id	sid	tid	token	lemma	pos
ejpam-4028	1	1	european	european	PROPN
ejpam-4028	1	2	journal	journal	PROPN
ejpam-4028	1	3	of	of	ADP
ejpam-4028	1	4	pure	pure	ADJ
ejpam-4028	1	5	and	and	CCONJ
ejpam-4028	1	6	applied	apply	VERB
ejpam-4028	1	7	mathematics	mathematic	NOUN
ejpam-4028	1	8	vol	vol	NOUN
ejpam-4028	1	9	.	.	PUNCT
ejpam-4028	2	1	14	14	NUM
ejpam-4028	2	2	,	,	PUNCT
ejpam-4028	2	3	no	no	INTJ
ejpam-4028	2	4	.	.	NOUN
ejpam-4028	2	5	3	3	NUM
ejpam-4028	2	6	,	,	PUNCT
ejpam-4028	2	7	2021	2021	NUM
ejpam-4028	2	8	,	,	PUNCT
ejpam-4028	2	9	923	923	NUM
ejpam-4028	2	10	-	-	SYM
ejpam-4028	2	11	941	941	NUM
ejpam-4028	2	12	issn	issn	PROPN
ejpam-4028	2	13	1307	1307	NUM
ejpam-4028	2	14	-	-	SYM
ejpam-4028	2	15	5543	5543	NUM
ejpam-4028	2	16	–	–	PUNCT
ejpam-4028	2	17	ejpam.com	ejpam.com	X
ejpam-4028	2	18	published	publish	VERB
ejpam-4028	2	19	by	by	ADP
ejpam-4028	2	20	new	new	PROPN
ejpam-4028	2	21	york	york	PROPN
ejpam-4028	2	22	business	business	PROPN
ejpam-4028	2	23	global	global	PROPN
ejpam-4028	2	24	some	some	DET
ejpam-4028	2	25	new	new	ADJ
ejpam-4028	2	26	results	result	NOUN
ejpam-4028	2	27	of	of	ADP
ejpam-4028	2	28	fixed	fix	VERB
ejpam-4028	2	29	point	point	NOUN
ejpam-4028	2	30	in	in	ADP
ejpam-4028	2	31	fuzzy	fuzzy	ADJ
ejpam-4028	2	32	soft	soft	ADJ
ejpam-4028	2	33	g	g	NOUN
ejpam-4028	2	34	-	-	PUNCT
ejpam-4028	2	35	metric	metric	ADJ
ejpam-4028	2	36	spaces	space	NOUN
ejpam-4028	2	37	abdelhamied	abdelhamie	VERB
ejpam-4028	2	38	farrag	farrag	PROPN
ejpam-4028	2	39	sayed1,∗	sayed1,∗	NOUN
ejpam-4028	2	40	,	,	PUNCT
ejpam-4028	2	41	abdullah	abdullah	PROPN
ejpam-4028	2	42	alahmari2	alahmari2	NOUN
ejpam-4028	3	1	1	1	NUM
ejpam-4028	3	2	department	department	NOUN
ejpam-4028	3	3	of	of	ADP
ejpam-4028	3	4	mathematics	mathematics	PROPN
ejpam-4028	3	5	,	,	PUNCT
ejpam-4028	3	6	al	al	PROPN
ejpam-4028	3	7	-	-	PUNCT
ejpam-4028	3	8	lith	lith	PROPN
ejpam-4028	3	9	university	university	NOUN
ejpam-4028	3	10	college	college	NOUN
ejpam-4028	3	11	,	,	PUNCT
ejpam-4028	3	12	umm	umm	INTJ
ejpam-4028	3	13	al	al	PROPN
ejpam-4028	3	14	-	-	PUNCT
ejpam-4028	3	15	qura	qura	PROPN
ejpam-4028	3	16	university	university	PROPN
ejpam-4028	3	17	,	,	PUNCT
ejpam-4028	3	18	p.o	p.o	PROPN
ejpam-4028	3	19	.	.	PROPN
ejpam-4028	3	20	box	box	PROPN
ejpam-4028	3	21	112	112	NUM
ejpam-4028	3	22	,	,	PUNCT
ejpam-4028	3	23	al	al	PROPN
ejpam-4028	3	24	-	-	PUNCT
ejpam-4028	3	25	lith	lith	PROPN
ejpam-4028	3	26	21961	21961	NUM
ejpam-4028	3	27	,	,	PUNCT
ejpam-4028	3	28	makkah	makkah	PROPN
ejpam-4028	3	29	al	al	PROPN
ejpam-4028	3	30	mukarramah	mukarramah	PROPN
ejpam-4028	3	31	,	,	PUNCT
ejpam-4028	3	32	kingdom	kingdom	NOUN
ejpam-4028	3	33	of	of	ADP
ejpam-4028	3	34	saudi	saudi	PROPN
ejpam-4028	3	35	arabia	arabia	PROPN
ejpam-4028	3	36	2	2	NUM
ejpam-4028	3	37	department	department	NOUN
ejpam-4028	3	38	of	of	ADP
ejpam-4028	3	39	mathematics	mathematic	NOUN
ejpam-4028	3	40	,	,	PUNCT
ejpam-4028	3	41	college	college	NOUN
ejpam-4028	3	42	of	of	ADP
ejpam-4028	3	43	applied	apply	VERB
ejpam-4028	3	44	sciences	science	NOUN
ejpam-4028	3	45	,	,	PUNCT
ejpam-4028	3	46	umm	umm	INTJ
ejpam-4028	3	47	al	al	PROPN
ejpam-4028	3	48	-	-	PUNCT
ejpam-4028	3	49	qura	qura	PROPN
ejpam-4028	3	50	university	university	NOUN
ejpam-4028	3	51	,	,	PUNCT
ejpam-4028	3	52	kingdom	kingdom	NOUN
ejpam-4028	3	53	of	of	ADP
ejpam-4028	3	54	saudi	saudi	PROPN
ejpam-4028	3	55	arabia	arabia	PROPN
ejpam-4028	3	56	.	.	PUNCT
ejpam-4028	4	1	abstract	abstract	ADJ
ejpam-4028	4	2	.	.	PUNCT
ejpam-4028	5	1	the	the	DET
ejpam-4028	5	2	main	main	ADJ
ejpam-4028	5	3	goal	goal	NOUN
ejpam-4028	5	4	of	of	ADP
ejpam-4028	5	5	the	the	DET
ejpam-4028	5	6	present	present	ADJ
ejpam-4028	5	7	paper	paper	NOUN
ejpam-4028	5	8	is	be	AUX
ejpam-4028	5	9	to	to	PART
ejpam-4028	5	10	study	study	VERB
ejpam-4028	5	11	and	and	CCONJ
ejpam-4028	5	12	prove	prove	VERB
ejpam-4028	5	13	some	some	DET
ejpam-4028	5	14	results	result	NOUN
ejpam-4028	5	15	of	of	ADP
ejpam-4028	5	16	fixed	fix	VERB
ejpam-4028	5	17	points	point	NOUN
ejpam-4028	5	18	for	for	ADP
ejpam-4028	5	19	mappings	mapping	NOUN
ejpam-4028	5	20	satisfying	satisfy	VERB
ejpam-4028	5	21	different	different	ADJ
ejpam-4028	5	22	conditions	condition	NOUN
ejpam-4028	5	23	in	in	ADP
ejpam-4028	5	24	fuzzy	fuzzy	ADJ
ejpam-4028	5	25	soft	soft	ADJ
ejpam-4028	5	26	g	g	NOUN
ejpam-4028	5	27	-	-	PUNCT
ejpam-4028	5	28	metric	metric	ADJ
ejpam-4028	5	29	spaces	space	NOUN
ejpam-4028	5	30	.	.	PUNCT
ejpam-4028	6	1	2020	2020	NUM
ejpam-4028	6	2	mathematics	mathematic	NOUN
ejpam-4028	6	3	subject	subject	NOUN
ejpam-4028	6	4	classifications	classification	NOUN
ejpam-4028	6	5	:	:	PUNCT
ejpam-4028	6	6	03e72	03e72	NUM
ejpam-4028	6	7	,	,	PUNCT
ejpam-4028	6	8	54a40	54a40	NUM
ejpam-4028	6	9	,	,	PUNCT
ejpam-4028	6	10	54e40	54e40	NUM
ejpam-4028	6	11	,	,	PUNCT
ejpam-4028	6	12	54e50	54e50	NUM
ejpam-4028	6	13	,	,	PUNCT
ejpam-4028	6	14	47h10	47h10	PRON
ejpam-4028	6	15	key	key	ADJ
ejpam-4028	6	16	words	word	NOUN
ejpam-4028	6	17	and	and	CCONJ
ejpam-4028	6	18	phrases	phrase	NOUN
ejpam-4028	6	19	:	:	PUNCT
ejpam-4028	6	20	fuzzy	fuzzy	ADJ
ejpam-4028	6	21	set	set	NOUN
ejpam-4028	6	22	,	,	PUNCT
ejpam-4028	6	23	fuzzy	fuzzy	ADJ
ejpam-4028	6	24	soft	soft	ADJ
ejpam-4028	6	25	set	set	NOUN
ejpam-4028	6	26	,	,	PUNCT
ejpam-4028	6	27	fuzzy	fuzzy	ADJ
ejpam-4028	6	28	soft	soft	ADJ
ejpam-4028	6	29	g	g	NOUN
ejpam-4028	6	30	-	-	PUNCT
ejpam-4028	6	31	metric	metric	ADJ
ejpam-4028	6	32	space	space	NOUN
ejpam-4028	6	33	,	,	PUNCT
ejpam-4028	6	34	fixed	fix	VERB
ejpam-4028	6	35	point	point	NOUN
ejpam-4028	6	36	1	1	NUM
ejpam-4028	6	37	.	.	PUNCT
ejpam-4028	7	1	introduction	introduction	NOUN
ejpam-4028	7	2	most	most	ADJ
ejpam-4028	7	3	of	of	ADP
ejpam-4028	7	4	the	the	DET
ejpam-4028	7	5	real	real	ADJ
ejpam-4028	7	6	life	life	NOUN
ejpam-4028	7	7	problems	problem	NOUN
ejpam-4028	7	8	have	have	VERB
ejpam-4028	7	9	various	various	ADJ
ejpam-4028	7	10	uncertainties	uncertainty	NOUN
ejpam-4028	7	11	and	and	CCONJ
ejpam-4028	7	12	that	that	SCONJ
ejpam-4028	7	13	classical	classical	ADJ
ejpam-4028	7	14	mathematics	mathematic	NOUN
ejpam-4028	7	15	may	may	AUX
ejpam-4028	7	16	not	not	PART
ejpam-4028	7	17	be	be	AUX
ejpam-4028	7	18	able	able	ADJ
ejpam-4028	7	19	to	to	PART
ejpam-4028	7	20	model	model	VERB
ejpam-4028	7	21	properly	properly	ADV
ejpam-4028	7	22	.	.	PUNCT
ejpam-4028	8	1	among	among	ADP
ejpam-4028	8	2	these	these	DET
ejpam-4028	8	3	uncertainties	uncertainty	NOUN
ejpam-4028	8	4	,	,	PUNCT
ejpam-4028	8	5	there	there	PRON
ejpam-4028	8	6	are	be	VERB
ejpam-4028	8	7	two	two	NUM
ejpam-4028	8	8	types	type	NOUN
ejpam-4028	8	9	of	of	ADP
ejpam-4028	8	10	mathematical	mathematical	ADJ
ejpam-4028	8	11	tools	tool	NOUN
ejpam-4028	8	12	for	for	ADP
ejpam-4028	8	13	dealing	deal	VERB
ejpam-4028	8	14	with	with	ADP
ejpam-4028	8	15	such	such	ADJ
ejpam-4028	8	16	problems	problem	NOUN
ejpam-4028	8	17	:	:	PUNCT
ejpam-4028	8	18	fuzzy	fuzzy	ADJ
ejpam-4028	8	19	set	set	NOUN
ejpam-4028	8	20	theory	theory	NOUN
ejpam-4028	8	21	[	[	X
ejpam-4028	8	22	32	32	NUM
ejpam-4028	8	23	]	]	PUNCT
ejpam-4028	8	24	and	and	CCONJ
ejpam-4028	8	25	theory	theory	NOUN
ejpam-4028	8	26	of	of	ADP
ejpam-4028	8	27	soft	soft	ADJ
ejpam-4028	8	28	sets	set	NOUN
ejpam-4028	8	29	due	due	ADP
ejpam-4028	8	30	to	to	ADP
ejpam-4028	8	31	molodstov	molodstov	NOUN
ejpam-4028	8	32	[	[	X
ejpam-4028	8	33	19	19	NUM
ejpam-4028	8	34	]	]	X
ejpam-4028	8	35	,	,	PUNCT
ejpam-4028	8	36	both	both	PRON
ejpam-4028	8	37	of	of	ADP
ejpam-4028	8	38	which	which	PRON
ejpam-4028	8	39	aid	aid	NOUN
ejpam-4028	8	40	in	in	ADP
ejpam-4028	8	41	the	the	DET
ejpam-4028	8	42	solution	solution	NOUN
ejpam-4028	8	43	of	of	ADP
ejpam-4028	8	44	problems	problem	NOUN
ejpam-4028	8	45	in	in	ADP
ejpam-4028	8	46	various	various	ADJ
ejpam-4028	8	47	fields	field	NOUN
ejpam-4028	8	48	.	.	PUNCT
ejpam-4028	9	1	maji	maji	PROPN
ejpam-4028	9	2	et	et	PROPN
ejpam-4028	9	3	al	al	PROPN
ejpam-4028	9	4	.	.	PUNCT
ejpam-4028	10	1	[	[	X
ejpam-4028	10	2	23	23	NUM
ejpam-4028	10	3	]	]	PUNCT
ejpam-4028	10	4	introduced	introduce	VERB
ejpam-4028	10	5	the	the	DET
ejpam-4028	10	6	fuzzy	fuzzy	ADJ
ejpam-4028	10	7	soft	soft	ADJ
ejpam-4028	10	8	set	set	NOUN
ejpam-4028	10	9	,	,	PUNCT
ejpam-4028	10	10	which	which	PRON
ejpam-4028	10	11	is	be	AUX
ejpam-4028	10	12	a	a	DET
ejpam-4028	10	13	hybrid	hybrid	NOUN
ejpam-4028	10	14	of	of	ADP
ejpam-4028	10	15	fuzzy	fuzzy	ADJ
ejpam-4028	10	16	and	and	CCONJ
ejpam-4028	10	17	soft	soft	ADJ
ejpam-4028	10	18	sets	set	NOUN
ejpam-4028	10	19	.	.	PUNCT
ejpam-4028	11	1	roy	roy	PROPN
ejpam-4028	11	2	and	and	CCONJ
ejpam-4028	11	3	maji	maji	PROPN
ejpam-4028	12	1	[	[	X
ejpam-4028	12	2	22	22	NUM
ejpam-4028	12	3	]	]	PUNCT
ejpam-4028	12	4	presented	present	VERB
ejpam-4028	12	5	some	some	DET
ejpam-4028	12	6	results	result	NOUN
ejpam-4028	12	7	on	on	ADP
ejpam-4028	12	8	the	the	DET
ejpam-4028	12	9	use	use	NOUN
ejpam-4028	12	10	of	of	ADP
ejpam-4028	12	11	fuzzy	fuzzy	ADJ
ejpam-4028	12	12	soft	soft	ADJ
ejpam-4028	12	13	sets	set	NOUN
ejpam-4028	12	14	in	in	ADP
ejpam-4028	12	15	decision	decision	NOUN
ejpam-4028	12	16	-	-	PUNCT
ejpam-4028	12	17	making	make	VERB
ejpam-4028	12	18	problems	problem	NOUN
ejpam-4028	12	19	.	.	PUNCT
ejpam-4028	13	1	the	the	DET
ejpam-4028	13	2	applications	application	NOUN
ejpam-4028	13	3	of	of	ADP
ejpam-4028	13	4	fuzzy	fuzzy	ADJ
ejpam-4028	13	5	soft	soft	ADJ
ejpam-4028	13	6	sets	set	NOUN
ejpam-4028	13	7	have	have	AUX
ejpam-4028	13	8	been	be	AUX
ejpam-4028	13	9	extensively	extensively	ADV
ejpam-4028	13	10	studied	study	VERB
ejpam-4028	13	11	(	(	PUNCT
ejpam-4028	13	12	see	see	VERB
ejpam-4028	13	13	,	,	PUNCT
ejpam-4028	13	14	e.g.	e.g.	ADV
ejpam-4028	13	15	,	,	PUNCT
ejpam-4028	13	16	[	[	X
ejpam-4028	13	17	1	1	NUM
ejpam-4028	13	18	,	,	PUNCT
ejpam-4028	13	19	3	3	NUM
ejpam-4028	13	20	,	,	PUNCT
ejpam-4028	13	21	4	4	NUM
ejpam-4028	13	22	,	,	PUNCT
ejpam-4028	13	23	6	6	NUM
ejpam-4028	13	24	,	,	PUNCT
ejpam-4028	13	25	12	12	NUM
ejpam-4028	13	26	,	,	PUNCT
ejpam-4028	13	27	15	15	NUM
ejpam-4028	13	28	,	,	PUNCT
ejpam-4028	13	29	16	16	NUM
ejpam-4028	13	30	,	,	PUNCT
ejpam-4028	13	31	18	18	NUM
ejpam-4028	13	32	,	,	PUNCT
ejpam-4028	13	33	31	31	NUM
ejpam-4028	13	34	]	]	PUNCT
ejpam-4028	13	35	)	)	PUNCT
ejpam-4028	13	36	.	.	PUNCT
ejpam-4028	14	1	beaulaa	beaulaa	PROPN
ejpam-4028	14	2	and	and	CCONJ
ejpam-4028	14	3	gunaseeli	gunaseeli	PROPN
ejpam-4028	14	4	defined	define	VERB
ejpam-4028	14	5	the	the	DET
ejpam-4028	14	6	fuzzy	fuzzy	ADJ
ejpam-4028	14	7	soft	soft	ADJ
ejpam-4028	14	8	metric	metric	ADJ
ejpam-4028	14	9	space	space	NOUN
ejpam-4028	14	10	in	in	ADP
ejpam-4028	14	11	[	[	X
ejpam-4028	14	12	7	7	NUM
ejpam-4028	14	13	]	]	PUNCT
ejpam-4028	14	14	,	,	PUNCT
ejpam-4028	14	15	and	and	CCONJ
ejpam-4028	14	16	sayed	say	VERB
ejpam-4028	14	17	and	and	CCONJ
ejpam-4028	14	18	alahmari	alahmari	ADJ
ejpam-4028	15	1	[	[	X
ejpam-4028	15	2	25	25	NUM
ejpam-4028	15	3	]	]	PUNCT
ejpam-4028	15	4	defined	define	VERB
ejpam-4028	15	5	the	the	DET
ejpam-4028	15	6	notions	notion	NOUN
ejpam-4028	15	7	of	of	ADP
ejpam-4028	15	8	some	some	DET
ejpam-4028	15	9	mappings	mapping	NOUN
ejpam-4028	15	10	and	and	CCONJ
ejpam-4028	15	11	proved	prove	VERB
ejpam-4028	15	12	several	several	ADJ
ejpam-4028	15	13	fixed	fix	VERB
ejpam-4028	15	14	point	point	NOUN
ejpam-4028	15	15	theorems	theorem	NOUN
ejpam-4028	15	16	in	in	ADP
ejpam-4028	15	17	fuzzy	fuzzy	ADJ
ejpam-4028	15	18	soft	soft	ADJ
ejpam-4028	15	19	metric	metric	ADJ
ejpam-4028	15	20	spaces	space	NOUN
ejpam-4028	15	21	.	.	PUNCT
ejpam-4028	16	1	mustafa	mustafa	PROPN
ejpam-4028	16	2	and	and	CCONJ
ejpam-4028	16	3	sims	sim	NOUN
ejpam-4028	16	4	[	[	X
ejpam-4028	16	5	20	20	NUM
ejpam-4028	16	6	]	]	PUNCT
ejpam-4028	16	7	introduced	introduce	VERB
ejpam-4028	16	8	the	the	DET
ejpam-4028	16	9	concept	concept	NOUN
ejpam-4028	16	10	of	of	ADP
ejpam-4028	16	11	g	g	NOUN
ejpam-4028	16	12	-	-	PUNCT
ejpam-4028	16	13	metric	metric	ADJ
ejpam-4028	16	14	space	space	NOUN
ejpam-4028	16	15	to	to	PART
ejpam-4028	16	16	extend	extend	VERB
ejpam-4028	16	17	and	and	CCONJ
ejpam-4028	16	18	generalize	generalize	VERB
ejpam-4028	16	19	the	the	DET
ejpam-4028	16	20	concept	concept	NOUN
ejpam-4028	16	21	of	of	ADP
ejpam-4028	16	22	metric	metric	ADJ
ejpam-4028	16	23	space	space	NOUN
ejpam-4028	16	24	.	.	PUNCT
ejpam-4028	17	1	since	since	SCONJ
ejpam-4028	17	2	then	then	ADV
ejpam-4028	17	3	,	,	PUNCT
ejpam-4028	17	4	a	a	DET
ejpam-4028	17	5	number	number	NOUN
ejpam-4028	17	6	of	of	ADP
ejpam-4028	17	7	authors	author	NOUN
ejpam-4028	17	8	have	have	AUX
ejpam-4028	17	9	investigated	investigate	VERB
ejpam-4028	17	10	a	a	DET
ejpam-4028	17	11	variety	variety	NOUN
ejpam-4028	17	12	of	of	ADP
ejpam-4028	17	13	well	well	ADV
ejpam-4028	17	14	-	-	PUNCT
ejpam-4028	17	15	known	know	VERB
ejpam-4028	17	16	results	result	NOUN
ejpam-4028	17	17	in	in	ADP
ejpam-4028	17	18	g	g	NOUN
ejpam-4028	17	19	-	-	PUNCT
ejpam-4028	17	20	metric	metric	ADJ
ejpam-4028	17	21	space	space	NOUN
ejpam-4028	17	22	(	(	PUNCT
ejpam-4028	17	23	see	see	VERB
ejpam-4028	17	24	,	,	PUNCT
ejpam-4028	17	25	e.g.	e.g.	ADV
ejpam-4028	17	26	,	,	PUNCT
ejpam-4028	17	27	[	[	X
ejpam-4028	17	28	5	5	NUM
ejpam-4028	17	29	,	,	PUNCT
ejpam-4028	17	30	13	13	NUM
ejpam-4028	17	31	,	,	PUNCT
ejpam-4028	17	32	21	21	NUM
ejpam-4028	17	33	,	,	PUNCT
ejpam-4028	17	34	24	24	NUM
ejpam-4028	17	35	,	,	PUNCT
ejpam-4028	17	36	26–30	26–30	NUM
ejpam-4028	17	37	]	]	PUNCT
ejpam-4028	17	38	)	)	PUNCT
ejpam-4028	17	39	.	.	PUNCT
ejpam-4028	18	1	güler	güler	NOUN
ejpam-4028	18	2	et	et	PROPN
ejpam-4028	18	3	al	al	PROPN
ejpam-4028	18	4	.	.	PUNCT
ejpam-4028	19	1	[	[	X
ejpam-4028	19	2	11	11	NUM
ejpam-4028	19	3	]	]	PUNCT
ejpam-4028	19	4	proposed	propose	VERB
ejpam-4028	19	5	the	the	DET
ejpam-4028	19	6	idea	idea	NOUN
ejpam-4028	19	7	of	of	ADP
ejpam-4028	19	8	a	a	DET
ejpam-4028	19	9	soft	soft	ADJ
ejpam-4028	19	10	gmetric	gmetric	ADJ
ejpam-4028	19	11	space	space	NOUN
ejpam-4028	19	12	based	base	VERB
ejpam-4028	19	13	on	on	ADP
ejpam-4028	19	14	a	a	DET
ejpam-4028	19	15	soft	soft	ADJ
ejpam-4028	19	16	element	element	NOUN
ejpam-4028	19	17	and	and	CCONJ
ejpam-4028	19	18	found	find	VERB
ejpam-4028	19	19	some	some	PRON
ejpam-4028	19	20	of	of	ADP
ejpam-4028	19	21	its	its	PRON
ejpam-4028	19	22	properties	property	NOUN
ejpam-4028	19	23	.	.	PUNCT
ejpam-4028	20	1	then	then	ADV
ejpam-4028	20	2	they	they	PRON
ejpam-4028	20	3	came	come	VERB
ejpam-4028	20	4	up	up	ADP
ejpam-4028	20	5	with	with	ADP
ejpam-4028	20	6	the	the	DET
ejpam-4028	20	7	concepts	concept	NOUN
ejpam-4028	20	8	”	"	PUNCT
ejpam-4028	20	9	soft	soft	ADJ
ejpam-4028	20	10	g	g	NOUN
ejpam-4028	20	11	-	-	PUNCT
ejpam-4028	20	12	convergence	convergence	NOUN
ejpam-4028	20	13	”	"	PUNCT
ejpam-4028	20	14	and	and	CCONJ
ejpam-4028	20	15	”	"	PUNCT
ejpam-4028	20	16	soft	soft	ADJ
ejpam-4028	20	17	continuity	continuity	NOUN
ejpam-4028	20	18	”	"	PUNCT
ejpam-4028	20	19	.	.	PUNCT
ejpam-4028	21	1	they	they	PRON
ejpam-4028	21	2	also	also	ADV
ejpam-4028	21	3	established	establish	VERB
ejpam-4028	21	4	that	that	SCONJ
ejpam-4028	21	5	fixed	fix	VERB
ejpam-4028	21	6	points	point	NOUN
ejpam-4028	21	7	in	in	ADP
ejpam-4028	21	8	soft	soft	ADJ
ejpam-4028	21	9	g	g	NOUN
ejpam-4028	21	10	-	-	PUNCT
ejpam-4028	21	11	metric	metric	ADJ
ejpam-4028	21	12	spaces	space	NOUN
ejpam-4028	21	13	exist	exist	VERB
ejpam-4028	21	14	and	and	CCONJ
ejpam-4028	21	15	are	be	AUX
ejpam-4028	21	16	unique	unique	ADJ
ejpam-4028	21	17	.	.	PUNCT
ejpam-4028	22	1	güler	güler	NOUN
ejpam-4028	22	2	and	and	CCONJ
ejpam-4028	22	3	yildirim	yildirim	PROPN
ejpam-4028	22	4	presented	present	VERB
ejpam-4028	22	5	∗corresponding	∗corresponde	VERB
ejpam-4028	22	6	author	author	NOUN
ejpam-4028	22	7	.	.	PUNCT
ejpam-4028	23	1	doi	doi	NOUN
ejpam-4028	23	2	:	:	PUNCT
ejpam-4028	23	3	https://doi.org/10.29020/nybg.ejpam.v14i3.4028	https://doi.org/10.29020/nybg.ejpam.v14i3.4028	ADJ
ejpam-4028	23	4	email	email	NOUN
ejpam-4028	23	5	addresses	address	NOUN
ejpam-4028	23	6	:	:	PUNCT
ejpam-4028	23	7	dr.afsayed@hotmail.com	dr.afsayed@hotmail.com	NOUN
ejpam-4028	23	8	,	,	PUNCT
ejpam-4028	23	9	afssayed@uqu.edu.sa	afssayed@uqu.edu.sa	NOUN
ejpam-4028	23	10	(	(	PUNCT
ejpam-4028	23	11	a.	a.	PROPN
ejpam-4028	23	12	f.	f.	PROPN
ejpam-4028	23	13	sayed	say	VERB
ejpam-4028	23	14	)	)	PUNCT
ejpam-4028	23	15	,	,	PUNCT
ejpam-4028	23	16	aaahmari@uqu.edu.sa	aaahmari@uqu.edu.sa	PROPN
ejpam-4028	23	17	(	(	PUNCT
ejpam-4028	23	18	a.	a.	NOUN
ejpam-4028	23	19	alahmari	alahmari	PROPN
ejpam-4028	23	20	)	)	PUNCT
ejpam-4028	23	21	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-4028	24	1	923	923	NUM
ejpam-4028	24	2	©	©	PROPN
ejpam-4028	24	3	2021	2021	NUM
ejpam-4028	24	4	ejpam	ejpam	VERB
ejpam-4028	24	5	all	all	DET
ejpam-4028	24	6	rights	right	NOUN
ejpam-4028	24	7	reserved	reserve	VERB
ejpam-4028	24	8	.	.	PUNCT
ejpam-4028	25	1	a.	a.	PROPN
ejpam-4028	25	2	f.	f.	PROPN
ejpam-4028	25	3	sayed	sayed	PROPN
ejpam-4028	25	4	,	,	PUNCT
ejpam-4028	25	5	a.	a.	NOUN
ejpam-4028	25	6	alahmari	alahmari	PROPN
ejpam-4028	25	7	/	/	SYM
ejpam-4028	25	8	eur	eur	PROPN
ejpam-4028	25	9	.	.	PUNCT
ejpam-4028	26	1	j.	j.	PROPN
ejpam-4028	26	2	pure	pure	PROPN
ejpam-4028	26	3	appl	appl	PROPN
ejpam-4028	26	4	.	.	PROPN
ejpam-4028	26	5	math	math	PROPN
ejpam-4028	26	6	,	,	PUNCT
ejpam-4028	26	7	14	14	NUM
ejpam-4028	26	8	(	(	PUNCT
ejpam-4028	26	9	3	3	NUM
ejpam-4028	26	10	)	)	PUNCT
ejpam-4028	26	11	(	(	PUNCT
ejpam-4028	26	12	2021	2021	NUM
ejpam-4028	26	13	)	)	PUNCT
ejpam-4028	26	14	,	,	PUNCT
ejpam-4028	26	15	923	923	NUM
ejpam-4028	26	16	-	-	SYM
ejpam-4028	26	17	941	941	NUM
ejpam-4028	26	18	924	924	NUM
ejpam-4028	26	19	soft	soft	ADJ
ejpam-4028	26	20	g	g	NOUN
ejpam-4028	26	21	-	-	PUNCT
ejpam-4028	26	22	cauchy	cauchy	ADJ
ejpam-4028	26	23	sequences	sequence	NOUN
ejpam-4028	26	24	and	and	CCONJ
ejpam-4028	26	25	soft	soft	ADJ
ejpam-4028	26	26	g	g	NOUN
ejpam-4028	26	27	-	-	PUNCT
ejpam-4028	26	28	complete	complete	ADJ
ejpam-4028	26	29	metric	metric	ADJ
ejpam-4028	26	30	spaces	space	NOUN
ejpam-4028	26	31	in	in	ADP
ejpam-4028	26	32	[	[	X
ejpam-4028	26	33	10	10	NUM
ejpam-4028	26	34	]	]	PUNCT
ejpam-4028	26	35	,	,	PUNCT
ejpam-4028	26	36	and	and	CCONJ
ejpam-4028	26	37	shrivastava	shrivastava	PROPN
ejpam-4028	26	38	et	et	PROPN
ejpam-4028	26	39	al	al	PROPN
ejpam-4028	26	40	.	.	PROPN
ejpam-4028	26	41	established	establish	VERB
ejpam-4028	26	42	fixed	fix	VERB
ejpam-4028	26	43	point	point	NOUN
ejpam-4028	26	44	results	result	NOUN
ejpam-4028	26	45	of	of	ADP
ejpam-4028	26	46	mapping	mapping	NOUN
ejpam-4028	26	47	defined	define	VERB
ejpam-4028	26	48	on	on	ADP
ejpam-4028	26	49	soft	soft	ADJ
ejpam-4028	26	50	g	g	NOUN
ejpam-4028	26	51	-	-	PUNCT
ejpam-4028	26	52	metric	metric	ADJ
ejpam-4028	26	53	spaces	space	NOUN
ejpam-4028	26	54	in	in	ADP
ejpam-4028	26	55	[	[	X
ejpam-4028	26	56	17	17	NUM
ejpam-4028	26	57	]	]	PUNCT
ejpam-4028	26	58	.	.	PUNCT
ejpam-4028	27	1	using	use	VERB
ejpam-4028	27	2	fuzzy	fuzzy	ADJ
ejpam-4028	27	3	soft	soft	ADJ
ejpam-4028	27	4	elements	element	NOUN
ejpam-4028	27	5	,	,	PUNCT
ejpam-4028	27	6	sayed	say	VERB
ejpam-4028	27	7	et	et	PROPN
ejpam-4028	27	8	al	al	PROPN
ejpam-4028	27	9	.	.	PROPN
ejpam-4028	27	10	proposed	propose	VERB
ejpam-4028	27	11	the	the	DET
ejpam-4028	27	12	concept	concept	NOUN
ejpam-4028	27	13	of	of	ADP
ejpam-4028	27	14	fuzzy	fuzzy	ADJ
ejpam-4028	27	15	soft	soft	ADJ
ejpam-4028	27	16	g	g	NOUN
ejpam-4028	27	17	-	-	PUNCT
ejpam-4028	27	18	metric	metric	ADJ
ejpam-4028	27	19	space	space	NOUN
ejpam-4028	27	20	in	in	ADP
ejpam-4028	27	21	[	[	X
ejpam-4028	27	22	2	2	NUM
ejpam-4028	27	23	]	]	PUNCT
ejpam-4028	27	24	.	.	PUNCT
ejpam-4028	28	1	they	they	PRON
ejpam-4028	28	2	also	also	ADV
ejpam-4028	28	3	investigated	investigate	VERB
ejpam-4028	28	4	on	on	ADP
ejpam-4028	28	5	fuzzy	fuzzy	ADJ
ejpam-4028	28	6	soft	soft	ADJ
ejpam-4028	28	7	continuity	continuity	NOUN
ejpam-4028	28	8	and	and	CCONJ
ejpam-4028	28	9	convergence	convergence	NOUN
ejpam-4028	28	10	in	in	ADP
ejpam-4028	28	11	fuzzy	fuzzy	ADJ
ejpam-4028	28	12	soft	soft	ADJ
ejpam-4028	28	13	g	g	NOUN
ejpam-4028	28	14	-	-	PUNCT
ejpam-4028	28	15	metric	metric	ADJ
ejpam-4028	28	16	spaces	space	NOUN
ejpam-4028	28	17	.	.	PUNCT
ejpam-4028	29	1	the	the	DET
ejpam-4028	29	2	main	main	ADJ
ejpam-4028	29	3	goal	goal	NOUN
ejpam-4028	29	4	of	of	ADP
ejpam-4028	29	5	the	the	DET
ejpam-4028	29	6	present	present	ADJ
ejpam-4028	29	7	paper	paper	NOUN
ejpam-4028	29	8	is	be	AUX
ejpam-4028	29	9	to	to	PART
ejpam-4028	29	10	study	study	VERB
ejpam-4028	29	11	and	and	CCONJ
ejpam-4028	29	12	prove	prove	VERB
ejpam-4028	29	13	some	some	DET
ejpam-4028	29	14	results	result	NOUN
ejpam-4028	29	15	of	of	ADP
ejpam-4028	29	16	fixed	fix	VERB
ejpam-4028	29	17	points	point	NOUN
ejpam-4028	29	18	for	for	ADP
ejpam-4028	29	19	mappings	mapping	NOUN
ejpam-4028	29	20	satisfying	satisfy	VERB
ejpam-4028	29	21	different	different	ADJ
ejpam-4028	29	22	conditions	condition	NOUN
ejpam-4028	29	23	in	in	ADP
ejpam-4028	29	24	fuzzy	fuzzy	ADJ
ejpam-4028	29	25	soft	soft	ADJ
ejpam-4028	29	26	g	g	NOUN
ejpam-4028	29	27	-	-	PUNCT
ejpam-4028	29	28	metric	metric	ADJ
ejpam-4028	29	29	spaces	space	NOUN
ejpam-4028	29	30	.	.	PUNCT
ejpam-4028	30	1	2	2	X
ejpam-4028	30	2	.	.	NUM
ejpam-4028	30	3	preliminaries	preliminary	NOUN
ejpam-4028	30	4	basic	basic	ADJ
ejpam-4028	30	5	definitions	definition	NOUN
ejpam-4028	30	6	of	of	ADP
ejpam-4028	30	7	fuzzy	fuzzy	ADJ
ejpam-4028	30	8	soft	soft	ADJ
ejpam-4028	30	9	sets	set	NOUN
ejpam-4028	30	10	and	and	CCONJ
ejpam-4028	30	11	fuzzy	fuzzy	ADJ
ejpam-4028	30	12	soft	soft	ADJ
ejpam-4028	30	13	g	g	NOUN
ejpam-4028	30	14	-	-	PUNCT
ejpam-4028	30	15	metric	metric	ADJ
ejpam-4028	30	16	spaces	space	NOUN
ejpam-4028	30	17	are	be	AUX
ejpam-4028	30	18	presented	present	VERB
ejpam-4028	30	19	in	in	ADP
ejpam-4028	30	20	this	this	DET
ejpam-4028	30	21	section	section	NOUN
ejpam-4028	30	22	.	.	PUNCT
ejpam-4028	31	1	throughout	throughout	ADP
ejpam-4028	31	2	this	this	DET
ejpam-4028	31	3	study	study	NOUN
ejpam-4028	31	4	,	,	PUNCT
ejpam-4028	31	5	we	we	PRON
ejpam-4028	31	6	will	will	AUX
ejpam-4028	31	7	use	use	VERB
ejpam-4028	31	8	the	the	DET
ejpam-4028	31	9	terms	term	NOUN
ejpam-4028	31	10	x	x	PART
ejpam-4028	31	11	to	to	PART
ejpam-4028	31	12	refer	refer	VERB
ejpam-4028	31	13	to	to	ADP
ejpam-4028	31	14	an	an	DET
ejpam-4028	31	15	initial	initial	ADJ
ejpam-4028	31	16	universe	universe	NOUN
ejpam-4028	31	17	,	,	PUNCT
ejpam-4028	31	18	e	e	NOUN
ejpam-4028	31	19	to	to	PART
ejpam-4028	31	20	refer	refer	VERB
ejpam-4028	31	21	to	to	ADP
ejpam-4028	31	22	the	the	DET
ejpam-4028	31	23	set	set	NOUN
ejpam-4028	31	24	of	of	ADP
ejpam-4028	31	25	all	all	DET
ejpam-4028	31	26	parameters	parameter	NOUN
ejpam-4028	31	27	for	for	ADP
ejpam-4028	31	28	x	x	X
ejpam-4028	31	29	,	,	PUNCT
ejpam-4028	31	30	and	and	CCONJ
ejpam-4028	31	31	i	i	PRON
ejpam-4028	31	32	=	=	PUNCT
ejpam-4028	32	1	[	[	X
ejpam-4028	32	2	0	0	NUM
ejpam-4028	32	3	,	,	PUNCT
ejpam-4028	32	4	1	1	NUM
ejpam-4028	32	5	]	]	PUNCT
ejpam-4028	32	6	to	to	PART
ejpam-4028	32	7	refer	refer	VERB
ejpam-4028	32	8	to	to	ADP
ejpam-4028	32	9	the	the	DET
ejpam-4028	32	10	initial	initial	ADJ
ejpam-4028	32	11	universe	universe	NOUN
ejpam-4028	32	12	.	.	PUNCT
ejpam-4028	33	1	definition	definition	NOUN
ejpam-4028	33	2	1	1	NUM
ejpam-4028	33	3	.	.	PUNCT
ejpam-4028	34	1	[	[	X
ejpam-4028	34	2	32	32	NUM
ejpam-4028	34	3	]	]	PUNCT
ejpam-4028	34	4	the	the	DET
ejpam-4028	34	5	membership	membership	NOUN
ejpam-4028	34	6	function	function	NOUN
ejpam-4028	34	7	µa(x	µa(x	NOUN
ejpam-4028	34	8	)	)	PUNCT
ejpam-4028	34	9	of	of	ADP
ejpam-4028	34	10	a	a	DET
ejpam-4028	34	11	fuzzy	fuzzy	ADJ
ejpam-4028	34	12	set	set	NOUN
ejpam-4028	34	13	a	a	PRON
ejpam-4028	34	14	is	be	AUX
ejpam-4028	34	15	a	a	DET
ejpam-4028	34	16	function	function	NOUN
ejpam-4028	34	17	µa	µa	NOUN
ejpam-4028	34	18	:	:	PUNCT
ejpam-4028	34	19	x	x	X
ejpam-4028	34	20	→	→	SYM
ejpam-4028	34	21	[	[	X
ejpam-4028	34	22	0	0	NUM
ejpam-4028	34	23	,	,	PUNCT
ejpam-4028	34	24	1	1	NUM
ejpam-4028	34	25	]	]	PUNCT
ejpam-4028	34	26	so	so	ADV
ejpam-4028	34	27	,	,	PUNCT
ejpam-4028	34	28	every	every	DET
ejpam-4028	34	29	element	element	NOUN
ejpam-4028	34	30	x	x	PUNCT
ejpam-4028	34	31	in	in	ADP
ejpam-4028	34	32	x	x	PROPN
ejpam-4028	34	33	has	have	VERB
ejpam-4028	34	34	membership	membership	NOUN
ejpam-4028	34	35	degree	degree	NOUN
ejpam-4028	34	36	:	:	PUNCT
ejpam-4028	34	37	µa(x	µa(x	NUM
ejpam-4028	34	38	)	)	PUNCT
ejpam-4028	34	39	∈	∈	PROPN
ejpam-4028	35	1	[	[	X
ejpam-4028	35	2	0	0	NUM
ejpam-4028	35	3	,	,	PUNCT
ejpam-4028	35	4	1	1	NUM
ejpam-4028	35	5	]	]	PUNCT
ejpam-4028	35	6	.	.	PUNCT
ejpam-4028	36	1	a	a	PRON
ejpam-4028	36	2	is	be	AUX
ejpam-4028	36	3	completely	completely	ADV
ejpam-4028	36	4	determined	determine	VERB
ejpam-4028	36	5	by	by	ADP
ejpam-4028	36	6	the	the	DET
ejpam-4028	36	7	set	set	NOUN
ejpam-4028	36	8	of	of	ADP
ejpam-4028	36	9	tuples	tuple	NOUN
ejpam-4028	36	10	:	:	PUNCT
ejpam-4028	36	11	a	a	PRON
ejpam-4028	36	12	=	=	X
ejpam-4028	36	13	{	{	PUNCT
ejpam-4028	36	14	(	(	PUNCT
ejpam-4028	36	15	x	x	NOUN
ejpam-4028	36	16	,	,	PUNCT
ejpam-4028	36	17	µa(x	µa(x	NOUN
ejpam-4028	36	18	)	)	PUNCT
ejpam-4028	36	19	)	)	PUNCT
ejpam-4028	37	1	:	:	PUNCT
ejpam-4028	37	2	x	x	X
ejpam-4028	37	3	∈	∈	NOUN
ejpam-4028	37	4	x	x	X
ejpam-4028	37	5	}	}	PUNCT
ejpam-4028	37	6	.	.	PUNCT
ejpam-4028	38	1	an	an	DET
ejpam-4028	38	2	empty	empty	ADJ
ejpam-4028	38	3	fuzzy	fuzzy	ADJ
ejpam-4028	38	4	set	set	NOUN
ejpam-4028	38	5	,	,	PUNCT
ejpam-4028	38	6	denoted	denote	VERB
ejpam-4028	38	7	by	by	ADP
ejpam-4028	38	8	0̃	0̃	PROPN
ejpam-4028	38	9	is	be	AUX
ejpam-4028	38	10	one	one	NUM
ejpam-4028	38	11	whose	whose	DET
ejpam-4028	38	12	membership	membership	NOUN
ejpam-4028	38	13	value	value	NOUN
ejpam-4028	38	14	is	be	AUX
ejpam-4028	38	15	0	0	NUM
ejpam-4028	38	16	,	,	PUNCT
ejpam-4028	38	17	∀x	∀x	X
ejpam-4028	38	18	∈	∈	PROPN
ejpam-4028	38	19	x.	x.	NOUN
ejpam-4028	38	20	in	in	ADP
ejpam-4028	38	21	contrast	contrast	NOUN
ejpam-4028	38	22	to	to	ADP
ejpam-4028	38	23	the	the	DET
ejpam-4028	38	24	above	above	ADJ
ejpam-4028	38	25	,	,	PUNCT
ejpam-4028	38	26	when	when	SCONJ
ejpam-4028	38	27	µa(x	µa(x	NOUN
ejpam-4028	38	28	)	)	PUNCT
ejpam-4028	38	29	=	=	SYM
ejpam-4028	38	30	1	1	NUM
ejpam-4028	38	31	,	,	PUNCT
ejpam-4028	38	32	then	then	ADV
ejpam-4028	38	33	the	the	DET
ejpam-4028	38	34	fuzzy	fuzzy	ADJ
ejpam-4028	38	35	set	set	VERB
ejpam-4028	38	36	a	a	PRON
ejpam-4028	38	37	is	be	AUX
ejpam-4028	38	38	the	the	DET
ejpam-4028	38	39	universal	universal	ADJ
ejpam-4028	38	40	fuzzy	fuzzy	ADJ
ejpam-4028	38	41	set	set	NOUN
ejpam-4028	38	42	,	,	PUNCT
ejpam-4028	38	43	denoted	denote	VERB
ejpam-4028	38	44	by	by	ADP
ejpam-4028	38	45	1̃.	1̃.	NUM
ejpam-4028	38	46	definition	definition	NOUN
ejpam-4028	38	47	2	2	NUM
ejpam-4028	38	48	.	.	PUNCT
ejpam-4028	39	1	[	[	X
ejpam-4028	39	2	8	8	NUM
ejpam-4028	39	3	]	]	PUNCT
ejpam-4028	39	4	a	a	DET
ejpam-4028	39	5	fuzzy	fuzzy	ADJ
ejpam-4028	39	6	soft	soft	ADJ
ejpam-4028	39	7	set	set	NOUN
ejpam-4028	39	8	fa	fa	NOUN
ejpam-4028	39	9	over	over	ADP
ejpam-4028	39	10	x	x	PRON
ejpam-4028	39	11	is	be	AUX
ejpam-4028	39	12	a	a	DET
ejpam-4028	39	13	pair	pair	NOUN
ejpam-4028	39	14	(	(	PUNCT
ejpam-4028	39	15	f	f	X
ejpam-4028	39	16	,	,	PUNCT
ejpam-4028	39	17	a	a	PRON
ejpam-4028	39	18	)	)	PUNCT
ejpam-4028	39	19	,	,	PUNCT
ejpam-4028	39	20	where	where	SCONJ
ejpam-4028	39	21	f	f	PROPN
ejpam-4028	39	22	is	be	AUX
ejpam-4028	39	23	a	a	DET
ejpam-4028	39	24	mapping	mapping	NOUN
ejpam-4028	39	25	f	f	NOUN
ejpam-4028	39	26	:	:	PUNCT
ejpam-4028	39	27	a→	a→	PUNCT
ejpam-4028	39	28	ix	ix	ADV
ejpam-4028	39	29	defined	define	VERB
ejpam-4028	39	30	by	by	ADP
ejpam-4028	39	31	fa(e	fa(e	NOUN
ejpam-4028	39	32	)	)	PUNCT
ejpam-4028	40	1	=	=	PRON
ejpam-4028	40	2	{	{	PUNCT
ejpam-4028	40	3	0̃	0̃	NOUN
ejpam-4028	40	4	,	,	PUNCT
ejpam-4028	40	5	if	if	SCONJ
ejpam-4028	40	6	e	e	NOUN
ejpam-4028	40	7	/∈	/∈	VERB
ejpam-4028	41	1	a	a	X
ejpam-4028	41	2	;	;	PUNCT
ejpam-4028	41	3	otherwise	otherwise	ADV
ejpam-4028	41	4	,	,	PUNCT
ejpam-4028	41	5	if	if	SCONJ
ejpam-4028	41	6	e	e	PROPN
ejpam-4028	41	7	∈	∈	PROPN
ejpam-4028	41	8	a.	a.	NOUN
ejpam-4028	41	9	definition	definition	NOUN
ejpam-4028	41	10	3	3	NUM
ejpam-4028	41	11	.	.	PUNCT
ejpam-4028	42	1	[	[	X
ejpam-4028	42	2	9	9	NUM
ejpam-4028	42	3	]	]	PUNCT
ejpam-4028	42	4	a	a	DET
ejpam-4028	42	5	fuzzy	fuzzy	ADJ
ejpam-4028	42	6	soft	soft	ADJ
ejpam-4028	42	7	set	set	NOUN
ejpam-4028	42	8	fa	fa	NOUN
ejpam-4028	42	9	over	over	ADP
ejpam-4028	42	10	x	x	VERB
ejpam-4028	42	11	is	be	AUX
ejpam-4028	42	12	said	say	VERB
ejpam-4028	42	13	to	to	PART
ejpam-4028	42	14	be	be	AUX
ejpam-4028	42	15	:	:	PUNCT
ejpam-4028	42	16	(	(	PUNCT
ejpam-4028	42	17	a	a	X
ejpam-4028	42	18	)	)	PUNCT
ejpam-4028	42	19	null	null	ADJ
ejpam-4028	42	20	fuzzy	fuzzy	ADJ
ejpam-4028	42	21	soft	soft	ADJ
ejpam-4028	42	22	set	set	NOUN
ejpam-4028	42	23	,	,	PUNCT
ejpam-4028	42	24	denoted	denote	VERB
ejpam-4028	42	25	by	by	ADP
ejpam-4028	42	26	φ̃	φ̃	PROPN
ejpam-4028	42	27	,	,	PUNCT
ejpam-4028	42	28	if	if	SCONJ
ejpam-4028	42	29	for	for	ADP
ejpam-4028	42	30	all	all	DET
ejpam-4028	42	31	e	e	PROPN
ejpam-4028	42	32	∈	∈	PROPN
ejpam-4028	42	33	a	a	PRON
ejpam-4028	42	34	,	,	PUNCT
ejpam-4028	42	35	fa(e	fa(e	X
ejpam-4028	42	36	)	)	PUNCT
ejpam-4028	43	1	=	=	SYM
ejpam-4028	43	2	0̃	0̃	NOUN
ejpam-4028	43	3	,	,	PUNCT
ejpam-4028	43	4	(	(	PUNCT
ejpam-4028	43	5	b	b	X
ejpam-4028	43	6	)	)	PUNCT
ejpam-4028	43	7	absolute	absolute	ADJ
ejpam-4028	43	8	fuzzy	fuzzy	ADJ
ejpam-4028	43	9	soft	soft	ADJ
ejpam-4028	43	10	set	set	NOUN
ejpam-4028	43	11	,	,	PUNCT
ejpam-4028	43	12	denoted	denote	VERB
ejpam-4028	43	13	by	by	ADP
ejpam-4028	43	14	ẽ	ẽ	PROPN
ejpam-4028	43	15	,	,	PUNCT
ejpam-4028	43	16	if	if	SCONJ
ejpam-4028	43	17	for	for	ADP
ejpam-4028	43	18	all	all	DET
ejpam-4028	43	19	e	e	PROPN
ejpam-4028	43	20	∈	∈	PROPN
ejpam-4028	43	21	a	a	PRON
ejpam-4028	43	22	,	,	PUNCT
ejpam-4028	43	23	fa(e	fa(e	X
ejpam-4028	43	24	)	)	PUNCT
ejpam-4028	43	25	=	=	SYM
ejpam-4028	44	1	1̃.	1̃.	NUM
ejpam-4028	44	2	the	the	DET
ejpam-4028	44	3	fuzzy	fuzzy	ADJ
ejpam-4028	44	4	soft	soft	ADJ
ejpam-4028	44	5	real	real	ADJ
ejpam-4028	44	6	numbers	number	NOUN
ejpam-4028	44	7	were	be	AUX
ejpam-4028	44	8	defined	define	VERB
ejpam-4028	44	9	in	in	ADP
ejpam-4028	44	10	[	[	X
ejpam-4028	44	11	14	14	NUM
ejpam-4028	44	12	]	]	PUNCT
ejpam-4028	44	13	,	,	PUNCT
ejpam-4028	44	14	denoted	denote	VERB
ejpam-4028	44	15	by	by	ADP
ejpam-4028	44	16	˜̃r	˜̃r	NUM
ejpam-4028	44	17	,	,	PUNCT
ejpam-4028	44	18	˜̃s	˜̃	NOUN
ejpam-4028	44	19	,	,	PUNCT
ejpam-4028	44	20	˜̃t	˜̃t	NOUN
ejpam-4028	44	21	,	,	PUNCT
ejpam-4028	44	22	...	...	PUNCT
ejpam-4028	44	23	etc	etc	X
ejpam-4028	44	24	,	,	PUNCT
ejpam-4028	44	25	and	and	CCONJ
ejpam-4028	44	26	¯̄r	¯̄r	PROPN
ejpam-4028	44	27	,	,	PUNCT
ejpam-4028	44	28	¯̄s	¯̄s	NOUN
ejpam-4028	44	29	,	,	PUNCT
ejpam-4028	44	30	¯̄t	¯̄t	PROPN
ejpam-4028	44	31	will	will	AUX
ejpam-4028	44	32	be	be	AUX
ejpam-4028	44	33	denoted	denote	VERB
ejpam-4028	44	34	in	in	ADP
ejpam-4028	44	35	particular	particular	ADJ
ejpam-4028	44	36	type	type	NOUN
ejpam-4028	44	37	of	of	ADP
ejpam-4028	44	38	fuzzy	fuzzy	ADJ
ejpam-4028	44	39	soft	soft	ADJ
ejpam-4028	44	40	real	real	ADJ
ejpam-4028	44	41	numbers	number	NOUN
ejpam-4028	44	42	such	such	ADJ
ejpam-4028	44	43	that	that	PRON
ejpam-4028	44	44	¯̄r(e	¯̄r(e	NOUN
ejpam-4028	44	45	)	)	PUNCT
ejpam-4028	44	46	is	be	AUX
ejpam-4028	44	47	a	a	DET
ejpam-4028	44	48	fuzzy	fuzzy	ADJ
ejpam-4028	44	49	number	number	NOUN
ejpam-4028	44	50	for	for	ADP
ejpam-4028	44	51	all	all	DET
ejpam-4028	44	52	e	e	PROPN
ejpam-4028	44	53	∈	∈	PROPN
ejpam-4028	44	54	e.	e.	PROPN
ejpam-4028	44	55	let	let	VERB
ejpam-4028	44	56	a	a	DET
ejpam-4028	44	57	⊆	⊆	NUM
ejpam-4028	44	58	e.	e.	PROPN
ejpam-4028	44	59	r(a)∗	r(a)∗	PROPN
ejpam-4028	44	60	be	be	AUX
ejpam-4028	44	61	a	a	DET
ejpam-4028	44	62	set	set	NOUN
ejpam-4028	44	63	of	of	ADP
ejpam-4028	44	64	all	all	DET
ejpam-4028	44	65	nonnegative	nonnegative	ADJ
ejpam-4028	44	66	fuzzy	fuzzy	ADJ
ejpam-4028	44	67	soft	soft	ADJ
ejpam-4028	44	68	real	real	ADJ
ejpam-4028	44	69	numbers	number	NOUN
ejpam-4028	44	70	and	and	CCONJ
ejpam-4028	44	71	fsc(fa	fsc(fa	NOUN
ejpam-4028	44	72	)	)	PUNCT
ejpam-4028	44	73	denotes	denote	VERB
ejpam-4028	44	74	a	a	DET
ejpam-4028	44	75	collection	collection	NOUN
ejpam-4028	44	76	of	of	ADP
ejpam-4028	44	77	all	all	DET
ejpam-4028	44	78	fuzzy	fuzzy	ADJ
ejpam-4028	44	79	soft	soft	ADJ
ejpam-4028	44	80	points	point	NOUN
ejpam-4028	44	81	of	of	ADP
ejpam-4028	44	82	a	a	DET
ejpam-4028	44	83	fuzzy	fuzzy	ADJ
ejpam-4028	44	84	soft	soft	ADJ
ejpam-4028	44	85	set	set	NOUN
ejpam-4028	44	86	fa	fa	NOUN
ejpam-4028	44	87	over	over	ADP
ejpam-4028	44	88	x.	x.	NOUN
ejpam-4028	44	89	definition	definition	NOUN
ejpam-4028	44	90	4	4	NUM
ejpam-4028	44	91	.	.	PUNCT
ejpam-4028	45	1	[	[	X
ejpam-4028	45	2	2	2	X
ejpam-4028	45	3	]	]	PUNCT
ejpam-4028	45	4	let	let	VERB
ejpam-4028	45	5	e	e	PRON
ejpam-4028	45	6	be	be	AUX
ejpam-4028	45	7	a	a	DET
ejpam-4028	45	8	nonempty	nonempty	ADJ
ejpam-4028	45	9	set	set	NOUN
ejpam-4028	45	10	of	of	ADP
ejpam-4028	45	11	parameters	parameter	NOUN
ejpam-4028	45	12	,	,	PUNCT
ejpam-4028	45	13	a	a	DET
ejpam-4028	45	14	⊆	⊆	NUM
ejpam-4028	45	15	e	e	NOUN
ejpam-4028	45	16	and	and	CCONJ
ejpam-4028	45	17	ẽ	ẽ	PROPN
ejpam-4028	45	18	be	be	AUX
ejpam-4028	45	19	the	the	DET
ejpam-4028	45	20	absolute	absolute	ADJ
ejpam-4028	45	21	fuzzy	fuzzy	ADJ
ejpam-4028	45	22	soft	soft	ADJ
ejpam-4028	45	23	.	.	PUNCT
ejpam-4028	46	1	a	a	DET
ejpam-4028	46	2	mapping	mapping	NOUN
ejpam-4028	46	3	g̃	g̃	PROPN
ejpam-4028	46	4	:	:	PUNCT
ejpam-4028	46	5	fsc(ẽ)×	fsc(ẽ)×	NUM
ejpam-4028	46	6	fsc(ẽ)×	fsc(ẽ)×	NUM
ejpam-4028	47	1	fsc(ẽ)→	fsc(ẽ)→	PROPN
ejpam-4028	47	2	r(a)∗	r(a)∗	PROPN
ejpam-4028	47	3	is	be	AUX
ejpam-4028	47	4	said	say	VERB
ejpam-4028	47	5	to	to	PART
ejpam-4028	47	6	be	be	AUX
ejpam-4028	47	7	a	a	DET
ejpam-4028	47	8	fuzzy	fuzzy	ADJ
ejpam-4028	47	9	soft	soft	ADJ
ejpam-4028	47	10	g	g	NOUN
ejpam-4028	47	11	-	-	NOUN
ejpam-4028	47	12	metric	metric	ADJ
ejpam-4028	47	13	on	on	ADP
ejpam-4028	47	14	ẽ	ẽ	PROPN
ejpam-4028	47	15	if	if	SCONJ
ejpam-4028	47	16	g̃	g̃	PROPN
ejpam-4028	47	17	satisfies	satisfy	VERB
ejpam-4028	47	18	the	the	DET
ejpam-4028	47	19	following	follow	VERB
ejpam-4028	47	20	conditions	condition	NOUN
ejpam-4028	47	21	:	:	PUNCT
ejpam-4028	47	22	(	(	PUNCT
ejpam-4028	47	23	fsg̃1	fsg̃1	NOUN
ejpam-4028	47	24	)	)	PUNCT
ejpam-4028	47	25	:	:	PUNCT
ejpam-4028	48	1	g̃(fe1	g̃(fe1	NUM
ejpam-4028	48	2	,	,	PUNCT
ejpam-4028	48	3	fe2	fe2	PROPN
ejpam-4028	48	4	,	,	PUNCT
ejpam-4028	48	5	fe3	fe3	PROPN
ejpam-4028	48	6	)	)	PUNCT
ejpam-4028	48	7	=	=	SYM
ejpam-4028	48	8	0̃	0̃	NOUN
ejpam-4028	48	9	if	if	SCONJ
ejpam-4028	48	10	fe1	fe1	PROPN
ejpam-4028	48	11	=	=	SYM
ejpam-4028	48	12	fe2	fe2	PROPN
ejpam-4028	48	13	=	=	PUNCT
ejpam-4028	48	14	fe3	fe3	PROPN
ejpam-4028	48	15	;	;	PUNCT
ejpam-4028	48	16	(	(	PUNCT
ejpam-4028	48	17	fsg̃2	fsg̃2	NOUN
ejpam-4028	48	18	)	)	PUNCT
ejpam-4028	48	19	:	:	PUNCT
ejpam-4028	48	20	0̃<̃g̃(fe1	0̃<̃g̃(fe1	NOUN
ejpam-4028	48	21	,	,	PUNCT
ejpam-4028	48	22	fe2	fe2	PROPN
ejpam-4028	48	23	,	,	PUNCT
ejpam-4028	48	24	fe3	fe3	PROPN
ejpam-4028	48	25	)	)	PUNCT
ejpam-4028	48	26	for	for	ADP
ejpam-4028	48	27	all	all	DET
ejpam-4028	48	28	fe1	fe1	PROPN
ejpam-4028	48	29	,	,	PUNCT
ejpam-4028	48	30	fe2∈̃fsc(ẽ	fe2∈̃fsc(ẽ	PROPN
ejpam-4028	48	31	)	)	PUNCT
ejpam-4028	48	32	with	with	ADP
ejpam-4028	48	33	fe1	fe1	PROPN
ejpam-4028	48	34	6=	6=	SYM
ejpam-4028	48	35	fe2	fe2	PROPN
ejpam-4028	48	36	;	;	PUNCT
ejpam-4028	48	37	(	(	PUNCT
ejpam-4028	48	38	fsg̃3	fsg̃3	NOUN
ejpam-4028	48	39	)	)	PUNCT
ejpam-4028	48	40	:	:	PUNCT
ejpam-4028	49	1	g̃(fe1	g̃(fe1	NUM
ejpam-4028	49	2	,	,	PUNCT
ejpam-4028	49	3	fe1	fe1	PROPN
ejpam-4028	49	4	,	,	PUNCT
ejpam-4028	49	5	fe2)≤̃g̃(fe1	fe2)≤̃g̃(fe1	PROPN
ejpam-4028	49	6	,	,	PUNCT
ejpam-4028	49	7	fe2	fe2	PROPN
ejpam-4028	49	8	,	,	PUNCT
ejpam-4028	49	9	fe3	fe3	PROPN
ejpam-4028	49	10	)	)	PUNCT
ejpam-4028	49	11	for	for	ADP
ejpam-4028	49	12	all	all	DET
ejpam-4028	49	13	fe1	fe1	PROPN
ejpam-4028	49	14	,	,	PUNCT
ejpam-4028	49	15	fe2	fe2	PROPN
ejpam-4028	49	16	,	,	PUNCT
ejpam-4028	49	17	fe3∈̃fsc(ẽ	fe3∈̃fsc(ẽ	PROPN
ejpam-4028	49	18	)	)	PUNCT
ejpam-4028	49	19	with	with	ADP
ejpam-4028	49	20	fe2	fe2	PROPN
ejpam-4028	49	21	6=	6=	PROPN
ejpam-4028	49	22	fe3	fe3	PROPN
ejpam-4028	49	23	;	;	PUNCT
ejpam-4028	49	24	a.	a.	PROPN
ejpam-4028	49	25	f.	f.	PROPN
ejpam-4028	49	26	sayed	sayed	PROPN
ejpam-4028	49	27	,	,	PUNCT
ejpam-4028	49	28	a.	a.	NOUN
ejpam-4028	49	29	alahmari	alahmari	PROPN
ejpam-4028	49	30	/	/	SYM
ejpam-4028	49	31	eur	eur	PROPN
ejpam-4028	49	32	.	.	PUNCT
ejpam-4028	50	1	j.	j.	PROPN
ejpam-4028	50	2	pure	pure	PROPN
ejpam-4028	50	3	appl	appl	PROPN
ejpam-4028	50	4	.	.	PROPN
ejpam-4028	50	5	math	math	PROPN
ejpam-4028	50	6	,	,	PUNCT
ejpam-4028	50	7	14	14	NUM
ejpam-4028	50	8	(	(	PUNCT
ejpam-4028	50	9	3	3	NUM
ejpam-4028	50	10	)	)	PUNCT
ejpam-4028	50	11	(	(	PUNCT
ejpam-4028	50	12	2021	2021	NUM
ejpam-4028	50	13	)	)	PUNCT
ejpam-4028	50	14	,	,	PUNCT
ejpam-4028	50	15	923	923	NUM
ejpam-4028	50	16	-	-	SYM
ejpam-4028	50	17	941	941	NUM
ejpam-4028	50	18	925	925	NUM
ejpam-4028	50	19	(	(	PUNCT
ejpam-4028	50	20	fsg̃4	fsg̃4	PROPN
ejpam-4028	50	21	)	)	PUNCT
ejpam-4028	50	22	:	:	PUNCT
ejpam-4028	51	1	g̃(fe1	g̃(fe1	NUM
ejpam-4028	51	2	,	,	PUNCT
ejpam-4028	51	3	fe2	fe2	PROPN
ejpam-4028	51	4	,	,	PUNCT
ejpam-4028	51	5	fe3	fe3	PROPN
ejpam-4028	51	6	)	)	PUNCT
ejpam-4028	51	7	=	=	SYM
ejpam-4028	52	1	g̃(fe1	g̃(fe1	PROPN
ejpam-4028	52	2	,	,	PUNCT
ejpam-4028	52	3	fe3	fe3	NOUN
ejpam-4028	52	4	,	,	PUNCT
ejpam-4028	52	5	fe2	fe2	PROPN
ejpam-4028	52	6	)	)	PUNCT
ejpam-4028	52	7	=	=	SYM
ejpam-4028	52	8	g̃(fe2	g̃(fe2	NOUN
ejpam-4028	52	9	,	,	PUNCT
ejpam-4028	52	10	fe3	fe3	PROPN
ejpam-4028	52	11	,	,	PUNCT
ejpam-4028	52	12	fe1	fe1	PROPN
ejpam-4028	52	13	)	)	PUNCT
ejpam-4028	52	14	=	=	SYM
ejpam-4028	52	15	...	...	PUNCT
ejpam-4028	52	16	;	;	PUNCT
ejpam-4028	52	17	(	(	PUNCT
ejpam-4028	52	18	fsg̃5	fsg̃5	NOUN
ejpam-4028	52	19	)	)	PUNCT
ejpam-4028	52	20	:	:	PUNCT
ejpam-4028	53	1	g̃(fe1	g̃(fe1	NUM
ejpam-4028	53	2	,	,	PUNCT
ejpam-4028	53	3	fe2	fe2	PROPN
ejpam-4028	53	4	,	,	PUNCT
ejpam-4028	53	5	fe3)≤̃g̃(fe1	fe3)≤̃g̃(fe1	PROPN
ejpam-4028	53	6	,	,	PUNCT
ejpam-4028	53	7	fe	fe	X
ejpam-4028	53	8	,	,	PUNCT
ejpam-4028	53	9	fe	fe	X
ejpam-4028	53	10	)	)	PUNCT
ejpam-4028	53	11	+	+	CCONJ
ejpam-4028	53	12	g̃(fe	g̃(fe	NOUN
ejpam-4028	53	13	,	,	PUNCT
ejpam-4028	53	14	fe2	fe2	PROPN
ejpam-4028	53	15	,	,	PUNCT
ejpam-4028	53	16	fe3	fe3	PROPN
ejpam-4028	53	17	)	)	PUNCT
ejpam-4028	53	18	for	for	ADP
ejpam-4028	53	19	all	all	DET
ejpam-4028	53	20	fe1	fe1	PROPN
ejpam-4028	53	21	,	,	PUNCT
ejpam-4028	53	22	fe2	fe2	PROPN
ejpam-4028	53	23	,	,	PUNCT
ejpam-4028	53	24	fe3	fe3	NOUN
ejpam-4028	53	25	,	,	PUNCT
ejpam-4028	53	26	fe∈̃fsc(ẽ	fe∈̃fsc(ẽ	PROPN
ejpam-4028	53	27	)	)	PUNCT
ejpam-4028	53	28	.	.	PUNCT
ejpam-4028	54	1	the	the	DET
ejpam-4028	54	2	fuzzy	fuzzy	ADJ
ejpam-4028	54	3	soft	soft	ADJ
ejpam-4028	54	4	set	set	VERB
ejpam-4028	54	5	ẽ	ẽ	PROPN
ejpam-4028	54	6	with	with	ADP
ejpam-4028	54	7	a	a	DET
ejpam-4028	54	8	fuzzy	fuzzy	ADJ
ejpam-4028	54	9	soft	soft	ADJ
ejpam-4028	54	10	g	g	NOUN
ejpam-4028	54	11	-	-	PUNCT
ejpam-4028	54	12	metric	metric	ADJ
ejpam-4028	54	13	g̃	g̃	PROPN
ejpam-4028	54	14	on	on	ADP
ejpam-4028	54	15	ẽ	ẽ	PROPN
ejpam-4028	54	16	is	be	AUX
ejpam-4028	54	17	said	say	VERB
ejpam-4028	54	18	to	to	PART
ejpam-4028	54	19	be	be	AUX
ejpam-4028	54	20	a	a	DET
ejpam-4028	54	21	fuzzy	fuzzy	ADJ
ejpam-4028	54	22	soft	soft	ADJ
ejpam-4028	54	23	g	g	NOUN
ejpam-4028	54	24	-	-	PUNCT
ejpam-4028	54	25	metric	metric	ADJ
ejpam-4028	54	26	space	space	NOUN
ejpam-4028	54	27	and	and	CCONJ
ejpam-4028	54	28	is	be	AUX
ejpam-4028	54	29	denoted	denote	VERB
ejpam-4028	54	30	by	by	ADP
ejpam-4028	54	31	(	(	PUNCT
ejpam-4028	54	32	ẽ	ẽ	PROPN
ejpam-4028	54	33	,	,	PUNCT
ejpam-4028	54	34	g̃	g̃	PROPN
ejpam-4028	54	35	)	)	PUNCT
ejpam-4028	54	36	.	.	PUNCT
ejpam-4028	55	1	definition	definition	NOUN
ejpam-4028	55	2	5	5	NUM
ejpam-4028	55	3	.	.	PUNCT
ejpam-4028	56	1	[	[	X
ejpam-4028	56	2	2	2	NUM
ejpam-4028	56	3	]	]	X
ejpam-4028	56	4	let	let	NOUN
ejpam-4028	56	5	(	(	PUNCT
ejpam-4028	56	6	ẽ	ẽ	NOUN
ejpam-4028	56	7	,	,	PUNCT
ejpam-4028	56	8	g̃	g̃	PROPN
ejpam-4028	56	9	)	)	PUNCT
ejpam-4028	56	10	be	be	VERB
ejpam-4028	56	11	a	a	DET
ejpam-4028	56	12	fuzzy	fuzzy	ADJ
ejpam-4028	56	13	soft	soft	ADJ
ejpam-4028	56	14	g	g	NOUN
ejpam-4028	56	15	-	-	PUNCT
ejpam-4028	56	16	metric	metric	ADJ
ejpam-4028	56	17	space	space	NOUN
ejpam-4028	56	18	and	and	CCONJ
ejpam-4028	56	19	{	{	PUNCT
ejpam-4028	56	20	fen	fen	PROPN
ejpam-4028	56	21	}	}	PUNCT
ejpam-4028	56	22	a	a	DET
ejpam-4028	56	23	sequence	sequence	NOUN
ejpam-4028	56	24	of	of	ADP
ejpam-4028	56	25	fuzzy	fuzzy	ADJ
ejpam-4028	56	26	soft	soft	ADJ
ejpam-4028	56	27	elements	element	NOUN
ejpam-4028	56	28	in	in	ADP
ejpam-4028	56	29	ẽ.	ẽ.	PROPN
ejpam-4028	56	30	the	the	DET
ejpam-4028	56	31	sequence	sequence	NOUN
ejpam-4028	56	32	{	{	PUNCT
ejpam-4028	56	33	fen	fen	PROPN
ejpam-4028	56	34	}	}	PUNCT
ejpam-4028	56	35	is	be	AUX
ejpam-4028	56	36	said	say	VERB
ejpam-4028	56	37	to	to	PART
ejpam-4028	56	38	be	be	AUX
ejpam-4028	56	39	fuzzy	fuzzy	ADJ
ejpam-4028	56	40	soft	soft	ADJ
ejpam-4028	56	41	g	g	NOUN
ejpam-4028	56	42	-	-	PUNCT
ejpam-4028	56	43	convergent	convergent	NOUN
ejpam-4028	56	44	to	to	ADP
ejpam-4028	56	45	fe	fe	NOUN
ejpam-4028	56	46	in	in	ADP
ejpam-4028	56	47	ẽ	ẽ	PROPN
ejpam-4028	56	48	if	if	SCONJ
ejpam-4028	56	49	for	for	ADP
ejpam-4028	56	50	every	every	DET
ejpam-4028	56	51	ε̃≥̃0̃	ε̃≥̃0̃	NOUN
ejpam-4028	56	52	,	,	PUNCT
ejpam-4028	56	53	chosen	choose	VERB
ejpam-4028	56	54	arbitrary	arbitrary	ADJ
ejpam-4028	56	55	,	,	PUNCT
ejpam-4028	56	56	there	there	PRON
ejpam-4028	56	57	exists	exist	VERB
ejpam-4028	56	58	a	a	DET
ejpam-4028	56	59	natural	natural	ADJ
ejpam-4028	56	60	number	number	NOUN
ejpam-4028	56	61	n	n	ADP
ejpam-4028	56	62	=	=	SYM
ejpam-4028	56	63	n(ε̃	n(ε̃	NOUN
ejpam-4028	56	64	)	)	PUNCT
ejpam-4028	56	65	such	such	ADJ
ejpam-4028	56	66	that	that	PRON
ejpam-4028	56	67	0̃≤̃g̃(fen	0̃≤̃g̃(fen	PROPN
ejpam-4028	56	68	,	,	PUNCT
ejpam-4028	56	69	fen	fen	PROPN
ejpam-4028	56	70	,	,	PUNCT
ejpam-4028	56	71	fe)<̃ε̃	fe)<̃ε̃	VERB
ejpam-4028	56	72	whenever	whenever	SCONJ
ejpam-4028	56	73	n	n	PRON
ejpam-4028	56	74	≥	≥	NOUN
ejpam-4028	56	75	n	n	CCONJ
ejpam-4028	56	76	i.e	i.e	PROPN
ejpam-4028	56	77	n	n	CCONJ
ejpam-4028	56	78	≥	≥	NOUN
ejpam-4028	56	79	n	n	PRON
ejpam-4028	56	80	⇒	⇒	NOUN
ejpam-4028	56	81	{	{	PUNCT
ejpam-4028	56	82	fen}∈̃	fen}∈̃	NOUN
ejpam-4028	56	83	˜̃b(fe	˜̃b(fe	NOUN
ejpam-4028	56	84	,	,	PUNCT
ejpam-4028	56	85	˜̃t	˜̃t	NOUN
ejpam-4028	56	86	,	,	PUNCT
ejpam-4028	56	87	ε̃	ε̃	PROPN
ejpam-4028	56	88	)	)	PUNCT
ejpam-4028	56	89	.	.	PUNCT
ejpam-4028	57	1	we	we	PRON
ejpam-4028	57	2	denote	denote	VERB
ejpam-4028	57	3	this	this	PRON
ejpam-4028	57	4	by	by	ADP
ejpam-4028	57	5	fen	fen	PROPN
ejpam-4028	57	6	→	→	SYM
ejpam-4028	57	7	fe	fe	PROPN
ejpam-4028	57	8	as	as	ADP
ejpam-4028	57	9	n→∞	n→∞	NUM
ejpam-4028	57	10	or	or	CCONJ
ejpam-4028	57	11	limn→∞{fen	limn→∞{fen	PROPN
ejpam-4028	57	12	}	}	PUNCT
ejpam-4028	57	13	=	=	SYM
ejpam-4028	57	14	fe	fe	X
ejpam-4028	57	15	.	.	PROPN
ejpam-4028	57	16	definition	definition	NOUN
ejpam-4028	57	17	6	6	NUM
ejpam-4028	57	18	.	.	PUNCT
ejpam-4028	58	1	[	[	X
ejpam-4028	58	2	2	2	NUM
ejpam-4028	58	3	]	]	X
ejpam-4028	58	4	let	let	NOUN
ejpam-4028	58	5	(	(	PUNCT
ejpam-4028	58	6	ẽ	ẽ	NOUN
ejpam-4028	58	7	,	,	PUNCT
ejpam-4028	58	8	g̃	g̃	PROPN
ejpam-4028	58	9	)	)	PUNCT
ejpam-4028	58	10	be	be	VERB
ejpam-4028	58	11	a	a	DET
ejpam-4028	58	12	fuzzy	fuzzy	ADJ
ejpam-4028	58	13	soft	soft	ADJ
ejpam-4028	58	14	g	g	NOUN
ejpam-4028	58	15	-	-	PUNCT
ejpam-4028	58	16	metric	metric	ADJ
ejpam-4028	58	17	space	space	NOUN
ejpam-4028	58	18	and	and	CCONJ
ejpam-4028	58	19	{	{	PUNCT
ejpam-4028	58	20	fen	fen	PROPN
ejpam-4028	58	21	}	}	PUNCT
ejpam-4028	58	22	be	be	VERB
ejpam-4028	58	23	sequence	sequence	NOUN
ejpam-4028	58	24	of	of	ADP
ejpam-4028	58	25	fuzzy	fuzzy	ADJ
ejpam-4028	58	26	soft	soft	ADJ
ejpam-4028	58	27	elements	element	NOUN
ejpam-4028	58	28	in	in	ADP
ejpam-4028	58	29	ẽ.	ẽ.	PROPN
ejpam-4028	58	30	then	then	ADV
ejpam-4028	58	31	the	the	DET
ejpam-4028	58	32	sequence	sequence	NOUN
ejpam-4028	58	33	{	{	PUNCT
ejpam-4028	58	34	fen	fen	PROPN
ejpam-4028	58	35	}	}	PUNCT
ejpam-4028	58	36	is	be	AUX
ejpam-4028	58	37	said	say	VERB
ejpam-4028	58	38	to	to	PART
ejpam-4028	58	39	be	be	AUX
ejpam-4028	58	40	fuzzy	fuzzy	ADJ
ejpam-4028	58	41	soft	soft	ADJ
ejpam-4028	58	42	g	g	NOUN
ejpam-4028	58	43	-	-	PUNCT
ejpam-4028	58	44	cauchy	cauchy	NOUN
ejpam-4028	58	45	if	if	SCONJ
ejpam-4028	58	46	for	for	ADP
ejpam-4028	58	47	every	every	DET
ejpam-4028	58	48	ε̃≥̃0̃	ε̃≥̃0̃	NOUN
ejpam-4028	58	49	,	,	PUNCT
ejpam-4028	58	50	there	there	PRON
ejpam-4028	58	51	exist	exist	VERB
ejpam-4028	58	52	δ̃>̃0̃	δ̃>̃0̃	NUM
ejpam-4028	58	53	and	and	CCONJ
ejpam-4028	58	54	a	a	DET
ejpam-4028	58	55	positive	positive	ADJ
ejpam-4028	58	56	integer	integer	NOUN
ejpam-4028	58	57	n	n	PROPN
ejpam-4028	58	58	=	=	SYM
ejpam-4028	58	59	n(ε̃	n(ε̃	PROPN
ejpam-4028	58	60	)	)	PUNCT
ejpam-4028	58	61	such	such	ADJ
ejpam-4028	58	62	that	that	DET
ejpam-4028	58	63	g̃(fen	g̃(fen	PROPN
ejpam-4028	58	64	,	,	PUNCT
ejpam-4028	58	65	fem	fem	NOUN
ejpam-4028	58	66	,	,	PUNCT
ejpam-4028	58	67	fel)<̃ε̃	fel)<̃ε̃	INTJ
ejpam-4028	58	68	for	for	ADP
ejpam-4028	58	69	all	all	DET
ejpam-4028	58	70	n	n	CCONJ
ejpam-4028	58	71	,	,	PUNCT
ejpam-4028	58	72	m	m	PROPN
ejpam-4028	58	73	,	,	PUNCT
ejpam-4028	58	74	l	l	PROPN
ejpam-4028	58	75	≥	≥	NOUN
ejpam-4028	58	76	n	n	NOUN
ejpam-4028	58	77	;	;	PUNCT
ejpam-4028	58	78	that	that	PRON
ejpam-4028	58	79	is	be	AUX
ejpam-4028	58	80	g̃(fen	g̃(fen	PROPN
ejpam-4028	58	81	,	,	PUNCT
ejpam-4028	58	82	fem	fem	NOUN
ejpam-4028	58	83	,	,	PUNCT
ejpam-4028	58	84	fel)→	fel)→	VERB
ejpam-4028	58	85	0̃	0̃	NOUN
ejpam-4028	58	86	as	as	ADP
ejpam-4028	58	87	n	n	NUM
ejpam-4028	58	88	,	,	PUNCT
ejpam-4028	58	89	m	m	PROPN
ejpam-4028	58	90	,	,	PUNCT
ejpam-4028	58	91	l→∞.	l→∞.	ADJ
ejpam-4028	58	92	definition	definition	NOUN
ejpam-4028	58	93	7	7	NUM
ejpam-4028	58	94	.	.	PUNCT
ejpam-4028	59	1	[	[	X
ejpam-4028	59	2	2	2	X
ejpam-4028	59	3	]	]	PUNCT
ejpam-4028	59	4	a	a	DET
ejpam-4028	59	5	fuzzy	fuzzy	ADJ
ejpam-4028	59	6	soft	soft	ADJ
ejpam-4028	59	7	g	g	NOUN
ejpam-4028	59	8	-	-	PUNCT
ejpam-4028	59	9	metric	metric	ADJ
ejpam-4028	59	10	space	space	NOUN
ejpam-4028	59	11	(	(	PUNCT
ejpam-4028	59	12	ẽ	ẽ	PROPN
ejpam-4028	59	13	,	,	PUNCT
ejpam-4028	59	14	g̃	g̃	PROPN
ejpam-4028	59	15	)	)	PUNCT
ejpam-4028	59	16	is	be	AUX
ejpam-4028	59	17	said	say	VERB
ejpam-4028	59	18	to	to	PART
ejpam-4028	59	19	be	be	AUX
ejpam-4028	59	20	fuzzy	fuzzy	ADJ
ejpam-4028	59	21	soft	soft	ADJ
ejpam-4028	59	22	g	g	NOUN
ejpam-4028	59	23	-	-	PUNCT
ejpam-4028	59	24	complete	complete	ADJ
ejpam-4028	59	25	if	if	SCONJ
ejpam-4028	59	26	every	every	DET
ejpam-4028	59	27	fuzzy	fuzzy	ADJ
ejpam-4028	59	28	soft	soft	ADJ
ejpam-4028	59	29	g	g	NOUN
ejpam-4028	59	30	-	-	PUNCT
ejpam-4028	59	31	cauchy	cauchy	ADJ
ejpam-4028	59	32	sequence	sequence	NOUN
ejpam-4028	59	33	in	in	ADP
ejpam-4028	59	34	(	(	PUNCT
ejpam-4028	59	35	ẽ	ẽ	PROPN
ejpam-4028	59	36	,	,	PUNCT
ejpam-4028	59	37	g̃	g̃	PROPN
ejpam-4028	59	38	)	)	PUNCT
ejpam-4028	59	39	is	be	AUX
ejpam-4028	59	40	fuzzy	fuzzy	ADJ
ejpam-4028	59	41	soft	soft	ADJ
ejpam-4028	59	42	g	g	NOUN
ejpam-4028	59	43	-	-	PUNCT
ejpam-4028	59	44	convergent	convergent	NOUN
ejpam-4028	59	45	in	in	ADP
ejpam-4028	59	46	(	(	PUNCT
ejpam-4028	59	47	ẽ	ẽ	PROPN
ejpam-4028	59	48	,	,	PUNCT
ejpam-4028	59	49	g̃	g̃	PROPN
ejpam-4028	59	50	)	)	PUNCT
ejpam-4028	59	51	.	.	PUNCT
ejpam-4028	60	1	definition	definition	NOUN
ejpam-4028	60	2	8	8	NUM
ejpam-4028	60	3	.	.	PUNCT
ejpam-4028	61	1	[	[	X
ejpam-4028	61	2	2	2	NUM
ejpam-4028	61	3	]	]	X
ejpam-4028	61	4	let	let	NOUN
ejpam-4028	61	5	(	(	PUNCT
ejpam-4028	61	6	ẽ	ẽ	NOUN
ejpam-4028	61	7	,	,	PUNCT
ejpam-4028	61	8	g̃	g̃	PROPN
ejpam-4028	61	9	)	)	PUNCT
ejpam-4028	61	10	,	,	PUNCT
ejpam-4028	61	11	(	(	PUNCT
ejpam-4028	61	12	˜́	˜́	PROPN
ejpam-4028	61	13	e	e	NOUN
ejpam-4028	61	14	,	,	PUNCT
ejpam-4028	61	15	˜́	˜́	PROPN
ejpam-4028	61	16	g	g	NOUN
ejpam-4028	61	17	)	)	PUNCT
ejpam-4028	61	18	be	be	AUX
ejpam-4028	61	19	two	two	NUM
ejpam-4028	61	20	fuzzy	fuzzy	ADJ
ejpam-4028	61	21	soft	soft	ADJ
ejpam-4028	61	22	g	g	NOUN
ejpam-4028	61	23	-	-	PUNCT
ejpam-4028	61	24	metric	metric	ADJ
ejpam-4028	61	25	spaces	space	NOUN
ejpam-4028	61	26	.	.	PUNCT
ejpam-4028	62	1	then	then	ADV
ejpam-4028	62	2	a	a	DET
ejpam-4028	62	3	function	function	NOUN
ejpam-4028	62	4	t	t	NOUN
ejpam-4028	62	5	:	:	PUNCT
ejpam-4028	62	6	ẽ	ẽ	PROPN
ejpam-4028	62	7	→	→	SYM
ejpam-4028	62	8	˜́	˜́	NOUN
ejpam-4028	62	9	e	e	NOUN
ejpam-4028	62	10	is	be	AUX
ejpam-4028	62	11	fuzzy	fuzzy	ADJ
ejpam-4028	62	12	soft	soft	ADJ
ejpam-4028	62	13	g	g	NOUN
ejpam-4028	62	14	-	-	NOUN
ejpam-4028	62	15	continuous	continuous	ADJ
ejpam-4028	62	16	at	at	ADP
ejpam-4028	62	17	a	a	DET
ejpam-4028	62	18	fuzzy	fuzzy	ADJ
ejpam-4028	62	19	soft	soft	ADJ
ejpam-4028	62	20	element	element	NOUN
ejpam-4028	62	21	fe∈̃fsc(ẽ	fe∈̃fsc(ẽ	PROPN
ejpam-4028	62	22	)	)	PUNCT
ejpam-4028	62	23	if	if	SCONJ
ejpam-4028	62	24	and	and	CCONJ
ejpam-4028	62	25	only	only	ADV
ejpam-4028	62	26	if	if	SCONJ
ejpam-4028	62	27	for	for	ADP
ejpam-4028	62	28	every	every	DET
ejpam-4028	62	29	ε̃>̃0̃	ε̃>̃0̃	NOUN
ejpam-4028	62	30	,	,	PUNCT
ejpam-4028	62	31	there	there	PRON
ejpam-4028	62	32	exists	exist	VERB
ejpam-4028	62	33	δ̃≥̃0̃	δ̃≥̃0̃	VERB
ejpam-4028	62	34	such	such	ADJ
ejpam-4028	62	35	that	that	SCONJ
ejpam-4028	62	36	fe1	fe1	PROPN
ejpam-4028	62	37	,	,	PUNCT
ejpam-4028	62	38	fe2∈̃fsc(ẽ	fe2∈̃fsc(ẽ	PROPN
ejpam-4028	62	39	)	)	PUNCT
ejpam-4028	62	40	and	and	CCONJ
ejpam-4028	62	41	g̃(fe	g̃(fe	NOUN
ejpam-4028	62	42	,	,	PUNCT
ejpam-4028	62	43	fe1	fe1	PROPN
ejpam-4028	62	44	,	,	PUNCT
ejpam-4028	62	45	fe2)<̃δ̃	fe2)<̃δ̃	PROPN
ejpam-4028	62	46	implies	imply	VERB
ejpam-4028	62	47	that	that	SCONJ
ejpam-4028	62	48	˜́	˜́	PROPN
ejpam-4028	62	49	g(tfe	g(tfe	PROPN
ejpam-4028	62	50	,	,	PUNCT
ejpam-4028	62	51	t	t	PROPN
ejpam-4028	62	52	fe1	fe1	PROPN
ejpam-4028	62	53	,	,	PUNCT
ejpam-4028	62	54	t	t	PROPN
ejpam-4028	62	55	fe2)<̃ε̃.	fe2)<̃ε̃.	VERB
ejpam-4028	62	56	a	a	DET
ejpam-4028	62	57	function	function	NOUN
ejpam-4028	62	58	t	t	NOUN
ejpam-4028	62	59	is	be	AUX
ejpam-4028	62	60	fuzzy	fuzzy	ADJ
ejpam-4028	62	61	soft	soft	ADJ
ejpam-4028	62	62	g	g	NOUN
ejpam-4028	62	63	-	-	PUNCT
ejpam-4028	62	64	continuous	continuous	ADJ
ejpam-4028	62	65	if	if	SCONJ
ejpam-4028	62	66	and	and	CCONJ
ejpam-4028	62	67	only	only	ADV
ejpam-4028	62	68	if	if	SCONJ
ejpam-4028	62	69	it	it	PRON
ejpam-4028	62	70	is	be	AUX
ejpam-4028	62	71	fuzzy	fuzzy	ADJ
ejpam-4028	62	72	soft	soft	ADJ
ejpam-4028	62	73	g	g	NOUN
ejpam-4028	62	74	-	-	NOUN
ejpam-4028	62	75	continuous	continuous	ADJ
ejpam-4028	62	76	at	at	ADP
ejpam-4028	62	77	all	all	ADV
ejpam-4028	62	78	fuzzy	fuzzy	ADJ
ejpam-4028	62	79	soft	soft	ADJ
ejpam-4028	62	80	elements	element	NOUN
ejpam-4028	62	81	fe∈̃fsc(ẽ	fe∈̃fsc(ẽ	PROPN
ejpam-4028	62	82	)	)	PUNCT
ejpam-4028	62	83	3	3	NUM
ejpam-4028	62	84	.	.	X
ejpam-4028	62	85	main	main	ADJ
ejpam-4028	62	86	results	result	NOUN
ejpam-4028	62	87	we	we	PRON
ejpam-4028	62	88	start	start	VERB
ejpam-4028	62	89	our	our	PRON
ejpam-4028	62	90	main	main	ADJ
ejpam-4028	62	91	results	result	NOUN
ejpam-4028	62	92	in	in	ADP
ejpam-4028	62	93	this	this	DET
ejpam-4028	62	94	paper	paper	NOUN
ejpam-4028	62	95	with	with	ADP
ejpam-4028	62	96	the	the	DET
ejpam-4028	62	97	following	follow	VERB
ejpam-4028	62	98	theorem	theorem	NOUN
ejpam-4028	62	99	(	(	PUNCT
ejpam-4028	62	100	theorem	theorem	VERB
ejpam-4028	62	101	4.2	4.2	NUM
ejpam-4028	62	102	in	in	ADP
ejpam-4028	62	103	[	[	PUNCT
ejpam-4028	62	104	2	2	NUM
ejpam-4028	62	105	]	]	PUNCT
ejpam-4028	62	106	)	)	PUNCT
ejpam-4028	62	107	theorem	theorem	NOUN
ejpam-4028	62	108	1	1	NUM
ejpam-4028	62	109	.	.	PUNCT
ejpam-4028	63	1	let	let	VERB
ejpam-4028	63	2	(	(	PUNCT
ejpam-4028	63	3	ẽ	ẽ	NOUN
ejpam-4028	63	4	,	,	PUNCT
ejpam-4028	63	5	g̃	g̃	PROPN
ejpam-4028	63	6	)	)	PUNCT
ejpam-4028	63	7	be	be	VERB
ejpam-4028	63	8	a	a	DET
ejpam-4028	63	9	fuzzy	fuzzy	ADJ
ejpam-4028	63	10	soft	soft	ADJ
ejpam-4028	63	11	g	g	NOUN
ejpam-4028	63	12	-	-	PUNCT
ejpam-4028	63	13	complete	complete	ADJ
ejpam-4028	63	14	and	and	CCONJ
ejpam-4028	63	15	t	t	NOUN
ejpam-4028	63	16	:	:	PUNCT
ejpam-4028	63	17	(	(	PUNCT
ejpam-4028	63	18	ẽ	ẽ	NOUN
ejpam-4028	63	19	,	,	PUNCT
ejpam-4028	63	20	g̃)→	g̃)→	PRON
ejpam-4028	63	21	(	(	PUNCT
ejpam-4028	63	22	ẽ	ẽ	PROPN
ejpam-4028	63	23	,	,	PUNCT
ejpam-4028	63	24	g̃	g̃	PROPN
ejpam-4028	63	25	)	)	PUNCT
ejpam-4028	63	26	be	be	VERB
ejpam-4028	63	27	a	a	DET
ejpam-4028	63	28	mapping	mapping	NOUN
ejpam-4028	63	29	that	that	PRON
ejpam-4028	63	30	satisfies	satisfy	VERB
ejpam-4028	63	31	the	the	DET
ejpam-4028	63	32	following	follow	VERB
ejpam-4028	63	33	condition	condition	NOUN
ejpam-4028	63	34	for	for	ADP
ejpam-4028	63	35	all	all	DET
ejpam-4028	63	36	fe1	fe1	PROPN
ejpam-4028	63	37	,	,	PUNCT
ejpam-4028	63	38	fe2	fe2	PROPN
ejpam-4028	63	39	,	,	PUNCT
ejpam-4028	63	40	fe3∈̃fsc(ẽ	fe3∈̃fsc(ẽ	PROPN
ejpam-4028	63	41	)	)	PUNCT
ejpam-4028	63	42	,	,	PUNCT
ejpam-4028	63	43	g̃(tfe1	g̃(tfe1	PROPN
ejpam-4028	63	44	,	,	PUNCT
ejpam-4028	63	45	tfe2	tfe2	NOUN
ejpam-4028	63	46	,	,	PUNCT
ejpam-4028	63	47	tfe3)≤̃¯̄ag̃(fe1	tfe3)≤̃¯̄ag̃(fe1	PROPN
ejpam-4028	63	48	,	,	PUNCT
ejpam-4028	63	49	tfe1	tfe1	NOUN
ejpam-4028	63	50	,	,	PUNCT
ejpam-4028	63	51	tfe1	tfe1	PROPN
ejpam-4028	63	52	)	)	PUNCT
ejpam-4028	64	1	+	+	CCONJ
ejpam-4028	64	2	¯̄bg̃(fe2	¯̄bg̃(fe2	NOUN
ejpam-4028	64	3	,	,	PUNCT
ejpam-4028	64	4	tfe2	tfe2	NOUN
ejpam-4028	64	5	,	,	PUNCT
ejpam-4028	64	6	tfe2)+	tfe2)+	X
ejpam-4028	64	7	¯̄cg̃(fe3	¯̄cg̃(fe3	PROPN
ejpam-4028	64	8	,	,	PUNCT
ejpam-4028	64	9	t	t	PROPN
ejpam-4028	64	10	fe3	fe3	PROPN
ejpam-4028	64	11	,	,	PUNCT
ejpam-4028	64	12	tfe3	tfe3	PROPN
ejpam-4028	64	13	)	)	PUNCT
ejpam-4028	65	1	+	+	CCONJ
ejpam-4028	65	2	¯̄dg̃(fe1	¯̄dg̃(fe1	PROPN
ejpam-4028	65	3	,	,	PUNCT
ejpam-4028	65	4	fe2	fe2	PROPN
ejpam-4028	65	5	,	,	PUNCT
ejpam-4028	65	6	fe3	fe3	PROPN
ejpam-4028	65	7	)	)	PUNCT
ejpam-4028	65	8	,	,	PUNCT
ejpam-4028	65	9	(	(	PUNCT
ejpam-4028	65	10	1	1	X
ejpam-4028	65	11	)	)	PUNCT
ejpam-4028	65	12	where	where	SCONJ
ejpam-4028	65	13	0̃≤̃¯̄a+	0̃≤̃¯̄a+	NOUN
ejpam-4028	65	14	¯̄b+	¯̄b+	PRON
ejpam-4028	65	15	¯̄c+	¯̄c+	VERB
ejpam-4028	65	16	¯̄d<̃1̃.	¯̄d<̃1̃.	PROPN
ejpam-4028	65	17	then	then	ADV
ejpam-4028	65	18	t	t	PROPN
ejpam-4028	65	19	has	have	VERB
ejpam-4028	65	20	a	a	DET
ejpam-4028	65	21	unique	unique	ADJ
ejpam-4028	65	22	fixed	fix	VERB
ejpam-4028	65	23	point	point	NOUN
ejpam-4028	65	24	,	,	PUNCT
ejpam-4028	65	25	say	say	VERB
ejpam-4028	65	26	fe	fe	INTJ
ejpam-4028	65	27	,	,	PUNCT
ejpam-4028	65	28	and	and	CCONJ
ejpam-4028	65	29	t	t	PROPN
ejpam-4028	65	30	is	be	AUX
ejpam-4028	65	31	a	a	DET
ejpam-4028	65	32	fuzzy	fuzzy	ADJ
ejpam-4028	65	33	soft	soft	ADJ
ejpam-4028	65	34	g	g	NOUN
ejpam-4028	65	35	-	-	NOUN
ejpam-4028	65	36	continuous	continuous	ADJ
ejpam-4028	65	37	at	at	ADP
ejpam-4028	65	38	fe	fe	NOUN
ejpam-4028	65	39	.	.	PUNCT
ejpam-4028	66	1	we	we	PRON
ejpam-4028	66	2	will	will	AUX
ejpam-4028	66	3	show	show	VERB
ejpam-4028	66	4	that	that	SCONJ
ejpam-4028	66	5	this	this	PRON
ejpam-4028	66	6	theorem	theorem	VERB
ejpam-4028	66	7	fails	fail	VERB
ejpam-4028	66	8	to	to	PART
ejpam-4028	66	9	verify	verify	VERB
ejpam-4028	66	10	if	if	SCONJ
ejpam-4028	66	11	the	the	DET
ejpam-4028	66	12	set	set	NOUN
ejpam-4028	66	13	of	of	ADP
ejpam-4028	66	14	parameter	parameter	NOUN
ejpam-4028	66	15	is	be	AUX
ejpam-4028	66	16	not	not	PART
ejpam-4028	66	17	finite	finite	ADJ
ejpam-4028	66	18	.	.	PUNCT
ejpam-4028	67	1	for	for	ADP
ejpam-4028	67	2	this	this	PRON
ejpam-4028	67	3	,	,	PUNCT
ejpam-4028	67	4	we	we	PRON
ejpam-4028	67	5	will	will	AUX
ejpam-4028	67	6	provide	provide	VERB
ejpam-4028	67	7	the	the	DET
ejpam-4028	67	8	following	follow	VERB
ejpam-4028	67	9	two	two	NUM
ejpam-4028	67	10	examples	example	NOUN
ejpam-4028	67	11	:	:	PUNCT
ejpam-4028	67	12	a.	a.	PROPN
ejpam-4028	67	13	f.	f.	PROPN
ejpam-4028	67	14	sayed	sayed	PROPN
ejpam-4028	67	15	,	,	PUNCT
ejpam-4028	67	16	a.	a.	NOUN
ejpam-4028	67	17	alahmari	alahmari	PROPN
ejpam-4028	67	18	/	/	SYM
ejpam-4028	67	19	eur	eur	PROPN
ejpam-4028	67	20	.	.	PUNCT
ejpam-4028	68	1	j.	j.	PROPN
ejpam-4028	68	2	pure	pure	PROPN
ejpam-4028	68	3	appl	appl	PROPN
ejpam-4028	68	4	.	.	PROPN
ejpam-4028	68	5	math	math	PROPN
ejpam-4028	68	6	,	,	PUNCT
ejpam-4028	68	7	14	14	NUM
ejpam-4028	68	8	(	(	PUNCT
ejpam-4028	68	9	3	3	NUM
ejpam-4028	68	10	)	)	PUNCT
ejpam-4028	68	11	(	(	PUNCT
ejpam-4028	68	12	2021	2021	NUM
ejpam-4028	68	13	)	)	PUNCT
ejpam-4028	68	14	,	,	PUNCT
ejpam-4028	68	15	923	923	NUM
ejpam-4028	68	16	-	-	SYM
ejpam-4028	68	17	941	941	NUM
ejpam-4028	68	18	926	926	NUM
ejpam-4028	68	19	example	example	NOUN
ejpam-4028	68	20	1	1	NUM
ejpam-4028	68	21	.	.	PUNCT
ejpam-4028	69	1	let	let	VERB
ejpam-4028	69	2	x	x	PUNCT
ejpam-4028	69	3	=	=	PUNCT
ejpam-4028	69	4	e	e	NOUN
ejpam-4028	69	5	=	=	PRON
ejpam-4028	69	6	{	{	PUNCT
ejpam-4028	69	7	1	1	NUM
ejpam-4028	69	8	n	n	NOUN
ejpam-4028	69	9	:	:	PUNCT
ejpam-4028	69	10	n	n	CCONJ
ejpam-4028	69	11	∈	∈	PROPN
ejpam-4028	69	12	n	n	CCONJ
ejpam-4028	69	13	}	}	PUNCT
ejpam-4028	69	14	.	.	PUNCT
ejpam-4028	70	1	consider	consider	VERB
ejpam-4028	70	2	the	the	DET
ejpam-4028	70	3	fuzzy	fuzzy	ADJ
ejpam-4028	70	4	soft	soft	ADJ
ejpam-4028	70	5	g	g	NOUN
ejpam-4028	70	6	-	-	PUNCT
ejpam-4028	70	7	metric	metric	ADJ
ejpam-4028	70	8	space	space	NOUN
ejpam-4028	70	9	(	(	PUNCT
ejpam-4028	70	10	ẽ	ẽ	NOUN
ejpam-4028	70	11	,	,	PUNCT
ejpam-4028	70	12	g̃	g̃	PROPN
ejpam-4028	70	13	)	)	PUNCT
ejpam-4028	70	14	,	,	PUNCT
ejpam-4028	70	15	where	where	SCONJ
ejpam-4028	70	16	g̃(fe1	g̃(fe1	PROPN
ejpam-4028	70	17	,	,	PUNCT
ejpam-4028	70	18	fe2	fe2	PROPN
ejpam-4028	70	19	,	,	PUNCT
ejpam-4028	70	20	fe3	fe3	PROPN
ejpam-4028	70	21	)	)	PUNCT
ejpam-4028	70	22	=	=	PUNCT
ejpam-4028	71	1	˜̃1	˜̃1	NOUN
ejpam-4028	71	2	3	3	NUM
ejpam-4028	71	3	{	{	PUNCT
ejpam-4028	71	4	|fe1	|fe1	PROPN
ejpam-4028	71	5	−	−	PROPN
ejpam-4028	71	6	fe2	fe2	PROPN
ejpam-4028	71	7	|+	|+	X
ejpam-4028	71	8	|fe2	|fe2	NOUN
ejpam-4028	71	9	−	−	PROPN
ejpam-4028	71	10	fe3	fe3	NOUN
ejpam-4028	71	11	|+	|+	NOUN
ejpam-4028	72	1	|fe1	|fe1	CCONJ
ejpam-4028	72	2	−	−	PROPN
ejpam-4028	72	3	fe3	fe3	NOUN
ejpam-4028	72	4	|	|	NOUN
ejpam-4028	72	5	}	}	PUNCT
ejpam-4028	72	6	,	,	PUNCT
ejpam-4028	72	7	∀fe1	∀fe1	PROPN
ejpam-4028	72	8	,	,	PUNCT
ejpam-4028	72	9	fe2	fe2	PROPN
ejpam-4028	72	10	,	,	PUNCT
ejpam-4028	72	11	fe3∈̃fsc(ẽ	fe3∈̃fsc(ẽ	PROPN
ejpam-4028	72	12	)	)	PUNCT
ejpam-4028	72	13	.	.	PUNCT
ejpam-4028	73	1	note	note	VERB
ejpam-4028	73	2	that	that	SCONJ
ejpam-4028	73	3	,	,	PUNCT
ejpam-4028	73	4	(	(	PUNCT
ejpam-4028	73	5	ẽ	ẽ	PROPN
ejpam-4028	73	6	,	,	PUNCT
ejpam-4028	73	7	g̃	g̃	PROPN
ejpam-4028	73	8	)	)	PUNCT
ejpam-4028	73	9	is	be	AUX
ejpam-4028	73	10	a	a	DET
ejpam-4028	73	11	symmetric	symmetric	ADJ
ejpam-4028	73	12	fuzzy	fuzzy	ADJ
ejpam-4028	73	13	soft	soft	ADJ
ejpam-4028	73	14	g	g	NOUN
ejpam-4028	73	15	-	-	PUNCT
ejpam-4028	73	16	metric(proposition	metric(proposition	NOUN
ejpam-4028	73	17	3.3	3.3	NUM
ejpam-4028	73	18	,	,	PUNCT
ejpam-4028	73	19	[	[	X
ejpam-4028	73	20	2	2	NUM
ejpam-4028	73	21	]	]	NUM
ejpam-4028	73	22	)	)	PUNCT
ejpam-4028	73	23	.	.	PUNCT
ejpam-4028	74	1	now	now	ADV
ejpam-4028	74	2	,	,	PUNCT
ejpam-4028	74	3	we	we	PRON
ejpam-4028	74	4	show	show	VERB
ejpam-4028	74	5	that	that	SCONJ
ejpam-4028	74	6	(	(	PUNCT
ejpam-4028	74	7	ẽ	ẽ	PROPN
ejpam-4028	74	8	,	,	PUNCT
ejpam-4028	74	9	g̃	g̃	PROPN
ejpam-4028	74	10	)	)	PUNCT
ejpam-4028	74	11	is	be	AUX
ejpam-4028	74	12	fuzzy	fuzzy	ADJ
ejpam-4028	74	13	soft	soft	ADJ
ejpam-4028	74	14	g	g	NOUN
ejpam-4028	74	15	-	-	PUNCT
ejpam-4028	74	16	complete	complete	ADJ
ejpam-4028	74	17	.	.	PUNCT
ejpam-4028	75	1	for	for	ADP
ejpam-4028	75	2	this	this	PRON
ejpam-4028	75	3	,	,	PUNCT
ejpam-4028	75	4	suppose	suppose	VERB
ejpam-4028	75	5	that	that	SCONJ
ejpam-4028	75	6	{	{	PUNCT
ejpam-4028	75	7	fen}n∈n	fen}n∈n	VERB
ejpam-4028	75	8	is	be	AUX
ejpam-4028	75	9	a	a	DET
ejpam-4028	75	10	fuzzy	fuzzy	ADJ
ejpam-4028	75	11	soft	soft	ADJ
ejpam-4028	75	12	g	g	NOUN
ejpam-4028	75	13	-	-	PUNCT
ejpam-4028	75	14	cauchy	cauchy	ADJ
ejpam-4028	75	15	sequence	sequence	NOUN
ejpam-4028	75	16	of	of	ADP
ejpam-4028	75	17	fuzzy	fuzzy	ADJ
ejpam-4028	75	18	soft	soft	ADJ
ejpam-4028	75	19	elements	element	NOUN
ejpam-4028	75	20	in	in	ADP
ejpam-4028	75	21	(	(	PUNCT
ejpam-4028	75	22	ẽ	ẽ	PROPN
ejpam-4028	75	23	,	,	PUNCT
ejpam-4028	75	24	g̃	g̃	PROPN
ejpam-4028	75	25	)	)	PUNCT
ejpam-4028	75	26	.	.	PUNCT
ejpam-4028	76	1	take	take	VERB
ejpam-4028	76	2	the	the	DET
ejpam-4028	76	3	fuzzy	fuzzy	ADJ
ejpam-4028	76	4	soft	soft	ADJ
ejpam-4028	76	5	real	real	ADJ
ejpam-4028	76	6	number	number	NOUN
ejpam-4028	76	7	ε̃	ε̃	PROPN
ejpam-4028	76	8	such	such	ADJ
ejpam-4028	76	9	that	that	SCONJ
ejpam-4028	76	10	ε̃(λ	ε̃(λ	PROPN
ejpam-4028	76	11	)	)	PUNCT
ejpam-4028	77	1	=	=	PUNCT
ejpam-4028	78	1	λ,∀λ	λ,∀λ	PUNCT
ejpam-4028	78	2	∈	∈	X
ejpam-4028	78	3	e	e	NOUN
ejpam-4028	78	4	,	,	PUNCT
ejpam-4028	78	5	that	that	PRON
ejpam-4028	78	6	is	be	AUX
ejpam-4028	78	7	ε̃	ε̃	PROPN
ejpam-4028	78	8	(	(	PUNCT
ejpam-4028	78	9	1	1	NUM
ejpam-4028	78	10	h	h	NOUN
ejpam-4028	78	11	)	)	PUNCT
ejpam-4028	78	12	=	=	SYM
ejpam-4028	78	13	1	1	NUM
ejpam-4028	78	14	h	h	NOUN
ejpam-4028	78	15	,	,	PUNCT
ejpam-4028	78	16	∀h	∀h	PROPN
ejpam-4028	78	17	∈	∈	PROPN
ejpam-4028	78	18	n.	n.	NOUN
ejpam-4028	78	19	then	then	ADV
ejpam-4028	78	20	,	,	PUNCT
ejpam-4028	78	21	∃k	∃k	PROPN
ejpam-4028	78	22	∈	∈	PROPN
ejpam-4028	78	23	n	n	CCONJ
ejpam-4028	78	24	such	such	ADJ
ejpam-4028	78	25	that	that	DET
ejpam-4028	78	26	g̃(fen	g̃(fen	PROPN
ejpam-4028	78	27	,	,	PUNCT
ejpam-4028	78	28	fem	fem	NOUN
ejpam-4028	78	29	,	,	PUNCT
ejpam-4028	78	30	fel)<̃ε̃	fel)<̃ε̃	INTJ
ejpam-4028	78	31	,	,	PUNCT
ejpam-4028	78	32	∀n	∀n	X
ejpam-4028	78	33	,	,	PUNCT
ejpam-4028	78	34	m	m	X
ejpam-4028	78	35	,	,	PUNCT
ejpam-4028	78	36	l	l	PROPN
ejpam-4028	78	37	≥	≥	X
ejpam-4028	78	38	k	k	NOUN
ejpam-4028	78	39	,	,	PUNCT
ejpam-4028	78	40	which	which	PRON
ejpam-4028	78	41	implies	imply	VERB
ejpam-4028	78	42	to	to	PART
ejpam-4028	78	43	g̃(fen	g̃(fen	VERB
ejpam-4028	78	44	,	,	PUNCT
ejpam-4028	78	45	fem	fem	X
ejpam-4028	78	46	,	,	PUNCT
ejpam-4028	78	47	fel	fel	PROPN
ejpam-4028	78	48	)	)	PUNCT
ejpam-4028	78	49	(	(	PUNCT
ejpam-4028	78	50	1	1	NUM
ejpam-4028	78	51	h	h	NOUN
ejpam-4028	78	52	)	)	PUNCT
ejpam-4028	78	53	<	<	X
ejpam-4028	78	54	ε̃	ε̃	PROPN
ejpam-4028	78	55	(	(	PUNCT
ejpam-4028	78	56	1	1	NUM
ejpam-4028	78	57	h),∀h	h),∀h	NOUN
ejpam-4028	78	58	∈	∈	PROPN
ejpam-4028	78	59	n.	n.	NOUN
ejpam-4028	78	60	hence	hence	ADV
ejpam-4028	78	61	˜̃1	˜̃1	VERB
ejpam-4028	78	62	3	3	NUM
ejpam-4028	78	63	(	(	PUNCT
ejpam-4028	78	64	|fen	|fen	PROPN
ejpam-4028	78	65	−	−	PROPN
ejpam-4028	78	66	fem	fem	PROPN
ejpam-4028	78	67	|+	|+	X
ejpam-4028	78	68	|fem	|fem	VERB
ejpam-4028	78	69	−	−	PROPN
ejpam-4028	78	70	fel	fel	PROPN
ejpam-4028	78	71	|+	|+	X
ejpam-4028	78	72	|fen	|fen	PRON
ejpam-4028	78	73	−	−	PROPN
ejpam-4028	78	74	fel	fel	NOUN
ejpam-4028	78	75	|	|	ADV
ejpam-4028	78	76	)	)	PUNCT
ejpam-4028	78	77	(	(	PUNCT
ejpam-4028	78	78	1	1	NUM
ejpam-4028	78	79	h	h	NOUN
ejpam-4028	78	80	)	)	PUNCT
ejpam-4028	78	81	<	<	X
ejpam-4028	78	82	1	1	NUM
ejpam-4028	78	83	h′	h′	PROPN
ejpam-4028	78	84	,	,	PUNCT
ejpam-4028	78	85	∀n	∀n	PROPN
ejpam-4028	78	86	,	,	PUNCT
ejpam-4028	78	87	m	m	X
ejpam-4028	78	88	,	,	PUNCT
ejpam-4028	78	89	l	l	PROPN
ejpam-4028	78	90	≥	≥	X
ejpam-4028	78	91	k	k	NOUN
ejpam-4028	78	92	,	,	PUNCT
ejpam-4028	78	93	h	h	NOUN
ejpam-4028	78	94	∈	∈	PROPN
ejpam-4028	78	95	n	n	PRON
ejpam-4028	78	96	which	which	PRON
ejpam-4028	78	97	implies	imply	VERB
ejpam-4028	78	98	to	to	ADP
ejpam-4028	78	99	˜̃1	˜̃1	NOUN
ejpam-4028	78	100	3	3	NUM
ejpam-4028	78	101	(	(	PUNCT
ejpam-4028	78	102	|fen	|fen	PROPN
ejpam-4028	78	103	−	−	PROPN
ejpam-4028	78	104	fem	fem	PROPN
ejpam-4028	78	105	|+	|+	X
ejpam-4028	78	106	|fem	|fem	VERB
ejpam-4028	78	107	−	−	PROPN
ejpam-4028	78	108	fel	fel	PROPN
ejpam-4028	78	109	|+	|+	X
ejpam-4028	78	110	|fen	|fen	PRON
ejpam-4028	78	111	−	−	PROPN
ejpam-4028	78	112	fel	fel	NOUN
ejpam-4028	78	113	|	|	NOUN
ejpam-4028	78	114	)	)	PUNCT
ejpam-4028	78	115	≤	≤	NUM
ejpam-4028	78	116	1	1	NUM
ejpam-4028	78	117	h′	h′	NOUN
ejpam-4028	78	118	,	,	PUNCT
ejpam-4028	78	119	∀n	∀n	PROPN
ejpam-4028	78	120	,	,	PUNCT
ejpam-4028	78	121	m	m	X
ejpam-4028	78	122	,	,	PUNCT
ejpam-4028	78	123	l	l	PROPN
ejpam-4028	78	124	≥	≥	X
ejpam-4028	78	125	k	k	NOUN
ejpam-4028	78	126	,	,	PUNCT
ejpam-4028	78	127	h	h	NOUN
ejpam-4028	78	128	∈	∈	PROPN
ejpam-4028	79	1	n	n	CCONJ
ejpam-4028	79	2	so	so	ADV
ejpam-4028	79	3	,	,	PUNCT
ejpam-4028	79	4	we	we	PRON
ejpam-4028	79	5	obtain	obtain	VERB
ejpam-4028	79	6	that	that	SCONJ
ejpam-4028	79	7	the	the	DET
ejpam-4028	79	8	sequence	sequence	NOUN
ejpam-4028	79	9	{	{	PUNCT
ejpam-4028	79	10	fen}n∈n	fen}n∈n	PRON
ejpam-4028	79	11	is	be	AUX
ejpam-4028	79	12	eventually	eventually	ADV
ejpam-4028	79	13	constant	constant	ADJ
ejpam-4028	79	14	,	,	PUNCT
ejpam-4028	79	15	and	and	CCONJ
ejpam-4028	79	16	hence	hence	ADV
ejpam-4028	79	17	fuzzy	fuzzy	ADJ
ejpam-4028	79	18	soft	soft	ADJ
ejpam-4028	79	19	g	g	NOUN
ejpam-4028	79	20	-	-	PUNCT
ejpam-4028	79	21	convergent	convergent	NOUN
ejpam-4028	79	22	.	.	PUNCT
ejpam-4028	80	1	hence	hence	ADV
ejpam-4028	80	2	(	(	PUNCT
ejpam-4028	80	3	ẽ	ẽ	PROPN
ejpam-4028	80	4	,	,	PUNCT
ejpam-4028	80	5	g̃	g̃	PROPN
ejpam-4028	80	6	)	)	PUNCT
ejpam-4028	80	7	is	be	AUX
ejpam-4028	80	8	fuzzy	fuzzy	ADJ
ejpam-4028	80	9	soft	soft	ADJ
ejpam-4028	80	10	g	g	NOUN
ejpam-4028	80	11	-	-	PUNCT
ejpam-4028	80	12	complete	complete	ADJ
ejpam-4028	80	13	.	.	PUNCT
ejpam-4028	81	1	now	now	ADV
ejpam-4028	81	2	suppose	suppose	VERB
ejpam-4028	81	3	t	t	NOUN
ejpam-4028	81	4	:	:	PUNCT
ejpam-4028	81	5	(	(	PUNCT
ejpam-4028	81	6	ẽ	ẽ	NOUN
ejpam-4028	81	7	,	,	PUNCT
ejpam-4028	81	8	g̃)→	g̃)→	PRON
ejpam-4028	81	9	(	(	PUNCT
ejpam-4028	81	10	ẽ	ẽ	PROPN
ejpam-4028	81	11	,	,	PUNCT
ejpam-4028	81	12	g̃	g̃	PROPN
ejpam-4028	81	13	)	)	PUNCT
ejpam-4028	81	14	is	be	AUX
ejpam-4028	81	15	defined	define	VERB
ejpam-4028	81	16	as	as	ADP
ejpam-4028	81	17	:	:	PUNCT
ejpam-4028	81	18	t	t	PROPN
ejpam-4028	81	19	(	(	PUNCT
ejpam-4028	81	20	fe	fe	X
ejpam-4028	81	21	)	)	PUNCT
ejpam-4028	81	22	=	=	SYM
ejpam-4028	81	23	˜̃1	˜̃1	NOUN
ejpam-4028	81	24	8(fe),∀fe	8(fe),∀fe	NOUN
ejpam-4028	81	25	∈	∈	PROPN
ejpam-4028	81	26	fsc(ẽ	fsc(ẽ	PROPN
ejpam-4028	81	27	)	)	PUNCT
ejpam-4028	81	28	note	note	NOUN
ejpam-4028	81	29	that	that	SCONJ
ejpam-4028	81	30	t	t	PROPN
ejpam-4028	81	31	satisfies	satisfy	VERB
ejpam-4028	81	32	the	the	DET
ejpam-4028	81	33	condition	condition	NOUN
ejpam-4028	81	34	(	(	PUNCT
ejpam-4028	81	35	1	1	NUM
ejpam-4028	81	36	)	)	PUNCT
ejpam-4028	81	37	.	.	PUNCT
ejpam-4028	82	1	for	for	ADP
ejpam-4028	82	2	any	any	DET
ejpam-4028	82	3	fe1	fe1	PROPN
ejpam-4028	82	4	,	,	PUNCT
ejpam-4028	82	5	fe2	fe2	PROPN
ejpam-4028	82	6	,	,	PUNCT
ejpam-4028	82	7	fe3∈̃fsc(ẽ	fe3∈̃fsc(ẽ	PROPN
ejpam-4028	82	8	)	)	PUNCT
ejpam-4028	82	9	and	and	CCONJ
ejpam-4028	82	10	η	η	PROPN
ejpam-4028	82	11	∈	∈	PROPN
ejpam-4028	82	12	e	e	NOUN
ejpam-4028	82	13	,	,	PUNCT
ejpam-4028	82	14	we	we	PRON
ejpam-4028	82	15	have	have	AUX
ejpam-4028	82	16	g̃(tfe1	g̃(tfe1	VERB
ejpam-4028	82	17	,	,	PUNCT
ejpam-4028	82	18	t	t	PROPN
ejpam-4028	82	19	fe2	fe2	PROPN
ejpam-4028	82	20	,	,	PUNCT
ejpam-4028	82	21	t	t	PROPN
ejpam-4028	82	22	fe3)(η	fe3)(η	PROPN
ejpam-4028	82	23	)	)	PUNCT
ejpam-4028	83	1	=	=	PRON
ejpam-4028	83	2	(	(	PUNCT
ejpam-4028	83	3	˜̃1	˜̃1	NOUN
ejpam-4028	83	4	3	3	NUM
ejpam-4028	83	5	{	{	PUNCT
ejpam-4028	83	6	˜̃1	˜̃1	NOUN
ejpam-4028	83	7	8	8	NUM
ejpam-4028	83	8	|fe1	|fe1	NUM
ejpam-4028	83	9	−	−	PROPN
ejpam-4028	83	10	fe2	fe2	PROPN
ejpam-4028	83	11	|+	|+	X
ejpam-4028	83	12	˜̃1	˜̃1	PUNCT
ejpam-4028	83	13	8	8	NUM
ejpam-4028	83	14	|fe2	|fe2	NOUN
ejpam-4028	83	15	−	−	NOUN
ejpam-4028	83	16	fe3	fe3	NOUN
ejpam-4028	83	17	|+	|+	NOUN
ejpam-4028	83	18	˜̃1	˜̃1	PUNCT
ejpam-4028	83	19	8	8	NUM
ejpam-4028	83	20	|fe1	|fe1	NUM
ejpam-4028	83	21	−	−	PROPN
ejpam-4028	83	22	fe3	fe3	NOUN
ejpam-4028	83	23	|	|	NOUN
ejpam-4028	83	24	}	}	PUNCT
ejpam-4028	83	25	)	)	PUNCT
ejpam-4028	83	26	(	(	PUNCT
ejpam-4028	83	27	η	η	NOUN
ejpam-4028	83	28	)	)	PUNCT
ejpam-4028	83	29	=	=	SYM
ejpam-4028	83	30	˜̃1	˜̃1	NOUN
ejpam-4028	83	31	24	24	NUM
ejpam-4028	83	32	{	{	PUNCT
ejpam-4028	83	33	|fe1	|fe1	PROPN
ejpam-4028	83	34	−	−	PROPN
ejpam-4028	83	35	fe2	fe2	PROPN
ejpam-4028	83	36	|+	|+	X
ejpam-4028	83	37	|fe2	|fe2	NOUN
ejpam-4028	83	38	−	−	PROPN
ejpam-4028	83	39	fe3	fe3	NOUN
ejpam-4028	83	40	|+	|+	NOUN
ejpam-4028	84	1	|fe1	|fe1	CCONJ
ejpam-4028	84	2	−	−	PROPN
ejpam-4028	84	3	fe3	fe3	NOUN
ejpam-4028	84	4	|	|	NOUN
ejpam-4028	84	5	}	}	PUNCT
ejpam-4028	84	6	=	=	SYM
ejpam-4028	84	7	˜̃1	˜̃1	PROPN
ejpam-4028	84	8	8g̃(fe1	8g̃(fe1	PROPN
ejpam-4028	84	9	,	,	PUNCT
ejpam-4028	84	10	fe2	fe2	PROPN
ejpam-4028	84	11	,	,	PUNCT
ejpam-4028	84	12	fe3)(η	fe3)(η	PROPN
ejpam-4028	84	13	)	)	PUNCT
ejpam-4028	84	14	≤̃˜̃1	≤̃˜̃1	PRON
ejpam-4028	84	15	8	8	NUM
ejpam-4028	84	16	{	{	PUNCT
ejpam-4028	84	17	g̃(fe1	g̃(fe1	PROPN
ejpam-4028	84	18	,	,	PUNCT
ejpam-4028	84	19	tfe1	tfe1	NOUN
ejpam-4028	84	20	,	,	PUNCT
ejpam-4028	84	21	tfe1	tfe1	PROPN
ejpam-4028	84	22	)	)	PUNCT
ejpam-4028	85	1	+	+	CCONJ
ejpam-4028	85	2	g̃(fe2	g̃(fe2	NOUN
ejpam-4028	85	3	,	,	PUNCT
ejpam-4028	85	4	tfe2	tfe2	NOUN
ejpam-4028	85	5	,	,	PUNCT
ejpam-4028	85	6	tfe2	tfe2	PROPN
ejpam-4028	85	7	)	)	PUNCT
ejpam-4028	86	1	+	+	CCONJ
ejpam-4028	86	2	g̃(fe3	g̃(fe3	NUM
ejpam-4028	86	3	,	,	PUNCT
ejpam-4028	86	4	tfe3	tfe3	NOUN
ejpam-4028	86	5	,	,	PUNCT
ejpam-4028	86	6	t	t	PROPN
ejpam-4028	86	7	fe3	fe3	PROPN
ejpam-4028	86	8	)	)	PUNCT
ejpam-4028	86	9	}	}	PUNCT
ejpam-4028	86	10	(	(	PUNCT
ejpam-4028	86	11	η	η	NOUN
ejpam-4028	86	12	)	)	PUNCT
ejpam-4028	86	13	.	.	PUNCT
ejpam-4028	87	1	hence	hence	ADV
ejpam-4028	87	2	,	,	PUNCT
ejpam-4028	87	3	we	we	PRON
ejpam-4028	87	4	obtain	obtain	VERB
ejpam-4028	87	5	g̃(tfe1	g̃(tfe1	PROPN
ejpam-4028	87	6	,	,	PUNCT
ejpam-4028	87	7	t	t	PROPN
ejpam-4028	87	8	fe2	fe2	PROPN
ejpam-4028	87	9	,	,	PUNCT
ejpam-4028	87	10	t	t	PROPN
ejpam-4028	87	11	fe3)≤̃˜̃1	fe3)≤̃˜̃1	NOUN
ejpam-4028	87	12	8g̃(fe1	8g̃(fe1	PROPN
ejpam-4028	87	13	,	,	PUNCT
ejpam-4028	87	14	t	t	PROPN
ejpam-4028	87	15	fe1	fe1	PROPN
ejpam-4028	87	16	,	,	PUNCT
ejpam-4028	87	17	t	t	PROPN
ejpam-4028	87	18	fe1	fe1	PROPN
ejpam-4028	87	19	)	)	PUNCT
ejpam-4028	88	1	+	+	NUM
ejpam-4028	88	2	˜̃1	˜̃1	NOUN
ejpam-4028	88	3	8g̃(fe2	8g̃(fe2	NOUN
ejpam-4028	88	4	,	,	PUNCT
ejpam-4028	88	5	tfe2	tfe2	NOUN
ejpam-4028	88	6	,	,	PUNCT
ejpam-4028	88	7	tfe2	tfe2	PROPN
ejpam-4028	88	8	)	)	PUNCT
ejpam-4028	89	1	+	+	NUM
ejpam-4028	89	2	˜̃1	˜̃1	NOUN
ejpam-4028	89	3	8g̃(fe3	8g̃(fe3	PROPN
ejpam-4028	89	4	,	,	PUNCT
ejpam-4028	89	5	t	t	PROPN
ejpam-4028	89	6	fe3	fe3	PROPN
ejpam-4028	89	7	,	,	PUNCT
ejpam-4028	89	8	t	t	PROPN
ejpam-4028	89	9	fe3	fe3	PROPN
ejpam-4028	89	10	)	)	PUNCT
ejpam-4028	89	11	+	+	NUM
ejpam-4028	89	12	˜̃1	˜̃1	PROPN
ejpam-4028	89	13	8g̃(fe1	8g̃(fe1	NUM
ejpam-4028	89	14	,	,	PUNCT
ejpam-4028	89	15	fe2	fe2	PROPN
ejpam-4028	89	16	,	,	PUNCT
ejpam-4028	89	17	fe3	fe3	PROPN
ejpam-4028	89	18	)	)	PUNCT
ejpam-4028	89	19	.	.	PUNCT
ejpam-4028	90	1	all	all	DET
ejpam-4028	90	2	conditions	condition	NOUN
ejpam-4028	90	3	of	of	ADP
ejpam-4028	90	4	theorem	theorem	NOUN
ejpam-4028	90	5	1	1	NUM
ejpam-4028	90	6	are	be	AUX
ejpam-4028	90	7	satisfied	satisfied	ADJ
ejpam-4028	90	8	but	but	CCONJ
ejpam-4028	90	9	t	t	PROPN
ejpam-4028	90	10	is	be	AUX
ejpam-4028	90	11	a	a	DET
ejpam-4028	90	12	fixed	fix	VERB
ejpam-4028	90	13	point	point	NOUN
ejpam-4028	90	14	free	free	ADJ
ejpam-4028	90	15	map	map	NOUN
ejpam-4028	90	16	.	.	PUNCT
ejpam-4028	90	17	example	example	NOUN
ejpam-4028	91	1	2	2	NUM
ejpam-4028	91	2	.	.	PUNCT
ejpam-4028	91	3	let	let	VERB
ejpam-4028	91	4	x	x	PUNCT
ejpam-4028	91	5	=	=	PUNCT
ejpam-4028	91	6	e	e	NOUN
ejpam-4028	91	7	=	=	PRON
ejpam-4028	91	8	{	{	PUNCT
ejpam-4028	91	9	1	1	NUM
ejpam-4028	91	10	n	n	NOUN
ejpam-4028	91	11	:	:	PUNCT
ejpam-4028	91	12	n	n	CCONJ
ejpam-4028	91	13	∈	∈	PROPN
ejpam-4028	91	14	n	n	CCONJ
ejpam-4028	91	15	}	}	PUNCT
ejpam-4028	91	16	.	.	PUNCT
ejpam-4028	92	1	consider	consider	VERB
ejpam-4028	92	2	the	the	DET
ejpam-4028	92	3	fuzzy	fuzzy	ADJ
ejpam-4028	92	4	soft	soft	ADJ
ejpam-4028	92	5	g	g	NOUN
ejpam-4028	92	6	-	-	PUNCT
ejpam-4028	92	7	metric	metric	ADJ
ejpam-4028	92	8	space	space	NOUN
ejpam-4028	92	9	(	(	PUNCT
ejpam-4028	92	10	ẽ	ẽ	NOUN
ejpam-4028	92	11	,	,	PUNCT
ejpam-4028	92	12	g̃	g̃	PROPN
ejpam-4028	92	13	)	)	PUNCT
ejpam-4028	92	14	,	,	PUNCT
ejpam-4028	92	15	where	where	SCONJ
ejpam-4028	92	16	the	the	DET
ejpam-4028	92	17	fuzzy	fuzzy	ADJ
ejpam-4028	92	18	soft	soft	ADJ
ejpam-4028	92	19	g	g	NOUN
ejpam-4028	92	20	-	-	PUNCT
ejpam-4028	92	21	metric	metric	ADJ
ejpam-4028	92	22	is	be	AUX
ejpam-4028	92	23	defined	define	VERB
ejpam-4028	92	24	as	as	ADP
ejpam-4028	92	25	:	:	PUNCT
ejpam-4028	92	26	g̃(fe1	g̃(fe1	NUM
ejpam-4028	92	27	,	,	PUNCT
ejpam-4028	92	28	fe2	fe2	PROPN
ejpam-4028	92	29	,	,	PUNCT
ejpam-4028	92	30	fe3	fe3	PROPN
ejpam-4028	92	31	)	)	PUNCT
ejpam-4028	92	32	=	=	PUNCT
ejpam-4028	93	1			PROPN
ejpam-4028	93	2	fe1	fe1	PROPN
ejpam-4028	93	3	+	+	CCONJ
ejpam-4028	93	4	fe2	fe2	PROPN
ejpam-4028	93	5	+	+	CCONJ
ejpam-4028	93	6	fe3	fe3	NOUN
ejpam-4028	93	7	+	+	CCONJ
ejpam-4028	93	8	1̃	1̃	NUM
ejpam-4028	93	9	,	,	PUNCT
ejpam-4028	93	10	if	if	SCONJ
ejpam-4028	93	11	fe1	fe1	PROPN
ejpam-4028	93	12	6=	6=	SYM
ejpam-4028	93	13	fe2	fe2	PROPN
ejpam-4028	93	14	6=	6=	PROPN
ejpam-4028	93	15	fe3	fe3	PROPN
ejpam-4028	93	16	6=	6=	NUM
ejpam-4028	93	17	0̃	0̃	NOUN
ejpam-4028	93	18	;	;	PUNCT
ejpam-4028	93	19	fe1	fe1	PROPN
ejpam-4028	93	20	+	+	CCONJ
ejpam-4028	93	21	fe3	fe3	PROPN
ejpam-4028	93	22	+	+	CCONJ
ejpam-4028	93	23	1̃	1̃	NUM
ejpam-4028	93	24	,	,	PUNCT
ejpam-4028	93	25	if	if	SCONJ
ejpam-4028	93	26	fe1	fe1	PROPN
ejpam-4028	93	27	=	=	SYM
ejpam-4028	93	28	fe2	fe2	PROPN
ejpam-4028	93	29	6=	6=	PROPN
ejpam-4028	93	30	fe3	fe3	PROPN
ejpam-4028	93	31	6=	6=	SYM
ejpam-4028	93	32	0̃	0̃	NOUN
ejpam-4028	93	33	;	;	PUNCT
ejpam-4028	93	34	fe2	fe2	PROPN
ejpam-4028	93	35	+	+	CCONJ
ejpam-4028	93	36	fe3	fe3	NOUN
ejpam-4028	93	37	+	+	CCONJ
ejpam-4028	93	38	˜̃2	˜̃2	NOUN
ejpam-4028	93	39	,	,	PUNCT
ejpam-4028	93	40	if	if	SCONJ
ejpam-4028	93	41	fe1	fe1	PROPN
ejpam-4028	93	42	=	=	SYM
ejpam-4028	93	43	0̃	0̃	PROPN
ejpam-4028	93	44	,	,	PUNCT
ejpam-4028	93	45	fe2	fe2	PROPN
ejpam-4028	93	46	6=	6=	PROPN
ejpam-4028	93	47	fe3	fe3	PROPN
ejpam-4028	93	48	6=	6=	SYM
ejpam-4028	93	49	0̃	0̃	NOUN
ejpam-4028	93	50	;	;	PUNCT
ejpam-4028	93	51	fe2	fe2	PROPN
ejpam-4028	94	1	+	+	CCONJ
ejpam-4028	94	2	˜̃3	˜̃3	PROPN
ejpam-4028	94	3	,	,	PUNCT
ejpam-4028	94	4	if	if	SCONJ
ejpam-4028	94	5	fe1	fe1	PROPN
ejpam-4028	94	6	=	=	SYM
ejpam-4028	94	7	0̃	0̃	PROPN
ejpam-4028	94	8	,	,	PUNCT
ejpam-4028	94	9	fe2	fe2	PROPN
ejpam-4028	94	10	=	=	SYM
ejpam-4028	94	11	fe3	fe3	PROPN
ejpam-4028	94	12	6=	6=	NUM
ejpam-4028	94	13	0̃	0̃	NOUN
ejpam-4028	94	14	;	;	PUNCT
ejpam-4028	94	15	fe3	fe3	NOUN
ejpam-4028	94	16	+	+	NOUN
ejpam-4028	94	17	˜̃2	˜̃2	NOUN
ejpam-4028	94	18	,	,	PUNCT
ejpam-4028	94	19	if	if	SCONJ
ejpam-4028	94	20	fe1	fe1	PROPN
ejpam-4028	94	21	=	=	SYM
ejpam-4028	94	22	fe2	fe2	PROPN
ejpam-4028	94	23	=	=	PROPN
ejpam-4028	94	24	0̃	0̃	PROPN
ejpam-4028	94	25	,	,	PUNCT
ejpam-4028	94	26	fe3	fe3	NOUN
ejpam-4028	94	27	6=	6=	PRON
ejpam-4028	94	28	0̃	0̃	NOUN
ejpam-4028	94	29	;	;	PUNCT
ejpam-4028	94	30	0̃	0̃	NOUN
ejpam-4028	94	31	,	,	PUNCT
ejpam-4028	94	32	if	if	SCONJ
ejpam-4028	94	33	fe1	fe1	PROPN
ejpam-4028	94	34	=	=	SYM
ejpam-4028	94	35	fe2	fe2	PROPN
ejpam-4028	94	36	=	=	PROPN
ejpam-4028	94	37	fe3	fe3	PROPN
ejpam-4028	94	38	,	,	PUNCT
ejpam-4028	94	39	a.	a.	PROPN
ejpam-4028	94	40	f.	f.	PROPN
ejpam-4028	94	41	sayed	sayed	PROPN
ejpam-4028	94	42	,	,	PUNCT
ejpam-4028	94	43	a.	a.	NOUN
ejpam-4028	94	44	alahmari	alahmari	PROPN
ejpam-4028	94	45	/	/	SYM
ejpam-4028	94	46	eur	eur	PROPN
ejpam-4028	94	47	.	.	PUNCT
ejpam-4028	95	1	j.	j.	PROPN
ejpam-4028	95	2	pure	pure	PROPN
ejpam-4028	95	3	appl	appl	PROPN
ejpam-4028	95	4	.	.	PROPN
ejpam-4028	95	5	math	math	PROPN
ejpam-4028	95	6	,	,	PUNCT
ejpam-4028	95	7	14	14	NUM
ejpam-4028	95	8	(	(	PUNCT
ejpam-4028	95	9	3	3	NUM
ejpam-4028	95	10	)	)	PUNCT
ejpam-4028	95	11	(	(	PUNCT
ejpam-4028	95	12	2021	2021	NUM
ejpam-4028	95	13	)	)	PUNCT
ejpam-4028	95	14	,	,	PUNCT
ejpam-4028	95	15	923	923	NUM
ejpam-4028	95	16	-	-	SYM
ejpam-4028	95	17	941	941	NUM
ejpam-4028	95	18	927	927	NUM
ejpam-4028	96	1	and	and	CCONJ
ejpam-4028	96	2	extend	extend	VERB
ejpam-4028	96	3	the	the	DET
ejpam-4028	96	4	definition	definition	NOUN
ejpam-4028	96	5	by	by	ADP
ejpam-4028	96	6	symmetry	symmetry	NOUN
ejpam-4028	96	7	in	in	ADP
ejpam-4028	96	8	its	its	PRON
ejpam-4028	96	9	arguments	argument	NOUN
ejpam-4028	96	10	.	.	PUNCT
ejpam-4028	97	1	it	it	PRON
ejpam-4028	97	2	is	be	AUX
ejpam-4028	97	3	easy	easy	ADJ
ejpam-4028	97	4	to	to	PART
ejpam-4028	97	5	show	show	VERB
ejpam-4028	97	6	that	that	SCONJ
ejpam-4028	97	7	(	(	PUNCT
ejpam-4028	97	8	ẽ	ẽ	PROPN
ejpam-4028	97	9	,	,	PUNCT
ejpam-4028	97	10	g̃	g̃	PROPN
ejpam-4028	97	11	)	)	PUNCT
ejpam-4028	97	12	is	be	AUX
ejpam-4028	97	13	a	a	DET
ejpam-4028	97	14	fuzzy	fuzzy	ADJ
ejpam-4028	97	15	soft	soft	ADJ
ejpam-4028	97	16	g	g	NOUN
ejpam-4028	97	17	-	-	PUNCT
ejpam-4028	97	18	metric	metric	NOUN
ejpam-4028	97	19	which	which	PRON
ejpam-4028	97	20	is	be	AUX
ejpam-4028	97	21	not	not	PART
ejpam-4028	97	22	symmetric	symmetric	ADJ
ejpam-4028	97	23	.	.	PUNCT
ejpam-4028	98	1	now	now	ADV
ejpam-4028	98	2	,	,	PUNCT
ejpam-4028	98	3	we	we	PRON
ejpam-4028	98	4	show	show	VERB
ejpam-4028	98	5	that	that	SCONJ
ejpam-4028	98	6	(	(	PUNCT
ejpam-4028	98	7	ẽ	ẽ	PROPN
ejpam-4028	98	8	,	,	PUNCT
ejpam-4028	98	9	g̃	g̃	PROPN
ejpam-4028	98	10	)	)	PUNCT
ejpam-4028	98	11	is	be	AUX
ejpam-4028	98	12	fuzzy	fuzzy	ADJ
ejpam-4028	98	13	soft	soft	ADJ
ejpam-4028	98	14	g	g	NOUN
ejpam-4028	98	15	-	-	PUNCT
ejpam-4028	98	16	complete	complete	ADJ
ejpam-4028	98	17	.	.	PUNCT
ejpam-4028	99	1	for	for	ADP
ejpam-4028	99	2	this	this	PRON
ejpam-4028	99	3	,	,	PUNCT
ejpam-4028	99	4	suppose	suppose	VERB
ejpam-4028	99	5	that	that	SCONJ
ejpam-4028	99	6	{	{	PUNCT
ejpam-4028	99	7	fen}n∈n	fen}n∈n	VERB
ejpam-4028	99	8	is	be	AUX
ejpam-4028	99	9	a	a	DET
ejpam-4028	99	10	fuzzy	fuzzy	ADJ
ejpam-4028	99	11	soft	soft	ADJ
ejpam-4028	99	12	g	g	NOUN
ejpam-4028	99	13	-	-	PUNCT
ejpam-4028	99	14	cauchy	cauchy	ADJ
ejpam-4028	99	15	sequence	sequence	NOUN
ejpam-4028	99	16	of	of	ADP
ejpam-4028	99	17	fuzzy	fuzzy	ADJ
ejpam-4028	99	18	soft	soft	ADJ
ejpam-4028	99	19	elements	element	NOUN
ejpam-4028	99	20	in	in	ADP
ejpam-4028	99	21	(	(	PUNCT
ejpam-4028	99	22	ẽ	ẽ	PROPN
ejpam-4028	99	23	,	,	PUNCT
ejpam-4028	99	24	g̃	g̃	PROPN
ejpam-4028	99	25	)	)	PUNCT
ejpam-4028	99	26	.	.	PUNCT
ejpam-4028	100	1	take	take	VERB
ejpam-4028	100	2	the	the	DET
ejpam-4028	100	3	fuzzy	fuzzy	ADJ
ejpam-4028	100	4	soft	soft	ADJ
ejpam-4028	100	5	real	real	ADJ
ejpam-4028	100	6	number	number	NOUN
ejpam-4028	100	7	ε̃	ε̃	PROPN
ejpam-4028	100	8	such	such	ADJ
ejpam-4028	100	9	that	that	SCONJ
ejpam-4028	100	10	ε̃(λ	ε̃(λ	PROPN
ejpam-4028	100	11	)	)	PUNCT
ejpam-4028	101	1	=	=	PUNCT
ejpam-4028	102	1	λ,∀λ	λ,∀λ	PUNCT
ejpam-4028	102	2	∈	∈	X
ejpam-4028	102	3	e	e	NOUN
ejpam-4028	102	4	,	,	PUNCT
ejpam-4028	102	5	that	that	PRON
ejpam-4028	102	6	is	be	AUX
ejpam-4028	102	7	ε̃	ε̃	PROPN
ejpam-4028	102	8	(	(	PUNCT
ejpam-4028	102	9	1	1	NUM
ejpam-4028	102	10	h	h	NOUN
ejpam-4028	102	11	)	)	PUNCT
ejpam-4028	102	12	=	=	SYM
ejpam-4028	102	13	1	1	NUM
ejpam-4028	102	14	h	h	NOUN
ejpam-4028	102	15	,	,	PUNCT
ejpam-4028	102	16	∀h	∀h	PROPN
ejpam-4028	102	17	∈	∈	PROPN
ejpam-4028	102	18	n.	n.	NOUN
ejpam-4028	102	19	then	then	ADV
ejpam-4028	102	20	,	,	PUNCT
ejpam-4028	102	21	∃k	∃k	PROPN
ejpam-4028	102	22	∈	∈	PROPN
ejpam-4028	102	23	n	n	CCONJ
ejpam-4028	102	24	such	such	ADJ
ejpam-4028	102	25	that	that	DET
ejpam-4028	102	26	g̃(fen	g̃(fen	PROPN
ejpam-4028	102	27	,	,	PUNCT
ejpam-4028	102	28	fem	fem	NOUN
ejpam-4028	102	29	,	,	PUNCT
ejpam-4028	102	30	fel)<̃ε̃,∀n	fel)<̃ε̃,∀n	PROPN
ejpam-4028	102	31	,	,	PUNCT
ejpam-4028	102	32	m	m	PROPN
ejpam-4028	102	33	,	,	PUNCT
ejpam-4028	102	34	l	l	PROPN
ejpam-4028	102	35	≥	≥	X
ejpam-4028	102	36	k	k	NOUN
ejpam-4028	102	37	,	,	PUNCT
ejpam-4028	102	38	which	which	PRON
ejpam-4028	102	39	implies	imply	VERB
ejpam-4028	102	40	to	to	PART
ejpam-4028	102	41	g̃(fen	g̃(fen	VERB
ejpam-4028	102	42	,	,	PUNCT
ejpam-4028	102	43	fem	fem	X
ejpam-4028	102	44	,	,	PUNCT
ejpam-4028	102	45	fel	fel	PROPN
ejpam-4028	102	46	)	)	PUNCT
ejpam-4028	102	47	(	(	PUNCT
ejpam-4028	102	48	1	1	NUM
ejpam-4028	102	49	h)<̃ε̃	h)<̃ε̃	NOUN
ejpam-4028	102	50	(	(	PUNCT
ejpam-4028	102	51	1	1	NUM
ejpam-4028	102	52	h),∀h	h),∀h	NOUN
ejpam-4028	102	53	∈	∈	PROPN
ejpam-4028	102	54	n	n	CCONJ
ejpam-4028	102	55	,	,	PUNCT
ejpam-4028	102	56	that	that	PRON
ejpam-4028	102	57	is	be	AUX
ejpam-4028	102	58	g̃(fen	g̃(fen	PROPN
ejpam-4028	102	59	,	,	PUNCT
ejpam-4028	102	60	fem	fem	X
ejpam-4028	102	61	,	,	PUNCT
ejpam-4028	102	62	fel	fel	PROPN
ejpam-4028	102	63	)	)	PUNCT
ejpam-4028	102	64	(	(	PUNCT
ejpam-4028	102	65	1	1	NUM
ejpam-4028	102	66	h)<̃	h)<̃	NOUN
ejpam-4028	102	67	1	1	NUM
ejpam-4028	102	68	h′	h′	PROPN
ejpam-4028	102	69	,	,	PUNCT
ejpam-4028	102	70	∀n	∀n	PROPN
ejpam-4028	102	71	,	,	PUNCT
ejpam-4028	102	72	m	m	PROPN
ejpam-4028	102	73	,	,	PUNCT
ejpam-4028	102	74	l	l	PROPN
ejpam-4028	102	75	≥	≥	NOUN
ejpam-4028	102	76	k,∀h	k,∀h	NOUN
ejpam-4028	102	77	∈	∈	PROPN
ejpam-4028	102	78	n.	n.	NOUN
ejpam-4028	102	79	this	this	PRON
ejpam-4028	102	80	is	be	AUX
ejpam-4028	102	81	possible	possible	ADJ
ejpam-4028	102	82	only	only	ADV
ejpam-4028	102	83	if	if	SCONJ
ejpam-4028	102	84	the	the	DET
ejpam-4028	102	85	sequence	sequence	NOUN
ejpam-4028	102	86	{	{	PUNCT
ejpam-4028	102	87	fen}n∈n	fen}n∈n	PRON
ejpam-4028	102	88	is	be	AUX
ejpam-4028	102	89	constant	constant	ADJ
ejpam-4028	102	90	,	,	PUNCT
ejpam-4028	102	91	and	and	CCONJ
ejpam-4028	102	92	therefore	therefore	ADV
ejpam-4028	102	93	it	it	PRON
ejpam-4028	102	94	is	be	AUX
ejpam-4028	102	95	fuzzy	fuzzy	ADJ
ejpam-4028	102	96	soft	soft	ADJ
ejpam-4028	102	97	g	g	NOUN
ejpam-4028	102	98	-	-	PUNCT
ejpam-4028	102	99	convergent	convergent	NOUN
ejpam-4028	102	100	.	.	PUNCT
ejpam-4028	103	1	we	we	PRON
ejpam-4028	103	2	conclude	conclude	VERB
ejpam-4028	103	3	that	that	SCONJ
ejpam-4028	103	4	(	(	PUNCT
ejpam-4028	103	5	ẽ	ẽ	PROPN
ejpam-4028	103	6	,	,	PUNCT
ejpam-4028	103	7	g̃	g̃	PROPN
ejpam-4028	103	8	)	)	PUNCT
ejpam-4028	103	9	is	be	AUX
ejpam-4028	103	10	fuzzy	fuzzy	ADJ
ejpam-4028	103	11	soft	soft	ADJ
ejpam-4028	103	12	g	g	NOUN
ejpam-4028	103	13	-	-	PUNCT
ejpam-4028	103	14	complete	complete	ADJ
ejpam-4028	103	15	.	.	PUNCT
ejpam-4028	104	1	now	now	ADV
ejpam-4028	104	2	suppose	suppose	VERB
ejpam-4028	104	3	t	t	NOUN
ejpam-4028	104	4	:	:	PUNCT
ejpam-4028	104	5	(	(	PUNCT
ejpam-4028	104	6	ẽ	ẽ	NOUN
ejpam-4028	104	7	,	,	PUNCT
ejpam-4028	104	8	g̃)→	g̃)→	PRON
ejpam-4028	104	9	(	(	PUNCT
ejpam-4028	104	10	ẽ	ẽ	PROPN
ejpam-4028	104	11	,	,	PUNCT
ejpam-4028	104	12	g̃	g̃	PROPN
ejpam-4028	104	13	)	)	PUNCT
ejpam-4028	104	14	is	be	AUX
ejpam-4028	104	15	defined	define	VERB
ejpam-4028	104	16	as	as	ADP
ejpam-4028	104	17	:	:	PUNCT
ejpam-4028	104	18	t	t	PROPN
ejpam-4028	104	19	(	(	PUNCT
ejpam-4028	104	20	fe	fe	X
ejpam-4028	104	21	)	)	PUNCT
ejpam-4028	104	22	=	=	SYM
ejpam-4028	104	23	˜̃1	˜̃1	NOUN
ejpam-4028	104	24	8(fe),∀fe	8(fe),∀fe	NOUN
ejpam-4028	104	25	∈	∈	PROPN
ejpam-4028	104	26	fsc(ẽ	fsc(ẽ	PROPN
ejpam-4028	104	27	)	)	PUNCT
ejpam-4028	104	28	note	note	NOUN
ejpam-4028	104	29	that	that	SCONJ
ejpam-4028	104	30	t	t	PROPN
ejpam-4028	104	31	satisfies	satisfy	VERB
ejpam-4028	104	32	the	the	DET
ejpam-4028	104	33	condition	condition	NOUN
ejpam-4028	104	34	(	(	PUNCT
ejpam-4028	104	35	1	1	NUM
ejpam-4028	104	36	)	)	PUNCT
ejpam-4028	104	37	.	.	PUNCT
ejpam-4028	105	1	for	for	ADP
ejpam-4028	105	2	any	any	DET
ejpam-4028	105	3	fe1	fe1	PROPN
ejpam-4028	105	4	,	,	PUNCT
ejpam-4028	105	5	fe2	fe2	PROPN
ejpam-4028	105	6	,	,	PUNCT
ejpam-4028	105	7	fe3∈̃fsc(ẽ	fe3∈̃fsc(ẽ	PROPN
ejpam-4028	105	8	)	)	PUNCT
ejpam-4028	105	9	and	and	CCONJ
ejpam-4028	105	10	η	η	PROPN
ejpam-4028	105	11	∈	∈	PROPN
ejpam-4028	105	12	e	e	NOUN
ejpam-4028	105	13	,	,	PUNCT
ejpam-4028	105	14	we	we	PRON
ejpam-4028	105	15	have	have	AUX
ejpam-4028	105	16	g̃(tfe1	g̃(tfe1	VERB
ejpam-4028	105	17	,	,	PUNCT
ejpam-4028	105	18	t	t	PROPN
ejpam-4028	105	19	fe2	fe2	PROPN
ejpam-4028	105	20	,	,	PUNCT
ejpam-4028	105	21	t	t	PROPN
ejpam-4028	105	22	fe3)(η	fe3)(η	PROPN
ejpam-4028	105	23	)	)	PUNCT
ejpam-4028	106	1	=	=	SYM
ejpam-4028	106	2	˜̃1	˜̃1	PROPN
ejpam-4028	106	3	8g̃(fe1	8g̃(fe1	PROPN
ejpam-4028	106	4	,	,	PUNCT
ejpam-4028	106	5	fe2	fe2	PROPN
ejpam-4028	106	6	,	,	PUNCT
ejpam-4028	106	7	fe3)(η	fe3)(η	PROPN
ejpam-4028	106	8	)	)	PUNCT
ejpam-4028	106	9	≤̃˜̃1	≤̃˜̃1	PRON
ejpam-4028	106	10	8{g̃(fe1	8{g̃(fe1	PROPN
ejpam-4028	106	11	,	,	PUNCT
ejpam-4028	106	12	tfe1	tfe1	NOUN
ejpam-4028	106	13	,	,	PUNCT
ejpam-4028	106	14	tfe1	tfe1	PROPN
ejpam-4028	106	15	)	)	PUNCT
ejpam-4028	107	1	+	+	CCONJ
ejpam-4028	107	2	g̃(fe2	g̃(fe2	NOUN
ejpam-4028	107	3	,	,	PUNCT
ejpam-4028	107	4	tfe2	tfe2	NOUN
ejpam-4028	107	5	,	,	PUNCT
ejpam-4028	107	6	t	t	PROPN
ejpam-4028	107	7	fe2	fe2	PROPN
ejpam-4028	107	8	)	)	PUNCT
ejpam-4028	107	9	+	+	NUM
ejpam-4028	107	10	g̃(fe3	g̃(fe3	NUM
ejpam-4028	107	11	,	,	PUNCT
ejpam-4028	107	12	t	t	PROPN
ejpam-4028	107	13	fe3	fe3	PROPN
ejpam-4028	107	14	,	,	PUNCT
ejpam-4028	107	15	t	t	PROPN
ejpam-4028	107	16	fe3	fe3	PROPN
ejpam-4028	107	17	)	)	PUNCT
ejpam-4028	108	1	+	+	CCONJ
ejpam-4028	108	2	g̃(fe1	g̃(fe1	PROPN
ejpam-4028	108	3	,	,	PUNCT
ejpam-4028	108	4	fe2	fe2	PROPN
ejpam-4028	108	5	,	,	PUNCT
ejpam-4028	108	6	fe3)}(η	fe3)}(η	PROPN
ejpam-4028	108	7	)	)	PUNCT
ejpam-4028	108	8	.	.	PUNCT
ejpam-4028	109	1	hence	hence	ADV
ejpam-4028	109	2	,	,	PUNCT
ejpam-4028	109	3	we	we	PRON
ejpam-4028	109	4	obtain	obtain	VERB
ejpam-4028	109	5	g̃(tfe1	g̃(tfe1	PROPN
ejpam-4028	109	6	,	,	PUNCT
ejpam-4028	109	7	t	t	PROPN
ejpam-4028	109	8	fe2	fe2	PROPN
ejpam-4028	109	9	,	,	PUNCT
ejpam-4028	109	10	t	t	PROPN
ejpam-4028	109	11	fe3)≤̃˜̃1	fe3)≤̃˜̃1	NOUN
ejpam-4028	109	12	8g̃(fe1	8g̃(fe1	PROPN
ejpam-4028	109	13	,	,	PUNCT
ejpam-4028	109	14	t	t	PROPN
ejpam-4028	109	15	fe1	fe1	PROPN
ejpam-4028	109	16	,	,	PUNCT
ejpam-4028	109	17	t	t	PROPN
ejpam-4028	109	18	fe1	fe1	PROPN
ejpam-4028	109	19	)	)	PUNCT
ejpam-4028	110	1	+	+	NUM
ejpam-4028	110	2	˜̃1	˜̃1	NOUN
ejpam-4028	110	3	8g̃(fe2	8g̃(fe2	NOUN
ejpam-4028	110	4	,	,	PUNCT
ejpam-4028	110	5	tfe2	tfe2	NOUN
ejpam-4028	110	6	,	,	PUNCT
ejpam-4028	110	7	tfe2	tfe2	PROPN
ejpam-4028	110	8	)	)	PUNCT
ejpam-4028	111	1	+	+	NUM
ejpam-4028	111	2	˜̃1	˜̃1	NOUN
ejpam-4028	111	3	8g̃(fe3	8g̃(fe3	PROPN
ejpam-4028	111	4	,	,	PUNCT
ejpam-4028	111	5	t	t	PROPN
ejpam-4028	111	6	fe3	fe3	PROPN
ejpam-4028	111	7	,	,	PUNCT
ejpam-4028	111	8	t	t	PROPN
ejpam-4028	111	9	fe3	fe3	PROPN
ejpam-4028	111	10	)	)	PUNCT
ejpam-4028	111	11	+	+	NUM
ejpam-4028	111	12	˜̃1	˜̃1	PROPN
ejpam-4028	111	13	8g̃(fe1	8g̃(fe1	NUM
ejpam-4028	111	14	,	,	PUNCT
ejpam-4028	111	15	fe2	fe2	PROPN
ejpam-4028	111	16	,	,	PUNCT
ejpam-4028	111	17	fe3	fe3	PROPN
ejpam-4028	111	18	)	)	PUNCT
ejpam-4028	111	19	.	.	PUNCT
ejpam-4028	112	1	all	all	DET
ejpam-4028	112	2	conditions	condition	NOUN
ejpam-4028	112	3	of	of	ADP
ejpam-4028	112	4	theorem	theorem	NOUN
ejpam-4028	112	5	1	1	NUM
ejpam-4028	112	6	are	be	AUX
ejpam-4028	112	7	satisfied	satisfied	ADJ
ejpam-4028	112	8	but	but	CCONJ
ejpam-4028	112	9	t	t	NOUN
ejpam-4028	112	10	can	can	AUX
ejpam-4028	112	11	be	be	AUX
ejpam-4028	112	12	seen	see	VERB
ejpam-4028	112	13	it	it	PRON
ejpam-4028	112	14	has	have	VERB
ejpam-4028	112	15	no	no	DET
ejpam-4028	112	16	fixed	fix	VERB
ejpam-4028	112	17	point	point	NOUN
ejpam-4028	112	18	.	.	PUNCT
ejpam-4028	113	1	next	next	ADV
ejpam-4028	113	2	,	,	PUNCT
ejpam-4028	113	3	we	we	PRON
ejpam-4028	113	4	see	see	VERB
ejpam-4028	113	5	that	that	SCONJ
ejpam-4028	113	6	keeping	keep	VERB
ejpam-4028	113	7	the	the	DET
ejpam-4028	113	8	set	set	NOUN
ejpam-4028	113	9	of	of	ADP
ejpam-4028	113	10	parameters	parameter	NOUN
ejpam-4028	113	11	finite	finite	VERB
ejpam-4028	113	12	,	,	PUNCT
ejpam-4028	113	13	one	one	PRON
ejpam-4028	113	14	can	can	AUX
ejpam-4028	113	15	obtain	obtain	VERB
ejpam-4028	113	16	the	the	DET
ejpam-4028	113	17	following	follow	VERB
ejpam-4028	113	18	new	new	ADJ
ejpam-4028	113	19	results	result	NOUN
ejpam-4028	113	20	.	.	PUNCT
ejpam-4028	114	1	theorem	theorem	NOUN
ejpam-4028	114	2	2	2	NUM
ejpam-4028	114	3	.	.	PUNCT
ejpam-4028	114	4	suppose	suppose	VERB
ejpam-4028	114	5	(	(	PUNCT
ejpam-4028	114	6	ẽ	ẽ	PROPN
ejpam-4028	114	7	,	,	PUNCT
ejpam-4028	114	8	g̃	g̃	PROPN
ejpam-4028	114	9	)	)	PUNCT
ejpam-4028	114	10	is	be	AUX
ejpam-4028	114	11	a	a	DET
ejpam-4028	114	12	fuzzy	fuzzy	ADJ
ejpam-4028	114	13	soft	soft	ADJ
ejpam-4028	114	14	g	g	NOUN
ejpam-4028	114	15	-	-	PUNCT
ejpam-4028	114	16	metric	metric	ADJ
ejpam-4028	114	17	space	space	NOUN
ejpam-4028	114	18	and	and	CCONJ
ejpam-4028	114	19	t	t	NOUN
ejpam-4028	114	20	:	:	PUNCT
ejpam-4028	114	21	(	(	PUNCT
ejpam-4028	114	22	ẽ	ẽ	NOUN
ejpam-4028	114	23	,	,	PUNCT
ejpam-4028	114	24	g̃)→	g̃)→	PRON
ejpam-4028	114	25	(	(	PUNCT
ejpam-4028	114	26	ẽ	ẽ	PROPN
ejpam-4028	114	27	,	,	PUNCT
ejpam-4028	114	28	g̃	g̃	PROPN
ejpam-4028	114	29	)	)	PUNCT
ejpam-4028	114	30	is	be	AUX
ejpam-4028	114	31	a	a	DET
ejpam-4028	114	32	mapping	mapping	NOUN
ejpam-4028	114	33	satisfying	satisfy	VERB
ejpam-4028	114	34	the	the	DET
ejpam-4028	114	35	following	follow	VERB
ejpam-4028	114	36	condition	condition	NOUN
ejpam-4028	114	37	:	:	PUNCT
ejpam-4028	115	1	¯̄ag̃(tfe1	¯̄ag̃(tfe1	NOUN
ejpam-4028	115	2	,	,	PUNCT
ejpam-4028	115	3	t	t	PROPN
ejpam-4028	115	4	fe2	fe2	X
ejpam-4028	115	5	,	,	PUNCT
ejpam-4028	115	6	tfe3)≤̃¯̄b	tfe3)≤̃¯̄b	PROPN
ejpam-4028	115	7			PUNCT
ejpam-4028	115	8	g̃(fe1	g̃(fe1	PROPN
ejpam-4028	115	9	,	,	PUNCT
ejpam-4028	115	10	t	t	PROPN
ejpam-4028	115	11	fe2	fe2	PROPN
ejpam-4028	115	12	,	,	PUNCT
ejpam-4028	115	13	tfe2	tfe2	PROPN
ejpam-4028	115	14	)	)	PUNCT
ejpam-4028	116	1	+	+	PROPN
ejpam-4028	116	2	g̃(fe1	g̃(fe1	PROPN
ejpam-4028	116	3	,	,	PUNCT
ejpam-4028	116	4	t	t	PROPN
ejpam-4028	116	5	fe3	fe3	PROPN
ejpam-4028	116	6	,	,	PUNCT
ejpam-4028	116	7	t	t	PROPN
ejpam-4028	116	8	fe3	fe3	PROPN
ejpam-4028	116	9	)	)	PUNCT
ejpam-4028	117	1	+	+	NOUN
ejpam-4028	117	2	g̃(fe3	g̃(fe3	NOUN
ejpam-4028	117	3	,	,	PUNCT
ejpam-4028	117	4	t	t	PROPN
ejpam-4028	117	5	fe1	fe1	PROPN
ejpam-4028	117	6	,	,	PUNCT
ejpam-4028	117	7	t	t	PROPN
ejpam-4028	117	8	fe1	fe1	PROPN
ejpam-4028	117	9	)	)	PUNCT
ejpam-4028	117	10	+	+	VERB
ejpam-4028	117	11	¯̄cg̃(fe1	¯̄cg̃(fe1	PROPN
ejpam-4028	117	12	,	,	PUNCT
ejpam-4028	117	13	fe2	fe2	PROPN
ejpam-4028	117	14	,	,	PUNCT
ejpam-4028	117	15	fe3	fe3	PROPN
ejpam-4028	117	16	)	)	PUNCT
ejpam-4028	117	17	(	(	PUNCT
ejpam-4028	117	18	2	2	X
ejpam-4028	117	19	)	)	PUNCT
ejpam-4028	117	20	∀fe1	∀fe1	PROPN
ejpam-4028	117	21	,	,	PUNCT
ejpam-4028	117	22	fe2	fe2	PROPN
ejpam-4028	117	23	,	,	PUNCT
ejpam-4028	117	24	fe3∈̃fsc(ẽ	fe3∈̃fsc(ẽ	PROPN
ejpam-4028	117	25	)	)	PUNCT
ejpam-4028	117	26	and	and	CCONJ
ejpam-4028	117	27	0̃≤̃¯̄a	0̃≤̃¯̄a	NUM
ejpam-4028	117	28	,	,	PUNCT
ejpam-4028	117	29	¯̄b	¯̄b	NOUN
ejpam-4028	117	30	,	,	PUNCT
ejpam-4028	117	31	¯̄c<̃1̃	¯̄c<̃1̃	VERB
ejpam-4028	117	32	with	with	ADP
ejpam-4028	117	33	˜̃3¯̄b+	˜̃3¯̄b+	NOUN
ejpam-4028	117	34	¯̄c<̃¯̄a	¯̄c<̃¯̄a	NOUN
ejpam-4028	117	35	.	.	PUNCT
ejpam-4028	118	1	then	then	ADV
ejpam-4028	118	2	t	t	PROPN
ejpam-4028	118	3	has	have	VERB
ejpam-4028	118	4	an	an	DET
ejpam-4028	118	5	unique	unique	ADJ
ejpam-4028	118	6	fixed	fix	VERB
ejpam-4028	118	7	point	point	NOUN
ejpam-4028	118	8	,	,	PUNCT
ejpam-4028	118	9	say	say	VERB
ejpam-4028	118	10	fe	fe	X
ejpam-4028	118	11	,	,	PUNCT
ejpam-4028	118	12	and	and	CCONJ
ejpam-4028	118	13	at	at	ADP
ejpam-4028	118	14	fe	fe	PROPN
ejpam-4028	118	15	,	,	PUNCT
ejpam-4028	118	16	t	t	PROPN
ejpam-4028	118	17	is	be	AUX
ejpam-4028	118	18	fuzzy	fuzzy	ADJ
ejpam-4028	118	19	soft	soft	ADJ
ejpam-4028	118	20	g	g	NOUN
ejpam-4028	118	21	-	-	PUNCT
ejpam-4028	118	22	continuous	continuous	ADJ
ejpam-4028	118	23	.	.	PUNCT
ejpam-4028	119	1	proof	proof	NOUN
ejpam-4028	119	2	.	.	PUNCT
ejpam-4028	120	1	assume	assume	VERB
ejpam-4028	120	2	that	that	SCONJ
ejpam-4028	120	3	fe0∈̃fsc(ẽ	fe0∈̃fsc(ẽ	NOUN
ejpam-4028	120	4	)	)	PUNCT
ejpam-4028	120	5	is	be	AUX
ejpam-4028	120	6	an	an	DET
ejpam-4028	120	7	arbitrary	arbitrary	ADJ
ejpam-4028	120	8	fuzzy	fuzzy	ADJ
ejpam-4028	120	9	soft	soft	ADJ
ejpam-4028	120	10	element	element	NOUN
ejpam-4028	120	11	and	and	CCONJ
ejpam-4028	120	12	define	define	VERB
ejpam-4028	120	13	the	the	DET
ejpam-4028	120	14	sequence	sequence	NOUN
ejpam-4028	120	15	{	{	PUNCT
ejpam-4028	120	16	gen}n∈n	gen}n∈n	PROPN
ejpam-4028	120	17	as	as	SCONJ
ejpam-4028	120	18	follows	follow	VERB
ejpam-4028	120	19	:	:	PUNCT
ejpam-4028	121	1	tge0	tge0	NOUN
ejpam-4028	121	2	=	=	SYM
ejpam-4028	121	3	ge1	ge1	PROPN
ejpam-4028	121	4	,	,	PUNCT
ejpam-4028	121	5	t	t	PROPN
ejpam-4028	121	6	ge1	ge1	PROPN
ejpam-4028	121	7	=	=	PUNCT
ejpam-4028	121	8	ge2	ge2	PROPN
ejpam-4028	121	9	,	,	PUNCT
ejpam-4028	121	10	t	t	PROPN
ejpam-4028	121	11	ge2	ge2	PROPN
ejpam-4028	121	12	=	=	X
ejpam-4028	121	13	ge3	ge3	PROPN
ejpam-4028	121	14	,	,	PUNCT
ejpam-4028	121	15	...	...	PUNCT
ejpam-4028	121	16	,	,	PUNCT
ejpam-4028	121	17	t	t	PROPN
ejpam-4028	121	18	gen	gen	PROPN
ejpam-4028	121	19	=	=	NOUN
ejpam-4028	121	20	gen+1	gen+1	PROPN
ejpam-4028	121	21	.	.	PUNCT
ejpam-4028	122	1	consider	consider	VERB
ejpam-4028	122	2	that	that	DET
ejpam-4028	122	3	gen	gen	PROPN
ejpam-4028	122	4	6=	6=	PROPN
ejpam-4028	122	5	gen+1	gen+1	NOUN
ejpam-4028	122	6	.	.	PUNCT
ejpam-4028	123	1	substituting	substitute	VERB
ejpam-4028	123	2	fe1	fe1	PROPN
ejpam-4028	123	3	=	=	SYM
ejpam-4028	123	4	gen	gen	PROPN
ejpam-4028	123	5	,	,	PUNCT
ejpam-4028	123	6	fe2	fe2	X
ejpam-4028	123	7	=	=	SYM
ejpam-4028	123	8	gen+1	gen+1	NOUN
ejpam-4028	123	9	and	and	CCONJ
ejpam-4028	123	10	fe3	fe3	NOUN
ejpam-4028	123	11	=	=	SYM
ejpam-4028	123	12	gen+1	gen+1	NOUN
ejpam-4028	123	13	in	in	ADP
ejpam-4028	123	14	(	(	PUNCT
ejpam-4028	123	15	2	2	NUM
ejpam-4028	123	16	)	)	PUNCT
ejpam-4028	123	17	,	,	PUNCT
ejpam-4028	123	18	we	we	PRON
ejpam-4028	123	19	obtain	obtain	VERB
ejpam-4028	123	20	¯̄ag̃(tgen	¯̄ag̃(tgen	PROPN
ejpam-4028	123	21	,	,	PUNCT
ejpam-4028	123	22	t	t	PROPN
ejpam-4028	123	23	gen+1	gen+1	NOUN
ejpam-4028	123	24	,	,	PUNCT
ejpam-4028	123	25	t	t	PROPN
ejpam-4028	123	26	gen+1)≤̃¯̄b	gen+1)≤̃¯̄b	PROPN
ejpam-4028	123	27			PUNCT
ejpam-4028	123	28	g̃(gen	g̃(gen	PROPN
ejpam-4028	123	29	,	,	PUNCT
ejpam-4028	123	30	t	t	PROPN
ejpam-4028	123	31	gen+1	gen+1	PROPN
ejpam-4028	123	32	,	,	PUNCT
ejpam-4028	123	33	t	t	PROPN
ejpam-4028	123	34	gen+1	gen+1	PROPN
ejpam-4028	123	35	)	)	PUNCT
ejpam-4028	124	1	+	+	NOUN
ejpam-4028	124	2	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	124	3	,	,	PUNCT
ejpam-4028	124	4	t	t	PROPN
ejpam-4028	124	5	gen+1	gen+1	NOUN
ejpam-4028	124	6	,	,	PUNCT
ejpam-4028	124	7	t	t	PROPN
ejpam-4028	124	8	gen+1	gen+1	PROPN
ejpam-4028	124	9	)	)	PUNCT
ejpam-4028	125	1	+	+	NOUN
ejpam-4028	125	2	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	125	3	,	,	PUNCT
ejpam-4028	125	4	t	t	PROPN
ejpam-4028	125	5	gen	gen	PROPN
ejpam-4028	125	6	,	,	PUNCT
ejpam-4028	125	7	t	t	PROPN
ejpam-4028	125	8	gen	gen	PROPN
ejpam-4028	125	9	)	)	PUNCT
ejpam-4028	125	10	+	+	VERB
ejpam-4028	125	11	¯̄cg̃(gen	¯̄cg̃(gen	PROPN
ejpam-4028	125	12	,	,	PUNCT
ejpam-4028	125	13	gen+1	gen+1	NOUN
ejpam-4028	125	14	,	,	PUNCT
ejpam-4028	125	15	gen+1	gen+1	NOUN
ejpam-4028	125	16	)	)	PUNCT
ejpam-4028	125	17	a.	a.	PROPN
ejpam-4028	125	18	f.	f.	PROPN
ejpam-4028	125	19	sayed	say	VERB
ejpam-4028	125	20	,	,	PUNCT
ejpam-4028	125	21	a.	a.	NOUN
ejpam-4028	125	22	alahmari	alahmari	PROPN
ejpam-4028	125	23	/	/	SYM
ejpam-4028	125	24	eur	eur	PROPN
ejpam-4028	125	25	.	.	PUNCT
ejpam-4028	126	1	j.	j.	PROPN
ejpam-4028	126	2	pure	pure	PROPN
ejpam-4028	126	3	appl	appl	PROPN
ejpam-4028	126	4	.	.	PROPN
ejpam-4028	126	5	math	math	PROPN
ejpam-4028	126	6	,	,	PUNCT
ejpam-4028	126	7	14	14	NUM
ejpam-4028	126	8	(	(	PUNCT
ejpam-4028	126	9	3	3	NUM
ejpam-4028	126	10	)	)	PUNCT
ejpam-4028	126	11	(	(	PUNCT
ejpam-4028	126	12	2021	2021	NUM
ejpam-4028	126	13	)	)	PUNCT
ejpam-4028	126	14	,	,	PUNCT
ejpam-4028	126	15	923	923	NUM
ejpam-4028	126	16	-	-	SYM
ejpam-4028	126	17	941	941	NUM
ejpam-4028	126	18	928	928	NUM
ejpam-4028	126	19	⇒	⇒	NOUN
ejpam-4028	126	20	¯̄ag̃(gen+1	¯̄ag̃(gen+1	NOUN
ejpam-4028	126	21	,	,	PUNCT
ejpam-4028	126	22	gen+2	gen+2	NOUN
ejpam-4028	126	23	,	,	PUNCT
ejpam-4028	126	24	gen+2)≤̃¯̄b	gen+2)≤̃¯̄b	PROPN
ejpam-4028	126	25			PUNCT
ejpam-4028	126	26	g̃(gen	g̃(gen	PROPN
ejpam-4028	126	27	,	,	PUNCT
ejpam-4028	126	28	gen+2	gen+2	NOUN
ejpam-4028	126	29	,	,	PUNCT
ejpam-4028	126	30	gen+2	gen+2	NOUN
ejpam-4028	126	31	)	)	PUNCT
ejpam-4028	127	1	+	+	NOUN
ejpam-4028	127	2	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	127	3	,	,	PUNCT
ejpam-4028	127	4	gen+2	gen+2	NOUN
ejpam-4028	127	5	,	,	PUNCT
ejpam-4028	127	6	gen+2	gen+2	NOUN
ejpam-4028	127	7	)	)	PUNCT
ejpam-4028	127	8	+	+	NOUN
ejpam-4028	127	9	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	127	10	,	,	PUNCT
ejpam-4028	127	11	gen+1	gen+1	NOUN
ejpam-4028	127	12	,	,	PUNCT
ejpam-4028	127	13	gen+1	gen+1	NOUN
ejpam-4028	127	14	)	)	PUNCT
ejpam-4028	127	15	+	+	VERB
ejpam-4028	127	16	¯̄cg̃(gen	¯̄cg̃(gen	PROPN
ejpam-4028	127	17	,	,	PUNCT
ejpam-4028	127	18	gen+1	gen+1	NOUN
ejpam-4028	127	19	,	,	PUNCT
ejpam-4028	127	20	gen+1	gen+1	NOUN
ejpam-4028	127	21	)	)	PUNCT
ejpam-4028	127	22	⇒	⇒	NOUN
ejpam-4028	127	23	¯̄ag̃(gen+1	¯̄ag̃(gen+1	NOUN
ejpam-4028	127	24	,	,	PUNCT
ejpam-4028	127	25	gen+2	gen+2	NOUN
ejpam-4028	127	26	,	,	PUNCT
ejpam-4028	127	27	gen+2)≤̃	gen+2)≤̃	PROPN
ejpam-4028	127	28	¯̄b+¯̄c	¯̄b+¯̄c	PROPN
ejpam-4028	127	29	(	(	PUNCT
ejpam-4028	127	30	¯̄a−˜̃2¯̄b	¯̄a−˜̃2¯̄b	NOUN
ejpam-4028	127	31	)	)	PUNCT
ejpam-4028	127	32	g̃(gen	g̃(gen	PROPN
ejpam-4028	127	33	,	,	PUNCT
ejpam-4028	127	34	gen+1	gen+1	NOUN
ejpam-4028	127	35	,	,	PUNCT
ejpam-4028	127	36	gen+1	gen+1	NOUN
ejpam-4028	127	37	)	)	PUNCT
ejpam-4028	127	38	⇒	⇒	NOUN
ejpam-4028	127	39	¯̄ag̃(gen+1	¯̄ag̃(gen+1	NOUN
ejpam-4028	127	40	,	,	PUNCT
ejpam-4028	127	41	gen+2	gen+2	NOUN
ejpam-4028	127	42	,	,	PUNCT
ejpam-4028	127	43	gen+2)≤̃¯̄kg̃(gen	gen+2)≤̃¯̄kg̃(gen	NOUN
ejpam-4028	127	44	,	,	PUNCT
ejpam-4028	127	45	gen+1	gen+1	NOUN
ejpam-4028	127	46	,	,	PUNCT
ejpam-4028	127	47	gen+1	gen+1	NOUN
ejpam-4028	127	48	)	)	PUNCT
ejpam-4028	127	49	,	,	PUNCT
ejpam-4028	128	1	where	where	SCONJ
ejpam-4028	128	2	¯̄k	¯̄k	PROPN
ejpam-4028	128	3	=	=	SYM
ejpam-4028	128	4	¯̄b+¯̄c	¯̄b+¯̄c	PROPN
ejpam-4028	128	5	(	(	PUNCT
ejpam-4028	128	6	¯̄a−˜̃2¯̄b	¯̄a−˜̃2¯̄b	NOUN
ejpam-4028	128	7	)	)	PUNCT
ejpam-4028	128	8	<	<	X
ejpam-4028	128	9	̃1̃.	̃1̃.	PROPN
ejpam-4028	128	10	on	on	ADP
ejpam-4028	128	11	continuing	continue	VERB
ejpam-4028	128	12	this	this	DET
ejpam-4028	128	13	process	process	NOUN
ejpam-4028	128	14	(	(	PUNCT
ejpam-4028	128	15	n+	n+	NOUN
ejpam-4028	128	16	1	1	NUM
ejpam-4028	128	17	)	)	PUNCT
ejpam-4028	128	18	times	time	NOUN
ejpam-4028	128	19	;	;	PUNCT
ejpam-4028	128	20	we	we	PRON
ejpam-4028	128	21	obtain	obtain	VERB
ejpam-4028	128	22	¯̄ag̃(gen+1	¯̄ag̃(gen+1	ADJ
ejpam-4028	128	23	,	,	PUNCT
ejpam-4028	128	24	gen+2	gen+2	NOUN
ejpam-4028	128	25	,	,	PUNCT
ejpam-4028	128	26	gen+2)≤̃¯̄k(n+1)g̃(ge0	gen+2)≤̃¯̄k(n+1)g̃(ge0	PROPN
ejpam-4028	128	27	,	,	PUNCT
ejpam-4028	128	28	ge1	ge1	NOUN
ejpam-4028	128	29	,	,	PUNCT
ejpam-4028	128	30	ge1	ge1	PROPN
ejpam-4028	128	31	)	)	PUNCT
ejpam-4028	128	32	.	.	PUNCT
ejpam-4028	129	1	similarly	similarly	ADV
ejpam-4028	129	2	,	,	PUNCT
ejpam-4028	129	3	we	we	PRON
ejpam-4028	129	4	will	will	AUX
ejpam-4028	129	5	conclude	conclude	VERB
ejpam-4028	129	6	that	that	PRON
ejpam-4028	129	7	¯̄ag̃(gen	¯̄ag̃(gen	NOUN
ejpam-4028	129	8	,	,	PUNCT
ejpam-4028	129	9	gen+1	gen+1	NOUN
ejpam-4028	129	10	,	,	PUNCT
ejpam-4028	129	11	gen+1)≤̃¯̄kng̃(ge0	gen+1)≤̃¯̄kng̃(ge0	NOUN
ejpam-4028	129	12	,	,	PUNCT
ejpam-4028	129	13	ge1	ge1	NOUN
ejpam-4028	129	14	,	,	PUNCT
ejpam-4028	129	15	ge1	ge1	PROPN
ejpam-4028	129	16	)	)	PUNCT
ejpam-4028	129	17	.	.	PUNCT
ejpam-4028	130	1	next	next	ADV
ejpam-4028	130	2	,	,	PUNCT
ejpam-4028	130	3	we	we	PRON
ejpam-4028	130	4	show	show	VERB
ejpam-4028	130	5	that	that	SCONJ
ejpam-4028	130	6	{	{	PUNCT
ejpam-4028	130	7	gen}n∈n	gen}n∈n	NOUN
ejpam-4028	130	8	is	be	AUX
ejpam-4028	130	9	a	a	DET
ejpam-4028	130	10	fuzzy	fuzzy	ADJ
ejpam-4028	130	11	soft	soft	ADJ
ejpam-4028	130	12	g	g	NOUN
ejpam-4028	130	13	-	-	PUNCT
ejpam-4028	130	14	cauchy	cauchy	ADJ
ejpam-4028	130	15	sequence	sequence	NOUN
ejpam-4028	130	16	.	.	PUNCT
ejpam-4028	131	1	then	then	ADV
ejpam-4028	131	2	for	for	ADP
ejpam-4028	131	3	all	all	DET
ejpam-4028	131	4	n	n	CCONJ
ejpam-4028	131	5	,	,	PUNCT
ejpam-4028	131	6	m	m	VERB
ejpam-4028	131	7	∈	∈	PROPN
ejpam-4028	131	8	n	n	CCONJ
ejpam-4028	131	9	,	,	PUNCT
ejpam-4028	131	10	n	n	CCONJ
ejpam-4028	131	11	<	<	X
ejpam-4028	131	12	m	m	PROPN
ejpam-4028	131	13	,	,	PUNCT
ejpam-4028	131	14	we	we	PRON
ejpam-4028	131	15	have	have	VERB
ejpam-4028	131	16	g̃(gen	g̃(gen	PROPN
ejpam-4028	131	17	,	,	PUNCT
ejpam-4028	131	18	gem	gem	NOUN
ejpam-4028	131	19	,	,	PUNCT
ejpam-4028	131	20	gem)≤̃g̃(gen	gem)≤̃g̃(gen	NOUN
ejpam-4028	131	21	,	,	PUNCT
ejpam-4028	131	22	gen+1	gen+1	NOUN
ejpam-4028	131	23	,	,	PUNCT
ejpam-4028	131	24	gen+1	gen+1	NOUN
ejpam-4028	131	25	)	)	PUNCT
ejpam-4028	132	1	+	+	CCONJ
ejpam-4028	132	2	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	132	3	,	,	PUNCT
ejpam-4028	132	4	gen+2	gen+2	NOUN
ejpam-4028	132	5	,	,	PUNCT
ejpam-4028	132	6	gen+2	gen+2	NOUN
ejpam-4028	132	7	)	)	PUNCT
ejpam-4028	133	1	+	+	CCONJ
ejpam-4028	133	2	...	...	PUNCT
ejpam-4028	134	1	+	+	CCONJ
ejpam-4028	134	2	g̃(gem−1	g̃(gem−1	NOUN
ejpam-4028	134	3	,	,	PUNCT
ejpam-4028	134	4	gem	gem	NOUN
ejpam-4028	134	5	,	,	PUNCT
ejpam-4028	134	6	gem	gem	NOUN
ejpam-4028	134	7	)	)	PUNCT
ejpam-4028	134	8	≤̃(¯̄kn	≤̃(¯̄kn	PROPN
ejpam-4028	134	9	+	+	CCONJ
ejpam-4028	134	10	¯̄k(n+1	¯̄k(n+1	PROPN
ejpam-4028	134	11	)	)	PUNCT
ejpam-4028	135	1	+	+	CCONJ
ejpam-4028	135	2	...	...	PUNCT
ejpam-4028	136	1	+	+	CCONJ
ejpam-4028	136	2	¯̄kmg̃(ge0	¯̄kmg̃(ge0	ADJ
ejpam-4028	136	3	,	,	PUNCT
ejpam-4028	136	4	ge1	ge1	NOUN
ejpam-4028	136	5	,	,	PUNCT
ejpam-4028	136	6	ge1	ge1	NOUN
ejpam-4028	136	7	)	)	PUNCT
ejpam-4028	136	8	≤̃	≤̃	PROPN
ejpam-4028	136	9	¯̄kn	¯̄kn	PROPN
ejpam-4028	136	10	1̃−¯̄k	1̃−¯̄k	NUM
ejpam-4028	136	11	g̃(ge0	g̃(ge0	PROPN
ejpam-4028	136	12	,	,	PUNCT
ejpam-4028	136	13	ge1	ge1	NOUN
ejpam-4028	136	14	,	,	PUNCT
ejpam-4028	136	15	ge1	ge1	PROPN
ejpam-4028	136	16	)	)	PUNCT
ejpam-4028	136	17	.	.	PUNCT
ejpam-4028	137	1	hence	hence	ADV
ejpam-4028	137	2	,	,	PUNCT
ejpam-4028	137	3	{	{	PUNCT
ejpam-4028	137	4	gen}n∈n	gen}n∈n	PROPN
ejpam-4028	137	5	is	be	AUX
ejpam-4028	137	6	a	a	DET
ejpam-4028	137	7	fuzzy	fuzzy	ADJ
ejpam-4028	137	8	soft	soft	ADJ
ejpam-4028	137	9	g	g	NOUN
ejpam-4028	137	10	-	-	PUNCT
ejpam-4028	137	11	cauchy	cauchy	ADJ
ejpam-4028	137	12	sequence	sequence	NOUN
ejpam-4028	137	13	.	.	PUNCT
ejpam-4028	138	1	since	since	SCONJ
ejpam-4028	138	2	(	(	PUNCT
ejpam-4028	138	3	ẽ	ẽ	PROPN
ejpam-4028	138	4	,	,	PUNCT
ejpam-4028	138	5	g̃	g̃	PROPN
ejpam-4028	138	6	)	)	PUNCT
ejpam-4028	138	7	is	be	AUX
ejpam-4028	138	8	fuzzy	fuzzy	ADJ
ejpam-4028	138	9	soft	soft	ADJ
ejpam-4028	138	10	g	g	NOUN
ejpam-4028	138	11	-	-	PUNCT
ejpam-4028	138	12	complete	complete	ADJ
ejpam-4028	138	13	,	,	PUNCT
ejpam-4028	138	14	there	there	PRON
ejpam-4028	138	15	exists	exist	VERB
ejpam-4028	138	16	fe∈̃fsc(ẽ	fe∈̃fsc(ẽ	PROPN
ejpam-4028	138	17	)	)	PUNCT
ejpam-4028	138	18	such	such	ADJ
ejpam-4028	138	19	that	that	SCONJ
ejpam-4028	138	20	{	{	PUNCT
ejpam-4028	138	21	gen}n∈n	gen}n∈n	PROPN
ejpam-4028	138	22	fuzzy	fuzzy	ADJ
ejpam-4028	138	23	soft	soft	ADJ
ejpam-4028	138	24	g	g	NOUN
ejpam-4028	138	25	-	-	PUNCT
ejpam-4028	138	26	converges	converge	NOUN
ejpam-4028	138	27	to	to	ADP
ejpam-4028	138	28	fe	fe	PROPN
ejpam-4028	138	29	.	.	PUNCT
ejpam-4028	139	1	next	next	ADV
ejpam-4028	139	2	,	,	PUNCT
ejpam-4028	139	3	we	we	PRON
ejpam-4028	139	4	will	will	AUX
ejpam-4028	139	5	show	show	VERB
ejpam-4028	139	6	that	that	SCONJ
ejpam-4028	139	7	fe	fe	PROPN
ejpam-4028	139	8	is	be	AUX
ejpam-4028	139	9	a	a	DET
ejpam-4028	139	10	fixed	fix	VERB
ejpam-4028	139	11	point	point	NOUN
ejpam-4028	139	12	of	of	ADP
ejpam-4028	139	13	t	t	PROPN
ejpam-4028	139	14	.	.	PUNCT
ejpam-4028	140	1	for	for	ADP
ejpam-4028	140	2	this	this	PRON
ejpam-4028	140	3	,	,	PUNCT
ejpam-4028	140	4	we	we	PRON
ejpam-4028	140	5	take	take	VERB
ejpam-4028	140	6	fe1	fe1	PROPN
ejpam-4028	140	7	=	=	SYM
ejpam-4028	140	8	gen	gen	PROPN
ejpam-4028	140	9	and	and	CCONJ
ejpam-4028	140	10	fe2	fe2	PROPN
ejpam-4028	140	11	=	=	SYM
ejpam-4028	140	12	fe3	fe3	PROPN
ejpam-4028	140	13	=	=	SYM
ejpam-4028	140	14	fe	fe	X
ejpam-4028	140	15	in	in	ADP
ejpam-4028	140	16	(	(	PUNCT
ejpam-4028	140	17	3.1	3.1	NUM
ejpam-4028	140	18	)	)	PUNCT
ejpam-4028	140	19	,	,	PUNCT
ejpam-4028	140	20	then	then	ADV
ejpam-4028	140	21	¯̄ag̃(tgen	¯̄ag̃(tgen	PROPN
ejpam-4028	140	22	,	,	PUNCT
ejpam-4028	140	23	t	t	PROPN
ejpam-4028	140	24	fe	fe	PROPN
ejpam-4028	140	25	,	,	PUNCT
ejpam-4028	140	26	t	t	PROPN
ejpam-4028	140	27	fe)≤̃¯̄b	fe)≤̃¯̄b	NOUN
ejpam-4028	140	28			PUNCT
ejpam-4028	140	29	g̃(gen	g̃(gen	PROPN
ejpam-4028	140	30	,	,	PUNCT
ejpam-4028	140	31	t	t	PROPN
ejpam-4028	140	32	fe	fe	PROPN
ejpam-4028	140	33	,	,	PUNCT
ejpam-4028	140	34	t	t	PROPN
ejpam-4028	140	35	fe	fe	X
ejpam-4028	140	36	)	)	PUNCT
ejpam-4028	141	1	+	+	NOUN
ejpam-4028	141	2	g̃(fe	g̃(fe	NOUN
ejpam-4028	141	3	,	,	PUNCT
ejpam-4028	141	4	tfe	tfe	NOUN
ejpam-4028	141	5	,	,	PUNCT
ejpam-4028	141	6	tfe	tfe	NOUN
ejpam-4028	141	7	)	)	PUNCT
ejpam-4028	141	8	+	+	NOUN
ejpam-4028	141	9	g̃(fe	g̃(fe	NOUN
ejpam-4028	141	10	,	,	PUNCT
ejpam-4028	141	11	t	t	PROPN
ejpam-4028	141	12	gen	gen	PROPN
ejpam-4028	141	13	,	,	PUNCT
ejpam-4028	141	14	t	t	PROPN
ejpam-4028	141	15	gen	gen	PROPN
ejpam-4028	141	16	)	)	PUNCT
ejpam-4028	141	17	+	+	VERB
ejpam-4028	141	18	¯̄cg̃(gen	¯̄cg̃(gen	PROPN
ejpam-4028	141	19	,	,	PUNCT
ejpam-4028	141	20	fe	fe	PROPN
ejpam-4028	141	21	,	,	PUNCT
ejpam-4028	141	22	fe	fe	NOUN
ejpam-4028	141	23	)	)	PUNCT
ejpam-4028	141	24	⇒	⇒	PROPN
ejpam-4028	141	25	¯̄ag̃(fe	¯̄ag̃(fe	PROPN
ejpam-4028	141	26	,	,	PUNCT
ejpam-4028	141	27	t	t	PROPN
ejpam-4028	141	28	fe	fe	PROPN
ejpam-4028	141	29	,	,	PUNCT
ejpam-4028	141	30	t	t	PROPN
ejpam-4028	141	31	fe)≤̃¯̄b	fe)≤̃¯̄b	NOUN
ejpam-4028	141	32			PUNCT
ejpam-4028	141	33	g̃(fe	g̃(fe	NOUN
ejpam-4028	141	34	,	,	PUNCT
ejpam-4028	141	35	t	t	PROPN
ejpam-4028	141	36	fe	fe	PROPN
ejpam-4028	141	37	,	,	PUNCT
ejpam-4028	141	38	t	t	PROPN
ejpam-4028	141	39	fe	fe	X
ejpam-4028	141	40	)	)	PUNCT
ejpam-4028	142	1	+	+	NOUN
ejpam-4028	142	2	g̃(fe	g̃(fe	NOUN
ejpam-4028	142	3	,	,	PUNCT
ejpam-4028	142	4	t	t	PROPN
ejpam-4028	142	5	fe	fe	PROPN
ejpam-4028	142	6	,	,	PUNCT
ejpam-4028	142	7	t	t	PROPN
ejpam-4028	142	8	fe	fe	X
ejpam-4028	142	9	)	)	PUNCT
ejpam-4028	142	10	+	+	NOUN
ejpam-4028	142	11	g̃(fe	g̃(fe	NOUN
ejpam-4028	142	12	,	,	PUNCT
ejpam-4028	142	13	fe	fe	X
ejpam-4028	142	14	,	,	PUNCT
ejpam-4028	142	15	fe	fe	X
ejpam-4028	142	16	)	)	PUNCT
ejpam-4028	142	17	+	+	VERB
ejpam-4028	142	18	¯̄cg̃(fe	¯̄cg̃(fe	PROPN
ejpam-4028	142	19	,	,	PUNCT
ejpam-4028	142	20	fe	fe	X
ejpam-4028	142	21	,	,	PUNCT
ejpam-4028	142	22	fe	fe	NOUN
ejpam-4028	142	23	)	)	PUNCT
ejpam-4028	142	24	.	.	PUNCT
ejpam-4028	143	1	⇒	⇒	PROPN
ejpam-4028	143	2	g̃(fe	g̃(fe	PROPN
ejpam-4028	143	3	,	,	PUNCT
ejpam-4028	143	4	tfe	tfe	NOUN
ejpam-4028	143	5	,	,	PUNCT
ejpam-4028	143	6	tfe)≤̃	tfe)≤̃	ADJ
ejpam-4028	143	7	˜̃2¯̄b	˜̃2¯̄b	NOUN
ejpam-4028	143	8	¯̄a	¯̄a	NOUN
ejpam-4028	143	9	g̃((fe	g̃((fe	NOUN
ejpam-4028	143	10	,	,	PUNCT
ejpam-4028	143	11	tfe	tfe	NOUN
ejpam-4028	143	12	,	,	PUNCT
ejpam-4028	143	13	tfe	tfe	NOUN
ejpam-4028	143	14	)	)	PUNCT
ejpam-4028	143	15	.	.	PUNCT
ejpam-4028	144	1	this	this	PRON
ejpam-4028	144	2	is	be	AUX
ejpam-4028	144	3	a	a	DET
ejpam-4028	144	4	contradiction	contradiction	NOUN
ejpam-4028	144	5	,	,	PUNCT
ejpam-4028	144	6	so	so	ADV
ejpam-4028	144	7	tfe	tfe	NOUN
ejpam-4028	144	8	=	=	SYM
ejpam-4028	144	9	fe	fe	X
ejpam-4028	144	10	i.e.	i.e.	X
ejpam-4028	144	11	fe	fe	X
ejpam-4028	144	12	is	be	AUX
ejpam-4028	144	13	a	a	DET
ejpam-4028	144	14	fixed	fix	VERB
ejpam-4028	144	15	point	point	NOUN
ejpam-4028	144	16	of	of	ADP
ejpam-4028	144	17	t	t	PROPN
ejpam-4028	144	18	now	now	ADV
ejpam-4028	144	19	,	,	PUNCT
ejpam-4028	144	20	to	to	PART
ejpam-4028	144	21	prove	prove	VERB
ejpam-4028	144	22	uniqueness	uniqueness	NOUN
ejpam-4028	144	23	,	,	PUNCT
ejpam-4028	144	24	assume	assume	VERB
ejpam-4028	144	25	that	that	SCONJ
ejpam-4028	144	26	fe	fe	PROPN
ejpam-4028	144	27	and	and	CCONJ
ejpam-4028	144	28	ge	ge	PROPN
ejpam-4028	144	29	are	be	AUX
ejpam-4028	144	30	two	two	NUM
ejpam-4028	144	31	fixed	fix	VERB
ejpam-4028	144	32	points	point	NOUN
ejpam-4028	144	33	of	of	ADP
ejpam-4028	144	34	t	t	PROPN
ejpam-4028	144	35	.	.	PUNCT
ejpam-4028	145	1	then	then	ADV
ejpam-4028	145	2	by	by	ADP
ejpam-4028	145	3	inequality	inequality	NOUN
ejpam-4028	145	4	(	(	PUNCT
ejpam-4028	145	5	2	2	NUM
ejpam-4028	145	6	)	)	PUNCT
ejpam-4028	145	7	,	,	PUNCT
ejpam-4028	145	8	we	we	PRON
ejpam-4028	145	9	have	have	VERB
ejpam-4028	145	10	¯̄ag̃(tfe	¯̄ag̃(tfe	NOUN
ejpam-4028	145	11	,	,	PUNCT
ejpam-4028	145	12	t	t	PROPN
ejpam-4028	145	13	ge	ge	PROPN
ejpam-4028	145	14	,	,	PUNCT
ejpam-4028	145	15	t	t	PROPN
ejpam-4028	145	16	ge)≤̃¯̄b	ge)≤̃¯̄b	PROPN
ejpam-4028	145	17			PUNCT
ejpam-4028	145	18	g̃(fe	g̃(fe	NOUN
ejpam-4028	145	19	,	,	PUNCT
ejpam-4028	145	20	t	t	PROPN
ejpam-4028	145	21	ge	ge	PROPN
ejpam-4028	145	22	,	,	PUNCT
ejpam-4028	145	23	t	t	PROPN
ejpam-4028	145	24	ge	ge	PROPN
ejpam-4028	145	25	)	)	PUNCT
ejpam-4028	146	1	+	+	NUM
ejpam-4028	146	2	g̃(ge	g̃(ge	NOUN
ejpam-4028	146	3	,	,	PUNCT
ejpam-4028	146	4	t	t	PROPN
ejpam-4028	146	5	ge	ge	PROPN
ejpam-4028	146	6	,	,	PUNCT
ejpam-4028	146	7	t	t	PROPN
ejpam-4028	146	8	ge	ge	PROPN
ejpam-4028	146	9	)	)	PUNCT
ejpam-4028	147	1	+	+	NUM
ejpam-4028	147	2	g̃(ge	g̃(ge	NOUN
ejpam-4028	147	3	,	,	PUNCT
ejpam-4028	147	4	t	t	PROPN
ejpam-4028	147	5	fe	fe	PROPN
ejpam-4028	147	6	,	,	PUNCT
ejpam-4028	147	7	t	t	PROPN
ejpam-4028	147	8	fe	fe	X
ejpam-4028	147	9	)	)	PUNCT
ejpam-4028	147	10	+	+	VERB
ejpam-4028	147	11	¯̄cg̃(fe	¯̄cg̃(fe	PROPN
ejpam-4028	147	12	,	,	PUNCT
ejpam-4028	147	13	ge	ge	PROPN
ejpam-4028	147	14	,	,	PUNCT
ejpam-4028	147	15	ge	ge	PROPN
ejpam-4028	147	16	)	)	PUNCT
ejpam-4028	147	17	⇒	⇒	PROPN
ejpam-4028	147	18	¯̄ag̃(fe	¯̄ag̃(fe	PROPN
ejpam-4028	147	19	,	,	PUNCT
ejpam-4028	147	20	ge	ge	PROPN
ejpam-4028	147	21	,	,	PUNCT
ejpam-4028	147	22	ge)≤̃¯̄b	ge)≤̃¯̄b	PROPN
ejpam-4028	147	23			NOUN
ejpam-4028	147	24	g̃(fe	g̃(fe	NOUN
ejpam-4028	147	25	,	,	PUNCT
ejpam-4028	147	26	ge	ge	PROPN
ejpam-4028	147	27	,	,	PUNCT
ejpam-4028	147	28	ge	ge	PROPN
ejpam-4028	147	29	)	)	PUNCT
ejpam-4028	148	1	+	+	NUM
ejpam-4028	148	2	g̃(ge	g̃(ge	NOUN
ejpam-4028	148	3	,	,	PUNCT
ejpam-4028	148	4	ge	ge	PROPN
ejpam-4028	148	5	,	,	PUNCT
ejpam-4028	148	6	ge	ge	PROPN
ejpam-4028	148	7	)	)	PUNCT
ejpam-4028	148	8	+	+	NUM
ejpam-4028	148	9	g̃(ge	g̃(ge	ADJ
ejpam-4028	148	10	,	,	PUNCT
ejpam-4028	148	11	fe	fe	X
ejpam-4028	148	12	,	,	PUNCT
ejpam-4028	148	13	fe	fe	X
ejpam-4028	148	14	)	)	PUNCT
ejpam-4028	148	15	+	+	VERB
ejpam-4028	148	16	¯̄cg̃(fe	¯̄cg̃(fe	PROPN
ejpam-4028	148	17	,	,	PUNCT
ejpam-4028	148	18	ge	ge	PROPN
ejpam-4028	148	19	,	,	PUNCT
ejpam-4028	148	20	ge	ge	PROPN
ejpam-4028	148	21	)	)	PUNCT
ejpam-4028	148	22	.	.	PUNCT
ejpam-4028	149	1	so	so	ADV
ejpam-4028	149	2	,	,	PUNCT
ejpam-4028	149	3	we	we	PRON
ejpam-4028	149	4	deduct	deduct	VERB
ejpam-4028	149	5	that	that	PRON
ejpam-4028	149	6	(	(	PUNCT
ejpam-4028	149	7	¯̄a−	¯̄a−	NOUN
ejpam-4028	149	8	¯̄b−	¯̄b−	PROPN
ejpam-4028	149	9	¯̄c)g̃(fe	¯̄c)g̃(fe	NOUN
ejpam-4028	149	10	,	,	PUNCT
ejpam-4028	149	11	ge	ge	PROPN
ejpam-4028	149	12	,	,	PUNCT
ejpam-4028	149	13	ge)≤̃¯̄bg̃(ge	ge)≤̃¯̄bg̃(ge	PROPN
ejpam-4028	149	14	,	,	PUNCT
ejpam-4028	149	15	fe	fe	X
ejpam-4028	149	16	,	,	PUNCT
ejpam-4028	149	17	fe	fe	NOUN
ejpam-4028	149	18	)	)	PUNCT
ejpam-4028	149	19	.	.	PUNCT
ejpam-4028	150	1	⇒	⇒	PROPN
ejpam-4028	150	2	g̃(fe	g̃(fe	PROPN
ejpam-4028	150	3	,	,	PUNCT
ejpam-4028	150	4	ge	ge	PROPN
ejpam-4028	150	5	,	,	PUNCT
ejpam-4028	150	6	ge)≤̃	ge)≤̃	PROPN
ejpam-4028	150	7	¯̄b	¯̄b	NOUN
ejpam-4028	150	8	(	(	PUNCT
ejpam-4028	150	9	¯̄a−¯̄b−¯̄c	¯̄a−¯̄b−¯̄c	ADJ
ejpam-4028	150	10	)	)	PUNCT
ejpam-4028	150	11	g̃(ge	g̃(ge	NOUN
ejpam-4028	150	12	,	,	PUNCT
ejpam-4028	150	13	fe	fe	X
ejpam-4028	150	14	,	,	PUNCT
ejpam-4028	150	15	fe	fe	NOUN
ejpam-4028	150	16	)	)	PUNCT
ejpam-4028	150	17	and	and	CCONJ
ejpam-4028	150	18	by	by	ADP
ejpam-4028	150	19	use	use	NOUN
ejpam-4028	150	20	of	of	ADP
ejpam-4028	150	21	the	the	DET
ejpam-4028	150	22	same	same	ADJ
ejpam-4028	150	23	argument	argument	NOUN
ejpam-4028	150	24	,	,	PUNCT
ejpam-4028	150	25	we	we	PRON
ejpam-4028	150	26	will	will	AUX
ejpam-4028	150	27	find	find	VERB
ejpam-4028	150	28	g̃(ge	g̃(ge	NOUN
ejpam-4028	150	29	,	,	PUNCT
ejpam-4028	150	30	fe	fe	NOUN
ejpam-4028	150	31	,	,	PUNCT
ejpam-4028	150	32	fe)≤̃	fe)≤̃	VERB
ejpam-4028	150	33	¯̄b	¯̄b	NOUN
ejpam-4028	150	34	(	(	PUNCT
ejpam-4028	150	35	¯̄a−¯̄b−¯̄c	¯̄a−¯̄b−¯̄c	ADJ
ejpam-4028	150	36	)	)	PUNCT
ejpam-4028	150	37	g̃(fe	g̃(fe	NOUN
ejpam-4028	150	38	,	,	PUNCT
ejpam-4028	150	39	ge	ge	PROPN
ejpam-4028	150	40	,	,	PUNCT
ejpam-4028	150	41	ge	ge	PROPN
ejpam-4028	150	42	)	)	PUNCT
ejpam-4028	150	43	.	.	PUNCT
ejpam-4028	151	1	a.	a.	PROPN
ejpam-4028	151	2	f.	f.	PROPN
ejpam-4028	151	3	sayed	sayed	PROPN
ejpam-4028	151	4	,	,	PUNCT
ejpam-4028	151	5	a.	a.	NOUN
ejpam-4028	151	6	alahmari	alahmari	PROPN
ejpam-4028	151	7	/	/	SYM
ejpam-4028	151	8	eur	eur	PROPN
ejpam-4028	151	9	.	.	PUNCT
ejpam-4028	152	1	j.	j.	PROPN
ejpam-4028	152	2	pure	pure	PROPN
ejpam-4028	152	3	appl	appl	PROPN
ejpam-4028	152	4	.	.	PROPN
ejpam-4028	152	5	math	math	PROPN
ejpam-4028	152	6	,	,	PUNCT
ejpam-4028	152	7	14	14	NUM
ejpam-4028	152	8	(	(	PUNCT
ejpam-4028	152	9	3	3	NUM
ejpam-4028	152	10	)	)	PUNCT
ejpam-4028	152	11	(	(	PUNCT
ejpam-4028	152	12	2021	2021	NUM
ejpam-4028	152	13	)	)	PUNCT
ejpam-4028	152	14	,	,	PUNCT
ejpam-4028	152	15	923	923	NUM
ejpam-4028	152	16	-	-	SYM
ejpam-4028	152	17	941	941	NUM
ejpam-4028	152	18	929	929	NUM
ejpam-4028	152	19	therefore	therefore	ADV
ejpam-4028	152	20	,	,	PUNCT
ejpam-4028	152	21	we	we	PRON
ejpam-4028	152	22	get	get	VERB
ejpam-4028	152	23	g̃(fe	g̃(fe	ADJ
ejpam-4028	152	24	,	,	PUNCT
ejpam-4028	152	25	ge	ge	PROPN
ejpam-4028	152	26	,	,	PUNCT
ejpam-4028	152	27	ge)≤̃	ge)≤̃	PROPN
ejpam-4028	152	28	(	(	PUNCT
ejpam-4028	152	29	¯̄b	¯̄b	PROPN
ejpam-4028	152	30	(	(	PUNCT
ejpam-4028	152	31	¯̄a−¯̄b−¯̄c	¯̄a−¯̄b−¯̄c	PROPN
ejpam-4028	152	32	)	)	PUNCT
ejpam-4028	152	33	)	)	PUNCT
ejpam-4028	152	34	2	2	NUM
ejpam-4028	152	35	g̃(fe	g̃(fe	NOUN
ejpam-4028	152	36	,	,	PUNCT
ejpam-4028	152	37	ge	ge	PROPN
ejpam-4028	152	38	,	,	PUNCT
ejpam-4028	152	39	ge	ge	PROPN
ejpam-4028	152	40	)	)	PUNCT
ejpam-4028	152	41	,	,	PUNCT
ejpam-4028	152	42	since	since	SCONJ
ejpam-4028	152	43	˜̃3¯̄b	˜̃3¯̄b	NOUN
ejpam-4028	152	44	+	+	CCONJ
ejpam-4028	152	45	¯̄c<̃¯̄a	¯̄c<̃¯̄a	NOUN
ejpam-4028	152	46	,	,	PUNCT
ejpam-4028	152	47	this	this	PRON
ejpam-4028	152	48	is	be	AUX
ejpam-4028	152	49	a	a	DET
ejpam-4028	152	50	contradiction	contradiction	NOUN
ejpam-4028	152	51	implies	imply	VERB
ejpam-4028	152	52	that	that	PRON
ejpam-4028	152	53	fe	fe	X
ejpam-4028	152	54	=	=	PROPN
ejpam-4028	152	55	ge	ge	PROPN
ejpam-4028	152	56	.	.	PUNCT
ejpam-4028	153	1	to	to	PART
ejpam-4028	153	2	show	show	VERB
ejpam-4028	153	3	that	that	SCONJ
ejpam-4028	153	4	t	t	PROPN
ejpam-4028	153	5	is	be	AUX
ejpam-4028	153	6	fuzzy	fuzzy	ADJ
ejpam-4028	153	7	soft	soft	ADJ
ejpam-4028	153	8	g	g	NOUN
ejpam-4028	153	9	-	-	NOUN
ejpam-4028	153	10	continuous	continuous	ADJ
ejpam-4028	153	11	at	at	ADP
ejpam-4028	153	12	fe	fe	NOUN
ejpam-4028	153	13	.	.	PUNCT
ejpam-4028	153	14	let	let	AUX
ejpam-4028	153	15	{	{	PUNCT
ejpam-4028	153	16	hen}n∈n	hen}n∈n	PRON
ejpam-4028	153	17	be	be	AUX
ejpam-4028	153	18	a	a	DET
ejpam-4028	153	19	sequence	sequence	NOUN
ejpam-4028	153	20	of	of	ADP
ejpam-4028	153	21	fuzzy	fuzzy	ADJ
ejpam-4028	153	22	soft	soft	ADJ
ejpam-4028	153	23	elements	element	NOUN
ejpam-4028	153	24	in	in	ADP
ejpam-4028	153	25	ẽ	ẽ	PROPN
ejpam-4028	153	26	such	such	ADJ
ejpam-4028	153	27	that	that	SCONJ
ejpam-4028	153	28	{	{	PUNCT
ejpam-4028	153	29	hen}n∈n	hen}n∈n	PROPN
ejpam-4028	153	30	→	→	SYM
ejpam-4028	153	31	fe	fe	PROPN
ejpam-4028	153	32	,	,	PUNCT
ejpam-4028	153	33	then	then	ADV
ejpam-4028	153	34	we	we	PRON
ejpam-4028	153	35	can	can	AUX
ejpam-4028	153	36	deduce	deduce	VERB
ejpam-4028	153	37	that	that	SCONJ
ejpam-4028	153	38	using	use	VERB
ejpam-4028	153	39	inequality	inequality	NOUN
ejpam-4028	153	40	(	(	PUNCT
ejpam-4028	153	41	2	2	NUM
ejpam-4028	153	42	)	)	PUNCT
ejpam-4028	153	43	,	,	PUNCT
ejpam-4028	153	44	we	we	PRON
ejpam-4028	153	45	have	have	VERB
ejpam-4028	153	46	¯̄ag̃(tfe	¯̄ag̃(tfe	NOUN
ejpam-4028	153	47	,	,	PUNCT
ejpam-4028	153	48	then	then	ADV
ejpam-4028	153	49	,	,	PUNCT
ejpam-4028	153	50	then)≤̃¯̄b	then)≤̃¯̄b	PROPN
ejpam-4028	153	51			PUNCT
ejpam-4028	153	52	g̃(fe	g̃(fe	NOUN
ejpam-4028	153	53	,	,	PUNCT
ejpam-4028	153	54	then	then	ADV
ejpam-4028	153	55	,	,	PUNCT
ejpam-4028	153	56	then	then	ADV
ejpam-4028	153	57	)	)	PUNCT
ejpam-4028	154	1	+	+	ADV
ejpam-4028	154	2	g̃(hen	g̃(hen	ADV
ejpam-4028	154	3	,	,	PUNCT
ejpam-4028	154	4	then	then	ADV
ejpam-4028	154	5	,	,	PUNCT
ejpam-4028	154	6	then	then	ADV
ejpam-4028	154	7	)	)	PUNCT
ejpam-4028	155	1	+	+	ADV
ejpam-4028	155	2	g̃(hen	g̃(hen	PROPN
ejpam-4028	155	3	,	,	PUNCT
ejpam-4028	155	4	t	t	PROPN
ejpam-4028	155	5	fe	fe	PROPN
ejpam-4028	155	6	,	,	PUNCT
ejpam-4028	155	7	t	t	PROPN
ejpam-4028	155	8	fe	fe	X
ejpam-4028	155	9	)	)	PUNCT
ejpam-4028	155	10	+	+	VERB
ejpam-4028	155	11	¯̄cg̃(fe	¯̄cg̃(fe	PROPN
ejpam-4028	155	12	,	,	PUNCT
ejpam-4028	155	13	hen	hen	NOUN
ejpam-4028	155	14	,	,	PUNCT
ejpam-4028	155	15	hen	hen	NOUN
ejpam-4028	155	16	)	)	PUNCT
ejpam-4028	155	17	⇒	⇒	NOUN
ejpam-4028	155	18	¯̄ag̃(fe	¯̄ag̃(fe	NOUN
ejpam-4028	155	19	,	,	PUNCT
ejpam-4028	155	20	then	then	ADV
ejpam-4028	155	21	,	,	PUNCT
ejpam-4028	155	22	then)≤̃¯̄b	then)≤̃¯̄b	PROPN
ejpam-4028	155	23			PUNCT
ejpam-4028	155	24	g̃(fe	g̃(fe	NOUN
ejpam-4028	155	25	,	,	PUNCT
ejpam-4028	155	26	then	then	ADV
ejpam-4028	155	27	,	,	PUNCT
ejpam-4028	155	28	then	then	ADV
ejpam-4028	155	29	)	)	PUNCT
ejpam-4028	156	1	+	+	ADV
ejpam-4028	156	2	g̃(hen	g̃(hen	ADV
ejpam-4028	156	3	,	,	PUNCT
ejpam-4028	156	4	then	then	ADV
ejpam-4028	156	5	,	,	PUNCT
ejpam-4028	156	6	then	then	ADV
ejpam-4028	156	7	)	)	PUNCT
ejpam-4028	157	1	+	+	ADV
ejpam-4028	157	2	g̃(hen	g̃(hen	PROPN
ejpam-4028	157	3	,	,	PUNCT
ejpam-4028	157	4	fe	fe	X
ejpam-4028	157	5	,	,	PUNCT
ejpam-4028	157	6	fe	fe	X
ejpam-4028	157	7	)	)	PUNCT
ejpam-4028	157	8	+	+	VERB
ejpam-4028	157	9	¯̄cg̃(fe	¯̄cg̃(fe	PROPN
ejpam-4028	157	10	,	,	PUNCT
ejpam-4028	157	11	hen	hen	NOUN
ejpam-4028	157	12	,	,	PUNCT
ejpam-4028	157	13	hen	hen	NOUN
ejpam-4028	157	14	)	)	PUNCT
ejpam-4028	157	15	taking	take	VERB
ejpam-4028	157	16	the	the	DET
ejpam-4028	157	17	limit	limit	NOUN
ejpam-4028	157	18	as	as	ADP
ejpam-4028	157	19	n→∞	n→∞	NUM
ejpam-4028	157	20	from	from	ADP
ejpam-4028	157	21	which	which	PRON
ejpam-4028	157	22	,	,	PUNCT
ejpam-4028	157	23	we	we	PRON
ejpam-4028	157	24	see	see	VERB
ejpam-4028	157	25	that	that	PRON
ejpam-4028	157	26	(	(	PUNCT
ejpam-4028	157	27	ā−	ā−	NOUN
ejpam-4028	157	28	˜̃2¯̄b)g̃(fe	˜̃2¯̄b)g̃(fe	VERB
ejpam-4028	157	29	,	,	PUNCT
ejpam-4028	157	30	then	then	ADV
ejpam-4028	157	31	,	,	PUNCT
ejpam-4028	157	32	then)→	then)→	ADP
ejpam-4028	157	33	0̃	0̃	NOUN
ejpam-4028	157	34	and	and	CCONJ
ejpam-4028	157	35	so	so	ADV
ejpam-4028	157	36	,	,	PUNCT
ejpam-4028	157	37	by	by	ADP
ejpam-4028	157	38	proposition	proposition	NOUN
ejpam-4028	157	39	(	(	PUNCT
ejpam-4028	157	40	4.1	4.1	NUM
ejpam-4028	157	41	)	)	PUNCT
ejpam-4028	157	42	in	in	ADP
ejpam-4028	157	43	[	[	X
ejpam-4028	157	44	2	2	X
ejpam-4028	157	45	]	]	PUNCT
ejpam-4028	157	46	we	we	PRON
ejpam-4028	157	47	have	have	VERB
ejpam-4028	157	48	that	that	SCONJ
ejpam-4028	157	49	the	the	DET
ejpam-4028	157	50	sequence	sequence	NOUN
ejpam-4028	157	51	{	{	PUNCT
ejpam-4028	157	52	then}n∈n	then}n∈n	PROPN
ejpam-4028	157	53	is	be	AUX
ejpam-4028	157	54	fuzzy	fuzzy	ADJ
ejpam-4028	157	55	soft	soft	ADJ
ejpam-4028	157	56	g	g	NOUN
ejpam-4028	157	57	-	-	PUNCT
ejpam-4028	157	58	convergent	convergent	NOUN
ejpam-4028	157	59	to	to	ADP
ejpam-4028	157	60	tfe	tfe	NOUN
ejpam-4028	157	61	=	=	SYM
ejpam-4028	157	62	fe	fe	X
ejpam-4028	157	63	,	,	PUNCT
ejpam-4028	157	64	therefore	therefore	ADV
ejpam-4028	157	65	proposition	proposition	NOUN
ejpam-4028	157	66	(	(	PUNCT
ejpam-4028	157	67	4.4	4.4	NUM
ejpam-4028	157	68	)	)	PUNCT
ejpam-4028	157	69	in	in	ADP
ejpam-4028	157	70	[	[	X
ejpam-4028	157	71	2	2	NUM
ejpam-4028	157	72	]	]	PUNCT
ejpam-4028	157	73	implies	imply	VERB
ejpam-4028	157	74	that	that	SCONJ
ejpam-4028	157	75	t	t	PROPN
ejpam-4028	157	76	is	be	AUX
ejpam-4028	157	77	fuzzy	fuzzy	ADJ
ejpam-4028	157	78	soft	soft	ADJ
ejpam-4028	157	79	g	g	NOUN
ejpam-4028	157	80	-	-	NOUN
ejpam-4028	157	81	continuous	continuous	ADJ
ejpam-4028	157	82	at	at	ADP
ejpam-4028	157	83	fe	fe	PROPN
ejpam-4028	157	84	.	.	PROPN
ejpam-4028	157	85	theorem	theorem	NOUN
ejpam-4028	157	86	3	3	X
ejpam-4028	157	87	.	.	PUNCT
ejpam-4028	157	88	suppose	suppose	VERB
ejpam-4028	157	89	(	(	PUNCT
ejpam-4028	157	90	ẽ	ẽ	PROPN
ejpam-4028	157	91	,	,	PUNCT
ejpam-4028	157	92	g̃	g̃	PROPN
ejpam-4028	157	93	)	)	PUNCT
ejpam-4028	157	94	is	be	AUX
ejpam-4028	157	95	a	a	DET
ejpam-4028	157	96	fuzzy	fuzzy	ADJ
ejpam-4028	157	97	soft	soft	ADJ
ejpam-4028	157	98	g	g	NOUN
ejpam-4028	157	99	-	-	PUNCT
ejpam-4028	157	100	metric	metric	ADJ
ejpam-4028	157	101	space	space	NOUN
ejpam-4028	157	102	and	and	CCONJ
ejpam-4028	157	103	t	t	NOUN
ejpam-4028	157	104	:	:	PUNCT
ejpam-4028	157	105	(	(	PUNCT
ejpam-4028	157	106	ẽ	ẽ	NOUN
ejpam-4028	157	107	,	,	PUNCT
ejpam-4028	157	108	g̃)→	g̃)→	PRON
ejpam-4028	157	109	(	(	PUNCT
ejpam-4028	157	110	ẽ	ẽ	PROPN
ejpam-4028	157	111	,	,	PUNCT
ejpam-4028	157	112	g̃	g̃	PROPN
ejpam-4028	157	113	)	)	PUNCT
ejpam-4028	157	114	is	be	AUX
ejpam-4028	157	115	a	a	DET
ejpam-4028	157	116	mapping	mapping	NOUN
ejpam-4028	157	117	satisfying	satisfy	VERB
ejpam-4028	157	118	the	the	DET
ejpam-4028	157	119	following	follow	VERB
ejpam-4028	157	120	condition	condition	NOUN
ejpam-4028	157	121	:	:	PUNCT
ejpam-4028	158	1	¯̄ag̃(tfe1	¯̄ag̃(tfe1	NOUN
ejpam-4028	158	2	,	,	PUNCT
ejpam-4028	158	3	t	t	PROPN
ejpam-4028	158	4	fe2	fe2	PROPN
ejpam-4028	158	5	,	,	PUNCT
ejpam-4028	158	6	t	t	PROPN
ejpam-4028	158	7	fe3	fe3	PROPN
ejpam-4028	158	8	)	)	PUNCT
ejpam-4028	158	9	+	+	CCONJ
ejpam-4028	158	10	¯̄b	¯̄b	NOUN
ejpam-4028	158	11	min	min	NOUN
ejpam-4028	158	12			PUNCT
ejpam-4028	158	13	g̃(tfe1	g̃(tfe1	PROPN
ejpam-4028	158	14	,	,	PUNCT
ejpam-4028	158	15	t	t	PROPN
ejpam-4028	158	16	fe2	fe2	PROPN
ejpam-4028	158	17	,	,	PUNCT
ejpam-4028	158	18	t	t	PROPN
ejpam-4028	158	19	fe3	fe3	PROPN
ejpam-4028	158	20	)	)	PUNCT
ejpam-4028	158	21	,	,	PUNCT
ejpam-4028	158	22	g̃(fe1	g̃(fe1	PROPN
ejpam-4028	158	23	,	,	PUNCT
ejpam-4028	158	24	t	t	PROPN
ejpam-4028	158	25	fe1	fe1	PROPN
ejpam-4028	158	26	,	,	PUNCT
ejpam-4028	158	27	t	t	PROPN
ejpam-4028	158	28	fe1	fe1	PROPN
ejpam-4028	158	29	)	)	PUNCT
ejpam-4028	158	30	,	,	PUNCT
ejpam-4028	158	31	g̃(fe2	g̃(fe2	PROPN
ejpam-4028	158	32	,	,	PUNCT
ejpam-4028	158	33	t	t	PROPN
ejpam-4028	158	34	fe2	fe2	PROPN
ejpam-4028	158	35	,	,	PUNCT
ejpam-4028	158	36	t	t	PROPN
ejpam-4028	158	37	fe2	fe2	PROPN
ejpam-4028	158	38	)	)	PUNCT
ejpam-4028	158	39	,	,	PUNCT
ejpam-4028	158	40	g̃(fe3	g̃(fe3	PROPN
ejpam-4028	158	41	,	,	PUNCT
ejpam-4028	158	42	t	t	PROPN
ejpam-4028	158	43	fe3	fe3	PROPN
ejpam-4028	158	44	,	,	PUNCT
ejpam-4028	158	45	t	t	PROPN
ejpam-4028	158	46	fe3	fe3	PROPN
ejpam-4028	158	47	)	)	PUNCT
ejpam-4028	159	1			PROPN
ejpam-4028	159	2	≤̃¯̄cg̃(fe1	≤̃¯̄cg̃(fe1	PROPN
ejpam-4028	159	3	,	,	PUNCT
ejpam-4028	159	4	fe2	fe2	PROPN
ejpam-4028	159	5	,	,	PUNCT
ejpam-4028	159	6	fe3	fe3	PROPN
ejpam-4028	159	7	)	)	PUNCT
ejpam-4028	159	8	(	(	PUNCT
ejpam-4028	159	9	3	3	X
ejpam-4028	159	10	)	)	PUNCT
ejpam-4028	159	11	∀fe1	∀fe1	PROPN
ejpam-4028	159	12	,	,	PUNCT
ejpam-4028	159	13	fe2	fe2	PROPN
ejpam-4028	159	14	,	,	PUNCT
ejpam-4028	159	15	fe3∈̃fsc(ẽ	fe3∈̃fsc(ẽ	PROPN
ejpam-4028	159	16	)	)	PUNCT
ejpam-4028	159	17	and	and	CCONJ
ejpam-4028	159	18	0̃≤̃¯̄a	0̃≤̃¯̄a	NUM
ejpam-4028	159	19	,	,	PUNCT
ejpam-4028	159	20	¯̄b	¯̄b	NOUN
ejpam-4028	159	21	,	,	PUNCT
ejpam-4028	159	22	¯̄c<̃1̃	¯̄c<̃1̃	VERB
ejpam-4028	159	23	with	with	ADP
ejpam-4028	159	24	¯̄c−	¯̄c−	PROPN
ejpam-4028	159	25	¯̄b<̃¯̄a	¯̄b<̃¯̄a	NOUN
ejpam-4028	159	26	.	.	PUNCT
ejpam-4028	160	1	then	then	ADV
ejpam-4028	160	2	t	t	PROPN
ejpam-4028	160	3	has	have	VERB
ejpam-4028	160	4	an	an	DET
ejpam-4028	160	5	unique	unique	ADJ
ejpam-4028	160	6	fixed	fix	VERB
ejpam-4028	160	7	point	point	NOUN
ejpam-4028	160	8	,	,	PUNCT
ejpam-4028	160	9	say	say	VERB
ejpam-4028	160	10	fe	fe	X
ejpam-4028	160	11	,	,	PUNCT
ejpam-4028	160	12	and	and	CCONJ
ejpam-4028	160	13	at	at	ADP
ejpam-4028	160	14	fe	fe	PROPN
ejpam-4028	160	15	,	,	PUNCT
ejpam-4028	160	16	t	t	PROPN
ejpam-4028	160	17	is	be	AUX
ejpam-4028	160	18	fuzzy	fuzzy	ADJ
ejpam-4028	160	19	soft	soft	ADJ
ejpam-4028	160	20	g	g	NOUN
ejpam-4028	160	21	-	-	PUNCT
ejpam-4028	160	22	continuous	continuous	ADJ
ejpam-4028	160	23	.	.	PUNCT
ejpam-4028	161	1	proof	proof	NOUN
ejpam-4028	161	2	.	.	PUNCT
ejpam-4028	162	1	assume	assume	VERB
ejpam-4028	162	2	that	that	SCONJ
ejpam-4028	162	3	fe0∈̃fsc(ẽ	fe0∈̃fsc(ẽ	NOUN
ejpam-4028	162	4	)	)	PUNCT
ejpam-4028	162	5	is	be	AUX
ejpam-4028	162	6	an	an	DET
ejpam-4028	162	7	arbitrary	arbitrary	ADJ
ejpam-4028	162	8	fuzzy	fuzzy	ADJ
ejpam-4028	162	9	soft	soft	ADJ
ejpam-4028	162	10	element	element	NOUN
ejpam-4028	162	11	and	and	CCONJ
ejpam-4028	162	12	define	define	VERB
ejpam-4028	162	13	the	the	DET
ejpam-4028	162	14	sequence	sequence	NOUN
ejpam-4028	162	15	{	{	PUNCT
ejpam-4028	162	16	gen}n∈n	gen}n∈n	PROPN
ejpam-4028	162	17	as	as	SCONJ
ejpam-4028	162	18	follows	follow	VERB
ejpam-4028	162	19	:	:	PUNCT
ejpam-4028	163	1	tge0	tge0	NOUN
ejpam-4028	163	2	=	=	SYM
ejpam-4028	163	3	ge1	ge1	PROPN
ejpam-4028	163	4	,	,	PUNCT
ejpam-4028	163	5	t	t	PROPN
ejpam-4028	163	6	ge1	ge1	PROPN
ejpam-4028	163	7	=	=	PUNCT
ejpam-4028	163	8	ge2	ge2	PROPN
ejpam-4028	163	9	,	,	PUNCT
ejpam-4028	163	10	t	t	PROPN
ejpam-4028	163	11	ge2	ge2	PROPN
ejpam-4028	163	12	=	=	X
ejpam-4028	163	13	ge3	ge3	PROPN
ejpam-4028	163	14	,	,	PUNCT
ejpam-4028	163	15	...	...	PUNCT
ejpam-4028	163	16	,	,	PUNCT
ejpam-4028	163	17	t	t	PROPN
ejpam-4028	163	18	gen	gen	PROPN
ejpam-4028	163	19	=	=	NOUN
ejpam-4028	163	20	gen+1	gen+1	PROPN
ejpam-4028	163	21	.	.	PUNCT
ejpam-4028	164	1	consider	consider	VERB
ejpam-4028	164	2	that	that	DET
ejpam-4028	164	3	gen	gen	PROPN
ejpam-4028	164	4	6=	6=	PROPN
ejpam-4028	164	5	gen+1	gen+1	NOUN
ejpam-4028	164	6	.	.	PUNCT
ejpam-4028	165	1	substituting	substitute	VERB
ejpam-4028	165	2	fe1	fe1	PROPN
ejpam-4028	165	3	=	=	SYM
ejpam-4028	165	4	gen	gen	PROPN
ejpam-4028	165	5	,	,	PUNCT
ejpam-4028	165	6	fe2	fe2	X
ejpam-4028	165	7	=	=	SYM
ejpam-4028	165	8	gen+1	gen+1	NOUN
ejpam-4028	165	9	and	and	CCONJ
ejpam-4028	165	10	fe3	fe3	NOUN
ejpam-4028	165	11	=	=	SYM
ejpam-4028	165	12	gen+1	gen+1	NOUN
ejpam-4028	165	13	in	in	ADP
ejpam-4028	165	14	(	(	PUNCT
ejpam-4028	165	15	3	3	NUM
ejpam-4028	165	16	)	)	PUNCT
ejpam-4028	165	17	,	,	PUNCT
ejpam-4028	165	18	we	we	PRON
ejpam-4028	165	19	obtain	obtain	VERB
ejpam-4028	165	20	¯̄ag̃(tgen	¯̄ag̃(tgen	PROPN
ejpam-4028	165	21	,	,	PUNCT
ejpam-4028	165	22	t	t	PROPN
ejpam-4028	165	23	gen+1	gen+1	NOUN
ejpam-4028	165	24	,	,	PUNCT
ejpam-4028	165	25	t	t	PROPN
ejpam-4028	165	26	gen+1	gen+1	PROPN
ejpam-4028	165	27	)	)	PUNCT
ejpam-4028	166	1	+	+	CCONJ
ejpam-4028	166	2	¯̄b	¯̄b	NOUN
ejpam-4028	166	3	min	min	NOUN
ejpam-4028	166	4			NOUN
ejpam-4028	166	5	g̃(tgen	g̃(tgen	ADJ
ejpam-4028	166	6	,	,	PUNCT
ejpam-4028	166	7	t	t	PROPN
ejpam-4028	166	8	gen+1	gen+1	NOUN
ejpam-4028	166	9	,	,	PUNCT
ejpam-4028	166	10	t	t	PROPN
ejpam-4028	166	11	gen+1	gen+1	PROPN
ejpam-4028	166	12	)	)	PUNCT
ejpam-4028	166	13	,	,	PUNCT
ejpam-4028	166	14	g̃(gen	g̃(gen	PROPN
ejpam-4028	166	15	,	,	PUNCT
ejpam-4028	166	16	t	t	PROPN
ejpam-4028	166	17	gen	gen	PROPN
ejpam-4028	166	18	,	,	PUNCT
ejpam-4028	166	19	t	t	PROPN
ejpam-4028	166	20	gen	gen	PROPN
ejpam-4028	166	21	)	)	PUNCT
ejpam-4028	166	22	,	,	PUNCT
ejpam-4028	166	23	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	166	24	,	,	PUNCT
ejpam-4028	166	25	t	t	PROPN
ejpam-4028	166	26	gen+1	gen+1	NOUN
ejpam-4028	166	27	,	,	PUNCT
ejpam-4028	166	28	t	t	PROPN
ejpam-4028	166	29	gen+1	gen+1	PROPN
ejpam-4028	166	30	)	)	PUNCT
ejpam-4028	166	31	,	,	PUNCT
ejpam-4028	166	32	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	166	33	,	,	PUNCT
ejpam-4028	166	34	t	t	PROPN
ejpam-4028	166	35	gen+1	gen+1	NOUN
ejpam-4028	166	36	,	,	PUNCT
ejpam-4028	166	37	t	t	PROPN
ejpam-4028	166	38	gen+1	gen+1	NOUN
ejpam-4028	166	39	)	)	PUNCT
ejpam-4028	167	1			PROPN
ejpam-4028	167	2	≤̃¯̄cg̃(gen	≤̃¯̄cg̃(gen	NOUN
ejpam-4028	167	3	,	,	PUNCT
ejpam-4028	167	4	gen+1gen+2	gen+1gen+2	PROPN
ejpam-4028	167	5	)	)	PUNCT
ejpam-4028	167	6	,	,	PUNCT
ejpam-4028	167	7	⇒	⇒	PROPN
ejpam-4028	167	8	¯̄ag̃(gen+1	¯̄ag̃(gen+1	VERB
ejpam-4028	167	9	,	,	PUNCT
ejpam-4028	167	10	gen+2	gen+2	NOUN
ejpam-4028	167	11	,	,	PUNCT
ejpam-4028	167	12	gen+2	gen+2	NOUN
ejpam-4028	167	13	)	)	PUNCT
ejpam-4028	168	1	+	+	CCONJ
ejpam-4028	168	2	¯̄b	¯̄b	NOUN
ejpam-4028	168	3	min	min	NOUN
ejpam-4028	168	4			PUNCT
ejpam-4028	168	5	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	168	6	,	,	PUNCT
ejpam-4028	168	7	gen+2	gen+2	NOUN
ejpam-4028	168	8	,	,	PUNCT
ejpam-4028	168	9	gen+2	gen+2	NOUN
ejpam-4028	168	10	)	)	PUNCT
ejpam-4028	168	11	,	,	PUNCT
ejpam-4028	168	12	g̃(gen	g̃(gen	PROPN
ejpam-4028	168	13	,	,	PUNCT
ejpam-4028	168	14	gen+1	gen+1	NOUN
ejpam-4028	168	15	,	,	PUNCT
ejpam-4028	168	16	gen+1	gen+1	NOUN
ejpam-4028	168	17	)	)	PUNCT
ejpam-4028	168	18	,	,	PUNCT
ejpam-4028	168	19	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	168	20	,	,	PUNCT
ejpam-4028	168	21	gen+2	gen+2	PROPN
ejpam-4028	168	22	,	,	PUNCT
ejpam-4028	168	23	t	t	PROPN
ejpam-4028	168	24	gen+2	gen+2	PROPN
ejpam-4028	168	25	)	)	PUNCT
ejpam-4028	168	26	,	,	PUNCT
ejpam-4028	168	27	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	168	28	,	,	PUNCT
ejpam-4028	168	29	gen+2	gen+2	NOUN
ejpam-4028	168	30	,	,	PUNCT
ejpam-4028	168	31	gen+2	gen+2	NOUN
ejpam-4028	168	32	)	)	PUNCT
ejpam-4028	169	1			PROPN
ejpam-4028	169	2	≤̃¯̄cg̃(gen	≤̃¯̄cg̃(gen	NOUN
ejpam-4028	169	3	,	,	PUNCT
ejpam-4028	169	4	gen+1	gen+1	NOUN
ejpam-4028	169	5	,	,	PUNCT
ejpam-4028	169	6	gen+1	gen+1	NOUN
ejpam-4028	169	7	)	)	PUNCT
ejpam-4028	169	8	⇒	⇒	NOUN
ejpam-4028	169	9	¯̄ag̃(gen+1	¯̄ag̃(gen+1	NOUN
ejpam-4028	169	10	,	,	PUNCT
ejpam-4028	169	11	gen+2	gen+2	NOUN
ejpam-4028	169	12	,	,	PUNCT
ejpam-4028	169	13	gen+2	gen+2	NOUN
ejpam-4028	169	14	)	)	PUNCT
ejpam-4028	170	1	+	+	CCONJ
ejpam-4028	170	2	¯̄b	¯̄b	NOUN
ejpam-4028	170	3	min	min	NOUN
ejpam-4028	170	4	{	{	PUNCT
ejpam-4028	170	5	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	170	6	,	,	PUNCT
ejpam-4028	170	7	gen+2	gen+2	NOUN
ejpam-4028	170	8	,	,	PUNCT
ejpam-4028	170	9	gen+2	gen+2	NOUN
ejpam-4028	170	10	)	)	PUNCT
ejpam-4028	170	11	,	,	PUNCT
ejpam-4028	170	12	g̃(gen	g̃(gen	PROPN
ejpam-4028	170	13	,	,	PUNCT
ejpam-4028	170	14	gen+1	gen+1	PROPN
ejpam-4028	170	15	,	,	PUNCT
ejpam-4028	170	16	t	t	PROPN
ejpam-4028	170	17	gen+1	gen+1	PROPN
ejpam-4028	170	18	)	)	PUNCT
ejpam-4028	170	19	}	}	PUNCT
ejpam-4028	170	20	≤̃¯̄cg̃(gen	≤̃¯̄cg̃(gen	NOUN
ejpam-4028	170	21	,	,	PUNCT
ejpam-4028	170	22	gen+1	gen+1	NOUN
ejpam-4028	170	23	,	,	PUNCT
ejpam-4028	170	24	gen+1	gen+1	NOUN
ejpam-4028	170	25	)	)	PUNCT
ejpam-4028	170	26	a.	a.	PROPN
ejpam-4028	170	27	f.	f.	PROPN
ejpam-4028	170	28	sayed	say	VERB
ejpam-4028	170	29	,	,	PUNCT
ejpam-4028	170	30	a.	a.	NOUN
ejpam-4028	170	31	alahmari	alahmari	PROPN
ejpam-4028	170	32	/	/	SYM
ejpam-4028	170	33	eur	eur	PROPN
ejpam-4028	170	34	.	.	PUNCT
ejpam-4028	171	1	j.	j.	PROPN
ejpam-4028	171	2	pure	pure	PROPN
ejpam-4028	171	3	appl	appl	PROPN
ejpam-4028	171	4	.	.	PROPN
ejpam-4028	171	5	math	math	PROPN
ejpam-4028	171	6	,	,	PUNCT
ejpam-4028	171	7	14	14	NUM
ejpam-4028	171	8	(	(	PUNCT
ejpam-4028	171	9	3	3	NUM
ejpam-4028	171	10	)	)	PUNCT
ejpam-4028	171	11	(	(	PUNCT
ejpam-4028	171	12	2021	2021	NUM
ejpam-4028	171	13	)	)	PUNCT
ejpam-4028	171	14	,	,	PUNCT
ejpam-4028	171	15	923	923	NUM
ejpam-4028	171	16	-	-	SYM
ejpam-4028	171	17	941	941	NUM
ejpam-4028	171	18	930	930	NUM
ejpam-4028	171	19	we	we	PRON
ejpam-4028	171	20	now	now	ADV
ejpam-4028	171	21	have	have	VERB
ejpam-4028	171	22	two	two	NUM
ejpam-4028	171	23	cases	case	NOUN
ejpam-4028	171	24	:	:	PUNCT
ejpam-4028	171	25	case	case	NOUN
ejpam-4028	171	26	(	(	PUNCT
ejpam-4028	171	27	1	1	NUM
ejpam-4028	171	28	):	):	PUNCT
ejpam-4028	171	29	if	if	SCONJ
ejpam-4028	171	30	min	min	PROPN
ejpam-4028	171	31	{	{	PUNCT
ejpam-4028	171	32	g̃(gen+1	g̃(gen+1	PROPN
ejpam-4028	171	33	,	,	PUNCT
ejpam-4028	171	34	gen+2	gen+2	NOUN
ejpam-4028	171	35	,	,	PUNCT
ejpam-4028	171	36	,	,	PUNCT
ejpam-4028	171	37	gen+2	gen+2	PROPN
ejpam-4028	171	38	)	)	PUNCT
ejpam-4028	171	39	,	,	PUNCT
ejpam-4028	171	40	g̃(gen	g̃(gen	PROPN
ejpam-4028	171	41	,	,	PUNCT
ejpam-4028	171	42	gen+1	gen+1	PROPN
ejpam-4028	171	43	,	,	PUNCT
ejpam-4028	171	44	t	t	PROPN
ejpam-4028	171	45	gen+1	gen+1	PROPN
ejpam-4028	171	46	)	)	PUNCT
ejpam-4028	171	47	}	}	PUNCT
ejpam-4028	171	48	=	=	SYM
ejpam-4028	171	49	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	171	50	,	,	PUNCT
ejpam-4028	171	51	gen+2	gen+2	NOUN
ejpam-4028	171	52	,	,	PUNCT
ejpam-4028	171	53	gen+2	gen+2	NOUN
ejpam-4028	171	54	)	)	PUNCT
ejpam-4028	171	55	,	,	PUNCT
ejpam-4028	171	56	then	then	ADV
ejpam-4028	171	57	¯̄ag̃(gen+1	¯̄ag̃(gen+1	VERB
ejpam-4028	171	58	,	,	PUNCT
ejpam-4028	171	59	gen+2	gen+2	NOUN
ejpam-4028	171	60	,	,	PUNCT
ejpam-4028	171	61	gen+2	gen+2	NOUN
ejpam-4028	171	62	)	)	PUNCT
ejpam-4028	172	1	+	+	NUM
ejpam-4028	172	2	¯̄bg̃(gen+1	¯̄bg̃(gen+1	ADJ
ejpam-4028	172	3	,	,	PUNCT
ejpam-4028	172	4	gen+2	gen+2	NOUN
ejpam-4028	172	5	,	,	PUNCT
ejpam-4028	172	6	gen+2)≤̃¯̄cg̃(gen	gen+2)≤̃¯̄cg̃(gen	NOUN
ejpam-4028	172	7	,	,	PUNCT
ejpam-4028	172	8	gen+1	gen+1	NOUN
ejpam-4028	172	9	,	,	PUNCT
ejpam-4028	172	10	gen+1	gen+1	NOUN
ejpam-4028	172	11	)	)	PUNCT
ejpam-4028	172	12	⇒	⇒	NOUN
ejpam-4028	172	13	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	172	14	,	,	PUNCT
ejpam-4028	172	15	gen+2	gen+2	NOUN
ejpam-4028	172	16	,	,	PUNCT
ejpam-4028	172	17	gen+2)≤̃	gen+2)≤̃	PROPN
ejpam-4028	172	18	¯̄c	¯̄c	PROPN
ejpam-4028	172	19	¯̄a+¯̄b	¯̄a+¯̄b	X
ejpam-4028	172	20	g̃(gen	g̃(gen	PROPN
ejpam-4028	172	21	,	,	PUNCT
ejpam-4028	172	22	gen+1	gen+1	NOUN
ejpam-4028	172	23	,	,	PUNCT
ejpam-4028	172	24	gen+1	gen+1	NOUN
ejpam-4028	172	25	)	)	PUNCT
ejpam-4028	172	26	case	case	NOUN
ejpam-4028	172	27	(	(	PUNCT
ejpam-4028	172	28	2	2	NUM
ejpam-4028	172	29	):	):	PUNCT
ejpam-4028	172	30	if	if	SCONJ
ejpam-4028	172	31	min	min	PROPN
ejpam-4028	172	32	{	{	PUNCT
ejpam-4028	172	33	g̃(gen+1	g̃(gen+1	PROPN
ejpam-4028	172	34	,	,	PUNCT
ejpam-4028	172	35	gen+2	gen+2	NOUN
ejpam-4028	172	36	,	,	PUNCT
ejpam-4028	172	37	,	,	PUNCT
ejpam-4028	172	38	gen+2	gen+2	PROPN
ejpam-4028	172	39	)	)	PUNCT
ejpam-4028	172	40	,	,	PUNCT
ejpam-4028	172	41	g̃(gen	g̃(gen	PROPN
ejpam-4028	172	42	,	,	PUNCT
ejpam-4028	172	43	gen+1	gen+1	PROPN
ejpam-4028	172	44	,	,	PUNCT
ejpam-4028	172	45	t	t	PROPN
ejpam-4028	172	46	gen+1	gen+1	PROPN
ejpam-4028	172	47	)	)	PUNCT
ejpam-4028	172	48	}	}	PUNCT
ejpam-4028	173	1	=	=	SYM
ejpam-4028	173	2	g̃(gen	g̃(gen	PROPN
ejpam-4028	173	3	,	,	PUNCT
ejpam-4028	173	4	gen+1	gen+1	NOUN
ejpam-4028	173	5	,	,	PUNCT
ejpam-4028	173	6	gen+1	gen+1	NOUN
ejpam-4028	173	7	)	)	PUNCT
ejpam-4028	173	8	,	,	PUNCT
ejpam-4028	173	9	then	then	ADV
ejpam-4028	173	10	¯̄ag̃(gen+1	¯̄ag̃(gen+1	VERB
ejpam-4028	173	11	,	,	PUNCT
ejpam-4028	173	12	gen+2	gen+2	NOUN
ejpam-4028	173	13	,	,	PUNCT
ejpam-4028	173	14	gen+2	gen+2	NOUN
ejpam-4028	173	15	)	)	PUNCT
ejpam-4028	174	1	+	+	CCONJ
ejpam-4028	174	2	¯̄bg̃(gen	¯̄bg̃(gen	NOUN
ejpam-4028	174	3	,	,	PUNCT
ejpam-4028	174	4	gen+1	gen+1	NOUN
ejpam-4028	174	5	,	,	PUNCT
ejpam-4028	174	6	gen+1)≤̃¯̄cg̃(gen	gen+1)≤̃¯̄cg̃(gen	PROPN
ejpam-4028	174	7	,	,	PUNCT
ejpam-4028	174	8	gen+1	gen+1	NOUN
ejpam-4028	174	9	,	,	PUNCT
ejpam-4028	174	10	gen+1	gen+1	NOUN
ejpam-4028	174	11	)	)	PUNCT
ejpam-4028	174	12	⇒	⇒	NOUN
ejpam-4028	174	13	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	174	14	,	,	PUNCT
ejpam-4028	174	15	gen+2	gen+2	NOUN
ejpam-4028	174	16	,	,	PUNCT
ejpam-4028	174	17	gen+2)≤̃	gen+2)≤̃	PROPN
ejpam-4028	174	18	¯̄c−¯̄b	¯̄c−¯̄b	X
ejpam-4028	175	1	¯̄a	¯̄a	AUX
ejpam-4028	175	2	g̃(gen	g̃(gen	PROPN
ejpam-4028	175	3	,	,	PUNCT
ejpam-4028	175	4	gen+1	gen+1	NOUN
ejpam-4028	175	5	,	,	PUNCT
ejpam-4028	175	6	gen+1	gen+1	NOUN
ejpam-4028	175	7	)	)	PUNCT
ejpam-4028	175	8	from	from	ADP
ejpam-4028	175	9	(	(	PUNCT
ejpam-4028	175	10	1	1	NUM
ejpam-4028	175	11	)	)	PUNCT
ejpam-4028	175	12	and	and	CCONJ
ejpam-4028	175	13	(	(	PUNCT
ejpam-4028	175	14	2	2	NUM
ejpam-4028	175	15	)	)	PUNCT
ejpam-4028	175	16	,	,	PUNCT
ejpam-4028	175	17	we	we	PRON
ejpam-4028	175	18	have	have	VERB
ejpam-4028	175	19	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	175	20	,	,	PUNCT
ejpam-4028	175	21	gen+2	gen+2	NOUN
ejpam-4028	175	22	,	,	PUNCT
ejpam-4028	175	23	gen+2)≤̃¯̄kg̃(gen	gen+2)≤̃¯̄kg̃(gen	NOUN
ejpam-4028	175	24	,	,	PUNCT
ejpam-4028	175	25	gen+1	gen+1	NOUN
ejpam-4028	175	26	,	,	PUNCT
ejpam-4028	175	27	gen+1	gen+1	NOUN
ejpam-4028	175	28	)	)	PUNCT
ejpam-4028	175	29	similarly	similarly	ADV
ejpam-4028	175	30	,	,	PUNCT
ejpam-4028	175	31	we	we	PRON
ejpam-4028	175	32	will	will	AUX
ejpam-4028	175	33	conclude	conclude	VERB
ejpam-4028	175	34	that	that	SCONJ
ejpam-4028	175	35	g̃(gen	g̃(gen	PROPN
ejpam-4028	175	36	,	,	PUNCT
ejpam-4028	175	37	gen+1	gen+1	NOUN
ejpam-4028	175	38	,	,	PUNCT
ejpam-4028	175	39	gen+1)≤̃¯̄kg̃(gen−1	gen+1)≤̃¯̄kg̃(gen−1	PROPN
ejpam-4028	175	40	,	,	PUNCT
ejpam-4028	175	41	gen	gen	PROPN
ejpam-4028	175	42	,	,	PUNCT
ejpam-4028	175	43	gen	gen	PROPN
ejpam-4028	175	44	)	)	PUNCT
ejpam-4028	175	45	and	and	CCONJ
ejpam-4028	175	46	so	so	ADV
ejpam-4028	175	47	g̃(gen	g̃(gen	PROPN
ejpam-4028	175	48	,	,	PUNCT
ejpam-4028	175	49	gen+1	gen+1	NOUN
ejpam-4028	175	50	,	,	PUNCT
ejpam-4028	175	51	gen+1)≤̃¯̄kng̃(ge0	gen+1)≤̃¯̄kng̃(ge0	NOUN
ejpam-4028	175	52	,	,	PUNCT
ejpam-4028	175	53	ge1	ge1	NOUN
ejpam-4028	175	54	,	,	PUNCT
ejpam-4028	175	55	ge1	ge1	PROPN
ejpam-4028	175	56	)	)	PUNCT
ejpam-4028	175	57	next	next	ADV
ejpam-4028	175	58	,	,	PUNCT
ejpam-4028	175	59	we	we	PRON
ejpam-4028	175	60	show	show	VERB
ejpam-4028	175	61	that	that	SCONJ
ejpam-4028	175	62	{	{	PUNCT
ejpam-4028	175	63	gen}n∈n	gen}n∈n	NOUN
ejpam-4028	175	64	is	be	AUX
ejpam-4028	175	65	a	a	DET
ejpam-4028	175	66	fuzzy	fuzzy	ADJ
ejpam-4028	175	67	soft	soft	ADJ
ejpam-4028	175	68	g	g	NOUN
ejpam-4028	175	69	-	-	PUNCT
ejpam-4028	175	70	cauchy	cauchy	ADJ
ejpam-4028	175	71	sequence	sequence	NOUN
ejpam-4028	175	72	.	.	PUNCT
ejpam-4028	176	1	then	then	ADV
ejpam-4028	176	2	for	for	ADP
ejpam-4028	176	3	all	all	DET
ejpam-4028	176	4	n	n	CCONJ
ejpam-4028	176	5	,	,	PUNCT
ejpam-4028	176	6	m	m	VERB
ejpam-4028	176	7	∈	∈	PROPN
ejpam-4028	176	8	n	n	CCONJ
ejpam-4028	176	9	,	,	PUNCT
ejpam-4028	176	10	n	n	CCONJ
ejpam-4028	176	11	<	<	X
ejpam-4028	176	12	m	m	PROPN
ejpam-4028	176	13	,	,	PUNCT
ejpam-4028	176	14	we	we	PRON
ejpam-4028	176	15	have	have	VERB
ejpam-4028	176	16	¯̄ag̃(gen	¯̄ag̃(gen	ADV
ejpam-4028	176	17	,	,	PUNCT
ejpam-4028	176	18	gem	gem	NOUN
ejpam-4028	176	19	,	,	PUNCT
ejpam-4028	176	20	gem)≤̃g̃(gen	gem)≤̃g̃(gen	NOUN
ejpam-4028	176	21	,	,	PUNCT
ejpam-4028	176	22	gen+1	gen+1	NOUN
ejpam-4028	176	23	,	,	PUNCT
ejpam-4028	176	24	gen+1	gen+1	NOUN
ejpam-4028	176	25	)	)	PUNCT
ejpam-4028	177	1	+	+	CCONJ
ejpam-4028	178	1	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	178	2	,	,	PUNCT
ejpam-4028	178	3	gen+2	gen+2	NOUN
ejpam-4028	178	4	,	,	PUNCT
ejpam-4028	178	5	gen+2	gen+2	NOUN
ejpam-4028	178	6	)	)	PUNCT
ejpam-4028	179	1	+	+	CCONJ
ejpam-4028	179	2	...	...	PUNCT
ejpam-4028	180	1	+	+	CCONJ
ejpam-4028	180	2	g̃(gem−1	g̃(gem−1	NOUN
ejpam-4028	180	3	,	,	PUNCT
ejpam-4028	180	4	gem	gem	NOUN
ejpam-4028	180	5	,	,	PUNCT
ejpam-4028	180	6	gem	gem	NOUN
ejpam-4028	180	7	)	)	PUNCT
ejpam-4028	180	8	≤̃(¯̄kn	≤̃(¯̄kn	PROPN
ejpam-4028	180	9	+	+	CCONJ
ejpam-4028	180	10	¯̄k(n+1	¯̄k(n+1	PROPN
ejpam-4028	180	11	)	)	PUNCT
ejpam-4028	181	1	+	+	CCONJ
ejpam-4028	181	2	...	...	PUNCT
ejpam-4028	182	1	+	+	CCONJ
ejpam-4028	182	2	¯̄k(m−1))g̃(ge0	¯̄k(m−1))g̃(ge0	NOUN
ejpam-4028	182	3	,	,	PUNCT
ejpam-4028	182	4	ge1	ge1	NOUN
ejpam-4028	182	5	,	,	PUNCT
ejpam-4028	182	6	ge1	ge1	NOUN
ejpam-4028	182	7	)	)	PUNCT
ejpam-4028	182	8	≤̃	≤̃	PROPN
ejpam-4028	182	9	¯̄kn	¯̄kn	PROPN
ejpam-4028	182	10	1̃−¯̄k	1̃−¯̄k	NUM
ejpam-4028	182	11	g̃(ge0	g̃(ge0	PROPN
ejpam-4028	182	12	,	,	PUNCT
ejpam-4028	182	13	ge1	ge1	PROPN
ejpam-4028	182	14	,	,	PUNCT
ejpam-4028	182	15	ge2	ge2	PROPN
ejpam-4028	182	16	)	)	PUNCT
ejpam-4028	182	17	.	.	PUNCT
ejpam-4028	183	1	hence	hence	ADV
ejpam-4028	183	2	,	,	PUNCT
ejpam-4028	183	3	{	{	PUNCT
ejpam-4028	183	4	gen}n∈n	gen}n∈n	PROPN
ejpam-4028	183	5	is	be	AUX
ejpam-4028	183	6	a	a	DET
ejpam-4028	183	7	fuzzy	fuzzy	ADJ
ejpam-4028	183	8	soft	soft	ADJ
ejpam-4028	183	9	g	g	NOUN
ejpam-4028	183	10	-	-	PUNCT
ejpam-4028	183	11	cauchy	cauchy	ADJ
ejpam-4028	183	12	sequence	sequence	NOUN
ejpam-4028	183	13	.	.	PUNCT
ejpam-4028	184	1	since	since	SCONJ
ejpam-4028	184	2	(	(	PUNCT
ejpam-4028	184	3	ẽ	ẽ	PROPN
ejpam-4028	184	4	,	,	PUNCT
ejpam-4028	184	5	g̃	g̃	PROPN
ejpam-4028	184	6	)	)	PUNCT
ejpam-4028	184	7	is	be	AUX
ejpam-4028	184	8	fuzzy	fuzzy	ADJ
ejpam-4028	184	9	soft	soft	ADJ
ejpam-4028	184	10	g	g	NOUN
ejpam-4028	184	11	-	-	PUNCT
ejpam-4028	184	12	complete	complete	ADJ
ejpam-4028	184	13	,	,	PUNCT
ejpam-4028	184	14	there	there	PRON
ejpam-4028	184	15	exists	exist	VERB
ejpam-4028	184	16	fe∈̃fsc(ẽ	fe∈̃fsc(ẽ	PROPN
ejpam-4028	184	17	)	)	PUNCT
ejpam-4028	184	18	such	such	ADJ
ejpam-4028	184	19	that	that	SCONJ
ejpam-4028	184	20	{	{	PUNCT
ejpam-4028	184	21	gen}n∈n	gen}n∈n	PROPN
ejpam-4028	184	22	fuzzy	fuzzy	ADJ
ejpam-4028	184	23	soft	soft	ADJ
ejpam-4028	184	24	g	g	NOUN
ejpam-4028	184	25	-	-	PUNCT
ejpam-4028	184	26	converges	converge	NOUN
ejpam-4028	184	27	to	to	ADP
ejpam-4028	184	28	fe	fe	PROPN
ejpam-4028	184	29	.	.	PUNCT
ejpam-4028	185	1	next	next	ADV
ejpam-4028	185	2	,	,	PUNCT
ejpam-4028	185	3	we	we	PRON
ejpam-4028	185	4	will	will	AUX
ejpam-4028	185	5	show	show	VERB
ejpam-4028	185	6	that	that	SCONJ
ejpam-4028	185	7	fe	fe	PROPN
ejpam-4028	185	8	is	be	AUX
ejpam-4028	185	9	a	a	DET
ejpam-4028	185	10	fixed	fix	VERB
ejpam-4028	185	11	point	point	NOUN
ejpam-4028	185	12	of	of	ADP
ejpam-4028	185	13	t	t	PROPN
ejpam-4028	185	14	.	.	PUNCT
ejpam-4028	186	1	for	for	ADP
ejpam-4028	186	2	this	this	PRON
ejpam-4028	186	3	,	,	PUNCT
ejpam-4028	186	4	we	we	PRON
ejpam-4028	186	5	take	take	VERB
ejpam-4028	186	6	fe1	fe1	PROPN
ejpam-4028	186	7	=	=	SYM
ejpam-4028	186	8	gen	gen	PROPN
ejpam-4028	186	9	and	and	CCONJ
ejpam-4028	186	10	fe2	fe2	PROPN
ejpam-4028	186	11	=	=	SYM
ejpam-4028	186	12	fe3	fe3	PROPN
ejpam-4028	186	13	=	=	SYM
ejpam-4028	186	14	fe	fe	X
ejpam-4028	186	15	in	in	ADP
ejpam-4028	186	16	(	(	PUNCT
ejpam-4028	186	17	3	3	NUM
ejpam-4028	186	18	)	)	PUNCT
ejpam-4028	186	19	,	,	PUNCT
ejpam-4028	186	20	then	then	ADV
ejpam-4028	186	21	¯̄ag̃(tgen	¯̄ag̃(tgen	PROPN
ejpam-4028	186	22	,	,	PUNCT
ejpam-4028	186	23	tfe	tfe	NOUN
ejpam-4028	186	24	,	,	PUNCT
ejpam-4028	186	25	tfe	tfe	NOUN
ejpam-4028	186	26	)	)	PUNCT
ejpam-4028	187	1	+	+	CCONJ
ejpam-4028	187	2	¯̄b	¯̄b	NOUN
ejpam-4028	187	3	min	min	NOUN
ejpam-4028	187	4			ADV
ejpam-4028	187	5	g̃(tgen	g̃(tgen	PROPN
ejpam-4028	187	6	,	,	PUNCT
ejpam-4028	187	7	tfe	tfe	NOUN
ejpam-4028	187	8	,	,	PUNCT
ejpam-4028	187	9	t	t	PROPN
ejpam-4028	187	10	fe	fe	PROPN
ejpam-4028	187	11	)	)	PUNCT
ejpam-4028	187	12	,	,	PUNCT
ejpam-4028	187	13	g̃(gen	g̃(gen	PROPN
ejpam-4028	187	14	,	,	PUNCT
ejpam-4028	187	15	t	t	PROPN
ejpam-4028	187	16	gen	gen	PROPN
ejpam-4028	187	17	,	,	PUNCT
ejpam-4028	187	18	t	t	PROPN
ejpam-4028	187	19	gen	gen	PROPN
ejpam-4028	187	20	)	)	PUNCT
ejpam-4028	187	21	,	,	PUNCT
ejpam-4028	187	22	g̃(fe	g̃(fe	NOUN
ejpam-4028	187	23	,	,	PUNCT
ejpam-4028	187	24	t	t	PROPN
ejpam-4028	187	25	fe	fe	PROPN
ejpam-4028	187	26	,	,	PUNCT
ejpam-4028	187	27	tfe	tfe	PROPN
ejpam-4028	187	28	)	)	PUNCT
ejpam-4028	187	29	,	,	PUNCT
ejpam-4028	187	30	g̃(fe	g̃(fe	NOUN
ejpam-4028	187	31	,	,	PUNCT
ejpam-4028	187	32	t	t	PROPN
ejpam-4028	187	33	fe	fe	PROPN
ejpam-4028	187	34	,	,	PUNCT
ejpam-4028	187	35	tfe	tfe	NOUN
ejpam-4028	187	36	)	)	PUNCT
ejpam-4028	188	1			PROPN
ejpam-4028	188	2	≤̃¯̄cg̃(gen	≤̃¯̄cg̃(gen	NOUN
ejpam-4028	188	3	,	,	PUNCT
ejpam-4028	188	4	fe	fe	X
ejpam-4028	188	5	,	,	PUNCT
ejpam-4028	188	6	fe	fe	NOUN
ejpam-4028	188	7	)	)	PUNCT
ejpam-4028	188	8	as	as	ADP
ejpam-4028	188	9	n→∞	n→∞	NUM
ejpam-4028	188	10	,	,	PUNCT
ejpam-4028	188	11	we	we	PRON
ejpam-4028	188	12	have	have	AUX
ejpam-4028	188	13	¯̄ag̃(fe	¯̄ag̃(fe	NOUN
ejpam-4028	188	14	,	,	PUNCT
ejpam-4028	188	15	t	t	PROPN
ejpam-4028	188	16	fe	fe	PROPN
ejpam-4028	188	17	,	,	PUNCT
ejpam-4028	188	18	t	t	PROPN
ejpam-4028	188	19	fe	fe	X
ejpam-4028	188	20	)	)	PUNCT
ejpam-4028	189	1	+	+	CCONJ
ejpam-4028	189	2	¯̄b	¯̄b	NOUN
ejpam-4028	189	3	min	min	NOUN
ejpam-4028	189	4			PUNCT
ejpam-4028	189	5	g̃(fe	g̃(fe	NOUN
ejpam-4028	189	6	,	,	PUNCT
ejpam-4028	189	7	t	t	PROPN
ejpam-4028	189	8	fe	fe	PROPN
ejpam-4028	189	9	,	,	PUNCT
ejpam-4028	189	10	t	t	PROPN
ejpam-4028	189	11	fe	fe	PROPN
ejpam-4028	189	12	)	)	PUNCT
ejpam-4028	189	13	,	,	PUNCT
ejpam-4028	189	14	g̃(fe	g̃(fe	NOUN
ejpam-4028	189	15	,	,	PUNCT
ejpam-4028	189	16	t	t	PROPN
ejpam-4028	189	17	fe	fe	PROPN
ejpam-4028	189	18	,	,	PUNCT
ejpam-4028	189	19	t	t	PROPN
ejpam-4028	189	20	fe	fe	PROPN
ejpam-4028	189	21	)	)	PUNCT
ejpam-4028	189	22	,	,	PUNCT
ejpam-4028	189	23	g̃(fe	g̃(fe	NOUN
ejpam-4028	189	24	,	,	PUNCT
ejpam-4028	189	25	t	t	PROPN
ejpam-4028	189	26	fe	fe	PROPN
ejpam-4028	189	27	,	,	PUNCT
ejpam-4028	189	28	t	t	PROPN
ejpam-4028	189	29	fe	fe	PROPN
ejpam-4028	189	30	)	)	PUNCT
ejpam-4028	189	31	,	,	PUNCT
ejpam-4028	189	32	g̃(fe	g̃(fe	NOUN
ejpam-4028	189	33	,	,	PUNCT
ejpam-4028	189	34	tfe	tfe	PROPN
ejpam-4028	189	35	,	,	PUNCT
ejpam-4028	189	36	t	t	PROPN
ejpam-4028	189	37	fe	fe	NOUN
ejpam-4028	189	38	)	)	PUNCT
ejpam-4028	189	39			PROPN
ejpam-4028	189	40	≤̃¯̄cg̃(fe	≤̃¯̄cg̃(fe	PROPN
ejpam-4028	189	41	,	,	PUNCT
ejpam-4028	189	42	fe	fe	X
ejpam-4028	189	43	,	,	PUNCT
ejpam-4028	189	44	fe	fe	NOUN
ejpam-4028	189	45	)	)	PUNCT
ejpam-4028	189	46	⇒	⇒	PROPN
ejpam-4028	189	47	¯̄ag̃(fe	¯̄ag̃(fe	PROPN
ejpam-4028	189	48	,	,	PUNCT
ejpam-4028	189	49	t	t	PROPN
ejpam-4028	189	50	fe	fe	PROPN
ejpam-4028	189	51	,	,	PUNCT
ejpam-4028	189	52	t	t	PROPN
ejpam-4028	189	53	fe)≤̃0̃	fe)≤̃0̃	PROPN
ejpam-4028	189	54	,	,	PUNCT
ejpam-4028	189	55	since	since	SCONJ
ejpam-4028	189	56	0̃≤̃¯̄a<̃1̃	0̃≤̃¯̄a<̃1̃	NOUN
ejpam-4028	189	57	this	this	PRON
ejpam-4028	189	58	is	be	AUX
ejpam-4028	189	59	a	a	DET
ejpam-4028	189	60	contradiction	contradiction	NOUN
ejpam-4028	189	61	,	,	PUNCT
ejpam-4028	189	62	so	so	ADV
ejpam-4028	189	63	tfe	tfe	NOUN
ejpam-4028	189	64	=	=	SYM
ejpam-4028	189	65	fe	fe	X
ejpam-4028	189	66	i.e.	i.e.	X
ejpam-4028	189	67	fe	fe	X
ejpam-4028	189	68	is	be	AUX
ejpam-4028	189	69	a	a	DET
ejpam-4028	189	70	fixed	fix	VERB
ejpam-4028	189	71	point	point	NOUN
ejpam-4028	189	72	of	of	ADP
ejpam-4028	189	73	t	t	PROPN
ejpam-4028	189	74	.	.	PUNCT
ejpam-4028	190	1	now	now	ADV
ejpam-4028	190	2	,	,	PUNCT
ejpam-4028	190	3	to	to	PART
ejpam-4028	190	4	prove	prove	VERB
ejpam-4028	190	5	uniqueness	uniqueness	NOUN
ejpam-4028	190	6	,	,	PUNCT
ejpam-4028	190	7	assume	assume	VERB
ejpam-4028	190	8	that	that	SCONJ
ejpam-4028	190	9	fe	fe	PROPN
ejpam-4028	190	10	and	and	CCONJ
ejpam-4028	190	11	ge	ge	PROPN
ejpam-4028	190	12	are	be	AUX
ejpam-4028	190	13	two	two	NUM
ejpam-4028	190	14	fixed	fix	VERB
ejpam-4028	190	15	points	point	NOUN
ejpam-4028	190	16	of	of	ADP
ejpam-4028	190	17	t	t	PROPN
ejpam-4028	190	18	.	.	PUNCT
ejpam-4028	191	1	then	then	ADV
ejpam-4028	191	2	by	by	ADP
ejpam-4028	191	3	inequality	inequality	NOUN
ejpam-4028	191	4	(	(	PUNCT
ejpam-4028	191	5	3	3	NUM
ejpam-4028	191	6	)	)	PUNCT
ejpam-4028	191	7	,	,	PUNCT
ejpam-4028	191	8	we	we	PRON
ejpam-4028	191	9	have	have	VERB
ejpam-4028	191	10	¯̄ag̃(tfe	¯̄ag̃(tfe	NOUN
ejpam-4028	191	11	,	,	PUNCT
ejpam-4028	191	12	t	t	PROPN
ejpam-4028	191	13	ge	ge	PROPN
ejpam-4028	191	14	,	,	PUNCT
ejpam-4028	191	15	t	t	PROPN
ejpam-4028	191	16	ge	ge	PROPN
ejpam-4028	191	17	)	)	PUNCT
ejpam-4028	192	1	+	+	CCONJ
ejpam-4028	192	2	¯̄b	¯̄b	NOUN
ejpam-4028	192	3	min	min	NOUN
ejpam-4028	192	4			PUNCT
ejpam-4028	192	5	g̃(tfe	g̃(tfe	PROPN
ejpam-4028	192	6	,	,	PUNCT
ejpam-4028	192	7	t	t	PROPN
ejpam-4028	192	8	ge	ge	PROPN
ejpam-4028	192	9	,	,	PUNCT
ejpam-4028	192	10	t	t	PROPN
ejpam-4028	192	11	ge	ge	PROPN
ejpam-4028	192	12	)	)	PUNCT
ejpam-4028	192	13	,	,	PUNCT
ejpam-4028	192	14	g̃(fe	g̃(fe	NOUN
ejpam-4028	192	15	,	,	PUNCT
ejpam-4028	192	16	tfe	tfe	PROPN
ejpam-4028	192	17	,	,	PUNCT
ejpam-4028	192	18	t	t	PROPN
ejpam-4028	192	19	ge	ge	PROPN
ejpam-4028	192	20	)	)	PUNCT
ejpam-4028	192	21	,	,	PUNCT
ejpam-4028	192	22	g̃(ge	g̃(ge	NOUN
ejpam-4028	192	23	,	,	PUNCT
ejpam-4028	192	24	t	t	PROPN
ejpam-4028	192	25	ge	ge	PROPN
ejpam-4028	192	26	,	,	PUNCT
ejpam-4028	192	27	t	t	PROPN
ejpam-4028	192	28	ge	ge	PROPN
ejpam-4028	192	29	)	)	PUNCT
ejpam-4028	192	30	,	,	PUNCT
ejpam-4028	192	31	g̃(ge	g̃(ge	NOUN
ejpam-4028	192	32	,	,	PUNCT
ejpam-4028	192	33	t	t	PROPN
ejpam-4028	192	34	ge	ge	PROPN
ejpam-4028	192	35	,	,	PUNCT
ejpam-4028	192	36	t	t	PROPN
ejpam-4028	192	37	ge	ge	PROPN
ejpam-4028	192	38	)	)	PUNCT
ejpam-4028	193	1			PROPN
ejpam-4028	193	2	≤̃¯̄cg̃(fe	≤̃¯̄cg̃(fe	NOUN
ejpam-4028	193	3	,	,	PUNCT
ejpam-4028	193	4	ge	ge	PROPN
ejpam-4028	193	5	,	,	PUNCT
ejpam-4028	193	6	ge	ge	PROPN
ejpam-4028	193	7	)	)	PUNCT
ejpam-4028	193	8	a.	a.	PROPN
ejpam-4028	193	9	f.	f.	PROPN
ejpam-4028	193	10	sayed	say	VERB
ejpam-4028	193	11	,	,	PUNCT
ejpam-4028	193	12	a.	a.	NOUN
ejpam-4028	193	13	alahmari	alahmari	PROPN
ejpam-4028	193	14	/	/	SYM
ejpam-4028	193	15	eur	eur	PROPN
ejpam-4028	193	16	.	.	PUNCT
ejpam-4028	194	1	j.	j.	PROPN
ejpam-4028	194	2	pure	pure	PROPN
ejpam-4028	194	3	appl	appl	PROPN
ejpam-4028	194	4	.	.	PROPN
ejpam-4028	194	5	math	math	PROPN
ejpam-4028	194	6	,	,	PUNCT
ejpam-4028	194	7	14	14	NUM
ejpam-4028	194	8	(	(	PUNCT
ejpam-4028	194	9	3	3	NUM
ejpam-4028	194	10	)	)	PUNCT
ejpam-4028	194	11	(	(	PUNCT
ejpam-4028	194	12	2021	2021	NUM
ejpam-4028	194	13	)	)	PUNCT
ejpam-4028	194	14	,	,	PUNCT
ejpam-4028	194	15	923	923	NUM
ejpam-4028	194	16	-	-	SYM
ejpam-4028	194	17	941	941	NUM
ejpam-4028	194	18	931	931	NUM
ejpam-4028	194	19	⇒	⇒	NOUN
ejpam-4028	194	20	g̃(fe	g̃(fe	NOUN
ejpam-4028	194	21	,	,	PUNCT
ejpam-4028	194	22	ge	ge	PROPN
ejpam-4028	194	23	,	,	PUNCT
ejpam-4028	194	24	ge)≤̃	ge)≤̃	PROPN
ejpam-4028	194	25	¯̄c	¯̄c	PROPN
ejpam-4028	194	26	¯̄ag̃(fe	¯̄ag̃(fe	NOUN
ejpam-4028	194	27	,	,	PUNCT
ejpam-4028	194	28	ge	ge	PROPN
ejpam-4028	194	29	,	,	PUNCT
ejpam-4028	194	30	ge	ge	PROPN
ejpam-4028	194	31	)	)	PUNCT
ejpam-4028	194	32	,	,	PUNCT
ejpam-4028	194	33	this	this	PRON
ejpam-4028	194	34	is	be	AUX
ejpam-4028	194	35	a	a	DET
ejpam-4028	194	36	contradiction	contradiction	NOUN
ejpam-4028	194	37	implies	imply	VERB
ejpam-4028	194	38	that	that	PRON
ejpam-4028	194	39	fe	fe	X
ejpam-4028	194	40	=	=	PROPN
ejpam-4028	194	41	ge	ge	PROPN
ejpam-4028	194	42	.	.	PUNCT
ejpam-4028	195	1	to	to	PART
ejpam-4028	195	2	show	show	VERB
ejpam-4028	195	3	that	that	SCONJ
ejpam-4028	195	4	t	t	PROPN
ejpam-4028	195	5	is	be	AUX
ejpam-4028	195	6	fuzzy	fuzzy	ADJ
ejpam-4028	195	7	soft	soft	ADJ
ejpam-4028	195	8	g	g	NOUN
ejpam-4028	195	9	-	-	NOUN
ejpam-4028	195	10	continuous	continuous	ADJ
ejpam-4028	195	11	at	at	ADP
ejpam-4028	195	12	fe	fe	NOUN
ejpam-4028	195	13	.	.	PUNCT
ejpam-4028	195	14	let	let	AUX
ejpam-4028	195	15	{	{	PUNCT
ejpam-4028	195	16	hen}n∈n	hen}n∈n	PRON
ejpam-4028	195	17	be	be	AUX
ejpam-4028	195	18	a	a	DET
ejpam-4028	195	19	sequence	sequence	NOUN
ejpam-4028	195	20	of	of	ADP
ejpam-4028	195	21	fuzzy	fuzzy	ADJ
ejpam-4028	195	22	soft	soft	ADJ
ejpam-4028	195	23	elements	element	NOUN
ejpam-4028	195	24	in	in	ADP
ejpam-4028	195	25	ẽ	ẽ	PROPN
ejpam-4028	195	26	such	such	ADJ
ejpam-4028	195	27	that	that	SCONJ
ejpam-4028	195	28	{	{	PUNCT
ejpam-4028	195	29	hen}n∈n	hen}n∈n	PROPN
ejpam-4028	195	30	→	→	SYM
ejpam-4028	195	31	fe	fe	PROPN
ejpam-4028	195	32	,	,	PUNCT
ejpam-4028	195	33	then	then	ADV
ejpam-4028	195	34	we	we	PRON
ejpam-4028	195	35	can	can	AUX
ejpam-4028	195	36	deduce	deduce	VERB
ejpam-4028	195	37	that	that	SCONJ
ejpam-4028	195	38	using	use	VERB
ejpam-4028	195	39	inequality	inequality	NOUN
ejpam-4028	195	40	(	(	PUNCT
ejpam-4028	195	41	3	3	NUM
ejpam-4028	195	42	)	)	PUNCT
ejpam-4028	195	43	,	,	PUNCT
ejpam-4028	195	44	we	we	PRON
ejpam-4028	195	45	have	have	VERB
ejpam-4028	195	46	¯̄ag̃(tfe	¯̄ag̃(tfe	NOUN
ejpam-4028	195	47	,	,	PUNCT
ejpam-4028	195	48	then	then	ADV
ejpam-4028	195	49	,	,	PUNCT
ejpam-4028	195	50	then	then	ADV
ejpam-4028	195	51	)	)	PUNCT
ejpam-4028	196	1	+	+	CCONJ
ejpam-4028	196	2	¯̄b	¯̄b	NOUN
ejpam-4028	196	3	min	min	NOUN
ejpam-4028	196	4			PUNCT
ejpam-4028	196	5	g̃(tfe	g̃(tfe	NOUN
ejpam-4028	196	6	,	,	PUNCT
ejpam-4028	196	7	then	then	ADV
ejpam-4028	196	8	,	,	PUNCT
ejpam-4028	196	9	then	then	ADV
ejpam-4028	196	10	)	)	PUNCT
ejpam-4028	196	11	,	,	PUNCT
ejpam-4028	196	12	g̃(fe	g̃(fe	NOUN
ejpam-4028	196	13	,	,	PUNCT
ejpam-4028	196	14	tfe	tfe	NOUN
ejpam-4028	196	15	,	,	PUNCT
ejpam-4028	196	16	tfe	tfe	NOUN
ejpam-4028	196	17	)	)	PUNCT
ejpam-4028	196	18	,	,	PUNCT
ejpam-4028	197	1	g̃(hen	g̃(hen	INTJ
ejpam-4028	197	2	,	,	PUNCT
ejpam-4028	197	3	then	then	ADV
ejpam-4028	197	4	,	,	PUNCT
ejpam-4028	197	5	then	then	ADV
ejpam-4028	197	6	)	)	PUNCT
ejpam-4028	197	7	,	,	PUNCT
ejpam-4028	197	8	g̃(hen	g̃(hen	INTJ
ejpam-4028	197	9	,	,	PUNCT
ejpam-4028	197	10	then	then	ADV
ejpam-4028	197	11	,	,	PUNCT
ejpam-4028	197	12	then	then	ADV
ejpam-4028	197	13	)	)	PUNCT
ejpam-4028	197	14			PROPN
ejpam-4028	197	15	≤̃¯̄cg̃(fe	≤̃¯̄cg̃(fe	NOUN
ejpam-4028	197	16	,	,	PUNCT
ejpam-4028	197	17	hen	hen	NOUN
ejpam-4028	197	18	,	,	PUNCT
ejpam-4028	197	19	hen	hen	NOUN
ejpam-4028	197	20	)	)	PUNCT
ejpam-4028	197	21	⇒	⇒	NOUN
ejpam-4028	197	22	¯̄ag̃(fe	¯̄ag̃(fe	NOUN
ejpam-4028	197	23	,	,	PUNCT
ejpam-4028	197	24	then	then	ADV
ejpam-4028	197	25	,	,	PUNCT
ejpam-4028	197	26	then	then	ADV
ejpam-4028	197	27	)	)	PUNCT
ejpam-4028	197	28	+	+	CCONJ
ejpam-4028	197	29	¯̄b	¯̄b	NOUN
ejpam-4028	197	30	min	min	NOUN
ejpam-4028	197	31			PUNCT
ejpam-4028	197	32	g̃(fe	g̃(fe	NOUN
ejpam-4028	197	33	,	,	PUNCT
ejpam-4028	197	34	then	then	ADV
ejpam-4028	197	35	,	,	PUNCT
ejpam-4028	197	36	then	then	ADV
ejpam-4028	197	37	)	)	PUNCT
ejpam-4028	197	38	,	,	PUNCT
ejpam-4028	197	39	g̃(fe	g̃(fe	NOUN
ejpam-4028	197	40	,	,	PUNCT
ejpam-4028	197	41	fe	fe	X
ejpam-4028	197	42	,	,	PUNCT
ejpam-4028	197	43	fe	fe	NOUN
ejpam-4028	197	44	)	)	PUNCT
ejpam-4028	197	45	,	,	PUNCT
ejpam-4028	197	46	g̃(hen	g̃(hen	INTJ
ejpam-4028	197	47	,	,	PUNCT
ejpam-4028	197	48	then	then	ADV
ejpam-4028	197	49	,	,	PUNCT
ejpam-4028	197	50	then	then	ADV
ejpam-4028	197	51	)	)	PUNCT
ejpam-4028	197	52	,	,	PUNCT
ejpam-4028	197	53	g̃(hen	g̃(hen	INTJ
ejpam-4028	197	54	,	,	PUNCT
ejpam-4028	197	55	then	then	ADV
ejpam-4028	197	56	,	,	PUNCT
ejpam-4028	197	57	then	then	ADV
ejpam-4028	197	58	)	)	PUNCT
ejpam-4028	197	59			PROPN
ejpam-4028	197	60	≤̃¯̄cg̃(fe	≤̃¯̄cg̃(fe	NOUN
ejpam-4028	197	61	,	,	PUNCT
ejpam-4028	197	62	hen	hen	NOUN
ejpam-4028	197	63	,	,	PUNCT
ejpam-4028	197	64	hen	hen	NOUN
ejpam-4028	197	65	)	)	PUNCT
ejpam-4028	197	66	taking	take	VERB
ejpam-4028	197	67	the	the	DET
ejpam-4028	197	68	limit	limit	NOUN
ejpam-4028	197	69	as	as	ADP
ejpam-4028	197	70	n→∞	n→∞	NUM
ejpam-4028	197	71	from	from	ADP
ejpam-4028	197	72	which	which	PRON
ejpam-4028	197	73	,	,	PUNCT
ejpam-4028	197	74	we	we	PRON
ejpam-4028	197	75	see	see	VERB
ejpam-4028	197	76	that	that	DET
ejpam-4028	197	77	g̃(fe	g̃(fe	NOUN
ejpam-4028	197	78	,	,	PUNCT
ejpam-4028	197	79	then	then	ADV
ejpam-4028	197	80	,	,	PUNCT
ejpam-4028	197	81	then	then	ADV
ejpam-4028	197	82	)	)	PUNCT
ejpam-4028	197	83	→	→	SYM
ejpam-4028	197	84	0̃	0̃	NOUN
ejpam-4028	197	85	and	and	CCONJ
ejpam-4028	197	86	so	so	ADV
ejpam-4028	197	87	,	,	PUNCT
ejpam-4028	197	88	by	by	ADP
ejpam-4028	197	89	proposition	proposition	NOUN
ejpam-4028	197	90	(	(	PUNCT
ejpam-4028	197	91	4.1	4.1	NUM
ejpam-4028	197	92	)	)	PUNCT
ejpam-4028	197	93	in	in	ADP
ejpam-4028	197	94	[	[	X
ejpam-4028	197	95	2	2	X
ejpam-4028	197	96	]	]	PUNCT
ejpam-4028	197	97	we	we	PRON
ejpam-4028	197	98	have	have	VERB
ejpam-4028	197	99	that	that	SCONJ
ejpam-4028	197	100	the	the	DET
ejpam-4028	197	101	sequence	sequence	NOUN
ejpam-4028	197	102	{	{	PUNCT
ejpam-4028	197	103	then}n∈n	then}n∈n	PROPN
ejpam-4028	197	104	is	be	AUX
ejpam-4028	197	105	fuzzy	fuzzy	ADJ
ejpam-4028	197	106	soft	soft	ADJ
ejpam-4028	197	107	g	g	NOUN
ejpam-4028	197	108	-	-	PUNCT
ejpam-4028	197	109	convergent	convergent	NOUN
ejpam-4028	197	110	to	to	ADP
ejpam-4028	197	111	tfe	tfe	NOUN
ejpam-4028	197	112	=	=	SYM
ejpam-4028	197	113	fe	fe	X
ejpam-4028	197	114	,	,	PUNCT
ejpam-4028	197	115	therefore	therefore	ADV
ejpam-4028	197	116	proposition	proposition	NOUN
ejpam-4028	197	117	(	(	PUNCT
ejpam-4028	197	118	4.4	4.4	NUM
ejpam-4028	197	119	)	)	PUNCT
ejpam-4028	197	120	in	in	ADP
ejpam-4028	197	121	[	[	X
ejpam-4028	197	122	2	2	NUM
ejpam-4028	197	123	]	]	PUNCT
ejpam-4028	197	124	implies	imply	VERB
ejpam-4028	197	125	that	that	SCONJ
ejpam-4028	197	126	t	t	PROPN
ejpam-4028	197	127	is	be	AUX
ejpam-4028	197	128	fuzzy	fuzzy	ADJ
ejpam-4028	197	129	soft	soft	ADJ
ejpam-4028	197	130	g	g	NOUN
ejpam-4028	197	131	-	-	NOUN
ejpam-4028	197	132	continuous	continuous	ADJ
ejpam-4028	197	133	at	at	ADP
ejpam-4028	197	134	fe	fe	PROPN
ejpam-4028	197	135	.	.	PUNCT
ejpam-4028	197	136	theorem	theorem	NOUN
ejpam-4028	197	137	4	4	NUM
ejpam-4028	197	138	.	.	PUNCT
ejpam-4028	197	139	suppose	suppose	VERB
ejpam-4028	197	140	(	(	PUNCT
ejpam-4028	197	141	ẽ	ẽ	PROPN
ejpam-4028	197	142	,	,	PUNCT
ejpam-4028	197	143	g̃	g̃	PROPN
ejpam-4028	197	144	)	)	PUNCT
ejpam-4028	197	145	is	be	AUX
ejpam-4028	197	146	a	a	DET
ejpam-4028	197	147	fuzzy	fuzzy	ADJ
ejpam-4028	197	148	soft	soft	ADJ
ejpam-4028	197	149	g	g	NOUN
ejpam-4028	197	150	-	-	PUNCT
ejpam-4028	197	151	metric	metric	ADJ
ejpam-4028	197	152	space	space	NOUN
ejpam-4028	197	153	and	and	CCONJ
ejpam-4028	197	154	t	t	NOUN
ejpam-4028	197	155	:	:	PUNCT
ejpam-4028	197	156	(	(	PUNCT
ejpam-4028	197	157	ẽ	ẽ	NOUN
ejpam-4028	197	158	,	,	PUNCT
ejpam-4028	197	159	g̃)→	g̃)→	PRON
ejpam-4028	197	160	(	(	PUNCT
ejpam-4028	197	161	ẽ	ẽ	PROPN
ejpam-4028	197	162	,	,	PUNCT
ejpam-4028	197	163	g̃	g̃	PROPN
ejpam-4028	197	164	)	)	PUNCT
ejpam-4028	197	165	is	be	AUX
ejpam-4028	197	166	a	a	DET
ejpam-4028	197	167	mapping	mapping	NOUN
ejpam-4028	197	168	satisfying	satisfy	VERB
ejpam-4028	197	169	the	the	DET
ejpam-4028	197	170	following	follow	VERB
ejpam-4028	197	171	condition	condition	NOUN
ejpam-4028	197	172	:	:	PUNCT
ejpam-4028	198	1	¯̄ag̃(tfe1	¯̄ag̃(tfe1	NOUN
ejpam-4028	198	2	,	,	PUNCT
ejpam-4028	198	3	tfe2	tfe2	NOUN
ejpam-4028	198	4	,	,	PUNCT
ejpam-4028	198	5	t	t	PROPN
ejpam-4028	198	6	fe3	fe3	PROPN
ejpam-4028	198	7	)	)	PUNCT
ejpam-4028	198	8	+	+	CCONJ
ejpam-4028	198	9	¯̄b	¯̄b	NOUN
ejpam-4028	198	10			NOUN
ejpam-4028	198	11	min	min	NOUN
ejpam-4028	198	12	{	{	PUNCT
ejpam-4028	198	13	g̃(tfe1	g̃(tfe1	PROPN
ejpam-4028	198	14	,	,	PUNCT
ejpam-4028	198	15	t	t	PROPN
ejpam-4028	198	16	fe2	fe2	PROPN
ejpam-4028	198	17	,	,	PUNCT
ejpam-4028	198	18	t	t	PROPN
ejpam-4028	198	19	fe2	fe2	PROPN
ejpam-4028	198	20	)	)	PUNCT
ejpam-4028	198	21	·	·	PUNCT
ejpam-4028	199	1	g̃(fe1	g̃(fe1	NUM
ejpam-4028	199	2	,	,	PUNCT
ejpam-4028	199	3	tfe1	tfe1	PROPN
ejpam-4028	199	4	,	,	PUNCT
ejpam-4028	199	5	t	t	PROPN
ejpam-4028	199	6	fe1	fe1	PROPN
ejpam-4028	199	7	)	)	PUNCT
ejpam-4028	199	8	,	,	PUNCT
ejpam-4028	199	9	g̃(fe1	g̃(fe1	PROPN
ejpam-4028	199	10	,	,	PUNCT
ejpam-4028	199	11	fe2	fe2	PROPN
ejpam-4028	199	12	,	,	PUNCT
ejpam-4028	199	13	t	t	PROPN
ejpam-4028	199	14	fe3	fe3	PROPN
ejpam-4028	199	15	)	)	PUNCT
ejpam-4028	199	16	·	·	PUNCT
ejpam-4028	200	1	g̃(fe2	g̃(fe2	NOUN
ejpam-4028	200	2	,	,	PUNCT
ejpam-4028	200	3	tfe2	tfe2	NOUN
ejpam-4028	200	4	,	,	PUNCT
ejpam-4028	200	5	tfe2	tfe2	PROPN
ejpam-4028	200	6	)	)	PUNCT
ejpam-4028	200	7	}	}	PUNCT
ejpam-4028	200	8	min	min	PROPN
ejpam-4028	200	9	{	{	PUNCT
ejpam-4028	200	10	g̃(tfe1	g̃(tfe1	PROPN
ejpam-4028	200	11	,	,	PUNCT
ejpam-4028	200	12	t	t	PROPN
ejpam-4028	200	13	fe2	fe2	PROPN
ejpam-4028	200	14	,	,	PUNCT
ejpam-4028	200	15	t	t	PROPN
ejpam-4028	200	16	fe3	fe3	PROPN
ejpam-4028	200	17	)	)	PUNCT
ejpam-4028	200	18	·	·	PUNCT
ejpam-4028	201	1	g̃(fe1	g̃(fe1	NUM
ejpam-4028	201	2	,	,	PUNCT
ejpam-4028	201	3	tfe1	tfe1	PROPN
ejpam-4028	201	4	,	,	PUNCT
ejpam-4028	201	5	t	t	PROPN
ejpam-4028	201	6	fe1	fe1	PROPN
ejpam-4028	201	7	)	)	PUNCT
ejpam-4028	201	8	,	,	PUNCT
ejpam-4028	201	9	g̃(fe1	g̃(fe1	PROPN
ejpam-4028	201	10	,	,	PUNCT
ejpam-4028	201	11	fe2	fe2	PROPN
ejpam-4028	201	12	,	,	PUNCT
ejpam-4028	201	13	fe3	fe3	PROPN
ejpam-4028	201	14	)	)	PUNCT
ejpam-4028	201	15	·	·	PUNCT
ejpam-4028	202	1	g̃(fe2	g̃(fe2	NOUN
ejpam-4028	202	2	,	,	PUNCT
ejpam-4028	202	3	t	t	PROPN
ejpam-4028	202	4	fe2	fe2	PROPN
ejpam-4028	202	5	,	,	PUNCT
ejpam-4028	202	6	t	t	PROPN
ejpam-4028	202	7	fe2	fe2	PROPN
ejpam-4028	202	8	)	)	PUNCT
ejpam-4028	202	9	}	}	PUNCT
ejpam-4028	202	10			PROPN
ejpam-4028	202	11	≤̃¯̄cg̃(fe1	≤̃¯̄cg̃(fe1	PROPN
ejpam-4028	202	12	,	,	PUNCT
ejpam-4028	202	13	fe2	fe2	PROPN
ejpam-4028	202	14	,	,	PUNCT
ejpam-4028	202	15	fe2	fe2	PROPN
ejpam-4028	202	16	)	)	PUNCT
ejpam-4028	202	17	(	(	PUNCT
ejpam-4028	202	18	4	4	X
ejpam-4028	202	19	)	)	PUNCT
ejpam-4028	202	20	∀fe1	∀fe1	PROPN
ejpam-4028	202	21	,	,	PUNCT
ejpam-4028	202	22	fe2	fe2	PROPN
ejpam-4028	202	23	,	,	PUNCT
ejpam-4028	202	24	fe3∈̃fsc(ẽ	fe3∈̃fsc(ẽ	PROPN
ejpam-4028	202	25	)	)	PUNCT
ejpam-4028	202	26	and	and	CCONJ
ejpam-4028	202	27	0̃≤̃¯̄a	0̃≤̃¯̄a	NUM
ejpam-4028	202	28	,	,	PUNCT
ejpam-4028	202	29	¯̄b	¯̄b	NOUN
ejpam-4028	202	30	,	,	PUNCT
ejpam-4028	202	31	¯̄c<̃1̃	¯̄c<̃1̃	VERB
ejpam-4028	202	32	with	with	ADP
ejpam-4028	202	33	¯̄c−	¯̄c−	PROPN
ejpam-4028	202	34	¯̄b<̃¯̄a	¯̄b<̃¯̄a	NOUN
ejpam-4028	202	35	.	.	PUNCT
ejpam-4028	203	1	then	then	ADV
ejpam-4028	203	2	t	t	PROPN
ejpam-4028	203	3	has	have	VERB
ejpam-4028	203	4	an	an	DET
ejpam-4028	203	5	unique	unique	ADJ
ejpam-4028	203	6	fixed	fix	VERB
ejpam-4028	203	7	point	point	NOUN
ejpam-4028	203	8	,	,	PUNCT
ejpam-4028	203	9	say	say	VERB
ejpam-4028	203	10	fe	fe	X
ejpam-4028	203	11	,	,	PUNCT
ejpam-4028	203	12	and	and	CCONJ
ejpam-4028	203	13	at	at	ADP
ejpam-4028	203	14	fe	fe	PROPN
ejpam-4028	203	15	,	,	PUNCT
ejpam-4028	203	16	t	t	PROPN
ejpam-4028	203	17	is	be	AUX
ejpam-4028	203	18	fuzzy	fuzzy	ADJ
ejpam-4028	203	19	soft	soft	ADJ
ejpam-4028	203	20	g	g	NOUN
ejpam-4028	203	21	-	-	PUNCT
ejpam-4028	203	22	continuous	continuous	ADJ
ejpam-4028	203	23	.	.	PUNCT
ejpam-4028	204	1	proof	proof	NOUN
ejpam-4028	204	2	.	.	PUNCT
ejpam-4028	205	1	assume	assume	VERB
ejpam-4028	205	2	that	that	SCONJ
ejpam-4028	205	3	fe0∈̃fsc(ẽ	fe0∈̃fsc(ẽ	NOUN
ejpam-4028	205	4	)	)	PUNCT
ejpam-4028	205	5	is	be	AUX
ejpam-4028	205	6	an	an	DET
ejpam-4028	205	7	arbitrary	arbitrary	ADJ
ejpam-4028	205	8	fuzzy	fuzzy	ADJ
ejpam-4028	205	9	soft	soft	ADJ
ejpam-4028	205	10	element	element	NOUN
ejpam-4028	205	11	and	and	CCONJ
ejpam-4028	205	12	define	define	VERB
ejpam-4028	205	13	the	the	DET
ejpam-4028	205	14	sequence	sequence	NOUN
ejpam-4028	205	15	{	{	PUNCT
ejpam-4028	205	16	gen}n∈n	gen}n∈n	PROPN
ejpam-4028	205	17	as	as	SCONJ
ejpam-4028	205	18	follows	follow	VERB
ejpam-4028	205	19	:	:	PUNCT
ejpam-4028	206	1	tge0	tge0	NOUN
ejpam-4028	206	2	=	=	SYM
ejpam-4028	206	3	ge1	ge1	PROPN
ejpam-4028	206	4	,	,	PUNCT
ejpam-4028	206	5	t	t	PROPN
ejpam-4028	206	6	ge1	ge1	PROPN
ejpam-4028	206	7	=	=	PUNCT
ejpam-4028	206	8	ge2	ge2	PROPN
ejpam-4028	206	9	,	,	PUNCT
ejpam-4028	206	10	t	t	PROPN
ejpam-4028	206	11	ge2	ge2	PROPN
ejpam-4028	206	12	=	=	X
ejpam-4028	206	13	ge3	ge3	PROPN
ejpam-4028	206	14	,	,	PUNCT
ejpam-4028	206	15	...	...	PUNCT
ejpam-4028	206	16	,	,	PUNCT
ejpam-4028	206	17	t	t	PROPN
ejpam-4028	206	18	gen	gen	PROPN
ejpam-4028	206	19	=	=	NOUN
ejpam-4028	206	20	gen+1	gen+1	PROPN
ejpam-4028	206	21	.	.	PUNCT
ejpam-4028	207	1	consider	consider	VERB
ejpam-4028	207	2	that	that	DET
ejpam-4028	207	3	gen	gen	PROPN
ejpam-4028	207	4	6=	6=	PROPN
ejpam-4028	207	5	gen+1	gen+1	NOUN
ejpam-4028	207	6	.	.	PUNCT
ejpam-4028	208	1	substituting	substitute	VERB
ejpam-4028	208	2	fe1	fe1	PROPN
ejpam-4028	208	3	=	=	SYM
ejpam-4028	208	4	gen	gen	PROPN
ejpam-4028	208	5	,	,	PUNCT
ejpam-4028	208	6	fe2	fe2	X
ejpam-4028	208	7	=	=	SYM
ejpam-4028	208	8	gen+1	gen+1	NOUN
ejpam-4028	208	9	and	and	CCONJ
ejpam-4028	208	10	fe3	fe3	NOUN
ejpam-4028	208	11	=	=	SYM
ejpam-4028	208	12	gen+1	gen+1	NOUN
ejpam-4028	208	13	in	in	ADP
ejpam-4028	208	14	(	(	PUNCT
ejpam-4028	208	15	4	4	NUM
ejpam-4028	208	16	)	)	PUNCT
ejpam-4028	208	17	,	,	PUNCT
ejpam-4028	208	18	we	we	PRON
ejpam-4028	208	19	obtain	obtain	VERB
ejpam-4028	208	20	¯̄ag̃(tgen	¯̄ag̃(tgen	PROPN
ejpam-4028	208	21	,	,	PUNCT
ejpam-4028	208	22	t	t	PROPN
ejpam-4028	208	23	gen+1	gen+1	NOUN
ejpam-4028	208	24	,	,	PUNCT
ejpam-4028	208	25	t	t	PROPN
ejpam-4028	208	26	gen+1	gen+1	PROPN
ejpam-4028	208	27	)	)	PUNCT
ejpam-4028	209	1	+	+	CCONJ
ejpam-4028	209	2	¯̄b	¯̄b	NOUN
ejpam-4028	209	3			NOUN
ejpam-4028	209	4	min	min	NOUN
ejpam-4028	209	5	{	{	PUNCT
ejpam-4028	209	6	g̃(tgen	g̃(tgen	INTJ
ejpam-4028	209	7	,	,	PUNCT
ejpam-4028	209	8	t	t	PROPN
ejpam-4028	209	9	gen+1	gen+1	NOUN
ejpam-4028	209	10	,	,	PUNCT
ejpam-4028	209	11	t	t	PROPN
ejpam-4028	209	12	gen+1	gen+1	PROPN
ejpam-4028	209	13	)	)	PUNCT
ejpam-4028	209	14	·	·	PUNCT
ejpam-4028	210	1	g̃(gen	g̃(gen	PROPN
ejpam-4028	210	2	,	,	PUNCT
ejpam-4028	210	3	t	t	PROPN
ejpam-4028	210	4	gen	gen	PROPN
ejpam-4028	210	5	,	,	PUNCT
ejpam-4028	210	6	t	t	PROPN
ejpam-4028	210	7	gen	gen	PROPN
ejpam-4028	210	8	)	)	PUNCT
ejpam-4028	210	9	,	,	PUNCT
ejpam-4028	210	10	g̃(gen	g̃(gen	PROPN
ejpam-4028	210	11	,	,	PUNCT
ejpam-4028	210	12	gen+1	gen+1	NOUN
ejpam-4028	210	13	,	,	PUNCT
ejpam-4028	210	14	gen+1	gen+1	NOUN
ejpam-4028	210	15	)	)	PUNCT
ejpam-4028	210	16	·	·	PUNCT
ejpam-4028	210	17	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	210	18	,	,	PUNCT
ejpam-4028	210	19	t	t	PROPN
ejpam-4028	210	20	gen+1	gen+1	NOUN
ejpam-4028	210	21	,	,	PUNCT
ejpam-4028	210	22	t	t	PROPN
ejpam-4028	210	23	gen+1	gen+1	PROPN
ejpam-4028	210	24	)	)	PUNCT
ejpam-4028	210	25	}	}	PUNCT
ejpam-4028	210	26	min	min	NOUN
ejpam-4028	210	27	{	{	PUNCT
ejpam-4028	210	28	g̃(tgen	g̃(tgen	INTJ
ejpam-4028	210	29	,	,	PUNCT
ejpam-4028	210	30	t	t	PROPN
ejpam-4028	210	31	gen+1	gen+1	NOUN
ejpam-4028	210	32	,	,	PUNCT
ejpam-4028	210	33	t	t	PROPN
ejpam-4028	210	34	gen+1	gen+1	PROPN
ejpam-4028	210	35	)	)	PUNCT
ejpam-4028	210	36	,	,	PUNCT
ejpam-4028	210	37	g̃(gen	g̃(gen	PROPN
ejpam-4028	210	38	,	,	PUNCT
ejpam-4028	210	39	t	t	PROPN
ejpam-4028	210	40	gen	gen	PROPN
ejpam-4028	210	41	,	,	PUNCT
ejpam-4028	210	42	t	t	PROPN
ejpam-4028	210	43	gen	gen	PROPN
ejpam-4028	210	44	)	)	PUNCT
ejpam-4028	210	45	,	,	PUNCT
ejpam-4028	210	46	g̃(gen	g̃(gen	PROPN
ejpam-4028	210	47	,	,	PUNCT
ejpam-4028	210	48	gen+1	gen+1	NOUN
ejpam-4028	210	49	,	,	PUNCT
ejpam-4028	210	50	gen+1	gen+1	NOUN
ejpam-4028	210	51	)	)	PUNCT
ejpam-4028	210	52	,	,	PUNCT
ejpam-4028	210	53	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	210	54	,	,	PUNCT
ejpam-4028	210	55	t	t	PROPN
ejpam-4028	210	56	gen+1	gen+1	NOUN
ejpam-4028	210	57	,	,	PUNCT
ejpam-4028	210	58	t	t	PROPN
ejpam-4028	210	59	gen+1	gen+1	PROPN
ejpam-4028	210	60	)	)	PUNCT
ejpam-4028	210	61	}	}	PUNCT
ejpam-4028	210	62			ADJ
ejpam-4028	210	63	≤̃¯̄cg̃(gen	≤̃¯̄cg̃(gen	NOUN
ejpam-4028	210	64	,	,	PUNCT
ejpam-4028	210	65	gen+1	gen+1	NOUN
ejpam-4028	210	66	,	,	PUNCT
ejpam-4028	210	67	gen+1	gen+1	NOUN
ejpam-4028	210	68	)	)	PUNCT
ejpam-4028	210	69	a.	a.	PROPN
ejpam-4028	210	70	f.	f.	PROPN
ejpam-4028	210	71	sayed	say	VERB
ejpam-4028	210	72	,	,	PUNCT
ejpam-4028	210	73	a.	a.	NOUN
ejpam-4028	210	74	alahmari	alahmari	PROPN
ejpam-4028	210	75	/	/	SYM
ejpam-4028	210	76	eur	eur	PROPN
ejpam-4028	210	77	.	.	PUNCT
ejpam-4028	211	1	j.	j.	PROPN
ejpam-4028	211	2	pure	pure	PROPN
ejpam-4028	211	3	appl	appl	PROPN
ejpam-4028	211	4	.	.	PROPN
ejpam-4028	211	5	math	math	PROPN
ejpam-4028	211	6	,	,	PUNCT
ejpam-4028	211	7	14	14	NUM
ejpam-4028	211	8	(	(	PUNCT
ejpam-4028	211	9	3	3	NUM
ejpam-4028	211	10	)	)	PUNCT
ejpam-4028	211	11	(	(	PUNCT
ejpam-4028	211	12	2021	2021	NUM
ejpam-4028	211	13	)	)	PUNCT
ejpam-4028	211	14	,	,	PUNCT
ejpam-4028	211	15	923	923	NUM
ejpam-4028	211	16	-	-	SYM
ejpam-4028	211	17	941	941	NUM
ejpam-4028	211	18	932	932	NUM
ejpam-4028	211	19	¯̄ag̃(gen+1	¯̄ag̃(gen+1	NOUN
ejpam-4028	211	20	,	,	PUNCT
ejpam-4028	211	21	gen+2	gen+2	NOUN
ejpam-4028	211	22	,	,	PUNCT
ejpam-4028	211	23	gen+2	gen+2	NOUN
ejpam-4028	211	24	)	)	PUNCT
ejpam-4028	212	1	+	+	CCONJ
ejpam-4028	212	2	¯̄b	¯̄b	NOUN
ejpam-4028	212	3			NOUN
ejpam-4028	212	4	min	min	NOUN
ejpam-4028	212	5	{	{	PUNCT
ejpam-4028	212	6	g̃(gen+1	g̃(gen+1	PROPN
ejpam-4028	212	7	,	,	PUNCT
ejpam-4028	212	8	gen+2	gen+2	NOUN
ejpam-4028	212	9	,	,	PUNCT
ejpam-4028	212	10	gen+2	gen+2	NOUN
ejpam-4028	212	11	)	)	PUNCT
ejpam-4028	212	12	·	·	PUNCT
ejpam-4028	213	1	g̃(gen	g̃(gen	PROPN
ejpam-4028	213	2	,	,	PUNCT
ejpam-4028	213	3	gen+1	gen+1	NOUN
ejpam-4028	213	4	,	,	PUNCT
ejpam-4028	213	5	gen+1	gen+1	NOUN
ejpam-4028	213	6	)	)	PUNCT
ejpam-4028	213	7	,	,	PUNCT
ejpam-4028	213	8	g̃(gen	g̃(gen	PROPN
ejpam-4028	213	9	,	,	PUNCT
ejpam-4028	213	10	gen+1	gen+1	NOUN
ejpam-4028	213	11	,	,	PUNCT
ejpam-4028	213	12	gen+1	gen+1	NOUN
ejpam-4028	213	13	)	)	PUNCT
ejpam-4028	213	14	·	·	PUNCT
ejpam-4028	213	15	g̃(gen+1	g̃(gen+1	VERB
ejpam-4028	213	16	,	,	PUNCT
ejpam-4028	213	17	gen+2	gen+2	NOUN
ejpam-4028	213	18	,	,	PUNCT
ejpam-4028	213	19	gen+2	gen+2	NOUN
ejpam-4028	213	20	)	)	PUNCT
ejpam-4028	213	21	}	}	PUNCT
ejpam-4028	213	22	min	min	NOUN
ejpam-4028	213	23	{	{	PUNCT
ejpam-4028	213	24	g̃(gen+1	g̃(gen+1	PROPN
ejpam-4028	213	25	,	,	PUNCT
ejpam-4028	213	26	gen+2	gen+2	NOUN
ejpam-4028	213	27	,	,	PUNCT
ejpam-4028	213	28	gen+2	gen+2	NOUN
ejpam-4028	213	29	)	)	PUNCT
ejpam-4028	213	30	,	,	PUNCT
ejpam-4028	213	31	g̃(gen	g̃(gen	PROPN
ejpam-4028	213	32	,	,	PUNCT
ejpam-4028	213	33	gen+1	gen+1	NOUN
ejpam-4028	213	34	,	,	PUNCT
ejpam-4028	213	35	gen+1	gen+1	NOUN
ejpam-4028	213	36	)	)	PUNCT
ejpam-4028	213	37	,	,	PUNCT
ejpam-4028	213	38	g̃(gen	g̃(gen	PROPN
ejpam-4028	213	39	,	,	PUNCT
ejpam-4028	213	40	gen+1	gen+1	NOUN
ejpam-4028	213	41	,	,	PUNCT
ejpam-4028	213	42	gen+1	gen+1	NOUN
ejpam-4028	213	43	)	)	PUNCT
ejpam-4028	213	44	,	,	PUNCT
ejpam-4028	213	45	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	213	46	,	,	PUNCT
ejpam-4028	213	47	gen+2	gen+2	NOUN
ejpam-4028	213	48	,	,	PUNCT
ejpam-4028	213	49	gen+2	gen+2	NOUN
ejpam-4028	213	50	)	)	PUNCT
ejpam-4028	213	51	}	}	PUNCT
ejpam-4028	213	52			ADJ
ejpam-4028	213	53	≤̃¯̄cg̃(gen	≤̃¯̄cg̃(gen	NOUN
ejpam-4028	213	54	,	,	PUNCT
ejpam-4028	213	55	gen+1	gen+1	NOUN
ejpam-4028	213	56	,	,	PUNCT
ejpam-4028	213	57	gen+1	gen+1	NOUN
ejpam-4028	213	58	)	)	PUNCT
ejpam-4028	213	59	(	(	PUNCT
ejpam-4028	213	60	5	5	X
ejpam-4028	213	61	)	)	PUNCT
ejpam-4028	213	62	⇒	⇒	NOUN
ejpam-4028	213	63	¯̄ag̃(gen+1	¯̄ag̃(gen+1	VERB
ejpam-4028	213	64	,	,	PUNCT
ejpam-4028	213	65	gen+2	gen+2	NOUN
ejpam-4028	213	66	,	,	PUNCT
ejpam-4028	213	67	gen+2	gen+2	NOUN
ejpam-4028	213	68	)	)	PUNCT
ejpam-4028	214	1	+	+	CCONJ
ejpam-4028	214	2	¯̄b	¯̄b	NOUN
ejpam-4028	214	3			ADJ
ejpam-4028	214	4	min	min	NOUN
ejpam-4028	214	5			NOUN
ejpam-4028	214	6	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	214	7	,	,	PUNCT
ejpam-4028	214	8	gen+2	gen+2	NOUN
ejpam-4028	214	9	,	,	PUNCT
ejpam-4028	214	10	gen+2	gen+2	NOUN
ejpam-4028	214	11	)	)	PUNCT
ejpam-4028	214	12	·	·	PUNCT
ejpam-4028	215	1	g̃(gen	g̃(gen	PROPN
ejpam-4028	215	2	,	,	PUNCT
ejpam-4028	215	3	gen+1	gen+1	NOUN
ejpam-4028	215	4	,	,	PUNCT
ejpam-4028	215	5	gen+1	gen+1	NOUN
ejpam-4028	215	6	)	)	PUNCT
ejpam-4028	215	7	,	,	PUNCT
ejpam-4028	215	8	g̃(gen	g̃(gen	PROPN
ejpam-4028	215	9	,	,	PUNCT
ejpam-4028	215	10	gen+1	gen+1	NOUN
ejpam-4028	215	11	,	,	PUNCT
ejpam-4028	215	12	gen+1	gen+1	NOUN
ejpam-4028	215	13	)	)	PUNCT
ejpam-4028	215	14	·	·	PUNCT
ejpam-4028	215	15	g̃(gen+1	g̃(gen+1	VERB
ejpam-4028	215	16	,	,	PUNCT
ejpam-4028	215	17	gen+2	gen+2	NOUN
ejpam-4028	215	18	,	,	PUNCT
ejpam-4028	215	19	gen+2	gen+2	NOUN
ejpam-4028	215	20	)	)	PUNCT
ejpam-4028	215	21			NOUN
ejpam-4028	215	22	min	min	NOUN
ejpam-4028	215	23	{	{	PUNCT
ejpam-4028	215	24	g̃(gen+1	g̃(gen+1	PROPN
ejpam-4028	215	25	,	,	PUNCT
ejpam-4028	215	26	gen+2	gen+2	NOUN
ejpam-4028	215	27	,	,	PUNCT
ejpam-4028	215	28	gen+2	gen+2	NOUN
ejpam-4028	215	29	)	)	PUNCT
ejpam-4028	215	30	,	,	PUNCT
ejpam-4028	215	31	g̃(gen	g̃(gen	PROPN
ejpam-4028	215	32	,	,	PUNCT
ejpam-4028	215	33	gen+1	gen+1	NOUN
ejpam-4028	215	34	,	,	PUNCT
ejpam-4028	215	35	gen+1	gen+1	NOUN
ejpam-4028	215	36	)	)	PUNCT
ejpam-4028	215	37	}	}	PUNCT
ejpam-4028	215	38			ADJ
ejpam-4028	215	39	≤̃¯̄cg̃(gen	≤̃¯̄cg̃(gen	NOUN
ejpam-4028	215	40	,	,	PUNCT
ejpam-4028	215	41	gen+1	gen+1	NOUN
ejpam-4028	215	42	,	,	PUNCT
ejpam-4028	215	43	gen+1	gen+1	NOUN
ejpam-4028	215	44	)	)	PUNCT
ejpam-4028	215	45	we	we	PRON
ejpam-4028	215	46	now	now	ADV
ejpam-4028	215	47	have	have	VERB
ejpam-4028	215	48	four	four	NUM
ejpam-4028	215	49	cases	case	NOUN
ejpam-4028	215	50	:	:	PUNCT
ejpam-4028	215	51	case	case	NOUN
ejpam-4028	215	52	(	(	PUNCT
ejpam-4028	215	53	1	1	NUM
ejpam-4028	215	54	):	):	PUNCT
ejpam-4028	215	55	if	if	SCONJ
ejpam-4028	215	56			PROPN
ejpam-4028	215	57	min	min	NOUN
ejpam-4028	215	58			NOUN
ejpam-4028	215	59	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	215	60	,	,	PUNCT
ejpam-4028	215	61	gen+2	gen+2	NOUN
ejpam-4028	215	62	,	,	PUNCT
ejpam-4028	215	63	gen+2	gen+2	NOUN
ejpam-4028	215	64	)	)	PUNCT
ejpam-4028	215	65	·	·	PUNCT
ejpam-4028	216	1	g̃(gen	g̃(gen	PROPN
ejpam-4028	216	2	,	,	PUNCT
ejpam-4028	216	3	gen+1	gen+1	NOUN
ejpam-4028	216	4	,	,	PUNCT
ejpam-4028	216	5	gen+1	gen+1	NOUN
ejpam-4028	216	6	)	)	PUNCT
ejpam-4028	216	7	,	,	PUNCT
ejpam-4028	216	8	g̃(gen	g̃(gen	PROPN
ejpam-4028	216	9	,	,	PUNCT
ejpam-4028	216	10	gen+1	gen+1	NOUN
ejpam-4028	216	11	,	,	PUNCT
ejpam-4028	216	12	gen+1	gen+1	NOUN
ejpam-4028	216	13	)	)	PUNCT
ejpam-4028	216	14	·	·	PUNCT
ejpam-4028	216	15	g̃(gen+1	g̃(gen+1	VERB
ejpam-4028	216	16	,	,	PUNCT
ejpam-4028	216	17	gen+2	gen+2	NOUN
ejpam-4028	216	18	,	,	PUNCT
ejpam-4028	216	19	gen+2	gen+2	NOUN
ejpam-4028	216	20	)	)	PUNCT
ejpam-4028	216	21			NOUN
ejpam-4028	216	22	min	min	NOUN
ejpam-4028	216	23	{	{	PUNCT
ejpam-4028	216	24	g̃(gen+1	g̃(gen+1	PROPN
ejpam-4028	216	25	,	,	PUNCT
ejpam-4028	216	26	gen+2	gen+2	NOUN
ejpam-4028	216	27	,	,	PUNCT
ejpam-4028	216	28	gen+2	gen+2	NOUN
ejpam-4028	216	29	)	)	PUNCT
ejpam-4028	216	30	,	,	PUNCT
ejpam-4028	216	31	g̃(gen	g̃(gen	PROPN
ejpam-4028	216	32	,	,	PUNCT
ejpam-4028	216	33	gen+1	gen+1	NOUN
ejpam-4028	216	34	,	,	PUNCT
ejpam-4028	216	35	gen+1	gen+1	NOUN
ejpam-4028	216	36	)	)	PUNCT
ejpam-4028	216	37	}	}	PUNCT
ejpam-4028	216	38	=	=	ADP
ejpam-4028	216	39	[	[	X
ejpam-4028	216	40	{	{	PUNCT
ejpam-4028	216	41	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	216	42	,	,	PUNCT
ejpam-4028	216	43	gen+2	gen+2	NOUN
ejpam-4028	216	44	,	,	PUNCT
ejpam-4028	216	45	gen+2	gen+2	NOUN
ejpam-4028	216	46	)	)	PUNCT
ejpam-4028	216	47	·	·	PUNCT
ejpam-4028	217	1	g̃(gen	g̃(gen	PROPN
ejpam-4028	217	2	,	,	PUNCT
ejpam-4028	217	3	gen+1	gen+1	NOUN
ejpam-4028	217	4	,	,	PUNCT
ejpam-4028	217	5	gen+1	gen+1	NOUN
ejpam-4028	217	6	)	)	PUNCT
ejpam-4028	217	7	}	}	PUNCT
ejpam-4028	217	8	g̃(gen	g̃(gen	PROPN
ejpam-4028	217	9	,	,	PUNCT
ejpam-4028	217	10	gen+1	gen+1	NOUN
ejpam-4028	217	11	,	,	PUNCT
ejpam-4028	217	12	gen+1	gen+1	NOUN
ejpam-4028	217	13	)	)	PUNCT
ejpam-4028	217	14	]	]	PUNCT
ejpam-4028	218	1	=	=	PUNCT
ejpam-4028	218	2	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	218	3	,	,	PUNCT
ejpam-4028	218	4	gen+2	gen+2	NOUN
ejpam-4028	218	5	,	,	PUNCT
ejpam-4028	218	6	gen+2	gen+2	NOUN
ejpam-4028	218	7	)	)	PUNCT
ejpam-4028	218	8	then	then	ADV
ejpam-4028	218	9	,	,	PUNCT
ejpam-4028	218	10	we	we	PRON
ejpam-4028	218	11	have	have	VERB
ejpam-4028	218	12	¯̄ag̃(gen+1	¯̄ag̃(gen+1	NOUN
ejpam-4028	218	13	,	,	PUNCT
ejpam-4028	218	14	gen+2	gen+2	NOUN
ejpam-4028	218	15	,	,	PUNCT
ejpam-4028	218	16	gen+2	gen+2	NOUN
ejpam-4028	218	17	)	)	PUNCT
ejpam-4028	219	1	+	+	NUM
ejpam-4028	219	2	¯̄bg̃(gen+1	¯̄bg̃(gen+1	ADJ
ejpam-4028	219	3	,	,	PUNCT
ejpam-4028	219	4	gen+2	gen+2	NOUN
ejpam-4028	219	5	,	,	PUNCT
ejpam-4028	219	6	gen+2)≤̃¯̄cg̃(gen	gen+2)≤̃¯̄cg̃(gen	NOUN
ejpam-4028	219	7	,	,	PUNCT
ejpam-4028	219	8	gen+1	gen+1	NOUN
ejpam-4028	219	9	,	,	PUNCT
ejpam-4028	219	10	gen+1	gen+1	NOUN
ejpam-4028	219	11	)	)	PUNCT
ejpam-4028	219	12	⇒	⇒	NOUN
ejpam-4028	219	13	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	219	14	,	,	PUNCT
ejpam-4028	219	15	gen+2	gen+2	NOUN
ejpam-4028	219	16	,	,	PUNCT
ejpam-4028	219	17	gen+2)≤̃	gen+2)≤̃	PROPN
ejpam-4028	219	18	¯̄c	¯̄c	PROPN
ejpam-4028	219	19	¯̄a+¯̄b	¯̄a+¯̄b	X
ejpam-4028	219	20	g̃(gen	g̃(gen	PROPN
ejpam-4028	219	21	,	,	PUNCT
ejpam-4028	219	22	gen+1	gen+1	NOUN
ejpam-4028	219	23	,	,	PUNCT
ejpam-4028	219	24	gen+1	gen+1	NOUN
ejpam-4028	219	25	)	)	PUNCT
ejpam-4028	219	26	case	case	NOUN
ejpam-4028	219	27	(	(	PUNCT
ejpam-4028	219	28	2	2	NUM
ejpam-4028	219	29	):	):	PUNCT
ejpam-4028	219	30	if	if	SCONJ
ejpam-4028	219	31			PROPN
ejpam-4028	219	32	min	min	NOUN
ejpam-4028	219	33			NOUN
ejpam-4028	219	34	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	219	35	,	,	PUNCT
ejpam-4028	219	36	gen+2	gen+2	NOUN
ejpam-4028	219	37	,	,	PUNCT
ejpam-4028	219	38	gen+2	gen+2	NOUN
ejpam-4028	219	39	)	)	PUNCT
ejpam-4028	219	40	·	·	PUNCT
ejpam-4028	220	1	g̃(gen	g̃(gen	PROPN
ejpam-4028	220	2	,	,	PUNCT
ejpam-4028	220	3	gen+1	gen+1	NOUN
ejpam-4028	220	4	,	,	PUNCT
ejpam-4028	220	5	gen+1	gen+1	NOUN
ejpam-4028	220	6	)	)	PUNCT
ejpam-4028	220	7	,	,	PUNCT
ejpam-4028	220	8	g̃(gen	g̃(gen	PROPN
ejpam-4028	220	9	,	,	PUNCT
ejpam-4028	220	10	gen+1	gen+1	NOUN
ejpam-4028	220	11	,	,	PUNCT
ejpam-4028	220	12	gen+1	gen+1	NOUN
ejpam-4028	220	13	)	)	PUNCT
ejpam-4028	220	14	·	·	PUNCT
ejpam-4028	220	15	g̃(gen+1	g̃(gen+1	VERB
ejpam-4028	220	16	,	,	PUNCT
ejpam-4028	220	17	gen+2	gen+2	NOUN
ejpam-4028	220	18	,	,	PUNCT
ejpam-4028	220	19	gen+2	gen+2	NOUN
ejpam-4028	220	20	)	)	PUNCT
ejpam-4028	220	21			NOUN
ejpam-4028	220	22	min	min	NOUN
ejpam-4028	220	23	{	{	PUNCT
ejpam-4028	220	24	g̃(gen+1	g̃(gen+1	PROPN
ejpam-4028	220	25	,	,	PUNCT
ejpam-4028	220	26	gen+2	gen+2	NOUN
ejpam-4028	220	27	,	,	PUNCT
ejpam-4028	220	28	gen+2	gen+2	NOUN
ejpam-4028	220	29	)	)	PUNCT
ejpam-4028	220	30	,	,	PUNCT
ejpam-4028	220	31	g̃(gen	g̃(gen	PROPN
ejpam-4028	220	32	,	,	PUNCT
ejpam-4028	220	33	gen+1	gen+1	NOUN
ejpam-4028	220	34	,	,	PUNCT
ejpam-4028	220	35	gen+1	gen+1	NOUN
ejpam-4028	220	36	)	)	PUNCT
ejpam-4028	220	37	}	}	PUNCT
ejpam-4028	220	38	=	=	ADP
ejpam-4028	220	39	[	[	X
ejpam-4028	220	40	{	{	PUNCT
ejpam-4028	220	41	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	220	42	,	,	PUNCT
ejpam-4028	220	43	gen+2	gen+2	NOUN
ejpam-4028	220	44	,	,	PUNCT
ejpam-4028	220	45	gen+2	gen+2	NOUN
ejpam-4028	220	46	)	)	PUNCT
ejpam-4028	220	47	·	·	PUNCT
ejpam-4028	221	1	g̃(gen	g̃(gen	PROPN
ejpam-4028	221	2	,	,	PUNCT
ejpam-4028	221	3	gen+1	gen+1	NOUN
ejpam-4028	221	4	,	,	PUNCT
ejpam-4028	221	5	gen+1	gen+1	NOUN
ejpam-4028	221	6	)	)	PUNCT
ejpam-4028	221	7	}	}	PUNCT
ejpam-4028	221	8	g̃(gen+1	g̃(gen+1	VERB
ejpam-4028	221	9	,	,	PUNCT
ejpam-4028	221	10	gen+2	gen+2	NOUN
ejpam-4028	221	11	,	,	PUNCT
ejpam-4028	221	12	gen+2	gen+2	NOUN
ejpam-4028	221	13	)	)	PUNCT
ejpam-4028	221	14	]	]	PUNCT
ejpam-4028	222	1	=	=	SYM
ejpam-4028	222	2	g̃(gen	g̃(gen	PROPN
ejpam-4028	222	3	,	,	PUNCT
ejpam-4028	222	4	gen+1	gen+1	NOUN
ejpam-4028	222	5	,	,	PUNCT
ejpam-4028	222	6	gen+1	gen+1	NOUN
ejpam-4028	222	7	)	)	PUNCT
ejpam-4028	222	8	then	then	ADV
ejpam-4028	222	9	,	,	PUNCT
ejpam-4028	222	10	we	we	PRON
ejpam-4028	222	11	have	have	VERB
ejpam-4028	222	12	¯̄ag̃(gen+1	¯̄ag̃(gen+1	NOUN
ejpam-4028	222	13	,	,	PUNCT
ejpam-4028	222	14	gen+2	gen+2	NOUN
ejpam-4028	222	15	,	,	PUNCT
ejpam-4028	222	16	gen+2	gen+2	NOUN
ejpam-4028	222	17	)	)	PUNCT
ejpam-4028	223	1	+	+	CCONJ
ejpam-4028	223	2	¯̄bg̃(gen	¯̄bg̃(gen	NOUN
ejpam-4028	223	3	,	,	PUNCT
ejpam-4028	223	4	gen+1	gen+1	NOUN
ejpam-4028	223	5	,	,	PUNCT
ejpam-4028	223	6	gen+1)≤̃¯̄cg̃(gen	gen+1)≤̃¯̄cg̃(gen	PROPN
ejpam-4028	223	7	,	,	PUNCT
ejpam-4028	223	8	gen+1	gen+1	NOUN
ejpam-4028	223	9	,	,	PUNCT
ejpam-4028	223	10	gen+1	gen+1	NOUN
ejpam-4028	223	11	)	)	PUNCT
ejpam-4028	223	12	⇒	⇒	NOUN
ejpam-4028	223	13	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	223	14	,	,	PUNCT
ejpam-4028	223	15	gen+2	gen+2	NOUN
ejpam-4028	223	16	,	,	PUNCT
ejpam-4028	223	17	gen+2)≤̃	gen+2)≤̃	PROPN
ejpam-4028	223	18	¯̄c−¯̄b	¯̄c−¯̄b	X
ejpam-4028	223	19	¯̄a	¯̄a	PROPN
ejpam-4028	223	20	g̃(gen	g̃(gen	PROPN
ejpam-4028	223	21	,	,	PUNCT
ejpam-4028	223	22	gen+1	gen+1	NOUN
ejpam-4028	223	23	,	,	PUNCT
ejpam-4028	223	24	gen+1	gen+1	NOUN
ejpam-4028	223	25	)	)	PUNCT
ejpam-4028	223	26	case	case	NOUN
ejpam-4028	223	27	(	(	PUNCT
ejpam-4028	223	28	3	3	NUM
ejpam-4028	223	29	):	):	PUNCT
ejpam-4028	223	30	if	if	SCONJ
ejpam-4028	223	31			PROPN
ejpam-4028	223	32	min	min	NOUN
ejpam-4028	223	33			NOUN
ejpam-4028	223	34	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	223	35	,	,	PUNCT
ejpam-4028	223	36	gen+2	gen+2	NOUN
ejpam-4028	223	37	,	,	PUNCT
ejpam-4028	223	38	gen+2	gen+2	NOUN
ejpam-4028	223	39	)	)	PUNCT
ejpam-4028	223	40	·	·	PUNCT
ejpam-4028	224	1	g̃(gen	g̃(gen	PROPN
ejpam-4028	224	2	,	,	PUNCT
ejpam-4028	224	3	gen+1	gen+1	NOUN
ejpam-4028	224	4	,	,	PUNCT
ejpam-4028	224	5	gen+1	gen+1	NOUN
ejpam-4028	224	6	)	)	PUNCT
ejpam-4028	224	7	,	,	PUNCT
ejpam-4028	224	8	g̃(gen	g̃(gen	PROPN
ejpam-4028	224	9	,	,	PUNCT
ejpam-4028	224	10	gen+1	gen+1	NOUN
ejpam-4028	224	11	,	,	PUNCT
ejpam-4028	224	12	gen+1	gen+1	NOUN
ejpam-4028	224	13	)	)	PUNCT
ejpam-4028	224	14	·	·	PUNCT
ejpam-4028	224	15	g̃(gen+1	g̃(gen+1	VERB
ejpam-4028	224	16	,	,	PUNCT
ejpam-4028	224	17	gen+2	gen+2	NOUN
ejpam-4028	224	18	,	,	PUNCT
ejpam-4028	224	19	gen+2	gen+2	NOUN
ejpam-4028	224	20	)	)	PUNCT
ejpam-4028	224	21			NOUN
ejpam-4028	224	22	min	min	NOUN
ejpam-4028	224	23	{	{	PUNCT
ejpam-4028	224	24	g̃(gen+1	g̃(gen+1	PROPN
ejpam-4028	224	25	,	,	PUNCT
ejpam-4028	224	26	gen+2	gen+2	NOUN
ejpam-4028	224	27	,	,	PUNCT
ejpam-4028	224	28	gen+2	gen+2	NOUN
ejpam-4028	224	29	)	)	PUNCT
ejpam-4028	224	30	,	,	PUNCT
ejpam-4028	224	31	g̃(gen	g̃(gen	PROPN
ejpam-4028	224	32	,	,	PUNCT
ejpam-4028	224	33	gen+1	gen+1	NOUN
ejpam-4028	224	34	,	,	PUNCT
ejpam-4028	224	35	gen+1	gen+1	NOUN
ejpam-4028	224	36	)	)	PUNCT
ejpam-4028	224	37	}	}	PUNCT
ejpam-4028	224	38	=	=	PROPN
ejpam-4028	224	39	[	[	X
ejpam-4028	224	40	{	{	PUNCT
ejpam-4028	224	41	g̃(gen	g̃(gen	PROPN
ejpam-4028	224	42	,	,	PUNCT
ejpam-4028	224	43	gen+1	gen+1	NOUN
ejpam-4028	224	44	,	,	PUNCT
ejpam-4028	224	45	gen+1	gen+1	NOUN
ejpam-4028	224	46	)	)	PUNCT
ejpam-4028	224	47	·	·	PUNCT
ejpam-4028	224	48	g̃(gen+1	g̃(gen+1	VERB
ejpam-4028	224	49	,	,	PUNCT
ejpam-4028	224	50	gen+2	gen+2	NOUN
ejpam-4028	224	51	,	,	PUNCT
ejpam-4028	224	52	gen+2	gen+2	NOUN
ejpam-4028	224	53	)	)	PUNCT
ejpam-4028	224	54	}	}	PUNCT
ejpam-4028	224	55	g̃(gen	g̃(gen	PROPN
ejpam-4028	224	56	,	,	PUNCT
ejpam-4028	224	57	gen+1	gen+1	NOUN
ejpam-4028	224	58	,	,	PUNCT
ejpam-4028	224	59	gen+1	gen+1	NOUN
ejpam-4028	224	60	)	)	PUNCT
ejpam-4028	224	61	]	]	PUNCT
ejpam-4028	225	1	=	=	PUNCT
ejpam-4028	225	2	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	225	3	,	,	PUNCT
ejpam-4028	225	4	gen+2	gen+2	NOUN
ejpam-4028	225	5	,	,	PUNCT
ejpam-4028	225	6	gen+2	gen+2	NOUN
ejpam-4028	225	7	)	)	PUNCT
ejpam-4028	225	8	then	then	ADV
ejpam-4028	225	9	,	,	PUNCT
ejpam-4028	225	10	we	we	PRON
ejpam-4028	225	11	have	have	VERB
ejpam-4028	225	12	¯̄ag̃(gen+1	¯̄ag̃(gen+1	NOUN
ejpam-4028	225	13	,	,	PUNCT
ejpam-4028	225	14	gen+2	gen+2	NOUN
ejpam-4028	225	15	,	,	PUNCT
ejpam-4028	225	16	gen+2	gen+2	NOUN
ejpam-4028	225	17	)	)	PUNCT
ejpam-4028	226	1	+	+	NUM
ejpam-4028	226	2	¯̄bg̃(gen+1	¯̄bg̃(gen+1	ADJ
ejpam-4028	226	3	,	,	PUNCT
ejpam-4028	226	4	gen+2	gen+2	NOUN
ejpam-4028	226	5	,	,	PUNCT
ejpam-4028	226	6	gen+2)≤̃¯̄cg̃(gen	gen+2)≤̃¯̄cg̃(gen	NOUN
ejpam-4028	226	7	,	,	PUNCT
ejpam-4028	226	8	gen+1	gen+1	NOUN
ejpam-4028	226	9	,	,	PUNCT
ejpam-4028	226	10	gen+1	gen+1	NOUN
ejpam-4028	226	11	)	)	PUNCT
ejpam-4028	226	12	⇒	⇒	NOUN
ejpam-4028	226	13	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	226	14	,	,	PUNCT
ejpam-4028	226	15	gen+2	gen+2	NOUN
ejpam-4028	226	16	,	,	PUNCT
ejpam-4028	226	17	gen+2)≤̃	gen+2)≤̃	PROPN
ejpam-4028	226	18	¯̄c	¯̄c	PROPN
ejpam-4028	226	19	¯̄a+¯̄b	¯̄a+¯̄b	X
ejpam-4028	226	20	g̃(gen	g̃(gen	PROPN
ejpam-4028	226	21	,	,	PUNCT
ejpam-4028	226	22	gen+1	gen+1	NOUN
ejpam-4028	226	23	,	,	PUNCT
ejpam-4028	226	24	gen+1	gen+1	NOUN
ejpam-4028	226	25	)	)	PUNCT
ejpam-4028	226	26	a.	a.	PROPN
ejpam-4028	226	27	f.	f.	PROPN
ejpam-4028	226	28	sayed	say	VERB
ejpam-4028	226	29	,	,	PUNCT
ejpam-4028	226	30	a.	a.	NOUN
ejpam-4028	226	31	alahmari	alahmari	PROPN
ejpam-4028	226	32	/	/	SYM
ejpam-4028	226	33	eur	eur	PROPN
ejpam-4028	226	34	.	.	PUNCT
ejpam-4028	227	1	j.	j.	PROPN
ejpam-4028	227	2	pure	pure	PROPN
ejpam-4028	227	3	appl	appl	PROPN
ejpam-4028	227	4	.	.	PROPN
ejpam-4028	227	5	math	math	PROPN
ejpam-4028	227	6	,	,	PUNCT
ejpam-4028	227	7	14	14	NUM
ejpam-4028	227	8	(	(	PUNCT
ejpam-4028	227	9	3	3	NUM
ejpam-4028	227	10	)	)	PUNCT
ejpam-4028	227	11	(	(	PUNCT
ejpam-4028	227	12	2021	2021	NUM
ejpam-4028	227	13	)	)	PUNCT
ejpam-4028	227	14	,	,	PUNCT
ejpam-4028	227	15	923	923	NUM
ejpam-4028	227	16	-	-	SYM
ejpam-4028	227	17	941	941	NUM
ejpam-4028	227	18	933	933	NUM
ejpam-4028	227	19	case	case	NOUN
ejpam-4028	227	20	(	(	PUNCT
ejpam-4028	227	21	4	4	NUM
ejpam-4028	227	22	):	):	PUNCT
ejpam-4028	227	23	if	if	SCONJ
ejpam-4028	227	24			PROPN
ejpam-4028	227	25	min	min	NOUN
ejpam-4028	227	26			NOUN
ejpam-4028	227	27	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	227	28	,	,	PUNCT
ejpam-4028	227	29	gen+2	gen+2	NOUN
ejpam-4028	227	30	,	,	PUNCT
ejpam-4028	227	31	gen+2	gen+2	NOUN
ejpam-4028	227	32	)	)	PUNCT
ejpam-4028	227	33	·	·	PUNCT
ejpam-4028	228	1	g̃(gen	g̃(gen	PROPN
ejpam-4028	228	2	,	,	PUNCT
ejpam-4028	228	3	gen+1	gen+1	NOUN
ejpam-4028	228	4	,	,	PUNCT
ejpam-4028	228	5	gen+1	gen+1	NOUN
ejpam-4028	228	6	)	)	PUNCT
ejpam-4028	228	7	,	,	PUNCT
ejpam-4028	228	8	g̃(gen	g̃(gen	PROPN
ejpam-4028	228	9	,	,	PUNCT
ejpam-4028	228	10	gen+1	gen+1	NOUN
ejpam-4028	228	11	,	,	PUNCT
ejpam-4028	228	12	gen+1	gen+1	NOUN
ejpam-4028	228	13	)	)	PUNCT
ejpam-4028	228	14	·	·	PUNCT
ejpam-4028	228	15	g̃(gen+1	g̃(gen+1	VERB
ejpam-4028	228	16	,	,	PUNCT
ejpam-4028	228	17	gen+2	gen+2	NOUN
ejpam-4028	228	18	,	,	PUNCT
ejpam-4028	228	19	gen+2	gen+2	NOUN
ejpam-4028	228	20	)	)	PUNCT
ejpam-4028	228	21			NOUN
ejpam-4028	228	22	min	min	NOUN
ejpam-4028	228	23	{	{	PUNCT
ejpam-4028	228	24	g̃(gen+1	g̃(gen+1	PROPN
ejpam-4028	228	25	,	,	PUNCT
ejpam-4028	228	26	gen+2	gen+2	NOUN
ejpam-4028	228	27	,	,	PUNCT
ejpam-4028	228	28	gen+2	gen+2	NOUN
ejpam-4028	228	29	)	)	PUNCT
ejpam-4028	228	30	,	,	PUNCT
ejpam-4028	228	31	g̃(gen	g̃(gen	PROPN
ejpam-4028	228	32	,	,	PUNCT
ejpam-4028	228	33	gen+1	gen+1	NOUN
ejpam-4028	228	34	,	,	PUNCT
ejpam-4028	228	35	gen+1	gen+1	NOUN
ejpam-4028	228	36	)	)	PUNCT
ejpam-4028	228	37	}	}	PUNCT
ejpam-4028	228	38	=	=	PROPN
ejpam-4028	228	39	[	[	X
ejpam-4028	228	40	{	{	PUNCT
ejpam-4028	228	41	g̃(gen	g̃(gen	PROPN
ejpam-4028	228	42	,	,	PUNCT
ejpam-4028	228	43	gen+1	gen+1	NOUN
ejpam-4028	228	44	,	,	PUNCT
ejpam-4028	228	45	gen+1	gen+1	NOUN
ejpam-4028	228	46	)	)	PUNCT
ejpam-4028	228	47	·	·	PUNCT
ejpam-4028	228	48	g̃(gen+1	g̃(gen+1	VERB
ejpam-4028	228	49	,	,	PUNCT
ejpam-4028	228	50	gen+2	gen+2	NOUN
ejpam-4028	228	51	,	,	PUNCT
ejpam-4028	228	52	gen+2	gen+2	NOUN
ejpam-4028	228	53	)	)	PUNCT
ejpam-4028	228	54	}	}	PUNCT
ejpam-4028	228	55	g̃(gen+1	g̃(gen+1	VERB
ejpam-4028	228	56	,	,	PUNCT
ejpam-4028	228	57	gen+2	gen+2	NOUN
ejpam-4028	228	58	,	,	PUNCT
ejpam-4028	228	59	gen+2	gen+2	NOUN
ejpam-4028	228	60	)	)	PUNCT
ejpam-4028	228	61	]	]	PUNCT
ejpam-4028	229	1	=	=	SYM
ejpam-4028	229	2	g̃(gen	g̃(gen	PROPN
ejpam-4028	229	3	,	,	PUNCT
ejpam-4028	229	4	gen+1	gen+1	NOUN
ejpam-4028	229	5	,	,	PUNCT
ejpam-4028	229	6	gen+1	gen+1	NOUN
ejpam-4028	229	7	)	)	PUNCT
ejpam-4028	229	8	then	then	ADV
ejpam-4028	229	9	,	,	PUNCT
ejpam-4028	229	10	we	we	PRON
ejpam-4028	229	11	have	have	VERB
ejpam-4028	229	12	¯̄ag̃(gen+1	¯̄ag̃(gen+1	NOUN
ejpam-4028	229	13	,	,	PUNCT
ejpam-4028	229	14	gen+2	gen+2	NOUN
ejpam-4028	229	15	,	,	PUNCT
ejpam-4028	229	16	gen+2	gen+2	NOUN
ejpam-4028	229	17	)	)	PUNCT
ejpam-4028	230	1	+	+	CCONJ
ejpam-4028	230	2	¯̄bg̃(gen	¯̄bg̃(gen	NOUN
ejpam-4028	230	3	,	,	PUNCT
ejpam-4028	230	4	gen+1	gen+1	NOUN
ejpam-4028	230	5	,	,	PUNCT
ejpam-4028	230	6	gen+1)≤̃¯̄cg̃(gen	gen+1)≤̃¯̄cg̃(gen	PROPN
ejpam-4028	230	7	,	,	PUNCT
ejpam-4028	230	8	gen+1	gen+1	NOUN
ejpam-4028	230	9	,	,	PUNCT
ejpam-4028	230	10	gen+1	gen+1	NOUN
ejpam-4028	230	11	)	)	PUNCT
ejpam-4028	230	12	⇒	⇒	NOUN
ejpam-4028	230	13	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	230	14	,	,	PUNCT
ejpam-4028	230	15	gen+2	gen+2	NOUN
ejpam-4028	230	16	,	,	PUNCT
ejpam-4028	230	17	gen+2)≤̃	gen+2)≤̃	PROPN
ejpam-4028	230	18	¯̄c−¯̄b	¯̄c−¯̄b	X
ejpam-4028	230	19	¯̄a	¯̄a	PROPN
ejpam-4028	230	20	g̃(gen	g̃(gen	PROPN
ejpam-4028	230	21	,	,	PUNCT
ejpam-4028	230	22	gen+1	gen+1	NOUN
ejpam-4028	230	23	,	,	PUNCT
ejpam-4028	230	24	gen+1	gen+1	NOUN
ejpam-4028	230	25	)	)	PUNCT
ejpam-4028	230	26	from	from	ADP
ejpam-4028	230	27	cases	case	NOUN
ejpam-4028	230	28	(	(	PUNCT
ejpam-4028	230	29	1	1	NUM
ejpam-4028	230	30	)	)	PUNCT
ejpam-4028	230	31	,	,	PUNCT
ejpam-4028	230	32	(	(	PUNCT
ejpam-4028	230	33	2	2	NUM
ejpam-4028	230	34	)	)	PUNCT
ejpam-4028	230	35	,	,	PUNCT
ejpam-4028	230	36	(	(	PUNCT
ejpam-4028	230	37	3	3	X
ejpam-4028	230	38	)	)	PUNCT
ejpam-4028	230	39	and	and	CCONJ
ejpam-4028	230	40	(	(	PUNCT
ejpam-4028	230	41	4	4	NUM
ejpam-4028	230	42	)	)	PUNCT
ejpam-4028	230	43	,	,	PUNCT
ejpam-4028	230	44	we	we	PRON
ejpam-4028	230	45	have	have	VERB
ejpam-4028	230	46	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	230	47	,	,	PUNCT
ejpam-4028	230	48	gen+2	gen+2	NOUN
ejpam-4028	230	49	,	,	PUNCT
ejpam-4028	230	50	gen+2)≤̃¯̄kg̃(gen	gen+2)≤̃¯̄kg̃(gen	NOUN
ejpam-4028	230	51	,	,	PUNCT
ejpam-4028	230	52	gen+1	gen+1	NOUN
ejpam-4028	230	53	,	,	PUNCT
ejpam-4028	230	54	gen+1	gen+1	NOUN
ejpam-4028	230	55	)	)	PUNCT
ejpam-4028	230	56	on	on	ADP
ejpam-4028	230	57	continuing	continue	VERB
ejpam-4028	230	58	this	this	DET
ejpam-4028	230	59	process	process	NOUN
ejpam-4028	230	60	(	(	PUNCT
ejpam-4028	230	61	n+	n+	NOUN
ejpam-4028	230	62	1	1	NUM
ejpam-4028	230	63	)	)	PUNCT
ejpam-4028	230	64	times	time	NOUN
ejpam-4028	230	65	,	,	PUNCT
ejpam-4028	230	66	we	we	PRON
ejpam-4028	230	67	have	have	VERB
ejpam-4028	230	68	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	230	69	,	,	PUNCT
ejpam-4028	230	70	gen+2	gen+2	NOUN
ejpam-4028	230	71	,	,	PUNCT
ejpam-4028	230	72	gen+2)≤̃¯̄kn+1g̃(ge0	gen+2)≤̃¯̄kn+1g̃(ge0	NOUN
ejpam-4028	230	73	,	,	PUNCT
ejpam-4028	230	74	ge1	ge1	NOUN
ejpam-4028	230	75	,	,	PUNCT
ejpam-4028	230	76	ge1	ge1	NOUN
ejpam-4028	230	77	)	)	PUNCT
ejpam-4028	230	78	similarly	similarly	ADV
ejpam-4028	230	79	,	,	PUNCT
ejpam-4028	230	80	we	we	PRON
ejpam-4028	230	81	will	will	AUX
ejpam-4028	230	82	conclude	conclude	VERB
ejpam-4028	230	83	that	that	SCONJ
ejpam-4028	230	84	g̃(gen	g̃(gen	PROPN
ejpam-4028	230	85	,	,	PUNCT
ejpam-4028	230	86	gen+1	gen+1	NOUN
ejpam-4028	230	87	,	,	PUNCT
ejpam-4028	230	88	gen+1)≤̃¯̄kng̃(ge0	gen+1)≤̃¯̄kng̃(ge0	NOUN
ejpam-4028	230	89	,	,	PUNCT
ejpam-4028	230	90	ge1	ge1	NOUN
ejpam-4028	230	91	,	,	PUNCT
ejpam-4028	230	92	ge1	ge1	PROPN
ejpam-4028	230	93	)	)	PUNCT
ejpam-4028	230	94	next	next	ADV
ejpam-4028	230	95	,	,	PUNCT
ejpam-4028	230	96	we	we	PRON
ejpam-4028	230	97	show	show	VERB
ejpam-4028	230	98	that	that	SCONJ
ejpam-4028	230	99	{	{	PUNCT
ejpam-4028	230	100	gen}n∈n	gen}n∈n	NOUN
ejpam-4028	230	101	is	be	AUX
ejpam-4028	230	102	a	a	DET
ejpam-4028	230	103	fuzzy	fuzzy	ADJ
ejpam-4028	230	104	soft	soft	ADJ
ejpam-4028	230	105	g	g	NOUN
ejpam-4028	230	106	-	-	PUNCT
ejpam-4028	230	107	cauchy	cauchy	ADJ
ejpam-4028	230	108	sequence	sequence	NOUN
ejpam-4028	230	109	.	.	PUNCT
ejpam-4028	231	1	then	then	ADV
ejpam-4028	231	2	for	for	ADP
ejpam-4028	231	3	all	all	DET
ejpam-4028	231	4	n	n	CCONJ
ejpam-4028	231	5	,	,	PUNCT
ejpam-4028	231	6	m	m	VERB
ejpam-4028	231	7	∈	∈	PROPN
ejpam-4028	231	8	n	n	CCONJ
ejpam-4028	231	9	,	,	PUNCT
ejpam-4028	231	10	n	n	CCONJ
ejpam-4028	231	11	<	<	X
ejpam-4028	231	12	m	m	PROPN
ejpam-4028	231	13	,	,	PUNCT
ejpam-4028	231	14	we	we	PRON
ejpam-4028	231	15	have	have	VERB
ejpam-4028	231	16	¯̄ag̃(gen	¯̄ag̃(gen	ADV
ejpam-4028	231	17	,	,	PUNCT
ejpam-4028	231	18	gem	gem	NOUN
ejpam-4028	231	19	,	,	PUNCT
ejpam-4028	231	20	gem)≤̃g̃(gen	gem)≤̃g̃(gen	NOUN
ejpam-4028	231	21	,	,	PUNCT
ejpam-4028	231	22	gen+1	gen+1	NOUN
ejpam-4028	231	23	,	,	PUNCT
ejpam-4028	231	24	gen+1	gen+1	NOUN
ejpam-4028	231	25	)	)	PUNCT
ejpam-4028	232	1	+	+	CCONJ
ejpam-4028	233	1	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	233	2	,	,	PUNCT
ejpam-4028	233	3	gen+2	gen+2	NOUN
ejpam-4028	233	4	,	,	PUNCT
ejpam-4028	233	5	gen+2	gen+2	NOUN
ejpam-4028	233	6	)	)	PUNCT
ejpam-4028	234	1	+	+	CCONJ
ejpam-4028	234	2	...	...	PUNCT
ejpam-4028	235	1	+	+	CCONJ
ejpam-4028	235	2	g̃(gem−1	g̃(gem−1	NOUN
ejpam-4028	235	3	,	,	PUNCT
ejpam-4028	235	4	gem	gem	NOUN
ejpam-4028	235	5	,	,	PUNCT
ejpam-4028	235	6	gem	gem	NOUN
ejpam-4028	235	7	)	)	PUNCT
ejpam-4028	235	8	≤̃(¯̄kn	≤̃(¯̄kn	PROPN
ejpam-4028	235	9	+	+	CCONJ
ejpam-4028	235	10	¯̄k(n+1	¯̄k(n+1	PROPN
ejpam-4028	235	11	)	)	PUNCT
ejpam-4028	236	1	+	+	CCONJ
ejpam-4028	236	2	...	...	PUNCT
ejpam-4028	237	1	+	+	CCONJ
ejpam-4028	237	2	¯̄k(m−1))g̃(ge0	¯̄k(m−1))g̃(ge0	NOUN
ejpam-4028	237	3	,	,	PUNCT
ejpam-4028	237	4	ge1	ge1	NOUN
ejpam-4028	237	5	,	,	PUNCT
ejpam-4028	237	6	ge1	ge1	NOUN
ejpam-4028	237	7	)	)	PUNCT
ejpam-4028	237	8	≤̃	≤̃	PROPN
ejpam-4028	237	9	¯̄kn	¯̄kn	PROPN
ejpam-4028	237	10	1̃−¯̄k	1̃−¯̄k	NUM
ejpam-4028	237	11	g̃(ge0	g̃(ge0	PROPN
ejpam-4028	237	12	,	,	PUNCT
ejpam-4028	237	13	ge1	ge1	PROPN
ejpam-4028	237	14	,	,	PUNCT
ejpam-4028	237	15	ge2	ge2	PROPN
ejpam-4028	237	16	)	)	PUNCT
ejpam-4028	237	17	.	.	PUNCT
ejpam-4028	238	1	hence	hence	ADV
ejpam-4028	238	2	,	,	PUNCT
ejpam-4028	238	3	{	{	PUNCT
ejpam-4028	238	4	gen}n∈n	gen}n∈n	PROPN
ejpam-4028	238	5	is	be	AUX
ejpam-4028	238	6	a	a	DET
ejpam-4028	238	7	fuzzy	fuzzy	ADJ
ejpam-4028	238	8	soft	soft	ADJ
ejpam-4028	238	9	g	g	NOUN
ejpam-4028	238	10	-	-	PUNCT
ejpam-4028	238	11	cauchy	cauchy	ADJ
ejpam-4028	238	12	sequence	sequence	NOUN
ejpam-4028	238	13	.	.	PUNCT
ejpam-4028	239	1	since	since	SCONJ
ejpam-4028	239	2	(	(	PUNCT
ejpam-4028	239	3	ẽ	ẽ	PROPN
ejpam-4028	239	4	,	,	PUNCT
ejpam-4028	239	5	g̃	g̃	PROPN
ejpam-4028	239	6	)	)	PUNCT
ejpam-4028	239	7	is	be	AUX
ejpam-4028	239	8	fuzzy	fuzzy	ADJ
ejpam-4028	239	9	soft	soft	ADJ
ejpam-4028	239	10	g	g	NOUN
ejpam-4028	239	11	-	-	PUNCT
ejpam-4028	239	12	complete	complete	ADJ
ejpam-4028	239	13	,	,	PUNCT
ejpam-4028	239	14	there	there	PRON
ejpam-4028	239	15	exists	exist	VERB
ejpam-4028	239	16	fe∈̃fsc(ẽ	fe∈̃fsc(ẽ	PROPN
ejpam-4028	239	17	)	)	PUNCT
ejpam-4028	239	18	such	such	ADJ
ejpam-4028	239	19	that	that	SCONJ
ejpam-4028	239	20	{	{	PUNCT
ejpam-4028	239	21	gen}n∈n	gen}n∈n	PROPN
ejpam-4028	239	22	fuzzy	fuzzy	ADJ
ejpam-4028	239	23	soft	soft	ADJ
ejpam-4028	239	24	g	g	NOUN
ejpam-4028	239	25	-	-	PUNCT
ejpam-4028	239	26	converges	converge	NOUN
ejpam-4028	239	27	to	to	ADP
ejpam-4028	239	28	fe	fe	PROPN
ejpam-4028	239	29	.	.	PUNCT
ejpam-4028	240	1	next	next	ADV
ejpam-4028	240	2	,	,	PUNCT
ejpam-4028	240	3	we	we	PRON
ejpam-4028	240	4	will	will	AUX
ejpam-4028	240	5	show	show	VERB
ejpam-4028	240	6	that	that	SCONJ
ejpam-4028	240	7	fe	fe	PROPN
ejpam-4028	240	8	is	be	AUX
ejpam-4028	240	9	a	a	DET
ejpam-4028	240	10	fixed	fix	VERB
ejpam-4028	240	11	point	point	NOUN
ejpam-4028	240	12	of	of	ADP
ejpam-4028	240	13	t	t	PROPN
ejpam-4028	240	14	.	.	PUNCT
ejpam-4028	241	1	for	for	ADP
ejpam-4028	241	2	this	this	PRON
ejpam-4028	241	3	,	,	PUNCT
ejpam-4028	241	4	we	we	PRON
ejpam-4028	241	5	take	take	VERB
ejpam-4028	241	6	fe1	fe1	PROPN
ejpam-4028	241	7	=	=	SYM
ejpam-4028	241	8	gen	gen	PROPN
ejpam-4028	241	9	and	and	CCONJ
ejpam-4028	241	10	fe2	fe2	PROPN
ejpam-4028	241	11	=	=	SYM
ejpam-4028	241	12	fe3	fe3	PROPN
ejpam-4028	241	13	=	=	SYM
ejpam-4028	241	14	fe	fe	PROPN
ejpam-4028	241	15	in	in	ADP
ejpam-4028	241	16	the	the	DET
ejpam-4028	241	17	inequality	inequality	NOUN
ejpam-4028	241	18	(	(	PUNCT
ejpam-4028	241	19	4	4	NUM
ejpam-4028	241	20	)	)	PUNCT
ejpam-4028	241	21	,	,	PUNCT
ejpam-4028	241	22	then	then	ADV
ejpam-4028	241	23	from	from	ADP
ejpam-4028	241	24	the	the	DET
ejpam-4028	241	25	inequality	inequality	NOUN
ejpam-4028	241	26	(	(	PUNCT
ejpam-4028	241	27	5	5	NUM
ejpam-4028	241	28	)	)	PUNCT
ejpam-4028	241	29	,	,	PUNCT
ejpam-4028	241	30	we	we	PRON
ejpam-4028	241	31	have	have	VERB
ejpam-4028	241	32	¯̄ag̃(tgen	¯̄ag̃(tgen	PROPN
ejpam-4028	241	33	,	,	PUNCT
ejpam-4028	241	34	t	t	PROPN
ejpam-4028	241	35	fe	fe	PROPN
ejpam-4028	241	36	,	,	PUNCT
ejpam-4028	241	37	t	t	PROPN
ejpam-4028	241	38	fe)+	fe)+	PROPN
ejpam-4028	241	39	¯̄b	¯̄b	PROPN
ejpam-4028	241	40			PROPN
ejpam-4028	241	41	min	min	NOUN
ejpam-4028	241	42			PROPN
ejpam-4028	241	43	g̃(tgen	g̃(tgen	PROPN
ejpam-4028	241	44	,	,	PUNCT
ejpam-4028	241	45	t	t	PROPN
ejpam-4028	241	46	fe	fe	PROPN
ejpam-4028	241	47	,	,	PUNCT
ejpam-4028	241	48	t	t	PROPN
ejpam-4028	241	49	fe	fe	X
ejpam-4028	241	50	)	)	PUNCT
ejpam-4028	241	51	·	·	PUNCT
ejpam-4028	242	1	g̃(gen	g̃(gen	PROPN
ejpam-4028	242	2	,	,	PUNCT
ejpam-4028	242	3	t	t	PROPN
ejpam-4028	242	4	gen	gen	PROPN
ejpam-4028	242	5	,	,	PUNCT
ejpam-4028	242	6	t	t	PROPN
ejpam-4028	242	7	gen	gen	PROPN
ejpam-4028	242	8	)	)	PUNCT
ejpam-4028	242	9	,	,	PUNCT
ejpam-4028	242	10	g̃(gen	g̃(gen	PROPN
ejpam-4028	242	11	,	,	PUNCT
ejpam-4028	242	12	fe	fe	PROPN
ejpam-4028	242	13	,	,	PUNCT
ejpam-4028	242	14	fe	fe	X
ejpam-4028	242	15	)	)	PUNCT
ejpam-4028	242	16	·	·	PUNCT
ejpam-4028	242	17	g̃(fe	g̃(fe	NOUN
ejpam-4028	242	18	,	,	PUNCT
ejpam-4028	242	19	t	t	PROPN
ejpam-4028	242	20	fe	fe	PROPN
ejpam-4028	242	21	,	,	PUNCT
ejpam-4028	242	22	t	t	PROPN
ejpam-4028	242	23	fe	fe	X
ejpam-4028	242	24	)	)	PUNCT
ejpam-4028	242	25			NOUN
ejpam-4028	242	26	min	min	NOUN
ejpam-4028	242	27			PROPN
ejpam-4028	242	28	g̃(tgen	g̃(tgen	PROPN
ejpam-4028	242	29	,	,	PUNCT
ejpam-4028	242	30	tfe	tfe	NOUN
ejpam-4028	242	31	,	,	PUNCT
ejpam-4028	242	32	tfe	tfe	NOUN
ejpam-4028	242	33	)	)	PUNCT
ejpam-4028	242	34	,	,	PUNCT
ejpam-4028	242	35	g̃(gen	g̃(gen	PROPN
ejpam-4028	242	36	,	,	PUNCT
ejpam-4028	242	37	t	t	PROPN
ejpam-4028	242	38	gen	gen	PROPN
ejpam-4028	242	39	,	,	PUNCT
ejpam-4028	242	40	t	t	PROPN
ejpam-4028	242	41	gen	gen	PROPN
ejpam-4028	242	42	)	)	PUNCT
ejpam-4028	242	43	,	,	PUNCT
ejpam-4028	242	44	g̃(gen	g̃(gen	PROPN
ejpam-4028	242	45	,	,	PUNCT
ejpam-4028	242	46	fe	fe	PROPN
ejpam-4028	242	47	,	,	PUNCT
ejpam-4028	242	48	fe	fe	NOUN
ejpam-4028	242	49	)	)	PUNCT
ejpam-4028	242	50	,	,	PUNCT
ejpam-4028	242	51	g̃(fe	g̃(fe	NOUN
ejpam-4028	242	52	,	,	PUNCT
ejpam-4028	242	53	t	t	PROPN
ejpam-4028	242	54	fe	fe	PROPN
ejpam-4028	242	55	,	,	PUNCT
ejpam-4028	242	56	t	t	PROPN
ejpam-4028	242	57	fe	fe	X
ejpam-4028	242	58	)	)	PUNCT
ejpam-4028	242	59			PROPN
ejpam-4028	242	60			VERB
ejpam-4028	242	61	≤̃¯̄cg̃(gen	≤̃¯̄cg̃(gen	NOUN
ejpam-4028	242	62	,	,	PUNCT
ejpam-4028	242	63	fe	fe	X
ejpam-4028	242	64	,	,	PUNCT
ejpam-4028	242	65	fe	fe	NOUN
ejpam-4028	242	66	)	)	PUNCT
ejpam-4028	242	67	as	as	ADP
ejpam-4028	242	68	n→∞	n→∞	NUM
ejpam-4028	242	69	,	,	PUNCT
ejpam-4028	242	70	we	we	PRON
ejpam-4028	242	71	have	have	VERB
ejpam-4028	242	72	¯̄ag̃(fe	¯̄ag̃(fe	NOUN
ejpam-4028	242	73	,	,	PUNCT
ejpam-4028	242	74	tfe	tfe	NOUN
ejpam-4028	242	75	,	,	PUNCT
ejpam-4028	242	76	tfe	tfe	NOUN
ejpam-4028	242	77	)	)	PUNCT
ejpam-4028	243	1	+	+	CCONJ
ejpam-4028	243	2	¯̄b	¯̄b	NOUN
ejpam-4028	243	3			NOUN
ejpam-4028	243	4	min	min	NOUN
ejpam-4028	243	5			PUNCT
ejpam-4028	243	6	g̃(fe	g̃(fe	NOUN
ejpam-4028	243	7	,	,	PUNCT
ejpam-4028	243	8	tfe	tfe	NOUN
ejpam-4028	243	9	,	,	PUNCT
ejpam-4028	243	10	tfe	tfe	NOUN
ejpam-4028	243	11	)	)	PUNCT
ejpam-4028	243	12	·	·	PUNCT
ejpam-4028	243	13	g̃(fe	g̃(fe	NOUN
ejpam-4028	243	14	,	,	PUNCT
ejpam-4028	243	15	fe	fe	X
ejpam-4028	243	16	,	,	PUNCT
ejpam-4028	243	17	fe	fe	NOUN
ejpam-4028	243	18	)	)	PUNCT
ejpam-4028	243	19	,	,	PUNCT
ejpam-4028	243	20	g̃(fe	g̃(fe	NOUN
ejpam-4028	243	21	,	,	PUNCT
ejpam-4028	243	22	fe	fe	X
ejpam-4028	243	23	,	,	PUNCT
ejpam-4028	243	24	fe	fe	X
ejpam-4028	243	25	)	)	PUNCT
ejpam-4028	243	26	·	·	PUNCT
ejpam-4028	243	27	g̃(fe	g̃(fe	NOUN
ejpam-4028	243	28	,	,	PUNCT
ejpam-4028	243	29	tfe	tfe	NOUN
ejpam-4028	243	30	,	,	PUNCT
ejpam-4028	243	31	tfe	tfe	NOUN
ejpam-4028	243	32	)	)	PUNCT
ejpam-4028	244	1			ADP
ejpam-4028	244	2	min	min	NOUN
ejpam-4028	244	3			PUNCT
ejpam-4028	244	4	g̃(fe	g̃(fe	PROPN
ejpam-4028	244	5	,	,	PUNCT
ejpam-4028	244	6	t	t	PROPN
ejpam-4028	244	7	fe	fe	PROPN
ejpam-4028	244	8	,	,	PUNCT
ejpam-4028	244	9	t	t	PROPN
ejpam-4028	244	10	fe	fe	PROPN
ejpam-4028	244	11	)	)	PUNCT
ejpam-4028	244	12	,	,	PUNCT
ejpam-4028	244	13	g̃(fe	g̃(fe	NOUN
ejpam-4028	244	14	,	,	PUNCT
ejpam-4028	244	15	t	t	PROPN
ejpam-4028	244	16	fe	fe	PROPN
ejpam-4028	244	17	,	,	PUNCT
ejpam-4028	244	18	t	t	PROPN
ejpam-4028	244	19	fe	fe	PROPN
ejpam-4028	244	20	)	)	PUNCT
ejpam-4028	244	21	,	,	PUNCT
ejpam-4028	244	22	g̃(fe	g̃(fe	NOUN
ejpam-4028	244	23	,	,	PUNCT
ejpam-4028	244	24	fe	fe	X
ejpam-4028	244	25	,	,	PUNCT
ejpam-4028	244	26	fe	fe	NOUN
ejpam-4028	244	27	)	)	PUNCT
ejpam-4028	244	28	,	,	PUNCT
ejpam-4028	244	29	g̃(fe	g̃(fe	NOUN
ejpam-4028	244	30	,	,	PUNCT
ejpam-4028	244	31	tfe	tfe	PROPN
ejpam-4028	244	32	,	,	PUNCT
ejpam-4028	244	33	t	t	PROPN
ejpam-4028	244	34	fe	fe	X
ejpam-4028	244	35	)	)	PUNCT
ejpam-4028	244	36			NOUN
ejpam-4028	244	37			VERB
ejpam-4028	244	38	≤̃¯̄cg̃(fe	≤̃¯̄cg̃(fe	NOUN
ejpam-4028	244	39	,	,	PUNCT
ejpam-4028	244	40	fe	fe	X
ejpam-4028	244	41	,	,	PUNCT
ejpam-4028	244	42	fe	fe	NOUN
ejpam-4028	244	43	)	)	PUNCT
ejpam-4028	244	44	⇒	⇒	PROPN
ejpam-4028	244	45	¯̄ag̃(fe	¯̄ag̃(fe	PROPN
ejpam-4028	244	46	,	,	PUNCT
ejpam-4028	244	47	t	t	PROPN
ejpam-4028	244	48	fe	fe	PROPN
ejpam-4028	244	49	,	,	PUNCT
ejpam-4028	244	50	t	t	PROPN
ejpam-4028	244	51	fe)≤̃0̃	fe)≤̃0̃	PROPN
ejpam-4028	244	52	,	,	PUNCT
ejpam-4028	244	53	since	since	SCONJ
ejpam-4028	244	54	0̃≤̃¯̄a<̃1̃.	0̃≤̃¯̄a<̃1̃.	NOUN
ejpam-4028	244	55	this	this	PRON
ejpam-4028	244	56	is	be	AUX
ejpam-4028	244	57	a	a	DET
ejpam-4028	244	58	contradiction	contradiction	NOUN
ejpam-4028	244	59	,	,	PUNCT
ejpam-4028	244	60	so	so	ADV
ejpam-4028	244	61	tfe	tfe	NOUN
ejpam-4028	244	62	=	=	SYM
ejpam-4028	244	63	fe	fe	X
ejpam-4028	244	64	i.e.	i.e.	X
ejpam-4028	244	65	fe	fe	X
ejpam-4028	244	66	is	be	AUX
ejpam-4028	244	67	a	a	DET
ejpam-4028	244	68	fixed	fix	VERB
ejpam-4028	244	69	point	point	NOUN
ejpam-4028	244	70	of	of	ADP
ejpam-4028	244	71	t	t	PROPN
ejpam-4028	244	72	.	.	PUNCT
ejpam-4028	245	1	now	now	ADV
ejpam-4028	245	2	,	,	PUNCT
ejpam-4028	245	3	to	to	PART
ejpam-4028	245	4	prove	prove	VERB
ejpam-4028	245	5	uniqueness	uniqueness	NOUN
ejpam-4028	245	6	,	,	PUNCT
ejpam-4028	245	7	assume	assume	VERB
ejpam-4028	245	8	that	that	SCONJ
ejpam-4028	245	9	fe	fe	PROPN
ejpam-4028	245	10	and	and	CCONJ
ejpam-4028	245	11	ge	ge	PROPN
ejpam-4028	245	12	are	be	AUX
ejpam-4028	245	13	two	two	NUM
ejpam-4028	245	14	fixed	fix	VERB
ejpam-4028	245	15	points	point	NOUN
ejpam-4028	245	16	of	of	ADP
ejpam-4028	245	17	t	t	PROPN
ejpam-4028	245	18	.	.	PUNCT
ejpam-4028	246	1	then	then	ADV
ejpam-4028	246	2	by	by	ADP
ejpam-4028	246	3	inequality	inequality	NOUN
ejpam-4028	246	4	(	(	PUNCT
ejpam-4028	246	5	5	5	NUM
ejpam-4028	246	6	)	)	PUNCT
ejpam-4028	246	7	,	,	PUNCT
ejpam-4028	246	8	we	we	PRON
ejpam-4028	246	9	have	have	VERB
ejpam-4028	246	10	a.	a.	PROPN
ejpam-4028	246	11	f.	f.	PROPN
ejpam-4028	246	12	sayed	sayed	PROPN
ejpam-4028	246	13	,	,	PUNCT
ejpam-4028	246	14	a.	a.	NOUN
ejpam-4028	246	15	alahmari	alahmari	PROPN
ejpam-4028	246	16	/	/	SYM
ejpam-4028	246	17	eur	eur	PROPN
ejpam-4028	246	18	.	.	PUNCT
ejpam-4028	247	1	j.	j.	PROPN
ejpam-4028	247	2	pure	pure	PROPN
ejpam-4028	247	3	appl	appl	PROPN
ejpam-4028	247	4	.	.	PROPN
ejpam-4028	247	5	math	math	PROPN
ejpam-4028	247	6	,	,	PUNCT
ejpam-4028	247	7	14	14	NUM
ejpam-4028	247	8	(	(	PUNCT
ejpam-4028	247	9	3	3	NUM
ejpam-4028	247	10	)	)	PUNCT
ejpam-4028	247	11	(	(	PUNCT
ejpam-4028	247	12	2021	2021	NUM
ejpam-4028	247	13	)	)	PUNCT
ejpam-4028	247	14	,	,	PUNCT
ejpam-4028	247	15	923	923	NUM
ejpam-4028	247	16	-	-	SYM
ejpam-4028	247	17	941	941	NUM
ejpam-4028	247	18	934	934	NUM
ejpam-4028	247	19	¯̄ag̃(tfe	¯̄ag̃(tfe	NOUN
ejpam-4028	247	20	,	,	PUNCT
ejpam-4028	247	21	t	t	PROPN
ejpam-4028	247	22	ge	ge	PROPN
ejpam-4028	247	23	,	,	PUNCT
ejpam-4028	247	24	t	t	PROPN
ejpam-4028	247	25	ge	ge	PROPN
ejpam-4028	247	26	)	)	PUNCT
ejpam-4028	248	1	+	+	CCONJ
ejpam-4028	248	2	¯̄b	¯̄b	NOUN
ejpam-4028	248	3			NOUN
ejpam-4028	248	4	min	min	PROPN
ejpam-4028	248	5			PROPN
ejpam-4028	248	6	g̃(tfe	g̃(tfe	PROPN
ejpam-4028	248	7	,	,	PUNCT
ejpam-4028	248	8	t	t	PROPN
ejpam-4028	248	9	ge	ge	PROPN
ejpam-4028	248	10	,	,	PUNCT
ejpam-4028	248	11	t	t	PROPN
ejpam-4028	248	12	ge	ge	PROPN
ejpam-4028	248	13	)	)	PUNCT
ejpam-4028	248	14	·	·	PUNCT
ejpam-4028	249	1	g̃(ge	g̃(ge	NOUN
ejpam-4028	249	2	,	,	PUNCT
ejpam-4028	249	3	t	t	PROPN
ejpam-4028	249	4	ge	ge	PROPN
ejpam-4028	249	5	,	,	PUNCT
ejpam-4028	249	6	t	t	PROPN
ejpam-4028	249	7	ge	ge	PROPN
ejpam-4028	249	8	)	)	PUNCT
ejpam-4028	249	9	,	,	PUNCT
ejpam-4028	249	10	g̃(fe	g̃(fe	NOUN
ejpam-4028	249	11	,	,	PUNCT
ejpam-4028	249	12	ge	ge	PROPN
ejpam-4028	249	13	,	,	PUNCT
ejpam-4028	249	14	ge	ge	PROPN
ejpam-4028	249	15	)	)	PUNCT
ejpam-4028	249	16	·	·	PUNCT
ejpam-4028	250	1	g̃(ge	g̃(ge	NOUN
ejpam-4028	250	2	,	,	PUNCT
ejpam-4028	250	3	t	t	PROPN
ejpam-4028	250	4	ge	ge	PROPN
ejpam-4028	250	5	,	,	PUNCT
ejpam-4028	250	6	t	t	PROPN
ejpam-4028	250	7	ge	ge	PROPN
ejpam-4028	250	8	)	)	PUNCT
ejpam-4028	251	1			PROPN
ejpam-4028	251	2	min	min	PROPN
ejpam-4028	251	3			PUNCT
ejpam-4028	251	4	g̃(tfe	g̃(tfe	PROPN
ejpam-4028	251	5	,	,	PUNCT
ejpam-4028	251	6	t	t	PROPN
ejpam-4028	251	7	ge	ge	PROPN
ejpam-4028	251	8	,	,	PUNCT
ejpam-4028	251	9	t	t	PROPN
ejpam-4028	251	10	ge	ge	PROPN
ejpam-4028	251	11	)	)	PUNCT
ejpam-4028	251	12	·	·	PUNCT
ejpam-4028	251	13	g̃(fe	g̃(fe	NOUN
ejpam-4028	251	14	,	,	PUNCT
ejpam-4028	251	15	t	t	PROPN
ejpam-4028	251	16	fe	fe	PROPN
ejpam-4028	251	17	,	,	PUNCT
ejpam-4028	251	18	t	t	PROPN
ejpam-4028	251	19	fe	fe	PROPN
ejpam-4028	251	20	)	)	PUNCT
ejpam-4028	251	21	,	,	PUNCT
ejpam-4028	251	22	g̃(fe	g̃(fe	NOUN
ejpam-4028	251	23	,	,	PUNCT
ejpam-4028	251	24	ge	ge	PROPN
ejpam-4028	251	25	,	,	PUNCT
ejpam-4028	251	26	ge	ge	PROPN
ejpam-4028	251	27	)	)	PUNCT
ejpam-4028	251	28	·	·	PUNCT
ejpam-4028	251	29	g̃(ge	g̃(ge	NOUN
ejpam-4028	251	30	,	,	PUNCT
ejpam-4028	251	31	t	t	PROPN
ejpam-4028	251	32	ge	ge	PROPN
ejpam-4028	251	33	,	,	PUNCT
ejpam-4028	251	34	t	t	PROPN
ejpam-4028	251	35	ge	ge	PROPN
ejpam-4028	251	36	)	)	PUNCT
ejpam-4028	252	1			ADV
ejpam-4028	252	2			VERB
ejpam-4028	252	3	≤̃¯̄cg̃(fe	≤̃¯̄cg̃(fe	NOUN
ejpam-4028	252	4	,	,	PUNCT
ejpam-4028	252	5	ge	ge	PROPN
ejpam-4028	252	6	,	,	PUNCT
ejpam-4028	252	7	ge	ge	PROPN
ejpam-4028	252	8	)	)	PUNCT
ejpam-4028	252	9	⇒	⇒	PROPN
ejpam-4028	252	10	¯̄ag̃(fe	¯̄ag̃(fe	PROPN
ejpam-4028	252	11	,	,	PUNCT
ejpam-4028	252	12	ge	ge	PROPN
ejpam-4028	252	13	,	,	PUNCT
ejpam-4028	252	14	ge	ge	PROPN
ejpam-4028	252	15	)	)	PUNCT
ejpam-4028	252	16	+	+	CCONJ
ejpam-4028	252	17	¯̄b	¯̄b	NOUN
ejpam-4028	252	18			NOUN
ejpam-4028	252	19	min	min	NOUN
ejpam-4028	252	20			PUNCT
ejpam-4028	252	21	g̃(fe	g̃(fe	PROPN
ejpam-4028	252	22	,	,	PUNCT
ejpam-4028	252	23	ge	ge	PROPN
ejpam-4028	252	24	,	,	PUNCT
ejpam-4028	252	25	ge	ge	PROPN
ejpam-4028	252	26	)	)	PUNCT
ejpam-4028	252	27	·	·	PUNCT
ejpam-4028	253	1	g̃(ge	g̃(ge	NOUN
ejpam-4028	253	2	,	,	PUNCT
ejpam-4028	253	3	ge	ge	PROPN
ejpam-4028	253	4	,	,	PUNCT
ejpam-4028	253	5	ge	ge	PROPN
ejpam-4028	253	6	)	)	PUNCT
ejpam-4028	253	7	,	,	PUNCT
ejpam-4028	253	8	g̃(fe	g̃(fe	NOUN
ejpam-4028	253	9	,	,	PUNCT
ejpam-4028	253	10	ge	ge	PROPN
ejpam-4028	253	11	,	,	PUNCT
ejpam-4028	253	12	ge	ge	PROPN
ejpam-4028	253	13	)	)	PUNCT
ejpam-4028	253	14	·	·	PUNCT
ejpam-4028	254	1	g̃(ge	g̃(ge	NOUN
ejpam-4028	254	2	,	,	PUNCT
ejpam-4028	254	3	ge	ge	PROPN
ejpam-4028	254	4	,	,	PUNCT
ejpam-4028	254	5	ge	ge	PROPN
ejpam-4028	254	6	)	)	PUNCT
ejpam-4028	255	1			ADP
ejpam-4028	255	2	min	min	NOUN
ejpam-4028	255	3			PUNCT
ejpam-4028	255	4	g̃(fe	g̃(fe	PROPN
ejpam-4028	255	5	,	,	PUNCT
ejpam-4028	255	6	ge	ge	PROPN
ejpam-4028	255	7	,	,	PUNCT
ejpam-4028	255	8	ge	ge	PROPN
ejpam-4028	255	9	)	)	PUNCT
ejpam-4028	255	10	·	·	PUNCT
ejpam-4028	255	11	g̃(fe	g̃(fe	NOUN
ejpam-4028	255	12	,	,	PUNCT
ejpam-4028	255	13	fe	fe	X
ejpam-4028	255	14	,	,	PUNCT
ejpam-4028	255	15	fe	fe	NOUN
ejpam-4028	255	16	)	)	PUNCT
ejpam-4028	255	17	,	,	PUNCT
ejpam-4028	255	18	g̃(fe	g̃(fe	NOUN
ejpam-4028	255	19	,	,	PUNCT
ejpam-4028	255	20	ge	ge	PROPN
ejpam-4028	255	21	,	,	PUNCT
ejpam-4028	255	22	ge	ge	PROPN
ejpam-4028	255	23	)	)	PUNCT
ejpam-4028	255	24	·	·	PUNCT
ejpam-4028	255	25	g̃(ge	g̃(ge	NOUN
ejpam-4028	255	26	,	,	PUNCT
ejpam-4028	255	27	ge	ge	PROPN
ejpam-4028	255	28	,	,	PUNCT
ejpam-4028	255	29	ge	ge	PROPN
ejpam-4028	255	30	)	)	PUNCT
ejpam-4028	256	1			ADP
ejpam-4028	256	2			VERB
ejpam-4028	256	3	≤̃¯̄cg̃(fe	≤̃¯̄cg̃(fe	NOUN
ejpam-4028	256	4	,	,	PUNCT
ejpam-4028	256	5	ge	ge	PROPN
ejpam-4028	256	6	,	,	PUNCT
ejpam-4028	256	7	ge	ge	PROPN
ejpam-4028	256	8	)	)	PUNCT
ejpam-4028	256	9	⇒	⇒	PROPN
ejpam-4028	256	10	g̃(fe	g̃(fe	NOUN
ejpam-4028	256	11	,	,	PUNCT
ejpam-4028	256	12	ge	ge	PROPN
ejpam-4028	256	13	,	,	PUNCT
ejpam-4028	256	14	ge)≤̃	ge)≤̃	PROPN
ejpam-4028	256	15	¯̄c	¯̄c	PROPN
ejpam-4028	256	16	¯̄ag̃(fe	¯̄ag̃(fe	NOUN
ejpam-4028	256	17	,	,	PUNCT
ejpam-4028	256	18	ge	ge	PROPN
ejpam-4028	256	19	,	,	PUNCT
ejpam-4028	256	20	ge	ge	PROPN
ejpam-4028	256	21	)	)	PUNCT
ejpam-4028	256	22	,	,	PUNCT
ejpam-4028	256	23	since	since	SCONJ
ejpam-4028	256	24	0̃≤̃	0̃≤̃	VERB
ejpam-4028	256	25	¯̄c	¯̄c	PROPN
ejpam-4028	256	26	¯̄a<̃1̃.	¯̄a<̃1̃.	NOUN
ejpam-4028	256	27	this	this	PRON
ejpam-4028	256	28	is	be	AUX
ejpam-4028	256	29	a	a	DET
ejpam-4028	256	30	contradiction	contradiction	NOUN
ejpam-4028	256	31	,	,	PUNCT
ejpam-4028	256	32	implies	imply	VERB
ejpam-4028	256	33	that	that	DET
ejpam-4028	256	34	fe	fe	X
ejpam-4028	256	35	=	=	PROPN
ejpam-4028	256	36	ge	ge	PROPN
ejpam-4028	256	37	.	.	PUNCT
ejpam-4028	257	1	to	to	PART
ejpam-4028	257	2	show	show	VERB
ejpam-4028	257	3	that	that	SCONJ
ejpam-4028	257	4	t	t	PROPN
ejpam-4028	257	5	is	be	AUX
ejpam-4028	257	6	fuzzy	fuzzy	ADJ
ejpam-4028	257	7	soft	soft	ADJ
ejpam-4028	257	8	g	g	NOUN
ejpam-4028	257	9	-	-	NOUN
ejpam-4028	257	10	continuous	continuous	ADJ
ejpam-4028	257	11	at	at	ADP
ejpam-4028	257	12	fe	fe	NOUN
ejpam-4028	257	13	.	.	PUNCT
ejpam-4028	257	14	let	let	AUX
ejpam-4028	257	15	{	{	PUNCT
ejpam-4028	257	16	hen}n∈n	hen}n∈n	PRON
ejpam-4028	257	17	be	be	AUX
ejpam-4028	257	18	a	a	DET
ejpam-4028	257	19	sequence	sequence	NOUN
ejpam-4028	257	20	of	of	ADP
ejpam-4028	257	21	fuzzy	fuzzy	ADJ
ejpam-4028	257	22	soft	soft	ADJ
ejpam-4028	257	23	elements	element	NOUN
ejpam-4028	257	24	in	in	ADP
ejpam-4028	257	25	ẽ	ẽ	PROPN
ejpam-4028	257	26	such	such	ADJ
ejpam-4028	257	27	that	that	SCONJ
ejpam-4028	257	28	{	{	PUNCT
ejpam-4028	257	29	hen}n∈n	hen}n∈n	PROPN
ejpam-4028	257	30	→	→	SYM
ejpam-4028	257	31	fe	fe	PROPN
ejpam-4028	257	32	,	,	PUNCT
ejpam-4028	257	33	then	then	ADV
ejpam-4028	257	34	we	we	PRON
ejpam-4028	257	35	can	can	AUX
ejpam-4028	257	36	deduce	deduce	VERB
ejpam-4028	257	37	that	that	SCONJ
ejpam-4028	257	38	using	use	VERB
ejpam-4028	257	39	inequality	inequality	NOUN
ejpam-4028	257	40	(	(	PUNCT
ejpam-4028	257	41	5	5	NUM
ejpam-4028	257	42	)	)	PUNCT
ejpam-4028	257	43	,	,	PUNCT
ejpam-4028	257	44	we	we	PRON
ejpam-4028	257	45	have	have	VERB
ejpam-4028	257	46	¯̄ag̃(tfe	¯̄ag̃(tfe	NOUN
ejpam-4028	257	47	,	,	PUNCT
ejpam-4028	257	48	then	then	ADV
ejpam-4028	257	49	,	,	PUNCT
ejpam-4028	257	50	then	then	ADV
ejpam-4028	257	51	)	)	PUNCT
ejpam-4028	258	1	+	+	CCONJ
ejpam-4028	258	2	¯̄b	¯̄b	NOUN
ejpam-4028	258	3			NOUN
ejpam-4028	258	4	min	min	PROPN
ejpam-4028	258	5			PROPN
ejpam-4028	258	6	g̃(tfe	g̃(tfe	PROPN
ejpam-4028	258	7	,	,	PUNCT
ejpam-4028	258	8	then	then	ADV
ejpam-4028	258	9	,	,	PUNCT
ejpam-4028	258	10	then	then	ADV
ejpam-4028	258	11	)	)	PUNCT
ejpam-4028	258	12	·	·	PUNCT
ejpam-4028	259	1	g̃(fe	g̃(fe	NOUN
ejpam-4028	259	2	,	,	PUNCT
ejpam-4028	259	3	tfe	tfe	NOUN
ejpam-4028	259	4	,	,	PUNCT
ejpam-4028	259	5	t	t	PROPN
ejpam-4028	259	6	fe	fe	PROPN
ejpam-4028	259	7	)	)	PUNCT
ejpam-4028	259	8	,	,	PUNCT
ejpam-4028	259	9	g̃(fe	g̃(fe	NOUN
ejpam-4028	259	10	,	,	PUNCT
ejpam-4028	259	11	hen	hen	NOUN
ejpam-4028	259	12	,	,	PUNCT
ejpam-4028	259	13	hen	hen	NOUN
ejpam-4028	259	14	)	)	PUNCT
ejpam-4028	259	15	·	·	PUNCT
ejpam-4028	260	1	g̃(fe	g̃(fe	NOUN
ejpam-4028	260	2	,	,	PUNCT
ejpam-4028	260	3	t	t	PROPN
ejpam-4028	260	4	fe	fe	PROPN
ejpam-4028	260	5	,	,	PUNCT
ejpam-4028	260	6	t	t	PROPN
ejpam-4028	260	7	fe	fe	X
ejpam-4028	260	8	)	)	PUNCT
ejpam-4028	260	9			PROPN
ejpam-4028	260	10	min	min	PROPN
ejpam-4028	260	11			PUNCT
ejpam-4028	260	12	g̃(tfe	g̃(tfe	PROPN
ejpam-4028	260	13	,	,	PUNCT
ejpam-4028	260	14	then	then	ADV
ejpam-4028	260	15	,	,	PUNCT
ejpam-4028	260	16	then	then	ADV
ejpam-4028	260	17	)	)	PUNCT
ejpam-4028	260	18	·	·	PUNCT
ejpam-4028	261	1	g̃(fe	g̃(fe	NOUN
ejpam-4028	261	2	,	,	PUNCT
ejpam-4028	261	3	t	t	PROPN
ejpam-4028	261	4	fe	fe	PROPN
ejpam-4028	261	5	,	,	PUNCT
ejpam-4028	261	6	t	t	PROPN
ejpam-4028	261	7	fe	fe	PROPN
ejpam-4028	261	8	)	)	PUNCT
ejpam-4028	261	9	,	,	PUNCT
ejpam-4028	261	10	g̃(fe	g̃(fe	NOUN
ejpam-4028	261	11	,	,	PUNCT
ejpam-4028	261	12	hen	hen	NOUN
ejpam-4028	261	13	,	,	PUNCT
ejpam-4028	261	14	hen	hen	NOUN
ejpam-4028	261	15	)	)	PUNCT
ejpam-4028	261	16	·	·	PUNCT
ejpam-4028	261	17	g̃(fe	g̃(fe	NOUN
ejpam-4028	261	18	,	,	PUNCT
ejpam-4028	261	19	tfe	tfe	NOUN
ejpam-4028	261	20	,	,	PUNCT
ejpam-4028	261	21	tfe	tfe	NOUN
ejpam-4028	261	22	)	)	PUNCT
ejpam-4028	261	23			NOUN
ejpam-4028	261	24			VERB
ejpam-4028	261	25	≤̃	≤̃	PROPN
ejpam-4028	261	26	¯̄cg̃(fe	¯̄cg̃(fe	PROPN
ejpam-4028	261	27	,	,	PUNCT
ejpam-4028	261	28	hen	hen	NOUN
ejpam-4028	261	29	,	,	PUNCT
ejpam-4028	261	30	hen	hen	NOUN
ejpam-4028	261	31	)	)	PUNCT
ejpam-4028	261	32	⇒	⇒	NOUN
ejpam-4028	261	33	¯̄ag̃(fe	¯̄ag̃(fe	NOUN
ejpam-4028	261	34	,	,	PUNCT
ejpam-4028	261	35	then	then	ADV
ejpam-4028	261	36	,	,	PUNCT
ejpam-4028	261	37	then	then	ADV
ejpam-4028	261	38	)	)	PUNCT
ejpam-4028	262	1	+	+	CCONJ
ejpam-4028	262	2	¯̄b	¯̄b	NOUN
ejpam-4028	262	3			NOUN
ejpam-4028	262	4	min	min	NOUN
ejpam-4028	262	5			NOUN
ejpam-4028	262	6	g̃(fe	g̃(fe	NOUN
ejpam-4028	262	7	,	,	PUNCT
ejpam-4028	262	8	then	then	ADV
ejpam-4028	262	9	,	,	PUNCT
ejpam-4028	262	10	then	then	ADV
ejpam-4028	262	11	)	)	PUNCT
ejpam-4028	262	12	·	·	PUNCT
ejpam-4028	262	13	g̃(fe	g̃(fe	NOUN
ejpam-4028	262	14	,	,	PUNCT
ejpam-4028	262	15	fe	fe	X
ejpam-4028	262	16	,	,	PUNCT
ejpam-4028	262	17	fe	fe	NOUN
ejpam-4028	262	18	)	)	PUNCT
ejpam-4028	262	19	,	,	PUNCT
ejpam-4028	262	20	g̃(fe	g̃(fe	NOUN
ejpam-4028	262	21	,	,	PUNCT
ejpam-4028	262	22	hen	hen	NOUN
ejpam-4028	262	23	,	,	PUNCT
ejpam-4028	262	24	hen	hen	NOUN
ejpam-4028	262	25	)	)	PUNCT
ejpam-4028	262	26	·	·	PUNCT
ejpam-4028	262	27	g̃(fe	g̃(fe	NOUN
ejpam-4028	262	28	,	,	PUNCT
ejpam-4028	262	29	fe	fe	X
ejpam-4028	262	30	,	,	PUNCT
ejpam-4028	262	31	fe	fe	NOUN
ejpam-4028	262	32	)	)	PUNCT
ejpam-4028	262	33			PROPN
ejpam-4028	262	34	min	min	NOUN
ejpam-4028	262	35			PUNCT
ejpam-4028	262	36	g̃(fe	g̃(fe	NOUN
ejpam-4028	262	37	,	,	PUNCT
ejpam-4028	262	38	then	then	ADV
ejpam-4028	262	39	,	,	PUNCT
ejpam-4028	262	40	then	then	ADV
ejpam-4028	262	41	)	)	PUNCT
ejpam-4028	262	42	·	·	PUNCT
ejpam-4028	262	43	g̃(fe	g̃(fe	NOUN
ejpam-4028	262	44	,	,	PUNCT
ejpam-4028	262	45	fe	fe	X
ejpam-4028	262	46	,	,	PUNCT
ejpam-4028	262	47	fe	fe	NOUN
ejpam-4028	262	48	)	)	PUNCT
ejpam-4028	262	49	,	,	PUNCT
ejpam-4028	262	50	g̃(fe	g̃(fe	NOUN
ejpam-4028	262	51	,	,	PUNCT
ejpam-4028	262	52	hen	hen	NOUN
ejpam-4028	262	53	,	,	PUNCT
ejpam-4028	262	54	hen	hen	NOUN
ejpam-4028	262	55	)	)	PUNCT
ejpam-4028	262	56	·	·	PUNCT
ejpam-4028	262	57	g̃(fe	g̃(fe	NOUN
ejpam-4028	262	58	,	,	PUNCT
ejpam-4028	262	59	fe	fe	X
ejpam-4028	262	60	,	,	PUNCT
ejpam-4028	262	61	fe	fe	NOUN
ejpam-4028	262	62	)	)	PUNCT
ejpam-4028	262	63			NOUN
ejpam-4028	262	64			ADJ
ejpam-4028	262	65	≤̃¯̄cg̃(fe	≤̃¯̄cg̃(fe	NOUN
ejpam-4028	262	66	,	,	PUNCT
ejpam-4028	262	67	hen	hen	NOUN
ejpam-4028	262	68	,	,	PUNCT
ejpam-4028	262	69	hen	hen	NOUN
ejpam-4028	262	70	)	)	PUNCT
ejpam-4028	262	71	taking	take	VERB
ejpam-4028	262	72	the	the	DET
ejpam-4028	262	73	limit	limit	NOUN
ejpam-4028	262	74	as	as	ADP
ejpam-4028	262	75	n→∞	n→∞	NUM
ejpam-4028	262	76	from	from	ADP
ejpam-4028	262	77	which	which	PRON
ejpam-4028	262	78	,	,	PUNCT
ejpam-4028	262	79	we	we	PRON
ejpam-4028	262	80	see	see	VERB
ejpam-4028	262	81	that	that	DET
ejpam-4028	262	82	g̃(fe	g̃(fe	NOUN
ejpam-4028	262	83	,	,	PUNCT
ejpam-4028	262	84	then	then	ADV
ejpam-4028	262	85	,	,	PUNCT
ejpam-4028	262	86	then	then	ADV
ejpam-4028	262	87	)	)	PUNCT
ejpam-4028	262	88	→	→	SYM
ejpam-4028	262	89	0̃	0̃	NOUN
ejpam-4028	262	90	and	and	CCONJ
ejpam-4028	262	91	so	so	ADV
ejpam-4028	262	92	,	,	PUNCT
ejpam-4028	262	93	by	by	ADP
ejpam-4028	262	94	proposition	proposition	NOUN
ejpam-4028	262	95	(	(	PUNCT
ejpam-4028	262	96	4.1	4.1	NUM
ejpam-4028	262	97	)	)	PUNCT
ejpam-4028	262	98	in	in	ADP
ejpam-4028	262	99	[	[	X
ejpam-4028	262	100	2	2	X
ejpam-4028	262	101	]	]	PUNCT
ejpam-4028	262	102	we	we	PRON
ejpam-4028	262	103	have	have	VERB
ejpam-4028	262	104	that	that	SCONJ
ejpam-4028	262	105	the	the	DET
ejpam-4028	262	106	sequence	sequence	NOUN
ejpam-4028	262	107	{	{	PUNCT
ejpam-4028	262	108	then}n∈n	then}n∈n	PROPN
ejpam-4028	262	109	is	be	AUX
ejpam-4028	262	110	fuzzy	fuzzy	ADJ
ejpam-4028	262	111	soft	soft	ADJ
ejpam-4028	262	112	g	g	NOUN
ejpam-4028	262	113	-	-	PUNCT
ejpam-4028	262	114	convergent	convergent	NOUN
ejpam-4028	262	115	to	to	ADP
ejpam-4028	262	116	tfe	tfe	NOUN
ejpam-4028	262	117	=	=	SYM
ejpam-4028	262	118	fe	fe	X
ejpam-4028	262	119	,	,	PUNCT
ejpam-4028	262	120	therefore	therefore	ADV
ejpam-4028	262	121	proposition	proposition	NOUN
ejpam-4028	262	122	(	(	PUNCT
ejpam-4028	262	123	4.4	4.4	NUM
ejpam-4028	262	124	)	)	PUNCT
ejpam-4028	262	125	in	in	ADP
ejpam-4028	262	126	[	[	X
ejpam-4028	262	127	2	2	NUM
ejpam-4028	262	128	]	]	PUNCT
ejpam-4028	262	129	implies	imply	VERB
ejpam-4028	262	130	that	that	SCONJ
ejpam-4028	262	131	t	t	PROPN
ejpam-4028	262	132	is	be	AUX
ejpam-4028	262	133	fuzzy	fuzzy	ADJ
ejpam-4028	262	134	soft	soft	ADJ
ejpam-4028	262	135	g	g	NOUN
ejpam-4028	262	136	-	-	NOUN
ejpam-4028	262	137	continuous	continuous	ADJ
ejpam-4028	262	138	at	at	ADP
ejpam-4028	262	139	fe	fe	PROPN
ejpam-4028	262	140	.	.	PUNCT
ejpam-4028	262	141	theorem	theorem	NOUN
ejpam-4028	262	142	5	5	NUM
ejpam-4028	262	143	.	.	PUNCT
ejpam-4028	262	144	suppose	suppose	VERB
ejpam-4028	262	145	(	(	PUNCT
ejpam-4028	262	146	ẽ	ẽ	PROPN
ejpam-4028	262	147	,	,	PUNCT
ejpam-4028	262	148	g̃	g̃	PROPN
ejpam-4028	262	149	)	)	PUNCT
ejpam-4028	262	150	is	be	AUX
ejpam-4028	262	151	a	a	DET
ejpam-4028	262	152	fuzzy	fuzzy	ADJ
ejpam-4028	262	153	soft	soft	ADJ
ejpam-4028	262	154	g	g	NOUN
ejpam-4028	262	155	-	-	PUNCT
ejpam-4028	262	156	metric	metric	ADJ
ejpam-4028	262	157	space	space	NOUN
ejpam-4028	262	158	and	and	CCONJ
ejpam-4028	262	159	t	t	NOUN
ejpam-4028	262	160	:	:	PUNCT
ejpam-4028	262	161	(	(	PUNCT
ejpam-4028	262	162	ẽ	ẽ	NOUN
ejpam-4028	262	163	,	,	PUNCT
ejpam-4028	262	164	g̃)→	g̃)→	PRON
ejpam-4028	262	165	(	(	PUNCT
ejpam-4028	262	166	ẽ	ẽ	PROPN
ejpam-4028	262	167	,	,	PUNCT
ejpam-4028	262	168	g̃	g̃	PROPN
ejpam-4028	262	169	)	)	PUNCT
ejpam-4028	262	170	is	be	AUX
ejpam-4028	262	171	a	a	DET
ejpam-4028	262	172	mapping	mapping	NOUN
ejpam-4028	262	173	satisfying	satisfy	VERB
ejpam-4028	262	174	the	the	DET
ejpam-4028	262	175	following	follow	VERB
ejpam-4028	262	176	condition	condition	NOUN
ejpam-4028	262	177	:	:	PUNCT
ejpam-4028	262	178	min	min	PROPN
ejpam-4028	262	179			PUNCT
ejpam-4028	262	180	[	[	PUNCT
ejpam-4028	262	181	g̃(fe1	g̃(fe1	PROPN
ejpam-4028	262	182	,	,	PUNCT
ejpam-4028	262	183	t	t	PROPN
ejpam-4028	262	184	fe1	fe1	PROPN
ejpam-4028	262	185	,	,	PUNCT
ejpam-4028	262	186	t	t	PROPN
ejpam-4028	262	187	fe1	fe1	PROPN
ejpam-4028	262	188	)	)	PUNCT
ejpam-4028	263	1	+	+	CCONJ
ejpam-4028	263	2	g̃(fe1	g̃(fe1	PROPN
ejpam-4028	263	3	,	,	PUNCT
ejpam-4028	263	4	t	t	PROPN
ejpam-4028	263	5	fe2	fe2	PROPN
ejpam-4028	263	6	,	,	PUNCT
ejpam-4028	263	7	t	t	PROPN
ejpam-4028	263	8	fe2	fe2	PROPN
ejpam-4028	263	9	)	)	PUNCT
ejpam-4028	263	10	]	]	PUNCT
ejpam-4028	263	11	,	,	PUNCT
ejpam-4028	263	12	g̃(tfe1	g̃(tfe1	PROPN
ejpam-4028	263	13	,	,	PUNCT
ejpam-4028	263	14	tfe2	tfe2	NOUN
ejpam-4028	263	15	,	,	PUNCT
ejpam-4028	263	16	tfe3	tfe3	PROPN
ejpam-4028	263	17	)	)	PUNCT
ejpam-4028	263	18	,	,	PUNCT
ejpam-4028	263	19	[	[	PUNCT
ejpam-4028	263	20	g̃(fe2	g̃(fe2	PROPN
ejpam-4028	263	21	,	,	PUNCT
ejpam-4028	263	22	t	t	PROPN
ejpam-4028	263	23	fe2	fe2	PROPN
ejpam-4028	263	24	,	,	PUNCT
ejpam-4028	263	25	t	t	PROPN
ejpam-4028	263	26	fe2	fe2	PROPN
ejpam-4028	263	27	)	)	PUNCT
ejpam-4028	264	1	+	+	NUM
ejpam-4028	264	2	g̃(fe2	g̃(fe2	NOUN
ejpam-4028	264	3	,	,	PUNCT
ejpam-4028	264	4	t	t	PROPN
ejpam-4028	264	5	fe1	fe1	PROPN
ejpam-4028	264	6	,	,	PUNCT
ejpam-4028	264	7	t	t	PROPN
ejpam-4028	264	8	fe1	fe1	PROPN
ejpam-4028	264	9	)	)	PUNCT
ejpam-4028	264	10	]	]	PUNCT
ejpam-4028	265	1			PROPN
ejpam-4028	265	2	≤̃¯̄ag̃(fe1	≤̃¯̄ag̃(fe1	PROPN
ejpam-4028	265	3	,	,	PUNCT
ejpam-4028	265	4	fe2	fe2	PROPN
ejpam-4028	265	5	,	,	PUNCT
ejpam-4028	265	6	fe3	fe3	PROPN
ejpam-4028	265	7	)	)	PUNCT
ejpam-4028	265	8	(	(	PUNCT
ejpam-4028	265	9	6	6	X
ejpam-4028	265	10	)	)	PUNCT
ejpam-4028	265	11	∀fe1	∀fe1	PROPN
ejpam-4028	265	12	,	,	PUNCT
ejpam-4028	265	13	fe2	fe2	PROPN
ejpam-4028	265	14	,	,	PUNCT
ejpam-4028	265	15	fe3∈̃fsc(ẽ	fe3∈̃fsc(ẽ	PROPN
ejpam-4028	265	16	)	)	PUNCT
ejpam-4028	265	17	and	and	CCONJ
ejpam-4028	265	18	0̃≤̃¯̄a<̃1̃.	0̃≤̃¯̄a<̃1̃.	NUM
ejpam-4028	265	19	then	then	ADV
ejpam-4028	265	20	t	t	PROPN
ejpam-4028	265	21	has	have	VERB
ejpam-4028	265	22	an	an	DET
ejpam-4028	265	23	unique	unique	ADJ
ejpam-4028	265	24	fixed	fix	VERB
ejpam-4028	265	25	point	point	NOUN
ejpam-4028	265	26	,	,	PUNCT
ejpam-4028	265	27	say	say	VERB
ejpam-4028	265	28	fe	fe	X
ejpam-4028	265	29	,	,	PUNCT
ejpam-4028	265	30	and	and	CCONJ
ejpam-4028	265	31	at	at	ADP
ejpam-4028	265	32	fe	fe	PROPN
ejpam-4028	265	33	,	,	PUNCT
ejpam-4028	265	34	t	t	PROPN
ejpam-4028	265	35	is	be	AUX
ejpam-4028	265	36	fuzzy	fuzzy	ADJ
ejpam-4028	265	37	soft	soft	ADJ
ejpam-4028	265	38	g	g	NOUN
ejpam-4028	265	39	-	-	PUNCT
ejpam-4028	265	40	continuous	continuous	ADJ
ejpam-4028	265	41	.	.	PUNCT
ejpam-4028	266	1	proof	proof	NOUN
ejpam-4028	266	2	.	.	PUNCT
ejpam-4028	267	1	assume	assume	VERB
ejpam-4028	267	2	that	that	SCONJ
ejpam-4028	267	3	fe0∈̃fsc(ẽ	fe0∈̃fsc(ẽ	NOUN
ejpam-4028	267	4	)	)	PUNCT
ejpam-4028	267	5	is	be	AUX
ejpam-4028	267	6	an	an	DET
ejpam-4028	267	7	arbitrary	arbitrary	ADJ
ejpam-4028	267	8	fuzzy	fuzzy	ADJ
ejpam-4028	267	9	soft	soft	ADJ
ejpam-4028	267	10	element	element	NOUN
ejpam-4028	267	11	and	and	CCONJ
ejpam-4028	267	12	define	define	VERB
ejpam-4028	267	13	the	the	DET
ejpam-4028	267	14	sequence	sequence	NOUN
ejpam-4028	267	15	{	{	PUNCT
ejpam-4028	267	16	gen}n∈n	gen}n∈n	PROPN
ejpam-4028	267	17	as	as	SCONJ
ejpam-4028	267	18	follows	follow	VERB
ejpam-4028	267	19	:	:	PUNCT
ejpam-4028	268	1	tge0	tge0	NOUN
ejpam-4028	268	2	=	=	SYM
ejpam-4028	268	3	ge1	ge1	PROPN
ejpam-4028	268	4	,	,	PUNCT
ejpam-4028	268	5	t	t	PROPN
ejpam-4028	268	6	ge1	ge1	PROPN
ejpam-4028	268	7	=	=	PUNCT
ejpam-4028	268	8	ge2	ge2	PROPN
ejpam-4028	268	9	,	,	PUNCT
ejpam-4028	268	10	t	t	PROPN
ejpam-4028	268	11	ge2	ge2	PROPN
ejpam-4028	268	12	=	=	X
ejpam-4028	268	13	ge3	ge3	PROPN
ejpam-4028	268	14	,	,	PUNCT
ejpam-4028	268	15	...	...	PUNCT
ejpam-4028	268	16	,	,	PUNCT
ejpam-4028	268	17	t	t	PROPN
ejpam-4028	268	18	gen	gen	PROPN
ejpam-4028	268	19	=	=	NOUN
ejpam-4028	268	20	gen+1	gen+1	PROPN
ejpam-4028	268	21	.	.	PUNCT
ejpam-4028	269	1	consider	consider	VERB
ejpam-4028	269	2	that	that	DET
ejpam-4028	269	3	gen	gen	PROPN
ejpam-4028	269	4	6=	6=	PROPN
ejpam-4028	269	5	gen+1	gen+1	NOUN
ejpam-4028	269	6	.	.	PUNCT
ejpam-4028	270	1	substituting	substitute	VERB
ejpam-4028	270	2	fe1	fe1	PROPN
ejpam-4028	270	3	=	=	SYM
ejpam-4028	270	4	gen	gen	PROPN
ejpam-4028	270	5	,	,	PUNCT
ejpam-4028	270	6	fe2	fe2	X
ejpam-4028	270	7	=	=	SYM
ejpam-4028	270	8	gen+1	gen+1	NOUN
ejpam-4028	270	9	and	and	CCONJ
ejpam-4028	270	10	fe3	fe3	NOUN
ejpam-4028	270	11	=	=	SYM
ejpam-4028	270	12	gen+1	gen+1	NOUN
ejpam-4028	270	13	in	in	ADP
ejpam-4028	270	14	(	(	PUNCT
ejpam-4028	270	15	6	6	NUM
ejpam-4028	270	16	)	)	PUNCT
ejpam-4028	270	17	,	,	PUNCT
ejpam-4028	270	18	we	we	PRON
ejpam-4028	270	19	obtain	obtain	VERB
ejpam-4028	270	20	a.	a.	PROPN
ejpam-4028	270	21	f.	f.	PROPN
ejpam-4028	270	22	sayed	sayed	PROPN
ejpam-4028	270	23	,	,	PUNCT
ejpam-4028	270	24	a.	a.	NOUN
ejpam-4028	270	25	alahmari	alahmari	PROPN
ejpam-4028	270	26	/	/	SYM
ejpam-4028	270	27	eur	eur	PROPN
ejpam-4028	270	28	.	.	PUNCT
ejpam-4028	271	1	j.	j.	PROPN
ejpam-4028	271	2	pure	pure	PROPN
ejpam-4028	271	3	appl	appl	PROPN
ejpam-4028	271	4	.	.	PROPN
ejpam-4028	271	5	math	math	PROPN
ejpam-4028	271	6	,	,	PUNCT
ejpam-4028	271	7	14	14	NUM
ejpam-4028	271	8	(	(	PUNCT
ejpam-4028	271	9	3	3	NUM
ejpam-4028	271	10	)	)	PUNCT
ejpam-4028	271	11	(	(	PUNCT
ejpam-4028	271	12	2021	2021	NUM
ejpam-4028	271	13	)	)	PUNCT
ejpam-4028	271	14	,	,	PUNCT
ejpam-4028	271	15	923	923	NUM
ejpam-4028	271	16	-	-	SYM
ejpam-4028	271	17	941	941	NUM
ejpam-4028	271	18	935	935	NUM
ejpam-4028	271	19	min	min	NOUN
ejpam-4028	271	20			PROPN
ejpam-4028	271	21	[	[	PUNCT
ejpam-4028	271	22	g̃(gen	g̃(gen	PROPN
ejpam-4028	271	23	,	,	PUNCT
ejpam-4028	271	24	t	t	PROPN
ejpam-4028	271	25	gen	gen	PROPN
ejpam-4028	271	26	,	,	PUNCT
ejpam-4028	271	27	t	t	PROPN
ejpam-4028	271	28	gen	gen	PROPN
ejpam-4028	271	29	)	)	PUNCT
ejpam-4028	272	1	+	+	CCONJ
ejpam-4028	272	2	g̃(gen	g̃(gen	PROPN
ejpam-4028	272	3	,	,	PUNCT
ejpam-4028	272	4	t	t	PROPN
ejpam-4028	272	5	gen+1	gen+1	PROPN
ejpam-4028	272	6	,	,	PUNCT
ejpam-4028	272	7	t	t	PROPN
ejpam-4028	272	8	gen+1	gen+1	PROPN
ejpam-4028	272	9	)	)	PUNCT
ejpam-4028	272	10	]	]	PUNCT
ejpam-4028	272	11	,	,	PUNCT
ejpam-4028	272	12	g̃(tgen	g̃(tgen	INTJ
ejpam-4028	272	13	,	,	PUNCT
ejpam-4028	272	14	t	t	PROPN
ejpam-4028	272	15	gen+1	gen+1	NOUN
ejpam-4028	272	16	,	,	PUNCT
ejpam-4028	272	17	t	t	PROPN
ejpam-4028	272	18	gen+1	gen+1	PROPN
ejpam-4028	272	19	)	)	PUNCT
ejpam-4028	272	20	,	,	PUNCT
ejpam-4028	272	21	[	[	PUNCT
ejpam-4028	272	22	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	272	23	,	,	PUNCT
ejpam-4028	272	24	t	t	PROPN
ejpam-4028	272	25	gen+1	gen+1	NOUN
ejpam-4028	272	26	,	,	PUNCT
ejpam-4028	272	27	t	t	PROPN
ejpam-4028	272	28	gen+1	gen+1	PROPN
ejpam-4028	272	29	)	)	PUNCT
ejpam-4028	273	1	+	+	CCONJ
ejpam-4028	273	2	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	273	3	,	,	PUNCT
ejpam-4028	273	4	t	t	PROPN
ejpam-4028	273	5	gen	gen	PROPN
ejpam-4028	273	6	,	,	PUNCT
ejpam-4028	273	7	t	t	PROPN
ejpam-4028	273	8	gen	gen	PROPN
ejpam-4028	273	9	)	)	PUNCT
ejpam-4028	273	10	]	]	PUNCT
ejpam-4028	274	1			PROPN
ejpam-4028	274	2	≤̃¯̄ag̃(gen	≤̃¯̄ag̃(gen	NOUN
ejpam-4028	274	3	,	,	PUNCT
ejpam-4028	274	4	gen+1	gen+1	NOUN
ejpam-4028	274	5	,	,	PUNCT
ejpam-4028	274	6	gen+1	gen+1	NOUN
ejpam-4028	274	7	)	)	PUNCT
ejpam-4028	274	8	⇒	⇒	PROPN
ejpam-4028	274	9	min	min	PROPN
ejpam-4028	274	10			PROPN
ejpam-4028	274	11	[	[	PUNCT
ejpam-4028	274	12	g̃(gen	g̃(gen	PROPN
ejpam-4028	274	13	,	,	PUNCT
ejpam-4028	274	14	gen+1	gen+1	NOUN
ejpam-4028	274	15	,	,	PUNCT
ejpam-4028	274	16	gen+1	gen+1	NOUN
ejpam-4028	274	17	)	)	PUNCT
ejpam-4028	274	18	+	+	CCONJ
ejpam-4028	274	19	g̃(gen	g̃(gen	PROPN
ejpam-4028	274	20	,	,	PUNCT
ejpam-4028	274	21	gen+2	gen+2	NOUN
ejpam-4028	274	22	,	,	PUNCT
ejpam-4028	274	23	gen+2	gen+2	NOUN
ejpam-4028	274	24	)	)	PUNCT
ejpam-4028	274	25	]	]	PUNCT
ejpam-4028	274	26	,	,	PUNCT
ejpam-4028	274	27	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	274	28	,	,	PUNCT
ejpam-4028	274	29	gen+2	gen+2	NOUN
ejpam-4028	274	30	,	,	PUNCT
ejpam-4028	274	31	gen+2	gen+2	NOUN
ejpam-4028	274	32	)	)	PUNCT
ejpam-4028	274	33	,	,	PUNCT
ejpam-4028	274	34	[	[	PUNCT
ejpam-4028	274	35	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	274	36	,	,	PUNCT
ejpam-4028	274	37	gen+2	gen+2	NOUN
ejpam-4028	274	38	,	,	PUNCT
ejpam-4028	274	39	gen+2	gen+2	NOUN
ejpam-4028	274	40	)	)	PUNCT
ejpam-4028	275	1	+	+	CCONJ
ejpam-4028	275	2	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	275	3	,	,	PUNCT
ejpam-4028	275	4	gen+1	gen+1	NOUN
ejpam-4028	275	5	,	,	PUNCT
ejpam-4028	275	6	gen+1	gen+1	NOUN
ejpam-4028	275	7	)	)	PUNCT
ejpam-4028	275	8	]	]	PUNCT
ejpam-4028	276	1			PROPN
ejpam-4028	276	2	≤̃¯̄ag̃(gen	≤̃¯̄ag̃(gen	NOUN
ejpam-4028	276	3	,	,	PUNCT
ejpam-4028	276	4	gen+1	gen+1	NOUN
ejpam-4028	276	5	,	,	PUNCT
ejpam-4028	276	6	gen+1	gen+1	NOUN
ejpam-4028	276	7	)	)	PUNCT
ejpam-4028	276	8	⇒	⇒	PROPN
ejpam-4028	276	9	min	min	NOUN
ejpam-4028	276	10	{	{	PUNCT
ejpam-4028	276	11	[	[	PUNCT
ejpam-4028	276	12	g̃(gen	g̃(gen	PROPN
ejpam-4028	276	13	,	,	PUNCT
ejpam-4028	276	14	gen+1	gen+1	NOUN
ejpam-4028	276	15	,	,	PUNCT
ejpam-4028	276	16	gen+1	gen+1	NOUN
ejpam-4028	276	17	)	)	PUNCT
ejpam-4028	276	18	+	+	CCONJ
ejpam-4028	276	19	g̃(gen	g̃(gen	PROPN
ejpam-4028	276	20	,	,	PUNCT
ejpam-4028	276	21	gen+2	gen+2	NOUN
ejpam-4028	276	22	,	,	PUNCT
ejpam-4028	276	23	gen+2	gen+2	NOUN
ejpam-4028	276	24	)	)	PUNCT
ejpam-4028	276	25	]	]	PUNCT
ejpam-4028	276	26	,	,	PUNCT
ejpam-4028	276	27	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	276	28	,	,	PUNCT
ejpam-4028	276	29	gen+2	gen+2	NOUN
ejpam-4028	276	30	,	,	PUNCT
ejpam-4028	276	31	gen+2	gen+2	NOUN
ejpam-4028	276	32	)	)	PUNCT
ejpam-4028	276	33	}	}	PUNCT
ejpam-4028	276	34	≤̃¯̄ag̃(gen	≤̃¯̄ag̃(gen	NOUN
ejpam-4028	276	35	,	,	PUNCT
ejpam-4028	276	36	gen+1	gen+1	NOUN
ejpam-4028	276	37	,	,	PUNCT
ejpam-4028	276	38	gen+1	gen+1	NOUN
ejpam-4028	276	39	)	)	PUNCT
ejpam-4028	276	40	(	(	PUNCT
ejpam-4028	276	41	7	7	X
ejpam-4028	276	42	)	)	PUNCT
ejpam-4028	276	43	we	we	PRON
ejpam-4028	276	44	now	now	ADV
ejpam-4028	276	45	have	have	VERB
ejpam-4028	276	46	two	two	NUM
ejpam-4028	276	47	cases	case	NOUN
ejpam-4028	276	48	:	:	PUNCT
ejpam-4028	276	49	case	case	NOUN
ejpam-4028	276	50	(	(	PUNCT
ejpam-4028	276	51	1	1	NUM
ejpam-4028	276	52	):	):	PUNCT
ejpam-4028	276	53	if	if	SCONJ
ejpam-4028	276	54	min	min	PROPN
ejpam-4028	276	55	{	{	PUNCT
ejpam-4028	276	56	[	[	PUNCT
ejpam-4028	276	57	g̃(gen	g̃(gen	PROPN
ejpam-4028	276	58	,	,	PUNCT
ejpam-4028	276	59	gen+1	gen+1	NOUN
ejpam-4028	276	60	,	,	PUNCT
ejpam-4028	276	61	gen+1	gen+1	NOUN
ejpam-4028	276	62	)	)	PUNCT
ejpam-4028	276	63	+	+	CCONJ
ejpam-4028	276	64	g̃(gen	g̃(gen	PROPN
ejpam-4028	276	65	,	,	PUNCT
ejpam-4028	276	66	gen+2	gen+2	NOUN
ejpam-4028	276	67	,	,	PUNCT
ejpam-4028	276	68	gen+2	gen+2	NOUN
ejpam-4028	276	69	)	)	PUNCT
ejpam-4028	276	70	]	]	PUNCT
ejpam-4028	276	71	,	,	PUNCT
ejpam-4028	276	72	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	276	73	,	,	PUNCT
ejpam-4028	276	74	gen+2	gen+2	NOUN
ejpam-4028	276	75	,	,	PUNCT
ejpam-4028	276	76	gen+2	gen+2	NOUN
ejpam-4028	276	77	)	)	PUNCT
ejpam-4028	276	78	}	}	PUNCT
ejpam-4028	276	79	=	=	SYM
ejpam-4028	276	80	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	276	81	,	,	PUNCT
ejpam-4028	276	82	gen+2	gen+2	NOUN
ejpam-4028	276	83	,	,	PUNCT
ejpam-4028	276	84	gen+2	gen+2	NOUN
ejpam-4028	276	85	)	)	PUNCT
ejpam-4028	276	86	then	then	ADV
ejpam-4028	276	87	,	,	PUNCT
ejpam-4028	276	88	(	(	PUNCT
ejpam-4028	276	89	7	7	X
ejpam-4028	276	90	)	)	PUNCT
ejpam-4028	276	91	is	be	AUX
ejpam-4028	276	92	reduced	reduce	VERB
ejpam-4028	276	93	to	to	PART
ejpam-4028	276	94	g̃(gen+1	g̃(gen+1	VERB
ejpam-4028	276	95	,	,	PUNCT
ejpam-4028	276	96	gen+2	gen+2	NOUN
ejpam-4028	276	97	,	,	PUNCT
ejpam-4028	276	98	gen+2)≤̃¯̄ag̃(gen	gen+2)≤̃¯̄ag̃(gen	X
ejpam-4028	276	99	,	,	PUNCT
ejpam-4028	276	100	gen+1	gen+1	NOUN
ejpam-4028	276	101	,	,	PUNCT
ejpam-4028	276	102	gen+1	gen+1	NOUN
ejpam-4028	276	103	)	)	PUNCT
ejpam-4028	276	104	case	case	NOUN
ejpam-4028	276	105	(	(	PUNCT
ejpam-4028	276	106	2	2	NUM
ejpam-4028	276	107	):	):	PUNCT
ejpam-4028	276	108	if	if	SCONJ
ejpam-4028	276	109	min	min	PROPN
ejpam-4028	276	110	{	{	PUNCT
ejpam-4028	276	111	[	[	PUNCT
ejpam-4028	276	112	g̃(gen	g̃(gen	PROPN
ejpam-4028	276	113	,	,	PUNCT
ejpam-4028	276	114	gen+1	gen+1	NOUN
ejpam-4028	276	115	,	,	PUNCT
ejpam-4028	276	116	gen+1	gen+1	NOUN
ejpam-4028	276	117	)	)	PUNCT
ejpam-4028	277	1	+	+	CCONJ
ejpam-4028	277	2	g̃(gen	g̃(gen	PROPN
ejpam-4028	277	3	,	,	PUNCT
ejpam-4028	277	4	gen+2	gen+2	NOUN
ejpam-4028	277	5	,	,	PUNCT
ejpam-4028	277	6	gen+2	gen+2	NOUN
ejpam-4028	277	7	)	)	PUNCT
ejpam-4028	277	8	]	]	PUNCT
ejpam-4028	277	9	,	,	PUNCT
ejpam-4028	277	10	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	277	11	,	,	PUNCT
ejpam-4028	277	12	gen+2	gen+2	NOUN
ejpam-4028	277	13	,	,	PUNCT
ejpam-4028	277	14	gen+2	gen+2	NOUN
ejpam-4028	277	15	)	)	PUNCT
ejpam-4028	277	16	}	}	PUNCT
ejpam-4028	277	17	=[	=[	NOUN
ejpam-4028	277	18	g̃(gen	g̃(gen	PROPN
ejpam-4028	277	19	,	,	PUNCT
ejpam-4028	277	20	gen+1	gen+1	NOUN
ejpam-4028	277	21	,	,	PUNCT
ejpam-4028	277	22	gen+1	gen+1	NOUN
ejpam-4028	277	23	)	)	PUNCT
ejpam-4028	278	1	+	+	CCONJ
ejpam-4028	278	2	g̃(gen	g̃(gen	PROPN
ejpam-4028	278	3	,	,	PUNCT
ejpam-4028	278	4	gen+2	gen+2	NOUN
ejpam-4028	278	5	,	,	PUNCT
ejpam-4028	278	6	gen+2	gen+2	NOUN
ejpam-4028	278	7	)	)	PUNCT
ejpam-4028	278	8	]	]	PUNCT
ejpam-4028	278	9	then	then	ADV
ejpam-4028	278	10	,	,	PUNCT
ejpam-4028	278	11	(	(	PUNCT
ejpam-4028	278	12	7	7	X
ejpam-4028	278	13	)	)	PUNCT
ejpam-4028	278	14	is	be	AUX
ejpam-4028	278	15	reduced	reduce	VERB
ejpam-4028	278	16	to	to	ADP
ejpam-4028	278	17	g̃(gen	g̃(gen	PROPN
ejpam-4028	278	18	,	,	PUNCT
ejpam-4028	278	19	gen+1	gen+1	NOUN
ejpam-4028	278	20	,	,	PUNCT
ejpam-4028	278	21	gen+1	gen+1	NOUN
ejpam-4028	278	22	)	)	PUNCT
ejpam-4028	279	1	+	+	CCONJ
ejpam-4028	279	2	g̃(gen	g̃(gen	PROPN
ejpam-4028	279	3	,	,	PUNCT
ejpam-4028	279	4	gen+2	gen+2	PROPN
ejpam-4028	279	5	,	,	PUNCT
ejpam-4028	279	6	gen+2)≤̃¯̄ag̃(gen	gen+2)≤̃¯̄ag̃(gen	X
ejpam-4028	279	7	,	,	PUNCT
ejpam-4028	279	8	gen+1	gen+1	NOUN
ejpam-4028	279	9	,	,	PUNCT
ejpam-4028	279	10	gen+1	gen+1	NOUN
ejpam-4028	279	11	)	)	PUNCT
ejpam-4028	279	12	g̃(gen	g̃(gen	PROPN
ejpam-4028	279	13	,	,	PUNCT
ejpam-4028	279	14	gen+1	gen+1	NOUN
ejpam-4028	279	15	,	,	PUNCT
ejpam-4028	279	16	gen+1	gen+1	NOUN
ejpam-4028	279	17	)	)	PUNCT
ejpam-4028	280	1	+	+	CCONJ
ejpam-4028	280	2	[	[	PUNCT
ejpam-4028	280	3	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	280	4	,	,	PUNCT
ejpam-4028	280	5	gen+2	gen+2	NOUN
ejpam-4028	280	6	,	,	PUNCT
ejpam-4028	280	7	gen+2)−	gen+2)−	PROPN
ejpam-4028	280	8	g̃(gen	g̃(gen	PROPN
ejpam-4028	280	9	,	,	PUNCT
ejpam-4028	280	10	gen+1	gen+1	NOUN
ejpam-4028	280	11	,	,	PUNCT
ejpam-4028	280	12	gen+1	gen+1	NOUN
ejpam-4028	280	13	)	)	PUNCT
ejpam-4028	280	14	]	]	PUNCT
ejpam-4028	280	15	≤̃¯̄ag̃(gen	≤̃¯̄ag̃(gen	X
ejpam-4028	280	16	,	,	PUNCT
ejpam-4028	280	17	gen+1	gen+1	NOUN
ejpam-4028	280	18	,	,	PUNCT
ejpam-4028	280	19	gen+1	gen+1	NOUN
ejpam-4028	280	20	)	)	PUNCT
ejpam-4028	280	21	⇒	⇒	NOUN
ejpam-4028	280	22	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	280	23	,	,	PUNCT
ejpam-4028	280	24	gen+2	gen+2	NOUN
ejpam-4028	280	25	,	,	PUNCT
ejpam-4028	280	26	gen+2)≤̃¯̄ag̃(gen	gen+2)≤̃¯̄ag̃(gen	X
ejpam-4028	280	27	,	,	PUNCT
ejpam-4028	280	28	gen+1	gen+1	NOUN
ejpam-4028	280	29	,	,	PUNCT
ejpam-4028	280	30	gen+1	gen+1	NOUN
ejpam-4028	280	31	)	)	PUNCT
ejpam-4028	280	32	on	on	ADP
ejpam-4028	280	33	continuing	continue	VERB
ejpam-4028	280	34	this	this	DET
ejpam-4028	280	35	process	process	NOUN
ejpam-4028	280	36	(	(	PUNCT
ejpam-4028	280	37	n+	n+	NOUN
ejpam-4028	280	38	1	1	NUM
ejpam-4028	280	39	)	)	PUNCT
ejpam-4028	280	40	times	time	NOUN
ejpam-4028	280	41	;	;	PUNCT
ejpam-4028	280	42	we	we	PRON
ejpam-4028	280	43	obtain	obtain	VERB
ejpam-4028	280	44	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	280	45	,	,	PUNCT
ejpam-4028	280	46	gen+2	gen+2	NOUN
ejpam-4028	280	47	,	,	PUNCT
ejpam-4028	280	48	gen+2)≤̃¯̄an+1g̃(ge0	gen+2)≤̃¯̄an+1g̃(ge0	NOUN
ejpam-4028	280	49	,	,	PUNCT
ejpam-4028	280	50	ge1	ge1	NOUN
ejpam-4028	280	51	,	,	PUNCT
ejpam-4028	280	52	ge1	ge1	NOUN
ejpam-4028	280	53	)	)	PUNCT
ejpam-4028	280	54	similarly	similarly	ADV
ejpam-4028	280	55	,	,	PUNCT
ejpam-4028	280	56	we	we	PRON
ejpam-4028	280	57	will	will	AUX
ejpam-4028	280	58	conclude	conclude	VERB
ejpam-4028	280	59	that	that	SCONJ
ejpam-4028	280	60	g̃(gen	g̃(gen	PROPN
ejpam-4028	280	61	,	,	PUNCT
ejpam-4028	280	62	gen+1	gen+1	NOUN
ejpam-4028	280	63	,	,	PUNCT
ejpam-4028	280	64	gen+1)≤̃¯̄ang̃(ge0	gen+1)≤̃¯̄ang̃(ge0	NOUN
ejpam-4028	280	65	,	,	PUNCT
ejpam-4028	280	66	ge1	ge1	NOUN
ejpam-4028	280	67	,	,	PUNCT
ejpam-4028	280	68	ge1	ge1	PROPN
ejpam-4028	280	69	)	)	PUNCT
ejpam-4028	280	70	next	next	ADV
ejpam-4028	280	71	,	,	PUNCT
ejpam-4028	280	72	we	we	PRON
ejpam-4028	280	73	show	show	VERB
ejpam-4028	280	74	that	that	SCONJ
ejpam-4028	280	75	{	{	PUNCT
ejpam-4028	280	76	gen}n∈n	gen}n∈n	NOUN
ejpam-4028	280	77	is	be	AUX
ejpam-4028	280	78	a	a	DET
ejpam-4028	280	79	fuzzy	fuzzy	ADJ
ejpam-4028	280	80	soft	soft	ADJ
ejpam-4028	280	81	g	g	NOUN
ejpam-4028	280	82	-	-	PUNCT
ejpam-4028	280	83	cauchy	cauchy	ADJ
ejpam-4028	280	84	sequence	sequence	NOUN
ejpam-4028	280	85	.	.	PUNCT
ejpam-4028	281	1	then	then	ADV
ejpam-4028	281	2	for	for	ADP
ejpam-4028	281	3	all	all	DET
ejpam-4028	281	4	n	n	CCONJ
ejpam-4028	281	5	,	,	PUNCT
ejpam-4028	281	6	m	m	VERB
ejpam-4028	281	7	∈	∈	PROPN
ejpam-4028	281	8	n	n	CCONJ
ejpam-4028	281	9	,	,	PUNCT
ejpam-4028	281	10	n	n	CCONJ
ejpam-4028	281	11	<	<	X
ejpam-4028	281	12	m	m	PROPN
ejpam-4028	281	13	,	,	PUNCT
ejpam-4028	281	14	we	we	PRON
ejpam-4028	281	15	have	have	VERB
ejpam-4028	281	16	g̃(gen	g̃(gen	PROPN
ejpam-4028	281	17	,	,	PUNCT
ejpam-4028	281	18	gem	gem	NOUN
ejpam-4028	281	19	,	,	PUNCT
ejpam-4028	281	20	gem)≤̃g̃(gen	gem)≤̃g̃(gen	NOUN
ejpam-4028	281	21	,	,	PUNCT
ejpam-4028	281	22	gen+1	gen+1	NOUN
ejpam-4028	281	23	,	,	PUNCT
ejpam-4028	281	24	gen+1	gen+1	NOUN
ejpam-4028	281	25	)	)	PUNCT
ejpam-4028	282	1	+	+	CCONJ
ejpam-4028	282	2	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	282	3	,	,	PUNCT
ejpam-4028	282	4	gen+2	gen+2	NOUN
ejpam-4028	282	5	,	,	PUNCT
ejpam-4028	282	6	gen+2	gen+2	NOUN
ejpam-4028	282	7	)	)	PUNCT
ejpam-4028	283	1	+	+	CCONJ
ejpam-4028	283	2	...	...	PUNCT
ejpam-4028	284	1	+	+	CCONJ
ejpam-4028	284	2	g̃(gem−1	g̃(gem−1	NOUN
ejpam-4028	284	3	,	,	PUNCT
ejpam-4028	284	4	gem	gem	NOUN
ejpam-4028	284	5	,	,	PUNCT
ejpam-4028	284	6	gem	gem	NOUN
ejpam-4028	284	7	)	)	PUNCT
ejpam-4028	284	8	≤̃(¯̄an	≤̃(¯̄an	NOUN
ejpam-4028	284	9	+	+	CCONJ
ejpam-4028	284	10	¯̄a(n+1	¯̄a(n+1	NOUN
ejpam-4028	284	11	)	)	PUNCT
ejpam-4028	285	1	+	+	CCONJ
ejpam-4028	285	2	...	...	PUNCT
ejpam-4028	286	1	+	+	CCONJ
ejpam-4028	286	2	¯̄amg̃(ge0	¯̄amg̃(ge0	ADJ
ejpam-4028	286	3	,	,	PUNCT
ejpam-4028	286	4	ge1	ge1	NOUN
ejpam-4028	286	5	,	,	PUNCT
ejpam-4028	286	6	ge1	ge1	NOUN
ejpam-4028	286	7	)	)	PUNCT
ejpam-4028	286	8	≤̃	≤̃	PROPN
ejpam-4028	286	9	¯̄an	¯̄an	PROPN
ejpam-4028	286	10	1̃−¯̄a	1̃−¯̄a	PROPN
ejpam-4028	286	11	g̃(ge0	g̃(ge0	PROPN
ejpam-4028	286	12	,	,	PUNCT
ejpam-4028	286	13	ge1	ge1	NOUN
ejpam-4028	286	14	,	,	PUNCT
ejpam-4028	286	15	ge1	ge1	PROPN
ejpam-4028	286	16	)	)	PUNCT
ejpam-4028	286	17	.	.	PUNCT
ejpam-4028	287	1	a.	a.	PROPN
ejpam-4028	287	2	f.	f.	PROPN
ejpam-4028	287	3	sayed	sayed	PROPN
ejpam-4028	287	4	,	,	PUNCT
ejpam-4028	287	5	a.	a.	NOUN
ejpam-4028	287	6	alahmari	alahmari	PROPN
ejpam-4028	287	7	/	/	SYM
ejpam-4028	287	8	eur	eur	PROPN
ejpam-4028	287	9	.	.	PUNCT
ejpam-4028	288	1	j.	j.	PROPN
ejpam-4028	288	2	pure	pure	PROPN
ejpam-4028	288	3	appl	appl	PROPN
ejpam-4028	288	4	.	.	PROPN
ejpam-4028	288	5	math	math	PROPN
ejpam-4028	288	6	,	,	PUNCT
ejpam-4028	288	7	14	14	NUM
ejpam-4028	288	8	(	(	PUNCT
ejpam-4028	288	9	3	3	NUM
ejpam-4028	288	10	)	)	PUNCT
ejpam-4028	288	11	(	(	PUNCT
ejpam-4028	288	12	2021	2021	NUM
ejpam-4028	288	13	)	)	PUNCT
ejpam-4028	288	14	,	,	PUNCT
ejpam-4028	288	15	923	923	NUM
ejpam-4028	288	16	-	-	SYM
ejpam-4028	288	17	941	941	NUM
ejpam-4028	288	18	936	936	NUM
ejpam-4028	288	19	hence	hence	ADV
ejpam-4028	288	20	,	,	PUNCT
ejpam-4028	288	21	{	{	PUNCT
ejpam-4028	288	22	gen}n∈n	gen}n∈n	PROPN
ejpam-4028	288	23	is	be	AUX
ejpam-4028	288	24	a	a	DET
ejpam-4028	288	25	fuzzy	fuzzy	ADJ
ejpam-4028	288	26	soft	soft	ADJ
ejpam-4028	288	27	g	g	NOUN
ejpam-4028	288	28	-	-	PUNCT
ejpam-4028	288	29	cauchy	cauchy	ADJ
ejpam-4028	288	30	sequence	sequence	NOUN
ejpam-4028	288	31	.	.	PUNCT
ejpam-4028	289	1	since	since	SCONJ
ejpam-4028	289	2	(	(	PUNCT
ejpam-4028	289	3	ẽ	ẽ	PROPN
ejpam-4028	289	4	,	,	PUNCT
ejpam-4028	289	5	g̃	g̃	PROPN
ejpam-4028	289	6	)	)	PUNCT
ejpam-4028	289	7	is	be	AUX
ejpam-4028	289	8	fuzzy	fuzzy	ADJ
ejpam-4028	289	9	soft	soft	ADJ
ejpam-4028	289	10	g	g	NOUN
ejpam-4028	289	11	-	-	PUNCT
ejpam-4028	289	12	complete	complete	ADJ
ejpam-4028	289	13	,	,	PUNCT
ejpam-4028	289	14	there	there	PRON
ejpam-4028	289	15	exists	exist	VERB
ejpam-4028	289	16	fe∈̃fsc(ẽ	fe∈̃fsc(ẽ	PROPN
ejpam-4028	289	17	)	)	PUNCT
ejpam-4028	289	18	such	such	ADJ
ejpam-4028	289	19	that	that	SCONJ
ejpam-4028	289	20	{	{	PUNCT
ejpam-4028	289	21	gen}n∈n	gen}n∈n	PROPN
ejpam-4028	289	22	fuzzy	fuzzy	ADJ
ejpam-4028	289	23	soft	soft	ADJ
ejpam-4028	289	24	g	g	NOUN
ejpam-4028	289	25	-	-	PUNCT
ejpam-4028	289	26	converges	converge	NOUN
ejpam-4028	289	27	to	to	ADP
ejpam-4028	289	28	fe	fe	PROPN
ejpam-4028	289	29	.	.	PUNCT
ejpam-4028	290	1	next	next	ADV
ejpam-4028	290	2	,	,	PUNCT
ejpam-4028	290	3	we	we	PRON
ejpam-4028	290	4	will	will	AUX
ejpam-4028	290	5	show	show	VERB
ejpam-4028	290	6	that	that	SCONJ
ejpam-4028	290	7	fe	fe	PROPN
ejpam-4028	290	8	is	be	AUX
ejpam-4028	290	9	a	a	DET
ejpam-4028	290	10	fixed	fix	VERB
ejpam-4028	290	11	point	point	NOUN
ejpam-4028	290	12	of	of	ADP
ejpam-4028	290	13	t	t	PROPN
ejpam-4028	290	14	.	.	PUNCT
ejpam-4028	291	1	for	for	ADP
ejpam-4028	291	2	this	this	PRON
ejpam-4028	291	3	,	,	PUNCT
ejpam-4028	291	4	we	we	PRON
ejpam-4028	291	5	take	take	VERB
ejpam-4028	291	6	fe1	fe1	PROPN
ejpam-4028	291	7	=	=	SYM
ejpam-4028	291	8	gen	gen	PROPN
ejpam-4028	291	9	and	and	CCONJ
ejpam-4028	291	10	fe2	fe2	PROPN
ejpam-4028	291	11	=	=	SYM
ejpam-4028	291	12	fe3	fe3	PROPN
ejpam-4028	291	13	=	=	SYM
ejpam-4028	291	14	fe	fe	X
ejpam-4028	291	15	in	in	ADP
ejpam-4028	291	16	(	(	PUNCT
ejpam-4028	291	17	6	6	NUM
ejpam-4028	291	18	)	)	PUNCT
ejpam-4028	291	19	,	,	PUNCT
ejpam-4028	291	20	then	then	ADV
ejpam-4028	291	21	min	min	PROPN
ejpam-4028	291	22			PROPN
ejpam-4028	291	23	[	[	PUNCT
ejpam-4028	291	24	g̃(gen	g̃(gen	PROPN
ejpam-4028	291	25	,	,	PUNCT
ejpam-4028	291	26	t	t	PROPN
ejpam-4028	291	27	gen	gen	PROPN
ejpam-4028	291	28	,	,	PUNCT
ejpam-4028	291	29	t	t	PROPN
ejpam-4028	291	30	gen	gen	PROPN
ejpam-4028	291	31	)	)	PUNCT
ejpam-4028	292	1	+	+	CCONJ
ejpam-4028	292	2	g̃(gen	g̃(gen	PROPN
ejpam-4028	292	3	,	,	PUNCT
ejpam-4028	292	4	tfe	tfe	PROPN
ejpam-4028	292	5	,	,	PUNCT
ejpam-4028	292	6	t	t	PROPN
ejpam-4028	292	7	fe	fe	PROPN
ejpam-4028	292	8	)	)	PUNCT
ejpam-4028	292	9	]	]	PUNCT
ejpam-4028	292	10	,	,	PUNCT
ejpam-4028	292	11	g̃(tgen	g̃(tgen	PROPN
ejpam-4028	292	12	,	,	PUNCT
ejpam-4028	292	13	t	t	PROPN
ejpam-4028	292	14	fe	fe	PROPN
ejpam-4028	292	15	,	,	PUNCT
ejpam-4028	292	16	t	t	PROPN
ejpam-4028	292	17	fe	fe	PROPN
ejpam-4028	292	18	)	)	PUNCT
ejpam-4028	292	19	,	,	PUNCT
ejpam-4028	292	20	[	[	PUNCT
ejpam-4028	292	21	g̃(fe	g̃(fe	NOUN
ejpam-4028	292	22	,	,	PUNCT
ejpam-4028	292	23	tfe	tfe	NOUN
ejpam-4028	292	24	,	,	PUNCT
ejpam-4028	292	25	t	t	PROPN
ejpam-4028	292	26	fe	fe	X
ejpam-4028	292	27	)	)	PUNCT
ejpam-4028	292	28	+	+	CCONJ
ejpam-4028	292	29	g̃(fe	g̃(fe	NOUN
ejpam-4028	292	30	,	,	PUNCT
ejpam-4028	292	31	t	t	PROPN
ejpam-4028	292	32	gen	gen	PROPN
ejpam-4028	292	33	,	,	PUNCT
ejpam-4028	292	34	t	t	PROPN
ejpam-4028	292	35	gen	gen	PROPN
ejpam-4028	292	36	)	)	PUNCT
ejpam-4028	292	37	]	]	PUNCT
ejpam-4028	293	1			PROPN
ejpam-4028	293	2	≤̃¯̄ag̃(gen	≤̃¯̄ag̃(gen	NOUN
ejpam-4028	293	3	,	,	PUNCT
ejpam-4028	293	4	fe	fe	X
ejpam-4028	293	5	,	,	PUNCT
ejpam-4028	293	6	fe	fe	NOUN
ejpam-4028	293	7	)	)	PUNCT
ejpam-4028	293	8	⇒	⇒	PROPN
ejpam-4028	293	9	min	min	PROPN
ejpam-4028	293	10			PROPN
ejpam-4028	293	11	[	[	PUNCT
ejpam-4028	293	12	g̃(fe	g̃(fe	NOUN
ejpam-4028	293	13	,	,	PUNCT
ejpam-4028	293	14	fe	fe	X
ejpam-4028	293	15	,	,	PUNCT
ejpam-4028	293	16	fe	fe	X
ejpam-4028	293	17	)	)	PUNCT
ejpam-4028	293	18	+	+	CCONJ
ejpam-4028	293	19	g̃(fe	g̃(fe	NOUN
ejpam-4028	293	20	,	,	PUNCT
ejpam-4028	293	21	tfe	tfe	NOUN
ejpam-4028	293	22	,	,	PUNCT
ejpam-4028	293	23	t	t	PROPN
ejpam-4028	293	24	fe	fe	PROPN
ejpam-4028	293	25	)	)	PUNCT
ejpam-4028	293	26	]	]	PUNCT
ejpam-4028	293	27	,	,	PUNCT
ejpam-4028	293	28	g̃(fe	g̃(fe	NOUN
ejpam-4028	293	29	,	,	PUNCT
ejpam-4028	293	30	t	t	PROPN
ejpam-4028	293	31	fe	fe	PROPN
ejpam-4028	293	32	,	,	PUNCT
ejpam-4028	293	33	t	t	PROPN
ejpam-4028	293	34	fe	fe	PROPN
ejpam-4028	293	35	)	)	PUNCT
ejpam-4028	293	36	,	,	PUNCT
ejpam-4028	293	37	[	[	PUNCT
ejpam-4028	293	38	g̃(fe	g̃(fe	NOUN
ejpam-4028	293	39	,	,	PUNCT
ejpam-4028	293	40	t	t	PROPN
ejpam-4028	293	41	fe	fe	PROPN
ejpam-4028	293	42	,	,	PUNCT
ejpam-4028	293	43	t	t	PROPN
ejpam-4028	293	44	fe	fe	X
ejpam-4028	293	45	)	)	PUNCT
ejpam-4028	293	46	+	+	CCONJ
ejpam-4028	293	47	g̃(fe	g̃(fe	NOUN
ejpam-4028	293	48	,	,	PUNCT
ejpam-4028	293	49	fe	fe	X
ejpam-4028	293	50	,	,	PUNCT
ejpam-4028	293	51	fe	fe	X
ejpam-4028	293	52	)	)	PUNCT
ejpam-4028	293	53	]	]	PUNCT
ejpam-4028	294	1			PROPN
ejpam-4028	294	2	≤̃¯̄ag̃(fe	≤̃¯̄ag̃(fe	NOUN
ejpam-4028	294	3	,	,	PUNCT
ejpam-4028	294	4	fe	fe	X
ejpam-4028	294	5	,	,	PUNCT
ejpam-4028	294	6	fe	fe	NOUN
ejpam-4028	294	7	)	)	PUNCT
ejpam-4028	294	8	⇒	⇒	PROPN
ejpam-4028	294	9	g̃(fe	g̃(fe	NOUN
ejpam-4028	294	10	,	,	PUNCT
ejpam-4028	294	11	tfe	tfe	PROPN
ejpam-4028	294	12	,	,	PUNCT
ejpam-4028	294	13	tfe)≤̃0̃	tfe)≤̃0̃	X
ejpam-4028	295	1	this	this	PRON
ejpam-4028	295	2	is	be	AUX
ejpam-4028	295	3	a	a	DET
ejpam-4028	295	4	contradiction	contradiction	NOUN
ejpam-4028	295	5	,	,	PUNCT
ejpam-4028	295	6	so	so	ADV
ejpam-4028	295	7	tfe	tfe	NOUN
ejpam-4028	295	8	=	=	SYM
ejpam-4028	295	9	fe	fe	X
ejpam-4028	295	10	i.e.	i.e.	X
ejpam-4028	295	11	fe	fe	X
ejpam-4028	295	12	is	be	AUX
ejpam-4028	295	13	a	a	DET
ejpam-4028	295	14	fixed	fix	VERB
ejpam-4028	295	15	point	point	NOUN
ejpam-4028	295	16	of	of	ADP
ejpam-4028	295	17	t	t	PROPN
ejpam-4028	295	18	.	.	PUNCT
ejpam-4028	296	1	now	now	ADV
ejpam-4028	296	2	,	,	PUNCT
ejpam-4028	296	3	to	to	PART
ejpam-4028	296	4	prove	prove	VERB
ejpam-4028	296	5	uniqueness	uniqueness	NOUN
ejpam-4028	296	6	,	,	PUNCT
ejpam-4028	296	7	assume	assume	VERB
ejpam-4028	296	8	that	that	SCONJ
ejpam-4028	296	9	fe	fe	PROPN
ejpam-4028	296	10	and	and	CCONJ
ejpam-4028	296	11	ge	ge	PROPN
ejpam-4028	296	12	are	be	AUX
ejpam-4028	296	13	two	two	NUM
ejpam-4028	296	14	fixed	fix	VERB
ejpam-4028	296	15	points	point	NOUN
ejpam-4028	296	16	of	of	ADP
ejpam-4028	296	17	t	t	PROPN
ejpam-4028	296	18	.	.	PUNCT
ejpam-4028	297	1	then	then	ADV
ejpam-4028	297	2	by	by	ADP
ejpam-4028	297	3	inequality	inequality	NOUN
ejpam-4028	297	4	(	(	PUNCT
ejpam-4028	297	5	6	6	NUM
ejpam-4028	297	6	)	)	PUNCT
ejpam-4028	297	7	,	,	PUNCT
ejpam-4028	297	8	we	we	PRON
ejpam-4028	297	9	have	have	VERB
ejpam-4028	297	10	min	min	PROPN
ejpam-4028	297	11			PROPN
ejpam-4028	297	12	[	[	PUNCT
ejpam-4028	297	13	g̃(fe	g̃(fe	NOUN
ejpam-4028	297	14	,	,	PUNCT
ejpam-4028	297	15	fe	fe	X
ejpam-4028	297	16	,	,	PUNCT
ejpam-4028	297	17	fe	fe	X
ejpam-4028	297	18	)	)	PUNCT
ejpam-4028	297	19	+	+	CCONJ
ejpam-4028	297	20	g̃(fe	g̃(fe	NOUN
ejpam-4028	297	21	,	,	PUNCT
ejpam-4028	297	22	ge	ge	PROPN
ejpam-4028	297	23	,	,	PUNCT
ejpam-4028	297	24	ge	ge	PROPN
ejpam-4028	297	25	)	)	PUNCT
ejpam-4028	297	26	]	]	PUNCT
ejpam-4028	297	27	,	,	PUNCT
ejpam-4028	297	28	g̃(fe	g̃(fe	NOUN
ejpam-4028	297	29	,	,	PUNCT
ejpam-4028	297	30	ge	ge	PROPN
ejpam-4028	297	31	,	,	PUNCT
ejpam-4028	297	32	ge	ge	PROPN
ejpam-4028	297	33	)	)	PUNCT
ejpam-4028	297	34	,	,	PUNCT
ejpam-4028	297	35	[	[	PUNCT
ejpam-4028	297	36	g̃(ge	g̃(ge	NOUN
ejpam-4028	297	37	,	,	PUNCT
ejpam-4028	297	38	ge	ge	PROPN
ejpam-4028	297	39	,	,	PUNCT
ejpam-4028	297	40	ge	ge	PROPN
ejpam-4028	297	41	)	)	PUNCT
ejpam-4028	298	1	+	+	NUM
ejpam-4028	298	2	g̃(ge	g̃(ge	ADJ
ejpam-4028	298	3	,	,	PUNCT
ejpam-4028	298	4	fe	fe	X
ejpam-4028	298	5	,	,	PUNCT
ejpam-4028	298	6	fe	fe	X
ejpam-4028	298	7	)	)	PUNCT
ejpam-4028	298	8	]	]	PUNCT
ejpam-4028	299	1			PROPN
ejpam-4028	299	2	≤̃¯̄ag̃(fe	≤̃¯̄ag̃(fe	NOUN
ejpam-4028	299	3	,	,	PUNCT
ejpam-4028	299	4	fe	fe	X
ejpam-4028	299	5	,	,	PUNCT
ejpam-4028	299	6	fe	fe	NOUN
ejpam-4028	299	7	)	)	PUNCT
ejpam-4028	299	8	⇒	⇒	PROPN
ejpam-4028	299	9	g̃(fe	g̃(fe	NOUN
ejpam-4028	299	10	,	,	PUNCT
ejpam-4028	299	11	ge	ge	PROPN
ejpam-4028	299	12	,	,	PUNCT
ejpam-4028	299	13	ge)≤̃¯̄ag̃(fe	ge)≤̃¯̄ag̃(fe	NOUN
ejpam-4028	299	14	,	,	PUNCT
ejpam-4028	299	15	ge	ge	PROPN
ejpam-4028	299	16	,	,	PUNCT
ejpam-4028	299	17	ge	ge	PROPN
ejpam-4028	299	18	)	)	PUNCT
ejpam-4028	299	19	,	,	PUNCT
ejpam-4028	299	20	this	this	PRON
ejpam-4028	299	21	is	be	AUX
ejpam-4028	299	22	a	a	DET
ejpam-4028	299	23	contradiction	contradiction	NOUN
ejpam-4028	299	24	implies	imply	VERB
ejpam-4028	299	25	that	that	PRON
ejpam-4028	299	26	fe	fe	X
ejpam-4028	299	27	=	=	PROPN
ejpam-4028	299	28	ge	ge	PROPN
ejpam-4028	299	29	.	.	PUNCT
ejpam-4028	300	1	to	to	PART
ejpam-4028	300	2	show	show	VERB
ejpam-4028	300	3	that	that	SCONJ
ejpam-4028	300	4	t	t	PROPN
ejpam-4028	300	5	is	be	AUX
ejpam-4028	300	6	fuzzy	fuzzy	ADJ
ejpam-4028	300	7	soft	soft	ADJ
ejpam-4028	300	8	g	g	NOUN
ejpam-4028	300	9	-	-	NOUN
ejpam-4028	300	10	continuous	continuous	ADJ
ejpam-4028	300	11	at	at	ADP
ejpam-4028	300	12	fe	fe	NOUN
ejpam-4028	300	13	.	.	PUNCT
ejpam-4028	300	14	let	let	AUX
ejpam-4028	300	15	{	{	PUNCT
ejpam-4028	300	16	hen}n∈n	hen}n∈n	PRON
ejpam-4028	300	17	be	be	AUX
ejpam-4028	300	18	a	a	DET
ejpam-4028	300	19	sequence	sequence	NOUN
ejpam-4028	300	20	of	of	ADP
ejpam-4028	300	21	fuzzy	fuzzy	ADJ
ejpam-4028	300	22	soft	soft	ADJ
ejpam-4028	300	23	elements	element	NOUN
ejpam-4028	300	24	in	in	ADP
ejpam-4028	300	25	ẽ	ẽ	PROPN
ejpam-4028	300	26	such	such	ADJ
ejpam-4028	300	27	that	that	SCONJ
ejpam-4028	300	28	{	{	PUNCT
ejpam-4028	300	29	hen}n∈n	hen}n∈n	PROPN
ejpam-4028	300	30	→	→	SYM
ejpam-4028	300	31	fe	fe	PROPN
ejpam-4028	300	32	,	,	PUNCT
ejpam-4028	300	33	then	then	ADV
ejpam-4028	300	34	we	we	PRON
ejpam-4028	300	35	can	can	AUX
ejpam-4028	300	36	deduce	deduce	VERB
ejpam-4028	300	37	that	that	SCONJ
ejpam-4028	300	38	using	use	VERB
ejpam-4028	300	39	inequality	inequality	NOUN
ejpam-4028	300	40	(	(	PUNCT
ejpam-4028	300	41	6	6	NUM
ejpam-4028	300	42	)	)	PUNCT
ejpam-4028	300	43	,	,	PUNCT
ejpam-4028	300	44	we	we	PRON
ejpam-4028	300	45	have	have	VERB
ejpam-4028	300	46	min	min	PROPN
ejpam-4028	300	47			PROPN
ejpam-4028	300	48	[	[	PUNCT
ejpam-4028	300	49	g̃(fe	g̃(fe	NOUN
ejpam-4028	300	50	,	,	PUNCT
ejpam-4028	300	51	tfe	tfe	NOUN
ejpam-4028	300	52	,	,	PUNCT
ejpam-4028	300	53	t	t	PROPN
ejpam-4028	300	54	fe	fe	X
ejpam-4028	300	55	)	)	PUNCT
ejpam-4028	300	56	+	+	CCONJ
ejpam-4028	300	57	g̃(fe	g̃(fe	NOUN
ejpam-4028	300	58	,	,	PUNCT
ejpam-4028	300	59	then	then	ADV
ejpam-4028	300	60	,	,	PUNCT
ejpam-4028	300	61	then	then	ADV
ejpam-4028	300	62	)	)	PUNCT
ejpam-4028	300	63	]	]	PUNCT
ejpam-4028	300	64	,	,	PUNCT
ejpam-4028	300	65	g̃(tfe	g̃(tfe	NOUN
ejpam-4028	300	66	,	,	PUNCT
ejpam-4028	300	67	then	then	ADV
ejpam-4028	300	68	,	,	PUNCT
ejpam-4028	300	69	then	then	ADV
ejpam-4028	300	70	)	)	PUNCT
ejpam-4028	300	71	,	,	PUNCT
ejpam-4028	300	72	[	[	PUNCT
ejpam-4028	300	73	g̃(hen	g̃(hen	ADV
ejpam-4028	300	74	,	,	PUNCT
ejpam-4028	300	75	then	then	ADV
ejpam-4028	300	76	,	,	PUNCT
ejpam-4028	300	77	then	then	ADV
ejpam-4028	300	78	)	)	PUNCT
ejpam-4028	301	1	+	+	CCONJ
ejpam-4028	301	2	g̃(hen	g̃(hen	ADV
ejpam-4028	301	3	,	,	PUNCT
ejpam-4028	301	4	t	t	PROPN
ejpam-4028	301	5	fe	fe	PROPN
ejpam-4028	301	6	,	,	PUNCT
ejpam-4028	301	7	t	t	PROPN
ejpam-4028	301	8	fe	fe	PROPN
ejpam-4028	301	9	)	)	PUNCT
ejpam-4028	301	10	]	]	PUNCT
ejpam-4028	302	1			PROPN
ejpam-4028	302	2	≤̃¯̄ag̃(fe	≤̃¯̄ag̃(fe	NOUN
ejpam-4028	302	3	,	,	PUNCT
ejpam-4028	302	4	hen	hen	NOUN
ejpam-4028	302	5	,	,	PUNCT
ejpam-4028	302	6	hen	hen	NOUN
ejpam-4028	302	7	)	)	PUNCT
ejpam-4028	302	8	⇒	⇒	NOUN
ejpam-4028	302	9	min	min	PROPN
ejpam-4028	302	10			PROPN
ejpam-4028	302	11	[	[	PUNCT
ejpam-4028	302	12	g̃(fe	g̃(fe	NOUN
ejpam-4028	302	13	,	,	PUNCT
ejpam-4028	302	14	fe	fe	X
ejpam-4028	302	15	,	,	PUNCT
ejpam-4028	302	16	fe	fe	X
ejpam-4028	302	17	)	)	PUNCT
ejpam-4028	302	18	+	+	CCONJ
ejpam-4028	302	19	g̃(fe	g̃(fe	NOUN
ejpam-4028	302	20	,	,	PUNCT
ejpam-4028	302	21	then	then	ADV
ejpam-4028	302	22	,	,	PUNCT
ejpam-4028	302	23	then	then	ADV
ejpam-4028	302	24	)	)	PUNCT
ejpam-4028	302	25	]	]	PUNCT
ejpam-4028	302	26	,	,	PUNCT
ejpam-4028	302	27	g̃(fe	g̃(fe	NOUN
ejpam-4028	302	28	,	,	PUNCT
ejpam-4028	302	29	then	then	ADV
ejpam-4028	302	30	,	,	PUNCT
ejpam-4028	302	31	then	then	ADV
ejpam-4028	302	32	)	)	PUNCT
ejpam-4028	302	33	,	,	PUNCT
ejpam-4028	302	34	[	[	PUNCT
ejpam-4028	302	35	g̃(hen	g̃(hen	ADV
ejpam-4028	302	36	,	,	PUNCT
ejpam-4028	302	37	then	then	ADV
ejpam-4028	302	38	,	,	PUNCT
ejpam-4028	302	39	then	then	ADV
ejpam-4028	302	40	)	)	PUNCT
ejpam-4028	303	1	+	+	CCONJ
ejpam-4028	303	2	g̃(hen	g̃(hen	ADV
ejpam-4028	303	3	,	,	PUNCT
ejpam-4028	303	4	fe	fe	X
ejpam-4028	303	5	,	,	PUNCT
ejpam-4028	303	6	fe	fe	X
ejpam-4028	303	7	)	)	PUNCT
ejpam-4028	303	8	]	]	PUNCT
ejpam-4028	304	1			PROPN
ejpam-4028	304	2	≤̃¯̄ag̃(fe	≤̃¯̄ag̃(fe	NOUN
ejpam-4028	304	3	,	,	PUNCT
ejpam-4028	304	4	hen	hen	NOUN
ejpam-4028	304	5	,	,	PUNCT
ejpam-4028	304	6	hen	hen	NOUN
ejpam-4028	304	7	)	)	PUNCT
ejpam-4028	304	8	taking	take	VERB
ejpam-4028	304	9	the	the	DET
ejpam-4028	304	10	limit	limit	NOUN
ejpam-4028	304	11	as	as	ADP
ejpam-4028	304	12	n→∞	n→∞	NUM
ejpam-4028	304	13	from	from	ADP
ejpam-4028	304	14	which	which	PRON
ejpam-4028	304	15	,	,	PUNCT
ejpam-4028	304	16	we	we	PRON
ejpam-4028	304	17	see	see	VERB
ejpam-4028	304	18	that	that	DET
ejpam-4028	304	19	g̃(fe	g̃(fe	NOUN
ejpam-4028	304	20	,	,	PUNCT
ejpam-4028	304	21	then	then	ADV
ejpam-4028	304	22	,	,	PUNCT
ejpam-4028	304	23	then	then	ADV
ejpam-4028	304	24	)	)	PUNCT
ejpam-4028	304	25	→	→	SYM
ejpam-4028	304	26	0̃	0̃	NOUN
ejpam-4028	304	27	and	and	CCONJ
ejpam-4028	304	28	so	so	ADV
ejpam-4028	304	29	,	,	PUNCT
ejpam-4028	304	30	by	by	ADP
ejpam-4028	304	31	proposition	proposition	NOUN
ejpam-4028	304	32	(	(	PUNCT
ejpam-4028	304	33	4.1	4.1	NUM
ejpam-4028	304	34	)	)	PUNCT
ejpam-4028	304	35	in	in	ADP
ejpam-4028	304	36	[	[	X
ejpam-4028	304	37	2	2	X
ejpam-4028	304	38	]	]	PUNCT
ejpam-4028	304	39	we	we	PRON
ejpam-4028	304	40	have	have	VERB
ejpam-4028	304	41	that	that	SCONJ
ejpam-4028	304	42	the	the	DET
ejpam-4028	304	43	sequence	sequence	NOUN
ejpam-4028	304	44	{	{	PUNCT
ejpam-4028	304	45	then}n∈n	then}n∈n	PROPN
ejpam-4028	304	46	is	be	AUX
ejpam-4028	304	47	fuzzy	fuzzy	ADJ
ejpam-4028	304	48	soft	soft	ADJ
ejpam-4028	304	49	g	g	NOUN
ejpam-4028	304	50	-	-	PUNCT
ejpam-4028	304	51	convergent	convergent	NOUN
ejpam-4028	304	52	to	to	ADP
ejpam-4028	304	53	tfe	tfe	NOUN
ejpam-4028	304	54	=	=	SYM
ejpam-4028	304	55	fe	fe	X
ejpam-4028	304	56	,	,	PUNCT
ejpam-4028	304	57	therefore	therefore	ADV
ejpam-4028	304	58	proposition	proposition	NOUN
ejpam-4028	304	59	(	(	PUNCT
ejpam-4028	304	60	4.4	4.4	NUM
ejpam-4028	304	61	)	)	PUNCT
ejpam-4028	304	62	in	in	ADP
ejpam-4028	304	63	[	[	X
ejpam-4028	304	64	2	2	NUM
ejpam-4028	304	65	]	]	PUNCT
ejpam-4028	304	66	implies	imply	VERB
ejpam-4028	304	67	that	that	SCONJ
ejpam-4028	304	68	t	t	PROPN
ejpam-4028	304	69	is	be	AUX
ejpam-4028	304	70	fuzzy	fuzzy	ADJ
ejpam-4028	304	71	soft	soft	ADJ
ejpam-4028	304	72	g	g	NOUN
ejpam-4028	304	73	-	-	NOUN
ejpam-4028	304	74	continuous	continuous	ADJ
ejpam-4028	304	75	at	at	ADP
ejpam-4028	304	76	fe	fe	PROPN
ejpam-4028	304	77	.	.	PUNCT
ejpam-4028	304	78	a.	a.	PROPN
ejpam-4028	304	79	f.	f.	PROPN
ejpam-4028	304	80	sayed	sayed	PROPN
ejpam-4028	304	81	,	,	PUNCT
ejpam-4028	304	82	a.	a.	NOUN
ejpam-4028	304	83	alahmari	alahmari	PROPN
ejpam-4028	304	84	/	/	SYM
ejpam-4028	304	85	eur	eur	PROPN
ejpam-4028	304	86	.	.	PUNCT
ejpam-4028	305	1	j.	j.	PROPN
ejpam-4028	305	2	pure	pure	PROPN
ejpam-4028	305	3	appl	appl	PROPN
ejpam-4028	305	4	.	.	PROPN
ejpam-4028	305	5	math	math	PROPN
ejpam-4028	305	6	,	,	PUNCT
ejpam-4028	305	7	14	14	NUM
ejpam-4028	305	8	(	(	PUNCT
ejpam-4028	305	9	3	3	NUM
ejpam-4028	305	10	)	)	PUNCT
ejpam-4028	305	11	(	(	PUNCT
ejpam-4028	305	12	2021	2021	NUM
ejpam-4028	305	13	)	)	PUNCT
ejpam-4028	305	14	,	,	PUNCT
ejpam-4028	305	15	923	923	NUM
ejpam-4028	305	16	-	-	SYM
ejpam-4028	305	17	941	941	NUM
ejpam-4028	305	18	937	937	NUM
ejpam-4028	305	19	theorem	theorem	NOUN
ejpam-4028	305	20	6	6	NUM
ejpam-4028	305	21	.	.	PUNCT
ejpam-4028	306	1	suppose	suppose	VERB
ejpam-4028	306	2	(	(	PUNCT
ejpam-4028	306	3	ẽ	ẽ	PROPN
ejpam-4028	306	4	,	,	PUNCT
ejpam-4028	306	5	g̃	g̃	PROPN
ejpam-4028	306	6	)	)	PUNCT
ejpam-4028	306	7	is	be	AUX
ejpam-4028	306	8	a	a	DET
ejpam-4028	306	9	fuzzy	fuzzy	ADJ
ejpam-4028	306	10	soft	soft	ADJ
ejpam-4028	306	11	g	g	NOUN
ejpam-4028	306	12	-	-	PUNCT
ejpam-4028	306	13	metric	metric	ADJ
ejpam-4028	306	14	space	space	NOUN
ejpam-4028	306	15	and	and	CCONJ
ejpam-4028	306	16	t	t	NOUN
ejpam-4028	306	17	:	:	PUNCT
ejpam-4028	306	18	(	(	PUNCT
ejpam-4028	306	19	ẽ	ẽ	NOUN
ejpam-4028	306	20	,	,	PUNCT
ejpam-4028	306	21	g̃)→	g̃)→	PRON
ejpam-4028	306	22	(	(	PUNCT
ejpam-4028	306	23	ẽ	ẽ	PROPN
ejpam-4028	306	24	,	,	PUNCT
ejpam-4028	306	25	g̃	g̃	PROPN
ejpam-4028	306	26	)	)	PUNCT
ejpam-4028	306	27	is	be	AUX
ejpam-4028	306	28	a	a	DET
ejpam-4028	306	29	mapping	mapping	NOUN
ejpam-4028	306	30	satisfying	satisfy	VERB
ejpam-4028	306	31	the	the	DET
ejpam-4028	306	32	following	follow	VERB
ejpam-4028	306	33	condition	condition	NOUN
ejpam-4028	306	34	:	:	PUNCT
ejpam-4028	307	1	g̃(tfe1	g̃(tfe1	NOUN
ejpam-4028	307	2	,	,	PUNCT
ejpam-4028	307	3	tfe2	tfe2	NOUN
ejpam-4028	307	4	,	,	PUNCT
ejpam-4028	307	5	tfe3)≤̃¯̄a	tfe3)≤̃¯̄a	PROPN
ejpam-4028	307	6	max	max	PROPN
ejpam-4028	307	7			PROPN
ejpam-4028	307	8	[	[	PUNCT
ejpam-4028	307	9	g̃(fe1	g̃(fe1	PROPN
ejpam-4028	307	10	,	,	PUNCT
ejpam-4028	307	11	t	t	PROPN
ejpam-4028	307	12	fe1	fe1	PROPN
ejpam-4028	307	13	,	,	PUNCT
ejpam-4028	307	14	tfe1	tfe1	PROPN
ejpam-4028	307	15	)	)	PUNCT
ejpam-4028	308	1	+	+	CCONJ
ejpam-4028	308	2	g̃(fe1	g̃(fe1	PROPN
ejpam-4028	308	3	,	,	PUNCT
ejpam-4028	308	4	tfe2	tfe2	NOUN
ejpam-4028	308	5	,	,	PUNCT
ejpam-4028	308	6	tfe2	tfe2	PROPN
ejpam-4028	308	7	)	)	PUNCT
ejpam-4028	308	8	]	]	PUNCT
ejpam-4028	308	9	,	,	PUNCT
ejpam-4028	308	10	g̃(fe1	g̃(fe1	PROPN
ejpam-4028	308	11	,	,	PUNCT
ejpam-4028	308	12	fe2	fe2	PROPN
ejpam-4028	308	13	,	,	PUNCT
ejpam-4028	308	14	fe3	fe3	PROPN
ejpam-4028	308	15	)	)	PUNCT
ejpam-4028	308	16	,	,	PUNCT
ejpam-4028	308	17	[	[	PUNCT
ejpam-4028	308	18	g̃(fe2	g̃(fe2	PROPN
ejpam-4028	308	19	,	,	PUNCT
ejpam-4028	308	20	t	t	PROPN
ejpam-4028	308	21	fe2	fe2	PROPN
ejpam-4028	308	22	,	,	PUNCT
ejpam-4028	308	23	tfe2	tfe2	PROPN
ejpam-4028	308	24	)	)	PUNCT
ejpam-4028	309	1	+	+	CCONJ
ejpam-4028	309	2	g̃(fe2	g̃(fe2	NOUN
ejpam-4028	309	3	,	,	PUNCT
ejpam-4028	309	4	tfe1	tfe1	PROPN
ejpam-4028	309	5	,	,	PUNCT
ejpam-4028	309	6	tfe1	tfe1	PROPN
ejpam-4028	309	7	)	)	PUNCT
ejpam-4028	309	8	]	]	PUNCT
ejpam-4028	310	1			PROPN
ejpam-4028	310	2	(	(	PUNCT
ejpam-4028	310	3	8)	8)	NUM
ejpam-4028	310	4	∀fe1	∀fe1	PROPN
ejpam-4028	310	5	,	,	PUNCT
ejpam-4028	310	6	fe2	fe2	PROPN
ejpam-4028	310	7	,	,	PUNCT
ejpam-4028	310	8	fe3∈̃fsc(ẽ	fe3∈̃fsc(ẽ	PROPN
ejpam-4028	310	9	)	)	PUNCT
ejpam-4028	310	10	and	and	CCONJ
ejpam-4028	310	11	0̃≤̃¯̄a<̃1̃.	0̃≤̃¯̄a<̃1̃.	NUM
ejpam-4028	310	12	then	then	ADV
ejpam-4028	310	13	t	t	PROPN
ejpam-4028	310	14	has	have	VERB
ejpam-4028	310	15	an	an	DET
ejpam-4028	310	16	unique	unique	ADJ
ejpam-4028	310	17	fixed	fix	VERB
ejpam-4028	310	18	point	point	NOUN
ejpam-4028	310	19	,	,	PUNCT
ejpam-4028	310	20	say	say	VERB
ejpam-4028	310	21	fe	fe	X
ejpam-4028	310	22	,	,	PUNCT
ejpam-4028	310	23	and	and	CCONJ
ejpam-4028	310	24	at	at	ADP
ejpam-4028	310	25	fe	fe	PROPN
ejpam-4028	310	26	,	,	PUNCT
ejpam-4028	310	27	t	t	PROPN
ejpam-4028	310	28	is	be	AUX
ejpam-4028	310	29	fuzzy	fuzzy	ADJ
ejpam-4028	310	30	soft	soft	ADJ
ejpam-4028	310	31	g	g	NOUN
ejpam-4028	310	32	-	-	PUNCT
ejpam-4028	310	33	continuous	continuous	ADJ
ejpam-4028	310	34	.	.	PUNCT
ejpam-4028	311	1	proof	proof	NOUN
ejpam-4028	311	2	.	.	PUNCT
ejpam-4028	312	1	assume	assume	VERB
ejpam-4028	312	2	that	that	SCONJ
ejpam-4028	312	3	fe0∈̃fsc(ẽ	fe0∈̃fsc(ẽ	NOUN
ejpam-4028	312	4	)	)	PUNCT
ejpam-4028	312	5	is	be	AUX
ejpam-4028	312	6	an	an	DET
ejpam-4028	312	7	arbitrary	arbitrary	ADJ
ejpam-4028	312	8	fuzzy	fuzzy	ADJ
ejpam-4028	312	9	soft	soft	ADJ
ejpam-4028	312	10	element	element	NOUN
ejpam-4028	312	11	and	and	CCONJ
ejpam-4028	312	12	define	define	VERB
ejpam-4028	312	13	the	the	DET
ejpam-4028	312	14	sequence	sequence	NOUN
ejpam-4028	312	15	{	{	PUNCT
ejpam-4028	312	16	gen}n∈n	gen}n∈n	PROPN
ejpam-4028	312	17	as	as	SCONJ
ejpam-4028	312	18	follows	follow	VERB
ejpam-4028	312	19	:	:	PUNCT
ejpam-4028	313	1	tge0	tge0	NOUN
ejpam-4028	313	2	=	=	SYM
ejpam-4028	313	3	ge1	ge1	PROPN
ejpam-4028	313	4	,	,	PUNCT
ejpam-4028	313	5	t	t	PROPN
ejpam-4028	313	6	ge1	ge1	PROPN
ejpam-4028	313	7	=	=	PUNCT
ejpam-4028	313	8	ge2	ge2	PROPN
ejpam-4028	313	9	,	,	PUNCT
ejpam-4028	313	10	t	t	PROPN
ejpam-4028	313	11	ge2	ge2	PROPN
ejpam-4028	313	12	=	=	X
ejpam-4028	313	13	ge3	ge3	PROPN
ejpam-4028	313	14	,	,	PUNCT
ejpam-4028	313	15	...	...	PUNCT
ejpam-4028	313	16	,	,	PUNCT
ejpam-4028	313	17	t	t	PROPN
ejpam-4028	313	18	gen	gen	PROPN
ejpam-4028	313	19	=	=	NOUN
ejpam-4028	313	20	gen+1	gen+1	PROPN
ejpam-4028	313	21	.	.	PUNCT
ejpam-4028	314	1	consider	consider	VERB
ejpam-4028	314	2	that	that	DET
ejpam-4028	314	3	gen	gen	PROPN
ejpam-4028	314	4	6=	6=	PROPN
ejpam-4028	314	5	gen+1	gen+1	NOUN
ejpam-4028	314	6	.	.	PUNCT
ejpam-4028	315	1	substituting	substitute	VERB
ejpam-4028	315	2	fe1	fe1	PROPN
ejpam-4028	315	3	=	=	SYM
ejpam-4028	315	4	gen	gen	PROPN
ejpam-4028	315	5	,	,	PUNCT
ejpam-4028	315	6	fe2	fe2	X
ejpam-4028	315	7	=	=	SYM
ejpam-4028	315	8	gen+1	gen+1	NOUN
ejpam-4028	315	9	and	and	CCONJ
ejpam-4028	315	10	fe3	fe3	NOUN
ejpam-4028	315	11	=	=	SYM
ejpam-4028	315	12	gen+1	gen+1	NOUN
ejpam-4028	315	13	in	in	ADP
ejpam-4028	315	14	(	(	PUNCT
ejpam-4028	315	15	8)	8)	NUM
ejpam-4028	315	16	,	,	PUNCT
ejpam-4028	315	17	we	we	PRON
ejpam-4028	315	18	obtain	obtain	VERB
ejpam-4028	315	19	g̃(tgen	g̃(tgen	ADJ
ejpam-4028	315	20	,	,	PUNCT
ejpam-4028	315	21	t	t	PROPN
ejpam-4028	315	22	gen+1	gen+1	NOUN
ejpam-4028	315	23	,	,	PUNCT
ejpam-4028	315	24	t	t	PROPN
ejpam-4028	315	25	gen+1)≤̃¯̄a	gen+1)≤̃¯̄a	PROPN
ejpam-4028	315	26	max	max	PROPN
ejpam-4028	315	27			PROPN
ejpam-4028	315	28	[	[	PUNCT
ejpam-4028	315	29	g̃(gen	g̃(gen	PROPN
ejpam-4028	315	30	,	,	PUNCT
ejpam-4028	315	31	t	t	PROPN
ejpam-4028	315	32	gen	gen	PROPN
ejpam-4028	315	33	,	,	PUNCT
ejpam-4028	315	34	t	t	PROPN
ejpam-4028	315	35	gen	gen	PROPN
ejpam-4028	315	36	)	)	PUNCT
ejpam-4028	316	1	+	+	CCONJ
ejpam-4028	316	2	g̃(gen	g̃(gen	PROPN
ejpam-4028	316	3	,	,	PUNCT
ejpam-4028	316	4	t	t	PROPN
ejpam-4028	316	5	gen+1	gen+1	PROPN
ejpam-4028	316	6	,	,	PUNCT
ejpam-4028	316	7	t	t	PROPN
ejpam-4028	316	8	gen+1	gen+1	PROPN
ejpam-4028	316	9	)	)	PUNCT
ejpam-4028	316	10	]	]	PUNCT
ejpam-4028	316	11	,	,	PUNCT
ejpam-4028	316	12	g̃(gen	g̃(gen	PROPN
ejpam-4028	316	13	,	,	PUNCT
ejpam-4028	316	14	gen+1	gen+1	NOUN
ejpam-4028	316	15	,	,	PUNCT
ejpam-4028	316	16	gen+1	gen+1	NOUN
ejpam-4028	316	17	)	)	PUNCT
ejpam-4028	316	18	,	,	PUNCT
ejpam-4028	316	19	[	[	PUNCT
ejpam-4028	316	20	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	316	21	,	,	PUNCT
ejpam-4028	316	22	t	t	PROPN
ejpam-4028	316	23	gen+1	gen+1	NOUN
ejpam-4028	316	24	,	,	PUNCT
ejpam-4028	316	25	t	t	PROPN
ejpam-4028	316	26	gen+1	gen+1	PROPN
ejpam-4028	316	27	)	)	PUNCT
ejpam-4028	317	1	+	+	CCONJ
ejpam-4028	317	2	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	317	3	,	,	PUNCT
ejpam-4028	317	4	t	t	PROPN
ejpam-4028	317	5	gen	gen	PROPN
ejpam-4028	317	6	,	,	PUNCT
ejpam-4028	317	7	t	t	PROPN
ejpam-4028	317	8	gen	gen	PROPN
ejpam-4028	317	9	)	)	PUNCT
ejpam-4028	317	10	]	]	PUNCT
ejpam-4028	318	1			PROPN
ejpam-4028	318	2	⇒	⇒	NOUN
ejpam-4028	318	3	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	318	4	,	,	PUNCT
ejpam-4028	318	5	gen+2	gen+2	NOUN
ejpam-4028	318	6	,	,	PUNCT
ejpam-4028	318	7	gen+2)≤̃¯̄a	gen+2)≤̃¯̄a	PROPN
ejpam-4028	318	8	max	max	PROPN
ejpam-4028	318	9			PROPN
ejpam-4028	318	10	[	[	PUNCT
ejpam-4028	318	11	g̃(gen	g̃(gen	PROPN
ejpam-4028	318	12	,	,	PUNCT
ejpam-4028	318	13	gen+1	gen+1	NOUN
ejpam-4028	318	14	,	,	PUNCT
ejpam-4028	318	15	gen+1	gen+1	NOUN
ejpam-4028	318	16	)	)	PUNCT
ejpam-4028	318	17	+	+	CCONJ
ejpam-4028	318	18	g̃(gen	g̃(gen	PROPN
ejpam-4028	318	19	,	,	PUNCT
ejpam-4028	318	20	gen+2	gen+2	NOUN
ejpam-4028	318	21	,	,	PUNCT
ejpam-4028	318	22	gen+2	gen+2	NOUN
ejpam-4028	318	23	)	)	PUNCT
ejpam-4028	318	24	]	]	PUNCT
ejpam-4028	318	25	,	,	PUNCT
ejpam-4028	318	26	g̃(gen	g̃(gen	PROPN
ejpam-4028	318	27	,	,	PUNCT
ejpam-4028	318	28	gen+1	gen+1	NOUN
ejpam-4028	318	29	,	,	PUNCT
ejpam-4028	318	30	gen+1	gen+1	NOUN
ejpam-4028	318	31	)	)	PUNCT
ejpam-4028	318	32	,	,	PUNCT
ejpam-4028	318	33	[	[	PUNCT
ejpam-4028	318	34	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	318	35	,	,	PUNCT
ejpam-4028	318	36	gen+2	gen+2	NOUN
ejpam-4028	318	37	,	,	PUNCT
ejpam-4028	318	38	gen+2	gen+2	NOUN
ejpam-4028	318	39	)	)	PUNCT
ejpam-4028	318	40	+	+	CCONJ
ejpam-4028	318	41	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	318	42	,	,	PUNCT
ejpam-4028	318	43	gen+1	gen+1	NOUN
ejpam-4028	318	44	,	,	PUNCT
ejpam-4028	318	45	gen+1	gen+1	NOUN
ejpam-4028	318	46	)	)	PUNCT
ejpam-4028	318	47	]	]	PUNCT
ejpam-4028	319	1			PROPN
ejpam-4028	319	2	⇒	⇒	NOUN
ejpam-4028	319	3	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	319	4	,	,	PUNCT
ejpam-4028	319	5	gen+2	gen+2	NOUN
ejpam-4028	319	6	,	,	PUNCT
ejpam-4028	319	7	gen+2)≤̃¯̄a	gen+2)≤̃¯̄a	PROPN
ejpam-4028	319	8	max	max	PROPN
ejpam-4028	319	9	{	{	PUNCT
ejpam-4028	319	10	[	[	PUNCT
ejpam-4028	319	11	g̃(gen	g̃(gen	PROPN
ejpam-4028	319	12	,	,	PUNCT
ejpam-4028	319	13	gen+1	gen+1	NOUN
ejpam-4028	319	14	,	,	PUNCT
ejpam-4028	319	15	gen+1	gen+1	NOUN
ejpam-4028	319	16	)	)	PUNCT
ejpam-4028	320	1	+	+	CCONJ
ejpam-4028	320	2	g̃(gen	g̃(gen	PROPN
ejpam-4028	320	3	,	,	PUNCT
ejpam-4028	320	4	gen+2	gen+2	NOUN
ejpam-4028	320	5	,	,	PUNCT
ejpam-4028	320	6	gen+2	gen+2	NOUN
ejpam-4028	320	7	)	)	PUNCT
ejpam-4028	320	8	]	]	PUNCT
ejpam-4028	320	9	,	,	PUNCT
ejpam-4028	320	10	g̃(gen	g̃(gen	PROPN
ejpam-4028	320	11	,	,	PUNCT
ejpam-4028	320	12	gen+1	gen+1	NOUN
ejpam-4028	320	13	,	,	PUNCT
ejpam-4028	320	14	gen+1	gen+1	NOUN
ejpam-4028	320	15	)	)	PUNCT
ejpam-4028	320	16	,	,	PUNCT
ejpam-4028	320	17	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	320	18	,	,	PUNCT
ejpam-4028	320	19	gen+2	gen+2	NOUN
ejpam-4028	320	20	,	,	PUNCT
ejpam-4028	320	21	gen+2	gen+2	NOUN
ejpam-4028	320	22	)	)	PUNCT
ejpam-4028	320	23	}	}	PUNCT
ejpam-4028	320	24	(	(	PUNCT
ejpam-4028	320	25	9	9	X
ejpam-4028	320	26	)	)	PUNCT
ejpam-4028	320	27	we	we	PRON
ejpam-4028	320	28	now	now	ADV
ejpam-4028	320	29	have	have	VERB
ejpam-4028	320	30	three	three	NUM
ejpam-4028	320	31	cases	case	NOUN
ejpam-4028	320	32	:	:	PUNCT
ejpam-4028	320	33	case	case	NOUN
ejpam-4028	320	34	(	(	PUNCT
ejpam-4028	320	35	1	1	NUM
ejpam-4028	320	36	):	):	PUNCT
ejpam-4028	320	37	if	if	SCONJ
ejpam-4028	320	38	max	max	PROPN
ejpam-4028	320	39	{	{	PUNCT
ejpam-4028	320	40	[	[	PUNCT
ejpam-4028	320	41	g̃(gen	g̃(gen	PROPN
ejpam-4028	320	42	,	,	PUNCT
ejpam-4028	320	43	gen+1	gen+1	NOUN
ejpam-4028	320	44	,	,	PUNCT
ejpam-4028	320	45	gen+1	gen+1	NOUN
ejpam-4028	320	46	)	)	PUNCT
ejpam-4028	320	47	+	+	CCONJ
ejpam-4028	320	48	g̃(gen	g̃(gen	PROPN
ejpam-4028	320	49	,	,	PUNCT
ejpam-4028	320	50	gen+2	gen+2	NOUN
ejpam-4028	320	51	,	,	PUNCT
ejpam-4028	320	52	gen+2	gen+2	NOUN
ejpam-4028	320	53	)	)	PUNCT
ejpam-4028	320	54	]	]	PUNCT
ejpam-4028	320	55	,	,	PUNCT
ejpam-4028	320	56	g̃(gen	g̃(gen	PROPN
ejpam-4028	320	57	,	,	PUNCT
ejpam-4028	320	58	gen+1	gen+1	NOUN
ejpam-4028	320	59	,	,	PUNCT
ejpam-4028	320	60	gen+1	gen+1	NOUN
ejpam-4028	320	61	)	)	PUNCT
ejpam-4028	320	62	,	,	PUNCT
ejpam-4028	320	63	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	320	64	,	,	PUNCT
ejpam-4028	320	65	gen+2	gen+2	NOUN
ejpam-4028	320	66	,	,	PUNCT
ejpam-4028	320	67	gen+2	gen+2	NOUN
ejpam-4028	320	68	)	)	PUNCT
ejpam-4028	320	69	}	}	PUNCT
ejpam-4028	320	70	=[	=[	NOUN
ejpam-4028	320	71	g̃(gen	g̃(gen	PROPN
ejpam-4028	320	72	,	,	PUNCT
ejpam-4028	320	73	gen+1	gen+1	NOUN
ejpam-4028	320	74	,	,	PUNCT
ejpam-4028	320	75	gen+1	gen+1	NOUN
ejpam-4028	320	76	)	)	PUNCT
ejpam-4028	321	1	+	+	CCONJ
ejpam-4028	321	2	g̃(gen	g̃(gen	PROPN
ejpam-4028	321	3	,	,	PUNCT
ejpam-4028	321	4	gen+2	gen+2	NOUN
ejpam-4028	321	5	,	,	PUNCT
ejpam-4028	321	6	gen+2	gen+2	NOUN
ejpam-4028	321	7	)	)	PUNCT
ejpam-4028	321	8	]	]	PUNCT
ejpam-4028	321	9	then	then	ADV
ejpam-4028	321	10	,	,	PUNCT
ejpam-4028	321	11	(	(	PUNCT
ejpam-4028	321	12	9	9	X
ejpam-4028	321	13	)	)	PUNCT
ejpam-4028	321	14	is	be	AUX
ejpam-4028	321	15	reduced	reduce	VERB
ejpam-4028	321	16	to	to	PART
ejpam-4028	321	17	g̃(gen+1	g̃(gen+1	VERB
ejpam-4028	321	18	,	,	PUNCT
ejpam-4028	321	19	gen+2	gen+2	NOUN
ejpam-4028	321	20	,	,	PUNCT
ejpam-4028	321	21	gen+2)≤̃¯̄a	gen+2)≤̃¯̄a	PROPN
ejpam-4028	321	22	[	[	PUNCT
ejpam-4028	321	23	g̃(gen	g̃(gen	PROPN
ejpam-4028	321	24	,	,	PUNCT
ejpam-4028	321	25	gen+1	gen+1	NOUN
ejpam-4028	321	26	,	,	PUNCT
ejpam-4028	321	27	gen+1	gen+1	NOUN
ejpam-4028	321	28	)	)	PUNCT
ejpam-4028	322	1	+	+	CCONJ
ejpam-4028	322	2	g̃(gen	g̃(gen	PROPN
ejpam-4028	322	3	,	,	PUNCT
ejpam-4028	322	4	gen+2	gen+2	NOUN
ejpam-4028	322	5	,	,	PUNCT
ejpam-4028	322	6	gen+2	gen+2	NOUN
ejpam-4028	322	7	)	)	PUNCT
ejpam-4028	322	8	]	]	PUNCT
ejpam-4028	323	1	⇒	⇒	PROPN
ejpam-4028	323	2	g̃(gen+1	g̃(gen+1	PROPN
ejpam-4028	323	3	,	,	PUNCT
ejpam-4028	323	4	gen+2	gen+2	NOUN
ejpam-4028	323	5	,	,	PUNCT
ejpam-4028	323	6	gen+2)≤̃	gen+2)≤̃	PROPN
ejpam-4028	323	7	¯̄a	¯̄a	PROPN
ejpam-4028	323	8	1̃−˜̃a	1̃−˜̃a	ADV
ejpam-4028	323	9	g̃(gen	g̃(gen	PROPN
ejpam-4028	323	10	,	,	PUNCT
ejpam-4028	323	11	gen+1	gen+1	NOUN
ejpam-4028	323	12	,	,	PUNCT
ejpam-4028	323	13	gen+1	gen+1	NOUN
ejpam-4028	323	14	)	)	PUNCT
ejpam-4028	323	15	case	case	NOUN
ejpam-4028	323	16	(	(	PUNCT
ejpam-4028	323	17	2	2	NUM
ejpam-4028	323	18	):	):	PUNCT
ejpam-4028	323	19	if	if	SCONJ
ejpam-4028	323	20	max	max	PROPN
ejpam-4028	323	21	{	{	PUNCT
ejpam-4028	323	22	[	[	PUNCT
ejpam-4028	323	23	g̃(gen	g̃(gen	PROPN
ejpam-4028	323	24	,	,	PUNCT
ejpam-4028	323	25	gen+1	gen+1	NOUN
ejpam-4028	323	26	,	,	PUNCT
ejpam-4028	323	27	gen+1	gen+1	NOUN
ejpam-4028	323	28	)	)	PUNCT
ejpam-4028	323	29	+	+	CCONJ
ejpam-4028	323	30	g̃(gen	g̃(gen	PROPN
ejpam-4028	323	31	,	,	PUNCT
ejpam-4028	323	32	gen+2	gen+2	NOUN
ejpam-4028	323	33	,	,	PUNCT
ejpam-4028	323	34	gen+2	gen+2	NOUN
ejpam-4028	323	35	)	)	PUNCT
ejpam-4028	323	36	]	]	PUNCT
ejpam-4028	323	37	,	,	PUNCT
ejpam-4028	323	38	g̃(gen	g̃(gen	PROPN
ejpam-4028	323	39	,	,	PUNCT
ejpam-4028	323	40	gen+1	gen+1	NOUN
ejpam-4028	323	41	,	,	PUNCT
ejpam-4028	323	42	gen+1	gen+1	NOUN
ejpam-4028	323	43	)	)	PUNCT
ejpam-4028	323	44	,	,	PUNCT
ejpam-4028	323	45	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	323	46	,	,	PUNCT
ejpam-4028	323	47	gen+2	gen+2	NOUN
ejpam-4028	323	48	,	,	PUNCT
ejpam-4028	323	49	gen+2	gen+2	NOUN
ejpam-4028	323	50	)	)	PUNCT
ejpam-4028	323	51	}	}	PUNCT
ejpam-4028	324	1	=	=	SYM
ejpam-4028	324	2	g̃(gen	g̃(gen	PROPN
ejpam-4028	324	3	,	,	PUNCT
ejpam-4028	324	4	gen+1	gen+1	NOUN
ejpam-4028	324	5	,	,	PUNCT
ejpam-4028	324	6	gen+1	gen+1	NOUN
ejpam-4028	324	7	)	)	PUNCT
ejpam-4028	324	8	then	then	ADV
ejpam-4028	324	9	,	,	PUNCT
ejpam-4028	324	10	(	(	PUNCT
ejpam-4028	324	11	9	9	X
ejpam-4028	324	12	)	)	PUNCT
ejpam-4028	324	13	is	be	AUX
ejpam-4028	324	14	reduced	reduce	VERB
ejpam-4028	324	15	to	to	ADP
ejpam-4028	324	16	⇒	⇒	NOUN
ejpam-4028	324	17	g̃(gen+1	g̃(gen+1	PROPN
ejpam-4028	324	18	,	,	PUNCT
ejpam-4028	324	19	gen+2	gen+2	NOUN
ejpam-4028	324	20	,	,	PUNCT
ejpam-4028	324	21	gen+2)≤̃¯̄ag̃(gen	gen+2)≤̃¯̄ag̃(gen	X
ejpam-4028	324	22	,	,	PUNCT
ejpam-4028	324	23	gen+1	gen+1	NOUN
ejpam-4028	324	24	,	,	PUNCT
ejpam-4028	324	25	gen+1	gen+1	NOUN
ejpam-4028	324	26	)	)	PUNCT
ejpam-4028	324	27	case	case	NOUN
ejpam-4028	324	28	(	(	PUNCT
ejpam-4028	324	29	3	3	NUM
ejpam-4028	324	30	):	):	PUNCT
ejpam-4028	324	31	ifmax	ifmax	X
ejpam-4028	324	32	{	{	PUNCT
ejpam-4028	324	33	[	[	PUNCT
ejpam-4028	324	34	g̃(gen	g̃(gen	PROPN
ejpam-4028	324	35	,	,	PUNCT
ejpam-4028	324	36	gen+1	gen+1	NOUN
ejpam-4028	324	37	,	,	PUNCT
ejpam-4028	324	38	gen+1	gen+1	NOUN
ejpam-4028	324	39	)	)	PUNCT
ejpam-4028	325	1	+	+	CCONJ
ejpam-4028	325	2	g̃(gen	g̃(gen	PROPN
ejpam-4028	325	3	,	,	PUNCT
ejpam-4028	325	4	gen+2	gen+2	NOUN
ejpam-4028	325	5	,	,	PUNCT
ejpam-4028	325	6	gen+2	gen+2	NOUN
ejpam-4028	325	7	)	)	PUNCT
ejpam-4028	325	8	]	]	PUNCT
ejpam-4028	325	9	,	,	PUNCT
ejpam-4028	325	10	g̃(gen	g̃(gen	PROPN
ejpam-4028	325	11	,	,	PUNCT
ejpam-4028	325	12	gen+1	gen+1	NOUN
ejpam-4028	325	13	,	,	PUNCT
ejpam-4028	325	14	gen+1	gen+1	NOUN
ejpam-4028	325	15	)	)	PUNCT
ejpam-4028	325	16	,	,	PUNCT
ejpam-4028	325	17	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	325	18	,	,	PUNCT
ejpam-4028	325	19	gen+2	gen+2	NOUN
ejpam-4028	325	20	,	,	PUNCT
ejpam-4028	325	21	gen+2	gen+2	NOUN
ejpam-4028	325	22	)	)	PUNCT
ejpam-4028	325	23	}	}	PUNCT
ejpam-4028	325	24	=	=	SYM
ejpam-4028	325	25	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	325	26	,	,	PUNCT
ejpam-4028	325	27	gen+2	gen+2	NOUN
ejpam-4028	325	28	,	,	PUNCT
ejpam-4028	325	29	gen+2	gen+2	NOUN
ejpam-4028	325	30	)	)	PUNCT
ejpam-4028	325	31	a.	a.	PROPN
ejpam-4028	325	32	f.	f.	PROPN
ejpam-4028	325	33	sayed	say	VERB
ejpam-4028	325	34	,	,	PUNCT
ejpam-4028	325	35	a.	a.	NOUN
ejpam-4028	325	36	alahmari	alahmari	PROPN
ejpam-4028	325	37	/	/	SYM
ejpam-4028	325	38	eur	eur	PROPN
ejpam-4028	325	39	.	.	PUNCT
ejpam-4028	326	1	j.	j.	PROPN
ejpam-4028	326	2	pure	pure	PROPN
ejpam-4028	326	3	appl	appl	PROPN
ejpam-4028	326	4	.	.	PROPN
ejpam-4028	326	5	math	math	PROPN
ejpam-4028	326	6	,	,	PUNCT
ejpam-4028	326	7	14	14	NUM
ejpam-4028	326	8	(	(	PUNCT
ejpam-4028	326	9	3	3	NUM
ejpam-4028	326	10	)	)	PUNCT
ejpam-4028	326	11	(	(	PUNCT
ejpam-4028	326	12	2021	2021	NUM
ejpam-4028	326	13	)	)	PUNCT
ejpam-4028	326	14	,	,	PUNCT
ejpam-4028	326	15	923	923	NUM
ejpam-4028	326	16	-	-	SYM
ejpam-4028	326	17	941	941	NUM
ejpam-4028	326	18	938	938	NUM
ejpam-4028	326	19	then	then	ADV
ejpam-4028	326	20	,	,	PUNCT
ejpam-4028	326	21	(	(	PUNCT
ejpam-4028	326	22	9	9	X
ejpam-4028	326	23	)	)	PUNCT
ejpam-4028	326	24	is	be	AUX
ejpam-4028	326	25	reduced	reduce	VERB
ejpam-4028	326	26	to	to	PART
ejpam-4028	326	27	g̃(gen+1	g̃(gen+1	VERB
ejpam-4028	326	28	,	,	PUNCT
ejpam-4028	326	29	gen+2	gen+2	NOUN
ejpam-4028	326	30	,	,	PUNCT
ejpam-4028	326	31	gen+2)≤̃¯̄ag̃(gen+1	gen+2)≤̃¯̄ag̃(gen+1	PROPN
ejpam-4028	326	32	,	,	PUNCT
ejpam-4028	326	33	gen+2	gen+2	NOUN
ejpam-4028	326	34	,	,	PUNCT
ejpam-4028	326	35	gen+2	gen+2	NOUN
ejpam-4028	326	36	)	)	PUNCT
ejpam-4028	326	37	,	,	PUNCT
ejpam-4028	326	38	which	which	PRON
ejpam-4028	326	39	is	be	AUX
ejpam-4028	326	40	a	a	DET
ejpam-4028	326	41	contradiction	contradiction	NOUN
ejpam-4028	326	42	.	.	PUNCT
ejpam-4028	327	1	from	from	ADP
ejpam-4028	327	2	cases	case	NOUN
ejpam-4028	327	3	(	(	PUNCT
ejpam-4028	327	4	1	1	NUM
ejpam-4028	327	5	)	)	PUNCT
ejpam-4028	327	6	,	,	PUNCT
ejpam-4028	327	7	(	(	PUNCT
ejpam-4028	327	8	2	2	X
ejpam-4028	327	9	)	)	PUNCT
ejpam-4028	327	10	and	and	CCONJ
ejpam-4028	327	11	(	(	PUNCT
ejpam-4028	327	12	3	3	NUM
ejpam-4028	327	13	)	)	PUNCT
ejpam-4028	327	14	;	;	PUNCT
ejpam-4028	327	15	we	we	PRON
ejpam-4028	327	16	have	have	VERB
ejpam-4028	327	17	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	327	18	,	,	PUNCT
ejpam-4028	327	19	gen+2	gen+2	NOUN
ejpam-4028	327	20	,	,	PUNCT
ejpam-4028	327	21	gen+2)≤̃¯̄ag̃(gen	gen+2)≤̃¯̄ag̃(gen	X
ejpam-4028	327	22	,	,	PUNCT
ejpam-4028	327	23	gen+1	gen+1	NOUN
ejpam-4028	327	24	,	,	PUNCT
ejpam-4028	327	25	gen+1	gen+1	NOUN
ejpam-4028	327	26	)	)	PUNCT
ejpam-4028	327	27	on	on	ADP
ejpam-4028	327	28	continuing	continue	VERB
ejpam-4028	327	29	this	this	DET
ejpam-4028	327	30	process	process	NOUN
ejpam-4028	327	31	(	(	PUNCT
ejpam-4028	327	32	n+	n+	NOUN
ejpam-4028	327	33	1	1	NUM
ejpam-4028	327	34	)	)	PUNCT
ejpam-4028	327	35	times	time	NOUN
ejpam-4028	327	36	;	;	PUNCT
ejpam-4028	327	37	we	we	PRON
ejpam-4028	327	38	have	have	VERB
ejpam-4028	327	39	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	327	40	,	,	PUNCT
ejpam-4028	327	41	gen+2	gen+2	NOUN
ejpam-4028	327	42	,	,	PUNCT
ejpam-4028	327	43	gen+2)≤̃¯̄an+1g̃(ge0	gen+2)≤̃¯̄an+1g̃(ge0	NOUN
ejpam-4028	327	44	,	,	PUNCT
ejpam-4028	327	45	ge1	ge1	NOUN
ejpam-4028	327	46	,	,	PUNCT
ejpam-4028	327	47	ge1	ge1	NOUN
ejpam-4028	327	48	)	)	PUNCT
ejpam-4028	327	49	similarly	similarly	ADV
ejpam-4028	327	50	,	,	PUNCT
ejpam-4028	327	51	we	we	PRON
ejpam-4028	327	52	will	will	AUX
ejpam-4028	327	53	conclude	conclude	VERB
ejpam-4028	327	54	that	that	SCONJ
ejpam-4028	327	55	g̃(gen	g̃(gen	PROPN
ejpam-4028	327	56	,	,	PUNCT
ejpam-4028	327	57	gen+1	gen+1	NOUN
ejpam-4028	327	58	,	,	PUNCT
ejpam-4028	327	59	gen)≤̃¯̄ag̃(gen	gen)≤̃¯̄ag̃(gen	INTJ
ejpam-4028	327	60	,	,	PUNCT
ejpam-4028	327	61	gen+1	gen+1	NOUN
ejpam-4028	327	62	,	,	PUNCT
ejpam-4028	327	63	gen+1	gen+1	NOUN
ejpam-4028	327	64	)	)	PUNCT
ejpam-4028	327	65	next	next	ADV
ejpam-4028	327	66	,	,	PUNCT
ejpam-4028	327	67	we	we	PRON
ejpam-4028	327	68	show	show	VERB
ejpam-4028	327	69	that	that	SCONJ
ejpam-4028	327	70	{	{	PUNCT
ejpam-4028	327	71	gen}n∈n	gen}n∈n	NOUN
ejpam-4028	327	72	is	be	AUX
ejpam-4028	327	73	a	a	DET
ejpam-4028	327	74	fuzzy	fuzzy	ADJ
ejpam-4028	327	75	soft	soft	ADJ
ejpam-4028	327	76	g	g	NOUN
ejpam-4028	327	77	-	-	PUNCT
ejpam-4028	327	78	cauchy	cauchy	ADJ
ejpam-4028	327	79	sequence	sequence	NOUN
ejpam-4028	327	80	.	.	PUNCT
ejpam-4028	328	1	then	then	ADV
ejpam-4028	328	2	for	for	ADP
ejpam-4028	328	3	all	all	DET
ejpam-4028	328	4	n	n	CCONJ
ejpam-4028	328	5	,	,	PUNCT
ejpam-4028	328	6	m	m	VERB
ejpam-4028	328	7	∈	∈	PROPN
ejpam-4028	328	8	n	n	CCONJ
ejpam-4028	328	9	,	,	PUNCT
ejpam-4028	328	10	n	n	CCONJ
ejpam-4028	328	11	<	<	X
ejpam-4028	328	12	m	m	PROPN
ejpam-4028	328	13	,	,	PUNCT
ejpam-4028	328	14	we	we	PRON
ejpam-4028	328	15	have	have	VERB
ejpam-4028	328	16	g̃(gen	g̃(gen	PROPN
ejpam-4028	328	17	,	,	PUNCT
ejpam-4028	328	18	gem	gem	NOUN
ejpam-4028	328	19	,	,	PUNCT
ejpam-4028	328	20	gem)≤̃g̃(gen	gem)≤̃g̃(gen	NOUN
ejpam-4028	328	21	,	,	PUNCT
ejpam-4028	328	22	gen+1	gen+1	NOUN
ejpam-4028	328	23	,	,	PUNCT
ejpam-4028	328	24	gen+1	gen+1	NOUN
ejpam-4028	328	25	)	)	PUNCT
ejpam-4028	329	1	+	+	CCONJ
ejpam-4028	329	2	g̃(gen+1	g̃(gen+1	NOUN
ejpam-4028	329	3	,	,	PUNCT
ejpam-4028	329	4	gen+2	gen+2	NOUN
ejpam-4028	329	5	,	,	PUNCT
ejpam-4028	329	6	gen+2	gen+2	NOUN
ejpam-4028	329	7	)	)	PUNCT
ejpam-4028	330	1	+	+	CCONJ
ejpam-4028	330	2	...	...	PUNCT
ejpam-4028	331	1	+	+	CCONJ
ejpam-4028	331	2	g̃(gem−1	g̃(gem−1	NOUN
ejpam-4028	331	3	,	,	PUNCT
ejpam-4028	331	4	gem	gem	NOUN
ejpam-4028	331	5	,	,	PUNCT
ejpam-4028	331	6	gem	gem	NOUN
ejpam-4028	331	7	)	)	PUNCT
ejpam-4028	331	8	≤̃(¯̄an	≤̃(¯̄an	NOUN
ejpam-4028	331	9	+	+	CCONJ
ejpam-4028	331	10	¯̄a(n+1	¯̄a(n+1	NOUN
ejpam-4028	331	11	)	)	PUNCT
ejpam-4028	332	1	+	+	CCONJ
ejpam-4028	332	2	...	...	PUNCT
ejpam-4028	333	1	+	+	CCONJ
ejpam-4028	333	2	¯̄amg̃(ge0	¯̄amg̃(ge0	ADJ
ejpam-4028	333	3	,	,	PUNCT
ejpam-4028	333	4	ge1	ge1	NOUN
ejpam-4028	333	5	,	,	PUNCT
ejpam-4028	333	6	ge1	ge1	NOUN
ejpam-4028	333	7	)	)	PUNCT
ejpam-4028	333	8	≤̃	≤̃	PROPN
ejpam-4028	333	9	¯̄an	¯̄an	PROPN
ejpam-4028	333	10	1̃−¯̄a	1̃−¯̄a	PROPN
ejpam-4028	333	11	g̃(ge0	g̃(ge0	PROPN
ejpam-4028	333	12	,	,	PUNCT
ejpam-4028	333	13	ge1	ge1	NOUN
ejpam-4028	333	14	,	,	PUNCT
ejpam-4028	333	15	ge1	ge1	PROPN
ejpam-4028	333	16	)	)	PUNCT
ejpam-4028	333	17	.	.	PUNCT
ejpam-4028	334	1	hence	hence	ADV
ejpam-4028	334	2	,	,	PUNCT
ejpam-4028	334	3	{	{	PUNCT
ejpam-4028	334	4	gen}n∈n	gen}n∈n	PROPN
ejpam-4028	334	5	is	be	AUX
ejpam-4028	334	6	a	a	DET
ejpam-4028	334	7	fuzzy	fuzzy	ADJ
ejpam-4028	334	8	soft	soft	ADJ
ejpam-4028	334	9	g	g	NOUN
ejpam-4028	334	10	-	-	PUNCT
ejpam-4028	334	11	cauchy	cauchy	ADJ
ejpam-4028	334	12	sequence	sequence	NOUN
ejpam-4028	334	13	.	.	PUNCT
ejpam-4028	335	1	since	since	SCONJ
ejpam-4028	335	2	(	(	PUNCT
ejpam-4028	335	3	ẽ	ẽ	PROPN
ejpam-4028	335	4	,	,	PUNCT
ejpam-4028	335	5	g̃	g̃	PROPN
ejpam-4028	335	6	)	)	PUNCT
ejpam-4028	335	7	is	be	AUX
ejpam-4028	335	8	fuzzy	fuzzy	ADJ
ejpam-4028	335	9	soft	soft	ADJ
ejpam-4028	335	10	g	g	NOUN
ejpam-4028	335	11	-	-	PUNCT
ejpam-4028	335	12	complete	complete	ADJ
ejpam-4028	335	13	,	,	PUNCT
ejpam-4028	335	14	there	there	PRON
ejpam-4028	335	15	exists	exist	VERB
ejpam-4028	335	16	fe∈̃fsc(ẽ	fe∈̃fsc(ẽ	PROPN
ejpam-4028	335	17	)	)	PUNCT
ejpam-4028	335	18	such	such	ADJ
ejpam-4028	335	19	that	that	SCONJ
ejpam-4028	335	20	{	{	PUNCT
ejpam-4028	335	21	gen}n∈n	gen}n∈n	PROPN
ejpam-4028	335	22	fuzzy	fuzzy	ADJ
ejpam-4028	335	23	soft	soft	ADJ
ejpam-4028	335	24	g	g	NOUN
ejpam-4028	335	25	-	-	PUNCT
ejpam-4028	335	26	converges	converge	NOUN
ejpam-4028	335	27	to	to	ADP
ejpam-4028	335	28	fe	fe	PROPN
ejpam-4028	335	29	.	.	PUNCT
ejpam-4028	336	1	next	next	ADV
ejpam-4028	336	2	,	,	PUNCT
ejpam-4028	336	3	we	we	PRON
ejpam-4028	336	4	will	will	AUX
ejpam-4028	336	5	show	show	VERB
ejpam-4028	336	6	that	that	SCONJ
ejpam-4028	336	7	fe	fe	PROPN
ejpam-4028	336	8	is	be	AUX
ejpam-4028	336	9	a	a	DET
ejpam-4028	336	10	fixed	fix	VERB
ejpam-4028	336	11	point	point	NOUN
ejpam-4028	336	12	of	of	ADP
ejpam-4028	336	13	t	t	PROPN
ejpam-4028	336	14	.	.	PUNCT
ejpam-4028	337	1	for	for	ADP
ejpam-4028	337	2	this	this	PRON
ejpam-4028	337	3	,	,	PUNCT
ejpam-4028	337	4	we	we	PRON
ejpam-4028	337	5	take	take	VERB
ejpam-4028	337	6	fe1	fe1	PROPN
ejpam-4028	337	7	=	=	SYM
ejpam-4028	337	8	gen	gen	PROPN
ejpam-4028	337	9	and	and	CCONJ
ejpam-4028	337	10	fe2	fe2	PROPN
ejpam-4028	337	11	=	=	SYM
ejpam-4028	337	12	fe3	fe3	PROPN
ejpam-4028	337	13	=	=	SYM
ejpam-4028	337	14	fe	fe	X
ejpam-4028	337	15	in	in	ADP
ejpam-4028	337	16	(	(	PUNCT
ejpam-4028	337	17	8)	8)	NUM
ejpam-4028	337	18	,	,	PUNCT
ejpam-4028	337	19	then	then	ADV
ejpam-4028	337	20	g̃(tgen	g̃(tgen	ADJ
ejpam-4028	337	21	,	,	PUNCT
ejpam-4028	337	22	tfe	tfe	NOUN
ejpam-4028	337	23	,	,	PUNCT
ejpam-4028	337	24	tfe)≤̃¯̄a	tfe)≤̃¯̄a	NOUN
ejpam-4028	337	25	max	max	PROPN
ejpam-4028	337	26			PROPN
ejpam-4028	337	27	[	[	PUNCT
ejpam-4028	337	28	g̃(gen	g̃(gen	PROPN
ejpam-4028	337	29	,	,	PUNCT
ejpam-4028	337	30	t	t	PROPN
ejpam-4028	337	31	gen	gen	PROPN
ejpam-4028	337	32	,	,	PUNCT
ejpam-4028	337	33	t	t	PROPN
ejpam-4028	337	34	gen	gen	PROPN
ejpam-4028	337	35	)	)	PUNCT
ejpam-4028	338	1	+	+	CCONJ
ejpam-4028	338	2	g̃(gen	g̃(gen	PROPN
ejpam-4028	338	3	,	,	PUNCT
ejpam-4028	338	4	tfe	tfe	NOUN
ejpam-4028	338	5	,	,	PUNCT
ejpam-4028	338	6	tfe	tfe	NOUN
ejpam-4028	338	7	)	)	PUNCT
ejpam-4028	338	8	]	]	PUNCT
ejpam-4028	338	9	,	,	PUNCT
ejpam-4028	338	10	g̃(gen	g̃(gen	PROPN
ejpam-4028	338	11	,	,	PUNCT
ejpam-4028	338	12	fe	fe	PROPN
ejpam-4028	338	13	,	,	PUNCT
ejpam-4028	338	14	fe	fe	NOUN
ejpam-4028	338	15	)	)	PUNCT
ejpam-4028	338	16	,	,	PUNCT
ejpam-4028	338	17	[	[	PUNCT
ejpam-4028	338	18	g̃(fe	g̃(fe	NOUN
ejpam-4028	338	19	,	,	PUNCT
ejpam-4028	338	20	tfe	tfe	NOUN
ejpam-4028	338	21	,	,	PUNCT
ejpam-4028	338	22	tfe	tfe	NOUN
ejpam-4028	338	23	)	)	PUNCT
ejpam-4028	338	24	+	+	CCONJ
ejpam-4028	339	1	g̃(fe	g̃(fe	NOUN
ejpam-4028	339	2	,	,	PUNCT
ejpam-4028	339	3	t	t	PROPN
ejpam-4028	339	4	gen	gen	PROPN
ejpam-4028	339	5	,	,	PUNCT
ejpam-4028	339	6	t	t	PROPN
ejpam-4028	339	7	gen	gen	PROPN
ejpam-4028	339	8	)	)	PUNCT
ejpam-4028	339	9	]	]	PUNCT
ejpam-4028	340	1			PROPN
ejpam-4028	340	2	⇒	⇒	PROPN
ejpam-4028	340	3	g̃(fe	g̃(fe	NOUN
ejpam-4028	340	4	,	,	PUNCT
ejpam-4028	340	5	t	t	PROPN
ejpam-4028	340	6	fe	fe	PROPN
ejpam-4028	340	7	,	,	PUNCT
ejpam-4028	340	8	t	t	PROPN
ejpam-4028	340	9	fe)≤̃¯̄a	fe)≤̃¯̄a	PROPN
ejpam-4028	340	10	max	max	PROPN
ejpam-4028	340	11			PROPN
ejpam-4028	340	12	[	[	PUNCT
ejpam-4028	340	13	g̃(fe	g̃(fe	NOUN
ejpam-4028	340	14	,	,	PUNCT
ejpam-4028	340	15	fe	fe	X
ejpam-4028	340	16	,	,	PUNCT
ejpam-4028	340	17	fe	fe	X
ejpam-4028	340	18	)	)	PUNCT
ejpam-4028	340	19	+	+	CCONJ
ejpam-4028	340	20	g̃(fe	g̃(fe	NOUN
ejpam-4028	340	21	,	,	PUNCT
ejpam-4028	340	22	tfe	tfe	NOUN
ejpam-4028	340	23	,	,	PUNCT
ejpam-4028	340	24	t	t	PROPN
ejpam-4028	340	25	fe	fe	PROPN
ejpam-4028	340	26	)	)	PUNCT
ejpam-4028	340	27	]	]	PUNCT
ejpam-4028	340	28	,	,	PUNCT
ejpam-4028	340	29	g̃(fe	g̃(fe	NOUN
ejpam-4028	340	30	,	,	PUNCT
ejpam-4028	340	31	fe	fe	X
ejpam-4028	340	32	,	,	PUNCT
ejpam-4028	340	33	fe	fe	NOUN
ejpam-4028	340	34	)	)	PUNCT
ejpam-4028	340	35	,	,	PUNCT
ejpam-4028	340	36	[	[	PUNCT
ejpam-4028	340	37	g̃(fe	g̃(fe	NOUN
ejpam-4028	340	38	,	,	PUNCT
ejpam-4028	340	39	t	t	PROPN
ejpam-4028	340	40	fe	fe	PROPN
ejpam-4028	340	41	,	,	PUNCT
ejpam-4028	340	42	t	t	PROPN
ejpam-4028	340	43	fe	fe	X
ejpam-4028	340	44	)	)	PUNCT
ejpam-4028	340	45	+	+	CCONJ
ejpam-4028	340	46	g̃(fe	g̃(fe	NOUN
ejpam-4028	340	47	,	,	PUNCT
ejpam-4028	340	48	fe	fe	X
ejpam-4028	340	49	,	,	PUNCT
ejpam-4028	340	50	fe	fe	X
ejpam-4028	340	51	)	)	PUNCT
ejpam-4028	340	52	]	]	PUNCT
ejpam-4028	341	1			PROPN
ejpam-4028	341	2	⇒	⇒	PROPN
ejpam-4028	341	3	g̃(fe	g̃(fe	NOUN
ejpam-4028	341	4	,	,	PUNCT
ejpam-4028	341	5	t	t	PROPN
ejpam-4028	341	6	fe	fe	PROPN
ejpam-4028	341	7	,	,	PUNCT
ejpam-4028	341	8	t	t	PROPN
ejpam-4028	341	9	fe)≤̃¯̄ag̃(fe	fe)≤̃¯̄ag̃(fe	PROPN
ejpam-4028	341	10	,	,	PUNCT
ejpam-4028	341	11	t	t	PROPN
ejpam-4028	341	12	fe	fe	PROPN
ejpam-4028	341	13	,	,	PUNCT
ejpam-4028	341	14	t	t	PROPN
ejpam-4028	341	15	fe	fe	PROPN
ejpam-4028	341	16	)	)	PUNCT
ejpam-4028	341	17	⇒	⇒	PROPN
ejpam-4028	341	18	(	(	PUNCT
ejpam-4028	341	19	1̃−	1̃−	NUM
ejpam-4028	341	20	¯̄a)g̃(fe	¯̄a)g̃(fe	NOUN
ejpam-4028	341	21	,	,	PUNCT
ejpam-4028	341	22	t	t	PROPN
ejpam-4028	341	23	fe	fe	PROPN
ejpam-4028	341	24	,	,	PUNCT
ejpam-4028	341	25	t	t	PROPN
ejpam-4028	341	26	fe)≤̃0̃	fe)≤̃0̃	VERB
ejpam-4028	341	27	this	this	PRON
ejpam-4028	341	28	is	be	AUX
ejpam-4028	341	29	a	a	DET
ejpam-4028	341	30	contradiction	contradiction	NOUN
ejpam-4028	341	31	,	,	PUNCT
ejpam-4028	341	32	so	so	ADV
ejpam-4028	341	33	tfe	tfe	NOUN
ejpam-4028	341	34	=	=	SYM
ejpam-4028	341	35	fe	fe	X
ejpam-4028	341	36	i.e.	i.e.	X
ejpam-4028	341	37	fe	fe	X
ejpam-4028	341	38	is	be	AUX
ejpam-4028	341	39	a	a	DET
ejpam-4028	341	40	fixed	fix	VERB
ejpam-4028	341	41	point	point	NOUN
ejpam-4028	341	42	of	of	ADP
ejpam-4028	341	43	t	t	PROPN
ejpam-4028	341	44	.	.	PUNCT
ejpam-4028	342	1	now	now	ADV
ejpam-4028	342	2	,	,	PUNCT
ejpam-4028	342	3	to	to	PART
ejpam-4028	342	4	prove	prove	VERB
ejpam-4028	342	5	uniqueness	uniqueness	NOUN
ejpam-4028	342	6	,	,	PUNCT
ejpam-4028	342	7	assume	assume	VERB
ejpam-4028	342	8	that	that	SCONJ
ejpam-4028	342	9	fe	fe	PROPN
ejpam-4028	342	10	and	and	CCONJ
ejpam-4028	342	11	ge	ge	PROPN
ejpam-4028	342	12	are	be	AUX
ejpam-4028	342	13	two	two	NUM
ejpam-4028	342	14	fixed	fix	VERB
ejpam-4028	342	15	points	point	NOUN
ejpam-4028	342	16	of	of	ADP
ejpam-4028	342	17	t	t	PROPN
ejpam-4028	342	18	.	.	PUNCT
ejpam-4028	343	1	then	then	ADV
ejpam-4028	343	2	by	by	ADP
ejpam-4028	343	3	inequality	inequality	NOUN
ejpam-4028	343	4	(	(	PUNCT
ejpam-4028	343	5	8)	8)	NUM
ejpam-4028	343	6	,	,	PUNCT
ejpam-4028	343	7	we	we	PRON
ejpam-4028	343	8	have	have	VERB
ejpam-4028	343	9	g̃(tfe	g̃(tfe	NOUN
ejpam-4028	343	10	,	,	PUNCT
ejpam-4028	343	11	t	t	PROPN
ejpam-4028	343	12	ge	ge	PROPN
ejpam-4028	343	13	,	,	PUNCT
ejpam-4028	343	14	t	t	PROPN
ejpam-4028	343	15	ge)≤̃¯̄a	ge)≤̃¯̄a	PROPN
ejpam-4028	343	16	max	max	PROPN
ejpam-4028	343	17			PROPN
ejpam-4028	343	18	[	[	PUNCT
ejpam-4028	343	19	g̃(fe	g̃(fe	NOUN
ejpam-4028	343	20	,	,	PUNCT
ejpam-4028	343	21	tfe	tfe	NOUN
ejpam-4028	343	22	,	,	PUNCT
ejpam-4028	343	23	tfe	tfe	NOUN
ejpam-4028	343	24	)	)	PUNCT
ejpam-4028	343	25	+	+	CCONJ
ejpam-4028	343	26	g̃(fe	g̃(fe	NOUN
ejpam-4028	343	27	,	,	PUNCT
ejpam-4028	343	28	t	t	PROPN
ejpam-4028	343	29	ge	ge	PROPN
ejpam-4028	343	30	,	,	PUNCT
ejpam-4028	343	31	t	t	PROPN
ejpam-4028	343	32	ge	ge	PROPN
ejpam-4028	343	33	)	)	PUNCT
ejpam-4028	343	34	]	]	PUNCT
ejpam-4028	343	35	,	,	PUNCT
ejpam-4028	343	36	g̃(fe	g̃(fe	NOUN
ejpam-4028	343	37	,	,	PUNCT
ejpam-4028	343	38	ge	ge	PROPN
ejpam-4028	343	39	,	,	PUNCT
ejpam-4028	343	40	ge	ge	PROPN
ejpam-4028	343	41	)	)	PUNCT
ejpam-4028	343	42	,	,	PUNCT
ejpam-4028	343	43	[	[	PUNCT
ejpam-4028	343	44	g̃(ge	g̃(ge	NOUN
ejpam-4028	343	45	,	,	PUNCT
ejpam-4028	343	46	t	t	PROPN
ejpam-4028	343	47	ge	ge	PROPN
ejpam-4028	343	48	,	,	PUNCT
ejpam-4028	343	49	t	t	PROPN
ejpam-4028	343	50	ge	ge	PROPN
ejpam-4028	343	51	)	)	PUNCT
ejpam-4028	344	1	+	+	CCONJ
ejpam-4028	344	2	g̃(ge	g̃(ge	NOUN
ejpam-4028	344	3	,	,	PUNCT
ejpam-4028	344	4	t	t	PROPN
ejpam-4028	344	5	fe	fe	PROPN
ejpam-4028	344	6	,	,	PUNCT
ejpam-4028	344	7	t	t	PROPN
ejpam-4028	344	8	fe	fe	PROPN
ejpam-4028	344	9	)	)	PUNCT
ejpam-4028	344	10	]	]	PUNCT
ejpam-4028	345	1			PROPN
ejpam-4028	345	2	⇒	⇒	PROPN
ejpam-4028	345	3	g̃(fe	g̃(fe	NOUN
ejpam-4028	345	4	,	,	PUNCT
ejpam-4028	345	5	ge	ge	PROPN
ejpam-4028	345	6	,	,	PUNCT
ejpam-4028	345	7	ge)≤̃¯̄a	ge)≤̃¯̄a	PROPN
ejpam-4028	345	8	max	max	PROPN
ejpam-4028	345	9			PROPN
ejpam-4028	345	10	[	[	PUNCT
ejpam-4028	345	11	g̃(fe	g̃(fe	NOUN
ejpam-4028	345	12	,	,	PUNCT
ejpam-4028	345	13	fe	fe	X
ejpam-4028	345	14	,	,	PUNCT
ejpam-4028	345	15	fe	fe	X
ejpam-4028	345	16	)	)	PUNCT
ejpam-4028	345	17	+	+	CCONJ
ejpam-4028	345	18	g̃(fe	g̃(fe	NOUN
ejpam-4028	345	19	,	,	PUNCT
ejpam-4028	345	20	ge	ge	PROPN
ejpam-4028	345	21	,	,	PUNCT
ejpam-4028	345	22	ge	ge	PROPN
ejpam-4028	345	23	)	)	PUNCT
ejpam-4028	345	24	]	]	PUNCT
ejpam-4028	345	25	,	,	PUNCT
ejpam-4028	345	26	g̃(fe	g̃(fe	NOUN
ejpam-4028	345	27	,	,	PUNCT
ejpam-4028	345	28	ge	ge	PROPN
ejpam-4028	345	29	,	,	PUNCT
ejpam-4028	345	30	ge	ge	PROPN
ejpam-4028	345	31	)	)	PUNCT
ejpam-4028	345	32	,	,	PUNCT
ejpam-4028	345	33	[	[	PUNCT
ejpam-4028	345	34	g̃(ge	g̃(ge	NOUN
ejpam-4028	345	35	,	,	PUNCT
ejpam-4028	345	36	ge	ge	PROPN
ejpam-4028	345	37	,	,	PUNCT
ejpam-4028	345	38	ge	ge	PROPN
ejpam-4028	345	39	)	)	PUNCT
ejpam-4028	346	1	+	+	NUM
ejpam-4028	346	2	g̃(ge	g̃(ge	ADJ
ejpam-4028	346	3	,	,	PUNCT
ejpam-4028	346	4	fe	fe	X
ejpam-4028	346	5	,	,	PUNCT
ejpam-4028	346	6	fe	fe	X
ejpam-4028	346	7	)	)	PUNCT
ejpam-4028	346	8	]	]	PUNCT
ejpam-4028	347	1			PROPN
ejpam-4028	347	2	⇒	⇒	PROPN
ejpam-4028	347	3	g̃(fe	g̃(fe	NOUN
ejpam-4028	347	4	,	,	PUNCT
ejpam-4028	347	5	ge	ge	PROPN
ejpam-4028	347	6	,	,	PUNCT
ejpam-4028	347	7	ge)≤̃¯̄a	ge)≤̃¯̄a	PROPN
ejpam-4028	347	8	max	max	PROPN
ejpam-4028	347	9	{	{	PUNCT
ejpam-4028	347	10	g̃(fe	g̃(fe	PROPN
ejpam-4028	347	11	,	,	PUNCT
ejpam-4028	347	12	ge	ge	PROPN
ejpam-4028	347	13	,	,	PUNCT
ejpam-4028	347	14	ge	ge	PROPN
ejpam-4028	347	15	)	)	PUNCT
ejpam-4028	347	16	,	,	PUNCT
ejpam-4028	347	17	g̃(ge	g̃(ge	NOUN
ejpam-4028	347	18	,	,	PUNCT
ejpam-4028	347	19	fe	fe	X
ejpam-4028	347	20	,	,	PUNCT
ejpam-4028	347	21	fe	fe	NOUN
ejpam-4028	347	22	)	)	PUNCT
ejpam-4028	347	23	}	}	PUNCT
ejpam-4028	347	24	we	we	PRON
ejpam-4028	347	25	now	now	ADV
ejpam-4028	347	26	have	have	AUX
ejpam-4028	347	27	two	two	NUM
ejpam-4028	347	28	cases	case	NOUN
ejpam-4028	347	29	:	:	PUNCT
ejpam-4028	347	30	case	case	NOUN
ejpam-4028	347	31	(	(	PUNCT
ejpam-4028	347	32	i	i	NOUN
ejpam-4028	347	33	):	):	PUNCT
ejpam-4028	347	34	if	if	SCONJ
ejpam-4028	347	35	max	max	PROPN
ejpam-4028	347	36	{	{	PUNCT
ejpam-4028	347	37	g̃(fe	g̃(fe	PROPN
ejpam-4028	347	38	,	,	PUNCT
ejpam-4028	347	39	ge	ge	PROPN
ejpam-4028	347	40	,	,	PUNCT
ejpam-4028	347	41	ge	ge	PROPN
ejpam-4028	347	42	)	)	PUNCT
ejpam-4028	347	43	,	,	PUNCT
ejpam-4028	347	44	g̃(ge	g̃(ge	NOUN
ejpam-4028	347	45	,	,	PUNCT
ejpam-4028	347	46	fe	fe	X
ejpam-4028	347	47	,	,	PUNCT
ejpam-4028	347	48	fe	fe	NOUN
ejpam-4028	347	49	)	)	PUNCT
ejpam-4028	347	50	}	}	PUNCT
ejpam-4028	347	51	=	=	SYM
ejpam-4028	347	52	g̃(fe	g̃(fe	NOUN
ejpam-4028	347	53	,	,	PUNCT
ejpam-4028	347	54	ge	ge	PROPN
ejpam-4028	347	55	,	,	PUNCT
ejpam-4028	347	56	ge	ge	PROPN
ejpam-4028	347	57	)	)	PUNCT
ejpam-4028	347	58	,	,	PUNCT
ejpam-4028	347	59	then	then	ADV
ejpam-4028	347	60	we	we	PRON
ejpam-4028	347	61	get	get	VERB
ejpam-4028	347	62	references	reference	NOUN
ejpam-4028	347	63	939	939	NUM
ejpam-4028	347	64	g̃(fe	g̃(fe	NOUN
ejpam-4028	347	65	,	,	PUNCT
ejpam-4028	347	66	ge	ge	PROPN
ejpam-4028	347	67	,	,	PUNCT
ejpam-4028	347	68	ge)≤̃¯̄ag̃(fe	ge)≤̃¯̄ag̃(fe	NOUN
ejpam-4028	347	69	,	,	PUNCT
ejpam-4028	347	70	ge	ge	PROPN
ejpam-4028	347	71	,	,	PUNCT
ejpam-4028	347	72	ge	ge	PROPN
ejpam-4028	347	73	)	)	PUNCT
ejpam-4028	347	74	this	this	PRON
ejpam-4028	347	75	is	be	AUX
ejpam-4028	347	76	a	a	DET
ejpam-4028	347	77	contradiction	contradiction	NOUN
ejpam-4028	347	78	implies	imply	VERB
ejpam-4028	347	79	that	that	DET
ejpam-4028	347	80	fe	fe	X
ejpam-4028	347	81	=	=	PUNCT
ejpam-4028	347	82	ge	ge	PROPN
ejpam-4028	347	83	case	case	PROPN
ejpam-4028	347	84	(	(	PUNCT
ejpam-4028	347	85	ii	ii	NUM
ejpam-4028	347	86	):	):	PUNCT
ejpam-4028	347	87	if	if	SCONJ
ejpam-4028	347	88	max	max	PROPN
ejpam-4028	347	89	{	{	PUNCT
ejpam-4028	347	90	g̃(fe	g̃(fe	PROPN
ejpam-4028	347	91	,	,	PUNCT
ejpam-4028	347	92	ge	ge	PROPN
ejpam-4028	347	93	,	,	PUNCT
ejpam-4028	347	94	ge	ge	PROPN
ejpam-4028	347	95	)	)	PUNCT
ejpam-4028	347	96	,	,	PUNCT
ejpam-4028	347	97	g̃(ge	g̃(ge	NOUN
ejpam-4028	347	98	,	,	PUNCT
ejpam-4028	347	99	fe	fe	X
ejpam-4028	347	100	,	,	PUNCT
ejpam-4028	347	101	fe	fe	NOUN
ejpam-4028	347	102	)	)	PUNCT
ejpam-4028	347	103	}	}	PUNCT
ejpam-4028	347	104	=	=	SYM
ejpam-4028	347	105	g̃(ge	g̃(ge	NOUN
ejpam-4028	347	106	,	,	PUNCT
ejpam-4028	347	107	fe	fe	X
ejpam-4028	347	108	,	,	PUNCT
ejpam-4028	347	109	fe	fe	NOUN
ejpam-4028	347	110	)	)	PUNCT
ejpam-4028	347	111	,	,	PUNCT
ejpam-4028	347	112	then	then	ADV
ejpam-4028	347	113	we	we	PRON
ejpam-4028	347	114	get	get	VERB
ejpam-4028	347	115	g̃(fe	g̃(fe	ADJ
ejpam-4028	347	116	,	,	PUNCT
ejpam-4028	347	117	ge	ge	PROPN
ejpam-4028	347	118	,	,	PUNCT
ejpam-4028	347	119	ge)≤̃¯̄ag̃(ge	ge)≤̃¯̄ag̃(ge	PROPN
ejpam-4028	347	120	,	,	PUNCT
ejpam-4028	347	121	fe	fe	X
ejpam-4028	347	122	,	,	PUNCT
ejpam-4028	347	123	fe	fe	NOUN
ejpam-4028	347	124	)	)	PUNCT
ejpam-4028	347	125	so	so	ADV
ejpam-4028	347	126	,	,	PUNCT
ejpam-4028	347	127	we	we	PRON
ejpam-4028	347	128	deduct	deduct	VERB
ejpam-4028	347	129	that	that	DET
ejpam-4028	347	130	g̃(fe	g̃(fe	NOUN
ejpam-4028	347	131	,	,	PUNCT
ejpam-4028	347	132	ge	ge	PROPN
ejpam-4028	347	133	,	,	PUNCT
ejpam-4028	347	134	ge)≤̃¯̄ag̃(ge	ge)≤̃¯̄ag̃(ge	PROPN
ejpam-4028	347	135	,	,	PUNCT
ejpam-4028	347	136	fe	fe	X
ejpam-4028	347	137	,	,	PUNCT
ejpam-4028	347	138	fe	fe	NOUN
ejpam-4028	347	139	)	)	PUNCT
ejpam-4028	347	140	.	.	PUNCT
ejpam-4028	348	1	by	by	ADP
ejpam-4028	348	2	repeated	repeat	VERB
ejpam-4028	348	3	use	use	NOUN
ejpam-4028	348	4	of	of	ADP
ejpam-4028	348	5	the	the	DET
ejpam-4028	348	6	same	same	ADJ
ejpam-4028	348	7	argument	argument	NOUN
ejpam-4028	348	8	,	,	PUNCT
ejpam-4028	348	9	we	we	PRON
ejpam-4028	348	10	will	will	AUX
ejpam-4028	348	11	find	find	VERB
ejpam-4028	348	12	g̃(ge	g̃(ge	NOUN
ejpam-4028	348	13	,	,	PUNCT
ejpam-4028	348	14	fe	fe	NOUN
ejpam-4028	348	15	,	,	PUNCT
ejpam-4028	348	16	fe)≤̃¯̄ag̃(fe	fe)≤̃¯̄ag̃(fe	PROPN
ejpam-4028	348	17	,	,	PUNCT
ejpam-4028	348	18	ge	ge	PROPN
ejpam-4028	348	19	,	,	PUNCT
ejpam-4028	348	20	ge	ge	PROPN
ejpam-4028	348	21	)	)	PUNCT
ejpam-4028	348	22	.	.	PUNCT
ejpam-4028	349	1	therefore	therefore	ADV
ejpam-4028	349	2	,	,	PUNCT
ejpam-4028	349	3	we	we	PRON
ejpam-4028	349	4	get	get	VERB
ejpam-4028	349	5	g̃(fe	g̃(fe	ADJ
ejpam-4028	349	6	,	,	PUNCT
ejpam-4028	349	7	ge	ge	PROPN
ejpam-4028	349	8	,	,	PUNCT
ejpam-4028	349	9	ge)≤̃¯̄a2g̃(ge	ge)≤̃¯̄a2g̃(ge	NOUN
ejpam-4028	349	10	,	,	PUNCT
ejpam-4028	349	11	fe	fe	X
ejpam-4028	349	12	,	,	PUNCT
ejpam-4028	349	13	fe	fe	NOUN
ejpam-4028	349	14	)	)	PUNCT
ejpam-4028	349	15	.	.	PUNCT
ejpam-4028	350	1	since	since	SCONJ
ejpam-4028	350	2	¯̄a<̃	¯̄a<̃	NOUN
ejpam-4028	350	3	(	(	PUNCT
ejpam-4028	350	4	˜̃	˜̃	NOUN
ejpam-4028	350	5	1/2	1/2	NUM
ejpam-4028	350	6	)	)	PUNCT
ejpam-4028	350	7	,	,	PUNCT
ejpam-4028	350	8	this	this	PRON
ejpam-4028	350	9	is	be	AUX
ejpam-4028	350	10	a	a	DET
ejpam-4028	350	11	contradiction	contradiction	NOUN
ejpam-4028	350	12	implies	imply	VERB
ejpam-4028	350	13	that	that	PRON
ejpam-4028	350	14	fe	fe	X
ejpam-4028	350	15	=	=	PUNCT
ejpam-4028	350	16	ge	ge	PROPN
ejpam-4028	350	17	to	to	PART
ejpam-4028	350	18	show	show	VERB
ejpam-4028	350	19	that	that	SCONJ
ejpam-4028	350	20	t	t	PROPN
ejpam-4028	350	21	is	be	AUX
ejpam-4028	350	22	fuzzy	fuzzy	ADJ
ejpam-4028	350	23	soft	soft	ADJ
ejpam-4028	350	24	g	g	NOUN
ejpam-4028	350	25	-	-	NOUN
ejpam-4028	350	26	continuous	continuous	ADJ
ejpam-4028	350	27	at	at	ADP
ejpam-4028	350	28	fe	fe	NOUN
ejpam-4028	350	29	.	.	PUNCT
ejpam-4028	351	1	let	let	VERB
ejpam-4028	351	2	{	{	PUNCT
ejpam-4028	351	3	hen}n∈n	hen}n∈n	PRON
ejpam-4028	351	4	be	be	AUX
ejpam-4028	351	5	a	a	DET
ejpam-4028	351	6	sequence	sequence	NOUN
ejpam-4028	351	7	of	of	ADP
ejpam-4028	351	8	fuzzy	fuzzy	ADJ
ejpam-4028	351	9	soft	soft	ADJ
ejpam-4028	351	10	elements	element	NOUN
ejpam-4028	351	11	in	in	ADP
ejpam-4028	351	12	ẽ	ẽ	PROPN
ejpam-4028	351	13	such	such	ADJ
ejpam-4028	351	14	that	that	SCONJ
ejpam-4028	351	15	{	{	PUNCT
ejpam-4028	351	16	hen}n∈n	hen}n∈n	PROPN
ejpam-4028	351	17	→	→	SYM
ejpam-4028	351	18	fe	fe	PROPN
ejpam-4028	351	19	,	,	PUNCT
ejpam-4028	351	20	then	then	ADV
ejpam-4028	351	21	by	by	ADP
ejpam-4028	351	22	using	use	VERB
ejpam-4028	351	23	inequality	inequality	NOUN
ejpam-4028	351	24	(	(	PUNCT
ejpam-4028	351	25	8)	8)	NUM
ejpam-4028	351	26	,	,	PUNCT
ejpam-4028	351	27	we	we	PRON
ejpam-4028	351	28	can	can	AUX
ejpam-4028	351	29	deduce	deduce	VERB
ejpam-4028	351	30	that	that	DET
ejpam-4028	351	31	g̃(fe	g̃(fe	NOUN
ejpam-4028	351	32	,	,	PUNCT
ejpam-4028	351	33	then	then	ADV
ejpam-4028	351	34	,	,	PUNCT
ejpam-4028	351	35	then	then	ADV
ejpam-4028	351	36	)	)	PUNCT
ejpam-4028	352	1	=	=	SYM
ejpam-4028	352	2	g̃(tfe	g̃(tfe	NOUN
ejpam-4028	352	3	,	,	PUNCT
ejpam-4028	352	4	then	then	ADV
ejpam-4028	352	5	,	,	PUNCT
ejpam-4028	352	6	then)≤̃	then)≤̃	PROPN
ejpam-4028	352	7	¯̄a	¯̄a	PROPN
ejpam-4028	352	8	max	max	PROPN
ejpam-4028	352	9			PROPN
ejpam-4028	352	10	[	[	PUNCT
ejpam-4028	352	11	g̃(fe	g̃(fe	NOUN
ejpam-4028	352	12	,	,	PUNCT
ejpam-4028	352	13	tfe	tfe	NOUN
ejpam-4028	352	14	,	,	PUNCT
ejpam-4028	352	15	tfe	tfe	NOUN
ejpam-4028	352	16	)	)	PUNCT
ejpam-4028	352	17	+	+	CCONJ
ejpam-4028	352	18	g̃(fe	g̃(fe	NOUN
ejpam-4028	352	19	,	,	PUNCT
ejpam-4028	352	20	then	then	ADV
ejpam-4028	352	21	,	,	PUNCT
ejpam-4028	352	22	then	then	ADV
ejpam-4028	352	23	)	)	PUNCT
ejpam-4028	352	24	]	]	PUNCT
ejpam-4028	352	25	,	,	PUNCT
ejpam-4028	352	26	g̃(fe	g̃(fe	NOUN
ejpam-4028	352	27	,	,	PUNCT
ejpam-4028	352	28	hen	hen	NOUN
ejpam-4028	352	29	,	,	PUNCT
ejpam-4028	352	30	hen	hen	NOUN
ejpam-4028	352	31	)	)	PUNCT
ejpam-4028	352	32	,	,	PUNCT
ejpam-4028	352	33	[	[	PUNCT
ejpam-4028	352	34	g̃(hen	g̃(hen	ADV
ejpam-4028	352	35	,	,	PUNCT
ejpam-4028	352	36	then	then	ADV
ejpam-4028	352	37	,	,	PUNCT
ejpam-4028	352	38	then	then	ADV
ejpam-4028	352	39	)	)	PUNCT
ejpam-4028	353	1	+	+	CCONJ
ejpam-4028	353	2	g̃(hen	g̃(hen	ADV
ejpam-4028	353	3	,	,	PUNCT
ejpam-4028	353	4	t	t	PROPN
ejpam-4028	353	5	fe	fe	PROPN
ejpam-4028	353	6	,	,	PUNCT
ejpam-4028	353	7	t	t	PROPN
ejpam-4028	353	8	fe	fe	PROPN
ejpam-4028	353	9	)	)	PUNCT
ejpam-4028	353	10	]	]	PUNCT
ejpam-4028	354	1			PROPN
ejpam-4028	354	2	⇒	⇒	PROPN
ejpam-4028	354	3	g̃(fe	g̃(fe	NOUN
ejpam-4028	354	4	,	,	PUNCT
ejpam-4028	354	5	then	then	ADV
ejpam-4028	354	6	,	,	PUNCT
ejpam-4028	354	7	then)≤̃¯̄ag̃(fe	then)≤̃¯̄ag̃(fe	PROPN
ejpam-4028	354	8	,	,	PUNCT
ejpam-4028	354	9	then	then	ADV
ejpam-4028	354	10	,	,	PUNCT
ejpam-4028	354	11	then	then	ADV
ejpam-4028	354	12	)	)	PUNCT
ejpam-4028	354	13	⇒	⇒	NOUN
ejpam-4028	354	14	(	(	PUNCT
ejpam-4028	354	15	1̃−	1̃−	NUM
ejpam-4028	354	16	¯̄a)g̃(fe	¯̄a)g̃(fe	NOUN
ejpam-4028	354	17	,	,	PUNCT
ejpam-4028	354	18	then	then	ADV
ejpam-4028	354	19	,	,	PUNCT
ejpam-4028	354	20	then)≤̃0̃	then)≤̃0̃	PROPN
ejpam-4028	354	21	taking	take	VERB
ejpam-4028	354	22	the	the	DET
ejpam-4028	354	23	limit	limit	NOUN
ejpam-4028	354	24	as	as	ADP
ejpam-4028	354	25	n→∞	n→∞	NUM
ejpam-4028	354	26	from	from	ADP
ejpam-4028	354	27	which	which	PRON
ejpam-4028	354	28	,	,	PUNCT
ejpam-4028	354	29	we	we	PRON
ejpam-4028	354	30	see	see	VERB
ejpam-4028	354	31	that	that	DET
ejpam-4028	354	32	g̃(fe	g̃(fe	NOUN
ejpam-4028	354	33	,	,	PUNCT
ejpam-4028	354	34	then	then	ADV
ejpam-4028	354	35	,	,	PUNCT
ejpam-4028	354	36	then	then	ADV
ejpam-4028	354	37	)	)	PUNCT
ejpam-4028	354	38	→	→	SYM
ejpam-4028	354	39	0̃	0̃	NOUN
ejpam-4028	354	40	and	and	CCONJ
ejpam-4028	354	41	so	so	ADV
ejpam-4028	354	42	,	,	PUNCT
ejpam-4028	354	43	by	by	ADP
ejpam-4028	354	44	proposition	proposition	NOUN
ejpam-4028	354	45	(	(	PUNCT
ejpam-4028	354	46	4.1	4.1	NUM
ejpam-4028	354	47	)	)	PUNCT
ejpam-4028	354	48	in	in	ADP
ejpam-4028	354	49	[	[	X
ejpam-4028	354	50	2	2	X
ejpam-4028	354	51	]	]	PUNCT
ejpam-4028	354	52	we	we	PRON
ejpam-4028	354	53	have	have	VERB
ejpam-4028	354	54	that	that	SCONJ
ejpam-4028	354	55	the	the	DET
ejpam-4028	354	56	sequence	sequence	NOUN
ejpam-4028	354	57	{	{	PUNCT
ejpam-4028	354	58	then}n∈n	then}n∈n	PROPN
ejpam-4028	354	59	is	be	AUX
ejpam-4028	354	60	fuzzy	fuzzy	ADJ
ejpam-4028	354	61	soft	soft	ADJ
ejpam-4028	354	62	g	g	NOUN
ejpam-4028	354	63	-	-	PUNCT
ejpam-4028	354	64	convergent	convergent	NOUN
ejpam-4028	354	65	to	to	ADP
ejpam-4028	354	66	tfe	tfe	NOUN
ejpam-4028	354	67	=	=	SYM
ejpam-4028	354	68	fe	fe	X
ejpam-4028	354	69	,	,	PUNCT
ejpam-4028	354	70	therefore	therefore	ADV
ejpam-4028	354	71	proposition	proposition	NOUN
ejpam-4028	354	72	(	(	PUNCT
ejpam-4028	354	73	4.4	4.4	NUM
ejpam-4028	354	74	)	)	PUNCT
ejpam-4028	354	75	in	in	ADP
ejpam-4028	354	76	[	[	X
ejpam-4028	354	77	2	2	NUM
ejpam-4028	354	78	]	]	PUNCT
ejpam-4028	354	79	implies	imply	VERB
ejpam-4028	354	80	that	that	SCONJ
ejpam-4028	354	81	t	t	PROPN
ejpam-4028	354	82	is	be	AUX
ejpam-4028	354	83	fuzzy	fuzzy	ADJ
ejpam-4028	354	84	soft	soft	ADJ
ejpam-4028	354	85	g	g	NOUN
ejpam-4028	354	86	-	-	NOUN
ejpam-4028	354	87	continuous	continuous	ADJ
ejpam-4028	354	88	at	at	ADP
ejpam-4028	354	89	fe	fe	NOUN
ejpam-4028	354	90	.	.	PROPN
ejpam-4028	354	91	4	4	NUM
ejpam-4028	354	92	.	.	X
ejpam-4028	354	93	conclusion	conclusion	NOUN
ejpam-4028	354	94	in	in	ADP
ejpam-4028	354	95	this	this	DET
ejpam-4028	354	96	paper	paper	NOUN
ejpam-4028	354	97	,	,	PUNCT
ejpam-4028	354	98	some	some	DET
ejpam-4028	354	99	new	new	ADJ
ejpam-4028	354	100	results	result	NOUN
ejpam-4028	354	101	of	of	ADP
ejpam-4028	354	102	fixed	fix	VERB
ejpam-4028	354	103	points	point	NOUN
ejpam-4028	354	104	for	for	ADP
ejpam-4028	354	105	mappings	mapping	NOUN
ejpam-4028	354	106	satisfying	satisfy	VERB
ejpam-4028	354	107	different	different	ADJ
ejpam-4028	354	108	conditions	condition	NOUN
ejpam-4028	354	109	in	in	ADP
ejpam-4028	354	110	fuzzy	fuzzy	ADJ
ejpam-4028	354	111	soft	soft	ADJ
ejpam-4028	354	112	g	g	NOUN
ejpam-4028	354	113	-	-	PUNCT
ejpam-4028	354	114	metric	metric	ADJ
ejpam-4028	354	115	spaces	space	NOUN
ejpam-4028	354	116	were	be	AUX
ejpam-4028	354	117	presented	present	VERB
ejpam-4028	354	118	and	and	CCONJ
ejpam-4028	354	119	proved	prove	VERB
ejpam-4028	354	120	.	.	PUNCT
ejpam-4028	355	1	we	we	PRON
ejpam-4028	355	2	’ll	’ll	AUX
ejpam-4028	355	3	hope	hope	VERB
ejpam-4028	355	4	to	to	PART
ejpam-4028	355	5	improve	improve	VERB
ejpam-4028	355	6	the	the	DET
ejpam-4028	355	7	search	search	NOUN
ejpam-4028	355	8	performance	performance	NOUN
ejpam-4028	355	9	even	even	ADV
ejpam-4028	355	10	more	more	ADV
ejpam-4028	355	11	in	in	ADP
ejpam-4028	355	12	the	the	DET
ejpam-4028	355	13	future	future	NOUN
ejpam-4028	355	14	for	for	ADP
ejpam-4028	355	15	some	some	DET
ejpam-4028	355	16	more	more	ADV
ejpam-4028	355	17	important	important	ADJ
ejpam-4028	355	18	results	result	NOUN
ejpam-4028	355	19	in	in	ADP
ejpam-4028	355	20	this	this	DET
ejpam-4028	355	21	space	space	NOUN
ejpam-4028	355	22	.	.	PUNCT
ejpam-4028	356	1	acknowledgements	acknowledgement	NOUN
ejpam-4028	356	2	the	the	DET
ejpam-4028	356	3	authors	author	NOUN
ejpam-4028	356	4	are	be	AUX
ejpam-4028	356	5	very	very	ADV
ejpam-4028	356	6	grateful	grateful	ADJ
ejpam-4028	356	7	to	to	ADP
ejpam-4028	356	8	the	the	DET
ejpam-4028	356	9	editor	editor	NOUN
ejpam-4028	356	10	and	and	CCONJ
ejpam-4028	356	11	the	the	DET
ejpam-4028	356	12	reviewers	reviewer	NOUN
ejpam-4028	356	13	for	for	ADP
ejpam-4028	356	14	their	their	PRON
ejpam-4028	356	15	valuable	valuable	ADJ
ejpam-4028	356	16	suggestions	suggestion	NOUN
ejpam-4028	356	17	.	.	PUNCT
ejpam-4028	357	1	references	reference	NOUN
ejpam-4028	357	2	[	[	X
ejpam-4028	357	3	1	1	NUM
ejpam-4028	357	4	]	]	X
ejpam-4028	357	5	b	b	NOUN
ejpam-4028	357	6	ahmad	ahmad	NOUN
ejpam-4028	357	7	and	and	CCONJ
ejpam-4028	357	8	a	a	DET
ejpam-4028	357	9	kharal	kharal	ADJ
ejpam-4028	357	10	.	.	PUNCT
ejpam-4028	358	1	on	on	ADP
ejpam-4028	358	2	fuzzy	fuzzy	ADJ
ejpam-4028	358	3	soft	soft	ADJ
ejpam-4028	358	4	sets	set	NOUN
ejpam-4028	358	5	.	.	PUNCT
ejpam-4028	359	1	adv	adv	PROPN
ejpam-4028	359	2	.	.	PUNCT
ejpam-4028	359	3	fuzzy	fuzzy	ADJ
ejpam-4028	359	4	syst	syst	PROPN
ejpam-4028	359	5	.	.	PROPN
ejpam-4028	359	6	,	,	PUNCT
ejpam-4028	359	7	2009:6	2009:6	NUM
ejpam-4028	359	8	pages	page	NOUN
ejpam-4028	359	9	,	,	PUNCT
ejpam-4028	359	10	2009	2009	NUM
ejpam-4028	359	11	.	.	PUNCT
ejpam-4028	360	1	[	[	X
ejpam-4028	360	2	2	2	X
ejpam-4028	360	3	]	]	PUNCT
ejpam-4028	360	4	a	a	DET
ejpam-4028	360	5	f	f	PROPN
ejpam-4028	360	6	sayed	say	VERB
ejpam-4028	360	7	a	a	DET
ejpam-4028	360	8	alahmari	alahmari	ADJ
ejpam-4028	360	9	and	and	CCONJ
ejpam-4028	360	10	s	s	NOUN
ejpam-4028	360	11	omran	omran	NOUN
ejpam-4028	360	12	.	.	PUNCT
ejpam-4028	361	1	on	on	ADP
ejpam-4028	361	2	fuzzy	fuzzy	ADJ
ejpam-4028	361	3	soft	soft	ADJ
ejpam-4028	361	4	g	g	NOUN
ejpam-4028	361	5	-	-	PUNCT
ejpam-4028	361	6	metric	metric	ADJ
ejpam-4028	361	7	spaces	space	NOUN
ejpam-4028	361	8	.	.	PUNCT
ejpam-4028	362	1	journal	journal	NOUN
ejpam-4028	362	2	of	of	ADP
ejpam-4028	362	3	advances	advance	NOUN
ejpam-4028	362	4	in	in	ADP
ejpam-4028	362	5	mathematics	mathematic	NOUN
ejpam-4028	362	6	and	and	CCONJ
ejpam-4028	362	7	computer	computer	NOUN
ejpam-4028	362	8	science	science	NOUN
ejpam-4028	362	9	,	,	PUNCT
ejpam-4028	362	10	27(6):1–15	27(6):1–15	NUM
ejpam-4028	362	11	,	,	PUNCT
ejpam-4028	362	12	2018	2018	NUM
ejpam-4028	362	13	.	.	PUNCT
ejpam-4028	363	1	references	reference	NOUN
ejpam-4028	363	2	940	940	NUM
ejpam-4028	364	1	[	[	X
ejpam-4028	364	2	3	3	NUM
ejpam-4028	364	3	]	]	X
ejpam-4028	364	4	m	m	VERB
ejpam-4028	364	5	akram	akram	NOUN
ejpam-4028	364	6	n	n	CCONJ
ejpam-4028	364	7	o	o	NOUN
ejpam-4028	364	8	alshehri	alshehri	NOUN
ejpam-4028	364	9	and	and	CCONJ
ejpam-4028	364	10	r	r	NOUN
ejpam-4028	364	11	s	s	PROPN
ejpam-4028	364	12	alghamdi	alghamdi	NOUN
ejpam-4028	364	13	.	.	PUNCT
ejpam-4028	365	1	fuzzy	fuzzy	ADJ
ejpam-4028	365	2	soft	soft	ADJ
ejpam-4028	365	3	k	k	NOUN
ejpam-4028	365	4	-	-	PUNCT
ejpam-4028	365	5	algebras	algebras	PROPN
ejpam-4028	365	6	.	.	PUNCT
ejpam-4028	366	1	utilitas	utilitas	PROPN
ejpam-4028	366	2	mathematica	mathematica	PROPN
ejpam-4028	366	3	,	,	PUNCT
ejpam-4028	366	4	90:307–325	90:307–325	PROPN
ejpam-4028	366	5	,	,	PUNCT
ejpam-4028	366	6	2013	2013	NUM
ejpam-4028	366	7	.	.	PUNCT
ejpam-4028	367	1	[	[	X
ejpam-4028	367	2	4	4	NUM
ejpam-4028	367	3	]	]	PUNCT
ejpam-4028	367	4	s	s	VERB
ejpam-4028	367	5	atmaca	atmaca	NOUN
ejpam-4028	367	6	and	and	CCONJ
ejpam-4028	367	7	i	i	PRON
ejpam-4028	367	8	zorlutuna	zorlutuna	AUX
ejpam-4028	367	9	.	.	PUNCT
ejpam-4028	368	1	on	on	ADP
ejpam-4028	368	2	fuzzy	fuzzy	ADJ
ejpam-4028	368	3	soft	soft	ADJ
ejpam-4028	368	4	topological	topological	ADJ
ejpam-4028	368	5	spaces	space	NOUN
ejpam-4028	368	6	.	.	PUNCT
ejpam-4028	369	1	ann	ann	PROPN
ejpam-4028	369	2	.	.	PUNCT
ejpam-4028	369	3	fuzzy	fuzzy	ADJ
ejpam-4028	369	4	math	math	NOUN
ejpam-4028	369	5	.	.	PUNCT
ejpam-4028	370	1	inform	inform	NOUN
ejpam-4028	370	2	.	.	PUNCT
ejpam-4028	370	3	,	,	PUNCT
ejpam-4028	370	4	5(2):377–386	5(2):377–386	NUM
ejpam-4028	370	5	,	,	PUNCT
ejpam-4028	370	6	2013	2013	NUM
ejpam-4028	370	7	.	.	PUNCT
ejpam-4028	371	1	[	[	X
ejpam-4028	371	2	5	5	NUM
ejpam-4028	371	3	]	]	PUNCT
ejpam-4028	371	4	w	w	NOUN
ejpam-4028	371	5	shatanawi	shatanawi	PROPN
ejpam-4028	371	6	m	m	PROPN
ejpam-4028	371	7	abbas	abbas	PROPN
ejpam-4028	371	8	h	h	PROPN
ejpam-4028	371	9	aydi	aydi	VERB
ejpam-4028	371	10	and	and	CCONJ
ejpam-4028	371	11	n	n	PRON
ejpam-4028	371	12	tahat	tahat	PROPN
ejpam-4028	371	13	.	.	PUNCT
ejpam-4028	372	1	common	common	ADJ
ejpam-4028	372	2	coupled	couple	VERB
ejpam-4028	372	3	coincidence	coincidence	NOUN
ejpam-4028	372	4	and	and	CCONJ
ejpam-4028	372	5	coupled	couple	VERB
ejpam-4028	372	6	fixed	fix	VERB
ejpam-4028	372	7	points	point	NOUN
ejpam-4028	372	8	in	in	ADP
ejpam-4028	372	9	g	g	NOUN
ejpam-4028	372	10	-	-	PUNCT
ejpam-4028	372	11	metric	metric	ADJ
ejpam-4028	372	12	spaces	space	NOUN
ejpam-4028	372	13	.	.	PUNCT
ejpam-4028	373	1	nonlinear	nonlinear	ADJ
ejpam-4028	373	2	analysis	analysis	NOUN
ejpam-4028	373	3	and	and	CCONJ
ejpam-4028	373	4	application	application	NOUN
ejpam-4028	373	5	,	,	PUNCT
ejpam-4028	373	6	2012(article	2012(article	NUM
ejpam-4028	374	1	i	i	PROPN
ejpam-4028	374	2	d	d	PROPN
ejpam-4028	374	3	jnaa-00162):16	jnaa-00162):16	PROPN
ejpam-4028	374	4	pages	page	NOUN
ejpam-4028	374	5	,	,	PUNCT
ejpam-4028	374	6	2012	2012	NUM
ejpam-4028	374	7	.	.	PUNCT
ejpam-4028	375	1	[	[	X
ejpam-4028	375	2	6	6	NUM
ejpam-4028	375	3	]	]	PUNCT
ejpam-4028	375	4	a	a	DET
ejpam-4028	375	5	aygüunoĝlu	aygüunoĝlu	NOUN
ejpam-4028	375	6	and	and	CCONJ
ejpam-4028	375	7	h	h	NOUN
ejpam-4028	375	8	aygün	aygün	PROPN
ejpam-4028	375	9	.	.	PUNCT
ejpam-4028	376	1	introduction	introduction	NOUN
ejpam-4028	376	2	to	to	ADP
ejpam-4028	376	3	fuzzy	fuzzy	ADJ
ejpam-4028	376	4	soft	soft	ADJ
ejpam-4028	376	5	groups	group	NOUN
ejpam-4028	376	6	.	.	PUNCT
ejpam-4028	377	1	comput	comput	NOUN
ejpam-4028	377	2	.	.	PUNCT
ejpam-4028	378	1	math	math	NOUN
ejpam-4028	378	2	.	.	PUNCT
ejpam-4028	379	1	appl	appl	PROPN
ejpam-4028	379	2	.	.	PROPN
ejpam-4028	379	3	,	,	PUNCT
ejpam-4028	379	4	58(6):1279–1286	58(6):1279–1286	NUM
ejpam-4028	379	5	,	,	PUNCT
ejpam-4028	379	6	2009	2009	NUM
ejpam-4028	379	7	.	.	PUNCT
ejpam-4028	380	1	[	[	X
ejpam-4028	380	2	7	7	X
ejpam-4028	380	3	]	]	PUNCT
ejpam-4028	380	4	t	t	PROPN
ejpam-4028	380	5	beaulaa	beaulaa	PROPN
ejpam-4028	380	6	and	and	CCONJ
ejpam-4028	380	7	c	c	PROPN
ejpam-4028	380	8	gunaseeli	gunaseeli	NOUN
ejpam-4028	380	9	.	.	PUNCT
ejpam-4028	381	1	on	on	ADP
ejpam-4028	381	2	fuzzy	fuzzy	ADJ
ejpam-4028	381	3	soft	soft	ADJ
ejpam-4028	381	4	metric	metric	ADJ
ejpam-4028	381	5	spaces	space	NOUN
ejpam-4028	381	6	.	.	PUNCT
ejpam-4028	382	1	malaya	malaya	PROPN
ejpam-4028	382	2	j.	j.	PROPN
ejpam-4028	382	3	mat	mat	PROPN
ejpam-4028	382	4	.	.	PROPN
ejpam-4028	382	5	,	,	PUNCT
ejpam-4028	382	6	2(3):197	2(3):197	NUM
ejpam-4028	382	7	–	–	PUNCT
ejpam-4028	382	8	202	202	NUM
ejpam-4028	382	9	,	,	PUNCT
ejpam-4028	382	10	2009	2009	NUM
ejpam-4028	382	11	.	.	PUNCT
ejpam-4028	383	1	[	[	X
ejpam-4028	383	2	8	8	X
ejpam-4028	383	3	]	]	X
ejpam-4028	383	4	p	p	X
ejpam-4028	383	5	k	k	PROPN
ejpam-4028	383	6	maji	maji	PROPN
ejpam-4028	383	7	r	r	PROPN
ejpam-4028	383	8	biswas	biswas	PROPN
ejpam-4028	383	9	and	and	CCONJ
ejpam-4028	383	10	a	a	DET
ejpam-4028	383	11	r	r	NOUN
ejpam-4028	383	12	roy	roy	PROPN
ejpam-4028	383	13	.	.	PROPN
ejpam-4028	383	14	fuzzy	fuzzy	ADJ
ejpam-4028	383	15	soft	soft	ADJ
ejpam-4028	383	16	sets	set	NOUN
ejpam-4028	383	17	.	.	PUNCT
ejpam-4028	384	1	j.	j.	PROPN
ejpam-4028	384	2	fuzzy	fuzzy	PROPN
ejpam-4028	384	3	math	math	PROPN
ejpam-4028	384	4	.	.	PUNCT
ejpam-4028	384	5	,	,	PUNCT
ejpam-4028	384	6	9(3):589–602	9(3):589–602	NOUN
ejpam-4028	384	7	,	,	PUNCT
ejpam-4028	384	8	2001	2001	NUM
ejpam-4028	384	9	.	.	PUNCT
ejpam-4028	385	1	[	[	X
ejpam-4028	385	2	9	9	X
ejpam-4028	385	3	]	]	X
ejpam-4028	385	4	p	p	X
ejpam-4028	385	5	k	k	PROPN
ejpam-4028	385	6	maji	maji	PROPN
ejpam-4028	385	7	r	r	PROPN
ejpam-4028	385	8	biswas	biswas	PROPN
ejpam-4028	385	9	and	and	CCONJ
ejpam-4028	385	10	a	a	DET
ejpam-4028	385	11	r	r	NOUN
ejpam-4028	385	12	roy	roy	PROPN
ejpam-4028	385	13	.	.	PROPN
ejpam-4028	385	14	soft	soft	ADJ
ejpam-4028	385	15	set	set	NOUN
ejpam-4028	385	16	theory	theory	NOUN
ejpam-4028	385	17	.	.	PUNCT
ejpam-4028	386	1	comput	comput	NOUN
ejpam-4028	386	2	.	.	PUNCT
ejpam-4028	387	1	math	math	NOUN
ejpam-4028	387	2	.	.	PUNCT
ejpam-4028	388	1	appl	appl	PROPN
ejpam-4028	388	2	.	.	PROPN
ejpam-4028	388	3	,	,	PUNCT
ejpam-4028	388	4	45:555–562	45:555–562	PROPN
ejpam-4028	388	5	,	,	PUNCT
ejpam-4028	388	6	2003	2003	NUM
ejpam-4028	388	7	.	.	PUNCT
ejpam-4028	389	1	[	[	X
ejpam-4028	389	2	10	10	NUM
ejpam-4028	389	3	]	]	X
ejpam-4028	389	4	a	a	DET
ejpam-4028	389	5	ç	ç	NOUN
ejpam-4028	389	6	güler	güler	NOUN
ejpam-4028	389	7	and	and	CCONJ
ejpam-4028	389	8	e	e	PROPN
ejpam-4028	389	9	d	d	PROPN
ejpam-4028	389	10	yildirim	yildirim	PROPN
ejpam-4028	389	11	.	.	PUNCT
ejpam-4028	390	1	a	a	PRON
ejpam-4028	390	2	not	not	PART
ejpam-4028	390	3	on	on	ADP
ejpam-4028	390	4	soft	soft	ADJ
ejpam-4028	390	5	g	g	NOUN
ejpam-4028	390	6	-	-	PUNCT
ejpam-4028	390	7	metric	metric	ADJ
ejpam-4028	390	8	spaces	space	NOUN
ejpam-4028	390	9	about	about	ADP
ejpam-4028	390	10	fixed	fix	VERB
ejpam-4028	390	11	point	point	NOUN
ejpam-4028	390	12	theorems	theorem	NOUN
ejpam-4028	390	13	.	.	PUNCT
ejpam-4028	391	1	ann	ann	PROPN
ejpam-4028	391	2	.	.	PUNCT
ejpam-4028	391	3	fuzzy	fuzzy	ADJ
ejpam-4028	391	4	math	math	NOUN
ejpam-4028	391	5	.	.	PUNCT
ejpam-4028	392	1	inform	inform	NOUN
ejpam-4028	392	2	.	.	PUNCT
ejpam-4028	392	3	,	,	PUNCT
ejpam-4028	392	4	12(5):691–701	12(5):691–701	NUM
ejpam-4028	392	5	,	,	PUNCT
ejpam-4028	392	6	2016	2016	NUM
ejpam-4028	392	7	.	.	PUNCT
ejpam-4028	393	1	[	[	X
ejpam-4028	393	2	11	11	NUM
ejpam-4028	393	3	]	]	X
ejpam-4028	393	4	a	a	DET
ejpam-4028	393	5	ç	ç	NOUN
ejpam-4028	393	6	güler	güler	NOUN
ejpam-4028	393	7	e	e	PROPN
ejpam-4028	393	8	d	d	PROPN
ejpam-4028	393	9	yildirim	yildirim	PROPN
ejpam-4028	393	10	and	and	CCONJ
ejpam-4028	393	11	o	o	PROPN
ejpam-4028	393	12	b	b	X
ejpam-4028	393	13	ozbakir	ozbakir	NOUN
ejpam-4028	393	14	.	.	PUNCT
ejpam-4028	394	1	a	a	DET
ejpam-4028	394	2	fixed	fix	VERB
ejpam-4028	394	3	point	point	NOUN
ejpam-4028	394	4	theorem	theorem	VERB
ejpam-4028	394	5	on	on	ADP
ejpam-4028	394	6	soft	soft	ADJ
ejpam-4028	394	7	g	g	NOUN
ejpam-4028	394	8	-	-	PUNCT
ejpam-4028	394	9	metric	metric	ADJ
ejpam-4028	394	10	spaces	space	NOUN
ejpam-4028	394	11	.	.	PUNCT
ejpam-4028	395	1	j.	j.	PROPN
ejpam-4028	395	2	nonlinear	nonlinear	PROPN
ejpam-4028	395	3	sci	sci	PROPN
ejpam-4028	395	4	.	.	PUNCT
ejpam-4028	395	5	appl	appl	PROPN
ejpam-4028	395	6	.	.	PROPN
ejpam-4028	395	7	,	,	PUNCT
ejpam-4028	395	8	9:885–894	9:885–894	NUM
ejpam-4028	395	9	,	,	PUNCT
ejpam-4028	395	10	2016	2016	NUM
ejpam-4028	395	11	.	.	PUNCT
ejpam-4028	396	1	[	[	X
ejpam-4028	396	2	12	12	NUM
ejpam-4028	396	3	]	]	X
ejpam-4028	396	4	z	z	PROPN
ejpam-4028	396	5	kong	kong	PROPN
ejpam-4028	397	1	l	l	PROPN
ejpam-4028	397	2	gao	gao	PROPN
ejpam-4028	397	3	and	and	CCONJ
ejpam-4028	397	4	l	l	PROPN
ejpam-4028	397	5	wang	wang	PROPN
ejpam-4028	397	6	.	.	PUNCT
ejpam-4028	398	1	comment	comment	NOUN
ejpam-4028	398	2	on	on	ADP
ejpam-4028	398	3	a	a	DET
ejpam-4028	398	4	fuzzy	fuzzy	ADJ
ejpam-4028	398	5	soft	soft	ADJ
ejpam-4028	398	6	set	set	ADJ
ejpam-4028	398	7	theoretic	theoretic	ADJ
ejpam-4028	398	8	approach	approach	NOUN
ejpam-4028	398	9	to	to	ADP
ejpam-4028	398	10	decision	decision	NOUN
ejpam-4028	398	11	making	make	VERB
ejpam-4028	398	12	problems	problem	NOUN
ejpam-4028	398	13	.	.	PUNCT
ejpam-4028	399	1	j.	j.	PROPN
ejpam-4028	399	2	comput	comput	PROPN
ejpam-4028	399	3	.	.	PUNCT
ejpam-4028	400	1	appl	appl	PROPN
ejpam-4028	400	2	.	.	PROPN
ejpam-4028	400	3	math	math	PROPN
ejpam-4028	400	4	.	.	PUNCT
ejpam-4028	400	5	,	,	PUNCT
ejpam-4028	400	6	223(2):540–542	223(2):540–542	NUM
ejpam-4028	400	7	,	,	PUNCT
ejpam-4028	400	8	2009	2009	NUM
ejpam-4028	400	9	.	.	PUNCT
ejpam-4028	401	1	[	[	X
ejpam-4028	401	2	13	13	NUM
ejpam-4028	401	3	]	]	SYM
ejpam-4028	401	4	f	f	PROPN
ejpam-4028	401	5	gu	gu	PROPN
ejpam-4028	401	6	and	and	CCONJ
ejpam-4028	401	7	w	w	PROPN
ejpam-4028	401	8	shatanawi	shatanawi	ADJ
ejpam-4028	401	9	.	.	PUNCT
ejpam-4028	402	1	common	common	ADJ
ejpam-4028	402	2	fixed	fix	VERB
ejpam-4028	402	3	point	point	NOUN
ejpam-4028	402	4	for	for	ADP
ejpam-4028	402	5	generalized	generalized	ADJ
ejpam-4028	402	6	weakly	weakly	ADJ
ejpam-4028	402	7	g	g	NOUN
ejpam-4028	402	8	-	-	PUNCT
ejpam-4028	402	9	contraction	contraction	NOUN
ejpam-4028	402	10	mappings	mapping	NOUN
ejpam-4028	402	11	satisfying	satisfy	VERB
ejpam-4028	402	12	common	common	ADJ
ejpam-4028	402	13	(	(	PUNCT
ejpam-4028	402	14	e.a	e.a	PROPN
ejpam-4028	402	15	)	)	PUNCT
ejpam-4028	402	16	property	property	NOUN
ejpam-4028	402	17	in	in	ADP
ejpam-4028	402	18	g	g	NOUN
ejpam-4028	402	19	-	-	PUNCT
ejpam-4028	402	20	metric	metric	ADJ
ejpam-4028	402	21	spaces	space	NOUN
ejpam-4028	402	22	.	.	PUNCT
ejpam-4028	403	1	fixed	fix	VERB
ejpam-4028	403	2	point	point	NOUN
ejpam-4028	403	3	theory	theory	NOUN
ejpam-4028	403	4	and	and	CCONJ
ejpam-4028	403	5	appl	appl	NOUN
ejpam-4028	403	6	.	.	PROPN
ejpam-4028	403	7	,	,	PUNCT
ejpam-4028	403	8	2013(309):1–15	2013(309):1–15	NUM
ejpam-4028	403	9	,	,	PUNCT
ejpam-4028	403	10	2013	2013	NUM
ejpam-4028	403	11	.	.	PUNCT
ejpam-4028	404	1	[	[	X
ejpam-4028	404	2	14	14	NUM
ejpam-4028	404	3	]	]	X
ejpam-4028	404	4	c	c	PROPN
ejpam-4028	404	5	gunaseeli	gunaseeli	PROPN
ejpam-4028	404	6	.	.	PUNCT
ejpam-4028	405	1	some	some	DET
ejpam-4028	405	2	contributions	contribution	NOUN
ejpam-4028	405	3	to	to	ADP
ejpam-4028	405	4	special	special	ADJ
ejpam-4028	405	5	fuzzy	fuzzy	ADJ
ejpam-4028	405	6	topological	topological	ADJ
ejpam-4028	405	7	spaces	space	NOUN
ejpam-4028	405	8	.	.	PUNCT
ejpam-4028	406	1	thesis	thesis	NOUN
ejpam-4028	406	2	submitted	submit	VERB
ejpam-4028	406	3	to	to	ADP
ejpam-4028	406	4	the	the	DET
ejpam-4028	406	5	bharathidasan	bharathidasan	ADJ
ejpam-4028	406	6	university	university	NOUN
ejpam-4028	406	7	,	,	PUNCT
ejpam-4028	406	8	tiruchirappalli	tiruchirappalli	NOUN
ejpam-4028	406	9	in	in	ADP
ejpam-4028	406	10	partial	partial	ADJ
ejpam-4028	406	11	fulfillment	fulfillment	NOUN
ejpam-4028	406	12	of	of	ADP
ejpam-4028	406	13	the	the	DET
ejpam-4028	406	14	requirements	requirement	NOUN
ejpam-4028	406	15	for	for	ADP
ejpam-4028	406	16	the	the	DET
ejpam-4028	406	17	degree	degree	NOUN
ejpam-4028	406	18	of	of	ADP
ejpam-4028	406	19	doctor	doctor	NOUN
ejpam-4028	406	20	of	of	ADP
ejpam-4028	406	21	philosophy	philosophy	NOUN
ejpam-4028	406	22	in	in	ADP
ejpam-4028	406	23	mathematics	mathematic	NOUN
ejpam-4028	406	24	,	,	PUNCT
ejpam-4028	406	25	ref.no.16690	ref.no.16690	NOUN
ejpam-4028	406	26	/	/	SYM
ejpam-4028	406	27	ph.d./mathematics	ph.d./mathematic	NOUN
ejpam-4028	406	28	full	full	ADJ
ejpam-4028	406	29	-	-	PUNCT
ejpam-4028	406	30	time	time	NOUN
ejpam-4028	406	31	/	/	SYM
ejpam-4028	406	32	july	july	PROPN
ejpam-4028	406	33	2012	2012	NUM
ejpam-4028	406	34	,	,	PUNCT
ejpam-4028	406	35	bharathidasan	bharathidasan	ADJ
ejpam-4028	406	36	university	university	NOUN
ejpam-4028	406	37	,	,	PUNCT
ejpam-4028	406	38	2012	2012	NUM
ejpam-4028	406	39	.	.	PUNCT
ejpam-4028	407	1	[	[	X
ejpam-4028	407	2	15	15	NUM
ejpam-4028	407	3	]	]	X
ejpam-4028	407	4	f	f	PROPN
ejpam-4028	407	5	feng	feng	PROPN
ejpam-4028	407	6	h	h	PROPN
ejpam-4028	407	7	fujita	fujita	PROPN
ejpam-4028	407	8	y	y	PROPN
ejpam-4028	407	9	b	b	PROPN
ejpam-4028	407	10	jun	jun	PROPN
ejpam-4028	407	11	and	and	CCONJ
ejpam-4028	407	12	m	m	PROPN
ejpam-4028	407	13	khan	khan	PROPN
ejpam-4028	407	14	.	.	PUNCT
ejpam-4028	408	1	decomposition	decomposition	NOUN
ejpam-4028	408	2	of	of	ADP
ejpam-4028	408	3	fuzzy	fuzzy	ADJ
ejpam-4028	408	4	soft	soft	ADJ
ejpam-4028	408	5	sets	set	NOUN
ejpam-4028	408	6	with	with	ADP
ejpam-4028	408	7	finite	finite	ADJ
ejpam-4028	408	8	value	value	NOUN
ejpam-4028	408	9	spaces	space	NOUN
ejpam-4028	408	10	.	.	PUNCT
ejpam-4028	409	1	the	the	DET
ejpam-4028	409	2	scientific	scientific	ADJ
ejpam-4028	409	3	world	world	NOUN
ejpam-4028	409	4	j.	j.	PROPN
ejpam-4028	409	5	,	,	PUNCT
ejpam-4028	409	6	2014(article	2014(article	NUM
ejpam-4028	410	1	i	i	PROPN
ejpam-4028	410	2	d	d	PROPN
ejpam-4028	410	3	902687):10	902687):10	NUM
ejpam-4028	410	4	pages	page	NOUN
ejpam-4028	410	5	,	,	PUNCT
ejpam-4028	410	6	2014	2014	NUM
ejpam-4028	410	7	.	.	PUNCT
ejpam-4028	411	1	[	[	X
ejpam-4028	411	2	16	16	NUM
ejpam-4028	411	3	]	]	PUNCT
ejpam-4028	411	4	a	a	DET
ejpam-4028	411	5	kharal	kharal	ADJ
ejpam-4028	411	6	and	and	CCONJ
ejpam-4028	411	7	b	b	PROPN
ejpam-4028	411	8	ahmad	ahmad	PROPN
ejpam-4028	411	9	.	.	PUNCT
ejpam-4028	412	1	mappings	mapping	NOUN
ejpam-4028	412	2	on	on	ADP
ejpam-4028	412	3	fuzzy	fuzzy	ADJ
ejpam-4028	412	4	soft	soft	ADJ
ejpam-4028	412	5	classes	class	NOUN
ejpam-4028	412	6	.	.	PUNCT
ejpam-4028	413	1	fuzzy	fuzzy	ADJ
ejpam-4028	413	2	syst	syst	PROPN
ejpam-4028	413	3	.	.	PROPN
ejpam-4028	413	4	,	,	PUNCT
ejpam-4028	413	5	2009(article	2009(article	NOUN
ejpam-4028	414	1	i	i	PRON
ejpam-4028	414	2	d	d	PROPN
ejpam-4028	414	3	407890):6	407890):6	PROPN
ejpam-4028	414	4	pages	page	NOUN
ejpam-4028	414	5	,	,	PUNCT
ejpam-4028	414	6	2009	2009	NUM
ejpam-4028	414	7	.	.	PUNCT
ejpam-4028	415	1	references	reference	NOUN
ejpam-4028	415	2	941	941	NUM
ejpam-4028	416	1	[	[	X
ejpam-4028	416	2	17	17	NUM
ejpam-4028	416	3	]	]	X
ejpam-4028	416	4	r	r	NOUN
ejpam-4028	416	5	shrivastava	shrivastava	PROPN
ejpam-4028	416	6	s	s	PART
ejpam-4028	416	7	khare	khare	PROPN
ejpam-4028	416	8	and	and	CCONJ
ejpam-4028	416	9	s	s	PROPN
ejpam-4028	416	10	garg	garg	NOUN
ejpam-4028	416	11	.	.	PUNCT
ejpam-4028	417	1	fixed	fix	VERB
ejpam-4028	417	2	point	point	NOUN
ejpam-4028	417	3	results	result	NOUN
ejpam-4028	417	4	with	with	ADP
ejpam-4028	417	5	soft	soft	ADJ
ejpam-4028	417	6	gmetrc	gmetrc	NOUN
ejpam-4028	417	7	spaces	space	NOUN
ejpam-4028	417	8	.	.	PUNCT
ejpam-4028	418	1	computer	computer	NOUN
ejpam-4028	418	2	engineering	engineering	NOUN
ejpam-4028	418	3	and	and	CCONJ
ejpam-4028	418	4	intelligent	intelligent	ADJ
ejpam-4028	418	5	systems	system	NOUN
ejpam-4028	418	6	,	,	PUNCT
ejpam-4028	418	7	9(7):29–40	9(7):29–40	NUM
ejpam-4028	418	8	,	,	PUNCT
ejpam-4028	418	9	2018	2018	NUM
ejpam-4028	418	10	.	.	PUNCT
ejpam-4028	419	1	[	[	X
ejpam-4028	419	2	18	18	NUM
ejpam-4028	419	3	]	]	X
ejpam-4028	419	4	f	f	PROPN
ejpam-4028	419	5	feng	feng	PROPN
ejpam-4028	419	6	y	y	PROPN
ejpam-4028	419	7	b	b	PROPN
ejpam-4028	419	8	jun	jun	PROPN
ejpam-4028	419	9	x	x	PROPN
ejpam-4028	419	10	y	y	PROPN
ejpam-4028	419	11	liu	liu	PROPN
ejpam-4028	419	12	and	and	CCONJ
ejpam-4028	419	13	l	l	PROPN
ejpam-4028	419	14	f	f	PROPN
ejpam-4028	419	15	li	li	PROPN
ejpam-4028	419	16	.	.	PUNCT
ejpam-4028	420	1	an	an	DET
ejpam-4028	420	2	adjustable	adjustable	ADJ
ejpam-4028	420	3	approach	approach	NOUN
ejpam-4028	420	4	to	to	ADP
ejpam-4028	420	5	fuzzy	fuzzy	ADJ
ejpam-4028	420	6	soft	soft	ADJ
ejpam-4028	420	7	set	set	NOUN
ejpam-4028	420	8	based	base	VERB
ejpam-4028	420	9	decision	decision	NOUN
ejpam-4028	420	10	making	making	NOUN
ejpam-4028	420	11	.	.	PUNCT
ejpam-4028	421	1	j.	j.	PROPN
ejpam-4028	421	2	comput	comput	PROPN
ejpam-4028	421	3	.	.	PUNCT
ejpam-4028	422	1	appl	appl	PROPN
ejpam-4028	422	2	.	.	PROPN
ejpam-4028	422	3	math	math	PROPN
ejpam-4028	422	4	.	.	PUNCT
ejpam-4028	422	5	,	,	PUNCT
ejpam-4028	422	6	234(1):10–20	234(1):10–20	NUM
ejpam-4028	422	7	,	,	PUNCT
ejpam-4028	422	8	2010	2010	NUM
ejpam-4028	422	9	.	.	PUNCT
ejpam-4028	423	1	[	[	X
ejpam-4028	423	2	19	19	NUM
ejpam-4028	423	3	]	]	X
ejpam-4028	423	4	d	d	X
ejpam-4028	423	5	molodtsov	molodtsov	PROPN
ejpam-4028	423	6	.	.	PUNCT
ejpam-4028	424	1	soft	soft	ADJ
ejpam-4028	424	2	set	set	ADJ
ejpam-4028	424	3	theory	theory	NOUN
ejpam-4028	424	4	first	first	ADJ
ejpam-4028	424	5	results	result	NOUN
ejpam-4028	424	6	.	.	PUNCT
ejpam-4028	425	1	comput	comput	NOUN
ejpam-4028	425	2	.	.	PUNCT
ejpam-4028	426	1	math	math	NOUN
ejpam-4028	426	2	.	.	PUNCT
ejpam-4028	427	1	appl	appl	PROPN
ejpam-4028	427	2	.	.	PROPN
ejpam-4028	427	3	,	,	PUNCT
ejpam-4028	427	4	8(4	8(4	NOUN
ejpam-4028	427	5	-	-	SYM
ejpam-4028	427	6	5):19–31	5):19–31	NUM
ejpam-4028	427	7	,	,	PUNCT
ejpam-4028	427	8	1999	1999	NUM
ejpam-4028	427	9	.	.	PUNCT
ejpam-4028	428	1	[	[	X
ejpam-4028	428	2	20	20	NUM
ejpam-4028	428	3	]	]	X
ejpam-4028	428	4	z	z	NOUN
ejpam-4028	428	5	mustafa	mustafa	PROPN
ejpam-4028	428	6	and	and	CCONJ
ejpam-4028	428	7	b	b	NOUN
ejpam-4028	428	8	sims	sim	NOUN
ejpam-4028	428	9	.	.	PUNCT
ejpam-4028	429	1	a	a	DET
ejpam-4028	429	2	new	new	ADJ
ejpam-4028	429	3	approach	approach	NOUN
ejpam-4028	429	4	to	to	ADP
ejpam-4028	429	5	generalized	generalize	VERB
ejpam-4028	429	6	metric	metric	ADJ
ejpam-4028	429	7	spaces	space	NOUN
ejpam-4028	429	8	.	.	PUNCT
ejpam-4028	430	1	j.	j.	PROPN
ejpam-4028	430	2	nonlinear	nonlinear	PROPN
ejpam-4028	430	3	convex	convex	PROPN
ejpam-4028	430	4	anal	anal	NOUN
ejpam-4028	430	5	.	.	PUNCT
ejpam-4028	430	6	,	,	PUNCT
ejpam-4028	430	7	7(2):289–297	7(2):289–297	NOUN
ejpam-4028	430	8	,	,	PUNCT
ejpam-4028	430	9	2006	2006	NUM
ejpam-4028	430	10	.	.	PUNCT
ejpam-4028	431	1	[	[	X
ejpam-4028	431	2	21	21	NUM
ejpam-4028	431	3	]	]	X
ejpam-4028	431	4	z	z	NOUN
ejpam-4028	431	5	mustafa	mustafa	PROPN
ejpam-4028	431	6	and	and	CCONJ
ejpam-4028	431	7	b	b	NOUN
ejpam-4028	431	8	sims	sim	NOUN
ejpam-4028	431	9	.	.	PUNCT
ejpam-4028	432	1	fixed	fix	VERB
ejpam-4028	432	2	point	point	NOUN
ejpam-4028	432	3	theorems	theorem	NOUN
ejpam-4028	432	4	for	for	ADP
ejpam-4028	432	5	contractive	contractive	ADJ
ejpam-4028	432	6	mappings	mapping	NOUN
ejpam-4028	432	7	in	in	ADP
ejpam-4028	432	8	complete	complete	ADJ
ejpam-4028	432	9	g	g	PROPN
ejpam-4028	432	10	-metric	-metric	ADJ
ejpam-4028	432	11	spaces	space	NOUN
ejpam-4028	432	12	.	.	PUNCT
ejpam-4028	433	1	fixed	fix	VERB
ejpam-4028	433	2	point	point	NOUN
ejpam-4028	433	3	theory	theory	NOUN
ejpam-4028	433	4	appl	appl	PROPN
ejpam-4028	433	5	.	.	PROPN
ejpam-4028	433	6	,	,	PUNCT
ejpam-4028	433	7	2009(article	2009(article	NOUN
ejpam-4028	434	1	i	i	PROPN
ejpam-4028	434	2	d	d	PROPN
ejpam-4028	434	3	917175):10	917175):10	NUM
ejpam-4028	434	4	pages	page	NOUN
ejpam-4028	434	5	,	,	PUNCT
ejpam-4028	434	6	2009	2009	NUM
ejpam-4028	434	7	.	.	PUNCT
ejpam-4028	435	1	[	[	X
ejpam-4028	435	2	22	22	NUM
ejpam-4028	435	3	]	]	PUNCT
ejpam-4028	435	4	a	a	DET
ejpam-4028	435	5	r	r	NOUN
ejpam-4028	435	6	roy	roy	PROPN
ejpam-4028	435	7	and	and	CCONJ
ejpam-4028	435	8	p	p	PROPN
ejpam-4028	435	9	k	k	PROPN
ejpam-4028	435	10	maji	maji	PROPN
ejpam-4028	435	11	.	.	PUNCT
ejpam-4028	436	1	a	a	DET
ejpam-4028	436	2	fuzzy	fuzzy	ADJ
ejpam-4028	436	3	soft	soft	ADJ
ejpam-4028	436	4	set	set	ADJ
ejpam-4028	436	5	theoretic	theoretic	ADJ
ejpam-4028	436	6	approach	approach	NOUN
ejpam-4028	436	7	to	to	ADP
ejpam-4028	436	8	decision	decision	NOUN
ejpam-4028	436	9	making	make	VERB
ejpam-4028	436	10	problems	problem	NOUN
ejpam-4028	436	11	.	.	PUNCT
ejpam-4028	437	1	j.	j.	PROPN
ejpam-4028	437	2	comput	comput	PROPN
ejpam-4028	437	3	.	.	PUNCT
ejpam-4028	438	1	appl	appl	PROPN
ejpam-4028	438	2	.	.	PROPN
ejpam-4028	438	3	math	math	PROPN
ejpam-4028	438	4	.	.	PUNCT
ejpam-4028	438	5	,	,	PUNCT
ejpam-4028	438	6	203(2):412–418	203(2):412–418	NUM
ejpam-4028	438	7	,	,	PUNCT
ejpam-4028	438	8	2007	2007	NUM
ejpam-4028	438	9	.	.	PUNCT
ejpam-4028	439	1	[	[	X
ejpam-4028	439	2	23	23	NUM
ejpam-4028	439	3	]	]	X
ejpam-4028	439	4	p	p	X
ejpam-4028	439	5	k	k	PROPN
ejpam-4028	439	6	maji	maji	PROPN
ejpam-4028	439	7	a	a	DET
ejpam-4028	439	8	r	r	NOUN
ejpam-4028	439	9	roy	roy	PROPN
ejpam-4028	439	10	and	and	CCONJ
ejpam-4028	439	11	r	r	PROPN
ejpam-4028	439	12	biswas	biswas	PROPN
ejpam-4028	439	13	.	.	PUNCT
ejpam-4028	440	1	an	an	DET
ejpam-4028	440	2	application	application	NOUN
ejpam-4028	440	3	of	of	ADP
ejpam-4028	440	4	soft	soft	ADJ
ejpam-4028	440	5	sets	set	NOUN
ejpam-4028	440	6	in	in	ADP
ejpam-4028	440	7	a	a	DET
ejpam-4028	440	8	decision	decision	NOUN
ejpam-4028	440	9	making	make	VERB
ejpam-4028	440	10	problem	problem	NOUN
ejpam-4028	440	11	.	.	PUNCT
ejpam-4028	441	1	comput	comput	NOUN
ejpam-4028	441	2	.	.	PUNCT
ejpam-4028	442	1	math	math	NOUN
ejpam-4028	442	2	.	.	PUNCT
ejpam-4028	443	1	appl	appl	PROPN
ejpam-4028	443	2	.	.	PROPN
ejpam-4028	443	3	,	,	PUNCT
ejpam-4028	443	4	44(8	44(8	NOUN
ejpam-4028	443	5	-	-	PUNCT
ejpam-4028	443	6	9):1077–1083	9):1077–1083	NOUN
ejpam-4028	443	7	,	,	PUNCT
ejpam-4028	443	8	2002	2002	NUM
ejpam-4028	443	9	.	.	PUNCT
ejpam-4028	444	1	[	[	X
ejpam-4028	444	2	24	24	NUM
ejpam-4028	444	3	]	]	X
ejpam-4028	444	4	y	y	PROPN
ejpam-4028	444	5	j	j	PROPN
ejpam-4028	444	6	cho	cho	PROPN
ejpam-4028	444	7	b	b	PROPN
ejpam-4028	445	1	e	e	PROPN
ejpam-4028	445	2	rhoades	rhoades	PROPN
ejpam-4028	445	3	r	r	PROPN
ejpam-4028	445	4	saadati	saadati	PROPN
ejpam-4028	445	5	b	b	PROPN
ejpam-4028	445	6	samet	samet	PROPN
ejpam-4028	445	7	and	and	CCONJ
ejpam-4028	445	8	w	w	PROPN
ejpam-4028	445	9	shatanawi	shatanawi	PROPN
ejpam-4028	445	10	.	.	PUNCT
ejpam-4028	446	1	nonlinear	nonlinear	PROPN
ejpam-4028	446	2	coupled	couple	VERB
ejpam-4028	446	3	fixed	fix	VERB
ejpam-4028	446	4	point	point	NOUN
ejpam-4028	446	5	theorems	theorem	NOUN
ejpam-4028	446	6	in	in	ADP
ejpam-4028	446	7	ordered	order	VERB
ejpam-4028	446	8	generalized	generalized	ADJ
ejpam-4028	446	9	metric	metric	ADJ
ejpam-4028	446	10	spaces	space	NOUN
ejpam-4028	446	11	with	with	ADP
ejpam-4028	446	12	integral	integral	ADJ
ejpam-4028	446	13	type	type	NOUN
ejpam-4028	446	14	.	.	PUNCT
ejpam-4028	447	1	fixed	fix	VERB
ejpam-4028	447	2	point	point	NOUN
ejpam-4028	447	3	theory	theory	NOUN
ejpam-4028	447	4	and	and	CCONJ
ejpam-4028	447	5	appl	appl	NOUN
ejpam-4028	447	6	.	.	PROPN
ejpam-4028	447	7	,	,	PUNCT
ejpam-4028	447	8	2012(8):1–14	2012(8):1–14	PROPN
ejpam-4028	447	9	,	,	PUNCT
ejpam-4028	447	10	2012	2012	NUM
ejpam-4028	447	11	.	.	PUNCT
ejpam-4028	448	1	[	[	X
ejpam-4028	448	2	25	25	NUM
ejpam-4028	448	3	]	]	PUNCT
ejpam-4028	448	4	a	a	DET
ejpam-4028	448	5	f	f	X
ejpam-4028	448	6	sayed	say	VERB
ejpam-4028	448	7	and	and	CCONJ
ejpam-4028	448	8	a	a	DET
ejpam-4028	448	9	alahmari	alahmari	NOUN
ejpam-4028	448	10	.	.	PUNCT
ejpam-4028	449	1	fuzzy	fuzzy	ADJ
ejpam-4028	449	2	soft	soft	ADJ
ejpam-4028	449	3	α−	α−	ADP
ejpam-4028	449	4	ψ−contractive	ψ−contractive	NUM
ejpam-4028	449	5	type	type	NOUN
ejpam-4028	449	6	mappings	mapping	NOUN
ejpam-4028	449	7	and	and	CCONJ
ejpam-4028	449	8	some	some	DET
ejpam-4028	449	9	fixed	fix	VERB
ejpam-4028	449	10	point	point	NOUN
ejpam-4028	449	11	theorems	theorem	NOUN
ejpam-4028	449	12	in	in	ADP
ejpam-4028	449	13	fuzzy	fuzzy	ADJ
ejpam-4028	449	14	soft	soft	ADJ
ejpam-4028	449	15	metric	metric	ADJ
ejpam-4028	449	16	spaces	space	NOUN
ejpam-4028	449	17	.	.	PUNCT
ejpam-4028	450	1	ann	ann	PROPN
ejpam-4028	450	2	.	.	PUNCT
ejpam-4028	450	3	fuzzy	fuzzy	ADJ
ejpam-4028	450	4	math	math	NOUN
ejpam-4028	450	5	.	.	PUNCT
ejpam-4028	451	1	inform	inform	NOUN
ejpam-4028	451	2	.	.	PUNCT
ejpam-4028	451	3	,	,	PUNCT
ejpam-4028	451	4	15(1):73	15(1):73	NUM
ejpam-4028	451	5	–	–	PUNCT
ejpam-4028	451	6	87	87	NUM
ejpam-4028	451	7	,	,	PUNCT
ejpam-4028	451	8	2018	2018	NUM
ejpam-4028	451	9	.	.	PUNCT
ejpam-4028	452	1	[	[	X
ejpam-4028	452	2	26	26	NUM
ejpam-4028	452	3	]	]	X
ejpam-4028	452	4	m	m	VERB
ejpam-4028	452	5	abbas	abbas	PROPN
ejpam-4028	452	6	t	t	PROPN
ejpam-4028	452	7	nazir	nazir	PROPN
ejpam-4028	452	8	w	w	PROPN
ejpam-4028	452	9	shatanawi	shatanawi	PROPN
ejpam-4028	452	10	and	and	CCONJ
ejpam-4028	452	11	z	z	PROPN
ejpam-4028	452	12	mustafa	mustafa	PROPN
ejpam-4028	452	13	.	.	PUNCT
ejpam-4028	453	1	fixed	fix	VERB
ejpam-4028	453	2	and	and	CCONJ
ejpam-4028	453	3	related	relate	VERB
ejpam-4028	453	4	fixed	fix	VERB
ejpam-4028	453	5	point	point	NOUN
ejpam-4028	453	6	theorems	theorem	NOUN
ejpam-4028	453	7	for	for	ADP
ejpam-4028	453	8	three	three	NUM
ejpam-4028	453	9	maps	map	NOUN
ejpam-4028	453	10	in	in	ADP
ejpam-4028	453	11	g	g	NOUN
ejpam-4028	453	12	-	-	PUNCT
ejpam-4028	453	13	metric	metric	ADJ
ejpam-4028	453	14	spaces	space	NOUN
ejpam-4028	453	15	.	.	PUNCT
ejpam-4028	454	1	hacet	hacet	PROPN
ejpam-4028	454	2	.	.	PUNCT
ejpam-4028	455	1	j.	j.	PROPN
ejpam-4028	455	2	math	math	PROPN
ejpam-4028	455	3	.	.	PUNCT
ejpam-4028	456	1	stat	stat	PROPN
ejpam-4028	456	2	.	.	PUNCT
ejpam-4028	456	3	,	,	PUNCT
ejpam-4028	457	1	41:291–306	41:291–306	PROPN
ejpam-4028	457	2	,	,	PUNCT
ejpam-4028	457	3	2012	2012	NUM
ejpam-4028	457	4	.	.	PUNCT
ejpam-4028	458	1	[	[	X
ejpam-4028	458	2	27	27	NUM
ejpam-4028	458	3	]	]	X
ejpam-4028	458	4	w	w	NOUN
ejpam-4028	458	5	shatanawi	shatanawi	ADJ
ejpam-4028	458	6	.	.	PUNCT
ejpam-4028	459	1	fixed	fix	VERB
ejpam-4028	459	2	point	point	NOUN
ejpam-4028	459	3	theory	theory	NOUN
ejpam-4028	459	4	for	for	ADP
ejpam-4028	459	5	contractive	contractive	ADJ
ejpam-4028	459	6	mappings	mapping	NOUN
ejpam-4028	459	7	satisfying	satisfy	VERB
ejpam-4028	459	8	φ	φ	NOUN
ejpam-4028	459	9	-	-	NOUN
ejpam-4028	459	10	maps	map	NOUN
ejpam-4028	459	11	in	in	ADP
ejpam-4028	459	12	g	g	NOUN
ejpam-4028	459	13	-	-	PUNCT
ejpam-4028	459	14	metric	metric	ADJ
ejpam-4028	459	15	spaces	space	NOUN
ejpam-4028	459	16	.	.	PUNCT
ejpam-4028	460	1	fixed	fix	VERB
ejpam-4028	460	2	point	point	NOUN
ejpam-4028	460	3	theory	theory	NOUN
ejpam-4028	460	4	appl	appl	PROPN
ejpam-4028	460	5	.	.	PROPN
ejpam-4028	460	6	,	,	PUNCT
ejpam-4028	460	7	2010(article	2010(article	NUM
ejpam-4028	461	1	i	i	PROPN
ejpam-4028	461	2	d	d	PROPN
ejpam-4028	461	3	181650):9	181650):9	PROPN
ejpam-4028	461	4	pages	page	NOUN
ejpam-4028	461	5	,	,	PUNCT
ejpam-4028	461	6	2010	2010	NUM
ejpam-4028	461	7	.	.	PUNCT
ejpam-4028	462	1	[	[	X
ejpam-4028	462	2	28	28	NUM
ejpam-4028	462	3	]	]	X
ejpam-4028	462	4	w	w	NOUN
ejpam-4028	462	5	shatanawi	shatanawi	ADJ
ejpam-4028	462	6	.	.	PUNCT
ejpam-4028	463	1	some	some	DET
ejpam-4028	463	2	fixed	fix	VERB
ejpam-4028	463	3	point	point	NOUN
ejpam-4028	463	4	theorems	theorem	NOUN
ejpam-4028	463	5	in	in	ADP
ejpam-4028	463	6	ordered	order	VERB
ejpam-4028	463	7	g	g	NOUN
ejpam-4028	463	8	-	-	PUNCT
ejpam-4028	463	9	metric	metric	ADJ
ejpam-4028	463	10	spaces	space	NOUN
ejpam-4028	463	11	and	and	CCONJ
ejpam-4028	463	12	applications	application	NOUN
ejpam-4028	463	13	.	.	PUNCT
ejpam-4028	464	1	abstr	abstr	PROPN
ejpam-4028	464	2	.	.	PUNCT
ejpam-4028	464	3	appl	appl	PROPN
ejpam-4028	464	4	.	.	PUNCT
ejpam-4028	465	1	anal	anal	PROPN
ejpam-4028	465	2	,	,	PUNCT
ejpam-4028	465	3	2011(article	2011(article	NUM
ejpam-4028	466	1	i	i	PROPN
ejpam-4028	466	2	d	d	PROPN
ejpam-4028	466	3	126205):11	126205):11	NUM
ejpam-4028	466	4	pages	page	NOUN
ejpam-4028	466	5	,	,	PUNCT
ejpam-4028	466	6	2011	2011	NUM
ejpam-4028	466	7	.	.	PUNCT
ejpam-4028	467	1	[	[	X
ejpam-4028	467	2	29	29	NUM
ejpam-4028	467	3	]	]	X
ejpam-4028	467	4	w	w	NOUN
ejpam-4028	467	5	shatanawi	shatanawi	ADJ
ejpam-4028	467	6	and	and	CCONJ
ejpam-4028	467	7	m	m	NOUN
ejpam-4028	467	8	abbas	abbas	NOUN
ejpam-4028	467	9	.	.	PUNCT
ejpam-4028	468	1	some	some	DET
ejpam-4028	468	2	fixed	fix	VERB
ejpam-4028	468	3	point	point	NOUN
ejpam-4028	468	4	results	result	NOUN
ejpam-4028	468	5	for	for	ADP
ejpam-4028	468	6	multi	multi	ADJ
ejpam-4028	468	7	valued	value	VERB
ejpam-4028	468	8	mappings	mapping	NOUN
ejpam-4028	468	9	in	in	ADP
ejpam-4028	468	10	ordered	order	VERB
ejpam-4028	468	11	g	g	NOUN
ejpam-4028	468	12	-	-	PUNCT
ejpam-4028	468	13	metric	metric	ADJ
ejpam-4028	468	14	spaces	space	NOUN
ejpam-4028	468	15	.	.	PUNCT
ejpam-4028	469	1	gazi	gazi	PROPN
ejpam-4028	469	2	university	university	PROPN
ejpam-4028	469	3	journal	journal	PROPN
ejpam-4028	469	4	of	of	ADP
ejpam-4028	469	5	science	science	NOUN
ejpam-4028	469	6	,	,	PUNCT
ejpam-4028	469	7	25:385–392	25:385–392	NUM
ejpam-4028	469	8	,	,	PUNCT
ejpam-4028	469	9	2012	2012	NUM
ejpam-4028	469	10	.	.	PUNCT
ejpam-4028	470	1	[	[	X
ejpam-4028	470	2	30	30	NUM
ejpam-4028	470	3	]	]	X
ejpam-4028	470	4	w	w	NOUN
ejpam-4028	470	5	shatanawi	shatanawi	ADJ
ejpam-4028	470	6	and	and	CCONJ
ejpam-4028	470	7	m	m	PROPN
ejpam-4028	470	8	postolache	postolache	NOUN
ejpam-4028	470	9	.	.	PUNCT
ejpam-4028	471	1	some	some	DET
ejpam-4028	471	2	fixed	fix	VERB
ejpam-4028	471	3	point	point	NOUN
ejpam-4028	471	4	results	result	NOUN
ejpam-4028	471	5	for	for	ADP
ejpam-4028	471	6	a	a	DET
ejpam-4028	471	7	g	g	NOUN
ejpam-4028	471	8	-	-	PUNCT
ejpam-4028	471	9	weak	weak	ADJ
ejpam-4028	471	10	contraction	contraction	NOUN
ejpam-4028	471	11	in	in	ADP
ejpam-4028	471	12	g	g	NOUN
ejpam-4028	471	13	-	-	PUNCT
ejpam-4028	471	14	metric	metric	ADJ
ejpam-4028	471	15	spaces	space	NOUN
ejpam-4028	471	16	.	.	PUNCT
ejpam-4028	472	1	abstr	abstr	PROPN
ejpam-4028	472	2	.	.	PUNCT
ejpam-4028	472	3	appl	appl	PROPN
ejpam-4028	472	4	.	.	PUNCT
ejpam-4028	473	1	anal	anal	PROPN
ejpam-4028	473	2	.	.	PROPN
ejpam-4028	473	3	,	,	PUNCT
ejpam-4028	473	4	2012(article	2012(article	NUM
ejpam-4028	474	1	i	i	PROPN
ejpam-4028	474	2	d	d	PROPN
ejpam-4028	474	3	815870):19	815870):19	NUM
ejpam-4028	474	4	pages	page	NOUN
ejpam-4028	474	5	,	,	PUNCT
ejpam-4028	474	6	2012	2012	NUM
ejpam-4028	474	7	.	.	PUNCT
ejpam-4028	475	1	[	[	X
ejpam-4028	475	2	31	31	NUM
ejpam-4028	475	3	]	]	PUNCT
ejpam-4028	475	4	t	t	PROPN
ejpam-4028	475	5	j	j	PROPN
ejpam-4028	476	1	neog	neog	NOUN
ejpam-4028	476	2	d	d	PROPN
ejpam-4028	476	3	k	k	PROPN
ejpam-4028	476	4	sut	sut	PROPN
ejpam-4028	476	5	and	and	CCONJ
ejpam-4028	476	6	g	g	PROPN
ejpam-4028	476	7	c	c	NOUN
ejpam-4028	476	8	hazarika	hazarika	NOUN
ejpam-4028	476	9	.	.	PUNCT
ejpam-4028	477	1	fuzzy	fuzzy	ADJ
ejpam-4028	477	2	soft	soft	ADJ
ejpam-4028	477	3	topological	topological	ADJ
ejpam-4028	477	4	spaces	space	NOUN
ejpam-4028	477	5	.	.	PUNCT
ejpam-4028	478	1	int	int	NOUN
ejpam-4028	478	2	.	.	PUNCT
ejpam-4028	479	1	j.	j.	PROPN
ejpam-4028	479	2	latest	late	ADJ
ejpam-4028	479	3	trends	trend	NOUN
ejpam-4028	479	4	in	in	ADP
ejpam-4028	479	5	math	math	NOUN
ejpam-4028	479	6	.	.	PUNCT
ejpam-4028	479	7	,	,	PUNCT
ejpam-4028	479	8	2:54–67	2:54–67	NUM
ejpam-4028	479	9	,	,	PUNCT
ejpam-4028	479	10	2012	2012	NUM
ejpam-4028	479	11	.	.	PUNCT
ejpam-4028	480	1	[	[	X
ejpam-4028	480	2	32	32	NUM
ejpam-4028	480	3	]	]	PUNCT
ejpam-4028	480	4	l	l	NOUN
ejpam-4028	480	5	a	a	DET
ejpam-4028	480	6	zadeh	zadeh	PROPN
ejpam-4028	480	7	.	.	PUNCT
ejpam-4028	480	8	fuzzy	fuzzy	ADJ
ejpam-4028	480	9	sets	set	NOUN
ejpam-4028	480	10	.	.	PUNCT
ejpam-4028	481	1	information	information	NOUN
ejpam-4028	481	2	and	and	CCONJ
ejpam-4028	481	3	control	control	NOUN
ejpam-4028	481	4	,	,	PUNCT
ejpam-4028	481	5	8:338–353	8:338–353	NUM
ejpam-4028	481	6	,	,	PUNCT
ejpam-4028	481	7	1965	1965	NUM
ejpam-4028	481	8	.	.	PUNCT