id	sid	tid	token	lemma	pos
ejpam-5431	1	1	european	european	PROPN
ejpam-5431	1	2	journal	journal	PROPN
ejpam-5431	1	3	of	of	ADP
ejpam-5431	1	4	pure	pure	ADJ
ejpam-5431	1	5	and	and	CCONJ
ejpam-5431	1	6	applied	apply	VERB
ejpam-5431	1	7	mathematics	mathematic	NOUN
ejpam-5431	1	8	vol	vol	NOUN
ejpam-5431	1	9	.	.	PROPN
ejpam-5431	2	1	17	17	NUM
ejpam-5431	2	2	,	,	PUNCT
ejpam-5431	2	3	no	no	INTJ
ejpam-5431	2	4	.	.	NOUN
ejpam-5431	2	5	4	4	NUM
ejpam-5431	2	6	,	,	PUNCT
ejpam-5431	2	7	2024	2024	NUM
ejpam-5431	2	8	,	,	PUNCT
ejpam-5431	2	9	3304	3304	NUM
ejpam-5431	2	10	-	-	SYM
ejpam-5431	2	11	3335	3335	NUM
ejpam-5431	2	12	issn	issn	VERB
ejpam-5431	2	13	1307	1307	NUM
ejpam-5431	2	14	-	-	SYM
ejpam-5431	2	15	5543	5543	NUM
ejpam-5431	2	16	–	–	PUNCT
ejpam-5431	2	17	ejpam.com	ejpam.com	X
ejpam-5431	2	18	published	publish	VERB
ejpam-5431	2	19	by	by	ADP
ejpam-5431	2	20	new	new	PROPN
ejpam-5431	2	21	york	york	PROPN
ejpam-5431	2	22	business	business	PROPN
ejpam-5431	2	23	global	global	ADJ
ejpam-5431	2	24	intuitionistic	intuitionistic	ADJ
ejpam-5431	2	25	fuzzy	fuzzy	ADJ
ejpam-5431	2	26	z	z	NOUN
ejpam-5431	2	27	-	-	PUNCT
ejpam-5431	2	28	contractions	contraction	NOUN
ejpam-5431	2	29	and	and	CCONJ
ejpam-5431	2	30	common	common	ADJ
ejpam-5431	2	31	fixed	fix	VERB
ejpam-5431	2	32	points	point	NOUN
ejpam-5431	2	33	with	with	ADP
ejpam-5431	2	34	applications	application	NOUN
ejpam-5431	2	35	maliha	maliha	VERB
ejpam-5431	2	36	rashid1	rashid1	ADV
ejpam-5431	2	37	,	,	PUNCT
ejpam-5431	2	38	,	,	PUNCT
ejpam-5431	2	39	naeem	naeem	PROPN
ejpam-5431	2	40	saleem2,3,∗	saleem2,3,∗	NOUN
ejpam-5431	2	41	,	,	PUNCT
ejpam-5431	2	42	quratulain	quratulain	NOUN
ejpam-5431	2	43	mumtaz1	mumtaz1	NOUN
ejpam-5431	2	44	,	,	PUNCT
ejpam-5431	2	45	,	,	PUNCT
ejpam-5431	2	46	maggie	maggie	NOUN
ejpam-5431	2	47	aphane3	aphane3	PROPN
ejpam-5431	2	48	,	,	PUNCT
ejpam-5431	2	49	,	,	PUNCT
ejpam-5431	2	50	inayatur	inayatur	ADJ
ejpam-5431	2	51	rehman4	rehman4	PROPN
ejpam-5431	2	52	1	1	NUM
ejpam-5431	2	53	department	department	NOUN
ejpam-5431	2	54	of	of	ADP
ejpam-5431	2	55	mathematics	mathematic	NOUN
ejpam-5431	2	56	and	and	CCONJ
ejpam-5431	2	57	statistics	statistic	NOUN
ejpam-5431	2	58	,	,	PUNCT
ejpam-5431	2	59	international	international	ADJ
ejpam-5431	2	60	islamic	islamic	PROPN
ejpam-5431	2	61	university	university	PROPN
ejpam-5431	2	62	,	,	PUNCT
ejpam-5431	2	63	islamabad	islamabad	PROPN
ejpam-5431	2	64	,	,	PUNCT
ejpam-5431	2	65	pakistan	pakistan	PROPN
ejpam-5431	2	66	2	2	NUM
ejpam-5431	2	67	department	department	NOUN
ejpam-5431	2	68	of	of	ADP
ejpam-5431	2	69	mathematics	mathematic	NOUN
ejpam-5431	2	70	,	,	PUNCT
ejpam-5431	2	71	university	university	NOUN
ejpam-5431	2	72	of	of	ADP
ejpam-5431	2	73	management	management	NOUN
ejpam-5431	2	74	and	and	CCONJ
ejpam-5431	2	75	technology	technology	NOUN
ejpam-5431	2	76	,	,	PUNCT
ejpam-5431	2	77	lahore	lahore	NOUN
ejpam-5431	2	78	54770	54770	NUM
ejpam-5431	2	79	,	,	PUNCT
ejpam-5431	2	80	pakistan	pakistan	PROPN
ejpam-5431	2	81	3	3	NUM
ejpam-5431	2	82	department	department	NOUN
ejpam-5431	2	83	of	of	ADP
ejpam-5431	2	84	mathematics	mathematic	NOUN
ejpam-5431	2	85	and	and	CCONJ
ejpam-5431	2	86	applied	apply	VERB
ejpam-5431	2	87	mathematics	mathematic	NOUN
ejpam-5431	2	88	,	,	PUNCT
ejpam-5431	2	89	sefako	sefako	VERB
ejpam-5431	2	90	makgatho	makgatho	PROPN
ejpam-5431	2	91	health	health	PROPN
ejpam-5431	2	92	sciences	sciences	PROPN
ejpam-5431	2	93	university	university	PROPN
ejpam-5431	2	94	,	,	PUNCT
ejpam-5431	2	95	ga	ga	PROPN
ejpam-5431	2	96	-	-	NOUN
ejpam-5431	2	97	rankuwa	rankuwa	ADJ
ejpam-5431	2	98	,	,	PUNCT
ejpam-5431	2	99	medunsa	medunsa	ADJ
ejpam-5431	2	100	,	,	PUNCT
ejpam-5431	2	101	pretoria	pretoria	PROPN
ejpam-5431	2	102	0204	0204	NUM
ejpam-5431	2	103	,	,	PUNCT
ejpam-5431	2	104	south	south	PROPN
ejpam-5431	2	105	africa	africa	PROPN
ejpam-5431	2	106	4	4	NUM
ejpam-5431	2	107	department	department	NOUN
ejpam-5431	2	108	of	of	ADP
ejpam-5431	2	109	mathematics	mathematic	NOUN
ejpam-5431	2	110	and	and	CCONJ
ejpam-5431	2	111	sciences	science	NOUN
ejpam-5431	2	112	,	,	PUNCT
ejpam-5431	2	113	college	college	NOUN
ejpam-5431	2	114	of	of	ADP
ejpam-5431	2	115	arts	art	NOUN
ejpam-5431	2	116	and	and	CCONJ
ejpam-5431	2	117	applied	apply	VERB
ejpam-5431	2	118	sciences	sciences	PROPN
ejpam-5431	2	119	dhofar	dhofar	PROPN
ejpam-5431	2	120	university	university	PROPN
ejpam-5431	2	121	,	,	PUNCT
ejpam-5431	2	122	salalah	salalah	PROPN
ejpam-5431	2	123	,	,	PUNCT
ejpam-5431	2	124	oman	oman	PROPN
ejpam-5431	2	125	abstract	abstract	NOUN
ejpam-5431	2	126	.	.	PUNCT
ejpam-5431	3	1	in	in	ADP
ejpam-5431	3	2	the	the	DET
ejpam-5431	3	3	context	context	NOUN
ejpam-5431	3	4	of	of	ADP
ejpam-5431	3	5	b	b	NOUN
ejpam-5431	3	6	-	-	PUNCT
ejpam-5431	3	7	metric	metric	ADJ
ejpam-5431	3	8	spaces	space	NOUN
ejpam-5431	3	9	,	,	PUNCT
ejpam-5431	3	10	this	this	DET
ejpam-5431	3	11	paper	paper	NOUN
ejpam-5431	3	12	introduces	introduce	VERB
ejpam-5431	3	13	two	two	NUM
ejpam-5431	3	14	concepts	concept	NOUN
ejpam-5431	3	15	:	:	PUNCT
ejpam-5431	3	16	admissible	admissible	ADJ
ejpam-5431	3	17	hybrid	hybrid	ADJ
ejpam-5431	3	18	intuitionistic	intuitionistic	ADJ
ejpam-5431	3	19	fuzzy	fuzzy	ADJ
ejpam-5431	3	20	z	z	NOUN
ejpam-5431	3	21	-	-	PUNCT
ejpam-5431	3	22	contractions	contraction	NOUN
ejpam-5431	3	23	and	and	CCONJ
ejpam-5431	3	24	pairwise	pairwise	NOUN
ejpam-5431	3	25	admissible	admissible	ADJ
ejpam-5431	3	26	hybrid	hybrid	ADJ
ejpam-5431	3	27	intuitionistic	intuitionistic	ADJ
ejpam-5431	3	28	fuzzy	fuzzy	ADJ
ejpam-5431	3	29	zcontractions	zcontraction	NOUN
ejpam-5431	3	30	,	,	PUNCT
ejpam-5431	3	31	and	and	CCONJ
ejpam-5431	3	32	establishes	establish	VERB
ejpam-5431	3	33	criteria	criterion	NOUN
ejpam-5431	3	34	for	for	ADP
ejpam-5431	3	35	intuitionistic	intuitionistic	ADJ
ejpam-5431	3	36	fuzzy	fuzzy	ADJ
ejpam-5431	3	37	fixed	fix	VERB
ejpam-5431	3	38	points	point	NOUN
ejpam-5431	3	39	under	under	ADP
ejpam-5431	3	40	such	such	ADJ
ejpam-5431	3	41	contractions	contraction	NOUN
ejpam-5431	3	42	.	.	PUNCT
ejpam-5431	4	1	it	it	PRON
ejpam-5431	4	2	is	be	AUX
ejpam-5431	4	3	demonstrated	demonstrate	VERB
ejpam-5431	4	4	that	that	SCONJ
ejpam-5431	4	5	a	a	DET
ejpam-5431	4	6	pair	pair	NOUN
ejpam-5431	4	7	of	of	ADP
ejpam-5431	4	8	set	set	NOUN
ejpam-5431	4	9	-	-	PUNCT
ejpam-5431	4	10	valued	value	VERB
ejpam-5431	4	11	maps	map	NOUN
ejpam-5431	4	12	possesses	possess	VERB
ejpam-5431	4	13	a	a	DET
ejpam-5431	4	14	common	common	ADJ
ejpam-5431	4	15	fixed	fix	VERB
ejpam-5431	4	16	point	point	NOUN
ejpam-5431	4	17	.	.	PUNCT
ejpam-5431	5	1	various	various	ADJ
ejpam-5431	5	2	illustrative	illustrative	ADJ
ejpam-5431	5	3	examples	example	NOUN
ejpam-5431	5	4	are	be	AUX
ejpam-5431	5	5	provided	provide	VERB
ejpam-5431	5	6	to	to	PART
ejpam-5431	5	7	validate	validate	VERB
ejpam-5431	5	8	these	these	DET
ejpam-5431	5	9	results	result	NOUN
ejpam-5431	5	10	.	.	PUNCT
ejpam-5431	6	1	moreover	moreover	ADV
ejpam-5431	6	2	,	,	PUNCT
ejpam-5431	6	3	the	the	DET
ejpam-5431	6	4	significant	significant	ADJ
ejpam-5431	6	5	implications	implication	NOUN
ejpam-5431	6	6	of	of	ADP
ejpam-5431	6	7	our	our	PRON
ejpam-5431	6	8	main	main	ADJ
ejpam-5431	6	9	theorem	theorem	NOUN
ejpam-5431	6	10	are	be	AUX
ejpam-5431	6	11	explored	explore	VERB
ejpam-5431	6	12	and	and	CCONJ
ejpam-5431	6	13	analyzed	analyze	VERB
ejpam-5431	6	14	across	across	ADP
ejpam-5431	6	15	different	different	ADJ
ejpam-5431	6	16	types	type	NOUN
ejpam-5431	6	17	of	of	ADP
ejpam-5431	6	18	simulation	simulation	NOUN
ejpam-5431	6	19	functions	function	NOUN
ejpam-5431	6	20	.	.	PUNCT
ejpam-5431	7	1	furthermore	furthermore	ADV
ejpam-5431	7	2	,	,	PUNCT
ejpam-5431	7	3	we	we	PRON
ejpam-5431	7	4	derive	derive	VERB
ejpam-5431	7	5	several	several	ADJ
ejpam-5431	7	6	fixed	fix	VERB
ejpam-5431	7	7	point	point	NOUN
ejpam-5431	7	8	results	result	NOUN
ejpam-5431	7	9	in	in	ADP
ejpam-5431	7	10	the	the	DET
ejpam-5431	7	11	context	context	NOUN
ejpam-5431	7	12	of	of	ADP
ejpam-5431	7	13	partially	partially	ADV
ejpam-5431	7	14	ordered	order	VERB
ejpam-5431	7	15	b	b	ADJ
ejpam-5431	7	16	-	-	ADJ
ejpam-5431	7	17	metric	metric	ADJ
ejpam-5431	7	18	spaces	space	NOUN
ejpam-5431	7	19	,	,	PUNCT
ejpam-5431	7	20	offering	offer	VERB
ejpam-5431	7	21	insights	insight	NOUN
ejpam-5431	7	22	from	from	ADP
ejpam-5431	7	23	an	an	DET
ejpam-5431	7	24	application	application	NOUN
ejpam-5431	7	25	-	-	PUNCT
ejpam-5431	7	26	oriented	orient	VERB
ejpam-5431	7	27	perspective	perspective	NOUN
ejpam-5431	7	28	.	.	PUNCT
ejpam-5431	8	1	these	these	DET
ejpam-5431	8	2	outcomes	outcome	NOUN
ejpam-5431	8	3	extend	extend	VERB
ejpam-5431	8	4	and	and	CCONJ
ejpam-5431	8	5	generalize	generalize	VERB
ejpam-5431	8	6	several	several	ADJ
ejpam-5431	8	7	prior	prior	ADJ
ejpam-5431	8	8	results	result	NOUN
ejpam-5431	8	9	documented	document	VERB
ejpam-5431	8	10	in	in	ADP
ejpam-5431	8	11	the	the	DET
ejpam-5431	8	12	literature	literature	NOUN
ejpam-5431	8	13	.	.	PUNCT
ejpam-5431	9	1	2020	2020	NUM
ejpam-5431	9	2	mathematics	mathematic	NOUN
ejpam-5431	9	3	subject	subject	NOUN
ejpam-5431	9	4	classifications	classification	NOUN
ejpam-5431	9	5	:	:	PUNCT
ejpam-5431	9	6	54h25	54h25	NUM
ejpam-5431	9	7	,	,	PUNCT
ejpam-5431	9	8	47h10	47h10	NUM
ejpam-5431	9	9	,	,	PUNCT
ejpam-5431	9	10	03e72	03e72	NUM
ejpam-5431	9	11	,	,	PUNCT
ejpam-5431	9	12	54e35	54e35	NUM
ejpam-5431	9	13	,	,	PUNCT
ejpam-5431	9	14	06a06	06a06	NOUN
ejpam-5431	9	15	key	key	ADJ
ejpam-5431	9	16	words	word	NOUN
ejpam-5431	9	17	and	and	CCONJ
ejpam-5431	9	18	phrases	phrase	NOUN
ejpam-5431	9	19	:	:	PUNCT
ejpam-5431	9	20	b	b	X
ejpam-5431	9	21	-	-	PUNCT
ejpam-5431	9	22	metric	metric	ADJ
ejpam-5431	9	23	space	space	NOUN
ejpam-5431	9	24	,	,	PUNCT
ejpam-5431	9	25	common	common	ADJ
ejpam-5431	9	26	intuitionistic	intuitionistic	ADJ
ejpam-5431	9	27	fuzzy	fuzzy	ADJ
ejpam-5431	9	28	fixed	fix	VERB
ejpam-5431	9	29	point	point	NOUN
ejpam-5431	9	30	,	,	PUNCT
ejpam-5431	9	31	intuitionistic	intuitionistic	ADJ
ejpam-5431	9	32	fuzzy	fuzzy	ADJ
ejpam-5431	9	33	set	set	NOUN
ejpam-5431	9	34	-	-	PUNCT
ejpam-5431	9	35	valued	value	VERB
ejpam-5431	9	36	map	map	NOUN
ejpam-5431	9	37	,	,	PUNCT
ejpam-5431	9	38	pairwise	pairwise	NOUN
ejpam-5431	9	39	intuitionistic	intuitionistic	ADJ
ejpam-5431	9	40	fuzzy	fuzzy	ADJ
ejpam-5431	9	41	z	z	NOUN
ejpam-5431	9	42	-	-	PUNCT
ejpam-5431	9	43	contraction	contraction	NOUN
ejpam-5431	9	44	,	,	PUNCT
ejpam-5431	9	45	simulation	simulation	NOUN
ejpam-5431	9	46	function	function	NOUN
ejpam-5431	9	47	1	1	NUM
ejpam-5431	9	48	.	.	PUNCT
ejpam-5431	10	1	introduction	introduction	NOUN
ejpam-5431	10	2	fixed	fix	VERB
ejpam-5431	10	3	point	point	NOUN
ejpam-5431	10	4	theory	theory	NOUN
ejpam-5431	10	5	is	be	AUX
ejpam-5431	10	6	a	a	DET
ejpam-5431	10	7	pivotal	pivotal	ADJ
ejpam-5431	10	8	area	area	NOUN
ejpam-5431	10	9	of	of	ADP
ejpam-5431	10	10	mathematical	mathematical	ADJ
ejpam-5431	10	11	analysis	analysis	NOUN
ejpam-5431	10	12	with	with	ADP
ejpam-5431	10	13	broad	broad	ADJ
ejpam-5431	10	14	implications	implication	NOUN
ejpam-5431	10	15	across	across	ADP
ejpam-5431	10	16	various	various	ADJ
ejpam-5431	10	17	disciplines	discipline	NOUN
ejpam-5431	10	18	,	,	PUNCT
ejpam-5431	10	19	including	include	VERB
ejpam-5431	10	20	functional	functional	ADJ
ejpam-5431	10	21	analysis	analysis	NOUN
ejpam-5431	10	22	,	,	PUNCT
ejpam-5431	10	23	topology	topology	NOUN
ejpam-5431	10	24	,	,	PUNCT
ejpam-5431	10	25	and	and	CCONJ
ejpam-5431	10	26	applied	apply	VERB
ejpam-5431	10	27	mathematics	mathematic	NOUN
ejpam-5431	10	28	.	.	PUNCT
ejpam-5431	11	1	one	one	NUM
ejpam-5431	11	2	of	of	ADP
ejpam-5431	11	3	the	the	DET
ejpam-5431	11	4	foundational	foundational	ADJ
ejpam-5431	11	5	results	result	NOUN
ejpam-5431	11	6	in	in	ADP
ejpam-5431	11	7	this	this	DET
ejpam-5431	11	8	field	field	NOUN
ejpam-5431	11	9	is	be	AUX
ejpam-5431	11	10	the	the	DET
ejpam-5431	11	11	banach	banach	ADV
ejpam-5431	11	12	fixed	fix	VERB
ejpam-5431	11	13	point	point	NOUN
ejpam-5431	11	14	theorem	theorem	ADJ
ejpam-5431	11	15	,	,	PUNCT
ejpam-5431	11	16	also	also	ADV
ejpam-5431	11	17	known	know	VERB
ejpam-5431	11	18	as	as	ADP
ejpam-5431	11	19	the	the	DET
ejpam-5431	11	20	contraction	contraction	NOUN
ejpam-5431	11	21	mapping	mapping	NOUN
ejpam-5431	11	22	principle	principle	NOUN
ejpam-5431	11	23	,	,	PUNCT
ejpam-5431	11	24	a	a	DET
ejpam-5431	11	25	cornerstone	cornerstone	NOUN
ejpam-5431	11	26	in	in	ADP
ejpam-5431	11	27	the	the	DET
ejpam-5431	11	28	study	study	NOUN
ejpam-5431	11	29	of	of	ADP
ejpam-5431	11	30	fixed	fix	VERB
ejpam-5431	11	31	points	point	NOUN
ejpam-5431	11	32	∗corresponding	∗corresponde	VERB
ejpam-5431	11	33	author	author	NOUN
ejpam-5431	11	34	.	.	PUNCT
ejpam-5431	12	1	doi	doi	NOUN
ejpam-5431	12	2	:	:	PUNCT
ejpam-5431	12	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5431	https://doi.org/10.29020/nybg.ejpam.v17i4.5431	NUM
ejpam-5431	12	4	email	email	NOUN
ejpam-5431	12	5	addresses	address	NOUN
ejpam-5431	12	6	:	:	PUNCT
ejpam-5431	13	1	maliha.rashid@iiu.edu.pk	maliha.rashid@iiu.edu.pk	PROPN
ejpam-5431	13	2	(	(	PUNCT
ejpam-5431	13	3	m.	m.	NOUN
ejpam-5431	13	4	rashid	rashid	PROPN
ejpam-5431	13	5	)	)	PUNCT
ejpam-5431	13	6	,	,	PUNCT
ejpam-5431	13	7	quratulain.msma749@iiu.edu.pk	quratulain.msma749@iiu.edu.pk	PRON
ejpam-5431	13	8	(	(	PUNCT
ejpam-5431	13	9	q.	q.	PROPN
ejpam-5431	13	10	mumtaz	mumtaz	PROPN
ejpam-5431	13	11	)	)	PUNCT
ejpam-5431	13	12	,	,	PUNCT
ejpam-5431	13	13	naeem.saleem2@gmail.com	naeem.saleem2@gmail.com	X
ejpam-5431	13	14	(	(	PUNCT
ejpam-5431	13	15	n.	n.	NOUN
ejpam-5431	13	16	saleem	saleem	PROPN
ejpam-5431	13	17	)	)	PUNCT
ejpam-5431	13	18	,	,	PUNCT
ejpam-5431	13	19	maggie.aphane@smu.ac.za	maggie.aphane@smu.ac.za	PROPN
ejpam-5431	13	20	(	(	PUNCT
ejpam-5431	13	21	m.	m.	NOUN
ejpam-5431	13	22	aphane	aphane	PROPN
ejpam-5431	13	23	)	)	PUNCT
ejpam-5431	13	24	,	,	PUNCT
ejpam-5431	13	25	irehman@du.edu.om	irehman@du.edu.om	PROPN
ejpam-5431	13	26	(	(	PUNCT
ejpam-5431	13	27	i.	i.	PROPN
ejpam-5431	13	28	rehman	rehman	PROPN
ejpam-5431	13	29	)	)	PUNCT
ejpam-5431	13	30	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5431	13	31	3304	3304	NUM
ejpam-5431	14	1	copyright	copyright	NOUN
ejpam-5431	14	2	:	:	PUNCT
ejpam-5431	14	3	©	©	PROPN
ejpam-5431	14	4	2024	2024	NUM
ejpam-5431	14	5	the	the	DET
ejpam-5431	14	6	author(s	author(s	NOUN
ejpam-5431	14	7	)	)	PUNCT
ejpam-5431	14	8	.	.	PUNCT
ejpam-5431	15	1	(	(	PUNCT
ejpam-5431	15	2	cc	cc	NOUN
ejpam-5431	15	3	by	by	ADP
ejpam-5431	15	4	-	-	PUNCT
ejpam-5431	15	5	nc	nc	PROPN
ejpam-5431	15	6	4.0	4.0	NUM
ejpam-5431	15	7	)	)	PUNCT
ejpam-5431	15	8	n.	n.	NOUN
ejpam-5431	15	9	saleem	saleem	PROPN
ejpam-5431	15	10	et	et	PROPN
ejpam-5431	15	11	al	al	PROPN
ejpam-5431	15	12	.	.	PUNCT
ejpam-5431	15	13	/	/	SYM
ejpam-5431	15	14	eur	eur	PROPN
ejpam-5431	15	15	.	.	PUNCT
ejpam-5431	16	1	j.	j.	PROPN
ejpam-5431	16	2	pure	pure	PROPN
ejpam-5431	16	3	appl	appl	PROPN
ejpam-5431	16	4	.	.	PROPN
ejpam-5431	16	5	math	math	PROPN
ejpam-5431	16	6	,	,	PUNCT
ejpam-5431	16	7	17	17	NUM
ejpam-5431	16	8	(	(	PUNCT
ejpam-5431	16	9	4	4	NUM
ejpam-5431	16	10	)	)	PUNCT
ejpam-5431	16	11	(	(	PUNCT
ejpam-5431	16	12	2024	2024	NUM
ejpam-5431	16	13	)	)	PUNCT
ejpam-5431	16	14	,	,	PUNCT
ejpam-5431	16	15	3304	3304	NUM
ejpam-5431	16	16	-	-	SYM
ejpam-5431	16	17	3335	3335	NUM
ejpam-5431	16	18	3305	3305	NUM
ejpam-5431	16	19	that	that	PRON
ejpam-5431	16	20	plays	play	VERB
ejpam-5431	16	21	a	a	DET
ejpam-5431	16	22	crucial	crucial	ADJ
ejpam-5431	16	23	role	role	NOUN
ejpam-5431	16	24	in	in	ADP
ejpam-5431	16	25	proving	prove	VERB
ejpam-5431	16	26	the	the	DET
ejpam-5431	16	27	existence	existence	NOUN
ejpam-5431	16	28	and	and	CCONJ
ejpam-5431	16	29	uniqueness	uniqueness	NOUN
ejpam-5431	16	30	of	of	ADP
ejpam-5431	16	31	solutions	solution	NOUN
ejpam-5431	16	32	across	across	ADP
ejpam-5431	16	33	a	a	DET
ejpam-5431	16	34	broad	broad	ADJ
ejpam-5431	16	35	spectrum	spectrum	NOUN
ejpam-5431	16	36	of	of	ADP
ejpam-5431	16	37	mathematical	mathematical	ADJ
ejpam-5431	16	38	problems	problem	NOUN
ejpam-5431	16	39	,	,	PUNCT
ejpam-5431	16	40	including	include	VERB
ejpam-5431	16	41	those	those	PRON
ejpam-5431	16	42	in	in	ADP
ejpam-5431	16	43	differential	differential	ADJ
ejpam-5431	16	44	and	and	CCONJ
ejpam-5431	16	45	integral	integral	ADJ
ejpam-5431	16	46	equations	equation	NOUN
ejpam-5431	16	47	.	.	PUNCT
ejpam-5431	17	1	the	the	DET
ejpam-5431	17	2	banach	banach	NOUN
ejpam-5431	17	3	contraction	contraction	NOUN
ejpam-5431	17	4	theorem	theorem	VERB
ejpam-5431	17	5	[	[	PUNCT
ejpam-5431	17	6	13	13	NUM
ejpam-5431	17	7	]	]	PUNCT
ejpam-5431	17	8	,	,	PUNCT
ejpam-5431	17	9	a	a	DET
ejpam-5431	17	10	seminal	seminal	ADJ
ejpam-5431	17	11	result	result	NOUN
ejpam-5431	17	12	in	in	ADP
ejpam-5431	17	13	this	this	DET
ejpam-5431	17	14	field	field	NOUN
ejpam-5431	17	15	,	,	PUNCT
ejpam-5431	17	16	has	have	AUX
ejpam-5431	17	17	profoundly	profoundly	ADV
ejpam-5431	17	18	influenced	influence	VERB
ejpam-5431	17	19	subsequent	subsequent	ADJ
ejpam-5431	17	20	research	research	NOUN
ejpam-5431	17	21	and	and	CCONJ
ejpam-5431	17	22	applications	application	NOUN
ejpam-5431	17	23	.	.	PUNCT
ejpam-5431	18	1	fixed	fix	VERB
ejpam-5431	18	2	point	point	NOUN
ejpam-5431	18	3	theory	theory	NOUN
ejpam-5431	18	4	is	be	AUX
ejpam-5431	18	5	instrumental	instrumental	ADJ
ejpam-5431	18	6	in	in	ADP
ejpam-5431	18	7	addressing	address	VERB
ejpam-5431	18	8	a	a	DET
ejpam-5431	18	9	variety	variety	NOUN
ejpam-5431	18	10	of	of	ADP
ejpam-5431	18	11	complex	complex	ADJ
ejpam-5431	18	12	issues	issue	NOUN
ejpam-5431	18	13	in	in	ADP
ejpam-5431	18	14	nonlinear	nonlinear	ADJ
ejpam-5431	18	15	analysis	analysis	NOUN
ejpam-5431	18	16	.	.	PUNCT
ejpam-5431	19	1	specifically	specifically	ADV
ejpam-5431	19	2	,	,	PUNCT
ejpam-5431	19	3	in	in	ADP
ejpam-5431	19	4	operator	operator	NOUN
ejpam-5431	19	5	equations	equation	NOUN
ejpam-5431	19	6	such	such	ADJ
ejpam-5431	19	7	as	as	ADP
ejpam-5431	19	8	gx	gx	PROPN
ejpam-5431	19	9	=	=	PROPN
ejpam-5431	19	10	0	0	PROPN
ejpam-5431	19	11	,	,	PUNCT
ejpam-5431	19	12	the	the	DET
ejpam-5431	19	13	existence	existence	NOUN
ejpam-5431	19	14	of	of	ADP
ejpam-5431	19	15	a	a	DET
ejpam-5431	19	16	fixed	fix	VERB
ejpam-5431	19	17	point	point	NOUN
ejpam-5431	19	18	fx	fx	NOUN
ejpam-5431	19	19	=	=	PUNCT
ejpam-5431	19	20	x	x	X
ejpam-5431	19	21	can	can	AUX
ejpam-5431	19	22	be	be	AUX
ejpam-5431	19	23	effectively	effectively	ADV
ejpam-5431	19	24	established	establish	VERB
ejpam-5431	19	25	for	for	ADP
ejpam-5431	19	26	self	self	NOUN
ejpam-5431	19	27	-	-	PUNCT
ejpam-5431	19	28	mappings	mapping	NOUN
ejpam-5431	19	29	within	within	ADP
ejpam-5431	19	30	the	the	DET
ejpam-5431	19	31	relevant	relevant	ADJ
ejpam-5431	19	32	domain	domain	NOUN
ejpam-5431	19	33	.	.	PUNCT
ejpam-5431	20	1	fixed	fix	VERB
ejpam-5431	20	2	point	point	NOUN
ejpam-5431	20	3	theory	theory	NOUN
ejpam-5431	20	4	has	have	AUX
ejpam-5431	20	5	evolved	evolve	VERB
ejpam-5431	20	6	significantly	significantly	ADV
ejpam-5431	20	7	,	,	PUNCT
ejpam-5431	20	8	with	with	ADP
ejpam-5431	20	9	numerous	numerous	ADJ
ejpam-5431	20	10	generalizations	generalization	NOUN
ejpam-5431	20	11	that	that	PRON
ejpam-5431	20	12	extend	extend	VERB
ejpam-5431	20	13	beyond	beyond	ADP
ejpam-5431	20	14	metric	metric	ADJ
ejpam-5431	20	15	spaces	space	NOUN
ejpam-5431	20	16	to	to	ADP
ejpam-5431	20	17	more	more	ADJ
ejpam-5431	20	18	abstract	abstract	ADJ
ejpam-5431	20	19	settings	setting	NOUN
ejpam-5431	20	20	such	such	ADJ
ejpam-5431	20	21	as	as	ADP
ejpam-5431	20	22	topological	topological	ADJ
ejpam-5431	20	23	vector	vector	NOUN
ejpam-5431	20	24	spaces	space	NOUN
ejpam-5431	20	25	,	,	PUNCT
ejpam-5431	20	26	normed	normed	ADJ
ejpam-5431	20	27	spaces	space	NOUN
ejpam-5431	20	28	,	,	PUNCT
ejpam-5431	20	29	and	and	CCONJ
ejpam-5431	20	30	ordered	order	VERB
ejpam-5431	20	31	structures	structure	NOUN
ejpam-5431	20	32	.	.	PUNCT
ejpam-5431	21	1	these	these	DET
ejpam-5431	21	2	generalizations	generalization	NOUN
ejpam-5431	21	3	have	have	AUX
ejpam-5431	21	4	been	be	AUX
ejpam-5431	21	5	instrumental	instrumental	ADJ
ejpam-5431	21	6	in	in	ADP
ejpam-5431	21	7	solving	solve	VERB
ejpam-5431	21	8	complex	complex	ADJ
ejpam-5431	21	9	problems	problem	NOUN
ejpam-5431	21	10	in	in	ADP
ejpam-5431	21	11	economics	economic	NOUN
ejpam-5431	21	12	,	,	PUNCT
ejpam-5431	21	13	computer	computer	NOUN
ejpam-5431	21	14	science	science	NOUN
ejpam-5431	21	15	,	,	PUNCT
ejpam-5431	21	16	and	and	CCONJ
ejpam-5431	21	17	engineering	engineering	NOUN
ejpam-5431	21	18	,	,	PUNCT
ejpam-5431	21	19	where	where	SCONJ
ejpam-5431	21	20	finding	find	VERB
ejpam-5431	21	21	equilibrium	equilibrium	NOUN
ejpam-5431	21	22	states	state	NOUN
ejpam-5431	21	23	or	or	CCONJ
ejpam-5431	21	24	stable	stable	ADJ
ejpam-5431	21	25	solutions	solution	NOUN
ejpam-5431	21	26	is	be	AUX
ejpam-5431	21	27	essential	essential	ADJ
ejpam-5431	21	28	.	.	PUNCT
ejpam-5431	22	1	fuzzy	fuzzy	ADJ
ejpam-5431	22	2	set	set	PROPN
ejpam-5431	22	3	theory	theory	NOUN
ejpam-5431	22	4	,	,	PUNCT
ejpam-5431	22	5	introduced	introduce	VERB
ejpam-5431	22	6	by	by	ADP
ejpam-5431	22	7	lotfi	lotfi	PROPN
ejpam-5431	22	8	a.	a.	PROPN
ejpam-5431	22	9	zadeh	zadeh	PROPN
ejpam-5431	23	1	[	[	X
ejpam-5431	23	2	2	2	X
ejpam-5431	23	3	]	]	PUNCT
ejpam-5431	23	4	in	in	ADP
ejpam-5431	23	5	1965	1965	NUM
ejpam-5431	23	6	,	,	PUNCT
ejpam-5431	23	7	revolutionized	revolutionize	VERB
ejpam-5431	23	8	classical	classical	ADJ
ejpam-5431	23	9	set	set	NOUN
ejpam-5431	23	10	theory	theory	NOUN
ejpam-5431	23	11	by	by	ADP
ejpam-5431	23	12	allowing	allow	VERB
ejpam-5431	23	13	partial	partial	ADJ
ejpam-5431	23	14	membership	membership	NOUN
ejpam-5431	23	15	of	of	ADP
ejpam-5431	23	16	elements	element	NOUN
ejpam-5431	23	17	in	in	ADP
ejpam-5431	23	18	a	a	DET
ejpam-5431	23	19	set	set	NOUN
ejpam-5431	23	20	.	.	PUNCT
ejpam-5431	24	1	this	this	DET
ejpam-5431	24	2	approach	approach	NOUN
ejpam-5431	24	3	is	be	AUX
ejpam-5431	24	4	particularly	particularly	ADV
ejpam-5431	24	5	useful	useful	ADJ
ejpam-5431	24	6	in	in	ADP
ejpam-5431	24	7	modeling	model	VERB
ejpam-5431	24	8	situations	situation	NOUN
ejpam-5431	24	9	characterized	characterize	VERB
ejpam-5431	24	10	by	by	ADP
ejpam-5431	24	11	uncertainty	uncertainty	NOUN
ejpam-5431	24	12	,	,	PUNCT
ejpam-5431	24	13	imprecision	imprecision	NOUN
ejpam-5431	24	14	,	,	PUNCT
ejpam-5431	24	15	or	or	CCONJ
ejpam-5431	24	16	vagueness	vagueness	NOUN
ejpam-5431	24	17	,	,	PUNCT
ejpam-5431	24	18	as	as	SCONJ
ejpam-5431	24	19	it	it	PRON
ejpam-5431	24	20	provides	provide	VERB
ejpam-5431	24	21	a	a	DET
ejpam-5431	24	22	more	more	ADV
ejpam-5431	24	23	flexible	flexible	ADJ
ejpam-5431	24	24	and	and	CCONJ
ejpam-5431	24	25	realistic	realistic	ADJ
ejpam-5431	24	26	representation	representation	NOUN
ejpam-5431	24	27	of	of	ADP
ejpam-5431	24	28	real	real	ADJ
ejpam-5431	24	29	-	-	PUNCT
ejpam-5431	24	30	world	world	NOUN
ejpam-5431	24	31	phenomena	phenomenon	NOUN
ejpam-5431	24	32	.	.	PUNCT
ejpam-5431	25	1	fuzzy	fuzzy	ADJ
ejpam-5431	25	2	sets	set	NOUN
ejpam-5431	25	3	have	have	AUX
ejpam-5431	25	4	found	find	VERB
ejpam-5431	25	5	extensive	extensive	ADJ
ejpam-5431	25	6	applications	application	NOUN
ejpam-5431	25	7	in	in	ADP
ejpam-5431	25	8	various	various	ADJ
ejpam-5431	25	9	fields	field	NOUN
ejpam-5431	25	10	such	such	ADJ
ejpam-5431	25	11	as	as	ADP
ejpam-5431	25	12	control	control	NOUN
ejpam-5431	25	13	systems	system	NOUN
ejpam-5431	25	14	,	,	PUNCT
ejpam-5431	25	15	decisionmaking	decisionmake	VERB
ejpam-5431	25	16	,	,	PUNCT
ejpam-5431	25	17	pattern	pattern	NOUN
ejpam-5431	25	18	recognition	recognition	NOUN
ejpam-5431	25	19	,	,	PUNCT
ejpam-5431	25	20	and	and	CCONJ
ejpam-5431	25	21	artificial	artificial	ADJ
ejpam-5431	25	22	intelligence	intelligence	NOUN
ejpam-5431	25	23	.	.	PUNCT
ejpam-5431	26	1	building	build	VERB
ejpam-5431	26	2	upon	upon	SCONJ
ejpam-5431	26	3	the	the	DET
ejpam-5431	26	4	foundation	foundation	NOUN
ejpam-5431	26	5	of	of	ADP
ejpam-5431	26	6	fuzzy	fuzzy	ADJ
ejpam-5431	26	7	sets	set	NOUN
ejpam-5431	26	8	,	,	PUNCT
ejpam-5431	26	9	krassimir	krassimir	NOUN
ejpam-5431	26	10	atanassov	atanassov	NOUN
ejpam-5431	26	11	[	[	X
ejpam-5431	26	12	23	23	NUM
ejpam-5431	26	13	]	]	PUNCT
ejpam-5431	26	14	introduced	introduce	VERB
ejpam-5431	26	15	intuitionistic	intuitionistic	ADJ
ejpam-5431	26	16	fuzzy	fuzzy	ADJ
ejpam-5431	26	17	sets	set	NOUN
ejpam-5431	26	18	(	(	PUNCT
ejpam-5431	26	19	ifs	ifs	PROPN
ejpam-5431	26	20	)	)	PUNCT
ejpam-5431	26	21	in	in	ADP
ejpam-5431	26	22	1986	1986	NUM
ejpam-5431	26	23	as	as	ADP
ejpam-5431	26	24	a	a	DET
ejpam-5431	26	25	further	further	ADJ
ejpam-5431	26	26	extension	extension	NOUN
ejpam-5431	26	27	to	to	PART
ejpam-5431	26	28	better	well	ADV
ejpam-5431	26	29	handle	handle	VERB
ejpam-5431	26	30	situations	situation	NOUN
ejpam-5431	26	31	where	where	SCONJ
ejpam-5431	26	32	there	there	PRON
ejpam-5431	26	33	is	be	VERB
ejpam-5431	26	34	hesitation	hesitation	NOUN
ejpam-5431	26	35	or	or	CCONJ
ejpam-5431	26	36	lack	lack	NOUN
ejpam-5431	26	37	of	of	ADP
ejpam-5431	26	38	complete	complete	ADJ
ejpam-5431	26	39	information	information	NOUN
ejpam-5431	26	40	.	.	PUNCT
ejpam-5431	27	1	in	in	ADP
ejpam-5431	27	2	intuitionistic	intuitionistic	ADJ
ejpam-5431	27	3	fuzzy	fuzzy	ADJ
ejpam-5431	27	4	sets	set	NOUN
ejpam-5431	27	5	,	,	PUNCT
ejpam-5431	27	6	each	each	DET
ejpam-5431	27	7	element	element	NOUN
ejpam-5431	27	8	is	be	AUX
ejpam-5431	27	9	described	describe	VERB
ejpam-5431	27	10	by	by	ADP
ejpam-5431	27	11	two	two	NUM
ejpam-5431	27	12	values	value	NOUN
ejpam-5431	27	13	:	:	PUNCT
ejpam-5431	27	14	the	the	DET
ejpam-5431	27	15	degree	degree	NOUN
ejpam-5431	27	16	of	of	ADP
ejpam-5431	27	17	membership	membership	NOUN
ejpam-5431	27	18	.	.	PUNCT
ejpam-5431	28	1	additionally	additionally	ADV
ejpam-5431	28	2	,	,	PUNCT
ejpam-5431	28	3	there	there	PRON
ejpam-5431	28	4	exists	exist	VERB
ejpam-5431	28	5	a	a	DET
ejpam-5431	28	6	hesitation	hesitation	NOUN
ejpam-5431	28	7	margin	margin	NOUN
ejpam-5431	28	8	,	,	PUNCT
ejpam-5431	28	9	often	often	ADV
ejpam-5431	28	10	referred	refer	VERB
ejpam-5431	28	11	to	to	ADP
ejpam-5431	28	12	as	as	ADP
ejpam-5431	28	13	the	the	DET
ejpam-5431	28	14	degree	degree	NOUN
ejpam-5431	28	15	of	of	ADP
ejpam-5431	28	16	indeterminacy	indeterminacy	NOUN
ejpam-5431	28	17	or	or	CCONJ
ejpam-5431	28	18	uncertainty	uncertainty	NOUN
ejpam-5431	28	19	.	.	PUNCT
ejpam-5431	29	1	this	this	DET
ejpam-5431	29	2	generalization	generalization	NOUN
ejpam-5431	29	3	has	have	AUX
ejpam-5431	29	4	proven	prove	VERB
ejpam-5431	29	5	useful	useful	ADJ
ejpam-5431	29	6	in	in	ADP
ejpam-5431	29	7	many	many	ADJ
ejpam-5431	29	8	applications	application	NOUN
ejpam-5431	29	9	,	,	PUNCT
ejpam-5431	29	10	particularly	particularly	ADV
ejpam-5431	29	11	in	in	ADP
ejpam-5431	29	12	decision	decision	NOUN
ejpam-5431	29	13	-	-	PUNCT
ejpam-5431	29	14	making	make	VERB
ejpam-5431	29	15	scenarios	scenario	NOUN
ejpam-5431	29	16	where	where	SCONJ
ejpam-5431	29	17	incomplete	incomplete	ADJ
ejpam-5431	29	18	or	or	CCONJ
ejpam-5431	29	19	ambiguous	ambiguous	ADJ
ejpam-5431	29	20	information	information	NOUN
ejpam-5431	29	21	exists	exist	VERB
ejpam-5431	29	22	.	.	PUNCT
ejpam-5431	30	1	notably	notably	ADV
ejpam-5431	30	2	,	,	PUNCT
ejpam-5431	30	3	gulzar	gulzar	PROPN
ejpam-5431	31	1	[	[	X
ejpam-5431	31	2	14	14	NUM
ejpam-5431	31	3	]	]	PUNCT
ejpam-5431	31	4	applied	apply	VERB
ejpam-5431	31	5	ifss	ifss	NOUN
ejpam-5431	31	6	to	to	ADP
ejpam-5431	31	7	group	group	NOUN
ejpam-5431	31	8	theory	theory	NOUN
ejpam-5431	31	9	,	,	PUNCT
ejpam-5431	31	10	while	while	SCONJ
ejpam-5431	31	11	kanwal	kanwal	PROPN
ejpam-5431	31	12	and	and	CCONJ
ejpam-5431	31	13	akbar	akbar	NOUN
ejpam-5431	32	1	[	[	X
ejpam-5431	32	2	27	27	NUM
ejpam-5431	32	3	]	]	PUNCT
ejpam-5431	32	4	used	use	VERB
ejpam-5431	32	5	them	they	PRON
ejpam-5431	32	6	to	to	PART
ejpam-5431	32	7	define	define	VERB
ejpam-5431	32	8	intuitionistic	intuitionistic	ADJ
ejpam-5431	32	9	fuzzy	fuzzy	ADJ
ejpam-5431	32	10	mappings	mapping	NOUN
ejpam-5431	32	11	and	and	CCONJ
ejpam-5431	32	12	identify	identify	VERB
ejpam-5431	32	13	common	common	ADJ
ejpam-5431	32	14	fixed	fix	VERB
ejpam-5431	32	15	points	point	NOUN
ejpam-5431	32	16	[	[	X
ejpam-5431	32	17	24	24	NUM
ejpam-5431	32	18	,	,	PUNCT
ejpam-5431	32	19	26	26	NUM
ejpam-5431	32	20	]	]	PUNCT
ejpam-5431	32	21	.	.	PUNCT
ejpam-5431	33	1	incorporating	incorporate	VERB
ejpam-5431	33	2	fuzzy	fuzzy	ADJ
ejpam-5431	33	3	sets	set	NOUN
ejpam-5431	33	4	into	into	ADP
ejpam-5431	33	5	traditional	traditional	ADJ
ejpam-5431	33	6	metric	metric	ADJ
ejpam-5431	33	7	spaces	space	NOUN
ejpam-5431	33	8	has	have	AUX
ejpam-5431	33	9	led	lead	VERB
ejpam-5431	33	10	to	to	ADP
ejpam-5431	33	11	significant	significant	ADJ
ejpam-5431	33	12	advancements	advancement	NOUN
ejpam-5431	33	13	.	.	PUNCT
ejpam-5431	34	1	deng	deng	PROPN
ejpam-5431	35	1	[	[	X
ejpam-5431	35	2	8	8	NUM
ejpam-5431	35	3	]	]	PUNCT
ejpam-5431	35	4	introduced	introduce	VERB
ejpam-5431	35	5	the	the	DET
ejpam-5431	35	6	concept	concept	NOUN
ejpam-5431	35	7	of	of	ADP
ejpam-5431	35	8	fuzzy	fuzzy	ADJ
ejpam-5431	35	9	pseudo	pseudo	NOUN
ejpam-5431	35	10	-	-	ADJ
ejpam-5431	35	11	metric	metric	ADJ
ejpam-5431	35	12	spaces	space	NOUN
ejpam-5431	35	13	,	,	PUNCT
ejpam-5431	35	14	which	which	PRON
ejpam-5431	35	15	extend	extend	VERB
ejpam-5431	35	16	the	the	DET
ejpam-5431	35	17	classical	classical	ADJ
ejpam-5431	35	18	metric	metric	ADJ
ejpam-5431	35	19	framework	framework	NOUN
ejpam-5431	35	20	to	to	PART
ejpam-5431	35	21	accommodate	accommodate	VERB
ejpam-5431	35	22	fuzzy	fuzzy	ADJ
ejpam-5431	35	23	topological	topological	ADJ
ejpam-5431	35	24	and	and	CCONJ
ejpam-5431	35	25	uniform	uniform	ADJ
ejpam-5431	35	26	structures	structure	NOUN
ejpam-5431	35	27	.	.	PUNCT
ejpam-5431	36	1	erceg	erceg	PROPN
ejpam-5431	36	2	[	[	X
ejpam-5431	36	3	17	17	NUM
ejpam-5431	36	4	]	]	PUNCT
ejpam-5431	36	5	further	far	ADV
ejpam-5431	36	6	explored	explore	VERB
ejpam-5431	36	7	the	the	DET
ejpam-5431	36	8	equivalence	equivalence	NOUN
ejpam-5431	36	9	of	of	ADP
ejpam-5431	36	10	pseudo	pseudo	NOUN
ejpam-5431	36	11	-	-	ADJ
ejpam-5431	36	12	quasi	quasi	NOUN
ejpam-5431	36	13	-	-	ADJ
ejpam-5431	36	14	metrics	metric	NOUN
ejpam-5431	36	15	to	to	PART
ejpam-5431	36	16	distance	distance	NOUN
ejpam-5431	36	17	functions	function	NOUN
ejpam-5431	36	18	in	in	ADP
ejpam-5431	36	19	fuzzy	fuzzy	ADJ
ejpam-5431	36	20	set	set	NOUN
ejpam-5431	36	21	theory	theory	NOUN
ejpam-5431	36	22	,	,	PUNCT
ejpam-5431	36	23	proposing	propose	VERB
ejpam-5431	36	24	additional	additional	ADJ
ejpam-5431	36	25	axioms	axiom	NOUN
ejpam-5431	36	26	for	for	ADP
ejpam-5431	36	27	metrics	metric	NOUN
ejpam-5431	36	28	and	and	CCONJ
ejpam-5431	36	29	uniformity	uniformity	NOUN
ejpam-5431	36	30	within	within	ADP
ejpam-5431	36	31	this	this	DET
ejpam-5431	36	32	context	context	NOUN
ejpam-5431	36	33	.	.	PUNCT
ejpam-5431	37	1	these	these	DET
ejpam-5431	37	2	developments	development	NOUN
ejpam-5431	37	3	underscore	underscore	VERB
ejpam-5431	37	4	the	the	DET
ejpam-5431	37	5	ongoing	ongoing	ADJ
ejpam-5431	37	6	effort	effort	NOUN
ejpam-5431	37	7	to	to	PART
ejpam-5431	37	8	apply	apply	VERB
ejpam-5431	37	9	mathematical	mathematical	ADJ
ejpam-5431	37	10	structures	structure	NOUN
ejpam-5431	37	11	to	to	ADP
ejpam-5431	37	12	fuzzy	fuzzy	ADJ
ejpam-5431	37	13	scenarios	scenario	NOUN
ejpam-5431	37	14	.	.	PUNCT
ejpam-5431	38	1	in	in	ADP
ejpam-5431	38	2	mathematical	mathematical	ADJ
ejpam-5431	38	3	analysis	analysis	NOUN
ejpam-5431	38	4	,	,	PUNCT
ejpam-5431	38	5	the	the	DET
ejpam-5431	38	6	concept	concept	NOUN
ejpam-5431	38	7	of	of	ADP
ejpam-5431	38	8	metric	metric	ADJ
ejpam-5431	38	9	spaces	space	NOUN
ejpam-5431	38	10	plays	play	VERB
ejpam-5431	38	11	a	a	DET
ejpam-5431	38	12	fundamental	fundamental	ADJ
ejpam-5431	38	13	role	role	NOUN
ejpam-5431	38	14	in	in	ADP
ejpam-5431	38	15	understanding	understand	VERB
ejpam-5431	38	16	various	various	ADJ
ejpam-5431	38	17	aspects	aspect	NOUN
ejpam-5431	38	18	of	of	ADP
ejpam-5431	38	19	distance	distance	NOUN
ejpam-5431	38	20	and	and	CCONJ
ejpam-5431	38	21	convergence	convergence	NOUN
ejpam-5431	38	22	.	.	PUNCT
ejpam-5431	39	1	extending	extend	VERB
ejpam-5431	39	2	the	the	DET
ejpam-5431	39	3	traditional	traditional	ADJ
ejpam-5431	39	4	notion	notion	NOUN
ejpam-5431	39	5	of	of	ADP
ejpam-5431	39	6	a	a	DET
ejpam-5431	39	7	metric	metric	ADJ
ejpam-5431	39	8	,	,	PUNCT
ejpam-5431	39	9	b	b	X
ejpam-5431	39	10	-	-	ADJ
ejpam-5431	39	11	metric	metric	ADJ
ejpam-5431	39	12	spaces	space	NOUN
ejpam-5431	39	13	provide	provide	VERB
ejpam-5431	39	14	a	a	DET
ejpam-5431	39	15	more	more	ADV
ejpam-5431	39	16	generalized	generalized	ADJ
ejpam-5431	39	17	framework	framework	NOUN
ejpam-5431	39	18	that	that	PRON
ejpam-5431	39	19	retains	retain	VERB
ejpam-5431	39	20	many	many	ADJ
ejpam-5431	39	21	essential	essential	ADJ
ejpam-5431	39	22	properties	property	NOUN
ejpam-5431	39	23	while	while	SCONJ
ejpam-5431	39	24	relaxing	relax	VERB
ejpam-5431	39	25	some	some	DET
ejpam-5431	39	26	strict	strict	ADJ
ejpam-5431	39	27	conditions	condition	NOUN
ejpam-5431	39	28	.	.	PUNCT
ejpam-5431	40	1	the	the	DET
ejpam-5431	40	2	development	development	NOUN
ejpam-5431	40	3	of	of	ADP
ejpam-5431	40	4	b	b	NOUN
ejpam-5431	40	5	-	-	PUNCT
ejpam-5431	40	6	metric	metric	ADJ
ejpam-5431	40	7	spaces	space	NOUN
ejpam-5431	40	8	drew	draw	VERB
ejpam-5431	40	9	upon	upon	SCONJ
ejpam-5431	40	10	a	a	DET
ejpam-5431	40	11	long	long	ADJ
ejpam-5431	40	12	history	history	NOUN
ejpam-5431	40	13	of	of	ADP
ejpam-5431	40	14	work	work	NOUN
ejpam-5431	40	15	on	on	ADP
ejpam-5431	40	16	metric	metric	ADJ
ejpam-5431	40	17	spaces	space	NOUN
ejpam-5431	40	18	and	and	CCONJ
ejpam-5431	40	19	their	their	PRON
ejpam-5431	40	20	generalizations	generalization	NOUN
ejpam-5431	40	21	.	.	PUNCT
ejpam-5431	41	1	several	several	ADJ
ejpam-5431	41	2	key	key	ADJ
ejpam-5431	41	3	contributions	contribution	NOUN
ejpam-5431	41	4	paved	pave	VERB
ejpam-5431	41	5	the	the	DET
ejpam-5431	41	6	way	way	NOUN
ejpam-5431	41	7	for	for	ADP
ejpam-5431	41	8	the	the	DET
ejpam-5431	41	9	formalization	formalization	NOUN
ejpam-5431	41	10	of	of	ADP
ejpam-5431	41	11	b	b	NOUN
ejpam-5431	41	12	-	-	PUNCT
ejpam-5431	41	13	metric	metric	ADJ
ejpam-5431	41	14	spaces	space	NOUN
ejpam-5431	41	15	:	:	PUNCT
ejpam-5431	41	16	this	this	DET
ejpam-5431	41	17	line	line	NOUN
ejpam-5431	41	18	of	of	ADP
ejpam-5431	41	19	inquiry	inquiry	NOUN
ejpam-5431	41	20	was	be	AUX
ejpam-5431	41	21	initiated	initiate	VERB
ejpam-5431	41	22	by	by	ADP
ejpam-5431	41	23	bakhtin	bakhtin	NOUN
ejpam-5431	41	24	[	[	X
ejpam-5431	41	25	5	5	NUM
ejpam-5431	41	26	]	]	PUNCT
ejpam-5431	41	27	and	and	CCONJ
ejpam-5431	41	28	bourbaki	bourbaki	VERB
ejpam-5431	41	29	[	[	X
ejpam-5431	41	30	7	7	NUM
ejpam-5431	41	31	]	]	PUNCT
ejpam-5431	41	32	.	.	PUNCT
ejpam-5431	42	1	czerwik	czerwik	PROPN
ejpam-5431	43	1	[	[	X
ejpam-5431	43	2	8	8	NUM
ejpam-5431	43	3	]	]	PUNCT
ejpam-5431	43	4	further	far	ADV
ejpam-5431	43	5	contributed	contribute	VERB
ejpam-5431	43	6	to	to	ADP
ejpam-5431	43	7	this	this	DET
ejpam-5431	43	8	area	area	NOUN
ejpam-5431	43	9	by	by	ADP
ejpam-5431	43	10	introducing	introduce	VERB
ejpam-5431	43	11	a	a	DET
ejpam-5431	43	12	concept	concept	NOUN
ejpam-5431	43	13	that	that	PRON
ejpam-5431	43	14	relaxes	relax	VERB
ejpam-5431	43	15	the	the	DET
ejpam-5431	43	16	constraints	constraint	NOUN
ejpam-5431	43	17	of	of	ADP
ejpam-5431	43	18	the	the	DET
ejpam-5431	43	19	traditional	traditional	ADJ
ejpam-5431	43	20	triangle	triangle	NOUN
ejpam-5431	43	21	inequality	inequality	NOUN
ejpam-5431	43	22	and	and	CCONJ
ejpam-5431	43	23	formally	formally	ADV
ejpam-5431	43	24	defined	define	VERB
ejpam-5431	43	25	b	b	X
ejpam-5431	43	26	-	-	PUNCT
ejpam-5431	43	27	mss	mss	NOUN
ejpam-5431	43	28	to	to	PART
ejpam-5431	43	29	enhance	enhance	VERB
ejpam-5431	43	30	the	the	DET
ejpam-5431	43	31	banach	banach	ADV
ejpam-5431	43	32	fixed	fix	VERB
ejpam-5431	43	33	point	point	NOUN
ejpam-5431	43	34	(	(	PUNCT
ejpam-5431	43	35	fp	fp	X
ejpam-5431	43	36	)	)	PUNCT
ejpam-5431	43	37	theorem	theorem	NOUN
ejpam-5431	43	38	.	.	PUNCT
ejpam-5431	44	1	since	since	SCONJ
ejpam-5431	44	2	then	then	ADV
ejpam-5431	44	3	,	,	PUNCT
ejpam-5431	44	4	n.	n.	PROPN
ejpam-5431	44	5	saleem	saleem	PROPN
ejpam-5431	44	6	et	et	PROPN
ejpam-5431	44	7	al	al	PROPN
ejpam-5431	44	8	.	.	PUNCT
ejpam-5431	44	9	/	/	SYM
ejpam-5431	44	10	eur	eur	PROPN
ejpam-5431	44	11	.	.	PUNCT
ejpam-5431	45	1	j.	j.	PROPN
ejpam-5431	45	2	pure	pure	PROPN
ejpam-5431	45	3	appl	appl	PROPN
ejpam-5431	45	4	.	.	PROPN
ejpam-5431	45	5	math	math	PROPN
ejpam-5431	45	6	,	,	PUNCT
ejpam-5431	45	7	17	17	NUM
ejpam-5431	45	8	(	(	PUNCT
ejpam-5431	45	9	4	4	NUM
ejpam-5431	45	10	)	)	PUNCT
ejpam-5431	45	11	(	(	PUNCT
ejpam-5431	45	12	2024	2024	NUM
ejpam-5431	45	13	)	)	PUNCT
ejpam-5431	45	14	,	,	PUNCT
ejpam-5431	45	15	3304	3304	NUM
ejpam-5431	45	16	-	-	SYM
ejpam-5431	45	17	3335	3335	NUM
ejpam-5431	45	18	3306	3306	NUM
ejpam-5431	45	19	there	there	PRON
ejpam-5431	45	20	has	have	AUX
ejpam-5431	45	21	been	be	AUX
ejpam-5431	45	22	a	a	DET
ejpam-5431	45	23	proliferation	proliferation	NOUN
ejpam-5431	45	24	of	of	ADP
ejpam-5431	45	25	research	research	NOUN
ejpam-5431	45	26	papers	paper	NOUN
ejpam-5431	45	27	examining	examine	VERB
ejpam-5431	45	28	single	single	ADV
ejpam-5431	45	29	-	-	PUNCT
ejpam-5431	45	30	valued	value	VERB
ejpam-5431	45	31	and	and	CCONJ
ejpam-5431	45	32	multi	multi	ADJ
ejpam-5431	45	33	-	-	ADJ
ejpam-5431	45	34	valued	value	VERB
ejpam-5431	45	35	operators	operator	NOUN
ejpam-5431	45	36	within	within	ADP
ejpam-5431	45	37	b	b	PROPN
ejpam-5431	45	38	-	-	PUNCT
ejpam-5431	45	39	mss	mss	NOUN
ejpam-5431	45	40	,	,	PUNCT
ejpam-5431	45	41	often	often	ADV
ejpam-5431	45	42	delving	delve	VERB
ejpam-5431	45	43	into	into	ADP
ejpam-5431	45	44	fp	fp	ADJ
ejpam-5431	45	45	theory	theory	NOUN
ejpam-5431	45	46	or	or	CCONJ
ejpam-5431	45	47	the	the	DET
ejpam-5431	45	48	variational	variational	ADJ
ejpam-5431	45	49	principle	principle	NOUN
ejpam-5431	45	50	(	(	PUNCT
ejpam-5431	45	51	refer	refer	VERB
ejpam-5431	45	52	to	to	ADP
ejpam-5431	45	53	[	[	X
ejpam-5431	45	54	1	1	NUM
ejpam-5431	45	55	,	,	PUNCT
ejpam-5431	45	56	9	9	NUM
ejpam-5431	45	57	,	,	PUNCT
ejpam-5431	45	58	10	10	NUM
ejpam-5431	45	59	,	,	PUNCT
ejpam-5431	45	60	12	12	NUM
ejpam-5431	45	61	,	,	PUNCT
ejpam-5431	45	62	22	22	NUM
ejpam-5431	45	63	]	]	PUNCT
ejpam-5431	45	64	)	)	PUNCT
ejpam-5431	45	65	.	.	PUNCT
ejpam-5431	46	1	the	the	DET
ejpam-5431	46	2	introduction	introduction	NOUN
ejpam-5431	46	3	of	of	ADP
ejpam-5431	46	4	γ	γ	NOUN
ejpam-5431	46	5	-	-	PUNCT
ejpam-5431	46	6	admissibility	admissibility	NOUN
ejpam-5431	46	7	has	have	AUX
ejpam-5431	46	8	played	play	VERB
ejpam-5431	46	9	a	a	DET
ejpam-5431	46	10	key	key	ADJ
ejpam-5431	46	11	role	role	NOUN
ejpam-5431	46	12	in	in	ADP
ejpam-5431	46	13	extending	extend	VERB
ejpam-5431	46	14	fixed	fix	VERB
ejpam-5431	46	15	point	point	NOUN
ejpam-5431	46	16	theory	theory	NOUN
ejpam-5431	46	17	to	to	ADP
ejpam-5431	46	18	more	more	ADJ
ejpam-5431	46	19	complex	complex	ADJ
ejpam-5431	46	20	spaces	space	NOUN
ejpam-5431	46	21	and	and	CCONJ
ejpam-5431	46	22	functions	function	NOUN
ejpam-5431	46	23	.	.	PUNCT
ejpam-5431	47	1	it	it	PRON
ejpam-5431	47	2	has	have	AUX
ejpam-5431	47	3	been	be	AUX
ejpam-5431	47	4	particularly	particularly	ADV
ejpam-5431	47	5	useful	useful	ADJ
ejpam-5431	47	6	in	in	ADP
ejpam-5431	47	7	the	the	DET
ejpam-5431	47	8	study	study	NOUN
ejpam-5431	47	9	of	of	ADP
ejpam-5431	47	10	non	non	ADJ
ejpam-5431	47	11	linear	linear	PROPN
ejpam-5431	47	12	analysis	analysis	NOUN
ejpam-5431	47	13	,	,	PUNCT
ejpam-5431	47	14	multi	multi	X
ejpam-5431	47	15	valued	value	VERB
ejpam-5431	47	16	mappings	mapping	NOUN
ejpam-5431	47	17	,	,	PUNCT
ejpam-5431	47	18	dynamic	dynamic	ADJ
ejpam-5431	47	19	system	system	NOUN
ejpam-5431	47	20	and	and	CCONJ
ejpam-5431	47	21	generalized	generalize	VERB
ejpam-5431	47	22	metric	metric	ADJ
ejpam-5431	47	23	spaces	space	NOUN
ejpam-5431	47	24	.	.	PUNCT
ejpam-5431	48	1	several	several	ADJ
ejpam-5431	48	2	researchers	researcher	NOUN
ejpam-5431	48	3	have	have	AUX
ejpam-5431	48	4	contributed	contribute	VERB
ejpam-5431	48	5	to	to	ADP
ejpam-5431	48	6	the	the	DET
ejpam-5431	48	7	development	development	NOUN
ejpam-5431	48	8	of	of	ADP
ejpam-5431	48	9	fixed	fix	VERB
ejpam-5431	48	10	point	point	NOUN
ejpam-5431	48	11	theorems	theorem	NOUN
ejpam-5431	48	12	involving	involve	VERB
ejpam-5431	48	13	beta	beta	ADJ
ejpam-5431	48	14	admissibility	admissibility	NOUN
ejpam-5431	48	15	.	.	PUNCT
ejpam-5431	49	1	samet	samet	PROPN
ejpam-5431	49	2	et	et	PROPN
ejpam-5431	49	3	al	al	PROPN
ejpam-5431	49	4	.	.	PUNCT
ejpam-5431	50	1	(	(	PUNCT
ejpam-5431	50	2	2012)[25	2012)[25	NOUN
ejpam-5431	50	3	]	]	X
ejpam-5431	50	4	explored	explore	VERB
ejpam-5431	50	5	fixed	fix	VERB
ejpam-5431	50	6	point	point	NOUN
ejpam-5431	50	7	theorems	theorem	NOUN
ejpam-5431	50	8	for	for	ADP
ejpam-5431	50	9	single	single	ADJ
ejpam-5431	50	10	and	and	CCONJ
ejpam-5431	50	11	multi	multi	ADJ
ejpam-5431	50	12	-	-	ADJ
ejpam-5431	50	13	valued	value	VERB
ejpam-5431	50	14	mappings	mapping	NOUN
ejpam-5431	50	15	in	in	ADP
ejpam-5431	50	16	spaces	space	NOUN
ejpam-5431	50	17	where	where	SCONJ
ejpam-5431	50	18	γ	γ	NOUN
ejpam-5431	50	19	-	-	PUNCT
ejpam-5431	50	20	admissibility	admissibility	NOUN
ejpam-5431	50	21	is	be	AUX
ejpam-5431	50	22	assumed	assume	VERB
ejpam-5431	50	23	,	,	PUNCT
ejpam-5431	50	24	contributing	contribute	VERB
ejpam-5431	50	25	to	to	ADP
ejpam-5431	50	26	the	the	DET
ejpam-5431	50	27	generalization	generalization	NOUN
ejpam-5431	50	28	of	of	ADP
ejpam-5431	50	29	classical	classical	ADJ
ejpam-5431	50	30	fixed	fix	VERB
ejpam-5431	50	31	point	point	NOUN
ejpam-5431	50	32	results	result	NOUN
ejpam-5431	50	33	.	.	PUNCT
ejpam-5431	51	1	rhoades	rhoade	NOUN
ejpam-5431	51	2	[	[	X
ejpam-5431	51	3	23	23	NUM
ejpam-5431	51	4	]	]	PUNCT
ejpam-5431	51	5	worked	work	VERB
ejpam-5431	51	6	on	on	ADP
ejpam-5431	51	7	extending	extend	VERB
ejpam-5431	51	8	fixed	fix	VERB
ejpam-5431	51	9	point	point	NOUN
ejpam-5431	51	10	theorems	theorem	NOUN
ejpam-5431	51	11	using	use	VERB
ejpam-5431	51	12	γ	γ	NOUN
ejpam-5431	51	13	-	-	NOUN
ejpam-5431	51	14	admissibility	admissibility	NOUN
ejpam-5431	51	15	in	in	ADP
ejpam-5431	51	16	partially	partially	ADV
ejpam-5431	51	17	ordered	order	VERB
ejpam-5431	51	18	spaces	space	NOUN
ejpam-5431	51	19	,	,	PUNCT
ejpam-5431	51	20	showing	show	VERB
ejpam-5431	51	21	how	how	SCONJ
ejpam-5431	51	22	this	this	DET
ejpam-5431	51	23	concept	concept	NOUN
ejpam-5431	51	24	could	could	AUX
ejpam-5431	51	25	be	be	AUX
ejpam-5431	51	26	applied	apply	VERB
ejpam-5431	51	27	to	to	ADP
ejpam-5431	51	28	more	more	ADV
ejpam-5431	51	29	structured	structured	ADJ
ejpam-5431	51	30	settings	setting	NOUN
ejpam-5431	51	31	.	.	PUNCT
ejpam-5431	52	1	the	the	DET
ejpam-5431	52	2	concept	concept	NOUN
ejpam-5431	52	3	of	of	ADP
ejpam-5431	52	4	γ	γ	PROPN
ejpam-5431	52	5	-	-	PUNCT
ejpam-5431	52	6	admissibility	admissibility	NOUN
ejpam-5431	52	7	serves	serve	VERB
ejpam-5431	52	8	as	as	ADP
ejpam-5431	52	9	a	a	DET
ejpam-5431	52	10	powerful	powerful	ADJ
ejpam-5431	52	11	generalization	generalization	NOUN
ejpam-5431	52	12	in	in	ADP
ejpam-5431	52	13	fixed	fix	VERB
ejpam-5431	52	14	point	point	NOUN
ejpam-5431	52	15	theory	theory	NOUN
ejpam-5431	52	16	,	,	PUNCT
ejpam-5431	52	17	allowing	allow	VERB
ejpam-5431	52	18	for	for	ADP
ejpam-5431	52	19	the	the	DET
ejpam-5431	52	20	study	study	NOUN
ejpam-5431	52	21	of	of	ADP
ejpam-5431	52	22	mappings	mapping	NOUN
ejpam-5431	52	23	that	that	PRON
ejpam-5431	52	24	do	do	AUX
ejpam-5431	52	25	not	not	PART
ejpam-5431	52	26	necessarily	necessarily	ADV
ejpam-5431	52	27	satisfy	satisfy	VERB
ejpam-5431	52	28	the	the	DET
ejpam-5431	52	29	strict	strict	ADJ
ejpam-5431	52	30	contractive	contractive	ADJ
ejpam-5431	52	31	conditions	condition	NOUN
ejpam-5431	52	32	required	require	VERB
ejpam-5431	52	33	in	in	ADP
ejpam-5431	52	34	classical	classical	ADJ
ejpam-5431	52	35	fixed	fix	VERB
ejpam-5431	52	36	point	point	NOUN
ejpam-5431	52	37	theorems	theorem	NOUN
ejpam-5431	52	38	.	.	PUNCT
ejpam-5431	53	1	by	by	ADP
ejpam-5431	53	2	introducing	introduce	VERB
ejpam-5431	53	3	a	a	DET
ejpam-5431	53	4	function	function	NOUN
ejpam-5431	53	5	γ	γ	NOUN
ejpam-5431	53	6	that	that	PRON
ejpam-5431	53	7	controls	control	VERB
ejpam-5431	53	8	the	the	DET
ejpam-5431	53	9	behavior	behavior	NOUN
ejpam-5431	53	10	of	of	ADP
ejpam-5431	53	11	the	the	DET
ejpam-5431	53	12	mapping	mapping	NOUN
ejpam-5431	53	13	,	,	PUNCT
ejpam-5431	53	14	γ	γ	PROPN
ejpam-5431	53	15	-	-	PUNCT
ejpam-5431	53	16	admissibility	admissibility	NOUN
ejpam-5431	53	17	provides	provide	VERB
ejpam-5431	53	18	the	the	DET
ejpam-5431	53	19	flexibility	flexibility	NOUN
ejpam-5431	53	20	needed	need	VERB
ejpam-5431	53	21	to	to	PART
ejpam-5431	53	22	extend	extend	VERB
ejpam-5431	53	23	fixed	fix	VERB
ejpam-5431	53	24	point	point	NOUN
ejpam-5431	53	25	results	result	NOUN
ejpam-5431	53	26	to	to	ADP
ejpam-5431	53	27	broader	broad	ADJ
ejpam-5431	53	28	classes	class	NOUN
ejpam-5431	53	29	of	of	ADP
ejpam-5431	53	30	spaces	space	NOUN
ejpam-5431	53	31	and	and	CCONJ
ejpam-5431	53	32	functions	function	NOUN
ejpam-5431	53	33	.	.	PUNCT
ejpam-5431	54	1	this	this	PRON
ejpam-5431	54	2	has	have	AUX
ejpam-5431	54	3	led	lead	VERB
ejpam-5431	54	4	to	to	ADP
ejpam-5431	54	5	significant	significant	ADJ
ejpam-5431	54	6	advances	advance	NOUN
ejpam-5431	54	7	in	in	ADP
ejpam-5431	54	8	nonlinear	nonlinear	ADJ
ejpam-5431	54	9	analysis	analysis	NOUN
ejpam-5431	54	10	,	,	PUNCT
ejpam-5431	54	11	dynamic	dynamic	ADJ
ejpam-5431	54	12	systems	system	NOUN
ejpam-5431	54	13	,	,	PUNCT
ejpam-5431	54	14	and	and	CCONJ
ejpam-5431	54	15	the	the	DET
ejpam-5431	54	16	study	study	NOUN
ejpam-5431	54	17	of	of	ADP
ejpam-5431	54	18	generalized	generalized	ADJ
ejpam-5431	54	19	metric	metric	ADJ
ejpam-5431	54	20	spaces	space	NOUN
ejpam-5431	54	21	.	.	PUNCT
ejpam-5431	55	1	the	the	DET
ejpam-5431	55	2	foundational	foundational	ADJ
ejpam-5431	55	3	work	work	NOUN
ejpam-5431	55	4	on	on	ADP
ejpam-5431	55	5	γadmissibility	γadmissibility	NOUN
ejpam-5431	55	6	continues	continue	VERB
ejpam-5431	55	7	to	to	PART
ejpam-5431	55	8	influence	influence	VERB
ejpam-5431	55	9	ongoing	ongoing	ADJ
ejpam-5431	55	10	research	research	NOUN
ejpam-5431	55	11	in	in	ADP
ejpam-5431	55	12	applied	applied	ADJ
ejpam-5431	55	13	mathematics	mathematic	NOUN
ejpam-5431	55	14	,	,	PUNCT
ejpam-5431	55	15	offering	offer	VERB
ejpam-5431	55	16	new	new	ADJ
ejpam-5431	55	17	tools	tool	NOUN
ejpam-5431	55	18	for	for	ADP
ejpam-5431	55	19	solving	solve	VERB
ejpam-5431	55	20	complex	complex	ADJ
ejpam-5431	55	21	problems	problem	NOUN
ejpam-5431	55	22	in	in	ADP
ejpam-5431	55	23	fields	field	NOUN
ejpam-5431	55	24	like	like	ADP
ejpam-5431	55	25	optimization	optimization	NOUN
ejpam-5431	55	26	,	,	PUNCT
ejpam-5431	55	27	economics	economic	NOUN
ejpam-5431	55	28	,	,	PUNCT
ejpam-5431	55	29	and	and	CCONJ
ejpam-5431	55	30	mathematical	mathematical	ADJ
ejpam-5431	55	31	modeling	modeling	NOUN
ejpam-5431	55	32	.	.	PUNCT
ejpam-5431	56	1	in	in	ADP
ejpam-5431	56	2	a	a	DET
ejpam-5431	56	3	related	related	ADJ
ejpam-5431	56	4	vein	vein	NOUN
ejpam-5431	56	5	,	,	PUNCT
ejpam-5431	56	6	the	the	DET
ejpam-5431	56	7	exploration	exploration	NOUN
ejpam-5431	56	8	of	of	ADP
ejpam-5431	56	9	fixed	fix	VERB
ejpam-5431	56	10	points	point	NOUN
ejpam-5431	56	11	arising	arise	VERB
ejpam-5431	56	12	from	from	ADP
ejpam-5431	56	13	hybrid	hybrid	ADJ
ejpam-5431	56	14	contractions	contraction	NOUN
ejpam-5431	56	15	represents	represent	VERB
ejpam-5431	56	16	a	a	DET
ejpam-5431	56	17	burgeoning	burgeon	VERB
ejpam-5431	56	18	area	area	NOUN
ejpam-5431	56	19	of	of	ADP
ejpam-5431	56	20	research	research	NOUN
ejpam-5431	56	21	within	within	ADP
ejpam-5431	56	22	fixed	fix	VERB
ejpam-5431	56	23	point	point	NOUN
ejpam-5431	56	24	theory	theory	NOUN
ejpam-5431	56	25	.	.	PUNCT
ejpam-5431	57	1	recent	recent	ADJ
ejpam-5431	57	2	contributions	contribution	NOUN
ejpam-5431	57	3	[	[	X
ejpam-5431	57	4	18	18	NUM
ejpam-5431	57	5	]	]	PUNCT
ejpam-5431	57	6	have	have	AUX
ejpam-5431	57	7	provided	provide	VERB
ejpam-5431	57	8	criteria	criterion	NOUN
ejpam-5431	57	9	for	for	ADP
ejpam-5431	57	10	establishing	establish	VERB
ejpam-5431	57	11	the	the	DET
ejpam-5431	57	12	existence	existence	NOUN
ejpam-5431	57	13	of	of	ADP
ejpam-5431	57	14	intuitionistic	intuitionistic	ADJ
ejpam-5431	57	15	fuzzy	fuzzy	ADJ
ejpam-5431	57	16	fixed	fix	VERB
ejpam-5431	57	17	points	point	NOUN
ejpam-5431	57	18	(	(	PUNCT
ejpam-5431	57	19	iffps	iffps	NOUN
ejpam-5431	57	20	)	)	PUNCT
ejpam-5431	57	21	within	within	ADP
ejpam-5431	57	22	b	b	NOUN
ejpam-5431	57	23	-	-	ADJ
ejpam-5431	57	24	metric	metric	ADJ
ejpam-5431	57	25	spaces	space	NOUN
ejpam-5431	57	26	,	,	PUNCT
ejpam-5431	57	27	focusing	focus	VERB
ejpam-5431	57	28	on	on	ADP
ejpam-5431	57	29	admissible	admissible	ADJ
ejpam-5431	57	30	hybrid	hybrid	ADJ
ejpam-5431	57	31	intuitionistic	intuitionistic	ADJ
ejpam-5431	57	32	fuzzy	fuzzy	ADJ
ejpam-5431	57	33	(	(	PUNCT
ejpam-5431	57	34	ahif	ahif	PROPN
ejpam-5431	57	35	)	)	PUNCT
ejpam-5431	57	36	z	z	NOUN
ejpam-5431	57	37	-	-	PUNCT
ejpam-5431	57	38	contractions	contraction	NOUN
ejpam-5431	57	39	and	and	CCONJ
ejpam-5431	57	40	hif	hif	PROPN
ejpam-5431	57	41	z	z	PROPN
ejpam-5431	57	42	-	-	PUNCT
ejpam-5431	57	43	contractions	contraction	NOUN
ejpam-5431	57	44	.	.	PUNCT
ejpam-5431	58	1	this	this	DET
ejpam-5431	58	2	article	article	NOUN
ejpam-5431	58	3	introduces	introduce	VERB
ejpam-5431	58	4	a	a	DET
ejpam-5431	58	5	modified	modify	VERB
ejpam-5431	58	6	form	form	NOUN
ejpam-5431	58	7	of	of	ADP
ejpam-5431	58	8	an	an	DET
ejpam-5431	58	9	admissible	admissible	ADJ
ejpam-5431	58	10	hybrid	hybrid	ADJ
ejpam-5431	58	11	intuitionistic	intuitionistic	ADJ
ejpam-5431	58	12	fuzzy	fuzzy	ADJ
ejpam-5431	58	13	z	z	NOUN
ejpam-5431	58	14	-	-	PUNCT
ejpam-5431	58	15	contraction	contraction	NOUN
ejpam-5431	58	16	within	within	ADP
ejpam-5431	58	17	the	the	DET
ejpam-5431	58	18	framework	framework	NOUN
ejpam-5431	58	19	of	of	ADP
ejpam-5431	58	20	ifs	ifs	PROPN
ejpam-5431	58	21	-	-	PUNCT
ejpam-5431	58	22	valued	value	VERB
ejpam-5431	58	23	mappings	mapping	NOUN
ejpam-5431	58	24	in	in	ADP
ejpam-5431	58	25	extended	extended	ADJ
ejpam-5431	58	26	b	b	X
ejpam-5431	58	27	-	-	ADJ
ejpam-5431	58	28	metric	metric	ADJ
ejpam-5431	58	29	spaces	space	NOUN
ejpam-5431	58	30	,	,	PUNCT
ejpam-5431	58	31	providing	provide	VERB
ejpam-5431	58	32	sufficient	sufficient	ADJ
ejpam-5431	58	33	conditions	condition	NOUN
ejpam-5431	58	34	for	for	ADP
ejpam-5431	58	35	intuitionistic	intuitionistic	ADJ
ejpam-5431	58	36	fuzzy	fuzzy	ADJ
ejpam-5431	58	37	fixed	fix	VERB
ejpam-5431	58	38	point	point	NOUN
ejpam-5431	58	39	(	(	PUNCT
ejpam-5431	58	40	iffp	iffp	NOUN
ejpam-5431	58	41	)	)	PUNCT
ejpam-5431	58	42	results	result	NOUN
ejpam-5431	58	43	.	.	PUNCT
ejpam-5431	59	1	several	several	ADJ
ejpam-5431	59	2	special	special	ADJ
ejpam-5431	59	3	cases	case	NOUN
ejpam-5431	59	4	of	of	ADP
ejpam-5431	59	5	the	the	DET
ejpam-5431	59	6	main	main	ADJ
ejpam-5431	59	7	result	result	NOUN
ejpam-5431	59	8	are	be	AUX
ejpam-5431	59	9	discussed	discuss	VERB
ejpam-5431	59	10	through	through	ADP
ejpam-5431	59	11	corollaries	corollary	NOUN
ejpam-5431	59	12	.	.	PUNCT
ejpam-5431	60	1	the	the	DET
ejpam-5431	60	2	application	application	NOUN
ejpam-5431	60	3	of	of	ADP
ejpam-5431	60	4	these	these	DET
ejpam-5431	60	5	findings	finding	NOUN
ejpam-5431	60	6	pertains	pertain	NOUN
ejpam-5431	60	7	to	to	ADP
ejpam-5431	60	8	the	the	DET
ejpam-5431	60	9	iffp	iffp	PROPN
ejpam-5431	60	10	result	result	NOUN
ejpam-5431	60	11	in	in	ADP
ejpam-5431	60	12	the	the	DET
ejpam-5431	60	13	context	context	NOUN
ejpam-5431	60	14	of	of	ADP
ejpam-5431	60	15	an	an	DET
ejpam-5431	60	16	orderes	ordere	NOUN
ejpam-5431	60	17	b	b	NOUN
ejpam-5431	60	18	-	-	PUNCT
ejpam-5431	60	19	metric	metric	ADJ
ejpam-5431	60	20	space	space	NOUN
ejpam-5431	60	21	.	.	PUNCT
ejpam-5431	61	1	each	each	DET
ejpam-5431	61	2	result	result	NOUN
ejpam-5431	61	3	is	be	AUX
ejpam-5431	61	4	supported	support	VERB
ejpam-5431	61	5	by	by	ADP
ejpam-5431	61	6	examples	example	NOUN
ejpam-5431	61	7	to	to	PART
ejpam-5431	61	8	validate	validate	VERB
ejpam-5431	61	9	the	the	DET
ejpam-5431	61	10	hypotheses	hypothesis	NOUN
ejpam-5431	61	11	.	.	PUNCT
ejpam-5431	62	1	to	to	ADP
ejpam-5431	62	2	the	the	DET
ejpam-5431	62	3	best	good	ADJ
ejpam-5431	62	4	of	of	ADP
ejpam-5431	62	5	our	our	PRON
ejpam-5431	62	6	knowledge	knowledge	NOUN
ejpam-5431	62	7	,	,	PUNCT
ejpam-5431	62	8	common	common	ADJ
ejpam-5431	62	9	fixed	fix	VERB
ejpam-5431	62	10	point	point	NOUN
ejpam-5431	62	11	theorems	theorem	NOUN
ejpam-5431	62	12	within	within	ADP
ejpam-5431	62	13	the	the	DET
ejpam-5431	62	14	framework	framework	NOUN
ejpam-5431	62	15	of	of	ADP
ejpam-5431	62	16	ifss	ifss	ADJ
ejpam-5431	62	17	utilizing	utilize	VERB
ejpam-5431	62	18	simulation	simulation	NOUN
ejpam-5431	62	19	functions	function	NOUN
ejpam-5431	62	20	have	have	AUX
ejpam-5431	62	21	not	not	PART
ejpam-5431	62	22	yet	yet	ADV
ejpam-5431	62	23	been	be	AUX
ejpam-5431	62	24	explored	explore	VERB
ejpam-5431	62	25	,	,	PUNCT
ejpam-5431	62	26	making	make	VERB
ejpam-5431	62	27	the	the	DET
ejpam-5431	62	28	concepts	concept	NOUN
ejpam-5431	62	29	presented	present	VERB
ejpam-5431	62	30	here	here	ADV
ejpam-5431	62	31	novel	novel	NOUN
ejpam-5431	62	32	.	.	PUNCT
ejpam-5431	63	1	2	2	X
ejpam-5431	63	2	.	.	X
ejpam-5431	63	3	preliminaries	preliminary	NOUN
ejpam-5431	63	4	the	the	DET
ejpam-5431	63	5	collections	collection	NOUN
ejpam-5431	63	6	of	of	ADP
ejpam-5431	63	7	natural	natural	ADJ
ejpam-5431	63	8	,	,	PUNCT
ejpam-5431	63	9	non	non	ADJ
ejpam-5431	63	10	-	-	ADJ
ejpam-5431	63	11	negative	negative	ADJ
ejpam-5431	63	12	real	real	ADJ
ejpam-5431	63	13	and	and	CCONJ
ejpam-5431	63	14	real	real	ADJ
ejpam-5431	63	15	numbers	number	NOUN
ejpam-5431	63	16	are	be	AUX
ejpam-5431	63	17	indicated	indicate	VERB
ejpam-5431	63	18	by	by	ADP
ejpam-5431	63	19	n	n	CCONJ
ejpam-5431	63	20	,	,	PUNCT
ejpam-5431	63	21	r+	r+	X
ejpam-5431	63	22	,	,	PUNCT
ejpam-5431	63	23	and	and	CCONJ
ejpam-5431	63	24	r	r	NOUN
ejpam-5431	63	25	,	,	PUNCT
ejpam-5431	63	26	respectively	respectively	ADV
ejpam-5431	63	27	.	.	PUNCT
ejpam-5431	64	1	definition	definition	NOUN
ejpam-5431	64	2	1	1	NUM
ejpam-5431	64	3	.	.	PUNCT
ejpam-5431	65	1	[	[	X
ejpam-5431	65	2	8	8	NUM
ejpam-5431	65	3	]	]	PUNCT
ejpam-5431	65	4	assume	assume	VERB
ejpam-5431	65	5	a	a	DET
ejpam-5431	65	6	set	set	NOUN
ejpam-5431	65	7	x	x	PUNCT
ejpam-5431	65	8	that	that	PRON
ejpam-5431	65	9	is	be	AUX
ejpam-5431	65	10	not	not	PART
ejpam-5431	65	11	empty	empty	ADJ
ejpam-5431	65	12	and	and	CCONJ
ejpam-5431	65	13	h	h	PRON
ejpam-5431	65	14	≥	≥	NOUN
ejpam-5431	65	15	1	1	NUM
ejpam-5431	65	16	is	be	AUX
ejpam-5431	65	17	a	a	DET
ejpam-5431	65	18	constant	constant	ADJ
ejpam-5431	65	19	.	.	PUNCT
ejpam-5431	65	20	suppose	suppose	VERB
ejpam-5431	65	21	that	that	SCONJ
ejpam-5431	65	22	the	the	DET
ejpam-5431	65	23	mapping	mapping	NOUN
ejpam-5431	65	24	δ	δ	NOUN
ejpam-5431	65	25	:	:	PUNCT
ejpam-5431	65	26	x	x	X
ejpam-5431	65	27	×x	×x	ADP
ejpam-5431	65	28	→	→	PUNCT
ejpam-5431	65	29	r+	r+	NOUN
ejpam-5431	65	30	meets	meet	VERB
ejpam-5431	65	31	the	the	DET
ejpam-5431	65	32	criteria	criterion	NOUN
ejpam-5431	65	33	below	below	ADP
ejpam-5431	65	34	for	for	ADP
ejpam-5431	65	35	all	all	DET
ejpam-5431	65	36	σ	σ	NOUN
ejpam-5431	65	37	,	,	PUNCT
ejpam-5431	65	38	τ,ϖ	τ,ϖ	PROPN
ejpam-5431	65	39	∈	∈	PROPN
ejpam-5431	65	40	x	x	X
ejpam-5431	65	41	;	;	PUNCT
ejpam-5431	65	42	(	(	PUNCT
ejpam-5431	65	43	i	i	NOUN
ejpam-5431	65	44	)	)	PUNCT
ejpam-5431	65	45	δ(σ	δ(σ	PROPN
ejpam-5431	65	46	,	,	PUNCT
ejpam-5431	65	47	τ	τ	X
ejpam-5431	65	48	)	)	PUNCT
ejpam-5431	66	1	=	=	SYM
ejpam-5431	66	2	0	0	PUNCT
ejpam-5431	67	1	if	if	SCONJ
ejpam-5431	67	2	and	and	CCONJ
ejpam-5431	67	3	only	only	ADV
ejpam-5431	67	4	if	if	SCONJ
ejpam-5431	67	5	σ	σ	PROPN
ejpam-5431	67	6	=	=	SYM
ejpam-5431	67	7	τ	τ	PROPN
ejpam-5431	67	8	;	;	PUNCT
ejpam-5431	67	9	n.	n.	PROPN
ejpam-5431	67	10	saleem	saleem	PROPN
ejpam-5431	67	11	et	et	PROPN
ejpam-5431	67	12	al	al	PROPN
ejpam-5431	67	13	.	.	PUNCT
ejpam-5431	67	14	/	/	SYM
ejpam-5431	67	15	eur	eur	PROPN
ejpam-5431	67	16	.	.	PUNCT
ejpam-5431	68	1	j.	j.	PROPN
ejpam-5431	68	2	pure	pure	PROPN
ejpam-5431	68	3	appl	appl	PROPN
ejpam-5431	68	4	.	.	PROPN
ejpam-5431	68	5	math	math	PROPN
ejpam-5431	68	6	,	,	PUNCT
ejpam-5431	68	7	17	17	NUM
ejpam-5431	68	8	(	(	PUNCT
ejpam-5431	68	9	4	4	NUM
ejpam-5431	68	10	)	)	PUNCT
ejpam-5431	68	11	(	(	PUNCT
ejpam-5431	68	12	2024	2024	NUM
ejpam-5431	68	13	)	)	PUNCT
ejpam-5431	68	14	,	,	PUNCT
ejpam-5431	68	15	3304	3304	NUM
ejpam-5431	68	16	-	-	SYM
ejpam-5431	68	17	3335	3335	NUM
ejpam-5431	68	18	3307	3307	NUM
ejpam-5431	68	19	(	(	PUNCT
ejpam-5431	68	20	ii	ii	NOUN
ejpam-5431	68	21	)	)	PUNCT
ejpam-5431	68	22	δ(σ	δ(σ	PROPN
ejpam-5431	68	23	,	,	PUNCT
ejpam-5431	68	24	τ	τ	X
ejpam-5431	68	25	)	)	PUNCT
ejpam-5431	68	26	=	=	SYM
ejpam-5431	68	27	δ(τ	δ(τ	PROPN
ejpam-5431	68	28	,	,	PUNCT
ejpam-5431	68	29	σ	σ	PROPN
ejpam-5431	68	30	)	)	PUNCT
ejpam-5431	68	31	;	;	PUNCT
ejpam-5431	68	32	(	(	PUNCT
ejpam-5431	68	33	iii	iii	X
ejpam-5431	68	34	)	)	PUNCT
ejpam-5431	68	35	δ(σ	δ(σ	PROPN
ejpam-5431	68	36	,	,	PUNCT
ejpam-5431	68	37	τ	τ	X
ejpam-5431	68	38	)	)	PUNCT
ejpam-5431	68	39	≤	≤	NOUN
ejpam-5431	68	40	h[δ(σ,ϖ	h[δ(σ,ϖ	PROPN
ejpam-5431	68	41	)	)	PUNCT
ejpam-5431	69	1	+	+	NUM
ejpam-5431	69	2	δ(ϖ	δ(ϖ	PROPN
ejpam-5431	69	3	,	,	PUNCT
ejpam-5431	69	4	τ	τ	PROPN
ejpam-5431	69	5	)	)	PUNCT
ejpam-5431	69	6	]	]	PUNCT
ejpam-5431	69	7	for	for	ADP
ejpam-5431	69	8	all	all	DET
ejpam-5431	69	9	σ	σ	PROPN
ejpam-5431	69	10	,	,	PUNCT
ejpam-5431	69	11	τ,ϖ	τ,ϖ	PROPN
ejpam-5431	69	12	∈	∈	PROPN
ejpam-5431	69	13	x.	x.	NOUN
ejpam-5431	69	14	then	then	ADV
ejpam-5431	69	15	,	,	PUNCT
ejpam-5431	69	16	the	the	DET
ejpam-5431	69	17	triplet	triplet	NOUN
ejpam-5431	69	18	(	(	PUNCT
ejpam-5431	69	19	x	x	NOUN
ejpam-5431	69	20	,	,	PUNCT
ejpam-5431	69	21	δ	δ	PROPN
ejpam-5431	69	22	,	,	PUNCT
ejpam-5431	69	23	h	h	NOUN
ejpam-5431	69	24	)	)	PUNCT
ejpam-5431	69	25	is	be	AUX
ejpam-5431	69	26	called	call	VERB
ejpam-5431	69	27	a	a	DET
ejpam-5431	69	28	b	b	PROPN
ejpam-5431	69	29	-	-	PUNCT
ejpam-5431	69	30	ms	ms	PROPN
ejpam-5431	69	31	.	.	PROPN
ejpam-5431	69	32	example	example	NOUN
ejpam-5431	70	1	2	2	NUM
ejpam-5431	70	2	.	.	PUNCT
ejpam-5431	71	1	let	let	VERB
ejpam-5431	71	2	x	x	SYM
ejpam-5431	71	3	=	=	PUNCT
ejpam-5431	71	4	lp(r	lp(r	X
ejpam-5431	71	5	)	)	PUNCT
ejpam-5431	71	6	with	with	ADP
ejpam-5431	71	7	0	0	NUM
ejpam-5431	71	8	<	<	X
ejpam-5431	71	9	p	p	X
ejpam-5431	71	10	<	<	X
ejpam-5431	71	11	1	1	NUM
ejpam-5431	71	12	,	,	PUNCT
ejpam-5431	71	13	where	where	SCONJ
ejpam-5431	71	14	lp(r	lp(r	PUNCT
ejpam-5431	71	15	)	)	PUNCT
ejpam-5431	71	16	=	=	SYM
ejpam-5431	71	17	{	{	PUNCT
ejpam-5431	71	18	σ	σ	NOUN
ejpam-5431	71	19	=	=	SYM
ejpam-5431	71	20	{	{	PUNCT
ejpam-5431	71	21	σn	σn	NOUN
ejpam-5431	71	22	}	}	PUNCT
ejpam-5431	71	23	⊂	⊂	NOUN
ejpam-5431	71	24	r	r	NOUN
ejpam-5431	71	25	:	:	PUNCT
ejpam-5431	71	26	∑+∞n=1|σn|p	∑+∞n=1|σn|p	NOUN
ejpam-5431	71	27	<	<	X
ejpam-5431	71	28	+	+	NOUN
ejpam-5431	71	29	∞	∞	NOUN
ejpam-5431	71	30	}	}	PUNCT
ejpam-5431	71	31	.	.	PUNCT
ejpam-5431	72	1	then	then	ADV
ejpam-5431	72	2	δ(σ	δ(σ	PROPN
ejpam-5431	72	3	,	,	PUNCT
ejpam-5431	72	4	τ	τ	X
ejpam-5431	72	5	)	)	PUNCT
ejpam-5431	72	6	=	=	NOUN
ejpam-5431	72	7	(	(	PUNCT
ejpam-5431	72	8	∑+∞	∑+∞	ADJ
ejpam-5431	72	9	n=1	n=1	PROPN
ejpam-5431	72	10	|σn	|σn	NUM
ejpam-5431	72	11	−	−	PROPN
ejpam-5431	72	12	yn|p	yn|p	NOUN
ejpam-5431	72	13	)	)	PUNCT
ejpam-5431	72	14	1	1	NUM
ejpam-5431	72	15	p	p	NOUN
ejpam-5431	72	16	is	be	AUX
ejpam-5431	72	17	a	a	DET
ejpam-5431	72	18	b	b	NOUN
ejpam-5431	72	19	-	-	PUNCT
ejpam-5431	72	20	ms	ms	NOUN
ejpam-5431	72	21	on	on	ADP
ejpam-5431	72	22	x	x	PUNCT
ejpam-5431	72	23	with	with	ADP
ejpam-5431	72	24	h	h	NOUN
ejpam-5431	72	25	=	=	SYM
ejpam-5431	72	26	2	2	NUM
ejpam-5431	72	27	1	1	NUM
ejpam-5431	72	28	p	p	NOUN
ejpam-5431	72	29	.	.	PUNCT
ejpam-5431	73	1	notice	notice	VERB
ejpam-5431	73	2	that	that	SCONJ
ejpam-5431	73	3	(	(	PUNCT
ejpam-5431	73	4	x	x	NOUN
ejpam-5431	73	5	,	,	PUNCT
ejpam-5431	73	6	δ	δ	PROPN
ejpam-5431	73	7	)	)	PUNCT
ejpam-5431	73	8	is	be	AUX
ejpam-5431	73	9	not	not	PART
ejpam-5431	73	10	a	a	DET
ejpam-5431	73	11	ms	ms	PROPN
ejpam-5431	73	12	.	.	PROPN
ejpam-5431	73	13	definition	definition	NOUN
ejpam-5431	73	14	3	3	NUM
ejpam-5431	73	15	.	.	PUNCT
ejpam-5431	74	1	[	[	X
ejpam-5431	74	2	6	6	NUM
ejpam-5431	74	3	]	]	PUNCT
ejpam-5431	74	4	let	let	VERB
ejpam-5431	74	5	(	(	PUNCT
ejpam-5431	74	6	x	x	NOUN
ejpam-5431	74	7	,	,	PUNCT
ejpam-5431	74	8	δ	δ	PROPN
ejpam-5431	74	9	,	,	PUNCT
ejpam-5431	74	10	h	h	NOUN
ejpam-5431	74	11	)	)	PUNCT
ejpam-5431	74	12	be	be	VERB
ejpam-5431	74	13	a	a	DET
ejpam-5431	74	14	b	b	PROPN
ejpam-5431	74	15	-	-	PUNCT
ejpam-5431	74	16	ms	ms	NOUN
ejpam-5431	74	17	.	.	PROPN
ejpam-5431	75	1	then	then	ADV
ejpam-5431	75	2	,	,	PUNCT
ejpam-5431	75	3	the	the	DET
ejpam-5431	75	4	subset	subset	NOUN
ejpam-5431	75	5	a	a	PRON
ejpam-5431	75	6	of	of	ADP
ejpam-5431	75	7	x	x	SYM
ejpam-5431	75	8	is	be	AUX
ejpam-5431	75	9	called	call	VERB
ejpam-5431	75	10	:	:	PUNCT
ejpam-5431	75	11	(	(	PUNCT
ejpam-5431	75	12	i	i	NOUN
ejpam-5431	75	13	)	)	PUNCT
ejpam-5431	75	14	compact	compact	ADJ
ejpam-5431	75	15	if	if	SCONJ
ejpam-5431	75	16	and	and	CCONJ
ejpam-5431	75	17	only	only	ADV
ejpam-5431	75	18	if	if	SCONJ
ejpam-5431	75	19	for	for	ADP
ejpam-5431	75	20	every	every	DET
ejpam-5431	75	21	sequence	sequence	NOUN
ejpam-5431	75	22	of	of	ADP
ejpam-5431	75	23	elements	element	NOUN
ejpam-5431	75	24	of	of	ADP
ejpam-5431	75	25	a	a	PRON
ejpam-5431	75	26	,	,	PUNCT
ejpam-5431	75	27	there	there	PRON
ejpam-5431	75	28	exists	exist	VERB
ejpam-5431	75	29	a	a	DET
ejpam-5431	75	30	subsequence	subsequence	NOUN
ejpam-5431	75	31	that	that	PRON
ejpam-5431	75	32	is	be	AUX
ejpam-5431	75	33	convergent	convergent	ADJ
ejpam-5431	75	34	to	to	ADP
ejpam-5431	75	35	an	an	DET
ejpam-5431	75	36	element	element	NOUN
ejpam-5431	75	37	of	of	ADP
ejpam-5431	75	38	a.	a.	PROPN
ejpam-5431	75	39	(	(	PUNCT
ejpam-5431	75	40	ii	ii	NOUN
ejpam-5431	75	41	)	)	PUNCT
ejpam-5431	75	42	closed	close	VERB
ejpam-5431	75	43	if	if	SCONJ
ejpam-5431	75	44	and	and	CCONJ
ejpam-5431	75	45	only	only	ADV
ejpam-5431	75	46	if	if	SCONJ
ejpam-5431	75	47	for	for	ADP
ejpam-5431	75	48	every	every	DET
ejpam-5431	75	49	sequence	sequence	NOUN
ejpam-5431	75	50	{	{	PUNCT
ejpam-5431	75	51	σn}n∈n	σn}n∈n	X
ejpam-5431	75	52	of	of	ADP
ejpam-5431	75	53	elements	element	NOUN
ejpam-5431	75	54	of	of	ADP
ejpam-5431	75	55	a	a	DET
ejpam-5431	75	56	converging	converging	NOUN
ejpam-5431	75	57	to	to	ADP
ejpam-5431	75	58	an	an	DET
ejpam-5431	75	59	element	element	NOUN
ejpam-5431	75	60	σ	σ	NOUN
ejpam-5431	75	61	,	,	PUNCT
ejpam-5431	75	62	we	we	PRON
ejpam-5431	75	63	have	have	VERB
ejpam-5431	75	64	σ	σ	PROPN
ejpam-5431	75	65	∈	∈	PROPN
ejpam-5431	75	66	a.	a.	NOUN
ejpam-5431	75	67	definition	definition	NOUN
ejpam-5431	75	68	4	4	NUM
ejpam-5431	75	69	.	.	PUNCT
ejpam-5431	76	1	[	[	X
ejpam-5431	76	2	19	19	NUM
ejpam-5431	76	3	]	]	PUNCT
ejpam-5431	76	4	a	a	DET
ejpam-5431	76	5	set	set	NOUN
ejpam-5431	76	6	a	a	PRON
ejpam-5431	76	7	,	,	PUNCT
ejpam-5431	76	8	containing	contain	VERB
ejpam-5431	76	9	one	one	NUM
ejpam-5431	76	10	or	or	CCONJ
ejpam-5431	76	11	more	more	ADJ
ejpam-5431	76	12	elements	element	NOUN
ejpam-5431	76	13	,	,	PUNCT
ejpam-5431	76	14	in	in	ADP
ejpam-5431	76	15	x	x	PROPN
ejpam-5431	76	16	is	be	AUX
ejpam-5431	76	17	called	call	VERB
ejpam-5431	76	18	proximal	proximal	ADJ
ejpam-5431	76	19	if	if	SCONJ
ejpam-5431	76	20	,	,	PUNCT
ejpam-5431	76	21	for	for	ADP
ejpam-5431	76	22	some	some	DET
ejpam-5431	76	23	σ	σ	NUM
ejpam-5431	76	24	∈	∈	PROPN
ejpam-5431	76	25	x	x	PRON
ejpam-5431	76	26	,	,	PUNCT
ejpam-5431	76	27	there	there	PRON
ejpam-5431	76	28	is	be	VERB
ejpam-5431	76	29	k	k	PROPN
ejpam-5431	76	30	∈	∈	PROPN
ejpam-5431	76	31	a	a	DET
ejpam-5431	76	32	such	such	ADJ
ejpam-5431	77	1	that	that	SCONJ
ejpam-5431	77	2	δ(σ	δ(σ	PROPN
ejpam-5431	77	3	,	,	PUNCT
ejpam-5431	77	4	k	k	NOUN
ejpam-5431	77	5	)	)	PUNCT
ejpam-5431	77	6	=	=	SYM
ejpam-5431	77	7	δ(σ	δ(σ	PROPN
ejpam-5431	77	8	,	,	PUNCT
ejpam-5431	77	9	a	a	PRON
ejpam-5431	77	10	)	)	PUNCT
ejpam-5431	77	11	.	.	PUNCT
ejpam-5431	77	12	denote	denote	VERB
ejpam-5431	77	13	by	by	ADP
ejpam-5431	77	14	n	n	PROPN
ejpam-5431	77	15	(	(	PUNCT
ejpam-5431	77	16	x	x	NOUN
ejpam-5431	77	17	)	)	PUNCT
ejpam-5431	77	18	,	,	PUNCT
ejpam-5431	77	19	cb(x	cb(x	NUM
ejpam-5431	77	20	)	)	PUNCT
ejpam-5431	77	21	,	,	PUNCT
ejpam-5431	77	22	pr(x	pr(x	NOUN
ejpam-5431	77	23	)	)	PUNCT
ejpam-5431	77	24	and	and	CCONJ
ejpam-5431	77	25	q(x	q(x	PROPN
ejpam-5431	77	26	)	)	PUNCT
ejpam-5431	77	27	,	,	PUNCT
ejpam-5431	77	28	the	the	DET
ejpam-5431	77	29	families	family	NOUN
ejpam-5431	77	30	of	of	ADP
ejpam-5431	77	31	nonempty	nonempty	ADJ
ejpam-5431	77	32	subsets	subset	NOUN
ejpam-5431	77	33	of	of	ADP
ejpam-5431	77	34	x	x	PRON
ejpam-5431	77	35	,	,	PUNCT
ejpam-5431	77	36	all	all	PRON
ejpam-5431	77	37	nonempty	nonempty	ADV
ejpam-5431	77	38	closed	close	VERB
ejpam-5431	77	39	and	and	CCONJ
ejpam-5431	77	40	bounded	bound	VERB
ejpam-5431	77	41	subsets	subset	NOUN
ejpam-5431	77	42	of	of	ADP
ejpam-5431	77	43	x	x	PRON
ejpam-5431	77	44	,	,	PUNCT
ejpam-5431	77	45	all	all	DET
ejpam-5431	77	46	nonempty	nonempty	ADJ
ejpam-5431	77	47	proximal	proximal	ADJ
ejpam-5431	77	48	subsets	subset	NOUN
ejpam-5431	77	49	of	of	ADP
ejpam-5431	77	50	x	x	PUNCT
ejpam-5431	77	51	and	and	CCONJ
ejpam-5431	77	52	all	all	DET
ejpam-5431	77	53	nonempty	nonempty	ADJ
ejpam-5431	77	54	compact	compact	ADJ
ejpam-5431	77	55	subsets	subset	NOUN
ejpam-5431	77	56	of	of	ADP
ejpam-5431	77	57	x	x	NOUN
ejpam-5431	77	58	,	,	PUNCT
ejpam-5431	77	59	respectively	respectively	ADV
ejpam-5431	77	60	.	.	PUNCT
ejpam-5431	78	1	let	let	AUX
ejpam-5431	78	2	(	(	PUNCT
ejpam-5431	78	3	x	x	NOUN
ejpam-5431	78	4	,	,	PUNCT
ejpam-5431	78	5	δ	δ	PROPN
ejpam-5431	78	6	)	)	PUNCT
ejpam-5431	78	7	be	be	VERB
ejpam-5431	78	8	a	a	DET
ejpam-5431	78	9	b	b	PROPN
ejpam-5431	78	10	-	-	PUNCT
ejpam-5431	78	11	ms	ms	NOUN
ejpam-5431	78	12	.	.	PROPN
ejpam-5431	78	13	for	for	ADP
ejpam-5431	78	14	a	a	DET
ejpam-5431	78	15	,	,	PUNCT
ejpam-5431	78	16	b	b	PROPN
ejpam-5431	78	17	∈	∈	PROPN
ejpam-5431	78	18	q(x	q(x	PROPN
ejpam-5431	78	19	)	)	PUNCT
ejpam-5431	78	20	,	,	PUNCT
ejpam-5431	78	21	the	the	DET
ejpam-5431	78	22	function	function	NOUN
ejpam-5431	78	23	ℵ	ℵ	NOUN
ejpam-5431	78	24	:	:	PUNCT
ejpam-5431	78	25	q(x)×q(x	q(x)×q(x	ADP
ejpam-5431	78	26	)	)	PUNCT
ejpam-5431	78	27	→	→	NOUN
ejpam-5431	78	28	r+	r+	X
ejpam-5431	78	29	,	,	PUNCT
ejpam-5431	78	30	defined	define	VERB
ejpam-5431	78	31	by	by	ADP
ejpam-5431	78	32	,	,	PUNCT
ejpam-5431	78	33	ℵ(a	ℵ(a	PROPN
ejpam-5431	78	34	,	,	PUNCT
ejpam-5431	78	35	b	b	NOUN
ejpam-5431	78	36	)	)	PUNCT
ejpam-5431	78	37	=	=	SYM
ejpam-5431	78	38	{	{	PUNCT
ejpam-5431	78	39	max{supσ∈a	max{supσ∈a	NUM
ejpam-5431	78	40	δ(σ	δ(σ	PROPN
ejpam-5431	78	41	,	,	PUNCT
ejpam-5431	78	42	b	b	NOUN
ejpam-5431	78	43	)	)	PUNCT
ejpam-5431	78	44	,	,	PUNCT
ejpam-5431	78	45	supx∈b	supx∈b	PROPN
ejpam-5431	78	46	δ(σ	δ(σ	PROPN
ejpam-5431	78	47	,	,	PUNCT
ejpam-5431	78	48	a	a	NOUN
ejpam-5431	78	49	)	)	PUNCT
ejpam-5431	78	50	}	}	PUNCT
ejpam-5431	78	51	,	,	PUNCT
ejpam-5431	78	52	if	if	SCONJ
ejpam-5431	78	53	it	it	PRON
ejpam-5431	78	54	exists	exist	VERB
ejpam-5431	78	55	+	+	ADJ
ejpam-5431	78	56	∞	∞	PROPN
ejpam-5431	78	57	,	,	PUNCT
ejpam-5431	78	58	otherwise	otherwise	ADV
ejpam-5431	78	59	,	,	PUNCT
ejpam-5431	78	60	is	be	AUX
ejpam-5431	78	61	named	name	VERB
ejpam-5431	78	62	as	as	ADP
ejpam-5431	78	63	generalized	generalized	ADJ
ejpam-5431	78	64	hausdorff	hausdorff	NOUN
ejpam-5431	78	65	distance	distance	NOUN
ejpam-5431	78	66	on	on	ADP
ejpam-5431	78	67	x	x	PUNCT
ejpam-5431	78	68	and	and	CCONJ
ejpam-5431	78	69	q(x	q(x	PROPN
ejpam-5431	78	70	,	,	PUNCT
ejpam-5431	78	71	δ	δ	PROPN
ejpam-5431	78	72	,	,	PUNCT
ejpam-5431	78	73	h	h	NOUN
ejpam-5431	78	74	)	)	PUNCT
ejpam-5431	78	75	is	be	AUX
ejpam-5431	78	76	hausdorff	hausdorff	PROPN
ejpam-5431	78	77	b	b	PROPN
ejpam-5431	78	78	-	-	PUNCT
ejpam-5431	78	79	m	m	NOUN
ejpam-5431	78	80	,	,	PUNCT
ejpam-5431	78	81	where	where	SCONJ
ejpam-5431	78	82	δ(σ	δ(σ	PROPN
ejpam-5431	78	83	,	,	PUNCT
ejpam-5431	78	84	b	b	NOUN
ejpam-5431	78	85	)	)	PUNCT
ejpam-5431	78	86	=	=	SYM
ejpam-5431	79	1	infτ∈b	infτ∈b	PROPN
ejpam-5431	79	2	δ(σ	δ(σ	PROPN
ejpam-5431	79	3	,	,	PUNCT
ejpam-5431	79	4	τ	τ	PROPN
ejpam-5431	79	5	)	)	PUNCT
ejpam-5431	79	6	.	.	PUNCT
ejpam-5431	80	1	lemma	lemma	PROPN
ejpam-5431	80	2	5	5	NUM
ejpam-5431	80	3	.	.	PUNCT
ejpam-5431	81	1	[	[	X
ejpam-5431	81	2	27	27	NUM
ejpam-5431	81	3	]	]	X
ejpam-5431	81	4	let	let	AUX
ejpam-5431	81	5	(	(	PUNCT
ejpam-5431	81	6	x	x	NOUN
ejpam-5431	81	7	,	,	PUNCT
ejpam-5431	81	8	δ	δ	PROPN
ejpam-5431	81	9	,	,	PUNCT
ejpam-5431	81	10	h	h	NOUN
ejpam-5431	81	11	)	)	PUNCT
ejpam-5431	81	12	be	be	VERB
ejpam-5431	81	13	a	a	DET
ejpam-5431	81	14	b	b	PROPN
ejpam-5431	81	15	-	-	PUNCT
ejpam-5431	81	16	ms	ms	NOUN
ejpam-5431	81	17	.	.	PROPN
ejpam-5431	81	18	for	for	ADP
ejpam-5431	81	19	a	a	DET
ejpam-5431	81	20	,	,	PUNCT
ejpam-5431	81	21	b	b	PROPN
ejpam-5431	81	22	∈	∈	PROPN
ejpam-5431	81	23	q(x	q(x	PROPN
ejpam-5431	81	24	)	)	PUNCT
ejpam-5431	81	25	and	and	CCONJ
ejpam-5431	81	26	σ	σ	PROPN
ejpam-5431	81	27	,	,	PUNCT
ejpam-5431	82	1	τ	τ	PROPN
ejpam-5431	82	2	∈	∈	PROPN
ejpam-5431	82	3	x	x	PRON
ejpam-5431	82	4	,	,	PUNCT
ejpam-5431	82	5	the	the	DET
ejpam-5431	82	6	specifications	specification	NOUN
ejpam-5431	82	7	listed	list	VERB
ejpam-5431	82	8	below	below	ADV
ejpam-5431	82	9	are	be	AUX
ejpam-5431	82	10	true	true	ADJ
ejpam-5431	82	11	:	:	PUNCT
ejpam-5431	82	12	(	(	PUNCT
ejpam-5431	82	13	i	i	NOUN
ejpam-5431	82	14	)	)	PUNCT
ejpam-5431	82	15	δ(σ	δ(σ	PROPN
ejpam-5431	82	16	,	,	PUNCT
ejpam-5431	82	17	b	b	NOUN
ejpam-5431	82	18	)	)	PUNCT
ejpam-5431	82	19	≤	≤	NOUN
ejpam-5431	82	20	ℵ(a	ℵ(a	PROPN
ejpam-5431	82	21	,	,	PUNCT
ejpam-5431	82	22	b	b	NOUN
ejpam-5431	82	23	)	)	PUNCT
ejpam-5431	82	24	for	for	ADP
ejpam-5431	82	25	every	every	DET
ejpam-5431	82	26	σ	σ	PROPN
ejpam-5431	82	27	∈	∈	PROPN
ejpam-5431	82	28	a.	a.	NOUN
ejpam-5431	82	29	(	(	PUNCT
ejpam-5431	82	30	ii	ii	NOUN
ejpam-5431	82	31	)	)	PUNCT
ejpam-5431	82	32	δ(σ	δ(σ	PROPN
ejpam-5431	82	33	,	,	PUNCT
ejpam-5431	82	34	b	b	NOUN
ejpam-5431	82	35	)	)	PUNCT
ejpam-5431	82	36	≤	≤	NOUN
ejpam-5431	82	37	δ(σ	δ(σ	PROPN
ejpam-5431	82	38	,	,	PUNCT
ejpam-5431	82	39	b	b	NOUN
ejpam-5431	82	40	)	)	PUNCT
ejpam-5431	82	41	for	for	ADP
ejpam-5431	82	42	any	any	DET
ejpam-5431	82	43	b	b	PROPN
ejpam-5431	82	44	∈	∈	PROPN
ejpam-5431	82	45	b.	b.	PROPN
ejpam-5431	82	46	(	(	PUNCT
ejpam-5431	82	47	iii	iii	NOUN
ejpam-5431	82	48	)	)	PUNCT
ejpam-5431	82	49	δ(σ	δ(σ	PROPN
ejpam-5431	82	50	,	,	PUNCT
ejpam-5431	82	51	a	a	PRON
ejpam-5431	82	52	)	)	PUNCT
ejpam-5431	82	53	≤	≤	NUM
ejpam-5431	82	54	h[δ(σ	h[δ(σ	NOUN
ejpam-5431	82	55	,	,	PUNCT
ejpam-5431	82	56	τ	τ	X
ejpam-5431	82	57	)	)	PUNCT
ejpam-5431	83	1	+	+	CCONJ
ejpam-5431	83	2	δ(τ	δ(τ	PROPN
ejpam-5431	83	3	,	,	PUNCT
ejpam-5431	83	4	a	a	NOUN
ejpam-5431	83	5	)	)	PUNCT
ejpam-5431	83	6	]	]	PUNCT
ejpam-5431	83	7	.	.	PUNCT
ejpam-5431	84	1	(	(	PUNCT
ejpam-5431	84	2	iv	iv	X
ejpam-5431	84	3	)	)	PUNCT
ejpam-5431	84	4	δ(σ	δ(σ	PROPN
ejpam-5431	84	5	,	,	PUNCT
ejpam-5431	84	6	a	a	PRON
ejpam-5431	84	7	)	)	PUNCT
ejpam-5431	84	8	=	=	SYM
ejpam-5431	84	9	0	0	NUM
ejpam-5431	85	1	⇔	⇔	PROPN
ejpam-5431	85	2	σ	σ	PROPN
ejpam-5431	85	3	∈	∈	PROPN
ejpam-5431	85	4	a.	a.	NOUN
ejpam-5431	85	5	(	(	PUNCT
ejpam-5431	85	6	v	v	NOUN
ejpam-5431	85	7	)	)	PUNCT
ejpam-5431	85	8	ℵ(a	ℵ(a	NOUN
ejpam-5431	85	9	,	,	PUNCT
ejpam-5431	85	10	b	b	NOUN
ejpam-5431	85	11	)	)	PUNCT
ejpam-5431	85	12	=	=	SYM
ejpam-5431	85	13	0	0	NUM
ejpam-5431	85	14	⇔	⇔	PROPN
ejpam-5431	85	15	a	a	PROPN
ejpam-5431	85	16	=	=	PROPN
ejpam-5431	85	17	b.	b.	PROPN
ejpam-5431	85	18	(	(	PUNCT
ejpam-5431	85	19	vi	vi	NOUN
ejpam-5431	85	20	)	)	PUNCT
ejpam-5431	85	21	ℵ(a	ℵ(a	NOUN
ejpam-5431	85	22	,	,	PUNCT
ejpam-5431	85	23	b	b	NOUN
ejpam-5431	85	24	)	)	PUNCT
ejpam-5431	86	1	=	=	SYM
ejpam-5431	86	2	ℵ(b	ℵ(b	NOUN
ejpam-5431	86	3	,	,	PUNCT
ejpam-5431	86	4	a	a	PRON
ejpam-5431	86	5	)	)	PUNCT
ejpam-5431	86	6	.	.	PUNCT
ejpam-5431	87	1	n.	n.	PROPN
ejpam-5431	87	2	saleem	saleem	PROPN
ejpam-5431	87	3	et	et	PROPN
ejpam-5431	87	4	al	al	PROPN
ejpam-5431	87	5	.	.	PUNCT
ejpam-5431	87	6	/	/	SYM
ejpam-5431	87	7	eur	eur	PROPN
ejpam-5431	87	8	.	.	PUNCT
ejpam-5431	88	1	j.	j.	PROPN
ejpam-5431	88	2	pure	pure	PROPN
ejpam-5431	88	3	appl	appl	PROPN
ejpam-5431	88	4	.	.	PROPN
ejpam-5431	88	5	math	math	PROPN
ejpam-5431	88	6	,	,	PUNCT
ejpam-5431	88	7	17	17	NUM
ejpam-5431	88	8	(	(	PUNCT
ejpam-5431	88	9	4	4	NUM
ejpam-5431	88	10	)	)	PUNCT
ejpam-5431	88	11	(	(	PUNCT
ejpam-5431	88	12	2024	2024	NUM
ejpam-5431	88	13	)	)	PUNCT
ejpam-5431	88	14	,	,	PUNCT
ejpam-5431	88	15	3304	3304	NUM
ejpam-5431	88	16	-	-	SYM
ejpam-5431	88	17	3335	3335	NUM
ejpam-5431	88	18	3308	3308	NUM
ejpam-5431	88	19	khojasteh	khojasteh	X
ejpam-5431	88	20	et	et	PROPN
ejpam-5431	88	21	al	al	PROPN
ejpam-5431	88	22	.	.	PUNCT
ejpam-5431	89	1	[	[	X
ejpam-5431	89	2	17	17	NUM
ejpam-5431	89	3	]	]	PUNCT
ejpam-5431	89	4	introduced	introduce	VERB
ejpam-5431	89	5	a	a	DET
ejpam-5431	89	6	family	family	NOUN
ejpam-5431	89	7	of	of	ADP
ejpam-5431	89	8	auxiliary	auxiliary	ADJ
ejpam-5431	89	9	functions	function	NOUN
ejpam-5431	89	10	known	know	VERB
ejpam-5431	89	11	as	as	ADP
ejpam-5431	89	12	sfs	sfs	PROPN
ejpam-5431	89	13	(	(	PUNCT
ejpam-5431	89	14	simulation	simulation	NOUN
ejpam-5431	89	15	functions	function	NOUN
ejpam-5431	89	16	)	)	PUNCT
ejpam-5431	89	17	to	to	PART
ejpam-5431	89	18	unify	unify	VERB
ejpam-5431	89	19	distinct	distinct	ADJ
ejpam-5431	89	20	types	type	NOUN
ejpam-5431	89	21	of	of	ADP
ejpam-5431	89	22	contraction	contraction	NOUN
ejpam-5431	89	23	.	.	PUNCT
ejpam-5431	90	1	definition	definition	NOUN
ejpam-5431	90	2	6	6	NUM
ejpam-5431	90	3	.	.	PUNCT
ejpam-5431	91	1	[	[	X
ejpam-5431	91	2	17	17	NUM
ejpam-5431	91	3	]	]	PUNCT
ejpam-5431	91	4	a	a	DET
ejpam-5431	91	5	sf	sf	PROPN
ejpam-5431	91	6	(	(	PUNCT
ejpam-5431	91	7	simulation	simulation	NOUN
ejpam-5431	91	8	function	function	PROPN
ejpam-5431	91	9	)	)	PUNCT
ejpam-5431	91	10	is	be	AUX
ejpam-5431	91	11	an	an	DET
ejpam-5431	91	12	operator	operator	NOUN
ejpam-5431	91	13	℘	℘	PROPN
ejpam-5431	91	14	:	:	PUNCT
ejpam-5431	91	15	r+	r+	NOUN
ejpam-5431	91	16	×	×	NOUN
ejpam-5431	91	17	r+	r+	NOUN
ejpam-5431	91	18	→	→	PUNCT
ejpam-5431	91	19	r	r	NOUN
ejpam-5431	91	20	that	that	PRON
ejpam-5431	91	21	meets	meet	VERB
ejpam-5431	91	22	the	the	DET
ejpam-5431	91	23	requirements	requirement	NOUN
ejpam-5431	91	24	listed	list	VERB
ejpam-5431	91	25	below	below	ADV
ejpam-5431	91	26	:	:	PUNCT
ejpam-5431	91	27	(	(	PUNCT
ejpam-5431	91	28	i	i	NOUN
ejpam-5431	91	29	)	)	PUNCT
ejpam-5431	91	30	℘(0	℘(0	PROPN
ejpam-5431	91	31	,	,	PUNCT
ejpam-5431	91	32	0	0	NUM
ejpam-5431	91	33	)	)	PUNCT
ejpam-5431	91	34	=	=	SYM
ejpam-5431	91	35	0	0	NUM
ejpam-5431	91	36	;	;	PUNCT
ejpam-5431	91	37	(	(	PUNCT
ejpam-5431	91	38	ii	ii	NOUN
ejpam-5431	91	39	)	)	PUNCT
ejpam-5431	91	40	℘(a	℘(a	PROPN
ejpam-5431	91	41	,	,	PUNCT
ejpam-5431	91	42	b	b	NOUN
ejpam-5431	91	43	)	)	PUNCT
ejpam-5431	91	44	<	<	X
ejpam-5431	91	45	b−	b−	PROPN
ejpam-5431	91	46	a	a	PRON
ejpam-5431	91	47	for	for	ADP
ejpam-5431	91	48	all	all	DET
ejpam-5431	91	49	a	a	PRON
ejpam-5431	91	50	,	,	PUNCT
ejpam-5431	91	51	b	b	X
ejpam-5431	91	52	>	>	X
ejpam-5431	91	53	0	0	NUM
ejpam-5431	91	54	;	;	PUNCT
ejpam-5431	91	55	(	(	PUNCT
ejpam-5431	91	56	iii	iii	X
ejpam-5431	91	57	)	)	PUNCT
ejpam-5431	91	58	if	if	SCONJ
ejpam-5431	91	59	{	{	PUNCT
ejpam-5431	91	60	an}n≥1	an}n≥1	INTJ
ejpam-5431	91	61	and	and	CCONJ
ejpam-5431	91	62	{	{	PUNCT
ejpam-5431	91	63	bn}n≥1	bn}n≥1	NOUN
ejpam-5431	91	64	are	be	AUX
ejpam-5431	91	65	sequences	sequence	NOUN
ejpam-5431	91	66	in	in	ADP
ejpam-5431	91	67	(	(	PUNCT
ejpam-5431	91	68	0,+∞	0,+∞	NUM
ejpam-5431	91	69	)	)	PUNCT
ejpam-5431	91	70	such	such	ADJ
ejpam-5431	91	71	that	that	PRON
ejpam-5431	91	72	limn→+∞	limn→+∞	VERB
ejpam-5431	91	73	an	an	DET
ejpam-5431	91	74	=	=	PUNCT
ejpam-5431	91	75	limn→+∞	limn→+∞	PROPN
ejpam-5431	91	76	bn	bn	INTJ
ejpam-5431	91	77	>	>	X
ejpam-5431	91	78	0	0	NUM
ejpam-5431	91	79	,	,	PUNCT
ejpam-5431	91	80	then	then	ADV
ejpam-5431	91	81	limn→+∞	limn→+∞	VERB
ejpam-5431	91	82	sup℘(an	sup℘(an	PROPN
ejpam-5431	91	83	,	,	PUNCT
ejpam-5431	91	84	bn	bn	ADJ
ejpam-5431	91	85	)	)	PUNCT
ejpam-5431	91	86	<	<	X
ejpam-5431	91	87	0	0	X
ejpam-5431	91	88	.	.	PUNCT
ejpam-5431	92	1	the	the	DET
ejpam-5431	92	2	collection	collection	NOUN
ejpam-5431	92	3	of	of	ADP
ejpam-5431	92	4	sfs	sfs	PROPN
ejpam-5431	92	5	is	be	AUX
ejpam-5431	92	6	denoted	denote	VERB
ejpam-5431	92	7	by	by	ADP
ejpam-5431	92	8	z.	z.	PROPN
ejpam-5431	92	9	example	example	NOUN
ejpam-5431	92	10	7	7	X
ejpam-5431	92	11	.	.	PUNCT
ejpam-5431	93	1	let	let	VERB
ejpam-5431	93	2	o	o	NOUN
ejpam-5431	93	3	and	and	CCONJ
ejpam-5431	93	4	ψ	ψ	X
ejpam-5431	93	5	be	be	AUX
ejpam-5431	93	6	two	two	NUM
ejpam-5431	93	7	altering	alter	VERB
ejpam-5431	93	8	distance	distance	NOUN
ejpam-5431	93	9	functions	function	NOUN
ejpam-5431	93	10	such	such	ADJ
ejpam-5431	93	11	that	that	SCONJ
ejpam-5431	93	12	ψ(t	ψ(t	PROPN
ejpam-5431	93	13	)	)	PUNCT
ejpam-5431	93	14	<	<	X
ejpam-5431	93	15	t	t	X
ejpam-5431	93	16	≤	≤	NUM
ejpam-5431	93	17	ϕ(t	ϕ(t	NUM
ejpam-5431	93	18	)	)	PUNCT
ejpam-5431	93	19	for	for	ADP
ejpam-5431	93	20	all	all	DET
ejpam-5431	93	21	t	t	PROPN
ejpam-5431	93	22	>	>	X
ejpam-5431	93	23	0	0	PROPN
ejpam-5431	93	24	,	,	PUNCT
ejpam-5431	93	25	also	also	ADV
ejpam-5431	93	26	ϕ	ϕ	PROPN
ejpam-5431	93	27	and	and	CCONJ
ejpam-5431	93	28	ψ	ψ	NOUN
ejpam-5431	93	29	are	be	AUX
ejpam-5431	93	30	continuous	continuous	ADJ
ejpam-5431	93	31	functions	function	NOUN
ejpam-5431	93	32	such	such	ADJ
ejpam-5431	93	33	that	that	SCONJ
ejpam-5431	93	34	ϕ(t	ϕ(t	NUM
ejpam-5431	93	35	)	)	PUNCT
ejpam-5431	94	1	=	=	SYM
ejpam-5431	94	2	ψ(t	ψ(t	PROPN
ejpam-5431	94	3	)	)	PUNCT
ejpam-5431	94	4	=	=	SYM
ejpam-5431	94	5	0	0	PUNCT
ejpam-5431	95	1	if	if	SCONJ
ejpam-5431	95	2	and	and	CCONJ
ejpam-5431	95	3	only	only	ADV
ejpam-5431	95	4	if	if	SCONJ
ejpam-5431	95	5	t	t	PROPN
ejpam-5431	95	6	=	=	SYM
ejpam-5431	95	7	0	0	PROPN
ejpam-5431	95	8	.	.	PUNCT
ejpam-5431	96	1	then	then	ADV
ejpam-5431	96	2	the	the	DET
ejpam-5431	96	3	mapping	mapping	PROPN
ejpam-5431	96	4	℘(a	℘(a	PROPN
ejpam-5431	96	5	,	,	PUNCT
ejpam-5431	96	6	b	b	NOUN
ejpam-5431	96	7	)	)	PUNCT
ejpam-5431	96	8	=	=	PUNCT
ejpam-5431	96	9	ψ(b)−	ψ(b)−	PROPN
ejpam-5431	96	10	ϕ(a	ϕ(a	NOUN
ejpam-5431	96	11	)	)	PUNCT
ejpam-5431	96	12	for	for	ADP
ejpam-5431	96	13	all	all	DET
ejpam-5431	96	14	a	a	PRON
ejpam-5431	96	15	,	,	PUNCT
ejpam-5431	96	16	b	b	X
ejpam-5431	96	17	∈	∈	PROPN
ejpam-5431	97	1	[	[	X
ejpam-5431	97	2	0,+∞	0,+∞	NUM
ejpam-5431	97	3	)	)	PUNCT
ejpam-5431	97	4	is	be	AUX
ejpam-5431	97	5	a	a	DET
ejpam-5431	97	6	sf	sf	NOUN
ejpam-5431	97	7	.	.	PUNCT
ejpam-5431	97	8	to	to	PART
ejpam-5431	97	9	study	study	VERB
ejpam-5431	97	10	even	even	ADV
ejpam-5431	97	11	more	more	ADJ
ejpam-5431	97	12	details	detail	NOUN
ejpam-5431	97	13	and	and	CCONJ
ejpam-5431	97	14	examples	example	NOUN
ejpam-5431	97	15	of	of	ADP
ejpam-5431	97	16	sf	sf	PRON
ejpam-5431	97	17	see	see	VERB
ejpam-5431	97	18	[	[	X
ejpam-5431	97	19	2	2	NUM
ejpam-5431	97	20	,	,	PUNCT
ejpam-5431	97	21	11	11	NUM
ejpam-5431	97	22	,	,	PUNCT
ejpam-5431	97	23	17	17	NUM
ejpam-5431	97	24	]	]	PUNCT
ejpam-5431	97	25	definition	definition	NOUN
ejpam-5431	97	26	8	8	NUM
ejpam-5431	97	27	.	.	PUNCT
ejpam-5431	98	1	[	[	X
ejpam-5431	98	2	17	17	NUM
ejpam-5431	98	3	]	]	X
ejpam-5431	98	4	let	let	VERB
ejpam-5431	98	5	(	(	PUNCT
ejpam-5431	98	6	x	x	NOUN
ejpam-5431	98	7	,	,	PUNCT
ejpam-5431	98	8	δ	δ	PROPN
ejpam-5431	98	9	)	)	PUNCT
ejpam-5431	98	10	be	be	VERB
ejpam-5431	98	11	a	a	DET
ejpam-5431	98	12	ms	ms	PROPN
ejpam-5431	98	13	.	.	PROPN
ejpam-5431	99	1	a	a	DET
ejpam-5431	99	2	correspondence	correspondence	NOUN
ejpam-5431	99	3	t	t	NOUN
ejpam-5431	99	4	:	:	PUNCT
ejpam-5431	99	5	x	x	X
ejpam-5431	99	6	→	→	PUNCT
ejpam-5431	99	7	x	x	X
ejpam-5431	99	8	is	be	AUX
ejpam-5431	99	9	named	name	VERB
ejpam-5431	99	10	as	as	ADP
ejpam-5431	99	11	zcontraction	zcontraction	NOUN
ejpam-5431	99	12	with	with	ADP
ejpam-5431	99	13	regard	regard	NOUN
ejpam-5431	99	14	to	to	ADP
ejpam-5431	99	15	℘	℘	PROPN
ejpam-5431	99	16	∈	∈	PROPN
ejpam-5431	99	17	z	z	NOUN
ejpam-5431	99	18	,	,	PUNCT
ejpam-5431	99	19	if	if	SCONJ
ejpam-5431	99	20	℘(δ(t	℘(δ(t	PROPN
ejpam-5431	99	21	σ	σ	PROPN
ejpam-5431	99	22	,	,	PUNCT
ejpam-5431	99	23	t	t	PROPN
ejpam-5431	99	24	τ	τ	PROPN
ejpam-5431	99	25	)	)	PUNCT
ejpam-5431	99	26	,	,	PUNCT
ejpam-5431	99	27	δ(σ	δ(σ	PROPN
ejpam-5431	99	28	,	,	PUNCT
ejpam-5431	99	29	τ	τ	PROPN
ejpam-5431	99	30	)	)	PUNCT
ejpam-5431	99	31	)	)	PUNCT
ejpam-5431	99	32	≥	≥	NOUN
ejpam-5431	99	33	0	0	NUM
ejpam-5431	99	34	for	for	ADP
ejpam-5431	99	35	all	all	DET
ejpam-5431	99	36	σ	σ	PROPN
ejpam-5431	99	37	,	,	PUNCT
ejpam-5431	99	38	τ	τ	PROPN
ejpam-5431	99	39	∈	∈	PROPN
ejpam-5431	99	40	x	x	PUNCT
ejpam-5431	99	41	remark	remark	NOUN
ejpam-5431	99	42	9	9	NUM
ejpam-5431	99	43	.	.	PUNCT
ejpam-5431	100	1	the	the	DET
ejpam-5431	100	2	description	description	NOUN
ejpam-5431	100	3	of	of	ADP
ejpam-5431	100	4	the	the	DET
ejpam-5431	100	5	sf	sf	PROPN
ejpam-5431	100	6	makes	make	VERB
ejpam-5431	100	7	it	it	PRON
ejpam-5431	100	8	evident	evident	ADJ
ejpam-5431	100	9	that	that	SCONJ
ejpam-5431	100	10	℘(a	℘(a	PROPN
ejpam-5431	100	11	,	,	PUNCT
ejpam-5431	100	12	b	b	NOUN
ejpam-5431	100	13	)	)	PUNCT
ejpam-5431	100	14	<	<	X
ejpam-5431	100	15	0	0	NUM
ejpam-5431	100	16	for	for	ADP
ejpam-5431	100	17	all	all	DET
ejpam-5431	100	18	a	a	DET
ejpam-5431	100	19	≥	≥	NOUN
ejpam-5431	100	20	b	b	X
ejpam-5431	100	21	>	>	X
ejpam-5431	100	22	0	0	NUM
ejpam-5431	100	23	.	.	PUNCT
ejpam-5431	101	1	therefore	therefore	ADV
ejpam-5431	101	2	,	,	PUNCT
ejpam-5431	101	3	if	if	SCONJ
ejpam-5431	101	4	t	t	PROPN
ejpam-5431	101	5	is	be	AUX
ejpam-5431	101	6	a	a	DET
ejpam-5431	101	7	z	z	NOUN
ejpam-5431	101	8	-	-	PUNCT
ejpam-5431	101	9	contraction	contraction	NOUN
ejpam-5431	101	10	with	with	ADP
ejpam-5431	101	11	respect	respect	NOUN
ejpam-5431	101	12	to	to	ADP
ejpam-5431	101	13	℘	℘	PROPN
ejpam-5431	101	14	∈	∈	PROPN
ejpam-5431	101	15	z	z	NOUN
ejpam-5431	101	16	then	then	ADV
ejpam-5431	101	17	δ(t	δ(t	PROPN
ejpam-5431	101	18	σ	σ	PROPN
ejpam-5431	101	19	,	,	PUNCT
ejpam-5431	101	20	t	t	PROPN
ejpam-5431	101	21	τ	τ	PROPN
ejpam-5431	101	22	)	)	PUNCT
ejpam-5431	101	23	<	<	X
ejpam-5431	101	24	δ(σ	δ(σ	PROPN
ejpam-5431	101	25	,	,	PUNCT
ejpam-5431	101	26	τ	τ	X
ejpam-5431	101	27	)	)	PUNCT
ejpam-5431	101	28	for	for	ADP
ejpam-5431	101	29	all	all	DET
ejpam-5431	101	30	distinct	distinct	PROPN
ejpam-5431	101	31	σ	σ	PROPN
ejpam-5431	101	32	,	,	PUNCT
ejpam-5431	101	33	τ	τ	PROPN
ejpam-5431	101	34	∈	∈	PROPN
ejpam-5431	101	35	x.	x.	NOUN
ejpam-5431	101	36	as	as	ADP
ejpam-5431	101	37	a	a	DET
ejpam-5431	101	38	result	result	NOUN
ejpam-5431	101	39	,	,	PUNCT
ejpam-5431	101	40	it	it	PRON
ejpam-5431	101	41	can	can	AUX
ejpam-5431	101	42	be	be	AUX
ejpam-5431	101	43	seen	see	VERB
ejpam-5431	101	44	that	that	SCONJ
ejpam-5431	101	45	every	every	DET
ejpam-5431	101	46	z	z	NOUN
ejpam-5431	101	47	contraction	contraction	NOUN
ejpam-5431	101	48	mapping	mapping	NOUN
ejpam-5431	101	49	is	be	AUX
ejpam-5431	101	50	contractive	contractive	ADJ
ejpam-5431	101	51	and	and	CCONJ
ejpam-5431	101	52	continuous	continuous	ADJ
ejpam-5431	101	53	.	.	PUNCT
ejpam-5431	102	1	theorem	theorem	ADJ
ejpam-5431	102	2	10	10	NUM
ejpam-5431	102	3	.	.	PUNCT
ejpam-5431	103	1	[	[	X
ejpam-5431	103	2	17	17	NUM
ejpam-5431	103	3	]	]	PUNCT
ejpam-5431	103	4	every	every	DET
ejpam-5431	103	5	z	z	NOUN
ejpam-5431	103	6	-	-	PUNCT
ejpam-5431	103	7	contraction	contraction	NOUN
ejpam-5431	103	8	on	on	ADP
ejpam-5431	103	9	a	a	DET
ejpam-5431	103	10	complete	complete	ADJ
ejpam-5431	103	11	ms	ms	NOUN
ejpam-5431	103	12	has	have	VERB
ejpam-5431	103	13	a	a	DET
ejpam-5431	103	14	unique	unique	ADJ
ejpam-5431	103	15	fp	fp	X
ejpam-5431	103	16	.	.	PUNCT
ejpam-5431	103	17	let	let	VERB
ejpam-5431	103	18	x	x	PRON
ejpam-5431	103	19	represent	represent	VERB
ejpam-5431	103	20	a	a	DET
ejpam-5431	103	21	universal	universal	ADJ
ejpam-5431	103	22	set	set	NOUN
ejpam-5431	103	23	.	.	PUNCT
ejpam-5431	104	1	a	a	DET
ejpam-5431	104	2	function	function	NOUN
ejpam-5431	104	3	with	with	ADP
ejpam-5431	104	4	a	a	DET
ejpam-5431	104	5	domain	domain	NOUN
ejpam-5431	104	6	of	of	ADP
ejpam-5431	104	7	x	x	PUNCT
ejpam-5431	104	8	and	and	CCONJ
ejpam-5431	104	9	values	value	NOUN
ejpam-5431	104	10	in	in	ADP
ejpam-5431	104	11	[	[	X
ejpam-5431	104	12	0	0	NUM
ejpam-5431	104	13	,	,	PUNCT
ejpam-5431	104	14	1	1	NUM
ejpam-5431	104	15	]	]	PUNCT
ejpam-5431	104	16	=	=	PUNCT
ejpam-5431	104	17	i	i	PRON
ejpam-5431	104	18	is	be	AUX
ejpam-5431	104	19	referred	refer	VERB
ejpam-5431	104	20	to	to	ADP
ejpam-5431	104	21	as	as	ADP
ejpam-5431	104	22	a	a	DET
ejpam-5431	104	23	fs	fs	NOUN
ejpam-5431	104	24	in	in	ADP
ejpam-5431	104	25	x.	x.	NOUN
ejpam-5431	104	26	if	if	SCONJ
ejpam-5431	104	27	a	a	PRON
ejpam-5431	104	28	is	be	AUX
ejpam-5431	104	29	a	a	DET
ejpam-5431	104	30	fuzzy	fuzzy	ADJ
ejpam-5431	104	31	set	set	NOUN
ejpam-5431	104	32	in	in	ADP
ejpam-5431	104	33	x	x	NOUN
ejpam-5431	104	34	,	,	PUNCT
ejpam-5431	104	35	then	then	ADV
ejpam-5431	104	36	the	the	DET
ejpam-5431	104	37	function	function	NOUN
ejpam-5431	104	38	value	value	NOUN
ejpam-5431	104	39	a(x	a(x	NOUN
ejpam-5431	104	40	)	)	PUNCT
ejpam-5431	104	41	is	be	AUX
ejpam-5431	104	42	called	call	VERB
ejpam-5431	104	43	the	the	DET
ejpam-5431	104	44	grade	grade	NOUN
ejpam-5431	104	45	of	of	ADP
ejpam-5431	104	46	membership	membership	NOUN
ejpam-5431	104	47	of	of	ADP
ejpam-5431	104	48	σ	σ	PROPN
ejpam-5431	104	49	in	in	ADP
ejpam-5431	104	50	a.	a.	NOUN
ejpam-5431	104	51	definition	definition	NOUN
ejpam-5431	104	52	11	11	NUM
ejpam-5431	104	53	.	.	PUNCT
ejpam-5431	105	1	[	[	X
ejpam-5431	105	2	4	4	X
ejpam-5431	105	3	]	]	PUNCT
ejpam-5431	105	4	let	let	VERB
ejpam-5431	105	5	x	x	PRON
ejpam-5431	105	6	be	be	AUX
ejpam-5431	105	7	a	a	DET
ejpam-5431	105	8	universal	universal	ADJ
ejpam-5431	105	9	set	set	NOUN
ejpam-5431	105	10	.	.	PUNCT
ejpam-5431	106	1	an	an	DET
ejpam-5431	106	2	ifs	ifs	PROPN
ejpam-5431	106	3	(	(	PUNCT
ejpam-5431	106	4	intuitionistic	intuitionistic	ADJ
ejpam-5431	106	5	fuzzy	fuzzy	ADJ
ejpam-5431	106	6	set	set	NOUN
ejpam-5431	106	7	)	)	PUNCT
ejpam-5431	106	8	a	a	PRON
ejpam-5431	106	9	is	be	AUX
ejpam-5431	106	10	described	describe	VERB
ejpam-5431	106	11	as	as	ADP
ejpam-5431	106	12	:	:	PUNCT
ejpam-5431	106	13	a	a	PRON
ejpam-5431	106	14	=	=	SYM
ejpam-5431	106	15	{	{	PUNCT
ejpam-5431	106	16	σ	σ	NUM
ejpam-5431	106	17	∈	∈	PROPN
ejpam-5431	106	18	x	x	X
ejpam-5431	106	19	;	;	PUNCT
ejpam-5431	106	20	(	(	PUNCT
ejpam-5431	106	21	µa(σ	µa(σ	NOUN
ejpam-5431	106	22	)	)	PUNCT
ejpam-5431	106	23	,	,	PUNCT
ejpam-5431	106	24	νa(σ	νa(σ	NUM
ejpam-5431	106	25	)	)	PUNCT
ejpam-5431	106	26	)	)	PUNCT
ejpam-5431	106	27	}	}	PUNCT
ejpam-5431	106	28	with	with	ADP
ejpam-5431	106	29	µa	µa	NOUN
ejpam-5431	106	30	:	:	PUNCT
ejpam-5431	106	31	x	x	X
ejpam-5431	106	32	→	→	SYM
ejpam-5431	107	1	[	[	X
ejpam-5431	107	2	0	0	NUM
ejpam-5431	107	3	,	,	PUNCT
ejpam-5431	107	4	1	1	NUM
ejpam-5431	107	5	]	]	PUNCT
ejpam-5431	107	6	and	and	CCONJ
ejpam-5431	107	7	νa	νa	VERB
ejpam-5431	107	8	:	:	PUNCT
ejpam-5431	107	9	x	x	X
ejpam-5431	107	10	→	→	SYM
ejpam-5431	107	11	[	[	X
ejpam-5431	107	12	0	0	NUM
ejpam-5431	107	13	,	,	PUNCT
ejpam-5431	107	14	1	1	NUM
ejpam-5431	107	15	]	]	PUNCT
ejpam-5431	107	16	denote	denote	VERB
ejpam-5431	107	17	the	the	DET
ejpam-5431	107	18	degree	degree	NOUN
ejpam-5431	107	19	of	of	ADP
ejpam-5431	107	20	membership	membership	NOUN
ejpam-5431	107	21	and	and	CCONJ
ejpam-5431	107	22	the	the	DET
ejpam-5431	107	23	degree	degree	NOUN
ejpam-5431	107	24	of	of	ADP
ejpam-5431	107	25	nonmembership	nonmembership	NOUN
ejpam-5431	107	26	of	of	ADP
ejpam-5431	107	27	each	each	DET
ejpam-5431	107	28	element	element	NOUN
ejpam-5431	107	29	σ	σ	PROPN
ejpam-5431	107	30	to	to	PART
ejpam-5431	107	31	set	set	VERB
ejpam-5431	107	32	a	a	DET
ejpam-5431	107	33	respectively	respectively	ADV
ejpam-5431	107	34	,	,	PUNCT
ejpam-5431	107	35	such	such	ADJ
ejpam-5431	107	36	that	that	SCONJ
ejpam-5431	107	37	0	0	NUM
ejpam-5431	107	38	≤	≤	NUM
ejpam-5431	107	39	µa(σ	µa(σ	NOUN
ejpam-5431	107	40	)	)	PUNCT
ejpam-5431	107	41	+	+	NUM
ejpam-5431	107	42	νa(σ	νa(σ	X
ejpam-5431	107	43	)	)	PUNCT
ejpam-5431	107	44	≤	≤	NOUN
ejpam-5431	107	45	1	1	NUM
ejpam-5431	107	46	for	for	ADP
ejpam-5431	107	47	all	all	DET
ejpam-5431	107	48	σ	σ	PROPN
ejpam-5431	107	49	∈	∈	PROPN
ejpam-5431	107	50	x.	x.	NOUN
ejpam-5431	107	51	n.	n.	PROPN
ejpam-5431	107	52	saleem	saleem	PROPN
ejpam-5431	107	53	et	et	PROPN
ejpam-5431	107	54	al	al	PROPN
ejpam-5431	107	55	.	.	PUNCT
ejpam-5431	107	56	/	/	SYM
ejpam-5431	107	57	eur	eur	PROPN
ejpam-5431	107	58	.	.	PUNCT
ejpam-5431	108	1	j.	j.	PROPN
ejpam-5431	108	2	pure	pure	PROPN
ejpam-5431	108	3	appl	appl	PROPN
ejpam-5431	108	4	.	.	PROPN
ejpam-5431	108	5	math	math	PROPN
ejpam-5431	108	6	,	,	PUNCT
ejpam-5431	108	7	17	17	NUM
ejpam-5431	108	8	(	(	PUNCT
ejpam-5431	108	9	4	4	NUM
ejpam-5431	108	10	)	)	PUNCT
ejpam-5431	108	11	(	(	PUNCT
ejpam-5431	108	12	2024	2024	NUM
ejpam-5431	108	13	)	)	PUNCT
ejpam-5431	108	14	,	,	PUNCT
ejpam-5431	108	15	3304	3304	NUM
ejpam-5431	108	16	-	-	SYM
ejpam-5431	108	17	3335	3335	NUM
ejpam-5431	108	18	3309	3309	NUM
ejpam-5431	108	19	x	x	SYM
ejpam-5431	108	20	σ1	σ1	PROPN
ejpam-5431	108	21	σ2	σ2	PROPN
ejpam-5431	108	22	σ3	σ3	PROPN
ejpam-5431	108	23	.	.	PUNCT
ejpam-5431	108	24	.	.	PUNCT
ejpam-5431	108	25	.	.	PUNCT
ejpam-5431	109	1	ifs(x	ifs(x	PROPN
ejpam-5431	109	2	)	)	PUNCT
ejpam-5431	109	3	x	x	PUNCT
ejpam-5431	110	1	[	[	X
ejpam-5431	110	2	0	0	NUM
ejpam-5431	110	3	,	,	PUNCT
ejpam-5431	110	4	1	1	NUM
ejpam-5431	110	5	]	]	X
ejpam-5431	110	6	tσ1	tσ1	NOUN
ejpam-5431	110	7	=	=	PUNCT
ejpam-5431	110	8	µσ1	µσ1	NOUN
ejpam-5431	110	9	:	:	PUNCT
ejpam-5431	110	10	σi	σi	ADJ
ejpam-5431	110	11	λ	λ	PART
ejpam-5431	110	12	ασj	ασj	VERB
ejpam-5431	110	13	γ	γ	X
ejpam-5431	110	14	β	β	NOUN
ejpam-5431	110	15	νσ1	νσ1	NOUN
ejpam-5431	110	16	:	:	PUNCT
ejpam-5431	110	17	σi	σi	PRON
ejpam-5431	110	18	σj	σj	VERB
ejpam-5431	110	19	such	such	ADJ
ejpam-5431	110	20	that	that	SCONJ
ejpam-5431	110	21	µσ1	µσ1	NOUN
ejpam-5431	110	22	+	+	CCONJ
ejpam-5431	110	23	νσ1	νσ1	NOUN
ejpam-5431	110	24	:	:	PUNCT
ejpam-5431	110	25	x	x	PUNCT
ejpam-5431	111	1	[	[	X
ejpam-5431	111	2	0	0	NUM
ejpam-5431	111	3	,	,	PUNCT
ejpam-5431	111	4	1	1	NUM
ejpam-5431	111	5	]	]	PUNCT
ejpam-5431	111	6	σi	σi	PRON
ejpam-5431	111	7	σj	σj	VERB
ejpam-5431	111	8	a	a	DET
ejpam-5431	111	9	b	b	NUM
ejpam-5431	111	10	figure	figure	NOUN
ejpam-5431	111	11	1	1	NUM
ejpam-5431	111	12	:	:	PUNCT
ejpam-5431	111	13	pictorial	pictorial	ADJ
ejpam-5431	111	14	representation	representation	NOUN
ejpam-5431	111	15	of	of	ADP
ejpam-5431	111	16	intuitionistic	intuitionistic	ADJ
ejpam-5431	111	17	fuzzy	fuzzy	ADJ
ejpam-5431	111	18	set	set	NOUN
ejpam-5431	111	19	-	-	PUNCT
ejpam-5431	111	20	valued	value	VERB
ejpam-5431	111	21	mappings	mapping	NOUN
ejpam-5431	111	22	.	.	PUNCT
ejpam-5431	112	1	example	example	NOUN
ejpam-5431	112	2	12	12	NUM
ejpam-5431	112	3	.	.	PUNCT
ejpam-5431	113	1	consider	consider	VERB
ejpam-5431	113	2	the	the	DET
ejpam-5431	113	3	following	follow	VERB
ejpam-5431	113	4	real	real	ADJ
ejpam-5431	113	5	-	-	PUNCT
ejpam-5431	113	6	world	world	NOUN
ejpam-5431	113	7	example	example	NOUN
ejpam-5431	113	8	of	of	ADP
ejpam-5431	113	9	an	an	DET
ejpam-5431	113	10	ifs	ifs	PROPN
ejpam-5431	113	11	representing	represent	VERB
ejpam-5431	113	12	the	the	DET
ejpam-5431	113	13	idea	idea	NOUN
ejpam-5431	113	14	of	of	ADP
ejpam-5431	113	15	”	"	PUNCT
ejpam-5431	113	16	customer	customer	NOUN
ejpam-5431	113	17	satisfaction	satisfaction	NOUN
ejpam-5431	113	18	”	"	PUNCT
ejpam-5431	113	19	for	for	ADP
ejpam-5431	113	20	a	a	DET
ejpam-5431	113	21	restaurant	restaurant	NOUN
ejpam-5431	113	22	.	.	PUNCT
ejpam-5431	114	1	we	we	PRON
ejpam-5431	114	2	will	will	AUX
ejpam-5431	114	3	design	design	VERB
ejpam-5431	114	4	eight	eight	NUM
ejpam-5431	114	5	customer	customer	NOUN
ejpam-5431	114	6	satisfaction	satisfaction	NOUN
ejpam-5431	114	7	elements	element	NOUN
ejpam-5431	114	8	and	and	CCONJ
ejpam-5431	114	9	give	give	VERB
ejpam-5431	114	10	membership	membership	NOUN
ejpam-5431	114	11	and	and	CCONJ
ejpam-5431	114	12	non	non	ADJ
ejpam-5431	114	13	-	-	ADJ
ejpam-5431	114	14	membership	membership	ADJ
ejpam-5431	114	15	values	value	NOUN
ejpam-5431	114	16	to	to	ADP
ejpam-5431	114	17	every	every	DET
ejpam-5431	114	18	single	single	ADJ
ejpam-5431	114	19	factor	factor	NOUN
ejpam-5431	114	20	.	.	PUNCT
ejpam-5431	115	1	table	table	NOUN
ejpam-5431	115	2	1	1	NUM
ejpam-5431	115	3	:	:	PUNCT
ejpam-5431	115	4	intuitionistic	intuitionistic	ADJ
ejpam-5431	115	5	fuzzy	fuzzy	ADJ
ejpam-5431	115	6	set	set	VERB
ejpam-5431	115	7	data	data	NOUN
ejpam-5431	115	8	factors	factor	NOUN
ejpam-5431	115	9	membership	membership	VERB
ejpam-5431	115	10	non	non	PROPN
ejpam-5431	115	11	membership	membership	NOUN
ejpam-5431	115	12	food	food	NOUN
ejpam-5431	115	13	quality	quality	NOUN
ejpam-5431	115	14	0.8	0.8	NUM
ejpam-5431	115	15	0.1	0.1	NUM
ejpam-5431	115	16	service	service	NOUN
ejpam-5431	115	17	speed	speed	NOUN
ejpam-5431	115	18	0.7	0.7	NUM
ejpam-5431	115	19	0.2	0.2	NUM
ejpam-5431	115	20	cleanliness	cleanliness	NOUN
ejpam-5431	115	21	0.6	0.6	NUM
ejpam-5431	115	22	0.2	0.2	NUM
ejpam-5431	115	23	atmosphere	atmosphere	NOUN
ejpam-5431	115	24	0.6	0.6	NUM
ejpam-5431	115	25	0.3	0.3	NUM
ejpam-5431	115	26	prices	price	NOUN
ejpam-5431	115	27	0.4	0.4	NUM
ejpam-5431	115	28	0.5	0.5	NUM
ejpam-5431	115	29	menu	menu	NOUN
ejpam-5431	115	30	variety	variety	NOUN
ejpam-5431	115	31	0.8	0.8	NUM
ejpam-5431	115	32	0.2	0.2	NUM
ejpam-5431	115	33	staff	staff	NOUN
ejpam-5431	115	34	friendliness	friendliness	VERB
ejpam-5431	115	35	0.6	0.6	NUM
ejpam-5431	115	36	0.4	0.4	NUM
ejpam-5431	115	37	noise	noise	NOUN
ejpam-5431	115	38	level	level	NOUN
ejpam-5431	115	39	0.5	0.5	NUM
ejpam-5431	115	40	0.3	0.3	NUM
ejpam-5431	115	41	definition	definition	NOUN
ejpam-5431	115	42	13	13	NUM
ejpam-5431	115	43	.	.	PUNCT
ejpam-5431	116	1	let	let	VERB
ejpam-5431	116	2	l	l	NOUN
ejpam-5431	116	3	=	=	PRON
ejpam-5431	116	4	{	{	PUNCT
ejpam-5431	116	5	(	(	PUNCT
ejpam-5431	116	6	⋉	⋉	PROPN
ejpam-5431	116	7	,	,	PUNCT
ejpam-5431	116	8	β);⋉+	β);⋉+	PUNCT
ejpam-5431	116	9	β	β	X
ejpam-5431	116	10	≤	≤	NUM
ejpam-5431	116	11	1	1	NUM
ejpam-5431	116	12	,	,	PUNCT
ejpam-5431	116	13	(	(	PUNCT
ejpam-5431	116	14	⋉	⋉	PROPN
ejpam-5431	116	15	,	,	PUNCT
ejpam-5431	116	16	β	β	NOUN
ejpam-5431	116	17	)	)	PUNCT
ejpam-5431	116	18	∈	∈	PROPN
ejpam-5431	116	19	(	(	PUNCT
ejpam-5431	116	20	0	0	NUM
ejpam-5431	116	21	,	,	PUNCT
ejpam-5431	116	22	1]×	1]×	NUM
ejpam-5431	116	23	[	[	X
ejpam-5431	116	24	0	0	NUM
ejpam-5431	116	25	,	,	PUNCT
ejpam-5431	116	26	1	1	NUM
ejpam-5431	116	27	)	)	PUNCT
ejpam-5431	116	28	}	}	PUNCT
ejpam-5431	116	29	and	and	CCONJ
ejpam-5431	116	30	a	a	PRON
ejpam-5431	116	31	is	be	AUX
ejpam-5431	116	32	an	an	DET
ejpam-5431	116	33	ifs	ifs	PROPN
ejpam-5431	116	34	,	,	PUNCT
ejpam-5431	116	35	then	then	ADV
ejpam-5431	116	36	(	(	PUNCT
ejpam-5431	116	37	⋉	⋉	PROPN
ejpam-5431	116	38	,	,	PUNCT
ejpam-5431	116	39	β)-cut	β)-cut	VERB
ejpam-5431	116	40	set	set	NOUN
ejpam-5431	116	41	of	of	ADP
ejpam-5431	116	42	a	a	PRON
ejpam-5431	116	43	is	be	AUX
ejpam-5431	116	44	defined	define	VERB
ejpam-5431	116	45	as	as	ADP
ejpam-5431	116	46	:	:	PUNCT
ejpam-5431	116	47	[	[	X
ejpam-5431	116	48	a](⋉,β	a](⋉,β	X
ejpam-5431	116	49	)	)	PUNCT
ejpam-5431	116	50	=	=	SYM
ejpam-5431	116	51	{	{	PUNCT
ejpam-5431	116	52	σ	σ	NUM
ejpam-5431	116	53	∈	∈	PROPN
ejpam-5431	116	54	x	x	X
ejpam-5431	116	55	:	:	PUNCT
ejpam-5431	116	56	µa(σ	µa(σ	X
ejpam-5431	116	57	)	)	PUNCT
ejpam-5431	116	58	≥	≥	PRON
ejpam-5431	116	59	⋉	⋉	PROPN
ejpam-5431	116	60	and	and	CCONJ
ejpam-5431	116	61	νa(σ	νa(σ	NUM
ejpam-5431	116	62	)	)	PUNCT
ejpam-5431	116	63	≤	≤	NOUN
ejpam-5431	116	64	β	β	X
ejpam-5431	116	65	}	}	PUNCT
ejpam-5431	116	66	let	let	VERB
ejpam-5431	116	67	x	x	PRON
ejpam-5431	116	68	be	be	AUX
ejpam-5431	116	69	a	a	DET
ejpam-5431	116	70	nonempty	nonempty	ADV
ejpam-5431	116	71	set	set	VERB
ejpam-5431	116	72	and	and	CCONJ
ejpam-5431	116	73	υ	υ	NOUN
ejpam-5431	116	74	be	be	AUX
ejpam-5431	116	75	a	a	DET
ejpam-5431	116	76	ms	ms	PROPN
ejpam-5431	116	77	.	.	PROPN
ejpam-5431	117	1	a	a	DET
ejpam-5431	117	2	mapping	mapping	NOUN
ejpam-5431	117	3	t	t	NOUN
ejpam-5431	117	4	:	:	PUNCT
ejpam-5431	117	5	x	x	X
ejpam-5431	117	6	→	→	SYM
ejpam-5431	117	7	ifs(x	ifs(x	PROPN
ejpam-5431	117	8	)	)	PUNCT
ejpam-5431	117	9	is	be	AUX
ejpam-5431	117	10	called	call	VERB
ejpam-5431	117	11	ifs	ifs	PROPN
ejpam-5431	117	12	-	-	PUNCT
ejpam-5431	117	13	valued	value	VERB
ejpam-5431	117	14	map	map	NOUN
ejpam-5431	117	15	.	.	PUNCT
ejpam-5431	118	1	an	an	DET
ejpam-5431	118	2	ifs	ifs	PROPN
ejpam-5431	118	3	-	-	PUNCT
ejpam-5431	118	4	valued	value	VERB
ejpam-5431	118	5	map	map	NOUN
ejpam-5431	118	6	t	t	PROPN
ejpam-5431	118	7	is	be	AUX
ejpam-5431	118	8	an	an	DET
ejpam-5431	118	9	if	if	SCONJ
ejpam-5431	118	10	subset	subset	NOUN
ejpam-5431	118	11	of	of	ADP
ejpam-5431	118	12	x	x	PUNCT
ejpam-5431	118	13	with	with	ADP
ejpam-5431	118	14	membership	membership	NOUN
ejpam-5431	118	15	function	function	NOUN
ejpam-5431	118	16	µt	µt	X
ejpam-5431	118	17	(	(	PUNCT
ejpam-5431	118	18	σ)(τ	σ)(τ	NUM
ejpam-5431	118	19	)	)	PUNCT
ejpam-5431	118	20	and	and	CCONJ
ejpam-5431	118	21	nonmembership	nonmembership	NOUN
ejpam-5431	118	22	function	function	NOUN
ejpam-5431	118	23	νt	νt	NOUN
ejpam-5431	118	24	(	(	PUNCT
ejpam-5431	118	25	σ)(τ	σ)(τ	NUM
ejpam-5431	118	26	)	)	PUNCT
ejpam-5431	118	27	.	.	PUNCT
ejpam-5431	119	1	an	an	DET
ejpam-5431	119	2	ifs	ifs	PROPN
ejpam-5431	119	3	a	a	PRON
ejpam-5431	119	4	in	in	ADP
ejpam-5431	119	5	a	a	DET
ejpam-5431	119	6	metric	metric	ADJ
ejpam-5431	119	7	linear	linear	NOUN
ejpam-5431	119	8	space	space	NOUN
ejpam-5431	119	9	v	v	NOUN
ejpam-5431	119	10	is	be	AUX
ejpam-5431	119	11	known	know	VERB
ejpam-5431	119	12	to	to	PART
ejpam-5431	119	13	be	be	AUX
ejpam-5431	119	14	an	an	DET
ejpam-5431	119	15	approximate	approximate	ADJ
ejpam-5431	119	16	quantity	quantity	NOUN
ejpam-5431	119	17	if	if	SCONJ
ejpam-5431	119	18	and	and	CCONJ
ejpam-5431	119	19	only	only	ADV
ejpam-5431	119	20	if	if	SCONJ
ejpam-5431	119	21	[	[	X
ejpam-5431	119	22	a](⋉,β	a](⋉,β	X
ejpam-5431	119	23	)	)	PUNCT
ejpam-5431	119	24	is	be	AUX
ejpam-5431	119	25	compact	compact	ADJ
ejpam-5431	119	26	and	and	CCONJ
ejpam-5431	119	27	convex	convex	VERB
ejpam-5431	119	28	in	in	ADP
ejpam-5431	119	29	v	v	NOUN
ejpam-5431	119	30	for	for	ADP
ejpam-5431	119	31	each	each	PRON
ejpam-5431	119	32	(	(	PUNCT
ejpam-5431	119	33	⋉	⋉	PROPN
ejpam-5431	119	34	,	,	PUNCT
ejpam-5431	119	35	β	β	NOUN
ejpam-5431	119	36	)	)	PUNCT
ejpam-5431	119	37	∈	∈	PROPN
ejpam-5431	119	38	(	(	PUNCT
ejpam-5431	119	39	0	0	NUM
ejpam-5431	119	40	,	,	PUNCT
ejpam-5431	119	41	1]×[0	1]×[0	NUM
ejpam-5431	119	42	,	,	PUNCT
ejpam-5431	119	43	1	1	NUM
ejpam-5431	119	44	)	)	PUNCT
ejpam-5431	119	45	with	with	ADP
ejpam-5431	119	46	supσ∈v	supσ∈v	PROPN
ejpam-5431	119	47	µa(σ	µa(σ	NOUN
ejpam-5431	119	48	)	)	PUNCT
ejpam-5431	120	1	=	=	SYM
ejpam-5431	120	2	1	1	NUM
ejpam-5431	120	3	and	and	CCONJ
ejpam-5431	120	4	infσ∈v	infσ∈v	NOUN
ejpam-5431	120	5	νa(σ	νa(σ	NOUN
ejpam-5431	120	6	)	)	PUNCT
ejpam-5431	120	7	=	=	SYM
ejpam-5431	121	1	0	0	X
ejpam-5431	121	2	.	.	PUNCT
ejpam-5431	122	1	the	the	DET
ejpam-5431	122	2	compilation	compilation	NOUN
ejpam-5431	122	3	of	of	ADP
ejpam-5431	122	4	all	all	DET
ejpam-5431	122	5	approximate	approximate	ADJ
ejpam-5431	122	6	quantities	quantity	NOUN
ejpam-5431	122	7	in	in	ADP
ejpam-5431	122	8	v	v	NOUN
ejpam-5431	122	9	is	be	AUX
ejpam-5431	122	10	denoted	denote	VERB
ejpam-5431	122	11	by	by	ADP
ejpam-5431	122	12	n.	n.	PROPN
ejpam-5431	122	13	saleem	saleem	PROPN
ejpam-5431	122	14	et	et	PROPN
ejpam-5431	122	15	al	al	PROPN
ejpam-5431	122	16	.	.	PUNCT
ejpam-5431	122	17	/	/	SYM
ejpam-5431	122	18	eur	eur	PROPN
ejpam-5431	122	19	.	.	PUNCT
ejpam-5431	123	1	j.	j.	PROPN
ejpam-5431	123	2	pure	pure	PROPN
ejpam-5431	123	3	appl	appl	PROPN
ejpam-5431	123	4	.	.	PROPN
ejpam-5431	123	5	math	math	PROPN
ejpam-5431	123	6	,	,	PUNCT
ejpam-5431	123	7	17	17	NUM
ejpam-5431	123	8	(	(	PUNCT
ejpam-5431	123	9	4	4	NUM
ejpam-5431	123	10	)	)	PUNCT
ejpam-5431	123	11	(	(	PUNCT
ejpam-5431	123	12	2024	2024	NUM
ejpam-5431	123	13	)	)	PUNCT
ejpam-5431	123	14	,	,	PUNCT
ejpam-5431	123	15	3304	3304	NUM
ejpam-5431	123	16	-	-	SYM
ejpam-5431	123	17	3335	3335	NUM
ejpam-5431	123	18	3310	3310	NUM
ejpam-5431	123	19	1	1	NUM
ejpam-5431	123	20	2	2	NUM
ejpam-5431	123	21	3	3	NUM
ejpam-5431	123	22	4	4	NUM
ejpam-5431	123	23	5	5	NUM
ejpam-5431	123	24	6	6	NUM
ejpam-5431	123	25	7	7	NUM
ejpam-5431	123	26	8	8	NUM
ejpam-5431	123	27	0.2	0.2	NUM
ejpam-5431	123	28	0.4	0.4	NUM
ejpam-5431	123	29	0.6	0.6	NUM
ejpam-5431	123	30	0.8	0.8	NUM
ejpam-5431	123	31	=	=	SYM
ejpam-5431	123	32	m(a	m(a	NOUN
ejpam-5431	123	33	)	)	PUNCT
ejpam-5431	123	34	=	=	SYM
ejpam-5431	123	35	n(a	n(a	NOUN
ejpam-5431	123	36	)	)	PUNCT
ejpam-5431	123	37	figure	figure	NOUN
ejpam-5431	123	38	2	2	NUM
ejpam-5431	123	39	:	:	PUNCT
ejpam-5431	123	40	scattered	scatter	VERB
ejpam-5431	123	41	plot	plot	NOUN
ejpam-5431	123	42	for	for	ADP
ejpam-5431	123	43	membership	membership	NOUN
ejpam-5431	123	44	and	and	CCONJ
ejpam-5431	123	45	non	non	ADJ
ejpam-5431	123	46	-	-	NOUN
ejpam-5431	123	47	membership	membership	NOUN
ejpam-5431	123	48	of	of	ADP
ejpam-5431	123	49	an	an	DET
ejpam-5431	123	50	ifs	ifs	PROPN
ejpam-5431	123	51	a	a	DET
ejpam-5431	123	52	w	w	PROPN
ejpam-5431	123	53	(	(	PUNCT
ejpam-5431	123	54	v	v	NOUN
ejpam-5431	123	55	)	)	PUNCT
ejpam-5431	123	56	.	.	PUNCT
ejpam-5431	124	1	if	if	SCONJ
ejpam-5431	124	2	there	there	PRON
ejpam-5431	124	3	is	be	VERB
ejpam-5431	124	4	(	(	PUNCT
ejpam-5431	124	5	⋉	⋉	PROPN
ejpam-5431	124	6	,	,	PUNCT
ejpam-5431	124	7	β	β	NOUN
ejpam-5431	124	8	)	)	PUNCT
ejpam-5431	124	9	∈	∈	PROPN
ejpam-5431	124	10	(	(	PUNCT
ejpam-5431	124	11	0	0	NUM
ejpam-5431	124	12	,	,	PUNCT
ejpam-5431	124	13	1]×[0	1]×[0	NUM
ejpam-5431	124	14	,	,	PUNCT
ejpam-5431	124	15	1	1	NUM
ejpam-5431	124	16	)	)	PUNCT
ejpam-5431	124	17	in	in	ADP
ejpam-5431	124	18	such	such	DET
ejpam-5431	124	19	a	a	DET
ejpam-5431	124	20	way	way	NOUN
ejpam-5431	124	21	that	that	SCONJ
ejpam-5431	124	22	[	[	X
ejpam-5431	124	23	a](⋉,β	a](⋉,β	NOUN
ejpam-5431	124	24	)	)	PUNCT
ejpam-5431	124	25	,	,	PUNCT
ejpam-5431	124	26	[	[	X
ejpam-5431	124	27	b](⋉,β	b](⋉,β	X
ejpam-5431	124	28	)	)	PUNCT
ejpam-5431	124	29	∈	∈	PROPN
ejpam-5431	124	30	q(x	q(x	PROPN
ejpam-5431	124	31	)	)	PUNCT
ejpam-5431	124	32	,	,	PUNCT
ejpam-5431	124	33	then	then	ADV
ejpam-5431	124	34	establish	establish	VERB
ejpam-5431	124	35	d(⋉,β)(a	d(⋉,β)(a	PROPN
ejpam-5431	124	36	,	,	PUNCT
ejpam-5431	124	37	b	b	NOUN
ejpam-5431	124	38	)	)	PUNCT
ejpam-5431	124	39	=	=	PUNCT
ejpam-5431	124	40	ℵ([a](⋉,β	ℵ([a](⋉,β	NOUN
ejpam-5431	124	41	)	)	PUNCT
ejpam-5431	124	42	,	,	PUNCT
ejpam-5431	124	43	[	[	X
ejpam-5431	124	44	b](⋉,β	b](⋉,β	NOUN
ejpam-5431	124	45	)	)	PUNCT
ejpam-5431	124	46	)	)	PUNCT
ejpam-5431	125	1	δ+∞(a	δ+∞(a	PROPN
ejpam-5431	125	2	,	,	PUNCT
ejpam-5431	125	3	b	b	NOUN
ejpam-5431	125	4	)	)	PUNCT
ejpam-5431	125	5	=	=	SYM
ejpam-5431	125	6	sup	sup	NOUN
ejpam-5431	125	7	(	(	PUNCT
ejpam-5431	125	8	⋉,β	⋉,β	NOUN
ejpam-5431	125	9	)	)	PUNCT
ejpam-5431	125	10	d(⋉,β)(a	d(⋉,β)(a	ADP
ejpam-5431	125	11	,	,	PUNCT
ejpam-5431	125	12	b	b	NOUN
ejpam-5431	125	13	)	)	PUNCT
ejpam-5431	125	14	.	.	PUNCT
ejpam-5431	126	1	definition	definition	NOUN
ejpam-5431	126	2	14	14	NUM
ejpam-5431	126	3	.	.	PUNCT
ejpam-5431	127	1	[	[	X
ejpam-5431	127	2	4	4	X
ejpam-5431	127	3	]	]	PUNCT
ejpam-5431	127	4	let	let	VERB
ejpam-5431	127	5	x	x	PRON
ejpam-5431	127	6	be	be	AUX
ejpam-5431	127	7	an	an	DET
ejpam-5431	127	8	arbitrary	arbitrary	ADJ
ejpam-5431	127	9	set	set	NOUN
ejpam-5431	127	10	,	,	PUNCT
ejpam-5431	127	11	a	a	DET
ejpam-5431	127	12	point	point	NOUN
ejpam-5431	127	13	ς	ς	X
ejpam-5431	127	14	∈	∈	PROPN
ejpam-5431	127	15	x	x	AUX
ejpam-5431	127	16	is	be	AUX
ejpam-5431	127	17	called	call	VERB
ejpam-5431	127	18	an	an	DET
ejpam-5431	127	19	iffp	iffp	NOUN
ejpam-5431	127	20	of	of	ADP
ejpam-5431	127	21	an	an	DET
ejpam-5431	127	22	ifm	ifm	NOUN
ejpam-5431	127	23	s	s	PART
ejpam-5431	127	24	:	:	PUNCT
ejpam-5431	127	25	x	x	SYM
ejpam-5431	127	26	→	→	SYM
ejpam-5431	127	27	ifs(x	ifs(x	PROPN
ejpam-5431	127	28	)	)	PUNCT
ejpam-5431	127	29	,	,	PUNCT
ejpam-5431	127	30	if	if	SCONJ
ejpam-5431	127	31	there	there	PRON
ejpam-5431	127	32	exists	exist	VERB
ejpam-5431	127	33	(	(	PUNCT
ejpam-5431	127	34	⋉	⋉	PROPN
ejpam-5431	127	35	,	,	PUNCT
ejpam-5431	127	36	β	β	NOUN
ejpam-5431	127	37	)	)	PUNCT
ejpam-5431	127	38	∈	∈	PROPN
ejpam-5431	127	39	(	(	PUNCT
ejpam-5431	127	40	0	0	NUM
ejpam-5431	127	41	,	,	PUNCT
ejpam-5431	127	42	1]×	1]×	NUM
ejpam-5431	128	1	[	[	X
ejpam-5431	128	2	0	0	NUM
ejpam-5431	128	3	,	,	PUNCT
ejpam-5431	128	4	1	1	NUM
ejpam-5431	128	5	)	)	PUNCT
ejpam-5431	128	6	so	so	SCONJ
ejpam-5431	128	7	that	that	SCONJ
ejpam-5431	128	8	ς	ς	PROPN
ejpam-5431	128	9	∈	∈	PROPN
ejpam-5431	128	10	[	[	X
ejpam-5431	128	11	sς](⋉,β	sς](⋉,β	NOUN
ejpam-5431	128	12	)	)	PUNCT
ejpam-5431	128	13	.	.	PUNCT
ejpam-5431	129	1	a	a	DET
ejpam-5431	129	2	point	point	NOUN
ejpam-5431	129	3	ς	ς	X
ejpam-5431	129	4	∈	∈	PROPN
ejpam-5431	129	5	x	x	PUNCT
ejpam-5431	129	6	is	be	AUX
ejpam-5431	129	7	referred	refer	VERB
ejpam-5431	129	8	to	to	ADP
ejpam-5431	129	9	as	as	ADP
ejpam-5431	129	10	fp	fp	PROPN
ejpam-5431	129	11	of	of	ADP
ejpam-5431	129	12	an	an	DET
ejpam-5431	129	13	ifm	ifm	NOUN
ejpam-5431	129	14	s	s	PART
ejpam-5431	129	15	:	:	PUNCT
ejpam-5431	129	16	x	x	SYM
ejpam-5431	129	17	→	→	SYM
ejpam-5431	129	18	ifs(x	ifs(x	PROPN
ejpam-5431	129	19	)	)	PUNCT
ejpam-5431	129	20	,	,	PUNCT
ejpam-5431	129	21	if	if	SCONJ
ejpam-5431	129	22	µ(sς)(ς	µ(sς)(ς	PROPN
ejpam-5431	129	23	)	)	PUNCT
ejpam-5431	129	24	≥	≥	NOUN
ejpam-5431	129	25	µ(sς)(σ	µ(sς)(σ	PROPN
ejpam-5431	129	26	)	)	PUNCT
ejpam-5431	129	27	and	and	CCONJ
ejpam-5431	129	28	ν(sς)(ς	ν(sς)(ς	PROPN
ejpam-5431	129	29	)	)	PUNCT
ejpam-5431	129	30	≤	≤	NUM
ejpam-5431	129	31	ν(sς)(σ	ν(sς)(σ	NOUN
ejpam-5431	129	32	)	)	PUNCT
ejpam-5431	129	33	for	for	ADP
ejpam-5431	129	34	all	all	PRON
ejpam-5431	129	35	σ	σ	PROPN
ejpam-5431	129	36	∈	∈	PROPN
ejpam-5431	129	37	x.	x.	NOUN
ejpam-5431	129	38	give	give	VERB
ejpam-5431	129	39	the	the	DET
ejpam-5431	129	40	set	set	NOUN
ejpam-5431	129	41	of	of	ADP
ejpam-5431	129	42	all	all	DET
ejpam-5431	129	43	fps	fps	NOUN
ejpam-5431	129	44	of	of	ADP
ejpam-5431	129	45	t	t	PROPN
ejpam-5431	129	46	,	,	PUNCT
ejpam-5431	129	47	the	the	DET
ejpam-5431	129	48	symbol	symbol	NOUN
ejpam-5431	129	49	fix(t	fix(t	PROPN
ejpam-5431	129	50	)	)	PUNCT
ejpam-5431	129	51	.	.	PUNCT
ejpam-5431	130	1	rus	rus	NOUN
ejpam-5431	131	1	[	[	X
ejpam-5431	131	2	24	24	NUM
ejpam-5431	131	3	]	]	PUNCT
ejpam-5431	131	4	introduced	introduce	VERB
ejpam-5431	131	5	the	the	DET
ejpam-5431	131	6	idea	idea	NOUN
ejpam-5431	131	7	of	of	ADP
ejpam-5431	131	8	comparison	comparison	NOUN
ejpam-5431	131	9	function	function	NOUN
ejpam-5431	131	10	(	(	PUNCT
ejpam-5431	131	11	cf	cf	NOUN
ejpam-5431	131	12	)	)	PUNCT
ejpam-5431	131	13	,	,	PUNCT
ejpam-5431	131	14	which	which	PRON
ejpam-5431	131	15	a	a	DET
ejpam-5431	131	16	lot	lot	NOUN
ejpam-5431	131	17	of	of	ADP
ejpam-5431	131	18	authors	author	NOUN
ejpam-5431	131	19	have	have	AUX
ejpam-5431	131	20	thoroughly	thoroughly	ADV
ejpam-5431	131	21	reviewed	review	VERB
ejpam-5431	131	22	to	to	PART
ejpam-5431	131	23	expand	expand	VERB
ejpam-5431	131	24	more	more	ADJ
ejpam-5431	131	25	generic	generic	ADJ
ejpam-5431	131	26	contraction	contraction	NOUN
ejpam-5431	131	27	type	type	NOUN
ejpam-5431	131	28	mappings	mapping	NOUN
ejpam-5431	131	29	.	.	PUNCT
ejpam-5431	132	1	definition	definition	NOUN
ejpam-5431	132	2	15	15	NUM
ejpam-5431	132	3	.	.	PUNCT
ejpam-5431	133	1	[	[	X
ejpam-5431	133	2	24	24	NUM
ejpam-5431	133	3	]	]	PUNCT
ejpam-5431	133	4	a	a	DET
ejpam-5431	133	5	function	function	NOUN
ejpam-5431	133	6	φ	φ	NOUN
ejpam-5431	133	7	:	:	PUNCT
ejpam-5431	133	8	r+	r+	X
ejpam-5431	133	9	→	→	PUNCT
ejpam-5431	133	10	r+	r+	NOUN
ejpam-5431	133	11	is	be	AUX
ejpam-5431	133	12	known	know	VERB
ejpam-5431	133	13	as	as	ADP
ejpam-5431	133	14	cf	cf	NOUN
ejpam-5431	133	15	(	(	PUNCT
ejpam-5431	133	16	comparison	comparison	NOUN
ejpam-5431	133	17	function	function	NOUN
ejpam-5431	133	18	)	)	PUNCT
ejpam-5431	133	19	if	if	SCONJ
ejpam-5431	133	20	it	it	PRON
ejpam-5431	133	21	does	do	AUX
ejpam-5431	133	22	not	not	PART
ejpam-5431	133	23	decrease	decrease	VERB
ejpam-5431	133	24	and	and	CCONJ
ejpam-5431	133	25	φn(t	φn(t	PUNCT
ejpam-5431	133	26	)	)	PUNCT
ejpam-5431	133	27	→	→	SYM
ejpam-5431	133	28	0	0	NUM
ejpam-5431	133	29	as	as	ADP
ejpam-5431	133	30	n→	n→	ADV
ejpam-5431	133	31	+	+	PROPN
ejpam-5431	133	32	∞	∞	PROPN
ejpam-5431	133	33	for	for	ADP
ejpam-5431	133	34	all	all	DET
ejpam-5431	133	35	t	t	PROPN
ejpam-5431	133	36	≥	≥	NOUN
ejpam-5431	133	37	0	0	NUM
ejpam-5431	133	38	.	.	PUNCT
ejpam-5431	134	1	definition	definition	NOUN
ejpam-5431	134	2	16	16	NUM
ejpam-5431	134	3	.	.	PUNCT
ejpam-5431	135	1	[	[	X
ejpam-5431	135	2	24	24	NUM
ejpam-5431	135	3	]	]	X
ejpam-5431	135	4	a	a	DET
ejpam-5431	135	5	nondecreasing	nondecreasing	ADJ
ejpam-5431	135	6	function	function	NOUN
ejpam-5431	135	7	φ	φ	NOUN
ejpam-5431	135	8	:	:	PUNCT
ejpam-5431	135	9	r+	r+	X
ejpam-5431	135	10	→	→	PUNCT
ejpam-5431	135	11	r+	r+	NOUN
ejpam-5431	135	12	is	be	AUX
ejpam-5431	135	13	called	call	VERB
ejpam-5431	135	14	:	:	PUNCT
ejpam-5431	135	15	(	(	PUNCT
ejpam-5431	135	16	i	i	NOUN
ejpam-5431	135	17	)	)	PUNCT
ejpam-5431	135	18	a	a	DET
ejpam-5431	135	19	c	c	NOUN
ejpam-5431	135	20	-	-	PUNCT
ejpam-5431	135	21	cf	cf	NOUN
ejpam-5431	135	22	if	if	SCONJ
ejpam-5431	135	23	it	it	PRON
ejpam-5431	135	24	fulfils	fulfil	VERB
ejpam-5431	135	25	the	the	DET
ejpam-5431	135	26	criteria	criterion	NOUN
ejpam-5431	135	27	that	that	PRON
ejpam-5431	135	28	∑+∞	∑+∞	ADJ
ejpam-5431	135	29	n=0	n=0	PROPN
ejpam-5431	135	30	φ	φ	NUM
ejpam-5431	135	31	n(t	n(t	PROPN
ejpam-5431	135	32	)	)	PUNCT
ejpam-5431	135	33	converges	converge	VERB
ejpam-5431	135	34	for	for	ADP
ejpam-5431	135	35	all	all	DET
ejpam-5431	135	36	t	t	PROPN
ejpam-5431	135	37	>	>	X
ejpam-5431	135	38	0	0	X
ejpam-5431	135	39	.	.	PUNCT
ejpam-5431	135	40	(	(	PUNCT
ejpam-5431	135	41	ii	ii	NOUN
ejpam-5431	135	42	)	)	PUNCT
ejpam-5431	135	43	a	a	DET
ejpam-5431	135	44	b	b	X
ejpam-5431	135	45	-	-	PUNCT
ejpam-5431	135	46	cf	cf	NOUN
ejpam-5431	135	47	if	if	SCONJ
ejpam-5431	135	48	it	it	PRON
ejpam-5431	135	49	meets	meet	VERB
ejpam-5431	135	50	the	the	DET
ejpam-5431	135	51	requirement	requirement	NOUN
ejpam-5431	135	52	that	that	SCONJ
ejpam-5431	135	53	∑+∞	∑+∞	ADJ
ejpam-5431	135	54	n=0	n=0	PROPN
ejpam-5431	135	55	s	s	PART
ejpam-5431	135	56	nφn(t	nφn(t	PROPN
ejpam-5431	135	57	)	)	PUNCT
ejpam-5431	135	58	converges	converge	VERB
ejpam-5431	135	59	for	for	ADP
ejpam-5431	135	60	all	all	DET
ejpam-5431	135	61	t	t	NOUN
ejpam-5431	135	62	∈	∈	PROPN
ejpam-5431	135	63	r+	r+	PUNCT
ejpam-5431	135	64	where	where	SCONJ
ejpam-5431	135	65	(	(	PUNCT
ejpam-5431	135	66	x	x	NOUN
ejpam-5431	135	67	,	,	PUNCT
ejpam-5431	135	68	δ	δ	PROPN
ejpam-5431	135	69	)	)	PUNCT
ejpam-5431	135	70	be	be	VERB
ejpam-5431	135	71	a	a	DET
ejpam-5431	135	72	b	b	NOUN
ejpam-5431	135	73	-	-	PUNCT
ejpam-5431	135	74	ms	ms	NOUN
ejpam-5431	135	75	with	with	ADP
ejpam-5431	135	76	s	s	PRON
ejpam-5431	135	77	≥	≥	NUM
ejpam-5431	135	78	1	1	NUM
ejpam-5431	135	79	.	.	PUNCT
ejpam-5431	135	80	example	example	NOUN
ejpam-5431	136	1	17	17	NUM
ejpam-5431	136	2	.	.	PUNCT
ejpam-5431	137	1	let	let	AUX
ejpam-5431	137	2	(	(	PUNCT
ejpam-5431	137	3	x	x	NOUN
ejpam-5431	137	4	,	,	PUNCT
ejpam-5431	137	5	δ	δ	PROPN
ejpam-5431	137	6	)	)	PUNCT
ejpam-5431	137	7	be	be	VERB
ejpam-5431	137	8	a	a	DET
ejpam-5431	137	9	b	b	NOUN
ejpam-5431	137	10	-	-	PUNCT
ejpam-5431	137	11	ms	ms	NOUN
ejpam-5431	137	12	with	with	ADP
ejpam-5431	137	13	coefficient	coefficient	NOUN
ejpam-5431	137	14	h	h	PROPN
ejpam-5431	137	15	≥	≥	NOUN
ejpam-5431	137	16	1	1	NUM
ejpam-5431	137	17	.	.	PUNCT
ejpam-5431	138	1	then	then	ADV
ejpam-5431	138	2	φ(t	φ(t	VERB
ejpam-5431	138	3	)	)	PUNCT
ejpam-5431	138	4	=	=	SYM
ejpam-5431	138	5	℘t	℘t	NOUN
ejpam-5431	138	6	;	;	PUNCT
ejpam-5431	138	7	t	t	PROPN
ejpam-5431	138	8	∈	∈	PROPN
ejpam-5431	138	9	r+	r+	NOUN
ejpam-5431	138	10	with	with	ADP
ejpam-5431	138	11	0	0	NUM
ejpam-5431	138	12	<	<	X
ejpam-5431	138	13	℘	℘	PROPN
ejpam-5431	138	14	<	<	X
ejpam-5431	138	15	1	1	NUM
ejpam-5431	138	16	h	h	NOUN
ejpam-5431	138	17	is	be	AUX
ejpam-5431	138	18	a	a	DET
ejpam-5431	138	19	b	b	NOUN
ejpam-5431	138	20	-	-	PUNCT
ejpam-5431	138	21	cf	cf	NOUN
ejpam-5431	138	22	.	.	PUNCT
ejpam-5431	139	1	the	the	DET
ejpam-5431	139	2	definition	definition	NOUN
ejpam-5431	139	3	of	of	ADP
ejpam-5431	139	4	b	b	NOUN
ejpam-5431	139	5	-	-	PUNCT
ejpam-5431	139	6	cf	cf	NOUN
ejpam-5431	139	7	becomes	become	VERB
ejpam-5431	139	8	equivalent	equivalent	ADJ
ejpam-5431	139	9	to	to	ADP
ejpam-5431	139	10	c	c	NOUN
ejpam-5431	139	11	-	-	PUNCT
ejpam-5431	139	12	cf	cf	NOUN
ejpam-5431	139	13	when	when	SCONJ
ejpam-5431	139	14	h	h	NOUN
ejpam-5431	139	15	=	=	NOUN
ejpam-5431	139	16	1	1	X
ejpam-5431	139	17	.	.	PUNCT
ejpam-5431	139	18	indicate	indicate	VERB
ejpam-5431	139	19	by	by	ADP
ejpam-5431	139	20	λb	λb	ADP
ejpam-5431	139	21	,	,	PUNCT
ejpam-5431	139	22	the	the	DET
ejpam-5431	139	23	family	family	NOUN
ejpam-5431	139	24	of	of	ADP
ejpam-5431	139	25	all	all	DET
ejpam-5431	139	26	functions	function	NOUN
ejpam-5431	139	27	φ	φ	NOUN
ejpam-5431	139	28	:	:	PUNCT
ejpam-5431	139	29	r+	r+	X
ejpam-5431	139	30	×	×	NOUN
ejpam-5431	139	31	r+	r+	PUNCT
ejpam-5431	139	32	fulfilling	fulfil	VERB
ejpam-5431	139	33	:	:	PUNCT
ejpam-5431	139	34	n.	n.	PROPN
ejpam-5431	139	35	saleem	saleem	PROPN
ejpam-5431	139	36	et	et	PROPN
ejpam-5431	139	37	al	al	PROPN
ejpam-5431	139	38	.	.	PUNCT
ejpam-5431	139	39	/	/	SYM
ejpam-5431	139	40	eur	eur	PROPN
ejpam-5431	139	41	.	.	PUNCT
ejpam-5431	140	1	j.	j.	PROPN
ejpam-5431	140	2	pure	pure	PROPN
ejpam-5431	140	3	appl	appl	PROPN
ejpam-5431	140	4	.	.	PROPN
ejpam-5431	140	5	math	math	PROPN
ejpam-5431	140	6	,	,	PUNCT
ejpam-5431	140	7	17	17	NUM
ejpam-5431	140	8	(	(	PUNCT
ejpam-5431	140	9	4	4	NUM
ejpam-5431	140	10	)	)	PUNCT
ejpam-5431	140	11	(	(	PUNCT
ejpam-5431	140	12	2024	2024	NUM
ejpam-5431	140	13	)	)	PUNCT
ejpam-5431	140	14	,	,	PUNCT
ejpam-5431	140	15	3304	3304	NUM
ejpam-5431	140	16	-	-	SYM
ejpam-5431	140	17	3335	3335	NUM
ejpam-5431	140	18	3311	3311	NUM
ejpam-5431	140	19	(	(	PUNCT
ejpam-5431	140	20	i	i	NOUN
ejpam-5431	140	21	)	)	PUNCT
ejpam-5431	140	22	φ	φ	PROPN
ejpam-5431	140	23	is	be	AUX
ejpam-5431	140	24	a	a	DET
ejpam-5431	140	25	b	b	NOUN
ejpam-5431	140	26	-	-	PUNCT
ejpam-5431	140	27	cf	cf	NOUN
ejpam-5431	140	28	;	;	PUNCT
ejpam-5431	140	29	(	(	PUNCT
ejpam-5431	140	30	ii	ii	NOUN
ejpam-5431	140	31	)	)	PUNCT
ejpam-5431	140	32	φ(t	φ(t	PROPN
ejpam-5431	140	33	)	)	PUNCT
ejpam-5431	140	34	=	=	SYM
ejpam-5431	140	35	0	0	PUNCT
ejpam-5431	141	1	if	if	SCONJ
ejpam-5431	141	2	and	and	CCONJ
ejpam-5431	141	3	only	only	ADV
ejpam-5431	141	4	if	if	SCONJ
ejpam-5431	141	5	t	t	PROPN
ejpam-5431	141	6	=	=	SYM
ejpam-5431	141	7	0	0	NUM
ejpam-5431	141	8	;	;	PUNCT
ejpam-5431	141	9	(	(	PUNCT
ejpam-5431	141	10	iii	iii	X
ejpam-5431	141	11	)	)	PUNCT
ejpam-5431	141	12	φ	φ	PROPN
ejpam-5431	141	13	is	be	AUX
ejpam-5431	141	14	continuous	continuous	ADJ
ejpam-5431	141	15	.	.	PUNCT
ejpam-5431	142	1	lemma	lemma	PROPN
ejpam-5431	142	2	18	18	NUM
ejpam-5431	142	3	.	.	PUNCT
ejpam-5431	143	1	[	[	X
ejpam-5431	143	2	24	24	NUM
ejpam-5431	143	3	]	]	PUNCT
ejpam-5431	143	4	for	for	ADP
ejpam-5431	143	5	a	a	DET
ejpam-5431	143	6	cf	cf	NOUN
ejpam-5431	143	7	φ	φ	NOUN
ejpam-5431	143	8	:	:	PUNCT
ejpam-5431	143	9	r+	r+	X
ejpam-5431	143	10	→	→	SYM
ejpam-5431	143	11	r+	r+	X
ejpam-5431	143	12	,	,	PUNCT
ejpam-5431	143	13	the	the	DET
ejpam-5431	143	14	characteristics	characteristic	NOUN
ejpam-5431	143	15	,	,	PUNCT
ejpam-5431	143	16	defined	define	VERB
ejpam-5431	143	17	below	below	ADV
ejpam-5431	143	18	,	,	PUNCT
ejpam-5431	143	19	are	be	AUX
ejpam-5431	143	20	true	true	ADJ
ejpam-5431	143	21	:	:	PUNCT
ejpam-5431	143	22	(	(	PUNCT
ejpam-5431	143	23	i	i	NOUN
ejpam-5431	143	24	)	)	PUNCT
ejpam-5431	143	25	each	each	PRON
ejpam-5431	143	26	iterate	iterate	VERB
ejpam-5431	143	27	φn	φn	NOUN
ejpam-5431	143	28	,	,	PUNCT
ejpam-5431	143	29	n	n	PRON
ejpam-5431	143	30	∈	∈	NOUN
ejpam-5431	143	31	n	n	VERB
ejpam-5431	143	32	is	be	AUX
ejpam-5431	143	33	also	also	ADV
ejpam-5431	143	34	a	a	DET
ejpam-5431	143	35	cf	cf	NOUN
ejpam-5431	143	36	;	;	PUNCT
ejpam-5431	143	37	(	(	PUNCT
ejpam-5431	143	38	ii	ii	NOUN
ejpam-5431	143	39	)	)	PUNCT
ejpam-5431	143	40	φ(t	φ(t	PROPN
ejpam-5431	143	41	)	)	PUNCT
ejpam-5431	143	42	<	<	X
ejpam-5431	143	43	t	t	PROPN
ejpam-5431	143	44	for	for	ADP
ejpam-5431	143	45	all	all	DET
ejpam-5431	143	46	t	t	PROPN
ejpam-5431	143	47	>	>	X
ejpam-5431	143	48	0	0	X
ejpam-5431	143	49	.	.	PUNCT
ejpam-5431	144	1	lemma	lemma	PROPN
ejpam-5431	144	2	19	19	NUM
ejpam-5431	144	3	.	.	PUNCT
ejpam-5431	145	1	[	[	X
ejpam-5431	145	2	24	24	NUM
ejpam-5431	145	3	]	]	PUNCT
ejpam-5431	145	4	let	let	VERB
ejpam-5431	145	5	φ	φ	PROPN
ejpam-5431	145	6	:	:	PUNCT
ejpam-5431	145	7	r+	r+	X
ejpam-5431	145	8	→	→	PUNCT
ejpam-5431	145	9	r+	r+	NUM
ejpam-5431	145	10	be	be	AUX
ejpam-5431	145	11	a	a	DET
ejpam-5431	145	12	b	b	NOUN
ejpam-5431	145	13	-	-	PUNCT
ejpam-5431	145	14	cf	cf	NOUN
ejpam-5431	145	15	.	.	PUNCT
ejpam-5431	146	1	then	then	ADV
ejpam-5431	146	2	,	,	PUNCT
ejpam-5431	146	3	the	the	DET
ejpam-5431	146	4	series	series	NOUN
ejpam-5431	146	5	∑+∞k=0h	∑+∞k=0h	PROPN
ejpam-5431	146	6	kφk(t	kφk(t	PROPN
ejpam-5431	146	7	)	)	PUNCT
ejpam-5431	146	8	converges	converge	VERB
ejpam-5431	146	9	for	for	ADP
ejpam-5431	146	10	each	each	DET
ejpam-5431	146	11	t	t	PROPN
ejpam-5431	146	12	∈	∈	PROPN
ejpam-5431	146	13	r+	r+	NOUN
ejpam-5431	146	14	.	.	PUNCT
ejpam-5431	147	1	3	3	X
ejpam-5431	147	2	.	.	X
ejpam-5431	147	3	main	main	ADJ
ejpam-5431	147	4	results	result	NOUN
ejpam-5431	147	5	within	within	ADP
ejpam-5431	147	6	this	this	DET
ejpam-5431	147	7	part	part	NOUN
ejpam-5431	147	8	,	,	PUNCT
ejpam-5431	147	9	we	we	PRON
ejpam-5431	147	10	’ll	’ll	AUX
ejpam-5431	147	11	discuss	discuss	VERB
ejpam-5431	147	12	the	the	DET
ejpam-5431	147	13	idea	idea	NOUN
ejpam-5431	147	14	of	of	ADP
ejpam-5431	147	15	γ	γ	NOUN
ejpam-5431	147	16	-	-	PUNCT
ejpam-5431	147	17	admissibility	admissibility	NOUN
ejpam-5431	147	18	of	of	ADP
ejpam-5431	147	19	ifs	ifs	PROPN
ejpam-5431	147	20	-	-	PUNCT
ejpam-5431	147	21	valued	value	VERB
ejpam-5431	147	22	maps	map	NOUN
ejpam-5431	147	23	,	,	PUNCT
ejpam-5431	147	24	which	which	PRON
ejpam-5431	147	25	is	be	AUX
ejpam-5431	147	26	inspired	inspire	VERB
ejpam-5431	147	27	by	by	ADP
ejpam-5431	147	28	the	the	DET
ejpam-5431	147	29	idea	idea	NOUN
ejpam-5431	147	30	of	of	ADP
ejpam-5431	147	31	γ	γ	NOUN
ejpam-5431	147	32	-	-	PUNCT
ejpam-5431	147	33	admissibility	admissibility	NOUN
ejpam-5431	147	34	raised	raise	VERB
ejpam-5431	147	35	by	by	ADP
ejpam-5431	147	36	samet	samet	PROPN
ejpam-5431	147	37	et	et	PROPN
ejpam-5431	147	38	al	al	PROPN
ejpam-5431	147	39	.	.	PUNCT
ejpam-5431	148	1	[	[	X
ejpam-5431	148	2	25	25	NUM
ejpam-5431	148	3	]	]	PUNCT
ejpam-5431	148	4	.	.	PUNCT
ejpam-5431	149	1	definition	definition	NOUN
ejpam-5431	149	2	20	20	NUM
ejpam-5431	149	3	.	.	PUNCT
ejpam-5431	150	1	let	let	AUX
ejpam-5431	150	2	(	(	PUNCT
ejpam-5431	150	3	x	x	NOUN
ejpam-5431	150	4	,	,	PUNCT
ejpam-5431	150	5	δ	δ	PROPN
ejpam-5431	150	6	)	)	PUNCT
ejpam-5431	150	7	be	be	VERB
ejpam-5431	150	8	a	a	DET
ejpam-5431	150	9	metric	metric	ADJ
ejpam-5431	150	10	linear	linear	ADJ
ejpam-5431	150	11	space	space	NOUN
ejpam-5431	150	12	.	.	PUNCT
ejpam-5431	151	1	a	a	DET
ejpam-5431	151	2	mapping	mapping	NOUN
ejpam-5431	151	3	t	t	NOUN
ejpam-5431	151	4	:	:	PUNCT
ejpam-5431	151	5	x	x	X
ejpam-5431	151	6	→	→	SYM
ejpam-5431	151	7	ifs(x	ifs(x	PROPN
ejpam-5431	151	8	)	)	PUNCT
ejpam-5431	151	9	is	be	AUX
ejpam-5431	151	10	called	call	VERB
ejpam-5431	151	11	an	an	DET
ejpam-5431	151	12	if	if	SCONJ
ejpam-5431	151	13	λ	λ	NOUN
ejpam-5431	151	14	-	-	NOUN
ejpam-5431	151	15	contraction	contraction	NOUN
ejpam-5431	151	16	,	,	PUNCT
ejpam-5431	151	17	if	if	SCONJ
ejpam-5431	151	18	there	there	PRON
ejpam-5431	151	19	is	be	VERB
ejpam-5431	151	20	λ	λ	PROPN
ejpam-5431	151	21	∈	∈	PROPN
ejpam-5431	151	22	(	(	PUNCT
ejpam-5431	151	23	0	0	NUM
ejpam-5431	151	24	,	,	PUNCT
ejpam-5431	151	25	1	1	NUM
ejpam-5431	151	26	)	)	PUNCT
ejpam-5431	151	27	in	in	ADP
ejpam-5431	151	28	a	a	DET
ejpam-5431	151	29	way	way	NOUN
ejpam-5431	151	30	that	that	PRON
ejpam-5431	151	31	for	for	ADP
ejpam-5431	151	32	each	each	DET
ejpam-5431	151	33	σ	σ	PROPN
ejpam-5431	151	34	,	,	PUNCT
ejpam-5431	151	35	τ	τ	PROPN
ejpam-5431	151	36	∈	∈	PROPN
ejpam-5431	151	37	x	x	NOUN
ejpam-5431	151	38	,	,	PUNCT
ejpam-5431	151	39	δ+∞(t	δ+∞(t	PROPN
ejpam-5431	151	40	(	(	PUNCT
ejpam-5431	151	41	σ	σ	PROPN
ejpam-5431	151	42	)	)	PUNCT
ejpam-5431	151	43	,	,	PUNCT
ejpam-5431	151	44	t	t	PROPN
ejpam-5431	151	45	(	(	PUNCT
ejpam-5431	151	46	τ	τ	PROPN
ejpam-5431	151	47	)	)	PUNCT
ejpam-5431	151	48	)	)	PUNCT
ejpam-5431	151	49	≤	≤	NOUN
ejpam-5431	151	50	λδ(σ	λδ(σ	NUM
ejpam-5431	151	51	,	,	PUNCT
ejpam-5431	151	52	τ	τ	X
ejpam-5431	151	53	)	)	PUNCT
ejpam-5431	151	54	.	.	PUNCT
ejpam-5431	152	1	definition	definition	NOUN
ejpam-5431	152	2	21	21	NUM
ejpam-5431	152	3	.	.	PUNCT
ejpam-5431	153	1	for	for	ADP
ejpam-5431	153	2	a	a	DET
ejpam-5431	153	3	b	b	NOUN
ejpam-5431	153	4	-	-	PUNCT
ejpam-5431	153	5	ms	ms	ADJ
ejpam-5431	153	6	(	(	PUNCT
ejpam-5431	153	7	x	x	PROPN
ejpam-5431	153	8	,	,	PUNCT
ejpam-5431	153	9	δ	δ	PROPN
ejpam-5431	153	10	,	,	PUNCT
ejpam-5431	153	11	h	h	NOUN
ejpam-5431	153	12	)	)	PUNCT
ejpam-5431	153	13	,	,	PUNCT
ejpam-5431	153	14	γ	γ	X
ejpam-5431	153	15	:	:	PUNCT
ejpam-5431	153	16	x	x	SYM
ejpam-5431	153	17	×	×	NOUN
ejpam-5431	153	18	x	x	INTJ
ejpam-5431	153	19	→	→	X
ejpam-5431	153	20	r+	r+	NOUN
ejpam-5431	153	21	and	and	CCONJ
ejpam-5431	153	22	ifss	ifss	NOUN
ejpam-5431	153	23	s	s	NOUN
ejpam-5431	153	24	and	and	CCONJ
ejpam-5431	153	25	t	t	PROPN
ejpam-5431	153	26	,	,	PUNCT
ejpam-5431	153	27	the	the	DET
ejpam-5431	153	28	ordered	order	VERB
ejpam-5431	153	29	pair	pair	NOUN
ejpam-5431	153	30	(	(	PUNCT
ejpam-5431	153	31	s	s	PROPN
ejpam-5431	153	32	,	,	PUNCT
ejpam-5431	153	33	t	t	PROPN
ejpam-5431	153	34	)	)	PUNCT
ejpam-5431	153	35	is	be	AUX
ejpam-5431	153	36	known	know	VERB
ejpam-5431	153	37	as	as	ADP
ejpam-5431	153	38	γ	γ	NOUN
ejpam-5431	153	39	-	-	ADJ
ejpam-5431	153	40	admissible	admissible	ADJ
ejpam-5431	153	41	if	if	SCONJ
ejpam-5431	153	42	the	the	DET
ejpam-5431	153	43	criteria	criterion	NOUN
ejpam-5431	153	44	bellow	bellow	ADV
ejpam-5431	153	45	are	be	AUX
ejpam-5431	153	46	met	meet	VERB
ejpam-5431	153	47	:	:	PUNCT
ejpam-5431	153	48	(	(	PUNCT
ejpam-5431	153	49	i	i	NOUN
ejpam-5431	153	50	)	)	PUNCT
ejpam-5431	153	51	for	for	ADP
ejpam-5431	153	52	each	each	DET
ejpam-5431	153	53	σ	σ	NOUN
ejpam-5431	153	54	∈	∈	PROPN
ejpam-5431	153	55	x	x	X
ejpam-5431	153	56	and	and	CCONJ
ejpam-5431	153	57	τ	τ	PROPN
ejpam-5431	153	58	∈	∈	PROPN
ejpam-5431	154	1	[	[	X
ejpam-5431	154	2	sσ](⋉(σ),β(σ	sσ](⋉(σ),β(σ	NOUN
ejpam-5431	154	3	)	)	PUNCT
ejpam-5431	154	4	)	)	PUNCT
ejpam-5431	154	5	,	,	PUNCT
ejpam-5431	154	6	where	where	SCONJ
ejpam-5431	154	7	(	(	PUNCT
ejpam-5431	154	8	⋉(σ	⋉(σ	NOUN
ejpam-5431	154	9	)	)	PUNCT
ejpam-5431	154	10	,	,	PUNCT
ejpam-5431	154	11	β(σ	β(σ	NOUN
ejpam-5431	154	12	)	)	PUNCT
ejpam-5431	154	13	)	)	PUNCT
ejpam-5431	155	1	∈	∈	PROPN
ejpam-5431	155	2	(	(	PUNCT
ejpam-5431	155	3	0	0	NUM
ejpam-5431	155	4	,	,	PUNCT
ejpam-5431	155	5	1	1	NUM
ejpam-5431	155	6	]	]	SYM
ejpam-5431	155	7	×	×	NOUN
ejpam-5431	156	1	[	[	X
ejpam-5431	156	2	0	0	NUM
ejpam-5431	156	3	,	,	PUNCT
ejpam-5431	156	4	1	1	NUM
ejpam-5431	156	5	)	)	PUNCT
ejpam-5431	156	6	,	,	PUNCT
ejpam-5431	156	7	with	with	ADP
ejpam-5431	156	8	γ(σ	γ(σ	PROPN
ejpam-5431	156	9	,	,	PUNCT
ejpam-5431	156	10	τ	τ	PROPN
ejpam-5431	156	11	)	)	PUNCT
ejpam-5431	156	12	≥	≥	NOUN
ejpam-5431	156	13	1	1	NUM
ejpam-5431	156	14	,	,	PUNCT
ejpam-5431	156	15	we	we	PRON
ejpam-5431	156	16	have	have	VERB
ejpam-5431	156	17	γ(τ,ϖ	γ(τ,ϖ	NOUN
ejpam-5431	156	18	)	)	PUNCT
ejpam-5431	156	19	≥	≥	NOUN
ejpam-5431	156	20	1	1	NUM
ejpam-5431	156	21	for	for	ADP
ejpam-5431	156	22	all	all	DET
ejpam-5431	156	23	ϖ	ϖ	PRON
ejpam-5431	156	24	∈	∈	PROPN
ejpam-5431	157	1	[	[	X
ejpam-5431	157	2	t	t	X
ejpam-5431	157	3	τ	τ	X
ejpam-5431	157	4	]	]	X
ejpam-5431	157	5	(	(	PUNCT
ejpam-5431	157	6	⋉(τ),β(τ	⋉(τ),β(τ	NOUN
ejpam-5431	157	7	)	)	PUNCT
ejpam-5431	157	8	)	)	PUNCT
ejpam-5431	158	1	̸=	̸=	PROPN
ejpam-5431	158	2	φ	φ	NUM
ejpam-5431	158	3	where	where	SCONJ
ejpam-5431	158	4	(	(	PUNCT
ejpam-5431	158	5	⋉(τ	⋉(τ	NOUN
ejpam-5431	158	6	)	)	PUNCT
ejpam-5431	158	7	,	,	PUNCT
ejpam-5431	158	8	β(τ	β(τ	PROPN
ejpam-5431	158	9	)	)	PUNCT
ejpam-5431	158	10	)	)	PUNCT
ejpam-5431	159	1	∈	∈	PROPN
ejpam-5431	159	2	(	(	PUNCT
ejpam-5431	159	3	0	0	NUM
ejpam-5431	159	4	,	,	PUNCT
ejpam-5431	159	5	1]×	1]×	NUM
ejpam-5431	159	6	[	[	X
ejpam-5431	159	7	0	0	NUM
ejpam-5431	159	8	,	,	PUNCT
ejpam-5431	159	9	1	1	NUM
ejpam-5431	159	10	)	)	PUNCT
ejpam-5431	159	11	(	(	PUNCT
ejpam-5431	159	12	ii	ii	NOUN
ejpam-5431	159	13	)	)	PUNCT
ejpam-5431	159	14	for	for	ADP
ejpam-5431	159	15	each	each	DET
ejpam-5431	159	16	σ	σ	NOUN
ejpam-5431	159	17	∈	∈	PROPN
ejpam-5431	159	18	x	x	X
ejpam-5431	159	19	and	and	CCONJ
ejpam-5431	159	20	τ	τ	PROPN
ejpam-5431	159	21	∈	∈	PROPN
ejpam-5431	160	1	[	[	X
ejpam-5431	160	2	t	t	NOUN
ejpam-5431	160	3	σ](⋉(σ),β(σ	σ](⋉(σ),β(σ	NOUN
ejpam-5431	160	4	)	)	PUNCT
ejpam-5431	160	5	)	)	PUNCT
ejpam-5431	160	6	,	,	PUNCT
ejpam-5431	160	7	where	where	SCONJ
ejpam-5431	160	8	(	(	PUNCT
ejpam-5431	160	9	⋉(σ	⋉(σ	NOUN
ejpam-5431	160	10	)	)	PUNCT
ejpam-5431	160	11	,	,	PUNCT
ejpam-5431	160	12	β(σ	β(σ	NOUN
ejpam-5431	160	13	)	)	PUNCT
ejpam-5431	160	14	)	)	PUNCT
ejpam-5431	161	1	∈	∈	PROPN
ejpam-5431	161	2	(	(	PUNCT
ejpam-5431	161	3	0	0	NUM
ejpam-5431	161	4	,	,	PUNCT
ejpam-5431	161	5	1	1	NUM
ejpam-5431	161	6	]	]	SYM
ejpam-5431	161	7	×	×	NOUN
ejpam-5431	161	8	[	[	X
ejpam-5431	161	9	0	0	NUM
ejpam-5431	161	10	,	,	PUNCT
ejpam-5431	161	11	1	1	NUM
ejpam-5431	161	12	)	)	PUNCT
ejpam-5431	161	13	with	with	ADP
ejpam-5431	161	14	γ(σ	γ(σ	PROPN
ejpam-5431	161	15	,	,	PUNCT
ejpam-5431	161	16	τ	τ	PROPN
ejpam-5431	161	17	)	)	PUNCT
ejpam-5431	161	18	≥	≥	NOUN
ejpam-5431	161	19	1	1	NUM
ejpam-5431	161	20	,	,	PUNCT
ejpam-5431	161	21	we	we	PRON
ejpam-5431	161	22	have	have	AUX
ejpam-5431	161	23	γ(τ,ϖ	γ(τ,ϖ	NOUN
ejpam-5431	161	24	)	)	PUNCT
ejpam-5431	161	25	≥	≥	NOUN
ejpam-5431	161	26	1	1	NUM
ejpam-5431	161	27	for	for	ADP
ejpam-5431	161	28	all	all	DET
ejpam-5431	161	29	ϖ	ϖ	PRON
ejpam-5431	161	30	∈	∈	NOUN
ejpam-5431	161	31	[	[	AUX
ejpam-5431	161	32	sτ	sτ	ADP
ejpam-5431	161	33	]	]	PUNCT
ejpam-5431	161	34	(	(	PUNCT
ejpam-5431	161	35	⋉(τ),β(τ	⋉(τ),β(τ	NOUN
ejpam-5431	161	36	)	)	PUNCT
ejpam-5431	161	37	)	)	PUNCT
ejpam-5431	162	1	̸=	̸=	PROPN
ejpam-5431	162	2	φ	φ	NUM
ejpam-5431	162	3	,	,	PUNCT
ejpam-5431	162	4	where	where	SCONJ
ejpam-5431	162	5	(	(	PUNCT
ejpam-5431	162	6	⋉(τ	⋉(τ	NOUN
ejpam-5431	162	7	)	)	PUNCT
ejpam-5431	162	8	,	,	PUNCT
ejpam-5431	162	9	β(τ	β(τ	PROPN
ejpam-5431	162	10	)	)	PUNCT
ejpam-5431	162	11	)	)	PUNCT
ejpam-5431	163	1	∈	∈	PROPN
ejpam-5431	163	2	(	(	PUNCT
ejpam-5431	163	3	0	0	NUM
ejpam-5431	163	4	,	,	PUNCT
ejpam-5431	163	5	1]×	1]×	NUM
ejpam-5431	163	6	[	[	X
ejpam-5431	163	7	0	0	NUM
ejpam-5431	163	8	,	,	PUNCT
ejpam-5431	163	9	1	1	NUM
ejpam-5431	163	10	)	)	PUNCT
ejpam-5431	163	11	.	.	PUNCT
ejpam-5431	164	1	if	if	SCONJ
ejpam-5431	164	2	s	s	NOUN
ejpam-5431	164	3	=	=	X
ejpam-5431	164	4	t	t	PROPN
ejpam-5431	164	5	,	,	PUNCT
ejpam-5431	164	6	then	then	ADV
ejpam-5431	164	7	t	t	PROPN
ejpam-5431	164	8	is	be	AUX
ejpam-5431	164	9	called	call	VERB
ejpam-5431	164	10	γ	γ	NOUN
ejpam-5431	164	11	-	-	ADJ
ejpam-5431	164	12	admissible	admissible	ADJ
ejpam-5431	164	13	.	.	PUNCT
ejpam-5431	165	1	definition	definition	NOUN
ejpam-5431	165	2	22	22	NUM
ejpam-5431	165	3	.	.	PUNCT
ejpam-5431	166	1	let	let	AUX
ejpam-5431	166	2	(	(	PUNCT
ejpam-5431	166	3	x	x	NOUN
ejpam-5431	166	4	,	,	PUNCT
ejpam-5431	166	5	δ	δ	PROPN
ejpam-5431	166	6	,	,	PUNCT
ejpam-5431	166	7	h	h	NOUN
ejpam-5431	166	8	)	)	PUNCT
ejpam-5431	166	9	be	be	VERB
ejpam-5431	166	10	a	a	DET
ejpam-5431	166	11	b	b	NOUN
ejpam-5431	166	12	-	-	PUNCT
ejpam-5431	166	13	ms	ms	NOUN
ejpam-5431	166	14	and	and	CCONJ
ejpam-5431	166	15	s	s	PROPN
ejpam-5431	166	16	,	,	PUNCT
ejpam-5431	166	17	t	t	X
ejpam-5431	166	18	:	:	PUNCT
ejpam-5431	166	19	x	x	X
ejpam-5431	166	20	→	→	SYM
ejpam-5431	166	21	ifs(x	ifs(x	PROPN
ejpam-5431	166	22	)	)	PUNCT
ejpam-5431	166	23	are	be	AUX
ejpam-5431	166	24	ifs	ifs	PROPN
ejpam-5431	166	25	-	-	PUNCT
ejpam-5431	166	26	valued	value	VERB
ejpam-5431	166	27	maps	map	NOUN
ejpam-5431	166	28	.	.	PUNCT
ejpam-5431	167	1	the	the	DET
ejpam-5431	167	2	ordered	order	VERB
ejpam-5431	167	3	pair	pair	NOUN
ejpam-5431	167	4	(	(	PUNCT
ejpam-5431	167	5	s	s	PROPN
ejpam-5431	167	6	,	,	PUNCT
ejpam-5431	167	7	t	t	PROPN
ejpam-5431	167	8	)	)	PUNCT
ejpam-5431	167	9	is	be	AUX
ejpam-5431	167	10	said	say	VERB
ejpam-5431	167	11	to	to	PART
ejpam-5431	167	12	be	be	AUX
ejpam-5431	167	13	ℵ-continuous	ℵ-continuous	ADJ
ejpam-5431	167	14	at	at	ADP
ejpam-5431	167	15	ς	ς	PROPN
ejpam-5431	167	16	∈	∈	PROPN
ejpam-5431	167	17	x	x	PUNCT
ejpam-5431	167	18	if	if	SCONJ
ejpam-5431	167	19	for	for	ADP
ejpam-5431	167	20	each	each	DET
ejpam-5431	167	21	sequence	sequence	NOUN
ejpam-5431	167	22	{	{	PUNCT
ejpam-5431	167	23	σn}n≥1	σn}n≥1	NOUN
ejpam-5431	167	24	in	in	ADP
ejpam-5431	167	25	x	x	PRON
ejpam-5431	167	26	,	,	PUNCT
ejpam-5431	167	27	(	(	PUNCT
ejpam-5431	167	28	i	i	NOUN
ejpam-5431	167	29	)	)	PUNCT
ejpam-5431	167	30	limn→+∞	limn→+∞	VERB
ejpam-5431	167	31	δ(σn	δ(σn	PROPN
ejpam-5431	167	32	,	,	PUNCT
ejpam-5431	167	33	ς	ς	PROPN
ejpam-5431	167	34	)	)	PUNCT
ejpam-5431	167	35	=	=	SYM
ejpam-5431	167	36	0	0	NUM
ejpam-5431	167	37	implies	imply	VERB
ejpam-5431	167	38	that	that	SCONJ
ejpam-5431	167	39	limn→+∞	limn→+∞	VERB
ejpam-5431	167	40	ℵ([sσn](⋉(σn),β(σn	ℵ([sσn](⋉(σn),β(σn	PROPN
ejpam-5431	167	41	)	)	PUNCT
ejpam-5431	167	42	)	)	PUNCT
ejpam-5431	167	43	,	,	PUNCT
ejpam-5431	168	1	[	[	X
ejpam-5431	168	2	t	t	NOUN
ejpam-5431	168	3	ς](⋉(ς),β(ς	ς](⋉(ς),β(ς	NUM
ejpam-5431	168	4	)	)	PUNCT
ejpam-5431	168	5	)	)	PUNCT
ejpam-5431	168	6	)	)	PUNCT
ejpam-5431	169	1	=	=	PUNCT
ejpam-5431	169	2	0	0	NUM
ejpam-5431	169	3	where	where	SCONJ
ejpam-5431	169	4	(	(	PUNCT
ejpam-5431	169	5	⋉(σn	⋉(σn	NOUN
ejpam-5431	169	6	)	)	PUNCT
ejpam-5431	169	7	,	,	PUNCT
ejpam-5431	169	8	β(σn	β(σn	NOUN
ejpam-5431	169	9	)	)	PUNCT
ejpam-5431	169	10	)	)	PUNCT
ejpam-5431	169	11	,	,	PUNCT
ejpam-5431	169	12	(	(	PUNCT
ejpam-5431	169	13	⋉(ς	⋉(ς	NOUN
ejpam-5431	169	14	)	)	PUNCT
ejpam-5431	169	15	,	,	PUNCT
ejpam-5431	169	16	β(ς	β(ς	NOUN
ejpam-5431	169	17	)	)	PUNCT
ejpam-5431	169	18	)	)	PUNCT
ejpam-5431	170	1	∈	∈	PROPN
ejpam-5431	170	2	(	(	PUNCT
ejpam-5431	170	3	0	0	NUM
ejpam-5431	170	4	,	,	PUNCT
ejpam-5431	170	5	1]×	1]×	NUM
ejpam-5431	170	6	[	[	X
ejpam-5431	170	7	0	0	NUM
ejpam-5431	170	8	,	,	PUNCT
ejpam-5431	170	9	1	1	NUM
ejpam-5431	170	10	)	)	PUNCT
ejpam-5431	170	11	.	.	PUNCT
ejpam-5431	171	1	(	(	PUNCT
ejpam-5431	171	2	ii	ii	NOUN
ejpam-5431	171	3	)	)	PUNCT
ejpam-5431	171	4	limn→+∞	limn→+∞	VERB
ejpam-5431	171	5	δ(σn	δ(σn	PROPN
ejpam-5431	171	6	,	,	PUNCT
ejpam-5431	171	7	ς	ς	PROPN
ejpam-5431	171	8	)	)	PUNCT
ejpam-5431	171	9	=	=	SYM
ejpam-5431	171	10	0	0	NUM
ejpam-5431	171	11	implies	imply	VERB
ejpam-5431	171	12	that	that	PRON
ejpam-5431	171	13	limn→+∞	limn→+∞	VERB
ejpam-5431	171	14	ℵ([t	ℵ([t	PRON
ejpam-5431	171	15	σn](⋉(σn),β(σn	σn](⋉(σn),β(σn	NUM
ejpam-5431	171	16	)	)	PUNCT
ejpam-5431	171	17	)	)	PUNCT
ejpam-5431	171	18	,	,	PUNCT
ejpam-5431	172	1	[	[	X
ejpam-5431	172	2	sς](⋉(ς),β(ς	sς](⋉(ς),β(ς	X
ejpam-5431	172	3	)	)	PUNCT
ejpam-5431	172	4	)	)	PUNCT
ejpam-5431	172	5	)	)	PUNCT
ejpam-5431	173	1	=	=	PUNCT
ejpam-5431	173	2	0	0	NUM
ejpam-5431	173	3	where	where	SCONJ
ejpam-5431	173	4	(	(	PUNCT
ejpam-5431	173	5	⋉(σn	⋉(σn	NOUN
ejpam-5431	173	6	)	)	PUNCT
ejpam-5431	173	7	,	,	PUNCT
ejpam-5431	173	8	β(σn	β(σn	NOUN
ejpam-5431	173	9	)	)	PUNCT
ejpam-5431	173	10	)	)	PUNCT
ejpam-5431	173	11	,	,	PUNCT
ejpam-5431	173	12	(	(	PUNCT
ejpam-5431	173	13	⋉(ς	⋉(ς	NOUN
ejpam-5431	173	14	)	)	PUNCT
ejpam-5431	173	15	,	,	PUNCT
ejpam-5431	173	16	β(ς	β(ς	NOUN
ejpam-5431	173	17	)	)	PUNCT
ejpam-5431	173	18	)	)	PUNCT
ejpam-5431	174	1	∈	∈	PROPN
ejpam-5431	174	2	(	(	PUNCT
ejpam-5431	174	3	0	0	NUM
ejpam-5431	174	4	,	,	PUNCT
ejpam-5431	174	5	1]×	1]×	NUM
ejpam-5431	174	6	[	[	X
ejpam-5431	174	7	0	0	NUM
ejpam-5431	174	8	,	,	PUNCT
ejpam-5431	174	9	1	1	NUM
ejpam-5431	174	10	)	)	PUNCT
ejpam-5431	174	11	.	.	PUNCT
ejpam-5431	175	1	n.	n.	PROPN
ejpam-5431	175	2	saleem	saleem	PROPN
ejpam-5431	175	3	et	et	PROPN
ejpam-5431	175	4	al	al	PROPN
ejpam-5431	175	5	.	.	PUNCT
ejpam-5431	175	6	/	/	SYM
ejpam-5431	175	7	eur	eur	PROPN
ejpam-5431	175	8	.	.	PUNCT
ejpam-5431	176	1	j.	j.	PROPN
ejpam-5431	176	2	pure	pure	PROPN
ejpam-5431	176	3	appl	appl	PROPN
ejpam-5431	176	4	.	.	PROPN
ejpam-5431	176	5	math	math	PROPN
ejpam-5431	176	6	,	,	PUNCT
ejpam-5431	176	7	17	17	NUM
ejpam-5431	176	8	(	(	PUNCT
ejpam-5431	176	9	4	4	NUM
ejpam-5431	176	10	)	)	PUNCT
ejpam-5431	176	11	(	(	PUNCT
ejpam-5431	176	12	2024	2024	NUM
ejpam-5431	176	13	)	)	PUNCT
ejpam-5431	176	14	,	,	PUNCT
ejpam-5431	176	15	3304	3304	NUM
ejpam-5431	176	16	-	-	SYM
ejpam-5431	176	17	3335	3335	NUM
ejpam-5431	176	18	3312	3312	NUM
ejpam-5431	176	19	definition	definition	NOUN
ejpam-5431	176	20	23	23	NUM
ejpam-5431	176	21	.	.	PUNCT
ejpam-5431	177	1	let	let	AUX
ejpam-5431	177	2	(	(	PUNCT
ejpam-5431	177	3	x	x	NOUN
ejpam-5431	177	4	,	,	PUNCT
ejpam-5431	177	5	δ	δ	PROPN
ejpam-5431	177	6	,	,	PUNCT
ejpam-5431	177	7	h	h	NOUN
ejpam-5431	177	8	)	)	PUNCT
ejpam-5431	177	9	be	be	VERB
ejpam-5431	177	10	a	a	DET
ejpam-5431	177	11	b	b	NOUN
ejpam-5431	177	12	-	-	PUNCT
ejpam-5431	177	13	ms	ms	NOUN
ejpam-5431	177	14	and	and	CCONJ
ejpam-5431	177	15	s	s	PROPN
ejpam-5431	177	16	and	and	CCONJ
ejpam-5431	177	17	t	t	PROPN
ejpam-5431	177	18	are	be	AUX
ejpam-5431	177	19	ifs	ifs	PROPN
ejpam-5431	177	20	-	-	PUNCT
ejpam-5431	177	21	valued	value	VERB
ejpam-5431	177	22	maps	map	NOUN
ejpam-5431	177	23	.	.	PUNCT
ejpam-5431	178	1	the	the	DET
ejpam-5431	178	2	mappings	mapping	NOUN
ejpam-5431	178	3	s	s	PART
ejpam-5431	178	4	and	and	CCONJ
ejpam-5431	178	5	t	t	PROPN
ejpam-5431	178	6	are	be	AUX
ejpam-5431	178	7	called	call	VERB
ejpam-5431	178	8	pairwise	pairwise	PROPN
ejpam-5431	178	9	ahif	ahif	PROPN
ejpam-5431	178	10	z	z	PROPN
ejpam-5431	178	11	-	-	PUNCT
ejpam-5431	178	12	contraction	contraction	NOUN
ejpam-5431	178	13	with	with	ADP
ejpam-5431	178	14	respect	respect	NOUN
ejpam-5431	178	15	to	to	ADP
ejpam-5431	178	16	℘	℘	PROPN
ejpam-5431	178	17	∈	∈	PROPN
ejpam-5431	178	18	z	z	NOUN
ejpam-5431	178	19	,	,	PUNCT
ejpam-5431	178	20	if	if	SCONJ
ejpam-5431	178	21	there	there	PRON
ejpam-5431	178	22	exists	exist	VERB
ejpam-5431	178	23	(	(	PUNCT
ejpam-5431	178	24	⋉	⋉	PROPN
ejpam-5431	178	25	,	,	PUNCT
ejpam-5431	178	26	β	β	NOUN
ejpam-5431	178	27	)	)	PUNCT
ejpam-5431	178	28	∈	∈	PROPN
ejpam-5431	178	29	(	(	PUNCT
ejpam-5431	178	30	0	0	NUM
ejpam-5431	178	31	,	,	PUNCT
ejpam-5431	178	32	1]×	1]×	NUM
ejpam-5431	179	1	[	[	X
ejpam-5431	179	2	0	0	NUM
ejpam-5431	179	3	,	,	PUNCT
ejpam-5431	179	4	1	1	NUM
ejpam-5431	179	5	)	)	PUNCT
ejpam-5431	179	6	a	a	DET
ejpam-5431	179	7	function	function	NOUN
ejpam-5431	179	8	γ	γ	X
ejpam-5431	179	9	:	:	PUNCT
ejpam-5431	179	10	x	x	PROPN
ejpam-5431	179	11	×x	×x	ADP
ejpam-5431	179	12	→	→	PUNCT
ejpam-5431	179	13	r+	r+	NOUN
ejpam-5431	179	14	and	and	CCONJ
ejpam-5431	179	15	a	a	DET
ejpam-5431	179	16	b	b	NOUN
ejpam-5431	179	17	-	-	PUNCT
ejpam-5431	179	18	cf	cf	NOUN
ejpam-5431	179	19	φ	φ	NOUN
ejpam-5431	179	20	:	:	PUNCT
ejpam-5431	179	21	r+	r+	X
ejpam-5431	179	22	×	×	NOUN
ejpam-5431	179	23	r+	r+	NOUN
ejpam-5431	179	24	in	in	ADP
ejpam-5431	179	25	a	a	DET
ejpam-5431	179	26	manner	manner	NOUN
ejpam-5431	179	27	that	that	SCONJ
ejpam-5431	179	28	the	the	DET
ejpam-5431	179	29	following	follow	VERB
ejpam-5431	179	30	prerequisites	prerequisite	NOUN
ejpam-5431	179	31	are	be	AUX
ejpam-5431	179	32	fulfilled	fulfil	VERB
ejpam-5431	179	33	:	:	PUNCT
ejpam-5431	179	34	(	(	PUNCT
ejpam-5431	179	35	i	i	NOUN
ejpam-5431	179	36	)	)	PUNCT
ejpam-5431	179	37	℘(γ(σ	℘(γ(σ	ADJ
ejpam-5431	179	38	,	,	PUNCT
ejpam-5431	179	39	τ)ℵ([sσ](⋉(σ),β(σ	τ)ℵ([sσ](⋉(σ),β(σ	NOUN
ejpam-5431	179	40	)	)	PUNCT
ejpam-5431	179	41	)	)	PUNCT
ejpam-5431	179	42	,	,	PUNCT
ejpam-5431	180	1	[	[	X
ejpam-5431	180	2	t	t	X
ejpam-5431	180	3	τ	τ	X
ejpam-5431	180	4	]	]	X
ejpam-5431	180	5	(	(	PUNCT
ejpam-5431	180	6	⋉(τ),β(τ	⋉(τ),β(τ	NOUN
ejpam-5431	180	7	)	)	PUNCT
ejpam-5431	180	8	)	)	PUNCT
ejpam-5431	180	9	)	)	PUNCT
ejpam-5431	180	10	,	,	PUNCT
ejpam-5431	180	11	φ(m	φ(m	ADJ
ejpam-5431	180	12	r	r	NOUN
ejpam-5431	180	13	(	(	PUNCT
ejpam-5431	180	14	s	s	PROPN
ejpam-5431	180	15	,	,	PUNCT
ejpam-5431	180	16	t	t	NOUN
ejpam-5431	180	17	)	)	PUNCT
ejpam-5431	180	18	(	(	PUNCT
ejpam-5431	180	19	σ	σ	PROPN
ejpam-5431	180	20	,	,	PUNCT
ejpam-5431	180	21	τ	τ	PROPN
ejpam-5431	180	22	)	)	PUNCT
ejpam-5431	180	23	)	)	PUNCT
ejpam-5431	180	24	)	)	PUNCT
ejpam-5431	180	25	≥	≥	NOUN
ejpam-5431	180	26	0	0	NUM
ejpam-5431	180	27	for	for	ADP
ejpam-5431	180	28	all	all	DET
ejpam-5431	180	29	σ	σ	PROPN
ejpam-5431	180	30	,	,	PUNCT
ejpam-5431	180	31	τ	τ	PROPN
ejpam-5431	180	32	∈	∈	PROPN
ejpam-5431	180	33	x	x	NOUN
ejpam-5431	180	34	,	,	PUNCT
ejpam-5431	180	35	where	where	SCONJ
ejpam-5431	180	36	m	m	VERB
ejpam-5431	180	37	r	r	NOUN
ejpam-5431	180	38	(	(	PUNCT
ejpam-5431	180	39	s	s	PROPN
ejpam-5431	180	40	,	,	PUNCT
ejpam-5431	180	41	t	t	NOUN
ejpam-5431	180	42	)	)	PUNCT
ejpam-5431	180	43	(	(	PUNCT
ejpam-5431	180	44	σ	σ	PROPN
ejpam-5431	180	45	,	,	PUNCT
ejpam-5431	180	46	τ	τ	X
ejpam-5431	180	47	)	)	PUNCT
ejpam-5431	180	48	=	=	PRON
ejpam-5431	180	49	{	{	PUNCT
ejpam-5431	181	1	[	[	X
ejpam-5431	181	2	a(σ	a(σ	PROPN
ejpam-5431	181	3	,	,	PUNCT
ejpam-5431	181	4	τ	τ	PROPN
ejpam-5431	181	5	)	)	PUNCT
ejpam-5431	181	6	]	]	PUNCT
ejpam-5431	181	7	1	1	NUM
ejpam-5431	181	8	r	r	NOUN
ejpam-5431	181	9	,	,	PUNCT
ejpam-5431	181	10	for	for	ADP
ejpam-5431	181	11	r	r	NOUN
ejpam-5431	181	12	>	>	X
ejpam-5431	181	13	0	0	NUM
ejpam-5431	181	14	,	,	PUNCT
ejpam-5431	181	15	σ	σ	PROPN
ejpam-5431	181	16	,	,	PUNCT
ejpam-5431	181	17	τ	τ	PROPN
ejpam-5431	181	18	∈	∈	PROPN
ejpam-5431	181	19	x	x	SYM
ejpam-5431	181	20	,	,	PUNCT
ejpam-5431	181	21	b(σ	b(σ	PROPN
ejpam-5431	181	22	,	,	PUNCT
ejpam-5431	181	23	τ	τ	PROPN
ejpam-5431	181	24	)	)	PUNCT
ejpam-5431	181	25	,	,	PUNCT
ejpam-5431	181	26	for	for	ADP
ejpam-5431	181	27	r	r	NOUN
ejpam-5431	181	28	=	=	SYM
ejpam-5431	181	29	0	0	NUM
ejpam-5431	181	30	,	,	PUNCT
ejpam-5431	181	31	σ	σ	PROPN
ejpam-5431	181	32	,	,	PUNCT
ejpam-5431	181	33	τ	τ	PROPN
ejpam-5431	181	34	∈	∈	PROPN
ejpam-5431	181	35	x.	x.	PUNCT
ejpam-5431	182	1	a(σ	a(σ	PROPN
ejpam-5431	182	2	,	,	PUNCT
ejpam-5431	182	3	τ	τ	X
ejpam-5431	182	4	)	)	PUNCT
ejpam-5431	182	5	=	=	SYM
ejpam-5431	182	6	k1(δ(σ	k1(δ(σ	X
ejpam-5431	182	7	,	,	PUNCT
ejpam-5431	182	8	τ	τ	NOUN
ejpam-5431	182	9	)	)	PUNCT
ejpam-5431	182	10	)	)	PUNCT
ejpam-5431	183	1	r	r	NOUN
ejpam-5431	183	2	+	+	CCONJ
ejpam-5431	183	3	k2(δ(σ	k2(δ(σ	X
ejpam-5431	183	4	,	,	PUNCT
ejpam-5431	183	5	[	[	X
ejpam-5431	183	6	sσ](⋉(σ),β(σ	sσ](⋉(σ),β(σ	NOUN
ejpam-5431	183	7	)	)	PUNCT
ejpam-5431	183	8	)	)	PUNCT
ejpam-5431	183	9	)	)	PUNCT
ejpam-5431	183	10	)	)	PUNCT
ejpam-5431	184	1	r	r	NOUN
ejpam-5431	184	2	+	+	CCONJ
ejpam-5431	184	3	k3(δ(y	k3(δ(y	ADV
ejpam-5431	184	4	,	,	PUNCT
ejpam-5431	184	5	[	[	X
ejpam-5431	184	6	t	t	X
ejpam-5431	184	7	τ	τ	X
ejpam-5431	184	8	]	]	X
ejpam-5431	184	9	(	(	PUNCT
ejpam-5431	184	10	⋉(τ),β(τ	⋉(τ),β(τ	NOUN
ejpam-5431	184	11	)	)	PUNCT
ejpam-5431	184	12	)	)	PUNCT
ejpam-5431	184	13	)	)	PUNCT
ejpam-5431	184	14	)	)	PUNCT
ejpam-5431	185	1	r	r	NOUN
ejpam-5431	185	2	+	+	PRON
ejpam-5431	185	3	k4	k4	NOUN
ejpam-5431	185	4	(	(	PUNCT
ejpam-5431	185	5	δ(τ	δ(τ	PROPN
ejpam-5431	185	6	,	,	PUNCT
ejpam-5431	186	1	[	[	X
ejpam-5431	186	2	t	t	X
ejpam-5431	186	3	τ	τ	X
ejpam-5431	186	4	]	]	X
ejpam-5431	186	5	(	(	PUNCT
ejpam-5431	186	6	⋉(τ),β(τ)))(1	⋉(τ),β(τ)))(1	NOUN
ejpam-5431	186	7	+	+	CCONJ
ejpam-5431	186	8	δ(σ	δ(σ	PROPN
ejpam-5431	186	9	,	,	PUNCT
ejpam-5431	186	10	[	[	X
ejpam-5431	186	11	sσ](⋉(σ),β(σ	sσ](⋉(σ),β(σ	NOUN
ejpam-5431	186	12	)	)	PUNCT
ejpam-5431	186	13	)	)	PUNCT
ejpam-5431	186	14	)	)	PUNCT
ejpam-5431	186	15	)	)	PUNCT
ejpam-5431	186	16	1	1	NUM
ejpam-5431	187	1	+	+	CCONJ
ejpam-5431	187	2	δ(σ	δ(σ	PROPN
ejpam-5431	187	3	,	,	PUNCT
ejpam-5431	187	4	τ	τ	X
ejpam-5431	187	5	)	)	PUNCT
ejpam-5431	187	6	)	)	PUNCT
ejpam-5431	187	7	r	r	PROPN
ejpam-5431	187	8	+	+	PROPN
ejpam-5431	187	9	k5	k5	PROPN
ejpam-5431	187	10	(	(	PUNCT
ejpam-5431	187	11	δ(τ	δ(τ	PROPN
ejpam-5431	187	12	,	,	PUNCT
ejpam-5431	188	1	[	[	X
ejpam-5431	188	2	sσ](⋉(σ),β(σ)))(1	sσ](⋉(σ),β(σ)))(1	X
ejpam-5431	188	3	+	+	ADJ
ejpam-5431	188	4	δ(σ	δ(σ	PROPN
ejpam-5431	188	5	,	,	PUNCT
ejpam-5431	188	6	[	[	X
ejpam-5431	188	7	t	t	X
ejpam-5431	188	8	τ	τ	X
ejpam-5431	188	9	]	]	X
ejpam-5431	188	10	(	(	PUNCT
ejpam-5431	188	11	⋉(τ),β(τ	⋉(τ),β(τ	NOUN
ejpam-5431	188	12	)	)	PUNCT
ejpam-5431	188	13	)	)	PUNCT
ejpam-5431	188	14	)	)	PUNCT
ejpam-5431	188	15	)	)	PUNCT
ejpam-5431	188	16	1	1	NUM
ejpam-5431	189	1	+	+	CCONJ
ejpam-5431	189	2	δ(σ	δ(σ	PROPN
ejpam-5431	189	3	,	,	PUNCT
ejpam-5431	189	4	τ	τ	X
ejpam-5431	189	5	)	)	PUNCT
ejpam-5431	189	6	)	)	PUNCT
ejpam-5431	189	7	r	r	NOUN
ejpam-5431	189	8	b(σ	b(σ	PROPN
ejpam-5431	189	9	,	,	PUNCT
ejpam-5431	189	10	τ	τ	X
ejpam-5431	189	11	)	)	PUNCT
ejpam-5431	189	12	=	=	SYM
ejpam-5431	189	13	(	(	PUNCT
ejpam-5431	189	14	δ(σ	δ(σ	PROPN
ejpam-5431	189	15	,	,	PUNCT
ejpam-5431	189	16	τ))k1	τ))k1	PRON
ejpam-5431	189	17	×	×	PROPN
ejpam-5431	189	18	(	(	PUNCT
ejpam-5431	189	19	δ(σ	δ(σ	PROPN
ejpam-5431	189	20	,	,	PUNCT
ejpam-5431	189	21	[	[	X
ejpam-5431	189	22	sσ](⋉(σ),β(σ	sσ](⋉(σ),β(σ	NOUN
ejpam-5431	189	23	)	)	PUNCT
ejpam-5431	189	24	)	)	PUNCT
ejpam-5431	189	25	)	)	PUNCT
ejpam-5431	189	26	)	)	PUNCT
ejpam-5431	189	27	k2	k2	ADJ
ejpam-5431	189	28	×	×	NOUN
ejpam-5431	189	29	(	(	PUNCT
ejpam-5431	189	30	δ(τ	δ(τ	PROPN
ejpam-5431	189	31	,	,	PUNCT
ejpam-5431	189	32	[	[	X
ejpam-5431	189	33	t	t	X
ejpam-5431	189	34	τ	τ	X
ejpam-5431	189	35	]	]	X
ejpam-5431	189	36	(	(	PUNCT
ejpam-5431	189	37	⋉(τ),β(τ	⋉(τ),β(τ	NOUN
ejpam-5431	189	38	)	)	PUNCT
ejpam-5431	189	39	)	)	PUNCT
ejpam-5431	189	40	)	)	PUNCT
ejpam-5431	189	41	)	)	PUNCT
ejpam-5431	190	1	k3	k3	VERB
ejpam-5431	190	2	×	×	NOUN
ejpam-5431	190	3	(	(	PUNCT
ejpam-5431	190	4	δ(τ	δ(τ	PROPN
ejpam-5431	190	5	,	,	PUNCT
ejpam-5431	191	1	[	[	X
ejpam-5431	191	2	t	t	X
ejpam-5431	191	3	τ	τ	X
ejpam-5431	191	4	]	]	X
ejpam-5431	191	5	(	(	PUNCT
ejpam-5431	191	6	⋉(τ),β(τ)))(1	⋉(τ),β(τ)))(1	NOUN
ejpam-5431	191	7	+	+	CCONJ
ejpam-5431	191	8	δ(σ	δ(σ	PROPN
ejpam-5431	191	9	,	,	PUNCT
ejpam-5431	191	10	[	[	X
ejpam-5431	191	11	sσ](⋉(σ),β(σ	sσ](⋉(σ),β(σ	NOUN
ejpam-5431	191	12	)	)	PUNCT
ejpam-5431	191	13	)	)	PUNCT
ejpam-5431	191	14	)	)	PUNCT
ejpam-5431	191	15	)	)	PUNCT
ejpam-5431	191	16	1	1	NUM
ejpam-5431	191	17	+	+	CCONJ
ejpam-5431	191	18	δ(σ	δ(σ	PROPN
ejpam-5431	191	19	,	,	PUNCT
ejpam-5431	191	20	τ	τ	X
ejpam-5431	191	21	)	)	PUNCT
ejpam-5431	191	22	)	)	PUNCT
ejpam-5431	192	1	k4	k4	PROPN
ejpam-5431	192	2	×	×	NOUN
ejpam-5431	192	3	(	(	PUNCT
ejpam-5431	192	4	δ(σ	δ(σ	PROPN
ejpam-5431	192	5	,	,	PUNCT
ejpam-5431	192	6	[	[	X
ejpam-5431	192	7	t	t	X
ejpam-5431	192	8	τ	τ	X
ejpam-5431	192	9	]	]	X
ejpam-5431	192	10	(	(	PUNCT
ejpam-5431	192	11	⋉(τ),β(τ	⋉(τ),β(τ	NOUN
ejpam-5431	192	12	)	)	PUNCT
ejpam-5431	192	13	)	)	PUNCT
ejpam-5431	192	14	)	)	PUNCT
ejpam-5431	193	1	+	+	CCONJ
ejpam-5431	193	2	δ(τ	δ(τ	NOUN
ejpam-5431	193	3	,	,	PUNCT
ejpam-5431	193	4	[	[	X
ejpam-5431	193	5	sσ](⋉(σ),β(σ	sσ](⋉(σ),β(σ	X
ejpam-5431	193	6	)	)	PUNCT
ejpam-5431	193	7	)	)	PUNCT
ejpam-5431	193	8	)	)	PUNCT
ejpam-5431	193	9	2h	2h	X
ejpam-5431	193	10	)	)	PUNCT
ejpam-5431	193	11	k5	k5	PROPN
ejpam-5431	193	12	(	(	PUNCT
ejpam-5431	193	13	ii	ii	NOUN
ejpam-5431	193	14	)	)	PUNCT
ejpam-5431	193	15	℘(γ(σ	℘(γ(σ	ADJ
ejpam-5431	193	16	,	,	PUNCT
ejpam-5431	193	17	τ)ℵ([t	τ)ℵ([t	PROPN
ejpam-5431	193	18	σ](⋉(σ),β(σ	σ](⋉(σ),β(σ	NOUN
ejpam-5431	193	19	)	)	PUNCT
ejpam-5431	193	20	)	)	PUNCT
ejpam-5431	193	21	,	,	PUNCT
ejpam-5431	193	22	[	[	X
ejpam-5431	193	23	sτ	sτ	ADP
ejpam-5431	193	24	]	]	PUNCT
ejpam-5431	193	25	(	(	PUNCT
ejpam-5431	193	26	⋉(τ),β(τ	⋉(τ),β(τ	NOUN
ejpam-5431	193	27	)	)	PUNCT
ejpam-5431	193	28	)	)	PUNCT
ejpam-5431	193	29	)	)	PUNCT
ejpam-5431	193	30	,	,	PUNCT
ejpam-5431	193	31	φ(m	φ(m	ADJ
ejpam-5431	193	32	r	r	NOUN
ejpam-5431	193	33	(	(	PUNCT
ejpam-5431	193	34	t	t	NOUN
ejpam-5431	193	35	,	,	PUNCT
ejpam-5431	193	36	s)(σ	s)(σ	PROPN
ejpam-5431	193	37	,	,	PUNCT
ejpam-5431	193	38	τ	τ	PROPN
ejpam-5431	193	39	)	)	PUNCT
ejpam-5431	193	40	)	)	PUNCT
ejpam-5431	193	41	)	)	PUNCT
ejpam-5431	193	42	≥	≥	NOUN
ejpam-5431	193	43	0	0	NUM
ejpam-5431	193	44	for	for	ADP
ejpam-5431	193	45	all	all	DET
ejpam-5431	193	46	σ	σ	PROPN
ejpam-5431	193	47	,	,	PUNCT
ejpam-5431	193	48	τ	τ	PROPN
ejpam-5431	193	49	∈	∈	PROPN
ejpam-5431	193	50	x	x	NOUN
ejpam-5431	193	51	,	,	PUNCT
ejpam-5431	193	52	where	where	SCONJ
ejpam-5431	193	53	m	m	VERB
ejpam-5431	193	54	r	r	NOUN
ejpam-5431	193	55	(	(	PUNCT
ejpam-5431	193	56	t	t	NOUN
ejpam-5431	193	57	,	,	PUNCT
ejpam-5431	193	58	s)(σ	s)(σ	PROPN
ejpam-5431	193	59	,	,	PUNCT
ejpam-5431	193	60	τ	τ	X
ejpam-5431	193	61	)	)	PUNCT
ejpam-5431	193	62	=	=	PRON
ejpam-5431	193	63	{	{	PUNCT
ejpam-5431	194	1	[	[	X
ejpam-5431	194	2	a(σ	a(σ	PROPN
ejpam-5431	194	3	,	,	PUNCT
ejpam-5431	194	4	τ	τ	PROPN
ejpam-5431	194	5	)	)	PUNCT
ejpam-5431	194	6	]	]	PUNCT
ejpam-5431	194	7	1	1	NUM
ejpam-5431	194	8	r	r	NOUN
ejpam-5431	194	9	,	,	PUNCT
ejpam-5431	194	10	for	for	ADP
ejpam-5431	194	11	r	r	NOUN
ejpam-5431	194	12	>	>	X
ejpam-5431	194	13	0	0	NUM
ejpam-5431	194	14	,	,	PUNCT
ejpam-5431	194	15	σ	σ	PROPN
ejpam-5431	194	16	,	,	PUNCT
ejpam-5431	194	17	τ	τ	PROPN
ejpam-5431	194	18	∈	∈	PROPN
ejpam-5431	194	19	x	x	SYM
ejpam-5431	194	20	,	,	PUNCT
ejpam-5431	194	21	b(σ	b(σ	PROPN
ejpam-5431	194	22	,	,	PUNCT
ejpam-5431	194	23	τ	τ	PROPN
ejpam-5431	194	24	)	)	PUNCT
ejpam-5431	194	25	,	,	PUNCT
ejpam-5431	194	26	for	for	ADP
ejpam-5431	194	27	r	r	NOUN
ejpam-5431	194	28	=	=	SYM
ejpam-5431	194	29	0	0	NUM
ejpam-5431	194	30	,	,	PUNCT
ejpam-5431	194	31	σ	σ	PROPN
ejpam-5431	194	32	,	,	PUNCT
ejpam-5431	194	33	τ	τ	PROPN
ejpam-5431	194	34	∈	∈	PROPN
ejpam-5431	194	35	x.	x.	PUNCT
ejpam-5431	195	1	a(σ	a(σ	PROPN
ejpam-5431	195	2	,	,	PUNCT
ejpam-5431	195	3	τ	τ	X
ejpam-5431	195	4	)	)	PUNCT
ejpam-5431	195	5	=	=	SYM
ejpam-5431	195	6	k1(δ(σ	k1(δ(σ	X
ejpam-5431	195	7	,	,	PUNCT
ejpam-5431	195	8	τ	τ	NOUN
ejpam-5431	195	9	)	)	PUNCT
ejpam-5431	195	10	)	)	PUNCT
ejpam-5431	196	1	r	r	NOUN
ejpam-5431	196	2	+	+	CCONJ
ejpam-5431	196	3	k2(δ(σ	k2(δ(σ	X
ejpam-5431	196	4	,	,	PUNCT
ejpam-5431	196	5	[	[	X
ejpam-5431	196	6	t	t	NOUN
ejpam-5431	196	7	σ](⋉(σ),β(σ	σ](⋉(σ),β(σ	NOUN
ejpam-5431	196	8	)	)	PUNCT
ejpam-5431	196	9	)	)	PUNCT
ejpam-5431	196	10	)	)	PUNCT
ejpam-5431	196	11	)	)	PUNCT
ejpam-5431	197	1	r	r	NOUN
ejpam-5431	197	2	+	+	NUM
ejpam-5431	197	3	k3(δ(τ	k3(δ(τ	NOUN
ejpam-5431	197	4	,	,	PUNCT
ejpam-5431	197	5	[	[	X
ejpam-5431	197	6	sτ	sτ	ADP
ejpam-5431	197	7	]	]	PUNCT
ejpam-5431	197	8	(	(	PUNCT
ejpam-5431	197	9	⋉(τ),β(τ	⋉(τ),β(τ	NOUN
ejpam-5431	197	10	)	)	PUNCT
ejpam-5431	197	11	)	)	PUNCT
ejpam-5431	197	12	)	)	PUNCT
ejpam-5431	197	13	)	)	PUNCT
ejpam-5431	198	1	r	r	NOUN
ejpam-5431	198	2	+	+	PRON
ejpam-5431	198	3	k4	k4	NOUN
ejpam-5431	198	4	(	(	PUNCT
ejpam-5431	198	5	δ(τ	δ(τ	PROPN
ejpam-5431	198	6	,	,	PUNCT
ejpam-5431	198	7	[	[	X
ejpam-5431	198	8	sτ	sτ	ADP
ejpam-5431	198	9	]	]	PUNCT
ejpam-5431	198	10	(	(	PUNCT
ejpam-5431	198	11	⋉(τ),β(τ)))(1	⋉(τ),β(τ)))(1	NOUN
ejpam-5431	198	12	+	+	CCONJ
ejpam-5431	198	13	δ(σ	δ(σ	PROPN
ejpam-5431	198	14	,	,	PUNCT
ejpam-5431	198	15	[	[	X
ejpam-5431	198	16	t	t	NOUN
ejpam-5431	198	17	σ](⋉(σ),β(σ	σ](⋉(σ),β(σ	NOUN
ejpam-5431	198	18	)	)	PUNCT
ejpam-5431	198	19	)	)	PUNCT
ejpam-5431	198	20	)	)	PUNCT
ejpam-5431	198	21	)	)	PUNCT
ejpam-5431	198	22	1	1	NUM
ejpam-5431	199	1	+	+	CCONJ
ejpam-5431	199	2	δ(σ	δ(σ	PROPN
ejpam-5431	199	3	,	,	PUNCT
ejpam-5431	199	4	τ	τ	X
ejpam-5431	199	5	)	)	PUNCT
ejpam-5431	199	6	)	)	PUNCT
ejpam-5431	199	7	r	r	PROPN
ejpam-5431	199	8	+	+	PROPN
ejpam-5431	199	9	k5	k5	PROPN
ejpam-5431	199	10	(	(	PUNCT
ejpam-5431	199	11	δ(τ	δ(τ	PROPN
ejpam-5431	199	12	,	,	PUNCT
ejpam-5431	200	1	[	[	X
ejpam-5431	200	2	t	t	X
ejpam-5431	200	3	σ](⋉(σ),β(τ)))(1	σ](⋉(σ),β(τ)))(1	X
ejpam-5431	200	4	+	+	CCONJ
ejpam-5431	200	5	δ(σ	δ(σ	PROPN
ejpam-5431	200	6	,	,	PUNCT
ejpam-5431	200	7	[	[	X
ejpam-5431	200	8	sτ	sτ	ADP
ejpam-5431	200	9	]	]	PUNCT
ejpam-5431	200	10	(	(	PUNCT
ejpam-5431	200	11	⋉(τ),β(τ	⋉(τ),β(τ	NOUN
ejpam-5431	200	12	)	)	PUNCT
ejpam-5431	200	13	)	)	PUNCT
ejpam-5431	200	14	)	)	PUNCT
ejpam-5431	200	15	)	)	PUNCT
ejpam-5431	200	16	1	1	NUM
ejpam-5431	201	1	+	+	CCONJ
ejpam-5431	201	2	δ(σ	δ(σ	PROPN
ejpam-5431	201	3	,	,	PUNCT
ejpam-5431	201	4	τ	τ	X
ejpam-5431	201	5	)	)	PUNCT
ejpam-5431	201	6	)	)	PUNCT
ejpam-5431	201	7	r	r	NOUN
ejpam-5431	201	8	b(σ	b(σ	PROPN
ejpam-5431	201	9	,	,	PUNCT
ejpam-5431	201	10	τ	τ	X
ejpam-5431	201	11	)	)	PUNCT
ejpam-5431	201	12	=	=	SYM
ejpam-5431	201	13	(	(	PUNCT
ejpam-5431	201	14	δ(σ	δ(σ	PROPN
ejpam-5431	201	15	,	,	PUNCT
ejpam-5431	201	16	τ))k1	τ))k1	PRON
ejpam-5431	201	17	×	×	PROPN
ejpam-5431	201	18	(	(	PUNCT
ejpam-5431	201	19	δ(σ	δ(σ	PROPN
ejpam-5431	201	20	,	,	PUNCT
ejpam-5431	201	21	[	[	X
ejpam-5431	201	22	t	t	NOUN
ejpam-5431	201	23	σ](⋉(σ),β(σ	σ](⋉(σ),β(σ	NOUN
ejpam-5431	201	24	)	)	PUNCT
ejpam-5431	201	25	)	)	PUNCT
ejpam-5431	201	26	)	)	PUNCT
ejpam-5431	201	27	)	)	PUNCT
ejpam-5431	201	28	k2	k2	ADJ
ejpam-5431	201	29	×	×	NOUN
ejpam-5431	201	30	(	(	PUNCT
ejpam-5431	201	31	δ(τ	δ(τ	PROPN
ejpam-5431	201	32	,	,	PUNCT
ejpam-5431	201	33	[	[	X
ejpam-5431	201	34	sτ	sτ	ADP
ejpam-5431	201	35	]	]	PUNCT
ejpam-5431	201	36	(	(	PUNCT
ejpam-5431	201	37	⋉(τ),β(τ	⋉(τ),β(τ	NOUN
ejpam-5431	201	38	)	)	PUNCT
ejpam-5431	201	39	)	)	PUNCT
ejpam-5431	201	40	)	)	PUNCT
ejpam-5431	201	41	)	)	PUNCT
ejpam-5431	202	1	k3	k3	VERB
ejpam-5431	202	2	×	×	NOUN
ejpam-5431	202	3	(	(	PUNCT
ejpam-5431	202	4	δ(τ	δ(τ	PROPN
ejpam-5431	202	5	,	,	PUNCT
ejpam-5431	202	6	[	[	X
ejpam-5431	202	7	sτ	sτ	ADP
ejpam-5431	202	8	]	]	PUNCT
ejpam-5431	202	9	(	(	PUNCT
ejpam-5431	202	10	⋉(τ),β(τ)))(1	⋉(τ),β(τ)))(1	NOUN
ejpam-5431	202	11	+	+	CCONJ
ejpam-5431	202	12	δ(σ	δ(σ	PROPN
ejpam-5431	202	13	,	,	PUNCT
ejpam-5431	202	14	[	[	X
ejpam-5431	202	15	t	t	NOUN
ejpam-5431	202	16	σ](⋉(σ),β(σ	σ](⋉(σ),β(σ	NOUN
ejpam-5431	202	17	)	)	PUNCT
ejpam-5431	202	18	)	)	PUNCT
ejpam-5431	202	19	)	)	PUNCT
ejpam-5431	202	20	)	)	PUNCT
ejpam-5431	202	21	1	1	NUM
ejpam-5431	203	1	+	+	CCONJ
ejpam-5431	203	2	δ(σ	δ(σ	PROPN
ejpam-5431	203	3	,	,	PUNCT
ejpam-5431	203	4	τ	τ	X
ejpam-5431	203	5	)	)	PUNCT
ejpam-5431	203	6	)	)	PUNCT
ejpam-5431	203	7	k4	k4	PROPN
ejpam-5431	203	8	n.	n.	PROPN
ejpam-5431	203	9	saleem	saleem	PROPN
ejpam-5431	203	10	et	et	PROPN
ejpam-5431	203	11	al	al	PROPN
ejpam-5431	203	12	.	.	PUNCT
ejpam-5431	203	13	/	/	SYM
ejpam-5431	203	14	eur	eur	PROPN
ejpam-5431	203	15	.	.	PUNCT
ejpam-5431	204	1	j.	j.	PROPN
ejpam-5431	204	2	pure	pure	PROPN
ejpam-5431	204	3	appl	appl	PROPN
ejpam-5431	204	4	.	.	PROPN
ejpam-5431	204	5	math	math	PROPN
ejpam-5431	204	6	,	,	PUNCT
ejpam-5431	204	7	17	17	NUM
ejpam-5431	204	8	(	(	PUNCT
ejpam-5431	204	9	4	4	NUM
ejpam-5431	204	10	)	)	PUNCT
ejpam-5431	204	11	(	(	PUNCT
ejpam-5431	204	12	2024	2024	NUM
ejpam-5431	204	13	)	)	PUNCT
ejpam-5431	204	14	,	,	PUNCT
ejpam-5431	204	15	3304	3304	NUM
ejpam-5431	204	16	-	-	SYM
ejpam-5431	204	17	3335	3335	NUM
ejpam-5431	204	18	3313	3313	NUM
ejpam-5431	204	19	×	×	NOUN
ejpam-5431	204	20	(	(	PUNCT
ejpam-5431	204	21	δ(σ	δ(σ	PROPN
ejpam-5431	204	22	,	,	PUNCT
ejpam-5431	204	23	[	[	X
ejpam-5431	204	24	sτ	sτ	ADP
ejpam-5431	204	25	]	]	PUNCT
ejpam-5431	204	26	(	(	PUNCT
ejpam-5431	204	27	⋉(τ),β(τ	⋉(τ),β(τ	NOUN
ejpam-5431	204	28	)	)	PUNCT
ejpam-5431	204	29	)	)	PUNCT
ejpam-5431	204	30	)	)	PUNCT
ejpam-5431	205	1	+	+	CCONJ
ejpam-5431	205	2	δ(τ	δ(τ	NOUN
ejpam-5431	205	3	,	,	PUNCT
ejpam-5431	205	4	[	[	X
ejpam-5431	205	5	t	t	X
ejpam-5431	205	6	σ](⋉(σ),β(σ	σ](⋉(σ),β(σ	NOUN
ejpam-5431	205	7	)	)	PUNCT
ejpam-5431	205	8	)	)	PUNCT
ejpam-5431	205	9	)	)	PUNCT
ejpam-5431	205	10	2h	2h	X
ejpam-5431	205	11	)	)	PUNCT
ejpam-5431	205	12	k5	k5	PROPN
ejpam-5431	205	13	where	where	SCONJ
ejpam-5431	205	14	(	(	PUNCT
ejpam-5431	205	15	⋉(σ	⋉(σ	NOUN
ejpam-5431	205	16	)	)	PUNCT
ejpam-5431	205	17	,	,	PUNCT
ejpam-5431	205	18	β(σ	β(σ	NOUN
ejpam-5431	205	19	)	)	PUNCT
ejpam-5431	205	20	)	)	PUNCT
ejpam-5431	205	21	,	,	PUNCT
ejpam-5431	205	22	(	(	PUNCT
ejpam-5431	205	23	⋉(τ	⋉(τ	X
ejpam-5431	205	24	)	)	PUNCT
ejpam-5431	205	25	,	,	PUNCT
ejpam-5431	205	26	β(τ	β(τ	PROPN
ejpam-5431	205	27	)	)	PUNCT
ejpam-5431	205	28	)	)	PUNCT
ejpam-5431	206	1	∈	∈	PROPN
ejpam-5431	206	2	(	(	PUNCT
ejpam-5431	206	3	0	0	NUM
ejpam-5431	206	4	,	,	PUNCT
ejpam-5431	206	5	1	1	NUM
ejpam-5431	206	6	]	]	SYM
ejpam-5431	206	7	×	×	NOUN
ejpam-5431	206	8	[	[	X
ejpam-5431	206	9	0	0	NUM
ejpam-5431	206	10	,	,	PUNCT
ejpam-5431	206	11	1	1	NUM
ejpam-5431	206	12	)	)	PUNCT
ejpam-5431	206	13	with	with	ADP
ejpam-5431	206	14	γ	γ	PROPN
ejpam-5431	206	15	≥	≥	X
ejpam-5431	206	16	0	0	NUM
ejpam-5431	206	17	and	and	CCONJ
ejpam-5431	206	18	ki	ki	PROPN
ejpam-5431	206	19	≥	≥	NUM
ejpam-5431	206	20	0	0	NUM
ejpam-5431	206	21	such	such	ADJ
ejpam-5431	206	22	as∑5	as∑5	NOUN
ejpam-5431	207	1	i=1	i=1	X
ejpam-5431	207	2	ki	ki	PROPN
ejpam-5431	208	1	=	=	SYM
ejpam-5431	208	2	1	1	X
ejpam-5431	208	3	.	.	PUNCT
ejpam-5431	208	4	remark	remark	PROPN
ejpam-5431	208	5	24	24	NUM
ejpam-5431	208	6	.	.	PUNCT
ejpam-5431	209	1	(	(	PUNCT
ejpam-5431	209	2	i	i	NOUN
ejpam-5431	209	3	)	)	PUNCT
ejpam-5431	209	4	if	if	SCONJ
ejpam-5431	209	5	the	the	DET
ejpam-5431	209	6	pair	pair	NOUN
ejpam-5431	209	7	(	(	PUNCT
ejpam-5431	209	8	s	s	PROPN
ejpam-5431	209	9	,	,	PUNCT
ejpam-5431	209	10	t	t	PROPN
ejpam-5431	209	11	)	)	PUNCT
ejpam-5431	209	12	is	be	AUX
ejpam-5431	209	13	ℵ-continuous	ℵ-continuous	ADJ
ejpam-5431	209	14	,	,	PUNCT
ejpam-5431	209	15	then	then	ADV
ejpam-5431	209	16	(	(	PUNCT
ejpam-5431	209	17	t	t	PROPN
ejpam-5431	209	18	,	,	PUNCT
ejpam-5431	209	19	s	s	AUX
ejpam-5431	209	20	)	)	PUNCT
ejpam-5431	209	21	is	be	AUX
ejpam-5431	209	22	also	also	ADV
ejpam-5431	209	23	ℵ-continuous	ℵ-continuous	ADJ
ejpam-5431	209	24	.	.	PUNCT
ejpam-5431	210	1	(	(	PUNCT
ejpam-5431	210	2	ii	ii	NOUN
ejpam-5431	210	3	)	)	PUNCT
ejpam-5431	210	4	if	if	SCONJ
ejpam-5431	210	5	(	(	PUNCT
ejpam-5431	210	6	s	s	X
ejpam-5431	210	7	,	,	PUNCT
ejpam-5431	210	8	t	t	PROPN
ejpam-5431	210	9	)	)	PUNCT
ejpam-5431	210	10	is	be	AUX
ejpam-5431	210	11	pairwise	pairwise	PROPN
ejpam-5431	210	12	ahif	ahif	PROPN
ejpam-5431	210	13	z	z	PROPN
ejpam-5431	210	14	-	-	PUNCT
ejpam-5431	210	15	contraction	contraction	NOUN
ejpam-5431	210	16	then	then	ADV
ejpam-5431	210	17	so	so	ADV
ejpam-5431	210	18	is	be	AUX
ejpam-5431	210	19	(	(	PUNCT
ejpam-5431	210	20	t	t	PROPN
ejpam-5431	210	21	,	,	PUNCT
ejpam-5431	210	22	s	s	PROPN
ejpam-5431	210	23	)	)	PUNCT
ejpam-5431	210	24	.	.	PUNCT
ejpam-5431	211	1	let	let	VERB
ejpam-5431	211	2	ifss(x	ifss(x	NOUN
ejpam-5431	211	3	)	)	PUNCT
ejpam-5431	211	4	be	be	AUX
ejpam-5431	211	5	a	a	DET
ejpam-5431	211	6	subset	subset	NOUN
ejpam-5431	211	7	of	of	ADP
ejpam-5431	211	8	ifs(x	ifs(x	PROPN
ejpam-5431	211	9	)	)	PUNCT
ejpam-5431	211	10	defined	define	VERB
ejpam-5431	211	11	by	by	ADP
ejpam-5431	211	12	:	:	PUNCT
ejpam-5431	211	13	ifss(x	ifss(x	NOUN
ejpam-5431	211	14	)	)	PUNCT
ejpam-5431	211	15	=	=	SYM
ejpam-5431	211	16	{	{	PUNCT
ejpam-5431	211	17	a	a	DET
ejpam-5431	211	18	∈	∈	PROPN
ejpam-5431	211	19	ifs(x	ifs(x	PROPN
ejpam-5431	211	20	)	)	PUNCT
ejpam-5431	211	21	:	:	PUNCT
ejpam-5431	212	1	[	[	X
ejpam-5431	212	2	a](⋉,β	a](⋉,β	X
ejpam-5431	212	3	)	)	PUNCT
ejpam-5431	212	4	∈	∈	PROPN
ejpam-5431	212	5	q(x	q(x	PROPN
ejpam-5431	212	6	)	)	PUNCT
ejpam-5431	212	7	,	,	PUNCT
ejpam-5431	212	8	(	(	PUNCT
ejpam-5431	212	9	⋉	⋉	PROPN
ejpam-5431	212	10	,	,	PUNCT
ejpam-5431	212	11	β	β	NOUN
ejpam-5431	212	12	)	)	PUNCT
ejpam-5431	212	13	∈	∈	PROPN
ejpam-5431	212	14	(	(	PUNCT
ejpam-5431	212	15	0	0	NUM
ejpam-5431	212	16	,	,	PUNCT
ejpam-5431	212	17	1]×	1]×	NUM
ejpam-5431	213	1	[	[	X
ejpam-5431	213	2	0	0	NUM
ejpam-5431	213	3	,	,	PUNCT
ejpam-5431	213	4	1	1	NUM
ejpam-5431	213	5	)	)	PUNCT
ejpam-5431	213	6	}	}	PUNCT
ejpam-5431	213	7	theorem	theorem	VERB
ejpam-5431	213	8	25	25	NUM
ejpam-5431	213	9	.	.	PUNCT
ejpam-5431	214	1	let	let	AUX
ejpam-5431	214	2	(	(	PUNCT
ejpam-5431	214	3	x	x	NOUN
ejpam-5431	214	4	,	,	PUNCT
ejpam-5431	214	5	δ	δ	PROPN
ejpam-5431	214	6	,	,	PUNCT
ejpam-5431	214	7	h	h	NOUN
ejpam-5431	214	8	)	)	PUNCT
ejpam-5431	214	9	be	be	AUX
ejpam-5431	214	10	a	a	DET
ejpam-5431	214	11	complete	complete	ADJ
ejpam-5431	214	12	b	b	NOUN
ejpam-5431	214	13	-	-	PUNCT
ejpam-5431	214	14	ms	ms	NOUN
ejpam-5431	214	15	and	and	CCONJ
ejpam-5431	214	16	s	s	PROPN
ejpam-5431	214	17	,	,	PUNCT
ejpam-5431	214	18	t	t	X
ejpam-5431	214	19	:	:	PUNCT
ejpam-5431	214	20	x	x	X
ejpam-5431	214	21	→	→	SYM
ejpam-5431	214	22	ifs(x	ifs(x	PROPN
ejpam-5431	214	23	)	)	PUNCT
ejpam-5431	214	24	be	be	VERB
ejpam-5431	214	25	pairwise	pairwise	PROPN
ejpam-5431	214	26	ahif	ahif	PROPN
ejpam-5431	214	27	z	z	PROPN
ejpam-5431	214	28	-	-	PUNCT
ejpam-5431	214	29	contraction	contraction	NOUN
ejpam-5431	214	30	pertaining	pertain	VERB
ejpam-5431	214	31	to	to	ADP
ejpam-5431	214	32	℘	℘	PROPN
ejpam-5431	214	33	∈	∈	PROPN
ejpam-5431	214	34	z.	z.	NOUN
ejpam-5431	214	35	furthermore	furthermore	ADV
ejpam-5431	214	36	,	,	PUNCT
ejpam-5431	214	37	suppose	suppose	VERB
ejpam-5431	214	38	that	that	SCONJ
ejpam-5431	214	39	:	:	PUNCT
ejpam-5431	214	40	(	(	PUNCT
ejpam-5431	214	41	i	i	NOUN
ejpam-5431	214	42	)	)	PUNCT
ejpam-5431	214	43	(	(	PUNCT
ejpam-5431	214	44	s	s	PROPN
ejpam-5431	214	45	,	,	PUNCT
ejpam-5431	214	46	t	t	PROPN
ejpam-5431	214	47	)	)	PUNCT
ejpam-5431	214	48	is	be	AUX
ejpam-5431	214	49	a	a	DET
ejpam-5431	214	50	γ	γ	ADJ
ejpam-5431	214	51	-	-	ADJ
ejpam-5431	214	52	admissible	admissible	ADJ
ejpam-5431	214	53	pair	pair	NOUN
ejpam-5431	214	54	;	;	PUNCT
ejpam-5431	214	55	(	(	PUNCT
ejpam-5431	214	56	ii	ii	NOUN
ejpam-5431	214	57	)	)	PUNCT
ejpam-5431	214	58	there	there	PRON
ejpam-5431	214	59	is	be	VERB
ejpam-5431	214	60	σ0	σ0	PROPN
ejpam-5431	214	61	∈	∈	PROPN
ejpam-5431	214	62	x	x	X
ejpam-5431	214	63	and	and	CCONJ
ejpam-5431	214	64	(	(	PUNCT
ejpam-5431	214	65	a	a	X
ejpam-5431	214	66	)	)	PUNCT
ejpam-5431	214	67	σ1	σ1	PROPN
ejpam-5431	214	68	∈	∈	PROPN
ejpam-5431	215	1	[	[	X
ejpam-5431	215	2	sσ0](⋉(σ0),β(σ0	sσ0](⋉(σ0),β(σ0	NOUN
ejpam-5431	215	3	)	)	PUNCT
ejpam-5431	215	4	)	)	PUNCT
ejpam-5431	215	5	such	such	ADJ
ejpam-5431	215	6	that	that	DET
ejpam-5431	215	7	γ(σ0	γ(σ0	NOUN
ejpam-5431	215	8	,	,	PUNCT
ejpam-5431	215	9	σ1	σ1	PROPN
ejpam-5431	215	10	)	)	PUNCT
ejpam-5431	215	11	≥	≥	NOUN
ejpam-5431	215	12	1	1	NUM
ejpam-5431	215	13	;	;	PUNCT
ejpam-5431	215	14	(	(	PUNCT
ejpam-5431	215	15	b	b	X
ejpam-5431	215	16	)	)	PUNCT
ejpam-5431	215	17	σ1	σ1	PROPN
ejpam-5431	215	18	∈	∈	PROPN
ejpam-5431	216	1	[	[	X
ejpam-5431	216	2	t	t	NOUN
ejpam-5431	216	3	σ0](⋉(σ0),β(σ0	σ0](⋉(σ0),β(σ0	PROPN
ejpam-5431	216	4	)	)	PUNCT
ejpam-5431	216	5	)	)	PUNCT
ejpam-5431	216	6	such	such	ADJ
ejpam-5431	216	7	that	that	DET
ejpam-5431	216	8	γ(σ0	γ(σ0	NOUN
ejpam-5431	216	9	,	,	PUNCT
ejpam-5431	216	10	σ1	σ1	PROPN
ejpam-5431	216	11	)	)	PUNCT
ejpam-5431	216	12	≥	≥	NOUN
ejpam-5431	216	13	1	1	NUM
ejpam-5431	216	14	;	;	PUNCT
ejpam-5431	216	15	(	(	PUNCT
ejpam-5431	216	16	iii	iii	X
ejpam-5431	216	17	)	)	PUNCT
ejpam-5431	216	18	(	(	PUNCT
ejpam-5431	216	19	s	s	PROPN
ejpam-5431	216	20	,	,	PUNCT
ejpam-5431	216	21	t	t	PROPN
ejpam-5431	216	22	)	)	PUNCT
ejpam-5431	216	23	is	be	AUX
ejpam-5431	216	24	ℵ-continuous	ℵ-continuous	ADJ
ejpam-5431	216	25	;	;	PUNCT
ejpam-5431	216	26	(	(	PUNCT
ejpam-5431	216	27	iv	iv	X
ejpam-5431	216	28	)	)	PUNCT
ejpam-5431	216	29	the	the	DET
ejpam-5431	216	30	sets	set	NOUN
ejpam-5431	216	31	[	[	X
ejpam-5431	216	32	sσ](⋉(σ),β(σ	sσ](⋉(σ),β(σ	NOUN
ejpam-5431	216	33	)	)	PUNCT
ejpam-5431	216	34	)	)	PUNCT
ejpam-5431	217	1	and	and	CCONJ
ejpam-5431	217	2	[	[	X
ejpam-5431	217	3	t	t	NOUN
ejpam-5431	217	4	σ](⋉(σ),β(σ	σ](⋉(σ),β(σ	NOUN
ejpam-5431	217	5	)	)	PUNCT
ejpam-5431	217	6	)	)	PUNCT
ejpam-5431	217	7	are	be	AUX
ejpam-5431	217	8	proximal	proximal	ADJ
ejpam-5431	217	9	for	for	ADP
ejpam-5431	217	10	each	each	DET
ejpam-5431	217	11	σ	σ	PROPN
ejpam-5431	217	12	∈	∈	PROPN
ejpam-5431	217	13	x.	x.	NOUN
ejpam-5431	218	1	then	then	ADV
ejpam-5431	218	2	s	s	VERB
ejpam-5431	218	3	and	and	CCONJ
ejpam-5431	218	4	t	t	PROPN
ejpam-5431	218	5	have	have	VERB
ejpam-5431	218	6	at	at	ADV
ejpam-5431	218	7	least	least	ADJ
ejpam-5431	218	8	single	single	ADJ
ejpam-5431	218	9	common	common	ADJ
ejpam-5431	218	10	iffp	iffp	NOUN
ejpam-5431	218	11	in	in	ADP
ejpam-5431	218	12	x.	x.	NOUN
ejpam-5431	218	13	proof	proof	NOUN
ejpam-5431	218	14	.	.	PUNCT
ejpam-5431	219	1	using	use	VERB
ejpam-5431	219	2	(	(	PUNCT
ejpam-5431	219	3	ii)(a	ii)(a	PROPN
ejpam-5431	219	4	)	)	PUNCT
ejpam-5431	219	5	,	,	PUNCT
ejpam-5431	219	6	we	we	PRON
ejpam-5431	219	7	have	have	VERB
ejpam-5431	219	8	(	(	PUNCT
ejpam-5431	219	9	⋉(σ0	⋉(σ0	NOUN
ejpam-5431	219	10	)	)	PUNCT
ejpam-5431	219	11	,	,	PUNCT
ejpam-5431	219	12	β(σ0	β(σ0	NUM
ejpam-5431	219	13	)	)	PUNCT
ejpam-5431	219	14	)	)	PUNCT
ejpam-5431	220	1	∈	∈	PROPN
ejpam-5431	220	2	(	(	PUNCT
ejpam-5431	220	3	0	0	NUM
ejpam-5431	220	4	,	,	PUNCT
ejpam-5431	220	5	1	1	NUM
ejpam-5431	220	6	]	]	SYM
ejpam-5431	220	7	×	×	NOUN
ejpam-5431	220	8	[	[	X
ejpam-5431	220	9	0	0	NUM
ejpam-5431	220	10	,	,	PUNCT
ejpam-5431	220	11	1	1	NUM
ejpam-5431	220	12	)	)	PUNCT
ejpam-5431	220	13	,	,	PUNCT
ejpam-5431	220	14	σ0	σ0	NOUN
ejpam-5431	220	15	∈	∈	PROPN
ejpam-5431	220	16	x	x	X
ejpam-5431	220	17	and	and	CCONJ
ejpam-5431	220	18	σ1	σ1	PROPN
ejpam-5431	220	19	∈	∈	PROPN
ejpam-5431	221	1	[	[	X
ejpam-5431	221	2	sσ0](⋉(σ0),β(σ0	sσ0](⋉(σ0),β(σ0	NOUN
ejpam-5431	221	3	)	)	PUNCT
ejpam-5431	221	4	)	)	PUNCT
ejpam-5431	221	5	such	such	ADJ
ejpam-5431	221	6	that	that	DET
ejpam-5431	221	7	γ(σ0	γ(σ0	NOUN
ejpam-5431	221	8	,	,	PUNCT
ejpam-5431	221	9	σ1	σ1	PROPN
ejpam-5431	221	10	)	)	PUNCT
ejpam-5431	221	11	≥	≥	NOUN
ejpam-5431	222	1	1	1	NUM
ejpam-5431	222	2	.	.	PUNCT
ejpam-5431	223	1	if	if	SCONJ
ejpam-5431	223	2	σ1	σ1	PROPN
ejpam-5431	223	3	=	=	SYM
ejpam-5431	223	4	σ0	σ0	PROPN
ejpam-5431	223	5	and	and	CCONJ
ejpam-5431	223	6	t	t	NOUN
ejpam-5431	223	7	=	=	SYM
ejpam-5431	223	8	s	s	PART
ejpam-5431	223	9	then	then	ADV
ejpam-5431	223	10	,	,	PUNCT
ejpam-5431	223	11	from	from	ADP
ejpam-5431	223	12	condition	condition	NOUN
ejpam-5431	223	13	(	(	PUNCT
ejpam-5431	223	14	i	i	NOUN
ejpam-5431	223	15	)	)	PUNCT
ejpam-5431	223	16	in	in	ADP
ejpam-5431	223	17	definition	definition	NOUN
ejpam-5431	223	18	(	(	PUNCT
ejpam-5431	223	19	23	23	NUM
ejpam-5431	223	20	)	)	PUNCT
ejpam-5431	223	21	,	,	PUNCT
ejpam-5431	223	22	we	we	PRON
ejpam-5431	223	23	have	have	VERB
ejpam-5431	223	24	0	0	NUM
ejpam-5431	223	25	≤	≤	NUM
ejpam-5431	223	26	℘(γ(σ	℘(γ(σ	ADJ
ejpam-5431	223	27	,	,	PUNCT
ejpam-5431	223	28	τ)ℵ([sσ0](⋉(σ0),β(σ0	τ)ℵ([sσ0](⋉(σ0),β(σ0	PROPN
ejpam-5431	223	29	)	)	PUNCT
ejpam-5431	223	30	)	)	PUNCT
ejpam-5431	223	31	,	,	PUNCT
ejpam-5431	224	1	[	[	X
ejpam-5431	224	2	t	t	NOUN
ejpam-5431	224	3	σ1](⋉(σ1),β(σ1	σ1](⋉(σ1),β(σ1	NUM
ejpam-5431	224	4	)	)	PUNCT
ejpam-5431	224	5	)	)	PUNCT
ejpam-5431	224	6	)	)	PUNCT
ejpam-5431	224	7	,	,	PUNCT
ejpam-5431	224	8	φ(m	φ(m	ADJ
ejpam-5431	224	9	r	r	NOUN
ejpam-5431	224	10	(	(	PUNCT
ejpam-5431	224	11	s	s	PROPN
ejpam-5431	224	12	,	,	PUNCT
ejpam-5431	224	13	t	t	NOUN
ejpam-5431	224	14	)	)	PUNCT
ejpam-5431	224	15	(	(	PUNCT
ejpam-5431	224	16	σ0	σ0	PROPN
ejpam-5431	224	17	,	,	PUNCT
ejpam-5431	224	18	σ1	σ1	PROPN
ejpam-5431	224	19	)	)	PUNCT
ejpam-5431	224	20	)	)	PUNCT
ejpam-5431	224	21	)	)	PUNCT
ejpam-5431	224	22	<	<	X
ejpam-5431	224	23	φ(m	φ(m	ADJ
ejpam-5431	224	24	r	r	NOUN
ejpam-5431	224	25	(	(	PUNCT
ejpam-5431	224	26	s	s	PROPN
ejpam-5431	224	27	,	,	PUNCT
ejpam-5431	224	28	t	t	NOUN
ejpam-5431	224	29	)	)	PUNCT
ejpam-5431	224	30	(	(	PUNCT
ejpam-5431	224	31	σ0	σ0	PROPN
ejpam-5431	224	32	,	,	PUNCT
ejpam-5431	224	33	σ1))−	σ1))−	NOUN
ejpam-5431	224	34	γ(σ0	γ(σ0	NOUN
ejpam-5431	224	35	,	,	PUNCT
ejpam-5431	224	36	σ1)ℵ([sσ0](⋉(σ0),β(σ0	σ1)ℵ([sσ0](⋉(σ0),β(σ0	PROPN
ejpam-5431	224	37	)	)	PUNCT
ejpam-5431	224	38	)	)	PUNCT
ejpam-5431	224	39	,	,	PUNCT
ejpam-5431	225	1	[	[	X
ejpam-5431	225	2	t	t	NOUN
ejpam-5431	225	3	σ1](⋉(σ1),β(σ1	σ1](⋉(σ1),β(σ1	NUM
ejpam-5431	225	4	)	)	PUNCT
ejpam-5431	225	5	)	)	PUNCT
ejpam-5431	225	6	)	)	PUNCT
ejpam-5431	225	7	which	which	PRON
ejpam-5431	225	8	is	be	AUX
ejpam-5431	225	9	analogous	analogous	ADJ
ejpam-5431	225	10	to	to	ADP
ejpam-5431	225	11	γ(σ0	γ(σ0	NOUN
ejpam-5431	225	12	,	,	PUNCT
ejpam-5431	225	13	σ1)ℵ([sσ0](⋉(σ0),β(σ0	σ1)ℵ([sσ0](⋉(σ0),β(σ0	PROPN
ejpam-5431	225	14	)	)	PUNCT
ejpam-5431	225	15	)	)	PUNCT
ejpam-5431	225	16	,	,	PUNCT
ejpam-5431	225	17	[	[	X
ejpam-5431	225	18	t	t	NOUN
ejpam-5431	225	19	σ1](⋉(σ1),β(σ1	σ1](⋉(σ1),β(σ1	NUM
ejpam-5431	225	20	)	)	PUNCT
ejpam-5431	225	21	)	)	PUNCT
ejpam-5431	225	22	)	)	PUNCT
ejpam-5431	225	23	≤	≤	NUM
ejpam-5431	225	24	φ(m	φ(m	ADJ
ejpam-5431	225	25	r	r	NOUN
ejpam-5431	225	26	(	(	PUNCT
ejpam-5431	225	27	s	s	PROPN
ejpam-5431	225	28	,	,	PUNCT
ejpam-5431	225	29	t	t	NOUN
ejpam-5431	225	30	)	)	PUNCT
ejpam-5431	225	31	(	(	PUNCT
ejpam-5431	225	32	σ0	σ0	PROPN
ejpam-5431	225	33	,	,	PUNCT
ejpam-5431	225	34	σ1	σ1	PROPN
ejpam-5431	225	35	)	)	PUNCT
ejpam-5431	225	36	)	)	PUNCT
ejpam-5431	225	37	(	(	PUNCT
ejpam-5431	225	38	1	1	X
ejpam-5431	225	39	)	)	PUNCT
ejpam-5431	225	40	then	then	ADV
ejpam-5431	225	41	for	for	ADP
ejpam-5431	225	42	r	r	PROPN
ejpam-5431	225	43	>	>	X
ejpam-5431	225	44	0	0	NUM
ejpam-5431	225	45	,	,	PUNCT
ejpam-5431	225	46	we	we	PRON
ejpam-5431	225	47	get	get	VERB
ejpam-5431	225	48	m	m	VERB
ejpam-5431	225	49	r	r	NOUN
ejpam-5431	225	50	(	(	PUNCT
ejpam-5431	225	51	s	s	PROPN
ejpam-5431	225	52	,	,	PUNCT
ejpam-5431	225	53	t	t	NOUN
ejpam-5431	225	54	)	)	PUNCT
ejpam-5431	225	55	(	(	PUNCT
ejpam-5431	225	56	σ0	σ0	PROPN
ejpam-5431	225	57	,	,	PUNCT
ejpam-5431	225	58	σ1	σ1	PROPN
ejpam-5431	225	59	)	)	PUNCT
ejpam-5431	225	60	=	=	PUNCT
ejpam-5431	226	1	[	[	X
ejpam-5431	226	2	a(σ0	a(σ0	NOUN
ejpam-5431	226	3	,	,	PUNCT
ejpam-5431	226	4	σ1	σ1	PROPN
ejpam-5431	226	5	)	)	PUNCT
ejpam-5431	226	6	]	]	PUNCT
ejpam-5431	226	7	1	1	NUM
ejpam-5431	226	8	r	r	NOUN
ejpam-5431	226	9	n.	n.	NOUN
ejpam-5431	226	10	saleem	saleem	PROPN
ejpam-5431	226	11	et	et	PROPN
ejpam-5431	226	12	al	al	PROPN
ejpam-5431	226	13	.	.	PUNCT
ejpam-5431	226	14	/	/	SYM
ejpam-5431	226	15	eur	eur	PROPN
ejpam-5431	226	16	.	.	PUNCT
ejpam-5431	227	1	j.	j.	PROPN
ejpam-5431	227	2	pure	pure	PROPN
ejpam-5431	227	3	appl	appl	PROPN
ejpam-5431	227	4	.	.	PROPN
ejpam-5431	227	5	math	math	PROPN
ejpam-5431	227	6	,	,	PUNCT
ejpam-5431	227	7	17	17	NUM
ejpam-5431	227	8	(	(	PUNCT
ejpam-5431	227	9	4	4	NUM
ejpam-5431	227	10	)	)	PUNCT
ejpam-5431	227	11	(	(	PUNCT
ejpam-5431	227	12	2024	2024	NUM
ejpam-5431	227	13	)	)	PUNCT
ejpam-5431	227	14	,	,	PUNCT
ejpam-5431	227	15	3304	3304	NUM
ejpam-5431	227	16	-	-	SYM
ejpam-5431	227	17	3335	3335	NUM
ejpam-5431	227	18	3314	3314	NUM
ejpam-5431	227	19	=	=	SYM
ejpam-5431	227	20	[	[	PUNCT
ejpam-5431	227	21	k1(δ(σ0	k1(δ(σ0	PROPN
ejpam-5431	227	22	,	,	PUNCT
ejpam-5431	227	23	σ1	σ1	PROPN
ejpam-5431	227	24	)	)	PUNCT
ejpam-5431	227	25	)	)	PUNCT
ejpam-5431	228	1	r	r	NOUN
ejpam-5431	228	2	+	+	CCONJ
ejpam-5431	228	3	k2(δ(σ0	k2(δ(σ0	NOUN
ejpam-5431	228	4	,	,	PUNCT
ejpam-5431	228	5	[	[	X
ejpam-5431	228	6	sσ0](⋉(σ0),β(σ0	sσ0](⋉(σ0),β(σ0	NOUN
ejpam-5431	228	7	)	)	PUNCT
ejpam-5431	228	8	)	)	PUNCT
ejpam-5431	228	9	)	)	PUNCT
ejpam-5431	228	10	)	)	PUNCT
ejpam-5431	229	1	r	r	NOUN
ejpam-5431	229	2	+	+	NUM
ejpam-5431	229	3	k3(δ(σ1	k3(δ(σ1	NOUN
ejpam-5431	229	4	,	,	PUNCT
ejpam-5431	229	5	[	[	X
ejpam-5431	229	6	t	t	NOUN
ejpam-5431	229	7	σ1](⋉(σ1),β(σ1	σ1](⋉(σ1),β(σ1	NUM
ejpam-5431	229	8	)	)	PUNCT
ejpam-5431	229	9	)	)	PUNCT
ejpam-5431	229	10	)	)	PUNCT
ejpam-5431	229	11	)	)	PUNCT
ejpam-5431	230	1	r	r	NOUN
ejpam-5431	231	1	+	+	PRON
ejpam-5431	231	2	k4	k4	ADJ
ejpam-5431	231	3	(	(	PUNCT
ejpam-5431	231	4	δ(σ1	δ(σ1	NOUN
ejpam-5431	231	5	,	,	PUNCT
ejpam-5431	231	6	[	[	X
ejpam-5431	231	7	t	t	X
ejpam-5431	231	8	σ1](⋉(σ1),β(σ1)))(1	σ1](⋉(σ1),β(σ1)))(1	NOUN
ejpam-5431	231	9	+	+	CCONJ
ejpam-5431	231	10	δ(σ0	δ(σ0	NOUN
ejpam-5431	231	11	,	,	PUNCT
ejpam-5431	231	12	[	[	X
ejpam-5431	231	13	sσ0](⋉(σ0),β(σ0	sσ0](⋉(σ0),β(σ0	NOUN
ejpam-5431	231	14	)	)	PUNCT
ejpam-5431	231	15	)	)	PUNCT
ejpam-5431	231	16	)	)	PUNCT
ejpam-5431	231	17	)	)	PUNCT
ejpam-5431	232	1	1	1	NUM
ejpam-5431	233	1	+	+	NUM
ejpam-5431	233	2	δ(σ0	δ(σ0	NOUN
ejpam-5431	233	3	,	,	PUNCT
ejpam-5431	233	4	σ1	σ1	NOUN
ejpam-5431	233	5	)	)	PUNCT
ejpam-5431	233	6	)	)	PUNCT
ejpam-5431	234	1	r	r	X
ejpam-5431	234	2	+	+	PROPN
ejpam-5431	234	3	k5	k5	PROPN
ejpam-5431	234	4	(	(	PUNCT
ejpam-5431	234	5	δ(σ1	δ(σ1	NOUN
ejpam-5431	234	6	,	,	PUNCT
ejpam-5431	234	7	[	[	X
ejpam-5431	234	8	sσ0](⋉(σ0),β(σ0)))(1	sσ0](⋉(σ0),β(σ0)))(1	NOUN
ejpam-5431	234	9	+	+	SYM
ejpam-5431	234	10	δ(σ0	δ(σ0	NOUN
ejpam-5431	234	11	,	,	PUNCT
ejpam-5431	234	12	[	[	X
ejpam-5431	234	13	t	t	NOUN
ejpam-5431	234	14	σ1](⋉(σ1),β(σ1	σ1](⋉(σ1),β(σ1	NUM
ejpam-5431	234	15	)	)	PUNCT
ejpam-5431	234	16	)	)	PUNCT
ejpam-5431	234	17	)	)	PUNCT
ejpam-5431	234	18	)	)	PUNCT
ejpam-5431	235	1	1	1	NUM
ejpam-5431	236	1	+	+	NUM
ejpam-5431	236	2	δ(σ0	δ(σ0	NOUN
ejpam-5431	236	3	,	,	PUNCT
ejpam-5431	236	4	σ1	σ1	NOUN
ejpam-5431	236	5	)	)	PUNCT
ejpam-5431	236	6	)	)	PUNCT
ejpam-5431	237	1	r	r	NOUN
ejpam-5431	237	2	]	]	PUNCT
ejpam-5431	237	3	1	1	NUM
ejpam-5431	237	4	r	r	NOUN
ejpam-5431	237	5	using	use	VERB
ejpam-5431	237	6	proximality	proximality	NOUN
ejpam-5431	237	7	of	of	ADP
ejpam-5431	237	8	s	s	PROPN
ejpam-5431	237	9	,	,	PUNCT
ejpam-5431	237	10	σ1	σ1	PROPN
ejpam-5431	237	11	∈	∈	PROPN
ejpam-5431	238	1	[	[	X
ejpam-5431	238	2	sσ0](⋉(σ0),β(σ0	sσ0](⋉(σ0),β(σ0	NOUN
ejpam-5431	238	3	)	)	PUNCT
ejpam-5431	238	4	)	)	PUNCT
ejpam-5431	239	1	m	m	VERB
ejpam-5431	239	2	r	r	NOUN
ejpam-5431	239	3	(	(	PUNCT
ejpam-5431	239	4	s	s	PROPN
ejpam-5431	239	5	,	,	PUNCT
ejpam-5431	239	6	t	t	NOUN
ejpam-5431	239	7	)	)	PUNCT
ejpam-5431	239	8	(	(	PUNCT
ejpam-5431	239	9	σ0	σ0	PROPN
ejpam-5431	239	10	,	,	PUNCT
ejpam-5431	239	11	σ1	σ1	PROPN
ejpam-5431	239	12	)	)	PUNCT
ejpam-5431	240	1	=	=	PUNCT
ejpam-5431	240	2	[	[	PUNCT
ejpam-5431	240	3	k1(δ(σ0	k1(δ(σ0	PROPN
ejpam-5431	240	4	,	,	PUNCT
ejpam-5431	240	5	σ1	σ1	PROPN
ejpam-5431	240	6	)	)	PUNCT
ejpam-5431	240	7	)	)	PUNCT
ejpam-5431	241	1	r	r	NOUN
ejpam-5431	241	2	+	+	CCONJ
ejpam-5431	241	3	k2(δ(σ0	k2(δ(σ0	NOUN
ejpam-5431	241	4	,	,	PUNCT
ejpam-5431	241	5	σ1	σ1	NOUN
ejpam-5431	241	6	)	)	PUNCT
ejpam-5431	241	7	)	)	PUNCT
ejpam-5431	242	1	r	r	NOUN
ejpam-5431	242	2	+	+	NUM
ejpam-5431	242	3	k3(δ(σ1	k3(δ(σ1	NOUN
ejpam-5431	242	4	,	,	PUNCT
ejpam-5431	242	5	[	[	X
ejpam-5431	242	6	t	t	NOUN
ejpam-5431	242	7	σ1](⋉(σ1),β(σ1	σ1](⋉(σ1),β(σ1	NUM
ejpam-5431	242	8	)	)	PUNCT
ejpam-5431	242	9	)	)	PUNCT
ejpam-5431	242	10	)	)	PUNCT
ejpam-5431	242	11	)	)	PUNCT
ejpam-5431	243	1	r	r	NOUN
ejpam-5431	244	1	+	+	PRON
ejpam-5431	244	2	k4	k4	ADJ
ejpam-5431	244	3	(	(	PUNCT
ejpam-5431	244	4	δ(σ1	δ(σ1	NOUN
ejpam-5431	244	5	,	,	PUNCT
ejpam-5431	244	6	[	[	X
ejpam-5431	244	7	t	t	X
ejpam-5431	244	8	σ1](⋉(σ1),β(σ1)))(1	σ1](⋉(σ1),β(σ1)))(1	NOUN
ejpam-5431	244	9	+	+	CCONJ
ejpam-5431	244	10	δ(σ0	δ(σ0	NOUN
ejpam-5431	244	11	,	,	PUNCT
ejpam-5431	244	12	σ1	σ1	PROPN
ejpam-5431	244	13	)	)	PUNCT
ejpam-5431	244	14	)	)	PUNCT
ejpam-5431	244	15	1	1	NUM
ejpam-5431	245	1	+	+	NUM
ejpam-5431	245	2	δ(σ0	δ(σ0	NOUN
ejpam-5431	245	3	,	,	PUNCT
ejpam-5431	245	4	σ1	σ1	NOUN
ejpam-5431	245	5	)	)	PUNCT
ejpam-5431	245	6	)	)	PUNCT
ejpam-5431	246	1	r	r	X
ejpam-5431	246	2	+	+	PROPN
ejpam-5431	246	3	k5	k5	PROPN
ejpam-5431	246	4	(	(	PUNCT
ejpam-5431	246	5	δ(σ1	δ(σ1	NOUN
ejpam-5431	246	6	,	,	PUNCT
ejpam-5431	246	7	σ1)(1	σ1)(1	NOUN
ejpam-5431	246	8	+	+	CCONJ
ejpam-5431	246	9	δ(σ0	δ(σ0	NOUN
ejpam-5431	246	10	,	,	PUNCT
ejpam-5431	246	11	[	[	X
ejpam-5431	246	12	t	t	NOUN
ejpam-5431	246	13	σ1](⋉(σ1),β(σ1	σ1](⋉(σ1),β(σ1	NUM
ejpam-5431	246	14	)	)	PUNCT
ejpam-5431	246	15	)	)	PUNCT
ejpam-5431	246	16	)	)	PUNCT
ejpam-5431	246	17	)	)	PUNCT
ejpam-5431	247	1	1	1	NUM
ejpam-5431	248	1	+	+	NUM
ejpam-5431	248	2	δ(σ0	δ(σ0	NOUN
ejpam-5431	248	3	,	,	PUNCT
ejpam-5431	248	4	σ1	σ1	NOUN
ejpam-5431	248	5	)	)	PUNCT
ejpam-5431	248	6	)	)	PUNCT
ejpam-5431	249	1	r	r	NOUN
ejpam-5431	249	2	]	]	PUNCT
ejpam-5431	249	3	1	1	NUM
ejpam-5431	249	4	r	r	NOUN
ejpam-5431	249	5	=	=	SYM
ejpam-5431	250	1	[	[	X
ejpam-5431	250	2	(	(	PUNCT
ejpam-5431	250	3	k1	k1	NOUN
ejpam-5431	250	4	+	+	CCONJ
ejpam-5431	250	5	k2)(δ(σ0	k2)(δ(σ0	PROPN
ejpam-5431	250	6	,	,	PUNCT
ejpam-5431	250	7	σ1	σ1	PROPN
ejpam-5431	250	8	)	)	PUNCT
ejpam-5431	250	9	)	)	PUNCT
ejpam-5431	251	1	r	r	NOUN
ejpam-5431	251	2	+	+	CCONJ
ejpam-5431	251	3	(	(	PUNCT
ejpam-5431	251	4	k3	k3	X
ejpam-5431	251	5	+	+	CCONJ
ejpam-5431	251	6	k4)(δ(σ1	k4)(δ(σ1	NOUN
ejpam-5431	251	7	,	,	PUNCT
ejpam-5431	251	8	[	[	X
ejpam-5431	251	9	t	t	NOUN
ejpam-5431	251	10	σ1](⋉(σ1),β(σ1	σ1](⋉(σ1),β(σ1	NUM
ejpam-5431	251	11	)	)	PUNCT
ejpam-5431	251	12	)	)	PUNCT
ejpam-5431	251	13	)	)	PUNCT
ejpam-5431	251	14	)	)	PUNCT
ejpam-5431	252	1	r	r	X
ejpam-5431	252	2	]	]	SYM
ejpam-5431	252	3	1	1	NUM
ejpam-5431	252	4	r	r	NOUN
ejpam-5431	252	5	for	for	ADP
ejpam-5431	252	6	σ1	σ1	NOUN
ejpam-5431	252	7	=	=	SYM
ejpam-5431	252	8	σ0	σ0	PROPN
ejpam-5431	252	9	and	and	CCONJ
ejpam-5431	252	10	t	t	PROPN
ejpam-5431	252	11	=	=	SYM
ejpam-5431	252	12	s	s	PROPN
ejpam-5431	252	13	,	,	PUNCT
ejpam-5431	252	14	we	we	PRON
ejpam-5431	252	15	get	get	VERB
ejpam-5431	252	16	m	m	VERB
ejpam-5431	252	17	r	r	NOUN
ejpam-5431	252	18	(	(	PUNCT
ejpam-5431	252	19	s	s	PROPN
ejpam-5431	252	20	,	,	PUNCT
ejpam-5431	252	21	t	t	NOUN
ejpam-5431	252	22	)	)	PUNCT
ejpam-5431	252	23	(	(	PUNCT
ejpam-5431	252	24	σ0	σ0	PROPN
ejpam-5431	252	25	,	,	PUNCT
ejpam-5431	252	26	σ1	σ1	PROPN
ejpam-5431	252	27	)	)	PUNCT
ejpam-5431	252	28	=	=	PUNCT
ejpam-5431	253	1	[	[	X
ejpam-5431	253	2	(	(	PUNCT
ejpam-5431	253	3	k1	k1	NOUN
ejpam-5431	253	4	+	+	CCONJ
ejpam-5431	253	5	k2)(δ(σ0	k2)(δ(σ0	PROPN
ejpam-5431	253	6	,	,	PUNCT
ejpam-5431	253	7	σ0	σ0	PROPN
ejpam-5431	253	8	)	)	PUNCT
ejpam-5431	253	9	)	)	PUNCT
ejpam-5431	254	1	r	r	NOUN
ejpam-5431	254	2	+	+	CCONJ
ejpam-5431	254	3	(	(	PUNCT
ejpam-5431	254	4	k3	k3	X
ejpam-5431	254	5	+	+	CCONJ
ejpam-5431	254	6	k4)(δ(σ1	k4)(δ(σ1	NOUN
ejpam-5431	254	7	,	,	PUNCT
ejpam-5431	254	8	[	[	X
ejpam-5431	254	9	sσ0](⋉(σ1),β(σ1	sσ0](⋉(σ1),β(σ1	NOUN
ejpam-5431	254	10	)	)	PUNCT
ejpam-5431	254	11	)	)	PUNCT
ejpam-5431	254	12	)	)	PUNCT
ejpam-5431	254	13	)	)	PUNCT
ejpam-5431	255	1	r	r	X
ejpam-5431	255	2	]	]	SYM
ejpam-5431	255	3	1	1	NUM
ejpam-5431	255	4	r	r	NOUN
ejpam-5431	255	5	=	=	SYM
ejpam-5431	255	6	0	0	NUM
ejpam-5431	255	7	similarly	similarly	ADV
ejpam-5431	255	8	b(σ0	b(σ0	NOUN
ejpam-5431	255	9	,	,	PUNCT
ejpam-5431	255	10	σ1	σ1	PROPN
ejpam-5431	255	11	)	)	PUNCT
ejpam-5431	255	12	=	=	PUNCT
ejpam-5431	256	1	0	0	X
ejpam-5431	256	2	.	.	PUNCT
ejpam-5431	257	1	hence	hence	ADV
ejpam-5431	257	2	(	(	PUNCT
ejpam-5431	257	3	1	1	X
ejpam-5431	257	4	)	)	PUNCT
ejpam-5431	257	5	becomes	become	VERB
ejpam-5431	257	6	,	,	PUNCT
ejpam-5431	257	7	γ(σ0	γ(σ0	NOUN
ejpam-5431	257	8	,	,	PUNCT
ejpam-5431	257	9	σ1)ℵ([sσ0](⋉(σ0),β(σ0	σ1)ℵ([sσ0](⋉(σ0),β(σ0	PROPN
ejpam-5431	257	10	)	)	PUNCT
ejpam-5431	257	11	)	)	PUNCT
ejpam-5431	257	12	,	,	PUNCT
ejpam-5431	258	1	[	[	X
ejpam-5431	258	2	t	t	NOUN
ejpam-5431	258	3	σ1](⋉(σ1),β(σ1	σ1](⋉(σ1),β(σ1	NUM
ejpam-5431	258	4	)	)	PUNCT
ejpam-5431	258	5	)	)	PUNCT
ejpam-5431	258	6	)	)	PUNCT
ejpam-5431	258	7	≤	≤	NUM
ejpam-5431	259	1	φ(0	φ(0	ADJ
ejpam-5431	259	2	)	)	PUNCT
ejpam-5431	259	3	=	=	SYM
ejpam-5431	259	4	0	0	NUM
ejpam-5431	259	5	which	which	PRON
ejpam-5431	259	6	implies	imply	VERB
ejpam-5431	259	7	that	that	SCONJ
ejpam-5431	259	8	ℵ([sσ0](⋉(σ0),β(σ0	ℵ([sσ0](⋉(σ0),β(σ0	VERB
ejpam-5431	259	9	)	)	PUNCT
ejpam-5431	259	10	)	)	PUNCT
ejpam-5431	259	11	,	,	PUNCT
ejpam-5431	260	1	[	[	X
ejpam-5431	260	2	t	t	NOUN
ejpam-5431	260	3	σ1](⋉(σ1),β(σ1	σ1](⋉(σ1),β(σ1	NUM
ejpam-5431	260	4	)	)	PUNCT
ejpam-5431	260	5	)	)	PUNCT
ejpam-5431	260	6	)	)	PUNCT
ejpam-5431	261	1	=	=	PUNCT
ejpam-5431	261	2	0	0	PROPN
ejpam-5431	262	1	that	that	PRON
ejpam-5431	262	2	is	be	AUX
ejpam-5431	262	3	,	,	PUNCT
ejpam-5431	262	4	σ1	σ1	PROPN
ejpam-5431	262	5	∈	∈	PROPN
ejpam-5431	263	1	[	[	X
ejpam-5431	263	2	sσ0](⋉(σ0),β(σ0	sσ0](⋉(σ0),β(σ0	NOUN
ejpam-5431	263	3	)	)	PUNCT
ejpam-5431	263	4	)	)	PUNCT
ejpam-5431	264	1	=	=	PUNCT
ejpam-5431	265	1	[	[	X
ejpam-5431	265	2	t	t	NOUN
ejpam-5431	265	3	σ1](⋉(σ1),β(σ1	σ1](⋉(σ1),β(σ1	NUM
ejpam-5431	265	4	)	)	PUNCT
ejpam-5431	265	5	)	)	PUNCT
ejpam-5431	266	1	which	which	PRON
ejpam-5431	266	2	means	mean	VERB
ejpam-5431	266	3	σ1	σ1	PROPN
ejpam-5431	266	4	is	be	AUX
ejpam-5431	266	5	iffp	iffp	PROPN
ejpam-5431	266	6	of	of	ADP
ejpam-5431	266	7	t	t	PROPN
ejpam-5431	266	8	.	.	PUNCT
ejpam-5431	267	1	since	since	SCONJ
ejpam-5431	267	2	σ1	σ1	PROPN
ejpam-5431	267	3	∈	∈	PROPN
ejpam-5431	268	1	[	[	X
ejpam-5431	268	2	sσ0](⋉(σ0),β(σ0	sσ0](⋉(σ0),β(σ0	NOUN
ejpam-5431	268	3	)	)	PUNCT
ejpam-5431	268	4	)	)	PUNCT
ejpam-5431	268	5	with	with	ADP
ejpam-5431	268	6	γ(σ0	γ(σ0	PROPN
ejpam-5431	268	7	,	,	PUNCT
ejpam-5431	268	8	σ1	σ1	PROPN
ejpam-5431	268	9	)	)	PUNCT
ejpam-5431	268	10	≥	≥	NOUN
ejpam-5431	268	11	1,so	1,so	NUM
ejpam-5431	268	12	by	by	ADP
ejpam-5431	268	13	(	(	PUNCT
ejpam-5431	268	14	i	i	NOUN
ejpam-5431	268	15	)	)	PUNCT
ejpam-5431	268	16	,	,	PUNCT
ejpam-5431	268	17	γ(σ1	γ(σ1	NOUN
ejpam-5431	268	18	,	,	PUNCT
ejpam-5431	268	19	ϖ	ϖ	NOUN
ejpam-5431	268	20	)	)	PUNCT
ejpam-5431	268	21	≥	≥	NOUN
ejpam-5431	268	22	1	1	NUM
ejpam-5431	268	23	for	for	ADP
ejpam-5431	268	24	all	all	DET
ejpam-5431	268	25	ϖ	ϖ	PRON
ejpam-5431	268	26	∈	∈	PROPN
ejpam-5431	269	1	[	[	X
ejpam-5431	269	2	t	t	NOUN
ejpam-5431	269	3	σ1](⋉(σ1),β(σ1	σ1](⋉(σ1),β(σ1	NUM
ejpam-5431	269	4	)	)	PUNCT
ejpam-5431	269	5	)	)	PUNCT
ejpam-5431	269	6	.	.	PUNCT
ejpam-5431	270	1	as	as	ADP
ejpam-5431	270	2	σ1	σ1	PROPN
ejpam-5431	270	3	∈	∈	PROPN
ejpam-5431	271	1	[	[	X
ejpam-5431	271	2	t	t	X
ejpam-5431	271	3	σ1](⋉(σ1),β(σ1)),we	σ1](⋉(σ1),β(σ1)),we	NOUN
ejpam-5431	271	4	have	have	VERB
ejpam-5431	271	5	γ(σ1	γ(σ1	NOUN
ejpam-5431	271	6	,	,	PUNCT
ejpam-5431	271	7	σ1	σ1	PROPN
ejpam-5431	271	8	)	)	PUNCT
ejpam-5431	271	9	≥	≥	NOUN
ejpam-5431	271	10	1	1	NUM
ejpam-5431	271	11	and	and	CCONJ
ejpam-5431	271	12	0	0	NUM
ejpam-5431	271	13	≤	≤	NUM
ejpam-5431	271	14	℘(γ(σ1	℘(γ(σ1	NOUN
ejpam-5431	271	15	,	,	PUNCT
ejpam-5431	271	16	σ1)ℵ([sσ1](⋉(σ1),β(σ1	σ1)ℵ([sσ1](⋉(σ1),β(σ1	PROPN
ejpam-5431	271	17	)	)	PUNCT
ejpam-5431	271	18	)	)	PUNCT
ejpam-5431	271	19	,	,	PUNCT
ejpam-5431	272	1	[	[	X
ejpam-5431	272	2	t	t	NOUN
ejpam-5431	272	3	σ1](⋉(σ1),β(σ1	σ1](⋉(σ1),β(σ1	NUM
ejpam-5431	272	4	)	)	PUNCT
ejpam-5431	272	5	)	)	PUNCT
ejpam-5431	272	6	)	)	PUNCT
ejpam-5431	272	7	,	,	PUNCT
ejpam-5431	272	8	φ(m	φ(m	ADJ
ejpam-5431	272	9	r	r	NOUN
ejpam-5431	272	10	(	(	PUNCT
ejpam-5431	272	11	s	s	PROPN
ejpam-5431	272	12	,	,	PUNCT
ejpam-5431	272	13	t	t	NOUN
ejpam-5431	272	14	)	)	PUNCT
ejpam-5431	272	15	(	(	PUNCT
ejpam-5431	272	16	σ1	σ1	PROPN
ejpam-5431	272	17	,	,	PUNCT
ejpam-5431	272	18	σ1	σ1	PROPN
ejpam-5431	272	19	)	)	PUNCT
ejpam-5431	272	20	)	)	PUNCT
ejpam-5431	272	21	)	)	PUNCT
ejpam-5431	272	22	which	which	PRON
ejpam-5431	272	23	is	be	AUX
ejpam-5431	272	24	equivalent	equivalent	ADJ
ejpam-5431	272	25	to	to	PART
ejpam-5431	272	26	γ(σ1	γ(σ1	VERB
ejpam-5431	272	27	,	,	PUNCT
ejpam-5431	272	28	σ1)ℵ([sσ1](⋉(σ1),β(σ1	σ1)ℵ([sσ1](⋉(σ1),β(σ1	PROPN
ejpam-5431	272	29	)	)	PUNCT
ejpam-5431	272	30	)	)	PUNCT
ejpam-5431	272	31	,	,	PUNCT
ejpam-5431	272	32	[	[	X
ejpam-5431	272	33	t	t	NOUN
ejpam-5431	272	34	σ1](⋉(σ1),β(σ1	σ1](⋉(σ1),β(σ1	NUM
ejpam-5431	272	35	)	)	PUNCT
ejpam-5431	272	36	)	)	PUNCT
ejpam-5431	272	37	)	)	PUNCT
ejpam-5431	272	38	≤	≤	NUM
ejpam-5431	272	39	φ(m	φ(m	ADJ
ejpam-5431	272	40	r	r	NOUN
ejpam-5431	272	41	(	(	PUNCT
ejpam-5431	272	42	s	s	PROPN
ejpam-5431	272	43	,	,	PUNCT
ejpam-5431	272	44	t	t	NOUN
ejpam-5431	272	45	)	)	PUNCT
ejpam-5431	272	46	(	(	PUNCT
ejpam-5431	272	47	σ1	σ1	PROPN
ejpam-5431	272	48	,	,	PUNCT
ejpam-5431	272	49	σ1	σ1	PROPN
ejpam-5431	272	50	)	)	PUNCT
ejpam-5431	272	51	)	)	PUNCT
ejpam-5431	272	52	(	(	PUNCT
ejpam-5431	272	53	2	2	X
ejpam-5431	272	54	)	)	PUNCT
ejpam-5431	272	55	n.	n.	NOUN
ejpam-5431	272	56	saleem	saleem	PROPN
ejpam-5431	272	57	et	et	PROPN
ejpam-5431	272	58	al	al	PROPN
ejpam-5431	272	59	.	.	PUNCT
ejpam-5431	272	60	/	/	SYM
ejpam-5431	272	61	eur	eur	PROPN
ejpam-5431	272	62	.	.	PUNCT
ejpam-5431	273	1	j.	j.	PROPN
ejpam-5431	273	2	pure	pure	PROPN
ejpam-5431	273	3	appl	appl	PROPN
ejpam-5431	273	4	.	.	PROPN
ejpam-5431	273	5	math	math	PROPN
ejpam-5431	273	6	,	,	PUNCT
ejpam-5431	273	7	17	17	NUM
ejpam-5431	273	8	(	(	PUNCT
ejpam-5431	273	9	4	4	NUM
ejpam-5431	273	10	)	)	PUNCT
ejpam-5431	273	11	(	(	PUNCT
ejpam-5431	273	12	2024	2024	NUM
ejpam-5431	273	13	)	)	PUNCT
ejpam-5431	273	14	,	,	PUNCT
ejpam-5431	273	15	3304	3304	NUM
ejpam-5431	273	16	-	-	SYM
ejpam-5431	273	17	3335	3335	NUM
ejpam-5431	273	18	3315	3315	NUM
ejpam-5431	273	19	then	then	ADV
ejpam-5431	273	20	for	for	ADP
ejpam-5431	273	21	r	r	PROPN
ejpam-5431	273	22	>	>	X
ejpam-5431	273	23	0	0	NUM
ejpam-5431	273	24	,	,	PUNCT
ejpam-5431	273	25	we	we	PRON
ejpam-5431	273	26	get	get	VERB
ejpam-5431	273	27	m	m	VERB
ejpam-5431	273	28	r	r	NOUN
ejpam-5431	273	29	(	(	PUNCT
ejpam-5431	273	30	s	s	PROPN
ejpam-5431	273	31	,	,	PUNCT
ejpam-5431	273	32	t	t	NOUN
ejpam-5431	273	33	)	)	PUNCT
ejpam-5431	273	34	(	(	PUNCT
ejpam-5431	273	35	σ1	σ1	PROPN
ejpam-5431	273	36	,	,	PUNCT
ejpam-5431	273	37	σ1	σ1	PROPN
ejpam-5431	273	38	)	)	PUNCT
ejpam-5431	273	39	=	=	PUNCT
ejpam-5431	274	1	[	[	X
ejpam-5431	274	2	a(σ1	a(σ1	NOUN
ejpam-5431	274	3	,	,	PUNCT
ejpam-5431	274	4	σ1	σ1	PROPN
ejpam-5431	274	5	)	)	PUNCT
ejpam-5431	274	6	]	]	PUNCT
ejpam-5431	275	1	1	1	NUM
ejpam-5431	275	2	r	r	NOUN
ejpam-5431	275	3	=	=	SYM
ejpam-5431	275	4	[	[	PUNCT
ejpam-5431	275	5	k1(δ(σ1	k1(δ(σ1	X
ejpam-5431	275	6	,	,	PUNCT
ejpam-5431	275	7	σ1	σ1	PROPN
ejpam-5431	275	8	)	)	PUNCT
ejpam-5431	275	9	)	)	PUNCT
ejpam-5431	276	1	r	r	NOUN
ejpam-5431	276	2	+	+	NUM
ejpam-5431	276	3	k2(δ(σ1	k2(δ(σ1	NOUN
ejpam-5431	276	4	,	,	PUNCT
ejpam-5431	276	5	[	[	NOUN
ejpam-5431	276	6	sσ1](⋉(σ1),β(σ1	sσ1](⋉(σ1),β(σ1	NOUN
ejpam-5431	276	7	)	)	PUNCT
ejpam-5431	276	8	)	)	PUNCT
ejpam-5431	276	9	)	)	PUNCT
ejpam-5431	276	10	)	)	PUNCT
ejpam-5431	277	1	r	r	NOUN
ejpam-5431	277	2	+	+	NUM
ejpam-5431	277	3	k3(δ(σ1	k3(δ(σ1	NOUN
ejpam-5431	277	4	,	,	PUNCT
ejpam-5431	277	5	[	[	X
ejpam-5431	277	6	t	t	NOUN
ejpam-5431	277	7	σ1](⋉(σ1),β(σ1	σ1](⋉(σ1),β(σ1	NUM
ejpam-5431	277	8	)	)	PUNCT
ejpam-5431	277	9	)	)	PUNCT
ejpam-5431	277	10	)	)	PUNCT
ejpam-5431	277	11	)	)	PUNCT
ejpam-5431	278	1	r	r	NOUN
ejpam-5431	279	1	+	+	PRON
ejpam-5431	279	2	k4	k4	ADJ
ejpam-5431	279	3	(	(	PUNCT
ejpam-5431	279	4	δ(σ1	δ(σ1	NOUN
ejpam-5431	279	5	,	,	PUNCT
ejpam-5431	279	6	[	[	X
ejpam-5431	279	7	t	t	X
ejpam-5431	279	8	σ1](⋉(σ1),β(σ1)))(1	σ1](⋉(σ1),β(σ1)))(1	NOUN
ejpam-5431	279	9	+	+	NUM
ejpam-5431	279	10	δ(σ1	δ(σ1	NOUN
ejpam-5431	279	11	,	,	PUNCT
ejpam-5431	279	12	[	[	NOUN
ejpam-5431	279	13	sσ1](⋉(σ1),β(σ1	sσ1](⋉(σ1),β(σ1	NOUN
ejpam-5431	279	14	)	)	PUNCT
ejpam-5431	279	15	)	)	PUNCT
ejpam-5431	279	16	)	)	PUNCT
ejpam-5431	279	17	)	)	PUNCT
ejpam-5431	280	1	1	1	NUM
ejpam-5431	281	1	+	+	NUM
ejpam-5431	281	2	δ(σ1	δ(σ1	NOUN
ejpam-5431	281	3	,	,	PUNCT
ejpam-5431	281	4	σ1	σ1	NOUN
ejpam-5431	281	5	)	)	PUNCT
ejpam-5431	281	6	)	)	PUNCT
ejpam-5431	282	1	r	r	X
ejpam-5431	282	2	+	+	PROPN
ejpam-5431	282	3	k5	k5	PROPN
ejpam-5431	282	4	(	(	PUNCT
ejpam-5431	282	5	δ(σ1	δ(σ1	NOUN
ejpam-5431	282	6	,	,	PUNCT
ejpam-5431	282	7	[	[	X
ejpam-5431	282	8	sσ1](⋉(σ1),β(σ1)))(1	sσ1](⋉(σ1),β(σ1)))(1	NOUN
ejpam-5431	282	9	+	+	NOUN
ejpam-5431	282	10	δ(σ1	δ(σ1	NOUN
ejpam-5431	282	11	,	,	PUNCT
ejpam-5431	282	12	[	[	X
ejpam-5431	282	13	t	t	NOUN
ejpam-5431	282	14	σ1](⋉(σ1),β(σ1	σ1](⋉(σ1),β(σ1	NUM
ejpam-5431	282	15	)	)	PUNCT
ejpam-5431	282	16	)	)	PUNCT
ejpam-5431	282	17	)	)	PUNCT
ejpam-5431	282	18	)	)	PUNCT
ejpam-5431	283	1	1	1	NUM
ejpam-5431	284	1	+	+	NUM
ejpam-5431	284	2	δ(σ1	δ(σ1	NOUN
ejpam-5431	284	3	,	,	PUNCT
ejpam-5431	284	4	σ1	σ1	NOUN
ejpam-5431	284	5	)	)	PUNCT
ejpam-5431	284	6	)	)	PUNCT
ejpam-5431	285	1	r	r	NOUN
ejpam-5431	285	2	]	]	PUNCT
ejpam-5431	285	3	1	1	NUM
ejpam-5431	285	4	r	r	NOUN
ejpam-5431	285	5	using	use	VERB
ejpam-5431	285	6	the	the	DET
ejpam-5431	285	7	proximality	proximality	NOUN
ejpam-5431	285	8	of	of	ADP
ejpam-5431	285	9	t	t	PROPN
ejpam-5431	285	10	,	,	PUNCT
ejpam-5431	285	11	we	we	PRON
ejpam-5431	285	12	get	get	VERB
ejpam-5431	285	13	m	m	VERB
ejpam-5431	285	14	r	r	NOUN
ejpam-5431	285	15	(	(	PUNCT
ejpam-5431	285	16	s	s	PROPN
ejpam-5431	285	17	,	,	PUNCT
ejpam-5431	285	18	t	t	NOUN
ejpam-5431	285	19	)	)	PUNCT
ejpam-5431	285	20	=	=	PUNCT
ejpam-5431	286	1	[	[	X
ejpam-5431	286	2	k1(0	k1(0	PROPN
ejpam-5431	286	3	)	)	PUNCT
ejpam-5431	286	4	+	+	CCONJ
ejpam-5431	286	5	k2(δ(σ1	k2(δ(σ1	NOUN
ejpam-5431	286	6	,	,	PUNCT
ejpam-5431	286	7	[	[	NOUN
ejpam-5431	286	8	sσ1](⋉(σ1),β(σ1	sσ1](⋉(σ1),β(σ1	NOUN
ejpam-5431	286	9	)	)	PUNCT
ejpam-5431	286	10	)	)	PUNCT
ejpam-5431	286	11	)	)	PUNCT
ejpam-5431	286	12	)	)	PUNCT
ejpam-5431	287	1	r	r	NOUN
ejpam-5431	287	2	+	+	NUM
ejpam-5431	287	3	k3(0	k3(0	PROPN
ejpam-5431	287	4	)	)	PUNCT
ejpam-5431	288	1	+	+	NUM
ejpam-5431	288	2	k4(0	k4(0	NOUN
ejpam-5431	288	3	)	)	PUNCT
ejpam-5431	289	1	+	+	PUNCT
ejpam-5431	289	2	k5(δ(σ1	k5(δ(σ1	ADV
ejpam-5431	289	3	,	,	PUNCT
ejpam-5431	289	4	[	[	X
ejpam-5431	289	5	sσ1](⋉(σ1),β(σ1	sσ1](⋉(σ1),β(σ1	NOUN
ejpam-5431	289	6	)	)	PUNCT
ejpam-5431	289	7	)	)	PUNCT
ejpam-5431	289	8	)	)	PUNCT
ejpam-5431	289	9	)	)	PUNCT
ejpam-5431	290	1	r	r	X
ejpam-5431	290	2	]	]	SYM
ejpam-5431	290	3	1	1	NUM
ejpam-5431	290	4	r	r	NOUN
ejpam-5431	290	5	=	=	SYM
ejpam-5431	290	6	0	0	NUM
ejpam-5431	290	7	similarly	similarly	ADV
ejpam-5431	290	8	b(σ1	b(σ1	ADJ
ejpam-5431	290	9	,	,	PUNCT
ejpam-5431	290	10	σ1	σ1	PROPN
ejpam-5431	290	11	)	)	PUNCT
ejpam-5431	290	12	=	=	SYM
ejpam-5431	291	1	0	0	X
ejpam-5431	291	2	.	.	PUNCT
ejpam-5431	292	1	therefore	therefore	ADV
ejpam-5431	292	2	(	(	PUNCT
ejpam-5431	292	3	2	2	X
ejpam-5431	292	4	)	)	PUNCT
ejpam-5431	292	5	becomes	become	VERB
ejpam-5431	292	6	,	,	PUNCT
ejpam-5431	292	7	γ(σ1	γ(σ1	NOUN
ejpam-5431	292	8	,	,	PUNCT
ejpam-5431	292	9	σ1)ℵ([sσ1](⋉(σ1),β(σ1	σ1)ℵ([sσ1](⋉(σ1),β(σ1	PROPN
ejpam-5431	292	10	)	)	PUNCT
ejpam-5431	292	11	)	)	PUNCT
ejpam-5431	292	12	,	,	PUNCT
ejpam-5431	293	1	[	[	X
ejpam-5431	293	2	t	t	NOUN
ejpam-5431	293	3	σ1](⋉(σ1),β(σ1	σ1](⋉(σ1),β(σ1	NUM
ejpam-5431	293	4	)	)	PUNCT
ejpam-5431	293	5	)	)	PUNCT
ejpam-5431	293	6	)	)	PUNCT
ejpam-5431	293	7	≤	≤	NUM
ejpam-5431	294	1	φ(0	φ(0	ADJ
ejpam-5431	294	2	)	)	PUNCT
ejpam-5431	295	1	=	=	SYM
ejpam-5431	295	2	0	0	NUM
ejpam-5431	295	3	which	which	PRON
ejpam-5431	295	4	yields	yield	VERB
ejpam-5431	295	5	ℵ([sσ1](⋉(σ1),β(σ1	ℵ([sσ1](⋉(σ1),β(σ1	NOUN
ejpam-5431	295	6	)	)	PUNCT
ejpam-5431	295	7	)	)	PUNCT
ejpam-5431	295	8	,	,	PUNCT
ejpam-5431	296	1	[	[	X
ejpam-5431	296	2	t	t	NOUN
ejpam-5431	296	3	σ1](⋉(σ1),β(σ1	σ1](⋉(σ1),β(σ1	NUM
ejpam-5431	296	4	)	)	PUNCT
ejpam-5431	296	5	)	)	PUNCT
ejpam-5431	296	6	)	)	PUNCT
ejpam-5431	297	1	=	=	SYM
ejpam-5431	297	2	0	0	NUM
ejpam-5431	297	3	implies	imply	VERB
ejpam-5431	297	4	that	that	SCONJ
ejpam-5431	297	5	[	[	X
ejpam-5431	297	6	sσ1](⋉(σ1),β(σ1	sσ1](⋉(σ1),β(σ1	NOUN
ejpam-5431	297	7	)	)	PUNCT
ejpam-5431	297	8	)	)	PUNCT
ejpam-5431	298	1	=	=	PUNCT
ejpam-5431	299	1	[	[	X
ejpam-5431	299	2	t	t	NOUN
ejpam-5431	299	3	σ1](⋉(σ1),β(σ1	σ1](⋉(σ1),β(σ1	NUM
ejpam-5431	299	4	)	)	PUNCT
ejpam-5431	299	5	)	)	PUNCT
ejpam-5431	299	6	that	that	ADV
ejpam-5431	299	7	is	be	AUX
ejpam-5431	299	8	,	,	PUNCT
ejpam-5431	299	9	σ1	σ1	PROPN
ejpam-5431	299	10	is	be	AUX
ejpam-5431	299	11	an	an	DET
ejpam-5431	299	12	iffp	iffp	NOUN
ejpam-5431	299	13	of	of	ADP
ejpam-5431	299	14	s	s	PROPN
ejpam-5431	299	15	,	,	PUNCT
ejpam-5431	299	16	which	which	PRON
ejpam-5431	299	17	yields	yield	VERB
ejpam-5431	299	18	σ1	σ1	PROPN
ejpam-5431	299	19	∈	∈	PROPN
ejpam-5431	300	1	[	[	X
ejpam-5431	300	2	t	t	NOUN
ejpam-5431	300	3	σ1](⋉(σ1),β(σ1	σ1](⋉(σ1),β(σ1	NUM
ejpam-5431	300	4	)	)	PUNCT
ejpam-5431	300	5	)	)	PUNCT
ejpam-5431	301	1	∩	∩	NOUN
ejpam-5431	301	2	[	[	X
ejpam-5431	301	3	sσ1](⋉(σ1),β(σ1	sσ1](⋉(σ1),β(σ1	NOUN
ejpam-5431	301	4	)	)	PUNCT
ejpam-5431	301	5	)	)	PUNCT
ejpam-5431	302	1	henceforth	henceforth	ADV
ejpam-5431	302	2	we	we	PRON
ejpam-5431	302	3	presume	presume	VERB
ejpam-5431	302	4	that	that	SCONJ
ejpam-5431	302	5	σ0	σ0	PROPN
ejpam-5431	302	6	̸=	̸=	PROPN
ejpam-5431	302	7	σ1	σ1	PROPN
ejpam-5431	302	8	and	and	CCONJ
ejpam-5431	302	9	s	s	VERB
ejpam-5431	302	10	̸=	̸=	PROPN
ejpam-5431	302	11	t	t	NOUN
ejpam-5431	302	12	so	so	ADV
ejpam-5431	302	13	,	,	PUNCT
ejpam-5431	302	14	σ1	σ1	PROPN
ejpam-5431	302	15	/∈	/∈	PUNCT
ejpam-5431	303	1	[	[	X
ejpam-5431	303	2	t	t	X
ejpam-5431	303	3	σ1](⋉(σ1),β(σ1))∩[sσ1](⋉(σ1),β(σ1	σ1](⋉(σ1),β(σ1))∩[sσ1](⋉(σ1),β(σ1	NOUN
ejpam-5431	303	4	)	)	PUNCT
ejpam-5431	303	5	)	)	PUNCT
ejpam-5431	303	6	which	which	PRON
ejpam-5431	303	7	implies	imply	VERB
ejpam-5431	303	8	that	that	SCONJ
ejpam-5431	303	9	σ1	σ1	PROPN
ejpam-5431	303	10	/∈	/∈	PUNCT
ejpam-5431	304	1	[	[	X
ejpam-5431	304	2	t	t	NOUN
ejpam-5431	304	3	σ1](⋉(σ1),β(σ1	σ1](⋉(σ1),β(σ1	NUM
ejpam-5431	304	4	)	)	PUNCT
ejpam-5431	304	5	)	)	PUNCT
ejpam-5431	304	6	.	.	PUNCT
ejpam-5431	305	1	so	so	ADV
ejpam-5431	305	2	that	that	DET
ejpam-5431	305	3	δ(σ1	δ(σ1	NOUN
ejpam-5431	305	4	,	,	PUNCT
ejpam-5431	305	5	[	[	X
ejpam-5431	305	6	t	t	NOUN
ejpam-5431	305	7	σ1](⋉(σ1),β(σ1	σ1](⋉(σ1),β(σ1	NUM
ejpam-5431	305	8	)	)	PUNCT
ejpam-5431	305	9	)	)	PUNCT
ejpam-5431	305	10	)	)	PUNCT
ejpam-5431	306	1	>	>	X
ejpam-5431	307	1	0	0	X
ejpam-5431	307	2	.	.	PUNCT
ejpam-5431	308	1	since	since	SCONJ
ejpam-5431	308	2	[	[	X
ejpam-5431	308	3	t	t	NOUN
ejpam-5431	308	4	σ1](⋉(σ1),β(σ1	σ1](⋉(σ1),β(σ1	NUM
ejpam-5431	308	5	)	)	PUNCT
ejpam-5431	308	6	)	)	PUNCT
ejpam-5431	308	7	∈	∈	PROPN
ejpam-5431	308	8	q(x	q(x	PROPN
ejpam-5431	308	9	)	)	PUNCT
ejpam-5431	308	10	and	and	CCONJ
ejpam-5431	308	11	σ1	σ1	PROPN
ejpam-5431	308	12	∈	∈	PROPN
ejpam-5431	309	1	[	[	X
ejpam-5431	309	2	sσ0](⋉(σ0),β(σ0	sσ0](⋉(σ0),β(σ0	NOUN
ejpam-5431	309	3	)	)	PUNCT
ejpam-5431	309	4	)	)	PUNCT
ejpam-5431	309	5	,	,	PUNCT
ejpam-5431	309	6	there	there	PRON
ejpam-5431	309	7	is	be	VERB
ejpam-5431	309	8	σ2	σ2	PROPN
ejpam-5431	309	9	∈	∈	PROPN
ejpam-5431	309	10	[	[	X
ejpam-5431	309	11	t	t	NOUN
ejpam-5431	309	12	σ1](⋉(σ1),β(σ1	σ1](⋉(σ1),β(σ1	NUM
ejpam-5431	309	13	)	)	PUNCT
ejpam-5431	309	14	)	)	PUNCT
ejpam-5431	309	15	with	with	ADP
ejpam-5431	309	16	σ1	σ1	PROPN
ejpam-5431	309	17	̸=	̸=	PROPN
ejpam-5431	309	18	σ2	σ2	PROPN
ejpam-5431	309	19	such	such	DET
ejpam-5431	309	20	that	that	DET
ejpam-5431	309	21	δ(σ1	δ(σ1	NOUN
ejpam-5431	309	22	,	,	PUNCT
ejpam-5431	309	23	σ2	σ2	NOUN
ejpam-5431	309	24	)	)	PUNCT
ejpam-5431	309	25	≤	≤	NUM
ejpam-5431	309	26	ℵ([sσ0](⋉(σ0),β(σ0	ℵ([sσ0](⋉(σ0),β(σ0	NOUN
ejpam-5431	309	27	)	)	PUNCT
ejpam-5431	309	28	)	)	PUNCT
ejpam-5431	309	29	,	,	PUNCT
ejpam-5431	310	1	[	[	X
ejpam-5431	310	2	t	t	NOUN
ejpam-5431	310	3	σ1](⋉(σ1),β(σ1	σ1](⋉(σ1),β(σ1	NUM
ejpam-5431	310	4	)	)	PUNCT
ejpam-5431	310	5	)	)	PUNCT
ejpam-5431	310	6	)	)	PUNCT
ejpam-5431	310	7	≤	≤	NUM
ejpam-5431	310	8	γ(σ0	γ(σ0	NOUN
ejpam-5431	310	9	,	,	PUNCT
ejpam-5431	310	10	σ1)ℵ([sσ0](⋉(σ0),β(σ0	σ1)ℵ([sσ0](⋉(σ0),β(σ0	PROPN
ejpam-5431	310	11	)	)	PUNCT
ejpam-5431	310	12	)	)	PUNCT
ejpam-5431	310	13	,	,	PUNCT
ejpam-5431	311	1	[	[	X
ejpam-5431	311	2	t	t	NOUN
ejpam-5431	311	3	σ1](⋉(σ1),β(σ1	σ1](⋉(σ1),β(σ1	NUM
ejpam-5431	311	4	)	)	PUNCT
ejpam-5431	311	5	)	)	PUNCT
ejpam-5431	311	6	)	)	PUNCT
ejpam-5431	311	7	(	(	PUNCT
ejpam-5431	311	8	3	3	X
ejpam-5431	311	9	)	)	PUNCT
ejpam-5431	311	10	using	use	VERB
ejpam-5431	311	11	(	(	PUNCT
ejpam-5431	311	12	2	2	NUM
ejpam-5431	311	13	)	)	PUNCT
ejpam-5431	311	14	and	and	CCONJ
ejpam-5431	311	15	(	(	PUNCT
ejpam-5431	311	16	3	3	NUM
ejpam-5431	311	17	)	)	PUNCT
ejpam-5431	311	18	,	,	PUNCT
ejpam-5431	311	19	we	we	PRON
ejpam-5431	311	20	get	get	VERB
ejpam-5431	311	21	δ(σ1	δ(σ1	NOUN
ejpam-5431	311	22	,	,	PUNCT
ejpam-5431	311	23	σ2	σ2	NOUN
ejpam-5431	311	24	)	)	PUNCT
ejpam-5431	311	25	≤	≤	NUM
ejpam-5431	311	26	φ(m	φ(m	ADJ
ejpam-5431	311	27	r	r	NOUN
ejpam-5431	311	28	(	(	PUNCT
ejpam-5431	311	29	s	s	PROPN
ejpam-5431	311	30	,	,	PUNCT
ejpam-5431	311	31	t	t	NOUN
ejpam-5431	311	32	)	)	PUNCT
ejpam-5431	311	33	(	(	PUNCT
ejpam-5431	311	34	σ0	σ0	PROPN
ejpam-5431	311	35	,	,	PUNCT
ejpam-5431	311	36	σ1	σ1	PROPN
ejpam-5431	311	37	)	)	PUNCT
ejpam-5431	311	38	)	)	PUNCT
ejpam-5431	311	39	provided	provide	VERB
ejpam-5431	311	40	that	that	SCONJ
ejpam-5431	311	41	(	(	PUNCT
ejpam-5431	311	42	s	s	PROPN
ejpam-5431	311	43	,	,	PUNCT
ejpam-5431	311	44	t	t	PROPN
ejpam-5431	311	45	)	)	PUNCT
ejpam-5431	311	46	is	be	AUX
ejpam-5431	311	47	γ	γ	X
ejpam-5431	311	48	-	-	ADJ
ejpam-5431	311	49	admissible	admissible	ADJ
ejpam-5431	311	50	pair	pair	NOUN
ejpam-5431	311	51	and	and	CCONJ
ejpam-5431	311	52	σ2	σ2	PROPN
ejpam-5431	311	53	∈	∈	PROPN
ejpam-5431	312	1	[	[	X
ejpam-5431	312	2	t	t	NOUN
ejpam-5431	312	3	σ1](⋉(σ1),β(σ1	σ1](⋉(σ1),β(σ1	NUM
ejpam-5431	312	4	)	)	PUNCT
ejpam-5431	312	5	)	)	PUNCT
ejpam-5431	312	6	,	,	PUNCT
ejpam-5431	312	7	we	we	PRON
ejpam-5431	312	8	have	have	VERB
ejpam-5431	312	9	γ(σ1	γ(σ1	NOUN
ejpam-5431	312	10	,	,	PUNCT
ejpam-5431	312	11	σ2	σ2	NOUN
ejpam-5431	312	12	)	)	PUNCT
ejpam-5431	312	13	≥	≥	NOUN
ejpam-5431	312	14	1	1	NUM
ejpam-5431	312	15	.	.	PUNCT
ejpam-5431	313	1	n.	n.	PROPN
ejpam-5431	313	2	saleem	saleem	PROPN
ejpam-5431	313	3	et	et	PROPN
ejpam-5431	313	4	al	al	PROPN
ejpam-5431	313	5	.	.	PUNCT
ejpam-5431	313	6	/	/	SYM
ejpam-5431	313	7	eur	eur	PROPN
ejpam-5431	313	8	.	.	PUNCT
ejpam-5431	314	1	j.	j.	PROPN
ejpam-5431	314	2	pure	pure	PROPN
ejpam-5431	314	3	appl	appl	PROPN
ejpam-5431	314	4	.	.	PROPN
ejpam-5431	314	5	math	math	PROPN
ejpam-5431	314	6	,	,	PUNCT
ejpam-5431	314	7	17	17	NUM
ejpam-5431	314	8	(	(	PUNCT
ejpam-5431	314	9	4	4	NUM
ejpam-5431	314	10	)	)	PUNCT
ejpam-5431	314	11	(	(	PUNCT
ejpam-5431	314	12	2024	2024	NUM
ejpam-5431	314	13	)	)	PUNCT
ejpam-5431	314	14	,	,	PUNCT
ejpam-5431	314	15	3304	3304	NUM
ejpam-5431	314	16	-	-	SYM
ejpam-5431	314	17	3335	3335	NUM
ejpam-5431	314	18	3316	3316	NUM
ejpam-5431	314	19	if	if	SCONJ
ejpam-5431	314	20	σ2	σ2	PROPN
ejpam-5431	314	21	∈	∈	PROPN
ejpam-5431	314	22	[	[	X
ejpam-5431	314	23	sσ2](⋉(σ2),β(σ2	sσ2](⋉(σ2),β(σ2	NOUN
ejpam-5431	314	24	)	)	PUNCT
ejpam-5431	314	25	)	)	PUNCT
ejpam-5431	314	26	,	,	PUNCT
ejpam-5431	314	27	then	then	ADV
ejpam-5431	314	28	taking	take	VERB
ejpam-5431	314	29	σ1	σ1	PROPN
ejpam-5431	314	30	=	=	PROPN
ejpam-5431	314	31	σ2	σ2	PROPN
ejpam-5431	314	32	and	and	CCONJ
ejpam-5431	314	33	t	t	NOUN
ejpam-5431	314	34	=	=	SYM
ejpam-5431	314	35	s	s	VERB
ejpam-5431	314	36	consistent	consistent	ADJ
ejpam-5431	314	37	with	with	ADP
ejpam-5431	314	38	earlier	early	ADJ
ejpam-5431	314	39	steps	step	NOUN
ejpam-5431	314	40	,	,	PUNCT
ejpam-5431	314	41	we	we	PRON
ejpam-5431	314	42	find	find	VERB
ejpam-5431	314	43	directly	directly	ADV
ejpam-5431	314	44	that	that	SCONJ
ejpam-5431	314	45	σ2	σ2	PROPN
ejpam-5431	314	46	∈	∈	PROPN
ejpam-5431	314	47	[	[	X
ejpam-5431	314	48	sσ2](⋉(σ2),β(σ2	sσ2](⋉(σ2),β(σ2	NUM
ejpam-5431	314	49	)	)	PUNCT
ejpam-5431	314	50	)	)	PUNCT
ejpam-5431	314	51	∩	∩	NOUN
ejpam-5431	315	1	[	[	X
ejpam-5431	315	2	t	t	NOUN
ejpam-5431	315	3	σ2](⋉(σ2),β(σ2	σ2](⋉(σ2),β(σ2	NUM
ejpam-5431	315	4	)	)	PUNCT
ejpam-5431	315	5	)	)	PUNCT
ejpam-5431	316	1	so	so	ADV
ejpam-5431	316	2	we	we	PRON
ejpam-5431	316	3	suppose	suppose	VERB
ejpam-5431	316	4	σ2	σ2	PROPN
ejpam-5431	316	5	̸=	̸=	PROPN
ejpam-5431	316	6	[	[	PUNCT
ejpam-5431	316	7	sσ2](⋉(σ1),β(σ1	sσ2](⋉(σ1),β(σ1	NOUN
ejpam-5431	316	8	)	)	PUNCT
ejpam-5431	316	9	)	)	PUNCT
ejpam-5431	316	10	>	>	X
ejpam-5431	317	1	0	0	X
ejpam-5431	317	2	.	.	PUNCT
ejpam-5431	318	1	so	so	ADV
ejpam-5431	318	2	that	that	SCONJ
ejpam-5431	318	3	δ(σ2	δ(σ2	ADJ
ejpam-5431	318	4	,	,	PUNCT
ejpam-5431	318	5	[	[	X
ejpam-5431	318	6	sσ2](⋉(σ2),β(σ2	sσ2](⋉(σ2),β(σ2	X
ejpam-5431	318	7	)	)	PUNCT
ejpam-5431	318	8	)	)	PUNCT
ejpam-5431	318	9	)	)	PUNCT
ejpam-5431	319	1	>	>	X
ejpam-5431	320	1	0	0	X
ejpam-5431	320	2	.	.	PUNCT
ejpam-5431	321	1	since	since	SCONJ
ejpam-5431	321	2	[	[	X
ejpam-5431	321	3	t	t	NOUN
ejpam-5431	321	4	σ1](⋉(σ1),β(σ1	σ1](⋉(σ1),β(σ1	NUM
ejpam-5431	321	5	)	)	PUNCT
ejpam-5431	321	6	)	)	PUNCT
ejpam-5431	321	7	,	,	PUNCT
ejpam-5431	321	8	[	[	X
ejpam-5431	321	9	sσ2](⋉(σ2),β(σ2	sσ2](⋉(σ2),β(σ2	X
ejpam-5431	321	10	)	)	PUNCT
ejpam-5431	321	11	)	)	PUNCT
ejpam-5431	321	12	∈	∈	PROPN
ejpam-5431	321	13	q(x	q(x	PROPN
ejpam-5431	321	14	)	)	PUNCT
ejpam-5431	321	15	and	and	CCONJ
ejpam-5431	321	16	σ2	σ2	PROPN
ejpam-5431	321	17	∈	∈	PROPN
ejpam-5431	321	18	[	[	X
ejpam-5431	321	19	t	t	NOUN
ejpam-5431	321	20	σ1](⋉(σ1),β(σ1	σ1](⋉(σ1),β(σ1	NUM
ejpam-5431	321	21	)	)	PUNCT
ejpam-5431	321	22	)	)	PUNCT
ejpam-5431	321	23	there	there	PRON
ejpam-5431	321	24	exists	exist	VERB
ejpam-5431	321	25	a	a	DET
ejpam-5431	321	26	point	point	NOUN
ejpam-5431	321	27	σ3	σ3	PROPN
ejpam-5431	321	28	∈	∈	PROPN
ejpam-5431	322	1	[	[	X
ejpam-5431	322	2	sσ2](⋉(σ2),β(σ2	sσ2](⋉(σ2),β(σ2	NOUN
ejpam-5431	322	3	)	)	PUNCT
ejpam-5431	322	4	)	)	PUNCT
ejpam-5431	322	5	with	with	ADP
ejpam-5431	322	6	σ2	σ2	PROPN
ejpam-5431	322	7	̸=	̸=	PROPN
ejpam-5431	322	8	σ3	σ3	PROPN
ejpam-5431	322	9	such	such	DET
ejpam-5431	322	10	that	that	DET
ejpam-5431	322	11	δ(σ2	δ(σ2	ADJ
ejpam-5431	322	12	,	,	PUNCT
ejpam-5431	322	13	σ3	σ3	NOUN
ejpam-5431	322	14	)	)	PUNCT
ejpam-5431	322	15	≤	≤	NOUN
ejpam-5431	322	16	ℵ([t	ℵ([t	NUM
ejpam-5431	322	17	σ1](⋉(σ1),β(σ1	σ1](⋉(σ1),β(σ1	PROPN
ejpam-5431	322	18	)	)	PUNCT
ejpam-5431	322	19	)	)	PUNCT
ejpam-5431	322	20	,	,	PUNCT
ejpam-5431	323	1	[	[	X
ejpam-5431	323	2	sσ2](⋉(σ2),β(σ2	sσ2](⋉(σ2),β(σ2	X
ejpam-5431	323	3	)	)	PUNCT
ejpam-5431	323	4	)	)	PUNCT
ejpam-5431	323	5	)	)	PUNCT
ejpam-5431	323	6	≤	≤	NUM
ejpam-5431	323	7	γ(σ1	γ(σ1	NOUN
ejpam-5431	323	8	,	,	PUNCT
ejpam-5431	323	9	σ2)ℵ([t	σ2)ℵ([t	PROPN
ejpam-5431	323	10	σ1](⋉(σ1),β(σ1	σ1](⋉(σ1),β(σ1	NUM
ejpam-5431	323	11	)	)	PUNCT
ejpam-5431	323	12	)	)	PUNCT
ejpam-5431	323	13	,	,	PUNCT
ejpam-5431	324	1	[	[	X
ejpam-5431	324	2	sσ2](⋉(σ2),β(σ2	sσ2](⋉(σ2),β(σ2	X
ejpam-5431	324	3	)	)	PUNCT
ejpam-5431	324	4	)	)	PUNCT
ejpam-5431	324	5	)	)	PUNCT
ejpam-5431	324	6	(	(	PUNCT
ejpam-5431	324	7	4	4	X
ejpam-5431	324	8	)	)	PUNCT
ejpam-5431	324	9	from	from	ADP
ejpam-5431	324	10	condition	condition	NOUN
ejpam-5431	324	11	(	(	PUNCT
ejpam-5431	324	12	ii	ii	NOUN
ejpam-5431	324	13	)	)	PUNCT
ejpam-5431	324	14	in	in	ADP
ejpam-5431	324	15	definition	definition	NOUN
ejpam-5431	324	16	(	(	PUNCT
ejpam-5431	324	17	23	23	NUM
ejpam-5431	324	18	)	)	PUNCT
ejpam-5431	324	19	,	,	PUNCT
ejpam-5431	324	20	we	we	PRON
ejpam-5431	324	21	get	get	VERB
ejpam-5431	324	22	0	0	NUM
ejpam-5431	324	23	≤	≤	NUM
ejpam-5431	324	24	℘(γ(σ1	℘(γ(σ1	NOUN
ejpam-5431	324	25	,	,	PUNCT
ejpam-5431	324	26	σ2)ℵ([t	σ2)ℵ([t	PROPN
ejpam-5431	324	27	σ1](⋉(σ1),β(σ1	σ1](⋉(σ1),β(σ1	NUM
ejpam-5431	324	28	)	)	PUNCT
ejpam-5431	324	29	)	)	PUNCT
ejpam-5431	324	30	,	,	PUNCT
ejpam-5431	325	1	[	[	X
ejpam-5431	325	2	sσ2](⋉(σ2),β(σ2	sσ2](⋉(σ2),β(σ2	X
ejpam-5431	325	3	)	)	PUNCT
ejpam-5431	325	4	)	)	PUNCT
ejpam-5431	325	5	)	)	PUNCT
ejpam-5431	325	6	,	,	PUNCT
ejpam-5431	325	7	φ(m	φ(m	ADJ
ejpam-5431	325	8	r	r	NOUN
ejpam-5431	325	9	(	(	PUNCT
ejpam-5431	325	10	t	t	NOUN
ejpam-5431	325	11	,	,	PUNCT
ejpam-5431	325	12	s)(σ1	s)(σ1	NOUN
ejpam-5431	325	13	,	,	PUNCT
ejpam-5431	325	14	σ2	σ2	NOUN
ejpam-5431	325	15	)	)	PUNCT
ejpam-5431	325	16	)	)	PUNCT
ejpam-5431	325	17	)	)	PUNCT
ejpam-5431	325	18	<	<	X
ejpam-5431	325	19	φ(m	φ(m	ADJ
ejpam-5431	325	20	r	r	NOUN
ejpam-5431	325	21	(	(	PUNCT
ejpam-5431	325	22	t	t	NOUN
ejpam-5431	325	23	,	,	PUNCT
ejpam-5431	325	24	s)(σ1	s)(σ1	NOUN
ejpam-5431	325	25	,	,	PUNCT
ejpam-5431	325	26	σ2))−	σ2))−	NOUN
ejpam-5431	325	27	γ(σ1	γ(σ1	NOUN
ejpam-5431	325	28	,	,	PUNCT
ejpam-5431	325	29	σ2)ℵ([t	σ2)ℵ([t	PROPN
ejpam-5431	325	30	σ1](⋉(σ1),β(σ1	σ1](⋉(σ1),β(σ1	NUM
ejpam-5431	325	31	)	)	PUNCT
ejpam-5431	325	32	)	)	PUNCT
ejpam-5431	325	33	,	,	PUNCT
ejpam-5431	326	1	[	[	X
ejpam-5431	326	2	sσ2](⋉(σ2),β(σ2	sσ2](⋉(σ2),β(σ2	X
ejpam-5431	326	3	)	)	PUNCT
ejpam-5431	326	4	)	)	PUNCT
ejpam-5431	326	5	)	)	PUNCT
ejpam-5431	327	1	which	which	PRON
ejpam-5431	327	2	can	can	AUX
ejpam-5431	327	3	be	be	AUX
ejpam-5431	327	4	written	write	VERB
ejpam-5431	327	5	as	as	ADP
ejpam-5431	327	6	γ(σ1	γ(σ1	NOUN
ejpam-5431	327	7	,	,	PUNCT
ejpam-5431	327	8	σ2)ℵ([t	σ2)ℵ([t	PROPN
ejpam-5431	327	9	σ1](⋉(σ1),β(σ1	σ1](⋉(σ1),β(σ1	NUM
ejpam-5431	327	10	)	)	PUNCT
ejpam-5431	327	11	)	)	PUNCT
ejpam-5431	328	1	,	,	PUNCT
ejpam-5431	329	1	[	[	X
ejpam-5431	329	2	sσ2](⋉(σ2),β(σ2	sσ2](⋉(σ2),β(σ2	X
ejpam-5431	329	3	)	)	PUNCT
ejpam-5431	329	4	)	)	PUNCT
ejpam-5431	329	5	)	)	PUNCT
ejpam-5431	330	1	≤	≤	NUM
ejpam-5431	330	2	φ(m	φ(m	ADJ
ejpam-5431	330	3	r	r	NOUN
ejpam-5431	330	4	(	(	PUNCT
ejpam-5431	330	5	t	t	NOUN
ejpam-5431	330	6	,	,	PUNCT
ejpam-5431	330	7	s)(σ1	s)(σ1	NOUN
ejpam-5431	330	8	,	,	PUNCT
ejpam-5431	330	9	σ2	σ2	NOUN
ejpam-5431	330	10	)	)	PUNCT
ejpam-5431	330	11	)	)	PUNCT
ejpam-5431	330	12	(	(	PUNCT
ejpam-5431	330	13	5	5	X
ejpam-5431	330	14	)	)	PUNCT
ejpam-5431	330	15	combining	combine	VERB
ejpam-5431	330	16	(	(	PUNCT
ejpam-5431	330	17	4	4	NUM
ejpam-5431	330	18	)	)	PUNCT
ejpam-5431	330	19	and	and	CCONJ
ejpam-5431	330	20	(	(	PUNCT
ejpam-5431	330	21	5	5	X
ejpam-5431	330	22	)	)	PUNCT
ejpam-5431	330	23	yields	yield	NOUN
ejpam-5431	330	24	,	,	PUNCT
ejpam-5431	330	25	δ(σ2	δ(σ2	ADJ
ejpam-5431	330	26	,	,	PUNCT
ejpam-5431	330	27	σ3	σ3	NOUN
ejpam-5431	330	28	)	)	PUNCT
ejpam-5431	330	29	≤	≤	NUM
ejpam-5431	331	1	φ(m	φ(m	ADJ
ejpam-5431	331	2	r	r	NOUN
ejpam-5431	331	3	(	(	PUNCT
ejpam-5431	331	4	t	t	NOUN
ejpam-5431	331	5	,	,	PUNCT
ejpam-5431	331	6	s)(σ1	s)(σ1	NOUN
ejpam-5431	331	7	,	,	PUNCT
ejpam-5431	331	8	σ2	σ2	NOUN
ejpam-5431	331	9	)	)	PUNCT
ejpam-5431	331	10	)	)	PUNCT
ejpam-5431	332	1	likewise	likewise	ADV
ejpam-5431	332	2	,	,	PUNCT
ejpam-5431	332	3	we	we	PRON
ejpam-5431	332	4	generate	generate	VERB
ejpam-5431	332	5	a	a	DET
ejpam-5431	332	6	sequence	sequence	NOUN
ejpam-5431	332	7	{	{	PUNCT
ejpam-5431	332	8	σn}n≥1	σn}n≥1	NOUN
ejpam-5431	332	9	with	with	ADP
ejpam-5431	332	10	σ2n+1	σ2n+1	PROPN
ejpam-5431	332	11	∈	∈	PROPN
ejpam-5431	332	12	[	[	X
ejpam-5431	332	13	sσ2n](⋉(σ2n),β(σ2n	sσ2n](⋉(σ2n),β(σ2n	NOUN
ejpam-5431	332	14	)	)	PUNCT
ejpam-5431	332	15	)	)	PUNCT
ejpam-5431	332	16	,	,	PUNCT
ejpam-5431	332	17	σ2n+2	σ2n+2	X
ejpam-5431	332	18	∈	∈	PROPN
ejpam-5431	333	1	[	[	X
ejpam-5431	333	2	t	t	X
ejpam-5431	333	3	σ2n+1](⋉(σ2n+1),β(σ2n+1	σ2n+1](⋉(σ2n+1),β(σ2n+1	NOUN
ejpam-5431	333	4	)	)	PUNCT
ejpam-5431	333	5	)	)	PUNCT
ejpam-5431	333	6	,	,	PUNCT
ejpam-5431	333	7	γ(σ2n	γ(σ2n	NOUN
ejpam-5431	333	8	,	,	PUNCT
ejpam-5431	333	9	σ2n+1	σ2n+1	PROPN
ejpam-5431	333	10	)	)	PUNCT
ejpam-5431	333	11	≥	≥	NOUN
ejpam-5431	333	12	1	1	NUM
ejpam-5431	333	13	and	and	CCONJ
ejpam-5431	333	14	γ(σ2n+1	γ(σ2n+1	NOUN
ejpam-5431	333	15	,	,	PUNCT
ejpam-5431	333	16	σ2n+2	σ2n+2	NOUN
ejpam-5431	333	17	)	)	PUNCT
ejpam-5431	333	18	≥	≥	NOUN
ejpam-5431	333	19	1	1	NUM
ejpam-5431	333	20	such	such	ADJ
ejpam-5431	333	21	that	that	DET
ejpam-5431	333	22	δ(σ2n+1	δ(σ2n+1	ADJ
ejpam-5431	333	23	,	,	PUNCT
ejpam-5431	333	24	σ2n+2	σ2n+2	NOUN
ejpam-5431	333	25	)	)	PUNCT
ejpam-5431	333	26	≤	≤	NUM
ejpam-5431	333	27	φ(m	φ(m	ADJ
ejpam-5431	333	28	r	r	NOUN
ejpam-5431	333	29	(	(	PUNCT
ejpam-5431	333	30	s	s	PROPN
ejpam-5431	333	31	,	,	PUNCT
ejpam-5431	333	32	t	t	NOUN
ejpam-5431	333	33	)	)	PUNCT
ejpam-5431	333	34	(	(	PUNCT
ejpam-5431	333	35	σ2n	σ2n	NOUN
ejpam-5431	333	36	,	,	PUNCT
ejpam-5431	333	37	σ(2n+1	σ(2n+1	ADJ
ejpam-5431	333	38	)	)	PUNCT
ejpam-5431	333	39	)	)	PUNCT
ejpam-5431	333	40	)	)	PUNCT
ejpam-5431	334	1	(	(	PUNCT
ejpam-5431	334	2	6	6	NUM
ejpam-5431	334	3	)	)	PUNCT
ejpam-5431	334	4	δ(σ2n+2	δ(σ2n+2	ADJ
ejpam-5431	334	5	,	,	PUNCT
ejpam-5431	334	6	σ2n+3	σ2n+3	ADJ
ejpam-5431	334	7	)	)	PUNCT
ejpam-5431	334	8	≤	≤	NUM
ejpam-5431	334	9	φ(m	φ(m	ADJ
ejpam-5431	334	10	r	r	NOUN
ejpam-5431	334	11	(	(	PUNCT
ejpam-5431	334	12	t	t	NOUN
ejpam-5431	334	13	,	,	PUNCT
ejpam-5431	334	14	s)(σ2n+1	s)(σ2n+1	ADJ
ejpam-5431	334	15	,	,	PUNCT
ejpam-5431	334	16	σ2n+2	σ2n+2	NOUN
ejpam-5431	334	17	)	)	PUNCT
ejpam-5431	334	18	)	)	PUNCT
ejpam-5431	334	19	(	(	PUNCT
ejpam-5431	334	20	7	7	X
ejpam-5431	334	21	)	)	PUNCT
ejpam-5431	334	22	now	now	ADV
ejpam-5431	334	23	we	we	PRON
ejpam-5431	334	24	investigate	investigate	VERB
ejpam-5431	334	25	(	(	PUNCT
ejpam-5431	334	26	6	6	NUM
ejpam-5431	334	27	)	)	PUNCT
ejpam-5431	334	28	and	and	CCONJ
ejpam-5431	334	29	(	(	PUNCT
ejpam-5431	334	30	7	7	X
ejpam-5431	334	31	)	)	PUNCT
ejpam-5431	334	32	under	under	ADP
ejpam-5431	334	33	the	the	DET
ejpam-5431	334	34	criteria	criterion	NOUN
ejpam-5431	334	35	below	below	ADV
ejpam-5431	334	36	,	,	PUNCT
ejpam-5431	334	37	case	case	NOUN
ejpam-5431	334	38	1	1	NUM
ejpam-5431	334	39	:	:	PUNCT
ejpam-5431	334	40	r	r	NOUN
ejpam-5431	334	41	>	>	X
ejpam-5431	334	42	0	0	NUM
ejpam-5431	335	1	in	in	ADP
ejpam-5431	335	2	this	this	DET
ejpam-5431	335	3	case	case	NOUN
ejpam-5431	335	4	,	,	PUNCT
ejpam-5431	335	5	from	from	ADP
ejpam-5431	335	6	condition	condition	NOUN
ejpam-5431	335	7	(	(	PUNCT
ejpam-5431	335	8	i	i	NOUN
ejpam-5431	335	9	)	)	PUNCT
ejpam-5431	335	10	in	in	ADP
ejpam-5431	335	11	definition	definition	NOUN
ejpam-5431	335	12	(	(	PUNCT
ejpam-5431	335	13	23	23	NUM
ejpam-5431	335	14	)	)	PUNCT
ejpam-5431	335	15	using	use	VERB
ejpam-5431	335	16	the	the	DET
ejpam-5431	335	17	proximality	proximality	NOUN
ejpam-5431	335	18	of	of	ADP
ejpam-5431	335	19	t	t	PROPN
ejpam-5431	335	20	and	and	CCONJ
ejpam-5431	335	21	s	s	AUX
ejpam-5431	335	22	in	in	ADP
ejpam-5431	335	23	(	(	PUNCT
ejpam-5431	335	24	6	6	NUM
ejpam-5431	335	25	)	)	PUNCT
ejpam-5431	335	26	we	we	PRON
ejpam-5431	335	27	have	have	VERB
ejpam-5431	335	28	m	m	PROPN
ejpam-5431	335	29	r	r	NOUN
ejpam-5431	335	30	(	(	PUNCT
ejpam-5431	335	31	s	s	PROPN
ejpam-5431	335	32	,	,	PUNCT
ejpam-5431	335	33	t	t	NOUN
ejpam-5431	335	34	)	)	PUNCT
ejpam-5431	335	35	(	(	PUNCT
ejpam-5431	335	36	σ2n	σ2n	NOUN
ejpam-5431	335	37	,	,	PUNCT
ejpam-5431	335	38	σ2n+1	σ2n+1	NOUN
ejpam-5431	335	39	)	)	PUNCT
ejpam-5431	335	40	=	=	PUNCT
ejpam-5431	336	1	[	[	X
ejpam-5431	336	2	a(σ2n	a(σ2n	NOUN
ejpam-5431	336	3	,	,	PUNCT
ejpam-5431	336	4	σ2n+1	σ2n+1	PROPN
ejpam-5431	336	5	)	)	PUNCT
ejpam-5431	336	6	]	]	PUNCT
ejpam-5431	336	7	1	1	NUM
ejpam-5431	336	8	r	r	NOUN
ejpam-5431	336	9	=	=	PUNCT
ejpam-5431	336	10	[	[	PUNCT
ejpam-5431	336	11	k1(δ(σ2n	k1(δ(σ2n	NOUN
ejpam-5431	336	12	,	,	PUNCT
ejpam-5431	336	13	σ2n+1	σ2n+1	NOUN
ejpam-5431	336	14	)	)	PUNCT
ejpam-5431	336	15	)	)	PUNCT
ejpam-5431	337	1	r	r	NOUN
ejpam-5431	337	2	+	+	NUM
ejpam-5431	337	3	k2(δ(σ2n	k2(δ(σ2n	X
ejpam-5431	337	4	,	,	PUNCT
ejpam-5431	337	5	[	[	X
ejpam-5431	337	6	sσ2n](⋉(σ2n),β(σ2n	sσ2n](⋉(σ2n),β(σ2n	NOUN
ejpam-5431	337	7	)	)	PUNCT
ejpam-5431	337	8	)	)	PUNCT
ejpam-5431	337	9	)	)	PUNCT
ejpam-5431	337	10	)	)	PUNCT
ejpam-5431	338	1	r	r	NOUN
ejpam-5431	338	2	+	+	CCONJ
ejpam-5431	338	3	k3(δ(σ2n+1	k3(δ(σ2n+1	PROPN
ejpam-5431	338	4	,	,	PUNCT
ejpam-5431	338	5	[	[	X
ejpam-5431	338	6	t	t	X
ejpam-5431	338	7	σ2n+1](⋉(σ2n+1),β(σ2n+1	σ2n+1](⋉(σ2n+1),β(σ2n+1	NOUN
ejpam-5431	338	8	)	)	PUNCT
ejpam-5431	338	9	)	)	PUNCT
ejpam-5431	338	10	)	)	PUNCT
ejpam-5431	338	11	)	)	PUNCT
ejpam-5431	339	1	r	r	NOUN
ejpam-5431	339	2	+	+	CCONJ
ejpam-5431	339	3	k4	k4	NOUN
ejpam-5431	339	4	(	(	PUNCT
ejpam-5431	339	5	δ(σ2n+1	δ(σ2n+1	NUM
ejpam-5431	339	6	,	,	PUNCT
ejpam-5431	339	7	[	[	X
ejpam-5431	339	8	t	t	X
ejpam-5431	339	9	σ2n+1](⋉(σ2n+1),β(σ2n+1)))(1	σ2n+1](⋉(σ2n+1),β(σ2n+1)))(1	NOUN
ejpam-5431	339	10	+	+	CCONJ
ejpam-5431	339	11	δ(σ2n	δ(σ2n	NOUN
ejpam-5431	339	12	,	,	PUNCT
ejpam-5431	339	13	[	[	X
ejpam-5431	339	14	sσ2n](⋉(σ2n),β(σ2n	sσ2n](⋉(σ2n),β(σ2n	NOUN
ejpam-5431	339	15	)	)	PUNCT
ejpam-5431	339	16	)	)	PUNCT
ejpam-5431	339	17	)	)	PUNCT
ejpam-5431	339	18	)	)	PUNCT
ejpam-5431	339	19	1	1	NUM
ejpam-5431	340	1	+	+	NUM
ejpam-5431	340	2	δ(σ2n	δ(σ2n	NOUN
ejpam-5431	340	3	,	,	PUNCT
ejpam-5431	340	4	σ2n+1	σ2n+1	NOUN
ejpam-5431	340	5	)	)	PUNCT
ejpam-5431	340	6	)	)	PUNCT
ejpam-5431	341	1	r	r	NOUN
ejpam-5431	341	2	+	+	CCONJ
ejpam-5431	341	3	k5	k5	PROPN
ejpam-5431	341	4	(	(	PUNCT
ejpam-5431	341	5	δ(σ2n+1	δ(σ2n+1	PROPN
ejpam-5431	341	6	,	,	PUNCT
ejpam-5431	341	7	[	[	X
ejpam-5431	341	8	sσ2n](⋉(σ2n),β(σ2n)))(1	sσ2n](⋉(σ2n),β(σ2n)))(1	X
ejpam-5431	341	9	+	+	CCONJ
ejpam-5431	341	10	δ(σ2n	δ(σ2n	NOUN
ejpam-5431	341	11	,	,	PUNCT
ejpam-5431	341	12	[	[	X
ejpam-5431	341	13	t	t	X
ejpam-5431	341	14	σ2n+1](⋉(σ2n+1),β(σ2n+1	σ2n+1](⋉(σ2n+1),β(σ2n+1	NOUN
ejpam-5431	341	15	)	)	PUNCT
ejpam-5431	341	16	)	)	PUNCT
ejpam-5431	341	17	)	)	PUNCT
ejpam-5431	341	18	)	)	PUNCT
ejpam-5431	341	19	1	1	NUM
ejpam-5431	342	1	+	+	NUM
ejpam-5431	342	2	δ(σ2n	δ(σ2n	NOUN
ejpam-5431	342	3	,	,	PUNCT
ejpam-5431	342	4	σ2n+1	σ2n+1	NOUN
ejpam-5431	342	5	)	)	PUNCT
ejpam-5431	342	6	)	)	PUNCT
ejpam-5431	343	1	r	r	NOUN
ejpam-5431	343	2	]	]	PUNCT
ejpam-5431	343	3	1	1	NUM
ejpam-5431	343	4	r	r	NOUN
ejpam-5431	343	5	n.	n.	NOUN
ejpam-5431	343	6	saleem	saleem	PROPN
ejpam-5431	343	7	et	et	PROPN
ejpam-5431	343	8	al	al	PROPN
ejpam-5431	343	9	.	.	PUNCT
ejpam-5431	343	10	/	/	SYM
ejpam-5431	343	11	eur	eur	PROPN
ejpam-5431	343	12	.	.	PUNCT
ejpam-5431	344	1	j.	j.	PROPN
ejpam-5431	344	2	pure	pure	PROPN
ejpam-5431	344	3	appl	appl	PROPN
ejpam-5431	344	4	.	.	PROPN
ejpam-5431	344	5	math	math	PROPN
ejpam-5431	344	6	,	,	PUNCT
ejpam-5431	344	7	17	17	NUM
ejpam-5431	344	8	(	(	PUNCT
ejpam-5431	344	9	4	4	NUM
ejpam-5431	344	10	)	)	PUNCT
ejpam-5431	344	11	(	(	PUNCT
ejpam-5431	344	12	2024	2024	NUM
ejpam-5431	344	13	)	)	PUNCT
ejpam-5431	344	14	,	,	PUNCT
ejpam-5431	344	15	3304	3304	NUM
ejpam-5431	344	16	-	-	SYM
ejpam-5431	344	17	3335	3335	NUM
ejpam-5431	344	18	3317	3317	NUM
ejpam-5431	344	19	=	=	PUNCT
ejpam-5431	344	20	[	[	PUNCT
ejpam-5431	344	21	k1(δ(σ2n	k1(δ(σ2n	NOUN
ejpam-5431	344	22	,	,	PUNCT
ejpam-5431	344	23	σ2n+1	σ2n+1	NOUN
ejpam-5431	344	24	)	)	PUNCT
ejpam-5431	344	25	)	)	PUNCT
ejpam-5431	345	1	r	r	NOUN
ejpam-5431	345	2	+	+	CCONJ
ejpam-5431	345	3	k2(δ(σ2n	k2(δ(σ2n	X
ejpam-5431	345	4	,	,	PUNCT
ejpam-5431	345	5	σ2n+1	σ2n+1	NOUN
ejpam-5431	345	6	)	)	PUNCT
ejpam-5431	345	7	)	)	PUNCT
ejpam-5431	346	1	r	r	NOUN
ejpam-5431	346	2	+	+	CCONJ
ejpam-5431	346	3	k3(δ(σ2n+1	k3(δ(σ2n+1	PROPN
ejpam-5431	346	4	,	,	PUNCT
ejpam-5431	346	5	σ2n+2	σ2n+2	NOUN
ejpam-5431	346	6	)	)	PUNCT
ejpam-5431	346	7	)	)	PUNCT
ejpam-5431	347	1	r	r	NOUN
ejpam-5431	347	2	+	+	CCONJ
ejpam-5431	347	3	k4	k4	ADJ
ejpam-5431	347	4	(	(	PUNCT
ejpam-5431	347	5	δ(σ2n+1	δ(σ2n+1	ADJ
ejpam-5431	347	6	,	,	PUNCT
ejpam-5431	347	7	σ2n+2)(1	σ2n+2)(1	NOUN
ejpam-5431	347	8	+	+	CCONJ
ejpam-5431	347	9	δ(σ2n	δ(σ2n	NOUN
ejpam-5431	347	10	,	,	PUNCT
ejpam-5431	347	11	σ2n+1	σ2n+1	NOUN
ejpam-5431	347	12	)	)	PUNCT
ejpam-5431	347	13	)	)	PUNCT
ejpam-5431	347	14	1	1	NUM
ejpam-5431	348	1	+	+	NUM
ejpam-5431	348	2	δ(σ2n	δ(σ2n	NOUN
ejpam-5431	348	3	,	,	PUNCT
ejpam-5431	348	4	σ2n+1	σ2n+1	NOUN
ejpam-5431	348	5	)	)	PUNCT
ejpam-5431	348	6	)	)	PUNCT
ejpam-5431	349	1	r	r	NOUN
ejpam-5431	349	2	+	+	CCONJ
ejpam-5431	349	3	k5	k5	PROPN
ejpam-5431	349	4	(	(	PUNCT
ejpam-5431	349	5	δ(σ2n+1	δ(σ2n+1	PROPN
ejpam-5431	349	6	,	,	PUNCT
ejpam-5431	349	7	σ2n+1)(1	σ2n+1)(1	NOUN
ejpam-5431	349	8	+	+	CCONJ
ejpam-5431	349	9	δ(σ2n	δ(σ2n	NOUN
ejpam-5431	349	10	,	,	PUNCT
ejpam-5431	349	11	σ2n+2	σ2n+2	NOUN
ejpam-5431	349	12	)	)	PUNCT
ejpam-5431	349	13	)	)	PUNCT
ejpam-5431	349	14	1	1	NUM
ejpam-5431	350	1	+	+	NUM
ejpam-5431	350	2	δ(σ2n	δ(σ2n	NOUN
ejpam-5431	350	3	,	,	PUNCT
ejpam-5431	350	4	σ2n+1	σ2n+1	NOUN
ejpam-5431	350	5	)	)	PUNCT
ejpam-5431	350	6	)	)	PUNCT
ejpam-5431	351	1	r	r	NOUN
ejpam-5431	351	2	]	]	PUNCT
ejpam-5431	351	3	1	1	NUM
ejpam-5431	351	4	r	r	NOUN
ejpam-5431	351	5	=	=	SYM
ejpam-5431	351	6	[	[	X
ejpam-5431	351	7	(	(	PUNCT
ejpam-5431	351	8	k1	k1	NOUN
ejpam-5431	351	9	+	+	CCONJ
ejpam-5431	351	10	k2)(δ(σ2n	k2)(δ(σ2n	NOUN
ejpam-5431	351	11	,	,	PUNCT
ejpam-5431	351	12	σ2n+1	σ2n+1	NOUN
ejpam-5431	351	13	)	)	PUNCT
ejpam-5431	351	14	)	)	PUNCT
ejpam-5431	352	1	r	r	NOUN
ejpam-5431	352	2	+	+	CCONJ
ejpam-5431	352	3	(	(	PUNCT
ejpam-5431	352	4	k3	k3	X
ejpam-5431	352	5	+	+	X
ejpam-5431	352	6	k4)(δ(σ2n+1	k4)(δ(σ2n+1	PROPN
ejpam-5431	352	7	,	,	PUNCT
ejpam-5431	352	8	σ2n+2	σ2n+2	NOUN
ejpam-5431	352	9	)	)	PUNCT
ejpam-5431	352	10	)	)	PUNCT
ejpam-5431	353	1	r	r	X
ejpam-5431	353	2	]	]	SYM
ejpam-5431	353	3	1	1	NUM
ejpam-5431	353	4	r	r	NOUN
ejpam-5431	353	5	(	(	PUNCT
ejpam-5431	353	6	8)	8)	NUM
ejpam-5431	353	7	using	use	VERB
ejpam-5431	353	8	(	(	PUNCT
ejpam-5431	353	9	8)	8)	NUM
ejpam-5431	353	10	in	in	ADP
ejpam-5431	353	11	(	(	PUNCT
ejpam-5431	353	12	6	6	NUM
ejpam-5431	353	13	)	)	PUNCT
ejpam-5431	353	14	,	,	PUNCT
ejpam-5431	353	15	we	we	PRON
ejpam-5431	353	16	get	get	VERB
ejpam-5431	353	17	δ(σ2n+1	δ(σ2n+1	ADJ
ejpam-5431	353	18	,	,	PUNCT
ejpam-5431	353	19	σ2n+2	σ2n+2	NOUN
ejpam-5431	353	20	)	)	PUNCT
ejpam-5431	353	21	≤	≤	NUM
ejpam-5431	353	22	φ([(k1	φ([(k1	NOUN
ejpam-5431	354	1	+	+	CCONJ
ejpam-5431	354	2	k2)(δ(σ2n	k2)(δ(σ2n	NOUN
ejpam-5431	354	3	,	,	PUNCT
ejpam-5431	354	4	σ2n+1	σ2n+1	NOUN
ejpam-5431	354	5	)	)	PUNCT
ejpam-5431	354	6	)	)	PUNCT
ejpam-5431	355	1	r	r	NOUN
ejpam-5431	355	2	+	+	CCONJ
ejpam-5431	355	3	(	(	PUNCT
ejpam-5431	355	4	k3	k3	X
ejpam-5431	355	5	+	+	X
ejpam-5431	355	6	k4)(δ(σ2n+1	k4)(δ(σ2n+1	PROPN
ejpam-5431	355	7	,	,	PUNCT
ejpam-5431	355	8	σ2n+2	σ2n+2	NOUN
ejpam-5431	355	9	)	)	PUNCT
ejpam-5431	355	10	)	)	PUNCT
ejpam-5431	356	1	r	r	X
ejpam-5431	356	2	]	]	SYM
ejpam-5431	356	3	1	1	NUM
ejpam-5431	356	4	r	r	NOUN
ejpam-5431	356	5	)	)	PUNCT
ejpam-5431	356	6	(	(	PUNCT
ejpam-5431	356	7	9	9	X
ejpam-5431	356	8	)	)	PUNCT
ejpam-5431	356	9	assume	assume	VERB
ejpam-5431	356	10	that	that	SCONJ
ejpam-5431	356	11	δ(σ2n	δ(σ2n	NOUN
ejpam-5431	356	12	,	,	PUNCT
ejpam-5431	356	13	σ2n+1	σ2n+1	NOUN
ejpam-5431	356	14	)	)	PUNCT
ejpam-5431	356	15	≤	≤	NOUN
ejpam-5431	356	16	δ(σ2n+1	δ(σ2n+1	NUM
ejpam-5431	356	17	,	,	PUNCT
ejpam-5431	356	18	σ2n+2	σ2n+2	X
ejpam-5431	356	19	)	)	PUNCT
ejpam-5431	356	20	,	,	PUNCT
ejpam-5431	356	21	then	then	ADV
ejpam-5431	356	22	since	since	SCONJ
ejpam-5431	356	23	φ	φ	PROPN
ejpam-5431	356	24	is	be	AUX
ejpam-5431	356	25	non	non	ADJ
ejpam-5431	356	26	-	-	ADJ
ejpam-5431	356	27	decreasing	decrease	VERB
ejpam-5431	356	28	,	,	PUNCT
ejpam-5431	356	29	we	we	PRON
ejpam-5431	356	30	get	get	VERB
ejpam-5431	356	31	δ(σ2n+1	δ(σ2n+1	ADJ
ejpam-5431	356	32	,	,	PUNCT
ejpam-5431	356	33	σ2n+2	σ2n+2	NOUN
ejpam-5431	356	34	)	)	PUNCT
ejpam-5431	356	35	≤	≤	PROPN
ejpam-5431	356	36	φ([(k1	φ([(k1	PROPN
ejpam-5431	356	37	+	+	NOUN
ejpam-5431	356	38	k2)(δ(σ2n+1	k2)(δ(σ2n+1	PROPN
ejpam-5431	356	39	,	,	PUNCT
ejpam-5431	356	40	σ2n+2	σ2n+2	NOUN
ejpam-5431	356	41	)	)	PUNCT
ejpam-5431	356	42	)	)	PUNCT
ejpam-5431	357	1	r	r	NOUN
ejpam-5431	357	2	+	+	CCONJ
ejpam-5431	357	3	(	(	PUNCT
ejpam-5431	357	4	k3	k3	X
ejpam-5431	357	5	+	+	X
ejpam-5431	357	6	k4)(δ(σ2n+1	k4)(δ(σ2n+1	PROPN
ejpam-5431	357	7	,	,	PUNCT
ejpam-5431	357	8	σ2n+2	σ2n+2	NOUN
ejpam-5431	357	9	)	)	PUNCT
ejpam-5431	357	10	)	)	PUNCT
ejpam-5431	358	1	r	r	X
ejpam-5431	358	2	]	]	SYM
ejpam-5431	358	3	1	1	NUM
ejpam-5431	358	4	r	r	NOUN
ejpam-5431	358	5	)	)	PUNCT
ejpam-5431	358	6	noting	note	VERB
ejpam-5431	358	7	that	that	SCONJ
ejpam-5431	358	8	k1	k1	PROPN
ejpam-5431	358	9	+	+	CCONJ
ejpam-5431	358	10	k2	k2	NOUN
ejpam-5431	358	11	+	+	CCONJ
ejpam-5431	358	12	k3	k3	ADJ
ejpam-5431	358	13	+	+	CCONJ
ejpam-5431	358	14	k4	k4	ADJ
ejpam-5431	358	15	≤	≤	NUM
ejpam-5431	358	16	1	1	NUM
ejpam-5431	358	17	,	,	PUNCT
ejpam-5431	358	18	δ(σ2n+1	δ(σ2n+1	NUM
ejpam-5431	358	19	,	,	PUNCT
ejpam-5431	358	20	σ2n+2	σ2n+2	NOUN
ejpam-5431	358	21	)	)	PUNCT
ejpam-5431	358	22	≤	≤	NOUN
ejpam-5431	358	23	φ([(δ(σ2n+1	φ([(δ(σ2n+1	NOUN
ejpam-5431	358	24	,	,	PUNCT
ejpam-5431	358	25	σ2n+2	σ2n+2	NOUN
ejpam-5431	358	26	)	)	PUNCT
ejpam-5431	358	27	)	)	PUNCT
ejpam-5431	359	1	r	r	X
ejpam-5431	359	2	]	]	SYM
ejpam-5431	359	3	1	1	NUM
ejpam-5431	359	4	r	r	NOUN
ejpam-5431	359	5	)	)	PUNCT
ejpam-5431	359	6	=	=	SYM
ejpam-5431	359	7	φ(δ(σ2n+1	φ(δ(σ2n+1	ADJ
ejpam-5431	359	8	,	,	PUNCT
ejpam-5431	359	9	σ2n+2	σ2n+2	NOUN
ejpam-5431	359	10	)	)	PUNCT
ejpam-5431	359	11	)	)	PUNCT
ejpam-5431	360	1	<	<	X
ejpam-5431	360	2	δ(σ2n+1	δ(σ2n+1	X
ejpam-5431	360	3	,	,	PUNCT
ejpam-5431	360	4	σ2n+2	σ2n+2	NOUN
ejpam-5431	360	5	)	)	PUNCT
ejpam-5431	360	6	a	a	DET
ejpam-5431	360	7	contradiction	contradiction	NOUN
ejpam-5431	360	8	.	.	PUNCT
ejpam-5431	361	1	consequently	consequently	ADV
ejpam-5431	361	2	,	,	PUNCT
ejpam-5431	361	3	we	we	PRON
ejpam-5431	361	4	have	have	VERB
ejpam-5431	361	5	δ(σ2n+1	δ(σ2n+1	NUM
ejpam-5431	361	6	,	,	PUNCT
ejpam-5431	361	7	σ2n+2	σ2n+2	NOUN
ejpam-5431	361	8	)	)	PUNCT
ejpam-5431	361	9	≤	≤	NOUN
ejpam-5431	361	10	δ(σ2n	δ(σ2n	NOUN
ejpam-5431	361	11	,	,	PUNCT
ejpam-5431	361	12	σ2n+1	σ2n+1	NOUN
ejpam-5431	361	13	)	)	PUNCT
ejpam-5431	361	14	so	so	ADV
ejpam-5431	361	15	,	,	PUNCT
ejpam-5431	361	16	(	(	PUNCT
ejpam-5431	361	17	9	9	X
ejpam-5431	361	18	)	)	PUNCT
ejpam-5431	361	19	becomes	become	VERB
ejpam-5431	361	20	δ(σ2n+1	δ(σ2n+1	ADJ
ejpam-5431	361	21	,	,	PUNCT
ejpam-5431	361	22	σ2n+2	σ2n+2	NOUN
ejpam-5431	361	23	)	)	PUNCT
ejpam-5431	361	24	≤	≤	NOUN
ejpam-5431	361	25	φ(δ(σ2n	φ(δ(σ2n	PROPN
ejpam-5431	361	26	,	,	PUNCT
ejpam-5431	361	27	σ2n+1	σ2n+1	PROPN
ejpam-5431	361	28	)	)	PUNCT
ejpam-5431	361	29	)	)	PUNCT
ejpam-5431	362	1	≤	≤	NOUN
ejpam-5431	362	2	φ2(δ(σ2n−1	φ2(δ(σ2n−1	ADJ
ejpam-5431	362	3	,	,	PUNCT
ejpam-5431	362	4	σ2n	σ2n	NOUN
ejpam-5431	362	5	)	)	PUNCT
ejpam-5431	362	6	)	)	PUNCT
ejpam-5431	362	7	...	...	PUNCT
ejpam-5431	363	1	≤	≤	PROPN
ejpam-5431	363	2	φ2n+1(δ(σ0	φ2n+1(δ(σ0	PROPN
ejpam-5431	363	3	,	,	PUNCT
ejpam-5431	363	4	σ1	σ1	PROPN
ejpam-5431	363	5	)	)	PUNCT
ejpam-5431	363	6	)	)	PUNCT
ejpam-5431	363	7	δ(σ2n+1	δ(σ2n+1	NUM
ejpam-5431	363	8	,	,	PUNCT
ejpam-5431	363	9	σ2n+2	σ2n+2	NOUN
ejpam-5431	363	10	)	)	PUNCT
ejpam-5431	363	11	≤	≤	PROPN
ejpam-5431	363	12	φ2n+1(δ(σ0	φ2n+1(δ(σ0	PROPN
ejpam-5431	363	13	,	,	PUNCT
ejpam-5431	363	14	σ1	σ1	PROPN
ejpam-5431	363	15	)	)	PUNCT
ejpam-5431	363	16	)	)	PUNCT
ejpam-5431	363	17	similarly	similarly	ADV
ejpam-5431	363	18	,	,	PUNCT
ejpam-5431	363	19	for	for	ADP
ejpam-5431	363	20	(	(	PUNCT
ejpam-5431	363	21	7	7	X
ejpam-5431	363	22	)	)	PUNCT
ejpam-5431	363	23	we	we	PRON
ejpam-5431	363	24	are	be	AUX
ejpam-5431	363	25	able	able	ADJ
ejpam-5431	363	26	to	to	PART
ejpam-5431	363	27	demonstrate	demonstrate	VERB
ejpam-5431	363	28	that	that	SCONJ
ejpam-5431	363	29	δ(σ2n+2	δ(σ2n+2	ADJ
ejpam-5431	363	30	,	,	PUNCT
ejpam-5431	363	31	σ2n+3	σ2n+3	PROPN
ejpam-5431	363	32	)	)	PUNCT
ejpam-5431	363	33	≤	≤	NOUN
ejpam-5431	363	34	φ2n+2(δ(σ0	φ2n+2(δ(σ0	PROPN
ejpam-5431	363	35	,	,	PUNCT
ejpam-5431	363	36	σ1	σ1	PROPN
ejpam-5431	363	37	)	)	PUNCT
ejpam-5431	363	38	)	)	PUNCT
ejpam-5431	363	39	from	from	ADP
ejpam-5431	363	40	above	above	ADP
ejpam-5431	363	41	two	two	NUM
ejpam-5431	363	42	equations	equation	NOUN
ejpam-5431	363	43	,	,	PUNCT
ejpam-5431	363	44	we	we	PRON
ejpam-5431	363	45	conclude	conclude	VERB
ejpam-5431	363	46	that	that	SCONJ
ejpam-5431	363	47	δ(σn	δ(σn	NOUN
ejpam-5431	363	48	,	,	PUNCT
ejpam-5431	363	49	σn+1	σn+1	NOUN
ejpam-5431	363	50	)	)	PUNCT
ejpam-5431	363	51	≤	≤	NOUN
ejpam-5431	363	52	φn(δ(σ0	φn(δ(σ0	PROPN
ejpam-5431	363	53	,	,	PUNCT
ejpam-5431	363	54	σ1	σ1	PROPN
ejpam-5431	363	55	)	)	PUNCT
ejpam-5431	363	56	)	)	PUNCT
ejpam-5431	363	57	(	(	PUNCT
ejpam-5431	363	58	10	10	X
ejpam-5431	363	59	)	)	PUNCT
ejpam-5431	363	60	n.	n.	NOUN
ejpam-5431	363	61	saleem	saleem	PROPN
ejpam-5431	363	62	et	et	PROPN
ejpam-5431	363	63	al	al	PROPN
ejpam-5431	363	64	.	.	PUNCT
ejpam-5431	363	65	/	/	SYM
ejpam-5431	363	66	eur	eur	PROPN
ejpam-5431	363	67	.	.	PUNCT
ejpam-5431	364	1	j.	j.	PROPN
ejpam-5431	364	2	pure	pure	PROPN
ejpam-5431	364	3	appl	appl	PROPN
ejpam-5431	364	4	.	.	PROPN
ejpam-5431	364	5	math	math	PROPN
ejpam-5431	364	6	,	,	PUNCT
ejpam-5431	364	7	17	17	NUM
ejpam-5431	364	8	(	(	PUNCT
ejpam-5431	364	9	4	4	NUM
ejpam-5431	364	10	)	)	PUNCT
ejpam-5431	364	11	(	(	PUNCT
ejpam-5431	364	12	2024	2024	NUM
ejpam-5431	364	13	)	)	PUNCT
ejpam-5431	364	14	,	,	PUNCT
ejpam-5431	364	15	3304	3304	NUM
ejpam-5431	364	16	-	-	SYM
ejpam-5431	364	17	3335	3335	NUM
ejpam-5431	364	18	3318	3318	NUM
ejpam-5431	364	19	take	take	VERB
ejpam-5431	364	20	m	m	PRON
ejpam-5431	364	21	,	,	PUNCT
ejpam-5431	364	22	n	n	PROPN
ejpam-5431	364	23	∈	∈	PROPN
ejpam-5431	364	24	n	n	CCONJ
ejpam-5431	364	25	where	where	SCONJ
ejpam-5431	364	26	m	m	VERB
ejpam-5431	364	27	>	>	X
ejpam-5431	364	28	n	n	CCONJ
ejpam-5431	364	29	,	,	PUNCT
ejpam-5431	364	30	then	then	ADV
ejpam-5431	364	31	δ(σn	δ(σn	NOUN
ejpam-5431	364	32	,	,	PUNCT
ejpam-5431	364	33	σm	σm	NOUN
ejpam-5431	364	34	)	)	PUNCT
ejpam-5431	364	35	≤	≤	NOUN
ejpam-5431	364	36	hδ(σn	hδ(σn	PROPN
ejpam-5431	364	37	,	,	PUNCT
ejpam-5431	364	38	σn+1	σn+1	PROPN
ejpam-5431	364	39	)	)	PUNCT
ejpam-5431	364	40	+	+	CCONJ
ejpam-5431	365	1	h2δ(σn+1	h2δ(σn+1	NOUN
ejpam-5431	365	2	,	,	PUNCT
ejpam-5431	365	3	σn+2	σn+2	NUM
ejpam-5431	365	4	)	)	PUNCT
ejpam-5431	365	5	+	+	CCONJ
ejpam-5431	365	6	·	·	PUNCT
ejpam-5431	365	7	·	·	PUNCT
ejpam-5431	365	8	·	·	PUNCT
ejpam-5431	366	1	+	+	NUM
ejpam-5431	366	2	hm−nδ(σm−1	hm−nδ(σm−1	PROPN
ejpam-5431	366	3	,	,	PUNCT
ejpam-5431	366	4	σm	σm	X
ejpam-5431	366	5	)	)	PUNCT
ejpam-5431	366	6	using	use	VERB
ejpam-5431	366	7	(	(	PUNCT
ejpam-5431	366	8	10	10	NUM
ejpam-5431	366	9	)	)	PUNCT
ejpam-5431	366	10	,	,	PUNCT
ejpam-5431	366	11	we	we	PRON
ejpam-5431	366	12	get	get	VERB
ejpam-5431	366	13	δ(σn	δ(σn	NOUN
ejpam-5431	366	14	,	,	PUNCT
ejpam-5431	366	15	σm	σm	NOUN
ejpam-5431	366	16	)	)	PUNCT
ejpam-5431	366	17	≤	≤	PROPN
ejpam-5431	366	18	hφn(δ(σ0	hφn(δ(σ0	PROPN
ejpam-5431	366	19	,	,	PUNCT
ejpam-5431	366	20	σ1	σ1	PROPN
ejpam-5431	366	21	)	)	PUNCT
ejpam-5431	366	22	)	)	PUNCT
ejpam-5431	367	1	+	+	CCONJ
ejpam-5431	367	2	h2φn+1(δ(σ0	h2φn+1(δ(σ0	PROPN
ejpam-5431	367	3	,	,	PUNCT
ejpam-5431	367	4	σ1	σ1	PROPN
ejpam-5431	367	5	)	)	PUNCT
ejpam-5431	367	6	)	)	PUNCT
ejpam-5431	368	1	+	+	CCONJ
ejpam-5431	368	2	·	·	PUNCT
ejpam-5431	368	3	·	·	PUNCT
ejpam-5431	368	4	·	·	PUNCT
ejpam-5431	368	5	+	+	PUNCT
ejpam-5431	368	6	hm−nφm−1(δ(σ0	hm−nφm−1(δ(σ0	ADJ
ejpam-5431	368	7	,	,	PUNCT
ejpam-5431	368	8	σ1	σ1	NOUN
ejpam-5431	368	9	)	)	PUNCT
ejpam-5431	368	10	)	)	PUNCT
ejpam-5431	369	1	=	=	SYM
ejpam-5431	369	2	hn−n+1φn(δ(σ0	hn−n+1φn(δ(σ0	NOUN
ejpam-5431	369	3	,	,	PUNCT
ejpam-5431	369	4	σ1	σ1	PROPN
ejpam-5431	369	5	)	)	PUNCT
ejpam-5431	369	6	)	)	PUNCT
ejpam-5431	370	1	+	+	CCONJ
ejpam-5431	370	2	hn−n+2φn+1(δ(σ0	hn−n+2φn+1(δ(σ0	PROPN
ejpam-5431	370	3	,	,	PUNCT
ejpam-5431	370	4	σ1	σ1	PROPN
ejpam-5431	370	5	)	)	PUNCT
ejpam-5431	370	6	)	)	PUNCT
ejpam-5431	371	1	+	+	CCONJ
ejpam-5431	371	2	·	·	PUNCT
ejpam-5431	371	3	·	·	PUNCT
ejpam-5431	371	4	·	·	PUNCT
ejpam-5431	371	5	+	+	NUM
ejpam-5431	371	6	hm−n+1−1φm−1(δ(σ0	hm−n+1−1φm−1(δ(σ0	PROPN
ejpam-5431	371	7	,	,	PUNCT
ejpam-5431	371	8	σ1	σ1	NOUN
ejpam-5431	371	9	)	)	PUNCT
ejpam-5431	371	10	)	)	PUNCT
ejpam-5431	372	1	=	=	SYM
ejpam-5431	372	2	1	1	NUM
ejpam-5431	372	3	hn−1	hn−1	PROPN
ejpam-5431	372	4	[	[	X
ejpam-5431	372	5	hnφn(δ(σ0	hnφn(δ(σ0	NOUN
ejpam-5431	372	6	,	,	PUNCT
ejpam-5431	372	7	σ1	σ1	PROPN
ejpam-5431	372	8	)	)	PUNCT
ejpam-5431	372	9	)	)	PUNCT
ejpam-5431	373	1	+	+	CCONJ
ejpam-5431	373	2	hn+1φn+1(δ(σ0	hn+1φn+1(δ(σ0	NOUN
ejpam-5431	373	3	,	,	PUNCT
ejpam-5431	373	4	σ1	σ1	PROPN
ejpam-5431	373	5	)	)	PUNCT
ejpam-5431	373	6	)	)	PUNCT
ejpam-5431	374	1	+	+	CCONJ
ejpam-5431	374	2	·	·	PUNCT
ejpam-5431	374	3	·	·	PUNCT
ejpam-5431	374	4	·	·	PUNCT
ejpam-5431	374	5	+	+	NUM
ejpam-5431	374	6	hm−1φm−1(δ(σ0	hm−1φm−1(δ(σ0	PROPN
ejpam-5431	374	7	,	,	PUNCT
ejpam-5431	374	8	σ1	σ1	PROPN
ejpam-5431	374	9	)	)	PUNCT
ejpam-5431	374	10	)	)	PUNCT
ejpam-5431	374	11	]	]	PUNCT
ejpam-5431	375	1	=	=	SYM
ejpam-5431	375	2	1	1	NUM
ejpam-5431	375	3	hn−1	hn−1	ADJ
ejpam-5431	375	4	m−1∑	m−1∑	PROPN
ejpam-5431	375	5	i	i	NOUN
ejpam-5431	375	6	=	=	PROPN
ejpam-5431	375	7	n	n	PROPN
ejpam-5431	375	8	hiφi(δ(σ0	hiφi(δ(σ0	PROPN
ejpam-5431	375	9	,	,	PUNCT
ejpam-5431	375	10	σ1	σ1	PROPN
ejpam-5431	375	11	)	)	PUNCT
ejpam-5431	375	12	)	)	PUNCT
ejpam-5431	375	13	≤	≤	ADV
ejpam-5431	375	14	1	1	NUM
ejpam-5431	375	15	hn−1	hn−1	NOUN
ejpam-5431	375	16	+	+	PROPN
ejpam-5431	375	17	∞∑	∞∑	PROPN
ejpam-5431	375	18	i=0	i=0	PROPN
ejpam-5431	375	19	hiφi(δ(σ0	hiφi(δ(σ0	PROPN
ejpam-5431	375	20	,	,	PUNCT
ejpam-5431	375	21	σ1	σ1	PROPN
ejpam-5431	375	22	)	)	PUNCT
ejpam-5431	375	23	)	)	PUNCT
ejpam-5431	375	24	thus	thus	ADV
ejpam-5431	375	25	δ(σn	δ(σn	NOUN
ejpam-5431	375	26	,	,	PUNCT
ejpam-5431	375	27	σm	σm	X
ejpam-5431	375	28	)	)	PUNCT
ejpam-5431	375	29	≤	≤	NOUN
ejpam-5431	375	30	1	1	NUM
ejpam-5431	375	31	hn−1	hn−1	NOUN
ejpam-5431	375	32	+	+	PROPN
ejpam-5431	375	33	∞∑	∞∑	PROPN
ejpam-5431	375	34	i=0	i=0	PROPN
ejpam-5431	375	35	hiφi(δ(σ0	hiφi(δ(σ0	PROPN
ejpam-5431	375	36	,	,	PUNCT
ejpam-5431	375	37	σ1	σ1	PROPN
ejpam-5431	375	38	)	)	PUNCT
ejpam-5431	375	39	)	)	PUNCT
ejpam-5431	375	40	(	(	PUNCT
ejpam-5431	375	41	11	11	NUM
ejpam-5431	375	42	)	)	PUNCT
ejpam-5431	375	43	since	since	SCONJ
ejpam-5431	375	44	φ	φ	PROPN
ejpam-5431	375	45	is	be	AUX
ejpam-5431	375	46	a	a	DET
ejpam-5431	375	47	b	b	NOUN
ejpam-5431	375	48	-	-	PUNCT
ejpam-5431	375	49	cf	cf	NOUN
ejpam-5431	375	50	,	,	PUNCT
ejpam-5431	375	51	it	it	PRON
ejpam-5431	375	52	follows	follow	VERB
ejpam-5431	375	53	that	that	SCONJ
ejpam-5431	375	54	the	the	DET
ejpam-5431	375	55	series	series	NOUN
ejpam-5431	375	56	∑+∞	∑+∞	ADJ
ejpam-5431	375	57	i=0	i=0	PROPN
ejpam-5431	375	58	h	h	NOUN
ejpam-5431	375	59	iφi(δ(σ0	iφi(δ(σ0	PROPN
ejpam-5431	375	60	,	,	PUNCT
ejpam-5431	375	61	σ1	σ1	PROPN
ejpam-5431	375	62	)	)	PUNCT
ejpam-5431	375	63	)	)	PUNCT
ejpam-5431	375	64	is	be	AUX
ejpam-5431	375	65	convergent	convergent	NOUN
ejpam-5431	375	66	.	.	PUNCT
ejpam-5431	376	1	setting	set	VERB
ejpam-5431	376	2	,	,	PUNCT
ejpam-5431	376	3	sk	sk	PROPN
ejpam-5431	376	4	=	=	PUNCT
ejpam-5431	376	5	k∑	k∑	PROPN
ejpam-5431	376	6	i=1	i=1	PROPN
ejpam-5431	376	7	hiφi(δ(σ0	hiφi(δ(σ0	PROPN
ejpam-5431	376	8	,	,	PUNCT
ejpam-5431	376	9	σ1	σ1	PROPN
ejpam-5431	376	10	)	)	PUNCT
ejpam-5431	376	11	)	)	PUNCT
ejpam-5431	377	1	then	then	ADV
ejpam-5431	377	2	(	(	PUNCT
ejpam-5431	377	3	11	11	NUM
ejpam-5431	377	4	)	)	PUNCT
ejpam-5431	377	5	becomes	become	VERB
ejpam-5431	377	6	δ(σn	δ(σn	NOUN
ejpam-5431	377	7	,	,	PUNCT
ejpam-5431	377	8	σm	σm	NOUN
ejpam-5431	377	9	)	)	PUNCT
ejpam-5431	377	10	≤	≤	NOUN
ejpam-5431	377	11	1	1	NUM
ejpam-5431	377	12	hn−1	hn−1	ADJ
ejpam-5431	377	13	(	(	PUNCT
ejpam-5431	377	14	sm−1	sm−1	NOUN
ejpam-5431	377	15	−	−	PROPN
ejpam-5431	377	16	sn−1	sn−1	PROPN
ejpam-5431	377	17	)	)	PUNCT
ejpam-5431	377	18	(	(	PUNCT
ejpam-5431	377	19	12	12	NUM
ejpam-5431	377	20	)	)	PUNCT
ejpam-5431	377	21	applying	apply	VERB
ejpam-5431	377	22	limit	limit	NOUN
ejpam-5431	377	23	as	as	ADP
ejpam-5431	377	24	n	n	CCONJ
ejpam-5431	377	25	,	,	PUNCT
ejpam-5431	377	26	m→	m→	PUNCT
ejpam-5431	378	1	+	+	NOUN
ejpam-5431	378	2	∞	∞	NUM
ejpam-5431	378	3	in	in	ADP
ejpam-5431	378	4	(	(	PUNCT
ejpam-5431	378	5	12	12	NUM
ejpam-5431	378	6	)	)	PUNCT
ejpam-5431	378	7	we	we	PRON
ejpam-5431	378	8	attain	attain	VERB
ejpam-5431	378	9	δ(σn	δ(σn	NOUN
ejpam-5431	378	10	,	,	PUNCT
ejpam-5431	378	11	σm	σm	NOUN
ejpam-5431	378	12	)	)	PUNCT
ejpam-5431	378	13	→	→	SYM
ejpam-5431	378	14	0	0	NUM
ejpam-5431	378	15	,	,	PUNCT
ejpam-5431	378	16	this	this	PRON
ejpam-5431	378	17	indicates	indicate	VERB
ejpam-5431	378	18	that	that	SCONJ
ejpam-5431	378	19	{	{	PUNCT
ejpam-5431	378	20	σn}n≥1	σn}n≥1	NOUN
ejpam-5431	378	21	is	be	AUX
ejpam-5431	378	22	a	a	DET
ejpam-5431	378	23	cauchy	cauchy	ADJ
ejpam-5431	378	24	sequence	sequence	NOUN
ejpam-5431	378	25	in	in	ADP
ejpam-5431	378	26	x.	x.	NOUN
ejpam-5431	378	27	completeness	completeness	PROPN
ejpam-5431	378	28	of	of	ADP
ejpam-5431	378	29	x	x	PRON
ejpam-5431	378	30	demonstrates	demonstrate	VERB
ejpam-5431	378	31	that	that	SCONJ
ejpam-5431	378	32	there	there	PRON
ejpam-5431	378	33	is	be	VERB
ejpam-5431	378	34	ς	ς	PROPN
ejpam-5431	378	35	∈	∈	PROPN
ejpam-5431	378	36	x	x	NOUN
ejpam-5431	378	37	,	,	PUNCT
ejpam-5431	378	38	so	so	SCONJ
ejpam-5431	378	39	that	that	SCONJ
ejpam-5431	378	40	lim	lim	PROPN
ejpam-5431	378	41	n→+∞	n→+∞	VERB
ejpam-5431	378	42	δ(σn	δ(σn	PROPN
ejpam-5431	378	43	,	,	PUNCT
ejpam-5431	378	44	ς	ς	PROPN
ejpam-5431	378	45	)	)	PUNCT
ejpam-5431	378	46	=	=	NOUN
ejpam-5431	379	1	0	0	X
ejpam-5431	379	2	.	.	PUNCT
ejpam-5431	380	1	now	now	ADV
ejpam-5431	380	2	we	we	PRON
ejpam-5431	380	3	show	show	VERB
ejpam-5431	380	4	that	that	SCONJ
ejpam-5431	380	5	ς	ς	PROPN
ejpam-5431	380	6	∈	∈	PROPN
ejpam-5431	381	1	[	[	X
ejpam-5431	381	2	t	t	NOUN
ejpam-5431	381	3	ς](⋉(ς),β(ς	ς](⋉(ς),β(ς	NUM
ejpam-5431	381	4	)	)	PUNCT
ejpam-5431	381	5	)	)	PUNCT
ejpam-5431	381	6	by	by	ADP
ejpam-5431	381	7	using	use	VERB
ejpam-5431	381	8	ti	ti	NOUN
ejpam-5431	381	9	in	in	ADP
ejpam-5431	381	10	x	x	PROPN
ejpam-5431	381	11	,	,	PUNCT
ejpam-5431	381	12	δ(ς	δ(ς	PROPN
ejpam-5431	381	13	,	,	PUNCT
ejpam-5431	381	14	[	[	X
ejpam-5431	381	15	t	t	NOUN
ejpam-5431	381	16	ς](⋉(ς),β(ς	ς](⋉(ς),β(ς	NUM
ejpam-5431	381	17	)	)	PUNCT
ejpam-5431	381	18	)	)	PUNCT
ejpam-5431	381	19	)	)	PUNCT
ejpam-5431	381	20	≤	≤	NUM
ejpam-5431	381	21	h(δ(ς	h(δ(ς	PROPN
ejpam-5431	381	22	,	,	PUNCT
ejpam-5431	381	23	σ2n+1	σ2n+1	NOUN
ejpam-5431	381	24	)	)	PUNCT
ejpam-5431	381	25	)	)	PUNCT
ejpam-5431	382	1	+	+	PUNCT
ejpam-5431	382	2	δ(σ2n+1	δ(σ2n+1	NUM
ejpam-5431	382	3	,	,	PUNCT
ejpam-5431	382	4	[	[	X
ejpam-5431	382	5	t	t	NOUN
ejpam-5431	382	6	ς](⋉(ς),β(ς	ς](⋉(ς),β(ς	NUM
ejpam-5431	382	7	)	)	PUNCT
ejpam-5431	382	8	)	)	PUNCT
ejpam-5431	382	9	)	)	PUNCT
ejpam-5431	383	1	=	=	SYM
ejpam-5431	383	2	h(δ(ς	h(δ(ς	X
ejpam-5431	383	3	,	,	PUNCT
ejpam-5431	383	4	σ2n+1	σ2n+1	NOUN
ejpam-5431	383	5	)	)	PUNCT
ejpam-5431	383	6	)	)	PUNCT
ejpam-5431	384	1	+	+	CCONJ
ejpam-5431	384	2	h(δ(σ2n+1	h(δ(σ2n+1	NOUN
ejpam-5431	384	3	)	)	PUNCT
ejpam-5431	384	4	)	)	PUNCT
ejpam-5431	384	5	.	.	PUNCT
ejpam-5431	385	1	using	use	VERB
ejpam-5431	385	2	δ(σ	δ(σ	PROPN
ejpam-5431	385	3	,	,	PUNCT
ejpam-5431	385	4	b	b	NOUN
ejpam-5431	385	5	)	)	PUNCT
ejpam-5431	385	6	≤	≤	NOUN
ejpam-5431	385	7	ℵ(a	ℵ(a	PROPN
ejpam-5431	385	8	,	,	PUNCT
ejpam-5431	385	9	b	b	NOUN
ejpam-5431	385	10	)	)	PUNCT
ejpam-5431	385	11	for	for	ADP
ejpam-5431	385	12	σ	σ	PROPN
ejpam-5431	385	13	∈	∈	PROPN
ejpam-5431	385	14	a	a	PRON
ejpam-5431	385	15	,	,	PUNCT
ejpam-5431	385	16	δ(ς	δ(ς	PROPN
ejpam-5431	385	17	,	,	PUNCT
ejpam-5431	385	18	[	[	X
ejpam-5431	385	19	t	t	NOUN
ejpam-5431	385	20	ς](⋉(ς)+β(ς	ς](⋉(ς)+β(ς	NUM
ejpam-5431	385	21	)	)	PUNCT
ejpam-5431	385	22	)	)	PUNCT
ejpam-5431	385	23	)	)	PUNCT
ejpam-5431	385	24	≤	≤	NOUN
ejpam-5431	385	25	hδ(ς	hδ(ς	NUM
ejpam-5431	385	26	,	,	PUNCT
ejpam-5431	385	27	σ2n+1	σ2n+1	PROPN
ejpam-5431	385	28	)	)	PUNCT
ejpam-5431	386	1	+	+	NUM
ejpam-5431	386	2	hℵ([sσ2n](⋉(σ2n),β(σ2n	hℵ([sσ2n](⋉(σ2n),β(σ2n	NOUN
ejpam-5431	386	3	)	)	PUNCT
ejpam-5431	386	4	)	)	PUNCT
ejpam-5431	386	5	,	,	PUNCT
ejpam-5431	387	1	[	[	X
ejpam-5431	387	2	t	t	NOUN
ejpam-5431	387	3	ς](⋉(ς),β(ς	ς](⋉(ς),β(ς	NUM
ejpam-5431	387	4	)	)	PUNCT
ejpam-5431	387	5	)	)	PUNCT
ejpam-5431	387	6	)	)	PUNCT
ejpam-5431	388	1	(	(	PUNCT
ejpam-5431	388	2	13	13	NUM
ejpam-5431	388	3	)	)	PUNCT
ejpam-5431	388	4	since	since	SCONJ
ejpam-5431	388	5	(	(	PUNCT
ejpam-5431	388	6	s	s	PROPN
ejpam-5431	388	7	,	,	PUNCT
ejpam-5431	388	8	t	t	NOUN
ejpam-5431	388	9	)	)	PUNCT
ejpam-5431	388	10	pair	pair	NOUN
ejpam-5431	388	11	is	be	AUX
ejpam-5431	388	12	ℵ-continuous	ℵ-continuous	ADJ
ejpam-5431	388	13	,	,	PUNCT
ejpam-5431	388	14	by	by	ADP
ejpam-5431	388	15	applying	apply	VERB
ejpam-5431	388	16	limit	limit	NOUN
ejpam-5431	388	17	as	as	ADP
ejpam-5431	388	18	n→	n→	ADV
ejpam-5431	388	19	+	+	ADJ
ejpam-5431	388	20	∞	∞	PROPN
ejpam-5431	388	21	in	in	ADP
ejpam-5431	388	22	(	(	PUNCT
ejpam-5431	388	23	13	13	NUM
ejpam-5431	388	24	)	)	PUNCT
ejpam-5431	388	25	,	,	PUNCT
ejpam-5431	388	26	we	we	PRON
ejpam-5431	388	27	get	get	VERB
ejpam-5431	388	28	n.	n.	PROPN
ejpam-5431	388	29	saleem	saleem	PROPN
ejpam-5431	389	1	et	et	PROPN
ejpam-5431	389	2	al	al	PROPN
ejpam-5431	389	3	.	.	PUNCT
ejpam-5431	389	4	/	/	SYM
ejpam-5431	389	5	eur	eur	PROPN
ejpam-5431	389	6	.	.	PUNCT
ejpam-5431	390	1	j.	j.	PROPN
ejpam-5431	390	2	pure	pure	PROPN
ejpam-5431	390	3	appl	appl	PROPN
ejpam-5431	390	4	.	.	PROPN
ejpam-5431	390	5	math	math	PROPN
ejpam-5431	390	6	,	,	PUNCT
ejpam-5431	390	7	17	17	NUM
ejpam-5431	390	8	(	(	PUNCT
ejpam-5431	390	9	4	4	NUM
ejpam-5431	390	10	)	)	PUNCT
ejpam-5431	390	11	(	(	PUNCT
ejpam-5431	390	12	2024	2024	NUM
ejpam-5431	390	13	)	)	PUNCT
ejpam-5431	390	14	,	,	PUNCT
ejpam-5431	390	15	3304	3304	NUM
ejpam-5431	390	16	-	-	SYM
ejpam-5431	390	17	3335	3335	NUM
ejpam-5431	390	18	3319	3319	NUM
ejpam-5431	390	19	δ(ς	δ(ς	PROPN
ejpam-5431	390	20	,	,	PUNCT
ejpam-5431	391	1	[	[	X
ejpam-5431	391	2	t	t	NOUN
ejpam-5431	391	3	ς](⋉(ς),β(ς	ς](⋉(ς),β(ς	NUM
ejpam-5431	391	4	)	)	PUNCT
ejpam-5431	391	5	)	)	PUNCT
ejpam-5431	391	6	)	)	PUNCT
ejpam-5431	392	1	=	=	SYM
ejpam-5431	392	2	0	0	NUM
ejpam-5431	393	1	this	this	PRON
ejpam-5431	393	2	indicate	indicate	VERB
ejpam-5431	393	3	that	that	SCONJ
ejpam-5431	393	4	ς	ς	PROPN
ejpam-5431	393	5	∈	∈	PROPN
ejpam-5431	393	6	[	[	X
ejpam-5431	393	7	t	t	NOUN
ejpam-5431	393	8	ς](⋉(ς),β(ς	ς](⋉(ς),β(ς	NUM
ejpam-5431	393	9	)	)	PUNCT
ejpam-5431	393	10	)	)	PUNCT
ejpam-5431	393	11	analogously	analogously	ADV
ejpam-5431	393	12	it	it	PRON
ejpam-5431	393	13	can	can	AUX
ejpam-5431	393	14	be	be	AUX
ejpam-5431	393	15	shown	show	VERB
ejpam-5431	393	16	that	that	SCONJ
ejpam-5431	393	17	ς	ς	PROPN
ejpam-5431	393	18	∈	∈	PROPN
ejpam-5431	393	19	[	[	X
ejpam-5431	393	20	sς](⋉(ς),β(ς	sς](⋉(ς),β(ς	X
ejpam-5431	393	21	)	)	PUNCT
ejpam-5431	393	22	)	)	PUNCT
ejpam-5431	393	23	.	.	PUNCT
ejpam-5431	394	1	thus	thus	ADV
ejpam-5431	394	2	ς	ς	PROPN
ejpam-5431	394	3	∈	∈	PROPN
ejpam-5431	394	4	[	[	X
ejpam-5431	394	5	t	t	NOUN
ejpam-5431	394	6	ς](⋉(ς),β(ς	ς](⋉(ς),β(ς	NUM
ejpam-5431	394	7	)	)	PUNCT
ejpam-5431	394	8	)	)	PUNCT
ejpam-5431	394	9	∩	∩	NOUN
ejpam-5431	394	10	[	[	X
ejpam-5431	394	11	sς](⋉(ς),β(ς	sς](⋉(ς),β(ς	X
ejpam-5431	394	12	)	)	PUNCT
ejpam-5431	394	13	)	)	PUNCT
ejpam-5431	394	14	that	that	ADV
ejpam-5431	394	15	is	be	AUX
ejpam-5431	394	16	,	,	PUNCT
ejpam-5431	394	17	ς	ς	PROPN
ejpam-5431	394	18	is	be	AUX
ejpam-5431	394	19	a	a	DET
ejpam-5431	394	20	common	common	ADJ
ejpam-5431	394	21	iffp	iffp	NOUN
ejpam-5431	394	22	of	of	ADP
ejpam-5431	394	23	mappings	mapping	NOUN
ejpam-5431	394	24	s	s	PART
ejpam-5431	394	25	and	and	CCONJ
ejpam-5431	394	26	t	t	PROPN
ejpam-5431	394	27	.	.	PUNCT
ejpam-5431	395	1	case	case	NOUN
ejpam-5431	395	2	2	2	NUM
ejpam-5431	395	3	:	:	PUNCT
ejpam-5431	395	4	r	r	NOUN
ejpam-5431	395	5	=	=	SYM
ejpam-5431	395	6	0	0	NUM
ejpam-5431	395	7	for	for	ADP
ejpam-5431	395	8	r	r	NOUN
ejpam-5431	395	9	=	=	SYM
ejpam-5431	395	10	0	0	NUM
ejpam-5431	395	11	,	,	PUNCT
ejpam-5431	395	12	taking	take	VERB
ejpam-5431	395	13	inequality	inequality	NOUN
ejpam-5431	395	14	(	(	PUNCT
ejpam-5431	395	15	6	6	NUM
ejpam-5431	395	16	)	)	PUNCT
ejpam-5431	395	17	with	with	ADP
ejpam-5431	395	18	condition	condition	NOUN
ejpam-5431	395	19	(	(	PUNCT
ejpam-5431	395	20	i	i	NOUN
ejpam-5431	395	21	)	)	PUNCT
ejpam-5431	395	22	,	,	PUNCT
ejpam-5431	395	23	we	we	PRON
ejpam-5431	395	24	have	have	VERB
ejpam-5431	395	25	m	m	PROPN
ejpam-5431	395	26	r	r	NOUN
ejpam-5431	395	27	(	(	PUNCT
ejpam-5431	395	28	s	s	PROPN
ejpam-5431	395	29	,	,	PUNCT
ejpam-5431	395	30	t	t	NOUN
ejpam-5431	395	31	)	)	PUNCT
ejpam-5431	395	32	(	(	PUNCT
ejpam-5431	395	33	σ2n	σ2n	NOUN
ejpam-5431	395	34	,	,	PUNCT
ejpam-5431	395	35	σ2n+1	σ2n+1	NOUN
ejpam-5431	395	36	)	)	PUNCT
ejpam-5431	395	37	=	=	SYM
ejpam-5431	395	38	b(σ2n	b(σ2n	NOUN
ejpam-5431	395	39	,	,	PUNCT
ejpam-5431	395	40	σ2n+1	σ2n+1	PROPN
ejpam-5431	395	41	)	)	PUNCT
ejpam-5431	395	42	=	=	SYM
ejpam-5431	395	43	(	(	PUNCT
ejpam-5431	395	44	δ(σ2n	δ(σ2n	NOUN
ejpam-5431	395	45	,	,	PUNCT
ejpam-5431	395	46	σ2n+1	σ2n+1	NOUN
ejpam-5431	395	47	)	)	PUNCT
ejpam-5431	395	48	)	)	PUNCT
ejpam-5431	396	1	k1	k1	PROPN
ejpam-5431	396	2	×	×	NOUN
ejpam-5431	396	3	(	(	PUNCT
ejpam-5431	396	4	δ(σ2n	δ(σ2n	NOUN
ejpam-5431	396	5	,	,	PUNCT
ejpam-5431	396	6	[	[	X
ejpam-5431	396	7	sσ2n](⋉(σ2n),β(σ2n	sσ2n](⋉(σ2n),β(σ2n	NOUN
ejpam-5431	396	8	)	)	PUNCT
ejpam-5431	396	9	)	)	PUNCT
ejpam-5431	396	10	)	)	PUNCT
ejpam-5431	396	11	)	)	PUNCT
ejpam-5431	397	1	k2	k2	PROPN
ejpam-5431	397	2	×	×	PROPN
ejpam-5431	397	3	(	(	PUNCT
ejpam-5431	397	4	δ(σ2n+1	δ(σ2n+1	X
ejpam-5431	397	5	,	,	PUNCT
ejpam-5431	397	6	[	[	X
ejpam-5431	397	7	t	t	X
ejpam-5431	397	8	σ2n+1](⋉(σ2n+1),β(σ2n+1	σ2n+1](⋉(σ2n+1),β(σ2n+1	NOUN
ejpam-5431	397	9	)	)	PUNCT
ejpam-5431	397	10	)	)	PUNCT
ejpam-5431	397	11	)	)	PUNCT
ejpam-5431	397	12	)	)	PUNCT
ejpam-5431	398	1	k3	k3	VERB
ejpam-5431	398	2	×	×	NOUN
ejpam-5431	398	3	(	(	PUNCT
ejpam-5431	398	4	δ(σ2n+1	δ(σ2n+1	X
ejpam-5431	398	5	,	,	PUNCT
ejpam-5431	398	6	[	[	X
ejpam-5431	398	7	t	t	X
ejpam-5431	398	8	σ2n+1](⋉(σ2n+1),β(σ2n+1)))(1	σ2n+1](⋉(σ2n+1),β(σ2n+1)))(1	NOUN
ejpam-5431	398	9	+	+	CCONJ
ejpam-5431	398	10	δ(σ2n	δ(σ2n	NOUN
ejpam-5431	398	11	,	,	PUNCT
ejpam-5431	398	12	[	[	X
ejpam-5431	398	13	sσ2n](⋉(σ2n),β(σ2n	sσ2n](⋉(σ2n),β(σ2n	NOUN
ejpam-5431	398	14	)	)	PUNCT
ejpam-5431	398	15	)	)	PUNCT
ejpam-5431	398	16	)	)	PUNCT
ejpam-5431	398	17	)	)	PUNCT
ejpam-5431	399	1	1	1	NUM
ejpam-5431	400	1	+	+	NUM
ejpam-5431	400	2	δ(σ2n	δ(σ2n	NOUN
ejpam-5431	400	3	,	,	PUNCT
ejpam-5431	400	4	σ2n+1	σ2n+1	NOUN
ejpam-5431	400	5	)	)	PUNCT
ejpam-5431	400	6	)	)	PUNCT
ejpam-5431	401	1	k4	k4	ADJ
ejpam-5431	401	2	×	×	NOUN
ejpam-5431	401	3	(	(	PUNCT
ejpam-5431	401	4	δ(σ2n	δ(σ2n	NOUN
ejpam-5431	401	5	,	,	PUNCT
ejpam-5431	401	6	[	[	X
ejpam-5431	401	7	t	t	X
ejpam-5431	401	8	σ2n+1](⋉(σ2n+1),β(σ2n+1	σ2n+1](⋉(σ2n+1),β(σ2n+1	NOUN
ejpam-5431	401	9	)	)	PUNCT
ejpam-5431	401	10	)	)	PUNCT
ejpam-5431	401	11	)	)	PUNCT
ejpam-5431	402	1	+	+	PUNCT
ejpam-5431	402	2	δ(σ2n+1	δ(σ2n+1	NUM
ejpam-5431	402	3	,	,	PUNCT
ejpam-5431	402	4	[	[	X
ejpam-5431	402	5	sσ2n](⋉(σ2n),β(σ2n	sσ2n](⋉(σ2n),β(σ2n	NOUN
ejpam-5431	402	6	)	)	PUNCT
ejpam-5431	402	7	)	)	PUNCT
ejpam-5431	402	8	)	)	PUNCT
ejpam-5431	403	1	2h	2h	X
ejpam-5431	403	2	)	)	PUNCT
ejpam-5431	404	1	k5	k5	PROPN
ejpam-5431	404	2	=	=	SYM
ejpam-5431	404	3	(	(	PUNCT
ejpam-5431	404	4	δ(σ2n	δ(σ2n	NOUN
ejpam-5431	404	5	,	,	PUNCT
ejpam-5431	404	6	σ2n+1	σ2n+1	NOUN
ejpam-5431	404	7	)	)	PUNCT
ejpam-5431	404	8	)	)	PUNCT
ejpam-5431	404	9	k1	k1	PROPN
ejpam-5431	404	10	×	×	NOUN
ejpam-5431	404	11	(	(	PUNCT
ejpam-5431	404	12	δ(σ2n	δ(σ2n	NOUN
ejpam-5431	404	13	,	,	PUNCT
ejpam-5431	404	14	σ2n+1	σ2n+1	NOUN
ejpam-5431	404	15	)	)	PUNCT
ejpam-5431	404	16	)	)	PUNCT
ejpam-5431	405	1	k2	k2	PROPN
ejpam-5431	405	2	×	×	PROPN
ejpam-5431	405	3	(	(	PUNCT
ejpam-5431	405	4	δ(σ2n+1	δ(σ2n+1	X
ejpam-5431	405	5	,	,	PUNCT
ejpam-5431	405	6	σ2n+2	σ2n+2	NOUN
ejpam-5431	405	7	)	)	PUNCT
ejpam-5431	405	8	)	)	PUNCT
ejpam-5431	405	9	k3	k3	VERB
ejpam-5431	405	10	×	×	NOUN
ejpam-5431	405	11	(	(	PUNCT
ejpam-5431	405	12	δ(σ2n	δ(σ2n	NOUN
ejpam-5431	405	13	,	,	PUNCT
ejpam-5431	405	14	σ2n+2)(1	σ2n+2)(1	NOUN
ejpam-5431	405	15	+	+	CCONJ
ejpam-5431	405	16	δ(σ2n	δ(σ2n	NOUN
ejpam-5431	405	17	,	,	PUNCT
ejpam-5431	405	18	σ2n+1	σ2n+1	NOUN
ejpam-5431	405	19	)	)	PUNCT
ejpam-5431	405	20	)	)	PUNCT
ejpam-5431	405	21	1	1	NUM
ejpam-5431	406	1	+	+	NUM
ejpam-5431	406	2	δ(σ2n	δ(σ2n	NOUN
ejpam-5431	406	3	,	,	PUNCT
ejpam-5431	406	4	σ2n+1	σ2n+1	NOUN
ejpam-5431	406	5	)	)	PUNCT
ejpam-5431	406	6	)	)	PUNCT
ejpam-5431	407	1	k4	k4	ADJ
ejpam-5431	407	2	×	×	NOUN
ejpam-5431	407	3	(	(	PUNCT
ejpam-5431	407	4	δ(σ2n	δ(σ2n	NOUN
ejpam-5431	407	5	,	,	PUNCT
ejpam-5431	407	6	σ2n+2	σ2n+2	X
ejpam-5431	407	7	)	)	PUNCT
ejpam-5431	408	1	+	+	CCONJ
ejpam-5431	408	2	δ(σ2n+1	δ(σ2n+1	NUM
ejpam-5431	408	3	,	,	PUNCT
ejpam-5431	408	4	σ2n+1	σ2n+1	PROPN
ejpam-5431	408	5	)	)	PUNCT
ejpam-5431	408	6	2h	2h	NUM
ejpam-5431	408	7	)	)	PUNCT
ejpam-5431	408	8	k5	k5	PROPN
ejpam-5431	408	9	≤	≤	PROPN
ejpam-5431	408	10	(	(	PUNCT
ejpam-5431	408	11	δ(σ2n	δ(σ2n	NOUN
ejpam-5431	408	12	,	,	PUNCT
ejpam-5431	408	13	σ2n+1	σ2n+1	NOUN
ejpam-5431	408	14	)	)	PUNCT
ejpam-5431	408	15	)	)	PUNCT
ejpam-5431	409	1	k1+k2	k1+k2	PROPN
ejpam-5431	409	2	×	×	NOUN
ejpam-5431	409	3	(	(	PUNCT
ejpam-5431	409	4	δ(σ2n+1	δ(σ2n+1	NUM
ejpam-5431	409	5	,	,	PUNCT
ejpam-5431	409	6	σ2n+2	σ2n+2	X
ejpam-5431	409	7	)	)	PUNCT
ejpam-5431	409	8	k3+k4	k3+k4	NOUN
ejpam-5431	409	9	)	)	PUNCT
ejpam-5431	409	10	×	×	NOUN
ejpam-5431	409	11	(	(	PUNCT
ejpam-5431	409	12	h(δ(σ2n	h(δ(σ2n	PROPN
ejpam-5431	409	13	,	,	PUNCT
ejpam-5431	409	14	σ2n+1	σ2n+1	PROPN
ejpam-5431	409	15	)	)	PUNCT
ejpam-5431	409	16	+	+	CCONJ
ejpam-5431	409	17	δ(σ2n+1	δ(σ2n+1	NUM
ejpam-5431	409	18	,	,	PUNCT
ejpam-5431	409	19	σ2n+2	σ2n+2	NOUN
ejpam-5431	409	20	)	)	PUNCT
ejpam-5431	409	21	)	)	PUNCT
ejpam-5431	409	22	2h	2h	NUM
ejpam-5431	409	23	)	)	PUNCT
ejpam-5431	409	24	k5	k5	PROPN
ejpam-5431	409	25	=	=	SYM
ejpam-5431	409	26	(	(	PUNCT
ejpam-5431	409	27	δ(σ2n	δ(σ2n	NOUN
ejpam-5431	409	28	,	,	PUNCT
ejpam-5431	409	29	σ2n+1	σ2n+1	NOUN
ejpam-5431	409	30	)	)	PUNCT
ejpam-5431	409	31	)	)	PUNCT
ejpam-5431	410	1	k1+k2	k1+k2	PROPN
ejpam-5431	410	2	×	×	NOUN
ejpam-5431	410	3	(	(	PUNCT
ejpam-5431	410	4	δ(σ2n+1	δ(σ2n+1	NUM
ejpam-5431	410	5	,	,	PUNCT
ejpam-5431	410	6	σ2n+2	σ2n+2	NOUN
ejpam-5431	410	7	)	)	PUNCT
ejpam-5431	410	8	)	)	PUNCT
ejpam-5431	411	1	k3+k4	k3+k4	PROPN
ejpam-5431	411	2	×	×	NOUN
ejpam-5431	411	3	(	(	PUNCT
ejpam-5431	411	4	δ(σ2n	δ(σ2n	NOUN
ejpam-5431	411	5	,	,	PUNCT
ejpam-5431	411	6	σ2n+1	σ2n+1	NOUN
ejpam-5431	411	7	)	)	PUNCT
ejpam-5431	411	8	+	+	CCONJ
ejpam-5431	411	9	δ(σ2n+1	δ(σ2n+1	NUM
ejpam-5431	411	10	,	,	PUNCT
ejpam-5431	411	11	σ2n+2	σ2n+2	NOUN
ejpam-5431	411	12	)	)	PUNCT
ejpam-5431	411	13	2	2	X
ejpam-5431	411	14	)	)	PUNCT
ejpam-5431	411	15	k5	k5	PROPN
ejpam-5431	411	16	(	(	PUNCT
ejpam-5431	411	17	14	14	NUM
ejpam-5431	411	18	)	)	PUNCT
ejpam-5431	411	19	it	it	PRON
ejpam-5431	411	20	is	be	AUX
ejpam-5431	411	21	widely	widely	ADV
ejpam-5431	411	22	acknowledged	acknowledge	VERB
ejpam-5431	411	23	that	that	SCONJ
ejpam-5431	411	24	,	,	PUNCT
ejpam-5431	411	25	for	for	ADP
ejpam-5431	411	26	any	any	DET
ejpam-5431	411	27	p	p	X
ejpam-5431	411	28	,	,	PUNCT
ejpam-5431	411	29	q	q	NOUN
ejpam-5431	411	30	,	,	PUNCT
ejpam-5431	411	31	l	l	NOUN
ejpam-5431	411	32	>	>	X
ejpam-5431	411	33	0	0	PUNCT
ejpam-5431	411	34	we	we	PRON
ejpam-5431	411	35	have	have	VERB
ejpam-5431	411	36	(	(	PUNCT
ejpam-5431	411	37	p+	p+	NOUN
ejpam-5431	411	38	q	q	PROPN
ejpam-5431	411	39	2	2	NUM
ejpam-5431	411	40	)	)	PUNCT
ejpam-5431	411	41	l	l	NOUN
ejpam-5431	411	42	≤	≤	NUM
ejpam-5431	412	1	pl	pl	X
ejpam-5431	412	2	+	+	CCONJ
ejpam-5431	412	3	ql	ql	X
ejpam-5431	412	4	2	2	NUM
ejpam-5431	412	5	(	(	PUNCT
ejpam-5431	412	6	15	15	NUM
ejpam-5431	412	7	)	)	PUNCT
ejpam-5431	412	8	applying	apply	VERB
ejpam-5431	412	9	(	(	PUNCT
ejpam-5431	412	10	15	15	NUM
ejpam-5431	412	11	)	)	PUNCT
ejpam-5431	412	12	to	to	ADP
ejpam-5431	412	13	(	(	PUNCT
ejpam-5431	412	14	14	14	NUM
ejpam-5431	412	15	)	)	PUNCT
ejpam-5431	412	16	,	,	PUNCT
ejpam-5431	412	17	we	we	PRON
ejpam-5431	412	18	get	get	VERB
ejpam-5431	412	19	m	m	VERB
ejpam-5431	412	20	r	r	NOUN
ejpam-5431	412	21	(	(	PUNCT
ejpam-5431	412	22	s	s	PROPN
ejpam-5431	412	23	,	,	PUNCT
ejpam-5431	412	24	t	t	NOUN
ejpam-5431	412	25	)	)	PUNCT
ejpam-5431	412	26	(	(	PUNCT
ejpam-5431	412	27	σ2n	σ2n	NOUN
ejpam-5431	412	28	,	,	PUNCT
ejpam-5431	412	29	σ2n+1	σ2n+1	NOUN
ejpam-5431	412	30	)	)	PUNCT
ejpam-5431	412	31	≤	≤	NOUN
ejpam-5431	412	32	(	(	PUNCT
ejpam-5431	412	33	δ(σ2n	δ(σ2n	NOUN
ejpam-5431	412	34	,	,	PUNCT
ejpam-5431	412	35	σ2n+1	σ2n+1	NOUN
ejpam-5431	412	36	)	)	PUNCT
ejpam-5431	412	37	)	)	PUNCT
ejpam-5431	413	1	k1+k2	k1+k2	PROPN
ejpam-5431	413	2	×	×	NOUN
ejpam-5431	413	3	(	(	PUNCT
ejpam-5431	413	4	δ(σ2n+1	δ(σ2n+1	NUM
ejpam-5431	413	5	,	,	PUNCT
ejpam-5431	413	6	σ2n+2	σ2n+2	NOUN
ejpam-5431	413	7	)	)	PUNCT
ejpam-5431	413	8	)	)	PUNCT
ejpam-5431	414	1	k3+k4	k3+k4	PROPN
ejpam-5431	414	2	×	×	INTJ
ejpam-5431	414	3	(	(	PUNCT
ejpam-5431	414	4	(	(	PUNCT
ejpam-5431	414	5	δ(σ2n	δ(σ2n	NOUN
ejpam-5431	414	6	,	,	PUNCT
ejpam-5431	414	7	σ2n+1	σ2n+1	NOUN
ejpam-5431	414	8	)	)	PUNCT
ejpam-5431	414	9	)	)	PUNCT
ejpam-5431	415	1	k5	k5	PROPN
ejpam-5431	415	2	2	2	NUM
ejpam-5431	415	3	+	+	CCONJ
ejpam-5431	415	4	(	(	PUNCT
ejpam-5431	415	5	δ(σ2n+1	δ(σ2n+1	NUM
ejpam-5431	415	6	,	,	PUNCT
ejpam-5431	415	7	σ2n+2	σ2n+2	NOUN
ejpam-5431	415	8	)	)	PUNCT
ejpam-5431	415	9	)	)	PUNCT
ejpam-5431	416	1	k5	k5	PROPN
ejpam-5431	416	2	2	2	NUM
ejpam-5431	416	3	)	)	PUNCT
ejpam-5431	416	4	(	(	PUNCT
ejpam-5431	416	5	16	16	X
ejpam-5431	416	6	)	)	PUNCT
ejpam-5431	416	7	n.	n.	NOUN
ejpam-5431	416	8	saleem	saleem	PROPN
ejpam-5431	416	9	et	et	PROPN
ejpam-5431	416	10	al	al	PROPN
ejpam-5431	416	11	.	.	PUNCT
ejpam-5431	416	12	/	/	SYM
ejpam-5431	416	13	eur	eur	PROPN
ejpam-5431	416	14	.	.	PUNCT
ejpam-5431	417	1	j.	j.	PROPN
ejpam-5431	417	2	pure	pure	PROPN
ejpam-5431	417	3	appl	appl	PROPN
ejpam-5431	417	4	.	.	PROPN
ejpam-5431	417	5	math	math	PROPN
ejpam-5431	417	6	,	,	PUNCT
ejpam-5431	417	7	17	17	NUM
ejpam-5431	417	8	(	(	PUNCT
ejpam-5431	417	9	4	4	NUM
ejpam-5431	417	10	)	)	PUNCT
ejpam-5431	417	11	(	(	PUNCT
ejpam-5431	417	12	2024	2024	NUM
ejpam-5431	417	13	)	)	PUNCT
ejpam-5431	417	14	,	,	PUNCT
ejpam-5431	417	15	3304	3304	NUM
ejpam-5431	417	16	-	-	SYM
ejpam-5431	417	17	3335	3335	NUM
ejpam-5431	417	18	3320	3320	NUM
ejpam-5431	417	19	using	use	VERB
ejpam-5431	417	20	(	(	PUNCT
ejpam-5431	417	21	16	16	NUM
ejpam-5431	417	22	)	)	PUNCT
ejpam-5431	417	23	in	in	ADP
ejpam-5431	417	24	(	(	PUNCT
ejpam-5431	417	25	6	6	NUM
ejpam-5431	417	26	)	)	PUNCT
ejpam-5431	417	27	,	,	PUNCT
ejpam-5431	417	28	we	we	PRON
ejpam-5431	417	29	get	get	VERB
ejpam-5431	417	30	δ(σ2n+1	δ(σ2n+1	ADJ
ejpam-5431	417	31	,	,	PUNCT
ejpam-5431	417	32	σ2n+2	σ2n+2	NOUN
ejpam-5431	417	33	)	)	PUNCT
ejpam-5431	417	34	≤	≤	NOUN
ejpam-5431	417	35	φ(δ(σ2n	φ(δ(σ2n	PROPN
ejpam-5431	417	36	,	,	PUNCT
ejpam-5431	417	37	σ2n+1	σ2n+1	PROPN
ejpam-5431	417	38	)	)	PUNCT
ejpam-5431	417	39	)	)	PUNCT
ejpam-5431	418	1	k1+k2	k1+k2	PROPN
ejpam-5431	418	2	×	×	NOUN
ejpam-5431	418	3	(	(	PUNCT
ejpam-5431	418	4	δ(σ2n+1	δ(σ2n+1	NUM
ejpam-5431	418	5	,	,	PUNCT
ejpam-5431	418	6	σ2n+2	σ2n+2	NOUN
ejpam-5431	418	7	)	)	PUNCT
ejpam-5431	418	8	)	)	PUNCT
ejpam-5431	419	1	k3+k4	k3+k4	PROPN
ejpam-5431	419	2	×	×	INTJ
ejpam-5431	419	3	(	(	PUNCT
ejpam-5431	419	4	(	(	PUNCT
ejpam-5431	419	5	δ(σ2n	δ(σ2n	NOUN
ejpam-5431	419	6	,	,	PUNCT
ejpam-5431	419	7	σ2n+1	σ2n+1	NOUN
ejpam-5431	419	8	)	)	PUNCT
ejpam-5431	419	9	)	)	PUNCT
ejpam-5431	420	1	k5	k5	PROPN
ejpam-5431	420	2	2	2	NUM
ejpam-5431	420	3	+	+	CCONJ
ejpam-5431	420	4	(	(	PUNCT
ejpam-5431	420	5	δ(σ2n+1	δ(σ2n+1	NUM
ejpam-5431	420	6	,	,	PUNCT
ejpam-5431	420	7	σ2n+2	σ2n+2	NOUN
ejpam-5431	420	8	)	)	PUNCT
ejpam-5431	420	9	)	)	PUNCT
ejpam-5431	421	1	k5	k5	PROPN
ejpam-5431	421	2	2	2	NUM
ejpam-5431	421	3	)	)	PUNCT
ejpam-5431	421	4	(	(	PUNCT
ejpam-5431	421	5	17	17	NUM
ejpam-5431	421	6	)	)	PUNCT
ejpam-5431	421	7	suppose	suppose	VERB
ejpam-5431	421	8	δ(σ2n	δ(σ2n	NOUN
ejpam-5431	421	9	,	,	PUNCT
ejpam-5431	421	10	σ2n+1	σ2n+1	NOUN
ejpam-5431	421	11	)	)	PUNCT
ejpam-5431	421	12	≤	≤	NOUN
ejpam-5431	421	13	δ(σ2n+1	δ(σ2n+1	NUM
ejpam-5431	421	14	,	,	PUNCT
ejpam-5431	421	15	σ2n+2	σ2n+2	X
ejpam-5431	421	16	)	)	PUNCT
ejpam-5431	421	17	and	and	CCONJ
ejpam-5431	421	18	noting	note	VERB
ejpam-5431	421	19	that	that	SCONJ
ejpam-5431	421	20	φ	φ	PROPN
ejpam-5431	421	21	is	be	AUX
ejpam-5431	421	22	non	non	ADJ
ejpam-5431	421	23	-	-	ADJ
ejpam-5431	421	24	decreasing	decrease	VERB
ejpam-5431	421	25	,	,	PUNCT
ejpam-5431	421	26	(	(	PUNCT
ejpam-5431	421	27	17	17	NUM
ejpam-5431	421	28	)	)	PUNCT
ejpam-5431	421	29	gives	give	VERB
ejpam-5431	421	30	:	:	PUNCT
ejpam-5431	421	31	δ(σ2n+1	δ(σ2n+1	NUM
ejpam-5431	421	32	,	,	PUNCT
ejpam-5431	421	33	σ2n+2	σ2n+2	NOUN
ejpam-5431	421	34	)	)	PUNCT
ejpam-5431	421	35	≤	≤	NOUN
ejpam-5431	422	1	φ((δ(σ2n+1	φ((δ(σ2n+1	ADJ
ejpam-5431	422	2	,	,	PUNCT
ejpam-5431	422	3	σ2n+2	σ2n+2	NOUN
ejpam-5431	422	4	)	)	PUNCT
ejpam-5431	422	5	)	)	PUNCT
ejpam-5431	423	1	k1+k2+k3+k4+k5	k1+k2+k3+k4+k5	PROPN
ejpam-5431	423	2	)	)	PUNCT
ejpam-5431	423	3	=	=	SYM
ejpam-5431	423	4	φ(δ(σ2n+1	φ(δ(σ2n+1	ADJ
ejpam-5431	423	5	,	,	PUNCT
ejpam-5431	423	6	σ2n+2	σ2n+2	NOUN
ejpam-5431	423	7	)	)	PUNCT
ejpam-5431	423	8	)	)	PUNCT
ejpam-5431	423	9	<	<	X
ejpam-5431	423	10	δ(σ2n+1	δ(σ2n+1	X
ejpam-5431	423	11	,	,	PUNCT
ejpam-5431	423	12	σ2n+2	σ2n+2	NOUN
ejpam-5431	423	13	)	)	PUNCT
ejpam-5431	423	14	a	a	DET
ejpam-5431	423	15	contradiction	contradiction	NOUN
ejpam-5431	423	16	.	.	PUNCT
ejpam-5431	424	1	so	so	ADV
ejpam-5431	424	2	we	we	PRON
ejpam-5431	424	3	have	have	VERB
ejpam-5431	424	4	δ(σ2n+1	δ(σ2n+1	NUM
ejpam-5431	424	5	,	,	PUNCT
ejpam-5431	424	6	σ2n+2	σ2n+2	NOUN
ejpam-5431	424	7	)	)	PUNCT
ejpam-5431	424	8	≤	≤	NOUN
ejpam-5431	424	9	δ(σ2n	δ(σ2n	NOUN
ejpam-5431	424	10	,	,	PUNCT
ejpam-5431	424	11	σ2n+1	σ2n+1	NOUN
ejpam-5431	424	12	)	)	PUNCT
ejpam-5431	424	13	therefore	therefore	ADV
ejpam-5431	424	14	(	(	PUNCT
ejpam-5431	424	15	17	17	NUM
ejpam-5431	424	16	)	)	PUNCT
ejpam-5431	424	17	becomes	become	VERB
ejpam-5431	424	18	δ(σ2n+1	δ(σ2n+1	ADJ
ejpam-5431	424	19	,	,	PUNCT
ejpam-5431	424	20	σ2n+2	σ2n+2	NOUN
ejpam-5431	424	21	)	)	PUNCT
ejpam-5431	424	22	≤	≤	NOUN
ejpam-5431	424	23	φ(δ(σ2n	φ(δ(σ2n	PROPN
ejpam-5431	424	24	,	,	PUNCT
ejpam-5431	424	25	σ2n+1	σ2n+1	PROPN
ejpam-5431	424	26	)	)	PUNCT
ejpam-5431	424	27	)	)	PUNCT
ejpam-5431	425	1	≤	≤	NOUN
ejpam-5431	425	2	φ2(δ(σ2n−1	φ2(δ(σ2n−1	ADJ
ejpam-5431	425	3	,	,	PUNCT
ejpam-5431	425	4	σ2n	σ2n	NOUN
ejpam-5431	425	5	)	)	PUNCT
ejpam-5431	425	6	)	)	PUNCT
ejpam-5431	425	7	...	...	PUNCT
ejpam-5431	426	1	≤	≤	PROPN
ejpam-5431	426	2	φ2n+1(δ(σ0	φ2n+1(δ(σ0	PROPN
ejpam-5431	426	3	,	,	PUNCT
ejpam-5431	426	4	σ1	σ1	PROPN
ejpam-5431	426	5	)	)	PUNCT
ejpam-5431	426	6	)	)	PUNCT
ejpam-5431	426	7	δ(σ2n+1	δ(σ2n+1	NUM
ejpam-5431	426	8	,	,	PUNCT
ejpam-5431	426	9	σ2n+2	σ2n+2	NOUN
ejpam-5431	426	10	)	)	PUNCT
ejpam-5431	426	11	≤	≤	PROPN
ejpam-5431	426	12	φ2n+1(δ(σ0	φ2n+1(δ(σ0	PROPN
ejpam-5431	426	13	,	,	PUNCT
ejpam-5431	426	14	σ1	σ1	PROPN
ejpam-5431	426	15	)	)	PUNCT
ejpam-5431	426	16	)	)	PUNCT
ejpam-5431	426	17	.	.	PUNCT
ejpam-5431	427	1	similarly	similarly	ADV
ejpam-5431	427	2	,	,	PUNCT
ejpam-5431	427	3	using	use	VERB
ejpam-5431	427	4	(	(	PUNCT
ejpam-5431	427	5	7	7	X
ejpam-5431	427	6	)	)	PUNCT
ejpam-5431	427	7	we	we	PRON
ejpam-5431	427	8	can	can	AUX
ejpam-5431	427	9	show	show	VERB
ejpam-5431	427	10	that	that	SCONJ
ejpam-5431	427	11	δ(σ2n+2	δ(σ2n+2	ADJ
ejpam-5431	427	12	,	,	PUNCT
ejpam-5431	427	13	σ2n+3	σ2n+3	PROPN
ejpam-5431	427	14	)	)	PUNCT
ejpam-5431	427	15	≤	≤	NOUN
ejpam-5431	427	16	φ2n+2(δ(σ0	φ2n+2(δ(σ0	PROPN
ejpam-5431	427	17	,	,	PUNCT
ejpam-5431	427	18	σ1	σ1	PROPN
ejpam-5431	427	19	)	)	PUNCT
ejpam-5431	427	20	)	)	PUNCT
ejpam-5431	427	21	combining	combine	VERB
ejpam-5431	427	22	above	above	ADP
ejpam-5431	427	23	two	two	NUM
ejpam-5431	427	24	equations	equation	NOUN
ejpam-5431	427	25	,	,	PUNCT
ejpam-5431	427	26	we	we	PRON
ejpam-5431	427	27	can	can	AUX
ejpam-5431	427	28	write	write	VERB
ejpam-5431	427	29	δ(σn	δ(σn	PROPN
ejpam-5431	427	30	,	,	PUNCT
ejpam-5431	427	31	σn+1	σn+1	NOUN
ejpam-5431	427	32	)	)	PUNCT
ejpam-5431	427	33	≤	≤	NOUN
ejpam-5431	427	34	φn(δ(σ0	φn(δ(σ0	PROPN
ejpam-5431	427	35	,	,	PUNCT
ejpam-5431	427	36	σ1	σ1	PROPN
ejpam-5431	427	37	)	)	PUNCT
ejpam-5431	427	38	)	)	PUNCT
ejpam-5431	427	39	.	.	PUNCT
ejpam-5431	428	1	(	(	PUNCT
ejpam-5431	428	2	18	18	NUM
ejpam-5431	428	3	)	)	PUNCT
ejpam-5431	428	4	adhering	adhere	VERB
ejpam-5431	428	5	to	to	ADP
ejpam-5431	428	6	the	the	DET
ejpam-5431	428	7	same	same	ADJ
ejpam-5431	428	8	process	process	NOUN
ejpam-5431	428	9	as	as	ADP
ejpam-5431	428	10	in	in	ADP
ejpam-5431	428	11	case	case	NOUN
ejpam-5431	428	12	1	1	NUM
ejpam-5431	428	13	,	,	PUNCT
ejpam-5431	428	14	this	this	PRON
ejpam-5431	428	15	can	can	AUX
ejpam-5431	428	16	be	be	AUX
ejpam-5431	428	17	deduced	deduce	VERB
ejpam-5431	428	18	from	from	ADP
ejpam-5431	428	19	(	(	PUNCT
ejpam-5431	428	20	18	18	NUM
ejpam-5431	428	21	)	)	PUNCT
ejpam-5431	428	22	that	that	PRON
ejpam-5431	428	23	{	{	PUNCT
ejpam-5431	428	24	σn}n≥1	σn}n≥1	NOUN
ejpam-5431	428	25	is	be	AUX
ejpam-5431	428	26	a	a	DET
ejpam-5431	428	27	cauchy	cauchy	ADJ
ejpam-5431	428	28	sequence	sequence	NOUN
ejpam-5431	428	29	in	in	ADP
ejpam-5431	428	30	x.	x.	NOUN
ejpam-5431	428	31	completeness	completeness	PROPN
ejpam-5431	428	32	of	of	ADP
ejpam-5431	428	33	x	x	PUNCT
ejpam-5431	428	34	reveals	reveal	VERB
ejpam-5431	428	35	that	that	SCONJ
ejpam-5431	428	36	there	there	PRON
ejpam-5431	428	37	is	be	VERB
ejpam-5431	428	38	an	an	DET
ejpam-5431	428	39	element	element	NOUN
ejpam-5431	428	40	ς	ς	PROPN
ejpam-5431	428	41	∈	∈	PROPN
ejpam-5431	428	42	x	x	PUNCT
ejpam-5431	428	43	such	such	ADJ
ejpam-5431	428	44	as	as	ADP
ejpam-5431	428	45	,	,	PUNCT
ejpam-5431	428	46	lim	lim	PROPN
ejpam-5431	428	47	n→+∞	n→+∞	PROPN
ejpam-5431	428	48	δ(σn	δ(σn	PROPN
ejpam-5431	428	49	,	,	PUNCT
ejpam-5431	428	50	ς	ς	PROPN
ejpam-5431	428	51	)	)	PUNCT
ejpam-5431	428	52	=	=	SYM
ejpam-5431	428	53	0	0	X
ejpam-5431	428	54	.	.	PUNCT
ejpam-5431	429	1	(	(	PUNCT
ejpam-5431	429	2	19	19	NUM
ejpam-5431	429	3	)	)	PUNCT
ejpam-5431	429	4	now	now	ADV
ejpam-5431	429	5	,	,	PUNCT
ejpam-5431	429	6	to	to	PART
ejpam-5431	429	7	illustrate	illustrate	VERB
ejpam-5431	429	8	that	that	SCONJ
ejpam-5431	429	9	ς	ς	PROPN
ejpam-5431	429	10	∈	∈	PROPN
ejpam-5431	430	1	[	[	X
ejpam-5431	430	2	t	t	NOUN
ejpam-5431	430	3	ς](⋉(ς),β(ς	ς](⋉(ς),β(ς	NUM
ejpam-5431	430	4	)	)	PUNCT
ejpam-5431	430	5	)	)	PUNCT
ejpam-5431	431	1	,	,	PUNCT
ejpam-5431	431	2	consider	consider	VERB
ejpam-5431	431	3	δ(ς	δ(ς	PROPN
ejpam-5431	431	4	,	,	PUNCT
ejpam-5431	431	5	[	[	X
ejpam-5431	431	6	t	t	NOUN
ejpam-5431	431	7	ς](⋉(ς),β(ς	ς](⋉(ς),β(ς	NUM
ejpam-5431	431	8	)	)	PUNCT
ejpam-5431	431	9	)	)	PUNCT
ejpam-5431	431	10	)	)	PUNCT
ejpam-5431	432	1	≤	≤	NUM
ejpam-5431	432	2	h(δ(ς	h(δ(ς	PROPN
ejpam-5431	432	3	,	,	PUNCT
ejpam-5431	432	4	σ2n+1	σ2n+1	PROPN
ejpam-5431	432	5	)	)	PUNCT
ejpam-5431	432	6	+	+	PUNCT
ejpam-5431	432	7	δ(σ2n+1	δ(σ2n+1	NUM
ejpam-5431	432	8	,	,	PUNCT
ejpam-5431	432	9	[	[	X
ejpam-5431	432	10	t	t	NOUN
ejpam-5431	432	11	ς](⋉(ς),β(ς	ς](⋉(ς),β(ς	NUM
ejpam-5431	432	12	)	)	PUNCT
ejpam-5431	432	13	)	)	PUNCT
ejpam-5431	432	14	)	)	PUNCT
ejpam-5431	432	15	)	)	PUNCT
ejpam-5431	433	1	≤	≤	NUM
ejpam-5431	433	2	h(δ(ς	h(δ(ς	PROPN
ejpam-5431	433	3	,	,	PUNCT
ejpam-5431	433	4	σ2n+1	σ2n+1	PROPN
ejpam-5431	433	5	)	)	PUNCT
ejpam-5431	433	6	+	+	CCONJ
ejpam-5431	433	7	ℵ([sσ2n](⋉(σ2n),β(σ2n	ℵ([sσ2n](⋉(σ2n),β(σ2n	PROPN
ejpam-5431	433	8	)	)	PUNCT
ejpam-5431	433	9	)	)	PUNCT
ejpam-5431	433	10	,	,	PUNCT
ejpam-5431	434	1	[	[	X
ejpam-5431	434	2	t	t	NOUN
ejpam-5431	434	3	ς](⋉(ς),β(ς	ς](⋉(ς),β(ς	NUM
ejpam-5431	434	4	)	)	PUNCT
ejpam-5431	434	5	)	)	PUNCT
ejpam-5431	434	6	)	)	PUNCT
ejpam-5431	434	7	)	)	PUNCT
ejpam-5431	435	1	(	(	PUNCT
ejpam-5431	435	2	20	20	X
ejpam-5431	435	3	)	)	PUNCT
ejpam-5431	435	4	using	use	VERB
ejpam-5431	435	5	ℵ-continuity	ℵ-continuity	NOUN
ejpam-5431	435	6	of	of	ADP
ejpam-5431	435	7	(	(	PUNCT
ejpam-5431	435	8	s	s	PROPN
ejpam-5431	435	9	,	,	PUNCT
ejpam-5431	435	10	t	t	NOUN
ejpam-5431	435	11	)	)	PUNCT
ejpam-5431	435	12	pair	pair	NOUN
ejpam-5431	435	13	,	,	PUNCT
ejpam-5431	435	14	by	by	ADP
ejpam-5431	435	15	allowing	allow	VERB
ejpam-5431	435	16	n	n	PRON
ejpam-5431	435	17	→	→	SYM
ejpam-5431	435	18	+	+	NOUN
ejpam-5431	435	19	∞	∞	PROPN
ejpam-5431	435	20	in	in	ADP
ejpam-5431	435	21	(	(	PUNCT
ejpam-5431	435	22	20	20	NUM
ejpam-5431	435	23	)	)	PUNCT
ejpam-5431	435	24	and	and	CCONJ
ejpam-5431	435	25	considering	consider	VERB
ejpam-5431	435	26	(	(	PUNCT
ejpam-5431	435	27	19	19	NUM
ejpam-5431	435	28	)	)	PUNCT
ejpam-5431	435	29	,	,	PUNCT
ejpam-5431	435	30	we	we	PRON
ejpam-5431	435	31	attain	attain	VERB
ejpam-5431	435	32	n.	n.	PROPN
ejpam-5431	435	33	saleem	saleem	PROPN
ejpam-5431	435	34	et	et	PROPN
ejpam-5431	435	35	al	al	PROPN
ejpam-5431	435	36	.	.	PUNCT
ejpam-5431	435	37	/	/	SYM
ejpam-5431	435	38	eur	eur	PROPN
ejpam-5431	435	39	.	.	PUNCT
ejpam-5431	436	1	j.	j.	PROPN
ejpam-5431	436	2	pure	pure	PROPN
ejpam-5431	436	3	appl	appl	PROPN
ejpam-5431	436	4	.	.	PROPN
ejpam-5431	436	5	math	math	PROPN
ejpam-5431	436	6	,	,	PUNCT
ejpam-5431	436	7	17	17	NUM
ejpam-5431	436	8	(	(	PUNCT
ejpam-5431	436	9	4	4	NUM
ejpam-5431	436	10	)	)	PUNCT
ejpam-5431	436	11	(	(	PUNCT
ejpam-5431	436	12	2024	2024	NUM
ejpam-5431	436	13	)	)	PUNCT
ejpam-5431	436	14	,	,	PUNCT
ejpam-5431	436	15	3304	3304	NUM
ejpam-5431	436	16	-	-	SYM
ejpam-5431	436	17	3335	3335	NUM
ejpam-5431	436	18	3321	3321	NUM
ejpam-5431	436	19	δ(ς	δ(ς	PROPN
ejpam-5431	436	20	,	,	PUNCT
ejpam-5431	436	21	[	[	X
ejpam-5431	436	22	t	t	NOUN
ejpam-5431	436	23	ς](⋉(ς),β(ς	ς](⋉(ς),β(ς	NUM
ejpam-5431	436	24	)	)	PUNCT
ejpam-5431	436	25	)	)	PUNCT
ejpam-5431	436	26	)	)	PUNCT
ejpam-5431	437	1	=	=	SYM
ejpam-5431	437	2	0	0	NUM
ejpam-5431	437	3	which	which	PRON
ejpam-5431	437	4	implies	imply	VERB
ejpam-5431	437	5	that	that	SCONJ
ejpam-5431	437	6	ς	ς	PROPN
ejpam-5431	437	7	∈	∈	PROPN
ejpam-5431	437	8	[	[	X
ejpam-5431	437	9	t	t	NOUN
ejpam-5431	437	10	ς](⋉(ς),β(ς	ς](⋉(ς),β(ς	NUM
ejpam-5431	437	11	)	)	PUNCT
ejpam-5431	437	12	)	)	PUNCT
ejpam-5431	437	13	.	.	PUNCT
ejpam-5431	438	1	correspondingly	correspondingly	ADV
ejpam-5431	438	2	we	we	PRON
ejpam-5431	438	3	can	can	AUX
ejpam-5431	438	4	prove	prove	VERB
ejpam-5431	438	5	that	that	SCONJ
ejpam-5431	438	6	δ(ς	δ(ς	PROPN
ejpam-5431	438	7	,	,	PUNCT
ejpam-5431	438	8	[	[	X
ejpam-5431	438	9	sς](⋉(ς),β(ς	sς](⋉(ς),β(ς	X
ejpam-5431	438	10	)	)	PUNCT
ejpam-5431	438	11	)	)	PUNCT
ejpam-5431	438	12	)	)	PUNCT
ejpam-5431	439	1	=	=	SYM
ejpam-5431	439	2	0	0	NUM
ejpam-5431	439	3	which	which	PRON
ejpam-5431	439	4	means	mean	VERB
ejpam-5431	439	5	that	that	SCONJ
ejpam-5431	439	6	ς	ς	PROPN
ejpam-5431	439	7	∈	∈	PROPN
ejpam-5431	439	8	[	[	X
ejpam-5431	439	9	sς](⋉(ς),β(ς	sς](⋉(ς),β(ς	X
ejpam-5431	439	10	)	)	PUNCT
ejpam-5431	439	11	)	)	PUNCT
ejpam-5431	439	12	.	.	PUNCT
ejpam-5431	440	1	thus	thus	ADV
ejpam-5431	440	2	we	we	PRON
ejpam-5431	440	3	have	have	VERB
ejpam-5431	440	4	ς	ς	PROPN
ejpam-5431	440	5	∈	∈	PROPN
ejpam-5431	440	6	[	[	X
ejpam-5431	440	7	t	t	NOUN
ejpam-5431	440	8	ς](⋉(ς),β(ς	ς](⋉(ς),β(ς	NUM
ejpam-5431	440	9	)	)	PUNCT
ejpam-5431	440	10	)	)	PUNCT
ejpam-5431	440	11	∩	∩	NOUN
ejpam-5431	440	12	[	[	X
ejpam-5431	440	13	sς](⋉(ς),β(ς	sς](⋉(ς),β(ς	X
ejpam-5431	440	14	)	)	PUNCT
ejpam-5431	440	15	)	)	PUNCT
ejpam-5431	440	16	that	that	ADV
ejpam-5431	440	17	is	be	AUX
ejpam-5431	440	18	,	,	PUNCT
ejpam-5431	440	19	ς	ς	PROPN
ejpam-5431	440	20	is	be	AUX
ejpam-5431	440	21	common	common	ADJ
ejpam-5431	440	22	iffp	iffp	NOUN
ejpam-5431	440	23	of	of	ADP
ejpam-5431	440	24	s	s	PRON
ejpam-5431	440	25	and	and	CCONJ
ejpam-5431	440	26	t	t	PROPN
ejpam-5431	440	27	.	.	PUNCT
ejpam-5431	441	1	example	example	NOUN
ejpam-5431	442	1	26	26	NUM
ejpam-5431	442	2	.	.	PUNCT
ejpam-5431	443	1	let	let	VERB
ejpam-5431	443	2	x	x	PUNCT
ejpam-5431	443	3	=	=	PUNCT
ejpam-5431	444	1	[	[	X
ejpam-5431	444	2	1,+∞	1,+∞	NUM
ejpam-5431	444	3	)	)	PUNCT
ejpam-5431	444	4	and	and	CCONJ
ejpam-5431	444	5	δ(σ	δ(σ	PROPN
ejpam-5431	444	6	,	,	PUNCT
ejpam-5431	444	7	τ	τ	X
ejpam-5431	444	8	)	)	PUNCT
ejpam-5431	444	9	=	=	SYM
ejpam-5431	444	10	|σ−τ	|σ−τ	PROPN
ejpam-5431	444	11	|2	|2	NUM
ejpam-5431	444	12	for	for	ADP
ejpam-5431	444	13	all	all	DET
ejpam-5431	444	14	σ	σ	PROPN
ejpam-5431	444	15	,	,	PUNCT
ejpam-5431	444	16	τ	τ	PROPN
ejpam-5431	444	17	∈	∈	PROPN
ejpam-5431	444	18	x.	x.	NOUN
ejpam-5431	444	19	then	then	ADV
ejpam-5431	444	20	(	(	PUNCT
ejpam-5431	444	21	x	x	NOUN
ejpam-5431	444	22	,	,	PUNCT
ejpam-5431	444	23	δ	δ	PROPN
ejpam-5431	444	24	,	,	PUNCT
ejpam-5431	444	25	h	h	NOUN
ejpam-5431	444	26	=	=	NOUN
ejpam-5431	444	27	2	2	X
ejpam-5431	444	28	)	)	PUNCT
ejpam-5431	444	29	is	be	AUX
ejpam-5431	444	30	a	a	DET
ejpam-5431	444	31	complete	complete	ADJ
ejpam-5431	444	32	b	b	NOUN
ejpam-5431	444	33	-	-	PUNCT
ejpam-5431	444	34	ms	ms	NOUN
ejpam-5431	444	35	.	.	PROPN
ejpam-5431	444	36	for	for	ADP
ejpam-5431	444	37	each	each	DET
ejpam-5431	444	38	σ	σ	NUM
ejpam-5431	444	39	∈	∈	PROPN
ejpam-5431	444	40	x	x	X
ejpam-5431	444	41	,	,	PUNCT
ejpam-5431	444	42	consider	consider	VERB
ejpam-5431	444	43	ifs	ifs	PROPN
ejpam-5431	444	44	-	-	PUNCT
ejpam-5431	444	45	valued	value	VERB
ejpam-5431	444	46	maps	map	NOUN
ejpam-5431	444	47	s	s	PROPN
ejpam-5431	444	48	,	,	PUNCT
ejpam-5431	444	49	t	t	X
ejpam-5431	444	50	:	:	PUNCT
ejpam-5431	444	51	x	x	X
ejpam-5431	444	52	→	→	SYM
ejpam-5431	444	53	ifs(x	ifs(x	PROPN
ejpam-5431	444	54	)	)	PUNCT
ejpam-5431	444	55	and	and	CCONJ
ejpam-5431	444	56	sσ	sσ	NOUN
ejpam-5431	444	57	,	,	PUNCT
ejpam-5431	444	58	t	t	PROPN
ejpam-5431	444	59	σ	σ	NOUN
ejpam-5431	444	60	are	be	AUX
ejpam-5431	444	61	ifss	ifss	ADJ
ejpam-5431	444	62	such	such	ADJ
ejpam-5431	444	63	that	that	SCONJ
ejpam-5431	444	64	µt	µt	PROPN
ejpam-5431	444	65	σ	σ	X
ejpam-5431	444	66	:	:	PUNCT
ejpam-5431	444	67	x	x	X
ejpam-5431	444	68	→	→	PUNCT
ejpam-5431	444	69	[	[	X
ejpam-5431	444	70	0	0	NUM
ejpam-5431	444	71	,	,	PUNCT
ejpam-5431	444	72	1	1	NUM
ejpam-5431	444	73	]	]	PUNCT
ejpam-5431	444	74	,	,	PUNCT
ejpam-5431	444	75	µsσ	µsσ	VERB
ejpam-5431	444	76	:	:	PUNCT
ejpam-5431	444	77	x	x	X
ejpam-5431	444	78	→	→	SYM
ejpam-5431	444	79	[	[	X
ejpam-5431	444	80	0	0	NUM
ejpam-5431	444	81	,	,	PUNCT
ejpam-5431	444	82	1	1	NUM
ejpam-5431	444	83	]	]	PUNCT
ejpam-5431	444	84	are	be	AUX
ejpam-5431	444	85	membership	membership	NOUN
ejpam-5431	444	86	functions	function	NOUN
ejpam-5431	444	87	of	of	ADP
ejpam-5431	444	88	t	t	PROPN
ejpam-5431	444	89	σ	σ	PROPN
ejpam-5431	444	90	and	and	CCONJ
ejpam-5431	444	91	sσ	sσ	VERB
ejpam-5431	444	92	respectively	respectively	ADV
ejpam-5431	444	93	and	and	CCONJ
ejpam-5431	444	94	νt	νt	PROPN
ejpam-5431	444	95	σ	σ	NOUN
ejpam-5431	444	96	:	:	PUNCT
ejpam-5431	444	97	x	x	X
ejpam-5431	444	98	→	→	PUNCT
ejpam-5431	445	1	[	[	X
ejpam-5431	445	2	0	0	NUM
ejpam-5431	445	3	,	,	PUNCT
ejpam-5431	445	4	1	1	NUM
ejpam-5431	445	5	]	]	PUNCT
ejpam-5431	445	6	and	and	CCONJ
ejpam-5431	445	7	νsσ	νsσ	NOUN
ejpam-5431	445	8	:	:	PUNCT
ejpam-5431	445	9	x	x	X
ejpam-5431	445	10	→	→	PUNCT
ejpam-5431	445	11	[	[	X
ejpam-5431	445	12	0	0	NUM
ejpam-5431	445	13	,	,	PUNCT
ejpam-5431	445	14	1	1	NUM
ejpam-5431	445	15	]	]	PUNCT
ejpam-5431	445	16	are	be	AUX
ejpam-5431	445	17	non	non	ADJ
ejpam-5431	445	18	-	-	ADJ
ejpam-5431	445	19	membership	membership	ADJ
ejpam-5431	445	20	functions	function	NOUN
ejpam-5431	445	21	of	of	ADP
ejpam-5431	445	22	t	t	PROPN
ejpam-5431	445	23	σ	σ	PROPN
ejpam-5431	445	24	and	and	CCONJ
ejpam-5431	445	25	sσ	sσ	VERB
ejpam-5431	445	26	respectively	respectively	ADV
ejpam-5431	445	27	with	with	ADP
ejpam-5431	445	28	µt	µt	DET
ejpam-5431	445	29	σ(t	σ(t	PROPN
ejpam-5431	445	30	)	)	PUNCT
ejpam-5431	446	1	+	+	CCONJ
ejpam-5431	446	2	νt	νt	PRON
ejpam-5431	446	3	σ(t	σ(t	NOUN
ejpam-5431	446	4	)	)	PUNCT
ejpam-5431	446	5	≤	≤	ADV
ejpam-5431	446	6	1	1	NUM
ejpam-5431	446	7	and	and	CCONJ
ejpam-5431	446	8	µsσ(t	µsσ(t	PROPN
ejpam-5431	446	9	)	)	PUNCT
ejpam-5431	446	10	+	+	NUM
ejpam-5431	446	11	νsσ(t	νsσ(t	NOUN
ejpam-5431	446	12	)	)	PUNCT
ejpam-5431	446	13	≤	≤	NUM
ejpam-5431	446	14	1	1	NUM
ejpam-5431	446	15	for	for	ADP
ejpam-5431	446	16	all	all	DET
ejpam-5431	446	17	t	t	NOUN
ejpam-5431	446	18	∈	∈	PROPN
ejpam-5431	446	19	x.	x.	NOUN
ejpam-5431	447	1	if	if	SCONJ
ejpam-5431	447	2	σ	σ	NOUN
ejpam-5431	447	3	=	=	SYM
ejpam-5431	447	4	1	1	NUM
ejpam-5431	447	5	:	:	PUNCT
ejpam-5431	447	6	µt1(t	µt1(t	PROPN
ejpam-5431	447	7	)	)	PUNCT
ejpam-5431	448	1	=	=	PRON
ejpam-5431	448	2	{	{	PUNCT
ejpam-5431	448	3	1	1	NUM
ejpam-5431	448	4	8	8	NUM
ejpam-5431	448	5	,	,	PUNCT
ejpam-5431	448	6	if	if	SCONJ
ejpam-5431	448	7	t	t	NOUN
ejpam-5431	448	8	=	=	SYM
ejpam-5431	448	9	1	1	NUM
ejpam-5431	448	10	2	2	NUM
ejpam-5431	448	11	5	5	NUM
ejpam-5431	448	12	,	,	PUNCT
ejpam-5431	448	13	if	if	SCONJ
ejpam-5431	448	14	t	t	PROPN
ejpam-5431	448	15	̸=	̸=	PROPN
ejpam-5431	448	16	1	1	NUM
ejpam-5431	448	17	νt1(t	νt1(t	PROPN
ejpam-5431	448	18	)	)	PUNCT
ejpam-5431	448	19	=	=	PRON
ejpam-5431	448	20	{	{	PUNCT
ejpam-5431	448	21	3	3	NUM
ejpam-5431	448	22	7	7	NUM
ejpam-5431	448	23	,	,	PUNCT
ejpam-5431	448	24	if	if	SCONJ
ejpam-5431	448	25	t	t	NOUN
ejpam-5431	448	26	=	=	SYM
ejpam-5431	448	27	1	1	NUM
ejpam-5431	448	28	4	4	NUM
ejpam-5431	448	29	7	7	NUM
ejpam-5431	448	30	,	,	PUNCT
ejpam-5431	448	31	if	if	SCONJ
ejpam-5431	448	32	t	t	PROPN
ejpam-5431	448	33	̸=	̸=	PROPN
ejpam-5431	448	34	1	1	NUM
ejpam-5431	448	35	µs1(t	µs1(t	PROPN
ejpam-5431	448	36	)	)	PUNCT
ejpam-5431	448	37	=	=	PRON
ejpam-5431	448	38	{	{	PUNCT
ejpam-5431	448	39	1	1	NUM
ejpam-5431	448	40	,	,	PUNCT
ejpam-5431	448	41	if	if	SCONJ
ejpam-5431	448	42	t	t	NOUN
ejpam-5431	448	43	=	=	SYM
ejpam-5431	448	44	1	1	NUM
ejpam-5431	448	45	1	1	NUM
ejpam-5431	448	46	5	5	NUM
ejpam-5431	448	47	,	,	PUNCT
ejpam-5431	448	48	if	if	SCONJ
ejpam-5431	448	49	t	t	PROPN
ejpam-5431	448	50	̸=	̸=	PROPN
ejpam-5431	448	51	1	1	NUM
ejpam-5431	448	52	νs1(t	νs1(t	ADJ
ejpam-5431	448	53	)	)	PUNCT
ejpam-5431	448	54	=	=	PRON
ejpam-5431	448	55	{	{	PUNCT
ejpam-5431	448	56	0	0	NUM
ejpam-5431	448	57	,	,	PUNCT
ejpam-5431	448	58	if	if	SCONJ
ejpam-5431	448	59	t	t	NOUN
ejpam-5431	448	60	=	=	SYM
ejpam-5431	448	61	1	1	NUM
ejpam-5431	448	62	4	4	NUM
ejpam-5431	448	63	9	9	NUM
ejpam-5431	448	64	,	,	PUNCT
ejpam-5431	448	65	if	if	SCONJ
ejpam-5431	448	66	t	t	PROPN
ejpam-5431	448	67	̸=	̸=	PROPN
ejpam-5431	448	68	1	1	NUM
ejpam-5431	448	69	.	.	PUNCT
ejpam-5431	449	1	if	if	SCONJ
ejpam-5431	449	2	σ	σ	PROPN
ejpam-5431	449	3	̸=	̸=	PROPN
ejpam-5431	449	4	1	1	NUM
ejpam-5431	449	5	;	;	PUNCT
ejpam-5431	449	6	µt	µt	DET
ejpam-5431	449	7	σ(t	σ(t	PROPN
ejpam-5431	449	8	)	)	PUNCT
ejpam-5431	449	9	=	=	PUNCT
ejpam-5431	449	10			PUNCT
ejpam-5431	449	11	⋉	⋉	PROPN
ejpam-5431	449	12	,	,	PUNCT
ejpam-5431	449	13	if	if	SCONJ
ejpam-5431	449	14	1	1	NUM
ejpam-5431	449	15	≤	≤	NUM
ejpam-5431	449	16	t	t	PROPN
ejpam-5431	449	17	≤	≤	NOUN
ejpam-5431	449	18	3σ	3σ	NUM
ejpam-5431	449	19	1−	1−	NUM
ejpam-5431	449	20	2	2	NUM
ejpam-5431	449	21	3⋉	3⋉	NUM
ejpam-5431	449	22	,	,	PUNCT
ejpam-5431	449	23	if	if	SCONJ
ejpam-5431	449	24	3σ	3σ	NUM
ejpam-5431	449	25	<	<	X
ejpam-5431	449	26	t	t	PROPN
ejpam-5431	449	27	≤	≤	PUNCT
ejpam-5431	449	28	5σ	5σ	PROPN
ejpam-5431	449	29	⋉	⋉	PROPN
ejpam-5431	449	30	6	6	NUM
ejpam-5431	449	31	,	,	PUNCT
ejpam-5431	449	32	if	if	SCONJ
ejpam-5431	449	33	5σ	5σ	PROPN
ejpam-5431	449	34	<	<	X
ejpam-5431	449	35	t	t	X
ejpam-5431	449	36	<	<	X
ejpam-5431	449	37	+	+	PROPN
ejpam-5431	449	38	∞	∞	NOUN
ejpam-5431	449	39	νt	νt	ADJ
ejpam-5431	449	40	σ(t	σ(t	NOUN
ejpam-5431	449	41	)	)	PUNCT
ejpam-5431	450	1	=	=	PUNCT
ejpam-5431	450	2			PUNCT
ejpam-5431	450	3	β	β	X
ejpam-5431	450	4	4	4	NUM
ejpam-5431	450	5	,	,	PUNCT
ejpam-5431	450	6	if	if	SCONJ
ejpam-5431	450	7	1	1	NUM
ejpam-5431	450	8	≤	≤	NUM
ejpam-5431	450	9	t	t	NOUN
ejpam-5431	450	10	≤	≤	NOUN
ejpam-5431	450	11	2σ	2σ	X
ejpam-5431	450	12	0	0	NUM
ejpam-5431	450	13	,	,	PUNCT
ejpam-5431	450	14	if	if	SCONJ
ejpam-5431	450	15	2σ	2σ	PRON
ejpam-5431	450	16	<	<	X
ejpam-5431	450	17	t	t	PROPN
ejpam-5431	450	18	≤	≤	PROPN
ejpam-5431	450	19	5σ	5σ	PROPN
ejpam-5431	450	20	β	β	NOUN
ejpam-5431	450	21	,	,	PUNCT
ejpam-5431	450	22	if	if	SCONJ
ejpam-5431	450	23	5σ	5σ	PROPN
ejpam-5431	450	24	<	<	X
ejpam-5431	450	25	t	t	X
ejpam-5431	450	26	<	<	X
ejpam-5431	450	27	+	+	PROPN
ejpam-5431	450	28	∞	∞	PROPN
ejpam-5431	450	29	µsσ(t	µsσ(t	PROPN
ejpam-5431	450	30	)	)	PUNCT
ejpam-5431	450	31	=	=	PUNCT
ejpam-5431	450	32			PUNCT
ejpam-5431	450	33	⋉	⋉	PROPN
ejpam-5431	450	34	,	,	PUNCT
ejpam-5431	450	35	if	if	SCONJ
ejpam-5431	450	36	1	1	NUM
ejpam-5431	450	37	≤	≤	NUM
ejpam-5431	450	38	t	t	PROPN
ejpam-5431	450	39	≤	≤	PROPN
ejpam-5431	450	40	5σ	5σ	PROPN
ejpam-5431	450	41	⋉	⋉	PROPN
ejpam-5431	450	42	3	3	NUM
ejpam-5431	450	43	,	,	PUNCT
ejpam-5431	450	44	if	if	SCONJ
ejpam-5431	450	45	5σ	5σ	PROPN
ejpam-5431	450	46	<	<	X
ejpam-5431	450	47	t	t	NOUN
ejpam-5431	450	48	≤	≤	NOUN
ejpam-5431	450	49	9σ	9σ	NOUN
ejpam-5431	450	50	2⋉	2⋉	NUM
ejpam-5431	450	51	19	19	NUM
ejpam-5431	450	52	,	,	PUNCT
ejpam-5431	450	53	if	if	SCONJ
ejpam-5431	450	54	9σ	9σ	NOUN
ejpam-5431	450	55	<	<	X
ejpam-5431	450	56	t	t	X
ejpam-5431	450	57	<	<	X
ejpam-5431	450	58	+	+	PROPN
ejpam-5431	450	59	∞	∞	PROPN
ejpam-5431	450	60	n.	n.	NOUN
ejpam-5431	450	61	saleem	saleem	PROPN
ejpam-5431	450	62	et	et	PROPN
ejpam-5431	450	63	al	al	PROPN
ejpam-5431	450	64	.	.	PUNCT
ejpam-5431	450	65	/	/	SYM
ejpam-5431	450	66	eur	eur	PROPN
ejpam-5431	450	67	.	.	PUNCT
ejpam-5431	451	1	j.	j.	PROPN
ejpam-5431	451	2	pure	pure	PROPN
ejpam-5431	451	3	appl	appl	PROPN
ejpam-5431	451	4	.	.	PROPN
ejpam-5431	451	5	math	math	PROPN
ejpam-5431	451	6	,	,	PUNCT
ejpam-5431	451	7	17	17	NUM
ejpam-5431	451	8	(	(	PUNCT
ejpam-5431	451	9	4	4	NUM
ejpam-5431	451	10	)	)	PUNCT
ejpam-5431	451	11	(	(	PUNCT
ejpam-5431	451	12	2024	2024	NUM
ejpam-5431	451	13	)	)	PUNCT
ejpam-5431	451	14	,	,	PUNCT
ejpam-5431	451	15	3304	3304	NUM
ejpam-5431	451	16	-	-	SYM
ejpam-5431	451	17	3335	3335	NUM
ejpam-5431	451	18	3322	3322	NUM
ejpam-5431	451	19	νsσ(t	νsσ(t	NOUN
ejpam-5431	451	20	)	)	PUNCT
ejpam-5431	451	21	=	=	PUNCT
ejpam-5431	452	1			PUNCT
ejpam-5431	452	2	β2	β2	ADJ
ejpam-5431	452	3	,	,	PUNCT
ejpam-5431	452	4	if	if	SCONJ
ejpam-5431	452	5	1	1	NUM
ejpam-5431	452	6	≤	≤	NUM
ejpam-5431	452	7	t	t	NOUN
ejpam-5431	452	8	≤	≤	NOUN
ejpam-5431	452	9	7σ	7σ	NOUN
ejpam-5431	452	10	β3	β3	NOUN
ejpam-5431	452	11	5	5	NUM
ejpam-5431	452	12	,	,	PUNCT
ejpam-5431	452	13	if	if	SCONJ
ejpam-5431	452	14	7σ	7σ	PROPN
ejpam-5431	452	15	<	<	X
ejpam-5431	452	16	t	t	X
ejpam-5431	452	17	≤	≤	NOUN
ejpam-5431	452	18	11σ	11σ	NUM
ejpam-5431	452	19	β	β	NOUN
ejpam-5431	452	20	,	,	PUNCT
ejpam-5431	452	21	if	if	SCONJ
ejpam-5431	452	22	11σ	11σ	NOUN
ejpam-5431	452	23	<	<	X
ejpam-5431	452	24	t	t	X
ejpam-5431	452	25	<	<	X
ejpam-5431	452	26	+	+	NOUN
ejpam-5431	452	27	∞.	∞.	PROPN
ejpam-5431	452	28	let	let	VERB
ejpam-5431	452	29	⋉	⋉	PROPN
ejpam-5431	452	30	=	=	SYM
ejpam-5431	452	31	3	3	NUM
ejpam-5431	452	32	8	8	NUM
ejpam-5431	452	33	and	and	CCONJ
ejpam-5431	452	34	β	β	X
ejpam-5431	452	35	=	=	NOUN
ejpam-5431	452	36	1	1	NUM
ejpam-5431	452	37	2	2	NUM
ejpam-5431	452	38	.	.	PUNCT
ejpam-5431	453	1	then	then	ADV
ejpam-5431	453	2	[	[	X
ejpam-5431	453	3	t	t	NOUN
ejpam-5431	453	4	σ](⋉,β	σ](⋉,β	PROPN
ejpam-5431	453	5	)	)	PUNCT
ejpam-5431	453	6	=	=	PRON
ejpam-5431	453	7	{	{	PUNCT
ejpam-5431	453	8	{	{	PUNCT
ejpam-5431	453	9	1	1	NUM
ejpam-5431	453	10	}	}	PUNCT
ejpam-5431	453	11	,	,	PUNCT
ejpam-5431	453	12	if	if	SCONJ
ejpam-5431	453	13	σ	σ	NOUN
ejpam-5431	453	14	=	=	SYM
ejpam-5431	453	15	1	1	NUM
ejpam-5431	454	1	[	[	SYM
ejpam-5431	454	2	1	1	NUM
ejpam-5431	454	3	,	,	PUNCT
ejpam-5431	454	4	5σ	5σ	NOUN
ejpam-5431	454	5	]	]	PUNCT
ejpam-5431	454	6	,	,	PUNCT
ejpam-5431	454	7	if	if	SCONJ
ejpam-5431	454	8	σ	σ	NUM
ejpam-5431	454	9	̸=	̸=	PROPN
ejpam-5431	454	10	1	1	NUM
ejpam-5431	454	11	and	and	CCONJ
ejpam-5431	454	12	[	[	X
ejpam-5431	454	13	sσ](⋉,β	sσ](⋉,β	PROPN
ejpam-5431	454	14	)	)	PUNCT
ejpam-5431	454	15	=	=	PRON
ejpam-5431	454	16	{	{	PUNCT
ejpam-5431	454	17	{	{	PUNCT
ejpam-5431	454	18	1	1	NUM
ejpam-5431	454	19	}	}	PUNCT
ejpam-5431	454	20	,	,	PUNCT
ejpam-5431	454	21	if	if	SCONJ
ejpam-5431	454	22	σ	σ	NOUN
ejpam-5431	454	23	=	=	SYM
ejpam-5431	454	24	1	1	NUM
ejpam-5431	455	1	[	[	SYM
ejpam-5431	455	2	1	1	NUM
ejpam-5431	455	3	,	,	PUNCT
ejpam-5431	455	4	5σ	5σ	NOUN
ejpam-5431	455	5	]	]	PUNCT
ejpam-5431	455	6	,	,	PUNCT
ejpam-5431	455	7	if	if	SCONJ
ejpam-5431	455	8	σ	σ	PRON
ejpam-5431	455	9	̸=	̸=	PROPN
ejpam-5431	455	10	1	1	NUM
ejpam-5431	455	11	.	.	PUNCT
ejpam-5431	455	12	clearly	clearly	ADV
ejpam-5431	455	13	sσ	sσ	ADJ
ejpam-5431	455	14	,	,	PUNCT
ejpam-5431	455	15	t	t	PROPN
ejpam-5431	455	16	σ	σ	PROPN
ejpam-5431	455	17	∈	∈	PROPN
ejpam-5431	455	18	ifs(x	ifs(x	PROPN
ejpam-5431	455	19	)	)	PUNCT
ejpam-5431	455	20	for	for	ADP
ejpam-5431	455	21	each	each	DET
ejpam-5431	455	22	σ	σ	PROPN
ejpam-5431	455	23	∈	∈	PROPN
ejpam-5431	455	24	x.	x.	NOUN
ejpam-5431	455	25	define	define	VERB
ejpam-5431	455	26	the	the	DET
ejpam-5431	455	27	functions	function	NOUN
ejpam-5431	455	28	γ	γ	X
ejpam-5431	455	29	:	:	PUNCT
ejpam-5431	455	30	x	x	SYM
ejpam-5431	455	31	×	×	NOUN
ejpam-5431	455	32	x	x	INTJ
ejpam-5431	455	33	→	→	X
ejpam-5431	455	34	r+	r+	NOUN
ejpam-5431	455	35	and	and	CCONJ
ejpam-5431	455	36	φ	φ	PROPN
ejpam-5431	455	37	:	:	PUNCT
ejpam-5431	455	38	r+	r+	X
ejpam-5431	455	39	→	→	SYM
ejpam-5431	455	40	r+	r+	NOUN
ejpam-5431	455	41	by	by	ADP
ejpam-5431	455	42	γ(σ	γ(σ	PROPN
ejpam-5431	455	43	,	,	PUNCT
ejpam-5431	455	44	τ	τ	X
ejpam-5431	455	45	)	)	PUNCT
ejpam-5431	455	46	=	=	PUNCT
ejpam-5431	456	1			PROPN
ejpam-5431	456	2	6	6	NUM
ejpam-5431	456	3	,	,	PUNCT
ejpam-5431	456	4	if	if	SCONJ
ejpam-5431	456	5	σ	σ	PROPN
ejpam-5431	456	6	=	=	SYM
ejpam-5431	456	7	τ	τ	X
ejpam-5431	456	8	=	=	SYM
ejpam-5431	456	9	1	1	NUM
ejpam-5431	456	10	1	1	NUM
ejpam-5431	456	11	430	430	NUM
ejpam-5431	456	12	,	,	PUNCT
ejpam-5431	456	13	if	if	SCONJ
ejpam-5431	456	14	σ	σ	PROPN
ejpam-5431	456	15	,	,	PUNCT
ejpam-5431	456	16	τ	τ	PROPN
ejpam-5431	456	17	∈	∈	PROPN
ejpam-5431	456	18	{	{	PUNCT
ejpam-5431	456	19	4	4	NUM
ejpam-5431	456	20	,	,	PUNCT
ejpam-5431	456	21	5	5	NUM
ejpam-5431	456	22	}	}	SYM
ejpam-5431	456	23	0	0	NUM
ejpam-5431	456	24	,	,	PUNCT
ejpam-5431	456	25	elsewhere	elsewhere	ADV
ejpam-5431	456	26	.	.	PUNCT
ejpam-5431	456	27	and	and	CCONJ
ejpam-5431	456	28	φ(t	φ(t	PROPN
ejpam-5431	456	29	)	)	PUNCT
ejpam-5431	456	30	=	=	PUNCT
ejpam-5431	456	31	t	t	PROPN
ejpam-5431	456	32	4	4	NUM
ejpam-5431	456	33	for	for	ADP
ejpam-5431	456	34	all	all	DET
ejpam-5431	456	35	t	t	PROPN
ejpam-5431	456	36	>	>	X
ejpam-5431	456	37	0	0	X
ejpam-5431	456	38	.	.	PUNCT
ejpam-5431	457	1	let	let	AUX
ejpam-5431	457	2	℘(a	℘(a	PROPN
ejpam-5431	457	3	,	,	PUNCT
ejpam-5431	457	4	b	b	NOUN
ejpam-5431	457	5	)	)	PUNCT
ejpam-5431	457	6	=	=	SYM
ejpam-5431	457	7	1	1	NUM
ejpam-5431	457	8	2b	2b	NUM
ejpam-5431	457	9	−	−	NOUN
ejpam-5431	457	10	a	a	PRON
ejpam-5431	457	11	for	for	ADP
ejpam-5431	457	12	all	all	DET
ejpam-5431	457	13	a	a	DET
ejpam-5431	457	14	,	,	PUNCT
ejpam-5431	457	15	b	b	X
ejpam-5431	457	16	∈	∈	PROPN
ejpam-5431	457	17	r+	r+	X
ejpam-5431	457	18	.	.	PUNCT
ejpam-5431	458	1	obviously	obviously	ADV
ejpam-5431	458	2	℘	℘	VERB
ejpam-5431	458	3	∈	∈	PROPN
ejpam-5431	458	4	z	z	NOUN
ejpam-5431	458	5	and	and	CCONJ
ejpam-5431	458	6	φ	φ	PROPN
ejpam-5431	458	7	∈	∈	PROPN
ejpam-5431	458	8	λb	λb	ADP
ejpam-5431	458	9	now	now	ADV
ejpam-5431	458	10	we	we	PRON
ejpam-5431	458	11	verify	verify	VERB
ejpam-5431	458	12	conditions	condition	NOUN
ejpam-5431	458	13	℘(γ(σ	℘(γ(σ	ADJ
ejpam-5431	458	14	,	,	PUNCT
ejpam-5431	458	15	τ)ℵ([sσ](⋉,β	τ)ℵ([sσ](⋉,β	NOUN
ejpam-5431	458	16	)	)	PUNCT
ejpam-5431	458	17	,	,	PUNCT
ejpam-5431	459	1	[	[	X
ejpam-5431	459	2	t	t	X
ejpam-5431	459	3	τ	τ	X
ejpam-5431	459	4	]	]	X
ejpam-5431	459	5	(	(	PUNCT
ejpam-5431	459	6	⋉,β	⋉,β	NOUN
ejpam-5431	459	7	)	)	PUNCT
ejpam-5431	459	8	)	)	PUNCT
ejpam-5431	459	9	,	,	PUNCT
ejpam-5431	459	10	φ(m	φ(m	ADJ
ejpam-5431	459	11	r	r	NOUN
ejpam-5431	459	12	(	(	PUNCT
ejpam-5431	459	13	s	s	PROPN
ejpam-5431	459	14	,	,	PUNCT
ejpam-5431	459	15	t	t	NOUN
ejpam-5431	459	16	)	)	PUNCT
ejpam-5431	459	17	(	(	PUNCT
ejpam-5431	459	18	σ	σ	PROPN
ejpam-5431	459	19	,	,	PUNCT
ejpam-5431	459	20	τ	τ	PROPN
ejpam-5431	459	21	)	)	PUNCT
ejpam-5431	459	22	)	)	PUNCT
ejpam-5431	459	23	)	)	PUNCT
ejpam-5431	459	24	≥	≥	NOUN
ejpam-5431	459	25	0	0	NUM
ejpam-5431	459	26	and	and	CCONJ
ejpam-5431	459	27	℘(γ(σ	℘(γ(σ	ADJ
ejpam-5431	459	28	,	,	PUNCT
ejpam-5431	459	29	τ)ℵ([t	τ)ℵ([t	PROPN
ejpam-5431	459	30	σ](⋉,β	σ](⋉,β	NUM
ejpam-5431	459	31	)	)	PUNCT
ejpam-5431	459	32	,	,	PUNCT
ejpam-5431	459	33	[	[	X
ejpam-5431	459	34	sτ	sτ	ADP
ejpam-5431	459	35	]	]	PUNCT
ejpam-5431	459	36	(	(	PUNCT
ejpam-5431	459	37	⋉,β	⋉,β	NOUN
ejpam-5431	459	38	)	)	PUNCT
ejpam-5431	459	39	)	)	PUNCT
ejpam-5431	459	40	,	,	PUNCT
ejpam-5431	459	41	φ(m	φ(m	ADJ
ejpam-5431	459	42	r	r	NOUN
ejpam-5431	459	43	(	(	PUNCT
ejpam-5431	459	44	t	t	NOUN
ejpam-5431	459	45	,	,	PUNCT
ejpam-5431	459	46	s)(σ	s)(σ	PROPN
ejpam-5431	459	47	,	,	PUNCT
ejpam-5431	459	48	τ	τ	PROPN
ejpam-5431	459	49	)	)	PUNCT
ejpam-5431	459	50	)	)	PUNCT
ejpam-5431	459	51	)	)	PUNCT
ejpam-5431	459	52	≥	≥	NOUN
ejpam-5431	459	53	0	0	NUM
ejpam-5431	459	54	for	for	ADP
ejpam-5431	459	55	r	r	NOUN
ejpam-5431	459	56	>	>	X
ejpam-5431	459	57	0	0	PUNCT
ejpam-5431	460	1	under	under	ADP
ejpam-5431	460	2	the	the	DET
ejpam-5431	460	3	these	these	DET
ejpam-5431	460	4	cases	case	NOUN
ejpam-5431	460	5	;	;	PUNCT
ejpam-5431	460	6	case	case	NOUN
ejpam-5431	460	7	1	1	NUM
ejpam-5431	460	8	if	if	SCONJ
ejpam-5431	460	9	σ	σ	NOUN
ejpam-5431	460	10	=	=	SYM
ejpam-5431	460	11	τ	τ	X
ejpam-5431	460	12	=	=	SYM
ejpam-5431	460	13	1	1	NUM
ejpam-5431	460	14	,	,	PUNCT
ejpam-5431	460	15	then	then	ADV
ejpam-5431	460	16	[	[	X
ejpam-5431	460	17	sσ](⋉,β	sσ](⋉,β	NOUN
ejpam-5431	460	18	)	)	PUNCT
ejpam-5431	460	19	=	=	PRON
ejpam-5431	460	20	{	{	PUNCT
ejpam-5431	460	21	1	1	NUM
ejpam-5431	460	22	}	}	PUNCT
ejpam-5431	460	23	=	=	PUNCT
ejpam-5431	461	1	[	[	X
ejpam-5431	461	2	t	t	X
ejpam-5431	461	3	τ	τ	X
ejpam-5431	461	4	]	]	X
ejpam-5431	461	5	(	(	PUNCT
ejpam-5431	461	6	⋉,β	⋉,β	NUM
ejpam-5431	461	7	)	)	PUNCT
ejpam-5431	461	8	,	,	PUNCT
ejpam-5431	461	9	this	this	PRON
ejpam-5431	461	10	implies	imply	VERB
ejpam-5431	461	11	that	that	SCONJ
ejpam-5431	461	12	ℵ([sσ](⋉,β	ℵ([sσ](⋉,β	PROPN
ejpam-5431	461	13	)	)	PUNCT
ejpam-5431	461	14	,	,	PUNCT
ejpam-5431	462	1	[	[	X
ejpam-5431	462	2	t	t	X
ejpam-5431	462	3	τ	τ	X
ejpam-5431	462	4	]	]	X
ejpam-5431	462	5	(	(	PUNCT
ejpam-5431	462	6	⋉,β	⋉,β	NOUN
ejpam-5431	462	7	)	)	PUNCT
ejpam-5431	462	8	)	)	PUNCT
ejpam-5431	463	1	=	=	SYM
ejpam-5431	463	2	0	0	PUNCT
ejpam-5431	464	1	so	so	ADV
ejpam-5431	464	2	,	,	PUNCT
ejpam-5431	464	3	℘(6(0	℘(6(0	PROPN
ejpam-5431	464	4	)	)	PUNCT
ejpam-5431	464	5	,	,	PUNCT
ejpam-5431	464	6	φ(m	φ(m	ADJ
ejpam-5431	464	7	r	r	NOUN
ejpam-5431	464	8	(	(	PUNCT
ejpam-5431	464	9	s	s	PROPN
ejpam-5431	464	10	,	,	PUNCT
ejpam-5431	464	11	t	t	NOUN
ejpam-5431	464	12	)	)	PUNCT
ejpam-5431	464	13	(	(	PUNCT
ejpam-5431	464	14	σ	σ	PROPN
ejpam-5431	464	15	,	,	PUNCT
ejpam-5431	464	16	τ	τ	PROPN
ejpam-5431	464	17	)	)	PUNCT
ejpam-5431	464	18	)	)	PUNCT
ejpam-5431	464	19	)	)	PUNCT
ejpam-5431	465	1	≥	≥	NOUN
ejpam-5431	465	2	0	0	X
ejpam-5431	465	3	.	.	PUNCT
ejpam-5431	466	1	similarly	similarly	ADV
ejpam-5431	466	2	℘(γ(σ	℘(γ(σ	ADJ
ejpam-5431	466	3	,	,	PUNCT
ejpam-5431	466	4	τ)ℵ([t	τ)ℵ([t	PROPN
ejpam-5431	466	5	σ](⋉,β	σ](⋉,β	NUM
ejpam-5431	466	6	)	)	PUNCT
ejpam-5431	466	7	,	,	PUNCT
ejpam-5431	466	8	[	[	X
ejpam-5431	466	9	sτ	sτ	ADP
ejpam-5431	466	10	]	]	PUNCT
ejpam-5431	466	11	(	(	PUNCT
ejpam-5431	466	12	⋉,β	⋉,β	NOUN
ejpam-5431	466	13	)	)	PUNCT
ejpam-5431	466	14	)	)	PUNCT
ejpam-5431	466	15	,	,	PUNCT
ejpam-5431	466	16	φ(m	φ(m	ADJ
ejpam-5431	466	17	r	r	NOUN
ejpam-5431	466	18	(	(	PUNCT
ejpam-5431	466	19	t	t	NOUN
ejpam-5431	466	20	,	,	PUNCT
ejpam-5431	466	21	s)(σ	s)(σ	PROPN
ejpam-5431	466	22	,	,	PUNCT
ejpam-5431	466	23	τ	τ	PROPN
ejpam-5431	466	24	)	)	PUNCT
ejpam-5431	466	25	)	)	PUNCT
ejpam-5431	466	26	)	)	PUNCT
ejpam-5431	466	27	≥	≥	NOUN
ejpam-5431	466	28	0	0	NUM
ejpam-5431	466	29	.	.	PUNCT
ejpam-5431	466	30	case	case	NOUN
ejpam-5431	466	31	2	2	NUM
ejpam-5431	466	32	if	if	SCONJ
ejpam-5431	466	33	σ	σ	PROPN
ejpam-5431	466	34	,	,	PUNCT
ejpam-5431	466	35	τ	τ	PROPN
ejpam-5431	466	36	∈	∈	PROPN
ejpam-5431	466	37	{	{	PUNCT
ejpam-5431	466	38	4	4	NUM
ejpam-5431	466	39	,	,	PUNCT
ejpam-5431	466	40	5	5	NUM
ejpam-5431	466	41	}	}	PUNCT
ejpam-5431	466	42	such	such	ADJ
ejpam-5431	466	43	that	that	SCONJ
ejpam-5431	466	44	σ	σ	PROPN
ejpam-5431	466	45	̸=	̸=	PROPN
ejpam-5431	466	46	τ	τ	X
ejpam-5431	466	47	,	,	PUNCT
ejpam-5431	466	48	let	let	VERB
ejpam-5431	466	49	σ	σ	NOUN
ejpam-5431	466	50	=	=	SYM
ejpam-5431	466	51	4	4	NUM
ejpam-5431	466	52	and	and	CCONJ
ejpam-5431	466	53	τ	τ	X
ejpam-5431	466	54	=	=	SYM
ejpam-5431	466	55	5	5	X
ejpam-5431	466	56	.	.	PUNCT
ejpam-5431	467	1	then	then	ADV
ejpam-5431	467	2	[	[	X
ejpam-5431	467	3	sσ](⋉,β	sσ](⋉,β	NOUN
ejpam-5431	467	4	)	)	PUNCT
ejpam-5431	467	5	=	=	PUNCT
ejpam-5431	468	1	[	[	X
ejpam-5431	468	2	1	1	NUM
ejpam-5431	468	3	,	,	PUNCT
ejpam-5431	468	4	20	20	NUM
ejpam-5431	468	5	]	]	PUNCT
ejpam-5431	468	6	and	and	CCONJ
ejpam-5431	469	1	[	[	X
ejpam-5431	469	2	t	t	X
ejpam-5431	469	3	τ	τ	X
ejpam-5431	469	4	]	]	X
ejpam-5431	469	5	(	(	PUNCT
ejpam-5431	469	6	⋉,β	⋉,β	X
ejpam-5431	469	7	)	)	PUNCT
ejpam-5431	469	8	=	=	PUNCT
ejpam-5431	470	1	[	[	X
ejpam-5431	470	2	1	1	NUM
ejpam-5431	470	3	,	,	PUNCT
ejpam-5431	470	4	25	25	NUM
ejpam-5431	470	5	]	]	PUNCT
ejpam-5431	470	6	.	.	PUNCT
ejpam-5431	471	1	ℵ([sσ](⋉,β	ℵ([sσ](⋉,β	PROPN
ejpam-5431	471	2	)	)	PUNCT
ejpam-5431	471	3	,	,	PUNCT
ejpam-5431	472	1	[	[	X
ejpam-5431	472	2	t	t	X
ejpam-5431	472	3	τ	τ	X
ejpam-5431	472	4	]	]	X
ejpam-5431	472	5	(	(	PUNCT
ejpam-5431	472	6	⋉,β	⋉,β	NOUN
ejpam-5431	472	7	)	)	PUNCT
ejpam-5431	472	8	)	)	PUNCT
ejpam-5431	472	9	=	=	SYM
ejpam-5431	472	10	ℵ([1	ℵ([1	NOUN
ejpam-5431	472	11	,	,	PUNCT
ejpam-5431	472	12	20	20	NUM
ejpam-5431	472	13	]	]	PUNCT
ejpam-5431	472	14	,	,	PUNCT
ejpam-5431	472	15	[	[	X
ejpam-5431	472	16	1	1	NUM
ejpam-5431	472	17	,	,	PUNCT
ejpam-5431	472	18	25	25	NUM
ejpam-5431	472	19	]	]	PUNCT
ejpam-5431	472	20	)	)	PUNCT
ejpam-5431	472	21	n.	n.	PROPN
ejpam-5431	472	22	saleem	saleem	PROPN
ejpam-5431	472	23	et	et	PROPN
ejpam-5431	472	24	al	al	PROPN
ejpam-5431	472	25	.	.	PUNCT
ejpam-5431	472	26	/	/	SYM
ejpam-5431	472	27	eur	eur	PROPN
ejpam-5431	472	28	.	.	PUNCT
ejpam-5431	473	1	j.	j.	PROPN
ejpam-5431	473	2	pure	pure	PROPN
ejpam-5431	473	3	appl	appl	PROPN
ejpam-5431	473	4	.	.	PROPN
ejpam-5431	473	5	math	math	PROPN
ejpam-5431	473	6	,	,	PUNCT
ejpam-5431	473	7	17	17	NUM
ejpam-5431	473	8	(	(	PUNCT
ejpam-5431	473	9	4	4	NUM
ejpam-5431	473	10	)	)	PUNCT
ejpam-5431	473	11	(	(	PUNCT
ejpam-5431	473	12	2024	2024	NUM
ejpam-5431	473	13	)	)	PUNCT
ejpam-5431	473	14	,	,	PUNCT
ejpam-5431	473	15	3304	3304	NUM
ejpam-5431	473	16	-	-	SYM
ejpam-5431	473	17	3335	3335	NUM
ejpam-5431	473	18	3323	3323	NUM
ejpam-5431	473	19	=	=	SYM
ejpam-5431	473	20	δ(20	δ(20	PROPN
ejpam-5431	473	21	,	,	PUNCT
ejpam-5431	473	22	25	25	NUM
ejpam-5431	473	23	)	)	PUNCT
ejpam-5431	473	24	=	=	PUNCT
ejpam-5431	474	1	25	25	NUM
ejpam-5431	474	2	m	m	NOUN
ejpam-5431	474	3	r	r	NOUN
ejpam-5431	474	4	(	(	PUNCT
ejpam-5431	474	5	s	s	PROPN
ejpam-5431	474	6	,	,	PUNCT
ejpam-5431	474	7	t	t	NOUN
ejpam-5431	474	8	)	)	PUNCT
ejpam-5431	474	9	(	(	PUNCT
ejpam-5431	474	10	4	4	NUM
ejpam-5431	474	11	,	,	PUNCT
ejpam-5431	474	12	5	5	NUM
ejpam-5431	474	13	)	)	PUNCT
ejpam-5431	474	14	=	=	NOUN
ejpam-5431	475	1	[	[	X
ejpam-5431	475	2	a(4	a(4	PROPN
ejpam-5431	475	3	,	,	PUNCT
ejpam-5431	475	4	5	5	NUM
ejpam-5431	475	5	)	)	PUNCT
ejpam-5431	475	6	]	]	PUNCT
ejpam-5431	475	7	1	1	NUM
ejpam-5431	475	8	r	r	NOUN
ejpam-5431	475	9	=	=	SYM
ejpam-5431	475	10	[	[	PUNCT
ejpam-5431	475	11	k1(δ(4	k1(δ(4	PROPN
ejpam-5431	475	12	,	,	PUNCT
ejpam-5431	475	13	5	5	NUM
ejpam-5431	475	14	)	)	PUNCT
ejpam-5431	475	15	)	)	PUNCT
ejpam-5431	475	16	r	r	NOUN
ejpam-5431	475	17	+	+	NUM
ejpam-5431	475	18	k2(δ(4	k2(δ(4	NOUN
ejpam-5431	475	19	,	,	PUNCT
ejpam-5431	475	20	[	[	X
ejpam-5431	475	21	s4](⋉,β	s4](⋉,β	NUM
ejpam-5431	475	22	)	)	PUNCT
ejpam-5431	475	23	)	)	PUNCT
ejpam-5431	475	24	)	)	PUNCT
ejpam-5431	476	1	r	r	NOUN
ejpam-5431	476	2	+	+	NUM
ejpam-5431	476	3	k3(δ(5	k3(δ(5	NOUN
ejpam-5431	476	4	,	,	PUNCT
ejpam-5431	476	5	[	[	X
ejpam-5431	476	6	t	t	NOUN
ejpam-5431	476	7	5](⋉,β	5](⋉,β	NUM
ejpam-5431	476	8	)	)	PUNCT
ejpam-5431	476	9	)	)	PUNCT
ejpam-5431	476	10	)	)	PUNCT
ejpam-5431	477	1	r	r	NOUN
ejpam-5431	477	2	+	+	PRON
ejpam-5431	477	3	k4	k4	NOUN
ejpam-5431	477	4	(	(	PUNCT
ejpam-5431	477	5	δ(5	δ(5	PROPN
ejpam-5431	477	6	,	,	PUNCT
ejpam-5431	478	1	[	[	X
ejpam-5431	478	2	t	t	X
ejpam-5431	478	3	5](⋉,β))(1	5](⋉,β))(1	NOUN
ejpam-5431	478	4	+	+	CCONJ
ejpam-5431	478	5	δ(4	δ(4	PROPN
ejpam-5431	478	6	,	,	PUNCT
ejpam-5431	478	7	[	[	X
ejpam-5431	478	8	s4](⋉,β	s4](⋉,β	NUM
ejpam-5431	478	9	)	)	PUNCT
ejpam-5431	478	10	)	)	PUNCT
ejpam-5431	478	11	)	)	PUNCT
ejpam-5431	478	12	1	1	NUM
ejpam-5431	479	1	+	+	X
ejpam-5431	479	2	δ(4	δ(4	NOUN
ejpam-5431	479	3	,	,	PUNCT
ejpam-5431	479	4	5	5	NUM
ejpam-5431	479	5	)	)	PUNCT
ejpam-5431	479	6	)	)	PUNCT
ejpam-5431	480	1	r	r	PROPN
ejpam-5431	480	2	+	+	PROPN
ejpam-5431	480	3	k5	k5	PROPN
ejpam-5431	480	4	(	(	PUNCT
ejpam-5431	480	5	δ(5	δ(5	PROPN
ejpam-5431	480	6	,	,	PUNCT
ejpam-5431	481	1	[	[	X
ejpam-5431	481	2	s4](⋉,β))(1	s4](⋉,β))(1	NOUN
ejpam-5431	481	3	+	+	NOUN
ejpam-5431	481	4	δ(4	δ(4	PROPN
ejpam-5431	481	5	,	,	PUNCT
ejpam-5431	481	6	[	[	X
ejpam-5431	481	7	t	t	NOUN
ejpam-5431	481	8	5](⋉,β	5](⋉,β	NUM
ejpam-5431	481	9	)	)	PUNCT
ejpam-5431	481	10	)	)	PUNCT
ejpam-5431	481	11	)	)	PUNCT
ejpam-5431	481	12	1	1	NUM
ejpam-5431	482	1	+	+	X
ejpam-5431	482	2	δ(4	δ(4	NOUN
ejpam-5431	482	3	,	,	PUNCT
ejpam-5431	482	4	5	5	NUM
ejpam-5431	482	5	)	)	PUNCT
ejpam-5431	482	6	)	)	PUNCT
ejpam-5431	483	1	r	r	NOUN
ejpam-5431	483	2	]	]	PUNCT
ejpam-5431	483	3	1	1	NUM
ejpam-5431	483	4	r	r	NOUN
ejpam-5431	483	5	taking	take	VERB
ejpam-5431	483	6	k1	k1	NOUN
ejpam-5431	483	7	=	=	SYM
ejpam-5431	483	8	k2	k2	NOUN
ejpam-5431	483	9	=	=	SYM
ejpam-5431	483	10	1	1	NUM
ejpam-5431	483	11	2	2	NUM
ejpam-5431	483	12	and	and	CCONJ
ejpam-5431	483	13	k3	k3	X
ejpam-5431	483	14	=	=	SYM
ejpam-5431	483	15	k4	k4	PROPN
ejpam-5431	483	16	=	=	PROPN
ejpam-5431	483	17	k5	k5	PROPN
ejpam-5431	483	18	=	=	SYM
ejpam-5431	483	19	0	0	PROPN
ejpam-5431	483	20	,	,	PUNCT
ejpam-5431	483	21	m	m	VERB
ejpam-5431	483	22	r	r	NOUN
ejpam-5431	483	23	(	(	PUNCT
ejpam-5431	483	24	s	s	PROPN
ejpam-5431	483	25	,	,	PUNCT
ejpam-5431	483	26	t	t	NOUN
ejpam-5431	483	27	)	)	PUNCT
ejpam-5431	483	28	(	(	PUNCT
ejpam-5431	483	29	4	4	NUM
ejpam-5431	483	30	,	,	PUNCT
ejpam-5431	483	31	5	5	NUM
ejpam-5431	483	32	)	)	PUNCT
ejpam-5431	483	33	=	=	NOUN
ejpam-5431	484	1	[	[	PUNCT
ejpam-5431	484	2	1	1	NUM
ejpam-5431	484	3	2	2	NUM
ejpam-5431	484	4	(	(	PUNCT
ejpam-5431	484	5	1)r	1)r	NOUN
ejpam-5431	484	6	+	+	CCONJ
ejpam-5431	484	7	1	1	NUM
ejpam-5431	484	8	2	2	NUM
ejpam-5431	484	9	(	(	PUNCT
ejpam-5431	484	10	0)r	0)r	ADP
ejpam-5431	484	11	]	]	X
ejpam-5431	484	12	1	1	NUM
ejpam-5431	484	13	r	r	NOUN
ejpam-5431	484	14	=	=	SYM
ejpam-5431	484	15	[	[	PUNCT
ejpam-5431	484	16	1	1	NUM
ejpam-5431	484	17	2	2	NUM
ejpam-5431	484	18	]	]	SYM
ejpam-5431	484	19	1	1	NUM
ejpam-5431	484	20	r	r	NOUN
ejpam-5431	484	21	→	→	SYM
ejpam-5431	484	22	1	1	NUM
ejpam-5431	484	23	as	as	ADP
ejpam-5431	484	24	r	r	NOUN
ejpam-5431	484	25	→	→	SYM
ejpam-5431	484	26	+	+	NUM
ejpam-5431	484	27	∞	∞	PROPN
ejpam-5431	484	28	therefore	therefore	ADV
ejpam-5431	484	29	,	,	PUNCT
ejpam-5431	484	30	℘	℘	PROPN
ejpam-5431	484	31	(	(	PUNCT
ejpam-5431	484	32	1	1	NUM
ejpam-5431	484	33	430	430	NUM
ejpam-5431	484	34	(	(	PUNCT
ejpam-5431	484	35	25	25	NUM
ejpam-5431	484	36	)	)	PUNCT
ejpam-5431	484	37	,	,	PUNCT
ejpam-5431	484	38	φ(1	φ(1	PROPN
ejpam-5431	484	39	)	)	PUNCT
ejpam-5431	484	40	)	)	PUNCT
ejpam-5431	485	1	=	=	SYM
ejpam-5431	486	1	1	1	NUM
ejpam-5431	486	2	2	2	NUM
ejpam-5431	486	3	(	(	PUNCT
ejpam-5431	486	4	1	1	NUM
ejpam-5431	486	5	4	4	NUM
ejpam-5431	486	6	)	)	PUNCT
ejpam-5431	486	7	−	−	PROPN
ejpam-5431	486	8	25	25	NUM
ejpam-5431	486	9	430	430	NUM
ejpam-5431	486	10	≥	≥	NOUN
ejpam-5431	486	11	0	0	NUM
ejpam-5431	486	12	similarly	similarly	ADV
ejpam-5431	486	13	,	,	PUNCT
ejpam-5431	486	14	℘(γ(σ	℘(γ(σ	ADJ
ejpam-5431	486	15	,	,	PUNCT
ejpam-5431	486	16	τ)ℵ([t	τ)ℵ([t	PROPN
ejpam-5431	486	17	σ](⋉,β	σ](⋉,β	NUM
ejpam-5431	486	18	)	)	PUNCT
ejpam-5431	486	19	,	,	PUNCT
ejpam-5431	486	20	[	[	X
ejpam-5431	486	21	sτ	sτ	ADP
ejpam-5431	486	22	]	]	PUNCT
ejpam-5431	486	23	(	(	PUNCT
ejpam-5431	486	24	⋉,β	⋉,β	NOUN
ejpam-5431	486	25	)	)	PUNCT
ejpam-5431	486	26	)	)	PUNCT
ejpam-5431	486	27	,	,	PUNCT
ejpam-5431	486	28	φ(m	φ(m	ADJ
ejpam-5431	486	29	r	r	NOUN
ejpam-5431	486	30	(	(	PUNCT
ejpam-5431	486	31	t	t	NOUN
ejpam-5431	486	32	,	,	PUNCT
ejpam-5431	486	33	s)(σ	s)(σ	PROPN
ejpam-5431	486	34	,	,	PUNCT
ejpam-5431	486	35	τ	τ	PROPN
ejpam-5431	486	36	)	)	PUNCT
ejpam-5431	486	37	)	)	PUNCT
ejpam-5431	486	38	)	)	PUNCT
ejpam-5431	486	39	≥	≥	NOUN
ejpam-5431	486	40	0	0	NUM
ejpam-5431	486	41	case	case	NOUN
ejpam-5431	486	42	3	3	NUM
ejpam-5431	486	43	if	if	SCONJ
ejpam-5431	486	44	σ	σ	PROPN
ejpam-5431	486	45	,	,	PUNCT
ejpam-5431	486	46	τ	τ	PROPN
ejpam-5431	486	47	∈	∈	PROPN
ejpam-5431	486	48	x	x	PUNCT
ejpam-5431	486	49	−	−	PROPN
ejpam-5431	486	50	{	{	PUNCT
ejpam-5431	486	51	1	1	NUM
ejpam-5431	486	52	,	,	PUNCT
ejpam-5431	486	53	4	4	NUM
ejpam-5431	486	54	,	,	PUNCT
ejpam-5431	486	55	5	5	NUM
ejpam-5431	486	56	}	}	PUNCT
ejpam-5431	486	57	.	.	PUNCT
ejpam-5431	487	1	then	then	ADV
ejpam-5431	487	2	γ(σ	γ(σ	PROPN
ejpam-5431	487	3	,	,	PUNCT
ejpam-5431	487	4	τ	τ	X
ejpam-5431	487	5	)	)	PUNCT
ejpam-5431	487	6	=	=	SYM
ejpam-5431	487	7	0	0	NUM
ejpam-5431	487	8	℘(0	℘(0	NOUN
ejpam-5431	487	9	,	,	PUNCT
ejpam-5431	487	10	φ(m	φ(m	ADJ
ejpam-5431	487	11	r	r	NOUN
ejpam-5431	487	12	(	(	PUNCT
ejpam-5431	487	13	s	s	PROPN
ejpam-5431	487	14	,	,	PUNCT
ejpam-5431	487	15	t	t	NOUN
ejpam-5431	487	16	)	)	PUNCT
ejpam-5431	487	17	(	(	PUNCT
ejpam-5431	487	18	σ	σ	PROPN
ejpam-5431	487	19	,	,	PUNCT
ejpam-5431	487	20	τ	τ	PROPN
ejpam-5431	487	21	)	)	PUNCT
ejpam-5431	487	22	)	)	PUNCT
ejpam-5431	487	23	=	=	SYM
ejpam-5431	487	24	1	1	NUM
ejpam-5431	487	25	2	2	NUM
ejpam-5431	487	26	φ(m	φ(m	NOUN
ejpam-5431	487	27	r	r	NOUN
ejpam-5431	487	28	(	(	PUNCT
ejpam-5431	487	29	s	s	PROPN
ejpam-5431	487	30	,	,	PUNCT
ejpam-5431	487	31	t	t	NOUN
ejpam-5431	487	32	)	)	PUNCT
ejpam-5431	487	33	(	(	PUNCT
ejpam-5431	487	34	σ	σ	PROPN
ejpam-5431	487	35	,	,	PUNCT
ejpam-5431	487	36	τ	τ	PROPN
ejpam-5431	487	37	)	)	PUNCT
ejpam-5431	487	38	)	)	PUNCT
ejpam-5431	487	39	)	)	PUNCT
ejpam-5431	487	40	≥	≥	X
ejpam-5431	487	41	0	0	NUM
ejpam-5431	487	42	similarly	similarly	ADV
ejpam-5431	487	43	,	,	PUNCT
ejpam-5431	487	44	℘(0	℘(0	NOUN
ejpam-5431	487	45	,	,	PUNCT
ejpam-5431	487	46	φ(m	φ(m	ADJ
ejpam-5431	487	47	r	r	NOUN
ejpam-5431	487	48	(	(	PUNCT
ejpam-5431	487	49	t	t	NOUN
ejpam-5431	487	50	,	,	PUNCT
ejpam-5431	487	51	s)(σ	s)(σ	PROPN
ejpam-5431	487	52	,	,	PUNCT
ejpam-5431	487	53	τ	τ	PROPN
ejpam-5431	487	54	)	)	PUNCT
ejpam-5431	487	55	)	)	PUNCT
ejpam-5431	487	56	)	)	PUNCT
ejpam-5431	487	57	≥	≥	NOUN
ejpam-5431	487	58	0	0	NUM
ejpam-5431	487	59	.	.	PUNCT
ejpam-5431	488	1	moreover	moreover	ADV
ejpam-5431	488	2	,	,	PUNCT
ejpam-5431	488	3	it	it	PRON
ejpam-5431	488	4	is	be	AUX
ejpam-5431	488	5	clear	clear	ADJ
ejpam-5431	488	6	that	that	SCONJ
ejpam-5431	488	7	the	the	DET
ejpam-5431	488	8	pair	pair	NOUN
ejpam-5431	488	9	(	(	PUNCT
ejpam-5431	488	10	s	s	PROPN
ejpam-5431	488	11	,	,	PUNCT
ejpam-5431	488	12	t	t	PROPN
ejpam-5431	488	13	)	)	PUNCT
ejpam-5431	488	14	is	be	AUX
ejpam-5431	488	15	γ	γ	X
ejpam-5431	488	16	-	-	ADJ
ejpam-5431	488	17	admissible	admissible	ADJ
ejpam-5431	488	18	,	,	PUNCT
ejpam-5431	488	19	ℵ-continuous	ℵ-continuous	ADJ
ejpam-5431	488	20	and	and	CCONJ
ejpam-5431	488	21	[	[	X
ejpam-5431	488	22	sσ](⋉,β	sσ](⋉,β	PROPN
ejpam-5431	488	23	)	)	PUNCT
ejpam-5431	488	24	,	,	PUNCT
ejpam-5431	489	1	[	[	X
ejpam-5431	489	2	t	t	NOUN
ejpam-5431	489	3	σ](⋉,β	σ](⋉,β	NOUN
ejpam-5431	489	4	)	)	PUNCT
ejpam-5431	489	5	are	be	AUX
ejpam-5431	489	6	proximal	proximal	ADJ
ejpam-5431	489	7	for	for	ADP
ejpam-5431	489	8	each	each	DET
ejpam-5431	489	9	σ	σ	PROPN
ejpam-5431	489	10	∈	∈	PROPN
ejpam-5431	489	11	x.	x.	NOUN
ejpam-5431	489	12	as	as	SCONJ
ejpam-5431	489	13	the	the	DET
ejpam-5431	489	14	conditions	condition	NOUN
ejpam-5431	489	15	outlined	outline	VERB
ejpam-5431	489	16	in	in	ADP
ejpam-5431	489	17	theorem	theorem	ADJ
ejpam-5431	489	18	2	2	NUM
ejpam-5431	489	19	are	be	AUX
ejpam-5431	489	20	fulfilled	fulfil	VERB
ejpam-5431	489	21	,	,	PUNCT
ejpam-5431	489	22	we	we	PRON
ejpam-5431	489	23	see	see	VERB
ejpam-5431	489	24	that	that	DET
ejpam-5431	489	25	s	s	VERB
ejpam-5431	489	26	and	and	CCONJ
ejpam-5431	489	27	t	t	PROPN
ejpam-5431	489	28	have	have	VERB
ejpam-5431	489	29	many	many	ADJ
ejpam-5431	489	30	common	common	ADJ
ejpam-5431	489	31	iffps	iffps	NOUN
ejpam-5431	489	32	.	.	PUNCT
ejpam-5431	490	1	here	here	ADV
ejpam-5431	490	2	is	be	AUX
ejpam-5431	490	3	another	another	DET
ejpam-5431	490	4	example(non	example(non	NOUN
ejpam-5431	490	5	-	-	PUNCT
ejpam-5431	490	6	trivial	trivial	ADJ
ejpam-5431	490	7	)	)	PUNCT
ejpam-5431	490	8	for	for	ADP
ejpam-5431	490	9	our	our	PRON
ejpam-5431	490	10	main	main	ADJ
ejpam-5431	490	11	result	result	NOUN
ejpam-5431	490	12	,	,	PUNCT
ejpam-5431	490	13	example	example	NOUN
ejpam-5431	490	14	27	27	NUM
ejpam-5431	490	15	.	.	PUNCT
ejpam-5431	491	1	let	let	VERB
ejpam-5431	491	2	x	x	SYM
ejpam-5431	491	3	=	=	PUNCT
ejpam-5431	491	4	lp(r	lp(r	X
ejpam-5431	491	5	)	)	PUNCT
ejpam-5431	491	6	with	with	ADP
ejpam-5431	491	7	0	0	NUM
ejpam-5431	491	8	<	<	X
ejpam-5431	491	9	p	p	X
ejpam-5431	491	10	<	<	X
ejpam-5431	491	11	1	1	NUM
ejpam-5431	491	12	,	,	PUNCT
ejpam-5431	491	13	where	where	SCONJ
ejpam-5431	491	14	lp(r	lp(r	PUNCT
ejpam-5431	491	15	)	)	PUNCT
ejpam-5431	491	16	=	=	SYM
ejpam-5431	491	17	{	{	PUNCT
ejpam-5431	491	18	σ	σ	NOUN
ejpam-5431	491	19	=	=	SYM
ejpam-5431	491	20	{	{	PUNCT
ejpam-5431	491	21	σn	σn	NOUN
ejpam-5431	491	22	}	}	PUNCT
ejpam-5431	491	23	⊂	⊂	NOUN
ejpam-5431	491	24	r	r	NOUN
ejpam-5431	491	25	:	:	PUNCT
ejpam-5431	491	26	∑+∞n=1|σn|p	∑+∞n=1|σn|p	NOUN
ejpam-5431	491	27	<	<	X
ejpam-5431	491	28	+	+	NOUN
ejpam-5431	491	29	∞	∞	NOUN
ejpam-5431	491	30	}	}	PUNCT
ejpam-5431	491	31	.	.	PUNCT
ejpam-5431	492	1	then	then	ADV
ejpam-5431	492	2	δ(σ	δ(σ	PROPN
ejpam-5431	492	3	,	,	PUNCT
ejpam-5431	492	4	τ	τ	X
ejpam-5431	492	5	)	)	PUNCT
ejpam-5431	492	6	=	=	NOUN
ejpam-5431	492	7	(	(	PUNCT
ejpam-5431	492	8	∑+∞	∑+∞	ADJ
ejpam-5431	492	9	n=1	n=1	PROPN
ejpam-5431	492	10	|σn	|σn	NUM
ejpam-5431	492	11	−	−	PROPN
ejpam-5431	492	12	yn|p	yn|p	NOUN
ejpam-5431	492	13	)	)	PUNCT
ejpam-5431	492	14	1	1	NUM
ejpam-5431	492	15	p	p	NOUN
ejpam-5431	492	16	is	be	AUX
ejpam-5431	492	17	a	a	DET
ejpam-5431	492	18	complete	complete	ADJ
ejpam-5431	492	19	b	b	NOUN
ejpam-5431	492	20	-	-	PUNCT
ejpam-5431	492	21	ms	ms	NOUN
ejpam-5431	492	22	on	on	ADP
ejpam-5431	492	23	x	x	PUNCT
ejpam-5431	492	24	with	with	ADP
ejpam-5431	492	25	h	h	NOUN
ejpam-5431	492	26	=	=	SYM
ejpam-5431	492	27	2	2	NUM
ejpam-5431	492	28	1	1	NUM
ejpam-5431	492	29	p	p	NOUN
ejpam-5431	492	30	,	,	PUNCT
ejpam-5431	492	31	consider	consider	VERB
ejpam-5431	492	32	ifs	ifs	PROPN
ejpam-5431	492	33	-	-	PUNCT
ejpam-5431	492	34	valued	value	VERB
ejpam-5431	492	35	maps	map	NOUN
ejpam-5431	492	36	s	s	PROPN
ejpam-5431	492	37	,	,	PUNCT
ejpam-5431	492	38	t	t	X
ejpam-5431	492	39	:	:	PUNCT
ejpam-5431	492	40	x	x	X
ejpam-5431	492	41	→	→	SYM
ejpam-5431	492	42	ifs(x	ifs(x	PROPN
ejpam-5431	492	43	)	)	PUNCT
ejpam-5431	492	44	and	and	CCONJ
ejpam-5431	492	45	sσ	sσ	NOUN
ejpam-5431	492	46	,	,	PUNCT
ejpam-5431	492	47	t	t	PROPN
ejpam-5431	492	48	σ	σ	NOUN
ejpam-5431	492	49	are	be	AUX
ejpam-5431	492	50	ifss	ifss	ADJ
ejpam-5431	492	51	such	such	ADJ
ejpam-5431	492	52	that	that	SCONJ
ejpam-5431	492	53	µt	µt	PROPN
ejpam-5431	492	54	σ	σ	X
ejpam-5431	492	55	:	:	PUNCT
ejpam-5431	492	56	x	x	X
ejpam-5431	492	57	→	→	PUNCT
ejpam-5431	492	58	[	[	X
ejpam-5431	492	59	0	0	NUM
ejpam-5431	492	60	,	,	PUNCT
ejpam-5431	492	61	1	1	NUM
ejpam-5431	492	62	]	]	PUNCT
ejpam-5431	492	63	,	,	PUNCT
ejpam-5431	492	64	µsσ	µsσ	VERB
ejpam-5431	492	65	:	:	PUNCT
ejpam-5431	492	66	x	x	X
ejpam-5431	492	67	→	→	SYM
ejpam-5431	492	68	[	[	X
ejpam-5431	492	69	0	0	NUM
ejpam-5431	492	70	,	,	PUNCT
ejpam-5431	492	71	1	1	NUM
ejpam-5431	492	72	]	]	PUNCT
ejpam-5431	492	73	are	be	AUX
ejpam-5431	492	74	membership	membership	NOUN
ejpam-5431	492	75	functions	function	NOUN
ejpam-5431	492	76	of	of	ADP
ejpam-5431	492	77	t	t	PROPN
ejpam-5431	492	78	σ	σ	PROPN
ejpam-5431	492	79	and	and	CCONJ
ejpam-5431	492	80	sσ	sσ	PROPN
ejpam-5431	492	81	n.	n.	PROPN
ejpam-5431	492	82	saleem	saleem	PROPN
ejpam-5431	493	1	et	et	PROPN
ejpam-5431	493	2	al	al	PROPN
ejpam-5431	493	3	.	.	PUNCT
ejpam-5431	493	4	/	/	SYM
ejpam-5431	493	5	eur	eur	PROPN
ejpam-5431	493	6	.	.	PUNCT
ejpam-5431	494	1	j.	j.	PROPN
ejpam-5431	494	2	pure	pure	PROPN
ejpam-5431	494	3	appl	appl	PROPN
ejpam-5431	494	4	.	.	PROPN
ejpam-5431	494	5	math	math	PROPN
ejpam-5431	494	6	,	,	PUNCT
ejpam-5431	494	7	17	17	NUM
ejpam-5431	494	8	(	(	PUNCT
ejpam-5431	494	9	4	4	NUM
ejpam-5431	494	10	)	)	PUNCT
ejpam-5431	494	11	(	(	PUNCT
ejpam-5431	494	12	2024	2024	NUM
ejpam-5431	494	13	)	)	PUNCT
ejpam-5431	494	14	,	,	PUNCT
ejpam-5431	494	15	3304	3304	NUM
ejpam-5431	494	16	-	-	SYM
ejpam-5431	494	17	3335	3335	NUM
ejpam-5431	494	18	3324	3324	NUM
ejpam-5431	494	19	respectively	respectively	ADV
ejpam-5431	494	20	and	and	CCONJ
ejpam-5431	494	21	νt	νt	PROPN
ejpam-5431	494	22	σ	σ	NOUN
ejpam-5431	494	23	:	:	PUNCT
ejpam-5431	494	24	x	x	X
ejpam-5431	495	1	→	→	PUNCT
ejpam-5431	495	2	[	[	X
ejpam-5431	495	3	0	0	NUM
ejpam-5431	495	4	,	,	PUNCT
ejpam-5431	495	5	1	1	NUM
ejpam-5431	495	6	]	]	PUNCT
ejpam-5431	495	7	and	and	CCONJ
ejpam-5431	495	8	νsσ	νsσ	NOUN
ejpam-5431	495	9	:	:	PUNCT
ejpam-5431	495	10	x	x	X
ejpam-5431	495	11	→	→	PUNCT
ejpam-5431	495	12	[	[	X
ejpam-5431	495	13	0	0	NUM
ejpam-5431	495	14	,	,	PUNCT
ejpam-5431	495	15	1	1	NUM
ejpam-5431	495	16	]	]	PUNCT
ejpam-5431	495	17	are	be	AUX
ejpam-5431	495	18	non	non	ADJ
ejpam-5431	495	19	-	-	ADJ
ejpam-5431	495	20	membership	membership	ADJ
ejpam-5431	495	21	functions	function	NOUN
ejpam-5431	495	22	of	of	ADP
ejpam-5431	495	23	t	t	PROPN
ejpam-5431	495	24	σ	σ	PROPN
ejpam-5431	495	25	and	and	CCONJ
ejpam-5431	495	26	sσ	sσ	VERB
ejpam-5431	495	27	respectively	respectively	ADV
ejpam-5431	495	28	with	with	ADP
ejpam-5431	495	29	µt	µt	PRON
ejpam-5431	495	30	σ(t)+νt	σ(t)+νt	VERB
ejpam-5431	495	31	σ(t	σ(t	PROPN
ejpam-5431	495	32	)	)	PUNCT
ejpam-5431	495	33	≤	≤	NUM
ejpam-5431	495	34	1	1	NUM
ejpam-5431	495	35	and	and	CCONJ
ejpam-5431	495	36	µsσ(t)+νsσ(t	µsσ(t)+νsσ(t	PROPN
ejpam-5431	495	37	)	)	PUNCT
ejpam-5431	495	38	≤	≤	ADV
ejpam-5431	495	39	1	1	NUM
ejpam-5431	495	40	for	for	ADP
ejpam-5431	495	41	all	all	DET
ejpam-5431	495	42	t	t	NOUN
ejpam-5431	495	43	∈	∈	NOUN
ejpam-5431	495	44	x.	x.	PUNCT
ejpam-5431	496	1	µtσ(t	µtσ(t	PROPN
ejpam-5431	496	2	)	)	PUNCT
ejpam-5431	496	3	=	=	PUNCT
ejpam-5431	497	1			PUNCT
ejpam-5431	497	2	1	1	NUM
ejpam-5431	497	3	8	8	NUM
ejpam-5431	497	4	,	,	PUNCT
ejpam-5431	497	5	if	if	SCONJ
ejpam-5431	497	6	t	t	PROPN
ejpam-5431	497	7	contains	contain	VERB
ejpam-5431	497	8	finite	finite	ADJ
ejpam-5431	497	9	number	number	NOUN
ejpam-5431	497	10	of	of	ADP
ejpam-5431	497	11	zero	zero	NUM
ejpam-5431	497	12	9	9	NUM
ejpam-5431	497	13	10	10	NUM
ejpam-5431	497	14	,	,	PUNCT
ejpam-5431	497	15	if	if	SCONJ
ejpam-5431	497	16	t	t	PROPN
ejpam-5431	497	17	contains	contain	VERB
ejpam-5431	497	18	infinite	infinite	ADJ
ejpam-5431	497	19	number	number	NOUN
ejpam-5431	497	20	of	of	ADP
ejpam-5431	497	21	zero	zero	NUM
ejpam-5431	497	22	1	1	NUM
ejpam-5431	497	23	100	100	NUM
ejpam-5431	497	24	,	,	PUNCT
ejpam-5431	497	25	if	if	SCONJ
ejpam-5431	497	26	t	t	PROPN
ejpam-5431	497	27	contains	contain	VERB
ejpam-5431	497	28	no	no	DET
ejpam-5431	497	29	zero	zero	NUM
ejpam-5431	497	30	νtσ(t	νtσ(t	PROPN
ejpam-5431	497	31	)	)	PUNCT
ejpam-5431	498	1	=	=	PUNCT
ejpam-5431	498	2			PUNCT
ejpam-5431	498	3	1	1	NUM
ejpam-5431	498	4	5	5	NUM
ejpam-5431	498	5	,	,	PUNCT
ejpam-5431	498	6	if	if	SCONJ
ejpam-5431	498	7	t	t	PROPN
ejpam-5431	498	8	contains	contain	VERB
ejpam-5431	498	9	finite	finite	ADJ
ejpam-5431	498	10	number	number	NOUN
ejpam-5431	498	11	of	of	ADP
ejpam-5431	498	12	zero	zero	NUM
ejpam-5431	498	13	1	1	NUM
ejpam-5431	498	14	120	120	NUM
ejpam-5431	498	15	,	,	PUNCT
ejpam-5431	498	16	if	if	SCONJ
ejpam-5431	498	17	t	t	PROPN
ejpam-5431	498	18	contains	contain	VERB
ejpam-5431	498	19	infinite	infinite	ADJ
ejpam-5431	498	20	number	number	NOUN
ejpam-5431	498	21	of	of	ADP
ejpam-5431	498	22	zero	zero	NUM
ejpam-5431	498	23	1	1	NUM
ejpam-5431	498	24	7	7	NUM
ejpam-5431	498	25	,	,	PUNCT
ejpam-5431	498	26	if	if	SCONJ
ejpam-5431	498	27	t	t	PROPN
ejpam-5431	498	28	contains	contain	VERB
ejpam-5431	498	29	no	no	DET
ejpam-5431	498	30	zero	zero	NUM
ejpam-5431	498	31	µsσ(t	µsσ(t	PROPN
ejpam-5431	498	32	)	)	PUNCT
ejpam-5431	498	33	=	=	PUNCT
ejpam-5431	499	1			PUNCT
ejpam-5431	499	2	1	1	NUM
ejpam-5431	499	3	50	50	NUM
ejpam-5431	499	4	,	,	PUNCT
ejpam-5431	499	5	if	if	SCONJ
ejpam-5431	499	6	t	t	PROPN
ejpam-5431	499	7	contains	contain	VERB
ejpam-5431	499	8	no	no	DET
ejpam-5431	499	9	zero	zero	NUM
ejpam-5431	499	10	2	2	NUM
ejpam-5431	499	11	5	5	NUM
ejpam-5431	499	12	,	,	PUNCT
ejpam-5431	499	13	if	if	SCONJ
ejpam-5431	499	14	t	t	PROPN
ejpam-5431	499	15	contains	contain	VERB
ejpam-5431	499	16	finite	finite	ADJ
ejpam-5431	499	17	number	number	NOUN
ejpam-5431	499	18	of	of	ADP
ejpam-5431	499	19	zero	zero	NUM
ejpam-5431	499	20	7	7	NUM
ejpam-5431	499	21	10	10	NUM
ejpam-5431	499	22	,	,	PUNCT
ejpam-5431	499	23	if	if	SCONJ
ejpam-5431	499	24	t	t	PROPN
ejpam-5431	499	25	contains	contain	VERB
ejpam-5431	499	26	infinite	infinite	ADJ
ejpam-5431	499	27	number	number	NOUN
ejpam-5431	499	28	of	of	ADP
ejpam-5431	499	29	zero	zero	NUM
ejpam-5431	499	30	νsσ(t	νsσ(t	PROPN
ejpam-5431	499	31	)	)	PUNCT
ejpam-5431	499	32	=	=	PUNCT
ejpam-5431	500	1			PUNCT
ejpam-5431	500	2	1	1	NUM
ejpam-5431	500	3	9	9	NUM
ejpam-5431	500	4	,	,	PUNCT
ejpam-5431	500	5	if	if	SCONJ
ejpam-5431	500	6	t	t	PROPN
ejpam-5431	500	7	contains	contain	VERB
ejpam-5431	500	8	no	no	DET
ejpam-5431	500	9	zero	zero	NUM
ejpam-5431	500	10	3	3	NUM
ejpam-5431	500	11	7	7	NUM
ejpam-5431	500	12	,	,	PUNCT
ejpam-5431	500	13	if	if	SCONJ
ejpam-5431	500	14	t	t	PROPN
ejpam-5431	500	15	contains	contain	VERB
ejpam-5431	500	16	finite	finite	ADJ
ejpam-5431	500	17	number	number	NOUN
ejpam-5431	500	18	of	of	ADP
ejpam-5431	500	19	zero	zero	NUM
ejpam-5431	500	20	2	2	NUM
ejpam-5431	500	21	15	15	NUM
ejpam-5431	500	22	,	,	PUNCT
ejpam-5431	500	23	if	if	SCONJ
ejpam-5431	500	24	t	t	PROPN
ejpam-5431	500	25	contains	contain	VERB
ejpam-5431	500	26	infinite	infinite	ADJ
ejpam-5431	500	27	number	number	NOUN
ejpam-5431	500	28	of	of	ADP
ejpam-5431	500	29	zero	zero	NUM
ejpam-5431	500	30	let	let	VERB
ejpam-5431	500	31	⋉	⋉	PROPN
ejpam-5431	500	32	=	=	SYM
ejpam-5431	500	33	1	1	NUM
ejpam-5431	500	34	2	2	NUM
ejpam-5431	500	35	and	and	CCONJ
ejpam-5431	500	36	β	β	X
ejpam-5431	500	37	=	=	SYM
ejpam-5431	500	38	1	1	NUM
ejpam-5431	500	39	6	6	NUM
ejpam-5431	500	40	,	,	PUNCT
ejpam-5431	500	41	then	then	ADV
ejpam-5431	500	42	[	[	X
ejpam-5431	500	43	tσ](⋉,β	tσ](⋉,β	NOUN
ejpam-5431	500	44	)	)	PUNCT
ejpam-5431	500	45	=	=	SYM
ejpam-5431	500	46	{	{	PUNCT
ejpam-5431	500	47	t	t	PROPN
ejpam-5431	500	48	contains	contain	VERB
ejpam-5431	500	49	infinitely	infinitely	ADV
ejpam-5431	500	50	many	many	ADJ
ejpam-5431	500	51	zeros	zero	NOUN
ejpam-5431	500	52	}	}	PUNCT
ejpam-5431	500	53	and	and	CCONJ
ejpam-5431	501	1	[	[	X
ejpam-5431	501	2	sσ](⋉,β	sσ](⋉,β	PROPN
ejpam-5431	501	3	)	)	PUNCT
ejpam-5431	501	4	=	=	PRON
ejpam-5431	501	5	{	{	PUNCT
ejpam-5431	501	6	t	t	PROPN
ejpam-5431	501	7	contains	contain	VERB
ejpam-5431	501	8	infinitely	infinitely	ADV
ejpam-5431	501	9	many	many	ADJ
ejpam-5431	501	10	zeros	zero	NOUN
ejpam-5431	501	11	}	}	PUNCT
ejpam-5431	501	12	clearly	clearly	ADV
ejpam-5431	501	13	sσ	sσ	ADJ
ejpam-5431	501	14	,	,	PUNCT
ejpam-5431	501	15	t	t	PROPN
ejpam-5431	501	16	σ	σ	PROPN
ejpam-5431	501	17	∈	∈	PROPN
ejpam-5431	501	18	ifs(x	ifs(x	PROPN
ejpam-5431	501	19	)	)	PUNCT
ejpam-5431	501	20	for	for	ADP
ejpam-5431	501	21	each	each	DET
ejpam-5431	501	22	σ	σ	PROPN
ejpam-5431	501	23	∈	∈	PROPN
ejpam-5431	501	24	x.	x.	NOUN
ejpam-5431	501	25	define	define	VERB
ejpam-5431	501	26	the	the	DET
ejpam-5431	501	27	functions	function	NOUN
ejpam-5431	501	28	γ	γ	X
ejpam-5431	501	29	:	:	PUNCT
ejpam-5431	501	30	x	x	X
ejpam-5431	501	31	×x	×x	ADP
ejpam-5431	501	32	→	→	PUNCT
ejpam-5431	501	33	r+	r+	X
ejpam-5431	501	34	and	and	CCONJ
ejpam-5431	501	35	φ	φ	NOUN
ejpam-5431	501	36	:	:	PUNCT
ejpam-5431	501	37	r+	r+	X
ejpam-5431	501	38	→	→	SYM
ejpam-5431	501	39	r+	r+	NOUN
ejpam-5431	501	40	by	by	ADP
ejpam-5431	501	41	γ(σ	γ(σ	PROPN
ejpam-5431	501	42	,	,	PUNCT
ejpam-5431	501	43	τ	τ	X
ejpam-5431	501	44	)	)	PUNCT
ejpam-5431	501	45	=	=	NOUN
ejpam-5431	501	46	{	{	PUNCT
ejpam-5431	501	47	7	7	NUM
ejpam-5431	501	48	,	,	PUNCT
ejpam-5431	501	49	if	if	SCONJ
ejpam-5431	501	50	σ	σ	PROPN
ejpam-5431	501	51	=	=	SYM
ejpam-5431	501	52	y	y	PROPN
ejpam-5431	501	53	10	10	NUM
ejpam-5431	501	54	,	,	PUNCT
ejpam-5431	501	55	elsewhere	elsewhere	ADV
ejpam-5431	501	56	.	.	PUNCT
ejpam-5431	501	57	and	and	CCONJ
ejpam-5431	501	58	φ(t	φ(t	PROPN
ejpam-5431	501	59	)	)	PUNCT
ejpam-5431	501	60	=	=	PUNCT
ejpam-5431	501	61	t	t	PROPN
ejpam-5431	501	62	4	4	NUM
ejpam-5431	501	63	for	for	ADP
ejpam-5431	501	64	all	all	DET
ejpam-5431	501	65	t	t	PROPN
ejpam-5431	501	66	>	>	X
ejpam-5431	501	67	0	0	X
ejpam-5431	501	68	.	.	PUNCT
ejpam-5431	502	1	let	let	AUX
ejpam-5431	502	2	℘(a	℘(a	PROPN
ejpam-5431	502	3	,	,	PUNCT
ejpam-5431	502	4	b	b	NOUN
ejpam-5431	502	5	)	)	PUNCT
ejpam-5431	502	6	=	=	SYM
ejpam-5431	502	7	b−a	b−a	ADP
ejpam-5431	502	8	10	10	NUM
ejpam-5431	502	9	for	for	ADP
ejpam-5431	502	10	all	all	DET
ejpam-5431	502	11	a	a	DET
ejpam-5431	502	12	,	,	PUNCT
ejpam-5431	502	13	b	b	X
ejpam-5431	502	14	∈	∈	PROPN
ejpam-5431	502	15	r+	r+	X
ejpam-5431	502	16	.	.	PUNCT
ejpam-5431	503	1	obviously	obviously	ADV
ejpam-5431	503	2	℘	℘	VERB
ejpam-5431	503	3	∈	∈	PROPN
ejpam-5431	503	4	z	z	NOUN
ejpam-5431	503	5	and	and	CCONJ
ejpam-5431	503	6	φ	φ	PROPN
ejpam-5431	503	7	∈	∈	PROPN
ejpam-5431	503	8	λb	λb	X
ejpam-5431	503	9	.	.	PUNCT
ejpam-5431	504	1	also	also	ADV
ejpam-5431	504	2	,	,	PUNCT
ejpam-5431	504	3	ℵ([sσ](⋉,β	ℵ([sσ](⋉,β	PROPN
ejpam-5431	504	4	)	)	PUNCT
ejpam-5431	504	5	,	,	PUNCT
ejpam-5431	504	6	[	[	X
ejpam-5431	504	7	tσ](⋉,β	tσ](⋉,β	NOUN
ejpam-5431	504	8	)	)	PUNCT
ejpam-5431	504	9	=	=	SYM
ejpam-5431	504	10	max	max	PROPN
ejpam-5431	504	11	(	(	PUNCT
ejpam-5431	504	12	∞∑	∞∑	NUM
ejpam-5431	504	13	i=1	i=1	X
ejpam-5431	504	14	|σi	|σi	X
ejpam-5431	504	15	−	−	PROPN
ejpam-5431	504	16	yi|p	yi|p	NOUN
ejpam-5431	504	17	)	)	PUNCT
ejpam-5431	504	18	1	1	NUM
ejpam-5431	505	1	p	p	NOUN
ejpam-5431	505	2	clearly	clearly	ADV
ejpam-5431	505	3	,	,	PUNCT
ejpam-5431	505	4	℘(γ(σ	℘(γ(σ	ADJ
ejpam-5431	505	5	,	,	PUNCT
ejpam-5431	505	6	τ)ℵ([t	τ)ℵ([t	PROPN
ejpam-5431	505	7	σ](⋉,β	σ](⋉,β	NUM
ejpam-5431	505	8	)	)	PUNCT
ejpam-5431	505	9	,	,	PUNCT
ejpam-5431	505	10	[	[	X
ejpam-5431	505	11	sτ	sτ	ADP
ejpam-5431	505	12	]	]	PUNCT
ejpam-5431	505	13	(	(	PUNCT
ejpam-5431	505	14	⋉,β	⋉,β	NOUN
ejpam-5431	505	15	)	)	PUNCT
ejpam-5431	505	16	)	)	PUNCT
ejpam-5431	505	17	,	,	PUNCT
ejpam-5431	505	18	φ(m	φ(m	ADJ
ejpam-5431	505	19	r	r	NOUN
ejpam-5431	505	20	(	(	PUNCT
ejpam-5431	505	21	t	t	NOUN
ejpam-5431	505	22	,	,	PUNCT
ejpam-5431	505	23	s)(σ	s)(σ	PROPN
ejpam-5431	505	24	,	,	PUNCT
ejpam-5431	505	25	τ	τ	PROPN
ejpam-5431	505	26	)	)	PUNCT
ejpam-5431	505	27	)	)	PUNCT
ejpam-5431	505	28	)	)	PUNCT
ejpam-5431	506	1	≥	≥	NOUN
ejpam-5431	506	2	0	0	PUNCT
ejpam-5431	507	1	as	as	SCONJ
ejpam-5431	507	2	it	it	PRON
ejpam-5431	507	3	can	can	AUX
ejpam-5431	507	4	be	be	AUX
ejpam-5431	507	5	seen	see	VERB
ejpam-5431	507	6	that	that	SCONJ
ejpam-5431	507	7	the	the	DET
ejpam-5431	507	8	pair	pair	NOUN
ejpam-5431	507	9	(	(	PUNCT
ejpam-5431	507	10	s	s	PROPN
ejpam-5431	507	11	,	,	PUNCT
ejpam-5431	507	12	t	t	PROPN
ejpam-5431	507	13	)	)	PUNCT
ejpam-5431	507	14	is	be	AUX
ejpam-5431	507	15	γ	γ	X
ejpam-5431	507	16	-	-	ADJ
ejpam-5431	507	17	admissible	admissible	ADJ
ejpam-5431	507	18	,	,	PUNCT
ejpam-5431	507	19	ℵ-continuous	ℵ-continuous	ADJ
ejpam-5431	507	20	and	and	CCONJ
ejpam-5431	507	21	[	[	X
ejpam-5431	507	22	sσ](⋉,β	sσ](⋉,β	PROPN
ejpam-5431	507	23	)	)	PUNCT
ejpam-5431	507	24	,	,	PUNCT
ejpam-5431	508	1	[	[	X
ejpam-5431	508	2	t	t	NOUN
ejpam-5431	508	3	σ](⋉,β	σ](⋉,β	NOUN
ejpam-5431	508	4	)	)	PUNCT
ejpam-5431	508	5	are	be	AUX
ejpam-5431	508	6	proximal	proximal	ADJ
ejpam-5431	508	7	for	for	ADP
ejpam-5431	508	8	each	each	DET
ejpam-5431	508	9	σ	σ	PROPN
ejpam-5431	508	10	∈	∈	PROPN
ejpam-5431	508	11	x.	x.	NOUN
ejpam-5431	508	12	since	since	SCONJ
ejpam-5431	508	13	the	the	DET
ejpam-5431	508	14	conditions	condition	NOUN
ejpam-5431	508	15	in	in	ADP
ejpam-5431	508	16	theorem	theorem	ADJ
ejpam-5431	508	17	2	2	NUM
ejpam-5431	508	18	are	be	AUX
ejpam-5431	508	19	fulfilled	fulfil	VERB
ejpam-5431	508	20	,	,	PUNCT
ejpam-5431	508	21	we	we	PRON
ejpam-5431	508	22	see	see	VERB
ejpam-5431	508	23	that	that	DET
ejpam-5431	508	24	s	s	VERB
ejpam-5431	508	25	and	and	CCONJ
ejpam-5431	508	26	t	t	PROPN
ejpam-5431	508	27	have	have	VERB
ejpam-5431	508	28	many	many	ADJ
ejpam-5431	508	29	common	common	ADJ
ejpam-5431	508	30	iffps	iffps	NOUN
ejpam-5431	508	31	.	.	PUNCT
ejpam-5431	509	1	n.	n.	PROPN
ejpam-5431	509	2	saleem	saleem	PROPN
ejpam-5431	509	3	et	et	PROPN
ejpam-5431	509	4	al	al	PROPN
ejpam-5431	509	5	.	.	PUNCT
ejpam-5431	509	6	/	/	SYM
ejpam-5431	509	7	eur	eur	PROPN
ejpam-5431	509	8	.	.	PUNCT
ejpam-5431	510	1	j.	j.	PROPN
ejpam-5431	510	2	pure	pure	PROPN
ejpam-5431	510	3	appl	appl	PROPN
ejpam-5431	510	4	.	.	PROPN
ejpam-5431	510	5	math	math	PROPN
ejpam-5431	510	6	,	,	PUNCT
ejpam-5431	510	7	17	17	NUM
ejpam-5431	510	8	(	(	PUNCT
ejpam-5431	510	9	4	4	NUM
ejpam-5431	510	10	)	)	PUNCT
ejpam-5431	510	11	(	(	PUNCT
ejpam-5431	510	12	2024	2024	NUM
ejpam-5431	510	13	)	)	PUNCT
ejpam-5431	510	14	,	,	PUNCT
ejpam-5431	510	15	3304	3304	NUM
ejpam-5431	510	16	-	-	SYM
ejpam-5431	510	17	3335	3335	NUM
ejpam-5431	510	18	3325	3325	NUM
ejpam-5431	510	19	0.5	0.5	NUM
ejpam-5431	510	20	1.0	1.0	NUM
ejpam-5431	510	21	1.5	1.5	NUM
ejpam-5431	510	22	2.0	2.0	NUM
ejpam-5431	510	23	2.5	2.5	NUM
ejpam-5431	510	24	3.0	3.0	NUM
ejpam-5431	510	25	ϱ	ϱ	ADP
ejpam-5431	510	26	5	5	NUM
ejpam-5431	510	27	10	10	NUM
ejpam-5431	510	28	15	15	NUM
ejpam-5431	510	29	[	[	X
ejpam-5431	510	30	tϱ]	tϱ]	NOUN
ejpam-5431	510	31	�	�	PROPN
ejpam-5431	510	32	�	�	PROPN
ejpam-5431	510	33	,β	,β	PUNCT
ejpam-5431	510	34	figure	figure	VERB
ejpam-5431	510	35	3	3	NUM
ejpam-5431	510	36	:	:	PUNCT
ejpam-5431	510	37	graph	graph	NOUN
ejpam-5431	510	38	representing	represent	VERB
ejpam-5431	510	39	common	common	ADJ
ejpam-5431	510	40	fixed	fix	VERB
ejpam-5431	510	41	points	point	NOUN
ejpam-5431	510	42	of	of	ADP
ejpam-5431	510	43	the	the	DET
ejpam-5431	510	44	given	give	VERB
ejpam-5431	510	45	mappings	mapping	NOUN
ejpam-5431	510	46	in	in	ADP
ejpam-5431	510	47	example	example	NOUN
ejpam-5431	510	48	25	25	NUM
ejpam-5431	510	49	.	.	NOUN
ejpam-5431	511	1	4	4	NUM
ejpam-5431	511	2	.	.	NUM
ejpam-5431	511	3	consequences	consequence	NOUN
ejpam-5431	511	4	in	in	ADP
ejpam-5431	511	5	this	this	DET
ejpam-5431	511	6	section	section	NOUN
ejpam-5431	511	7	,	,	PUNCT
ejpam-5431	511	8	we	we	PRON
ejpam-5431	511	9	demonstrate	demonstrate	VERB
ejpam-5431	511	10	how	how	SCONJ
ejpam-5431	511	11	our	our	PRON
ejpam-5431	511	12	primary	primary	ADJ
ejpam-5431	511	13	theorem	theorem	NOUN
ejpam-5431	511	14	can	can	AUX
ejpam-5431	511	15	be	be	AUX
ejpam-5431	511	16	used	use	VERB
ejpam-5431	511	17	to	to	PART
ejpam-5431	511	18	obtain	obtain	VERB
ejpam-5431	511	19	a	a	DET
ejpam-5431	511	20	few	few	ADJ
ejpam-5431	511	21	intriguing	intriguing	ADJ
ejpam-5431	511	22	fixed	fix	VERB
ejpam-5431	511	23	point	point	NOUN
ejpam-5431	511	24	conclusions	conclusion	NOUN
ejpam-5431	511	25	,	,	PUNCT
ejpam-5431	511	26	particularly	particularly	ADV
ejpam-5431	511	27	when	when	SCONJ
ejpam-5431	511	28	using	use	VERB
ejpam-5431	511	29	different	different	ADJ
ejpam-5431	511	30	simulation	simulation	NOUN
ejpam-5431	511	31	function	function	NOUN
ejpam-5431	511	32	variations	variation	NOUN
ejpam-5431	511	33	.	.	PUNCT
ejpam-5431	512	1	all	all	PRON
ejpam-5431	512	2	of	of	ADP
ejpam-5431	512	3	the	the	DET
ejpam-5431	512	4	results	result	NOUN
ejpam-5431	512	5	reported	report	VERB
ejpam-5431	512	6	here	here	ADV
ejpam-5431	512	7	are	be	AUX
ejpam-5431	512	8	also	also	ADV
ejpam-5431	512	9	new	new	ADJ
ejpam-5431	512	10	as	as	ADV
ejpam-5431	512	11	far	far	ADV
ejpam-5431	512	12	as	as	SCONJ
ejpam-5431	512	13	we	we	PRON
ejpam-5431	512	14	can	can	AUX
ejpam-5431	512	15	tell	tell	VERB
ejpam-5431	512	16	.	.	PUNCT
ejpam-5431	513	1	corollary	corollary	ADJ
ejpam-5431	513	2	1	1	NUM
ejpam-5431	513	3	.	.	PUNCT
ejpam-5431	514	1	let	let	AUX
ejpam-5431	514	2	(	(	PUNCT
ejpam-5431	514	3	x	x	NOUN
ejpam-5431	514	4	,	,	PUNCT
ejpam-5431	514	5	δ	δ	PROPN
ejpam-5431	514	6	,	,	PUNCT
ejpam-5431	514	7	h	h	NOUN
ejpam-5431	514	8	)	)	PUNCT
ejpam-5431	514	9	be	be	AUX
ejpam-5431	514	10	a	a	DET
ejpam-5431	514	11	complete	complete	ADJ
ejpam-5431	514	12	b	b	NOUN
ejpam-5431	514	13	-	-	PUNCT
ejpam-5431	514	14	ms	ms	NOUN
ejpam-5431	514	15	and	and	CCONJ
ejpam-5431	514	16	t	t	PROPN
ejpam-5431	514	17	be	be	AUX
ejpam-5431	514	18	an	an	DET
ejpam-5431	514	19	ahif	ahif	PROPN
ejpam-5431	514	20	z	z	PROPN
ejpam-5431	514	21	-	-	PUNCT
ejpam-5431	514	22	contraction	contraction	NOUN
ejpam-5431	514	23	regarding	regard	VERB
ejpam-5431	514	24	℘	℘	PROPN
ejpam-5431	514	25	∈	∈	PROPN
ejpam-5431	514	26	z.	z.	NOUN
ejpam-5431	514	27	let	let	VERB
ejpam-5431	514	28	’s	’s	NOUN
ejpam-5431	514	29	also	also	ADV
ejpam-5431	514	30	consider	consider	VERB
ejpam-5431	514	31	that	that	PRON
ejpam-5431	514	32	:	:	PUNCT
ejpam-5431	514	33	(	(	PUNCT
ejpam-5431	514	34	i	i	NOUN
ejpam-5431	514	35	)	)	PUNCT
ejpam-5431	514	36	t	t	PROPN
ejpam-5431	514	37	is	be	AUX
ejpam-5431	514	38	a	a	DET
ejpam-5431	514	39	γ	γ	NOUN
ejpam-5431	514	40	-	-	ADJ
ejpam-5431	514	41	admissible	admissible	ADJ
ejpam-5431	514	42	ifs	ifs	PROPN
ejpam-5431	514	43	-	-	PUNCT
ejpam-5431	514	44	valued	value	VERB
ejpam-5431	514	45	map	map	NOUN
ejpam-5431	514	46	;	;	PUNCT
ejpam-5431	514	47	(	(	PUNCT
ejpam-5431	514	48	ii	ii	NOUN
ejpam-5431	514	49	)	)	PUNCT
ejpam-5431	514	50	there	there	PRON
ejpam-5431	514	51	are	be	VERB
ejpam-5431	514	52	σ0	σ0	PROPN
ejpam-5431	514	53	∈	∈	PROPN
ejpam-5431	514	54	x	x	X
ejpam-5431	514	55	and	and	CCONJ
ejpam-5431	514	56	σ1	σ1	PROPN
ejpam-5431	514	57	∈	∈	PROPN
ejpam-5431	515	1	[	[	X
ejpam-5431	515	2	t	t	NOUN
ejpam-5431	515	3	σ0](⋉,β	σ0](⋉,β	NUM
ejpam-5431	515	4	)	)	PUNCT
ejpam-5431	515	5	such	such	ADJ
ejpam-5431	515	6	that	that	DET
ejpam-5431	515	7	γ(σ0	γ(σ0	NOUN
ejpam-5431	515	8	,	,	PUNCT
ejpam-5431	515	9	σ1	σ1	PROPN
ejpam-5431	515	10	)	)	PUNCT
ejpam-5431	515	11	≥	≥	NOUN
ejpam-5431	515	12	1	1	NUM
ejpam-5431	515	13	,	,	PUNCT
ejpam-5431	516	1	where	where	SCONJ
ejpam-5431	516	2	(	(	PUNCT
ejpam-5431	516	3	⋉	⋉	PROPN
ejpam-5431	516	4	,	,	PUNCT
ejpam-5431	516	5	β	β	NOUN
ejpam-5431	516	6	)	)	PUNCT
ejpam-5431	516	7	∈	∈	PROPN
ejpam-5431	516	8	(	(	PUNCT
ejpam-5431	516	9	0	0	NUM
ejpam-5431	516	10	,	,	PUNCT
ejpam-5431	516	11	1]×	1]×	NUM
ejpam-5431	516	12	[	[	X
ejpam-5431	516	13	0	0	NUM
ejpam-5431	516	14	,	,	PUNCT
ejpam-5431	516	15	1	1	NUM
ejpam-5431	516	16	)	)	PUNCT
ejpam-5431	516	17	;	;	PUNCT
ejpam-5431	516	18	(	(	PUNCT
ejpam-5431	516	19	iii	iii	X
ejpam-5431	516	20	)	)	PUNCT
ejpam-5431	516	21	t	t	PROPN
ejpam-5431	516	22	is	be	AUX
ejpam-5431	516	23	ℵ-continuous	ℵ-continuous	ADJ
ejpam-5431	516	24	;	;	PUNCT
ejpam-5431	516	25	(	(	PUNCT
ejpam-5431	516	26	iv	iv	X
ejpam-5431	516	27	)	)	PUNCT
ejpam-5431	517	1	[	[	X
ejpam-5431	517	2	t	t	NOUN
ejpam-5431	517	3	σ](⋉,β	σ](⋉,β	NOUN
ejpam-5431	517	4	)	)	PUNCT
ejpam-5431	517	5	is	be	AUX
ejpam-5431	517	6	proximal	proximal	ADJ
ejpam-5431	517	7	for	for	ADP
ejpam-5431	517	8	every	every	DET
ejpam-5431	517	9	σ	σ	PROPN
ejpam-5431	517	10	∈	∈	PROPN
ejpam-5431	517	11	x.	x.	NOUN
ejpam-5431	518	1	then	then	ADV
ejpam-5431	518	2	,	,	PUNCT
ejpam-5431	518	3	t	t	PROPN
ejpam-5431	518	4	has	have	VERB
ejpam-5431	518	5	at	at	ADV
ejpam-5431	518	6	least	least	ADJ
ejpam-5431	518	7	one	one	NUM
ejpam-5431	518	8	iffp	iffp	NOUN
ejpam-5431	518	9	in	in	ADP
ejpam-5431	518	10	x.	x.	NOUN
ejpam-5431	518	11	proof	proof	NOUN
ejpam-5431	518	12	.	.	PUNCT
ejpam-5431	519	1	if	if	SCONJ
ejpam-5431	519	2	we	we	PRON
ejpam-5431	519	3	take	take	VERB
ejpam-5431	519	4	the	the	DET
ejpam-5431	519	5	mapping	mapping	NOUN
ejpam-5431	519	6	t	t	NOUN
ejpam-5431	520	1	=	=	SYM
ejpam-5431	520	2	s	s	NOUN
ejpam-5431	520	3	in	in	ADP
ejpam-5431	520	4	theorem	theorem	NOUN
ejpam-5431	520	5	2	2	NUM
ejpam-5431	520	6	,	,	PUNCT
ejpam-5431	520	7	then	then	ADV
ejpam-5431	520	8	it	it	PRON
ejpam-5431	520	9	can	can	AUX
ejpam-5431	520	10	easily	easily	ADV
ejpam-5431	520	11	be	be	AUX
ejpam-5431	520	12	seen	see	VERB
ejpam-5431	520	13	that	that	SCONJ
ejpam-5431	520	14	the	the	DET
ejpam-5431	520	15	ahif	ahif	PROPN
ejpam-5431	520	16	z	z	PROPN
ejpam-5431	520	17	-	-	PUNCT
ejpam-5431	520	18	contraction	contraction	PROPN
ejpam-5431	520	19	t	t	PROPN
ejpam-5431	520	20	has	have	VERB
ejpam-5431	520	21	many	many	ADJ
ejpam-5431	520	22	iffps	iffps	NOUN
ejpam-5431	520	23	in	in	ADP
ejpam-5431	520	24	x.	x.	NOUN
ejpam-5431	520	25	corollary	corollary	NOUN
ejpam-5431	520	26	2	2	X
ejpam-5431	520	27	.	.	PUNCT
ejpam-5431	521	1	let	let	AUX
ejpam-5431	521	2	(	(	PUNCT
ejpam-5431	521	3	x	x	NOUN
ejpam-5431	521	4	,	,	PUNCT
ejpam-5431	521	5	δ	δ	PROPN
ejpam-5431	521	6	,	,	PUNCT
ejpam-5431	521	7	h	h	NOUN
ejpam-5431	521	8	)	)	PUNCT
ejpam-5431	521	9	be	be	AUX
ejpam-5431	521	10	a	a	DET
ejpam-5431	521	11	complete	complete	ADJ
ejpam-5431	521	12	b	b	NOUN
ejpam-5431	521	13	-	-	PUNCT
ejpam-5431	521	14	ms	ms	NOUN
ejpam-5431	521	15	and	and	CCONJ
ejpam-5431	521	16	t	t	PROPN
ejpam-5431	521	17	be	be	AUX
ejpam-5431	521	18	an	an	DET
ejpam-5431	521	19	ifs	ifs	PROPN
ejpam-5431	521	20	-	-	PUNCT
ejpam-5431	521	21	valued	value	VERB
ejpam-5431	521	22	map	map	NOUN
ejpam-5431	521	23	satisfying	satisfying	ADJ
ejpam-5431	521	24	:	:	PUNCT
ejpam-5431	521	25	(	(	PUNCT
ejpam-5431	521	26	i	i	NOUN
ejpam-5431	521	27	)	)	PUNCT
ejpam-5431	521	28	t	t	PROPN
ejpam-5431	521	29	is	be	AUX
ejpam-5431	521	30	γ	γ	NOUN
ejpam-5431	521	31	-	-	ADJ
ejpam-5431	521	32	admissible	admissible	ADJ
ejpam-5431	521	33	ifs	ifs	PROPN
ejpam-5431	521	34	-	-	PUNCT
ejpam-5431	521	35	valued	value	VERB
ejpam-5431	521	36	map	map	NOUN
ejpam-5431	521	37	;	;	PUNCT
ejpam-5431	521	38	(	(	PUNCT
ejpam-5431	521	39	ii	ii	NOUN
ejpam-5431	521	40	)	)	PUNCT
ejpam-5431	521	41	there	there	PRON
ejpam-5431	521	42	exists	exist	VERB
ejpam-5431	521	43	σ0	σ0	PROPN
ejpam-5431	521	44	∈	∈	PROPN
ejpam-5431	521	45	x	x	X
ejpam-5431	521	46	and	and	CCONJ
ejpam-5431	521	47	σ	σ	NUM
ejpam-5431	521	48	∈	∈	PROPN
ejpam-5431	522	1	[	[	X
ejpam-5431	522	2	t	t	NOUN
ejpam-5431	522	3	σ0](⋉,β	σ0](⋉,β	NUM
ejpam-5431	522	4	)	)	PUNCT
ejpam-5431	522	5	such	such	ADJ
ejpam-5431	522	6	that	that	DET
ejpam-5431	522	7	γ(σ0	γ(σ0	NOUN
ejpam-5431	522	8	,	,	PUNCT
ejpam-5431	522	9	σ1	σ1	PROPN
ejpam-5431	522	10	)	)	PUNCT
ejpam-5431	522	11	≥	≥	NOUN
ejpam-5431	522	12	1	1	NUM
ejpam-5431	523	1	where	where	SCONJ
ejpam-5431	523	2	(	(	PUNCT
ejpam-5431	523	3	⋉	⋉	PROPN
ejpam-5431	523	4	,	,	PUNCT
ejpam-5431	523	5	β	β	NOUN
ejpam-5431	523	6	)	)	PUNCT
ejpam-5431	523	7	∈	∈	PROPN
ejpam-5431	523	8	(	(	PUNCT
ejpam-5431	523	9	0	0	NUM
ejpam-5431	523	10	,	,	PUNCT
ejpam-5431	523	11	1]×	1]×	NUM
ejpam-5431	524	1	[	[	X
ejpam-5431	524	2	0	0	NUM
ejpam-5431	524	3	,	,	PUNCT
ejpam-5431	524	4	1	1	NUM
ejpam-5431	524	5	)	)	PUNCT
ejpam-5431	524	6	;	;	PUNCT
ejpam-5431	524	7	(	(	PUNCT
ejpam-5431	524	8	iii	iii	X
ejpam-5431	524	9	)	)	PUNCT
ejpam-5431	524	10	t	t	PROPN
ejpam-5431	524	11	is	be	AUX
ejpam-5431	524	12	ℵ-continuous	ℵ-continuous	ADJ
ejpam-5431	524	13	;	;	PUNCT
ejpam-5431	524	14	(	(	PUNCT
ejpam-5431	524	15	iv	iv	X
ejpam-5431	524	16	)	)	PUNCT
ejpam-5431	525	1	[	[	X
ejpam-5431	525	2	t	t	NOUN
ejpam-5431	525	3	σ](⋉,β	σ](⋉,β	NOUN
ejpam-5431	525	4	)	)	PUNCT
ejpam-5431	525	5	is	be	AUX
ejpam-5431	525	6	proximal	proximal	ADJ
ejpam-5431	525	7	for	for	ADP
ejpam-5431	525	8	each	each	DET
ejpam-5431	525	9	σ	σ	PROPN
ejpam-5431	525	10	∈	∈	PROPN
ejpam-5431	525	11	x.	x.	NOUN
ejpam-5431	525	12	n.	n.	PROPN
ejpam-5431	525	13	saleem	saleem	PROPN
ejpam-5431	525	14	et	et	PROPN
ejpam-5431	525	15	al	al	PROPN
ejpam-5431	525	16	.	.	PUNCT
ejpam-5431	525	17	/	/	SYM
ejpam-5431	525	18	eur	eur	PROPN
ejpam-5431	525	19	.	.	PUNCT
ejpam-5431	526	1	j.	j.	PROPN
ejpam-5431	526	2	pure	pure	PROPN
ejpam-5431	526	3	appl	appl	PROPN
ejpam-5431	526	4	.	.	PROPN
ejpam-5431	526	5	math	math	PROPN
ejpam-5431	526	6	,	,	PUNCT
ejpam-5431	526	7	17	17	NUM
ejpam-5431	526	8	(	(	PUNCT
ejpam-5431	526	9	4	4	NUM
ejpam-5431	526	10	)	)	PUNCT
ejpam-5431	526	11	(	(	PUNCT
ejpam-5431	526	12	2024	2024	NUM
ejpam-5431	526	13	)	)	PUNCT
ejpam-5431	526	14	,	,	PUNCT
ejpam-5431	526	15	3304	3304	NUM
ejpam-5431	526	16	-	-	SYM
ejpam-5431	526	17	3335	3335	NUM
ejpam-5431	526	18	3326	3326	NUM
ejpam-5431	526	19	additionally	additionally	ADV
ejpam-5431	526	20	,	,	PUNCT
ejpam-5431	526	21	assume	assume	VERB
ejpam-5431	526	22	that	that	SCONJ
ejpam-5431	526	23	there	there	PRON
ejpam-5431	526	24	exists	exist	VERB
ejpam-5431	526	25	℘	℘	PROPN
ejpam-5431	526	26	∈	∈	PROPN
ejpam-5431	526	27	z	z	PROPN
ejpam-5431	526	28	,	,	PUNCT
ejpam-5431	526	29	φ	φ	PROPN
ejpam-5431	526	30	∈	∈	PROPN
ejpam-5431	526	31	λb	λb	X
ejpam-5431	526	32	and	and	CCONJ
ejpam-5431	526	33	an	an	DET
ejpam-5431	526	34	operator	operator	NOUN
ejpam-5431	526	35	γ	γ	NOUN
ejpam-5431	526	36	:	:	PUNCT
ejpam-5431	526	37	x	x	X
ejpam-5431	526	38	×x	×x	ADP
ejpam-5431	526	39	→	→	NOUN
ejpam-5431	526	40	r+	r+	NOUN
ejpam-5431	526	41	in	in	ADP
ejpam-5431	526	42	a	a	DET
ejpam-5431	526	43	way	way	NOUN
ejpam-5431	526	44	that	that	PRON
ejpam-5431	526	45	for	for	ADP
ejpam-5431	526	46	all	all	DET
ejpam-5431	526	47	σ	σ	PROPN
ejpam-5431	526	48	,	,	PUNCT
ejpam-5431	526	49	τ	τ	PROPN
ejpam-5431	526	50	∈	∈	PROPN
ejpam-5431	526	51	x	x	NOUN
ejpam-5431	526	52	,	,	PUNCT
ejpam-5431	526	53	℘(γ(σ	℘(γ(σ	ADJ
ejpam-5431	526	54	,	,	PUNCT
ejpam-5431	526	55	τ)ℵ([t	τ)ℵ([t	PROPN
ejpam-5431	526	56	σ](⋉,β	σ](⋉,β	NUM
ejpam-5431	526	57	)	)	PUNCT
ejpam-5431	526	58	,	,	PUNCT
ejpam-5431	526	59	[	[	X
ejpam-5431	526	60	t	t	X
ejpam-5431	526	61	τ	τ	X
ejpam-5431	526	62	]	]	X
ejpam-5431	526	63	(	(	PUNCT
ejpam-5431	526	64	⋉,β	⋉,β	NOUN
ejpam-5431	526	65	)	)	PUNCT
ejpam-5431	526	66	)	)	PUNCT
ejpam-5431	526	67	,	,	PUNCT
ejpam-5431	526	68	φ([a(σ	φ([a(σ	NOUN
ejpam-5431	526	69	,	,	PUNCT
ejpam-5431	526	70	τ	τ	X
ejpam-5431	526	71	)	)	PUNCT
ejpam-5431	526	72	]	]	PUNCT
ejpam-5431	526	73	1	1	NUM
ejpam-5431	526	74	r	r	NOUN
ejpam-5431	526	75	)	)	PUNCT
ejpam-5431	526	76	)	)	PUNCT
ejpam-5431	527	1	≥	≥	NOUN
ejpam-5431	527	2	0	0	NUM
ejpam-5431	527	3	(	(	PUNCT
ejpam-5431	527	4	21	21	NUM
ejpam-5431	527	5	)	)	PUNCT
ejpam-5431	527	6	then	then	ADV
ejpam-5431	527	7	,	,	PUNCT
ejpam-5431	527	8	t	t	PROPN
ejpam-5431	527	9	has	have	VERB
ejpam-5431	527	10	at	at	ADV
ejpam-5431	527	11	least	least	ADJ
ejpam-5431	527	12	one	one	NUM
ejpam-5431	527	13	iffp	iffp	NOUN
ejpam-5431	527	14	in	in	ADP
ejpam-5431	527	15	x.	x.	NOUN
ejpam-5431	527	16	proof	proof	NOUN
ejpam-5431	527	17	.	.	PUNCT
ejpam-5431	528	1	set	set	VERB
ejpam-5431	528	2	ρ(τ	ρ(τ	NOUN
ejpam-5431	528	3	,	,	PUNCT
ejpam-5431	528	4	κ	κ	NOUN
ejpam-5431	528	5	)	)	PUNCT
ejpam-5431	528	6	=	=	SYM
ejpam-5431	529	1	ϕ(κ)−	ϕ(κ)−	PROPN
ejpam-5431	529	2	τ	τ	X
ejpam-5431	529	3	for	for	ADP
ejpam-5431	529	4	all	all	DET
ejpam-5431	529	5	τ	τ	PROPN
ejpam-5431	529	6	,	,	PUNCT
ejpam-5431	529	7	κ	κ	PROPN
ejpam-5431	529	8	∈	∈	PROPN
ejpam-5431	529	9	r+	r+	NOUN
ejpam-5431	529	10	in	in	ADP
ejpam-5431	529	11	theorem	theorem	NOUN
ejpam-5431	529	12	25	25	NUM
ejpam-5431	529	13	.	.	PUNCT
ejpam-5431	530	1	then	then	ADV
ejpam-5431	530	2	,	,	PUNCT
ejpam-5431	530	3	21	21	NUM
ejpam-5431	530	4	follows	follow	VERB
ejpam-5431	530	5	easily	easily	ADV
ejpam-5431	530	6	.	.	PUNCT
ejpam-5431	531	1	note	note	VERB
ejpam-5431	531	2	that	that	SCONJ
ejpam-5431	531	3	ϕ(κ	ϕ(κ	PROPN
ejpam-5431	531	4	)	)	PUNCT
ejpam-5431	531	5	−	−	PROPN
ejpam-5431	532	1	τ	τ	PROPN
ejpam-5431	532	2	∈	∈	PROPN
ejpam-5431	532	3	z.	z.	PROPN
ejpam-5431	532	4	consequently	consequently	ADV
ejpam-5431	532	5	theorem	theorem	VERB
ejpam-5431	532	6	25	25	NUM
ejpam-5431	532	7	can	can	AUX
ejpam-5431	532	8	be	be	AUX
ejpam-5431	532	9	applied	apply	VERB
ejpam-5431	532	10	to	to	PART
ejpam-5431	532	11	find	find	VERB
ejpam-5431	532	12	u	u	PRON
ejpam-5431	532	13	∈	∈	PROPN
ejpam-5431	532	14	x	x	PUNCT
ejpam-5431	533	1	such	such	ADJ
ejpam-5431	533	2	that	that	SCONJ
ejpam-5431	533	3	u	u	PROPN
ejpam-5431	533	4	∈	∈	PROPN
ejpam-5431	533	5	[	[	X
ejpam-5431	533	6	tu](⋉,β	tu](⋉,β	X
ejpam-5431	533	7	)	)	PUNCT
ejpam-5431	533	8	.	.	PUNCT
ejpam-5431	534	1	corollary	corollary	ADJ
ejpam-5431	534	2	3	3	X
ejpam-5431	534	3	.	.	PUNCT
ejpam-5431	535	1	let	let	AUX
ejpam-5431	535	2	(	(	PUNCT
ejpam-5431	535	3	x	x	NOUN
ejpam-5431	535	4	,	,	PUNCT
ejpam-5431	535	5	δ	δ	PROPN
ejpam-5431	535	6	)	)	PUNCT
ejpam-5431	535	7	be	be	VERB
ejpam-5431	535	8	a	a	DET
ejpam-5431	535	9	complete	complete	ADJ
ejpam-5431	535	10	b	b	NOUN
ejpam-5431	535	11	-	-	PUNCT
ejpam-5431	535	12	ms	ms	NOUN
ejpam-5431	535	13	and	and	CCONJ
ejpam-5431	535	14	t	t	NOUN
ejpam-5431	535	15	:	:	PUNCT
ejpam-5431	535	16	x	x	X
ejpam-5431	535	17	→	→	SYM
ejpam-5431	535	18	ifs(x	ifs(x	PROPN
ejpam-5431	535	19	)	)	PUNCT
ejpam-5431	535	20	be	be	VERB
ejpam-5431	535	21	an	an	DET
ejpam-5431	535	22	ifs	ifs	PROPN
ejpam-5431	535	23	-	-	PUNCT
ejpam-5431	535	24	valued	value	VERB
ejpam-5431	535	25	map	map	NOUN
ejpam-5431	535	26	satisfying	satisfy	VERB
ejpam-5431	535	27	the	the	DET
ejpam-5431	535	28	condition	condition	NOUN
ejpam-5431	535	29	:	:	PUNCT
ejpam-5431	535	30	γ(σ	γ(σ	ADJ
ejpam-5431	535	31	,	,	PUNCT
ejpam-5431	535	32	τ)ℵ([t	τ)ℵ([t	PROPN
ejpam-5431	535	33	σ](⋉,β	σ](⋉,β	NUM
ejpam-5431	535	34	)	)	PUNCT
ejpam-5431	535	35	,	,	PUNCT
ejpam-5431	536	1	[	[	X
ejpam-5431	536	2	t	t	X
ejpam-5431	536	3	τ	τ	X
ejpam-5431	536	4	]	]	X
ejpam-5431	536	5	(	(	PUNCT
ejpam-5431	536	6	⋉,β	⋉,β	NOUN
ejpam-5431	536	7	)	)	PUNCT
ejpam-5431	536	8	)	)	PUNCT
ejpam-5431	536	9	≤	≤	NUM
ejpam-5431	536	10	φ(m	φ(m	NOUN
ejpam-5431	536	11	r	r	NOUN
ejpam-5431	536	12	t	t	NOUN
ejpam-5431	536	13	(	(	PUNCT
ejpam-5431	536	14	σ	σ	PROPN
ejpam-5431	536	15	,	,	PUNCT
ejpam-5431	536	16	τ	τ	PROPN
ejpam-5431	536	17	)	)	PUNCT
ejpam-5431	536	18	)	)	PUNCT
ejpam-5431	536	19	(	(	PUNCT
ejpam-5431	536	20	22	22	NUM
ejpam-5431	536	21	)	)	PUNCT
ejpam-5431	536	22	for	for	ADP
ejpam-5431	536	23	all	all	DET
ejpam-5431	536	24	σ	σ	PROPN
ejpam-5431	536	25	,	,	PUNCT
ejpam-5431	536	26	τ	τ	PROPN
ejpam-5431	536	27	∈	∈	PROPN
ejpam-5431	536	28	x	x	NOUN
ejpam-5431	536	29	,	,	PUNCT
ejpam-5431	536	30	where	where	SCONJ
ejpam-5431	536	31	φ	φ	PROPN
ejpam-5431	536	32	∈	∈	PROPN
ejpam-5431	536	33	λb	λb	X
ejpam-5431	536	34	and	and	CCONJ
ejpam-5431	536	35	γ	γ	X
ejpam-5431	536	36	:	:	PUNCT
ejpam-5431	536	37	x	x	PROPN
ejpam-5431	536	38	×x	×x	ADP
ejpam-5431	536	39	→	→	PUNCT
ejpam-5431	536	40	r+	r+	PRON
ejpam-5431	536	41	is	be	AUX
ejpam-5431	536	42	a	a	DET
ejpam-5431	536	43	function	function	NOUN
ejpam-5431	536	44	.	.	PUNCT
ejpam-5431	537	1	furthermore	furthermore	ADV
ejpam-5431	537	2	,	,	PUNCT
ejpam-5431	537	3	it	it	PRON
ejpam-5431	537	4	can	can	AUX
ejpam-5431	537	5	be	be	AUX
ejpam-5431	537	6	assumed	assume	VERB
ejpam-5431	537	7	that	that	SCONJ
ejpam-5431	537	8	:	:	PUNCT
ejpam-5431	537	9	(	(	PUNCT
ejpam-5431	537	10	i	i	NOUN
ejpam-5431	537	11	)	)	PUNCT
ejpam-5431	537	12	t	t	PROPN
ejpam-5431	537	13	is	be	AUX
ejpam-5431	537	14	γ	γ	X
ejpam-5431	537	15	-	-	ADJ
ejpam-5431	537	16	admissible	admissible	ADJ
ejpam-5431	537	17	;	;	PUNCT
ejpam-5431	537	18	(	(	PUNCT
ejpam-5431	537	19	ii	ii	NOUN
ejpam-5431	537	20	)	)	PUNCT
ejpam-5431	537	21	there	there	PRON
ejpam-5431	537	22	are	be	VERB
ejpam-5431	537	23	σ0	σ0	PROPN
ejpam-5431	537	24	∈	∈	PROPN
ejpam-5431	537	25	x	x	X
ejpam-5431	537	26	and	and	CCONJ
ejpam-5431	537	27	σ1	σ1	PROPN
ejpam-5431	537	28	∈	∈	PROPN
ejpam-5431	538	1	[	[	X
ejpam-5431	538	2	t	t	NOUN
ejpam-5431	538	3	σ0](⋉,β	σ0](⋉,β	NUM
ejpam-5431	538	4	)	)	PUNCT
ejpam-5431	538	5	with	with	ADP
ejpam-5431	538	6	γ(σ0	γ(σ0	PROPN
ejpam-5431	538	7	,	,	PUNCT
ejpam-5431	538	8	σ1	σ1	PROPN
ejpam-5431	538	9	)	)	PUNCT
ejpam-5431	538	10	≥	≥	NOUN
ejpam-5431	538	11	1	1	NUM
ejpam-5431	538	12	(	(	PUNCT
ejpam-5431	538	13	iii	iii	NOUN
ejpam-5431	538	14	)	)	PUNCT
ejpam-5431	538	15	t	t	PROPN
ejpam-5431	538	16	is	be	AUX
ejpam-5431	538	17	ℵ-continuous	ℵ-continuous	ADJ
ejpam-5431	538	18	;	;	PUNCT
ejpam-5431	538	19	(	(	PUNCT
ejpam-5431	538	20	iv	iv	X
ejpam-5431	538	21	)	)	PUNCT
ejpam-5431	539	1	[	[	X
ejpam-5431	539	2	t	t	NOUN
ejpam-5431	539	3	σ](⋉,β	σ](⋉,β	NOUN
ejpam-5431	539	4	)	)	PUNCT
ejpam-5431	539	5	is	be	AUX
ejpam-5431	539	6	proximal	proximal	ADJ
ejpam-5431	539	7	for	for	ADP
ejpam-5431	539	8	each	each	DET
ejpam-5431	539	9	σ	σ	NOUN
ejpam-5431	539	10	∈	∈	PROPN
ejpam-5431	539	11	x	x	X
ejpam-5431	539	12	;	;	PUNCT
ejpam-5431	539	13	then	then	ADV
ejpam-5431	539	14	there	there	PRON
ejpam-5431	539	15	is	be	VERB
ejpam-5431	539	16	ς	ς	PROPN
ejpam-5431	539	17	∈	∈	PROPN
ejpam-5431	539	18	x	x	PUNCT
ejpam-5431	539	19	such	such	ADJ
ejpam-5431	539	20	that	that	SCONJ
ejpam-5431	539	21	ς	ς	PROPN
ejpam-5431	539	22	∈	∈	PROPN
ejpam-5431	540	1	[	[	X
ejpam-5431	540	2	t	t	NOUN
ejpam-5431	540	3	ς](⋉,β	ς](⋉,β	NUM
ejpam-5431	540	4	)	)	PUNCT
ejpam-5431	540	5	.	.	PUNCT
ejpam-5431	541	1	proof	proof	NOUN
ejpam-5431	541	2	.	.	PUNCT
ejpam-5431	542	1	take	take	VERB
ejpam-5431	542	2	℘	℘	NOUN
ejpam-5431	542	3	:	:	PUNCT
ejpam-5431	542	4	=	=	SYM
ejpam-5431	542	5	℘(a	℘(a	PROPN
ejpam-5431	542	6	,	,	PUNCT
ejpam-5431	542	7	b	b	NOUN
ejpam-5431	542	8	)	)	PUNCT
ejpam-5431	542	9	=	=	PUNCT
ejpam-5431	543	1	φ(b	φ(b	PROPN
ejpam-5431	543	2	)	)	PUNCT
ejpam-5431	543	3	−	−	NOUN
ejpam-5431	543	4	a	a	PRON
ejpam-5431	543	5	for	for	ADP
ejpam-5431	543	6	each	each	DET
ejpam-5431	543	7	a	a	NOUN
ejpam-5431	543	8	,	,	PUNCT
ejpam-5431	543	9	b	b	X
ejpam-5431	543	10	∈	∈	PROPN
ejpam-5431	543	11	r+	r+	NOUN
ejpam-5431	543	12	in	in	ADP
ejpam-5431	543	13	corollary	corollary	ADJ
ejpam-5431	543	14	(	(	PUNCT
ejpam-5431	543	15	1	1	NUM
ejpam-5431	543	16	)	)	PUNCT
ejpam-5431	543	17	.	.	PUNCT
ejpam-5431	544	1	then	then	ADV
ejpam-5431	544	2	(	(	PUNCT
ejpam-5431	544	3	22	22	NUM
ejpam-5431	544	4	)	)	PUNCT
ejpam-5431	544	5	follows	follow	VERB
ejpam-5431	544	6	easily	easily	ADV
ejpam-5431	544	7	.	.	PUNCT
ejpam-5431	545	1	notice	notice	VERB
ejpam-5431	545	2	that	that	SCONJ
ejpam-5431	545	3	φ(b	φ(b	ADP
ejpam-5431	545	4	)	)	PUNCT
ejpam-5431	545	5	−	−	ADP
ejpam-5431	545	6	a	a	DET
ejpam-5431	545	7	∈	∈	PROPN
ejpam-5431	545	8	z.	z.	PROPN
ejpam-5431	545	9	accordingly	accordingly	ADV
ejpam-5431	545	10	,	,	PUNCT
ejpam-5431	545	11	by	by	ADP
ejpam-5431	545	12	utilizing	utilize	VERB
ejpam-5431	545	13	corollary	corollary	ADJ
ejpam-5431	545	14	(	(	PUNCT
ejpam-5431	545	15	1	1	NUM
ejpam-5431	545	16	)	)	PUNCT
ejpam-5431	545	17	,	,	PUNCT
ejpam-5431	545	18	ς	ς	PROPN
ejpam-5431	545	19	∈	∈	PROPN
ejpam-5431	545	20	x	x	AUX
ejpam-5431	545	21	can	can	AUX
ejpam-5431	545	22	be	be	AUX
ejpam-5431	545	23	determined	determine	VERB
ejpam-5431	545	24	such	such	ADJ
ejpam-5431	545	25	that	that	SCONJ
ejpam-5431	545	26	ς	ς	PROPN
ejpam-5431	545	27	∈	∈	PROPN
ejpam-5431	546	1	[	[	X
ejpam-5431	546	2	t	t	NOUN
ejpam-5431	546	3	ς](⋉,β	ς](⋉,β	NUM
ejpam-5431	546	4	)	)	PUNCT
ejpam-5431	546	5	.	.	PUNCT
ejpam-5431	547	1	the	the	DET
ejpam-5431	547	2	ensuing	ensue	VERB
ejpam-5431	547	3	generalization	generalization	NOUN
ejpam-5431	547	4	and	and	CCONJ
ejpam-5431	547	5	fuzzification	fuzzification	NOUN
ejpam-5431	547	6	of	of	ADP
ejpam-5431	547	7	rhoades	rhoade	NOUN
ejpam-5431	547	8	’	'	PUNCT
ejpam-5431	547	9	outcome	outcome	NOUN
ejpam-5431	547	10	[	[	X
ejpam-5431	547	11	23	23	NUM
ejpam-5431	547	12	]	]	PUNCT
ejpam-5431	547	13	are	be	AUX
ejpam-5431	547	14	as	as	SCONJ
ejpam-5431	547	15	follows	follow	VERB
ejpam-5431	547	16	:	:	PUNCT
ejpam-5431	547	17	corollary	corollary	ADJ
ejpam-5431	547	18	4	4	X
ejpam-5431	547	19	.	.	PUNCT
ejpam-5431	548	1	let	let	AUX
ejpam-5431	548	2	(	(	PUNCT
ejpam-5431	548	3	x	x	NOUN
ejpam-5431	548	4	,	,	PUNCT
ejpam-5431	548	5	δ	δ	PROPN
ejpam-5431	548	6	,	,	PUNCT
ejpam-5431	548	7	h	h	NOUN
ejpam-5431	548	8	)	)	PUNCT
ejpam-5431	548	9	be	be	AUX
ejpam-5431	548	10	a	a	DET
ejpam-5431	548	11	complete	complete	ADJ
ejpam-5431	548	12	b	b	NOUN
ejpam-5431	548	13	-	-	PUNCT
ejpam-5431	548	14	ms	ms	NOUN
ejpam-5431	548	15	and	and	CCONJ
ejpam-5431	548	16	t	t	NOUN
ejpam-5431	548	17	:	:	PUNCT
ejpam-5431	548	18	x	x	X
ejpam-5431	548	19	→	→	SYM
ejpam-5431	548	20	ifs(x	ifs(x	PROPN
ejpam-5431	548	21	)	)	PUNCT
ejpam-5431	548	22	be	be	VERB
ejpam-5431	548	23	an	an	DET
ejpam-5431	548	24	ifs	ifs	PROPN
ejpam-5431	548	25	-	-	PUNCT
ejpam-5431	548	26	valued	value	VERB
ejpam-5431	548	27	map	map	NOUN
ejpam-5431	548	28	satisfying	satisfy	VERB
ejpam-5431	548	29	the	the	DET
ejpam-5431	548	30	following	following	NOUN
ejpam-5431	548	31	:	:	PUNCT
ejpam-5431	548	32	ℵ([t	ℵ([t	PRON
ejpam-5431	548	33	σ](⋉,β	σ](⋉,β	NUM
ejpam-5431	548	34	)	)	PUNCT
ejpam-5431	548	35	,	,	PUNCT
ejpam-5431	549	1	[	[	X
ejpam-5431	549	2	t	t	X
ejpam-5431	549	3	τ	τ	X
ejpam-5431	549	4	]	]	X
ejpam-5431	549	5	(	(	PUNCT
ejpam-5431	549	6	⋉,β	⋉,β	NOUN
ejpam-5431	549	7	)	)	PUNCT
ejpam-5431	549	8	)	)	PUNCT
ejpam-5431	549	9	≤	≤	NUM
ejpam-5431	549	10	φ(m	φ(m	NOUN
ejpam-5431	549	11	r	r	NOUN
ejpam-5431	549	12	t	t	NOUN
ejpam-5431	549	13	(	(	PUNCT
ejpam-5431	549	14	σ	σ	PROPN
ejpam-5431	549	15	,	,	PUNCT
ejpam-5431	549	16	τ))−	τ))−	NOUN
ejpam-5431	549	17	φ2(m	φ2(m	X
ejpam-5431	549	18	r	r	NOUN
ejpam-5431	549	19	t	t	PROPN
ejpam-5431	549	20	(	(	PUNCT
ejpam-5431	549	21	σ	σ	PROPN
ejpam-5431	549	22	,	,	PUNCT
ejpam-5431	549	23	τ	τ	PROPN
ejpam-5431	549	24	)	)	PUNCT
ejpam-5431	549	25	)	)	PUNCT
ejpam-5431	549	26	(	(	PUNCT
ejpam-5431	549	27	23	23	NUM
ejpam-5431	549	28	)	)	PUNCT
ejpam-5431	549	29	for	for	ADP
ejpam-5431	549	30	all	all	DET
ejpam-5431	549	31	σ	σ	PROPN
ejpam-5431	549	32	,	,	PUNCT
ejpam-5431	549	33	τ	τ	PROPN
ejpam-5431	549	34	∈	∈	PROPN
ejpam-5431	549	35	x	x	NOUN
ejpam-5431	549	36	,	,	PUNCT
ejpam-5431	549	37	where	where	SCONJ
ejpam-5431	549	38	φ	φ	PROPN
ejpam-5431	549	39	:	:	PUNCT
ejpam-5431	549	40	r+	r+	X
ejpam-5431	549	41	→	→	SYM
ejpam-5431	549	42	r+	r+	NOUN
ejpam-5431	549	43	is	be	AUX
ejpam-5431	549	44	lower	low	ADJ
ejpam-5431	549	45	semicontinuous	semicontinuous	ADJ
ejpam-5431	549	46	and	and	CCONJ
ejpam-5431	549	47	φ−1(0	φ−1(0	NOUN
ejpam-5431	549	48	)	)	PUNCT
ejpam-5431	549	49	=	=	PUNCT
ejpam-5431	549	50	{	{	PUNCT
ejpam-5431	549	51	0	0	NUM
ejpam-5431	549	52	}	}	PUNCT
ejpam-5431	549	53	.	.	PUNCT
ejpam-5431	550	1	further	far	ADV
ejpam-5431	550	2	let	let	VERB
ejpam-5431	550	3	us	we	PRON
ejpam-5431	550	4	suppose	suppose	VERB
ejpam-5431	550	5	that	that	SCONJ
ejpam-5431	550	6	:	:	PUNCT
ejpam-5431	550	7	(	(	PUNCT
ejpam-5431	550	8	i	i	NOUN
ejpam-5431	550	9	)	)	PUNCT
ejpam-5431	550	10	t	t	PROPN
ejpam-5431	550	11	is	be	AUX
ejpam-5431	550	12	ℵ-continuous	ℵ-continuous	ADJ
ejpam-5431	550	13	;	;	PUNCT
ejpam-5431	550	14	(	(	PUNCT
ejpam-5431	550	15	ii	ii	NOUN
ejpam-5431	550	16	)	)	PUNCT
ejpam-5431	551	1	[	[	X
ejpam-5431	551	2	t	t	NOUN
ejpam-5431	551	3	σ](⋉,β	σ](⋉,β	NOUN
ejpam-5431	551	4	)	)	PUNCT
ejpam-5431	551	5	is	be	AUX
ejpam-5431	551	6	proximal	proximal	ADJ
ejpam-5431	551	7	for	for	ADP
ejpam-5431	551	8	each	each	DET
ejpam-5431	551	9	σ	σ	PROPN
ejpam-5431	551	10	∈	∈	PROPN
ejpam-5431	551	11	x.	x.	NOUN
ejpam-5431	552	1	then	then	ADV
ejpam-5431	552	2	,	,	PUNCT
ejpam-5431	552	3	there	there	PRON
ejpam-5431	552	4	exists	exist	VERB
ejpam-5431	552	5	ς	ς	PROPN
ejpam-5431	552	6	∈	∈	PROPN
ejpam-5431	552	7	x	x	PUNCT
ejpam-5431	552	8	such	such	ADJ
ejpam-5431	552	9	that	that	SCONJ
ejpam-5431	552	10	ς	ς	PROPN
ejpam-5431	552	11	∈	∈	PROPN
ejpam-5431	553	1	[	[	X
ejpam-5431	553	2	t	t	NOUN
ejpam-5431	553	3	ς](⋉,β	ς](⋉,β	NUM
ejpam-5431	553	4	)	)	PUNCT
ejpam-5431	553	5	.	.	PUNCT
ejpam-5431	554	1	n.	n.	PROPN
ejpam-5431	554	2	saleem	saleem	PROPN
ejpam-5431	554	3	et	et	PROPN
ejpam-5431	554	4	al	al	PROPN
ejpam-5431	554	5	.	.	PUNCT
ejpam-5431	554	6	/	/	SYM
ejpam-5431	554	7	eur	eur	PROPN
ejpam-5431	554	8	.	.	PUNCT
ejpam-5431	555	1	j.	j.	PROPN
ejpam-5431	555	2	pure	pure	PROPN
ejpam-5431	555	3	appl	appl	PROPN
ejpam-5431	555	4	.	.	PROPN
ejpam-5431	555	5	math	math	PROPN
ejpam-5431	555	6	,	,	PUNCT
ejpam-5431	555	7	17	17	NUM
ejpam-5431	555	8	(	(	PUNCT
ejpam-5431	555	9	4	4	NUM
ejpam-5431	555	10	)	)	PUNCT
ejpam-5431	555	11	(	(	PUNCT
ejpam-5431	555	12	2024	2024	NUM
ejpam-5431	555	13	)	)	PUNCT
ejpam-5431	555	14	,	,	PUNCT
ejpam-5431	555	15	3304	3304	NUM
ejpam-5431	555	16	-	-	SYM
ejpam-5431	555	17	3335	3335	NUM
ejpam-5431	555	18	3327	3327	NUM
ejpam-5431	555	19	proof	proof	NOUN
ejpam-5431	555	20	.	.	PUNCT
ejpam-5431	556	1	in	in	ADP
ejpam-5431	556	2	corollary	corollary	ADJ
ejpam-5431	556	3	(	(	PUNCT
ejpam-5431	556	4	1	1	NUM
ejpam-5431	556	5	)	)	PUNCT
ejpam-5431	556	6	,	,	PUNCT
ejpam-5431	556	7	take	take	VERB
ejpam-5431	556	8	℘	℘	NOUN
ejpam-5431	556	9	:	:	PUNCT
ejpam-5431	556	10	=	=	SYM
ejpam-5431	556	11	℘(a	℘(a	PROPN
ejpam-5431	556	12	,	,	PUNCT
ejpam-5431	556	13	b	b	NOUN
ejpam-5431	556	14	)	)	PUNCT
ejpam-5431	556	15	=	=	VERB
ejpam-5431	556	16	b−φ(b)−a	b−φ(b)−a	X
ejpam-5431	556	17	for	for	ADP
ejpam-5431	556	18	all	all	DET
ejpam-5431	556	19	a	a	DET
ejpam-5431	556	20	,	,	PUNCT
ejpam-5431	556	21	b	b	X
ejpam-5431	556	22	∈	∈	PROPN
ejpam-5431	556	23	r+	r+	NOUN
ejpam-5431	556	24	and	and	CCONJ
ejpam-5431	556	25	γ(σ	γ(σ	PROPN
ejpam-5431	556	26	,	,	PUNCT
ejpam-5431	556	27	τ	τ	X
ejpam-5431	556	28	)	)	PUNCT
ejpam-5431	556	29	=	=	SYM
ejpam-5431	556	30	1	1	NUM
ejpam-5431	556	31	for	for	ADP
ejpam-5431	556	32	all	all	DET
ejpam-5431	556	33	σ	σ	PROPN
ejpam-5431	556	34	,	,	PUNCT
ejpam-5431	556	35	τ	τ	PROPN
ejpam-5431	556	36	∈	∈	PROPN
ejpam-5431	556	37	x.	x.	NOUN
ejpam-5431	556	38	then	then	ADV
ejpam-5431	556	39	(	(	PUNCT
ejpam-5431	556	40	23	23	NUM
ejpam-5431	556	41	)	)	PUNCT
ejpam-5431	556	42	is	be	AUX
ejpam-5431	556	43	attained	attain	VERB
ejpam-5431	556	44	.	.	PUNCT
ejpam-5431	557	1	observe	observe	VERB
ejpam-5431	557	2	that	that	SCONJ
ejpam-5431	557	3	b−φ(b)−	b−φ(b)−	VERB
ejpam-5431	557	4	a	a	DET
ejpam-5431	557	5	∈	∈	PROPN
ejpam-5431	557	6	z.	z.	PROPN
ejpam-5431	557	7	thus	thus	ADV
ejpam-5431	557	8	,	,	PUNCT
ejpam-5431	557	9	by	by	ADP
ejpam-5431	557	10	corollary	corollary	ADJ
ejpam-5431	557	11	(	(	PUNCT
ejpam-5431	557	12	1	1	NUM
ejpam-5431	557	13	)	)	PUNCT
ejpam-5431	557	14	,	,	PUNCT
ejpam-5431	557	15	t	t	PROPN
ejpam-5431	557	16	has	have	VERB
ejpam-5431	557	17	an	an	DET
ejpam-5431	557	18	iffp	iffp	NOUN
ejpam-5431	557	19	in	in	ADP
ejpam-5431	557	20	x.	x.	PROPN
ejpam-5431	557	21	corollary	corollary	PROPN
ejpam-5431	557	22	5	5	PROPN
ejpam-5431	557	23	.	.	PUNCT
ejpam-5431	557	24	nadler	nadler	PROPN
ejpam-5431	557	25	’s	’s	PART
ejpam-5431	557	26	type	type	NOUN
ejpam-5431	558	1	[	[	X
ejpam-5431	558	2	16	16	NUM
ejpam-5431	558	3	]	]	PUNCT
ejpam-5431	558	4	)	)	PUNCT
ejpam-5431	558	5	let	let	VERB
ejpam-5431	558	6	(	(	PUNCT
ejpam-5431	558	7	x	x	NOUN
ejpam-5431	558	8	,	,	PUNCT
ejpam-5431	558	9	δ	δ	PROPN
ejpam-5431	558	10	,	,	PUNCT
ejpam-5431	558	11	h	h	NOUN
ejpam-5431	558	12	)	)	PUNCT
ejpam-5431	558	13	be	be	AUX
ejpam-5431	558	14	a	a	DET
ejpam-5431	558	15	complete	complete	ADJ
ejpam-5431	558	16	b	b	NOUN
ejpam-5431	558	17	-	-	PUNCT
ejpam-5431	558	18	ms	ms	NOUN
ejpam-5431	558	19	and	and	CCONJ
ejpam-5431	558	20	t	t	NOUN
ejpam-5431	558	21	:	:	PUNCT
ejpam-5431	558	22	x	x	X
ejpam-5431	558	23	→	→	SYM
ejpam-5431	558	24	ifs(x	ifs(x	PROPN
ejpam-5431	558	25	)	)	PUNCT
ejpam-5431	558	26	be	be	VERB
ejpam-5431	558	27	an	an	DET
ejpam-5431	558	28	ifs	ifs	PROPN
ejpam-5431	558	29	-	-	PUNCT
ejpam-5431	558	30	valued	value	VERB
ejpam-5431	558	31	map	map	NOUN
ejpam-5431	558	32	satisfying	satisfying	ADJ
ejpam-5431	558	33	:	:	PUNCT
ejpam-5431	558	34	ℵ([t	ℵ([t	PRON
ejpam-5431	558	35	σ](⋉,β	σ](⋉,β	PROPN
ejpam-5431	558	36	)	)	PUNCT
ejpam-5431	558	37	,	,	PUNCT
ejpam-5431	559	1	[	[	X
ejpam-5431	559	2	t	t	X
ejpam-5431	559	3	τ	τ	X
ejpam-5431	559	4	]	]	X
ejpam-5431	559	5	(	(	PUNCT
ejpam-5431	559	6	⋉,β	⋉,β	NOUN
ejpam-5431	559	7	)	)	PUNCT
ejpam-5431	559	8	)	)	PUNCT
ejpam-5431	560	1	≤	≤	NOUN
ejpam-5431	560	2	λδ(σ	λδ(σ	NUM
ejpam-5431	560	3	,	,	PUNCT
ejpam-5431	560	4	τ	τ	X
ejpam-5431	560	5	)	)	PUNCT
ejpam-5431	560	6	(	(	PUNCT
ejpam-5431	560	7	24	24	NUM
ejpam-5431	560	8	)	)	PUNCT
ejpam-5431	560	9	for	for	ADP
ejpam-5431	560	10	all	all	DET
ejpam-5431	560	11	σ	σ	PROPN
ejpam-5431	560	12	,	,	PUNCT
ejpam-5431	560	13	τ	τ	PROPN
ejpam-5431	560	14	∈	∈	PROPN
ejpam-5431	560	15	x	x	NOUN
ejpam-5431	560	16	,	,	PUNCT
ejpam-5431	560	17	where	where	SCONJ
ejpam-5431	560	18	λ	λ	PROPN
ejpam-5431	560	19	∈	∈	PROPN
ejpam-5431	560	20	(	(	PUNCT
ejpam-5431	560	21	0	0	NUM
ejpam-5431	560	22	,	,	PUNCT
ejpam-5431	560	23	1	1	NUM
ejpam-5431	560	24	)	)	PUNCT
ejpam-5431	560	25	.	.	PUNCT
ejpam-5431	560	26	assume	assume	VERB
ejpam-5431	560	27	also	also	ADV
ejpam-5431	560	28	that	that	SCONJ
ejpam-5431	560	29	:	:	PUNCT
ejpam-5431	560	30	(	(	PUNCT
ejpam-5431	560	31	i	i	NOUN
ejpam-5431	560	32	)	)	PUNCT
ejpam-5431	560	33	t	t	PROPN
ejpam-5431	560	34	is	be	AUX
ejpam-5431	560	35	ℵ-continuous	ℵ-continuous	ADJ
ejpam-5431	560	36	;	;	PUNCT
ejpam-5431	560	37	(	(	PUNCT
ejpam-5431	560	38	ii	ii	NOUN
ejpam-5431	560	39	)	)	PUNCT
ejpam-5431	561	1	[	[	X
ejpam-5431	561	2	t	t	NOUN
ejpam-5431	561	3	σ](⋉,β	σ](⋉,β	NOUN
ejpam-5431	561	4	)	)	PUNCT
ejpam-5431	561	5	is	be	AUX
ejpam-5431	561	6	proximal	proximal	ADJ
ejpam-5431	561	7	for	for	ADP
ejpam-5431	561	8	each	each	DET
ejpam-5431	561	9	σ	σ	PROPN
ejpam-5431	561	10	∈	∈	PROPN
ejpam-5431	561	11	x.	x.	NOUN
ejpam-5431	562	1	then	then	ADV
ejpam-5431	562	2	t	t	PROPN
ejpam-5431	562	3	has	have	VERB
ejpam-5431	562	4	an	an	DET
ejpam-5431	562	5	iffp	iffp	NOUN
ejpam-5431	562	6	in	in	ADP
ejpam-5431	562	7	x.	x.	NOUN
ejpam-5431	562	8	proof	proof	NOUN
ejpam-5431	562	9	.	.	PUNCT
ejpam-5431	563	1	consider	consider	VERB
ejpam-5431	563	2	γ(σ	γ(σ	PROPN
ejpam-5431	563	3	,	,	PUNCT
ejpam-5431	563	4	τ	τ	X
ejpam-5431	563	5	)	)	PUNCT
ejpam-5431	563	6	=	=	SYM
ejpam-5431	563	7	1	1	NUM
ejpam-5431	563	8	,	,	PUNCT
ejpam-5431	563	9	℘	℘	NOUN
ejpam-5431	563	10	:	:	PUNCT
ejpam-5431	563	11	=	=	SYM
ejpam-5431	563	12	℘(a	℘(a	PROPN
ejpam-5431	563	13	,	,	PUNCT
ejpam-5431	563	14	b	b	NOUN
ejpam-5431	563	15	)	)	PUNCT
ejpam-5431	563	16	=	=	SYM
ejpam-5431	563	17	λb	λb	ADP
ejpam-5431	563	18	−	−	PROPN
ejpam-5431	563	19	a	a	PRON
ejpam-5431	563	20	for	for	ADP
ejpam-5431	563	21	all	all	DET
ejpam-5431	563	22	a	a	PRON
ejpam-5431	563	23	,	,	PUNCT
ejpam-5431	563	24	b	b	X
ejpam-5431	563	25	∈	∈	PROPN
ejpam-5431	563	26	r+	r+	NOUN
ejpam-5431	563	27	and	and	CCONJ
ejpam-5431	563	28	insert	insert	VERB
ejpam-5431	563	29	φ(a	φ(a	ADJ
ejpam-5431	563	30	)	)	PUNCT
ejpam-5431	563	31	=	=	SYM
ejpam-5431	563	32	λa	λa	NOUN
ejpam-5431	563	33	for	for	ADP
ejpam-5431	563	34	all	all	DET
ejpam-5431	563	35	a	a	DET
ejpam-5431	563	36	≥	≥	NOUN
ejpam-5431	563	37	0	0	NUM
ejpam-5431	563	38	,	,	PUNCT
ejpam-5431	563	39	with	with	ADP
ejpam-5431	563	40	λ	λ	PROPN
ejpam-5431	563	41	∈	∈	PROPN
ejpam-5431	563	42	(	(	PUNCT
ejpam-5431	563	43	0	0	NUM
ejpam-5431	563	44	,	,	PUNCT
ejpam-5431	563	45	1	1	NUM
ejpam-5431	563	46	)	)	PUNCT
ejpam-5431	563	47	in	in	ADP
ejpam-5431	563	48	corollary	corollary	ADJ
ejpam-5431	563	49	(	(	PUNCT
ejpam-5431	563	50	1	1	NUM
ejpam-5431	563	51	)	)	PUNCT
ejpam-5431	563	52	.	.	PUNCT
ejpam-5431	564	1	then	then	ADV
ejpam-5431	564	2	(	(	PUNCT
ejpam-5431	564	3	24	24	NUM
ejpam-5431	564	4	)	)	PUNCT
ejpam-5431	564	5	is	be	AUX
ejpam-5431	564	6	achievable	achievable	ADJ
ejpam-5431	564	7	.	.	PUNCT
ejpam-5431	565	1	it	it	PRON
ejpam-5431	565	2	can	can	AUX
ejpam-5431	565	3	be	be	AUX
ejpam-5431	565	4	obsereved	obsereve	VERB
ejpam-5431	565	5	that	that	SCONJ
ejpam-5431	565	6	λb	λb	ADP
ejpam-5431	565	7	−	−	PROPN
ejpam-5431	565	8	a	a	DET
ejpam-5431	565	9	∈	∈	PROPN
ejpam-5431	565	10	z.	z.	PROPN
ejpam-5431	565	11	corollary	corollary	NOUN
ejpam-5431	565	12	(	(	PUNCT
ejpam-5431	565	13	1	1	NUM
ejpam-5431	565	14	)	)	PUNCT
ejpam-5431	565	15	yields	yield	NOUN
ejpam-5431	565	16	that	that	SCONJ
ejpam-5431	565	17	there	there	PRON
ejpam-5431	565	18	is	be	VERB
ejpam-5431	565	19	ς	ς	PROPN
ejpam-5431	565	20	∈	∈	PROPN
ejpam-5431	565	21	x	x	PUNCT
ejpam-5431	565	22	such	such	ADJ
ejpam-5431	565	23	that	that	SCONJ
ejpam-5431	565	24	ς	ς	PROPN
ejpam-5431	565	25	∈	∈	PROPN
ejpam-5431	566	1	[	[	X
ejpam-5431	566	2	t	t	NOUN
ejpam-5431	566	3	ς](⋉,β	ς](⋉,β	NUM
ejpam-5431	566	4	)	)	PUNCT
ejpam-5431	566	5	.	.	PUNCT
ejpam-5431	567	1	the	the	DET
ejpam-5431	567	2	subsequent	subsequent	ADJ
ejpam-5431	567	3	corollary	corollary	NOUN
ejpam-5431	567	4	builds	build	NOUN
ejpam-5431	567	5	upon	upon	SCONJ
ejpam-5431	567	6	heilpern	heilpern	NOUN
ejpam-5431	567	7	’s	’s	PART
ejpam-5431	567	8	initial	initial	ADJ
ejpam-5431	567	9	metric	metric	ADJ
ejpam-5431	567	10	fp	fp	X
ejpam-5431	567	11	theorem	theorem	NOUN
ejpam-5431	567	12	[	[	X
ejpam-5431	567	13	15	15	NUM
ejpam-5431	567	14	]	]	PUNCT
ejpam-5431	567	15	:	:	PUNCT
ejpam-5431	567	16	corollary	corollary	ADJ
ejpam-5431	567	17	6	6	NUM
ejpam-5431	567	18	.	.	PUNCT
ejpam-5431	568	1	let	let	VERB
ejpam-5431	568	2	(	(	PUNCT
ejpam-5431	568	3	x	x	NOUN
ejpam-5431	568	4	,	,	PUNCT
ejpam-5431	568	5	δ	δ	PROPN
ejpam-5431	568	6	,	,	PUNCT
ejpam-5431	568	7	h	h	NOUN
ejpam-5431	568	8	)	)	PUNCT
ejpam-5431	568	9	ba	ba	NOUN
ejpam-5431	569	1	e	e	X
ejpam-5431	569	2	complete	complete	VERB
ejpam-5431	569	3	b	b	X
ejpam-5431	569	4	-	-	PUNCT
ejpam-5431	569	5	ms	ms	NOUN
ejpam-5431	569	6	and	and	CCONJ
ejpam-5431	569	7	t	t	PROPN
ejpam-5431	569	8	:	:	PUNCT
ejpam-5431	569	9	x	x	X
ejpam-5431	569	10	→w	→w	PUNCT
ejpam-5431	569	11	(	(	PUNCT
ejpam-5431	569	12	x	x	X
ejpam-5431	569	13	)	)	PUNCT
ejpam-5431	569	14	be	be	VERB
ejpam-5431	569	15	an	an	DET
ejpam-5431	569	16	ifs	ifs	PROPN
ejpam-5431	569	17	-	-	PUNCT
ejpam-5431	569	18	valued	value	VERB
ejpam-5431	569	19	map	map	NOUN
ejpam-5431	569	20	satisfying	satisfying	ADJ
ejpam-5431	569	21	:	:	PUNCT
ejpam-5431	569	22	δ+∞(t	δ+∞(t	PROPN
ejpam-5431	569	23	σ	σ	PROPN
ejpam-5431	569	24	,	,	PUNCT
ejpam-5431	569	25	t	t	PROPN
ejpam-5431	569	26	τ	τ	PROPN
ejpam-5431	569	27	)	)	PUNCT
ejpam-5431	569	28	≤	≤	NOUN
ejpam-5431	569	29	λδ(σ	λδ(σ	NUM
ejpam-5431	569	30	,	,	PUNCT
ejpam-5431	569	31	τ	τ	X
ejpam-5431	569	32	)	)	PUNCT
ejpam-5431	569	33	(	(	PUNCT
ejpam-5431	569	34	25	25	NUM
ejpam-5431	569	35	)	)	PUNCT
ejpam-5431	569	36	for	for	ADP
ejpam-5431	569	37	all	all	DET
ejpam-5431	569	38	σ	σ	PROPN
ejpam-5431	569	39	,	,	PUNCT
ejpam-5431	569	40	τ	τ	PROPN
ejpam-5431	569	41	∈	∈	PROPN
ejpam-5431	569	42	x	x	NOUN
ejpam-5431	569	43	,	,	PUNCT
ejpam-5431	569	44	where	where	SCONJ
ejpam-5431	569	45	λ	λ	PROPN
ejpam-5431	569	46	∈	∈	PROPN
ejpam-5431	569	47	(	(	PUNCT
ejpam-5431	569	48	0	0	NUM
ejpam-5431	569	49	,	,	PUNCT
ejpam-5431	569	50	1	1	NUM
ejpam-5431	569	51	)	)	PUNCT
ejpam-5431	569	52	.	.	PUNCT
ejpam-5431	570	1	in	in	ADP
ejpam-5431	570	2	addition	addition	NOUN
ejpam-5431	570	3	,	,	PUNCT
ejpam-5431	570	4	suppose	suppose	VERB
ejpam-5431	570	5	that	that	SCONJ
ejpam-5431	570	6	:	:	PUNCT
ejpam-5431	570	7	(	(	PUNCT
ejpam-5431	570	8	i	i	NOUN
ejpam-5431	570	9	)	)	PUNCT
ejpam-5431	570	10	t	t	PROPN
ejpam-5431	570	11	is	be	AUX
ejpam-5431	570	12	ℵ-continuous	ℵ-continuous	ADJ
ejpam-5431	570	13	;	;	PUNCT
ejpam-5431	570	14	(	(	PUNCT
ejpam-5431	570	15	ii	ii	NOUN
ejpam-5431	570	16	)	)	PUNCT
ejpam-5431	570	17	t	t	PROPN
ejpam-5431	570	18	σ	σ	PROPN
ejpam-5431	570	19	is	be	AUX
ejpam-5431	570	20	proximal	proximal	ADJ
ejpam-5431	570	21	for	for	ADP
ejpam-5431	570	22	each	each	DET
ejpam-5431	570	23	σ	σ	PROPN
ejpam-5431	570	24	∈	∈	PROPN
ejpam-5431	570	25	x.	x.	NOUN
ejpam-5431	571	1	then	then	ADV
ejpam-5431	571	2	,	,	PUNCT
ejpam-5431	571	3	there	there	PRON
ejpam-5431	571	4	is	be	VERB
ejpam-5431	571	5	ς	ς	PROPN
ejpam-5431	571	6	∈	∈	PROPN
ejpam-5431	571	7	x	x	PUNCT
ejpam-5431	571	8	such	such	ADJ
ejpam-5431	571	9	that	that	SCONJ
ejpam-5431	571	10	{	{	PUNCT
ejpam-5431	571	11	ς	ς	NOUN
ejpam-5431	571	12	}	}	PUNCT
ejpam-5431	571	13	∈	∈	PROPN
ejpam-5431	571	14	x	x	PUNCT
ejpam-5431	571	15	such	such	ADJ
ejpam-5431	571	16	as	as	ADP
ejpam-5431	571	17	{	{	PUNCT
ejpam-5431	571	18	ς	ς	NOUN
ejpam-5431	571	19	}	}	PUNCT
ejpam-5431	571	20	⊂	⊂	PROPN
ejpam-5431	571	21	t	t	PROPN
ejpam-5431	571	22	ς	ς	PROPN
ejpam-5431	571	23	.	.	PUNCT
ejpam-5431	571	24	proof	proof	NOUN
ejpam-5431	571	25	.	.	PUNCT
ejpam-5431	572	1	since	since	SCONJ
ejpam-5431	572	2	ℵ([t	ℵ([t	PRON
ejpam-5431	572	3	σ](⋉,β	σ](⋉,β	NUM
ejpam-5431	572	4	)	)	PUNCT
ejpam-5431	572	5	,	,	PUNCT
ejpam-5431	572	6	[	[	X
ejpam-5431	572	7	t	t	X
ejpam-5431	572	8	τ	τ	X
ejpam-5431	572	9	]	]	X
ejpam-5431	572	10	(	(	PUNCT
ejpam-5431	572	11	⋉,β	⋉,β	NOUN
ejpam-5431	572	12	)	)	PUNCT
ejpam-5431	572	13	)	)	PUNCT
ejpam-5431	572	14	≤	≤	PUNCT
ejpam-5431	572	15	δ+∞(t	δ+∞(t	PROPN
ejpam-5431	572	16	σ	σ	PROPN
ejpam-5431	572	17	,	,	PUNCT
ejpam-5431	572	18	t	t	PROPN
ejpam-5431	572	19	τ	τ	PROPN
ejpam-5431	572	20	)	)	PUNCT
ejpam-5431	572	21	for	for	ADP
ejpam-5431	572	22	all	all	DET
ejpam-5431	572	23	σ	σ	PROPN
ejpam-5431	572	24	,	,	PUNCT
ejpam-5431	572	25	τ	τ	PROPN
ejpam-5431	572	26	∈	∈	PROPN
ejpam-5431	572	27	x	x	X
ejpam-5431	572	28	,	,	PUNCT
ejpam-5431	572	29	by	by	ADP
ejpam-5431	572	30	employing	employ	VERB
ejpam-5431	572	31	corollary	corollary	ADJ
ejpam-5431	572	32	5	5	NUM
ejpam-5431	572	33	,	,	PUNCT
ejpam-5431	572	34	we	we	PRON
ejpam-5431	572	35	can	can	AUX
ejpam-5431	572	36	identify	identify	VERB
ejpam-5431	572	37	ς	ς	PROPN
ejpam-5431	572	38	∈	∈	NOUN
ejpam-5431	572	39	x	x	PUNCT
ejpam-5431	573	1	so	so	SCONJ
ejpam-5431	573	2	that	that	SCONJ
ejpam-5431	573	3	{	{	PUNCT
ejpam-5431	573	4	ς	ς	NOUN
ejpam-5431	573	5	}	}	PUNCT
ejpam-5431	573	6	⊂	⊂	PROPN
ejpam-5431	573	7	t	t	PROPN
ejpam-5431	574	1	ς	ς	PROPN
ejpam-5431	574	2	=	=	PUNCT
ejpam-5431	575	1	[	[	X
ejpam-5431	575	2	t	t	NOUN
ejpam-5431	575	3	ς](⋉,β	ς](⋉,β	NUM
ejpam-5431	575	4	)	)	PUNCT
ejpam-5431	575	5	∈w	∈w	NOUN
ejpam-5431	575	6	(	(	PUNCT
ejpam-5431	575	7	x	x	NOUN
ejpam-5431	575	8	)	)	PUNCT
ejpam-5431	575	9	.	.	PUNCT
ejpam-5431	576	1	the	the	DET
ejpam-5431	576	2	definition	definition	NOUN
ejpam-5431	576	3	of	of	ADP
ejpam-5431	576	4	single	single	ADV
ejpam-5431	576	5	-	-	PUNCT
ejpam-5431	576	6	valued	value	VERB
ejpam-5431	576	7	γ	γ	NOUN
ejpam-5431	576	8	-	-	ADJ
ejpam-5431	576	9	admissible	admissible	ADJ
ejpam-5431	576	10	map	map	NOUN
ejpam-5431	576	11	proposed	propose	VERB
ejpam-5431	576	12	by	by	ADP
ejpam-5431	576	13	samet	samet	NOUN
ejpam-5431	576	14	in	in	ADP
ejpam-5431	576	15	[	[	X
ejpam-5431	576	16	25	25	NUM
ejpam-5431	576	17	]	]	PUNCT
ejpam-5431	576	18	is	be	AUX
ejpam-5431	576	19	provided	provide	VERB
ejpam-5431	576	20	here	here	ADV
ejpam-5431	576	21	:	:	PUNCT
ejpam-5431	576	22	definition	definition	NOUN
ejpam-5431	576	23	28	28	NUM
ejpam-5431	576	24	.	.	PUNCT
ejpam-5431	577	1	let	let	VERB
ejpam-5431	577	2	o	o	NOUN
ejpam-5431	577	3	:	:	PUNCT
ejpam-5431	577	4	x	x	SYM
ejpam-5431	577	5	→	→	SYM
ejpam-5431	577	6	x	x	X
ejpam-5431	577	7	and	and	CCONJ
ejpam-5431	577	8	γ	γ	X
ejpam-5431	577	9	:	:	PUNCT
ejpam-5431	577	10	x	x	PROPN
ejpam-5431	577	11	×x	×x	ADP
ejpam-5431	577	12	→	→	PUNCT
ejpam-5431	577	13	r+	r+	NOUN
ejpam-5431	577	14	be	be	AUX
ejpam-5431	577	15	mappings	mapping	NOUN
ejpam-5431	577	16	.	.	PUNCT
ejpam-5431	578	1	then	then	ADV
ejpam-5431	578	2	,	,	PUNCT
ejpam-5431	578	3	o	o	PROPN
ejpam-5431	578	4	is	be	AUX
ejpam-5431	578	5	named	name	VERB
ejpam-5431	578	6	as	as	ADP
ejpam-5431	578	7	γ	γ	NOUN
ejpam-5431	578	8	-	-	ADJ
ejpam-5431	578	9	admissible	admissible	ADJ
ejpam-5431	578	10	if	if	SCONJ
ejpam-5431	578	11	for	for	ADP
ejpam-5431	578	12	all	all	DET
ejpam-5431	578	13	x	x	NOUN
ejpam-5431	578	14	,	,	PUNCT
ejpam-5431	578	15	τ	τ	PROPN
ejpam-5431	578	16	∈	∈	PROPN
ejpam-5431	578	17	x	x	SYM
ejpam-5431	578	18	,	,	PUNCT
ejpam-5431	578	19	γ(σ	γ(σ	PROPN
ejpam-5431	578	20	,	,	PUNCT
ejpam-5431	578	21	τ	τ	PROPN
ejpam-5431	578	22	)	)	PUNCT
ejpam-5431	578	23	≥	≥	NOUN
ejpam-5431	578	24	1	1	NUM
ejpam-5431	578	25	⇒	⇒	NOUN
ejpam-5431	578	26	γ(oσ	γ(oσ	PROPN
ejpam-5431	578	27	,	,	PUNCT
ejpam-5431	578	28	oτ	oτ	NOUN
ejpam-5431	578	29	)	)	PUNCT
ejpam-5431	578	30	≥	≥	NOUN
ejpam-5431	578	31	1	1	NUM
ejpam-5431	578	32	.	.	PUNCT
ejpam-5431	579	1	(	(	PUNCT
ejpam-5431	579	2	26	26	NUM
ejpam-5431	579	3	)	)	PUNCT
ejpam-5431	579	4	chifu	chifu	VERB
ejpam-5431	579	5	and	and	CCONJ
ejpam-5431	579	6	karapinar	karapinar	NOUN
ejpam-5431	579	7	came	come	VERB
ejpam-5431	579	8	up	up	ADP
ejpam-5431	579	9	with	with	ADP
ejpam-5431	579	10	this	this	DET
ejpam-5431	579	11	corollary	corollary	NOUN
ejpam-5431	579	12	without	without	ADP
ejpam-5431	579	13	relying	rely	VERB
ejpam-5431	579	14	on	on	ADP
ejpam-5431	579	15	triangular	triangular	ADJ
ejpam-5431	579	16	γorbital	γorbital	ADJ
ejpam-5431	579	17	admissibility	admissibility	NOUN
ejpam-5431	579	18	of	of	ADP
ejpam-5431	579	19	o	o	PROPN
ejpam-5431	579	20	:	:	PUNCT
ejpam-5431	579	21	n.	n.	PROPN
ejpam-5431	579	22	saleem	saleem	PROPN
ejpam-5431	579	23	et	et	PROPN
ejpam-5431	579	24	al	al	PROPN
ejpam-5431	579	25	.	.	PUNCT
ejpam-5431	579	26	/	/	SYM
ejpam-5431	579	27	eur	eur	PROPN
ejpam-5431	579	28	.	.	PUNCT
ejpam-5431	580	1	j.	j.	PROPN
ejpam-5431	580	2	pure	pure	PROPN
ejpam-5431	580	3	appl	appl	PROPN
ejpam-5431	580	4	.	.	PROPN
ejpam-5431	580	5	math	math	PROPN
ejpam-5431	580	6	,	,	PUNCT
ejpam-5431	580	7	17	17	NUM
ejpam-5431	580	8	(	(	PUNCT
ejpam-5431	580	9	4	4	NUM
ejpam-5431	580	10	)	)	PUNCT
ejpam-5431	580	11	(	(	PUNCT
ejpam-5431	580	12	2024	2024	NUM
ejpam-5431	580	13	)	)	PUNCT
ejpam-5431	580	14	,	,	PUNCT
ejpam-5431	580	15	3304	3304	NUM
ejpam-5431	580	16	-	-	SYM
ejpam-5431	580	17	3335	3335	NUM
ejpam-5431	580	18	3328	3328	NUM
ejpam-5431	580	19	corollary	corollary	NOUN
ejpam-5431	580	20	7	7	NUM
ejpam-5431	580	21	.	.	PUNCT
ejpam-5431	581	1	let	let	AUX
ejpam-5431	581	2	(	(	PUNCT
ejpam-5431	581	3	x	x	NOUN
ejpam-5431	581	4	,	,	PUNCT
ejpam-5431	581	5	δ	δ	PROPN
ejpam-5431	581	6	,	,	PUNCT
ejpam-5431	581	7	h	h	NOUN
ejpam-5431	581	8	)	)	PUNCT
ejpam-5431	581	9	be	be	AUX
ejpam-5431	581	10	a	a	DET
ejpam-5431	581	11	complete	complete	ADJ
ejpam-5431	581	12	b	b	NOUN
ejpam-5431	581	13	-	-	PUNCT
ejpam-5431	581	14	ms	ms	NOUN
ejpam-5431	581	15	and	and	CCONJ
ejpam-5431	581	16	o	o	NOUN
ejpam-5431	581	17	:	:	PUNCT
ejpam-5431	581	18	x	x	X
ejpam-5431	581	19	→	→	PUNCT
ejpam-5431	581	20	x	x	PUNCT
ejpam-5431	581	21	be	be	AUX
ejpam-5431	581	22	a	a	DET
ejpam-5431	581	23	γ	γ	NOUN
ejpam-5431	581	24	-	-	ADJ
ejpam-5431	581	25	admissible	admissible	ADJ
ejpam-5431	581	26	singlevalued	singlevalue	VERB
ejpam-5431	581	27	mapping	mapping	NOUN
ejpam-5431	581	28	fulfilling	fulfil	VERB
ejpam-5431	581	29	:	:	PUNCT
ejpam-5431	581	30	℘(γ(σ	℘(γ(σ	ADJ
ejpam-5431	581	31	,	,	PUNCT
ejpam-5431	581	32	τ)ℵ(oσ	τ)ℵ(oσ	X
ejpam-5431	581	33	,	,	PUNCT
ejpam-5431	581	34	oτ	oτ	NOUN
ejpam-5431	581	35	)	)	PUNCT
ejpam-5431	581	36	,	,	PUNCT
ejpam-5431	581	37	φ(m	φ(m	ADJ
ejpam-5431	581	38	r	r	NOUN
ejpam-5431	581	39	o(σ	o(σ	PROPN
ejpam-5431	581	40	,	,	PUNCT
ejpam-5431	581	41	τ	τ	PROPN
ejpam-5431	581	42	)	)	PUNCT
ejpam-5431	581	43	)	)	PUNCT
ejpam-5431	581	44	≥	≥	NOUN
ejpam-5431	581	45	0	0	NUM
ejpam-5431	581	46	(	(	PUNCT
ejpam-5431	581	47	27	27	NUM
ejpam-5431	581	48	)	)	PUNCT
ejpam-5431	581	49	for	for	ADP
ejpam-5431	581	50	all	all	DET
ejpam-5431	581	51	σ	σ	PROPN
ejpam-5431	581	52	,	,	PUNCT
ejpam-5431	581	53	τ	τ	PROPN
ejpam-5431	581	54	∈	∈	PROPN
ejpam-5431	581	55	x	x	NOUN
ejpam-5431	581	56	,	,	PUNCT
ejpam-5431	581	57	where	where	SCONJ
ejpam-5431	581	58	φ	φ	PROPN
ejpam-5431	581	59	∈	∈	PROPN
ejpam-5431	581	60	λb	λb	PROPN
ejpam-5431	581	61	,	,	PUNCT
ejpam-5431	581	62	m	m	VERB
ejpam-5431	581	63	r	r	NOUN
ejpam-5431	581	64	o(σ	o(σ	PROPN
ejpam-5431	581	65	,	,	PUNCT
ejpam-5431	581	66	τ	τ	X
ejpam-5431	581	67	)	)	PUNCT
ejpam-5431	581	68	=	=	PRON
ejpam-5431	581	69	{	{	PUNCT
ejpam-5431	582	1	[	[	X
ejpam-5431	582	2	w	w	X
ejpam-5431	582	3	(	(	PUNCT
ejpam-5431	582	4	σ	σ	PROPN
ejpam-5431	582	5	,	,	PUNCT
ejpam-5431	582	6	τ	τ	PROPN
ejpam-5431	582	7	)	)	PUNCT
ejpam-5431	582	8	]	]	PUNCT
ejpam-5431	582	9	1	1	NUM
ejpam-5431	582	10	r	r	NOUN
ejpam-5431	582	11	,	,	PUNCT
ejpam-5431	582	12	for	for	ADP
ejpam-5431	582	13	r	r	NOUN
ejpam-5431	582	14	>	>	X
ejpam-5431	582	15	0	0	NUM
ejpam-5431	582	16	,	,	PUNCT
ejpam-5431	582	17	σ	σ	PROPN
ejpam-5431	582	18	,	,	PUNCT
ejpam-5431	582	19	τ	τ	PROPN
ejpam-5431	582	20	∈	∈	PROPN
ejpam-5431	582	21	x	x	PUNCT
ejpam-5431	582	22	d(σ	d(σ	PROPN
ejpam-5431	582	23	,	,	PUNCT
ejpam-5431	582	24	τ	τ	PROPN
ejpam-5431	582	25	)	)	PUNCT
ejpam-5431	582	26	,	,	PUNCT
ejpam-5431	582	27	for	for	ADP
ejpam-5431	582	28	r	r	NOUN
ejpam-5431	582	29	=	=	SYM
ejpam-5431	582	30	0	0	NUM
ejpam-5431	582	31	,	,	PUNCT
ejpam-5431	582	32	σ	σ	PROPN
ejpam-5431	582	33	,	,	PUNCT
ejpam-5431	582	34	τ	τ	PROPN
ejpam-5431	582	35	∈	∈	PROPN
ejpam-5431	582	36	x	x	SYM
ejpam-5431	582	37	,	,	PUNCT
ejpam-5431	582	38	w	w	PROPN
ejpam-5431	582	39	(	(	PUNCT
ejpam-5431	582	40	σ	σ	PROPN
ejpam-5431	582	41	,	,	PUNCT
ejpam-5431	582	42	τ	τ	X
ejpam-5431	582	43	)	)	PUNCT
ejpam-5431	582	44	=	=	SYM
ejpam-5431	582	45	k1(δ(σ	k1(δ(σ	X
ejpam-5431	582	46	,	,	PUNCT
ejpam-5431	582	47	τ	τ	NOUN
ejpam-5431	582	48	)	)	PUNCT
ejpam-5431	582	49	)	)	PUNCT
ejpam-5431	583	1	r	r	NOUN
ejpam-5431	583	2	+	+	CCONJ
ejpam-5431	583	3	k2(δ(σ	k2(δ(σ	PROPN
ejpam-5431	583	4	,	,	PUNCT
ejpam-5431	583	5	oσ	oσ	NOUN
ejpam-5431	583	6	)	)	PUNCT
ejpam-5431	583	7	)	)	PUNCT
ejpam-5431	584	1	r	r	NOUN
ejpam-5431	584	2	+	+	NUM
ejpam-5431	584	3	k3(δ(τ	k3(δ(τ	NUM
ejpam-5431	584	4	,	,	PUNCT
ejpam-5431	584	5	oτ	oτ	NOUN
ejpam-5431	584	6	)	)	PUNCT
ejpam-5431	584	7	)	)	PUNCT
ejpam-5431	585	1	r	r	NOUN
ejpam-5431	585	2	+	+	PRON
ejpam-5431	585	3	k4	k4	NOUN
ejpam-5431	585	4	(	(	PUNCT
ejpam-5431	585	5	δ(τ	δ(τ	NOUN
ejpam-5431	585	6	,	,	PUNCT
ejpam-5431	585	7	oτ)(1	oτ)(1	ADJ
ejpam-5431	585	8	+	+	CCONJ
ejpam-5431	585	9	δ(σ	δ(σ	NOUN
ejpam-5431	585	10	,	,	PUNCT
ejpam-5431	585	11	oσ	oσ	NOUN
ejpam-5431	585	12	)	)	PUNCT
ejpam-5431	585	13	)	)	PUNCT
ejpam-5431	585	14	1	1	NUM
ejpam-5431	586	1	+	+	CCONJ
ejpam-5431	586	2	δ(σ	δ(σ	PROPN
ejpam-5431	586	3	,	,	PUNCT
ejpam-5431	586	4	τ	τ	X
ejpam-5431	586	5	)	)	PUNCT
ejpam-5431	586	6	)	)	PUNCT
ejpam-5431	586	7	r	r	NOUN
ejpam-5431	586	8	+	+	NUM
ejpam-5431	586	9	k5	k5	PROPN
ejpam-5431	586	10	(	(	PUNCT
ejpam-5431	586	11	δ(τ	δ(τ	PROPN
ejpam-5431	586	12	,	,	PUNCT
ejpam-5431	586	13	oσ)(1	oσ)(1	ADP
ejpam-5431	586	14	+	+	ADJ
ejpam-5431	586	15	δ(σ	δ(σ	PROPN
ejpam-5431	586	16	,	,	PUNCT
ejpam-5431	586	17	oτ	oτ	NOUN
ejpam-5431	586	18	)	)	PUNCT
ejpam-5431	586	19	)	)	PUNCT
ejpam-5431	586	20	1	1	NUM
ejpam-5431	586	21	+	+	CCONJ
ejpam-5431	586	22	δ(σ	δ(σ	PROPN
ejpam-5431	586	23	,	,	PUNCT
ejpam-5431	586	24	τ	τ	X
ejpam-5431	586	25	)	)	PUNCT
ejpam-5431	586	26	)	)	PUNCT
ejpam-5431	586	27	r	r	NOUN
ejpam-5431	586	28	and	and	CCONJ
ejpam-5431	586	29	d(σ	d(σ	PROPN
ejpam-5431	586	30	,	,	PUNCT
ejpam-5431	586	31	τ	τ	X
ejpam-5431	586	32	)	)	PUNCT
ejpam-5431	586	33	=	=	SYM
ejpam-5431	586	34	(	(	PUNCT
ejpam-5431	586	35	δ(σ	δ(σ	PROPN
ejpam-5431	586	36	,	,	PUNCT
ejpam-5431	586	37	τ))k1	τ))k1	PRON
ejpam-5431	586	38	×	×	NOUN
ejpam-5431	586	39	(	(	PUNCT
ejpam-5431	586	40	δ(σ	δ(σ	PROPN
ejpam-5431	586	41	,	,	PUNCT
ejpam-5431	586	42	oσ))k2	oσ))k2	NOUN
ejpam-5431	586	43	×	×	NOUN
ejpam-5431	586	44	(	(	PUNCT
ejpam-5431	586	45	δ(τ	δ(τ	PROPN
ejpam-5431	586	46	,	,	PUNCT
ejpam-5431	586	47	oτ))k3	oτ))k3	NUM
ejpam-5431	586	48	×	×	NOUN
ejpam-5431	586	49	(	(	PUNCT
ejpam-5431	586	50	δ(τ	δ(τ	PROPN
ejpam-5431	586	51	,	,	PUNCT
ejpam-5431	586	52	oτ)(1	oτ)(1	ADJ
ejpam-5431	586	53	+	+	CCONJ
ejpam-5431	586	54	δ(σ	δ(σ	NOUN
ejpam-5431	586	55	,	,	PUNCT
ejpam-5431	586	56	oσ	oσ	NOUN
ejpam-5431	586	57	)	)	PUNCT
ejpam-5431	586	58	)	)	PUNCT
ejpam-5431	586	59	1	1	NUM
ejpam-5431	587	1	+	+	CCONJ
ejpam-5431	587	2	δ(σ	δ(σ	PROPN
ejpam-5431	587	3	,	,	PUNCT
ejpam-5431	587	4	τ	τ	X
ejpam-5431	587	5	)	)	PUNCT
ejpam-5431	587	6	)	)	PUNCT
ejpam-5431	587	7	k4	k4	PROPN
ejpam-5431	587	8	×	×	NOUN
ejpam-5431	587	9	(	(	PUNCT
ejpam-5431	587	10	δ(σ	δ(σ	PROPN
ejpam-5431	587	11	,	,	PUNCT
ejpam-5431	587	12	oτ	oτ	PROPN
ejpam-5431	587	13	)	)	PUNCT
ejpam-5431	587	14	+	+	CCONJ
ejpam-5431	587	15	δ(τ	δ(τ	PROPN
ejpam-5431	587	16	,	,	PUNCT
ejpam-5431	587	17	oσ	oσ	PROPN
ejpam-5431	587	18	)	)	PUNCT
ejpam-5431	587	19	2h	2h	NUM
ejpam-5431	587	20	)	)	PUNCT
ejpam-5431	587	21	k5	k5	NOUN
ejpam-5431	587	22	with	with	ADP
ejpam-5431	587	23	r	r	PROPN
ejpam-5431	587	24	≥	≥	NOUN
ejpam-5431	587	25	0	0	NUM
ejpam-5431	587	26	and	and	CCONJ
ejpam-5431	587	27	ki	ki	PROPN
ejpam-5431	587	28	≥	≥	NUM
ejpam-5431	587	29	0	0	NUM
ejpam-5431	587	30	(	(	PUNCT
ejpam-5431	587	31	i	i	NOUN
ejpam-5431	587	32	=	=	NOUN
ejpam-5431	587	33	1	1	NUM
ejpam-5431	587	34	,	,	PUNCT
ejpam-5431	587	35	5	5	NUM
ejpam-5431	587	36	)	)	PUNCT
ejpam-5431	588	1	such	such	ADJ
ejpam-5431	588	2	that	that	DET
ejpam-5431	588	3	∑5	∑5	PROPN
ejpam-5431	588	4	i=1	i=1	PROPN
ejpam-5431	588	5	ki	ki	PROPN
ejpam-5431	588	6	=	=	NOUN
ejpam-5431	588	7	1	1	X
ejpam-5431	588	8	.	.	PUNCT
ejpam-5431	588	9	then	then	ADV
ejpam-5431	588	10	,	,	PUNCT
ejpam-5431	588	11	there	there	PRON
ejpam-5431	588	12	exists	exist	VERB
ejpam-5431	588	13	ς	ς	PROPN
ejpam-5431	588	14	∈	∈	PROPN
ejpam-5431	588	15	x	x	PUNCT
ejpam-5431	588	16	such	such	ADJ
ejpam-5431	588	17	that	that	DET
ejpam-5431	588	18	oς	oς	ADP
ejpam-5431	588	19	=	=	SYM
ejpam-5431	588	20	ς	ς	PROPN
ejpam-5431	588	21	.	.	PUNCT
ejpam-5431	588	22	proof	proof	NOUN
ejpam-5431	588	23	.	.	PUNCT
ejpam-5431	589	1	let	let	VERB
ejpam-5431	589	2	(	(	PUNCT
ejpam-5431	589	3	⋉	⋉	PROPN
ejpam-5431	589	4	,	,	PUNCT
ejpam-5431	589	5	β	β	NOUN
ejpam-5431	589	6	)	)	PUNCT
ejpam-5431	589	7	∈	∈	PROPN
ejpam-5431	589	8	(	(	PUNCT
ejpam-5431	589	9	0	0	NUM
ejpam-5431	589	10	,	,	PUNCT
ejpam-5431	589	11	1	1	NUM
ejpam-5431	589	12	]	]	SYM
ejpam-5431	589	13	×	×	NOUN
ejpam-5431	590	1	[	[	X
ejpam-5431	590	2	0	0	NUM
ejpam-5431	590	3	,	,	PUNCT
ejpam-5431	590	4	1	1	NUM
ejpam-5431	590	5	)	)	PUNCT
ejpam-5431	590	6	and	and	CCONJ
ejpam-5431	590	7	for	for	ADP
ejpam-5431	590	8	each	each	DET
ejpam-5431	590	9	σ	σ	NUM
ejpam-5431	590	10	∈	∈	PROPN
ejpam-5431	590	11	x	x	NOUN
ejpam-5431	590	12	,	,	PUNCT
ejpam-5431	590	13	consider	consider	VERB
ejpam-5431	590	14	an	an	DET
ejpam-5431	590	15	ifs	ifs	NOUN
ejpam-5431	590	16	-	-	PUNCT
ejpam-5431	590	17	valued	value	VERB
ejpam-5431	590	18	map	map	NOUN
ejpam-5431	590	19	t	t	NOUN
ejpam-5431	590	20	and	and	CCONJ
ejpam-5431	590	21	for	for	ADP
ejpam-5431	590	22	σ	σ	PROPN
ejpam-5431	590	23	∈	∈	PROPN
ejpam-5431	590	24	x	x	PROPN
ejpam-5431	590	25	,	,	PUNCT
ejpam-5431	590	26	t	t	PROPN
ejpam-5431	590	27	σ	σ	PROPN
ejpam-5431	590	28	is	be	AUX
ejpam-5431	590	29	an	an	DET
ejpam-5431	590	30	ifs	if	NOUN
ejpam-5431	590	31	such	such	ADJ
ejpam-5431	590	32	that	that	SCONJ
ejpam-5431	590	33	µt	µt	PROPN
ejpam-5431	590	34	σ	σ	X
ejpam-5431	590	35	:	:	PUNCT
ejpam-5431	590	36	x	x	X
ejpam-5431	590	37	→	→	PUNCT
ejpam-5431	591	1	[	[	X
ejpam-5431	591	2	0	0	NUM
ejpam-5431	591	3	,	,	PUNCT
ejpam-5431	591	4	1	1	NUM
ejpam-5431	591	5	]	]	PUNCT
ejpam-5431	591	6	is	be	AUX
ejpam-5431	591	7	membership	membership	NOUN
ejpam-5431	591	8	function	function	NOUN
ejpam-5431	591	9	and	and	CCONJ
ejpam-5431	591	10	νt	νt	PROPN
ejpam-5431	591	11	σ	σ	NOUN
ejpam-5431	591	12	:	:	PUNCT
ejpam-5431	592	1	x	x	X
ejpam-5431	592	2	→	→	PUNCT
ejpam-5431	592	3	[	[	X
ejpam-5431	592	4	0	0	NUM
ejpam-5431	592	5	,	,	PUNCT
ejpam-5431	592	6	1	1	NUM
ejpam-5431	592	7	]	]	PUNCT
ejpam-5431	592	8	is	be	AUX
ejpam-5431	592	9	nonmembership	nonmembership	NOUN
ejpam-5431	592	10	function	function	NOUN
ejpam-5431	592	11	.	.	PUNCT
ejpam-5431	593	1	we	we	PRON
ejpam-5431	593	2	define	define	VERB
ejpam-5431	593	3	these	these	DET
ejpam-5431	593	4	maps	map	NOUN
ejpam-5431	593	5	as	as	ADP
ejpam-5431	593	6	µt	µt	PROPN
ejpam-5431	593	7	σ(a	σ(a	PROPN
ejpam-5431	593	8	)	)	PUNCT
ejpam-5431	593	9	=	=	PRON
ejpam-5431	593	10	{	{	PUNCT
ejpam-5431	594	1	⋉	⋉	PROPN
ejpam-5431	594	2	,	,	PUNCT
ejpam-5431	594	3	if	if	SCONJ
ejpam-5431	594	4	a	a	PRON
ejpam-5431	594	5	=	=	X
ejpam-5431	594	6	oσ	oσ	ADJ
ejpam-5431	594	7	0	0	NUM
ejpam-5431	594	8	,	,	PUNCT
ejpam-5431	594	9	if	if	SCONJ
ejpam-5431	594	10	a	a	DET
ejpam-5431	594	11	̸=	̸=	PROPN
ejpam-5431	594	12	oσ	oσ	ADV
ejpam-5431	594	13	,	,	PUNCT
ejpam-5431	594	14	and	and	CCONJ
ejpam-5431	594	15	νt	νt	PROPN
ejpam-5431	594	16	σ(a	σ(a	PROPN
ejpam-5431	594	17	)	)	PUNCT
ejpam-5431	594	18	=	=	PRON
ejpam-5431	594	19	{	{	PUNCT
ejpam-5431	594	20	0	0	NUM
ejpam-5431	594	21	,	,	PUNCT
ejpam-5431	594	22	if	if	SCONJ
ejpam-5431	594	23	a	a	PRON
ejpam-5431	594	24	=	=	X
ejpam-5431	594	25	oσ	oσ	ADJ
ejpam-5431	594	26	β	β	NOUN
ejpam-5431	594	27	,	,	PUNCT
ejpam-5431	594	28	if	if	SCONJ
ejpam-5431	594	29	a	a	DET
ejpam-5431	594	30	̸=	̸=	PROPN
ejpam-5431	594	31	oσ	oσ	ADV
ejpam-5431	594	32	,	,	PUNCT
ejpam-5431	594	33	then	then	ADV
ejpam-5431	594	34	,	,	PUNCT
ejpam-5431	595	1	[	[	X
ejpam-5431	595	2	t	t	NOUN
ejpam-5431	595	3	x](⋉,β	x](⋉,β	NUM
ejpam-5431	595	4	)	)	PUNCT
ejpam-5431	595	5	=	=	PRON
ejpam-5431	595	6	{	{	PUNCT
ejpam-5431	595	7	a	a	DET
ejpam-5431	595	8	∈	∈	NOUN
ejpam-5431	595	9	x	x	X
ejpam-5431	595	10	:	:	PUNCT
ejpam-5431	595	11	µt	µt	PROPN
ejpam-5431	595	12	σ(a	σ(a	PROPN
ejpam-5431	595	13	)	)	PUNCT
ejpam-5431	595	14	≥	≥	NOUN
ejpam-5431	595	15	⋉	⋉	ADV
ejpam-5431	595	16	and	and	CCONJ
ejpam-5431	595	17	νt	νt	PROPN
ejpam-5431	595	18	σ(a	σ(a	PROPN
ejpam-5431	595	19	)	)	PUNCT
ejpam-5431	595	20	≤	≤	NOUN
ejpam-5431	595	21	β	β	X
ejpam-5431	595	22	}	}	PUNCT
ejpam-5431	595	23	.	.	PUNCT
ejpam-5431	596	1	obviously	obviously	ADV
ejpam-5431	596	2	,	,	PUNCT
ejpam-5431	596	3	{	{	PUNCT
ejpam-5431	596	4	oσ	oσ	PROPN
ejpam-5431	596	5	}	}	PUNCT
ejpam-5431	596	6	∈	∈	PROPN
ejpam-5431	596	7	q(x	q(x	PROPN
ejpam-5431	596	8	)	)	PUNCT
ejpam-5431	596	9	.	.	PUNCT
ejpam-5431	596	10	notice	notice	VERB
ejpam-5431	596	11	that	that	SCONJ
ejpam-5431	596	12	in	in	ADP
ejpam-5431	596	13	this	this	DET
ejpam-5431	596	14	case	case	NOUN
ejpam-5431	596	15	,	,	PUNCT
ejpam-5431	596	16	ℵ([t	ℵ([t	PRON
ejpam-5431	596	17	σ](⋉,β	σ](⋉,β	NUM
ejpam-5431	596	18	)	)	PUNCT
ejpam-5431	596	19	,	,	PUNCT
ejpam-5431	596	20	[	[	X
ejpam-5431	596	21	t	t	X
ejpam-5431	596	22	τ	τ	X
ejpam-5431	596	23	]	]	X
ejpam-5431	596	24	(	(	PUNCT
ejpam-5431	596	25	⋉,β	⋉,β	NOUN
ejpam-5431	596	26	)	)	PUNCT
ejpam-5431	596	27	)	)	PUNCT
ejpam-5431	597	1	=	=	SYM
ejpam-5431	597	2	δ(oσ	δ(oσ	X
ejpam-5431	597	3	,	,	PUNCT
ejpam-5431	597	4	oτ	oτ	NOUN
ejpam-5431	597	5	)	)	PUNCT
ejpam-5431	597	6	.	.	PUNCT
ejpam-5431	598	1	therefore	therefore	ADV
ejpam-5431	598	2	,	,	PUNCT
ejpam-5431	598	3	corollary	corollary	ADJ
ejpam-5431	598	4	(	(	PUNCT
ejpam-5431	598	5	1	1	NUM
ejpam-5431	598	6	)	)	PUNCT
ejpam-5431	598	7	can	can	AUX
ejpam-5431	598	8	be	be	AUX
ejpam-5431	598	9	applied	apply	VERB
ejpam-5431	598	10	to	to	PART
ejpam-5431	598	11	obtain	obtain	VERB
ejpam-5431	598	12	ς	ς	PROPN
ejpam-5431	598	13	∈	∈	NOUN
ejpam-5431	598	14	x	x	PUNCT
ejpam-5431	598	15	such	such	ADJ
ejpam-5431	598	16	that	that	SCONJ
ejpam-5431	598	17	ς	ς	PROPN
ejpam-5431	598	18	∈	∈	PROPN
ejpam-5431	599	1	[	[	X
ejpam-5431	599	2	t	t	NOUN
ejpam-5431	599	3	ς](⋉,β	ς](⋉,β	NUM
ejpam-5431	599	4	)	)	PUNCT
ejpam-5431	599	5	=	=	PRON
ejpam-5431	599	6	{	{	PUNCT
ejpam-5431	599	7	oς	oς	ADP
ejpam-5431	599	8	}	}	PUNCT
ejpam-5431	599	9	,	,	PUNCT
ejpam-5431	599	10	which	which	PRON
ejpam-5431	599	11	further	far	ADV
ejpam-5431	599	12	implies	imply	VERB
ejpam-5431	599	13	that	that	SCONJ
ejpam-5431	599	14	ς	ς	PROPN
ejpam-5431	599	15	=	=	PUNCT
ejpam-5431	599	16	oς	oς	PROPN
ejpam-5431	599	17	.	.	PUNCT
ejpam-5431	599	18	n.	n.	PROPN
ejpam-5431	599	19	saleem	saleem	PROPN
ejpam-5431	599	20	et	et	PROPN
ejpam-5431	599	21	al	al	PROPN
ejpam-5431	599	22	.	.	PUNCT
ejpam-5431	599	23	/	/	SYM
ejpam-5431	599	24	eur	eur	PROPN
ejpam-5431	599	25	.	.	PUNCT
ejpam-5431	600	1	j.	j.	PROPN
ejpam-5431	600	2	pure	pure	PROPN
ejpam-5431	600	3	appl	appl	PROPN
ejpam-5431	600	4	.	.	PROPN
ejpam-5431	600	5	math	math	PROPN
ejpam-5431	600	6	,	,	PUNCT
ejpam-5431	600	7	17	17	NUM
ejpam-5431	600	8	(	(	PUNCT
ejpam-5431	600	9	4	4	NUM
ejpam-5431	600	10	)	)	PUNCT
ejpam-5431	600	11	(	(	PUNCT
ejpam-5431	600	12	2024	2024	NUM
ejpam-5431	600	13	)	)	PUNCT
ejpam-5431	600	14	,	,	PUNCT
ejpam-5431	600	15	3304	3304	NUM
ejpam-5431	600	16	-	-	SYM
ejpam-5431	600	17	3335	3335	NUM
ejpam-5431	600	18	3329	3329	NUM
ejpam-5431	600	19	5	5	NUM
ejpam-5431	600	20	.	.	PUNCT
ejpam-5431	601	1	application	application	NOUN
ejpam-5431	601	2	one	one	NUM
ejpam-5431	601	3	of	of	ADP
ejpam-5431	601	4	the	the	DET
ejpam-5431	601	5	most	most	ADV
ejpam-5431	601	6	helpful	helpful	ADJ
ejpam-5431	601	7	subfields	subfield	NOUN
ejpam-5431	601	8	of	of	ADP
ejpam-5431	601	9	fixed	fix	VERB
ejpam-5431	601	10	theory	theory	NOUN
ejpam-5431	601	11	,	,	PUNCT
ejpam-5431	601	12	fp	fp	PROPN
ejpam-5431	601	13	theory	theory	NOUN
ejpam-5431	601	14	in	in	ADP
ejpam-5431	601	15	partially	partially	ADV
ejpam-5431	601	16	ordered	order	VERB
ejpam-5431	601	17	sets	set	NOUN
ejpam-5431	601	18	has	have	VERB
ejpam-5431	601	19	many	many	ADJ
ejpam-5431	601	20	applications	application	NOUN
ejpam-5431	601	21	,	,	PUNCT
ejpam-5431	601	22	including	include	VERB
ejpam-5431	601	23	solving	solve	VERB
ejpam-5431	601	24	matrix	matrix	NOUN
ejpam-5431	601	25	equations	equation	NOUN
ejpam-5431	601	26	and	and	CCONJ
ejpam-5431	601	27	solving	solve	VERB
ejpam-5431	601	28	boundary	boundary	ADJ
ejpam-5431	601	29	value	value	NOUN
ejpam-5431	601	30	issues	issue	NOUN
ejpam-5431	601	31	.	.	PUNCT
ejpam-5431	602	1	see	see	VERB
ejpam-5431	602	2	[	[	X
ejpam-5431	602	3	3	3	NUM
ejpam-5431	602	4	,	,	PUNCT
ejpam-5431	602	5	20	20	NUM
ejpam-5431	602	6	,	,	PUNCT
ejpam-5431	602	7	21	21	NUM
ejpam-5431	602	8	]	]	PUNCT
ejpam-5431	602	9	for	for	ADP
ejpam-5431	602	10	a	a	DET
ejpam-5431	602	11	few	few	ADJ
ejpam-5431	602	12	articles	article	NOUN
ejpam-5431	602	13	that	that	PRON
ejpam-5431	602	14	go	go	VERB
ejpam-5431	602	15	in	in	ADP
ejpam-5431	602	16	this	this	DET
ejpam-5431	602	17	direction	direction	NOUN
ejpam-5431	602	18	.	.	PUNCT
ejpam-5431	603	1	here	here	ADV
ejpam-5431	603	2	,	,	PUNCT
ejpam-5431	603	3	we	we	PRON
ejpam-5431	603	4	will	will	AUX
ejpam-5431	603	5	utilize	utilize	VERB
ejpam-5431	603	6	our	our	PRON
ejpam-5431	603	7	principal	principal	ADJ
ejpam-5431	603	8	discovery	discovery	NOUN
ejpam-5431	603	9	to	to	PART
ejpam-5431	603	10	derive	derive	VERB
ejpam-5431	603	11	its	its	PRON
ejpam-5431	603	12	counterpart	counterpart	NOUN
ejpam-5431	603	13	within	within	ADP
ejpam-5431	603	14	the	the	DET
ejpam-5431	603	15	framework	framework	NOUN
ejpam-5431	603	16	of	of	ADP
ejpam-5431	603	17	ordered	order	VERB
ejpam-5431	603	18	b	b	PROPN
ejpam-5431	603	19	-	-	PUNCT
ejpam-5431	603	20	ms	ms	NOUN
ejpam-5431	603	21	.	.	PROPN
ejpam-5431	603	22	importantly	importantly	ADV
ejpam-5431	603	23	,	,	PUNCT
ejpam-5431	603	24	a	a	DET
ejpam-5431	603	25	b	b	X
ejpam-5431	603	26	-	-	PUNCT
ejpam-5431	603	27	ms	ms	NOUN
ejpam-5431	603	28	can	can	AUX
ejpam-5431	603	29	be	be	AUX
ejpam-5431	603	30	equipped	equip	VERB
ejpam-5431	603	31	with	with	ADP
ejpam-5431	603	32	a	a	DET
ejpam-5431	603	33	partial	partial	ADJ
ejpam-5431	603	34	ordering	ordering	NOUN
ejpam-5431	603	35	.	.	PUNCT
ejpam-5431	604	1	to	to	PART
ejpam-5431	604	2	elaborate	elaborate	VERB
ejpam-5431	604	3	,	,	PUNCT
ejpam-5431	604	4	if	if	SCONJ
ejpam-5431	604	5	(	(	PUNCT
ejpam-5431	604	6	x,⪯	x,⪯	NUM
ejpam-5431	604	7	)	)	PUNCT
ejpam-5431	604	8	is	be	AUX
ejpam-5431	604	9	a	a	DET
ejpam-5431	604	10	partially	partially	ADV
ejpam-5431	604	11	ordered	order	VERB
ejpam-5431	604	12	set	set	NOUN
ejpam-5431	604	13	,	,	PUNCT
ejpam-5431	604	14	then	then	ADV
ejpam-5431	604	15	(	(	PUNCT
ejpam-5431	604	16	x	x	NOUN
ejpam-5431	604	17	,	,	PUNCT
ejpam-5431	604	18	δ	δ	PROPN
ejpam-5431	604	19	,	,	PUNCT
ejpam-5431	604	20	h,⪯	h,⪯	CCONJ
ejpam-5431	604	21	)	)	PUNCT
ejpam-5431	604	22	is	be	AUX
ejpam-5431	604	23	recognized	recognize	VERB
ejpam-5431	604	24	as	as	ADP
ejpam-5431	604	25	an	an	DET
ejpam-5431	604	26	ordered	ordered	ADJ
ejpam-5431	604	27	b	b	NOUN
ejpam-5431	604	28	-	-	PUNCT
ejpam-5431	604	29	ms	ms	NOUN
ejpam-5431	604	30	.	.	PROPN
ejpam-5431	604	31	as	as	ADP
ejpam-5431	604	32	a	a	DET
ejpam-5431	604	33	result	result	NOUN
ejpam-5431	604	34	,	,	PUNCT
ejpam-5431	604	35	we	we	PRON
ejpam-5431	604	36	define	define	VERB
ejpam-5431	604	37	,	,	PUNCT
ejpam-5431	604	38	σ	σ	PROPN
ejpam-5431	604	39	,	,	PUNCT
ejpam-5431	604	40	τ	τ	PROPN
ejpam-5431	604	41	∈	∈	PROPN
ejpam-5431	604	42	x	x	NOUN
ejpam-5431	604	43	are	be	AUX
ejpam-5431	604	44	comparable	comparable	ADJ
ejpam-5431	604	45	if	if	SCONJ
ejpam-5431	604	46	either	either	CCONJ
ejpam-5431	604	47	σ	σ	PROPN
ejpam-5431	604	48	⪯	⪯	PROPN
ejpam-5431	604	49	τ	τ	PROPN
ejpam-5431	604	50	or	or	CCONJ
ejpam-5431	604	51	τ	τ	PROPN
ejpam-5431	604	52	⪯	⪯	PROPN
ejpam-5431	604	53	σ	σ	PROPN
ejpam-5431	604	54	is	be	AUX
ejpam-5431	604	55	fulfilled	fulfil	VERB
ejpam-5431	604	56	.	.	PUNCT
ejpam-5431	605	1	consider	consider	VERB
ejpam-5431	605	2	£	£	SYM
ejpam-5431	605	3	,	,	PUNCT
ejpam-5431	605	4	ℜ	ℜ	NOUN
ejpam-5431	605	5	⊆	⊆	NUM
ejpam-5431	605	6	x	x	SYM
ejpam-5431	605	7	,	,	PUNCT
ejpam-5431	605	8	then	then	ADV
ejpam-5431	605	9	£	£	SYM
ejpam-5431	605	10	⪯	⪯	VERB
ejpam-5431	605	11	ℜ	ℜ	PROPN
ejpam-5431	605	12	if	if	SCONJ
ejpam-5431	605	13	for	for	ADP
ejpam-5431	605	14	all	all	DET
ejpam-5431	605	15	l	l	NOUN
ejpam-5431	605	16	∈	∈	NOUN
ejpam-5431	606	1	£	£	NOUN
ejpam-5431	606	2	,	,	PUNCT
ejpam-5431	606	3	there	there	PRON
ejpam-5431	606	4	is	be	VERB
ejpam-5431	606	5	r	r	NOUN
ejpam-5431	606	6	∈	∈	PROPN
ejpam-5431	606	7	ℜ	ℜ	PROPN
ejpam-5431	606	8	with	with	ADP
ejpam-5431	606	9	l	l	PROPN
ejpam-5431	606	10	⪯	⪯	PROPN
ejpam-5431	606	11	r.	r.	PROPN
ejpam-5431	606	12	theorem	theorem	PROPN
ejpam-5431	606	13	29	29	NUM
ejpam-5431	606	14	.	.	PUNCT
ejpam-5431	607	1	let	let	AUX
ejpam-5431	607	2	(	(	PUNCT
ejpam-5431	607	3	x	x	NOUN
ejpam-5431	607	4	,	,	PUNCT
ejpam-5431	607	5	δ	δ	PROPN
ejpam-5431	607	6	,	,	PUNCT
ejpam-5431	607	7	h,⪯	h,⪯	CCONJ
ejpam-5431	607	8	)	)	PUNCT
ejpam-5431	607	9	be	be	VERB
ejpam-5431	607	10	a	a	DET
ejpam-5431	607	11	complete	complete	ADJ
ejpam-5431	607	12	ordered	order	VERB
ejpam-5431	607	13	b	b	X
ejpam-5431	607	14	-	-	PUNCT
ejpam-5431	607	15	ms	ms	NOUN
ejpam-5431	607	16	and	and	CCONJ
ejpam-5431	607	17	s	s	PROPN
ejpam-5431	607	18	,	,	PUNCT
ejpam-5431	607	19	t	t	PROPN
ejpam-5431	607	20	are	be	AUX
ejpam-5431	607	21	ifs	ifs	PROPN
ejpam-5431	607	22	-	-	PUNCT
ejpam-5431	607	23	valued	value	VERB
ejpam-5431	607	24	maps	map	NOUN
ejpam-5431	607	25	.	.	PUNCT
ejpam-5431	608	1	consider	consider	VERB
ejpam-5431	608	2	that	that	SCONJ
ejpam-5431	608	3	there	there	PRON
ejpam-5431	608	4	is	be	VERB
ejpam-5431	608	5	℘	℘	PROPN
ejpam-5431	608	6	∈	∈	PROPN
ejpam-5431	608	7	z	z	PROPN
ejpam-5431	608	8	,	,	PUNCT
ejpam-5431	608	9	φ	φ	PROPN
ejpam-5431	608	10	∈	∈	PROPN
ejpam-5431	608	11	λb	λb	X
ejpam-5431	608	12	and	and	CCONJ
ejpam-5431	608	13	an	an	DET
ejpam-5431	608	14	operator	operator	NOUN
ejpam-5431	608	15	γ	γ	NOUN
ejpam-5431	608	16	:	:	PUNCT
ejpam-5431	608	17	x	x	PROPN
ejpam-5431	608	18	×x	×x	ADP
ejpam-5431	608	19	→	→	PUNCT
ejpam-5431	608	20	r+	r+	NOUN
ejpam-5431	608	21	such	such	ADJ
ejpam-5431	608	22	that	that	SCONJ
ejpam-5431	608	23	℘(γ(σ	℘(γ(σ	ADJ
ejpam-5431	608	24	,	,	PUNCT
ejpam-5431	608	25	τ))ℵ([sσ](⋉(σ),β(σ	τ))ℵ([sσ](⋉(σ),β(σ	NOUN
ejpam-5431	608	26	)	)	PUNCT
ejpam-5431	608	27	)	)	PUNCT
ejpam-5431	608	28	,	,	PUNCT
ejpam-5431	609	1	[	[	X
ejpam-5431	609	2	t	t	X
ejpam-5431	609	3	τ	τ	X
ejpam-5431	609	4	]	]	X
ejpam-5431	609	5	(	(	PUNCT
ejpam-5431	609	6	⋉(τ),β(τ	⋉(τ),β(τ	NOUN
ejpam-5431	609	7	)	)	PUNCT
ejpam-5431	609	8	)	)	PUNCT
ejpam-5431	609	9	)	)	PUNCT
ejpam-5431	609	10	,	,	PUNCT
ejpam-5431	609	11	φ(m	φ(m	ADJ
ejpam-5431	609	12	r	r	NOUN
ejpam-5431	609	13	(	(	PUNCT
ejpam-5431	609	14	s	s	PROPN
ejpam-5431	609	15	,	,	PUNCT
ejpam-5431	609	16	t	t	NOUN
ejpam-5431	609	17	)	)	PUNCT
ejpam-5431	609	18	(	(	PUNCT
ejpam-5431	609	19	σ	σ	PROPN
ejpam-5431	609	20	,	,	PUNCT
ejpam-5431	609	21	τ	τ	PROPN
ejpam-5431	609	22	)	)	PUNCT
ejpam-5431	609	23	)	)	PUNCT
ejpam-5431	609	24	≥	≥	NOUN
ejpam-5431	609	25	0	0	NUM
ejpam-5431	609	26	(	(	PUNCT
ejpam-5431	609	27	28	28	NUM
ejpam-5431	609	28	)	)	PUNCT
ejpam-5431	609	29	for	for	ADP
ejpam-5431	609	30	all	all	DET
ejpam-5431	609	31	σ	σ	PROPN
ejpam-5431	609	32	,	,	PUNCT
ejpam-5431	609	33	τ	τ	PROPN
ejpam-5431	609	34	∈	∈	PROPN
ejpam-5431	609	35	x	x	PUNCT
ejpam-5431	609	36	with	with	ADP
ejpam-5431	609	37	[	[	X
ejpam-5431	609	38	sσ](⋉(σ),β(σ	sσ](⋉(σ),β(σ	NOUN
ejpam-5431	609	39	)	)	PUNCT
ejpam-5431	609	40	)	)	PUNCT
ejpam-5431	609	41	⪯	⪯	NOUN
ejpam-5431	610	1	[	[	X
ejpam-5431	610	2	t	t	X
ejpam-5431	610	3	τ	τ	X
ejpam-5431	610	4	]	]	X
ejpam-5431	610	5	(	(	PUNCT
ejpam-5431	610	6	⋉(τ),β(τ	⋉(τ),β(τ	NOUN
ejpam-5431	610	7	)	)	PUNCT
ejpam-5431	610	8	)	)	PUNCT
ejpam-5431	610	9	and	and	CCONJ
ejpam-5431	610	10	℘(γ(σ	℘(γ(σ	PROPN
ejpam-5431	610	11	,	,	PUNCT
ejpam-5431	610	12	τ))ℵ([t	τ))ℵ([t	PRON
ejpam-5431	610	13	σ](⋉(σ),β(σ	σ](⋉(σ),β(σ	NOUN
ejpam-5431	610	14	)	)	PUNCT
ejpam-5431	610	15	)	)	PUNCT
ejpam-5431	610	16	,	,	PUNCT
ejpam-5431	611	1	[	[	X
ejpam-5431	611	2	sτ	sτ	ADP
ejpam-5431	611	3	]	]	PUNCT
ejpam-5431	611	4	(	(	PUNCT
ejpam-5431	611	5	⋉(τ),β(τ	⋉(τ),β(τ	NOUN
ejpam-5431	611	6	)	)	PUNCT
ejpam-5431	611	7	)	)	PUNCT
ejpam-5431	611	8	)	)	PUNCT
ejpam-5431	611	9	,	,	PUNCT
ejpam-5431	611	10	φ(m	φ(m	ADJ
ejpam-5431	611	11	r	r	NOUN
ejpam-5431	611	12	(	(	PUNCT
ejpam-5431	611	13	s	s	PROPN
ejpam-5431	611	14	,	,	PUNCT
ejpam-5431	611	15	t	t	NOUN
ejpam-5431	611	16	)	)	PUNCT
ejpam-5431	611	17	(	(	PUNCT
ejpam-5431	611	18	σ	σ	PROPN
ejpam-5431	611	19	,	,	PUNCT
ejpam-5431	611	20	τ	τ	PROPN
ejpam-5431	611	21	)	)	PUNCT
ejpam-5431	611	22	)	)	PUNCT
ejpam-5431	611	23	≥	≥	NOUN
ejpam-5431	611	24	0	0	NUM
ejpam-5431	611	25	(	(	PUNCT
ejpam-5431	611	26	29	29	NUM
ejpam-5431	611	27	)	)	PUNCT
ejpam-5431	611	28	for	for	ADP
ejpam-5431	611	29	all	all	DET
ejpam-5431	611	30	σ	σ	PROPN
ejpam-5431	611	31	,	,	PUNCT
ejpam-5431	611	32	τ	τ	PROPN
ejpam-5431	611	33	∈	∈	PROPN
ejpam-5431	611	34	x	x	PUNCT
ejpam-5431	611	35	with	with	ADP
ejpam-5431	611	36	[	[	X
ejpam-5431	611	37	t	t	NOUN
ejpam-5431	611	38	σ](⋉(σ),β(σ	σ](⋉(σ),β(σ	NOUN
ejpam-5431	611	39	)	)	PUNCT
ejpam-5431	611	40	)	)	PUNCT
ejpam-5431	611	41	⪯	⪯	NOUN
ejpam-5431	611	42	[	[	X
ejpam-5431	611	43	sτ	sτ	ADP
ejpam-5431	611	44	]	]	PUNCT
ejpam-5431	611	45	(	(	PUNCT
ejpam-5431	611	46	⋉(τ),β(τ	⋉(τ),β(τ	NOUN
ejpam-5431	611	47	)	)	PUNCT
ejpam-5431	611	48	)	)	PUNCT
ejpam-5431	611	49	.	.	PUNCT
ejpam-5431	612	1	we	we	PRON
ejpam-5431	612	2	further	far	ADV
ejpam-5431	612	3	require	require	VERB
ejpam-5431	612	4	that	that	SCONJ
ejpam-5431	612	5	the	the	DET
ejpam-5431	612	6	following	follow	VERB
ejpam-5431	612	7	conditions	condition	NOUN
ejpam-5431	612	8	be	be	AUX
ejpam-5431	612	9	satisfied	satisfied	ADJ
ejpam-5431	612	10	:	:	PUNCT
ejpam-5431	612	11	(	(	PUNCT
ejpam-5431	612	12	i	i	NOUN
ejpam-5431	612	13	)	)	PUNCT
ejpam-5431	612	14	there	there	PRON
ejpam-5431	612	15	is	be	VERB
ejpam-5431	612	16	σ0	σ0	PROPN
ejpam-5431	612	17	∈	∈	PROPN
ejpam-5431	612	18	x	x	X
ejpam-5431	612	19	and	and	CCONJ
ejpam-5431	612	20	a	a	X
ejpam-5431	612	21	)	)	PUNCT
ejpam-5431	612	22	σ1	σ1	PROPN
ejpam-5431	612	23	∈	∈	PROPN
ejpam-5431	613	1	[	[	X
ejpam-5431	613	2	sσ0](⋉(σ0),β(σ0	sσ0](⋉(σ0),β(σ0	NOUN
ejpam-5431	613	3	)	)	PUNCT
ejpam-5431	613	4	)	)	PUNCT
ejpam-5431	613	5	such	such	ADJ
ejpam-5431	613	6	that	that	SCONJ
ejpam-5431	613	7	[	[	X
ejpam-5431	613	8	sσ0](⋉(σ0),β(σ0	sσ0](⋉(σ0),β(σ0	NOUN
ejpam-5431	613	9	)	)	PUNCT
ejpam-5431	613	10	)	)	PUNCT
ejpam-5431	613	11	⪯	⪯	NOUN
ejpam-5431	614	1	[	[	X
ejpam-5431	614	2	t	t	NOUN
ejpam-5431	614	3	σ1](⋉(σ1),β(σ1	σ1](⋉(σ1),β(σ1	NUM
ejpam-5431	614	4	)	)	PUNCT
ejpam-5431	614	5	)	)	PUNCT
ejpam-5431	615	1	;	;	PUNCT
ejpam-5431	615	2	b	b	X
ejpam-5431	615	3	)	)	PUNCT
ejpam-5431	615	4	σ1	σ1	PROPN
ejpam-5431	615	5	∈	∈	PROPN
ejpam-5431	616	1	[	[	X
ejpam-5431	616	2	t	t	NOUN
ejpam-5431	616	3	σ0](⋉(σ0),β(σ0	σ0](⋉(σ0),β(σ0	PROPN
ejpam-5431	616	4	)	)	PUNCT
ejpam-5431	616	5	)	)	PUNCT
ejpam-5431	617	1	such	such	ADJ
ejpam-5431	617	2	that	that	PRON
ejpam-5431	617	3	[	[	X
ejpam-5431	617	4	t	t	NOUN
ejpam-5431	617	5	σ0](⋉(σ0),β(σ0	σ0](⋉(σ0),β(σ0	PROPN
ejpam-5431	617	6	)	)	PUNCT
ejpam-5431	617	7	)	)	PUNCT
ejpam-5431	617	8	⪯	⪯	NOUN
ejpam-5431	617	9	[	[	X
ejpam-5431	617	10	sσ1](⋉(σ1),β(σ1	sσ1](⋉(σ1),β(σ1	NOUN
ejpam-5431	617	11	)	)	PUNCT
ejpam-5431	617	12	)	)	PUNCT
ejpam-5431	617	13	(	(	PUNCT
ejpam-5431	617	14	ii	ii	NOUN
ejpam-5431	617	15	)	)	PUNCT
ejpam-5431	617	16	for	for	ADP
ejpam-5431	617	17	each	each	DET
ejpam-5431	617	18	σ	σ	NOUN
ejpam-5431	617	19	∈	∈	PROPN
ejpam-5431	617	20	x	x	X
ejpam-5431	617	21	and	and	CCONJ
ejpam-5431	617	22	a	a	X
ejpam-5431	617	23	)	)	PUNCT
ejpam-5431	617	24	τ	τ	PROPN
ejpam-5431	617	25	∈	∈	PROPN
ejpam-5431	618	1	[	[	X
ejpam-5431	618	2	sσ](⋉(σ),β(σ	sσ](⋉(σ),β(σ	NOUN
ejpam-5431	618	3	)	)	PUNCT
ejpam-5431	618	4	)	)	PUNCT
ejpam-5431	618	5	with	with	ADP
ejpam-5431	618	6	[	[	X
ejpam-5431	618	7	sσ](⋉(σ),β(σ	sσ](⋉(σ),β(σ	NOUN
ejpam-5431	618	8	)	)	PUNCT
ejpam-5431	618	9	)	)	PUNCT
ejpam-5431	618	10	⪯	⪯	NOUN
ejpam-5431	619	1	[	[	X
ejpam-5431	619	2	t	t	X
ejpam-5431	619	3	τ	τ	X
ejpam-5431	619	4	]	]	X
ejpam-5431	619	5	(	(	PUNCT
ejpam-5431	619	6	⋉(τ),β(τ	⋉(τ),β(τ	NOUN
ejpam-5431	619	7	)	)	PUNCT
ejpam-5431	619	8	)	)	PUNCT
ejpam-5431	619	9	,	,	PUNCT
ejpam-5431	619	10	we	we	PRON
ejpam-5431	619	11	have	have	VERB
ejpam-5431	619	12	[	[	X
ejpam-5431	619	13	t	t	X
ejpam-5431	619	14	τ	τ	X
ejpam-5431	619	15	]	]	X
ejpam-5431	619	16	(	(	PUNCT
ejpam-5431	619	17	⋉(τ),β(τ	⋉(τ),β(τ	NOUN
ejpam-5431	619	18	)	)	PUNCT
ejpam-5431	619	19	)	)	PUNCT
ejpam-5431	619	20	⪯	⪯	NOUN
ejpam-5431	620	1	[	[	X
ejpam-5431	620	2	sϖ](⋉(ϖ),β(ϖ	sϖ](⋉(ϖ),β(ϖ	X
ejpam-5431	620	3	)	)	PUNCT
ejpam-5431	620	4	)	)	PUNCT
ejpam-5431	621	1	for	for	ADP
ejpam-5431	621	2	all	all	DET
ejpam-5431	621	3	ϖ	ϖ	PRON
ejpam-5431	621	4	∈	∈	PROPN
ejpam-5431	621	5	[	[	X
ejpam-5431	621	6	t	t	X
ejpam-5431	621	7	τ	τ	X
ejpam-5431	621	8	]	]	X
ejpam-5431	621	9	(	(	PUNCT
ejpam-5431	621	10	⋉(τ),β(τ	⋉(τ),β(τ	NOUN
ejpam-5431	621	11	)	)	PUNCT
ejpam-5431	621	12	)	)	PUNCT
ejpam-5431	621	13	;	;	PUNCT
ejpam-5431	621	14	b	b	X
ejpam-5431	621	15	)	)	PUNCT
ejpam-5431	621	16	τ	τ	PROPN
ejpam-5431	621	17	∈	∈	PROPN
ejpam-5431	621	18	[	[	X
ejpam-5431	621	19	t	t	NOUN
ejpam-5431	621	20	σ](⋉(σ),β(σ	σ](⋉(σ),β(σ	NOUN
ejpam-5431	621	21	)	)	PUNCT
ejpam-5431	621	22	)	)	PUNCT
ejpam-5431	621	23	with	with	ADP
ejpam-5431	621	24	[	[	X
ejpam-5431	621	25	t	t	NOUN
ejpam-5431	621	26	σ](⋉(σ),β(σ	σ](⋉(σ),β(σ	NOUN
ejpam-5431	621	27	)	)	PUNCT
ejpam-5431	621	28	)	)	PUNCT
ejpam-5431	622	1	⪯	⪯	NOUN
ejpam-5431	622	2	[	[	X
ejpam-5431	622	3	sτ	sτ	ADP
ejpam-5431	622	4	]	]	PUNCT
ejpam-5431	622	5	(	(	PUNCT
ejpam-5431	622	6	⋉(τ),β(τ	⋉(τ),β(τ	NOUN
ejpam-5431	622	7	)	)	PUNCT
ejpam-5431	622	8	)	)	PUNCT
ejpam-5431	622	9	,	,	PUNCT
ejpam-5431	622	10	we	we	PRON
ejpam-5431	622	11	have	have	AUX
ejpam-5431	622	12	[	[	PUNCT
ejpam-5431	622	13	sτ	sτ	NOUN
ejpam-5431	622	14	]	]	PUNCT
ejpam-5431	622	15	(	(	PUNCT
ejpam-5431	622	16	⋉(τ),β(τ	⋉(τ),β(τ	NOUN
ejpam-5431	622	17	)	)	PUNCT
ejpam-5431	622	18	)	)	PUNCT
ejpam-5431	623	1	⪯	⪯	NOUN
ejpam-5431	624	1	[	[	X
ejpam-5431	624	2	t	t	PROPN
ejpam-5431	624	3	ϖ](⋉(ϖ),β(ϖ	ϖ](⋉(ϖ),β(ϖ	PROPN
ejpam-5431	624	4	)	)	PUNCT
ejpam-5431	624	5	)	)	PUNCT
ejpam-5431	625	1	for	for	ADP
ejpam-5431	625	2	all	all	DET
ejpam-5431	625	3	ϖ	ϖ	PRON
ejpam-5431	625	4	∈	∈	NOUN
ejpam-5431	625	5	[	[	X
ejpam-5431	625	6	sτ	sτ	ADP
ejpam-5431	625	7	]	]	PUNCT
ejpam-5431	625	8	(	(	PUNCT
ejpam-5431	625	9	⋉(τ),β(τ	⋉(τ),β(τ	NOUN
ejpam-5431	625	10	)	)	PUNCT
ejpam-5431	625	11	)	)	PUNCT
ejpam-5431	625	12	(	(	PUNCT
ejpam-5431	625	13	iii	iii	X
ejpam-5431	625	14	)	)	PUNCT
ejpam-5431	625	15	the	the	DET
ejpam-5431	625	16	pair	pair	NOUN
ejpam-5431	625	17	(	(	PUNCT
ejpam-5431	625	18	s	s	PROPN
ejpam-5431	625	19	,	,	PUNCT
ejpam-5431	625	20	t	t	PROPN
ejpam-5431	625	21	)	)	PUNCT
ejpam-5431	625	22	is	be	AUX
ejpam-5431	625	23	ℵ-continuous	ℵ-continuous	ADJ
ejpam-5431	625	24	;	;	PUNCT
ejpam-5431	625	25	(	(	PUNCT
ejpam-5431	625	26	iv	iv	X
ejpam-5431	625	27	)	)	PUNCT
ejpam-5431	625	28	the	the	DET
ejpam-5431	625	29	sets	set	NOUN
ejpam-5431	625	30	[	[	X
ejpam-5431	625	31	sσ](⋉(σ),β(σ	sσ](⋉(σ),β(σ	NOUN
ejpam-5431	625	32	)	)	PUNCT
ejpam-5431	625	33	)	)	PUNCT
ejpam-5431	626	1	and	and	CCONJ
ejpam-5431	626	2	[	[	X
ejpam-5431	626	3	t	t	NOUN
ejpam-5431	626	4	σ](⋉(σ),β(σ	σ](⋉(σ),β(σ	NOUN
ejpam-5431	626	5	)	)	PUNCT
ejpam-5431	626	6	)	)	PUNCT
ejpam-5431	626	7	are	be	AUX
ejpam-5431	626	8	proximal	proximal	ADJ
ejpam-5431	626	9	for	for	ADP
ejpam-5431	626	10	each	each	DET
ejpam-5431	626	11	σ	σ	PROPN
ejpam-5431	626	12	∈	∈	PROPN
ejpam-5431	626	13	x.	x.	NOUN
ejpam-5431	627	1	then	then	ADV
ejpam-5431	627	2	,	,	PUNCT
ejpam-5431	627	3	s	s	X
ejpam-5431	627	4	and	and	CCONJ
ejpam-5431	627	5	t	t	PROPN
ejpam-5431	627	6	have	have	VERB
ejpam-5431	627	7	at	at	ADV
ejpam-5431	627	8	least	least	ADV
ejpam-5431	627	9	one	one	NUM
ejpam-5431	627	10	common	common	ADJ
ejpam-5431	627	11	iffp	iffp	NOUN
ejpam-5431	627	12	.	.	PUNCT
ejpam-5431	628	1	proof	proof	NOUN
ejpam-5431	628	2	.	.	PUNCT
ejpam-5431	629	1	let	let	VERB
ejpam-5431	629	2	the	the	DET
ejpam-5431	629	3	function	function	NOUN
ejpam-5431	629	4	γ	γ	X
ejpam-5431	629	5	:	:	PUNCT
ejpam-5431	629	6	x	x	PROPN
ejpam-5431	629	7	×x	×x	ADP
ejpam-5431	629	8	→	→	PUNCT
ejpam-5431	629	9	r+	r+	PRON
ejpam-5431	629	10	be	be	AUX
ejpam-5431	629	11	defined	define	VERB
ejpam-5431	629	12	by	by	ADP
ejpam-5431	629	13	γ(σ	γ(σ	PROPN
ejpam-5431	629	14	,	,	PUNCT
ejpam-5431	629	15	τ	τ	X
ejpam-5431	629	16	)	)	PUNCT
ejpam-5431	630	1	=	=	PRON
ejpam-5431	630	2	{	{	PUNCT
ejpam-5431	630	3	1	1	NUM
ejpam-5431	630	4	,	,	PUNCT
ejpam-5431	630	5	if	if	SCONJ
ejpam-5431	630	6	[	[	X
ejpam-5431	630	7	sσ](⋉(σ),β(σ	sσ](⋉(σ),β(σ	NOUN
ejpam-5431	630	8	)	)	PUNCT
ejpam-5431	630	9	)	)	PUNCT
ejpam-5431	631	1	⪯	⪯	NOUN
ejpam-5431	632	1	[	[	X
ejpam-5431	632	2	t	t	X
ejpam-5431	632	3	τ	τ	X
ejpam-5431	632	4	]	]	X
ejpam-5431	632	5	(	(	PUNCT
ejpam-5431	632	6	⋉(τ),β(τ	⋉(τ),β(τ	NOUN
ejpam-5431	632	7	)	)	PUNCT
ejpam-5431	632	8	)	)	PUNCT
ejpam-5431	632	9	or	or	CCONJ
ejpam-5431	632	10	[	[	X
ejpam-5431	632	11	t	t	NOUN
ejpam-5431	632	12	σ](⋉(σ),β(σ	σ](⋉(σ),β(σ	NOUN
ejpam-5431	632	13	)	)	PUNCT
ejpam-5431	632	14	)	)	PUNCT
ejpam-5431	633	1	⪯	⪯	NOUN
ejpam-5431	633	2	[	[	X
ejpam-5431	633	3	sτ	sτ	ADP
ejpam-5431	633	4	]	]	PUNCT
ejpam-5431	633	5	(	(	PUNCT
ejpam-5431	633	6	⋉(τ),β(τ	⋉(τ),β(τ	NOUN
ejpam-5431	633	7	)	)	PUNCT
ejpam-5431	633	8	)	)	PUNCT
ejpam-5431	633	9	,	,	PUNCT
ejpam-5431	633	10	0	0	NUM
ejpam-5431	633	11	,	,	PUNCT
ejpam-5431	633	12	otherwise	otherwise	ADV
ejpam-5431	633	13	.	.	PUNCT
ejpam-5431	634	1	to	to	PART
ejpam-5431	634	2	show	show	VERB
ejpam-5431	634	3	that	that	SCONJ
ejpam-5431	634	4	the	the	DET
ejpam-5431	634	5	pair	pair	NOUN
ejpam-5431	634	6	(	(	PUNCT
ejpam-5431	634	7	s	s	PROPN
ejpam-5431	634	8	,	,	PUNCT
ejpam-5431	634	9	t	t	PROPN
ejpam-5431	634	10	)	)	PUNCT
ejpam-5431	634	11	is	be	AUX
ejpam-5431	634	12	γ	γ	X
ejpam-5431	634	13	-	-	ADJ
ejpam-5431	634	14	admissible	admissible	ADJ
ejpam-5431	634	15	,	,	PUNCT
ejpam-5431	634	16	take	take	NOUN
ejpam-5431	634	17	(	(	PUNCT
ejpam-5431	634	18	i	i	NOUN
ejpam-5431	634	19	)	)	PUNCT
ejpam-5431	634	20	σ	σ	PROPN
ejpam-5431	634	21	∈	∈	PROPN
ejpam-5431	634	22	x	x	X
ejpam-5431	634	23	and	and	CCONJ
ejpam-5431	634	24	τ	τ	PROPN
ejpam-5431	634	25	∈	∈	PROPN
ejpam-5431	635	1	[	[	X
ejpam-5431	635	2	sσ](⋉(σ),β(σ	sσ](⋉(σ),β(σ	NOUN
ejpam-5431	635	3	)	)	PUNCT
ejpam-5431	635	4	)	)	PUNCT
ejpam-5431	635	5	with	with	ADP
ejpam-5431	635	6	γ(σ	γ(σ	PROPN
ejpam-5431	635	7	,	,	PUNCT
ejpam-5431	635	8	τ	τ	PROPN
ejpam-5431	635	9	)	)	PUNCT
ejpam-5431	635	10	≥	≥	NOUN
ejpam-5431	635	11	1	1	NUM
ejpam-5431	635	12	then	then	ADV
ejpam-5431	635	13	,	,	PUNCT
ejpam-5431	636	1	[	[	X
ejpam-5431	636	2	sσ](⋉(σ),β(σ	sσ](⋉(σ),β(σ	NOUN
ejpam-5431	636	3	)	)	PUNCT
ejpam-5431	636	4	)	)	PUNCT
ejpam-5431	637	1	⪯	⪯	NOUN
ejpam-5431	638	1	[	[	X
ejpam-5431	638	2	t	t	X
ejpam-5431	638	3	τ	τ	X
ejpam-5431	638	4	]	]	X
ejpam-5431	638	5	(	(	PUNCT
ejpam-5431	638	6	⋉(τ),β(τ	⋉(τ),β(τ	NOUN
ejpam-5431	638	7	)	)	PUNCT
ejpam-5431	638	8	)	)	PUNCT
ejpam-5431	638	9	and	and	CCONJ
ejpam-5431	638	10	by	by	ADP
ejpam-5431	638	11	hypothesis	hypothesis	NOUN
ejpam-5431	638	12	(	(	PUNCT
ejpam-5431	638	13	ii)(a),we	ii)(a),we	PROPN
ejpam-5431	638	14	have	have	VERB
ejpam-5431	638	15	[	[	X
ejpam-5431	638	16	t	t	X
ejpam-5431	638	17	τ	τ	X
ejpam-5431	638	18	]	]	X
ejpam-5431	638	19	(	(	PUNCT
ejpam-5431	638	20	⋉(τ),β(τ	⋉(τ),β(τ	NOUN
ejpam-5431	638	21	)	)	PUNCT
ejpam-5431	638	22	)	)	PUNCT
ejpam-5431	638	23	⪯	⪯	NOUN
ejpam-5431	639	1	[	[	X
ejpam-5431	639	2	sϖ](⋉(ϖ),β(ϖ	sϖ](⋉(ϖ),β(ϖ	X
ejpam-5431	639	3	)	)	PUNCT
ejpam-5431	639	4	)	)	PUNCT
ejpam-5431	640	1	for	for	ADP
ejpam-5431	640	2	all	all	DET
ejpam-5431	640	3	ϖ	ϖ	PRON
ejpam-5431	640	4	∈	∈	PROPN
ejpam-5431	640	5	[	[	X
ejpam-5431	640	6	t	t	X
ejpam-5431	640	7	τ	τ	X
ejpam-5431	640	8	]	]	X
ejpam-5431	640	9	(	(	PUNCT
ejpam-5431	640	10	⋉(τ),β(τ	⋉(τ),β(τ	NOUN
ejpam-5431	640	11	)	)	PUNCT
ejpam-5431	640	12	)	)	PUNCT
ejpam-5431	640	13	.	.	PUNCT
ejpam-5431	641	1	it	it	PRON
ejpam-5431	641	2	follows	follow	VERB
ejpam-5431	641	3	that	that	SCONJ
ejpam-5431	641	4	γ(τ,ϖ	γ(τ,ϖ	NOUN
ejpam-5431	641	5	)	)	PUNCT
ejpam-5431	641	6	≥	≥	NOUN
ejpam-5431	641	7	1	1	NUM
ejpam-5431	641	8	for	for	ADP
ejpam-5431	641	9	all	all	DET
ejpam-5431	641	10	ϖ	ϖ	PRON
ejpam-5431	641	11	∈	∈	PROPN
ejpam-5431	642	1	[	[	X
ejpam-5431	642	2	t	t	X
ejpam-5431	642	3	τ	τ	X
ejpam-5431	642	4	]	]	X
ejpam-5431	642	5	(	(	PUNCT
ejpam-5431	642	6	⋉(τ),β(τ	⋉(τ),β(τ	NOUN
ejpam-5431	642	7	)	)	PUNCT
ejpam-5431	642	8	)	)	PUNCT
ejpam-5431	642	9	.	.	PUNCT
ejpam-5431	643	1	n.	n.	PROPN
ejpam-5431	643	2	saleem	saleem	PROPN
ejpam-5431	643	3	et	et	PROPN
ejpam-5431	643	4	al	al	PROPN
ejpam-5431	643	5	.	.	PUNCT
ejpam-5431	643	6	/	/	SYM
ejpam-5431	643	7	eur	eur	PROPN
ejpam-5431	643	8	.	.	PUNCT
ejpam-5431	644	1	j.	j.	PROPN
ejpam-5431	644	2	pure	pure	PROPN
ejpam-5431	644	3	appl	appl	PROPN
ejpam-5431	644	4	.	.	PROPN
ejpam-5431	644	5	math	math	PROPN
ejpam-5431	644	6	,	,	PUNCT
ejpam-5431	644	7	17	17	NUM
ejpam-5431	644	8	(	(	PUNCT
ejpam-5431	644	9	4	4	NUM
ejpam-5431	644	10	)	)	PUNCT
ejpam-5431	644	11	(	(	PUNCT
ejpam-5431	644	12	2024	2024	NUM
ejpam-5431	644	13	)	)	PUNCT
ejpam-5431	644	14	,	,	PUNCT
ejpam-5431	644	15	3304	3304	NUM
ejpam-5431	644	16	-	-	SYM
ejpam-5431	644	17	3335	3335	NUM
ejpam-5431	644	18	3330	3330	NUM
ejpam-5431	644	19	(	(	PUNCT
ejpam-5431	644	20	ii	ii	NOUN
ejpam-5431	644	21	)	)	PUNCT
ejpam-5431	644	22	σ	σ	PROPN
ejpam-5431	644	23	∈	∈	PROPN
ejpam-5431	644	24	x	x	X
ejpam-5431	644	25	and	and	CCONJ
ejpam-5431	644	26	τ	τ	PROPN
ejpam-5431	644	27	∈	∈	PROPN
ejpam-5431	645	1	[	[	X
ejpam-5431	645	2	t	t	NOUN
ejpam-5431	645	3	σ](⋉(σ),β(σ	σ](⋉(σ),β(σ	NOUN
ejpam-5431	645	4	)	)	PUNCT
ejpam-5431	645	5	)	)	PUNCT
ejpam-5431	645	6	with	with	ADP
ejpam-5431	645	7	γ(σ	γ(σ	PROPN
ejpam-5431	645	8	,	,	PUNCT
ejpam-5431	645	9	τ	τ	PROPN
ejpam-5431	645	10	)	)	PUNCT
ejpam-5431	645	11	≥	≥	NOUN
ejpam-5431	645	12	1	1	NUM
ejpam-5431	645	13	then	then	ADV
ejpam-5431	645	14	,	,	PUNCT
ejpam-5431	645	15	[	[	X
ejpam-5431	645	16	t	t	X
ejpam-5431	645	17	σ](⋉(σ),β(σ	σ](⋉(σ),β(σ	NOUN
ejpam-5431	645	18	)	)	PUNCT
ejpam-5431	645	19	)	)	PUNCT
ejpam-5431	646	1	⪯	⪯	NOUN
ejpam-5431	646	2	[	[	X
ejpam-5431	646	3	sτ	sτ	ADP
ejpam-5431	646	4	]	]	PUNCT
ejpam-5431	646	5	(	(	PUNCT
ejpam-5431	646	6	⋉(τ),β(τ	⋉(τ),β(τ	NOUN
ejpam-5431	646	7	)	)	PUNCT
ejpam-5431	646	8	)	)	PUNCT
ejpam-5431	646	9	and	and	CCONJ
ejpam-5431	646	10	by	by	ADP
ejpam-5431	646	11	hypothesis	hypothesis	NOUN
ejpam-5431	646	12	(	(	PUNCT
ejpam-5431	646	13	ii)(b),we	ii)(b),we	NOUN
ejpam-5431	646	14	have	have	VERB
ejpam-5431	646	15	[	[	PUNCT
ejpam-5431	646	16	sτ	sτ	NOUN
ejpam-5431	646	17	]	]	PUNCT
ejpam-5431	646	18	(	(	PUNCT
ejpam-5431	646	19	⋉(τ),β(τ	⋉(τ),β(τ	NOUN
ejpam-5431	646	20	)	)	PUNCT
ejpam-5431	646	21	)	)	PUNCT
ejpam-5431	647	1	⪯	⪯	NOUN
ejpam-5431	648	1	[	[	X
ejpam-5431	648	2	t	t	PROPN
ejpam-5431	648	3	ϖ](⋉(ϖ),β(ϖ	ϖ](⋉(ϖ),β(ϖ	PROPN
ejpam-5431	648	4	)	)	PUNCT
ejpam-5431	648	5	)	)	PUNCT
ejpam-5431	649	1	for	for	ADP
ejpam-5431	649	2	all	all	DET
ejpam-5431	649	3	ϖ	ϖ	PRON
ejpam-5431	649	4	∈	∈	NOUN
ejpam-5431	649	5	[	[	X
ejpam-5431	649	6	sτ	sτ	ADP
ejpam-5431	649	7	]	]	PUNCT
ejpam-5431	649	8	(	(	PUNCT
ejpam-5431	649	9	⋉(τ),β(τ	⋉(τ),β(τ	NOUN
ejpam-5431	649	10	)	)	PUNCT
ejpam-5431	649	11	)	)	PUNCT
ejpam-5431	649	12	.	.	PUNCT
ejpam-5431	650	1	it	it	PRON
ejpam-5431	650	2	follows	follow	VERB
ejpam-5431	650	3	that	that	SCONJ
ejpam-5431	650	4	γ(τ,ϖ	γ(τ,ϖ	NOUN
ejpam-5431	650	5	)	)	PUNCT
ejpam-5431	650	6	≥	≥	NOUN
ejpam-5431	650	7	1	1	NUM
ejpam-5431	650	8	for	for	ADP
ejpam-5431	650	9	all	all	DET
ejpam-5431	650	10	ϖ	ϖ	PRON
ejpam-5431	650	11	∈	∈	NOUN
ejpam-5431	650	12	[	[	AUX
ejpam-5431	650	13	sτ	sτ	ADP
ejpam-5431	650	14	]	]	PUNCT
ejpam-5431	650	15	(	(	PUNCT
ejpam-5431	650	16	⋉(τ),β(τ	⋉(τ),β(τ	NOUN
ejpam-5431	650	17	)	)	PUNCT
ejpam-5431	650	18	)	)	PUNCT
ejpam-5431	650	19	.	.	PUNCT
ejpam-5431	651	1	moreover	moreover	ADV
ejpam-5431	651	2	,	,	PUNCT
ejpam-5431	651	3	by	by	ADP
ejpam-5431	651	4	inequalities	inequality	NOUN
ejpam-5431	651	5	(	(	PUNCT
ejpam-5431	651	6	28	28	NUM
ejpam-5431	651	7	)	)	PUNCT
ejpam-5431	651	8	and	and	CCONJ
ejpam-5431	651	9	(	(	PUNCT
ejpam-5431	651	10	29	29	NUM
ejpam-5431	651	11	)	)	PUNCT
ejpam-5431	651	12	,	,	PUNCT
ejpam-5431	651	13	we	we	PRON
ejpam-5431	651	14	find	find	VERB
ejpam-5431	651	15	that	that	SCONJ
ejpam-5431	651	16	the	the	DET
ejpam-5431	651	17	pair	pair	NOUN
ejpam-5431	651	18	(	(	PUNCT
ejpam-5431	651	19	s	s	PROPN
ejpam-5431	651	20	,	,	PUNCT
ejpam-5431	651	21	t	t	PROPN
ejpam-5431	651	22	)	)	PUNCT
ejpam-5431	651	23	is	be	AUX
ejpam-5431	651	24	an	an	DET
ejpam-5431	651	25	ahif	ahif	NOUN
ejpam-5431	651	26	zcontraction	zcontraction	NOUN
ejpam-5431	651	27	regarding	regard	VERB
ejpam-5431	651	28	℘	℘	PROPN
ejpam-5431	651	29	∈	∈	PROPN
ejpam-5431	651	30	z.	z.	NOUN
ejpam-5431	651	31	as	as	ADP
ejpam-5431	651	32	a	a	DET
ejpam-5431	651	33	result	result	NOUN
ejpam-5431	651	34	,	,	PUNCT
ejpam-5431	651	35	it	it	PRON
ejpam-5431	651	36	can	can	AUX
ejpam-5431	651	37	be	be	AUX
ejpam-5431	651	38	seen	see	VERB
ejpam-5431	651	39	that	that	SCONJ
ejpam-5431	651	40	all	all	DET
ejpam-5431	651	41	the	the	DET
ejpam-5431	651	42	axioms	axiom	NOUN
ejpam-5431	651	43	of	of	ADP
ejpam-5431	651	44	the	the	DET
ejpam-5431	651	45	theorem	theorem	ADJ
ejpam-5431	651	46	2	2	NUM
ejpam-5431	651	47	are	be	AUX
ejpam-5431	651	48	met	meet	VERB
ejpam-5431	651	49	.	.	PUNCT
ejpam-5431	652	1	thus	thus	ADV
ejpam-5431	652	2	s	s	VERB
ejpam-5431	652	3	and	and	CCONJ
ejpam-5431	652	4	t	t	PROPN
ejpam-5431	652	5	have	have	VERB
ejpam-5431	652	6	at	at	ADV
ejpam-5431	652	7	least	least	ADV
ejpam-5431	652	8	one	one	NUM
ejpam-5431	652	9	common	common	ADJ
ejpam-5431	652	10	iffp	iffp	NOUN
ejpam-5431	652	11	in	in	ADP
ejpam-5431	652	12	x.	x.	PROPN
ejpam-5431	652	13	example	example	NOUN
ejpam-5431	652	14	30	30	NUM
ejpam-5431	652	15	.	.	PUNCT
ejpam-5431	653	1	let	let	VERB
ejpam-5431	653	2	x	x	PUNCT
ejpam-5431	653	3	=	=	PRON
ejpam-5431	653	4	n	n	PART
ejpam-5431	653	5	be	be	AUX
ejpam-5431	653	6	a	a	DET
ejpam-5431	653	7	partially	partially	ADV
ejpam-5431	653	8	ordered	order	VERB
ejpam-5431	653	9	set	set	VERB
ejpam-5431	653	10	such	such	DET
ejpam-5431	653	11	that	that	SCONJ
ejpam-5431	653	12	a	a	DET
ejpam-5431	653	13	⪯	⪯	NOUN
ejpam-5431	653	14	b	b	NOUN
ejpam-5431	653	15	if	if	SCONJ
ejpam-5431	654	1	and	and	CCONJ
ejpam-5431	654	2	only	only	ADV
ejpam-5431	654	3	if	if	SCONJ
ejpam-5431	654	4	b|a	b|a	ADP
ejpam-5431	654	5	for	for	ADP
ejpam-5431	654	6	all	all	DET
ejpam-5431	654	7	a	a	PRON
ejpam-5431	654	8	,	,	PUNCT
ejpam-5431	654	9	b	b	X
ejpam-5431	654	10	∈	∈	PROPN
ejpam-5431	654	11	x.	x.	NOUN
ejpam-5431	654	12	define	define	VERB
ejpam-5431	654	13	δ(σ	δ(σ	PROPN
ejpam-5431	654	14	,	,	PUNCT
ejpam-5431	654	15	τ	τ	X
ejpam-5431	654	16	)	)	PUNCT
ejpam-5431	654	17	=	=	SYM
ejpam-5431	655	1	|σ	|σ	PROPN
ejpam-5431	655	2	−	−	NOUN
ejpam-5431	655	3	τ	τ	X
ejpam-5431	655	4	|3	|3	NOUN
ejpam-5431	655	5	for	for	ADP
ejpam-5431	655	6	all	all	DET
ejpam-5431	655	7	σ	σ	PROPN
ejpam-5431	655	8	,	,	PUNCT
ejpam-5431	655	9	τ	τ	PROPN
ejpam-5431	655	10	∈	∈	PROPN
ejpam-5431	655	11	x.	x.	NOUN
ejpam-5431	655	12	then	then	ADV
ejpam-5431	655	13	(	(	PUNCT
ejpam-5431	655	14	x	x	NOUN
ejpam-5431	655	15	,	,	PUNCT
ejpam-5431	655	16	δ	δ	PROPN
ejpam-5431	655	17	,	,	PUNCT
ejpam-5431	655	18	h	h	NOUN
ejpam-5431	655	19	=	=	NOUN
ejpam-5431	655	20	4	4	X
ejpam-5431	655	21	)	)	PUNCT
ejpam-5431	655	22	is	be	AUX
ejpam-5431	655	23	a	a	DET
ejpam-5431	655	24	complete	complete	ADJ
ejpam-5431	655	25	b	b	NOUN
ejpam-5431	655	26	-	-	PUNCT
ejpam-5431	655	27	ms	ms	NOUN
ejpam-5431	655	28	but	but	CCONJ
ejpam-5431	655	29	not	not	PART
ejpam-5431	655	30	a	a	DET
ejpam-5431	655	31	ms	ms	NOUN
ejpam-5431	655	32	.	.	PROPN
ejpam-5431	655	33	for	for	ADP
ejpam-5431	655	34	each	each	DET
ejpam-5431	655	35	σ	σ	NUM
ejpam-5431	655	36	∈	∈	PROPN
ejpam-5431	655	37	x	x	PRON
ejpam-5431	655	38	consider	consider	VERB
ejpam-5431	655	39	two	two	NUM
ejpam-5431	655	40	ifs	ifs	PROPN
ejpam-5431	655	41	-	-	PUNCT
ejpam-5431	655	42	valued	value	VERB
ejpam-5431	655	43	maps	map	NOUN
ejpam-5431	655	44	s	s	PROPN
ejpam-5431	655	45	,	,	PUNCT
ejpam-5431	655	46	t	t	X
ejpam-5431	655	47	:	:	PUNCT
ejpam-5431	655	48	x	x	X
ejpam-5431	655	49	→	→	SYM
ejpam-5431	655	50	ifs(x	ifs(x	PROPN
ejpam-5431	655	51	)	)	PUNCT
ejpam-5431	655	52	and	and	CCONJ
ejpam-5431	655	53	for	for	ADP
ejpam-5431	655	54	σ	σ	PROPN
ejpam-5431	655	55	∈	∈	PROPN
ejpam-5431	655	56	x	x	PROPN
ejpam-5431	655	57	,	,	PUNCT
ejpam-5431	655	58	t	t	PROPN
ejpam-5431	655	59	σ	σ	PROPN
ejpam-5431	655	60	,	,	PUNCT
ejpam-5431	655	61	sσ	sσ	PROPN
ejpam-5431	655	62	are	be	AUX
ejpam-5431	655	63	ifss	ifss	ADJ
ejpam-5431	655	64	such	such	ADJ
ejpam-5431	655	65	that	that	DET
ejpam-5431	655	66	µsσ	µsσ	NOUN
ejpam-5431	655	67	,	,	PUNCT
ejpam-5431	655	68	µt	µt	PROPN
ejpam-5431	655	69	σ	σ	X
ejpam-5431	655	70	:	:	PUNCT
ejpam-5431	655	71	x	x	X
ejpam-5431	655	72	→	→	PUNCT
ejpam-5431	655	73	[	[	X
ejpam-5431	655	74	0	0	NUM
ejpam-5431	655	75	,	,	PUNCT
ejpam-5431	655	76	1	1	NUM
ejpam-5431	655	77	]	]	PUNCT
ejpam-5431	655	78	are	be	AUX
ejpam-5431	655	79	membership	membership	NOUN
ejpam-5431	655	80	functions	function	NOUN
ejpam-5431	655	81	and	and	CCONJ
ejpam-5431	655	82	νsσ	νsσ	NOUN
ejpam-5431	655	83	,	,	PUNCT
ejpam-5431	655	84	νt	νt	PROPN
ejpam-5431	655	85	σ	σ	NOUN
ejpam-5431	655	86	:	:	PUNCT
ejpam-5431	655	87	x	x	X
ejpam-5431	655	88	→	→	PUNCT
ejpam-5431	656	1	[	[	X
ejpam-5431	656	2	0	0	NUM
ejpam-5431	656	3	,	,	PUNCT
ejpam-5431	656	4	1	1	NUM
ejpam-5431	656	5	]	]	PUNCT
ejpam-5431	656	6	are	be	AUX
ejpam-5431	656	7	non	non	ADJ
ejpam-5431	656	8	-	-	ADJ
ejpam-5431	656	9	membership	membership	ADJ
ejpam-5431	656	10	functions	function	NOUN
ejpam-5431	656	11	of	of	ADP
ejpam-5431	656	12	s	s	PRON
ejpam-5431	656	13	and	and	CCONJ
ejpam-5431	656	14	t	t	NOUN
ejpam-5431	656	15	respectively	respectively	ADV
ejpam-5431	656	16	with	with	ADP
ejpam-5431	656	17	µsσ(a	µsσ(a	NOUN
ejpam-5431	656	18	)	)	PUNCT
ejpam-5431	656	19	+	+	CCONJ
ejpam-5431	656	20	νsσ(a	νsσ(a	NOUN
ejpam-5431	656	21	)	)	PUNCT
ejpam-5431	656	22	≤	≤	NOUN
ejpam-5431	656	23	1	1	NUM
ejpam-5431	656	24	and	and	CCONJ
ejpam-5431	656	25	µt	µt	PRON
ejpam-5431	656	26	σ(a	σ(a	PROPN
ejpam-5431	656	27	)	)	PUNCT
ejpam-5431	657	1	+	+	NUM
ejpam-5431	657	2	νt	νt	X
ejpam-5431	657	3	σ(a	σ(a	PROPN
ejpam-5431	657	4	)	)	PUNCT
ejpam-5431	657	5	≤	≤	NOUN
ejpam-5431	657	6	1	1	NUM
ejpam-5431	657	7	for	for	ADP
ejpam-5431	657	8	all	all	DET
ejpam-5431	657	9	a	a	DET
ejpam-5431	657	10	∈	∈	NOUN
ejpam-5431	657	11	x.	x.	NOUN
ejpam-5431	658	1	we	we	PRON
ejpam-5431	658	2	define	define	VERB
ejpam-5431	658	3	these	these	DET
ejpam-5431	658	4	maps	map	NOUN
ejpam-5431	658	5	as	as	ADP
ejpam-5431	658	6	:	:	PUNCT
ejpam-5431	658	7	case	case	NOUN
ejpam-5431	658	8	1	1	NUM
ejpam-5431	658	9	:	:	PUNCT
ejpam-5431	658	10	if	if	SCONJ
ejpam-5431	658	11	σ	σ	PROPN
ejpam-5431	658	12	is	be	AUX
ejpam-5431	658	13	even	even	ADV
ejpam-5431	658	14	;	;	PUNCT
ejpam-5431	658	15	µt	µt	PROPN
ejpam-5431	658	16	σ(a	σ(a	PROPN
ejpam-5431	658	17	)	)	PUNCT
ejpam-5431	658	18	=	=	PUNCT
ejpam-5431	658	19			PUNCT
ejpam-5431	658	20	⋉	⋉	PROPN
ejpam-5431	658	21	,	,	PUNCT
ejpam-5431	658	22	if	if	SCONJ
ejpam-5431	658	23	a	a	DET
ejpam-5431	658	24	=	=	X
ejpam-5431	658	25	σ	σ	X
ejpam-5431	658	26	2	2	NUM
ejpam-5431	658	27	⋉	⋉	NOUN
ejpam-5431	658	28	3	3	NUM
ejpam-5431	658	29	,	,	PUNCT
ejpam-5431	658	30	if	if	SCONJ
ejpam-5431	658	31	a	a	DET
ejpam-5431	658	32	=	=	X
ejpam-5431	658	33	σ	σ	PROPN
ejpam-5431	658	34	0	0	PROPN
ejpam-5431	658	35	,	,	PUNCT
ejpam-5431	658	36	elsewhere	elsewhere	ADV
ejpam-5431	658	37	νt	νt	ADP
ejpam-5431	658	38	σ(a	σ(a	PROPN
ejpam-5431	658	39	)	)	PUNCT
ejpam-5431	658	40	=	=	PUNCT
ejpam-5431	659	1			PUNCT
ejpam-5431	659	2	β	β	X
ejpam-5431	659	3	5	5	NUM
ejpam-5431	659	4	,	,	PUNCT
ejpam-5431	659	5	if	if	SCONJ
ejpam-5431	659	6	a	a	DET
ejpam-5431	659	7	=	=	X
ejpam-5431	659	8	σ	σ	PROPN
ejpam-5431	659	9	2	2	NUM
ejpam-5431	659	10	β	β	SYM
ejpam-5431	659	11	2	2	NUM
ejpam-5431	659	12	,	,	PUNCT
ejpam-5431	659	13	if	if	SCONJ
ejpam-5431	659	14	a	a	DET
ejpam-5431	659	15	=	=	X
ejpam-5431	659	16	σ	σ	NUM
ejpam-5431	659	17	β	β	PROPN
ejpam-5431	659	18	,	,	PUNCT
ejpam-5431	659	19	elsewhere	elsewhere	ADV
ejpam-5431	659	20	µsσ(a	µsσ(a	ADP
ejpam-5431	659	21	)	)	PUNCT
ejpam-5431	659	22	=	=	PUNCT
ejpam-5431	659	23			PUNCT
ejpam-5431	659	24	⋉	⋉	PROPN
ejpam-5431	659	25	,	,	PUNCT
ejpam-5431	659	26	if	if	SCONJ
ejpam-5431	659	27	a	a	PRON
ejpam-5431	659	28	=	=	SYM
ejpam-5431	659	29	σ	σ	PROPN
ejpam-5431	659	30	2	2	NUM
ejpam-5431	659	31	1−	1−	NUM
ejpam-5431	659	32	⋉	⋉	ADV
ejpam-5431	659	33	3	3	NUM
ejpam-5431	659	34	,	,	PUNCT
ejpam-5431	659	35	if	if	SCONJ
ejpam-5431	659	36	a	a	PRON
ejpam-5431	659	37	=	=	X
ejpam-5431	659	38	σ	σ	PROPN
ejpam-5431	659	39	0	0	PROPN
ejpam-5431	659	40	,	,	PUNCT
ejpam-5431	659	41	elsewhere	elsewhere	ADV
ejpam-5431	659	42	νsσ(a	νsσ(a	PROPN
ejpam-5431	659	43	)	)	PUNCT
ejpam-5431	659	44	=	=	PUNCT
ejpam-5431	660	1			PUNCT
ejpam-5431	660	2	β	β	X
ejpam-5431	660	3	6	6	NUM
ejpam-5431	660	4	,	,	PUNCT
ejpam-5431	660	5	if	if	SCONJ
ejpam-5431	660	6	a	a	DET
ejpam-5431	660	7	=	=	X
ejpam-5431	660	8	σ	σ	PROPN
ejpam-5431	660	9	2	2	NUM
ejpam-5431	660	10	β	β	SYM
ejpam-5431	660	11	3	3	NUM
ejpam-5431	660	12	,	,	PUNCT
ejpam-5431	660	13	if	if	SCONJ
ejpam-5431	660	14	a	a	DET
ejpam-5431	660	15	=	=	X
ejpam-5431	660	16	σ	σ	NUM
ejpam-5431	660	17	β	β	PROPN
ejpam-5431	660	18	,	,	PUNCT
ejpam-5431	660	19	elsewhere	elsewhere	ADV
ejpam-5431	660	20	.	.	PUNCT
ejpam-5431	661	1	case	case	NOUN
ejpam-5431	661	2	2	2	NUM
ejpam-5431	661	3	:	:	PUNCT
ejpam-5431	661	4	if	if	SCONJ
ejpam-5431	661	5	σ	σ	PROPN
ejpam-5431	661	6	is	be	AUX
ejpam-5431	661	7	odd	odd	ADJ
ejpam-5431	661	8	;	;	PUNCT
ejpam-5431	661	9	µt	µt	PRON
ejpam-5431	661	10	σ(a	σ(a	PROPN
ejpam-5431	661	11	)	)	PUNCT
ejpam-5431	661	12	=	=	PUNCT
ejpam-5431	662	1			PUNCT
ejpam-5431	662	2	1−⋉	1−⋉	NUM
ejpam-5431	662	3	,	,	PUNCT
ejpam-5431	662	4	if	if	SCONJ
ejpam-5431	662	5	a	a	PRON
ejpam-5431	662	6	=	=	X
ejpam-5431	662	7	σ	σ	NOUN
ejpam-5431	662	8	+	+	PROPN
ejpam-5431	662	9	1	1	NUM
ejpam-5431	662	10	⋉	⋉	PROPN
ejpam-5431	662	11	,	,	PUNCT
ejpam-5431	662	12	if	if	SCONJ
ejpam-5431	662	13	a	a	DET
ejpam-5431	662	14	=	=	X
ejpam-5431	662	15	σ	σ	PROPN
ejpam-5431	662	16	⋉3	⋉3	PROPN
ejpam-5431	662	17	,	,	PUNCT
ejpam-5431	662	18	elsewhere	elsewhere	ADV
ejpam-5431	662	19	νt	νt	ADP
ejpam-5431	662	20	σ(a	σ(a	PROPN
ejpam-5431	662	21	)	)	PUNCT
ejpam-5431	662	22	=	=	PUNCT
ejpam-5431	663	1			PROPN
ejpam-5431	663	2	0	0	NUM
ejpam-5431	663	3	,	,	PUNCT
ejpam-5431	663	4	if	if	SCONJ
ejpam-5431	663	5	a	a	DET
ejpam-5431	663	6	=	=	X
ejpam-5431	663	7	σ	σ	NOUN
ejpam-5431	663	8	+	+	PROPN
ejpam-5431	663	9	1	1	NUM
ejpam-5431	663	10	β2	β2	NOUN
ejpam-5431	663	11	,	,	PUNCT
ejpam-5431	663	12	if	if	SCONJ
ejpam-5431	663	13	a	a	DET
ejpam-5431	663	14	=	=	X
ejpam-5431	663	15	σ	σ	PROPN
ejpam-5431	663	16	β4	β4	PROPN
ejpam-5431	663	17	,	,	PUNCT
ejpam-5431	663	18	elsewhere	elsewhere	ADV
ejpam-5431	663	19	n.	n.	PROPN
ejpam-5431	663	20	saleem	saleem	PROPN
ejpam-5431	663	21	et	et	PROPN
ejpam-5431	663	22	al	al	PROPN
ejpam-5431	663	23	.	.	PUNCT
ejpam-5431	663	24	/	/	SYM
ejpam-5431	663	25	eur	eur	PROPN
ejpam-5431	663	26	.	.	PUNCT
ejpam-5431	664	1	j.	j.	PROPN
ejpam-5431	664	2	pure	pure	PROPN
ejpam-5431	664	3	appl	appl	PROPN
ejpam-5431	664	4	.	.	PROPN
ejpam-5431	664	5	math	math	PROPN
ejpam-5431	664	6	,	,	PUNCT
ejpam-5431	664	7	17	17	NUM
ejpam-5431	664	8	(	(	PUNCT
ejpam-5431	664	9	4	4	NUM
ejpam-5431	664	10	)	)	PUNCT
ejpam-5431	664	11	(	(	PUNCT
ejpam-5431	664	12	2024	2024	NUM
ejpam-5431	664	13	)	)	PUNCT
ejpam-5431	664	14	,	,	PUNCT
ejpam-5431	664	15	3304	3304	NUM
ejpam-5431	664	16	-	-	SYM
ejpam-5431	664	17	3335	3335	NUM
ejpam-5431	664	18	3331	3331	NUM
ejpam-5431	664	19	µsσ(a	µsσ(a	NOUN
ejpam-5431	664	20	)	)	PUNCT
ejpam-5431	664	21	=	=	PUNCT
ejpam-5431	664	22			PUNCT
ejpam-5431	664	23	⋉	⋉	ADV
ejpam-5431	664	24	2	2	NUM
ejpam-5431	664	25	,	,	PUNCT
ejpam-5431	664	26	if	if	SCONJ
ejpam-5431	664	27	a	a	DET
ejpam-5431	664	28	=	=	X
ejpam-5431	664	29	σ	σ	NOUN
ejpam-5431	664	30	+	+	PROPN
ejpam-5431	664	31	1	1	NUM
ejpam-5431	664	32	⋉	⋉	PROPN
ejpam-5431	664	33	,	,	PUNCT
ejpam-5431	664	34	if	if	SCONJ
ejpam-5431	664	35	a	a	PRON
ejpam-5431	664	36	=	=	X
ejpam-5431	664	37	σ	σ	PROPN
ejpam-5431	664	38	0	0	PROPN
ejpam-5431	664	39	,	,	PUNCT
ejpam-5431	664	40	elsewhere	elsewhere	ADV
ejpam-5431	664	41	νsσ(a	νsσ(a	PROPN
ejpam-5431	664	42	)	)	PUNCT
ejpam-5431	664	43	=	=	PUNCT
ejpam-5431	665	1			PUNCT
ejpam-5431	665	2	β	β	NOUN
ejpam-5431	665	3	,	,	PUNCT
ejpam-5431	665	4	if	if	SCONJ
ejpam-5431	665	5	a	a	DET
ejpam-5431	665	6	=	=	X
ejpam-5431	665	7	σ	σ	NOUN
ejpam-5431	665	8	+	+	PROPN
ejpam-5431	665	9	1	1	NUM
ejpam-5431	665	10	β2	β2	NOUN
ejpam-5431	665	11	,	,	PUNCT
ejpam-5431	665	12	if	if	SCONJ
ejpam-5431	665	13	a	a	DET
ejpam-5431	665	14	=	=	X
ejpam-5431	665	15	σ	σ	PROPN
ejpam-5431	665	16	β3	β3	PROPN
ejpam-5431	665	17	,	,	PUNCT
ejpam-5431	665	18	elsewhere	elsewhere	ADV
ejpam-5431	665	19	.	.	PUNCT
ejpam-5431	666	1	let	let	VERB
ejpam-5431	666	2	⋉	⋉	PROPN
ejpam-5431	666	3	=	=	SYM
ejpam-5431	666	4	3	3	NUM
ejpam-5431	666	5	5	5	NUM
ejpam-5431	666	6	and	and	CCONJ
ejpam-5431	666	7	β	β	X
ejpam-5431	666	8	=	=	NOUN
ejpam-5431	666	9	1	1	NUM
ejpam-5431	666	10	5	5	NUM
ejpam-5431	666	11	.	.	PUNCT
ejpam-5431	667	1	then	then	ADV
ejpam-5431	667	2	[	[	X
ejpam-5431	667	3	t	t	NOUN
ejpam-5431	667	4	σ](⋉,β	σ](⋉,β	PROPN
ejpam-5431	667	5	)	)	PUNCT
ejpam-5431	667	6	=	=	PRON
ejpam-5431	667	7	{	{	PUNCT
ejpam-5431	667	8	{	{	PUNCT
ejpam-5431	667	9	σ	σ	NOUN
ejpam-5431	667	10	2	2	NUM
ejpam-5431	667	11	}	}	PUNCT
ejpam-5431	667	12	,	,	PUNCT
ejpam-5431	667	13	if	if	SCONJ
ejpam-5431	667	14	σ	σ	PROPN
ejpam-5431	667	15	is	be	AUX
ejpam-5431	667	16	even	even	ADV
ejpam-5431	667	17	{	{	PUNCT
ejpam-5431	667	18	σ	σ	X
ejpam-5431	667	19	}	}	PUNCT
ejpam-5431	667	20	,	,	PUNCT
ejpam-5431	667	21	if	if	SCONJ
ejpam-5431	667	22	σ	σ	PROPN
ejpam-5431	667	23	is	be	AUX
ejpam-5431	667	24	odd	odd	ADJ
ejpam-5431	667	25	and	and	CCONJ
ejpam-5431	667	26	[	[	X
ejpam-5431	667	27	sσ](⋉,β	sσ](⋉,β	PROPN
ejpam-5431	667	28	)	)	PUNCT
ejpam-5431	668	1	=	=	PRON
ejpam-5431	668	2	{	{	PUNCT
ejpam-5431	668	3	{	{	PUNCT
ejpam-5431	668	4	σ	σ	NOUN
ejpam-5431	668	5	2	2	NUM
ejpam-5431	668	6	}	}	PUNCT
ejpam-5431	668	7	,	,	PUNCT
ejpam-5431	668	8	if	if	SCONJ
ejpam-5431	668	9	σ	σ	PROPN
ejpam-5431	668	10	is	be	AUX
ejpam-5431	668	11	even	even	ADV
ejpam-5431	668	12	{	{	PUNCT
ejpam-5431	668	13	σ	σ	X
ejpam-5431	668	14	}	}	PUNCT
ejpam-5431	668	15	,	,	PUNCT
ejpam-5431	668	16	if	if	SCONJ
ejpam-5431	668	17	σ	σ	PROPN
ejpam-5431	668	18	is	be	AUX
ejpam-5431	668	19	odd	odd	ADJ
ejpam-5431	668	20	.	.	PUNCT
ejpam-5431	669	1	clearly	clearly	ADV
ejpam-5431	669	2	sσ	sσ	ADJ
ejpam-5431	669	3	,	,	PUNCT
ejpam-5431	669	4	t	t	PROPN
ejpam-5431	669	5	σ	σ	PROPN
ejpam-5431	669	6	∈	∈	PROPN
ejpam-5431	669	7	ifs(x	ifs(x	PROPN
ejpam-5431	669	8	)	)	PUNCT
ejpam-5431	669	9	for	for	ADP
ejpam-5431	669	10	each	each	DET
ejpam-5431	669	11	σ	σ	PROPN
ejpam-5431	669	12	∈	∈	PROPN
ejpam-5431	669	13	x.	x.	NOUN
ejpam-5431	669	14	define	define	VERB
ejpam-5431	669	15	the	the	DET
ejpam-5431	669	16	functions	function	NOUN
ejpam-5431	669	17	γ	γ	X
ejpam-5431	669	18	:	:	PUNCT
ejpam-5431	669	19	x	x	SYM
ejpam-5431	669	20	×	×	NOUN
ejpam-5431	669	21	x	x	INTJ
ejpam-5431	669	22	→	→	X
ejpam-5431	669	23	r+	r+	NOUN
ejpam-5431	669	24	and	and	CCONJ
ejpam-5431	669	25	φ	φ	PROPN
ejpam-5431	669	26	:	:	PUNCT
ejpam-5431	669	27	r+	r+	X
ejpam-5431	669	28	→	→	SYM
ejpam-5431	669	29	r+	r+	NOUN
ejpam-5431	669	30	by	by	ADP
ejpam-5431	669	31	γ(σ	γ(σ	PROPN
ejpam-5431	669	32	,	,	PUNCT
ejpam-5431	669	33	τ	τ	X
ejpam-5431	669	34	)	)	PUNCT
ejpam-5431	669	35	=	=	PUNCT
ejpam-5431	670	1			PROPN
ejpam-5431	670	2	6	6	NUM
ejpam-5431	670	3	,	,	PUNCT
ejpam-5431	670	4	if	if	SCONJ
ejpam-5431	670	5	σ	σ	PROPN
ejpam-5431	670	6	=	=	SYM
ejpam-5431	670	7	τ	τ	X
ejpam-5431	670	8	=	=	SYM
ejpam-5431	670	9	1	1	NUM
ejpam-5431	670	10	1	1	NUM
ejpam-5431	670	11	150	150	NUM
ejpam-5431	670	12	,	,	PUNCT
ejpam-5431	670	13	if	if	SCONJ
ejpam-5431	670	14	σ	σ	PROPN
ejpam-5431	670	15	,	,	PUNCT
ejpam-5431	670	16	τ	τ	PROPN
ejpam-5431	670	17	∈	∈	PROPN
ejpam-5431	670	18	{	{	PUNCT
ejpam-5431	670	19	2	2	NUM
ejpam-5431	670	20	,	,	PUNCT
ejpam-5431	670	21	3	3	NUM
ejpam-5431	670	22	}	}	PUNCT
ejpam-5431	670	23	such	such	ADJ
ejpam-5431	670	24	that	that	SCONJ
ejpam-5431	670	25	σ	σ	NOUN
ejpam-5431	670	26	̸=	̸=	PROPN
ejpam-5431	670	27	τ	τ	X
ejpam-5431	670	28	0	0	NUM
ejpam-5431	670	29	,	,	PUNCT
ejpam-5431	670	30	otherwise	otherwise	ADV
ejpam-5431	670	31	.	.	PUNCT
ejpam-5431	670	32	and	and	CCONJ
ejpam-5431	670	33	φ(t	φ(t	PROPN
ejpam-5431	670	34	)	)	PUNCT
ejpam-5431	670	35	=	=	PUNCT
ejpam-5431	670	36	t	t	PROPN
ejpam-5431	670	37	4	4	NUM
ejpam-5431	670	38	for	for	ADP
ejpam-5431	670	39	all	all	DET
ejpam-5431	670	40	t	t	PROPN
ejpam-5431	670	41	>	>	X
ejpam-5431	670	42	0	0	X
ejpam-5431	670	43	.	.	PUNCT
ejpam-5431	671	1	let	let	AUX
ejpam-5431	671	2	℘(a	℘(a	PROPN
ejpam-5431	671	3	,	,	PUNCT
ejpam-5431	671	4	b	b	NOUN
ejpam-5431	671	5	)	)	PUNCT
ejpam-5431	671	6	=	=	SYM
ejpam-5431	671	7	1	1	NUM
ejpam-5431	671	8	2b	2b	NUM
ejpam-5431	671	9	−	−	NOUN
ejpam-5431	671	10	a	a	PRON
ejpam-5431	671	11	for	for	ADP
ejpam-5431	671	12	all	all	DET
ejpam-5431	671	13	a	a	DET
ejpam-5431	671	14	,	,	PUNCT
ejpam-5431	671	15	b	b	X
ejpam-5431	671	16	∈	∈	PROPN
ejpam-5431	671	17	r+	r+	X
ejpam-5431	671	18	.	.	PUNCT
ejpam-5431	672	1	obviously	obviously	ADV
ejpam-5431	672	2	℘	℘	VERB
ejpam-5431	672	3	∈	∈	PROPN
ejpam-5431	672	4	z	z	NOUN
ejpam-5431	672	5	and	and	CCONJ
ejpam-5431	672	6	φ	φ	PROPN
ejpam-5431	672	7	∈	∈	PROPN
ejpam-5431	672	8	λb	λb	ADP
ejpam-5431	672	9	now	now	ADV
ejpam-5431	672	10	we	we	PRON
ejpam-5431	672	11	verify	verify	VERB
ejpam-5431	672	12	conditions	condition	NOUN
ejpam-5431	672	13	℘(γ(σ	℘(γ(σ	ADJ
ejpam-5431	672	14	,	,	PUNCT
ejpam-5431	672	15	τ)ℵ([sσ](⋉,β	τ)ℵ([sσ](⋉,β	NOUN
ejpam-5431	672	16	)	)	PUNCT
ejpam-5431	672	17	,	,	PUNCT
ejpam-5431	673	1	[	[	X
ejpam-5431	673	2	t	t	X
ejpam-5431	673	3	τ	τ	X
ejpam-5431	673	4	]	]	X
ejpam-5431	673	5	(	(	PUNCT
ejpam-5431	673	6	⋉,β	⋉,β	NOUN
ejpam-5431	673	7	)	)	PUNCT
ejpam-5431	673	8	)	)	PUNCT
ejpam-5431	673	9	,	,	PUNCT
ejpam-5431	673	10	φ(m	φ(m	ADJ
ejpam-5431	673	11	r	r	NOUN
ejpam-5431	673	12	(	(	PUNCT
ejpam-5431	673	13	s	s	PROPN
ejpam-5431	673	14	,	,	PUNCT
ejpam-5431	673	15	t	t	NOUN
ejpam-5431	673	16	)	)	PUNCT
ejpam-5431	673	17	(	(	PUNCT
ejpam-5431	673	18	σ	σ	PROPN
ejpam-5431	673	19	,	,	PUNCT
ejpam-5431	673	20	τ	τ	PROPN
ejpam-5431	673	21	)	)	PUNCT
ejpam-5431	673	22	)	)	PUNCT
ejpam-5431	673	23	)	)	PUNCT
ejpam-5431	673	24	≥	≥	NOUN
ejpam-5431	673	25	0	0	NUM
ejpam-5431	673	26	and	and	CCONJ
ejpam-5431	673	27	℘(γ(σ	℘(γ(σ	ADJ
ejpam-5431	673	28	,	,	PUNCT
ejpam-5431	673	29	τ)ℵ([t	τ)ℵ([t	PROPN
ejpam-5431	673	30	σ](⋉,β	σ](⋉,β	NUM
ejpam-5431	673	31	)	)	PUNCT
ejpam-5431	673	32	,	,	PUNCT
ejpam-5431	673	33	[	[	X
ejpam-5431	673	34	sτ	sτ	ADP
ejpam-5431	673	35	]	]	PUNCT
ejpam-5431	673	36	(	(	PUNCT
ejpam-5431	673	37	⋉,β	⋉,β	NOUN
ejpam-5431	673	38	)	)	PUNCT
ejpam-5431	673	39	)	)	PUNCT
ejpam-5431	673	40	,	,	PUNCT
ejpam-5431	673	41	φ(m	φ(m	ADJ
ejpam-5431	673	42	r	r	NOUN
ejpam-5431	673	43	(	(	PUNCT
ejpam-5431	673	44	t	t	NOUN
ejpam-5431	673	45	,	,	PUNCT
ejpam-5431	673	46	s)(σ	s)(σ	PROPN
ejpam-5431	673	47	,	,	PUNCT
ejpam-5431	673	48	τ	τ	PROPN
ejpam-5431	673	49	)	)	PUNCT
ejpam-5431	673	50	)	)	PUNCT
ejpam-5431	673	51	)	)	PUNCT
ejpam-5431	673	52	≥	≥	NOUN
ejpam-5431	673	53	0	0	NUM
ejpam-5431	673	54	for	for	ADP
ejpam-5431	673	55	r	r	NOUN
ejpam-5431	673	56	>	>	X
ejpam-5431	673	57	0	0	PUNCT
ejpam-5431	674	1	under	under	ADP
ejpam-5431	674	2	the	the	DET
ejpam-5431	674	3	following	follow	VERB
ejpam-5431	674	4	cases	case	NOUN
ejpam-5431	674	5	;	;	PUNCT
ejpam-5431	674	6	case	case	NOUN
ejpam-5431	674	7	1	1	NUM
ejpam-5431	674	8	:	:	PUNCT
ejpam-5431	674	9	if	if	SCONJ
ejpam-5431	674	10	σ	σ	PROPN
ejpam-5431	674	11	=	=	SYM
ejpam-5431	674	12	τ	τ	X
ejpam-5431	674	13	=	=	SYM
ejpam-5431	674	14	1	1	NUM
ejpam-5431	674	15	,	,	PUNCT
ejpam-5431	674	16	then	then	ADV
ejpam-5431	674	17	[	[	X
ejpam-5431	674	18	sσ](⋉,β	sσ](⋉,β	NOUN
ejpam-5431	674	19	)	)	PUNCT
ejpam-5431	674	20	=	=	PUNCT
ejpam-5431	675	1	[	[	X
ejpam-5431	675	2	t	t	X
ejpam-5431	675	3	τ	τ	X
ejpam-5431	675	4	]	]	X
ejpam-5431	675	5	(	(	PUNCT
ejpam-5431	675	6	⋉,β	⋉,β	NOUN
ejpam-5431	675	7	)	)	PUNCT
ejpam-5431	675	8	=	=	PRON
ejpam-5431	675	9	{	{	PUNCT
ejpam-5431	675	10	1	1	NUM
ejpam-5431	675	11	}	}	PUNCT
ejpam-5431	675	12	this	this	PRON
ejpam-5431	675	13	implies	imply	VERB
ejpam-5431	675	14	that	that	SCONJ
ejpam-5431	675	15	ℵ([sσ](⋉,β	ℵ([sσ](⋉,β	PROPN
ejpam-5431	675	16	)	)	PUNCT
ejpam-5431	675	17	,	,	PUNCT
ejpam-5431	676	1	[	[	X
ejpam-5431	676	2	t	t	X
ejpam-5431	676	3	τ	τ	X
ejpam-5431	676	4	]	]	X
ejpam-5431	676	5	(	(	PUNCT
ejpam-5431	676	6	⋉,β	⋉,β	NOUN
ejpam-5431	676	7	)	)	PUNCT
ejpam-5431	676	8	)	)	PUNCT
ejpam-5431	677	1	=	=	SYM
ejpam-5431	677	2	0	0	PUNCT
ejpam-5431	678	1	so	so	ADV
ejpam-5431	678	2	,	,	PUNCT
ejpam-5431	678	3	℘(6(0	℘(6(0	PROPN
ejpam-5431	678	4	)	)	PUNCT
ejpam-5431	678	5	,	,	PUNCT
ejpam-5431	678	6	φ(m	φ(m	ADJ
ejpam-5431	678	7	r	r	NOUN
ejpam-5431	678	8	(	(	PUNCT
ejpam-5431	678	9	s	s	PROPN
ejpam-5431	678	10	,	,	PUNCT
ejpam-5431	678	11	t	t	NOUN
ejpam-5431	678	12	)	)	PUNCT
ejpam-5431	678	13	(	(	PUNCT
ejpam-5431	678	14	σ	σ	PROPN
ejpam-5431	678	15	,	,	PUNCT
ejpam-5431	678	16	τ	τ	PROPN
ejpam-5431	678	17	)	)	PUNCT
ejpam-5431	678	18	)	)	PUNCT
ejpam-5431	678	19	)	)	PUNCT
ejpam-5431	679	1	≥	≥	NOUN
ejpam-5431	679	2	0	0	NUM
ejpam-5431	680	1	similarly	similarly	ADV
ejpam-5431	680	2	℘(γ(σ	℘(γ(σ	ADJ
ejpam-5431	680	3	,	,	PUNCT
ejpam-5431	680	4	τ)ℵ([t	τ)ℵ([t	PROPN
ejpam-5431	680	5	σ](⋉,β	σ](⋉,β	NUM
ejpam-5431	680	6	)	)	PUNCT
ejpam-5431	680	7	,	,	PUNCT
ejpam-5431	680	8	[	[	X
ejpam-5431	680	9	sτ	sτ	ADP
ejpam-5431	680	10	]	]	PUNCT
ejpam-5431	680	11	(	(	PUNCT
ejpam-5431	680	12	⋉,β	⋉,β	NOUN
ejpam-5431	680	13	)	)	PUNCT
ejpam-5431	680	14	)	)	PUNCT
ejpam-5431	680	15	,	,	PUNCT
ejpam-5431	680	16	φ(m	φ(m	ADJ
ejpam-5431	680	17	r	r	NOUN
ejpam-5431	680	18	(	(	PUNCT
ejpam-5431	680	19	t	t	NOUN
ejpam-5431	680	20	,	,	PUNCT
ejpam-5431	680	21	s)(σ	s)(σ	PROPN
ejpam-5431	680	22	,	,	PUNCT
ejpam-5431	680	23	τ	τ	PROPN
ejpam-5431	680	24	)	)	PUNCT
ejpam-5431	680	25	)	)	PUNCT
ejpam-5431	680	26	)	)	PUNCT
ejpam-5431	680	27	≥	≥	X
ejpam-5431	680	28	0	0	NUM
ejpam-5431	680	29	n.	n.	PROPN
ejpam-5431	680	30	saleem	saleem	PROPN
ejpam-5431	680	31	et	et	PROPN
ejpam-5431	680	32	al	al	PROPN
ejpam-5431	680	33	.	.	PUNCT
ejpam-5431	680	34	/	/	SYM
ejpam-5431	680	35	eur	eur	PROPN
ejpam-5431	680	36	.	.	PUNCT
ejpam-5431	681	1	j.	j.	PROPN
ejpam-5431	681	2	pure	pure	PROPN
ejpam-5431	681	3	appl	appl	PROPN
ejpam-5431	681	4	.	.	PROPN
ejpam-5431	681	5	math	math	PROPN
ejpam-5431	681	6	,	,	PUNCT
ejpam-5431	681	7	17	17	NUM
ejpam-5431	681	8	(	(	PUNCT
ejpam-5431	681	9	4	4	NUM
ejpam-5431	681	10	)	)	PUNCT
ejpam-5431	681	11	(	(	PUNCT
ejpam-5431	681	12	2024	2024	NUM
ejpam-5431	681	13	)	)	PUNCT
ejpam-5431	681	14	,	,	PUNCT
ejpam-5431	681	15	3304	3304	NUM
ejpam-5431	681	16	-	-	SYM
ejpam-5431	681	17	3335	3335	NUM
ejpam-5431	681	18	3332	3332	NUM
ejpam-5431	681	19	case	case	NOUN
ejpam-5431	681	20	2	2	NUM
ejpam-5431	681	21	:	:	PUNCT
ejpam-5431	681	22	if	if	SCONJ
ejpam-5431	681	23	σ	σ	PROPN
ejpam-5431	681	24	,	,	PUNCT
ejpam-5431	681	25	τ	τ	PROPN
ejpam-5431	681	26	∈	∈	PROPN
ejpam-5431	681	27	{	{	PUNCT
ejpam-5431	681	28	2	2	NUM
ejpam-5431	681	29	,	,	PUNCT
ejpam-5431	681	30	3	3	NUM
ejpam-5431	681	31	}	}	PUNCT
ejpam-5431	681	32	such	such	ADJ
ejpam-5431	681	33	that	that	SCONJ
ejpam-5431	681	34	σ	σ	PROPN
ejpam-5431	681	35	̸=	̸=	PROPN
ejpam-5431	681	36	τ	τ	X
ejpam-5431	681	37	,	,	PUNCT
ejpam-5431	681	38	let	let	VERB
ejpam-5431	681	39	σ	σ	NOUN
ejpam-5431	681	40	=	=	SYM
ejpam-5431	681	41	2	2	NUM
ejpam-5431	681	42	and	and	CCONJ
ejpam-5431	681	43	τ	τ	X
ejpam-5431	681	44	=	=	SYM
ejpam-5431	681	45	3	3	X
ejpam-5431	681	46	.	.	PUNCT
ejpam-5431	682	1	then	then	ADV
ejpam-5431	682	2	[	[	X
ejpam-5431	682	3	sσ](⋉,β	sσ](⋉,β	NOUN
ejpam-5431	682	4	)	)	PUNCT
ejpam-5431	683	1	=	=	PRON
ejpam-5431	683	2	{	{	PUNCT
ejpam-5431	683	3	1	1	NUM
ejpam-5431	683	4	}	}	PUNCT
ejpam-5431	683	5	and	and	CCONJ
ejpam-5431	684	1	[	[	X
ejpam-5431	684	2	t	t	X
ejpam-5431	684	3	τ	τ	X
ejpam-5431	684	4	]	]	X
ejpam-5431	684	5	(	(	PUNCT
ejpam-5431	684	6	⋉,β	⋉,β	NOUN
ejpam-5431	684	7	)	)	PUNCT
ejpam-5431	684	8	=	=	PRON
ejpam-5431	684	9	{	{	PUNCT
ejpam-5431	684	10	3	3	NUM
ejpam-5431	684	11	}	}	PUNCT
ejpam-5431	684	12	which	which	PRON
ejpam-5431	684	13	implies	imply	VERB
ejpam-5431	684	14	that	that	SCONJ
ejpam-5431	684	15	ℵ([sσ](⋉,β	ℵ([sσ](⋉,β	PROPN
ejpam-5431	684	16	)	)	PUNCT
ejpam-5431	684	17	,	,	PUNCT
ejpam-5431	685	1	[	[	X
ejpam-5431	685	2	t	t	X
ejpam-5431	685	3	τ	τ	X
ejpam-5431	685	4	]	]	X
ejpam-5431	685	5	(	(	PUNCT
ejpam-5431	685	6	⋉,β	⋉,β	NOUN
ejpam-5431	685	7	)	)	PUNCT
ejpam-5431	685	8	)	)	PUNCT
ejpam-5431	686	1	=	=	SYM
ejpam-5431	686	2	ℵ({1	ℵ({1	NOUN
ejpam-5431	686	3	}	}	PUNCT
ejpam-5431	686	4	,	,	PUNCT
ejpam-5431	686	5	{	{	PUNCT
ejpam-5431	686	6	3	3	NUM
ejpam-5431	686	7	}	}	PUNCT
ejpam-5431	686	8	)	)	PUNCT
ejpam-5431	687	1	=	=	SYM
ejpam-5431	687	2	δ(1	δ(1	NOUN
ejpam-5431	687	3	,	,	PUNCT
ejpam-5431	687	4	3	3	NUM
ejpam-5431	687	5	)	)	PUNCT
ejpam-5431	687	6	=	=	SYM
ejpam-5431	687	7	8	8	NUM
ejpam-5431	687	8	m	m	VERB
ejpam-5431	687	9	r	r	NOUN
ejpam-5431	687	10	(	(	PUNCT
ejpam-5431	687	11	s	s	PROPN
ejpam-5431	687	12	,	,	PUNCT
ejpam-5431	687	13	t	t	NOUN
ejpam-5431	687	14	)	)	PUNCT
ejpam-5431	687	15	(	(	PUNCT
ejpam-5431	687	16	2	2	NUM
ejpam-5431	687	17	,	,	PUNCT
ejpam-5431	687	18	3	3	NUM
ejpam-5431	687	19	)	)	PUNCT
ejpam-5431	687	20	=	=	NOUN
ejpam-5431	688	1	[	[	X
ejpam-5431	688	2	a(2	a(2	PROPN
ejpam-5431	688	3	,	,	PUNCT
ejpam-5431	688	4	3	3	NUM
ejpam-5431	688	5	)	)	PUNCT
ejpam-5431	688	6	]	]	PUNCT
ejpam-5431	688	7	1	1	NUM
ejpam-5431	688	8	r	r	NOUN
ejpam-5431	688	9	=	=	PUNCT
ejpam-5431	688	10	[	[	PUNCT
ejpam-5431	688	11	k1(δ(2	k1(δ(2	ADJ
ejpam-5431	688	12	,	,	PUNCT
ejpam-5431	688	13	3	3	NUM
ejpam-5431	688	14	)	)	PUNCT
ejpam-5431	688	15	)	)	PUNCT
ejpam-5431	689	1	r	r	NOUN
ejpam-5431	689	2	+	+	CCONJ
ejpam-5431	689	3	k2(δ(2	k2(δ(2	PROPN
ejpam-5431	689	4	,	,	PUNCT
ejpam-5431	689	5	[	[	X
ejpam-5431	689	6	s2](⋉,β	s2](⋉,β	NOUN
ejpam-5431	689	7	)	)	PUNCT
ejpam-5431	689	8	)	)	PUNCT
ejpam-5431	689	9	)	)	PUNCT
ejpam-5431	690	1	r	r	NOUN
ejpam-5431	690	2	+	+	NUM
ejpam-5431	690	3	k3(δ(3	k3(δ(3	NOUN
ejpam-5431	690	4	,	,	PUNCT
ejpam-5431	690	5	[	[	X
ejpam-5431	690	6	t	t	NOUN
ejpam-5431	690	7	3](⋉,β	3](⋉,β	NUM
ejpam-5431	690	8	)	)	PUNCT
ejpam-5431	690	9	)	)	PUNCT
ejpam-5431	690	10	)	)	PUNCT
ejpam-5431	691	1	r	r	NOUN
ejpam-5431	691	2	+	+	PRON
ejpam-5431	691	3	k4	k4	NOUN
ejpam-5431	691	4	(	(	PUNCT
ejpam-5431	691	5	δ(3	δ(3	PROPN
ejpam-5431	691	6	,	,	PUNCT
ejpam-5431	691	7	[	[	X
ejpam-5431	691	8	t	t	X
ejpam-5431	691	9	3](⋉,β))(1	3](⋉,β))(1	NOUN
ejpam-5431	691	10	+	+	CCONJ
ejpam-5431	691	11	δ(2	δ(2	PROPN
ejpam-5431	691	12	,	,	PUNCT
ejpam-5431	691	13	[	[	X
ejpam-5431	691	14	s2](⋉,β	s2](⋉,β	NOUN
ejpam-5431	691	15	)	)	PUNCT
ejpam-5431	691	16	)	)	PUNCT
ejpam-5431	691	17	)	)	PUNCT
ejpam-5431	692	1	1	1	NUM
ejpam-5431	693	1	+	+	CCONJ
ejpam-5431	693	2	δ(2	δ(2	PROPN
ejpam-5431	693	3	,	,	PUNCT
ejpam-5431	693	4	3	3	NUM
ejpam-5431	693	5	)	)	PUNCT
ejpam-5431	693	6	)	)	PUNCT
ejpam-5431	694	1	r	r	NOUN
ejpam-5431	694	2	+	+	PROPN
ejpam-5431	694	3	k5	k5	PROPN
ejpam-5431	694	4	(	(	PUNCT
ejpam-5431	694	5	δ(3	δ(3	PROPN
ejpam-5431	694	6	,	,	PUNCT
ejpam-5431	694	7	[	[	X
ejpam-5431	694	8	s2](⋉,β))(1	s2](⋉,β))(1	NOUN
ejpam-5431	694	9	+	+	X
ejpam-5431	694	10	δ(2	δ(2	PROPN
ejpam-5431	694	11	,	,	PUNCT
ejpam-5431	694	12	[	[	X
ejpam-5431	694	13	t	t	NOUN
ejpam-5431	694	14	3](⋉,β	3](⋉,β	NUM
ejpam-5431	694	15	)	)	PUNCT
ejpam-5431	694	16	)	)	PUNCT
ejpam-5431	694	17	)	)	PUNCT
ejpam-5431	694	18	1	1	NUM
ejpam-5431	695	1	+	+	CCONJ
ejpam-5431	695	2	δ(2	δ(2	PROPN
ejpam-5431	695	3	,	,	PUNCT
ejpam-5431	695	4	3	3	NUM
ejpam-5431	695	5	)	)	PUNCT
ejpam-5431	695	6	)	)	PUNCT
ejpam-5431	695	7	r	r	NOUN
ejpam-5431	695	8	]	]	PUNCT
ejpam-5431	695	9	1	1	NUM
ejpam-5431	695	10	r	r	NOUN
ejpam-5431	695	11	taking	take	VERB
ejpam-5431	695	12	k1	k1	NOUN
ejpam-5431	695	13	=	=	SYM
ejpam-5431	695	14	k2	k2	NOUN
ejpam-5431	695	15	=	=	SYM
ejpam-5431	695	16	1	1	NUM
ejpam-5431	695	17	2	2	NUM
ejpam-5431	695	18	and	and	CCONJ
ejpam-5431	695	19	k3	k3	X
ejpam-5431	695	20	=	=	SYM
ejpam-5431	695	21	k4	k4	PROPN
ejpam-5431	695	22	=	=	PROPN
ejpam-5431	695	23	k5	k5	PROPN
ejpam-5431	695	24	=	=	SYM
ejpam-5431	695	25	0	0	PROPN
ejpam-5431	695	26	,	,	PUNCT
ejpam-5431	695	27	m	m	VERB
ejpam-5431	695	28	r	r	NOUN
ejpam-5431	695	29	(	(	PUNCT
ejpam-5431	695	30	s	s	PROPN
ejpam-5431	695	31	,	,	PUNCT
ejpam-5431	695	32	t	t	NOUN
ejpam-5431	695	33	)	)	PUNCT
ejpam-5431	695	34	(	(	PUNCT
ejpam-5431	695	35	2	2	NUM
ejpam-5431	695	36	,	,	PUNCT
ejpam-5431	695	37	3	3	NUM
ejpam-5431	695	38	)	)	PUNCT
ejpam-5431	695	39	=	=	NOUN
ejpam-5431	696	1	[	[	PUNCT
ejpam-5431	696	2	1	1	NUM
ejpam-5431	696	3	2	2	NUM
ejpam-5431	696	4	(	(	PUNCT
ejpam-5431	696	5	1)r	1)r	NOUN
ejpam-5431	696	6	+	+	CCONJ
ejpam-5431	696	7	1	1	NUM
ejpam-5431	696	8	2	2	NUM
ejpam-5431	696	9	(	(	PUNCT
ejpam-5431	696	10	1)r	1)r	NUM
ejpam-5431	696	11	]	]	PUNCT
ejpam-5431	696	12	1	1	NUM
ejpam-5431	696	13	r	r	NOUN
ejpam-5431	696	14	=	=	PUNCT
ejpam-5431	696	15	{	{	PUNCT
ejpam-5431	696	16	1	1	NUM
ejpam-5431	696	17	}	}	SYM
ejpam-5431	696	18	1	1	NUM
ejpam-5431	696	19	r	r	NOUN
ejpam-5431	696	20	=	=	SYM
ejpam-5431	696	21	1	1	NUM
ejpam-5431	696	22	therefore	therefore	ADV
ejpam-5431	696	23	,	,	PUNCT
ejpam-5431	696	24	℘	℘	PROPN
ejpam-5431	696	25	(	(	PUNCT
ejpam-5431	696	26	1	1	NUM
ejpam-5431	696	27	150	150	NUM
ejpam-5431	696	28	(	(	PUNCT
ejpam-5431	696	29	8)	8)	NUM
ejpam-5431	696	30	,	,	PUNCT
ejpam-5431	696	31	φ(1	φ(1	PROPN
ejpam-5431	696	32	)	)	PUNCT
ejpam-5431	696	33	)	)	PUNCT
ejpam-5431	696	34	≥	≥	X
ejpam-5431	696	35	0	0	NUM
ejpam-5431	696	36	similarly	similarly	ADV
ejpam-5431	696	37	,	,	PUNCT
ejpam-5431	696	38	℘(γ(σ	℘(γ(σ	ADJ
ejpam-5431	696	39	,	,	PUNCT
ejpam-5431	696	40	τ)ℵ([t	τ)ℵ([t	PROPN
ejpam-5431	696	41	σ](⋉,β	σ](⋉,β	NUM
ejpam-5431	696	42	)	)	PUNCT
ejpam-5431	696	43	,	,	PUNCT
ejpam-5431	696	44	[	[	X
ejpam-5431	696	45	sτ	sτ	ADP
ejpam-5431	696	46	]	]	PUNCT
ejpam-5431	696	47	(	(	PUNCT
ejpam-5431	696	48	⋉,β	⋉,β	NOUN
ejpam-5431	696	49	)	)	PUNCT
ejpam-5431	696	50	)	)	PUNCT
ejpam-5431	696	51	,	,	PUNCT
ejpam-5431	696	52	φ(m	φ(m	ADJ
ejpam-5431	696	53	r	r	NOUN
ejpam-5431	696	54	(	(	PUNCT
ejpam-5431	696	55	t	t	NOUN
ejpam-5431	696	56	,	,	PUNCT
ejpam-5431	696	57	s)(σ	s)(σ	PROPN
ejpam-5431	696	58	,	,	PUNCT
ejpam-5431	696	59	τ	τ	PROPN
ejpam-5431	696	60	)	)	PUNCT
ejpam-5431	696	61	)	)	PUNCT
ejpam-5431	696	62	)	)	PUNCT
ejpam-5431	697	1	≥	≥	NOUN
ejpam-5431	697	2	0	0	NUM
ejpam-5431	697	3	case	case	NOUN
ejpam-5431	697	4	3	3	NUM
ejpam-5431	697	5	if	if	SCONJ
ejpam-5431	697	6	σ	σ	PROPN
ejpam-5431	697	7	,	,	PUNCT
ejpam-5431	697	8	τ	τ	PROPN
ejpam-5431	697	9	∈	∈	PROPN
ejpam-5431	697	10	x	x	PUNCT
ejpam-5431	697	11	−	−	PROPN
ejpam-5431	697	12	{	{	PUNCT
ejpam-5431	697	13	1	1	NUM
ejpam-5431	697	14	,	,	PUNCT
ejpam-5431	697	15	2	2	NUM
ejpam-5431	697	16	,	,	PUNCT
ejpam-5431	697	17	3	3	NUM
ejpam-5431	697	18	}	}	PUNCT
ejpam-5431	697	19	,	,	PUNCT
ejpam-5431	697	20	then	then	ADV
ejpam-5431	697	21	γ(σ	γ(σ	PROPN
ejpam-5431	697	22	,	,	PUNCT
ejpam-5431	697	23	τ	τ	X
ejpam-5431	697	24	)	)	PUNCT
ejpam-5431	697	25	=	=	SYM
ejpam-5431	697	26	0	0	NUM
ejpam-5431	697	27	which	which	PRON
ejpam-5431	697	28	implies	imply	VERB
ejpam-5431	697	29	that	that	SCONJ
ejpam-5431	697	30	℘(0	℘(0	NOUN
ejpam-5431	697	31	,	,	PUNCT
ejpam-5431	697	32	φ(m	φ(m	ADJ
ejpam-5431	697	33	r	r	NOUN
ejpam-5431	697	34	(	(	PUNCT
ejpam-5431	697	35	s	s	PROPN
ejpam-5431	697	36	,	,	PUNCT
ejpam-5431	697	37	t	t	NOUN
ejpam-5431	697	38	)	)	PUNCT
ejpam-5431	697	39	(	(	PUNCT
ejpam-5431	697	40	σ	σ	PROPN
ejpam-5431	697	41	,	,	PUNCT
ejpam-5431	697	42	τ	τ	PROPN
ejpam-5431	697	43	)	)	PUNCT
ejpam-5431	697	44	)	)	PUNCT
ejpam-5431	698	1	=	=	SYM
ejpam-5431	698	2	1	1	NUM
ejpam-5431	698	3	2	2	NUM
ejpam-5431	698	4	φ(m	φ(m	NOUN
ejpam-5431	698	5	r	r	NOUN
ejpam-5431	698	6	(	(	PUNCT
ejpam-5431	698	7	s	s	PROPN
ejpam-5431	698	8	,	,	PUNCT
ejpam-5431	698	9	t	t	NOUN
ejpam-5431	698	10	)	)	PUNCT
ejpam-5431	698	11	(	(	PUNCT
ejpam-5431	698	12	σ	σ	PROPN
ejpam-5431	698	13	,	,	PUNCT
ejpam-5431	698	14	τ	τ	PROPN
ejpam-5431	698	15	)	)	PUNCT
ejpam-5431	698	16	)	)	PUNCT
ejpam-5431	698	17	)	)	PUNCT
ejpam-5431	698	18	≥	≥	X
ejpam-5431	698	19	0	0	NUM
ejpam-5431	698	20	similarly	similarly	ADV
ejpam-5431	698	21	,	,	PUNCT
ejpam-5431	698	22	℘(0	℘(0	NOUN
ejpam-5431	698	23	,	,	PUNCT
ejpam-5431	698	24	φ(m	φ(m	ADJ
ejpam-5431	698	25	r	r	NOUN
ejpam-5431	698	26	(	(	PUNCT
ejpam-5431	698	27	t	t	NOUN
ejpam-5431	698	28	,	,	PUNCT
ejpam-5431	698	29	s)(σ	s)(σ	PROPN
ejpam-5431	698	30	,	,	PUNCT
ejpam-5431	698	31	τ	τ	PROPN
ejpam-5431	698	32	)	)	PUNCT
ejpam-5431	698	33	)	)	PUNCT
ejpam-5431	698	34	)	)	PUNCT
ejpam-5431	698	35	≥	≥	NOUN
ejpam-5431	698	36	0	0	NUM
ejpam-5431	698	37	.	.	PUNCT
ejpam-5431	699	1	moreover	moreover	ADV
ejpam-5431	699	2	,	,	PUNCT
ejpam-5431	699	3	it	it	PRON
ejpam-5431	699	4	is	be	AUX
ejpam-5431	699	5	clear	clear	ADJ
ejpam-5431	699	6	that	that	SCONJ
ejpam-5431	699	7	the	the	DET
ejpam-5431	699	8	pair	pair	NOUN
ejpam-5431	699	9	(	(	PUNCT
ejpam-5431	699	10	s	s	PROPN
ejpam-5431	699	11	,	,	PUNCT
ejpam-5431	699	12	t	t	PROPN
ejpam-5431	699	13	)	)	PUNCT
ejpam-5431	699	14	is	be	AUX
ejpam-5431	699	15	γ	γ	X
ejpam-5431	699	16	-	-	ADJ
ejpam-5431	699	17	admissible	admissible	ADJ
ejpam-5431	699	18	,	,	PUNCT
ejpam-5431	699	19	ℵ-continuous	ℵ-continuous	ADJ
ejpam-5431	699	20	and	and	CCONJ
ejpam-5431	699	21	the	the	DET
ejpam-5431	699	22	sets	set	NOUN
ejpam-5431	699	23	[	[	X
ejpam-5431	699	24	sσ](⋉,β	sσ](⋉,β	PROPN
ejpam-5431	699	25	)	)	PUNCT
ejpam-5431	699	26	,	,	PUNCT
ejpam-5431	700	1	[	[	X
ejpam-5431	700	2	t	t	NOUN
ejpam-5431	700	3	σ](⋉,β	σ](⋉,β	NOUN
ejpam-5431	700	4	)	)	PUNCT
ejpam-5431	700	5	are	be	AUX
ejpam-5431	700	6	proximal	proximal	ADJ
ejpam-5431	700	7	for	for	ADP
ejpam-5431	700	8	each	each	DET
ejpam-5431	700	9	σ	σ	PROPN
ejpam-5431	700	10	∈	∈	PROPN
ejpam-5431	700	11	x.	x.	NOUN
ejpam-5431	700	12	hence	hence	NOUN
ejpam-5431	700	13	s	s	PROPN
ejpam-5431	700	14	and	and	CCONJ
ejpam-5431	700	15	t	t	PROPN
ejpam-5431	700	16	have	have	VERB
ejpam-5431	700	17	at	at	ADV
ejpam-5431	700	18	least	least	ADV
ejpam-5431	700	19	one	one	NUM
ejpam-5431	700	20	common	common	ADJ
ejpam-5431	700	21	iffp	iffp	NOUN
ejpam-5431	700	22	in	in	ADP
ejpam-5431	700	23	x.	x.	PROPN
ejpam-5431	700	24	n.	n.	PROPN
ejpam-5431	700	25	saleem	saleem	PROPN
ejpam-5431	700	26	et	et	PROPN
ejpam-5431	700	27	al	al	PROPN
ejpam-5431	700	28	.	.	PUNCT
ejpam-5431	700	29	/	/	SYM
ejpam-5431	700	30	eur	eur	PROPN
ejpam-5431	700	31	.	.	PUNCT
ejpam-5431	701	1	j.	j.	PROPN
ejpam-5431	701	2	pure	pure	PROPN
ejpam-5431	701	3	appl	appl	PROPN
ejpam-5431	701	4	.	.	PROPN
ejpam-5431	701	5	math	math	PROPN
ejpam-5431	701	6	,	,	PUNCT
ejpam-5431	701	7	17	17	NUM
ejpam-5431	701	8	(	(	PUNCT
ejpam-5431	701	9	4	4	NUM
ejpam-5431	701	10	)	)	PUNCT
ejpam-5431	701	11	(	(	PUNCT
ejpam-5431	701	12	2024	2024	NUM
ejpam-5431	701	13	)	)	PUNCT
ejpam-5431	701	14	,	,	PUNCT
ejpam-5431	701	15	3304	3304	NUM
ejpam-5431	701	16	-	-	SYM
ejpam-5431	701	17	3335	3335	NUM
ejpam-5431	701	18	3333	3333	NUM
ejpam-5431	701	19	6	6	NUM
ejpam-5431	701	20	.	.	PUNCT
ejpam-5431	702	1	conclusion	conclusion	NOUN
ejpam-5431	702	2	in	in	ADP
ejpam-5431	702	3	this	this	DET
ejpam-5431	702	4	paper	paper	NOUN
ejpam-5431	702	5	,	,	PUNCT
ejpam-5431	702	6	we	we	PRON
ejpam-5431	702	7	introduce	introduce	VERB
ejpam-5431	702	8	the	the	DET
ejpam-5431	702	9	concept	concept	NOUN
ejpam-5431	702	10	of	of	ADP
ejpam-5431	702	11	admissible	admissible	ADJ
ejpam-5431	702	12	hybrid	hybrid	ADJ
ejpam-5431	702	13	intuitionistic	intuitionistic	ADJ
ejpam-5431	702	14	fuzzy	fuzzy	ADJ
ejpam-5431	702	15	(	(	PUNCT
ejpam-5431	702	16	ahif	ahif	PROPN
ejpam-5431	702	17	)	)	PUNCT
ejpam-5431	702	18	z	z	NOUN
ejpam-5431	702	19	-	-	PUNCT
ejpam-5431	702	20	contractions	contraction	NOUN
ejpam-5431	702	21	within	within	ADP
ejpam-5431	702	22	the	the	DET
ejpam-5431	702	23	framework	framework	NOUN
ejpam-5431	702	24	of	of	ADP
ejpam-5431	702	25	complete	complete	ADJ
ejpam-5431	702	26	b	b	X
ejpam-5431	702	27	-	-	ADJ
ejpam-5431	702	28	metric	metric	ADJ
ejpam-5431	702	29	spaces	space	NOUN
ejpam-5431	702	30	(	(	PUNCT
ejpam-5431	702	31	b	b	X
ejpam-5431	702	32	-	-	PUNCT
ejpam-5431	702	33	mss	mss	NOUN
ejpam-5431	702	34	)	)	PUNCT
ejpam-5431	702	35	,	,	PUNCT
ejpam-5431	702	36	a	a	DET
ejpam-5431	702	37	significant	significant	ADJ
ejpam-5431	702	38	innovation	innovation	NOUN
ejpam-5431	702	39	that	that	PRON
ejpam-5431	702	40	aims	aim	VERB
ejpam-5431	702	41	to	to	PART
ejpam-5431	702	42	extend	extend	VERB
ejpam-5431	702	43	and	and	CCONJ
ejpam-5431	702	44	generalize	generalize	VERB
ejpam-5431	702	45	existing	exist	VERB
ejpam-5431	702	46	results	result	NOUN
ejpam-5431	702	47	in	in	ADP
ejpam-5431	702	48	intuitionistic	intuitionistic	ADJ
ejpam-5431	702	49	fuzzy	fuzzy	ADJ
ejpam-5431	702	50	fixed	fix	VERB
ejpam-5431	702	51	point	point	NOUN
ejpam-5431	702	52	(	(	PUNCT
ejpam-5431	702	53	iffp	iffp	NOUN
ejpam-5431	702	54	)	)	PUNCT
ejpam-5431	702	55	theory	theory	NOUN
ejpam-5431	702	56	.	.	PUNCT
ejpam-5431	703	1	by	by	ADP
ejpam-5431	703	2	developing	develop	VERB
ejpam-5431	703	3	new	new	ADJ
ejpam-5431	703	4	definitions	definition	NOUN
ejpam-5431	703	5	and	and	CCONJ
ejpam-5431	703	6	constructing	construct	VERB
ejpam-5431	703	7	a	a	DET
ejpam-5431	703	8	theorem	theorem	NOUN
ejpam-5431	703	9	that	that	PRON
ejpam-5431	703	10	ensures	ensure	VERB
ejpam-5431	703	11	the	the	DET
ejpam-5431	703	12	existence	existence	NOUN
ejpam-5431	703	13	of	of	ADP
ejpam-5431	703	14	at	at	ADV
ejpam-5431	703	15	least	least	ADV
ejpam-5431	703	16	one	one	NUM
ejpam-5431	703	17	common	common	ADJ
ejpam-5431	703	18	iffp	iffp	NOUN
ejpam-5431	703	19	,	,	PUNCT
ejpam-5431	703	20	our	our	PRON
ejpam-5431	703	21	work	work	NOUN
ejpam-5431	703	22	advances	advance	VERB
ejpam-5431	703	23	the	the	DET
ejpam-5431	703	24	understanding	understanding	NOUN
ejpam-5431	703	25	of	of	ADP
ejpam-5431	703	26	fixed	fix	VERB
ejpam-5431	703	27	points	point	NOUN
ejpam-5431	703	28	in	in	ADP
ejpam-5431	703	29	the	the	DET
ejpam-5431	703	30	context	context	NOUN
ejpam-5431	703	31	of	of	ADP
ejpam-5431	703	32	b	b	NOUN
ejpam-5431	703	33	-	-	PUNCT
ejpam-5431	703	34	metric	metric	ADJ
ejpam-5431	703	35	spaces	space	NOUN
ejpam-5431	703	36	,	,	PUNCT
ejpam-5431	703	37	a	a	DET
ejpam-5431	703	38	structure	structure	NOUN
ejpam-5431	703	39	that	that	PRON
ejpam-5431	703	40	has	have	AUX
ejpam-5431	703	41	gained	gain	VERB
ejpam-5431	703	42	considerable	considerable	ADJ
ejpam-5431	703	43	attention	attention	NOUN
ejpam-5431	703	44	due	due	ADP
ejpam-5431	703	45	to	to	ADP
ejpam-5431	703	46	its	its	PRON
ejpam-5431	703	47	flexibility	flexibility	NOUN
ejpam-5431	703	48	in	in	ADP
ejpam-5431	703	49	handling	handle	VERB
ejpam-5431	703	50	generalized	generalized	ADJ
ejpam-5431	703	51	distance	distance	NOUN
ejpam-5431	703	52	measures	measure	NOUN
ejpam-5431	703	53	.	.	PUNCT
ejpam-5431	704	1	the	the	DET
ejpam-5431	704	2	importance	importance	NOUN
ejpam-5431	704	3	of	of	ADP
ejpam-5431	704	4	our	our	PRON
ejpam-5431	704	5	work	work	NOUN
ejpam-5431	704	6	lies	lie	VERB
ejpam-5431	704	7	in	in	ADP
ejpam-5431	704	8	its	its	PRON
ejpam-5431	704	9	ability	ability	NOUN
ejpam-5431	704	10	to	to	PART
ejpam-5431	704	11	unify	unify	VERB
ejpam-5431	704	12	and	and	CCONJ
ejpam-5431	704	13	expand	expand	VERB
ejpam-5431	704	14	upon	upon	SCONJ
ejpam-5431	704	15	prior	prior	ADJ
ejpam-5431	704	16	theorems	theorem	NOUN
ejpam-5431	704	17	,	,	PUNCT
ejpam-5431	704	18	which	which	PRON
ejpam-5431	704	19	were	be	AUX
ejpam-5431	704	20	limited	limit	VERB
ejpam-5431	704	21	in	in	ADP
ejpam-5431	704	22	scope	scope	NOUN
ejpam-5431	704	23	to	to	ADP
ejpam-5431	704	24	more	more	ADV
ejpam-5431	704	25	restrictive	restrictive	ADJ
ejpam-5431	704	26	spaces	space	NOUN
ejpam-5431	704	27	and	and	CCONJ
ejpam-5431	704	28	less	less	ADV
ejpam-5431	704	29	generalized	generalized	ADJ
ejpam-5431	704	30	contractions	contraction	NOUN
ejpam-5431	704	31	.	.	PUNCT
ejpam-5431	705	1	through	through	ADP
ejpam-5431	705	2	the	the	DET
ejpam-5431	705	3	introduction	introduction	NOUN
ejpam-5431	705	4	of	of	ADP
ejpam-5431	705	5	ahif	ahif	PROPN
ejpam-5431	705	6	z	z	PROPN
ejpam-5431	705	7	-	-	PUNCT
ejpam-5431	705	8	contractions	contraction	NOUN
ejpam-5431	705	9	,	,	PUNCT
ejpam-5431	705	10	we	we	PRON
ejpam-5431	705	11	establish	establish	VERB
ejpam-5431	705	12	a	a	DET
ejpam-5431	705	13	broader	broad	ADJ
ejpam-5431	705	14	framework	framework	NOUN
ejpam-5431	705	15	for	for	ADP
ejpam-5431	705	16	studying	study	VERB
ejpam-5431	705	17	common	common	ADJ
ejpam-5431	705	18	fixed	fix	VERB
ejpam-5431	705	19	points	point	NOUN
ejpam-5431	705	20	in	in	ADP
ejpam-5431	705	21	intuitionistic	intuitionistic	ADJ
ejpam-5431	705	22	fuzzy	fuzzy	ADJ
ejpam-5431	705	23	settings	setting	NOUN
ejpam-5431	705	24	.	.	PUNCT
ejpam-5431	706	1	our	our	PRON
ejpam-5431	706	2	results	result	NOUN
ejpam-5431	706	3	are	be	AUX
ejpam-5431	706	4	not	not	PART
ejpam-5431	706	5	only	only	ADV
ejpam-5431	706	6	theoretical	theoretical	ADJ
ejpam-5431	706	7	but	but	CCONJ
ejpam-5431	706	8	also	also	ADV
ejpam-5431	706	9	practical	practical	ADJ
ejpam-5431	706	10	,	,	PUNCT
ejpam-5431	706	11	as	as	SCONJ
ejpam-5431	706	12	demonstrated	demonstrate	VERB
ejpam-5431	706	13	by	by	ADP
ejpam-5431	706	14	the	the	DET
ejpam-5431	706	15	example	example	NOUN
ejpam-5431	706	16	that	that	PRON
ejpam-5431	706	17	showcases	showcase	VERB
ejpam-5431	706	18	the	the	DET
ejpam-5431	706	19	application	application	NOUN
ejpam-5431	706	20	of	of	ADP
ejpam-5431	706	21	these	these	DET
ejpam-5431	706	22	findings	finding	NOUN
ejpam-5431	706	23	in	in	ADP
ejpam-5431	706	24	ordered	order	VERB
ejpam-5431	706	25	b	b	X
ejpam-5431	706	26	-	-	ADJ
ejpam-5431	706	27	metric	metric	ADJ
ejpam-5431	706	28	spaces	space	NOUN
ejpam-5431	706	29	.	.	PUNCT
ejpam-5431	707	1	this	this	DET
ejpam-5431	707	2	example	example	NOUN
ejpam-5431	707	3	illustrates	illustrate	VERB
ejpam-5431	707	4	the	the	DET
ejpam-5431	707	5	relevance	relevance	NOUN
ejpam-5431	707	6	of	of	ADP
ejpam-5431	707	7	our	our	PRON
ejpam-5431	707	8	work	work	NOUN
ejpam-5431	707	9	for	for	ADP
ejpam-5431	707	10	real	real	ADJ
ejpam-5431	707	11	-	-	PUNCT
ejpam-5431	707	12	world	world	NOUN
ejpam-5431	707	13	problems	problem	NOUN
ejpam-5431	707	14	where	where	SCONJ
ejpam-5431	707	15	common	common	ADJ
ejpam-5431	707	16	iffps	iffps	NOUN
ejpam-5431	707	17	play	play	VERB
ejpam-5431	707	18	a	a	DET
ejpam-5431	707	19	crucial	crucial	ADJ
ejpam-5431	707	20	role	role	NOUN
ejpam-5431	707	21	,	,	PUNCT
ejpam-5431	707	22	further	far	ADV
ejpam-5431	707	23	highlighting	highlight	VERB
ejpam-5431	707	24	the	the	DET
ejpam-5431	707	25	utility	utility	NOUN
ejpam-5431	707	26	of	of	ADP
ejpam-5431	707	27	our	our	PRON
ejpam-5431	707	28	contributions	contribution	NOUN
ejpam-5431	707	29	.	.	PUNCT
ejpam-5431	708	1	moreover	moreover	ADV
ejpam-5431	708	2	,	,	PUNCT
ejpam-5431	708	3	our	our	PRON
ejpam-5431	708	4	work	work	NOUN
ejpam-5431	708	5	builds	build	VERB
ejpam-5431	708	6	upon	upon	SCONJ
ejpam-5431	708	7	foundational	foundational	ADJ
ejpam-5431	708	8	fixed	fix	VERB
ejpam-5431	708	9	point	point	NOUN
ejpam-5431	708	10	theorems	theorem	NOUN
ejpam-5431	708	11	and	and	CCONJ
ejpam-5431	708	12	intuitionistic	intuitionistic	ADJ
ejpam-5431	708	13	fuzzy	fuzzy	ADJ
ejpam-5431	708	14	set	set	NOUN
ejpam-5431	708	15	theory	theory	NOUN
ejpam-5431	708	16	by	by	ADP
ejpam-5431	708	17	providing	provide	VERB
ejpam-5431	708	18	new	new	ADJ
ejpam-5431	708	19	pathways	pathway	NOUN
ejpam-5431	708	20	for	for	ADP
ejpam-5431	708	21	exploration	exploration	NOUN
ejpam-5431	708	22	within	within	ADP
ejpam-5431	708	23	the	the	DET
ejpam-5431	708	24	framework	framework	NOUN
ejpam-5431	708	25	of	of	ADP
ejpam-5431	708	26	bmetric	bmetric	ADJ
ejpam-5431	708	27	spaces	space	NOUN
ejpam-5431	708	28	.	.	PUNCT
ejpam-5431	709	1	the	the	DET
ejpam-5431	709	2	construction	construction	NOUN
ejpam-5431	709	3	of	of	ADP
ejpam-5431	709	4	ahif	ahif	PROPN
ejpam-5431	709	5	z	z	PROPN
ejpam-5431	709	6	-	-	PUNCT
ejpam-5431	709	7	contractions	contraction	NOUN
ejpam-5431	709	8	and	and	CCONJ
ejpam-5431	709	9	the	the	DET
ejpam-5431	709	10	corresponding	corresponding	ADJ
ejpam-5431	709	11	fixed	fix	VERB
ejpam-5431	709	12	point	point	NOUN
ejpam-5431	709	13	results	result	NOUN
ejpam-5431	709	14	represent	represent	VERB
ejpam-5431	709	15	a	a	DET
ejpam-5431	709	16	significant	significant	ADJ
ejpam-5431	709	17	extension	extension	NOUN
ejpam-5431	709	18	of	of	ADP
ejpam-5431	709	19	existing	exist	VERB
ejpam-5431	709	20	literature	literature	NOUN
ejpam-5431	709	21	.	.	PUNCT
ejpam-5431	710	1	these	these	DET
ejpam-5431	710	2	contributions	contribution	NOUN
ejpam-5431	710	3	refine	refine	VERB
ejpam-5431	710	4	and	and	CCONJ
ejpam-5431	710	5	broaden	broaden	VERB
ejpam-5431	710	6	the	the	DET
ejpam-5431	710	7	applicability	applicability	NOUN
ejpam-5431	710	8	of	of	ADP
ejpam-5431	710	9	iffp	iffp	PROPN
ejpam-5431	710	10	results	result	NOUN
ejpam-5431	710	11	,	,	PUNCT
ejpam-5431	710	12	offering	offer	VERB
ejpam-5431	710	13	new	new	ADJ
ejpam-5431	710	14	perspectives	perspective	NOUN
ejpam-5431	710	15	for	for	ADP
ejpam-5431	710	16	researchers	researcher	NOUN
ejpam-5431	710	17	interested	interested	ADJ
ejpam-5431	710	18	in	in	ADP
ejpam-5431	710	19	the	the	DET
ejpam-5431	710	20	interplay	interplay	NOUN
ejpam-5431	710	21	between	between	ADP
ejpam-5431	710	22	b	b	NOUN
ejpam-5431	710	23	-	-	PUNCT
ejpam-5431	710	24	metric	metric	ADJ
ejpam-5431	710	25	spaces	space	NOUN
ejpam-5431	710	26	and	and	CCONJ
ejpam-5431	710	27	intuitionistic	intuitionistic	ADJ
ejpam-5431	710	28	fuzzy	fuzzy	ADJ
ejpam-5431	710	29	systems	system	NOUN
ejpam-5431	710	30	.	.	PUNCT
ejpam-5431	711	1	the	the	DET
ejpam-5431	711	2	introduction	introduction	NOUN
ejpam-5431	711	3	of	of	ADP
ejpam-5431	711	4	the	the	DET
ejpam-5431	711	5	ahif	ahif	PROPN
ejpam-5431	711	6	z	z	PROPN
ejpam-5431	711	7	-	-	PUNCT
ejpam-5431	711	8	contraction	contraction	NOUN
ejpam-5431	711	9	,	,	PUNCT
ejpam-5431	711	10	along	along	ADP
ejpam-5431	711	11	with	with	ADP
ejpam-5431	711	12	its	its	PRON
ejpam-5431	711	13	practical	practical	ADJ
ejpam-5431	711	14	implications	implication	NOUN
ejpam-5431	711	15	,	,	PUNCT
ejpam-5431	711	16	signals	signal	VERB
ejpam-5431	711	17	a	a	DET
ejpam-5431	711	18	meaningful	meaningful	ADJ
ejpam-5431	711	19	advancement	advancement	NOUN
ejpam-5431	711	20	in	in	ADP
ejpam-5431	711	21	fixed	fix	VERB
ejpam-5431	711	22	point	point	NOUN
ejpam-5431	711	23	theory	theory	NOUN
ejpam-5431	711	24	,	,	PUNCT
ejpam-5431	711	25	particularly	particularly	ADV
ejpam-5431	711	26	within	within	ADP
ejpam-5431	711	27	the	the	DET
ejpam-5431	711	28	context	context	NOUN
ejpam-5431	711	29	of	of	ADP
ejpam-5431	711	30	intuitionistic	intuitionistic	ADJ
ejpam-5431	711	31	fuzzy	fuzzy	ADJ
ejpam-5431	711	32	systems	system	NOUN
ejpam-5431	711	33	in	in	ADP
ejpam-5431	711	34	b	b	NOUN
ejpam-5431	711	35	-	-	ADJ
ejpam-5431	711	36	metric	metric	ADJ
ejpam-5431	711	37	spaces	space	NOUN
ejpam-5431	711	38	.	.	PUNCT
ejpam-5431	712	1	by	by	ADP
ejpam-5431	712	2	demonstrating	demonstrate	VERB
ejpam-5431	712	3	the	the	DET
ejpam-5431	712	4	existence	existence	NOUN
ejpam-5431	712	5	of	of	ADP
ejpam-5431	712	6	common	common	ADJ
ejpam-5431	712	7	fixed	fix	VERB
ejpam-5431	712	8	points	point	NOUN
ejpam-5431	712	9	in	in	ADP
ejpam-5431	712	10	an	an	DET
ejpam-5431	712	11	ordered	ordered	ADJ
ejpam-5431	712	12	b	b	NOUN
ejpam-5431	712	13	-	-	PUNCT
ejpam-5431	712	14	metric	metric	ADJ
ejpam-5431	712	15	space	space	NOUN
ejpam-5431	712	16	,	,	PUNCT
ejpam-5431	712	17	we	we	PRON
ejpam-5431	712	18	not	not	PART
ejpam-5431	712	19	only	only	ADV
ejpam-5431	712	20	validate	validate	VERB
ejpam-5431	712	21	our	our	PRON
ejpam-5431	712	22	theoretical	theoretical	ADJ
ejpam-5431	712	23	results	result	NOUN
ejpam-5431	712	24	but	but	CCONJ
ejpam-5431	712	25	also	also	ADV
ejpam-5431	712	26	provide	provide	VERB
ejpam-5431	712	27	a	a	DET
ejpam-5431	712	28	robust	robust	ADJ
ejpam-5431	712	29	example	example	NOUN
ejpam-5431	712	30	that	that	PRON
ejpam-5431	712	31	may	may	AUX
ejpam-5431	712	32	inspire	inspire	VERB
ejpam-5431	712	33	further	further	ADJ
ejpam-5431	712	34	applications	application	NOUN
ejpam-5431	712	35	across	across	ADP
ejpam-5431	712	36	various	various	ADJ
ejpam-5431	712	37	domains	domain	NOUN
ejpam-5431	712	38	.	.	PUNCT
ejpam-5431	713	1	this	this	DET
ejpam-5431	713	2	research	research	NOUN
ejpam-5431	713	3	contributes	contribute	VERB
ejpam-5431	713	4	to	to	ADP
ejpam-5431	713	5	the	the	DET
ejpam-5431	713	6	growing	grow	VERB
ejpam-5431	713	7	body	body	NOUN
ejpam-5431	713	8	of	of	ADP
ejpam-5431	713	9	work	work	NOUN
ejpam-5431	713	10	on	on	ADP
ejpam-5431	713	11	generalized	generalized	ADJ
ejpam-5431	713	12	metric	metric	ADJ
ejpam-5431	713	13	spaces	space	NOUN
ejpam-5431	713	14	and	and	CCONJ
ejpam-5431	713	15	intuitionistic	intuitionistic	ADJ
ejpam-5431	713	16	fuzzy	fuzzy	ADJ
ejpam-5431	713	17	systems	system	NOUN
ejpam-5431	713	18	,	,	PUNCT
ejpam-5431	713	19	and	and	CCONJ
ejpam-5431	713	20	we	we	PRON
ejpam-5431	713	21	anticipate	anticipate	VERB
ejpam-5431	713	22	that	that	SCONJ
ejpam-5431	713	23	it	it	PRON
ejpam-5431	713	24	will	will	AUX
ejpam-5431	713	25	foster	foster	VERB
ejpam-5431	713	26	additional	additional	ADJ
ejpam-5431	713	27	exploration	exploration	NOUN
ejpam-5431	713	28	and	and	CCONJ
ejpam-5431	713	29	innovation	innovation	NOUN
ejpam-5431	713	30	in	in	ADP
ejpam-5431	713	31	these	these	DET
ejpam-5431	713	32	areas	area	NOUN
ejpam-5431	713	33	,	,	PUNCT
ejpam-5431	713	34	leading	lead	VERB
ejpam-5431	713	35	to	to	ADP
ejpam-5431	713	36	new	new	ADJ
ejpam-5431	713	37	developments	development	NOUN
ejpam-5431	713	38	in	in	ADP
ejpam-5431	713	39	both	both	DET
ejpam-5431	713	40	theory	theory	NOUN
ejpam-5431	713	41	and	and	CCONJ
ejpam-5431	713	42	application	application	NOUN
ejpam-5431	713	43	.	.	PUNCT
ejpam-5431	714	1	open	open	ADJ
ejpam-5431	714	2	problem	problem	NOUN
ejpam-5431	714	3	:	:	PUNCT
ejpam-5431	714	4	discuss	discuss	VERB
ejpam-5431	714	5	the	the	DET
ejpam-5431	714	6	limitations	limitation	NOUN
ejpam-5431	714	7	and	and	CCONJ
ejpam-5431	714	8	potential	potential	ADJ
ejpam-5431	714	9	challenges	challenge	NOUN
ejpam-5431	714	10	that	that	PRON
ejpam-5431	714	11	may	may	AUX
ejpam-5431	714	12	arise	arise	VERB
ejpam-5431	714	13	when	when	SCONJ
ejpam-5431	714	14	extending	extend	VERB
ejpam-5431	714	15	the	the	DET
ejpam-5431	714	16	proven	prove	VERB
ejpam-5431	714	17	results	result	NOUN
ejpam-5431	714	18	to	to	ADP
ejpam-5431	714	19	suzuki	suzuki	NOUN
ejpam-5431	714	20	-	-	PUNCT
ejpam-5431	714	21	type	type	NOUN
ejpam-5431	714	22	fuzzy	fuzzy	ADJ
ejpam-5431	714	23	weak	weak	ADJ
ejpam-5431	714	24	ϕ-contraction	ϕ-contraction	NOUN
ejpam-5431	714	25	,	,	PUNCT
ejpam-5431	714	26	and	and	CCONJ
ejpam-5431	714	27	propose	propose	VERB
ejpam-5431	714	28	future	future	ADJ
ejpam-5431	714	29	research	research	NOUN
ejpam-5431	714	30	directions	direction	NOUN
ejpam-5431	714	31	to	to	PART
ejpam-5431	714	32	address	address	VERB
ejpam-5431	714	33	these	these	DET
ejpam-5431	714	34	issues	issue	NOUN
ejpam-5431	714	35	.	.	PUNCT
ejpam-5431	715	1	author	author	NOUN
ejpam-5431	715	2	contributions	contribution	NOUN
ejpam-5431	715	3	:	:	PUNCT
ejpam-5431	715	4	conceptualization	conceptualization	NOUN
ejpam-5431	715	5	,	,	PUNCT
ejpam-5431	715	6	m.r	m.r	PROPN
ejpam-5431	715	7	.	.	PROPN
ejpam-5431	715	8	,	,	PUNCT
ejpam-5431	715	9	n.s	n.s	PROPN
ejpam-5431	715	10	.	.	PROPN
ejpam-5431	715	11	and	and	CCONJ
ejpam-5431	715	12	q.m	q.m	PROPN
ejpam-5431	715	13	.	.	PROPN
ejpam-5431	715	14	;	;	PUNCT
ejpam-5431	715	15	formal	formal	ADJ
ejpam-5431	715	16	analysis	analysis	NOUN
ejpam-5431	715	17	,	,	PUNCT
ejpam-5431	715	18	n.s	n.s	PROPN
ejpam-5431	715	19	.	.	PROPN
ejpam-5431	715	20	,	,	PUNCT
ejpam-5431	715	21	m.a	m.a	PROPN
ejpam-5431	715	22	.	.	PROPN
ejpam-5431	715	23	and	and	CCONJ
ejpam-5431	715	24	m.r	m.r	PROPN
ejpam-5431	715	25	.	.	PROPN
ejpam-5431	715	26	;	;	PUNCT
ejpam-5431	715	27	investigation	investigation	NOUN
ejpam-5431	715	28	,	,	PUNCT
ejpam-5431	715	29	n.s	n.s	PROPN
ejpam-5431	715	30	.	.	PROPN
ejpam-5431	715	31	,	,	PUNCT
ejpam-5431	715	32	q.m	q.m	PROPN
ejpam-5431	715	33	.	.	PROPN
ejpam-5431	715	34	and	and	CCONJ
ejpam-5431	715	35	m.a	m.a	PROPN
ejpam-5431	715	36	.	.	PROPN
ejpam-5431	715	37	;	;	PUNCT
ejpam-5431	715	38	writing	write	VERB
ejpam-5431	715	39	original	original	ADJ
ejpam-5431	715	40	draft	draft	NOUN
ejpam-5431	715	41	preparation	preparation	NOUN
ejpam-5431	715	42	,	,	PUNCT
ejpam-5431	715	43	q.m	q.m	PROPN
ejpam-5431	715	44	.	.	PROPN
ejpam-5431	715	45	,	,	PUNCT
ejpam-5431	715	46	m.a	m.a	PROPN
ejpam-5431	715	47	.	.	PROPN
ejpam-5431	715	48	and	and	CCONJ
ejpam-5431	715	49	i.r	i.r	PROPN
ejpam-5431	715	50	.	.	PROPN
ejpam-5431	715	51	;	;	PUNCT
ejpam-5431	715	52	writing	writing	NOUN
ejpam-5431	715	53	,	,	PUNCT
ejpam-5431	715	54	review	review	NOUN
ejpam-5431	715	55	and	and	CCONJ
ejpam-5431	715	56	editing	editing	NOUN
ejpam-5431	715	57	,	,	PUNCT
ejpam-5431	715	58	n.s	n.s	PROPN
ejpam-5431	715	59	.	.	PROPN
ejpam-5431	715	60	,	,	PUNCT
ejpam-5431	715	61	i.r	i.r	PROPN
ejpam-5431	715	62	.	.	PROPN
ejpam-5431	715	63	and	and	CCONJ
ejpam-5431	715	64	q.m	q.m	PROPN
ejpam-5431	715	65	.	.	PROPN
ejpam-5431	716	1	all	all	DET
ejpam-5431	716	2	authors	author	NOUN
ejpam-5431	716	3	have	have	AUX
ejpam-5431	716	4	read	read	VERB
ejpam-5431	716	5	and	and	CCONJ
ejpam-5431	716	6	agreed	agree	VERB
ejpam-5431	716	7	to	to	ADP
ejpam-5431	716	8	the	the	DET
ejpam-5431	716	9	published	publish	VERB
ejpam-5431	716	10	version	version	NOUN
ejpam-5431	716	11	of	of	ADP
ejpam-5431	716	12	the	the	DET
ejpam-5431	716	13	manuscript	manuscript	NOUN
ejpam-5431	716	14	.	.	PUNCT
ejpam-5431	717	1	references	reference	NOUN
ejpam-5431	717	2	3334	3334	NUM
ejpam-5431	717	3	funding	funding	NOUN
ejpam-5431	717	4	:	:	PUNCT
ejpam-5431	717	5	this	this	DET
ejpam-5431	717	6	research	research	NOUN
ejpam-5431	717	7	received	receive	VERB
ejpam-5431	717	8	no	no	DET
ejpam-5431	717	9	external	external	ADJ
ejpam-5431	717	10	funding	funding	NOUN
ejpam-5431	717	11	.	.	PUNCT
ejpam-5431	718	1	data	datum	NOUN
ejpam-5431	718	2	availability	availability	NOUN
ejpam-5431	718	3	statement	statement	NOUN
ejpam-5431	718	4	:	:	PUNCT
ejpam-5431	718	5	the	the	DET
ejpam-5431	718	6	data	datum	NOUN
ejpam-5431	718	7	used	use	VERB
ejpam-5431	718	8	to	to	PART
ejpam-5431	718	9	support	support	VERB
ejpam-5431	718	10	the	the	DET
ejpam-5431	718	11	findings	finding	NOUN
ejpam-5431	718	12	of	of	ADP
ejpam-5431	718	13	this	this	DET
ejpam-5431	718	14	study	study	NOUN
ejpam-5431	718	15	are	be	AUX
ejpam-5431	718	16	available	available	ADJ
ejpam-5431	718	17	from	from	ADP
ejpam-5431	718	18	the	the	DET
ejpam-5431	718	19	corresponding	corresponding	ADJ
ejpam-5431	718	20	author	author	NOUN
ejpam-5431	718	21	upon	upon	SCONJ
ejpam-5431	718	22	request	request	NOUN
ejpam-5431	718	23	.	.	PUNCT
ejpam-5431	719	1	conflict	conflict	NOUN
ejpam-5431	719	2	of	of	ADP
ejpam-5431	719	3	interest	interest	NOUN
ejpam-5431	719	4	:	:	PUNCT
ejpam-5431	719	5	the	the	DET
ejpam-5431	719	6	authors	author	NOUN
ejpam-5431	719	7	declare	declare	VERB
ejpam-5431	719	8	no	no	DET
ejpam-5431	719	9	conflict	conflict	NOUN
ejpam-5431	719	10	of	of	ADP
ejpam-5431	719	11	interest	interest	NOUN
ejpam-5431	719	12	.	.	PUNCT
ejpam-5431	720	1	references	reference	NOUN
ejpam-5431	720	2	[	[	X
ejpam-5431	720	3	1	1	X
ejpam-5431	720	4	]	]	PUNCT
ejpam-5431	721	1	s.	s.	PROPN
ejpam-5431	721	2	aleksic	aleksic	PROPN
ejpam-5431	721	3	et	et	PROPN
ejpam-5431	721	4	al	al	PROPN
ejpam-5431	721	5	.	.	PUNCT
ejpam-5431	721	6	picard	picard	PROPN
ejpam-5431	721	7	’s	’s	PART
ejpam-5431	721	8	sequences	sequence	NOUN
ejpam-5431	721	9	in	in	ADP
ejpam-5431	721	10	b	b	NOUN
ejpam-5431	721	11	-	-	PUNCT
ejpam-5431	721	12	metric	metric	ADJ
ejpam-5431	721	13	spaces	space	NOUN
ejpam-5431	721	14	.	.	PUNCT
ejpam-5431	722	1	fixed	fix	VERB
ejpam-5431	722	2	point	point	NOUN
ejpam-5431	722	3	theory	theory	NOUN
ejpam-5431	722	4	,	,	PUNCT
ejpam-5431	722	5	21(1):35	21(1):35	PROPN
ejpam-5431	722	6	–	–	PUNCT
ejpam-5431	722	7	46	46	NUM
ejpam-5431	722	8	,	,	PUNCT
ejpam-5431	722	9	2020	2020	NUM
ejpam-5431	722	10	.	.	PUNCT
ejpam-5431	723	1	[	[	X
ejpam-5431	723	2	2	2	X
ejpam-5431	723	3	]	]	PUNCT
ejpam-5431	723	4	h.	h.	PROPN
ejpam-5431	723	5	h.	h.	PROPN
ejpam-5431	723	6	alsulami	alsulami	PROPN
ejpam-5431	723	7	,	,	PUNCT
ejpam-5431	723	8	e.	e.	PROPN
ejpam-5431	723	9	karapinar	karapinar	PROPN
ejpam-5431	723	10	,	,	PUNCT
ejpam-5431	723	11	f.	f.	PROPN
ejpam-5431	723	12	khojasteh	khojasteh	PROPN
ejpam-5431	723	13	,	,	PUNCT
ejpam-5431	723	14	and	and	CCONJ
ejpam-5431	723	15	a.	a.	PROPN
ejpam-5431	723	16	f.	f.	PROPN
ejpam-5431	723	17	roldán	roldán	PROPN
ejpam-5431	723	18	-	-	PUNCT
ejpam-5431	723	19	lópez	lópez	PROPN
ejpam-5431	723	20	de	de	PROPN
ejpam-5431	723	21	hierro	hierro	PROPN
ejpam-5431	723	22	.	.	PUNCT
ejpam-5431	724	1	a	a	DET
ejpam-5431	724	2	proposal	proposal	NOUN
ejpam-5431	724	3	to	to	ADP
ejpam-5431	724	4	the	the	DET
ejpam-5431	724	5	study	study	NOUN
ejpam-5431	724	6	of	of	ADP
ejpam-5431	724	7	contractions	contraction	NOUN
ejpam-5431	724	8	in	in	ADP
ejpam-5431	724	9	quasi	quasi	ADJ
ejpam-5431	724	10	-	-	ADJ
ejpam-5431	724	11	metric	metric	ADJ
ejpam-5431	724	12	spaces	space	NOUN
ejpam-5431	724	13	.	.	PUNCT
ejpam-5431	725	1	discrete	discrete	ADJ
ejpam-5431	725	2	dynamics	dynamic	NOUN
ejpam-5431	725	3	in	in	ADP
ejpam-5431	725	4	nature	nature	NOUN
ejpam-5431	725	5	and	and	CCONJ
ejpam-5431	725	6	society	society	NOUN
ejpam-5431	725	7	,	,	PUNCT
ejpam-5431	725	8	2014	2014	NUM
ejpam-5431	725	9	.	.	PUNCT
ejpam-5431	726	1	[	[	X
ejpam-5431	726	2	3	3	X
ejpam-5431	726	3	]	]	X
ejpam-5431	726	4	m.	m.	NOUN
ejpam-5431	726	5	arshad	arshad	PROPN
ejpam-5431	726	6	,	,	PUNCT
ejpam-5431	726	7	a.	a.	PROPN
ejpam-5431	726	8	shoaib	shoaib	PROPN
ejpam-5431	726	9	,	,	PUNCT
ejpam-5431	726	10	m.	m.	NOUN
ejpam-5431	726	11	abbas	abbas	PROPN
ejpam-5431	726	12	,	,	PUNCT
ejpam-5431	726	13	and	and	CCONJ
ejpam-5431	726	14	a.	a.	PROPN
ejpam-5431	726	15	azam	azam	PROPN
ejpam-5431	726	16	.	.	PUNCT
ejpam-5431	727	1	fixed	fix	VERB
ejpam-5431	727	2	points	point	NOUN
ejpam-5431	727	3	of	of	ADP
ejpam-5431	727	4	a	a	DET
ejpam-5431	727	5	pair	pair	NOUN
ejpam-5431	727	6	of	of	ADP
ejpam-5431	727	7	kannan	kannan	PROPN
ejpam-5431	727	8	type	type	NOUN
ejpam-5431	727	9	mappings	mapping	NOUN
ejpam-5431	727	10	on	on	ADP
ejpam-5431	727	11	a	a	DET
ejpam-5431	727	12	closed	closed	ADJ
ejpam-5431	727	13	ball	ball	NOUN
ejpam-5431	727	14	in	in	ADP
ejpam-5431	727	15	ordered	order	VERB
ejpam-5431	727	16	partial	partial	ADJ
ejpam-5431	727	17	metric	metric	ADJ
ejpam-5431	727	18	spaces	space	NOUN
ejpam-5431	727	19	.	.	PUNCT
ejpam-5431	728	1	miskolc	miskolc	ADJ
ejpam-5431	728	2	mathematical	mathematical	ADJ
ejpam-5431	728	3	notes	note	NOUN
ejpam-5431	728	4	,	,	PUNCT
ejpam-5431	728	5	14(3):769–784	14(3):769–784	PROPN
ejpam-5431	728	6	,	,	PUNCT
ejpam-5431	728	7	2013	2013	NUM
ejpam-5431	728	8	.	.	PUNCT
ejpam-5431	729	1	[	[	X
ejpam-5431	729	2	4	4	X
ejpam-5431	729	3	]	]	PUNCT
ejpam-5431	729	4	k.	k.	PROPN
ejpam-5431	729	5	atanassov	atanassov	PROPN
ejpam-5431	729	6	.	.	PUNCT
ejpam-5431	730	1	intuitionistic	intuitionistic	ADJ
ejpam-5431	730	2	fuzzy	fuzzy	ADJ
ejpam-5431	730	3	sets	set	NOUN
ejpam-5431	730	4	.	.	PUNCT
ejpam-5431	731	1	fuzzy	fuzzy	ADJ
ejpam-5431	731	2	sets	set	NOUN
ejpam-5431	731	3	and	and	CCONJ
ejpam-5431	731	4	systems	system	NOUN
ejpam-5431	731	5	,	,	PUNCT
ejpam-5431	731	6	20:87–96	20:87–96	NUM
ejpam-5431	731	7	,	,	PUNCT
ejpam-5431	731	8	1986	1986	NUM
ejpam-5431	731	9	.	.	PUNCT
ejpam-5431	732	1	[	[	X
ejpam-5431	732	2	5	5	NUM
ejpam-5431	732	3	]	]	PUNCT
ejpam-5431	732	4	i.	i.	PROPN
ejpam-5431	732	5	a.	a.	PROPN
ejpam-5431	732	6	bakhtin	bakhtin	PROPN
ejpam-5431	732	7	.	.	PUNCT
ejpam-5431	733	1	the	the	DET
ejpam-5431	733	2	contraction	contraction	NOUN
ejpam-5431	733	3	principle	principle	NOUN
ejpam-5431	733	4	in	in	ADP
ejpam-5431	733	5	quasi	quasi	ADJ
ejpam-5431	733	6	metric	metric	ADJ
ejpam-5431	733	7	spaces	space	NOUN
ejpam-5431	733	8	.	.	PUNCT
ejpam-5431	734	1	funct	funct	ADJ
ejpam-5431	734	2	.	.	PUNCT
ejpam-5431	735	1	anal	anal	PROPN
ejpam-5431	735	2	.	.	PUNCT
ejpam-5431	736	1	unianowsk	unianowsk	PROPN
ejpam-5431	736	2	gos	gos	PROPN
ejpam-5431	736	3	.	.	PUNCT
ejpam-5431	736	4	ped	ped	PROPN
ejpam-5431	736	5	.	.	PROPN
ejpam-5431	736	6	inst	inst	PROPN
ejpam-5431	736	7	,	,	PUNCT
ejpam-5431	736	8	30:26–37	30:26–37	PROPN
ejpam-5431	736	9	,	,	PUNCT
ejpam-5431	736	10	1989	1989	NUM
ejpam-5431	736	11	.	.	PUNCT
ejpam-5431	737	1	[	[	X
ejpam-5431	737	2	6	6	NUM
ejpam-5431	737	3	]	]	PUNCT
ejpam-5431	737	4	m.	m.	NOUN
ejpam-5431	737	5	boriceanu	boriceanu	PROPN
ejpam-5431	737	6	.	.	PUNCT
ejpam-5431	738	1	fixed	fix	VERB
ejpam-5431	738	2	point	point	NOUN
ejpam-5431	738	3	theory	theory	NOUN
ejpam-5431	738	4	for	for	ADP
ejpam-5431	738	5	multivalued	multivalued	ADJ
ejpam-5431	738	6	generalized	generalized	ADJ
ejpam-5431	738	7	contraction	contraction	NOUN
ejpam-5431	738	8	on	on	ADP
ejpam-5431	738	9	a	a	DET
ejpam-5431	738	10	set	set	NOUN
ejpam-5431	738	11	with	with	ADP
ejpam-5431	738	12	two	two	NUM
ejpam-5431	738	13	b	b	NOUN
ejpam-5431	738	14	-	-	PUNCT
ejpam-5431	738	15	metrics	metric	NOUN
ejpam-5431	738	16	.	.	PUNCT
ejpam-5431	739	1	studia	studia	PROPN
ejpam-5431	739	2	universitatis	universitatis	PROPN
ejpam-5431	739	3	babes	babes	PROPN
ejpam-5431	739	4	-	-	PUNCT
ejpam-5431	739	5	bolyai	bolyai	NOUN
ejpam-5431	739	6	,	,	PUNCT
ejpam-5431	739	7	mathematica	mathematica	PROPN
ejpam-5431	739	8	,	,	PUNCT
ejpam-5431	739	9	2009	2009	NUM
ejpam-5431	739	10	.	.	PUNCT
ejpam-5431	740	1	[	[	X
ejpam-5431	740	2	7	7	X
ejpam-5431	740	3	]	]	X
ejpam-5431	740	4	n.	n.	NOUN
ejpam-5431	740	5	bourbaki	bourbaki	PROPN
ejpam-5431	740	6	.	.	PUNCT
ejpam-5431	741	1	topologie	topologie	NOUN
ejpam-5431	741	2	generale	generale	PROPN
ejpam-5431	741	3	.	.	PUNCT
ejpam-5431	742	1	herman	herman	PROPN
ejpam-5431	742	2	,	,	PUNCT
ejpam-5431	742	3	paris	paris	PROPN
ejpam-5431	742	4	,	,	PUNCT
ejpam-5431	742	5	france	france	PROPN
ejpam-5431	742	6	,	,	PUNCT
ejpam-5431	742	7	1974	1974	NUM
ejpam-5431	742	8	.	.	PUNCT
ejpam-5431	743	1	[	[	X
ejpam-5431	743	2	8	8	NUM
ejpam-5431	743	3	]	]	X
ejpam-5431	743	4	s.	s.	PROPN
ejpam-5431	743	5	czerwik	czerwik	PROPN
ejpam-5431	743	6	.	.	PUNCT
ejpam-5431	744	1	contraction	contraction	NOUN
ejpam-5431	744	2	mappings	mapping	NOUN
ejpam-5431	744	3	in	in	ADP
ejpam-5431	744	4	b	b	NOUN
ejpam-5431	744	5	-	-	ADJ
ejpam-5431	744	6	metric	metric	ADJ
ejpam-5431	744	7	spaces	space	NOUN
ejpam-5431	744	8	.	.	PUNCT
ejpam-5431	745	1	acta	acta	PROPN
ejpam-5431	745	2	mathematica	mathematica	PROPN
ejpam-5431	745	3	et	et	PROPN
ejpam-5431	745	4	informatica	informatica	PROPN
ejpam-5431	745	5	universitatis	universitatis	PROPN
ejpam-5431	745	6	ostraviensis	ostraviensis	PROPN
ejpam-5431	745	7	,	,	PUNCT
ejpam-5431	745	8	1(1):5–11	1(1):5–11	NUM
ejpam-5431	745	9	,	,	PUNCT
ejpam-5431	745	10	1993	1993	NUM
ejpam-5431	745	11	.	.	PUNCT
ejpam-5431	746	1	[	[	X
ejpam-5431	746	2	9	9	NUM
ejpam-5431	746	3	]	]	X
ejpam-5431	746	4	s.	s.	PROPN
ejpam-5431	746	5	czerwik	czerwik	PROPN
ejpam-5431	746	6	.	.	PUNCT
ejpam-5431	747	1	nonlinear	nonlinear	ADJ
ejpam-5431	747	2	set	set	NOUN
ejpam-5431	747	3	-	-	PUNCT
ejpam-5431	747	4	valued	value	VERB
ejpam-5431	747	5	contraction	contraction	NOUN
ejpam-5431	747	6	mappings	mapping	NOUN
ejpam-5431	747	7	in	in	ADP
ejpam-5431	747	8	b	b	NOUN
ejpam-5431	747	9	-	-	ADJ
ejpam-5431	747	10	metric	metric	ADJ
ejpam-5431	747	11	spaces	space	NOUN
ejpam-5431	747	12	.	.	PUNCT
ejpam-5431	748	1	atti	atti	PROPN
ejpam-5431	748	2	sem	sem	PROPN
ejpam-5431	748	3	.	.	PROPN
ejpam-5431	749	1	mat	mat	PROPN
ejpam-5431	749	2	.	.	PROPN
ejpam-5431	749	3	fis	fis	PROPN
ejpam-5431	749	4	.	.	PUNCT
ejpam-5431	750	1	univ	univ	PROPN
ejpam-5431	750	2	.	.	PUNCT
ejpam-5431	751	1	modena	modena	PROPN
ejpam-5431	751	2	,	,	PUNCT
ejpam-5431	751	3	46:263–276	46:263–276	PROPN
ejpam-5431	751	4	,	,	PUNCT
ejpam-5431	751	5	1998	1998	NUM
ejpam-5431	751	6	.	.	PUNCT
ejpam-5431	752	1	[	[	X
ejpam-5431	752	2	10	10	NUM
ejpam-5431	752	3	]	]	X
ejpam-5431	752	4	s.	s.	PROPN
ejpam-5431	752	5	czerwik	czerwik	PROPN
ejpam-5431	752	6	,	,	PUNCT
ejpam-5431	752	7	k.	k.	PROPN
ejpam-5431	752	8	dlutek	dlutek	PROPN
ejpam-5431	752	9	,	,	PUNCT
ejpam-5431	752	10	and	and	CCONJ
ejpam-5431	752	11	s.	s.	PROPN
ejpam-5431	752	12	singh	singh	PROPN
ejpam-5431	752	13	.	.	PUNCT
ejpam-5431	753	1	round	round	PROPN
ejpam-5431	753	2	-	-	PUNCT
ejpam-5431	753	3	off	off	ADP
ejpam-5431	753	4	stability	stability	NOUN
ejpam-5431	753	5	of	of	ADP
ejpam-5431	753	6	iteration	iteration	NOUN
ejpam-5431	753	7	procedures	procedure	NOUN
ejpam-5431	753	8	for	for	ADP
ejpam-5431	753	9	operators	operator	NOUN
ejpam-5431	753	10	in	in	ADP
ejpam-5431	753	11	b	b	NOUN
ejpam-5431	753	12	-	-	PUNCT
ejpam-5431	753	13	metric	metric	ADJ
ejpam-5431	753	14	spaces	space	NOUN
ejpam-5431	753	15	.	.	PUNCT
ejpam-5431	754	1	j.	j.	PROPN
ejpam-5431	754	2	nat	nat	PROPN
ejpam-5431	754	3	.	.	PUNCT
ejpam-5431	755	1	phys	phy	NOUN
ejpam-5431	755	2	.	.	PUNCT
ejpam-5431	756	1	sci	sci	PROPN
ejpam-5431	756	2	.	.	PROPN
ejpam-5431	756	3	,	,	PUNCT
ejpam-5431	756	4	11	11	NUM
ejpam-5431	756	5	,	,	PUNCT
ejpam-5431	756	6	1997	1997	NUM
ejpam-5431	756	7	.	.	PUNCT
ejpam-5431	757	1	[	[	X
ejpam-5431	757	2	11	11	NUM
ejpam-5431	757	3	]	]	PUNCT
ejpam-5431	757	4	a.	a.	NOUN
ejpam-5431	757	5	f.	f.	PROPN
ejpam-5431	757	6	roldán	roldán	PROPN
ejpam-5431	757	7	-	-	PUNCT
ejpam-5431	757	8	lópez	lópez	PROPN
ejpam-5431	757	9	de	de	PROPN
ejpam-5431	757	10	hierro	hierro	PROPN
ejpam-5431	757	11	,	,	PUNCT
ejpam-5431	757	12	e.	e.	PROPN
ejpam-5431	757	13	karapinar	karapinar	PROPN
ejpam-5431	757	14	,	,	PUNCT
ejpam-5431	757	15	c.	c.	PROPN
ejpam-5431	757	16	roldán	roldán	PROPN
ejpam-5431	757	17	-	-	PUNCT
ejpam-5431	757	18	lópez	lópez	PROPN
ejpam-5431	757	19	de	de	X
ejpam-5431	757	20	hierro	hierro	PROPN
ejpam-5431	757	21	,	,	PUNCT
ejpam-5431	757	22	and	and	CCONJ
ejpam-5431	757	23	j.	j.	PROPN
ejpam-5431	757	24	mart́ınez	mart́ınez	PROPN
ejpam-5431	757	25	-	-	PUNCT
ejpam-5431	757	26	moreno	moreno	PROPN
ejpam-5431	757	27	.	.	PUNCT
ejpam-5431	758	1	coincidence	coincidence	NOUN
ejpam-5431	758	2	point	point	NOUN
ejpam-5431	758	3	theorems	theorem	NOUN
ejpam-5431	758	4	on	on	ADP
ejpam-5431	758	5	metric	metric	ADJ
ejpam-5431	758	6	spaces	space	NOUN
ejpam-5431	758	7	via	via	ADP
ejpam-5431	758	8	simulation	simulation	NOUN
ejpam-5431	758	9	functions	function	NOUN
ejpam-5431	758	10	.	.	PUNCT
ejpam-5431	759	1	journal	journal	NOUN
ejpam-5431	759	2	of	of	ADP
ejpam-5431	759	3	computational	computational	ADJ
ejpam-5431	759	4	and	and	CCONJ
ejpam-5431	759	5	applied	applied	ADJ
ejpam-5431	759	6	mathematics	mathematic	NOUN
ejpam-5431	759	7	,	,	PUNCT
ejpam-5431	759	8	275:345–355	275:345–355	NUM
ejpam-5431	759	9	,	,	PUNCT
ejpam-5431	759	10	2015	2015	NUM
ejpam-5431	759	11	.	.	PUNCT
ejpam-5431	760	1	[	[	X
ejpam-5431	760	2	12	12	NUM
ejpam-5431	760	3	]	]	X
ejpam-5431	760	4	r.	r.	PROPN
ejpam-5431	760	5	george	george	PROPN
ejpam-5431	760	6	and	and	CCONJ
ejpam-5431	760	7	b.	b.	PROPN
ejpam-5431	760	8	fisher	fisher	PROPN
ejpam-5431	760	9	.	.	PUNCT
ejpam-5431	761	1	some	some	DET
ejpam-5431	761	2	generalized	generalized	ADJ
ejpam-5431	761	3	results	result	NOUN
ejpam-5431	761	4	of	of	ADP
ejpam-5431	761	5	fixed	fix	VERB
ejpam-5431	761	6	points	point	NOUN
ejpam-5431	761	7	in	in	ADP
ejpam-5431	761	8	cone	cone	PROPN
ejpam-5431	761	9	b	b	X
ejpam-5431	761	10	-	-	PUNCT
ejpam-5431	761	11	metric	metric	ADJ
ejpam-5431	761	12	spaces	space	NOUN
ejpam-5431	761	13	.	.	PUNCT
ejpam-5431	762	1	mathematica	mathematica	PROPN
ejpam-5431	762	2	moravica	moravica	PROPN
ejpam-5431	762	3	,	,	PUNCT
ejpam-5431	762	4	17(2):39–50	17(2):39–50	NUM
ejpam-5431	762	5	,	,	PUNCT
ejpam-5431	762	6	2013	2013	NUM
ejpam-5431	762	7	.	.	PUNCT
ejpam-5431	763	1	[	[	X
ejpam-5431	763	2	13	13	NUM
ejpam-5431	763	3	]	]	PUNCT
ejpam-5431	763	4	m.	m.	NOUN
ejpam-5431	763	5	gulzar	gulzar	PROPN
ejpam-5431	763	6	,	,	PUNCT
ejpam-5431	763	7	d.	d.	PROPN
ejpam-5431	763	8	alghazzawi	alghazzawi	PROPN
ejpam-5431	763	9	,	,	PUNCT
ejpam-5431	763	10	m.	m.	PROPN
ejpam-5431	763	11	h.	h.	PROPN
ejpam-5431	763	12	mateen	mateen	PROPN
ejpam-5431	763	13	,	,	PUNCT
ejpam-5431	763	14	and	and	CCONJ
ejpam-5431	763	15	n.	n.	PROPN
ejpam-5431	763	16	kausar	kausar	PROPN
ejpam-5431	763	17	.	.	PUNCT
ejpam-5431	764	1	a	a	DET
ejpam-5431	764	2	certain	certain	ADJ
ejpam-5431	764	3	class	class	NOUN
ejpam-5431	764	4	of	of	ADP
ejpam-5431	764	5	tintuitionistic	tintuitionistic	ADJ
ejpam-5431	764	6	fuzzy	fuzzy	ADJ
ejpam-5431	764	7	subgroups	subgroup	NOUN
ejpam-5431	764	8	.	.	PUNCT
ejpam-5431	765	1	ieee	ieee	NOUN
ejpam-5431	765	2	access	access	NOUN
ejpam-5431	765	3	,	,	PUNCT
ejpam-5431	765	4	8:163260–163268	8:163260–163268	NUM
ejpam-5431	765	5	,	,	PUNCT
ejpam-5431	765	6	2020	2020	NUM
ejpam-5431	765	7	.	.	PUNCT
ejpam-5431	766	1	references	reference	NOUN
ejpam-5431	766	2	3335	3335	NUM
ejpam-5431	766	3	[	[	X
ejpam-5431	766	4	14	14	NUM
ejpam-5431	766	5	]	]	PUNCT
ejpam-5431	766	6	m.	m.	NOUN
ejpam-5431	766	7	gulzar	gulzar	PROPN
ejpam-5431	766	8	,	,	PUNCT
ejpam-5431	766	9	m.	m.	PROPN
ejpam-5431	766	10	h.	h.	PROPN
ejpam-5431	766	11	mateen	mateen	PROPN
ejpam-5431	766	12	,	,	PUNCT
ejpam-5431	766	13	d.	d.	PROPN
ejpam-5431	766	14	alghazzawi	alghazzawi	PROPN
ejpam-5431	766	15	,	,	PUNCT
ejpam-5431	766	16	and	and	CCONJ
ejpam-5431	766	17	n.	n.	PROPN
ejpam-5431	766	18	kausar	kausar	PROPN
ejpam-5431	766	19	.	.	PUNCT
ejpam-5431	767	1	a	a	DET
ejpam-5431	767	2	novel	novel	ADJ
ejpam-5431	767	3	applications	application	NOUN
ejpam-5431	767	4	of	of	ADP
ejpam-5431	767	5	complex	complex	ADJ
ejpam-5431	767	6	intuitionistic	intuitionistic	ADJ
ejpam-5431	767	7	fuzzy	fuzzy	ADJ
ejpam-5431	767	8	sets	set	NOUN
ejpam-5431	767	9	in	in	ADP
ejpam-5431	767	10	group	group	NOUN
ejpam-5431	767	11	theory	theory	NOUN
ejpam-5431	767	12	.	.	PUNCT
ejpam-5431	768	1	ieee	ieee	NOUN
ejpam-5431	768	2	access	access	NOUN
ejpam-5431	768	3	,	,	PUNCT
ejpam-5431	768	4	8:196075–196085	8:196075–196085	NUM
ejpam-5431	768	5	,	,	PUNCT
ejpam-5431	768	6	2020	2020	NUM
ejpam-5431	768	7	.	.	PUNCT
ejpam-5431	769	1	[	[	X
ejpam-5431	769	2	15	15	NUM
ejpam-5431	769	3	]	]	X
ejpam-5431	769	4	s.	s.	PROPN
ejpam-5431	769	5	heilpern	heilpern	PROPN
ejpam-5431	769	6	.	.	PUNCT
ejpam-5431	770	1	fuzzy	fuzzy	ADJ
ejpam-5431	770	2	mappings	mapping	NOUN
ejpam-5431	770	3	and	and	CCONJ
ejpam-5431	770	4	fixed	fix	VERB
ejpam-5431	770	5	point	point	NOUN
ejpam-5431	770	6	theorem	theorem	VERB
ejpam-5431	770	7	.	.	PROPN
ejpam-5431	770	8	journal	journal	PROPN
ejpam-5431	770	9	of	of	ADP
ejpam-5431	770	10	mathematical	mathematical	ADJ
ejpam-5431	770	11	analysis	analysis	NOUN
ejpam-5431	770	12	and	and	CCONJ
ejpam-5431	770	13	applications	application	NOUN
ejpam-5431	770	14	,	,	PUNCT
ejpam-5431	770	15	83(2):566–569	83(2):566–569	PROPN
ejpam-5431	770	16	,	,	PUNCT
ejpam-5431	770	17	1981	1981	NUM
ejpam-5431	770	18	.	.	PUNCT
ejpam-5431	771	1	[	[	X
ejpam-5431	771	2	16	16	NUM
ejpam-5431	771	3	]	]	PUNCT
ejpam-5431	771	4	s.	s.	PROPN
ejpam-5431	771	5	b.	b.	PROPN
ejpam-5431	771	6	nadler	nadler	PROPN
ejpam-5431	771	7	jr	jr	PROPN
ejpam-5431	771	8	.	.	PUNCT
ejpam-5431	771	9	multi	multi	ADJ
ejpam-5431	771	10	-	-	ADJ
ejpam-5431	771	11	valued	value	VERB
ejpam-5431	771	12	contraction	contraction	NOUN
ejpam-5431	771	13	mappings	mapping	NOUN
ejpam-5431	771	14	.	.	PUNCT
ejpam-5431	772	1	1969	1969	NUM
ejpam-5431	772	2	.	.	PUNCT
ejpam-5431	773	1	[	[	X
ejpam-5431	773	2	17	17	NUM
ejpam-5431	773	3	]	]	X
ejpam-5431	773	4	f.	f.	PROPN
ejpam-5431	773	5	khojasteh	khojasteh	PROPN
ejpam-5431	773	6	et	et	PROPN
ejpam-5431	773	7	al	al	PROPN
ejpam-5431	773	8	.	.	PUNCT
ejpam-5431	774	1	a	a	DET
ejpam-5431	774	2	new	new	ADJ
ejpam-5431	774	3	approach	approach	NOUN
ejpam-5431	774	4	to	to	ADP
ejpam-5431	774	5	the	the	DET
ejpam-5431	774	6	study	study	NOUN
ejpam-5431	774	7	of	of	ADP
ejpam-5431	774	8	fixed	fix	VERB
ejpam-5431	774	9	point	point	NOUN
ejpam-5431	774	10	theory	theory	NOUN
ejpam-5431	774	11	for	for	ADP
ejpam-5431	774	12	simulation	simulation	NOUN
ejpam-5431	774	13	functions	function	NOUN
ejpam-5431	774	14	.	.	PUNCT
ejpam-5431	775	1	filomat	filomat	NOUN
ejpam-5431	775	2	,	,	PUNCT
ejpam-5431	775	3	29(6):1189–1194	29(6):1189–1194	PROPN
ejpam-5431	775	4	,	,	PUNCT
ejpam-5431	775	5	2015	2015	NUM
ejpam-5431	775	6	.	.	PUNCT
ejpam-5431	776	1	[	[	X
ejpam-5431	776	2	18	18	NUM
ejpam-5431	776	3	]	]	X
ejpam-5431	776	4	n.	n.	PROPN
ejpam-5431	776	5	konwar	konwar	PROPN
ejpam-5431	776	6	.	.	PUNCT
ejpam-5431	777	1	extension	extension	NOUN
ejpam-5431	777	2	of	of	ADP
ejpam-5431	777	3	fixed	fix	VERB
ejpam-5431	777	4	point	point	NOUN
ejpam-5431	777	5	results	result	NOUN
ejpam-5431	777	6	in	in	ADP
ejpam-5431	777	7	intuitionistic	intuitionistic	ADJ
ejpam-5431	777	8	fuzzy	fuzzy	ADJ
ejpam-5431	777	9	b	b	X
ejpam-5431	777	10	metric	metric	ADJ
ejpam-5431	777	11	space	space	NOUN
ejpam-5431	777	12	.	.	PUNCT
ejpam-5431	778	1	journal	journal	NOUN
ejpam-5431	778	2	of	of	ADP
ejpam-5431	778	3	intelligent	intelligent	ADJ
ejpam-5431	778	4	and	and	CCONJ
ejpam-5431	778	5	fuzzy	fuzzy	ADJ
ejpam-5431	778	6	systems	system	NOUN
ejpam-5431	778	7	,	,	PUNCT
ejpam-5431	778	8	39(5):7831–7841	39(5):7831–7841	NUM
ejpam-5431	778	9	,	,	PUNCT
ejpam-5431	778	10	2020	2020	NUM
ejpam-5431	778	11	.	.	PUNCT
ejpam-5431	779	1	[	[	X
ejpam-5431	779	2	19	19	NUM
ejpam-5431	779	3	]	]	PUNCT
ejpam-5431	779	4	s.	s.	PROPN
ejpam-5431	779	5	s.	s.	PROPN
ejpam-5431	779	6	mohammed	mohammed	PROPN
ejpam-5431	779	7	and	and	CCONJ
ejpam-5431	779	8	i.	i.	PROPN
ejpam-5431	779	9	a.	a.	PROPN
ejpam-5431	779	10	fulatan	fulatan	PROPN
ejpam-5431	779	11	.	.	PUNCT
ejpam-5431	780	1	fuzzy	fuzzy	ADJ
ejpam-5431	780	2	fixed	fix	VERB
ejpam-5431	780	3	point	point	NOUN
ejpam-5431	780	4	results	result	NOUN
ejpam-5431	780	5	via	via	ADP
ejpam-5431	780	6	simulation	simulation	NOUN
ejpam-5431	780	7	functions	function	NOUN
ejpam-5431	780	8	.	.	PUNCT
ejpam-5431	781	1	mathematical	mathematical	ADJ
ejpam-5431	781	2	sciences	sciences	PROPN
ejpam-5431	781	3	,	,	PUNCT
ejpam-5431	781	4	16(2):137–148	16(2):137–148	NUM
ejpam-5431	781	5	,	,	PUNCT
ejpam-5431	781	6	2022	2022	NUM
ejpam-5431	781	7	.	.	PUNCT
ejpam-5431	782	1	[	[	X
ejpam-5431	782	2	20	20	NUM
ejpam-5431	782	3	]	]	PUNCT
ejpam-5431	782	4	j.	j.	PROPN
ejpam-5431	782	5	j.	j.	PROPN
ejpam-5431	782	6	nieto	nieto	PROPN
ejpam-5431	782	7	and	and	CCONJ
ejpam-5431	782	8	r.	r.	PROPN
ejpam-5431	782	9	rodŕıguez	rodŕıguez	PROPN
ejpam-5431	782	10	-	-	PUNCT
ejpam-5431	782	11	lópez	lópez	ADV
ejpam-5431	782	12	.	.	PUNCT
ejpam-5431	783	1	existence	existence	NOUN
ejpam-5431	783	2	and	and	CCONJ
ejpam-5431	783	3	uniqueness	uniqueness	NOUN
ejpam-5431	783	4	of	of	ADP
ejpam-5431	783	5	fixed	fix	VERB
ejpam-5431	783	6	point	point	NOUN
ejpam-5431	783	7	in	in	ADP
ejpam-5431	783	8	partially	partially	ADV
ejpam-5431	783	9	ordered	order	VERB
ejpam-5431	783	10	sets	set	NOUN
ejpam-5431	783	11	and	and	CCONJ
ejpam-5431	783	12	applications	application	NOUN
ejpam-5431	783	13	to	to	ADP
ejpam-5431	783	14	ordinary	ordinary	ADJ
ejpam-5431	783	15	differential	differential	ADJ
ejpam-5431	783	16	equations	equation	NOUN
ejpam-5431	783	17	.	.	PUNCT
ejpam-5431	784	1	acta	acta	PROPN
ejpam-5431	784	2	mathematica	mathematica	PROPN
ejpam-5431	784	3	sinica	sinica	PROPN
ejpam-5431	784	4	,	,	PUNCT
ejpam-5431	784	5	english	english	ADJ
ejpam-5431	784	6	series	series	NOUN
ejpam-5431	784	7	,	,	PUNCT
ejpam-5431	784	8	23(12):2205–2212	23(12):2205–2212	PRON
ejpam-5431	784	9	,	,	PUNCT
ejpam-5431	784	10	2007	2007	NUM
ejpam-5431	784	11	.	.	PUNCT
ejpam-5431	785	1	[	[	X
ejpam-5431	785	2	21	21	NUM
ejpam-5431	785	3	]	]	PUNCT
ejpam-5431	785	4	a.	a.	NOUN
ejpam-5431	785	5	ran	run	VERB
ejpam-5431	785	6	and	and	CCONJ
ejpam-5431	785	7	m.	m.	NOUN
ejpam-5431	785	8	reurings	reuring	NOUN
ejpam-5431	785	9	.	.	PUNCT
ejpam-5431	786	1	a	a	DET
ejpam-5431	786	2	fixed	fix	VERB
ejpam-5431	786	3	point	point	NOUN
ejpam-5431	786	4	theorem	theorem	VERB
ejpam-5431	786	5	in	in	ADP
ejpam-5431	786	6	partially	partially	ADV
ejpam-5431	786	7	ordered	order	VERB
ejpam-5431	786	8	sets	set	NOUN
ejpam-5431	786	9	and	and	CCONJ
ejpam-5431	786	10	some	some	DET
ejpam-5431	786	11	applications	application	NOUN
ejpam-5431	786	12	to	to	PART
ejpam-5431	786	13	matrix	matrix	VERB
ejpam-5431	786	14	equations	equation	NOUN
ejpam-5431	786	15	.	.	PUNCT
ejpam-5431	787	1	proceedings	proceeding	NOUN
ejpam-5431	787	2	of	of	ADP
ejpam-5431	787	3	the	the	DET
ejpam-5431	787	4	american	american	PROPN
ejpam-5431	787	5	mathematical	mathematical	PROPN
ejpam-5431	787	6	society	society	NOUN
ejpam-5431	787	7	,	,	PUNCT
ejpam-5431	787	8	132(5):1435–1443	132(5):1435–1443	PROPN
ejpam-5431	787	9	,	,	PUNCT
ejpam-5431	787	10	2004	2004	NUM
ejpam-5431	787	11	.	.	PUNCT
ejpam-5431	788	1	[	[	X
ejpam-5431	788	2	22	22	NUM
ejpam-5431	788	3	]	]	PUNCT
ejpam-5431	788	4	m.	m.	NOUN
ejpam-5431	788	5	rashid	rashid	PROPN
ejpam-5431	788	6	,	,	PUNCT
ejpam-5431	788	7	a.	a.	PROPN
ejpam-5431	788	8	azam	azam	PROPN
ejpam-5431	788	9	,	,	PUNCT
ejpam-5431	788	10	f.	f.	PROPN
ejpam-5431	788	11	dar	dar	PROPN
ejpam-5431	788	12	,	,	PUNCT
ejpam-5431	788	13	f.	f.	PROPN
ejpam-5431	788	14	ali	ali	PROPN
ejpam-5431	788	15	,	,	PUNCT
ejpam-5431	788	16	and	and	CCONJ
ejpam-5431	788	17	m.	m.	PROPN
ejpam-5431	788	18	a.	a.	PROPN
ejpam-5431	788	19	al	al	PROPN
ejpam-5431	788	20	-	-	PUNCT
ejpam-5431	788	21	kadhi	kadhi	PROPN
ejpam-5431	788	22	.	.	PUNCT
ejpam-5431	789	1	a	a	DET
ejpam-5431	789	2	comprehensive	comprehensive	ADJ
ejpam-5431	789	3	study	study	NOUN
ejpam-5431	789	4	on	on	ADP
ejpam-5431	789	5	advancement	advancement	NOUN
ejpam-5431	789	6	in	in	ADP
ejpam-5431	789	7	hybrid	hybrid	ADJ
ejpam-5431	789	8	contraction	contraction	NOUN
ejpam-5431	789	9	and	and	CCONJ
ejpam-5431	789	10	graphical	graphical	ADJ
ejpam-5431	789	11	analysis	analysis	NOUN
ejpam-5431	789	12	of	of	ADP
ejpam-5431	789	13	-fuzzy	-fuzzy	NOUN
ejpam-5431	789	14	fixed	fix	VERB
ejpam-5431	789	15	points	point	NOUN
ejpam-5431	789	16	with	with	ADP
ejpam-5431	789	17	application	application	NOUN
ejpam-5431	789	18	.	.	PUNCT
ejpam-5431	790	1	mathematics	mathematic	NOUN
ejpam-5431	790	2	,	,	PUNCT
ejpam-5431	790	3	11(21):4489	11(21):4489	NUM
ejpam-5431	790	4	,	,	PUNCT
ejpam-5431	790	5	2023	2023	NUM
ejpam-5431	790	6	.	.	PUNCT
ejpam-5431	791	1	[	[	X
ejpam-5431	791	2	23	23	NUM
ejpam-5431	791	3	]	]	X
ejpam-5431	791	4	b.	b.	PROPN
ejpam-5431	791	5	rhoades	rhoades	PROPN
ejpam-5431	791	6	.	.	PUNCT
ejpam-5431	792	1	some	some	DET
ejpam-5431	792	2	theorems	theorem	NOUN
ejpam-5431	792	3	on	on	ADP
ejpam-5431	792	4	weakly	weakly	ADJ
ejpam-5431	792	5	contractive	contractive	ADJ
ejpam-5431	792	6	maps	map	NOUN
ejpam-5431	792	7	.	.	PUNCT
ejpam-5431	793	1	nonlinear	nonlinear	ADJ
ejpam-5431	793	2	analysis	analysis	NOUN
ejpam-5431	793	3	:	:	PUNCT
ejpam-5431	793	4	theory	theory	NOUN
ejpam-5431	793	5	,	,	PUNCT
ejpam-5431	793	6	methods	method	NOUN
ejpam-5431	793	7	and	and	CCONJ
ejpam-5431	793	8	applications	application	NOUN
ejpam-5431	793	9	,	,	PUNCT
ejpam-5431	793	10	47(4):2683–2693	47(4):2683–2693	NUM
ejpam-5431	793	11	,	,	PUNCT
ejpam-5431	793	12	2001	2001	NUM
ejpam-5431	793	13	.	.	PUNCT
ejpam-5431	794	1	[	[	X
ejpam-5431	794	2	24	24	NUM
ejpam-5431	794	3	]	]	PUNCT
ejpam-5431	794	4	i.	i.	PROPN
ejpam-5431	794	5	a.	a.	PROPN
ejpam-5431	794	6	rus	rus	PROPN
ejpam-5431	794	7	.	.	PUNCT
ejpam-5431	794	8	generalized	generalized	ADJ
ejpam-5431	794	9	contractions	contraction	NOUN
ejpam-5431	794	10	and	and	CCONJ
ejpam-5431	794	11	applications	application	NOUN
ejpam-5431	794	12	.	.	PUNCT
ejpam-5431	795	1	2001	2001	NUM
ejpam-5431	795	2	.	.	PUNCT
ejpam-5431	796	1	[	[	X
ejpam-5431	796	2	25	25	NUM
ejpam-5431	796	3	]	]	PUNCT
ejpam-5431	796	4	b.	b.	PROPN
ejpam-5431	796	5	samet	samet	PROPN
ejpam-5431	796	6	,	,	PUNCT
ejpam-5431	796	7	c.	c.	PROPN
ejpam-5431	796	8	vetro	vetro	PROPN
ejpam-5431	796	9	,	,	PUNCT
ejpam-5431	796	10	and	and	CCONJ
ejpam-5431	796	11	p.	p.	PROPN
ejpam-5431	796	12	vetro	vetro	PROPN
ejpam-5431	796	13	.	.	PUNCT
ejpam-5431	797	1	fixed	fix	VERB
ejpam-5431	797	2	point	point	NOUN
ejpam-5431	797	3	theorems	theorem	NOUN
ejpam-5431	797	4	for	for	ADP
ejpam-5431	797	5	a	a	DET
ejpam-5431	797	6	-	-	PUNCT
ejpam-5431	797	7	contractive	contractive	ADJ
ejpam-5431	797	8	type	type	NOUN
ejpam-5431	797	9	mappings	mapping	NOUN
ejpam-5431	797	10	.	.	PUNCT
ejpam-5431	798	1	nonlinear	nonlinear	ADJ
ejpam-5431	798	2	analysis	analysis	NOUN
ejpam-5431	798	3	:	:	PUNCT
ejpam-5431	798	4	theory	theory	NOUN
ejpam-5431	798	5	,	,	PUNCT
ejpam-5431	798	6	methods	method	NOUN
ejpam-5431	798	7	and	and	CCONJ
ejpam-5431	798	8	applications	application	NOUN
ejpam-5431	798	9	,	,	PUNCT
ejpam-5431	798	10	75(4):2154–2165	75(4):2154–2165	NOUN
ejpam-5431	798	11	,	,	PUNCT
ejpam-5431	798	12	2012	2012	NUM
ejpam-5431	798	13	.	.	PUNCT
ejpam-5431	799	1	[	[	X
ejpam-5431	799	2	26	26	NUM
ejpam-5431	799	3	]	]	X
ejpam-5431	799	4	y.	y.	PROPN
ejpam-5431	799	5	h.	h.	PROPN
ejpam-5431	799	6	shen	shen	PROPN
ejpam-5431	799	7	,	,	PUNCT
ejpam-5431	799	8	f.	f.	PROPN
ejpam-5431	799	9	x.	x.	PROPN
ejpam-5431	799	10	wang	wang	PROPN
ejpam-5431	799	11	,	,	PUNCT
ejpam-5431	799	12	and	and	CCONJ
ejpam-5431	799	13	w.	w.	PROPN
ejpam-5431	799	14	chen	chen	PROPN
ejpam-5431	799	15	.	.	PUNCT
ejpam-5431	800	1	a	a	DET
ejpam-5431	800	2	note	note	NOUN
ejpam-5431	800	3	on	on	ADP
ejpam-5431	800	4	intuitionistic	intuitionistic	ADJ
ejpam-5431	800	5	fuzzy	fuzzy	ADJ
ejpam-5431	800	6	mappings	mapping	NOUN
ejpam-5431	800	7	.	.	PUNCT
ejpam-5431	801	1	2012	2012	NUM
ejpam-5431	801	2	.	.	PUNCT
ejpam-5431	802	1	[	[	X
ejpam-5431	802	2	27	27	NUM
ejpam-5431	802	3	]	]	PUNCT
ejpam-5431	802	4	s.	s.	PROPN
ejpam-5431	802	5	l.	l.	PROPN
ejpam-5431	802	6	singh	singh	PROPN
ejpam-5431	802	7	and	and	CCONJ
ejpam-5431	802	8	b.	b.	PROPN
ejpam-5431	802	9	prasad	prasad	PROPN
ejpam-5431	802	10	.	.	PUNCT
ejpam-5431	803	1	some	some	DET
ejpam-5431	803	2	coincidence	coincidence	NOUN
ejpam-5431	803	3	theorems	theorem	NOUN
ejpam-5431	803	4	and	and	CCONJ
ejpam-5431	803	5	stability	stability	NOUN
ejpam-5431	803	6	of	of	ADP
ejpam-5431	803	7	iterative	iterative	NOUN
ejpam-5431	803	8	procedures	procedure	NOUN
ejpam-5431	803	9	.	.	PUNCT
ejpam-5431	804	1	computers	computer	NOUN
ejpam-5431	804	2	and	and	CCONJ
ejpam-5431	804	3	mathematics	mathematic	NOUN
ejpam-5431	804	4	with	with	ADP
ejpam-5431	804	5	applications	application	NOUN
ejpam-5431	804	6	,	,	PUNCT
ejpam-5431	804	7	55(11):2512–2520	55(11):2512–2520	NUM
ejpam-5431	804	8	,	,	PUNCT
ejpam-5431	804	9	2008	2008	NUM
ejpam-5431	804	10	.	.	PUNCT