id	sid	tid	token	lemma	pos
ejpam-5699	1	1	european	european	PROPN
ejpam-5699	1	2	journal	journal	PROPN
ejpam-5699	1	3	of	of	ADP
ejpam-5699	1	4	pure	pure	ADJ
ejpam-5699	1	5	and	and	CCONJ
ejpam-5699	1	6	applied	applied	ADJ
ejpam-5699	1	7	mathematics	mathematic	NOUN
ejpam-5699	1	8	2025	2025	NUM
ejpam-5699	1	9	,	,	PUNCT
ejpam-5699	1	10	vol	vol	NOUN
ejpam-5699	1	11	.	.	PROPN
ejpam-5699	1	12	18	18	NUM
ejpam-5699	1	13	,	,	PUNCT
ejpam-5699	1	14	issue	issue	NOUN
ejpam-5699	1	15	1	1	NUM
ejpam-5699	1	16	,	,	PUNCT
ejpam-5699	1	17	article	article	NOUN
ejpam-5699	1	18	number	number	NOUN
ejpam-5699	1	19	5699	5699	NUM
ejpam-5699	1	20	issn	issn	PROPN
ejpam-5699	1	21	1307	1307	NUM
ejpam-5699	1	22	-	-	SYM
ejpam-5699	1	23	5543	5543	NUM
ejpam-5699	1	24	–	–	PUNCT
ejpam-5699	1	25	ejpam.com	ejpam.com	X
ejpam-5699	1	26	published	publish	VERB
ejpam-5699	1	27	by	by	ADP
ejpam-5699	1	28	new	new	PROPN
ejpam-5699	1	29	york	york	PROPN
ejpam-5699	1	30	business	business	PROPN
ejpam-5699	1	31	global	global	ADJ
ejpam-5699	1	32	bipolar	bipolar	ADV
ejpam-5699	1	33	-	-	PUNCT
ejpam-5699	1	34	valued	value	VERB
ejpam-5699	1	35	intuitionistic	intuitionistic	ADJ
ejpam-5699	1	36	fuzzy	fuzzy	ADJ
ejpam-5699	1	37	positive	positive	ADJ
ejpam-5699	1	38	implicative	implicative	ADJ
ejpam-5699	1	39	ideals	ideal	NOUN
ejpam-5699	1	40	in	in	ADP
ejpam-5699	1	41	bck	bck	PROPN
ejpam-5699	1	42	-	-	PUNCT
ejpam-5699	1	43	algebras	algebras	PROPN
ejpam-5699	1	44	d.	d.	PROPN
ejpam-5699	1	45	ramesh1	ramesh1	PROPN
ejpam-5699	1	46	,	,	PUNCT
ejpam-5699	1	47	shake	shake	VERB
ejpam-5699	1	48	baji2	baji2	NOUN
ejpam-5699	1	49	,	,	PUNCT
ejpam-5699	1	50	aiyared	aiyare	VERB
ejpam-5699	1	51	iampan3,∗	iampan3,∗	NOUN
ejpam-5699	1	52	,	,	PUNCT
ejpam-5699	1	53	r.	r.	PROPN
ejpam-5699	1	54	durga	durga	PROPN
ejpam-5699	1	55	prasad4	prasad4	PROPN
ejpam-5699	1	56	,	,	PUNCT
ejpam-5699	1	57	b.	b.	PROPN
ejpam-5699	1	58	satyanarayana5	satyanarayana5	NOUN
ejpam-5699	2	1	1	1	NUM
ejpam-5699	2	2	department	department	NOUN
ejpam-5699	2	3	of	of	ADP
ejpam-5699	2	4	engineering	engineering	NOUN
ejpam-5699	2	5	mathematics	mathematic	NOUN
ejpam-5699	2	6	,	,	PUNCT
ejpam-5699	2	7	college	college	NOUN
ejpam-5699	2	8	of	of	ADP
ejpam-5699	2	9	engineering	engineering	PROPN
ejpam-5699	2	10	,	,	PUNCT
ejpam-5699	2	11	koneru	koneru	PROPN
ejpam-5699	2	12	lakshmaiah	lakshmaiah	PROPN
ejpam-5699	2	13	education	education	PROPN
ejpam-5699	2	14	foundation	foundation	PROPN
ejpam-5699	2	15	,	,	PUNCT
ejpam-5699	2	16	vaddeswaram	vaddeswaram	PROPN
ejpam-5699	2	17	,	,	PUNCT
ejpam-5699	2	18	andhra	andhra	PROPN
ejpam-5699	2	19	pradesh-522302	pradesh-522302	NOUN
ejpam-5699	2	20	,	,	PUNCT
ejpam-5699	2	21	india	india	PROPN
ejpam-5699	2	22	2	2	NUM
ejpam-5699	2	23	department	department	NOUN
ejpam-5699	2	24	of	of	ADP
ejpam-5699	2	25	mathematics	mathematic	NOUN
ejpam-5699	2	26	,	,	PUNCT
ejpam-5699	2	27	sir	sir	PROPN
ejpam-5699	2	28	c.r	c.r	PROPN
ejpam-5699	2	29	.	.	PROPN
ejpam-5699	2	30	reddy	reddy	PROPN
ejpam-5699	2	31	college	college	PROPN
ejpam-5699	2	32	of	of	ADP
ejpam-5699	2	33	engineering	engineering	NOUN
ejpam-5699	2	34	,	,	PUNCT
ejpam-5699	2	35	eluru-534007	eluru-534007	NOUN
ejpam-5699	2	36	,	,	PUNCT
ejpam-5699	2	37	andhra	andhra	PROPN
ejpam-5699	2	38	pradesh	pradesh	PROPN
ejpam-5699	2	39	,	,	PUNCT
ejpam-5699	2	40	india	india	PROPN
ejpam-5699	2	41	3	3	PROPN
ejpam-5699	2	42	department	department	PROPN
ejpam-5699	2	43	of	of	ADP
ejpam-5699	2	44	mathematics	mathematic	NOUN
ejpam-5699	2	45	,	,	PUNCT
ejpam-5699	2	46	school	school	NOUN
ejpam-5699	2	47	of	of	ADP
ejpam-5699	2	48	science	science	NOUN
ejpam-5699	2	49	,	,	PUNCT
ejpam-5699	2	50	university	university	NOUN
ejpam-5699	2	51	of	of	ADP
ejpam-5699	2	52	phayao	phayao	NOUN
ejpam-5699	2	53	,	,	PUNCT
ejpam-5699	2	54	mae	mae	PROPN
ejpam-5699	2	55	ka	ka	PROPN
ejpam-5699	2	56	,	,	PUNCT
ejpam-5699	2	57	mueang	mueang	PROPN
ejpam-5699	2	58	,	,	PUNCT
ejpam-5699	2	59	phayao	phayao	NOUN
ejpam-5699	2	60	56000	56000	NUM
ejpam-5699	2	61	,	,	PUNCT
ejpam-5699	2	62	thailand	thailand	PROPN
ejpam-5699	2	63	4	4	NUM
ejpam-5699	2	64	department	department	NOUN
ejpam-5699	2	65	of	of	ADP
ejpam-5699	2	66	mathematics	mathematic	NOUN
ejpam-5699	2	67	,	,	PUNCT
ejpam-5699	2	68	kg	kg	PROPN
ejpam-5699	2	69	reddy	reddy	PROPN
ejpam-5699	2	70	college	college	PROPN
ejpam-5699	2	71	of	of	ADP
ejpam-5699	2	72	engineering	engineering	NOUN
ejpam-5699	2	73	and	and	CCONJ
ejpam-5699	2	74	technology	technology	NOUN
ejpam-5699	2	75	,	,	PUNCT
ejpam-5699	2	76	hyderabad	hyderabad	PROPN
ejpam-5699	2	77	,	,	PUNCT
ejpam-5699	2	78	telangana-501504	telangana-501504	NOUN
ejpam-5699	2	79	,	,	PUNCT
ejpam-5699	2	80	india	india	PROPN
ejpam-5699	2	81	5	5	NUM
ejpam-5699	2	82	department	department	NOUN
ejpam-5699	2	83	of	of	ADP
ejpam-5699	2	84	mathematics	mathematic	NOUN
ejpam-5699	2	85	,	,	PUNCT
ejpam-5699	2	86	acharya	acharya	PROPN
ejpam-5699	2	87	nagarjuna	nagarjuna	PROPN
ejpam-5699	2	88	university	university	PROPN
ejpam-5699	2	89	,	,	PUNCT
ejpam-5699	2	90	nagarjuna	nagarjuna	PROPN
ejpam-5699	2	91	nagar	nagar	PROPN
ejpam-5699	2	92	,	,	PUNCT
ejpam-5699	2	93	guntur-522510	guntur-522510	PROPN
ejpam-5699	2	94	,	,	PUNCT
ejpam-5699	2	95	andhra	andhra	PROPN
ejpam-5699	2	96	pradesh	pradesh	PROPN
ejpam-5699	2	97	,	,	PUNCT
ejpam-5699	2	98	india	india	PROPN
ejpam-5699	2	99	abstract	abstract	NOUN
ejpam-5699	2	100	.	.	PUNCT
ejpam-5699	3	1	this	this	DET
ejpam-5699	3	2	study	study	NOUN
ejpam-5699	3	3	develops	develop	VERB
ejpam-5699	3	4	a	a	DET
ejpam-5699	3	5	novel	novel	ADJ
ejpam-5699	3	6	framework	framework	NOUN
ejpam-5699	3	7	for	for	ADP
ejpam-5699	3	8	bipolar	bipolar	ADV
ejpam-5699	3	9	-	-	PUNCT
ejpam-5699	3	10	valued	value	VERB
ejpam-5699	3	11	intuitionistic	intuitionistic	ADJ
ejpam-5699	3	12	fuzzy	fuzzy	ADJ
ejpam-5699	3	13	positive	positive	ADJ
ejpam-5699	3	14	implicative	implicative	ADJ
ejpam-5699	3	15	ideals	ideal	NOUN
ejpam-5699	3	16	(	(	PUNCT
ejpam-5699	3	17	bpvifpiis	bpvifpiis	ADJ
ejpam-5699	3	18	)	)	PUNCT
ejpam-5699	3	19	in	in	ADP
ejpam-5699	3	20	bck	bck	NOUN
ejpam-5699	3	21	-	-	PUNCT
ejpam-5699	3	22	algebras	algebras	PROPN
ejpam-5699	3	23	by	by	ADP
ejpam-5699	3	24	integrating	integrate	VERB
ejpam-5699	3	25	bipolar	bipolar	ADJ
ejpam-5699	3	26	-	-	PUNCT
ejpam-5699	3	27	valued	value	VERB
ejpam-5699	3	28	intuitionistic	intuitionistic	ADJ
ejpam-5699	3	29	fuzzy	fuzzy	ADJ
ejpam-5699	3	30	set	set	NOUN
ejpam-5699	3	31	theory	theory	NOUN
ejpam-5699	3	32	with	with	ADP
ejpam-5699	3	33	algebraic	algebraic	ADJ
ejpam-5699	3	34	structures	structure	NOUN
ejpam-5699	3	35	.	.	PUNCT
ejpam-5699	4	1	the	the	DET
ejpam-5699	4	2	primary	primary	ADJ
ejpam-5699	4	3	objective	objective	NOUN
ejpam-5699	4	4	is	be	AUX
ejpam-5699	4	5	to	to	PART
ejpam-5699	4	6	define	define	VERB
ejpam-5699	4	7	and	and	CCONJ
ejpam-5699	4	8	explore	explore	VERB
ejpam-5699	4	9	the	the	DET
ejpam-5699	4	10	properties	property	NOUN
ejpam-5699	4	11	of	of	ADP
ejpam-5699	4	12	bpvifpiis	bpvifpiis	ADJ
ejpam-5699	4	13	in	in	ADP
ejpam-5699	4	14	bck	bck	PROPN
ejpam-5699	4	15	-	-	PUNCT
ejpam-5699	4	16	algebras	algebras	X
ejpam-5699	4	17	,	,	PUNCT
ejpam-5699	4	18	providing	provide	VERB
ejpam-5699	4	19	rigorous	rigorous	ADJ
ejpam-5699	4	20	theoretical	theoretical	ADJ
ejpam-5699	4	21	foundations	foundation	NOUN
ejpam-5699	4	22	supported	support	VERB
ejpam-5699	4	23	by	by	ADP
ejpam-5699	4	24	illustrative	illustrative	ADJ
ejpam-5699	4	25	examples	example	NOUN
ejpam-5699	4	26	.	.	PUNCT
ejpam-5699	5	1	key	key	ADJ
ejpam-5699	5	2	conditions	condition	NOUN
ejpam-5699	5	3	under	under	ADP
ejpam-5699	5	4	which	which	PRON
ejpam-5699	5	5	a	a	DET
ejpam-5699	5	6	bipolar	bipolar	ADV
ejpam-5699	5	7	-	-	PUNCT
ejpam-5699	5	8	valued	value	VERB
ejpam-5699	5	9	intuitionistic	intuitionistic	ADJ
ejpam-5699	5	10	fuzzy	fuzzy	ADJ
ejpam-5699	5	11	set	set	NOUN
ejpam-5699	5	12	qualifies	qualifie	NOUN
ejpam-5699	5	13	as	as	ADP
ejpam-5699	5	14	a	a	DET
ejpam-5699	5	15	bpvifpii	bpvifpii	NOUN
ejpam-5699	5	16	are	be	AUX
ejpam-5699	5	17	established	establish	VERB
ejpam-5699	5	18	.	.	PUNCT
ejpam-5699	6	1	the	the	DET
ejpam-5699	6	2	findings	finding	NOUN
ejpam-5699	6	3	reveal	reveal	VERB
ejpam-5699	6	4	significant	significant	ADJ
ejpam-5699	6	5	connections	connection	NOUN
ejpam-5699	6	6	between	between	ADP
ejpam-5699	6	7	bpvifpiis	bpvifpiis	ADJ
ejpam-5699	6	8	and	and	CCONJ
ejpam-5699	6	9	other	other	ADJ
ejpam-5699	6	10	fuzzy	fuzzy	ADJ
ejpam-5699	6	11	ideals	ideal	NOUN
ejpam-5699	6	12	,	,	PUNCT
ejpam-5699	6	13	highlighting	highlight	VERB
ejpam-5699	6	14	their	their	PRON
ejpam-5699	6	15	role	role	NOUN
ejpam-5699	6	16	in	in	ADP
ejpam-5699	6	17	advancing	advance	VERB
ejpam-5699	6	18	the	the	DET
ejpam-5699	6	19	understanding	understanding	NOUN
ejpam-5699	6	20	of	of	ADP
ejpam-5699	6	21	uncertainty	uncertainty	NOUN
ejpam-5699	6	22	and	and	CCONJ
ejpam-5699	6	23	algebraic	algebraic	ADJ
ejpam-5699	6	24	reasoning	reasoning	NOUN
ejpam-5699	6	25	.	.	PUNCT
ejpam-5699	7	1	this	this	DET
ejpam-5699	7	2	research	research	NOUN
ejpam-5699	7	3	opens	open	VERB
ejpam-5699	7	4	avenues	avenue	NOUN
ejpam-5699	7	5	for	for	ADP
ejpam-5699	7	6	further	further	ADJ
ejpam-5699	7	7	exploration	exploration	NOUN
ejpam-5699	7	8	of	of	ADP
ejpam-5699	7	9	bipolar	bipolar	ADJ
ejpam-5699	7	10	fuzzy	fuzzy	ADJ
ejpam-5699	7	11	structures	structure	NOUN
ejpam-5699	7	12	in	in	ADP
ejpam-5699	7	13	algebra	algebra	NOUN
ejpam-5699	7	14	and	and	CCONJ
ejpam-5699	7	15	their	their	PRON
ejpam-5699	7	16	practical	practical	ADJ
ejpam-5699	7	17	implications	implication	NOUN
ejpam-5699	7	18	in	in	ADP
ejpam-5699	7	19	decision	decision	NOUN
ejpam-5699	7	20	-	-	PUNCT
ejpam-5699	7	21	making	make	VERB
ejpam-5699	7	22	processes	process	NOUN
ejpam-5699	7	23	involving	involve	VERB
ejpam-5699	7	24	uncertain	uncertain	ADJ
ejpam-5699	7	25	data	datum	NOUN
ejpam-5699	7	26	.	.	PUNCT
ejpam-5699	8	1	2020	2020	NUM
ejpam-5699	8	2	mathematics	mathematics	PROPN
ejpam-5699	8	3	subject	subject	NOUN
ejpam-5699	8	4	classifications	classification	NOUN
ejpam-5699	8	5	:	:	PUNCT
ejpam-5699	8	6	06f35	06f35	NUM
ejpam-5699	8	7	;	;	PUNCT
ejpam-5699	8	8	03e72	03e72	NUM
ejpam-5699	8	9	key	key	ADJ
ejpam-5699	8	10	words	word	NOUN
ejpam-5699	8	11	and	and	CCONJ
ejpam-5699	8	12	phrases	phrase	NOUN
ejpam-5699	8	13	:	:	PUNCT
ejpam-5699	8	14	bipolar	bipolar	ADJ
ejpam-5699	8	15	-	-	PUNCT
ejpam-5699	8	16	valued	value	VERB
ejpam-5699	8	17	fuzzy	fuzzy	ADJ
ejpam-5699	8	18	set	set	NOUN
ejpam-5699	8	19	(	(	PUNCT
ejpam-5699	8	20	bpvfs	bpvfs	NOUN
ejpam-5699	8	21	)	)	PUNCT
ejpam-5699	8	22	,	,	PUNCT
ejpam-5699	8	23	bipolar	bipolar	ADJ
ejpam-5699	8	24	-	-	PUNCT
ejpam-5699	8	25	valued	value	VERB
ejpam-5699	8	26	intuitionistic	intuitionistic	ADJ
ejpam-5699	8	27	fuzzy	fuzzy	ADJ
ejpam-5699	8	28	set	set	NOUN
ejpam-5699	8	29	(	(	PUNCT
ejpam-5699	8	30	bpvifs	bpvifs	PROPN
ejpam-5699	8	31	)	)	PUNCT
ejpam-5699	8	32	,	,	PUNCT
ejpam-5699	8	33	bipolar	bipolar	ADJ
ejpam-5699	8	34	-	-	PUNCT
ejpam-5699	8	35	valued	value	VERB
ejpam-5699	8	36	intuitionistic	intuitionistic	ADJ
ejpam-5699	8	37	fuzzy	fuzzy	ADJ
ejpam-5699	8	38	ideal	ideal	NOUN
ejpam-5699	8	39	(	(	PUNCT
ejpam-5699	8	40	bpvifi	bpvifi	NOUN
ejpam-5699	8	41	)	)	PUNCT
ejpam-5699	8	42	,	,	PUNCT
ejpam-5699	8	43	bipolar	bipolar	ADJ
ejpam-5699	8	44	-	-	PUNCT
ejpam-5699	8	45	valued	value	VERB
ejpam-5699	8	46	intuitionistic	intuitionistic	ADJ
ejpam-5699	8	47	fuzzy	fuzzy	ADJ
ejpam-5699	8	48	positive	positive	ADJ
ejpam-5699	8	49	implicative	implicative	ADJ
ejpam-5699	8	50	ideal	ideal	NOUN
ejpam-5699	8	51	(	(	PUNCT
ejpam-5699	8	52	bpvifpii	bpvifpii	NOUN
ejpam-5699	8	53	)	)	PUNCT
ejpam-5699	8	54	∗corresponding	∗corresponde	VERB
ejpam-5699	8	55	author	author	NOUN
ejpam-5699	8	56	.	.	PUNCT
ejpam-5699	9	1	doi	doi	NOUN
ejpam-5699	9	2	:	:	PUNCT
ejpam-5699	9	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5699	https://doi.org/10.29020/nybg.ejpam.v18i1.5699	ADJ
ejpam-5699	9	4	email	email	NOUN
ejpam-5699	9	5	addresses	address	NOUN
ejpam-5699	9	6	:	:	PUNCT
ejpam-5699	9	7	ram.fuzzy@gmail.com	ram.fuzzy@gmail.com	PROPN
ejpam-5699	9	8	(	(	PUNCT
ejpam-5699	9	9	d.	d.	PROPN
ejpam-5699	9	10	ramesh	ramesh	PROPN
ejpam-5699	9	11	)	)	PUNCT
ejpam-5699	9	12	,	,	PUNCT
ejpam-5699	9	13	shakebaji6@gmail.com	shakebaji6@gmail.com	X
ejpam-5699	9	14	(	(	PUNCT
ejpam-5699	9	15	s.	s.	PROPN
ejpam-5699	9	16	baji	baji	PROPN
ejpam-5699	9	17	)	)	PUNCT
ejpam-5699	9	18	,	,	PUNCT
ejpam-5699	9	19	aiyared.ia@up.ac.th	aiyared.ia@up.ac.th	NOUN
ejpam-5699	9	20	(	(	PUNCT
ejpam-5699	9	21	a.	a.	NOUN
ejpam-5699	9	22	iampan	iampan	PROPN
ejpam-5699	9	23	)	)	PUNCT
ejpam-5699	9	24	,	,	PUNCT
ejpam-5699	9	25	durgaprasad.fuzzy@gmail.com	durgaprasad.fuzzy@gmail.com	X
ejpam-5699	9	26	(	(	PUNCT
ejpam-5699	9	27	r.	r.	PROPN
ejpam-5699	9	28	d.	d.	PROPN
ejpam-5699	9	29	prasad	prasad	PROPN
ejpam-5699	9	30	)	)	PUNCT
ejpam-5699	9	31	,	,	PUNCT
ejpam-5699	9	32	drbsn63@yahoo.co.in	drbsn63@yahoo.co.in	NOUN
ejpam-5699	9	33	(	(	PUNCT
ejpam-5699	9	34	b.	b.	PROPN
ejpam-5699	9	35	satyanarayana	satyanarayana	PROPN
ejpam-5699	9	36	)	)	PUNCT
ejpam-5699	9	37	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5699	10	1	1	1	NUM
ejpam-5699	10	2	copyright	copyright	NOUN
ejpam-5699	10	3	:	:	PUNCT
ejpam-5699	10	4	©	©	PROPN
ejpam-5699	10	5	2025	2025	NUM
ejpam-5699	10	6	the	the	DET
ejpam-5699	10	7	author(s	author(s	NOUN
ejpam-5699	10	8	)	)	PUNCT
ejpam-5699	10	9	.	.	PUNCT
ejpam-5699	11	1	(	(	PUNCT
ejpam-5699	11	2	cc	cc	NOUN
ejpam-5699	11	3	by	by	ADP
ejpam-5699	11	4	-	-	PUNCT
ejpam-5699	11	5	nc	nc	PROPN
ejpam-5699	11	6	4.0	4.0	NUM
ejpam-5699	11	7	)	)	PUNCT
ejpam-5699	11	8	d.	d.	PROPN
ejpam-5699	11	9	ramesh	ramesh	PROPN
ejpam-5699	11	10	et	et	PROPN
ejpam-5699	11	11	al	al	PROPN
ejpam-5699	11	12	.	.	PUNCT
ejpam-5699	11	13	/	/	SYM
ejpam-5699	11	14	eur	eur	PROPN
ejpam-5699	11	15	.	.	PUNCT
ejpam-5699	12	1	j.	j.	PROPN
ejpam-5699	12	2	pure	pure	PROPN
ejpam-5699	12	3	appl	appl	PROPN
ejpam-5699	12	4	.	.	PROPN
ejpam-5699	12	5	math	math	PROPN
ejpam-5699	12	6	,	,	PUNCT
ejpam-5699	12	7	18	18	NUM
ejpam-5699	12	8	(	(	PUNCT
ejpam-5699	12	9	1	1	NUM
ejpam-5699	12	10	)	)	PUNCT
ejpam-5699	12	11	(	(	PUNCT
ejpam-5699	12	12	2025	2025	NUM
ejpam-5699	12	13	)	)	PUNCT
ejpam-5699	12	14	,	,	PUNCT
ejpam-5699	12	15	5699	5699	NUM
ejpam-5699	12	16	2	2	NUM
ejpam-5699	12	17	of	of	ADP
ejpam-5699	12	18	20	20	NUM
ejpam-5699	12	19	1	1	NUM
ejpam-5699	12	20	.	.	PUNCT
ejpam-5699	13	1	introduction	introduction	NOUN
ejpam-5699	13	2	in	in	ADP
ejpam-5699	13	3	this	this	DET
ejpam-5699	13	4	article	article	NOUN
ejpam-5699	13	5	,	,	PUNCT
ejpam-5699	13	6	we	we	PRON
ejpam-5699	13	7	will	will	AUX
ejpam-5699	13	8	utilize	utilize	VERB
ejpam-5699	13	9	the	the	DET
ejpam-5699	13	10	following	follow	VERB
ejpam-5699	13	11	list	list	NOUN
ejpam-5699	13	12	of	of	ADP
ejpam-5699	13	13	abbreviations	abbreviation	NOUN
ejpam-5699	13	14	:	:	PUNCT
ejpam-5699	13	15	•	•	PUNCT
ejpam-5699	13	16	bck	bck	VERB
ejpam-5699	13	17	-	-	PUNCT
ejpam-5699	13	18	a	a	NOUN
ejpam-5699	13	19	:	:	PUNCT
ejpam-5699	13	20	bck	bck	NOUN
ejpam-5699	13	21	-	-	PUNCT
ejpam-5699	13	22	algebra	algebra	NOUN
ejpam-5699	13	23	•	•	NOUN
ejpam-5699	13	24	fs	fs	PROPN
ejpam-5699	13	25	:	:	PUNCT
ejpam-5699	13	26	fuzzy	fuzzy	ADJ
ejpam-5699	13	27	set	set	VERB
ejpam-5699	13	28	•	•	NUM
ejpam-5699	13	29	bpvfs	bpvfs	NOUN
ejpam-5699	13	30	:	:	PUNCT
ejpam-5699	13	31	bipolar	bipolar	ADJ
ejpam-5699	13	32	-	-	PUNCT
ejpam-5699	13	33	valued	value	VERB
ejpam-5699	13	34	fuzzy	fuzzy	ADJ
ejpam-5699	13	35	set	set	VERB
ejpam-5699	13	36	•	•	NUM
ejpam-5699	13	37	ifs	ifs	PROPN
ejpam-5699	13	38	:	:	PUNCT
ejpam-5699	13	39	intuitionistic	intuitionistic	ADJ
ejpam-5699	13	40	fuzzy	fuzzy	ADJ
ejpam-5699	13	41	set	set	VERB
ejpam-5699	13	42	•	•	PROPN
ejpam-5699	13	43	bpvifs	bpvif	NOUN
ejpam-5699	13	44	:	:	PUNCT
ejpam-5699	13	45	bipolar	bipolar	ADJ
ejpam-5699	13	46	-	-	PUNCT
ejpam-5699	13	47	valued	value	VERB
ejpam-5699	13	48	intuitionistic	intuitionistic	ADJ
ejpam-5699	13	49	fuzzy	fuzzy	ADJ
ejpam-5699	13	50	set	set	VERB
ejpam-5699	13	51	•	•	NUM
ejpam-5699	13	52	bpvifsa	bpvifsa	NOUN
ejpam-5699	13	53	:	:	PUNCT
ejpam-5699	13	54	bipolar	bipolar	ADJ
ejpam-5699	13	55	-	-	PUNCT
ejpam-5699	13	56	valued	value	VERB
ejpam-5699	13	57	intuitionistic	intuitionistic	ADJ
ejpam-5699	13	58	fuzzy	fuzzy	ADJ
ejpam-5699	13	59	subalgebra	subalgebra	NOUN
ejpam-5699	13	60	•	•	NOUN
ejpam-5699	13	61	bpvifi	bpvifi	NOUN
ejpam-5699	13	62	:	:	PUNCT
ejpam-5699	13	63	bipolar	bipolar	ADJ
ejpam-5699	13	64	-	-	PUNCT
ejpam-5699	13	65	valued	value	VERB
ejpam-5699	13	66	intuitionistic	intuitionistic	ADJ
ejpam-5699	13	67	fuzzy	fuzzy	ADJ
ejpam-5699	13	68	ideal	ideal	ADJ
ejpam-5699	13	69	•	•	NOUN
ejpam-5699	13	70	bpvifpii	bpvifpii	NOUN
ejpam-5699	13	71	:	:	PUNCT
ejpam-5699	13	72	bipolar	bipolar	ADJ
ejpam-5699	13	73	-	-	PUNCT
ejpam-5699	13	74	valued	value	VERB
ejpam-5699	13	75	intuitionistic	intuitionistic	ADJ
ejpam-5699	13	76	fuzzy	fuzzy	ADJ
ejpam-5699	13	77	positive	positive	ADJ
ejpam-5699	13	78	implicative	implicative	ADJ
ejpam-5699	13	79	ideal	ideal	NOUN
ejpam-5699	13	80	in	in	ADP
ejpam-5699	13	81	many	many	ADJ
ejpam-5699	13	82	practical	practical	ADJ
ejpam-5699	13	83	scenarios	scenario	NOUN
ejpam-5699	13	84	,	,	PUNCT
ejpam-5699	13	85	the	the	DET
ejpam-5699	13	86	handling	handling	NOUN
ejpam-5699	13	87	of	of	ADP
ejpam-5699	13	88	information	information	NOUN
ejpam-5699	13	89	and	and	CCONJ
ejpam-5699	13	90	the	the	DET
ejpam-5699	13	91	process	process	NOUN
ejpam-5699	13	92	of	of	ADP
ejpam-5699	13	93	decisionmaking	decisionmake	VERB
ejpam-5699	13	94	often	often	ADV
ejpam-5699	13	95	encounter	encounter	VERB
ejpam-5699	13	96	situations	situation	NOUN
ejpam-5699	13	97	where	where	SCONJ
ejpam-5699	13	98	data	datum	NOUN
ejpam-5699	13	99	or	or	CCONJ
ejpam-5699	13	100	results	result	NOUN
ejpam-5699	13	101	lack	lack	VERB
ejpam-5699	13	102	a	a	DET
ejpam-5699	13	103	clear	clear	ADJ
ejpam-5699	13	104	definition	definition	NOUN
ejpam-5699	13	105	.	.	PUNCT
ejpam-5699	14	1	this	this	DET
ejpam-5699	14	2	intrinsic	intrinsic	ADJ
ejpam-5699	14	3	absence	absence	NOUN
ejpam-5699	14	4	of	of	ADP
ejpam-5699	14	5	accuracy	accuracy	NOUN
ejpam-5699	14	6	and	and	CCONJ
ejpam-5699	14	7	precision	precision	NOUN
ejpam-5699	14	8	is	be	AUX
ejpam-5699	14	9	commonly	commonly	ADV
ejpam-5699	14	10	known	know	VERB
ejpam-5699	14	11	as	as	ADP
ejpam-5699	14	12	uncertainty	uncertainty	NOUN
ejpam-5699	14	13	.	.	PUNCT
ejpam-5699	15	1	uncertainty	uncertainty	NOUN
ejpam-5699	15	2	can	can	AUX
ejpam-5699	15	3	come	come	VERB
ejpam-5699	15	4	up	up	ADP
ejpam-5699	15	5	for	for	ADP
ejpam-5699	15	6	a	a	DET
ejpam-5699	15	7	few	few	ADJ
ejpam-5699	15	8	reasons	reason	NOUN
ejpam-5699	15	9	,	,	PUNCT
ejpam-5699	15	10	like	like	ADP
ejpam-5699	15	11	not	not	PART
ejpam-5699	15	12	having	have	VERB
ejpam-5699	15	13	all	all	DET
ejpam-5699	15	14	the	the	DET
ejpam-5699	15	15	data	datum	NOUN
ejpam-5699	15	16	,	,	PUNCT
ejpam-5699	15	17	mistakes	mistake	NOUN
ejpam-5699	15	18	in	in	ADP
ejpam-5699	15	19	object	object	NOUN
ejpam-5699	15	20	measurement	measurement	NOUN
ejpam-5699	15	21	,	,	PUNCT
ejpam-5699	15	22	errors	error	NOUN
ejpam-5699	15	23	in	in	ADP
ejpam-5699	15	24	collecting	collect	VERB
ejpam-5699	15	25	data	datum	NOUN
ejpam-5699	15	26	,	,	PUNCT
ejpam-5699	15	27	and	and	CCONJ
ejpam-5699	15	28	the	the	DET
ejpam-5699	15	29	natural	natural	ADJ
ejpam-5699	15	30	differences	difference	NOUN
ejpam-5699	15	31	in	in	ADP
ejpam-5699	15	32	complex	complex	ADJ
ejpam-5699	15	33	systems	system	NOUN
ejpam-5699	15	34	.	.	PUNCT
ejpam-5699	16	1	dealing	deal	VERB
ejpam-5699	16	2	with	with	ADP
ejpam-5699	16	3	uncertainty	uncertainty	NOUN
ejpam-5699	16	4	and	and	CCONJ
ejpam-5699	16	5	handling	handle	VERB
ejpam-5699	16	6	it	it	PRON
ejpam-5699	16	7	properly	properly	ADV
ejpam-5699	16	8	is	be	AUX
ejpam-5699	16	9	crucial	crucial	ADJ
ejpam-5699	16	10	for	for	ADP
ejpam-5699	16	11	making	make	VERB
ejpam-5699	16	12	good	good	ADJ
ejpam-5699	16	13	decisions	decision	NOUN
ejpam-5699	16	14	,	,	PUNCT
ejpam-5699	16	15	particularly	particularly	ADV
ejpam-5699	16	16	in	in	ADP
ejpam-5699	16	17	areas	area	NOUN
ejpam-5699	16	18	like	like	ADP
ejpam-5699	16	19	business	business	NOUN
ejpam-5699	16	20	,	,	PUNCT
ejpam-5699	16	21	engineering	engineering	NOUN
ejpam-5699	16	22	,	,	PUNCT
ejpam-5699	16	23	artificial	artificial	ADJ
ejpam-5699	16	24	intelligence	intelligence	NOUN
ejpam-5699	16	25	,	,	PUNCT
ejpam-5699	16	26	etc	etc	X
ejpam-5699	16	27	.	.	X
ejpam-5699	16	28	a	a	DET
ejpam-5699	16	29	very	very	ADV
ejpam-5699	16	30	effective	effective	ADJ
ejpam-5699	16	31	way	way	NOUN
ejpam-5699	16	32	to	to	PART
ejpam-5699	16	33	deal	deal	VERB
ejpam-5699	16	34	with	with	ADP
ejpam-5699	16	35	the	the	DET
ejpam-5699	16	36	challenge	challenge	NOUN
ejpam-5699	16	37	of	of	ADP
ejpam-5699	16	38	uncertainty	uncertainty	NOUN
ejpam-5699	16	39	is	be	AUX
ejpam-5699	16	40	through	through	ADP
ejpam-5699	16	41	the	the	DET
ejpam-5699	16	42	application	application	NOUN
ejpam-5699	16	43	of	of	ADP
ejpam-5699	16	44	fuzzy	fuzzy	ADJ
ejpam-5699	16	45	set	set	NOUN
ejpam-5699	16	46	theory	theory	NOUN
ejpam-5699	16	47	.	.	PUNCT
ejpam-5699	17	1	this	this	DET
ejpam-5699	17	2	idea	idea	NOUN
ejpam-5699	17	3	was	be	AUX
ejpam-5699	17	4	introduced	introduce	VERB
ejpam-5699	17	5	in	in	ADP
ejpam-5699	17	6	the	the	DET
ejpam-5699	17	7	mid-20th	mid-20th	NUM
ejpam-5699	17	8	century	century	NOUN
ejpam-5699	17	9	by	by	ADP
ejpam-5699	17	10	zadeh	zadeh	PROPN
ejpam-5699	18	1	[	[	X
ejpam-5699	18	2	31	31	NUM
ejpam-5699	18	3	]	]	PUNCT
ejpam-5699	18	4	.	.	PUNCT
ejpam-5699	19	1	this	this	DET
ejpam-5699	19	2	theory	theory	NOUN
ejpam-5699	19	3	is	be	AUX
ejpam-5699	19	4	like	like	ADP
ejpam-5699	19	5	a	a	DET
ejpam-5699	19	6	mathematical	mathematical	ADJ
ejpam-5699	19	7	tool	tool	NOUN
ejpam-5699	19	8	that	that	PRON
ejpam-5699	19	9	helps	help	VERB
ejpam-5699	19	10	us	we	PRON
ejpam-5699	19	11	handle	handle	VERB
ejpam-5699	19	12	uncertainty	uncertainty	NOUN
ejpam-5699	19	13	and	and	CCONJ
ejpam-5699	19	14	imprecision	imprecision	NOUN
ejpam-5699	19	15	in	in	ADP
ejpam-5699	19	16	a	a	DET
ejpam-5699	19	17	neat	neat	ADJ
ejpam-5699	19	18	and	and	CCONJ
ejpam-5699	19	19	structured	structured	ADJ
ejpam-5699	19	20	way	way	NOUN
ejpam-5699	19	21	.	.	PUNCT
ejpam-5699	20	1	research	research	NOUN
ejpam-5699	20	2	on	on	ADP
ejpam-5699	20	3	bck	bck	PROPN
ejpam-5699	20	4	/	/	SYM
ejpam-5699	20	5	bci	bci	PROPN
ejpam-5699	20	6	algebras	algebra	NOUN
ejpam-5699	20	7	was	be	AUX
ejpam-5699	20	8	initiated	initiate	VERB
ejpam-5699	20	9	by	by	ADP
ejpam-5699	20	10	imai	imai	PROPN
ejpam-5699	20	11	and	and	CCONJ
ejpam-5699	20	12	iséki	iséki	NUM
ejpam-5699	21	1	[	[	X
ejpam-5699	21	2	6	6	NUM
ejpam-5699	21	3	,	,	PUNCT
ejpam-5699	21	4	7	7	NUM
ejpam-5699	21	5	]	]	PUNCT
ejpam-5699	21	6	in	in	ADP
ejpam-5699	21	7	1966	1966	NUM
ejpam-5699	21	8	,	,	PUNCT
ejpam-5699	21	9	as	as	SCONJ
ejpam-5699	21	10	evidenced	evidence	VERB
ejpam-5699	21	11	by	by	ADP
ejpam-5699	21	12	their	their	PRON
ejpam-5699	21	13	work	work	NOUN
ejpam-5699	21	14	on	on	ADP
ejpam-5699	21	15	set	set	NOUN
ejpam-5699	21	16	-	-	PUNCT
ejpam-5699	21	17	theoretic	theoretic	NOUN
ejpam-5699	21	18	difference	difference	NOUN
ejpam-5699	21	19	and	and	CCONJ
ejpam-5699	21	20	propositional	propositional	ADJ
ejpam-5699	21	21	logics	logic	NOUN
ejpam-5699	21	22	.	.	PUNCT
ejpam-5699	22	1	several	several	ADJ
ejpam-5699	22	2	researchers	researcher	NOUN
ejpam-5699	22	3	,	,	PUNCT
ejpam-5699	22	4	including	include	VERB
ejpam-5699	22	5	jun	jun	PROPN
ejpam-5699	22	6	(	(	PUNCT
ejpam-5699	22	7	[	[	X
ejpam-5699	22	8	11	11	NUM
ejpam-5699	22	9	,	,	PUNCT
ejpam-5699	22	10	21	21	NUM
ejpam-5699	22	11	]	]	PUNCT
ejpam-5699	22	12	)	)	PUNCT
ejpam-5699	22	13	,	,	PUNCT
ejpam-5699	22	14	liu	liu	PROPN
ejpam-5699	23	1	[	[	X
ejpam-5699	23	2	18	18	NUM
ejpam-5699	23	3	]	]	PUNCT
ejpam-5699	23	4	,	,	PUNCT
ejpam-5699	23	5	and	and	CCONJ
ejpam-5699	23	6	lee	lee	PROPN
ejpam-5699	24	1	[	[	X
ejpam-5699	24	2	16	16	NUM
ejpam-5699	24	3	]	]	PUNCT
ejpam-5699	24	4	,	,	PUNCT
ejpam-5699	24	5	have	have	AUX
ejpam-5699	24	6	extensively	extensively	ADV
ejpam-5699	24	7	explored	explore	VERB
ejpam-5699	24	8	the	the	DET
ejpam-5699	24	9	fuzzy	fuzzy	ADJ
ejpam-5699	24	10	structures	structure	NOUN
ejpam-5699	24	11	inherent	inherent	ADJ
ejpam-5699	24	12	in	in	ADP
ejpam-5699	24	13	bck	bck	PROPN
ejpam-5699	24	14	/	/	SYM
ejpam-5699	24	15	bci	bci	PROPN
ejpam-5699	24	16	algebras	algebra	NOUN
ejpam-5699	24	17	.	.	PUNCT
ejpam-5699	25	1	others	other	NOUN
ejpam-5699	25	2	(	(	PUNCT
ejpam-5699	25	3	[	[	X
ejpam-5699	25	4	5	5	NUM
ejpam-5699	25	5	,	,	PUNCT
ejpam-5699	25	6	8	8	NUM
ejpam-5699	25	7	,	,	PUNCT
ejpam-5699	25	8	17	17	NUM
ejpam-5699	25	9	,	,	PUNCT
ejpam-5699	25	10	27	27	NUM
ejpam-5699	25	11	,	,	PUNCT
ejpam-5699	25	12	28	28	NUM
ejpam-5699	25	13	]	]	PUNCT
ejpam-5699	25	14	)	)	PUNCT
ejpam-5699	25	15	have	have	AUX
ejpam-5699	25	16	also	also	ADV
ejpam-5699	25	17	made	make	VERB
ejpam-5699	25	18	significant	significant	ADJ
ejpam-5699	25	19	contributions	contribution	NOUN
ejpam-5699	25	20	to	to	ADP
ejpam-5699	25	21	this	this	DET
ejpam-5699	25	22	field	field	NOUN
ejpam-5699	25	23	from	from	ADP
ejpam-5699	25	24	various	various	ADJ
ejpam-5699	25	25	perspectives	perspective	NOUN
ejpam-5699	25	26	on	on	ADP
ejpam-5699	25	27	various	various	ADJ
ejpam-5699	25	28	branches	branch	NOUN
ejpam-5699	25	29	of	of	ADP
ejpam-5699	25	30	algebra	algebra	PROPN
ejpam-5699	25	31	.	.	PUNCT
ejpam-5699	26	1	bpvfss	bpvfss	ADJ
ejpam-5699	26	2	(	(	PUNCT
ejpam-5699	26	3	bpvfs	bpvfs	NOUN
ejpam-5699	26	4	)	)	PUNCT
ejpam-5699	26	5	,	,	PUNCT
ejpam-5699	26	6	an	an	DET
ejpam-5699	26	7	extension	extension	NOUN
ejpam-5699	26	8	of	of	ADP
ejpam-5699	26	9	fuzzy	fuzzy	ADJ
ejpam-5699	26	10	sets	set	NOUN
ejpam-5699	26	11	(	(	PUNCT
ejpam-5699	26	12	[	[	X
ejpam-5699	26	13	32	32	NUM
ejpam-5699	26	14	,	,	PUNCT
ejpam-5699	26	15	33	33	NUM
ejpam-5699	26	16	]	]	PUNCT
ejpam-5699	26	17	)	)	PUNCT
ejpam-5699	26	18	,	,	PUNCT
ejpam-5699	26	19	are	be	AUX
ejpam-5699	26	20	designed	design	VERB
ejpam-5699	26	21	to	to	PART
ejpam-5699	26	22	address	address	VERB
ejpam-5699	26	23	scenarios	scenario	NOUN
ejpam-5699	26	24	in	in	ADP
ejpam-5699	26	25	which	which	PRON
ejpam-5699	26	26	both	both	CCONJ
ejpam-5699	26	27	negative	negative	ADJ
ejpam-5699	26	28	and	and	CCONJ
ejpam-5699	26	29	positive	positive	ADJ
ejpam-5699	26	30	membership	membership	NOUN
ejpam-5699	26	31	degrees	degree	NOUN
ejpam-5699	26	32	hold	hold	VERB
ejpam-5699	26	33	significance	significance	NOUN
ejpam-5699	26	34	.	.	PUNCT
ejpam-5699	27	1	this	this	DET
ejpam-5699	27	2	extension	extension	NOUN
ejpam-5699	27	3	allows	allow	VERB
ejpam-5699	27	4	us	we	PRON
ejpam-5699	27	5	to	to	PART
ejpam-5699	27	6	consider	consider	VERB
ejpam-5699	27	7	the	the	DET
ejpam-5699	27	8	negative	negative	ADJ
ejpam-5699	27	9	and	and	CCONJ
ejpam-5699	27	10	positive	positive	ADJ
ejpam-5699	27	11	aspects	aspect	NOUN
ejpam-5699	27	12	of	of	ADP
ejpam-5699	27	13	membership	membership	NOUN
ejpam-5699	27	14	and	and	CCONJ
ejpam-5699	27	15	identify	identify	VERB
ejpam-5699	27	16	their	their	PRON
ejpam-5699	27	17	respective	respective	ADJ
ejpam-5699	27	18	roles	role	NOUN
ejpam-5699	27	19	.	.	PUNCT
ejpam-5699	28	1	unlike	unlike	ADP
ejpam-5699	28	2	a	a	DET
ejpam-5699	28	3	conventional	conventional	ADJ
ejpam-5699	28	4	fuzzy	fuzzy	ADJ
ejpam-5699	28	5	set	set	NOUN
ejpam-5699	28	6	,	,	PUNCT
ejpam-5699	28	7	where	where	SCONJ
ejpam-5699	28	8	an	an	DET
ejpam-5699	28	9	element	element	NOUN
ejpam-5699	28	10	is	be	AUX
ejpam-5699	28	11	either	either	CCONJ
ejpam-5699	28	12	entirely	entirely	ADV
ejpam-5699	28	13	connected	connect	VERB
ejpam-5699	28	14	(	(	PUNCT
ejpam-5699	28	15	membership	membership	NOUN
ejpam-5699	28	16	value	value	NOUN
ejpam-5699	28	17	=	=	NOUN
ejpam-5699	28	18	1	1	NUM
ejpam-5699	28	19	)	)	PUNCT
ejpam-5699	28	20	or	or	CCONJ
ejpam-5699	28	21	partially	partially	ADV
ejpam-5699	28	22	connected	connect	VERB
ejpam-5699	28	23	(	(	PUNCT
ejpam-5699	28	24	membership	membership	NOUN
ejpam-5699	28	25	value	value	NOUN
ejpam-5699	28	26	=	=	SYM
ejpam-5699	28	27	(	(	PUNCT
ejpam-5699	28	28	0	0	NUM
ejpam-5699	28	29	,	,	PUNCT
ejpam-5699	28	30	1	1	NUM
ejpam-5699	28	31	)	)	PUNCT
ejpam-5699	28	32	)	)	PUNCT
ejpam-5699	28	33	,	,	PUNCT
ejpam-5699	28	34	bpvfss	bpvfss	NOUN
ejpam-5699	28	35	offer	offer	VERB
ejpam-5699	28	36	a	a	DET
ejpam-5699	28	37	more	more	ADV
ejpam-5699	28	38	detailed	detailed	ADJ
ejpam-5699	28	39	representation	representation	NOUN
ejpam-5699	28	40	.	.	PUNCT
ejpam-5699	29	1	alternatively	alternatively	ADV
ejpam-5699	29	2	,	,	PUNCT
ejpam-5699	29	3	a	a	DET
ejpam-5699	29	4	bpvfs	bpvfs	NOUN
ejpam-5699	29	5	permits	permit	VERB
ejpam-5699	29	6	the	the	DET
ejpam-5699	29	7	assignment	assignment	NOUN
ejpam-5699	29	8	of	of	ADP
ejpam-5699	29	9	degrees	degree	NOUN
ejpam-5699	29	10	to	to	ADP
ejpam-5699	29	11	members	member	NOUN
ejpam-5699	29	12	within	within	ADP
ejpam-5699	29	13	the	the	DET
ejpam-5699	29	14	range	range	NOUN
ejpam-5699	29	15	of	of	ADP
ejpam-5699	29	16	[	[	X
ejpam-5699	29	17	−1	−1	NOUN
ejpam-5699	29	18	,	,	PUNCT
ejpam-5699	29	19	1	1	NUM
ejpam-5699	29	20	]	]	PUNCT
ejpam-5699	29	21	.	.	PUNCT
ejpam-5699	30	1	these	these	DET
ejpam-5699	30	2	degrees	degree	NOUN
ejpam-5699	30	3	signify	signify	VERB
ejpam-5699	30	4	the	the	DET
ejpam-5699	30	5	extent	extent	NOUN
ejpam-5699	30	6	to	to	PART
ejpam-5699	30	7	which	which	PRON
ejpam-5699	30	8	an	an	DET
ejpam-5699	30	9	element	element	NOUN
ejpam-5699	30	10	is	be	AUX
ejpam-5699	30	11	connected	connect	VERB
ejpam-5699	30	12	positively	positively	ADV
ejpam-5699	30	13	or	or	CCONJ
ejpam-5699	30	14	negatively	negatively	ADV
ejpam-5699	30	15	to	to	ADP
ejpam-5699	30	16	the	the	DET
ejpam-5699	30	17	set	set	NOUN
ejpam-5699	30	18	.	.	PUNCT
ejpam-5699	31	1	this	this	DET
ejpam-5699	31	2	extension	extension	NOUN
ejpam-5699	31	3	offers	offer	VERB
ejpam-5699	31	4	a	a	DET
ejpam-5699	31	5	complete	complete	ADJ
ejpam-5699	31	6	view	view	NOUN
ejpam-5699	31	7	of	of	ADP
ejpam-5699	31	8	uncertain	uncertain	ADJ
ejpam-5699	31	9	and	and	CCONJ
ejpam-5699	31	10	changing	change	VERB
ejpam-5699	31	11	information	information	NOUN
ejpam-5699	31	12	,	,	PUNCT
ejpam-5699	31	13	particularly	particularly	ADV
ejpam-5699	31	14	valuable	valuable	ADJ
ejpam-5699	31	15	in	in	ADP
ejpam-5699	31	16	practical	practical	ADJ
ejpam-5699	31	17	scenarios	scenario	NOUN
ejpam-5699	31	18	where	where	SCONJ
ejpam-5699	31	19	both	both	DET
ejpam-5699	31	20	negative	negative	ADJ
ejpam-5699	31	21	and	and	CCONJ
ejpam-5699	31	22	positive	positive	ADJ
ejpam-5699	31	23	aspects	aspect	NOUN
ejpam-5699	31	24	matter	matter	NOUN
ejpam-5699	31	25	.	.	PUNCT
ejpam-5699	32	1	the	the	DET
ejpam-5699	32	2	concept	concept	NOUN
ejpam-5699	32	3	of	of	ADP
ejpam-5699	32	4	a	a	DET
ejpam-5699	32	5	bpvfs	bpvfs	NOUN
ejpam-5699	32	6	was	be	AUX
ejpam-5699	32	7	applied	apply	VERB
ejpam-5699	32	8	to	to	PART
ejpam-5699	32	9	study	study	VERB
ejpam-5699	32	10	different	different	ADJ
ejpam-5699	32	11	ideas	idea	NOUN
ejpam-5699	32	12	in	in	ADP
ejpam-5699	32	13	bck	bck	PROPN
ejpam-5699	32	14	/	/	SYM
ejpam-5699	32	15	bci	bci	NOUN
ejpam-5699	32	16	-	-	PUNCT
ejpam-5699	32	17	algebras	algebra	NOUN
ejpam-5699	32	18	,	,	PUNCT
ejpam-5699	32	19	like	like	ADP
ejpam-5699	32	20	a	a	DET
ejpam-5699	32	21	-	-	PUNCT
ejpam-5699	32	22	ideals	ideal	NOUN
ejpam-5699	32	23	of	of	ADP
ejpam-5699	32	24	bci	bci	NOUN
ejpam-5699	32	25	-	-	PUNCT
ejpam-5699	32	26	algebras	algebras	X
ejpam-5699	33	1	[	[	X
ejpam-5699	33	2	16	16	NUM
ejpam-5699	33	3	]	]	PUNCT
ejpam-5699	33	4	,	,	PUNCT
ejpam-5699	33	5	subalgebras	subalgebras	PROPN
ejpam-5699	33	6	and	and	CCONJ
ejpam-5699	33	7	ideals	ideal	NOUN
ejpam-5699	33	8	of	of	ADP
ejpam-5699	33	9	bck	bck	PROPN
ejpam-5699	33	10	/	/	SYM
ejpam-5699	33	11	bci	bci	NOUN
ejpam-5699	33	12	-	-	PUNCT
ejpam-5699	33	13	algebras	algebras	X
ejpam-5699	34	1	[	[	X
ejpam-5699	34	2	15	15	NUM
ejpam-5699	34	3	]	]	PUNCT
ejpam-5699	34	4	,	,	PUNCT
ejpam-5699	34	5	and	and	CCONJ
ejpam-5699	34	6	d.	d.	PROPN
ejpam-5699	34	7	ramesh	ramesh	PROPN
ejpam-5699	34	8	et	et	PROPN
ejpam-5699	34	9	al	al	PROPN
ejpam-5699	34	10	.	.	PUNCT
ejpam-5699	34	11	/	/	SYM
ejpam-5699	34	12	eur	eur	PROPN
ejpam-5699	34	13	.	.	PUNCT
ejpam-5699	35	1	j.	j.	PROPN
ejpam-5699	35	2	pure	pure	PROPN
ejpam-5699	35	3	appl	appl	PROPN
ejpam-5699	35	4	.	.	PROPN
ejpam-5699	35	5	math	math	PROPN
ejpam-5699	35	6	,	,	PUNCT
ejpam-5699	35	7	18	18	NUM
ejpam-5699	35	8	(	(	PUNCT
ejpam-5699	35	9	1	1	NUM
ejpam-5699	35	10	)	)	PUNCT
ejpam-5699	35	11	(	(	PUNCT
ejpam-5699	35	12	2025	2025	NUM
ejpam-5699	35	13	)	)	PUNCT
ejpam-5699	35	14	,	,	PUNCT
ejpam-5699	35	15	5699	5699	NUM
ejpam-5699	35	16	3	3	NUM
ejpam-5699	35	17	of	of	ADP
ejpam-5699	35	18	20	20	NUM
ejpam-5699	35	19	many	many	ADJ
ejpam-5699	35	20	others	other	NOUN
ejpam-5699	35	21	,	,	PUNCT
ejpam-5699	35	22	as	as	SCONJ
ejpam-5699	35	23	explained	explain	VERB
ejpam-5699	35	24	in	in	ADP
ejpam-5699	35	25	[	[	X
ejpam-5699	35	26	9	9	NUM
ejpam-5699	35	27	,	,	PUNCT
ejpam-5699	35	28	10	10	NUM
ejpam-5699	35	29	]	]	PUNCT
ejpam-5699	35	30	.	.	PUNCT
ejpam-5699	36	1	recent	recent	ADJ
ejpam-5699	36	2	research	research	NOUN
ejpam-5699	36	3	in	in	ADP
ejpam-5699	36	4	[	[	X
ejpam-5699	36	5	1	1	NUM
ejpam-5699	36	6	]	]	PUNCT
ejpam-5699	36	7	explores	explore	VERB
ejpam-5699	36	8	bipolar	bipolar	ADV
ejpam-5699	36	9	-	-	PUNCT
ejpam-5699	36	10	valued	value	VERB
ejpam-5699	36	11	fuzzy	fuzzy	ADJ
ejpam-5699	36	12	bci	bci	ADJ
ejpam-5699	36	13	-	-	ADJ
ejpam-5699	36	14	implicative	implicative	ADJ
ejpam-5699	36	15	ideals	ideal	NOUN
ejpam-5699	36	16	of	of	ADP
ejpam-5699	36	17	bci	bci	NOUN
ejpam-5699	36	18	-	-	PUNCT
ejpam-5699	36	19	algebras	algebras	X
ejpam-5699	36	20	.	.	PUNCT
ejpam-5699	37	1	muhiuddin	muhiuddin	PROPN
ejpam-5699	37	2	et	et	PROPN
ejpam-5699	37	3	al	al	PROPN
ejpam-5699	37	4	.	.	PUNCT
ejpam-5699	38	1	[	[	X
ejpam-5699	38	2	22	22	NUM
ejpam-5699	38	3	]	]	PUNCT
ejpam-5699	38	4	look	look	VERB
ejpam-5699	38	5	at	at	ADP
ejpam-5699	38	6	positive	positive	ADJ
ejpam-5699	38	7	implicative	implicative	ADJ
ejpam-5699	38	8	and	and	CCONJ
ejpam-5699	38	9	closed	closed	ADJ
ejpam-5699	38	10	bipolar	bipolar	ADV
ejpam-5699	38	11	-	-	PUNCT
ejpam-5699	38	12	valued	value	VERB
ejpam-5699	38	13	fuzzy	fuzzy	ADJ
ejpam-5699	38	14	ideals	ideal	NOUN
ejpam-5699	38	15	in	in	ADP
ejpam-5699	38	16	bck	bck	NOUN
ejpam-5699	38	17	-	-	PUNCT
ejpam-5699	38	18	as	as	ADP
ejpam-5699	38	19	.	.	PUNCT
ejpam-5699	39	1	many	many	ADJ
ejpam-5699	39	2	other	other	ADJ
ejpam-5699	39	3	scholars	scholar	NOUN
ejpam-5699	39	4	have	have	AUX
ejpam-5699	39	5	also	also	ADV
ejpam-5699	39	6	added	add	VERB
ejpam-5699	39	7	to	to	ADP
ejpam-5699	39	8	this	this	DET
ejpam-5699	39	9	field	field	NOUN
ejpam-5699	39	10	,	,	PUNCT
ejpam-5699	39	11	exploring	explore	VERB
ejpam-5699	39	12	different	different	ADJ
ejpam-5699	39	13	aspects	aspect	NOUN
ejpam-5699	39	14	of	of	ADP
ejpam-5699	39	15	algebra	algebra	NOUN
ejpam-5699	39	16	in	in	ADP
ejpam-5699	39	17	various	various	ADJ
ejpam-5699	39	18	ways	way	NOUN
ejpam-5699	39	19	(	(	PUNCT
ejpam-5699	39	20	[	[	X
ejpam-5699	39	21	12	12	NUM
ejpam-5699	39	22	,	,	PUNCT
ejpam-5699	39	23	13	13	NUM
ejpam-5699	39	24	,	,	PUNCT
ejpam-5699	39	25	23	23	NUM
ejpam-5699	39	26	,	,	PUNCT
ejpam-5699	39	27	25	25	NUM
ejpam-5699	39	28	,	,	PUNCT
ejpam-5699	39	29	29	29	NUM
ejpam-5699	39	30	]	]	PUNCT
ejpam-5699	39	31	)	)	PUNCT
ejpam-5699	39	32	.	.	PUNCT
ejpam-5699	40	1	after	after	ADP
ejpam-5699	40	2	presenting	present	VERB
ejpam-5699	40	3	the	the	DET
ejpam-5699	40	4	idea	idea	NOUN
ejpam-5699	40	5	of	of	ADP
ejpam-5699	40	6	the	the	DET
ejpam-5699	40	7	fuzzy	fuzzy	ADJ
ejpam-5699	40	8	set	set	NOUN
ejpam-5699	40	9	concept	concept	NOUN
ejpam-5699	40	10	,	,	PUNCT
ejpam-5699	40	11	many	many	ADJ
ejpam-5699	40	12	studies	study	NOUN
ejpam-5699	40	13	have	have	AUX
ejpam-5699	40	14	been	be	AUX
ejpam-5699	40	15	carried	carry	VERB
ejpam-5699	40	16	out	out	ADP
ejpam-5699	40	17	to	to	PART
ejpam-5699	40	18	investigate	investigate	VERB
ejpam-5699	40	19	the	the	DET
ejpam-5699	40	20	extension	extension	NOUN
ejpam-5699	40	21	of	of	ADP
ejpam-5699	40	22	this	this	DET
ejpam-5699	40	23	concept	concept	NOUN
ejpam-5699	40	24	.	.	PUNCT
ejpam-5699	41	1	in	in	ADP
ejpam-5699	41	2	1986	1986	NUM
ejpam-5699	41	3	,	,	PUNCT
ejpam-5699	41	4	atanasov	atanasov	NOUN
ejpam-5699	41	5	introduced	introduce	VERB
ejpam-5699	41	6	the	the	DET
ejpam-5699	41	7	idea	idea	NOUN
ejpam-5699	41	8	of	of	ADP
ejpam-5699	41	9	ifss	ifss	NOUN
ejpam-5699	41	10	,	,	PUNCT
ejpam-5699	41	11	representing	represent	VERB
ejpam-5699	41	12	an	an	DET
ejpam-5699	41	13	advancement	advancement	NOUN
ejpam-5699	41	14	in	in	ADP
ejpam-5699	41	15	fuzzy	fuzzy	ADJ
ejpam-5699	41	16	set	set	NOUN
ejpam-5699	41	17	theory	theory	NOUN
ejpam-5699	41	18	.	.	PUNCT
ejpam-5699	42	1	ezhilmaran	ezhilmaran	ADJ
ejpam-5699	42	2	and	and	CCONJ
ejpam-5699	42	3	shankar	shankar	PROPN
ejpam-5699	42	4	[	[	X
ejpam-5699	42	5	29	29	NUM
ejpam-5699	42	6	]	]	PUNCT
ejpam-5699	42	7	present	present	VERB
ejpam-5699	42	8	the	the	DET
ejpam-5699	42	9	idea	idea	NOUN
ejpam-5699	42	10	of	of	ADP
ejpam-5699	42	11	bpvifss	bpvifss	NOUN
ejpam-5699	42	12	.	.	PUNCT
ejpam-5699	43	1	this	this	DET
ejpam-5699	43	2	classification	classification	NOUN
ejpam-5699	43	3	of	of	ADP
ejpam-5699	43	4	fuzzy	fuzzy	ADJ
ejpam-5699	43	5	sets	set	NOUN
ejpam-5699	43	6	encompasses	encompass	VERB
ejpam-5699	43	7	not	not	PART
ejpam-5699	43	8	only	only	ADV
ejpam-5699	43	9	negative	negative	ADJ
ejpam-5699	43	10	and	and	CCONJ
ejpam-5699	43	11	positive	positive	ADJ
ejpam-5699	43	12	levels	level	NOUN
ejpam-5699	43	13	of	of	ADP
ejpam-5699	43	14	belongingness	belongingness	NOUN
ejpam-5699	43	15	but	but	CCONJ
ejpam-5699	43	16	also	also	ADV
ejpam-5699	43	17	negative	negative	ADJ
ejpam-5699	43	18	and	and	CCONJ
ejpam-5699	43	19	positive	positive	ADJ
ejpam-5699	43	20	levels	level	NOUN
ejpam-5699	43	21	of	of	ADP
ejpam-5699	43	22	non	non	ADJ
ejpam-5699	43	23	-	-	NOUN
ejpam-5699	43	24	belongingness	belongingness	ADJ
ejpam-5699	43	25	for	for	ADP
ejpam-5699	43	26	elements	element	NOUN
ejpam-5699	43	27	within	within	ADP
ejpam-5699	43	28	a	a	DET
ejpam-5699	43	29	given	give	VERB
ejpam-5699	43	30	set	set	NOUN
ejpam-5699	43	31	.	.	PUNCT
ejpam-5699	44	1	recently	recently	ADV
ejpam-5699	44	2	,	,	PUNCT
ejpam-5699	44	3	in	in	ADP
ejpam-5699	44	4	[	[	X
ejpam-5699	44	5	26	26	NUM
ejpam-5699	44	6	]	]	PUNCT
ejpam-5699	44	7	,	,	PUNCT
ejpam-5699	44	8	satyanarayana	satyanarayana	PROPN
ejpam-5699	44	9	et	et	PROPN
ejpam-5699	44	10	al	al	PROPN
ejpam-5699	44	11	.	.	PROPN
ejpam-5699	44	12	introduced	introduce	VERB
ejpam-5699	44	13	the	the	DET
ejpam-5699	44	14	concept	concept	NOUN
ejpam-5699	44	15	of	of	ADP
ejpam-5699	44	16	bpvifii	bpvifii	NOUN
ejpam-5699	44	17	in	in	ADP
ejpam-5699	44	18	bck	bck	PROPN
ejpam-5699	44	19	-	-	PUNCT
ejpam-5699	44	20	a.	a.	NOUN
ejpam-5699	44	21	the	the	DET
ejpam-5699	44	22	proposed	propose	VERB
ejpam-5699	44	23	theory	theory	NOUN
ejpam-5699	44	24	of	of	ADP
ejpam-5699	44	25	bipolar	bipolar	ADV
ejpam-5699	44	26	-	-	PUNCT
ejpam-5699	44	27	valued	value	VERB
ejpam-5699	44	28	intuitionistic	intuitionistic	ADJ
ejpam-5699	44	29	fuzzy	fuzzy	ADJ
ejpam-5699	44	30	positive	positive	ADJ
ejpam-5699	44	31	implicative	implicative	ADJ
ejpam-5699	44	32	ideals	ideal	NOUN
ejpam-5699	44	33	(	(	PUNCT
ejpam-5699	44	34	bpvifpiis	bpvifpiis	ADJ
ejpam-5699	44	35	)	)	PUNCT
ejpam-5699	44	36	in	in	ADP
ejpam-5699	44	37	bck	bck	PROPN
ejpam-5699	44	38	-	-	PUNCT
ejpam-5699	44	39	algebras	algebras	PROPN
ejpam-5699	44	40	is	be	AUX
ejpam-5699	44	41	motivated	motivate	VERB
ejpam-5699	44	42	by	by	ADP
ejpam-5699	44	43	the	the	DET
ejpam-5699	44	44	need	need	NOUN
ejpam-5699	44	45	to	to	PART
ejpam-5699	44	46	address	address	VERB
ejpam-5699	44	47	limitations	limitation	NOUN
ejpam-5699	44	48	in	in	ADP
ejpam-5699	44	49	existing	exist	VERB
ejpam-5699	44	50	frameworks	framework	NOUN
ejpam-5699	44	51	for	for	ADP
ejpam-5699	44	52	handling	handle	VERB
ejpam-5699	44	53	uncertainty	uncertainty	NOUN
ejpam-5699	44	54	in	in	ADP
ejpam-5699	44	55	algebraic	algebraic	ADJ
ejpam-5699	44	56	structures	structure	NOUN
ejpam-5699	44	57	.	.	PUNCT
ejpam-5699	45	1	traditional	traditional	ADJ
ejpam-5699	45	2	fuzzy	fuzzy	ADJ
ejpam-5699	45	3	and	and	CCONJ
ejpam-5699	45	4	intuitionistic	intuitionistic	ADJ
ejpam-5699	45	5	fuzzy	fuzzy	ADJ
ejpam-5699	45	6	set	set	NOUN
ejpam-5699	45	7	theories	theory	NOUN
ejpam-5699	45	8	provide	provide	VERB
ejpam-5699	45	9	tools	tool	NOUN
ejpam-5699	45	10	for	for	ADP
ejpam-5699	45	11	modeling	model	VERB
ejpam-5699	45	12	uncertainty	uncertainty	NOUN
ejpam-5699	45	13	,	,	PUNCT
ejpam-5699	45	14	yet	yet	CCONJ
ejpam-5699	45	15	they	they	PRON
ejpam-5699	45	16	often	often	ADV
ejpam-5699	45	17	fail	fail	VERB
ejpam-5699	45	18	to	to	PART
ejpam-5699	45	19	account	account	VERB
ejpam-5699	45	20	for	for	ADP
ejpam-5699	45	21	the	the	DET
ejpam-5699	45	22	dual	dual	ADJ
ejpam-5699	45	23	nature	nature	NOUN
ejpam-5699	45	24	of	of	ADP
ejpam-5699	45	25	positive	positive	ADJ
ejpam-5699	45	26	and	and	CCONJ
ejpam-5699	45	27	negative	negative	ADJ
ejpam-5699	45	28	membership	membership	NOUN
ejpam-5699	45	29	degrees	degree	VERB
ejpam-5699	45	30	simultaneously	simultaneously	ADV
ejpam-5699	45	31	.	.	PUNCT
ejpam-5699	46	1	this	this	DET
ejpam-5699	46	2	duality	duality	NOUN
ejpam-5699	46	3	becomes	become	VERB
ejpam-5699	46	4	crucial	crucial	ADJ
ejpam-5699	46	5	in	in	ADP
ejpam-5699	46	6	applications	application	NOUN
ejpam-5699	46	7	where	where	SCONJ
ejpam-5699	46	8	both	both	CCONJ
ejpam-5699	46	9	positive	positive	ADJ
ejpam-5699	46	10	and	and	CCONJ
ejpam-5699	46	11	negative	negative	ADJ
ejpam-5699	46	12	aspects	aspect	NOUN
ejpam-5699	46	13	of	of	ADP
ejpam-5699	46	14	membership	membership	NOUN
ejpam-5699	46	15	and	and	CCONJ
ejpam-5699	46	16	non	non	ADJ
ejpam-5699	46	17	-	-	ADJ
ejpam-5699	46	18	membership	membership	NOUN
ejpam-5699	46	19	must	must	AUX
ejpam-5699	46	20	be	be	AUX
ejpam-5699	46	21	analyzed	analyze	VERB
ejpam-5699	46	22	,	,	PUNCT
ejpam-5699	46	23	such	such	ADJ
ejpam-5699	46	24	as	as	ADP
ejpam-5699	46	25	in	in	ADP
ejpam-5699	46	26	decision	decision	NOUN
ejpam-5699	46	27	-	-	PUNCT
ejpam-5699	46	28	making	make	VERB
ejpam-5699	46	29	scenarios	scenario	NOUN
ejpam-5699	46	30	involving	involve	VERB
ejpam-5699	46	31	conflicting	conflicting	ADJ
ejpam-5699	46	32	or	or	CCONJ
ejpam-5699	46	33	imprecise	imprecise	ADJ
ejpam-5699	46	34	data	datum	NOUN
ejpam-5699	46	35	.	.	PUNCT
ejpam-5699	47	1	by	by	ADP
ejpam-5699	47	2	extending	extend	VERB
ejpam-5699	47	3	these	these	DET
ejpam-5699	47	4	concepts	concept	NOUN
ejpam-5699	47	5	into	into	ADP
ejpam-5699	47	6	the	the	DET
ejpam-5699	47	7	domain	domain	NOUN
ejpam-5699	47	8	of	of	ADP
ejpam-5699	47	9	bck	bck	PROPN
ejpam-5699	47	10	-	-	PUNCT
ejpam-5699	47	11	algebras	algebras	PROPN
ejpam-5699	47	12	,	,	PUNCT
ejpam-5699	47	13	the	the	DET
ejpam-5699	47	14	study	study	NOUN
ejpam-5699	47	15	aims	aim	VERB
ejpam-5699	47	16	to	to	PART
ejpam-5699	47	17	enrich	enrich	VERB
ejpam-5699	47	18	the	the	DET
ejpam-5699	47	19	theoretical	theoretical	ADJ
ejpam-5699	47	20	foundations	foundation	NOUN
ejpam-5699	47	21	of	of	ADP
ejpam-5699	47	22	algebraic	algebraic	ADJ
ejpam-5699	47	23	reasoning	reasoning	NOUN
ejpam-5699	47	24	under	under	ADP
ejpam-5699	47	25	uncertainty	uncertainty	NOUN
ejpam-5699	47	26	,	,	PUNCT
ejpam-5699	47	27	offering	offer	VERB
ejpam-5699	47	28	a	a	DET
ejpam-5699	47	29	more	more	ADV
ejpam-5699	47	30	comprehensive	comprehensive	ADJ
ejpam-5699	47	31	mathematical	mathematical	ADJ
ejpam-5699	47	32	model	model	NOUN
ejpam-5699	47	33	.	.	PUNCT
ejpam-5699	48	1	the	the	DET
ejpam-5699	48	2	existence	existence	NOUN
ejpam-5699	48	3	of	of	ADP
ejpam-5699	48	4	previous	previous	ADJ
ejpam-5699	48	5	studies	study	NOUN
ejpam-5699	48	6	on	on	ADP
ejpam-5699	48	7	related	related	ADJ
ejpam-5699	48	8	bipolar	bipolar	ADJ
ejpam-5699	48	9	fuzzy	fuzzy	ADJ
ejpam-5699	48	10	structures	structure	NOUN
ejpam-5699	48	11	,	,	PUNCT
ejpam-5699	48	12	such	such	ADJ
ejpam-5699	48	13	as	as	ADP
ejpam-5699	48	14	bipolar	bipolar	ADJ
ejpam-5699	48	15	complex	complex	ADJ
ejpam-5699	48	16	fuzzy	fuzzy	ADJ
ejpam-5699	48	17	subgroups	subgroup	NOUN
ejpam-5699	48	18	[	[	X
ejpam-5699	48	19	30	30	NUM
ejpam-5699	48	20	]	]	PUNCT
ejpam-5699	48	21	,	,	PUNCT
ejpam-5699	48	22	bipolar	bipolar	ADJ
ejpam-5699	48	23	complex	complex	ADJ
ejpam-5699	48	24	fuzzy	fuzzy	ADJ
ejpam-5699	48	25	semigroups	semigroup	NOUN
ejpam-5699	49	1	[	[	X
ejpam-5699	49	2	24	24	NUM
ejpam-5699	49	3	]	]	PUNCT
ejpam-5699	49	4	,	,	PUNCT
ejpam-5699	49	5	and	and	CCONJ
ejpam-5699	49	6	t	t	PROPN
ejpam-5699	49	7	-bipolar	-bipolar	ADJ
ejpam-5699	49	8	soft	soft	ADJ
ejpam-5699	49	9	groups	group	NOUN
ejpam-5699	49	10	and	and	CCONJ
ejpam-5699	49	11	their	their	PRON
ejpam-5699	49	12	fundamental	fundamental	ADJ
ejpam-5699	49	13	laws	law	NOUN
ejpam-5699	49	14	[	[	X
ejpam-5699	49	15	19	19	NUM
ejpam-5699	49	16	]	]	PUNCT
ejpam-5699	49	17	,	,	PUNCT
ejpam-5699	49	18	provides	provide	VERB
ejpam-5699	49	19	a	a	DET
ejpam-5699	49	20	solid	solid	ADJ
ejpam-5699	49	21	foundation	foundation	NOUN
ejpam-5699	49	22	for	for	ADP
ejpam-5699	49	23	advancing	advance	VERB
ejpam-5699	49	24	this	this	DET
ejpam-5699	49	25	field	field	NOUN
ejpam-5699	49	26	.	.	PUNCT
ejpam-5699	50	1	these	these	DET
ejpam-5699	50	2	works	work	NOUN
ejpam-5699	50	3	have	have	AUX
ejpam-5699	50	4	successfully	successfully	ADV
ejpam-5699	50	5	demonstrated	demonstrate	VERB
ejpam-5699	50	6	the	the	DET
ejpam-5699	50	7	versatility	versatility	NOUN
ejpam-5699	50	8	of	of	ADP
ejpam-5699	50	9	bipolar	bipolar	ADJ
ejpam-5699	50	10	fuzzy	fuzzy	ADJ
ejpam-5699	50	11	sets	set	NOUN
ejpam-5699	50	12	in	in	ADP
ejpam-5699	50	13	addressing	address	VERB
ejpam-5699	50	14	complex	complex	ADJ
ejpam-5699	50	15	algebraic	algebraic	ADJ
ejpam-5699	50	16	problems	problem	NOUN
ejpam-5699	50	17	,	,	PUNCT
ejpam-5699	50	18	including	include	VERB
ejpam-5699	50	19	γ	γ	NOUN
ejpam-5699	50	20	-	-	PUNCT
ejpam-5699	50	21	semigroups	semigroup	NOUN
ejpam-5699	50	22	[	[	X
ejpam-5699	50	23	20	20	NUM
ejpam-5699	50	24	]	]	PUNCT
ejpam-5699	50	25	and	and	CCONJ
ejpam-5699	50	26	bipolar	bipolar	ADJ
ejpam-5699	50	27	complex	complex	ADJ
ejpam-5699	50	28	fuzzy	fuzzy	ADJ
ejpam-5699	50	29	submodules	submodule	NOUN
ejpam-5699	50	30	[	[	X
ejpam-5699	50	31	2	2	NUM
ejpam-5699	50	32	]	]	PUNCT
ejpam-5699	50	33	.	.	PUNCT
ejpam-5699	51	1	however	however	ADV
ejpam-5699	51	2	,	,	PUNCT
ejpam-5699	51	3	to	to	ADP
ejpam-5699	51	4	the	the	DET
ejpam-5699	51	5	best	good	ADJ
ejpam-5699	51	6	of	of	ADP
ejpam-5699	51	7	our	our	PRON
ejpam-5699	51	8	knowledge	knowledge	NOUN
ejpam-5699	51	9	,	,	PUNCT
ejpam-5699	51	10	no	no	DET
ejpam-5699	51	11	existing	exist	VERB
ejpam-5699	51	12	literature	literature	NOUN
ejpam-5699	51	13	has	have	AUX
ejpam-5699	51	14	explored	explore	VERB
ejpam-5699	51	15	the	the	DET
ejpam-5699	51	16	bipolar	bipolar	ADV
ejpam-5699	51	17	-	-	PUNCT
ejpam-5699	51	18	valued	value	VERB
ejpam-5699	51	19	intuitionistic	intuitionistic	ADJ
ejpam-5699	51	20	fuzzification	fuzzification	NOUN
ejpam-5699	51	21	of	of	ADP
ejpam-5699	51	22	positive	positive	ADJ
ejpam-5699	51	23	implicative	implicative	ADJ
ejpam-5699	51	24	ideals	ideal	NOUN
ejpam-5699	51	25	in	in	ADP
ejpam-5699	51	26	bck	bck	PROPN
ejpam-5699	51	27	/	/	SYM
ejpam-5699	51	28	bci	bci	PROPN
ejpam-5699	51	29	algebras	algebra	NOUN
ejpam-5699	51	30	.	.	PUNCT
ejpam-5699	52	1	this	this	DET
ejpam-5699	52	2	absence	absence	NOUN
ejpam-5699	52	3	motivated	motivate	VERB
ejpam-5699	52	4	us	we	PRON
ejpam-5699	52	5	to	to	PART
ejpam-5699	52	6	initiate	initiate	VERB
ejpam-5699	52	7	theoretical	theoretical	ADJ
ejpam-5699	52	8	research	research	NOUN
ejpam-5699	52	9	on	on	ADP
ejpam-5699	52	10	this	this	DET
ejpam-5699	52	11	specific	specific	ADJ
ejpam-5699	52	12	topic	topic	NOUN
ejpam-5699	52	13	,	,	PUNCT
ejpam-5699	52	14	aiming	aim	VERB
ejpam-5699	52	15	to	to	PART
ejpam-5699	52	16	bridge	bridge	VERB
ejpam-5699	52	17	the	the	DET
ejpam-5699	52	18	gap	gap	NOUN
ejpam-5699	52	19	in	in	ADP
ejpam-5699	52	20	the	the	DET
ejpam-5699	52	21	current	current	ADJ
ejpam-5699	52	22	body	body	NOUN
ejpam-5699	52	23	of	of	ADP
ejpam-5699	52	24	knowledge	knowledge	NOUN
ejpam-5699	52	25	.	.	PUNCT
ejpam-5699	53	1	in	in	ADP
ejpam-5699	53	2	addition	addition	NOUN
ejpam-5699	53	3	to	to	ADP
ejpam-5699	53	4	its	its	PRON
ejpam-5699	53	5	theoretical	theoretical	ADJ
ejpam-5699	53	6	contributions	contribution	NOUN
ejpam-5699	53	7	,	,	PUNCT
ejpam-5699	53	8	the	the	DET
ejpam-5699	53	9	proposed	propose	VERB
ejpam-5699	53	10	framework	framework	NOUN
ejpam-5699	53	11	has	have	VERB
ejpam-5699	53	12	significant	significant	ADJ
ejpam-5699	53	13	practical	practical	ADJ
ejpam-5699	53	14	potential	potential	NOUN
ejpam-5699	53	15	.	.	PUNCT
ejpam-5699	54	1	bpvifpiis	bpvifpiis	PROPN
ejpam-5699	54	2	can	can	AUX
ejpam-5699	54	3	be	be	AUX
ejpam-5699	54	4	applied	apply	VERB
ejpam-5699	54	5	in	in	ADP
ejpam-5699	54	6	decision	decision	NOUN
ejpam-5699	54	7	-	-	PUNCT
ejpam-5699	54	8	making	make	VERB
ejpam-5699	54	9	systems	system	NOUN
ejpam-5699	54	10	where	where	SCONJ
ejpam-5699	54	11	conflicting	conflicting	ADJ
ejpam-5699	54	12	or	or	CCONJ
ejpam-5699	54	13	dual	dual	ADJ
ejpam-5699	54	14	aspects	aspect	NOUN
ejpam-5699	54	15	of	of	ADP
ejpam-5699	54	16	data	datum	NOUN
ejpam-5699	54	17	must	must	AUX
ejpam-5699	54	18	be	be	AUX
ejpam-5699	54	19	considered	consider	VERB
ejpam-5699	54	20	,	,	PUNCT
ejpam-5699	54	21	such	such	ADJ
ejpam-5699	54	22	as	as	ADP
ejpam-5699	54	23	in	in	ADP
ejpam-5699	54	24	medical	medical	ADJ
ejpam-5699	54	25	diagnostics	diagnostic	NOUN
ejpam-5699	54	26	,	,	PUNCT
ejpam-5699	54	27	where	where	SCONJ
ejpam-5699	54	28	symptoms	symptom	NOUN
ejpam-5699	54	29	may	may	AUX
ejpam-5699	54	30	simultaneously	simultaneously	ADV
ejpam-5699	54	31	support	support	VERB
ejpam-5699	54	32	and	and	CCONJ
ejpam-5699	54	33	contradict	contradict	VERB
ejpam-5699	54	34	potential	potential	ADJ
ejpam-5699	54	35	diagnoses	diagnosis	NOUN
ejpam-5699	54	36	.	.	PUNCT
ejpam-5699	55	1	similarly	similarly	ADV
ejpam-5699	55	2	,	,	PUNCT
ejpam-5699	55	3	this	this	DET
ejpam-5699	55	4	framework	framework	NOUN
ejpam-5699	55	5	is	be	AUX
ejpam-5699	55	6	relevant	relevant	ADJ
ejpam-5699	55	7	in	in	ADP
ejpam-5699	55	8	machine	machine	NOUN
ejpam-5699	55	9	learning	learning	NOUN
ejpam-5699	55	10	and	and	CCONJ
ejpam-5699	55	11	artificial	artificial	ADJ
ejpam-5699	55	12	intelligence	intelligence	NOUN
ejpam-5699	55	13	,	,	PUNCT
ejpam-5699	55	14	particularly	particularly	ADV
ejpam-5699	55	15	in	in	ADP
ejpam-5699	55	16	bipolar	bipolar	ADJ
ejpam-5699	55	17	sentiment	sentiment	NOUN
ejpam-5699	55	18	analysis	analysis	NOUN
ejpam-5699	55	19	or	or	CCONJ
ejpam-5699	55	20	systems	system	NOUN
ejpam-5699	55	21	that	that	PRON
ejpam-5699	55	22	require	require	VERB
ejpam-5699	55	23	evaluating	evaluate	VERB
ejpam-5699	55	24	both	both	CCONJ
ejpam-5699	55	25	positive	positive	ADJ
ejpam-5699	55	26	and	and	CCONJ
ejpam-5699	55	27	negative	negative	ADJ
ejpam-5699	55	28	influences	influence	NOUN
ejpam-5699	55	29	on	on	ADP
ejpam-5699	55	30	decisions	decision	NOUN
ejpam-5699	55	31	.	.	PUNCT
ejpam-5699	56	1	by	by	ADP
ejpam-5699	56	2	enabling	enable	VERB
ejpam-5699	56	3	the	the	DET
ejpam-5699	56	4	simultaneous	simultaneous	ADJ
ejpam-5699	56	5	analysis	analysis	NOUN
ejpam-5699	56	6	of	of	ADP
ejpam-5699	56	7	positive	positive	ADJ
ejpam-5699	56	8	and	and	CCONJ
ejpam-5699	56	9	negative	negative	ADJ
ejpam-5699	56	10	membership	membership	NOUN
ejpam-5699	56	11	values	value	NOUN
ejpam-5699	56	12	,	,	PUNCT
ejpam-5699	56	13	bpvifpiis	bpvifpiis	ADJ
ejpam-5699	56	14	provide	provide	VERB
ejpam-5699	56	15	a	a	DET
ejpam-5699	56	16	robust	robust	ADJ
ejpam-5699	56	17	tool	tool	NOUN
ejpam-5699	56	18	for	for	ADP
ejpam-5699	56	19	applications	application	NOUN
ejpam-5699	56	20	where	where	SCONJ
ejpam-5699	56	21	traditional	traditional	ADJ
ejpam-5699	56	22	fuzzy	fuzzy	ADJ
ejpam-5699	56	23	models	model	NOUN
ejpam-5699	56	24	are	be	AUX
ejpam-5699	56	25	insufficient	insufficient	ADJ
ejpam-5699	56	26	.	.	PUNCT
ejpam-5699	57	1	to	to	PART
ejpam-5699	57	2	enhance	enhance	VERB
ejpam-5699	57	3	clarity	clarity	NOUN
ejpam-5699	57	4	,	,	PUNCT
ejpam-5699	57	5	we	we	PRON
ejpam-5699	57	6	have	have	AUX
ejpam-5699	57	7	illustrated	illustrate	VERB
ejpam-5699	57	8	the	the	DET
ejpam-5699	57	9	research	research	NOUN
ejpam-5699	57	10	process	process	NOUN
ejpam-5699	57	11	in	in	ADP
ejpam-5699	57	12	a	a	DET
ejpam-5699	57	13	flowchart	flowchart	NOUN
ejpam-5699	57	14	(	(	PUNCT
ejpam-5699	57	15	figure	figure	NOUN
ejpam-5699	57	16	1	1	NUM
ejpam-5699	57	17	)	)	PUNCT
ejpam-5699	57	18	,	,	PUNCT
ejpam-5699	57	19	which	which	PRON
ejpam-5699	57	20	provides	provide	VERB
ejpam-5699	57	21	a	a	DET
ejpam-5699	57	22	structured	structured	ADJ
ejpam-5699	57	23	overview	overview	NOUN
ejpam-5699	57	24	of	of	ADP
ejpam-5699	57	25	the	the	DET
ejpam-5699	57	26	development	development	NOUN
ejpam-5699	57	27	of	of	ADP
ejpam-5699	57	28	bpvifpiis	bpvifpiis	NOUN
ejpam-5699	57	29	.	.	PUNCT
ejpam-5699	58	1	we	we	PRON
ejpam-5699	58	2	believe	believe	VERB
ejpam-5699	58	3	this	this	DET
ejpam-5699	58	4	graphical	graphical	ADJ
ejpam-5699	58	5	representation	representation	NOUN
ejpam-5699	58	6	will	will	AUX
ejpam-5699	58	7	facilitate	facilitate	VERB
ejpam-5699	58	8	a	a	DET
ejpam-5699	58	9	deeper	deep	ADJ
ejpam-5699	58	10	understanding	understanding	NOUN
ejpam-5699	58	11	of	of	ADP
ejpam-5699	58	12	the	the	DET
ejpam-5699	58	13	proposed	propose	VERB
ejpam-5699	58	14	concepts	concept	NOUN
ejpam-5699	58	15	and	and	CCONJ
ejpam-5699	58	16	their	their	PRON
ejpam-5699	58	17	significance	significance	NOUN
ejpam-5699	58	18	within	within	ADP
ejpam-5699	58	19	the	the	DET
ejpam-5699	58	20	broader	broad	ADJ
ejpam-5699	58	21	context	context	NOUN
ejpam-5699	58	22	of	of	ADP
ejpam-5699	58	23	algebraic	algebraic	ADJ
ejpam-5699	58	24	and	and	CCONJ
ejpam-5699	58	25	fuzzy	fuzzy	ADJ
ejpam-5699	58	26	set	set	NOUN
ejpam-5699	58	27	theory	theory	NOUN
ejpam-5699	58	28	.	.	PUNCT
ejpam-5699	59	1	d.	d.	PROPN
ejpam-5699	59	2	ramesh	ramesh	PROPN
ejpam-5699	59	3	et	et	PROPN
ejpam-5699	59	4	al	al	PROPN
ejpam-5699	59	5	.	.	PUNCT
ejpam-5699	59	6	/	/	SYM
ejpam-5699	59	7	eur	eur	PROPN
ejpam-5699	59	8	.	.	PUNCT
ejpam-5699	60	1	j.	j.	PROPN
ejpam-5699	60	2	pure	pure	PROPN
ejpam-5699	60	3	appl	appl	PROPN
ejpam-5699	60	4	.	.	PROPN
ejpam-5699	60	5	math	math	PROPN
ejpam-5699	60	6	,	,	PUNCT
ejpam-5699	60	7	18	18	NUM
ejpam-5699	60	8	(	(	PUNCT
ejpam-5699	60	9	1	1	NUM
ejpam-5699	60	10	)	)	PUNCT
ejpam-5699	60	11	(	(	PUNCT
ejpam-5699	60	12	2025	2025	NUM
ejpam-5699	60	13	)	)	PUNCT
ejpam-5699	60	14	,	,	PUNCT
ejpam-5699	60	15	5699	5699	NUM
ejpam-5699	60	16	4	4	NUM
ejpam-5699	60	17	of	of	ADP
ejpam-5699	60	18	20	20	NUM
ejpam-5699	60	19	this	this	DET
ejpam-5699	60	20	article	article	NOUN
ejpam-5699	60	21	presents	present	VERB
ejpam-5699	60	22	a	a	DET
ejpam-5699	60	23	comprehensive	comprehensive	ADJ
ejpam-5699	60	24	exploration	exploration	NOUN
ejpam-5699	60	25	of	of	ADP
ejpam-5699	60	26	bpvifpiis	bpvifpiis	NOUN
ejpam-5699	60	27	within	within	ADP
ejpam-5699	60	28	the	the	DET
ejpam-5699	60	29	framework	framework	NOUN
ejpam-5699	60	30	of	of	ADP
ejpam-5699	60	31	bck	bck	PROPN
ejpam-5699	60	32	-	-	PUNCT
ejpam-5699	60	33	algebras	algebras	PROPN
ejpam-5699	60	34	,	,	PUNCT
ejpam-5699	60	35	accompanied	accompany	VERB
ejpam-5699	60	36	by	by	ADP
ejpam-5699	60	37	illustrative	illustrative	ADJ
ejpam-5699	60	38	examples	example	NOUN
ejpam-5699	60	39	that	that	PRON
ejpam-5699	60	40	illuminate	illuminate	VERB
ejpam-5699	60	41	the	the	DET
ejpam-5699	60	42	core	core	NOUN
ejpam-5699	60	43	concepts	concept	NOUN
ejpam-5699	60	44	.	.	PUNCT
ejpam-5699	61	1	the	the	DET
ejpam-5699	61	2	study	study	NOUN
ejpam-5699	61	3	meticulously	meticulously	ADV
ejpam-5699	61	4	establishes	establish	VERB
ejpam-5699	61	5	the	the	DET
ejpam-5699	61	6	conditions	condition	NOUN
ejpam-5699	61	7	under	under	ADP
ejpam-5699	61	8	which	which	PRON
ejpam-5699	61	9	a	a	DET
ejpam-5699	61	10	bpvifs	bpvifs	PROPN
ejpam-5699	61	11	qualifies	qualify	VERB
ejpam-5699	61	12	as	as	ADP
ejpam-5699	61	13	a	a	DET
ejpam-5699	61	14	bpvifpii	bpvifpii	NOUN
ejpam-5699	61	15	and	and	CCONJ
ejpam-5699	61	16	when	when	SCONJ
ejpam-5699	61	17	a	a	DET
ejpam-5699	61	18	bpvifi	bpvifi	NOUN
ejpam-5699	61	19	attains	attain	VERB
ejpam-5699	61	20	the	the	DET
ejpam-5699	61	21	structure	structure	NOUN
ejpam-5699	61	22	of	of	ADP
ejpam-5699	61	23	a	a	DET
ejpam-5699	61	24	bpvifpii	bpvifpii	NOUN
ejpam-5699	61	25	.	.	PUNCT
ejpam-5699	62	1	by	by	ADP
ejpam-5699	62	2	combining	combine	VERB
ejpam-5699	62	3	rigorous	rigorous	ADJ
ejpam-5699	62	4	theoretical	theoretical	ADJ
ejpam-5699	62	5	analysis	analysis	NOUN
ejpam-5699	62	6	with	with	ADP
ejpam-5699	62	7	practical	practical	ADJ
ejpam-5699	62	8	examples	example	NOUN
ejpam-5699	62	9	,	,	PUNCT
ejpam-5699	62	10	this	this	DET
ejpam-5699	62	11	work	work	NOUN
ejpam-5699	62	12	not	not	PART
ejpam-5699	62	13	only	only	ADV
ejpam-5699	62	14	expands	expand	VERB
ejpam-5699	62	15	the	the	DET
ejpam-5699	62	16	algebraic	algebraic	ADJ
ejpam-5699	62	17	understanding	understanding	NOUN
ejpam-5699	62	18	of	of	ADP
ejpam-5699	62	19	fuzzy	fuzzy	ADJ
ejpam-5699	62	20	structures	structure	NOUN
ejpam-5699	62	21	but	but	CCONJ
ejpam-5699	62	22	also	also	ADV
ejpam-5699	62	23	highlights	highlight	VERB
ejpam-5699	62	24	the	the	DET
ejpam-5699	62	25	critical	critical	ADJ
ejpam-5699	62	26	connections	connection	NOUN
ejpam-5699	62	27	between	between	ADP
ejpam-5699	62	28	these	these	DET
ejpam-5699	62	29	fuzzy	fuzzy	ADJ
ejpam-5699	62	30	ideals	ideal	NOUN
ejpam-5699	62	31	and	and	CCONJ
ejpam-5699	62	32	their	their	PRON
ejpam-5699	62	33	broader	broad	ADJ
ejpam-5699	62	34	implications	implication	NOUN
ejpam-5699	62	35	in	in	ADP
ejpam-5699	62	36	algebraic	algebraic	ADJ
ejpam-5699	62	37	reasoning	reasoning	NOUN
ejpam-5699	62	38	and	and	CCONJ
ejpam-5699	62	39	uncertainty	uncertainty	NOUN
ejpam-5699	62	40	modeling	modeling	NOUN
ejpam-5699	62	41	.	.	PUNCT
ejpam-5699	63	1	figure	figure	NOUN
ejpam-5699	63	2	1	1	NUM
ejpam-5699	63	3	:	:	PUNCT
ejpam-5699	63	4	the	the	DET
ejpam-5699	63	5	research	research	NOUN
ejpam-5699	63	6	process	process	NOUN
ejpam-5699	63	7	2	2	NUM
ejpam-5699	63	8	.	.	PUNCT
ejpam-5699	63	9	preliminaries	preliminary	NOUN
ejpam-5699	63	10	definition	definition	NOUN
ejpam-5699	63	11	1	1	NUM
ejpam-5699	63	12	.	.	PUNCT
ejpam-5699	64	1	[	[	X
ejpam-5699	64	2	7	7	X
ejpam-5699	64	3	]	]	X
ejpam-5699	64	4	a	a	DET
ejpam-5699	64	5	bck	bck	NOUN
ejpam-5699	64	6	-	-	PUNCT
ejpam-5699	64	7	a	a	NOUN
ejpam-5699	64	8	g	g	NOUN
ejpam-5699	64	9	=	=	SYM
ejpam-5699	64	10	(	(	PUNCT
ejpam-5699	64	11	g	g	PROPN
ejpam-5699	64	12	,	,	PUNCT
ejpam-5699	64	13	⋄	⋄	PROPN
ejpam-5699	64	14	,	,	PUNCT
ejpam-5699	64	15	0	0	NUM
ejpam-5699	64	16	)	)	PUNCT
ejpam-5699	64	17	is	be	AUX
ejpam-5699	64	18	an	an	DET
ejpam-5699	64	19	algebra	algebra	NOUN
ejpam-5699	64	20	of	of	ADP
ejpam-5699	64	21	type	type	NOUN
ejpam-5699	64	22	(	(	PUNCT
ejpam-5699	64	23	2	2	NUM
ejpam-5699	64	24	,	,	PUNCT
ejpam-5699	64	25	0	0	NUM
ejpam-5699	64	26	)	)	PUNCT
ejpam-5699	64	27	,	,	PUNCT
ejpam-5699	64	28	where	where	SCONJ
ejpam-5699	64	29	g	g	PROPN
ejpam-5699	64	30	is	be	AUX
ejpam-5699	64	31	a	a	DET
ejpam-5699	64	32	nonempty	nonempty	ADJ
ejpam-5699	64	33	set	set	NOUN
ejpam-5699	64	34	,	,	PUNCT
ejpam-5699	64	35	⋄	⋄	PROPN
ejpam-5699	64	36	is	be	AUX
ejpam-5699	64	37	a	a	DET
ejpam-5699	64	38	binary	binary	ADJ
ejpam-5699	64	39	operation	operation	NOUN
ejpam-5699	64	40	on	on	ADP
ejpam-5699	64	41	g	g	PROPN
ejpam-5699	64	42	,	,	PUNCT
ejpam-5699	64	43	and	and	CCONJ
ejpam-5699	64	44	0	0	NUM
ejpam-5699	64	45	is	be	AUX
ejpam-5699	64	46	a	a	DET
ejpam-5699	64	47	fixed	fix	VERB
ejpam-5699	64	48	element	element	NOUN
ejpam-5699	64	49	of	of	ADP
ejpam-5699	64	50	g	g	PROPN
ejpam-5699	64	51	if	if	SCONJ
ejpam-5699	64	52	it	it	PRON
ejpam-5699	64	53	satisfies	satisfy	VERB
ejpam-5699	64	54	the	the	DET
ejpam-5699	64	55	following	follow	VERB
ejpam-5699	64	56	axioms	axiom	NOUN
ejpam-5699	64	57	:	:	PUNCT
ejpam-5699	64	58	for	for	ADP
ejpam-5699	64	59	all	all	DET
ejpam-5699	64	60	g1	g1	NOUN
ejpam-5699	64	61	,	,	PUNCT
ejpam-5699	64	62	è1	è1	NOUN
ejpam-5699	64	63	,	,	PUNCT
ejpam-5699	64	64	11	11	NUM
ejpam-5699	64	65	∈	∈	NOUN
ejpam-5699	64	66	g	g	NOUN
ejpam-5699	64	67	,	,	PUNCT
ejpam-5699	64	68	(	(	PUNCT
ejpam-5699	64	69	bck-1	bck-1	NOUN
ejpam-5699	64	70	)	)	PUNCT
ejpam-5699	64	71	(	(	PUNCT
ejpam-5699	64	72	(	(	PUNCT
ejpam-5699	64	73	g1	g1	PROPN
ejpam-5699	64	74	⋄	⋄	PROPN
ejpam-5699	64	75	è1	è1	PROPN
ejpam-5699	64	76	)	)	PUNCT
ejpam-5699	64	77	⋄	⋄	NOUN
ejpam-5699	64	78	(	(	PUNCT
ejpam-5699	64	79	g1	g1	VERB
ejpam-5699	64	80	⋄	⋄	PROPN
ejpam-5699	64	81	11	11	NUM
ejpam-5699	64	82	)	)	PUNCT
ejpam-5699	64	83	)	)	PUNCT
ejpam-5699	65	1	⋄	⋄	NOUN
ejpam-5699	65	2	(	(	PUNCT
ejpam-5699	65	3	11	11	NUM
ejpam-5699	65	4	⋄	⋄	PROPN
ejpam-5699	65	5	è1	è1	PROPN
ejpam-5699	65	6	)	)	PUNCT
ejpam-5699	65	7	=	=	SYM
ejpam-5699	65	8	0	0	NUM
ejpam-5699	65	9	,	,	PUNCT
ejpam-5699	65	10	(	(	PUNCT
ejpam-5699	65	11	bck-2	bck-2	NOUN
ejpam-5699	65	12	)	)	PUNCT
ejpam-5699	65	13	(	(	PUNCT
ejpam-5699	65	14	g1	g1	PROPN
ejpam-5699	65	15	⋄	⋄	PROPN
ejpam-5699	65	16	(	(	PUNCT
ejpam-5699	65	17	g1	g1	PROPN
ejpam-5699	65	18	⋄	⋄	PROPN
ejpam-5699	65	19	è1	è1	PROPN
ejpam-5699	65	20	)	)	PUNCT
ejpam-5699	65	21	)	)	PUNCT
ejpam-5699	65	22	⋄	⋄	PROPN
ejpam-5699	65	23	è1	è1	PROPN
ejpam-5699	65	24	=	=	SYM
ejpam-5699	65	25	0	0	NUM
ejpam-5699	65	26	,	,	PUNCT
ejpam-5699	65	27	(	(	PUNCT
ejpam-5699	65	28	bck-3	bck-3	NOUN
ejpam-5699	65	29	)	)	PUNCT
ejpam-5699	65	30	g1	g1	PROPN
ejpam-5699	65	31	⋄	⋄	PROPN
ejpam-5699	65	32	g1	g1	PROPN
ejpam-5699	65	33	=	=	SYM
ejpam-5699	65	34	0	0	NUM
ejpam-5699	65	35	,	,	PUNCT
ejpam-5699	65	36	(	(	PUNCT
ejpam-5699	65	37	bck-4	bck-4	ADV
ejpam-5699	65	38	)	)	PUNCT
ejpam-5699	65	39	0	0	NUM
ejpam-5699	65	40	⋄	⋄	PROPN
ejpam-5699	65	41	g1	g1	PROPN
ejpam-5699	65	42	=	=	SYM
ejpam-5699	65	43	0	0	NUM
ejpam-5699	65	44	,	,	PUNCT
ejpam-5699	65	45	(	(	PUNCT
ejpam-5699	65	46	bck-5	bck-5	ADV
ejpam-5699	65	47	)	)	PUNCT
ejpam-5699	65	48	g1	g1	PROPN
ejpam-5699	65	49	⋄	⋄	NOUN
ejpam-5699	65	50	è1	è1	PROPN
ejpam-5699	65	51	=	=	SYM
ejpam-5699	65	52	0	0	NUM
ejpam-5699	65	53	and	and	CCONJ
ejpam-5699	65	54	è1	è1	PROPN
ejpam-5699	65	55	⋄	⋄	PROPN
ejpam-5699	65	56	g1	g1	NOUN
ejpam-5699	65	57	=	=	SYM
ejpam-5699	65	58	0	0	NUM
ejpam-5699	65	59	⇒	⇒	PROPN
ejpam-5699	65	60	g1	g1	PROPN
ejpam-5699	65	61	=	=	SYM
ejpam-5699	65	62	è1	è1	PROPN
ejpam-5699	65	63	.	.	PUNCT
ejpam-5699	66	1	for	for	ADP
ejpam-5699	66	2	convenience	convenience	NOUN
ejpam-5699	66	3	,	,	PUNCT
ejpam-5699	66	4	we	we	PRON
ejpam-5699	66	5	will	will	AUX
ejpam-5699	66	6	let	let	VERB
ejpam-5699	66	7	g	g	PROPN
ejpam-5699	66	8	represent	represent	VERB
ejpam-5699	66	9	the	the	DET
ejpam-5699	66	10	bck	bck	VERB
ejpam-5699	66	11	-	-	PUNCT
ejpam-5699	66	12	a	a	NOUN
ejpam-5699	66	13	g	g	NOUN
ejpam-5699	66	14	=	=	SYM
ejpam-5699	66	15	(	(	PUNCT
ejpam-5699	66	16	g	g	PROPN
ejpam-5699	66	17	,	,	PUNCT
ejpam-5699	66	18	⋄	⋄	PROPN
ejpam-5699	66	19	,	,	PUNCT
ejpam-5699	66	20	0	0	NUM
ejpam-5699	66	21	)	)	PUNCT
ejpam-5699	66	22	until	until	SCONJ
ejpam-5699	66	23	otherwise	otherwise	ADV
ejpam-5699	66	24	specified	specify	VERB
ejpam-5699	66	25	.	.	PUNCT
ejpam-5699	67	1	we	we	PRON
ejpam-5699	67	2	are	be	AUX
ejpam-5699	67	3	able	able	ADJ
ejpam-5699	67	4	to	to	PART
ejpam-5699	67	5	define	define	VERB
ejpam-5699	67	6	a	a	DET
ejpam-5699	67	7	binary	binary	ADJ
ejpam-5699	67	8	operation	operation	NOUN
ejpam-5699	67	9	≤	≤	NOUN
ejpam-5699	67	10	on	on	ADP
ejpam-5699	67	11	g	g	NOUN
ejpam-5699	67	12	by	by	ADP
ejpam-5699	67	13	assuming	assume	VERB
ejpam-5699	67	14	g1	g1	NOUN
ejpam-5699	67	15	≤	≤	NOUN
ejpam-5699	67	16	è1	è1	PROPN
ejpam-5699	67	17	if	if	SCONJ
ejpam-5699	67	18	and	and	CCONJ
ejpam-5699	67	19	only	only	ADV
ejpam-5699	67	20	if	if	SCONJ
ejpam-5699	67	21	g1	g1	PROPN
ejpam-5699	67	22	⋄	⋄	PROPN
ejpam-5699	67	23	è1	è1	PROPN
ejpam-5699	67	24	=	=	SYM
ejpam-5699	67	25	0	0	NUM
ejpam-5699	67	26	.	.	PUNCT
ejpam-5699	68	1	in	in	ADP
ejpam-5699	68	2	a	a	DET
ejpam-5699	68	3	bck	bck	NOUN
ejpam-5699	68	4	-	-	PUNCT
ejpam-5699	68	5	a	a	NOUN
ejpam-5699	68	6	g	g	NOUN
ejpam-5699	68	7	,	,	PUNCT
ejpam-5699	68	8	the	the	DET
ejpam-5699	68	9	following	follow	VERB
ejpam-5699	68	10	properties	property	NOUN
ejpam-5699	68	11	hold	hold	VERB
ejpam-5699	68	12	.	.	PUNCT
ejpam-5699	69	1	g1	g1	VERB
ejpam-5699	69	2	⋄	⋄	NOUN
ejpam-5699	69	3	0	0	NUM
ejpam-5699	69	4	=	=	SYM
ejpam-5699	69	5	g1	g1	NOUN
ejpam-5699	69	6	,	,	PUNCT
ejpam-5699	69	7	(	(	PUNCT
ejpam-5699	69	8	1	1	X
ejpam-5699	69	9	)	)	PUNCT
ejpam-5699	69	10	d.	d.	PROPN
ejpam-5699	69	11	ramesh	ramesh	PROPN
ejpam-5699	69	12	et	et	PROPN
ejpam-5699	69	13	al	al	PROPN
ejpam-5699	69	14	.	.	PUNCT
ejpam-5699	69	15	/	/	SYM
ejpam-5699	69	16	eur	eur	PROPN
ejpam-5699	69	17	.	.	PUNCT
ejpam-5699	70	1	j.	j.	PROPN
ejpam-5699	70	2	pure	pure	PROPN
ejpam-5699	70	3	appl	appl	PROPN
ejpam-5699	70	4	.	.	PROPN
ejpam-5699	70	5	math	math	PROPN
ejpam-5699	70	6	,	,	PUNCT
ejpam-5699	70	7	18	18	NUM
ejpam-5699	70	8	(	(	PUNCT
ejpam-5699	70	9	1	1	NUM
ejpam-5699	70	10	)	)	PUNCT
ejpam-5699	70	11	(	(	PUNCT
ejpam-5699	70	12	2025	2025	NUM
ejpam-5699	70	13	)	)	PUNCT
ejpam-5699	70	14	,	,	PUNCT
ejpam-5699	70	15	5699	5699	NUM
ejpam-5699	70	16	5	5	NUM
ejpam-5699	70	17	of	of	ADP
ejpam-5699	70	18	20	20	NUM
ejpam-5699	70	19	g1	g1	PROPN
ejpam-5699	70	20	⋄	⋄	PROPN
ejpam-5699	70	21	è1	è1	ADJ
ejpam-5699	70	22	≤	≤	NUM
ejpam-5699	70	23	g1	g1	NOUN
ejpam-5699	70	24	,	,	PUNCT
ejpam-5699	70	25	(	(	PUNCT
ejpam-5699	70	26	2	2	NUM
ejpam-5699	70	27	)	)	PUNCT
ejpam-5699	70	28	(	(	PUNCT
ejpam-5699	70	29	g1	g1	PROPN
ejpam-5699	70	30	⋄	⋄	PROPN
ejpam-5699	70	31	è1	è1	PROPN
ejpam-5699	70	32	)	)	PUNCT
ejpam-5699	70	33	⋄	⋄	NOUN
ejpam-5699	70	34	11	11	NUM
ejpam-5699	70	35	=	=	SYM
ejpam-5699	70	36	(	(	PUNCT
ejpam-5699	70	37	g1	g1	VERB
ejpam-5699	70	38	⋄	⋄	PROPN
ejpam-5699	70	39	11	11	NUM
ejpam-5699	70	40	)	)	PUNCT
ejpam-5699	70	41	⋄	⋄	PROPN
ejpam-5699	70	42	è1	è1	PROPN
ejpam-5699	70	43	,	,	PUNCT
ejpam-5699	70	44	(	(	PUNCT
ejpam-5699	70	45	3	3	X
ejpam-5699	70	46	)	)	PUNCT
ejpam-5699	70	47	(	(	PUNCT
ejpam-5699	70	48	g1	g1	VERB
ejpam-5699	70	49	⋄	⋄	PROPN
ejpam-5699	70	50	11	11	NUM
ejpam-5699	70	51	)	)	PUNCT
ejpam-5699	70	52	⋄	⋄	NOUN
ejpam-5699	70	53	(	(	PUNCT
ejpam-5699	70	54	è1	è1	ADP
ejpam-5699	70	55	⋄	⋄	PROPN
ejpam-5699	70	56	11	11	NUM
ejpam-5699	70	57	)	)	PUNCT
ejpam-5699	70	58	≤	≤	PROPN
ejpam-5699	70	59	g1	g1	PROPN
ejpam-5699	70	60	⋄	⋄	PROPN
ejpam-5699	70	61	è1	è1	PROPN
ejpam-5699	70	62	,	,	PUNCT
ejpam-5699	70	63	(	(	PUNCT
ejpam-5699	70	64	4	4	X
ejpam-5699	70	65	)	)	PUNCT
ejpam-5699	70	66	g1	g1	PROPN
ejpam-5699	70	67	⋄	⋄	PROPN
ejpam-5699	70	68	(	(	PUNCT
ejpam-5699	70	69	g1	g1	PROPN
ejpam-5699	70	70	⋄	⋄	PROPN
ejpam-5699	70	71	(	(	PUNCT
ejpam-5699	70	72	g1	g1	PROPN
ejpam-5699	70	73	⋄	⋄	PROPN
ejpam-5699	70	74	è1	è1	PROPN
ejpam-5699	70	75	)	)	PUNCT
ejpam-5699	70	76	)	)	PUNCT
ejpam-5699	71	1	=	=	PUNCT
ejpam-5699	71	2	g1	g1	PROPN
ejpam-5699	71	3	⋄	⋄	PROPN
ejpam-5699	71	4	è1	è1	PROPN
ejpam-5699	71	5	,	,	PUNCT
ejpam-5699	71	6	(	(	PUNCT
ejpam-5699	71	7	5	5	X
ejpam-5699	71	8	)	)	PUNCT
ejpam-5699	71	9	g1	g1	NOUN
ejpam-5699	71	10	≤	≤	X
ejpam-5699	71	11	è1	è1	ADJ
ejpam-5699	71	12	⇒	⇒	NOUN
ejpam-5699	71	13	g1	g1	PROPN
ejpam-5699	71	14	⋄	⋄	PROPN
ejpam-5699	71	15	11	11	NUM
ejpam-5699	71	16	≤	≤	NOUN
ejpam-5699	71	17	è1	è1	ADP
ejpam-5699	71	18	⋄	⋄	NOUN
ejpam-5699	71	19	11	11	NUM
ejpam-5699	71	20	and	and	CCONJ
ejpam-5699	71	21	11	11	NUM
ejpam-5699	71	22	⋄	⋄	NOUN
ejpam-5699	71	23	è1	è1	ADJ
ejpam-5699	71	24	≤	≤	ADJ
ejpam-5699	71	25	11	11	NUM
ejpam-5699	71	26	⋄	⋄	NOUN
ejpam-5699	71	27	g1	g1	NOUN
ejpam-5699	71	28	,	,	PUNCT
ejpam-5699	71	29	(	(	PUNCT
ejpam-5699	71	30	6	6	X
ejpam-5699	71	31	)	)	PUNCT
ejpam-5699	71	32	g1	g1	PROPN
ejpam-5699	71	33	⋄	⋄	PROPN
ejpam-5699	71	34	è1	è1	ADJ
ejpam-5699	71	35	≤	≤	ADJ
ejpam-5699	71	36	11	11	NUM
ejpam-5699	71	37	⇒	⇒	NOUN
ejpam-5699	71	38	g1	g1	PROPN
ejpam-5699	71	39	⋄	⋄	PROPN
ejpam-5699	71	40	11	11	NUM
ejpam-5699	71	41	≤	≤	NOUN
ejpam-5699	71	42	è1	è1	NOUN
ejpam-5699	71	43	,	,	PUNCT
ejpam-5699	71	44	(	(	PUNCT
ejpam-5699	71	45	7	7	X
ejpam-5699	71	46	)	)	PUNCT
ejpam-5699	71	47	for	for	ADP
ejpam-5699	71	48	all	all	DET
ejpam-5699	71	49	g1,è1	g1,è1	PROPN
ejpam-5699	71	50	,	,	PUNCT
ejpam-5699	71	51	11	11	NUM
ejpam-5699	71	52	∈	∈	PROPN
ejpam-5699	71	53	g.	g.	NOUN
ejpam-5699	71	54	theorem	theorem	VERB
ejpam-5699	71	55	1	1	NUM
ejpam-5699	71	56	.	.	PUNCT
ejpam-5699	72	1	[	[	X
ejpam-5699	72	2	6	6	NUM
ejpam-5699	72	3	]	]	PUNCT
ejpam-5699	72	4	in	in	ADP
ejpam-5699	72	5	a	a	DET
ejpam-5699	72	6	bck	bck	NOUN
ejpam-5699	72	7	-	-	PUNCT
ejpam-5699	72	8	a	a	NOUN
ejpam-5699	72	9	g	g	NOUN
ejpam-5699	72	10	,	,	PUNCT
ejpam-5699	72	11	the	the	DET
ejpam-5699	72	12	following	follow	VERB
ejpam-5699	72	13	holds	hold	VERB
ejpam-5699	72	14	for	for	ADP
ejpam-5699	72	15	all	all	DET
ejpam-5699	72	16	g1,è1	g1,è1	PROPN
ejpam-5699	72	17	,	,	PUNCT
ejpam-5699	72	18	11	11	NUM
ejpam-5699	72	19	∈	∈	NOUN
ejpam-5699	72	20	g	g	NOUN
ejpam-5699	72	21	,	,	PUNCT
ejpam-5699	72	22	(	(	PUNCT
ejpam-5699	72	23	i	i	NOUN
ejpam-5699	72	24	)	)	PUNCT
ejpam-5699	72	25	(	(	PUNCT
ejpam-5699	72	26	(	(	PUNCT
ejpam-5699	72	27	g1	g1	VERB
ejpam-5699	72	28	⋄	⋄	PROPN
ejpam-5699	72	29	11	11	NUM
ejpam-5699	72	30	)	)	PUNCT
ejpam-5699	72	31	⋄	⋄	NOUN
ejpam-5699	72	32	11	11	NUM
ejpam-5699	72	33	)	)	PUNCT
ejpam-5699	72	34	⋄	⋄	NOUN
ejpam-5699	72	35	(	(	PUNCT
ejpam-5699	72	36	è1	è1	ADP
ejpam-5699	72	37	⋄	⋄	PROPN
ejpam-5699	72	38	11	11	NUM
ejpam-5699	72	39	)	)	PUNCT
ejpam-5699	72	40	≤	≤	NOUN
ejpam-5699	72	41	(	(	PUNCT
ejpam-5699	72	42	g1	g1	PROPN
ejpam-5699	72	43	⋄	⋄	PROPN
ejpam-5699	72	44	è1	è1	PROPN
ejpam-5699	72	45	)	)	PUNCT
ejpam-5699	72	46	⋄	⋄	PROPN
ejpam-5699	72	47	11	11	NUM
ejpam-5699	72	48	,	,	PUNCT
ejpam-5699	72	49	(	(	PUNCT
ejpam-5699	72	50	ii	ii	NOUN
ejpam-5699	72	51	)	)	PUNCT
ejpam-5699	72	52	(	(	PUNCT
ejpam-5699	72	53	g1	g1	VERB
ejpam-5699	72	54	⋄	⋄	PROPN
ejpam-5699	72	55	11	11	NUM
ejpam-5699	72	56	)	)	PUNCT
ejpam-5699	72	57	⋄	⋄	NOUN
ejpam-5699	72	58	(	(	PUNCT
ejpam-5699	72	59	g1	g1	PROPN
ejpam-5699	72	60	⋄	⋄	PROPN
ejpam-5699	72	61	(	(	PUNCT
ejpam-5699	72	62	g1	g1	VERB
ejpam-5699	72	63	⋄	⋄	PROPN
ejpam-5699	72	64	11	11	NUM
ejpam-5699	72	65	)	)	PUNCT
ejpam-5699	72	66	)	)	PUNCT
ejpam-5699	73	1	=	=	PRON
ejpam-5699	74	1	(	(	PUNCT
ejpam-5699	74	2	g1	g1	VERB
ejpam-5699	74	3	⋄	⋄	PROPN
ejpam-5699	74	4	11	11	NUM
ejpam-5699	74	5	)	)	PUNCT
ejpam-5699	74	6	⋄	⋄	NOUN
ejpam-5699	74	7	11	11	NUM
ejpam-5699	74	8	,	,	PUNCT
ejpam-5699	74	9	(	(	PUNCT
ejpam-5699	74	10	iii	iii	NOUN
ejpam-5699	74	11	)	)	PUNCT
ejpam-5699	74	12	(	(	PUNCT
ejpam-5699	74	13	g1	g1	PROPN
ejpam-5699	74	14	⋄	⋄	PROPN
ejpam-5699	74	15	(	(	PUNCT
ejpam-5699	74	16	è1	è1	PROPN
ejpam-5699	74	17	⋄	⋄	NOUN
ejpam-5699	74	18	(	(	PUNCT
ejpam-5699	74	19	è1	è1	PROPN
ejpam-5699	74	20	⋄	⋄	PROPN
ejpam-5699	74	21	g1	g1	PROPN
ejpam-5699	74	22	)	)	PUNCT
ejpam-5699	74	23	)	)	PUNCT
ejpam-5699	74	24	)	)	PUNCT
ejpam-5699	75	1	⋄	⋄	NOUN
ejpam-5699	75	2	(	(	PUNCT
ejpam-5699	75	3	è1	è1	PROPN
ejpam-5699	75	4	⋄	⋄	PROPN
ejpam-5699	75	5	(	(	PUNCT
ejpam-5699	75	6	g1	g1	PROPN
ejpam-5699	75	7	⋄	⋄	PROPN
ejpam-5699	75	8	(	(	PUNCT
ejpam-5699	75	9	è1	è1	PROPN
ejpam-5699	75	10	⋄	⋄	NOUN
ejpam-5699	75	11	(	(	PUNCT
ejpam-5699	75	12	è1	è1	PROPN
ejpam-5699	75	13	⋄	⋄	PROPN
ejpam-5699	75	14	g1	g1	PROPN
ejpam-5699	75	15	)	)	PUNCT
ejpam-5699	75	16	)	)	PUNCT
ejpam-5699	75	17	)	)	PUNCT
ejpam-5699	75	18	)	)	PUNCT
ejpam-5699	75	19	≤	≤	PROPN
ejpam-5699	75	20	g1	g1	VERB
ejpam-5699	75	21	⋄	⋄	PROPN
ejpam-5699	75	22	è1	è1	PROPN
ejpam-5699	75	23	.	.	PUNCT
ejpam-5699	76	1	definition	definition	NOUN
ejpam-5699	76	2	2	2	NUM
ejpam-5699	76	3	.	.	PUNCT
ejpam-5699	77	1	[	[	X
ejpam-5699	77	2	6	6	NUM
ejpam-5699	77	3	]	]	PUNCT
ejpam-5699	77	4	a	a	DET
ejpam-5699	77	5	bck	bck	NOUN
ejpam-5699	77	6	-	-	PUNCT
ejpam-5699	77	7	a	a	DET
ejpam-5699	77	8	g	g	NOUN
ejpam-5699	77	9	is	be	AUX
ejpam-5699	77	10	considered	consider	VERB
ejpam-5699	77	11	to	to	PART
ejpam-5699	77	12	be	be	AUX
ejpam-5699	77	13	a	a	DET
ejpam-5699	77	14	positive	positive	ADJ
ejpam-5699	77	15	implicative	implicative	NOUN
ejpam-5699	77	16	if	if	SCONJ
ejpam-5699	77	17	the	the	DET
ejpam-5699	77	18	following	follow	VERB
ejpam-5699	77	19	condition	condition	NOUN
ejpam-5699	77	20	holds	hold	VERB
ejpam-5699	77	21	(	(	PUNCT
ejpam-5699	77	22	g1	g1	VERB
ejpam-5699	77	23	⋄	⋄	PROPN
ejpam-5699	77	24	11	11	NUM
ejpam-5699	77	25	)	)	PUNCT
ejpam-5699	77	26	⋄	⋄	NOUN
ejpam-5699	77	27	(	(	PUNCT
ejpam-5699	77	28	è1	è1	ADP
ejpam-5699	77	29	⋄	⋄	NOUN
ejpam-5699	77	30	11	11	NUM
ejpam-5699	77	31	)	)	PUNCT
ejpam-5699	77	32	=	=	PRON
ejpam-5699	77	33	(	(	PUNCT
ejpam-5699	77	34	g1	g1	PROPN
ejpam-5699	77	35	⋄	⋄	PROPN
ejpam-5699	77	36	è1	è1	PROPN
ejpam-5699	77	37	)	)	PUNCT
ejpam-5699	77	38	⋄	⋄	PROPN
ejpam-5699	77	39	11	11	NUM
ejpam-5699	77	40	,	,	PUNCT
ejpam-5699	77	41	(	(	PUNCT
ejpam-5699	77	42	8)	8)	NUM
ejpam-5699	77	43	for	for	ADP
ejpam-5699	77	44	all	all	DET
ejpam-5699	77	45	g1,è1	g1,è1	PROPN
ejpam-5699	77	46	,	,	PUNCT
ejpam-5699	77	47	11	11	NUM
ejpam-5699	77	48	∈	∈	NOUN
ejpam-5699	77	49	g.	g.	NOUN
ejpam-5699	77	50	definition	definition	NOUN
ejpam-5699	77	51	3	3	NUM
ejpam-5699	77	52	.	.	PUNCT
ejpam-5699	78	1	[	[	X
ejpam-5699	78	2	6	6	NUM
ejpam-5699	78	3	]	]	PUNCT
ejpam-5699	78	4	a	a	DET
ejpam-5699	78	5	bck	bck	NOUN
ejpam-5699	78	6	-	-	PUNCT
ejpam-5699	78	7	a	a	DET
ejpam-5699	78	8	g	g	NOUN
ejpam-5699	78	9	is	be	AUX
ejpam-5699	78	10	considered	consider	VERB
ejpam-5699	78	11	to	to	PART
ejpam-5699	78	12	be	be	AUX
ejpam-5699	78	13	a	a	DET
ejpam-5699	78	14	commutative	commutative	ADJ
ejpam-5699	78	15	if	if	SCONJ
ejpam-5699	78	16	the	the	DET
ejpam-5699	78	17	following	follow	VERB
ejpam-5699	78	18	condition	condition	NOUN
ejpam-5699	78	19	holds	hold	VERB
ejpam-5699	78	20	g1	g1	PROPN
ejpam-5699	78	21	⋄	⋄	PROPN
ejpam-5699	78	22	(	(	PUNCT
ejpam-5699	78	23	g1	g1	PROPN
ejpam-5699	78	24	⋄	⋄	PROPN
ejpam-5699	78	25	è1	è1	PROPN
ejpam-5699	78	26	)	)	PUNCT
ejpam-5699	78	27	=	=	SYM
ejpam-5699	78	28	è1	è1	NOUN
ejpam-5699	78	29	⋄	⋄	NOUN
ejpam-5699	78	30	(	(	PUNCT
ejpam-5699	78	31	è1	è1	PROPN
ejpam-5699	78	32	⋄	⋄	PROPN
ejpam-5699	78	33	g1	g1	PROPN
ejpam-5699	78	34	)	)	PUNCT
ejpam-5699	78	35	,	,	PUNCT
ejpam-5699	78	36	(	(	PUNCT
ejpam-5699	78	37	9	9	X
ejpam-5699	78	38	)	)	PUNCT
ejpam-5699	78	39	for	for	ADP
ejpam-5699	78	40	all	all	DET
ejpam-5699	78	41	g1,è1	g1,è1	PROPN
ejpam-5699	78	42	∈	∈	PROPN
ejpam-5699	78	43	g.	g.	NOUN
ejpam-5699	78	44	definition	definition	NOUN
ejpam-5699	78	45	4	4	NUM
ejpam-5699	78	46	.	.	PUNCT
ejpam-5699	79	1	[	[	X
ejpam-5699	79	2	6	6	NUM
ejpam-5699	79	3	]	]	PUNCT
ejpam-5699	79	4	a	a	DET
ejpam-5699	79	5	bck	bck	NOUN
ejpam-5699	79	6	-	-	PUNCT
ejpam-5699	79	7	a	a	DET
ejpam-5699	79	8	g	g	NOUN
ejpam-5699	79	9	is	be	AUX
ejpam-5699	79	10	considered	consider	VERB
ejpam-5699	79	11	to	to	PART
ejpam-5699	79	12	be	be	AUX
ejpam-5699	79	13	an	an	DET
ejpam-5699	79	14	implicative	implicative	ADJ
ejpam-5699	79	15	if	if	SCONJ
ejpam-5699	79	16	the	the	DET
ejpam-5699	79	17	following	follow	VERB
ejpam-5699	79	18	condition	condition	NOUN
ejpam-5699	79	19	holds	hold	VERB
ejpam-5699	79	20	g1	g1	PROPN
ejpam-5699	79	21	⋄	⋄	PROPN
ejpam-5699	79	22	(	(	PUNCT
ejpam-5699	79	23	è1	è1	PROPN
ejpam-5699	79	24	⋄	⋄	NOUN
ejpam-5699	79	25	g1	g1	PROPN
ejpam-5699	79	26	)	)	PUNCT
ejpam-5699	79	27	=	=	SYM
ejpam-5699	79	28	g1	g1	NOUN
ejpam-5699	79	29	,	,	PUNCT
ejpam-5699	79	30	(	(	PUNCT
ejpam-5699	79	31	10	10	NUM
ejpam-5699	79	32	)	)	PUNCT
ejpam-5699	79	33	for	for	ADP
ejpam-5699	79	34	all	all	DET
ejpam-5699	79	35	g1,è1	g1,è1	PROPN
ejpam-5699	79	36	∈	∈	PROPN
ejpam-5699	79	37	g.	g.	NOUN
ejpam-5699	79	38	definition	definition	NOUN
ejpam-5699	79	39	5	5	NUM
ejpam-5699	79	40	.	.	PUNCT
ejpam-5699	80	1	[	[	X
ejpam-5699	80	2	6	6	NUM
ejpam-5699	80	3	]	]	PUNCT
ejpam-5699	80	4	a	a	DET
ejpam-5699	80	5	subalgebra	subalgebra	NOUN
ejpam-5699	80	6	of	of	ADP
ejpam-5699	80	7	a	a	DET
ejpam-5699	80	8	bck	bck	NOUN
ejpam-5699	80	9	-	-	PUNCT
ejpam-5699	80	10	a	a	DET
ejpam-5699	80	11	g	g	NOUN
ejpam-5699	80	12	is	be	AUX
ejpam-5699	80	13	defined	define	VERB
ejpam-5699	80	14	as	as	ADP
ejpam-5699	80	15	a	a	DET
ejpam-5699	80	16	non	non	ADJ
ejpam-5699	80	17	-	-	ADJ
ejpam-5699	80	18	empty	empty	ADJ
ejpam-5699	80	19	subset	subset	NOUN
ejpam-5699	80	20	i	i	PRON
ejpam-5699	80	21	of	of	ADP
ejpam-5699	80	22	g	g	PROPN
ejpam-5699	80	23	satisfying	satisfy	VERB
ejpam-5699	80	24	the	the	DET
ejpam-5699	80	25	following	follow	VERB
ejpam-5699	80	26	condition	condition	NOUN
ejpam-5699	80	27	:	:	PUNCT
ejpam-5699	80	28	g1	g1	PROPN
ejpam-5699	80	29	⋄	⋄	PROPN
ejpam-5699	80	30	è1	è1	PROPN
ejpam-5699	80	31	∈	∈	PROPN
ejpam-5699	80	32	i	i	PRON
ejpam-5699	80	33	,	,	PUNCT
ejpam-5699	80	34	(	(	PUNCT
ejpam-5699	80	35	11	11	NUM
ejpam-5699	80	36	)	)	PUNCT
ejpam-5699	80	37	for	for	ADP
ejpam-5699	80	38	all	all	DET
ejpam-5699	80	39	g1,è1	g1,è1	PROPN
ejpam-5699	80	40	∈	∈	PROPN
ejpam-5699	80	41	i.	i.	NOUN
ejpam-5699	80	42	definition	definition	NOUN
ejpam-5699	80	43	6	6	NUM
ejpam-5699	80	44	.	.	PUNCT
ejpam-5699	81	1	[	[	X
ejpam-5699	81	2	6	6	NUM
ejpam-5699	81	3	]	]	PUNCT
ejpam-5699	81	4	an	an	DET
ejpam-5699	81	5	ideal	ideal	NOUN
ejpam-5699	81	6	of	of	ADP
ejpam-5699	81	7	a	a	DET
ejpam-5699	81	8	bck	bck	NOUN
ejpam-5699	81	9	-	-	PUNCT
ejpam-5699	81	10	a	a	DET
ejpam-5699	81	11	g	g	NOUN
ejpam-5699	81	12	is	be	AUX
ejpam-5699	81	13	defined	define	VERB
ejpam-5699	81	14	as	as	ADP
ejpam-5699	81	15	a	a	DET
ejpam-5699	81	16	non	non	ADJ
ejpam-5699	81	17	-	-	ADJ
ejpam-5699	81	18	empty	empty	ADJ
ejpam-5699	81	19	subset	subset	NOUN
ejpam-5699	81	20	i	i	PRON
ejpam-5699	81	21	of	of	ADP
ejpam-5699	81	22	g	g	PROPN
ejpam-5699	81	23	satisfying	satisfy	VERB
ejpam-5699	81	24	the	the	DET
ejpam-5699	81	25	following	follow	VERB
ejpam-5699	81	26	condition	condition	NOUN
ejpam-5699	81	27	:	:	PUNCT
ejpam-5699	81	28	(	(	PUNCT
ejpam-5699	81	29	i1	i1	PROPN
ejpam-5699	81	30	)	)	PUNCT
ejpam-5699	81	31	0	0	PUNCT
ejpam-5699	82	1	∈	∈	PROPN
ejpam-5699	82	2	i	i	PRON
ejpam-5699	82	3	,	,	PUNCT
ejpam-5699	82	4	(	(	PUNCT
ejpam-5699	82	5	i2	i2	NOUN
ejpam-5699	82	6	)	)	PUNCT
ejpam-5699	82	7	g1	g1	PROPN
ejpam-5699	82	8	⋄	⋄	PROPN
ejpam-5699	82	9	è1	è1	PROPN
ejpam-5699	82	10	∈	∈	PROPN
ejpam-5699	82	11	i	i	PRON
ejpam-5699	82	12	,	,	PUNCT
ejpam-5699	82	13	è1	è1	NOUN
ejpam-5699	82	14	∈	∈	NOUN
ejpam-5699	82	15	i	i	PRON
ejpam-5699	82	16	⇒	⇒	VERB
ejpam-5699	82	17	g1	g1	PROPN
ejpam-5699	82	18	∈	∈	PROPN
ejpam-5699	82	19	i	i	PROPN
ejpam-5699	82	20	,	,	PUNCT
ejpam-5699	82	21	d.	d.	PROPN
ejpam-5699	82	22	ramesh	ramesh	PROPN
ejpam-5699	82	23	et	et	PROPN
ejpam-5699	82	24	al	al	PROPN
ejpam-5699	82	25	.	.	PUNCT
ejpam-5699	82	26	/	/	SYM
ejpam-5699	82	27	eur	eur	PROPN
ejpam-5699	82	28	.	.	PUNCT
ejpam-5699	83	1	j.	j.	PROPN
ejpam-5699	83	2	pure	pure	PROPN
ejpam-5699	83	3	appl	appl	PROPN
ejpam-5699	83	4	.	.	PROPN
ejpam-5699	83	5	math	math	PROPN
ejpam-5699	83	6	,	,	PUNCT
ejpam-5699	83	7	18	18	NUM
ejpam-5699	83	8	(	(	PUNCT
ejpam-5699	83	9	1	1	NUM
ejpam-5699	83	10	)	)	PUNCT
ejpam-5699	83	11	(	(	PUNCT
ejpam-5699	83	12	2025	2025	NUM
ejpam-5699	83	13	)	)	PUNCT
ejpam-5699	83	14	,	,	PUNCT
ejpam-5699	83	15	5699	5699	NUM
ejpam-5699	83	16	6	6	NUM
ejpam-5699	83	17	of	of	ADP
ejpam-5699	83	18	20	20	NUM
ejpam-5699	83	19	for	for	ADP
ejpam-5699	83	20	all	all	DET
ejpam-5699	83	21	g1,è1	g1,è1	PROPN
ejpam-5699	83	22	∈	∈	PROPN
ejpam-5699	83	23	g.	g.	NOUN
ejpam-5699	83	24	definition	definition	NOUN
ejpam-5699	83	25	7	7	NUM
ejpam-5699	83	26	.	.	PUNCT
ejpam-5699	84	1	[	[	X
ejpam-5699	84	2	6	6	NUM
ejpam-5699	84	3	]	]	PUNCT
ejpam-5699	84	4	a	a	DET
ejpam-5699	84	5	commutative	commutative	ADJ
ejpam-5699	84	6	ideal	ideal	NOUN
ejpam-5699	84	7	of	of	ADP
ejpam-5699	84	8	a	a	DET
ejpam-5699	84	9	bck	bck	NOUN
ejpam-5699	84	10	-	-	PUNCT
ejpam-5699	84	11	a	a	DET
ejpam-5699	84	12	g	g	NOUN
ejpam-5699	84	13	is	be	AUX
ejpam-5699	84	14	defined	define	VERB
ejpam-5699	84	15	as	as	ADP
ejpam-5699	84	16	a	a	DET
ejpam-5699	84	17	non	non	ADJ
ejpam-5699	84	18	-	-	ADJ
ejpam-5699	84	19	empty	empty	ADJ
ejpam-5699	84	20	subset	subset	NOUN
ejpam-5699	84	21	i	i	PRON
ejpam-5699	84	22	of	of	ADP
ejpam-5699	84	23	g	g	PROPN
ejpam-5699	84	24	satisfying	satisfy	VERB
ejpam-5699	84	25	the	the	DET
ejpam-5699	84	26	condition	condition	NOUN
ejpam-5699	84	27	(	(	PUNCT
ejpam-5699	84	28	i1	i1	PROPN
ejpam-5699	84	29	)	)	PUNCT
ejpam-5699	84	30	and	and	CCONJ
ejpam-5699	84	31	the	the	DET
ejpam-5699	84	32	following	follow	VERB
ejpam-5699	84	33	(	(	PUNCT
ejpam-5699	84	34	ci1	ci1	PROPN
ejpam-5699	84	35	)	)	PUNCT
ejpam-5699	84	36	(	(	PUNCT
ejpam-5699	84	37	g1	g1	PROPN
ejpam-5699	84	38	⋄	⋄	PROPN
ejpam-5699	84	39	è1	è1	PROPN
ejpam-5699	84	40	)	)	PUNCT
ejpam-5699	84	41	⋄	⋄	NOUN
ejpam-5699	84	42	11	11	NUM
ejpam-5699	84	43	∈	∈	PROPN
ejpam-5699	84	44	i	i	PRON
ejpam-5699	84	45	,	,	PUNCT
ejpam-5699	84	46	11	11	NUM
ejpam-5699	84	47	∈	∈	NOUN
ejpam-5699	84	48	i	i	PRON
ejpam-5699	84	49	⇒	⇒	VERB
ejpam-5699	84	50	g1	g1	PROPN
ejpam-5699	84	51	⋄	⋄	PROPN
ejpam-5699	84	52	(	(	PUNCT
ejpam-5699	84	53	è1	è1	PROPN
ejpam-5699	84	54	⋄	⋄	NOUN
ejpam-5699	84	55	(	(	PUNCT
ejpam-5699	84	56	è1	è1	PROPN
ejpam-5699	84	57	⋄	⋄	PROPN
ejpam-5699	84	58	g1	g1	PROPN
ejpam-5699	84	59	)	)	PUNCT
ejpam-5699	84	60	)	)	PUNCT
ejpam-5699	85	1	∈	∈	PROPN
ejpam-5699	86	1	i	i	PRON
ejpam-5699	86	2	,	,	PUNCT
ejpam-5699	86	3	for	for	ADP
ejpam-5699	86	4	all	all	DET
ejpam-5699	86	5	g1,è1	g1,è1	PROPN
ejpam-5699	86	6	,	,	PUNCT
ejpam-5699	86	7	11	11	NUM
ejpam-5699	86	8	∈	∈	NOUN
ejpam-5699	86	9	g.	g.	NOUN
ejpam-5699	86	10	definition	definition	NOUN
ejpam-5699	86	11	8	8	NUM
ejpam-5699	86	12	.	.	PUNCT
ejpam-5699	87	1	[	[	X
ejpam-5699	87	2	6	6	NUM
ejpam-5699	87	3	]	]	PUNCT
ejpam-5699	87	4	a	a	DET
ejpam-5699	87	5	positive	positive	ADJ
ejpam-5699	87	6	implicative	implicative	ADJ
ejpam-5699	87	7	ideal	ideal	NOUN
ejpam-5699	87	8	of	of	ADP
ejpam-5699	87	9	a	a	DET
ejpam-5699	87	10	bck	bck	NOUN
ejpam-5699	87	11	-	-	PUNCT
ejpam-5699	87	12	a	a	DET
ejpam-5699	87	13	g	g	NOUN
ejpam-5699	87	14	is	be	AUX
ejpam-5699	87	15	defined	define	VERB
ejpam-5699	87	16	as	as	ADP
ejpam-5699	87	17	a	a	DET
ejpam-5699	87	18	non	non	ADJ
ejpam-5699	87	19	-	-	ADJ
ejpam-5699	87	20	empty	empty	ADJ
ejpam-5699	87	21	subset	subset	NOUN
ejpam-5699	87	22	i	i	PRON
ejpam-5699	87	23	of	of	ADP
ejpam-5699	87	24	g	g	PROPN
ejpam-5699	87	25	satisfying	satisfy	VERB
ejpam-5699	87	26	the	the	DET
ejpam-5699	87	27	condition	condition	NOUN
ejpam-5699	87	28	(	(	PUNCT
ejpam-5699	87	29	i1	i1	PROPN
ejpam-5699	87	30	)	)	PUNCT
ejpam-5699	87	31	and	and	CCONJ
ejpam-5699	87	32	the	the	DET
ejpam-5699	87	33	following	follow	VERB
ejpam-5699	87	34	(	(	PUNCT
ejpam-5699	87	35	pii1	pii1	NOUN
ejpam-5699	87	36	)	)	PUNCT
ejpam-5699	87	37	(	(	PUNCT
ejpam-5699	87	38	g1	g1	PROPN
ejpam-5699	87	39	⋄	⋄	PROPN
ejpam-5699	87	40	è1	è1	PROPN
ejpam-5699	87	41	)	)	PUNCT
ejpam-5699	87	42	⋄	⋄	NOUN
ejpam-5699	87	43	11	11	NUM
ejpam-5699	87	44	∈	∈	PROPN
ejpam-5699	87	45	i	i	PRON
ejpam-5699	87	46	,	,	PUNCT
ejpam-5699	87	47	è1	è1	PROPN
ejpam-5699	87	48	⋄	⋄	PROPN
ejpam-5699	87	49	11	11	NUM
ejpam-5699	87	50	∈	∈	NOUN
ejpam-5699	87	51	i	i	PRON
ejpam-5699	87	52	⇒	⇒	VERB
ejpam-5699	87	53	g1	g1	PROPN
ejpam-5699	87	54	⋄	⋄	PROPN
ejpam-5699	87	55	11	11	NUM
ejpam-5699	87	56	∈	∈	PROPN
ejpam-5699	88	1	i	i	PRON
ejpam-5699	88	2	,	,	PUNCT
ejpam-5699	88	3	for	for	ADP
ejpam-5699	88	4	all	all	DET
ejpam-5699	88	5	g1,è1	g1,è1	PROPN
ejpam-5699	88	6	,	,	PUNCT
ejpam-5699	88	7	11	11	NUM
ejpam-5699	88	8	∈	∈	NOUN
ejpam-5699	88	9	g.	g.	NOUN
ejpam-5699	88	10	definition	definition	NOUN
ejpam-5699	88	11	9	9	NUM
ejpam-5699	88	12	.	.	PUNCT
ejpam-5699	89	1	[	[	X
ejpam-5699	89	2	6	6	NUM
ejpam-5699	89	3	]	]	PUNCT
ejpam-5699	89	4	an	an	DET
ejpam-5699	89	5	implicative	implicative	ADJ
ejpam-5699	89	6	ideal	ideal	NOUN
ejpam-5699	89	7	of	of	ADP
ejpam-5699	89	8	a	a	DET
ejpam-5699	89	9	bck	bck	NOUN
ejpam-5699	89	10	-	-	PUNCT
ejpam-5699	89	11	a	a	DET
ejpam-5699	89	12	g	g	NOUN
ejpam-5699	89	13	is	be	AUX
ejpam-5699	89	14	defined	define	VERB
ejpam-5699	89	15	as	as	ADP
ejpam-5699	89	16	a	a	DET
ejpam-5699	89	17	non	non	ADJ
ejpam-5699	89	18	-	-	ADJ
ejpam-5699	89	19	empty	empty	ADJ
ejpam-5699	89	20	subset	subset	NOUN
ejpam-5699	89	21	i	i	PRON
ejpam-5699	89	22	of	of	ADP
ejpam-5699	89	23	g	g	PROPN
ejpam-5699	89	24	satisfying	satisfy	VERB
ejpam-5699	89	25	the	the	DET
ejpam-5699	89	26	condition	condition	NOUN
ejpam-5699	89	27	(	(	PUNCT
ejpam-5699	89	28	i1	i1	PROPN
ejpam-5699	89	29	)	)	PUNCT
ejpam-5699	89	30	and	and	CCONJ
ejpam-5699	89	31	the	the	DET
ejpam-5699	89	32	following	follow	VERB
ejpam-5699	89	33	(	(	PUNCT
ejpam-5699	89	34	ii1	ii1	NOUN
ejpam-5699	89	35	)	)	PUNCT
ejpam-5699	89	36	(	(	PUNCT
ejpam-5699	89	37	g1	g1	PROPN
ejpam-5699	89	38	⋄	⋄	PROPN
ejpam-5699	89	39	(	(	PUNCT
ejpam-5699	89	40	è1	è1	PROPN
ejpam-5699	89	41	⋄	⋄	PROPN
ejpam-5699	89	42	g1	g1	PROPN
ejpam-5699	89	43	)	)	PUNCT
ejpam-5699	89	44	)	)	PUNCT
ejpam-5699	90	1	⋄	⋄	NOUN
ejpam-5699	90	2	11	11	NUM
ejpam-5699	90	3	∈	∈	PROPN
ejpam-5699	91	1	i	i	PRON
ejpam-5699	91	2	,	,	PUNCT
ejpam-5699	91	3	11	11	NUM
ejpam-5699	91	4	∈	∈	NOUN
ejpam-5699	91	5	i	i	PRON
ejpam-5699	91	6	⇒	⇒	VERB
ejpam-5699	91	7	g1	g1	PROPN
ejpam-5699	91	8	∈	∈	PROPN
ejpam-5699	91	9	i	i	PROPN
ejpam-5699	91	10	,	,	PUNCT
ejpam-5699	91	11	for	for	ADP
ejpam-5699	91	12	all	all	DET
ejpam-5699	91	13	g1,è1	g1,è1	PROPN
ejpam-5699	91	14	,	,	PUNCT
ejpam-5699	91	15	11	11	NUM
ejpam-5699	91	16	∈	∈	NOUN
ejpam-5699	91	17	g.	g.	NOUN
ejpam-5699	91	18	definition	definition	NOUN
ejpam-5699	91	19	10	10	NUM
ejpam-5699	91	20	.	.	PUNCT
ejpam-5699	92	1	[	[	X
ejpam-5699	92	2	31	31	NUM
ejpam-5699	92	3	]	]	PUNCT
ejpam-5699	92	4	let	let	VERB
ejpam-5699	92	5	g	g	PRON
ejpam-5699	92	6	be	be	AUX
ejpam-5699	92	7	a	a	DET
ejpam-5699	92	8	non	non	ADJ
ejpam-5699	92	9	-	-	ADJ
ejpam-5699	92	10	empty	empty	ADJ
ejpam-5699	92	11	set	set	NOUN
ejpam-5699	92	12	.	.	PUNCT
ejpam-5699	93	1	an	an	DET
ejpam-5699	93	2	fs	f	NOUN
ejpam-5699	93	3	in	in	ADP
ejpam-5699	93	4	g	g	PROPN
ejpam-5699	93	5	is	be	AUX
ejpam-5699	93	6	a	a	DET
ejpam-5699	93	7	mapping	mapping	NOUN
ejpam-5699	93	8	m	m	NOUN
ejpam-5699	93	9	:	:	PUNCT
ejpam-5699	93	10	g	g	X
ejpam-5699	93	11	→	→	SYM
ejpam-5699	93	12	[	[	X
ejpam-5699	93	13	0	0	NUM
ejpam-5699	93	14	,	,	PUNCT
ejpam-5699	93	15	1	1	NUM
ejpam-5699	93	16	]	]	PUNCT
ejpam-5699	93	17	.	.	PUNCT
ejpam-5699	94	1	definition	definition	NOUN
ejpam-5699	94	2	11	11	NUM
ejpam-5699	94	3	.	.	PUNCT
ejpam-5699	95	1	[	[	X
ejpam-5699	95	2	31	31	NUM
ejpam-5699	95	3	]	]	PUNCT
ejpam-5699	95	4	the	the	DET
ejpam-5699	95	5	complement	complement	NOUN
ejpam-5699	95	6	of	of	ADP
ejpam-5699	95	7	an	an	DET
ejpam-5699	95	8	fs	fs	NOUN
ejpam-5699	95	9	m	m	AUX
ejpam-5699	95	10	denoted	denote	VERB
ejpam-5699	95	11	by	by	ADP
ejpam-5699	95	12	m	m	PROPN
ejpam-5699	95	13	is	be	AUX
ejpam-5699	95	14	also	also	ADV
ejpam-5699	95	15	an	an	DET
ejpam-5699	95	16	fs	fs	NOUN
ejpam-5699	95	17	defined	define	VERB
ejpam-5699	95	18	as	as	ADP
ejpam-5699	95	19	m(g1	m(g1	NOUN
ejpam-5699	95	20	)	)	PUNCT
ejpam-5699	95	21	=	=	SYM
ejpam-5699	96	1	1−m(g1	1−m(g1	NUM
ejpam-5699	96	2	)	)	PUNCT
ejpam-5699	96	3	for	for	ADP
ejpam-5699	96	4	all	all	DET
ejpam-5699	96	5	g1	g1	PROPN
ejpam-5699	96	6	∈	∈	PROPN
ejpam-5699	96	7	g.	g.	NOUN
ejpam-5699	96	8	also	also	ADV
ejpam-5699	96	9	(	(	PUNCT
ejpam-5699	96	10	m	m	NOUN
ejpam-5699	96	11	)	)	PUNCT
ejpam-5699	96	12	=	=	SYM
ejpam-5699	96	13	m.	m.	NOUN
ejpam-5699	96	14	definition	definition	NOUN
ejpam-5699	96	15	12	12	NUM
ejpam-5699	96	16	.	.	PUNCT
ejpam-5699	97	1	[	[	X
ejpam-5699	97	2	14	14	NUM
ejpam-5699	97	3	]	]	X
ejpam-5699	97	4	a	a	DET
ejpam-5699	97	5	bpvfs	bpvfs	NOUN
ejpam-5699	97	6	b	b	NOUN
ejpam-5699	97	7	of	of	ADP
ejpam-5699	97	8	g	g	PROPN
ejpam-5699	97	9	is	be	AUX
ejpam-5699	97	10	defined	define	VERB
ejpam-5699	97	11	as	as	ADP
ejpam-5699	97	12	b	b	X
ejpam-5699	97	13	=	=	PRON
ejpam-5699	97	14	{	{	PUNCT
ejpam-5699	97	15	(	(	PUNCT
ejpam-5699	97	16	g1,m+	g1,m+	X
ejpam-5699	97	17	b(g1),m−	b(g1),m−	PROPN
ejpam-5699	97	18	b(g1))|g1	b(g1))|g1	NOUN
ejpam-5699	97	19	∈	∈	NOUN
ejpam-5699	97	20	g	g	PROPN
ejpam-5699	97	21	}	}	PUNCT
ejpam-5699	97	22	,	,	PUNCT
ejpam-5699	97	23	where	where	SCONJ
ejpam-5699	97	24	m+	m+	NUM
ejpam-5699	97	25	b	b	NOUN
ejpam-5699	97	26	:	:	PUNCT
ejpam-5699	97	27	g	g	NOUN
ejpam-5699	97	28	→	→	SYM
ejpam-5699	97	29	[	[	X
ejpam-5699	97	30	0	0	NUM
ejpam-5699	97	31	,	,	PUNCT
ejpam-5699	97	32	1	1	NUM
ejpam-5699	97	33	]	]	PUNCT
ejpam-5699	97	34	and	and	CCONJ
ejpam-5699	97	35	m−	m−	PROPN
ejpam-5699	97	36	b	b	PROPN
ejpam-5699	97	37	:	:	PUNCT
ejpam-5699	97	38	g	g	PROPN
ejpam-5699	97	39	→	→	SYM
ejpam-5699	97	40	[	[	X
ejpam-5699	97	41	−1	−1	NOUN
ejpam-5699	97	42	,	,	PUNCT
ejpam-5699	97	43	0	0	NUM
ejpam-5699	97	44	]	]	PUNCT
ejpam-5699	97	45	are	be	AUX
ejpam-5699	97	46	mappings	mapping	NOUN
ejpam-5699	97	47	.	.	PUNCT
ejpam-5699	98	1	the	the	DET
ejpam-5699	98	2	degree	degree	NOUN
ejpam-5699	98	3	of	of	ADP
ejpam-5699	98	4	positive	positive	ADJ
ejpam-5699	98	5	membership	membership	NOUN
ejpam-5699	98	6	m+	m+	NUM
ejpam-5699	98	7	b	b	PROPN
ejpam-5699	98	8	indicates	indicate	VERB
ejpam-5699	98	9	how	how	SCONJ
ejpam-5699	98	10	the	the	DET
ejpam-5699	98	11	member	member	NOUN
ejpam-5699	98	12	of	of	ADP
ejpam-5699	98	13	g	g	PROPN
ejpam-5699	98	14	satisfies	satisfy	VERB
ejpam-5699	98	15	the	the	DET
ejpam-5699	98	16	property	property	NOUN
ejpam-5699	98	17	related	relate	VERB
ejpam-5699	98	18	to	to	ADP
ejpam-5699	98	19	the	the	DET
ejpam-5699	98	20	bpvfs	bpvfs	NOUN
ejpam-5699	98	21	b	b	NOUN
ejpam-5699	98	22	,	,	PUNCT
ejpam-5699	98	23	while	while	SCONJ
ejpam-5699	98	24	the	the	DET
ejpam-5699	98	25	negative	negative	ADJ
ejpam-5699	98	26	degree	degree	NOUN
ejpam-5699	98	27	of	of	ADP
ejpam-5699	98	28	membership	membership	NOUN
ejpam-5699	98	29	m−	m−	PROPN
ejpam-5699	98	30	b	b	PROPN
ejpam-5699	98	31	indicates	indicate	VERB
ejpam-5699	98	32	the	the	DET
ejpam-5699	98	33	grade	grade	NOUN
ejpam-5699	98	34	of	of	ADP
ejpam-5699	98	35	satisfaction	satisfaction	NOUN
ejpam-5699	98	36	that	that	SCONJ
ejpam-5699	98	37	the	the	DET
ejpam-5699	98	38	member	member	NOUN
ejpam-5699	98	39	of	of	ADP
ejpam-5699	98	40	g	g	PROPN
ejpam-5699	98	41	has	have	VERB
ejpam-5699	98	42	toward	toward	ADP
ejpam-5699	98	43	some	some	DET
ejpam-5699	98	44	implicit	implicit	ADJ
ejpam-5699	98	45	counter	counter	ADJ
ejpam-5699	98	46	property	property	NOUN
ejpam-5699	98	47	of	of	ADP
ejpam-5699	98	48	b.	b.	PROPN
ejpam-5699	98	49	we	we	PRON
ejpam-5699	98	50	shall	shall	AUX
ejpam-5699	98	51	use	use	VERB
ejpam-5699	98	52	the	the	DET
ejpam-5699	98	53	symbol	symbol	NOUN
ejpam-5699	98	54	b	b	NOUN
ejpam-5699	98	55	=	=	PUNCT
ejpam-5699	98	56	(	(	PUNCT
ejpam-5699	98	57	g1,m+	g1,m+	NOUN
ejpam-5699	98	58	b	b	NOUN
ejpam-5699	98	59	,	,	PUNCT
ejpam-5699	98	60	m−	m−	PROPN
ejpam-5699	98	61	b	b	PROPN
ejpam-5699	98	62	)	)	PUNCT
ejpam-5699	98	63	for	for	ADP
ejpam-5699	98	64	a	a	DET
ejpam-5699	98	65	bpvfs	bpvfs	NOUN
ejpam-5699	98	66	b	b	X
ejpam-5699	98	67	=	=	PRON
ejpam-5699	98	68	{	{	PUNCT
ejpam-5699	98	69	(	(	PUNCT
ejpam-5699	98	70	g1,m+	g1,m+	X
ejpam-5699	98	71	b(g1),m−	b(g1),m−	PROPN
ejpam-5699	98	72	b(g1))|g1	b(g1))|g1	NOUN
ejpam-5699	98	73	∈	∈	NOUN
ejpam-5699	98	74	g	g	PROPN
ejpam-5699	98	75	}	}	PUNCT
ejpam-5699	98	76	.	.	PUNCT
ejpam-5699	99	1	definition	definition	NOUN
ejpam-5699	99	2	13	13	NUM
ejpam-5699	99	3	.	.	PUNCT
ejpam-5699	100	1	[	[	X
ejpam-5699	100	2	15	15	NUM
ejpam-5699	100	3	]	]	X
ejpam-5699	100	4	a	a	DET
ejpam-5699	100	5	bpvfs	bpvfs	NOUN
ejpam-5699	100	6	b	b	X
ejpam-5699	100	7	=	=	PUNCT
ejpam-5699	100	8	(	(	PUNCT
ejpam-5699	100	9	g1,m+	g1,m+	NOUN
ejpam-5699	100	10	b	b	NOUN
ejpam-5699	100	11	,	,	PUNCT
ejpam-5699	100	12	m−	m−	PROPN
ejpam-5699	100	13	b	b	NOUN
ejpam-5699	100	14	)	)	PUNCT
ejpam-5699	100	15	in	in	ADP
ejpam-5699	100	16	g	g	PROPN
ejpam-5699	100	17	is	be	AUX
ejpam-5699	100	18	said	say	VERB
ejpam-5699	100	19	to	to	PART
ejpam-5699	100	20	be	be	AUX
ejpam-5699	100	21	a	a	DET
ejpam-5699	100	22	bipolar	bipolar	ADJ
ejpam-5699	100	23	fuzzy	fuzzy	ADJ
ejpam-5699	100	24	subalgebra	subalgebra	NOUN
ejpam-5699	100	25	if	if	SCONJ
ejpam-5699	100	26	the	the	DET
ejpam-5699	100	27	following	follow	VERB
ejpam-5699	100	28	conditions	condition	NOUN
ejpam-5699	100	29	are	be	AUX
ejpam-5699	100	30	satisfied	satisfied	ADJ
ejpam-5699	100	31	:	:	PUNCT
ejpam-5699	100	32	m+	m+	NUM
ejpam-5699	100	33	b(g1	b(g1	ADJ
ejpam-5699	100	34	⋄	⋄	PROPN
ejpam-5699	100	35	è1	è1	PROPN
ejpam-5699	100	36	)	)	PUNCT
ejpam-5699	100	37	≥	≥	NOUN
ejpam-5699	100	38	min{m+	min{m+	PROPN
ejpam-5699	100	39	b(g1),m+	b(g1),m+	PROPN
ejpam-5699	100	40	b(è1	b(è1	NOUN
ejpam-5699	100	41	)	)	PUNCT
ejpam-5699	100	42	}	}	PUNCT
ejpam-5699	100	43	,	,	PUNCT
ejpam-5699	100	44	m−	m−	PROPN
ejpam-5699	100	45	b(g1	b(g1	PROPN
ejpam-5699	100	46	⋄	⋄	PROPN
ejpam-5699	100	47	è1	è1	PROPN
ejpam-5699	100	48	)	)	PUNCT
ejpam-5699	100	49	≤	≤	NOUN
ejpam-5699	100	50	max{m−	max{m−	NOUN
ejpam-5699	100	51	b(g1),m−	b(g1),m−	NOUN
ejpam-5699	100	52	b(è1	b(è1	NOUN
ejpam-5699	100	53	)	)	PUNCT
ejpam-5699	100	54	}	}	PUNCT
ejpam-5699	100	55	,	,	PUNCT
ejpam-5699	100	56	for	for	ADP
ejpam-5699	100	57	all	all	DET
ejpam-5699	100	58	g1,è1	g1,è1	PROPN
ejpam-5699	100	59	∈	∈	PROPN
ejpam-5699	100	60	g.	g.	NOUN
ejpam-5699	100	61	definition	definition	NOUN
ejpam-5699	100	62	14	14	NUM
ejpam-5699	100	63	.	.	PUNCT
ejpam-5699	101	1	[	[	X
ejpam-5699	101	2	15	15	NUM
ejpam-5699	101	3	]	]	X
ejpam-5699	101	4	a	a	DET
ejpam-5699	101	5	bpvfs	bpvfs	NOUN
ejpam-5699	101	6	b	b	X
ejpam-5699	101	7	=	=	PUNCT
ejpam-5699	101	8	(	(	PUNCT
ejpam-5699	101	9	g1,m+	g1,m+	NOUN
ejpam-5699	101	10	b	b	NOUN
ejpam-5699	101	11	,	,	PUNCT
ejpam-5699	101	12	m−	m−	PROPN
ejpam-5699	101	13	b	b	NOUN
ejpam-5699	101	14	)	)	PUNCT
ejpam-5699	101	15	in	in	ADP
ejpam-5699	101	16	g	g	PROPN
ejpam-5699	101	17	is	be	AUX
ejpam-5699	101	18	said	say	VERB
ejpam-5699	101	19	to	to	PART
ejpam-5699	101	20	be	be	AUX
ejpam-5699	101	21	a	a	DET
ejpam-5699	101	22	bipolar	bipolar	ADJ
ejpam-5699	101	23	fuzzy	fuzzy	ADJ
ejpam-5699	101	24	ideal	ideal	NOUN
ejpam-5699	101	25	if	if	SCONJ
ejpam-5699	101	26	the	the	DET
ejpam-5699	101	27	following	follow	VERB
ejpam-5699	101	28	conditions	condition	NOUN
ejpam-5699	101	29	are	be	AUX
ejpam-5699	101	30	satisfied	satisfied	ADJ
ejpam-5699	101	31	:	:	PUNCT
ejpam-5699	101	32	m+	m+	NUM
ejpam-5699	101	33	b(0	b(0	NOUN
ejpam-5699	101	34	)	)	PUNCT
ejpam-5699	101	35	≥	≥	NOUN
ejpam-5699	101	36	m+	m+	NUM
ejpam-5699	101	37	b(g1	b(g1	NOUN
ejpam-5699	101	38	)	)	PUNCT
ejpam-5699	101	39	,	,	PUNCT
ejpam-5699	101	40	m−	m−	PROPN
ejpam-5699	101	41	b(0	b(0	PROPN
ejpam-5699	101	42	)	)	PUNCT
ejpam-5699	101	43	≤	≤	NOUN
ejpam-5699	101	44	m−	m−	PROPN
ejpam-5699	101	45	b(g1	b(g1	NOUN
ejpam-5699	101	46	)	)	PUNCT
ejpam-5699	101	47	and	and	CCONJ
ejpam-5699	101	48	m+	m+	NUM
ejpam-5699	101	49	b(g1	b(g1	NOUN
ejpam-5699	101	50	)	)	PUNCT
ejpam-5699	101	51	≥	≥	NOUN
ejpam-5699	101	52	min{m+	min{m+	VERB
ejpam-5699	101	53	b(g1	b(g1	ADJ
ejpam-5699	101	54	⋄	⋄	PROPN
ejpam-5699	101	55	è1),m+	è1),m+	NOUN
ejpam-5699	101	56	b(è1	b(è1	NOUN
ejpam-5699	101	57	)	)	PUNCT
ejpam-5699	101	58	}	}	PUNCT
ejpam-5699	101	59	,	,	PUNCT
ejpam-5699	101	60	m−	m−	PROPN
ejpam-5699	101	61	b(g1	b(g1	NOUN
ejpam-5699	101	62	)	)	PUNCT
ejpam-5699	101	63	≤	≤	NOUN
ejpam-5699	101	64	max{m−	max{m−	NOUN
ejpam-5699	101	65	b(g1	b(g1	ADJ
ejpam-5699	101	66	⋄	⋄	PROPN
ejpam-5699	101	67	è1),m−	è1),m−	PROPN
ejpam-5699	101	68	b(è1	b(è1	NOUN
ejpam-5699	101	69	)	)	PUNCT
ejpam-5699	101	70	}	}	PUNCT
ejpam-5699	101	71	,	,	PUNCT
ejpam-5699	101	72	for	for	ADP
ejpam-5699	101	73	all	all	DET
ejpam-5699	101	74	g1,è1	g1,è1	PROPN
ejpam-5699	101	75	∈	∈	PROPN
ejpam-5699	101	76	g.	g.	PROPN
ejpam-5699	101	77	d.	d.	PROPN
ejpam-5699	101	78	ramesh	ramesh	PROPN
ejpam-5699	102	1	et	et	PROPN
ejpam-5699	102	2	al	al	PROPN
ejpam-5699	102	3	.	.	PUNCT
ejpam-5699	102	4	/	/	SYM
ejpam-5699	102	5	eur	eur	PROPN
ejpam-5699	102	6	.	.	PUNCT
ejpam-5699	103	1	j.	j.	PROPN
ejpam-5699	103	2	pure	pure	PROPN
ejpam-5699	103	3	appl	appl	PROPN
ejpam-5699	103	4	.	.	PROPN
ejpam-5699	103	5	math	math	PROPN
ejpam-5699	103	6	,	,	PUNCT
ejpam-5699	103	7	18	18	NUM
ejpam-5699	103	8	(	(	PUNCT
ejpam-5699	103	9	1	1	NUM
ejpam-5699	103	10	)	)	PUNCT
ejpam-5699	103	11	(	(	PUNCT
ejpam-5699	103	12	2025	2025	NUM
ejpam-5699	103	13	)	)	PUNCT
ejpam-5699	103	14	,	,	PUNCT
ejpam-5699	103	15	5699	5699	NUM
ejpam-5699	103	16	7	7	NUM
ejpam-5699	103	17	of	of	ADP
ejpam-5699	103	18	20	20	NUM
ejpam-5699	103	19	definition	definition	NOUN
ejpam-5699	103	20	15	15	NUM
ejpam-5699	103	21	.	.	PUNCT
ejpam-5699	104	1	[	[	X
ejpam-5699	104	2	22	22	NUM
ejpam-5699	104	3	]	]	X
ejpam-5699	104	4	a	a	DET
ejpam-5699	104	5	bpvfs	bpvfs	NOUN
ejpam-5699	104	6	b	b	X
ejpam-5699	104	7	=	=	PUNCT
ejpam-5699	104	8	(	(	PUNCT
ejpam-5699	104	9	g1,m+	g1,m+	NOUN
ejpam-5699	104	10	b	b	NOUN
ejpam-5699	104	11	,	,	PUNCT
ejpam-5699	104	12	m−	m−	PROPN
ejpam-5699	104	13	b	b	NOUN
ejpam-5699	104	14	)	)	PUNCT
ejpam-5699	104	15	in	in	ADP
ejpam-5699	104	16	g	g	PROPN
ejpam-5699	104	17	is	be	AUX
ejpam-5699	104	18	said	say	VERB
ejpam-5699	104	19	to	to	PART
ejpam-5699	104	20	be	be	AUX
ejpam-5699	104	21	a	a	DET
ejpam-5699	104	22	bipolar	bipolar	ADJ
ejpam-5699	104	23	fuzzy	fuzzy	ADJ
ejpam-5699	104	24	implicative	implicative	ADJ
ejpam-5699	104	25	ideal	ideal	NOUN
ejpam-5699	104	26	of	of	ADP
ejpam-5699	104	27	g	g	PROPN
ejpam-5699	104	28	if	if	SCONJ
ejpam-5699	104	29	it	it	PRON
ejpam-5699	104	30	satisfies	satisfy	VERB
ejpam-5699	104	31	m+	m+	NUM
ejpam-5699	104	32	b(0	b(0	NOUN
ejpam-5699	104	33	)	)	PUNCT
ejpam-5699	104	34	≥	≥	NOUN
ejpam-5699	104	35	m+	m+	NUM
ejpam-5699	104	36	b(g1	b(g1	NOUN
ejpam-5699	104	37	)	)	PUNCT
ejpam-5699	104	38	,	,	PUNCT
ejpam-5699	104	39	m−	m−	PROPN
ejpam-5699	104	40	b(0	b(0	PROPN
ejpam-5699	104	41	)	)	PUNCT
ejpam-5699	104	42	≤	≤	NOUN
ejpam-5699	104	43	m−	m−	PROPN
ejpam-5699	104	44	b(g1	b(g1	NOUN
ejpam-5699	104	45	)	)	PUNCT
ejpam-5699	104	46	and	and	CCONJ
ejpam-5699	104	47	m+	m+	NUM
ejpam-5699	104	48	b(g1	b(g1	NOUN
ejpam-5699	104	49	)	)	PUNCT
ejpam-5699	104	50	≥	≥	NOUN
ejpam-5699	104	51	min{m+	min{m+	PROPN
ejpam-5699	104	52	b((g1	b((g1	PROPN
ejpam-5699	104	53	⋄	⋄	PROPN
ejpam-5699	104	54	(	(	PUNCT
ejpam-5699	104	55	è1	è1	PROPN
ejpam-5699	104	56	⋄	⋄	PROPN
ejpam-5699	104	57	g1	g1	PROPN
ejpam-5699	104	58	)	)	PUNCT
ejpam-5699	104	59	)	)	PUNCT
ejpam-5699	105	1	⋄	⋄	PROPN
ejpam-5699	105	2	11),m+	11),m+	NUM
ejpam-5699	105	3	b(11	b(11	NOUN
ejpam-5699	105	4	)	)	PUNCT
ejpam-5699	105	5	}	}	PUNCT
ejpam-5699	105	6	,	,	PUNCT
ejpam-5699	105	7	m−	m−	PROPN
ejpam-5699	105	8	b(g1	b(g1	NOUN
ejpam-5699	105	9	)	)	PUNCT
ejpam-5699	105	10	≤	≤	NOUN
ejpam-5699	105	11	max{m−	max{m−	NOUN
ejpam-5699	105	12	b((g1	b((g1	NOUN
ejpam-5699	105	13	⋄	⋄	NOUN
ejpam-5699	105	14	(	(	PUNCT
ejpam-5699	105	15	è1	è1	PROPN
ejpam-5699	105	16	⋄	⋄	PROPN
ejpam-5699	105	17	g1	g1	PROPN
ejpam-5699	105	18	)	)	PUNCT
ejpam-5699	105	19	)	)	PUNCT
ejpam-5699	106	1	⋄	⋄	PROPN
ejpam-5699	106	2	11),m−	11),m−	NUM
ejpam-5699	106	3	b(11	b(11	NOUN
ejpam-5699	106	4	)	)	PUNCT
ejpam-5699	106	5	}	}	PUNCT
ejpam-5699	106	6	,	,	PUNCT
ejpam-5699	106	7	for	for	ADP
ejpam-5699	106	8	all	all	DET
ejpam-5699	106	9	g1,è1	g1,è1	PROPN
ejpam-5699	106	10	,	,	PUNCT
ejpam-5699	106	11	11	11	NUM
ejpam-5699	106	12	∈	∈	NOUN
ejpam-5699	106	13	g.	g.	NOUN
ejpam-5699	106	14	definition	definition	NOUN
ejpam-5699	106	15	16	16	NUM
ejpam-5699	106	16	.	.	PUNCT
ejpam-5699	107	1	a	a	DET
ejpam-5699	107	2	bpvfs	bpvfs	NOUN
ejpam-5699	107	3	b	b	NOUN
ejpam-5699	107	4	=	=	PUNCT
ejpam-5699	107	5	(	(	PUNCT
ejpam-5699	107	6	g1,m+	g1,m+	NOUN
ejpam-5699	107	7	b	b	NOUN
ejpam-5699	107	8	,	,	PUNCT
ejpam-5699	107	9	m−	m−	PROPN
ejpam-5699	107	10	b	b	NOUN
ejpam-5699	107	11	)	)	PUNCT
ejpam-5699	107	12	in	in	ADP
ejpam-5699	107	13	g	g	PROPN
ejpam-5699	107	14	is	be	AUX
ejpam-5699	107	15	said	say	VERB
ejpam-5699	107	16	to	to	PART
ejpam-5699	107	17	be	be	AUX
ejpam-5699	107	18	a	a	DET
ejpam-5699	107	19	bipolar	bipolar	ADJ
ejpam-5699	107	20	fuzzy	fuzzy	ADJ
ejpam-5699	107	21	commutative	commutative	ADJ
ejpam-5699	107	22	ideal	ideal	NOUN
ejpam-5699	107	23	of	of	ADP
ejpam-5699	107	24	g	g	PROPN
ejpam-5699	107	25	if	if	SCONJ
ejpam-5699	107	26	it	it	PRON
ejpam-5699	107	27	satisfies	satisfy	VERB
ejpam-5699	107	28	m+	m+	NUM
ejpam-5699	107	29	b(0	b(0	NOUN
ejpam-5699	107	30	)	)	PUNCT
ejpam-5699	107	31	≥	≥	NOUN
ejpam-5699	107	32	m+	m+	NUM
ejpam-5699	107	33	b(g1	b(g1	NOUN
ejpam-5699	107	34	)	)	PUNCT
ejpam-5699	107	35	,	,	PUNCT
ejpam-5699	107	36	m−	m−	PROPN
ejpam-5699	107	37	b(0	b(0	PROPN
ejpam-5699	107	38	)	)	PUNCT
ejpam-5699	107	39	≤	≤	NOUN
ejpam-5699	107	40	m−	m−	PROPN
ejpam-5699	107	41	b(g1	b(g1	NOUN
ejpam-5699	107	42	)	)	PUNCT
ejpam-5699	107	43	and	and	CCONJ
ejpam-5699	107	44	m+	m+	NUM
ejpam-5699	107	45	b(g1	b(g1	ADJ
ejpam-5699	107	46	⋄	⋄	PROPN
ejpam-5699	107	47	(	(	PUNCT
ejpam-5699	107	48	è1	è1	PROPN
ejpam-5699	107	49	⋄	⋄	NOUN
ejpam-5699	107	50	(	(	PUNCT
ejpam-5699	107	51	è1	è1	PROPN
ejpam-5699	107	52	⋄	⋄	PROPN
ejpam-5699	107	53	g1	g1	PROPN
ejpam-5699	107	54	)	)	PUNCT
ejpam-5699	107	55	)	)	PUNCT
ejpam-5699	107	56	)	)	PUNCT
ejpam-5699	107	57	≥	≥	PROPN
ejpam-5699	107	58	min{m+	min{m+	PROPN
ejpam-5699	107	59	b((g1	b((g1	PROPN
ejpam-5699	107	60	⋄	⋄	PROPN
ejpam-5699	107	61	è1	è1	PROPN
ejpam-5699	107	62	)	)	PUNCT
ejpam-5699	107	63	⋄	⋄	PROPN
ejpam-5699	107	64	11),m+	11),m+	NUM
ejpam-5699	107	65	b(11	b(11	NOUN
ejpam-5699	107	66	)	)	PUNCT
ejpam-5699	107	67	}	}	PUNCT
ejpam-5699	107	68	,	,	PUNCT
ejpam-5699	107	69	m−	m−	PROPN
ejpam-5699	107	70	b(g1	b(g1	PROPN
ejpam-5699	107	71	⋄	⋄	PROPN
ejpam-5699	107	72	(	(	PUNCT
ejpam-5699	107	73	è1	è1	PROPN
ejpam-5699	107	74	⋄	⋄	NOUN
ejpam-5699	107	75	(	(	PUNCT
ejpam-5699	107	76	è1	è1	PROPN
ejpam-5699	107	77	⋄	⋄	PROPN
ejpam-5699	107	78	g1	g1	PROPN
ejpam-5699	107	79	)	)	PUNCT
ejpam-5699	107	80	)	)	PUNCT
ejpam-5699	107	81	)	)	PUNCT
ejpam-5699	107	82	≤	≤	NUM
ejpam-5699	107	83	max{m−	max{m−	NOUN
ejpam-5699	107	84	b((g1	b((g1	NOUN
ejpam-5699	107	85	⋄	⋄	PROPN
ejpam-5699	107	86	è1	è1	PROPN
ejpam-5699	107	87	)	)	PUNCT
ejpam-5699	107	88	⋄	⋄	PROPN
ejpam-5699	107	89	11),m−	11),m−	NUM
ejpam-5699	107	90	b(11	b(11	NOUN
ejpam-5699	107	91	)	)	PUNCT
ejpam-5699	107	92	}	}	PUNCT
ejpam-5699	107	93	,	,	PUNCT
ejpam-5699	107	94	for	for	ADP
ejpam-5699	107	95	all	all	DET
ejpam-5699	107	96	g1,è1	g1,è1	PROPN
ejpam-5699	107	97	,	,	PUNCT
ejpam-5699	107	98	11	11	NUM
ejpam-5699	107	99	∈	∈	NOUN
ejpam-5699	107	100	g.	g.	NOUN
ejpam-5699	107	101	definition	definition	NOUN
ejpam-5699	107	102	17	17	NUM
ejpam-5699	107	103	.	.	PUNCT
ejpam-5699	108	1	[	[	X
ejpam-5699	108	2	22	22	NUM
ejpam-5699	108	3	]	]	X
ejpam-5699	108	4	a	a	DET
ejpam-5699	108	5	bpvfs	bpvfs	NOUN
ejpam-5699	108	6	b	b	X
ejpam-5699	108	7	=	=	PUNCT
ejpam-5699	108	8	(	(	PUNCT
ejpam-5699	108	9	g1,m+	g1,m+	NOUN
ejpam-5699	108	10	b	b	NOUN
ejpam-5699	108	11	,	,	PUNCT
ejpam-5699	108	12	m−	m−	PROPN
ejpam-5699	108	13	b	b	NOUN
ejpam-5699	108	14	)	)	PUNCT
ejpam-5699	108	15	in	in	ADP
ejpam-5699	108	16	g	g	PROPN
ejpam-5699	108	17	is	be	AUX
ejpam-5699	108	18	said	say	VERB
ejpam-5699	108	19	to	to	PART
ejpam-5699	108	20	be	be	AUX
ejpam-5699	108	21	a	a	DET
ejpam-5699	108	22	bipolar	bipolar	ADJ
ejpam-5699	108	23	fuzzy	fuzzy	ADJ
ejpam-5699	108	24	positive	positive	ADJ
ejpam-5699	108	25	implicative	implicative	ADJ
ejpam-5699	108	26	ideal	ideal	NOUN
ejpam-5699	108	27	of	of	ADP
ejpam-5699	108	28	g	g	PROPN
ejpam-5699	108	29	if	if	SCONJ
ejpam-5699	108	30	it	it	PRON
ejpam-5699	108	31	satisfies	satisfy	VERB
ejpam-5699	108	32	m+	m+	NUM
ejpam-5699	108	33	b(0	b(0	NOUN
ejpam-5699	108	34	)	)	PUNCT
ejpam-5699	108	35	≥	≥	NOUN
ejpam-5699	108	36	m+	m+	NUM
ejpam-5699	108	37	b(g1	b(g1	NOUN
ejpam-5699	108	38	)	)	PUNCT
ejpam-5699	108	39	,	,	PUNCT
ejpam-5699	108	40	m−	m−	PROPN
ejpam-5699	108	41	b(0	b(0	PROPN
ejpam-5699	108	42	)	)	PUNCT
ejpam-5699	108	43	≤	≤	NOUN
ejpam-5699	108	44	m−	m−	PROPN
ejpam-5699	108	45	b(g1	b(g1	NOUN
ejpam-5699	108	46	)	)	PUNCT
ejpam-5699	108	47	and	and	CCONJ
ejpam-5699	108	48	m+	m+	NUM
ejpam-5699	108	49	b(g1	b(g1	ADJ
ejpam-5699	108	50	⋄	⋄	PROPN
ejpam-5699	108	51	11	11	NUM
ejpam-5699	108	52	)	)	PUNCT
ejpam-5699	108	53	≥	≥	NOUN
ejpam-5699	108	54	min{m+	min{m+	PROPN
ejpam-5699	108	55	b((g1	b((g1	PROPN
ejpam-5699	108	56	⋄	⋄	PROPN
ejpam-5699	108	57	è1	è1	PROPN
ejpam-5699	108	58	)	)	PUNCT
ejpam-5699	108	59	⋄	⋄	PROPN
ejpam-5699	108	60	11),m+	11),m+	NUM
ejpam-5699	108	61	b(è1	b(è1	NOUN
ejpam-5699	108	62	⋄	⋄	PROPN
ejpam-5699	108	63	11	11	NUM
ejpam-5699	108	64	)	)	PUNCT
ejpam-5699	108	65	}	}	PUNCT
ejpam-5699	108	66	,	,	PUNCT
ejpam-5699	108	67	m−	m−	PROPN
ejpam-5699	108	68	b(g1	b(g1	ADJ
ejpam-5699	108	69	⋄	⋄	PROPN
ejpam-5699	108	70	11	11	NUM
ejpam-5699	108	71	)	)	PUNCT
ejpam-5699	108	72	≤	≤	NOUN
ejpam-5699	108	73	max{m−	max{m−	NOUN
ejpam-5699	108	74	b((g1	b((g1	NOUN
ejpam-5699	108	75	⋄	⋄	PROPN
ejpam-5699	108	76	è1	è1	PROPN
ejpam-5699	108	77	)	)	PUNCT
ejpam-5699	108	78	⋄	⋄	NOUN
ejpam-5699	108	79	11),m−	11),m−	NUM
ejpam-5699	108	80	b(è1	b(è1	NOUN
ejpam-5699	108	81	⋄	⋄	PROPN
ejpam-5699	108	82	11	11	NUM
ejpam-5699	108	83	)	)	PUNCT
ejpam-5699	108	84	}	}	PUNCT
ejpam-5699	108	85	,	,	PUNCT
ejpam-5699	108	86	for	for	ADP
ejpam-5699	108	87	all	all	DET
ejpam-5699	108	88	g1,è1	g1,è1	PROPN
ejpam-5699	108	89	,	,	PUNCT
ejpam-5699	108	90	11	11	NUM
ejpam-5699	108	91	∈	∈	NOUN
ejpam-5699	108	92	g.	g.	NOUN
ejpam-5699	108	93	definition	definition	NOUN
ejpam-5699	108	94	18	18	NUM
ejpam-5699	108	95	.	.	PUNCT
ejpam-5699	109	1	[	[	X
ejpam-5699	109	2	3	3	X
ejpam-5699	109	3	]	]	X
ejpam-5699	109	4	an	an	DET
ejpam-5699	109	5	ifs	ifs	PROPN
ejpam-5699	109	6	b	b	PROPN
ejpam-5699	109	7	in	in	ADP
ejpam-5699	109	8	a	a	DET
ejpam-5699	109	9	non	non	ADJ
ejpam-5699	109	10	-	-	ADJ
ejpam-5699	109	11	empty	empty	ADJ
ejpam-5699	109	12	set	set	NOUN
ejpam-5699	109	13	g	g	PROPN
ejpam-5699	109	14	is	be	AUX
ejpam-5699	109	15	an	an	DET
ejpam-5699	109	16	object	object	NOUN
ejpam-5699	109	17	having	have	VERB
ejpam-5699	109	18	the	the	DET
ejpam-5699	109	19	form	form	NOUN
ejpam-5699	109	20	b	b	NOUN
ejpam-5699	109	21	=	=	SYM
ejpam-5699	109	22	{	{	PUNCT
ejpam-5699	109	23	(	(	PUNCT
ejpam-5699	109	24	g1,m(g1),n	g1,m(g1),n	X
ejpam-5699	109	25	(	(	PUNCT
ejpam-5699	109	26	g1))|g1	g1))|g1	NOUN
ejpam-5699	109	27	∈	∈	PROPN
ejpam-5699	109	28	g	g	NOUN
ejpam-5699	109	29	}	}	PUNCT
ejpam-5699	109	30	where	where	SCONJ
ejpam-5699	109	31	m(g1),n	m(g1),n	PROPN
ejpam-5699	109	32	(	(	PUNCT
ejpam-5699	109	33	g1	g1	PROPN
ejpam-5699	109	34	)	)	PUNCT
ejpam-5699	109	35	are	be	AUX
ejpam-5699	109	36	level	level	NOUN
ejpam-5699	109	37	of	of	ADP
ejpam-5699	109	38	belongingness	belongingness	NOUN
ejpam-5699	109	39	and	and	CCONJ
ejpam-5699	109	40	level	level	NOUN
ejpam-5699	109	41	of	of	ADP
ejpam-5699	109	42	non	non	ADJ
ejpam-5699	109	43	-	-	NOUN
ejpam-5699	109	44	belongingness	belongingness	NOUN
ejpam-5699	109	45	of	of	ADP
ejpam-5699	109	46	g1	g1	PROPN
ejpam-5699	109	47	∈	∈	PROPN
ejpam-5699	109	48	g	g	NOUN
ejpam-5699	109	49	respectively	respectively	ADV
ejpam-5699	109	50	and	and	CCONJ
ejpam-5699	109	51	0	0	NUM
ejpam-5699	109	52	≤	≤	NUM
ejpam-5699	109	53	m(g1	m(g1	NOUN
ejpam-5699	109	54	)	)	PUNCT
ejpam-5699	109	55	+	+	NUM
ejpam-5699	109	56	n	n	CCONJ
ejpam-5699	109	57	(	(	PUNCT
ejpam-5699	109	58	g1	g1	PROPN
ejpam-5699	109	59	)	)	PUNCT
ejpam-5699	109	60	≤	≤	NOUN
ejpam-5699	109	61	1	1	NUM
ejpam-5699	109	62	for	for	ADP
ejpam-5699	109	63	all	all	DET
ejpam-5699	109	64	g1	g1	PROPN
ejpam-5699	109	65	∈	∈	PROPN
ejpam-5699	109	66	g.	g.	NOUN
ejpam-5699	109	67	we	we	PRON
ejpam-5699	109	68	shall	shall	AUX
ejpam-5699	109	69	use	use	VERB
ejpam-5699	109	70	the	the	DET
ejpam-5699	109	71	symbol	symbol	NOUN
ejpam-5699	109	72	b	b	NOUN
ejpam-5699	109	73	=	=	PUNCT
ejpam-5699	109	74	(	(	PUNCT
ejpam-5699	109	75	g1,m	g1,m	PROPN
ejpam-5699	109	76	,	,	PUNCT
ejpam-5699	109	77	n	n	PROPN
ejpam-5699	109	78	)	)	PUNCT
ejpam-5699	109	79	for	for	ADP
ejpam-5699	109	80	an	an	DET
ejpam-5699	109	81	ifs	ifs	PROPN
ejpam-5699	109	82	b	b	PROPN
ejpam-5699	109	83	=	=	PRON
ejpam-5699	109	84	{	{	PUNCT
ejpam-5699	109	85	(	(	PUNCT
ejpam-5699	109	86	g1,m(g1),n	g1,m(g1),n	X
ejpam-5699	109	87	(	(	PUNCT
ejpam-5699	109	88	g1))|g1	g1))|g1	NOUN
ejpam-5699	109	89	∈	∈	PROPN
ejpam-5699	109	90	g	g	NOUN
ejpam-5699	109	91	}	}	PUNCT
ejpam-5699	109	92	.	.	PUNCT
ejpam-5699	110	1	definition	definition	NOUN
ejpam-5699	110	2	19	19	NUM
ejpam-5699	110	3	.	.	PUNCT
ejpam-5699	111	1	[	[	X
ejpam-5699	111	2	4	4	X
ejpam-5699	111	3	]	]	X
ejpam-5699	111	4	a	a	DET
ejpam-5699	111	5	bpvifs	bpvifs	PROPN
ejpam-5699	111	6	b	b	PROPN
ejpam-5699	111	7	in	in	ADP
ejpam-5699	111	8	a	a	DET
ejpam-5699	111	9	non	non	ADJ
ejpam-5699	111	10	-	-	ADJ
ejpam-5699	111	11	empty	empty	ADJ
ejpam-5699	111	12	set	set	NOUN
ejpam-5699	111	13	g	g	PROPN
ejpam-5699	111	14	is	be	AUX
ejpam-5699	111	15	an	an	DET
ejpam-5699	111	16	object	object	NOUN
ejpam-5699	111	17	having	have	VERB
ejpam-5699	111	18	the	the	DET
ejpam-5699	111	19	form	form	NOUN
ejpam-5699	111	20	b	b	NOUN
ejpam-5699	111	21	=	=	SYM
ejpam-5699	111	22	{	{	PUNCT
ejpam-5699	111	23	(	(	PUNCT
ejpam-5699	111	24	g1,m+	g1,m+	X
ejpam-5699	111	25	b(g1),m−	b(g1),m−	PROPN
ejpam-5699	111	26	b(g1),n+	b(g1),n+	PROPN
ejpam-5699	111	27	b	b	PROPN
ejpam-5699	111	28	(	(	PUNCT
ejpam-5699	111	29	g1),n−	g1),n−	PROPN
ejpam-5699	111	30	b	b	PROPN
ejpam-5699	111	31	(	(	PUNCT
ejpam-5699	111	32	g1))|g1	g1))|g1	NOUN
ejpam-5699	111	33	∈	∈	PROPN
ejpam-5699	111	34	g	g	NOUN
ejpam-5699	111	35	}	}	PUNCT
ejpam-5699	111	36	,	,	PUNCT
ejpam-5699	111	37	where	where	SCONJ
ejpam-5699	111	38	m+	m+	NOUN
ejpam-5699	111	39	b(g1	b(g1	NOUN
ejpam-5699	111	40	)	)	PUNCT
ejpam-5699	111	41	:	:	PUNCT
ejpam-5699	112	1	g	g	X
ejpam-5699	112	2	→	→	SYM
ejpam-5699	112	3	[	[	X
ejpam-5699	112	4	0	0	NUM
ejpam-5699	112	5	,	,	PUNCT
ejpam-5699	112	6	1	1	NUM
ejpam-5699	112	7	]	]	PUNCT
ejpam-5699	112	8	,	,	PUNCT
ejpam-5699	112	9	m−	m−	PROPN
ejpam-5699	112	10	b(g1	b(g1	ADJ
ejpam-5699	112	11	)	)	PUNCT
ejpam-5699	112	12	:	:	PUNCT
ejpam-5699	113	1	g	g	X
ejpam-5699	113	2	→	→	SYM
ejpam-5699	113	3	[	[	X
ejpam-5699	113	4	−1	−1	NOUN
ejpam-5699	113	5	,	,	PUNCT
ejpam-5699	113	6	0	0	NUM
ejpam-5699	113	7	]	]	PUNCT
ejpam-5699	113	8	,	,	PUNCT
ejpam-5699	113	9	n+	n+	PUNCT
ejpam-5699	113	10	b	b	X
ejpam-5699	113	11	(	(	PUNCT
ejpam-5699	113	12	g1	g1	PROPN
ejpam-5699	113	13	)	)	PUNCT
ejpam-5699	113	14	:	:	PUNCT
ejpam-5699	114	1	g	g	X
ejpam-5699	114	2	→	→	SYM
ejpam-5699	114	3	[	[	X
ejpam-5699	114	4	0	0	NUM
ejpam-5699	114	5	,	,	PUNCT
ejpam-5699	114	6	1	1	NUM
ejpam-5699	114	7	]	]	PUNCT
ejpam-5699	114	8	,	,	PUNCT
ejpam-5699	114	9	and	and	CCONJ
ejpam-5699	114	10	n−	n−	PROPN
ejpam-5699	114	11	b	b	X
ejpam-5699	114	12	(	(	PUNCT
ejpam-5699	114	13	g1	g1	PROPN
ejpam-5699	114	14	)	)	PUNCT
ejpam-5699	114	15	:	:	PUNCT
ejpam-5699	114	16	g	g	X
ejpam-5699	114	17	→	→	SYM
ejpam-5699	114	18	[	[	X
ejpam-5699	114	19	−1	−1	NOUN
ejpam-5699	114	20	,	,	PUNCT
ejpam-5699	114	21	0	0	NUM
ejpam-5699	114	22	]	]	PUNCT
ejpam-5699	114	23	are	be	AUX
ejpam-5699	114	24	such	such	ADJ
ejpam-5699	114	25	that	that	SCONJ
ejpam-5699	114	26	0	0	NUM
ejpam-5699	114	27	≤	≤	NUM
ejpam-5699	114	28	m+	m+	NUM
ejpam-5699	114	29	b(g1	b(g1	NOUN
ejpam-5699	114	30	)	)	PUNCT
ejpam-5699	115	1	+	+	PROPN
ejpam-5699	115	2	n+	n+	ADP
ejpam-5699	115	3	b	b	X
ejpam-5699	115	4	(	(	PUNCT
ejpam-5699	115	5	g1	g1	PROPN
ejpam-5699	115	6	)	)	PUNCT
ejpam-5699	115	7	≤	≤	NOUN
ejpam-5699	115	8	1	1	NUM
ejpam-5699	115	9	and	and	CCONJ
ejpam-5699	115	10	−1	−1	NOUN
ejpam-5699	115	11	≤	≤	NOUN
ejpam-5699	115	12	m−	m−	PROPN
ejpam-5699	115	13	b(g1	b(g1	NOUN
ejpam-5699	115	14	)	)	PUNCT
ejpam-5699	116	1	+	+	PROPN
ejpam-5699	116	2	n−	n−	PROPN
ejpam-5699	116	3	b	b	X
ejpam-5699	116	4	(	(	PUNCT
ejpam-5699	116	5	g1	g1	PROPN
ejpam-5699	116	6	)	)	PUNCT
ejpam-5699	116	7	≤	≤	NOUN
ejpam-5699	116	8	0	0	NUM
ejpam-5699	116	9	.	.	PUNCT
ejpam-5699	117	1	in	in	ADP
ejpam-5699	117	2	this	this	PRON
ejpam-5699	117	3	,	,	PUNCT
ejpam-5699	117	4	m+b	m+b	NUM
ejpam-5699	117	5	is	be	AUX
ejpam-5699	117	6	used	use	VERB
ejpam-5699	117	7	to	to	PART
ejpam-5699	117	8	indicate	indicate	VERB
ejpam-5699	117	9	the	the	DET
ejpam-5699	117	10	level	level	NOUN
ejpam-5699	117	11	of	of	ADP
ejpam-5699	117	12	positive	positive	ADJ
ejpam-5699	117	13	membership	membership	NOUN
ejpam-5699	117	14	level	level	NOUN
ejpam-5699	117	15	,	,	PUNCT
ejpam-5699	117	16	showing	show	VERB
ejpam-5699	117	17	the	the	DET
ejpam-5699	117	18	extent	extent	NOUN
ejpam-5699	117	19	to	to	PART
ejpam-5699	117	20	which	which	PRON
ejpam-5699	117	21	a	a	DET
ejpam-5699	117	22	member	member	NOUN
ejpam-5699	117	23	of	of	ADP
ejpam-5699	117	24	g	g	PROPN
ejpam-5699	117	25	satisfies	satisfy	VERB
ejpam-5699	117	26	a	a	DET
ejpam-5699	117	27	property	property	NOUN
ejpam-5699	117	28	within	within	ADP
ejpam-5699	117	29	a	a	DET
ejpam-5699	117	30	bpvifs	bpvifs	PROPN
ejpam-5699	117	31	b.	b.	PROPN
ejpam-5699	117	32	on	on	ADP
ejpam-5699	117	33	the	the	DET
ejpam-5699	117	34	other	other	ADJ
ejpam-5699	117	35	side	side	NOUN
ejpam-5699	117	36	,	,	PUNCT
ejpam-5699	117	37	m−b	m−b	PROPN
ejpam-5699	117	38	indicates	indicate	VERB
ejpam-5699	117	39	the	the	DET
ejpam-5699	117	40	level	level	NOUN
ejpam-5699	117	41	of	of	ADP
ejpam-5699	117	42	negative	negative	ADJ
ejpam-5699	117	43	membership	membership	NOUN
ejpam-5699	117	44	,	,	PUNCT
ejpam-5699	117	45	showing	show	VERB
ejpam-5699	117	46	the	the	DET
ejpam-5699	117	47	extent	extent	NOUN
ejpam-5699	117	48	to	to	PART
ejpam-5699	117	49	which	which	PRON
ejpam-5699	117	50	a	a	DET
ejpam-5699	117	51	member	member	NOUN
ejpam-5699	117	52	of	of	ADP
ejpam-5699	117	53	g	g	PROPN
ejpam-5699	117	54	satisfies	satisfy	VERB
ejpam-5699	117	55	the	the	DET
ejpam-5699	117	56	implicit	implicit	ADJ
ejpam-5699	117	57	counter	counter	NOUN
ejpam-5699	117	58	property	property	NOUN
ejpam-5699	117	59	associated	associate	VERB
ejpam-5699	117	60	with	with	ADP
ejpam-5699	117	61	the	the	DET
ejpam-5699	117	62	bpvifs	bpvifs	PROPN
ejpam-5699	117	63	.	.	PUNCT
ejpam-5699	118	1	the	the	DET
ejpam-5699	118	2	terms	term	NOUN
ejpam-5699	118	3	n+	n+	ADP
ejpam-5699	118	4	b	b	X
ejpam-5699	118	5	(	(	PUNCT
ejpam-5699	118	6	g1	g1	PROPN
ejpam-5699	118	7	)	)	PUNCT
ejpam-5699	118	8	and	and	CCONJ
ejpam-5699	118	9	n−	n−	PROPN
ejpam-5699	118	10	b	b	X
ejpam-5699	118	11	(	(	PUNCT
ejpam-5699	118	12	g1	g1	PROPN
ejpam-5699	118	13	)	)	PUNCT
ejpam-5699	118	14	refer	refer	VERB
ejpam-5699	118	15	to	to	ADP
ejpam-5699	118	16	the	the	DET
ejpam-5699	118	17	level	level	NOUN
ejpam-5699	118	18	of	of	ADP
ejpam-5699	118	19	positive	positive	ADJ
ejpam-5699	118	20	non	non	ADJ
ejpam-5699	118	21	-	-	ADJ
ejpam-5699	118	22	membership	membership	NOUN
ejpam-5699	118	23	and	and	CCONJ
ejpam-5699	118	24	level	level	VERB
ejpam-5699	118	25	negative	negative	ADJ
ejpam-5699	118	26	nonmembership	nonmembership	NOUN
ejpam-5699	118	27	respectively	respectively	ADV
ejpam-5699	118	28	.	.	PUNCT
ejpam-5699	119	1	we	we	PRON
ejpam-5699	119	2	calculate	calculate	VERB
ejpam-5699	119	3	n+	n+	ADP
ejpam-5699	119	4	b	b	X
ejpam-5699	119	5	(	(	PUNCT
ejpam-5699	119	6	g1	g1	PROPN
ejpam-5699	119	7	)	)	PUNCT
ejpam-5699	119	8	and	and	CCONJ
ejpam-5699	119	9	n−	n−	PROPN
ejpam-5699	119	10	b	b	X
ejpam-5699	119	11	(	(	PUNCT
ejpam-5699	119	12	g1	g1	PROPN
ejpam-5699	119	13	)	)	PUNCT
ejpam-5699	119	14	as	as	ADP
ejpam-5699	119	15	n+	n+	ADP
ejpam-5699	119	16	b	b	X
ejpam-5699	119	17	(	(	PUNCT
ejpam-5699	119	18	g1	g1	PROPN
ejpam-5699	119	19	)	)	PUNCT
ejpam-5699	119	20	=	=	SYM
ejpam-5699	120	1	1	1	NUM
ejpam-5699	120	2	−	−	NUM
ejpam-5699	120	3	m+	m+	NOUN
ejpam-5699	120	4	b(g1	b(g1	NOUN
ejpam-5699	120	5	)	)	PUNCT
ejpam-5699	120	6	and	and	CCONJ
ejpam-5699	120	7	n−	n−	PROPN
ejpam-5699	120	8	b	b	X
ejpam-5699	120	9	(	(	PUNCT
ejpam-5699	120	10	g1	g1	PROPN
ejpam-5699	120	11	)	)	PUNCT
ejpam-5699	120	12	=	=	SYM
ejpam-5699	120	13	−1−m−	−1−m−	ADV
ejpam-5699	120	14	b(g1	b(g1	NOUN
ejpam-5699	120	15	)	)	PUNCT
ejpam-5699	120	16	.	.	PUNCT
ejpam-5699	121	1	d.	d.	PROPN
ejpam-5699	121	2	ramesh	ramesh	PROPN
ejpam-5699	121	3	et	et	PROPN
ejpam-5699	121	4	al	al	PROPN
ejpam-5699	121	5	.	.	PUNCT
ejpam-5699	121	6	/	/	SYM
ejpam-5699	121	7	eur	eur	PROPN
ejpam-5699	121	8	.	.	PUNCT
ejpam-5699	122	1	j.	j.	PROPN
ejpam-5699	122	2	pure	pure	PROPN
ejpam-5699	122	3	appl	appl	PROPN
ejpam-5699	122	4	.	.	PROPN
ejpam-5699	122	5	math	math	PROPN
ejpam-5699	122	6	,	,	PUNCT
ejpam-5699	122	7	18	18	NUM
ejpam-5699	122	8	(	(	PUNCT
ejpam-5699	122	9	1	1	NUM
ejpam-5699	122	10	)	)	PUNCT
ejpam-5699	122	11	(	(	PUNCT
ejpam-5699	122	12	2025	2025	NUM
ejpam-5699	122	13	)	)	PUNCT
ejpam-5699	122	14	,	,	PUNCT
ejpam-5699	122	15	5699	5699	NUM
ejpam-5699	122	16	8	8	NUM
ejpam-5699	122	17	of	of	ADP
ejpam-5699	122	18	20	20	NUM
ejpam-5699	122	19	definition	definition	NOUN
ejpam-5699	122	20	20	20	NUM
ejpam-5699	122	21	.	.	PUNCT
ejpam-5699	123	1	a	a	DET
ejpam-5699	123	2	bpvifs	bpvifs	PROPN
ejpam-5699	123	3	b	b	PROPN
ejpam-5699	123	4	=	=	PUNCT
ejpam-5699	123	5	(	(	PUNCT
ejpam-5699	123	6	m+	m+	NUM
ejpam-5699	123	7	b	b	NOUN
ejpam-5699	123	8	,	,	PUNCT
ejpam-5699	123	9	m−	m−	PROPN
ejpam-5699	123	10	b	b	PROPN
ejpam-5699	123	11	,	,	PUNCT
ejpam-5699	123	12	n+	n+	NOUN
ejpam-5699	123	13	b	b	NOUN
ejpam-5699	123	14	,	,	PUNCT
ejpam-5699	123	15	n−	n−	PROPN
ejpam-5699	123	16	b	b	NOUN
ejpam-5699	123	17	)	)	PUNCT
ejpam-5699	123	18	in	in	ADP
ejpam-5699	123	19	g	g	PROPN
ejpam-5699	123	20	is	be	AUX
ejpam-5699	123	21	a	a	DET
ejpam-5699	123	22	bpvifi	bpvifi	NOUN
ejpam-5699	123	23	of	of	ADP
ejpam-5699	123	24	g	g	NOUN
ejpam-5699	123	25	if	if	SCONJ
ejpam-5699	123	26	it	it	PRON
ejpam-5699	123	27	satisfies	satisfy	VERB
ejpam-5699	123	28	m+	m+	NUM
ejpam-5699	123	29	b(0	b(0	NOUN
ejpam-5699	123	30	)	)	PUNCT
ejpam-5699	123	31	≥	≥	NOUN
ejpam-5699	123	32	m+	m+	NUM
ejpam-5699	123	33	b(g1	b(g1	NOUN
ejpam-5699	123	34	)	)	PUNCT
ejpam-5699	123	35	,	,	PUNCT
ejpam-5699	123	36	m−	m−	PROPN
ejpam-5699	123	37	b(0	b(0	PROPN
ejpam-5699	123	38	)	)	PUNCT
ejpam-5699	123	39	≤	≤	NOUN
ejpam-5699	123	40	m−	m−	PROPN
ejpam-5699	123	41	b(g1	b(g1	NOUN
ejpam-5699	123	42	)	)	PUNCT
ejpam-5699	123	43	,	,	PUNCT
ejpam-5699	123	44	n+	n+	ADP
ejpam-5699	123	45	b	b	X
ejpam-5699	123	46	(	(	PUNCT
ejpam-5699	123	47	0	0	NUM
ejpam-5699	123	48	)	)	PUNCT
ejpam-5699	123	49	≤	≤	NUM
ejpam-5699	123	50	n+	n+	PUNCT
ejpam-5699	123	51	b	b	X
ejpam-5699	123	52	(	(	PUNCT
ejpam-5699	123	53	g1	g1	PROPN
ejpam-5699	123	54	)	)	PUNCT
ejpam-5699	123	55	,	,	PUNCT
ejpam-5699	123	56	n−	n−	PROPN
ejpam-5699	123	57	b	b	X
ejpam-5699	123	58	(	(	PUNCT
ejpam-5699	123	59	0	0	NUM
ejpam-5699	123	60	)	)	PUNCT
ejpam-5699	123	61	≥	≥	NOUN
ejpam-5699	123	62	n−	n−	PROPN
ejpam-5699	123	63	b	b	X
ejpam-5699	123	64	(	(	PUNCT
ejpam-5699	123	65	g1	g1	PROPN
ejpam-5699	123	66	)	)	PUNCT
ejpam-5699	123	67	,	,	PUNCT
ejpam-5699	123	68	and	and	CCONJ
ejpam-5699	123	69	m+	m+	NUM
ejpam-5699	123	70	b(g1	b(g1	NOUN
ejpam-5699	123	71	)	)	PUNCT
ejpam-5699	123	72	≥	≥	NOUN
ejpam-5699	123	73	min{m+	min{m+	VERB
ejpam-5699	123	74	b(g1	b(g1	ADJ
ejpam-5699	123	75	⋄	⋄	PROPN
ejpam-5699	123	76	è1),m+	è1),m+	NOUN
ejpam-5699	123	77	b(è1	b(è1	NOUN
ejpam-5699	123	78	)	)	PUNCT
ejpam-5699	123	79	}	}	PUNCT
ejpam-5699	123	80	,	,	PUNCT
ejpam-5699	123	81	m−	m−	PROPN
ejpam-5699	123	82	b(g1	b(g1	NOUN
ejpam-5699	123	83	)	)	PUNCT
ejpam-5699	123	84	≤	≤	NOUN
ejpam-5699	124	1	max{m−	max{m−	NOUN
ejpam-5699	124	2	b(g1	b(g1	ADJ
ejpam-5699	124	3	⋄	⋄	PROPN
ejpam-5699	124	4	è1),m−	è1),m−	PROPN
ejpam-5699	124	5	b(è1	b(è1	NOUN
ejpam-5699	124	6	)	)	PUNCT
ejpam-5699	124	7	}	}	PUNCT
ejpam-5699	124	8	,	,	PUNCT
ejpam-5699	124	9	n+	n+	ADP
ejpam-5699	124	10	b	b	X
ejpam-5699	124	11	(	(	PUNCT
ejpam-5699	124	12	g1	g1	PROPN
ejpam-5699	124	13	)	)	PUNCT
ejpam-5699	124	14	≤	≤	NUM
ejpam-5699	124	15	max{n+	max{n+	PROPN
ejpam-5699	124	16	b	b	PROPN
ejpam-5699	124	17	(	(	PUNCT
ejpam-5699	124	18	g1	g1	PROPN
ejpam-5699	124	19	⋄	⋄	PROPN
ejpam-5699	124	20	è1),n+	è1),n+	PROPN
ejpam-5699	124	21	b	b	PROPN
ejpam-5699	124	22	(	(	PUNCT
ejpam-5699	124	23	è1	è1	NOUN
ejpam-5699	124	24	)	)	PUNCT
ejpam-5699	124	25	}	}	PUNCT
ejpam-5699	124	26	,	,	PUNCT
ejpam-5699	124	27	n−	n−	PROPN
ejpam-5699	124	28	b	b	X
ejpam-5699	124	29	(	(	PUNCT
ejpam-5699	124	30	g1	g1	PROPN
ejpam-5699	124	31	)	)	PUNCT
ejpam-5699	124	32	≥	≥	NOUN
ejpam-5699	124	33	min{n−	min{n−	PROPN
ejpam-5699	124	34	b	b	PROPN
ejpam-5699	124	35	(	(	PUNCT
ejpam-5699	124	36	g1	g1	PROPN
ejpam-5699	124	37	⋄	⋄	PROPN
ejpam-5699	124	38	è1),n−	è1),n−	PROPN
ejpam-5699	124	39	b	b	PROPN
ejpam-5699	124	40	(	(	PUNCT
ejpam-5699	124	41	è1	è1	NOUN
ejpam-5699	124	42	)	)	PUNCT
ejpam-5699	124	43	}	}	PUNCT
ejpam-5699	124	44	,	,	PUNCT
ejpam-5699	124	45	for	for	ADP
ejpam-5699	124	46	all	all	DET
ejpam-5699	124	47	g1,è1	g1,è1	PROPN
ejpam-5699	124	48	∈	∈	PROPN
ejpam-5699	124	49	g.	g.	NOUN
ejpam-5699	124	50	theorem	theorem	VERB
ejpam-5699	124	51	2	2	NUM
ejpam-5699	124	52	.	.	PUNCT
ejpam-5699	124	53	a	a	DET
ejpam-5699	124	54	bpvifs	bpvifs	PROPN
ejpam-5699	124	55	b	b	PROPN
ejpam-5699	124	56	=	=	PUNCT
ejpam-5699	124	57	(	(	PUNCT
ejpam-5699	124	58	m+	m+	NUM
ejpam-5699	124	59	b	b	NOUN
ejpam-5699	124	60	,	,	PUNCT
ejpam-5699	124	61	m−	m−	PROPN
ejpam-5699	124	62	b	b	PROPN
ejpam-5699	124	63	,	,	PUNCT
ejpam-5699	124	64	n+	n+	NOUN
ejpam-5699	124	65	b	b	NOUN
ejpam-5699	124	66	,	,	PUNCT
ejpam-5699	124	67	n−	n−	PROPN
ejpam-5699	124	68	b	b	NOUN
ejpam-5699	124	69	)	)	PUNCT
ejpam-5699	124	70	in	in	ADP
ejpam-5699	124	71	g	g	PROPN
ejpam-5699	124	72	is	be	AUX
ejpam-5699	124	73	a	a	DET
ejpam-5699	124	74	bpvifi	bpvifi	NOUN
ejpam-5699	124	75	of	of	ADP
ejpam-5699	124	76	g	g	NOUN
ejpam-5699	124	77	if	if	SCONJ
ejpam-5699	125	1	and	and	CCONJ
ejpam-5699	125	2	only	only	ADV
ejpam-5699	125	3	if	if	SCONJ
ejpam-5699	125	4	it	it	PRON
ejpam-5699	125	5	satisfies	satisfy	VERB
ejpam-5699	125	6	the	the	DET
ejpam-5699	125	7	condition	condition	NOUN
ejpam-5699	125	8	if	if	SCONJ
ejpam-5699	125	9	g1	g1	PROPN
ejpam-5699	125	10	⋄	⋄	PROPN
ejpam-5699	125	11	è1	è1	ADJ
ejpam-5699	125	12	≤	≤	NOUN
ejpam-5699	125	13	11	11	NUM
ejpam-5699	125	14	for	for	ADP
ejpam-5699	125	15	all	all	DET
ejpam-5699	125	16	g1,è1	g1,è1	PROPN
ejpam-5699	125	17	,	,	PUNCT
ejpam-5699	125	18	11	11	NUM
ejpam-5699	125	19	∈	∈	NOUN
ejpam-5699	125	20	g	g	NOUN
ejpam-5699	125	21	,	,	PUNCT
ejpam-5699	125	22	then	then	PROPN
ejpam-5699	125	23	m+	m+	NUM
ejpam-5699	125	24	b(g1	b(g1	NOUN
ejpam-5699	125	25	)	)	PUNCT
ejpam-5699	125	26	≥	≥	NOUN
ejpam-5699	125	27	min{m+	min{m+	PROPN
ejpam-5699	125	28	b(è1),m+	b(è1),m+	PROPN
ejpam-5699	125	29	b(11	b(11	PROPN
ejpam-5699	125	30	)	)	PUNCT
ejpam-5699	125	31	}	}	PUNCT
ejpam-5699	125	32	,	,	PUNCT
ejpam-5699	125	33	m−	m−	PROPN
ejpam-5699	125	34	b(g1	b(g1	NOUN
ejpam-5699	125	35	)	)	PUNCT
ejpam-5699	125	36	≤	≤	NOUN
ejpam-5699	125	37	max{m−	max{m−	PROPN
ejpam-5699	125	38	b(è1),m−	b(è1),m−	PROPN
ejpam-5699	125	39	b(11	b(11	NOUN
ejpam-5699	125	40	)	)	PUNCT
ejpam-5699	125	41	}	}	PUNCT
ejpam-5699	125	42	,	,	PUNCT
ejpam-5699	125	43	n+	n+	ADP
ejpam-5699	125	44	b	b	X
ejpam-5699	125	45	(	(	PUNCT
ejpam-5699	125	46	g1	g1	PROPN
ejpam-5699	125	47	)	)	PUNCT
ejpam-5699	125	48	≤	≤	NUM
ejpam-5699	125	49	max{n+	max{n+	PROPN
ejpam-5699	125	50	b	b	PROPN
ejpam-5699	125	51	(	(	PUNCT
ejpam-5699	125	52	è1),n+	è1),n+	PROPN
ejpam-5699	125	53	b	b	PROPN
ejpam-5699	125	54	(	(	PUNCT
ejpam-5699	125	55	11	11	NUM
ejpam-5699	125	56	)	)	PUNCT
ejpam-5699	125	57	}	}	PUNCT
ejpam-5699	125	58	,	,	PUNCT
ejpam-5699	125	59	n−	n−	PROPN
ejpam-5699	125	60	b	b	X
ejpam-5699	125	61	(	(	PUNCT
ejpam-5699	125	62	g1	g1	PROPN
ejpam-5699	125	63	)	)	PUNCT
ejpam-5699	125	64	≥	≥	NOUN
ejpam-5699	125	65	min{n−	min{n−	PROPN
ejpam-5699	125	66	b	b	PROPN
ejpam-5699	125	67	(	(	PUNCT
ejpam-5699	125	68	è1),n−	è1),n−	PROPN
ejpam-5699	125	69	b	b	PROPN
ejpam-5699	125	70	(	(	PUNCT
ejpam-5699	125	71	11	11	NUM
ejpam-5699	125	72	)	)	PUNCT
ejpam-5699	125	73	}	}	PUNCT
ejpam-5699	125	74	,	,	PUNCT
ejpam-5699	125	75			NOUN
ejpam-5699	125	76	(	(	PUNCT
ejpam-5699	125	77	12	12	NUM
ejpam-5699	125	78	)	)	PUNCT
ejpam-5699	125	79	proof	proof	NOUN
ejpam-5699	125	80	.	.	PUNCT
ejpam-5699	126	1	assume	assume	VERB
ejpam-5699	126	2	that	that	SCONJ
ejpam-5699	126	3	b	b	X
ejpam-5699	126	4	=	=	SYM
ejpam-5699	126	5	(	(	PUNCT
ejpam-5699	126	6	m+	m+	NUM
ejpam-5699	126	7	b	b	NOUN
ejpam-5699	126	8	,	,	PUNCT
ejpam-5699	126	9	m−	m−	PROPN
ejpam-5699	126	10	b	b	PROPN
ejpam-5699	126	11	,	,	PUNCT
ejpam-5699	126	12	n+	n+	NOUN
ejpam-5699	126	13	b	b	NOUN
ejpam-5699	126	14	,	,	PUNCT
ejpam-5699	126	15	n−	n−	PROPN
ejpam-5699	126	16	b	b	X
ejpam-5699	126	17	)	)	PUNCT
ejpam-5699	126	18	is	be	AUX
ejpam-5699	126	19	a	a	DET
ejpam-5699	126	20	bpifi	bpifi	NOUN
ejpam-5699	126	21	of	of	ADP
ejpam-5699	126	22	g.	g.	NOUN
ejpam-5699	126	23	let	let	VERB
ejpam-5699	126	24	g1,è1	g1,è1	PROPN
ejpam-5699	126	25	,	,	PUNCT
ejpam-5699	126	26	11	11	NUM
ejpam-5699	126	27	∈	∈	NOUN
ejpam-5699	126	28	g	g	NOUN
ejpam-5699	126	29	be	be	VERB
ejpam-5699	126	30	such	such	ADJ
ejpam-5699	126	31	that	that	SCONJ
ejpam-5699	126	32	g1	g1	PROPN
ejpam-5699	126	33	⋄	⋄	PROPN
ejpam-5699	126	34	è1	è1	PROPN
ejpam-5699	126	35	≤	≤	ADJ
ejpam-5699	126	36	11	11	NUM
ejpam-5699	126	37	.	.	PUNCT
ejpam-5699	127	1	then	then	ADV
ejpam-5699	127	2	(	(	PUNCT
ejpam-5699	127	3	g1	g1	PROPN
ejpam-5699	127	4	⋄	⋄	PROPN
ejpam-5699	127	5	è1	è1	PROPN
ejpam-5699	127	6	)	)	PUNCT
ejpam-5699	127	7	⋄	⋄	NOUN
ejpam-5699	127	8	11	11	NUM
ejpam-5699	127	9	=	=	SYM
ejpam-5699	127	10	0	0	NUM
ejpam-5699	127	11	.	.	PUNCT
ejpam-5699	128	1	thus	thus	ADV
ejpam-5699	128	2	,	,	PUNCT
ejpam-5699	128	3	m+	m+	X
ejpam-5699	128	4	b(g1	b(g1	NOUN
ejpam-5699	128	5	)	)	PUNCT
ejpam-5699	128	6	≥	≥	NOUN
ejpam-5699	128	7	min{m+	min{m+	VERB
ejpam-5699	128	8	b(g1	b(g1	ADJ
ejpam-5699	128	9	⋄	⋄	PROPN
ejpam-5699	128	10	è1),m+	è1),m+	NOUN
ejpam-5699	128	11	b(è1	b(è1	NOUN
ejpam-5699	128	12	)	)	PUNCT
ejpam-5699	128	13	}	}	PUNCT
ejpam-5699	128	14	≥	≥	PART
ejpam-5699	128	15	min{min{m+	min{min{m+	PROPN
ejpam-5699	128	16	b((g1	b((g1	PROPN
ejpam-5699	128	17	⋄	⋄	PROPN
ejpam-5699	128	18	è1	è1	PROPN
ejpam-5699	128	19	)	)	PUNCT
ejpam-5699	128	20	⋄	⋄	PROPN
ejpam-5699	128	21	11),m+	11),m+	NUM
ejpam-5699	128	22	b(11)},m+	b(11)},m+	NOUN
ejpam-5699	128	23	b(è1	b(è1	NOUN
ejpam-5699	128	24	)	)	PUNCT
ejpam-5699	128	25	}	}	PUNCT
ejpam-5699	128	26	≥	≥	VERB
ejpam-5699	128	27	min{min{m+	min{min{m+	NOUN
ejpam-5699	128	28	b(0),m+	b(0),m+	NUM
ejpam-5699	128	29	b(11)},m+	b(11)},m+	NOUN
ejpam-5699	128	30	b(è1	b(è1	NOUN
ejpam-5699	128	31	)	)	PUNCT
ejpam-5699	128	32	}	}	PUNCT
ejpam-5699	129	1	=	=	PUNCT
ejpam-5699	129	2	min{m+	min{m+	PROPN
ejpam-5699	129	3	b(è1),m+	b(è1),m+	PROPN
ejpam-5699	129	4	b(11	b(11	PROPN
ejpam-5699	129	5	)	)	PUNCT
ejpam-5699	129	6	}	}	PUNCT
ejpam-5699	129	7	,	,	PUNCT
ejpam-5699	129	8	m−	m−	PROPN
ejpam-5699	129	9	b(g1	b(g1	NOUN
ejpam-5699	129	10	)	)	PUNCT
ejpam-5699	129	11	≤	≤	NOUN
ejpam-5699	129	12	max{m−	max{m−	NOUN
ejpam-5699	129	13	b(g1	b(g1	ADJ
ejpam-5699	129	14	⋄	⋄	PROPN
ejpam-5699	129	15	è1),m−	è1),m−	PROPN
ejpam-5699	129	16	b(è1	b(è1	NOUN
ejpam-5699	129	17	)	)	PUNCT
ejpam-5699	129	18	}	}	PUNCT
ejpam-5699	129	19	≤	≤	NUM
ejpam-5699	129	20	max{max{m−	max{max{m−	PROPN
ejpam-5699	129	21	b((g1	b((g1	PROPN
ejpam-5699	129	22	⋄	⋄	PROPN
ejpam-5699	129	23	è1	è1	PROPN
ejpam-5699	129	24	)	)	PUNCT
ejpam-5699	129	25	⋄	⋄	PROPN
ejpam-5699	129	26	11),m−	11),m−	NUM
ejpam-5699	129	27	b(11)},m−	b(11)},m−	ADJ
ejpam-5699	129	28	b(è1	b(è1	NOUN
ejpam-5699	129	29	)	)	PUNCT
ejpam-5699	129	30	}	}	PUNCT
ejpam-5699	129	31	≤	≤	NUM
ejpam-5699	129	32	max{max{m−	max{max{m−	PROPN
ejpam-5699	129	33	b(0),m−	b(0),m−	PROPN
ejpam-5699	129	34	b(11)},m−	b(11)},m−	ADP
ejpam-5699	129	35	b(è1	b(è1	NOUN
ejpam-5699	129	36	)	)	PUNCT
ejpam-5699	129	37	}	}	PUNCT
ejpam-5699	130	1	=	=	SYM
ejpam-5699	130	2	max{m−	max{m−	PROPN
ejpam-5699	130	3	b(è1),m−	b(è1),m−	PROPN
ejpam-5699	130	4	b(11	b(11	NOUN
ejpam-5699	130	5	)	)	PUNCT
ejpam-5699	130	6	}	}	PUNCT
ejpam-5699	130	7	,	,	PUNCT
ejpam-5699	130	8	n+	n+	ADP
ejpam-5699	130	9	b	b	X
ejpam-5699	130	10	(	(	PUNCT
ejpam-5699	130	11	g1	g1	PROPN
ejpam-5699	130	12	)	)	PUNCT
ejpam-5699	130	13	≤	≤	NUM
ejpam-5699	130	14	max{n+	max{n+	PROPN
ejpam-5699	130	15	b	b	PROPN
ejpam-5699	130	16	(	(	PUNCT
ejpam-5699	130	17	g1	g1	PROPN
ejpam-5699	130	18	⋄	⋄	PROPN
ejpam-5699	130	19	è1),n+	è1),n+	PROPN
ejpam-5699	130	20	b	b	PROPN
ejpam-5699	130	21	(	(	PUNCT
ejpam-5699	130	22	è1	è1	NOUN
ejpam-5699	130	23	)	)	PUNCT
ejpam-5699	130	24	}	}	PUNCT
ejpam-5699	130	25	≤	≤	NUM
ejpam-5699	130	26	max{max{n+	max{max{n+	PROPN
ejpam-5699	130	27	b	b	PROPN
ejpam-5699	130	28	(	(	PUNCT
ejpam-5699	130	29	(	(	PUNCT
ejpam-5699	130	30	g1	g1	PROPN
ejpam-5699	130	31	⋄	⋄	PROPN
ejpam-5699	130	32	è1	è1	PROPN
ejpam-5699	130	33	)	)	PUNCT
ejpam-5699	130	34	⋄	⋄	PROPN
ejpam-5699	131	1	11),n+	11),n+	NUM
ejpam-5699	131	2	b	b	PROPN
ejpam-5699	131	3	(	(	PUNCT
ejpam-5699	131	4	11)},n+	11)},n+	PROPN
ejpam-5699	131	5	b	b	PROPN
ejpam-5699	131	6	(	(	PUNCT
ejpam-5699	131	7	è1	è1	NOUN
ejpam-5699	131	8	)	)	PUNCT
ejpam-5699	131	9	}	}	PUNCT
ejpam-5699	131	10	≤	≤	NUM
ejpam-5699	131	11	max{max{n+	max{max{n+	PROPN
ejpam-5699	131	12	b	b	X
ejpam-5699	131	13	(	(	PUNCT
ejpam-5699	131	14	0),n+	0),n+	PROPN
ejpam-5699	131	15	b	b	PROPN
ejpam-5699	131	16	(	(	PUNCT
ejpam-5699	131	17	11)},n+	11)},n+	PROPN
ejpam-5699	131	18	b	b	PROPN
ejpam-5699	131	19	(	(	PUNCT
ejpam-5699	131	20	è1	è1	NOUN
ejpam-5699	131	21	)	)	PUNCT
ejpam-5699	131	22	}	}	PUNCT
ejpam-5699	131	23	=	=	PUNCT
ejpam-5699	131	24	max{n+	max{n+	NOUN
ejpam-5699	131	25	b	b	PROPN
ejpam-5699	131	26	(	(	PUNCT
ejpam-5699	131	27	è1),n+	è1),n+	PROPN
ejpam-5699	131	28	b	b	PROPN
ejpam-5699	131	29	(	(	PUNCT
ejpam-5699	131	30	11	11	NUM
ejpam-5699	131	31	)	)	PUNCT
ejpam-5699	131	32	}	}	PUNCT
ejpam-5699	131	33	,	,	PUNCT
ejpam-5699	131	34	n−	n−	PROPN
ejpam-5699	131	35	b	b	X
ejpam-5699	131	36	(	(	PUNCT
ejpam-5699	131	37	g1	g1	PROPN
ejpam-5699	131	38	)	)	PUNCT
ejpam-5699	131	39	≥	≥	NOUN
ejpam-5699	131	40	min{n−	min{n−	PROPN
ejpam-5699	131	41	b	b	PROPN
ejpam-5699	131	42	(	(	PUNCT
ejpam-5699	131	43	g1	g1	PROPN
ejpam-5699	131	44	⋄	⋄	PROPN
ejpam-5699	131	45	è1),n−	è1),n−	PROPN
ejpam-5699	131	46	b	b	PROPN
ejpam-5699	131	47	(	(	PUNCT
ejpam-5699	131	48	è1	è1	NOUN
ejpam-5699	131	49	)	)	PUNCT
ejpam-5699	131	50	}	}	PUNCT
ejpam-5699	131	51	≥	≥	AUX
ejpam-5699	131	52	min{min{n−	min{min{n−	PROPN
ejpam-5699	131	53	b	b	PROPN
ejpam-5699	131	54	(	(	PUNCT
ejpam-5699	131	55	(	(	PUNCT
ejpam-5699	131	56	g1	g1	PROPN
ejpam-5699	131	57	⋄	⋄	PROPN
ejpam-5699	131	58	è1	è1	PROPN
ejpam-5699	131	59	)	)	PUNCT
ejpam-5699	131	60	⋄	⋄	PROPN
ejpam-5699	132	1	11),n−	11),n−	NUM
ejpam-5699	132	2	b	b	PROPN
ejpam-5699	132	3	(	(	PUNCT
ejpam-5699	132	4	11)},n−	11)},n−	NUM
ejpam-5699	132	5	b	b	PROPN
ejpam-5699	132	6	(	(	PUNCT
ejpam-5699	132	7	è1	è1	NOUN
ejpam-5699	132	8	)	)	PUNCT
ejpam-5699	132	9	}	}	PUNCT
ejpam-5699	132	10	≥	≥	AUX
ejpam-5699	132	11	min{min{n−	min{min{n−	PROPN
ejpam-5699	132	12	b	b	PROPN
ejpam-5699	132	13	(	(	PUNCT
ejpam-5699	132	14	0),n−	0),n−	PROPN
ejpam-5699	132	15	b	b	NOUN
ejpam-5699	132	16	(	(	PUNCT
ejpam-5699	132	17	11)},n−	11)},n−	NUM
ejpam-5699	132	18	b	b	PROPN
ejpam-5699	132	19	(	(	PUNCT
ejpam-5699	132	20	è1	è1	NOUN
ejpam-5699	132	21	)	)	PUNCT
ejpam-5699	132	22	}	}	PUNCT
ejpam-5699	132	23	=	=	SYM
ejpam-5699	132	24	min{n−	min{n−	PROPN
ejpam-5699	132	25	b	b	PROPN
ejpam-5699	132	26	(	(	PUNCT
ejpam-5699	132	27	è1),n−	è1),n−	PROPN
ejpam-5699	132	28	b	b	PROPN
ejpam-5699	132	29	(	(	PUNCT
ejpam-5699	132	30	11	11	NUM
ejpam-5699	132	31	)	)	PUNCT
ejpam-5699	132	32	}	}	PUNCT
ejpam-5699	132	33	.	.	PUNCT
ejpam-5699	133	1	hence	hence	ADV
ejpam-5699	133	2	,	,	PUNCT
ejpam-5699	133	3	(	(	PUNCT
ejpam-5699	133	4	12	12	NUM
ejpam-5699	133	5	)	)	PUNCT
ejpam-5699	133	6	is	be	AUX
ejpam-5699	133	7	valid	valid	ADJ
ejpam-5699	133	8	.	.	PUNCT
ejpam-5699	134	1	conversely	conversely	ADV
ejpam-5699	134	2	,	,	PUNCT
ejpam-5699	134	3	let	let	VERB
ejpam-5699	134	4	b	b	X
ejpam-5699	134	5	=	=	SYM
ejpam-5699	134	6	(	(	PUNCT
ejpam-5699	134	7	m+	m+	NUM
ejpam-5699	134	8	b	b	NOUN
ejpam-5699	134	9	,	,	PUNCT
ejpam-5699	134	10	m−	m−	PROPN
ejpam-5699	134	11	b	b	PROPN
ejpam-5699	134	12	,	,	PUNCT
ejpam-5699	134	13	n+	n+	NOUN
ejpam-5699	134	14	b	b	NOUN
ejpam-5699	134	15	,	,	PUNCT
ejpam-5699	134	16	n−	n−	PROPN
ejpam-5699	134	17	b	b	AUX
ejpam-5699	134	18	)	)	PUNCT
ejpam-5699	134	19	be	be	AUX
ejpam-5699	134	20	a	a	DET
ejpam-5699	134	21	bpifs	bpif	NOUN
ejpam-5699	134	22	in	in	ADP
ejpam-5699	134	23	g	g	PROPN
ejpam-5699	134	24	that	that	SCONJ
ejpam-5699	134	25	satisfies	satisfie	NOUN
ejpam-5699	134	26	(	(	PUNCT
ejpam-5699	134	27	12	12	NUM
ejpam-5699	134	28	)	)	PUNCT
ejpam-5699	134	29	.	.	PUNCT
ejpam-5699	135	1	since	since	SCONJ
ejpam-5699	135	2	0	0	NUM
ejpam-5699	135	3	⋄	⋄	PROPN
ejpam-5699	135	4	g1	g1	VERB
ejpam-5699	135	5	≤	≤	PUNCT
ejpam-5699	135	6	g1	g1	NOUN
ejpam-5699	135	7	for	for	ADP
ejpam-5699	135	8	all	all	DET
ejpam-5699	135	9	g1	g1	PROPN
ejpam-5699	135	10	∈	∈	PROPN
ejpam-5699	135	11	g	g	NOUN
ejpam-5699	135	12	,	,	PUNCT
ejpam-5699	135	13	we	we	PRON
ejpam-5699	135	14	have	have	VERB
ejpam-5699	135	15	m+	m+	VERB
ejpam-5699	135	16	b(0	b(0	NOUN
ejpam-5699	135	17	)	)	PUNCT
ejpam-5699	135	18	≥	≥	NOUN
ejpam-5699	135	19	m+	m+	NUM
ejpam-5699	135	20	b(g1	b(g1	NOUN
ejpam-5699	135	21	)	)	PUNCT
ejpam-5699	135	22	,	,	PUNCT
ejpam-5699	135	23	m−	m−	PROPN
ejpam-5699	135	24	b(0	b(0	PROPN
ejpam-5699	135	25	)	)	PUNCT
ejpam-5699	135	26	≤	≤	NOUN
ejpam-5699	135	27	m−	m−	PROPN
ejpam-5699	135	28	b(g1	b(g1	NOUN
ejpam-5699	135	29	)	)	PUNCT
ejpam-5699	135	30	,	,	PUNCT
ejpam-5699	135	31	n+	n+	ADP
ejpam-5699	135	32	b	b	X
ejpam-5699	135	33	(	(	PUNCT
ejpam-5699	135	34	0	0	NUM
ejpam-5699	135	35	)	)	PUNCT
ejpam-5699	135	36	≤	≤	NOUN
ejpam-5699	136	1	d.	d.	PROPN
ejpam-5699	136	2	ramesh	ramesh	PROPN
ejpam-5699	136	3	et	et	PROPN
ejpam-5699	136	4	al	al	PROPN
ejpam-5699	136	5	.	.	PUNCT
ejpam-5699	136	6	/	/	SYM
ejpam-5699	136	7	eur	eur	PROPN
ejpam-5699	136	8	.	.	PUNCT
ejpam-5699	137	1	j.	j.	PROPN
ejpam-5699	137	2	pure	pure	PROPN
ejpam-5699	137	3	appl	appl	PROPN
ejpam-5699	137	4	.	.	PROPN
ejpam-5699	137	5	math	math	PROPN
ejpam-5699	137	6	,	,	PUNCT
ejpam-5699	137	7	18	18	NUM
ejpam-5699	137	8	(	(	PUNCT
ejpam-5699	137	9	1	1	NUM
ejpam-5699	137	10	)	)	PUNCT
ejpam-5699	137	11	(	(	PUNCT
ejpam-5699	137	12	2025	2025	NUM
ejpam-5699	137	13	)	)	PUNCT
ejpam-5699	137	14	,	,	PUNCT
ejpam-5699	137	15	5699	5699	NUM
ejpam-5699	137	16	9	9	NUM
ejpam-5699	137	17	of	of	ADP
ejpam-5699	137	18	20	20	NUM
ejpam-5699	137	19	n+	n+	SYM
ejpam-5699	137	20	b	b	PROPN
ejpam-5699	137	21	(	(	PUNCT
ejpam-5699	137	22	g1	g1	PROPN
ejpam-5699	137	23	)	)	PUNCT
ejpam-5699	137	24	,	,	PUNCT
ejpam-5699	137	25	and	and	CCONJ
ejpam-5699	137	26	n−	n−	PROPN
ejpam-5699	137	27	b	b	X
ejpam-5699	137	28	(	(	PUNCT
ejpam-5699	137	29	0	0	NUM
ejpam-5699	137	30	)	)	PUNCT
ejpam-5699	137	31	≥	≥	NOUN
ejpam-5699	137	32	n−	n−	PROPN
ejpam-5699	137	33	b	b	X
ejpam-5699	137	34	(	(	PUNCT
ejpam-5699	137	35	g1	g1	PROPN
ejpam-5699	137	36	)	)	PUNCT
ejpam-5699	137	37	.	.	PUNCT
ejpam-5699	138	1	also	also	ADV
ejpam-5699	138	2	,	,	PUNCT
ejpam-5699	138	3	since	since	SCONJ
ejpam-5699	138	4	g1	g1	PROPN
ejpam-5699	138	5	⋄	⋄	PROPN
ejpam-5699	138	6	(	(	PUNCT
ejpam-5699	138	7	g1	g1	PROPN
ejpam-5699	138	8	⋄	⋄	PROPN
ejpam-5699	138	9	è1	è1	PROPN
ejpam-5699	138	10	)	)	PUNCT
ejpam-5699	138	11	≤	≤	NOUN
ejpam-5699	138	12	è1	è1	NOUN
ejpam-5699	138	13	for	for	ADP
ejpam-5699	138	14	all	all	DET
ejpam-5699	138	15	g1,è1	g1,è1	PROPN
ejpam-5699	138	16	∈	∈	PROPN
ejpam-5699	138	17	g	g	NOUN
ejpam-5699	138	18	,	,	PUNCT
ejpam-5699	138	19	we	we	PRON
ejpam-5699	138	20	have	have	VERB
ejpam-5699	138	21	m+	m+	VERB
ejpam-5699	138	22	b(g1	b(g1	NOUN
ejpam-5699	138	23	)	)	PUNCT
ejpam-5699	139	1	≥	≥	NOUN
ejpam-5699	140	1	min{m+	min{m+	VERB
ejpam-5699	140	2	b(g1	b(g1	ADJ
ejpam-5699	140	3	⋄	⋄	PROPN
ejpam-5699	140	4	è1),m+	è1),m+	NOUN
ejpam-5699	140	5	b(è1	b(è1	NOUN
ejpam-5699	140	6	)	)	PUNCT
ejpam-5699	140	7	}	}	PUNCT
ejpam-5699	140	8	,	,	PUNCT
ejpam-5699	140	9	m−	m−	PROPN
ejpam-5699	140	10	b(g1	b(g1	NOUN
ejpam-5699	140	11	)	)	PUNCT
ejpam-5699	140	12	≤	≤	NOUN
ejpam-5699	141	1	max{m−	max{m−	NOUN
ejpam-5699	141	2	b(g1	b(g1	ADJ
ejpam-5699	141	3	⋄	⋄	PROPN
ejpam-5699	141	4	è1),m−	è1),m−	PROPN
ejpam-5699	141	5	b(è1	b(è1	NOUN
ejpam-5699	141	6	)	)	PUNCT
ejpam-5699	141	7	}	}	PUNCT
ejpam-5699	141	8	,	,	PUNCT
ejpam-5699	141	9	n+	n+	ADP
ejpam-5699	141	10	b	b	X
ejpam-5699	141	11	(	(	PUNCT
ejpam-5699	141	12	g1	g1	PROPN
ejpam-5699	141	13	)	)	PUNCT
ejpam-5699	141	14	≤	≤	NUM
ejpam-5699	141	15	max{n+	max{n+	PROPN
ejpam-5699	141	16	b	b	PROPN
ejpam-5699	141	17	(	(	PUNCT
ejpam-5699	141	18	g1	g1	PROPN
ejpam-5699	141	19	⋄	⋄	PROPN
ejpam-5699	141	20	è1),n+	è1),n+	PROPN
ejpam-5699	141	21	b	b	PROPN
ejpam-5699	141	22	(	(	PUNCT
ejpam-5699	141	23	è1	è1	NOUN
ejpam-5699	141	24	)	)	PUNCT
ejpam-5699	141	25	}	}	PUNCT
ejpam-5699	141	26	,	,	PUNCT
ejpam-5699	141	27	n−	n−	PROPN
ejpam-5699	141	28	b	b	X
ejpam-5699	141	29	(	(	PUNCT
ejpam-5699	141	30	g1	g1	PROPN
ejpam-5699	141	31	)	)	PUNCT
ejpam-5699	141	32	≥	≥	NOUN
ejpam-5699	141	33	min{n−	min{n−	PROPN
ejpam-5699	141	34	b	b	PROPN
ejpam-5699	141	35	(	(	PUNCT
ejpam-5699	141	36	g1	g1	PROPN
ejpam-5699	141	37	⋄	⋄	PROPN
ejpam-5699	141	38	è1),n−	è1),n−	PROPN
ejpam-5699	141	39	b	b	PROPN
ejpam-5699	141	40	(	(	PUNCT
ejpam-5699	141	41	è1	è1	NOUN
ejpam-5699	141	42	)	)	PUNCT
ejpam-5699	141	43	}	}	PUNCT
ejpam-5699	141	44	.	.	PUNCT
ejpam-5699	142	1	therefore	therefore	ADV
ejpam-5699	142	2	,	,	PUNCT
ejpam-5699	142	3	b	b	X
ejpam-5699	142	4	=	=	SYM
ejpam-5699	142	5	(	(	PUNCT
ejpam-5699	142	6	m+	m+	NUM
ejpam-5699	142	7	b	b	NOUN
ejpam-5699	142	8	,	,	PUNCT
ejpam-5699	142	9	m−	m−	PROPN
ejpam-5699	142	10	b	b	PROPN
ejpam-5699	142	11	,	,	PUNCT
ejpam-5699	142	12	n+	n+	NOUN
ejpam-5699	142	13	b	b	NOUN
ejpam-5699	142	14	,	,	PUNCT
ejpam-5699	142	15	n−	n−	PROPN
ejpam-5699	142	16	b	b	X
ejpam-5699	142	17	)	)	PUNCT
ejpam-5699	142	18	is	be	AUX
ejpam-5699	142	19	a	a	DET
ejpam-5699	142	20	bpifi	bpifi	NOUN
ejpam-5699	142	21	of	of	ADP
ejpam-5699	142	22	g.	g.	PROPN
ejpam-5699	142	23	3	3	NUM
ejpam-5699	142	24	.	.	X
ejpam-5699	142	25	bipolar	bipolar	ADJ
ejpam-5699	142	26	valued	value	VERB
ejpam-5699	142	27	intuitionistic	intuitionistic	ADJ
ejpam-5699	142	28	fuzzy	fuzzy	ADJ
ejpam-5699	142	29	positive	positive	ADJ
ejpam-5699	142	30	implicative	implicative	ADJ
ejpam-5699	142	31	ideals	ideal	NOUN
ejpam-5699	142	32	definition	definition	NOUN
ejpam-5699	142	33	21	21	NUM
ejpam-5699	142	34	.	.	PUNCT
ejpam-5699	143	1	a	a	DET
ejpam-5699	143	2	bpvifs	bpvifs	PROPN
ejpam-5699	143	3	b	b	PROPN
ejpam-5699	143	4	=	=	PUNCT
ejpam-5699	143	5	(	(	PUNCT
ejpam-5699	143	6	m+	m+	NUM
ejpam-5699	143	7	b	b	NOUN
ejpam-5699	143	8	,	,	PUNCT
ejpam-5699	143	9	m−	m−	PROPN
ejpam-5699	143	10	b	b	PROPN
ejpam-5699	143	11	,	,	PUNCT
ejpam-5699	143	12	n+	n+	NOUN
ejpam-5699	143	13	b	b	NOUN
ejpam-5699	143	14	,	,	PUNCT
ejpam-5699	143	15	n−	n−	PROPN
ejpam-5699	143	16	b	b	NOUN
ejpam-5699	143	17	)	)	PUNCT
ejpam-5699	143	18	in	in	ADP
ejpam-5699	143	19	g	g	PROPN
ejpam-5699	143	20	is	be	AUX
ejpam-5699	143	21	a	a	DET
ejpam-5699	143	22	bpvifpii	bpvifpii	NOUN
ejpam-5699	143	23	of	of	ADP
ejpam-5699	143	24	g	g	NOUN
ejpam-5699	143	25	if	if	SCONJ
ejpam-5699	143	26	it	it	PRON
ejpam-5699	143	27	satisfies	satisfy	VERB
ejpam-5699	143	28	for	for	ADP
ejpam-5699	143	29	all	all	DET
ejpam-5699	143	30	g1,è1	g1,è1	PROPN
ejpam-5699	143	31	,	,	PUNCT
ejpam-5699	143	32	11	11	NUM
ejpam-5699	143	33	∈	∈	NOUN
ejpam-5699	143	34	g	g	NOUN
ejpam-5699	143	35	,	,	PUNCT
ejpam-5699	143	36	m+	m+	NUM
ejpam-5699	143	37	b(0	b(0	NOUN
ejpam-5699	143	38	)	)	PUNCT
ejpam-5699	143	39	≥	≥	NOUN
ejpam-5699	143	40	m+	m+	NUM
ejpam-5699	143	41	b(g1	b(g1	NOUN
ejpam-5699	143	42	)	)	PUNCT
ejpam-5699	143	43	,	,	PUNCT
ejpam-5699	143	44	m−	m−	PROPN
ejpam-5699	143	45	b(0	b(0	PROPN
ejpam-5699	143	46	)	)	PUNCT
ejpam-5699	143	47	≤	≤	NOUN
ejpam-5699	143	48	m−	m−	PROPN
ejpam-5699	143	49	b(g1	b(g1	NOUN
ejpam-5699	143	50	)	)	PUNCT
ejpam-5699	143	51	,	,	PUNCT
ejpam-5699	143	52	n+	n+	ADP
ejpam-5699	143	53	b	b	X
ejpam-5699	143	54	(	(	PUNCT
ejpam-5699	143	55	0	0	NUM
ejpam-5699	143	56	)	)	PUNCT
ejpam-5699	143	57	≤	≤	NUM
ejpam-5699	143	58	n+	n+	PUNCT
ejpam-5699	144	1	b	b	X
ejpam-5699	144	2	(	(	PUNCT
ejpam-5699	144	3	g1	g1	PROPN
ejpam-5699	144	4	)	)	PUNCT
ejpam-5699	144	5	,	,	PUNCT
ejpam-5699	144	6	n−	n−	PROPN
ejpam-5699	144	7	b	b	X
ejpam-5699	144	8	(	(	PUNCT
ejpam-5699	144	9	0	0	NUM
ejpam-5699	144	10	)	)	PUNCT
ejpam-5699	144	11	≥	≥	NOUN
ejpam-5699	144	12	n−	n−	PROPN
ejpam-5699	144	13	b	b	X
ejpam-5699	144	14	(	(	PUNCT
ejpam-5699	144	15	g1	g1	PROPN
ejpam-5699	144	16	)	)	PUNCT
ejpam-5699	144	17	,	,	PUNCT
ejpam-5699	144	18	and	and	CCONJ
ejpam-5699	144	19	m+	m+	NOUN
ejpam-5699	144	20	b(g1	b(g1	ADJ
ejpam-5699	144	21	⋄	⋄	PROPN
ejpam-5699	144	22	11	11	NUM
ejpam-5699	144	23	)	)	PUNCT
ejpam-5699	144	24	≥	≥	NOUN
ejpam-5699	144	25	min{m+	min{m+	PROPN
ejpam-5699	144	26	b((g1	b((g1	PROPN
ejpam-5699	144	27	⋄	⋄	PROPN
ejpam-5699	144	28	è1	è1	PROPN
ejpam-5699	144	29	)	)	PUNCT
ejpam-5699	144	30	⋄	⋄	PROPN
ejpam-5699	144	31	11),m+	11),m+	NUM
ejpam-5699	144	32	b(è1	b(è1	NOUN
ejpam-5699	144	33	⋄	⋄	PROPN
ejpam-5699	144	34	11	11	NUM
ejpam-5699	144	35	)	)	PUNCT
ejpam-5699	144	36	}	}	PUNCT
ejpam-5699	144	37	,	,	PUNCT
ejpam-5699	144	38	m−	m−	PROPN
ejpam-5699	144	39	b(g1	b(g1	ADJ
ejpam-5699	144	40	⋄	⋄	PROPN
ejpam-5699	144	41	11	11	NUM
ejpam-5699	144	42	)	)	PUNCT
ejpam-5699	144	43	≤	≤	NOUN
ejpam-5699	144	44	max{m−	max{m−	NOUN
ejpam-5699	144	45	b((g1	b((g1	NOUN
ejpam-5699	144	46	⋄	⋄	PROPN
ejpam-5699	144	47	è1	è1	PROPN
ejpam-5699	144	48	)	)	PUNCT
ejpam-5699	144	49	⋄	⋄	NOUN
ejpam-5699	144	50	11),m−	11),m−	NUM
ejpam-5699	144	51	b(è1	b(è1	NOUN
ejpam-5699	144	52	⋄	⋄	PROPN
ejpam-5699	144	53	11	11	NUM
ejpam-5699	144	54	)	)	PUNCT
ejpam-5699	144	55	}	}	PUNCT
ejpam-5699	144	56	,	,	PUNCT
ejpam-5699	144	57	n+	n+	ADP
ejpam-5699	144	58	b	b	X
ejpam-5699	144	59	(	(	PUNCT
ejpam-5699	144	60	g1	g1	VERB
ejpam-5699	144	61	⋄	⋄	PROPN
ejpam-5699	144	62	11	11	NUM
ejpam-5699	144	63	)	)	PUNCT
ejpam-5699	144	64	≤	≤	NUM
ejpam-5699	144	65	max{n+	max{n+	PROPN
ejpam-5699	144	66	b	b	PROPN
ejpam-5699	144	67	(	(	PUNCT
ejpam-5699	144	68	(	(	PUNCT
ejpam-5699	144	69	g1	g1	PROPN
ejpam-5699	144	70	⋄	⋄	PROPN
ejpam-5699	144	71	è1	è1	PROPN
ejpam-5699	144	72	)	)	PUNCT
ejpam-5699	144	73	⋄	⋄	PROPN
ejpam-5699	144	74	11),n+	11),n+	NUM
ejpam-5699	144	75	b	b	PROPN
ejpam-5699	144	76	(	(	PUNCT
ejpam-5699	144	77	è1	è1	ADJ
ejpam-5699	144	78	⋄	⋄	NOUN
ejpam-5699	144	79	11	11	NUM
ejpam-5699	144	80	)	)	PUNCT
ejpam-5699	144	81	}	}	PUNCT
ejpam-5699	144	82	,	,	PUNCT
ejpam-5699	144	83	n−	n−	PROPN
ejpam-5699	144	84	b	b	X
ejpam-5699	144	85	(	(	PUNCT
ejpam-5699	144	86	g1	g1	VERB
ejpam-5699	144	87	⋄	⋄	PROPN
ejpam-5699	144	88	11	11	NUM
ejpam-5699	144	89	)	)	PUNCT
ejpam-5699	144	90	≥	≥	NOUN
ejpam-5699	144	91	min{n−	min{n−	PROPN
ejpam-5699	144	92	b	b	PROPN
ejpam-5699	144	93	(	(	PUNCT
ejpam-5699	144	94	(	(	PUNCT
ejpam-5699	144	95	g1	g1	PROPN
ejpam-5699	144	96	⋄	⋄	PROPN
ejpam-5699	144	97	è1	è1	PROPN
ejpam-5699	144	98	)	)	PUNCT
ejpam-5699	144	99	⋄	⋄	PROPN
ejpam-5699	144	100	11),n−	11),n−	NUM
ejpam-5699	144	101	b	b	PROPN
ejpam-5699	144	102	(	(	PUNCT
ejpam-5699	144	103	è1	è1	ADJ
ejpam-5699	144	104	⋄	⋄	NOUN
ejpam-5699	144	105	11	11	NUM
ejpam-5699	144	106	)	)	PUNCT
ejpam-5699	144	107	}	}	PUNCT
ejpam-5699	144	108	.	.	PUNCT
ejpam-5699	145	1	example	example	NOUN
ejpam-5699	146	1	1	1	X
ejpam-5699	146	2	.	.	X
ejpam-5699	146	3	consider	consider	VERB
ejpam-5699	146	4	g	g	NOUN
ejpam-5699	146	5	=	=	SYM
ejpam-5699	146	6	{	{	PUNCT
ejpam-5699	146	7	0	0	NUM
ejpam-5699	146	8	,	,	PUNCT
ejpam-5699	146	9	1	1	NUM
ejpam-5699	146	10	,	,	PUNCT
ejpam-5699	146	11	2	2	NUM
ejpam-5699	146	12	,	,	PUNCT
ejpam-5699	146	13	3	3	NUM
ejpam-5699	146	14	}	}	PUNCT
ejpam-5699	146	15	be	be	AUX
ejpam-5699	146	16	a	a	DET
ejpam-5699	146	17	set	set	NOUN
ejpam-5699	146	18	in	in	ADP
ejpam-5699	146	19	which	which	PRON
ejpam-5699	146	20	the	the	DET
ejpam-5699	146	21	binary	binary	PROPN
ejpam-5699	146	22	operation	operation	PROPN
ejpam-5699	146	23	⋄	⋄	PROPN
ejpam-5699	146	24	is	be	AUX
ejpam-5699	146	25	defined	define	VERB
ejpam-5699	146	26	as	as	SCONJ
ejpam-5699	146	27	follows	follow	VERB
ejpam-5699	146	28	:	:	PUNCT
ejpam-5699	146	29	0	0	NUM
ejpam-5699	146	30	⋄	⋄	PROPN
ejpam-5699	146	31	g1	g1	PROPN
ejpam-5699	146	32	=	=	SYM
ejpam-5699	146	33	0	0	NUM
ejpam-5699	146	34	∀g1	∀g1	PROPN
ejpam-5699	146	35	∈	∈	PROPN
ejpam-5699	146	36	g	g	PROPN
ejpam-5699	146	37	1	1	NUM
ejpam-5699	146	38	⋄	⋄	PROPN
ejpam-5699	146	39	g1	g1	NOUN
ejpam-5699	146	40	=	=	SYM
ejpam-5699	146	41	{	{	PUNCT
ejpam-5699	146	42	0	0	NUM
ejpam-5699	146	43	,	,	PUNCT
ejpam-5699	146	44	if	if	SCONJ
ejpam-5699	146	45	g1	g1	PROPN
ejpam-5699	146	46	∈	∈	PROPN
ejpam-5699	146	47	{	{	PUNCT
ejpam-5699	146	48	1	1	NUM
ejpam-5699	146	49	,	,	PUNCT
ejpam-5699	146	50	3	3	NUM
ejpam-5699	146	51	}	}	SYM
ejpam-5699	146	52	1	1	NUM
ejpam-5699	146	53	,	,	PUNCT
ejpam-5699	146	54	if	if	SCONJ
ejpam-5699	146	55	g1	g1	PROPN
ejpam-5699	146	56	∈	∈	PROPN
ejpam-5699	146	57	{	{	PUNCT
ejpam-5699	146	58	0	0	NUM
ejpam-5699	146	59	,	,	PUNCT
ejpam-5699	146	60	2	2	NUM
ejpam-5699	146	61	}	}	SYM
ejpam-5699	146	62	2	2	NUM
ejpam-5699	146	63	⋄	⋄	NOUN
ejpam-5699	146	64	g1	g1	NOUN
ejpam-5699	146	65	=	=	SYM
ejpam-5699	146	66	{	{	PUNCT
ejpam-5699	146	67	0	0	NUM
ejpam-5699	146	68	,	,	PUNCT
ejpam-5699	146	69	if	if	SCONJ
ejpam-5699	146	70	g1	g1	PROPN
ejpam-5699	146	71	∈	∈	PROPN
ejpam-5699	146	72	{	{	PUNCT
ejpam-5699	146	73	2	2	NUM
ejpam-5699	146	74	,	,	PUNCT
ejpam-5699	146	75	3	3	NUM
ejpam-5699	146	76	}	}	SYM
ejpam-5699	146	77	2	2	NUM
ejpam-5699	146	78	,	,	PUNCT
ejpam-5699	146	79	if	if	SCONJ
ejpam-5699	146	80	g1	g1	PROPN
ejpam-5699	146	81	∈	∈	PROPN
ejpam-5699	146	82	{	{	PUNCT
ejpam-5699	146	83	0	0	NUM
ejpam-5699	146	84	,	,	PUNCT
ejpam-5699	146	85	1	1	NUM
ejpam-5699	146	86	}	}	SYM
ejpam-5699	146	87	3	3	NUM
ejpam-5699	146	88	⋄	⋄	PROPN
ejpam-5699	146	89	g1	g1	NOUN
ejpam-5699	146	90	=	=	PUNCT
ejpam-5699	146	91			NOUN
ejpam-5699	146	92	0	0	NUM
ejpam-5699	146	93	,	,	PUNCT
ejpam-5699	146	94	if	if	SCONJ
ejpam-5699	146	95	g1	g1	NOUN
ejpam-5699	146	96	=	=	SYM
ejpam-5699	146	97	3	3	NUM
ejpam-5699	146	98	1	1	NUM
ejpam-5699	146	99	,	,	PUNCT
ejpam-5699	146	100	if	if	SCONJ
ejpam-5699	146	101	g1	g1	NOUN
ejpam-5699	146	102	=	=	SYM
ejpam-5699	146	103	2	2	NUM
ejpam-5699	146	104	2	2	NUM
ejpam-5699	146	105	,	,	PUNCT
ejpam-5699	146	106	if	if	SCONJ
ejpam-5699	146	107	g1	g1	NOUN
ejpam-5699	146	108	=	=	SYM
ejpam-5699	146	109	1	1	NUM
ejpam-5699	146	110	3	3	NUM
ejpam-5699	146	111	,	,	PUNCT
ejpam-5699	146	112	if	if	SCONJ
ejpam-5699	146	113	g1	g1	NOUN
ejpam-5699	146	114	=	=	SYM
ejpam-5699	146	115	0	0	PUNCT
ejpam-5699	147	1	then	then	ADV
ejpam-5699	147	2	g	g	PROPN
ejpam-5699	147	3	is	be	AUX
ejpam-5699	147	4	a	a	DET
ejpam-5699	147	5	bck	bck	NOUN
ejpam-5699	147	6	-	-	PUNCT
ejpam-5699	147	7	a.	a.	NOUN
ejpam-5699	147	8	let	let	VERB
ejpam-5699	147	9	us	we	PRON
ejpam-5699	147	10	define	define	VERB
ejpam-5699	147	11	a	a	DET
ejpam-5699	147	12	bpvifs	bpvifs	PROPN
ejpam-5699	147	13	b	b	PROPN
ejpam-5699	147	14	=	=	PUNCT
ejpam-5699	147	15	(	(	PUNCT
ejpam-5699	147	16	m+	m+	NUM
ejpam-5699	147	17	b	b	NOUN
ejpam-5699	147	18	,	,	PUNCT
ejpam-5699	147	19	m−	m−	PROPN
ejpam-5699	147	20	b	b	PROPN
ejpam-5699	147	21	,	,	PUNCT
ejpam-5699	147	22	n+	n+	NOUN
ejpam-5699	147	23	b	b	NOUN
ejpam-5699	147	24	,	,	PUNCT
ejpam-5699	147	25	n−	n−	PROPN
ejpam-5699	147	26	b	b	NOUN
ejpam-5699	147	27	)	)	PUNCT
ejpam-5699	147	28	in	in	ADP
ejpam-5699	147	29	g	g	PROPN
ejpam-5699	147	30	as	as	SCONJ
ejpam-5699	147	31	shown	show	VERB
ejpam-5699	147	32	in	in	ADP
ejpam-5699	147	33	table	table	NOUN
ejpam-5699	147	34	1	1	NUM
ejpam-5699	147	35	.	.	PUNCT
ejpam-5699	147	36	by	by	ADP
ejpam-5699	147	37	using	use	VERB
ejpam-5699	147	38	standard	standard	ADJ
ejpam-5699	147	39	computation	computation	NOUN
ejpam-5699	147	40	,	,	PUNCT
ejpam-5699	147	41	it	it	PRON
ejpam-5699	147	42	is	be	AUX
ejpam-5699	147	43	clear	clear	ADJ
ejpam-5699	147	44	that	that	SCONJ
ejpam-5699	147	45	b	b	X
ejpam-5699	147	46	=	=	SYM
ejpam-5699	147	47	(	(	PUNCT
ejpam-5699	147	48	m+	m+	NUM
ejpam-5699	147	49	b	b	NOUN
ejpam-5699	147	50	,	,	PUNCT
ejpam-5699	147	51	m−	m−	PROPN
ejpam-5699	147	52	b	b	PROPN
ejpam-5699	147	53	,	,	PUNCT
ejpam-5699	147	54	n+	n+	NOUN
ejpam-5699	147	55	b	b	NOUN
ejpam-5699	147	56	,	,	PUNCT
ejpam-5699	147	57	n−	n−	PROPN
ejpam-5699	147	58	b	b	X
ejpam-5699	147	59	)	)	PUNCT
ejpam-5699	147	60	is	be	AUX
ejpam-5699	147	61	a	a	DET
ejpam-5699	147	62	bpvifpii	bpvifpii	NOUN
ejpam-5699	147	63	of	of	ADP
ejpam-5699	147	64	g.	g.	PROPN
ejpam-5699	147	65	example	example	NOUN
ejpam-5699	147	66	2	2	X
ejpam-5699	147	67	.	.	X
ejpam-5699	147	68	consider	consider	VERB
ejpam-5699	147	69	g	g	NOUN
ejpam-5699	147	70	=	=	SYM
ejpam-5699	147	71	{	{	PUNCT
ejpam-5699	147	72	0	0	NUM
ejpam-5699	147	73	,	,	PUNCT
ejpam-5699	147	74	1	1	NUM
ejpam-5699	147	75	,	,	PUNCT
ejpam-5699	147	76	2	2	NUM
ejpam-5699	147	77	,	,	PUNCT
ejpam-5699	147	78	3	3	NUM
ejpam-5699	147	79	,	,	PUNCT
ejpam-5699	147	80	4	4	NUM
ejpam-5699	147	81	}	}	PUNCT
ejpam-5699	147	82	be	be	AUX
ejpam-5699	147	83	a	a	DET
ejpam-5699	147	84	set	set	NOUN
ejpam-5699	147	85	in	in	ADP
ejpam-5699	147	86	which	which	PRON
ejpam-5699	147	87	the	the	DET
ejpam-5699	147	88	binary	binary	PROPN
ejpam-5699	147	89	operation	operation	PROPN
ejpam-5699	147	90	⋄	⋄	PROPN
ejpam-5699	147	91	is	be	AUX
ejpam-5699	147	92	defined	define	VERB
ejpam-5699	147	93	as	as	SCONJ
ejpam-5699	147	94	follows	follow	VERB
ejpam-5699	147	95	:	:	PUNCT
ejpam-5699	147	96	0	0	NUM
ejpam-5699	147	97	⋄	⋄	PROPN
ejpam-5699	147	98	g1	g1	PROPN
ejpam-5699	147	99	=	=	SYM
ejpam-5699	147	100	0	0	NUM
ejpam-5699	147	101	∀g1	∀g1	PROPN
ejpam-5699	148	1	∈	∈	PROPN
ejpam-5699	148	2	g	g	PROPN
ejpam-5699	148	3	d.	d.	PROPN
ejpam-5699	148	4	ramesh	ramesh	PROPN
ejpam-5699	148	5	et	et	PROPN
ejpam-5699	148	6	al	al	PROPN
ejpam-5699	148	7	.	.	PUNCT
ejpam-5699	148	8	/	/	SYM
ejpam-5699	148	9	eur	eur	PROPN
ejpam-5699	148	10	.	.	PUNCT
ejpam-5699	149	1	j.	j.	PROPN
ejpam-5699	149	2	pure	pure	PROPN
ejpam-5699	149	3	appl	appl	PROPN
ejpam-5699	149	4	.	.	PROPN
ejpam-5699	149	5	math	math	PROPN
ejpam-5699	149	6	,	,	PUNCT
ejpam-5699	149	7	18	18	NUM
ejpam-5699	149	8	(	(	PUNCT
ejpam-5699	149	9	1	1	NUM
ejpam-5699	149	10	)	)	PUNCT
ejpam-5699	149	11	(	(	PUNCT
ejpam-5699	149	12	2025	2025	NUM
ejpam-5699	149	13	)	)	PUNCT
ejpam-5699	149	14	,	,	PUNCT
ejpam-5699	149	15	5699	5699	NUM
ejpam-5699	149	16	10	10	NUM
ejpam-5699	149	17	of	of	ADP
ejpam-5699	149	18	20	20	NUM
ejpam-5699	149	19	table	table	NOUN
ejpam-5699	149	20	1	1	NUM
ejpam-5699	149	21	:	:	PUNCT
ejpam-5699	149	22	bpvifpii	bpvifpii	NOUN
ejpam-5699	149	23	g1	g1	PROPN
ejpam-5699	149	24	m+	m+	VERB
ejpam-5699	149	25	b(g1	b(g1	NOUN
ejpam-5699	149	26	)	)	PUNCT
ejpam-5699	149	27	m−	m−	PROPN
ejpam-5699	149	28	b(g1	b(g1	NOUN
ejpam-5699	149	29	)	)	PUNCT
ejpam-5699	149	30	n+	n+	PROPN
ejpam-5699	150	1	b	b	X
ejpam-5699	150	2	(	(	PUNCT
ejpam-5699	150	3	g1	g1	PROPN
ejpam-5699	150	4	)	)	PUNCT
ejpam-5699	150	5	n−	n−	PROPN
ejpam-5699	150	6	b	b	X
ejpam-5699	150	7	(	(	PUNCT
ejpam-5699	150	8	g1	g1	PROPN
ejpam-5699	150	9	)	)	PUNCT
ejpam-5699	150	10	0	0	NUM
ejpam-5699	150	11	0.65	0.65	NUM
ejpam-5699	150	12	−0.85	−0.85	NOUN
ejpam-5699	150	13	0.35	0.35	NUM
ejpam-5699	150	14	−0.15	−0.15	NOUN
ejpam-5699	150	15	1	1	NUM
ejpam-5699	150	16	0.53	0.53	NUM
ejpam-5699	150	17	−0.53	−0.53	NUM
ejpam-5699	150	18	0.47	0.47	NUM
ejpam-5699	150	19	−0.47	−0.47	SYM
ejpam-5699	150	20	2	2	NUM
ejpam-5699	150	21	0.31	0.31	NUM
ejpam-5699	150	22	−0.23	−0.23	PRON
ejpam-5699	150	23	0.69	0.69	NUM
ejpam-5699	150	24	−0.77	−0.77	NOUN
ejpam-5699	150	25	3	3	NUM
ejpam-5699	150	26	0.31	0.31	NUM
ejpam-5699	150	27	−0.23	−0.23	PRON
ejpam-5699	150	28	0.69	0.69	NUM
ejpam-5699	150	29	−0.77	−0.77	NUM
ejpam-5699	150	30	1	1	NUM
ejpam-5699	150	31	⋄	⋄	NOUN
ejpam-5699	150	32	g1	g1	NOUN
ejpam-5699	150	33	=	=	SYM
ejpam-5699	150	34	{	{	PUNCT
ejpam-5699	150	35	0	0	NUM
ejpam-5699	150	36	,	,	PUNCT
ejpam-5699	150	37	if	if	SCONJ
ejpam-5699	150	38	g1	g1	PROPN
ejpam-5699	150	39	∈	∈	PROPN
ejpam-5699	150	40	{	{	PUNCT
ejpam-5699	150	41	1	1	NUM
ejpam-5699	150	42	,	,	PUNCT
ejpam-5699	150	43	2	2	NUM
ejpam-5699	150	44	,	,	PUNCT
ejpam-5699	150	45	3	3	NUM
ejpam-5699	150	46	,	,	PUNCT
ejpam-5699	150	47	4	4	NUM
ejpam-5699	150	48	}	}	SYM
ejpam-5699	150	49	1	1	NUM
ejpam-5699	150	50	,	,	PUNCT
ejpam-5699	150	51	if	if	SCONJ
ejpam-5699	150	52	g1	g1	NOUN
ejpam-5699	150	53	=	=	SYM
ejpam-5699	150	54	0	0	NUM
ejpam-5699	150	55	2	2	NUM
ejpam-5699	150	56	⋄	⋄	NOUN
ejpam-5699	150	57	g1	g1	NOUN
ejpam-5699	150	58	=	=	SYM
ejpam-5699	150	59	{	{	PUNCT
ejpam-5699	150	60	0	0	NUM
ejpam-5699	150	61	,	,	PUNCT
ejpam-5699	150	62	if	if	SCONJ
ejpam-5699	150	63	g1	g1	PROPN
ejpam-5699	150	64	∈	∈	PROPN
ejpam-5699	150	65	{	{	PUNCT
ejpam-5699	150	66	2	2	NUM
ejpam-5699	150	67	,	,	PUNCT
ejpam-5699	150	68	3	3	NUM
ejpam-5699	150	69	}	}	SYM
ejpam-5699	150	70	2	2	NUM
ejpam-5699	150	71	,	,	PUNCT
ejpam-5699	150	72	if	if	SCONJ
ejpam-5699	150	73	g1	g1	PROPN
ejpam-5699	150	74	∈	∈	PROPN
ejpam-5699	150	75	{	{	PUNCT
ejpam-5699	150	76	0	0	NUM
ejpam-5699	150	77	,	,	PUNCT
ejpam-5699	150	78	1	1	NUM
ejpam-5699	150	79	,	,	PUNCT
ejpam-5699	150	80	4	4	NUM
ejpam-5699	150	81	}	}	SYM
ejpam-5699	150	82	3	3	NUM
ejpam-5699	150	83	⋄	⋄	NOUN
ejpam-5699	150	84	g1	g1	NOUN
ejpam-5699	150	85	=	=	SYM
ejpam-5699	150	86	{	{	PUNCT
ejpam-5699	150	87	0	0	NUM
ejpam-5699	150	88	,	,	PUNCT
ejpam-5699	150	89	if	if	SCONJ
ejpam-5699	150	90	g1	g1	NOUN
ejpam-5699	150	91	=	=	SYM
ejpam-5699	150	92	3	3	NUM
ejpam-5699	150	93	3	3	NUM
ejpam-5699	150	94	,	,	PUNCT
ejpam-5699	150	95	if	if	SCONJ
ejpam-5699	150	96	g1	g1	PROPN
ejpam-5699	150	97	∈	∈	PROPN
ejpam-5699	150	98	{	{	PUNCT
ejpam-5699	150	99	0	0	NUM
ejpam-5699	150	100	,	,	PUNCT
ejpam-5699	150	101	1	1	NUM
ejpam-5699	150	102	,	,	PUNCT
ejpam-5699	150	103	2	2	NUM
ejpam-5699	150	104	,	,	PUNCT
ejpam-5699	150	105	4	4	NUM
ejpam-5699	150	106	}	}	SYM
ejpam-5699	150	107	4	4	NUM
ejpam-5699	150	108	⋄	⋄	NOUN
ejpam-5699	150	109	g1	g1	NOUN
ejpam-5699	150	110	=	=	SYM
ejpam-5699	150	111	{	{	PUNCT
ejpam-5699	150	112	0	0	NUM
ejpam-5699	150	113	,	,	PUNCT
ejpam-5699	150	114	if	if	SCONJ
ejpam-5699	150	115	g1	g1	NOUN
ejpam-5699	150	116	=	=	NOUN
ejpam-5699	150	117	4	4	NUM
ejpam-5699	150	118	4	4	NUM
ejpam-5699	150	119	,	,	PUNCT
ejpam-5699	150	120	if	if	SCONJ
ejpam-5699	150	121	g1	g1	PROPN
ejpam-5699	150	122	∈	∈	PROPN
ejpam-5699	150	123	{	{	PUNCT
ejpam-5699	150	124	0	0	NUM
ejpam-5699	150	125	,	,	PUNCT
ejpam-5699	150	126	1	1	NUM
ejpam-5699	150	127	,	,	PUNCT
ejpam-5699	150	128	2	2	NUM
ejpam-5699	150	129	,	,	PUNCT
ejpam-5699	150	130	3	3	NUM
ejpam-5699	150	131	}	}	PUNCT
ejpam-5699	150	132	then	then	ADV
ejpam-5699	150	133	g	g	PROPN
ejpam-5699	150	134	is	be	AUX
ejpam-5699	150	135	a	a	DET
ejpam-5699	150	136	bck	bck	NOUN
ejpam-5699	150	137	-	-	PUNCT
ejpam-5699	150	138	a.	a.	NOUN
ejpam-5699	150	139	let	let	VERB
ejpam-5699	150	140	us	we	PRON
ejpam-5699	150	141	define	define	VERB
ejpam-5699	150	142	a	a	DET
ejpam-5699	150	143	bpvifs	bpvifs	PROPN
ejpam-5699	150	144	b	b	PROPN
ejpam-5699	150	145	=	=	PUNCT
ejpam-5699	150	146	(	(	PUNCT
ejpam-5699	150	147	m+	m+	NUM
ejpam-5699	150	148	b	b	NOUN
ejpam-5699	150	149	,	,	PUNCT
ejpam-5699	150	150	m−	m−	PROPN
ejpam-5699	150	151	b	b	PROPN
ejpam-5699	150	152	,	,	PUNCT
ejpam-5699	150	153	n+	n+	NOUN
ejpam-5699	150	154	b	b	NOUN
ejpam-5699	150	155	,	,	PUNCT
ejpam-5699	150	156	n−	n−	PROPN
ejpam-5699	150	157	b	b	NOUN
ejpam-5699	150	158	)	)	PUNCT
ejpam-5699	150	159	in	in	ADP
ejpam-5699	150	160	g	g	PROPN
ejpam-5699	150	161	as	as	SCONJ
ejpam-5699	150	162	shown	show	VERB
ejpam-5699	150	163	in	in	ADP
ejpam-5699	150	164	table	table	NOUN
ejpam-5699	150	165	2	2	NUM
ejpam-5699	150	166	.	.	PUNCT
ejpam-5699	150	167	table	table	NOUN
ejpam-5699	150	168	2	2	NUM
ejpam-5699	150	169	:	:	PUNCT
ejpam-5699	150	170	bpvifpii	bpvifpii	NOUN
ejpam-5699	150	171	g1	g1	NOUN
ejpam-5699	150	172	m+	m+	VERB
ejpam-5699	150	173	b(g1	b(g1	NOUN
ejpam-5699	150	174	)	)	PUNCT
ejpam-5699	150	175	m−	m−	PROPN
ejpam-5699	150	176	b(g1	b(g1	NOUN
ejpam-5699	150	177	)	)	PUNCT
ejpam-5699	150	178	n+	n+	PROPN
ejpam-5699	151	1	b	b	X
ejpam-5699	151	2	(	(	PUNCT
ejpam-5699	151	3	g1	g1	PROPN
ejpam-5699	151	4	)	)	PUNCT
ejpam-5699	151	5	n−	n−	PROPN
ejpam-5699	151	6	b	b	X
ejpam-5699	151	7	(	(	PUNCT
ejpam-5699	151	8	g1	g1	PROPN
ejpam-5699	151	9	)	)	PUNCT
ejpam-5699	151	10	0	0	NUM
ejpam-5699	151	11	0.91	0.91	NUM
ejpam-5699	151	12	−0.79	−0.79	SYM
ejpam-5699	151	13	0.09	0.09	NUM
ejpam-5699	151	14	−0.21	−0.21	NOUN
ejpam-5699	151	15	1	1	NUM
ejpam-5699	151	16	0.75	0.75	NUM
ejpam-5699	151	17	−0.59	−0.59	NUM
ejpam-5699	151	18	0.25	0.25	NUM
ejpam-5699	151	19	−0.41	−0.41	NOUN
ejpam-5699	151	20	2	2	NUM
ejpam-5699	151	21	0.53	0.53	NUM
ejpam-5699	151	22	−0.38	−0.38	ADP
ejpam-5699	151	23	0.47	0.47	NUM
ejpam-5699	151	24	−0.62	−0.62	ADP
ejpam-5699	151	25	3	3	NUM
ejpam-5699	151	26	0.32	0.32	NUM
ejpam-5699	151	27	−0.29	−0.29	SYM
ejpam-5699	151	28	0.68	0.68	NUM
ejpam-5699	151	29	−0.71	−0.71	ADP
ejpam-5699	151	30	4	4	NUM
ejpam-5699	151	31	0.11	0.11	NUM
ejpam-5699	151	32	−0.11	−0.11	NOUN
ejpam-5699	151	33	0.89	0.89	NUM
ejpam-5699	151	34	−0.89	−0.89	NOUN
ejpam-5699	151	35	by	by	ADP
ejpam-5699	151	36	using	use	VERB
ejpam-5699	151	37	standard	standard	ADJ
ejpam-5699	151	38	computation	computation	NOUN
ejpam-5699	151	39	,	,	PUNCT
ejpam-5699	151	40	it	it	PRON
ejpam-5699	151	41	is	be	AUX
ejpam-5699	151	42	clear	clear	ADJ
ejpam-5699	151	43	that	that	SCONJ
ejpam-5699	151	44	b	b	X
ejpam-5699	151	45	=	=	SYM
ejpam-5699	151	46	(	(	PUNCT
ejpam-5699	151	47	m+	m+	NUM
ejpam-5699	151	48	b	b	NOUN
ejpam-5699	151	49	,	,	PUNCT
ejpam-5699	151	50	m−	m−	PROPN
ejpam-5699	151	51	b	b	PROPN
ejpam-5699	151	52	,	,	PUNCT
ejpam-5699	151	53	n+	n+	NOUN
ejpam-5699	151	54	b	b	NOUN
ejpam-5699	151	55	,	,	PUNCT
ejpam-5699	151	56	n−	n−	PROPN
ejpam-5699	151	57	b	b	X
ejpam-5699	151	58	)	)	PUNCT
ejpam-5699	151	59	is	be	AUX
ejpam-5699	151	60	a	a	DET
ejpam-5699	151	61	bpvifpii	bpvifpii	NOUN
ejpam-5699	151	62	of	of	ADP
ejpam-5699	151	63	g.	g.	PROPN
ejpam-5699	151	64	theorem	theorem	VERB
ejpam-5699	151	65	3	3	X
ejpam-5699	151	66	.	.	PUNCT
ejpam-5699	152	1	every	every	DET
ejpam-5699	152	2	bpvifpii	bpvifpii	NOUN
ejpam-5699	152	3	of	of	ADP
ejpam-5699	152	4	g	g	PROPN
ejpam-5699	152	5	is	be	AUX
ejpam-5699	152	6	also	also	ADV
ejpam-5699	152	7	a	a	DET
ejpam-5699	152	8	bpvifi	bpvifi	NOUN
ejpam-5699	152	9	of	of	ADP
ejpam-5699	152	10	g.	g.	PROPN
ejpam-5699	152	11	proof	proof	NOUN
ejpam-5699	152	12	.	.	PUNCT
ejpam-5699	153	1	let	let	VERB
ejpam-5699	153	2	b	b	NOUN
ejpam-5699	153	3	=	=	SYM
ejpam-5699	153	4	(	(	PUNCT
ejpam-5699	153	5	m+	m+	NUM
ejpam-5699	153	6	b	b	NOUN
ejpam-5699	153	7	,	,	PUNCT
ejpam-5699	153	8	m−	m−	PROPN
ejpam-5699	153	9	b	b	PROPN
ejpam-5699	153	10	,	,	PUNCT
ejpam-5699	153	11	n+	n+	NOUN
ejpam-5699	153	12	b	b	NOUN
ejpam-5699	153	13	,	,	PUNCT
ejpam-5699	153	14	n−	n−	PROPN
ejpam-5699	153	15	b	b	AUX
ejpam-5699	153	16	)	)	PUNCT
ejpam-5699	153	17	be	be	AUX
ejpam-5699	153	18	a	a	DET
ejpam-5699	153	19	bpvifpii	bpvifpii	NOUN
ejpam-5699	153	20	of	of	ADP
ejpam-5699	153	21	g	g	NOUN
ejpam-5699	153	22	,	,	PUNCT
ejpam-5699	153	23	and	and	CCONJ
ejpam-5699	153	24	put	put	VERB
ejpam-5699	153	25	11	11	NUM
ejpam-5699	153	26	=	=	SYM
ejpam-5699	153	27	0	0	NUM
ejpam-5699	153	28	in	in	ADP
ejpam-5699	153	29	definition	definition	NOUN
ejpam-5699	153	30	21	21	NUM
ejpam-5699	153	31	.	.	PUNCT
ejpam-5699	154	1	then	then	ADV
ejpam-5699	154	2	,	,	PUNCT
ejpam-5699	154	3	using	use	VERB
ejpam-5699	154	4	(	(	PUNCT
ejpam-5699	154	5	1	1	NUM
ejpam-5699	154	6	)	)	PUNCT
ejpam-5699	154	7	,	,	PUNCT
ejpam-5699	154	8	we	we	PRON
ejpam-5699	154	9	obtain	obtain	VERB
ejpam-5699	154	10	m+	m+	NOUN
ejpam-5699	154	11	b(g1	b(g1	ADJ
ejpam-5699	154	12	⋄	⋄	PROPN
ejpam-5699	154	13	0	0	NUM
ejpam-5699	154	14	)	)	PUNCT
ejpam-5699	154	15	≥	≥	NOUN
ejpam-5699	154	16	min{m+	min{m+	PROPN
ejpam-5699	154	17	b((g1	b((g1	PROPN
ejpam-5699	154	18	⋄	⋄	PROPN
ejpam-5699	154	19	è1	è1	PROPN
ejpam-5699	154	20	)	)	PUNCT
ejpam-5699	154	21	⋄	⋄	PROPN
ejpam-5699	154	22	0),m+	0),m+	PROPN
ejpam-5699	154	23	b(è1	b(è1	VERB
ejpam-5699	154	24	⋄	⋄	PROPN
ejpam-5699	154	25	0	0	NUM
ejpam-5699	154	26	)	)	PUNCT
ejpam-5699	154	27	}	}	PUNCT
ejpam-5699	154	28	⇒	⇒	VERB
ejpam-5699	154	29	m+	m+	NUM
ejpam-5699	154	30	b(g1	b(g1	NOUN
ejpam-5699	154	31	)	)	PUNCT
ejpam-5699	154	32	≥	≥	NOUN
ejpam-5699	155	1	min{m+	min{m+	VERB
ejpam-5699	155	2	b(g1	b(g1	ADJ
ejpam-5699	155	3	⋄	⋄	PROPN
ejpam-5699	155	4	è1),m+	è1),m+	NOUN
ejpam-5699	155	5	b(è1	b(è1	NOUN
ejpam-5699	155	6	)	)	PUNCT
ejpam-5699	155	7	}	}	PUNCT
ejpam-5699	155	8	,	,	PUNCT
ejpam-5699	155	9	m−	m−	PROPN
ejpam-5699	155	10	b(g1	b(g1	ADJ
ejpam-5699	155	11	⋄	⋄	PROPN
ejpam-5699	155	12	0	0	NUM
ejpam-5699	155	13	)	)	PUNCT
ejpam-5699	155	14	≤	≤	NOUN
ejpam-5699	155	15	max{m−	max{m−	NOUN
ejpam-5699	155	16	b((g1	b((g1	NOUN
ejpam-5699	155	17	⋄	⋄	PROPN
ejpam-5699	155	18	è1	è1	PROPN
ejpam-5699	155	19	)	)	PUNCT
ejpam-5699	155	20	⋄	⋄	NOUN
ejpam-5699	155	21	0),m−	0),m−	PUNCT
ejpam-5699	155	22	b(è1	b(è1	VERB
ejpam-5699	155	23	⋄	⋄	PROPN
ejpam-5699	155	24	0	0	NUM
ejpam-5699	155	25	)	)	PUNCT
ejpam-5699	155	26	}	}	PUNCT
ejpam-5699	155	27	⇒	⇒	VERB
ejpam-5699	155	28	m−	m−	PROPN
ejpam-5699	155	29	b(g1	b(g1	NOUN
ejpam-5699	155	30	)	)	PUNCT
ejpam-5699	155	31	≤	≤	NOUN
ejpam-5699	155	32	max{m−	max{m−	NOUN
ejpam-5699	155	33	b(g1	b(g1	ADJ
ejpam-5699	155	34	⋄	⋄	PROPN
ejpam-5699	155	35	è1),m−	è1),m−	PROPN
ejpam-5699	155	36	b(è1	b(è1	NOUN
ejpam-5699	155	37	)	)	PUNCT
ejpam-5699	155	38	}	}	PUNCT
ejpam-5699	155	39	,	,	PUNCT
ejpam-5699	155	40	n+	n+	ADP
ejpam-5699	155	41	b	b	X
ejpam-5699	155	42	(	(	PUNCT
ejpam-5699	155	43	g1	g1	VERB
ejpam-5699	155	44	⋄	⋄	PROPN
ejpam-5699	155	45	0	0	NUM
ejpam-5699	155	46	)	)	PUNCT
ejpam-5699	155	47	≤	≤	NUM
ejpam-5699	156	1	max{n+	max{n+	PROPN
ejpam-5699	156	2	b	b	PROPN
ejpam-5699	156	3	(	(	PUNCT
ejpam-5699	156	4	(	(	PUNCT
ejpam-5699	156	5	g1	g1	PROPN
ejpam-5699	156	6	⋄	⋄	PROPN
ejpam-5699	156	7	è1	è1	PROPN
ejpam-5699	156	8	)	)	PUNCT
ejpam-5699	156	9	⋄	⋄	NOUN
ejpam-5699	157	1	0),n+	0),n+	NUM
ejpam-5699	157	2	b	b	X
ejpam-5699	157	3	(	(	PUNCT
ejpam-5699	157	4	è1	è1	PROPN
ejpam-5699	157	5	⋄	⋄	NOUN
ejpam-5699	157	6	0	0	NUM
ejpam-5699	157	7	)	)	PUNCT
ejpam-5699	157	8	}	}	PUNCT
ejpam-5699	157	9	⇒	⇒	NOUN
ejpam-5699	157	10	n+	n+	ADP
ejpam-5699	157	11	b	b	X
ejpam-5699	157	12	(	(	PUNCT
ejpam-5699	157	13	g1	g1	PROPN
ejpam-5699	157	14	)	)	PUNCT
ejpam-5699	157	15	≤	≤	NUM
ejpam-5699	157	16	max{n+	max{n+	PROPN
ejpam-5699	157	17	b	b	PROPN
ejpam-5699	157	18	(	(	PUNCT
ejpam-5699	157	19	g1	g1	PROPN
ejpam-5699	157	20	⋄	⋄	PROPN
ejpam-5699	157	21	è1),n+	è1),n+	PROPN
ejpam-5699	157	22	b	b	PROPN
ejpam-5699	157	23	(	(	PUNCT
ejpam-5699	157	24	è1	è1	NOUN
ejpam-5699	157	25	)	)	PUNCT
ejpam-5699	157	26	}	}	PUNCT
ejpam-5699	157	27	,	,	PUNCT
ejpam-5699	157	28	d.	d.	PROPN
ejpam-5699	157	29	ramesh	ramesh	PROPN
ejpam-5699	157	30	et	et	PROPN
ejpam-5699	157	31	al	al	PROPN
ejpam-5699	157	32	.	.	PUNCT
ejpam-5699	157	33	/	/	SYM
ejpam-5699	157	34	eur	eur	PROPN
ejpam-5699	157	35	.	.	PUNCT
ejpam-5699	158	1	j.	j.	PROPN
ejpam-5699	158	2	pure	pure	PROPN
ejpam-5699	158	3	appl	appl	PROPN
ejpam-5699	158	4	.	.	PROPN
ejpam-5699	158	5	math	math	PROPN
ejpam-5699	158	6	,	,	PUNCT
ejpam-5699	158	7	18	18	NUM
ejpam-5699	158	8	(	(	PUNCT
ejpam-5699	158	9	1	1	NUM
ejpam-5699	158	10	)	)	PUNCT
ejpam-5699	158	11	(	(	PUNCT
ejpam-5699	158	12	2025	2025	NUM
ejpam-5699	158	13	)	)	PUNCT
ejpam-5699	158	14	,	,	PUNCT
ejpam-5699	158	15	5699	5699	NUM
ejpam-5699	158	16	11	11	NUM
ejpam-5699	158	17	of	of	ADP
ejpam-5699	158	18	20	20	NUM
ejpam-5699	158	19	n−	n−	PROPN
ejpam-5699	158	20	b	b	X
ejpam-5699	158	21	(	(	PUNCT
ejpam-5699	158	22	g1	g1	VERB
ejpam-5699	158	23	⋄	⋄	PROPN
ejpam-5699	158	24	0	0	NUM
ejpam-5699	158	25	)	)	PUNCT
ejpam-5699	158	26	≥	≥	NOUN
ejpam-5699	158	27	min{n−	min{n−	PROPN
ejpam-5699	158	28	b	b	PROPN
ejpam-5699	158	29	(	(	PUNCT
ejpam-5699	158	30	(	(	PUNCT
ejpam-5699	158	31	g1	g1	PROPN
ejpam-5699	158	32	⋄	⋄	PROPN
ejpam-5699	158	33	è1	è1	PROPN
ejpam-5699	158	34	)	)	PUNCT
ejpam-5699	158	35	⋄	⋄	PROPN
ejpam-5699	159	1	0),n−	0),n−	PROPN
ejpam-5699	160	1	b	b	NOUN
ejpam-5699	161	1	(	(	PUNCT
ejpam-5699	161	2	è1	è1	ADJ
ejpam-5699	161	3	⋄	⋄	NOUN
ejpam-5699	161	4	0	0	NUM
ejpam-5699	161	5	)	)	PUNCT
ejpam-5699	161	6	}	}	PUNCT
ejpam-5699	161	7	⇒	⇒	VERB
ejpam-5699	161	8	n−(g1	n−(g1	NUM
ejpam-5699	161	9	)	)	PUNCT
ejpam-5699	161	10	≥	≥	PROPN
ejpam-5699	161	11	min{n−	min{n−	PROPN
ejpam-5699	161	12	b	b	PROPN
ejpam-5699	161	13	(	(	PUNCT
ejpam-5699	161	14	g1	g1	PROPN
ejpam-5699	161	15	⋄	⋄	PROPN
ejpam-5699	161	16	è1),n−	è1),n−	PROPN
ejpam-5699	161	17	b	b	PROPN
ejpam-5699	161	18	(	(	PUNCT
ejpam-5699	161	19	è1	è1	NOUN
ejpam-5699	161	20	)	)	PUNCT
ejpam-5699	161	21	}	}	PUNCT
ejpam-5699	161	22	,	,	PUNCT
ejpam-5699	161	23	for	for	ADP
ejpam-5699	161	24	all	all	DET
ejpam-5699	161	25	g1,è1	g1,è1	PROPN
ejpam-5699	161	26	,	,	PUNCT
ejpam-5699	161	27	11	11	NUM
ejpam-5699	161	28	∈	∈	NOUN
ejpam-5699	161	29	g.	g.	NOUN
ejpam-5699	161	30	this	this	PRON
ejpam-5699	161	31	shows	show	VERB
ejpam-5699	161	32	that	that	SCONJ
ejpam-5699	161	33	b	b	X
ejpam-5699	161	34	=	=	SYM
ejpam-5699	161	35	(	(	PUNCT
ejpam-5699	161	36	m+	m+	NUM
ejpam-5699	161	37	b	b	NOUN
ejpam-5699	161	38	,	,	PUNCT
ejpam-5699	161	39	m−	m−	PROPN
ejpam-5699	161	40	b	b	PROPN
ejpam-5699	161	41	,	,	PUNCT
ejpam-5699	161	42	n+	n+	NOUN
ejpam-5699	161	43	b	b	NOUN
ejpam-5699	161	44	,	,	PUNCT
ejpam-5699	161	45	n−	n−	PROPN
ejpam-5699	161	46	b	b	X
ejpam-5699	161	47	)	)	PUNCT
ejpam-5699	161	48	is	be	AUX
ejpam-5699	161	49	a	a	DET
ejpam-5699	161	50	bpvifpii	bpvifpii	NOUN
ejpam-5699	161	51	of	of	ADP
ejpam-5699	161	52	g.	g.	PROPN
ejpam-5699	161	53	the	the	DET
ejpam-5699	161	54	following	follow	VERB
ejpam-5699	161	55	example	example	NOUN
ejpam-5699	161	56	shows	show	VERB
ejpam-5699	161	57	that	that	SCONJ
ejpam-5699	161	58	the	the	DET
ejpam-5699	161	59	converse	converse	NOUN
ejpam-5699	161	60	of	of	ADP
ejpam-5699	161	61	theorem	theorem	NOUN
ejpam-5699	161	62	3	3	NUM
ejpam-5699	161	63	may	may	AUX
ejpam-5699	161	64	not	not	PART
ejpam-5699	161	65	be	be	AUX
ejpam-5699	161	66	true	true	ADJ
ejpam-5699	161	67	.	.	PUNCT
ejpam-5699	162	1	example	example	NOUN
ejpam-5699	163	1	3	3	X
ejpam-5699	163	2	.	.	PUNCT
ejpam-5699	163	3	let	let	VERB
ejpam-5699	163	4	g1	g1	PROPN
ejpam-5699	163	5	=	=	PRON
ejpam-5699	163	6	{	{	PUNCT
ejpam-5699	163	7	0	0	NUM
ejpam-5699	163	8	,	,	PUNCT
ejpam-5699	163	9	1	1	NUM
ejpam-5699	163	10	,	,	PUNCT
ejpam-5699	163	11	2	2	NUM
ejpam-5699	163	12	,	,	PUNCT
ejpam-5699	163	13	3	3	NUM
ejpam-5699	163	14	}	}	PUNCT
ejpam-5699	163	15	be	be	AUX
ejpam-5699	163	16	a	a	DET
ejpam-5699	163	17	set	set	NOUN
ejpam-5699	163	18	in	in	ADP
ejpam-5699	163	19	which	which	PRON
ejpam-5699	163	20	the	the	DET
ejpam-5699	163	21	binary	binary	PROPN
ejpam-5699	163	22	operation	operation	PROPN
ejpam-5699	163	23	⋄	⋄	PROPN
ejpam-5699	163	24	is	be	AUX
ejpam-5699	163	25	defined	define	VERB
ejpam-5699	163	26	as	as	ADP
ejpam-5699	163	27	given	give	VERB
ejpam-5699	163	28	below	below	ADP
ejpam-5699	163	29	0	0	NUM
ejpam-5699	163	30	⋄	⋄	PROPN
ejpam-5699	163	31	g1	g1	PROPN
ejpam-5699	163	32	=	=	SYM
ejpam-5699	163	33	0	0	NUM
ejpam-5699	163	34	∀g1	∀g1	PROPN
ejpam-5699	163	35	∈	∈	PROPN
ejpam-5699	163	36	g	g	PROPN
ejpam-5699	163	37	1	1	NUM
ejpam-5699	163	38	⋄	⋄	PROPN
ejpam-5699	163	39	g1	g1	NOUN
ejpam-5699	163	40	=	=	SYM
ejpam-5699	163	41	{	{	PUNCT
ejpam-5699	163	42	0	0	NUM
ejpam-5699	163	43	,	,	PUNCT
ejpam-5699	163	44	if	if	SCONJ
ejpam-5699	163	45	g1	g1	PROPN
ejpam-5699	163	46	∈	∈	PROPN
ejpam-5699	163	47	{	{	PUNCT
ejpam-5699	163	48	1	1	NUM
ejpam-5699	163	49	,	,	PUNCT
ejpam-5699	163	50	2	2	NUM
ejpam-5699	163	51	}	}	SYM
ejpam-5699	163	52	1	1	NUM
ejpam-5699	163	53	,	,	PUNCT
ejpam-5699	163	54	if	if	SCONJ
ejpam-5699	163	55	g1	g1	PROPN
ejpam-5699	163	56	∈	∈	PROPN
ejpam-5699	163	57	{	{	PUNCT
ejpam-5699	163	58	0	0	NUM
ejpam-5699	163	59	,	,	PUNCT
ejpam-5699	163	60	3	3	NUM
ejpam-5699	163	61	}	}	SYM
ejpam-5699	163	62	2	2	NUM
ejpam-5699	163	63	⋄	⋄	NOUN
ejpam-5699	163	64	g1	g1	NOUN
ejpam-5699	163	65	=	=	PUNCT
ejpam-5699	164	1			NOUN
ejpam-5699	164	2	0	0	NUM
ejpam-5699	164	3	,	,	PUNCT
ejpam-5699	164	4	if	if	SCONJ
ejpam-5699	164	5	g1	g1	NOUN
ejpam-5699	164	6	=	=	SYM
ejpam-5699	164	7	2	2	NUM
ejpam-5699	164	8	1	1	NUM
ejpam-5699	164	9	,	,	PUNCT
ejpam-5699	164	10	if	if	SCONJ
ejpam-5699	164	11	g1	g1	NOUN
ejpam-5699	164	12	=	=	SYM
ejpam-5699	164	13	1	1	NUM
ejpam-5699	164	14	2	2	NUM
ejpam-5699	164	15	,	,	PUNCT
ejpam-5699	164	16	if	if	SCONJ
ejpam-5699	164	17	g1	g1	PROPN
ejpam-5699	164	18	∈	∈	PROPN
ejpam-5699	164	19	{	{	PUNCT
ejpam-5699	164	20	0	0	NUM
ejpam-5699	164	21	,	,	PUNCT
ejpam-5699	164	22	3	3	NUM
ejpam-5699	164	23	}	}	SYM
ejpam-5699	164	24	3	3	NUM
ejpam-5699	164	25	⋄	⋄	PROPN
ejpam-5699	164	26	g1	g1	NOUN
ejpam-5699	164	27	=	=	SYM
ejpam-5699	164	28	{	{	PUNCT
ejpam-5699	164	29	0	0	NUM
ejpam-5699	164	30	,	,	PUNCT
ejpam-5699	164	31	if	if	SCONJ
ejpam-5699	164	32	g1	g1	NOUN
ejpam-5699	164	33	=	=	SYM
ejpam-5699	164	34	3	3	NUM
ejpam-5699	164	35	3	3	NUM
ejpam-5699	164	36	,	,	PUNCT
ejpam-5699	164	37	if	if	SCONJ
ejpam-5699	164	38	g1	g1	PROPN
ejpam-5699	164	39	∈	∈	PROPN
ejpam-5699	164	40	{	{	PUNCT
ejpam-5699	164	41	0	0	NUM
ejpam-5699	164	42	,	,	PUNCT
ejpam-5699	164	43	1	1	NUM
ejpam-5699	164	44	,	,	PUNCT
ejpam-5699	164	45	2	2	NUM
ejpam-5699	164	46	}	}	PUNCT
ejpam-5699	164	47	then	then	ADV
ejpam-5699	164	48	g	g	PROPN
ejpam-5699	164	49	is	be	AUX
ejpam-5699	164	50	a	a	DET
ejpam-5699	164	51	bck	bck	NOUN
ejpam-5699	164	52	-	-	PUNCT
ejpam-5699	164	53	a.	a.	NOUN
ejpam-5699	164	54	let	let	NOUN
ejpam-5699	164	55	b	b	NOUN
ejpam-5699	164	56	=	=	SYM
ejpam-5699	164	57	(	(	PUNCT
ejpam-5699	164	58	m+	m+	NUM
ejpam-5699	164	59	b	b	NOUN
ejpam-5699	164	60	,	,	PUNCT
ejpam-5699	164	61	m−	m−	PROPN
ejpam-5699	164	62	b	b	PROPN
ejpam-5699	164	63	,	,	PUNCT
ejpam-5699	164	64	n+	n+	NOUN
ejpam-5699	164	65	b	b	NOUN
ejpam-5699	164	66	,	,	PUNCT
ejpam-5699	164	67	n−	n−	PROPN
ejpam-5699	164	68	b	b	AUX
ejpam-5699	164	69	)	)	PUNCT
ejpam-5699	164	70	be	be	AUX
ejpam-5699	164	71	a	a	DET
ejpam-5699	164	72	bpvifs	bpvifs	PROPN
ejpam-5699	164	73	in	in	ADP
ejpam-5699	164	74	g	g	PROPN
ejpam-5699	164	75	defined	define	VERB
ejpam-5699	164	76	as	as	SCONJ
ejpam-5699	164	77	shown	show	VERB
ejpam-5699	164	78	in	in	ADP
ejpam-5699	164	79	table	table	NOUN
ejpam-5699	164	80	3	3	NUM
ejpam-5699	164	81	.	.	PUNCT
ejpam-5699	164	82	table	table	NOUN
ejpam-5699	164	83	3	3	NUM
ejpam-5699	164	84	:	:	PUNCT
ejpam-5699	164	85	bpvifi	bpvifi	NOUN
ejpam-5699	164	86	g1	g1	PROPN
ejpam-5699	164	87	m+	m+	VERB
ejpam-5699	164	88	b(g1	b(g1	NOUN
ejpam-5699	164	89	)	)	PUNCT
ejpam-5699	164	90	m−	m−	PROPN
ejpam-5699	164	91	b(g1	b(g1	NOUN
ejpam-5699	164	92	)	)	PUNCT
ejpam-5699	164	93	n+	n+	PROPN
ejpam-5699	165	1	b	b	X
ejpam-5699	165	2	(	(	PUNCT
ejpam-5699	165	3	g1	g1	PROPN
ejpam-5699	165	4	)	)	PUNCT
ejpam-5699	165	5	n−	n−	PROPN
ejpam-5699	165	6	b	b	X
ejpam-5699	165	7	(	(	PUNCT
ejpam-5699	165	8	g1	g1	PROPN
ejpam-5699	165	9	)	)	PUNCT
ejpam-5699	165	10	0	0	NUM
ejpam-5699	165	11	0.95	0.95	NUM
ejpam-5699	165	12	−0.87	−0.87	NUM
ejpam-5699	165	13	0.05	0.05	NUM
ejpam-5699	165	14	−0.13	−0.13	NOUN
ejpam-5699	165	15	1	1	NUM
ejpam-5699	165	16	0.73	0.73	NUM
ejpam-5699	165	17	−0.43	−0.43	NUM
ejpam-5699	165	18	0.27	0.27	NUM
ejpam-5699	165	19	−0.57	−0.57	CCONJ
ejpam-5699	165	20	2	2	NUM
ejpam-5699	165	21	0.73	0.73	NUM
ejpam-5699	165	22	−0.43	−0.43	NUM
ejpam-5699	165	23	0.27	0.27	NUM
ejpam-5699	165	24	−0.57	−0.57	NUM
ejpam-5699	165	25	3	3	NUM
ejpam-5699	165	26	0.33	0.33	NUM
ejpam-5699	165	27	−0.15	−0.15	NOUN
ejpam-5699	165	28	0.67	0.67	NUM
ejpam-5699	165	29	−0.85	−0.85	INTJ
ejpam-5699	165	30	it	it	PRON
ejpam-5699	165	31	is	be	AUX
ejpam-5699	165	32	easy	easy	ADJ
ejpam-5699	165	33	to	to	PART
ejpam-5699	165	34	check	check	VERB
ejpam-5699	165	35	that	that	DET
ejpam-5699	165	36	b	b	NOUN
ejpam-5699	165	37	=	=	SYM
ejpam-5699	165	38	(	(	PUNCT
ejpam-5699	165	39	m+	m+	NUM
ejpam-5699	165	40	b	b	NOUN
ejpam-5699	165	41	,	,	PUNCT
ejpam-5699	165	42	m−	m−	PROPN
ejpam-5699	165	43	b	b	PROPN
ejpam-5699	165	44	,	,	PUNCT
ejpam-5699	165	45	n+	n+	NOUN
ejpam-5699	165	46	b	b	NOUN
ejpam-5699	165	47	,	,	PUNCT
ejpam-5699	165	48	n−	n−	PROPN
ejpam-5699	165	49	b	b	X
ejpam-5699	165	50	)	)	PUNCT
ejpam-5699	165	51	is	be	AUX
ejpam-5699	165	52	a	a	DET
ejpam-5699	165	53	bpvifi	bpvifi	NOUN
ejpam-5699	165	54	of	of	ADP
ejpam-5699	165	55	g.	g.	PROPN
ejpam-5699	165	56	however	however	ADV
ejpam-5699	165	57	,	,	PUNCT
ejpam-5699	165	58	it	it	PRON
ejpam-5699	165	59	is	be	AUX
ejpam-5699	165	60	not	not	PART
ejpam-5699	165	61	a	a	DET
ejpam-5699	165	62	bpvifpii	bpvifpii	NOUN
ejpam-5699	165	63	of	of	ADP
ejpam-5699	165	64	g	g	NOUN
ejpam-5699	165	65	because	because	SCONJ
ejpam-5699	165	66	m+	m+	NUM
ejpam-5699	166	1	b(2	b(2	PROPN
ejpam-5699	166	2	⋄	⋄	NOUN
ejpam-5699	166	3	1	1	NUM
ejpam-5699	166	4	)	)	PUNCT
ejpam-5699	166	5	=	=	SYM
ejpam-5699	166	6	m+	m+	NUM
ejpam-5699	166	7	b(1	b(1	PROPN
ejpam-5699	166	8	)	)	PUNCT
ejpam-5699	166	9	=	=	PUNCT
ejpam-5699	167	1	0.73	0.73	NUM
ejpam-5699	167	2	<	<	NOUN
ejpam-5699	167	3	0.95	0.95	NUM
ejpam-5699	167	4	=	=	SYM
ejpam-5699	167	5	m+	m+	NUM
ejpam-5699	167	6	b(0	b(0	NOUN
ejpam-5699	167	7	)	)	PUNCT
ejpam-5699	167	8	=	=	PUNCT
ejpam-5699	167	9	min{m+	min{m+	PROPN
ejpam-5699	167	10	b((2	b((2	PROPN
ejpam-5699	167	11	⋄	⋄	PROPN
ejpam-5699	167	12	1	1	NUM
ejpam-5699	167	13	)	)	PUNCT
ejpam-5699	167	14	⋄	⋄	PROPN
ejpam-5699	167	15	1),m+	1),m+	PROPN
ejpam-5699	167	16	b(1	b(1	PROPN
ejpam-5699	167	17	⋄	⋄	PROPN
ejpam-5699	167	18	1	1	NUM
ejpam-5699	167	19	)	)	PUNCT
ejpam-5699	167	20	}	}	PUNCT
ejpam-5699	167	21	,	,	PUNCT
ejpam-5699	167	22	m−	m−	PROPN
ejpam-5699	167	23	b(2⋄1	b(2⋄1	PROPN
ejpam-5699	167	24	)	)	PUNCT
ejpam-5699	168	1	=	=	PROPN
ejpam-5699	168	2	m−	m−	PROPN
ejpam-5699	168	3	b(1	b(1	PROPN
ejpam-5699	168	4	)	)	PUNCT
ejpam-5699	168	5	=	=	PUNCT
ejpam-5699	169	1	−0.43	−0.43	X
ejpam-5699	169	2	>	>	X
ejpam-5699	169	3	−0.87	−0.87	PROPN
ejpam-5699	169	4	=	=	PUNCT
ejpam-5699	169	5	m−	m−	PROPN
ejpam-5699	169	6	b(0	b(0	PROPN
ejpam-5699	169	7	)	)	PUNCT
ejpam-5699	169	8	=	=	SYM
ejpam-5699	169	9	max{m−	max{m−	NOUN
ejpam-5699	169	10	b((2⋄1)⋄1),m−	b((2⋄1)⋄1),m−	PROPN
ejpam-5699	169	11	b(1⋄1	b(1⋄1	NOUN
ejpam-5699	169	12	)	)	PUNCT
ejpam-5699	169	13	}	}	PUNCT
ejpam-5699	169	14	,	,	PUNCT
ejpam-5699	169	15	n+	n+	ADP
ejpam-5699	169	16	b	b	X
ejpam-5699	169	17	(	(	PUNCT
ejpam-5699	169	18	2	2	NUM
ejpam-5699	169	19	⋄	⋄	NOUN
ejpam-5699	169	20	1	1	NUM
ejpam-5699	169	21	)	)	PUNCT
ejpam-5699	169	22	=	=	PUNCT
ejpam-5699	170	1	n+	n+	PUNCT
ejpam-5699	170	2	b	b	X
ejpam-5699	170	3	(	(	PUNCT
ejpam-5699	170	4	1	1	NUM
ejpam-5699	170	5	)	)	PUNCT
ejpam-5699	170	6	=	=	SYM
ejpam-5699	171	1	0.27	0.27	NUM
ejpam-5699	171	2	>	>	SYM
ejpam-5699	171	3	0.05	0.05	NUM
ejpam-5699	171	4	=	=	SYM
ejpam-5699	171	5	n+	n+	ADP
ejpam-5699	171	6	b	b	X
ejpam-5699	171	7	(	(	PUNCT
ejpam-5699	171	8	0	0	NUM
ejpam-5699	171	9	)	)	PUNCT
ejpam-5699	171	10	=	=	PUNCT
ejpam-5699	171	11	max{n+	max{n+	NOUN
ejpam-5699	171	12	b	b	X
ejpam-5699	171	13	(	(	PUNCT
ejpam-5699	171	14	(	(	PUNCT
ejpam-5699	171	15	2	2	NUM
ejpam-5699	171	16	⋄	⋄	NOUN
ejpam-5699	171	17	1	1	NUM
ejpam-5699	171	18	)	)	PUNCT
ejpam-5699	171	19	⋄	⋄	PROPN
ejpam-5699	171	20	1),n+	1),n+	NUM
ejpam-5699	171	21	b	b	PROPN
ejpam-5699	171	22	(	(	PUNCT
ejpam-5699	171	23	1	1	NUM
ejpam-5699	171	24	⋄	⋄	NOUN
ejpam-5699	171	25	1	1	NUM
ejpam-5699	171	26	)	)	PUNCT
ejpam-5699	171	27	}	}	PUNCT
ejpam-5699	171	28	,	,	PUNCT
ejpam-5699	171	29	n−	n−	PROPN
ejpam-5699	171	30	b	b	X
ejpam-5699	171	31	(	(	PUNCT
ejpam-5699	171	32	2	2	NUM
ejpam-5699	171	33	⋄	⋄	NOUN
ejpam-5699	171	34	1	1	NUM
ejpam-5699	171	35	)	)	PUNCT
ejpam-5699	171	36	=	=	PUNCT
ejpam-5699	171	37	n−	n−	NUM
ejpam-5699	171	38	b	b	X
ejpam-5699	171	39	(	(	PUNCT
ejpam-5699	171	40	1	1	NUM
ejpam-5699	171	41	)	)	PUNCT
ejpam-5699	171	42	=	=	PUNCT
ejpam-5699	172	1	−0.57	−0.57	PUNCT
ejpam-5699	172	2	<	<	X
ejpam-5699	173	1	−0.13	−0.13	X
ejpam-5699	173	2	=	=	PUNCT
ejpam-5699	173	3	n−	n−	PROPN
ejpam-5699	173	4	b	b	X
ejpam-5699	173	5	(	(	PUNCT
ejpam-5699	173	6	0	0	NUM
ejpam-5699	173	7	)	)	PUNCT
ejpam-5699	173	8	=	=	SYM
ejpam-5699	173	9	min{n−	min{n−	PROPN
ejpam-5699	173	10	b	b	PROPN
ejpam-5699	173	11	(	(	PUNCT
ejpam-5699	173	12	(	(	PUNCT
ejpam-5699	173	13	2	2	NUM
ejpam-5699	173	14	⋄	⋄	NOUN
ejpam-5699	173	15	1	1	NUM
ejpam-5699	173	16	)	)	PUNCT
ejpam-5699	173	17	⋄	⋄	PROPN
ejpam-5699	173	18	1),n−	1),n−	NUM
ejpam-5699	173	19	b	b	X
ejpam-5699	173	20	(	(	PUNCT
ejpam-5699	173	21	1	1	NUM
ejpam-5699	173	22	⋄	⋄	NOUN
ejpam-5699	173	23	1	1	NUM
ejpam-5699	173	24	)	)	PUNCT
ejpam-5699	173	25	}	}	PUNCT
ejpam-5699	173	26	.	.	PUNCT
ejpam-5699	174	1	corollary	corollary	ADJ
ejpam-5699	174	2	1	1	NUM
ejpam-5699	174	3	.	.	PUNCT
ejpam-5699	175	1	let	let	VERB
ejpam-5699	175	2	b	b	NOUN
ejpam-5699	175	3	=	=	SYM
ejpam-5699	175	4	(	(	PUNCT
ejpam-5699	175	5	m+	m+	NUM
ejpam-5699	175	6	b	b	NOUN
ejpam-5699	175	7	,	,	PUNCT
ejpam-5699	175	8	m−	m−	PROPN
ejpam-5699	175	9	b	b	PROPN
ejpam-5699	175	10	,	,	PUNCT
ejpam-5699	175	11	n+	n+	NOUN
ejpam-5699	175	12	b	b	NOUN
ejpam-5699	175	13	,	,	PUNCT
ejpam-5699	175	14	n−	n−	PROPN
ejpam-5699	175	15	b	b	AUX
ejpam-5699	175	16	)	)	PUNCT
ejpam-5699	175	17	be	be	AUX
ejpam-5699	175	18	a	a	DET
ejpam-5699	175	19	bpvifpii	bpvifpii	NOUN
ejpam-5699	175	20	of	of	ADP
ejpam-5699	175	21	g.	g.	PROPN
ejpam-5699	175	22	if	if	SCONJ
ejpam-5699	175	23	g1	g1	NOUN
ejpam-5699	175	24	≤	≤	PUNCT
ejpam-5699	175	25	è1	è1	NOUN
ejpam-5699	175	26	in	in	ADP
ejpam-5699	175	27	g	g	NOUN
ejpam-5699	175	28	,	,	PUNCT
ejpam-5699	175	29	then	then	ADV
ejpam-5699	176	1	m+	m+	PRON
ejpam-5699	176	2	b(g1	b(g1	NOUN
ejpam-5699	176	3	)	)	PUNCT
ejpam-5699	176	4	≥	≥	NOUN
ejpam-5699	176	5	m+	m+	NUM
ejpam-5699	176	6	b(è1	b(è1	NOUN
ejpam-5699	176	7	)	)	PUNCT
ejpam-5699	176	8	,	,	PUNCT
ejpam-5699	176	9	m−	m−	PROPN
ejpam-5699	176	10	b(g1	b(g1	NOUN
ejpam-5699	176	11	)	)	PUNCT
ejpam-5699	176	12	≤	≤	NOUN
ejpam-5699	176	13	m−	m−	PROPN
ejpam-5699	176	14	b(è1	b(è1	NOUN
ejpam-5699	176	15	)	)	PUNCT
ejpam-5699	176	16	,	,	PUNCT
ejpam-5699	176	17	n+	n+	ADP
ejpam-5699	176	18	b	b	X
ejpam-5699	176	19	(	(	PUNCT
ejpam-5699	176	20	g1	g1	PROPN
ejpam-5699	176	21	)	)	PUNCT
ejpam-5699	176	22	≤	≤	NUM
ejpam-5699	176	23	n+	n+	PUNCT
ejpam-5699	177	1	b	b	X
ejpam-5699	177	2	(	(	PUNCT
ejpam-5699	177	3	è1	è1	NOUN
ejpam-5699	177	4	)	)	PUNCT
ejpam-5699	177	5	,	,	PUNCT
ejpam-5699	177	6	and	and	CCONJ
ejpam-5699	177	7	n−	n−	PROPN
ejpam-5699	177	8	b	b	X
ejpam-5699	177	9	(	(	PUNCT
ejpam-5699	177	10	g1	g1	PROPN
ejpam-5699	177	11	)	)	PUNCT
ejpam-5699	177	12	≥	≥	NOUN
ejpam-5699	177	13	n−	n−	PROPN
ejpam-5699	177	14	b	b	PROPN
ejpam-5699	177	15	(	(	PUNCT
ejpam-5699	177	16	è1	è1	NOUN
ejpam-5699	177	17	)	)	PUNCT
ejpam-5699	177	18	.	.	PUNCT
ejpam-5699	178	1	i.e.	i.e.	X
ejpam-5699	178	2	,	,	PUNCT
ejpam-5699	178	3	m+	m+	NUM
ejpam-5699	178	4	b	b	NOUN
ejpam-5699	178	5	,	,	PUNCT
ejpam-5699	178	6	n−	n−	PROPN
ejpam-5699	178	7	b	b	NOUN
ejpam-5699	178	8	are	be	AUX
ejpam-5699	178	9	order	order	NOUN
ejpam-5699	178	10	-	-	PUNCT
ejpam-5699	178	11	reversing	reverse	VERB
ejpam-5699	178	12	and	and	CCONJ
ejpam-5699	178	13	m−	m−	PROPN
ejpam-5699	178	14	b	b	PROPN
ejpam-5699	178	15	,	,	PUNCT
ejpam-5699	178	16	n+	n+	PRON
ejpam-5699	178	17	b	b	NUM
ejpam-5699	178	18	are	be	AUX
ejpam-5699	178	19	order	order	NOUN
ejpam-5699	178	20	-	-	PUNCT
ejpam-5699	178	21	preserving	preserve	VERB
ejpam-5699	178	22	.	.	PUNCT
ejpam-5699	179	1	corollary	corollary	ADJ
ejpam-5699	179	2	2	2	NUM
ejpam-5699	179	3	.	.	PUNCT
ejpam-5699	180	1	in	in	ADP
ejpam-5699	180	2	g	g	NOUN
ejpam-5699	180	3	,	,	PUNCT
ejpam-5699	180	4	every	every	DET
ejpam-5699	180	5	bpvifpii	bpvifpii	NOUN
ejpam-5699	180	6	of	of	ADP
ejpam-5699	180	7	g	g	PROPN
ejpam-5699	180	8	is	be	AUX
ejpam-5699	180	9	a	a	DET
ejpam-5699	180	10	bpvifsa	bpvifsa	NOUN
ejpam-5699	180	11	.	.	PUNCT
ejpam-5699	181	1	d.	d.	PROPN
ejpam-5699	181	2	ramesh	ramesh	PROPN
ejpam-5699	181	3	et	et	PROPN
ejpam-5699	181	4	al	al	PROPN
ejpam-5699	181	5	.	.	PUNCT
ejpam-5699	181	6	/	/	SYM
ejpam-5699	181	7	eur	eur	PROPN
ejpam-5699	181	8	.	.	PUNCT
ejpam-5699	182	1	j.	j.	PROPN
ejpam-5699	182	2	pure	pure	PROPN
ejpam-5699	182	3	appl	appl	PROPN
ejpam-5699	182	4	.	.	PROPN
ejpam-5699	182	5	math	math	PROPN
ejpam-5699	182	6	,	,	PUNCT
ejpam-5699	182	7	18	18	NUM
ejpam-5699	182	8	(	(	PUNCT
ejpam-5699	182	9	1	1	NUM
ejpam-5699	182	10	)	)	PUNCT
ejpam-5699	182	11	(	(	PUNCT
ejpam-5699	182	12	2025	2025	NUM
ejpam-5699	182	13	)	)	PUNCT
ejpam-5699	182	14	,	,	PUNCT
ejpam-5699	182	15	5699	5699	NUM
ejpam-5699	182	16	12	12	NUM
ejpam-5699	182	17	of	of	ADP
ejpam-5699	182	18	20	20	NUM
ejpam-5699	182	19	theorem	theorem	ADJ
ejpam-5699	182	20	4	4	NUM
ejpam-5699	182	21	.	.	PUNCT
ejpam-5699	183	1	if	if	SCONJ
ejpam-5699	183	2	b	b	X
ejpam-5699	183	3	=	=	SYM
ejpam-5699	183	4	(	(	PUNCT
ejpam-5699	183	5	m+	m+	NUM
ejpam-5699	183	6	b	b	NOUN
ejpam-5699	183	7	,	,	PUNCT
ejpam-5699	183	8	m−	m−	PROPN
ejpam-5699	183	9	b	b	PROPN
ejpam-5699	183	10	,	,	PUNCT
ejpam-5699	183	11	n+	n+	NOUN
ejpam-5699	183	12	b	b	NOUN
ejpam-5699	183	13	,	,	PUNCT
ejpam-5699	183	14	n−	n−	PROPN
ejpam-5699	183	15	b	b	X
ejpam-5699	183	16	)	)	PUNCT
ejpam-5699	183	17	is	be	AUX
ejpam-5699	183	18	a	a	DET
ejpam-5699	183	19	bpvifpii	bpvifpii	NOUN
ejpam-5699	183	20	in	in	ADP
ejpam-5699	183	21	g	g	NOUN
ejpam-5699	183	22	,	,	PUNCT
ejpam-5699	183	23	and	and	CCONJ
ejpam-5699	183	24	j	j	PROPN
ejpam-5699	183	25	(	(	PUNCT
ejpam-5699	183	26	0	0	NUM
ejpam-5699	183	27	)	)	PUNCT
ejpam-5699	183	28	=	=	PRON
ejpam-5699	183	29	{	{	PUNCT
ejpam-5699	183	30	g1	g1	PROPN
ejpam-5699	183	31	∈	∈	PROPN
ejpam-5699	183	32	g|m+	g|m+	PUNCT
ejpam-5699	183	33	b(g1	b(g1	NOUN
ejpam-5699	183	34	)	)	PUNCT
ejpam-5699	184	1	=	=	SYM
ejpam-5699	184	2	m+	m+	NUM
ejpam-5699	184	3	b(0),m−	b(0),m−	NOUN
ejpam-5699	184	4	b(g1	b(g1	NOUN
ejpam-5699	184	5	)	)	PUNCT
ejpam-5699	185	1	=	=	SYM
ejpam-5699	185	2	m−	m−	PROPN
ejpam-5699	185	3	b(0),n+	b(0),n+	NUM
ejpam-5699	185	4	b	b	PROPN
ejpam-5699	185	5	(	(	PUNCT
ejpam-5699	185	6	g1	g1	PROPN
ejpam-5699	185	7	)	)	PUNCT
ejpam-5699	185	8	=	=	PUNCT
ejpam-5699	186	1	n+	n+	NUM
ejpam-5699	186	2	b	b	X
ejpam-5699	186	3	(	(	PUNCT
ejpam-5699	186	4	0),n−	0),n−	PROPN
ejpam-5699	186	5	b	b	X
ejpam-5699	186	6	(	(	PUNCT
ejpam-5699	186	7	g1)=	g1)=	X
ejpam-5699	186	8	n−(0	n−(0	NOUN
ejpam-5699	186	9	)	)	PUNCT
ejpam-5699	186	10	}	}	PUNCT
ejpam-5699	186	11	,	,	PUNCT
ejpam-5699	186	12	then	then	ADV
ejpam-5699	186	13	j	j	PROPN
ejpam-5699	186	14	(	(	PUNCT
ejpam-5699	186	15	0	0	NUM
ejpam-5699	186	16	)	)	PUNCT
ejpam-5699	186	17	is	be	AUX
ejpam-5699	186	18	a	a	DET
ejpam-5699	186	19	positive	positive	ADJ
ejpam-5699	186	20	implicative	implicative	ADJ
ejpam-5699	186	21	ideal	ideal	NOUN
ejpam-5699	186	22	of	of	ADP
ejpam-5699	186	23	g.	g.	PROPN
ejpam-5699	186	24	proof	proof	NOUN
ejpam-5699	186	25	.	.	PUNCT
ejpam-5699	187	1	let	let	VERB
ejpam-5699	187	2	g1,è1	g1,è1	PROPN
ejpam-5699	187	3	∈	∈	PROPN
ejpam-5699	187	4	g	g	NOUN
ejpam-5699	187	5	be	be	AUX
ejpam-5699	187	6	such	such	ADJ
ejpam-5699	187	7	that	that	PRON
ejpam-5699	187	8	(	(	PUNCT
ejpam-5699	187	9	g1⋄è1)⋄11,è1⋄11	g1⋄è1)⋄11,è1⋄11	PROPN
ejpam-5699	187	10	∈	∈	PROPN
ejpam-5699	187	11	j	j	PROPN
ejpam-5699	187	12	(	(	PUNCT
ejpam-5699	187	13	0	0	NUM
ejpam-5699	187	14	)	)	PUNCT
ejpam-5699	187	15	.	.	PUNCT
ejpam-5699	188	1	since	since	SCONJ
ejpam-5699	188	2	b	b	PROPN
ejpam-5699	188	3	=	=	SYM
ejpam-5699	188	4	(	(	PUNCT
ejpam-5699	188	5	g1,m+	g1,m+	NOUN
ejpam-5699	188	6	b	b	NOUN
ejpam-5699	188	7	,	,	PUNCT
ejpam-5699	188	8	m−	m−	PROPN
ejpam-5699	188	9	b	b	PROPN
ejpam-5699	188	10	,	,	PUNCT
ejpam-5699	188	11	n+	n+	ADP
ejpam-5699	188	12	b	b	NUM
ejpam-5699	188	13	,	,	PUNCT
ejpam-5699	188	14	n−	n−	PROPN
ejpam-5699	188	15	b	b	X
ejpam-5699	188	16	)	)	PUNCT
ejpam-5699	188	17	is	be	AUX
ejpam-5699	188	18	a	a	DET
ejpam-5699	188	19	bpvifpii	bpvifpii	NOUN
ejpam-5699	188	20	in	in	ADP
ejpam-5699	188	21	g	g	PROPN
ejpam-5699	188	22	,	,	PUNCT
ejpam-5699	188	23	we	we	PRON
ejpam-5699	188	24	have	have	VERB
ejpam-5699	188	25	m+	m+	NUM
ejpam-5699	188	26	b(g1⋄11	b(g1⋄11	NOUN
ejpam-5699	188	27	)	)	PUNCT
ejpam-5699	189	1	≥	≥	NOUN
ejpam-5699	189	2	min{m+	min{m+	PROPN
ejpam-5699	189	3	b((g1⋄è1)⋄11),m+	b((g1⋄è1)⋄11),m+	PUNCT
ejpam-5699	189	4	b(è1⋄11	b(è1⋄11	NOUN
ejpam-5699	189	5	)	)	PUNCT
ejpam-5699	189	6	}	}	PUNCT
ejpam-5699	189	7	=	=	PUNCT
ejpam-5699	189	8	min{m+	min{m+	PROPN
ejpam-5699	189	9	b(0),m+	b(0),m+	NUM
ejpam-5699	189	10	b(0	b(0	NOUN
ejpam-5699	189	11	)	)	PUNCT
ejpam-5699	189	12	}	}	PUNCT
ejpam-5699	189	13	=	=	SYM
ejpam-5699	189	14	m+	m+	NUM
ejpam-5699	189	15	b(0	b(0	NOUN
ejpam-5699	189	16	)	)	PUNCT
ejpam-5699	189	17	,	,	PUNCT
ejpam-5699	189	18	m−	m−	PROPN
ejpam-5699	189	19	b(g1	b(g1	ADJ
ejpam-5699	189	20	⋄	⋄	PROPN
ejpam-5699	189	21	11	11	NUM
ejpam-5699	189	22	)	)	PUNCT
ejpam-5699	189	23	≤	≤	NOUN
ejpam-5699	189	24	max{m−	max{m−	NOUN
ejpam-5699	189	25	b((g1	b((g1	NOUN
ejpam-5699	189	26	⋄	⋄	PROPN
ejpam-5699	189	27	è1	è1	PROPN
ejpam-5699	189	28	)	)	PUNCT
ejpam-5699	189	29	⋄	⋄	NOUN
ejpam-5699	189	30	11),m−	11),m−	NUM
ejpam-5699	189	31	b(è1	b(è1	NOUN
ejpam-5699	189	32	⋄	⋄	PROPN
ejpam-5699	189	33	11	11	NUM
ejpam-5699	189	34	)	)	PUNCT
ejpam-5699	189	35	}	}	PUNCT
ejpam-5699	189	36	=	=	SYM
ejpam-5699	189	37	max{m−	max{m−	NOUN
ejpam-5699	189	38	b(0),m−	b(0),m−	ADJ
ejpam-5699	189	39	b(0	b(0	NOUN
ejpam-5699	189	40	)	)	PUNCT
ejpam-5699	189	41	}	}	PUNCT
ejpam-5699	189	42	=	=	SYM
ejpam-5699	189	43	m−	m−	PROPN
ejpam-5699	189	44	b(0	b(0	PROPN
ejpam-5699	189	45	)	)	PUNCT
ejpam-5699	189	46	,	,	PUNCT
ejpam-5699	189	47	n+	n+	ADP
ejpam-5699	189	48	b	b	X
ejpam-5699	189	49	(	(	PUNCT
ejpam-5699	189	50	g1	g1	VERB
ejpam-5699	189	51	⋄	⋄	PROPN
ejpam-5699	189	52	11	11	NUM
ejpam-5699	189	53	)	)	PUNCT
ejpam-5699	189	54	≤	≤	NUM
ejpam-5699	189	55	max{n+	max{n+	PROPN
ejpam-5699	189	56	b	b	PROPN
ejpam-5699	189	57	(	(	PUNCT
ejpam-5699	189	58	(	(	PUNCT
ejpam-5699	189	59	g1	g1	PROPN
ejpam-5699	189	60	⋄	⋄	PROPN
ejpam-5699	189	61	è1	è1	PROPN
ejpam-5699	189	62	)	)	PUNCT
ejpam-5699	189	63	⋄	⋄	PROPN
ejpam-5699	190	1	11),n+	11),n+	NUM
ejpam-5699	190	2	b	b	PROPN
ejpam-5699	190	3	(	(	PUNCT
ejpam-5699	190	4	è1	è1	ADJ
ejpam-5699	190	5	⋄	⋄	PROPN
ejpam-5699	190	6	11	11	NUM
ejpam-5699	190	7	)	)	PUNCT
ejpam-5699	190	8	}	}	PUNCT
ejpam-5699	190	9	=	=	PUNCT
ejpam-5699	190	10	max{n+	max{n+	NOUN
ejpam-5699	190	11	b	b	X
ejpam-5699	190	12	(	(	PUNCT
ejpam-5699	190	13	0),n+	0),n+	PROPN
ejpam-5699	190	14	b	b	PROPN
ejpam-5699	190	15	(	(	PUNCT
ejpam-5699	190	16	0	0	NUM
ejpam-5699	190	17	)	)	PUNCT
ejpam-5699	190	18	}	}	PUNCT
ejpam-5699	190	19	=	=	PUNCT
ejpam-5699	190	20	n+	n+	PUNCT
ejpam-5699	190	21	b	b	X
ejpam-5699	190	22	(	(	PUNCT
ejpam-5699	190	23	0	0	NUM
ejpam-5699	190	24	)	)	PUNCT
ejpam-5699	190	25	,	,	PUNCT
ejpam-5699	190	26	n−	n−	PROPN
ejpam-5699	190	27	b	b	X
ejpam-5699	190	28	(	(	PUNCT
ejpam-5699	190	29	g1	g1	VERB
ejpam-5699	190	30	⋄	⋄	PROPN
ejpam-5699	190	31	11	11	NUM
ejpam-5699	190	32	)	)	PUNCT
ejpam-5699	190	33	≥	≥	NOUN
ejpam-5699	190	34	min{n−	min{n−	PROPN
ejpam-5699	190	35	b	b	PROPN
ejpam-5699	190	36	(	(	PUNCT
ejpam-5699	190	37	(	(	PUNCT
ejpam-5699	190	38	g1	g1	PROPN
ejpam-5699	190	39	⋄	⋄	PROPN
ejpam-5699	190	40	è1	è1	PROPN
ejpam-5699	190	41	)	)	PUNCT
ejpam-5699	190	42	⋄	⋄	PROPN
ejpam-5699	190	43	11),n−	11),n−	NUM
ejpam-5699	190	44	b	b	PROPN
ejpam-5699	190	45	(	(	PUNCT
ejpam-5699	190	46	è1	è1	ADJ
ejpam-5699	190	47	⋄	⋄	PROPN
ejpam-5699	190	48	11	11	NUM
ejpam-5699	190	49	)	)	PUNCT
ejpam-5699	190	50	}	}	PUNCT
ejpam-5699	190	51	=	=	SYM
ejpam-5699	190	52	min{n−	min{n−	PROPN
ejpam-5699	190	53	b	b	PROPN
ejpam-5699	190	54	(	(	PUNCT
ejpam-5699	190	55	0),n−	0),n−	PROPN
ejpam-5699	190	56	b	b	X
ejpam-5699	190	57	(	(	PUNCT
ejpam-5699	190	58	0	0	NUM
ejpam-5699	190	59	)	)	PUNCT
ejpam-5699	190	60	}	}	PUNCT
ejpam-5699	190	61	=	=	PUNCT
ejpam-5699	190	62	n−	n−	NUM
ejpam-5699	190	63	b	b	X
ejpam-5699	190	64	(	(	PUNCT
ejpam-5699	190	65	0	0	NUM
ejpam-5699	190	66	)	)	PUNCT
ejpam-5699	190	67	.	.	PUNCT
ejpam-5699	191	1	on	on	ADP
ejpam-5699	191	2	the	the	DET
ejpam-5699	191	3	other	other	ADJ
ejpam-5699	191	4	hand	hand	NOUN
ejpam-5699	191	5	,	,	PUNCT
ejpam-5699	191	6	we	we	PRON
ejpam-5699	191	7	know	know	VERB
ejpam-5699	191	8	from	from	ADP
ejpam-5699	191	9	(	(	PUNCT
ejpam-5699	191	10	bpvifpii-1	bpvifpii-1	X
ejpam-5699	191	11	)	)	PUNCT
ejpam-5699	191	12	that	that	SCONJ
ejpam-5699	191	13	m+	m+	NUM
ejpam-5699	191	14	b(0	b(0	NOUN
ejpam-5699	191	15	)	)	PUNCT
ejpam-5699	191	16	≥	≥	NOUN
ejpam-5699	191	17	m+	m+	NUM
ejpam-5699	191	18	b(g1	b(g1	NOUN
ejpam-5699	191	19	)	)	PUNCT
ejpam-5699	191	20	,	,	PUNCT
ejpam-5699	191	21	m−	m−	PROPN
ejpam-5699	191	22	b(0	b(0	PROPN
ejpam-5699	191	23	)	)	PUNCT
ejpam-5699	191	24	≤	≤	NOUN
ejpam-5699	191	25	m−	m−	PROPN
ejpam-5699	191	26	b(g1	b(g1	NOUN
ejpam-5699	191	27	)	)	PUNCT
ejpam-5699	191	28	,	,	PUNCT
ejpam-5699	191	29	n+	n+	ADP
ejpam-5699	191	30	b	b	X
ejpam-5699	191	31	(	(	PUNCT
ejpam-5699	191	32	0	0	NUM
ejpam-5699	191	33	)	)	PUNCT
ejpam-5699	191	34	≤	≤	NUM
ejpam-5699	191	35	n+	n+	PUNCT
ejpam-5699	192	1	b	b	X
ejpam-5699	192	2	(	(	PUNCT
ejpam-5699	192	3	g1	g1	PROPN
ejpam-5699	192	4	)	)	PUNCT
ejpam-5699	192	5	,	,	PUNCT
ejpam-5699	192	6	and	and	CCONJ
ejpam-5699	192	7	n−	n−	PROPN
ejpam-5699	192	8	b	b	X
ejpam-5699	192	9	(	(	PUNCT
ejpam-5699	192	10	0	0	NUM
ejpam-5699	192	11	)	)	PUNCT
ejpam-5699	192	12	≥	≥	NOUN
ejpam-5699	192	13	n−	n−	PROPN
ejpam-5699	192	14	b	b	X
ejpam-5699	192	15	(	(	PUNCT
ejpam-5699	192	16	g1	g1	PROPN
ejpam-5699	192	17	)	)	PUNCT
ejpam-5699	192	18	for	for	ADP
ejpam-5699	192	19	all	all	DET
ejpam-5699	192	20	g1	g1	PROPN
ejpam-5699	192	21	∈	∈	PROPN
ejpam-5699	192	22	g.	g.	NOUN
ejpam-5699	192	23	thus	thus	ADV
ejpam-5699	192	24	,	,	PUNCT
ejpam-5699	192	25	m+	m+	NOUN
ejpam-5699	192	26	b(g1	b(g1	ADJ
ejpam-5699	192	27	⋄	⋄	PROPN
ejpam-5699	192	28	11	11	NUM
ejpam-5699	192	29	)	)	PUNCT
ejpam-5699	192	30	=	=	SYM
ejpam-5699	192	31	m+	m+	NUM
ejpam-5699	192	32	b(0	b(0	NOUN
ejpam-5699	192	33	)	)	PUNCT
ejpam-5699	192	34	,	,	PUNCT
ejpam-5699	192	35	m−	m−	PROPN
ejpam-5699	192	36	b(g1	b(g1	ADJ
ejpam-5699	192	37	⋄	⋄	PROPN
ejpam-5699	192	38	11	11	NUM
ejpam-5699	192	39	)	)	PUNCT
ejpam-5699	193	1	=	=	SYM
ejpam-5699	194	1	m−	m−	PROPN
ejpam-5699	194	2	b(0),n+	b(0),n+	NUM
ejpam-5699	194	3	b	b	X
ejpam-5699	194	4	(	(	PUNCT
ejpam-5699	194	5	g1	g1	VERB
ejpam-5699	194	6	⋄	⋄	PROPN
ejpam-5699	194	7	11	11	NUM
ejpam-5699	194	8	)	)	PUNCT
ejpam-5699	194	9	=	=	PUNCT
ejpam-5699	195	1	n+	n+	PUNCT
ejpam-5699	195	2	b	b	X
ejpam-5699	195	3	(	(	PUNCT
ejpam-5699	195	4	0	0	NUM
ejpam-5699	195	5	)	)	PUNCT
ejpam-5699	195	6	,	,	PUNCT
ejpam-5699	195	7	and	and	CCONJ
ejpam-5699	195	8	n−	n−	PROPN
ejpam-5699	195	9	b	b	X
ejpam-5699	195	10	(	(	PUNCT
ejpam-5699	195	11	g1	g1	VERB
ejpam-5699	195	12	⋄	⋄	PROPN
ejpam-5699	195	13	11	11	NUM
ejpam-5699	195	14	)	)	PUNCT
ejpam-5699	196	1	=	=	PUNCT
ejpam-5699	196	2	n−	n−	NUM
ejpam-5699	196	3	b	b	X
ejpam-5699	196	4	(	(	PUNCT
ejpam-5699	196	5	0	0	NUM
ejpam-5699	196	6	)	)	PUNCT
ejpam-5699	196	7	.	.	PUNCT
ejpam-5699	197	1	this	this	PRON
ejpam-5699	197	2	implies	imply	VERB
ejpam-5699	197	3	g1	g1	PROPN
ejpam-5699	197	4	⋄	⋄	PROPN
ejpam-5699	197	5	11	11	NUM
ejpam-5699	197	6	∈	∈	PROPN
ejpam-5699	197	7	j	j	X
ejpam-5699	197	8	(	(	PUNCT
ejpam-5699	197	9	0	0	NUM
ejpam-5699	197	10	)	)	PUNCT
ejpam-5699	197	11	.	.	PUNCT
ejpam-5699	198	1	obviously	obviously	ADV
ejpam-5699	198	2	,	,	PUNCT
ejpam-5699	198	3	0	0	NUM
ejpam-5699	198	4	∈	∈	PROPN
ejpam-5699	198	5	j	j	PROPN
ejpam-5699	198	6	(	(	PUNCT
ejpam-5699	198	7	0	0	NUM
ejpam-5699	198	8	)	)	PUNCT
ejpam-5699	198	9	.	.	PUNCT
ejpam-5699	199	1	therefore	therefore	ADV
ejpam-5699	199	2	,	,	PUNCT
ejpam-5699	199	3	j	j	PROPN
ejpam-5699	199	4	(	(	PUNCT
ejpam-5699	199	5	0	0	NUM
ejpam-5699	199	6	)	)	PUNCT
ejpam-5699	199	7	is	be	AUX
ejpam-5699	199	8	a	a	DET
ejpam-5699	199	9	positive	positive	ADJ
ejpam-5699	199	10	implicative	implicative	ADJ
ejpam-5699	199	11	ideal	ideal	NOUN
ejpam-5699	199	12	of	of	ADP
ejpam-5699	199	13	g.	g.	PROPN
ejpam-5699	199	14	theorem	theorem	VERB
ejpam-5699	199	15	5	5	NUM
ejpam-5699	199	16	.	.	PUNCT
ejpam-5699	199	17	in	in	ADP
ejpam-5699	199	18	a	a	DET
ejpam-5699	199	19	positive	positive	ADJ
ejpam-5699	199	20	implicative	implicative	ADJ
ejpam-5699	199	21	bck	bck	NOUN
ejpam-5699	199	22	-	-	PUNCT
ejpam-5699	199	23	a	a	NOUN
ejpam-5699	199	24	g	g	NOUN
ejpam-5699	199	25	,	,	PUNCT
ejpam-5699	199	26	every	every	DET
ejpam-5699	199	27	bpvifi	bpvifi	NOUN
ejpam-5699	199	28	of	of	ADP
ejpam-5699	199	29	g	g	PROPN
ejpam-5699	199	30	is	be	AUX
ejpam-5699	199	31	a	a	DET
ejpam-5699	199	32	bpvifpii	bpvifpii	NOUN
ejpam-5699	199	33	of	of	ADP
ejpam-5699	199	34	g.	g.	PROPN
ejpam-5699	199	35	proof	proof	NOUN
ejpam-5699	199	36	.	.	PUNCT
ejpam-5699	200	1	let	let	VERB
ejpam-5699	200	2	g	g	PRON
ejpam-5699	200	3	be	be	AUX
ejpam-5699	200	4	a	a	DET
ejpam-5699	200	5	positive	positive	ADJ
ejpam-5699	200	6	implicative	implicative	ADJ
ejpam-5699	200	7	bck	bck	NOUN
ejpam-5699	200	8	-	-	PUNCT
ejpam-5699	200	9	a	a	NOUN
ejpam-5699	200	10	,	,	PUNCT
ejpam-5699	200	11	and	and	CCONJ
ejpam-5699	200	12	b	b	X
ejpam-5699	200	13	=	=	SYM
ejpam-5699	200	14	(	(	PUNCT
ejpam-5699	200	15	m+	m+	NUM
ejpam-5699	200	16	b	b	NOUN
ejpam-5699	200	17	,	,	PUNCT
ejpam-5699	200	18	m−	m−	PROPN
ejpam-5699	200	19	b	b	PROPN
ejpam-5699	200	20	,	,	PUNCT
ejpam-5699	200	21	n+	n+	NOUN
ejpam-5699	200	22	b	b	NOUN
ejpam-5699	200	23	,	,	PUNCT
ejpam-5699	200	24	n−	n−	PROPN
ejpam-5699	200	25	b	b	AUX
ejpam-5699	200	26	)	)	PUNCT
ejpam-5699	200	27	be	be	AUX
ejpam-5699	200	28	a	a	DET
ejpam-5699	200	29	bpvifi	bpvifi	NOUN
ejpam-5699	200	30	of	of	ADP
ejpam-5699	200	31	g.	g.	PROPN
ejpam-5699	200	32	if	if	SCONJ
ejpam-5699	200	33	we	we	PRON
ejpam-5699	200	34	replace	replace	VERB
ejpam-5699	200	35	g1	g1	NOUN
ejpam-5699	200	36	with	with	ADP
ejpam-5699	200	37	g1	g1	PROPN
ejpam-5699	200	38	⋄	⋄	PROPN
ejpam-5699	200	39	11	11	NUM
ejpam-5699	200	40	and	and	CCONJ
ejpam-5699	200	41	è1	è1	ADJ
ejpam-5699	200	42	with	with	ADP
ejpam-5699	200	43	è1	è1	ADJ
ejpam-5699	200	44	⋄	⋄	PROPN
ejpam-5699	200	45	11	11	NUM
ejpam-5699	200	46	in	in	ADP
ejpam-5699	200	47	bpvifi-2	bpvifi-2	PROPN
ejpam-5699	200	48	,	,	PUNCT
ejpam-5699	200	49	3	3	NUM
ejpam-5699	200	50	,	,	PUNCT
ejpam-5699	200	51	4	4	NUM
ejpam-5699	200	52	,	,	PUNCT
ejpam-5699	200	53	5	5	NUM
ejpam-5699	200	54	,	,	PUNCT
ejpam-5699	200	55	then	then	ADV
ejpam-5699	200	56	m+	m+	NUM
ejpam-5699	200	57	b(g1	b(g1	ADJ
ejpam-5699	200	58	⋄	⋄	PROPN
ejpam-5699	200	59	11	11	NUM
ejpam-5699	200	60	)	)	PUNCT
ejpam-5699	201	1	≥	≥	NOUN
ejpam-5699	201	2	min{m+	min{m+	PROPN
ejpam-5699	201	3	b((g1	b((g1	PROPN
ejpam-5699	201	4	⋄	⋄	PROPN
ejpam-5699	201	5	11	11	NUM
ejpam-5699	201	6	)	)	PUNCT
ejpam-5699	201	7	⋄	⋄	NOUN
ejpam-5699	201	8	(	(	PUNCT
ejpam-5699	201	9	è1	è1	PROPN
ejpam-5699	201	10	⋄	⋄	PROPN
ejpam-5699	201	11	11)),m+	11)),m+	NUM
ejpam-5699	201	12	b(è1	b(è1	NOUN
ejpam-5699	201	13	⋄	⋄	PROPN
ejpam-5699	201	14	11	11	NUM
ejpam-5699	201	15	)	)	PUNCT
ejpam-5699	201	16	}	}	PUNCT
ejpam-5699	201	17	=	=	SYM
ejpam-5699	201	18	min{m+	min{m+	PROPN
ejpam-5699	201	19	b((g1	b((g1	PROPN
ejpam-5699	201	20	⋄	⋄	PROPN
ejpam-5699	201	21	è1	è1	PROPN
ejpam-5699	201	22	)	)	PUNCT
ejpam-5699	201	23	⋄	⋄	PROPN
ejpam-5699	201	24	11),m+	11),m+	NUM
ejpam-5699	201	25	b(è1	b(è1	NOUN
ejpam-5699	201	26	⋄	⋄	PROPN
ejpam-5699	201	27	11	11	NUM
ejpam-5699	201	28	)	)	PUNCT
ejpam-5699	201	29	}	}	PUNCT
ejpam-5699	201	30	,	,	PUNCT
ejpam-5699	201	31	m−	m−	PROPN
ejpam-5699	201	32	b(g1	b(g1	ADJ
ejpam-5699	201	33	⋄	⋄	PROPN
ejpam-5699	201	34	11	11	NUM
ejpam-5699	201	35	)	)	PUNCT
ejpam-5699	201	36	≤	≤	NOUN
ejpam-5699	201	37	max{m−	max{m−	NOUN
ejpam-5699	201	38	b((g1	b((g1	NOUN
ejpam-5699	201	39	⋄	⋄	NOUN
ejpam-5699	201	40	11	11	NUM
ejpam-5699	201	41	)	)	PUNCT
ejpam-5699	201	42	⋄	⋄	NOUN
ejpam-5699	201	43	(	(	PUNCT
ejpam-5699	201	44	è1	è1	ADP
ejpam-5699	201	45	⋄	⋄	PROPN
ejpam-5699	201	46	11)),m−	11)),m−	NUM
ejpam-5699	201	47	b(è1	b(è1	NOUN
ejpam-5699	201	48	⋄	⋄	PROPN
ejpam-5699	201	49	11	11	NUM
ejpam-5699	201	50	)	)	PUNCT
ejpam-5699	201	51	}	}	PUNCT
ejpam-5699	201	52	=	=	SYM
ejpam-5699	201	53	max{m−	max{m−	NOUN
ejpam-5699	201	54	b((g1	b((g1	NOUN
ejpam-5699	201	55	⋄	⋄	PROPN
ejpam-5699	201	56	è1	è1	PROPN
ejpam-5699	201	57	)	)	PUNCT
ejpam-5699	201	58	⋄	⋄	NOUN
ejpam-5699	201	59	11),m−	11),m−	NUM
ejpam-5699	201	60	b(è1	b(è1	NOUN
ejpam-5699	201	61	⋄	⋄	PROPN
ejpam-5699	201	62	11	11	NUM
ejpam-5699	201	63	)	)	PUNCT
ejpam-5699	201	64	}	}	PUNCT
ejpam-5699	201	65	,	,	PUNCT
ejpam-5699	201	66	n+	n+	ADP
ejpam-5699	201	67	b	b	X
ejpam-5699	201	68	(	(	PUNCT
ejpam-5699	201	69	g1	g1	VERB
ejpam-5699	201	70	⋄	⋄	PROPN
ejpam-5699	201	71	11	11	NUM
ejpam-5699	201	72	)	)	PUNCT
ejpam-5699	201	73	≤	≤	NUM
ejpam-5699	201	74	max{n+	max{n+	PROPN
ejpam-5699	201	75	b	b	PROPN
ejpam-5699	201	76	(	(	PUNCT
ejpam-5699	201	77	(	(	PUNCT
ejpam-5699	201	78	g1	g1	VERB
ejpam-5699	201	79	⋄	⋄	PROPN
ejpam-5699	201	80	11	11	NUM
ejpam-5699	201	81	)	)	PUNCT
ejpam-5699	201	82	⋄	⋄	NOUN
ejpam-5699	201	83	(	(	PUNCT
ejpam-5699	201	84	è1	è1	NOUN
ejpam-5699	201	85	⋄	⋄	NOUN
ejpam-5699	201	86	11)),n+	11)),n+	NUM
ejpam-5699	201	87	b	b	NOUN
ejpam-5699	201	88	(	(	PUNCT
ejpam-5699	201	89	è1	è1	ADJ
ejpam-5699	201	90	⋄	⋄	PROPN
ejpam-5699	201	91	11	11	NUM
ejpam-5699	201	92	)	)	PUNCT
ejpam-5699	201	93	}	}	PUNCT
ejpam-5699	201	94	=	=	PUNCT
ejpam-5699	201	95	max{n+	max{n+	NOUN
ejpam-5699	201	96	b	b	X
ejpam-5699	201	97	(	(	PUNCT
ejpam-5699	201	98	(	(	PUNCT
ejpam-5699	201	99	g1	g1	PROPN
ejpam-5699	201	100	⋄	⋄	PROPN
ejpam-5699	201	101	è1	è1	PROPN
ejpam-5699	201	102	)	)	PUNCT
ejpam-5699	201	103	⋄	⋄	PROPN
ejpam-5699	202	1	11),n+	11),n+	NUM
ejpam-5699	202	2	b	b	PROPN
ejpam-5699	202	3	(	(	PUNCT
ejpam-5699	202	4	è1	è1	ADJ
ejpam-5699	202	5	⋄	⋄	NOUN
ejpam-5699	202	6	11	11	NUM
ejpam-5699	202	7	)	)	PUNCT
ejpam-5699	202	8	}	}	PUNCT
ejpam-5699	202	9	,	,	PUNCT
ejpam-5699	202	10	n−	n−	PROPN
ejpam-5699	202	11	b	b	X
ejpam-5699	202	12	(	(	PUNCT
ejpam-5699	202	13	g1	g1	VERB
ejpam-5699	202	14	⋄	⋄	PROPN
ejpam-5699	202	15	11	11	NUM
ejpam-5699	202	16	)	)	PUNCT
ejpam-5699	202	17	≥	≥	NOUN
ejpam-5699	202	18	min{n−	min{n−	PROPN
ejpam-5699	202	19	b	b	PROPN
ejpam-5699	202	20	(	(	PUNCT
ejpam-5699	202	21	(	(	PUNCT
ejpam-5699	202	22	g1	g1	VERB
ejpam-5699	202	23	⋄	⋄	PROPN
ejpam-5699	202	24	11	11	NUM
ejpam-5699	202	25	)	)	PUNCT
ejpam-5699	202	26	⋄	⋄	NOUN
ejpam-5699	202	27	(	(	PUNCT
ejpam-5699	202	28	è1	è1	ADP
ejpam-5699	202	29	⋄	⋄	PROPN
ejpam-5699	202	30	11)),n−	11)),n−	NUM
ejpam-5699	202	31	b	b	NOUN
ejpam-5699	202	32	(	(	PUNCT
ejpam-5699	202	33	è1	è1	ADJ
ejpam-5699	202	34	⋄	⋄	PROPN
ejpam-5699	202	35	11	11	NUM
ejpam-5699	202	36	)	)	PUNCT
ejpam-5699	202	37	}	}	PUNCT
ejpam-5699	202	38	=	=	SYM
ejpam-5699	202	39	min{n−	min{n−	PROPN
ejpam-5699	202	40	b	b	PROPN
ejpam-5699	202	41	(	(	PUNCT
ejpam-5699	202	42	(	(	PUNCT
ejpam-5699	202	43	g1	g1	PROPN
ejpam-5699	202	44	⋄	⋄	PROPN
ejpam-5699	202	45	è1	è1	PROPN
ejpam-5699	202	46	)	)	PUNCT
ejpam-5699	202	47	⋄	⋄	PROPN
ejpam-5699	202	48	11),n−	11),n−	NUM
ejpam-5699	202	49	b	b	PROPN
ejpam-5699	202	50	(	(	PUNCT
ejpam-5699	202	51	è1	è1	ADJ
ejpam-5699	202	52	⋄	⋄	NOUN
ejpam-5699	202	53	11	11	NUM
ejpam-5699	202	54	)	)	PUNCT
ejpam-5699	202	55	}	}	PUNCT
ejpam-5699	202	56	,	,	PUNCT
ejpam-5699	202	57	for	for	ADP
ejpam-5699	202	58	all	all	DET
ejpam-5699	202	59	g1,è1	g1,è1	PROPN
ejpam-5699	202	60	,	,	PUNCT
ejpam-5699	202	61	11	11	NUM
ejpam-5699	202	62	∈	∈	NOUN
ejpam-5699	202	63	g.	g.	NOUN
ejpam-5699	202	64	obviously	obviously	ADV
ejpam-5699	202	65	,	,	PUNCT
ejpam-5699	202	66	m+	m+	NUM
ejpam-5699	202	67	b(0	b(0	NOUN
ejpam-5699	202	68	)	)	PUNCT
ejpam-5699	202	69	≥	≥	NOUN
ejpam-5699	202	70	m+	m+	NUM
ejpam-5699	202	71	b(g1	b(g1	NOUN
ejpam-5699	202	72	)	)	PUNCT
ejpam-5699	202	73	,	,	PUNCT
ejpam-5699	202	74	m−	m−	PROPN
ejpam-5699	202	75	b(0	b(0	PROPN
ejpam-5699	202	76	)	)	PUNCT
ejpam-5699	202	77	≤	≤	NOUN
ejpam-5699	202	78	m−	m−	PROPN
ejpam-5699	202	79	b(g1	b(g1	NOUN
ejpam-5699	202	80	)	)	PUNCT
ejpam-5699	202	81	,	,	PUNCT
ejpam-5699	202	82	n+	n+	ADP
ejpam-5699	202	83	b	b	X
ejpam-5699	202	84	(	(	PUNCT
ejpam-5699	202	85	0	0	NUM
ejpam-5699	202	86	)	)	PUNCT
ejpam-5699	202	87	≤	≤	NUM
ejpam-5699	202	88	n+	n+	PUNCT
ejpam-5699	202	89	b	b	X
ejpam-5699	202	90	(	(	PUNCT
ejpam-5699	202	91	g1	g1	PROPN
ejpam-5699	202	92	)	)	PUNCT
ejpam-5699	202	93	,	,	PUNCT
ejpam-5699	202	94	and	and	CCONJ
ejpam-5699	202	95	n−	n−	PROPN
ejpam-5699	202	96	b	b	X
ejpam-5699	202	97	(	(	PUNCT
ejpam-5699	202	98	0	0	NUM
ejpam-5699	202	99	)	)	PUNCT
ejpam-5699	202	100	≥	≥	NOUN
ejpam-5699	202	101	n−	n−	PROPN
ejpam-5699	202	102	b	b	X
ejpam-5699	202	103	(	(	PUNCT
ejpam-5699	202	104	g1	g1	PROPN
ejpam-5699	202	105	)	)	PUNCT
ejpam-5699	202	106	for	for	ADP
ejpam-5699	202	107	all	all	DET
ejpam-5699	202	108	g1	g1	PROPN
ejpam-5699	202	109	∈	∈	PROPN
ejpam-5699	202	110	g.	g.	NOUN
ejpam-5699	202	111	therefore	therefore	ADV
ejpam-5699	202	112	,	,	PUNCT
ejpam-5699	202	113	b	b	X
ejpam-5699	202	114	=	=	SYM
ejpam-5699	202	115	(	(	PUNCT
ejpam-5699	202	116	m+	m+	NUM
ejpam-5699	202	117	b	b	NOUN
ejpam-5699	202	118	,	,	PUNCT
ejpam-5699	202	119	m−	m−	PROPN
ejpam-5699	202	120	b	b	PROPN
ejpam-5699	202	121	,	,	PUNCT
ejpam-5699	202	122	n+	n+	NOUN
ejpam-5699	202	123	b	b	NOUN
ejpam-5699	202	124	,	,	PUNCT
ejpam-5699	202	125	n−	n−	PROPN
ejpam-5699	202	126	b	b	X
ejpam-5699	202	127	)	)	PUNCT
ejpam-5699	202	128	is	be	AUX
ejpam-5699	202	129	a	a	DET
ejpam-5699	202	130	bpvifpii	bpvifpii	NOUN
ejpam-5699	202	131	of	of	ADP
ejpam-5699	202	132	g.	g.	PROPN
ejpam-5699	202	133	theorem	theorem	VERB
ejpam-5699	202	134	6	6	NUM
ejpam-5699	202	135	.	.	PUNCT
ejpam-5699	203	1	a	a	DET
ejpam-5699	203	2	bpvifs	bpvifs	PROPN
ejpam-5699	203	3	b	b	PROPN
ejpam-5699	203	4	=	=	PUNCT
ejpam-5699	203	5	(	(	PUNCT
ejpam-5699	203	6	m+	m+	NUM
ejpam-5699	203	7	b	b	NOUN
ejpam-5699	203	8	,	,	PUNCT
ejpam-5699	203	9	m−	m−	PROPN
ejpam-5699	203	10	b	b	PROPN
ejpam-5699	203	11	,	,	PUNCT
ejpam-5699	203	12	n+	n+	NOUN
ejpam-5699	203	13	b	b	NOUN
ejpam-5699	203	14	,	,	PUNCT
ejpam-5699	203	15	n−	n−	PROPN
ejpam-5699	203	16	b	b	NOUN
ejpam-5699	203	17	)	)	PUNCT
ejpam-5699	203	18	in	in	ADP
ejpam-5699	203	19	g	g	PROPN
ejpam-5699	203	20	is	be	AUX
ejpam-5699	203	21	a	a	DET
ejpam-5699	203	22	bpvifpii	bpvifpii	NOUN
ejpam-5699	203	23	of	of	ADP
ejpam-5699	203	24	g	g	NOUN
ejpam-5699	203	25	if	if	SCONJ
ejpam-5699	204	1	and	and	CCONJ
ejpam-5699	204	2	only	only	ADV
ejpam-5699	204	3	if	if	SCONJ
ejpam-5699	204	4	it	it	PRON
ejpam-5699	204	5	is	be	AUX
ejpam-5699	204	6	a	a	DET
ejpam-5699	204	7	bpvifi	bpvifi	NOUN
ejpam-5699	204	8	satisfying	satisfy	VERB
ejpam-5699	204	9	the	the	DET
ejpam-5699	204	10	following	follow	VERB
ejpam-5699	204	11	condition:	condition:	NOUN
ejpam-5699	204	12	m+	m+	NUM
ejpam-5699	204	13	b(g1	b(g1	PROPN
ejpam-5699	204	14	⋄	⋄	PROPN
ejpam-5699	204	15	è1	è1	PROPN
ejpam-5699	204	16	)	)	PUNCT
ejpam-5699	204	17	≥	≥	NOUN
ejpam-5699	204	18	m+	m+	NUM
ejpam-5699	204	19	b((g1	b((g1	PROPN
ejpam-5699	204	20	⋄	⋄	PROPN
ejpam-5699	204	21	è1	è1	PROPN
ejpam-5699	204	22	)	)	PUNCT
ejpam-5699	204	23	⋄	⋄	PROPN
ejpam-5699	204	24	è1	è1	PROPN
ejpam-5699	204	25	)	)	PUNCT
ejpam-5699	204	26	,	,	PUNCT
ejpam-5699	204	27	m−	m−	PROPN
ejpam-5699	204	28	b(g1	b(g1	PROPN
ejpam-5699	204	29	⋄	⋄	PROPN
ejpam-5699	204	30	è1	è1	PROPN
ejpam-5699	204	31	)	)	PUNCT
ejpam-5699	204	32	≤	≤	NOUN
ejpam-5699	205	1	m−	m−	PROPN
ejpam-5699	205	2	b((g1	b((g1	VERB
ejpam-5699	205	3	⋄	⋄	PROPN
ejpam-5699	205	4	è1	è1	PROPN
ejpam-5699	205	5	)	)	PUNCT
ejpam-5699	205	6	⋄	⋄	PROPN
ejpam-5699	205	7	è1	è1	PROPN
ejpam-5699	205	8	)	)	PUNCT
ejpam-5699	205	9	,	,	PUNCT
ejpam-5699	205	10	n+	n+	ADP
ejpam-5699	205	11	b	b	X
ejpam-5699	205	12	(	(	PUNCT
ejpam-5699	205	13	g1	g1	PROPN
ejpam-5699	205	14	⋄	⋄	PROPN
ejpam-5699	205	15	è1	è1	PROPN
ejpam-5699	205	16	)	)	PUNCT
ejpam-5699	205	17	≤	≤	NUM
ejpam-5699	205	18	n+	n+	PUNCT
ejpam-5699	205	19	b	b	X
ejpam-5699	205	20	(	(	PUNCT
ejpam-5699	205	21	(	(	PUNCT
ejpam-5699	205	22	g1	g1	PROPN
ejpam-5699	205	23	⋄	⋄	PROPN
ejpam-5699	205	24	è1	è1	PROPN
ejpam-5699	205	25	)	)	PUNCT
ejpam-5699	205	26	⋄	⋄	PROPN
ejpam-5699	205	27	è1	è1	PROPN
ejpam-5699	205	28	)	)	PUNCT
ejpam-5699	205	29	,	,	PUNCT
ejpam-5699	205	30	n−	n−	PROPN
ejpam-5699	205	31	b	b	X
ejpam-5699	205	32	(	(	PUNCT
ejpam-5699	205	33	g1	g1	PROPN
ejpam-5699	205	34	⋄	⋄	PROPN
ejpam-5699	205	35	è1	è1	PROPN
ejpam-5699	205	36	)	)	PUNCT
ejpam-5699	205	37	≥	≥	NOUN
ejpam-5699	205	38	n−	n−	PROPN
ejpam-5699	205	39	b	b	X
ejpam-5699	205	40	(	(	PUNCT
ejpam-5699	205	41	(	(	PUNCT
ejpam-5699	205	42	g1	g1	PROPN
ejpam-5699	205	43	⋄	⋄	PROPN
ejpam-5699	205	44	è1	è1	PROPN
ejpam-5699	205	45	)	)	PUNCT
ejpam-5699	205	46	⋄	⋄	PROPN
ejpam-5699	205	47	è1	è1	PROPN
ejpam-5699	205	48	)	)	PUNCT
ejpam-5699	205	49	,	,	PUNCT
ejpam-5699	205	50			NOUN
ejpam-5699	205	51	(	(	PUNCT
ejpam-5699	205	52	13	13	NUM
ejpam-5699	205	53	)	)	PUNCT
ejpam-5699	205	54	for	for	ADP
ejpam-5699	205	55	all	all	DET
ejpam-5699	205	56	g1,è1	g1,è1	PROPN
ejpam-5699	205	57	∈	∈	PROPN
ejpam-5699	205	58	g.	g.	PROPN
ejpam-5699	205	59	d.	d.	PROPN
ejpam-5699	205	60	ramesh	ramesh	PROPN
ejpam-5699	205	61	et	et	PROPN
ejpam-5699	205	62	al	al	PROPN
ejpam-5699	205	63	.	.	PUNCT
ejpam-5699	205	64	/	/	SYM
ejpam-5699	205	65	eur	eur	PROPN
ejpam-5699	205	66	.	.	PUNCT
ejpam-5699	206	1	j.	j.	PROPN
ejpam-5699	206	2	pure	pure	PROPN
ejpam-5699	206	3	appl	appl	PROPN
ejpam-5699	206	4	.	.	PROPN
ejpam-5699	206	5	math	math	PROPN
ejpam-5699	206	6	,	,	PUNCT
ejpam-5699	206	7	18	18	NUM
ejpam-5699	206	8	(	(	PUNCT
ejpam-5699	206	9	1	1	NUM
ejpam-5699	206	10	)	)	PUNCT
ejpam-5699	206	11	(	(	PUNCT
ejpam-5699	206	12	2025	2025	NUM
ejpam-5699	206	13	)	)	PUNCT
ejpam-5699	206	14	,	,	PUNCT
ejpam-5699	206	15	5699	5699	NUM
ejpam-5699	206	16	13	13	NUM
ejpam-5699	206	17	of	of	ADP
ejpam-5699	206	18	20	20	NUM
ejpam-5699	206	19	proof	proof	NOUN
ejpam-5699	206	20	.	.	PUNCT
ejpam-5699	207	1	assume	assume	VERB
ejpam-5699	207	2	that	that	SCONJ
ejpam-5699	207	3	b	b	X
ejpam-5699	207	4	=	=	SYM
ejpam-5699	207	5	(	(	PUNCT
ejpam-5699	207	6	m+	m+	NUM
ejpam-5699	207	7	b	b	NOUN
ejpam-5699	207	8	,	,	PUNCT
ejpam-5699	207	9	m−	m−	PROPN
ejpam-5699	207	10	b	b	PROPN
ejpam-5699	207	11	,	,	PUNCT
ejpam-5699	207	12	n+	n+	NOUN
ejpam-5699	207	13	b	b	NOUN
ejpam-5699	207	14	,	,	PUNCT
ejpam-5699	207	15	n−	n−	PROPN
ejpam-5699	207	16	b	b	X
ejpam-5699	207	17	)	)	PUNCT
ejpam-5699	207	18	is	be	AUX
ejpam-5699	207	19	a	a	DET
ejpam-5699	207	20	bpvifpii	bpvifpii	NOUN
ejpam-5699	207	21	of	of	ADP
ejpam-5699	207	22	g.	g.	PROPN
ejpam-5699	207	23	write	write	VERB
ejpam-5699	207	24	11	11	NUM
ejpam-5699	207	25	=	=	SYM
ejpam-5699	207	26	è1	è1	NOUN
ejpam-5699	207	27	in	in	ADP
ejpam-5699	207	28	definition	definition	NOUN
ejpam-5699	207	29	21	21	NUM
ejpam-5699	207	30	,	,	PUNCT
ejpam-5699	207	31	we	we	PRON
ejpam-5699	207	32	obtain	obtain	VERB
ejpam-5699	207	33	m+	m+	NUM
ejpam-5699	207	34	b(g1	b(g1	ADJ
ejpam-5699	207	35	⋄	⋄	PROPN
ejpam-5699	207	36	è1	è1	PROPN
ejpam-5699	207	37	)	)	PUNCT
ejpam-5699	207	38	≥	≥	NOUN
ejpam-5699	207	39	min{m+	min{m+	PROPN
ejpam-5699	207	40	b((g1	b((g1	PROPN
ejpam-5699	207	41	⋄	⋄	PROPN
ejpam-5699	207	42	è1	è1	PROPN
ejpam-5699	207	43	)	)	PUNCT
ejpam-5699	207	44	⋄	⋄	PROPN
ejpam-5699	207	45	è1),m+	è1),m+	NOUN
ejpam-5699	207	46	b(è1	b(è1	NOUN
ejpam-5699	207	47	⋄	⋄	PROPN
ejpam-5699	207	48	è1	è1	PROPN
ejpam-5699	207	49	)	)	PUNCT
ejpam-5699	207	50	}	}	PUNCT
ejpam-5699	207	51	=	=	SYM
ejpam-5699	207	52	min{m+	min{m+	PROPN
ejpam-5699	207	53	b((g1	b((g1	PROPN
ejpam-5699	207	54	⋄	⋄	PROPN
ejpam-5699	207	55	è1	è1	PROPN
ejpam-5699	207	56	)	)	PUNCT
ejpam-5699	207	57	⋄	⋄	PROPN
ejpam-5699	207	58	è1),m+	è1),m+	NOUN
ejpam-5699	207	59	b(0	b(0	NOUN
ejpam-5699	207	60	)	)	PUNCT
ejpam-5699	207	61	}	}	PUNCT
ejpam-5699	207	62	=	=	SYM
ejpam-5699	208	1	m+	m+	NUM
ejpam-5699	208	2	b((g1	b((g1	PROPN
ejpam-5699	208	3	⋄	⋄	PROPN
ejpam-5699	208	4	è1	è1	PROPN
ejpam-5699	208	5	)	)	PUNCT
ejpam-5699	208	6	⋄	⋄	PROPN
ejpam-5699	208	7	è1	è1	PROPN
ejpam-5699	208	8	)	)	PUNCT
ejpam-5699	208	9	,	,	PUNCT
ejpam-5699	208	10	m−	m−	PROPN
ejpam-5699	208	11	b(g1	b(g1	PROPN
ejpam-5699	208	12	⋄	⋄	PROPN
ejpam-5699	208	13	è1	è1	PROPN
ejpam-5699	208	14	)	)	PUNCT
ejpam-5699	208	15	≤	≤	NOUN
ejpam-5699	208	16	max{m−	max{m−	NOUN
ejpam-5699	208	17	b((g1	b((g1	NOUN
ejpam-5699	208	18	⋄	⋄	PROPN
ejpam-5699	208	19	è1	è1	PROPN
ejpam-5699	208	20	)	)	PUNCT
ejpam-5699	208	21	⋄	⋄	PROPN
ejpam-5699	208	22	è1),m−	è1),m−	VERB
ejpam-5699	208	23	b(è1	b(è1	NOUN
ejpam-5699	208	24	⋄	⋄	PROPN
ejpam-5699	208	25	è1	è1	PROPN
ejpam-5699	208	26	)	)	PUNCT
ejpam-5699	208	27	}	}	PUNCT
ejpam-5699	208	28	=	=	SYM
ejpam-5699	209	1	max{m−	max{m−	NOUN
ejpam-5699	209	2	b((g1	b((g1	NOUN
ejpam-5699	209	3	⋄	⋄	PROPN
ejpam-5699	209	4	è1	è1	PROPN
ejpam-5699	209	5	)	)	PUNCT
ejpam-5699	209	6	⋄	⋄	PROPN
ejpam-5699	209	7	è1),m−	è1),m−	PROPN
ejpam-5699	209	8	b(0	b(0	NOUN
ejpam-5699	209	9	)	)	PUNCT
ejpam-5699	209	10	}	}	PUNCT
ejpam-5699	210	1	=	=	SYM
ejpam-5699	210	2	m−	m−	PROPN
ejpam-5699	210	3	b((g1	b((g1	VERB
ejpam-5699	210	4	⋄	⋄	PROPN
ejpam-5699	210	5	è1	è1	PROPN
ejpam-5699	210	6	)	)	PUNCT
ejpam-5699	210	7	⋄	⋄	PROPN
ejpam-5699	210	8	è1	è1	PROPN
ejpam-5699	210	9	)	)	PUNCT
ejpam-5699	210	10	,	,	PUNCT
ejpam-5699	210	11	n+	n+	ADP
ejpam-5699	210	12	b	b	X
ejpam-5699	210	13	(	(	PUNCT
ejpam-5699	210	14	g1	g1	PROPN
ejpam-5699	210	15	⋄	⋄	PROPN
ejpam-5699	210	16	è1	è1	PROPN
ejpam-5699	210	17	)	)	PUNCT
ejpam-5699	210	18	≤	≤	NUM
ejpam-5699	211	1	max{n+	max{n+	PROPN
ejpam-5699	211	2	b	b	PROPN
ejpam-5699	211	3	(	(	PUNCT
ejpam-5699	211	4	(	(	PUNCT
ejpam-5699	211	5	g1	g1	PROPN
ejpam-5699	211	6	⋄	⋄	PROPN
ejpam-5699	211	7	è1	è1	PROPN
ejpam-5699	211	8	)	)	PUNCT
ejpam-5699	211	9	⋄	⋄	PROPN
ejpam-5699	211	10	è1),n+	è1),n+	PROPN
ejpam-5699	211	11	b	b	PROPN
ejpam-5699	211	12	(	(	PUNCT
ejpam-5699	211	13	è1	è1	PROPN
ejpam-5699	211	14	⋄	⋄	PROPN
ejpam-5699	211	15	è1	è1	NOUN
ejpam-5699	211	16	)	)	PUNCT
ejpam-5699	211	17	}	}	PUNCT
ejpam-5699	211	18	=	=	PUNCT
ejpam-5699	211	19	max{n+	max{n+	NOUN
ejpam-5699	211	20	b	b	X
ejpam-5699	211	21	(	(	PUNCT
ejpam-5699	211	22	(	(	PUNCT
ejpam-5699	211	23	g1	g1	PROPN
ejpam-5699	211	24	⋄	⋄	PROPN
ejpam-5699	211	25	è1	è1	PROPN
ejpam-5699	211	26	)	)	PUNCT
ejpam-5699	211	27	⋄	⋄	PROPN
ejpam-5699	211	28	è1),n+	è1),n+	PROPN
ejpam-5699	211	29	b	b	PROPN
ejpam-5699	211	30	(	(	PUNCT
ejpam-5699	211	31	0	0	NUM
ejpam-5699	211	32	)	)	PUNCT
ejpam-5699	211	33	}	}	PUNCT
ejpam-5699	211	34	=	=	PUNCT
ejpam-5699	211	35	n+	n+	PUNCT
ejpam-5699	211	36	b	b	X
ejpam-5699	211	37	(	(	PUNCT
ejpam-5699	211	38	(	(	PUNCT
ejpam-5699	211	39	g1	g1	PROPN
ejpam-5699	211	40	⋄	⋄	PROPN
ejpam-5699	211	41	è1	è1	PROPN
ejpam-5699	211	42	)	)	PUNCT
ejpam-5699	211	43	⋄	⋄	PROPN
ejpam-5699	211	44	è1	è1	PROPN
ejpam-5699	211	45	)	)	PUNCT
ejpam-5699	211	46	,	,	PUNCT
ejpam-5699	211	47	n−	n−	PROPN
ejpam-5699	211	48	b	b	X
ejpam-5699	211	49	(	(	PUNCT
ejpam-5699	211	50	g1	g1	PROPN
ejpam-5699	211	51	⋄	⋄	PROPN
ejpam-5699	211	52	è1	è1	PROPN
ejpam-5699	211	53	)	)	PUNCT
ejpam-5699	211	54	≥	≥	NOUN
ejpam-5699	211	55	min{n−	min{n−	PROPN
ejpam-5699	211	56	b	b	PROPN
ejpam-5699	211	57	(	(	PUNCT
ejpam-5699	211	58	(	(	PUNCT
ejpam-5699	211	59	g1	g1	PROPN
ejpam-5699	211	60	⋄	⋄	PROPN
ejpam-5699	211	61	è1	è1	PROPN
ejpam-5699	211	62	)	)	PUNCT
ejpam-5699	211	63	⋄	⋄	PROPN
ejpam-5699	211	64	è1),n−	è1),n−	PROPN
ejpam-5699	211	65	b	b	PROPN
ejpam-5699	211	66	(	(	PUNCT
ejpam-5699	211	67	è1	è1	PROPN
ejpam-5699	211	68	⋄	⋄	PROPN
ejpam-5699	211	69	è1	è1	NOUN
ejpam-5699	211	70	)	)	PUNCT
ejpam-5699	211	71	}	}	PUNCT
ejpam-5699	211	72	=	=	SYM
ejpam-5699	211	73	min{n−	min{n−	PROPN
ejpam-5699	211	74	b	b	PROPN
ejpam-5699	211	75	(	(	PUNCT
ejpam-5699	211	76	(	(	PUNCT
ejpam-5699	211	77	g1	g1	PROPN
ejpam-5699	211	78	⋄	⋄	PROPN
ejpam-5699	211	79	è1	è1	PROPN
ejpam-5699	211	80	)	)	PUNCT
ejpam-5699	211	81	⋄	⋄	PROPN
ejpam-5699	211	82	è1),n−	è1),n−	PROPN
ejpam-5699	211	83	b	b	PROPN
ejpam-5699	211	84	(	(	PUNCT
ejpam-5699	211	85	0	0	NUM
ejpam-5699	211	86	)	)	PUNCT
ejpam-5699	211	87	}	}	PUNCT
ejpam-5699	211	88	=	=	PUNCT
ejpam-5699	211	89	n−	n−	NUM
ejpam-5699	211	90	b	b	X
ejpam-5699	211	91	(	(	PUNCT
ejpam-5699	211	92	(	(	PUNCT
ejpam-5699	211	93	g1	g1	PROPN
ejpam-5699	211	94	⋄	⋄	PROPN
ejpam-5699	211	95	è1	è1	PROPN
ejpam-5699	211	96	)	)	PUNCT
ejpam-5699	211	97	⋄	⋄	PROPN
ejpam-5699	211	98	è1	è1	PROPN
ejpam-5699	211	99	)	)	PUNCT
ejpam-5699	211	100	,	,	PUNCT
ejpam-5699	211	101	for	for	ADP
ejpam-5699	211	102	all	all	DET
ejpam-5699	211	103	g1,è1	g1,è1	PROPN
ejpam-5699	211	104	∈	∈	PROPN
ejpam-5699	211	105	g.	g.	NOUN
ejpam-5699	211	106	thus	thus	ADV
ejpam-5699	211	107	,	,	PUNCT
ejpam-5699	211	108	condition	condition	NOUN
ejpam-5699	211	109	(	(	PUNCT
ejpam-5699	211	110	13	13	NUM
ejpam-5699	211	111	)	)	PUNCT
ejpam-5699	211	112	holds	hold	VERB
ejpam-5699	211	113	.	.	PUNCT
ejpam-5699	212	1	conversely	conversely	ADV
ejpam-5699	212	2	,	,	PUNCT
ejpam-5699	212	3	let	let	VERB
ejpam-5699	212	4	b	b	X
ejpam-5699	212	5	=	=	SYM
ejpam-5699	212	6	(	(	PUNCT
ejpam-5699	212	7	m+	m+	NUM
ejpam-5699	212	8	b	b	NOUN
ejpam-5699	212	9	,	,	PUNCT
ejpam-5699	212	10	m−	m−	PROPN
ejpam-5699	212	11	b	b	PROPN
ejpam-5699	212	12	,	,	PUNCT
ejpam-5699	212	13	n+	n+	NOUN
ejpam-5699	212	14	b	b	NOUN
ejpam-5699	212	15	,	,	PUNCT
ejpam-5699	212	16	n−	n−	PROPN
ejpam-5699	212	17	b	b	AUX
ejpam-5699	212	18	)	)	PUNCT
ejpam-5699	212	19	be	be	AUX
ejpam-5699	212	20	a	a	DET
ejpam-5699	212	21	bpvifi	bpvifi	NOUN
ejpam-5699	212	22	of	of	ADP
ejpam-5699	212	23	g	g	NOUN
ejpam-5699	212	24	satisfying	satisfy	VERB
ejpam-5699	212	25	the	the	DET
ejpam-5699	212	26	condition	condition	NOUN
ejpam-5699	212	27	(	(	PUNCT
ejpam-5699	212	28	13	13	NUM
ejpam-5699	212	29	)	)	PUNCT
ejpam-5699	212	30	.	.	PUNCT
ejpam-5699	213	1	by	by	ADP
ejpam-5699	213	2	using	use	VERB
ejpam-5699	213	3	bck-1	bck-1	NOUN
ejpam-5699	213	4	,	,	PUNCT
ejpam-5699	213	5	(	(	PUNCT
ejpam-5699	213	6	3	3	NUM
ejpam-5699	213	7	)	)	PUNCT
ejpam-5699	213	8	,	,	PUNCT
ejpam-5699	213	9	and	and	CCONJ
ejpam-5699	213	10	(	(	PUNCT
ejpam-5699	213	11	6	6	NUM
ejpam-5699	213	12	)	)	PUNCT
ejpam-5699	213	13	,	,	PUNCT
ejpam-5699	213	14	we	we	PRON
ejpam-5699	213	15	obtain	obtain	VERB
ejpam-5699	213	16	for	for	ADP
ejpam-5699	213	17	all	all	DET
ejpam-5699	213	18	g1,è1	g1,è1	PROPN
ejpam-5699	213	19	,	,	PUNCT
ejpam-5699	213	20	11	11	NUM
ejpam-5699	213	21	∈	∈	NOUN
ejpam-5699	213	22	g	g	NOUN
ejpam-5699	213	23	,	,	PUNCT
ejpam-5699	213	24	(	(	PUNCT
ejpam-5699	213	25	(	(	PUNCT
ejpam-5699	213	26	g1	g1	VERB
ejpam-5699	213	27	⋄	⋄	PROPN
ejpam-5699	213	28	11	11	NUM
ejpam-5699	213	29	)	)	PUNCT
ejpam-5699	213	30	⋄	⋄	NOUN
ejpam-5699	213	31	(	(	PUNCT
ejpam-5699	213	32	g1	g1	PROPN
ejpam-5699	213	33	⋄	⋄	PROPN
ejpam-5699	213	34	è1	è1	PROPN
ejpam-5699	213	35	)	)	PUNCT
ejpam-5699	213	36	)	)	PUNCT
ejpam-5699	213	37	≤	≤	NOUN
ejpam-5699	213	38	(	(	PUNCT
ejpam-5699	213	39	è1	è1	NOUN
ejpam-5699	213	40	⋄	⋄	PROPN
ejpam-5699	213	41	11	11	NUM
ejpam-5699	213	42	)	)	PUNCT
ejpam-5699	213	43	⇒	⇒	NOUN
ejpam-5699	213	44	(	(	PUNCT
ejpam-5699	213	45	(	(	PUNCT
ejpam-5699	213	46	g1	g1	VERB
ejpam-5699	213	47	⋄	⋄	PROPN
ejpam-5699	213	48	11	11	NUM
ejpam-5699	213	49	)	)	PUNCT
ejpam-5699	213	50	⋄	⋄	NOUN
ejpam-5699	213	51	(	(	PUNCT
ejpam-5699	213	52	è1	è1	NOUN
ejpam-5699	213	53	⋄	⋄	PROPN
ejpam-5699	213	54	11	11	NUM
ejpam-5699	213	55	)	)	PUNCT
ejpam-5699	213	56	)	)	PUNCT
ejpam-5699	213	57	≤	≤	NOUN
ejpam-5699	213	58	(	(	PUNCT
ejpam-5699	213	59	g1	g1	PROPN
ejpam-5699	213	60	⋄	⋄	PROPN
ejpam-5699	213	61	è1	è1	PROPN
ejpam-5699	213	62	)	)	PUNCT
ejpam-5699	213	63	⇒	⇒	NOUN
ejpam-5699	213	64	(	(	PUNCT
ejpam-5699	213	65	(	(	PUNCT
ejpam-5699	213	66	g1	g1	VERB
ejpam-5699	213	67	⋄	⋄	PROPN
ejpam-5699	213	68	11	11	NUM
ejpam-5699	213	69	)	)	PUNCT
ejpam-5699	213	70	⋄	⋄	NOUN
ejpam-5699	213	71	(	(	PUNCT
ejpam-5699	213	72	è1	è1	NOUN
ejpam-5699	213	73	⋄	⋄	PROPN
ejpam-5699	213	74	11	11	NUM
ejpam-5699	213	75	)	)	PUNCT
ejpam-5699	213	76	)	)	PUNCT
ejpam-5699	214	1	⋄	⋄	NOUN
ejpam-5699	214	2	11	11	NUM
ejpam-5699	214	3	≤	≤	NOUN
ejpam-5699	214	4	(	(	PUNCT
ejpam-5699	214	5	g1	g1	PROPN
ejpam-5699	214	6	⋄	⋄	PROPN
ejpam-5699	214	7	è1	è1	PROPN
ejpam-5699	214	8	)	)	PUNCT
ejpam-5699	214	9	⋄	⋄	PROPN
ejpam-5699	214	10	11	11	NUM
ejpam-5699	214	11	⇒	⇒	NOUN
ejpam-5699	214	12	(	(	PUNCT
ejpam-5699	214	13	(	(	PUNCT
ejpam-5699	214	14	g1	g1	VERB
ejpam-5699	214	15	⋄	⋄	PROPN
ejpam-5699	214	16	11	11	NUM
ejpam-5699	214	17	)	)	PUNCT
ejpam-5699	214	18	⋄	⋄	NOUN
ejpam-5699	214	19	11	11	NUM
ejpam-5699	214	20	)	)	PUNCT
ejpam-5699	214	21	⋄	⋄	NOUN
ejpam-5699	214	22	(	(	PUNCT
ejpam-5699	214	23	è1	è1	ADP
ejpam-5699	214	24	⋄	⋄	PROPN
ejpam-5699	214	25	11	11	NUM
ejpam-5699	214	26	)	)	PUNCT
ejpam-5699	214	27	≤	≤	NOUN
ejpam-5699	214	28	(	(	PUNCT
ejpam-5699	214	29	g1	g1	PROPN
ejpam-5699	214	30	⋄	⋄	PROPN
ejpam-5699	214	31	è1	è1	PROPN
ejpam-5699	214	32	)	)	PUNCT
ejpam-5699	214	33	⋄	⋄	NOUN
ejpam-5699	214	34	11	11	NUM
ejpam-5699	214	35	.	.	PUNCT
ejpam-5699	215	1	it	it	PRON
ejpam-5699	215	2	follows	follow	VERB
ejpam-5699	215	3	from	from	ADP
ejpam-5699	215	4	corollary	corollary	ADJ
ejpam-5699	215	5	1	1	NUM
ejpam-5699	215	6	that	that	NOUN
ejpam-5699	215	7	m+	m+	NOUN
ejpam-5699	215	8	b(((g1	b(((g1	VERB
ejpam-5699	215	9	⋄	⋄	NOUN
ejpam-5699	215	10	11	11	NUM
ejpam-5699	215	11	)	)	PUNCT
ejpam-5699	215	12	⋄	⋄	NOUN
ejpam-5699	215	13	11	11	NUM
ejpam-5699	215	14	)	)	PUNCT
ejpam-5699	215	15	⋄	⋄	NOUN
ejpam-5699	215	16	(	(	PUNCT
ejpam-5699	215	17	è1	è1	NOUN
ejpam-5699	215	18	⋄	⋄	PROPN
ejpam-5699	215	19	11	11	NUM
ejpam-5699	215	20	)	)	PUNCT
ejpam-5699	215	21	)	)	PUNCT
ejpam-5699	215	22	≥	≥	NOUN
ejpam-5699	215	23	m+	m+	NUM
ejpam-5699	215	24	b((g1	b((g1	PROPN
ejpam-5699	215	25	⋄	⋄	PROPN
ejpam-5699	215	26	è1	è1	PROPN
ejpam-5699	215	27	)	)	PUNCT
ejpam-5699	215	28	⋄	⋄	NOUN
ejpam-5699	215	29	11	11	NUM
ejpam-5699	215	30	)	)	PUNCT
ejpam-5699	215	31	,	,	PUNCT
ejpam-5699	215	32	m−	m−	PROPN
ejpam-5699	215	33	b(((g1	b(((g1	VERB
ejpam-5699	215	34	⋄	⋄	PROPN
ejpam-5699	215	35	11	11	NUM
ejpam-5699	215	36	)	)	PUNCT
ejpam-5699	215	37	⋄	⋄	NOUN
ejpam-5699	215	38	11	11	NUM
ejpam-5699	215	39	)	)	PUNCT
ejpam-5699	215	40	⋄	⋄	NOUN
ejpam-5699	215	41	(	(	PUNCT
ejpam-5699	215	42	è1	è1	NOUN
ejpam-5699	215	43	⋄	⋄	PROPN
ejpam-5699	215	44	11	11	NUM
ejpam-5699	215	45	)	)	PUNCT
ejpam-5699	215	46	)	)	PUNCT
ejpam-5699	215	47	≤	≤	NUM
ejpam-5699	216	1	m−	m−	PROPN
ejpam-5699	216	2	b((g1	b((g1	VERB
ejpam-5699	216	3	⋄	⋄	PROPN
ejpam-5699	216	4	è1	è1	PROPN
ejpam-5699	216	5	)	)	PUNCT
ejpam-5699	216	6	⋄	⋄	NOUN
ejpam-5699	216	7	11	11	NUM
ejpam-5699	216	8	)	)	PUNCT
ejpam-5699	216	9	,	,	PUNCT
ejpam-5699	216	10	n+	n+	ADP
ejpam-5699	216	11	b	b	X
ejpam-5699	216	12	(	(	PUNCT
ejpam-5699	216	13	(	(	PUNCT
ejpam-5699	216	14	(	(	PUNCT
ejpam-5699	216	15	g1	g1	VERB
ejpam-5699	216	16	⋄	⋄	PROPN
ejpam-5699	216	17	11	11	NUM
ejpam-5699	216	18	)	)	PUNCT
ejpam-5699	216	19	⋄	⋄	NOUN
ejpam-5699	216	20	11	11	NUM
ejpam-5699	216	21	)	)	PUNCT
ejpam-5699	216	22	⋄	⋄	NOUN
ejpam-5699	216	23	(	(	PUNCT
ejpam-5699	216	24	è1	è1	NOUN
ejpam-5699	216	25	⋄	⋄	PROPN
ejpam-5699	216	26	11	11	NUM
ejpam-5699	216	27	)	)	PUNCT
ejpam-5699	216	28	)	)	PUNCT
ejpam-5699	216	29	≤	≤	NUM
ejpam-5699	217	1	n+	n+	PUNCT
ejpam-5699	217	2	b	b	X
ejpam-5699	217	3	(	(	PUNCT
ejpam-5699	217	4	(	(	PUNCT
ejpam-5699	217	5	g1	g1	PROPN
ejpam-5699	217	6	⋄	⋄	PROPN
ejpam-5699	217	7	è1	è1	PROPN
ejpam-5699	217	8	)	)	PUNCT
ejpam-5699	217	9	⋄	⋄	NOUN
ejpam-5699	217	10	11	11	NUM
ejpam-5699	217	11	)	)	PUNCT
ejpam-5699	217	12	,	,	PUNCT
ejpam-5699	217	13	n−	n−	PROPN
ejpam-5699	217	14	b	b	X
ejpam-5699	217	15	(	(	PUNCT
ejpam-5699	217	16	(	(	PUNCT
ejpam-5699	217	17	(	(	PUNCT
ejpam-5699	217	18	g1	g1	VERB
ejpam-5699	217	19	⋄	⋄	PROPN
ejpam-5699	217	20	11	11	NUM
ejpam-5699	217	21	)	)	PUNCT
ejpam-5699	217	22	⋄	⋄	NOUN
ejpam-5699	217	23	11	11	NUM
ejpam-5699	217	24	)	)	PUNCT
ejpam-5699	217	25	⋄	⋄	NOUN
ejpam-5699	217	26	(	(	PUNCT
ejpam-5699	217	27	è1	è1	NOUN
ejpam-5699	217	28	⋄	⋄	PROPN
ejpam-5699	217	29	11	11	NUM
ejpam-5699	217	30	)	)	PUNCT
ejpam-5699	217	31	)	)	PUNCT
ejpam-5699	217	32	≥	≥	PROPN
ejpam-5699	217	33	n−	n−	PROPN
ejpam-5699	217	34	b	b	X
ejpam-5699	217	35	(	(	PUNCT
ejpam-5699	217	36	(	(	PUNCT
ejpam-5699	217	37	g1	g1	PROPN
ejpam-5699	217	38	⋄	⋄	PROPN
ejpam-5699	217	39	è1	è1	PROPN
ejpam-5699	217	40	)	)	PUNCT
ejpam-5699	217	41	⋄	⋄	NOUN
ejpam-5699	217	42	11	11	NUM
ejpam-5699	217	43	)	)	PUNCT
ejpam-5699	217	44	,	,	PUNCT
ejpam-5699	217	45			NOUN
ejpam-5699	217	46	(	(	PUNCT
ejpam-5699	217	47	14	14	NUM
ejpam-5699	217	48	)	)	PUNCT
ejpam-5699	217	49	for	for	ADP
ejpam-5699	217	50	all	all	DET
ejpam-5699	217	51	g1,è1	g1,è1	PROPN
ejpam-5699	217	52	,	,	PUNCT
ejpam-5699	217	53	11	11	NUM
ejpam-5699	217	54	∈	∈	NOUN
ejpam-5699	217	55	g.	g.	NOUN
ejpam-5699	217	56	now	now	ADV
ejpam-5699	217	57	,	,	PUNCT
ejpam-5699	217	58	by	by	ADP
ejpam-5699	217	59	using	use	VERB
ejpam-5699	217	60	(	(	PUNCT
ejpam-5699	217	61	13	13	NUM
ejpam-5699	217	62	)	)	PUNCT
ejpam-5699	217	63	,	,	PUNCT
ejpam-5699	217	64	definition	definition	NOUN
ejpam-5699	217	65	20	20	NUM
ejpam-5699	217	66	,	,	PUNCT
ejpam-5699	217	67	and	and	CCONJ
ejpam-5699	217	68	(	(	PUNCT
ejpam-5699	217	69	14	14	NUM
ejpam-5699	217	70	)	)	PUNCT
ejpam-5699	217	71	,	,	PUNCT
ejpam-5699	217	72	we	we	PRON
ejpam-5699	217	73	obtain	obtain	VERB
ejpam-5699	217	74	m+	m+	NOUN
ejpam-5699	217	75	b(g1	b(g1	ADJ
ejpam-5699	217	76	⋄	⋄	PROPN
ejpam-5699	217	77	11	11	NUM
ejpam-5699	217	78	)	)	PUNCT
ejpam-5699	217	79	≥	≥	NOUN
ejpam-5699	217	80	m+	m+	NUM
ejpam-5699	217	81	b((g1	b((g1	NOUN
ejpam-5699	217	82	⋄	⋄	PROPN
ejpam-5699	217	83	11	11	NUM
ejpam-5699	217	84	)	)	PUNCT
ejpam-5699	217	85	⋄	⋄	NOUN
ejpam-5699	217	86	11	11	NUM
ejpam-5699	217	87	)	)	PUNCT
ejpam-5699	217	88	≥	≥	NOUN
ejpam-5699	218	1	min{m+	min{m+	PROPN
ejpam-5699	218	2	b(((g1	b(((g1	PART
ejpam-5699	218	3	⋄	⋄	NOUN
ejpam-5699	218	4	11	11	NUM
ejpam-5699	218	5	)	)	PUNCT
ejpam-5699	218	6	⋄	⋄	NOUN
ejpam-5699	218	7	11	11	NUM
ejpam-5699	218	8	)	)	PUNCT
ejpam-5699	218	9	⋄	⋄	NOUN
ejpam-5699	218	10	(	(	PUNCT
ejpam-5699	218	11	è1	è1	PROPN
ejpam-5699	218	12	⋄	⋄	PROPN
ejpam-5699	218	13	11)),m+	11)),m+	NUM
ejpam-5699	218	14	b(è1	b(è1	NOUN
ejpam-5699	218	15	⋄	⋄	PROPN
ejpam-5699	218	16	11	11	NUM
ejpam-5699	218	17	)	)	PUNCT
ejpam-5699	218	18	}	}	PUNCT
ejpam-5699	218	19	≥	≥	NOUN
ejpam-5699	218	20	min{m+	min{m+	PROPN
ejpam-5699	218	21	b((g1	b((g1	PROPN
ejpam-5699	218	22	⋄	⋄	PROPN
ejpam-5699	218	23	è1	è1	PROPN
ejpam-5699	218	24	)	)	PUNCT
ejpam-5699	218	25	⋄	⋄	PROPN
ejpam-5699	218	26	11),m+	11),m+	NUM
ejpam-5699	218	27	b(è1	b(è1	NOUN
ejpam-5699	218	28	⋄	⋄	PROPN
ejpam-5699	218	29	11	11	NUM
ejpam-5699	218	30	)	)	PUNCT
ejpam-5699	218	31	}	}	PUNCT
ejpam-5699	218	32	,	,	PUNCT
ejpam-5699	218	33	m−	m−	PROPN
ejpam-5699	218	34	b(g1	b(g1	ADJ
ejpam-5699	218	35	⋄	⋄	PROPN
ejpam-5699	218	36	11	11	NUM
ejpam-5699	218	37	)	)	PUNCT
ejpam-5699	218	38	≤	≤	NOUN
ejpam-5699	218	39	m−	m−	PROPN
ejpam-5699	218	40	b((g1	b((g1	VERB
ejpam-5699	218	41	⋄	⋄	PROPN
ejpam-5699	218	42	11	11	NUM
ejpam-5699	218	43	)	)	PUNCT
ejpam-5699	218	44	⋄	⋄	NOUN
ejpam-5699	218	45	11	11	NUM
ejpam-5699	218	46	)	)	PUNCT
ejpam-5699	218	47	≤	≤	NOUN
ejpam-5699	218	48	max{m−	max{m−	NOUN
ejpam-5699	218	49	b(((g1	b(((g1	VERB
ejpam-5699	218	50	⋄	⋄	NOUN
ejpam-5699	218	51	11	11	NUM
ejpam-5699	218	52	)	)	PUNCT
ejpam-5699	218	53	⋄	⋄	NOUN
ejpam-5699	218	54	11	11	NUM
ejpam-5699	218	55	)	)	PUNCT
ejpam-5699	218	56	⋄	⋄	NOUN
ejpam-5699	219	1	(	(	PUNCT
ejpam-5699	219	2	è1	è1	ADP
ejpam-5699	219	3	⋄	⋄	PROPN
ejpam-5699	219	4	11)),m−	11)),m−	NUM
ejpam-5699	219	5	b(è1	b(è1	NOUN
ejpam-5699	219	6	⋄	⋄	PROPN
ejpam-5699	219	7	11	11	NUM
ejpam-5699	219	8	)	)	PUNCT
ejpam-5699	219	9	}	}	PUNCT
ejpam-5699	219	10	≤	≤	NOUN
ejpam-5699	219	11	max{m−	max{m−	NOUN
ejpam-5699	219	12	b((g1	b((g1	NOUN
ejpam-5699	219	13	⋄	⋄	PROPN
ejpam-5699	219	14	è1	è1	PROPN
ejpam-5699	219	15	)	)	PUNCT
ejpam-5699	219	16	⋄	⋄	NOUN
ejpam-5699	219	17	11),m−	11),m−	NUM
ejpam-5699	219	18	b(è1	b(è1	NOUN
ejpam-5699	219	19	⋄	⋄	PROPN
ejpam-5699	219	20	11	11	NUM
ejpam-5699	219	21	)	)	PUNCT
ejpam-5699	219	22	}	}	PUNCT
ejpam-5699	219	23	,	,	PUNCT
ejpam-5699	219	24	n+	n+	ADP
ejpam-5699	219	25	b	b	X
ejpam-5699	219	26	(	(	PUNCT
ejpam-5699	219	27	g1	g1	VERB
ejpam-5699	219	28	⋄	⋄	PROPN
ejpam-5699	219	29	11	11	NUM
ejpam-5699	219	30	)	)	PUNCT
ejpam-5699	219	31	≤	≤	NUM
ejpam-5699	220	1	n+	n+	PUNCT
ejpam-5699	221	1	b	b	X
ejpam-5699	221	2	(	(	PUNCT
ejpam-5699	221	3	(	(	PUNCT
ejpam-5699	221	4	g1	g1	VERB
ejpam-5699	221	5	⋄	⋄	PROPN
ejpam-5699	221	6	11	11	NUM
ejpam-5699	221	7	)	)	PUNCT
ejpam-5699	221	8	⋄	⋄	NOUN
ejpam-5699	221	9	11	11	NUM
ejpam-5699	221	10	)	)	PUNCT
ejpam-5699	221	11	≤	≤	NUM
ejpam-5699	221	12	max{n+	max{n+	PROPN
ejpam-5699	221	13	b	b	PROPN
ejpam-5699	221	14	(	(	PUNCT
ejpam-5699	221	15	(	(	PUNCT
ejpam-5699	221	16	(	(	PUNCT
ejpam-5699	221	17	g1	g1	VERB
ejpam-5699	221	18	⋄	⋄	PROPN
ejpam-5699	221	19	11	11	NUM
ejpam-5699	221	20	)	)	PUNCT
ejpam-5699	221	21	⋄	⋄	NOUN
ejpam-5699	221	22	11	11	NUM
ejpam-5699	221	23	)	)	PUNCT
ejpam-5699	221	24	⋄	⋄	NOUN
ejpam-5699	221	25	(	(	PUNCT
ejpam-5699	221	26	è1	è1	NOUN
ejpam-5699	221	27	⋄	⋄	NOUN
ejpam-5699	221	28	11)),n+	11)),n+	NUM
ejpam-5699	221	29	b	b	NOUN
ejpam-5699	221	30	(	(	PUNCT
ejpam-5699	221	31	è1	è1	ADJ
ejpam-5699	221	32	⋄	⋄	PROPN
ejpam-5699	221	33	11	11	NUM
ejpam-5699	221	34	)	)	PUNCT
ejpam-5699	221	35	}	}	PUNCT
ejpam-5699	221	36	d.	d.	PROPN
ejpam-5699	221	37	ramesh	ramesh	PROPN
ejpam-5699	221	38	et	et	PROPN
ejpam-5699	221	39	al	al	PROPN
ejpam-5699	221	40	.	.	PUNCT
ejpam-5699	221	41	/	/	SYM
ejpam-5699	221	42	eur	eur	PROPN
ejpam-5699	221	43	.	.	PUNCT
ejpam-5699	222	1	j.	j.	PROPN
ejpam-5699	222	2	pure	pure	PROPN
ejpam-5699	222	3	appl	appl	PROPN
ejpam-5699	222	4	.	.	PROPN
ejpam-5699	222	5	math	math	PROPN
ejpam-5699	222	6	,	,	PUNCT
ejpam-5699	222	7	18	18	NUM
ejpam-5699	222	8	(	(	PUNCT
ejpam-5699	222	9	1	1	NUM
ejpam-5699	222	10	)	)	PUNCT
ejpam-5699	222	11	(	(	PUNCT
ejpam-5699	222	12	2025	2025	NUM
ejpam-5699	222	13	)	)	PUNCT
ejpam-5699	222	14	,	,	PUNCT
ejpam-5699	222	15	5699	5699	NUM
ejpam-5699	222	16	14	14	NUM
ejpam-5699	222	17	of	of	ADP
ejpam-5699	222	18	20	20	NUM
ejpam-5699	222	19	≤	≤	NUM
ejpam-5699	222	20	max{n+	max{n+	PROPN
ejpam-5699	222	21	b	b	PROPN
ejpam-5699	222	22	(	(	PUNCT
ejpam-5699	222	23	(	(	PUNCT
ejpam-5699	222	24	g1	g1	PROPN
ejpam-5699	222	25	⋄	⋄	PROPN
ejpam-5699	222	26	è1	è1	PROPN
ejpam-5699	222	27	)	)	PUNCT
ejpam-5699	222	28	⋄	⋄	PROPN
ejpam-5699	223	1	11),n+	11),n+	NUM
ejpam-5699	223	2	b	b	PROPN
ejpam-5699	223	3	(	(	PUNCT
ejpam-5699	223	4	è1	è1	ADJ
ejpam-5699	223	5	⋄	⋄	NOUN
ejpam-5699	223	6	11	11	NUM
ejpam-5699	223	7	)	)	PUNCT
ejpam-5699	223	8	}	}	PUNCT
ejpam-5699	223	9	,	,	PUNCT
ejpam-5699	223	10	n−	n−	PROPN
ejpam-5699	223	11	b	b	X
ejpam-5699	223	12	(	(	PUNCT
ejpam-5699	223	13	g1	g1	VERB
ejpam-5699	223	14	⋄	⋄	PROPN
ejpam-5699	223	15	11	11	NUM
ejpam-5699	223	16	)	)	PUNCT
ejpam-5699	223	17	≥	≥	NOUN
ejpam-5699	223	18	n−	n−	PROPN
ejpam-5699	223	19	b	b	X
ejpam-5699	223	20	(	(	PUNCT
ejpam-5699	223	21	(	(	PUNCT
ejpam-5699	223	22	g1	g1	VERB
ejpam-5699	223	23	⋄	⋄	PROPN
ejpam-5699	223	24	11	11	NUM
ejpam-5699	223	25	)	)	PUNCT
ejpam-5699	223	26	⋄	⋄	NOUN
ejpam-5699	223	27	11	11	NUM
ejpam-5699	223	28	)	)	PUNCT
ejpam-5699	223	29	≥	≥	NOUN
ejpam-5699	223	30	min{n−	min{n−	PROPN
ejpam-5699	223	31	b	b	PROPN
ejpam-5699	223	32	(	(	PUNCT
ejpam-5699	223	33	(	(	PUNCT
ejpam-5699	223	34	(	(	PUNCT
ejpam-5699	223	35	g1	g1	VERB
ejpam-5699	223	36	⋄	⋄	PROPN
ejpam-5699	223	37	11	11	NUM
ejpam-5699	223	38	)	)	PUNCT
ejpam-5699	223	39	⋄	⋄	NOUN
ejpam-5699	223	40	11	11	NUM
ejpam-5699	223	41	)	)	PUNCT
ejpam-5699	223	42	⋄	⋄	NOUN
ejpam-5699	223	43	(	(	PUNCT
ejpam-5699	223	44	è1	è1	ADP
ejpam-5699	223	45	⋄	⋄	PROPN
ejpam-5699	223	46	11)),n−	11)),n−	NUM
ejpam-5699	223	47	b	b	NOUN
ejpam-5699	223	48	(	(	PUNCT
ejpam-5699	223	49	è1	è1	ADJ
ejpam-5699	223	50	⋄	⋄	PROPN
ejpam-5699	223	51	11	11	NUM
ejpam-5699	223	52	)	)	PUNCT
ejpam-5699	223	53	}	}	PUNCT
ejpam-5699	223	54	≥	≥	VERB
ejpam-5699	223	55	min{n−	min{n−	PROPN
ejpam-5699	223	56	b	b	PROPN
ejpam-5699	223	57	(	(	PUNCT
ejpam-5699	223	58	(	(	PUNCT
ejpam-5699	223	59	g1	g1	PROPN
ejpam-5699	223	60	⋄	⋄	PROPN
ejpam-5699	223	61	è1	è1	PROPN
ejpam-5699	223	62	)	)	PUNCT
ejpam-5699	223	63	⋄	⋄	PROPN
ejpam-5699	224	1	11),n−	11),n−	NUM
ejpam-5699	224	2	b	b	PROPN
ejpam-5699	224	3	(	(	PUNCT
ejpam-5699	224	4	è1	è1	ADJ
ejpam-5699	224	5	⋄	⋄	NOUN
ejpam-5699	224	6	11	11	NUM
ejpam-5699	224	7	)	)	PUNCT
ejpam-5699	224	8	}	}	PUNCT
ejpam-5699	224	9	.	.	PUNCT
ejpam-5699	225	1	therefore	therefore	ADV
ejpam-5699	225	2	,	,	PUNCT
ejpam-5699	225	3	b	b	X
ejpam-5699	225	4	=	=	SYM
ejpam-5699	225	5	(	(	PUNCT
ejpam-5699	225	6	m+	m+	NUM
ejpam-5699	225	7	b	b	NOUN
ejpam-5699	225	8	,	,	PUNCT
ejpam-5699	225	9	m−	m−	PROPN
ejpam-5699	225	10	b	b	PROPN
ejpam-5699	225	11	,	,	PUNCT
ejpam-5699	225	12	n+	n+	NOUN
ejpam-5699	225	13	b	b	NOUN
ejpam-5699	225	14	,	,	PUNCT
ejpam-5699	225	15	n−	n−	PROPN
ejpam-5699	225	16	b	b	X
ejpam-5699	225	17	)	)	PUNCT
ejpam-5699	225	18	is	be	AUX
ejpam-5699	225	19	a	a	DET
ejpam-5699	225	20	bpvifpii	bpvifpii	NOUN
ejpam-5699	225	21	of	of	ADP
ejpam-5699	225	22	g.	g.	PROPN
ejpam-5699	225	23	theorem	theorem	VERB
ejpam-5699	225	24	7	7	NUM
ejpam-5699	225	25	.	.	PUNCT
ejpam-5699	226	1	a	a	DET
ejpam-5699	226	2	bpvifs	bpvifs	PROPN
ejpam-5699	226	3	b	b	PROPN
ejpam-5699	226	4	=	=	PUNCT
ejpam-5699	226	5	(	(	PUNCT
ejpam-5699	226	6	m+	m+	NUM
ejpam-5699	226	7	b	b	NOUN
ejpam-5699	226	8	,	,	PUNCT
ejpam-5699	226	9	m−	m−	PROPN
ejpam-5699	226	10	b	b	PROPN
ejpam-5699	226	11	,	,	PUNCT
ejpam-5699	226	12	n+	n+	NOUN
ejpam-5699	226	13	b	b	NOUN
ejpam-5699	226	14	,	,	PUNCT
ejpam-5699	226	15	n−	n−	PROPN
ejpam-5699	226	16	b	b	NOUN
ejpam-5699	226	17	)	)	PUNCT
ejpam-5699	226	18	in	in	ADP
ejpam-5699	226	19	g	g	PROPN
ejpam-5699	226	20	is	be	AUX
ejpam-5699	226	21	a	a	DET
ejpam-5699	226	22	bpvifpii	bpvifpii	NOUN
ejpam-5699	226	23	of	of	ADP
ejpam-5699	226	24	g	g	NOUN
ejpam-5699	226	25	if	if	SCONJ
ejpam-5699	227	1	and	and	CCONJ
ejpam-5699	227	2	only	only	ADV
ejpam-5699	227	3	if	if	SCONJ
ejpam-5699	227	4	it	it	PRON
ejpam-5699	227	5	satisfies	satisfy	VERB
ejpam-5699	227	6	(	(	PUNCT
ejpam-5699	227	7	bpvifi-1	bpvifi-1	X
ejpam-5699	227	8	)	)	PUNCT
ejpam-5699	227	9	and	and	CCONJ
ejpam-5699	227	10	the	the	DET
ejpam-5699	227	11	following	follow	VERB
ejpam-5699	227	12	condition:	condition:	NOUN
ejpam-5699	227	13	m+	m+	NUM
ejpam-5699	227	14	b(g1	b(g1	PROPN
ejpam-5699	227	15	⋄	⋄	PROPN
ejpam-5699	227	16	è1	è1	PROPN
ejpam-5699	227	17	)	)	PUNCT
ejpam-5699	227	18	≥	≥	NOUN
ejpam-5699	227	19	min{m+	min{m+	PROPN
ejpam-5699	227	20	b(((g1	b(((g1	PART
ejpam-5699	227	21	⋄	⋄	PROPN
ejpam-5699	227	22	è1	è1	PROPN
ejpam-5699	227	23	)	)	PUNCT
ejpam-5699	227	24	⋄	⋄	PROPN
ejpam-5699	227	25	è1	è1	PROPN
ejpam-5699	227	26	)	)	PUNCT
ejpam-5699	227	27	⋄	⋄	PROPN
ejpam-5699	227	28	11),m+	11),m+	NUM
ejpam-5699	227	29	b(11	b(11	NOUN
ejpam-5699	227	30	)	)	PUNCT
ejpam-5699	227	31	}	}	PUNCT
ejpam-5699	227	32	,	,	PUNCT
ejpam-5699	227	33	m−	m−	PROPN
ejpam-5699	227	34	b(g1	b(g1	PROPN
ejpam-5699	227	35	⋄	⋄	PROPN
ejpam-5699	227	36	è1	è1	PROPN
ejpam-5699	227	37	)	)	PUNCT
ejpam-5699	227	38	≤	≤	NOUN
ejpam-5699	227	39	max{m−	max{m−	NOUN
ejpam-5699	227	40	b(((g1	b(((g1	VERB
ejpam-5699	227	41	⋄	⋄	NOUN
ejpam-5699	227	42	è1	è1	NOUN
ejpam-5699	227	43	)	)	PUNCT
ejpam-5699	227	44	⋄	⋄	PROPN
ejpam-5699	227	45	è1	è1	PROPN
ejpam-5699	227	46	)	)	PUNCT
ejpam-5699	227	47	⋄	⋄	PROPN
ejpam-5699	227	48	11),m−	11),m−	NUM
ejpam-5699	227	49	b(11	b(11	NOUN
ejpam-5699	227	50	)	)	PUNCT
ejpam-5699	227	51	}	}	PUNCT
ejpam-5699	227	52	,	,	PUNCT
ejpam-5699	227	53	n+	n+	ADP
ejpam-5699	227	54	b	b	X
ejpam-5699	227	55	(	(	PUNCT
ejpam-5699	227	56	g1	g1	PROPN
ejpam-5699	227	57	⋄	⋄	PROPN
ejpam-5699	227	58	è1	è1	PROPN
ejpam-5699	227	59	)	)	PUNCT
ejpam-5699	227	60	≤	≤	NUM
ejpam-5699	228	1	max{n+	max{n+	PROPN
ejpam-5699	228	2	b	b	PROPN
ejpam-5699	228	3	(	(	PUNCT
ejpam-5699	228	4	(	(	PUNCT
ejpam-5699	228	5	(	(	PUNCT
ejpam-5699	228	6	g1	g1	PROPN
ejpam-5699	228	7	⋄	⋄	PROPN
ejpam-5699	228	8	è1	è1	PROPN
ejpam-5699	228	9	)	)	PUNCT
ejpam-5699	228	10	⋄	⋄	PROPN
ejpam-5699	228	11	è1	è1	PROPN
ejpam-5699	228	12	)	)	PUNCT
ejpam-5699	228	13	⋄	⋄	NOUN
ejpam-5699	229	1	11),n+	11),n+	NUM
ejpam-5699	229	2	b	b	PROPN
ejpam-5699	229	3	(	(	PUNCT
ejpam-5699	229	4	11	11	NUM
ejpam-5699	229	5	)	)	PUNCT
ejpam-5699	229	6	}	}	PUNCT
ejpam-5699	229	7	,	,	PUNCT
ejpam-5699	229	8	n−	n−	PROPN
ejpam-5699	229	9	b	b	X
ejpam-5699	229	10	(	(	PUNCT
ejpam-5699	229	11	g1	g1	PROPN
ejpam-5699	229	12	⋄	⋄	PROPN
ejpam-5699	229	13	è1	è1	PROPN
ejpam-5699	229	14	)	)	PUNCT
ejpam-5699	229	15	≥	≥	NOUN
ejpam-5699	229	16	min{n−	min{n−	PROPN
ejpam-5699	229	17	b	b	PROPN
ejpam-5699	229	18	(	(	PUNCT
ejpam-5699	229	19	(	(	PUNCT
ejpam-5699	229	20	(	(	PUNCT
ejpam-5699	229	21	g1	g1	PROPN
ejpam-5699	229	22	⋄	⋄	PROPN
ejpam-5699	229	23	è1	è1	PROPN
ejpam-5699	229	24	)	)	PUNCT
ejpam-5699	229	25	⋄	⋄	PROPN
ejpam-5699	229	26	è1	è1	PROPN
ejpam-5699	229	27	)	)	PUNCT
ejpam-5699	229	28	⋄	⋄	PROPN
ejpam-5699	229	29	11),n−	11),n−	NUM
ejpam-5699	229	30	b	b	PROPN
ejpam-5699	229	31	(	(	PUNCT
ejpam-5699	229	32	11	11	NUM
ejpam-5699	229	33	)	)	PUNCT
ejpam-5699	229	34	}	}	PUNCT
ejpam-5699	229	35	,	,	PUNCT
ejpam-5699	229	36			NOUN
ejpam-5699	229	37	(	(	PUNCT
ejpam-5699	229	38	15	15	NUM
ejpam-5699	229	39	)	)	PUNCT
ejpam-5699	229	40	for	for	ADP
ejpam-5699	229	41	all	all	DET
ejpam-5699	229	42	g1,è1	g1,è1	PROPN
ejpam-5699	229	43	,	,	PUNCT
ejpam-5699	229	44	11	11	NUM
ejpam-5699	229	45	∈	∈	NOUN
ejpam-5699	229	46	g.	g.	NOUN
ejpam-5699	229	47	proof	proof	NOUN
ejpam-5699	229	48	.	.	PUNCT
ejpam-5699	230	1	assume	assume	VERB
ejpam-5699	230	2	that	that	SCONJ
ejpam-5699	230	3	b	b	X
ejpam-5699	230	4	=	=	SYM
ejpam-5699	230	5	(	(	PUNCT
ejpam-5699	230	6	m+	m+	NUM
ejpam-5699	230	7	b	b	NOUN
ejpam-5699	230	8	,	,	PUNCT
ejpam-5699	230	9	m−	m−	PROPN
ejpam-5699	230	10	b	b	PROPN
ejpam-5699	230	11	,	,	PUNCT
ejpam-5699	230	12	n+	n+	NOUN
ejpam-5699	230	13	b	b	NOUN
ejpam-5699	230	14	,	,	PUNCT
ejpam-5699	230	15	n−	n−	PROPN
ejpam-5699	230	16	b	b	X
ejpam-5699	230	17	)	)	PUNCT
ejpam-5699	230	18	is	be	AUX
ejpam-5699	230	19	a	a	DET
ejpam-5699	230	20	bpvifpii	bpvifpii	NOUN
ejpam-5699	230	21	of	of	ADP
ejpam-5699	230	22	g.	g.	PROPN
ejpam-5699	230	23	then	then	ADV
ejpam-5699	230	24	,	,	PUNCT
ejpam-5699	230	25	b	b	X
ejpam-5699	230	26	=	=	SYM
ejpam-5699	230	27	(	(	PUNCT
ejpam-5699	230	28	m+	m+	NUM
ejpam-5699	230	29	b	b	NOUN
ejpam-5699	230	30	,	,	PUNCT
ejpam-5699	230	31	m−	m−	PROPN
ejpam-5699	230	32	b	b	PROPN
ejpam-5699	230	33	,	,	PUNCT
ejpam-5699	230	34	n+	n+	NOUN
ejpam-5699	230	35	b	b	NOUN
ejpam-5699	230	36	,	,	PUNCT
ejpam-5699	230	37	n−	n−	PROPN
ejpam-5699	230	38	b	b	X
ejpam-5699	230	39	)	)	PUNCT
ejpam-5699	230	40	is	be	AUX
ejpam-5699	230	41	a	a	DET
ejpam-5699	230	42	bpvifi	bpvifi	NOUN
ejpam-5699	230	43	of	of	ADP
ejpam-5699	230	44	g	g	NOUN
ejpam-5699	230	45	by	by	ADP
ejpam-5699	230	46	theorem	theorem	NOUN
ejpam-5699	230	47	3	3	NUM
ejpam-5699	230	48	,	,	PUNCT
ejpam-5699	230	49	and	and	CCONJ
ejpam-5699	230	50	thus	thus	ADV
ejpam-5699	230	51	,	,	PUNCT
ejpam-5699	230	52	it	it	PRON
ejpam-5699	230	53	satisfies	satisfy	VERB
ejpam-5699	230	54	(	(	PUNCT
ejpam-5699	230	55	bpvifi-1	bpvifi-1	NUM
ejpam-5699	230	56	)	)	PUNCT
ejpam-5699	230	57	.	.	PUNCT
ejpam-5699	231	1	now	now	ADV
ejpam-5699	231	2	,	,	PUNCT
ejpam-5699	231	3	m+	m+	AUX
ejpam-5699	231	4	b(g1	b(g1	ADJ
ejpam-5699	231	5	⋄	⋄	PROPN
ejpam-5699	231	6	è1	è1	PROPN
ejpam-5699	231	7	)	)	PUNCT
ejpam-5699	231	8	≥	≥	NOUN
ejpam-5699	231	9	min{m+	min{m+	PROPN
ejpam-5699	231	10	b((g1	b((g1	PROPN
ejpam-5699	231	11	⋄	⋄	PROPN
ejpam-5699	231	12	è1	è1	PROPN
ejpam-5699	231	13	)	)	PUNCT
ejpam-5699	231	14	⋄	⋄	PROPN
ejpam-5699	231	15	11),m+	11),m+	NUM
ejpam-5699	231	16	b(11	b(11	NOUN
ejpam-5699	231	17	)	)	PUNCT
ejpam-5699	231	18	}	}	PUNCT
ejpam-5699	231	19	=	=	PUNCT
ejpam-5699	231	20	min{m+	min{m+	PROPN
ejpam-5699	231	21	b(((g1	b(((g1	PART
ejpam-5699	231	22	⋄	⋄	PROPN
ejpam-5699	231	23	è1	è1	NOUN
ejpam-5699	231	24	)	)	PUNCT
ejpam-5699	231	25	⋄	⋄	NOUN
ejpam-5699	231	26	11	11	NUM
ejpam-5699	231	27	)	)	PUNCT
ejpam-5699	231	28	⋄	⋄	NOUN
ejpam-5699	231	29	(	(	PUNCT
ejpam-5699	231	30	è1	è1	ADP
ejpam-5699	231	31	⋄	⋄	PROPN
ejpam-5699	231	32	è1)),m+	è1)),m+	PROPN
ejpam-5699	231	33	b(11	b(11	PROPN
ejpam-5699	231	34	)	)	PUNCT
ejpam-5699	231	35	}	}	PUNCT
ejpam-5699	232	1	=	=	PUNCT
ejpam-5699	232	2	min{m+	min{m+	PROPN
ejpam-5699	232	3	b(((g1	b(((g1	PART
ejpam-5699	232	4	⋄	⋄	NOUN
ejpam-5699	232	5	11	11	NUM
ejpam-5699	232	6	)	)	PUNCT
ejpam-5699	232	7	⋄	⋄	PROPN
ejpam-5699	232	8	è1	è1	PROPN
ejpam-5699	232	9	)	)	PUNCT
ejpam-5699	232	10	⋄	⋄	NOUN
ejpam-5699	232	11	(	(	PUNCT
ejpam-5699	232	12	è1	è1	ADP
ejpam-5699	232	13	⋄	⋄	PROPN
ejpam-5699	232	14	è1)),m+	è1)),m+	PROPN
ejpam-5699	232	15	b(11	b(11	PROPN
ejpam-5699	232	16	)	)	PUNCT
ejpam-5699	232	17	}	}	PUNCT
ejpam-5699	232	18	≥	≥	X
ejpam-5699	232	19	min{m+	min{m+	PROPN
ejpam-5699	232	20	b((g1	b((g1	PROPN
ejpam-5699	232	21	⋄	⋄	PROPN
ejpam-5699	232	22	11	11	NUM
ejpam-5699	232	23	)	)	PUNCT
ejpam-5699	232	24	⋄	⋄	PROPN
ejpam-5699	232	25	è1),m+	è1),m+	NOUN
ejpam-5699	232	26	b(11	b(11	NOUN
ejpam-5699	232	27	)	)	PUNCT
ejpam-5699	232	28	}	}	PUNCT
ejpam-5699	232	29	≥	≥	AUX
ejpam-5699	232	30	min{m+	min{m+	PROPN
ejpam-5699	232	31	b(((g1	b(((g1	PART
ejpam-5699	232	32	⋄	⋄	NOUN
ejpam-5699	232	33	11	11	NUM
ejpam-5699	232	34	)	)	PUNCT
ejpam-5699	232	35	⋄	⋄	PROPN
ejpam-5699	232	36	è1	è1	PROPN
ejpam-5699	232	37	)	)	PUNCT
ejpam-5699	232	38	⋄	⋄	PROPN
ejpam-5699	232	39	è1),m+	è1),m+	NOUN
ejpam-5699	232	40	b(11	b(11	NOUN
ejpam-5699	232	41	)	)	PUNCT
ejpam-5699	232	42	}	}	PUNCT
ejpam-5699	233	1	=	=	PUNCT
ejpam-5699	233	2	min{m+	min{m+	PROPN
ejpam-5699	233	3	b(((g1	b(((g1	PART
ejpam-5699	233	4	⋄	⋄	PROPN
ejpam-5699	233	5	è1	è1	PROPN
ejpam-5699	233	6	)	)	PUNCT
ejpam-5699	233	7	⋄	⋄	PROPN
ejpam-5699	233	8	è1	è1	PROPN
ejpam-5699	233	9	)	)	PUNCT
ejpam-5699	233	10	⋄	⋄	PROPN
ejpam-5699	233	11	11),m+	11),m+	NUM
ejpam-5699	233	12	b(11	b(11	NOUN
ejpam-5699	233	13	)	)	PUNCT
ejpam-5699	233	14	}	}	PUNCT
ejpam-5699	233	15	,	,	PUNCT
ejpam-5699	233	16	m−	m−	PROPN
ejpam-5699	233	17	b(g1	b(g1	PROPN
ejpam-5699	233	18	⋄	⋄	PROPN
ejpam-5699	233	19	è1	è1	PROPN
ejpam-5699	233	20	)	)	PUNCT
ejpam-5699	233	21	≤	≤	NOUN
ejpam-5699	233	22	max{m−	max{m−	NOUN
ejpam-5699	233	23	b((g1	b((g1	NOUN
ejpam-5699	233	24	⋄	⋄	PROPN
ejpam-5699	233	25	è1	è1	PROPN
ejpam-5699	233	26	)	)	PUNCT
ejpam-5699	233	27	⋄	⋄	PROPN
ejpam-5699	233	28	11),m−	11),m−	NUM
ejpam-5699	233	29	b(11	b(11	NOUN
ejpam-5699	233	30	)	)	PUNCT
ejpam-5699	233	31	}	}	PUNCT
ejpam-5699	234	1	=	=	SYM
ejpam-5699	234	2	max{m−	max{m−	NOUN
ejpam-5699	234	3	b(((g1	b(((g1	VERB
ejpam-5699	234	4	⋄	⋄	NOUN
ejpam-5699	234	5	è1	è1	NOUN
ejpam-5699	234	6	)	)	PUNCT
ejpam-5699	234	7	⋄	⋄	NOUN
ejpam-5699	234	8	11	11	NUM
ejpam-5699	234	9	)	)	PUNCT
ejpam-5699	234	10	⋄	⋄	NOUN
ejpam-5699	234	11	(	(	PUNCT
ejpam-5699	234	12	è1	è1	PROPN
ejpam-5699	234	13	⋄	⋄	PROPN
ejpam-5699	234	14	è1)),m−	è1)),m−	NOUN
ejpam-5699	234	15	b(11	b(11	NOUN
ejpam-5699	234	16	)	)	PUNCT
ejpam-5699	234	17	}	}	PUNCT
ejpam-5699	235	1	=	=	SYM
ejpam-5699	235	2	max{m−	max{m−	NOUN
ejpam-5699	235	3	b(((g1	b(((g1	VERB
ejpam-5699	235	4	⋄	⋄	NOUN
ejpam-5699	235	5	11	11	NUM
ejpam-5699	235	6	)	)	PUNCT
ejpam-5699	235	7	⋄	⋄	PROPN
ejpam-5699	235	8	è1	è1	PROPN
ejpam-5699	235	9	)	)	PUNCT
ejpam-5699	235	10	⋄	⋄	NOUN
ejpam-5699	235	11	(	(	PUNCT
ejpam-5699	235	12	è1	è1	PROPN
ejpam-5699	235	13	⋄	⋄	PROPN
ejpam-5699	235	14	è1)),m−	è1)),m−	NOUN
ejpam-5699	235	15	b(11	b(11	PROPN
ejpam-5699	235	16	)	)	PUNCT
ejpam-5699	235	17	}	}	PUNCT
ejpam-5699	235	18	≤	≤	NOUN
ejpam-5699	235	19	max{m−	max{m−	NOUN
ejpam-5699	235	20	b((g1	b((g1	NOUN
ejpam-5699	235	21	⋄	⋄	NOUN
ejpam-5699	235	22	11	11	NUM
ejpam-5699	235	23	)	)	PUNCT
ejpam-5699	235	24	⋄	⋄	NOUN
ejpam-5699	235	25	è1),m−	è1),m−	PROPN
ejpam-5699	235	26	b(11	b(11	NOUN
ejpam-5699	235	27	)	)	PUNCT
ejpam-5699	235	28	}	}	PUNCT
ejpam-5699	235	29	≤	≤	NOUN
ejpam-5699	235	30	max{m−	max{m−	NOUN
ejpam-5699	235	31	b(((g1	b(((g1	VERB
ejpam-5699	235	32	⋄	⋄	NOUN
ejpam-5699	235	33	11	11	NUM
ejpam-5699	235	34	)	)	PUNCT
ejpam-5699	235	35	⋄	⋄	PROPN
ejpam-5699	235	36	è1	è1	PROPN
ejpam-5699	235	37	)	)	PUNCT
ejpam-5699	235	38	⋄	⋄	PROPN
ejpam-5699	235	39	è1),m−	è1),m−	PROPN
ejpam-5699	235	40	b(11	b(11	NOUN
ejpam-5699	235	41	)	)	PUNCT
ejpam-5699	235	42	}	}	PUNCT
ejpam-5699	236	1	=	=	SYM
ejpam-5699	236	2	max{m−	max{m−	NOUN
ejpam-5699	236	3	b(((g1	b(((g1	VERB
ejpam-5699	236	4	⋄	⋄	NOUN
ejpam-5699	236	5	è1	è1	NOUN
ejpam-5699	236	6	)	)	PUNCT
ejpam-5699	236	7	⋄	⋄	PROPN
ejpam-5699	236	8	è1	è1	PROPN
ejpam-5699	236	9	)	)	PUNCT
ejpam-5699	236	10	⋄	⋄	PROPN
ejpam-5699	236	11	11),m−	11),m−	NUM
ejpam-5699	236	12	b(11	b(11	NOUN
ejpam-5699	236	13	)	)	PUNCT
ejpam-5699	236	14	}	}	PUNCT
ejpam-5699	236	15	,	,	PUNCT
ejpam-5699	236	16	n+	n+	ADP
ejpam-5699	236	17	b	b	X
ejpam-5699	236	18	(	(	PUNCT
ejpam-5699	236	19	g1	g1	PROPN
ejpam-5699	236	20	⋄	⋄	PROPN
ejpam-5699	236	21	è1	è1	PROPN
ejpam-5699	236	22	)	)	PUNCT
ejpam-5699	236	23	≤	≤	NUM
ejpam-5699	237	1	max{n+	max{n+	PROPN
ejpam-5699	237	2	b	b	PROPN
ejpam-5699	237	3	(	(	PUNCT
ejpam-5699	237	4	(	(	PUNCT
ejpam-5699	237	5	g1	g1	PROPN
ejpam-5699	237	6	⋄	⋄	PROPN
ejpam-5699	237	7	è1	è1	PROPN
ejpam-5699	237	8	)	)	PUNCT
ejpam-5699	237	9	⋄	⋄	PROPN
ejpam-5699	238	1	11),n+	11),n+	NUM
ejpam-5699	238	2	b	b	PROPN
ejpam-5699	238	3	(	(	PUNCT
ejpam-5699	238	4	11	11	NUM
ejpam-5699	238	5	)	)	PUNCT
ejpam-5699	238	6	}	}	PUNCT
ejpam-5699	238	7	=	=	PUNCT
ejpam-5699	238	8	max{n+	max{n+	NOUN
ejpam-5699	238	9	b	b	X
ejpam-5699	238	10	(	(	PUNCT
ejpam-5699	238	11	(	(	PUNCT
ejpam-5699	238	12	(	(	PUNCT
ejpam-5699	238	13	g1	g1	PROPN
ejpam-5699	238	14	⋄	⋄	PROPN
ejpam-5699	238	15	è1	è1	PROPN
ejpam-5699	238	16	)	)	PUNCT
ejpam-5699	238	17	⋄	⋄	NOUN
ejpam-5699	238	18	11	11	NUM
ejpam-5699	238	19	)	)	PUNCT
ejpam-5699	238	20	⋄	⋄	NOUN
ejpam-5699	238	21	(	(	PUNCT
ejpam-5699	238	22	è1	è1	NOUN
ejpam-5699	238	23	⋄	⋄	PROPN
ejpam-5699	238	24	è1)),n+	è1)),n+	PROPN
ejpam-5699	238	25	b	b	PROPN
ejpam-5699	238	26	(	(	PUNCT
ejpam-5699	238	27	11	11	NUM
ejpam-5699	238	28	)	)	PUNCT
ejpam-5699	238	29	}	}	PUNCT
ejpam-5699	238	30	=	=	PUNCT
ejpam-5699	238	31	max{n+	max{n+	NOUN
ejpam-5699	238	32	b	b	X
ejpam-5699	238	33	(	(	PUNCT
ejpam-5699	238	34	(	(	PUNCT
ejpam-5699	238	35	(	(	PUNCT
ejpam-5699	238	36	g1	g1	VERB
ejpam-5699	238	37	⋄	⋄	PROPN
ejpam-5699	238	38	11	11	NUM
ejpam-5699	238	39	)	)	PUNCT
ejpam-5699	238	40	⋄	⋄	PROPN
ejpam-5699	238	41	è1	è1	PROPN
ejpam-5699	238	42	)	)	PUNCT
ejpam-5699	238	43	⋄	⋄	NOUN
ejpam-5699	238	44	(	(	PUNCT
ejpam-5699	238	45	è1	è1	NOUN
ejpam-5699	238	46	⋄	⋄	PROPN
ejpam-5699	238	47	è1)),n+	è1)),n+	PROPN
ejpam-5699	238	48	b	b	PROPN
ejpam-5699	238	49	(	(	PUNCT
ejpam-5699	238	50	11	11	NUM
ejpam-5699	238	51	)	)	PUNCT
ejpam-5699	238	52	}	}	PUNCT
ejpam-5699	238	53	≤	≤	NUM
ejpam-5699	238	54	max{n+	max{n+	PROPN
ejpam-5699	238	55	b	b	PROPN
ejpam-5699	238	56	(	(	PUNCT
ejpam-5699	238	57	(	(	PUNCT
ejpam-5699	238	58	g1	g1	VERB
ejpam-5699	238	59	⋄	⋄	PROPN
ejpam-5699	238	60	11	11	NUM
ejpam-5699	238	61	)	)	PUNCT
ejpam-5699	238	62	⋄	⋄	PROPN
ejpam-5699	238	63	è1),n+	è1),n+	PROPN
ejpam-5699	238	64	b	b	PROPN
ejpam-5699	238	65	(	(	PUNCT
ejpam-5699	238	66	11	11	NUM
ejpam-5699	238	67	)	)	PUNCT
ejpam-5699	238	68	}	}	PUNCT
ejpam-5699	238	69	≤	≤	NUM
ejpam-5699	238	70	max{n+	max{n+	PROPN
ejpam-5699	238	71	b	b	PROPN
ejpam-5699	238	72	(	(	PUNCT
ejpam-5699	238	73	(	(	PUNCT
ejpam-5699	238	74	(	(	PUNCT
ejpam-5699	238	75	g1	g1	VERB
ejpam-5699	238	76	⋄	⋄	PROPN
ejpam-5699	238	77	11	11	NUM
ejpam-5699	238	78	)	)	PUNCT
ejpam-5699	238	79	⋄	⋄	PROPN
ejpam-5699	238	80	è1	è1	PROPN
ejpam-5699	238	81	)	)	PUNCT
ejpam-5699	238	82	⋄	⋄	PROPN
ejpam-5699	238	83	è1),n+	è1),n+	PROPN
ejpam-5699	238	84	b	b	PROPN
ejpam-5699	238	85	(	(	PUNCT
ejpam-5699	238	86	11	11	NUM
ejpam-5699	238	87	)	)	PUNCT
ejpam-5699	238	88	}	}	PUNCT
ejpam-5699	238	89	d.	d.	PROPN
ejpam-5699	238	90	ramesh	ramesh	PROPN
ejpam-5699	238	91	et	et	PROPN
ejpam-5699	238	92	al	al	PROPN
ejpam-5699	238	93	.	.	PUNCT
ejpam-5699	238	94	/	/	SYM
ejpam-5699	238	95	eur	eur	PROPN
ejpam-5699	238	96	.	.	PUNCT
ejpam-5699	239	1	j.	j.	PROPN
ejpam-5699	239	2	pure	pure	PROPN
ejpam-5699	239	3	appl	appl	PROPN
ejpam-5699	239	4	.	.	PROPN
ejpam-5699	239	5	math	math	PROPN
ejpam-5699	239	6	,	,	PUNCT
ejpam-5699	239	7	18	18	NUM
ejpam-5699	239	8	(	(	PUNCT
ejpam-5699	239	9	1	1	NUM
ejpam-5699	239	10	)	)	PUNCT
ejpam-5699	239	11	(	(	PUNCT
ejpam-5699	239	12	2025	2025	NUM
ejpam-5699	239	13	)	)	PUNCT
ejpam-5699	239	14	,	,	PUNCT
ejpam-5699	239	15	5699	5699	NUM
ejpam-5699	239	16	15	15	NUM
ejpam-5699	239	17	of	of	ADP
ejpam-5699	239	18	20	20	NUM
ejpam-5699	239	19	=	=	SYM
ejpam-5699	239	20	max{n+	max{n+	PROPN
ejpam-5699	239	21	b	b	PROPN
ejpam-5699	239	22	(	(	PUNCT
ejpam-5699	239	23	(	(	PUNCT
ejpam-5699	239	24	(	(	PUNCT
ejpam-5699	239	25	g1	g1	PROPN
ejpam-5699	239	26	⋄	⋄	PROPN
ejpam-5699	239	27	è1	è1	PROPN
ejpam-5699	239	28	)	)	PUNCT
ejpam-5699	239	29	⋄	⋄	PROPN
ejpam-5699	239	30	è1	è1	PROPN
ejpam-5699	239	31	)	)	PUNCT
ejpam-5699	239	32	⋄	⋄	NOUN
ejpam-5699	240	1	11),n+	11),n+	NUM
ejpam-5699	240	2	b	b	PROPN
ejpam-5699	240	3	(	(	PUNCT
ejpam-5699	240	4	11	11	NUM
ejpam-5699	240	5	)	)	PUNCT
ejpam-5699	240	6	}	}	PUNCT
ejpam-5699	240	7	,	,	PUNCT
ejpam-5699	240	8	n−	n−	PROPN
ejpam-5699	240	9	b	b	X
ejpam-5699	240	10	(	(	PUNCT
ejpam-5699	240	11	g1	g1	PROPN
ejpam-5699	240	12	⋄	⋄	PROPN
ejpam-5699	240	13	è1	è1	PROPN
ejpam-5699	240	14	)	)	PUNCT
ejpam-5699	240	15	≥	≥	NOUN
ejpam-5699	240	16	min{n−	min{n−	PROPN
ejpam-5699	240	17	b	b	PROPN
ejpam-5699	240	18	(	(	PUNCT
ejpam-5699	240	19	(	(	PUNCT
ejpam-5699	240	20	g1	g1	PROPN
ejpam-5699	240	21	⋄	⋄	PROPN
ejpam-5699	240	22	è1	è1	PROPN
ejpam-5699	240	23	)	)	PUNCT
ejpam-5699	240	24	⋄	⋄	PROPN
ejpam-5699	240	25	11),n−	11),n−	NUM
ejpam-5699	240	26	b	b	PROPN
ejpam-5699	240	27	(	(	PUNCT
ejpam-5699	240	28	11	11	NUM
ejpam-5699	240	29	)	)	PUNCT
ejpam-5699	240	30	}	}	PUNCT
ejpam-5699	240	31	=	=	SYM
ejpam-5699	240	32	min{n−	min{n−	PROPN
ejpam-5699	240	33	b	b	PROPN
ejpam-5699	240	34	(	(	PUNCT
ejpam-5699	240	35	(	(	PUNCT
ejpam-5699	240	36	(	(	PUNCT
ejpam-5699	240	37	g1	g1	PROPN
ejpam-5699	240	38	⋄	⋄	PROPN
ejpam-5699	240	39	è1	è1	PROPN
ejpam-5699	240	40	)	)	PUNCT
ejpam-5699	240	41	⋄	⋄	NOUN
ejpam-5699	240	42	11	11	NUM
ejpam-5699	240	43	)	)	PUNCT
ejpam-5699	240	44	⋄	⋄	NOUN
ejpam-5699	240	45	(	(	PUNCT
ejpam-5699	240	46	è1	è1	PROPN
ejpam-5699	240	47	⋄	⋄	PROPN
ejpam-5699	240	48	è1)),n−	è1)),n−	NOUN
ejpam-5699	240	49	b	b	NOUN
ejpam-5699	240	50	(	(	PUNCT
ejpam-5699	240	51	11	11	NUM
ejpam-5699	240	52	)	)	PUNCT
ejpam-5699	240	53	}	}	PUNCT
ejpam-5699	240	54	=	=	SYM
ejpam-5699	240	55	min{n−	min{n−	PROPN
ejpam-5699	240	56	b	b	PROPN
ejpam-5699	240	57	(	(	PUNCT
ejpam-5699	240	58	(	(	PUNCT
ejpam-5699	240	59	(	(	PUNCT
ejpam-5699	240	60	g1	g1	VERB
ejpam-5699	240	61	⋄	⋄	PROPN
ejpam-5699	240	62	11	11	NUM
ejpam-5699	240	63	)	)	PUNCT
ejpam-5699	240	64	⋄	⋄	PROPN
ejpam-5699	240	65	è1	è1	PROPN
ejpam-5699	240	66	)	)	PUNCT
ejpam-5699	240	67	⋄	⋄	NOUN
ejpam-5699	240	68	(	(	PUNCT
ejpam-5699	240	69	è1	è1	PROPN
ejpam-5699	240	70	⋄	⋄	PROPN
ejpam-5699	240	71	è1)),n−	è1)),n−	NOUN
ejpam-5699	240	72	b	b	NOUN
ejpam-5699	240	73	(	(	PUNCT
ejpam-5699	240	74	11	11	NUM
ejpam-5699	240	75	)	)	PUNCT
ejpam-5699	240	76	}	}	PUNCT
ejpam-5699	240	77	≥	≥	VERB
ejpam-5699	240	78	min{n−	min{n−	PROPN
ejpam-5699	240	79	b	b	PROPN
ejpam-5699	240	80	(	(	PUNCT
ejpam-5699	240	81	(	(	PUNCT
ejpam-5699	240	82	g1	g1	VERB
ejpam-5699	240	83	⋄	⋄	PROPN
ejpam-5699	240	84	11	11	NUM
ejpam-5699	240	85	)	)	PUNCT
ejpam-5699	240	86	⋄	⋄	PROPN
ejpam-5699	240	87	è1),n−	è1),n−	PROPN
ejpam-5699	240	88	b	b	PROPN
ejpam-5699	240	89	(	(	PUNCT
ejpam-5699	240	90	11	11	NUM
ejpam-5699	240	91	)	)	PUNCT
ejpam-5699	240	92	}	}	PUNCT
ejpam-5699	240	93	≥	≥	VERB
ejpam-5699	240	94	min{n−	min{n−	PROPN
ejpam-5699	240	95	b	b	PROPN
ejpam-5699	240	96	(	(	PUNCT
ejpam-5699	240	97	(	(	PUNCT
ejpam-5699	240	98	(	(	PUNCT
ejpam-5699	240	99	g1	g1	VERB
ejpam-5699	240	100	⋄	⋄	PROPN
ejpam-5699	240	101	11	11	NUM
ejpam-5699	240	102	)	)	PUNCT
ejpam-5699	240	103	⋄	⋄	PROPN
ejpam-5699	240	104	è1	è1	PROPN
ejpam-5699	240	105	)	)	PUNCT
ejpam-5699	241	1	⋄	⋄	PROPN
ejpam-5699	241	2	è1),n−	è1),n−	PROPN
ejpam-5699	241	3	b	b	PROPN
ejpam-5699	241	4	(	(	PUNCT
ejpam-5699	241	5	11	11	NUM
ejpam-5699	241	6	)	)	PUNCT
ejpam-5699	241	7	}	}	PUNCT
ejpam-5699	242	1	=	=	SYM
ejpam-5699	242	2	min{n−	min{n−	PROPN
ejpam-5699	242	3	b	b	PROPN
ejpam-5699	242	4	(	(	PUNCT
ejpam-5699	242	5	(	(	PUNCT
ejpam-5699	242	6	(	(	PUNCT
ejpam-5699	242	7	g1	g1	PROPN
ejpam-5699	242	8	⋄	⋄	PROPN
ejpam-5699	242	9	è1	è1	PROPN
ejpam-5699	242	10	)	)	PUNCT
ejpam-5699	242	11	⋄	⋄	PROPN
ejpam-5699	242	12	è1	è1	PROPN
ejpam-5699	242	13	)	)	PUNCT
ejpam-5699	242	14	⋄	⋄	PROPN
ejpam-5699	243	1	11),n−	11),n−	NUM
ejpam-5699	243	2	b	b	PROPN
ejpam-5699	243	3	(	(	PUNCT
ejpam-5699	243	4	11	11	NUM
ejpam-5699	243	5	)	)	PUNCT
ejpam-5699	243	6	}	}	PUNCT
ejpam-5699	243	7	,	,	PUNCT
ejpam-5699	243	8	for	for	ADP
ejpam-5699	243	9	all	all	DET
ejpam-5699	243	10	g1,è1	g1,è1	PROPN
ejpam-5699	243	11	,	,	PUNCT
ejpam-5699	243	12	11	11	NUM
ejpam-5699	243	13	∈	∈	NOUN
ejpam-5699	243	14	g.	g.	NOUN
ejpam-5699	243	15	hence	hence	ADV
ejpam-5699	243	16	,	,	PUNCT
ejpam-5699	243	17	(	(	PUNCT
ejpam-5699	243	18	15	15	NUM
ejpam-5699	243	19	)	)	PUNCT
ejpam-5699	243	20	holds	hold	VERB
ejpam-5699	243	21	.	.	PUNCT
ejpam-5699	244	1	conversely	conversely	ADV
ejpam-5699	244	2	,	,	PUNCT
ejpam-5699	244	3	let	let	VERB
ejpam-5699	244	4	b	b	X
ejpam-5699	244	5	=	=	SYM
ejpam-5699	244	6	(	(	PUNCT
ejpam-5699	244	7	m+	m+	NUM
ejpam-5699	244	8	b	b	NOUN
ejpam-5699	244	9	,	,	PUNCT
ejpam-5699	244	10	m−	m−	PROPN
ejpam-5699	244	11	b	b	PROPN
ejpam-5699	244	12	,	,	PUNCT
ejpam-5699	244	13	n+	n+	NOUN
ejpam-5699	244	14	b	b	NOUN
ejpam-5699	244	15	,	,	PUNCT
ejpam-5699	244	16	n−	n−	PROPN
ejpam-5699	244	17	b	b	AUX
ejpam-5699	244	18	)	)	PUNCT
ejpam-5699	244	19	be	be	AUX
ejpam-5699	244	20	a	a	DET
ejpam-5699	244	21	bpvifs	bpvif	NOUN
ejpam-5699	244	22	in	in	ADP
ejpam-5699	244	23	g	g	PROPN
ejpam-5699	244	24	which	which	DET
ejpam-5699	244	25	satisfies	satisfy	VERB
ejpam-5699	244	26	(	(	PUNCT
ejpam-5699	244	27	bpvifi1	bpvifi1	NOUN
ejpam-5699	244	28	)	)	PUNCT
ejpam-5699	244	29	and	and	CCONJ
ejpam-5699	244	30	(	(	PUNCT
ejpam-5699	244	31	15	15	NUM
ejpam-5699	244	32	)	)	PUNCT
ejpam-5699	244	33	.	.	PUNCT
ejpam-5699	245	1	then	then	ADV
ejpam-5699	245	2	,	,	PUNCT
ejpam-5699	245	3	m+	m+	NOUN
ejpam-5699	245	4	b(g1	b(g1	NOUN
ejpam-5699	245	5	)	)	PUNCT
ejpam-5699	246	1	=	=	SYM
ejpam-5699	246	2	m+	m+	NOUN
ejpam-5699	246	3	b(g1	b(g1	ADJ
ejpam-5699	246	4	⋄	⋄	PROPN
ejpam-5699	246	5	0	0	NUM
ejpam-5699	246	6	)	)	PUNCT
ejpam-5699	246	7	≥	≥	NOUN
ejpam-5699	247	1	min{m+	min{m+	PROPN
ejpam-5699	247	2	b(((g1	b(((g1	PROPN
ejpam-5699	247	3	⋄	⋄	NOUN
ejpam-5699	247	4	0	0	NUM
ejpam-5699	247	5	)	)	PUNCT
ejpam-5699	247	6	⋄	⋄	NOUN
ejpam-5699	247	7	0	0	NUM
ejpam-5699	247	8	)	)	PUNCT
ejpam-5699	247	9	⋄	⋄	NOUN
ejpam-5699	247	10	11),m+	11),m+	NUM
ejpam-5699	247	11	b(11	b(11	NOUN
ejpam-5699	247	12	)	)	PUNCT
ejpam-5699	247	13	}	}	PUNCT
ejpam-5699	247	14	=	=	SYM
ejpam-5699	247	15	min{m+	min{m+	PROPN
ejpam-5699	247	16	b(g1	b(g1	ADJ
ejpam-5699	247	17	⋄	⋄	PROPN
ejpam-5699	247	18	11),m+	11),m+	NUM
ejpam-5699	247	19	b(11	b(11	NOUN
ejpam-5699	247	20	)	)	PUNCT
ejpam-5699	247	21	}	}	PUNCT
ejpam-5699	247	22	,	,	PUNCT
ejpam-5699	247	23	m−	m−	PROPN
ejpam-5699	247	24	b(g1	b(g1	NOUN
ejpam-5699	247	25	)	)	PUNCT
ejpam-5699	248	1	=	=	SYM
ejpam-5699	248	2	m−	m−	PROPN
ejpam-5699	248	3	b(g1	b(g1	ADJ
ejpam-5699	248	4	⋄	⋄	PROPN
ejpam-5699	248	5	0	0	NUM
ejpam-5699	248	6	)	)	PUNCT
ejpam-5699	248	7	≤	≤	NOUN
ejpam-5699	248	8	max{m−	max{m−	NOUN
ejpam-5699	248	9	b(((g1	b(((g1	VERB
ejpam-5699	248	10	⋄	⋄	NOUN
ejpam-5699	248	11	0	0	NUM
ejpam-5699	248	12	)	)	PUNCT
ejpam-5699	248	13	⋄	⋄	NOUN
ejpam-5699	248	14	0	0	NUM
ejpam-5699	248	15	)	)	PUNCT
ejpam-5699	248	16	⋄	⋄	NOUN
ejpam-5699	248	17	11),m−	11),m−	NUM
ejpam-5699	248	18	b(11	b(11	NOUN
ejpam-5699	248	19	)	)	PUNCT
ejpam-5699	248	20	}	}	PUNCT
ejpam-5699	249	1	=	=	SYM
ejpam-5699	249	2	max{m−	max{m−	NOUN
ejpam-5699	249	3	b(g1	b(g1	ADJ
ejpam-5699	249	4	⋄	⋄	PROPN
ejpam-5699	249	5	11),m−	11),m−	NUM
ejpam-5699	249	6	b(11	b(11	NOUN
ejpam-5699	249	7	)	)	PUNCT
ejpam-5699	249	8	}	}	PUNCT
ejpam-5699	249	9	,	,	PUNCT
ejpam-5699	249	10	n+	n+	ADP
ejpam-5699	249	11	b	b	X
ejpam-5699	249	12	(	(	PUNCT
ejpam-5699	249	13	g1	g1	PROPN
ejpam-5699	249	14	)	)	PUNCT
ejpam-5699	249	15	=	=	PUNCT
ejpam-5699	250	1	n+	n+	NUM
ejpam-5699	250	2	b	b	PROPN
ejpam-5699	250	3	(	(	PUNCT
ejpam-5699	250	4	g1	g1	VERB
ejpam-5699	250	5	⋄	⋄	PROPN
ejpam-5699	250	6	0	0	NUM
ejpam-5699	250	7	)	)	PUNCT
ejpam-5699	250	8	≤	≤	NUM
ejpam-5699	251	1	max{n+	max{n+	PROPN
ejpam-5699	251	2	b	b	PROPN
ejpam-5699	251	3	(	(	PUNCT
ejpam-5699	251	4	(	(	PUNCT
ejpam-5699	251	5	(	(	PUNCT
ejpam-5699	251	6	g1	g1	VERB
ejpam-5699	251	7	⋄	⋄	PROPN
ejpam-5699	251	8	0	0	NUM
ejpam-5699	251	9	)	)	PUNCT
ejpam-5699	251	10	⋄	⋄	NOUN
ejpam-5699	251	11	0	0	NUM
ejpam-5699	251	12	)	)	PUNCT
ejpam-5699	251	13	⋄	⋄	NOUN
ejpam-5699	252	1	11),n+	11),n+	NUM
ejpam-5699	252	2	b	b	PROPN
ejpam-5699	252	3	(	(	PUNCT
ejpam-5699	252	4	11	11	NUM
ejpam-5699	252	5	)	)	PUNCT
ejpam-5699	252	6	}	}	PUNCT
ejpam-5699	252	7	=	=	PUNCT
ejpam-5699	252	8	max{n+	max{n+	NOUN
ejpam-5699	252	9	b	b	X
ejpam-5699	252	10	(	(	PUNCT
ejpam-5699	252	11	g1	g1	PROPN
ejpam-5699	252	12	⋄	⋄	PROPN
ejpam-5699	252	13	11),n+	11),n+	NUM
ejpam-5699	252	14	b	b	PROPN
ejpam-5699	252	15	(	(	PUNCT
ejpam-5699	252	16	11	11	NUM
ejpam-5699	252	17	)	)	PUNCT
ejpam-5699	252	18	}	}	PUNCT
ejpam-5699	252	19	,	,	PUNCT
ejpam-5699	252	20	n−	n−	PROPN
ejpam-5699	252	21	b	b	X
ejpam-5699	252	22	(	(	PUNCT
ejpam-5699	252	23	g1	g1	PROPN
ejpam-5699	252	24	)	)	PUNCT
ejpam-5699	252	25	=	=	PUNCT
ejpam-5699	252	26	n−	n−	PROPN
ejpam-5699	252	27	b	b	X
ejpam-5699	252	28	(	(	PUNCT
ejpam-5699	252	29	g1	g1	VERB
ejpam-5699	252	30	⋄	⋄	PROPN
ejpam-5699	252	31	0	0	NUM
ejpam-5699	252	32	)	)	PUNCT
ejpam-5699	252	33	≥	≥	NOUN
ejpam-5699	252	34	min{n−	min{n−	PROPN
ejpam-5699	252	35	b	b	PROPN
ejpam-5699	252	36	(	(	PUNCT
ejpam-5699	252	37	(	(	PUNCT
ejpam-5699	252	38	(	(	PUNCT
ejpam-5699	252	39	g1	g1	VERB
ejpam-5699	252	40	⋄	⋄	PROPN
ejpam-5699	252	41	0	0	NUM
ejpam-5699	252	42	)	)	PUNCT
ejpam-5699	252	43	⋄	⋄	NOUN
ejpam-5699	252	44	0	0	NUM
ejpam-5699	252	45	)	)	PUNCT
ejpam-5699	252	46	⋄	⋄	PROPN
ejpam-5699	252	47	11),n−	11),n−	NUM
ejpam-5699	252	48	b	b	PROPN
ejpam-5699	252	49	(	(	PUNCT
ejpam-5699	252	50	11	11	NUM
ejpam-5699	252	51	)	)	PUNCT
ejpam-5699	252	52	}	}	PUNCT
ejpam-5699	252	53	=	=	SYM
ejpam-5699	252	54	min{n−	min{n−	PROPN
ejpam-5699	252	55	b	b	PROPN
ejpam-5699	252	56	(	(	PUNCT
ejpam-5699	252	57	g1	g1	PROPN
ejpam-5699	252	58	⋄	⋄	PROPN
ejpam-5699	252	59	11),n−	11),n−	NUM
ejpam-5699	252	60	b	b	PROPN
ejpam-5699	252	61	(	(	PUNCT
ejpam-5699	252	62	11	11	NUM
ejpam-5699	252	63	)	)	PUNCT
ejpam-5699	252	64	}	}	PUNCT
ejpam-5699	252	65	,	,	PUNCT
ejpam-5699	252	66	for	for	ADP
ejpam-5699	252	67	all	all	DET
ejpam-5699	252	68	g1	g1	NOUN
ejpam-5699	252	69	,	,	PUNCT
ejpam-5699	252	70	11	11	NUM
ejpam-5699	252	71	∈	∈	NOUN
ejpam-5699	252	72	g.	g.	NOUN
ejpam-5699	252	73	thus	thus	ADV
ejpam-5699	252	74	,	,	PUNCT
ejpam-5699	252	75	b	b	X
ejpam-5699	252	76	=	=	SYM
ejpam-5699	252	77	(	(	PUNCT
ejpam-5699	252	78	m+	m+	NUM
ejpam-5699	252	79	b	b	NOUN
ejpam-5699	252	80	,	,	PUNCT
ejpam-5699	252	81	m−	m−	PROPN
ejpam-5699	252	82	b	b	PROPN
ejpam-5699	252	83	,	,	PUNCT
ejpam-5699	252	84	n+	n+	NOUN
ejpam-5699	252	85	b	b	NOUN
ejpam-5699	252	86	,	,	PUNCT
ejpam-5699	252	87	n−	n−	PROPN
ejpam-5699	252	88	b	b	X
ejpam-5699	252	89	)	)	PUNCT
ejpam-5699	252	90	is	be	AUX
ejpam-5699	252	91	a	a	DET
ejpam-5699	252	92	bpvifi	bpvifi	NOUN
ejpam-5699	252	93	of	of	ADP
ejpam-5699	252	94	g.	g.	NOUN
ejpam-5699	252	95	taking	take	VERB
ejpam-5699	252	96	11	11	NUM
ejpam-5699	252	97	=	=	SYM
ejpam-5699	252	98	0	0	NUM
ejpam-5699	252	99	in	in	ADP
ejpam-5699	252	100	(	(	PUNCT
ejpam-5699	252	101	15	15	NUM
ejpam-5699	252	102	)	)	PUNCT
ejpam-5699	252	103	,	,	PUNCT
ejpam-5699	252	104	we	we	PRON
ejpam-5699	252	105	obtain	obtain	VERB
ejpam-5699	252	106	m+	m+	NUM
ejpam-5699	252	107	b(g1	b(g1	ADJ
ejpam-5699	252	108	⋄	⋄	PROPN
ejpam-5699	252	109	è1	è1	PROPN
ejpam-5699	252	110	)	)	PUNCT
ejpam-5699	252	111	≥	≥	NOUN
ejpam-5699	252	112	min{m+	min{m+	PROPN
ejpam-5699	252	113	b(((g1	b(((g1	PART
ejpam-5699	252	114	⋄	⋄	PROPN
ejpam-5699	252	115	è1	è1	PROPN
ejpam-5699	252	116	)	)	PUNCT
ejpam-5699	252	117	⋄	⋄	PROPN
ejpam-5699	252	118	è1	è1	PROPN
ejpam-5699	252	119	)	)	PUNCT
ejpam-5699	252	120	⋄	⋄	NOUN
ejpam-5699	252	121	0),m+	0),m+	PROPN
ejpam-5699	252	122	b(0	b(0	NOUN
ejpam-5699	252	123	)	)	PUNCT
ejpam-5699	252	124	}	}	PUNCT
ejpam-5699	253	1	=	=	SYM
ejpam-5699	253	2	m+	m+	NUM
ejpam-5699	253	3	b((g1	b((g1	PROPN
ejpam-5699	253	4	⋄	⋄	PROPN
ejpam-5699	253	5	è1	è1	PROPN
ejpam-5699	253	6	)	)	PUNCT
ejpam-5699	253	7	⋄	⋄	PROPN
ejpam-5699	253	8	è1	è1	PROPN
ejpam-5699	253	9	)	)	PUNCT
ejpam-5699	253	10	,	,	PUNCT
ejpam-5699	253	11	m−	m−	PROPN
ejpam-5699	253	12	b(g1	b(g1	PROPN
ejpam-5699	253	13	⋄	⋄	PROPN
ejpam-5699	253	14	è1	è1	PROPN
ejpam-5699	253	15	)	)	PUNCT
ejpam-5699	253	16	≤	≤	NOUN
ejpam-5699	253	17	max{m−	max{m−	NOUN
ejpam-5699	253	18	b(((g1	b(((g1	VERB
ejpam-5699	253	19	⋄	⋄	NOUN
ejpam-5699	253	20	è1	è1	NOUN
ejpam-5699	253	21	)	)	PUNCT
ejpam-5699	253	22	⋄	⋄	PROPN
ejpam-5699	253	23	è1	è1	PROPN
ejpam-5699	253	24	)	)	PUNCT
ejpam-5699	253	25	⋄	⋄	NOUN
ejpam-5699	253	26	0),m−	0),m−	PUNCT
ejpam-5699	253	27	b(0	b(0	NOUN
ejpam-5699	253	28	)	)	PUNCT
ejpam-5699	253	29	}	}	PUNCT
ejpam-5699	253	30	=	=	SYM
ejpam-5699	253	31	m−	m−	PROPN
ejpam-5699	253	32	b((g1	b((g1	VERB
ejpam-5699	253	33	⋄	⋄	PROPN
ejpam-5699	253	34	è1	è1	PROPN
ejpam-5699	253	35	)	)	PUNCT
ejpam-5699	253	36	⋄	⋄	PROPN
ejpam-5699	253	37	è1	è1	PROPN
ejpam-5699	253	38	)	)	PUNCT
ejpam-5699	253	39	,	,	PUNCT
ejpam-5699	253	40	n+	n+	ADP
ejpam-5699	253	41	b	b	X
ejpam-5699	253	42	(	(	PUNCT
ejpam-5699	253	43	g1	g1	PROPN
ejpam-5699	253	44	⋄	⋄	PROPN
ejpam-5699	253	45	è1	è1	PROPN
ejpam-5699	253	46	)	)	PUNCT
ejpam-5699	253	47	≤	≤	NUM
ejpam-5699	254	1	max{n+	max{n+	PROPN
ejpam-5699	254	2	b	b	PROPN
ejpam-5699	254	3	(	(	PUNCT
ejpam-5699	254	4	(	(	PUNCT
ejpam-5699	254	5	(	(	PUNCT
ejpam-5699	254	6	g1	g1	PROPN
ejpam-5699	254	7	⋄	⋄	PROPN
ejpam-5699	254	8	è1	è1	PROPN
ejpam-5699	254	9	)	)	PUNCT
ejpam-5699	254	10	⋄	⋄	PROPN
ejpam-5699	254	11	è1	è1	PROPN
ejpam-5699	254	12	)	)	PUNCT
ejpam-5699	254	13	⋄	⋄	NOUN
ejpam-5699	255	1	0),n+	0),n+	NUM
ejpam-5699	255	2	b	b	X
ejpam-5699	255	3	(	(	PUNCT
ejpam-5699	255	4	0	0	NUM
ejpam-5699	255	5	)	)	PUNCT
ejpam-5699	255	6	}	}	PUNCT
ejpam-5699	255	7	=	=	PUNCT
ejpam-5699	255	8	n+	n+	PUNCT
ejpam-5699	255	9	b	b	X
ejpam-5699	255	10	(	(	PUNCT
ejpam-5699	255	11	(	(	PUNCT
ejpam-5699	255	12	g1	g1	PROPN
ejpam-5699	255	13	⋄	⋄	PROPN
ejpam-5699	255	14	è1	è1	PROPN
ejpam-5699	255	15	)	)	PUNCT
ejpam-5699	255	16	⋄	⋄	PROPN
ejpam-5699	255	17	è1	è1	PROPN
ejpam-5699	255	18	)	)	PUNCT
ejpam-5699	255	19	,	,	PUNCT
ejpam-5699	255	20	n−	n−	PROPN
ejpam-5699	255	21	b	b	X
ejpam-5699	255	22	(	(	PUNCT
ejpam-5699	255	23	g1	g1	PROPN
ejpam-5699	255	24	⋄	⋄	PROPN
ejpam-5699	255	25	è1	è1	PROPN
ejpam-5699	255	26	)	)	PUNCT
ejpam-5699	255	27	≥	≥	NOUN
ejpam-5699	255	28	min{n−	min{n−	PROPN
ejpam-5699	255	29	b	b	PROPN
ejpam-5699	255	30	(	(	PUNCT
ejpam-5699	255	31	(	(	PUNCT
ejpam-5699	255	32	(	(	PUNCT
ejpam-5699	255	33	g1	g1	PROPN
ejpam-5699	255	34	⋄	⋄	PROPN
ejpam-5699	255	35	è1	è1	PROPN
ejpam-5699	255	36	)	)	PUNCT
ejpam-5699	255	37	⋄	⋄	PROPN
ejpam-5699	255	38	è1	è1	PROPN
ejpam-5699	255	39	)	)	PUNCT
ejpam-5699	255	40	⋄	⋄	PROPN
ejpam-5699	255	41	0),n−	0),n−	PROPN
ejpam-5699	255	42	b	b	X
ejpam-5699	255	43	(	(	PUNCT
ejpam-5699	255	44	0	0	NUM
ejpam-5699	255	45	)	)	PUNCT
ejpam-5699	255	46	}	}	PUNCT
ejpam-5699	256	1	=	=	PUNCT
ejpam-5699	256	2	n−	n−	NUM
ejpam-5699	256	3	b	b	X
ejpam-5699	256	4	(	(	PUNCT
ejpam-5699	256	5	(	(	PUNCT
ejpam-5699	256	6	g1	g1	PROPN
ejpam-5699	256	7	⋄	⋄	PROPN
ejpam-5699	256	8	è1	è1	PROPN
ejpam-5699	256	9	)	)	PUNCT
ejpam-5699	256	10	⋄	⋄	PROPN
ejpam-5699	256	11	è1	è1	PROPN
ejpam-5699	256	12	)	)	PUNCT
ejpam-5699	256	13	,	,	PUNCT
ejpam-5699	256	14	for	for	ADP
ejpam-5699	256	15	all	all	DET
ejpam-5699	256	16	g1,è1	g1,è1	PROPN
ejpam-5699	256	17	∈	∈	PROPN
ejpam-5699	256	18	g.	g.	NOUN
ejpam-5699	256	19	it	it	PRON
ejpam-5699	256	20	follows	follow	VERB
ejpam-5699	256	21	from	from	ADP
ejpam-5699	256	22	theorem	theorem	NOUN
ejpam-5699	256	23	6	6	NUM
ejpam-5699	256	24	that	that	PRON
ejpam-5699	256	25	b	b	X
ejpam-5699	256	26	=	=	SYM
ejpam-5699	256	27	(	(	PUNCT
ejpam-5699	256	28	m+	m+	NUM
ejpam-5699	256	29	b	b	NOUN
ejpam-5699	256	30	,	,	PUNCT
ejpam-5699	256	31	m−	m−	PROPN
ejpam-5699	256	32	b	b	PROPN
ejpam-5699	256	33	,	,	PUNCT
ejpam-5699	256	34	n+	n+	NOUN
ejpam-5699	256	35	b	b	NOUN
ejpam-5699	256	36	,	,	PUNCT
ejpam-5699	256	37	n−	n−	PROPN
ejpam-5699	256	38	b	b	X
ejpam-5699	256	39	)	)	PUNCT
ejpam-5699	256	40	is	be	AUX
ejpam-5699	256	41	a	a	DET
ejpam-5699	256	42	bpvifpii	bpvifpii	NOUN
ejpam-5699	256	43	of	of	ADP
ejpam-5699	256	44	g.	g.	PROPN
ejpam-5699	256	45	d.	d.	PROPN
ejpam-5699	256	46	ramesh	ramesh	PROPN
ejpam-5699	256	47	et	et	PROPN
ejpam-5699	256	48	al	al	PROPN
ejpam-5699	256	49	.	.	PUNCT
ejpam-5699	256	50	/	/	SYM
ejpam-5699	256	51	eur	eur	PROPN
ejpam-5699	256	52	.	.	PUNCT
ejpam-5699	257	1	j.	j.	PROPN
ejpam-5699	257	2	pure	pure	PROPN
ejpam-5699	257	3	appl	appl	PROPN
ejpam-5699	257	4	.	.	PROPN
ejpam-5699	257	5	math	math	PROPN
ejpam-5699	257	6	,	,	PUNCT
ejpam-5699	257	7	18	18	NUM
ejpam-5699	257	8	(	(	PUNCT
ejpam-5699	257	9	1	1	NUM
ejpam-5699	257	10	)	)	PUNCT
ejpam-5699	257	11	(	(	PUNCT
ejpam-5699	257	12	2025	2025	NUM
ejpam-5699	257	13	)	)	PUNCT
ejpam-5699	257	14	,	,	PUNCT
ejpam-5699	257	15	5699	5699	NUM
ejpam-5699	257	16	16	16	NUM
ejpam-5699	257	17	of	of	ADP
ejpam-5699	257	18	20	20	NUM
ejpam-5699	257	19	theorem	theorem	NOUN
ejpam-5699	257	20	8	8	NUM
ejpam-5699	257	21	.	.	PUNCT
ejpam-5699	258	1	let	let	VERB
ejpam-5699	258	2	b	b	NOUN
ejpam-5699	258	3	=	=	SYM
ejpam-5699	258	4	(	(	PUNCT
ejpam-5699	258	5	m+	m+	NUM
ejpam-5699	258	6	b	b	NOUN
ejpam-5699	258	7	,	,	PUNCT
ejpam-5699	258	8	m−	m−	PROPN
ejpam-5699	258	9	b	b	PROPN
ejpam-5699	258	10	,	,	PUNCT
ejpam-5699	258	11	n+	n+	NOUN
ejpam-5699	258	12	b	b	NOUN
ejpam-5699	258	13	,	,	PUNCT
ejpam-5699	258	14	n−	n−	PROPN
ejpam-5699	258	15	b	b	AUX
ejpam-5699	258	16	)	)	PUNCT
ejpam-5699	258	17	be	be	AUX
ejpam-5699	258	18	a	a	DET
ejpam-5699	258	19	bpvifi	bpvifi	NOUN
ejpam-5699	258	20	of	of	ADP
ejpam-5699	258	21	g.	g.	PROPN
ejpam-5699	259	1	then	then	ADV
ejpam-5699	259	2	b	b	X
ejpam-5699	259	3	=	=	PUNCT
ejpam-5699	259	4	(	(	PUNCT
ejpam-5699	259	5	m+	m+	NUM
ejpam-5699	259	6	b	b	NOUN
ejpam-5699	259	7	,	,	PUNCT
ejpam-5699	259	8	m−	m−	PROPN
ejpam-5699	259	9	b	b	PROPN
ejpam-5699	259	10	,	,	PUNCT
ejpam-5699	259	11	n+	n+	NOUN
ejpam-5699	259	12	b	b	NOUN
ejpam-5699	259	13	,	,	PUNCT
ejpam-5699	259	14	n−	n−	PROPN
ejpam-5699	259	15	b	b	X
ejpam-5699	259	16	)	)	PUNCT
ejpam-5699	259	17	is	be	AUX
ejpam-5699	259	18	a	a	DET
ejpam-5699	259	19	bpvifpii	bpvifpii	NOUN
ejpam-5699	259	20	of	of	ADP
ejpam-5699	259	21	g	g	NOUN
ejpam-5699	259	22	if	if	SCONJ
ejpam-5699	260	1	and	and	CCONJ
ejpam-5699	260	2	only	only	ADV
ejpam-5699	260	3	if	if	SCONJ
ejpam-5699	260	4	it	it	PRON
ejpam-5699	260	5	satisfies	satisfy	VERB
ejpam-5699	260	6	the	the	DET
ejpam-5699	260	7	condition	condition	PROPN
ejpam-5699	260	8	m+	m+	NOUN
ejpam-5699	260	9	b((g1	b((g1	VERB
ejpam-5699	260	10	⋄	⋄	PROPN
ejpam-5699	260	11	11	11	NUM
ejpam-5699	260	12	)	)	PUNCT
ejpam-5699	260	13	⋄	⋄	NOUN
ejpam-5699	260	14	(	(	PUNCT
ejpam-5699	260	15	è1	è1	NOUN
ejpam-5699	260	16	⋄	⋄	PROPN
ejpam-5699	260	17	11	11	NUM
ejpam-5699	260	18	)	)	PUNCT
ejpam-5699	260	19	)	)	PUNCT
ejpam-5699	260	20	≥	≥	NOUN
ejpam-5699	260	21	m+	m+	NUM
ejpam-5699	260	22	b((g1	b((g1	PROPN
ejpam-5699	260	23	⋄	⋄	PROPN
ejpam-5699	260	24	è1	è1	PROPN
ejpam-5699	260	25	)	)	PUNCT
ejpam-5699	260	26	⋄	⋄	NOUN
ejpam-5699	260	27	11	11	NUM
ejpam-5699	260	28	)	)	PUNCT
ejpam-5699	260	29	,	,	PUNCT
ejpam-5699	260	30	m−	m−	PROPN
ejpam-5699	260	31	b((g1	b((g1	VERB
ejpam-5699	260	32	⋄	⋄	PROPN
ejpam-5699	260	33	11	11	NUM
ejpam-5699	260	34	)	)	PUNCT
ejpam-5699	260	35	⋄	⋄	NOUN
ejpam-5699	260	36	(	(	PUNCT
ejpam-5699	260	37	è1	è1	NOUN
ejpam-5699	260	38	⋄	⋄	PROPN
ejpam-5699	260	39	11	11	NUM
ejpam-5699	260	40	)	)	PUNCT
ejpam-5699	260	41	)	)	PUNCT
ejpam-5699	260	42	≤	≤	NUM
ejpam-5699	261	1	m−	m−	PROPN
ejpam-5699	261	2	b((g1	b((g1	VERB
ejpam-5699	261	3	⋄	⋄	PROPN
ejpam-5699	261	4	è1	è1	PROPN
ejpam-5699	261	5	)	)	PUNCT
ejpam-5699	261	6	⋄	⋄	NOUN
ejpam-5699	261	7	11	11	NUM
ejpam-5699	261	8	)	)	PUNCT
ejpam-5699	261	9	,	,	PUNCT
ejpam-5699	261	10	n+	n+	ADP
ejpam-5699	261	11	b	b	X
ejpam-5699	261	12	(	(	PUNCT
ejpam-5699	261	13	(	(	PUNCT
ejpam-5699	261	14	g1	g1	VERB
ejpam-5699	261	15	⋄	⋄	PROPN
ejpam-5699	261	16	11	11	NUM
ejpam-5699	261	17	)	)	PUNCT
ejpam-5699	261	18	⋄	⋄	NOUN
ejpam-5699	261	19	(	(	PUNCT
ejpam-5699	261	20	è1	è1	NOUN
ejpam-5699	261	21	⋄	⋄	PROPN
ejpam-5699	261	22	11	11	NUM
ejpam-5699	261	23	)	)	PUNCT
ejpam-5699	261	24	)	)	PUNCT
ejpam-5699	261	25	≤	≤	NUM
ejpam-5699	262	1	n+	n+	PUNCT
ejpam-5699	262	2	b	b	X
ejpam-5699	262	3	(	(	PUNCT
ejpam-5699	262	4	(	(	PUNCT
ejpam-5699	262	5	g1	g1	PROPN
ejpam-5699	262	6	⋄	⋄	PROPN
ejpam-5699	262	7	è1	è1	PROPN
ejpam-5699	262	8	)	)	PUNCT
ejpam-5699	262	9	⋄	⋄	NOUN
ejpam-5699	262	10	11	11	NUM
ejpam-5699	262	11	)	)	PUNCT
ejpam-5699	262	12	,	,	PUNCT
ejpam-5699	262	13	n−	n−	PROPN
ejpam-5699	262	14	b	b	X
ejpam-5699	262	15	(	(	PUNCT
ejpam-5699	262	16	(	(	PUNCT
ejpam-5699	262	17	g1	g1	VERB
ejpam-5699	262	18	⋄	⋄	PROPN
ejpam-5699	262	19	11	11	NUM
ejpam-5699	262	20	)	)	PUNCT
ejpam-5699	262	21	⋄	⋄	NOUN
ejpam-5699	262	22	(	(	PUNCT
ejpam-5699	262	23	è1	è1	NOUN
ejpam-5699	262	24	⋄	⋄	PROPN
ejpam-5699	262	25	11	11	NUM
ejpam-5699	262	26	)	)	PUNCT
ejpam-5699	262	27	)	)	PUNCT
ejpam-5699	262	28	≥	≥	PROPN
ejpam-5699	262	29	n−	n−	PROPN
ejpam-5699	262	30	b	b	X
ejpam-5699	262	31	(	(	PUNCT
ejpam-5699	262	32	(	(	PUNCT
ejpam-5699	262	33	g1	g1	PROPN
ejpam-5699	262	34	⋄	⋄	PROPN
ejpam-5699	262	35	è1	è1	PROPN
ejpam-5699	262	36	)	)	PUNCT
ejpam-5699	262	37	⋄	⋄	NOUN
ejpam-5699	262	38	11	11	NUM
ejpam-5699	262	39	)	)	PUNCT
ejpam-5699	262	40	,	,	PUNCT
ejpam-5699	262	41			NOUN
ejpam-5699	262	42	(	(	PUNCT
ejpam-5699	262	43	16	16	NUM
ejpam-5699	262	44	)	)	PUNCT
ejpam-5699	262	45	for	for	ADP
ejpam-5699	262	46	all	all	DET
ejpam-5699	262	47	g1,è1	g1,è1	PROPN
ejpam-5699	262	48	,	,	PUNCT
ejpam-5699	262	49	11	11	NUM
ejpam-5699	262	50	∈	∈	NOUN
ejpam-5699	262	51	g.	g.	NOUN
ejpam-5699	262	52	proof	proof	NOUN
ejpam-5699	262	53	.	.	PUNCT
ejpam-5699	263	1	assume	assume	VERB
ejpam-5699	263	2	that	that	SCONJ
ejpam-5699	263	3	b	b	X
ejpam-5699	263	4	=	=	SYM
ejpam-5699	263	5	(	(	PUNCT
ejpam-5699	263	6	m+	m+	NUM
ejpam-5699	263	7	b	b	NOUN
ejpam-5699	263	8	,	,	PUNCT
ejpam-5699	263	9	m−	m−	PROPN
ejpam-5699	263	10	b	b	PROPN
ejpam-5699	263	11	,	,	PUNCT
ejpam-5699	263	12	n+	n+	NOUN
ejpam-5699	263	13	b	b	NOUN
ejpam-5699	263	14	,	,	PUNCT
ejpam-5699	263	15	n−	n−	PROPN
ejpam-5699	263	16	b	b	X
ejpam-5699	263	17	)	)	PUNCT
ejpam-5699	263	18	is	be	AUX
ejpam-5699	263	19	a	a	DET
ejpam-5699	263	20	bpvifpii	bpvifpii	NOUN
ejpam-5699	263	21	of	of	ADP
ejpam-5699	263	22	g.	g.	PROPN
ejpam-5699	263	23	then	then	ADV
ejpam-5699	263	24	,	,	PUNCT
ejpam-5699	263	25	by	by	ADP
ejpam-5699	263	26	theorem	theorem	NOUN
ejpam-5699	263	27	3	3	NUM
ejpam-5699	263	28	,	,	PUNCT
ejpam-5699	263	29	b	b	NOUN
ejpam-5699	263	30	=	=	SYM
ejpam-5699	263	31	(	(	PUNCT
ejpam-5699	263	32	m+	m+	NUM
ejpam-5699	263	33	b	b	NOUN
ejpam-5699	263	34	,	,	PUNCT
ejpam-5699	263	35	m−	m−	PROPN
ejpam-5699	263	36	b	b	PROPN
ejpam-5699	263	37	,	,	PUNCT
ejpam-5699	263	38	n+	n+	NOUN
ejpam-5699	263	39	b	b	NOUN
ejpam-5699	263	40	,	,	PUNCT
ejpam-5699	263	41	n−	n−	PROPN
ejpam-5699	263	42	b	b	X
ejpam-5699	263	43	)	)	PUNCT
ejpam-5699	263	44	is	be	AUX
ejpam-5699	263	45	a	a	DET
ejpam-5699	263	46	bpvifi	bpvifi	NOUN
ejpam-5699	263	47	of	of	ADP
ejpam-5699	263	48	g	g	NOUN
ejpam-5699	263	49	and	and	CCONJ
ejpam-5699	263	50	satisfies	satisfie	NOUN
ejpam-5699	263	51	(	(	PUNCT
ejpam-5699	263	52	13	13	NUM
ejpam-5699	263	53	)	)	PUNCT
ejpam-5699	263	54	.	.	PUNCT
ejpam-5699	264	1	since	since	SCONJ
ejpam-5699	264	2	(	(	PUNCT
ejpam-5699	264	3	(	(	PUNCT
ejpam-5699	264	4	g1	g1	PROPN
ejpam-5699	264	5	⋄	⋄	PROPN
ejpam-5699	264	6	(	(	PUNCT
ejpam-5699	264	7	è1	è1	ADP
ejpam-5699	264	8	⋄	⋄	PROPN
ejpam-5699	264	9	11	11	NUM
ejpam-5699	264	10	)	)	PUNCT
ejpam-5699	264	11	)	)	PUNCT
ejpam-5699	264	12	⋄	⋄	NOUN
ejpam-5699	264	13	11	11	NUM
ejpam-5699	264	14	)	)	PUNCT
ejpam-5699	264	15	⋄	⋄	NOUN
ejpam-5699	264	16	11	11	NUM
ejpam-5699	264	17	=	=	SYM
ejpam-5699	264	18	(	(	PUNCT
ejpam-5699	264	19	(	(	PUNCT
ejpam-5699	264	20	g1	g1	VERB
ejpam-5699	264	21	⋄	⋄	PROPN
ejpam-5699	264	22	11	11	NUM
ejpam-5699	264	23	)	)	PUNCT
ejpam-5699	264	24	⋄	⋄	NOUN
ejpam-5699	264	25	(	(	PUNCT
ejpam-5699	264	26	è1	è1	NOUN
ejpam-5699	264	27	⋄	⋄	PROPN
ejpam-5699	264	28	11	11	NUM
ejpam-5699	264	29	)	)	PUNCT
ejpam-5699	264	30	)	)	PUNCT
ejpam-5699	264	31	⋄	⋄	NOUN
ejpam-5699	264	32	11	11	NUM
ejpam-5699	264	33	≤	≤	NOUN
ejpam-5699	264	34	(	(	PUNCT
ejpam-5699	264	35	g1	g1	PROPN
ejpam-5699	264	36	⋄	⋄	PROPN
ejpam-5699	264	37	è1	è1	PROPN
ejpam-5699	264	38	)	)	PUNCT
ejpam-5699	264	39	⋄	⋄	NOUN
ejpam-5699	264	40	11	11	NUM
ejpam-5699	264	41	for	for	ADP
ejpam-5699	264	42	all	all	DET
ejpam-5699	264	43	g1,è1	g1,è1	PROPN
ejpam-5699	264	44	,	,	PUNCT
ejpam-5699	264	45	11	11	NUM
ejpam-5699	264	46	∈	∈	NOUN
ejpam-5699	264	47	g	g	NOUN
ejpam-5699	264	48	,	,	PUNCT
ejpam-5699	264	49	it	it	PRON
ejpam-5699	264	50	follows	follow	VERB
ejpam-5699	264	51	from	from	ADP
ejpam-5699	264	52	corollary	corollary	ADJ
ejpam-5699	265	1	1	1	NUM
ejpam-5699	265	2	that	that	PROPN
ejpam-5699	265	3	m+	m+	NOUN
ejpam-5699	265	4	b(((g1	b(((g1	PART
ejpam-5699	265	5	⋄	⋄	NOUN
ejpam-5699	265	6	(	(	PUNCT
ejpam-5699	265	7	è1	è1	NOUN
ejpam-5699	265	8	⋄	⋄	PROPN
ejpam-5699	265	9	11	11	NUM
ejpam-5699	265	10	)	)	PUNCT
ejpam-5699	265	11	)	)	PUNCT
ejpam-5699	266	1	⋄	⋄	NOUN
ejpam-5699	266	2	11	11	NUM
ejpam-5699	266	3	)	)	PUNCT
ejpam-5699	266	4	⋄	⋄	NOUN
ejpam-5699	266	5	11	11	NUM
ejpam-5699	266	6	)	)	PUNCT
ejpam-5699	266	7	≥	≥	NOUN
ejpam-5699	266	8	m+	m+	NUM
ejpam-5699	266	9	b((g1	b((g1	PROPN
ejpam-5699	266	10	⋄	⋄	PROPN
ejpam-5699	266	11	è1	è1	PROPN
ejpam-5699	266	12	)	)	PUNCT
ejpam-5699	266	13	⋄	⋄	NOUN
ejpam-5699	266	14	11	11	NUM
ejpam-5699	266	15	)	)	PUNCT
ejpam-5699	266	16	,	,	PUNCT
ejpam-5699	266	17	m−	m−	PROPN
ejpam-5699	266	18	b(((g1	b(((g1	VERB
ejpam-5699	266	19	⋄	⋄	PROPN
ejpam-5699	266	20	(	(	PUNCT
ejpam-5699	266	21	è1	è1	NOUN
ejpam-5699	266	22	⋄	⋄	PROPN
ejpam-5699	266	23	11	11	NUM
ejpam-5699	266	24	)	)	PUNCT
ejpam-5699	266	25	)	)	PUNCT
ejpam-5699	266	26	⋄	⋄	NOUN
ejpam-5699	266	27	11	11	NUM
ejpam-5699	266	28	)	)	PUNCT
ejpam-5699	266	29	⋄	⋄	NOUN
ejpam-5699	266	30	11	11	NUM
ejpam-5699	266	31	)	)	PUNCT
ejpam-5699	266	32	≤	≤	NOUN
ejpam-5699	267	1	m−	m−	PROPN
ejpam-5699	267	2	b((g1	b((g1	VERB
ejpam-5699	267	3	⋄	⋄	PROPN
ejpam-5699	267	4	è1	è1	PROPN
ejpam-5699	267	5	)	)	PUNCT
ejpam-5699	267	6	⋄	⋄	NOUN
ejpam-5699	267	7	11	11	NUM
ejpam-5699	267	8	)	)	PUNCT
ejpam-5699	267	9	,	,	PUNCT
ejpam-5699	267	10	n+	n+	ADP
ejpam-5699	267	11	b	b	X
ejpam-5699	267	12	(	(	PUNCT
ejpam-5699	267	13	(	(	PUNCT
ejpam-5699	267	14	(	(	PUNCT
ejpam-5699	267	15	g1	g1	PROPN
ejpam-5699	267	16	⋄	⋄	PROPN
ejpam-5699	267	17	(	(	PUNCT
ejpam-5699	267	18	è1	è1	ADP
ejpam-5699	267	19	⋄	⋄	PROPN
ejpam-5699	267	20	11	11	NUM
ejpam-5699	267	21	)	)	PUNCT
ejpam-5699	267	22	)	)	PUNCT
ejpam-5699	268	1	⋄	⋄	NOUN
ejpam-5699	268	2	11	11	NUM
ejpam-5699	268	3	)	)	PUNCT
ejpam-5699	268	4	⋄	⋄	NOUN
ejpam-5699	268	5	11	11	NUM
ejpam-5699	268	6	)	)	PUNCT
ejpam-5699	268	7	≤	≤	NUM
ejpam-5699	268	8	n+	n+	PUNCT
ejpam-5699	268	9	b	b	X
ejpam-5699	268	10	(	(	PUNCT
ejpam-5699	268	11	(	(	PUNCT
ejpam-5699	268	12	g1	g1	PROPN
ejpam-5699	268	13	⋄	⋄	PROPN
ejpam-5699	268	14	è1	è1	PROPN
ejpam-5699	268	15	)	)	PUNCT
ejpam-5699	268	16	⋄	⋄	NOUN
ejpam-5699	268	17	11	11	NUM
ejpam-5699	268	18	)	)	PUNCT
ejpam-5699	268	19	,	,	PUNCT
ejpam-5699	268	20	n−	n−	PROPN
ejpam-5699	268	21	b	b	X
ejpam-5699	268	22	(	(	PUNCT
ejpam-5699	268	23	(	(	PUNCT
ejpam-5699	268	24	(	(	PUNCT
ejpam-5699	268	25	g1	g1	PROPN
ejpam-5699	268	26	⋄	⋄	PROPN
ejpam-5699	268	27	(	(	PUNCT
ejpam-5699	268	28	è1	è1	ADP
ejpam-5699	268	29	⋄	⋄	PROPN
ejpam-5699	268	30	11	11	NUM
ejpam-5699	268	31	)	)	PUNCT
ejpam-5699	268	32	)	)	PUNCT
ejpam-5699	269	1	⋄	⋄	NOUN
ejpam-5699	269	2	11	11	NUM
ejpam-5699	269	3	)	)	PUNCT
ejpam-5699	269	4	⋄	⋄	NOUN
ejpam-5699	269	5	11	11	NUM
ejpam-5699	269	6	)	)	PUNCT
ejpam-5699	269	7	≥	≥	NOUN
ejpam-5699	269	8	n−	n−	PROPN
ejpam-5699	269	9	b	b	X
ejpam-5699	269	10	(	(	PUNCT
ejpam-5699	269	11	(	(	PUNCT
ejpam-5699	269	12	g1	g1	PROPN
ejpam-5699	269	13	⋄	⋄	PROPN
ejpam-5699	269	14	è1	è1	PROPN
ejpam-5699	269	15	)	)	PUNCT
ejpam-5699	269	16	⋄	⋄	NOUN
ejpam-5699	269	17	11	11	NUM
ejpam-5699	269	18	)	)	PUNCT
ejpam-5699	269	19	,	,	PUNCT
ejpam-5699	269	20			NOUN
ejpam-5699	269	21	(	(	PUNCT
ejpam-5699	269	22	17	17	NUM
ejpam-5699	269	23	)	)	PUNCT
ejpam-5699	269	24	for	for	ADP
ejpam-5699	269	25	all	all	DET
ejpam-5699	269	26	g1,è1	g1,è1	PROPN
ejpam-5699	269	27	,	,	PUNCT
ejpam-5699	269	28	11	11	NUM
ejpam-5699	269	29	∈	∈	NOUN
ejpam-5699	269	30	g.	g.	NOUN
ejpam-5699	269	31	now	now	ADV
ejpam-5699	269	32	,	,	PUNCT
ejpam-5699	269	33	by	by	ADP
ejpam-5699	269	34	using	use	VERB
ejpam-5699	269	35	(	(	PUNCT
ejpam-5699	269	36	3	3	NUM
ejpam-5699	269	37	)	)	PUNCT
ejpam-5699	269	38	,	,	PUNCT
ejpam-5699	269	39	(	(	PUNCT
ejpam-5699	269	40	13	13	NUM
ejpam-5699	269	41	)	)	PUNCT
ejpam-5699	269	42	,	,	PUNCT
ejpam-5699	269	43	and	and	CCONJ
ejpam-5699	269	44	(	(	PUNCT
ejpam-5699	269	45	17	17	NUM
ejpam-5699	269	46	)	)	PUNCT
ejpam-5699	269	47	,	,	PUNCT
ejpam-5699	269	48	we	we	PRON
ejpam-5699	269	49	obtain	obtain	VERB
ejpam-5699	269	50	m+	m+	NUM
ejpam-5699	269	51	b((g1	b((g1	NOUN
ejpam-5699	269	52	⋄	⋄	PROPN
ejpam-5699	269	53	11	11	NUM
ejpam-5699	269	54	)	)	PUNCT
ejpam-5699	269	55	⋄	⋄	NOUN
ejpam-5699	269	56	(	(	PUNCT
ejpam-5699	269	57	è1	è1	NOUN
ejpam-5699	269	58	⋄	⋄	PROPN
ejpam-5699	269	59	11	11	NUM
ejpam-5699	269	60	)	)	PUNCT
ejpam-5699	269	61	)	)	PUNCT
ejpam-5699	270	1	=	=	PUNCT
ejpam-5699	270	2	m+	m+	NUM
ejpam-5699	270	3	b((g1	b((g1	PROPN
ejpam-5699	270	4	⋄	⋄	PROPN
ejpam-5699	270	5	(	(	PUNCT
ejpam-5699	270	6	è1	è1	NOUN
ejpam-5699	270	7	⋄	⋄	PROPN
ejpam-5699	270	8	11	11	NUM
ejpam-5699	270	9	)	)	PUNCT
ejpam-5699	270	10	)	)	PUNCT
ejpam-5699	270	11	⋄	⋄	NOUN
ejpam-5699	270	12	11	11	NUM
ejpam-5699	270	13	)	)	PUNCT
ejpam-5699	270	14	≥	≥	NOUN
ejpam-5699	271	1	m+	m+	NUM
ejpam-5699	271	2	b(((g1	b(((g1	PART
ejpam-5699	271	3	⋄	⋄	NOUN
ejpam-5699	271	4	(	(	PUNCT
ejpam-5699	271	5	è1	è1	NOUN
ejpam-5699	271	6	⋄	⋄	PROPN
ejpam-5699	271	7	11	11	NUM
ejpam-5699	271	8	)	)	PUNCT
ejpam-5699	271	9	)	)	PUNCT
ejpam-5699	271	10	⋄	⋄	NOUN
ejpam-5699	271	11	11	11	NUM
ejpam-5699	271	12	)	)	PUNCT
ejpam-5699	271	13	⋄	⋄	NOUN
ejpam-5699	271	14	11	11	NUM
ejpam-5699	271	15	)	)	PUNCT
ejpam-5699	271	16	≥	≥	NOUN
ejpam-5699	271	17	m+	m+	NUM
ejpam-5699	271	18	b((g1	b((g1	PROPN
ejpam-5699	271	19	⋄	⋄	PROPN
ejpam-5699	271	20	è1	è1	PROPN
ejpam-5699	271	21	)	)	PUNCT
ejpam-5699	271	22	⋄	⋄	NOUN
ejpam-5699	271	23	11	11	NUM
ejpam-5699	271	24	)	)	PUNCT
ejpam-5699	272	1	,	,	PUNCT
ejpam-5699	272	2	m−	m−	PROPN
ejpam-5699	272	3	b((g1	b((g1	VERB
ejpam-5699	272	4	⋄	⋄	PROPN
ejpam-5699	272	5	11	11	NUM
ejpam-5699	272	6	)	)	PUNCT
ejpam-5699	272	7	⋄	⋄	NOUN
ejpam-5699	272	8	(	(	PUNCT
ejpam-5699	272	9	è1	è1	NOUN
ejpam-5699	272	10	⋄	⋄	PROPN
ejpam-5699	272	11	11	11	NUM
ejpam-5699	272	12	)	)	PUNCT
ejpam-5699	272	13	)	)	PUNCT
ejpam-5699	273	1	=	=	SYM
ejpam-5699	273	2	m−	m−	PROPN
ejpam-5699	273	3	b((g1	b((g1	VERB
ejpam-5699	273	4	⋄	⋄	PROPN
ejpam-5699	273	5	(	(	PUNCT
ejpam-5699	273	6	è1	è1	NOUN
ejpam-5699	273	7	⋄	⋄	PROPN
ejpam-5699	273	8	11	11	NUM
ejpam-5699	273	9	)	)	PUNCT
ejpam-5699	273	10	)	)	PUNCT
ejpam-5699	273	11	⋄	⋄	NOUN
ejpam-5699	273	12	11	11	NUM
ejpam-5699	273	13	)	)	PUNCT
ejpam-5699	273	14	≤	≤	NOUN
ejpam-5699	273	15	m−	m−	PROPN
ejpam-5699	273	16	b(((g1	b(((g1	PART
ejpam-5699	273	17	⋄	⋄	NOUN
ejpam-5699	273	18	(	(	PUNCT
ejpam-5699	273	19	è1	è1	NOUN
ejpam-5699	273	20	⋄	⋄	PROPN
ejpam-5699	273	21	11	11	NUM
ejpam-5699	273	22	)	)	PUNCT
ejpam-5699	273	23	)	)	PUNCT
ejpam-5699	273	24	⋄	⋄	NOUN
ejpam-5699	273	25	11	11	NUM
ejpam-5699	273	26	)	)	PUNCT
ejpam-5699	273	27	⋄	⋄	NOUN
ejpam-5699	273	28	11	11	NUM
ejpam-5699	273	29	)	)	PUNCT
ejpam-5699	273	30	≤	≤	NOUN
ejpam-5699	274	1	m−	m−	PROPN
ejpam-5699	274	2	b((g1	b((g1	VERB
ejpam-5699	274	3	⋄	⋄	PROPN
ejpam-5699	274	4	è1	è1	PROPN
ejpam-5699	274	5	)	)	PUNCT
ejpam-5699	274	6	⋄	⋄	NOUN
ejpam-5699	274	7	11	11	NUM
ejpam-5699	274	8	)	)	PUNCT
ejpam-5699	274	9	,	,	PUNCT
ejpam-5699	274	10	n+	n+	ADP
ejpam-5699	274	11	b	b	X
ejpam-5699	274	12	(	(	PUNCT
ejpam-5699	274	13	(	(	PUNCT
ejpam-5699	274	14	g1	g1	VERB
ejpam-5699	274	15	⋄	⋄	PROPN
ejpam-5699	274	16	11	11	NUM
ejpam-5699	274	17	)	)	PUNCT
ejpam-5699	274	18	⋄	⋄	NOUN
ejpam-5699	274	19	(	(	PUNCT
ejpam-5699	274	20	è1	è1	NOUN
ejpam-5699	274	21	⋄	⋄	PROPN
ejpam-5699	274	22	11	11	NUM
ejpam-5699	274	23	)	)	PUNCT
ejpam-5699	274	24	)	)	PUNCT
ejpam-5699	275	1	=	=	PUNCT
ejpam-5699	275	2	n+	n+	PUNCT
ejpam-5699	275	3	b	b	X
ejpam-5699	275	4	(	(	PUNCT
ejpam-5699	275	5	(	(	PUNCT
ejpam-5699	275	6	g1	g1	PROPN
ejpam-5699	275	7	⋄	⋄	PROPN
ejpam-5699	275	8	(	(	PUNCT
ejpam-5699	275	9	è1	è1	ADP
ejpam-5699	275	10	⋄	⋄	PROPN
ejpam-5699	275	11	11	11	NUM
ejpam-5699	275	12	)	)	PUNCT
ejpam-5699	275	13	)	)	PUNCT
ejpam-5699	276	1	⋄	⋄	NOUN
ejpam-5699	276	2	11	11	NUM
ejpam-5699	276	3	)	)	PUNCT
ejpam-5699	276	4	≤	≤	NUM
ejpam-5699	276	5	n+	n+	PUNCT
ejpam-5699	276	6	b	b	X
ejpam-5699	276	7	(	(	PUNCT
ejpam-5699	276	8	(	(	PUNCT
ejpam-5699	276	9	(	(	PUNCT
ejpam-5699	276	10	g1	g1	PROPN
ejpam-5699	276	11	⋄	⋄	PROPN
ejpam-5699	276	12	(	(	PUNCT
ejpam-5699	276	13	è1	è1	ADP
ejpam-5699	276	14	⋄	⋄	PROPN
ejpam-5699	276	15	11	11	NUM
ejpam-5699	276	16	)	)	PUNCT
ejpam-5699	276	17	)	)	PUNCT
ejpam-5699	277	1	⋄	⋄	NOUN
ejpam-5699	277	2	11	11	NUM
ejpam-5699	277	3	)	)	PUNCT
ejpam-5699	277	4	⋄	⋄	NOUN
ejpam-5699	277	5	11	11	NUM
ejpam-5699	277	6	)	)	PUNCT
ejpam-5699	277	7	≤	≤	NUM
ejpam-5699	277	8	n+	n+	PUNCT
ejpam-5699	277	9	b	b	X
ejpam-5699	277	10	(	(	PUNCT
ejpam-5699	277	11	(	(	PUNCT
ejpam-5699	277	12	g1	g1	PROPN
ejpam-5699	277	13	⋄	⋄	PROPN
ejpam-5699	277	14	è1	è1	PROPN
ejpam-5699	277	15	)	)	PUNCT
ejpam-5699	277	16	⋄	⋄	NOUN
ejpam-5699	277	17	11	11	NUM
ejpam-5699	277	18	)	)	PUNCT
ejpam-5699	277	19	,	,	PUNCT
ejpam-5699	277	20	n−	n−	PROPN
ejpam-5699	277	21	b	b	X
ejpam-5699	277	22	(	(	PUNCT
ejpam-5699	277	23	(	(	PUNCT
ejpam-5699	277	24	g1	g1	VERB
ejpam-5699	277	25	⋄	⋄	PROPN
ejpam-5699	277	26	11	11	NUM
ejpam-5699	277	27	)	)	PUNCT
ejpam-5699	277	28	⋄	⋄	NOUN
ejpam-5699	277	29	(	(	PUNCT
ejpam-5699	277	30	è1	è1	NOUN
ejpam-5699	277	31	⋄	⋄	PROPN
ejpam-5699	277	32	11	11	NUM
ejpam-5699	277	33	)	)	PUNCT
ejpam-5699	277	34	)	)	PUNCT
ejpam-5699	278	1	=	=	PUNCT
ejpam-5699	278	2	n−	n−	NUM
ejpam-5699	278	3	b	b	X
ejpam-5699	278	4	(	(	PUNCT
ejpam-5699	278	5	(	(	PUNCT
ejpam-5699	278	6	g1	g1	PROPN
ejpam-5699	278	7	⋄	⋄	PROPN
ejpam-5699	278	8	(	(	PUNCT
ejpam-5699	278	9	è1	è1	ADP
ejpam-5699	278	10	⋄	⋄	PROPN
ejpam-5699	278	11	11	11	NUM
ejpam-5699	278	12	)	)	PUNCT
ejpam-5699	278	13	)	)	PUNCT
ejpam-5699	278	14	⋄	⋄	NOUN
ejpam-5699	278	15	11	11	NUM
ejpam-5699	278	16	)	)	PUNCT
ejpam-5699	278	17	≥	≥	NOUN
ejpam-5699	278	18	n−	n−	PROPN
ejpam-5699	278	19	b	b	X
ejpam-5699	278	20	(	(	PUNCT
ejpam-5699	278	21	(	(	PUNCT
ejpam-5699	278	22	(	(	PUNCT
ejpam-5699	278	23	g1	g1	PROPN
ejpam-5699	278	24	⋄	⋄	PROPN
ejpam-5699	278	25	(	(	PUNCT
ejpam-5699	278	26	è1	è1	ADP
ejpam-5699	278	27	⋄	⋄	PROPN
ejpam-5699	278	28	11	11	NUM
ejpam-5699	278	29	)	)	PUNCT
ejpam-5699	278	30	)	)	PUNCT
ejpam-5699	278	31	⋄	⋄	NOUN
ejpam-5699	278	32	11	11	NUM
ejpam-5699	278	33	)	)	PUNCT
ejpam-5699	278	34	⋄	⋄	NOUN
ejpam-5699	278	35	11	11	NUM
ejpam-5699	278	36	)	)	PUNCT
ejpam-5699	278	37	≥	≥	NOUN
ejpam-5699	278	38	n−	n−	PROPN
ejpam-5699	278	39	b	b	X
ejpam-5699	278	40	(	(	PUNCT
ejpam-5699	278	41	(	(	PUNCT
ejpam-5699	278	42	g1	g1	PROPN
ejpam-5699	278	43	⋄	⋄	PROPN
ejpam-5699	278	44	è1	è1	PROPN
ejpam-5699	278	45	)	)	PUNCT
ejpam-5699	278	46	⋄	⋄	NOUN
ejpam-5699	278	47	11	11	NUM
ejpam-5699	278	48	)	)	PUNCT
ejpam-5699	278	49	,	,	PUNCT
ejpam-5699	278	50	for	for	ADP
ejpam-5699	278	51	all	all	DET
ejpam-5699	278	52	g1,è1	g1,è1	PROPN
ejpam-5699	278	53	,	,	PUNCT
ejpam-5699	278	54	11	11	NUM
ejpam-5699	278	55	∈	∈	NOUN
ejpam-5699	278	56	g.	g.	NOUN
ejpam-5699	278	57	hence	hence	ADV
ejpam-5699	278	58	,	,	PUNCT
ejpam-5699	278	59	(	(	PUNCT
ejpam-5699	278	60	16	16	NUM
ejpam-5699	278	61	)	)	PUNCT
ejpam-5699	278	62	is	be	AUX
ejpam-5699	278	63	valid	valid	ADJ
ejpam-5699	278	64	.	.	PUNCT
ejpam-5699	279	1	conversely	conversely	ADV
ejpam-5699	279	2	,	,	PUNCT
ejpam-5699	279	3	let	let	VERB
ejpam-5699	279	4	b	b	X
ejpam-5699	279	5	=	=	SYM
ejpam-5699	279	6	(	(	PUNCT
ejpam-5699	279	7	m+	m+	NUM
ejpam-5699	279	8	b	b	NOUN
ejpam-5699	279	9	,	,	PUNCT
ejpam-5699	279	10	m−	m−	PROPN
ejpam-5699	279	11	b	b	PROPN
ejpam-5699	279	12	,	,	PUNCT
ejpam-5699	279	13	n+	n+	NOUN
ejpam-5699	279	14	b	b	NOUN
ejpam-5699	279	15	,	,	PUNCT
ejpam-5699	279	16	n−	n−	PROPN
ejpam-5699	279	17	b	b	AUX
ejpam-5699	279	18	)	)	PUNCT
ejpam-5699	279	19	be	be	AUX
ejpam-5699	279	20	a	a	DET
ejpam-5699	279	21	bpvifi	bpvifi	NOUN
ejpam-5699	279	22	of	of	ADP
ejpam-5699	279	23	g	g	NOUN
ejpam-5699	279	24	which	which	PRON
ejpam-5699	279	25	satisfies	satisfy	VERB
ejpam-5699	279	26	(	(	PUNCT
ejpam-5699	279	27	16	16	NUM
ejpam-5699	279	28	)	)	PUNCT
ejpam-5699	279	29	.	.	PUNCT
ejpam-5699	280	1	write	write	VERB
ejpam-5699	280	2	11	11	NUM
ejpam-5699	280	3	=	=	SYM
ejpam-5699	280	4	è1	è1	NOUN
ejpam-5699	280	5	in	in	ADP
ejpam-5699	280	6	(	(	PUNCT
ejpam-5699	280	7	16	16	NUM
ejpam-5699	280	8	)	)	PUNCT
ejpam-5699	280	9	,	,	PUNCT
ejpam-5699	280	10	we	we	PRON
ejpam-5699	280	11	obtain	obtain	VERB
ejpam-5699	280	12	m+	m+	NUM
ejpam-5699	280	13	b((g1	b((g1	NOUN
ejpam-5699	280	14	⋄	⋄	PROPN
ejpam-5699	280	15	è1	è1	PROPN
ejpam-5699	280	16	)	)	PUNCT
ejpam-5699	280	17	⋄	⋄	NOUN
ejpam-5699	281	1	(	(	PUNCT
ejpam-5699	281	2	è1	è1	PROPN
ejpam-5699	281	3	⋄	⋄	PROPN
ejpam-5699	281	4	è1	è1	NOUN
ejpam-5699	281	5	)	)	PUNCT
ejpam-5699	281	6	)	)	PUNCT
ejpam-5699	282	1	=	=	SYM
ejpam-5699	282	2	m+	m+	NUM
ejpam-5699	282	3	b((g1	b((g1	PROPN
ejpam-5699	282	4	⋄	⋄	PROPN
ejpam-5699	282	5	è1	è1	PROPN
ejpam-5699	282	6	)	)	PUNCT
ejpam-5699	282	7	⋄	⋄	NOUN
ejpam-5699	282	8	0	0	NUM
ejpam-5699	282	9	)	)	PUNCT
ejpam-5699	282	10	=	=	PRON
ejpam-5699	283	1	m+	m+	NUM
ejpam-5699	283	2	b(g1	b(g1	ADJ
ejpam-5699	283	3	⋄	⋄	PROPN
ejpam-5699	283	4	è1	è1	PROPN
ejpam-5699	283	5	)	)	PUNCT
ejpam-5699	283	6	≥	≥	NOUN
ejpam-5699	283	7	m+	m+	NUM
ejpam-5699	283	8	b((g1	b((g1	PROPN
ejpam-5699	283	9	⋄	⋄	PROPN
ejpam-5699	283	10	è1	è1	PROPN
ejpam-5699	283	11	)	)	PUNCT
ejpam-5699	283	12	⋄	⋄	PROPN
ejpam-5699	283	13	è1	è1	PROPN
ejpam-5699	283	14	)	)	PUNCT
ejpam-5699	283	15	,	,	PUNCT
ejpam-5699	283	16	d.	d.	PROPN
ejpam-5699	283	17	ramesh	ramesh	PROPN
ejpam-5699	283	18	et	et	PROPN
ejpam-5699	283	19	al	al	PROPN
ejpam-5699	283	20	.	.	PUNCT
ejpam-5699	283	21	/	/	SYM
ejpam-5699	283	22	eur	eur	PROPN
ejpam-5699	283	23	.	.	PUNCT
ejpam-5699	284	1	j.	j.	PROPN
ejpam-5699	284	2	pure	pure	PROPN
ejpam-5699	284	3	appl	appl	PROPN
ejpam-5699	284	4	.	.	PROPN
ejpam-5699	284	5	math	math	PROPN
ejpam-5699	284	6	,	,	PUNCT
ejpam-5699	284	7	18	18	NUM
ejpam-5699	284	8	(	(	PUNCT
ejpam-5699	284	9	1	1	NUM
ejpam-5699	284	10	)	)	PUNCT
ejpam-5699	284	11	(	(	PUNCT
ejpam-5699	284	12	2025	2025	NUM
ejpam-5699	284	13	)	)	PUNCT
ejpam-5699	284	14	,	,	PUNCT
ejpam-5699	284	15	5699	5699	NUM
ejpam-5699	284	16	17	17	NUM
ejpam-5699	284	17	of	of	ADP
ejpam-5699	284	18	20	20	NUM
ejpam-5699	284	19	m−	m−	PROPN
ejpam-5699	284	20	b((g1	b((g1	PROPN
ejpam-5699	284	21	⋄	⋄	PROPN
ejpam-5699	284	22	è1	è1	PROPN
ejpam-5699	284	23	)	)	PUNCT
ejpam-5699	284	24	⋄	⋄	NOUN
ejpam-5699	284	25	(	(	PUNCT
ejpam-5699	284	26	è1	è1	PROPN
ejpam-5699	284	27	⋄	⋄	PROPN
ejpam-5699	284	28	è1	è1	NOUN
ejpam-5699	284	29	)	)	PUNCT
ejpam-5699	284	30	)	)	PUNCT
ejpam-5699	285	1	=	=	SYM
ejpam-5699	285	2	m−	m−	PROPN
ejpam-5699	285	3	b((g1	b((g1	VERB
ejpam-5699	285	4	⋄	⋄	PROPN
ejpam-5699	285	5	è1	è1	PROPN
ejpam-5699	285	6	)	)	PUNCT
ejpam-5699	285	7	⋄	⋄	NOUN
ejpam-5699	285	8	0	0	NUM
ejpam-5699	285	9	)	)	PUNCT
ejpam-5699	286	1	=	=	NOUN
ejpam-5699	286	2	m−	m−	PROPN
ejpam-5699	286	3	b(g1	b(g1	PROPN
ejpam-5699	286	4	⋄	⋄	PROPN
ejpam-5699	286	5	è1	è1	PROPN
ejpam-5699	286	6	)	)	PUNCT
ejpam-5699	286	7	≤	≤	NOUN
ejpam-5699	286	8	m−	m−	PROPN
ejpam-5699	286	9	b((g1	b((g1	VERB
ejpam-5699	286	10	⋄	⋄	PROPN
ejpam-5699	286	11	è1	è1	PROPN
ejpam-5699	286	12	)	)	PUNCT
ejpam-5699	286	13	⋄	⋄	PROPN
ejpam-5699	286	14	è1	è1	PROPN
ejpam-5699	286	15	)	)	PUNCT
ejpam-5699	286	16	,	,	PUNCT
ejpam-5699	286	17	n+	n+	ADP
ejpam-5699	286	18	b	b	X
ejpam-5699	286	19	(	(	PUNCT
ejpam-5699	286	20	(	(	PUNCT
ejpam-5699	286	21	g1	g1	PROPN
ejpam-5699	286	22	⋄	⋄	PROPN
ejpam-5699	286	23	è1	è1	PROPN
ejpam-5699	286	24	)	)	PUNCT
ejpam-5699	286	25	⋄	⋄	NOUN
ejpam-5699	286	26	(	(	PUNCT
ejpam-5699	286	27	è1	è1	PROPN
ejpam-5699	286	28	⋄	⋄	PROPN
ejpam-5699	286	29	è1	è1	NOUN
ejpam-5699	286	30	)	)	PUNCT
ejpam-5699	286	31	)	)	PUNCT
ejpam-5699	287	1	=	=	PUNCT
ejpam-5699	287	2	n+	n+	NUM
ejpam-5699	287	3	b	b	X
ejpam-5699	287	4	(	(	PUNCT
ejpam-5699	287	5	(	(	PUNCT
ejpam-5699	287	6	g1	g1	PROPN
ejpam-5699	287	7	⋄	⋄	PROPN
ejpam-5699	287	8	è1	è1	PROPN
ejpam-5699	287	9	)	)	PUNCT
ejpam-5699	287	10	⋄	⋄	NOUN
ejpam-5699	287	11	0	0	NUM
ejpam-5699	287	12	)	)	PUNCT
ejpam-5699	287	13	=	=	PRON
ejpam-5699	288	1	n+	n+	NUM
ejpam-5699	288	2	b	b	X
ejpam-5699	288	3	(	(	PUNCT
ejpam-5699	288	4	g1	g1	PROPN
ejpam-5699	288	5	⋄	⋄	PROPN
ejpam-5699	288	6	è1	è1	PROPN
ejpam-5699	288	7	)	)	PUNCT
ejpam-5699	288	8	≤	≤	NUM
ejpam-5699	288	9	n+	n+	PUNCT
ejpam-5699	289	1	b	b	X
ejpam-5699	289	2	(	(	PUNCT
ejpam-5699	289	3	(	(	PUNCT
ejpam-5699	289	4	g1	g1	PROPN
ejpam-5699	289	5	⋄	⋄	PROPN
ejpam-5699	289	6	è1	è1	PROPN
ejpam-5699	289	7	)	)	PUNCT
ejpam-5699	289	8	⋄	⋄	PROPN
ejpam-5699	289	9	è1	è1	PROPN
ejpam-5699	289	10	)	)	PUNCT
ejpam-5699	289	11	,	,	PUNCT
ejpam-5699	289	12	n−	n−	PROPN
ejpam-5699	289	13	b	b	X
ejpam-5699	289	14	(	(	PUNCT
ejpam-5699	289	15	(	(	PUNCT
ejpam-5699	289	16	g1	g1	PROPN
ejpam-5699	289	17	⋄	⋄	PROPN
ejpam-5699	289	18	è1	è1	PROPN
ejpam-5699	289	19	)	)	PUNCT
ejpam-5699	289	20	⋄	⋄	NOUN
ejpam-5699	290	1	(	(	PUNCT
ejpam-5699	290	2	è1	è1	PROPN
ejpam-5699	290	3	⋄	⋄	PROPN
ejpam-5699	290	4	è1	è1	NOUN
ejpam-5699	290	5	)	)	PUNCT
ejpam-5699	290	6	)	)	PUNCT
ejpam-5699	291	1	=	=	PUNCT
ejpam-5699	291	2	n−	n−	NUM
ejpam-5699	291	3	b	b	X
ejpam-5699	291	4	(	(	PUNCT
ejpam-5699	291	5	(	(	PUNCT
ejpam-5699	291	6	g1	g1	PROPN
ejpam-5699	291	7	⋄	⋄	PROPN
ejpam-5699	291	8	è1	è1	PROPN
ejpam-5699	291	9	)	)	PUNCT
ejpam-5699	291	10	⋄	⋄	NOUN
ejpam-5699	291	11	0	0	NUM
ejpam-5699	291	12	)	)	PUNCT
ejpam-5699	291	13	=	=	PUNCT
ejpam-5699	291	14	n−	n−	NOUN
ejpam-5699	291	15	b	b	X
ejpam-5699	291	16	(	(	PUNCT
ejpam-5699	291	17	g1	g1	PROPN
ejpam-5699	291	18	⋄	⋄	PROPN
ejpam-5699	291	19	è1	è1	PROPN
ejpam-5699	291	20	)	)	PUNCT
ejpam-5699	291	21	≥	≥	NOUN
ejpam-5699	291	22	n−	n−	PROPN
ejpam-5699	291	23	b	b	X
ejpam-5699	291	24	(	(	PUNCT
ejpam-5699	291	25	(	(	PUNCT
ejpam-5699	291	26	g1	g1	PROPN
ejpam-5699	291	27	⋄	⋄	PROPN
ejpam-5699	291	28	è1	è1	PROPN
ejpam-5699	291	29	)	)	PUNCT
ejpam-5699	291	30	⋄	⋄	PROPN
ejpam-5699	291	31	è1	è1	PROPN
ejpam-5699	291	32	)	)	PUNCT
ejpam-5699	291	33	.	.	PUNCT
ejpam-5699	292	1	therefore	therefore	ADV
ejpam-5699	292	2	,	,	PUNCT
ejpam-5699	292	3	b	b	X
ejpam-5699	292	4	=	=	SYM
ejpam-5699	292	5	(	(	PUNCT
ejpam-5699	292	6	m+	m+	NUM
ejpam-5699	292	7	b	b	NOUN
ejpam-5699	292	8	,	,	PUNCT
ejpam-5699	292	9	m−	m−	PROPN
ejpam-5699	292	10	b	b	PROPN
ejpam-5699	292	11	,	,	PUNCT
ejpam-5699	292	12	n+	n+	NOUN
ejpam-5699	292	13	b	b	NOUN
ejpam-5699	292	14	,	,	PUNCT
ejpam-5699	292	15	n−	n−	PROPN
ejpam-5699	292	16	b	b	X
ejpam-5699	292	17	)	)	PUNCT
ejpam-5699	292	18	is	be	AUX
ejpam-5699	292	19	a	a	DET
ejpam-5699	292	20	bpvifpii	bpvifpii	NOUN
ejpam-5699	292	21	of	of	ADP
ejpam-5699	292	22	g	g	NOUN
ejpam-5699	292	23	by	by	ADP
ejpam-5699	292	24	theorem	theorem	NOUN
ejpam-5699	292	25	6	6	NUM
ejpam-5699	292	26	.	.	PUNCT
ejpam-5699	292	27	theorem	theorem	NOUN
ejpam-5699	292	28	9	9	NUM
ejpam-5699	292	29	.	.	PUNCT
ejpam-5699	293	1	let	let	VERB
ejpam-5699	293	2	b	b	NOUN
ejpam-5699	293	3	=	=	SYM
ejpam-5699	293	4	(	(	PUNCT
ejpam-5699	293	5	m+	m+	NUM
ejpam-5699	293	6	b	b	NOUN
ejpam-5699	293	7	,	,	PUNCT
ejpam-5699	293	8	m−	m−	PROPN
ejpam-5699	293	9	b	b	PROPN
ejpam-5699	293	10	,	,	PUNCT
ejpam-5699	293	11	n+	n+	NOUN
ejpam-5699	293	12	b	b	NOUN
ejpam-5699	293	13	,	,	PUNCT
ejpam-5699	293	14	n−	n−	PROPN
ejpam-5699	293	15	b	b	AUX
ejpam-5699	293	16	)	)	PUNCT
ejpam-5699	293	17	be	be	AUX
ejpam-5699	293	18	a	a	DET
ejpam-5699	293	19	bpvifs	bpvifs	PROPN
ejpam-5699	293	20	in	in	ADP
ejpam-5699	293	21	g.	g.	PROPN
ejpam-5699	294	1	then	then	ADV
ejpam-5699	294	2	b	b	X
ejpam-5699	294	3	=	=	SYM
ejpam-5699	294	4	(	(	PUNCT
ejpam-5699	294	5	m+	m+	NUM
ejpam-5699	294	6	b	b	NOUN
ejpam-5699	294	7	,	,	PUNCT
ejpam-5699	294	8	m−	m−	PROPN
ejpam-5699	294	9	b	b	PROPN
ejpam-5699	294	10	,	,	PUNCT
ejpam-5699	294	11	n+	n+	NOUN
ejpam-5699	294	12	b	b	NOUN
ejpam-5699	294	13	,	,	PUNCT
ejpam-5699	294	14	n−	n−	PROPN
ejpam-5699	294	15	b	b	X
ejpam-5699	294	16	)	)	PUNCT
ejpam-5699	294	17	is	be	AUX
ejpam-5699	294	18	a	a	DET
ejpam-5699	294	19	bpvifpii	bpvifpii	NOUN
ejpam-5699	294	20	of	of	ADP
ejpam-5699	294	21	g	g	NOUN
ejpam-5699	294	22	if	if	SCONJ
ejpam-5699	295	1	and	and	CCONJ
ejpam-5699	295	2	only	only	ADV
ejpam-5699	295	3	if	if	SCONJ
ejpam-5699	295	4	it	it	PRON
ejpam-5699	295	5	satisfies	satisfy	VERB
ejpam-5699	295	6	the	the	DET
ejpam-5699	295	7	condition	condition	NOUN
ejpam-5699	295	8	(	(	PUNCT
ejpam-5699	295	9	(	(	PUNCT
ejpam-5699	295	10	(	(	PUNCT
ejpam-5699	295	11	g1	g1	PROPN
ejpam-5699	295	12	⋄	⋄	PROPN
ejpam-5699	295	13	è1	è1	PROPN
ejpam-5699	295	14	)	)	PUNCT
ejpam-5699	295	15	⋄	⋄	PROPN
ejpam-5699	295	16	è1	è1	PROPN
ejpam-5699	295	17	)	)	PUNCT
ejpam-5699	295	18	⋄	⋄	PROPN
ejpam-5699	295	19	u	u	NOUN
ejpam-5699	295	20	)	)	PUNCT
ejpam-5699	295	21	≤	≤	NOUN
ejpam-5699	295	22	v	v	ADP
ejpam-5699	295	23	⇒	⇒	NOUN
ejpam-5699	295	24			PROPN
ejpam-5699	295	25	m+	m+	NUM
ejpam-5699	295	26	b(g1	b(g1	ADJ
ejpam-5699	295	27	⋄	⋄	PROPN
ejpam-5699	295	28	è1	è1	PROPN
ejpam-5699	295	29	)	)	PUNCT
ejpam-5699	295	30	≥	≥	NOUN
ejpam-5699	295	31	min{m+	min{m+	PROPN
ejpam-5699	295	32	b(u),m+	b(u),m+	PROPN
ejpam-5699	295	33	b(v	b(v	PROPN
ejpam-5699	295	34	)	)	PUNCT
ejpam-5699	295	35	}	}	PUNCT
ejpam-5699	295	36	,	,	PUNCT
ejpam-5699	295	37	m−	m−	PROPN
ejpam-5699	295	38	b(g1	b(g1	PROPN
ejpam-5699	295	39	⋄	⋄	PROPN
ejpam-5699	295	40	è1	è1	PROPN
ejpam-5699	295	41	)	)	PUNCT
ejpam-5699	295	42	≤	≤	NOUN
ejpam-5699	295	43	max{m−	max{m−	NOUN
ejpam-5699	295	44	b(u),m−	b(u),m−	PROPN
ejpam-5699	295	45	b(v	b(v	NOUN
ejpam-5699	295	46	)	)	PUNCT
ejpam-5699	295	47	}	}	PUNCT
ejpam-5699	295	48	,	,	PUNCT
ejpam-5699	295	49	n+	n+	ADP
ejpam-5699	295	50	b	b	X
ejpam-5699	295	51	(	(	PUNCT
ejpam-5699	295	52	g1	g1	PROPN
ejpam-5699	295	53	⋄	⋄	PROPN
ejpam-5699	295	54	è1	è1	PROPN
ejpam-5699	295	55	)	)	PUNCT
ejpam-5699	295	56	≤	≤	NUM
ejpam-5699	296	1	max{n+	max{n+	PROPN
ejpam-5699	296	2	b	b	PROPN
ejpam-5699	296	3	(	(	PUNCT
ejpam-5699	296	4	u),n+	u),n+	PROPN
ejpam-5699	296	5	b	b	PROPN
ejpam-5699	296	6	(	(	PUNCT
ejpam-5699	296	7	v	v	NOUN
ejpam-5699	296	8	)	)	PUNCT
ejpam-5699	296	9	}	}	PUNCT
ejpam-5699	296	10	,	,	PUNCT
ejpam-5699	296	11	n−	n−	PROPN
ejpam-5699	296	12	b	b	X
ejpam-5699	296	13	(	(	PUNCT
ejpam-5699	296	14	g1	g1	PROPN
ejpam-5699	296	15	⋄	⋄	PROPN
ejpam-5699	296	16	è1	è1	PROPN
ejpam-5699	296	17	)	)	PUNCT
ejpam-5699	296	18	≥	≥	NOUN
ejpam-5699	296	19	min{n−	min{n−	PROPN
ejpam-5699	296	20	b	b	PROPN
ejpam-5699	296	21	(	(	PUNCT
ejpam-5699	296	22	u),n−	u),n−	PROPN
ejpam-5699	296	23	b	b	PROPN
ejpam-5699	296	24	(	(	PUNCT
ejpam-5699	296	25	v	v	NOUN
ejpam-5699	296	26	)	)	PUNCT
ejpam-5699	296	27	}	}	PUNCT
ejpam-5699	296	28	,	,	PUNCT
ejpam-5699	296	29			NOUN
ejpam-5699	296	30	(	(	PUNCT
ejpam-5699	296	31	18	18	NUM
ejpam-5699	296	32	)	)	PUNCT
ejpam-5699	296	33	for	for	ADP
ejpam-5699	296	34	all	all	DET
ejpam-5699	296	35	g1,è1	g1,è1	PROPN
ejpam-5699	296	36	,	,	PUNCT
ejpam-5699	296	37	u	u	NOUN
ejpam-5699	296	38	,	,	PUNCT
ejpam-5699	296	39	v	v	PROPN
ejpam-5699	296	40	∈	∈	NOUN
ejpam-5699	296	41	g.	g.	NOUN
ejpam-5699	296	42	proof	proof	NOUN
ejpam-5699	296	43	.	.	PUNCT
ejpam-5699	297	1	assume	assume	VERB
ejpam-5699	297	2	that	that	SCONJ
ejpam-5699	297	3	b	b	X
ejpam-5699	297	4	=	=	SYM
ejpam-5699	297	5	(	(	PUNCT
ejpam-5699	297	6	m+	m+	NUM
ejpam-5699	297	7	b	b	NOUN
ejpam-5699	297	8	,	,	PUNCT
ejpam-5699	297	9	m−	m−	PROPN
ejpam-5699	297	10	b	b	PROPN
ejpam-5699	297	11	,	,	PUNCT
ejpam-5699	297	12	n+	n+	NOUN
ejpam-5699	297	13	b	b	NOUN
ejpam-5699	297	14	,	,	PUNCT
ejpam-5699	297	15	n−	n−	PROPN
ejpam-5699	297	16	b	b	X
ejpam-5699	297	17	)	)	PUNCT
ejpam-5699	297	18	is	be	AUX
ejpam-5699	297	19	a	a	DET
ejpam-5699	297	20	bpvifpii	bpvifpii	NOUN
ejpam-5699	297	21	of	of	ADP
ejpam-5699	297	22	g.	g.	PROPN
ejpam-5699	297	23	then	then	ADV
ejpam-5699	297	24	,	,	PUNCT
ejpam-5699	297	25	by	by	ADP
ejpam-5699	297	26	theorem	theorem	NOUN
ejpam-5699	297	27	3	3	NUM
ejpam-5699	297	28	,	,	PUNCT
ejpam-5699	297	29	b	b	NOUN
ejpam-5699	297	30	=	=	SYM
ejpam-5699	297	31	(	(	PUNCT
ejpam-5699	297	32	m+	m+	NUM
ejpam-5699	297	33	b	b	NOUN
ejpam-5699	297	34	,	,	PUNCT
ejpam-5699	297	35	m−	m−	PROPN
ejpam-5699	297	36	b	b	PROPN
ejpam-5699	297	37	,	,	PUNCT
ejpam-5699	297	38	n+	n+	NOUN
ejpam-5699	297	39	b	b	NOUN
ejpam-5699	297	40	,	,	PUNCT
ejpam-5699	297	41	n−	n−	PROPN
ejpam-5699	297	42	b	b	X
ejpam-5699	297	43	)	)	PUNCT
ejpam-5699	297	44	is	be	AUX
ejpam-5699	297	45	a	a	DET
ejpam-5699	297	46	bpvifi	bpvifi	NOUN
ejpam-5699	297	47	of	of	ADP
ejpam-5699	297	48	g.	g.	PROPN
ejpam-5699	297	49	let	let	VERB
ejpam-5699	297	50	g1,è1	g1,è1	PROPN
ejpam-5699	297	51	,	,	PUNCT
ejpam-5699	297	52	u	u	NOUN
ejpam-5699	297	53	,	,	PUNCT
ejpam-5699	297	54	v	v	ADP
ejpam-5699	297	55	∈	∈	PROPN
ejpam-5699	297	56	g	g	NOUN
ejpam-5699	297	57	be	be	AUX
ejpam-5699	297	58	such	such	ADJ
ejpam-5699	297	59	that	that	SCONJ
ejpam-5699	297	60	(	(	PUNCT
ejpam-5699	297	61	(	(	PUNCT
ejpam-5699	297	62	(	(	PUNCT
ejpam-5699	297	63	g1	g1	PROPN
ejpam-5699	297	64	⋄	⋄	PROPN
ejpam-5699	297	65	è1	è1	PROPN
ejpam-5699	297	66	)	)	PUNCT
ejpam-5699	297	67	⋄	⋄	PROPN
ejpam-5699	297	68	è1	è1	PROPN
ejpam-5699	297	69	)	)	PUNCT
ejpam-5699	297	70	⋄	⋄	PROPN
ejpam-5699	297	71	u	u	NOUN
ejpam-5699	297	72	)	)	PUNCT
ejpam-5699	297	73	≤	≤	NOUN
ejpam-5699	297	74	v.	v.	CCONJ
ejpam-5699	297	75	now	now	ADV
ejpam-5699	297	76	,	,	PUNCT
ejpam-5699	297	77	by	by	ADP
ejpam-5699	297	78	applying	apply	VERB
ejpam-5699	297	79	(	(	PUNCT
ejpam-5699	297	80	13	13	NUM
ejpam-5699	297	81	)	)	PUNCT
ejpam-5699	297	82	and	and	CCONJ
ejpam-5699	297	83	theorem	theorem	VERB
ejpam-5699	297	84	2	2	NUM
ejpam-5699	297	85	,	,	PUNCT
ejpam-5699	297	86	we	we	PRON
ejpam-5699	297	87	obtain	obtain	VERB
ejpam-5699	297	88	m+	m+	NUM
ejpam-5699	297	89	b(g1	b(g1	ADJ
ejpam-5699	297	90	⋄	⋄	PROPN
ejpam-5699	297	91	è1	è1	PROPN
ejpam-5699	297	92	)	)	PUNCT
ejpam-5699	297	93	≥	≥	NOUN
ejpam-5699	297	94	m+	m+	NUM
ejpam-5699	297	95	b((g1	b((g1	PROPN
ejpam-5699	297	96	⋄	⋄	PROPN
ejpam-5699	297	97	è1	è1	PROPN
ejpam-5699	297	98	)	)	PUNCT
ejpam-5699	297	99	⋄	⋄	PROPN
ejpam-5699	297	100	è1	è1	PROPN
ejpam-5699	297	101	)	)	PUNCT
ejpam-5699	297	102	≥	≥	NOUN
ejpam-5699	297	103	min{m+	min{m+	PROPN
ejpam-5699	297	104	b(u),m+	b(u),m+	PROPN
ejpam-5699	297	105	b(v	b(v	PROPN
ejpam-5699	297	106	)	)	PUNCT
ejpam-5699	297	107	}	}	PUNCT
ejpam-5699	297	108	,	,	PUNCT
ejpam-5699	297	109	m−	m−	PROPN
ejpam-5699	297	110	b(g1	b(g1	PROPN
ejpam-5699	297	111	⋄	⋄	PROPN
ejpam-5699	297	112	è1	è1	PROPN
ejpam-5699	297	113	)	)	PUNCT
ejpam-5699	297	114	≤	≤	NOUN
ejpam-5699	298	1	m−	m−	PROPN
ejpam-5699	298	2	b((g1	b((g1	VERB
ejpam-5699	298	3	⋄	⋄	PROPN
ejpam-5699	298	4	è1	è1	PROPN
ejpam-5699	298	5	)	)	PUNCT
ejpam-5699	298	6	⋄	⋄	PROPN
ejpam-5699	298	7	è1	è1	PROPN
ejpam-5699	298	8	)	)	PUNCT
ejpam-5699	298	9	≤	≤	NOUN
ejpam-5699	298	10	max{m−	max{m−	NOUN
ejpam-5699	298	11	b(u),m−	b(u),m−	PROPN
ejpam-5699	298	12	b(v	b(v	NOUN
ejpam-5699	298	13	)	)	PUNCT
ejpam-5699	298	14	}	}	PUNCT
ejpam-5699	298	15	,	,	PUNCT
ejpam-5699	298	16	n+	n+	ADP
ejpam-5699	298	17	b	b	X
ejpam-5699	298	18	(	(	PUNCT
ejpam-5699	298	19	g1	g1	PROPN
ejpam-5699	298	20	⋄	⋄	PROPN
ejpam-5699	298	21	è1	è1	PROPN
ejpam-5699	298	22	)	)	PUNCT
ejpam-5699	298	23	≤	≤	NUM
ejpam-5699	298	24	n+	n+	PUNCT
ejpam-5699	298	25	b	b	X
ejpam-5699	298	26	(	(	PUNCT
ejpam-5699	298	27	(	(	PUNCT
ejpam-5699	298	28	g1	g1	PROPN
ejpam-5699	298	29	⋄	⋄	PROPN
ejpam-5699	298	30	è1	è1	PROPN
ejpam-5699	298	31	)	)	PUNCT
ejpam-5699	298	32	⋄	⋄	PROPN
ejpam-5699	298	33	è1	è1	PROPN
ejpam-5699	298	34	)	)	PUNCT
ejpam-5699	298	35	≤	≤	NUM
ejpam-5699	299	1	max{n+	max{n+	PROPN
ejpam-5699	299	2	b	b	PROPN
ejpam-5699	299	3	(	(	PUNCT
ejpam-5699	299	4	u),n+	u),n+	PROPN
ejpam-5699	299	5	b	b	PROPN
ejpam-5699	299	6	(	(	PUNCT
ejpam-5699	299	7	v	v	NOUN
ejpam-5699	299	8	)	)	PUNCT
ejpam-5699	299	9	}	}	PUNCT
ejpam-5699	299	10	,	,	PUNCT
ejpam-5699	299	11	n−	n−	PROPN
ejpam-5699	299	12	b	b	X
ejpam-5699	299	13	(	(	PUNCT
ejpam-5699	299	14	g1	g1	PROPN
ejpam-5699	299	15	⋄	⋄	PROPN
ejpam-5699	299	16	è1	è1	PROPN
ejpam-5699	299	17	)	)	PUNCT
ejpam-5699	299	18	≥	≥	NOUN
ejpam-5699	299	19	n−	n−	PROPN
ejpam-5699	299	20	b	b	X
ejpam-5699	299	21	(	(	PUNCT
ejpam-5699	299	22	(	(	PUNCT
ejpam-5699	299	23	g1	g1	PROPN
ejpam-5699	299	24	⋄	⋄	PROPN
ejpam-5699	299	25	è1	è1	PROPN
ejpam-5699	299	26	)	)	PUNCT
ejpam-5699	299	27	⋄	⋄	PROPN
ejpam-5699	299	28	è1	è1	PROPN
ejpam-5699	299	29	)	)	PUNCT
ejpam-5699	299	30	≥	≥	NOUN
ejpam-5699	299	31	min{n−	min{n−	PROPN
ejpam-5699	299	32	b	b	PROPN
ejpam-5699	299	33	(	(	PUNCT
ejpam-5699	299	34	u),n−	u),n−	PROPN
ejpam-5699	299	35	b	b	PROPN
ejpam-5699	299	36	(	(	PUNCT
ejpam-5699	299	37	v	v	NOUN
ejpam-5699	299	38	)	)	PUNCT
ejpam-5699	299	39	}	}	PUNCT
ejpam-5699	299	40	.	.	PUNCT
ejpam-5699	300	1	therefore	therefore	ADV
ejpam-5699	300	2	,	,	PUNCT
ejpam-5699	300	3	(	(	PUNCT
ejpam-5699	300	4	18	18	NUM
ejpam-5699	300	5	)	)	PUNCT
ejpam-5699	300	6	is	be	AUX
ejpam-5699	300	7	valid	valid	ADJ
ejpam-5699	300	8	.	.	PUNCT
ejpam-5699	301	1	conversely	conversely	ADV
ejpam-5699	301	2	,	,	PUNCT
ejpam-5699	301	3	let	let	VERB
ejpam-5699	301	4	b	b	X
ejpam-5699	301	5	=	=	SYM
ejpam-5699	301	6	(	(	PUNCT
ejpam-5699	301	7	m+	m+	NUM
ejpam-5699	301	8	b	b	NOUN
ejpam-5699	301	9	,	,	PUNCT
ejpam-5699	301	10	m−	m−	PROPN
ejpam-5699	301	11	b	b	PROPN
ejpam-5699	301	12	,	,	PUNCT
ejpam-5699	301	13	n+	n+	NOUN
ejpam-5699	301	14	b	b	NOUN
ejpam-5699	301	15	,	,	PUNCT
ejpam-5699	301	16	n−	n−	PROPN
ejpam-5699	301	17	b	b	AUX
ejpam-5699	301	18	)	)	PUNCT
ejpam-5699	301	19	be	be	AUX
ejpam-5699	301	20	a	a	DET
ejpam-5699	301	21	bpvifs	bpvif	NOUN
ejpam-5699	301	22	in	in	ADP
ejpam-5699	301	23	g	g	PROPN
ejpam-5699	301	24	that	that	SCONJ
ejpam-5699	301	25	satisfies	satisfie	NOUN
ejpam-5699	301	26	(	(	PUNCT
ejpam-5699	301	27	18	18	NUM
ejpam-5699	301	28	)	)	PUNCT
ejpam-5699	301	29	.	.	PUNCT
ejpam-5699	302	1	let	let	VERB
ejpam-5699	302	2	g1	g1	PROPN
ejpam-5699	302	3	,	,	PUNCT
ejpam-5699	302	4	u	u	NOUN
ejpam-5699	302	5	,	,	PUNCT
ejpam-5699	302	6	v	v	ADP
ejpam-5699	302	7	∈	∈	PROPN
ejpam-5699	302	8	g	g	NOUN
ejpam-5699	302	9	be	be	VERB
ejpam-5699	302	10	such	such	ADJ
ejpam-5699	302	11	that	that	SCONJ
ejpam-5699	302	12	g1	g1	PROPN
ejpam-5699	302	13	⋄	⋄	PROPN
ejpam-5699	302	14	u	u	NOUN
ejpam-5699	302	15	≤	≤	X
ejpam-5699	303	1	v.	v.	CCONJ
ejpam-5699	303	2	then	then	ADV
ejpam-5699	303	3	,	,	PUNCT
ejpam-5699	303	4	(	(	PUNCT
ejpam-5699	303	5	(	(	PUNCT
ejpam-5699	303	6	(	(	PUNCT
ejpam-5699	303	7	g1	g1	VERB
ejpam-5699	303	8	⋄	⋄	PROPN
ejpam-5699	303	9	0	0	NUM
ejpam-5699	303	10	)	)	PUNCT
ejpam-5699	303	11	⋄	⋄	NOUN
ejpam-5699	303	12	0	0	NUM
ejpam-5699	303	13	)	)	PUNCT
ejpam-5699	303	14	⋄	⋄	PROPN
ejpam-5699	303	15	u	u	NOUN
ejpam-5699	303	16	)	)	PUNCT
ejpam-5699	303	17	⋄	⋄	PROPN
ejpam-5699	303	18	v	v	NOUN
ejpam-5699	303	19	=	=	SYM
ejpam-5699	303	20	0	0	NUM
ejpam-5699	303	21	,	,	PUNCT
ejpam-5699	303	22	and	and	CCONJ
ejpam-5699	303	23	so	so	ADV
ejpam-5699	303	24	m+	m+	NUM
ejpam-5699	303	25	b(g1	b(g1	NOUN
ejpam-5699	303	26	)	)	PUNCT
ejpam-5699	304	1	=	=	SYM
ejpam-5699	304	2	m+	m+	NOUN
ejpam-5699	304	3	b(g1	b(g1	ADJ
ejpam-5699	304	4	⋄	⋄	PROPN
ejpam-5699	304	5	0	0	NUM
ejpam-5699	304	6	)	)	PUNCT
ejpam-5699	304	7	≥	≥	NOUN
ejpam-5699	305	1	min{m+	min{m+	PROPN
ejpam-5699	305	2	b(u),m+	b(u),m+	PROPN
ejpam-5699	305	3	b(v	b(v	PROPN
ejpam-5699	305	4	)	)	PUNCT
ejpam-5699	305	5	}	}	PUNCT
ejpam-5699	305	6	,	,	PUNCT
ejpam-5699	305	7	m−	m−	PROPN
ejpam-5699	305	8	b(g1	b(g1	NOUN
ejpam-5699	305	9	)	)	PUNCT
ejpam-5699	306	1	=	=	SYM
ejpam-5699	306	2	m−	m−	PROPN
ejpam-5699	306	3	b(g1	b(g1	ADJ
ejpam-5699	306	4	⋄	⋄	PROPN
ejpam-5699	306	5	0	0	NUM
ejpam-5699	306	6	)	)	PUNCT
ejpam-5699	306	7	≤	≤	NOUN
ejpam-5699	306	8	max{m−	max{m−	NOUN
ejpam-5699	306	9	b(u),m−	b(u),m−	ADJ
ejpam-5699	306	10	b(v	b(v	NOUN
ejpam-5699	306	11	)	)	PUNCT
ejpam-5699	306	12	}	}	PUNCT
ejpam-5699	306	13	,	,	PUNCT
ejpam-5699	306	14	n+	n+	ADP
ejpam-5699	306	15	b	b	X
ejpam-5699	306	16	(	(	PUNCT
ejpam-5699	306	17	g1	g1	PROPN
ejpam-5699	306	18	)	)	PUNCT
ejpam-5699	306	19	=	=	PUNCT
ejpam-5699	307	1	n+	n+	NUM
ejpam-5699	307	2	b	b	PROPN
ejpam-5699	307	3	(	(	PUNCT
ejpam-5699	307	4	g1	g1	VERB
ejpam-5699	307	5	⋄	⋄	PROPN
ejpam-5699	307	6	0	0	NUM
ejpam-5699	307	7	)	)	PUNCT
ejpam-5699	307	8	≤	≤	NUM
ejpam-5699	308	1	max{n+	max{n+	PROPN
ejpam-5699	308	2	b	b	PROPN
ejpam-5699	308	3	(	(	PUNCT
ejpam-5699	308	4	u),n+	u),n+	PROPN
ejpam-5699	308	5	b	b	PROPN
ejpam-5699	308	6	(	(	PUNCT
ejpam-5699	308	7	v	v	NOUN
ejpam-5699	308	8	)	)	PUNCT
ejpam-5699	308	9	}	}	PUNCT
ejpam-5699	308	10	,	,	PUNCT
ejpam-5699	308	11	n−	n−	PROPN
ejpam-5699	308	12	b	b	X
ejpam-5699	308	13	(	(	PUNCT
ejpam-5699	308	14	g1	g1	PROPN
ejpam-5699	308	15	)	)	PUNCT
ejpam-5699	308	16	=	=	PUNCT
ejpam-5699	308	17	n−	n−	PROPN
ejpam-5699	308	18	b	b	X
ejpam-5699	308	19	(	(	PUNCT
ejpam-5699	308	20	g1	g1	VERB
ejpam-5699	308	21	⋄	⋄	PROPN
ejpam-5699	308	22	0	0	NUM
ejpam-5699	308	23	)	)	PUNCT
ejpam-5699	308	24	≥	≥	NOUN
ejpam-5699	308	25	min{n−	min{n−	PROPN
ejpam-5699	308	26	b	b	PROPN
ejpam-5699	308	27	(	(	PUNCT
ejpam-5699	308	28	u),n−	u),n−	PROPN
ejpam-5699	308	29	b	b	PROPN
ejpam-5699	308	30	(	(	PUNCT
ejpam-5699	308	31	v	v	NOUN
ejpam-5699	308	32	)	)	PUNCT
ejpam-5699	308	33	}	}	PUNCT
ejpam-5699	308	34	.	.	PUNCT
ejpam-5699	309	1	d.	d.	PROPN
ejpam-5699	309	2	ramesh	ramesh	PROPN
ejpam-5699	309	3	et	et	PROPN
ejpam-5699	309	4	al	al	PROPN
ejpam-5699	309	5	.	.	PUNCT
ejpam-5699	309	6	/	/	SYM
ejpam-5699	309	7	eur	eur	PROPN
ejpam-5699	309	8	.	.	PUNCT
ejpam-5699	310	1	j.	j.	PROPN
ejpam-5699	310	2	pure	pure	PROPN
ejpam-5699	310	3	appl	appl	PROPN
ejpam-5699	310	4	.	.	PROPN
ejpam-5699	310	5	math	math	PROPN
ejpam-5699	310	6	,	,	PUNCT
ejpam-5699	310	7	18	18	NUM
ejpam-5699	310	8	(	(	PUNCT
ejpam-5699	310	9	1	1	NUM
ejpam-5699	310	10	)	)	PUNCT
ejpam-5699	310	11	(	(	PUNCT
ejpam-5699	310	12	2025	2025	NUM
ejpam-5699	310	13	)	)	PUNCT
ejpam-5699	310	14	,	,	PUNCT
ejpam-5699	310	15	5699	5699	NUM
ejpam-5699	310	16	18	18	NUM
ejpam-5699	310	17	of	of	ADP
ejpam-5699	310	18	20	20	NUM
ejpam-5699	310	19	thus	thus	ADV
ejpam-5699	310	20	,	,	PUNCT
ejpam-5699	310	21	by	by	ADP
ejpam-5699	310	22	theorem	theorem	NOUN
ejpam-5699	310	23	2	2	NUM
ejpam-5699	310	24	,	,	PUNCT
ejpam-5699	310	25	b	b	NOUN
ejpam-5699	310	26	=	=	SYM
ejpam-5699	310	27	(	(	PUNCT
ejpam-5699	310	28	m+	m+	NUM
ejpam-5699	310	29	b	b	NOUN
ejpam-5699	310	30	,	,	PUNCT
ejpam-5699	310	31	m−	m−	PROPN
ejpam-5699	310	32	b	b	PROPN
ejpam-5699	310	33	,	,	PUNCT
ejpam-5699	310	34	n+	n+	NOUN
ejpam-5699	310	35	b	b	NOUN
ejpam-5699	310	36	,	,	PUNCT
ejpam-5699	310	37	n−	n−	PROPN
ejpam-5699	310	38	b	b	X
ejpam-5699	310	39	)	)	PUNCT
ejpam-5699	310	40	is	be	AUX
ejpam-5699	310	41	a	a	DET
ejpam-5699	310	42	bpvifi	bpvifi	NOUN
ejpam-5699	310	43	of	of	ADP
ejpam-5699	310	44	g.	g.	PROPN
ejpam-5699	310	45	since	since	SCONJ
ejpam-5699	310	46	(	(	PUNCT
ejpam-5699	310	47	(	(	PUNCT
ejpam-5699	310	48	(	(	PUNCT
ejpam-5699	310	49	g1	g1	PROPN
ejpam-5699	310	50	⋄è1)⋄è1)⋄	⋄è1)⋄è1)⋄	PROPN
ejpam-5699	310	51	(	(	PUNCT
ejpam-5699	310	52	(	(	PUNCT
ejpam-5699	310	53	g1	g1	PROPN
ejpam-5699	310	54	⋄	⋄	PROPN
ejpam-5699	310	55	è1	è1	PROPN
ejpam-5699	310	56	)	)	PUNCT
ejpam-5699	310	57	⋄	⋄	PROPN
ejpam-5699	310	58	è1	è1	PROPN
ejpam-5699	310	59	)	)	PUNCT
ejpam-5699	310	60	)	)	PUNCT
ejpam-5699	311	1	⋄	⋄	NOUN
ejpam-5699	311	2	0	0	NUM
ejpam-5699	312	1	=	=	SYM
ejpam-5699	312	2	0	0	NUM
ejpam-5699	312	3	for	for	ADP
ejpam-5699	312	4	all	all	DET
ejpam-5699	312	5	g1,è1	g1,è1	PROPN
ejpam-5699	312	6	∈	∈	PROPN
ejpam-5699	312	7	g	g	NOUN
ejpam-5699	312	8	,	,	PUNCT
ejpam-5699	312	9	it	it	PRON
ejpam-5699	312	10	follows	follow	VERB
ejpam-5699	312	11	from	from	ADP
ejpam-5699	312	12	(	(	PUNCT
ejpam-5699	312	13	18	18	NUM
ejpam-5699	312	14	)	)	PUNCT
ejpam-5699	312	15	that	that	PRON
ejpam-5699	312	16	m+	m+	VERB
ejpam-5699	312	17	b(g1	b(g1	ADJ
ejpam-5699	312	18	⋄	⋄	PROPN
ejpam-5699	312	19	è1	è1	PROPN
ejpam-5699	312	20	)	)	PUNCT
ejpam-5699	312	21	≥	≥	NOUN
ejpam-5699	312	22	min{m+	min{m+	PROPN
ejpam-5699	312	23	b((g1	b((g1	PROPN
ejpam-5699	312	24	⋄	⋄	PROPN
ejpam-5699	312	25	è1	è1	PROPN
ejpam-5699	312	26	)	)	PUNCT
ejpam-5699	312	27	⋄	⋄	PROPN
ejpam-5699	312	28	è1),m+	è1),m+	NOUN
ejpam-5699	312	29	b(0	b(0	NOUN
ejpam-5699	312	30	)	)	PUNCT
ejpam-5699	312	31	}	}	PUNCT
ejpam-5699	313	1	=	=	SYM
ejpam-5699	313	2	m+	m+	NUM
ejpam-5699	313	3	b((g1	b((g1	PROPN
ejpam-5699	313	4	⋄	⋄	PROPN
ejpam-5699	313	5	è1	è1	PROPN
ejpam-5699	313	6	)	)	PUNCT
ejpam-5699	313	7	⋄	⋄	PROPN
ejpam-5699	313	8	è1	è1	PROPN
ejpam-5699	313	9	)	)	PUNCT
ejpam-5699	313	10	,	,	PUNCT
ejpam-5699	313	11	m−	m−	PROPN
ejpam-5699	313	12	b(g1	b(g1	PROPN
ejpam-5699	313	13	⋄	⋄	PROPN
ejpam-5699	313	14	è1	è1	PROPN
ejpam-5699	313	15	)	)	PUNCT
ejpam-5699	313	16	≤	≤	NOUN
ejpam-5699	313	17	max{m−	max{m−	NOUN
ejpam-5699	313	18	b((g1	b((g1	NOUN
ejpam-5699	313	19	⋄	⋄	PROPN
ejpam-5699	313	20	è1	è1	PROPN
ejpam-5699	313	21	)	)	PUNCT
ejpam-5699	313	22	⋄	⋄	PROPN
ejpam-5699	313	23	è1),m−	è1),m−	PROPN
ejpam-5699	313	24	b(0	b(0	NOUN
ejpam-5699	313	25	)	)	PUNCT
ejpam-5699	313	26	}	}	PUNCT
ejpam-5699	314	1	=	=	SYM
ejpam-5699	314	2	m−	m−	PROPN
ejpam-5699	314	3	b((g1	b((g1	VERB
ejpam-5699	314	4	⋄	⋄	PROPN
ejpam-5699	314	5	è1	è1	PROPN
ejpam-5699	314	6	)	)	PUNCT
ejpam-5699	314	7	⋄	⋄	PROPN
ejpam-5699	314	8	è1	è1	PROPN
ejpam-5699	314	9	)	)	PUNCT
ejpam-5699	314	10	,	,	PUNCT
ejpam-5699	314	11	n+	n+	ADP
ejpam-5699	314	12	b	b	X
ejpam-5699	314	13	(	(	PUNCT
ejpam-5699	314	14	g1	g1	PROPN
ejpam-5699	314	15	⋄	⋄	PROPN
ejpam-5699	314	16	è1	è1	PROPN
ejpam-5699	314	17	)	)	PUNCT
ejpam-5699	314	18	≤	≤	NUM
ejpam-5699	315	1	max{n+	max{n+	PROPN
ejpam-5699	315	2	b	b	PROPN
ejpam-5699	315	3	(	(	PUNCT
ejpam-5699	315	4	(	(	PUNCT
ejpam-5699	315	5	g1	g1	PROPN
ejpam-5699	315	6	⋄	⋄	PROPN
ejpam-5699	315	7	è1	è1	PROPN
ejpam-5699	315	8	)	)	PUNCT
ejpam-5699	315	9	⋄	⋄	PROPN
ejpam-5699	315	10	è1),n+	è1),n+	PROPN
ejpam-5699	315	11	b	b	PROPN
ejpam-5699	315	12	(	(	PUNCT
ejpam-5699	315	13	0	0	NUM
ejpam-5699	315	14	)	)	PUNCT
ejpam-5699	315	15	}	}	PUNCT
ejpam-5699	315	16	=	=	PUNCT
ejpam-5699	315	17	n+	n+	PUNCT
ejpam-5699	315	18	b	b	X
ejpam-5699	315	19	(	(	PUNCT
ejpam-5699	315	20	(	(	PUNCT
ejpam-5699	315	21	g1	g1	PROPN
ejpam-5699	315	22	⋄	⋄	PROPN
ejpam-5699	315	23	è1	è1	PROPN
ejpam-5699	315	24	)	)	PUNCT
ejpam-5699	315	25	⋄	⋄	PROPN
ejpam-5699	315	26	è1	è1	PROPN
ejpam-5699	315	27	)	)	PUNCT
ejpam-5699	315	28	,	,	PUNCT
ejpam-5699	315	29	n−	n−	PROPN
ejpam-5699	315	30	b	b	X
ejpam-5699	315	31	(	(	PUNCT
ejpam-5699	315	32	g1	g1	PROPN
ejpam-5699	315	33	⋄	⋄	PROPN
ejpam-5699	315	34	è1	è1	PROPN
ejpam-5699	315	35	)	)	PUNCT
ejpam-5699	315	36	≥	≥	NOUN
ejpam-5699	315	37	min{n−	min{n−	PROPN
ejpam-5699	315	38	b	b	PROPN
ejpam-5699	315	39	(	(	PUNCT
ejpam-5699	315	40	(	(	PUNCT
ejpam-5699	315	41	g1	g1	PROPN
ejpam-5699	315	42	⋄	⋄	PROPN
ejpam-5699	315	43	è1	è1	PROPN
ejpam-5699	315	44	)	)	PUNCT
ejpam-5699	315	45	⋄	⋄	PROPN
ejpam-5699	315	46	è1),n−	è1),n−	PROPN
ejpam-5699	315	47	b	b	PROPN
ejpam-5699	315	48	(	(	PUNCT
ejpam-5699	315	49	0	0	NUM
ejpam-5699	315	50	)	)	PUNCT
ejpam-5699	315	51	}	}	PUNCT
ejpam-5699	315	52	=	=	PUNCT
ejpam-5699	315	53	n−	n−	NUM
ejpam-5699	315	54	b	b	X
ejpam-5699	315	55	(	(	PUNCT
ejpam-5699	315	56	(	(	PUNCT
ejpam-5699	315	57	g1	g1	PROPN
ejpam-5699	315	58	⋄	⋄	PROPN
ejpam-5699	315	59	è1	è1	PROPN
ejpam-5699	315	60	)	)	PUNCT
ejpam-5699	315	61	⋄	⋄	PROPN
ejpam-5699	315	62	è1	è1	PROPN
ejpam-5699	315	63	)	)	PUNCT
ejpam-5699	315	64	.	.	PUNCT
ejpam-5699	316	1	therefore	therefore	ADV
ejpam-5699	316	2	,	,	PUNCT
ejpam-5699	316	3	by	by	ADP
ejpam-5699	316	4	theorem	theorem	NOUN
ejpam-5699	316	5	6	6	NUM
ejpam-5699	316	6	,	,	PUNCT
ejpam-5699	316	7	b	b	NOUN
ejpam-5699	316	8	=	=	SYM
ejpam-5699	316	9	(	(	PUNCT
ejpam-5699	316	10	m+	m+	NUM
ejpam-5699	316	11	b	b	NOUN
ejpam-5699	316	12	,	,	PUNCT
ejpam-5699	316	13	m−	m−	PROPN
ejpam-5699	316	14	b	b	PROPN
ejpam-5699	316	15	,	,	PUNCT
ejpam-5699	316	16	n+	n+	NOUN
ejpam-5699	316	17	b	b	NOUN
ejpam-5699	316	18	,	,	PUNCT
ejpam-5699	316	19	n−	n−	PROPN
ejpam-5699	316	20	b	b	X
ejpam-5699	316	21	)	)	PUNCT
ejpam-5699	316	22	is	be	AUX
ejpam-5699	316	23	a	a	DET
ejpam-5699	316	24	bpvifpii	bpvifpii	NOUN
ejpam-5699	316	25	of	of	ADP
ejpam-5699	316	26	g.	g.	PROPN
ejpam-5699	316	27	4	4	NUM
ejpam-5699	316	28	.	.	PUNCT
ejpam-5699	316	29	conclusion	conclusion	NOUN
ejpam-5699	316	30	this	this	DET
ejpam-5699	316	31	study	study	NOUN
ejpam-5699	316	32	introduces	introduce	VERB
ejpam-5699	316	33	the	the	DET
ejpam-5699	316	34	concept	concept	NOUN
ejpam-5699	316	35	of	of	ADP
ejpam-5699	316	36	bipolar	bipolar	ADV
ejpam-5699	316	37	-	-	PUNCT
ejpam-5699	316	38	valued	value	VERB
ejpam-5699	316	39	intuitionistic	intuitionistic	ADJ
ejpam-5699	316	40	fuzzy	fuzzy	ADJ
ejpam-5699	316	41	positive	positive	ADJ
ejpam-5699	316	42	implicative	implicative	ADJ
ejpam-5699	316	43	ideals	ideal	NOUN
ejpam-5699	316	44	(	(	PUNCT
ejpam-5699	316	45	bpvifpiis	bpvifpiis	ADJ
ejpam-5699	316	46	)	)	PUNCT
ejpam-5699	316	47	within	within	ADP
ejpam-5699	316	48	bck	bck	PROPN
ejpam-5699	316	49	-	-	PUNCT
ejpam-5699	316	50	algebras	algebras	X
ejpam-5699	316	51	,	,	PUNCT
ejpam-5699	316	52	offering	offer	VERB
ejpam-5699	316	53	a	a	DET
ejpam-5699	316	54	robust	robust	ADJ
ejpam-5699	316	55	theoretical	theoretical	ADJ
ejpam-5699	316	56	framework	framework	NOUN
ejpam-5699	316	57	that	that	PRON
ejpam-5699	316	58	expands	expand	VERB
ejpam-5699	316	59	the	the	DET
ejpam-5699	316	60	algebraic	algebraic	ADJ
ejpam-5699	316	61	treatment	treatment	NOUN
ejpam-5699	316	62	of	of	ADP
ejpam-5699	316	63	fuzzy	fuzzy	ADJ
ejpam-5699	316	64	structures	structure	NOUN
ejpam-5699	316	65	.	.	PUNCT
ejpam-5699	317	1	the	the	DET
ejpam-5699	317	2	research	research	NOUN
ejpam-5699	317	3	thoroughly	thoroughly	ADV
ejpam-5699	317	4	examines	examine	VERB
ejpam-5699	317	5	the	the	DET
ejpam-5699	317	6	conditions	condition	NOUN
ejpam-5699	317	7	under	under	ADP
ejpam-5699	317	8	which	which	PRON
ejpam-5699	317	9	a	a	DET
ejpam-5699	317	10	bipolar	bipolar	ADV
ejpam-5699	317	11	-	-	PUNCT
ejpam-5699	317	12	valued	value	VERB
ejpam-5699	317	13	intuitionistic	intuitionistic	ADJ
ejpam-5699	317	14	fuzzy	fuzzy	ADJ
ejpam-5699	317	15	set	set	NOUN
ejpam-5699	317	16	qualifies	qualifie	NOUN
ejpam-5699	317	17	as	as	ADP
ejpam-5699	317	18	a	a	DET
ejpam-5699	317	19	bpvifpii	bpvifpii	NOUN
ejpam-5699	317	20	and	and	CCONJ
ejpam-5699	317	21	explores	explore	VERB
ejpam-5699	317	22	its	its	PRON
ejpam-5699	317	23	connections	connection	NOUN
ejpam-5699	317	24	with	with	ADP
ejpam-5699	317	25	bpvifis	bpvifis	PROPN
ejpam-5699	317	26	,	,	PUNCT
ejpam-5699	317	27	supported	support	VERB
ejpam-5699	317	28	by	by	ADP
ejpam-5699	317	29	illustrative	illustrative	ADJ
ejpam-5699	317	30	examples	example	NOUN
ejpam-5699	317	31	and	and	CCONJ
ejpam-5699	317	32	rigorous	rigorous	ADJ
ejpam-5699	317	33	proofs	proof	NOUN
ejpam-5699	317	34	.	.	PUNCT
ejpam-5699	318	1	to	to	PART
ejpam-5699	318	2	provide	provide	VERB
ejpam-5699	318	3	a	a	DET
ejpam-5699	318	4	clearer	clear	ADJ
ejpam-5699	318	5	understanding	understanding	NOUN
ejpam-5699	318	6	of	of	ADP
ejpam-5699	318	7	the	the	DET
ejpam-5699	318	8	research	research	NOUN
ejpam-5699	318	9	process	process	NOUN
ejpam-5699	318	10	,	,	PUNCT
ejpam-5699	318	11	figure	figure	VERB
ejpam-5699	318	12	1	1	NUM
ejpam-5699	318	13	presents	present	VERB
ejpam-5699	318	14	a	a	DET
ejpam-5699	318	15	detailed	detailed	ADJ
ejpam-5699	318	16	flowchart	flowchart	NOUN
ejpam-5699	318	17	outlining	outline	VERB
ejpam-5699	318	18	the	the	DET
ejpam-5699	318	19	logical	logical	ADJ
ejpam-5699	318	20	progression	progression	NOUN
ejpam-5699	318	21	of	of	ADP
ejpam-5699	318	22	this	this	DET
ejpam-5699	318	23	study	study	NOUN
ejpam-5699	318	24	.	.	PUNCT
ejpam-5699	319	1	this	this	DET
ejpam-5699	319	2	diagram	diagram	NOUN
ejpam-5699	319	3	highlights	highlight	VERB
ejpam-5699	319	4	key	key	ADJ
ejpam-5699	319	5	stages	stage	NOUN
ejpam-5699	319	6	,	,	PUNCT
ejpam-5699	319	7	starting	start	VERB
ejpam-5699	319	8	from	from	ADP
ejpam-5699	319	9	the	the	DET
ejpam-5699	319	10	foundational	foundational	ADJ
ejpam-5699	319	11	definitions	definition	NOUN
ejpam-5699	319	12	of	of	ADP
ejpam-5699	319	13	fuzzy	fuzzy	ADJ
ejpam-5699	319	14	and	and	CCONJ
ejpam-5699	319	15	intuitionistic	intuitionistic	ADJ
ejpam-5699	319	16	fuzzy	fuzzy	ADJ
ejpam-5699	319	17	sets	set	NOUN
ejpam-5699	319	18	,	,	PUNCT
ejpam-5699	319	19	extending	extend	VERB
ejpam-5699	319	20	through	through	ADP
ejpam-5699	319	21	the	the	DET
ejpam-5699	319	22	development	development	NOUN
ejpam-5699	319	23	of	of	ADP
ejpam-5699	319	24	bipolar	bipolar	ADV
ejpam-5699	319	25	-	-	PUNCT
ejpam-5699	319	26	valued	value	VERB
ejpam-5699	319	27	intuitionistic	intuitionistic	ADJ
ejpam-5699	319	28	fuzzy	fuzzy	ADJ
ejpam-5699	319	29	structures	structure	NOUN
ejpam-5699	319	30	,	,	PUNCT
ejpam-5699	319	31	and	and	CCONJ
ejpam-5699	319	32	culminating	culminate	VERB
ejpam-5699	319	33	in	in	ADP
ejpam-5699	319	34	the	the	DET
ejpam-5699	319	35	formalization	formalization	NOUN
ejpam-5699	319	36	of	of	ADP
ejpam-5699	319	37	bpvifpiis	bpvifpiis	ADJ
ejpam-5699	319	38	in	in	ADP
ejpam-5699	319	39	bck	bck	NOUN
ejpam-5699	319	40	-	-	PUNCT
ejpam-5699	319	41	algebras	algebras	PROPN
ejpam-5699	319	42	.	.	PUNCT
ejpam-5699	320	1	the	the	DET
ejpam-5699	320	2	flowchart	flowchart	NOUN
ejpam-5699	320	3	serves	serve	VERB
ejpam-5699	320	4	as	as	ADP
ejpam-5699	320	5	a	a	DET
ejpam-5699	320	6	visual	visual	ADJ
ejpam-5699	320	7	guide	guide	NOUN
ejpam-5699	320	8	,	,	PUNCT
ejpam-5699	320	9	summarizing	summarize	VERB
ejpam-5699	320	10	the	the	DET
ejpam-5699	320	11	theoretical	theoretical	ADJ
ejpam-5699	320	12	steps	step	NOUN
ejpam-5699	320	13	and	and	CCONJ
ejpam-5699	320	14	linking	link	VERB
ejpam-5699	320	15	them	they	PRON
ejpam-5699	320	16	to	to	ADP
ejpam-5699	320	17	their	their	PRON
ejpam-5699	320	18	practical	practical	ADJ
ejpam-5699	320	19	implications	implication	NOUN
ejpam-5699	320	20	,	,	PUNCT
ejpam-5699	320	21	thereby	thereby	ADV
ejpam-5699	320	22	facilitating	facilitate	VERB
ejpam-5699	320	23	a	a	DET
ejpam-5699	320	24	comprehensive	comprehensive	ADJ
ejpam-5699	320	25	grasp	grasp	NOUN
ejpam-5699	320	26	of	of	ADP
ejpam-5699	320	27	the	the	DET
ejpam-5699	320	28	study	study	NOUN
ejpam-5699	320	29	’s	’s	PART
ejpam-5699	320	30	contributions	contribution	NOUN
ejpam-5699	320	31	.	.	PUNCT
ejpam-5699	321	1	this	this	DET
ejpam-5699	321	2	work	work	NOUN
ejpam-5699	321	3	not	not	PART
ejpam-5699	321	4	only	only	ADV
ejpam-5699	321	5	establishes	establish	VERB
ejpam-5699	321	6	new	new	ADJ
ejpam-5699	321	7	theoretical	theoretical	ADJ
ejpam-5699	321	8	foundations	foundation	NOUN
ejpam-5699	321	9	but	but	CCONJ
ejpam-5699	321	10	also	also	ADV
ejpam-5699	321	11	underscores	underscore	VERB
ejpam-5699	321	12	the	the	DET
ejpam-5699	321	13	practical	practical	ADJ
ejpam-5699	321	14	potential	potential	NOUN
ejpam-5699	321	15	of	of	ADP
ejpam-5699	321	16	bpvifpiis	bpvifpiis	ADJ
ejpam-5699	321	17	in	in	ADP
ejpam-5699	321	18	decision	decision	NOUN
ejpam-5699	321	19	-	-	PUNCT
ejpam-5699	321	20	making	make	VERB
ejpam-5699	321	21	systems	system	NOUN
ejpam-5699	321	22	,	,	PUNCT
ejpam-5699	321	23	sentiment	sentiment	NOUN
ejpam-5699	321	24	analysis	analysis	NOUN
ejpam-5699	321	25	,	,	PUNCT
ejpam-5699	321	26	and	and	CCONJ
ejpam-5699	321	27	artificial	artificial	ADJ
ejpam-5699	321	28	intelligence	intelligence	NOUN
ejpam-5699	321	29	.	.	PUNCT
ejpam-5699	322	1	future	future	ADJ
ejpam-5699	322	2	research	research	NOUN
ejpam-5699	322	3	will	will	AUX
ejpam-5699	322	4	focus	focus	VERB
ejpam-5699	322	5	on	on	ADP
ejpam-5699	322	6	exploring	explore	VERB
ejpam-5699	322	7	these	these	DET
ejpam-5699	322	8	applications	application	NOUN
ejpam-5699	322	9	and	and	CCONJ
ejpam-5699	322	10	extending	extend	VERB
ejpam-5699	322	11	the	the	DET
ejpam-5699	322	12	proposed	propose	VERB
ejpam-5699	322	13	framework	framework	NOUN
ejpam-5699	322	14	to	to	ADP
ejpam-5699	322	15	related	related	ADJ
ejpam-5699	322	16	structures	structure	NOUN
ejpam-5699	322	17	,	,	PUNCT
ejpam-5699	322	18	such	such	ADJ
ejpam-5699	322	19	as	as	ADP
ejpam-5699	322	20	bipolar	bipolar	ADJ
ejpam-5699	322	21	-	-	PUNCT
ejpam-5699	322	22	valued	value	VERB
ejpam-5699	322	23	intuitionistic	intuitionistic	ADJ
ejpam-5699	322	24	fuzzy	fuzzy	ADJ
ejpam-5699	322	25	soft	soft	ADJ
ejpam-5699	322	26	ideals	ideal	NOUN
ejpam-5699	322	27	and	and	CCONJ
ejpam-5699	322	28	(	(	PUNCT
ejpam-5699	322	29	∈,∈	∈,∈	X
ejpam-5699	322	30	∨q)-bpvifis	∨q)-bpvifi	VERB
ejpam-5699	322	31	,	,	PUNCT
ejpam-5699	322	32	further	far	ADV
ejpam-5699	322	33	enriching	enrich	VERB
ejpam-5699	322	34	the	the	DET
ejpam-5699	322	35	field	field	NOUN
ejpam-5699	322	36	of	of	ADP
ejpam-5699	322	37	algebraic	algebraic	ADJ
ejpam-5699	322	38	reasoning	reasoning	NOUN
ejpam-5699	322	39	under	under	ADP
ejpam-5699	322	40	uncertainty	uncertainty	NOUN
ejpam-5699	322	41	.	.	PUNCT
ejpam-5699	323	1	acknowledgements	acknowledgement	NOUN
ejpam-5699	323	2	this	this	DET
ejpam-5699	323	3	research	research	NOUN
ejpam-5699	323	4	was	be	AUX
ejpam-5699	323	5	supported	support	VERB
ejpam-5699	323	6	by	by	ADP
ejpam-5699	323	7	university	university	NOUN
ejpam-5699	323	8	of	of	ADP
ejpam-5699	323	9	phayao	phayao	NOUN
ejpam-5699	323	10	and	and	CCONJ
ejpam-5699	323	11	thailand	thailand	PROPN
ejpam-5699	323	12	science	science	PROPN
ejpam-5699	323	13	research	research	PROPN
ejpam-5699	323	14	and	and	CCONJ
ejpam-5699	323	15	innovation	innovation	NOUN
ejpam-5699	323	16	fund	fund	NOUN
ejpam-5699	323	17	(	(	PUNCT
ejpam-5699	323	18	fundamental	fundamental	ADJ
ejpam-5699	323	19	fund	fund	NOUN
ejpam-5699	323	20	2025	2025	NUM
ejpam-5699	323	21	,	,	PUNCT
ejpam-5699	323	22	grant	grant	VERB
ejpam-5699	323	23	no	no	NOUN
ejpam-5699	323	24	.	.	PROPN
ejpam-5699	324	1	5027/2567	5027/2567	NUM
ejpam-5699	324	2	)	)	PUNCT
ejpam-5699	324	3	.	.	PUNCT
ejpam-5699	325	1	d.	d.	PROPN
ejpam-5699	325	2	ramesh	ramesh	PROPN
ejpam-5699	325	3	et	et	PROPN
ejpam-5699	325	4	al	al	PROPN
ejpam-5699	325	5	.	.	PUNCT
ejpam-5699	325	6	/	/	SYM
ejpam-5699	325	7	eur	eur	PROPN
ejpam-5699	325	8	.	.	PUNCT
ejpam-5699	326	1	j.	j.	PROPN
ejpam-5699	326	2	pure	pure	PROPN
ejpam-5699	326	3	appl	appl	PROPN
ejpam-5699	326	4	.	.	PROPN
ejpam-5699	326	5	math	math	PROPN
ejpam-5699	326	6	,	,	PUNCT
ejpam-5699	326	7	18	18	NUM
ejpam-5699	326	8	(	(	PUNCT
ejpam-5699	326	9	1	1	NUM
ejpam-5699	326	10	)	)	PUNCT
ejpam-5699	326	11	(	(	PUNCT
ejpam-5699	326	12	2025	2025	NUM
ejpam-5699	326	13	)	)	PUNCT
ejpam-5699	326	14	,	,	PUNCT
ejpam-5699	326	15	5699	5699	NUM
ejpam-5699	326	16	19	19	NUM
ejpam-5699	326	17	of	of	ADP
ejpam-5699	326	18	20	20	NUM
ejpam-5699	326	19	references	reference	NOUN
ejpam-5699	326	20	[	[	X
ejpam-5699	326	21	1	1	NUM
ejpam-5699	326	22	]	]	PUNCT
ejpam-5699	326	23	d.	d.	PROPN
ejpam-5699	326	24	al	al	PROPN
ejpam-5699	326	25	-	-	PUNCT
ejpam-5699	326	26	kadi	kadi	PROPN
ejpam-5699	326	27	and	and	CCONJ
ejpam-5699	326	28	g.	g.	PROPN
ejpam-5699	326	29	muhiuddin	muhiuddin	PROPN
ejpam-5699	326	30	.	.	PUNCT
ejpam-5699	327	1	bipolar	bipolar	ADJ
ejpam-5699	327	2	fuzzy	fuzzy	ADJ
ejpam-5699	327	3	bci	bci	ADJ
ejpam-5699	327	4	-	-	ADJ
ejpam-5699	327	5	implicative	implicative	ADJ
ejpam-5699	327	6	ideals	ideal	NOUN
ejpam-5699	327	7	of	of	ADP
ejpam-5699	327	8	bci	bci	NOUN
ejpam-5699	327	9	-	-	PUNCT
ejpam-5699	327	10	algebras	algebra	NOUN
ejpam-5699	327	11	.	.	PUNCT
ejpam-5699	328	1	annals	annal	NOUN
ejpam-5699	328	2	of	of	ADP
ejpam-5699	328	3	communications	communication	NOUN
ejpam-5699	328	4	of	of	ADP
ejpam-5699	328	5	mathematics	mathematic	NOUN
ejpam-5699	328	6	,	,	PUNCT
ejpam-5699	328	7	3(1):88–96	3(1):88–96	NUM
ejpam-5699	328	8	,	,	PUNCT
ejpam-5699	328	9	2020	2020	NUM
ejpam-5699	328	10	.	.	PUNCT
ejpam-5699	329	1	[	[	X
ejpam-5699	329	2	2	2	X
ejpam-5699	329	3	]	]	PUNCT
ejpam-5699	329	4	t.	t.	NOUN
ejpam-5699	329	5	alsuraiheed	alsuraiheed	NOUN
ejpam-5699	329	6	,	,	PUNCT
ejpam-5699	329	7	u.	u.	PROPN
ejpam-5699	329	8	u.	u.	PROPN
ejpam-5699	329	9	rehman	rehman	PROPN
ejpam-5699	329	10	,	,	PUNCT
ejpam-5699	329	11	m.	m.	NOUN
ejpam-5699	329	12	a.	a.	PROPN
ejpam-5699	329	13	khan	khan	PROPN
ejpam-5699	329	14	,	,	PUNCT
ejpam-5699	329	15	and	and	CCONJ
ejpam-5699	329	16	t.	t.	PROPN
ejpam-5699	329	17	mahmood	mahmood	PROPN
ejpam-5699	329	18	.	.	PUNCT
ejpam-5699	330	1	bipolar	bipolar	ADJ
ejpam-5699	330	2	complex	complex	ADJ
ejpam-5699	330	3	fuzzy	fuzzy	ADJ
ejpam-5699	330	4	submodules	submodule	NOUN
ejpam-5699	330	5	.	.	PUNCT
ejpam-5699	331	1	physica	physica	PROPN
ejpam-5699	331	2	scripta	scripta	PROPN
ejpam-5699	331	3	,	,	PUNCT
ejpam-5699	331	4	99(6):065225	99(6):065225	NUM
ejpam-5699	331	5	,	,	PUNCT
ejpam-5699	331	6	2024	2024	NUM
ejpam-5699	331	7	.	.	PUNCT
ejpam-5699	332	1	[	[	X
ejpam-5699	332	2	3	3	X
ejpam-5699	332	3	]	]	PUNCT
ejpam-5699	332	4	k.	k.	PROPN
ejpam-5699	332	5	t.	t.	PROPN
ejpam-5699	332	6	atanassov	atanassov	PROPN
ejpam-5699	332	7	.	.	PUNCT
ejpam-5699	333	1	intuitionistic	intuitionistic	ADJ
ejpam-5699	333	2	fuzzy	fuzzy	ADJ
ejpam-5699	333	3	sets	set	NOUN
ejpam-5699	333	4	.	.	PUNCT
ejpam-5699	334	1	fuzzy	fuzzy	ADJ
ejpam-5699	334	2	sets	set	NOUN
ejpam-5699	334	3	and	and	CCONJ
ejpam-5699	334	4	systems	system	NOUN
ejpam-5699	334	5	,	,	PUNCT
ejpam-5699	334	6	20(1):87–96	20(1):87–96	NUM
ejpam-5699	334	7	,	,	PUNCT
ejpam-5699	334	8	1986	1986	NUM
ejpam-5699	334	9	.	.	PUNCT
ejpam-5699	335	1	[	[	X
ejpam-5699	335	2	4	4	X
ejpam-5699	335	3	]	]	X
ejpam-5699	335	4	d.	d.	PROPN
ejpam-5699	335	5	ezhilmaran	ezhilmaran	PROPN
ejpam-5699	335	6	and	and	CCONJ
ejpam-5699	335	7	k.	k.	PROPN
ejpam-5699	335	8	sankar	sankar	PROPN
ejpam-5699	335	9	.	.	PUNCT
ejpam-5699	336	1	morphism	morphism	NOUN
ejpam-5699	336	2	of	of	ADP
ejpam-5699	336	3	bipolar	bipolar	ADJ
ejpam-5699	336	4	intuitionistic	intuitionistic	ADJ
ejpam-5699	336	5	fuzzy	fuzzy	ADJ
ejpam-5699	336	6	graphs	graph	NOUN
ejpam-5699	336	7	.	.	PUNCT
ejpam-5699	337	1	journal	journal	NOUN
ejpam-5699	337	2	of	of	ADP
ejpam-5699	337	3	discrete	discrete	ADJ
ejpam-5699	337	4	mathematical	mathematical	ADJ
ejpam-5699	337	5	sciences	science	NOUN
ejpam-5699	337	6	and	and	CCONJ
ejpam-5699	337	7	cryptography	cryptography	NOUN
ejpam-5699	337	8	,	,	PUNCT
ejpam-5699	337	9	18(5):605–621	18(5):605–621	NUM
ejpam-5699	337	10	,	,	PUNCT
ejpam-5699	337	11	2015	2015	NUM
ejpam-5699	337	12	.	.	PUNCT
ejpam-5699	338	1	[	[	X
ejpam-5699	338	2	5	5	X
ejpam-5699	338	3	]	]	PUNCT
ejpam-5699	338	4	h.	h.	PROPN
ejpam-5699	338	5	harizavi	harizavi	PROPN
ejpam-5699	338	6	,	,	PUNCT
ejpam-5699	338	7	t.	t.	NOUN
ejpam-5699	338	8	koochakpoor	koochakpoor	PROPN
ejpam-5699	338	9	,	,	PUNCT
ejpam-5699	338	10	and	and	CCONJ
ejpam-5699	338	11	r.	r.	PROPN
ejpam-5699	338	12	boorzoei	boorzoei	PROPN
ejpam-5699	338	13	.	.	PUNCT
ejpam-5699	339	1	quotient	quotient	VERB
ejpam-5699	339	2	hyper	hyper	ADJ
ejpam-5699	339	3	pseudo	pseudo	NOUN
ejpam-5699	339	4	bck	bck	NOUN
ejpam-5699	339	5	-	-	PUNCT
ejpam-5699	339	6	algebras	algebras	X
ejpam-5699	339	7	.	.	PUNCT
ejpam-5699	340	1	discussiones	discussione	NOUN
ejpam-5699	340	2	mathematicae	mathematicae	VERB
ejpam-5699	340	3	general	general	ADJ
ejpam-5699	340	4	algebra	algebra	PROPN
ejpam-5699	340	5	and	and	CCONJ
ejpam-5699	340	6	applications	application	NOUN
ejpam-5699	340	7	,	,	PUNCT
ejpam-5699	340	8	33(2):147–165	33(2):147–165	PROPN
ejpam-5699	340	9	,	,	PUNCT
ejpam-5699	340	10	2013	2013	NUM
ejpam-5699	340	11	.	.	PUNCT
ejpam-5699	341	1	[	[	X
ejpam-5699	341	2	6	6	NUM
ejpam-5699	341	3	]	]	X
ejpam-5699	341	4	y.	y.	PROPN
ejpam-5699	341	5	imai	imai	PROPN
ejpam-5699	341	6	and	and	CCONJ
ejpam-5699	341	7	k.	k.	PROPN
ejpam-5699	341	8	iséki	iséki	PROPN
ejpam-5699	341	9	.	.	PROPN
ejpam-5699	342	1	on	on	ADP
ejpam-5699	342	2	axiom	axiom	NOUN
ejpam-5699	342	3	systems	system	NOUN
ejpam-5699	342	4	of	of	ADP
ejpam-5699	342	5	propositional	propositional	ADJ
ejpam-5699	342	6	calculi	calculi	PROPN
ejpam-5699	342	7	.	.	PUNCT
ejpam-5699	343	1	xiv	xiv	PROPN
ejpam-5699	343	2	.	.	PUNCT
ejpam-5699	344	1	proceedings	proceeding	NOUN
ejpam-5699	344	2	of	of	ADP
ejpam-5699	344	3	the	the	DET
ejpam-5699	344	4	japan	japan	PROPN
ejpam-5699	344	5	academy	academy	PROPN
ejpam-5699	344	6	,	,	PUNCT
ejpam-5699	344	7	42(1):19–22	42(1):19–22	NUM
ejpam-5699	344	8	,	,	PUNCT
ejpam-5699	344	9	1966	1966	NUM
ejpam-5699	344	10	.	.	PUNCT
ejpam-5699	345	1	[	[	X
ejpam-5699	345	2	7	7	X
ejpam-5699	345	3	]	]	X
ejpam-5699	345	4	k.	k.	PROPN
ejpam-5699	345	5	iséki	iséki	PROPN
ejpam-5699	345	6	.	.	PROPN
ejpam-5699	346	1	on	on	ADP
ejpam-5699	346	2	axiom	axiom	NOUN
ejpam-5699	346	3	systems	system	NOUN
ejpam-5699	346	4	of	of	ADP
ejpam-5699	346	5	propositional	propositional	ADJ
ejpam-5699	346	6	calculus	calculus	NOUN
ejpam-5699	346	7	.	.	PUNCT
ejpam-5699	347	1	proceedings	proceeding	NOUN
ejpam-5699	347	2	of	of	ADP
ejpam-5699	347	3	the	the	DET
ejpam-5699	347	4	japan	japan	PROPN
ejpam-5699	347	5	academy	academy	PROPN
ejpam-5699	347	6	,	,	PUNCT
ejpam-5699	347	7	42(1):26–29	42(1):26–29	NUM
ejpam-5699	347	8	,	,	PUNCT
ejpam-5699	347	9	1966	1966	NUM
ejpam-5699	347	10	.	.	PUNCT
ejpam-5699	348	1	[	[	X
ejpam-5699	348	2	8	8	NUM
ejpam-5699	348	3	]	]	X
ejpam-5699	348	4	c.	c.	PROPN
ejpam-5699	348	5	jana	jana	PROPN
ejpam-5699	348	6	,	,	PUNCT
ejpam-5699	348	7	t.	t.	PROPN
ejpam-5699	348	8	senapati	senapati	PROPN
ejpam-5699	348	9	,	,	PUNCT
ejpam-5699	348	10	and	and	CCONJ
ejpam-5699	348	11	m.	m.	NOUN
ejpam-5699	348	12	pal	pal	NOUN
ejpam-5699	348	13	.	.	PUNCT
ejpam-5699	349	1	(	(	PUNCT
ejpam-5699	349	2	∈,∈	∈,∈	X
ejpam-5699	349	3	∨q)-intuitionistic	∨q)-intuitionistic	ADJ
ejpam-5699	349	4	fuzzy	fuzzy	ADJ
ejpam-5699	349	5	bci	bci	NOUN
ejpam-5699	349	6	-	-	PUNCT
ejpam-5699	349	7	subalgebras	subalgebras	PROPN
ejpam-5699	349	8	of	of	ADP
ejpam-5699	349	9	a	a	DET
ejpam-5699	349	10	bci	bci	NOUN
ejpam-5699	349	11	-	-	NOUN
ejpam-5699	349	12	algebra	algebra	NOUN
ejpam-5699	349	13	.	.	PUNCT
ejpam-5699	350	1	journal	journal	NOUN
ejpam-5699	350	2	of	of	ADP
ejpam-5699	350	3	intelligent	intelligent	ADJ
ejpam-5699	350	4	and	and	CCONJ
ejpam-5699	350	5	fuzzy	fuzzy	ADJ
ejpam-5699	350	6	systems	system	NOUN
ejpam-5699	350	7	,	,	PUNCT
ejpam-5699	350	8	31(1):613–621	31(1):613–621	PROPN
ejpam-5699	350	9	,	,	PUNCT
ejpam-5699	350	10	2016	2016	NUM
ejpam-5699	350	11	.	.	PUNCT
ejpam-5699	351	1	[	[	X
ejpam-5699	351	2	9	9	NUM
ejpam-5699	351	3	]	]	X
ejpam-5699	351	4	y.	y.	PROPN
ejpam-5699	351	5	b.	b.	PROPN
ejpam-5699	351	6	jun	jun	PROPN
ejpam-5699	351	7	,	,	PUNCT
ejpam-5699	351	8	m.	m.	PROPN
ejpam-5699	351	9	s.	s.	PROPN
ejpam-5699	351	10	kang	kang	PROPN
ejpam-5699	351	11	,	,	PUNCT
ejpam-5699	351	12	and	and	CCONJ
ejpam-5699	351	13	h.	h.	PROPN
ejpam-5699	351	14	s.	s.	PROPN
ejpam-5699	351	15	kim	kim	PROPN
ejpam-5699	351	16	.	.	PUNCT
ejpam-5699	352	1	bipolar	bipolar	ADJ
ejpam-5699	352	2	fuzzy	fuzzy	ADJ
ejpam-5699	352	3	hyper	hyper	ADJ
ejpam-5699	352	4	bck	bck	NOUN
ejpam-5699	352	5	-	-	PUNCT
ejpam-5699	352	6	ideals	ideal	NOUN
ejpam-5699	352	7	in	in	ADP
ejpam-5699	352	8	hyper	hyper	ADJ
ejpam-5699	352	9	bck	bck	NOUN
ejpam-5699	352	10	-	-	PUNCT
ejpam-5699	352	11	algebras	algebras	PROPN
ejpam-5699	352	12	.	.	PUNCT
ejpam-5699	353	1	iranian	iranian	PROPN
ejpam-5699	353	2	journal	journal	PROPN
ejpam-5699	353	3	of	of	ADP
ejpam-5699	353	4	fuzzy	fuzzy	ADJ
ejpam-5699	353	5	systems	system	NOUN
ejpam-5699	353	6	,	,	PUNCT
ejpam-5699	353	7	8(2):105–120	8(2):105–120	NUM
ejpam-5699	353	8	,	,	PUNCT
ejpam-5699	353	9	2011	2011	NUM
ejpam-5699	353	10	.	.	PUNCT
ejpam-5699	354	1	[	[	X
ejpam-5699	354	2	10	10	NUM
ejpam-5699	354	3	]	]	X
ejpam-5699	354	4	y.	y.	PROPN
ejpam-5699	354	5	b.	b.	PROPN
ejpam-5699	354	6	jun	jun	PROPN
ejpam-5699	354	7	,	,	PUNCT
ejpam-5699	354	8	m.	m.	PROPN
ejpam-5699	354	9	s.	s.	PROPN
ejpam-5699	354	10	kang	kang	PROPN
ejpam-5699	354	11	,	,	PUNCT
ejpam-5699	354	12	and	and	CCONJ
ejpam-5699	354	13	s.	s.	PROPN
ejpam-5699	354	14	z.	z.	PROPN
ejpam-5699	354	15	song	song	PROPN
ejpam-5699	354	16	.	.	PUNCT
ejpam-5699	355	1	several	several	ADJ
ejpam-5699	355	2	types	type	NOUN
ejpam-5699	355	3	of	of	ADP
ejpam-5699	355	4	bipolar	bipolar	ADJ
ejpam-5699	355	5	fuzzy	fuzzy	ADJ
ejpam-5699	355	6	hyper	hyper	ADJ
ejpam-5699	355	7	bckideals	bckideal	NOUN
ejpam-5699	355	8	in	in	ADP
ejpam-5699	355	9	hyper	hyper	ADJ
ejpam-5699	355	10	bck	bck	NOUN
ejpam-5699	355	11	-	-	PUNCT
ejpam-5699	355	12	algebras	algebras	PROPN
ejpam-5699	355	13	.	.	PUNCT
ejpam-5699	356	1	honam	honam	PROPN
ejpam-5699	356	2	mathematical	mathematical	PROPN
ejpam-5699	356	3	journal	journal	PROPN
ejpam-5699	356	4	,	,	PUNCT
ejpam-5699	356	5	34(2):145–159	34(2):145–159	PROPN
ejpam-5699	356	6	,	,	PUNCT
ejpam-5699	356	7	2012	2012	NUM
ejpam-5699	356	8	.	.	PUNCT
ejpam-5699	357	1	[	[	X
ejpam-5699	357	2	11	11	NUM
ejpam-5699	357	3	]	]	X
ejpam-5699	357	4	y.	y.	PROPN
ejpam-5699	357	5	b.	b.	PROPN
ejpam-5699	357	6	jun	jun	PROPN
ejpam-5699	357	7	,	,	PUNCT
ejpam-5699	357	8	g.	g.	PROPN
ejpam-5699	357	9	muhiuddin	muhiuddin	PROPN
ejpam-5699	357	10	,	,	PUNCT
ejpam-5699	357	11	and	and	CCONJ
ejpam-5699	357	12	a.	a.	NOUN
ejpam-5699	357	13	m.	m.	NOUN
ejpam-5699	357	14	al	al	PROPN
ejpam-5699	357	15	-	-	PUNCT
ejpam-5699	357	16	roqi	roqi	PROPN
ejpam-5699	357	17	.	.	PUNCT
ejpam-5699	358	1	ideal	ideal	ADJ
ejpam-5699	358	2	theory	theory	NOUN
ejpam-5699	358	3	of	of	ADP
ejpam-5699	358	4	bck	bck	PROPN
ejpam-5699	358	5	/	/	SYM
ejpam-5699	358	6	bci	bci	NOUN
ejpam-5699	358	7	-	-	PUNCT
ejpam-5699	358	8	algebras	algebra	NOUN
ejpam-5699	358	9	based	base	VERB
ejpam-5699	358	10	on	on	ADP
ejpam-5699	358	11	double	double	ADJ
ejpam-5699	358	12	-	-	PUNCT
ejpam-5699	358	13	framed	frame	VERB
ejpam-5699	358	14	soft	soft	ADJ
ejpam-5699	358	15	sets	set	NOUN
ejpam-5699	358	16	.	.	PUNCT
ejpam-5699	359	1	applied	apply	VERB
ejpam-5699	359	2	mathematics	mathematic	NOUN
ejpam-5699	359	3	and	and	CCONJ
ejpam-5699	359	4	information	information	NOUN
ejpam-5699	359	5	sciences	science	NOUN
ejpam-5699	359	6	,	,	PUNCT
ejpam-5699	359	7	7(5):1879	7(5):1879	NUM
ejpam-5699	359	8	,	,	PUNCT
ejpam-5699	359	9	2013	2013	NUM
ejpam-5699	359	10	.	.	PUNCT
ejpam-5699	360	1	[	[	X
ejpam-5699	360	2	12	12	NUM
ejpam-5699	360	3	]	]	X
ejpam-5699	360	4	y.	y.	PROPN
ejpam-5699	360	5	b.	b.	PROPN
ejpam-5699	360	6	jun	jun	PROPN
ejpam-5699	360	7	and	and	CCONJ
ejpam-5699	360	8	c.	c.	PROPN
ejpam-5699	360	9	h.	h.	PROPN
ejpam-5699	360	10	park	park	PROPN
ejpam-5699	360	11	.	.	PUNCT
ejpam-5699	361	1	filters	filter	NOUN
ejpam-5699	361	2	of	of	ADP
ejpam-5699	361	3	bch	bch	PROPN
ejpam-5699	361	4	-	-	PUNCT
ejpam-5699	361	5	algebras	algebras	PROPN
ejpam-5699	361	6	based	base	VERB
ejpam-5699	361	7	on	on	ADP
ejpam-5699	361	8	bipolar	bipolar	ADV
ejpam-5699	361	9	-	-	PUNCT
ejpam-5699	361	10	valued	value	VERB
ejpam-5699	361	11	fuzzy	fuzzy	ADJ
ejpam-5699	361	12	sets	set	NOUN
ejpam-5699	361	13	.	.	PUNCT
ejpam-5699	362	1	international	international	ADJ
ejpam-5699	362	2	mathematical	mathematical	PROPN
ejpam-5699	362	3	forum	forum	PROPN
ejpam-5699	362	4	,	,	PUNCT
ejpam-5699	362	5	4:631–643	4:631–643	PROPN
ejpam-5699	362	6	,	,	PUNCT
ejpam-5699	362	7	2009	2009	NUM
ejpam-5699	362	8	.	.	PUNCT
ejpam-5699	363	1	[	[	X
ejpam-5699	363	2	13	13	NUM
ejpam-5699	363	3	]	]	PUNCT
ejpam-5699	363	4	k.	k.	PROPN
ejpam-5699	363	5	kawila	kawila	PROPN
ejpam-5699	363	6	,	,	PUNCT
ejpam-5699	363	7	c.	c.	PROPN
ejpam-5699	363	8	udomsetchai	udomsetchai	PROPN
ejpam-5699	363	9	,	,	PUNCT
ejpam-5699	363	10	and	and	CCONJ
ejpam-5699	363	11	a.	a.	NOUN
ejpam-5699	363	12	iampan	iampan	PROPN
ejpam-5699	363	13	.	.	PUNCT
ejpam-5699	364	1	bipolar	bipolar	ADJ
ejpam-5699	364	2	fuzzy	fuzzy	ADJ
ejpam-5699	364	3	up	up	ADP
ejpam-5699	364	4	-	-	PUNCT
ejpam-5699	364	5	algebras	algebras	X
ejpam-5699	364	6	.	.	PUNCT
ejpam-5699	365	1	mathematical	mathematical	ADJ
ejpam-5699	365	2	and	and	CCONJ
ejpam-5699	365	3	computational	computational	ADJ
ejpam-5699	365	4	applications	application	NOUN
ejpam-5699	365	5	,	,	PUNCT
ejpam-5699	365	6	23(4):69	23(4):69	NUM
ejpam-5699	365	7	,	,	PUNCT
ejpam-5699	365	8	2018	2018	NUM
ejpam-5699	365	9	.	.	PUNCT
ejpam-5699	366	1	[	[	X
ejpam-5699	366	2	14	14	NUM
ejpam-5699	366	3	]	]	PUNCT
ejpam-5699	366	4	k.	k.	PROPN
ejpam-5699	366	5	j.	j.	PROPN
ejpam-5699	366	6	lee	lee	PROPN
ejpam-5699	366	7	.	.	PUNCT
ejpam-5699	367	1	bipolar	bipolar	ADJ
ejpam-5699	367	2	-	-	PUNCT
ejpam-5699	367	3	valued	value	VERB
ejpam-5699	367	4	fuzzy	fuzzy	ADJ
ejpam-5699	367	5	sets	set	NOUN
ejpam-5699	367	6	and	and	CCONJ
ejpam-5699	367	7	their	their	PRON
ejpam-5699	367	8	operations	operation	NOUN
ejpam-5699	367	9	.	.	PUNCT
ejpam-5699	368	1	in	in	ADP
ejpam-5699	368	2	proceedings	proceeding	NOUN
ejpam-5699	368	3	of	of	ADP
ejpam-5699	368	4	international	international	ADJ
ejpam-5699	368	5	conference	conference	NOUN
ejpam-5699	368	6	on	on	ADP
ejpam-5699	368	7	intelligent	intelligent	ADJ
ejpam-5699	368	8	technologies	technology	NOUN
ejpam-5699	368	9	,	,	PUNCT
ejpam-5699	368	10	pages	page	NOUN
ejpam-5699	368	11	307–312	307–312	NUM
ejpam-5699	368	12	,	,	PUNCT
ejpam-5699	368	13	bangkok	bangkok	PROPN
ejpam-5699	368	14	,	,	PUNCT
ejpam-5699	368	15	thailand	thailand	PROPN
ejpam-5699	368	16	,	,	PUNCT
ejpam-5699	368	17	2000	2000	NUM
ejpam-5699	368	18	.	.	PUNCT
ejpam-5699	369	1	[	[	X
ejpam-5699	369	2	15	15	NUM
ejpam-5699	369	3	]	]	PUNCT
ejpam-5699	369	4	k.	k.	PROPN
ejpam-5699	369	5	j.	j.	PROPN
ejpam-5699	369	6	lee	lee	PROPN
ejpam-5699	369	7	.	.	PUNCT
ejpam-5699	369	8	bipolar	bipolar	ADJ
ejpam-5699	369	9	fuzzy	fuzzy	ADJ
ejpam-5699	369	10	subalgebras	subalgebra	NOUN
ejpam-5699	369	11	and	and	CCONJ
ejpam-5699	369	12	bipolar	bipolar	ADJ
ejpam-5699	369	13	fuzzy	fuzzy	ADJ
ejpam-5699	369	14	ideals	ideal	NOUN
ejpam-5699	369	15	of	of	ADP
ejpam-5699	369	16	bck	bck	PROPN
ejpam-5699	369	17	/	/	SYM
ejpam-5699	369	18	bci	bci	NOUN
ejpam-5699	369	19	-	-	PUNCT
ejpam-5699	369	20	algebras	algebra	NOUN
ejpam-5699	369	21	.	.	PUNCT
ejpam-5699	369	22	bulletin	bulletin	NOUN
ejpam-5699	369	23	of	of	ADP
ejpam-5699	369	24	the	the	DET
ejpam-5699	369	25	malaysian	malaysian	PROPN
ejpam-5699	369	26	mathematical	mathematical	PROPN
ejpam-5699	369	27	sciences	sciences	PROPN
ejpam-5699	369	28	society	society	NOUN
ejpam-5699	369	29	,	,	PUNCT
ejpam-5699	369	30	32(3):361–373	32(3):361–373	PROPN
ejpam-5699	369	31	,	,	PUNCT
ejpam-5699	369	32	2009	2009	NUM
ejpam-5699	369	33	.	.	PUNCT
ejpam-5699	370	1	[	[	X
ejpam-5699	370	2	16	16	NUM
ejpam-5699	370	3	]	]	PUNCT
ejpam-5699	370	4	k.	k.	PROPN
ejpam-5699	370	5	j.	j.	PROPN
ejpam-5699	370	6	lee	lee	PROPN
ejpam-5699	370	7	and	and	CCONJ
ejpam-5699	370	8	y.	y.	PROPN
ejpam-5699	370	9	b.	b.	PROPN
ejpam-5699	370	10	jun	jun	PROPN
ejpam-5699	370	11	.	.	PUNCT
ejpam-5699	371	1	bipolar	bipolar	ADJ
ejpam-5699	371	2	fuzzy	fuzzy	ADJ
ejpam-5699	371	3	a	a	NOUN
ejpam-5699	371	4	-	-	PUNCT
ejpam-5699	371	5	ideals	ideal	NOUN
ejpam-5699	371	6	of	of	ADP
ejpam-5699	371	7	bci	bci	NOUN
ejpam-5699	371	8	-	-	PUNCT
ejpam-5699	371	9	algebras	algebra	NOUN
ejpam-5699	371	10	.	.	PUNCT
ejpam-5699	372	1	communications	communication	NOUN
ejpam-5699	372	2	of	of	ADP
ejpam-5699	372	3	the	the	DET
ejpam-5699	372	4	korean	korean	ADJ
ejpam-5699	372	5	mathematical	mathematical	ADJ
ejpam-5699	372	6	society	society	NOUN
ejpam-5699	372	7	,	,	PUNCT
ejpam-5699	372	8	26(4):531–542	26(4):531–542	PROPN
ejpam-5699	372	9	,	,	PUNCT
ejpam-5699	372	10	2011	2011	NUM
ejpam-5699	372	11	.	.	PUNCT
ejpam-5699	373	1	[	[	X
ejpam-5699	373	2	17	17	NUM
ejpam-5699	373	3	]	]	X
ejpam-5699	373	4	c.	c.	PROPN
ejpam-5699	373	5	lele	lele	PROPN
ejpam-5699	373	6	and	and	CCONJ
ejpam-5699	373	7	s.	s.	PROPN
ejpam-5699	373	8	moutari	moutari	PROPN
ejpam-5699	373	9	.	.	PUNCT
ejpam-5699	374	1	foldness	foldness	NOUN
ejpam-5699	374	2	of	of	ADP
ejpam-5699	374	3	commutative	commutative	ADJ
ejpam-5699	374	4	ideals	ideal	NOUN
ejpam-5699	374	5	in	in	ADP
ejpam-5699	374	6	bck	bck	NOUN
ejpam-5699	374	7	-	-	PUNCT
ejpam-5699	374	8	algebras	algebras	PROPN
ejpam-5699	374	9	.	.	PUNCT
ejpam-5699	375	1	discussiones	discussione	NOUN
ejpam-5699	375	2	mathematicae	mathematicae	VERB
ejpam-5699	375	3	general	general	ADJ
ejpam-5699	375	4	algebra	algebra	PROPN
ejpam-5699	375	5	and	and	CCONJ
ejpam-5699	375	6	applications	application	NOUN
ejpam-5699	375	7	,	,	PUNCT
ejpam-5699	375	8	26(1):111–135	26(1):111–135	NOUN
ejpam-5699	375	9	,	,	PUNCT
ejpam-5699	375	10	2006	2006	NUM
ejpam-5699	375	11	.	.	PUNCT
ejpam-5699	376	1	[	[	X
ejpam-5699	376	2	18	18	NUM
ejpam-5699	376	3	]	]	X
ejpam-5699	376	4	y.	y.	PROPN
ejpam-5699	376	5	l.	l.	PROPN
ejpam-5699	376	6	liu	liu	PROPN
ejpam-5699	376	7	,	,	PUNCT
ejpam-5699	376	8	y.	y.	PROPN
ejpam-5699	376	9	xu	xu	PROPN
ejpam-5699	376	10	,	,	PUNCT
ejpam-5699	376	11	and	and	CCONJ
ejpam-5699	376	12	j.	j.	PROPN
ejpam-5699	376	13	meng	meng	PROPN
ejpam-5699	376	14	.	.	PUNCT
ejpam-5699	377	1	bci	bci	ADJ
ejpam-5699	377	2	-	-	ADJ
ejpam-5699	377	3	implicative	implicative	ADJ
ejpam-5699	377	4	ideals	ideal	NOUN
ejpam-5699	377	5	of	of	ADP
ejpam-5699	377	6	bci	bci	NOUN
ejpam-5699	377	7	-	-	PUNCT
ejpam-5699	377	8	algebras	algebra	NOUN
ejpam-5699	377	9	.	.	PUNCT
ejpam-5699	378	1	information	information	NOUN
ejpam-5699	378	2	sciences	sciences	PROPN
ejpam-5699	378	3	,	,	PUNCT
ejpam-5699	378	4	177(22):4987–4996	177(22):4987–4996	NUM
ejpam-5699	378	5	,	,	PUNCT
ejpam-5699	378	6	2007	2007	NUM
ejpam-5699	378	7	.	.	PUNCT
ejpam-5699	379	1	[	[	X
ejpam-5699	379	2	19	19	NUM
ejpam-5699	379	3	]	]	PUNCT
ejpam-5699	379	4	t.	t.	PROPN
ejpam-5699	379	5	mahmood	mahmood	PROPN
ejpam-5699	379	6	,	,	PUNCT
ejpam-5699	379	7	k.	k.	PROPN
ejpam-5699	379	8	hussain	hussain	PROPN
ejpam-5699	379	9	,	,	PUNCT
ejpam-5699	379	10	j.	j.	PROPN
ejpam-5699	379	11	ahmmad	ahmmad	PROPN
ejpam-5699	379	12	,	,	PUNCT
ejpam-5699	379	13	s.	s.	PROPN
ejpam-5699	379	14	shahab	shahab	PROPN
ejpam-5699	379	15	,	,	PUNCT
ejpam-5699	379	16	u.	u.	PROPN
ejpam-5699	379	17	u.	u.	PROPN
ejpam-5699	379	18	rehman	rehman	PROPN
ejpam-5699	379	19	,	,	PUNCT
ejpam-5699	379	20	and	and	CCONJ
ejpam-5699	379	21	m.	m.	PROPN
ejpam-5699	379	22	anjum	anjum	PROPN
ejpam-5699	379	23	.	.	PUNCT
ejpam-5699	380	1	t	t	PROPN
ejpam-5699	380	2	-bipolar	-bipolar	ADJ
ejpam-5699	380	3	soft	soft	ADJ
ejpam-5699	380	4	groups	group	NOUN
ejpam-5699	380	5	and	and	CCONJ
ejpam-5699	380	6	their	their	PRON
ejpam-5699	380	7	fundamental	fundamental	ADJ
ejpam-5699	380	8	laws	law	NOUN
ejpam-5699	380	9	.	.	PUNCT
ejpam-5699	381	1	journal	journal	NOUN
ejpam-5699	381	2	of	of	ADP
ejpam-5699	381	3	intelligent	intelligent	ADJ
ejpam-5699	381	4	and	and	CCONJ
ejpam-5699	381	5	fuzzy	fuzzy	ADJ
ejpam-5699	381	6	systems	system	NOUN
ejpam-5699	381	7	,	,	PUNCT
ejpam-5699	381	8	46(4):9479–9490	46(4):9479–9490	NUM
ejpam-5699	381	9	,	,	PUNCT
ejpam-5699	381	10	2024	2024	NUM
ejpam-5699	381	11	.	.	PUNCT
ejpam-5699	382	1	[	[	X
ejpam-5699	382	2	20	20	NUM
ejpam-5699	382	3	]	]	PUNCT
ejpam-5699	382	4	t.	t.	PROPN
ejpam-5699	382	5	mahmood	mahmood	PROPN
ejpam-5699	382	6	,	,	PUNCT
ejpam-5699	382	7	u.	u.	PROPN
ejpam-5699	382	8	u.	u.	PROPN
ejpam-5699	382	9	rehman	rehman	PROPN
ejpam-5699	382	10	,	,	PUNCT
ejpam-5699	382	11	and	and	CCONJ
ejpam-5699	382	12	m.	m.	NOUN
ejpam-5699	382	13	albaity	albaity	NOUN
ejpam-5699	382	14	.	.	PUNCT
ejpam-5699	383	1	analysis	analysis	NOUN
ejpam-5699	383	2	of	of	ADP
ejpam-5699	383	3	γ	γ	NOUN
ejpam-5699	383	4	-	-	PUNCT
ejpam-5699	383	5	semigroups	semigroup	NOUN
ejpam-5699	383	6	based	base	VERB
ejpam-5699	383	7	on	on	ADP
ejpam-5699	383	8	d.	d.	PROPN
ejpam-5699	383	9	ramesh	ramesh	PROPN
ejpam-5699	383	10	et	et	PROPN
ejpam-5699	383	11	al	al	PROPN
ejpam-5699	383	12	.	.	PUNCT
ejpam-5699	383	13	/	/	SYM
ejpam-5699	383	14	eur	eur	PROPN
ejpam-5699	383	15	.	.	PUNCT
ejpam-5699	384	1	j.	j.	PROPN
ejpam-5699	384	2	pure	pure	PROPN
ejpam-5699	384	3	appl	appl	PROPN
ejpam-5699	384	4	.	.	PROPN
ejpam-5699	384	5	math	math	PROPN
ejpam-5699	384	6	,	,	PUNCT
ejpam-5699	384	7	18	18	NUM
ejpam-5699	384	8	(	(	PUNCT
ejpam-5699	384	9	1	1	NUM
ejpam-5699	384	10	)	)	PUNCT
ejpam-5699	384	11	(	(	PUNCT
ejpam-5699	384	12	2025	2025	NUM
ejpam-5699	384	13	)	)	PUNCT
ejpam-5699	384	14	,	,	PUNCT
ejpam-5699	384	15	5699	5699	NUM
ejpam-5699	384	16	20	20	NUM
ejpam-5699	384	17	of	of	ADP
ejpam-5699	384	18	20	20	NUM
ejpam-5699	384	19	bipolar	bipolar	ADJ
ejpam-5699	384	20	complex	complex	ADJ
ejpam-5699	384	21	fuzzy	fuzzy	ADJ
ejpam-5699	384	22	sets	set	NOUN
ejpam-5699	384	23	.	.	PUNCT
ejpam-5699	385	1	computational	computational	ADJ
ejpam-5699	385	2	and	and	CCONJ
ejpam-5699	385	3	applied	applied	ADJ
ejpam-5699	385	4	mathematics	mathematic	NOUN
ejpam-5699	385	5	,	,	PUNCT
ejpam-5699	385	6	42:262	42:262	NUM
ejpam-5699	385	7	,	,	PUNCT
ejpam-5699	385	8	2023	2023	NUM
ejpam-5699	385	9	.	.	PUNCT
ejpam-5699	386	1	[	[	X
ejpam-5699	386	2	21	21	NUM
ejpam-5699	386	3	]	]	X
ejpam-5699	386	4	j.	j.	PROPN
ejpam-5699	386	5	meng	meng	PROPN
ejpam-5699	386	6	and	and	CCONJ
ejpam-5699	386	7	x.-é	x.-é	PROPN
ejpam-5699	386	8	guo	guo	PROPN
ejpam-5699	386	9	.	.	PUNCT
ejpam-5699	387	1	on	on	ADP
ejpam-5699	387	2	fuzzy	fuzzy	ADJ
ejpam-5699	387	3	ideals	ideal	NOUN
ejpam-5699	387	4	in	in	ADP
ejpam-5699	387	5	bck	bck	PROPN
ejpam-5699	387	6	/	/	SYM
ejpam-5699	387	7	bci	bci	NOUN
ejpam-5699	387	8	-	-	PUNCT
ejpam-5699	387	9	algebras	algebras	X
ejpam-5699	387	10	.	.	PUNCT
ejpam-5699	388	1	fuzzy	fuzzy	ADJ
ejpam-5699	388	2	sets	set	NOUN
ejpam-5699	388	3	and	and	CCONJ
ejpam-5699	388	4	systems	system	NOUN
ejpam-5699	388	5	,	,	PUNCT
ejpam-5699	388	6	149(3):509–525	149(3):509–525	NUM
ejpam-5699	388	7	,	,	PUNCT
ejpam-5699	388	8	2005	2005	NUM
ejpam-5699	388	9	.	.	PUNCT
ejpam-5699	389	1	[	[	X
ejpam-5699	389	2	22	22	NUM
ejpam-5699	389	3	]	]	X
ejpam-5699	389	4	g.	g.	PROPN
ejpam-5699	389	5	muhiuddin	muhiuddin	PROPN
ejpam-5699	389	6	,	,	PUNCT
ejpam-5699	389	7	d.	d.	PROPN
ejpam-5699	389	8	al	al	PROPN
ejpam-5699	389	9	-	-	PUNCT
ejpam-5699	389	10	kadi	kadi	PROPN
ejpam-5699	389	11	,	,	PUNCT
ejpam-5699	389	12	a.	a.	NOUN
ejpam-5699	389	13	mahboob	mahboob	PROPN
ejpam-5699	389	14	,	,	PUNCT
ejpam-5699	389	15	and	and	CCONJ
ejpam-5699	389	16	k.	k.	PROPN
ejpam-5699	389	17	p.	p.	PROPN
ejpam-5699	389	18	shum	shum	PROPN
ejpam-5699	389	19	.	.	PUNCT
ejpam-5699	390	1	new	new	ADJ
ejpam-5699	390	2	types	type	NOUN
ejpam-5699	390	3	of	of	ADP
ejpam-5699	390	4	bipolar	bipolar	ADJ
ejpam-5699	390	5	fuzzy	fuzzy	ADJ
ejpam-5699	390	6	ideals	ideal	NOUN
ejpam-5699	390	7	of	of	ADP
ejpam-5699	390	8	bck	bck	NOUN
ejpam-5699	390	9	-	-	PUNCT
ejpam-5699	390	10	algebras	algebras	PROPN
ejpam-5699	390	11	.	.	PUNCT
ejpam-5699	391	1	international	international	ADJ
ejpam-5699	391	2	journal	journal	NOUN
ejpam-5699	391	3	of	of	ADP
ejpam-5699	391	4	analysis	analysis	NOUN
ejpam-5699	391	5	and	and	CCONJ
ejpam-5699	391	6	applications	application	NOUN
ejpam-5699	391	7	,	,	PUNCT
ejpam-5699	391	8	18(5):859–875	18(5):859–875	PROPN
ejpam-5699	391	9	,	,	PUNCT
ejpam-5699	391	10	2020	2020	NUM
ejpam-5699	391	11	.	.	PUNCT
ejpam-5699	392	1	[	[	X
ejpam-5699	392	2	23	23	NUM
ejpam-5699	392	3	]	]	X
ejpam-5699	392	4	g.	g.	PROPN
ejpam-5699	392	5	muhiuddin	muhiuddin	PROPN
ejpam-5699	392	6	,	,	PUNCT
ejpam-5699	392	7	h.	h.	PROPN
ejpam-5699	392	8	harizavi	harizavi	PROPN
ejpam-5699	392	9	,	,	PUNCT
ejpam-5699	392	10	and	and	CCONJ
ejpam-5699	392	11	y.	y.	PROPN
ejpam-5699	392	12	b.	b.	PROPN
ejpam-5699	392	13	jun	jun	PROPN
ejpam-5699	392	14	.	.	PROPN
ejpam-5699	392	15	bipolar	bipolar	ADJ
ejpam-5699	392	16	-	-	PUNCT
ejpam-5699	392	17	valued	value	VERB
ejpam-5699	392	18	fuzzy	fuzzy	ADJ
ejpam-5699	392	19	soft	soft	ADJ
ejpam-5699	392	20	hyper	hyper	ADJ
ejpam-5699	392	21	bckideals	bckideal	NOUN
ejpam-5699	392	22	in	in	ADP
ejpam-5699	392	23	hyper	hyper	ADJ
ejpam-5699	392	24	bck	bck	NOUN
ejpam-5699	392	25	-	-	PUNCT
ejpam-5699	392	26	algebras	algebras	PROPN
ejpam-5699	392	27	.	.	PUNCT
ejpam-5699	393	1	discrete	discrete	ADJ
ejpam-5699	393	2	mathematics	mathematic	NOUN
ejpam-5699	393	3	,	,	PUNCT
ejpam-5699	393	4	algorithms	algorithm	NOUN
ejpam-5699	393	5	and	and	CCONJ
ejpam-5699	393	6	applications	application	NOUN
ejpam-5699	393	7	,	,	PUNCT
ejpam-5699	393	8	12(02):2050018	12(02):2050018	NUM
ejpam-5699	393	9	,	,	PUNCT
ejpam-5699	393	10	2020	2020	NUM
ejpam-5699	393	11	.	.	PUNCT
ejpam-5699	394	1	[	[	X
ejpam-5699	394	2	24	24	NUM
ejpam-5699	394	3	]	]	X
ejpam-5699	394	4	u.	u.	PROPN
ejpam-5699	394	5	u.	u.	PROPN
ejpam-5699	394	6	rehman	rehman	PROPN
ejpam-5699	394	7	,	,	PUNCT
ejpam-5699	394	8	t.	t.	PROPN
ejpam-5699	394	9	mahmood	mahmood	PROPN
ejpam-5699	394	10	,	,	PUNCT
ejpam-5699	394	11	and	and	CCONJ
ejpam-5699	394	12	m.	m.	PROPN
ejpam-5699	394	13	naeem	naeem	PROPN
ejpam-5699	394	14	.	.	PUNCT
ejpam-5699	395	1	bipolar	bipolar	ADJ
ejpam-5699	395	2	complex	complex	ADJ
ejpam-5699	395	3	fuzzy	fuzzy	ADJ
ejpam-5699	395	4	semigroups	semigroup	NOUN
ejpam-5699	395	5	.	.	PUNCT
ejpam-5699	396	1	aims	aim	VERB
ejpam-5699	396	2	mathematics	mathematic	NOUN
ejpam-5699	396	3	,	,	PUNCT
ejpam-5699	396	4	8(2):3997–4021	8(2):3997–4021	NOUN
ejpam-5699	396	5	,	,	PUNCT
ejpam-5699	396	6	2023	2023	NUM
ejpam-5699	396	7	.	.	PUNCT
ejpam-5699	397	1	[	[	X
ejpam-5699	397	2	25	25	NUM
ejpam-5699	397	3	]	]	PUNCT
ejpam-5699	397	4	s.	s.	PROPN
ejpam-5699	397	5	sabarinathan	sabarinathan	PROPN
ejpam-5699	397	6	,	,	PUNCT
ejpam-5699	397	7	p.	p.	NOUN
ejpam-5699	397	8	muralikrishna	muralikrishna	NOUN
ejpam-5699	397	9	,	,	PUNCT
ejpam-5699	397	10	and	and	CCONJ
ejpam-5699	397	11	d.	d.	PROPN
ejpam-5699	397	12	c.	c.	PROPN
ejpam-5699	397	13	kumar	kumar	PROPN
ejpam-5699	397	14	.	.	PUNCT
ejpam-5699	398	1	bipolar	bipolar	PROPN
ejpam-5699	398	2	valued	value	VERB
ejpam-5699	398	3	fuzzy	fuzzy	ADJ
ejpam-5699	398	4	h	h	NOUN
ejpam-5699	398	5	-	-	PUNCT
ejpam-5699	398	6	ideals	ideal	NOUN
ejpam-5699	398	7	of	of	ADP
ejpam-5699	398	8	bf	bf	NOUN
ejpam-5699	398	9	-	-	PUNCT
ejpam-5699	398	10	algebras	algebras	PROPN
ejpam-5699	398	11	.	.	PUNCT
ejpam-5699	399	1	international	international	ADJ
ejpam-5699	399	2	journal	journal	PROPN
ejpam-5699	399	3	of	of	ADP
ejpam-5699	399	4	pure	pure	ADJ
ejpam-5699	399	5	and	and	CCONJ
ejpam-5699	399	6	applied	applied	ADJ
ejpam-5699	399	7	mathematics	mathematic	NOUN
ejpam-5699	399	8	,	,	PUNCT
ejpam-5699	399	9	112(5):87–92	112(5):87–92	NUM
ejpam-5699	399	10	,	,	PUNCT
ejpam-5699	399	11	2017	2017	NUM
ejpam-5699	399	12	.	.	PUNCT
ejpam-5699	400	1	[	[	X
ejpam-5699	400	2	26	26	NUM
ejpam-5699	400	3	]	]	X
ejpam-5699	400	4	b.	b.	PROPN
ejpam-5699	400	5	satyanarayana	satyanarayana	PROPN
ejpam-5699	400	6	,	,	PUNCT
ejpam-5699	400	7	s.	s.	PROPN
ejpam-5699	400	8	baji	baji	PROPN
ejpam-5699	400	9	,	,	PUNCT
ejpam-5699	400	10	and	and	CCONJ
ejpam-5699	400	11	d.	d.	PROPN
ejpam-5699	400	12	ramesh	ramesh	PROPN
ejpam-5699	400	13	.	.	PUNCT
ejpam-5699	401	1	bipolar	bipolar	ADJ
ejpam-5699	401	2	intuitionistic	intuitionistic	ADJ
ejpam-5699	401	3	fuzzy	fuzzy	ADJ
ejpam-5699	401	4	implicative	implicative	ADJ
ejpam-5699	401	5	ideals	ideal	NOUN
ejpam-5699	401	6	of	of	ADP
ejpam-5699	401	7	bck	bck	NOUN
ejpam-5699	401	8	-	-	PUNCT
ejpam-5699	401	9	algebra	algebra	NOUN
ejpam-5699	401	10	.	.	PUNCT
ejpam-5699	402	1	asia	asia	PROPN
ejpam-5699	402	2	pacific	pacific	PROPN
ejpam-5699	402	3	journal	journal	PROPN
ejpam-5699	402	4	of	of	ADP
ejpam-5699	402	5	mathematics	mathematic	NOUN
ejpam-5699	402	6	,	,	PUNCT
ejpam-5699	402	7	10:47	10:47	NUM
ejpam-5699	402	8	,	,	PUNCT
ejpam-5699	402	9	2023	2023	NUM
ejpam-5699	402	10	.	.	PUNCT
ejpam-5699	403	1	[	[	X
ejpam-5699	403	2	27	27	NUM
ejpam-5699	403	3	]	]	X
ejpam-5699	403	4	b.	b.	PROPN
ejpam-5699	403	5	satyanarayana	satyanarayana	PROPN
ejpam-5699	403	6	,	,	PUNCT
ejpam-5699	403	7	d.	d.	PROPN
ejpam-5699	403	8	ramesh	ramesh	PROPN
ejpam-5699	403	9	,	,	PUNCT
ejpam-5699	403	10	and	and	CCONJ
ejpam-5699	403	11	m.	m.	NOUN
ejpam-5699	403	12	v.	v.	PROPN
ejpam-5699	403	13	kumar	kumar	PROPN
ejpam-5699	403	14	.	.	PUNCT
ejpam-5699	404	1	on	on	ADP
ejpam-5699	404	2	fuzzy	fuzzy	ADJ
ejpam-5699	404	3	ideals	ideal	NOUN
ejpam-5699	404	4	in	in	ADP
ejpam-5699	404	5	bf	bf	NOUN
ejpam-5699	404	6	-	-	PUNCT
ejpam-5699	404	7	algebras	algebras	PROPN
ejpam-5699	404	8	.	.	PUNCT
ejpam-5699	405	1	international	international	ADJ
ejpam-5699	405	2	journal	journal	PROPN
ejpam-5699	405	3	of	of	ADP
ejpam-5699	405	4	mathematical	mathematical	ADJ
ejpam-5699	405	5	sciences	sciences	PROPN
ejpam-5699	405	6	and	and	CCONJ
ejpam-5699	405	7	engineering	engineering	NOUN
ejpam-5699	405	8	applications	application	NOUN
ejpam-5699	405	9	,	,	PUNCT
ejpam-5699	405	10	4(5):263	4(5):263	NUM
ejpam-5699	405	11	–	–	PUNCT
ejpam-5699	405	12	274	274	NUM
ejpam-5699	405	13	,	,	PUNCT
ejpam-5699	405	14	2010	2010	NUM
ejpam-5699	405	15	.	.	PUNCT
ejpam-5699	406	1	[	[	X
ejpam-5699	406	2	28	28	NUM
ejpam-5699	406	3	]	]	X
ejpam-5699	406	4	b.	b.	PROPN
ejpam-5699	406	5	satyanarayana	satyanarayana	PROPN
ejpam-5699	406	6	,	,	PUNCT
ejpam-5699	406	7	d.	d.	PROPN
ejpam-5699	406	8	ramesh	ramesh	PROPN
ejpam-5699	406	9	,	,	PUNCT
ejpam-5699	406	10	and	and	CCONJ
ejpam-5699	406	11	p.	p.	PROPN
ejpam-5699	406	12	h.	h.	PROPN
ejpam-5699	406	13	sundari	sundari	PROPN
ejpam-5699	406	14	.	.	PUNCT
ejpam-5699	407	1	on	on	ADP
ejpam-5699	407	2	quotient	quotient	NOUN
ejpam-5699	407	3	bf	bf	NOUN
ejpam-5699	407	4	-	-	PUNCT
ejpam-5699	407	5	algebras	algebras	NOUN
ejpam-5699	407	6	via	via	ADP
ejpam-5699	407	7	interval	interval	NOUN
ejpam-5699	407	8	-	-	PUNCT
ejpam-5699	407	9	valued	value	VERB
ejpam-5699	407	10	fuzzy	fuzzy	ADJ
ejpam-5699	407	11	ideals	ideal	NOUN
ejpam-5699	407	12	.	.	PUNCT
ejpam-5699	408	1	international	international	ADJ
ejpam-5699	408	2	journal	journal	NOUN
ejpam-5699	408	3	of	of	ADP
ejpam-5699	408	4	fuzzy	fuzzy	ADJ
ejpam-5699	408	5	mathematical	mathematical	ADJ
ejpam-5699	408	6	archive	archive	NOUN
ejpam-5699	408	7	,	,	PUNCT
ejpam-5699	408	8	10(2):179–184	10(2):179–184	PROPN
ejpam-5699	408	9	,	,	PUNCT
ejpam-5699	408	10	2016	2016	NUM
ejpam-5699	408	11	.	.	PUNCT
ejpam-5699	409	1	[	[	X
ejpam-5699	409	2	29	29	NUM
ejpam-5699	409	3	]	]	PUNCT
ejpam-5699	409	4	t.	t.	NOUN
ejpam-5699	409	5	senapati	senapati	PROPN
ejpam-5699	409	6	.	.	PUNCT
ejpam-5699	410	1	on	on	ADP
ejpam-5699	410	2	bipolar	bipolar	ADJ
ejpam-5699	410	3	fuzzy	fuzzy	ADJ
ejpam-5699	410	4	b	b	NOUN
ejpam-5699	410	5	-	-	PUNCT
ejpam-5699	410	6	subalgebras	subalgebras	PROPN
ejpam-5699	410	7	of	of	ADP
ejpam-5699	410	8	b	b	PROPN
ejpam-5699	410	9	-	-	PUNCT
ejpam-5699	410	10	algebras	algebras	PROPN
ejpam-5699	410	11	.	.	PUNCT
ejpam-5699	411	1	in	in	ADP
ejpam-5699	411	2	emerging	emerge	VERB
ejpam-5699	411	3	research	research	NOUN
ejpam-5699	411	4	on	on	ADP
ejpam-5699	411	5	applied	apply	VERB
ejpam-5699	411	6	fuzzy	fuzzy	ADJ
ejpam-5699	411	7	sets	set	NOUN
ejpam-5699	411	8	and	and	CCONJ
ejpam-5699	411	9	intuitionistic	intuitionistic	ADJ
ejpam-5699	411	10	fuzzy	fuzzy	ADJ
ejpam-5699	411	11	matrices	matrix	NOUN
ejpam-5699	411	12	,	,	PUNCT
ejpam-5699	411	13	pages	page	NOUN
ejpam-5699	411	14	254–267	254–267	NUM
ejpam-5699	411	15	.	.	PUNCT
ejpam-5699	412	1	igi	igi	PROPN
ejpam-5699	412	2	global	global	PROPN
ejpam-5699	412	3	,	,	PUNCT
ejpam-5699	412	4	2017	2017	NUM
ejpam-5699	412	5	.	.	PUNCT
ejpam-5699	413	1	[	[	X
ejpam-5699	413	2	30	30	NUM
ejpam-5699	413	3	]	]	PUNCT
ejpam-5699	413	4	x.	x.	PROPN
ejpam-5699	413	5	yang	yang	PROPN
ejpam-5699	413	6	,	,	PUNCT
ejpam-5699	413	7	t.	t.	PROPN
ejpam-5699	413	8	mahmood	mahmood	PROPN
ejpam-5699	413	9	,	,	PUNCT
ejpam-5699	413	10	and	and	CCONJ
ejpam-5699	413	11	u.	u.	PROPN
ejpam-5699	413	12	u.	u.	PROPN
ejpam-5699	413	13	rehman	rehman	PROPN
ejpam-5699	413	14	.	.	PUNCT
ejpam-5699	414	1	bipolar	bipolar	ADJ
ejpam-5699	414	2	complex	complex	ADJ
ejpam-5699	414	3	fuzzy	fuzzy	ADJ
ejpam-5699	414	4	subgroups	subgroup	NOUN
ejpam-5699	414	5	.	.	PUNCT
ejpam-5699	415	1	mathematics	mathematic	NOUN
ejpam-5699	415	2	,	,	PUNCT
ejpam-5699	415	3	10(16):2882	10(16):2882	NUM
ejpam-5699	415	4	,	,	PUNCT
ejpam-5699	415	5	2022	2022	NUM
ejpam-5699	415	6	.	.	PUNCT
ejpam-5699	416	1	[	[	X
ejpam-5699	416	2	31	31	NUM
ejpam-5699	416	3	]	]	PUNCT
ejpam-5699	416	4	l.	l.	PROPN
ejpam-5699	416	5	a.	a.	PROPN
ejpam-5699	416	6	zadeh	zadeh	PROPN
ejpam-5699	416	7	.	.	PUNCT
ejpam-5699	416	8	fuzzy	fuzzy	ADJ
ejpam-5699	416	9	sets	set	NOUN
ejpam-5699	416	10	.	.	PUNCT
ejpam-5699	417	1	information	information	NOUN
ejpam-5699	417	2	and	and	CCONJ
ejpam-5699	417	3	control	control	NOUN
ejpam-5699	417	4	,	,	PUNCT
ejpam-5699	417	5	8(3):338–353	8(3):338–353	NUM
ejpam-5699	417	6	,	,	PUNCT
ejpam-5699	417	7	1965	1965	NUM
ejpam-5699	417	8	.	.	PUNCT
ejpam-5699	418	1	[	[	X
ejpam-5699	418	2	32	32	NUM
ejpam-5699	418	3	]	]	PUNCT
ejpam-5699	418	4	w.-r	w.-r	PROPN
ejpam-5699	418	5	.	.	PUNCT
ejpam-5699	419	1	zhang	zhang	PROPN
ejpam-5699	419	2	.	.	PUNCT
ejpam-5699	419	3	bipolar	bipolar	ADJ
ejpam-5699	419	4	fuzzy	fuzzy	ADJ
ejpam-5699	419	5	sets	set	NOUN
ejpam-5699	419	6	.	.	PUNCT
ejpam-5699	420	1	in	in	ADP
ejpam-5699	420	2	1998	1998	NUM
ejpam-5699	420	3	ieee	ieee	NOUN
ejpam-5699	420	4	international	international	ADJ
ejpam-5699	420	5	conference	conference	NOUN
ejpam-5699	420	6	on	on	ADP
ejpam-5699	420	7	fuzzy	fuzzy	ADJ
ejpam-5699	420	8	systems	system	NOUN
ejpam-5699	420	9	proceedings	proceeding	NOUN
ejpam-5699	420	10	vol	vol	NOUN
ejpam-5699	420	11	.	.	PROPN
ejpam-5699	420	12	1	1	NUM
ejpam-5699	420	13	,	,	PUNCT
ejpam-5699	420	14	ieee	ieee	NOUN
ejpam-5699	420	15	world	world	PROPN
ejpam-5699	420	16	congress	congress	PROPN
ejpam-5699	420	17	on	on	ADP
ejpam-5699	420	18	computational	computational	ADJ
ejpam-5699	420	19	intelligence	intelligence	NOUN
ejpam-5699	420	20	(	(	PUNCT
ejpam-5699	420	21	cat	cat	NOUN
ejpam-5699	420	22	.	.	PUNCT
ejpam-5699	421	1	no	no	INTJ
ejpam-5699	421	2	.	.	PUNCT
ejpam-5699	422	1	98ch36228	98ch36228	NUM
ejpam-5699	422	2	)	)	PUNCT
ejpam-5699	422	3	,	,	PUNCT
ejpam-5699	422	4	pages	page	VERB
ejpam-5699	422	5	835–840	835–840	NUM
ejpam-5699	422	6	.	.	PUNCT
ejpam-5699	423	1	ieee	ieee	PROPN
ejpam-5699	423	2	,	,	PUNCT
ejpam-5699	423	3	1998	1998	NUM
ejpam-5699	423	4	.	.	PUNCT
ejpam-5699	424	1	[	[	X
ejpam-5699	424	2	33	33	NUM
ejpam-5699	424	3	]	]	PUNCT
ejpam-5699	424	4	w.-r	w.-r	PROPN
ejpam-5699	424	5	.	.	PUNCT
ejpam-5699	425	1	zhang	zhang	PROPN
ejpam-5699	425	2	.	.	PUNCT
ejpam-5699	425	3	bipolar	bipolar	ADJ
ejpam-5699	425	4	logic	logic	NOUN
ejpam-5699	425	5	and	and	CCONJ
ejpam-5699	425	6	bipolar	bipolar	ADJ
ejpam-5699	425	7	fuzzy	fuzzy	ADJ
ejpam-5699	425	8	logic	logic	NOUN
ejpam-5699	425	9	-	-	PUNCT
ejpam-5699	425	10	a	a	DET
ejpam-5699	425	11	unification	unification	NOUN
ejpam-5699	425	12	of	of	ADP
ejpam-5699	425	13	truth	truth	NOUN
ejpam-5699	425	14	,	,	PUNCT
ejpam-5699	425	15	fuzziness	fuzziness	NOUN
ejpam-5699	425	16	,	,	PUNCT
ejpam-5699	425	17	and	and	CCONJ
ejpam-5699	425	18	bipolarity	bipolarity	NOUN
ejpam-5699	425	19	.	.	PUNCT
ejpam-5699	426	1	in	in	ADP
ejpam-5699	426	2	2002	2002	NUM
ejpam-5699	426	3	annual	annual	ADJ
ejpam-5699	426	4	meeting	meeting	NOUN
ejpam-5699	426	5	of	of	ADP
ejpam-5699	426	6	the	the	DET
ejpam-5699	426	7	north	north	ADJ
ejpam-5699	426	8	american	american	ADJ
ejpam-5699	426	9	fuzzy	fuzzy	ADJ
ejpam-5699	426	10	information	information	NOUN
ejpam-5699	426	11	processing	process	VERB
ejpam-5699	426	12	society	society	NOUN
ejpam-5699	426	13	proceedings	proceeding	NOUN
ejpam-5699	426	14	,	,	PUNCT
ejpam-5699	426	15	nafips	nafips	NOUN
ejpam-5699	426	16	-	-	PUNCT
ejpam-5699	426	17	flint	flint	NOUN
ejpam-5699	426	18	2002	2002	NUM
ejpam-5699	426	19	(	(	PUNCT
ejpam-5699	426	20	cat	cat	NOUN
ejpam-5699	426	21	.	.	PUNCT
ejpam-5699	427	1	no	no	INTJ
ejpam-5699	427	2	.	.	PUNCT
ejpam-5699	428	1	02th8622	02th8622	NUM
ejpam-5699	428	2	)	)	PUNCT
ejpam-5699	428	3	,	,	PUNCT
ejpam-5699	428	4	pages	page	NOUN
ejpam-5699	428	5	286–291	286–291	NUM
ejpam-5699	428	6	.	.	PUNCT
ejpam-5699	428	7	ieee	ieee	PROPN
ejpam-5699	428	8	,	,	PUNCT
ejpam-5699	428	9	2002	2002	NUM
ejpam-5699	428	10	.	.	PUNCT