id	sid	tid	token	lemma	pos
ejpam-5429	1	1	european	european	PROPN
ejpam-5429	1	2	journal	journal	PROPN
ejpam-5429	1	3	of	of	ADP
ejpam-5429	1	4	pure	pure	ADJ
ejpam-5429	1	5	and	and	CCONJ
ejpam-5429	1	6	applied	apply	VERB
ejpam-5429	1	7	mathematics	mathematic	NOUN
ejpam-5429	1	8	vol	vol	NOUN
ejpam-5429	1	9	.	.	PROPN
ejpam-5429	2	1	17	17	NUM
ejpam-5429	2	2	,	,	PUNCT
ejpam-5429	2	3	no	no	INTJ
ejpam-5429	2	4	.	.	NOUN
ejpam-5429	2	5	4	4	NUM
ejpam-5429	2	6	,	,	PUNCT
ejpam-5429	2	7	2024	2024	NUM
ejpam-5429	2	8	,	,	PUNCT
ejpam-5429	2	9	3129	3129	NUM
ejpam-5429	2	10	-	-	SYM
ejpam-5429	2	11	3155	3155	NUM
ejpam-5429	2	12	issn	issn	PROPN
ejpam-5429	2	13	1307	1307	NUM
ejpam-5429	2	14	-	-	SYM
ejpam-5429	2	15	5543	5543	NUM
ejpam-5429	2	16	–	–	PUNCT
ejpam-5429	3	1	ejpam.com	ejpam.com	X
ejpam-5429	3	2	published	publish	VERB
ejpam-5429	3	3	by	by	ADP
ejpam-5429	3	4	new	new	PROPN
ejpam-5429	3	5	york	york	PROPN
ejpam-5429	3	6	business	business	PROPN
ejpam-5429	3	7	global	global	PROPN
ejpam-5429	3	8	quadri	quadri	PROPN
ejpam-5429	3	9	-	-	PUNCT
ejpam-5429	3	10	polar	polar	ADJ
ejpam-5429	3	11	fuzzy	fuzzy	ADJ
ejpam-5429	3	12	fantastic	fantastic	ADJ
ejpam-5429	3	13	ideals	ideal	NOUN
ejpam-5429	3	14	in	in	ADP
ejpam-5429	3	15	bci	bci	NOUN
ejpam-5429	3	16	-	-	NOUN
ejpam-5429	3	17	algebras	algebra	NOUN
ejpam-5429	3	18	:	:	PUNCT
ejpam-5429	3	19	a	a	DET
ejpam-5429	3	20	topsis	topsis	NOUN
ejpam-5429	3	21	framework	framework	NOUN
ejpam-5429	3	22	and	and	CCONJ
ejpam-5429	3	23	application	application	NOUN
ejpam-5429	3	24	m.	m.	NOUN
ejpam-5429	3	25	balamurugan1	balamurugan1	PROPN
ejpam-5429	3	26	,	,	PUNCT
ejpam-5429	3	27	khalil	khalil	PROPN
ejpam-5429	3	28	h.	h.	PROPN
ejpam-5429	3	29	hakami2,∗	hakami2,∗	PROPN
ejpam-5429	3	30	,	,	PUNCT
ejpam-5429	3	31	moin	moin	NOUN
ejpam-5429	3	32	a.	a.	NOUN
ejpam-5429	3	33	ansari2	ansari2	PROPN
ejpam-5429	3	34	,	,	PUNCT
ejpam-5429	3	35	*	*	PROPN
ejpam-5429	3	36	,	,	PUNCT
ejpam-5429	3	37	anas	anas	PROPN
ejpam-5429	3	38	al	al	PROPN
ejpam-5429	3	39	-	-	PUNCT
ejpam-5429	3	40	masarwah3	masarwah3	PROPN
ejpam-5429	3	41	,	,	PUNCT
ejpam-5429	3	42	k.	k.	X
ejpam-5429	3	43	loganathan4	loganathan4	PROPN
ejpam-5429	3	44	1	1	NUM
ejpam-5429	3	45	department	department	NOUN
ejpam-5429	3	46	of	of	ADP
ejpam-5429	3	47	mathematics	mathematic	NOUN
ejpam-5429	3	48	,	,	PUNCT
ejpam-5429	3	49	vel	vel	PROPN
ejpam-5429	3	50	tech	tech	PROPN
ejpam-5429	3	51	rangarajan	rangarajan	PROPN
ejpam-5429	3	52	dr	dr	PROPN
ejpam-5429	3	53	.	.	PROPN
ejpam-5429	3	54	sagunthala	sagunthala	PROPN
ejpam-5429	3	55	r&d	r&d	PROPN
ejpam-5429	3	56	institute	institute	PROPN
ejpam-5429	3	57	of	of	ADP
ejpam-5429	3	58	science	science	NOUN
ejpam-5429	3	59	and	and	CCONJ
ejpam-5429	3	60	technology	technology	NOUN
ejpam-5429	3	61	,	,	PUNCT
ejpam-5429	3	62	chennai	chennai	PROPN
ejpam-5429	3	63	,	,	PUNCT
ejpam-5429	3	64	tamil	tamil	PROPN
ejpam-5429	3	65	nadu	nadu	PROPN
ejpam-5429	3	66	,	,	PUNCT
ejpam-5429	3	67	india	india	PROPN
ejpam-5429	3	68	2	2	NUM
ejpam-5429	3	69	department	department	NOUN
ejpam-5429	3	70	of	of	ADP
ejpam-5429	3	71	mathematics	mathematic	NOUN
ejpam-5429	3	72	,	,	PUNCT
ejpam-5429	3	73	college	college	NOUN
ejpam-5429	3	74	of	of	ADP
ejpam-5429	3	75	science	science	PROPN
ejpam-5429	3	76	,	,	PUNCT
ejpam-5429	3	77	jazan	jazan	PROPN
ejpam-5429	3	78	university	university	PROPN
ejpam-5429	3	79	,	,	PUNCT
ejpam-5429	3	80	p.o	p.o	PROPN
ejpam-5429	3	81	.	.	PROPN
ejpam-5429	3	82	box	box	PROPN
ejpam-5429	3	83	.	.	PUNCT
ejpam-5429	4	1	114	114	NUM
ejpam-5429	4	2	,	,	PUNCT
ejpam-5429	4	3	jazan	jazan	NOUN
ejpam-5429	4	4	45142	45142	NUM
ejpam-5429	4	5	,	,	PUNCT
ejpam-5429	4	6	kingdom	kingdom	NOUN
ejpam-5429	4	7	of	of	ADP
ejpam-5429	4	8	saudi	saudi	PROPN
ejpam-5429	4	9	arabia	arabia	PROPN
ejpam-5429	4	10	3	3	NUM
ejpam-5429	4	11	department	department	NOUN
ejpam-5429	4	12	of	of	ADP
ejpam-5429	4	13	mathematics	mathematic	NOUN
ejpam-5429	4	14	,	,	PUNCT
ejpam-5429	4	15	faculty	faculty	NOUN
ejpam-5429	4	16	of	of	ADP
ejpam-5429	4	17	science	science	NOUN
ejpam-5429	4	18	,	,	PUNCT
ejpam-5429	4	19	ajloun	ajloun	ADJ
ejpam-5429	4	20	national	national	ADJ
ejpam-5429	4	21	university	university	PROPN
ejpam-5429	4	22	,	,	PUNCT
ejpam-5429	4	23	p.o	p.o	PROPN
ejpam-5429	4	24	.	.	PROPN
ejpam-5429	4	25	box	box	PROPN
ejpam-5429	4	26	43	43	NUM
ejpam-5429	4	27	,	,	PUNCT
ejpam-5429	4	28	ajloun	ajloun	ADJ
ejpam-5429	4	29	26810	26810	NUM
ejpam-5429	4	30	,	,	PUNCT
ejpam-5429	4	31	jordan	jordan	PROPN
ejpam-5429	4	32	4	4	NUM
ejpam-5429	4	33	department	department	NOUN
ejpam-5429	4	34	of	of	ADP
ejpam-5429	4	35	mathematics	mathematic	NOUN
ejpam-5429	4	36	and	and	CCONJ
ejpam-5429	4	37	statistics	statistic	NOUN
ejpam-5429	4	38	,	,	PUNCT
ejpam-5429	4	39	manipal	manipal	PROPN
ejpam-5429	4	40	university	university	PROPN
ejpam-5429	4	41	jaipur	jaipur	PROPN
ejpam-5429	4	42	,	,	PUNCT
ejpam-5429	4	43	jaipur-303007	jaipur-303007	NOUN
ejpam-5429	4	44	,	,	PUNCT
ejpam-5429	4	45	india	india	PROPN
ejpam-5429	4	46	abstract	abstract	NOUN
ejpam-5429	4	47	.	.	PUNCT
ejpam-5429	5	1	a	a	DET
ejpam-5429	5	2	quadri	quadri	NOUN
ejpam-5429	5	3	-	-	PUNCT
ejpam-5429	5	4	polar	polar	ADJ
ejpam-5429	5	5	fuzzy	fuzzy	ADJ
ejpam-5429	5	6	(	(	PUNCT
ejpam-5429	5	7	qp	qp	ADP
ejpam-5429	5	8	-	-	PUNCT
ejpam-5429	5	9	f	f	NOUN
ejpam-5429	5	10	)	)	PUNCT
ejpam-5429	5	11	set	set	NOUN
ejpam-5429	5	12	is	be	AUX
ejpam-5429	5	13	an	an	DET
ejpam-5429	5	14	extension	extension	NOUN
ejpam-5429	5	15	of	of	ADP
ejpam-5429	5	16	a	a	DET
ejpam-5429	5	17	traditional	traditional	ADJ
ejpam-5429	5	18	fuzzy	fuzzy	ADJ
ejpam-5429	5	19	set	set	NOUN
ejpam-5429	5	20	that	that	PRON
ejpam-5429	5	21	uses	use	VERB
ejpam-5429	5	22	four	four	NUM
ejpam-5429	5	23	degrees	degree	NOUN
ejpam-5429	5	24	of	of	ADP
ejpam-5429	5	25	membership	membership	NOUN
ejpam-5429	5	26	to	to	PART
ejpam-5429	5	27	represent	represent	VERB
ejpam-5429	5	28	different	different	ADJ
ejpam-5429	5	29	aspects	aspect	NOUN
ejpam-5429	5	30	of	of	ADP
ejpam-5429	5	31	belonging	belong	VERB
ejpam-5429	5	32	to	to	PART
ejpam-5429	5	33	provide	provide	VERB
ejpam-5429	5	34	a	a	DET
ejpam-5429	5	35	more	more	ADV
ejpam-5429	5	36	detailed	detailed	ADJ
ejpam-5429	5	37	framework	framework	NOUN
ejpam-5429	5	38	for	for	ADP
ejpam-5429	5	39	handling	handle	VERB
ejpam-5429	5	40	uncertainty	uncertainty	NOUN
ejpam-5429	5	41	and	and	CCONJ
ejpam-5429	5	42	vagueness	vagueness	NOUN
ejpam-5429	5	43	.	.	PUNCT
ejpam-5429	6	1	in	in	ADP
ejpam-5429	6	2	this	this	DET
ejpam-5429	6	3	paper	paper	NOUN
ejpam-5429	6	4	,	,	PUNCT
ejpam-5429	6	5	we	we	PRON
ejpam-5429	6	6	propose	propose	VERB
ejpam-5429	6	7	the	the	DET
ejpam-5429	6	8	notion	notion	NOUN
ejpam-5429	6	9	of	of	ADP
ejpam-5429	6	10	quadripolar-(ϖ,ϑ)-fuzzy	quadripolar-(ϖ,ϑ)-fuzzy	ADV
ejpam-5429	6	11	fantastic	fantastic	ADJ
ejpam-5429	6	12	ideals	ideal	NOUN
ejpam-5429	6	13	(	(	PUNCT
ejpam-5429	6	14	qp-(ϖ,ϑ)-ffi(s	qp-(ϖ,ϑ)-ffi(s	NOUN
ejpam-5429	6	15	)	)	PUNCT
ejpam-5429	6	16	)	)	PUNCT
ejpam-5429	6	17	in	in	ADP
ejpam-5429	6	18	bci	bci	PROPN
ejpam-5429	6	19	-	-	PUNCT
ejpam-5429	6	20	algebras	algebra	NOUN
ejpam-5429	6	21	based	base	VERB
ejpam-5429	6	22	on	on	ADP
ejpam-5429	6	23	qp	qp	PROPN
ejpam-5429	6	24	-	-	PUNCT
ejpam-5429	6	25	f	f	PROPN
ejpam-5429	6	26	set	set	NOUN
ejpam-5429	6	27	.	.	PUNCT
ejpam-5429	7	1	also	also	ADV
ejpam-5429	7	2	,	,	PUNCT
ejpam-5429	7	3	the	the	DET
ejpam-5429	7	4	notion	notion	NOUN
ejpam-5429	7	5	of	of	ADP
ejpam-5429	7	6	quadri	quadri	NOUN
ejpam-5429	7	7	-	-	PUNCT
ejpam-5429	7	8	polar-(∈σ̃,∈σ̃	polar-(∈σ̃,∈σ̃	NOUN
ejpam-5429	7	9	∨qτ̃	∨qτ̃	ADJ
ejpam-5429	7	10	)	)	PUNCT
ejpam-5429	7	11	-fuzzy	-fuzzy	PROPN
ejpam-5429	7	12	fantastic	fantastic	ADJ
ejpam-5429	7	13	ideals	ideal	NOUN
ejpam-5429	7	14	(	(	PUNCT
ejpam-5429	7	15	qp-(∈σ̃,∈σ̃	qp-(∈σ̃,∈σ̃	PROPN
ejpam-5429	7	16	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	7	17	)	)	PUNCT
ejpam-5429	7	18	-ffi(s	-ffi(s	PROPN
ejpam-5429	7	19	)	)	PUNCT
ejpam-5429	7	20	)	)	PUNCT
ejpam-5429	7	21	is	be	AUX
ejpam-5429	7	22	introduced	introduce	VERB
ejpam-5429	7	23	,	,	PUNCT
ejpam-5429	7	24	and	and	CCONJ
ejpam-5429	7	25	the	the	DET
ejpam-5429	7	26	characterizations	characterization	NOUN
ejpam-5429	7	27	for	for	ADP
ejpam-5429	7	28	an	an	DET
ejpam-5429	7	29	∈σ̃-qp	∈σ̃-qp	PROPN
ejpam-5429	7	30	-	-	PUNCT
ejpam-5429	7	31	f	f	NOUN
ejpam-5429	7	32	set	set	NOUN
ejpam-5429	7	33	and	and	CCONJ
ejpam-5429	7	34	qτ̃	qτ̃	NOUN
ejpam-5429	7	35	-qp	-qp	NOUN
ejpam-5429	7	36	-	-	PUNCT
ejpam-5429	7	37	f	f	NOUN
ejpam-5429	7	38	set	set	NOUN
ejpam-5429	7	39	to	to	PART
ejpam-5429	7	40	be	be	AUX
ejpam-5429	7	41	quadri	quadri	NOUN
ejpam-5429	7	42	-	-	ADJ
ejpam-5429	7	43	polar	polar	ADJ
ejpam-5429	7	44	fuzzy	fuzzy	ADJ
ejpam-5429	7	45	ideals	ideal	NOUN
ejpam-5429	7	46	(	(	PUNCT
ejpam-5429	7	47	qp	qp	NOUN
ejpam-5429	7	48	-	-	PUNCT
ejpam-5429	7	49	fi	fi	NOUN
ejpam-5429	7	50	)	)	PUNCT
ejpam-5429	7	51	in	in	ADP
ejpam-5429	7	52	bci	bci	NOUN
ejpam-5429	7	53	-	-	PUNCT
ejpam-5429	7	54	algebras	algebra	NOUN
ejpam-5429	7	55	are	be	AUX
ejpam-5429	7	56	established	establish	VERB
ejpam-5429	7	57	.	.	PUNCT
ejpam-5429	8	1	furthermore	furthermore	ADV
ejpam-5429	8	2	,	,	PUNCT
ejpam-5429	8	3	we	we	PRON
ejpam-5429	8	4	present	present	VERB
ejpam-5429	8	5	the	the	DET
ejpam-5429	8	6	qp	qp	PROPN
ejpam-5429	8	7	-	-	PUNCT
ejpam-5429	8	8	f	f	PROPN
ejpam-5429	8	9	topsis	topsis	NOUN
ejpam-5429	8	10	technique	technique	NOUN
ejpam-5429	8	11	for	for	ADP
ejpam-5429	8	12	multi	multi	ADJ
ejpam-5429	8	13	-	-	ADJ
ejpam-5429	8	14	criteria	criterion	NOUN
ejpam-5429	8	15	group	group	NOUN
ejpam-5429	8	16	decision	decision	NOUN
ejpam-5429	8	17	-	-	PUNCT
ejpam-5429	8	18	making	make	VERB
ejpam-5429	8	19	(	(	PUNCT
ejpam-5429	8	20	mcgdm	mcgdm	NOUN
ejpam-5429	8	21	)	)	PUNCT
ejpam-5429	8	22	,	,	PUNCT
ejpam-5429	8	23	which	which	PRON
ejpam-5429	8	24	is	be	AUX
ejpam-5429	8	25	a	a	DET
ejpam-5429	8	26	natural	natural	ADJ
ejpam-5429	8	27	extension	extension	NOUN
ejpam-5429	8	28	of	of	ADP
ejpam-5429	8	29	the	the	DET
ejpam-5429	8	30	topsis	topsis	NOUN
ejpam-5429	8	31	method	method	NOUN
ejpam-5429	8	32	and	and	CCONJ
ejpam-5429	8	33	used	use	VERB
ejpam-5429	8	34	to	to	PART
ejpam-5429	8	35	rank	rank	VERB
ejpam-5429	8	36	and	and	CCONJ
ejpam-5429	8	37	choose	choose	VERB
ejpam-5429	8	38	the	the	DET
ejpam-5429	8	39	best	good	ADJ
ejpam-5429	8	40	alternatives	alternative	NOUN
ejpam-5429	8	41	under	under	ADP
ejpam-5429	8	42	qp	qp	NOUN
ejpam-5429	8	43	-	-	PUNCT
ejpam-5429	8	44	f	f	X
ejpam-5429	8	45	positive	positive	ADJ
ejpam-5429	8	46	and	and	CCONJ
ejpam-5429	8	47	negative	negative	ADJ
ejpam-5429	8	48	ideal	ideal	ADJ
ejpam-5429	8	49	solutions	solution	NOUN
ejpam-5429	8	50	.	.	PUNCT
ejpam-5429	9	1	finally	finally	ADV
ejpam-5429	9	2	,	,	PUNCT
ejpam-5429	9	3	practical	practical	ADJ
ejpam-5429	9	4	examples	example	NOUN
ejpam-5429	9	5	interpreting	interpret	VERB
ejpam-5429	9	6	the	the	DET
ejpam-5429	9	7	applicability	applicability	NOUN
ejpam-5429	9	8	of	of	ADP
ejpam-5429	9	9	our	our	PRON
ejpam-5429	9	10	proposed	propose	VERB
ejpam-5429	9	11	qp	qp	PROPN
ejpam-5429	9	12	-	-	PUNCT
ejpam-5429	9	13	f	f	NOUN
ejpam-5429	9	14	-	-	PUNCT
ejpam-5429	9	15	topsis	topsis	NOUN
ejpam-5429	9	16	are	be	AUX
ejpam-5429	9	17	solved	solve	VERB
ejpam-5429	9	18	.	.	PUNCT
ejpam-5429	10	1	2020	2020	NUM
ejpam-5429	10	2	mathematics	mathematics	PROPN
ejpam-5429	10	3	subject	subject	NOUN
ejpam-5429	10	4	classifications	classification	NOUN
ejpam-5429	10	5	:	:	PUNCT
ejpam-5429	10	6	03b47	03b47	NOUN
ejpam-5429	10	7	,	,	PUNCT
ejpam-5429	10	8	03e72	03e72	NUM
ejpam-5429	10	9	,	,	PUNCT
ejpam-5429	10	10	08a72	08a72	NOUN
ejpam-5429	10	11	key	key	ADJ
ejpam-5429	10	12	words	word	NOUN
ejpam-5429	10	13	and	and	CCONJ
ejpam-5429	10	14	phrases	phrase	NOUN
ejpam-5429	10	15	:	:	PUNCT
ejpam-5429	10	16	bck	bck	VERB
ejpam-5429	10	17	/	/	SYM
ejpam-5429	10	18	bci	bci	NOUN
ejpam-5429	10	19	-	-	PUNCT
ejpam-5429	10	20	algebras	algebra	NOUN
ejpam-5429	10	21	,	,	PUNCT
ejpam-5429	10	22	q	q	ADJ
ejpam-5429	10	23	-	-	ADJ
ejpam-5429	10	24	polar	polar	ADJ
ejpam-5429	10	25	fuzzy	fuzzy	ADJ
ejpam-5429	10	26	fantastic	fantastic	ADJ
ejpam-5429	10	27	ideal	ideal	NOUN
ejpam-5429	10	28	,	,	PUNCT
ejpam-5429	10	29	q	q	NOUN
ejpam-5429	10	30	-	-	PUNCT
ejpam-5429	10	31	polar-(ω	polar-(ω	ADJ
ejpam-5429	10	32	,	,	PUNCT
ejpam-5429	10	33	ϑ)-fuzzy	ϑ)-fuzzy	PUNCT
ejpam-5429	10	34	fantastic	fantastic	ADJ
ejpam-5429	10	35	ideal	ideal	NOUN
ejpam-5429	10	36	,	,	PUNCT
ejpam-5429	10	37	q	q	NOUN
ejpam-5429	10	38	-	-	PUNCT
ejpam-5429	10	39	polar-(∈σ̃,∈σ̃	polar-(∈σ̃,∈σ̃	PRON
ejpam-5429	10	40	∨qτ̃	∨qτ̃	ADJ
ejpam-5429	10	41	)	)	PUNCT
ejpam-5429	10	42	-fuzzy	-fuzzy	PROPN
ejpam-5429	10	43	fantastic	fantastic	ADJ
ejpam-5429	10	44	ideal	ideal	ADJ
ejpam-5429	10	45	∗corresponding	∗corresponde	VERB
ejpam-5429	10	46	author	author	NOUN
ejpam-5429	10	47	.	.	PUNCT
ejpam-5429	11	1	doi	doi	NOUN
ejpam-5429	11	2	:	:	PUNCT
ejpam-5429	11	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5429	https://doi.org/10.29020/nybg.ejpam.v17i4.5429	ADJ
ejpam-5429	11	4	email	email	NOUN
ejpam-5429	11	5	addresses	address	NOUN
ejpam-5429	11	6	:	:	PUNCT
ejpam-5429	11	7	drbalamuruganm@veltech.edu.in	drbalamuruganm@veltech.edu.in	NOUN
ejpam-5429	11	8	(	(	PUNCT
ejpam-5429	11	9	m.	m.	NOUN
ejpam-5429	11	10	balamurugan	balamurugan	PROPN
ejpam-5429	11	11	)	)	PUNCT
ejpam-5429	11	12	,	,	PUNCT
ejpam-5429	11	13	khakami@jazanu.edu.sa	khakami@jazanu.edu.sa	PROPN
ejpam-5429	11	14	(	(	PUNCT
ejpam-5429	11	15	khalil	khalil	PROPN
ejpam-5429	11	16	h.	h.	PROPN
ejpam-5429	11	17	hakami	hakami	PROPN
ejpam-5429	11	18	)	)	PUNCT
ejpam-5429	11	19	,	,	PUNCT
ejpam-5429	11	20	maansari@jazanu.edu.sa	maansari@jazanu.edu.sa	PROPN
ejpam-5429	11	21	(	(	PUNCT
ejpam-5429	11	22	moin	moin	X
ejpam-5429	11	23	a.	a.	NOUN
ejpam-5429	11	24	ansari	ansari	PROPN
ejpam-5429	11	25	)	)	PUNCT
ejpam-5429	11	26	,	,	PUNCT
ejpam-5429	11	27	anas.almasarwah@anu.edu.jo	anas.almasarwah@anu.edu.jo	PROPN
ejpam-5429	11	28	(	(	PUNCT
ejpam-5429	11	29	anas	anas	PROPN
ejpam-5429	11	30	al	al	PROPN
ejpam-5429	11	31	-	-	PROPN
ejpam-5429	11	32	masarwah	masarwah	PROPN
ejpam-5429	11	33	)	)	PUNCT
ejpam-5429	11	34	,	,	PUNCT
ejpam-5429	11	35	loganathankaruppusamy304@gmail.com	loganathankaruppusamy304@gmail.com	X
ejpam-5429	12	1	(	(	PUNCT
ejpam-5429	12	2	k.	k.	PROPN
ejpam-5429	12	3	loganathan	loganathan	PROPN
ejpam-5429	12	4	)	)	PUNCT
ejpam-5429	12	5	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5429	12	6	3129	3129	NUM
ejpam-5429	13	1	copyright	copyright	NOUN
ejpam-5429	13	2	:	:	PUNCT
ejpam-5429	13	3	©	©	PROPN
ejpam-5429	13	4	2024	2024	NUM
ejpam-5429	13	5	the	the	DET
ejpam-5429	13	6	author(s	author(s	NOUN
ejpam-5429	13	7	)	)	PUNCT
ejpam-5429	13	8	.	.	PUNCT
ejpam-5429	14	1	(	(	PUNCT
ejpam-5429	14	2	cc	cc	NOUN
ejpam-5429	14	3	by	by	ADP
ejpam-5429	14	4	-	-	PUNCT
ejpam-5429	14	5	nc	nc	PROPN
ejpam-5429	14	6	4.0	4.0	NUM
ejpam-5429	14	7	)	)	PUNCT
ejpam-5429	14	8	k.	k.	PROPN
ejpam-5429	14	9	h.	h.	PROPN
ejpam-5429	14	10	hakami	hakami	PROPN
ejpam-5429	14	11	et	et	PROPN
ejpam-5429	14	12	al	al	PROPN
ejpam-5429	14	13	.	.	PUNCT
ejpam-5429	14	14	/	/	SYM
ejpam-5429	14	15	eur	eur	PROPN
ejpam-5429	14	16	.	.	PUNCT
ejpam-5429	15	1	j.	j.	PROPN
ejpam-5429	15	2	pure	pure	PROPN
ejpam-5429	15	3	appl	appl	PROPN
ejpam-5429	15	4	.	.	PROPN
ejpam-5429	15	5	math	math	PROPN
ejpam-5429	15	6	,	,	PUNCT
ejpam-5429	15	7	17	17	NUM
ejpam-5429	15	8	(	(	PUNCT
ejpam-5429	15	9	4	4	NUM
ejpam-5429	15	10	)	)	PUNCT
ejpam-5429	15	11	(	(	PUNCT
ejpam-5429	15	12	2024	2024	NUM
ejpam-5429	15	13	)	)	PUNCT
ejpam-5429	15	14	,	,	PUNCT
ejpam-5429	15	15	3129	3129	NUM
ejpam-5429	15	16	-	-	SYM
ejpam-5429	15	17	3155	3155	NUM
ejpam-5429	15	18	3130	3130	NUM
ejpam-5429	15	19	1	1	NUM
ejpam-5429	15	20	.	.	PUNCT
ejpam-5429	15	21	introduction	introduction	NOUN
ejpam-5429	15	22	axiom	axiom	NOUN
ejpam-5429	15	23	systems	system	NOUN
ejpam-5429	15	24	,	,	PUNCT
ejpam-5429	15	25	developed	develop	VERB
ejpam-5429	15	26	by	by	ADP
ejpam-5429	15	27	imai	imai	PROPN
ejpam-5429	15	28	et	et	PROPN
ejpam-5429	15	29	al	al	PROPN
ejpam-5429	15	30	.	.	PUNCT
ejpam-5429	16	1	[	[	X
ejpam-5429	16	2	20	20	NUM
ejpam-5429	16	3	,	,	PUNCT
ejpam-5429	16	4	21	21	NUM
ejpam-5429	16	5	]	]	PUNCT
ejpam-5429	16	6	and	and	CCONJ
ejpam-5429	16	7	used	use	VERB
ejpam-5429	16	8	in	in	ADP
ejpam-5429	16	9	propositional	propositional	ADJ
ejpam-5429	16	10	calculi	calculi	NOUN
ejpam-5429	16	11	,	,	PUNCT
ejpam-5429	16	12	are	be	AUX
ejpam-5429	16	13	collections	collection	NOUN
ejpam-5429	16	14	of	of	ADP
ejpam-5429	16	15	axioms	axiom	NOUN
ejpam-5429	16	16	and	and	CCONJ
ejpam-5429	16	17	inference	inference	NOUN
ejpam-5429	16	18	guidelines	guideline	NOUN
ejpam-5429	16	19	used	use	VERB
ejpam-5429	16	20	to	to	PART
ejpam-5429	16	21	derive	derive	VERB
ejpam-5429	16	22	theorems	theorem	NOUN
ejpam-5429	16	23	and	and	CCONJ
ejpam-5429	16	24	prove	prove	VERB
ejpam-5429	16	25	the	the	DET
ejpam-5429	16	26	correctness	correctness	NOUN
ejpam-5429	16	27	of	of	ADP
ejpam-5429	16	28	logical	logical	ADJ
ejpam-5429	16	29	arguments	argument	NOUN
ejpam-5429	16	30	.	.	PUNCT
ejpam-5429	17	1	theorem	theorem	ADJ
ejpam-5429	17	2	logic	logic	NOUN
ejpam-5429	17	3	and	and	CCONJ
ejpam-5429	17	4	propositional	propositional	ADJ
ejpam-5429	17	5	calculus	calculus	NOUN
ejpam-5429	17	6	are	be	AUX
ejpam-5429	17	7	other	other	ADJ
ejpam-5429	17	8	names	name	NOUN
ejpam-5429	17	9	for	for	ADP
ejpam-5429	17	10	propositional	propositional	ADJ
ejpam-5429	17	11	logic	logic	NOUN
ejpam-5429	17	12	,	,	PUNCT
ejpam-5429	17	13	which	which	PRON
ejpam-5429	17	14	deals	deal	VERB
ejpam-5429	17	15	with	with	ADP
ejpam-5429	17	16	the	the	DET
ejpam-5429	17	17	manipulation	manipulation	NOUN
ejpam-5429	17	18	and	and	CCONJ
ejpam-5429	17	19	analysis	analysis	NOUN
ejpam-5429	17	20	of	of	ADP
ejpam-5429	17	21	statements	statement	NOUN
ejpam-5429	17	22	using	use	VERB
ejpam-5429	17	23	logical	logical	ADJ
ejpam-5429	17	24	operators	operator	NOUN
ejpam-5429	17	25	like	like	ADP
ejpam-5429	17	26	or	or	CCONJ
ejpam-5429	17	27	,	,	PUNCT
ejpam-5429	17	28	and	and	CCONJ
ejpam-5429	17	29	,	,	PUNCT
ejpam-5429	17	30	and	and	CCONJ
ejpam-5429	17	31	not	not	PART
ejpam-5429	17	32	.	.	PUNCT
ejpam-5429	18	1	various	various	ADJ
ejpam-5429	18	2	mathematical	mathematical	ADJ
ejpam-5429	18	3	systems	system	NOUN
ejpam-5429	18	4	,	,	PUNCT
ejpam-5429	18	5	including	include	VERB
ejpam-5429	18	6	propositional	propositional	ADJ
ejpam-5429	18	7	logic	logic	NOUN
ejpam-5429	18	8	,	,	PUNCT
ejpam-5429	18	9	can	can	AUX
ejpam-5429	18	10	be	be	AUX
ejpam-5429	18	11	modeled	model	VERB
ejpam-5429	18	12	and	and	CCONJ
ejpam-5429	18	13	analyzed	analyze	VERB
ejpam-5429	18	14	using	use	VERB
ejpam-5429	18	15	algebraic	algebraic	ADJ
ejpam-5429	18	16	structures	structure	NOUN
ejpam-5429	18	17	,	,	PUNCT
ejpam-5429	18	18	particularly	particularly	ADV
ejpam-5429	18	19	boolean	boolean	ADJ
ejpam-5429	18	20	algebra	algebra	NOUN
ejpam-5429	18	21	,	,	PUNCT
ejpam-5429	18	22	which	which	PRON
ejpam-5429	18	23	is	be	AUX
ejpam-5429	18	24	closely	closely	ADV
ejpam-5429	18	25	related	relate	VERB
ejpam-5429	18	26	to	to	ADP
ejpam-5429	18	27	propositional	propositional	ADJ
ejpam-5429	18	28	logic	logic	NOUN
ejpam-5429	18	29	.	.	PUNCT
ejpam-5429	19	1	iseki	iseki	PROPN
ejpam-5429	20	1	[	[	X
ejpam-5429	20	2	22	22	NUM
ejpam-5429	20	3	,	,	PUNCT
ejpam-5429	20	4	23	23	NUM
ejpam-5429	20	5	]	]	PUNCT
ejpam-5429	20	6	introduced	introduce	VERB
ejpam-5429	20	7	the	the	DET
ejpam-5429	20	8	concept	concept	NOUN
ejpam-5429	20	9	of	of	ADP
ejpam-5429	20	10	bck	bck	PROPN
ejpam-5429	20	11	/	/	SYM
ejpam-5429	20	12	bci	bci	NOUN
ejpam-5429	20	13	-	-	PUNCT
ejpam-5429	20	14	algebras	algebra	NOUN
ejpam-5429	20	15	.	.	PUNCT
ejpam-5429	21	1	bci	bci	NOUN
ejpam-5429	21	2	-	-	PUNCT
ejpam-5429	21	3	algebras	algebras	X
ejpam-5429	21	4	,	,	PUNCT
ejpam-5429	21	5	also	also	ADV
ejpam-5429	21	6	known	know	VERB
ejpam-5429	21	7	as	as	ADP
ejpam-5429	21	8	bck	bck	NOUN
ejpam-5429	21	9	-	-	PUNCT
ejpam-5429	21	10	algebras	algebras	X
ejpam-5429	21	11	,	,	PUNCT
ejpam-5429	21	12	generalize	generalize	VERB
ejpam-5429	21	13	boolean	boolean	ADJ
ejpam-5429	21	14	algebras	algebra	NOUN
ejpam-5429	21	15	and	and	CCONJ
ejpam-5429	21	16	other	other	ADJ
ejpam-5429	21	17	related	relate	VERB
ejpam-5429	21	18	algebraic	algebraic	ADJ
ejpam-5429	21	19	structures	structure	NOUN
ejpam-5429	21	20	.	.	PUNCT
ejpam-5429	22	1	the	the	DET
ejpam-5429	22	2	idea	idea	NOUN
ejpam-5429	22	3	of	of	ADP
ejpam-5429	22	4	fantastic	fantastic	ADJ
ejpam-5429	22	5	ideals	ideal	NOUN
ejpam-5429	22	6	in	in	ADP
ejpam-5429	22	7	bci	bci	NOUN
ejpam-5429	22	8	-	-	PUNCT
ejpam-5429	22	9	algebras	algebras	PROPN
ejpam-5429	22	10	is	be	AUX
ejpam-5429	22	11	a	a	DET
ejpam-5429	22	12	significant	significant	ADJ
ejpam-5429	22	13	algebraic	algebraic	ADJ
ejpam-5429	22	14	substructure	substructure	NOUN
ejpam-5429	22	15	presented	present	VERB
ejpam-5429	22	16	and	and	CCONJ
ejpam-5429	22	17	discussed	discuss	VERB
ejpam-5429	22	18	by	by	ADP
ejpam-5429	22	19	saeid	saeid	PROPN
ejpam-5429	22	20	[	[	X
ejpam-5429	22	21	1	1	NUM
ejpam-5429	22	22	]	]	PUNCT
ejpam-5429	22	23	.	.	PUNCT
ejpam-5429	23	1	zadeh	zadeh	NOUN
ejpam-5429	24	1	[	[	X
ejpam-5429	24	2	39	39	NUM
ejpam-5429	24	3	]	]	PUNCT
ejpam-5429	24	4	proposed	propose	VERB
ejpam-5429	24	5	the	the	DET
ejpam-5429	24	6	concept	concept	NOUN
ejpam-5429	24	7	of	of	ADP
ejpam-5429	24	8	fuzzy	fuzzy	ADJ
ejpam-5429	24	9	(	(	PUNCT
ejpam-5429	24	10	uncertainty	uncertainty	NOUN
ejpam-5429	24	11	)	)	PUNCT
ejpam-5429	24	12	sets	set	NOUN
ejpam-5429	24	13	,	,	PUNCT
ejpam-5429	24	14	which	which	PRON
ejpam-5429	24	15	address	address	VERB
ejpam-5429	24	16	ambiguity	ambiguity	NOUN
ejpam-5429	24	17	and	and	CCONJ
ejpam-5429	24	18	vagueness	vagueness	NOUN
ejpam-5429	24	19	in	in	ADP
ejpam-5429	24	20	real	real	ADJ
ejpam-5429	24	21	world	world	NOUN
ejpam-5429	24	22	circumstances	circumstance	NOUN
ejpam-5429	24	23	.	.	PUNCT
ejpam-5429	25	1	a	a	DET
ejpam-5429	25	2	membership	membership	NOUN
ejpam-5429	25	3	function	function	NOUN
ejpam-5429	25	4	with	with	ADP
ejpam-5429	25	5	a	a	DET
ejpam-5429	25	6	range	range	NOUN
ejpam-5429	25	7	of	of	ADP
ejpam-5429	25	8	[	[	X
ejpam-5429	25	9	0,1	0,1	NUM
ejpam-5429	25	10	]	]	PUNCT
ejpam-5429	25	11	is	be	AUX
ejpam-5429	25	12	used	use	VERB
ejpam-5429	25	13	to	to	PART
ejpam-5429	25	14	illustrate	illustrate	VERB
ejpam-5429	25	15	an	an	DET
ejpam-5429	25	16	uncertainty	uncertainty	NOUN
ejpam-5429	25	17	structure	structure	NOUN
ejpam-5429	25	18	.	.	PUNCT
ejpam-5429	26	1	throughout	throughout	ADP
ejpam-5429	26	2	the	the	DET
ejpam-5429	26	3	history	history	NOUN
ejpam-5429	26	4	of	of	ADP
ejpam-5429	26	5	uncertainty	uncertainty	NOUN
ejpam-5429	26	6	set	set	NOUN
ejpam-5429	26	7	,	,	PUNCT
ejpam-5429	26	8	there	there	PRON
ejpam-5429	26	9	are	be	VERB
ejpam-5429	26	10	many	many	ADJ
ejpam-5429	26	11	kinds	kind	NOUN
ejpam-5429	26	12	of	of	ADP
ejpam-5429	26	13	uncertainty	uncertainty	NOUN
ejpam-5429	26	14	set	set	VERB
ejpam-5429	26	15	extensions	extension	NOUN
ejpam-5429	26	16	,	,	PUNCT
ejpam-5429	27	1	for	for	ADP
ejpam-5429	27	2	example	example	NOUN
ejpam-5429	27	3	bipolar	bipolar	ADJ
ejpam-5429	27	4	[	[	X
ejpam-5429	27	5	13	13	NUM
ejpam-5429	27	6	]	]	PUNCT
ejpam-5429	27	7	and	and	CCONJ
ejpam-5429	27	8	multipolar	multipolar	ADJ
ejpam-5429	27	9	[	[	X
ejpam-5429	27	10	3	3	X
ejpam-5429	27	11	]	]	PUNCT
ejpam-5429	27	12	uncertainty	uncertainty	NOUN
ejpam-5429	27	13	sets	set	NOUN
ejpam-5429	27	14	,	,	PUNCT
ejpam-5429	27	15	etc	etc	X
ejpam-5429	27	16	.	.	X
ejpam-5429	28	1	the	the	DET
ejpam-5429	28	2	bipolar	bipolar	ADJ
ejpam-5429	28	3	and	and	CCONJ
ejpam-5429	28	4	multipolar	multipolar	ADJ
ejpam-5429	28	5	uncertainty	uncertainty	NOUN
ejpam-5429	28	6	sets	set	NOUN
ejpam-5429	28	7	are	be	AUX
ejpam-5429	28	8	in	in	ADP
ejpam-5429	28	9	fact	fact	NOUN
ejpam-5429	28	10	a	a	DET
ejpam-5429	28	11	generalization	generalization	NOUN
ejpam-5429	28	12	of	of	ADP
ejpam-5429	28	13	an	an	DET
ejpam-5429	28	14	uncertainty	uncertainty	NOUN
ejpam-5429	28	15	set	set	VERB
ejpam-5429	28	16	with	with	ADP
ejpam-5429	28	17	a	a	DET
ejpam-5429	28	18	membership	membership	NOUN
ejpam-5429	28	19	degree	degree	NOUN
ejpam-5429	28	20	range	range	NOUN
ejpam-5429	28	21	[	[	X
ejpam-5429	28	22	−1	−1	NOUN
ejpam-5429	28	23	,	,	PUNCT
ejpam-5429	28	24	1	1	NUM
ejpam-5429	28	25	]	]	PUNCT
ejpam-5429	28	26	and	and	CCONJ
ejpam-5429	28	27	[	[	X
ejpam-5429	28	28	0	0	NUM
ejpam-5429	28	29	,	,	PUNCT
ejpam-5429	28	30	1]q	1]q	NUM
ejpam-5429	28	31	,	,	PUNCT
ejpam-5429	28	32	respectively	respectively	ADV
ejpam-5429	28	33	.	.	PUNCT
ejpam-5429	29	1	in	in	ADP
ejpam-5429	29	2	[	[	X
ejpam-5429	29	3	5	5	NUM
ejpam-5429	29	4	,	,	PUNCT
ejpam-5429	29	5	17	17	NUM
ejpam-5429	29	6	]	]	PUNCT
ejpam-5429	29	7	,	,	PUNCT
ejpam-5429	29	8	the	the	DET
ejpam-5429	29	9	few	few	ADJ
ejpam-5429	29	10	aspects	aspect	NOUN
ejpam-5429	29	11	of	of	ADP
ejpam-5429	29	12	the	the	DET
ejpam-5429	29	13	bipolar	bipolar	ADJ
ejpam-5429	29	14	fuzzy	fuzzy	ADJ
ejpam-5429	29	15	concept	concept	NOUN
ejpam-5429	29	16	are	be	AUX
ejpam-5429	29	17	applied	apply	VERB
ejpam-5429	29	18	to	to	ADP
ejpam-5429	29	19	algebraic	algebraic	ADJ
ejpam-5429	29	20	structures	structure	NOUN
ejpam-5429	29	21	.	.	PUNCT
ejpam-5429	30	1	the	the	PRON
ejpam-5429	30	2	qp	qp	PROPN
ejpam-5429	30	3	-	-	PUNCT
ejpam-5429	30	4	fs	fs	PROPN
ejpam-5429	30	5	has	have	VERB
ejpam-5429	30	6	an	an	DET
ejpam-5429	30	7	extensive	extensive	ADJ
ejpam-5429	30	8	range	range	NOUN
ejpam-5429	30	9	of	of	ADP
ejpam-5429	30	10	implementations	implementation	NOUN
ejpam-5429	30	11	to	to	PART
ejpam-5429	30	12	address	address	VERB
ejpam-5429	30	13	ambiguity	ambiguity	NOUN
ejpam-5429	30	14	and	and	CCONJ
ejpam-5429	30	15	vagueness	vagueness	NOUN
ejpam-5429	30	16	in	in	ADP
ejpam-5429	30	17	real	real	ADJ
ejpam-5429	30	18	world	world	NOUN
ejpam-5429	30	19	issues	issue	NOUN
ejpam-5429	30	20	related	relate	VERB
ejpam-5429	30	21	to	to	ADP
ejpam-5429	30	22	the	the	DET
ejpam-5429	30	23	quadri	quadri	NOUN
ejpam-5429	30	24	-	-	PUNCT
ejpam-5429	30	25	polar	polar	ADJ
ejpam-5429	30	26	data	datum	NOUN
ejpam-5429	30	27	,	,	PUNCT
ejpam-5429	30	28	quadri	quadri	NOUN
ejpam-5429	30	29	-	-	PUNCT
ejpam-5429	30	30	index	index	NOUN
ejpam-5429	30	31	and	and	CCONJ
ejpam-5429	30	32	quadri	quadri	NOUN
ejpam-5429	30	33	-	-	PUNCT
ejpam-5429	30	34	attributes	attribute	VERB
ejpam-5429	30	35	information	information	NOUN
ejpam-5429	30	36	.	.	PUNCT
ejpam-5429	31	1	researchers	researcher	NOUN
ejpam-5429	31	2	in	in	ADP
ejpam-5429	31	3	a	a	DET
ejpam-5429	31	4	lot	lot	NOUN
ejpam-5429	31	5	of	of	ADP
ejpam-5429	31	6	different	different	ADJ
ejpam-5429	31	7	areas	area	NOUN
ejpam-5429	31	8	are	be	AUX
ejpam-5429	31	9	very	very	ADV
ejpam-5429	31	10	interested	interested	ADJ
ejpam-5429	31	11	in	in	ADP
ejpam-5429	31	12	the	the	DET
ejpam-5429	31	13	multi	multi	ADJ
ejpam-5429	31	14	-	-	ADJ
ejpam-5429	31	15	polar	polar	ADJ
ejpam-5429	31	16	uncertainty	uncertainty	NOUN
ejpam-5429	31	17	set	set	VERB
ejpam-5429	31	18	theory	theory	NOUN
ejpam-5429	31	19	.	.	PUNCT
ejpam-5429	32	1	these	these	DET
ejpam-5429	32	2	areas	area	NOUN
ejpam-5429	32	3	include	include	VERB
ejpam-5429	32	4	lie	lie	NOUN
ejpam-5429	32	5	algebras	algebra	NOUN
ejpam-5429	32	6	[	[	X
ejpam-5429	32	7	4	4	NUM
ejpam-5429	32	8	]	]	PUNCT
ejpam-5429	32	9	,	,	PUNCT
ejpam-5429	32	10	ordered	order	VERB
ejpam-5429	32	11	semihypergroups	semihypergroup	NOUN
ejpam-5429	33	1	[	[	X
ejpam-5429	33	2	30	30	NUM
ejpam-5429	33	3	]	]	PUNCT
ejpam-5429	33	4	,	,	PUNCT
ejpam-5429	33	5	subgroups	subgroup	NOUN
ejpam-5429	33	6	[	[	X
ejpam-5429	33	7	16	16	NUM
ejpam-5429	33	8	]	]	PUNCT
ejpam-5429	33	9	and	and	CCONJ
ejpam-5429	33	10	bck	bck	PROPN
ejpam-5429	33	11	/	/	SYM
ejpam-5429	33	12	bci	bci	NOUN
ejpam-5429	33	13	-	-	PUNCT
ejpam-5429	33	14	algebras	algebras	X
ejpam-5429	34	1	[	[	X
ejpam-5429	34	2	7	7	NUM
ejpam-5429	34	3	,	,	PUNCT
ejpam-5429	34	4	36	36	NUM
ejpam-5429	34	5	]	]	PUNCT
ejpam-5429	34	6	.	.	PUNCT
ejpam-5429	35	1	rosenfeld	rosenfeld	PROPN
ejpam-5429	36	1	[	[	X
ejpam-5429	36	2	38	38	NUM
ejpam-5429	36	3	]	]	PUNCT
ejpam-5429	36	4	introduced	introduce	VERB
ejpam-5429	36	5	fuzzy	fuzzy	ADJ
ejpam-5429	36	6	groups	group	NOUN
ejpam-5429	36	7	,	,	PUNCT
ejpam-5429	36	8	while	while	SCONJ
ejpam-5429	36	9	bhakat	bhakat	PROPN
ejpam-5429	36	10	et	et	PROPN
ejpam-5429	36	11	al	al	PROPN
ejpam-5429	37	1	[	[	X
ejpam-5429	37	2	12	12	NUM
ejpam-5429	37	3	]	]	PUNCT
ejpam-5429	37	4	developed	develop	VERB
ejpam-5429	37	5	a	a	DET
ejpam-5429	37	6	specific	specific	ADJ
ejpam-5429	37	7	type	type	NOUN
ejpam-5429	37	8	denoted	denote	VERB
ejpam-5429	37	9	as	as	ADP
ejpam-5429	37	10	(	(	PUNCT
ejpam-5429	37	11	∈,∈	∈,∈	X
ejpam-5429	37	12	∨q	∨q	NOUN
ejpam-5429	37	13	)	)	PUNCT
ejpam-5429	37	14	,	,	PUNCT
ejpam-5429	37	15	based	base	VERB
ejpam-5429	37	16	on	on	ADP
ejpam-5429	37	17	point	point	NOUN
ejpam-5429	37	18	fuzzy	fuzzy	ADJ
ejpam-5429	37	19	sets	set	NOUN
ejpam-5429	37	20	within	within	ADP
ejpam-5429	37	21	group	group	NOUN
ejpam-5429	37	22	theory	theory	NOUN
ejpam-5429	37	23	.	.	PUNCT
ejpam-5429	38	1	jun	jun	PROPN
ejpam-5429	39	1	[	[	X
ejpam-5429	39	2	27	27	NUM
ejpam-5429	39	3	,	,	PUNCT
ejpam-5429	39	4	28	28	NUM
ejpam-5429	39	5	]	]	PUNCT
ejpam-5429	39	6	and	and	CCONJ
ejpam-5429	39	7	muhiuddin	muhiuddin	VERB
ejpam-5429	39	8	et	et	PROPN
ejpam-5429	39	9	al	al	PROPN
ejpam-5429	39	10	.	.	PUNCT
ejpam-5429	40	1	[	[	X
ejpam-5429	40	2	35	35	NUM
ejpam-5429	40	3	]	]	PUNCT
ejpam-5429	40	4	extended	extend	VERB
ejpam-5429	40	5	this	this	DET
ejpam-5429	40	6	concept	concept	NOUN
ejpam-5429	40	7	to	to	ADP
ejpam-5429	40	8	(	(	PUNCT
ejpam-5429	40	9	α	α	NOUN
ejpam-5429	40	10	,	,	PUNCT
ejpam-5429	40	11	β)-fuzzy	β)-fuzzy	PUNCT
ejpam-5429	40	12	subalgebra	subalgebra	PROPN
ejpam-5429	40	13	.	.	PUNCT
ejpam-5429	41	1	ibrara	ibrara	PROPN
ejpam-5429	41	2	et	et	PROPN
ejpam-5429	41	3	al	al	PROPN
ejpam-5429	41	4	.	.	PUNCT
ejpam-5429	42	1	[	[	X
ejpam-5429	42	2	19	19	NUM
ejpam-5429	42	3	]	]	PUNCT
ejpam-5429	42	4	,	,	PUNCT
ejpam-5429	42	5	dudek	dudek	PROPN
ejpam-5429	42	6	et	et	PROPN
ejpam-5429	42	7	al	al	PROPN
ejpam-5429	42	8	.	.	PUNCT
ejpam-5429	43	1	[	[	X
ejpam-5429	43	2	14	14	NUM
ejpam-5429	43	3	]	]	PUNCT
ejpam-5429	43	4	,	,	PUNCT
ejpam-5429	43	5	and	and	CCONJ
ejpam-5429	43	6	narayanan	narayanan	PROPN
ejpam-5429	43	7	et	et	PROPN
ejpam-5429	43	8	al	al	PROPN
ejpam-5429	43	9	.	.	PUNCT
ejpam-5429	44	1	[	[	X
ejpam-5429	44	2	37	37	NUM
ejpam-5429	44	3	]	]	PUNCT
ejpam-5429	44	4	furthered	further	VERB
ejpam-5429	44	5	this	this	DET
ejpam-5429	44	6	idea	idea	NOUN
ejpam-5429	44	7	with	with	ADP
ejpam-5429	44	8	extensions	extension	NOUN
ejpam-5429	44	9	to	to	ADP
ejpam-5429	44	10	semigroups	semigroup	NOUN
ejpam-5429	44	11	,	,	PUNCT
ejpam-5429	44	12	hemirings	hemiring	NOUN
ejpam-5429	44	13	,	,	PUNCT
ejpam-5429	44	14	and	and	CCONJ
ejpam-5429	44	15	near	near	ADP
ejpam-5429	44	16	-	-	PUNCT
ejpam-5429	44	17	rings	ring	NOUN
ejpam-5429	44	18	,	,	PUNCT
ejpam-5429	44	19	respectively	respectively	ADV
ejpam-5429	44	20	.	.	PUNCT
ejpam-5429	45	1	al	al	PROPN
ejpam-5429	45	2	-	-	PROPN
ejpam-5429	45	3	masarwah	masarwah	PROPN
ejpam-5429	45	4	et	et	PROPN
ejpam-5429	45	5	al	al	PROPN
ejpam-5429	45	6	.	.	PUNCT
ejpam-5429	46	1	[	[	X
ejpam-5429	46	2	6	6	NUM
ejpam-5429	46	3	,	,	PUNCT
ejpam-5429	46	4	8	8	NUM
ejpam-5429	46	5	]	]	PUNCT
ejpam-5429	46	6	explored	explore	VERB
ejpam-5429	46	7	(	(	PUNCT
ejpam-5429	46	8	α	α	X
ejpam-5429	46	9	,	,	PUNCT
ejpam-5429	46	10	β	β	NOUN
ejpam-5429	46	11	)	)	PUNCT
ejpam-5429	46	12	type	type	NOUN
ejpam-5429	46	13	subalgebras	subalgebras	PROPN
ejpam-5429	46	14	using	use	VERB
ejpam-5429	46	15	m	m	PROPN
ejpam-5429	46	16	-	-	PUNCT
ejpam-5429	46	17	f	f	PROPN
ejpam-5429	46	18	points	point	NOUN
ejpam-5429	46	19	within	within	ADP
ejpam-5429	46	20	bck	bck	PROPN
ejpam-5429	46	21	-	-	PUNCT
ejpam-5429	46	22	algebras	algebras	PROPN
ejpam-5429	46	23	.	.	PUNCT
ejpam-5429	47	1	ma	ma	PROPN
ejpam-5429	47	2	et	et	PROPN
ejpam-5429	47	3	al	al	PROPN
ejpam-5429	47	4	.	.	PUNCT
ejpam-5429	48	1	[	[	X
ejpam-5429	48	2	33	33	NUM
ejpam-5429	48	3	]	]	PUNCT
ejpam-5429	48	4	introduced	introduce	VERB
ejpam-5429	48	5	(	(	PUNCT
ejpam-5429	48	6	∈γ	∈γ	NUM
ejpam-5429	48	7	,	,	PUNCT
ejpam-5429	48	8	∈γ	∈γ	NOUN
ejpam-5429	48	9	∨qδ)-fuzzy	∨qδ)-fuzzy	NOUN
ejpam-5429	48	10	ideals	ideal	NOUN
ejpam-5429	48	11	,	,	PUNCT
ejpam-5429	48	12	while	while	SCONJ
ejpam-5429	48	13	jana	jana	PROPN
ejpam-5429	48	14	et	et	PROPN
ejpam-5429	48	15	al	al	PROPN
ejpam-5429	48	16	.	.	PUNCT
ejpam-5429	49	1	[	[	X
ejpam-5429	49	2	24	24	NUM
ejpam-5429	49	3	]	]	PUNCT
ejpam-5429	49	4	proposed	propose	VERB
ejpam-5429	49	5	(	(	PUNCT
ejpam-5429	49	6	∈γ	∈γ	NUM
ejpam-5429	49	7	,	,	PUNCT
ejpam-5429	49	8	∈γ	∈γ	NUM
ejpam-5429	49	9	∨qδ	∨qδ	NUM
ejpam-5429	49	10	)	)	PUNCT
ejpam-5429	49	11	fuzzy	fuzzy	ADJ
ejpam-5429	49	12	soft	soft	ADJ
ejpam-5429	49	13	bci	bci	NOUN
ejpam-5429	49	14	-	-	PUNCT
ejpam-5429	49	15	algebras	algebra	NOUN
ejpam-5429	49	16	.	.	PUNCT
ejpam-5429	49	17	zulfiqar	zulfiqar	PROPN
ejpam-5429	49	18	et	et	PROPN
ejpam-5429	49	19	al	al	PROPN
ejpam-5429	49	20	.	.	PUNCT
ejpam-5429	50	1	[	[	X
ejpam-5429	50	2	42	42	NUM
ejpam-5429	50	3	,	,	PUNCT
ejpam-5429	50	4	43	43	NUM
ejpam-5429	50	5	]	]	PUNCT
ejpam-5429	50	6	introduced	introduce	VERB
ejpam-5429	50	7	the	the	DET
ejpam-5429	50	8	idea	idea	NOUN
ejpam-5429	50	9	of	of	ADP
ejpam-5429	50	10	(	(	PUNCT
ejpam-5429	50	11	∈γ	∈γ	NUM
ejpam-5429	50	12	,	,	PUNCT
ejpam-5429	50	13	∈γ	∈γ	NOUN
ejpam-5429	50	14	∨qδ)-fuzzy	∨qδ)-fuzzy	VERB
ejpam-5429	50	15	subcommutative	subcommutative	ADJ
ejpam-5429	50	16	ideals	ideal	NOUN
ejpam-5429	50	17	and	and	CCONJ
ejpam-5429	50	18	fuzzy	fuzzy	ADJ
ejpam-5429	50	19	fantastic	fantastic	ADJ
ejpam-5429	50	20	ideals	ideal	NOUN
ejpam-5429	50	21	in	in	ADP
ejpam-5429	50	22	bci	bci	PROPN
ejpam-5429	50	23	/	/	SYM
ejpam-5429	50	24	bch	bch	PROPN
ejpam-5429	50	25	-	-	PUNCT
ejpam-5429	50	26	algebras	algebras	PROPN
ejpam-5429	50	27	.	.	PUNCT
ejpam-5429	51	1	zhan	zhan	PROPN
ejpam-5429	52	1	[	[	X
ejpam-5429	52	2	41	41	NUM
ejpam-5429	52	3	]	]	PUNCT
ejpam-5429	52	4	contributed	contribute	VERB
ejpam-5429	52	5	with	with	ADP
ejpam-5429	52	6	(	(	PUNCT
ejpam-5429	52	7	∈γ	∈γ	NUM
ejpam-5429	52	8	,	,	PUNCT
ejpam-5429	52	9	∈γ	∈γ	NOUN
ejpam-5429	52	10	∨qδ)-fuzzy	∨qδ)-fuzzy	VERB
ejpam-5429	52	11	soft	soft	ADJ
ejpam-5429	52	12	γ	γ	NOUN
ejpam-5429	52	13	-	-	ADJ
ejpam-5429	52	14	hyper	hyper	ADJ
ejpam-5429	52	15	ideals	ideal	NOUN
ejpam-5429	52	16	.	.	PUNCT
ejpam-5429	53	1	abuhijleh	abuhijleh	PROPN
ejpam-5429	53	2	et	et	PROPN
ejpam-5429	53	3	al	al	PROPN
ejpam-5429	53	4	.	.	PUNCT
ejpam-5429	54	1	[	[	X
ejpam-5429	54	2	2	2	X
ejpam-5429	54	3	]	]	PUNCT
ejpam-5429	54	4	introduced	introduce	VERB
ejpam-5429	54	5	the	the	DET
ejpam-5429	54	6	complex	complex	ADJ
ejpam-5429	54	7	fuzzy	fuzzy	ADJ
ejpam-5429	54	8	groups	group	NOUN
ejpam-5429	54	9	.	.	PUNCT
ejpam-5429	55	1	fallath	fallath	PROPN
ejpam-5429	55	2	et	et	PROPN
ejpam-5429	55	3	al	al	PROPN
ejpam-5429	55	4	.	.	PUNCT
ejpam-5429	56	1	[	[	X
ejpam-5429	56	2	15	15	NUM
ejpam-5429	56	3	]	]	PUNCT
ejpam-5429	56	4	introduced	introduce	VERB
ejpam-5429	56	5	cosets	coset	NOUN
ejpam-5429	56	6	and	and	CCONJ
ejpam-5429	56	7	normals	normal	NOUN
ejpam-5429	56	8	of	of	ADP
ejpam-5429	56	9	(	(	PUNCT
ejpam-5429	56	10	γ	γ	X
ejpam-5429	56	11	,	,	PUNCT
ejpam-5429	56	12	δ)-fuzzy	δ)-fuzzy	ADJ
ejpam-5429	56	13	hxsubgroups	hxsubgroup	NOUN
ejpam-5429	56	14	.	.	PUNCT
ejpam-5429	57	1	balamurugan	balamurugan	PROPN
ejpam-5429	57	2	et	et	PROPN
ejpam-5429	57	3	al	al	PROPN
ejpam-5429	57	4	.	.	PUNCT
ejpam-5429	58	1	[	[	X
ejpam-5429	58	2	10	10	NUM
ejpam-5429	58	3	,	,	PUNCT
ejpam-5429	58	4	18	18	NUM
ejpam-5429	58	5	]	]	PUNCT
ejpam-5429	58	6	introduced	introduce	VERB
ejpam-5429	58	7	anti	anti	ADJ
ejpam-5429	58	8	-	-	ADJ
ejpam-5429	58	9	intuitionistic	intuitionistic	ADJ
ejpam-5429	58	10	fuzzy	fuzzy	ADJ
ejpam-5429	58	11	soft	soft	ADJ
ejpam-5429	58	12	ideals	ideal	NOUN
ejpam-5429	58	13	in	in	ADP
ejpam-5429	58	14	bck	bck	PROPN
ejpam-5429	58	15	/	/	SYM
ejpam-5429	58	16	bci	bci	PROPN
ejpam-5429	58	17	/	/	SYM
ejpam-5429	58	18	bg	bg	PROPN
ejpam-5429	58	19	-	-	PUNCT
ejpam-5429	58	20	algebras	algebras	PROPN
ejpam-5429	58	21	.	.	PUNCT
ejpam-5429	59	1	balamurugan	balamurugan	PROPN
ejpam-5429	59	2	et	et	PROPN
ejpam-5429	59	3	al	al	PROPN
ejpam-5429	59	4	.	.	PUNCT
ejpam-5429	60	1	[	[	X
ejpam-5429	60	2	11	11	NUM
ejpam-5429	60	3	,	,	PUNCT
ejpam-5429	60	4	34	34	NUM
ejpam-5429	60	5	]	]	PUNCT
ejpam-5429	60	6	introduced	introduce	VERB
ejpam-5429	60	7	tripolar	tripolar	ADJ
ejpam-5429	60	8	picture	picture	NOUN
ejpam-5429	60	9	fuzzy	fuzzy	ADJ
ejpam-5429	60	10	ideals	ideal	NOUN
ejpam-5429	60	11	and	and	CCONJ
ejpam-5429	60	12	bipolar	bipolar	ADJ
ejpam-5429	60	13	intuitionistic	intuitionistic	ADJ
ejpam-5429	60	14	fuzzy	fuzzy	ADJ
ejpam-5429	60	15	soft	soft	ADJ
ejpam-5429	60	16	ideals	ideal	NOUN
ejpam-5429	60	17	in	in	ADP
ejpam-5429	60	18	bck	bck	PROPN
ejpam-5429	60	19	/	/	SYM
ejpam-5429	60	20	bci	bci	NOUN
ejpam-5429	60	21	-	-	PUNCT
ejpam-5429	60	22	algebras	algebras	X
ejpam-5429	60	23	.	.	PUNCT
ejpam-5429	61	1	moin	moin	PROPN
ejpam-5429	61	2	et	et	PROPN
ejpam-5429	61	3	al	al	PROPN
ejpam-5429	61	4	.	.	PUNCT
ejpam-5429	62	1	[	[	X
ejpam-5429	62	2	9	9	NUM
ejpam-5429	62	3	]	]	PUNCT
ejpam-5429	62	4	introduced	introduce	VERB
ejpam-5429	62	5	and	and	CCONJ
ejpam-5429	62	6	studied	study	VERB
ejpam-5429	62	7	a	a	DET
ejpam-5429	62	8	graph	graph	NOUN
ejpam-5429	62	9	associated	associate	VERB
ejpam-5429	62	10	to	to	ADP
ejpam-5429	62	11	up	up	ADV
ejpam-5429	62	12	-	-	PUNCT
ejpam-5429	62	13	algebras	algebras	X
ejpam-5429	62	14	.	.	PUNCT
ejpam-5429	63	1	fuzzy	fuzzy	ADJ
ejpam-5429	63	2	bi	bi	NOUN
ejpam-5429	63	3	-	-	NOUN
ejpam-5429	63	4	ideals	ideal	NOUN
ejpam-5429	63	5	in	in	ADP
ejpam-5429	63	6	ternary	ternary	ADJ
ejpam-5429	63	7	semirings	semiring	NOUN
ejpam-5429	63	8	are	be	AUX
ejpam-5429	63	9	studied	study	VERB
ejpam-5429	63	10	and	and	CCONJ
ejpam-5429	63	11	explored	explore	VERB
ejpam-5429	63	12	by	by	ADP
ejpam-5429	63	13	kavikumar	kavikumar	PROPN
ejpam-5429	63	14	[	[	X
ejpam-5429	63	15	29	29	NUM
ejpam-5429	63	16	]	]	PUNCT
ejpam-5429	63	17	.	.	PUNCT
ejpam-5429	64	1	in	in	ADP
ejpam-5429	64	2	this	this	DET
ejpam-5429	64	3	work	work	NOUN
ejpam-5429	64	4	,	,	PUNCT
ejpam-5429	64	5	we	we	PRON
ejpam-5429	64	6	combine	combine	VERB
ejpam-5429	64	7	qp	qp	NOUN
ejpam-5429	64	8	-	-	PUNCT
ejpam-5429	64	9	f	f	PROPN
ejpam-5429	64	10	sets	set	NOUN
ejpam-5429	64	11	with	with	ADP
ejpam-5429	64	12	bci	bci	NOUN
ejpam-5429	64	13	-	-	PUNCT
ejpam-5429	64	14	algebras	algebras	PROPN
ejpam-5429	64	15	to	to	PART
ejpam-5429	64	16	extend	extend	VERB
ejpam-5429	64	17	fuzzy	fuzzy	ADJ
ejpam-5429	64	18	set	set	NOUN
ejpam-5429	64	19	theory	theory	NOUN
ejpam-5429	64	20	and	and	CCONJ
ejpam-5429	64	21	provide	provide	VERB
ejpam-5429	64	22	new	new	ADJ
ejpam-5429	64	23	approaches	approach	NOUN
ejpam-5429	64	24	for	for	ADP
ejpam-5429	64	25	studying	study	VERB
ejpam-5429	64	26	quadri	quadri	NOUN
ejpam-5429	64	27	-	-	PUNCT
ejpam-5429	64	28	polar	polar	ADJ
ejpam-5429	64	29	fuzzy	fuzzy	ADJ
ejpam-5429	64	30	bci	bci	NOUN
ejpam-5429	64	31	-	-	PUNCT
ejpam-5429	64	32	algebras	algebras	X
ejpam-5429	64	33	.	.	PUNCT
ejpam-5429	65	1	we	we	PRON
ejpam-5429	65	2	introduce	introduce	VERB
ejpam-5429	65	3	a	a	DET
ejpam-5429	65	4	new	new	ADJ
ejpam-5429	65	5	class	class	NOUN
ejpam-5429	65	6	of	of	ADP
ejpam-5429	65	7	generalized	generalized	ADJ
ejpam-5429	65	8	qp-(ϖ,ϑ)-ffi	qp-(ϖ,ϑ)-ffi	PROPN
ejpam-5429	65	9	.	.	PUNCT
ejpam-5429	66	1	the	the	DET
ejpam-5429	66	2	properties	property	NOUN
ejpam-5429	66	3	of	of	ADP
ejpam-5429	66	4	qp-(ϖ,ϑ)-ffi(s	qp-(ϖ,ϑ)-ffi(s	NOUN
ejpam-5429	66	5	)	)	PUNCT
ejpam-5429	66	6	are	be	AUX
ejpam-5429	66	7	highlighted	highlight	VERB
ejpam-5429	66	8	.	.	PUNCT
ejpam-5429	67	1	k.	k.	PROPN
ejpam-5429	67	2	h.	h.	PROPN
ejpam-5429	67	3	hakami	hakami	PROPN
ejpam-5429	67	4	et	et	PROPN
ejpam-5429	67	5	al	al	PROPN
ejpam-5429	67	6	.	.	PUNCT
ejpam-5429	67	7	/	/	SYM
ejpam-5429	67	8	eur	eur	PROPN
ejpam-5429	67	9	.	.	PUNCT
ejpam-5429	68	1	j.	j.	PROPN
ejpam-5429	68	2	pure	pure	PROPN
ejpam-5429	68	3	appl	appl	PROPN
ejpam-5429	68	4	.	.	PROPN
ejpam-5429	68	5	math	math	PROPN
ejpam-5429	68	6	,	,	PUNCT
ejpam-5429	68	7	17	17	NUM
ejpam-5429	68	8	(	(	PUNCT
ejpam-5429	68	9	4	4	NUM
ejpam-5429	68	10	)	)	PUNCT
ejpam-5429	68	11	(	(	PUNCT
ejpam-5429	68	12	2024	2024	NUM
ejpam-5429	68	13	)	)	PUNCT
ejpam-5429	68	14	,	,	PUNCT
ejpam-5429	68	15	3129	3129	NUM
ejpam-5429	68	16	-	-	SYM
ejpam-5429	68	17	3155	3155	NUM
ejpam-5429	68	18	3131	3131	NUM
ejpam-5429	69	1	we	we	PRON
ejpam-5429	69	2	then	then	ADV
ejpam-5429	69	3	discuss	discuss	VERB
ejpam-5429	69	4	qp-(∈σ̃,∈σ̃	qp-(∈σ̃,∈σ̃	PROPN
ejpam-5429	69	5	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	69	6	)	)	PUNCT
ejpam-5429	69	7	ffi(s	ffi(s	PROPN
ejpam-5429	69	8	)	)	PUNCT
ejpam-5429	69	9	and	and	CCONJ
ejpam-5429	69	10	explore	explore	VERB
ejpam-5429	69	11	their	their	PRON
ejpam-5429	69	12	properties	property	NOUN
ejpam-5429	69	13	.	.	PUNCT
ejpam-5429	70	1	characterization	characterization	NOUN
ejpam-5429	70	2	theorems	theorem	NOUN
ejpam-5429	70	3	for	for	ADP
ejpam-5429	70	4	qp-(∈σ̃,∈σ̃	qp-(∈σ̃,∈σ̃	PROPN
ejpam-5429	70	5	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	70	6	)	)	PUNCT
ejpam-5429	70	7	-ffi(s	-ffi(s	PROPN
ejpam-5429	70	8	)	)	PUNCT
ejpam-5429	70	9	are	be	AUX
ejpam-5429	70	10	also	also	ADV
ejpam-5429	70	11	established	establish	VERB
ejpam-5429	70	12	.	.	PUNCT
ejpam-5429	71	1	finally	finally	ADV
ejpam-5429	71	2	,	,	PUNCT
ejpam-5429	71	3	we	we	PRON
ejpam-5429	71	4	present	present	VERB
ejpam-5429	71	5	a	a	DET
ejpam-5429	71	6	q	q	ADJ
ejpam-5429	71	7	-	-	PUNCT
ejpam-5429	71	8	pf	pf	NOUN
ejpam-5429	71	9	topsis	topsis	NOUN
ejpam-5429	71	10	methodology	methodology	NOUN
ejpam-5429	71	11	,	,	PUNCT
ejpam-5429	71	12	discuss	discuss	VERB
ejpam-5429	71	13	potential	potential	ADJ
ejpam-5429	71	14	applications	application	NOUN
ejpam-5429	71	15	,	,	PUNCT
ejpam-5429	71	16	compare	compare	VERB
ejpam-5429	71	17	it	it	PRON
ejpam-5429	71	18	with	with	ADP
ejpam-5429	71	19	existing	exist	VERB
ejpam-5429	71	20	topsis	topsis	NOUN
ejpam-5429	71	21	methods	method	NOUN
ejpam-5429	71	22	,	,	PUNCT
ejpam-5429	71	23	and	and	CCONJ
ejpam-5429	71	24	propose	propose	VERB
ejpam-5429	71	25	future	future	ADJ
ejpam-5429	71	26	directions	direction	NOUN
ejpam-5429	71	27	.	.	PUNCT
ejpam-5429	72	1	to	to	PART
ejpam-5429	72	2	explain	explain	VERB
ejpam-5429	72	3	the	the	DET
ejpam-5429	72	4	novelty	novelty	NOUN
ejpam-5429	72	5	of	of	ADP
ejpam-5429	72	6	this	this	DET
ejpam-5429	72	7	structure	structure	NOUN
ejpam-5429	72	8	,	,	PUNCT
ejpam-5429	72	9	some	some	DET
ejpam-5429	72	10	contributions	contribution	NOUN
ejpam-5429	72	11	by	by	ADP
ejpam-5429	72	12	several	several	ADJ
ejpam-5429	72	13	researchers	researcher	NOUN
ejpam-5429	72	14	towards	towards	ADP
ejpam-5429	72	15	qp	qp	NOUN
ejpam-5429	72	16	-	-	PUNCT
ejpam-5429	72	17	ffi(s	ffi(s	NOUN
ejpam-5429	72	18	)	)	PUNCT
ejpam-5429	72	19	,	,	PUNCT
ejpam-5429	72	20	qp-(ϖ,ϑ)-ffis	qp-(ϖ,ϑ)-ffis	ADJ
ejpam-5429	72	21	and	and	CCONJ
ejpam-5429	72	22	qp-(∈σ̃,∈σ̃	qp-(∈σ̃,∈σ̃	PRON
ejpam-5429	72	23	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	72	24	)	)	PUNCT
ejpam-5429	72	25	-ffi(s	-ffi(s	PROPN
ejpam-5429	72	26	)	)	PUNCT
ejpam-5429	72	27	in	in	ADP
ejpam-5429	72	28	bci	bci	NOUN
ejpam-5429	72	29	-	-	PUNCT
ejpam-5429	72	30	algebras	algebra	NOUN
ejpam-5429	72	31	are	be	AUX
ejpam-5429	72	32	presented	present	VERB
ejpam-5429	72	33	in	in	ADP
ejpam-5429	72	34	table	table	NOUN
ejpam-5429	72	35	1	1	NUM
ejpam-5429	72	36	.	.	PUNCT
ejpam-5429	72	37	table	table	NOUN
ejpam-5429	72	38	1	1	NUM
ejpam-5429	72	39	:	:	PUNCT
ejpam-5429	72	40	contributions	contribution	NOUN
ejpam-5429	72	41	of	of	ADP
ejpam-5429	72	42	several	several	ADJ
ejpam-5429	72	43	researchers	researcher	NOUN
ejpam-5429	72	44	toward	toward	ADP
ejpam-5429	72	45	ceratin	ceratin	PROPN
ejpam-5429	72	46	generalizations	generalization	NOUN
ejpam-5429	72	47	of	of	ADP
ejpam-5429	72	48	qp	qp	PROPN
ejpam-5429	72	49	-	-	PUNCT
ejpam-5429	72	50	ffi(s	ffi(s	NOUN
ejpam-5429	72	51	)	)	PUNCT
ejpam-5429	72	52	.	.	PUNCT
ejpam-5429	73	1	authors	author	NOUN
ejpam-5429	73	2	year	year	VERB
ejpam-5429	73	3	contributions	contribution	NOUN
ejpam-5429	73	4	rosenfeld	rosenfeld	PROPN
ejpam-5429	74	1	[	[	X
ejpam-5429	74	2	38	38	NUM
ejpam-5429	74	3	]	]	SYM
ejpam-5429	74	4	1971	1971	NUM
ejpam-5429	74	5	creation	creation	NOUN
ejpam-5429	74	6	of	of	ADP
ejpam-5429	74	7	fuzzy	fuzzy	ADJ
ejpam-5429	74	8	subgroups	subgroup	NOUN
ejpam-5429	74	9	.	.	PUNCT
ejpam-5429	75	1	xi	xi	X
ejpam-5429	76	1	[	[	X
ejpam-5429	76	2	40	40	NUM
ejpam-5429	76	3	]	]	PUNCT
ejpam-5429	76	4	1991	1991	NUM
ejpam-5429	76	5	creation	creation	NOUN
ejpam-5429	76	6	of	of	ADP
ejpam-5429	76	7	fuzzy	fuzzy	ADJ
ejpam-5429	76	8	ideals	ideal	NOUN
ejpam-5429	76	9	.	.	PUNCT
ejpam-5429	77	1	bhakat	bhakat	PROPN
ejpam-5429	77	2	and	and	CCONJ
ejpam-5429	77	3	das	das	PROPN
ejpam-5429	77	4	[	[	X
ejpam-5429	77	5	12	12	NUM
ejpam-5429	77	6	]	]	PUNCT
ejpam-5429	77	7	1996	1996	NUM
ejpam-5429	77	8	certain	certain	ADJ
ejpam-5429	77	9	extensions	extension	NOUN
ejpam-5429	77	10	of	of	ADP
ejpam-5429	77	11	fuzzy	fuzzy	ADJ
ejpam-5429	77	12	subgroups	subgroup	NOUN
ejpam-5429	77	13	.	.	PUNCT
ejpam-5429	78	1	jun	jun	PROPN
ejpam-5429	79	1	[	[	X
ejpam-5429	79	2	26	26	NUM
ejpam-5429	79	3	]	]	SYM
ejpam-5429	79	4	2004	2004	NUM
ejpam-5429	79	5	creation	creation	NOUN
ejpam-5429	79	6	of	of	ADP
ejpam-5429	79	7	(	(	PUNCT
ejpam-5429	79	8	α	α	NOUN
ejpam-5429	79	9	,	,	PUNCT
ejpam-5429	79	10	β)-fuzzy	β)-fuzzy	PUNCT
ejpam-5429	79	11	ideals	ideal	NOUN
ejpam-5429	79	12	.	.	PUNCT
ejpam-5429	80	1	lee	lee	PROPN
ejpam-5429	81	1	[	[	X
ejpam-5429	81	2	32	32	NUM
ejpam-5429	81	3	]	]	SYM
ejpam-5429	81	4	2009	2009	NUM
ejpam-5429	81	5	creation	creation	NOUN
ejpam-5429	81	6	of	of	ADP
ejpam-5429	81	7	bipolar	bipolar	ADJ
ejpam-5429	81	8	fuzzy	fuzzy	ADJ
ejpam-5429	81	9	ideals	ideal	NOUN
ejpam-5429	81	10	.	.	PUNCT
ejpam-5429	82	1	jana	jana	PROPN
ejpam-5429	82	2	et	et	PROPN
ejpam-5429	82	3	al	al	PROPN
ejpam-5429	82	4	.	.	PUNCT
ejpam-5429	83	1	[	[	X
ejpam-5429	83	2	25	25	NUM
ejpam-5429	83	3	]	]	SYM
ejpam-5429	83	4	2017	2017	NUM
ejpam-5429	83	5	extensions	extension	NOUN
ejpam-5429	83	6	of	of	ADP
ejpam-5429	83	7	bipolar	bipolar	ADJ
ejpam-5429	83	8	fuzzy	fuzzy	ADJ
ejpam-5429	83	9	ideals	ideal	NOUN
ejpam-5429	83	10	.	.	PUNCT
ejpam-5429	84	1	al	al	PROPN
ejpam-5429	84	2	-	-	PUNCT
ejpam-5429	84	3	masarwah	masarwah	PROPN
ejpam-5429	84	4	and	and	CCONJ
ejpam-5429	84	5	ahmad	ahmad	PROPN
ejpam-5429	85	1	[	[	X
ejpam-5429	85	2	6–8	6–8	X
ejpam-5429	85	3	]	]	SYM
ejpam-5429	85	4	2018	2018	NUM
ejpam-5429	85	5	creation	creation	NOUN
ejpam-5429	85	6	of	of	ADP
ejpam-5429	85	7	multi	multi	ADJ
ejpam-5429	85	8	p	p	PROPN
ejpam-5429	85	9	-	-	PUNCT
ejpam-5429	85	10	fis	fis	PROPN
ejpam-5429	85	11	.	.	PUNCT
ejpam-5429	86	1	alqahtani	alqahtani	PROPN
ejpam-5429	86	2	et	et	PROPN
ejpam-5429	86	3	al	al	PROPN
ejpam-5429	86	4	.	.	PROPN
ejpam-5429	87	1	present	present	ADJ
ejpam-5429	87	2	creation	creation	NOUN
ejpam-5429	87	3	of	of	ADP
ejpam-5429	87	4	qp-(∈σ̃,∈σ̃	qp-(∈σ̃,∈σ̃	PROPN
ejpam-5429	87	5	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	87	6	)	)	PUNCT
ejpam-5429	87	7	-ffi(s	-ffi(s	PROPN
ejpam-5429	87	8	)	)	PUNCT
ejpam-5429	87	9	.	.	PUNCT
ejpam-5429	88	1	2	2	X
ejpam-5429	88	2	.	.	X
ejpam-5429	88	3	preliminaries	preliminary	NOUN
ejpam-5429	88	4	bci	bci	NOUN
ejpam-5429	88	5	-	-	PUNCT
ejpam-5429	88	6	algebras	algebra	NOUN
ejpam-5429	88	7	are	be	AUX
ejpam-5429	88	8	types	type	NOUN
ejpam-5429	88	9	of	of	ADP
ejpam-5429	88	10	algebraic	algebraic	ADJ
ejpam-5429	88	11	structures	structure	NOUN
ejpam-5429	88	12	used	use	VERB
ejpam-5429	88	13	in	in	ADP
ejpam-5429	88	14	the	the	DET
ejpam-5429	88	15	study	study	NOUN
ejpam-5429	88	16	of	of	ADP
ejpam-5429	88	17	non	non	ADJ
ejpam-5429	88	18	-	-	ADJ
ejpam-5429	88	19	classical	classical	ADJ
ejpam-5429	88	20	logics	logic	NOUN
ejpam-5429	88	21	,	,	PUNCT
ejpam-5429	88	22	particularly	particularly	ADV
ejpam-5429	88	23	in	in	ADP
ejpam-5429	88	24	the	the	DET
ejpam-5429	88	25	context	context	NOUN
ejpam-5429	88	26	of	of	ADP
ejpam-5429	88	27	certain	certain	ADJ
ejpam-5429	88	28	types	type	NOUN
ejpam-5429	88	29	of	of	ADP
ejpam-5429	88	30	implication	implication	NOUN
ejpam-5429	88	31	algebras	algebra	NOUN
ejpam-5429	88	32	.	.	PUNCT
ejpam-5429	89	1	these	these	DET
ejpam-5429	89	2	algebras	algebra	NOUN
ejpam-5429	89	3	generalize	generalize	VERB
ejpam-5429	89	4	certain	certain	ADJ
ejpam-5429	89	5	aspects	aspect	NOUN
ejpam-5429	89	6	of	of	ADP
ejpam-5429	89	7	set	set	NOUN
ejpam-5429	89	8	theory	theory	NOUN
ejpam-5429	89	9	,	,	PUNCT
ejpam-5429	89	10	logic	logic	NOUN
ejpam-5429	89	11	and	and	CCONJ
ejpam-5429	89	12	have	have	VERB
ejpam-5429	89	13	applications	application	NOUN
ejpam-5429	89	14	in	in	ADP
ejpam-5429	89	15	some	some	DET
ejpam-5429	89	16	areas	area	NOUN
ejpam-5429	89	17	,	,	PUNCT
ejpam-5429	89	18	such	such	ADJ
ejpam-5429	89	19	as	as	ADP
ejpam-5429	89	20	theoretical	theoretical	ADJ
ejpam-5429	89	21	computer	computer	NOUN
ejpam-5429	89	22	science	science	NOUN
ejpam-5429	89	23	and	and	CCONJ
ejpam-5429	89	24	mathematical	mathematical	ADJ
ejpam-5429	89	25	logic	logic	NOUN
ejpam-5429	89	26	.	.	PUNCT
ejpam-5429	90	1	a	a	DET
ejpam-5429	90	2	bci	bci	NOUN
ejpam-5429	90	3	-	-	NOUN
ejpam-5429	90	4	algebra	algebra	NOUN
ejpam-5429	90	5	is	be	AUX
ejpam-5429	90	6	a	a	DET
ejpam-5429	90	7	structure	structure	NOUN
ejpam-5429	90	8	(	(	PUNCT
ejpam-5429	90	9	ℵ̃	ℵ̃	PROPN
ejpam-5429	90	10	;	;	PUNCT
ejpam-5429	90	11	≬	≬	PROPN
ejpam-5429	90	12	,	,	PUNCT
ejpam-5429	90	13	0	0	NUM
ejpam-5429	90	14	)	)	PUNCT
ejpam-5429	90	15	consisting	consist	VERB
ejpam-5429	90	16	of	of	ADP
ejpam-5429	90	17	a	a	DET
ejpam-5429	90	18	non	non	ADJ
ejpam-5429	90	19	-	-	ADJ
ejpam-5429	90	20	void	void	ADJ
ejpam-5429	90	21	set	set	NOUN
ejpam-5429	90	22	ℵ̃	ℵ̃	PROPN
ejpam-5429	90	23	,	,	PUNCT
ejpam-5429	90	24	a	a	DET
ejpam-5429	90	25	binary	binary	ADJ
ejpam-5429	90	26	operation	operation	NOUN
ejpam-5429	90	27	≬	≬	PROPN
ejpam-5429	90	28	on	on	ADP
ejpam-5429	90	29	ℵ̃	ℵ̃	PROPN
ejpam-5429	90	30	,	,	PUNCT
ejpam-5429	90	31	and	and	CCONJ
ejpam-5429	90	32	a	a	DET
ejpam-5429	90	33	constant	constant	ADJ
ejpam-5429	90	34	0	0	NUM
ejpam-5429	90	35	∈	∈	PROPN
ejpam-5429	90	36	ℵ̃	ℵ̃	PROPN
ejpam-5429	90	37	,	,	PUNCT
ejpam-5429	90	38	satisfying	satisfy	VERB
ejpam-5429	90	39	the	the	DET
ejpam-5429	90	40	following	follow	VERB
ejpam-5429	90	41	axioms	axiom	NOUN
ejpam-5429	90	42	:	:	PUNCT
ejpam-5429	90	43	∀ς̇	∀ς̇	NOUN
ejpam-5429	90	44	,	,	PUNCT
ejpam-5429	90	45	ϱ̇	ϱ̇	PROPN
ejpam-5429	90	46	,	,	PUNCT
ejpam-5429	90	47	κ̇	κ̇	PROPN
ejpam-5429	90	48	∈	∈	PROPN
ejpam-5429	90	49	ℵ̃	ℵ̃	PROPN
ejpam-5429	90	50	(	(	PUNCT
ejpam-5429	90	51	i1	i1	PROPN
ejpam-5429	90	52	)	)	PUNCT
ejpam-5429	90	53	(	(	PUNCT
ejpam-5429	90	54	(	(	PUNCT
ejpam-5429	90	55	ς̇	ς̇	PROPN
ejpam-5429	90	56	≬	≬	PROPN
ejpam-5429	90	57	ϱ̇	ϱ̇	PROPN
ejpam-5429	90	58	)	)	PUNCT
ejpam-5429	90	59	≬	≬	PROPN
ejpam-5429	90	60	(	(	PUNCT
ejpam-5429	90	61	ς̇	ς̇	PROPN
ejpam-5429	90	62	≬	≬	PROPN
ejpam-5429	90	63	κ̇	κ̇	PROPN
ejpam-5429	90	64	)	)	PUNCT
ejpam-5429	90	65	)	)	PUNCT
ejpam-5429	91	1	≬	≬	PROPN
ejpam-5429	91	2	(	(	PUNCT
ejpam-5429	91	3	κ̇	κ̇	INTJ
ejpam-5429	91	4	≬	≬	PROPN
ejpam-5429	91	5	ϱ̇	ϱ̇	PROPN
ejpam-5429	91	6	)	)	PUNCT
ejpam-5429	91	7	=	=	SYM
ejpam-5429	91	8	0	0	NUM
ejpam-5429	91	9	,	,	PUNCT
ejpam-5429	91	10	(	(	PUNCT
ejpam-5429	91	11	i2	i2	PROPN
ejpam-5429	91	12	)	)	PUNCT
ejpam-5429	91	13	(	(	PUNCT
ejpam-5429	91	14	ς̇	ς̇	NOUN
ejpam-5429	91	15	≬	≬	PROPN
ejpam-5429	91	16	(	(	PUNCT
ejpam-5429	91	17	ς̇	ς̇	PROPN
ejpam-5429	91	18	≬	≬	PROPN
ejpam-5429	91	19	ϱ̇	ϱ̇	PROPN
ejpam-5429	91	20	)	)	PUNCT
ejpam-5429	91	21	)	)	PUNCT
ejpam-5429	92	1	≬	≬	PROPN
ejpam-5429	92	2	ϱ̇	ϱ̇	PROPN
ejpam-5429	93	1	=	=	SYM
ejpam-5429	93	2	0	0	NUM
ejpam-5429	93	3	,	,	PUNCT
ejpam-5429	93	4	(	(	PUNCT
ejpam-5429	93	5	i3	i3	NOUN
ejpam-5429	93	6	)	)	PUNCT
ejpam-5429	93	7	ς̇	ς̇	NOUN
ejpam-5429	93	8	≬	≬	PROPN
ejpam-5429	93	9	ς̇	ς̇	NOUN
ejpam-5429	93	10	=	=	SYM
ejpam-5429	93	11	0	0	PROPN
ejpam-5429	93	12	,	,	PUNCT
ejpam-5429	93	13	(	(	PUNCT
ejpam-5429	93	14	i4	i4	PROPN
ejpam-5429	93	15	)	)	PUNCT
ejpam-5429	93	16	ς̇	ς̇	NOUN
ejpam-5429	93	17	≬	≬	PROPN
ejpam-5429	93	18	ϱ̇	ϱ̇	PROPN
ejpam-5429	94	1	=	=	SYM
ejpam-5429	94	2	0	0	NUM
ejpam-5429	94	3	,	,	PUNCT
ejpam-5429	94	4	ϱ̇	ϱ̇	PROPN
ejpam-5429	94	5	≬	≬	PROPN
ejpam-5429	94	6	ς̇	ς̇	NOUN
ejpam-5429	94	7	=	=	SYM
ejpam-5429	94	8	0	0	PROPN
ejpam-5429	94	9	⇒	⇒	NOUN
ejpam-5429	94	10	ς̇	ς̇	NOUN
ejpam-5429	94	11	=	=	SYM
ejpam-5429	94	12	ϱ̇.	ϱ̇.	PROPN
ejpam-5429	94	13	a	a	DET
ejpam-5429	94	14	subset	subset	NOUN
ejpam-5429	94	15	i	i	PRON
ejpam-5429	94	16	of	of	ADP
ejpam-5429	94	17	ℵ̃	ℵ̃	PROPN
ejpam-5429	94	18	is	be	AUX
ejpam-5429	94	19	referred	refer	VERB
ejpam-5429	94	20	to	to	ADP
ejpam-5429	94	21	an	an	DET
ejpam-5429	94	22	ideal	ideal	NOUN
ejpam-5429	94	23	of	of	ADP
ejpam-5429	94	24	ℵ̃	ℵ̃	PROPN
ejpam-5429	94	25	(	(	PUNCT
ejpam-5429	94	26	see	see	VERB
ejpam-5429	94	27	[	[	X
ejpam-5429	94	28	22	22	NUM
ejpam-5429	94	29	,	,	PUNCT
ejpam-5429	94	30	23	23	NUM
ejpam-5429	94	31	]	]	PUNCT
ejpam-5429	94	32	)	)	PUNCT
ejpam-5429	94	33	if	if	SCONJ
ejpam-5429	94	34	it	it	PRON
ejpam-5429	94	35	meets	meet	VERB
ejpam-5429	94	36	:	:	PUNCT
ejpam-5429	94	37	0	0	NUM
ejpam-5429	95	1	∈	∈	NOUN
ejpam-5429	96	1	i	i	PRON
ejpam-5429	96	2	and	and	CCONJ
ejpam-5429	96	3	(	(	PUNCT
ejpam-5429	96	4	∀ς̇	∀ς̇	PROPN
ejpam-5429	96	5	,	,	PUNCT
ejpam-5429	96	6	ϱ̇	ϱ̇	PROPN
ejpam-5429	96	7	∈	∈	PROPN
ejpam-5429	96	8	i	i	PRON
ejpam-5429	96	9	)	)	PUNCT
ejpam-5429	96	10	(	(	PUNCT
ejpam-5429	96	11	ς̇	ς̇	NOUN
ejpam-5429	96	12	≬	≬	PROPN
ejpam-5429	96	13	ϱ̇	ϱ̇	PROPN
ejpam-5429	96	14	∈	∈	PROPN
ejpam-5429	97	1	i	i	PRON
ejpam-5429	97	2	,	,	PUNCT
ejpam-5429	97	3	ϱ̇	ϱ̇	PROPN
ejpam-5429	97	4	∈	∈	PROPN
ejpam-5429	97	5	i	i	PRON
ejpam-5429	97	6	⇒	⇒	VERB
ejpam-5429	97	7	ς̇	ς̇	PROPN
ejpam-5429	97	8	∈	∈	PROPN
ejpam-5429	97	9	i	i	PROPN
ejpam-5429	97	10	)	)	PUNCT
ejpam-5429	97	11	.	.	PUNCT
ejpam-5429	98	1	(	(	PUNCT
ejpam-5429	98	2	1	1	X
ejpam-5429	98	3	)	)	PUNCT
ejpam-5429	98	4	a	a	DET
ejpam-5429	98	5	subset	subset	NOUN
ejpam-5429	98	6	i	i	PRON
ejpam-5429	98	7	of	of	ADP
ejpam-5429	98	8	ℵ̃	ℵ̃	PROPN
ejpam-5429	98	9	is	be	AUX
ejpam-5429	98	10	referred	refer	VERB
ejpam-5429	98	11	to	to	ADP
ejpam-5429	98	12	a	a	DET
ejpam-5429	98	13	fantastic	fantastic	ADJ
ejpam-5429	98	14	ideal	ideal	NOUN
ejpam-5429	98	15	of	of	ADP
ejpam-5429	98	16	ℵ̃	ℵ̃	PROPN
ejpam-5429	98	17	(	(	PUNCT
ejpam-5429	98	18	see	see	VERB
ejpam-5429	98	19	[	[	X
ejpam-5429	98	20	1	1	NUM
ejpam-5429	98	21	]	]	PUNCT
ejpam-5429	98	22	)	)	PUNCT
ejpam-5429	98	23	if	if	SCONJ
ejpam-5429	98	24	it	it	PRON
ejpam-5429	98	25	meets	meet	VERB
ejpam-5429	98	26	:	:	PUNCT
ejpam-5429	98	27	0	0	NUM
ejpam-5429	99	1	∈	∈	NOUN
ejpam-5429	100	1	i	i	PRON
ejpam-5429	100	2	and	and	CCONJ
ejpam-5429	100	3	(	(	PUNCT
ejpam-5429	100	4	∀ς̇	∀ς̇	PROPN
ejpam-5429	100	5	,	,	PUNCT
ejpam-5429	100	6	ϱ̇	ϱ̇	PROPN
ejpam-5429	100	7	,	,	PUNCT
ejpam-5429	100	8	κ̇	κ̇	PROPN
ejpam-5429	100	9	∈	∈	PROPN
ejpam-5429	100	10	i)((ς̇	i)((ς̇	VERB
ejpam-5429	100	11	≬	≬	PROPN
ejpam-5429	100	12	ϱ̇	ϱ̇	PROPN
ejpam-5429	100	13	)	)	PUNCT
ejpam-5429	101	1	≬	≬	PROPN
ejpam-5429	101	2	κ̇	κ̇	INTJ
ejpam-5429	101	3	∈	∈	PROPN
ejpam-5429	102	1	i	i	PRON
ejpam-5429	102	2	,	,	PUNCT
ejpam-5429	102	3	κ̇	κ̇	PROPN
ejpam-5429	102	4	∈	∈	PROPN
ejpam-5429	102	5	i	i	PRON
ejpam-5429	102	6	⇒	⇒	VERB
ejpam-5429	102	7	ς̇	ς̇	PROPN
ejpam-5429	102	8	≬	≬	PROPN
ejpam-5429	102	9	(	(	PUNCT
ejpam-5429	102	10	ϱ̇	ϱ̇	PROPN
ejpam-5429	102	11	≬	≬	PROPN
ejpam-5429	102	12	(	(	PUNCT
ejpam-5429	102	13	ϱ̇	ϱ̇	PROPN
ejpam-5429	102	14	≬	≬	PROPN
ejpam-5429	102	15	ς̇	ς̇	NOUN
ejpam-5429	102	16	)	)	PUNCT
ejpam-5429	102	17	)	)	PUNCT
ejpam-5429	103	1	∈	∈	PROPN
ejpam-5429	103	2	i	i	NOUN
ejpam-5429	103	3	)	)	PUNCT
ejpam-5429	103	4	.	.	PUNCT
ejpam-5429	104	1	(	(	PUNCT
ejpam-5429	104	2	2	2	X
ejpam-5429	104	3	)	)	PUNCT
ejpam-5429	104	4	definition	definition	NOUN
ejpam-5429	104	5	1	1	NUM
ejpam-5429	104	6	.	.	PUNCT
ejpam-5429	105	1	[	[	X
ejpam-5429	105	2	31	31	NUM
ejpam-5429	105	3	]	]	PUNCT
ejpam-5429	105	4	a	a	DET
ejpam-5429	105	5	mapping	mapping	NOUN
ejpam-5429	105	6	ã̧	ã̧	PROPN
ejpam-5429	105	7	:	:	PUNCT
ejpam-5429	105	8	ℵ̃	ℵ̃	PROPN
ejpam-5429	105	9	→	→	SYM
ejpam-5429	106	1	[	[	X
ejpam-5429	106	2	0	0	NUM
ejpam-5429	106	3	,	,	PUNCT
ejpam-5429	106	4	1	1	NUM
ejpam-5429	106	5	]	]	PUNCT
ejpam-5429	106	6	is	be	AUX
ejpam-5429	106	7	a	a	DET
ejpam-5429	106	8	fuzzy	fuzzy	ADJ
ejpam-5429	106	9	set	set	VERB
ejpam-5429	106	10	fs	f	NOUN
ejpam-5429	106	11	for	for	ADP
ejpam-5429	106	12	the	the	DET
ejpam-5429	106	13	set	set	VERB
ejpam-5429	106	14	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	106	15	k.	k.	PROPN
ejpam-5429	106	16	h.	h.	PROPN
ejpam-5429	106	17	hakami	hakami	PROPN
ejpam-5429	106	18	et	et	PROPN
ejpam-5429	106	19	al	al	PROPN
ejpam-5429	106	20	.	.	PUNCT
ejpam-5429	106	21	/	/	SYM
ejpam-5429	106	22	eur	eur	PROPN
ejpam-5429	106	23	.	.	PUNCT
ejpam-5429	107	1	j.	j.	PROPN
ejpam-5429	107	2	pure	pure	PROPN
ejpam-5429	107	3	appl	appl	PROPN
ejpam-5429	107	4	.	.	PROPN
ejpam-5429	107	5	math	math	PROPN
ejpam-5429	107	6	,	,	PUNCT
ejpam-5429	107	7	17	17	NUM
ejpam-5429	107	8	(	(	PUNCT
ejpam-5429	107	9	4	4	NUM
ejpam-5429	107	10	)	)	PUNCT
ejpam-5429	107	11	(	(	PUNCT
ejpam-5429	107	12	2024	2024	NUM
ejpam-5429	107	13	)	)	PUNCT
ejpam-5429	107	14	,	,	PUNCT
ejpam-5429	107	15	3129	3129	NUM
ejpam-5429	107	16	-	-	SYM
ejpam-5429	107	17	3155	3155	NUM
ejpam-5429	107	18	3132	3132	NUM
ejpam-5429	107	19	a	a	DET
ejpam-5429	107	20	fs	fs	X
ejpam-5429	107	21	ã̧	ã̧	PROPN
ejpam-5429	107	22	of	of	ADP
ejpam-5429	107	23	ℵ̃	ℵ̃	PROPN
ejpam-5429	107	24	is	be	AUX
ejpam-5429	107	25	a	a	DET
ejpam-5429	107	26	fi	fi	NOUN
ejpam-5429	107	27	of	of	ADP
ejpam-5429	107	28	ℵ̃	ℵ̃	PROPN
ejpam-5429	107	29	if	if	SCONJ
ejpam-5429	107	30	it	it	PRON
ejpam-5429	107	31	meets	meet	VERB
ejpam-5429	107	32	:	:	PUNCT
ejpam-5429	107	33	(	(	PUNCT
ejpam-5429	107	34	∀ς̇	∀ς̇	NOUN
ejpam-5429	107	35	,	,	PUNCT
ejpam-5429	107	36	ϱ̇	ϱ̇	PROPN
ejpam-5429	107	37	∈	∈	PROPN
ejpam-5429	107	38	ℵ̃	ℵ̃	PROPN
ejpam-5429	107	39	,	,	PUNCT
ejpam-5429	107	40	ã̧(0	ã̧(0	NOUN
ejpam-5429	107	41	)	)	PUNCT
ejpam-5429	107	42	≥	≥	NOUN
ejpam-5429	107	43	ã̧(ς̇	ã̧(ς̇	NOUN
ejpam-5429	107	44	)	)	PUNCT
ejpam-5429	107	45	and	and	CCONJ
ejpam-5429	107	46	ã̧(ς̇	ã̧(ς̇	NOUN
ejpam-5429	107	47	)	)	PUNCT
ejpam-5429	107	48	≥	≥	NOUN
ejpam-5429	107	49	ã̧(ς̇	ã̧(ς̇	ADP
ejpam-5429	107	50	≬	≬	PROPN
ejpam-5429	107	51	ϱ̇	ϱ̇	PROPN
ejpam-5429	107	52	)	)	PUNCT
ejpam-5429	107	53	∧	∧	NOUN
ejpam-5429	107	54	ã̧(ϱ̇	ã̧(ϱ̇	NOUN
ejpam-5429	107	55	)	)	PUNCT
ejpam-5429	107	56	)	)	PUNCT
ejpam-5429	107	57	.	.	PUNCT
ejpam-5429	108	1	(	(	PUNCT
ejpam-5429	108	2	3	3	X
ejpam-5429	108	3	)	)	PUNCT
ejpam-5429	108	4	a	a	DET
ejpam-5429	108	5	fs	fs	NOUN
ejpam-5429	108	6	ã̧	ã̧	PROPN
ejpam-5429	108	7	of	of	ADP
ejpam-5429	108	8	ℵ̃	ℵ̃	PROPN
ejpam-5429	108	9	is	be	AUX
ejpam-5429	108	10	a	a	DET
ejpam-5429	108	11	ffi	ffi	PROPN
ejpam-5429	108	12	of	of	ADP
ejpam-5429	108	13	ℵ̃	ℵ̃	PROPN
ejpam-5429	108	14	if	if	SCONJ
ejpam-5429	108	15	it	it	PRON
ejpam-5429	108	16	meets	meet	VERB
ejpam-5429	108	17	:	:	PUNCT
ejpam-5429	108	18	(	(	PUNCT
ejpam-5429	108	19	∀ς̇	∀ς̇	NOUN
ejpam-5429	108	20	,	,	PUNCT
ejpam-5429	108	21	ϱ̇	ϱ̇	PROPN
ejpam-5429	108	22	∈	∈	PROPN
ejpam-5429	108	23	ℵ̃	ℵ̃	PROPN
ejpam-5429	108	24	,	,	PUNCT
ejpam-5429	108	25	ã̧(0	ã̧(0	NOUN
ejpam-5429	108	26	)	)	PUNCT
ejpam-5429	108	27	≥	≥	NOUN
ejpam-5429	108	28	ã̧(ς̇	ã̧(ς̇	NOUN
ejpam-5429	108	29	)	)	PUNCT
ejpam-5429	108	30	and	and	CCONJ
ejpam-5429	108	31	ã̧(ς̇	ã̧(ς̇	ADP
ejpam-5429	108	32	≬	≬	PROPN
ejpam-5429	108	33	(	(	PUNCT
ejpam-5429	108	34	ϱ̇	ϱ̇	PROPN
ejpam-5429	108	35	≬	≬	PROPN
ejpam-5429	108	36	(	(	PUNCT
ejpam-5429	108	37	ϱ̇	ϱ̇	PROPN
ejpam-5429	108	38	≬	≬	PROPN
ejpam-5429	108	39	ς̇	ς̇	NOUN
ejpam-5429	108	40	)	)	PUNCT
ejpam-5429	108	41	)	)	PUNCT
ejpam-5429	108	42	)	)	PUNCT
ejpam-5429	108	43	≥	≥	PRON
ejpam-5429	108	44	ã̧((ς̇	ã̧((ς̇	VERB
ejpam-5429	108	45	≬	≬	PROPN
ejpam-5429	108	46	ϱ̇	ϱ̇	PROPN
ejpam-5429	108	47	)	)	PUNCT
ejpam-5429	108	48	≬	≬	PROPN
ejpam-5429	108	49	κ̇	κ̇	PROPN
ejpam-5429	108	50	)	)	PUNCT
ejpam-5429	108	51	∧	∧	PROPN
ejpam-5429	108	52	ã̧(κ̇	ã̧(κ̇	PROPN
ejpam-5429	108	53	)	)	PUNCT
ejpam-5429	108	54	)	)	PUNCT
ejpam-5429	108	55	.	.	PUNCT
ejpam-5429	109	1	(	(	PUNCT
ejpam-5429	109	2	4	4	X
ejpam-5429	109	3	)	)	PUNCT
ejpam-5429	109	4	3	3	NUM
ejpam-5429	109	5	.	.	X
ejpam-5429	109	6	quadri	quadri	NOUN
ejpam-5429	109	7	-	-	PUNCT
ejpam-5429	109	8	polar	polar	ADJ
ejpam-5429	109	9	fuzzy	fuzzy	ADJ
ejpam-5429	109	10	fantastic	fantastic	ADJ
ejpam-5429	109	11	ideals	ideal	NOUN
ejpam-5429	109	12	definition	definition	NOUN
ejpam-5429	109	13	2	2	NUM
ejpam-5429	109	14	.	.	PUNCT
ejpam-5429	110	1	a	a	DET
ejpam-5429	110	2	mapping	mapping	NOUN
ejpam-5429	110	3	ð̃	ð̃	PROPN
ejpam-5429	110	4	:	:	PUNCT
ejpam-5429	110	5	ℵ̃	ℵ̃	PROPN
ejpam-5429	110	6	→	→	SYM
ejpam-5429	110	7	[	[	X
ejpam-5429	110	8	0	0	NUM
ejpam-5429	110	9	,	,	PUNCT
ejpam-5429	110	10	1]4	1]4	PROPN
ejpam-5429	110	11	is	be	AUX
ejpam-5429	110	12	a	a	DET
ejpam-5429	110	13	qp	qp	NOUN
ejpam-5429	110	14	-	-	PUNCT
ejpam-5429	110	15	f	f	NOUN
ejpam-5429	110	16	for	for	ADP
ejpam-5429	110	17	the	the	DET
ejpam-5429	110	18	set	set	NOUN
ejpam-5429	110	19	ℵ̃	ℵ̃	PROPN
ejpam-5429	110	20	,	,	PUNCT
ejpam-5429	110	21	where	where	SCONJ
ejpam-5429	110	22	for	for	ADP
ejpam-5429	110	23	any	any	DET
ejpam-5429	110	24	ς̇	ς̇	NOUN
ejpam-5429	110	25	∈	∈	PROPN
ejpam-5429	110	26	ℵ̃	ℵ̃	PROPN
ejpam-5429	110	27	,	,	PUNCT
ejpam-5429	110	28	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	110	29	)	)	PUNCT
ejpam-5429	110	30	=	=	SYM
ejpam-5429	110	31	(	(	PUNCT
ejpam-5429	110	32	ð̃1(ς̇	ð̃1(ς̇	NOUN
ejpam-5429	110	33	)	)	PUNCT
ejpam-5429	110	34	,	,	PUNCT
ejpam-5429	110	35	ð̃2(ς̇	ð̃2(ς̇	NUM
ejpam-5429	110	36	)	)	PUNCT
ejpam-5429	110	37	,	,	PUNCT
ejpam-5429	110	38	ð̃3(ς̇	ð̃3(ς̇	PRON
ejpam-5429	110	39	)	)	PUNCT
ejpam-5429	110	40	,	,	PUNCT
ejpam-5429	110	41	ð̃4(ς̇	ð̃4(ς̇	NOUN
ejpam-5429	110	42	)	)	PUNCT
ejpam-5429	110	43	)	)	PUNCT
ejpam-5429	110	44	and	and	CCONJ
ejpam-5429	110	45	ð̃q(ς̇	ð̃q(ς̇	NOUN
ejpam-5429	110	46	)	)	PUNCT
ejpam-5429	110	47	∈	∈	PROPN
ejpam-5429	111	1	[	[	X
ejpam-5429	111	2	0	0	NUM
ejpam-5429	111	3	,	,	PUNCT
ejpam-5429	111	4	1	1	NUM
ejpam-5429	111	5	]	]	PUNCT
ejpam-5429	111	6	,	,	PUNCT
ejpam-5429	111	7	for	for	ADP
ejpam-5429	111	8	q	q	NOUN
ejpam-5429	111	9	=	=	SYM
ejpam-5429	111	10	1	1	NUM
ejpam-5429	111	11	,	,	PUNCT
ejpam-5429	111	12	2	2	NUM
ejpam-5429	111	13	,	,	PUNCT
ejpam-5429	111	14	3	3	NUM
ejpam-5429	111	15	,	,	PUNCT
ejpam-5429	111	16	4	4	NUM
ejpam-5429	111	17	.	.	PUNCT
ejpam-5429	111	18	definition	definition	NOUN
ejpam-5429	111	19	3	3	NUM
ejpam-5429	111	20	.	.	PUNCT
ejpam-5429	112	1	a	a	DET
ejpam-5429	112	2	qp	qp	PROPN
ejpam-5429	112	3	-	-	PUNCT
ejpam-5429	112	4	f	f	NOUN
ejpam-5429	112	5	set	set	NOUN
ejpam-5429	112	6	ð̃	ð̃	PROPN
ejpam-5429	112	7	of	of	ADP
ejpam-5429	112	8	ℵ̃	ℵ̃	PROPN
ejpam-5429	112	9	is	be	AUX
ejpam-5429	112	10	a	a	DET
ejpam-5429	112	11	qp	qp	PROPN
ejpam-5429	112	12	-	-	PUNCT
ejpam-5429	112	13	ffi	ffi	PROPN
ejpam-5429	112	14	if	if	SCONJ
ejpam-5429	112	15	,	,	PUNCT
ejpam-5429	112	16	∀ς̇	∀ς̇	PROPN
ejpam-5429	112	17	,	,	PUNCT
ejpam-5429	112	18	ϱ̇	ϱ̇	PROPN
ejpam-5429	112	19	,	,	PUNCT
ejpam-5429	112	20	κ̇	κ̇	PROPN
ejpam-5429	112	21	∈	∈	PROPN
ejpam-5429	112	22	ℵ̃	ℵ̃	PROPN
ejpam-5429	112	23	and	and	CCONJ
ejpam-5429	112	24	q	q	NOUN
ejpam-5429	112	25	=	=	NOUN
ejpam-5429	112	26	1	1	NUM
ejpam-5429	112	27	,	,	PUNCT
ejpam-5429	112	28	2	2	NUM
ejpam-5429	112	29	,	,	PUNCT
ejpam-5429	112	30	3	3	NUM
ejpam-5429	112	31	,	,	PUNCT
ejpam-5429	112	32	4	4	NUM
ejpam-5429	112	33	,	,	PUNCT
ejpam-5429	112	34	ð̃(0	ð̃(0	NOUN
ejpam-5429	112	35	)	)	PUNCT
ejpam-5429	112	36	≥	≥	NOUN
ejpam-5429	112	37	ð̃(ς̇	ð̃(ς̇	PUNCT
ejpam-5429	112	38	)	)	PUNCT
ejpam-5429	112	39	and	and	CCONJ
ejpam-5429	112	40	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	112	41	≬	≬	PROPN
ejpam-5429	112	42	(	(	PUNCT
ejpam-5429	112	43	ϱ̇	ϱ̇	PROPN
ejpam-5429	112	44	≬	≬	PROPN
ejpam-5429	112	45	(	(	PUNCT
ejpam-5429	112	46	ϱ̇	ϱ̇	PROPN
ejpam-5429	112	47	≬	≬	PROPN
ejpam-5429	112	48	ς̇	ς̇	NOUN
ejpam-5429	112	49	)	)	PUNCT
ejpam-5429	112	50	)	)	PUNCT
ejpam-5429	112	51	)	)	PUNCT
ejpam-5429	113	1	≥	≥	X
ejpam-5429	113	2	ð̃((ς̇	ð̃((ς̇	X
ejpam-5429	114	1	≬	≬	PROPN
ejpam-5429	114	2	ϱ̇	ϱ̇	PROPN
ejpam-5429	114	3	)	)	PUNCT
ejpam-5429	114	4	≬	≬	PROPN
ejpam-5429	114	5	κ̇	κ̇	PROPN
ejpam-5429	114	6	)	)	PUNCT
ejpam-5429	114	7	∧	∧	PROPN
ejpam-5429	114	8	ð̃(κ̇	ð̃(κ̇	PROPN
ejpam-5429	114	9	)	)	PUNCT
ejpam-5429	114	10	.	.	PUNCT
ejpam-5429	115	1	that	that	PRON
ejpam-5429	115	2	is	be	AUX
ejpam-5429	115	3	,	,	PUNCT
ejpam-5429	115	4	ð̃q(0	ð̃q(0	PROPN
ejpam-5429	115	5	)	)	PUNCT
ejpam-5429	115	6	≥	≥	NOUN
ejpam-5429	115	7	ð̃q(ς̇	ð̃q(ς̇	NOUN
ejpam-5429	115	8	)	)	PUNCT
ejpam-5429	115	9	and	and	CCONJ
ejpam-5429	115	10	ð̃q(ς̇	ð̃q(ς̇	VERB
ejpam-5429	115	11	≬	≬	PROPN
ejpam-5429	115	12	(	(	PUNCT
ejpam-5429	115	13	ϱ̇	ϱ̇	PROPN
ejpam-5429	115	14	≬	≬	PROPN
ejpam-5429	115	15	(	(	PUNCT
ejpam-5429	115	16	ϱ̇	ϱ̇	PROPN
ejpam-5429	115	17	≬	≬	PROPN
ejpam-5429	115	18	ς̇	ς̇	NOUN
ejpam-5429	115	19	)	)	PUNCT
ejpam-5429	115	20	)	)	PUNCT
ejpam-5429	115	21	)	)	PUNCT
ejpam-5429	116	1	≥	≥	X
ejpam-5429	116	2	ð̃q((ς̇	ð̃q((ς̇	X
ejpam-5429	116	3	≬	≬	PROPN
ejpam-5429	116	4	ϱ̇	ϱ̇	PROPN
ejpam-5429	116	5	)	)	PUNCT
ejpam-5429	116	6	≬	≬	PROPN
ejpam-5429	116	7	κ̇	κ̇	PROPN
ejpam-5429	116	8	)	)	PUNCT
ejpam-5429	116	9	∧	∧	PROPN
ejpam-5429	116	10	ð̃q(κ̇	ð̃q(κ̇	PROPN
ejpam-5429	116	11	)	)	PUNCT
ejpam-5429	116	12	.	.	PUNCT
ejpam-5429	117	1	example	example	NOUN
ejpam-5429	118	1	1	1	X
ejpam-5429	118	2	.	.	X
ejpam-5429	118	3	consider	consider	VERB
ejpam-5429	118	4	ℵ̃	ℵ̃	PROPN
ejpam-5429	118	5	=	=	SYM
ejpam-5429	118	6	{	{	PUNCT
ejpam-5429	118	7	0	0	NUM
ejpam-5429	118	8	,	,	PUNCT
ejpam-5429	118	9	ς̇	ς̇	NOUN
ejpam-5429	118	10	,	,	PUNCT
ejpam-5429	118	11	ϱ̇	ϱ̇	PROPN
ejpam-5429	118	12	,	,	PUNCT
ejpam-5429	118	13	κ̇	κ̇	PROPN
ejpam-5429	118	14	}	}	PUNCT
ejpam-5429	118	15	with	with	ADP
ejpam-5429	118	16	the	the	DET
ejpam-5429	118	17	binary	binary	ADJ
ejpam-5429	118	18	operation	operation	NOUN
ejpam-5429	118	19	≬	≬	PROPN
ejpam-5429	118	20	defined	define	VERB
ejpam-5429	118	21	by	by	ADP
ejpam-5429	118	22	table	table	NOUN
ejpam-5429	118	23	2	2	NUM
ejpam-5429	118	24	:	:	PUNCT
ejpam-5429	118	25	table	table	NOUN
ejpam-5429	118	26	2	2	NUM
ejpam-5429	118	27	.	.	PUNCT
ejpam-5429	118	28	cayley	cayley	ADJ
ejpam-5429	118	29	table	table	NOUN
ejpam-5429	118	30	representing	represent	VERB
ejpam-5429	118	31	by	by	ADP
ejpam-5429	118	32	“	"	PUNCT
ejpam-5429	118	33	≬	≬	PROPN
ejpam-5429	118	34	”	"	PUNCT
ejpam-5429	118	35	≬	≬	PROPN
ejpam-5429	118	36	0	0	NUM
ejpam-5429	118	37	ς̇	ς̇	NOUN
ejpam-5429	118	38	ϱ̇	ϱ̇	PROPN
ejpam-5429	118	39	κ̇	κ̇	VERB
ejpam-5429	118	40	0	0	NUM
ejpam-5429	118	41	0	0	NUM
ejpam-5429	118	42	0	0	NUM
ejpam-5429	118	43	0	0	NUM
ejpam-5429	118	44	0	0	NUM
ejpam-5429	118	45	ς̇	ς̇	NOUN
ejpam-5429	118	46	ς̇	ς̇	NOUN
ejpam-5429	118	47	0	0	NUM
ejpam-5429	118	48	0	0	NUM
ejpam-5429	119	1	ς̇	ς̇	NOUN
ejpam-5429	119	2	ϱ̇	ϱ̇	PROPN
ejpam-5429	120	1	ϱ̇	ϱ̇	PROPN
ejpam-5429	120	2	ς̇	ς̇	NOUN
ejpam-5429	120	3	0	0	NUM
ejpam-5429	121	1	ϱ̇	ϱ̇	PROPN
ejpam-5429	121	2	κ̇	κ̇	INTJ
ejpam-5429	121	3	κ̇	κ̇	INTJ
ejpam-5429	121	4	κ̇	κ̇	INTJ
ejpam-5429	122	1	κ̇	κ̇	INTJ
ejpam-5429	122	2	0	0	PUNCT
ejpam-5429	122	3	thus	thus	ADV
ejpam-5429	122	4	,	,	PUNCT
ejpam-5429	122	5	(	(	PUNCT
ejpam-5429	122	6	ℵ̃	ℵ̃	PROPN
ejpam-5429	122	7	;	;	PUNCT
ejpam-5429	122	8	≬	≬	PROPN
ejpam-5429	122	9	,	,	PUNCT
ejpam-5429	122	10	0	0	NUM
ejpam-5429	122	11	)	)	PUNCT
ejpam-5429	122	12	forms	form	VERB
ejpam-5429	122	13	a	a	DET
ejpam-5429	122	14	bci	bci	NOUN
ejpam-5429	122	15	-	-	NOUN
ejpam-5429	122	16	algebra	algebra	NOUN
ejpam-5429	122	17	.	.	PUNCT
ejpam-5429	123	1	consider	consider	VERB
ejpam-5429	123	2	a	a	DET
ejpam-5429	123	3	qp	qp	NOUN
ejpam-5429	123	4	-	-	PUNCT
ejpam-5429	123	5	f	f	NOUN
ejpam-5429	123	6	set	set	NOUN
ejpam-5429	123	7	ð̃	ð̃	PROPN
ejpam-5429	123	8	defined	define	VERB
ejpam-5429	123	9	on	on	ADP
ejpam-5429	123	10	ℵ̃	ℵ̃	PROPN
ejpam-5429	123	11	as	as	SCONJ
ejpam-5429	123	12	follows	follow	VERB
ejpam-5429	123	13	:	:	PUNCT
ejpam-5429	123	14	ð̃(ς̇	ð̃(ς̇	X
ejpam-5429	123	15	)	)	PUNCT
ejpam-5429	123	16	=	=	SYM
ejpam-5429	124	1			PUNCT
ejpam-5429	124	2	⟨0	⟨0	NOUN
ejpam-5429	124	3	,	,	PUNCT
ejpam-5429	124	4	(	(	PUNCT
ejpam-5429	124	5	.58	.58	NUM
ejpam-5429	124	6	,	,	PUNCT
ejpam-5429	124	7	.65	.65	NUM
ejpam-5429	124	8	,	,	PUNCT
ejpam-5429	124	9	.75	.75	NUM
ejpam-5429	124	10	,	,	PUNCT
ejpam-5429	124	11	.54)⟩	.54)⟩	PROPN
ejpam-5429	124	12	,	,	PUNCT
ejpam-5429	124	13	⟨ς̇	⟨ς̇	PRON
ejpam-5429	124	14	,	,	PUNCT
ejpam-5429	124	15	(	(	PUNCT
ejpam-5429	124	16	.48	.48	NUM
ejpam-5429	124	17	,	,	PUNCT
ejpam-5429	124	18	.21	.21	NUM
ejpam-5429	124	19	,	,	PUNCT
ejpam-5429	124	20	.45	.45	NUM
ejpam-5429	124	21	,	,	PUNCT
ejpam-5429	124	22	.30)⟩	.30)⟩	ADV
ejpam-5429	124	23	,	,	PUNCT
ejpam-5429	124	24	⟨ϱ̇	⟨ϱ̇	NOUN
ejpam-5429	124	25	,	,	PUNCT
ejpam-5429	124	26	(	(	PUNCT
ejpam-5429	124	27	.28	.28	NUM
ejpam-5429	124	28	,	,	PUNCT
ejpam-5429	124	29	.52	.52	NUM
ejpam-5429	124	30	,	,	PUNCT
ejpam-5429	124	31	.54	.54	NUM
ejpam-5429	124	32	,	,	PUNCT
ejpam-5429	124	33	.30)⟩	.30)⟩	ADV
ejpam-5429	124	34	,	,	PUNCT
ejpam-5429	124	35	⟨κ̇	⟨κ̇	VERB
ejpam-5429	124	36	,	,	PUNCT
ejpam-5429	124	37	(	(	PUNCT
ejpam-5429	124	38	.28	.28	NUM
ejpam-5429	124	39	,	,	PUNCT
ejpam-5429	124	40	.41	.41	NUM
ejpam-5429	124	41	,	,	PUNCT
ejpam-5429	124	42	.36	.36	NUM
ejpam-5429	124	43	,	,	PUNCT
ejpam-5429	124	44	.54)⟩.	.54)⟩.	PRON
ejpam-5429	125	1			PROPN
ejpam-5429	125	2	thus	thus	ADV
ejpam-5429	125	3	,	,	PUNCT
ejpam-5429	125	4	ð̃	ð̃	PROPN
ejpam-5429	125	5	is	be	AUX
ejpam-5429	125	6	a	a	DET
ejpam-5429	125	7	qp	qp	PROPN
ejpam-5429	125	8	-	-	PUNCT
ejpam-5429	125	9	ffi	ffi	PROPN
ejpam-5429	125	10	of	of	ADP
ejpam-5429	125	11	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	125	12	theorem	theorem	VERB
ejpam-5429	125	13	1	1	NUM
ejpam-5429	125	14	.	.	PUNCT
ejpam-5429	126	1	a	a	DET
ejpam-5429	126	2	qp	qp	PROPN
ejpam-5429	126	3	-	-	PUNCT
ejpam-5429	126	4	f	f	NOUN
ejpam-5429	126	5	set	set	NOUN
ejpam-5429	126	6	ð̃	ð̃	PROPN
ejpam-5429	126	7	is	be	AUX
ejpam-5429	126	8	a	a	DET
ejpam-5429	126	9	qp	qp	PROPN
ejpam-5429	126	10	-	-	PUNCT
ejpam-5429	126	11	ffi	ffi	PROPN
ejpam-5429	126	12	of	of	ADP
ejpam-5429	126	13	ℵ̃	ℵ̃	PROPN
ejpam-5429	126	14	⇔	⇔	PROPN
ejpam-5429	126	15	for	for	ADP
ejpam-5429	126	16	any	any	DET
ejpam-5429	126	17	ρ̃	ρ̃	PROPN
ejpam-5429	126	18	∈	∈	PROPN
ejpam-5429	126	19	(	(	PUNCT
ejpam-5429	126	20	0	0	NUM
ejpam-5429	126	21	,	,	PUNCT
ejpam-5429	126	22	1]4	1]4	NUM
ejpam-5429	126	23	,	,	PUNCT
ejpam-5429	126	24	the	the	DET
ejpam-5429	126	25	ρ̃-cut	ρ̃-cut	VERB
ejpam-5429	126	26	subset	subset	NOUN
ejpam-5429	126	27	ð̃ρ̃	ð̃ρ̃	X
ejpam-5429	126	28	=	=	SYM
ejpam-5429	126	29	{	{	PUNCT
ejpam-5429	126	30	ς̇	ς̇	NOUN
ejpam-5429	126	31	∈	∈	PROPN
ejpam-5429	126	32	ℵ̃	ℵ̃	PROPN
ejpam-5429	126	33	|	|	NOUN
ejpam-5429	126	34	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	126	35	)	)	PUNCT
ejpam-5429	126	36	≥	≥	NOUN
ejpam-5429	126	37	ρ̃	ρ̃	PROPN
ejpam-5429	126	38	}	}	PUNCT
ejpam-5429	126	39	is	be	AUX
ejpam-5429	126	40	a	a	DET
ejpam-5429	126	41	fantastic	fantastic	ADJ
ejpam-5429	126	42	ideal	ideal	NOUN
ejpam-5429	126	43	of	of	ADP
ejpam-5429	126	44	ℵ̃.	ℵ̃.	NOUN
ejpam-5429	126	45	proof	proof	NOUN
ejpam-5429	126	46	.	.	PUNCT
ejpam-5429	127	1	let	let	VERB
ejpam-5429	127	2	ð̃	ð̃	PRON
ejpam-5429	127	3	be	be	AUX
ejpam-5429	127	4	a	a	DET
ejpam-5429	127	5	qp	qp	PROPN
ejpam-5429	127	6	-	-	PUNCT
ejpam-5429	127	7	ffi	ffi	PROPN
ejpam-5429	127	8	of	of	ADP
ejpam-5429	127	9	ℵ̃	ℵ̃	PROPN
ejpam-5429	127	10	and	and	CCONJ
ejpam-5429	127	11	ρ̃	ρ̃	PROPN
ejpam-5429	127	12	∈	∈	PROPN
ejpam-5429	127	13	(	(	PUNCT
ejpam-5429	127	14	0	0	NUM
ejpam-5429	127	15	,	,	PUNCT
ejpam-5429	127	16	1]4	1]4	PROPN
ejpam-5429	127	17	be	be	AUX
ejpam-5429	127	18	such	such	ADJ
ejpam-5429	128	1	that	that	SCONJ
ejpam-5429	128	2	ð̃ρ̃	ð̃ρ̃	NOUN
ejpam-5429	128	3	=	=	PUNCT
ejpam-5429	128	4	{	{	PUNCT
ejpam-5429	128	5	ς̇	ς̇	NOUN
ejpam-5429	128	6	∈	∈	PROPN
ejpam-5429	128	7	ℵ̃	ℵ̃	PROPN
ejpam-5429	128	8	|	|	NOUN
ejpam-5429	128	9	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	128	10	)	)	PUNCT
ejpam-5429	128	11	≥	≥	NOUN
ejpam-5429	128	12	ρ̃	ρ̃	PROPN
ejpam-5429	128	13	}	}	PUNCT
ejpam-5429	128	14	.	.	PUNCT
ejpam-5429	129	1	let	let	VERB
ejpam-5429	129	2	ς̇	ς̇	NOUN
ejpam-5429	129	3	,	,	PUNCT
ejpam-5429	129	4	ϱ̇	ϱ̇	PROPN
ejpam-5429	129	5	,	,	PUNCT
ejpam-5429	129	6	κ̇	κ̇	PROPN
ejpam-5429	129	7	∈	∈	NOUN
ejpam-5429	129	8	ð̃ρ̃.	ð̃ρ̃.	NOUN
ejpam-5429	129	9	then	then	ADV
ejpam-5429	129	10	,	,	PUNCT
ejpam-5429	129	11	ð̃((ς̇	ð̃((ς̇	VERB
ejpam-5429	129	12	≬	≬	PROPN
ejpam-5429	129	13	ϱ̇	ϱ̇	PROPN
ejpam-5429	129	14	)	)	PUNCT
ejpam-5429	129	15	≬	≬	PROPN
ejpam-5429	129	16	κ̇	κ̇	PROPN
ejpam-5429	129	17	)	)	PUNCT
ejpam-5429	129	18	≥	≥	NOUN
ejpam-5429	129	19	ρ̃	ρ̃	PROPN
ejpam-5429	129	20	and	and	CCONJ
ejpam-5429	129	21	ð̃(κ̇	ð̃(κ̇	PROPN
ejpam-5429	129	22	)	)	PUNCT
ejpam-5429	129	23	≥	≥	NOUN
ejpam-5429	129	24	ρ̃.	ρ̃.	NUM
ejpam-5429	129	25	it	it	PRON
ejpam-5429	129	26	follows	follow	VERB
ejpam-5429	129	27	from	from	ADP
ejpam-5429	129	28	definition	definition	NOUN
ejpam-5429	129	29	3.2	3.2	NUM
ejpam-5429	129	30	that	that	PRON
ejpam-5429	129	31	,	,	PUNCT
ejpam-5429	129	32	k.	k.	PROPN
ejpam-5429	129	33	h.	h.	PROPN
ejpam-5429	129	34	hakami	hakami	PROPN
ejpam-5429	129	35	et	et	PROPN
ejpam-5429	129	36	al	al	PROPN
ejpam-5429	129	37	.	.	PUNCT
ejpam-5429	129	38	/	/	SYM
ejpam-5429	129	39	eur	eur	PROPN
ejpam-5429	129	40	.	.	PUNCT
ejpam-5429	130	1	j.	j.	PROPN
ejpam-5429	130	2	pure	pure	PROPN
ejpam-5429	130	3	appl	appl	PROPN
ejpam-5429	130	4	.	.	PROPN
ejpam-5429	130	5	math	math	PROPN
ejpam-5429	130	6	,	,	PUNCT
ejpam-5429	130	7	17	17	NUM
ejpam-5429	130	8	(	(	PUNCT
ejpam-5429	130	9	4	4	NUM
ejpam-5429	130	10	)	)	PUNCT
ejpam-5429	130	11	(	(	PUNCT
ejpam-5429	130	12	2024	2024	NUM
ejpam-5429	130	13	)	)	PUNCT
ejpam-5429	130	14	,	,	PUNCT
ejpam-5429	130	15	3129	3129	NUM
ejpam-5429	130	16	-	-	SYM
ejpam-5429	130	17	3155	3155	NUM
ejpam-5429	130	18	3133	3133	NUM
ejpam-5429	130	19	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	131	1	≬	≬	PROPN
ejpam-5429	131	2	(	(	PUNCT
ejpam-5429	131	3	ϱ̇	ϱ̇	PROPN
ejpam-5429	131	4	≬	≬	PROPN
ejpam-5429	131	5	(	(	PUNCT
ejpam-5429	131	6	ϱ̇	ϱ̇	PROPN
ejpam-5429	131	7	≬	≬	PROPN
ejpam-5429	131	8	ς̇	ς̇	NOUN
ejpam-5429	131	9	)	)	PUNCT
ejpam-5429	131	10	)	)	PUNCT
ejpam-5429	131	11	)	)	PUNCT
ejpam-5429	132	1	≥	≥	X
ejpam-5429	132	2	ð̃((ς̇	ð̃((ς̇	X
ejpam-5429	133	1	≬	≬	PROPN
ejpam-5429	133	2	ϱ̇	ϱ̇	PROPN
ejpam-5429	133	3	)	)	PUNCT
ejpam-5429	133	4	≬	≬	PROPN
ejpam-5429	133	5	κ̇	κ̇	PROPN
ejpam-5429	133	6	)	)	PUNCT
ejpam-5429	133	7	∧	∧	PROPN
ejpam-5429	133	8	ð̃(κ̇	ð̃(κ̇	PROPN
ejpam-5429	133	9	)	)	PUNCT
ejpam-5429	133	10	=	=	SYM
ejpam-5429	133	11	ρ̃	ρ̃	PROPN
ejpam-5429	133	12	∧	∧	NOUN
ejpam-5429	133	13	ρ̃	ρ̃	PROPN
ejpam-5429	133	14	=	=	SYM
ejpam-5429	133	15	ρ̃.	ρ̃.	PROPN
ejpam-5429	133	16	therefore	therefore	ADV
ejpam-5429	133	17	,	,	PUNCT
ejpam-5429	133	18	ς̇	ς̇	PROPN
ejpam-5429	133	19	≬	≬	PROPN
ejpam-5429	133	20	(	(	PUNCT
ejpam-5429	133	21	ϱ̇	ϱ̇	PROPN
ejpam-5429	133	22	≬	≬	PROPN
ejpam-5429	133	23	(	(	PUNCT
ejpam-5429	133	24	ϱ̇	ϱ̇	PROPN
ejpam-5429	133	25	≬	≬	PROPN
ejpam-5429	133	26	ς̇	ς̇	NOUN
ejpam-5429	133	27	)	)	PUNCT
ejpam-5429	133	28	)	)	PUNCT
ejpam-5429	134	1	∈	∈	PROPN
ejpam-5429	134	2	ð̃ρ̃.	ð̃ρ̃.	PROPN
ejpam-5429	134	3	hence	hence	ADV
ejpam-5429	134	4	,	,	PUNCT
ejpam-5429	134	5	ð̃ρ̃	ð̃ρ̃	PROPN
ejpam-5429	134	6	is	be	AUX
ejpam-5429	134	7	a	a	DET
ejpam-5429	134	8	fantastic	fantastic	ADJ
ejpam-5429	134	9	ideal	ideal	NOUN
ejpam-5429	134	10	of	of	ADP
ejpam-5429	134	11	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	134	12	conversely	conversely	ADV
ejpam-5429	134	13	,	,	PUNCT
ejpam-5429	134	14	assume	assume	VERB
ejpam-5429	134	15	ð̃ρ̃	ð̃ρ̃	PROPN
ejpam-5429	134	16	is	be	AUX
ejpam-5429	134	17	a	a	DET
ejpam-5429	134	18	fantastic	fantastic	ADJ
ejpam-5429	134	19	ideal	ideal	NOUN
ejpam-5429	134	20	of	of	ADP
ejpam-5429	134	21	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	134	22	suppose	suppose	VERB
ejpam-5429	135	1	that	that	SCONJ
ejpam-5429	135	2	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	135	3	≬	≬	PROPN
ejpam-5429	135	4	(	(	PUNCT
ejpam-5429	135	5	ϱ̇	ϱ̇	PROPN
ejpam-5429	135	6	≬	≬	PROPN
ejpam-5429	135	7	(	(	PUNCT
ejpam-5429	135	8	ϱ̇	ϱ̇	PROPN
ejpam-5429	135	9	≬	≬	PROPN
ejpam-5429	135	10	ς̇	ς̇	NOUN
ejpam-5429	135	11	)	)	PUNCT
ejpam-5429	135	12	)	)	PUNCT
ejpam-5429	135	13	)	)	PUNCT
ejpam-5429	136	1	<	<	X
ejpam-5429	136	2	ð̃((ς̇	ð̃((ς̇	X
ejpam-5429	136	3	≬	≬	PROPN
ejpam-5429	136	4	ϱ̇	ϱ̇	PROPN
ejpam-5429	136	5	)	)	PUNCT
ejpam-5429	136	6	≬	≬	PROPN
ejpam-5429	136	7	κ̇	κ̇	PROPN
ejpam-5429	136	8	)	)	PUNCT
ejpam-5429	136	9	∧	∧	PROPN
ejpam-5429	136	10	ð̃(κ̇	ð̃(κ̇	PROPN
ejpam-5429	136	11	)	)	PUNCT
ejpam-5429	136	12	.	.	PUNCT
ejpam-5429	137	1	then	then	ADV
ejpam-5429	137	2	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	137	3	≬	≬	PROPN
ejpam-5429	137	4	(	(	PUNCT
ejpam-5429	137	5	ϱ̇	ϱ̇	PROPN
ejpam-5429	137	6	≬	≬	PROPN
ejpam-5429	137	7	(	(	PUNCT
ejpam-5429	137	8	ϱ̇	ϱ̇	PROPN
ejpam-5429	137	9	≬	≬	PROPN
ejpam-5429	137	10	ς̇	ς̇	NOUN
ejpam-5429	137	11	)	)	PUNCT
ejpam-5429	137	12	)	)	PUNCT
ejpam-5429	137	13	)	)	PUNCT
ejpam-5429	138	1	<	<	X
ejpam-5429	138	2	ρ̃	ρ̃	PROPN
ejpam-5429	138	3	≤	≤	NOUN
ejpam-5429	138	4	ð̃((ς̇	ð̃((ς̇	PUNCT
ejpam-5429	139	1	≬	≬	PROPN
ejpam-5429	139	2	ϱ̇	ϱ̇	PROPN
ejpam-5429	139	3	)	)	PUNCT
ejpam-5429	139	4	≬	≬	PROPN
ejpam-5429	139	5	κ̇	κ̇	PROPN
ejpam-5429	139	6	)	)	PUNCT
ejpam-5429	139	7	∧	∧	PROPN
ejpam-5429	139	8	ð̃(κ̇	ð̃(κ̇	PROPN
ejpam-5429	139	9	)	)	PUNCT
ejpam-5429	139	10	.	.	PUNCT
ejpam-5429	140	1	but	but	CCONJ
ejpam-5429	140	2	ð̃((ς̇	ð̃((ς̇	X
ejpam-5429	140	3	≬	≬	PROPN
ejpam-5429	140	4	ϱ̇	ϱ̇	PROPN
ejpam-5429	140	5	)	)	PUNCT
ejpam-5429	140	6	≬	≬	PROPN
ejpam-5429	140	7	κ̇	κ̇	PROPN
ejpam-5429	140	8	)	)	PUNCT
ejpam-5429	140	9	≥	≥	NOUN
ejpam-5429	140	10	ρ̃	ρ̃	PROPN
ejpam-5429	140	11	and	and	CCONJ
ejpam-5429	140	12	ð̃(κ̇	ð̃(κ̇	PROPN
ejpam-5429	140	13	)	)	PUNCT
ejpam-5429	140	14	≥	≥	NOUN
ejpam-5429	140	15	ρ̃.	ρ̃.	NUM
ejpam-5429	140	16	so	so	ADV
ejpam-5429	140	17	,	,	PUNCT
ejpam-5429	140	18	ς̇	ς̇	PROPN
ejpam-5429	140	19	≬	≬	PROPN
ejpam-5429	140	20	(	(	PUNCT
ejpam-5429	140	21	ϱ̇	ϱ̇	PROPN
ejpam-5429	140	22	≬	≬	PROPN
ejpam-5429	140	23	(	(	PUNCT
ejpam-5429	140	24	ϱ̇	ϱ̇	PROPN
ejpam-5429	140	25	≬	≬	PROPN
ejpam-5429	140	26	ς̇	ς̇	NOUN
ejpam-5429	140	27	)	)	PUNCT
ejpam-5429	140	28	)	)	PUNCT
ejpam-5429	141	1	̸∈	̸∈	PROPN
ejpam-5429	141	2	ð̃ρ̃	ð̃ρ̃	PROPN
ejpam-5429	141	3	,	,	PUNCT
ejpam-5429	141	4	a	a	DET
ejpam-5429	141	5	contradiction	contradiction	NOUN
ejpam-5429	141	6	.	.	PUNCT
ejpam-5429	142	1	therefore	therefore	ADV
ejpam-5429	142	2	,	,	PUNCT
ejpam-5429	142	3	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	142	4	≬	≬	PROPN
ejpam-5429	142	5	(	(	PUNCT
ejpam-5429	142	6	ϱ̇	ϱ̇	PROPN
ejpam-5429	142	7	≬	≬	PROPN
ejpam-5429	142	8	(	(	PUNCT
ejpam-5429	142	9	ϱ̇	ϱ̇	PROPN
ejpam-5429	142	10	≬	≬	PROPN
ejpam-5429	142	11	ς̇	ς̇	NOUN
ejpam-5429	142	12	)	)	PUNCT
ejpam-5429	142	13	)	)	PUNCT
ejpam-5429	142	14	)	)	PUNCT
ejpam-5429	143	1	≥	≥	X
ejpam-5429	143	2	ð̃((ς̇	ð̃((ς̇	X
ejpam-5429	144	1	≬	≬	PROPN
ejpam-5429	144	2	ϱ̇	ϱ̇	PROPN
ejpam-5429	144	3	)	)	PUNCT
ejpam-5429	144	4	≬	≬	PROPN
ejpam-5429	144	5	κ̇	κ̇	PROPN
ejpam-5429	144	6	)	)	PUNCT
ejpam-5429	144	7	∧	∧	PROPN
ejpam-5429	144	8	ð̃(κ̇	ð̃(κ̇	PROPN
ejpam-5429	144	9	)	)	PUNCT
ejpam-5429	144	10	.	.	PUNCT
ejpam-5429	145	1	hence	hence	ADV
ejpam-5429	145	2	,	,	PUNCT
ejpam-5429	145	3	ð̃ρ̃	ð̃ρ̃	PROPN
ejpam-5429	145	4	is	be	AUX
ejpam-5429	145	5	a	a	DET
ejpam-5429	145	6	ffi	ffi	PROPN
ejpam-5429	145	7	of	of	ADP
ejpam-5429	145	8	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	145	9	consider	consider	VERB
ejpam-5429	145	10	a	a	DET
ejpam-5429	145	11	qp	qp	NOUN
ejpam-5429	145	12	-	-	PUNCT
ejpam-5429	145	13	f	f	NOUN
ejpam-5429	145	14	set	set	NOUN
ejpam-5429	145	15	ð̃	ð̃	PROPN
ejpam-5429	145	16	defined	define	VERB
ejpam-5429	145	17	on	on	ADP
ejpam-5429	145	18	ℵ̃	ℵ̃	PROPN
ejpam-5429	145	19	,	,	PUNCT
ejpam-5429	145	20	where	where	SCONJ
ejpam-5429	145	21	ð̃(ς̇	ð̃(ς̇	NOUN
ejpam-5429	145	22	)	)	PUNCT
ejpam-5429	145	23	=	=	PRON
ejpam-5429	145	24	{	{	PUNCT
ejpam-5429	145	25	ρ̃	ρ̃	PROPN
ejpam-5429	145	26	∈	∈	PROPN
ejpam-5429	145	27	(	(	PUNCT
ejpam-5429	145	28	0	0	NUM
ejpam-5429	145	29	,	,	PUNCT
ejpam-5429	145	30	1]q	1]q	NUM
ejpam-5429	145	31	,	,	PUNCT
ejpam-5429	145	32	if	if	SCONJ
ejpam-5429	145	33	ς̇	ς̇	PROPN
ejpam-5429	145	34	∈	∈	PROPN
ejpam-5429	145	35	ℵ̃	ℵ̃	PROPN
ejpam-5429	145	36	0̃	0̃	NOUN
ejpam-5429	145	37	,	,	PUNCT
ejpam-5429	145	38	if	if	SCONJ
ejpam-5429	145	39	ς̇	ς̇	PROPN
ejpam-5429	145	40	/∈	/∈	PUNCT
ejpam-5429	146	1	ℵ̃	ℵ̃	PROPN
ejpam-5429	146	2	,	,	PUNCT
ejpam-5429	146	3	then	then	ADV
ejpam-5429	146	4	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	146	5	is	be	AUX
ejpam-5429	146	6	a	a	DET
ejpam-5429	146	7	qp	qp	PROPN
ejpam-5429	146	8	-	-	PUNCT
ejpam-5429	146	9	f	f	NOUN
ejpam-5429	146	10	point	point	NOUN
ejpam-5429	146	11	with	with	ADP
ejpam-5429	146	12	support	support	NOUN
ejpam-5429	146	13	ℵ̃	ℵ̃	PROPN
ejpam-5429	146	14	and	and	CCONJ
ejpam-5429	146	15	the	the	DET
ejpam-5429	146	16	value	value	NOUN
ejpam-5429	146	17	ρ̃	ρ̃	PROPN
ejpam-5429	146	18	,	,	PUNCT
ejpam-5429	146	19	and	and	CCONJ
ejpam-5429	146	20	it	it	PRON
ejpam-5429	146	21	is	be	AUX
ejpam-5429	146	22	symbolized	symbolize	VERB
ejpam-5429	146	23	by	by	ADP
ejpam-5429	146	24	ς̇ρ̃.	ς̇ρ̃.	X
ejpam-5429	146	25	theorem	theorem	NOUN
ejpam-5429	146	26	2	2	NUM
ejpam-5429	146	27	.	.	PUNCT
ejpam-5429	147	1	every	every	DET
ejpam-5429	147	2	fantastic	fantastic	ADJ
ejpam-5429	147	3	ideal	ideal	NOUN
ejpam-5429	147	4	of	of	ADP
ejpam-5429	147	5	ℵ̃	ℵ̃	PROPN
ejpam-5429	147	6	is	be	AUX
ejpam-5429	147	7	a	a	DET
ejpam-5429	147	8	qp	qp	PROPN
ejpam-5429	147	9	-	-	PUNCT
ejpam-5429	147	10	ffi	ffi	PROPN
ejpam-5429	147	11	of	of	ADP
ejpam-5429	147	12	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	147	13	proof	proof	NOUN
ejpam-5429	147	14	.	.	PUNCT
ejpam-5429	148	1	suppose	suppose	VERB
ejpam-5429	148	2	ð̃ρ̃	ð̃ρ̃	NOUN
ejpam-5429	148	3	is	be	AUX
ejpam-5429	148	4	a	a	DET
ejpam-5429	148	5	fantastic	fantastic	ADJ
ejpam-5429	148	6	ideal	ideal	NOUN
ejpam-5429	148	7	of	of	ADP
ejpam-5429	148	8	ℵ̃	ℵ̃	PROPN
ejpam-5429	148	9	and	and	CCONJ
ejpam-5429	148	10	let	let	VERB
ejpam-5429	148	11	ð̃	ð̃	NOUN
ejpam-5429	148	12	be	be	AUX
ejpam-5429	148	13	an	an	DET
ejpam-5429	148	14	qp	qp	NOUN
ejpam-5429	148	15	-	-	PUNCT
ejpam-5429	148	16	fs	f	NOUN
ejpam-5429	148	17	in	in	ADP
ejpam-5429	148	18	ℵ̃	ℵ̃	PROPN
ejpam-5429	148	19	defined	define	VERB
ejpam-5429	148	20	by	by	ADP
ejpam-5429	148	21	ð̃(ς̇	ð̃(ς̇	NOUN
ejpam-5429	148	22	)	)	PUNCT
ejpam-5429	149	1	=	=	PRON
ejpam-5429	149	2	{	{	PUNCT
ejpam-5429	149	3	ρ̃	ρ̃	PROPN
ejpam-5429	149	4	∈	∈	PROPN
ejpam-5429	149	5	(	(	PUNCT
ejpam-5429	149	6	0	0	NUM
ejpam-5429	149	7	,	,	PUNCT
ejpam-5429	149	8	1]q	1]q	NUM
ejpam-5429	149	9	,	,	PUNCT
ejpam-5429	149	10	if	if	SCONJ
ejpam-5429	149	11	ς̇	ς̇	PROPN
ejpam-5429	149	12	∈	∈	PROPN
ejpam-5429	149	13	ℵ̃	ℵ̃	PROPN
ejpam-5429	149	14	0̃	0̃	NOUN
ejpam-5429	149	15	,	,	PUNCT
ejpam-5429	149	16	if	if	SCONJ
ejpam-5429	149	17	ς̇	ς̇	NOUN
ejpam-5429	149	18	/∈	/∈	PUNCT
ejpam-5429	150	1	ℵ̃	ℵ̃	PROPN
ejpam-5429	150	2	let	let	VERB
ejpam-5429	150	3	ς̇	ς̇	NOUN
ejpam-5429	150	4	,	,	PUNCT
ejpam-5429	150	5	ϱ̇	ϱ̇	PROPN
ejpam-5429	150	6	∈	∈	PROPN
ejpam-5429	150	7	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	150	8	to	to	PART
ejpam-5429	150	9	verify	verify	VERB
ejpam-5429	150	10	that	that	SCONJ
ejpam-5429	150	11	ð̃	ð̃	PROPN
ejpam-5429	150	12	is	be	AUX
ejpam-5429	150	13	a	a	DET
ejpam-5429	150	14	qp	qp	PROPN
ejpam-5429	150	15	-	-	PUNCT
ejpam-5429	150	16	ffi	ffi	PROPN
ejpam-5429	150	17	of	of	ADP
ejpam-5429	150	18	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	150	19	case	case	NOUN
ejpam-5429	150	20	1	1	NUM
ejpam-5429	150	21	:	:	PUNCT
ejpam-5429	150	22	if	if	SCONJ
ejpam-5429	150	23	(	(	PUNCT
ejpam-5429	150	24	ς̇	ς̇	PROPN
ejpam-5429	150	25	≬	≬	PROPN
ejpam-5429	150	26	ϱ̇	ϱ̇	NUM
ejpam-5429	150	27	)	)	PUNCT
ejpam-5429	150	28	≬	≬	PROPN
ejpam-5429	150	29	κ̇	κ̇	NOUN
ejpam-5429	150	30	∈	∈	PROPN
ejpam-5429	150	31	ð̃	ð̃	PROPN
ejpam-5429	150	32	and	and	CCONJ
ejpam-5429	150	33	κ̇	κ̇	PROPN
ejpam-5429	150	34	∈	∈	PROPN
ejpam-5429	150	35	ð̃	ð̃	PROPN
ejpam-5429	150	36	,	,	PUNCT
ejpam-5429	150	37	then	then	ADV
ejpam-5429	150	38	(	(	PUNCT
ejpam-5429	150	39	ς̇	ς̇	PROPN
ejpam-5429	150	40	≬	≬	PROPN
ejpam-5429	150	41	(	(	PUNCT
ejpam-5429	150	42	ϱ̇	ϱ̇	PROPN
ejpam-5429	150	43	≬	≬	PROPN
ejpam-5429	150	44	(	(	PUNCT
ejpam-5429	150	45	ϱ̇	ϱ̇	PROPN
ejpam-5429	150	46	≬	≬	PROPN
ejpam-5429	150	47	ς̇	ς̇	NOUN
ejpam-5429	150	48	)	)	PUNCT
ejpam-5429	150	49	)	)	PUNCT
ejpam-5429	150	50	)	)	PUNCT
ejpam-5429	151	1	∈	∈	PROPN
ejpam-5429	151	2	ð̃.	ð̃.	NOUN
ejpam-5429	151	3	thus	thus	ADV
ejpam-5429	151	4	ð̃((ς̇	ð̃((ς̇	X
ejpam-5429	151	5	≬	≬	PROPN
ejpam-5429	151	6	ϱ̇	ϱ̇	PROPN
ejpam-5429	151	7	)	)	PUNCT
ejpam-5429	151	8	≬	≬	PROPN
ejpam-5429	151	9	κ̇	κ̇	PROPN
ejpam-5429	151	10	)	)	PUNCT
ejpam-5429	151	11	=	=	SYM
ejpam-5429	151	12	ð̃(κ̇	ð̃(κ̇	X
ejpam-5429	151	13	)	)	PUNCT
ejpam-5429	151	14	=	=	SYM
ejpam-5429	151	15	ρ̃.	ρ̃.	PROPN
ejpam-5429	151	16	hence	hence	ADV
ejpam-5429	151	17	by	by	ADP
ejpam-5429	151	18	definition	definition	NOUN
ejpam-5429	151	19	3.2	3.2	NUM
ejpam-5429	151	20	,	,	PUNCT
ejpam-5429	151	21	we	we	PRON
ejpam-5429	151	22	have	have	VERB
ejpam-5429	151	23	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	151	24	≬	≬	PROPN
ejpam-5429	151	25	(	(	PUNCT
ejpam-5429	151	26	ϱ̇	ϱ̇	PROPN
ejpam-5429	151	27	≬	≬	PROPN
ejpam-5429	151	28	(	(	PUNCT
ejpam-5429	151	29	ϱ̇	ϱ̇	PROPN
ejpam-5429	151	30	≬	≬	PROPN
ejpam-5429	151	31	ς̇	ς̇	NOUN
ejpam-5429	151	32	)	)	PUNCT
ejpam-5429	151	33	)	)	PUNCT
ejpam-5429	151	34	)	)	PUNCT
ejpam-5429	152	1	≥	≥	X
ejpam-5429	152	2	ð̃((ς̇	ð̃((ς̇	X
ejpam-5429	153	1	≬	≬	PROPN
ejpam-5429	153	2	ϱ̇	ϱ̇	PROPN
ejpam-5429	153	3	)	)	PUNCT
ejpam-5429	153	4	≬	≬	PROPN
ejpam-5429	153	5	κ̇	κ̇	PROPN
ejpam-5429	153	6	)	)	PUNCT
ejpam-5429	153	7	∧	∧	PROPN
ejpam-5429	153	8	ð̃(κ̇	ð̃(κ̇	PROPN
ejpam-5429	153	9	)	)	PUNCT
ejpam-5429	153	10	=	=	SYM
ejpam-5429	153	11	ρ̃	ρ̃	PROPN
ejpam-5429	153	12	∧	∧	NOUN
ejpam-5429	153	13	ρ̃	ρ̃	PROPN
ejpam-5429	153	14	=	=	SYM
ejpam-5429	153	15	ρ̃.	ρ̃.	PROPN
ejpam-5429	153	16	case	case	NOUN
ejpam-5429	153	17	2	2	NUM
ejpam-5429	153	18	:	:	PUNCT
ejpam-5429	153	19	if	if	SCONJ
ejpam-5429	153	20	(	(	PUNCT
ejpam-5429	153	21	ς̇	ς̇	PROPN
ejpam-5429	153	22	≬	≬	PROPN
ejpam-5429	153	23	ϱ̇	ϱ̇	NUM
ejpam-5429	153	24	)	)	PUNCT
ejpam-5429	153	25	≬	≬	PROPN
ejpam-5429	153	26	κ̇	κ̇	VERB
ejpam-5429	153	27	̸∈	̸∈	PROPN
ejpam-5429	153	28	ð̃	ð̃	PROPN
ejpam-5429	153	29	and	and	CCONJ
ejpam-5429	153	30	κ̇	κ̇	PROPN
ejpam-5429	153	31	̸∈	̸∈	PROPN
ejpam-5429	153	32	ð̃	ð̃	PROPN
ejpam-5429	153	33	,	,	PUNCT
ejpam-5429	153	34	then	then	ADV
ejpam-5429	153	35	(	(	PUNCT
ejpam-5429	153	36	ς̇	ς̇	PROPN
ejpam-5429	153	37	≬	≬	PROPN
ejpam-5429	153	38	(	(	PUNCT
ejpam-5429	153	39	ϱ̇	ϱ̇	PROPN
ejpam-5429	153	40	≬	≬	PROPN
ejpam-5429	153	41	(	(	PUNCT
ejpam-5429	153	42	ϱ̇	ϱ̇	PROPN
ejpam-5429	153	43	≬	≬	PROPN
ejpam-5429	153	44	ς̇	ς̇	NOUN
ejpam-5429	153	45	)	)	PUNCT
ejpam-5429	153	46	)	)	PUNCT
ejpam-5429	153	47	)	)	PUNCT
ejpam-5429	154	1	̸∈	̸∈	PROPN
ejpam-5429	154	2	ð̃.	ð̃.	PROPN
ejpam-5429	154	3	thus	thus	ADV
ejpam-5429	154	4	,	,	PUNCT
ejpam-5429	154	5	ð̃((ς̇	ð̃((ς̇	VERB
ejpam-5429	154	6	≬	≬	PROPN
ejpam-5429	154	7	ϱ̇	ϱ̇	PROPN
ejpam-5429	154	8	)	)	PUNCT
ejpam-5429	154	9	≬	≬	PROPN
ejpam-5429	154	10	κ̇	κ̇	PROPN
ejpam-5429	154	11	)	)	PUNCT
ejpam-5429	154	12	=	=	PUNCT
ejpam-5429	154	13	ð̃(κ̇	ð̃(κ̇	PROPN
ejpam-5429	154	14	)	)	PUNCT
ejpam-5429	154	15	=	=	SYM
ejpam-5429	154	16	0̃.	0̃.	NOUN
ejpam-5429	154	17	hence	hence	ADV
ejpam-5429	154	18	by	by	ADP
ejpam-5429	154	19	definition	definition	NOUN
ejpam-5429	154	20	3.2	3.2	NUM
ejpam-5429	154	21	,	,	PUNCT
ejpam-5429	154	22	we	we	PRON
ejpam-5429	154	23	have	have	VERB
ejpam-5429	154	24	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	154	25	≬	≬	PROPN
ejpam-5429	154	26	(	(	PUNCT
ejpam-5429	154	27	ϱ̇	ϱ̇	PROPN
ejpam-5429	154	28	≬	≬	PROPN
ejpam-5429	154	29	(	(	PUNCT
ejpam-5429	154	30	ϱ̇	ϱ̇	PROPN
ejpam-5429	154	31	≬	≬	PROPN
ejpam-5429	154	32	ς̇	ς̇	NOUN
ejpam-5429	154	33	)	)	PUNCT
ejpam-5429	154	34	)	)	PUNCT
ejpam-5429	154	35	)	)	PUNCT
ejpam-5429	155	1	≥	≥	X
ejpam-5429	155	2	ð̃((ς̇	ð̃((ς̇	X
ejpam-5429	156	1	≬	≬	PROPN
ejpam-5429	156	2	ϱ̇	ϱ̇	PROPN
ejpam-5429	156	3	)	)	PUNCT
ejpam-5429	156	4	≬	≬	PROPN
ejpam-5429	156	5	κ̇	κ̇	PROPN
ejpam-5429	156	6	)	)	PUNCT
ejpam-5429	156	7	∧	∧	PROPN
ejpam-5429	156	8	ð̃(κ̇	ð̃(κ̇	PROPN
ejpam-5429	156	9	)	)	PUNCT
ejpam-5429	156	10	=	=	SYM
ejpam-5429	156	11	0̃	0̃	NOUN
ejpam-5429	156	12	∧	∧	NOUN
ejpam-5429	156	13	0̃	0̃	NOUN
ejpam-5429	156	14	=	=	SYM
ejpam-5429	156	15	0̃.	0̃.	NOUN
ejpam-5429	156	16	case	case	NOUN
ejpam-5429	156	17	3	3	NUM
ejpam-5429	156	18	:	:	PUNCT
ejpam-5429	156	19	if	if	SCONJ
ejpam-5429	156	20	either	either	PRON
ejpam-5429	156	21	(	(	PUNCT
ejpam-5429	156	22	ς̇	ς̇	PROPN
ejpam-5429	156	23	≬	≬	PROPN
ejpam-5429	156	24	ϱ̇	ϱ̇	NUM
ejpam-5429	156	25	)	)	PUNCT
ejpam-5429	156	26	≬	≬	PROPN
ejpam-5429	156	27	κ̇	κ̇	NOUN
ejpam-5429	156	28	∈	∈	PROPN
ejpam-5429	156	29	ð̃	ð̃	PROPN
ejpam-5429	156	30	or	or	CCONJ
ejpam-5429	156	31	κ̇	κ̇	PROPN
ejpam-5429	156	32	∈	∈	PROPN
ejpam-5429	156	33	ð̃	ð̃	PROPN
ejpam-5429	156	34	,	,	PUNCT
ejpam-5429	156	35	then	then	ADV
ejpam-5429	156	36	either	either	ADV
ejpam-5429	156	37	ð̃((ς̇	ð̃((ς̇	VERB
ejpam-5429	156	38	≬	≬	PROPN
ejpam-5429	156	39	ϱ̇	ϱ̇	PROPN
ejpam-5429	156	40	)	)	PUNCT
ejpam-5429	156	41	≬	≬	PROPN
ejpam-5429	156	42	κ̇	κ̇	PROPN
ejpam-5429	156	43	)	)	PUNCT
ejpam-5429	156	44	=	=	SYM
ejpam-5429	156	45	0̃	0̃	NOUN
ejpam-5429	156	46	or	or	CCONJ
ejpam-5429	156	47	ð̃(κ̇	ð̃(κ̇	PROPN
ejpam-5429	156	48	)	)	PUNCT
ejpam-5429	156	49	=	=	SYM
ejpam-5429	157	1	0̃.	0̃.	NOUN
ejpam-5429	158	1	so	so	ADV
ejpam-5429	158	2	,	,	PUNCT
ejpam-5429	158	3	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	158	4	≬	≬	PROPN
ejpam-5429	158	5	(	(	PUNCT
ejpam-5429	158	6	ϱ̇	ϱ̇	PROPN
ejpam-5429	158	7	≬	≬	PROPN
ejpam-5429	158	8	(	(	PUNCT
ejpam-5429	158	9	ϱ̇	ϱ̇	PROPN
ejpam-5429	158	10	≬	≬	PROPN
ejpam-5429	158	11	ς̇	ς̇	NOUN
ejpam-5429	158	12	)	)	PUNCT
ejpam-5429	158	13	)	)	PUNCT
ejpam-5429	158	14	)	)	PUNCT
ejpam-5429	159	1	≥	≥	X
ejpam-5429	159	2	ð̃((ς̇	ð̃((ς̇	X
ejpam-5429	160	1	≬	≬	PROPN
ejpam-5429	160	2	ϱ̇	ϱ̇	PROPN
ejpam-5429	160	3	)	)	PUNCT
ejpam-5429	160	4	≬	≬	PROPN
ejpam-5429	160	5	κ̇	κ̇	PROPN
ejpam-5429	160	6	)	)	PUNCT
ejpam-5429	160	7	∧	∧	PROPN
ejpam-5429	160	8	ð̃(κ̇	ð̃(κ̇	PROPN
ejpam-5429	160	9	)	)	PUNCT
ejpam-5429	160	10	.	.	PUNCT
ejpam-5429	161	1	hence	hence	ADV
ejpam-5429	161	2	,	,	PUNCT
ejpam-5429	161	3	ð̃	ð̃	PROPN
ejpam-5429	161	4	is	be	AUX
ejpam-5429	161	5	a	a	DET
ejpam-5429	161	6	qp	qp	PROPN
ejpam-5429	161	7	-	-	PUNCT
ejpam-5429	161	8	ffi	ffi	PROPN
ejpam-5429	161	9	of	of	ADP
ejpam-5429	161	10	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	161	11	k.	k.	PROPN
ejpam-5429	161	12	h.	h.	PROPN
ejpam-5429	161	13	hakami	hakami	PROPN
ejpam-5429	161	14	et	et	PROPN
ejpam-5429	161	15	al	al	PROPN
ejpam-5429	161	16	.	.	PUNCT
ejpam-5429	161	17	/	/	SYM
ejpam-5429	161	18	eur	eur	PROPN
ejpam-5429	161	19	.	.	PUNCT
ejpam-5429	162	1	j.	j.	PROPN
ejpam-5429	162	2	pure	pure	PROPN
ejpam-5429	162	3	appl	appl	PROPN
ejpam-5429	162	4	.	.	PROPN
ejpam-5429	162	5	math	math	PROPN
ejpam-5429	162	6	,	,	PUNCT
ejpam-5429	162	7	17	17	NUM
ejpam-5429	162	8	(	(	PUNCT
ejpam-5429	162	9	4	4	NUM
ejpam-5429	162	10	)	)	PUNCT
ejpam-5429	162	11	(	(	PUNCT
ejpam-5429	162	12	2024	2024	NUM
ejpam-5429	162	13	)	)	PUNCT
ejpam-5429	162	14	,	,	PUNCT
ejpam-5429	162	15	3129	3129	NUM
ejpam-5429	162	16	-	-	SYM
ejpam-5429	162	17	3155	3155	NUM
ejpam-5429	162	18	3134	3134	NUM
ejpam-5429	162	19	4	4	NUM
ejpam-5429	162	20	.	.	X
ejpam-5429	162	21	quadri	quadri	NOUN
ejpam-5429	162	22	-	-	PUNCT
ejpam-5429	162	23	polar	polar	PROPN
ejpam-5429	162	24	(	(	PUNCT
ejpam-5429	162	25	ϖ,ϑ)-fuzzy	ϖ,ϑ)-fuzzy	ADJ
ejpam-5429	162	26	fantastic	fantastic	ADJ
ejpam-5429	162	27	ideals	ideal	NOUN
ejpam-5429	162	28	in	in	ADP
ejpam-5429	162	29	this	this	DET
ejpam-5429	162	30	section	section	NOUN
ejpam-5429	162	31	,	,	PUNCT
ejpam-5429	162	32	we	we	PRON
ejpam-5429	162	33	introduce	introduce	VERB
ejpam-5429	162	34	the	the	DET
ejpam-5429	162	35	concept	concept	NOUN
ejpam-5429	162	36	of	of	ADP
ejpam-5429	162	37	a	a	DET
ejpam-5429	162	38	qp-(ϖ,ϑ)ffi(s	qp-(ϖ,ϑ)ffi(s	NOUN
ejpam-5429	162	39	)	)	PUNCT
ejpam-5429	162	40	in	in	ADP
ejpam-5429	162	41	bci	bci	NOUN
ejpam-5429	162	42	-	-	PUNCT
ejpam-5429	162	43	algebras	algebra	NOUN
ejpam-5429	162	44	and	and	CCONJ
ejpam-5429	162	45	explore	explore	VERB
ejpam-5429	162	46	various	various	ADJ
ejpam-5429	162	47	properties	property	NOUN
ejpam-5429	162	48	associated	associate	VERB
ejpam-5429	162	49	with	with	ADP
ejpam-5429	162	50	it	it	PRON
ejpam-5429	162	51	.	.	PUNCT
ejpam-5429	163	1	here	here	ADV
ejpam-5429	163	2	,	,	PUNCT
ejpam-5429	163	3	we	we	PRON
ejpam-5429	163	4	use	use	VERB
ejpam-5429	163	5	ϖ	ϖ	NOUN
ejpam-5429	163	6	and	and	CCONJ
ejpam-5429	163	7	ϑ	ϑ	X
ejpam-5429	163	8	to	to	PART
ejpam-5429	163	9	represent	represent	VERB
ejpam-5429	163	10	symbols	symbol	NOUN
ejpam-5429	163	11	such	such	ADJ
ejpam-5429	163	12	as	as	ADP
ejpam-5429	163	13	∈σ̃,∈σ̃	∈σ̃,∈σ̃	PROPN
ejpam-5429	163	14	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	163	15	,	,	PUNCT
ejpam-5429	163	16	qτ̃	qτ̃	PROPN
ejpam-5429	163	17	or	or	CCONJ
ejpam-5429	163	18	∈σ̃	∈σ̃	PROPN
ejpam-5429	163	19	∧qτ̃	∧qτ̃	PROPN
ejpam-5429	163	20	,	,	PUNCT
ejpam-5429	163	21	unless	unless	SCONJ
ejpam-5429	163	22	specified	specify	VERB
ejpam-5429	163	23	otherwise	otherwise	ADV
ejpam-5429	163	24	.	.	PUNCT
ejpam-5429	164	1	consider	consider	VERB
ejpam-5429	164	2	a	a	DET
ejpam-5429	164	3	qp	qp	NOUN
ejpam-5429	164	4	-	-	PUNCT
ejpam-5429	164	5	f	f	NOUN
ejpam-5429	164	6	point	point	NOUN
ejpam-5429	164	7	denoted	denote	VERB
ejpam-5429	164	8	as	as	ADP
ejpam-5429	164	9	ς̇ρ̃	ς̇ρ̃	PROPN
ejpam-5429	164	10	and	and	CCONJ
ejpam-5429	164	11	a	a	DET
ejpam-5429	164	12	qp	qp	PROPN
ejpam-5429	164	13	-	-	PUNCT
ejpam-5429	164	14	f	f	NOUN
ejpam-5429	164	15	set	set	NOUN
ejpam-5429	164	16	ð̃	ð̃	PROPN
ejpam-5429	164	17	defined	define	VERB
ejpam-5429	164	18	on	on	ADP
ejpam-5429	164	19	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	164	20	then	then	ADV
ejpam-5429	164	21	(	(	PUNCT
ejpam-5429	164	22	1	1	X
ejpam-5429	164	23	)	)	PUNCT
ejpam-5429	164	24	ς̇ρ̃	ς̇ρ̃	NOUN
ejpam-5429	165	1	∈σ̃	∈σ̃	PROPN
ejpam-5429	165	2	ð̃	ð̃	PROPN
ejpam-5429	165	3	if	if	SCONJ
ejpam-5429	165	4	ð̃(ς̇	ð̃(ς̇	NOUN
ejpam-5429	165	5	)	)	PUNCT
ejpam-5429	165	6	≥	≥	NOUN
ejpam-5429	166	1	ρ̃	ρ̃	PROPN
ejpam-5429	166	2	>	>	X
ejpam-5429	166	3	σ̃.	σ̃.	PROPN
ejpam-5429	166	4	(	(	PUNCT
ejpam-5429	166	5	2	2	NUM
ejpam-5429	166	6	)	)	PUNCT
ejpam-5429	166	7	ς̇ρ̃qτ̃	ς̇ρ̃qτ̃	NOUN
ejpam-5429	166	8	ð̃	ð̃	PROPN
ejpam-5429	166	9	if	if	SCONJ
ejpam-5429	166	10	ð̃(ς̇	ð̃(ς̇	NOUN
ejpam-5429	166	11	)	)	PUNCT
ejpam-5429	166	12	+	+	CCONJ
ejpam-5429	166	13	ρ̃	ρ̃	PROPN
ejpam-5429	166	14	>	>	SYM
ejpam-5429	166	15	2τ̃	2τ̃	PROPN
ejpam-5429	166	16	.	.	PUNCT
ejpam-5429	167	1	(	(	PUNCT
ejpam-5429	167	2	3	3	X
ejpam-5429	167	3	)	)	PUNCT
ejpam-5429	167	4	ς̇ρ̃	ς̇ρ̃	NOUN
ejpam-5429	167	5	∈σ̃	∈σ̃	VERB
ejpam-5429	167	6	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	167	7	ð̃	ð̃	PROPN
ejpam-5429	167	8	if	if	SCONJ
ejpam-5429	167	9	ς̇ρ̃	ς̇ρ̃	PROPN
ejpam-5429	167	10	∈σ̃	∈σ̃	PROPN
ejpam-5429	167	11	ð̃	ð̃	PROPN
ejpam-5429	167	12	or	or	CCONJ
ejpam-5429	167	13	ς̇ρ̃qτ̃	ς̇ρ̃qτ̃	NOUN
ejpam-5429	167	14	ð̃.	ð̃.	NOUN
ejpam-5429	167	15	(	(	PUNCT
ejpam-5429	167	16	4	4	NUM
ejpam-5429	167	17	)	)	PUNCT
ejpam-5429	167	18	ς̇ρ̃	ς̇ρ̃	PROPN
ejpam-5429	167	19	∈σ̃	∈σ̃	PROPN
ejpam-5429	167	20	∧qτ̃	∧qτ̃	PROPN
ejpam-5429	167	21	ð̃	ð̃	PROPN
ejpam-5429	167	22	if	if	SCONJ
ejpam-5429	167	23	ς̇ρ̃	ς̇ρ̃	PROPN
ejpam-5429	167	24	∈σ̃	∈σ̃	PROPN
ejpam-5429	167	25	ð̃	ð̃	PROPN
ejpam-5429	167	26	and	and	CCONJ
ejpam-5429	167	27	ς̇ρ̃qτ̃	ς̇ρ̃qτ̃	NOUN
ejpam-5429	167	28	ð̃.	ð̃.	NOUN
ejpam-5429	167	29	(	(	PUNCT
ejpam-5429	167	30	5	5	NUM
ejpam-5429	167	31	)	)	PUNCT
ejpam-5429	167	32	ς̇ρ̃ϖð̃	ς̇ρ̃ϖð̃	ADV
ejpam-5429	167	33	does	do	AUX
ejpam-5429	167	34	not	not	PART
ejpam-5429	167	35	hold	hold	VERB
ejpam-5429	167	36	for	for	ADP
ejpam-5429	167	37	ϖ	ϖ	NOUN
ejpam-5429	167	38	=	=	SYM
ejpam-5429	167	39	{	{	PUNCT
ejpam-5429	167	40	∈σ̃	∈σ̃	PROPN
ejpam-5429	167	41	,	,	PUNCT
ejpam-5429	167	42	qτ̃	qτ̃	X
ejpam-5429	167	43	,	,	PUNCT
ejpam-5429	167	44	∈σ̃	∈σ̃	PROPN
ejpam-5429	167	45	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	167	46	,	,	PUNCT
ejpam-5429	167	47	∈σ̃	∈σ̃	PROPN
ejpam-5429	167	48	∧qτ̃},∀σ̃	∧qτ̃},∀σ̃	ADP
ejpam-5429	167	49	,	,	PUNCT
ejpam-5429	167	50	τ̃	τ̃	PROPN
ejpam-5429	167	51	∈	∈	PROPN
ejpam-5429	168	1	[	[	X
ejpam-5429	168	2	0	0	NUM
ejpam-5429	168	3	,	,	PUNCT
ejpam-5429	168	4	1]4	1]4	NUM
ejpam-5429	168	5	,	,	PUNCT
ejpam-5429	168	6	where	where	SCONJ
ejpam-5429	168	7	σ̃	σ̃	PROPN
ejpam-5429	168	8	=	=	SYM
ejpam-5429	168	9	(	(	PUNCT
ejpam-5429	168	10	σ̃1	σ̃1	PROPN
ejpam-5429	168	11	,	,	PUNCT
ejpam-5429	168	12	σ̃2	σ̃2	PROPN
ejpam-5429	168	13	,	,	PUNCT
ejpam-5429	168	14	σ̃3	σ̃3	PROPN
ejpam-5429	168	15	,	,	PUNCT
ejpam-5429	168	16	σ̃4	σ̃4	NOUN
ejpam-5429	168	17	)	)	PUNCT
ejpam-5429	168	18	<	<	X
ejpam-5429	168	19	τ̃	τ̃	PROPN
ejpam-5429	169	1	=	=	SYM
ejpam-5429	169	2	(	(	PUNCT
ejpam-5429	169	3	τ̃1	τ̃1	PROPN
ejpam-5429	169	4	,	,	PUNCT
ejpam-5429	169	5	τ̃2	τ̃2	PROPN
ejpam-5429	169	6	,	,	PUNCT
ejpam-5429	169	7	τ̃3	τ̃3	PROPN
ejpam-5429	169	8	,	,	PUNCT
ejpam-5429	169	9	τ̃4	τ̃4	PROPN
ejpam-5429	169	10	)	)	PUNCT
ejpam-5429	169	11	.	.	PUNCT
ejpam-5429	170	1	a	a	DET
ejpam-5429	170	2	qp	qp	PROPN
ejpam-5429	170	3	-	-	PUNCT
ejpam-5429	170	4	f	f	NOUN
ejpam-5429	170	5	point	point	NOUN
ejpam-5429	170	6	ς̇ρ̃	ς̇ρ̃	NOUN
ejpam-5429	170	7	∈	∈	PROPN
ejpam-5429	170	8	ð̃	ð̃	PROPN
ejpam-5429	171	1	if	if	SCONJ
ejpam-5429	171	2	ð̃(ς̇	ð̃(ς̇	NOUN
ejpam-5429	171	3	)	)	PUNCT
ejpam-5429	171	4	≥	≥	NOUN
ejpam-5429	171	5	ρ̃.	ρ̃.	NUM
ejpam-5429	171	6	that	that	PRON
ejpam-5429	171	7	is	be	AUX
ejpam-5429	171	8	ð̃q(ς̇	ð̃q(ς̇	PRON
ejpam-5429	171	9	)	)	PUNCT
ejpam-5429	171	10	≥	≥	NOUN
ejpam-5429	171	11	ρ̃q,∀q	ρ̃q,∀q	NOUN
ejpam-5429	171	12	=	=	SYM
ejpam-5429	171	13	1	1	NUM
ejpam-5429	171	14	,	,	PUNCT
ejpam-5429	171	15	2	2	NUM
ejpam-5429	171	16	,	,	PUNCT
ejpam-5429	171	17	3	3	NUM
ejpam-5429	171	18	,	,	PUNCT
ejpam-5429	171	19	4	4	NUM
ejpam-5429	171	20	.	.	PUNCT
ejpam-5429	171	21	also	also	ADV
ejpam-5429	171	22	,	,	PUNCT
ejpam-5429	171	23	ς̇ρ̃qð̃	ς̇ρ̃qð̃	PROPN
ejpam-5429	171	24	if	if	SCONJ
ejpam-5429	171	25	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	171	26	)	)	PUNCT
ejpam-5429	172	1	+	+	CCONJ
ejpam-5429	172	2	ρ̃	ρ̃	PROPN
ejpam-5429	172	3	>	>	SYM
ejpam-5429	172	4	1̂.	1̂.	NUM
ejpam-5429	172	5	that	that	PRON
ejpam-5429	172	6	is	be	AUX
ejpam-5429	172	7	,	,	PUNCT
ejpam-5429	172	8	ð̃q(ς̇	ð̃q(ς̇	PUNCT
ejpam-5429	172	9	)	)	PUNCT
ejpam-5429	173	1	+	+	NUM
ejpam-5429	173	2	ρ̃q	ρ̃q	NOUN
ejpam-5429	173	3	>	>	X
ejpam-5429	173	4	1̂,∀q	1̂,∀q	NUM
ejpam-5429	173	5	=	=	SYM
ejpam-5429	173	6	1	1	NUM
ejpam-5429	173	7	,	,	PUNCT
ejpam-5429	173	8	2	2	NUM
ejpam-5429	173	9	,	,	PUNCT
ejpam-5429	173	10	3	3	NUM
ejpam-5429	173	11	,	,	PUNCT
ejpam-5429	173	12	4	4	NUM
ejpam-5429	173	13	.	.	PUNCT
ejpam-5429	173	14	by	by	ADP
ejpam-5429	173	15	ς̇ρ̃	ς̇ρ̃	PROPN
ejpam-5429	173	16	∈	∈	PROPN
ejpam-5429	173	17	∨qð̃(resp	∨qð̃(resp	NOUN
ejpam-5429	173	18	.	.	PUNCT
ejpam-5429	173	19	,	,	PUNCT
ejpam-5429	173	20	ς̇ρ̃	ς̇ρ̃	PROPN
ejpam-5429	173	21	∈	∈	PROPN
ejpam-5429	173	22	∧qð̃	∧qð̃	PROPN
ejpam-5429	173	23	)	)	PUNCT
ejpam-5429	173	24	⇒	⇒	NOUN
ejpam-5429	173	25	ς̇ρ̃	ς̇ρ̃	PROPN
ejpam-5429	173	26	∈	∈	PROPN
ejpam-5429	173	27	ð̃	ð̃	PROPN
ejpam-5429	173	28	or	or	CCONJ
ejpam-5429	173	29	ς̇ρ̃qð̃(resp	ς̇ρ̃qð̃(resp	NOUN
ejpam-5429	173	30	.	.	PUNCT
ejpam-5429	173	31	,	,	PUNCT
ejpam-5429	173	32	ς̇ρ̃	ς̇ρ̃	PROPN
ejpam-5429	173	33	∈	∈	PROPN
ejpam-5429	173	34	ð̃	ð̃	PROPN
ejpam-5429	173	35	and	and	CCONJ
ejpam-5429	173	36	ς̇ρ̃qð̃	ς̇ρ̃qð̃	PROPN
ejpam-5429	173	37	)	)	PUNCT
ejpam-5429	173	38	.	.	PUNCT
ejpam-5429	174	1	if	if	SCONJ
ejpam-5429	174	2	ϕ	ϕ	PROPN
ejpam-5429	174	3	̸=	̸=	PROPN
ejpam-5429	174	4	c̃	c̃	PROPN
ejpam-5429	174	5	⊆	⊆	NUM
ejpam-5429	174	6	ℵ̃	ℵ̃	PROPN
ejpam-5429	174	7	,	,	PUNCT
ejpam-5429	174	8	then	then	ADV
ejpam-5429	174	9	the	the	DET
ejpam-5429	174	10	quadri	quadri	PROPN
ejpam-5429	174	11	-	-	PUNCT
ejpam-5429	174	12	polar	polar	ADJ
ejpam-5429	174	13	characteristic	characteristic	ADJ
ejpam-5429	174	14	fuzzy	fuzzy	ADJ
ejpam-5429	174	15	set	set	NOUN
ejpam-5429	174	16	(	(	PUNCT
ejpam-5429	174	17	qp	qp	NOUN
ejpam-5429	174	18	-	-	PUNCT
ejpam-5429	174	19	cf	cf	NOUN
ejpam-5429	174	20	)	)	PUNCT
ejpam-5429	174	21	of	of	ADP
ejpam-5429	174	22	c̃	c̃	PROPN
ejpam-5429	174	23	,	,	PUNCT
ejpam-5429	174	24	say	say	VERB
ejpam-5429	174	25	χ̂c̃	χ̂c̃	NUM
ejpam-5429	174	26	,	,	PUNCT
ejpam-5429	174	27	where	where	SCONJ
ejpam-5429	174	28	χ̂c̃	χ̂c̃	NOUN
ejpam-5429	174	29	=	=	PRON
ejpam-5429	174	30	{	{	PUNCT
ejpam-5429	174	31	1̂	1̂	NUM
ejpam-5429	174	32	=	=	SYM
ejpam-5429	174	33	(	(	PUNCT
ejpam-5429	174	34	1	1	NUM
ejpam-5429	174	35	,	,	PUNCT
ejpam-5429	174	36	1	1	NUM
ejpam-5429	174	37	,	,	PUNCT
ejpam-5429	174	38	1	1	NUM
ejpam-5429	174	39	,	,	PUNCT
ejpam-5429	174	40	1	1	NUM
ejpam-5429	174	41	)	)	PUNCT
ejpam-5429	174	42	,	,	PUNCT
ejpam-5429	174	43	if	if	SCONJ
ejpam-5429	174	44	ς̇	ς̇	PROPN
ejpam-5429	174	45	∈	∈	PROPN
ejpam-5429	174	46	c̃	c̃	PROPN
ejpam-5429	174	47	0̃	0̃	PROPN
ejpam-5429	174	48	=	=	SYM
ejpam-5429	174	49	(	(	PUNCT
ejpam-5429	174	50	0	0	NUM
ejpam-5429	174	51	,	,	PUNCT
ejpam-5429	174	52	0	0	NUM
ejpam-5429	174	53	,	,	PUNCT
ejpam-5429	174	54	0	0	NUM
ejpam-5429	174	55	,	,	PUNCT
ejpam-5429	174	56	0	0	NUM
ejpam-5429	174	57	)	)	PUNCT
ejpam-5429	174	58	,	,	PUNCT
ejpam-5429	174	59	if	if	SCONJ
ejpam-5429	174	60	ς̇	ς̇	PROPN
ejpam-5429	174	61	̸∈	̸∈	PROPN
ejpam-5429	174	62	c̃	c̃	PROPN
ejpam-5429	174	63	clearly	clearly	ADV
ejpam-5429	174	64	,	,	PUNCT
ejpam-5429	174	65	a	a	DET
ejpam-5429	174	66	qp	qp	NOUN
ejpam-5429	174	67	-	-	PUNCT
ejpam-5429	174	68	cf	cf	NOUN
ejpam-5429	174	69	is	be	AUX
ejpam-5429	174	70	a	a	DET
ejpam-5429	174	71	qp	qp	PROPN
ejpam-5429	174	72	-	-	PUNCT
ejpam-5429	174	73	f	f	PROPN
ejpam-5429	174	74	subset	subset	NOUN
ejpam-5429	174	75	of	of	ADP
ejpam-5429	174	76	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	174	77	definition	definition	NOUN
ejpam-5429	174	78	4	4	NUM
ejpam-5429	174	79	.	.	PUNCT
ejpam-5429	175	1	a	a	DET
ejpam-5429	175	2	qp	qp	PROPN
ejpam-5429	175	3	-	-	PUNCT
ejpam-5429	175	4	f	f	NOUN
ejpam-5429	175	5	set	set	NOUN
ejpam-5429	175	6	ð̃	ð̃	PROPN
ejpam-5429	175	7	is	be	AUX
ejpam-5429	175	8	a	a	DET
ejpam-5429	175	9	qp-(ϖ,ϑ)-ffi	qp-(ϖ,ϑ)-ffi	NOUN
ejpam-5429	175	10	of	of	ADP
ejpam-5429	175	11	ℵ̃	ℵ̃	PROPN
ejpam-5429	175	12	,	,	PUNCT
ejpam-5429	175	13	if	if	SCONJ
ejpam-5429	175	14	(	(	PUNCT
ejpam-5429	175	15	(	(	PUNCT
ejpam-5429	175	16	ς̇	ς̇	PROPN
ejpam-5429	175	17	≬	≬	PROPN
ejpam-5429	175	18	ϱ̇	ϱ̇	NUM
ejpam-5429	175	19	)	)	PUNCT
ejpam-5429	175	20	≬	≬	PROPN
ejpam-5429	175	21	κ̇)ρ̃ϖð̃	κ̇)ρ̃ϖð̃	NOUN
ejpam-5429	175	22	,	,	PUNCT
ejpam-5429	175	23	κ̇η̃ϖð̃	κ̇η̃ϖð̃	PROPN
ejpam-5429	175	24	⇒	⇒	NOUN
ejpam-5429	175	25	(	(	PUNCT
ejpam-5429	175	26	ς̇	ς̇	NOUN
ejpam-5429	175	27	≬	≬	PROPN
ejpam-5429	175	28	(	(	PUNCT
ejpam-5429	175	29	ϱ̇	ϱ̇	PROPN
ejpam-5429	175	30	≬	≬	PROPN
ejpam-5429	175	31	(	(	PUNCT
ejpam-5429	175	32	ϱ̇	ϱ̇	PROPN
ejpam-5429	175	33	≬	≬	PROPN
ejpam-5429	175	34	ς̇)))ρ̃∧η̃ϑð̃	ς̇)))ρ̃∧η̃ϑð̃	NOUN
ejpam-5429	175	35	,	,	PUNCT
ejpam-5429	175	36	where	where	SCONJ
ejpam-5429	175	37	ϖ	ϖ	X
ejpam-5429	175	38	̸=∈σ̃	̸=∈σ̃	PROPN
ejpam-5429	175	39	∧qτ̃	∧qτ̃	PROPN
ejpam-5429	175	40	,	,	PUNCT
ejpam-5429	175	41	∀σ̃	∀σ̃	PROPN
ejpam-5429	175	42	<	<	X
ejpam-5429	175	43	ρ̃	ρ̃	PROPN
ejpam-5429	175	44	,	,	PUNCT
ejpam-5429	175	45	η̃	η̃	PROPN
ejpam-5429	175	46	≤	≤	NOUN
ejpam-5429	175	47	1̂	1̂	NUM
ejpam-5429	175	48	and	and	CCONJ
ejpam-5429	175	49	(	(	PUNCT
ejpam-5429	175	50	(	(	PUNCT
ejpam-5429	175	51	ς̇	ς̇	PROPN
ejpam-5429	175	52	≬	≬	PROPN
ejpam-5429	175	53	ϱ̇	ϱ̇	NUM
ejpam-5429	175	54	)	)	PUNCT
ejpam-5429	175	55	≬	≬	PROPN
ejpam-5429	175	56	κ̇	κ̇	PROPN
ejpam-5429	175	57	)	)	PUNCT
ejpam-5429	175	58	,	,	PUNCT
ejpam-5429	175	59	κ̇	κ̇	PROPN
ejpam-5429	175	60	∈	∈	PROPN
ejpam-5429	175	61	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	175	62	consider	consider	VERB
ejpam-5429	175	63	a	a	DET
ejpam-5429	175	64	qp	qp	NOUN
ejpam-5429	175	65	-	-	PUNCT
ejpam-5429	175	66	f	f	NOUN
ejpam-5429	175	67	set	set	NOUN
ejpam-5429	175	68	ð̃	ð̃	PROPN
ejpam-5429	175	69	defined	define	VERB
ejpam-5429	175	70	on	on	ADP
ejpam-5429	175	71	ℵ̃	ℵ̃	PROPN
ejpam-5429	175	72	such	such	DET
ejpam-5429	175	73	that	that	SCONJ
ejpam-5429	175	74	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	175	75	)	)	PUNCT
ejpam-5429	175	76	≤	≤	PROPN
ejpam-5429	175	77	τ̃	τ̃	PUNCT
ejpam-5429	175	78	,	,	PUNCT
ejpam-5429	175	79	∀ς̇	∀ς̇	PROPN
ejpam-5429	175	80	∈	∈	PROPN
ejpam-5429	175	81	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	175	82	let	let	VERB
ejpam-5429	175	83	ς̇	ς̇	PROPN
ejpam-5429	175	84	∈	∈	PROPN
ejpam-5429	175	85	ℵ̃	ℵ̃	PROPN
ejpam-5429	175	86	and	and	CCONJ
ejpam-5429	175	87	σ̃	σ̃	PROPN
ejpam-5429	175	88	<	<	X
ejpam-5429	175	89	ρ̃	ρ̃	PROPN
ejpam-5429	175	90	≤	≤	NOUN
ejpam-5429	175	91	1̂	1̂	NOUN
ejpam-5429	175	92	be	be	AUX
ejpam-5429	175	93	such	such	ADJ
ejpam-5429	175	94	that	that	SCONJ
ejpam-5429	175	95	ς̇ρ̃	ς̇ρ̃	PROPN
ejpam-5429	175	96	∈	∈	PROPN
ejpam-5429	175	97	∧qτ̃	∧qτ̃	PROPN
ejpam-5429	175	98	ð̃.	ð̃.	PROPN
ejpam-5429	175	99	then	then	ADV
ejpam-5429	175	100	,	,	PUNCT
ejpam-5429	175	101	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	175	102	)	)	PUNCT
ejpam-5429	175	103	≥	≥	NOUN
ejpam-5429	175	104	ρ̃	ρ̃	PROPN
ejpam-5429	175	105	>	>	SYM
ejpam-5429	175	106	σ̃	σ̃	PROPN
ejpam-5429	175	107	and	and	CCONJ
ejpam-5429	175	108	ð̃(ς̇	ð̃(ς̇	NOUN
ejpam-5429	175	109	)	)	PUNCT
ejpam-5429	176	1	+	+	CCONJ
ejpam-5429	176	2	ρ̃	ρ̃	PROPN
ejpam-5429	176	3	>	>	SYM
ejpam-5429	176	4	2τ̃	2τ̃	PROPN
ejpam-5429	176	5	.	.	PUNCT
ejpam-5429	177	1	thus	thus	ADV
ejpam-5429	177	2	,	,	PUNCT
ejpam-5429	177	3	2τ̃	2τ̃	PROPN
ejpam-5429	177	4	<	<	X
ejpam-5429	177	5	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	177	6	)	)	PUNCT
ejpam-5429	177	7	+	+	CCONJ
ejpam-5429	177	8	ρ̃	ρ̃	PROPN
ejpam-5429	177	9	≤	≤	NOUN
ejpam-5429	177	10	ð̃(ς̇	ð̃(ς̇	PUNCT
ejpam-5429	177	11	)	)	PUNCT
ejpam-5429	178	1	+	+	CCONJ
ejpam-5429	178	2	ð̃(ς̇	ð̃(ς̇	NOUN
ejpam-5429	178	3	)	)	PUNCT
ejpam-5429	178	4	=	=	SYM
ejpam-5429	178	5	2ð̃(ς̇	2ð̃(ς̇	X
ejpam-5429	178	6	)	)	PUNCT
ejpam-5429	178	7	⇒	⇒	NOUN
ejpam-5429	178	8	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	178	9	)	)	PUNCT
ejpam-5429	178	10	>	>	PUNCT
ejpam-5429	179	1	τ̃.	τ̃.	NOUN
ejpam-5429	179	2	hence	hence	ADV
ejpam-5429	179	3	,	,	PUNCT
ejpam-5429	179	4	{	{	PUNCT
ejpam-5429	179	5	ς̇ρ̃	ς̇ρ̃	NOUN
ejpam-5429	179	6	|	|	ADV
ejpam-5429	179	7	ς̇ρ̃	ς̇ρ̃	PROPN
ejpam-5429	179	8	∈σ̃	∈σ̃	PROPN
ejpam-5429	179	9	∧qτ̃	∧qτ̃	PROPN
ejpam-5429	179	10	ð̃	ð̃	PROPN
ejpam-5429	179	11	}	}	PUNCT
ejpam-5429	179	12	=	=	SYM
ejpam-5429	179	13	ϕ.	ϕ.	PROPN
ejpam-5429	179	14	therefore	therefore	ADV
ejpam-5429	179	15	,	,	PUNCT
ejpam-5429	179	16	we	we	PRON
ejpam-5429	179	17	exclude	exclude	VERB
ejpam-5429	179	18	the	the	DET
ejpam-5429	179	19	case	case	NOUN
ejpam-5429	179	20	ϖ	ϖ	X
ejpam-5429	179	21	=	=	SYM
ejpam-5429	179	22	∈σ̃	∈σ̃	PROPN
ejpam-5429	179	23	∧qτ̃	∧qτ̃	VERB
ejpam-5429	179	24	in	in	ADP
ejpam-5429	179	25	definition	definition	NOUN
ejpam-5429	179	26	4.1	4.1	NUM
ejpam-5429	179	27	is	be	AUX
ejpam-5429	179	28	neglected	neglect	VERB
ejpam-5429	179	29	.	.	PUNCT
ejpam-5429	180	1	theorem	theorem	NOUN
ejpam-5429	180	2	3	3	X
ejpam-5429	180	3	.	.	PUNCT
ejpam-5429	181	1	let	let	VERB
ejpam-5429	181	2	ð̃	ð̃	PRON
ejpam-5429	181	3	be	be	AUX
ejpam-5429	181	4	a	a	DET
ejpam-5429	181	5	qp-(ϖ,ϑ)-ffi	qp-(ϖ,ϑ)-ffi	NOUN
ejpam-5429	181	6	and	and	CCONJ
ejpam-5429	181	7	σ̃	σ̃	PROPN
ejpam-5429	181	8	+	+	NOUN
ejpam-5429	181	9	1̂	1̂	NUM
ejpam-5429	181	10	=	=	SYM
ejpam-5429	181	11	2τ̃	2τ̃	PROPN
ejpam-5429	181	12	of	of	ADP
ejpam-5429	181	13	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	181	14	then	then	ADV
ejpam-5429	181	15	,	,	PUNCT
ejpam-5429	181	16	the	the	DET
ejpam-5429	181	17	set	set	NOUN
ejpam-5429	181	18	ð̃σ̃	ð̃σ̃	NOUN
ejpam-5429	181	19	=	=	PRON
ejpam-5429	181	20	{	{	PUNCT
ejpam-5429	181	21	ς̇	ς̇	NOUN
ejpam-5429	181	22	∈	∈	PROPN
ejpam-5429	181	23	ℵ̃	ℵ̃	PROPN
ejpam-5429	181	24	|	|	ADV
ejpam-5429	181	25	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	181	26	)	)	PUNCT
ejpam-5429	181	27	>	>	PUNCT
ejpam-5429	182	1	σ̃	σ̃	PROPN
ejpam-5429	182	2	}	}	PUNCT
ejpam-5429	182	3	is	be	AUX
ejpam-5429	182	4	a	a	DET
ejpam-5429	182	5	fi	fi	NOUN
ejpam-5429	182	6	of	of	ADP
ejpam-5429	182	7	ℵ̃.	ℵ̃.	NOUN
ejpam-5429	182	8	proof	proof	NOUN
ejpam-5429	182	9	.	.	PUNCT
ejpam-5429	183	1	let	let	VERB
ejpam-5429	183	2	ς̇	ς̇	NOUN
ejpam-5429	183	3	,	,	PUNCT
ejpam-5429	183	4	ϱ̇	ϱ̇	PROPN
ejpam-5429	183	5	,	,	PUNCT
ejpam-5429	183	6	κ̇	κ̇	PROPN
ejpam-5429	183	7	∈	∈	PROPN
ejpam-5429	183	8	ℵ̃	ℵ̃	PROPN
ejpam-5429	183	9	be	be	VERB
ejpam-5429	183	10	such	such	ADJ
ejpam-5429	183	11	that	that	DET
ejpam-5429	183	12	ς̇	ς̇	NOUN
ejpam-5429	183	13	,	,	PUNCT
ejpam-5429	183	14	ϱ̇	ϱ̇	PROPN
ejpam-5429	183	15	,	,	PUNCT
ejpam-5429	183	16	κ̇	κ̇	PROPN
ejpam-5429	183	17	∈	∈	NOUN
ejpam-5429	183	18	ð̃σ̃.	ð̃σ̃.	NOUN
ejpam-5429	183	19	then	then	ADV
ejpam-5429	183	20	,	,	PUNCT
ejpam-5429	183	21	ð̃((ς̇	ð̃((ς̇	VERB
ejpam-5429	183	22	≬	≬	PROPN
ejpam-5429	183	23	ϱ̇	ϱ̇	PROPN
ejpam-5429	183	24	)	)	PUNCT
ejpam-5429	183	25	≬	≬	PROPN
ejpam-5429	183	26	κ̇	κ̇	PROPN
ejpam-5429	183	27	)	)	PUNCT
ejpam-5429	183	28	>	>	PUNCT
ejpam-5429	184	1	σ̃	σ̃	PROPN
ejpam-5429	184	2	and	and	CCONJ
ejpam-5429	184	3	ð̃(κ̇	ð̃(κ̇	PROPN
ejpam-5429	184	4	)	)	PUNCT
ejpam-5429	184	5	>	>	PUNCT
ejpam-5429	185	1	σ̃.	σ̃.	PROPN
ejpam-5429	185	2	assume	assume	VERB
ejpam-5429	185	3	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	185	4	≬	≬	PROPN
ejpam-5429	185	5	(	(	PUNCT
ejpam-5429	185	6	ϱ̇	ϱ̇	PROPN
ejpam-5429	185	7	≬	≬	PROPN
ejpam-5429	185	8	(	(	PUNCT
ejpam-5429	185	9	ϱ̇	ϱ̇	PROPN
ejpam-5429	185	10	≬	≬	PROPN
ejpam-5429	185	11	ς̇	ς̇	NOUN
ejpam-5429	185	12	)	)	PUNCT
ejpam-5429	185	13	)	)	PUNCT
ejpam-5429	185	14	)	)	PUNCT
ejpam-5429	186	1	≤	≤	X
ejpam-5429	186	2	σ̃.	σ̃.	NOUN
ejpam-5429	186	3	if	if	SCONJ
ejpam-5429	186	4	ϖ	ϖ	X
ejpam-5429	186	5	∈	∈	PROPN
ejpam-5429	186	6	{	{	PUNCT
ejpam-5429	186	7	∈σ̃	∈σ̃	PROPN
ejpam-5429	186	8	,	,	PUNCT
ejpam-5429	186	9	∈σ̃	∈σ̃	PROPN
ejpam-5429	186	10	∨qτ̃	∨qτ̃	ADJ
ejpam-5429	186	11	}	}	PUNCT
ejpam-5429	186	12	,	,	PUNCT
ejpam-5429	186	13	then	then	ADV
ejpam-5429	186	14	k.	k.	PROPN
ejpam-5429	186	15	h.	h.	PROPN
ejpam-5429	186	16	hakami	hakami	PROPN
ejpam-5429	186	17	et	et	PROPN
ejpam-5429	186	18	al	al	PROPN
ejpam-5429	186	19	.	.	PUNCT
ejpam-5429	186	20	/	/	SYM
ejpam-5429	186	21	eur	eur	PROPN
ejpam-5429	186	22	.	.	PUNCT
ejpam-5429	187	1	j.	j.	PROPN
ejpam-5429	187	2	pure	pure	PROPN
ejpam-5429	187	3	appl	appl	PROPN
ejpam-5429	187	4	.	.	PROPN
ejpam-5429	187	5	math	math	PROPN
ejpam-5429	187	6	,	,	PUNCT
ejpam-5429	187	7	17	17	NUM
ejpam-5429	187	8	(	(	PUNCT
ejpam-5429	187	9	4	4	NUM
ejpam-5429	187	10	)	)	PUNCT
ejpam-5429	187	11	(	(	PUNCT
ejpam-5429	187	12	2024	2024	NUM
ejpam-5429	187	13	)	)	PUNCT
ejpam-5429	187	14	,	,	PUNCT
ejpam-5429	187	15	3129	3129	NUM
ejpam-5429	187	16	-	-	SYM
ejpam-5429	187	17	3155	3155	NUM
ejpam-5429	187	18	3135	3135	NUM
ejpam-5429	187	19	(	(	PUNCT
ejpam-5429	187	20	(	(	PUNCT
ejpam-5429	187	21	ς̇	ς̇	PROPN
ejpam-5429	187	22	≬	≬	PROPN
ejpam-5429	187	23	ϱ̇	ϱ̇	NUM
ejpam-5429	187	24	)	)	PUNCT
ejpam-5429	187	25	≬	≬	PROPN
ejpam-5429	187	26	κ̇)ð̃(ς̇)ϖð̃	κ̇)ð̃(ς̇)ϖð̃	ADV
ejpam-5429	187	27	and	and	CCONJ
ejpam-5429	187	28	κ̇ð̃(ϱ̇)ϖð̃.	κ̇ð̃(ϱ̇)ϖð̃.	NOUN
ejpam-5429	187	29	but	but	CCONJ
ejpam-5429	187	30	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	187	31	≬	≬	PROPN
ejpam-5429	187	32	(	(	PUNCT
ejpam-5429	187	33	ϱ̇	ϱ̇	PROPN
ejpam-5429	187	34	≬	≬	PROPN
ejpam-5429	187	35	(	(	PUNCT
ejpam-5429	187	36	ϱ̇	ϱ̇	PROPN
ejpam-5429	187	37	≬	≬	PROPN
ejpam-5429	187	38	ς̇	ς̇	NOUN
ejpam-5429	187	39	)	)	PUNCT
ejpam-5429	187	40	)	)	PUNCT
ejpam-5429	187	41	)	)	PUNCT
ejpam-5429	187	42	≤	≤	PUNCT
ejpam-5429	188	1	σ̃	σ̃	PROPN
ejpam-5429	188	2	<	<	X
ejpam-5429	188	3	ð̃((ς̇	ð̃((ς̇	X
ejpam-5429	188	4	≬	≬	PROPN
ejpam-5429	188	5	ϱ̇	ϱ̇	PROPN
ejpam-5429	188	6	)	)	PUNCT
ejpam-5429	188	7	≬	≬	PROPN
ejpam-5429	188	8	κ̇	κ̇	PROPN
ejpam-5429	188	9	)	)	PUNCT
ejpam-5429	188	10	∧	∧	PROPN
ejpam-5429	188	11	ð̃(κ̇	ð̃(κ̇	PROPN
ejpam-5429	188	12	)	)	PUNCT
ejpam-5429	188	13	and	and	CCONJ
ejpam-5429	188	14	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	188	15	≬	≬	PROPN
ejpam-5429	188	16	(	(	PUNCT
ejpam-5429	188	17	ϱ̇	ϱ̇	PROPN
ejpam-5429	188	18	≬	≬	PROPN
ejpam-5429	188	19	(	(	PUNCT
ejpam-5429	188	20	ϱ̇	ϱ̇	PROPN
ejpam-5429	188	21	≬	≬	PROPN
ejpam-5429	188	22	ς̇	ς̇	NOUN
ejpam-5429	188	23	)	)	PUNCT
ejpam-5429	188	24	)	)	PUNCT
ejpam-5429	188	25	)	)	PUNCT
ejpam-5429	189	1	+	+	NUM
ejpam-5429	189	2	ð̃((ς̇	ð̃((ς̇	X
ejpam-5429	189	3	≬	≬	PROPN
ejpam-5429	189	4	ϱ̇	ϱ̇	PROPN
ejpam-5429	189	5	)	)	PUNCT
ejpam-5429	189	6	≬	≬	PROPN
ejpam-5429	189	7	κ̇	κ̇	PROPN
ejpam-5429	189	8	)	)	PUNCT
ejpam-5429	189	9	∧	∧	PROPN
ejpam-5429	189	10	ð̃(κ̇	ð̃(κ̇	PROPN
ejpam-5429	189	11	)	)	PUNCT
ejpam-5429	189	12	≤	≤	PUNCT
ejpam-5429	190	1	σ̃	σ̃	PROPN
ejpam-5429	190	2	+	+	NUM
ejpam-5429	190	3	1̂	1̂	NUM
ejpam-5429	190	4	=	=	SYM
ejpam-5429	190	5	2τ̃	2τ̃	PROPN
ejpam-5429	190	6	.	.	PUNCT
ejpam-5429	191	1	so	so	ADV
ejpam-5429	191	2	,	,	PUNCT
ejpam-5429	191	3	(	(	PUNCT
ejpam-5429	191	4	ς̇	ς̇	PROPN
ejpam-5429	191	5	≬	≬	PROPN
ejpam-5429	191	6	(	(	PUNCT
ejpam-5429	191	7	ϱ̇	ϱ̇	PROPN
ejpam-5429	191	8	≬	≬	PROPN
ejpam-5429	191	9	(	(	PUNCT
ejpam-5429	191	10	ϱ̇	ϱ̇	PROPN
ejpam-5429	191	11	≬	≬	PROPN
ejpam-5429	191	12	ς̇)))˜̃ð(ς̇)∧ð̃(η̇	ς̇)))˜̃ð(ς̇)∧ð̃(η̇	PROPN
ejpam-5429	191	13	)	)	PUNCT
ejpam-5429	191	14	ϑð̃,∀ϑ	ϑð̃,∀ϑ	X
ejpam-5429	191	15	∈	∈	PROPN
ejpam-5429	191	16	{	{	PUNCT
ejpam-5429	191	17	∈σ̃	∈σ̃	PROPN
ejpam-5429	191	18	,	,	PUNCT
ejpam-5429	191	19	qτ̃	qτ̃	X
ejpam-5429	191	20	,	,	PUNCT
ejpam-5429	191	21	∈σ̃	∈σ̃	PROPN
ejpam-5429	191	22	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	191	23	,	,	PUNCT
ejpam-5429	191	24	∈σ̃	∈σ̃	PROPN
ejpam-5429	191	25	∧qτ̃	∧qτ̃	PROPN
ejpam-5429	191	26	}	}	PUNCT
ejpam-5429	191	27	,	,	PUNCT
ejpam-5429	191	28	a	a	DET
ejpam-5429	191	29	contradiction	contradiction	NOUN
ejpam-5429	191	30	.	.	PUNCT
ejpam-5429	192	1	hence	hence	ADV
ejpam-5429	192	2	,	,	PUNCT
ejpam-5429	192	3	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	192	4	≬	≬	PROPN
ejpam-5429	192	5	(	(	PUNCT
ejpam-5429	192	6	ϱ̇	ϱ̇	PROPN
ejpam-5429	192	7	≬	≬	PROPN
ejpam-5429	192	8	(	(	PUNCT
ejpam-5429	192	9	ϱ̇	ϱ̇	PROPN
ejpam-5429	192	10	≬	≬	PROPN
ejpam-5429	192	11	ς̇	ς̇	NOUN
ejpam-5429	192	12	)	)	PUNCT
ejpam-5429	192	13	)	)	PUNCT
ejpam-5429	192	14	)	)	PUNCT
ejpam-5429	192	15	>	>	PUNCT
ejpam-5429	193	1	σ̃	σ̃	PROPN
ejpam-5429	193	2	⇒	⇒	VERB
ejpam-5429	193	3	ς̇	ς̇	PROPN
ejpam-5429	193	4	≬	≬	PROPN
ejpam-5429	193	5	(	(	PUNCT
ejpam-5429	193	6	ϱ̇	ϱ̇	PROPN
ejpam-5429	193	7	≬	≬	PROPN
ejpam-5429	193	8	(	(	PUNCT
ejpam-5429	193	9	ϱ̇	ϱ̇	PROPN
ejpam-5429	193	10	≬	≬	PROPN
ejpam-5429	193	11	ς̇	ς̇	NOUN
ejpam-5429	193	12	)	)	PUNCT
ejpam-5429	193	13	)	)	PUNCT
ejpam-5429	194	1	∈	∈	PROPN
ejpam-5429	194	2	ð̃σ̃.	ð̃σ̃.	NOUN
ejpam-5429	194	3	also	also	ADV
ejpam-5429	194	4	,	,	PUNCT
ejpam-5429	194	5	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	194	6	≬	≬	PROPN
ejpam-5429	194	7	(	(	PUNCT
ejpam-5429	194	8	ϱ̇	ϱ̇	PROPN
ejpam-5429	194	9	≬	≬	PROPN
ejpam-5429	194	10	(	(	PUNCT
ejpam-5429	194	11	ϱ̇	ϱ̇	PROPN
ejpam-5429	194	12	≬	≬	PROPN
ejpam-5429	194	13	ς̇	ς̇	NOUN
ejpam-5429	194	14	)	)	PUNCT
ejpam-5429	194	15	)	)	PUNCT
ejpam-5429	194	16	)	)	PUNCT
ejpam-5429	195	1	+	+	CCONJ
ejpam-5429	195	2	1̂	1̂	NOUN
ejpam-5429	195	3	>	>	X
ejpam-5429	195	4	σ̃	σ̃	PROPN
ejpam-5429	195	5	+	+	PUNCT
ejpam-5429	195	6	1̂	1̂	NUM
ejpam-5429	195	7	=	=	SYM
ejpam-5429	195	8	2τ̃	2τ̃	NUM
ejpam-5429	195	9	⇒	⇒	NOUN
ejpam-5429	195	10	(	(	PUNCT
ejpam-5429	195	11	ς̇	ς̇	NOUN
ejpam-5429	195	12	≬	≬	PROPN
ejpam-5429	195	13	(	(	PUNCT
ejpam-5429	195	14	ϱ̇	ϱ̇	PROPN
ejpam-5429	195	15	≬	≬	PROPN
ejpam-5429	195	16	(	(	PUNCT
ejpam-5429	195	17	ϱ̇	ϱ̇	PROPN
ejpam-5429	195	18	≬	≬	PROPN
ejpam-5429	195	19	ς̇)))1̂qτ̃	ς̇)))1̂qτ̃	PROPN
ejpam-5429	195	20	ð̃.	ð̃.	PROPN
ejpam-5429	195	21	but	but	CCONJ
ejpam-5429	195	22	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	195	23	≬	≬	PROPN
ejpam-5429	195	24	(	(	PUNCT
ejpam-5429	195	25	ϱ̇	ϱ̇	PROPN
ejpam-5429	195	26	≬	≬	PROPN
ejpam-5429	195	27	(	(	PUNCT
ejpam-5429	195	28	ϱ̇	ϱ̇	PROPN
ejpam-5429	195	29	≬	≬	PROPN
ejpam-5429	195	30	ς̇	ς̇	NOUN
ejpam-5429	195	31	)	)	PUNCT
ejpam-5429	195	32	)	)	PUNCT
ejpam-5429	195	33	)	)	PUNCT
ejpam-5429	196	1	≤	≤	X
ejpam-5429	197	1	σ̃	σ̃	PROPN
ejpam-5429	197	2	⇒	⇒	NOUN
ejpam-5429	197	3	(	(	PUNCT
ejpam-5429	197	4	ς̇	ς̇	NOUN
ejpam-5429	197	5	≬	≬	PROPN
ejpam-5429	197	6	(	(	PUNCT
ejpam-5429	197	7	ϱ̇	ϱ̇	PROPN
ejpam-5429	197	8	≬	≬	PROPN
ejpam-5429	197	9	(	(	PUNCT
ejpam-5429	197	10	ϱ̇	ϱ̇	PROPN
ejpam-5429	197	11	≬	≬	PROPN
ejpam-5429	197	12	ς̇)))1̂∈σ̃ð̃	ς̇)))1̂∈σ̃ð̃	PROPN
ejpam-5429	197	13	and	and	CCONJ
ejpam-5429	197	14	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	197	15	≬	≬	PROPN
ejpam-5429	197	16	(	(	PUNCT
ejpam-5429	197	17	ϱ̇	ϱ̇	PROPN
ejpam-5429	197	18	≬	≬	PROPN
ejpam-5429	197	19	(	(	PUNCT
ejpam-5429	197	20	ϱ̇	ϱ̇	PROPN
ejpam-5429	197	21	≬	≬	PROPN
ejpam-5429	197	22	ς̇	ς̇	NOUN
ejpam-5429	197	23	)	)	PUNCT
ejpam-5429	197	24	)	)	PUNCT
ejpam-5429	197	25	)	)	PUNCT
ejpam-5429	198	1	+	+	CCONJ
ejpam-5429	198	2	1̂	1̂	NOUN
ejpam-5429	198	3	≤	≤	X
ejpam-5429	199	1	σ̃	σ̃	PROPN
ejpam-5429	199	2	+	+	NUM
ejpam-5429	199	3	1̂	1̂	NUM
ejpam-5429	199	4	=	=	SYM
ejpam-5429	199	5	2τ̃	2τ̃	NUM
ejpam-5429	199	6	⇒	⇒	NOUN
ejpam-5429	199	7	(	(	PUNCT
ejpam-5429	199	8	ς̇	ς̇	NOUN
ejpam-5429	199	9	≬	≬	PROPN
ejpam-5429	199	10	(	(	PUNCT
ejpam-5429	199	11	ϱ̇	ϱ̇	PROPN
ejpam-5429	199	12	≬	≬	PROPN
ejpam-5429	199	13	(	(	PUNCT
ejpam-5429	199	14	ϱ̇	ϱ̇	PROPN
ejpam-5429	199	15	≬	≬	PROPN
ejpam-5429	199	16	ς̇)))1̂qτ̃	ς̇)))1̂qτ̃	PROPN
ejpam-5429	199	17	ð̃	ð̃	PROPN
ejpam-5429	199	18	,	,	PUNCT
ejpam-5429	199	19	a	a	DET
ejpam-5429	199	20	contradiction	contradiction	NOUN
ejpam-5429	199	21	.	.	PUNCT
ejpam-5429	200	1	thus	thus	ADV
ejpam-5429	201	1	,	,	PUNCT
ejpam-5429	201	2	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	201	3	≬	≬	PROPN
ejpam-5429	201	4	(	(	PUNCT
ejpam-5429	201	5	ϱ̇	ϱ̇	PROPN
ejpam-5429	201	6	≬	≬	PROPN
ejpam-5429	201	7	(	(	PUNCT
ejpam-5429	201	8	ϱ̇	ϱ̇	PROPN
ejpam-5429	201	9	≬	≬	PROPN
ejpam-5429	201	10	ς̇	ς̇	NOUN
ejpam-5429	201	11	)	)	PUNCT
ejpam-5429	201	12	)	)	PUNCT
ejpam-5429	201	13	)	)	PUNCT
ejpam-5429	201	14	>	>	PUNCT
ejpam-5429	201	15	σ̃	σ̃	PROPN
ejpam-5429	201	16	⇒	⇒	VERB
ejpam-5429	201	17	ς̇	ς̇	PROPN
ejpam-5429	201	18	≬	≬	PROPN
ejpam-5429	201	19	(	(	PUNCT
ejpam-5429	201	20	ϱ̇	ϱ̇	PROPN
ejpam-5429	201	21	≬	≬	PROPN
ejpam-5429	201	22	(	(	PUNCT
ejpam-5429	201	23	ϱ̇	ϱ̇	PROPN
ejpam-5429	201	24	≬	≬	PROPN
ejpam-5429	201	25	ς̇	ς̇	NOUN
ejpam-5429	201	26	)	)	PUNCT
ejpam-5429	201	27	)	)	PUNCT
ejpam-5429	202	1	∈	∈	PROPN
ejpam-5429	202	2	ð̃σ̃.	ð̃σ̃.	NOUN
ejpam-5429	202	3	therefore	therefore	ADV
ejpam-5429	202	4	,	,	PUNCT
ejpam-5429	202	5	ð̃σ̃	ð̃σ̃	NOUN
ejpam-5429	202	6	is	be	AUX
ejpam-5429	202	7	a	a	DET
ejpam-5429	202	8	fi	fi	NOUN
ejpam-5429	202	9	of	of	ADP
ejpam-5429	202	10	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	202	11	theorem	theorem	NOUN
ejpam-5429	202	12	4	4	X
ejpam-5429	202	13	.	.	PUNCT
ejpam-5429	203	1	let	let	VERB
ejpam-5429	203	2	ϕ	ϕ	PROPN
ejpam-5429	203	3	̸=	̸=	PROPN
ejpam-5429	203	4	c̃	c̃	PROPN
ejpam-5429	203	5	⊆	⊆	NUM
ejpam-5429	203	6	ℵ̃	ℵ̃	PROPN
ejpam-5429	203	7	and	and	CCONJ
ejpam-5429	203	8	σ̃	σ̃	PROPN
ejpam-5429	203	9	+	+	PROPN
ejpam-5429	203	10	1̂	1̂	NUM
ejpam-5429	203	11	=	=	SYM
ejpam-5429	203	12	2τ̃	2τ̃	PROPN
ejpam-5429	203	13	.	.	PUNCT
ejpam-5429	204	1	then	then	ADV
ejpam-5429	204	2	c̃	c̃	PROPN
ejpam-5429	204	3	is	be	AUX
ejpam-5429	204	4	a	a	DET
ejpam-5429	204	5	fi	fi	NOUN
ejpam-5429	204	6	of	of	ADP
ejpam-5429	204	7	ℵ̃	ℵ̃	PROPN
ejpam-5429	204	8	if	if	SCONJ
ejpam-5429	205	1	and	and	CCONJ
ejpam-5429	205	2	only	only	ADV
ejpam-5429	205	3	if	if	SCONJ
ejpam-5429	205	4	the	the	DET
ejpam-5429	205	5	qp	qp	PROPN
ejpam-5429	205	6	-	-	PUNCT
ejpam-5429	205	7	f	f	PROPN
ejpam-5429	205	8	subset	subset	NOUN
ejpam-5429	205	9	ð̃	ð̃	PROPN
ejpam-5429	205	10	of	of	ADP
ejpam-5429	205	11	ℵ̃	ℵ̃	PROPN
ejpam-5429	205	12	,	,	PUNCT
ejpam-5429	205	13	which	which	PRON
ejpam-5429	205	14	is	be	AUX
ejpam-5429	205	15	defined	define	VERB
ejpam-5429	205	16	as	as	SCONJ
ejpam-5429	205	17	follows	follow	VERB
ejpam-5429	205	18	:	:	PUNCT
ejpam-5429	205	19	(	(	PUNCT
ejpam-5429	205	20	1	1	X
ejpam-5429	205	21	)	)	PUNCT
ejpam-5429	205	22	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	205	23	)	)	PUNCT
ejpam-5429	205	24	≥	≥	NOUN
ejpam-5429	205	25	τ̃	τ̃	PROPN
ejpam-5429	205	26	,	,	PUNCT
ejpam-5429	205	27	∀ς̇	∀ς̇	PROPN
ejpam-5429	205	28	∈	∈	PROPN
ejpam-5429	205	29	c̃	c̃	PROPN
ejpam-5429	205	30	,	,	PUNCT
ejpam-5429	205	31	(	(	PUNCT
ejpam-5429	205	32	2	2	X
ejpam-5429	205	33	)	)	PUNCT
ejpam-5429	205	34	ð̃(ς̇	ð̃(ς̇	NOUN
ejpam-5429	205	35	)	)	PUNCT
ejpam-5429	205	36	≤	≤	NUM
ejpam-5429	205	37	σ̃,∀ς̇	σ̃,∀ς̇	NOUN
ejpam-5429	205	38	̸∈	̸∈	PROPN
ejpam-5429	205	39	c̃	c̃	PROPN
ejpam-5429	205	40	is	be	AUX
ejpam-5429	205	41	a	a	DET
ejpam-5429	205	42	qp-(∈σ̃,∈σ̃	qp-(∈σ̃,∈σ̃	NOUN
ejpam-5429	205	43	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	205	44	)	)	PUNCT
ejpam-5429	205	45	-ffi	-ffi	PROPN
ejpam-5429	205	46	of	of	ADP
ejpam-5429	205	47	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	205	48	proof	proof	NOUN
ejpam-5429	205	49	.	.	PUNCT
ejpam-5429	206	1	let	let	VERB
ejpam-5429	206	2	c̃	c̃	PROPN
ejpam-5429	206	3	be	be	AUX
ejpam-5429	206	4	a	a	DET
ejpam-5429	206	5	fi	fi	NOUN
ejpam-5429	206	6	of	of	ADP
ejpam-5429	206	7	ℵ̃	ℵ̃	PROPN
ejpam-5429	206	8	,	,	PUNCT
ejpam-5429	206	9	ς̇	ς̇	PROPN
ejpam-5429	206	10	,	,	PUNCT
ejpam-5429	206	11	ϱ̇	ϱ̇	PROPN
ejpam-5429	206	12	,	,	PUNCT
ejpam-5429	206	13	κ̇	κ̇	PROPN
ejpam-5429	206	14	∈	∈	PROPN
ejpam-5429	206	15	ℵ̃	ℵ̃	PROPN
ejpam-5429	206	16	and	and	CCONJ
ejpam-5429	206	17	let	let	VERB
ejpam-5429	206	18	σ̃	σ̃	PROPN
ejpam-5429	206	19	<	<	X
ejpam-5429	206	20	ρ̃	ρ̃	PROPN
ejpam-5429	206	21	,	,	PUNCT
ejpam-5429	206	22	η̃	η̃	PROPN
ejpam-5429	206	23	≤	≤	NOUN
ejpam-5429	206	24	1̂	1̂	NOUN
ejpam-5429	206	25	be	be	AUX
ejpam-5429	206	26	such	such	ADJ
ejpam-5429	206	27	that	that	SCONJ
ejpam-5429	206	28	(	(	PUNCT
ejpam-5429	206	29	(	(	PUNCT
ejpam-5429	206	30	ς̇	ς̇	PROPN
ejpam-5429	206	31	≬	≬	PROPN
ejpam-5429	206	32	ϱ̇	ϱ̇	PROPN
ejpam-5429	206	33	)	)	PUNCT
ejpam-5429	206	34	≬	≬	PROPN
ejpam-5429	206	35	κ̇)ρ̃	κ̇)ρ̃	PROPN
ejpam-5429	206	36	∈σ̃	∈σ̃	PROPN
ejpam-5429	206	37	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	206	38	ð̃	ð̃	PROPN
ejpam-5429	206	39	and	and	CCONJ
ejpam-5429	206	40	κ̇η̃	κ̇η̃	PROPN
ejpam-5429	206	41	∈σ̃	∈σ̃	PROPN
ejpam-5429	207	1	ð̃.	ð̃.	PROPN
ejpam-5429	207	2	then	then	ADV
ejpam-5429	207	3	ð̃(((ς̇	ð̃(((ς̇	X
ejpam-5429	207	4	≬	≬	PROPN
ejpam-5429	207	5	ϱ̇	ϱ̇	PROPN
ejpam-5429	207	6	)	)	PUNCT
ejpam-5429	207	7	≬	≬	PROPN
ejpam-5429	207	8	κ̇	κ̇	PROPN
ejpam-5429	207	9	)	)	PUNCT
ejpam-5429	207	10	)	)	PUNCT
ejpam-5429	207	11	≥	≥	X
ejpam-5429	207	12	ρ̃	ρ̃	PROPN
ejpam-5429	207	13	>	>	SYM
ejpam-5429	207	14	σ̃	σ̃	PROPN
ejpam-5429	207	15	and	and	CCONJ
ejpam-5429	207	16	ð̃(κ̇	ð̃(κ̇	PROPN
ejpam-5429	207	17	)	)	PUNCT
ejpam-5429	207	18	≥	≥	NOUN
ejpam-5429	207	19	η̃	η̃	PROPN
ejpam-5429	207	20	>	>	X
ejpam-5429	208	1	σ̃.	σ̃.	PROPN
ejpam-5429	208	2	thus	thus	ADV
ejpam-5429	208	3	,	,	PUNCT
ejpam-5429	208	4	ς̇	ς̇	PROPN
ejpam-5429	208	5	≬	≬	PROPN
ejpam-5429	208	6	(	(	PUNCT
ejpam-5429	208	7	ϱ̇	ϱ̇	PROPN
ejpam-5429	208	8	≬	≬	PROPN
ejpam-5429	208	9	(	(	PUNCT
ejpam-5429	208	10	ϱ̇	ϱ̇	PROPN
ejpam-5429	208	11	≬	≬	PROPN
ejpam-5429	208	12	ς̇	ς̇	NOUN
ejpam-5429	208	13	)	)	PUNCT
ejpam-5429	208	14	)	)	PUNCT
ejpam-5429	209	1	∈	∈	PROPN
ejpam-5429	209	2	c̃	c̃	PROPN
ejpam-5429	209	3	⇒	⇒	NOUN
ejpam-5429	209	4	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	209	5	≬	≬	PROPN
ejpam-5429	209	6	(	(	PUNCT
ejpam-5429	209	7	ϱ̇	ϱ̇	PROPN
ejpam-5429	209	8	≬	≬	PROPN
ejpam-5429	209	9	(	(	PUNCT
ejpam-5429	209	10	ϱ̇	ϱ̇	PROPN
ejpam-5429	209	11	≬	≬	PROPN
ejpam-5429	209	12	ς̇	ς̇	NOUN
ejpam-5429	209	13	)	)	PUNCT
ejpam-5429	209	14	)	)	PUNCT
ejpam-5429	209	15	)	)	PUNCT
ejpam-5429	209	16	≥	≥	PRON
ejpam-5429	209	17	τ̃	τ̃	X
ejpam-5429	209	18	.	.	PUNCT
ejpam-5429	210	1	if	if	SCONJ
ejpam-5429	210	2	ρ̃	ρ̃	PROPN
ejpam-5429	210	3	∧	∧	PROPN
ejpam-5429	210	4	η̃	η̃	PROPN
ejpam-5429	210	5	≤	≤	PROPN
ejpam-5429	210	6	τ̃	τ̃	PROPN
ejpam-5429	210	7	,	,	PUNCT
ejpam-5429	210	8	then	then	ADV
ejpam-5429	210	9	k.	k.	PROPN
ejpam-5429	210	10	h.	h.	PROPN
ejpam-5429	210	11	hakami	hakami	PROPN
ejpam-5429	210	12	et	et	PROPN
ejpam-5429	210	13	al	al	PROPN
ejpam-5429	210	14	.	.	PUNCT
ejpam-5429	210	15	/	/	SYM
ejpam-5429	210	16	eur	eur	PROPN
ejpam-5429	210	17	.	.	PUNCT
ejpam-5429	211	1	j.	j.	PROPN
ejpam-5429	211	2	pure	pure	PROPN
ejpam-5429	211	3	appl	appl	PROPN
ejpam-5429	211	4	.	.	PROPN
ejpam-5429	211	5	math	math	PROPN
ejpam-5429	211	6	,	,	PUNCT
ejpam-5429	211	7	17	17	NUM
ejpam-5429	211	8	(	(	PUNCT
ejpam-5429	211	9	4	4	NUM
ejpam-5429	211	10	)	)	PUNCT
ejpam-5429	211	11	(	(	PUNCT
ejpam-5429	211	12	2024	2024	NUM
ejpam-5429	211	13	)	)	PUNCT
ejpam-5429	211	14	,	,	PUNCT
ejpam-5429	211	15	3129	3129	NUM
ejpam-5429	211	16	-	-	SYM
ejpam-5429	211	17	3155	3155	NUM
ejpam-5429	211	18	3136	3136	NUM
ejpam-5429	211	19	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	212	1	≬	≬	PROPN
ejpam-5429	212	2	(	(	PUNCT
ejpam-5429	212	3	ϱ̇	ϱ̇	PROPN
ejpam-5429	212	4	≬	≬	PROPN
ejpam-5429	212	5	(	(	PUNCT
ejpam-5429	212	6	ϱ̇	ϱ̇	PROPN
ejpam-5429	212	7	≬	≬	PROPN
ejpam-5429	212	8	ς̇	ς̇	NOUN
ejpam-5429	212	9	)	)	PUNCT
ejpam-5429	212	10	)	)	PUNCT
ejpam-5429	212	11	)	)	PUNCT
ejpam-5429	212	12	≥	≥	PRON
ejpam-5429	213	1	τ̃	τ̃	NOUN
ejpam-5429	213	2	≥	≥	NOUN
ejpam-5429	213	3	ρ̃	ρ̃	PROPN
ejpam-5429	213	4	∧	∧	PROPN
ejpam-5429	213	5	η̃	η̃	PROPN
ejpam-5429	213	6	>	>	SYM
ejpam-5429	213	7	σ̃	σ̃	PROPN
ejpam-5429	213	8	⇒	⇒	NOUN
ejpam-5429	213	9	(	(	PUNCT
ejpam-5429	213	10	ς̇	ς̇	NOUN
ejpam-5429	213	11	≬	≬	PROPN
ejpam-5429	213	12	(	(	PUNCT
ejpam-5429	213	13	ϱ̇	ϱ̇	PROPN
ejpam-5429	213	14	≬	≬	PROPN
ejpam-5429	213	15	(	(	PUNCT
ejpam-5429	213	16	ϱ̇	ϱ̇	PROPN
ejpam-5429	213	17	≬	≬	PROPN
ejpam-5429	213	18	ς̇)))ρ̃∧η̃	ς̇)))ρ̃∧η̃	VERB
ejpam-5429	213	19	∈σ̃	∈σ̃	PROPN
ejpam-5429	213	20	ð̃.	ð̃.	NOUN
ejpam-5429	213	21	if	if	SCONJ
ejpam-5429	213	22	ρ̃	ρ̃	PROPN
ejpam-5429	213	23	∧	∧	PROPN
ejpam-5429	213	24	η̃	η̃	PROPN
ejpam-5429	213	25	>	>	PUNCT
ejpam-5429	213	26	τ̃	τ̃	PROPN
ejpam-5429	213	27	,	,	PUNCT
ejpam-5429	213	28	then	then	ADV
ejpam-5429	213	29	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	213	30	≬	≬	PROPN
ejpam-5429	213	31	(	(	PUNCT
ejpam-5429	213	32	ϱ̇	ϱ̇	PROPN
ejpam-5429	213	33	≬	≬	PROPN
ejpam-5429	213	34	(	(	PUNCT
ejpam-5429	213	35	ϱ̇	ϱ̇	PROPN
ejpam-5429	213	36	≬	≬	PROPN
ejpam-5429	213	37	ς̇	ς̇	NOUN
ejpam-5429	213	38	)	)	PUNCT
ejpam-5429	213	39	)	)	PUNCT
ejpam-5429	213	40	)	)	PUNCT
ejpam-5429	214	1	+	+	CCONJ
ejpam-5429	214	2	ρ̃	ρ̃	PROPN
ejpam-5429	214	3	∧	∧	PROPN
ejpam-5429	214	4	η̃	η̃	PROPN
ejpam-5429	214	5	>	>	X
ejpam-5429	214	6	τ̃	τ̃	PROPN
ejpam-5429	215	1	+	+	PUNCT
ejpam-5429	215	2	τ̃	τ̃	ADJ
ejpam-5429	215	3	=	=	SYM
ejpam-5429	215	4	2τ̃	2τ̃	ADJ
ejpam-5429	215	5	⇒	⇒	NOUN
ejpam-5429	215	6	(	(	PUNCT
ejpam-5429	215	7	ς̇	ς̇	NOUN
ejpam-5429	215	8	≬	≬	PROPN
ejpam-5429	215	9	(	(	PUNCT
ejpam-5429	215	10	ϱ̇	ϱ̇	PROPN
ejpam-5429	215	11	≬	≬	PROPN
ejpam-5429	215	12	(	(	PUNCT
ejpam-5429	215	13	ϱ̇	ϱ̇	PROPN
ejpam-5429	215	14	≬	≬	PROPN
ejpam-5429	215	15	ς̇)))ρ̃∧η̃qτ̃	ς̇)))ρ̃∧η̃qτ̃	PROPN
ejpam-5429	215	16	ð̃.	ð̃.	NOUN
ejpam-5429	215	17	thus	thus	ADV
ejpam-5429	215	18	,	,	PUNCT
ejpam-5429	215	19	(	(	PUNCT
ejpam-5429	215	20	ς̇	ς̇	PROPN
ejpam-5429	215	21	≬	≬	PROPN
ejpam-5429	215	22	(	(	PUNCT
ejpam-5429	215	23	ϱ̇	ϱ̇	PROPN
ejpam-5429	215	24	≬	≬	PROPN
ejpam-5429	215	25	(	(	PUNCT
ejpam-5429	215	26	ϱ̇	ϱ̇	PROPN
ejpam-5429	215	27	≬	≬	PROPN
ejpam-5429	215	28	ς̇)))ρ̃∧η̃	ς̇)))ρ̃∧η̃	VERB
ejpam-5429	215	29	∈σ̃	∈σ̃	NOUN
ejpam-5429	215	30	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	215	31	ð̃.	ð̃.	NOUN
ejpam-5429	215	32	hence	hence	ADV
ejpam-5429	215	33	,	,	PUNCT
ejpam-5429	215	34	ð̃	ð̃	PROPN
ejpam-5429	215	35	is	be	AUX
ejpam-5429	215	36	an	an	DET
ejpam-5429	215	37	qp-(∈σ̃,∈σ̃	qp-(∈σ̃,∈σ̃	PROPN
ejpam-5429	215	38	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	215	39	)	)	PUNCT
ejpam-5429	215	40	ffi	ffi	PROPN
ejpam-5429	215	41	of	of	ADP
ejpam-5429	215	42	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	215	43	on	on	ADP
ejpam-5429	215	44	the	the	DET
ejpam-5429	215	45	contrary	contrary	NOUN
ejpam-5429	215	46	,	,	PUNCT
ejpam-5429	215	47	assume	assume	VERB
ejpam-5429	215	48	ð̃	ð̃	PROPN
ejpam-5429	215	49	is	be	AUX
ejpam-5429	215	50	a	a	DET
ejpam-5429	215	51	qp-(∈σ̃,∈σ̃	qp-(∈σ̃,∈σ̃	NOUN
ejpam-5429	215	52	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	215	53	)	)	PUNCT
ejpam-5429	215	54	ffi	ffi	PROPN
ejpam-5429	215	55	of	of	ADP
ejpam-5429	215	56	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	215	57	then	then	ADV
ejpam-5429	215	58	c̃	c̃	PROPN
ejpam-5429	215	59	is	be	AUX
ejpam-5429	215	60	equal	equal	ADJ
ejpam-5429	215	61	to	to	ADP
ejpam-5429	215	62	ð̃σ̃.	ð̃σ̃.	PROPN
ejpam-5429	215	63	consequently	consequently	ADV
ejpam-5429	215	64	,	,	PUNCT
ejpam-5429	215	65	according	accord	VERB
ejpam-5429	215	66	to	to	ADP
ejpam-5429	215	67	theorem	theorem	NOUN
ejpam-5429	215	68	4.1	4.1	NUM
ejpam-5429	215	69	,	,	PUNCT
ejpam-5429	215	70	c̃	c̃	PROPN
ejpam-5429	215	71	is	be	AUX
ejpam-5429	215	72	a	a	DET
ejpam-5429	215	73	fi	fi	NOUN
ejpam-5429	215	74	of	of	ADP
ejpam-5429	215	75	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	215	76	corollary	corollary	ADJ
ejpam-5429	215	77	1	1	NUM
ejpam-5429	215	78	.	.	PUNCT
ejpam-5429	216	1	let	let	VERB
ejpam-5429	216	2	σ̃	σ̃	PROPN
ejpam-5429	216	3	+	+	NOUN
ejpam-5429	216	4	1̂	1̂	NUM
ejpam-5429	216	5	=	=	SYM
ejpam-5429	216	6	2τ̃	2τ̃	PROPN
ejpam-5429	216	7	and	and	CCONJ
ejpam-5429	216	8	ϕ	ϕ	PROPN
ejpam-5429	216	9	̸=	̸=	PROPN
ejpam-5429	216	10	c̃	c̃	PROPN
ejpam-5429	216	11	⊆	⊆	NUM
ejpam-5429	216	12	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	216	13	then	then	ADV
ejpam-5429	216	14	,	,	PUNCT
ejpam-5429	216	15	c̃	c̃	PROPN
ejpam-5429	216	16	is	be	AUX
ejpam-5429	216	17	a	a	DET
ejpam-5429	216	18	fi	fi	NOUN
ejpam-5429	216	19	of	of	ADP
ejpam-5429	216	20	ℵ̃	ℵ̃	PROPN
ejpam-5429	216	21	if	if	SCONJ
ejpam-5429	217	1	and	and	CCONJ
ejpam-5429	217	2	only	only	ADV
ejpam-5429	217	3	if	if	SCONJ
ejpam-5429	217	4	the	the	DET
ejpam-5429	217	5	characteristic	characteristic	ADJ
ejpam-5429	217	6	function	function	NOUN
ejpam-5429	217	7	χ̂c̃	χ̂c̃	PROPN
ejpam-5429	217	8	is	be	AUX
ejpam-5429	217	9	a	a	DET
ejpam-5429	217	10	qp-(∈σ̃,∈σ̃	qp-(∈σ̃,∈σ̃	PROPN
ejpam-5429	217	11	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	217	12	)	)	PUNCT
ejpam-5429	217	13	ffi	ffi	PROPN
ejpam-5429	217	14	of	of	ADP
ejpam-5429	217	15	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	217	16	theorem	theorem	ADJ
ejpam-5429	217	17	5	5	NUM
ejpam-5429	217	18	.	.	PUNCT
ejpam-5429	218	1	let	let	VERB
ejpam-5429	218	2	ϕ	ϕ	NOUN
ejpam-5429	218	3	̸=	̸=	PROPN
ejpam-5429	218	4	c̃	c̃	PROPN
ejpam-5429	218	5	⊆	⊆	NUM
ejpam-5429	218	6	ℵ̃	ℵ̃	PROPN
ejpam-5429	218	7	and	and	CCONJ
ejpam-5429	218	8	σ̃	σ̃	PROPN
ejpam-5429	218	9	+	+	PROPN
ejpam-5429	218	10	1̂	1̂	NUM
ejpam-5429	218	11	=	=	SYM
ejpam-5429	218	12	2τ̃	2τ̃	PROPN
ejpam-5429	218	13	.	.	PUNCT
ejpam-5429	219	1	then	then	ADV
ejpam-5429	219	2	,	,	PUNCT
ejpam-5429	219	3	c̃	c̃	PROPN
ejpam-5429	219	4	is	be	AUX
ejpam-5429	219	5	a	a	DET
ejpam-5429	219	6	fi	fi	NOUN
ejpam-5429	219	7	of	of	ADP
ejpam-5429	219	8	ℵ̃	ℵ̃	PROPN
ejpam-5429	219	9	if	if	SCONJ
ejpam-5429	220	1	and	and	CCONJ
ejpam-5429	220	2	only	only	ADV
ejpam-5429	220	3	if	if	SCONJ
ejpam-5429	220	4	the	the	DET
ejpam-5429	220	5	qp	qp	PROPN
ejpam-5429	220	6	-	-	PUNCT
ejpam-5429	220	7	f	f	PROPN
ejpam-5429	220	8	subset	subset	NOUN
ejpam-5429	220	9	ð̃	ð̃	PROPN
ejpam-5429	220	10	of	of	ADP
ejpam-5429	220	11	ℵ̃	ℵ̃	PROPN
ejpam-5429	220	12	defined	define	VERB
ejpam-5429	220	13	by	by	ADP
ejpam-5429	220	14	the	the	DET
ejpam-5429	220	15	following	following	ADJ
ejpam-5429	220	16	conditions	condition	NOUN
ejpam-5429	220	17	:	:	PUNCT
ejpam-5429	220	18	(	(	PUNCT
ejpam-5429	220	19	1	1	X
ejpam-5429	220	20	)	)	PUNCT
ejpam-5429	220	21	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	220	22	)	)	PUNCT
ejpam-5429	220	23	≥	≥	NOUN
ejpam-5429	220	24	τ̃	τ̃	PROPN
ejpam-5429	220	25	,	,	PUNCT
ejpam-5429	220	26	∀ς̇	∀ς̇	PROPN
ejpam-5429	220	27	∈	∈	PROPN
ejpam-5429	220	28	c̃	c̃	PROPN
ejpam-5429	220	29	,	,	PUNCT
ejpam-5429	220	30	(	(	PUNCT
ejpam-5429	220	31	2	2	X
ejpam-5429	220	32	)	)	PUNCT
ejpam-5429	220	33	ð̃(ς̇	ð̃(ς̇	NOUN
ejpam-5429	220	34	)	)	PUNCT
ejpam-5429	220	35	≤	≤	NUM
ejpam-5429	220	36	σ̃,∀ς̇	σ̃,∀ς̇	NOUN
ejpam-5429	220	37	̸∈	̸∈	PROPN
ejpam-5429	220	38	c̃	c̃	PROPN
ejpam-5429	220	39	is	be	AUX
ejpam-5429	220	40	a	a	DET
ejpam-5429	220	41	qp-(qτ̃	qp-(qτ̃	PROPN
ejpam-5429	220	42	,	,	PUNCT
ejpam-5429	220	43	∈σ̃	∈σ̃	PROPN
ejpam-5429	220	44	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	220	45	)	)	PUNCT
ejpam-5429	220	46	-ffi	-ffi	PROPN
ejpam-5429	220	47	of	of	ADP
ejpam-5429	220	48	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	220	49	proof	proof	NOUN
ejpam-5429	220	50	.	.	PUNCT
ejpam-5429	221	1	let	let	VERB
ejpam-5429	221	2	c̃	c̃	PROPN
ejpam-5429	221	3	be	be	AUX
ejpam-5429	221	4	a	a	DET
ejpam-5429	221	5	fi	fi	NOUN
ejpam-5429	221	6	of	of	ADP
ejpam-5429	221	7	ℵ̃	ℵ̃	PROPN
ejpam-5429	221	8	,	,	PUNCT
ejpam-5429	221	9	ς̇	ς̇	PROPN
ejpam-5429	221	10	,	,	PUNCT
ejpam-5429	221	11	ϱ̇	ϱ̇	PROPN
ejpam-5429	221	12	,	,	PUNCT
ejpam-5429	221	13	κ̇	κ̇	PROPN
ejpam-5429	221	14	∈	∈	PROPN
ejpam-5429	221	15	ℵ̃	ℵ̃	PROPN
ejpam-5429	221	16	and	and	CCONJ
ejpam-5429	221	17	let	let	VERB
ejpam-5429	221	18	σ̃	σ̃	PROPN
ejpam-5429	221	19	<	<	X
ejpam-5429	221	20	ρ̃	ρ̃	PROPN
ejpam-5429	221	21	,	,	PUNCT
ejpam-5429	221	22	η̃	η̃	PROPN
ejpam-5429	221	23	≤	≤	NOUN
ejpam-5429	221	24	1̂	1̂	NOUN
ejpam-5429	221	25	be	be	AUX
ejpam-5429	221	26	such	such	ADJ
ejpam-5429	221	27	that	that	SCONJ
ejpam-5429	221	28	(	(	PUNCT
ejpam-5429	221	29	(	(	PUNCT
ejpam-5429	221	30	ς̇	ς̇	PROPN
ejpam-5429	221	31	≬	≬	PROPN
ejpam-5429	221	32	ϱ̇	ϱ̇	PROPN
ejpam-5429	221	33	)	)	PUNCT
ejpam-5429	221	34	≬	≬	PROPN
ejpam-5429	221	35	κ̇)ρ̃qτ̃	κ̇)ρ̃qτ̃	PROPN
ejpam-5429	221	36	ð̃	ð̃	PROPN
ejpam-5429	221	37	and	and	CCONJ
ejpam-5429	221	38	κ̇η̃qτ̃	κ̇η̃qτ̃	PROPN
ejpam-5429	221	39	ð̃.	ð̃.	NOUN
ejpam-5429	221	40	then	then	ADV
ejpam-5429	221	41	ð̃(((ς̇	ð̃(((ς̇	X
ejpam-5429	221	42	≬	≬	PROPN
ejpam-5429	221	43	ϱ̇	ϱ̇	PROPN
ejpam-5429	221	44	)	)	PUNCT
ejpam-5429	221	45	≬	≬	PROPN
ejpam-5429	221	46	κ̇	κ̇	NOUN
ejpam-5429	221	47	)	)	PUNCT
ejpam-5429	221	48	)	)	PUNCT
ejpam-5429	222	1	+	+	CCONJ
ejpam-5429	222	2	ρ̃	ρ̃	PROPN
ejpam-5429	222	3	>	>	SYM
ejpam-5429	222	4	2τ̃	2τ̃	PROPN
ejpam-5429	222	5	⇒	⇒	NOUN
ejpam-5429	222	6	ð̃((ς̇	ð̃((ς̇	PUNCT
ejpam-5429	222	7	≬	≬	PROPN
ejpam-5429	222	8	ϱ̇	ϱ̇	PROPN
ejpam-5429	222	9	)	)	PUNCT
ejpam-5429	222	10	≬	≬	PROPN
ejpam-5429	222	11	κ̇	κ̇	PROPN
ejpam-5429	222	12	)	)	PUNCT
ejpam-5429	222	13	>	>	PUNCT
ejpam-5429	223	1	2τ̃	2τ̃	NUM
ejpam-5429	223	2	−	−	ADP
ejpam-5429	223	3	ρ̃	ρ̃	PROPN
ejpam-5429	223	4	≥	≥	NOUN
ejpam-5429	223	5	2τ̃	2τ̃	NUM
ejpam-5429	223	6	−	−	PROPN
ejpam-5429	223	7	1̂	1̂	NUM
ejpam-5429	223	8	=	=	SYM
ejpam-5429	223	9	σ̃	σ̃	PROPN
ejpam-5429	223	10	and	and	CCONJ
ejpam-5429	223	11	ð̃(κ̇	ð̃(κ̇	PROPN
ejpam-5429	223	12	)	)	PUNCT
ejpam-5429	223	13	+	+	NUM
ejpam-5429	224	1	η̃	η̃	PROPN
ejpam-5429	224	2	>	>	SYM
ejpam-5429	224	3	2τ̃	2τ̃	PROPN
ejpam-5429	224	4	⇒	⇒	NOUN
ejpam-5429	224	5	ð̃(κ̇	ð̃(κ̇	NOUN
ejpam-5429	224	6	)	)	PUNCT
ejpam-5429	224	7	>	>	X
ejpam-5429	225	1	2τ̃	2τ̃	NUM
ejpam-5429	225	2	−	−	PROPN
ejpam-5429	225	3	η̃	η̃	PROPN
ejpam-5429	225	4	≥	≥	NOUN
ejpam-5429	225	5	2τ̃	2τ̃	NUM
ejpam-5429	225	6	−	−	PROPN
ejpam-5429	225	7	1̂	1̂	NUM
ejpam-5429	225	8	=	=	SYM
ejpam-5429	226	1	σ̃.	σ̃.	PROPN
ejpam-5429	226	2	thus	thus	ADV
ejpam-5429	226	3	,	,	PUNCT
ejpam-5429	226	4	ς̇	ς̇	PROPN
ejpam-5429	226	5	≬	≬	PROPN
ejpam-5429	226	6	(	(	PUNCT
ejpam-5429	226	7	ϱ̇	ϱ̇	PROPN
ejpam-5429	226	8	≬	≬	PROPN
ejpam-5429	226	9	(	(	PUNCT
ejpam-5429	226	10	ϱ̇	ϱ̇	PROPN
ejpam-5429	226	11	≬	≬	PROPN
ejpam-5429	226	12	ς̇	ς̇	NOUN
ejpam-5429	226	13	)	)	PUNCT
ejpam-5429	226	14	)	)	PUNCT
ejpam-5429	227	1	∈	∈	PROPN
ejpam-5429	227	2	c̃	c̃	PROPN
ejpam-5429	227	3	⇒	⇒	NOUN
ejpam-5429	227	4	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	227	5	≬	≬	PROPN
ejpam-5429	227	6	(	(	PUNCT
ejpam-5429	227	7	ϱ̇	ϱ̇	PROPN
ejpam-5429	227	8	≬	≬	PROPN
ejpam-5429	227	9	(	(	PUNCT
ejpam-5429	227	10	ϱ̇	ϱ̇	PROPN
ejpam-5429	227	11	≬	≬	PROPN
ejpam-5429	227	12	ς̇	ς̇	NOUN
ejpam-5429	227	13	)	)	PUNCT
ejpam-5429	227	14	)	)	PUNCT
ejpam-5429	227	15	)	)	PUNCT
ejpam-5429	227	16	≥	≥	PRON
ejpam-5429	227	17	τ̃	τ̃	PROPN
ejpam-5429	227	18	.	.	PUNCT
ejpam-5429	228	1	now	now	ADV
ejpam-5429	228	2	,	,	PUNCT
ejpam-5429	228	3	if	if	SCONJ
ejpam-5429	228	4	ρ̃	ρ̃	PROPN
ejpam-5429	228	5	∧	∧	PROPN
ejpam-5429	228	6	η̃	η̃	PROPN
ejpam-5429	228	7	≤	≤	PROPN
ejpam-5429	228	8	τ̃	τ̃	PROPN
ejpam-5429	228	9	,	,	PUNCT
ejpam-5429	228	10	then	then	ADV
ejpam-5429	228	11	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	228	12	≬	≬	PROPN
ejpam-5429	228	13	(	(	PUNCT
ejpam-5429	228	14	ϱ̇	ϱ̇	PROPN
ejpam-5429	228	15	≬	≬	PROPN
ejpam-5429	228	16	(	(	PUNCT
ejpam-5429	228	17	ϱ̇	ϱ̇	PROPN
ejpam-5429	228	18	≬	≬	PROPN
ejpam-5429	228	19	ς̇	ς̇	NOUN
ejpam-5429	228	20	)	)	PUNCT
ejpam-5429	228	21	)	)	PUNCT
ejpam-5429	228	22	)	)	PUNCT
ejpam-5429	228	23	≥	≥	PRON
ejpam-5429	229	1	τ̃	τ̃	NOUN
ejpam-5429	229	2	≥	≥	NOUN
ejpam-5429	229	3	ρ̃	ρ̃	PROPN
ejpam-5429	229	4	∧	∧	PROPN
ejpam-5429	229	5	η̃	η̃	PROPN
ejpam-5429	229	6	>	>	X
ejpam-5429	229	7	σ̃.	σ̃.	PROPN
ejpam-5429	229	8	hence	hence	ADV
ejpam-5429	229	9	,	,	PUNCT
ejpam-5429	229	10	(	(	PUNCT
ejpam-5429	229	11	ς̇	ς̇	PROPN
ejpam-5429	229	12	≬	≬	PROPN
ejpam-5429	229	13	(	(	PUNCT
ejpam-5429	229	14	ϱ̇	ϱ̇	PROPN
ejpam-5429	229	15	≬	≬	PROPN
ejpam-5429	229	16	(	(	PUNCT
ejpam-5429	229	17	ϱ̇	ϱ̇	PROPN
ejpam-5429	229	18	≬	≬	PROPN
ejpam-5429	229	19	ς̇)))ρ̃∧η̃	ς̇)))ρ̃∧η̃	VERB
ejpam-5429	229	20	∈σ̃	∈σ̃	PROPN
ejpam-5429	229	21	ð̃.	ð̃.	NOUN
ejpam-5429	229	22	if	if	SCONJ
ejpam-5429	229	23	ρ̃	ρ̃	PROPN
ejpam-5429	229	24	∧	∧	PROPN
ejpam-5429	229	25	η̃	η̃	PROPN
ejpam-5429	229	26	>	>	PUNCT
ejpam-5429	229	27	τ̃	τ̃	PROPN
ejpam-5429	229	28	,	,	PUNCT
ejpam-5429	229	29	then	then	ADV
ejpam-5429	229	30	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	229	31	≬	≬	PROPN
ejpam-5429	229	32	(	(	PUNCT
ejpam-5429	229	33	ϱ̇	ϱ̇	PROPN
ejpam-5429	229	34	≬	≬	PROPN
ejpam-5429	229	35	(	(	PUNCT
ejpam-5429	229	36	ϱ̇	ϱ̇	PROPN
ejpam-5429	229	37	≬	≬	PROPN
ejpam-5429	229	38	ς̇	ς̇	NOUN
ejpam-5429	229	39	)	)	PUNCT
ejpam-5429	229	40	)	)	PUNCT
ejpam-5429	229	41	)	)	PUNCT
ejpam-5429	230	1	+	+	CCONJ
ejpam-5429	230	2	ρ̃	ρ̃	PROPN
ejpam-5429	230	3	∧	∧	PROPN
ejpam-5429	230	4	ϖ̃	ϖ̃	PROPN
ejpam-5429	230	5	>	>	X
ejpam-5429	230	6	τ̃	τ̃	PROPN
ejpam-5429	230	7	+	+	PUNCT
ejpam-5429	230	8	τ̃	τ̃	ADJ
ejpam-5429	230	9	=	=	SYM
ejpam-5429	230	10	2τ̃	2τ̃	ADJ
ejpam-5429	230	11	⇒	⇒	NOUN
ejpam-5429	230	12	(	(	PUNCT
ejpam-5429	230	13	ς̇	ς̇	NOUN
ejpam-5429	230	14	≬	≬	PROPN
ejpam-5429	230	15	(	(	PUNCT
ejpam-5429	230	16	ϱ̇	ϱ̇	PROPN
ejpam-5429	230	17	≬	≬	PROPN
ejpam-5429	230	18	(	(	PUNCT
ejpam-5429	230	19	ϱ̇	ϱ̇	PROPN
ejpam-5429	230	20	≬	≬	PROPN
ejpam-5429	230	21	ς̇)))ρ̃∧η̃qτ̃	ς̇)))ρ̃∧η̃qτ̃	PROPN
ejpam-5429	230	22	ð̃.	ð̃.	NOUN
ejpam-5429	230	23	therefore	therefore	ADV
ejpam-5429	230	24	,	,	PUNCT
ejpam-5429	230	25	(	(	PUNCT
ejpam-5429	230	26	ς̇	ς̇	PROPN
ejpam-5429	230	27	≬	≬	PROPN
ejpam-5429	230	28	(	(	PUNCT
ejpam-5429	230	29	ϱ̇	ϱ̇	PROPN
ejpam-5429	230	30	≬	≬	PROPN
ejpam-5429	230	31	(	(	PUNCT
ejpam-5429	230	32	ϱ̇	ϱ̇	PROPN
ejpam-5429	230	33	≬	≬	PROPN
ejpam-5429	230	34	ς̇)))ρ̃∧η̃	ς̇)))ρ̃∧η̃	VERB
ejpam-5429	230	35	∈	∈	PROPN
ejpam-5429	230	36	∨qτ̃	∨qτ̃	ADJ
ejpam-5429	230	37	ð̃.	ð̃.	PROPN
ejpam-5429	230	38	thus	thus	ADV
ejpam-5429	230	39	,	,	PUNCT
ejpam-5429	230	40	ð̃	ð̃	PROPN
ejpam-5429	230	41	is	be	AUX
ejpam-5429	230	42	an	an	DET
ejpam-5429	230	43	qp-(qτ̃	qp-(qτ̃	PROPN
ejpam-5429	230	44	,	,	PUNCT
ejpam-5429	230	45	∈σ̃	∈σ̃	PROPN
ejpam-5429	230	46	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	230	47	)	)	PUNCT
ejpam-5429	230	48	-ffi	-ffi	PROPN
ejpam-5429	230	49	of	of	ADP
ejpam-5429	230	50	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	230	51	on	on	ADP
ejpam-5429	230	52	the	the	DET
ejpam-5429	230	53	contrary	contrary	NOUN
ejpam-5429	230	54	,	,	PUNCT
ejpam-5429	230	55	assume	assume	VERB
ejpam-5429	230	56	ð̃	ð̃	PROPN
ejpam-5429	230	57	is	be	AUX
ejpam-5429	230	58	a	a	DET
ejpam-5429	230	59	qp-(qτ̃	qp-(qτ̃	PROPN
ejpam-5429	230	60	,	,	PUNCT
ejpam-5429	230	61	∈σ̃	∈σ̃	PROPN
ejpam-5429	230	62	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	230	63	)	)	PUNCT
ejpam-5429	230	64	-ffi	-ffi	PROPN
ejpam-5429	230	65	of	of	ADP
ejpam-5429	230	66	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	230	67	then	then	ADV
ejpam-5429	230	68	,	,	PUNCT
ejpam-5429	230	69	c̃	c̃	PROPN
ejpam-5429	230	70	is	be	AUX
ejpam-5429	230	71	equal	equal	ADJ
ejpam-5429	230	72	to	to	ADP
ejpam-5429	230	73	ð̃σ̃.	ð̃σ̃.	PROPN
ejpam-5429	230	74	consequently	consequently	ADV
ejpam-5429	230	75	,	,	PUNCT
ejpam-5429	230	76	according	accord	VERB
ejpam-5429	230	77	to	to	ADP
ejpam-5429	230	78	theorem	theorem	NOUN
ejpam-5429	230	79	4.1	4.1	NUM
ejpam-5429	230	80	,	,	PUNCT
ejpam-5429	230	81	c̃	c̃	PROPN
ejpam-5429	230	82	is	be	AUX
ejpam-5429	230	83	a	a	DET
ejpam-5429	230	84	fi	fi	NOUN
ejpam-5429	230	85	of	of	ADP
ejpam-5429	230	86	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	230	87	k.	k.	PROPN
ejpam-5429	230	88	h.	h.	PROPN
ejpam-5429	230	89	hakami	hakami	PROPN
ejpam-5429	230	90	et	et	PROPN
ejpam-5429	230	91	al	al	PROPN
ejpam-5429	230	92	.	.	PUNCT
ejpam-5429	230	93	/	/	SYM
ejpam-5429	230	94	eur	eur	PROPN
ejpam-5429	230	95	.	.	PUNCT
ejpam-5429	231	1	j.	j.	PROPN
ejpam-5429	231	2	pure	pure	PROPN
ejpam-5429	231	3	appl	appl	PROPN
ejpam-5429	231	4	.	.	PROPN
ejpam-5429	231	5	math	math	PROPN
ejpam-5429	231	6	,	,	PUNCT
ejpam-5429	231	7	17	17	NUM
ejpam-5429	231	8	(	(	PUNCT
ejpam-5429	231	9	4	4	NUM
ejpam-5429	231	10	)	)	PUNCT
ejpam-5429	231	11	(	(	PUNCT
ejpam-5429	231	12	2024	2024	NUM
ejpam-5429	231	13	)	)	PUNCT
ejpam-5429	231	14	,	,	PUNCT
ejpam-5429	231	15	3129	3129	NUM
ejpam-5429	231	16	-	-	SYM
ejpam-5429	231	17	3155	3155	NUM
ejpam-5429	231	18	3137	3137	NUM
ejpam-5429	231	19	corollary	corollary	NOUN
ejpam-5429	231	20	2	2	NUM
ejpam-5429	231	21	.	.	PUNCT
ejpam-5429	232	1	let	let	VERB
ejpam-5429	232	2	ϕ	ϕ	PROPN
ejpam-5429	232	3	̸=	̸=	PROPN
ejpam-5429	232	4	c̃	c̃	PROPN
ejpam-5429	232	5	⊆	⊆	NUM
ejpam-5429	232	6	ℵ̃	ℵ̃	PROPN
ejpam-5429	232	7	and	and	CCONJ
ejpam-5429	232	8	σ̃	σ̃	PROPN
ejpam-5429	232	9	+	+	PROPN
ejpam-5429	232	10	1̂	1̂	NUM
ejpam-5429	232	11	=	=	SYM
ejpam-5429	232	12	2τ̃	2τ̃	PROPN
ejpam-5429	232	13	.	.	PUNCT
ejpam-5429	233	1	then	then	ADV
ejpam-5429	233	2	,	,	PUNCT
ejpam-5429	233	3	c̃	c̃	PROPN
ejpam-5429	233	4	is	be	AUX
ejpam-5429	233	5	a	a	DET
ejpam-5429	233	6	fi	fi	NOUN
ejpam-5429	233	7	of	of	ADP
ejpam-5429	233	8	ℵ̃	ℵ̃	PROPN
ejpam-5429	233	9	if	if	SCONJ
ejpam-5429	234	1	and	and	CCONJ
ejpam-5429	234	2	only	only	ADV
ejpam-5429	234	3	if	if	SCONJ
ejpam-5429	234	4	the	the	DET
ejpam-5429	234	5	characteristic	characteristic	ADJ
ejpam-5429	234	6	function	function	NOUN
ejpam-5429	234	7	χ̂c̃	χ̂c̃	PROPN
ejpam-5429	234	8	is	be	AUX
ejpam-5429	234	9	a	a	DET
ejpam-5429	234	10	qp(qτ̃	qp(qτ̃	NOUN
ejpam-5429	234	11	,	,	PUNCT
ejpam-5429	234	12	∈σ̃	∈σ̃	PROPN
ejpam-5429	234	13	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	234	14	)	)	PUNCT
ejpam-5429	234	15	-ffi	-ffi	PROPN
ejpam-5429	234	16	of	of	ADP
ejpam-5429	234	17	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	234	18	theorem	theorem	VERB
ejpam-5429	234	19	6	6	NUM
ejpam-5429	234	20	.	.	PUNCT
ejpam-5429	235	1	let	let	VERB
ejpam-5429	235	2	ϕ	ϕ	PROPN
ejpam-5429	235	3	̸=	̸=	PROPN
ejpam-5429	235	4	c̃	c̃	PROPN
ejpam-5429	235	5	⊆	⊆	NUM
ejpam-5429	235	6	ℵ̃	ℵ̃	PROPN
ejpam-5429	235	7	and	and	CCONJ
ejpam-5429	235	8	σ̃	σ̃	PROPN
ejpam-5429	235	9	+	+	PROPN
ejpam-5429	235	10	1̂	1̂	NUM
ejpam-5429	235	11	=	=	SYM
ejpam-5429	235	12	2τ̃	2τ̃	PROPN
ejpam-5429	235	13	.	.	PUNCT
ejpam-5429	236	1	then	then	ADV
ejpam-5429	236	2	,	,	PUNCT
ejpam-5429	236	3	c̃	c̃	PROPN
ejpam-5429	236	4	is	be	AUX
ejpam-5429	236	5	a	a	DET
ejpam-5429	236	6	fi	fi	NOUN
ejpam-5429	236	7	of	of	ADP
ejpam-5429	236	8	ℵ̃	ℵ̃	PROPN
ejpam-5429	236	9	if	if	SCONJ
ejpam-5429	237	1	and	and	CCONJ
ejpam-5429	237	2	only	only	ADV
ejpam-5429	237	3	if	if	SCONJ
ejpam-5429	237	4	qp	qp	NOUN
ejpam-5429	237	5	-	-	PUNCT
ejpam-5429	237	6	f	f	NOUN
ejpam-5429	237	7	subset	subset	NOUN
ejpam-5429	237	8	ð̃	ð̃	PROPN
ejpam-5429	237	9	of	of	ADP
ejpam-5429	237	10	ℵ̃	ℵ̃	PROPN
ejpam-5429	237	11	defined	define	VERB
ejpam-5429	237	12	by	by	ADP
ejpam-5429	237	13	the	the	DET
ejpam-5429	237	14	following	following	ADJ
ejpam-5429	237	15	conditions	condition	NOUN
ejpam-5429	237	16	:	:	PUNCT
ejpam-5429	237	17	(	(	PUNCT
ejpam-5429	237	18	1	1	X
ejpam-5429	237	19	)	)	PUNCT
ejpam-5429	237	20	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	237	21	)	)	PUNCT
ejpam-5429	237	22	≥	≥	NOUN
ejpam-5429	237	23	τ̃	τ̃	PROPN
ejpam-5429	237	24	,	,	PUNCT
ejpam-5429	237	25	∀ς̇	∀ς̇	PROPN
ejpam-5429	237	26	∈	∈	PROPN
ejpam-5429	237	27	c̃	c̃	PROPN
ejpam-5429	237	28	,	,	PUNCT
ejpam-5429	237	29	(	(	PUNCT
ejpam-5429	237	30	2	2	X
ejpam-5429	237	31	)	)	PUNCT
ejpam-5429	237	32	ð̃(ς̇	ð̃(ς̇	NOUN
ejpam-5429	237	33	)	)	PUNCT
ejpam-5429	237	34	≤	≤	NUM
ejpam-5429	237	35	σ̃,∀ς̇	σ̃,∀ς̇	NOUN
ejpam-5429	237	36	̸∈	̸∈	PROPN
ejpam-5429	237	37	c̃	c̃	PROPN
ejpam-5429	237	38	is	be	AUX
ejpam-5429	237	39	a	a	DET
ejpam-5429	237	40	qp-(∈σ̃	qp-(∈σ̃	NUM
ejpam-5429	237	41	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	237	42	,	,	PUNCT
ejpam-5429	237	43	∈σ̃	∈σ̃	PROPN
ejpam-5429	237	44	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	237	45	)	)	PUNCT
ejpam-5429	237	46	ffi	ffi	PROPN
ejpam-5429	237	47	of	of	ADP
ejpam-5429	237	48	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	237	49	proof	proof	NOUN
ejpam-5429	237	50	.	.	PUNCT
ejpam-5429	238	1	let	let	VERB
ejpam-5429	238	2	c̃	c̃	PROPN
ejpam-5429	238	3	be	be	AUX
ejpam-5429	238	4	a	a	DET
ejpam-5429	238	5	fi	fi	NOUN
ejpam-5429	238	6	of	of	ADP
ejpam-5429	238	7	ℵ̃	ℵ̃	PROPN
ejpam-5429	238	8	,	,	PUNCT
ejpam-5429	238	9	ς̇	ς̇	PROPN
ejpam-5429	238	10	,	,	PUNCT
ejpam-5429	238	11	ϱ̇	ϱ̇	PROPN
ejpam-5429	238	12	,	,	PUNCT
ejpam-5429	238	13	κ̇	κ̇	PROPN
ejpam-5429	238	14	∈	∈	PROPN
ejpam-5429	238	15	ℵ̃	ℵ̃	PROPN
ejpam-5429	238	16	and	and	CCONJ
ejpam-5429	238	17	let	let	VERB
ejpam-5429	238	18	σ̃	σ̃	PROPN
ejpam-5429	238	19	<	<	X
ejpam-5429	238	20	ρ̃	ρ̃	PROPN
ejpam-5429	238	21	,	,	PUNCT
ejpam-5429	238	22	η̃	η̃	PROPN
ejpam-5429	238	23	≤	≤	NOUN
ejpam-5429	238	24	1̂	1̂	NOUN
ejpam-5429	238	25	be	be	AUX
ejpam-5429	238	26	such	such	ADJ
ejpam-5429	238	27	that	that	SCONJ
ejpam-5429	238	28	(	(	PUNCT
ejpam-5429	238	29	(	(	PUNCT
ejpam-5429	238	30	ς̇	ς̇	PROPN
ejpam-5429	238	31	≬	≬	PROPN
ejpam-5429	238	32	ϱ̇	ϱ̇	PROPN
ejpam-5429	238	33	)	)	PUNCT
ejpam-5429	238	34	≬	≬	PROPN
ejpam-5429	238	35	κ̇)ρ̃	κ̇)ρ̃	PROPN
ejpam-5429	238	36	∈σ̃	∈σ̃	PROPN
ejpam-5429	238	37	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	238	38	ð̃	ð̃	PROPN
ejpam-5429	238	39	⇒	⇒	NOUN
ejpam-5429	238	40	(	(	PUNCT
ejpam-5429	238	41	(	(	PUNCT
ejpam-5429	238	42	ς̇	ς̇	PROPN
ejpam-5429	238	43	≬	≬	PROPN
ejpam-5429	238	44	ϱ̇	ϱ̇	PROPN
ejpam-5429	238	45	)	)	PUNCT
ejpam-5429	238	46	≬	≬	PROPN
ejpam-5429	238	47	κ̇)ρ̃	κ̇)ρ̃	PROPN
ejpam-5429	238	48	∈σ̃	∈σ̃	PROPN
ejpam-5429	238	49	ð̃	ð̃	PROPN
ejpam-5429	238	50	or	or	CCONJ
ejpam-5429	238	51	(	(	PUNCT
ejpam-5429	238	52	(	(	PUNCT
ejpam-5429	238	53	ς̇	ς̇	PROPN
ejpam-5429	238	54	≬	≬	PROPN
ejpam-5429	238	55	ϱ̇	ϱ̇	PROPN
ejpam-5429	238	56	)	)	PUNCT
ejpam-5429	238	57	≬	≬	PROPN
ejpam-5429	238	58	κ̇)ρ̃qτ̃	κ̇)ρ̃qτ̃	PROPN
ejpam-5429	238	59	ð̃	ð̃	PROPN
ejpam-5429	238	60	and	and	CCONJ
ejpam-5429	238	61	κ̇η̃	κ̇η̃	PROPN
ejpam-5429	238	62	∈σ̃	∈σ̃	PROPN
ejpam-5429	238	63	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	238	64	ð̃	ð̃	PROPN
ejpam-5429	238	65	⇒	⇒	VERB
ejpam-5429	238	66	κ̇η̃	κ̇η̃	PROPN
ejpam-5429	238	67	∈σ̃	∈σ̃	PROPN
ejpam-5429	238	68	ð̃	ð̃	PROPN
ejpam-5429	238	69	or	or	CCONJ
ejpam-5429	238	70	κ̇η̃qτ̃	κ̇η̃qτ̃	PROPN
ejpam-5429	238	71	ð̃.	ð̃.	NOUN
ejpam-5429	238	72	if	if	SCONJ
ejpam-5429	238	73	(	(	PUNCT
ejpam-5429	238	74	(	(	PUNCT
ejpam-5429	238	75	ς̇	ς̇	PROPN
ejpam-5429	238	76	≬	≬	PROPN
ejpam-5429	238	77	ϱ̇	ϱ̇	PROPN
ejpam-5429	238	78	)	)	PUNCT
ejpam-5429	238	79	≬	≬	PROPN
ejpam-5429	238	80	κ̇)ρ̃	κ̇)ρ̃	PROPN
ejpam-5429	238	81	∈σ̃	∈σ̃	PROPN
ejpam-5429	238	82	ð̃	ð̃	PROPN
ejpam-5429	238	83	,	,	PUNCT
ejpam-5429	238	84	and	and	CCONJ
ejpam-5429	238	85	κ̇η̃qτ̃	κ̇η̃qτ̃	PROPN
ejpam-5429	238	86	ð̃	ð̃	PROPN
ejpam-5429	238	87	,	,	PUNCT
ejpam-5429	238	88	then	then	ADV
ejpam-5429	238	89	ð̃((ς̇	ð̃((ς̇	VERB
ejpam-5429	238	90	≬	≬	PROPN
ejpam-5429	238	91	ϱ̇	ϱ̇	PROPN
ejpam-5429	238	92	)	)	PUNCT
ejpam-5429	238	93	≬	≬	PROPN
ejpam-5429	238	94	κ̇	κ̇	PROPN
ejpam-5429	238	95	)	)	PUNCT
ejpam-5429	238	96	≥	≥	NOUN
ejpam-5429	238	97	ρ̃	ρ̃	PROPN
ejpam-5429	238	98	>	>	SYM
ejpam-5429	238	99	σ̃	σ̃	PROPN
ejpam-5429	238	100	and	and	CCONJ
ejpam-5429	238	101	ð̃(κ̇	ð̃(κ̇	PROPN
ejpam-5429	238	102	)	)	PUNCT
ejpam-5429	239	1	+	+	NUM
ejpam-5429	239	2	η̃	η̃	PROPN
ejpam-5429	239	3	>	>	SYM
ejpam-5429	239	4	2τ̃	2τ̃	PROPN
ejpam-5429	239	5	⇒	⇒	NOUN
ejpam-5429	239	6	ð̃(κ̇	ð̃(κ̇	NOUN
ejpam-5429	239	7	)	)	PUNCT
ejpam-5429	239	8	>	>	X
ejpam-5429	240	1	2τ̃	2τ̃	NUM
ejpam-5429	240	2	−	−	PROPN
ejpam-5429	240	3	η̃	η̃	PROPN
ejpam-5429	240	4	≥	≥	NOUN
ejpam-5429	240	5	2τ̃	2τ̃	NUM
ejpam-5429	240	6	−	−	PROPN
ejpam-5429	240	7	1̂	1̂	NUM
ejpam-5429	240	8	=	=	SYM
ejpam-5429	241	1	σ̃.	σ̃.	PROPN
ejpam-5429	241	2	thus	thus	ADV
ejpam-5429	241	3	,	,	PUNCT
ejpam-5429	241	4	ς̇	ς̇	PROPN
ejpam-5429	241	5	≬	≬	PROPN
ejpam-5429	241	6	(	(	PUNCT
ejpam-5429	241	7	ϱ̇	ϱ̇	PROPN
ejpam-5429	241	8	≬	≬	PROPN
ejpam-5429	241	9	(	(	PUNCT
ejpam-5429	241	10	ϱ̇	ϱ̇	PROPN
ejpam-5429	241	11	≬	≬	PROPN
ejpam-5429	241	12	ς̇	ς̇	NOUN
ejpam-5429	241	13	)	)	PUNCT
ejpam-5429	241	14	)	)	PUNCT
ejpam-5429	242	1	∈	∈	PROPN
ejpam-5429	242	2	c̃.	c̃.	PROPN
ejpam-5429	242	3	analogous	analogous	ADJ
ejpam-5429	242	4	as	as	ADP
ejpam-5429	242	5	in	in	ADP
ejpam-5429	242	6	theorems	theorem	NOUN
ejpam-5429	242	7	4.3	4.3	NUM
ejpam-5429	242	8	and	and	CCONJ
ejpam-5429	242	9	4.5	4.5	NUM
ejpam-5429	242	10	,	,	PUNCT
ejpam-5429	242	11	(	(	PUNCT
ejpam-5429	242	12	ς̇	ς̇	NOUN
ejpam-5429	242	13	≬	≬	PROPN
ejpam-5429	242	14	(	(	PUNCT
ejpam-5429	242	15	ϱ̇	ϱ̇	PROPN
ejpam-5429	242	16	≬	≬	PROPN
ejpam-5429	242	17	(	(	PUNCT
ejpam-5429	242	18	ϱ̇	ϱ̇	PROPN
ejpam-5429	242	19	≬	≬	PROPN
ejpam-5429	242	20	ς̇)))ρ̃∧η̃	ς̇)))ρ̃∧η̃	VERB
ejpam-5429	242	21	∈σ̃	∈σ̃	NOUN
ejpam-5429	242	22	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	242	23	ð̃.	ð̃.	NOUN
ejpam-5429	242	24	hence	hence	ADV
ejpam-5429	242	25	,	,	PUNCT
ejpam-5429	242	26	ð̃	ð̃	PROPN
ejpam-5429	242	27	is	be	AUX
ejpam-5429	242	28	a	a	DET
ejpam-5429	242	29	q	q	NOUN
ejpam-5429	242	30	-	-	PUNCT
ejpam-5429	242	31	p-(∈σ̃	p-(∈σ̃	ADJ
ejpam-5429	242	32	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	242	33	,	,	PUNCT
ejpam-5429	242	34	∈σ̃	∈σ̃	PROPN
ejpam-5429	242	35	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	242	36	)	)	PUNCT
ejpam-5429	242	37	-ffi	-ffi	PROPN
ejpam-5429	242	38	of	of	ADP
ejpam-5429	242	39	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	242	40	the	the	DET
ejpam-5429	242	41	other	other	ADJ
ejpam-5429	242	42	scenarios	scenario	NOUN
ejpam-5429	242	43	can	can	AUX
ejpam-5429	242	44	be	be	AUX
ejpam-5429	242	45	approached	approach	VERB
ejpam-5429	242	46	in	in	ADP
ejpam-5429	242	47	a	a	DET
ejpam-5429	242	48	similar	similar	ADJ
ejpam-5429	242	49	manner	manner	NOUN
ejpam-5429	242	50	to	to	ADP
ejpam-5429	242	51	this	this	DET
ejpam-5429	242	52	one	one	NOUN
ejpam-5429	242	53	.	.	PUNCT
ejpam-5429	243	1	on	on	ADP
ejpam-5429	243	2	the	the	DET
ejpam-5429	243	3	contrary	contrary	NOUN
ejpam-5429	243	4	,	,	PUNCT
ejpam-5429	243	5	assume	assume	VERB
ejpam-5429	243	6	ð̃	ð̃	PROPN
ejpam-5429	243	7	is	be	AUX
ejpam-5429	243	8	a	a	DET
ejpam-5429	243	9	qp-(∈σ̃	qp-(∈σ̃	NUM
ejpam-5429	243	10	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	243	11	,	,	PUNCT
ejpam-5429	243	12	∈σ̃	∈σ̃	PROPN
ejpam-5429	243	13	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	243	14	)	)	PUNCT
ejpam-5429	243	15	-ffi	-ffi	PROPN
ejpam-5429	243	16	of	of	ADP
ejpam-5429	243	17	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	243	18	then	then	ADV
ejpam-5429	243	19	,	,	PUNCT
ejpam-5429	243	20	c̃	c̃	PROPN
ejpam-5429	243	21	is	be	AUX
ejpam-5429	243	22	equal	equal	ADJ
ejpam-5429	243	23	to	to	ADP
ejpam-5429	243	24	ð̃σ̃.	ð̃σ̃.	PROPN
ejpam-5429	243	25	consequently	consequently	ADV
ejpam-5429	243	26	,	,	PUNCT
ejpam-5429	243	27	according	accord	VERB
ejpam-5429	243	28	to	to	ADP
ejpam-5429	243	29	theorem	theorem	NOUN
ejpam-5429	243	30	4.1	4.1	NUM
ejpam-5429	243	31	,	,	PUNCT
ejpam-5429	243	32	c̃	c̃	PROPN
ejpam-5429	243	33	is	be	AUX
ejpam-5429	243	34	a	a	DET
ejpam-5429	243	35	fi	fi	NOUN
ejpam-5429	243	36	of	of	ADP
ejpam-5429	243	37	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	243	38	corollary	corollary	ADJ
ejpam-5429	243	39	3	3	X
ejpam-5429	243	40	.	.	PUNCT
ejpam-5429	244	1	let	let	VERB
ejpam-5429	244	2	ϕ	ϕ	PROPN
ejpam-5429	244	3	̸=	̸=	PROPN
ejpam-5429	244	4	c̃	c̃	PROPN
ejpam-5429	244	5	⊆	⊆	NUM
ejpam-5429	244	6	ℵ̃	ℵ̃	PROPN
ejpam-5429	244	7	and	and	CCONJ
ejpam-5429	244	8	σ̃	σ̃	PROPN
ejpam-5429	244	9	+	+	PROPN
ejpam-5429	244	10	1̂	1̂	NUM
ejpam-5429	244	11	=	=	SYM
ejpam-5429	244	12	2τ̃	2τ̃	PROPN
ejpam-5429	244	13	.	.	PUNCT
ejpam-5429	245	1	then	then	ADV
ejpam-5429	245	2	,	,	PUNCT
ejpam-5429	245	3	c̃	c̃	PROPN
ejpam-5429	245	4	is	be	AUX
ejpam-5429	245	5	a	a	DET
ejpam-5429	245	6	fi	fi	NOUN
ejpam-5429	245	7	of	of	ADP
ejpam-5429	245	8	ℵ̃	ℵ̃	PROPN
ejpam-5429	245	9	if	if	SCONJ
ejpam-5429	246	1	and	and	CCONJ
ejpam-5429	246	2	only	only	ADV
ejpam-5429	246	3	if	if	SCONJ
ejpam-5429	246	4	the	the	DET
ejpam-5429	246	5	characteristic	characteristic	ADJ
ejpam-5429	246	6	function	function	NOUN
ejpam-5429	246	7	χ̂c̃	χ̂c̃	PROPN
ejpam-5429	246	8	is	be	AUX
ejpam-5429	246	9	a	a	DET
ejpam-5429	246	10	qp-(∈σ̃	qp-(∈σ̃	NOUN
ejpam-5429	246	11	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	246	12	,	,	PUNCT
ejpam-5429	246	13	∈σ̃	∈σ̃	PROPN
ejpam-5429	246	14	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	246	15	)	)	PUNCT
ejpam-5429	246	16	-ffi	-ffi	PROPN
ejpam-5429	246	17	of	of	ADP
ejpam-5429	246	18	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	246	19	theorem	theorem	VERB
ejpam-5429	246	20	7	7	NUM
ejpam-5429	246	21	.	.	PUNCT
ejpam-5429	247	1	every	every	DET
ejpam-5429	247	2	qp-(qτ̃	qp-(qτ̃	PROPN
ejpam-5429	247	3	,	,	PUNCT
ejpam-5429	247	4	∈σ̃	∈σ̃	PROPN
ejpam-5429	247	5	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	247	6	)	)	PUNCT
ejpam-5429	247	7	-ffi	-ffi	PROPN
ejpam-5429	247	8	of	of	ADP
ejpam-5429	247	9	ℵ̃	ℵ̃	PROPN
ejpam-5429	247	10	is	be	AUX
ejpam-5429	247	11	a	a	DET
ejpam-5429	247	12	qp-(∈σ̃,∈σ̃	qp-(∈σ̃,∈σ̃	NOUN
ejpam-5429	247	13	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	247	14	)	)	PUNCT
ejpam-5429	247	15	-ffi	-ffi	PROPN
ejpam-5429	247	16	of	of	ADP
ejpam-5429	247	17	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	247	18	proof	proof	NOUN
ejpam-5429	247	19	.	.	PUNCT
ejpam-5429	248	1	let	let	VERB
ejpam-5429	248	2	ð̃	ð̃	PRON
ejpam-5429	248	3	be	be	AUX
ejpam-5429	248	4	a	a	DET
ejpam-5429	248	5	qp-(qτ̃	qp-(qτ̃	PROPN
ejpam-5429	248	6	,	,	PUNCT
ejpam-5429	248	7	∈σ̃	∈σ̃	PROPN
ejpam-5429	248	8	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	248	9	)	)	PUNCT
ejpam-5429	248	10	-ffi	-ffi	PROPN
ejpam-5429	248	11	of	of	ADP
ejpam-5429	248	12	ℵ̃	ℵ̃	PROPN
ejpam-5429	248	13	,	,	PUNCT
ejpam-5429	248	14	ς̇	ς̇	PROPN
ejpam-5429	248	15	,	,	PUNCT
ejpam-5429	248	16	ϱ̇	ϱ̇	PROPN
ejpam-5429	248	17	,	,	PUNCT
ejpam-5429	248	18	κ̇	κ̇	PROPN
ejpam-5429	248	19	∈	∈	PROPN
ejpam-5429	248	20	ℵ̃	ℵ̃	PROPN
ejpam-5429	248	21	and	and	CCONJ
ejpam-5429	248	22	let	let	VERB
ejpam-5429	248	23	σ̃	σ̃	PROPN
ejpam-5429	248	24	<	<	X
ejpam-5429	248	25	ρ̃	ρ̃	PROPN
ejpam-5429	248	26	,	,	PUNCT
ejpam-5429	248	27	η̃	η̃	PROPN
ejpam-5429	248	28	≤	≤	NOUN
ejpam-5429	248	29	1̂	1̂	NOUN
ejpam-5429	248	30	be	be	AUX
ejpam-5429	248	31	such	such	ADJ
ejpam-5429	248	32	that	that	DET
ejpam-5429	248	33	ς̇	ς̇	PROPN
ejpam-5429	248	34	≬	≬	PROPN
ejpam-5429	248	35	(	(	PUNCT
ejpam-5429	248	36	ϱ̇	ϱ̇	PROPN
ejpam-5429	248	37	≬	≬	PROPN
ejpam-5429	248	38	(	(	PUNCT
ejpam-5429	248	39	ϱ̇	ϱ̇	PROPN
ejpam-5429	248	40	≬	≬	PROPN
ejpam-5429	248	41	ς̇))ρ̃	ς̇))ρ̃	VERB
ejpam-5429	248	42	∈σ̃	∈σ̃	PROPN
ejpam-5429	248	43	ð̃	ð̃	PROPN
ejpam-5429	248	44	and	and	CCONJ
ejpam-5429	248	45	κ̇η̃	κ̇η̃	PROPN
ejpam-5429	248	46	∈τ̃	∈τ̃	PROPN
ejpam-5429	248	47	ð̃.	ð̃.	PROPN
ejpam-5429	248	48	then	then	ADV
ejpam-5429	248	49	,	,	PUNCT
ejpam-5429	248	50	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	248	51	≬	≬	PROPN
ejpam-5429	248	52	(	(	PUNCT
ejpam-5429	248	53	ϱ̇	ϱ̇	PROPN
ejpam-5429	248	54	≬	≬	PROPN
ejpam-5429	248	55	(	(	PUNCT
ejpam-5429	248	56	ϱ̇	ϱ̇	PROPN
ejpam-5429	248	57	≬	≬	PROPN
ejpam-5429	248	58	ς̇	ς̇	NOUN
ejpam-5429	248	59	)	)	PUNCT
ejpam-5429	248	60	)	)	PUNCT
ejpam-5429	248	61	)	)	PUNCT
ejpam-5429	248	62	≥	≥	X
ejpam-5429	249	1	ρ̃	ρ̃	PROPN
ejpam-5429	249	2	>	>	SYM
ejpam-5429	249	3	σ̃	σ̃	PROPN
ejpam-5429	249	4	and	and	CCONJ
ejpam-5429	249	5	ð̃(κ̇	ð̃(κ̇	PROPN
ejpam-5429	249	6	)	)	PUNCT
ejpam-5429	249	7	≥	≥	NOUN
ejpam-5429	250	1	η̃	η̃	PROPN
ejpam-5429	250	2	>	>	X
ejpam-5429	251	1	σ̃.	σ̃.	PROPN
ejpam-5429	251	2	suppose	suppose	VERB
ejpam-5429	251	3	that	that	SCONJ
ejpam-5429	251	4	(	(	PUNCT
ejpam-5429	251	5	ς̇	ς̇	NOUN
ejpam-5429	251	6	≬	≬	PROPN
ejpam-5429	251	7	(	(	PUNCT
ejpam-5429	251	8	ϱ̇	ϱ̇	PROPN
ejpam-5429	251	9	≬	≬	PROPN
ejpam-5429	251	10	(	(	PUNCT
ejpam-5429	251	11	ϱ̇	ϱ̇	PROPN
ejpam-5429	251	12	≬	≬	PROPN
ejpam-5429	251	13	ς̇)))ρ̃∧η̃∈σ̃	ς̇)))ρ̃∧η̃∈σ̃	PROPN
ejpam-5429	251	14	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	251	15	ð̃.	ð̃.	PROPN
ejpam-5429	251	16	then	then	ADV
ejpam-5429	251	17	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	251	18	≬	≬	PROPN
ejpam-5429	251	19	(	(	PUNCT
ejpam-5429	251	20	ϱ̇	ϱ̇	PROPN
ejpam-5429	251	21	≬	≬	PROPN
ejpam-5429	251	22	(	(	PUNCT
ejpam-5429	251	23	ϱ̇	ϱ̇	PROPN
ejpam-5429	251	24	≬	≬	PROPN
ejpam-5429	251	25	ς̇	ς̇	NOUN
ejpam-5429	251	26	)	)	PUNCT
ejpam-5429	251	27	)	)	PUNCT
ejpam-5429	251	28	)	)	PUNCT
ejpam-5429	252	1	+	+	CCONJ
ejpam-5429	252	2	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	252	3	≬	≬	PROPN
ejpam-5429	252	4	(	(	PUNCT
ejpam-5429	252	5	ϱ̇	ϱ̇	PROPN
ejpam-5429	252	6	≬	≬	PROPN
ejpam-5429	252	7	(	(	PUNCT
ejpam-5429	252	8	ϱ̇	ϱ̇	PROPN
ejpam-5429	252	9	≬	≬	PROPN
ejpam-5429	252	10	ς̇	ς̇	NOUN
ejpam-5429	252	11	)	)	PUNCT
ejpam-5429	252	12	)	)	PUNCT
ejpam-5429	252	13	)	)	PUNCT
ejpam-5429	253	1	<	<	X
ejpam-5429	253	2	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	253	3	≬	≬	PROPN
ejpam-5429	253	4	(	(	PUNCT
ejpam-5429	253	5	ϱ̇	ϱ̇	PROPN
ejpam-5429	253	6	≬	≬	PROPN
ejpam-5429	253	7	(	(	PUNCT
ejpam-5429	253	8	ϱ̇	ϱ̇	PROPN
ejpam-5429	253	9	≬	≬	PROPN
ejpam-5429	253	10	ς̇	ς̇	NOUN
ejpam-5429	253	11	)	)	PUNCT
ejpam-5429	253	12	)	)	PUNCT
ejpam-5429	253	13	)	)	PUNCT
ejpam-5429	254	1	+	+	CCONJ
ejpam-5429	254	2	ρ̃	ρ̃	PROPN
ejpam-5429	254	3	∧	∧	NOUN
ejpam-5429	254	4	ϖ̃	ϖ̃	PROPN
ejpam-5429	254	5	≤	≤	NOUN
ejpam-5429	254	6	2τ̃	2τ̃	PROPN
ejpam-5429	254	7	.	.	PUNCT
ejpam-5429	255	1	therefore	therefore	ADV
ejpam-5429	255	2	,	,	PUNCT
ejpam-5429	255	3	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	255	4	≬	≬	PROPN
ejpam-5429	255	5	(	(	PUNCT
ejpam-5429	255	6	ϱ̇	ϱ̇	PROPN
ejpam-5429	255	7	≬	≬	PROPN
ejpam-5429	255	8	(	(	PUNCT
ejpam-5429	255	9	ϱ̇	ϱ̇	PROPN
ejpam-5429	255	10	≬	≬	PROPN
ejpam-5429	255	11	ς̇	ς̇	NOUN
ejpam-5429	255	12	)	)	PUNCT
ejpam-5429	255	13	)	)	PUNCT
ejpam-5429	255	14	)	)	PUNCT
ejpam-5429	256	1	<	<	X
ejpam-5429	256	2	τ̃	τ̃	PROPN
ejpam-5429	256	3	.	.	PUNCT
ejpam-5429	257	1	now	now	ADV
ejpam-5429	257	2	,	,	PUNCT
ejpam-5429	257	3	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	257	4	≬	≬	PROPN
ejpam-5429	257	5	(	(	PUNCT
ejpam-5429	257	6	ϱ̇	ϱ̇	PROPN
ejpam-5429	257	7	≬	≬	PROPN
ejpam-5429	257	8	(	(	PUNCT
ejpam-5429	257	9	ϱ̇	ϱ̇	PROPN
ejpam-5429	257	10	≬	≬	PROPN
ejpam-5429	257	11	ς̇	ς̇	NOUN
ejpam-5429	257	12	)	)	PUNCT
ejpam-5429	257	13	)	)	PUNCT
ejpam-5429	257	14	)	)	PUNCT
ejpam-5429	258	1	∨	∨	NUM
ejpam-5429	259	1	σ̃	σ̃	PROPN
ejpam-5429	259	2	<	<	X
ejpam-5429	259	3	ð̃((ς̇	ð̃((ς̇	X
ejpam-5429	259	4	≬	≬	PROPN
ejpam-5429	259	5	ϱ̇	ϱ̇	PROPN
ejpam-5429	259	6	)	)	PUNCT
ejpam-5429	259	7	∧	∧	PROPN
ejpam-5429	259	8	ð̃(κ̇	ð̃(κ̇	PROPN
ejpam-5429	259	9	)	)	PUNCT
ejpam-5429	259	10	∧	∧	PROPN
ejpam-5429	259	11	τ̃	τ̃	PROPN
ejpam-5429	259	12	.	.	PUNCT
ejpam-5429	260	1	choose	choose	VERB
ejpam-5429	260	2	σ̃	σ̃	PROPN
ejpam-5429	260	3	<	<	X
ejpam-5429	260	4	r̂	r̂	NOUN
ejpam-5429	260	5	≤	≤	NOUN
ejpam-5429	260	6	1̂	1̂	NOUN
ejpam-5429	261	1	then	then	ADV
ejpam-5429	261	2	k.	k.	PROPN
ejpam-5429	261	3	h.	h.	PROPN
ejpam-5429	261	4	hakami	hakami	PROPN
ejpam-5429	261	5	et	et	PROPN
ejpam-5429	261	6	al	al	PROPN
ejpam-5429	261	7	.	.	PUNCT
ejpam-5429	261	8	/	/	SYM
ejpam-5429	261	9	eur	eur	PROPN
ejpam-5429	261	10	.	.	PUNCT
ejpam-5429	262	1	j.	j.	PROPN
ejpam-5429	262	2	pure	pure	PROPN
ejpam-5429	262	3	appl	appl	PROPN
ejpam-5429	262	4	.	.	PROPN
ejpam-5429	262	5	math	math	PROPN
ejpam-5429	262	6	,	,	PUNCT
ejpam-5429	262	7	17	17	NUM
ejpam-5429	262	8	(	(	PUNCT
ejpam-5429	262	9	4	4	NUM
ejpam-5429	262	10	)	)	PUNCT
ejpam-5429	262	11	(	(	PUNCT
ejpam-5429	262	12	2024	2024	NUM
ejpam-5429	262	13	)	)	PUNCT
ejpam-5429	262	14	,	,	PUNCT
ejpam-5429	262	15	3129	3129	NUM
ejpam-5429	262	16	-	-	SYM
ejpam-5429	262	17	3155	3155	NUM
ejpam-5429	262	18	3138	3138	NUM
ejpam-5429	263	1	2τ̃	2τ̃	NUM
ejpam-5429	263	2	−	−	PROPN
ejpam-5429	263	3	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	264	1	≬	≬	PROPN
ejpam-5429	264	2	(	(	PUNCT
ejpam-5429	264	3	ϱ̇	ϱ̇	PROPN
ejpam-5429	264	4	≬	≬	PROPN
ejpam-5429	264	5	(	(	PUNCT
ejpam-5429	264	6	ϱ̇	ϱ̇	PROPN
ejpam-5429	264	7	≬	≬	PROPN
ejpam-5429	264	8	ς̇	ς̇	NOUN
ejpam-5429	264	9	)	)	PUNCT
ejpam-5429	264	10	)	)	PUNCT
ejpam-5429	264	11	)	)	PUNCT
ejpam-5429	265	1	∨	∨	NUM
ejpam-5429	266	1	σ̃	σ̃	PROPN
ejpam-5429	266	2	≥	≥	NUM
ejpam-5429	266	3	r̂	r̂	NOUN
ejpam-5429	266	4	>	>	X
ejpam-5429	266	5	2τ̃	2τ̃	NUM
ejpam-5429	267	1	−	−	NOUN
ejpam-5429	267	2	ð̃((ς̇	ð̃((ς̇	X
ejpam-5429	268	1	≬	≬	PROPN
ejpam-5429	268	2	ϱ̇	ϱ̇	PROPN
ejpam-5429	268	3	)	)	PUNCT
ejpam-5429	268	4	∧	∧	PROPN
ejpam-5429	268	5	ð̃(κ̇	ð̃(κ̇	PROPN
ejpam-5429	268	6	)	)	PUNCT
ejpam-5429	268	7	∧	∧	PROPN
ejpam-5429	268	8	τ̃	τ̃	PROPN
ejpam-5429	268	9	.	.	PUNCT
ejpam-5429	269	1	therefore	therefore	ADV
ejpam-5429	269	2	,	,	PUNCT
ejpam-5429	269	3	2τ̃	2τ̃	PROPN
ejpam-5429	269	4	−	−	PROPN
ejpam-5429	269	5	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	269	6	≬	≬	PROPN
ejpam-5429	269	7	(	(	PUNCT
ejpam-5429	269	8	ϱ̇	ϱ̇	PROPN
ejpam-5429	269	9	≬	≬	PROPN
ejpam-5429	269	10	(	(	PUNCT
ejpam-5429	269	11	ϱ̇	ϱ̇	PROPN
ejpam-5429	269	12	≬	≬	PROPN
ejpam-5429	269	13	ς̇	ς̇	NOUN
ejpam-5429	269	14	)	)	PUNCT
ejpam-5429	269	15	)	)	PUNCT
ejpam-5429	269	16	)	)	PUNCT
ejpam-5429	270	1	∧	∧	NOUN
ejpam-5429	270	2	(	(	PUNCT
ejpam-5429	270	3	2τ̃	2τ̃	PROPN
ejpam-5429	270	4	−	−	PROPN
ejpam-5429	270	5	σ̃	σ̃	PROPN
ejpam-5429	270	6	)	)	PUNCT
ejpam-5429	270	7	≥	≥	NOUN
ejpam-5429	270	8	(	(	PUNCT
ejpam-5429	270	9	2τ̃	2τ̃	PROPN
ejpam-5429	270	10	−	−	PROPN
ejpam-5429	270	11	ð̃((ς̇	ð̃((ς̇	X
ejpam-5429	270	12	≬	≬	PROPN
ejpam-5429	270	13	ϱ̇	ϱ̇	PROPN
ejpam-5429	270	14	)	)	PUNCT
ejpam-5429	270	15	)	)	PUNCT
ejpam-5429	270	16	∨	∨	NUM
ejpam-5429	270	17	(	(	PUNCT
ejpam-5429	270	18	2τ̃	2τ̃	PROPN
ejpam-5429	270	19	−	−	PROPN
ejpam-5429	270	20	ð̃(κ̇	ð̃(κ̇	NOUN
ejpam-5429	270	21	)	)	PUNCT
ejpam-5429	270	22	)	)	PUNCT
ejpam-5429	270	23	∨	∨	PROPN
ejpam-5429	270	24	τ̃	τ̃	PROPN
ejpam-5429	270	25	.	.	PUNCT
ejpam-5429	271	1	thus	thus	ADV
ejpam-5429	271	2	,	,	PUNCT
ejpam-5429	271	3	r̂	r̂	NOUN
ejpam-5429	271	4	>	>	X
ejpam-5429	271	5	2τ̃	2τ̃	NUM
ejpam-5429	272	1	−	−	NOUN
ejpam-5429	272	2	ð̃((ς̇	ð̃((ς̇	PUNCT
ejpam-5429	272	3	≬	≬	PROPN
ejpam-5429	272	4	ϱ̇	ϱ̇	PROPN
ejpam-5429	272	5	)	)	PUNCT
ejpam-5429	272	6	,	,	PUNCT
ejpam-5429	272	7	r̂	r̂	NOUN
ejpam-5429	272	8	>	>	X
ejpam-5429	273	1	2τ̃	2τ̃	NUM
ejpam-5429	273	2	−	−	PROPN
ejpam-5429	273	3	ð̃(κ̇	ð̃(κ̇	NOUN
ejpam-5429	273	4	)	)	PUNCT
ejpam-5429	273	5	and	and	CCONJ
ejpam-5429	273	6	2τ̃	2τ̃	NUM
ejpam-5429	274	1	−	−	PROPN
ejpam-5429	274	2	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	275	1	≬	≬	PROPN
ejpam-5429	275	2	(	(	PUNCT
ejpam-5429	275	3	ϱ̇	ϱ̇	PROPN
ejpam-5429	275	4	≬	≬	PROPN
ejpam-5429	275	5	(	(	PUNCT
ejpam-5429	275	6	ϱ̇	ϱ̇	PROPN
ejpam-5429	275	7	≬	≬	PROPN
ejpam-5429	275	8	ς̇	ς̇	NOUN
ejpam-5429	275	9	)	)	PUNCT
ejpam-5429	275	10	)	)	PUNCT
ejpam-5429	275	11	)	)	PUNCT
ejpam-5429	275	12	>	>	PUNCT
ejpam-5429	275	13	r̂	r̂	NOUN
ejpam-5429	276	1	so	so	ADV
ejpam-5429	276	2	,	,	PUNCT
ejpam-5429	276	3	ð̃((ς̇	ð̃((ς̇	VERB
ejpam-5429	276	4	≬	≬	PROPN
ejpam-5429	276	5	ϱ̇	ϱ̇	PROPN
ejpam-5429	276	6	)	)	PUNCT
ejpam-5429	277	1	+	+	CCONJ
ejpam-5429	277	2	r̂	r̂	NOUN
ejpam-5429	277	3	>	>	X
ejpam-5429	277	4	2τ̃	2τ̃	PROPN
ejpam-5429	277	5	,	,	PUNCT
ejpam-5429	277	6	ð̃(κ̇	ð̃(κ̇	NOUN
ejpam-5429	277	7	)	)	PUNCT
ejpam-5429	277	8	+	+	NUM
ejpam-5429	277	9	r̂	r̂	NOUN
ejpam-5429	277	10	>	>	X
ejpam-5429	277	11	2τ̃	2τ̃	PROPN
ejpam-5429	277	12	and	and	CCONJ
ejpam-5429	277	13	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	277	14	≬	≬	PROPN
ejpam-5429	277	15	(	(	PUNCT
ejpam-5429	277	16	ϱ̇	ϱ̇	PROPN
ejpam-5429	277	17	≬	≬	PROPN
ejpam-5429	277	18	(	(	PUNCT
ejpam-5429	277	19	ϱ̇	ϱ̇	PROPN
ejpam-5429	277	20	≬	≬	PROPN
ejpam-5429	277	21	ς̇	ς̇	NOUN
ejpam-5429	277	22	)	)	PUNCT
ejpam-5429	277	23	)	)	PUNCT
ejpam-5429	277	24	)	)	PUNCT
ejpam-5429	278	1	+	+	PUNCT
ejpam-5429	278	2	r̂	r̂	NOUN
ejpam-5429	278	3	<	<	X
ejpam-5429	278	4	2τ̃	2τ̃	PROPN
ejpam-5429	278	5	.	.	PUNCT
ejpam-5429	279	1	thus	thus	ADV
ejpam-5429	279	2	,	,	PUNCT
ejpam-5429	279	3	ς̇	ς̇	PROPN
ejpam-5429	279	4	≬	≬	PROPN
ejpam-5429	279	5	(	(	PUNCT
ejpam-5429	279	6	ϱ̇	ϱ̇	PROPN
ejpam-5429	279	7	≬	≬	PROPN
ejpam-5429	279	8	(	(	PUNCT
ejpam-5429	279	9	ϱ̇	ϱ̇	PROPN
ejpam-5429	279	10	≬	≬	PROPN
ejpam-5429	279	11	ς̇))r̂qτ̃	ς̇))r̂qτ̃	NUM
ejpam-5429	279	12	ð̃	ð̃	PROPN
ejpam-5429	279	13	,	,	PUNCT
ejpam-5429	279	14	κ̇r̂qτ̃	κ̇r̂qτ̃	NOUN
ejpam-5429	279	15	ð̃	ð̃	PROPN
ejpam-5429	279	16	but	but	CCONJ
ejpam-5429	279	17	(	(	PUNCT
ejpam-5429	279	18	ς̇	ς̇	NOUN
ejpam-5429	279	19	≬	≬	PROPN
ejpam-5429	279	20	(	(	PUNCT
ejpam-5429	279	21	ϱ̇	ϱ̇	PROPN
ejpam-5429	279	22	≬	≬	PROPN
ejpam-5429	279	23	(	(	PUNCT
ejpam-5429	279	24	ϱ̇	ϱ̇	PROPN
ejpam-5429	279	25	≬	≬	PROPN
ejpam-5429	279	26	ς̇)))r̂	ς̇)))r̂	PROPN
ejpam-5429	279	27	∈σ̃	∈σ̃	PROPN
ejpam-5429	279	28	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	279	29	ð̃	ð̃	PROPN
ejpam-5429	279	30	,	,	PUNCT
ejpam-5429	279	31	a	a	DET
ejpam-5429	279	32	contradiction	contradiction	NOUN
ejpam-5429	279	33	.	.	PUNCT
ejpam-5429	280	1	hence	hence	ADV
ejpam-5429	280	2	,	,	PUNCT
ejpam-5429	280	3	ð̃	ð̃	PROPN
ejpam-5429	280	4	is	be	AUX
ejpam-5429	280	5	a	a	DET
ejpam-5429	280	6	qp-(∈σ̃,∈σ̃	qp-(∈σ̃,∈σ̃	NOUN
ejpam-5429	280	7	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	280	8	)	)	PUNCT
ejpam-5429	280	9	-ffi	-ffi	PROPN
ejpam-5429	280	10	of	of	ADP
ejpam-5429	280	11	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	280	12	theorem	theorem	VERB
ejpam-5429	280	13	8	8	NUM
ejpam-5429	280	14	.	.	PUNCT
ejpam-5429	281	1	every	every	DET
ejpam-5429	281	2	qp-(∈σ̃	qp-(∈σ̃	PRON
ejpam-5429	281	3	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	281	4	,	,	PUNCT
ejpam-5429	281	5	∈σ̃	∈σ̃	PROPN
ejpam-5429	281	6	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	281	7	)	)	PUNCT
ejpam-5429	281	8	-ffi	-ffi	PROPN
ejpam-5429	281	9	of	of	ADP
ejpam-5429	281	10	ℵ̃	ℵ̃	PROPN
ejpam-5429	281	11	is	be	AUX
ejpam-5429	281	12	a	a	DET
ejpam-5429	281	13	qp-(∈σ̃,∈σ̃	qp-(∈σ̃,∈σ̃	NOUN
ejpam-5429	281	14	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	281	15	)	)	PUNCT
ejpam-5429	281	16	-ffi	-ffi	PROPN
ejpam-5429	281	17	of	of	ADP
ejpam-5429	281	18	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	281	19	proof	proof	NOUN
ejpam-5429	281	20	.	.	PUNCT
ejpam-5429	282	1	the	the	DET
ejpam-5429	282	2	proof	proof	NOUN
ejpam-5429	282	3	is	be	AUX
ejpam-5429	282	4	based	base	VERB
ejpam-5429	282	5	on	on	ADP
ejpam-5429	282	6	the	the	DET
ejpam-5429	282	7	observation	observation	NOUN
ejpam-5429	282	8	that	that	SCONJ
ejpam-5429	282	9	if	if	SCONJ
ejpam-5429	282	10	ς̇ρ̃	ς̇ρ̃	PROPN
ejpam-5429	282	11	∈σ̃	∈σ̃	PROPN
ejpam-5429	282	12	ð̃	ð̃	PROPN
ejpam-5429	282	13	,	,	PUNCT
ejpam-5429	282	14	then	then	ADV
ejpam-5429	282	15	ς̇ρ̃	ς̇ρ̃	PROPN
ejpam-5429	282	16	∈σ̃	∈σ̃	VERB
ejpam-5429	282	17	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	282	18	ð̃.	ð̃.	PROPN
ejpam-5429	282	19	theorem	theorem	VERB
ejpam-5429	282	20	9	9	NUM
ejpam-5429	282	21	.	.	PUNCT
ejpam-5429	283	1	every	every	DET
ejpam-5429	283	2	qp-(∈σ̃,∈σ̃)ffi	qp-(∈σ̃,∈σ̃)ffi	PROPN
ejpam-5429	283	3	is	be	AUX
ejpam-5429	283	4	a	a	DET
ejpam-5429	283	5	qp-(∈σ̃	qp-(∈σ̃	PROPN
ejpam-5429	283	6	,	,	PUNCT
ejpam-5429	283	7	∈σ̃	∈σ̃	PROPN
ejpam-5429	283	8	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	283	9	)	)	PUNCT
ejpam-5429	283	10	ffi	ffi	PROPN
ejpam-5429	283	11	of	of	ADP
ejpam-5429	283	12	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	283	13	proof	proof	NOUN
ejpam-5429	283	14	.	.	PUNCT
ejpam-5429	284	1	let	let	VERB
ejpam-5429	284	2	ð̃	ð̃	PRON
ejpam-5429	284	3	be	be	AUX
ejpam-5429	284	4	a	a	DET
ejpam-5429	284	5	qp-(∈σ̃,∈σ̃)-ffi	qp-(∈σ̃,∈σ̃)-ffi	PROPN
ejpam-5429	284	6	of	of	ADP
ejpam-5429	284	7	ℵ̃	ℵ̃	PROPN
ejpam-5429	284	8	,	,	PUNCT
ejpam-5429	284	9	ς̇	ς̇	PROPN
ejpam-5429	284	10	,	,	PUNCT
ejpam-5429	284	11	ϱ̇	ϱ̇	PROPN
ejpam-5429	284	12	,	,	PUNCT
ejpam-5429	284	13	κ̇	κ̇	PROPN
ejpam-5429	284	14	∈	∈	PROPN
ejpam-5429	284	15	ℵ̃	ℵ̃	PROPN
ejpam-5429	284	16	and	and	CCONJ
ejpam-5429	284	17	let	let	VERB
ejpam-5429	284	18	σ̃	σ̃	PROPN
ejpam-5429	284	19	<	<	X
ejpam-5429	284	20	ρ̃	ρ̃	PROPN
ejpam-5429	284	21	,	,	PUNCT
ejpam-5429	284	22	η̃	η̃	PROPN
ejpam-5429	284	23	≤	≤	NOUN
ejpam-5429	284	24	1̂.	1̂.	NUM
ejpam-5429	285	1	so	so	ADV
ejpam-5429	285	2	the	the	DET
ejpam-5429	285	3	qp	qp	PROPN
ejpam-5429	285	4	-	-	PUNCT
ejpam-5429	285	5	f	f	PROPN
ejpam-5429	285	6	points	point	NOUN
ejpam-5429	285	7	(	(	PUNCT
ejpam-5429	285	8	(	(	PUNCT
ejpam-5429	285	9	ς̇	ς̇	PROPN
ejpam-5429	285	10	≬	≬	PROPN
ejpam-5429	285	11	ϱ̇	ϱ̇	PROPN
ejpam-5429	285	12	)	)	PUNCT
ejpam-5429	285	13	≬	≬	PROPN
ejpam-5429	285	14	κ̇)ρ̃	κ̇)ρ̃	PROPN
ejpam-5429	285	15	∈σ̃	∈σ̃	PROPN
ejpam-5429	285	16	ð̃	ð̃	PROPN
ejpam-5429	285	17	and	and	CCONJ
ejpam-5429	285	18	κ̇η̃	κ̇η̃	PROPN
ejpam-5429	285	19	∈σ̃	∈σ̃	PROPN
ejpam-5429	286	1	ð̃.	ð̃.	PROPN
ejpam-5429	286	2	then	then	ADV
ejpam-5429	286	3	(	(	PUNCT
ejpam-5429	286	4	(	(	PUNCT
ejpam-5429	286	5	ς̇	ς̇	PROPN
ejpam-5429	286	6	≬	≬	PROPN
ejpam-5429	286	7	ϱ̇	ϱ̇	PROPN
ejpam-5429	286	8	)	)	PUNCT
ejpam-5429	286	9	≬	≬	PROPN
ejpam-5429	286	10	κ̇)ρ̃	κ̇)ρ̃	PROPN
ejpam-5429	286	11	∈σ̃	∈σ̃	PROPN
ejpam-5429	286	12	ð̃	ð̃	PROPN
ejpam-5429	286	13	and	and	CCONJ
ejpam-5429	286	14	κ̇η̃	κ̇η̃	PROPN
ejpam-5429	286	15	∈σ̃	∈σ̃	PROPN
ejpam-5429	286	16	ð̃	ð̃	PROPN
ejpam-5429	286	17	⇒	⇒	NOUN
ejpam-5429	286	18	(	(	PUNCT
ejpam-5429	286	19	ς̇	ς̇	NOUN
ejpam-5429	286	20	≬	≬	PROPN
ejpam-5429	286	21	(	(	PUNCT
ejpam-5429	286	22	ϱ̇	ϱ̇	PROPN
ejpam-5429	286	23	≬	≬	PROPN
ejpam-5429	286	24	(	(	PUNCT
ejpam-5429	286	25	ϱ̇	ϱ̇	PROPN
ejpam-5429	286	26	≬	≬	PROPN
ejpam-5429	286	27	ς̇)))ρ̃∧η̃	ς̇)))ρ̃∧η̃	VERB
ejpam-5429	286	28	∈σ̃	∈σ̃	NOUN
ejpam-5429	286	29	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	286	30	ð̃.	ð̃.	PROPN
ejpam-5429	286	31	thus	thus	ADV
ejpam-5429	286	32	,	,	PUNCT
ejpam-5429	286	33	ð̃	ð̃	PROPN
ejpam-5429	286	34	is	be	AUX
ejpam-5429	286	35	a	a	DET
ejpam-5429	286	36	qp-(∈σ̃,∈σ̃	qp-(∈σ̃,∈σ̃	NOUN
ejpam-5429	286	37	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	286	38	)	)	PUNCT
ejpam-5429	286	39	-ffi	-ffi	PROPN
ejpam-5429	286	40	of	of	ADP
ejpam-5429	286	41	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	286	42	5	5	NUM
ejpam-5429	286	43	.	.	PUNCT
ejpam-5429	286	44	quadri	quadri	NOUN
ejpam-5429	286	45	-	-	PUNCT
ejpam-5429	286	46	polar	polar	PROPN
ejpam-5429	286	47	(	(	PUNCT
ejpam-5429	286	48	∈σ̃,∈σ̃	∈σ̃,∈σ̃	VERB
ejpam-5429	286	49	∨qτ̃	∨qτ̃	ADJ
ejpam-5429	286	50	)	)	PUNCT
ejpam-5429	286	51	-fuzzy	-fuzzy	PROPN
ejpam-5429	286	52	fantastic	fantastic	ADJ
ejpam-5429	286	53	ideals	ideal	NOUN
ejpam-5429	286	54	in	in	ADP
ejpam-5429	286	55	this	this	DET
ejpam-5429	286	56	section	section	NOUN
ejpam-5429	286	57	,	,	PUNCT
ejpam-5429	286	58	we	we	PRON
ejpam-5429	286	59	present	present	VERB
ejpam-5429	286	60	the	the	DET
ejpam-5429	286	61	notion	notion	NOUN
ejpam-5429	286	62	of	of	ADP
ejpam-5429	286	63	a	a	DET
ejpam-5429	286	64	qp-(∈σ̃,∈σ̃	qp-(∈σ̃,∈σ̃	PROPN
ejpam-5429	286	65	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	286	66	)	)	PUNCT
ejpam-5429	286	67	-ffi(s	-ffi(s	PROPN
ejpam-5429	286	68	)	)	PUNCT
ejpam-5429	286	69	and	and	CCONJ
ejpam-5429	286	70	explore	explore	VERB
ejpam-5429	286	71	several	several	ADJ
ejpam-5429	286	72	of	of	ADP
ejpam-5429	286	73	its	its	PRON
ejpam-5429	286	74	essential	essential	ADJ
ejpam-5429	286	75	characteristics	characteristic	NOUN
ejpam-5429	286	76	and	and	CCONJ
ejpam-5429	286	77	properties	property	NOUN
ejpam-5429	286	78	.	.	PUNCT
ejpam-5429	287	1	definition	definition	NOUN
ejpam-5429	287	2	5	5	NUM
ejpam-5429	287	3	.	.	PUNCT
ejpam-5429	288	1	a	a	DET
ejpam-5429	288	2	qp	qp	PROPN
ejpam-5429	288	3	-	-	PUNCT
ejpam-5429	288	4	f	f	NOUN
ejpam-5429	288	5	set	set	NOUN
ejpam-5429	288	6	ð̃	ð̃	PROPN
ejpam-5429	288	7	of	of	ADP
ejpam-5429	288	8	ℵ̃	ℵ̃	PROPN
ejpam-5429	288	9	is	be	AUX
ejpam-5429	288	10	a	a	DET
ejpam-5429	288	11	qp-(∈σ̃,∈σ̃	qp-(∈σ̃,∈σ̃	NOUN
ejpam-5429	288	12	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	288	13	)	)	PUNCT
ejpam-5429	288	14	-ffi	-ffi	PROPN
ejpam-5429	288	15	of	of	ADP
ejpam-5429	288	16	ℵ̃	ℵ̃	PROPN
ejpam-5429	288	17	if	if	SCONJ
ejpam-5429	288	18	it	it	PRON
ejpam-5429	288	19	satisfies	satisfy	VERB
ejpam-5429	288	20	condition	condition	NOUN
ejpam-5429	288	21	(	(	PUNCT
ejpam-5429	288	22	1	1	NUM
ejpam-5429	288	23	)	)	PUNCT
ejpam-5429	288	24	,	,	PUNCT
ejpam-5429	288	25	as	as	SCONJ
ejpam-5429	288	26	follows	follow	VERB
ejpam-5429	288	27	:	:	PUNCT
ejpam-5429	288	28	(	(	PUNCT
ejpam-5429	288	29	1	1	X
ejpam-5429	288	30	)	)	PUNCT
ejpam-5429	288	31	(	(	PUNCT
ejpam-5429	288	32	(	(	PUNCT
ejpam-5429	288	33	ς̇	ς̇	PROPN
ejpam-5429	288	34	≬	≬	PROPN
ejpam-5429	288	35	ϱ̇	ϱ̇	PROPN
ejpam-5429	288	36	)	)	PUNCT
ejpam-5429	289	1	≬	≬	PROPN
ejpam-5429	289	2	κ̇)ρ̃	κ̇)ρ̃	PROPN
ejpam-5429	289	3	∈σ̃	∈σ̃	PROPN
ejpam-5429	289	4	ð̃	ð̃	PROPN
ejpam-5429	289	5	,	,	PUNCT
ejpam-5429	289	6	κ̇η̃	κ̇η̃	PROPN
ejpam-5429	289	7	∈σ̃	∈σ̃	PROPN
ejpam-5429	289	8	ð̃	ð̃	PROPN
ejpam-5429	289	9	⇒	⇒	NOUN
ejpam-5429	289	10	(	(	PUNCT
ejpam-5429	289	11	ς̇	ς̇	NOUN
ejpam-5429	289	12	≬	≬	PROPN
ejpam-5429	289	13	(	(	PUNCT
ejpam-5429	289	14	ϱ̇	ϱ̇	PROPN
ejpam-5429	289	15	≬	≬	PROPN
ejpam-5429	289	16	(	(	PUNCT
ejpam-5429	289	17	ϱ̇	ϱ̇	PROPN
ejpam-5429	289	18	≬	≬	PROPN
ejpam-5429	289	19	ς̇)))ρ̃∧η̃	ς̇)))ρ̃∧η̃	VERB
ejpam-5429	289	20	∈σ̃	∈σ̃	PROPN
ejpam-5429	289	21	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	289	22	ð̃,∀σ̃	ð̃,∀σ̃	X
ejpam-5429	289	23	<	<	X
ejpam-5429	289	24	ρ̃	ρ̃	PROPN
ejpam-5429	289	25	,	,	PUNCT
ejpam-5429	289	26	η̃	η̃	PROPN
ejpam-5429	289	27	≤	≤	NOUN
ejpam-5429	289	28	1̂	1̂	NOUN
ejpam-5429	289	29	and	and	CCONJ
ejpam-5429	289	30	ς̇	ς̇	NOUN
ejpam-5429	289	31	,	,	PUNCT
ejpam-5429	289	32	ϱ̇	ϱ̇	PROPN
ejpam-5429	289	33	,	,	PUNCT
ejpam-5429	289	34	κ̇	κ̇	PROPN
ejpam-5429	289	35	∈	∈	PROPN
ejpam-5429	289	36	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	289	37	example	example	NOUN
ejpam-5429	289	38	2	2	X
ejpam-5429	289	39	.	.	X
ejpam-5429	289	40	consider	consider	VERB
ejpam-5429	289	41	the	the	DET
ejpam-5429	289	42	bck	bck	NOUN
ejpam-5429	289	43	-	-	PUNCT
ejpam-5429	289	44	algebra	algebra	NOUN
ejpam-5429	289	45	(	(	PUNCT
ejpam-5429	289	46	ℵ̃	ℵ̃	PROPN
ejpam-5429	289	47	;	;	PUNCT
ejpam-5429	289	48	≬	≬	PROPN
ejpam-5429	289	49	,	,	PUNCT
ejpam-5429	289	50	0	0	NUM
ejpam-5429	289	51	)	)	PUNCT
ejpam-5429	289	52	and	and	CCONJ
ejpam-5429	289	53	a	a	DET
ejpam-5429	289	54	qp	qp	PROPN
ejpam-5429	289	55	-	-	PUNCT
ejpam-5429	289	56	f	f	NOUN
ejpam-5429	289	57	set	set	NOUN
ejpam-5429	289	58	ð̃	ð̃	PROPN
ejpam-5429	289	59	as	as	SCONJ
ejpam-5429	289	60	illustrated	illustrate	VERB
ejpam-5429	289	61	in	in	ADP
ejpam-5429	289	62	example	example	NOUN
ejpam-5429	289	63	3.1	3.1	NUM
ejpam-5429	289	64	.	.	PUNCT
ejpam-5429	290	1	it	it	PRON
ejpam-5429	290	2	is	be	AUX
ejpam-5429	290	3	evident	evident	ADJ
ejpam-5429	290	4	from	from	ADP
ejpam-5429	290	5	definition	definition	NOUN
ejpam-5429	290	6	5.1	5.1	NUM
ejpam-5429	290	7	,	,	PUNCT
ejpam-5429	290	8	ð̃	ð̃	PROPN
ejpam-5429	290	9	is	be	AUX
ejpam-5429	290	10	a	a	DET
ejpam-5429	290	11	qp-(∈(0.2,0.1,0.3,0.2),∈(0.2,0.1,0.3,0.2	qp-(∈(0.2,0.1,0.3,0.2),∈(0.2,0.1,0.3,0.2	NOUN
ejpam-5429	290	12	)	)	PUNCT
ejpam-5429	290	13	∨q(0.61,0.68,0.78,0.57))-ffi	∨q(0.61,0.68,0.78,0.57))-ffi	NOUN
ejpam-5429	290	14	of	of	ADP
ejpam-5429	290	15	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	290	16	theorem	theorem	VERB
ejpam-5429	290	17	10	10	NUM
ejpam-5429	290	18	.	.	PUNCT
ejpam-5429	291	1	for	for	ADP
ejpam-5429	291	2	a	a	DET
ejpam-5429	291	3	qp	qp	PROPN
ejpam-5429	291	4	-	-	PUNCT
ejpam-5429	291	5	f	f	NOUN
ejpam-5429	291	6	set	set	NOUN
ejpam-5429	291	7	ð̃	ð̃	PROPN
ejpam-5429	291	8	of	of	ADP
ejpam-5429	291	9	ℵ̃	ℵ̃	PROPN
ejpam-5429	291	10	,	,	PUNCT
ejpam-5429	291	11	condition	condition	NOUN
ejpam-5429	291	12	(	(	PUNCT
ejpam-5429	291	13	1	1	NUM
ejpam-5429	291	14	)	)	PUNCT
ejpam-5429	291	15	in	in	ADP
ejpam-5429	291	16	definition	definition	NOUN
ejpam-5429	291	17	5.1	5.1	NUM
ejpam-5429	291	18	is	be	AUX
ejpam-5429	291	19	similar	similar	ADJ
ejpam-5429	291	20	with	with	ADP
ejpam-5429	291	21	condition	condition	NOUN
ejpam-5429	291	22	(	(	PUNCT
ejpam-5429	291	23	2	2	NUM
ejpam-5429	291	24	)	)	PUNCT
ejpam-5429	291	25	,	,	PUNCT
ejpam-5429	291	26	as	as	SCONJ
ejpam-5429	291	27	follows	follow	VERB
ejpam-5429	291	28	:	:	PUNCT
ejpam-5429	291	29	(	(	PUNCT
ejpam-5429	291	30	2	2	X
ejpam-5429	291	31	)	)	PUNCT
ejpam-5429	292	1	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	293	1	≬	≬	PROPN
ejpam-5429	293	2	(	(	PUNCT
ejpam-5429	293	3	ϱ̇	ϱ̇	PROPN
ejpam-5429	293	4	≬	≬	PROPN
ejpam-5429	293	5	(	(	PUNCT
ejpam-5429	293	6	ϱ̇	ϱ̇	PROPN
ejpam-5429	293	7	≬	≬	PROPN
ejpam-5429	293	8	ς̇	ς̇	NOUN
ejpam-5429	293	9	)	)	PUNCT
ejpam-5429	293	10	)	)	PUNCT
ejpam-5429	293	11	)	)	PUNCT
ejpam-5429	294	1	∨	∨	NUM
ejpam-5429	294	2	σ̃	σ̃	PROPN
ejpam-5429	294	3	≥	≥	NOUN
ejpam-5429	294	4	ð̃((ς̇	ð̃((ς̇	X
ejpam-5429	295	1	≬	≬	PROPN
ejpam-5429	295	2	ϱ̇	ϱ̇	PROPN
ejpam-5429	295	3	)	)	PUNCT
ejpam-5429	295	4	≬	≬	PROPN
ejpam-5429	295	5	κ̇	κ̇	PROPN
ejpam-5429	295	6	)	)	PUNCT
ejpam-5429	295	7	∧	∧	PROPN
ejpam-5429	295	8	ð̃(κ̇	ð̃(κ̇	PROPN
ejpam-5429	295	9	)	)	PUNCT
ejpam-5429	295	10	,	,	PUNCT
ejpam-5429	295	11	τ̃	τ̃	PROPN
ejpam-5429	295	12	,	,	PUNCT
ejpam-5429	295	13	∀ς̇	∀ς̇	PROPN
ejpam-5429	295	14	,	,	PUNCT
ejpam-5429	295	15	ϱ̇	ϱ̇	PROPN
ejpam-5429	295	16	∈	∈	PROPN
ejpam-5429	295	17	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	295	18	k.	k.	PROPN
ejpam-5429	295	19	h.	h.	PROPN
ejpam-5429	295	20	hakami	hakami	PROPN
ejpam-5429	295	21	et	et	PROPN
ejpam-5429	295	22	al	al	PROPN
ejpam-5429	295	23	.	.	PUNCT
ejpam-5429	295	24	/	/	SYM
ejpam-5429	295	25	eur	eur	PROPN
ejpam-5429	295	26	.	.	PUNCT
ejpam-5429	296	1	j.	j.	PROPN
ejpam-5429	296	2	pure	pure	PROPN
ejpam-5429	296	3	appl	appl	PROPN
ejpam-5429	296	4	.	.	PROPN
ejpam-5429	296	5	math	math	PROPN
ejpam-5429	296	6	,	,	PUNCT
ejpam-5429	296	7	17	17	NUM
ejpam-5429	296	8	(	(	PUNCT
ejpam-5429	296	9	4	4	NUM
ejpam-5429	296	10	)	)	PUNCT
ejpam-5429	296	11	(	(	PUNCT
ejpam-5429	296	12	2024	2024	NUM
ejpam-5429	296	13	)	)	PUNCT
ejpam-5429	296	14	,	,	PUNCT
ejpam-5429	296	15	3129	3129	NUM
ejpam-5429	296	16	-	-	SYM
ejpam-5429	296	17	3155	3155	NUM
ejpam-5429	296	18	3139	3139	NUM
ejpam-5429	296	19	proof	proof	NOUN
ejpam-5429	296	20	.	.	PUNCT
ejpam-5429	297	1	(	(	PUNCT
ejpam-5429	297	2	1	1	X
ejpam-5429	297	3	)	)	PUNCT
ejpam-5429	297	4	⇒	⇒	NOUN
ejpam-5429	297	5	(	(	PUNCT
ejpam-5429	297	6	2	2	NUM
ejpam-5429	297	7	)	)	PUNCT
ejpam-5429	297	8	.	.	PUNCT
ejpam-5429	298	1	assume	assume	VERB
ejpam-5429	298	2	that	that	SCONJ
ejpam-5429	298	3	(	(	PUNCT
ejpam-5429	298	4	2	2	X
ejpam-5429	298	5	)	)	PUNCT
ejpam-5429	298	6	does	do	AUX
ejpam-5429	298	7	not	not	PART
ejpam-5429	298	8	hold	hold	VERB
ejpam-5429	298	9	.	.	PUNCT
ejpam-5429	299	1	then	then	ADV
ejpam-5429	299	2	,	,	PUNCT
ejpam-5429	299	3	∃ς̇	∃ς̇	PROPN
ejpam-5429	299	4	,	,	PUNCT
ejpam-5429	299	5	ϱ̇	ϱ̇	PROPN
ejpam-5429	299	6	,	,	PUNCT
ejpam-5429	299	7	κ̇	κ̇	PROPN
ejpam-5429	299	8	∈	∈	PROPN
ejpam-5429	299	9	ℵ̃	ℵ̃	PROPN
ejpam-5429	300	1	such	such	ADJ
ejpam-5429	300	2	that	that	SCONJ
ejpam-5429	300	3	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	300	4	≬	≬	PROPN
ejpam-5429	300	5	(	(	PUNCT
ejpam-5429	300	6	ϱ̇	ϱ̇	PROPN
ejpam-5429	300	7	≬	≬	PROPN
ejpam-5429	300	8	(	(	PUNCT
ejpam-5429	300	9	ϱ̇	ϱ̇	PROPN
ejpam-5429	300	10	≬	≬	PROPN
ejpam-5429	300	11	ς̇	ς̇	NOUN
ejpam-5429	300	12	)	)	PUNCT
ejpam-5429	300	13	)	)	PUNCT
ejpam-5429	300	14	)	)	PUNCT
ejpam-5429	300	15	∨	∨	NUM
ejpam-5429	301	1	σ̃	σ̃	PROPN
ejpam-5429	301	2	<	<	X
ejpam-5429	301	3	ð̃((ς̇	ð̃((ς̇	X
ejpam-5429	301	4	≬	≬	PROPN
ejpam-5429	301	5	ϱ̇	ϱ̇	PROPN
ejpam-5429	301	6	)	)	PUNCT
ejpam-5429	301	7	≬	≬	PROPN
ejpam-5429	301	8	κ̇	κ̇	PROPN
ejpam-5429	301	9	)	)	PUNCT
ejpam-5429	301	10	∧	∧	PROPN
ejpam-5429	301	11	ð̃(κ̇	ð̃(κ̇	PROPN
ejpam-5429	301	12	)	)	PUNCT
ejpam-5429	301	13	∧	∧	PROPN
ejpam-5429	301	14	τ̃	τ̃	PROPN
ejpam-5429	301	15	.	.	PUNCT
ejpam-5429	302	1	then	then	ADV
ejpam-5429	302	2	,	,	PUNCT
ejpam-5429	302	3	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	302	4	≬	≬	PROPN
ejpam-5429	302	5	(	(	PUNCT
ejpam-5429	302	6	ϱ̇	ϱ̇	PROPN
ejpam-5429	302	7	≬	≬	PROPN
ejpam-5429	302	8	(	(	PUNCT
ejpam-5429	302	9	ϱ̇	ϱ̇	PROPN
ejpam-5429	302	10	≬	≬	PROPN
ejpam-5429	302	11	ς̇	ς̇	NOUN
ejpam-5429	302	12	)	)	PUNCT
ejpam-5429	302	13	)	)	PUNCT
ejpam-5429	302	14	)	)	PUNCT
ejpam-5429	303	1	∨	∨	NUM
ejpam-5429	304	1	σ̃	σ̃	PROPN
ejpam-5429	304	2	<	<	X
ejpam-5429	304	3	ρ̃	ρ̃	PROPN
ejpam-5429	304	4	≤	≤	NOUN
ejpam-5429	304	5	ð̃((ς̇	ð̃((ς̇	PUNCT
ejpam-5429	305	1	≬	≬	PROPN
ejpam-5429	305	2	ϱ̇	ϱ̇	PROPN
ejpam-5429	305	3	)	)	PUNCT
ejpam-5429	305	4	≬	≬	PROPN
ejpam-5429	305	5	κ̇	κ̇	PROPN
ejpam-5429	305	6	)	)	PUNCT
ejpam-5429	305	7	∧	∧	PROPN
ejpam-5429	305	8	ð̃(κ̇	ð̃(κ̇	PROPN
ejpam-5429	305	9	)	)	PUNCT
ejpam-5429	305	10	∧	∧	PROPN
ejpam-5429	305	11	τ̃	τ̃	PROPN
ejpam-5429	305	12	.	.	PUNCT
ejpam-5429	306	1	thus	thus	ADV
ejpam-5429	306	2	,	,	PUNCT
ejpam-5429	306	3	(	(	PUNCT
ejpam-5429	306	4	(	(	PUNCT
ejpam-5429	306	5	ς̇	ς̇	PROPN
ejpam-5429	306	6	≬	≬	PROPN
ejpam-5429	306	7	ϱ̇	ϱ̇	PROPN
ejpam-5429	306	8	)	)	PUNCT
ejpam-5429	306	9	≬	≬	PROPN
ejpam-5429	306	10	κ̇)ρ̃	κ̇)ρ̃	PROPN
ejpam-5429	306	11	∈σ̃	∈σ̃	PROPN
ejpam-5429	306	12	ð̃	ð̃	PROPN
ejpam-5429	306	13	and	and	CCONJ
ejpam-5429	306	14	κ̇ρ̃	κ̇ρ̃	PROPN
ejpam-5429	306	15	∈σ̃	∈σ̃	PROPN
ejpam-5429	306	16	ð̃.	ð̃.	PROPN
ejpam-5429	306	17	but	but	CCONJ
ejpam-5429	306	18	(	(	PUNCT
ejpam-5429	306	19	ς̇	ς̇	NOUN
ejpam-5429	306	20	≬	≬	PROPN
ejpam-5429	306	21	(	(	PUNCT
ejpam-5429	306	22	ϱ̇	ϱ̇	PROPN
ejpam-5429	306	23	≬	≬	PROPN
ejpam-5429	306	24	(	(	PUNCT
ejpam-5429	306	25	ϱ̇	ϱ̇	PROPN
ejpam-5429	306	26	≬	≬	PROPN
ejpam-5429	306	27	ς̇)))ρ̃∈σ̃	ς̇)))ρ̃∈σ̃	NOUN
ejpam-5429	306	28	∨	∨	PROPN
ejpam-5429	306	29	∈σ̃ð̃	∈σ̃ð̃	PROPN
ejpam-5429	306	30	,	,	PUNCT
ejpam-5429	306	31	a	a	DET
ejpam-5429	306	32	contradiction	contradiction	NOUN
ejpam-5429	306	33	.	.	PUNCT
ejpam-5429	307	1	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	307	2	≬	≬	PROPN
ejpam-5429	307	3	(	(	PUNCT
ejpam-5429	307	4	ϱ̇	ϱ̇	PROPN
ejpam-5429	307	5	≬	≬	PROPN
ejpam-5429	307	6	(	(	PUNCT
ejpam-5429	307	7	ϱ̇	ϱ̇	PROPN
ejpam-5429	307	8	≬	≬	PROPN
ejpam-5429	307	9	ς̇	ς̇	NOUN
ejpam-5429	307	10	)	)	PUNCT
ejpam-5429	307	11	)	)	PUNCT
ejpam-5429	307	12	)	)	PUNCT
ejpam-5429	308	1	∨	∨	NUM
ejpam-5429	308	2	σ̃	σ̃	PROPN
ejpam-5429	308	3	≥	≥	NOUN
ejpam-5429	308	4	ð̃((ς̇	ð̃((ς̇	X
ejpam-5429	309	1	≬	≬	PROPN
ejpam-5429	309	2	ϱ̇	ϱ̇	PROPN
ejpam-5429	309	3	)	)	PUNCT
ejpam-5429	309	4	≬	≬	PROPN
ejpam-5429	309	5	κ̇	κ̇	PROPN
ejpam-5429	309	6	)	)	PUNCT
ejpam-5429	309	7	∧	∧	PROPN
ejpam-5429	309	8	ð̃(κ̇	ð̃(κ̇	PROPN
ejpam-5429	309	9	)	)	PUNCT
ejpam-5429	309	10	∧	∧	PROPN
ejpam-5429	309	11	τ̃	τ̃	PROPN
ejpam-5429	309	12	.	.	PUNCT
ejpam-5429	310	1	(	(	PUNCT
ejpam-5429	310	2	2	2	X
ejpam-5429	310	3	)	)	PUNCT
ejpam-5429	310	4	⇒	⇒	NOUN
ejpam-5429	310	5	(	(	PUNCT
ejpam-5429	310	6	1	1	X
ejpam-5429	310	7	)	)	PUNCT
ejpam-5429	310	8	let	let	VERB
ejpam-5429	310	9	(	(	PUNCT
ejpam-5429	310	10	(	(	PUNCT
ejpam-5429	310	11	ς̇	ς̇	PROPN
ejpam-5429	310	12	≬	≬	PROPN
ejpam-5429	310	13	ϱ̇	ϱ̇	PROPN
ejpam-5429	310	14	)	)	PUNCT
ejpam-5429	310	15	≬	≬	PROPN
ejpam-5429	310	16	κ̇)ρ̃	κ̇)ρ̃	PROPN
ejpam-5429	310	17	∈σ̃	∈σ̃	PROPN
ejpam-5429	310	18	ð̃	ð̃	PROPN
ejpam-5429	310	19	,	,	PUNCT
ejpam-5429	310	20	κ̇η̃	κ̇η̃	PROPN
ejpam-5429	310	21	∈σ̃	∈σ̃	PROPN
ejpam-5429	311	1	ð̃.	ð̃.	PROPN
ejpam-5429	311	2	then	then	ADV
ejpam-5429	311	3	,	,	PUNCT
ejpam-5429	311	4	ð̃((ς̇	ð̃((ς̇	VERB
ejpam-5429	311	5	≬	≬	PROPN
ejpam-5429	311	6	ϱ̇	ϱ̇	PROPN
ejpam-5429	311	7	)	)	PUNCT
ejpam-5429	311	8	≬	≬	PROPN
ejpam-5429	311	9	κ̇	κ̇	PROPN
ejpam-5429	311	10	)	)	PUNCT
ejpam-5429	311	11	≥	≥	NOUN
ejpam-5429	311	12	ρ̃	ρ̃	PROPN
ejpam-5429	311	13	>	>	SYM
ejpam-5429	311	14	σ̃	σ̃	PROPN
ejpam-5429	311	15	and	and	CCONJ
ejpam-5429	311	16	ð̃(κ̇	ð̃(κ̇	PROPN
ejpam-5429	311	17	)	)	PUNCT
ejpam-5429	311	18	≥	≥	NOUN
ejpam-5429	312	1	η̃	η̃	PROPN
ejpam-5429	312	2	>	>	X
ejpam-5429	312	3	σ̃.	σ̃.	PROPN
ejpam-5429	312	4	if	if	SCONJ
ejpam-5429	312	5	(	(	PUNCT
ejpam-5429	312	6	ς̇	ς̇	NOUN
ejpam-5429	312	7	≬	≬	PROPN
ejpam-5429	312	8	(	(	PUNCT
ejpam-5429	312	9	ϱ̇	ϱ̇	PROPN
ejpam-5429	312	10	≬	≬	PROPN
ejpam-5429	312	11	(	(	PUNCT
ejpam-5429	312	12	ϱ̇	ϱ̇	PROPN
ejpam-5429	312	13	≬	≬	PROPN
ejpam-5429	312	14	ς̇)))ρ̃∧η̃	ς̇)))ρ̃∧η̃	VERB
ejpam-5429	312	15	∈σ̃	∈σ̃	PROPN
ejpam-5429	312	16	,	,	PUNCT
ejpam-5429	312	17	then	then	ADV
ejpam-5429	312	18	(	(	PUNCT
ejpam-5429	312	19	1	1	X
ejpam-5429	312	20	)	)	PUNCT
ejpam-5429	312	21	is	be	AUX
ejpam-5429	312	22	hold	hold	ADJ
ejpam-5429	312	23	.	.	PUNCT
ejpam-5429	313	1	if	if	SCONJ
ejpam-5429	313	2	(	(	PUNCT
ejpam-5429	313	3	ς̇	ς̇	NOUN
ejpam-5429	313	4	≬	≬	PROPN
ejpam-5429	313	5	(	(	PUNCT
ejpam-5429	313	6	ϱ̇	ϱ̇	PROPN
ejpam-5429	313	7	≬	≬	PROPN
ejpam-5429	313	8	(	(	PUNCT
ejpam-5429	313	9	ϱ̇	ϱ̇	PROPN
ejpam-5429	313	10	≬	≬	PROPN
ejpam-5429	313	11	ς̇)))ρ̃∧η̃	ς̇)))ρ̃∧η̃	VERB
ejpam-5429	313	12	∈σ̃	∈σ̃	PROPN
ejpam-5429	313	13	ð̃	ð̃	PROPN
ejpam-5429	313	14	,	,	PUNCT
ejpam-5429	313	15	then	then	ADV
ejpam-5429	313	16	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	313	17	≬	≬	PROPN
ejpam-5429	313	18	(	(	PUNCT
ejpam-5429	313	19	ϱ̇	ϱ̇	PROPN
ejpam-5429	313	20	≬	≬	PROPN
ejpam-5429	313	21	(	(	PUNCT
ejpam-5429	313	22	ϱ̇	ϱ̇	PROPN
ejpam-5429	313	23	≬	≬	PROPN
ejpam-5429	313	24	ς̇	ς̇	NOUN
ejpam-5429	313	25	)	)	PUNCT
ejpam-5429	313	26	)	)	PUNCT
ejpam-5429	313	27	)	)	PUNCT
ejpam-5429	314	1	<	<	X
ejpam-5429	314	2	ρ̃	ρ̃	PROPN
ejpam-5429	314	3	∧	∧	PROPN
ejpam-5429	314	4	η̃.	η̃.	PROPN
ejpam-5429	314	5	since	since	SCONJ
ejpam-5429	314	6	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	314	7	≬	≬	PROPN
ejpam-5429	314	8	(	(	PUNCT
ejpam-5429	314	9	ϱ̇	ϱ̇	PROPN
ejpam-5429	314	10	≬	≬	PROPN
ejpam-5429	314	11	(	(	PUNCT
ejpam-5429	314	12	ϱ̇	ϱ̇	PROPN
ejpam-5429	314	13	≬	≬	PROPN
ejpam-5429	314	14	ς̇	ς̇	NOUN
ejpam-5429	314	15	)	)	PUNCT
ejpam-5429	314	16	)	)	PUNCT
ejpam-5429	314	17	)	)	PUNCT
ejpam-5429	314	18	∨	∨	NUM
ejpam-5429	315	1	σ̃	σ̃	PROPN
ejpam-5429	315	2	≥	≥	NOUN
ejpam-5429	315	3	ð̃(ς̇	ð̃(ς̇	NOUN
ejpam-5429	315	4	)	)	PUNCT
ejpam-5429	315	5	∧	∧	NOUN
ejpam-5429	315	6	ð̃(ϱ̇	ð̃(ϱ̇	NOUN
ejpam-5429	315	7	)	)	PUNCT
ejpam-5429	315	8	∧	∧	PROPN
ejpam-5429	315	9	τ̃	τ̃	PROPN
ejpam-5429	315	10	≥	≥	NOUN
ejpam-5429	315	11	ρ̃	ρ̃	PROPN
ejpam-5429	315	12	∧	∧	NOUN
ejpam-5429	315	13	ϖ̃	ϖ̃	PROPN
ejpam-5429	315	14	∧	∧	PROPN
ejpam-5429	315	15	τ̃	τ̃	PROPN
ejpam-5429	315	16	.	.	PUNCT
ejpam-5429	316	1	therefore	therefore	ADV
ejpam-5429	316	2	,	,	PUNCT
ejpam-5429	316	3	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	316	4	≬	≬	PROPN
ejpam-5429	316	5	(	(	PUNCT
ejpam-5429	316	6	ϱ̇	ϱ̇	PROPN
ejpam-5429	316	7	≬	≬	PROPN
ejpam-5429	316	8	(	(	PUNCT
ejpam-5429	316	9	ϱ̇	ϱ̇	PROPN
ejpam-5429	316	10	≬	≬	PROPN
ejpam-5429	316	11	ς̇	ς̇	NOUN
ejpam-5429	316	12	)	)	PUNCT
ejpam-5429	316	13	)	)	PUNCT
ejpam-5429	316	14	)	)	PUNCT
ejpam-5429	316	15	≥	≥	PRON
ejpam-5429	316	16	τ̃	τ̃	NOUN
ejpam-5429	316	17	and	and	CCONJ
ejpam-5429	316	18	ρ̃	ρ̃	PROPN
ejpam-5429	316	19	∧	∧	PROPN
ejpam-5429	316	20	ϖ̃	ϖ̃	PROPN
ejpam-5429	316	21	>	>	X
ejpam-5429	316	22	τ̃	τ̃	PROPN
ejpam-5429	316	23	.	.	PUNCT
ejpam-5429	317	1	thus	thus	ADV
ejpam-5429	317	2	,	,	PUNCT
ejpam-5429	317	3	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	317	4	≬	≬	PROPN
ejpam-5429	317	5	(	(	PUNCT
ejpam-5429	317	6	ϱ̇	ϱ̇	PROPN
ejpam-5429	317	7	≬	≬	PROPN
ejpam-5429	317	8	(	(	PUNCT
ejpam-5429	317	9	ϱ̇	ϱ̇	PROPN
ejpam-5429	317	10	≬	≬	PROPN
ejpam-5429	317	11	ς̇	ς̇	NOUN
ejpam-5429	317	12	)	)	PUNCT
ejpam-5429	317	13	)	)	PUNCT
ejpam-5429	317	14	)	)	PUNCT
ejpam-5429	318	1	+	+	CCONJ
ejpam-5429	318	2	ρ̃	ρ̃	PROPN
ejpam-5429	318	3	∧	∧	PROPN
ejpam-5429	318	4	η̃	η̃	PROPN
ejpam-5429	318	5	>	>	X
ejpam-5429	318	6	τ̃	τ̃	PROPN
ejpam-5429	319	1	+	+	PUNCT
ejpam-5429	319	2	τ̃	τ̃	ADJ
ejpam-5429	319	3	=	=	SYM
ejpam-5429	319	4	2τ̃	2τ̃	ADJ
ejpam-5429	319	5	⇒	⇒	NOUN
ejpam-5429	319	6	(	(	PUNCT
ejpam-5429	319	7	ς̇	ς̇	NOUN
ejpam-5429	319	8	≬	≬	PROPN
ejpam-5429	319	9	(	(	PUNCT
ejpam-5429	319	10	ϱ̇	ϱ̇	PROPN
ejpam-5429	319	11	≬	≬	PROPN
ejpam-5429	319	12	(	(	PUNCT
ejpam-5429	319	13	ϱ̇	ϱ̇	PROPN
ejpam-5429	319	14	≬	≬	PROPN
ejpam-5429	319	15	ς̇)))ρ̃∧η̃qτ̃	ς̇)))ρ̃∧η̃qτ̃	PROPN
ejpam-5429	319	16	ð̃.	ð̃.	NOUN
ejpam-5429	319	17	hence	hence	ADV
ejpam-5429	319	18	,	,	PUNCT
ejpam-5429	319	19	(	(	PUNCT
ejpam-5429	319	20	ς̇	ς̇	PROPN
ejpam-5429	319	21	≬	≬	PROPN
ejpam-5429	319	22	(	(	PUNCT
ejpam-5429	319	23	ϱ̇	ϱ̇	PROPN
ejpam-5429	319	24	≬	≬	PROPN
ejpam-5429	319	25	(	(	PUNCT
ejpam-5429	319	26	ϱ̇	ϱ̇	PROPN
ejpam-5429	319	27	≬	≬	PROPN
ejpam-5429	319	28	ς̇)))ρ̃∧η̃	ς̇)))ρ̃∧η̃	VERB
ejpam-5429	319	29	∈σ̃	∈σ̃	PROPN
ejpam-5429	319	30	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	319	31	ð̃.	ð̃.	NOUN
ejpam-5429	319	32	corollary	corollary	ADJ
ejpam-5429	319	33	4	4	NUM
ejpam-5429	319	34	.	.	PUNCT
ejpam-5429	320	1	a	a	DET
ejpam-5429	320	2	qp	qp	PROPN
ejpam-5429	320	3	-	-	PUNCT
ejpam-5429	320	4	f	f	NOUN
ejpam-5429	320	5	set	set	NOUN
ejpam-5429	320	6	ð̃	ð̃	PROPN
ejpam-5429	320	7	of	of	ADP
ejpam-5429	320	8	ℵ̃	ℵ̃	PROPN
ejpam-5429	320	9	is	be	AUX
ejpam-5429	320	10	a	a	DET
ejpam-5429	320	11	qp-(∈σ̃,∈σ̃	qp-(∈σ̃,∈σ̃	NOUN
ejpam-5429	320	12	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	320	13	)	)	PUNCT
ejpam-5429	320	14	-ffi	-ffi	PROPN
ejpam-5429	320	15	of	of	ADP
ejpam-5429	320	16	ℵ̃	ℵ̃	PROPN
ejpam-5429	320	17	if	if	SCONJ
ejpam-5429	320	18	it	it	PRON
ejpam-5429	320	19	satisfies	satisfy	VERB
ejpam-5429	320	20	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	320	21	≬	≬	PROPN
ejpam-5429	320	22	(	(	PUNCT
ejpam-5429	320	23	ϱ̇	ϱ̇	PROPN
ejpam-5429	320	24	≬	≬	PROPN
ejpam-5429	320	25	(	(	PUNCT
ejpam-5429	320	26	ϱ̇	ϱ̇	PROPN
ejpam-5429	320	27	≬	≬	PROPN
ejpam-5429	320	28	ς̇	ς̇	NOUN
ejpam-5429	320	29	)	)	PUNCT
ejpam-5429	320	30	)	)	PUNCT
ejpam-5429	320	31	)	)	PUNCT
ejpam-5429	321	1	∨	∨	NUM
ejpam-5429	321	2	σ̃	σ̃	PROPN
ejpam-5429	321	3	≥	≥	NOUN
ejpam-5429	321	4	ð̃((ς̇	ð̃((ς̇	X
ejpam-5429	322	1	≬	≬	PROPN
ejpam-5429	322	2	ϱ̇	ϱ̇	PROPN
ejpam-5429	322	3	)	)	PUNCT
ejpam-5429	322	4	≬	≬	PROPN
ejpam-5429	322	5	κ̇	κ̇	PROPN
ejpam-5429	322	6	)	)	PUNCT
ejpam-5429	322	7	∧	∧	PROPN
ejpam-5429	322	8	ð̃(κ̇	ð̃(κ̇	PROPN
ejpam-5429	322	9	)	)	PUNCT
ejpam-5429	322	10	,	,	PUNCT
ejpam-5429	322	11	τ̃	τ̃	PROPN
ejpam-5429	322	12	,	,	PUNCT
ejpam-5429	322	13	∀ς̇	∀ς̇	PROPN
ejpam-5429	322	14	,	,	PUNCT
ejpam-5429	322	15	ϱ̇	ϱ̇	PROPN
ejpam-5429	322	16	∈	∈	PROPN
ejpam-5429	322	17	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	322	18	theorem	theorem	VERB
ejpam-5429	322	19	11	11	NUM
ejpam-5429	322	20	.	.	PUNCT
ejpam-5429	323	1	the	the	DET
ejpam-5429	323	2	intersection	intersection	NOUN
ejpam-5429	323	3	of	of	ADP
ejpam-5429	323	4	any	any	DET
ejpam-5429	323	5	collection	collection	NOUN
ejpam-5429	323	6	of	of	ADP
ejpam-5429	323	7	qp-(∈σ̃,∈σ̃	qp-(∈σ̃,∈σ̃	PROPN
ejpam-5429	323	8	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	323	9	)	)	PUNCT
ejpam-5429	323	10	-ffis	-ffis	NOUN
ejpam-5429	323	11	of	of	ADP
ejpam-5429	323	12	ℵ̃	ℵ̃	PROPN
ejpam-5429	323	13	is	be	AUX
ejpam-5429	323	14	a	a	DET
ejpam-5429	323	15	qp-(∈σ̃,∈σ̃	qp-(∈σ̃,∈σ̃	NOUN
ejpam-5429	323	16	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	323	17	)	)	PUNCT
ejpam-5429	323	18	-ffi	-ffi	PROPN
ejpam-5429	323	19	of	of	ADP
ejpam-5429	323	20	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	323	21	proof	proof	NOUN
ejpam-5429	323	22	.	.	PUNCT
ejpam-5429	324	1	let	let	VERB
ejpam-5429	324	2	{	{	PUNCT
ejpam-5429	324	3	ð̃i}i∈i	ð̃i}i∈i	INTJ
ejpam-5429	324	4	be	be	AUX
ejpam-5429	324	5	a	a	DET
ejpam-5429	324	6	collection	collection	NOUN
ejpam-5429	324	7	of	of	ADP
ejpam-5429	324	8	qp-(∈σ̃,∈σ̃	qp-(∈σ̃,∈σ̃	PROPN
ejpam-5429	324	9	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	324	10	)	)	PUNCT
ejpam-5429	324	11	-ffis	-ffis	NOUN
ejpam-5429	324	12	of	of	ADP
ejpam-5429	324	13	ℵ̃	ℵ̃	PROPN
ejpam-5429	324	14	and	and	CCONJ
ejpam-5429	324	15	(	(	PUNCT
ejpam-5429	324	16	ς̇	ς̇	PROPN
ejpam-5429	324	17	≬	≬	PROPN
ejpam-5429	324	18	ϱ̇	ϱ̇	NUM
ejpam-5429	324	19	)	)	PUNCT
ejpam-5429	324	20	≬	≬	PROPN
ejpam-5429	324	21	κ̇	κ̇	PROPN
ejpam-5429	324	22	,	,	PUNCT
ejpam-5429	324	23	κ̇	κ̇	PROPN
ejpam-5429	324	24	∈	∈	PROPN
ejpam-5429	324	25	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	324	26	then	then	ADV
ejpam-5429	324	27	,	,	PUNCT
ejpam-5429	324	28	ð̃i(ς̇	ð̃i(ς̇	CCONJ
ejpam-5429	324	29	≬	≬	PROPN
ejpam-5429	324	30	(	(	PUNCT
ejpam-5429	324	31	ϱ̇	ϱ̇	PROPN
ejpam-5429	324	32	≬	≬	PROPN
ejpam-5429	324	33	(	(	PUNCT
ejpam-5429	324	34	ϱ̇	ϱ̇	PROPN
ejpam-5429	324	35	≬	≬	PROPN
ejpam-5429	324	36	ς̇	ς̇	NOUN
ejpam-5429	324	37	)	)	PUNCT
ejpam-5429	324	38	)	)	PUNCT
ejpam-5429	324	39	)	)	PUNCT
ejpam-5429	325	1	∨	∨	NUM
ejpam-5429	326	1	σ̃	σ̃	PROPN
ejpam-5429	326	2	≥	≥	NOUN
ejpam-5429	326	3	ð̃i((ς̇	ð̃i((ς̇	PROPN
ejpam-5429	326	4	≬	≬	PROPN
ejpam-5429	326	5	ϱ̇)κ̇	ϱ̇)κ̇	NOUN
ejpam-5429	326	6	)	)	PUNCT
ejpam-5429	326	7	∧	∧	PROPN
ejpam-5429	326	8	ð̃i(κ̇	ð̃i(κ̇	NOUN
ejpam-5429	326	9	)	)	PUNCT
ejpam-5429	326	10	∧	∧	PROPN
ejpam-5429	326	11	τ̃	τ̃	PROPN
ejpam-5429	326	12	.	.	PUNCT
ejpam-5429	327	1	thus	thus	ADV
ejpam-5429	327	2	,	,	PUNCT
ejpam-5429	327	3	(	(	PUNCT
ejpam-5429	327	4	∧i∈i	∧i∈i	X
ejpam-5429	327	5	ð̃i)(ς̇	ð̃i)(ς̇	VERB
ejpam-5429	327	6	≬	≬	PROPN
ejpam-5429	327	7	(	(	PUNCT
ejpam-5429	327	8	ϱ̇	ϱ̇	PROPN
ejpam-5429	327	9	≬	≬	PROPN
ejpam-5429	327	10	(	(	PUNCT
ejpam-5429	327	11	ϱ̇	ϱ̇	PROPN
ejpam-5429	327	12	≬	≬	PROPN
ejpam-5429	327	13	ς̇	ς̇	NOUN
ejpam-5429	327	14	)	)	PUNCT
ejpam-5429	327	15	)	)	PUNCT
ejpam-5429	327	16	)	)	PUNCT
ejpam-5429	328	1	∨	∨	NUM
ejpam-5429	329	1	σ̃	σ̃	NOUN
ejpam-5429	329	2	=	=	PUNCT
ejpam-5429	329	3	∧i∈i	∧i∈i	NOUN
ejpam-5429	329	4	ð̃i(ς̇	ð̃i(ς̇	ADP
ejpam-5429	329	5	≬	≬	PROPN
ejpam-5429	329	6	(	(	PUNCT
ejpam-5429	329	7	ϱ̇	ϱ̇	PROPN
ejpam-5429	329	8	≬	≬	PROPN
ejpam-5429	329	9	(	(	PUNCT
ejpam-5429	329	10	ϱ̇	ϱ̇	PROPN
ejpam-5429	329	11	≬	≬	PROPN
ejpam-5429	329	12	ς̇	ς̇	NOUN
ejpam-5429	329	13	)	)	PUNCT
ejpam-5429	329	14	)	)	PUNCT
ejpam-5429	329	15	)	)	PUNCT
ejpam-5429	330	1	∨	∨	NUM
ejpam-5429	330	2	σ̃	σ̃	PROPN
ejpam-5429	330	3	≥	≥	NOUN
ejpam-5429	330	4	∧i∈i(ð̃i((ς̇	∧i∈i(ð̃i((ς̇	NUM
ejpam-5429	330	5	≬	≬	PROPN
ejpam-5429	330	6	ϱ̇	ϱ̇	PROPN
ejpam-5429	330	7	)	)	PUNCT
ejpam-5429	330	8	≬	≬	PROPN
ejpam-5429	330	9	κ̇	κ̇	PROPN
ejpam-5429	330	10	)	)	PUNCT
ejpam-5429	330	11	∧	∧	PROPN
ejpam-5429	330	12	ð̃i(κ̇	ð̃i(κ̇	NOUN
ejpam-5429	330	13	)	)	PUNCT
ejpam-5429	330	14	∧	∧	PROPN
ejpam-5429	330	15	τ̃	τ̃	PROPN
ejpam-5429	330	16	)	)	PUNCT
ejpam-5429	330	17	≥	≥	NOUN
ejpam-5429	330	18	(	(	PUNCT
ejpam-5429	330	19	∧i∈i	∧i∈i	X
ejpam-5429	330	20	ð̃j)((ς̇	ð̃j)((ς̇	PUNCT
ejpam-5429	330	21	≬	≬	PROPN
ejpam-5429	330	22	ϱ̇	ϱ̇	PROPN
ejpam-5429	330	23	)	)	PUNCT
ejpam-5429	330	24	≬	≬	PROPN
ejpam-5429	330	25	κ̇	κ̇	PROPN
ejpam-5429	330	26	)	)	PUNCT
ejpam-5429	330	27	∧	∧	PROPN
ejpam-5429	330	28	(	(	PUNCT
ejpam-5429	330	29	∧i∈i	∧i∈i	NUM
ejpam-5429	330	30	ð̃i)(κ̇	ð̃i)(κ̇	NOUN
ejpam-5429	330	31	)	)	PUNCT
ejpam-5429	330	32	∧	∧	PROPN
ejpam-5429	330	33	τ̃	τ̃	PROPN
ejpam-5429	330	34	.	.	PUNCT
ejpam-5429	331	1	k.	k.	PROPN
ejpam-5429	331	2	h.	h.	PROPN
ejpam-5429	331	3	hakami	hakami	PROPN
ejpam-5429	331	4	et	et	PROPN
ejpam-5429	331	5	al	al	PROPN
ejpam-5429	331	6	.	.	PUNCT
ejpam-5429	331	7	/	/	SYM
ejpam-5429	331	8	eur	eur	PROPN
ejpam-5429	331	9	.	.	PUNCT
ejpam-5429	332	1	j.	j.	PROPN
ejpam-5429	332	2	pure	pure	PROPN
ejpam-5429	332	3	appl	appl	PROPN
ejpam-5429	332	4	.	.	PROPN
ejpam-5429	332	5	math	math	PROPN
ejpam-5429	332	6	,	,	PUNCT
ejpam-5429	332	7	17	17	NUM
ejpam-5429	332	8	(	(	PUNCT
ejpam-5429	332	9	4	4	NUM
ejpam-5429	332	10	)	)	PUNCT
ejpam-5429	332	11	(	(	PUNCT
ejpam-5429	332	12	2024	2024	NUM
ejpam-5429	332	13	)	)	PUNCT
ejpam-5429	332	14	,	,	PUNCT
ejpam-5429	332	15	3129	3129	NUM
ejpam-5429	332	16	-	-	SYM
ejpam-5429	332	17	3155	3155	NUM
ejpam-5429	332	18	3140	3140	NUM
ejpam-5429	332	19	therefore	therefore	ADV
ejpam-5429	332	20	,	,	PUNCT
ejpam-5429	332	21	(	(	PUNCT
ejpam-5429	332	22	∧i∈i	∧i∈i	X
ejpam-5429	332	23	ð̃i)(ς̇	ð̃i)(ς̇	VERB
ejpam-5429	332	24	≬	≬	PROPN
ejpam-5429	332	25	(	(	PUNCT
ejpam-5429	332	26	ϱ̇	ϱ̇	PROPN
ejpam-5429	332	27	≬	≬	PROPN
ejpam-5429	332	28	(	(	PUNCT
ejpam-5429	332	29	ϱ̇	ϱ̇	PROPN
ejpam-5429	332	30	≬	≬	PROPN
ejpam-5429	332	31	ς̇	ς̇	NOUN
ejpam-5429	332	32	)	)	PUNCT
ejpam-5429	332	33	)	)	PUNCT
ejpam-5429	332	34	)	)	PUNCT
ejpam-5429	333	1	∨	∨	NUM
ejpam-5429	334	1	σ̃	σ̃	PROPN
ejpam-5429	334	2	≥	≥	NUM
ejpam-5429	334	3	(	(	PUNCT
ejpam-5429	334	4	∧i∈i	∧i∈i	X
ejpam-5429	334	5	ð̃i)((ς̇	ð̃i)((ς̇	PUNCT
ejpam-5429	334	6	≬	≬	PROPN
ejpam-5429	334	7	ϱ̇	ϱ̇	PROPN
ejpam-5429	334	8	)	)	PUNCT
ejpam-5429	334	9	≬	≬	PROPN
ejpam-5429	334	10	κ̇	κ̇	PROPN
ejpam-5429	334	11	)	)	PUNCT
ejpam-5429	334	12	∧	∧	PROPN
ejpam-5429	334	13	(	(	PUNCT
ejpam-5429	334	14	∧i∈i	∧i∈i	NUM
ejpam-5429	334	15	ð̃i)(κ̇	ð̃i)(κ̇	NOUN
ejpam-5429	334	16	)	)	PUNCT
ejpam-5429	334	17	∧	∧	PROPN
ejpam-5429	334	18	τ̃	τ̃	PROPN
ejpam-5429	334	19	.	.	PUNCT
ejpam-5429	335	1	hence	hence	ADV
ejpam-5429	335	2	,	,	PUNCT
ejpam-5429	335	3	∧i∈i	∧i∈i	NOUN
ejpam-5429	335	4	ð̃i	ð̃i	NOUN
ejpam-5429	335	5	is	be	AUX
ejpam-5429	335	6	a	a	DET
ejpam-5429	335	7	qp-(∈σ̃,∈σ̃	qp-(∈σ̃,∈σ̃	PROPN
ejpam-5429	335	8	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	335	9	)	)	PUNCT
ejpam-5429	335	10	ffi	ffi	PROPN
ejpam-5429	335	11	of	of	ADP
ejpam-5429	335	12	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	335	13	for	for	ADP
ejpam-5429	335	14	any	any	DET
ejpam-5429	335	15	qp	qp	PROPN
ejpam-5429	335	16	-	-	PUNCT
ejpam-5429	335	17	f	f	NOUN
ejpam-5429	335	18	set	set	NOUN
ejpam-5429	335	19	ð̃	ð̃	PROPN
ejpam-5429	335	20	of	of	ADP
ejpam-5429	335	21	ℵ̃	ℵ̃	PROPN
ejpam-5429	335	22	and	and	CCONJ
ejpam-5429	335	23	ρ̃	ρ̃	PROPN
ejpam-5429	335	24	∈	∈	PROPN
ejpam-5429	336	1	[	[	X
ejpam-5429	336	2	0	0	NUM
ejpam-5429	336	3	,	,	PUNCT
ejpam-5429	336	4	1]q	1]q	NUM
ejpam-5429	336	5	,	,	PUNCT
ejpam-5429	336	6	we	we	PRON
ejpam-5429	336	7	define	define	VERB
ejpam-5429	336	8	:	:	PUNCT
ejpam-5429	336	9	(	(	PUNCT
ejpam-5429	336	10	1	1	X
ejpam-5429	336	11	)	)	PUNCT
ejpam-5429	336	12	ð̃σ̃ρ̃	ð̃σ̃ρ̃	PROPN
ejpam-5429	337	1	=	=	PUNCT
ejpam-5429	337	2	{	{	PUNCT
ejpam-5429	337	3	ς̇	ς̇	NOUN
ejpam-5429	337	4	∈	∈	PROPN
ejpam-5429	337	5	ℵ̃	ℵ̃	PROPN
ejpam-5429	337	6	|	|	NOUN
ejpam-5429	337	7	ς̇ρ̃	ς̇ρ̃	NOUN
ejpam-5429	337	8	∈σ̃	∈σ̃	PUNCT
ejpam-5429	337	9	ð̃	ð̃	PROPN
ejpam-5429	337	10	}	}	PUNCT
ejpam-5429	337	11	,	,	PUNCT
ejpam-5429	337	12	(	(	PUNCT
ejpam-5429	337	13	2	2	X
ejpam-5429	337	14	)	)	PUNCT
ejpam-5429	337	15	⟨ð̃⟩τ̃ρ̃	⟨ð̃⟩τ̃ρ̃	PROPN
ejpam-5429	337	16	=	=	PUNCT
ejpam-5429	337	17	{	{	PUNCT
ejpam-5429	337	18	ς̇	ς̇	NOUN
ejpam-5429	337	19	∈	∈	PROPN
ejpam-5429	337	20	ℵ̃	ℵ̃	PROPN
ejpam-5429	337	21	|	|	NOUN
ejpam-5429	337	22	ς̇ρ̃qτ̃	ς̇ρ̃qτ̃	PROPN
ejpam-5429	337	23	ð̃	ð̃	PROPN
ejpam-5429	337	24	}	}	PUNCT
ejpam-5429	337	25	,	,	PUNCT
ejpam-5429	337	26	(	(	PUNCT
ejpam-5429	337	27	3	3	X
ejpam-5429	337	28	)	)	PUNCT
ejpam-5429	337	29	[	[	X
ejpam-5429	337	30	ð̃]τ̃ρ̃	ð̃]τ̃ρ̃	X
ejpam-5429	337	31	=	=	SYM
ejpam-5429	337	32	{	{	PUNCT
ejpam-5429	337	33	ς̇	ς̇	NOUN
ejpam-5429	337	34	∈	∈	PROPN
ejpam-5429	337	35	ℵ̃	ℵ̃	PROPN
ejpam-5429	337	36	|	|	NOUN
ejpam-5429	337	37	ς̇ρ̃	ς̇ρ̃	PROPN
ejpam-5429	337	38	∈σ̃	∈σ̃	VERB
ejpam-5429	337	39	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	337	40	ð̃	ð̃	PROPN
ejpam-5429	337	41	}	}	PUNCT
ejpam-5429	337	42	.	.	PUNCT
ejpam-5429	338	1	it	it	PRON
ejpam-5429	338	2	is	be	AUX
ejpam-5429	338	3	clear	clear	ADJ
ejpam-5429	338	4	that	that	SCONJ
ejpam-5429	338	5	[	[	X
ejpam-5429	338	6	ð̃]τ̃ρ̃	ð̃]τ̃ρ̃	X
ejpam-5429	338	7	=	=	PUNCT
ejpam-5429	338	8	ð̃σ̃ρ̃	ð̃σ̃ρ̃	PROPN
ejpam-5429	338	9	∪	∪	X
ejpam-5429	338	10	⟨ð̃⟩τ̃ρ̃.	⟨ð̃⟩τ̃ρ̃.	VERB
ejpam-5429	338	11	the	the	DET
ejpam-5429	338	12	ensuing	ensue	VERB
ejpam-5429	338	13	theorems	theorem	NOUN
ejpam-5429	338	14	elucidate	elucidate	VERB
ejpam-5429	338	15	the	the	DET
ejpam-5429	338	16	connection	connection	NOUN
ejpam-5429	338	17	between	between	ADP
ejpam-5429	338	18	qp-(∈σ̃,∈σ̃	qp-(∈σ̃,∈σ̃	PROPN
ejpam-5429	338	19	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	338	20	)	)	PUNCT
ejpam-5429	338	21	-ffis	-ffis	PROPN
ejpam-5429	338	22	and	and	CCONJ
ejpam-5429	338	23	the	the	DET
ejpam-5429	338	24	crisp	crisp	ADJ
ejpam-5429	338	25	fis	fis	NOUN
ejpam-5429	338	26	in	in	ADP
ejpam-5429	338	27	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	338	28	theorem	theorem	NOUN
ejpam-5429	338	29	12	12	NUM
ejpam-5429	338	30	.	.	PUNCT
ejpam-5429	339	1	let	let	VERB
ejpam-5429	339	2	ð̃	ð̃	PRON
ejpam-5429	339	3	be	be	AUX
ejpam-5429	339	4	a	a	DET
ejpam-5429	339	5	qp	qp	PROPN
ejpam-5429	339	6	-	-	PUNCT
ejpam-5429	339	7	f	f	PROPN
ejpam-5429	339	8	set	set	NOUN
ejpam-5429	339	9	of	of	ADP
ejpam-5429	339	10	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	339	11	then	then	ADV
ejpam-5429	339	12	,	,	PUNCT
ejpam-5429	339	13	ð̃	ð̃	PROPN
ejpam-5429	339	14	is	be	AUX
ejpam-5429	339	15	a	a	DET
ejpam-5429	339	16	qp-(∈σ̃,∈σ̃	qp-(∈σ̃,∈σ̃	NOUN
ejpam-5429	339	17	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	339	18	)	)	PUNCT
ejpam-5429	339	19	-ffi	-ffi	PROPN
ejpam-5429	339	20	of	of	ADP
ejpam-5429	339	21	ℵ̃	ℵ̃	PROPN
ejpam-5429	339	22	⇔	⇔	PROPN
ejpam-5429	339	23	ð̃σ̃ρ̃	ð̃σ̃ρ̃	PROPN
ejpam-5429	340	1	̸=	̸=	PROPN
ejpam-5429	340	2	ϕ	ϕ	PROPN
ejpam-5429	340	3	is	be	AUX
ejpam-5429	340	4	a	a	DET
ejpam-5429	340	5	fi	fi	NOUN
ejpam-5429	340	6	of	of	ADP
ejpam-5429	340	7	ℵ̃	ℵ̃	PROPN
ejpam-5429	340	8	,	,	PUNCT
ejpam-5429	340	9	∀σ̃	∀σ̃	PROPN
ejpam-5429	340	10	<	<	X
ejpam-5429	340	11	ρ̃	ρ̃	PROPN
ejpam-5429	340	12	≤	≤	PROPN
ejpam-5429	340	13	τ̃	τ̃	PROPN
ejpam-5429	340	14	.	.	PUNCT
ejpam-5429	341	1	proof	proof	NOUN
ejpam-5429	341	2	.	.	PUNCT
ejpam-5429	342	1	let	let	VERB
ejpam-5429	342	2	ð̃	ð̃	PRON
ejpam-5429	342	3	be	be	AUX
ejpam-5429	342	4	a	a	DET
ejpam-5429	342	5	qp-(∈σ̃,∈σ̃	qp-(∈σ̃,∈σ̃	NOUN
ejpam-5429	342	6	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	342	7	)	)	PUNCT
ejpam-5429	342	8	-ffi	-ffi	PROPN
ejpam-5429	342	9	of	of	ADP
ejpam-5429	342	10	ℵ̃	ℵ̃	PROPN
ejpam-5429	342	11	and	and	CCONJ
ejpam-5429	342	12	let	let	VERB
ejpam-5429	342	13	ς̇	ς̇	NOUN
ejpam-5429	342	14	,	,	PUNCT
ejpam-5429	342	15	ϱ̇	ϱ̇	PROPN
ejpam-5429	342	16	,	,	PUNCT
ejpam-5429	342	17	κ̇	κ̇	PROPN
ejpam-5429	342	18	∈	∈	PROPN
ejpam-5429	342	19	ð̃σ̃ρ̃	ð̃σ̃ρ̃	PROPN
ejpam-5429	342	20	for	for	ADP
ejpam-5429	342	21	σ̃	σ̃	PROPN
ejpam-5429	342	22	<	<	X
ejpam-5429	342	23	ρ̃	ρ̃	PROPN
ejpam-5429	342	24	≤	≤	NOUN
ejpam-5429	342	25	τ̃	τ̃	PROPN
ejpam-5429	342	26	.	.	PUNCT
ejpam-5429	343	1	then	then	ADV
ejpam-5429	343	2	ð̃((ς̇	ð̃((ς̇	X
ejpam-5429	343	3	≬	≬	PROPN
ejpam-5429	343	4	ϱ̇	ϱ̇	PROPN
ejpam-5429	343	5	)	)	PUNCT
ejpam-5429	343	6	≬	≬	PROPN
ejpam-5429	343	7	κ̇	κ̇	PROPN
ejpam-5429	343	8	)	)	PUNCT
ejpam-5429	343	9	≥	≥	NOUN
ejpam-5429	343	10	ρ̃	ρ̃	PROPN
ejpam-5429	343	11	>	>	SYM
ejpam-5429	343	12	σ̃	σ̃	PROPN
ejpam-5429	343	13	and	and	CCONJ
ejpam-5429	343	14	ð̃(κ̇	ð̃(κ̇	PROPN
ejpam-5429	343	15	)	)	PUNCT
ejpam-5429	343	16	≥	≥	NOUN
ejpam-5429	344	1	ρ̃	ρ̃	PROPN
ejpam-5429	344	2	>	>	X
ejpam-5429	344	3	σ̃.	σ̃.	PROPN
ejpam-5429	344	4	thus	thus	ADV
ejpam-5429	344	5	,	,	PUNCT
ejpam-5429	344	6	we	we	PRON
ejpam-5429	344	7	have	have	VERB
ejpam-5429	344	8	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	344	9	≬	≬	PROPN
ejpam-5429	344	10	(	(	PUNCT
ejpam-5429	344	11	ϱ̇	ϱ̇	PROPN
ejpam-5429	344	12	≬	≬	PROPN
ejpam-5429	344	13	(	(	PUNCT
ejpam-5429	344	14	ϱ̇	ϱ̇	PROPN
ejpam-5429	344	15	≬	≬	PROPN
ejpam-5429	344	16	ς̇	ς̇	NOUN
ejpam-5429	344	17	)	)	PUNCT
ejpam-5429	344	18	)	)	PUNCT
ejpam-5429	344	19	)	)	PUNCT
ejpam-5429	345	1	∨	∨	NUM
ejpam-5429	345	2	σ̃	σ̃	PROPN
ejpam-5429	345	3	≥	≥	NOUN
ejpam-5429	345	4	ð̃((ς̇	ð̃((ς̇	X
ejpam-5429	346	1	≬	≬	PROPN
ejpam-5429	346	2	ϱ̇	ϱ̇	PROPN
ejpam-5429	346	3	)	)	PUNCT
ejpam-5429	346	4	≬	≬	PROPN
ejpam-5429	346	5	κ̇	κ̇	PROPN
ejpam-5429	346	6	)	)	PUNCT
ejpam-5429	346	7	∧	∧	PROPN
ejpam-5429	346	8	ð̃(κ̇	ð̃(κ̇	PROPN
ejpam-5429	346	9	)	)	PUNCT
ejpam-5429	346	10	∧	∧	PROPN
ejpam-5429	346	11	τ̃	τ̃	PROPN
ejpam-5429	346	12	≥	≥	NOUN
ejpam-5429	346	13	ρ̃	ρ̃	PROPN
ejpam-5429	346	14	∧	∧	NOUN
ejpam-5429	346	15	ρ̃	ρ̃	PROPN
ejpam-5429	346	16	∧	∧	NOUN
ejpam-5429	346	17	τ̃	τ̃	PROPN
ejpam-5429	346	18	=	=	SYM
ejpam-5429	346	19	ρ̃	ρ̃	PROPN
ejpam-5429	346	20	∧	∧	NOUN
ejpam-5429	346	21	τ̃	τ̃	PROPN
ejpam-5429	346	22	=	=	SYM
ejpam-5429	346	23	ρ̃	ρ̃	PROPN
ejpam-5429	346	24	>	>	X
ejpam-5429	346	25	σ̃.	σ̃.	PROPN
ejpam-5429	346	26	therefore	therefore	ADV
ejpam-5429	346	27	,	,	PUNCT
ejpam-5429	346	28	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	346	29	≬	≬	PROPN
ejpam-5429	346	30	(	(	PUNCT
ejpam-5429	346	31	ϱ̇	ϱ̇	PROPN
ejpam-5429	346	32	≬	≬	PROPN
ejpam-5429	346	33	(	(	PUNCT
ejpam-5429	346	34	ϱ̇	ϱ̇	PROPN
ejpam-5429	346	35	≬	≬	PROPN
ejpam-5429	346	36	ς̇	ς̇	NOUN
ejpam-5429	346	37	)	)	PUNCT
ejpam-5429	346	38	)	)	PUNCT
ejpam-5429	346	39	)	)	PUNCT
ejpam-5429	346	40	≥	≥	PROPN
ejpam-5429	347	1	ρ̃	ρ̃	PROPN
ejpam-5429	347	2	⇒	⇒	NOUN
ejpam-5429	347	3	ς̇	ς̇	NOUN
ejpam-5429	347	4	≬	≬	PROPN
ejpam-5429	347	5	(	(	PUNCT
ejpam-5429	347	6	ϱ̇	ϱ̇	PROPN
ejpam-5429	347	7	≬	≬	PROPN
ejpam-5429	347	8	(	(	PUNCT
ejpam-5429	347	9	ϱ̇	ϱ̇	PROPN
ejpam-5429	347	10	≬	≬	PROPN
ejpam-5429	347	11	ς̇	ς̇	NOUN
ejpam-5429	347	12	)	)	PUNCT
ejpam-5429	347	13	)	)	PUNCT
ejpam-5429	348	1	∈	∈	PROPN
ejpam-5429	348	2	ð̃σ̃ρ̃	ð̃σ̃ρ̃	PROPN
ejpam-5429	348	3	.	.	PUNCT
ejpam-5429	349	1	thus	thus	ADV
ejpam-5429	349	2	,	,	PUNCT
ejpam-5429	349	3	ð̃σ̃ρ̃	ð̃σ̃ρ̃	PROPN
ejpam-5429	349	4	is	be	AUX
ejpam-5429	349	5	a	a	DET
ejpam-5429	349	6	fi	fi	NOUN
ejpam-5429	349	7	of	of	ADP
ejpam-5429	349	8	u.	u.	NOUN
ejpam-5429	349	9	on	on	ADP
ejpam-5429	349	10	the	the	DET
ejpam-5429	349	11	other	other	ADJ
ejpam-5429	349	12	hand	hand	NOUN
ejpam-5429	349	13	,	,	PUNCT
ejpam-5429	349	14	suppose	suppose	VERB
ejpam-5429	349	15	that	that	SCONJ
ejpam-5429	349	16	ð̃σ̃ρ̃	ð̃σ̃ρ̃	PROPN
ejpam-5429	349	17	is	be	AUX
ejpam-5429	349	18	a	a	DET
ejpam-5429	349	19	fi	fi	NOUN
ejpam-5429	349	20	of	of	ADP
ejpam-5429	349	21	u,∀σ̃	u,∀σ̃	NOUN
ejpam-5429	349	22	<	<	X
ejpam-5429	349	23	ρ̃	ρ̃	PROPN
ejpam-5429	349	24	≤	≤	PROPN
ejpam-5429	349	25	τ̃	τ̃	PROPN
ejpam-5429	349	26	.	.	PUNCT
ejpam-5429	350	1	assume	assume	VERB
ejpam-5429	350	2	ς̇	ς̇	PROPN
ejpam-5429	350	3	,	,	PUNCT
ejpam-5429	350	4	ϱ̇	ϱ̇	PROPN
ejpam-5429	350	5	,	,	PUNCT
ejpam-5429	350	6	κ̇	κ̇	PROPN
ejpam-5429	350	7	∈	∈	PROPN
ejpam-5429	350	8	ℵ̃	ℵ̃	PROPN
ejpam-5429	350	9	such	such	ADJ
ejpam-5429	350	10	that	that	SCONJ
ejpam-5429	350	11	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	350	12	≬	≬	PROPN
ejpam-5429	350	13	(	(	PUNCT
ejpam-5429	350	14	ϱ̇	ϱ̇	PROPN
ejpam-5429	350	15	≬	≬	PROPN
ejpam-5429	350	16	(	(	PUNCT
ejpam-5429	350	17	ϱ̇	ϱ̇	PROPN
ejpam-5429	350	18	≬	≬	PROPN
ejpam-5429	350	19	ς̇	ς̇	NOUN
ejpam-5429	350	20	)	)	PUNCT
ejpam-5429	350	21	)	)	PUNCT
ejpam-5429	350	22	)	)	PUNCT
ejpam-5429	351	1	∨	∨	NUM
ejpam-5429	352	1	σ̃	σ̃	PROPN
ejpam-5429	352	2	<	<	X
ejpam-5429	352	3	ð̃((ς̇	ð̃((ς̇	X
ejpam-5429	352	4	≬	≬	PROPN
ejpam-5429	352	5	ϱ̇	ϱ̇	PROPN
ejpam-5429	352	6	)	)	PUNCT
ejpam-5429	352	7	≬	≬	PROPN
ejpam-5429	352	8	κ̇	κ̇	PROPN
ejpam-5429	352	9	)	)	PUNCT
ejpam-5429	352	10	∧	∧	PROPN
ejpam-5429	352	11	ð̃(κ̇	ð̃(κ̇	PROPN
ejpam-5429	352	12	)	)	PUNCT
ejpam-5429	352	13	∧	∧	PROPN
ejpam-5429	352	14	τ̃	τ̃	PROPN
ejpam-5429	352	15	.	.	PUNCT
ejpam-5429	353	1	select	select	VERB
ejpam-5429	354	1	σ̃	σ̃	NOUN
ejpam-5429	354	2	<	<	X
ejpam-5429	354	3	ρ̃	ρ̃	PROPN
ejpam-5429	354	4	≤	≤	NOUN
ejpam-5429	354	5	τ̃	τ̃	VERB
ejpam-5429	355	1	such	such	ADJ
ejpam-5429	355	2	that	that	SCONJ
ejpam-5429	355	3	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	355	4	≬	≬	PROPN
ejpam-5429	355	5	(	(	PUNCT
ejpam-5429	355	6	ϱ̇	ϱ̇	PROPN
ejpam-5429	355	7	≬	≬	PROPN
ejpam-5429	355	8	(	(	PUNCT
ejpam-5429	355	9	ϱ̇	ϱ̇	PROPN
ejpam-5429	355	10	≬	≬	PROPN
ejpam-5429	355	11	ς̇	ς̇	NOUN
ejpam-5429	355	12	)	)	PUNCT
ejpam-5429	355	13	)	)	PUNCT
ejpam-5429	355	14	)	)	PUNCT
ejpam-5429	355	15	∨	∨	NUM
ejpam-5429	356	1	σ̃	σ̃	PROPN
ejpam-5429	356	2	<	<	X
ejpam-5429	356	3	r̂	r̂	X
ejpam-5429	356	4	=	=	SYM
ejpam-5429	356	5	ð̃((ς̇	ð̃((ς̇	X
ejpam-5429	356	6	≬	≬	PROPN
ejpam-5429	356	7	ϱ̇	ϱ̇	PROPN
ejpam-5429	356	8	)	)	PUNCT
ejpam-5429	356	9	≬	≬	PROPN
ejpam-5429	356	10	κ̇	κ̇	PROPN
ejpam-5429	356	11	)	)	PUNCT
ejpam-5429	356	12	∧	∧	PROPN
ejpam-5429	356	13	ð̃(κ̇	ð̃(κ̇	PROPN
ejpam-5429	356	14	)	)	PUNCT
ejpam-5429	356	15	∧	∧	PROPN
ejpam-5429	356	16	τ̃	τ̃	PROPN
ejpam-5429	356	17	.	.	PUNCT
ejpam-5429	357	1	then	then	ADV
ejpam-5429	357	2	,	,	PUNCT
ejpam-5429	357	3	(	(	PUNCT
ejpam-5429	357	4	(	(	PUNCT
ejpam-5429	357	5	ς̇	ς̇	PROPN
ejpam-5429	357	6	≬	≬	PROPN
ejpam-5429	357	7	ϱ̇	ϱ̇	PROPN
ejpam-5429	357	8	)	)	PUNCT
ejpam-5429	357	9	≬	≬	PROPN
ejpam-5429	357	10	κ̇)ρ̃	κ̇)ρ̃	PROPN
ejpam-5429	357	11	∈σ̃	∈σ̃	PROPN
ejpam-5429	357	12	ð̃	ð̃	PROPN
ejpam-5429	357	13	,	,	PUNCT
ejpam-5429	357	14	κ̇ρ̃	κ̇ρ̃	PROPN
ejpam-5429	357	15	∈σ̃	∈σ̃	PROPN
ejpam-5429	357	16	ð̃	ð̃	PROPN
ejpam-5429	357	17	,	,	PUNCT
ejpam-5429	357	18	but	but	CCONJ
ejpam-5429	357	19	(	(	PUNCT
ejpam-5429	357	20	ς̇	ς̇	NOUN
ejpam-5429	357	21	≬	≬	PROPN
ejpam-5429	357	22	(	(	PUNCT
ejpam-5429	357	23	ϱ̇	ϱ̇	PROPN
ejpam-5429	357	24	≬	≬	PROPN
ejpam-5429	357	25	(	(	PUNCT
ejpam-5429	357	26	ϱ̇	ϱ̇	PROPN
ejpam-5429	357	27	≬	≬	PROPN
ejpam-5429	357	28	ς̇))r̂∈σ̃	ς̇))r̂∈σ̃	NUM
ejpam-5429	357	29	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	357	30	ð̃.	ð̃.	NOUN
ejpam-5429	357	31	since	since	SCONJ
ejpam-5429	357	32	ð̃σ̃ρ̃	ð̃σ̃ρ̃	PROPN
ejpam-5429	357	33	is	be	AUX
ejpam-5429	357	34	a	a	DET
ejpam-5429	357	35	fi	fi	NOUN
ejpam-5429	357	36	of	of	ADP
ejpam-5429	357	37	ℵ̃	ℵ̃	PROPN
ejpam-5429	357	38	,	,	PUNCT
ejpam-5429	357	39	ς̇	ς̇	NOUN
ejpam-5429	357	40	≬	≬	PROPN
ejpam-5429	357	41	(	(	PUNCT
ejpam-5429	357	42	ϱ̇	ϱ̇	PROPN
ejpam-5429	357	43	≬	≬	PROPN
ejpam-5429	357	44	(	(	PUNCT
ejpam-5429	357	45	ϱ̇	ϱ̇	PROPN
ejpam-5429	357	46	≬	≬	PROPN
ejpam-5429	357	47	ς̇	ς̇	NOUN
ejpam-5429	357	48	)	)	PUNCT
ejpam-5429	357	49	)	)	PUNCT
ejpam-5429	358	1	∈	∈	PROPN
ejpam-5429	358	2	ð̃σ̃ρ̃	ð̃σ̃ρ̃	PROPN
ejpam-5429	358	3	,	,	PUNCT
ejpam-5429	358	4	a	a	DET
ejpam-5429	358	5	contradiction	contradiction	NOUN
ejpam-5429	358	6	.	.	PUNCT
ejpam-5429	359	1	hence	hence	ADV
ejpam-5429	359	2	,	,	PUNCT
ejpam-5429	359	3	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	359	4	≬	≬	PROPN
ejpam-5429	359	5	(	(	PUNCT
ejpam-5429	359	6	ϱ̇	ϱ̇	PROPN
ejpam-5429	359	7	≬	≬	PROPN
ejpam-5429	359	8	(	(	PUNCT
ejpam-5429	359	9	ϱ̇	ϱ̇	PROPN
ejpam-5429	359	10	≬	≬	PROPN
ejpam-5429	359	11	ς̇	ς̇	NOUN
ejpam-5429	359	12	)	)	PUNCT
ejpam-5429	359	13	)	)	PUNCT
ejpam-5429	359	14	)	)	PUNCT
ejpam-5429	360	1	∨	∨	NUM
ejpam-5429	360	2	σ̃	σ̃	PROPN
ejpam-5429	360	3	≥	≥	NOUN
ejpam-5429	360	4	ð̃((ς̇	ð̃((ς̇	X
ejpam-5429	361	1	≬	≬	PROPN
ejpam-5429	361	2	ϱ̇	ϱ̇	PROPN
ejpam-5429	361	3	)	)	PUNCT
ejpam-5429	361	4	≬	≬	PROPN
ejpam-5429	361	5	κ̇	κ̇	PROPN
ejpam-5429	361	6	)	)	PUNCT
ejpam-5429	361	7	∧	∧	PROPN
ejpam-5429	361	8	ð̃(κ̇	ð̃(κ̇	PROPN
ejpam-5429	361	9	)	)	PUNCT
ejpam-5429	361	10	∧	∧	PROPN
ejpam-5429	361	11	τ̃	τ̃	PROPN
ejpam-5429	361	12	.	.	PUNCT
ejpam-5429	362	1	therefore	therefore	ADV
ejpam-5429	362	2	,	,	PUNCT
ejpam-5429	362	3	ð̃	ð̃	PROPN
ejpam-5429	362	4	is	be	AUX
ejpam-5429	362	5	a	a	DET
ejpam-5429	362	6	qp(∈σ̃,∈σ̃	qp(∈σ̃,∈σ̃	NOUN
ejpam-5429	362	7	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	362	8	)	)	PUNCT
ejpam-5429	362	9	ffi	ffi	PROPN
ejpam-5429	362	10	of	of	ADP
ejpam-5429	362	11	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	362	12	by	by	ADP
ejpam-5429	362	13	setting	set	VERB
ejpam-5429	362	14	σ̃	σ̃	PROPN
ejpam-5429	362	15	=	=	SYM
ejpam-5429	362	16	0̃	0̃	PROPN
ejpam-5429	362	17	and	and	CCONJ
ejpam-5429	362	18	τ̃	τ̃	PROPN
ejpam-5429	362	19	=	=	SYM
ejpam-5429	362	20	0̂.5	0̂.5	PROPN
ejpam-5429	362	21	in	in	ADP
ejpam-5429	362	22	theorem	theorem	NOUN
ejpam-5429	362	23	5.3	5.3	NUM
ejpam-5429	362	24	,	,	PUNCT
ejpam-5429	362	25	we	we	PRON
ejpam-5429	362	26	can	can	AUX
ejpam-5429	362	27	derive	derive	VERB
ejpam-5429	362	28	the	the	DET
ejpam-5429	362	29	subsequent	subsequent	ADJ
ejpam-5429	362	30	corollary	corollary	NOUN
ejpam-5429	362	31	.	.	PUNCT
ejpam-5429	363	1	k.	k.	PROPN
ejpam-5429	363	2	h.	h.	PROPN
ejpam-5429	363	3	hakami	hakami	PROPN
ejpam-5429	363	4	et	et	PROPN
ejpam-5429	363	5	al	al	PROPN
ejpam-5429	363	6	.	.	PUNCT
ejpam-5429	363	7	/	/	SYM
ejpam-5429	363	8	eur	eur	PROPN
ejpam-5429	363	9	.	.	PUNCT
ejpam-5429	364	1	j.	j.	PROPN
ejpam-5429	364	2	pure	pure	PROPN
ejpam-5429	364	3	appl	appl	PROPN
ejpam-5429	364	4	.	.	PROPN
ejpam-5429	364	5	math	math	PROPN
ejpam-5429	364	6	,	,	PUNCT
ejpam-5429	364	7	17	17	NUM
ejpam-5429	364	8	(	(	PUNCT
ejpam-5429	364	9	4	4	NUM
ejpam-5429	364	10	)	)	PUNCT
ejpam-5429	364	11	(	(	PUNCT
ejpam-5429	364	12	2024	2024	NUM
ejpam-5429	364	13	)	)	PUNCT
ejpam-5429	364	14	,	,	PUNCT
ejpam-5429	364	15	3129	3129	NUM
ejpam-5429	364	16	-	-	SYM
ejpam-5429	364	17	3155	3155	NUM
ejpam-5429	364	18	3141	3141	NUM
ejpam-5429	364	19	corollary	corollary	NOUN
ejpam-5429	364	20	5	5	NUM
ejpam-5429	364	21	.	.	PUNCT
ejpam-5429	365	1	let	let	VERB
ejpam-5429	365	2	ð̃	ð̃	PRON
ejpam-5429	365	3	be	be	AUX
ejpam-5429	365	4	a	a	DET
ejpam-5429	365	5	qp	qp	PROPN
ejpam-5429	365	6	-	-	PUNCT
ejpam-5429	365	7	f	f	PROPN
ejpam-5429	365	8	set	set	NOUN
ejpam-5429	365	9	of	of	ADP
ejpam-5429	365	10	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	365	11	then	then	ADV
ejpam-5429	365	12	ð̃	ð̃	PROPN
ejpam-5429	365	13	is	be	AUX
ejpam-5429	365	14	a	a	DET
ejpam-5429	365	15	qp-(∈,∈	qp-(∈,∈	X
ejpam-5429	365	16	∨q)ffi	∨q)ffi	PROPN
ejpam-5429	365	17	of	of	ADP
ejpam-5429	365	18	ℵ̃	ℵ̃	PROPN
ejpam-5429	365	19	⇔	⇔	X
ejpam-5429	365	20	ð̃ρ̃	ð̃ρ̃	PROPN
ejpam-5429	366	1	=	=	PUNCT
ejpam-5429	366	2	{	{	PUNCT
ejpam-5429	366	3	ς̇	ς̇	NOUN
ejpam-5429	366	4	∈	∈	PROPN
ejpam-5429	366	5	ℵ̃	ℵ̃	PROPN
ejpam-5429	366	6	|	|	ADV
ejpam-5429	366	7	ς̇ρ̃	ς̇ρ̃	NOUN
ejpam-5429	366	8	∈	∈	NOUN
ejpam-5429	366	9	ð̃	ð̃	PROPN
ejpam-5429	366	10	}	}	PUNCT
ejpam-5429	366	11	=	=	NOUN
ejpam-5429	366	12	̸	̸	NUM
ejpam-5429	366	13	ϕ	ϕ	NOUN
ejpam-5429	366	14	is	be	AUX
ejpam-5429	366	15	a	a	DET
ejpam-5429	366	16	fi	fi	NOUN
ejpam-5429	366	17	of	of	ADP
ejpam-5429	366	18	ℵ̃,∀ρ̃	ℵ̃,∀ρ̃	NOUN
ejpam-5429	366	19	∈	∈	PROPN
ejpam-5429	366	20	(	(	PUNCT
ejpam-5429	366	21	0	0	NUM
ejpam-5429	366	22	,	,	PUNCT
ejpam-5429	366	23	0.5]q	0.5]q	NOUN
ejpam-5429	366	24	.	.	PUNCT
ejpam-5429	367	1	theorem	theorem	VERB
ejpam-5429	367	2	13	13	NUM
ejpam-5429	367	3	.	.	PUNCT
ejpam-5429	368	1	let	let	VERB
ejpam-5429	368	2	ð̃	ð̃	PRON
ejpam-5429	368	3	be	be	AUX
ejpam-5429	368	4	a	a	DET
ejpam-5429	368	5	qp	qp	PROPN
ejpam-5429	368	6	-	-	PUNCT
ejpam-5429	368	7	f	f	PROPN
ejpam-5429	368	8	set	set	NOUN
ejpam-5429	368	9	of	of	ADP
ejpam-5429	368	10	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	368	11	then	then	ADV
ejpam-5429	368	12	(	(	PUNCT
ejpam-5429	368	13	1	1	X
ejpam-5429	368	14	)	)	PUNCT
ejpam-5429	368	15	ð̃	ð̃	PROPN
ejpam-5429	368	16	is	be	AUX
ejpam-5429	368	17	a	a	DET
ejpam-5429	368	18	qp-(∈σ̃,∈σ̃	qp-(∈σ̃,∈σ̃	NOUN
ejpam-5429	368	19	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	368	20	)	)	PUNCT
ejpam-5429	368	21	-ffis	-ffis	NOUN
ejpam-5429	368	22	of	of	ADP
ejpam-5429	368	23	ℵ̃	ℵ̃	PROPN
ejpam-5429	368	24	⇔	⇔	PROPN
ejpam-5429	368	25	ð̃σ̃ρ̃	ð̃σ̃ρ̃	PROPN
ejpam-5429	369	1	̸=	̸=	PROPN
ejpam-5429	369	2	ϕ	ϕ	PROPN
ejpam-5429	369	3	is	be	AUX
ejpam-5429	369	4	a	a	DET
ejpam-5429	369	5	fi	fi	NOUN
ejpam-5429	369	6	of	of	ADP
ejpam-5429	369	7	ℵ̃,∀σ̃	ℵ̃,∀σ̃	NOUN
ejpam-5429	369	8	<	<	X
ejpam-5429	369	9	ρ̃	ρ̃	PROPN
ejpam-5429	369	10	≤	≤	PROPN
ejpam-5429	369	11	τ̃	τ̃	PROPN
ejpam-5429	369	12	.	.	PUNCT
ejpam-5429	370	1	(	(	PUNCT
ejpam-5429	370	2	2	2	X
ejpam-5429	370	3	)	)	PUNCT
ejpam-5429	370	4	if	if	SCONJ
ejpam-5429	370	5	1̂	1̂	NOUN
ejpam-5429	370	6	+	+	CCONJ
ejpam-5429	370	7	σ̃	σ̃	NOUN
ejpam-5429	370	8	=	=	SYM
ejpam-5429	371	1	2τ̃	2τ̃	PROPN
ejpam-5429	371	2	,	,	PUNCT
ejpam-5429	371	3	then	then	ADV
ejpam-5429	371	4	ð̃	ð̃	PROPN
ejpam-5429	371	5	is	be	AUX
ejpam-5429	371	6	a	a	DET
ejpam-5429	371	7	qp-(∈σ̃,∈σ̃	qp-(∈σ̃,∈σ̃	NOUN
ejpam-5429	371	8	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	371	9	)	)	PUNCT
ejpam-5429	371	10	-ffi	-ffi	PROPN
ejpam-5429	371	11	of	of	ADP
ejpam-5429	371	12	ℵ̃	ℵ̃	PROPN
ejpam-5429	371	13	⇔	⇔	X
ejpam-5429	371	14	⟨ð̃⟩τ̃ρ̃	⟨ð̃⟩τ̃ρ̃	PROPN
ejpam-5429	371	15	̸=	̸=	PROPN
ejpam-5429	371	16	ϕ	ϕ	NOUN
ejpam-5429	371	17	is	be	AUX
ejpam-5429	371	18	a	a	DET
ejpam-5429	371	19	fi	fi	NOUN
ejpam-5429	371	20	of	of	ADP
ejpam-5429	371	21	ℵ̃,∀τ̃	ℵ̃,∀τ̃	PUNCT
ejpam-5429	371	22	<	<	X
ejpam-5429	371	23	ρ̃	ρ̃	PROPN
ejpam-5429	371	24	≤	≤	NOUN
ejpam-5429	371	25	1̂.	1̂.	NUM
ejpam-5429	371	26	(	(	PUNCT
ejpam-5429	371	27	3	3	X
ejpam-5429	371	28	)	)	PUNCT
ejpam-5429	371	29	if	if	SCONJ
ejpam-5429	371	30	1̂	1̂	NOUN
ejpam-5429	371	31	+	+	CCONJ
ejpam-5429	372	1	σ̃	σ̃	NOUN
ejpam-5429	372	2	=	=	SYM
ejpam-5429	372	3	2τ̃	2τ̃	PROPN
ejpam-5429	372	4	,	,	PUNCT
ejpam-5429	372	5	then	then	ADV
ejpam-5429	372	6	ð̃	ð̃	PROPN
ejpam-5429	372	7	is	be	AUX
ejpam-5429	372	8	a	a	DET
ejpam-5429	372	9	qp-(∈σ̃,∈σ̃	qp-(∈σ̃,∈σ̃	NOUN
ejpam-5429	372	10	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	372	11	)	)	PUNCT
ejpam-5429	372	12	-ffi	-ffi	PROPN
ejpam-5429	372	13	of	of	ADP
ejpam-5429	372	14	ℵ̃	ℵ̃	PROPN
ejpam-5429	372	15	⇔	⇔	PROPN
ejpam-5429	372	16	[	[	X
ejpam-5429	372	17	ð̃]τ̃ρ̃	ð̃]τ̃ρ̃	X
ejpam-5429	372	18	̸=	̸=	PROPN
ejpam-5429	372	19	ϕ	ϕ	NOUN
ejpam-5429	372	20	is	be	AUX
ejpam-5429	372	21	a	a	DET
ejpam-5429	372	22	fi	fi	NOUN
ejpam-5429	372	23	of	of	ADP
ejpam-5429	372	24	ℵ̃,∀σ̃	ℵ̃,∀σ̃	NOUN
ejpam-5429	372	25	<	<	X
ejpam-5429	372	26	ρ̃	ρ̃	PROPN
ejpam-5429	372	27	≤	≤	ADV
ejpam-5429	372	28	1̂.	1̂.	NUM
ejpam-5429	372	29	proof	proof	NOUN
ejpam-5429	372	30	.	.	PUNCT
ejpam-5429	373	1	(	(	PUNCT
ejpam-5429	373	2	1	1	X
ejpam-5429	373	3	)	)	PUNCT
ejpam-5429	373	4	let	let	VERB
ejpam-5429	373	5	ð̃	ð̃	PRON
ejpam-5429	373	6	be	be	AUX
ejpam-5429	373	7	a	a	DET
ejpam-5429	373	8	qp-(∈σ̃,∈σ̃	qp-(∈σ̃,∈σ̃	NOUN
ejpam-5429	373	9	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	373	10	)	)	PUNCT
ejpam-5429	373	11	-ffi	-ffi	PROPN
ejpam-5429	373	12	of	of	ADP
ejpam-5429	373	13	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	373	14	let	let	VERB
ejpam-5429	373	15	ς̇	ς̇	NOUN
ejpam-5429	373	16	∈	∈	PROPN
ejpam-5429	374	1	ð̃τ̃ρ̃.	ð̃τ̃ρ̃.	X
ejpam-5429	374	2	then	then	ADV
ejpam-5429	374	3	ð̃(0	ð̃(0	X
ejpam-5429	374	4	)	)	PUNCT
ejpam-5429	374	5	∨	∨	NUM
ejpam-5429	375	1	σ̃	σ̃	PROPN
ejpam-5429	375	2	≥	≥	NOUN
ejpam-5429	375	3	ð̃(ς̇	ð̃(ς̇	NOUN
ejpam-5429	375	4	)	)	PUNCT
ejpam-5429	375	5	∧	∧	PROPN
ejpam-5429	375	6	τ̃	τ̃	PROPN
ejpam-5429	375	7	≥	≥	NOUN
ejpam-5429	375	8	ρ̃	ρ̃	PROPN
ejpam-5429	375	9	∧	∧	PROPN
ejpam-5429	375	10	τ̃	τ̃	PROPN
ejpam-5429	375	11	>	>	X
ejpam-5429	375	12	σ̃.	σ̃.	PROPN
ejpam-5429	375	13	hence	hence	ADV
ejpam-5429	375	14	,	,	PUNCT
ejpam-5429	375	15	ð̃(0	ð̃(0	PROPN
ejpam-5429	375	16	)	)	PUNCT
ejpam-5429	375	17	≥	≥	NOUN
ejpam-5429	376	1	ρ̃	ρ̃	PROPN
ejpam-5429	376	2	⇒	⇒	NOUN
ejpam-5429	376	3	0	0	PUNCT
ejpam-5429	377	1	∈	∈	PROPN
ejpam-5429	377	2	ð̃τ̃ρ̃.	ð̃τ̃ρ̃.	AUX
ejpam-5429	377	3	let	let	VERB
ejpam-5429	377	4	ς̇	ς̇	NOUN
ejpam-5429	377	5	,	,	PUNCT
ejpam-5429	377	6	ϱ̇	ϱ̇	PROPN
ejpam-5429	377	7	,	,	PUNCT
ejpam-5429	377	8	κ̇	κ̇	PROPN
ejpam-5429	377	9	∈	∈	PROPN
ejpam-5429	378	1	ð̃τ̃ρ̃.	ð̃τ̃ρ̃.	X
ejpam-5429	378	2	then	then	ADV
ejpam-5429	378	3	,	,	PUNCT
ejpam-5429	378	4	ð̃((ς̇	ð̃((ς̇	VERB
ejpam-5429	378	5	≬	≬	PROPN
ejpam-5429	378	6	ϱ̇	ϱ̇	PROPN
ejpam-5429	378	7	)	)	PUNCT
ejpam-5429	378	8	≬	≬	PROPN
ejpam-5429	378	9	κ̇	κ̇	PROPN
ejpam-5429	378	10	)	)	PUNCT
ejpam-5429	378	11	≥	≥	NOUN
ejpam-5429	378	12	ρ̃	ρ̃	PROPN
ejpam-5429	378	13	>	>	SYM
ejpam-5429	378	14	σ̃	σ̃	PROPN
ejpam-5429	378	15	and	and	CCONJ
ejpam-5429	378	16	ð̃(κ̇	ð̃(κ̇	PROPN
ejpam-5429	378	17	)	)	PUNCT
ejpam-5429	378	18	≥	≥	NOUN
ejpam-5429	378	19	ρ̃	ρ̃	PROPN
ejpam-5429	378	20	>	>	X
ejpam-5429	378	21	σ̃.	σ̃.	PROPN
ejpam-5429	378	22	by	by	ADP
ejpam-5429	378	23	theorem	theorem	ADJ
ejpam-5429	378	24	5.1	5.1	NUM
ejpam-5429	378	25	(	(	PUNCT
ejpam-5429	378	26	2	2	NUM
ejpam-5429	378	27	)	)	PUNCT
ejpam-5429	378	28	,	,	PUNCT
ejpam-5429	378	29	we	we	PRON
ejpam-5429	378	30	have	have	VERB
ejpam-5429	378	31	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	378	32	≬	≬	PROPN
ejpam-5429	378	33	(	(	PUNCT
ejpam-5429	378	34	ϱ̇	ϱ̇	PROPN
ejpam-5429	378	35	≬	≬	PROPN
ejpam-5429	378	36	(	(	PUNCT
ejpam-5429	378	37	ϱ̇	ϱ̇	PROPN
ejpam-5429	378	38	≬	≬	PROPN
ejpam-5429	378	39	ς̇	ς̇	NOUN
ejpam-5429	378	40	)	)	PUNCT
ejpam-5429	378	41	)	)	PUNCT
ejpam-5429	378	42	)	)	PUNCT
ejpam-5429	379	1	∨	∨	NUM
ejpam-5429	379	2	σ̃	σ̃	PROPN
ejpam-5429	379	3	≥	≥	NOUN
ejpam-5429	379	4	ð̃((ς̇	ð̃((ς̇	X
ejpam-5429	380	1	≬	≬	PROPN
ejpam-5429	380	2	ϱ̇	ϱ̇	PROPN
ejpam-5429	380	3	)	)	PUNCT
ejpam-5429	380	4	≬	≬	PROPN
ejpam-5429	380	5	κ̇	κ̇	PROPN
ejpam-5429	380	6	)	)	PUNCT
ejpam-5429	380	7	∧	∧	PROPN
ejpam-5429	380	8	τ̃	τ̃	PROPN
ejpam-5429	380	9	≥	≥	NOUN
ejpam-5429	380	10	ρ̃	ρ̃	PROPN
ejpam-5429	380	11	∧	∧	NOUN
ejpam-5429	380	12	ρ̃	ρ̃	PROPN
ejpam-5429	380	13	∧	∧	NOUN
ejpam-5429	380	14	τ̃	τ̃	PROPN
ejpam-5429	380	15	=	=	SYM
ejpam-5429	380	16	ρ̃	ρ̃	PROPN
ejpam-5429	380	17	∧	∧	NOUN
ejpam-5429	380	18	τ̃	τ̃	PROPN
ejpam-5429	380	19	=	=	SYM
ejpam-5429	380	20	ρ̃	ρ̃	PROPN
ejpam-5429	380	21	>	>	X
ejpam-5429	380	22	σ̃.	σ̃.	PROPN
ejpam-5429	380	23	therefore	therefore	ADV
ejpam-5429	380	24	,	,	PUNCT
ejpam-5429	380	25	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	380	26	≬	≬	PROPN
ejpam-5429	380	27	(	(	PUNCT
ejpam-5429	380	28	ϱ̇	ϱ̇	PROPN
ejpam-5429	380	29	≬	≬	PROPN
ejpam-5429	380	30	(	(	PUNCT
ejpam-5429	380	31	ϱ̇	ϱ̇	PROPN
ejpam-5429	380	32	≬	≬	PROPN
ejpam-5429	380	33	ς̇	ς̇	NOUN
ejpam-5429	380	34	)	)	PUNCT
ejpam-5429	380	35	)	)	PUNCT
ejpam-5429	380	36	)	)	PUNCT
ejpam-5429	380	37	≥	≥	PROPN
ejpam-5429	381	1	ρ̃	ρ̃	PROPN
ejpam-5429	381	2	⇒	⇒	NOUN
ejpam-5429	381	3	ς̇	ς̇	NOUN
ejpam-5429	381	4	≬	≬	PROPN
ejpam-5429	381	5	(	(	PUNCT
ejpam-5429	381	6	ϱ̇	ϱ̇	PROPN
ejpam-5429	381	7	≬	≬	PROPN
ejpam-5429	381	8	(	(	PUNCT
ejpam-5429	381	9	ϱ̇	ϱ̇	PROPN
ejpam-5429	381	10	≬	≬	PROPN
ejpam-5429	381	11	ς̇	ς̇	NOUN
ejpam-5429	381	12	)	)	PUNCT
ejpam-5429	381	13	)	)	PUNCT
ejpam-5429	382	1	∈	∈	PROPN
ejpam-5429	383	1	ð̃σ̃ρ̃	ð̃σ̃ρ̃	PROPN
ejpam-5429	383	2	.	.	PUNCT
ejpam-5429	384	1	hence	hence	ADV
ejpam-5429	384	2	,	,	PUNCT
ejpam-5429	384	3	ð̃σ̃ρ̃	ð̃σ̃ρ̃	PROPN
ejpam-5429	384	4	is	be	AUX
ejpam-5429	384	5	a	a	DET
ejpam-5429	384	6	fi	fi	NOUN
ejpam-5429	384	7	of	of	ADP
ejpam-5429	384	8	ℵ̃.	ℵ̃.	NOUN
ejpam-5429	384	9	conversely	conversely	ADV
ejpam-5429	384	10	,	,	PUNCT
ejpam-5429	384	11	assume	assume	VERB
ejpam-5429	384	12	ð̃σ̃ρ̃	ð̃σ̃ρ̃	PROPN
ejpam-5429	384	13	is	be	AUX
ejpam-5429	384	14	a	a	DET
ejpam-5429	384	15	fi	fi	NOUN
ejpam-5429	384	16	of	of	ADP
ejpam-5429	384	17	ℵ̃	ℵ̃	PROPN
ejpam-5429	384	18	,	,	PUNCT
ejpam-5429	384	19	∀ρ̃	∀ρ̃	PROPN
ejpam-5429	384	20	∈	∈	PROPN
ejpam-5429	384	21	(	(	PUNCT
ejpam-5429	384	22	σ	σ	PROPN
ejpam-5429	384	23	,	,	PUNCT
ejpam-5429	384	24	τ	τ	X
ejpam-5429	384	25	]	]	PUNCT
ejpam-5429	384	26	.	.	PUNCT
ejpam-5429	385	1	let	let	VERB
ejpam-5429	385	2	ς̇	ς̇	PROPN
ejpam-5429	385	3	∈	∈	PROPN
ejpam-5429	385	4	ℵ̃	ℵ̃	PROPN
ejpam-5429	385	5	be	be	AUX
ejpam-5429	385	6	such	such	ADJ
ejpam-5429	385	7	that	that	SCONJ
ejpam-5429	385	8	ð̃(0)∨σ	ð̃(0)∨σ	PUNCT
ejpam-5429	385	9	<	<	X
ejpam-5429	385	10	ρ̃	ρ̃	PROPN
ejpam-5429	385	11	=	=	SYM
ejpam-5429	385	12	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	385	13	)	)	PUNCT
ejpam-5429	385	14	∧	∧	PROPN
ejpam-5429	385	15	τ̃	τ̃	PROPN
ejpam-5429	385	16	.	.	PUNCT
ejpam-5429	386	1	then	then	ADV
ejpam-5429	386	2	ς̇ρ̃	ς̇ρ̃	PROPN
ejpam-5429	386	3	∈σ̃	∈σ̃	PROPN
ejpam-5429	386	4	ð̃	ð̃	PROPN
ejpam-5429	386	5	,	,	PUNCT
ejpam-5429	386	6	but	but	CCONJ
ejpam-5429	386	7	0ρ̃∈σ̃	0ρ̃∈σ̃	PROPN
ejpam-5429	386	8	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	386	9	ð̃	ð̃	PROPN
ejpam-5429	386	10	,	,	PUNCT
ejpam-5429	386	11	a	a	DET
ejpam-5429	386	12	contradiction	contradiction	NOUN
ejpam-5429	386	13	.	.	PUNCT
ejpam-5429	387	1	suppose	suppose	VERB
ejpam-5429	387	2	ς̇	ς̇	PROPN
ejpam-5429	387	3	,	,	PUNCT
ejpam-5429	387	4	ϱ̇	ϱ̇	PROPN
ejpam-5429	387	5	,	,	PUNCT
ejpam-5429	387	6	κ̇	κ̇	PROPN
ejpam-5429	387	7	∈	∈	PROPN
ejpam-5429	387	8	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	387	9	then	then	ADV
ejpam-5429	387	10	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	387	11	≬	≬	PROPN
ejpam-5429	387	12	(	(	PUNCT
ejpam-5429	387	13	ϱ̇	ϱ̇	PROPN
ejpam-5429	387	14	≬	≬	PROPN
ejpam-5429	387	15	(	(	PUNCT
ejpam-5429	387	16	ϱ̇	ϱ̇	PROPN
ejpam-5429	387	17	≬	≬	PROPN
ejpam-5429	387	18	ς̇	ς̇	NOUN
ejpam-5429	387	19	)	)	PUNCT
ejpam-5429	387	20	)	)	PUNCT
ejpam-5429	387	21	)	)	PUNCT
ejpam-5429	388	1	∨	∨	NUM
ejpam-5429	389	1	σ̃	σ̃	PROPN
ejpam-5429	389	2	<	<	X
ejpam-5429	389	3	ð̃((ς̇	ð̃((ς̇	X
ejpam-5429	389	4	≬	≬	PROPN
ejpam-5429	389	5	ϱ̇	ϱ̇	PROPN
ejpam-5429	389	6	)	)	PUNCT
ejpam-5429	389	7	≬	≬	PROPN
ejpam-5429	389	8	κ̇	κ̇	PROPN
ejpam-5429	389	9	)	)	PUNCT
ejpam-5429	389	10	∧	∧	PROPN
ejpam-5429	389	11	ð̃(κ̇	ð̃(κ̇	PROPN
ejpam-5429	389	12	)	)	PUNCT
ejpam-5429	389	13	∧	∧	PROPN
ejpam-5429	389	14	τ̃	τ̃	PROPN
ejpam-5429	389	15	.	.	PUNCT
ejpam-5429	390	1	select	select	VERB
ejpam-5429	390	2	some	some	DET
ejpam-5429	390	3	ρ̃	ρ̃	PROPN
ejpam-5429	390	4	∈	∈	PROPN
ejpam-5429	390	5	(	(	PUNCT
ejpam-5429	390	6	σ̃	σ̃	PROPN
ejpam-5429	390	7	,	,	PUNCT
ejpam-5429	390	8	τ̃	τ̃	PROPN
ejpam-5429	390	9	]	]	PUNCT
ejpam-5429	390	10	such	such	ADJ
ejpam-5429	390	11	that	that	SCONJ
ejpam-5429	390	12	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	390	13	≬	≬	PROPN
ejpam-5429	390	14	(	(	PUNCT
ejpam-5429	390	15	ϱ̇	ϱ̇	PROPN
ejpam-5429	390	16	≬	≬	PROPN
ejpam-5429	390	17	(	(	PUNCT
ejpam-5429	390	18	ϱ̇	ϱ̇	PROPN
ejpam-5429	390	19	≬	≬	PROPN
ejpam-5429	390	20	ς̇	ς̇	NOUN
ejpam-5429	390	21	)	)	PUNCT
ejpam-5429	390	22	)	)	PUNCT
ejpam-5429	390	23	)	)	PUNCT
ejpam-5429	391	1	∨	∨	NUM
ejpam-5429	392	1	σ̃	σ̃	PROPN
ejpam-5429	392	2	<	<	X
ejpam-5429	392	3	ρ̃	ρ̃	PROPN
ejpam-5429	392	4	=	=	SYM
ejpam-5429	392	5	ð̃((ς̇	ð̃((ς̇	X
ejpam-5429	392	6	≬	≬	PROPN
ejpam-5429	392	7	ϱ̇	ϱ̇	PROPN
ejpam-5429	392	8	)	)	PUNCT
ejpam-5429	392	9	≬	≬	PROPN
ejpam-5429	392	10	κ̇	κ̇	PROPN
ejpam-5429	392	11	)	)	PUNCT
ejpam-5429	392	12	∧	∧	PROPN
ejpam-5429	392	13	ð̃(κ̇	ð̃(κ̇	PROPN
ejpam-5429	392	14	)	)	PUNCT
ejpam-5429	392	15	∧	∧	PROPN
ejpam-5429	392	16	τ̃	τ̃	PROPN
ejpam-5429	392	17	.	.	PUNCT
ejpam-5429	393	1	then	then	ADV
ejpam-5429	393	2	(	(	PUNCT
ejpam-5429	393	3	(	(	PUNCT
ejpam-5429	393	4	ς̇	ς̇	PROPN
ejpam-5429	393	5	≬	≬	PROPN
ejpam-5429	393	6	ϱ̇	ϱ̇	PROPN
ejpam-5429	393	7	)	)	PUNCT
ejpam-5429	393	8	≬	≬	PROPN
ejpam-5429	393	9	κ̇)ρ̃	κ̇)ρ̃	PROPN
ejpam-5429	393	10	∈σ̃	∈σ̃	PROPN
ejpam-5429	393	11	ð̃	ð̃	PROPN
ejpam-5429	393	12	,	,	PUNCT
ejpam-5429	393	13	κ̇ρ̃	κ̇ρ̃	PROPN
ejpam-5429	393	14	∈σ	∈σ	PROPN
ejpam-5429	393	15	ð̃	ð̃	PROPN
ejpam-5429	393	16	,	,	PUNCT
ejpam-5429	393	17	but	but	CCONJ
ejpam-5429	393	18	(	(	PUNCT
ejpam-5429	393	19	ς̇	ς̇	NOUN
ejpam-5429	393	20	≬	≬	PROPN
ejpam-5429	393	21	(	(	PUNCT
ejpam-5429	393	22	ϱ̇	ϱ̇	PROPN
ejpam-5429	393	23	≬	≬	PROPN
ejpam-5429	393	24	(	(	PUNCT
ejpam-5429	393	25	ϱ̇	ϱ̇	PROPN
ejpam-5429	393	26	≬	≬	PROPN
ejpam-5429	393	27	ς̇)))ρ̃∈σ̃	ς̇)))ρ̃∈σ̃	VERB
ejpam-5429	393	28	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	393	29	ð̃.	ð̃.	PROPN
ejpam-5429	393	30	since	since	SCONJ
ejpam-5429	393	31	ð̃σ̃ρ̃	ð̃σ̃ρ̃	PROPN
ejpam-5429	393	32	is	be	AUX
ejpam-5429	393	33	a	a	DET
ejpam-5429	393	34	fi	fi	NOUN
ejpam-5429	393	35	of	of	ADP
ejpam-5429	393	36	ℵ̃	ℵ̃	PROPN
ejpam-5429	393	37	,	,	PUNCT
ejpam-5429	393	38	we	we	PRON
ejpam-5429	393	39	have	have	VERB
ejpam-5429	393	40	ς̇	ς̇	NOUN
ejpam-5429	393	41	≬	≬	PROPN
ejpam-5429	393	42	(	(	PUNCT
ejpam-5429	393	43	ϱ̇	ϱ̇	PROPN
ejpam-5429	393	44	≬	≬	PROPN
ejpam-5429	393	45	(	(	PUNCT
ejpam-5429	393	46	ϱ̇	ϱ̇	PROPN
ejpam-5429	393	47	≬	≬	PROPN
ejpam-5429	393	48	ς̇	ς̇	NOUN
ejpam-5429	393	49	)	)	PUNCT
ejpam-5429	393	50	)	)	PUNCT
ejpam-5429	394	1	∈	∈	PROPN
ejpam-5429	394	2	ð̃σ̃ρ̃	ð̃σ̃ρ̃	PROPN
ejpam-5429	394	3	,	,	PUNCT
ejpam-5429	394	4	a	a	DET
ejpam-5429	394	5	contradiction	contradiction	NOUN
ejpam-5429	394	6	.	.	PUNCT
ejpam-5429	395	1	hence	hence	ADV
ejpam-5429	395	2	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	395	3	≬	≬	PROPN
ejpam-5429	395	4	(	(	PUNCT
ejpam-5429	395	5	ϱ̇	ϱ̇	PROPN
ejpam-5429	395	6	≬	≬	PROPN
ejpam-5429	395	7	(	(	PUNCT
ejpam-5429	395	8	ϱ̇	ϱ̇	PROPN
ejpam-5429	395	9	≬	≬	PROPN
ejpam-5429	395	10	ς̇	ς̇	NOUN
ejpam-5429	395	11	)	)	PUNCT
ejpam-5429	395	12	)	)	PUNCT
ejpam-5429	395	13	)	)	PUNCT
ejpam-5429	396	1	∨	∨	NUM
ejpam-5429	396	2	σ̃	σ̃	PROPN
ejpam-5429	396	3	≥	≥	NOUN
ejpam-5429	396	4	ð̃((ς̇	ð̃((ς̇	X
ejpam-5429	397	1	≬	≬	PROPN
ejpam-5429	397	2	ϱ̇	ϱ̇	PROPN
ejpam-5429	397	3	)	)	PUNCT
ejpam-5429	397	4	≬	≬	PROPN
ejpam-5429	397	5	κ̇	κ̇	PROPN
ejpam-5429	397	6	)	)	PUNCT
ejpam-5429	397	7	∧	∧	PROPN
ejpam-5429	397	8	ð̃(κ̇	ð̃(κ̇	PROPN
ejpam-5429	397	9	)	)	PUNCT
ejpam-5429	397	10	∧	∧	PROPN
ejpam-5429	397	11	τ̃	τ̃	PROPN
ejpam-5429	397	12	.	.	PUNCT
ejpam-5429	398	1	k.	k.	PROPN
ejpam-5429	398	2	h.	h.	PROPN
ejpam-5429	398	3	hakami	hakami	PROPN
ejpam-5429	398	4	et	et	PROPN
ejpam-5429	398	5	al	al	PROPN
ejpam-5429	398	6	.	.	PUNCT
ejpam-5429	398	7	/	/	SYM
ejpam-5429	398	8	eur	eur	PROPN
ejpam-5429	398	9	.	.	PUNCT
ejpam-5429	399	1	j.	j.	PROPN
ejpam-5429	399	2	pure	pure	PROPN
ejpam-5429	399	3	appl	appl	PROPN
ejpam-5429	399	4	.	.	PROPN
ejpam-5429	399	5	math	math	PROPN
ejpam-5429	399	6	,	,	PUNCT
ejpam-5429	399	7	17	17	NUM
ejpam-5429	399	8	(	(	PUNCT
ejpam-5429	399	9	4	4	NUM
ejpam-5429	399	10	)	)	PUNCT
ejpam-5429	399	11	(	(	PUNCT
ejpam-5429	399	12	2024	2024	NUM
ejpam-5429	399	13	)	)	PUNCT
ejpam-5429	399	14	,	,	PUNCT
ejpam-5429	399	15	3129	3129	NUM
ejpam-5429	399	16	-	-	SYM
ejpam-5429	399	17	3155	3155	NUM
ejpam-5429	399	18	3142	3142	NUM
ejpam-5429	399	19	therefore	therefore	ADV
ejpam-5429	399	20	ð̃	ð̃	PROPN
ejpam-5429	399	21	be	be	VERB
ejpam-5429	399	22	a	a	DET
ejpam-5429	399	23	qp-(∈σ̃,∈σ̃	qp-(∈σ̃,∈σ̃	NOUN
ejpam-5429	399	24	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	399	25	)	)	PUNCT
ejpam-5429	399	26	-ffi	-ffi	PROPN
ejpam-5429	399	27	of	of	ADP
ejpam-5429	399	28	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	399	29	(	(	PUNCT
ejpam-5429	399	30	2	2	NUM
ejpam-5429	399	31	)	)	PUNCT
ejpam-5429	399	32	the	the	DET
ejpam-5429	399	33	proof	proof	NOUN
ejpam-5429	399	34	follows	follow	VERB
ejpam-5429	399	35	a	a	DET
ejpam-5429	399	36	similar	similar	ADJ
ejpam-5429	399	37	pattern	pattern	NOUN
ejpam-5429	399	38	as	as	ADP
ejpam-5429	399	39	in	in	ADP
ejpam-5429	399	40	(	(	PUNCT
ejpam-5429	399	41	1	1	NUM
ejpam-5429	399	42	)	)	PUNCT
ejpam-5429	399	43	,	,	PUNCT
ejpam-5429	399	44	and	and	CCONJ
ejpam-5429	399	45	therefore	therefore	ADV
ejpam-5429	399	46	,	,	PUNCT
ejpam-5429	399	47	we	we	PRON
ejpam-5429	399	48	omit	omit	VERB
ejpam-5429	399	49	it	it	PRON
ejpam-5429	399	50	for	for	ADP
ejpam-5429	399	51	brevity	brevity	NOUN
ejpam-5429	399	52	.	.	PUNCT
ejpam-5429	400	1	(	(	PUNCT
ejpam-5429	400	2	3	3	X
ejpam-5429	400	3	)	)	PUNCT
ejpam-5429	400	4	let	let	VERB
ejpam-5429	400	5	ð̃	ð̃	PROPN
ejpam-5429	400	6	is	be	AUX
ejpam-5429	400	7	a	a	DET
ejpam-5429	400	8	qp-(∈σ̃,∈σ̃	qp-(∈σ̃,∈σ̃	NOUN
ejpam-5429	400	9	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	400	10	)	)	PUNCT
ejpam-5429	400	11	ffi	ffi	PROPN
ejpam-5429	400	12	of	of	ADP
ejpam-5429	400	13	ℵ̃	ℵ̃	PROPN
ejpam-5429	400	14	and	and	CCONJ
ejpam-5429	400	15	ρ̃	ρ̃	PROPN
ejpam-5429	400	16	∈	∈	PROPN
ejpam-5429	400	17	(	(	PUNCT
ejpam-5429	400	18	σ̃	σ̃	PROPN
ejpam-5429	400	19	,	,	PUNCT
ejpam-5429	400	20	1̂	1̂	NOUN
ejpam-5429	400	21	]	]	PUNCT
ejpam-5429	400	22	.	.	PUNCT
ejpam-5429	401	1	then	then	ADV
ejpam-5429	401	2	∀ς̇	∀ς̇	PROPN
ejpam-5429	401	3	∈	∈	PROPN
ejpam-5429	402	1	[	[	X
ejpam-5429	402	2	ð̃]τ̃ρ̃	ð̃]τ̃ρ̃	X
ejpam-5429	402	3	,	,	PUNCT
ejpam-5429	402	4	ς̇ρ̃	ς̇ρ̃	X
ejpam-5429	402	5	∈σ̃	∈σ̃	VERB
ejpam-5429	402	6	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	402	7	ð̃	ð̃	PROPN
ejpam-5429	402	8	⇒	⇒	PROPN
ejpam-5429	402	9	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	402	10	)	)	PUNCT
ejpam-5429	402	11	≥	≥	NOUN
ejpam-5429	402	12	ρ̃	ρ̃	PROPN
ejpam-5429	402	13	>	>	SYM
ejpam-5429	402	14	σ̃	σ̃	PROPN
ejpam-5429	402	15	or	or	CCONJ
ejpam-5429	402	16	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	402	17	)	)	PUNCT
ejpam-5429	402	18	>	>	PUNCT
ejpam-5429	403	1	2τ̃	2τ̃	NUM
ejpam-5429	404	1	−	−	ADP
ejpam-5429	404	2	ρ̃	ρ̃	PROPN
ejpam-5429	404	3	>	>	SYM
ejpam-5429	404	4	2τ̃	2τ̃	NUM
ejpam-5429	404	5	−	−	PROPN
ejpam-5429	404	6	1̂	1̂	NUM
ejpam-5429	404	7	=	=	SYM
ejpam-5429	404	8	σ̃.	σ̃.	PROPN
ejpam-5429	404	9	since	since	SCONJ
ejpam-5429	404	10	ð̃	ð̃	PROPN
ejpam-5429	404	11	is	be	AUX
ejpam-5429	404	12	a	a	DET
ejpam-5429	404	13	qp-(∈	qp-(∈	NOUN
ejpam-5429	404	14	σ̃,∈	σ̃,∈	PROPN
ejpam-5429	404	15	σ̃	σ̃	PROPN
ejpam-5429	404	16	∨	∨	PROPN
ejpam-5429	404	17	qτ̃	qτ̃	X
ejpam-5429	404	18	)	)	PUNCT
ejpam-5429	404	19	ffi	ffi	PROPN
ejpam-5429	404	20	of	of	ADP
ejpam-5429	404	21	ℵ̃	ℵ̃	PROPN
ejpam-5429	404	22	,	,	PUNCT
ejpam-5429	404	23	ð̃(0	ð̃(0	NOUN
ejpam-5429	404	24	)	)	PUNCT
ejpam-5429	404	25	∨	∨	NOUN
ejpam-5429	404	26	σ̃	σ̃	PROPN
ejpam-5429	404	27	≥	≥	NOUN
ejpam-5429	404	28	ð̃(ς̇	ð̃(ς̇	NOUN
ejpam-5429	404	29	)	)	PUNCT
ejpam-5429	404	30	∧	∧	PROPN
ejpam-5429	404	31	τ̃	τ̃	PROPN
ejpam-5429	404	32	>	>	PUNCT
ejpam-5429	404	33	σ̃	σ̃	PROPN
ejpam-5429	404	34	∧	∧	NOUN
ejpam-5429	404	35	τ̃	τ̃	PROPN
ejpam-5429	404	36	=	=	SYM
ejpam-5429	404	37	σ̃	σ̃	PROPN
ejpam-5429	404	38	,	,	PUNCT
ejpam-5429	404	39	and	and	CCONJ
ejpam-5429	404	40	so	so	ADV
ejpam-5429	404	41	ð̃(0	ð̃(0	NOUN
ejpam-5429	404	42	)	)	PUNCT
ejpam-5429	404	43	≥	≥	NOUN
ejpam-5429	405	1	σ̃	σ̃	PROPN
ejpam-5429	405	2	⇒	⇒	VERB
ejpam-5429	405	3	ð̃(0	ð̃(0	NOUN
ejpam-5429	405	4	)	)	PUNCT
ejpam-5429	405	5	≥	≥	NOUN
ejpam-5429	405	6	ð̃(ς̇	ð̃(ς̇	NOUN
ejpam-5429	405	7	)	)	PUNCT
ejpam-5429	405	8	∧	∧	PROPN
ejpam-5429	405	9	τ̃	τ̃	PROPN
ejpam-5429	405	10	.	.	PUNCT
ejpam-5429	406	1	case	case	NOUN
ejpam-5429	406	2	1	1	NUM
ejpam-5429	406	3	:	:	PUNCT
ejpam-5429	406	4	let	let	VERB
ejpam-5429	406	5	ρ̃	ρ̃	PROPN
ejpam-5429	406	6	∈	∈	PROPN
ejpam-5429	406	7	(	(	PUNCT
ejpam-5429	406	8	σ̃	σ̃	PROPN
ejpam-5429	406	9	,	,	PUNCT
ejpam-5429	406	10	τ̃	τ̃	PROPN
ejpam-5429	406	11	]	]	PUNCT
ejpam-5429	406	12	.	.	PUNCT
ejpam-5429	407	1	then	then	ADV
ejpam-5429	407	2	2τ̃	2τ̃	NUM
ejpam-5429	407	3	−	−	PROPN
ejpam-5429	407	4	ρ̃	ρ̃	PROPN
ejpam-5429	407	5	≥	≥	PRON
ejpam-5429	407	6	τ̃	τ̃	PROPN
ejpam-5429	407	7	≥	≥	NOUN
ejpam-5429	407	8	ρ̃	ρ̃	PROPN
ejpam-5429	407	9	,	,	PUNCT
ejpam-5429	407	10	ð̃(0	ð̃(0	NOUN
ejpam-5429	407	11	)	)	PUNCT
ejpam-5429	407	12	≥	≥	NOUN
ejpam-5429	407	13	ð̃(ς̇	ð̃(ς̇	NOUN
ejpam-5429	407	14	)	)	PUNCT
ejpam-5429	407	15	∧	∧	PROPN
ejpam-5429	407	16	τ̃	τ̃	PROPN
ejpam-5429	407	17	≥	≥	NOUN
ejpam-5429	407	18	ρ̃	ρ̃	PROPN
ejpam-5429	407	19	∧	∧	NOUN
ejpam-5429	407	20	τ̃	τ̃	PROPN
ejpam-5429	407	21	=	=	SYM
ejpam-5429	407	22	ρ̃	ρ̃	PROPN
ejpam-5429	407	23	or	or	CCONJ
ejpam-5429	407	24	ð̃(0	ð̃(0	NUM
ejpam-5429	407	25	)	)	PUNCT
ejpam-5429	407	26	≥	≥	NOUN
ejpam-5429	407	27	ð̃(ς̇	ð̃(ς̇	NOUN
ejpam-5429	407	28	)	)	PUNCT
ejpam-5429	408	1	∧	∧	PROPN
ejpam-5429	408	2	τ̃	τ̃	PROPN
ejpam-5429	408	3	>	>	X
ejpam-5429	408	4	(	(	PUNCT
ejpam-5429	408	5	2τ̃	2τ̃	PROPN
ejpam-5429	408	6	−	−	PROPN
ejpam-5429	408	7	ρ̃	ρ̃	PROPN
ejpam-5429	408	8	)	)	PUNCT
ejpam-5429	408	9	∧	∧	NOUN
ejpam-5429	408	10	τ̃	τ̃	PROPN
ejpam-5429	408	11	=	=	SYM
ejpam-5429	408	12	ρ̃	ρ̃	PROPN
ejpam-5429	408	13	∧	∧	NOUN
ejpam-5429	408	14	τ̃	τ̃	PROPN
ejpam-5429	408	15	=	=	SYM
ejpam-5429	408	16	ρ̃.	ρ̃.	PROPN
ejpam-5429	408	17	thus	thus	ADV
ejpam-5429	408	18	,	,	PUNCT
ejpam-5429	408	19	0ρ̃	0ρ̃	VERB
ejpam-5429	408	20	∈σ̃	∈σ̃	PROPN
ejpam-5429	409	1	ð̃.	ð̃.	NOUN
ejpam-5429	409	2	case	case	NOUN
ejpam-5429	409	3	2	2	X
ejpam-5429	409	4	:	:	PUNCT
ejpam-5429	409	5	let	let	VERB
ejpam-5429	409	6	ρ̃	ρ̃	PROPN
ejpam-5429	409	7	∈	∈	PROPN
ejpam-5429	409	8	(	(	PUNCT
ejpam-5429	409	9	τ̃	τ̃	PROPN
ejpam-5429	409	10	,	,	PUNCT
ejpam-5429	409	11	1̂	1̂	PROPN
ejpam-5429	409	12	]	]	PUNCT
ejpam-5429	409	13	.	.	PUNCT
ejpam-5429	410	1	then	then	ADV
ejpam-5429	410	2	2τ̃	2τ̃	NUM
ejpam-5429	410	3	−	−	PROPN
ejpam-5429	410	4	ρ̃	ρ̃	PROPN
ejpam-5429	410	5	<	<	X
ejpam-5429	410	6	τ̃	τ̃	X
ejpam-5429	410	7	<	<	X
ejpam-5429	410	8	ρ̃	ρ̃	PROPN
ejpam-5429	410	9	,	,	PUNCT
ejpam-5429	410	10	ð̃(0	ð̃(0	NOUN
ejpam-5429	410	11	)	)	PUNCT
ejpam-5429	410	12	≥	≥	NOUN
ejpam-5429	410	13	ð̃(ς̇	ð̃(ς̇	NOUN
ejpam-5429	410	14	)	)	PUNCT
ejpam-5429	411	1	∧	∧	NOUN
ejpam-5429	411	2	τ̃	τ̃	PROPN
ejpam-5429	411	3	=	=	SYM
ejpam-5429	411	4	ρ̃	ρ̃	PROPN
ejpam-5429	411	5	∧	∧	NOUN
ejpam-5429	411	6	τ̃	τ̃	PROPN
ejpam-5429	411	7	=	=	SYM
ejpam-5429	411	8	τ̃	τ̃	PROPN
ejpam-5429	411	9	>	>	X
ejpam-5429	412	1	2τ̃	2τ̃	NUM
ejpam-5429	413	1	−	−	ADP
ejpam-5429	413	2	ρ̃	ρ̃	PROPN
ejpam-5429	413	3	or	or	CCONJ
ejpam-5429	413	4	ð̃(0	ð̃(0	NUM
ejpam-5429	413	5	)	)	PUNCT
ejpam-5429	413	6	≥	≥	NOUN
ejpam-5429	413	7	ð̃(ς̇	ð̃(ς̇	NOUN
ejpam-5429	413	8	)	)	PUNCT
ejpam-5429	413	9	∧	∧	PROPN
ejpam-5429	413	10	τ̃	τ̃	PROPN
ejpam-5429	413	11	>	>	X
ejpam-5429	413	12	(	(	PUNCT
ejpam-5429	413	13	2τ̃	2τ̃	PROPN
ejpam-5429	413	14	−	−	PROPN
ejpam-5429	413	15	ρ̃	ρ̃	PROPN
ejpam-5429	413	16	)	)	PUNCT
ejpam-5429	413	17	∧	∧	NOUN
ejpam-5429	413	18	τ̃	τ̃	PUNCT
ejpam-5429	413	19	=	=	PUNCT
ejpam-5429	414	1	2τ̃	2τ̃	NUM
ejpam-5429	414	2	−	−	NUM
ejpam-5429	415	1	ρ̃.	ρ̃.	PROPN
ejpam-5429	415	2	hence	hence	ADV
ejpam-5429	415	3	,	,	PUNCT
ejpam-5429	415	4	0ρ̃qτ̃	0ρ̃qτ̃	PROPN
ejpam-5429	415	5	ð̃	ð̃	PROPN
ejpam-5429	415	6	⇒	⇒	VERB
ejpam-5429	415	7	0ρ̃	0ρ̃	VERB
ejpam-5429	416	1	∈σ̃	∈σ̃	VERB
ejpam-5429	416	2	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	416	3	ð̃.	ð̃.	NOUN
ejpam-5429	416	4	let	let	VERB
ejpam-5429	416	5	(	(	PUNCT
ejpam-5429	416	6	ς̇	ς̇	NOUN
ejpam-5429	416	7	≬	≬	PROPN
ejpam-5429	416	8	ϱ̇	ϱ̇	NUM
ejpam-5429	416	9	)	)	PUNCT
ejpam-5429	417	1	≬	≬	PROPN
ejpam-5429	417	2	κ̇	κ̇	PROPN
ejpam-5429	417	3	,	,	PUNCT
ejpam-5429	417	4	κ̇	κ̇	PROPN
ejpam-5429	417	5	∈	∈	PROPN
ejpam-5429	418	1	[	[	X
ejpam-5429	418	2	ð̃]τ̃ρ̃.	ð̃]τ̃ρ̃.	X
ejpam-5429	418	3	then	then	ADV
ejpam-5429	418	4	(	(	PUNCT
ejpam-5429	418	5	(	(	PUNCT
ejpam-5429	418	6	ς̇	ς̇	PROPN
ejpam-5429	418	7	≬	≬	PROPN
ejpam-5429	418	8	ϱ̇	ϱ̇	PROPN
ejpam-5429	418	9	)	)	PUNCT
ejpam-5429	418	10	≬	≬	PROPN
ejpam-5429	418	11	κ̇)ρ̃	κ̇)ρ̃	PROPN
ejpam-5429	418	12	,	,	PUNCT
ejpam-5429	418	13	κ̇ρ̃	κ̇ρ̃	PROPN
ejpam-5429	418	14	∈σ̃	∈σ̃	PROPN
ejpam-5429	418	15	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	418	16	ð̃	ð̃	PROPN
ejpam-5429	418	17	,	,	PUNCT
ejpam-5429	418	18	ð̃((ς̇≬ϱ̇	ð̃((ς̇≬ϱ̇	NUM
ejpam-5429	418	19	)	)	PUNCT
ejpam-5429	418	20	≬	≬	PROPN
ejpam-5429	418	21	κ̇	κ̇	PROPN
ejpam-5429	418	22	)	)	PUNCT
ejpam-5429	418	23	≥	≥	NOUN
ejpam-5429	418	24	ρ̃	ρ̃	PROPN
ejpam-5429	418	25	>	>	SYM
ejpam-5429	418	26	σ̃	σ̃	PROPN
ejpam-5429	418	27	or	or	CCONJ
ejpam-5429	418	28	ð̃((ς̇	ð̃((ς̇	PUNCT
ejpam-5429	418	29	≬	≬	PROPN
ejpam-5429	418	30	ϱ̇	ϱ̇	PROPN
ejpam-5429	418	31	)	)	PUNCT
ejpam-5429	418	32	≬	≬	PROPN
ejpam-5429	418	33	κ̇	κ̇	PROPN
ejpam-5429	418	34	)	)	PUNCT
ejpam-5429	418	35	>	>	X
ejpam-5429	418	36	2τ	2τ	NUM
ejpam-5429	419	1	−	−	PROPN
ejpam-5429	419	2	ρ̃	ρ̃	PROPN
ejpam-5429	419	3	>	>	SYM
ejpam-5429	420	1	2τ̃	2τ̃	NUM
ejpam-5429	420	2	−	−	NOUN
ejpam-5429	420	3	1̂	1̂	NUM
ejpam-5429	421	1	=	=	SYM
ejpam-5429	421	2	σ̃	σ̃	PROPN
ejpam-5429	421	3	and	and	CCONJ
ejpam-5429	421	4	ð̃(κ̇	ð̃(κ̇	PROPN
ejpam-5429	421	5	)	)	PUNCT
ejpam-5429	421	6	≥	≥	NOUN
ejpam-5429	421	7	ρ̃	ρ̃	PROPN
ejpam-5429	421	8	>	>	SYM
ejpam-5429	421	9	σ̃	σ̃	PROPN
ejpam-5429	421	10	or	or	CCONJ
ejpam-5429	421	11	≥	≥	NOUN
ejpam-5429	421	12	(	(	PUNCT
ejpam-5429	421	13	2τ̃	2τ̃	PROPN
ejpam-5429	421	14	−	−	PROPN
ejpam-5429	421	15	ρ̃	ρ̃	PROPN
ejpam-5429	421	16	)	)	PUNCT
ejpam-5429	421	17	∧	∧	PROPN
ejpam-5429	421	18	τ̃	τ̃	PROPN
ejpam-5429	421	19	ð̃(κ̇	ð̃(κ̇	PROPN
ejpam-5429	421	20	)	)	PUNCT
ejpam-5429	421	21	>	>	X
ejpam-5429	422	1	2τ̃	2τ̃	NUM
ejpam-5429	422	2	−	−	PUNCT
ejpam-5429	423	1	ρ̃	ρ̃	PROPN
ejpam-5429	423	2	=	=	SYM
ejpam-5429	423	3	2τ̃	2τ̃	NUM
ejpam-5429	423	4	−	−	PROPN
ejpam-5429	423	5	ρ̃	ρ̃	PROPN
ejpam-5429	423	6	>	>	SYM
ejpam-5429	423	7	2τ̃	2τ̃	NUM
ejpam-5429	423	8	−	−	PROPN
ejpam-5429	423	9	1̂	1̂	NUM
ejpam-5429	423	10	=	=	SYM
ejpam-5429	424	1	σ̃.	σ̃.	PROPN
ejpam-5429	424	2	since	since	SCONJ
ejpam-5429	424	3	ð̃	ð̃	PROPN
ejpam-5429	424	4	is	be	AUX
ejpam-5429	424	5	a	a	DET
ejpam-5429	424	6	qp-(∈σ̃,∈σ̃	qp-(∈σ̃,∈σ̃	NOUN
ejpam-5429	424	7	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	424	8	)	)	PUNCT
ejpam-5429	424	9	-ffi	-ffi	PROPN
ejpam-5429	424	10	of	of	ADP
ejpam-5429	424	11	ℵ̃	ℵ̃	PROPN
ejpam-5429	424	12	,	,	PUNCT
ejpam-5429	424	13	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	424	14	≬	≬	PROPN
ejpam-5429	424	15	(	(	PUNCT
ejpam-5429	424	16	ϱ̇	ϱ̇	PROPN
ejpam-5429	424	17	≬	≬	PROPN
ejpam-5429	424	18	(	(	PUNCT
ejpam-5429	424	19	ϱ̇	ϱ̇	PROPN
ejpam-5429	424	20	≬	≬	PROPN
ejpam-5429	424	21	ς̇	ς̇	NOUN
ejpam-5429	424	22	)	)	PUNCT
ejpam-5429	424	23	)	)	PUNCT
ejpam-5429	424	24	)	)	PUNCT
ejpam-5429	425	1	∨	∨	NUM
ejpam-5429	425	2	σ̃	σ̃	PROPN
ejpam-5429	425	3	≥	≥	NOUN
ejpam-5429	425	4	ð̃((ς̇	ð̃((ς̇	X
ejpam-5429	426	1	≬	≬	PROPN
ejpam-5429	426	2	ϱ̇	ϱ̇	PROPN
ejpam-5429	426	3	)	)	PUNCT
ejpam-5429	426	4	≬	≬	PROPN
ejpam-5429	426	5	κ̇	κ̇	PROPN
ejpam-5429	426	6	)	)	PUNCT
ejpam-5429	426	7	∧	∧	PROPN
ejpam-5429	426	8	ð̃(κ̇	ð̃(κ̇	PROPN
ejpam-5429	426	9	)	)	PUNCT
ejpam-5429	426	10	∧	∧	NOUN
ejpam-5429	426	11	τ̃	τ̃	PROPN
ejpam-5429	426	12	>	>	PUNCT
ejpam-5429	426	13	σ̃	σ̃	PROPN
ejpam-5429	426	14	∧	∧	NOUN
ejpam-5429	426	15	σ̃	σ̃	PROPN
ejpam-5429	426	16	∧	∧	PROPN
ejpam-5429	426	17	τ̃	τ̃	X
ejpam-5429	426	18	>	>	X
ejpam-5429	426	19	σ̃	σ̃	PROPN
ejpam-5429	426	20	∧	∧	NOUN
ejpam-5429	426	21	τ̃	τ̃	PROPN
ejpam-5429	427	1	=	=	SYM
ejpam-5429	427	2	σ̃.	σ̃.	PROPN
ejpam-5429	427	3	therefore	therefore	ADV
ejpam-5429	427	4	,	,	PUNCT
ejpam-5429	427	5	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	427	6	≬	≬	PROPN
ejpam-5429	427	7	(	(	PUNCT
ejpam-5429	427	8	ϱ̇	ϱ̇	PROPN
ejpam-5429	427	9	≬	≬	PROPN
ejpam-5429	427	10	(	(	PUNCT
ejpam-5429	427	11	ϱ̇	ϱ̇	PROPN
ejpam-5429	427	12	≬	≬	PROPN
ejpam-5429	427	13	ς̇	ς̇	NOUN
ejpam-5429	427	14	)	)	PUNCT
ejpam-5429	427	15	)	)	PUNCT
ejpam-5429	427	16	)	)	PUNCT
ejpam-5429	427	17	≥	≥	X
ejpam-5429	428	1	σ̃	σ̃	PROPN
ejpam-5429	428	2	⇒	⇒	VERB
ejpam-5429	428	3	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	429	1	≬	≬	PROPN
ejpam-5429	429	2	(	(	PUNCT
ejpam-5429	429	3	ϱ̇	ϱ̇	PROPN
ejpam-5429	429	4	≬	≬	PROPN
ejpam-5429	429	5	(	(	PUNCT
ejpam-5429	429	6	ϱ̇	ϱ̇	PROPN
ejpam-5429	429	7	≬	≬	PROPN
ejpam-5429	429	8	ς̇	ς̇	NOUN
ejpam-5429	429	9	)	)	PUNCT
ejpam-5429	429	10	)	)	PUNCT
ejpam-5429	429	11	)	)	PUNCT
ejpam-5429	430	1	≥	≥	X
ejpam-5429	430	2	ð̃((ς̇	ð̃((ς̇	X
ejpam-5429	431	1	≬	≬	PROPN
ejpam-5429	431	2	ϱ̇	ϱ̇	PROPN
ejpam-5429	431	3	)	)	PUNCT
ejpam-5429	431	4	≬	≬	PROPN
ejpam-5429	431	5	κ̇	κ̇	PROPN
ejpam-5429	431	6	)	)	PUNCT
ejpam-5429	431	7	∧	∧	PROPN
ejpam-5429	431	8	ð̃(κ̇	ð̃(κ̇	PROPN
ejpam-5429	431	9	)	)	PUNCT
ejpam-5429	431	10	∧	∧	PROPN
ejpam-5429	431	11	τ̃	τ̃	PROPN
ejpam-5429	431	12	.	.	PUNCT
ejpam-5429	431	13	case	case	NOUN
ejpam-5429	431	14	1	1	NUM
ejpam-5429	431	15	:	:	PUNCT
ejpam-5429	431	16	let	let	VERB
ejpam-5429	431	17	ρ̃	ρ̃	PROPN
ejpam-5429	431	18	∈	∈	PROPN
ejpam-5429	431	19	(	(	PUNCT
ejpam-5429	431	20	σ̃	σ̃	PROPN
ejpam-5429	431	21	,	,	PUNCT
ejpam-5429	431	22	τ̃	τ̃	PROPN
ejpam-5429	431	23	]	]	PUNCT
ejpam-5429	431	24	.	.	PUNCT
ejpam-5429	432	1	then	then	ADV
ejpam-5429	432	2	2τ̃	2τ̃	NUM
ejpam-5429	432	3	−	−	PROPN
ejpam-5429	432	4	ρ̃	ρ̃	PROPN
ejpam-5429	432	5	≥	≥	PRON
ejpam-5429	432	6	τ̃	τ̃	PROPN
ejpam-5429	432	7	≥	≥	NOUN
ejpam-5429	432	8	ρ̃	ρ̃	PROPN
ejpam-5429	432	9	,	,	PUNCT
ejpam-5429	432	10	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	432	11	≬	≬	PROPN
ejpam-5429	432	12	(	(	PUNCT
ejpam-5429	432	13	ϱ̇	ϱ̇	PROPN
ejpam-5429	432	14	≬	≬	PROPN
ejpam-5429	432	15	(	(	PUNCT
ejpam-5429	432	16	ϱ̇	ϱ̇	PROPN
ejpam-5429	432	17	≬	≬	PROPN
ejpam-5429	432	18	ς̇	ς̇	NOUN
ejpam-5429	432	19	)	)	PUNCT
ejpam-5429	432	20	)	)	PUNCT
ejpam-5429	432	21	)	)	PUNCT
ejpam-5429	433	1	≥	≥	X
ejpam-5429	433	2	ð̃((ς̇	ð̃((ς̇	X
ejpam-5429	434	1	≬	≬	PROPN
ejpam-5429	434	2	ϱ̇	ϱ̇	PROPN
ejpam-5429	434	3	)	)	PUNCT
ejpam-5429	434	4	≬	≬	PROPN
ejpam-5429	434	5	κ̇	κ̇	PROPN
ejpam-5429	434	6	)	)	PUNCT
ejpam-5429	434	7	∧	∧	PROPN
ejpam-5429	434	8	ð̃(κ̇	ð̃(κ̇	PROPN
ejpam-5429	434	9	)	)	PUNCT
ejpam-5429	434	10	∧	∧	PROPN
ejpam-5429	434	11	τ̃	τ̃	PROPN
ejpam-5429	434	12	≥	≥	NOUN
ejpam-5429	434	13	ρ̃	ρ̃	PROPN
ejpam-5429	434	14	∧	∧	NOUN
ejpam-5429	434	15	ρ̃	ρ̃	PROPN
ejpam-5429	434	16	∧	∧	NOUN
ejpam-5429	434	17	τ̃	τ̃	PROPN
ejpam-5429	434	18	=	=	SYM
ejpam-5429	434	19	ρ̃	ρ̃	PROPN
ejpam-5429	434	20	∧	∧	NOUN
ejpam-5429	434	21	τ̃	τ̃	PROPN
ejpam-5429	434	22	=	=	SYM
ejpam-5429	434	23	ρ̃	ρ̃	PROPN
ejpam-5429	434	24	k.	k.	PROPN
ejpam-5429	434	25	h.	h.	PROPN
ejpam-5429	434	26	hakami	hakami	PROPN
ejpam-5429	434	27	et	et	PROPN
ejpam-5429	434	28	al	al	PROPN
ejpam-5429	434	29	.	.	PUNCT
ejpam-5429	434	30	/	/	SYM
ejpam-5429	434	31	eur	eur	PROPN
ejpam-5429	434	32	.	.	PUNCT
ejpam-5429	435	1	j.	j.	PROPN
ejpam-5429	435	2	pure	pure	PROPN
ejpam-5429	435	3	appl	appl	PROPN
ejpam-5429	435	4	.	.	PROPN
ejpam-5429	435	5	math	math	PROPN
ejpam-5429	435	6	,	,	PUNCT
ejpam-5429	435	7	17	17	NUM
ejpam-5429	435	8	(	(	PUNCT
ejpam-5429	435	9	4	4	NUM
ejpam-5429	435	10	)	)	PUNCT
ejpam-5429	435	11	(	(	PUNCT
ejpam-5429	435	12	2024	2024	NUM
ejpam-5429	435	13	)	)	PUNCT
ejpam-5429	435	14	,	,	PUNCT
ejpam-5429	435	15	3129	3129	NUM
ejpam-5429	435	16	-	-	SYM
ejpam-5429	435	17	3155	3155	NUM
ejpam-5429	435	18	3143	3143	NUM
ejpam-5429	435	19	or	or	CCONJ
ejpam-5429	435	20	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	435	21	≬	≬	PROPN
ejpam-5429	435	22	(	(	PUNCT
ejpam-5429	435	23	ϱ̇	ϱ̇	PROPN
ejpam-5429	435	24	≬	≬	PROPN
ejpam-5429	435	25	(	(	PUNCT
ejpam-5429	435	26	ϱ̇	ϱ̇	PROPN
ejpam-5429	435	27	≬	≬	PROPN
ejpam-5429	435	28	ς̇	ς̇	NOUN
ejpam-5429	435	29	)	)	PUNCT
ejpam-5429	435	30	)	)	PUNCT
ejpam-5429	435	31	)	)	PUNCT
ejpam-5429	436	1	≥	≥	X
ejpam-5429	436	2	ð̃((ς̇	ð̃((ς̇	X
ejpam-5429	437	1	≬	≬	PROPN
ejpam-5429	437	2	ϱ̇	ϱ̇	PROPN
ejpam-5429	437	3	)	)	PUNCT
ejpam-5429	437	4	≬	≬	PROPN
ejpam-5429	437	5	κ̇	κ̇	PROPN
ejpam-5429	437	6	)	)	PUNCT
ejpam-5429	437	7	∧	∧	PROPN
ejpam-5429	437	8	ð̃(κ̇	ð̃(κ̇	PROPN
ejpam-5429	437	9	)	)	PUNCT
ejpam-5429	437	10	∧	∧	PROPN
ejpam-5429	437	11	τ̃	τ̃	PROPN
ejpam-5429	437	12	≥	≥	NOUN
ejpam-5429	437	13	ρ̃	ρ̃	PROPN
ejpam-5429	437	14	∧	∧	PROPN
ejpam-5429	437	15	(	(	PUNCT
ejpam-5429	437	16	2τ̃	2τ̃	PROPN
ejpam-5429	437	17	−	−	PROPN
ejpam-5429	437	18	ρ̃	ρ̃	PROPN
ejpam-5429	437	19	)	)	PUNCT
ejpam-5429	437	20	∧	∧	NOUN
ejpam-5429	437	21	τ̃	τ̃	PROPN
ejpam-5429	437	22	=	=	SYM
ejpam-5429	437	23	ρ̃	ρ̃	PROPN
ejpam-5429	437	24	∧	∧	NOUN
ejpam-5429	437	25	τ̃	τ̃	PROPN
ejpam-5429	437	26	∧	∧	NOUN
ejpam-5429	437	27	τ̃	τ̃	PROPN
ejpam-5429	437	28	=	=	SYM
ejpam-5429	437	29	ρ̃	ρ̃	PROPN
ejpam-5429	437	30	∧	∧	NOUN
ejpam-5429	437	31	τ̃	τ̃	PROPN
ejpam-5429	437	32	=	=	SYM
ejpam-5429	437	33	ρ̃	ρ̃	PROPN
ejpam-5429	437	34	or	or	CCONJ
ejpam-5429	437	35	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	437	36	≬	≬	PROPN
ejpam-5429	437	37	(	(	PUNCT
ejpam-5429	437	38	ϱ̇	ϱ̇	PROPN
ejpam-5429	437	39	≬	≬	PROPN
ejpam-5429	437	40	(	(	PUNCT
ejpam-5429	437	41	ϱ̇	ϱ̇	PROPN
ejpam-5429	437	42	≬	≬	PROPN
ejpam-5429	437	43	ς̇	ς̇	NOUN
ejpam-5429	437	44	)	)	PUNCT
ejpam-5429	437	45	)	)	PUNCT
ejpam-5429	437	46	)	)	PUNCT
ejpam-5429	438	1	≥	≥	X
ejpam-5429	438	2	ð̃((ς̇	ð̃((ς̇	X
ejpam-5429	439	1	≬	≬	PROPN
ejpam-5429	439	2	ϱ̇	ϱ̇	PROPN
ejpam-5429	439	3	)	)	PUNCT
ejpam-5429	439	4	≬	≬	PROPN
ejpam-5429	439	5	κ̇	κ̇	PROPN
ejpam-5429	439	6	)	)	PUNCT
ejpam-5429	439	7	∧	∧	PROPN
ejpam-5429	439	8	ð̃(κ̇	ð̃(κ̇	PROPN
ejpam-5429	439	9	)	)	PUNCT
ejpam-5429	439	10	∧	∧	PROPN
ejpam-5429	439	11	τ̃	τ̃	PROPN
ejpam-5429	439	12	≥	≥	X
ejpam-5429	439	13	(	(	PUNCT
ejpam-5429	439	14	2τ̃	2τ̃	PROPN
ejpam-5429	439	15	−	−	PART
ejpam-5429	439	16	ρ̃	ρ̃	PROPN
ejpam-5429	439	17	)	)	PUNCT
ejpam-5429	439	18	∧	∧	NOUN
ejpam-5429	439	19	(	(	PUNCT
ejpam-5429	439	20	2τ̃	2τ̃	PROPN
ejpam-5429	439	21	−	−	PROPN
ejpam-5429	439	22	ρ̃	ρ̃	PROPN
ejpam-5429	439	23	)	)	PUNCT
ejpam-5429	439	24	∧	∧	NOUN
ejpam-5429	439	25	τ̃	τ̃	PROPN
ejpam-5429	439	26	=	=	SYM
ejpam-5429	439	27	τ̃	τ̃	PROPN
ejpam-5429	439	28	∧	∧	NOUN
ejpam-5429	439	29	τ̃	τ̃	PROPN
ejpam-5429	439	30	∧	∧	NOUN
ejpam-5429	439	31	τ̃	τ̃	PROPN
ejpam-5429	439	32	=	=	SYM
ejpam-5429	440	1	τ̃	τ̃	PROPN
ejpam-5429	440	2	>	>	X
ejpam-5429	440	3	ρ̃.	ρ̃.	PROPN
ejpam-5429	440	4	hence	hence	ADV
ejpam-5429	440	5	,	,	PUNCT
ejpam-5429	440	6	(	(	PUNCT
ejpam-5429	440	7	ς̇	ς̇	PROPN
ejpam-5429	440	8	≬	≬	PROPN
ejpam-5429	440	9	(	(	PUNCT
ejpam-5429	440	10	ϱ̇	ϱ̇	PROPN
ejpam-5429	440	11	≬	≬	PROPN
ejpam-5429	440	12	(	(	PUNCT
ejpam-5429	440	13	ϱ̇	ϱ̇	PROPN
ejpam-5429	440	14	≬	≬	PROPN
ejpam-5429	440	15	ς̇)))ρ̃	ς̇)))ρ̃	PROPN
ejpam-5429	440	16	∈σ̃	∈σ̃	PROPN
ejpam-5429	441	1	ð̃.	ð̃.	NOUN
ejpam-5429	441	2	case	case	NOUN
ejpam-5429	441	3	2	2	X
ejpam-5429	441	4	:	:	PUNCT
ejpam-5429	441	5	let	let	VERB
ejpam-5429	441	6	ρ̃	ρ̃	PROPN
ejpam-5429	441	7	∈	∈	PROPN
ejpam-5429	441	8	(	(	PUNCT
ejpam-5429	441	9	τ̃	τ̃	PROPN
ejpam-5429	441	10	,	,	PUNCT
ejpam-5429	441	11	1̂	1̂	PROPN
ejpam-5429	441	12	]	]	PUNCT
ejpam-5429	441	13	.	.	PUNCT
ejpam-5429	442	1	then	then	ADV
ejpam-5429	442	2	2τ̃	2τ̃	NUM
ejpam-5429	442	3	−	−	PROPN
ejpam-5429	442	4	ρ̃	ρ̃	PROPN
ejpam-5429	442	5	<	<	X
ejpam-5429	442	6	τ̃	τ̃	X
ejpam-5429	442	7	<	<	X
ejpam-5429	442	8	ρ̃	ρ̃	PROPN
ejpam-5429	442	9	,	,	PUNCT
ejpam-5429	442	10	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	442	11	≬	≬	PROPN
ejpam-5429	442	12	(	(	PUNCT
ejpam-5429	442	13	ϱ̇	ϱ̇	PROPN
ejpam-5429	442	14	≬	≬	PROPN
ejpam-5429	442	15	(	(	PUNCT
ejpam-5429	442	16	ϱ̇	ϱ̇	PROPN
ejpam-5429	442	17	≬	≬	PROPN
ejpam-5429	442	18	ς̇	ς̇	NOUN
ejpam-5429	442	19	)	)	PUNCT
ejpam-5429	442	20	)	)	PUNCT
ejpam-5429	442	21	)	)	PUNCT
ejpam-5429	443	1	≥	≥	X
ejpam-5429	443	2	ð̃((ς̇	ð̃((ς̇	X
ejpam-5429	444	1	≬	≬	PROPN
ejpam-5429	444	2	ϱ̇	ϱ̇	PROPN
ejpam-5429	444	3	)	)	PUNCT
ejpam-5429	444	4	≬	≬	PROPN
ejpam-5429	444	5	κ̇	κ̇	PROPN
ejpam-5429	444	6	)	)	PUNCT
ejpam-5429	444	7	∧	∧	PROPN
ejpam-5429	444	8	ð̃(κ̇	ð̃(κ̇	PROPN
ejpam-5429	444	9	)	)	PUNCT
ejpam-5429	444	10	∧	∧	PROPN
ejpam-5429	444	11	τ̃	τ̃	PROPN
ejpam-5429	444	12	≥	≥	NOUN
ejpam-5429	444	13	ρ̃	ρ̃	PROPN
ejpam-5429	444	14	∧	∧	NOUN
ejpam-5429	444	15	ρ̃	ρ̃	PROPN
ejpam-5429	444	16	∧	∧	NOUN
ejpam-5429	444	17	τ̃	τ̃	PROPN
ejpam-5429	444	18	=	=	SYM
ejpam-5429	444	19	ρ̃	ρ̃	PROPN
ejpam-5429	444	20	∧	∧	NOUN
ejpam-5429	444	21	τ̃	τ̃	PROPN
ejpam-5429	444	22	=	=	SYM
ejpam-5429	444	23	τ̃	τ̃	PROPN
ejpam-5429	444	24	>	>	X
ejpam-5429	445	1	2τ̃	2τ̃	NUM
ejpam-5429	445	2	−	−	ADP
ejpam-5429	445	3	ρ̃	ρ̃	PROPN
ejpam-5429	445	4	or	or	CCONJ
ejpam-5429	445	5	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	445	6	≬	≬	PROPN
ejpam-5429	445	7	(	(	PUNCT
ejpam-5429	445	8	ϱ̇	ϱ̇	PROPN
ejpam-5429	445	9	≬	≬	PROPN
ejpam-5429	445	10	(	(	PUNCT
ejpam-5429	445	11	ϱ̇	ϱ̇	PROPN
ejpam-5429	445	12	≬	≬	PROPN
ejpam-5429	445	13	ς̇	ς̇	NOUN
ejpam-5429	445	14	)	)	PUNCT
ejpam-5429	445	15	)	)	PUNCT
ejpam-5429	445	16	)	)	PUNCT
ejpam-5429	446	1	≥	≥	X
ejpam-5429	446	2	ð̃((ς̇	ð̃((ς̇	X
ejpam-5429	447	1	≬	≬	PROPN
ejpam-5429	447	2	ϱ̇	ϱ̇	PROPN
ejpam-5429	447	3	)	)	PUNCT
ejpam-5429	447	4	≬	≬	PROPN
ejpam-5429	447	5	κ̇	κ̇	PROPN
ejpam-5429	447	6	)	)	PUNCT
ejpam-5429	447	7	∧	∧	PROPN
ejpam-5429	447	8	ð̃(κ̇	ð̃(κ̇	PROPN
ejpam-5429	447	9	)	)	PUNCT
ejpam-5429	447	10	∧	∧	PROPN
ejpam-5429	447	11	τ̃	τ̃	PROPN
ejpam-5429	447	12	≥	≥	NOUN
ejpam-5429	447	13	ρ̃	ρ̃	PROPN
ejpam-5429	447	14	∧	∧	PROPN
ejpam-5429	447	15	(	(	PUNCT
ejpam-5429	447	16	2τ̃	2τ̃	PROPN
ejpam-5429	447	17	−	−	PROPN
ejpam-5429	447	18	ρ̃	ρ̃	PROPN
ejpam-5429	447	19	)	)	PUNCT
ejpam-5429	447	20	∧	∧	PROPN
ejpam-5429	447	21	τ̃	τ̃	PROPN
ejpam-5429	447	22	≥	≥	NOUN
ejpam-5429	447	23	τ̃	τ̃	NOUN
ejpam-5429	447	24	∧	∧	PROPN
ejpam-5429	447	25	(	(	PUNCT
ejpam-5429	447	26	2τ̃	2τ̃	PROPN
ejpam-5429	447	27	−	−	PART
ejpam-5429	447	28	ρ̃	ρ̃	PROPN
ejpam-5429	447	29	)	)	PUNCT
ejpam-5429	447	30	∧	∧	PROPN
ejpam-5429	447	31	τ̃	τ̃	PROPN
ejpam-5429	447	32	≥	≥	NOUN
ejpam-5429	447	33	τ̃	τ̃	NOUN
ejpam-5429	447	34	∧	∧	PROPN
ejpam-5429	447	35	(	(	PUNCT
ejpam-5429	447	36	2τ̃	2τ̃	PROPN
ejpam-5429	447	37	−	−	PROPN
ejpam-5429	447	38	ρ̃	ρ̃	PROPN
ejpam-5429	447	39	)	)	PUNCT
ejpam-5429	447	40	=	=	PUNCT
ejpam-5429	447	41	(	(	PUNCT
ejpam-5429	447	42	2τ̃	2τ̃	PROPN
ejpam-5429	447	43	−	−	NOUN
ejpam-5429	447	44	ρ̃	ρ̃	PROPN
ejpam-5429	447	45	)	)	PUNCT
ejpam-5429	447	46	or	or	CCONJ
ejpam-5429	447	47	ð̃(ς̇	ð̃(ς̇	PROPN
ejpam-5429	447	48	≬	≬	PROPN
ejpam-5429	447	49	(	(	PUNCT
ejpam-5429	447	50	ϱ̇	ϱ̇	PROPN
ejpam-5429	447	51	≬	≬	PROPN
ejpam-5429	447	52	(	(	PUNCT
ejpam-5429	447	53	ϱ̇	ϱ̇	PROPN
ejpam-5429	447	54	≬	≬	PROPN
ejpam-5429	447	55	ς̇	ς̇	NOUN
ejpam-5429	447	56	)	)	PUNCT
ejpam-5429	447	57	)	)	PUNCT
ejpam-5429	447	58	)	)	PUNCT
ejpam-5429	448	1	≥	≥	X
ejpam-5429	448	2	ð̃((ς̇	ð̃((ς̇	X
ejpam-5429	449	1	≬	≬	PROPN
ejpam-5429	449	2	ϱ̇	ϱ̇	PROPN
ejpam-5429	449	3	)	)	PUNCT
ejpam-5429	449	4	≬	≬	PROPN
ejpam-5429	449	5	κ̇	κ̇	PROPN
ejpam-5429	449	6	)	)	PUNCT
ejpam-5429	449	7	∧	∧	PROPN
ejpam-5429	449	8	ð̃(κ̇	ð̃(κ̇	PROPN
ejpam-5429	449	9	)	)	PUNCT
ejpam-5429	449	10	∧	∧	PROPN
ejpam-5429	449	11	τ̃	τ̃	PROPN
ejpam-5429	449	12	≥	≥	X
ejpam-5429	449	13	(	(	PUNCT
ejpam-5429	449	14	2τ̃	2τ̃	PROPN
ejpam-5429	449	15	−	−	PART
ejpam-5429	449	16	ρ̃	ρ̃	PROPN
ejpam-5429	449	17	)	)	PUNCT
ejpam-5429	449	18	∧	∧	NOUN
ejpam-5429	449	19	(	(	PUNCT
ejpam-5429	449	20	2τ̃	2τ̃	PROPN
ejpam-5429	449	21	−	−	PROPN
ejpam-5429	449	22	ρ̃	ρ̃	PROPN
ejpam-5429	449	23	)	)	PUNCT
ejpam-5429	449	24	∧	∧	PROPN
ejpam-5429	449	25	τ̃	τ̃	PROPN
ejpam-5429	449	26	≥	≥	X
ejpam-5429	449	27	(	(	PUNCT
ejpam-5429	449	28	2τ̃	2τ̃	PROPN
ejpam-5429	449	29	−	−	PROPN
ejpam-5429	449	30	ρ̃	ρ̃	PROPN
ejpam-5429	449	31	)	)	PUNCT
ejpam-5429	449	32	∧	∧	PROPN
ejpam-5429	449	33	τ̃	τ̃	PROPN
ejpam-5429	449	34	>	>	X
ejpam-5429	449	35	(	(	PUNCT
ejpam-5429	449	36	2τ̃	2τ̃	PROPN
ejpam-5429	449	37	−	−	PROPN
ejpam-5429	449	38	ρ̃	ρ̃	PROPN
ejpam-5429	449	39	)	)	PUNCT
ejpam-5429	449	40	.	.	PUNCT
ejpam-5429	450	1	thus	thus	ADV
ejpam-5429	450	2	,	,	PUNCT
ejpam-5429	450	3	(	(	PUNCT
ejpam-5429	450	4	ς̇	ς̇	PROPN
ejpam-5429	450	5	≬	≬	PROPN
ejpam-5429	450	6	(	(	PUNCT
ejpam-5429	450	7	ϱ̇	ϱ̇	PROPN
ejpam-5429	450	8	≬	≬	PROPN
ejpam-5429	450	9	(	(	PUNCT
ejpam-5429	450	10	ϱ̇	ϱ̇	PROPN
ejpam-5429	450	11	≬	≬	PROPN
ejpam-5429	450	12	ς̇)))ρ̃qτ̃	ς̇)))ρ̃qτ̃	ADJ
ejpam-5429	450	13	ð̃.	ð̃.	NOUN
ejpam-5429	450	14	hence	hence	ADV
ejpam-5429	450	15	,	,	PUNCT
ejpam-5429	450	16	(	(	PUNCT
ejpam-5429	450	17	ς̇	ς̇	PROPN
ejpam-5429	450	18	≬	≬	PROPN
ejpam-5429	450	19	(	(	PUNCT
ejpam-5429	450	20	ϱ̇	ϱ̇	PROPN
ejpam-5429	450	21	≬	≬	PROPN
ejpam-5429	450	22	(	(	PUNCT
ejpam-5429	450	23	ϱ̇	ϱ̇	PROPN
ejpam-5429	450	24	≬	≬	PROPN
ejpam-5429	450	25	ς̇)))ρ̃	ς̇)))ρ̃	PROPN
ejpam-5429	450	26	∈σ̃	∈σ̃	PROPN
ejpam-5429	450	27	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	450	28	ð̃	ð̃	PROPN
ejpam-5429	450	29	⇒	⇒	NOUN
ejpam-5429	450	30	(	(	PUNCT
ejpam-5429	450	31	ς̇	ς̇	NOUN
ejpam-5429	450	32	≬	≬	PROPN
ejpam-5429	450	33	(	(	PUNCT
ejpam-5429	450	34	ϱ̇	ϱ̇	PROPN
ejpam-5429	450	35	≬	≬	PROPN
ejpam-5429	450	36	(	(	PUNCT
ejpam-5429	450	37	ϱ̇	ϱ̇	PROPN
ejpam-5429	450	38	≬	≬	PROPN
ejpam-5429	450	39	ς̇	ς̇	NOUN
ejpam-5429	450	40	)	)	PUNCT
ejpam-5429	450	41	)	)	PUNCT
ejpam-5429	450	42	)	)	PUNCT
ejpam-5429	451	1	∈	∈	PROPN
ejpam-5429	452	1	[	[	X
ejpam-5429	452	2	ð̃]τ̃ρ̃.	ð̃]τ̃ρ̃.	X
ejpam-5429	452	3	k.	k.	PROPN
ejpam-5429	452	4	h.	h.	PROPN
ejpam-5429	452	5	hakami	hakami	PROPN
ejpam-5429	452	6	et	et	PROPN
ejpam-5429	452	7	al	al	PROPN
ejpam-5429	452	8	.	.	PUNCT
ejpam-5429	452	9	/	/	SYM
ejpam-5429	452	10	eur	eur	PROPN
ejpam-5429	452	11	.	.	PUNCT
ejpam-5429	453	1	j.	j.	PROPN
ejpam-5429	453	2	pure	pure	PROPN
ejpam-5429	453	3	appl	appl	PROPN
ejpam-5429	453	4	.	.	PROPN
ejpam-5429	453	5	math	math	PROPN
ejpam-5429	453	6	,	,	PUNCT
ejpam-5429	453	7	17	17	NUM
ejpam-5429	453	8	(	(	PUNCT
ejpam-5429	453	9	4	4	NUM
ejpam-5429	453	10	)	)	PUNCT
ejpam-5429	453	11	(	(	PUNCT
ejpam-5429	453	12	2024	2024	NUM
ejpam-5429	453	13	)	)	PUNCT
ejpam-5429	453	14	,	,	PUNCT
ejpam-5429	453	15	3129	3129	NUM
ejpam-5429	453	16	-	-	SYM
ejpam-5429	453	17	3155	3155	NUM
ejpam-5429	453	18	3144	3144	NUM
ejpam-5429	453	19	therefore	therefore	ADV
ejpam-5429	453	20	[	[	X
ejpam-5429	453	21	ð̃]τ̃ρ̃	ð̃]τ̃ρ̃	X
ejpam-5429	453	22	is	be	AUX
ejpam-5429	453	23	a	a	DET
ejpam-5429	453	24	fi	fi	NOUN
ejpam-5429	453	25	of	of	ADP
ejpam-5429	453	26	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	453	27	by	by	ADP
ejpam-5429	453	28	substituting	substitute	VERB
ejpam-5429	453	29	σ̃	σ̃	PROPN
ejpam-5429	453	30	=	=	SYM
ejpam-5429	453	31	0̃	0̃	PROPN
ejpam-5429	453	32	and	and	CCONJ
ejpam-5429	453	33	τ̃	τ̃	PROPN
ejpam-5429	453	34	=	=	SYM
ejpam-5429	453	35	0̂.5	0̂.5	PROPN
ejpam-5429	453	36	into	into	ADP
ejpam-5429	453	37	theorem	theorem	NOUN
ejpam-5429	453	38	5.4	5.4	NUM
ejpam-5429	453	39	,	,	PUNCT
ejpam-5429	453	40	we	we	PRON
ejpam-5429	453	41	can	can	AUX
ejpam-5429	453	42	derive	derive	VERB
ejpam-5429	453	43	the	the	DET
ejpam-5429	453	44	ensuing	ensue	VERB
ejpam-5429	453	45	corollary	corollary	NOUN
ejpam-5429	453	46	.	.	PUNCT
ejpam-5429	454	1	corollary	corollary	ADJ
ejpam-5429	454	2	6	6	NUM
ejpam-5429	454	3	.	.	PUNCT
ejpam-5429	455	1	let	let	VERB
ejpam-5429	455	2	ð̃	ð̃	PRON
ejpam-5429	455	3	be	be	AUX
ejpam-5429	455	4	a	a	DET
ejpam-5429	455	5	qp	qp	PROPN
ejpam-5429	455	6	-	-	PUNCT
ejpam-5429	455	7	f	f	PROPN
ejpam-5429	455	8	set	set	NOUN
ejpam-5429	455	9	of	of	ADP
ejpam-5429	455	10	ℵ̃.	ℵ̃.	PROPN
ejpam-5429	455	11	then	then	ADV
ejpam-5429	455	12	(	(	PUNCT
ejpam-5429	455	13	1	1	X
ejpam-5429	455	14	)	)	PUNCT
ejpam-5429	455	15	ð̃	ð̃	PROPN
ejpam-5429	455	16	is	be	AUX
ejpam-5429	455	17	a	a	DET
ejpam-5429	455	18	qp-(∈,∈	qp-(∈,∈	X
ejpam-5429	455	19	∨q)-ffi	∨q)-ffi	PROPN
ejpam-5429	455	20	of	of	ADP
ejpam-5429	455	21	ℵ̃	ℵ̃	PROPN
ejpam-5429	455	22	⇔	⇔	PROPN
ejpam-5429	455	23	ð̃σ̃ρ̃	ð̃σ̃ρ̃	PROPN
ejpam-5429	456	1	(	(	PUNCT
ejpam-5429	456	2	̸=	̸=	PROPN
ejpam-5429	456	3	ϕ	ϕ	NOUN
ejpam-5429	456	4	)	)	PUNCT
ejpam-5429	456	5	is	be	AUX
ejpam-5429	456	6	a	a	DET
ejpam-5429	456	7	fi	fi	NOUN
ejpam-5429	456	8	of	of	ADP
ejpam-5429	456	9	ℵ̃,∀ρ̃	ℵ̃,∀ρ̃	NOUN
ejpam-5429	456	10	∈	∈	PROPN
ejpam-5429	456	11	(	(	PUNCT
ejpam-5429	456	12	0	0	NUM
ejpam-5429	456	13	,	,	PUNCT
ejpam-5429	456	14	0.5]q	0.5]q	NOUN
ejpam-5429	456	15	.	.	PUNCT
ejpam-5429	457	1	(	(	PUNCT
ejpam-5429	457	2	2	2	X
ejpam-5429	457	3	)	)	PUNCT
ejpam-5429	457	4	ð̃	ð̃	PROPN
ejpam-5429	457	5	is	be	AUX
ejpam-5429	457	6	a	a	DET
ejpam-5429	457	7	qp-(∈,∈	qp-(∈,∈	X
ejpam-5429	457	8	∨q)-ffi	∨q)-ffi	PROPN
ejpam-5429	457	9	of	of	ADP
ejpam-5429	457	10	ℵ̃	ℵ̃	PROPN
ejpam-5429	457	11	⇔	⇔	PROPN
ejpam-5429	457	12	⟨ð̃⟩τ̃ρ̃	⟨ð̃⟩τ̃ρ̃	PROPN
ejpam-5429	457	13	(	(	PUNCT
ejpam-5429	457	14	̸=	̸=	PROPN
ejpam-5429	457	15	ϕ	ϕ	NOUN
ejpam-5429	457	16	)	)	PUNCT
ejpam-5429	457	17	is	be	AUX
ejpam-5429	457	18	a	a	DET
ejpam-5429	457	19	fi	fi	NOUN
ejpam-5429	457	20	of	of	ADP
ejpam-5429	457	21	ℵ̃,∀ρ̃	ℵ̃,∀ρ̃	NOUN
ejpam-5429	457	22	∈	∈	PROPN
ejpam-5429	457	23	(	(	PUNCT
ejpam-5429	457	24	0.5	0.5	NUM
ejpam-5429	457	25	,	,	PUNCT
ejpam-5429	457	26	1]q	1]q	NUM
ejpam-5429	457	27	.	.	PUNCT
ejpam-5429	458	1	(	(	PUNCT
ejpam-5429	458	2	3	3	X
ejpam-5429	458	3	)	)	PUNCT
ejpam-5429	458	4	ð̃	ð̃	PROPN
ejpam-5429	458	5	is	be	AUX
ejpam-5429	458	6	a	a	DET
ejpam-5429	458	7	qp-(∈,∈	qp-(∈,∈	X
ejpam-5429	458	8	∨q)-ffi	∨q)-ffi	PROPN
ejpam-5429	458	9	of	of	ADP
ejpam-5429	458	10	ℵ̃	ℵ̃	PROPN
ejpam-5429	458	11	⇔	⇔	X
ejpam-5429	459	1	[	[	X
ejpam-5429	459	2	ð̃]τ̃ρ̃	ð̃]τ̃ρ̃	X
ejpam-5429	459	3	(	(	PUNCT
ejpam-5429	459	4	̸=	̸=	PROPN
ejpam-5429	459	5	ϕ	ϕ	NOUN
ejpam-5429	459	6	)	)	PUNCT
ejpam-5429	459	7	is	be	AUX
ejpam-5429	459	8	a	a	DET
ejpam-5429	459	9	fi	fi	NOUN
ejpam-5429	459	10	of	of	ADP
ejpam-5429	459	11	ℵ̃	ℵ̃	PROPN
ejpam-5429	459	12	,	,	PUNCT
ejpam-5429	459	13	∀ρ̃	∀ρ̃	PROPN
ejpam-5429	459	14	∈	∈	PROPN
ejpam-5429	459	15	(	(	PUNCT
ejpam-5429	459	16	0	0	NUM
ejpam-5429	459	17	,	,	PUNCT
ejpam-5429	459	18	1]q	1]q	NUM
ejpam-5429	459	19	.	.	PROPN
ejpam-5429	460	1	6	6	NUM
ejpam-5429	460	2	.	.	X
ejpam-5429	460	3	quadri	quadri	NOUN
ejpam-5429	460	4	-	-	PUNCT
ejpam-5429	460	5	polar	polar	ADJ
ejpam-5429	460	6	fuzzy	fuzzy	ADJ
ejpam-5429	460	7	topsis	topsis	NOUN
ejpam-5429	460	8	approach	approach	NOUN
ejpam-5429	460	9	in	in	ADP
ejpam-5429	460	10	this	this	DET
ejpam-5429	460	11	section	section	NOUN
ejpam-5429	460	12	,	,	PUNCT
ejpam-5429	460	13	we	we	PRON
ejpam-5429	460	14	present	present	VERB
ejpam-5429	460	15	a	a	DET
ejpam-5429	460	16	q	q	ADJ
ejpam-5429	460	17	-	-	PUNCT
ejpam-5429	460	18	pf	pf	NOUN
ejpam-5429	460	19	topsis	topsis	NOUN
ejpam-5429	460	20	approach	approach	NOUN
ejpam-5429	460	21	for	for	ADP
ejpam-5429	460	22	multi	multi	ADJ
ejpam-5429	460	23	-	-	ADJ
ejpam-5429	460	24	criteria	criterion	NOUN
ejpam-5429	460	25	group	group	NOUN
ejpam-5429	460	26	decisionmaking	decisionmake	VERB
ejpam-5429	460	27	(	(	PUNCT
ejpam-5429	460	28	mcgdm	mcgdm	ADJ
ejpam-5429	460	29	)	)	PUNCT
ejpam-5429	460	30	problems	problem	NOUN
ejpam-5429	460	31	.	.	PUNCT
ejpam-5429	461	1	for	for	ADP
ejpam-5429	461	2	these	these	DET
ejpam-5429	461	3	problems	problem	NOUN
ejpam-5429	461	4	,	,	PUNCT
ejpam-5429	461	5	we	we	PRON
ejpam-5429	461	6	use	use	VERB
ejpam-5429	461	7	a	a	DET
ejpam-5429	461	8	topsis	topsis	NOUN
ejpam-5429	461	9	method	method	NOUN
ejpam-5429	461	10	based	base	VERB
ejpam-5429	461	11	on	on	ADP
ejpam-5429	461	12	qpf	qpf	NOUN
ejpam-5429	461	13	-	-	NOUN
ejpam-5429	461	14	sets	set	NOUN
ejpam-5429	461	15	to	to	PART
ejpam-5429	461	16	address	address	VERB
ejpam-5429	461	17	a	a	DET
ejpam-5429	461	18	set	set	NOUN
ejpam-5429	461	19	of	of	ADP
ejpam-5429	461	20	alternatives	alternative	NOUN
ejpam-5429	461	21	a̧	a̧	NOUN
ejpam-5429	461	22	=	=	SYM
ejpam-5429	461	23	{	{	PUNCT
ejpam-5429	461	24	ς̇1	ς̇1	PROPN
ejpam-5429	461	25	,	,	PUNCT
ejpam-5429	461	26	ς̇2	ς̇2	PROPN
ejpam-5429	461	27	,	,	PUNCT
ejpam-5429	461	28	ς̇3	ς̇3	PROPN
ejpam-5429	461	29	,	,	PUNCT
ejpam-5429	461	30	ς̇4	ς̇4	PROPN
ejpam-5429	461	31	}	}	PUNCT
ejpam-5429	461	32	and	and	CCONJ
ejpam-5429	461	33	a	a	DET
ejpam-5429	461	34	set	set	NOUN
ejpam-5429	461	35	c	c	NOUN
ejpam-5429	461	36	=	=	SYM
ejpam-5429	461	37	{	{	PUNCT
ejpam-5429	461	38	c1	c1	PROPN
ejpam-5429	461	39	,	,	PUNCT
ejpam-5429	461	40	c2	c2	PROPN
ejpam-5429	461	41	,	,	PUNCT
ejpam-5429	461	42	c3	c3	PROPN
ejpam-5429	461	43	,	,	PUNCT
ejpam-5429	461	44	c4	c4	PROPN
ejpam-5429	461	45	}	}	PUNCT
ejpam-5429	461	46	classified	classify	VERB
ejpam-5429	461	47	by	by	ADP
ejpam-5429	461	48	q.	q.	NOUN
ejpam-5429	461	49	decision	decision	NOUN
ejpam-5429	461	50	-	-	PUNCT
ejpam-5429	461	51	makers	maker	NOUN
ejpam-5429	461	52	must	must	AUX
ejpam-5429	461	53	evaluate	evaluate	VERB
ejpam-5429	461	54	the	the	DET
ejpam-5429	461	55	four	four	NUM
ejpam-5429	461	56	possibilities	possibility	NOUN
ejpam-5429	461	57	based	base	VERB
ejpam-5429	461	58	on	on	ADP
ejpam-5429	461	59	the	the	DET
ejpam-5429	461	60	q	q	ADJ
ejpam-5429	461	61	-	-	PUNCT
ejpam-5429	461	62	pf	pf	NOUN
ejpam-5429	461	63	criteria	criterion	NOUN
ejpam-5429	461	64	.	.	PUNCT
ejpam-5429	462	1	the	the	DET
ejpam-5429	462	2	possible	possible	ADJ
ejpam-5429	462	3	ratings	rating	NOUN
ejpam-5429	462	4	of	of	ADP
ejpam-5429	462	5	alternatives	alternative	NOUN
ejpam-5429	462	6	are	be	AUX
ejpam-5429	462	7	evaluated	evaluate	VERB
ejpam-5429	462	8	in	in	ADP
ejpam-5429	462	9	terms	term	NOUN
ejpam-5429	462	10	of	of	ADP
ejpam-5429	462	11	q	q	PUNCT
ejpam-5429	462	12	different	different	ADJ
ejpam-5429	462	13	attributes	attribute	NOUN
ejpam-5429	462	14	among	among	ADP
ejpam-5429	462	15	four	four	NUM
ejpam-5429	462	16	membership	membership	NOUN
ejpam-5429	462	17	values	value	NOUN
ejpam-5429	462	18	,	,	PUNCT
ejpam-5429	462	19	represented	represent	VERB
ejpam-5429	462	20	as	as	ADP
ejpam-5429	462	21	(	(	PUNCT
ejpam-5429	462	22	i	i	NOUN
ejpam-5429	462	23	=	=	NOUN
ejpam-5429	462	24	1	1	NUM
ejpam-5429	462	25	,	,	PUNCT
ejpam-5429	462	26	2	2	NUM
ejpam-5429	462	27	,	,	PUNCT
ejpam-5429	462	28	3	3	NUM
ejpam-5429	462	29	,	,	PUNCT
ejpam-5429	462	30	4	4	NUM
ejpam-5429	462	31	)	)	PUNCT
ejpam-5429	462	32	.	.	PUNCT
ejpam-5429	463	1	step	step	NOUN
ejpam-5429	463	2	1	1	NUM
ejpam-5429	463	3	:	:	PUNCT
ejpam-5429	463	4	the	the	DET
ejpam-5429	463	5	degree	degree	NOUN
ejpam-5429	463	6	of	of	ADP
ejpam-5429	463	7	each	each	DET
ejpam-5429	463	8	alternative	alternative	ADJ
ejpam-5429	463	9	ς̇j	ς̇j	PROPN
ejpam-5429	463	10	∈	∈	PROPN
ejpam-5429	463	11	a̧	a̧	NOUN
ejpam-5429	463	12	,	,	PUNCT
ejpam-5429	463	13	j	j	PROPN
ejpam-5429	463	14	=	=	SYM
ejpam-5429	463	15	1	1	NUM
ejpam-5429	463	16	,	,	PUNCT
ejpam-5429	463	17	2	2	NUM
ejpam-5429	463	18	,	,	PUNCT
ejpam-5429	463	19	3	3	NUM
ejpam-5429	463	20	,	,	PUNCT
ejpam-5429	463	21	4	4	NUM
ejpam-5429	463	22	)	)	PUNCT
ejpam-5429	463	23	over	over	ADP
ejpam-5429	463	24	all	all	DET
ejpam-5429	463	25	the	the	DET
ejpam-5429	463	26	criteria	criterion	NOUN
ejpam-5429	463	27	(	(	PUNCT
ejpam-5429	463	28	ck	ck	INTJ
ejpam-5429	463	29	∈	∈	PROPN
ejpam-5429	463	30	c	c	NOUN
ejpam-5429	463	31	,	,	PUNCT
ejpam-5429	463	32	k	k	X
ejpam-5429	463	33	=	=	SYM
ejpam-5429	463	34	1	1	NUM
ejpam-5429	463	35	,	,	PUNCT
ejpam-5429	463	36	2	2	NUM
ejpam-5429	463	37	,	,	PUNCT
ejpam-5429	463	38	3	3	NUM
ejpam-5429	463	39	,	,	PUNCT
ejpam-5429	463	40	4	4	NUM
ejpam-5429	463	41	)	)	PUNCT
ejpam-5429	463	42	may	may	AUX
ejpam-5429	463	43	be	be	AUX
ejpam-5429	463	44	expressed	express	VERB
ejpam-5429	463	45	as	as	ADP
ejpam-5429	463	46	q	q	NOUN
ejpam-5429	463	47	-	-	PUNCT
ejpam-5429	463	48	pfes	pfe	NOUN
ejpam-5429	463	49	.	.	PUNCT
ejpam-5429	464	1	ð̃jk(ς̇	ð̃jk(ς̇	X
ejpam-5429	464	2	)	)	PUNCT
ejpam-5429	465	1	=	=	PRON
ejpam-5429	465	2	(	(	PUNCT
ejpam-5429	465	3	ρ1	ρ1	NOUN
ejpam-5429	465	4	o	o	NOUN
ejpam-5429	465	5	ð̃jk(ς̇	ð̃jk(ς̇	PROPN
ejpam-5429	465	6	)	)	PUNCT
ejpam-5429	465	7	,	,	PUNCT
ejpam-5429	465	8	ρ2	ρ2	NOUN
ejpam-5429	465	9	o	o	NOUN
ejpam-5429	465	10	ð̃jk(ς̇	ð̃jk(ς̇	PROPN
ejpam-5429	465	11	)	)	PUNCT
ejpam-5429	465	12	,	,	PUNCT
ejpam-5429	465	13	ρ3	ρ3	NOUN
ejpam-5429	465	14	o	o	NOUN
ejpam-5429	465	15	ð̃jk(ς̇	ð̃jk(ς̇	PROPN
ejpam-5429	465	16	)	)	PUNCT
ejpam-5429	465	17	,	,	PUNCT
ejpam-5429	465	18	ρ4	ρ4	ADV
ejpam-5429	465	19	o	o	NOUN
ejpam-5429	465	20	ð̃jk(ς̇	ð̃jk(ς̇	PROPN
ejpam-5429	465	21	)	)	PUNCT
ejpam-5429	465	22	)	)	PUNCT
ejpam-5429	465	23	,	,	PUNCT
ejpam-5429	465	24	where	where	SCONJ
ejpam-5429	465	25	=	=	PRON
ejpam-5429	465	26	(	(	PUNCT
ejpam-5429	465	27	ρ1	ρ1	NOUN
ejpam-5429	465	28	o	o	NOUN
ejpam-5429	465	29	ð̃jk(ς̇	ð̃jk(ς̇	PROPN
ejpam-5429	465	30	)	)	PUNCT
ejpam-5429	466	1	|	|	ADV
ejpam-5429	466	2	i	i	PRON
ejpam-5429	466	3	=	=	NOUN
ejpam-5429	466	4	1	1	NUM
ejpam-5429	466	5	,	,	PUNCT
ejpam-5429	466	6	2	2	NUM
ejpam-5429	466	7	,	,	PUNCT
ejpam-5429	466	8	...	...	PUNCT
ejpam-5429	466	9	,	,	PUNCT
ejpam-5429	466	10	q	q	NOUN
ejpam-5429	466	11	)	)	PUNCT
ejpam-5429	466	12	.	.	PUNCT
ejpam-5429	467	1	the	the	DET
ejpam-5429	467	2	tabular	tabular	PROPN
ejpam-5429	467	3	representation	representation	NOUN
ejpam-5429	467	4	of	of	ADP
ejpam-5429	467	5	the	the	DET
ejpam-5429	467	6	q	q	ADJ
ejpam-5429	467	7	-	-	PUNCT
ejpam-5429	467	8	pf	pf	NOUN
ejpam-5429	467	9	decision	decision	NOUN
ejpam-5429	467	10	matrix	matrix	NOUN
ejpam-5429	467	11	is	be	AUX
ejpam-5429	467	12	given	give	VERB
ejpam-5429	467	13	by	by	ADP
ejpam-5429	467	14	table	table	NOUN
ejpam-5429	467	15	2	2	NUM
ejpam-5429	467	16	,	,	PUNCT
ejpam-5429	467	17	which	which	PRON
ejpam-5429	467	18	describes	describe	VERB
ejpam-5429	467	19	the	the	DET
ejpam-5429	467	20	ratings	rating	NOUN
ejpam-5429	467	21	of	of	ADP
ejpam-5429	467	22	alternatives	alternative	NOUN
ejpam-5429	467	23	.	.	PUNCT
ejpam-5429	468	1	table	table	NOUN
ejpam-5429	468	2	3	3	NUM
ejpam-5429	468	3	.	.	PUNCT
ejpam-5429	468	4	tablular	tablular	ADJ
ejpam-5429	468	5	representation	representation	NOUN
ejpam-5429	468	6	of	of	ADP
ejpam-5429	468	7	q	q	ADJ
ejpam-5429	468	8	-	-	PUNCT
ejpam-5429	468	9	pf	pf	NOUN
ejpam-5429	468	10	decision	decision	NOUN
ejpam-5429	468	11	matrix	matrix	NOUN
ejpam-5429	468	12	.	.	PUNCT
ejpam-5429	469	1	alternatives	alternative	NOUN
ejpam-5429	469	2	c1	c1	PROPN
ejpam-5429	469	3	c2	c2	PROPN
ejpam-5429	469	4	c3	c3	PROPN
ejpam-5429	469	5	c4	c4	NOUN
ejpam-5429	469	6	ς̇1	ς̇1	PROPN
ejpam-5429	469	7	ð̃11(ς̇1	ð̃11(ς̇1	PROPN
ejpam-5429	469	8	)	)	PUNCT
ejpam-5429	469	9	ð̃12(ς̇1	ð̃12(ς̇1	PROPN
ejpam-5429	469	10	)	)	PUNCT
ejpam-5429	469	11	ð̃13(ς̇1	ð̃13(ς̇1	PROPN
ejpam-5429	469	12	)	)	PUNCT
ejpam-5429	469	13	ð̃14(ς̇1	ð̃14(ς̇1	PROPN
ejpam-5429	469	14	)	)	PUNCT
ejpam-5429	469	15	ς̇2	ς̇2	PROPN
ejpam-5429	469	16	ð̃21(ς̇2	ð̃21(ς̇2	PROPN
ejpam-5429	469	17	)	)	PUNCT
ejpam-5429	469	18	ð̃22(ς̇2	ð̃22(ς̇2	PROPN
ejpam-5429	469	19	)	)	PUNCT
ejpam-5429	469	20	ð̃23(ς̇2	ð̃23(ς̇2	PROPN
ejpam-5429	469	21	)	)	PUNCT
ejpam-5429	469	22	ð̃24(ς̇2	ð̃24(ς̇2	PROPN
ejpam-5429	469	23	)	)	PUNCT
ejpam-5429	469	24	ς̇3	ς̇3	PROPN
ejpam-5429	469	25	ð̃31(ς̇3	ð̃31(ς̇3	PROPN
ejpam-5429	469	26	)	)	PUNCT
ejpam-5429	469	27	ð̃32(ς̇3	ð̃32(ς̇3	PUNCT
ejpam-5429	469	28	)	)	PUNCT
ejpam-5429	470	1	ð̃33(ς̇3	ð̃33(ς̇3	PROPN
ejpam-5429	470	2	)	)	PUNCT
ejpam-5429	471	1	ð̃34(ς̇3	ð̃34(ς̇3	PROPN
ejpam-5429	471	2	)	)	PUNCT
ejpam-5429	472	1	ς̇4	ς̇4	PROPN
ejpam-5429	472	2	ð̃41(ς̇4	ð̃41(ς̇4	PROPN
ejpam-5429	472	3	)	)	PUNCT
ejpam-5429	472	4	ð̃42(ς̇4	ð̃42(ς̇4	PROPN
ejpam-5429	472	5	)	)	PUNCT
ejpam-5429	472	6	ð̃43(ς̇4	ð̃43(ς̇4	PROPN
ejpam-5429	472	7	)	)	PUNCT
ejpam-5429	472	8	ð̃44(ς̇4	ð̃44(ς̇4	NOUN
ejpam-5429	472	9	)	)	PUNCT
ejpam-5429	472	10	step	step	NOUN
ejpam-5429	472	11	2	2	NUM
ejpam-5429	472	12	:	:	PUNCT
ejpam-5429	472	13	we	we	PRON
ejpam-5429	472	14	build	build	VERB
ejpam-5429	472	15	the	the	DET
ejpam-5429	472	16	optimistic	optimistic	ADJ
ejpam-5429	472	17	or	or	CCONJ
ejpam-5429	472	18	pessimistic	pessimistic	ADJ
ejpam-5429	472	19	q	q	ADJ
ejpam-5429	472	20	-	-	PUNCT
ejpam-5429	472	21	pf	pf	NOUN
ejpam-5429	472	22	decision	decision	NOUN
ejpam-5429	472	23	matrix	matrix	NOUN
ejpam-5429	472	24	by	by	ADP
ejpam-5429	472	25	adding	add	VERB
ejpam-5429	472	26	the	the	DET
ejpam-5429	472	27	maximal	maximal	ADJ
ejpam-5429	472	28	and	and	CCONJ
ejpam-5429	472	29	smallest	small	ADJ
ejpam-5429	472	30	values	value	NOUN
ejpam-5429	472	31	to	to	PART
ejpam-5429	472	32	equalize	equalize	VERB
ejpam-5429	472	33	the	the	DET
ejpam-5429	472	34	length	length	NOUN
ejpam-5429	472	35	of	of	ADP
ejpam-5429	472	36	all	all	DET
ejpam-5429	472	37	q	q	NOUN
ejpam-5429	472	38	-	-	PUNCT
ejpam-5429	472	39	pfes	pfe	NOUN
ejpam-5429	472	40	.	.	PUNCT
ejpam-5429	473	1	step	step	NOUN
ejpam-5429	473	2	3	3	NUM
ejpam-5429	473	3	:	:	PUNCT
ejpam-5429	473	4	weights	weight	NOUN
ejpam-5429	473	5	can	can	AUX
ejpam-5429	473	6	be	be	AUX
ejpam-5429	473	7	assigned	assign	VERB
ejpam-5429	473	8	to	to	ADP
ejpam-5429	473	9	each	each	DET
ejpam-5429	473	10	q	q	ADJ
ejpam-5429	473	11	-	-	PUNCT
ejpam-5429	473	12	pf	pf	PROPN
ejpam-5429	473	13	criteria	criterion	NOUN
ejpam-5429	473	14	of	of	ADP
ejpam-5429	473	15	alternatives	alternative	NOUN
ejpam-5429	473	16	by	by	ADP
ejpam-5429	473	17	decision	decision	NOUN
ejpam-5429	473	18	-	-	PUNCT
ejpam-5429	473	19	makers	maker	NOUN
ejpam-5429	473	20	based	base	VERB
ejpam-5429	473	21	on	on	ADP
ejpam-5429	473	22	their	their	PRON
ejpam-5429	473	23	choice	choice	NOUN
ejpam-5429	473	24	and	and	CCONJ
ejpam-5429	473	25	importance	importance	NOUN
ejpam-5429	473	26	of	of	ADP
ejpam-5429	473	27	each	each	DET
ejpam-5429	473	28	criterion	criterion	NOUN
ejpam-5429	473	29	.	.	PUNCT
ejpam-5429	474	1	we	we	PRON
ejpam-5429	474	2	assume	assume	VERB
ejpam-5429	474	3	that	that	SCONJ
ejpam-5429	474	4	the	the	DET
ejpam-5429	474	5	weights	weight	NOUN
ejpam-5429	474	6	assigned	assign	VERB
ejpam-5429	474	7	by	by	ADP
ejpam-5429	474	8	the	the	DET
ejpam-5429	474	9	decision	decision	NOUN
ejpam-5429	474	10	-	-	PUNCT
ejpam-5429	474	11	makers	maker	NOUN
ejpam-5429	474	12	are	be	AUX
ejpam-5429	474	13	w̧	w̧	X
ejpam-5429	474	14	=	=	SYM
ejpam-5429	474	15	(	(	PUNCT
ejpam-5429	474	16	w1	w1	NOUN
ejpam-5429	474	17	,	,	PUNCT
ejpam-5429	474	18	w2	w2	NOUN
ejpam-5429	474	19	,	,	PUNCT
ejpam-5429	474	20	w3	w3	PROPN
ejpam-5429	474	21	,	,	PUNCT
ejpam-5429	474	22	wq	wq	PROPN
ejpam-5429	474	23	)	)	PUNCT
ejpam-5429	474	24	∈	∈	PROPN
ejpam-5429	474	25	(	(	PUNCT
ejpam-5429	474	26	0	0	NUM
ejpam-5429	474	27	,	,	PUNCT
ejpam-5429	474	28	1	1	NUM
ejpam-5429	474	29	]	]	PUNCT
ejpam-5429	474	30	,	,	PUNCT
ejpam-5429	474	31	k.	k.	PROPN
ejpam-5429	474	32	h.	h.	PROPN
ejpam-5429	474	33	hakami	hakami	PROPN
ejpam-5429	474	34	et	et	PROPN
ejpam-5429	474	35	al	al	PROPN
ejpam-5429	474	36	.	.	PUNCT
ejpam-5429	474	37	/	/	SYM
ejpam-5429	474	38	eur	eur	PROPN
ejpam-5429	474	39	.	.	PUNCT
ejpam-5429	475	1	j.	j.	PROPN
ejpam-5429	475	2	pure	pure	PROPN
ejpam-5429	475	3	appl	appl	PROPN
ejpam-5429	475	4	.	.	PROPN
ejpam-5429	475	5	math	math	PROPN
ejpam-5429	475	6	,	,	PUNCT
ejpam-5429	475	7	17	17	NUM
ejpam-5429	475	8	(	(	PUNCT
ejpam-5429	475	9	4	4	NUM
ejpam-5429	475	10	)	)	PUNCT
ejpam-5429	475	11	(	(	PUNCT
ejpam-5429	475	12	2024	2024	NUM
ejpam-5429	475	13	)	)	PUNCT
ejpam-5429	475	14	,	,	PUNCT
ejpam-5429	475	15	3129	3129	NUM
ejpam-5429	475	16	-	-	SYM
ejpam-5429	475	17	3155	3155	NUM
ejpam-5429	475	18	3145	3145	NUM
ejpam-5429	475	19	satisfying	satisfy	VERB
ejpam-5429	475	20	the	the	DET
ejpam-5429	475	21	normalized	normalize	VERB
ejpam-5429	475	22	condition∑q	condition∑q	PROPN
ejpam-5429	475	23	k=1wk	k=1wk	X
ejpam-5429	475	24	=	=	SYM
ejpam-5429	475	25	1	1	NUM
ejpam-5429	475	26	,	,	PUNCT
ejpam-5429	475	27	q	q	NOUN
ejpam-5429	476	1	=	=	SYM
ejpam-5429	476	2	1	1	NUM
ejpam-5429	476	3	,	,	PUNCT
ejpam-5429	476	4	2	2	NUM
ejpam-5429	476	5	,	,	PUNCT
ejpam-5429	476	6	3	3	NUM
ejpam-5429	476	7	,	,	PUNCT
ejpam-5429	476	8	4	4	NUM
ejpam-5429	476	9	..	..	PUNCT
ejpam-5429	476	10	step	step	NOUN
ejpam-5429	476	11	4	4	NUM
ejpam-5429	476	12	:	:	PUNCT
ejpam-5429	476	13	the	the	DET
ejpam-5429	476	14	weighted	weight	VERB
ejpam-5429	476	15	q	q	ADJ
ejpam-5429	476	16	-	-	PUNCT
ejpam-5429	476	17	pf	pf	NOUN
ejpam-5429	476	18	decision	decision	NOUN
ejpam-5429	476	19	matrix	matrix	NOUN
ejpam-5429	476	20	is	be	AUX
ejpam-5429	476	21	calculated	calculate	VERB
ejpam-5429	476	22	in	in	ADP
ejpam-5429	476	23	table	table	NOUN
ejpam-5429	476	24	4	4	NUM
ejpam-5429	476	25	.	.	PUNCT
ejpam-5429	476	26	table	table	NOUN
ejpam-5429	476	27	4	4	NUM
ejpam-5429	476	28	.	.	PUNCT
ejpam-5429	476	29	tabular	tabular	PROPN
ejpam-5429	476	30	representation	representation	NOUN
ejpam-5429	476	31	of	of	ADP
ejpam-5429	476	32	a	a	DET
ejpam-5429	476	33	weighted	weighted	ADJ
ejpam-5429	476	34	q	q	ADJ
ejpam-5429	476	35	-	-	PUNCT
ejpam-5429	476	36	pf	pf	NOUN
ejpam-5429	476	37	decision	decision	NOUN
ejpam-5429	476	38	matrix	matrix	NOUN
ejpam-5429	476	39	.	.	PUNCT
ejpam-5429	477	1	alternatives	alternative	NOUN
ejpam-5429	477	2	c1	c1	PROPN
ejpam-5429	477	3	c2	c2	PROPN
ejpam-5429	477	4	c3	c3	PROPN
ejpam-5429	477	5	c4	c4	PROPN
ejpam-5429	477	6	ς̇1	ς̇1	PROPN
ejpam-5429	477	7	ð̃(ς̇1)11	ð̃(ς̇1)11	PROPN
ejpam-5429	478	1	′	′	NUM
ejpam-5429	478	2	ð̃(ς̇1)12	ð̃(ς̇1)12	PROPN
ejpam-5429	478	3	′	′	NUM
ejpam-5429	479	1	ð̃(ς̇1)13	ð̃(ς̇1)13	INTJ
ejpam-5429	479	2	′	′	NUM
ejpam-5429	480	1	ð̃(ς̇1)14	ð̃(ς̇1)14	NOUN
ejpam-5429	480	2	′	′	NUM
ejpam-5429	481	1	ς̇2	ς̇2	PROPN
ejpam-5429	481	2	ð̃(ς̇2)21	ð̃(ς̇2)21	PROPN
ejpam-5429	481	3	′	′	NUM
ejpam-5429	482	1	ð̃(ς̇2)22	ð̃(ς̇2)22	NOUN
ejpam-5429	483	1	′	′	NUM
ejpam-5429	483	2	ð̃(ς̇2)23	ð̃(ς̇2)23	NOUN
ejpam-5429	483	3	′	′	NUM
ejpam-5429	484	1	ð̃(ς̇2)24	ð̃(ς̇2)24	NOUN
ejpam-5429	484	2	′	′	NUM
ejpam-5429	485	1	ς̇3	ς̇3	PROPN
ejpam-5429	485	2	ð̃(ς̇3)31	ð̃(ς̇3)31	PROPN
ejpam-5429	485	3	′	′	NUM
ejpam-5429	485	4	ð̃(ς̇3)32	ð̃(ς̇3)32	PROPN
ejpam-5429	485	5	′	′	PROPN
ejpam-5429	486	1	ð̃(ς̇3)33	ð̃(ς̇3)33	PROPN
ejpam-5429	486	2	′	′	NUM
ejpam-5429	487	1	ð̃(ς̇3)34	ð̃(ς̇3)34	PROPN
ejpam-5429	487	2	′	′	NUM
ejpam-5429	488	1	ς̇4	ς̇4	NUM
ejpam-5429	488	2	ð̃(ς̇4)41	ð̃(ς̇4)41	PROPN
ejpam-5429	488	3	′	′	NUM
ejpam-5429	489	1	ð̃(ς̇4)42	ð̃(ς̇4)42	PROPN
ejpam-5429	489	2	′	′	NUM
ejpam-5429	490	1	ð̃(ς̇4)43	ð̃(ς̇4)43	PROPN
ejpam-5429	490	2	′	′	NUM
ejpam-5429	491	1	ð̃(ς̇4)44	ð̃(ς̇4)44	NOUN
ejpam-5429	491	2	′	′	NUM
ejpam-5429	491	3	for	for	ADP
ejpam-5429	491	4	each	each	DET
ejpam-5429	491	5	possible	possible	ADJ
ejpam-5429	491	6	j	j	PROPN
ejpam-5429	491	7	and	and	CCONJ
ejpam-5429	491	8	k	k	PROPN
ejpam-5429	491	9	,	,	PUNCT
ejpam-5429	491	10	ð̃jk	ð̃jk	VERB
ejpam-5429	491	11	′	′	NUM
ejpam-5429	491	12	(	(	PUNCT
ejpam-5429	491	13	ς̇	ς̇	NOUN
ejpam-5429	491	14	)	)	PUNCT
ejpam-5429	491	15	=	=	PUNCT
ejpam-5429	492	1	(	(	PUNCT
ejpam-5429	492	2	ρ1	ρ1	NOUN
ejpam-5429	492	3	o	o	NOUN
ejpam-5429	493	1	ð̃jk	ð̃jk	VERB
ejpam-5429	493	2	′	′	NUM
ejpam-5429	493	3	(	(	PUNCT
ejpam-5429	493	4	ς̇	ς̇	NOUN
ejpam-5429	493	5	)	)	PUNCT
ejpam-5429	493	6	,	,	PUNCT
ejpam-5429	493	7	ρ2	ρ2	NOUN
ejpam-5429	493	8	o	o	NOUN
ejpam-5429	493	9	ð̃jk	ð̃jk	PRON
ejpam-5429	493	10	′	′	NUM
ejpam-5429	493	11	(	(	PUNCT
ejpam-5429	493	12	ς̇	ς̇	NOUN
ejpam-5429	493	13	)	)	PUNCT
ejpam-5429	493	14	,	,	PUNCT
ejpam-5429	493	15	ρ3	ρ3	NOUN
ejpam-5429	493	16	o	o	NOUN
ejpam-5429	494	1	ð̃jk	ð̃jk	VERB
ejpam-5429	494	2	′	′	NUM
ejpam-5429	494	3	(	(	PUNCT
ejpam-5429	494	4	ς̇	ς̇	NOUN
ejpam-5429	494	5	)	)	PUNCT
ejpam-5429	494	6	,	,	PUNCT
ejpam-5429	494	7	ρ4	ρ4	ADV
ejpam-5429	494	8	o	o	NOUN
ejpam-5429	494	9	ð̃jk	ð̃jk	VERB
ejpam-5429	494	10	′	′	NUM
ejpam-5429	494	11	(	(	PUNCT
ejpam-5429	494	12	ς̇	ς̇	NOUN
ejpam-5429	494	13	)	)	PUNCT
ejpam-5429	494	14	)	)	PUNCT
ejpam-5429	494	15	,	,	PUNCT
ejpam-5429	494	16	step	step	NOUN
ejpam-5429	494	17	5	5	NUM
ejpam-5429	494	18	:	:	PUNCT
ejpam-5429	494	19	the	the	DET
ejpam-5429	494	20	qp	qp	PROPN
ejpam-5429	494	21	-	-	PUNCT
ejpam-5429	494	22	f	f	PROPN
ejpam-5429	494	23	positive	positive	ADJ
ejpam-5429	494	24	ideal	ideal	ADJ
ejpam-5429	494	25	solution	solution	NOUN
ejpam-5429	494	26	(	(	PUNCT
ejpam-5429	494	27	qp	qp	NOUN
ejpam-5429	494	28	-	-	PUNCT
ejpam-5429	494	29	fpis	fpi	VERB
ejpam-5429	494	30	)	)	PUNCT
ejpam-5429	494	31	and	and	CCONJ
ejpam-5429	494	32	qp	qp	PROPN
ejpam-5429	494	33	-	-	PUNCT
ejpam-5429	494	34	f	f	PROPN
ejpam-5429	494	35	negative	negative	ADJ
ejpam-5429	494	36	ideal	ideal	ADJ
ejpam-5429	494	37	solution	solution	NOUN
ejpam-5429	494	38	(	(	PUNCT
ejpam-5429	494	39	qp	qp	NOUN
ejpam-5429	494	40	-	-	PUNCT
ejpam-5429	494	41	fnis	fnis	NOUN
ejpam-5429	494	42	)	)	PUNCT
ejpam-5429	494	43	of	of	ADP
ejpam-5429	494	44	alternatives	alternative	NOUN
ejpam-5429	494	45	under	under	ADP
ejpam-5429	494	46	the	the	DET
ejpam-5429	494	47	qp	qp	PROPN
ejpam-5429	494	48	-	-	PUNCT
ejpam-5429	494	49	f	f	PROPN
ejpam-5429	494	50	environment	environment	NOUN
ejpam-5429	494	51	can	can	AUX
ejpam-5429	494	52	be	be	AUX
ejpam-5429	494	53	calculated	calculate	VERB
ejpam-5429	494	54	by	by	ADP
ejpam-5429	494	55	equations	equation	NOUN
ejpam-5429	494	56	(	(	PUNCT
ejpam-5429	494	57	5	5	NUM
ejpam-5429	494	58	)	)	PUNCT
ejpam-5429	494	59	and	and	CCONJ
ejpam-5429	494	60	(	(	PUNCT
ejpam-5429	494	61	6	6	NUM
ejpam-5429	494	62	)	)	PUNCT
ejpam-5429	494	63	as	as	ADP
ejpam-5429	494	64	qp	qp	NOUN
ejpam-5429	494	65	−	−	PROPN
ejpam-5429	494	66	fpis	fpi	VERB
ejpam-5429	494	67	=	=	X
ejpam-5429	494	68	{	{	PUNCT
ejpam-5429	494	69	(	(	PUNCT
ejpam-5429	494	70	ð̃1	ð̃1	NOUN
ejpam-5429	494	71	′	′	NUM
ejpam-5429	494	72	(	(	PUNCT
ejpam-5429	494	73	ς̇))+	ς̇))+	PROPN
ejpam-5429	494	74	,	,	PUNCT
ejpam-5429	494	75	(	(	PUNCT
ejpam-5429	494	76	ð̃2	ð̃2	PROPN
ejpam-5429	494	77	′	′	NUM
ejpam-5429	494	78	(	(	PUNCT
ejpam-5429	494	79	ς̇))+	ς̇))+	PROPN
ejpam-5429	494	80	,	,	PUNCT
ejpam-5429	494	81	(	(	PUNCT
ejpam-5429	494	82	ð̃3	ð̃3	X
ejpam-5429	494	83	′	′	NUM
ejpam-5429	494	84	(	(	PUNCT
ejpam-5429	494	85	ς̇))+	ς̇))+	PROPN
ejpam-5429	494	86	,	,	PUNCT
ejpam-5429	494	87	(	(	PUNCT
ejpam-5429	494	88	ð̃4	ð̃4	PROPN
ejpam-5429	494	89	′	′	NUM
ejpam-5429	494	90	(	(	PUNCT
ejpam-5429	494	91	ς̇))+	ς̇))+	PROPN
ejpam-5429	494	92	}	}	PUNCT
ejpam-5429	494	93	,	,	PUNCT
ejpam-5429	494	94	(	(	PUNCT
ejpam-5429	494	95	5	5	X
ejpam-5429	494	96	)	)	PUNCT
ejpam-5429	494	97	qp	qp	ADP
ejpam-5429	494	98	−	−	PROPN
ejpam-5429	494	99	fnis	fnis	NOUN
ejpam-5429	494	100	=	=	SYM
ejpam-5429	494	101	{	{	PUNCT
ejpam-5429	494	102	(	(	PUNCT
ejpam-5429	494	103	ð̃1	ð̃1	SYM
ejpam-5429	494	104	′	′	NUM
ejpam-5429	494	105	(	(	PUNCT
ejpam-5429	494	106	ς̇))−	ς̇))−	NUM
ejpam-5429	494	107	,	,	PUNCT
ejpam-5429	494	108	(	(	PUNCT
ejpam-5429	494	109	ð̃2	ð̃2	PROPN
ejpam-5429	494	110	′	′	NUM
ejpam-5429	494	111	(	(	PUNCT
ejpam-5429	494	112	ς̇))−	ς̇))−	NUM
ejpam-5429	494	113	,	,	PUNCT
ejpam-5429	494	114	(	(	PUNCT
ejpam-5429	494	115	ð̃3	ð̃3	NUM
ejpam-5429	494	116	′	′	NUM
ejpam-5429	494	117	(	(	PUNCT
ejpam-5429	494	118	ς̇))−	ς̇))−	NUM
ejpam-5429	494	119	,	,	PUNCT
ejpam-5429	494	120	(	(	PUNCT
ejpam-5429	494	121	ð̃4	ð̃4	PROPN
ejpam-5429	494	122	′	′	NUM
ejpam-5429	494	123	(	(	PUNCT
ejpam-5429	494	124	ς̇))−	ς̇))−	NOUN
ejpam-5429	494	125	}	}	PUNCT
ejpam-5429	494	126	,	,	PUNCT
ejpam-5429	494	127	(	(	PUNCT
ejpam-5429	494	128	6	6	NUM
ejpam-5429	494	129	)	)	PUNCT
ejpam-5429	494	130	where	where	SCONJ
ejpam-5429	494	131	(	(	PUNCT
ejpam-5429	494	132	ð̃k	ð̃k	NOUN
ejpam-5429	494	133	′	′	NUM
ejpam-5429	495	1	(	(	PUNCT
ejpam-5429	496	1	ς̇))+	ς̇))+	NOUN
ejpam-5429	496	2	=	=	SYM
ejpam-5429	496	3	sup	sup	PROPN
ejpam-5429	496	4	j	j	PROPN
ejpam-5429	496	5	(	(	PUNCT
ejpam-5429	496	6	ð̃k	ð̃k	PROPN
ejpam-5429	497	1	′	′	NUM
ejpam-5429	497	2	(	(	PUNCT
ejpam-5429	497	3	ς̇	ς̇	NOUN
ejpam-5429	497	4	)	)	PUNCT
ejpam-5429	497	5	)	)	PUNCT
ejpam-5429	498	1	=	=	PUNCT
ejpam-5429	498	2	sup	sup	PROPN
ejpam-5429	498	3	j	j	PROPN
ejpam-5429	498	4	(	(	PUNCT
ejpam-5429	498	5	ρ1	ρ1	NOUN
ejpam-5429	498	6	o	o	NOUN
ejpam-5429	499	1	ð̃jk	ð̃jk	VERB
ejpam-5429	499	2	′	′	NUM
ejpam-5429	499	3	(	(	PUNCT
ejpam-5429	499	4	ς̇	ς̇	NOUN
ejpam-5429	499	5	)	)	PUNCT
ejpam-5429	499	6	,	,	PUNCT
ejpam-5429	499	7	ρ2	ρ2	NOUN
ejpam-5429	499	8	o	o	NOUN
ejpam-5429	499	9	ð̃jk	ð̃jk	PRON
ejpam-5429	499	10	′	′	NUM
ejpam-5429	499	11	(	(	PUNCT
ejpam-5429	499	12	ς̇	ς̇	NOUN
ejpam-5429	499	13	)	)	PUNCT
ejpam-5429	499	14	,	,	PUNCT
ejpam-5429	499	15	ρ3	ρ3	NOUN
ejpam-5429	499	16	o	o	NOUN
ejpam-5429	500	1	ð̃jk	ð̃jk	VERB
ejpam-5429	500	2	′	′	NUM
ejpam-5429	500	3	(	(	PUNCT
ejpam-5429	500	4	ς̇	ς̇	NOUN
ejpam-5429	500	5	)	)	PUNCT
ejpam-5429	500	6	,	,	PUNCT
ejpam-5429	500	7	ρ4	ρ4	ADV
ejpam-5429	500	8	o	o	NOUN
ejpam-5429	500	9	ð̃jk	ð̃jk	VERB
ejpam-5429	500	10	′	′	NUM
ejpam-5429	500	11	(	(	PUNCT
ejpam-5429	500	12	ς̇	ς̇	NOUN
ejpam-5429	500	13	)	)	PUNCT
ejpam-5429	500	14	)	)	PUNCT
ejpam-5429	501	1	=	=	PUNCT
ejpam-5429	501	2	(	(	PUNCT
ejpam-5429	501	3	(	(	PUNCT
ejpam-5429	501	4	ρ1	ρ1	NOUN
ejpam-5429	501	5	o	o	INTJ
ejpam-5429	501	6	ð̃k	ð̃k	NOUN
ejpam-5429	502	1	′	′	NUM
ejpam-5429	502	2	(	(	PUNCT
ejpam-5429	502	3	ς̇))+	ς̇))+	PROPN
ejpam-5429	502	4	,	,	PUNCT
ejpam-5429	502	5	(	(	PUNCT
ejpam-5429	502	6	ρ2	ρ2	NOUN
ejpam-5429	502	7	o	o	INTJ
ejpam-5429	502	8	ð̃k	ð̃k	NOUN
ejpam-5429	503	1	′	′	NUM
ejpam-5429	503	2	(	(	PUNCT
ejpam-5429	503	3	ς̇))+	ς̇))+	PROPN
ejpam-5429	503	4	,	,	PUNCT
ejpam-5429	503	5	(	(	PUNCT
ejpam-5429	503	6	ρ3	ρ3	NOUN
ejpam-5429	503	7	o	o	X
ejpam-5429	503	8	ð̃k	ð̃k	NOUN
ejpam-5429	504	1	′	′	NUM
ejpam-5429	504	2	(	(	PUNCT
ejpam-5429	504	3	ς̇))+	ς̇))+	PROPN
ejpam-5429	504	4	,	,	PUNCT
ejpam-5429	504	5	(	(	PUNCT
ejpam-5429	505	1	ρ4	ρ4	ADV
ejpam-5429	505	2	o	o	X
ejpam-5429	505	3	ð̃k	ð̃k	NOUN
ejpam-5429	506	1	′	′	NUM
ejpam-5429	506	2	(	(	PUNCT
ejpam-5429	506	3	ς̇))+	ς̇))+	NOUN
ejpam-5429	506	4	)	)	PUNCT
ejpam-5429	506	5	,	,	PUNCT
ejpam-5429	506	6	and	and	CCONJ
ejpam-5429	506	7	(	(	PUNCT
ejpam-5429	506	8	ð̃k	ð̃k	NOUN
ejpam-5429	506	9	′	′	NUM
ejpam-5429	507	1	(	(	PUNCT
ejpam-5429	507	2	ς̇))−	ς̇))−	PROPN
ejpam-5429	507	3	=	=	PROPN
ejpam-5429	507	4	inf	inf	PROPN
ejpam-5429	507	5	j	j	PROPN
ejpam-5429	507	6	(	(	PUNCT
ejpam-5429	507	7	ð̃k	ð̃k	PROPN
ejpam-5429	507	8	′	′	NUM
ejpam-5429	507	9	(	(	PUNCT
ejpam-5429	507	10	ς̇	ς̇	NOUN
ejpam-5429	507	11	)	)	PUNCT
ejpam-5429	507	12	)	)	PUNCT
ejpam-5429	508	1	=	=	SYM
ejpam-5429	508	2	inf	inf	PROPN
ejpam-5429	508	3	j	j	PROPN
ejpam-5429	508	4	(	(	PUNCT
ejpam-5429	508	5	ρ1	ρ1	NOUN
ejpam-5429	508	6	o	o	NOUN
ejpam-5429	509	1	ð̃jk	ð̃jk	VERB
ejpam-5429	509	2	′	′	NUM
ejpam-5429	509	3	(	(	PUNCT
ejpam-5429	509	4	ς̇	ς̇	NOUN
ejpam-5429	509	5	)	)	PUNCT
ejpam-5429	509	6	,	,	PUNCT
ejpam-5429	509	7	ρ2	ρ2	NOUN
ejpam-5429	509	8	o	o	NOUN
ejpam-5429	509	9	ð̃jk	ð̃jk	PRON
ejpam-5429	509	10	′	′	NUM
ejpam-5429	509	11	(	(	PUNCT
ejpam-5429	509	12	ς̇	ς̇	NOUN
ejpam-5429	509	13	)	)	PUNCT
ejpam-5429	509	14	,	,	PUNCT
ejpam-5429	509	15	ρ3	ρ3	NOUN
ejpam-5429	509	16	o	o	NOUN
ejpam-5429	510	1	ð̃jk	ð̃jk	VERB
ejpam-5429	510	2	′	′	NUM
ejpam-5429	510	3	(	(	PUNCT
ejpam-5429	510	4	ς̇	ς̇	NOUN
ejpam-5429	510	5	)	)	PUNCT
ejpam-5429	510	6	,	,	PUNCT
ejpam-5429	510	7	ρ4	ρ4	ADV
ejpam-5429	510	8	o	o	NOUN
ejpam-5429	510	9	ð̃jk	ð̃jk	VERB
ejpam-5429	510	10	′	′	NUM
ejpam-5429	510	11	(	(	PUNCT
ejpam-5429	510	12	ς̇	ς̇	NOUN
ejpam-5429	510	13	)	)	PUNCT
ejpam-5429	510	14	)	)	PUNCT
ejpam-5429	511	1	=	=	PUNCT
ejpam-5429	511	2	(	(	PUNCT
ejpam-5429	511	3	(	(	PUNCT
ejpam-5429	511	4	ρ1	ρ1	NOUN
ejpam-5429	511	5	o	o	INTJ
ejpam-5429	511	6	ð̃k	ð̃k	NOUN
ejpam-5429	512	1	′	′	NUM
ejpam-5429	512	2	(	(	PUNCT
ejpam-5429	512	3	ς̇))−	ς̇))−	NUM
ejpam-5429	512	4	,	,	PUNCT
ejpam-5429	512	5	(	(	PUNCT
ejpam-5429	512	6	ρ2	ρ2	NOUN
ejpam-5429	512	7	o	o	INTJ
ejpam-5429	512	8	ð̃k	ð̃k	NOUN
ejpam-5429	513	1	′	′	NUM
ejpam-5429	513	2	(	(	PUNCT
ejpam-5429	513	3	ς̇))−	ς̇))−	NUM
ejpam-5429	513	4	,	,	PUNCT
ejpam-5429	513	5	(	(	PUNCT
ejpam-5429	513	6	ρ3	ρ3	NOUN
ejpam-5429	513	7	o	o	X
ejpam-5429	513	8	ð̃k	ð̃k	NOUN
ejpam-5429	514	1	′	′	NUM
ejpam-5429	514	2	(	(	PUNCT
ejpam-5429	514	3	ς̇))−	ς̇))−	NUM
ejpam-5429	514	4	,	,	PUNCT
ejpam-5429	514	5	(	(	PUNCT
ejpam-5429	515	1	ρ4	ρ4	ADV
ejpam-5429	515	2	o	o	X
ejpam-5429	515	3	ð̃k	ð̃k	NOUN
ejpam-5429	516	1	′	′	NUM
ejpam-5429	516	2	(	(	PUNCT
ejpam-5429	516	3	ς̇))−	ς̇))−	NOUN
ejpam-5429	516	4	)	)	PUNCT
ejpam-5429	516	5	.	.	PUNCT
ejpam-5429	517	1	step	step	NOUN
ejpam-5429	517	2	6	6	NUM
ejpam-5429	517	3	:	:	PUNCT
ejpam-5429	517	4	the	the	DET
ejpam-5429	517	5	qp	qp	PROPN
ejpam-5429	517	6	-	-	PUNCT
ejpam-5429	517	7	f	f	PROPN
ejpam-5429	517	8	euclidean	euclidean	ADJ
ejpam-5429	517	9	distance	distance	NOUN
ejpam-5429	517	10	of	of	ADP
ejpam-5429	517	11	each	each	DET
ejpam-5429	517	12	alternative	alternative	ADJ
ejpam-5429	517	13	ς̇j	ς̇j	PROPN
ejpam-5429	517	14	from	from	ADP
ejpam-5429	517	15	qp	qp	NOUN
ejpam-5429	517	16	-	-	PUNCT
ejpam-5429	517	17	fpis	fpi	VERB
ejpam-5429	517	18	and	and	CCONJ
ejpam-5429	517	19	qpfnis	qpfni	NOUN
ejpam-5429	517	20	can	can	AUX
ejpam-5429	517	21	be	be	AUX
ejpam-5429	517	22	calculated	calculate	VERB
ejpam-5429	517	23	by	by	ADP
ejpam-5429	517	24	equations	equation	NOUN
ejpam-5429	517	25	(	(	PUNCT
ejpam-5429	517	26	7	7	NUM
ejpam-5429	517	27	)	)	PUNCT
ejpam-5429	517	28	and	and	CCONJ
ejpam-5429	517	29	(	(	PUNCT
ejpam-5429	517	30	8)	8)	NUM
ejpam-5429	517	31	.	.	PUNCT
ejpam-5429	518	1	d	d	NOUN
ejpam-5429	518	2	′	′	NUM
ejpam-5429	519	1	e(ς̇j	e(ς̇j	PROPN
ejpam-5429	519	2	,	,	PUNCT
ejpam-5429	519	3	qp	qp	ADP
ejpam-5429	519	4	−	−	PROPN
ejpam-5429	519	5	fpis	fpi	VERB
ejpam-5429	519	6	)	)	PUNCT
ejpam-5429	520	1	=	=	PUNCT
ejpam-5429	520	2	√√√√	√√√√	PRON
ejpam-5429	520	3	1	1	NUM
ejpam-5429	520	4	16	16	NUM
ejpam-5429	520	5	4∑	4∑	NOUN
ejpam-5429	520	6	k=1	k=1	PUNCT
ejpam-5429	521	1	[	[	PUNCT
ejpam-5429	521	2	4∑	4∑	NUM
ejpam-5429	521	3	l=1	l=1	PROPN
ejpam-5429	521	4	{	{	PUNCT
ejpam-5429	521	5	4∑	4∑	NOUN
ejpam-5429	521	6	i=1	i=1	X
ejpam-5429	521	7	(	(	PUNCT
ejpam-5429	521	8	ρi	ρi	INTJ
ejpam-5429	521	9	o	o	PROPN
ejpam-5429	521	10	ð̃jk′	ð̃jk′	PROPN
ejpam-5429	521	11	(	(	PUNCT
ejpam-5429	521	12	ς̇)−	ς̇)−	PROPN
ejpam-5429	521	13	ρi	ρi	NOUN
ejpam-5429	521	14	o	o	X
ejpam-5429	521	15	ð̃k′	ð̃k′	INTJ
ejpam-5429	521	16	(	(	PUNCT
ejpam-5429	521	17	ς̇)+	ς̇)+	NOUN
ejpam-5429	521	18	}	}	PUNCT
ejpam-5429	521	19	]	]	PUNCT
ejpam-5429	521	20	,	,	PUNCT
ejpam-5429	521	21	(	(	PUNCT
ejpam-5429	521	22	7	7	X
ejpam-5429	521	23	)	)	PUNCT
ejpam-5429	521	24	k.	k.	PROPN
ejpam-5429	522	1	h.	h.	PROPN
ejpam-5429	522	2	hakami	hakami	PROPN
ejpam-5429	522	3	et	et	PROPN
ejpam-5429	522	4	al	al	PROPN
ejpam-5429	522	5	.	.	PUNCT
ejpam-5429	522	6	/	/	SYM
ejpam-5429	522	7	eur	eur	PROPN
ejpam-5429	522	8	.	.	PUNCT
ejpam-5429	523	1	j.	j.	PROPN
ejpam-5429	523	2	pure	pure	PROPN
ejpam-5429	523	3	appl	appl	PROPN
ejpam-5429	523	4	.	.	PROPN
ejpam-5429	523	5	math	math	PROPN
ejpam-5429	523	6	,	,	PUNCT
ejpam-5429	523	7	17	17	NUM
ejpam-5429	523	8	(	(	PUNCT
ejpam-5429	523	9	4	4	NUM
ejpam-5429	523	10	)	)	PUNCT
ejpam-5429	523	11	(	(	PUNCT
ejpam-5429	523	12	2024	2024	NUM
ejpam-5429	523	13	)	)	PUNCT
ejpam-5429	523	14	,	,	PUNCT
ejpam-5429	523	15	3129	3129	NUM
ejpam-5429	523	16	-	-	SYM
ejpam-5429	523	17	3155	3155	NUM
ejpam-5429	523	18	3146	3146	NUM
ejpam-5429	523	19	and	and	CCONJ
ejpam-5429	523	20	d	d	NOUN
ejpam-5429	523	21	′	′	NUM
ejpam-5429	523	22	e(ς̇j	e(ς̇j	PROPN
ejpam-5429	523	23	,	,	PUNCT
ejpam-5429	523	24	qp	qp	VERB
ejpam-5429	523	25	−	−	PROPN
ejpam-5429	523	26	fnis	fnis	NOUN
ejpam-5429	523	27	)	)	PUNCT
ejpam-5429	524	1	=	=	PUNCT
ejpam-5429	524	2	√√√√	√√√√	PRON
ejpam-5429	524	3	1	1	NUM
ejpam-5429	524	4	16	16	NUM
ejpam-5429	524	5	4∑	4∑	NOUN
ejpam-5429	524	6	k=1	k=1	PUNCT
ejpam-5429	525	1	[	[	PUNCT
ejpam-5429	525	2	4∑	4∑	NUM
ejpam-5429	525	3	l=1	l=1	PROPN
ejpam-5429	525	4	{	{	PUNCT
ejpam-5429	525	5	4∑	4∑	NOUN
ejpam-5429	525	6	i=1	i=1	X
ejpam-5429	525	7	(	(	PUNCT
ejpam-5429	525	8	ρi	ρi	INTJ
ejpam-5429	525	9	o	o	PROPN
ejpam-5429	525	10	ð̃jk′	ð̃jk′	PROPN
ejpam-5429	525	11	(	(	PUNCT
ejpam-5429	525	12	ς̇)−	ς̇)−	PROPN
ejpam-5429	525	13	ρi	ρi	NOUN
ejpam-5429	525	14	o	o	X
ejpam-5429	525	15	ð̃k′	ð̃k′	PROPN
ejpam-5429	525	16	(	(	PUNCT
ejpam-5429	525	17	ς̇)−	ς̇)−	PROPN
ejpam-5429	525	18	}	}	PUNCT
ejpam-5429	525	19	]	]	PUNCT
ejpam-5429	525	20	,	,	PUNCT
ejpam-5429	525	21	(	(	PUNCT
ejpam-5429	525	22	8)	8)	NUM
ejpam-5429	525	23	step	step	NOUN
ejpam-5429	525	24	7	7	NUM
ejpam-5429	525	25	:	:	PUNCT
ejpam-5429	525	26	the	the	DET
ejpam-5429	525	27	relative	relative	ADJ
ejpam-5429	525	28	qp	qp	PROPN
ejpam-5429	525	29	-	-	PROPN
ejpam-5429	525	30	f	f	PROPN
ejpam-5429	525	31	closeness	closeness	NOUN
ejpam-5429	525	32	coefficient	coefficient	NOUN
ejpam-5429	525	33	of	of	ADP
ejpam-5429	525	34	each	each	DET
ejpam-5429	525	35	alternative	alternative	ADJ
ejpam-5429	525	36	ς̇j	ς̇j	NOUN
ejpam-5429	525	37	using	use	VERB
ejpam-5429	525	38	the	the	DET
ejpam-5429	525	39	following	follow	VERB
ejpam-5429	525	40	formula	formula	NOUN
ejpam-5429	525	41	as	as	SCONJ
ejpam-5429	525	42	described	describe	VERB
ejpam-5429	525	43	by	by	ADP
ejpam-5429	525	44	(	(	PUNCT
ejpam-5429	525	45	9	9	NUM
ejpam-5429	525	46	)	)	PUNCT
ejpam-5429	525	47	,	,	PUNCT
ejpam-5429	526	1	e	e	NOUN
ejpam-5429	526	2	′	′	NUM
ejpam-5429	527	1	j	j	X
ejpam-5429	528	1	=	=	SYM
ejpam-5429	529	1	d	d	NOUN
ejpam-5429	529	2	′	′	NUM
ejpam-5429	529	3	e(ς̇j	e(ς̇j	PROPN
ejpam-5429	529	4	,	,	PUNCT
ejpam-5429	529	5	qp	qp	VERB
ejpam-5429	529	6	−	−	PROPN
ejpam-5429	529	7	fnis	fnis	NOUN
ejpam-5429	529	8	)	)	PUNCT
ejpam-5429	530	1	d	d	NOUN
ejpam-5429	530	2	′	′	NUM
ejpam-5429	531	1	e(ς̇j	e(ς̇j	PROPN
ejpam-5429	531	2	,	,	PUNCT
ejpam-5429	531	3	qp	qp	ADP
ejpam-5429	531	4	−	−	PROPN
ejpam-5429	531	5	fpis	fpi	VERB
ejpam-5429	531	6	)	)	PUNCT
ejpam-5429	532	1	+	+	PUNCT
ejpam-5429	532	2	d	d	NOUN
ejpam-5429	532	3	′	′	NUM
ejpam-5429	532	4	e(ς̇j	e(ς̇j	PROPN
ejpam-5429	532	5	,	,	PUNCT
ejpam-5429	532	6	qp	qp	ADP
ejpam-5429	532	7	−	−	PROPN
ejpam-5429	532	8	fnis	fnis	PROPN
ejpam-5429	532	9	)	)	PUNCT
ejpam-5429	532	10	,	,	PUNCT
ejpam-5429	532	11	j	j	PROPN
ejpam-5429	532	12	=	=	SYM
ejpam-5429	532	13	1	1	NUM
ejpam-5429	532	14	,	,	PUNCT
ejpam-5429	532	15	2	2	NUM
ejpam-5429	532	16	,	,	PUNCT
ejpam-5429	532	17	3	3	NUM
ejpam-5429	532	18	,	,	PUNCT
ejpam-5429	532	19	4	4	NUM
ejpam-5429	532	20	.	.	PUNCT
ejpam-5429	532	21	(	(	PUNCT
ejpam-5429	532	22	9	9	X
ejpam-5429	532	23	)	)	PUNCT
ejpam-5429	532	24	the	the	DET
ejpam-5429	532	25	alternative	alternative	NOUN
ejpam-5429	532	26	with	with	ADP
ejpam-5429	532	27	the	the	DET
ejpam-5429	532	28	highest	high	ADJ
ejpam-5429	532	29	qp	qp	ADP
ejpam-5429	532	30	-	-	PUNCT
ejpam-5429	532	31	f	f	PROPN
ejpam-5429	532	32	closeness	closeness	NOUN
ejpam-5429	532	33	coefficient	coefficient	NOUN
ejpam-5429	532	34	is	be	AUX
ejpam-5429	532	35	the	the	DET
ejpam-5429	532	36	best	good	ADJ
ejpam-5429	532	37	one	one	NUM
ejpam-5429	532	38	,	,	PUNCT
ejpam-5429	532	39	and	and	CCONJ
ejpam-5429	532	40	we	we	PRON
ejpam-5429	532	41	can	can	AUX
ejpam-5429	532	42	rank	rank	VERB
ejpam-5429	532	43	each	each	DET
ejpam-5429	532	44	alternative	alternative	NOUN
ejpam-5429	532	45	in	in	ADP
ejpam-5429	532	46	order	order	NOUN
ejpam-5429	532	47	.	.	PUNCT
ejpam-5429	533	1	we	we	PRON
ejpam-5429	533	2	present	present	VERB
ejpam-5429	533	3	our	our	PRON
ejpam-5429	533	4	proposed	propose	VERB
ejpam-5429	533	5	decision	decision	NOUN
ejpam-5429	533	6	-	-	PUNCT
ejpam-5429	533	7	making	make	VERB
ejpam-5429	533	8	method	method	NOUN
ejpam-5429	533	9	in	in	ADP
ejpam-5429	533	10	algorithm	algorithm	NOUN
ejpam-5429	533	11	1	1	NUM
ejpam-5429	533	12	.	.	PUNCT
ejpam-5429	534	1	in	in	ADP
ejpam-5429	534	2	section	section	NOUN
ejpam-5429	534	3	6.1	6.1	NUM
ejpam-5429	534	4	,	,	PUNCT
ejpam-5429	534	5	we	we	PRON
ejpam-5429	534	6	examine	examine	VERB
ejpam-5429	534	7	the	the	DET
ejpam-5429	534	8	practical	practical	ADJ
ejpam-5429	534	9	usage	usage	NOUN
ejpam-5429	534	10	of	of	ADP
ejpam-5429	534	11	our	our	PRON
ejpam-5429	534	12	suggested	suggest	VERB
ejpam-5429	534	13	model	model	NOUN
ejpam-5429	534	14	.	.	PUNCT
ejpam-5429	535	1	specifically	specifically	ADV
ejpam-5429	535	2	,	,	PUNCT
ejpam-5429	535	3	we	we	PRON
ejpam-5429	535	4	algorithm	algorithm	VERB
ejpam-5429	535	5	1	1	NUM
ejpam-5429	535	6	.	.	PUNCT
ejpam-5429	536	1	the	the	DET
ejpam-5429	536	2	algorithm	algorithm	NOUN
ejpam-5429	536	3	of	of	ADP
ejpam-5429	536	4	the	the	DET
ejpam-5429	536	5	proposed	propose	VERB
ejpam-5429	536	6	approaches	approach	NOUN
ejpam-5429	536	7	for	for	ADP
ejpam-5429	536	8	dealing	deal	VERB
ejpam-5429	536	9	mcgdm	mcgdm	ADJ
ejpam-5429	536	10	problems	problem	NOUN
ejpam-5429	536	11	.	.	PUNCT
ejpam-5429	537	1	step	step	NOUN
ejpam-5429	537	2	1	1	NUM
ejpam-5429	537	3	.	.	PUNCT
ejpam-5429	537	4	input	input	NOUN
ejpam-5429	537	5	.	.	PUNCT
ejpam-5429	538	1	step	step	NOUN
ejpam-5429	538	2	2	2	NUM
ejpam-5429	538	3	.	.	PUNCT
ejpam-5429	538	4	determine	determine	VERB
ejpam-5429	538	5	the	the	DET
ejpam-5429	538	6	optimistic	optimistic	ADJ
ejpam-5429	538	7	or	or	CCONJ
ejpam-5429	538	8	pessimistic	pessimistic	ADJ
ejpam-5429	538	9	q	q	ADJ
ejpam-5429	538	10	-	-	PUNCT
ejpam-5429	538	11	pf	pf	NOUN
ejpam-5429	538	12	decision	decision	NOUN
ejpam-5429	538	13	matrix	matrix	NOUN
ejpam-5429	538	14	.	.	PUNCT
ejpam-5429	539	1	step	step	NOUN
ejpam-5429	539	2	3	3	NUM
ejpam-5429	539	3	.	.	PUNCT
ejpam-5429	539	4	calculate	calculate	VERB
ejpam-5429	539	5	the	the	DET
ejpam-5429	539	6	normalized	normalize	VERB
ejpam-5429	539	7	weights	weight	NOUN
ejpam-5429	539	8	.	.	PUNCT
ejpam-5429	540	1	step	step	NOUN
ejpam-5429	540	2	4	4	NUM
ejpam-5429	540	3	.	.	PUNCT
ejpam-5429	540	4	calculate	calculate	VERB
ejpam-5429	540	5	the	the	DET
ejpam-5429	540	6	weight	weight	NOUN
ejpam-5429	540	7	for	for	ADP
ejpam-5429	540	8	the	the	DET
ejpam-5429	540	9	pessimistic	pessimistic	ADJ
ejpam-5429	540	10	qp	qp	NOUN
ejpam-5429	540	11	-	-	PUNCT
ejpam-5429	540	12	f	f	NOUN
ejpam-5429	540	13	decision	decision	NOUN
ejpam-5429	540	14	matrix	matrix	NOUN
ejpam-5429	540	15	.	.	PUNCT
ejpam-5429	541	1	step	step	NOUN
ejpam-5429	541	2	5	5	NUM
ejpam-5429	541	3	.	.	PUNCT
ejpam-5429	541	4	compute	compute	VERB
ejpam-5429	541	5	the	the	DET
ejpam-5429	541	6	qp	qp	PROPN
ejpam-5429	541	7	-	-	PUNCT
ejpam-5429	541	8	fpis	fpi	VERB
ejpam-5429	541	9	,	,	PUNCT
ejpam-5429	541	10	and	and	CCONJ
ejpam-5429	541	11	qp	qp	NOUN
ejpam-5429	541	12	-	-	PUNCT
ejpam-5429	541	13	fnis	fnis	NOUN
ejpam-5429	541	14	.	.	PUNCT
ejpam-5429	542	1	step	step	NOUN
ejpam-5429	542	2	6	6	NUM
ejpam-5429	542	3	.	.	PUNCT
ejpam-5429	543	1	qp	qp	PROPN
ejpam-5429	543	2	-	-	PUNCT
ejpam-5429	543	3	f	f	PROPN
ejpam-5429	543	4	euclidean	euclidean	ADJ
ejpam-5429	543	5	distance	distance	NOUN
ejpam-5429	543	6	of	of	ADP
ejpam-5429	543	7	each	each	DET
ejpam-5429	543	8	alternative	alternative	ADJ
ejpam-5429	543	9	ς̇j	ς̇j	PROPN
ejpam-5429	543	10	from	from	ADP
ejpam-5429	543	11	qfpis	qfpis	NOUN
ejpam-5429	543	12	and	and	CCONJ
ejpam-5429	543	13	qp	qp	NOUN
ejpam-5429	543	14	-	-	PUNCT
ejpam-5429	543	15	fpis	fpi	VERB
ejpam-5429	543	16	.	.	PUNCT
ejpam-5429	544	1	step	step	NOUN
ejpam-5429	544	2	7	7	NUM
ejpam-5429	544	3	.	.	PUNCT
ejpam-5429	544	4	calculate	calculate	VERB
ejpam-5429	544	5	the	the	DET
ejpam-5429	544	6	relative	relative	ADJ
ejpam-5429	544	7	qp	qp	PROPN
ejpam-5429	544	8	-	-	PROPN
ejpam-5429	544	9	f	f	PROPN
ejpam-5429	544	10	closeness	closeness	NOUN
ejpam-5429	544	11	coefficients	coefficient	VERB
ejpam-5429	544	12	ej′	ej′	PRON
ejpam-5429	544	13	.	.	PUNCT
ejpam-5429	545	1	step	step	NOUN
ejpam-5429	545	2	8	8	NUM
ejpam-5429	545	3	.	.	PUNCT
ejpam-5429	546	1	output	output	NOUN
ejpam-5429	546	2	.	.	PUNCT
ejpam-5429	547	1	rank	rank	VERB
ejpam-5429	547	2	the	the	DET
ejpam-5429	547	3	possibilities	possibility	NOUN
ejpam-5429	547	4	for	for	ADP
ejpam-5429	547	5	the	the	DET
ejpam-5429	547	6	final	final	ADJ
ejpam-5429	547	7	decision	decision	NOUN
ejpam-5429	547	8	and	and	CCONJ
ejpam-5429	547	9	choose	choose	VERB
ejpam-5429	547	10	the	the	DET
ejpam-5429	547	11	best	good	ADJ
ejpam-5429	547	12	one	one	NUM
ejpam-5429	547	13	.	.	PUNCT
ejpam-5429	548	1	show	show	VERB
ejpam-5429	548	2	how	how	SCONJ
ejpam-5429	548	3	qp	qp	NOUN
ejpam-5429	548	4	-	-	PUNCT
ejpam-5429	548	5	f	f	PROPN
ejpam-5429	548	6	is	be	AUX
ejpam-5429	548	7	useful	useful	ADJ
ejpam-5429	548	8	in	in	ADP
ejpam-5429	548	9	the	the	DET
ejpam-5429	548	10	selection	selection	NOUN
ejpam-5429	548	11	of	of	ADP
ejpam-5429	548	12	solar	solar	ADJ
ejpam-5429	548	13	power	power	NOUN
ejpam-5429	548	14	plant	plant	NOUN
ejpam-5429	548	15	stations	station	NOUN
ejpam-5429	548	16	in	in	ADP
ejpam-5429	548	17	a	a	DET
ejpam-5429	548	18	rural	rural	ADJ
ejpam-5429	548	19	region	region	NOUN
ejpam-5429	548	20	.	.	PUNCT
ejpam-5429	549	1	selection	selection	NOUN
ejpam-5429	549	2	of	of	ADP
ejpam-5429	549	3	solar	solar	ADJ
ejpam-5429	549	4	power	power	NOUN
ejpam-5429	549	5	plant	plant	NOUN
ejpam-5429	549	6	station	station	NOUN
ejpam-5429	549	7	in	in	ADP
ejpam-5429	549	8	a	a	DET
ejpam-5429	549	9	rural	rural	ADJ
ejpam-5429	549	10	area	area	NOUN
ejpam-5429	549	11	assume	assume	VERB
ejpam-5429	549	12	that	that	SCONJ
ejpam-5429	549	13	the	the	DET
ejpam-5429	549	14	government	government	NOUN
ejpam-5429	549	15	want	want	VERB
ejpam-5429	549	16	to	to	PART
ejpam-5429	549	17	build	build	VERB
ejpam-5429	549	18	a	a	DET
ejpam-5429	549	19	solar	solar	ADJ
ejpam-5429	549	20	power	power	NOUN
ejpam-5429	549	21	plant	plant	NOUN
ejpam-5429	549	22	station	station	NOUN
ejpam-5429	549	23	in	in	ADP
ejpam-5429	549	24	a	a	DET
ejpam-5429	549	25	rural	rural	ADJ
ejpam-5429	549	26	area	area	NOUN
ejpam-5429	549	27	.	.	PUNCT
ejpam-5429	550	1	the	the	DET
ejpam-5429	550	2	government	government	NOUN
ejpam-5429	550	3	has	have	VERB
ejpam-5429	550	4	four	four	NUM
ejpam-5429	550	5	options	option	NOUN
ejpam-5429	550	6	for	for	ADP
ejpam-5429	550	7	the	the	DET
ejpam-5429	550	8	location	location	NOUN
ejpam-5429	550	9	of	of	ADP
ejpam-5429	550	10	a	a	DET
ejpam-5429	550	11	new	new	ADJ
ejpam-5429	550	12	solar	solar	ADJ
ejpam-5429	550	13	power	power	NOUN
ejpam-5429	550	14	plant	plant	NOUN
ejpam-5429	550	15	.	.	PUNCT
ejpam-5429	551	1	each	each	DET
ejpam-5429	551	2	site	site	NOUN
ejpam-5429	551	3	was	be	AUX
ejpam-5429	551	4	appraised	appraise	VERB
ejpam-5429	551	5	by	by	ADP
ejpam-5429	551	6	a	a	DET
ejpam-5429	551	7	group	group	NOUN
ejpam-5429	551	8	of	of	ADP
ejpam-5429	551	9	decision	decision	NOUN
ejpam-5429	551	10	makers	maker	NOUN
ejpam-5429	551	11	based	base	VERB
ejpam-5429	551	12	on	on	ADP
ejpam-5429	551	13	the	the	DET
ejpam-5429	551	14	following	follow	VERB
ejpam-5429	551	15	criteria	criterion	NOUN
ejpam-5429	551	16	as	as	SCONJ
ejpam-5429	551	17	follows	follow	VERB
ejpam-5429	551	18	:	:	PUNCT
ejpam-5429	552	1	1	1	X
ejpam-5429	552	2	.	.	PUNCT
ejpam-5429	552	3	“	"	PUNCT
ejpam-5429	552	4	solar	solar	ADJ
ejpam-5429	552	5	irradiance	irradiance	NOUN
ejpam-5429	552	6	(	(	PUNCT
ejpam-5429	552	7	t1	t1	NOUN
ejpam-5429	552	8	)	)	PUNCT
ejpam-5429	552	9	”	"	PUNCT
ejpam-5429	552	10	,	,	PUNCT
ejpam-5429	552	11	which	which	PRON
ejpam-5429	552	12	could	could	AUX
ejpam-5429	552	13	have	have	VERB
ejpam-5429	552	14	the	the	DET
ejpam-5429	552	15	characteristics	characteristic	NOUN
ejpam-5429	552	16	shown	show	VERB
ejpam-5429	552	17	below	below	ADP
ejpam-5429	552	18	:	:	PUNCT
ejpam-5429	552	19	•	•	NUM
ejpam-5429	552	20	solar	solar	ADJ
ejpam-5429	552	21	irradiance	irradiance	NOUN
ejpam-5429	552	22	density	density	NOUN
ejpam-5429	552	23	:	:	PUNCT
ejpam-5429	552	24	the	the	DET
ejpam-5429	552	25	amount	amount	NOUN
ejpam-5429	552	26	of	of	ADP
ejpam-5429	552	27	solar	solar	ADJ
ejpam-5429	552	28	power	power	NOUN
ejpam-5429	552	29	received	receive	VERB
ejpam-5429	552	30	per	per	ADP
ejpam-5429	552	31	unit	unit	NOUN
ejpam-5429	552	32	area	area	NOUN
ejpam-5429	552	33	.	.	PUNCT
ejpam-5429	553	1	•	•	NUM
ejpam-5429	553	2	sun	sun	NOUN
ejpam-5429	553	3	light	light	PROPN
ejpam-5429	553	4	duration	duration	NOUN
ejpam-5429	553	5	:	:	PUNCT
ejpam-5429	553	6	the	the	DET
ejpam-5429	553	7	number	number	NOUN
ejpam-5429	553	8	of	of	ADP
ejpam-5429	553	9	sunlight	sunlight	NOUN
ejpam-5429	553	10	hours	hour	NOUN
ejpam-5429	553	11	per	per	ADP
ejpam-5429	553	12	day	day	NOUN
ejpam-5429	553	13	.	.	PUNCT
ejpam-5429	554	1	•	•	NUM
ejpam-5429	554	2	solar	solar	ADJ
ejpam-5429	554	3	tracking	tracking	NOUN
ejpam-5429	554	4	:	:	PUNCT
ejpam-5429	554	5	the	the	DET
ejpam-5429	554	6	technology	technology	NOUN
ejpam-5429	554	7	used	use	VERB
ejpam-5429	554	8	to	to	PART
ejpam-5429	554	9	follow	follow	VERB
ejpam-5429	554	10	the	the	DET
ejpam-5429	554	11	sun	sun	NOUN
ejpam-5429	554	12	’s	’s	PART
ejpam-5429	554	13	path	path	NOUN
ejpam-5429	554	14	to	to	PART
ejpam-5429	554	15	maximize	maximize	VERB
ejpam-5429	554	16	energy	energy	NOUN
ejpam-5429	554	17	capture	capture	NOUN
ejpam-5429	554	18	.	.	PUNCT
ejpam-5429	555	1	•	•	NOUN
ejpam-5429	555	2	temporal	temporal	ADJ
ejpam-5429	555	3	variability	variability	NOUN
ejpam-5429	555	4	:	:	PUNCT
ejpam-5429	555	5	the	the	DET
ejpam-5429	555	6	fluctuation	fluctuation	NOUN
ejpam-5429	555	7	of	of	ADP
ejpam-5429	555	8	solar	solar	ADJ
ejpam-5429	555	9	irradiance	irradiance	NOUN
ejpam-5429	555	10	over	over	ADP
ejpam-5429	555	11	time	time	NOUN
ejpam-5429	555	12	,	,	PUNCT
ejpam-5429	555	13	including	include	VERB
ejpam-5429	555	14	daily	daily	ADJ
ejpam-5429	555	15	and	and	CCONJ
ejpam-5429	555	16	seasonal	seasonal	ADJ
ejpam-5429	555	17	changes	change	NOUN
ejpam-5429	555	18	.	.	PUNCT
ejpam-5429	556	1	k.	k.	PROPN
ejpam-5429	556	2	h.	h.	PROPN
ejpam-5429	556	3	hakami	hakami	PROPN
ejpam-5429	556	4	et	et	PROPN
ejpam-5429	556	5	al	al	PROPN
ejpam-5429	556	6	.	.	PUNCT
ejpam-5429	556	7	/	/	SYM
ejpam-5429	556	8	eur	eur	PROPN
ejpam-5429	556	9	.	.	PUNCT
ejpam-5429	557	1	j.	j.	PROPN
ejpam-5429	557	2	pure	pure	PROPN
ejpam-5429	557	3	appl	appl	PROPN
ejpam-5429	557	4	.	.	PROPN
ejpam-5429	557	5	math	math	PROPN
ejpam-5429	557	6	,	,	PUNCT
ejpam-5429	557	7	17	17	NUM
ejpam-5429	557	8	(	(	PUNCT
ejpam-5429	557	9	4	4	NUM
ejpam-5429	557	10	)	)	PUNCT
ejpam-5429	557	11	(	(	PUNCT
ejpam-5429	557	12	2024	2024	NUM
ejpam-5429	557	13	)	)	PUNCT
ejpam-5429	557	14	,	,	PUNCT
ejpam-5429	557	15	3129	3129	NUM
ejpam-5429	557	16	-	-	SYM
ejpam-5429	557	17	3155	3155	NUM
ejpam-5429	557	18	3147	3147	NUM
ejpam-5429	557	19	2	2	NUM
ejpam-5429	557	20	.	.	PUNCT
ejpam-5429	558	1	“	"	PUNCT
ejpam-5429	558	2	land	land	NOUN
ejpam-5429	558	3	availability	availability	NOUN
ejpam-5429	558	4	(	(	PUNCT
ejpam-5429	558	5	t2	t2	NOUN
ejpam-5429	558	6	)	)	PUNCT
ejpam-5429	558	7	”	"	PUNCT
ejpam-5429	558	8	,	,	PUNCT
ejpam-5429	558	9	which	which	PRON
ejpam-5429	558	10	could	could	AUX
ejpam-5429	558	11	have	have	VERB
ejpam-5429	558	12	the	the	DET
ejpam-5429	558	13	characteristics	characteristic	NOUN
ejpam-5429	558	14	shown	show	VERB
ejpam-5429	558	15	below	below	ADP
ejpam-5429	558	16	:	:	PUNCT
ejpam-5429	558	17	•	•	NUM
ejpam-5429	558	18	land	land	NOUN
ejpam-5429	558	19	size	size	NOUN
ejpam-5429	558	20	:	:	PUNCT
ejpam-5429	558	21	the	the	DET
ejpam-5429	558	22	total	total	ADJ
ejpam-5429	558	23	area	area	NOUN
ejpam-5429	558	24	available	available	ADJ
ejpam-5429	558	25	for	for	ADP
ejpam-5429	558	26	the	the	DET
ejpam-5429	558	27	solar	solar	ADJ
ejpam-5429	558	28	power	power	NOUN
ejpam-5429	558	29	plant	plant	NOUN
ejpam-5429	558	30	.	.	PUNCT
ejpam-5429	559	1	•	•	NUM
ejpam-5429	559	2	land	land	NOUN
ejpam-5429	559	3	ownership	ownership	NOUN
ejpam-5429	559	4	:	:	PUNCT
ejpam-5429	559	5	the	the	DET
ejpam-5429	559	6	ownership	ownership	NOUN
ejpam-5429	559	7	status	status	NOUN
ejpam-5429	559	8	of	of	ADP
ejpam-5429	559	9	the	the	DET
ejpam-5429	559	10	land	land	NOUN
ejpam-5429	559	11	,	,	PUNCT
ejpam-5429	559	12	such	such	ADJ
ejpam-5429	559	13	as	as	ADP
ejpam-5429	559	14	government	government	NOUN
ejpam-5429	559	15	-	-	PUNCT
ejpam-5429	559	16	owned	own	VERB
ejpam-5429	559	17	,	,	PUNCT
ejpam-5429	559	18	privately	privately	ADV
ejpam-5429	559	19	-	-	PUNCT
ejpam-5429	559	20	owned	own	VERB
ejpam-5429	559	21	,	,	PUNCT
ejpam-5429	559	22	or	or	CCONJ
ejpam-5429	559	23	leased	lease	VERB
ejpam-5429	559	24	.	.	PUNCT
ejpam-5429	560	1	•	•	NUM
ejpam-5429	560	2	land	land	NOUN
ejpam-5429	560	3	access	access	NOUN
ejpam-5429	560	4	:	:	PUNCT
ejpam-5429	560	5	the	the	DET
ejpam-5429	560	6	ease	ease	NOUN
ejpam-5429	560	7	of	of	ADP
ejpam-5429	560	8	access	access	NOUN
ejpam-5429	560	9	to	to	ADP
ejpam-5429	560	10	the	the	DET
ejpam-5429	560	11	land	land	NOUN
ejpam-5429	560	12	for	for	ADP
ejpam-5429	560	13	construction	construction	NOUN
ejpam-5429	560	14	and	and	CCONJ
ejpam-5429	560	15	maintenance	maintenance	NOUN
ejpam-5429	560	16	.	.	PUNCT
ejpam-5429	561	1	•land	•land	PROPN
ejpam-5429	561	2	cost	cost	NOUN
ejpam-5429	561	3	:	:	PUNCT
ejpam-5429	561	4	the	the	DET
ejpam-5429	561	5	cost	cost	NOUN
ejpam-5429	561	6	of	of	ADP
ejpam-5429	561	7	acquiring	acquire	VERB
ejpam-5429	561	8	or	or	CCONJ
ejpam-5429	561	9	leasing	lease	VERB
ejpam-5429	561	10	the	the	DET
ejpam-5429	561	11	land	land	NOUN
ejpam-5429	561	12	for	for	ADP
ejpam-5429	561	13	the	the	DET
ejpam-5429	561	14	project	project	NOUN
ejpam-5429	561	15	.	.	PUNCT
ejpam-5429	562	1	3	3	X
ejpam-5429	562	2	.	.	PUNCT
ejpam-5429	562	3	“	"	PUNCT
ejpam-5429	562	4	environmental	environmental	ADJ
ejpam-5429	562	5	impacts	impact	NOUN
ejpam-5429	562	6	(	(	PUNCT
ejpam-5429	562	7	t3	t3	NOUN
ejpam-5429	562	8	)	)	PUNCT
ejpam-5429	562	9	”	"	PUNCT
ejpam-5429	562	10	,	,	PUNCT
ejpam-5429	562	11	which	which	PRON
ejpam-5429	562	12	could	could	AUX
ejpam-5429	562	13	have	have	VERB
ejpam-5429	562	14	the	the	DET
ejpam-5429	562	15	characteristics	characteristic	NOUN
ejpam-5429	562	16	shown	show	VERB
ejpam-5429	562	17	below	below	ADP
ejpam-5429	562	18	:	:	PUNCT
ejpam-5429	562	19	•	•	NUM
ejpam-5429	562	20	land	land	NOUN
ejpam-5429	562	21	use	use	NOUN
ejpam-5429	562	22	:	:	PUNCT
ejpam-5429	562	23	the	the	DET
ejpam-5429	562	24	current	current	ADJ
ejpam-5429	562	25	and	and	CCONJ
ejpam-5429	562	26	previous	previous	ADJ
ejpam-5429	562	27	use	use	NOUN
ejpam-5429	562	28	of	of	ADP
ejpam-5429	562	29	the	the	DET
ejpam-5429	562	30	land	land	NOUN
ejpam-5429	562	31	and	and	CCONJ
ejpam-5429	562	32	the	the	DET
ejpam-5429	562	33	impact	impact	NOUN
ejpam-5429	562	34	of	of	ADP
ejpam-5429	562	35	converting	convert	VERB
ejpam-5429	562	36	it	it	PRON
ejpam-5429	562	37	to	to	ADP
ejpam-5429	562	38	a	a	DET
ejpam-5429	562	39	solar	solar	ADJ
ejpam-5429	562	40	power	power	NOUN
ejpam-5429	562	41	plant	plant	NOUN
ejpam-5429	562	42	.	.	PUNCT
ejpam-5429	563	1	•	•	NUM
ejpam-5429	563	2	water	water	NOUN
ejpam-5429	563	3	consumption	consumption	NOUN
ejpam-5429	563	4	:	:	PUNCT
ejpam-5429	563	5	the	the	DET
ejpam-5429	563	6	amount	amount	NOUN
ejpam-5429	563	7	of	of	ADP
ejpam-5429	563	8	water	water	NOUN
ejpam-5429	563	9	required	require	VERB
ejpam-5429	563	10	for	for	ADP
ejpam-5429	563	11	cleaning	clean	VERB
ejpam-5429	563	12	solar	solar	ADJ
ejpam-5429	563	13	panels	panel	NOUN
ejpam-5429	563	14	and	and	CCONJ
ejpam-5429	563	15	other	other	ADJ
ejpam-5429	563	16	operations	operation	NOUN
ejpam-5429	563	17	.	.	PUNCT
ejpam-5429	564	1	•	•	NUM
ejpam-5429	564	2	biodiversity	biodiversity	NOUN
ejpam-5429	564	3	:	:	PUNCT
ejpam-5429	564	4	the	the	DET
ejpam-5429	564	5	effect	effect	NOUN
ejpam-5429	564	6	of	of	ADP
ejpam-5429	564	7	the	the	DET
ejpam-5429	564	8	solar	solar	ADJ
ejpam-5429	564	9	power	power	NOUN
ejpam-5429	564	10	plant	plant	NOUN
ejpam-5429	564	11	on	on	ADP
ejpam-5429	564	12	local	local	ADJ
ejpam-5429	564	13	wildlife	wildlife	NOUN
ejpam-5429	564	14	and	and	CCONJ
ejpam-5429	564	15	plant	plant	NOUN
ejpam-5429	564	16	species	specie	NOUN
ejpam-5429	564	17	.	.	PUNCT
ejpam-5429	565	1	•	•	NUM
ejpam-5429	565	2	materials	material	NOUN
ejpam-5429	565	3	and	and	CCONJ
ejpam-5429	565	4	waste	waste	NOUN
ejpam-5429	565	5	:	:	PUNCT
ejpam-5429	565	6	the	the	DET
ejpam-5429	565	7	environmental	environmental	ADJ
ejpam-5429	565	8	impact	impact	NOUN
ejpam-5429	565	9	of	of	ADP
ejpam-5429	565	10	materials	material	NOUN
ejpam-5429	565	11	used	use	VERB
ejpam-5429	565	12	in	in	ADP
ejpam-5429	565	13	the	the	DET
ejpam-5429	565	14	construction	construction	NOUN
ejpam-5429	565	15	and	and	CCONJ
ejpam-5429	565	16	the	the	DET
ejpam-5429	565	17	waste	waste	NOUN
ejpam-5429	565	18	generated	generate	VERB
ejpam-5429	565	19	.	.	PUNCT
ejpam-5429	566	1	4	4	X
ejpam-5429	566	2	.	.	X
ejpam-5429	566	3	“	"	PUNCT
ejpam-5429	566	4	proximity	proximity	NOUN
ejpam-5429	566	5	to	to	ADP
ejpam-5429	566	6	grid	grid	NOUN
ejpam-5429	566	7	connections	connection	NOUN
ejpam-5429	566	8	(	(	PUNCT
ejpam-5429	566	9	t4)”,which	t4)”,which	X
ejpam-5429	566	10	could	could	AUX
ejpam-5429	566	11	have	have	AUX
ejpam-5429	566	12	the	the	DET
ejpam-5429	566	13	characteristics	characteristic	NOUN
ejpam-5429	566	14	shown	show	VERB
ejpam-5429	566	15	below	below	ADP
ejpam-5429	566	16	:	:	PUNCT
ejpam-5429	566	17	•	•	NUM
ejpam-5429	566	18	grid	grid	NOUN
ejpam-5429	566	19	connection	connection	NOUN
ejpam-5429	566	20	cost	cost	NOUN
ejpam-5429	566	21	:	:	PUNCT
ejpam-5429	566	22	the	the	DET
ejpam-5429	566	23	expense	expense	NOUN
ejpam-5429	566	24	associated	associate	VERB
ejpam-5429	566	25	with	with	ADP
ejpam-5429	566	26	connecting	connect	VERB
ejpam-5429	566	27	the	the	DET
ejpam-5429	566	28	solar	solar	ADJ
ejpam-5429	566	29	power	power	NOUN
ejpam-5429	566	30	plant	plant	NOUN
ejpam-5429	566	31	to	to	ADP
ejpam-5429	566	32	the	the	DET
ejpam-5429	566	33	nearest	near	ADJ
ejpam-5429	566	34	grid	grid	NOUN
ejpam-5429	566	35	infrastructure	infrastructure	NOUN
ejpam-5429	566	36	.	.	PUNCT
ejpam-5429	567	1	•	•	NUM
ejpam-5429	567	2	electricity	electricity	NOUN
ejpam-5429	567	3	demand	demand	NOUN
ejpam-5429	567	4	:	:	PUNCT
ejpam-5429	567	5	the	the	DET
ejpam-5429	567	6	local	local	ADJ
ejpam-5429	567	7	demand	demand	NOUN
ejpam-5429	567	8	for	for	ADP
ejpam-5429	567	9	electricity	electricity	NOUN
ejpam-5429	567	10	and	and	CCONJ
ejpam-5429	567	11	how	how	SCONJ
ejpam-5429	567	12	the	the	DET
ejpam-5429	567	13	new	new	ADJ
ejpam-5429	567	14	plant	plant	NOUN
ejpam-5429	567	15	will	will	AUX
ejpam-5429	567	16	meet	meet	VERB
ejpam-5429	567	17	or	or	CCONJ
ejpam-5429	567	18	exceed	exceed	VERB
ejpam-5429	567	19	this	this	DET
ejpam-5429	567	20	demand	demand	NOUN
ejpam-5429	567	21	.	.	PUNCT
ejpam-5429	568	1	•	•	NUM
ejpam-5429	568	2	grid	grid	NOUN
ejpam-5429	568	3	stability	stability	NOUN
ejpam-5429	568	4	:	:	PUNCT
ejpam-5429	568	5	the	the	DET
ejpam-5429	568	6	ability	ability	NOUN
ejpam-5429	568	7	of	of	ADP
ejpam-5429	568	8	the	the	DET
ejpam-5429	568	9	existing	exist	VERB
ejpam-5429	568	10	grid	grid	NOUN
ejpam-5429	568	11	to	to	PART
ejpam-5429	568	12	handle	handle	VERB
ejpam-5429	568	13	the	the	DET
ejpam-5429	568	14	additional	additional	ADJ
ejpam-5429	568	15	load	load	NOUN
ejpam-5429	568	16	from	from	ADP
ejpam-5429	568	17	the	the	DET
ejpam-5429	568	18	solar	solar	ADJ
ejpam-5429	568	19	power	power	NOUN
ejpam-5429	568	20	plant	plant	NOUN
ejpam-5429	568	21	.	.	PUNCT
ejpam-5429	569	1	•	•	NOUN
ejpam-5429	569	2	grid	grid	NOUN
ejpam-5429	569	3	capacity	capacity	NOUN
ejpam-5429	569	4	:	:	PUNCT
ejpam-5429	569	5	the	the	DET
ejpam-5429	569	6	existing	exist	VERB
ejpam-5429	569	7	capacity	capacity	NOUN
ejpam-5429	569	8	of	of	ADP
ejpam-5429	569	9	the	the	DET
ejpam-5429	569	10	grid	grid	NOUN
ejpam-5429	569	11	to	to	PART
ejpam-5429	569	12	integrate	integrate	VERB
ejpam-5429	569	13	the	the	DET
ejpam-5429	569	14	new	new	ADJ
ejpam-5429	569	15	power	power	NOUN
ejpam-5429	569	16	supply	supply	NOUN
ejpam-5429	569	17	without	without	ADP
ejpam-5429	569	18	significant	significant	ADJ
ejpam-5429	569	19	upgrades	upgrade	NOUN
ejpam-5429	569	20	.	.	PUNCT
ejpam-5429	570	1	5	5	X
ejpam-5429	570	2	.	.	PUNCT
ejpam-5429	570	3	“	"	PUNCT
ejpam-5429	570	4	local	local	ADJ
ejpam-5429	570	5	regulations	regulation	NOUN
ejpam-5429	570	6	(	(	PUNCT
ejpam-5429	570	7	t5	t5	PROPN
ejpam-5429	570	8	)	)	PUNCT
ejpam-5429	570	9	”	"	PUNCT
ejpam-5429	570	10	,	,	PUNCT
ejpam-5429	570	11	which	which	PRON
ejpam-5429	570	12	could	could	AUX
ejpam-5429	570	13	have	have	VERB
ejpam-5429	570	14	the	the	DET
ejpam-5429	570	15	characteristics	characteristic	NOUN
ejpam-5429	570	16	shown	show	VERB
ejpam-5429	570	17	below	below	ADP
ejpam-5429	570	18	:	:	PUNCT
ejpam-5429	570	19	•	•	NUM
ejpam-5429	570	20	zoning	zoning	NOUN
ejpam-5429	570	21	laws	law	NOUN
ejpam-5429	570	22	:	:	PUNCT
ejpam-5429	570	23	regulations	regulation	NOUN
ejpam-5429	570	24	that	that	PRON
ejpam-5429	570	25	dictate	dictate	VERB
ejpam-5429	570	26	land	land	NOUN
ejpam-5429	570	27	use	use	NOUN
ejpam-5429	570	28	in	in	ADP
ejpam-5429	570	29	the	the	DET
ejpam-5429	570	30	area	area	NOUN
ejpam-5429	570	31	.	.	PUNCT
ejpam-5429	571	1	•	•	NUM
ejpam-5429	571	2	permitting	permit	VERB
ejpam-5429	571	3	process	process	NOUN
ejpam-5429	571	4	:	:	PUNCT
ejpam-5429	571	5	the	the	DET
ejpam-5429	571	6	complexity	complexity	NOUN
ejpam-5429	571	7	and	and	CCONJ
ejpam-5429	571	8	duration	duration	NOUN
ejpam-5429	571	9	of	of	ADP
ejpam-5429	571	10	obtaining	obtain	VERB
ejpam-5429	571	11	the	the	DET
ejpam-5429	571	12	necessary	necessary	ADJ
ejpam-5429	571	13	permits	permit	NOUN
ejpam-5429	571	14	for	for	ADP
ejpam-5429	571	15	construction	construction	NOUN
ejpam-5429	571	16	and	and	CCONJ
ejpam-5429	571	17	operation	operation	NOUN
ejpam-5429	571	18	.	.	PUNCT
ejpam-5429	572	1	•	•	NOUN
ejpam-5429	572	2	incentives	incentive	NOUN
ejpam-5429	572	3	and	and	CCONJ
ejpam-5429	572	4	subsidies	subsidy	NOUN
ejpam-5429	572	5	:	:	PUNCT
ejpam-5429	572	6	availability	availability	NOUN
ejpam-5429	572	7	of	of	ADP
ejpam-5429	572	8	government	government	NOUN
ejpam-5429	572	9	incentives	incentive	NOUN
ejpam-5429	572	10	,	,	PUNCT
ejpam-5429	572	11	tax	tax	NOUN
ejpam-5429	572	12	credits	credit	NOUN
ejpam-5429	572	13	,	,	PUNCT
ejpam-5429	572	14	and	and	CCONJ
ejpam-5429	572	15	subsidies	subsidy	NOUN
ejpam-5429	572	16	for	for	ADP
ejpam-5429	572	17	renewable	renewable	ADJ
ejpam-5429	572	18	energy	energy	NOUN
ejpam-5429	572	19	projects	project	NOUN
ejpam-5429	572	20	.	.	PUNCT
ejpam-5429	573	1	•	•	NOUN
ejpam-5429	573	2	compliance	compliance	NOUN
ejpam-5429	573	3	requirements	requirement	NOUN
ejpam-5429	573	4	:	:	PUNCT
ejpam-5429	573	5	environmental	environmental	ADJ
ejpam-5429	573	6	and	and	CCONJ
ejpam-5429	573	7	operational	operational	ADJ
ejpam-5429	573	8	regulations	regulation	NOUN
ejpam-5429	573	9	that	that	PRON
ejpam-5429	573	10	need	need	VERB
ejpam-5429	573	11	to	to	PART
ejpam-5429	573	12	be	be	AUX
ejpam-5429	573	13	met	meet	VERB
ejpam-5429	573	14	for	for	SCONJ
ejpam-5429	573	15	the	the	DET
ejpam-5429	573	16	project	project	NOUN
ejpam-5429	573	17	to	to	PART
ejpam-5429	573	18	proceed	proceed	VERB
ejpam-5429	573	19	.	.	PUNCT
ejpam-5429	574	1	the	the	DET
ejpam-5429	574	2	five	five	NUM
ejpam-5429	574	3	criteria	criterion	NOUN
ejpam-5429	574	4	and	and	CCONJ
ejpam-5429	574	5	their	their	PRON
ejpam-5429	574	6	attributes	attribute	NOUN
ejpam-5429	574	7	are	be	AUX
ejpam-5429	574	8	shown	show	VERB
ejpam-5429	574	9	below	below	ADP
ejpam-5429	574	10	:	:	PUNCT
ejpam-5429	574	11	1	1	X
ejpam-5429	574	12	.	.	X
ejpam-5429	575	1	the	the	DET
ejpam-5429	575	2	qp	qp	PROPN
ejpam-5429	575	3	-	-	PUNCT
ejpam-5429	575	4	f	f	PROPN
ejpam-5429	575	5	initial	initial	ADJ
ejpam-5429	575	6	decision	decision	NOUN
ejpam-5429	575	7	matrix	matrix	NOUN
ejpam-5429	575	8	is	be	AUX
ejpam-5429	575	9	represented	represent	VERB
ejpam-5429	575	10	in	in	ADP
ejpam-5429	575	11	table	table	NOUN
ejpam-5429	575	12	5	5	NUM
ejpam-5429	575	13	.	.	PUNCT
ejpam-5429	575	14	k.	k.	PROPN
ejpam-5429	575	15	h.	h.	PROPN
ejpam-5429	575	16	hakami	hakami	PROPN
ejpam-5429	575	17	et	et	PROPN
ejpam-5429	575	18	al	al	PROPN
ejpam-5429	575	19	.	.	PUNCT
ejpam-5429	575	20	/	/	SYM
ejpam-5429	575	21	eur	eur	PROPN
ejpam-5429	575	22	.	.	PUNCT
ejpam-5429	576	1	j.	j.	PROPN
ejpam-5429	576	2	pure	pure	PROPN
ejpam-5429	576	3	appl	appl	PROPN
ejpam-5429	576	4	.	.	PROPN
ejpam-5429	576	5	math	math	PROPN
ejpam-5429	576	6	,	,	PUNCT
ejpam-5429	576	7	17	17	NUM
ejpam-5429	576	8	(	(	PUNCT
ejpam-5429	576	9	4	4	NUM
ejpam-5429	576	10	)	)	PUNCT
ejpam-5429	576	11	(	(	PUNCT
ejpam-5429	576	12	2024	2024	NUM
ejpam-5429	576	13	)	)	PUNCT
ejpam-5429	576	14	,	,	PUNCT
ejpam-5429	576	15	3129	3129	NUM
ejpam-5429	576	16	-	-	SYM
ejpam-5429	576	17	3155	3155	NUM
ejpam-5429	576	18	3148	3148	NUM
ejpam-5429	576	19	table	table	NOUN
ejpam-5429	576	20	5	5	NUM
ejpam-5429	576	21	.	.	PUNCT
ejpam-5429	576	22	qp	qp	PROPN
ejpam-5429	576	23	-	-	PUNCT
ejpam-5429	576	24	f	f	PROPN
ejpam-5429	576	25	initial	initial	ADJ
ejpam-5429	576	26	decision	decision	NOUN
ejpam-5429	576	27	matrix	matrix	NOUN
ejpam-5429	576	28	.	.	PUNCT
ejpam-5429	577	1	alternatives	alternative	NOUN
ejpam-5429	577	2	qp	qp	ADP
ejpam-5429	577	3	-	-	PUNCT
ejpam-5429	577	4	f	f	PROPN
ejpam-5429	577	5	criteria	criterion	NOUN
ejpam-5429	577	6	c1	c1	NOUN
ejpam-5429	577	7	-	-	PUNCT
ejpam-5429	577	8	solar	solar	ADJ
ejpam-5429	577	9	radiance	radiance	NOUN
ejpam-5429	577	10	ς̇1	ς̇1	PROPN
ejpam-5429	577	11	{	{	PUNCT
ejpam-5429	577	12	(	(	PUNCT
ejpam-5429	577	13	.18,.73,.43,.67),(.32,.64,.49,.72),(.38,.66,.54,.64	.18,.73,.43,.67),(.32,.64,.49,.72),(.38,.66,.54,.64	NOUN
ejpam-5429	577	14	)	)	PUNCT
ejpam-5429	577	15	}	}	PUNCT
ejpam-5429	578	1	ς̇2	ς̇2	NOUN
ejpam-5429	578	2	{	{	PUNCT
ejpam-5429	578	3	(	(	PUNCT
ejpam-5429	578	4	.46,.76,.45,.27),(.56,.91,.36,.48	.46,.76,.45,.27),(.56,.91,.36,.48	PROPN
ejpam-5429	578	5	)	)	PUNCT
ejpam-5429	578	6	}	}	PUNCT
ejpam-5429	578	7	ς̇3	ς̇3	PROPN
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ejpam-5429	578	9	(	(	PUNCT
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ejpam-5429	578	11	)	)	PUNCT
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ejpam-5429	579	1	ς̇4	ς̇4	ADJ
ejpam-5429	579	2	{	{	PUNCT
ejpam-5429	579	3	(	(	PUNCT
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ejpam-5429	579	5	)	)	PUNCT
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ejpam-5429	579	9	(	(	PUNCT
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ejpam-5429	579	11	)	)	PUNCT
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ejpam-5429	579	15	-	-	PUNCT
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ejpam-5429	579	19	-	-	PUNCT
ejpam-5429	579	20	local	local	ADJ
ejpam-5429	579	21	availability	availability	NOUN
ejpam-5429	579	22	ς̇1	ς̇1	PROPN
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ejpam-5429	579	24	(	(	PUNCT
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ejpam-5429	579	26	)	)	PUNCT
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ejpam-5429	580	3	(	(	PUNCT
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ejpam-5429	580	5	)	)	PUNCT
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ejpam-5429	580	9	(	(	PUNCT
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ejpam-5429	580	11	)	)	PUNCT
ejpam-5429	580	12	}	}	PUNCT
ejpam-5429	581	1	ς̇4	ς̇4	ADJ
ejpam-5429	581	2	{	{	PUNCT
ejpam-5429	581	3	(	(	PUNCT
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ejpam-5429	581	5	)	)	PUNCT
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ejpam-5429	581	9	(	(	PUNCT
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ejpam-5429	581	11	)	)	PUNCT
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ejpam-5429	581	13	’	'	PUNCT
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ejpam-5429	581	15	qp	qp	ADP
ejpam-5429	581	16	-	-	PUNCT
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ejpam-5429	581	20	-	-	ADJ
ejpam-5429	581	21	environmental	environmental	ADJ
ejpam-5429	581	22	impacts	impact	NOUN
ejpam-5429	581	23	ς̇1	ς̇1	PROPN
ejpam-5429	581	24	{	{	PUNCT
ejpam-5429	581	25	(	(	PUNCT
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ejpam-5429	581	27	)	)	PUNCT
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ejpam-5429	582	2	{	{	PUNCT
ejpam-5429	582	3	(	(	PUNCT
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ejpam-5429	582	5	)	)	PUNCT
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ejpam-5429	582	9	(	(	PUNCT
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ejpam-5429	582	11	)	)	PUNCT
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ejpam-5429	583	1	ς̇4	ς̇4	ADJ
ejpam-5429	583	2	{	{	PUNCT
ejpam-5429	583	3	(	(	PUNCT
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ejpam-5429	583	5	)	)	PUNCT
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ejpam-5429	583	7	ς̇5	ς̇5	PROPN
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ejpam-5429	583	9	(	(	PUNCT
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ejpam-5429	583	11	)	)	PUNCT
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ejpam-5429	583	15	-	-	PUNCT
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ejpam-5429	583	19	-	-	PUNCT
ejpam-5429	583	20	local	local	ADJ
ejpam-5429	583	21	regulations	regulation	NOUN
ejpam-5429	583	22	ς̇1	ς̇1	PROPN
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ejpam-5429	583	26	)	)	PUNCT
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ejpam-5429	584	2	{	{	PUNCT
ejpam-5429	584	3	(	(	PUNCT
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ejpam-5429	584	6	)	)	PUNCT
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ejpam-5429	584	10	(	(	PUNCT
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ejpam-5429	584	12	)	)	PUNCT
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ejpam-5429	585	3	(	(	PUNCT
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ejpam-5429	585	5	)	)	PUNCT
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ejpam-5429	585	9	(	(	PUNCT
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ejpam-5429	585	13	2	2	X
ejpam-5429	585	14	.	.	PUNCT
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ejpam-5429	586	5	qp	qp	ADP
ejpam-5429	586	6	-	-	PUNCT
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ejpam-5429	586	10	6	6	NUM
ejpam-5429	586	11	.	.	NOUN
ejpam-5429	586	12	3	3	X
ejpam-5429	586	13	.	.	PUNCT
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ejpam-5429	587	4	normalised	normalise	VERB
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ejpam-5429	587	9	,	,	PUNCT
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ejpam-5429	587	11	=	=	SYM
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ejpam-5429	587	13	,	,	PUNCT
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ejpam-5429	587	15	=	=	SYM
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ejpam-5429	587	17	,	,	PUNCT
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ejpam-5429	587	19	=	=	PUNCT
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ejpam-5429	587	21	,	,	PUNCT
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ejpam-5429	587	33	.	.	X
ejpam-5429	588	1	the	the	DET
ejpam-5429	588	2	weight	weight	NOUN
ejpam-5429	588	3	pessimistic	pessimistic	NOUN
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ejpam-5429	588	7	-	-	PUNCT
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ejpam-5429	588	17	k.	k.	PROPN
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ejpam-5429	589	6	,	,	PUNCT
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ejpam-5429	589	8	(	(	PUNCT
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ejpam-5429	589	16	-	-	SYM
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ejpam-5429	589	21	.	.	PUNCT
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ejpam-5429	590	4	-	-	PUNCT
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ejpam-5429	591	3	-	-	PUNCT
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ejpam-5429	591	7	-	-	PUNCT
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ejpam-5429	592	11	)	)	PUNCT
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ejpam-5429	597	19	-	-	PUNCT
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ejpam-5429	600	13	-	-	PUNCT
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ejpam-5429	600	18	-	-	PUNCT
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ejpam-5429	600	25	-	-	PUNCT
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ejpam-5429	603	7	-	-	PUNCT
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ejpam-5429	608	15	-	-	PUNCT
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ejpam-5429	608	26	)	)	PUNCT
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ejpam-5429	608	32	)	)	PUNCT
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ejpam-5429	608	38	)	)	PUNCT
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ejpam-5429	609	155	8)	8)	NUM
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ejpam-5429	611	15	,	,	PUNCT
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ejpam-5429	611	18	fpis	fpi	VERB
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ejpam-5429	612	7	,	,	PUNCT
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ejpam-5429	612	10	fpis	fpi	VERB
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ejpam-5429	613	1	=	=	SYM
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ejpam-5429	614	14	,	,	PUNCT
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ejpam-5429	614	25	fpis	fpi	VERB
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ejpam-5429	615	1	=	=	SYM
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ejpam-5429	615	7	,	,	PUNCT
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ejpam-5429	615	9	-	-	PUNCT
ejpam-5429	615	10	fnis	fnis	NOUN
ejpam-5429	615	11	)	)	PUNCT
ejpam-5429	616	1	=	=	SYM
ejpam-5429	616	2	.1627	.1627	NOUN
ejpam-5429	616	3	,	,	PUNCT
ejpam-5429	616	4	d	d	NOUN
ejpam-5429	616	5	′	′	NUM
ejpam-5429	616	6	e(ς̇3	e(ς̇3	NOUN
ejpam-5429	616	7	,	,	PUNCT
ejpam-5429	616	8	qp	qp	NOUN
ejpam-5429	616	9	-	-	PUNCT
ejpam-5429	616	10	fnis	fnis	NOUN
ejpam-5429	616	11	)	)	PUNCT
ejpam-5429	617	1	=	=	SYM
ejpam-5429	617	2	.1740	.1740	PROPN
ejpam-5429	617	3	,	,	PUNCT
ejpam-5429	617	4	d	d	NOUN
ejpam-5429	617	5	′	′	NUM
ejpam-5429	617	6	e(ς̇4	e(ς̇4	NOUN
ejpam-5429	617	7	,	,	PUNCT
ejpam-5429	617	8	qp	qp	NOUN
ejpam-5429	617	9	-	-	PUNCT
ejpam-5429	617	10	fnis	fnis	NOUN
ejpam-5429	617	11	)	)	PUNCT
ejpam-5429	617	12	=	=	PUNCT
ejpam-5429	618	1	.1461	.1461	NOUN
ejpam-5429	618	2	,	,	PUNCT
ejpam-5429	618	3	d	d	NOUN
ejpam-5429	618	4	′	′	NUM
ejpam-5429	618	5	e(ς̇5	e(ς̇5	NOUN
ejpam-5429	618	6	,	,	PUNCT
ejpam-5429	618	7	qp	qp	NOUN
ejpam-5429	618	8	-	-	PUNCT
ejpam-5429	618	9	fnis	fnis	NOUN
ejpam-5429	618	10	)	)	PUNCT
ejpam-5429	618	11	=	=	SYM
ejpam-5429	619	1	.1218	.1218	PROPN
ejpam-5429	619	2	.	.	PUNCT
ejpam-5429	620	1	using	use	VERB
ejpam-5429	620	2	equation	equation	NOUN
ejpam-5429	620	3	(	(	PUNCT
ejpam-5429	620	4	9	9	NUM
ejpam-5429	620	5	)	)	PUNCT
ejpam-5429	620	6	,	,	PUNCT
ejpam-5429	620	7	the	the	DET
ejpam-5429	620	8	relative	relative	ADJ
ejpam-5429	620	9	qp	qp	PROPN
ejpam-5429	620	10	-	-	PROPN
ejpam-5429	620	11	f	f	PROPN
ejpam-5429	620	12	closeness	closeness	NOUN
ejpam-5429	620	13	coefficients	coefficient	VERB
ejpam-5429	620	14	ej′	ej′	PRON
ejpam-5429	620	15	are	be	AUX
ejpam-5429	620	16	calculated	calculate	VERB
ejpam-5429	620	17	as	as	ADP
ejpam-5429	620	18	:	:	PUNCT
ejpam-5429	620	19	e1′	e1′	PROPN
ejpam-5429	620	20	=	=	SYM
ejpam-5429	620	21	.6565	.6565	PROPN
ejpam-5429	620	22	,	,	PUNCT
ejpam-5429	620	23	e2′	e2′	NOUN
ejpam-5429	620	24	=	=	SYM
ejpam-5429	620	25	.5572	.5572	PROPN
ejpam-5429	620	26	,	,	PUNCT
ejpam-5429	620	27	e3′	e3′	NOUN
ejpam-5429	620	28	=	=	SYM
ejpam-5429	620	29	.5860	.5860	PROPN
ejpam-5429	620	30	,	,	PUNCT
ejpam-5429	620	31	e4′	e4′	NOUN
ejpam-5429	621	1	=	=	SYM
ejpam-5429	621	2	.5270	.5270	PROPN
ejpam-5429	621	3	,	,	PUNCT
ejpam-5429	621	4	e5′	e5′	PROPN
ejpam-5429	621	5	=	=	PUNCT
ejpam-5429	621	6	.4055	.4055	PROPN
ejpam-5429	621	7	.	.	PUNCT
ejpam-5429	622	1	according	accord	VERB
ejpam-5429	622	2	to	to	ADP
ejpam-5429	622	3	the	the	DET
ejpam-5429	622	4	foregoing	forego	VERB
ejpam-5429	622	5	computations	computation	NOUN
ejpam-5429	622	6	,	,	PUNCT
ejpam-5429	622	7	the	the	DET
ejpam-5429	622	8	final	final	ADJ
ejpam-5429	622	9	ranking	ranking	NOUN
ejpam-5429	622	10	of	of	ADP
ejpam-5429	622	11	power	power	NOUN
ejpam-5429	622	12	plant	plant	NOUN
ejpam-5429	622	13	selection	selection	NOUN
ejpam-5429	622	14	is	be	AUX
ejpam-5429	622	15	as	as	SCONJ
ejpam-5429	622	16	follows	follow	VERB
ejpam-5429	622	17	:	:	PUNCT
ejpam-5429	622	18	ς̇1	ς̇1	PROPN
ejpam-5429	622	19	>	>	X
ejpam-5429	622	20	ς̇3	ς̇3	PROPN
ejpam-5429	622	21	>	>	PUNCT
ejpam-5429	623	1	ς̇2	ς̇2	PROPN
ejpam-5429	623	2	>	>	X
ejpam-5429	623	3	ς̇4	ς̇4	X
ejpam-5429	623	4	>	>	PUNCT
ejpam-5429	623	5	ς̇5	ς̇5	PROPN
ejpam-5429	623	6	.	.	PROPN
ejpam-5429	623	7	hence	hence	ADV
ejpam-5429	623	8	,	,	PUNCT
ejpam-5429	623	9	solar	solar	ADJ
ejpam-5429	623	10	power	power	NOUN
ejpam-5429	623	11	plant	plant	NOUN
ejpam-5429	623	12	station	station	NOUN
ejpam-5429	623	13	ς̇1	ς̇1	PROPN
ejpam-5429	623	14	is	be	AUX
ejpam-5429	623	15	selected	select	VERB
ejpam-5429	623	16	in	in	ADP
ejpam-5429	623	17	the	the	DET
ejpam-5429	623	18	rural	rural	ADJ
ejpam-5429	623	19	area	area	NOUN
ejpam-5429	623	20	.	.	PUNCT
ejpam-5429	624	1	as	as	ADP
ejpam-5429	624	2	a	a	DET
ejpam-5429	624	3	result	result	NOUN
ejpam-5429	624	4	of	of	ADP
ejpam-5429	624	5	the	the	DET
ejpam-5429	624	6	evaluation	evaluation	NOUN
ejpam-5429	624	7	among	among	ADP
ejpam-5429	624	8	the	the	DET
ejpam-5429	624	9	alternatives	alternative	NOUN
ejpam-5429	624	10	,	,	PUNCT
ejpam-5429	624	11	the	the	DET
ejpam-5429	624	12	most	most	ADV
ejpam-5429	624	13	risky	risky	ADJ
ejpam-5429	624	14	structure	structure	NOUN
ejpam-5429	624	15	is	be	AUX
ejpam-5429	624	16	ς̇1	ς̇1	PROPN
ejpam-5429	624	17	.	.	PUNCT
ejpam-5429	625	1	the	the	DET
ejpam-5429	625	2	positive	positive	ADJ
ejpam-5429	625	3	ideal	ideal	ADJ
ejpam-5429	625	4	solution	solution	NOUN
ejpam-5429	625	5	,	,	PUNCT
ejpam-5429	625	6	negative	negative	ADJ
ejpam-5429	625	7	ideal	ideal	ADJ
ejpam-5429	625	8	solution	solution	NOUN
ejpam-5429	625	9	and	and	CCONJ
ejpam-5429	625	10	ranking	ranking	NOUN
ejpam-5429	625	11	of	of	ADP
ejpam-5429	625	12	alternatives	alternative	NOUN
ejpam-5429	625	13	based	base	VERB
ejpam-5429	625	14	on	on	ADP
ejpam-5429	625	15	closeness	closeness	NOUN
ejpam-5429	625	16	coefficients	coefficient	NOUN
ejpam-5429	625	17	is	be	AUX
ejpam-5429	625	18	shown	show	VERB
ejpam-5429	625	19	in	in	ADP
ejpam-5429	625	20	figure	figure	NOUN
ejpam-5429	625	21	1	1	NUM
ejpam-5429	625	22	.	.	PUNCT
ejpam-5429	625	23	fig	fig	NOUN
ejpam-5429	625	24	.	.	PUNCT
ejpam-5429	626	1	1	1	NUM
ejpam-5429	626	2	:	:	PUNCT
ejpam-5429	626	3	positive	positive	ADJ
ejpam-5429	626	4	ideal	ideal	ADJ
ejpam-5429	626	5	solution	solution	NOUN
ejpam-5429	626	6	,	,	PUNCT
ejpam-5429	626	7	negative	negative	ADJ
ejpam-5429	626	8	ideal	ideal	ADJ
ejpam-5429	626	9	solution	solution	NOUN
ejpam-5429	626	10	and	and	CCONJ
ejpam-5429	626	11	ranking	ranking	NOUN
ejpam-5429	626	12	of	of	ADP
ejpam-5429	626	13	alternatives	alternative	NOUN
ejpam-5429	626	14	references	reference	NOUN
ejpam-5429	626	15	3152	3152	NUM
ejpam-5429	626	16	7	7	NUM
ejpam-5429	626	17	.	.	PUNCT
ejpam-5429	627	1	conclusions	conclusion	NOUN
ejpam-5429	627	2	quadri	quadri	PROPN
ejpam-5429	627	3	-	-	PUNCT
ejpam-5429	627	4	polar	polar	ADJ
ejpam-5429	627	5	structures	structure	NOUN
ejpam-5429	627	6	are	be	AUX
ejpam-5429	627	7	often	often	ADV
ejpam-5429	627	8	preferred	prefer	VERB
ejpam-5429	627	9	over	over	ADP
ejpam-5429	627	10	clear	clear	ADV
ejpam-5429	627	11	-	-	PUNCT
ejpam-5429	627	12	cut	cut	VERB
ejpam-5429	627	13	circumstances	circumstance	NOUN
ejpam-5429	627	14	.	.	PUNCT
ejpam-5429	628	1	various	various	ADJ
ejpam-5429	628	2	forms	form	NOUN
ejpam-5429	628	3	of	of	ADP
ejpam-5429	628	4	information	information	NOUN
ejpam-5429	628	5	can	can	AUX
ejpam-5429	628	6	be	be	AUX
ejpam-5429	628	7	used	use	VERB
ejpam-5429	628	8	to	to	PART
ejpam-5429	628	9	manipulate	manipulate	VERB
ejpam-5429	628	10	the	the	DET
ejpam-5429	628	11	membership	membership	NOUN
ejpam-5429	628	12	degrees	degree	NOUN
ejpam-5429	628	13	to	to	PART
ejpam-5429	628	14	facilitate	facilitate	VERB
ejpam-5429	628	15	the	the	DET
ejpam-5429	628	16	handling	handling	NOUN
ejpam-5429	628	17	of	of	ADP
ejpam-5429	628	18	quadri	quadri	NOUN
ejpam-5429	628	19	-	-	PUNCT
ejpam-5429	628	20	polar	polar	ADJ
ejpam-5429	628	21	fuzzy	fuzzy	ADJ
ejpam-5429	628	22	information	information	NOUN
ejpam-5429	628	23	.	.	PUNCT
ejpam-5429	629	1	we	we	PRON
ejpam-5429	629	2	have	have	AUX
ejpam-5429	629	3	proposed	propose	VERB
ejpam-5429	629	4	a	a	DET
ejpam-5429	629	5	novel	novel	ADJ
ejpam-5429	629	6	class	class	NOUN
ejpam-5429	629	7	of	of	ADP
ejpam-5429	629	8	generalized	generalized	ADJ
ejpam-5429	629	9	qpffi(s	qpffi(s	NOUN
ejpam-5429	629	10	)	)	PUNCT
ejpam-5429	629	11	of	of	ADP
ejpam-5429	629	12	ℵ̃	ℵ̃	PROPN
ejpam-5429	629	13	called	call	VERB
ejpam-5429	629	14	,	,	PUNCT
ejpam-5429	629	15	a	a	DET
ejpam-5429	629	16	qp-(ϖ,ϑ)-ffi(s	qp-(ϖ,ϑ)-ffi(s	NOUN
ejpam-5429	629	17	)	)	PUNCT
ejpam-5429	629	18	and	and	CCONJ
ejpam-5429	629	19	compared	compare	VERB
ejpam-5429	629	20	to	to	ADP
ejpam-5429	629	21	the	the	DET
ejpam-5429	629	22	generalizations	generalization	NOUN
ejpam-5429	629	23	of	of	ADP
ejpam-5429	629	24	present	present	ADJ
ejpam-5429	629	25	fuzzy	fuzzy	ADJ
ejpam-5429	629	26	sets	set	NOUN
ejpam-5429	629	27	,	,	PUNCT
ejpam-5429	629	28	it	it	PRON
ejpam-5429	629	29	is	be	AUX
ejpam-5429	629	30	shown	show	VERB
ejpam-5429	629	31	to	to	PART
ejpam-5429	629	32	be	be	AUX
ejpam-5429	629	33	a	a	DET
ejpam-5429	629	34	more	more	ADV
ejpam-5429	629	35	flexible	flexible	ADJ
ejpam-5429	629	36	approach	approach	NOUN
ejpam-5429	629	37	that	that	PRON
ejpam-5429	629	38	can	can	AUX
ejpam-5429	629	39	be	be	AUX
ejpam-5429	629	40	evaluated	evaluate	VERB
ejpam-5429	629	41	in	in	ADP
ejpam-5429	629	42	quadripolar	quadripolar	ADJ
ejpam-5429	629	43	ways	way	NOUN
ejpam-5429	629	44	based	base	VERB
ejpam-5429	629	45	on	on	ADP
ejpam-5429	629	46	practical	practical	ADJ
ejpam-5429	629	47	interests	interest	NOUN
ejpam-5429	629	48	and	and	CCONJ
ejpam-5429	629	49	requirements	requirement	NOUN
ejpam-5429	629	50	.	.	PUNCT
ejpam-5429	630	1	we	we	PRON
ejpam-5429	630	2	defined	define	VERB
ejpam-5429	630	3	and	and	CCONJ
ejpam-5429	630	4	analyzed	analyze	VERB
ejpam-5429	630	5	the	the	DET
ejpam-5429	630	6	concept	concept	NOUN
ejpam-5429	630	7	of	of	ADP
ejpam-5429	630	8	qp-(∈σ̃,∈σ̃	qp-(∈σ̃,∈σ̃	PROPN
ejpam-5429	630	9	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	630	10	)	)	PUNCT
ejpam-5429	630	11	-ffi(s	-ffi(s	PROPN
ejpam-5429	630	12	)	)	PUNCT
ejpam-5429	630	13	.	.	PUNCT
ejpam-5429	631	1	moreover	moreover	ADV
ejpam-5429	631	2	,	,	PUNCT
ejpam-5429	631	3	we	we	PRON
ejpam-5429	631	4	presented	present	VERB
ejpam-5429	631	5	various	various	ADJ
ejpam-5429	631	6	characterizations	characterization	NOUN
ejpam-5429	631	7	of	of	ADP
ejpam-5429	631	8	qp-(∈σ̃,∈σ̃	qp-(∈σ̃,∈σ̃	PROPN
ejpam-5429	631	9	∨qτ̃	∨qτ̃	PROPN
ejpam-5429	631	10	)	)	PUNCT
ejpam-5429	631	11	-ffis	-ffis	PROPN
ejpam-5429	631	12	.	.	PUNCT
ejpam-5429	632	1	it	it	PRON
ejpam-5429	632	2	is	be	AUX
ejpam-5429	632	3	used	use	VERB
ejpam-5429	632	4	to	to	PART
ejpam-5429	632	5	manage	manage	VERB
ejpam-5429	632	6	data	datum	NOUN
ejpam-5429	632	7	that	that	PRON
ejpam-5429	632	8	includes	include	VERB
ejpam-5429	632	9	quadri	quadri	PROPN
ejpam-5429	632	10	-	-	PUNCT
ejpam-5429	632	11	polar	polar	ADJ
ejpam-5429	632	12	information	information	NOUN
ejpam-5429	632	13	suggested	suggest	VERB
ejpam-5429	632	14	by	by	ADP
ejpam-5429	632	15	decision	decision	NOUN
ejpam-5429	632	16	-	-	PUNCT
ejpam-5429	632	17	makers	maker	NOUN
ejpam-5429	632	18	.	.	PUNCT
ejpam-5429	633	1	the	the	DET
ejpam-5429	633	2	final	final	ADJ
ejpam-5429	633	3	decision	decision	NOUN
ejpam-5429	633	4	on	on	ADP
ejpam-5429	633	5	the	the	DET
ejpam-5429	633	6	proposed	propose	VERB
ejpam-5429	633	7	approach	approach	NOUN
ejpam-5429	633	8	is	be	AUX
ejpam-5429	633	9	determined	determine	VERB
ejpam-5429	633	10	by	by	ADP
ejpam-5429	633	11	the	the	DET
ejpam-5429	633	12	decision	decision	NOUN
ejpam-5429	633	13	-	-	PUNCT
ejpam-5429	633	14	maker	maker	NOUN
ejpam-5429	633	15	’s	’s	PART
ejpam-5429	633	16	optimistic	optimistic	ADJ
ejpam-5429	633	17	or	or	CCONJ
ejpam-5429	633	18	pessimistic	pessimistic	ADJ
ejpam-5429	633	19	outlook	outlook	NOUN
ejpam-5429	633	20	.	.	PUNCT
ejpam-5429	634	1	in	in	ADP
ejpam-5429	634	2	practical	practical	ADJ
ejpam-5429	634	3	perspective	perspective	NOUN
ejpam-5429	634	4	,	,	PUNCT
ejpam-5429	634	5	we	we	PRON
ejpam-5429	634	6	have	have	AUX
ejpam-5429	634	7	devised	devise	VERB
ejpam-5429	634	8	a	a	DET
ejpam-5429	634	9	q	q	ADJ
ejpam-5429	634	10	-	-	PUNCT
ejpam-5429	634	11	pf	pf	NOUN
ejpam-5429	634	12	topsis	topsis	NOUN
ejpam-5429	634	13	approach	approach	NOUN
ejpam-5429	634	14	to	to	PART
ejpam-5429	634	15	address	address	VERB
ejpam-5429	634	16	mcgdm	mcgdm	ADJ
ejpam-5429	634	17	problems	problem	NOUN
ejpam-5429	634	18	.	.	PUNCT
ejpam-5429	635	1	this	this	DET
ejpam-5429	635	2	method	method	NOUN
ejpam-5429	635	3	represents	represent	VERB
ejpam-5429	635	4	a	a	DET
ejpam-5429	635	5	natural	natural	ADJ
ejpam-5429	635	6	extension	extension	NOUN
ejpam-5429	635	7	of	of	ADP
ejpam-5429	635	8	the	the	DET
ejpam-5429	635	9	topsis	topsis	NOUN
ejpam-5429	635	10	method	method	NOUN
ejpam-5429	635	11	tailored	tailor	VERB
ejpam-5429	635	12	to	to	ADP
ejpam-5429	635	13	our	our	PRON
ejpam-5429	635	14	specific	specific	ADJ
ejpam-5429	635	15	model	model	NOUN
ejpam-5429	635	16	.	.	PUNCT
ejpam-5429	636	1	ultimately	ultimately	ADV
ejpam-5429	636	2	,	,	PUNCT
ejpam-5429	636	3	we	we	PRON
ejpam-5429	636	4	have	have	AUX
ejpam-5429	636	5	implemented	implement	VERB
ejpam-5429	636	6	our	our	PRON
ejpam-5429	636	7	methodology	methodology	NOUN
ejpam-5429	636	8	in	in	ADP
ejpam-5429	636	9	addressing	address	VERB
ejpam-5429	636	10	real	real	ADJ
ejpam-5429	636	11	-	-	PUNCT
ejpam-5429	636	12	world	world	NOUN
ejpam-5429	636	13	issues	issue	NOUN
ejpam-5429	636	14	.	.	PUNCT
ejpam-5429	637	1	in	in	ADP
ejpam-5429	637	2	the	the	DET
ejpam-5429	637	3	future	future	NOUN
ejpam-5429	637	4	,	,	PUNCT
ejpam-5429	637	5	we	we	PRON
ejpam-5429	637	6	will	will	AUX
ejpam-5429	637	7	delve	delve	VERB
ejpam-5429	637	8	into	into	ADP
ejpam-5429	637	9	additional	additional	ADJ
ejpam-5429	637	10	decision	decision	NOUN
ejpam-5429	637	11	-	-	PUNCT
ejpam-5429	637	12	making	make	VERB
ejpam-5429	637	13	methods	method	NOUN
ejpam-5429	637	14	associated	associate	VERB
ejpam-5429	637	15	with	with	ADP
ejpam-5429	637	16	the	the	DET
ejpam-5429	637	17	proposed	propose	VERB
ejpam-5429	637	18	concept	concept	NOUN
ejpam-5429	637	19	,	,	PUNCT
ejpam-5429	637	20	such	such	ADJ
ejpam-5429	637	21	as	as	ADP
ejpam-5429	637	22	q	q	ADJ
ejpam-5429	637	23	-	-	ADJ
ejpam-5429	637	24	polar	polar	ADJ
ejpam-5429	637	25	fuzzy	fuzzy	ADJ
ejpam-5429	637	26	semi	semi	ADJ
ejpam-5429	637	27	-	-	ADJ
ejpam-5429	637	28	hyper	hyper	ADJ
ejpam-5429	637	29	groups	group	NOUN
ejpam-5429	637	30	,	,	PUNCT
ejpam-5429	637	31	q	q	ADJ
ejpam-5429	637	32	-	-	ADJ
ejpam-5429	637	33	polar	polar	ADJ
ejpam-5429	637	34	fuzzy	fuzzy	ADJ
ejpam-5429	637	35	rough	rough	ADJ
ejpam-5429	637	36	sets	set	NOUN
ejpam-5429	637	37	,	,	PUNCT
ejpam-5429	637	38	q	q	ADJ
ejpam-5429	637	39	-	-	PUNCT
ejpam-5429	637	40	polar	polar	ADJ
ejpam-5429	637	41	fuzzy	fuzzy	ADJ
ejpam-5429	637	42	in	in	ADP
ejpam-5429	637	43	different	different	ADJ
ejpam-5429	637	44	logical	logical	ADJ
ejpam-5429	637	45	algebras	algebras	PROPN
ejpam-5429	637	46	environment	environment	PROPN
ejpam-5429	637	47	.	.	PUNCT
ejpam-5429	638	1	acknowledgements	acknowledgement	NOUN
ejpam-5429	638	2	the	the	DET
ejpam-5429	638	3	authors	author	NOUN
ejpam-5429	638	4	gratefully	gratefully	ADV
ejpam-5429	638	5	acknowledge	acknowledge	VERB
ejpam-5429	638	6	the	the	DET
ejpam-5429	638	7	funding	funding	NOUN
ejpam-5429	638	8	of	of	ADP
ejpam-5429	638	9	the	the	DET
ejpam-5429	638	10	deanship	deanship	NOUN
ejpam-5429	638	11	of	of	ADP
ejpam-5429	638	12	graduate	graduate	NOUN
ejpam-5429	638	13	studies	study	NOUN
ejpam-5429	638	14	and	and	CCONJ
ejpam-5429	638	15	scientific	scientific	ADJ
ejpam-5429	638	16	research	research	NOUN
ejpam-5429	638	17	,	,	PUNCT
ejpam-5429	638	18	jazan	jazan	PROPN
ejpam-5429	638	19	university	university	PROPN
ejpam-5429	638	20	,	,	PUNCT
ejpam-5429	638	21	saudi	saudi	PROPN
ejpam-5429	638	22	arabia	arabia	PROPN
ejpam-5429	638	23	,	,	PUNCT
ejpam-5429	638	24	through	through	ADP
ejpam-5429	638	25	project	project	NOUN
ejpam-5429	638	26	number	number	NOUN
ejpam-5429	638	27	:	:	PUNCT
ejpam-5429	638	28	gssrd-24	gssrd-24	PROPN
ejpam-5429	638	29	.	.	PUNCT
ejpam-5429	639	1	references	reference	NOUN
ejpam-5429	639	2	[	[	X
ejpam-5429	639	3	1	1	NUM
ejpam-5429	639	4	]	]	PUNCT
ejpam-5429	639	5	saeid	saeid	PROPN
ejpam-5429	639	6	a.b	a.b	PROPN
ejpam-5429	639	7	.	.	PROPN
ejpam-5429	639	8	fantastic	fantastic	ADJ
ejpam-5429	639	9	ideals	ideal	NOUN
ejpam-5429	639	10	in	in	ADP
ejpam-5429	639	11	bci	bci	NOUN
ejpam-5429	639	12	-	-	PUNCT
ejpam-5429	639	13	algebras	algebra	NOUN
ejpam-5429	639	14	.	.	PUNCT
ejpam-5429	640	1	world	world	PROPN
ejpam-5429	640	2	applied	apply	VERB
ejpam-5429	640	3	sciences	science	NOUN
ejpam-5429	640	4	journal	journal	NOUN
ejpam-5429	640	5	,	,	PUNCT
ejpam-5429	640	6	8(5):550	8(5):550	NUM
ejpam-5429	640	7	–	–	PUNCT
ejpam-5429	640	8	554	554	NUM
ejpam-5429	640	9	,	,	PUNCT
ejpam-5429	640	10	2010	2010	NUM
ejpam-5429	640	11	.	.	PUNCT
ejpam-5429	641	1	[	[	X
ejpam-5429	641	2	2	2	NUM
ejpam-5429	641	3	]	]	X
ejpam-5429	641	4	e.a	e.a	PROPN
ejpam-5429	641	5	.	.	PROPN
ejpam-5429	641	6	abuhijleh	abuhijleh	PROPN
ejpam-5429	641	7	,	,	PUNCT
ejpam-5429	641	8	m.	m.	NOUN
ejpam-5429	641	9	massadeh	massadeh	PROPN
ejpam-5429	641	10	,	,	PUNCT
ejpam-5429	641	11	a.	a.	NOUN
ejpam-5429	641	12	sheimat	sheimat	NOUN
ejpam-5429	641	13	,	,	PUNCT
ejpam-5429	641	14	and	and	CCONJ
ejpam-5429	641	15	a.	a.	PROPN
ejpam-5429	641	16	alkouri	alkouri	PROPN
ejpam-5429	641	17	.	.	PUNCT
ejpam-5429	642	1	complex	complex	ADJ
ejpam-5429	642	2	fuzzy	fuzzy	ADJ
ejpam-5429	642	3	groups	group	NOUN
ejpam-5429	642	4	based	base	VERB
ejpam-5429	642	5	on	on	ADP
ejpam-5429	642	6	rosenfled	rosenfle	VERB
ejpam-5429	642	7	’s	’s	PART
ejpam-5429	642	8	approach	approach	NOUN
ejpam-5429	642	9	.	.	PUNCT
ejpam-5429	643	1	wseas	wseas	PROPN
ejpam-5429	643	2	trans	trans	PROPN
ejpam-5429	643	3	.	.	PROPN
ejpam-5429	643	4	math	math	PROPN
ejpam-5429	643	5	.	.	PUNCT
ejpam-5429	644	1	,	,	PUNCT
ejpam-5429	645	1	20:368–377	20:368–377	NUM
ejpam-5429	645	2	,	,	PUNCT
ejpam-5429	645	3	2021	2021	NUM
ejpam-5429	645	4	.	.	PUNCT
ejpam-5429	646	1	[	[	X
ejpam-5429	646	2	3	3	X
ejpam-5429	646	3	]	]	PUNCT
ejpam-5429	646	4	m.	m.	NOUN
ejpam-5429	646	5	akram	akram	PROPN
ejpam-5429	646	6	and	and	CCONJ
ejpam-5429	646	7	a.	a.	PROPN
ejpam-5429	646	8	adeel	adeel	PROPN
ejpam-5429	646	9	.	.	PUNCT
ejpam-5429	647	1	novel	novel	ADJ
ejpam-5429	647	2	topsis	topsis	NOUN
ejpam-5429	647	3	method	method	NOUN
ejpam-5429	647	4	for	for	ADP
ejpam-5429	647	5	group	group	NOUN
ejpam-5429	647	6	decision	decision	NOUN
ejpam-5429	647	7	-	-	PUNCT
ejpam-5429	647	8	making	making	NOUN
ejpam-5429	647	9	based	base	VERB
ejpam-5429	647	10	on	on	ADP
ejpam-5429	647	11	hesitant	hesitant	ADJ
ejpam-5429	647	12	m	m	ADJ
ejpam-5429	647	13	-	-	ADJ
ejpam-5429	647	14	polar	polar	ADJ
ejpam-5429	647	15	fuzzy	fuzzy	ADJ
ejpam-5429	647	16	model	model	NOUN
ejpam-5429	647	17	.	.	PUNCT
ejpam-5429	648	1	j.	j.	PROPN
ejpam-5429	648	2	int	int	PROPN
ejpam-5429	648	3	.	.	PUNCT
ejpam-5429	649	1	fuzzy	fuzzy	ADJ
ejpam-5429	649	2	syst	syst	PROPN
ejpam-5429	649	3	.	.	PUNCT
ejpam-5429	649	4	,	,	PUNCT
ejpam-5429	649	5	37(6):8077–8096	37(6):8077–8096	NUM
ejpam-5429	649	6	,	,	PUNCT
ejpam-5429	649	7	2019	2019	NUM
ejpam-5429	649	8	.	.	PUNCT
ejpam-5429	650	1	[	[	X
ejpam-5429	650	2	4	4	NUM
ejpam-5429	650	3	]	]	PUNCT
ejpam-5429	650	4	m.	m.	NOUN
ejpam-5429	650	5	akram	akram	PROPN
ejpam-5429	650	6	,	,	PUNCT
ejpam-5429	650	7	a.	a.	NOUN
ejpam-5429	650	8	farooq	farooq	PROPN
ejpam-5429	650	9	,	,	PUNCT
ejpam-5429	650	10	and	and	CCONJ
ejpam-5429	650	11	k.	k.	PROPN
ejpam-5429	650	12	p.	p.	PROPN
ejpam-5429	650	13	shum	shum	PROPN
ejpam-5429	650	14	.	.	PUNCT
ejpam-5429	651	1	on	on	ADP
ejpam-5429	651	2	m	m	ADJ
ejpam-5429	651	3	-	-	ADJ
ejpam-5429	651	4	polar	polar	ADJ
ejpam-5429	651	5	fuzzy	fuzzy	ADJ
ejpam-5429	651	6	lie	lie	NOUN
ejpam-5429	651	7	subalgebras	subalgebras	PROPN
ejpam-5429	651	8	.	.	PUNCT
ejpam-5429	652	1	italian	italian	ADJ
ejpam-5429	652	2	j.	j.	PROPN
ejpam-5429	652	3	pure	pure	PROPN
ejpam-5429	652	4	appl	appl	PROPN
ejpam-5429	652	5	.	.	PUNCT
ejpam-5429	652	6	math	math	PROPN
ejpam-5429	652	7	.	.	PUNCT
ejpam-5429	652	8	,	,	PUNCT
ejpam-5429	652	9	36:445–454	36:445–454	PROPN
ejpam-5429	652	10	,	,	PUNCT
ejpam-5429	652	11	2016	2016	NUM
ejpam-5429	652	12	.	.	PUNCT
ejpam-5429	653	1	[	[	X
ejpam-5429	653	2	5	5	NUM
ejpam-5429	653	3	]	]	PUNCT
ejpam-5429	653	4	a.	a.	PROPN
ejpam-5429	653	5	al	al	PROPN
ejpam-5429	653	6	-	-	PROPN
ejpam-5429	653	7	masarwah	masarwah	PROPN
ejpam-5429	653	8	and	and	CCONJ
ejpam-5429	653	9	ahmad	ahmad	PROPN
ejpam-5429	653	10	a.g	a.g	PROPN
ejpam-5429	653	11	.	.	PROPN
ejpam-5429	653	12	on	on	ADP
ejpam-5429	653	13	some	some	DET
ejpam-5429	653	14	properties	property	NOUN
ejpam-5429	653	15	of	of	ADP
ejpam-5429	653	16	doubt	doubt	NOUN
ejpam-5429	653	17	bipolar	bipolar	ADJ
ejpam-5429	653	18	fuzzy	fuzzy	ADJ
ejpam-5429	653	19	h	h	NOUN
ejpam-5429	653	20	-	-	PUNCT
ejpam-5429	653	21	ideals	ideal	NOUN
ejpam-5429	653	22	in	in	ADP
ejpam-5429	653	23	bck	bck	PROPN
ejpam-5429	653	24	/	/	SYM
ejpam-5429	653	25	bci	bci	NOUN
ejpam-5429	653	26	-	-	PUNCT
ejpam-5429	653	27	algebras	algebra	NOUN
ejpam-5429	653	28	.	.	PUNCT
ejpam-5429	654	1	eur	eur	PROPN
ejpam-5429	654	2	.	.	PUNCT
ejpam-5429	655	1	j.	j.	PROPN
ejpam-5429	655	2	pure	pure	PROPN
ejpam-5429	655	3	appl	appl	PROPN
ejpam-5429	655	4	.	.	PUNCT
ejpam-5429	655	5	math	math	PROPN
ejpam-5429	655	6	.	.	PUNCT
ejpam-5429	655	7	,	,	PUNCT
ejpam-5429	655	8	11(3):652–670	11(3):652–670	NUM
ejpam-5429	655	9	,	,	PUNCT
ejpam-5429	655	10	2018	2018	NUM
ejpam-5429	655	11	.	.	PUNCT
ejpam-5429	656	1	[	[	X
ejpam-5429	656	2	6	6	NUM
ejpam-5429	656	3	]	]	PUNCT
ejpam-5429	656	4	a.	a.	PROPN
ejpam-5429	656	5	al	al	PROPN
ejpam-5429	656	6	-	-	PROPN
ejpam-5429	656	7	masarwah	masarwah	PROPN
ejpam-5429	656	8	and	and	CCONJ
ejpam-5429	656	9	a.g	a.g	PROPN
ejpam-5429	656	10	.	.	PROPN
ejpam-5429	656	11	ahmad	ahmad	PROPN
ejpam-5429	656	12	.	.	PUNCT
ejpam-5429	657	1	m	m	PROPN
ejpam-5429	657	2	-	-	ADJ
ejpam-5429	657	3	polar	polar	ADJ
ejpam-5429	657	4	(	(	PUNCT
ejpam-5429	657	5	α	α	NOUN
ejpam-5429	657	6	,	,	PUNCT
ejpam-5429	657	7	β)-fuzzy	β)-fuzzy	PUNCT
ejpam-5429	657	8	ideals	ideal	NOUN
ejpam-5429	657	9	in	in	ADP
ejpam-5429	657	10	bck	bck	PROPN
ejpam-5429	657	11	/	/	SYM
ejpam-5429	657	12	bci	bci	NOUN
ejpam-5429	657	13	-	-	PUNCT
ejpam-5429	657	14	algebras	algebra	NOUN
ejpam-5429	657	15	.	.	PUNCT
ejpam-5429	657	16	symmetry	symmetry	PROPN
ejpam-5429	657	17	,	,	PUNCT
ejpam-5429	657	18	11(1):1–18	11(1):1–18	NUM
ejpam-5429	657	19	,	,	PUNCT
ejpam-5429	657	20	2019	2019	NUM
ejpam-5429	657	21	.	.	PUNCT
ejpam-5429	658	1	references	reference	NOUN
ejpam-5429	658	2	3153	3153	NUM
ejpam-5429	659	1	[	[	X
ejpam-5429	659	2	7	7	NUM
ejpam-5429	659	3	]	]	PUNCT
ejpam-5429	659	4	a.	a.	PROPN
ejpam-5429	659	5	al	al	PROPN
ejpam-5429	659	6	-	-	PROPN
ejpam-5429	659	7	masarwah	masarwah	PROPN
ejpam-5429	659	8	and	and	CCONJ
ejpam-5429	659	9	a.g	a.g	PROPN
ejpam-5429	659	10	.	.	PROPN
ejpam-5429	659	11	ahmad	ahmad	PROPN
ejpam-5429	659	12	.	.	PUNCT
ejpam-5429	660	1	m	m	ADJ
ejpam-5429	660	2	-	-	ADJ
ejpam-5429	660	3	polar	polar	ADJ
ejpam-5429	660	4	fuzzy	fuzzy	ADJ
ejpam-5429	660	5	ideals	ideal	NOUN
ejpam-5429	660	6	of	of	ADP
ejpam-5429	660	7	bck	bck	PROPN
ejpam-5429	660	8	/	/	SYM
ejpam-5429	660	9	bci	bci	NOUN
ejpam-5429	660	10	-	-	PUNCT
ejpam-5429	660	11	algebras	algebras	X
ejpam-5429	660	12	.	.	PUNCT
ejpam-5429	661	1	j.	j.	PROPN
ejpam-5429	661	2	king	king	PROPN
ejpam-5429	661	3	saud	saud	PROPN
ejpam-5429	661	4	univ	univ	PROPN
ejpam-5429	661	5	.	.	PUNCT
ejpam-5429	662	1	sci	sci	PROPN
ejpam-5429	662	2	.	.	PROPN
ejpam-5429	662	3	,	,	PUNCT
ejpam-5429	662	4	31(4):1220–1226	31(4):1220–1226	NUM
ejpam-5429	662	5	,	,	PUNCT
ejpam-5429	662	6	2019	2019	NUM
ejpam-5429	662	7	.	.	PUNCT
ejpam-5429	663	1	[	[	X
ejpam-5429	663	2	8	8	NUM
ejpam-5429	663	3	]	]	PUNCT
ejpam-5429	663	4	a.	a.	PROPN
ejpam-5429	663	5	al	al	PROPN
ejpam-5429	663	6	-	-	PROPN
ejpam-5429	663	7	masarwah	masarwah	PROPN
ejpam-5429	663	8	and	and	CCONJ
ejpam-5429	663	9	a.g	a.g	PROPN
ejpam-5429	663	10	.	.	PROPN
ejpam-5429	663	11	ahmad	ahmad	PROPN
ejpam-5429	663	12	.	.	PUNCT
ejpam-5429	664	1	subalgebras	subalgebras	PROPN
ejpam-5429	664	2	of	of	ADP
ejpam-5429	664	3	type	type	NOUN
ejpam-5429	664	4	(	(	PUNCT
ejpam-5429	664	5	α	α	NOUN
ejpam-5429	664	6	,	,	PUNCT
ejpam-5429	664	7	β	β	NOUN
ejpam-5429	664	8	)	)	PUNCT
ejpam-5429	664	9	based	base	VERB
ejpam-5429	664	10	on	on	ADP
ejpam-5429	664	11	m	m	ADJ
ejpam-5429	664	12	-	-	ADJ
ejpam-5429	664	13	polar	polar	ADJ
ejpam-5429	664	14	fuzzy	fuzzy	ADJ
ejpam-5429	664	15	points	point	NOUN
ejpam-5429	664	16	in	in	ADP
ejpam-5429	664	17	bck	bck	PROPN
ejpam-5429	664	18	/	/	SYM
ejpam-5429	664	19	bci	bci	NOUN
ejpam-5429	664	20	-	-	PUNCT
ejpam-5429	664	21	algebras	algebra	NOUN
ejpam-5429	664	22	.	.	PUNCT
ejpam-5429	665	1	aims	aim	VERB
ejpam-5429	665	2	mathematics	mathematic	NOUN
ejpam-5429	665	3	,	,	PUNCT
ejpam-5429	665	4	5(2):1035–1049	5(2):1035–1049	PROPN
ejpam-5429	665	5	,	,	PUNCT
ejpam-5429	665	6	2020	2020	NUM
ejpam-5429	665	7	.	.	PUNCT
ejpam-5429	666	1	[	[	X
ejpam-5429	666	2	9	9	NUM
ejpam-5429	666	3	]	]	SYM
ejpam-5429	666	4	moin	moin	NOUN
ejpam-5429	666	5	a.	a.	NOUN
ejpam-5429	666	6	ansari	ansari	PROPN
ejpam-5429	666	7	,	,	PUNCT
ejpam-5429	666	8	a.	a.	NOUN
ejpam-5429	666	9	haider	haider	PROPN
ejpam-5429	666	10	,	,	PUNCT
ejpam-5429	666	11	and	and	CCONJ
ejpam-5429	666	12	a.n.a	a.n.a	PROPN
ejpam-5429	666	13	.	.	PUNCT
ejpam-5429	667	1	koam	koam	PROPN
ejpam-5429	667	2	.	.	PUNCT
ejpam-5429	668	1	on	on	ADP
ejpam-5429	668	2	a	a	DET
ejpam-5429	668	3	graph	graph	NOUN
ejpam-5429	668	4	associated	associate	VERB
ejpam-5429	668	5	to	to	ADP
ejpam-5429	668	6	up	up	ADV
ejpam-5429	668	7	-	-	PUNCT
ejpam-5429	668	8	algebras	algebras	X
ejpam-5429	668	9	.	.	PUNCT
ejpam-5429	668	10	mathematical	mathematical	ADJ
ejpam-5429	668	11	and	and	CCONJ
ejpam-5429	668	12	computational	computational	ADJ
ejpam-5429	668	13	applications	application	NOUN
ejpam-5429	668	14	,	,	PUNCT
ejpam-5429	668	15	23(4):61	23(4):61	NUM
ejpam-5429	668	16	,	,	PUNCT
ejpam-5429	668	17	2018	2018	NUM
ejpam-5429	668	18	.	.	PUNCT
ejpam-5429	669	1	[	[	X
ejpam-5429	669	2	10	10	NUM
ejpam-5429	669	3	]	]	X
ejpam-5429	669	4	m.	m.	NOUN
ejpam-5429	669	5	balamurugan	balamurugan	NOUN
ejpam-5429	669	6	,	,	PUNCT
ejpam-5429	669	7	n.	n.	PROPN
ejpam-5429	669	8	alessa	alessa	PROPN
ejpam-5429	669	9	,	,	PUNCT
ejpam-5429	669	10	k.	k.	PROPN
ejpam-5429	669	11	loganathan	loganathan	PROPN
ejpam-5429	669	12	,	,	PUNCT
ejpam-5429	669	13	and	and	CCONJ
ejpam-5429	669	14	n.	n.	PROPN
ejpam-5429	669	15	amar	amar	PROPN
ejpam-5429	669	16	nath	nath	PROPN
ejpam-5429	669	17	.	.	PUNCT
ejpam-5429	670	1	(	(	PUNCT
ejpam-5429	670	2	∈́	∈́	PROPN
ejpam-5429	670	3	,	,	PUNCT
ejpam-5429	670	4	∈́	∈́	PROPN
ejpam-5429	670	5	∨	∨	NUM
ejpam-5429	670	6	q́ǩ)-uniintuitionistic	q́ǩ)-uniintuitionistic	ADJ
ejpam-5429	670	7	fuzzy	fuzzy	ADJ
ejpam-5429	670	8	soft	soft	ADJ
ejpam-5429	670	9	h	h	NOUN
ejpam-5429	670	10	-	-	PUNCT
ejpam-5429	670	11	ideals	ideal	NOUN
ejpam-5429	670	12	in	in	ADP
ejpam-5429	670	13	subtraction	subtraction	NOUN
ejpam-5429	670	14	bg	bg	PROPN
ejpam-5429	670	15	-	-	PUNCT
ejpam-5429	670	16	algebras	algebras	PROPN
ejpam-5429	670	17	.	.	PUNCT
ejpam-5429	671	1	mathematics	mathematic	NOUN
ejpam-5429	671	2	,	,	PUNCT
ejpam-5429	671	3	11(10	11(10	NUM
ejpam-5429	671	4	)	)	PUNCT
ejpam-5429	671	5	,	,	PUNCT
ejpam-5429	671	6	2296:1–15	2296:1–15	NUM
ejpam-5429	671	7	,	,	PUNCT
ejpam-5429	671	8	2023	2023	NUM
ejpam-5429	671	9	.	.	PUNCT
ejpam-5429	672	1	[	[	X
ejpam-5429	672	2	11	11	NUM
ejpam-5429	672	3	]	]	PUNCT
ejpam-5429	672	4	m.	m.	NOUN
ejpam-5429	672	5	balamurugan	balamurugan	NOUN
ejpam-5429	672	6	,	,	PUNCT
ejpam-5429	672	7	n.	n.	PROPN
ejpam-5429	672	8	alessa	alessa	PROPN
ejpam-5429	672	9	,	,	PUNCT
ejpam-5429	672	10	k.	k.	PROPN
ejpam-5429	672	11	loganathan	loganathan	PROPN
ejpam-5429	672	12	,	,	PUNCT
ejpam-5429	672	13	and	and	CCONJ
ejpam-5429	672	14	m.	m.	NOUN
ejpam-5429	672	15	sudheer	sudheer	PROPN
ejpam-5429	672	16	kumar	kumar	PROPN
ejpam-5429	672	17	.	.	PUNCT
ejpam-5429	673	1	bipolar	bipolar	ADJ
ejpam-5429	673	2	intuitionistic	intuitionistic	ADJ
ejpam-5429	673	3	fuzzy	fuzzy	ADJ
ejpam-5429	673	4	soft	soft	ADJ
ejpam-5429	673	5	ideals	ideal	NOUN
ejpam-5429	673	6	of	of	ADP
ejpam-5429	673	7	bck	bck	PROPN
ejpam-5429	673	8	/	/	SYM
ejpam-5429	673	9	bci	bci	NOUN
ejpam-5429	673	10	-	-	PUNCT
ejpam-5429	673	11	algebras	algebra	NOUN
ejpam-5429	673	12	and	and	CCONJ
ejpam-5429	673	13	its	its	PRON
ejpam-5429	673	14	applications	application	NOUN
ejpam-5429	673	15	in	in	ADP
ejpam-5429	673	16	decision	decision	NOUN
ejpam-5429	673	17	-	-	PUNCT
ejpam-5429	673	18	making	making	NOUN
ejpam-5429	673	19	.	.	PUNCT
ejpam-5429	674	1	mathematics	mathematic	NOUN
ejpam-5429	674	2	,	,	PUNCT
ejpam-5429	674	3	11(21):4471	11(21):4471	NUM
ejpam-5429	674	4	,	,	PUNCT
ejpam-5429	674	5	2023	2023	NUM
ejpam-5429	674	6	.	.	PUNCT
ejpam-5429	675	1	[	[	X
ejpam-5429	675	2	12	12	NUM
ejpam-5429	675	3	]	]	X
ejpam-5429	675	4	s.k	s.k	PROPN
ejpam-5429	675	5	.	.	PROPN
ejpam-5429	675	6	bhakat	bhakat	PROPN
ejpam-5429	675	7	and	and	CCONJ
ejpam-5429	675	8	p.	p.	PROPN
ejpam-5429	675	9	das	das	PROPN
ejpam-5429	675	10	.	.	PUNCT
ejpam-5429	676	1	(	(	PUNCT
ejpam-5429	676	2	∈,∈	∈,∈	X
ejpam-5429	676	3	∨q)-fuzzy	∨q)-fuzzy	ADJ
ejpam-5429	676	4	subgroups	subgroup	NOUN
ejpam-5429	676	5	.	.	PUNCT
ejpam-5429	677	1	fuzzy	fuzzy	ADJ
ejpam-5429	677	2	sets	set	NOUN
ejpam-5429	677	3	syst	syst	PROPN
ejpam-5429	677	4	.	.	PUNCT
ejpam-5429	677	5	,	,	PUNCT
ejpam-5429	677	6	80(3):359–368	80(3):359–368	NUM
ejpam-5429	677	7	,	,	PUNCT
ejpam-5429	677	8	1996	1996	NUM
ejpam-5429	677	9	.	.	PUNCT
ejpam-5429	678	1	[	[	X
ejpam-5429	678	2	13	13	NUM
ejpam-5429	678	3	]	]	PUNCT
ejpam-5429	678	4	j.	j.	PROPN
ejpam-5429	678	5	chen	chen	PROPN
ejpam-5429	678	6	,	,	PUNCT
ejpam-5429	678	7	s.	s.	PROPN
ejpam-5429	678	8	li	li	PROPN
ejpam-5429	678	9	,	,	PUNCT
ejpam-5429	678	10	s.	s.	PROPN
ejpam-5429	678	11	ma	ma	PROPN
ejpam-5429	678	12	,	,	PUNCT
ejpam-5429	678	13	and	and	CCONJ
ejpam-5429	678	14	x.	x.	PROPN
ejpam-5429	678	15	wang	wang	PROPN
ejpam-5429	678	16	.	.	PUNCT
ejpam-5429	679	1	m	m	PROPN
ejpam-5429	679	2	-	-	ADJ
ejpam-5429	679	3	polar	polar	ADJ
ejpam-5429	679	4	fuzzy	fuzzy	ADJ
ejpam-5429	679	5	sets	set	VERB
ejpam-5429	679	6	an	an	DET
ejpam-5429	679	7	extension	extension	NOUN
ejpam-5429	679	8	of	of	ADP
ejpam-5429	679	9	bipolar	bipolar	ADJ
ejpam-5429	679	10	fuzzy	fuzzy	ADJ
ejpam-5429	679	11	sets	set	NOUN
ejpam-5429	679	12	.	.	PUNCT
ejpam-5429	680	1	the	the	DET
ejpam-5429	680	2	sci	sci	PROPN
ejpam-5429	680	3	world	world	PROPN
ejpam-5429	680	4	j.	j.	PROPN
ejpam-5429	680	5	,	,	PUNCT
ejpam-5429	680	6	article	article	NOUN
ejpam-5429	680	7	i	i	PROPN
ejpam-5429	680	8	d	d	PROPN
ejpam-5429	680	9	416530:1–8	416530:1–8	PROPN
ejpam-5429	680	10	,	,	PUNCT
ejpam-5429	680	11	2014	2014	NUM
ejpam-5429	680	12	.	.	PUNCT
ejpam-5429	681	1	[	[	X
ejpam-5429	681	2	14	14	NUM
ejpam-5429	681	3	]	]	X
ejpam-5429	681	4	w.a	w.a	PROPN
ejpam-5429	681	5	.	.	PROPN
ejpam-5429	681	6	dudek	dudek	PROPN
ejpam-5429	681	7	,	,	PUNCT
ejpam-5429	681	8	m.	m.	NOUN
ejpam-5429	681	9	shabir	shabir	PROPN
ejpam-5429	681	10	,	,	PUNCT
ejpam-5429	681	11	and	and	CCONJ
ejpam-5429	681	12	m.	m.	PROPN
ejpam-5429	681	13	irfan	irfan	PROPN
ejpam-5429	681	14	ali	ali	PROPN
ejpam-5429	681	15	.	.	PUNCT
ejpam-5429	682	1	(	(	PUNCT
ejpam-5429	682	2	α	α	NOUN
ejpam-5429	682	3	,	,	PUNCT
ejpam-5429	682	4	β)-fuzzy	β)-fuzzy	PUNCT
ejpam-5429	682	5	ideals	ideal	NOUN
ejpam-5429	682	6	of	of	ADP
ejpam-5429	682	7	hemirings	hemiring	NOUN
ejpam-5429	682	8	.	.	PUNCT
ejpam-5429	683	1	comput	comput	PROPN
ejpam-5429	683	2	math	math	PROPN
ejpam-5429	683	3	appl	appl	PROPN
ejpam-5429	683	4	.	.	PROPN
ejpam-5429	684	1	,	,	PUNCT
ejpam-5429	684	2	58(2):310–321	58(2):310–321	NUM
ejpam-5429	684	3	,	,	PUNCT
ejpam-5429	684	4	2009	2009	NUM
ejpam-5429	684	5	.	.	PUNCT
ejpam-5429	685	1	[	[	X
ejpam-5429	685	2	15	15	NUM
ejpam-5429	685	3	]	]	X
ejpam-5429	685	4	a.	a.	NOUN
ejpam-5429	685	5	fallath	fallath	PROPN
ejpam-5429	685	6	,	,	PUNCT
ejpam-5429	685	7	m.o	m.o	PROPN
ejpam-5429	685	8	.	.	PROPN
ejpam-5429	685	9	massadeh	massadeh	PROPN
ejpam-5429	685	10	,	,	PUNCT
ejpam-5429	685	11	and	and	CCONJ
ejpam-5429	685	12	a.u	a.u	PROPN
ejpam-5429	685	13	.	.	PROPN
ejpam-5429	685	14	alkouri	alkouri	PROPN
ejpam-5429	685	15	.	.	PUNCT
ejpam-5429	686	1	normal	normal	ADJ
ejpam-5429	686	2	and	and	CCONJ
ejpam-5429	686	3	cosets	coset	NOUN
ejpam-5429	686	4	of	of	ADP
ejpam-5429	686	5	(	(	PUNCT
ejpam-5429	686	6	γ	γ	PROPN
ejpam-5429	686	7	,	,	PUNCT
ejpam-5429	686	8	δ)-fuzzy	δ)-fuzzy	ADJ
ejpam-5429	686	9	hx	hx	PROPN
ejpam-5429	686	10	-	-	PUNCT
ejpam-5429	686	11	subgroups	subgroup	NOUN
ejpam-5429	686	12	.	.	PUNCT
ejpam-5429	687	1	j.	j.	PROPN
ejpam-5429	687	2	appl	appl	PROPN
ejpam-5429	687	3	.	.	PROPN
ejpam-5429	687	4	math	math	PROPN
ejpam-5429	687	5	.	.	PUNCT
ejpam-5429	688	1	inform	inform	NOUN
ejpam-5429	688	2	.	.	PUNCT
ejpam-5429	688	3	,	,	PUNCT
ejpam-5429	688	4	40:719–727	40:719–727	PROPN
ejpam-5429	688	5	,	,	PUNCT
ejpam-5429	688	6	2022	2022	NUM
ejpam-5429	688	7	.	.	PUNCT
ejpam-5429	689	1	[	[	X
ejpam-5429	689	2	16	16	NUM
ejpam-5429	689	3	]	]	X
ejpam-5429	689	4	a.	a.	PROPN
ejpam-5429	689	5	farooq	farooq	PROPN
ejpam-5429	689	6	,	,	PUNCT
ejpam-5429	689	7	g.	g.	PROPN
ejpam-5429	689	8	alia	alia	PROPN
ejpam-5429	689	9	,	,	PUNCT
ejpam-5429	689	10	and	and	CCONJ
ejpam-5429	689	11	m.	m.	PROPN
ejpam-5429	689	12	akram	akram	PROPN
ejpam-5429	689	13	.	.	PUNCT
ejpam-5429	690	1	on	on	ADP
ejpam-5429	690	2	m	m	ADJ
ejpam-5429	690	3	-	-	ADJ
ejpam-5429	690	4	polar	polar	ADJ
ejpam-5429	690	5	fuzzy	fuzzy	ADJ
ejpam-5429	690	6	groups	group	NOUN
ejpam-5429	690	7	.	.	PUNCT
ejpam-5429	691	1	int	int	NOUN
ejpam-5429	691	2	.	.	PUNCT
ejpam-5429	692	1	j.	j.	PROPN
ejpam-5429	692	2	algebra	algebra	PROPN
ejpam-5429	692	3	stat	stat	PROPN
ejpam-5429	692	4	.	.	PUNCT
ejpam-5429	692	5	,	,	PUNCT
ejpam-5429	693	1	5(2):115–127	5(2):115–127	NUM
ejpam-5429	693	2	,	,	PUNCT
ejpam-5429	693	3	2016	2016	NUM
ejpam-5429	693	4	.	.	PUNCT
ejpam-5429	694	1	[	[	X
ejpam-5429	694	2	17	17	NUM
ejpam-5429	694	3	]	]	PUNCT
ejpam-5429	694	4	k.	k.	PROPN
ejpam-5429	694	5	hayat	hayat	PROPN
ejpam-5429	694	6	,	,	PUNCT
ejpam-5429	694	7	t.	t.	PROPN
ejpam-5429	694	8	mahmood	mahmood	PROPN
ejpam-5429	694	9	,	,	PUNCT
ejpam-5429	694	10	and	and	CCONJ
ejpam-5429	694	11	b.y	b.y	PROPN
ejpam-5429	694	12	.	.	PROPN
ejpam-5429	694	13	cao	cao	PROPN
ejpam-5429	694	14	.	.	PUNCT
ejpam-5429	695	1	on	on	ADP
ejpam-5429	695	2	bipolar	bipolar	ADJ
ejpam-5429	695	3	anti	anti	ADJ
ejpam-5429	695	4	fuzzy	fuzzy	ADJ
ejpam-5429	695	5	h	h	NOUN
ejpam-5429	695	6	-	-	PUNCT
ejpam-5429	695	7	ideals	ideal	NOUN
ejpam-5429	695	8	in	in	ADP
ejpam-5429	695	9	hemi	hemi	NOUN
ejpam-5429	695	10	-	-	PUNCT
ejpam-5429	695	11	rings	ring	NOUN
ejpam-5429	695	12	.	.	PUNCT
ejpam-5429	696	1	fuzzy	fuzzy	PROPN
ejpam-5429	696	2	inf	inf	PROPN
ejpam-5429	696	3	.	.	PUNCT
ejpam-5429	697	1	eng	eng	PROPN
ejpam-5429	697	2	.	.	PROPN
ejpam-5429	697	3	,	,	PUNCT
ejpam-5429	697	4	9(1):1–19	9(1):1–19	NUM
ejpam-5429	697	5	,	,	PUNCT
ejpam-5429	697	6	2017	2017	NUM
ejpam-5429	697	7	.	.	PUNCT
ejpam-5429	698	1	[	[	X
ejpam-5429	698	2	18	18	NUM
ejpam-5429	698	3	]	]	PUNCT
ejpam-5429	698	4	a.	a.	NOUN
ejpam-5429	698	5	iamapan	iamapan	PROPN
ejpam-5429	698	6	,	,	PUNCT
ejpam-5429	698	7	m.	m.	NOUN
ejpam-5429	698	8	balamurugan	balamurugan	NOUN
ejpam-5429	698	9	,	,	PUNCT
ejpam-5429	698	10	and	and	CCONJ
ejpam-5429	698	11	v.	v.	ADP
ejpam-5429	698	12	govindan	govindan	PROPN
ejpam-5429	698	13	.	.	PUNCT
ejpam-5429	699	1	(	(	PUNCT
ejpam-5429	699	2	∈,∈	∈,∈	X
ejpam-5429	699	3	∨qk̃)-anti	∨qk̃)-anti	VERB
ejpam-5429	699	4	-	-	ADJ
ejpam-5429	699	5	intuitionistic	intuitionistic	ADJ
ejpam-5429	699	6	fuzzy	fuzzy	ADJ
ejpam-5429	699	7	soft	soft	ADJ
ejpam-5429	699	8	b	b	NOUN
ejpam-5429	699	9	-	-	PUNCT
ejpam-5429	699	10	ideals	ideal	NOUN
ejpam-5429	699	11	in	in	ADP
ejpam-5429	699	12	bck	bck	PROPN
ejpam-5429	699	13	/	/	SYM
ejpam-5429	699	14	bci	bci	NOUN
ejpam-5429	699	15	-	-	PUNCT
ejpam-5429	699	16	algebras	algebra	NOUN
ejpam-5429	699	17	.	.	PUNCT
ejpam-5429	700	1	mathematics	mathematic	NOUN
ejpam-5429	700	2	and	and	CCONJ
ejpam-5429	700	3	statistics	statistic	NOUN
ejpam-5429	700	4	,	,	PUNCT
ejpam-5429	700	5	10(3):515–522	10(3):515–522	PROPN
ejpam-5429	700	6	,	,	PUNCT
ejpam-5429	700	7	2022	2022	NUM
ejpam-5429	700	8	.	.	PUNCT
ejpam-5429	701	1	[	[	X
ejpam-5429	701	2	19	19	NUM
ejpam-5429	701	3	]	]	PUNCT
ejpam-5429	701	4	m.	m.	NOUN
ejpam-5429	701	5	ibrar	ibrar	NOUN
ejpam-5429	701	6	,	,	PUNCT
ejpam-5429	701	7	a.	a.	PROPN
ejpam-5429	701	8	khan	khan	PROPN
ejpam-5429	701	9	,	,	PUNCT
ejpam-5429	701	10	and	and	CCONJ
ejpam-5429	701	11	b.	b.	PROPN
ejpam-5429	701	12	davvaz	davvaz	PROPN
ejpam-5429	701	13	.	.	PUNCT
ejpam-5429	702	1	characterizations	characterization	NOUN
ejpam-5429	702	2	of	of	ADP
ejpam-5429	702	3	regular	regular	ADJ
ejpam-5429	702	4	ordered	order	VERB
ejpam-5429	702	5	semigroups	semigroup	NOUN
ejpam-5429	702	6	in	in	ADP
ejpam-5429	702	7	terms	term	NOUN
ejpam-5429	702	8	of	of	ADP
ejpam-5429	702	9	(	(	PUNCT
ejpam-5429	702	10	α	α	X
ejpam-5429	702	11	,	,	PUNCT
ejpam-5429	702	12	β)−bipolar	β)−bipolar	ADJ
ejpam-5429	702	13	fuzzy	fuzzy	ADJ
ejpam-5429	702	14	generalized	generalize	VERB
ejpam-5429	702	15	bi	bi	NOUN
ejpam-5429	702	16	-	-	NOUN
ejpam-5429	702	17	ideals	ideal	NOUN
ejpam-5429	702	18	.	.	PUNCT
ejpam-5429	703	1	j.	j.	PROPN
ejpam-5429	703	2	intelli	intelli	PROPN
ejpam-5429	703	3	fuzzy	fuzzy	PROPN
ejpam-5429	703	4	syst	syst	PROPN
ejpam-5429	703	5	.	.	PUNCT
ejpam-5429	703	6	,	,	PUNCT
ejpam-5429	704	1	33:365–376	33:365–376	PROPN
ejpam-5429	704	2	,	,	PUNCT
ejpam-5429	704	3	2017	2017	NUM
ejpam-5429	704	4	.	.	PUNCT
ejpam-5429	705	1	[	[	X
ejpam-5429	705	2	20	20	NUM
ejpam-5429	705	3	]	]	X
ejpam-5429	705	4	y.	y.	PROPN
ejpam-5429	705	5	imai	imai	PROPN
ejpam-5429	705	6	and	and	CCONJ
ejpam-5429	705	7	k.	k.	PROPN
ejpam-5429	705	8	iseki	iseki	PROPN
ejpam-5429	705	9	.	.	PUNCT
ejpam-5429	706	1	on	on	ADP
ejpam-5429	706	2	axiom	axiom	NOUN
ejpam-5429	706	3	systems	system	NOUN
ejpam-5429	706	4	of	of	ADP
ejpam-5429	706	5	propositional	propositional	ADJ
ejpam-5429	706	6	calculi	calculi	PROPN
ejpam-5429	706	7	.	.	PUNCT
ejpam-5429	707	1	i.	i.	PROPN
ejpam-5429	707	2	proc	proc	PROPN
ejpam-5429	707	3	.	.	PUNCT
ejpam-5429	708	1	japan	japan	PROPN
ejpam-5429	708	2	acad	acad	PROPN
ejpam-5429	708	3	.	.	PROPN
ejpam-5429	708	4	,	,	PUNCT
ejpam-5429	708	5	41(6):436–439	41(6):436–439	PROPN
ejpam-5429	708	6	,	,	PUNCT
ejpam-5429	708	7	1965	1965	NUM
ejpam-5429	708	8	.	.	PUNCT
ejpam-5429	709	1	[	[	X
ejpam-5429	709	2	21	21	NUM
ejpam-5429	709	3	]	]	PUNCT
ejpam-5429	709	4	k.	k.	PROPN
ejpam-5429	709	5	iseki	iseki	PROPN
ejpam-5429	709	6	.	.	PUNCT
ejpam-5429	710	1	an	an	DET
ejpam-5429	710	2	algebra	algebra	NOUN
ejpam-5429	710	3	related	relate	VERB
ejpam-5429	710	4	with	with	ADP
ejpam-5429	710	5	a	a	DET
ejpam-5429	710	6	propositional	propositional	ADJ
ejpam-5429	710	7	calculus	calculus	NOUN
ejpam-5429	710	8	.	.	PUNCT
ejpam-5429	711	1	proc	proc	PROPN
ejpam-5429	711	2	.	.	PUNCT
ejpam-5429	712	1	japan	japan	PROPN
ejpam-5429	712	2	acad	acad	PROPN
ejpam-5429	712	3	.	.	PROPN
ejpam-5429	712	4	,	,	PUNCT
ejpam-5429	712	5	42(1):26–29	42(1):26–29	NUM
ejpam-5429	712	6	,	,	PUNCT
ejpam-5429	712	7	1966	1966	NUM
ejpam-5429	712	8	.	.	PUNCT
ejpam-5429	713	1	references	reference	NOUN
ejpam-5429	713	2	3154	3154	NUM
ejpam-5429	713	3	[	[	X
ejpam-5429	713	4	22	22	NUM
ejpam-5429	713	5	]	]	PUNCT
ejpam-5429	713	6	k.	k.	PROPN
ejpam-5429	713	7	iseki	iseki	PROPN
ejpam-5429	713	8	.	.	PUNCT
ejpam-5429	714	1	on	on	ADP
ejpam-5429	714	2	bci	bci	PROPN
ejpam-5429	714	3	-	-	PUNCT
ejpam-5429	714	4	algebras	algebra	NOUN
ejpam-5429	714	5	.	.	PUNCT
ejpam-5429	714	6	math	math	NOUN
ejpam-5429	714	7	.	.	PUNCT
ejpam-5429	715	1	seminar	seminar	NOUN
ejpam-5429	715	2	notes	note	NOUN
ejpam-5429	715	3	,	,	PUNCT
ejpam-5429	715	4	8(1):125–130	8(1):125–130	NOUN
ejpam-5429	715	5	,	,	PUNCT
ejpam-5429	715	6	1980	1980	NUM
ejpam-5429	715	7	.	.	PUNCT
ejpam-5429	716	1	[	[	X
ejpam-5429	716	2	23	23	NUM
ejpam-5429	716	3	]	]	PUNCT
ejpam-5429	716	4	k.	k.	PROPN
ejpam-5429	716	5	iseki	iseki	PROPN
ejpam-5429	716	6	and	and	CCONJ
ejpam-5429	716	7	tanaka	tanaka	PROPN
ejpam-5429	716	8	s.	s.	PROPN
ejpam-5429	717	1	an	an	DET
ejpam-5429	717	2	introduction	introduction	NOUN
ejpam-5429	717	3	to	to	ADP
ejpam-5429	717	4	the	the	DET
ejpam-5429	717	5	theory	theory	NOUN
ejpam-5429	717	6	of	of	ADP
ejpam-5429	717	7	bck	bck	PROPN
ejpam-5429	717	8	-	-	PUNCT
ejpam-5429	717	9	algebras	algebras	PROPN
ejpam-5429	717	10	.	.	PUNCT
ejpam-5429	718	1	math	math	PROPN
ejpam-5429	718	2	japan	japan	PROPN
ejpam-5429	718	3	,	,	PUNCT
ejpam-5429	718	4	23(1	23(1	NUM
ejpam-5429	718	5	)	)	PUNCT
ejpam-5429	718	6	,	,	PUNCT
ejpam-5429	718	7	1978	1978	NUM
ejpam-5429	718	8	.	.	PUNCT
ejpam-5429	719	1	[	[	X
ejpam-5429	719	2	24	24	NUM
ejpam-5429	719	3	]	]	X
ejpam-5429	719	4	c.	c.	PROPN
ejpam-5429	719	5	jana	jana	PROPN
ejpam-5429	719	6	and	and	CCONJ
ejpam-5429	719	7	m.	m.	PROPN
ejpam-5429	719	8	pal	pal	NOUN
ejpam-5429	719	9	.	.	PUNCT
ejpam-5429	720	1	(	(	PUNCT
ejpam-5429	720	2	∈γ	∈γ	NUM
ejpam-5429	720	3	,	,	PUNCT
ejpam-5429	720	4	∈γ	∈γ	NOUN
ejpam-5429	720	5	∨qδ)-fuzzy	∨qδ)-fuzzy	VERB
ejpam-5429	720	6	soft	soft	ADJ
ejpam-5429	720	7	bci	bci	NOUN
ejpam-5429	720	8	-	-	PUNCT
ejpam-5429	720	9	algebras	algebra	NOUN
ejpam-5429	720	10	.	.	PUNCT
ejpam-5429	721	1	missouri	missouri	PROPN
ejpam-5429	721	2	j.	j.	PROPN
ejpam-5429	721	3	math	math	PROPN
ejpam-5429	721	4	sci	sci	PROPN
ejpam-5429	721	5	.	.	PROPN
ejpam-5429	721	6	,	,	PUNCT
ejpam-5429	721	7	29(2):197–215	29(2):197–215	NUM
ejpam-5429	721	8	,	,	PUNCT
ejpam-5429	721	9	2017	2017	NUM
ejpam-5429	721	10	.	.	PUNCT
ejpam-5429	722	1	[	[	X
ejpam-5429	722	2	25	25	NUM
ejpam-5429	722	3	]	]	X
ejpam-5429	722	4	c.	c.	PROPN
ejpam-5429	722	5	jana	jana	PROPN
ejpam-5429	722	6	,	,	PUNCT
ejpam-5429	722	7	m.	m.	NOUN
ejpam-5429	722	8	pal	pal	NOUN
ejpam-5429	722	9	,	,	PUNCT
ejpam-5429	722	10	and	and	CCONJ
ejpam-5429	722	11	a.b	a.b	PROPN
ejpam-5429	722	12	.	.	PROPN
ejpam-5429	722	13	saeid	saeid	PROPN
ejpam-5429	722	14	.	.	PUNCT
ejpam-5429	723	1	(	(	PUNCT
ejpam-5429	723	2	∈,∈	∈,∈	X
ejpam-5429	723	3	∨q)-bipolar	∨q)-bipolar	ADJ
ejpam-5429	723	4	fuzzy	fuzzy	ADJ
ejpam-5429	723	5	bck	bck	PROPN
ejpam-5429	723	6	/	/	SYM
ejpam-5429	723	7	bci	bci	NOUN
ejpam-5429	723	8	-	-	PUNCT
ejpam-5429	723	9	algebras	algebras	X
ejpam-5429	723	10	.	.	PUNCT
ejpam-5429	724	1	missouri	missouri	PROPN
ejpam-5429	724	2	j.	j.	PROPN
ejpam-5429	724	3	math	math	PROPN
ejpam-5429	724	4	.	.	PUNCT
ejpam-5429	725	1	sci	sci	PROPN
ejpam-5429	725	2	.	.	PROPN
ejpam-5429	725	3	,	,	PUNCT
ejpam-5429	725	4	29:1–23	29:1–23	NUM
ejpam-5429	725	5	,	,	PUNCT
ejpam-5429	725	6	2017	2017	NUM
ejpam-5429	725	7	.	.	PUNCT
ejpam-5429	726	1	[	[	X
ejpam-5429	726	2	26	26	NUM
ejpam-5429	726	3	]	]	X
ejpam-5429	726	4	y.b	y.b	PROPN
ejpam-5429	726	5	.	.	PROPN
ejpam-5429	726	6	jun	jun	PROPN
ejpam-5429	726	7	.	.	PROPN
ejpam-5429	727	1	on	on	ADP
ejpam-5429	727	2	(	(	PUNCT
ejpam-5429	727	3	α	α	NOUN
ejpam-5429	727	4	,	,	PUNCT
ejpam-5429	727	5	β)-fuzzy	β)-fuzzy	PUNCT
ejpam-5429	727	6	ideals	ideal	NOUN
ejpam-5429	727	7	of	of	ADP
ejpam-5429	727	8	bck	bck	PROPN
ejpam-5429	727	9	/	/	SYM
ejpam-5429	727	10	bci	bci	NOUN
ejpam-5429	727	11	-	-	PUNCT
ejpam-5429	727	12	algebras	algebra	NOUN
ejpam-5429	727	13	.	.	PUNCT
ejpam-5429	727	14	sci	sci	PROPN
ejpam-5429	727	15	.	.	PROPN
ejpam-5429	727	16	math	math	PROPN
ejpam-5429	727	17	.	.	PUNCT
ejpam-5429	728	1	jpn	jpn	PROPN
ejpam-5429	728	2	.	.	PROPN
ejpam-5429	728	3	,	,	PUNCT
ejpam-5429	728	4	pages	page	NOUN
ejpam-5429	728	5	101–105	101–105	NUM
ejpam-5429	728	6	,	,	PUNCT
ejpam-5429	728	7	2004	2004	NUM
ejpam-5429	728	8	.	.	PUNCT
ejpam-5429	729	1	[	[	X
ejpam-5429	729	2	27	27	NUM
ejpam-5429	729	3	]	]	X
ejpam-5429	729	4	y.b	y.b	PROPN
ejpam-5429	729	5	.	.	PROPN
ejpam-5429	729	6	jun	jun	PROPN
ejpam-5429	729	7	.	.	PROPN
ejpam-5429	730	1	on	on	ADP
ejpam-5429	730	2	(	(	PUNCT
ejpam-5429	730	3	α	α	X
ejpam-5429	730	4	,	,	PUNCT
ejpam-5429	730	5	β)-fuzzy	β)-fuzzy	PUNCT
ejpam-5429	730	6	subalgebras	subalgebras	PROPN
ejpam-5429	730	7	of	of	ADP
ejpam-5429	730	8	bck	bck	PROPN
ejpam-5429	730	9	/	/	SYM
ejpam-5429	730	10	bci	bci	NOUN
ejpam-5429	730	11	-	-	PUNCT
ejpam-5429	730	12	algebras	algebra	NOUN
ejpam-5429	730	13	.	.	PUNCT
ejpam-5429	731	1	bull	bull	PROPN
ejpam-5429	731	2	korean	korean	ADJ
ejpam-5429	731	3	math	math	PROPN
ejpam-5429	731	4	soc	soc	PROPN
ejpam-5429	731	5	.	.	PUNCT
ejpam-5429	731	6	,	,	PUNCT
ejpam-5429	731	7	42(4):703–711	42(4):703–711	NOUN
ejpam-5429	731	8	,	,	PUNCT
ejpam-5429	731	9	2005	2005	NUM
ejpam-5429	731	10	.	.	PUNCT
ejpam-5429	732	1	[	[	X
ejpam-5429	732	2	28	28	NUM
ejpam-5429	732	3	]	]	X
ejpam-5429	732	4	y.b	y.b	PROPN
ejpam-5429	732	5	.	.	PROPN
ejpam-5429	732	6	jun	jun	PROPN
ejpam-5429	732	7	.	.	PROPN
ejpam-5429	732	8	fuzzy	fuzzy	ADJ
ejpam-5429	732	9	subalgebras	subalgebra	NOUN
ejpam-5429	732	10	of	of	ADP
ejpam-5429	732	11	type	type	NOUN
ejpam-5429	732	12	(	(	PUNCT
ejpam-5429	732	13	α	α	NOUN
ejpam-5429	732	14	,	,	PUNCT
ejpam-5429	732	15	β)-fuzzy	β)-fuzzy	PUNCT
ejpam-5429	732	16	subalgebras	subalgebras	PROPN
ejpam-5429	732	17	in	in	ADP
ejpam-5429	732	18	bck	bck	PROPN
ejpam-5429	732	19	/	/	SYM
ejpam-5429	732	20	bci	bci	NOUN
ejpam-5429	732	21	-	-	PUNCT
ejpam-5429	732	22	algebras	algebra	NOUN
ejpam-5429	732	23	.	.	PUNCT
ejpam-5429	733	1	kyungpook	kyungpook	PROPN
ejpam-5429	733	2	math	math	PROPN
ejpam-5429	733	3	.	.	PUNCT
ejpam-5429	734	1	j.	j.	PROPN
ejpam-5429	734	2	,	,	PUNCT
ejpam-5429	734	3	4:403–410	4:403–410	PROPN
ejpam-5429	734	4	,	,	PUNCT
ejpam-5429	734	5	2007	2007	NUM
ejpam-5429	734	6	.	.	PUNCT
ejpam-5429	735	1	[	[	X
ejpam-5429	735	2	29	29	NUM
ejpam-5429	735	3	]	]	SYM
ejpam-5429	735	4	kavikumar	kavikumar	PROPN
ejpam-5429	735	5	,	,	PUNCT
ejpam-5429	735	6	azme	azme	NOUN
ejpam-5429	735	7	khamis	khamis	PROPN
ejpam-5429	735	8	,	,	PUNCT
ejpam-5429	735	9	and	and	CCONJ
ejpam-5429	735	10	young	young	ADJ
ejpam-5429	735	11	bae	bae	PROPN
ejpam-5429	735	12	jun	jun	PROPN
ejpam-5429	735	13	.	.	PROPN
ejpam-5429	736	1	fuzzy	fuzzy	ADJ
ejpam-5429	736	2	bi	bi	NOUN
ejpam-5429	736	3	-	-	NOUN
ejpam-5429	736	4	ideals	ideal	NOUN
ejpam-5429	736	5	in	in	ADP
ejpam-5429	736	6	ternary	ternary	ADJ
ejpam-5429	736	7	semirings	semiring	NOUN
ejpam-5429	736	8	.	.	PUNCT
ejpam-5429	737	1	international	international	ADJ
ejpam-5429	737	2	journal	journal	PROPN
ejpam-5429	737	3	of	of	ADP
ejpam-5429	737	4	computational	computational	ADJ
ejpam-5429	737	5	and	and	CCONJ
ejpam-5429	737	6	mathematical	mathematical	ADJ
ejpam-5429	737	7	sciences	science	NOUN
ejpam-5429	737	8	,	,	PUNCT
ejpam-5429	737	9	3(4):164	3(4):164	NUM
ejpam-5429	737	10	–	–	PUNCT
ejpam-5429	737	11	168	168	NUM
ejpam-5429	737	12	,	,	PUNCT
ejpam-5429	737	13	2009	2009	NUM
ejpam-5429	737	14	.	.	PUNCT
ejpam-5429	738	1	[	[	X
ejpam-5429	738	2	30	30	NUM
ejpam-5429	738	3	]	]	X
ejpam-5429	738	4	o.	o.	PROPN
ejpam-5429	738	5	kazanc	kazanc	PROPN
ejpam-5429	738	6	,	,	PUNCT
ejpam-5429	738	7	s.	s.	PROPN
ejpam-5429	738	8	hoskova	hoskova	PROPN
ejpam-5429	738	9	-	-	PUNCT
ejpam-5429	738	10	mayerova	mayerova	NOUN
ejpam-5429	738	11	,	,	PUNCT
ejpam-5429	738	12	and	and	CCONJ
ejpam-5429	738	13	b.	b.	PROPN
ejpam-5429	738	14	davvaz	davvaz	PROPN
ejpam-5429	738	15	.	.	PUNCT
ejpam-5429	739	1	multipolar	multipolar	ADJ
ejpam-5429	739	2	fuzzy	fuzzy	ADJ
ejpam-5429	739	3	hyperideals	hyperideal	NOUN
ejpam-5429	739	4	in	in	ADP
ejpam-5429	739	5	ordered	order	VERB
ejpam-5429	739	6	semihypergroups	semihypergroup	NOUN
ejpam-5429	739	7	.	.	PUNCT
ejpam-5429	740	1	mathematics	mathematic	NOUN
ejpam-5429	740	2	,	,	PUNCT
ejpam-5429	740	3	pages	page	NOUN
ejpam-5429	740	4	1–11	1–11	PROPN
ejpam-5429	740	5	,	,	PUNCT
ejpam-5429	740	6	2022	2022	NUM
ejpam-5429	740	7	.	.	PUNCT
ejpam-5429	741	1	[	[	X
ejpam-5429	741	2	31	31	NUM
ejpam-5429	741	3	]	]	PUNCT
ejpam-5429	741	4	zadeh	zadeh	PROPN
ejpam-5429	741	5	l.a	l.a	PROPN
ejpam-5429	741	6	.	.	PROPN
ejpam-5429	741	7	fuzzy	fuzzy	ADJ
ejpam-5429	741	8	sets	set	NOUN
ejpam-5429	741	9	.	.	PUNCT
ejpam-5429	742	1	information	information	NOUN
ejpam-5429	742	2	and	and	CCONJ
ejpam-5429	742	3	control	control	NOUN
ejpam-5429	742	4	,	,	PUNCT
ejpam-5429	742	5	8(3):338–353	8(3):338–353	NUM
ejpam-5429	742	6	,	,	PUNCT
ejpam-5429	742	7	1965	1965	NUM
ejpam-5429	742	8	.	.	PUNCT
ejpam-5429	743	1	[	[	X
ejpam-5429	743	2	32	32	NUM
ejpam-5429	743	3	]	]	X
ejpam-5429	743	4	k.j	k.j	PROPN
ejpam-5429	743	5	.	.	PROPN
ejpam-5429	743	6	lee	lee	PROPN
ejpam-5429	743	7	.	.	PUNCT
ejpam-5429	744	1	bipolar	bipolar	ADJ
ejpam-5429	744	2	fuzzy	fuzzy	ADJ
ejpam-5429	744	3	subalgebras	subalgebra	NOUN
ejpam-5429	744	4	and	and	CCONJ
ejpam-5429	744	5	bipolar	bipolar	ADJ
ejpam-5429	744	6	fuzzy	fuzzy	ADJ
ejpam-5429	744	7	ideals	ideal	NOUN
ejpam-5429	744	8	of	of	ADP
ejpam-5429	744	9	bck	bck	PROPN
ejpam-5429	744	10	/	/	SYM
ejpam-5429	744	11	bci	bci	NOUN
ejpam-5429	744	12	-	-	PUNCT
ejpam-5429	744	13	algebras	algebra	NOUN
ejpam-5429	744	14	.	.	PUNCT
ejpam-5429	745	1	bull	bull	NOUN
ejpam-5429	745	2	.	.	PUNCT
ejpam-5429	746	1	malays	malays	PROPN
ejpam-5429	746	2	.	.	PUNCT
ejpam-5429	747	1	math	math	NOUN
ejpam-5429	747	2	.	.	PUNCT
ejpam-5429	748	1	sci	sci	PROPN
ejpam-5429	748	2	.	.	PROPN
ejpam-5429	748	3	soc	soc	PROPN
ejpam-5429	748	4	.	.	PUNCT
ejpam-5429	748	5	,	,	PUNCT
ejpam-5429	749	1	32(3):361–373	32(3):361–373	NUM
ejpam-5429	749	2	,	,	PUNCT
ejpam-5429	749	3	2009	2009	NUM
ejpam-5429	749	4	.	.	PUNCT
ejpam-5429	750	1	[	[	X
ejpam-5429	750	2	33	33	NUM
ejpam-5429	750	3	]	]	PUNCT
ejpam-5429	750	4	x.	x.	PROPN
ejpam-5429	750	5	ma	ma	PROPN
ejpam-5429	750	6	,	,	PUNCT
ejpam-5429	750	7	j.	j.	PROPN
ejpam-5429	750	8	zhan	zhan	PROPN
ejpam-5429	750	9	,	,	PUNCT
ejpam-5429	750	10	and	and	CCONJ
ejpam-5429	750	11	y.b	y.b	PROPN
ejpam-5429	750	12	.	.	PROPN
ejpam-5429	750	13	jun	jun	PROPN
ejpam-5429	750	14	.	.	PUNCT
ejpam-5429	751	1	some	some	DET
ejpam-5429	751	2	kinds	kind	NOUN
ejpam-5429	751	3	of	of	ADP
ejpam-5429	751	4	(	(	PUNCT
ejpam-5429	751	5	∈γ	∈γ	NUM
ejpam-5429	751	6	,	,	PUNCT
ejpam-5429	751	7	∈γ	∈γ	NOUN
ejpam-5429	751	8	∨qδ)-fuzzy	∨qδ)-fuzzy	VERB
ejpam-5429	751	9	ideals	ideal	NOUN
ejpam-5429	751	10	of	of	ADP
ejpam-5429	751	11	bci	bci	NOUN
ejpam-5429	751	12	-	-	PUNCT
ejpam-5429	751	13	algebras	algebra	NOUN
ejpam-5429	751	14	.	.	PUNCT
ejpam-5429	752	1	comput	comput	PROPN
ejpam-5429	752	2	math	math	PROPN
ejpam-5429	752	3	appl	appl	PROPN
ejpam-5429	752	4	.	.	PROPN
ejpam-5429	752	5	,	,	PUNCT
ejpam-5429	752	6	61(4):1005–1015	61(4):1005–1015	PROPN
ejpam-5429	752	7	,	,	PUNCT
ejpam-5429	752	8	2011	2011	NUM
ejpam-5429	753	1	.	.	PUNCT
ejpam-5429	754	1	[	[	X
ejpam-5429	754	2	34	34	NUM
ejpam-5429	754	3	]	]	X
ejpam-5429	754	4	g.	g.	PROPN
ejpam-5429	754	5	muhiuddin	muhiuddin	PROPN
ejpam-5429	754	6	,	,	PUNCT
ejpam-5429	754	7	n.	n.	PROPN
ejpam-5429	754	8	abughazalah	abughazalah	NOUN
ejpam-5429	754	9	,	,	PUNCT
ejpam-5429	754	10	a.	a.	NOUN
ejpam-5429	754	11	aljuhani	aljuhani	PROPN
ejpam-5429	754	12	,	,	PUNCT
ejpam-5429	754	13	and	and	CCONJ
ejpam-5429	754	14	m.	m.	NOUN
ejpam-5429	754	15	balamurugan	balamurugan	VERB
ejpam-5429	754	16	.	.	PUNCT
ejpam-5429	755	1	tripolar	tripolar	ADJ
ejpam-5429	755	2	picture	picture	NOUN
ejpam-5429	755	3	fuzzy	fuzzy	ADJ
ejpam-5429	755	4	ideals	ideal	NOUN
ejpam-5429	755	5	of	of	ADP
ejpam-5429	755	6	bck	bck	NOUN
ejpam-5429	755	7	-	-	PUNCT
ejpam-5429	755	8	algebras	algebras	PROPN
ejpam-5429	755	9	.	.	PUNCT
ejpam-5429	755	10	symmetry	symmetry	PROPN
ejpam-5429	755	11	,	,	PUNCT
ejpam-5429	755	12	14(8	14(8	NUM
ejpam-5429	755	13	)	)	PUNCT
ejpam-5429	755	14	,	,	PUNCT
ejpam-5429	755	15	1562:1–20	1562:1–20	NUM
ejpam-5429	755	16	,	,	PUNCT
ejpam-5429	755	17	2022	2022	NUM
ejpam-5429	755	18	.	.	PUNCT
ejpam-5429	756	1	[	[	X
ejpam-5429	756	2	35	35	NUM
ejpam-5429	756	3	]	]	X
ejpam-5429	756	4	g.	g.	PROPN
ejpam-5429	756	5	muhiuddin	muhiuddin	PROPN
ejpam-5429	756	6	and	and	CCONJ
ejpam-5429	756	7	a.m.	a.m.	PROPN
ejpam-5429	757	1	al	al	PROPN
ejpam-5429	757	2	-	-	PUNCT
ejpam-5429	757	3	roqi	roqi	ADV
ejpam-5429	757	4	.	.	PUNCT
ejpam-5429	758	1	subalgebras	subalgebras	PROPN
ejpam-5429	758	2	of	of	ADP
ejpam-5429	758	3	bck	bck	PROPN
ejpam-5429	758	4	/	/	SYM
ejpam-5429	758	5	bci	bci	NOUN
ejpam-5429	758	6	-	-	PUNCT
ejpam-5429	758	7	algebras	algebra	NOUN
ejpam-5429	758	8	based	base	VERB
ejpam-5429	758	9	on	on	ADP
ejpam-5429	758	10	(	(	PUNCT
ejpam-5429	758	11	α	α	NOUN
ejpam-5429	758	12	,	,	PUNCT
ejpam-5429	758	13	β)type	β)type	ADP
ejpam-5429	758	14	fuzzy	fuzzy	ADJ
ejpam-5429	758	15	sets	set	NOUN
ejpam-5429	758	16	.	.	PUNCT
ejpam-5429	759	1	comput	comput	PROPN
ejpam-5429	759	2	anal	anal	ADJ
ejpam-5429	759	3	appl	appl	PROPN
ejpam-5429	759	4	,	,	PUNCT
ejpam-5429	759	5	18(6):1057–1064	18(6):1057–1064	NUM
ejpam-5429	759	6	,	,	PUNCT
ejpam-5429	759	7	2015	2015	NUM
ejpam-5429	759	8	.	.	PUNCT
ejpam-5429	760	1	[	[	X
ejpam-5429	760	2	36	36	NUM
ejpam-5429	760	3	]	]	X
ejpam-5429	760	4	g.	g.	PROPN
ejpam-5429	760	5	muhiuddin	muhiuddin	PROPN
ejpam-5429	760	6	,	,	PUNCT
ejpam-5429	760	7	r.a	r.a	PROPN
ejpam-5429	760	8	.	.	PROPN
ejpam-5429	760	9	takallo	takallo	PROPN
ejpam-5429	760	10	,	,	PUNCT
ejpam-5429	760	11	m.m	m.m	PROPN
ejpam-5429	760	12	.	.	PROPN
ejpam-5429	760	13	nd	nd	PROPN
ejpam-5429	760	14	borzooei	borzooei	PROPN
ejpam-5429	760	15	,	,	PUNCT
ejpam-5429	760	16	and	and	CCONJ
ejpam-5429	760	17	y.b	y.b	PROPN
ejpam-5429	760	18	.	.	PROPN
ejpam-5429	760	19	jun	jun	PROPN
ejpam-5429	760	20	.	.	PROPN
ejpam-5429	761	1	m	m	PROPN
ejpam-5429	761	2	-	-	ADJ
ejpam-5429	761	3	polar	polar	ADJ
ejpam-5429	761	4	fuzzy	fuzzy	ADJ
ejpam-5429	761	5	q	q	NOUN
ejpam-5429	761	6	-	-	PUNCT
ejpam-5429	761	7	ideals	ideal	NOUN
ejpam-5429	761	8	in	in	ADP
ejpam-5429	761	9	bci	bci	NOUN
ejpam-5429	761	10	-	-	PUNCT
ejpam-5429	761	11	algebras	algebras	PROPN
ejpam-5429	761	12	.	.	PUNCT
ejpam-5429	762	1	j.	j.	PROPN
ejpam-5429	762	2	king	king	PROPN
ejpam-5429	762	3	saud	saud	PROPN
ejpam-5429	762	4	univ	univ	PROPN
ejpam-5429	762	5	.	.	PUNCT
ejpam-5429	763	1	sci	sci	PROPN
ejpam-5429	763	2	.	.	PROPN
ejpam-5429	763	3	,	,	PUNCT
ejpam-5429	763	4	32(6):2803–2809	32(6):2803–2809	PROPN
ejpam-5429	763	5	,	,	PUNCT
ejpam-5429	763	6	2020	2020	NUM
ejpam-5429	763	7	.	.	PUNCT
ejpam-5429	764	1	[	[	X
ejpam-5429	764	2	37	37	NUM
ejpam-5429	764	3	]	]	PUNCT
ejpam-5429	764	4	a.	a.	PROPN
ejpam-5429	764	5	l.	l.	PROPN
ejpam-5429	764	6	narayanan	narayanan	PROPN
ejpam-5429	764	7	and	and	CCONJ
ejpam-5429	764	8	t.	t.	PROPN
ejpam-5429	764	9	manikantan	manikantan	PROPN
ejpam-5429	764	10	.	.	PUNCT
ejpam-5429	765	1	(	(	PUNCT
ejpam-5429	765	2	∈,∈	∈,∈	X
ejpam-5429	765	3	∨q)-fuzzy	∨q)-fuzzy	ADJ
ejpam-5429	765	4	subnearrings	subnearring	NOUN
ejpam-5429	765	5	and	and	CCONJ
ejpam-5429	765	6	(	(	PUNCT
ejpam-5429	765	7	∈,∈	∈,∈	X
ejpam-5429	765	8	∨q)fuzzy	∨q)fuzzy	ADJ
ejpam-5429	765	9	ideals	ideal	NOUN
ejpam-5429	765	10	of	of	ADP
ejpam-5429	765	11	near	near	ADJ
ejpam-5429	765	12	-	-	PUNCT
ejpam-5429	765	13	rings	ring	NOUN
ejpam-5429	765	14	.	.	PUNCT
ejpam-5429	766	1	j.	j.	PROPN
ejpam-5429	766	2	appl	appl	PROPN
ejpam-5429	766	3	math	math	PROPN
ejpam-5429	766	4	comput	comput	PROPN
ejpam-5429	766	5	.	.	PUNCT
ejpam-5429	766	6	,	,	PUNCT
ejpam-5429	766	7	18(1):419–430	18(1):419–430	NUM
ejpam-5429	766	8	,	,	PUNCT
ejpam-5429	766	9	2009	2009	NUM
ejpam-5429	766	10	.	.	PUNCT
ejpam-5429	767	1	[	[	X
ejpam-5429	767	2	38	38	NUM
ejpam-5429	767	3	]	]	PUNCT
ejpam-5429	767	4	a.	a.	NOUN
ejpam-5429	767	5	rosenfeld	rosenfeld	PROPN
ejpam-5429	767	6	.	.	PUNCT
ejpam-5429	768	1	fuzzy	fuzzy	ADJ
ejpam-5429	768	2	groups	group	NOUN
ejpam-5429	768	3	.	.	PUNCT
ejpam-5429	769	1	j.	j.	PROPN
ejpam-5429	769	2	math	math	PROPN
ejpam-5429	769	3	anal	anal	PROPN
ejpam-5429	769	4	appl	appl	PROPN
ejpam-5429	769	5	.	.	PROPN
ejpam-5429	769	6	,	,	PUNCT
ejpam-5429	769	7	35(3):512–517	35(3):512–517	PROPN
ejpam-5429	769	8	,	,	PUNCT
ejpam-5429	769	9	1971	1971	NUM
ejpam-5429	769	10	.	.	PUNCT
ejpam-5429	770	1	references	reference	NOUN
ejpam-5429	770	2	3155	3155	NUM
ejpam-5429	770	3	[	[	X
ejpam-5429	770	4	39	39	NUM
ejpam-5429	770	5	]	]	PUNCT
ejpam-5429	770	6	zhang	zhang	PROPN
ejpam-5429	770	7	w.r	w.r	PROPN
ejpam-5429	770	8	.	.	PROPN
ejpam-5429	770	9	bipolar	bipolar	ADJ
ejpam-5429	770	10	fuzzy	fuzzy	ADJ
ejpam-5429	770	11	sets	set	NOUN
ejpam-5429	770	12	and	and	CCONJ
ejpam-5429	770	13	relations	relation	NOUN
ejpam-5429	770	14	a	a	DET
ejpam-5429	770	15	computational	computational	ADJ
ejpam-5429	770	16	framework	framework	NOUN
ejpam-5429	770	17	for	for	ADP
ejpam-5429	770	18	cognitive	cognitive	ADJ
ejpam-5429	770	19	and	and	CCONJ
ejpam-5429	770	20	modeling	modeling	NOUN
ejpam-5429	770	21	and	and	CCONJ
ejpam-5429	770	22	multiagent	multiagent	ADJ
ejpam-5429	770	23	decision	decision	NOUN
ejpam-5429	770	24	analysis	analysis	NOUN
ejpam-5429	770	25	.	.	PUNCT
ejpam-5429	771	1	proceedings	proceeding	NOUN
ejpam-5429	771	2	of	of	ADP
ejpam-5429	771	3	the	the	DET
ejpam-5429	771	4	first	first	ADJ
ejpam-5429	771	5	international	international	ADJ
ejpam-5429	771	6	joint	joint	ADJ
ejpam-5429	771	7	conference	conference	NOUN
ejpam-5429	771	8	of	of	ADP
ejpam-5429	771	9	the	the	DET
ejpam-5429	771	10	north	north	ADJ
ejpam-5429	771	11	american	american	ADJ
ejpam-5429	771	12	fuzzy	fuzzy	ADJ
ejpam-5429	771	13	information	information	NOUN
ejpam-5429	771	14	processing	processing	NOUN
ejpam-5429	771	15	society	society	NOUN
ejpam-5429	771	16	biannual	biannual	ADJ
ejpam-5429	771	17	conference	conference	NOUN
ejpam-5429	771	18	,	,	PUNCT
ejpam-5429	771	19	the	the	DET
ejpam-5429	771	20	industry	industry	NOUN
ejpam-5429	771	21	fuzzy	fuzzy	ADJ
ejpam-5429	771	22	control	control	NOUN
ejpam-5429	771	23	and	and	CCONJ
ejpam-5429	771	24	intelligent	intelligent	ADJ
ejpam-5429	771	25	,	,	PUNCT
ejpam-5429	771	26	pages	page	NOUN
ejpam-5429	771	27	305–309	305–309	NUM
ejpam-5429	771	28	,	,	PUNCT
ejpam-5429	771	29	1994	1994	NUM
ejpam-5429	771	30	.	.	PUNCT
ejpam-5429	772	1	[	[	X
ejpam-5429	772	2	40	40	NUM
ejpam-5429	772	3	]	]	X
ejpam-5429	772	4	o.g	o.g	PROPN
ejpam-5429	772	5	.	.	PROPN
ejpam-5429	772	6	xi	xi	PROPN
ejpam-5429	772	7	.	.	PUNCT
ejpam-5429	772	8	fuzzy	fuzzy	ADJ
ejpam-5429	772	9	bck	bck	PROPN
ejpam-5429	772	10	-	-	PUNCT
ejpam-5429	772	11	algebras	algebras	PROPN
ejpam-5429	772	12	.	.	PUNCT
ejpam-5429	773	1	math	math	PROPN
ejpam-5429	773	2	.	.	PUNCT
ejpam-5429	774	1	jpn	jpn	PROPN
ejpam-5429	774	2	.	.	PROPN
ejpam-5429	774	3	,	,	PUNCT
ejpam-5429	775	1	36:935–942	36:935–942	NUM
ejpam-5429	775	2	,	,	PUNCT
ejpam-5429	775	3	1991	1991	NUM
ejpam-5429	775	4	.	.	PUNCT
ejpam-5429	776	1	[	[	X
ejpam-5429	776	2	41	41	NUM
ejpam-5429	776	3	]	]	X
ejpam-5429	776	4	j.	j.	PROPN
ejpam-5429	776	5	zhan	zhan	PROPN
ejpam-5429	776	6	.	.	PUNCT
ejpam-5429	777	1	fuzzy	fuzzy	ADJ
ejpam-5429	777	2	soft	soft	ADJ
ejpam-5429	777	3	γ	γ	NOUN
ejpam-5429	777	4	-	-	NOUN
ejpam-5429	777	5	hyperrings	hyperring	NOUN
ejpam-5429	777	6	.	.	PUNCT
ejpam-5429	778	1	iran	iran	PROPN
ejpam-5429	778	2	j.	j.	PROPN
ejpam-5429	778	3	sci	sci	PROPN
ejpam-5429	778	4	technol	technol	PROPN
ejpam-5429	778	5	.	.	PROPN
ejpam-5429	778	6	,	,	PUNCT
ejpam-5429	778	7	36(2):125–135	36(2):125–135	NUM
ejpam-5429	778	8	,	,	PUNCT
ejpam-5429	778	9	2012	2012	NUM
ejpam-5429	778	10	.	.	PUNCT
ejpam-5429	779	1	[	[	X
ejpam-5429	779	2	42	42	NUM
ejpam-5429	779	3	]	]	PUNCT
ejpam-5429	779	4	m.	m.	PROPN
ejpam-5429	779	5	zulfiqar	zulfiqar	PROPN
ejpam-5429	779	6	.	.	PUNCT
ejpam-5429	780	1	some	some	DET
ejpam-5429	780	2	characterizations	characterization	NOUN
ejpam-5429	780	3	of	of	ADP
ejpam-5429	780	4	(	(	PUNCT
ejpam-5429	780	5	∈γ	∈γ	NUM
ejpam-5429	780	6	,	,	PUNCT
ejpam-5429	780	7	∈γ	∈γ	NUM
ejpam-5429	780	8	,	,	PUNCT
ejpam-5429	780	9	∨qδ)-fuzzy	∨qδ)-fuzzy	VERB
ejpam-5429	780	10	fantastic	fantastic	ADJ
ejpam-5429	780	11	ideals	ideal	NOUN
ejpam-5429	780	12	in	in	ADP
ejpam-5429	780	13	bchalgebras	bchalgebras	PROPN
ejpam-5429	780	14	.	.	PUNCT
ejpam-5429	781	1	acta	acta	PROPN
ejpam-5429	781	2	sci	sci	PROPN
ejpam-5429	781	3	technol	technol	NOUN
ejpam-5429	781	4	.	.	PROPN
ejpam-5429	781	5	,	,	PUNCT
ejpam-5429	781	6	35(1):123–129	35(1):123–129	PROPN
ejpam-5429	781	7	,	,	PUNCT
ejpam-5429	781	8	2013	2013	NUM
ejpam-5429	782	1	.	.	PUNCT
ejpam-5429	783	1	[	[	X
ejpam-5429	783	2	43	43	NUM
ejpam-5429	783	3	]	]	X
ejpam-5429	783	4	m.	m.	NOUN
ejpam-5429	783	5	zulfiqar	zulfiqar	PROPN
ejpam-5429	783	6	and	and	CCONJ
ejpam-5429	783	7	m.	m.	PROPN
ejpam-5429	783	8	shabir	shabir	PROPN
ejpam-5429	783	9	.	.	PUNCT
ejpam-5429	784	1	(	(	PUNCT
ejpam-5429	784	2	∈γ	∈γ	NUM
ejpam-5429	784	3	,	,	PUNCT
ejpam-5429	784	4	∈γ	∈γ	NOUN
ejpam-5429	784	5	∨qδ)-fuzzy	∨qδ)-fuzzy	VERB
ejpam-5429	784	6	soft	soft	ADJ
ejpam-5429	784	7	bci	bci	NOUN
ejpam-5429	784	8	-	-	PUNCT
ejpam-5429	784	9	algebras	algebra	NOUN
ejpam-5429	784	10	.	.	PUNCT
ejpam-5429	785	1	university	university	NOUN
ejpam-5429	785	2	politehnica	politehnica	PROPN
ejpam-5429	785	3	of	of	ADP
ejpam-5429	785	4	bucharest	buchar	ADJ
ejpam-5429	785	5	scientific	scientific	ADJ
ejpam-5429	785	6	bulletin	bulletin	NOUN
ejpam-5429	785	7	-	-	PUNCT
ejpam-5429	785	8	series	series	NOUN
ejpam-5429	785	9	a	a	PRON
ejpam-5429	785	10	-	-	PUNCT
ejpam-5429	785	11	applied	apply	VERB
ejpam-5429	785	12	mathematics	mathematic	NOUN
ejpam-5429	785	13	and	and	CCONJ
ejpam-5429	785	14	physics	physics	NOUN
ejpam-5429	785	15	,	,	PUNCT
ejpam-5429	785	16	75(4):217–230	75(4):217–230	PROPN
ejpam-5429	785	17	,	,	PUNCT
ejpam-5429	785	18	2013	2013	NUM
ejpam-5429	785	19	.	.	PUNCT