543	18	(	(	PUNCT
ejpam-4637	543	19	φ	φ	PROPN
ejpam-4637	543	20	,	,	PUNCT
ejpam-4637	543	21	ρ)(∆1	ρ)(∆1	PROPN
ejpam-4637	543	22	,	,	PUNCT
ejpam-4637	543	23	e	e	NOUN
ejpam-4637	543	24	)	)	PUNCT
ejpam-4637	543	25	is	be	AUX
ejpam-4637	543	26	a	a	DET
ejpam-4637	543	27	svns	svns	NOUN
ejpam-4637	543	28	hyper	hyper	ADJ
ejpam-4637	543	29	up	up	ADP
ejpam-4637	543	30	-	-	PUNCT
ejpam-4637	543	31	subalgebra	subalgebra	NOUN
ejpam-4637	543	32	of	of	ADP
ejpam-4637	543	33	x2	x2	PROPN
ejpam-4637	543	34	.	.	PUNCT
ejpam-4637	544	1	a.	a.	PROPN
ejpam-4637	544	2	cano	cano	PROPN
ejpam-4637	544	3	,	,	PUNCT
ejpam-4637	544	4	g.	g.	PROPN
ejpam-4637	544	5	petalcorin	petalcorin	PROPN
ejpam-4637	544	6	/	/	SYM
ejpam-4637	544	7	eur	eur	PROPN
ejpam-4637	544	8	.	.	PUNCT
ejpam-4637	545	1	j.	j.	PROPN
ejpam-4637	545	2	pure	pure	PROPN
ejpam-4637	545	3	appl	appl	PROPN
ejpam-4637	545	4	.	.	PROPN
ejpam-4637	545	5	math	math	PROPN
ejpam-4637	545	6	,	,	PUNCT
ejpam-4637	545	7	16	16	NUM
ejpam-4637	545	8	(	(	PUNCT
ejpam-4637	545	9	1	1	NUM
ejpam-4637	545	10	)	)	PUNCT
ejpam-4637	545	11	(	(	PUNCT
ejpam-4637	545	12	2023	2023	NUM
ejpam-4637	545	13	)	)	PUNCT
ejpam-4637	545	14	,	,	PUNCT
ejpam-4637	545	15	548	548	NUM
ejpam-4637	545	16	-	-	SYM
ejpam-4637	545	17	576	576	NUM
ejpam-4637	545	18	573	573	NUM
ejpam-4637	545	19	proof	proof	NOUN
ejpam-4637	545	20	.	.	PUNCT
ejpam-4637	546	1	let	let	AUX
ejpam-4637	546	2	(	(	PUNCT
ejpam-4637	546	3	φ	φ	PROPN
ejpam-4637	546	4	,	,	PUNCT
ejpam-4637	546	5	ρ	ρ	PROPN
ejpam-4637	546	6	)	)	PUNCT
ejpam-4637	546	7	be	be	VERB
ejpam-4637	546	8	a	a	DET
ejpam-4637	546	9	svns	svns	NOUN
ejpam-4637	546	10	homomorphism	homomorphism	NOUN
ejpam-4637	546	11	from	from	ADP
ejpam-4637	546	12	x1	x1	PROPN
ejpam-4637	546	13	to	to	ADP
ejpam-4637	546	14	x2	x2	NUM
ejpam-4637	546	15	,	,	PUNCT
ejpam-4637	546	16	(	(	PUNCT
ejpam-4637	546	17	∆1	∆1	NOUN
ejpam-4637	546	18	,	,	PUNCT
ejpam-4637	546	19	e	e	NOUN
ejpam-4637	546	20	)	)	PUNCT
ejpam-4637	546	21	is	be	AUX
ejpam-4637	546	22	a	a	DET
ejpam-4637	546	23	svns	svns	NOUN
ejpam-4637	546	24	hyper	hyper	ADJ
ejpam-4637	546	25	up	up	ADP
ejpam-4637	546	26	-subalgebra	-subalgebra	NOUN
ejpam-4637	546	27	of	of	ADP
ejpam-4637	546	28	x1	x1	PROPN
ejpam-4637	546	29	,	,	PUNCT
ejpam-4637	546	30	b	b	PROPN
ejpam-4637	546	31	∈	∈	PROPN
ejpam-4637	546	32	ρ(e	ρ(e	PROPN
ejpam-4637	546	33	)	)	PUNCT
ejpam-4637	546	34	,	,	PUNCT
ejpam-4637	546	35	and	and	CCONJ
ejpam-4637	546	36	x	x	X
ejpam-4637	546	37	,	,	PUNCT
ejpam-4637	546	38	y	y	PROPN
ejpam-4637	546	39	∈	∈	PROPN
ejpam-4637	546	40	x2	x2	PROPN
ejpam-4637	546	41	.	.	PUNCT
ejpam-4637	547	1	(	(	PUNCT
ejpam-4637	547	2	i	i	NOUN
ejpam-4637	547	3	)	)	PUNCT
ejpam-4637	547	4	for	for	ADP
ejpam-4637	547	5	φ−1(x	φ−1(x	NOUN
ejpam-4637	547	6	)	)	PUNCT
ejpam-4637	548	1	=	=	NOUN
ejpam-4637	548	2	∅	∅	NOUN
ejpam-4637	548	3	or	or	CCONJ
ejpam-4637	548	4	φ−1(y	φ−1(y	PROPN
ejpam-4637	548	5	)	)	PUNCT
ejpam-4637	549	1	=	=	NOUN
ejpam-4637	549	2	∅	∅	NOUN
ejpam-4637	549	3	,	,	PUNCT
ejpam-4637	549	4	the	the	DET
ejpam-4637	549	5	proof	proof	NOUN
ejpam-4637	549	6	is	be	AUX
ejpam-4637	549	7	straightforward	straightforward	ADJ
ejpam-4637	549	8	.	.	PUNCT
ejpam-4637	550	1	(	(	PUNCT
ejpam-4637	550	2	ii	ii	NOUN
ejpam-4637	550	3	)	)	PUNCT
ejpam-4637	550	4	assume	assume	VERB
ejpam-4637	550	5	that	that	SCONJ
ejpam-4637	550	6	there	there	PRON
ejpam-4637	550	7	exist	exist	VERB
ejpam-4637	550	8	x0	x0	PROPN
ejpam-4637	550	9	,	,	PUNCT
ejpam-4637	550	10	y0	y0	PROPN
ejpam-4637	550	11	∈	∈	NOUN
ejpam-4637	551	1	x1	x1	NUM
ejpam-4637	551	2	such	such	ADJ
ejpam-4637	551	3	that	that	DET
ejpam-4637	551	4	φ(x0	φ(x0	NOUN
ejpam-4637	551	5	)	)	PUNCT
ejpam-4637	551	6	=	=	SYM
ejpam-4637	552	1	x	x	PUNCT
ejpam-4637	552	2	and	and	CCONJ
ejpam-4637	552	3	φ(y0	φ(y0	NOUN
ejpam-4637	552	4	)	)	PUNCT
ejpam-4637	553	1	=	=	PUNCT
ejpam-4637	554	1	y.	y.	NOUN
ejpam-4637	554	2	then	then	ADV
ejpam-4637	554	3	x	x	SYM
ejpam-4637	554	4	◦	◦	NOUN
ejpam-4637	554	5	2	2	NUM
ejpam-4637	554	6	y	y	NOUN
ejpam-4637	554	7	=	=	PUNCT
ejpam-4637	554	8	φ(x0	φ(x0	NOUN
ejpam-4637	554	9	)	)	PUNCT
ejpam-4637	554	10	◦	◦	NOUN
ejpam-4637	554	11	2	2	NUM
ejpam-4637	554	12	φ(y0	φ(y0	NOUN
ejpam-4637	554	13	)	)	PUNCT
ejpam-4637	554	14	=	=	NOUN
ejpam-4637	554	15	φ(x0	φ(x0	NOUN
ejpam-4637	554	16	◦	◦	NOUN
ejpam-4637	554	17	1	1	NUM
ejpam-4637	554	18	y0	y0	NOUN
ejpam-4637	554	19	)	)	PUNCT
ejpam-4637	554	20	.	.	PUNCT
ejpam-4637	555	1	now	now	ADV
ejpam-4637	555	2	,	,	PUNCT
ejpam-4637	555	3	∗tφ(∆1)(b)(x	∗tφ(∆1)(b)(x	PROPN
ejpam-4637	555	4	◦	◦	NOUN
ejpam-4637	555	5	2	2	NUM
ejpam-4637	555	6	y	y	NOUN
ejpam-4637	555	7	)	)	PUNCT
ejpam-4637	555	8	=	=	SYM
ejpam-4637	555	9	inf	inf	PROPN
ejpam-4637	555	10	z∈x	z∈x	PROPN
ejpam-4637	555	11	◦	◦	NOUN
ejpam-4637	555	12	2y	2y	NUM
ejpam-4637	555	13	tφ(∆1)(b)(z	tφ(∆1)(b)(z	NOUN
ejpam-4637	555	14	)	)	PUNCT
ejpam-4637	555	15	=	=	SYM
ejpam-4637	555	16	inf	inf	NOUN
ejpam-4637	556	1	z0∈x0	z0∈x0	NUM
ejpam-4637	556	2	◦	◦	NOUN
ejpam-4637	556	3	1y0	1y0	NUM
ejpam-4637	556	4	[	[	PUNCT
ejpam-4637	556	5	max	max	PROPN
ejpam-4637	556	6	φ(z0)=z	φ(z0)=z	PROPN
ejpam-4637	556	7	max	max	PROPN
ejpam-4637	556	8	ρ(a)=b	ρ(a)=b	NUM
ejpam-4637	556	9	t∆1(a)(z0	t∆1(a)(z0	NOUN
ejpam-4637	556	10	)	)	PUNCT
ejpam-4637	556	11	]	]	PUNCT
ejpam-4637	556	12	≥	≥	PROPN
ejpam-4637	556	13	inf	inf	PROPN
ejpam-4637	556	14	z0∈x0	z0∈x0	NUM
ejpam-4637	556	15	◦	◦	NOUN
ejpam-4637	556	16	1y0	1y0	NUM
ejpam-4637	556	17	[	[	PUNCT
ejpam-4637	556	18	max	max	PROPN
ejpam-4637	556	19	ρ(a)=b	ρ(a)=b	NUM
ejpam-4637	556	20	t∆1(a)(z0	t∆1(a)(z0	NOUN
ejpam-4637	556	21	)	)	PUNCT
ejpam-4637	556	22	]	]	PUNCT
ejpam-4637	557	1	=	=	PUNCT
ejpam-4637	557	2	max	max	PROPN
ejpam-4637	557	3	ρ(a)=b	ρ(a)=b	CCONJ
ejpam-4637	557	4	[	[	PUNCT
ejpam-4637	557	5	inf	inf	NOUN
ejpam-4637	557	6	z0∈x0	z0∈x0	NUM
ejpam-4637	557	7	◦	◦	NOUN
ejpam-4637	557	8	1y0	1y0	NUM
ejpam-4637	557	9	t∆1(a)(z0	t∆1(a)(z0	NOUN
ejpam-4637	557	10	)	)	PUNCT
ejpam-4637	557	11	]	]	PUNCT
ejpam-4637	558	1	=	=	PUNCT
ejpam-4637	558	2	max	max	PROPN
ejpam-4637	558	3	ρ(a)=b	ρ(a)=b	CCONJ
ejpam-4637	558	4	[	[	PUNCT
ejpam-4637	558	5	∗t∆1(a)(x0	∗t∆1(a)(x0	PROPN
ejpam-4637	558	6	◦	◦	NOUN
ejpam-4637	558	7	1	1	NUM
ejpam-4637	558	8	y0	y0	NOUN
ejpam-4637	558	9	)	)	PUNCT
ejpam-4637	558	10	]	]	PUNCT
ejpam-4637	558	11	≥	≥	PROPN
ejpam-4637	558	12	max	max	PROPN
ejpam-4637	558	13	ρ(a)=b	ρ(a)=b	PROPN
ejpam-4637	558	14	[	[	PUNCT
ejpam-4637	558	15	min{t∆1(a)(x0	min{t∆1(a)(x0	NOUN
ejpam-4637	558	16	)	)	PUNCT
ejpam-4637	558	17	,	,	PUNCT
ejpam-4637	558	18	t∆1(a)(y0	t∆1(a)(y0	NOUN
ejpam-4637	558	19	)	)	PUNCT
ejpam-4637	558	20	}	}	PUNCT
ejpam-4637	558	21	]	]	PUNCT
ejpam-4637	559	1	=	=	PUNCT
ejpam-4637	559	2	min{max	min{max	NOUN
ejpam-4637	559	3	ρ(a)=b	ρ(a)=b	NUM
ejpam-4637	559	4	t∆1(a)(x0	t∆1(a)(x0	ADV
ejpam-4637	559	5	)	)	PUNCT
ejpam-4637	559	6	,	,	PUNCT
ejpam-4637	559	7	max	max	PROPN
ejpam-4637	559	8	ρ(a)=b	ρ(a)=b	CCONJ
ejpam-4637	559	9	t∆1(a)(y0	t∆1(a)(y0	NOUN
ejpam-4637	559	10	)	)	PUNCT
ejpam-4637	559	11	}	}	PUNCT
ejpam-4637	559	12	since	since	SCONJ
ejpam-4637	559	13	the	the	DET
ejpam-4637	559	14	inequality	inequality	NOUN
ejpam-4637	559	15	is	be	AUX
ejpam-4637	559	16	satisfied	satisfied	ADJ
ejpam-4637	559	17	for	for	ADP
ejpam-4637	559	18	all	all	DET
ejpam-4637	559	19	x0	x0	PROPN
ejpam-4637	559	20	,	,	PUNCT
ejpam-4637	559	21	y0	y0	NOUN
ejpam-4637	559	22	∈	∈	NOUN
ejpam-4637	559	23	x1	x1	NUM
ejpam-4637	559	24	satisfying	satisfying	NOUN
ejpam-4637	559	25	φ(x0	φ(x0	NOUN
ejpam-4637	559	26	)	)	PUNCT
ejpam-4637	559	27	=	=	SYM
ejpam-4637	560	1	x	x	PUNCT
ejpam-4637	560	2	and	and	CCONJ
ejpam-4637	560	3	φ(y0	φ(y0	NOUN
ejpam-4637	560	4	)	)	PUNCT
ejpam-4637	561	1	=	=	SYM
ejpam-4637	561	2	y	y	PROPN
ejpam-4637	561	3	,	,	PUNCT
ejpam-4637	561	4	it	it	PRON
ejpam-4637	561	5	follows	follow	VERB
ejpam-4637	561	6	that	that	SCONJ
ejpam-4637	561	7	∗tφ(∆1)(b)(x	∗tφ(∆1)(b)(x	PROPN
ejpam-4637	561	8	◦	◦	NOUN
ejpam-4637	561	9	2	2	NUM
ejpam-4637	561	10	y	y	NOUN
ejpam-4637	561	11	)	)	PUNCT
ejpam-4637	561	12	≥	≥	PROPN
ejpam-4637	561	13	min	min	PROPN
ejpam-4637	561	14	{	{	PUNCT
ejpam-4637	561	15	max	max	PROPN
ejpam-4637	561	16	φ(x0)=x	φ(x0)=x	PROPN
ejpam-4637	561	17	max	max	PROPN
ejpam-4637	561	18	ρ(a)=b	ρ(a)=b	NUM
ejpam-4637	561	19	t∆1(a)(x0	t∆1(a)(x0	ADV
ejpam-4637	561	20	)	)	PUNCT
ejpam-4637	561	21	,	,	PUNCT
ejpam-4637	561	22	max	max	PROPN
ejpam-4637	561	23	φ(y0)=y	φ(y0)=y	PROPN
ejpam-4637	561	24	max	max	PROPN
ejpam-4637	561	25	ρ(a)=b	ρ(a)=b	CCONJ
ejpam-4637	561	26	t∆1(a)(y0	t∆1(a)(y0	NOUN
ejpam-4637	561	27	)	)	PUNCT
ejpam-4637	561	28	}	}	PUNCT
ejpam-4637	561	29	=	=	SYM
ejpam-4637	561	30	min{tφ(∆1)(b)(x	min{tφ(∆1)(b)(x	PROPN
ejpam-4637	561	31	)	)	PUNCT
ejpam-4637	561	32	,	,	PUNCT
ejpam-4637	561	33	tφ(∆1)(b)(y	tφ(∆1)(b)(y	NOUN
ejpam-4637	561	34	)	)	PUNCT
ejpam-4637	561	35	}	}	PUNCT
ejpam-4637	561	36	.	.	PUNCT
ejpam-4637	562	1	also	also	ADV
ejpam-4637	562	2	,	,	PUNCT
ejpam-4637	562	3	∗iφ(∆1)(b)(x	∗iφ(∆1)(b)(x	PROPN
ejpam-4637	562	4	◦	◦	NOUN
ejpam-4637	562	5	2	2	NUM
ejpam-4637	562	6	y	y	NOUN
ejpam-4637	562	7	)	)	PUNCT
ejpam-4637	563	1	=	=	SYM
ejpam-4637	563	2	sup	sup	NUM
ejpam-4637	563	3	z∈x	z∈x	NOUN
ejpam-4637	563	4	◦	◦	NOUN
ejpam-4637	563	5	2y	2y	NUM
ejpam-4637	563	6	iφ(∆1)(b)(z	iφ(∆1)(b)(z	NOUN
ejpam-4637	563	7	)	)	PUNCT
ejpam-4637	563	8	=	=	SYM
ejpam-4637	563	9	sup	sup	NOUN
ejpam-4637	563	10	z0∈x0	z0∈x0	NUM
ejpam-4637	563	11	◦	◦	NOUN
ejpam-4637	563	12	1y0	1y0	NUM
ejpam-4637	563	13	[	[	PUNCT
ejpam-4637	563	14	min	min	X
ejpam-4637	563	15	φ(z0)=z	φ(z0)=z	NOUN
ejpam-4637	563	16	min	min	PROPN
ejpam-4637	563	17	ρ(a)=b	ρ(a)=b	NUM
ejpam-4637	563	18	i∆1(a)(z0	i∆1(a)(z0	NOUN
ejpam-4637	563	19	)	)	PUNCT
ejpam-4637	563	20	]	]	PUNCT
ejpam-4637	563	21	≤	≤	NUM
ejpam-4637	563	22	sup	sup	NOUN
ejpam-4637	563	23	z0∈x0	z0∈x0	NUM
ejpam-4637	563	24	◦	◦	NOUN
ejpam-4637	563	25	1y0	1y0	NUM
ejpam-4637	563	26	[	[	PUNCT
ejpam-4637	563	27	min	min	NOUN
ejpam-4637	563	28	ρ(a)=b	ρ(a)=b	SYM
ejpam-4637	563	29	i∆1(a)(z0	i∆1(a)(z0	NOUN
ejpam-4637	563	30	)	)	PUNCT
ejpam-4637	563	31	]	]	PUNCT
ejpam-4637	564	1	=	=	PUNCT
ejpam-4637	564	2	min	min	NOUN
ejpam-4637	565	1	ρ(a)=b	ρ(a)=b	INTJ
ejpam-4637	565	2	[	[	PUNCT
ejpam-4637	565	3	sup	sup	NOUN
ejpam-4637	565	4	z0∈x0	z0∈x0	NUM
ejpam-4637	565	5	◦	◦	NOUN
ejpam-4637	565	6	1y0	1y0	NUM
ejpam-4637	565	7	i∆1(a)(z0	i∆1(a)(z0	NOUN
ejpam-4637	565	8	)	)	PUNCT
ejpam-4637	565	9	]	]	PUNCT
ejpam-4637	566	1	=	=	PUNCT
ejpam-4637	566	2	min	min	NOUN
ejpam-4637	567	1	ρ(a)=b	ρ(a)=b	INTJ
ejpam-4637	567	2	[	[	PUNCT
ejpam-4637	567	3	∗i∆1(a)(x0	∗i∆1(a)(x0	PROPN
ejpam-4637	567	4	◦	◦	NOUN
ejpam-4637	567	5	1	1	NUM
ejpam-4637	567	6	y0	y0	NOUN
ejpam-4637	567	7	)	)	PUNCT
ejpam-4637	567	8	]	]	PUNCT
ejpam-4637	567	9	≤	≤	NUM
ejpam-4637	567	10	min	min	NOUN
ejpam-4637	567	11	ρ(a)=b	ρ(a)=b	NUM
ejpam-4637	567	12	[	[	PUNCT
ejpam-4637	567	13	max{i∆1(a)(x0	max{i∆1(a)(x0	NOUN
ejpam-4637	567	14	)	)	PUNCT
ejpam-4637	567	15	,	,	PUNCT
ejpam-4637	567	16	i∆1(a)(y0	i∆1(a)(y0	NOUN
ejpam-4637	567	17	)	)	PUNCT
ejpam-4637	567	18	}	}	PUNCT
ejpam-4637	567	19	]	]	PUNCT
ejpam-4637	567	20	=	=	SYM
ejpam-4637	567	21	max	max	PROPN
ejpam-4637	567	22	{	{	PUNCT
ejpam-4637	567	23	min	min	NOUN
ejpam-4637	567	24	ρ(a)=b	ρ(a)=b	X
ejpam-4637	567	25	i∆1(a)(x0	i∆1(a)(x0	ADJ
ejpam-4637	567	26	)	)	PUNCT
ejpam-4637	567	27	,	,	PUNCT
ejpam-4637	567	28	min	min	PROPN
ejpam-4637	567	29	ρ(a)=b	ρ(a)=b	CCONJ
ejpam-4637	567	30	i∆1(a)(y0	i∆1(a)(y0	NOUN
ejpam-4637	567	31	)	)	PUNCT
ejpam-4637	567	32	}	}	PUNCT
ejpam-4637	567	33	a.	a.	PROPN
ejpam-4637	567	34	cano	cano	PROPN
ejpam-4637	567	35	,	,	PUNCT
ejpam-4637	567	36	g.	g.	PROPN
ejpam-4637	567	37	petalcorin	petalcorin	PROPN
ejpam-4637	567	38	/	/	SYM
ejpam-4637	567	39	eur	eur	PROPN
ejpam-4637	567	40	.	.	PUNCT
ejpam-4637	568	1	j.	j.	PROPN
ejpam-4637	568	2	pure	pure	PROPN
ejpam-4637	568	3	appl	appl	PROPN
ejpam-4637	568	4	.	.	PROPN
ejpam-4637	568	5	math	math	PROPN
ejpam-4637	568	6	,	,	PUNCT
ejpam-4637	568	7	16	16	NUM
ejpam-4637	568	8	(	(	PUNCT
ejpam-4637	568	9	1	1	NUM
ejpam-4637	568	10	)	)	PUNCT
ejpam-4637	568	11	(	(	PUNCT
ejpam-4637	568	12	2023	2023	NUM
ejpam-4637	568	13	)	)	PUNCT
ejpam-4637	568	14	,	,	PUNCT
ejpam-4637	568	15	548	548	NUM
ejpam-4637	568	16	-	-	SYM
ejpam-4637	568	17	576	576	NUM
ejpam-4637	568	18	574	574	NUM
ejpam-4637	568	19	since	since	SCONJ
ejpam-4637	568	20	the	the	DET
ejpam-4637	568	21	inequality	inequality	NOUN
ejpam-4637	568	22	is	be	AUX
ejpam-4637	568	23	satisfied	satisfied	ADJ
ejpam-4637	568	24	for	for	ADP
ejpam-4637	568	25	all	all	DET
ejpam-4637	568	26	x0	x0	PROPN
ejpam-4637	568	27	,	,	PUNCT
ejpam-4637	568	28	y0	y0	NOUN
ejpam-4637	568	29	∈	∈	NOUN
ejpam-4637	568	30	x1	x1	NUM
ejpam-4637	568	31	satisfying	satisfying	NOUN
ejpam-4637	568	32	φ(x0	φ(x0	NOUN
ejpam-4637	568	33	)	)	PUNCT
ejpam-4637	568	34	=	=	SYM
ejpam-4637	569	1	x	x	PUNCT
ejpam-4637	569	2	and	and	CCONJ
ejpam-4637	569	3	φ(y0	φ(y0	NOUN
ejpam-4637	569	4	)	)	PUNCT
ejpam-4637	570	1	=	=	SYM
ejpam-4637	570	2	y	y	PROPN
ejpam-4637	570	3	,	,	PUNCT
ejpam-4637	570	4	it	it	PRON
ejpam-4637	570	5	follows	follow	VERB
ejpam-4637	570	6	that	that	SCONJ
ejpam-4637	570	7	∗iφ(∆1)(b)(x	∗iφ(∆1)(b)(x	PROPN
ejpam-4637	570	8	◦	◦	NOUN
ejpam-4637	570	9	2	2	NUM
ejpam-4637	570	10	y	y	NOUN
ejpam-4637	570	11	)	)	PUNCT
ejpam-4637	570	12	≤	≤	NUM
ejpam-4637	570	13	max	max	PROPN
ejpam-4637	570	14	{	{	PUNCT
ejpam-4637	570	15	min	min	PROPN
ejpam-4637	570	16	φ(x0)=x	φ(x0)=x	PROPN
ejpam-4637	570	17	min	min	NOUN
ejpam-4637	570	18	ρ(a)=b	ρ(a)=b	X
ejpam-4637	570	19	i∆1(a)(x0	i∆1(a)(x0	ADJ
ejpam-4637	570	20	)	)	PUNCT
ejpam-4637	570	21	,	,	PUNCT
ejpam-4637	570	22	max	max	PROPN
ejpam-4637	570	23	φ(y0)=y	φ(y0)=y	PROPN
ejpam-4637	570	24	max	max	PROPN
ejpam-4637	570	25	ρ(a)=b	ρ(a)=b	CCONJ
ejpam-4637	570	26	i∆1(a)(y0	i∆1(a)(y0	PROPN
ejpam-4637	570	27	)	)	PUNCT
ejpam-4637	570	28	}	}	PUNCT
ejpam-4637	570	29	=	=	SYM
ejpam-4637	570	30	max{iφ(∆1)(b)(x	max{iφ(∆1)(b)(x	NOUN
ejpam-4637	570	31	)	)	PUNCT
ejpam-4637	570	32	,	,	PUNCT
ejpam-4637	570	33	iφ(∆1)(b)(y	iφ(∆1)(b)(y	PROPN
ejpam-4637	570	34	)	)	PUNCT
ejpam-4637	570	35	}	}	PUNCT
ejpam-4637	570	36	.	.	PUNCT
ejpam-4637	571	1	similarly	similarly	ADV
ejpam-4637	571	2	,	,	PUNCT
ejpam-4637	571	3	∗fφ(∆1)(b)(x	∗fφ(∆1)(b)(x	PROPN
ejpam-4637	571	4	◦	◦	NOUN
ejpam-4637	571	5	2	2	NUM
ejpam-4637	571	6	y	y	NOUN
ejpam-4637	571	7	)	)	PUNCT
ejpam-4637	571	8	≤	≤	NOUN
ejpam-4637	572	1	max{fφ(∆1)(b)(x),fφ(∆1)(b)(y	max{fφ(∆1)(b)(x),fφ(∆1)(b)(y	PROPN
ejpam-4637	572	2	)	)	PUNCT
ejpam-4637	572	3	}	}	PUNCT
ejpam-4637	572	4	.	.	PUNCT
ejpam-4637	573	1	hence	hence	ADV
ejpam-4637	573	2	,	,	PUNCT
ejpam-4637	573	3	(	(	PUNCT
ejpam-4637	573	4	φ	φ	PROPN
ejpam-4637	573	5	,	,	PUNCT
ejpam-4637	573	6	ρ)(∆1	ρ)(∆1	PROPN
ejpam-4637	573	7	,	,	PUNCT
ejpam-4637	573	8	e	e	NOUN
ejpam-4637	573	9	)	)	PUNCT
ejpam-4637	573	10	is	be	AUX
ejpam-4637	573	11	a	a	DET
ejpam-4637	573	12	svns	svns	NOUN
ejpam-4637	573	13	hyper	hyper	ADJ
ejpam-4637	573	14	up	up	ADP
ejpam-4637	573	15	-subalgebra	-subalgebra	NOUN
ejpam-4637	573	16	of	of	ADP
ejpam-4637	573	17	x2	x2	PROPN
ejpam-4637	573	18	.	.	PUNCT
ejpam-4637	574	1	theorem	theorem	VERB
ejpam-4637	574	2	9	9	NUM
ejpam-4637	574	3	.	.	PUNCT
ejpam-4637	575	1	let	let	AUX
ejpam-4637	575	2	(	(	PUNCT
ejpam-4637	575	3	φ	φ	PROPN
ejpam-4637	575	4	,	,	PUNCT
ejpam-4637	575	5	ρ	ρ	PROPN
ejpam-4637	575	6	)	)	PUNCT
ejpam-4637	575	7	be	be	VERB
ejpam-4637	575	8	a	a	DET
ejpam-4637	575	9	svns	svns	NOUN
ejpam-4637	575	10	homomorphism	homomorphism	NOUN
ejpam-4637	575	11	from	from	ADP
ejpam-4637	575	12	(	(	PUNCT
ejpam-4637	575	13	x1	x1	PROPN
ejpam-4637	575	14	,	,	PUNCT
ejpam-4637	575	15	◦	◦	NOUN
ejpam-4637	575	16	1,≪1	1,≪1	NUM
ejpam-4637	575	17	,	,	PUNCT
ejpam-4637	575	18	01	01	NUM
ejpam-4637	575	19	)	)	PUNCT
ejpam-4637	575	20	to	to	ADP
ejpam-4637	575	21	(	(	PUNCT
ejpam-4637	575	22	x2	x2	INTJ
ejpam-4637	575	23	,	,	PUNCT
ejpam-4637	575	24	◦	◦	NOUN
ejpam-4637	575	25	2,≪2	2,≪2	NUM
ejpam-4637	575	26	,	,	PUNCT
ejpam-4637	575	27	02	02	NUM
ejpam-4637	575	28	)	)	PUNCT
ejpam-4637	575	29	.	.	PUNCT
ejpam-4637	576	1	if	if	SCONJ
ejpam-4637	576	2	(	(	PUNCT
ejpam-4637	576	3	∆2	∆2	X
ejpam-4637	576	4	,	,	PUNCT
ejpam-4637	576	5	e	e	NOUN
ejpam-4637	576	6	)	)	PUNCT
ejpam-4637	576	7	is	be	AUX
ejpam-4637	576	8	a	a	DET
ejpam-4637	576	9	svns	svns	NOUN
ejpam-4637	576	10	hyper	hyper	ADJ
ejpam-4637	576	11	up	up	ADP
ejpam-4637	576	12	-	-	PUNCT
ejpam-4637	576	13	subalgebra	subalgebra	NOUN
ejpam-4637	576	14	of	of	ADP
ejpam-4637	576	15	x2	x2	PROPN
ejpam-4637	576	16	,	,	PUNCT
ejpam-4637	576	17	then	then	ADV
ejpam-4637	576	18	(	(	PUNCT
ejpam-4637	576	19	φ	φ	NOUN
ejpam-4637	576	20	,	,	PUNCT
ejpam-4637	576	21	ρ)−1(∆2	ρ)−1(∆2	ADJ
ejpam-4637	576	22	,	,	PUNCT
ejpam-4637	576	23	e	e	X
ejpam-4637	576	24	)	)	PUNCT
ejpam-4637	576	25	is	be	AUX
ejpam-4637	576	26	a	a	DET
ejpam-4637	576	27	svns	svns	NOUN
ejpam-4637	576	28	hyper	hyper	ADJ
ejpam-4637	576	29	up	up	ADP
ejpam-4637	576	30	-	-	PUNCT
ejpam-4637	576	31	subalgebra	subalgebra	NOUN
ejpam-4637	576	32	of	of	ADP
ejpam-4637	576	33	x1	x1	PROPN
ejpam-4637	576	34	.	.	PUNCT
ejpam-4637	577	1	proof	proof	NOUN
ejpam-4637	577	2	.	.	PUNCT
ejpam-4637	578	1	let	let	AUX
ejpam-4637	578	2	(	(	PUNCT
ejpam-4637	578	3	φ	φ	PROPN
ejpam-4637	578	4	,	,	PUNCT
ejpam-4637	578	5	ρ	ρ	PROPN
ejpam-4637	578	6	)	)	PUNCT
ejpam-4637	578	7	be	be	VERB
ejpam-4637	578	8	a	a	DET
ejpam-4637	578	9	svns	svns	NOUN
ejpam-4637	578	10	homomorphism	homomorphism	NOUN
ejpam-4637	578	11	from	from	ADP
ejpam-4637	578	12	x1	x1	PROPN
ejpam-4637	578	13	to	to	ADP
ejpam-4637	578	14	x2	x2	NUM
ejpam-4637	578	15	,	,	PUNCT
ejpam-4637	578	16	(	(	PUNCT
ejpam-4637	578	17	∆2	∆2	X
ejpam-4637	578	18	,	,	PUNCT
ejpam-4637	578	19	e	e	NOUN
ejpam-4637	578	20	)	)	PUNCT
ejpam-4637	578	21	be	be	AUX
ejpam-4637	578	22	a	a	DET
ejpam-4637	578	23	svns	svns	NOUN
ejpam-4637	578	24	hyper	hyper	ADJ
ejpam-4637	578	25	up	up	ADP
ejpam-4637	578	26	-subalgebra	-subalgebra	NOUN
ejpam-4637	578	27	of	of	ADP
ejpam-4637	578	28	x2	x2	PROPN
ejpam-4637	578	29	,	,	PUNCT
ejpam-4637	578	30	a	a	DET
ejpam-4637	578	31	∈	∈	PROPN
ejpam-4637	578	32	ρ−1(e	ρ−1(e	PROPN
ejpam-4637	578	33	)	)	PUNCT
ejpam-4637	578	34	,	,	PUNCT
ejpam-4637	578	35	x	x	X
ejpam-4637	578	36	,	,	PUNCT
ejpam-4637	578	37	y	y	PROPN
ejpam-4637	578	38	∈	∈	PROPN
ejpam-4637	579	1	x1	x1	PROPN
ejpam-4637	579	2	.	.	PUNCT
ejpam-4637	580	1	now	now	ADV
ejpam-4637	580	2	,	,	PUNCT
ejpam-4637	580	3	∗tφ−1(∆2)(a)(x	∗tφ−1(∆2)(a)(x	PROPN
ejpam-4637	580	4	◦	◦	NOUN
ejpam-4637	580	5	1	1	NUM
ejpam-4637	580	6	y	y	NOUN
ejpam-4637	580	7	)	)	PUNCT
ejpam-4637	581	1	=	=	SYM
ejpam-4637	581	2	∗t∆2(ρ(a))(φ(x	∗t∆2(ρ(a))(φ(x	NOUN
ejpam-4637	581	3	◦	◦	NOUN
ejpam-4637	581	4	1	1	NUM
ejpam-4637	581	5	y	y	NOUN
ejpam-4637	581	6	)	)	PUNCT
ejpam-4637	581	7	)	)	PUNCT
ejpam-4637	582	1	=	=	SYM
ejpam-4637	582	2	∗t∆2(ρ(a))(φ(x	∗t∆2(ρ(a))(φ(x	NOUN
ejpam-4637	582	3	)	)	PUNCT
ejpam-4637	582	4	◦	◦	NOUN
ejpam-4637	582	5	2	2	NUM
ejpam-4637	582	6	φ(y	φ(y	NOUN
ejpam-4637	582	7	)	)	PUNCT
ejpam-4637	582	8	)	)	PUNCT
ejpam-4637	582	9	≥	≥	PROPN
ejpam-4637	582	10	min{t∆2(ρ(a))(φ(x	min{t∆2(ρ(a))(φ(x	NOUN
ejpam-4637	582	11	)	)	PUNCT
ejpam-4637	582	12	)	)	PUNCT
ejpam-4637	582	13	,	,	PUNCT
ejpam-4637	582	14	t∆2(ρ(a))(φ(y	t∆2(ρ(a))(φ(y	NOUN
ejpam-4637	582	15	)	)	PUNCT
ejpam-4637	582	16	)	)	PUNCT
ejpam-4637	582	17	}	}	PUNCT
ejpam-4637	582	18	=	=	SYM
ejpam-4637	582	19	min{tφ−1(∆2)(a)(x	min{tφ−1(∆2)(a)(x	NOUN
ejpam-4637	582	20	)	)	PUNCT
ejpam-4637	582	21	,	,	PUNCT
ejpam-4637	582	22	tφ−1(∆2)(a)(y	tφ−1(∆2)(a)(y	NOUN
ejpam-4637	582	23	)	)	PUNCT
ejpam-4637	582	24	}	}	PUNCT
ejpam-4637	582	25	,	,	PUNCT
ejpam-4637	582	26	∗iφ−1(∆2)(a)(x	∗iφ−1(∆2)(a)(x	PROPN
ejpam-4637	582	27	◦	◦	NOUN
ejpam-4637	582	28	1	1	NUM
ejpam-4637	582	29	y	y	NOUN
ejpam-4637	582	30	)	)	PUNCT
ejpam-4637	583	1	=	=	PUNCT
ejpam-4637	583	2	∗i∆2(ρ(a))(φ(x	∗i∆2(ρ(a))(φ(x	VERB
ejpam-4637	583	3	◦	◦	NOUN
ejpam-4637	583	4	1	1	NUM
ejpam-4637	583	5	y	y	NOUN
ejpam-4637	583	6	)	)	PUNCT
ejpam-4637	583	7	)	)	PUNCT
ejpam-4637	584	1	=	=	PUNCT
ejpam-4637	584	2	∗i∆2(ρ(a))(φ(x	∗i∆2(ρ(a))(φ(x	NOUN
ejpam-4637	584	3	)	)	PUNCT
ejpam-4637	584	4	◦	◦	NOUN
ejpam-4637	584	5	2	2	NUM
ejpam-4637	584	6	φ(y	φ(y	NOUN
ejpam-4637	584	7	)	)	PUNCT
ejpam-4637	584	8	)	)	PUNCT
ejpam-4637	584	9	≤	≤	NUM
ejpam-4637	584	10	max{i∆2(ρ(a))(φ(x	max{i∆2(ρ(a))(φ(x	NUM
ejpam-4637	584	11	)	)	PUNCT
ejpam-4637	584	12	)	)	PUNCT
ejpam-4637	584	13	,	,	PUNCT
ejpam-4637	584	14	i∆2(ρ(a))(φ(y	i∆2(ρ(a))(φ(y	PROPN
ejpam-4637	584	15	)	)	PUNCT
ejpam-4637	584	16	)	)	PUNCT
ejpam-4637	584	17	}	}	PUNCT
ejpam-4637	585	1	=	=	SYM
ejpam-4637	585	2	max{iφ−1(∆2)(a)(x	max{iφ−1(∆2)(a)(x	NOUN
ejpam-4637	585	3	)	)	PUNCT
ejpam-4637	585	4	,	,	PUNCT
ejpam-4637	585	5	iφ−1(∆2)(a)(y	iφ−1(∆2)(a)(y	PROPN
ejpam-4637	585	6	)	)	PUNCT
ejpam-4637	585	7	}	}	PUNCT
ejpam-4637	585	8	,	,	PUNCT
ejpam-4637	585	9	and	and	CCONJ
ejpam-4637	585	10	similarly	similarly	ADV
ejpam-4637	585	11	,	,	PUNCT
ejpam-4637	585	12	∗fφ−1(∆2)(a)(x	∗fφ−1(∆2)(a)(x	PROPN
ejpam-4637	585	13	◦	◦	NOUN
ejpam-4637	585	14	1	1	NUM
ejpam-4637	585	15	y	y	NOUN
ejpam-4637	585	16	)	)	PUNCT
ejpam-4637	585	17	=	=	SYM
ejpam-4637	585	18	max{fφ−1(∆2)(a)(x),fφ−1(∆2)(a)(y	max{fφ−1(∆2)(a)(x),fφ−1(∆2)(a)(y	PROPN
ejpam-4637	585	19	)	)	PUNCT
ejpam-4637	585	20	}	}	PUNCT
ejpam-4637	585	21	.	.	PUNCT
ejpam-4637	586	1	thus	thus	ADV
ejpam-4637	586	2	,	,	PUNCT
ejpam-4637	586	3	(	(	PUNCT
ejpam-4637	586	4	φ	φ	NOUN
ejpam-4637	586	5	,	,	PUNCT
ejpam-4637	586	6	ρ)−1(∆2	ρ)−1(∆2	ADJ
ejpam-4637	586	7	,	,	PUNCT
ejpam-4637	586	8	s2	s2	PROPN
ejpam-4637	586	9	)	)	PUNCT
ejpam-4637	586	10	is	be	AUX
ejpam-4637	586	11	a	a	DET
ejpam-4637	586	12	svns	svns	NOUN
ejpam-4637	586	13	hyper	hyper	ADJ
ejpam-4637	586	14	up	up	ADP
ejpam-4637	586	15	-subalgebra	-subalgebra	NOUN
ejpam-4637	586	16	of	of	ADP
ejpam-4637	586	17	x1	x1	PROPN
ejpam-4637	586	18	.	.	PROPN
ejpam-4637	587	1	4	4	X
ejpam-4637	587	2	.	.	X
ejpam-4637	587	3	conclusions	conclusion	NOUN
ejpam-4637	587	4	in	in	ADP
ejpam-4637	587	5	this	this	DET
ejpam-4637	587	6	paper	paper	NOUN
ejpam-4637	587	7	,	,	PUNCT
ejpam-4637	587	8	we	we	PRON
ejpam-4637	587	9	have	have	AUX
ejpam-4637	587	10	introduced	introduce	VERB
ejpam-4637	587	11	the	the	DET
ejpam-4637	587	12	svn	svn	NOUN
ejpam-4637	587	13	and	and	CCONJ
ejpam-4637	587	14	svns	svns	NOUN
ejpam-4637	587	15	hyper	hyper	ADJ
ejpam-4637	587	16	up	up	ADP
ejpam-4637	587	17	-subalgebra	-subalgebra	NOUN
ejpam-4637	587	18	together	together	ADV
ejpam-4637	587	19	with	with	ADP
ejpam-4637	587	20	their	their	PRON
ejpam-4637	587	21	properties	property	NOUN
ejpam-4637	587	22	.	.	PUNCT
ejpam-4637	588	1	aside	aside	ADV
ejpam-4637	588	2	from	from	ADP
ejpam-4637	588	3	that	that	PRON
ejpam-4637	588	4	,	,	PUNCT
ejpam-4637	588	5	the	the	DET
ejpam-4637	588	6	concept	concept	NOUN
ejpam-4637	588	7	of	of	ADP
ejpam-4637	588	8	cartesian	cartesian	ADJ
ejpam-4637	588	9	product	product	NOUN
ejpam-4637	588	10	of	of	ADP
ejpam-4637	588	11	svns	svn	NOUN
ejpam-4637	588	12	hyper	hyper	ADJ
ejpam-4637	588	13	up	up	ADP
ejpam-4637	588	14	-subalgebra	-subalgebra	PROPN
ejpam-4637	588	15	and	and	CCONJ
ejpam-4637	588	16	the	the	DET
ejpam-4637	588	17	homomorphic	homomorphic	ADJ
ejpam-4637	588	18	image	image	NOUN
ejpam-4637	588	19	and	and	CCONJ
ejpam-4637	588	20	preimage	preimage	NOUN
ejpam-4637	588	21	of	of	ADP
ejpam-4637	588	22	svns	svns	PROPN
ejpam-4637	588	23	hyper	hyper	ADJ
ejpam-4637	588	24	up	up	NOUN
ejpam-4637	588	25	-subalgebra	-subalgebra	NOUN
ejpam-4637	588	26	have	have	AUX
ejpam-4637	588	27	been	be	AUX
ejpam-4637	588	28	investigated	investigate	VERB
ejpam-4637	588	29	.	.	PUNCT
ejpam-4637	589	1	this	this	DET
ejpam-4637	589	2	study	study	NOUN
ejpam-4637	589	3	contributes	contribute	VERB
ejpam-4637	589	4	to	to	ADP
ejpam-4637	589	5	the	the	DET
ejpam-4637	589	6	development	development	NOUN
ejpam-4637	589	7	of	of	ADP
ejpam-4637	589	8	the	the	DET
ejpam-4637	589	9	notion	notion	NOUN
ejpam-4637	589	10	of	of	ADP
ejpam-4637	589	11	hyper	hyper	ADJ
ejpam-4637	589	12	up	up	ADP
ejpam-4637	589	13	-algebra	-algebra	NOUN
ejpam-4637	589	14	under	under	ADP
ejpam-4637	589	15	neutrosophic	neutrosophic	ADJ
ejpam-4637	589	16	soft	soft	ADJ
ejpam-4637	589	17	environment	environment	NOUN
ejpam-4637	589	18	.	.	PUNCT
ejpam-4637	590	1	it	it	PRON
ejpam-4637	590	2	also	also	ADV
ejpam-4637	590	3	opens	open	VERB
ejpam-4637	590	4	a	a	DET
ejpam-4637	590	5	door	door	NOUN
ejpam-4637	590	6	for	for	ADP
ejpam-4637	590	7	further	further	ADJ
ejpam-4637	590	8	study	study	NOUN
ejpam-4637	590	9	by	by	ADP
ejpam-4637	590	10	establishing	establish	VERB
ejpam-4637	590	11	svns	svn	NOUN
ejpam-4637	590	12	hyper	hyper	ADJ
ejpam-4637	590	13	up	up	ADV
ejpam-4637	590	14	-filter	-filter	PROPN
ejpam-4637	590	15	,	,	PUNCT
ejpam-4637	590	16	svns	svn	VERB
ejpam-4637	590	17	hyper	hyper	VERB
ejpam-4637	590	18	up	up	ADP
ejpam-4637	590	19	-ideals	-ideal	NOUN
ejpam-4637	590	20	and	and	CCONJ
ejpam-4637	590	21	some	some	PRON
ejpam-4637	590	22	of	of	ADP
ejpam-4637	590	23	their	their	PRON
ejpam-4637	590	24	variations	variation	NOUN
ejpam-4637	590	25	.	.	PUNCT
ejpam-4637	591	1	references	reference	NOUN
ejpam-4637	591	2	575	575	NUM
ejpam-4637	591	3	acknowledgements	acknowledgement	NOUN
ejpam-4637	591	4	the	the	DET
ejpam-4637	591	5	authors	author	NOUN
ejpam-4637	591	6	would	would	AUX
ejpam-4637	591	7	like	like	VERB
ejpam-4637	591	8	to	to	PART
ejpam-4637	591	9	thank	thank	VERB
ejpam-4637	591	10	the	the	DET
ejpam-4637	591	11	philippines	philippines	PROPN
ejpam-4637	591	12	department	department	PROPN
ejpam-4637	591	13	of	of	ADP
ejpam-4637	591	14	science	science	NOUN
ejpam-4637	591	15	and	and	CCONJ
ejpam-4637	591	16	technologyaccelerated	technologyaccelerated	ADJ
ejpam-4637	591	17	science	science	NOUN
ejpam-4637	591	18	and	and	CCONJ
ejpam-4637	591	19	technology	technology	NOUN
ejpam-4637	591	20	human	human	ADJ
ejpam-4637	591	21	resource	resource	NOUN
ejpam-4637	591	22	development	development	NOUN
ejpam-4637	591	23	program	program	NOUN
ejpam-4637	591	24	(	(	PUNCT
ejpam-4637	591	25	dostasthrdp	dostasthrdp	PROPN
ejpam-4637	591	26	)	)	PUNCT
ejpam-4637	591	27	and	and	CCONJ
ejpam-4637	591	28	mindanao	mindanao	PROPN
ejpam-4637	591	29	state	state	PROPN
ejpam-4637	591	30	university	university	PROPN
ejpam-4637	591	31	iligan	iligan	PROPN
ejpam-4637	591	32	institute	institute	PROPN
ejpam-4637	591	33	of	of	ADP
ejpam-4637	591	34	technology	technology	NOUN
ejpam-4637	591	35	for	for	ADP
ejpam-4637	591	36	the	the	DET
ejpam-4637	591	37	research	research	NOUN
ejpam-4637	591	38	funds	fund	NOUN
ejpam-4637	591	39	and	and	CCONJ
ejpam-4637	591	40	all	all	DET
ejpam-4637	591	41	the	the	DET
ejpam-4637	591	42	reviewers	reviewer	NOUN
ejpam-4637	591	43	for	for	ADP
ejpam-4637	591	44	their	their	PRON
ejpam-4637	591	45	comments	comment	NOUN
ejpam-4637	591	46	and	and	CCONJ
ejpam-4637	591	47	suggestions	suggestion	NOUN
ejpam-4637	591	48	to	to	PART
ejpam-4637	591	49	improve	improve	VERB
ejpam-4637	591	50	this	this	DET
ejpam-4637	591	51	paper	paper	NOUN
ejpam-4637	591	52	.	.	PUNCT
ejpam-4637	592	1	references	reference	NOUN
ejpam-4637	592	2	[	[	X
ejpam-4637	592	3	1	1	NUM
ejpam-4637	592	4	]	]	PUNCT
ejpam-4637	592	5	m.	m.	NOUN
ejpam-4637	592	6	abu	abu	PROPN
ejpam-4637	592	7	qamar	qamar	PROPN
ejpam-4637	592	8	a.	a.	NOUN
ejpam-4637	592	9	ghafur	ghafur	PROPN
ejpam-4637	592	10	ahmad	ahmad	NOUN
ejpam-4637	592	11	and	and	CCONJ
ejpam-4637	592	12	n.	n.	PROPN
ejpam-4637	592	13	hassan	hassan	PROPN
ejpam-4637	592	14	.	.	PUNCT
ejpam-4637	593	1	on	on	ADP
ejpam-4637	593	2	q	q	ADJ
ejpam-4637	593	3	-	-	ADJ
ejpam-4637	593	4	neutrosophic	neutrosophic	ADJ
ejpam-4637	593	5	soft	soft	ADJ
ejpam-4637	593	6	fields	field	NOUN
ejpam-4637	593	7	.	.	PUNCT
ejpam-4637	594	1	neutrosophic	neutrosophic	ADJ
ejpam-4637	594	2	sets	set	NOUN
ejpam-4637	594	3	and	and	CCONJ
ejpam-4637	594	4	systems	system	NOUN
ejpam-4637	594	5	,	,	PUNCT
ejpam-4637	594	6	32:80–93	32:80–93	NUM
ejpam-4637	594	7	,	,	PUNCT
ejpam-4637	594	8	2020	2020	NUM
ejpam-4637	594	9	.	.	PUNCT
ejpam-4637	595	1	[	[	X
ejpam-4637	595	2	2	2	NUM
ejpam-4637	595	3	]	]	X
ejpam-4637	595	4	r.m	r.m	PROPN
ejpam-4637	595	5	.	.	PROPN
ejpam-4637	595	6	amairanto	amairanto	PROPN
ejpam-4637	595	7	and	and	CCONJ
ejpam-4637	595	8	r.t	r.t	PROPN
ejpam-4637	595	9	.	.	PROPN
ejpam-4637	595	10	isla	isla	PROPN
ejpam-4637	595	11	.	.	PUNCT
ejpam-4637	596	1	hyper	hyper	PROPN
ejpam-4637	596	2	homomorphism	homomorphism	PROPN
ejpam-4637	596	3	and	and	CCONJ
ejpam-4637	596	4	hyper	hyper	ADJ
ejpam-4637	596	5	product	product	NOUN
ejpam-4637	596	6	of	of	ADP
ejpam-4637	596	7	hyper	hyper	ADJ
ejpam-4637	596	8	up	up	ADP
ejpam-4637	596	9	-	-	PUNCT
ejpam-4637	596	10	algebras	algebras	X
ejpam-4637	596	11	.	.	PUNCT
ejpam-4637	597	1	european	european	PROPN
ejpam-4637	597	2	journal	journal	PROPN
ejpam-4637	597	3	of	of	ADP
ejpam-4637	597	4	pure	pure	ADJ
ejpam-4637	597	5	and	and	CCONJ
ejpam-4637	597	6	applied	applied	ADJ
ejpam-4637	597	7	mathematics	mathematic	NOUN
ejpam-4637	597	8	,	,	PUNCT
ejpam-4637	597	9	13:483–497	13:483–497	NUM
ejpam-4637	597	10	,	,	PUNCT
ejpam-4637	597	11	2020	2020	NUM
ejpam-4637	597	12	.	.	PUNCT
ejpam-4637	598	1	[	[	X
ejpam-4637	598	2	3	3	X
ejpam-4637	598	3	]	]	X
ejpam-4637	598	4	k.t	k.t	PROPN
ejpam-4637	598	5	.	.	PROPN
ejpam-4637	598	6	atanassov	atanassov	PROPN
ejpam-4637	598	7	.	.	PUNCT
ejpam-4637	599	1	intuitionistic	intuitionistic	ADJ
ejpam-4637	599	2	fuzzy	fuzzy	ADJ
ejpam-4637	599	3	sets	set	NOUN
ejpam-4637	599	4	.	.	PUNCT
ejpam-4637	600	1	fuzzy	fuzzy	ADJ
ejpam-4637	600	2	sets	set	NOUN
ejpam-4637	600	3	and	and	CCONJ
ejpam-4637	600	4	systems	system	NOUN
ejpam-4637	600	5	,	,	PUNCT
ejpam-4637	600	6	20(1):87–96	20(1):87–96	NUM
ejpam-4637	600	7	,	,	PUNCT
ejpam-4637	600	8	1986	1986	NUM
ejpam-4637	600	9	.	.	PUNCT
ejpam-4637	601	1	[	[	X
ejpam-4637	601	2	4	4	X
ejpam-4637	601	3	]	]	PUNCT
ejpam-4637	601	4	t.	t.	NOUN
ejpam-4637	601	5	bera	bera	NOUN
ejpam-4637	601	6	and	and	CCONJ
ejpam-4637	601	7	n.	n.	PROPN
ejpam-4637	601	8	k.	k.	PROPN
ejpam-4637	601	9	mahapatra	mahapatra	PROPN
ejpam-4637	601	10	.	.	PUNCT
ejpam-4637	602	1	on	on	ADP
ejpam-4637	602	2	neutrosophic	neutrosophic	ADJ
ejpam-4637	602	3	soft	soft	ADJ
ejpam-4637	602	4	linear	linear	ADJ
ejpam-4637	602	5	spaces	space	NOUN
ejpam-4637	602	6	.	.	PUNCT
ejpam-4637	603	1	fuzzy	fuzzy	ADJ
ejpam-4637	603	2	information	information	NOUN
ejpam-4637	603	3	and	and	CCONJ
ejpam-4637	603	4	engineering	engineering	NOUN
ejpam-4637	603	5	,	,	PUNCT
ejpam-4637	603	6	9:299–324	9:299–324	NUM
ejpam-4637	603	7	,	,	PUNCT
ejpam-4637	603	8	2017	2017	NUM
ejpam-4637	603	9	.	.	PUNCT
ejpam-4637	604	1	[	[	X
ejpam-4637	604	2	5	5	X
ejpam-4637	604	3	]	]	PUNCT
ejpam-4637	604	4	t.	t.	NOUN
ejpam-4637	604	5	bera	bera	NOUN
ejpam-4637	604	6	and	and	CCONJ
ejpam-4637	604	7	n.	n.	PROPN
ejpam-4637	604	8	k.	k.	PROPN
ejpam-4637	604	9	mahapatra	mahapatra	PROPN
ejpam-4637	604	10	.	.	PUNCT
ejpam-4637	605	1	on	on	ADP
ejpam-4637	605	2	neutrosophic	neutrosophic	ADJ
ejpam-4637	605	3	soft	soft	ADJ
ejpam-4637	605	4	topological	topological	ADJ
ejpam-4637	605	5	space	space	NOUN
ejpam-4637	605	6	.	.	PUNCT
ejpam-4637	606	1	neutrosophic	neutrosophic	ADJ
ejpam-4637	606	2	sets	set	NOUN
ejpam-4637	606	3	and	and	CCONJ
ejpam-4637	606	4	systems	system	NOUN
ejpam-4637	606	5	,	,	PUNCT
ejpam-4637	606	6	19:1–15	19:1–15	NUM
ejpam-4637	606	7	,	,	PUNCT
ejpam-4637	606	8	2018	2018	NUM
ejpam-4637	606	9	.	.	PUNCT
ejpam-4637	607	1	[	[	X
ejpam-4637	607	2	6	6	NUM
ejpam-4637	607	3	]	]	PUNCT
ejpam-4637	607	4	i.	i.	NOUN
ejpam-4637	607	5	deli	deli	PROPN
ejpam-4637	607	6	and	and	CCONJ
ejpam-4637	607	7	s.	s.	PROPN
ejpam-4637	607	8	broumi	broumi	PROPN
ejpam-4637	607	9	.	.	PUNCT
ejpam-4637	608	1	neutrosophic	neutrosophic	ADJ
ejpam-4637	608	2	soft	soft	ADJ
ejpam-4637	608	3	sets	set	NOUN
ejpam-4637	608	4	and	and	CCONJ
ejpam-4637	608	5	neutrosophic	neutrosophic	ADJ
ejpam-4637	608	6	soft	soft	ADJ
ejpam-4637	608	7	matrices	matrix	NOUN
ejpam-4637	608	8	based	base	VERB
ejpam-4637	608	9	on	on	ADP
ejpam-4637	608	10	decision	decision	NOUN
ejpam-4637	608	11	making	making	NOUN
ejpam-4637	608	12	.	.	PUNCT
ejpam-4637	609	1	journal	journal	NOUN
ejpam-4637	609	2	of	of	ADP
ejpam-4637	609	3	intelligent	intelligent	ADJ
ejpam-4637	609	4	and	and	CCONJ
ejpam-4637	609	5	fuzzy	fuzzy	ADJ
ejpam-4637	609	6	systems	system	NOUN
ejpam-4637	609	7	,	,	PUNCT
ejpam-4637	609	8	28:2233–2241	28:2233–2241	NUM
ejpam-4637	609	9	,	,	PUNCT
ejpam-4637	609	10	2014	2014	NUM
ejpam-4637	609	11	.	.	PUNCT
ejpam-4637	610	1	[	[	X
ejpam-4637	610	2	7	7	X
ejpam-4637	610	3	]	]	PUNCT
ejpam-4637	610	4	m.	m.	NOUN
ejpam-4637	610	5	akram	akram	PROPN
ejpam-4637	610	6	h.	h.	PROPN
ejpam-4637	610	7	gulzar	gulzar	PROPN
ejpam-4637	610	8	and	and	CCONJ
ejpam-4637	610	9	k.	k.	PROPN
ejpam-4637	610	10	p.	p.	PROPN
ejpam-4637	610	11	shum	shum	PROPN
ejpam-4637	610	12	.	.	PUNCT
ejpam-4637	611	1	certain	certain	ADJ
ejpam-4637	611	2	notions	notion	NOUN
ejpam-4637	611	3	of	of	ADP
ejpam-4637	611	4	single	single	ADV
ejpam-4637	611	5	-	-	PUNCT
ejpam-4637	611	6	valued	value	VERB
ejpam-4637	611	7	neutrosophic	neutrosophic	ADJ
ejpam-4637	611	8	k	k	PROPN
ejpam-4637	611	9	-	-	PUNCT
ejpam-4637	611	10	algebras	algebras	PROPN
ejpam-4637	611	11	.	.	PUNCT
ejpam-4637	612	1	italian	italian	ADJ
ejpam-4637	612	2	journal	journal	NOUN
ejpam-4637	612	3	of	of	ADP
ejpam-4637	612	4	pure	pure	ADJ
ejpam-4637	612	5	and	and	CCONJ
ejpam-4637	612	6	applied	applied	ADJ
ejpam-4637	612	7	mathematics	mathematic	NOUN
ejpam-4637	612	8	,	,	PUNCT
ejpam-4637	612	9	pages	page	NOUN
ejpam-4637	612	10	271–289	271–289	NUM
ejpam-4637	612	11	,	,	PUNCT
ejpam-4637	612	12	2019	2019	NUM
ejpam-4637	612	13	.	.	PUNCT
ejpam-4637	613	1	[	[	X
ejpam-4637	613	2	8	8	NUM
ejpam-4637	613	3	]	]	X
ejpam-4637	613	4	m.	m.	NOUN
ejpam-4637	613	5	hamidi	hamidi	PROPN
ejpam-4637	613	6	and	and	CCONJ
ejpam-4637	613	7	f.	f.	PROPN
ejpam-4637	613	8	smarandache	smarandache	PROPN
ejpam-4637	613	9	.	.	PUNCT
ejpam-4637	614	1	single	single	ADJ
ejpam-4637	614	2	-	-	PUNCT
ejpam-4637	614	3	valued	value	VERB
ejpam-4637	614	4	neutro	neutro	PROPN
ejpam-4637	614	5	hyper	hyper	X
ejpam-4637	614	6	bck	bck	PROPN
ejpam-4637	614	7	-	-	PUNCT
ejpam-4637	614	8	subalgebras	subalgebras	PROPN
ejpam-4637	614	9	.	.	PUNCT
ejpam-4637	615	1	hindawi	hindawi	ADJ
ejpam-4637	615	2	journal	journal	PROPN
ejpam-4637	615	3	of	of	ADP
ejpam-4637	615	4	mathematics	mathematic	NOUN
ejpam-4637	615	5	,	,	PUNCT
ejpam-4637	615	6	pages	page	NOUN
ejpam-4637	615	7	1–11	1–11	PROPN
ejpam-4637	615	8	,	,	PUNCT
ejpam-4637	615	9	2021	2021	NUM
ejpam-4637	615	10	.	.	PUNCT
ejpam-4637	616	1	[	[	X
ejpam-4637	616	2	9	9	NUM
ejpam-4637	616	3	]	]	SYM
ejpam-4637	616	4	k.atanassov	k.atanassov	NOUN
ejpam-4637	616	5	and	and	CCONJ
ejpam-4637	616	6	g.gargov	g.gargov	ADJ
ejpam-4637	616	7	.	.	PUNCT
ejpam-4637	617	1	interval	interval	NOUN
ejpam-4637	617	2	valued	value	VERB
ejpam-4637	617	3	intuitionistic	intuitionistic	ADJ
ejpam-4637	617	4	fuzzy	fuzzy	ADJ
ejpam-4637	617	5	sets	set	NOUN
ejpam-4637	617	6	.	.	PUNCT
ejpam-4637	618	1	fuzzy	fuzzy	ADJ
ejpam-4637	618	2	sets	set	NOUN
ejpam-4637	618	3	and	and	CCONJ
ejpam-4637	618	4	systems	system	NOUN
ejpam-4637	618	5	,	,	PUNCT
ejpam-4637	618	6	31(3):343–349	31(3):343–349	NUM
ejpam-4637	618	7	,	,	PUNCT
ejpam-4637	618	8	1989	1989	NUM
ejpam-4637	618	9	.	.	PUNCT
ejpam-4637	619	1	[	[	X
ejpam-4637	619	2	10	10	NUM
ejpam-4637	619	3	]	]	X
ejpam-4637	619	4	l.zadeh	l.zadeh	NOUN
ejpam-4637	619	5	.	.	PUNCT
ejpam-4637	619	6	fuzzy	fuzzy	ADJ
ejpam-4637	619	7	sets	set	NOUN
ejpam-4637	619	8	.	.	PUNCT
ejpam-4637	620	1	information	information	NOUN
ejpam-4637	620	2	and	and	CCONJ
ejpam-4637	620	3	control	control	NOUN
ejpam-4637	620	4	,	,	PUNCT
ejpam-4637	620	5	8(3):338–353	8(3):338–353	NUM
ejpam-4637	620	6	,	,	PUNCT
ejpam-4637	620	7	1965	1965	NUM
ejpam-4637	620	8	.	.	PUNCT
ejpam-4637	621	1	[	[	X
ejpam-4637	621	2	11	11	NUM
ejpam-4637	621	3	]	]	X
ejpam-4637	621	4	f.	f.	PROPN
ejpam-4637	621	5	smarandache	smarandache	PROPN
ejpam-4637	621	6	m.	m.	PROPN
ejpam-4637	621	7	akram	akram	PROPN
ejpam-4637	621	8	,	,	PUNCT
ejpam-4637	621	9	h.	h.	PROPN
ejpam-4637	621	10	gulzar	gulzar	PROPN
ejpam-4637	621	11	.	.	PUNCT
ejpam-4637	622	1	neutrosophic	neutrosophic	ADJ
ejpam-4637	622	2	soft	soft	ADJ
ejpam-4637	622	3	topological	topological	ADJ
ejpam-4637	622	4	k	k	PROPN
ejpam-4637	622	5	-	-	PUNCT
ejpam-4637	622	6	algebras	algebras	PROPN
ejpam-4637	622	7	.	.	PUNCT
ejpam-4637	622	8	neutrosophic	neutrosophic	ADJ
ejpam-4637	622	9	sets	set	NOUN
ejpam-4637	622	10	and	and	CCONJ
ejpam-4637	622	11	systems	system	NOUN
ejpam-4637	622	12	,	,	PUNCT
ejpam-4637	622	13	25:104–124	25:104–124	NUM
ejpam-4637	622	14	,	,	PUNCT
ejpam-4637	622	15	2019	2019	NUM
ejpam-4637	622	16	.	.	PUNCT
ejpam-4637	623	1	[	[	X
ejpam-4637	623	2	12	12	NUM
ejpam-4637	623	3	]	]	X
ejpam-4637	623	4	p.k	p.k	PROPN
ejpam-4637	623	5	.	.	PROPN
ejpam-4637	623	6	maji	maji	PROPN
ejpam-4637	623	7	.	.	PUNCT
ejpam-4637	624	1	neutrosophic	neutrosophic	ADJ
ejpam-4637	624	2	soft	soft	ADJ
ejpam-4637	624	3	set	set	NOUN
ejpam-4637	624	4	.	.	PUNCT
ejpam-4637	625	1	annals	annal	NOUN
ejpam-4637	625	2	of	of	ADP
ejpam-4637	625	3	fuzzy	fuzzy	ADJ
ejpam-4637	625	4	mathematics	mathematic	NOUN
ejpam-4637	625	5	and	and	CCONJ
ejpam-4637	625	6	informatics	informatic	NOUN
ejpam-4637	625	7	,	,	PUNCT
ejpam-4637	625	8	5(1):157–168	5(1):157–168	NOUN
ejpam-4637	625	9	,	,	PUNCT
ejpam-4637	625	10	2013	2013	NUM
ejpam-4637	625	11	.	.	PUNCT
ejpam-4637	626	1	[	[	X
ejpam-4637	626	2	13	13	NUM
ejpam-4637	626	3	]	]	X
ejpam-4637	626	4	f.	f.	PROPN
ejpam-4637	626	5	marty	marty	PROPN
ejpam-4637	626	6	.	.	PUNCT
ejpam-4637	627	1	sur	sur	PROPN
ejpam-4637	627	2	une	une	PROPN
ejpam-4637	627	3	generalisation	generalisation	PROPN
ejpam-4637	627	4	de	de	X
ejpam-4637	627	5	la	la	PROPN
ejpam-4637	627	6	notion	notion	PROPN
ejpam-4637	627	7	de	de	X
ejpam-4637	627	8	groupe	groupe	PROPN
ejpam-4637	627	9	.	.	PUNCT
ejpam-4637	628	1	in	in	ADP
ejpam-4637	628	2	8th	8th	ADJ
ejpam-4637	628	3	congress	congress	PROPN
ejpam-4637	628	4	des	des	PROPN
ejpam-4637	628	5	mathematician	mathematician	PROPN
ejpam-4637	628	6	scandinaves	scandinaves	PROPN
ejpam-4637	628	7	,	,	PUNCT
ejpam-4637	628	8	pages	page	NOUN
ejpam-4637	628	9	45–49	45–49	PROPN
ejpam-4637	628	10	,	,	PUNCT
ejpam-4637	628	11	stockholm	stockholm	PROPN
ejpam-4637	628	12	1934	1934	NUM
ejpam-4637	628	13	.	.	PUNCT
ejpam-4637	629	1	references	reference	NOUN
ejpam-4637	629	2	576	576	NUM
ejpam-4637	629	3	[	[	X
ejpam-4637	629	4	14	14	NUM
ejpam-4637	629	5	]	]	X
ejpam-4637	629	6	d.	d.	PROPN
ejpam-4637	629	7	molodtsov	molodtsov	PROPN
ejpam-4637	629	8	.	.	PUNCT
ejpam-4637	630	1	soft	soft	ADJ
ejpam-4637	630	2	set	set	ADJ
ejpam-4637	630	3	theory	theory	NOUN
ejpam-4637	630	4	first	first	ADJ
ejpam-4637	630	5	result	result	NOUN
ejpam-4637	630	6	.	.	PUNCT
ejpam-4637	631	1	computers	computer	NOUN
ejpam-4637	631	2	and	and	CCONJ
ejpam-4637	631	3	mathematics	mathematic	NOUN
ejpam-4637	631	4	with	with	ADP
ejpam-4637	631	5	applications	application	NOUN
ejpam-4637	631	6	,	,	PUNCT
ejpam-4637	631	7	37:19–31	37:19–31	NUM
ejpam-4637	631	8	,	,	PUNCT
ejpam-4637	631	9	1999	1999	NUM
ejpam-4637	631	10	.	.	PUNCT
ejpam-4637	632	1	[	[	X
ejpam-4637	632	2	15	15	NUM
ejpam-4637	632	3	]	]	X
ejpam-4637	632	4	d.a	d.a	PROPN
ejpam-4637	632	5	.	.	PROPN
ejpam-4637	632	6	romano	romano	NOUN
ejpam-4637	632	7	.	.	PUNCT
ejpam-4637	633	1	hyper	hyper	PROPN
ejpam-4637	633	2	up	up	ADP
ejpam-4637	633	3	-	-	PUNCT
ejpam-4637	633	4	algebras	algebras	PROPN
ejpam-4637	633	5	.	.	PUNCT
ejpam-4637	634	1	journal	journal	PROPN
ejpam-4637	634	2	of	of	ADP
ejpam-4637	634	3	hyperstructures	hyperstructure	NOUN
ejpam-4637	634	4	,	,	PUNCT
ejpam-4637	634	5	8(2):112–122	8(2):112–122	NUM
ejpam-4637	634	6	,	,	PUNCT
ejpam-4637	634	7	2019	2019	NUM
ejpam-4637	634	8	.	.	PUNCT
ejpam-4637	635	1	[	[	X
ejpam-4637	635	2	16	16	NUM
ejpam-4637	635	3	]	]	X
ejpam-4637	635	4	d.	d.	PROPN
ejpam-4637	635	5	preethi	preethi	PROPN
ejpam-4637	635	6	s.	s.	PROPN
ejpam-4637	635	7	rajareega	rajareega	PROPN
ejpam-4637	635	8	j.	j.	PROPN
ejpam-4637	635	9	vimala	vimala	PROPN
ejpam-4637	635	10	g.	g.	PROPN
ejpam-4637	635	11	selvachandran	selvachandran	PROPN
ejpam-4637	635	12	and	and	CCONJ
ejpam-4637	635	13	f.	f.	PROPN
ejpam-4637	635	14	smarandache	smarandache	PROPN
ejpam-4637	635	15	.	.	PUNCT
ejpam-4637	636	1	singlevalued	singlevalue	VERB
ejpam-4637	636	2	neutrosophic	neutrosophic	ADJ
ejpam-4637	636	3	hyperrings	hyperring	NOUN
ejpam-4637	636	4	and	and	CCONJ
ejpam-4637	636	5	single	single	ADV
ejpam-4637	636	6	-	-	PUNCT
ejpam-4637	636	7	valued	value	VERB
ejpam-4637	636	8	neutrosophic	neutrosophic	ADJ
ejpam-4637	636	9	hyperideals	hyperideal	NOUN
ejpam-4637	636	10	.	.	PUNCT
ejpam-4637	637	1	neutrosophic	neutrosophic	ADJ
ejpam-4637	637	2	sets	set	NOUN
ejpam-4637	637	3	and	and	CCONJ
ejpam-4637	637	4	systems	system	NOUN
ejpam-4637	637	5	,	,	PUNCT
ejpam-4637	637	6	vol	vol	NOUN
ejpam-4637	637	7	.	.	PROPN
ejpam-4637	637	8	29	29	NUM
ejpam-4637	637	9	,	,	PUNCT
ejpam-4637	637	10	2019	2019	NUM
ejpam-4637	637	11	,	,	PUNCT
ejpam-4637	637	12	29:121–128	29:121–128	NUM
ejpam-4637	637	13	,	,	PUNCT
ejpam-4637	637	14	2019	2019	NUM
ejpam-4637	637	15	.	.	PUNCT
ejpam-4637	638	1	[	[	X
ejpam-4637	638	2	17	17	NUM
ejpam-4637	638	3	]	]	X
ejpam-4637	638	4	s.	s.	PROPN
ejpam-4637	638	5	rajareega	rajareega	PROPN
ejpam-4637	638	6	d.	d.	PROPN
ejpam-4637	638	7	preethi	preethi	PROPN
ejpam-4637	638	8	j.	j.	PROPN
ejpam-4637	638	9	vimala	vimala	PROPN
ejpam-4637	638	10	g.	g.	PROPN
ejpam-4637	638	11	selvachandran	selvachandran	PROPN
ejpam-4637	638	12	and	and	CCONJ
ejpam-4637	638	13	f.	f.	PROPN
ejpam-4637	638	14	smarandache	smarandache	PROPN
ejpam-4637	638	15	.	.	PUNCT
ejpam-4637	639	1	some	some	DET
ejpam-4637	639	2	results	result	NOUN
ejpam-4637	639	3	on	on	ADP
ejpam-4637	639	4	single	single	ADJ
ejpam-4637	639	5	valued	value	VERB
ejpam-4637	639	6	neutrosophic	neutrosophic	ADJ
ejpam-4637	639	7	hypergroup	hypergroup	NOUN
ejpam-4637	639	8	.	.	PUNCT
ejpam-4637	640	1	neutrosophic	neutrosophic	ADJ
ejpam-4637	640	2	sets	set	NOUN
ejpam-4637	640	3	and	and	CCONJ
ejpam-4637	640	4	systems	system	NOUN
ejpam-4637	640	5	,	,	PUNCT
ejpam-4637	640	6	31:80–85	31:80–85	NUM
ejpam-4637	640	7	,	,	PUNCT
ejpam-4637	640	8	2020	2020	NUM
ejpam-4637	640	9	.	.	PUNCT
ejpam-4637	641	1	[	[	X
ejpam-4637	641	2	18	18	NUM
ejpam-4637	641	3	]	]	X
ejpam-4637	641	4	f.	f.	PROPN
ejpam-4637	641	5	smarandache	smarandache	PROPN
ejpam-4637	641	6	.	.	PUNCT
ejpam-4637	642	1	neutrosophic	neutrosophic	PROPN
ejpam-4637	642	2	set	set	NOUN
ejpam-4637	642	3	is	be	AUX
ejpam-4637	642	4	a	a	DET
ejpam-4637	642	5	generalization	generalization	NOUN
ejpam-4637	642	6	of	of	ADP
ejpam-4637	642	7	intuitionistic	intuitionistic	ADJ
ejpam-4637	642	8	fuzzy	fuzzy	ADJ
ejpam-4637	642	9	set	set	NOUN
ejpam-4637	642	10	,	,	PUNCT
ejpam-4637	642	11	inconsistent	inconsistent	ADJ
ejpam-4637	642	12	intuitionistic	intuitionistic	ADJ
ejpam-4637	642	13	fuzzy	fuzzy	ADJ
ejpam-4637	642	14	set	set	NOUN
ejpam-4637	642	15	(	(	PUNCT
ejpam-4637	642	16	picture	picture	NOUN
ejpam-4637	642	17	fuzzy	fuzzy	ADJ
ejpam-4637	642	18	set	set	NOUN
ejpam-4637	642	19	,	,	PUNCT
ejpam-4637	642	20	ternary	ternary	ADJ
ejpam-4637	642	21	fuzzy	fuzzy	ADJ
ejpam-4637	642	22	set	set	NOUN
ejpam-4637	642	23	)	)	PUNCT
ejpam-4637	642	24	,	,	PUNCT
ejpam-4637	642	25	pythagorean	pythagorean	PROPN
ejpam-4637	642	26	fuzzy	fuzzy	ADJ
ejpam-4637	642	27	set	set	NOUN
ejpam-4637	642	28	(	(	PUNCT
ejpam-4637	642	29	atanassov	atanassov	PROPN
ejpam-4637	642	30	’s	’s	PART
ejpam-4637	642	31	intuitionistic	intuitionistic	ADJ
ejpam-4637	642	32	fuzzy	fuzzy	ADJ
ejpam-4637	642	33	set	set	NOUN
ejpam-4637	642	34	of	of	ADP
ejpam-4637	642	35	second	second	ADJ
ejpam-4637	642	36	type	type	NOUN
ejpam-4637	642	37	)	)	PUNCT
ejpam-4637	642	38	,	,	PUNCT
ejpam-4637	642	39	q	q	ADJ
ejpam-4637	642	40	-	-	PUNCT
ejpam-4637	642	41	rung	rung	ADJ
ejpam-4637	642	42	orthopair	orthopair	ADJ
ejpam-4637	642	43	fuzzy	fuzzy	ADJ
ejpam-4637	642	44	set	set	NOUN
ejpam-4637	642	45	,	,	PUNCT
ejpam-4637	642	46	spherical	spherical	ADJ
ejpam-4637	642	47	fuzzy	fuzzy	ADJ
ejpam-4637	642	48	set	set	NOUN
ejpam-4637	642	49	,	,	PUNCT
ejpam-4637	642	50	and	and	CCONJ
ejpam-4637	642	51	n	n	CCONJ
ejpam-4637	642	52	-	-	PUNCT
ejpam-4637	642	53	hyperspherical	hyperspherical	ADJ
ejpam-4637	642	54	fuzzy	fuzzy	ADJ
ejpam-4637	642	55	set	set	NOUN
ejpam-4637	642	56	,	,	PUNCT
ejpam-4637	642	57	while	while	SCONJ
ejpam-4637	642	58	neutrosophication	neutrosophication	NOUN
ejpam-4637	642	59	is	be	AUX
ejpam-4637	642	60	a	a	DET
ejpam-4637	642	61	generalization	generalization	NOUN
ejpam-4637	642	62	of	of	ADP
ejpam-4637	642	63	regret	regret	PROPN
ejpam-4637	642	64	theory	theory	PROPN
ejpam-4637	642	65	,	,	PUNCT
ejpam-4637	642	66	grey	grey	ADJ
ejpam-4637	642	67	system	system	NOUN
ejpam-4637	642	68	theory	theory	NOUN
ejpam-4637	642	69	,	,	PUNCT
ejpam-4637	642	70	and	and	CCONJ
ejpam-4637	642	71	three	three	NUM
ejpam-4637	642	72	-	-	PUNCT
ejpam-4637	642	73	ways	way	NOUN
ejpam-4637	642	74	decision	decision	NOUN
ejpam-4637	642	75	(	(	PUNCT
ejpam-4637	642	76	revisited	revisit	VERB
ejpam-4637	642	77	)	)	PUNCT
ejpam-4637	642	78	.	.	PUNCT
ejpam-4637	643	1	journal	journal	PROPN
ejpam-4637	643	2	of	of	ADP
ejpam-4637	643	3	new	new	ADJ
ejpam-4637	643	4	theory	theory	NOUN
ejpam-4637	643	5	,	,	PUNCT
ejpam-4637	643	6	29:01–35	29:01–35	NUM
ejpam-4637	643	7	,	,	PUNCT
ejpam-4637	643	8	2019	2019	NUM
ejpam-4637	643	9	.	.	PUNCT
ejpam-4637	644	1	[	[	X
ejpam-4637	644	2	19	19	NUM
ejpam-4637	644	3	]	]	PUNCT
ejpam-4637	644	4	m.	m.	NOUN
ejpam-4637	644	5	songsaeng	songsaeng	PROPN
ejpam-4637	644	6	and	and	CCONJ
ejpam-4637	644	7	a.	a.	NOUN
ejpam-4637	644	8	iampan	iampan	PROPN
ejpam-4637	644	9	.	.	PUNCT
ejpam-4637	645	1	neutrosophic	neutrosophic	PROPN
ejpam-4637	645	2	set	set	PROPN
ejpam-4637	645	3	theory	theory	NOUN
ejpam-4637	645	4	applied	apply	VERB
ejpam-4637	645	5	to	to	ADP
ejpam-4637	645	6	up	up	ADV
ejpam-4637	645	7	-	-	PUNCT
ejpam-4637	645	8	algebras	algebras	X
ejpam-4637	645	9	.	.	PUNCT
ejpam-4637	646	1	european	european	PROPN
ejpam-4637	646	2	journal	journal	PROPN
ejpam-4637	646	3	of	of	ADP
ejpam-4637	646	4	pure	pure	ADJ
ejpam-4637	646	5	and	and	CCONJ
ejpam-4637	646	6	applied	applied	ADJ
ejpam-4637	646	7	mathematics	mathematic	NOUN
ejpam-4637	646	8	,	,	PUNCT
ejpam-4637	646	9	12(4):1382–1409	12(4):1382–1409	NUM
ejpam-4637	646	10	,	,	PUNCT
ejpam-4637	646	11	2019	2019	NUM
ejpam-4637	646	12	.	.	PUNCT
ejpam-4637	647	1	[	[	X
ejpam-4637	647	2	20	20	NUM
ejpam-4637	647	3	]	]	PUNCT
ejpam-4637	647	4	m.	m.	NOUN
ejpam-4637	647	5	songsaeng	songsaeng	PROPN
ejpam-4637	647	6	and	and	CCONJ
ejpam-4637	647	7	a.	a.	NOUN
ejpam-4637	647	8	iampan	iampan	PROPN
ejpam-4637	647	9	.	.	PUNCT
ejpam-4637	648	1	a	a	DET
ejpam-4637	648	2	novel	novel	ADJ
ejpam-4637	648	3	approach	approach	NOUN
ejpam-4637	648	4	to	to	ADP
ejpam-4637	648	5	neutrosophic	neutrosophic	ADJ
ejpam-4637	648	6	sets	set	NOUN
ejpam-4637	648	7	in	in	ADP
ejpam-4637	648	8	up	up	ADP
ejpam-4637	648	9	-	-	PUNCT
ejpam-4637	648	10	algebras	algebras	X
ejpam-4637	648	11	.	.	PUNCT
ejpam-4637	649	1	journal	journal	PROPN
ejpam-4637	649	2	of	of	ADP
ejpam-4637	649	3	mathematics	mathematic	NOUN
ejpam-4637	649	4	and	and	CCONJ
ejpam-4637	649	5	computer	computer	NOUN
ejpam-4637	649	6	science	science	NOUN
ejpam-4637	649	7	,	,	PUNCT
ejpam-4637	649	8	21:78–98	21:78–98	NUM
ejpam-4637	649	9	,	,	PUNCT
ejpam-4637	649	10	2020	2020	NUM
ejpam-4637	649	11	.	.	PUNCT
ejpam-4637	650	1	[	[	X
ejpam-4637	650	2	21	21	NUM
ejpam-4637	650	3	]	]	X
ejpam-4637	650	4	y.	y.	PROPN
ejpam-4637	650	5	b.	b.	PROPN
ejpam-4637	650	6	jun	jun	PROPN
ejpam-4637	650	7	m.	m.	PROPN
ejpam-4637	650	8	m.	m.	PROPN
ejpam-4637	650	9	zahedi	zahedi	PROPN
ejpam-4637	650	10	x.	x.	PROPN
ejpam-4637	650	11	l.	l.	PROPN
ejpam-4637	650	12	xin	xin	PROPN
ejpam-4637	650	13	and	and	CCONJ
ejpam-4637	650	14	r.	r.	PROPN
ejpam-4637	650	15	a.	a.	PROPN
ejpam-4637	650	16	borzooei	borzooei	PROPN
ejpam-4637	650	17	.	.	PUNCT
ejpam-4637	651	1	on	on	ADP
ejpam-4637	651	2	hyper	hyper	ADJ
ejpam-4637	651	3	bck	bck	NOUN
ejpam-4637	651	4	-	-	PUNCT
ejpam-4637	651	5	algebras	algebras	PROPN
ejpam-4637	651	6	.	.	PUNCT
ejpam-4637	652	1	italian	italian	ADJ
ejpam-4637	652	2	journal	journal	NOUN
ejpam-4637	652	3	of	of	ADP
ejpam-4637	652	4	pure	pure	ADJ
ejpam-4637	652	5	and	and	CCONJ
ejpam-4637	652	6	applied	applied	ADJ
ejpam-4637	652	7	mathematics	mathematic	NOUN
ejpam-4637	652	8	,	,	PUNCT
ejpam-4637	652	9	10:127–136	10:127–136	NUM
ejpam-4637	652	10	,	,	PUNCT
ejpam-4637	652	11	2020	2020	NUM
ejpam-4637	652	12	.	.	PUNCT
ejpam-4637	653	1	[	[	X
ejpam-4637	653	2	22	22	NUM
ejpam-4637	653	3	]	]	PUNCT
ejpam-4637	653	4	h.	h.	PROPN
ejpam-4637	653	5	wang	wang	PROPN
ejpam-4637	653	6	f.	f.	PROPN
ejpam-4637	653	7	smarandache	smarandache	PROPN
ejpam-4637	653	8	y.	y.	PROPN
ejpam-4637	653	9	zhang	zhang	PROPN
ejpam-4637	653	10	and	and	CCONJ
ejpam-4637	653	11	r.	r.	PROPN
ejpam-4637	653	12	sunderraman	sunderraman	PROPN
ejpam-4637	653	13	.	.	PUNCT
ejpam-4637	654	1	single	single	ADJ
ejpam-4637	654	2	valued	value	VERB
ejpam-4637	654	3	neutrosophic	neutrosophic	ADJ
ejpam-4637	654	4	sets	set	NOUN
ejpam-4637	654	5	.	.	PUNCT
ejpam-4637	655	1	multi	multi	ADJ
ejpam-4637	655	2	-	-	ADJ
ejpam-4637	655	3	spacemultistructure	spacemultistructure	ADJ
ejpam-4637	655	4	,	,	PUNCT
ejpam-4637	655	5	4:410–413	4:410–413	NUM
ejpam-4637	655	6	,	,	PUNCT
ejpam-4637	655	7	2010	2010	NUM
ejpam-4637	655	8	.	.	PUNCT