id	sid	tid	token	lemma	pos
ejpam-6798	1	1	european	european	PROPN
ejpam-6798	1	2	journal	journal	PROPN
ejpam-6798	1	3	of	of	ADP
ejpam-6798	1	4	pure	pure	ADJ
ejpam-6798	1	5	and	and	CCONJ
ejpam-6798	1	6	applied	applied	ADJ
ejpam-6798	1	7	mathematics	mathematic	NOUN
ejpam-6798	1	8	2025	2025	NUM
ejpam-6798	1	9	,	,	PUNCT
ejpam-6798	1	10	vol	vol	NOUN
ejpam-6798	1	11	.	.	PROPN
ejpam-6798	1	12	18	18	NUM
ejpam-6798	1	13	,	,	PUNCT
ejpam-6798	1	14	issue	issue	NOUN
ejpam-6798	1	15	4	4	NUM
ejpam-6798	1	16	,	,	PUNCT
ejpam-6798	1	17	article	article	NOUN
ejpam-6798	1	18	number	number	NOUN
ejpam-6798	1	19	6798	6798	NUM
ejpam-6798	1	20	issn	issn	PROPN
ejpam-6798	1	21	1307	1307	NUM
ejpam-6798	1	22	-	-	SYM
ejpam-6798	1	23	5543	5543	NUM
ejpam-6798	1	24	–	–	PUNCT
ejpam-6798	1	25	ejpam.com	ejpam.com	X
ejpam-6798	1	26	published	publish	VERB
ejpam-6798	1	27	by	by	ADP
ejpam-6798	1	28	new	new	PROPN
ejpam-6798	1	29	york	york	PROPN
ejpam-6798	1	30	business	business	PROPN
ejpam-6798	1	31	global	global	PROPN
ejpam-6798	1	32	an	an	DET
ejpam-6798	1	33	innovative	innovative	ADJ
ejpam-6798	1	34	method	method	NOUN
ejpam-6798	1	35	for	for	ADP
ejpam-6798	1	36	employing	employ	VERB
ejpam-6798	1	37	complex	complex	ADJ
ejpam-6798	1	38	intuitionistic	intuitionistic	ADJ
ejpam-6798	1	39	fuzzy	fuzzy	ADJ
ejpam-6798	1	40	ideals	ideal	NOUN
ejpam-6798	1	41	in	in	ADP
ejpam-6798	1	42	bck	bck	PROPN
ejpam-6798	1	43	/	/	SYM
ejpam-6798	1	44	bci	bci	NOUN
ejpam-6798	1	45	-	-	PUNCT
ejpam-6798	1	46	algebras	algebras	PROPN
ejpam-6798	1	47	muhammad	muhammad	PROPN
ejpam-6798	1	48	jawad1	jawad1	PROPN
ejpam-6798	1	49	,	,	PUNCT
ejpam-6798	1	50	sarka	sarka	PROPN
ejpam-6798	1	51	hoskova	hoskova	PROPN
ejpam-6798	1	52	-	-	PUNCT
ejpam-6798	1	53	mayerova2,∗	mayerova2,∗	PROPN
ejpam-6798	1	54	,	,	PUNCT
ejpam-6798	1	55	niat	niat	PROPN
ejpam-6798	1	56	nigar1	nigar1	PROPN
ejpam-6798	1	57	,	,	PUNCT
ejpam-6798	1	58	muhammad	muhammad	PROPN
ejpam-6798	1	59	haris	haris	PROPN
ejpam-6798	1	60	mateen1,∗	mateen1,∗	PROPN
ejpam-6798	1	61	1	1	NUM
ejpam-6798	1	62	school	school	NOUN
ejpam-6798	1	63	of	of	ADP
ejpam-6798	1	64	mathematics	mathematic	NOUN
ejpam-6798	1	65	,	,	PUNCT
ejpam-6798	1	66	minhaj	minhaj	PROPN
ejpam-6798	1	67	university	university	PROPN
ejpam-6798	1	68	lahore	lahore	NOUN
ejpam-6798	1	69	,	,	PUNCT
ejpam-6798	1	70	pakistan	pakistan	PROPN
ejpam-6798	1	71	2	2	NUM
ejpam-6798	1	72	department	department	NOUN
ejpam-6798	1	73	of	of	ADP
ejpam-6798	1	74	mathematics	mathematics	PROPN
ejpam-6798	1	75	and	and	CCONJ
ejpam-6798	1	76	physics	physics	PROPN
ejpam-6798	1	77	,	,	PUNCT
ejpam-6798	1	78	university	university	PROPN
ejpam-6798	1	79	of	of	ADP
ejpam-6798	1	80	defence	defence	NOUN
ejpam-6798	1	81	,	,	PUNCT
ejpam-6798	1	82	brno	brno	NOUN
ejpam-6798	1	83	,	,	PUNCT
ejpam-6798	1	84	66210	66210	NUM
ejpam-6798	1	85	,	,	PUNCT
ejpam-6798	1	86	czech	czech	PROPN
ejpam-6798	1	87	republic	republic	NOUN
ejpam-6798	1	88	abstract	abstract	NOUN
ejpam-6798	1	89	.	.	PUNCT
ejpam-6798	2	1	the	the	DET
ejpam-6798	2	2	complex	complex	ADJ
ejpam-6798	2	3	intuitionistic	intuitionistic	ADJ
ejpam-6798	2	4	fuzzy	fuzzy	ADJ
ejpam-6798	2	5	set	set	NOUN
ejpam-6798	2	6	is	be	AUX
ejpam-6798	2	7	a	a	DET
ejpam-6798	2	8	more	more	ADV
ejpam-6798	2	9	generalized	generalized	ADJ
ejpam-6798	2	10	version	version	NOUN
ejpam-6798	2	11	of	of	ADP
ejpam-6798	2	12	the	the	DET
ejpam-6798	2	13	complex	complex	ADJ
ejpam-6798	2	14	fuzzy	fuzzy	ADJ
ejpam-6798	2	15	set	set	NOUN
ejpam-6798	2	16	.	.	PUNCT
ejpam-6798	3	1	it	it	PRON
ejpam-6798	3	2	is	be	AUX
ejpam-6798	3	3	made	make	VERB
ejpam-6798	3	4	by	by	ADP
ejpam-6798	3	5	including	include	VERB
ejpam-6798	3	6	the	the	DET
ejpam-6798	3	7	complex	complex	ADJ
ejpam-6798	3	8	degree	degree	NOUN
ejpam-6798	3	9	of	of	ADP
ejpam-6798	3	10	non	non	ADJ
ejpam-6798	3	11	-	-	ADJ
ejpam-6798	3	12	grading	grade	VERB
ejpam-6798	3	13	functions	function	NOUN
ejpam-6798	3	14	,	,	PUNCT
ejpam-6798	3	15	which	which	PRON
ejpam-6798	3	16	are	be	AUX
ejpam-6798	3	17	also	also	ADV
ejpam-6798	3	18	important	important	ADJ
ejpam-6798	3	19	in	in	ADP
ejpam-6798	3	20	the	the	DET
ejpam-6798	3	21	decision	decision	NOUN
ejpam-6798	3	22	-	-	PUNCT
ejpam-6798	3	23	making	make	VERB
ejpam-6798	3	24	process	process	NOUN
ejpam-6798	3	25	,	,	PUNCT
ejpam-6798	3	26	and	and	CCONJ
ejpam-6798	3	27	studying	study	VERB
ejpam-6798	3	28	their	their	PRON
ejpam-6798	3	29	basic	basic	ADJ
ejpam-6798	3	30	properties	property	NOUN
ejpam-6798	3	31	.	.	PUNCT
ejpam-6798	4	1	the	the	DET
ejpam-6798	4	2	complex	complex	ADJ
ejpam-6798	4	3	intuitionistic	intuitionistic	ADJ
ejpam-6798	4	4	fuzzy	fuzzy	ADJ
ejpam-6798	4	5	set	set	NOUN
ejpam-6798	4	6	extends	extend	VERB
ejpam-6798	4	7	theories	theory	NOUN
ejpam-6798	4	8	like	like	ADP
ejpam-6798	4	9	the	the	DET
ejpam-6798	4	10	complex	complex	ADJ
ejpam-6798	4	11	fuzzy	fuzzy	ADJ
ejpam-6798	4	12	set	set	NOUN
ejpam-6798	4	13	,	,	PUNCT
ejpam-6798	4	14	intuitionistic	intuitionistic	ADJ
ejpam-6798	4	15	fuzzy	fuzzy	ADJ
ejpam-6798	4	16	set	set	NOUN
ejpam-6798	4	17	,	,	PUNCT
ejpam-6798	4	18	and	and	CCONJ
ejpam-6798	4	19	fuzzy	fuzzy	ADJ
ejpam-6798	4	20	set	set	NOUN
ejpam-6798	4	21	.	.	PUNCT
ejpam-6798	5	1	the	the	DET
ejpam-6798	5	2	goal	goal	NOUN
ejpam-6798	5	3	of	of	ADP
ejpam-6798	5	4	this	this	DET
ejpam-6798	5	5	paper	paper	NOUN
ejpam-6798	5	6	is	be	AUX
ejpam-6798	5	7	to	to	PART
ejpam-6798	5	8	apply	apply	VERB
ejpam-6798	5	9	complex	complex	ADJ
ejpam-6798	5	10	intuitionistic	intuitionistic	ADJ
ejpam-6798	5	11	fuzzy	fuzzy	ADJ
ejpam-6798	5	12	sets	set	NOUN
ejpam-6798	5	13	in	in	ADP
ejpam-6798	5	14	bck	bck	PROPN
ejpam-6798	5	15	/	/	SYM
ejpam-6798	5	16	bci	bci	NOUN
ejpam-6798	5	17	-	-	PUNCT
ejpam-6798	5	18	algebras	algebras	X
ejpam-6798	5	19	(	(	PUNCT
ejpam-6798	5	20	m	m	NOUN
ejpam-6798	5	21	)	)	PUNCT
ejpam-6798	5	22	,	,	PUNCT
ejpam-6798	5	23	explain	explain	VERB
ejpam-6798	5	24	what	what	PRON
ejpam-6798	5	25	a	a	DET
ejpam-6798	5	26	complex	complex	ADJ
ejpam-6798	5	27	intuitionistic	intuitionistic	ADJ
ejpam-6798	5	28	fuzzy	fuzzy	ADJ
ejpam-6798	5	29	ideal	ideal	NOUN
ejpam-6798	5	30	is	be	AUX
ejpam-6798	5	31	,	,	PUNCT
ejpam-6798	5	32	and	and	CCONJ
ejpam-6798	5	33	explore	explore	VERB
ejpam-6798	5	34	some	some	PRON
ejpam-6798	5	35	of	of	ADP
ejpam-6798	5	36	its	its	PRON
ejpam-6798	5	37	properties	property	NOUN
ejpam-6798	5	38	.	.	PUNCT
ejpam-6798	6	1	we	we	PRON
ejpam-6798	6	2	introduce	introduce	VERB
ejpam-6798	6	3	the	the	DET
ejpam-6798	6	4	notion	notion	NOUN
ejpam-6798	6	5	of	of	ADP
ejpam-6798	6	6	a	a	DET
ejpam-6798	6	7	complex	complex	ADJ
ejpam-6798	6	8	intuitionistic	intuitionistic	ADJ
ejpam-6798	6	9	fuzzy	fuzzy	ADJ
ejpam-6798	6	10	sub	sub	NOUN
ejpam-6798	6	11	-	-	NOUN
ejpam-6798	6	12	algebra	algebra	NOUN
ejpam-6798	6	13	in	in	ADP
ejpam-6798	6	14	m	m	PROPN
ejpam-6798	6	15	,	,	PUNCT
ejpam-6798	6	16	and	and	CCONJ
ejpam-6798	6	17	its	its	PRON
ejpam-6798	6	18	characteristics	characteristic	NOUN
ejpam-6798	6	19	are	be	AUX
ejpam-6798	6	20	investigated	investigate	VERB
ejpam-6798	6	21	.	.	PUNCT
ejpam-6798	7	1	we	we	PRON
ejpam-6798	7	2	also	also	ADV
ejpam-6798	7	3	look	look	VERB
ejpam-6798	7	4	into	into	ADP
ejpam-6798	7	5	the	the	DET
ejpam-6798	7	6	level	level	NOUN
ejpam-6798	7	7	operators	operator	NOUN
ejpam-6798	7	8	and	and	CCONJ
ejpam-6798	7	9	models	model	NOUN
ejpam-6798	7	10	of	of	ADP
ejpam-6798	7	11	these	these	DET
ejpam-6798	7	12	complex	complex	ADJ
ejpam-6798	7	13	intuitionistic	intuitionistic	ADJ
ejpam-6798	7	14	fuzzy	fuzzy	ADJ
ejpam-6798	7	15	sub	sub	NOUN
ejpam-6798	7	16	-	-	ADJ
ejpam-6798	7	17	algebras	algebras	ADJ
ejpam-6798	7	18	and	and	CCONJ
ejpam-6798	7	19	explain	explain	VERB
ejpam-6798	7	20	their	their	PRON
ejpam-6798	7	21	importance	importance	NOUN
ejpam-6798	7	22	in	in	ADP
ejpam-6798	7	23	m	m	PROPN
ejpam-6798	7	24	.	.	PUNCT
ejpam-6798	8	1	finally	finally	ADV
ejpam-6798	8	2	,	,	PUNCT
ejpam-6798	8	3	we	we	PRON
ejpam-6798	8	4	discuss	discuss	VERB
ejpam-6798	8	5	the	the	DET
ejpam-6798	8	6	laws	law	NOUN
ejpam-6798	8	7	and	and	CCONJ
ejpam-6798	8	8	operations	operation	NOUN
ejpam-6798	8	9	of	of	ADP
ejpam-6798	8	10	a	a	DET
ejpam-6798	8	11	complex	complex	ADJ
ejpam-6798	8	12	intuitionistic	intuitionistic	ADJ
ejpam-6798	8	13	fuzzy	fuzzy	ADJ
ejpam-6798	8	14	set	set	NOUN
ejpam-6798	8	15	in	in	ADP
ejpam-6798	8	16	m	m	PROPN
ejpam-6798	8	17	,	,	PUNCT
ejpam-6798	8	18	such	such	ADJ
ejpam-6798	8	19	as	as	ADP
ejpam-6798	8	20	complement	complement	NOUN
ejpam-6798	8	21	,	,	PUNCT
ejpam-6798	8	22	intersection	intersection	NOUN
ejpam-6798	8	23	,	,	PUNCT
ejpam-6798	8	24	union	union	NOUN
ejpam-6798	8	25	,	,	PUNCT
ejpam-6798	8	26	boundedness	boundedness	NOUN
ejpam-6798	8	27	,	,	PUNCT
ejpam-6798	8	28	and	and	CCONJ
ejpam-6798	8	29	simple	simple	ADJ
ejpam-6798	8	30	differences	difference	NOUN
ejpam-6798	8	31	of	of	ADP
ejpam-6798	8	32	complex	complex	ADJ
ejpam-6798	8	33	intuitionistic	intuitionistic	ADJ
ejpam-6798	8	34	fuzzy	fuzzy	ADJ
ejpam-6798	8	35	ideals	ideal	NOUN
ejpam-6798	8	36	.	.	PUNCT
ejpam-6798	9	1	2020	2020	NUM
ejpam-6798	9	2	mathematics	mathematic	NOUN
ejpam-6798	9	3	subject	subject	NOUN
ejpam-6798	9	4	classifications	classification	NOUN
ejpam-6798	9	5	:	:	PUNCT
ejpam-6798	9	6	03g25	03g25	NUM
ejpam-6798	9	7	,	,	PUNCT
ejpam-6798	9	8	08a72	08a72	NUM
ejpam-6798	9	9	,	,	PUNCT
ejpam-6798	9	10	08e35	08e35	VERB
ejpam-6798	9	11	key	key	ADJ
ejpam-6798	9	12	words	word	NOUN
ejpam-6798	9	13	and	and	CCONJ
ejpam-6798	9	14	phrases	phrase	NOUN
ejpam-6798	9	15	:	:	PUNCT
ejpam-6798	9	16	complex	complex	ADJ
ejpam-6798	9	17	intuitionistic	intuitionistic	ADJ
ejpam-6798	9	18	fuzzy	fuzzy	ADJ
ejpam-6798	9	19	sub	sub	NOUN
ejpam-6798	9	20	-	-	ADJ
ejpam-6798	9	21	algebra	algebra	ADJ
ejpam-6798	9	22	,	,	PUNCT
ejpam-6798	9	23	fuzzy	fuzzy	ADJ
ejpam-6798	9	24	logic	logic	NOUN
ejpam-6798	9	25	,	,	PUNCT
ejpam-6798	9	26	bck	bck	NOUN
ejpam-6798	9	27	/	/	SYM
ejpam-6798	9	28	bcialgebras	bcialgebra	NOUN
ejpam-6798	9	29	,	,	PUNCT
ejpam-6798	9	30	complex	complex	ADJ
ejpam-6798	9	31	intuitionistic	intuitionistic	ADJ
ejpam-6798	9	32	fuzzy	fuzzy	ADJ
ejpam-6798	9	33	environment	environment	NOUN
ejpam-6798	9	34	1	1	NUM
ejpam-6798	9	35	.	.	PUNCT
ejpam-6798	10	1	introduction	introduction	NOUN
ejpam-6798	10	2	the	the	DET
ejpam-6798	10	3	concept	concept	NOUN
ejpam-6798	10	4	of	of	ADP
ejpam-6798	10	5	bck	bck	PROPN
ejpam-6798	10	6	/	/	SYM
ejpam-6798	10	7	bci	bci	NOUN
ejpam-6798	10	8	-	-	ADJ
ejpam-6798	10	9	algebra	algebra	NOUN
ejpam-6798	10	10	developed	develop	VERB
ejpam-6798	10	11	from	from	ADP
ejpam-6798	10	12	two	two	NUM
ejpam-6798	10	13	distinct	distinct	ADJ
ejpam-6798	10	14	techniques	technique	NOUN
ejpam-6798	10	15	:	:	PUNCT
ejpam-6798	10	16	(	(	PUNCT
ejpam-6798	10	17	1	1	X
ejpam-6798	10	18	)	)	PUNCT
ejpam-6798	10	19	set	set	NOUN
ejpam-6798	10	20	theory	theory	NOUN
ejpam-6798	10	21	,	,	PUNCT
ejpam-6798	10	22	and	and	CCONJ
ejpam-6798	10	23	(	(	PUNCT
ejpam-6798	10	24	2	2	X
ejpam-6798	10	25	)	)	PUNCT
ejpam-6798	10	26	non	non	ADJ
ejpam-6798	10	27	-	-	ADJ
ejpam-6798	10	28	classical	classical	ADJ
ejpam-6798	10	29	and	and	CCONJ
ejpam-6798	10	30	classical	classical	ADJ
ejpam-6798	10	31	propositional	propositional	ADJ
ejpam-6798	10	32	calculi	calculi	NOUN
ejpam-6798	10	33	.	.	PUNCT
ejpam-6798	11	1	currently	currently	ADV
ejpam-6798	11	2	,	,	PUNCT
ejpam-6798	11	3	bck	bck	PROPN
ejpam-6798	11	4	/	/	SYM
ejpam-6798	11	5	bcialgebras	bcialgebra	NOUN
ejpam-6798	11	6	are	be	AUX
ejpam-6798	11	7	utilized	utilize	VERB
ejpam-6798	11	8	in	in	ADP
ejpam-6798	11	9	a	a	DET
ejpam-6798	11	10	variety	variety	NOUN
ejpam-6798	11	11	of	of	ADP
ejpam-6798	11	12	mathematical	mathematical	ADJ
ejpam-6798	11	13	fields	field	NOUN
ejpam-6798	11	14	,	,	PUNCT
ejpam-6798	11	15	including	include	VERB
ejpam-6798	11	16	topology	topology	NOUN
ejpam-6798	11	17	,	,	PUNCT
ejpam-6798	11	18	probability	probability	NOUN
ejpam-6798	11	19	theory	theory	NOUN
ejpam-6798	11	20	,	,	PUNCT
ejpam-6798	11	21	functional	functional	ADJ
ejpam-6798	11	22	analysis	analysis	NOUN
ejpam-6798	11	23	,	,	PUNCT
ejpam-6798	11	24	group	group	NOUN
ejpam-6798	11	25	theory	theory	NOUN
ejpam-6798	11	26	,	,	PUNCT
ejpam-6798	11	27	fuzzy	fuzzy	ADJ
ejpam-6798	11	28	set	set	NOUN
ejpam-6798	11	29	theory	theory	NOUN
ejpam-6798	11	30	,	,	PUNCT
ejpam-6798	11	31	and	and	CCONJ
ejpam-6798	11	32	others	other	NOUN
ejpam-6798	11	33	.	.	PUNCT
ejpam-6798	12	1	zhang	zhang	X
ejpam-6798	13	1	[	[	X
ejpam-6798	13	2	1	1	X
ejpam-6798	13	3	]	]	PUNCT
ejpam-6798	13	4	presented	present	VERB
ejpam-6798	13	5	the	the	DET
ejpam-6798	13	6	bck	bck	PROPN
ejpam-6798	13	7	and	and	CCONJ
ejpam-6798	13	8	bci	bci	PROPN
ejpam-6798	13	9	algebra	algebra	NOUN
ejpam-6798	13	10	concepts	concept	NOUN
ejpam-6798	13	11	and	and	CCONJ
ejpam-6798	13	12	improved	improve	VERB
ejpam-6798	13	13	their	their	PRON
ejpam-6798	13	14	definitions	definition	NOUN
ejpam-6798	13	15	by	by	ADP
ejpam-6798	13	16	providing	provide	VERB
ejpam-6798	13	17	new	new	ADJ
ejpam-6798	13	18	equivalent	equivalent	ADJ
ejpam-6798	13	19	conditions	condition	NOUN
ejpam-6798	13	20	.	.	PUNCT
ejpam-6798	14	1	liu	liu	PROPN
ejpam-6798	15	1	[	[	X
ejpam-6798	15	2	2	2	NUM
ejpam-6798	15	3	]	]	PUNCT
ejpam-6798	15	4	established	establish	VERB
ejpam-6798	15	5	the	the	DET
ejpam-6798	15	6	new	new	ADJ
ejpam-6798	15	7	concepts	concept	NOUN
ejpam-6798	15	8	of	of	ADP
ejpam-6798	15	9	fuzzy	fuzzy	ADJ
ejpam-6798	15	10	bci	bci	ADJ
ejpam-6798	15	11	-	-	ADJ
ejpam-6798	15	12	implicative	implicative	ADJ
ejpam-6798	15	13	∗corresponding	∗corresponde	VERB
ejpam-6798	15	14	author	author	NOUN
ejpam-6798	15	15	.	.	PUNCT
ejpam-6798	16	1	∗corresponding	∗corresponde	VERB
ejpam-6798	16	2	author	author	NOUN
ejpam-6798	16	3	.	.	PUNCT
ejpam-6798	17	1	doi	doi	NOUN
ejpam-6798	17	2	:	:	PUNCT
ejpam-6798	17	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6798	https://doi.org/10.29020/nybg.ejpam.v18i4.6798	ADJ
ejpam-6798	17	4	email	email	NOUN
ejpam-6798	17	5	addresses	address	NOUN
ejpam-6798	17	6	:	:	PUNCT
ejpam-6798	17	7	sarka.mayerova@unob.cz	sarka.mayerova@unob.cz	NOUN
ejpam-6798	17	8	(	(	PUNCT
ejpam-6798	17	9	s.	s.	PROPN
ejpam-6798	17	10	hoskova	hoskova	PROPN
ejpam-6798	17	11	-	-	PUNCT
ejpam-6798	17	12	mayerova	mayerova	X
ejpam-6798	17	13	)	)	PUNCT
ejpam-6798	17	14	,	,	PUNCT
ejpam-6798	17	15	harism.math@gmail.com	harism.math@gmail.com	X
ejpam-6798	17	16	(	(	PUNCT
ejpam-6798	17	17	m.	m.	PROPN
ejpam-6798	17	18	h.	h.	PROPN
ejpam-6798	17	19	mateen	mateen	PROPN
ejpam-6798	17	20	)	)	PUNCT
ejpam-6798	17	21	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6798	18	1	1	1	NUM
ejpam-6798	18	2	copyright	copyright	NOUN
ejpam-6798	18	3	:	:	PUNCT
ejpam-6798	18	4	©	©	PROPN
ejpam-6798	18	5	2025	2025	NUM
ejpam-6798	18	6	the	the	DET
ejpam-6798	18	7	author(s	author(s	NOUN
ejpam-6798	18	8	)	)	PUNCT
ejpam-6798	18	9	.	.	PUNCT
ejpam-6798	19	1	(	(	PUNCT
ejpam-6798	19	2	cc	cc	NOUN
ejpam-6798	19	3	by	by	ADP
ejpam-6798	19	4	-	-	PUNCT
ejpam-6798	19	5	nc	nc	PROPN
ejpam-6798	19	6	4.0	4.0	NUM
ejpam-6798	19	7	)	)	PUNCT
ejpam-6798	19	8	m.	m.	NOUN
ejpam-6798	19	9	jawad	jawad	PROPN
ejpam-6798	19	10	et	et	PROPN
ejpam-6798	19	11	al	al	PROPN
ejpam-6798	19	12	.	.	PUNCT
ejpam-6798	19	13	/	/	SYM
ejpam-6798	19	14	eur	eur	PROPN
ejpam-6798	19	15	.	.	PUNCT
ejpam-6798	20	1	j.	j.	PROPN
ejpam-6798	20	2	pure	pure	PROPN
ejpam-6798	20	3	appl	appl	PROPN
ejpam-6798	20	4	.	.	PROPN
ejpam-6798	20	5	math	math	PROPN
ejpam-6798	20	6	,	,	PUNCT
ejpam-6798	20	7	18	18	NUM
ejpam-6798	20	8	(	(	PUNCT
ejpam-6798	20	9	4	4	NUM
ejpam-6798	20	10	)	)	PUNCT
ejpam-6798	20	11	(	(	PUNCT
ejpam-6798	20	12	2025	2025	NUM
ejpam-6798	20	13	)	)	PUNCT
ejpam-6798	20	14	,	,	PUNCT
ejpam-6798	20	15	6798	6798	NUM
ejpam-6798	20	16	2	2	NUM
ejpam-6798	20	17	of	of	ADP
ejpam-6798	20	18	22	22	NUM
ejpam-6798	20	19	ideals	ideal	NOUN
ejpam-6798	20	20	and	and	CCONJ
ejpam-6798	20	21	fuzzy	fuzzy	ADJ
ejpam-6798	20	22	bci	bci	ADJ
ejpam-6798	20	23	-	-	ADJ
ejpam-6798	20	24	positive	positive	ADJ
ejpam-6798	20	25	implicative	implicative	ADJ
ejpam-6798	20	26	ideals	ideal	NOUN
ejpam-6798	20	27	in	in	ADP
ejpam-6798	20	28	bci	bci	NOUN
ejpam-6798	20	29	-	-	PUNCT
ejpam-6798	20	30	algebras	algebras	PROPN
ejpam-6798	20	31	and	and	CCONJ
ejpam-6798	20	32	explored	explore	VERB
ejpam-6798	20	33	their	their	PRON
ejpam-6798	20	34	characteristics	characteristic	NOUN
ejpam-6798	20	35	.	.	PUNCT
ejpam-6798	21	1	the	the	DET
ejpam-6798	21	2	relations	relation	NOUN
ejpam-6798	21	3	between	between	ADP
ejpam-6798	21	4	distinct	distinct	ADJ
ejpam-6798	21	5	fuzzy	fuzzy	ADJ
ejpam-6798	21	6	ideals	ideal	NOUN
ejpam-6798	21	7	demonstrate	demonstrate	VERB
ejpam-6798	21	8	that	that	SCONJ
ejpam-6798	21	9	a	a	DET
ejpam-6798	21	10	fuzzy	fuzzy	ADJ
ejpam-6798	21	11	set	set	NOUN
ejpam-6798	21	12	(	(	PUNCT
ejpam-6798	21	13	fs	fs	PROPN
ejpam-6798	21	14	)	)	PUNCT
ejpam-6798	21	15	µ	µ	NOUN
ejpam-6798	21	16	of	of	ADP
ejpam-6798	21	17	a	a	DET
ejpam-6798	21	18	bci	bci	NOUN
ejpam-6798	21	19	-	-	NOUN
ejpam-6798	21	20	algebra	algebra	NOUN
ejpam-6798	21	21	is	be	AUX
ejpam-6798	21	22	a	a	DET
ejpam-6798	21	23	fuzzy	fuzzy	ADJ
ejpam-6798	21	24	bci	bci	ADJ
ejpam-6798	21	25	-	-	ADJ
ejpam-6798	21	26	implicative	implicative	ADJ
ejpam-6798	21	27	ideal	ideal	NOUN
ejpam-6798	22	1	if	if	SCONJ
ejpam-6798	22	2	and	and	CCONJ
ejpam-6798	22	3	only	only	ADV
ejpam-6798	22	4	if	if	SCONJ
ejpam-6798	22	5	µ	µ	NOUN
ejpam-6798	22	6	is	be	AUX
ejpam-6798	22	7	both	both	CCONJ
ejpam-6798	22	8	a	a	DET
ejpam-6798	22	9	fuzzy	fuzzy	ADJ
ejpam-6798	22	10	bcicommutative	bcicommutative	ADJ
ejpam-6798	22	11	ideal	ideal	NOUN
ejpam-6798	22	12	and	and	CCONJ
ejpam-6798	22	13	a	a	DET
ejpam-6798	22	14	fuzzy	fuzzy	ADJ
ejpam-6798	22	15	bci	bci	ADJ
ejpam-6798	22	16	-	-	ADJ
ejpam-6798	22	17	positive	positive	ADJ
ejpam-6798	22	18	implicative	implicative	ADJ
ejpam-6798	22	19	ideal	ideal	NOUN
ejpam-6798	22	20	.	.	PUNCT
ejpam-6798	23	1	meng	meng	PROPN
ejpam-6798	24	1	[	[	X
ejpam-6798	24	2	3	3	NUM
ejpam-6798	24	3	]	]	PUNCT
ejpam-6798	24	4	investigated	investigate	VERB
ejpam-6798	24	5	the	the	DET
ejpam-6798	24	6	idea	idea	NOUN
ejpam-6798	24	7	of	of	ADP
ejpam-6798	24	8	fuzzy	fuzzy	ADJ
ejpam-6798	24	9	implicative	implicative	ADJ
ejpam-6798	24	10	ideals	ideal	NOUN
ejpam-6798	24	11	in	in	ADP
ejpam-6798	24	12	bck	bck	NOUN
ejpam-6798	24	13	-	-	PUNCT
ejpam-6798	24	14	algebras	algebras	PROPN
ejpam-6798	24	15	and	and	CCONJ
ejpam-6798	24	16	presented	present	VERB
ejpam-6798	24	17	various	various	ADJ
ejpam-6798	24	18	characterizations	characterization	NOUN
ejpam-6798	24	19	of	of	ADP
ejpam-6798	24	20	these	these	DET
ejpam-6798	24	21	ideals	ideal	NOUN
ejpam-6798	24	22	.	.	PUNCT
ejpam-6798	25	1	jun	jun	PROPN
ejpam-6798	26	1	[	[	X
ejpam-6798	26	2	4	4	NUM
ejpam-6798	26	3	]	]	PUNCT
ejpam-6798	26	4	utilized	utilize	VERB
ejpam-6798	26	5	the	the	DET
ejpam-6798	26	6	concept	concept	NOUN
ejpam-6798	26	7	of	of	ADP
ejpam-6798	26	8	soft	soft	ADJ
ejpam-6798	26	9	sets	set	NOUN
ejpam-6798	26	10	to	to	ADP
ejpam-6798	26	11	the	the	DET
ejpam-6798	26	12	concept	concept	NOUN
ejpam-6798	26	13	of	of	ADP
ejpam-6798	26	14	bck	bck	PROPN
ejpam-6798	26	15	/	/	SYM
ejpam-6798	26	16	bci	bci	PROPN
ejpam-6798	26	17	algebras	algebra	NOUN
ejpam-6798	26	18	.	.	PUNCT
ejpam-6798	27	1	the	the	DET
ejpam-6798	27	2	concepts	concept	NOUN
ejpam-6798	27	3	of	of	ADP
ejpam-6798	27	4	soft	soft	ADJ
ejpam-6798	27	5	bck	bck	NOUN
ejpam-6798	27	6	/	/	SYM
ejpam-6798	27	7	bci	bci	PROPN
ejpam-6798	27	8	algebras	algebra	NOUN
ejpam-6798	27	9	and	and	CCONJ
ejpam-6798	27	10	soft	soft	ADJ
ejpam-6798	27	11	sub	sub	NOUN
ejpam-6798	27	12	-	-	ADJ
ejpam-6798	27	13	algebras	algebras	ADJ
ejpam-6798	27	14	were	be	AUX
ejpam-6798	27	15	presented	present	VERB
ejpam-6798	27	16	,	,	PUNCT
ejpam-6798	27	17	and	and	CCONJ
ejpam-6798	27	18	their	their	PRON
ejpam-6798	27	19	fundamental	fundamental	ADJ
ejpam-6798	27	20	characteristics	characteristic	NOUN
ejpam-6798	27	21	were	be	AUX
ejpam-6798	27	22	established	establish	VERB
ejpam-6798	27	23	.	.	PUNCT
ejpam-6798	28	1	senapati	senapati	PROPN
ejpam-6798	28	2	and	and	CCONJ
ejpam-6798	28	3	shum	shum	ADJ
ejpam-6798	29	1	[	[	X
ejpam-6798	29	2	5	5	NUM
ejpam-6798	29	3	]	]	PUNCT
ejpam-6798	29	4	introduced	introduce	VERB
ejpam-6798	29	5	the	the	DET
ejpam-6798	29	6	cubic	cubic	ADJ
ejpam-6798	29	7	set	set	NOUN
ejpam-6798	29	8	notion	notion	NOUN
ejpam-6798	29	9	to	to	ADP
ejpam-6798	29	10	implicative	implicative	ADJ
ejpam-6798	29	11	ideals	ideal	NOUN
ejpam-6798	29	12	of	of	ADP
ejpam-6798	29	13	bck	bck	NOUN
ejpam-6798	29	14	-	-	PUNCT
ejpam-6798	29	15	algebras	algebras	PROPN
ejpam-6798	29	16	and	and	CCONJ
ejpam-6798	29	17	characterised	characterise	VERB
ejpam-6798	29	18	their	their	PRON
ejpam-6798	29	19	basic	basic	ADJ
ejpam-6798	29	20	attributes	attribute	NOUN
ejpam-6798	29	21	.	.	PUNCT
ejpam-6798	30	1	andres	andres	PROPN
ejpam-6798	30	2	-	-	PUNCT
ejpam-6798	30	3	sanchez	sanchez	PROPN
ejpam-6798	30	4	[	[	X
ejpam-6798	30	5	6	6	NUM
ejpam-6798	30	6	]	]	PUNCT
ejpam-6798	30	7	developed	develop	VERB
ejpam-6798	30	8	fuzzy	fuzzy	ADJ
ejpam-6798	30	9	sets	set	NOUN
ejpam-6798	30	10	in	in	ADP
ejpam-6798	30	11	quantities	quantity	NOUN
ejpam-6798	30	12	correlated	correlate	VERB
ejpam-6798	30	13	with	with	ADP
ejpam-6798	30	14	a	a	DET
ejpam-6798	30	15	set	set	NOUN
ejpam-6798	30	16	of	of	ADP
ejpam-6798	30	17	objects	object	NOUN
ejpam-6798	30	18	,	,	PUNCT
ejpam-6798	30	19	with	with	ADP
ejpam-6798	30	20	the	the	DET
ejpam-6798	30	21	degree	degree	NOUN
ejpam-6798	30	22	of	of	ADP
ejpam-6798	30	23	membership	membership	NOUN
ejpam-6798	30	24	of	of	ADP
ejpam-6798	30	25	[	[	X
ejpam-6798	30	26	0	0	NUM
ejpam-6798	30	27	,	,	PUNCT
ejpam-6798	30	28	1	1	NUM
ejpam-6798	30	29	]	]	PUNCT
ejpam-6798	30	30	expressing	express	VERB
ejpam-6798	30	31	the	the	DET
ejpam-6798	30	32	degree	degree	NOUN
ejpam-6798	30	33	of	of	ADP
ejpam-6798	30	34	elements	element	NOUN
ejpam-6798	30	35	belonging	belong	VERB
ejpam-6798	30	36	to	to	ADP
ejpam-6798	30	37	the	the	DET
ejpam-6798	30	38	set	set	NOUN
ejpam-6798	30	39	.	.	PUNCT
ejpam-6798	31	1	mardani	mardani	PROPN
ejpam-6798	31	2	et	et	PROPN
ejpam-6798	31	3	al	al	PROPN
ejpam-6798	31	4	.	.	PUNCT
ejpam-6798	32	1	[	[	X
ejpam-6798	32	2	7	7	X
ejpam-6798	32	3	]	]	PUNCT
ejpam-6798	32	4	established	establish	VERB
ejpam-6798	32	5	among	among	ADP
ejpam-6798	32	6	the	the	DET
ejpam-6798	32	7	available	available	ADJ
ejpam-6798	32	8	strategies	strategy	NOUN
ejpam-6798	32	9	for	for	ADP
ejpam-6798	32	10	dealing	deal	VERB
ejpam-6798	32	11	with	with	ADP
ejpam-6798	32	12	uncertainty	uncertainty	NOUN
ejpam-6798	32	13	issues	issue	NOUN
ejpam-6798	32	14	,	,	PUNCT
ejpam-6798	32	15	fuzzy	fuzzy	ADJ
ejpam-6798	32	16	mathematics	mathematic	NOUN
ejpam-6798	32	17	mainly	mainly	ADV
ejpam-6798	32	18	focuses	focus	VERB
ejpam-6798	32	19	on	on	ADP
ejpam-6798	32	20	items	item	NOUN
ejpam-6798	32	21	with	with	ADP
ejpam-6798	32	22	specifically	specifically	ADV
ejpam-6798	32	23	internal	internal	ADJ
ejpam-6798	32	24	definitions	definition	NOUN
ejpam-6798	32	25	but	but	CCONJ
ejpam-6798	32	26	uncertain	uncertain	ADJ
ejpam-6798	32	27	outward	outward	ADJ
ejpam-6798	32	28	deployment	deployment	NOUN
ejpam-6798	32	29	as	as	ADP
ejpam-6798	32	30	membership	membership	NOUN
ejpam-6798	32	31	degree	degree	NOUN
ejpam-6798	32	32	;	;	PUNCT
ejpam-6798	32	33	however	however	ADV
ejpam-6798	32	34	,	,	PUNCT
ejpam-6798	32	35	the	the	DET
ejpam-6798	32	36	independency	independency	NOUN
ejpam-6798	32	37	value	value	NOUN
ejpam-6798	32	38	as	as	ADP
ejpam-6798	32	39	a	a	DET
ejpam-6798	32	40	key	key	ADJ
ejpam-6798	32	41	component	component	NOUN
ejpam-6798	32	42	of	of	ADP
ejpam-6798	32	43	elements	element	NOUN
ejpam-6798	32	44	was	be	AUX
ejpam-6798	32	45	ignored	ignore	VERB
ejpam-6798	32	46	in	in	ADP
ejpam-6798	32	47	the	the	DET
ejpam-6798	32	48	frameworks	framework	NOUN
ejpam-6798	32	49	.	.	PUNCT
ejpam-6798	33	1	the	the	DET
ejpam-6798	33	2	intuitionistic	intuitionistic	ADJ
ejpam-6798	33	3	fuzzy	fuzzy	ADJ
ejpam-6798	33	4	set	set	NOUN
ejpam-6798	33	5	(	(	PUNCT
ejpam-6798	33	6	ifs	ifs	PROPN
ejpam-6798	33	7	)	)	PUNCT
ejpam-6798	33	8	theory	theory	NOUN
ejpam-6798	33	9	has	have	VERB
ejpam-6798	33	10	a	a	DET
ejpam-6798	33	11	broad	broad	ADJ
ejpam-6798	33	12	range	range	NOUN
ejpam-6798	33	13	of	of	ADP
ejpam-6798	33	14	uses	use	NOUN
ejpam-6798	33	15	in	in	ADP
ejpam-6798	33	16	many	many	ADJ
ejpam-6798	33	17	domains	domain	NOUN
ejpam-6798	33	18	,	,	PUNCT
ejpam-6798	33	19	such	such	ADJ
ejpam-6798	33	20	as	as	ADP
ejpam-6798	33	21	medical	medical	ADJ
ejpam-6798	33	22	diagnosis	diagnosis	NOUN
ejpam-6798	33	23	[	[	X
ejpam-6798	33	24	8	8	NUM
ejpam-6798	33	25	,	,	PUNCT
ejpam-6798	33	26	9	9	NUM
ejpam-6798	33	27	]	]	PUNCT
ejpam-6798	33	28	,	,	PUNCT
ejpam-6798	33	29	pattern	pattern	NOUN
ejpam-6798	33	30	recognition	recognition	NOUN
ejpam-6798	34	1	[	[	X
ejpam-6798	34	2	10	10	NUM
ejpam-6798	34	3	]	]	PUNCT
ejpam-6798	34	4	,	,	PUNCT
ejpam-6798	34	5	engineering	engineering	NOUN
ejpam-6798	34	6	systems	system	NOUN
ejpam-6798	34	7	[	[	X
ejpam-6798	34	8	11	11	NUM
ejpam-6798	34	9	]	]	PUNCT
ejpam-6798	34	10	,	,	PUNCT
ejpam-6798	34	11	and	and	CCONJ
ejpam-6798	34	12	decisionmaking	decisionmake	VERB
ejpam-6798	34	13	[	[	X
ejpam-6798	34	14	12	12	NUM
ejpam-6798	34	15	]	]	PUNCT
ejpam-6798	34	16	.	.	PUNCT
ejpam-6798	35	1	in	in	ADP
ejpam-6798	35	2	today	today	NOUN
ejpam-6798	35	3	’s	’s	PART
ejpam-6798	35	4	world	world	NOUN
ejpam-6798	35	5	,	,	PUNCT
ejpam-6798	35	6	scientists	scientist	NOUN
ejpam-6798	35	7	and	and	CCONJ
ejpam-6798	35	8	technologists	technologist	NOUN
ejpam-6798	35	9	routinely	routinely	ADV
ejpam-6798	35	10	meet	meet	VERB
ejpam-6798	35	11	complex	complex	ADJ
ejpam-6798	35	12	processes	process	NOUN
ejpam-6798	35	13	and	and	CCONJ
ejpam-6798	35	14	phenomena	phenomenon	NOUN
ejpam-6798	35	15	that	that	PRON
ejpam-6798	35	16	are	be	AUX
ejpam-6798	35	17	beyond	beyond	ADP
ejpam-6798	35	18	full	full	ADJ
ejpam-6798	35	19	and	and	CCONJ
ejpam-6798	35	20	exact	exact	ADJ
ejpam-6798	35	21	insight	insight	NOUN
ejpam-6798	35	22	.	.	PUNCT
ejpam-6798	36	1	therefore	therefore	ADV
ejpam-6798	36	2	,	,	PUNCT
ejpam-6798	36	3	it	it	PRON
ejpam-6798	36	4	is	be	AUX
ejpam-6798	36	5	essential	essential	ADJ
ejpam-6798	36	6	to	to	PART
ejpam-6798	36	7	include	include	VERB
ejpam-6798	36	8	accurate	accurate	ADJ
ejpam-6798	36	9	mathematical	mathematical	ADJ
ejpam-6798	36	10	models	model	NOUN
ejpam-6798	36	11	into	into	ADP
ejpam-6798	36	12	systems	system	NOUN
ejpam-6798	36	13	that	that	PRON
ejpam-6798	36	14	exhibit	exhibit	VERB
ejpam-6798	36	15	a	a	DET
ejpam-6798	36	16	high	high	ADJ
ejpam-6798	36	17	level	level	NOUN
ejpam-6798	36	18	of	of	ADP
ejpam-6798	36	19	uncertainty	uncertainty	NOUN
ejpam-6798	36	20	.	.	PUNCT
ejpam-6798	37	1	the	the	DET
ejpam-6798	37	2	reason	reason	NOUN
ejpam-6798	37	3	for	for	ADP
ejpam-6798	37	4	developing	develop	VERB
ejpam-6798	37	5	fuzzy	fuzzy	ADJ
ejpam-6798	37	6	set	set	NOUN
ejpam-6798	37	7	theory	theory	NOUN
ejpam-6798	37	8	stemmed	stem	VERB
ejpam-6798	37	9	from	from	ADP
ejpam-6798	37	10	the	the	DET
ejpam-6798	37	11	need	need	NOUN
ejpam-6798	37	12	to	to	PART
ejpam-6798	37	13	broaden	broaden	VERB
ejpam-6798	37	14	traditional	traditional	ADJ
ejpam-6798	37	15	set	set	NOUN
ejpam-6798	37	16	theory	theory	NOUN
ejpam-6798	37	17	in	in	ADP
ejpam-6798	37	18	order	order	NOUN
ejpam-6798	37	19	to	to	PART
ejpam-6798	37	20	efficiently	efficiently	ADV
ejpam-6798	37	21	address	address	VERB
ejpam-6798	37	22	a	a	DET
ejpam-6798	37	23	certain	certain	ADJ
ejpam-6798	37	24	purpose	purpose	NOUN
ejpam-6798	37	25	.	.	PUNCT
ejpam-6798	38	1	the	the	DET
ejpam-6798	38	2	methodology	methodology	NOUN
ejpam-6798	38	3	offered	offer	VERB
ejpam-6798	38	4	herein	herein	NOUN
ejpam-6798	38	5	provides	provide	VERB
ejpam-6798	38	6	a	a	DET
ejpam-6798	38	7	systematic	systematic	ADJ
ejpam-6798	38	8	strategy	strategy	NOUN
ejpam-6798	38	9	for	for	ADP
ejpam-6798	38	10	developing	develop	VERB
ejpam-6798	38	11	and	and	CCONJ
ejpam-6798	38	12	evaluating	evaluate	VERB
ejpam-6798	38	13	various	various	ADJ
ejpam-6798	38	14	models	model	NOUN
ejpam-6798	38	15	that	that	PRON
ejpam-6798	38	16	effectively	effectively	ADV
ejpam-6798	38	17	capture	capture	VERB
ejpam-6798	38	18	and	and	CCONJ
ejpam-6798	38	19	tackle	tackle	VERB
ejpam-6798	38	20	the	the	DET
ejpam-6798	38	21	inherent	inherent	ADJ
ejpam-6798	38	22	uncertainties	uncertainty	NOUN
ejpam-6798	38	23	in	in	ADP
ejpam-6798	38	24	a	a	DET
ejpam-6798	38	25	particular	particular	ADJ
ejpam-6798	38	26	environment	environment	NOUN
ejpam-6798	38	27	.	.	PUNCT
ejpam-6798	39	1	this	this	DET
ejpam-6798	39	2	theory	theory	NOUN
ejpam-6798	39	3	is	be	AUX
ejpam-6798	39	4	critical	critical	ADJ
ejpam-6798	39	5	for	for	ADP
ejpam-6798	39	6	the	the	DET
ejpam-6798	39	7	development	development	NOUN
ejpam-6798	39	8	of	of	ADP
ejpam-6798	39	9	such	such	ADJ
ejpam-6798	39	10	structures	structure	NOUN
ejpam-6798	39	11	.	.	PUNCT
ejpam-6798	40	1	furthermore	furthermore	ADV
ejpam-6798	40	2	,	,	PUNCT
ejpam-6798	40	3	it	it	PRON
ejpam-6798	40	4	improves	improve	VERB
ejpam-6798	40	5	our	our	PRON
ejpam-6798	40	6	ability	ability	NOUN
ejpam-6798	40	7	to	to	PART
ejpam-6798	40	8	investigate	investigate	VERB
ejpam-6798	40	9	and	and	CCONJ
ejpam-6798	40	10	adapt	adapt	VERB
ejpam-6798	40	11	to	to	ADP
ejpam-6798	40	12	the	the	DET
ejpam-6798	40	13	complex	complex	ADJ
ejpam-6798	40	14	and	and	CCONJ
ejpam-6798	40	15	unpredictable	unpredictable	ADJ
ejpam-6798	40	16	properties	property	NOUN
ejpam-6798	40	17	of	of	ADP
ejpam-6798	40	18	systems	system	NOUN
ejpam-6798	40	19	within	within	ADP
ejpam-6798	40	20	a	a	DET
ejpam-6798	40	21	wide	wide	ADJ
ejpam-6798	40	22	range	range	NOUN
ejpam-6798	40	23	of	of	ADP
ejpam-6798	40	24	scientific	scientific	ADJ
ejpam-6798	40	25	and	and	CCONJ
ejpam-6798	40	26	technical	technical	ADJ
ejpam-6798	40	27	disciplines	discipline	NOUN
ejpam-6798	40	28	.	.	PUNCT
ejpam-6798	41	1	the	the	DET
ejpam-6798	41	2	uses	use	NOUN
ejpam-6798	41	3	of	of	ADP
ejpam-6798	41	4	fuzzy	fuzzy	ADJ
ejpam-6798	41	5	set	set	NOUN
ejpam-6798	41	6	concept	concept	NOUN
ejpam-6798	41	7	have	have	AUX
ejpam-6798	41	8	been	be	AUX
ejpam-6798	41	9	demonstrated	demonstrate	VERB
ejpam-6798	41	10	across	across	ADP
ejpam-6798	41	11	a	a	DET
ejpam-6798	41	12	wide	wide	ADJ
ejpam-6798	41	13	range	range	NOUN
ejpam-6798	41	14	of	of	ADP
ejpam-6798	41	15	scientific	scientific	ADJ
ejpam-6798	41	16	areas	area	NOUN
ejpam-6798	41	17	and	and	CCONJ
ejpam-6798	41	18	natural	natural	ADJ
ejpam-6798	41	19	phenomena	phenomenon	NOUN
ejpam-6798	41	20	.	.	PUNCT
ejpam-6798	42	1	fuzzy	fuzzy	ADJ
ejpam-6798	42	2	sets	set	NOUN
ejpam-6798	42	3	(	(	PUNCT
ejpam-6798	42	4	fss	fss	ADV
ejpam-6798	42	5	)	)	PUNCT
ejpam-6798	42	6	have	have	AUX
ejpam-6798	42	7	proven	prove	VERB
ejpam-6798	42	8	to	to	PART
ejpam-6798	42	9	be	be	AUX
ejpam-6798	42	10	an	an	DET
ejpam-6798	42	11	adaptable	adaptable	ADJ
ejpam-6798	42	12	strategy	strategy	NOUN
ejpam-6798	42	13	for	for	ADP
ejpam-6798	42	14	dealing	deal	VERB
ejpam-6798	42	15	with	with	ADP
ejpam-6798	42	16	complex	complex	ADJ
ejpam-6798	42	17	and	and	CCONJ
ejpam-6798	42	18	uncertain	uncertain	ADJ
ejpam-6798	42	19	situations	situation	NOUN
ejpam-6798	42	20	in	in	ADP
ejpam-6798	42	21	a	a	DET
ejpam-6798	42	22	variety	variety	NOUN
ejpam-6798	42	23	of	of	ADP
ejpam-6798	42	24	contexts	contexts	NOUN
ejpam-6798	42	25	.	.	PUNCT
ejpam-6798	43	1	fs	f	NOUN
ejpam-6798	43	2	relies	rely	VERB
ejpam-6798	43	3	primarily	primarily	ADV
ejpam-6798	43	4	on	on	ADP
ejpam-6798	43	5	membership	membership	NOUN
ejpam-6798	43	6	functions	function	NOUN
ejpam-6798	43	7	that	that	PRON
ejpam-6798	43	8	operate	operate	VERB
ejpam-6798	43	9	in	in	ADP
ejpam-6798	43	10	a	a	DET
ejpam-6798	43	11	single	single	ADJ
ejpam-6798	43	12	dimension	dimension	NOUN
ejpam-6798	43	13	,	,	PUNCT
ejpam-6798	43	14	making	make	VERB
ejpam-6798	43	15	it	it	PRON
ejpam-6798	43	16	difficult	difficult	ADJ
ejpam-6798	43	17	to	to	PART
ejpam-6798	43	18	describe	describe	VERB
ejpam-6798	43	19	complex	complex	ADJ
ejpam-6798	43	20	relationships	relationship	NOUN
ejpam-6798	43	21	and	and	CCONJ
ejpam-6798	43	22	variables	variable	NOUN
ejpam-6798	43	23	over	over	ADP
ejpam-6798	43	24	several	several	ADJ
ejpam-6798	43	25	dimensions	dimension	NOUN
ejpam-6798	43	26	.	.	PUNCT
ejpam-6798	44	1	ordinary	ordinary	ADJ
ejpam-6798	44	2	fs	fs	PROPN
ejpam-6798	44	3	serves	serve	VERB
ejpam-6798	44	4	as	as	ADP
ejpam-6798	44	5	a	a	DET
ejpam-6798	44	6	valuable	valuable	ADJ
ejpam-6798	44	7	mathematical	mathematical	ADJ
ejpam-6798	44	8	tool	tool	NOUN
ejpam-6798	44	9	in	in	ADP
ejpam-6798	44	10	such	such	ADJ
ejpam-6798	44	11	circumstances	circumstance	NOUN
ejpam-6798	44	12	.	.	PUNCT
ejpam-6798	45	1	complex	complex	ADJ
ejpam-6798	45	2	fuzzy	fuzzy	ADJ
ejpam-6798	45	3	sets	set	NOUN
ejpam-6798	45	4	have	have	VERB
ejpam-6798	45	5	the	the	DET
ejpam-6798	45	6	ability	ability	NOUN
ejpam-6798	45	7	to	to	PART
ejpam-6798	45	8	represent	represent	VERB
ejpam-6798	45	9	uncertainty	uncertainty	NOUN
ejpam-6798	45	10	in	in	ADP
ejpam-6798	45	11	a	a	DET
ejpam-6798	45	12	more	more	ADV
ejpam-6798	45	13	detailed	detailed	ADJ
ejpam-6798	45	14	fashion	fashion	NOUN
ejpam-6798	45	15	by	by	ADP
ejpam-6798	45	16	adding	add	VERB
ejpam-6798	45	17	many	many	ADJ
ejpam-6798	45	18	dimensions	dimension	NOUN
ejpam-6798	45	19	or	or	CCONJ
ejpam-6798	45	20	membership	membership	NOUN
ejpam-6798	45	21	attributes	attribute	NOUN
ejpam-6798	45	22	.	.	PUNCT
ejpam-6798	46	1	this	this	PRON
ejpam-6798	46	2	allows	allow	VERB
ejpam-6798	46	3	for	for	ADP
ejpam-6798	46	4	a	a	DET
ejpam-6798	46	5	more	more	ADV
ejpam-6798	46	6	thorough	thorough	ADJ
ejpam-6798	46	7	and	and	CCONJ
ejpam-6798	46	8	effective	effective	ADJ
ejpam-6798	46	9	analysis	analysis	NOUN
ejpam-6798	46	10	of	of	ADP
ejpam-6798	46	11	circumstances	circumstance	NOUN
ejpam-6798	46	12	with	with	ADP
ejpam-6798	46	13	complex	complex	ADJ
ejpam-6798	46	14	physical	physical	ADJ
ejpam-6798	46	15	characteristics	characteristic	NOUN
ejpam-6798	46	16	,	,	PUNCT
ejpam-6798	46	17	as	as	ADV
ejpam-6798	46	18	well	well	ADV
ejpam-6798	46	19	as	as	ADP
ejpam-6798	46	20	an	an	DET
ejpam-6798	46	21	individual	individual	NOUN
ejpam-6798	46	22	’s	’s	PART
ejpam-6798	46	23	ability	ability	NOUN
ejpam-6798	46	24	to	to	PART
ejpam-6798	46	25	make	make	VERB
ejpam-6798	46	26	informed	informed	ADJ
ejpam-6798	46	27	decisions	decision	NOUN
ejpam-6798	46	28	in	in	ADP
ejpam-6798	46	29	complicated	complicated	ADJ
ejpam-6798	46	30	situations	situation	NOUN
ejpam-6798	46	31	and	and	CCONJ
ejpam-6798	46	32	challenging	challenging	ADJ
ejpam-6798	46	33	.	.	PUNCT
ejpam-6798	47	1	in	in	ADP
ejpam-6798	47	2	today	today	NOUN
ejpam-6798	47	3	’s	’s	PART
ejpam-6798	47	4	society	society	NOUN
ejpam-6798	47	5	,	,	PUNCT
ejpam-6798	47	6	the	the	DET
ejpam-6798	47	7	advancement	advancement	NOUN
ejpam-6798	47	8	of	of	ADP
ejpam-6798	47	9	computer	computer	NOUN
ejpam-6798	47	10	technology	technology	NOUN
ejpam-6798	47	11	,	,	PUNCT
ejpam-6798	47	12	the	the	DET
ejpam-6798	47	13	availability	availability	NOUN
ejpam-6798	47	14	of	of	ADP
ejpam-6798	47	15	highspeed	highspeed	NOUN
ejpam-6798	47	16	processors	processor	NOUN
ejpam-6798	47	17	,	,	PUNCT
ejpam-6798	47	18	and	and	CCONJ
ejpam-6798	47	19	the	the	DET
ejpam-6798	47	20	widespread	widespread	ADJ
ejpam-6798	47	21	use	use	NOUN
ejpam-6798	47	22	of	of	ADP
ejpam-6798	47	23	programming	programming	NOUN
ejpam-6798	47	24	languages	language	NOUN
ejpam-6798	47	25	have	have	AUX
ejpam-6798	47	26	provided	provide	VERB
ejpam-6798	47	27	researchers	researcher	NOUN
ejpam-6798	47	28	with	with	ADP
ejpam-6798	47	29	new	new	ADJ
ejpam-6798	47	30	opportunities	opportunity	NOUN
ejpam-6798	47	31	to	to	PART
ejpam-6798	47	32	investigate	investigate	VERB
ejpam-6798	47	33	and	and	CCONJ
ejpam-6798	47	34	develop	develop	VERB
ejpam-6798	47	35	algorithms	algorithm	NOUN
ejpam-6798	47	36	that	that	PRON
ejpam-6798	47	37	specifically	specifically	ADV
ejpam-6798	47	38	address	address	VERB
ejpam-6798	47	39	intricate	intricate	ADJ
ejpam-6798	47	40	physical	physical	ADJ
ejpam-6798	47	41	phenomena	phenomenon	NOUN
ejpam-6798	47	42	in	in	ADP
ejpam-6798	47	43	a	a	DET
ejpam-6798	47	44	variety	variety	NOUN
ejpam-6798	47	45	of	of	ADP
ejpam-6798	47	46	scientific	scientific	ADJ
ejpam-6798	47	47	fields	field	NOUN
ejpam-6798	47	48	.	.	PUNCT
ejpam-6798	48	1	the	the	DET
ejpam-6798	48	2	field	field	NOUN
ejpam-6798	48	3	of	of	ADP
ejpam-6798	48	4	general	general	ADJ
ejpam-6798	48	5	operator	operator	NOUN
ejpam-6798	48	6	theory	theory	NOUN
ejpam-6798	48	7	presents	present	VERB
ejpam-6798	48	8	a	a	DET
ejpam-6798	48	9	theoretical	theoretical	ADJ
ejpam-6798	48	10	structure	structure	NOUN
ejpam-6798	48	11	for	for	ADP
ejpam-6798	48	12	understanding	understand	VERB
ejpam-6798	48	13	the	the	DET
ejpam-6798	48	14	mathematical	mathematical	ADJ
ejpam-6798	48	15	prinm	prinm	NOUN
ejpam-6798	48	16	.	.	PUNCT
ejpam-6798	49	1	jawad	jawad	PROPN
ejpam-6798	49	2	et	et	PROPN
ejpam-6798	49	3	al	al	PROPN
ejpam-6798	49	4	.	.	PUNCT
ejpam-6798	49	5	/	/	SYM
ejpam-6798	49	6	eur	eur	PROPN
ejpam-6798	49	7	.	.	PUNCT
ejpam-6798	50	1	j.	j.	PROPN
ejpam-6798	50	2	pure	pure	PROPN
ejpam-6798	50	3	appl	appl	PROPN
ejpam-6798	50	4	.	.	PROPN
ejpam-6798	50	5	math	math	PROPN
ejpam-6798	50	6	,	,	PUNCT
ejpam-6798	50	7	18	18	NUM
ejpam-6798	50	8	(	(	PUNCT
ejpam-6798	50	9	4	4	NUM
ejpam-6798	50	10	)	)	PUNCT
ejpam-6798	50	11	(	(	PUNCT
ejpam-6798	50	12	2025	2025	NUM
ejpam-6798	50	13	)	)	PUNCT
ejpam-6798	50	14	,	,	PUNCT
ejpam-6798	50	15	6798	6798	NUM
ejpam-6798	50	16	3	3	NUM
ejpam-6798	50	17	of	of	ADP
ejpam-6798	50	18	22	22	NUM
ejpam-6798	50	19	ciples	ciple	NOUN
ejpam-6798	50	20	that	that	PRON
ejpam-6798	50	21	serve	serve	VERB
ejpam-6798	50	22	as	as	ADP
ejpam-6798	50	23	the	the	DET
ejpam-6798	50	24	foundation	foundation	NOUN
ejpam-6798	50	25	for	for	ADP
ejpam-6798	50	26	numerous	numerous	ADJ
ejpam-6798	50	27	technical	technical	ADJ
ejpam-6798	50	28	approaches	approach	NOUN
ejpam-6798	50	29	utilized	utilize	VERB
ejpam-6798	50	30	in	in	ADP
ejpam-6798	50	31	a	a	DET
ejpam-6798	50	32	variety	variety	NOUN
ejpam-6798	50	33	of	of	ADP
ejpam-6798	50	34	fields	field	NOUN
ejpam-6798	50	35	.	.	PUNCT
ejpam-6798	51	1	the	the	DET
ejpam-6798	51	2	complex	complex	ADJ
ejpam-6798	51	3	intuitionistic	intuitionistic	ADJ
ejpam-6798	51	4	fuzzy	fuzzy	ADJ
ejpam-6798	51	5	environment	environment	NOUN
ejpam-6798	51	6	displays	display	VERB
ejpam-6798	51	7	mathematical	mathematical	ADJ
ejpam-6798	51	8	patterns	pattern	NOUN
ejpam-6798	51	9	that	that	PRON
ejpam-6798	51	10	can	can	AUX
ejpam-6798	51	11	be	be	AUX
ejpam-6798	51	12	easily	easily	ADV
ejpam-6798	51	13	understood	understand	VERB
ejpam-6798	51	14	within	within	ADP
ejpam-6798	51	15	the	the	DET
ejpam-6798	51	16	framework	framework	NOUN
ejpam-6798	51	17	of	of	ADP
ejpam-6798	51	18	general	general	ADJ
ejpam-6798	51	19	operator	operator	NOUN
ejpam-6798	51	20	theory	theory	NOUN
ejpam-6798	51	21	.	.	PUNCT
ejpam-6798	52	1	by	by	ADP
ejpam-6798	52	2	embracing	embrace	VERB
ejpam-6798	52	3	this	this	DET
ejpam-6798	52	4	expansion	expansion	NOUN
ejpam-6798	52	5	,	,	PUNCT
ejpam-6798	52	6	software	software	NOUN
ejpam-6798	52	7	applications	application	NOUN
ejpam-6798	52	8	that	that	PRON
ejpam-6798	52	9	have	have	VERB
ejpam-6798	52	10	the	the	DET
ejpam-6798	52	11	capacity	capacity	NOUN
ejpam-6798	52	12	to	to	PART
ejpam-6798	52	13	solve	solve	VERB
ejpam-6798	52	14	a	a	DET
ejpam-6798	52	15	broad	broad	ADJ
ejpam-6798	52	16	range	range	NOUN
ejpam-6798	52	17	of	of	ADP
ejpam-6798	52	18	problems	problem	NOUN
ejpam-6798	52	19	and	and	CCONJ
ejpam-6798	52	20	advance	advance	VERB
ejpam-6798	52	21	a	a	DET
ejpam-6798	52	22	number	number	NOUN
ejpam-6798	52	23	of	of	ADP
ejpam-6798	52	24	academic	academic	ADJ
ejpam-6798	52	25	disciplines	discipline	NOUN
ejpam-6798	52	26	can	can	AUX
ejpam-6798	52	27	be	be	AUX
ejpam-6798	52	28	developed	develop	VERB
ejpam-6798	52	29	.	.	PUNCT
ejpam-6798	53	1	the	the	DET
ejpam-6798	53	2	vague	vague	ADJ
ejpam-6798	53	3	and	and	CCONJ
ejpam-6798	53	4	uncertain	uncertain	ADJ
ejpam-6798	53	5	are	be	AUX
ejpam-6798	53	6	essential	essential	ADJ
ejpam-6798	53	7	parts	part	NOUN
ejpam-6798	53	8	of	of	ADP
ejpam-6798	53	9	mankind	mankind	NOUN
ejpam-6798	53	10	’s	’s	PART
ejpam-6798	53	11	existence	existence	NOUN
ejpam-6798	53	12	.	.	PUNCT
ejpam-6798	54	1	accurate	accurate	ADJ
ejpam-6798	54	2	estimates	estimate	NOUN
ejpam-6798	54	3	or	or	CCONJ
ejpam-6798	54	4	hypotheses	hypothesis	NOUN
ejpam-6798	54	5	are	be	AUX
ejpam-6798	54	6	unattainable	unattainable	ADJ
ejpam-6798	54	7	and	and	CCONJ
ejpam-6798	54	8	significantly	significantly	ADV
ejpam-6798	54	9	detrimental	detrimental	ADJ
ejpam-6798	54	10	to	to	ADP
ejpam-6798	54	11	human	human	ADJ
ejpam-6798	54	12	intelligence	intelligence	NOUN
ejpam-6798	54	13	.	.	PUNCT
ejpam-6798	55	1	several	several	ADJ
ejpam-6798	55	2	mathematical	mathematical	ADJ
ejpam-6798	55	3	concepts	concept	NOUN
ejpam-6798	55	4	,	,	PUNCT
ejpam-6798	55	5	including	include	VERB
ejpam-6798	55	6	fuzzy	fuzzy	ADJ
ejpam-6798	55	7	sets	set	NOUN
ejpam-6798	55	8	(	(	PUNCT
ejpam-6798	55	9	fss	fss	NOUN
ejpam-6798	55	10	)	)	PUNCT
ejpam-6798	55	11	,	,	PUNCT
ejpam-6798	55	12	have	have	AUX
ejpam-6798	55	13	emerged	emerge	VERB
ejpam-6798	55	14	as	as	ADP
ejpam-6798	55	15	effective	effective	ADJ
ejpam-6798	55	16	strategies	strategy	NOUN
ejpam-6798	55	17	to	to	PART
ejpam-6798	55	18	tackle	tackle	VERB
ejpam-6798	55	19	this	this	DET
ejpam-6798	55	20	challenge	challenge	NOUN
ejpam-6798	55	21	.	.	PUNCT
ejpam-6798	56	1	to	to	PART
ejpam-6798	56	2	address	address	VERB
ejpam-6798	56	3	this	this	DET
ejpam-6798	56	4	uncertainty	uncertainty	NOUN
ejpam-6798	56	5	in	in	ADP
ejpam-6798	56	6	the	the	DET
ejpam-6798	56	7	data	datum	NOUN
ejpam-6798	56	8	,	,	PUNCT
ejpam-6798	56	9	zadeh	zadeh	PROPN
ejpam-6798	57	1	[	[	X
ejpam-6798	57	2	13	13	NUM
ejpam-6798	57	3	]	]	PUNCT
ejpam-6798	57	4	established	establish	VERB
ejpam-6798	57	5	the	the	DET
ejpam-6798	57	6	concept	concept	NOUN
ejpam-6798	57	7	of	of	ADP
ejpam-6798	57	8	a	a	DET
ejpam-6798	57	9	fs	f	NOUN
ejpam-6798	57	10	,	,	PUNCT
ejpam-6798	57	11	and	and	CCONJ
ejpam-6798	57	12	defined	define	VERB
ejpam-6798	57	13	as	as	ADP
ejpam-6798	57	14	µ	µ	NOUN
ejpam-6798	57	15	→	→	SYM
ejpam-6798	57	16	a	a	X
ejpam-6798	57	17	:	:	PUNCT
ejpam-6798	57	18	{	{	PUNCT
ejpam-6798	57	19	(	(	PUNCT
ejpam-6798	57	20	s	s	X
ejpam-6798	57	21	,	,	PUNCT
ejpam-6798	57	22	µ(s	µ(	NOUN
ejpam-6798	57	23	)	)	PUNCT
ejpam-6798	57	24	)	)	PUNCT
ejpam-6798	57	25	;	;	PUNCT
ejpam-6798	57	26	s	s	VERB
ejpam-6798	57	27	∈	∈	PROPN
ejpam-6798	57	28	a	a	PRON
ejpam-6798	57	29	}	}	PUNCT
ejpam-6798	57	30	,	,	PUNCT
ejpam-6798	57	31	where	where	SCONJ
ejpam-6798	57	32	µ(s	µ(	NOUN
ejpam-6798	57	33	)	)	PUNCT
ejpam-6798	57	34	∈	∈	NOUN
ejpam-6798	58	1	[	[	X
ejpam-6798	58	2	0	0	NUM
ejpam-6798	58	3	,	,	PUNCT
ejpam-6798	58	4	1	1	NUM
ejpam-6798	58	5	]	]	PUNCT
ejpam-6798	58	6	known	know	VERB
ejpam-6798	58	7	as	as	ADP
ejpam-6798	58	8	membership	membership	NOUN
ejpam-6798	58	9	value	value	NOUN
ejpam-6798	58	10	.	.	PUNCT
ejpam-6798	59	1	rosenfeld	rosenfeld	PROPN
ejpam-6798	60	1	[	[	X
ejpam-6798	60	2	14	14	NUM
ejpam-6798	60	3	]	]	PUNCT
ejpam-6798	60	4	introduced	introduce	VERB
ejpam-6798	60	5	the	the	DET
ejpam-6798	60	6	fuzzy	fuzzy	ADJ
ejpam-6798	60	7	subgroup	subgroup	NOUN
ejpam-6798	60	8	(	(	PUNCT
ejpam-6798	60	9	fsg	fsg	PROPN
ejpam-6798	60	10	)	)	PUNCT
ejpam-6798	60	11	and	and	CCONJ
ejpam-6798	60	12	investigated	investigate	VERB
ejpam-6798	60	13	the	the	DET
ejpam-6798	60	14	algebraic	algebraic	ADJ
ejpam-6798	60	15	characteristics	characteristic	NOUN
ejpam-6798	60	16	of	of	ADP
ejpam-6798	60	17	the	the	DET
ejpam-6798	60	18	service	service	NOUN
ejpam-6798	60	19	.	.	PUNCT
ejpam-6798	61	1	das	das	PROPN
ejpam-6798	61	2	[	[	X
ejpam-6798	61	3	15	15	NUM
ejpam-6798	61	4	]	]	PUNCT
ejpam-6798	61	5	initiated	initiate	VERB
ejpam-6798	61	6	the	the	DET
ejpam-6798	61	7	concept	concept	NOUN
ejpam-6798	61	8	of	of	ADP
ejpam-6798	61	9	“	"	PUNCT
ejpam-6798	61	10	level	level	NOUN
ejpam-6798	61	11	subgroups	subgroup	NOUN
ejpam-6798	61	12	”	"	PUNCT
ejpam-6798	61	13	of	of	ADP
ejpam-6798	61	14	a	a	DET
ejpam-6798	61	15	fsg	fsg	NOUN
ejpam-6798	61	16	.	.	PUNCT
ejpam-6798	62	1	meng	meng	PROPN
ejpam-6798	63	1	[	[	X
ejpam-6798	63	2	16	16	NUM
ejpam-6798	63	3	]	]	PUNCT
ejpam-6798	63	4	developed	develop	VERB
ejpam-6798	63	5	a	a	DET
ejpam-6798	63	6	fuzzy	fuzzy	ADJ
ejpam-6798	63	7	concept	concept	NOUN
ejpam-6798	63	8	using	use	VERB
ejpam-6798	63	9	a	a	DET
ejpam-6798	63	10	fs	fs	NOUN
ejpam-6798	63	11	in	in	ADP
ejpam-6798	63	12	a	a	DET
ejpam-6798	63	13	bci	bci	NOUN
ejpam-6798	63	14	-	-	NOUN
ejpam-6798	63	15	algebra	algebra	NOUN
ejpam-6798	63	16	.	.	PUNCT
ejpam-6798	64	1	specifically	specifically	ADV
ejpam-6798	64	2	,	,	PUNCT
ejpam-6798	64	3	certain	certain	ADJ
ejpam-6798	64	4	concepts	concept	NOUN
ejpam-6798	64	5	of	of	ADP
ejpam-6798	64	6	noether	noether	ADJ
ejpam-6798	64	7	bck	bck	PROPN
ejpam-6798	64	8	/	/	SYM
ejpam-6798	64	9	bci	bci	NOUN
ejpam-6798	64	10	-	-	PUNCT
ejpam-6798	64	11	algebras	algebra	NOUN
ejpam-6798	64	12	employ	employ	VERB
ejpam-6798	64	13	fuzzy	fuzzy	ADJ
ejpam-6798	64	14	ideals	ideal	NOUN
ejpam-6798	64	15	.	.	PUNCT
ejpam-6798	65	1	atanassov	atanassov	PROPN
ejpam-6798	66	1	[	[	X
ejpam-6798	66	2	17	17	NUM
ejpam-6798	66	3	]	]	PUNCT
ejpam-6798	66	4	developed	develop	VERB
ejpam-6798	66	5	a	a	DET
ejpam-6798	66	6	new	new	ADJ
ejpam-6798	66	7	notion	notion	NOUN
ejpam-6798	66	8	of	of	ADP
ejpam-6798	66	9	ifs	ifs	PROPN
ejpam-6798	66	10	and	and	CCONJ
ejpam-6798	66	11	described	describe	VERB
ejpam-6798	66	12	as	as	ADP
ejpam-6798	66	13	a	a	DET
ejpam-6798	66	14	=	=	X
ejpam-6798	66	15	{	{	PUNCT
ejpam-6798	66	16	(	(	PUNCT
ejpam-6798	66	17	s	s	NOUN
ejpam-6798	66	18	,	,	PUNCT
ejpam-6798	66	19	µ(s	µ(	NOUN
ejpam-6798	66	20	)	)	PUNCT
ejpam-6798	66	21	,	,	PUNCT
ejpam-6798	66	22	ν(s	ν(s	NOUN
ejpam-6798	66	23	)	)	PUNCT
ejpam-6798	66	24	)	)	PUNCT
ejpam-6798	67	1	:	:	PUNCT
ejpam-6798	67	2	s	s	VERB
ejpam-6798	67	3	∈	∈	PROPN
ejpam-6798	67	4	h	h	NOUN
ejpam-6798	67	5	}	}	PUNCT
ejpam-6798	67	6	,	,	PUNCT
ejpam-6798	67	7	where	where	SCONJ
ejpam-6798	67	8	µ(s	µ(	NOUN
ejpam-6798	67	9	)	)	PUNCT
ejpam-6798	67	10	and	and	CCONJ
ejpam-6798	67	11	ν(s	ν(s	NOUN
ejpam-6798	67	12	)	)	PUNCT
ejpam-6798	67	13	are	be	AUX
ejpam-6798	67	14	the	the	DET
ejpam-6798	67	15	membership	membership	NOUN
ejpam-6798	67	16	degree	degree	NOUN
ejpam-6798	67	17	(	(	PUNCT
ejpam-6798	67	18	md	md	PROPN
ejpam-6798	67	19	)	)	PUNCT
ejpam-6798	67	20	and	and	CCONJ
ejpam-6798	67	21	non	non	PROPN
ejpam-6798	67	22	-	-	PROPN
ejpam-6798	67	23	md	md	PROPN
ejpam-6798	67	24	of	of	ADP
ejpam-6798	67	25	an	an	DET
ejpam-6798	67	26	element	element	NOUN
ejpam-6798	67	27	,	,	PUNCT
ejpam-6798	67	28	as	as	ADV
ejpam-6798	67	29	well	well	ADV
ejpam-6798	67	30	as	as	ADP
ejpam-6798	67	31	0	0	NUM
ejpam-6798	67	32	<	<	X
ejpam-6798	67	33	µ(s)+ν(s	µ(s)+ν(s	NOUN
ejpam-6798	67	34	)	)	PUNCT
ejpam-6798	67	35	≤	≤	NUM
ejpam-6798	67	36	1	1	NUM
ejpam-6798	67	37	.	.	PUNCT
ejpam-6798	68	1	additionally	additionally	ADV
ejpam-6798	68	2	,	,	PUNCT
ejpam-6798	68	3	it	it	PRON
ejpam-6798	68	4	demonstrated	demonstrate	VERB
ejpam-6798	68	5	various	various	ADJ
ejpam-6798	68	6	attributes	attribute	NOUN
ejpam-6798	68	7	associated	associate	VERB
ejpam-6798	68	8	with	with	ADP
ejpam-6798	68	9	relations	relation	NOUN
ejpam-6798	68	10	and	and	CCONJ
ejpam-6798	68	11	operations	operation	NOUN
ejpam-6798	68	12	over	over	ADP
ejpam-6798	68	13	sets	set	NOUN
ejpam-6798	68	14	,	,	PUNCT
ejpam-6798	68	15	as	as	ADV
ejpam-6798	68	16	well	well	ADV
ejpam-6798	68	17	as	as	ADP
ejpam-6798	68	18	the	the	DET
ejpam-6798	68	19	definition	definition	NOUN
ejpam-6798	68	20	of	of	ADP
ejpam-6798	68	21	topological	topological	ADJ
ejpam-6798	68	22	operators	operator	NOUN
ejpam-6798	68	23	and	and	CCONJ
ejpam-6798	68	24	modal	modal	NOUN
ejpam-6798	68	25	over	over	ADP
ejpam-6798	68	26	the	the	DET
ejpam-6798	68	27	set	set	NOUN
ejpam-6798	68	28	of	of	ADP
ejpam-6798	68	29	ifss	ifss	NOUN
ejpam-6798	68	30	were	be	AUX
ejpam-6798	68	31	discussed	discuss	VERB
ejpam-6798	68	32	.	.	PUNCT
ejpam-6798	69	1	akram	akram	PROPN
ejpam-6798	70	1	[	[	X
ejpam-6798	70	2	18	18	NUM
ejpam-6798	70	3	]	]	PUNCT
ejpam-6798	70	4	proposed	propose	VERB
ejpam-6798	70	5	the	the	DET
ejpam-6798	70	6	notion	notion	NOUN
ejpam-6798	70	7	of	of	ADP
ejpam-6798	70	8	an	an	DET
ejpam-6798	70	9	intuitionistic	intuitionistic	ADJ
ejpam-6798	70	10	fuzzy	fuzzy	ADJ
ejpam-6798	70	11	(	(	PUNCT
ejpam-6798	70	12	if	if	SCONJ
ejpam-6798	70	13	)	)	PUNCT
ejpam-6798	70	14	closed	close	VERB
ejpam-6798	70	15	ideal	ideal	NOUN
ejpam-6798	70	16	of	of	ADP
ejpam-6798	70	17	a	a	DET
ejpam-6798	70	18	bci	bci	NOUN
ejpam-6798	70	19	-	-	NOUN
ejpam-6798	70	20	algebra	algebra	NOUN
ejpam-6798	70	21	,	,	PUNCT
ejpam-6798	70	22	applied	apply	VERB
ejpam-6798	70	23	the	the	DET
ejpam-6798	70	24	idea	idea	NOUN
ejpam-6798	70	25	of	of	ADP
ejpam-6798	70	26	ifs	ifs	PROPN
ejpam-6798	70	27	to	to	PART
ejpam-6798	70	28	closed	closed	ADJ
ejpam-6798	70	29	ideals	ideal	NOUN
ejpam-6798	70	30	in	in	ADP
ejpam-6798	70	31	bci	bci	NOUN
ejpam-6798	70	32	-	-	PUNCT
ejpam-6798	70	33	algebras	algebra	NOUN
ejpam-6798	70	34	,	,	PUNCT
ejpam-6798	70	35	and	and	CCONJ
ejpam-6798	70	36	various	various	ADJ
ejpam-6798	70	37	attached	attached	ADJ
ejpam-6798	70	38	characteristics	characteristic	NOUN
ejpam-6798	70	39	were	be	AUX
ejpam-6798	70	40	examined	examine	VERB
ejpam-6798	70	41	.	.	PUNCT
ejpam-6798	71	1	muhiuddin	muhiuddin	VERB
ejpam-6798	71	2	et	et	PROPN
ejpam-6798	71	3	al	al	PROPN
ejpam-6798	71	4	.	.	PUNCT
ejpam-6798	72	1	[	[	X
ejpam-6798	72	2	19	19	NUM
ejpam-6798	72	3	]	]	PUNCT
ejpam-6798	72	4	established	establish	VERB
ejpam-6798	72	5	the	the	DET
ejpam-6798	72	6	(	(	PUNCT
ejpam-6798	72	7	α	α	NOUN
ejpam-6798	72	8	,	,	PUNCT
ejpam-6798	72	9	β)-if	β)-if	ADJ
ejpam-6798	72	10	soft	soft	ADJ
ejpam-6798	72	11	ideal	ideal	NOUN
ejpam-6798	72	12	of	of	ADP
ejpam-6798	72	13	the	the	DET
ejpam-6798	72	14	bck	bck	PROPN
ejpam-6798	72	15	/	/	SYM
ejpam-6798	72	16	bci	bci	PROPN
ejpam-6798	72	17	algebras	algebra	NOUN
ejpam-6798	72	18	,	,	PUNCT
ejpam-6798	72	19	where	where	SCONJ
ejpam-6798	72	20	α	α	NOUN
ejpam-6798	72	21	and	and	CCONJ
ejpam-6798	72	22	β	β	PROPN
ejpam-6798	72	23	represent	represent	VERB
ejpam-6798	72	24	the	the	DET
ejpam-6798	72	25	membership	membership	NOUN
ejpam-6798	72	26	values	value	NOUN
ejpam-6798	72	27	of	of	ADP
ejpam-6798	72	28	an	an	DET
ejpam-6798	72	29	if	if	SCONJ
ejpam-6798	72	30	soft	soft	ADJ
ejpam-6798	72	31	point	point	NOUN
ejpam-6798	72	32	,	,	PUNCT
ejpam-6798	72	33	ifs	ifs	PROPN
ejpam-6798	72	34	and	and	CCONJ
ejpam-6798	72	35	their	their	PRON
ejpam-6798	72	36	related	related	ADJ
ejpam-6798	72	37	characteristics	characteristic	NOUN
ejpam-6798	72	38	were	be	AUX
ejpam-6798	72	39	examined	examine	VERB
ejpam-6798	72	40	.	.	PUNCT
ejpam-6798	73	1	senapati	senapati	PROPN
ejpam-6798	73	2	et	et	PROPN
ejpam-6798	73	3	al	al	PROPN
ejpam-6798	73	4	.	.	PUNCT
ejpam-6798	74	1	[	[	X
ejpam-6798	74	2	20	20	NUM
ejpam-6798	74	3	]	]	PUNCT
ejpam-6798	74	4	introduced	introduce	VERB
ejpam-6798	74	5	the	the	DET
ejpam-6798	74	6	concepts	concept	NOUN
ejpam-6798	74	7	of	of	ADP
ejpam-6798	74	8	intuitionistic	intuitionistic	ADJ
ejpam-6798	74	9	fuzzy	fuzzy	ADJ
ejpam-6798	74	10	translation	translation	NOUN
ejpam-6798	74	11	to	to	PART
ejpam-6798	74	12	intuitionistic	intuitionistic	ADJ
ejpam-6798	74	13	fuzzy	fuzzy	ADJ
ejpam-6798	74	14	sub	sub	NOUN
ejpam-6798	74	15	-	-	ADJ
ejpam-6798	74	16	algebras	algebra	NOUN
ejpam-6798	74	17	and	and	CCONJ
ejpam-6798	74	18	ideals	ideal	NOUN
ejpam-6798	74	19	in	in	ADP
ejpam-6798	74	20	bck	bck	PROPN
ejpam-6798	74	21	/	/	SYM
ejpam-6798	74	22	bci	bci	NOUN
ejpam-6798	74	23	-	-	PUNCT
ejpam-6798	74	24	algebras	algebra	NOUN
ejpam-6798	74	25	.	.	PUNCT
ejpam-6798	75	1	also	also	ADV
ejpam-6798	75	2	,	,	PUNCT
ejpam-6798	75	3	the	the	DET
ejpam-6798	75	4	relationships	relationship	NOUN
ejpam-6798	75	5	between	between	ADP
ejpam-6798	75	6	intuitionistic	intuitionistic	ADJ
ejpam-6798	75	7	fuzzy	fuzzy	ADJ
ejpam-6798	75	8	translations	translation	NOUN
ejpam-6798	75	9	and	and	CCONJ
ejpam-6798	75	10	intuitionistic	intuitionistic	ADJ
ejpam-6798	75	11	fuzzy	fuzzy	ADJ
ejpam-6798	75	12	extensions	extension	NOUN
ejpam-6798	75	13	of	of	ADP
ejpam-6798	75	14	intuitionistic	intuitionistic	ADJ
ejpam-6798	75	15	fuzzy	fuzzy	ADJ
ejpam-6798	75	16	sub	sub	NOUN
ejpam-6798	75	17	-	-	ADJ
ejpam-6798	75	18	algebras	algebra	NOUN
ejpam-6798	75	19	and	and	CCONJ
ejpam-6798	75	20	ideals	ideal	NOUN
ejpam-6798	75	21	were	be	AUX
ejpam-6798	75	22	investigated	investigate	VERB
ejpam-6798	75	23	.	.	PUNCT
ejpam-6798	76	1	senapati	senapati	PROPN
ejpam-6798	76	2	et	et	PROPN
ejpam-6798	76	3	al	al	PROPN
ejpam-6798	76	4	.	.	PUNCT
ejpam-6798	77	1	[	[	X
ejpam-6798	77	2	21	21	NUM
ejpam-6798	77	3	]	]	PUNCT
ejpam-6798	77	4	investigated	investigate	VERB
ejpam-6798	77	5	the	the	DET
ejpam-6798	77	6	cubic	cubic	ADJ
ejpam-6798	77	7	intuitionistic	intuitionistic	ADJ
ejpam-6798	77	8	implicative	implicative	ADJ
ejpam-6798	77	9	ideals	ideal	NOUN
ejpam-6798	77	10	in	in	ADP
ejpam-6798	77	11	 	 	SPACE
ejpam-6798	77	12	bck	bck	NOUN
ejpam-6798	77	13	-	-	PUNCT
ejpam-6798	77	14	algebras	algebras	PROPN
ejpam-6798	77	15	and	and	CCONJ
ejpam-6798	77	16	the	the	DET
ejpam-6798	77	17	relationship	relationship	NOUN
ejpam-6798	77	18	between	between	ADP
ejpam-6798	77	19	a	a	DET
ejpam-6798	77	20	cubic	cubic	ADJ
ejpam-6798	77	21	intuitionistic	intuitionistic	ADJ
ejpam-6798	77	22	sub	sub	NOUN
ejpam-6798	77	23	-	-	ADJ
ejpam-6798	77	24	algebra	algebra	ADJ
ejpam-6798	77	25	,	,	PUNCT
ejpam-6798	77	26	a	a	DET
ejpam-6798	77	27	cubic	cubic	ADJ
ejpam-6798	77	28	intuitionistic	intuitionistic	ADJ
ejpam-6798	77	29	ideal	ideal	NOUN
ejpam-6798	77	30	and	and	CCONJ
ejpam-6798	77	31	a	a	DET
ejpam-6798	77	32	cubic	cubic	ADJ
ejpam-6798	77	33	intuitionistic	intuitionistic	ADJ
ejpam-6798	77	34	implicative	implicative	ADJ
ejpam-6798	77	35	ideal	ideal	NOUN
ejpam-6798	77	36	were	be	AUX
ejpam-6798	77	37	investigated	investigate	VERB
ejpam-6798	77	38	.	.	PUNCT
ejpam-6798	78	1	furthermore	furthermore	ADV
ejpam-6798	78	2	,	,	PUNCT
ejpam-6798	78	3	the	the	DET
ejpam-6798	78	4	conditions	condition	NOUN
ejpam-6798	78	5	for	for	ADP
ejpam-6798	78	6	a	a	DET
ejpam-6798	78	7	cubic	cubic	ADJ
ejpam-6798	78	8	intuitionistic	intuitionistic	ADJ
ejpam-6798	78	9	ideal	ideal	NOUN
ejpam-6798	78	10	to	to	PART
ejpam-6798	78	11	be	be	AUX
ejpam-6798	78	12	a	a	DET
ejpam-6798	78	13	cubic	cubic	ADJ
ejpam-6798	78	14	intuitionistic	intuitionistic	ADJ
ejpam-6798	78	15	implicative	implicative	ADJ
ejpam-6798	78	16	ideal	ideal	NOUN
ejpam-6798	78	17	were	be	AUX
ejpam-6798	78	18	described	describe	VERB
ejpam-6798	78	19	.	.	PUNCT
ejpam-6798	79	1	a	a	DET
ejpam-6798	79	2	complex	complex	ADJ
ejpam-6798	79	3	fuzzy	fuzzy	ADJ
ejpam-6798	79	4	set	set	NOUN
ejpam-6798	79	5	(	(	PUNCT
ejpam-6798	79	6	cfs	cfs	PROPN
ejpam-6798	79	7	)	)	PUNCT
ejpam-6798	79	8	is	be	AUX
ejpam-6798	79	9	more	more	ADV
ejpam-6798	79	10	efficient	efficient	ADJ
ejpam-6798	79	11	and	and	CCONJ
ejpam-6798	79	12	flexible	flexible	ADJ
ejpam-6798	79	13	than	than	ADP
ejpam-6798	79	14	fss	fss	ADJ
ejpam-6798	79	15	.	.	PUNCT
ejpam-6798	80	1	ramote	ramote	VERB
ejpam-6798	80	2	et	et	PROPN
ejpam-6798	80	3	al	al	PROPN
ejpam-6798	80	4	.	.	PUNCT
ejpam-6798	81	1	[	[	X
ejpam-6798	81	2	22	22	NUM
ejpam-6798	81	3	]	]	PUNCT
ejpam-6798	81	4	presented	present	VERB
ejpam-6798	81	5	the	the	DET
ejpam-6798	81	6	concept	concept	NOUN
ejpam-6798	81	7	of	of	ADP
ejpam-6798	81	8	complex	complex	ADJ
ejpam-6798	81	9	fuzzy	fuzzy	ADJ
ejpam-6798	81	10	logic	logic	NOUN
ejpam-6798	81	11	(	(	PUNCT
ejpam-6798	81	12	cfl	cfl	NOUN
ejpam-6798	81	13	)	)	PUNCT
ejpam-6798	81	14	.	.	PUNCT
ejpam-6798	82	1	cfl	cfl	NOUN
ejpam-6798	82	2	is	be	AUX
ejpam-6798	82	3	a	a	DET
ejpam-6798	82	4	generalization	generalization	NOUN
ejpam-6798	82	5	of	of	ADP
ejpam-6798	82	6	traditional	traditional	ADJ
ejpam-6798	82	7	fuzzy	fuzzy	ADJ
ejpam-6798	82	8	logic	logic	NOUN
ejpam-6798	82	9	,	,	PUNCT
ejpam-6798	82	10	based	base	VERB
ejpam-6798	82	11	on	on	ADP
ejpam-6798	82	12	cfss	cfss	PROPN
ejpam-6798	82	13	.	.	PUNCT
ejpam-6798	83	1	ramote	ramote	VERB
ejpam-6798	83	2	et	et	PROPN
ejpam-6798	83	3	al	al	PROPN
ejpam-6798	83	4	.	.	PUNCT
ejpam-6798	84	1	[	[	X
ejpam-6798	84	2	22	22	NUM
ejpam-6798	84	3	]	]	PUNCT
ejpam-6798	84	4	established	establish	VERB
ejpam-6798	84	5	the	the	DET
ejpam-6798	84	6	novel	novel	ADJ
ejpam-6798	84	7	concept	concept	NOUN
ejpam-6798	84	8	of	of	ADP
ejpam-6798	84	9	cfss	cfss	ADJ
ejpam-6798	84	10	,	,	PUNCT
ejpam-6798	84	11	which	which	PRON
ejpam-6798	84	12	was	be	AUX
ejpam-6798	84	13	defined	define	VERB
ejpam-6798	84	14	as	as	ADP
ejpam-6798	84	15	{	{	PUNCT
ejpam-6798	84	16	s	s	NOUN
ejpam-6798	84	17	,	,	PUNCT
ejpam-6798	84	18	ν(s	ν(s	NOUN
ejpam-6798	84	19	)	)	PUNCT
ejpam-6798	84	20	=	=	SYM
ejpam-6798	84	21	µ(s)eιθ(s	µ(s)eιθ(s	ADJ
ejpam-6798	84	22	)	)	PUNCT
ejpam-6798	84	23	:	:	PUNCT
ejpam-6798	84	24	s	s	VERB
ejpam-6798	84	25	∈	∈	PROPN
ejpam-6798	84	26	h	h	NOUN
ejpam-6798	84	27	}	}	PUNCT
ejpam-6798	84	28	,	,	PUNCT
ejpam-6798	84	29	where	where	SCONJ
ejpam-6798	84	30	µ(s	µ(	NOUN
ejpam-6798	84	31	)	)	PUNCT
ejpam-6798	84	32	→	→	PUNCT
ejpam-6798	85	1	[	[	X
ejpam-6798	85	2	0	0	NUM
ejpam-6798	85	3	,	,	PUNCT
ejpam-6798	85	4	1	1	NUM
ejpam-6798	85	5	]	]	PUNCT
ejpam-6798	85	6	is	be	AUX
ejpam-6798	85	7	the	the	DET
ejpam-6798	85	8	md	md	PROPN
ejpam-6798	85	9	of	of	ADP
ejpam-6798	85	10	the	the	DET
ejpam-6798	85	11	real	real	ADJ
ejpam-6798	85	12	part	part	NOUN
ejpam-6798	85	13	and	and	CCONJ
ejpam-6798	85	14	θ(p	θ(p	NOUN
ejpam-6798	85	15	)	)	PUNCT
ejpam-6798	85	16	→	→	PUNCT
ejpam-6798	86	1	[	[	X
ejpam-6798	86	2	0	0	NUM
ejpam-6798	86	3	,	,	PUNCT
ejpam-6798	86	4	2π	2π	NOUN
ejpam-6798	86	5	]	]	PUNCT
ejpam-6798	86	6	is	be	AUX
ejpam-6798	86	7	a	a	DET
ejpam-6798	86	8	md	md	PROPN
ejpam-6798	86	9	of	of	ADP
ejpam-6798	86	10	the	the	DET
ejpam-6798	86	11	imaginary	imaginary	ADJ
ejpam-6798	86	12	part	part	NOUN
ejpam-6798	86	13	of	of	ADP
ejpam-6798	86	14	a	a	DET
ejpam-6798	86	15	complex	complex	ADJ
ejpam-6798	86	16	number	number	NOUN
ejpam-6798	86	17	.	.	PUNCT
ejpam-6798	87	1	the	the	DET
ejpam-6798	87	2	range	range	NOUN
ejpam-6798	87	3	of	of	ADP
ejpam-6798	87	4	membership	membership	NOUN
ejpam-6798	87	5	functions	function	NOUN
ejpam-6798	87	6	(	(	PUNCT
ejpam-6798	87	7	mf	mf	X
ejpam-6798	87	8	)	)	PUNCT
ejpam-6798	87	9	in	in	ADP
ejpam-6798	87	10	a	a	DET
ejpam-6798	87	11	cfs	cfs	NOUN
ejpam-6798	87	12	is	be	AUX
ejpam-6798	87	13	extended	extend	VERB
ejpam-6798	87	14	from	from	ADP
ejpam-6798	87	15	a	a	DET
ejpam-6798	87	16	unit	unit	NOUN
ejpam-6798	87	17	interval	interval	NOUN
ejpam-6798	87	18	to	to	ADP
ejpam-6798	87	19	the	the	DET
ejpam-6798	87	20	complex	complex	ADJ
ejpam-6798	87	21	plane	plane	NOUN
ejpam-6798	87	22	(	(	PUNCT
ejpam-6798	87	23	cp	cp	NOUN
ejpam-6798	87	24	)	)	PUNCT
ejpam-6798	87	25	with	with	ADP
ejpam-6798	87	26	the	the	DET
ejpam-6798	87	27	unit	unit	NOUN
ejpam-6798	87	28	disc	disc	NOUN
ejpam-6798	87	29	.	.	PUNCT
ejpam-6798	88	1	the	the	DET
ejpam-6798	88	2	cfs	cfs	PROPN
ejpam-6798	88	3	helps	help	VERB
ejpam-6798	88	4	equally	equally	ADV
ejpam-6798	88	5	in	in	ADP
ejpam-6798	88	6	the	the	DET
ejpam-6798	88	7	process	process	NOUN
ejpam-6798	88	8	of	of	ADP
ejpam-6798	88	9	evaluating	evaluate	VERB
ejpam-6798	88	10	the	the	DET
ejpam-6798	88	11	system	system	NOUN
ejpam-6798	88	12	because	because	SCONJ
ejpam-6798	88	13	it	it	PRON
ejpam-6798	88	14	considers	consider	VERB
ejpam-6798	88	15	magnitude	magnitude	NOUN
ejpam-6798	88	16	term	term	NOUN
ejpam-6798	88	17	as	as	ADV
ejpam-6798	88	18	well	well	ADV
ejpam-6798	88	19	as	as	ADP
ejpam-6798	88	20	phase	phase	NOUN
ejpam-6798	88	21	term	term	NOUN
ejpam-6798	88	22	,	,	PUNCT
ejpam-6798	88	23	where	where	SCONJ
ejpam-6798	88	24	phase	phase	NOUN
ejpam-6798	88	25	term	term	NOUN
ejpam-6798	88	26	presents	present	VERB
ejpam-6798	88	27	the	the	DET
ejpam-6798	88	28	orientation	orientation	NOUN
ejpam-6798	88	29	of	of	ADP
ejpam-6798	88	30	data	datum	NOUN
ejpam-6798	88	31	item	item	NOUN
ejpam-6798	88	32	in	in	ADP
ejpam-6798	88	33	complex	complex	ADJ
ejpam-6798	88	34	unit	unit	NOUN
ejpam-6798	88	35	disk	disk	NOUN
ejpam-6798	88	36	plan	plan	NOUN
ejpam-6798	88	37	.	.	PUNCT
ejpam-6798	89	1	the	the	DET
ejpam-6798	89	2	primary	primary	ADJ
ejpam-6798	89	3	set	set	VERB
ejpam-6798	89	4	theoretic	theoretic	NOUN
ejpam-6798	89	5	operations	operation	NOUN
ejpam-6798	89	6	,	,	PUNCT
ejpam-6798	89	7	like	like	ADP
ejpam-6798	89	8	intersection	intersection	NOUN
ejpam-6798	89	9	,	,	PUNCT
ejpam-6798	89	10	union	union	NOUN
ejpam-6798	89	11	,	,	PUNCT
ejpam-6798	89	12	and	and	CCONJ
ejpam-6798	89	13	complement	complement	NOUN
ejpam-6798	89	14	,	,	PUNCT
ejpam-6798	89	15	were	be	AUX
ejpam-6798	89	16	discussed	discuss	VERB
ejpam-6798	89	17	in	in	ADP
ejpam-6798	89	18	detail	detail	NOUN
ejpam-6798	89	19	under	under	ADP
ejpam-6798	89	20	the	the	DET
ejpam-6798	89	21	influence	influence	NOUN
ejpam-6798	89	22	of	of	ADP
ejpam-6798	89	23	cfs	cfs	PROPN
ejpam-6798	89	24	.	.	PUNCT
ejpam-6798	90	1	jun	jun	PROPN
ejpam-6798	90	2	and	and	CCONJ
ejpam-6798	90	3	xin	xin	PROPN
ejpam-6798	91	1	[	[	X
ejpam-6798	91	2	23	23	NUM
ejpam-6798	91	3	]	]	PUNCT
ejpam-6798	91	4	presented	present	VERB
ejpam-6798	91	5	the	the	DET
ejpam-6798	91	6	principle	principle	NOUN
ejpam-6798	91	7	of	of	ADP
ejpam-6798	91	8	cfss	cfss	ADJ
ejpam-6798	91	9	to	to	PART
ejpam-6798	91	10	bck	bck	VERB
ejpam-6798	91	11	/	/	SYM
ejpam-6798	91	12	bci	bci	NOUN
ejpam-6798	91	13	-	-	PUNCT
ejpam-6798	91	14	algebras	algebras	X
ejpam-6798	91	15	.	.	PUNCT
ejpam-6798	92	1	in	in	ADP
ejpam-6798	92	2	a	a	DET
ejpam-6798	92	3	bck	bck	NOUN
ejpam-6798	92	4	/	/	SYM
ejpam-6798	92	5	bci	bci	PROPN
ejpam-6798	92	6	algebra	algebra	NOUN
ejpam-6798	92	7	,	,	PUNCT
ejpam-6798	92	8	the	the	DET
ejpam-6798	92	9	concepts	concept	NOUN
ejpam-6798	92	10	of	of	ADP
ejpam-6798	92	11	complex	complex	ADJ
ejpam-6798	92	12	left	left	NOUN
ejpam-6798	92	13	(	(	PUNCT
ejpam-6798	92	14	right	right	ADJ
ejpam-6798	92	15	)	)	PUNCT
ejpam-6798	92	16	reduced	reduce	VERB
ejpam-6798	92	17	ideal	ideal	ADJ
ejpam-6798	92	18	and	and	CCONJ
ejpam-6798	92	19	complex	complex	ADJ
ejpam-6798	92	20	m.	m.	NOUN
ejpam-6798	92	21	jawad	jawad	PROPN
ejpam-6798	92	22	et	et	PROPN
ejpam-6798	92	23	al	al	PROPN
ejpam-6798	92	24	.	.	PUNCT
ejpam-6798	92	25	/	/	SYM
ejpam-6798	92	26	eur	eur	PROPN
ejpam-6798	92	27	.	.	PUNCT
ejpam-6798	93	1	j.	j.	PROPN
ejpam-6798	93	2	pure	pure	PROPN
ejpam-6798	93	3	appl	appl	PROPN
ejpam-6798	93	4	.	.	PROPN
ejpam-6798	93	5	math	math	PROPN
ejpam-6798	93	6	,	,	PUNCT
ejpam-6798	93	7	18	18	NUM
ejpam-6798	93	8	(	(	PUNCT
ejpam-6798	93	9	4	4	NUM
ejpam-6798	93	10	)	)	PUNCT
ejpam-6798	93	11	(	(	PUNCT
ejpam-6798	93	12	2025	2025	NUM
ejpam-6798	93	13	)	)	PUNCT
ejpam-6798	93	14	,	,	PUNCT
ejpam-6798	93	15	6798	6798	NUM
ejpam-6798	93	16	4	4	NUM
ejpam-6798	93	17	of	of	ADP
ejpam-6798	93	18	22	22	NUM
ejpam-6798	93	19	subalgebra	subalgebra	NOUN
ejpam-6798	93	20	were	be	AUX
ejpam-6798	93	21	presented	present	VERB
ejpam-6798	93	22	,	,	PUNCT
ejpam-6798	93	23	and	and	CCONJ
ejpam-6798	93	24	their	their	PRON
ejpam-6798	93	25	linked	link	VERB
ejpam-6798	93	26	properties	property	NOUN
ejpam-6798	93	27	were	be	AUX
ejpam-6798	93	28	discussed	discuss	VERB
ejpam-6798	93	29	.	.	PUNCT
ejpam-6798	94	1	balamurugan	balamurugan	VERB
ejpam-6798	94	2	et	et	PROPN
ejpam-6798	94	3	al	al	PROPN
ejpam-6798	94	4	.	.	PUNCT
ejpam-6798	95	1	[	[	X
ejpam-6798	95	2	24	24	NUM
ejpam-6798	95	3	]	]	PUNCT
ejpam-6798	95	4	established	establish	VERB
ejpam-6798	95	5	the	the	DET
ejpam-6798	95	6	notion	notion	NOUN
ejpam-6798	95	7	of	of	ADP
ejpam-6798	95	8	complex	complex	ADJ
ejpam-6798	95	9	fuzzy	fuzzy	ADJ
ejpam-6798	95	10	sub	sub	NOUN
ejpam-6798	95	11	-	-	ADJ
ejpam-6798	95	12	algebras	algebras	ADJ
ejpam-6798	95	13	(	(	PUNCT
ejpam-6798	95	14	cfsa	cfsa	PROPN
ejpam-6798	95	15	)	)	PUNCT
ejpam-6798	95	16	in	in	ADP
ejpam-6798	95	17	bck	bck	PROPN
ejpam-6798	95	18	/	/	SYM
ejpam-6798	95	19	bci	bci	NOUN
ejpam-6798	95	20	-	-	NOUN
ejpam-6798	95	21	algebra	algebra	NOUN
ejpam-6798	95	22	and	and	CCONJ
ejpam-6798	95	23	their	their	PRON
ejpam-6798	95	24	characteristics	characteristic	NOUN
ejpam-6798	95	25	were	be	AUX
ejpam-6798	95	26	discussed	discuss	VERB
ejpam-6798	95	27	.	.	PUNCT
ejpam-6798	96	1	also	also	ADV
ejpam-6798	96	2	,	,	PUNCT
ejpam-6798	96	3	numerous	numerous	ADJ
ejpam-6798	96	4	laws	law	NOUN
ejpam-6798	96	5	and	and	CCONJ
ejpam-6798	96	6	operations	operation	NOUN
ejpam-6798	96	7	of	of	ADP
ejpam-6798	96	8	a	a	DET
ejpam-6798	96	9	complex	complex	ADJ
ejpam-6798	96	10	fuzzy	fuzzy	ADJ
ejpam-6798	96	11	system	system	NOUN
ejpam-6798	96	12	,	,	PUNCT
ejpam-6798	96	13	such	such	ADJ
ejpam-6798	96	14	as	as	ADP
ejpam-6798	96	15	bounded	bounded	ADJ
ejpam-6798	96	16	differences	difference	NOUN
ejpam-6798	96	17	,	,	PUNCT
ejpam-6798	96	18	union	union	NOUN
ejpam-6798	96	19	,	,	PUNCT
ejpam-6798	96	20	simple	simple	ADJ
ejpam-6798	96	21	differences	difference	NOUN
ejpam-6798	96	22	,	,	PUNCT
ejpam-6798	96	23	intersection	intersection	NOUN
ejpam-6798	96	24	,	,	PUNCT
ejpam-6798	96	25	and	and	CCONJ
ejpam-6798	96	26	complement	complement	NOUN
ejpam-6798	96	27	of	of	ADP
ejpam-6798	96	28	complex	complex	ADJ
ejpam-6798	96	29	fuzzy	fuzzy	ADJ
ejpam-6798	96	30	(	(	PUNCT
ejpam-6798	96	31	cf	cf	NOUN
ejpam-6798	96	32	)	)	PUNCT
ejpam-6798	96	33	ideals	ideal	NOUN
ejpam-6798	96	34	within	within	ADP
ejpam-6798	96	35	bck	bck	PROPN
ejpam-6798	96	36	/	/	SYM
ejpam-6798	96	37	bci	bci	NOUN
ejpam-6798	96	38	-	-	PUNCT
ejpam-6798	96	39	algebras	algebras	PROPN
ejpam-6798	96	40	were	be	AUX
ejpam-6798	96	41	investigated	investigate	VERB
ejpam-6798	96	42	.	.	PUNCT
ejpam-6798	97	1	alolaiyan	alolaiyan	VERB
ejpam-6798	97	2	et	et	PROPN
ejpam-6798	97	3	al	al	PROPN
ejpam-6798	97	4	.	.	PUNCT
ejpam-6798	98	1	[	[	X
ejpam-6798	98	2	25	25	NUM
ejpam-6798	98	3	]	]	PUNCT
ejpam-6798	98	4	proposed	propose	VERB
ejpam-6798	98	5	(	(	PUNCT
ejpam-6798	98	6	α	α	X
ejpam-6798	98	7	,	,	PUNCT
ejpam-6798	98	8	β)-cfss	β)-cfss	PUNCT
ejpam-6798	98	9	and	and	CCONJ
ejpam-6798	98	10	subgroups	subgroup	NOUN
ejpam-6798	98	11	,	,	PUNCT
ejpam-6798	98	12	indicating	indicate	VERB
ejpam-6798	98	13	that	that	SCONJ
ejpam-6798	98	14	all	all	DET
ejpam-6798	98	15	complex	complex	ADJ
ejpam-6798	98	16	fuzzy	fuzzy	ADJ
ejpam-6798	98	17	subgroups	subgroup	NOUN
ejpam-6798	98	18	were	be	AUX
ejpam-6798	98	19	(	(	PUNCT
ejpam-6798	98	20	α	α	NOUN
ejpam-6798	98	21	,	,	PUNCT
ejpam-6798	98	22	β)-cfsgs	β)-cfsgs	PUNCT
ejpam-6798	98	23	.	.	PUNCT
ejpam-6798	99	1	furthermore	furthermore	ADV
ejpam-6798	99	2	,	,	PUNCT
ejpam-6798	99	3	(	(	PUNCT
ejpam-6798	99	4	α	α	NOUN
ejpam-6798	99	5	,	,	PUNCT
ejpam-6798	99	6	β)-cf	β)-cf	ADJ
ejpam-6798	99	7	cosets	coset	NOUN
ejpam-6798	99	8	,	,	PUNCT
ejpam-6798	99	9	(	(	PUNCT
ejpam-6798	99	10	α	α	NOUN
ejpam-6798	99	11	,	,	PUNCT
ejpam-6798	99	12	β)-cf	β)-cf	ADJ
ejpam-6798	99	13	normal	normal	ADJ
ejpam-6798	99	14	subgroup	subgroup	NOUN
ejpam-6798	99	15	,	,	PUNCT
ejpam-6798	99	16	and	and	CCONJ
ejpam-6798	99	17	(	(	PUNCT
ejpam-6798	99	18	α	α	NOUN
ejpam-6798	99	19	,	,	PUNCT
ejpam-6798	99	20	β)-complex	β)-complex	ADJ
ejpam-6798	99	21	fuzzification	fuzzification	NOUN
ejpam-6798	99	22	of	of	ADP
ejpam-6798	99	23	lagrange	lagrange	PROPN
ejpam-6798	99	24	’s	’s	PART
ejpam-6798	99	25	theorem	theorem	ADJ
ejpam-6798	99	26	analog	analog	NOUN
ejpam-6798	99	27	to	to	PART
ejpam-6798	99	28	lagrange	lagrange	PROPN
ejpam-6798	99	29	’s	’s	PART
ejpam-6798	99	30	theorem	theorem	NOUN
ejpam-6798	99	31	of	of	ADP
ejpam-6798	99	32	classical	classical	ADJ
ejpam-6798	99	33	group	group	NOUN
ejpam-6798	99	34	theory	theory	NOUN
ejpam-6798	99	35	were	be	AUX
ejpam-6798	99	36	investigated	investigate	VERB
ejpam-6798	99	37	.	.	PUNCT
ejpam-6798	100	1	zhang	zhang	X
ejpam-6798	101	1	[	[	X
ejpam-6798	101	2	1	1	NUM
ejpam-6798	101	3	]	]	PUNCT
ejpam-6798	101	4	established	establish	VERB
ejpam-6798	101	5	essential	essential	ADJ
ejpam-6798	101	6	ideas	idea	NOUN
ejpam-6798	101	7	about	about	ADP
ejpam-6798	101	8	fuzzy	fuzzy	ADJ
ejpam-6798	101	9	complex	complex	ADJ
ejpam-6798	101	10	numbers	number	NOUN
ejpam-6798	101	11	(	(	PUNCT
ejpam-6798	101	12	fcns	fcns	NOUN
ejpam-6798	101	13	)	)	PUNCT
ejpam-6798	101	14	such	such	ADJ
ejpam-6798	101	15	as	as	ADP
ejpam-6798	101	16	fuzzy	fuzzy	ADJ
ejpam-6798	101	17	distance	distance	NOUN
ejpam-6798	101	18	and	and	CCONJ
ejpam-6798	101	19	fuzzy	fuzzy	ADJ
ejpam-6798	101	20	limit	limit	NOUN
ejpam-6798	101	21	.	.	PUNCT
ejpam-6798	102	1	furthermore	furthermore	ADV
ejpam-6798	102	2	,	,	PUNCT
ejpam-6798	102	3	some	some	DET
ejpam-6798	102	4	fundamental	fundamental	ADJ
ejpam-6798	102	5	properties	property	NOUN
ejpam-6798	102	6	of	of	ADP
ejpam-6798	102	7	fuzzy	fuzzy	ADJ
ejpam-6798	102	8	limits	limit	NOUN
ejpam-6798	102	9	,	,	PUNCT
ejpam-6798	102	10	fuzzy	fuzzy	ADJ
ejpam-6798	102	11	complex	complex	ADJ
ejpam-6798	102	12	numbers	number	NOUN
ejpam-6798	102	13	,	,	PUNCT
ejpam-6798	102	14	and	and	CCONJ
ejpam-6798	102	15	fuzzy	fuzzy	ADJ
ejpam-6798	102	16	distance	distance	NOUN
ejpam-6798	102	17	were	be	AUX
ejpam-6798	102	18	provided	provide	VERB
ejpam-6798	102	19	.	.	PUNCT
ejpam-6798	103	1	also	also	ADV
ejpam-6798	103	2	,	,	PUNCT
ejpam-6798	103	3	several	several	ADJ
ejpam-6798	103	4	essential	essential	ADJ
ejpam-6798	103	5	theorems	theorem	NOUN
ejpam-6798	103	6	of	of	ADP
ejpam-6798	103	7	fcns	fcns	NOUN
ejpam-6798	103	8	,	,	PUNCT
ejpam-6798	103	9	such	such	ADJ
ejpam-6798	103	10	as	as	ADP
ejpam-6798	103	11	the	the	DET
ejpam-6798	103	12	nested	nest	VERB
ejpam-6798	103	13	closed	closed	ADJ
ejpam-6798	103	14	rectangles	rectangle	NOUN
ejpam-6798	103	15	theorem	theorem	VERB
ejpam-6798	103	16	,	,	PUNCT
ejpam-6798	103	17	the	the	DET
ejpam-6798	103	18	accumulation	accumulation	NOUN
ejpam-6798	103	19	principle	principle	NOUN
ejpam-6798	103	20	,	,	PUNCT
ejpam-6798	103	21	and	and	CCONJ
ejpam-6798	103	22	cauchy	cauchy	PROPN
ejpam-6798	103	23	’s	’s	PART
ejpam-6798	103	24	criterion	criterion	NOUN
ejpam-6798	103	25	for	for	ADP
ejpam-6798	103	26	convergence	convergence	NOUN
ejpam-6798	103	27	were	be	AUX
ejpam-6798	103	28	discussed	discuss	VERB
ejpam-6798	103	29	.	.	PUNCT
ejpam-6798	104	1	alkouri	alkouri	PROPN
ejpam-6798	104	2	and	and	CCONJ
ejpam-6798	104	3	salleh	salleh	NOUN
ejpam-6798	105	1	[	[	X
ejpam-6798	105	2	?	?	PUNCT
ejpam-6798	105	3	]	]	PUNCT
ejpam-6798	105	4	established	establish	VERB
ejpam-6798	105	5	a	a	DET
ejpam-6798	105	6	new	new	ADJ
ejpam-6798	105	7	notion	notion	NOUN
ejpam-6798	105	8	of	of	ADP
ejpam-6798	105	9	complex	complex	ADJ
ejpam-6798	105	10	intutionistic	intutionistic	ADJ
ejpam-6798	105	11	fuzzy	fuzzy	ADJ
ejpam-6798	105	12	set	set	NOUN
ejpam-6798	105	13	(	(	PUNCT
ejpam-6798	105	14	cifs	cifs	PROPN
ejpam-6798	105	15	)	)	PUNCT
ejpam-6798	105	16	defined	define	VERB
ejpam-6798	105	17	as	as	ADP
ejpam-6798	105	18	{	{	PUNCT
ejpam-6798	105	19	s	s	NOUN
ejpam-6798	105	20	,	,	PUNCT
ejpam-6798	105	21	µ(s	µ(	NOUN
ejpam-6798	105	22	)	)	PUNCT
ejpam-6798	105	23	=	=	SYM
ejpam-6798	105	24	γ(s)eιθ(s	γ(s)eιθ(s	NOUN
ejpam-6798	105	25	)	)	PUNCT
ejpam-6798	105	26	,	,	PUNCT
ejpam-6798	105	27	ν(s	ν(s	PROPN
ejpam-6798	105	28	)	)	PUNCT
ejpam-6798	106	1	=	=	PUNCT
ejpam-6798	106	2	γ(s)eιθ(s	γ(s)eιθ(s	PROPN
ejpam-6798	106	3	)	)	PUNCT
ejpam-6798	106	4	:	:	PUNCT
ejpam-6798	106	5	s	s	VERB
ejpam-6798	106	6	∈	∈	PROPN
ejpam-6798	106	7	h	h	NOUN
ejpam-6798	106	8	}	}	PUNCT
ejpam-6798	106	9	,	,	PUNCT
ejpam-6798	106	10	which	which	PRON
ejpam-6798	106	11	is	be	AUX
ejpam-6798	106	12	extended	extend	VERB
ejpam-6798	106	13	by	by	ADP
ejpam-6798	106	14	adding	add	VERB
ejpam-6798	106	15	a	a	DET
ejpam-6798	106	16	non	non	ADJ
ejpam-6798	106	17	-	-	ADJ
ejpam-6798	106	18	md	md	ADJ
ejpam-6798	106	19	term	term	NOUN
ejpam-6798	106	20	to	to	ADP
ejpam-6798	106	21	the	the	DET
ejpam-6798	106	22	basic	basic	ADJ
ejpam-6798	106	23	notion	notion	NOUN
ejpam-6798	106	24	of	of	ADP
ejpam-6798	106	25	a	a	DET
ejpam-6798	106	26	cfs	cfs	NOUN
ejpam-6798	106	27	,	,	PUNCT
ejpam-6798	106	28	where	where	SCONJ
ejpam-6798	106	29	γ(s	γ(	NOUN
ejpam-6798	106	30	)	)	PUNCT
ejpam-6798	106	31	→	→	PUNCT
ejpam-6798	107	1	[	[	X
ejpam-6798	107	2	0	0	NUM
ejpam-6798	107	3	,	,	PUNCT
ejpam-6798	107	4	1	1	NUM
ejpam-6798	107	5	]	]	PUNCT
ejpam-6798	107	6	is	be	AUX
ejpam-6798	107	7	the	the	DET
ejpam-6798	107	8	md	md	PROPN
ejpam-6798	107	9	of	of	ADP
ejpam-6798	107	10	the	the	DET
ejpam-6798	107	11	real	real	ADJ
ejpam-6798	107	12	part	part	NOUN
ejpam-6798	107	13	,	,	PUNCT
ejpam-6798	107	14	γ(s	γ(s	PROPN
ejpam-6798	107	15	)	)	PUNCT
ejpam-6798	107	16	→	→	PUNCT
ejpam-6798	108	1	[	[	X
ejpam-6798	108	2	0	0	NUM
ejpam-6798	108	3	,	,	PUNCT
ejpam-6798	108	4	1	1	NUM
ejpam-6798	108	5	]	]	PUNCT
ejpam-6798	108	6	is	be	AUX
ejpam-6798	108	7	the	the	DET
ejpam-6798	108	8	non	non	PROPN
ejpam-6798	108	9	-	-	NOUN
ejpam-6798	108	10	md	md	PROPN
ejpam-6798	108	11	of	of	ADP
ejpam-6798	108	12	the	the	DET
ejpam-6798	108	13	real	real	ADJ
ejpam-6798	108	14	part	part	NOUN
ejpam-6798	108	15	,	,	PUNCT
ejpam-6798	108	16	θ(s	θ(s	PROPN
ejpam-6798	108	17	)	)	PUNCT
ejpam-6798	108	18	→	→	PUNCT
ejpam-6798	109	1	[	[	X
ejpam-6798	109	2	0	0	NUM
ejpam-6798	109	3	,	,	PUNCT
ejpam-6798	109	4	2π	2π	NOUN
ejpam-6798	109	5	]	]	PUNCT
ejpam-6798	109	6	is	be	AUX
ejpam-6798	109	7	the	the	DET
ejpam-6798	109	8	md	md	PROPN
ejpam-6798	109	9	of	of	ADP
ejpam-6798	109	10	the	the	DET
ejpam-6798	109	11	imaginary	imaginary	ADJ
ejpam-6798	109	12	part	part	NOUN
ejpam-6798	109	13	and	and	CCONJ
ejpam-6798	109	14	θ(s	θ(s	NOUN
ejpam-6798	109	15	)	)	PUNCT
ejpam-6798	109	16	→	→	PUNCT
ejpam-6798	110	1	[	[	X
ejpam-6798	110	2	0	0	NUM
ejpam-6798	110	3	,	,	PUNCT
ejpam-6798	110	4	2π	2π	NOUN
ejpam-6798	110	5	]	]	PUNCT
ejpam-6798	110	6	is	be	AUX
ejpam-6798	110	7	a	a	DET
ejpam-6798	110	8	non	non	ADJ
ejpam-6798	110	9	-	-	ADJ
ejpam-6798	110	10	md	md	PROPN
ejpam-6798	110	11	of	of	ADP
ejpam-6798	110	12	the	the	DET
ejpam-6798	110	13	imaginary	imaginary	ADJ
ejpam-6798	110	14	part	part	NOUN
ejpam-6798	110	15	of	of	ADP
ejpam-6798	110	16	a	a	DET
ejpam-6798	110	17	complex	complex	ADJ
ejpam-6798	110	18	number	number	NOUN
ejpam-6798	110	19	such	such	ADJ
ejpam-6798	110	20	that	that	SCONJ
ejpam-6798	110	21	0	0	NUM
ejpam-6798	110	22	<	<	X
ejpam-6798	110	23	µ(s	µ(	NOUN
ejpam-6798	110	24	)	)	PUNCT
ejpam-6798	110	25	+	+	NUM
ejpam-6798	110	26	ν(s	ν(s	NOUN
ejpam-6798	110	27	)	)	PUNCT
ejpam-6798	110	28	=	=	NOUN
ejpam-6798	110	29	1	1	NUM
ejpam-6798	110	30	and	and	CCONJ
ejpam-6798	110	31	0	0	NUM
ejpam-6798	110	32	<	<	X
ejpam-6798	110	33	θ(s	θ(s	PROPN
ejpam-6798	110	34	)	)	PUNCT
ejpam-6798	110	35	+	+	NUM
ejpam-6798	110	36	θ	θ	X
ejpam-6798	111	1	=	=	PUNCT
ejpam-6798	111	2	2π	2π	NOUN
ejpam-6798	111	3	,	,	PUNCT
ejpam-6798	111	4	for	for	ADP
ejpam-6798	111	5	all	all	DET
ejpam-6798	111	6	complex	complex	ADJ
ejpam-6798	111	7	numbers	number	NOUN
ejpam-6798	111	8	s	s	X
ejpam-6798	111	9	∈	∈	PROPN
ejpam-6798	111	10	h.	h.	NOUN
ejpam-6798	111	11	the	the	DET
ejpam-6798	111	12	novelty	novelty	NOUN
ejpam-6798	111	13	of	of	ADP
ejpam-6798	111	14	cifs	cif	NOUN
ejpam-6798	111	15	lies	lie	VERB
ejpam-6798	111	16	in	in	ADP
ejpam-6798	111	17	its	its	PRON
ejpam-6798	111	18	capabilities	capability	NOUN
ejpam-6798	111	19	to	to	PART
ejpam-6798	111	20	achieve	achieve	VERB
ejpam-6798	111	21	a	a	DET
ejpam-6798	111	22	wider	wide	ADJ
ejpam-6798	111	23	range	range	NOUN
ejpam-6798	111	24	of	of	ADP
ejpam-6798	111	25	values	value	NOUN
ejpam-6798	111	26	for	for	ADP
ejpam-6798	111	27	both	both	PRON
ejpam-6798	111	28	mf	mf	NOUN
ejpam-6798	111	29	and	and	CCONJ
ejpam-6798	111	30	non	non	PROPN
ejpam-6798	111	31	-	-	ADJ
ejpam-6798	111	32	mf	mf	PROPN
ejpam-6798	111	33	.	.	PROPN
ejpam-6798	111	34	gong	gong	PROPN
ejpam-6798	111	35	and	and	CCONJ
ejpam-6798	111	36	wang	wang	PROPN
ejpam-6798	112	1	[	[	X
ejpam-6798	112	2	26	26	NUM
ejpam-6798	112	3	]	]	PUNCT
ejpam-6798	112	4	proposed	propose	VERB
ejpam-6798	112	5	a	a	DET
ejpam-6798	112	6	range	range	NOUN
ejpam-6798	112	7	of	of	ADP
ejpam-6798	112	8	operation	operation	NOUN
ejpam-6798	112	9	characteristic	characteristic	NOUN
ejpam-6798	112	10	of	of	ADP
ejpam-6798	112	11	cifs	cif	NOUN
ejpam-6798	112	12	were	be	AUX
ejpam-6798	112	13	examined	examine	VERB
ejpam-6798	112	14	under	under	ADP
ejpam-6798	112	15	the	the	DET
ejpam-6798	112	16	condition	condition	NOUN
ejpam-6798	112	17	that	that	SCONJ
ejpam-6798	112	18	both	both	CCONJ
ejpam-6798	112	19	the	the	DET
ejpam-6798	112	20	non	non	ADJ
ejpam-6798	112	21	-	-	ADJ
ejpam-6798	112	22	membership	membership	ADJ
ejpam-6798	112	23	phase	phase	NOUN
ejpam-6798	112	24	and	and	CCONJ
ejpam-6798	112	25	membership	membership	NOUN
ejpam-6798	112	26	phase	phase	NOUN
ejpam-6798	112	27	were	be	AUX
ejpam-6798	112	28	limited	limit	VERB
ejpam-6798	112	29	to	to	ADP
ejpam-6798	112	30	the	the	DET
ejpam-6798	112	31	interval	interval	NOUN
ejpam-6798	112	32	[	[	X
ejpam-6798	112	33	0	0	NUM
ejpam-6798	112	34	,	,	PUNCT
ejpam-6798	112	35	2π	2π	NOUN
ejpam-6798	112	36	]	]	PUNCT
ejpam-6798	112	37	.	.	PUNCT
ejpam-6798	113	1	generally	generally	ADV
ejpam-6798	113	2	,	,	PUNCT
ejpam-6798	113	3	membership	membership	NOUN
ejpam-6798	113	4	and	and	CCONJ
ejpam-6798	113	5	non	non	ADJ
ejpam-6798	113	6	-	-	ADJ
ejpam-6798	113	7	membership	membership	ADJ
ejpam-6798	113	8	values	value	NOUN
ejpam-6798	113	9	have	have	VERB
ejpam-6798	113	10	little	little	ADJ
ejpam-6798	113	11	practical	practical	ADJ
ejpam-6798	113	12	significance	significance	NOUN
ejpam-6798	113	13	,	,	PUNCT
ejpam-6798	113	14	and	and	CCONJ
ejpam-6798	113	15	there	there	PRON
ejpam-6798	113	16	was	be	VERB
ejpam-6798	113	17	no	no	DET
ejpam-6798	113	18	study	study	NOUN
ejpam-6798	113	19	of	of	ADP
ejpam-6798	113	20	proximity	proximity	NOUN
ejpam-6798	113	21	and	and	CCONJ
ejpam-6798	113	22	equality	equality	NOUN
ejpam-6798	113	23	measures	measure	NOUN
ejpam-6798	113	24	for	for	ADP
ejpam-6798	113	25	cifs	cif	NOUN
ejpam-6798	113	26	.	.	PUNCT
ejpam-6798	114	1	the	the	DET
ejpam-6798	114	2	distance	distance	NOUN
ejpam-6798	114	3	measure	measure	NOUN
ejpam-6798	114	4	(	(	PUNCT
ejpam-6798	114	5	dm	dm	NOUN
ejpam-6798	114	6	)	)	PUNCT
ejpam-6798	114	7	was	be	AUX
ejpam-6798	114	8	used	use	VERB
ejpam-6798	114	9	to	to	PART
ejpam-6798	114	10	explain	explain	VERB
ejpam-6798	114	11	the	the	DET
ejpam-6798	114	12	(	(	PUNCT
ejpam-6798	114	13	α	α	NOUN
ejpam-6798	114	14	,	,	PUNCT
ejpam-6798	114	15	β)-equalities	β)-equalities	PUNCT
ejpam-6798	114	16	of	of	ADP
ejpam-6798	114	17	cifs	cif	NOUN
ejpam-6798	114	18	.	.	PUNCT
ejpam-6798	115	1	the	the	DET
ejpam-6798	115	2	(	(	PUNCT
ejpam-6798	115	3	α	α	NOUN
ejpam-6798	115	4	,	,	PUNCT
ejpam-6798	115	5	β)-equal	β)-equal	PUNCT
ejpam-6798	115	6	describes	describe	VERB
ejpam-6798	115	7	two	two	NUM
ejpam-6798	115	8	cifs	cif	NOUN
ejpam-6798	115	9	in	in	ADP
ejpam-6798	115	10	which	which	PRON
ejpam-6798	115	11	the	the	DET
ejpam-6798	115	12	difference	difference	NOUN
ejpam-6798	115	13	between	between	ADP
ejpam-6798	115	14	their	their	PRON
ejpam-6798	115	15	nonmembership	nonmembership	NOUN
ejpam-6798	115	16	degrees	degree	NOUN
ejpam-6798	115	17	(	(	PUNCT
ejpam-6798	115	18	mnd	mnd	PROPN
ejpam-6798	115	19	)	)	PUNCT
ejpam-6798	115	20	and	and	CCONJ
ejpam-6798	115	21	membership	membership	NOUN
ejpam-6798	115	22	degrees	degree	NOUN
ejpam-6798	115	23	(	(	PUNCT
ejpam-6798	115	24	md	md	PROPN
ejpam-6798	115	25	)	)	PUNCT
ejpam-6798	115	26	is	be	AUX
ejpam-6798	115	27	less	less	ADJ
ejpam-6798	115	28	than	than	ADP
ejpam-6798	115	29	β	β	PRON
ejpam-6798	115	30	and	and	CCONJ
ejpam-6798	115	31	1	1	NUM
ejpam-6798	115	32	−	−	PROPN
ejpam-6798	115	33	α	α	NOUN
ejpam-6798	115	34	,	,	PUNCT
ejpam-6798	115	35	respectively	respectively	ADV
ejpam-6798	115	36	.	.	PUNCT
ejpam-6798	116	1	gulzar	gulzar	PROPN
ejpam-6798	116	2	et	et	PROPN
ejpam-6798	116	3	al	al	PROPN
ejpam-6798	116	4	.	.	PUNCT
ejpam-6798	117	1	[	[	X
ejpam-6798	117	2	27	27	NUM
ejpam-6798	117	3	]	]	PUNCT
ejpam-6798	117	4	developed	develop	VERB
ejpam-6798	117	5	the	the	DET
ejpam-6798	117	6	notion	notion	NOUN
ejpam-6798	117	7	of	of	ADP
ejpam-6798	117	8	direct	direct	ADJ
ejpam-6798	117	9	product	product	NOUN
ejpam-6798	117	10	between	between	ADP
ejpam-6798	117	11	two	two	NUM
ejpam-6798	117	12	complex	complex	NOUN
ejpam-6798	117	13	if	if	SCONJ
ejpam-6798	117	14	subrings	subring	NOUN
ejpam-6798	117	15	and	and	CCONJ
ejpam-6798	117	16	the	the	DET
ejpam-6798	117	17	level	level	NOUN
ejpam-6798	117	18	sub	sub	NOUN
ejpam-6798	117	19	-	-	NOUN
ejpam-6798	117	20	sets	set	NOUN
ejpam-6798	117	21	of	of	ADP
ejpam-6798	117	22	the	the	DET
ejpam-6798	117	23	direct	direct	ADJ
ejpam-6798	117	24	product	product	NOUN
ejpam-6798	117	25	of	of	ADP
ejpam-6798	117	26	two	two	NUM
ejpam-6798	117	27	complex	complex	NOUN
ejpam-6798	117	28	if	if	SCONJ
ejpam-6798	117	29	subsets	subset	NOUN
ejpam-6798	117	30	were	be	AUX
ejpam-6798	117	31	defined	define	VERB
ejpam-6798	117	32	.	.	PUNCT
ejpam-6798	118	1	the	the	DET
ejpam-6798	118	2	complex	complex	ADJ
ejpam-6798	118	3	intuitionistic	intuitionistic	ADJ
ejpam-6798	118	4	fuzzy	fuzzy	ADJ
ejpam-6798	118	5	sub	sub	NOUN
ejpam-6798	118	6	-	-	NOUN
ejpam-6798	118	7	algebra	algebra	NOUN
ejpam-6798	118	8	has	have	VERB
ejpam-6798	118	9	a	a	DET
ejpam-6798	118	10	broader	broad	ADJ
ejpam-6798	118	11	conceptual	conceptual	ADJ
ejpam-6798	118	12	range	range	NOUN
ejpam-6798	118	13	compared	compare	VERB
ejpam-6798	118	14	to	to	ADP
ejpam-6798	118	15	previously	previously	ADV
ejpam-6798	118	16	existing	exist	VERB
ejpam-6798	118	17	theories	theory	NOUN
ejpam-6798	118	18	.	.	PUNCT
ejpam-6798	119	1	the	the	DET
ejpam-6798	119	2	complex	complex	ADJ
ejpam-6798	119	3	intuitionistic	intuitionistic	ADJ
ejpam-6798	119	4	fuzzy	fuzzy	ADJ
ejpam-6798	119	5	sub	sub	NOUN
ejpam-6798	119	6	-	-	NOUN
ejpam-6798	119	7	algebra	algebra	ADJ
ejpam-6798	119	8	is	be	AUX
ejpam-6798	119	9	a	a	DET
ejpam-6798	119	10	generalization	generalization	NOUN
ejpam-6798	119	11	of	of	ADP
ejpam-6798	119	12	the	the	DET
ejpam-6798	119	13	complex	complex	ADJ
ejpam-6798	119	14	fuzzy	fuzzy	ADJ
ejpam-6798	119	15	sub	sub	NOUN
ejpam-6798	119	16	-	-	NOUN
ejpam-6798	119	17	algebra	algebra	ADJ
ejpam-6798	119	18	,	,	PUNCT
ejpam-6798	119	19	which	which	PRON
ejpam-6798	119	20	does	do	AUX
ejpam-6798	119	21	not	not	PART
ejpam-6798	119	22	deal	deal	VERB
ejpam-6798	119	23	with	with	ADP
ejpam-6798	119	24	the	the	DET
ejpam-6798	119	25	degree	degree	NOUN
ejpam-6798	119	26	of	of	ADP
ejpam-6798	119	27	non	non	ADJ
ejpam-6798	119	28	-	-	NOUN
ejpam-6798	119	29	membership	membership	NOUN
ejpam-6798	119	30	.	.	PUNCT
ejpam-6798	120	1	also	also	ADV
ejpam-6798	120	2	,	,	PUNCT
ejpam-6798	120	3	complex	complex	ADJ
ejpam-6798	120	4	intuitionistic	intuitionistic	ADJ
ejpam-6798	120	5	fuzzy	fuzzy	ADJ
ejpam-6798	120	6	sub	sub	NOUN
ejpam-6798	120	7	-	-	NOUN
ejpam-6798	120	8	algebra	algebra	ADJ
ejpam-6798	120	9	is	be	AUX
ejpam-6798	120	10	a	a	DET
ejpam-6798	120	11	generalization	generalization	NOUN
ejpam-6798	120	12	of	of	ADP
ejpam-6798	120	13	intuitionistic	intuitionistic	ADJ
ejpam-6798	120	14	fuzzy	fuzzy	ADJ
ejpam-6798	120	15	sub	sub	NOUN
ejpam-6798	120	16	-	-	NOUN
ejpam-6798	120	17	algebra	algebra	ADJ
ejpam-6798	120	18	,	,	PUNCT
ejpam-6798	120	19	which	which	PRON
ejpam-6798	120	20	does	do	AUX
ejpam-6798	120	21	not	not	PART
ejpam-6798	120	22	deal	deal	VERB
ejpam-6798	120	23	with	with	ADP
ejpam-6798	120	24	phase	phase	NOUN
ejpam-6798	120	25	terms	term	NOUN
ejpam-6798	120	26	.	.	PUNCT
ejpam-6798	121	1	the	the	DET
ejpam-6798	121	2	complex	complex	ADJ
ejpam-6798	121	3	intuitionistic	intuitionistic	ADJ
ejpam-6798	121	4	fuzzy	fuzzy	ADJ
ejpam-6798	121	5	sub	sub	ADJ
ejpam-6798	121	6	-	-	ADJ
ejpam-6798	121	7	algebra	algebra	ADJ
ejpam-6798	121	8	deals	deal	NOUN
ejpam-6798	121	9	both	both	DET
ejpam-6798	121	10	degree	degree	NOUN
ejpam-6798	121	11	of	of	ADP
ejpam-6798	121	12	membership	membership	NOUN
ejpam-6798	121	13	and	and	CCONJ
ejpam-6798	121	14	degree	degree	NOUN
ejpam-6798	121	15	of	of	ADP
ejpam-6798	121	16	non	non	ADJ
ejpam-6798	121	17	-	-	NOUN
ejpam-6798	121	18	membership	membership	NOUN
ejpam-6798	121	19	,	,	PUNCT
ejpam-6798	121	20	as	as	ADV
ejpam-6798	121	21	well	well	ADV
ejpam-6798	121	22	as	as	ADP
ejpam-6798	121	23	phase	phase	NOUN
ejpam-6798	121	24	term	term	NOUN
ejpam-6798	121	25	and	and	CCONJ
ejpam-6798	121	26	amplitude	amplitude	NOUN
ejpam-6798	121	27	terms	term	NOUN
ejpam-6798	121	28	.	.	PUNCT
ejpam-6798	122	1	motivation	motivation	NOUN
ejpam-6798	122	2	and	and	CCONJ
ejpam-6798	122	3	contribution	contribution	NOUN
ejpam-6798	122	4	for	for	ADP
ejpam-6798	122	5	proposed	propose	VERB
ejpam-6798	122	6	concept	concept	NOUN
ejpam-6798	122	7	:	:	PUNCT
ejpam-6798	122	8	•	•	NUM
ejpam-6798	122	9	ramot	ramot	NOUN
ejpam-6798	122	10	et	et	PROPN
ejpam-6798	122	11	al	al	PROPN
ejpam-6798	122	12	.	.	PUNCT
ejpam-6798	123	1	[	[	X
ejpam-6798	123	2	22	22	NUM
ejpam-6798	123	3	]	]	PUNCT
ejpam-6798	123	4	initiated	initiate	VERB
ejpam-6798	123	5	the	the	DET
ejpam-6798	123	6	concept	concept	NOUN
ejpam-6798	123	7	of	of	ADP
ejpam-6798	123	8	a	a	DET
ejpam-6798	123	9	cfs	cfs	NOUN
ejpam-6798	123	10	by	by	ADP
ejpam-6798	123	11	extending	extend	VERB
ejpam-6798	123	12	the	the	DET
ejpam-6798	123	13	mf	mf	NOUN
ejpam-6798	123	14	from	from	ADP
ejpam-6798	123	15	real	real	ADJ
ejpam-6798	123	16	to	to	ADP
ejpam-6798	123	17	complex	complex	ADJ
ejpam-6798	123	18	numbers	number	NOUN
ejpam-6798	123	19	with	with	ADP
ejpam-6798	123	20	the	the	DET
ejpam-6798	123	21	unit	unit	NOUN
ejpam-6798	123	22	disc	disc	NOUN
ejpam-6798	123	23	.	.	PUNCT
ejpam-6798	124	1	because	because	SCONJ
ejpam-6798	124	2	the	the	DET
ejpam-6798	124	3	cfs	cfs	NOUN
ejpam-6798	124	4	only	only	ADV
ejpam-6798	124	5	evaluated	evaluate	VERB
ejpam-6798	124	6	the	the	DET
ejpam-6798	124	7	md	md	PROPN
ejpam-6798	124	8	rather	rather	ADV
ejpam-6798	124	9	than	than	ADP
ejpam-6798	124	10	the	the	DET
ejpam-6798	124	11	non	non	ADJ
ejpam-6798	124	12	-	-	ADJ
ejpam-6798	124	13	md	md	ADJ
ejpam-6798	124	14	element	element	NOUN
ejpam-6798	124	15	of	of	ADP
ejpam-6798	124	16	data	datum	NOUN
ejpam-6798	124	17	components	component	NOUN
ejpam-6798	124	18	,	,	PUNCT
ejpam-6798	124	19	which	which	PRON
ejpam-6798	124	20	also	also	ADV
ejpam-6798	124	21	performs	perform	VERB
ejpam-6798	124	22	an	an	DET
ejpam-6798	124	23	equal	equal	ADJ
ejpam-6798	124	24	m.	m.	NOUN
ejpam-6798	124	25	jawad	jawad	PROPN
ejpam-6798	124	26	et	et	PROPN
ejpam-6798	124	27	al	al	PROPN
ejpam-6798	124	28	.	.	PUNCT
ejpam-6798	124	29	/	/	SYM
ejpam-6798	124	30	eur	eur	PROPN
ejpam-6798	124	31	.	.	PUNCT
ejpam-6798	125	1	j.	j.	PROPN
ejpam-6798	125	2	pure	pure	PROPN
ejpam-6798	125	3	appl	appl	PROPN
ejpam-6798	125	4	.	.	PROPN
ejpam-6798	125	5	math	math	PROPN
ejpam-6798	125	6	,	,	PUNCT
ejpam-6798	125	7	18	18	NUM
ejpam-6798	125	8	(	(	PUNCT
ejpam-6798	125	9	4	4	NUM
ejpam-6798	125	10	)	)	PUNCT
ejpam-6798	125	11	(	(	PUNCT
ejpam-6798	125	12	2025	2025	NUM
ejpam-6798	125	13	)	)	PUNCT
ejpam-6798	125	14	,	,	PUNCT
ejpam-6798	125	15	6798	6798	NUM
ejpam-6798	125	16	5	5	NUM
ejpam-6798	125	17	of	of	ADP
ejpam-6798	125	18	22	22	NUM
ejpam-6798	125	19	interest	interest	NOUN
ejpam-6798	125	20	in	in	ADP
ejpam-6798	125	21	the	the	DET
ejpam-6798	125	22	decision	decision	NOUN
ejpam-6798	125	23	-	-	PUNCT
ejpam-6798	125	24	making	make	VERB
ejpam-6798	125	25	method	method	NOUN
ejpam-6798	125	26	for	for	ADP
ejpam-6798	125	27	system	system	NOUN
ejpam-6798	125	28	evaluation	evaluation	NOUN
ejpam-6798	126	1	,	,	PUNCT
ejpam-6798	126	2	it	it	PRON
ejpam-6798	126	3	provided	provide	VERB
ejpam-6798	126	4	weight	weight	NOUN
ejpam-6798	126	5	to	to	ADP
ejpam-6798	126	6	the	the	DET
ejpam-6798	126	7	md	md	PROPN
ejpam-6798	126	8	.	.	PROPN
ejpam-6798	126	9	•	•	PROPN
ejpam-6798	126	10	latif	latif	PROPN
ejpam-6798	126	11	and	and	CCONJ
ejpam-6798	126	12	shuaib	shuaib	NOUN
ejpam-6798	126	13	[	[	X
ejpam-6798	126	14	28	28	NUM
ejpam-6798	126	15	]	]	PUNCT
ejpam-6798	126	16	developed	develop	VERB
ejpam-6798	126	17	the	the	DET
ejpam-6798	126	18	idea	idea	NOUN
ejpam-6798	126	19	of	of	ADP
ejpam-6798	126	20	t	t	PROPN
ejpam-6798	126	21	-	-	PUNCT
ejpam-6798	126	22	if	if	SCONJ
ejpam-6798	126	23	conjugate	conjugate	ADJ
ejpam-6798	126	24	element	element	NOUN
ejpam-6798	126	25	and	and	CCONJ
ejpam-6798	126	26	discovered	discover	VERB
ejpam-6798	126	27	the	the	DET
ejpam-6798	126	28	t	t	PROPN
ejpam-6798	126	29	-	-	PUNCT
ejpam-6798	126	30	if	if	SCONJ
ejpam-6798	126	31	conjugacy	conjugacy	PROPN
ejpam-6798	126	32	classes	class	NOUN
ejpam-6798	126	33	of	of	ADP
ejpam-6798	126	34	t	t	PROPN
ejpam-6798	126	35	-	-	PUNCT
ejpam-6798	126	36	if	if	SCONJ
ejpam-6798	126	37	sub	sub	NOUN
ejpam-6798	126	38	-	-	NOUN
ejpam-6798	126	39	group	group	NOUN
ejpam-6798	126	40	.	.	PUNCT
ejpam-6798	127	1	the	the	DET
ejpam-6798	127	2	idea	idea	NOUN
ejpam-6798	127	3	of	of	ADP
ejpam-6798	127	4	t	t	PROPN
ejpam-6798	127	5	-	-	PUNCT
ejpam-6798	127	6	if	if	SCONJ
ejpam-6798	127	7	p	p	ADJ
ejpam-6798	127	8	sub	sub	NOUN
ejpam-6798	127	9	-	-	NOUN
ejpam-6798	127	10	group	group	NOUN
ejpam-6798	127	11	,	,	PUNCT
ejpam-6798	127	12	the	the	DET
ejpam-6798	127	13	t	t	NOUN
ejpam-6798	127	14	-	-	PUNCT
ejpam-6798	127	15	if	if	NOUN
ejpam-6798	127	16	sylow	sylow	NOUN
ejpam-6798	127	17	p	p	NOUN
ejpam-6798	127	18	sub	sub	NOUN
ejpam-6798	127	19	-	-	NOUN
ejpam-6798	127	20	group	group	NOUN
ejpam-6798	127	21	,	,	PUNCT
ejpam-6798	127	22	and	and	CCONJ
ejpam-6798	127	23	the	the	DET
ejpam-6798	127	24	t	t	NOUN
ejpam-6798	127	25	-	-	PUNCT
ejpam-6798	127	26	intuitionistic	intuitionistic	ADJ
ejpam-6798	127	27	fuzzification	fuzzification	NOUN
ejpam-6798	127	28	of	of	ADP
ejpam-6798	127	29	sylow	sylow	NOUN
ejpam-6798	127	30	’s	’s	PART
ejpam-6798	127	31	theorems	theorem	NOUN
ejpam-6798	127	32	were	be	AUX
ejpam-6798	127	33	also	also	ADV
ejpam-6798	127	34	explained	explain	VERB
ejpam-6798	127	35	.	.	PUNCT
ejpam-6798	128	1	gulzar	gulzar	PROPN
ejpam-6798	128	2	et	et	PROPN
ejpam-6798	128	3	al	al	PROPN
ejpam-6798	128	4	.	.	PUNCT
ejpam-6798	129	1	[	[	X
ejpam-6798	129	2	29	29	NUM
ejpam-6798	129	3	]	]	PUNCT
ejpam-6798	129	4	proposed	propose	VERB
ejpam-6798	129	5	the	the	DET
ejpam-6798	129	6	t	t	NOUN
ejpam-6798	129	7	-	-	PUNCT
ejpam-6798	129	8	if	if	NOUN
ejpam-6798	129	9	centralizer	centralizer	NOUN
ejpam-6798	129	10	and	and	CCONJ
ejpam-6798	129	11	normalizer	normalizer	NOUN
ejpam-6798	129	12	for	for	ADP
ejpam-6798	129	13	t	t	PROPN
ejpam-6798	129	14	-	-	PUNCT
ejpam-6798	130	1	if	if	SCONJ
ejpam-6798	130	2	subgroups	subgroup	NOUN
ejpam-6798	130	3	.	.	PUNCT
ejpam-6798	131	1	additionally	additionally	ADV
ejpam-6798	131	2	,	,	PUNCT
ejpam-6798	131	3	the	the	DET
ejpam-6798	131	4	concept	concept	NOUN
ejpam-6798	131	5	of	of	ADP
ejpam-6798	131	6	t	t	PROPN
ejpam-6798	131	7	-	-	PUNCT
ejpam-6798	131	8	if	if	SCONJ
ejpam-6798	131	9	cyclic	cyclic	ADJ
ejpam-6798	131	10	and	and	CCONJ
ejpam-6798	131	11	abelian	abelian	ADJ
ejpam-6798	131	12	subgroups	subgroup	NOUN
ejpam-6798	131	13	were	be	AUX
ejpam-6798	131	14	introduced	introduce	VERB
ejpam-6798	131	15	.	.	PUNCT
ejpam-6798	132	1	•	•	NUM
ejpam-6798	132	2	salleh	salleh	NOUN
ejpam-6798	133	1	[	[	X
ejpam-6798	133	2	30	30	NUM
ejpam-6798	133	3	]	]	PUNCT
ejpam-6798	133	4	proposed	propose	VERB
ejpam-6798	133	5	the	the	DET
ejpam-6798	133	6	notion	notion	NOUN
ejpam-6798	133	7	of	of	ADP
ejpam-6798	133	8	cf	cf	NOUN
ejpam-6798	133	9	space	space	NOUN
ejpam-6798	133	10	and	and	CCONJ
ejpam-6798	133	11	cf	cf	NOUN
ejpam-6798	133	12	sub	sub	NOUN
ejpam-6798	133	13	-	-	NOUN
ejpam-6798	133	14	groups	group	NOUN
ejpam-6798	133	15	.	.	PUNCT
ejpam-6798	134	1	the	the	DET
ejpam-6798	134	2	idea	idea	NOUN
ejpam-6798	134	3	of	of	ADP
ejpam-6798	134	4	fuzzy	fuzzy	ADJ
ejpam-6798	134	5	space	space	NOUN
ejpam-6798	134	6	extended	extend	VERB
ejpam-6798	134	7	beyond	beyond	ADP
ejpam-6798	134	8	the	the	DET
ejpam-6798	134	9	real	real	ADJ
ejpam-6798	134	10	range	range	NOUN
ejpam-6798	134	11	of	of	ADP
ejpam-6798	134	12	mfs	mfs	NOUN
ejpam-6798	134	13	to	to	ADP
ejpam-6798	134	14	the	the	DET
ejpam-6798	134	15	complex	complex	ADJ
ejpam-6798	134	16	range	range	NOUN
ejpam-6798	134	17	of	of	ADP
ejpam-6798	134	18	mfs	mfs	PROPN
ejpam-6798	134	19	,	,	PUNCT
ejpam-6798	134	20	which	which	PRON
ejpam-6798	134	21	was	be	AUX
ejpam-6798	134	22	represented	represent	VERB
ejpam-6798	134	23	by	by	ADP
ejpam-6798	134	24	the	the	DET
ejpam-6798	134	25	unit	unit	NOUN
ejpam-6798	134	26	disc	disc	NOUN
ejpam-6798	134	27	in	in	ADP
ejpam-6798	134	28	the	the	DET
ejpam-6798	134	29	complex	complex	ADJ
ejpam-6798	134	30	plane	plane	NOUN
ejpam-6798	134	31	.	.	PUNCT
ejpam-6798	135	1	ali	ali	PROPN
ejpam-6798	135	2	et	et	PROPN
ejpam-6798	135	3	al	al	PROPN
ejpam-6798	135	4	.	.	PUNCT
ejpam-6798	136	1	[	[	X
ejpam-6798	136	2	31	31	NUM
ejpam-6798	136	3	]	]	PUNCT
ejpam-6798	136	4	introduced	introduce	VERB
ejpam-6798	136	5	the	the	DET
ejpam-6798	136	6	idea	idea	NOUN
ejpam-6798	136	7	of	of	ADP
ejpam-6798	136	8	(	(	PUNCT
ejpam-6798	136	9	ϵ	ϵ	X
ejpam-6798	136	10	,	,	PUNCT
ejpam-6798	136	11	δ)-cafss	δ)-cafss	PROPN
ejpam-6798	136	12	,	,	PUNCT
ejpam-6798	136	13	which	which	PRON
ejpam-6798	136	14	give	give	VERB
ejpam-6798	136	15	a	a	DET
ejpam-6798	136	16	more	more	ADV
ejpam-6798	136	17	thorough	thorough	ADJ
ejpam-6798	136	18	representation	representation	NOUN
ejpam-6798	136	19	of	of	ADP
ejpam-6798	136	20	the	the	DET
ejpam-6798	136	21	ambiguity	ambiguity	NOUN
ejpam-6798	136	22	of	of	ADP
ejpam-6798	136	23	information	information	NOUN
ejpam-6798	136	24	than	than	ADP
ejpam-6798	136	25	cafss	cafss	ADV
ejpam-6798	136	26	by	by	ADP
ejpam-6798	136	27	incorporating	incorporate	VERB
ejpam-6798	136	28	both	both	DET
ejpam-6798	136	29	the	the	DET
ejpam-6798	136	30	magnitude	magnitude	NOUN
ejpam-6798	136	31	and	and	CCONJ
ejpam-6798	136	32	phase	phase	NOUN
ejpam-6798	136	33	of	of	ADP
ejpam-6798	136	34	the	the	DET
ejpam-6798	136	35	mfs	mfs	PROPN
ejpam-6798	136	36	.	.	PUNCT
ejpam-6798	137	1	also	also	ADV
ejpam-6798	137	2	,	,	PUNCT
ejpam-6798	137	3	the	the	DET
ejpam-6798	137	4	(	(	PUNCT
ejpam-6798	137	5	ϵ	ϵ	NOUN
ejpam-6798	137	6	,	,	PUNCT
ejpam-6798	137	7	δ)-complex	δ)-complex	ADJ
ejpam-6798	137	8	anti	anti	ADJ
ejpam-6798	137	9	-	-	ADJ
ejpam-6798	137	10	fuzzy	fuzzy	ADJ
ejpam-6798	137	11	subgroups	subgroup	NOUN
ejpam-6798	137	12	(	(	PUNCT
ejpam-6798	137	13	cafsg	cafsg	NOUN
ejpam-6798	137	14	)	)	PUNCT
ejpam-6798	137	15	in	in	ADP
ejpam-6798	137	16	the	the	DET
ejpam-6798	137	17	environment	environment	NOUN
ejpam-6798	137	18	of	of	ADP
ejpam-6798	137	19	cafs	cafs	NOUN
ejpam-6798	137	20	were	be	AUX
ejpam-6798	137	21	explained	explain	VERB
ejpam-6798	137	22	.	.	PUNCT
ejpam-6798	138	1	gulzar	gulzar	PROPN
ejpam-6798	138	2	et	et	PROPN
ejpam-6798	138	3	al	al	PROPN
ejpam-6798	138	4	.	.	PUNCT
ejpam-6798	139	1	[	[	X
ejpam-6798	139	2	32	32	NUM
ejpam-6798	139	3	]	]	PUNCT
ejpam-6798	139	4	introduced	introduce	VERB
ejpam-6798	139	5	the	the	DET
ejpam-6798	139	6	idea	idea	NOUN
ejpam-6798	139	7	of	of	ADP
ejpam-6798	139	8	complex	complex	ADJ
ejpam-6798	139	9	if	if	SCONJ
ejpam-6798	139	10	subgroups	subgroup	NOUN
ejpam-6798	139	11	and	and	CCONJ
ejpam-6798	139	12	showed	show	VERB
ejpam-6798	139	13	that	that	SCONJ
ejpam-6798	139	14	each	each	DET
ejpam-6798	139	15	complex	complex	NOUN
ejpam-6798	139	16	if	if	SCONJ
ejpam-6798	139	17	subgroup	subgroup	NOUN
ejpam-6798	139	18	can	can	AUX
ejpam-6798	139	19	be	be	AUX
ejpam-6798	139	20	split	split	VERB
ejpam-6798	139	21	into	into	ADP
ejpam-6798	139	22	two	two	NUM
ejpam-6798	139	23	if	if	SCONJ
ejpam-6798	139	24	subgroups	subgroup	NOUN
ejpam-6798	139	25	.	.	PUNCT
ejpam-6798	140	1	•	•	NUM
ejpam-6798	140	2	jawad	jawad	PROPN
ejpam-6798	140	3	et	et	PROPN
ejpam-6798	140	4	al	al	PROPN
ejpam-6798	140	5	.	.	PUNCT
ejpam-6798	141	1	[	[	X
ejpam-6798	141	2	33	33	NUM
ejpam-6798	141	3	]	]	PUNCT
ejpam-6798	141	4	investigated	investigate	VERB
ejpam-6798	141	5	into	into	ADP
ejpam-6798	141	6	group	group	NOUN
ejpam-6798	141	7	isomorphism	isomorphism	NOUN
ejpam-6798	141	8	under	under	ADP
ejpam-6798	141	9	the	the	DET
ejpam-6798	141	10	influence	influence	NOUN
ejpam-6798	141	11	of	of	ADP
ejpam-6798	141	12	cifs	cif	NOUN
ejpam-6798	141	13	,	,	PUNCT
ejpam-6798	141	14	a	a	DET
ejpam-6798	141	15	more	more	ADV
ejpam-6798	141	16	general	general	ADJ
ejpam-6798	141	17	form	form	NOUN
ejpam-6798	141	18	of	of	ADP
ejpam-6798	141	19	the	the	DET
ejpam-6798	141	20	cfs	cfs	NOUN
ejpam-6798	141	21	that	that	PRON
ejpam-6798	141	22	included	include	VERB
ejpam-6798	141	23	the	the	DET
ejpam-6798	141	24	non	non	ADJ
ejpam-6798	141	25	-	-	ADJ
ejpam-6798	141	26	mf	mf	ADJ
ejpam-6798	141	27	degree	degree	NOUN
ejpam-6798	141	28	.	.	PUNCT
ejpam-6798	142	1	the	the	DET
ejpam-6798	142	2	complex	complex	ADJ
ejpam-6798	142	3	algebraic	algebraic	ADJ
ejpam-6798	142	4	structure	structure	NOUN
ejpam-6798	142	5	offered	offer	VERB
ejpam-6798	142	6	useful	useful	ADJ
ejpam-6798	142	7	tools	tool	NOUN
ejpam-6798	142	8	for	for	ADP
ejpam-6798	142	9	understanding	understand	VERB
ejpam-6798	142	10	complex	complex	ADJ
ejpam-6798	142	11	techniques	technique	NOUN
ejpam-6798	142	12	.	.	PUNCT
ejpam-6798	143	1	•	•	NUM
ejpam-6798	143	2	the	the	DET
ejpam-6798	143	3	idea	idea	NOUN
ejpam-6798	143	4	of	of	ADP
ejpam-6798	143	5	complex	complex	ADJ
ejpam-6798	143	6	fuzzy	fuzzy	ADJ
ejpam-6798	143	7	ideals	ideal	NOUN
ejpam-6798	143	8	in	in	ADP
ejpam-6798	143	9	a	a	DET
ejpam-6798	143	10	bck	bck	NOUN
ejpam-6798	143	11	/	/	SYM
ejpam-6798	143	12	bci	bci	NOUN
ejpam-6798	143	13	-	-	NOUN
ejpam-6798	143	14	algebra	algebra	NOUN
ejpam-6798	143	15	was	be	AUX
ejpam-6798	143	16	first	first	ADV
ejpam-6798	143	17	put	put	VERB
ejpam-6798	143	18	forwarded	forward	VERB
ejpam-6798	143	19	by	by	ADP
ejpam-6798	143	20	balamurugan	balamurugan	NOUN
ejpam-6798	143	21	et	et	PROPN
ejpam-6798	143	22	al	al	PROPN
ejpam-6798	143	23	.	.	PUNCT
ejpam-6798	144	1	[	[	X
ejpam-6798	144	2	24	24	NUM
ejpam-6798	144	3	]	]	PUNCT
ejpam-6798	144	4	.	.	PUNCT
ejpam-6798	145	1	our	our	PRON
ejpam-6798	145	2	work	work	NOUN
ejpam-6798	145	3	is	be	AUX
ejpam-6798	145	4	motivated	motivate	VERB
ejpam-6798	145	5	by	by	ADP
ejpam-6798	145	6	the	the	DET
ejpam-6798	145	7	reality	reality	NOUN
ejpam-6798	145	8	that	that	SCONJ
ejpam-6798	145	9	a	a	DET
ejpam-6798	145	10	cfs	cfs	NOUN
ejpam-6798	145	11	considers	consider	VERB
ejpam-6798	145	12	only	only	ADV
ejpam-6798	145	13	the	the	DET
ejpam-6798	145	14	md	md	PROPN
ejpam-6798	145	15	but	but	CCONJ
ejpam-6798	145	16	does	do	AUX
ejpam-6798	145	17	not	not	PART
ejpam-6798	145	18	weigh	weigh	VERB
ejpam-6798	145	19	the	the	DET
ejpam-6798	145	20	non	non	NOUN
ejpam-6798	145	21	-	-	PROPN
ejpam-6798	145	22	md	md	PROPN
ejpam-6798	145	23	of	of	ADP
ejpam-6798	145	24	data	datum	NOUN
ejpam-6798	145	25	elements	element	NOUN
ejpam-6798	145	26	.	.	PUNCT
ejpam-6798	146	1	however	however	ADV
ejpam-6798	146	2	,	,	PUNCT
ejpam-6798	146	3	we	we	PRON
ejpam-6798	146	4	apply	apply	VERB
ejpam-6798	146	5	the	the	DET
ejpam-6798	146	6	cifs	cif	NOUN
ejpam-6798	146	7	in	in	ADP
ejpam-6798	146	8	bck	bck	PROPN
ejpam-6798	146	9	/	/	SYM
ejpam-6798	146	10	bci	bci	NOUN
ejpam-6798	146	11	-	-	NOUN
ejpam-6798	146	12	algebra	algebra	NOUN
ejpam-6798	146	13	,	,	PUNCT
ejpam-6798	146	14	which	which	PRON
ejpam-6798	146	15	is	be	AUX
ejpam-6798	146	16	the	the	DET
ejpam-6798	146	17	most	most	ADV
ejpam-6798	146	18	vital	vital	ADJ
ejpam-6798	146	19	component	component	NOUN
ejpam-6798	146	20	of	of	ADP
ejpam-6798	146	21	algebraic	algebraic	ADJ
ejpam-6798	146	22	structure	structure	NOUN
ejpam-6798	146	23	.	.	PUNCT
ejpam-6798	147	1	•	•	NUM
ejpam-6798	147	2	the	the	DET
ejpam-6798	147	3	idea	idea	NOUN
ejpam-6798	147	4	of	of	ADP
ejpam-6798	147	5	complex	complex	ADJ
ejpam-6798	147	6	if	if	SCONJ
ejpam-6798	147	7	ideals	ideal	NOUN
ejpam-6798	147	8	is	be	AUX
ejpam-6798	147	9	not	not	PART
ejpam-6798	147	10	yet	yet	ADV
ejpam-6798	147	11	applied	apply	VERB
ejpam-6798	147	12	to	to	ADP
ejpam-6798	147	13	the	the	DET
ejpam-6798	147	14	basic	basic	ADJ
ejpam-6798	147	15	algebraic	algebraic	ADJ
ejpam-6798	147	16	structure	structure	NOUN
ejpam-6798	147	17	of	of	ADP
ejpam-6798	147	18	bck	bck	PROPN
ejpam-6798	147	19	/	/	SYM
ejpam-6798	147	20	bci	bci	NOUN
ejpam-6798	147	21	-	-	NOUN
ejpam-6798	147	22	algebra	algebra	NOUN
ejpam-6798	147	23	.	.	PUNCT
ejpam-6798	148	1	in	in	ADP
ejpam-6798	148	2	this	this	DET
ejpam-6798	148	3	proposed	propose	VERB
ejpam-6798	148	4	work	work	NOUN
ejpam-6798	148	5	,	,	PUNCT
ejpam-6798	148	6	we	we	PRON
ejpam-6798	148	7	discuss	discuss	VERB
ejpam-6798	148	8	the	the	DET
ejpam-6798	148	9	various	various	ADJ
ejpam-6798	148	10	basic	basic	ADJ
ejpam-6798	148	11	characteristics	characteristic	NOUN
ejpam-6798	148	12	of	of	ADP
ejpam-6798	148	13	bck	bck	PROPN
ejpam-6798	148	14	/	/	SYM
ejpam-6798	148	15	bci	bci	NOUN
ejpam-6798	148	16	-	-	NOUN
ejpam-6798	148	17	algebra	algebra	NOUN
ejpam-6798	148	18	under	under	ADP
ejpam-6798	148	19	the	the	DET
ejpam-6798	148	20	influence	influence	NOUN
ejpam-6798	148	21	of	of	ADP
ejpam-6798	148	22	cifs	cif	NOUN
ejpam-6798	148	23	.	.	PUNCT
ejpam-6798	149	1	table	table	NOUN
ejpam-6798	149	2	1	1	NUM
ejpam-6798	149	3	:	:	PUNCT
ejpam-6798	149	4	list	list	NOUN
ejpam-6798	149	5	of	of	ADP
ejpam-6798	149	6	abbreviations	abbreviation	NOUN
ejpam-6798	149	7	and	and	CCONJ
ejpam-6798	149	8	symbols	symbol	NOUN
ejpam-6798	149	9	.	.	PUNCT
ejpam-6798	150	1	symbols	symbol	NOUN
ejpam-6798	150	2	abbreviations	abbreviations	PROPN
ejpam-6798	150	3	m	m	VERB
ejpam-6798	150	4	bck	bck	PROPN
ejpam-6798	150	5	/	/	SYM
ejpam-6798	150	6	bci	bci	NOUN
ejpam-6798	150	7	-	-	ADJ
ejpam-6798	150	8	algebra	algebra	ADJ
ejpam-6798	150	9	ifi	ifi	PROPN
ejpam-6798	150	10	intuitionistic	intuitionistic	ADJ
ejpam-6798	150	11	fuzzy	fuzzy	ADJ
ejpam-6798	150	12	ideal	ideal	PROPN
ejpam-6798	150	13	ifs	ifs	PROPN
ejpam-6798	150	14	intuitionistic	intuitionistic	ADJ
ejpam-6798	150	15	fuzzy	fuzzy	ADJ
ejpam-6798	150	16	set	set	VERB
ejpam-6798	150	17	ifsa	ifsa	PROPN
ejpam-6798	150	18	intuitionistic	intuitionistic	ADJ
ejpam-6798	150	19	fuzzy	fuzzy	ADJ
ejpam-6798	150	20	sub	sub	ADJ
ejpam-6798	150	21	-	-	ADJ
ejpam-6798	150	22	algebra	algebra	ADJ
ejpam-6798	150	23	cifi	cifi	NOUN
ejpam-6798	150	24	complex	complex	ADJ
ejpam-6798	150	25	intuitionistic	intuitionistic	ADJ
ejpam-6798	150	26	fuzzy	fuzzy	ADJ
ejpam-6798	150	27	ideal	ideal	ADJ
ejpam-6798	150	28	cifs	cif	VERB
ejpam-6798	150	29	complex	complex	ADJ
ejpam-6798	150	30	intuitionistic	intuitionistic	ADJ
ejpam-6798	150	31	fuzzy	fuzzy	ADJ
ejpam-6798	150	32	set	set	VERB
ejpam-6798	150	33	cifsa	cifsa	ADJ
ejpam-6798	150	34	complex	complex	ADJ
ejpam-6798	150	35	intuitionistic	intuitionistic	ADJ
ejpam-6798	150	36	fuzzy	fuzzy	ADJ
ejpam-6798	150	37	sub	sub	ADJ
ejpam-6798	150	38	-	-	ADJ
ejpam-6798	150	39	algebra	algebra	ADJ
ejpam-6798	150	40	m.	m.	NOUN
ejpam-6798	150	41	jawad	jawad	PROPN
ejpam-6798	150	42	et	et	PROPN
ejpam-6798	150	43	al	al	PROPN
ejpam-6798	150	44	.	.	PUNCT
ejpam-6798	150	45	/	/	SYM
ejpam-6798	150	46	eur	eur	PROPN
ejpam-6798	150	47	.	.	PUNCT
ejpam-6798	151	1	j.	j.	PROPN
ejpam-6798	151	2	pure	pure	PROPN
ejpam-6798	151	3	appl	appl	PROPN
ejpam-6798	151	4	.	.	PROPN
ejpam-6798	151	5	math	math	PROPN
ejpam-6798	151	6	,	,	PUNCT
ejpam-6798	151	7	18	18	NUM
ejpam-6798	151	8	(	(	PUNCT
ejpam-6798	151	9	4	4	NUM
ejpam-6798	151	10	)	)	PUNCT
ejpam-6798	151	11	(	(	PUNCT
ejpam-6798	151	12	2025	2025	NUM
ejpam-6798	151	13	)	)	PUNCT
ejpam-6798	151	14	,	,	PUNCT
ejpam-6798	151	15	6798	6798	NUM
ejpam-6798	151	16	6	6	NUM
ejpam-6798	151	17	of	of	ADP
ejpam-6798	151	18	22	22	NUM
ejpam-6798	151	19	2	2	NUM
ejpam-6798	151	20	.	.	PUNCT
ejpam-6798	151	21	preliminaries	preliminary	NOUN
ejpam-6798	151	22	we	we	PRON
ejpam-6798	151	23	start	start	VERB
ejpam-6798	151	24	by	by	ADP
ejpam-6798	151	25	analyzing	analyze	VERB
ejpam-6798	151	26	the	the	DET
ejpam-6798	151	27	basic	basic	ADJ
ejpam-6798	151	28	concepts	concept	NOUN
ejpam-6798	151	29	of	of	ADP
ejpam-6798	151	30	cfsa	cfsa	NOUN
ejpam-6798	151	31	and	and	CCONJ
ejpam-6798	151	32	cifsa	cifsa	NOUN
ejpam-6798	151	33	,	,	PUNCT
ejpam-6798	151	34	both	both	PRON
ejpam-6798	151	35	are	be	AUX
ejpam-6798	151	36	necessary	necessary	ADJ
ejpam-6798	151	37	for	for	ADP
ejpam-6798	151	38	study	study	NOUN
ejpam-6798	151	39	.	.	PUNCT
ejpam-6798	152	1	definition	definition	NOUN
ejpam-6798	152	2	1	1	NUM
ejpam-6798	152	3	.	.	PUNCT
ejpam-6798	153	1	[	[	X
ejpam-6798	153	2	34	34	NUM
ejpam-6798	153	3	]	]	PUNCT
ejpam-6798	153	4	let	let	VERB
ejpam-6798	153	5	u	u	PRON
ejpam-6798	153	6	be	be	AUX
ejpam-6798	153	7	a	a	DET
ejpam-6798	153	8	non	non	ADJ
ejpam-6798	153	9	-	-	ADJ
ejpam-6798	153	10	empty	empty	ADJ
ejpam-6798	153	11	set	set	NOUN
ejpam-6798	153	12	has	have	VERB
ejpam-6798	153	13	an	an	DET
ejpam-6798	153	14	identity	identity	NOUN
ejpam-6798	153	15	element	element	NOUN
ejpam-6798	153	16	denoted	denote	VERB
ejpam-6798	153	17	as	as	ADP
ejpam-6798	153	18	0	0	NUM
ejpam-6798	153	19	and	and	CCONJ
ejpam-6798	153	20	a	a	DET
ejpam-6798	153	21	binary	binary	ADJ
ejpam-6798	153	22	operation	operation	NOUN
ejpam-6798	153	23	“	"	PUNCT
ejpam-6798	153	24	⋆	⋆	X
ejpam-6798	153	25	”	"	PUNCT
ejpam-6798	153	26	then	then	ADV
ejpam-6798	153	27	u	u	PROPN
ejpam-6798	153	28	is	be	AUX
ejpam-6798	153	29	called	call	VERB
ejpam-6798	153	30	bci	bci	NOUN
ejpam-6798	153	31	-	-	NOUN
ejpam-6798	153	32	algebra	algebra	NOUN
ejpam-6798	153	33	if	if	SCONJ
ejpam-6798	153	34	the	the	DET
ejpam-6798	153	35	following	follow	VERB
ejpam-6798	153	36	axioms	axiom	NOUN
ejpam-6798	153	37	holds	hold	VERB
ejpam-6798	153	38	.	.	PUNCT
ejpam-6798	154	1	(	(	PUNCT
ejpam-6798	154	2	i	i	NOUN
ejpam-6798	154	3	)	)	PUNCT
ejpam-6798	154	4	(	(	PUNCT
ejpam-6798	154	5	(	(	PUNCT
ejpam-6798	154	6	s	s	X
ejpam-6798	154	7	⋆	⋆	NOUN
ejpam-6798	154	8	l	l	NOUN
ejpam-6798	154	9	)	)	PUNCT
ejpam-6798	154	10	⋆	⋆	X
ejpam-6798	154	11	(	(	PUNCT
ejpam-6798	154	12	s	s	X
ejpam-6798	154	13	⋆	⋆	ADJ
ejpam-6798	154	14	z	z	NOUN
ejpam-6798	154	15	)	)	PUNCT
ejpam-6798	154	16	)	)	PUNCT
ejpam-6798	155	1	⋆	⋆	X
ejpam-6798	155	2	(	(	PUNCT
ejpam-6798	155	3	z	z	NOUN
ejpam-6798	155	4	⋆	⋆	NOUN
ejpam-6798	155	5	l	l	NOUN
ejpam-6798	155	6	)	)	PUNCT
ejpam-6798	155	7	=	=	SYM
ejpam-6798	155	8	0	0	NUM
ejpam-6798	155	9	,	,	PUNCT
ejpam-6798	155	10	∀s	∀s	PROPN
ejpam-6798	155	11	,	,	PUNCT
ejpam-6798	155	12	l	l	PROPN
ejpam-6798	155	13	,	,	PUNCT
ejpam-6798	155	14	z	z	PROPN
ejpam-6798	155	15	∈	∈	PROPN
ejpam-6798	155	16	m	m	PRON
ejpam-6798	155	17	,	,	PUNCT
ejpam-6798	155	18	(	(	PUNCT
ejpam-6798	155	19	ii	ii	NOUN
ejpam-6798	155	20	)	)	PUNCT
ejpam-6798	155	21	(	(	PUNCT
ejpam-6798	155	22	s	s	X
ejpam-6798	155	23	⋆	⋆	X
ejpam-6798	155	24	(	(	PUNCT
ejpam-6798	155	25	s	s	X
ejpam-6798	155	26	⋆	⋆	NOUN
ejpam-6798	155	27	l	l	NOUN
ejpam-6798	155	28	)	)	PUNCT
ejpam-6798	155	29	⋆	⋆	X
ejpam-6798	155	30	l	l	NOUN
ejpam-6798	155	31	)	)	PUNCT
ejpam-6798	155	32	=	=	SYM
ejpam-6798	155	33	0	0	NUM
ejpam-6798	155	34	,	,	PUNCT
ejpam-6798	155	35	∀s	∀s	PROPN
ejpam-6798	155	36	,	,	PUNCT
ejpam-6798	155	37	l,∈	l,∈	X
ejpam-6798	155	38	m	m	VERB
ejpam-6798	155	39	,	,	PUNCT
ejpam-6798	155	40	(	(	PUNCT
ejpam-6798	155	41	iii	iii	NOUN
ejpam-6798	155	42	)	)	PUNCT
ejpam-6798	155	43	(	(	PUNCT
ejpam-6798	155	44	s	s	AUX
ejpam-6798	155	45	⋆	⋆	X
ejpam-6798	155	46	s	s	NOUN
ejpam-6798	155	47	)	)	PUNCT
ejpam-6798	155	48	=	=	SYM
ejpam-6798	155	49	0	0	NUM
ejpam-6798	155	50	,	,	PUNCT
ejpam-6798	155	51	∀s	∀s	PROPN
ejpam-6798	155	52	∈	∈	PROPN
ejpam-6798	155	53	m	m	PRON
ejpam-6798	155	54	,	,	PUNCT
ejpam-6798	155	55	(	(	PUNCT
ejpam-6798	155	56	iv	iv	X
ejpam-6798	155	57	)	)	PUNCT
ejpam-6798	155	58	(	(	PUNCT
ejpam-6798	155	59	s	s	X
ejpam-6798	155	60	⋆	⋆	NOUN
ejpam-6798	155	61	l	l	NOUN
ejpam-6798	155	62	=	=	SYM
ejpam-6798	155	63	0	0	NUM
ejpam-6798	155	64	,	,	PUNCT
ejpam-6798	155	65	l	l	NOUN
ejpam-6798	155	66	⋆	⋆	X
ejpam-6798	155	67	s	s	NOUN
ejpam-6798	155	68	=	=	SYM
ejpam-6798	155	69	0	0	NUM
ejpam-6798	155	70	⇒	⇒	NOUN
ejpam-6798	155	71	s	s	PART
ejpam-6798	155	72	=	=	NOUN
ejpam-6798	155	73	l	l	NOUN
ejpam-6798	155	74	)	)	PUNCT
ejpam-6798	155	75	,	,	PUNCT
ejpam-6798	155	76	∀s	∀s	PROPN
ejpam-6798	155	77	,	,	PUNCT
ejpam-6798	155	78	l,∈	l,∈	X
ejpam-6798	155	79	m	m	VERB
ejpam-6798	155	80	.	.	PUNCT
ejpam-6798	156	1	then	then	ADV
ejpam-6798	156	2	,	,	PUNCT
ejpam-6798	156	3	we	we	PRON
ejpam-6798	156	4	describe	describe	VERB
ejpam-6798	156	5	m	m	PRON
ejpam-6798	156	6	as	as	ADP
ejpam-6798	156	7	a	a	DET
ejpam-6798	156	8	bci	bci	NOUN
ejpam-6798	156	9	-	-	NOUN
ejpam-6798	156	10	algebra	algebra	NOUN
ejpam-6798	156	11	.	.	PUNCT
ejpam-6798	157	1	moreover	moreover	ADV
ejpam-6798	157	2	,	,	PUNCT
ejpam-6798	157	3	a	a	DET
ejpam-6798	157	4	bci	bci	NOUN
ejpam-6798	157	5	-	-	NOUN
ejpam-6798	157	6	algebra	algebra	NOUN
ejpam-6798	157	7	m	m	VERB
ejpam-6798	157	8	also	also	ADV
ejpam-6798	157	9	fulfills	fulfill	VERB
ejpam-6798	157	10	:	:	PUNCT
ejpam-6798	157	11	(	(	PUNCT
ejpam-6798	157	12	v	v	NOUN
ejpam-6798	157	13	)	)	PUNCT
ejpam-6798	157	14	(	(	PUNCT
ejpam-6798	157	15	0	0	NUM
ejpam-6798	157	16	⋆	⋆	NOUN
ejpam-6798	157	17	s	s	NOUN
ejpam-6798	157	18	=	=	NOUN
ejpam-6798	157	19	0	0	NUM
ejpam-6798	157	20	)	)	PUNCT
ejpam-6798	157	21	,	,	PUNCT
ejpam-6798	157	22	∀s	∀s	PROPN
ejpam-6798	157	23	∈	∈	PROPN
ejpam-6798	157	24	m	m	NOUN
ejpam-6798	157	25	,	,	PUNCT
ejpam-6798	157	26	then	then	ADV
ejpam-6798	157	27	m	m	VERB
ejpam-6798	157	28	as	as	ADP
ejpam-6798	157	29	a	a	DET
ejpam-6798	157	30	bck	bck	NOUN
ejpam-6798	157	31	-	-	PUNCT
ejpam-6798	157	32	algebra	algebra	NOUN
ejpam-6798	157	33	.	.	PUNCT
ejpam-6798	158	1	definition	definition	NOUN
ejpam-6798	158	2	2	2	NUM
ejpam-6798	158	3	.	.	PUNCT
ejpam-6798	159	1	[	[	X
ejpam-6798	159	2	17	17	NUM
ejpam-6798	159	3	]	]	PUNCT
ejpam-6798	159	4	a	a	DET
ejpam-6798	159	5	ifs	ifs	PROPN
ejpam-6798	159	6	l	l	NOUN
ejpam-6798	159	7	defined	define	VERB
ejpam-6798	159	8	on	on	ADP
ejpam-6798	159	9	m	m	PROPN
ejpam-6798	159	10	is	be	AUX
ejpam-6798	159	11	given	give	VERB
ejpam-6798	159	12	by	by	ADP
ejpam-6798	159	13	:	:	PUNCT
ejpam-6798	159	14	l	l	NOUN
ejpam-6798	159	15	=	=	SYM
ejpam-6798	159	16	{	{	PUNCT
ejpam-6798	159	17	(	(	PUNCT
ejpam-6798	159	18	s	s	X
ejpam-6798	159	19	,	,	PUNCT
ejpam-6798	159	20	µl(s	µl(s	NUM
ejpam-6798	159	21	)	)	PUNCT
ejpam-6798	159	22	,	,	PUNCT
ejpam-6798	159	23	νl(s	νl(	NOUN
ejpam-6798	159	24	)	)	PUNCT
ejpam-6798	159	25	)	)	PUNCT
ejpam-6798	159	26	:	:	PUNCT
ejpam-6798	159	27	s	s	VERB
ejpam-6798	159	28	∈	∈	PROPN
ejpam-6798	159	29	m	m	PRON
ejpam-6798	159	30	}	}	PUNCT
ejpam-6798	159	31	,	,	PUNCT
ejpam-6798	159	32	where	where	SCONJ
ejpam-6798	159	33	µ(s	µ(	NOUN
ejpam-6798	159	34	)	)	PUNCT
ejpam-6798	159	35	and	and	CCONJ
ejpam-6798	159	36	ν(s	ν(s	NOUN
ejpam-6798	159	37	)	)	PUNCT
ejpam-6798	159	38	represent	represent	VERB
ejpam-6798	159	39	membership	membership	NOUN
ejpam-6798	159	40	degree	degree	NOUN
ejpam-6798	159	41	(	(	PUNCT
ejpam-6798	159	42	md	md	PROPN
ejpam-6798	159	43	)	)	PUNCT
ejpam-6798	159	44	and	and	CCONJ
ejpam-6798	159	45	non	non	PROPN
ejpam-6798	159	46	-	-	PROPN
ejpam-6798	159	47	md	md	PROPN
ejpam-6798	159	48	of	of	ADP
ejpam-6798	159	49	element	element	NOUN
ejpam-6798	159	50	of	of	ADP
ejpam-6798	159	51	universe	universe	NOUN
ejpam-6798	159	52	set	set	NOUN
ejpam-6798	159	53	m	m	VERB
ejpam-6798	159	54	which	which	PRON
ejpam-6798	159	55	belong	belong	VERB
ejpam-6798	159	56	to	to	ADP
ejpam-6798	159	57	[	[	X
ejpam-6798	159	58	0	0	NUM
ejpam-6798	159	59	,	,	PUNCT
ejpam-6798	159	60	1	1	NUM
ejpam-6798	159	61	]	]	PUNCT
ejpam-6798	159	62	such	such	ADJ
ejpam-6798	159	63	that	that	SCONJ
ejpam-6798	159	64	0	0	NUM
ejpam-6798	159	65	<	<	X
ejpam-6798	159	66	µ(s	µ(	NOUN
ejpam-6798	159	67	)	)	PUNCT
ejpam-6798	160	1	+	+	CCONJ
ejpam-6798	160	2	ν(s	ν(s	NOUN
ejpam-6798	160	3	)	)	PUNCT
ejpam-6798	160	4	≤	≤	NOUN
ejpam-6798	160	5	1	1	NUM
ejpam-6798	160	6	,	,	PUNCT
ejpam-6798	160	7	∀s	∀s	PROPN
ejpam-6798	160	8	∈	∈	PROPN
ejpam-6798	160	9	m	m	NOUN
ejpam-6798	160	10	.	.	PUNCT
ejpam-6798	161	1	definition	definition	NOUN
ejpam-6798	161	2	3	3	NUM
ejpam-6798	161	3	.	.	PUNCT
ejpam-6798	162	1	[	[	X
ejpam-6798	162	2	35	35	NUM
ejpam-6798	162	3	]	]	PUNCT
ejpam-6798	162	4	an	an	DET
ejpam-6798	162	5	ifs	ifs	PROPN
ejpam-6798	162	6	l	l	PROPN
ejpam-6798	162	7	of	of	ADP
ejpam-6798	162	8	m	m	PROPN
ejpam-6798	162	9	is	be	AUX
ejpam-6798	162	10	known	know	VERB
ejpam-6798	162	11	as	as	ADP
ejpam-6798	162	12	an	an	DET
ejpam-6798	162	13	ifsa	ifsa	NOUN
ejpam-6798	162	14	of	of	ADP
ejpam-6798	162	15	m	m	PROPN
ejpam-6798	162	16	if	if	SCONJ
ejpam-6798	162	17	it	it	PRON
ejpam-6798	162	18	meets	meet	VERB
ejpam-6798	162	19	(	(	PUNCT
ejpam-6798	162	20	i	i	NOUN
ejpam-6798	162	21	)	)	PUNCT
ejpam-6798	162	22	µl(0	µl(0	PROPN
ejpam-6798	162	23	)	)	PUNCT
ejpam-6798	162	24	≥	≥	NOUN
ejpam-6798	162	25	µl(s	µl(s	NUM
ejpam-6798	162	26	)	)	PUNCT
ejpam-6798	162	27	,	,	PUNCT
ejpam-6798	162	28	(	(	PUNCT
ejpam-6798	162	29	ii	ii	NOUN
ejpam-6798	162	30	)	)	PUNCT
ejpam-6798	162	31	νl(0	νl(0	PROPN
ejpam-6798	162	32	)	)	PUNCT
ejpam-6798	162	33	≤	≤	NOUN
ejpam-6798	162	34	νl(s	νl(	NOUN
ejpam-6798	162	35	)	)	PUNCT
ejpam-6798	162	36	,	,	PUNCT
ejpam-6798	162	37	(	(	PUNCT
ejpam-6798	162	38	iii	iii	X
ejpam-6798	162	39	)	)	PUNCT
ejpam-6798	162	40	µl(s	µl(	NOUN
ejpam-6798	162	41	⋆	⋆	X
ejpam-6798	162	42	l	l	NOUN
ejpam-6798	162	43	)	)	PUNCT
ejpam-6798	162	44	≥	≥	NOUN
ejpam-6798	162	45	µl(s	µl(	NOUN
ejpam-6798	162	46	)	)	PUNCT
ejpam-6798	162	47	∧	∧	NOUN
ejpam-6798	162	48	µl(l	µl(l	NUM
ejpam-6798	162	49	)	)	PUNCT
ejpam-6798	162	50	,	,	PUNCT
ejpam-6798	162	51	∀s	∀s	PROPN
ejpam-6798	162	52	,	,	PUNCT
ejpam-6798	162	53	l	l	PROPN
ejpam-6798	162	54	∈	∈	PROPN
ejpam-6798	162	55	m	m	PRON
ejpam-6798	162	56	,	,	PUNCT
ejpam-6798	162	57	(	(	PUNCT
ejpam-6798	162	58	iv	iv	X
ejpam-6798	162	59	)	)	PUNCT
ejpam-6798	162	60	νl(s	νl(s	PUNCT
ejpam-6798	162	61	⋆	⋆	X
ejpam-6798	162	62	l	l	NOUN
ejpam-6798	162	63	)	)	PUNCT
ejpam-6798	162	64	≤	≤	NOUN
ejpam-6798	162	65	νl(s	νl(	NOUN
ejpam-6798	162	66	)	)	PUNCT
ejpam-6798	162	67	∨	∨	NUM
ejpam-6798	162	68	νl(l	νl(l	NUM
ejpam-6798	162	69	)	)	PUNCT
ejpam-6798	162	70	,	,	PUNCT
ejpam-6798	162	71	∀s	∀s	PROPN
ejpam-6798	162	72	,	,	PUNCT
ejpam-6798	162	73	l	l	PROPN
ejpam-6798	162	74	∈	∈	PROPN
ejpam-6798	162	75	m	m	VERB
ejpam-6798	162	76	.	.	PUNCT
ejpam-6798	163	1	definition	definition	NOUN
ejpam-6798	163	2	4	4	NUM
ejpam-6798	163	3	.	.	PUNCT
ejpam-6798	164	1	[	[	X
ejpam-6798	164	2	36	36	NUM
ejpam-6798	164	3	]	]	PUNCT
ejpam-6798	164	4	an	an	DET
ejpam-6798	164	5	ifs	ifs	PROPN
ejpam-6798	164	6	l	l	PROPN
ejpam-6798	164	7	of	of	ADP
ejpam-6798	164	8	m	m	PROPN
ejpam-6798	164	9	is	be	AUX
ejpam-6798	164	10	known	know	VERB
ejpam-6798	164	11	as	as	ADP
ejpam-6798	164	12	an	an	DET
ejpam-6798	164	13	ifi	ifi	NOUN
ejpam-6798	164	14	of	of	ADP
ejpam-6798	164	15	m	m	PROPN
ejpam-6798	164	16	if	if	SCONJ
ejpam-6798	164	17	it	it	PRON
ejpam-6798	164	18	meets	meet	VERB
ejpam-6798	164	19	(	(	PUNCT
ejpam-6798	164	20	i	i	NOUN
ejpam-6798	164	21	)	)	PUNCT
ejpam-6798	164	22	µl(s	µl(s	NUM
ejpam-6798	164	23	)	)	PUNCT
ejpam-6798	164	24	≥	≥	PRON
ejpam-6798	164	25	µl(s	µl(s	PRON
ejpam-6798	164	26	⋆	⋆	X
ejpam-6798	164	27	l	l	NOUN
ejpam-6798	164	28	)	)	PUNCT
ejpam-6798	164	29	∧	∧	NOUN
ejpam-6798	164	30	µl(l	µl(l	NUM
ejpam-6798	164	31	)	)	PUNCT
ejpam-6798	164	32	,	,	PUNCT
ejpam-6798	164	33	∀s	∀s	PROPN
ejpam-6798	164	34	,	,	PUNCT
ejpam-6798	165	1	l	l	PROPN
ejpam-6798	165	2	∈	∈	PROPN
ejpam-6798	165	3	m	m	PRON
ejpam-6798	165	4	,	,	PUNCT
ejpam-6798	165	5	(	(	PUNCT
ejpam-6798	165	6	ii	ii	NOUN
ejpam-6798	165	7	)	)	PUNCT
ejpam-6798	165	8	νl(s	νl(	NOUN
ejpam-6798	165	9	)	)	PUNCT
ejpam-6798	165	10	≤	≤	NOUN
ejpam-6798	165	11	νl(s	νl(s	PUNCT
ejpam-6798	165	12	⋆	⋆	X
ejpam-6798	165	13	l	l	NOUN
ejpam-6798	165	14	)	)	PUNCT
ejpam-6798	165	15	∨	∨	NOUN
ejpam-6798	165	16	νl(l	νl(l	NUM
ejpam-6798	165	17	)	)	PUNCT
ejpam-6798	165	18	,	,	PUNCT
ejpam-6798	165	19	∀s	∀s	PROPN
ejpam-6798	165	20	,	,	PUNCT
ejpam-6798	166	1	l	l	PROPN
ejpam-6798	166	2	∈	∈	PROPN
ejpam-6798	166	3	m	m	VERB
ejpam-6798	166	4	.	.	PUNCT
ejpam-6798	167	1	definition	definition	NOUN
ejpam-6798	167	2	5	5	NUM
ejpam-6798	167	3	.	.	PUNCT
ejpam-6798	168	1	[	[	X
ejpam-6798	168	2	37	37	NUM
ejpam-6798	168	3	]	]	PUNCT
ejpam-6798	168	4	a	a	DET
ejpam-6798	168	5	cifs	cif	NOUN
ejpam-6798	168	6	,	,	PUNCT
ejpam-6798	168	7	defined	define	VERB
ejpam-6798	168	8	on	on	ADP
ejpam-6798	168	9	m	m	PROPN
ejpam-6798	168	10	is	be	AUX
ejpam-6798	168	11	described	describe	VERB
ejpam-6798	168	12	by	by	ADP
ejpam-6798	168	13	a	a	DET
ejpam-6798	168	14	complex	complex	ADV
ejpam-6798	168	15	-	-	PUNCT
ejpam-6798	168	16	valued	value	VERB
ejpam-6798	168	17	grade	grade	NOUN
ejpam-6798	168	18	of	of	ADP
ejpam-6798	168	19	the	the	DET
ejpam-6798	168	20	non	non	ADJ
ejpam-6798	168	21	-	-	ADJ
ejpam-6798	168	22	membership	membership	ADJ
ejpam-6798	168	23	function	function	NOUN
ejpam-6798	168	24	,	,	PUNCT
ejpam-6798	168	25	membership	membership	NOUN
ejpam-6798	168	26	function	function	NOUN
ejpam-6798	168	27	νl(s	νl(	NOUN
ejpam-6798	168	28	)	)	PUNCT
ejpam-6798	168	29	,	,	PUNCT
ejpam-6798	168	30	µl(s	µl(s	NUM
ejpam-6798	168	31	)	)	PUNCT
ejpam-6798	168	32	that	that	PRON
ejpam-6798	168	33	assigns	assign	VERB
ejpam-6798	168	34	any	any	DET
ejpam-6798	168	35	element	element	NOUN
ejpam-6798	168	36	in	in	ADP
ejpam-6798	168	37	l.	l.	PROPN
ejpam-6798	168	38	the	the	DET
ejpam-6798	168	39	cifs	cif	NOUN
ejpam-6798	168	40	may	may	AUX
ejpam-6798	168	41	be	be	AUX
ejpam-6798	168	42	expressed	express	VERB
ejpam-6798	168	43	by	by	ADP
ejpam-6798	168	44	the	the	DET
ejpam-6798	168	45	set	set	NOUN
ejpam-6798	168	46	of	of	ADP
ejpam-6798	168	47	ordered	order	VERB
ejpam-6798	168	48	pairs	pair	NOUN
ejpam-6798	168	49	l	l	NOUN
ejpam-6798	168	50	=	=	SYM
ejpam-6798	168	51	{	{	PUNCT
ejpam-6798	168	52	(	(	PUNCT
ejpam-6798	168	53	s	s	X
ejpam-6798	168	54	,	,	PUNCT
ejpam-6798	168	55	µl(s	µl(s	NUM
ejpam-6798	168	56	)	)	PUNCT
ejpam-6798	168	57	,	,	PUNCT
ejpam-6798	168	58	νl(s	νl(	NOUN
ejpam-6798	168	59	)	)	PUNCT
ejpam-6798	168	60	)	)	PUNCT
ejpam-6798	168	61	:	:	PUNCT
ejpam-6798	169	1	s	s	VERB
ejpam-6798	169	2	∈	∈	PROPN
ejpam-6798	169	3	m	m	NOUN
ejpam-6798	169	4	}	}	PUNCT
ejpam-6798	169	5	where	where	SCONJ
ejpam-6798	169	6	µl(s	µl(	NOUN
ejpam-6798	169	7	)	)	PUNCT
ejpam-6798	169	8	=	=	SYM
ejpam-6798	169	9	γl(s)e	γl(s)e	NUM
ejpam-6798	169	10	ιθl(s	ιθl(s	PROPN
ejpam-6798	169	11	)	)	PUNCT
ejpam-6798	169	12	,	,	PUNCT
ejpam-6798	169	13	ι	ι	PROPN
ejpam-6798	170	1	=	=	NOUN
ejpam-6798	170	2	√	√	NUM
ejpam-6798	170	3	−1	−1	NOUN
ejpam-6798	170	4	,	,	PUNCT
ejpam-6798	170	5	γl(s	γl(	NOUN
ejpam-6798	170	6	)	)	PUNCT
ejpam-6798	170	7	∈	∈	PROPN
ejpam-6798	171	1	[	[	X
ejpam-6798	171	2	0	0	NUM
ejpam-6798	171	3	,	,	PUNCT
ejpam-6798	171	4	1	1	NUM
ejpam-6798	171	5	]	]	PUNCT
ejpam-6798	171	6	and	and	CCONJ
ejpam-6798	171	7	θl(s	θl(s	NUM
ejpam-6798	171	8	)	)	PUNCT
ejpam-6798	171	9	∈	∈	PROPN
ejpam-6798	172	1	[	[	X
ejpam-6798	172	2	0	0	NUM
ejpam-6798	172	3	,	,	PUNCT
ejpam-6798	172	4	2π	2π	NOUN
ejpam-6798	172	5	]	]	X
ejpam-6798	172	6	.	.	PUNCT
ejpam-6798	172	7	νl(s	νl(s	X
ejpam-6798	172	8	)	)	PUNCT
ejpam-6798	172	9	=	=	SYM
ejpam-6798	172	10	γl(s)e	γl(s)e	NUM
ejpam-6798	172	11	ιθl(s	ιθl(s	PROPN
ejpam-6798	172	12	)	)	PUNCT
ejpam-6798	172	13	,	,	PUNCT
ejpam-6798	172	14	ι	ι	PROPN
ejpam-6798	173	1	=	=	NOUN
ejpam-6798	173	2	√	√	NUM
ejpam-6798	173	3	−1	−1	NOUN
ejpam-6798	173	4	,	,	PUNCT
ejpam-6798	173	5	γl(s	γl(	NOUN
ejpam-6798	173	6	)	)	PUNCT
ejpam-6798	173	7	∈	∈	PROPN
ejpam-6798	174	1	[	[	X
ejpam-6798	174	2	0	0	NUM
ejpam-6798	174	3	,	,	PUNCT
ejpam-6798	174	4	1	1	NUM
ejpam-6798	174	5	]	]	PUNCT
ejpam-6798	174	6	and	and	CCONJ
ejpam-6798	174	7	θl(s	θl(s	NUM
ejpam-6798	174	8	)	)	PUNCT
ejpam-6798	174	9	∈	∈	PROPN
ejpam-6798	175	1	[	[	X
ejpam-6798	175	2	0	0	NUM
ejpam-6798	175	3	,	,	PUNCT
ejpam-6798	175	4	2π	2π	NOUN
ejpam-6798	175	5	]	]	PUNCT
ejpam-6798	175	6	.	.	PUNCT
ejpam-6798	176	1	definition	definition	NOUN
ejpam-6798	176	2	6	6	NUM
ejpam-6798	176	3	.	.	PUNCT
ejpam-6798	177	1	[	[	X
ejpam-6798	177	2	38	38	NUM
ejpam-6798	177	3	]	]	PUNCT
ejpam-6798	177	4	let	let	VERB
ejpam-6798	177	5	l	l	NOUN
ejpam-6798	177	6	=	=	PRON
ejpam-6798	177	7	{	{	PUNCT
ejpam-6798	177	8	(	(	PUNCT
ejpam-6798	177	9	s	s	X
ejpam-6798	177	10	,	,	PUNCT
ejpam-6798	177	11	µl(s	µl(s	NUM
ejpam-6798	177	12	)	)	PUNCT
ejpam-6798	177	13	,	,	PUNCT
ejpam-6798	177	14	νl(s	νl(	NOUN
ejpam-6798	177	15	)	)	PUNCT
ejpam-6798	177	16	)	)	PUNCT
ejpam-6798	177	17	:	:	PUNCT
ejpam-6798	177	18	s	s	VERB
ejpam-6798	177	19	∈	∈	PROPN
ejpam-6798	177	20	m	m	PRON
ejpam-6798	177	21	}	}	PUNCT
ejpam-6798	177	22	and	and	CCONJ
ejpam-6798	177	23	b	b	X
ejpam-6798	177	24	=	=	SYM
ejpam-6798	177	25	{	{	PUNCT
ejpam-6798	177	26	(	(	PUNCT
ejpam-6798	177	27	s	s	NOUN
ejpam-6798	177	28	,	,	PUNCT
ejpam-6798	177	29	µb(s	µb(	NOUN
ejpam-6798	177	30	)	)	PUNCT
ejpam-6798	177	31	,	,	PUNCT
ejpam-6798	177	32	νb(s	νb(	NOUN
ejpam-6798	177	33	)	)	PUNCT
ejpam-6798	177	34	)	)	PUNCT
ejpam-6798	177	35	:	:	PUNCT
ejpam-6798	177	36	s	s	AUX
ejpam-6798	177	37	∈	∈	PROPN
ejpam-6798	177	38	m	m	AUX
ejpam-6798	177	39	}	}	PUNCT
ejpam-6798	177	40	be	be	AUX
ejpam-6798	177	41	complex	complex	ADJ
ejpam-6798	177	42	sub	sub	NOUN
ejpam-6798	177	43	-	-	NOUN
ejpam-6798	177	44	sets	set	NOUN
ejpam-6798	177	45	of	of	ADP
ejpam-6798	177	46	a	a	DET
ejpam-6798	177	47	non	non	ADJ
ejpam-6798	177	48	-	-	ADJ
ejpam-6798	177	49	void	void	ADJ
ejpam-6798	177	50	set	set	NOUN
ejpam-6798	177	51	m	m	PROPN
ejpam-6798	177	52	with	with	ADP
ejpam-6798	177	53	membership	membership	NOUN
ejpam-6798	177	54	functions	function	NOUN
ejpam-6798	177	55	µl(s	µl(	NOUN
ejpam-6798	177	56	)	)	PUNCT
ejpam-6798	177	57	=	=	SYM
ejpam-6798	177	58	γl(s)e	γl(s)e	NUM
ejpam-6798	177	59	ιθl(s	ιθl(s	PROPN
ejpam-6798	177	60	)	)	PUNCT
ejpam-6798	177	61	,	,	PUNCT
ejpam-6798	177	62	µb(s	µb(	NOUN
ejpam-6798	177	63	)	)	PUNCT
ejpam-6798	178	1	=	=	SYM
ejpam-6798	178	2	γb(s)e	γb(s)e	NOUN
ejpam-6798	178	3	ιθb(s	ιθb(	NOUN
ejpam-6798	178	4	)	)	PUNCT
ejpam-6798	178	5	respectively	respectively	ADV
ejpam-6798	178	6	and	and	CCONJ
ejpam-6798	178	7	non	non	ADJ
ejpam-6798	178	8	-	-	ADJ
ejpam-6798	178	9	membership	membership	ADJ
ejpam-6798	178	10	functions	function	NOUN
ejpam-6798	178	11	νl(s	νl(	NOUN
ejpam-6798	178	12	)	)	PUNCT
ejpam-6798	178	13	=	=	SYM
ejpam-6798	178	14	γl(s)e	γl(s)e	NUM
ejpam-6798	178	15	ιθl(s	ιθl(s	PROPN
ejpam-6798	178	16	)	)	PUNCT
ejpam-6798	178	17	,	,	PUNCT
ejpam-6798	178	18	νb(s	νb(	NOUN
ejpam-6798	178	19	)	)	PUNCT
ejpam-6798	178	20	=	=	SYM
ejpam-6798	178	21	γb(s)e	γb(s)e	NOUN
ejpam-6798	178	22	ιθb(s	ιθb(	NOUN
ejpam-6798	178	23	)	)	PUNCT
ejpam-6798	178	24	respectively	respectively	ADV
ejpam-6798	178	25	.	.	PUNCT
ejpam-6798	179	1	by	by	ADP
ejpam-6798	179	2	µl(s	µl(	NOUN
ejpam-6798	179	3	)	)	PUNCT
ejpam-6798	179	4	≤	≤	NOUN
ejpam-6798	179	5	µb(s	µb(	NOUN
ejpam-6798	179	6	)	)	PUNCT
ejpam-6798	179	7	,	,	PUNCT
ejpam-6798	179	8	this	this	PRON
ejpam-6798	179	9	implies	imply	VERB
ejpam-6798	179	10	that	that	SCONJ
ejpam-6798	179	11	γl(s	γl(	NOUN
ejpam-6798	179	12	)	)	PUNCT
ejpam-6798	179	13	≤	≤	NOUN
ejpam-6798	179	14	γb(s	γb(	NOUN
ejpam-6798	179	15	)	)	PUNCT
ejpam-6798	179	16	,	,	PUNCT
ejpam-6798	179	17	θl(s	θl(s	NOUN
ejpam-6798	179	18	)	)	PUNCT
ejpam-6798	179	19	≤	≤	NOUN
ejpam-6798	179	20	θb(s	θb(s	PUNCT
ejpam-6798	179	21	)	)	PUNCT
ejpam-6798	179	22	and	and	CCONJ
ejpam-6798	179	23	νl(s	νl(	NOUN
ejpam-6798	179	24	)	)	PUNCT
ejpam-6798	179	25	≤	≤	NOUN
ejpam-6798	179	26	νb(s	νb(	NOUN
ejpam-6798	179	27	)	)	PUNCT
ejpam-6798	179	28	,	,	PUNCT
ejpam-6798	179	29	we	we	PRON
ejpam-6798	179	30	mean	mean	VERB
ejpam-6798	179	31	that	that	SCONJ
ejpam-6798	179	32	γl(s	γl(	NOUN
ejpam-6798	179	33	)	)	PUNCT
ejpam-6798	179	34	≤	≤	NOUN
ejpam-6798	179	35	γb(s	γb(	NOUN
ejpam-6798	179	36	)	)	PUNCT
ejpam-6798	179	37	,	,	PUNCT
ejpam-6798	179	38	θl(s	θl(s	NOUN
ejpam-6798	179	39	)	)	PUNCT
ejpam-6798	179	40	≤	≤	NOUN
ejpam-6798	179	41	θb(s	θb(s	PUNCT
ejpam-6798	179	42	)	)	PUNCT
ejpam-6798	179	43	.	.	PUNCT
ejpam-6798	180	1	m.	m.	PROPN
ejpam-6798	180	2	jawad	jawad	PROPN
ejpam-6798	180	3	et	et	PROPN
ejpam-6798	180	4	al	al	PROPN
ejpam-6798	180	5	.	.	PUNCT
ejpam-6798	180	6	/	/	SYM
ejpam-6798	180	7	eur	eur	PROPN
ejpam-6798	180	8	.	.	PUNCT
ejpam-6798	181	1	j.	j.	PROPN
ejpam-6798	181	2	pure	pure	PROPN
ejpam-6798	181	3	appl	appl	PROPN
ejpam-6798	181	4	.	.	PROPN
ejpam-6798	181	5	math	math	PROPN
ejpam-6798	181	6	,	,	PUNCT
ejpam-6798	181	7	18	18	NUM
ejpam-6798	181	8	(	(	PUNCT
ejpam-6798	181	9	4	4	NUM
ejpam-6798	181	10	)	)	PUNCT
ejpam-6798	181	11	(	(	PUNCT
ejpam-6798	181	12	2025	2025	NUM
ejpam-6798	181	13	)	)	PUNCT
ejpam-6798	181	14	,	,	PUNCT
ejpam-6798	181	15	6798	6798	NUM
ejpam-6798	181	16	7	7	NUM
ejpam-6798	181	17	of	of	ADP
ejpam-6798	181	18	22	22	NUM
ejpam-6798	181	19	3	3	NUM
ejpam-6798	181	20	.	.	PUNCT
ejpam-6798	182	1	complex	complex	ADJ
ejpam-6798	182	2	intuitionistic	intuitionistic	ADJ
ejpam-6798	182	3	fuzzy	fuzzy	ADJ
ejpam-6798	182	4	sub	sub	NOUN
ejpam-6798	182	5	-	-	ADJ
ejpam-6798	182	6	algebras(cifsas	algebras(cifsa	NOUN
ejpam-6798	182	7	)	)	PUNCT
ejpam-6798	182	8	of	of	ADP
ejpam-6798	182	9	bck	bck	PROPN
ejpam-6798	182	10	/	/	SYM
ejpam-6798	182	11	bci	bci	NOUN
ejpam-6798	182	12	-	-	PUNCT
ejpam-6798	182	13	algebras	algebras	NOUN
ejpam-6798	182	14	in	in	ADP
ejpam-6798	182	15	this	this	DET
ejpam-6798	182	16	part	part	NOUN
ejpam-6798	182	17	,	,	PUNCT
ejpam-6798	182	18	we	we	PRON
ejpam-6798	182	19	explore	explore	VERB
ejpam-6798	182	20	fundamental	fundamental	ADJ
ejpam-6798	182	21	notions	notion	NOUN
ejpam-6798	182	22	related	relate	VERB
ejpam-6798	182	23	to	to	ADP
ejpam-6798	182	24	cifss	cifss	NOUN
ejpam-6798	182	25	,	,	PUNCT
ejpam-6798	182	26	including	include	VERB
ejpam-6798	182	27	cifs	cif	NOUN
ejpam-6798	182	28	on	on	ADP
ejpam-6798	182	29	the	the	DET
ejpam-6798	182	30	universal	universal	ADJ
ejpam-6798	182	31	set	set	VERB
ejpam-6798	182	32	m	m	PROPN
ejpam-6798	182	33	and	and	CCONJ
ejpam-6798	182	34	modal	modal	ADJ
ejpam-6798	182	35	operators	operator	NOUN
ejpam-6798	182	36	are	be	AUX
ejpam-6798	182	37	defined	define	VERB
ejpam-6798	182	38	.	.	PUNCT
ejpam-6798	183	1	definition	definition	NOUN
ejpam-6798	183	2	7	7	NUM
ejpam-6798	183	3	.	.	PUNCT
ejpam-6798	184	1	let	let	VERB
ejpam-6798	184	2	l	l	NOUN
ejpam-6798	184	3	be	be	AUX
ejpam-6798	184	4	an	an	DET
ejpam-6798	184	5	ifs	ifs	PROPN
ejpam-6798	184	6	of	of	ADP
ejpam-6798	184	7	m	m	PROPN
ejpam-6798	184	8	.	.	PUNCT
ejpam-6798	185	1	then	then	ADV
ejpam-6798	185	2	,	,	PUNCT
ejpam-6798	185	3	modal	modal	ADJ
ejpam-6798	185	4	operators	operator	NOUN
ejpam-6798	185	5	and	and	CCONJ
ejpam-6798	185	6	level	level	NOUN
ejpam-6798	185	7	operators	operator	NOUN
ejpam-6798	185	8	(	(	PUNCT
ejpam-6798	185	9	i	i	NOUN
ejpam-6798	185	10	)	)	PUNCT
ejpam-6798	185	11	,	,	PUNCT
ejpam-6798	185	12	(	(	PUNCT
ejpam-6798	185	13	ii	ii	NOUN
ejpam-6798	185	14	)	)	PUNCT
ejpam-6798	185	15	,	,	PUNCT
ejpam-6798	185	16	(	(	PUNCT
ejpam-6798	185	17	iii	iii	NOUN
ejpam-6798	185	18	)	)	PUNCT
ejpam-6798	185	19	,	,	PUNCT
ejpam-6798	185	20	(	(	PUNCT
ejpam-6798	185	21	iv	iv	X
ejpam-6798	185	22	)	)	PUNCT
ejpam-6798	185	23	are	be	AUX
ejpam-6798	185	24	defined	define	VERB
ejpam-6798	185	25	by	by	ADP
ejpam-6798	185	26	(	(	PUNCT
ejpam-6798	185	27	i	i	NOUN
ejpam-6798	185	28	)	)	PUNCT
ejpam-6798	185	29	⊕l	⊕l	NOUN
ejpam-6798	185	30	=	=	SYM
ejpam-6798	185	31	{	{	PUNCT
ejpam-6798	185	32	(	(	PUNCT
ejpam-6798	185	33	s	s	X
ejpam-6798	185	34	,	,	PUNCT
ejpam-6798	185	35	µl(s	µl(	NOUN
ejpam-6798	185	36	)	)	PUNCT
ejpam-6798	185	37	2	2	NUM
ejpam-6798	185	38	)	)	PUNCT
ejpam-6798	185	39	,	,	PUNCT
ejpam-6798	185	40	νl(s)2	νl(s)2	PROPN
ejpam-6798	185	41	)	)	PUNCT
ejpam-6798	185	42	:	:	PUNCT
ejpam-6798	185	43	∀s	∀s	X
ejpam-6798	185	44	∈	∈	PROPN
ejpam-6798	185	45	m	m	PRON
ejpam-6798	185	46	}	}	PUNCT
ejpam-6798	185	47	,	,	PUNCT
ejpam-6798	185	48	(	(	PUNCT
ejpam-6798	185	49	ii	ii	NOUN
ejpam-6798	185	50	)	)	PUNCT
ejpam-6798	185	51	⊗l	⊗l	NOUN
ejpam-6798	185	52	=	=	SYM
ejpam-6798	185	53	{	{	PUNCT
ejpam-6798	185	54	(	(	PUNCT
ejpam-6798	185	55	s	s	X
ejpam-6798	185	56	,	,	PUNCT
ejpam-6798	185	57	µl(s)+1	µl(s)+1	NOUN
ejpam-6798	185	58	2	2	NUM
ejpam-6798	185	59	,	,	PUNCT
ejpam-6798	185	60	νl(s)+1	νl(s)+1	PROPN
ejpam-6798	185	61	2	2	NUM
ejpam-6798	185	62	)	)	PUNCT
ejpam-6798	185	63	:	:	PUNCT
ejpam-6798	185	64	∀s	∀s	PROPN
ejpam-6798	185	65	∈	∈	PROPN
ejpam-6798	185	66	m	m	PRON
ejpam-6798	185	67	}	}	PUNCT
ejpam-6798	185	68	,	,	PUNCT
ejpam-6798	185	69	(	(	PUNCT
ejpam-6798	185	70	iii	iii	X
ejpam-6798	185	71	)	)	PUNCT
ejpam-6798	185	72	†l	†l	NOUN
ejpam-6798	185	73	=	=	PRON
ejpam-6798	185	74	{	{	PUNCT
ejpam-6798	185	75	(	(	PUNCT
ejpam-6798	185	76	s	s	PROPN
ejpam-6798	185	77	,	,	PUNCT
ejpam-6798	185	78	12	12	NUM
ejpam-6798	185	79	∨	∨	NUM
ejpam-6798	185	80	µl(s	µl(s	NUM
ejpam-6798	185	81	)	)	PUNCT
ejpam-6798	185	82	,	,	PUNCT
ejpam-6798	185	83	1	1	NUM
ejpam-6798	185	84	2	2	NUM
ejpam-6798	185	85	∧	∧	PROPN
ejpam-6798	185	86	νl(s	νl(	NOUN
ejpam-6798	185	87	)	)	PUNCT
ejpam-6798	185	88	)	)	PUNCT
ejpam-6798	185	89	:	:	PUNCT
ejpam-6798	186	1	∀s	∀s	PROPN
ejpam-6798	186	2	∈	∈	PROPN
ejpam-6798	186	3	m	m	PRON
ejpam-6798	186	4	}	}	PUNCT
ejpam-6798	186	5	,	,	PUNCT
ejpam-6798	186	6	(	(	PUNCT
ejpam-6798	186	7	iv	iv	X
ejpam-6798	186	8	)	)	PUNCT
ejpam-6798	186	9	‡l	‡l	NOUN
ejpam-6798	186	10	=	=	PUNCT
ejpam-6798	186	11	{	{	PUNCT
ejpam-6798	186	12	(	(	PUNCT
ejpam-6798	186	13	s	s	PROPN
ejpam-6798	186	14	,	,	PUNCT
ejpam-6798	186	15	12	12	NUM
ejpam-6798	186	16	∧	∧	PROPN
ejpam-6798	186	17	µl(s	µl(s	NUM
ejpam-6798	186	18	)	)	PUNCT
ejpam-6798	186	19	,	,	PUNCT
ejpam-6798	186	20	1	1	NUM
ejpam-6798	186	21	2	2	NUM
ejpam-6798	186	22	∨	∨	NUM
ejpam-6798	186	23	νl(s	νl(	NOUN
ejpam-6798	186	24	)	)	PUNCT
ejpam-6798	186	25	)	)	PUNCT
ejpam-6798	186	26	:	:	PUNCT
ejpam-6798	186	27	∀s	∀s	PROPN
ejpam-6798	186	28	∈	∈	PROPN
ejpam-6798	186	29	m	m	PRON
ejpam-6798	186	30	}	}	PUNCT
ejpam-6798	186	31	.	.	PUNCT
ejpam-6798	187	1	definition	definition	NOUN
ejpam-6798	187	2	8	8	NUM
ejpam-6798	187	3	.	.	PUNCT
ejpam-6798	188	1	a	a	DET
ejpam-6798	188	2	cifs	cifs	NOUN
ejpam-6798	188	3	l	l	NOUN
ejpam-6798	188	4	=	=	SYM
ejpam-6798	188	5	(	(	PUNCT
ejpam-6798	188	6	s	s	X
ejpam-6798	188	7	,	,	PUNCT
ejpam-6798	188	8	µl(s	µl(s	NUM
ejpam-6798	188	9	)	)	PUNCT
ejpam-6798	188	10	,	,	PUNCT
ejpam-6798	188	11	νl(s	νl(	NOUN
ejpam-6798	188	12	)	)	PUNCT
ejpam-6798	188	13	)	)	PUNCT
ejpam-6798	188	14	is	be	AUX
ejpam-6798	188	15	considered	consider	VERB
ejpam-6798	188	16	a	a	DET
ejpam-6798	188	17	cifsa	cifsa	NOUN
ejpam-6798	188	18	of	of	ADP
ejpam-6798	188	19	m	m	PROPN
ejpam-6798	188	20	if	if	SCONJ
ejpam-6798	188	21	s	s	VERB
ejpam-6798	188	22	,	,	PUNCT
ejpam-6798	188	23	l	l	PROPN
ejpam-6798	188	24	∈	∈	PROPN
ejpam-6798	188	25	m	m	X
ejpam-6798	188	26	,	,	PUNCT
ejpam-6798	188	27	and	and	CCONJ
ejpam-6798	188	28	it	it	PRON
ejpam-6798	188	29	satisfies	satisfy	VERB
ejpam-6798	188	30	following	follow	VERB
ejpam-6798	188	31	:	:	PUNCT
ejpam-6798	188	32	(	(	PUNCT
ejpam-6798	188	33	i	i	NOUN
ejpam-6798	188	34	)	)	PUNCT
ejpam-6798	188	35	µl(0)e	µl(0)e	PROPN
ejpam-6798	188	36	ιθl(0	ιθl(0	NOUN
ejpam-6798	188	37	)	)	PUNCT
ejpam-6798	188	38	≥	≥	PRON
ejpam-6798	188	39	µl(s)e	µl(s)e	ADJ
ejpam-6798	188	40	ιθl(s	ιθl(s	PROPN
ejpam-6798	188	41	)	)	PUNCT
ejpam-6798	188	42	,	,	PUNCT
ejpam-6798	188	43	(	(	PUNCT
ejpam-6798	188	44	ii	ii	NOUN
ejpam-6798	188	45	)	)	PUNCT
ejpam-6798	188	46	µl(s	µl(	NOUN
ejpam-6798	188	47	⋆	⋆	VERB
ejpam-6798	188	48	l)e	l)e	X
ejpam-6798	188	49	ιθl(s⋆l	ιθl(s⋆l	NOUN
ejpam-6798	188	50	)	)	PUNCT
ejpam-6798	188	51	≥	≥	NOUN
ejpam-6798	188	52	µl(s)e	µl(s)e	X
ejpam-6798	188	53	ιθl(s	ιθl(s	PROPN
ejpam-6798	188	54	)	)	PUNCT
ejpam-6798	188	55	∧	∧	PROPN
ejpam-6798	188	56	µl(l)e	µl(l)e	X
ejpam-6798	188	57	ιθl(l	ιθl(l	PROPN
ejpam-6798	188	58	)	)	PUNCT
ejpam-6798	188	59	,	,	PUNCT
ejpam-6798	188	60	(	(	PUNCT
ejpam-6798	188	61	iii	iii	X
ejpam-6798	188	62	)	)	PUNCT
ejpam-6798	188	63	νl(0)e	νl(0)e	NOUN
ejpam-6798	188	64	ιθl(0	ιθl(0	NOUN
ejpam-6798	188	65	)	)	PUNCT
ejpam-6798	188	66	≤	≤	PROPN
ejpam-6798	189	1	νl(s)e	νl(s)e	NUM
ejpam-6798	189	2	ιθl(s	ιθl(s	PROPN
ejpam-6798	189	3	)	)	PUNCT
ejpam-6798	189	4	,	,	PUNCT
ejpam-6798	189	5	(	(	PUNCT
ejpam-6798	189	6	iv	iv	X
ejpam-6798	189	7	)	)	PUNCT
ejpam-6798	189	8	νl(s	νl(s	PUNCT
ejpam-6798	189	9	⋆	⋆	X
ejpam-6798	189	10	l)e	l)e	X
ejpam-6798	189	11	ιθl(s⋆l	ιθl(s⋆l	NOUN
ejpam-6798	189	12	)	)	PUNCT
ejpam-6798	189	13	≤	≤	NOUN
ejpam-6798	189	14	νl(s)e	νl(s)e	NUM
ejpam-6798	189	15	ιθl(s	ιθl(s	PROPN
ejpam-6798	189	16	)	)	PUNCT
ejpam-6798	189	17	∨	∨	NUM
ejpam-6798	189	18	νl(l)e	νl(l)e	X
ejpam-6798	189	19	ιθl(l	ιθl(l	PROPN
ejpam-6798	189	20	)	)	PUNCT
ejpam-6798	189	21	.	.	PUNCT
ejpam-6798	190	1	example	example	NOUN
ejpam-6798	191	1	1	1	X
ejpam-6798	191	2	.	.	X
ejpam-6798	191	3	take	take	VERB
ejpam-6798	191	4	a	a	DET
ejpam-6798	191	5	bck	bck	NOUN
ejpam-6798	191	6	algebra	algebra	NOUN
ejpam-6798	191	7	m	m	VERB
ejpam-6798	191	8	=	=	SYM
ejpam-6798	191	9	{	{	PUNCT
ejpam-6798	191	10	0	0	NUM
ejpam-6798	191	11	,	,	PUNCT
ejpam-6798	191	12	s	s	X
ejpam-6798	191	13	,	,	PUNCT
ejpam-6798	191	14	l	l	NOUN
ejpam-6798	191	15	,	,	PUNCT
ejpam-6798	191	16	z	z	NOUN
ejpam-6798	191	17	}	}	PUNCT
ejpam-6798	191	18	,	,	PUNCT
ejpam-6798	191	19	where	where	SCONJ
ejpam-6798	191	20	the	the	DET
ejpam-6798	191	21	binary	binary	ADJ
ejpam-6798	191	22	operation	operation	NOUN
ejpam-6798	191	23	is	be	AUX
ejpam-6798	191	24	defined	define	VERB
ejpam-6798	191	25	by	by	ADP
ejpam-6798	191	26	the	the	DET
ejpam-6798	191	27	caley	caley	NOUN
ejpam-6798	191	28	table	table	NOUN
ejpam-6798	191	29	2	2	NUM
ejpam-6798	191	30	.	.	PUNCT
ejpam-6798	191	31	now	now	ADV
ejpam-6798	191	32	explain	explain	VERB
ejpam-6798	191	33	a	a	DET
ejpam-6798	191	34	cifs	cif	NOUN
ejpam-6798	191	35	on	on	ADP
ejpam-6798	191	36	m	m	NOUN
ejpam-6798	191	37	as	as	ADP
ejpam-6798	191	38	:	:	PUNCT
ejpam-6798	191	39	l	l	NOUN
ejpam-6798	191	40	=	=	SYM
ejpam-6798	191	41	{	{	PUNCT
ejpam-6798	191	42	(	(	PUNCT
ejpam-6798	191	43	0	0	NUM
ejpam-6798	191	44	,	,	PUNCT
ejpam-6798	191	45	0.8eι0.5π	0.8eι0.5π	PROPN
ejpam-6798	191	46	,	,	PUNCT
ejpam-6798	191	47	0.6eι0.25π	0.6eι0.25π	NOUN
ejpam-6798	191	48	)	)	PUNCT
ejpam-6798	191	49	,	,	PUNCT
ejpam-6798	191	50	(	(	PUNCT
ejpam-6798	191	51	s	s	X
ejpam-6798	191	52	,	,	PUNCT
ejpam-6798	191	53	0.8eι0.5π	0.8eι0.5π	PROPN
ejpam-6798	191	54	,	,	PUNCT
ejpam-6798	191	55	0.6eι0.25π	0.6eι0.25π	NOUN
ejpam-6798	191	56	)	)	PUNCT
ejpam-6798	191	57	,	,	PUNCT
ejpam-6798	191	58	(	(	PUNCT
ejpam-6798	191	59	l	l	NOUN
ejpam-6798	191	60	,	,	PUNCT
ejpam-6798	191	61	0.5eι0.2π	0.5eι0.2π	PROPN
ejpam-6798	191	62	,	,	PUNCT
ejpam-6798	191	63	0.3eι0.1π	0.3eι0.1π	PROPN
ejpam-6798	191	64	)	)	PUNCT
ejpam-6798	191	65	,	,	PUNCT
ejpam-6798	191	66	(	(	PUNCT
ejpam-6798	191	67	z	z	X
ejpam-6798	191	68	,	,	PUNCT
ejpam-6798	191	69	0.8eι0.5π	0.8eι0.5π	PROPN
ejpam-6798	191	70	,	,	PUNCT
ejpam-6798	191	71	0.6eι0.25π	0.6eι0.25π	NOUN
ejpam-6798	191	72	)	)	PUNCT
ejpam-6798	191	73	}	}	PUNCT
ejpam-6798	191	74	.	.	PUNCT
ejpam-6798	192	1	it	it	PRON
ejpam-6798	192	2	is	be	AUX
ejpam-6798	192	3	simple	simple	ADJ
ejpam-6798	192	4	to	to	PART
ejpam-6798	192	5	demonstrate	demonstrate	VERB
ejpam-6798	192	6	that	that	SCONJ
ejpam-6798	192	7	l	l	NOUN
ejpam-6798	192	8	is	be	AUX
ejpam-6798	192	9	a	a	DET
ejpam-6798	192	10	cifs	cif	NOUN
ejpam-6798	192	11	of	of	ADP
ejpam-6798	192	12	m	m	PROPN
ejpam-6798	192	13	.	.	PUNCT
ejpam-6798	193	1	table	table	NOUN
ejpam-6798	193	2	2	2	NUM
ejpam-6798	193	3	:	:	PUNCT
ejpam-6798	193	4	cayley	cayley	PROPN
ejpam-6798	193	5	’s	’s	PART
ejpam-6798	193	6	table	table	NOUN
ejpam-6798	193	7	describing	describe	VERB
ejpam-6798	193	8	the	the	DET
ejpam-6798	193	9	binary	binary	ADJ
ejpam-6798	193	10	operation	operation	NOUN
ejpam-6798	193	11	expressed	express	VERB
ejpam-6798	193	12	by	by	ADP
ejpam-6798	193	13	“	"	PUNCT
ejpam-6798	193	14	⋆	⋆	VERB
ejpam-6798	193	15	”	"	PUNCT
ejpam-6798	193	16	.	.	PUNCT
ejpam-6798	194	1	⋆	⋆	VERB
ejpam-6798	194	2	0	0	NUM
ejpam-6798	194	3	s	s	PART
ejpam-6798	194	4	l	l	NOUN
ejpam-6798	194	5	z	z	NOUN
ejpam-6798	194	6	s	s	NOUN
ejpam-6798	194	7	0	0	NUM
ejpam-6798	194	8	0	0	NUM
ejpam-6798	194	9	0	0	NUM
ejpam-6798	194	10	0	0	NUM
ejpam-6798	194	11	0	0	NUM
ejpam-6798	195	1	s	s	NOUN
ejpam-6798	195	2	s	s	X
ejpam-6798	195	3	s	s	NOUN
ejpam-6798	195	4	0	0	NUM
ejpam-6798	195	5	0	0	NUM
ejpam-6798	195	6	s	s	NOUN
ejpam-6798	195	7	s	s	NOUN
ejpam-6798	195	8	l	l	NOUN
ejpam-6798	195	9	l	l	NOUN
ejpam-6798	195	10	l	l	NOUN
ejpam-6798	195	11	0	0	PUNCT
ejpam-6798	195	12	l	l	NOUN
ejpam-6798	195	13	s	s	NOUN
ejpam-6798	195	14	z	z	NOUN
ejpam-6798	195	15	z	z	NOUN
ejpam-6798	195	16	z	z	NOUN
ejpam-6798	195	17	z	z	NOUN
ejpam-6798	195	18	0	0	NUM
ejpam-6798	196	1	s	s	AUX
ejpam-6798	196	2	p	p	X
ejpam-6798	196	3	q	q	NOUN
ejpam-6798	196	4	r	r	NOUN
ejpam-6798	196	5	s	s	NOUN
ejpam-6798	196	6	r	r	NOUN
ejpam-6798	196	7	s	s	PART
ejpam-6798	196	8	example	example	NOUN
ejpam-6798	196	9	2	2	NUM
ejpam-6798	196	10	.	.	X
ejpam-6798	196	11	take	take	VERB
ejpam-6798	196	12	a	a	DET
ejpam-6798	196	13	bck	bck	NOUN
ejpam-6798	196	14	-	-	PUNCT
ejpam-6798	196	15	algebra	algebra	NOUN
ejpam-6798	196	16	m	m	NOUN
ejpam-6798	196	17	=	=	SYM
ejpam-6798	196	18	{	{	PUNCT
ejpam-6798	196	19	0	0	NUM
ejpam-6798	196	20	,	,	PUNCT
ejpam-6798	196	21	s	s	X
ejpam-6798	196	22	,	,	PUNCT
ejpam-6798	196	23	l	l	NOUN
ejpam-6798	196	24	,	,	PUNCT
ejpam-6798	196	25	z	z	NOUN
ejpam-6798	196	26	,	,	PUNCT
ejpam-6798	196	27	w	w	PROPN
ejpam-6798	196	28	}	}	PUNCT
ejpam-6798	196	29	,	,	PUNCT
ejpam-6798	196	30	where	where	SCONJ
ejpam-6798	196	31	the	the	DET
ejpam-6798	196	32	binary	binary	ADJ
ejpam-6798	196	33	operation	operation	NOUN
ejpam-6798	196	34	is	be	AUX
ejpam-6798	196	35	defined	define	VERB
ejpam-6798	196	36	by	by	ADP
ejpam-6798	196	37	the	the	DET
ejpam-6798	196	38	caley	caley	NOUN
ejpam-6798	196	39	table	table	NOUN
ejpam-6798	196	40	3	3	NUM
ejpam-6798	196	41	.	.	PUNCT
ejpam-6798	197	1	now	now	ADV
ejpam-6798	197	2	explain	explain	VERB
ejpam-6798	197	3	a	a	DET
ejpam-6798	197	4	cifs	cif	NOUN
ejpam-6798	197	5	on	on	ADP
ejpam-6798	197	6	m	m	NOUN
ejpam-6798	197	7	as	as	ADP
ejpam-6798	197	8	:	:	PUNCT
ejpam-6798	197	9	l	l	NOUN
ejpam-6798	197	10	=	=	SYM
ejpam-6798	197	11	{	{	PUNCT
ejpam-6798	197	12	(	(	PUNCT
ejpam-6798	197	13	0	0	NUM
ejpam-6798	197	14	,	,	PUNCT
ejpam-6798	197	15	0.9eι0.6π	0.9eι0.6π	NUM
ejpam-6798	197	16	,	,	PUNCT
ejpam-6798	197	17	0.7eι0.4π	0.7eι0.4π	PROPN
ejpam-6798	197	18	)	)	PUNCT
ejpam-6798	197	19	,	,	PUNCT
ejpam-6798	197	20	(	(	PUNCT
ejpam-6798	197	21	s	s	X
ejpam-6798	197	22	,	,	PUNCT
ejpam-6798	197	23	0.7eι0.5π	0.7eι0.5π	PROPN
ejpam-6798	197	24	,	,	PUNCT
ejpam-6798	197	25	0.5eι0.3π	0.5eι0.3π	PROPN
ejpam-6798	197	26	)	)	PUNCT
ejpam-6798	197	27	,	,	PUNCT
ejpam-6798	197	28	(	(	PUNCT
ejpam-6798	197	29	l	l	NOUN
ejpam-6798	197	30	,	,	PUNCT
ejpam-6798	197	31	0.4eι0.3π	0.4eι0.3π	NOUN
ejpam-6798	197	32	,	,	PUNCT
ejpam-6798	197	33	0.2eι0.1π	0.2eι0.1π	PROPN
ejpam-6798	197	34	)	)	PUNCT
ejpam-6798	197	35	,	,	PUNCT
ejpam-6798	197	36	(	(	PUNCT
ejpam-6798	197	37	z	z	X
ejpam-6798	197	38	,	,	PUNCT
ejpam-6798	197	39	0.4eι0.3π	0.4eι0.3π	PROPN
ejpam-6798	197	40	,	,	PUNCT
ejpam-6798	197	41	0.2eι0.1π	0.2eι0.1π	PROPN
ejpam-6798	197	42	)	)	PUNCT
ejpam-6798	197	43	,	,	PUNCT
ejpam-6798	197	44	(	(	PUNCT
ejpam-6798	197	45	w	w	PROPN
ejpam-6798	197	46	,	,	PUNCT
ejpam-6798	197	47	0.4eι0.3π	0.4eι0.3π	PROPN
ejpam-6798	197	48	,	,	PUNCT
ejpam-6798	197	49	0.2eι0.1π	0.2eι0.1π	PROPN
ejpam-6798	197	50	)	)	PUNCT
ejpam-6798	197	51	}	}	PUNCT
ejpam-6798	197	52	.	.	PUNCT
ejpam-6798	198	1	it	it	PRON
ejpam-6798	198	2	is	be	AUX
ejpam-6798	198	3	simple	simple	ADJ
ejpam-6798	198	4	to	to	PART
ejpam-6798	198	5	demonstrate	demonstrate	VERB
ejpam-6798	198	6	that	that	SCONJ
ejpam-6798	198	7	l	l	NOUN
ejpam-6798	198	8	is	be	AUX
ejpam-6798	198	9	a	a	DET
ejpam-6798	198	10	cifs	cif	NOUN
ejpam-6798	198	11	of	of	ADP
ejpam-6798	198	12	m	m	PROPN
ejpam-6798	198	13	.	.	PUNCT
ejpam-6798	199	1	m.	m.	PROPN
ejpam-6798	199	2	jawad	jawad	PROPN
ejpam-6798	199	3	et	et	PROPN
ejpam-6798	199	4	al	al	PROPN
ejpam-6798	199	5	.	.	PUNCT
ejpam-6798	199	6	/	/	SYM
ejpam-6798	199	7	eur	eur	PROPN
ejpam-6798	199	8	.	.	PUNCT
ejpam-6798	200	1	j.	j.	PROPN
ejpam-6798	200	2	pure	pure	PROPN
ejpam-6798	200	3	appl	appl	PROPN
ejpam-6798	200	4	.	.	PROPN
ejpam-6798	200	5	math	math	PROPN
ejpam-6798	200	6	,	,	PUNCT
ejpam-6798	200	7	18	18	NUM
ejpam-6798	200	8	(	(	PUNCT
ejpam-6798	200	9	4	4	NUM
ejpam-6798	200	10	)	)	PUNCT
ejpam-6798	200	11	(	(	PUNCT
ejpam-6798	200	12	2025	2025	NUM
ejpam-6798	200	13	)	)	PUNCT
ejpam-6798	200	14	,	,	PUNCT
ejpam-6798	200	15	6798	6798	NUM
ejpam-6798	200	16	8	8	NUM
ejpam-6798	200	17	of	of	ADP
ejpam-6798	200	18	22	22	NUM
ejpam-6798	200	19	table	table	NOUN
ejpam-6798	200	20	3	3	NUM
ejpam-6798	200	21	:	:	PUNCT
ejpam-6798	200	22	cayley	cayley	PROPN
ejpam-6798	200	23	’s	’s	PART
ejpam-6798	200	24	table	table	NOUN
ejpam-6798	200	25	describing	describe	VERB
ejpam-6798	200	26	the	the	DET
ejpam-6798	200	27	binary	binary	ADJ
ejpam-6798	200	28	operation	operation	NOUN
ejpam-6798	200	29	expressed	express	VERB
ejpam-6798	200	30	by	by	ADP
ejpam-6798	200	31	“	"	PUNCT
ejpam-6798	200	32	⋆	⋆	VERB
ejpam-6798	200	33	”	"	PUNCT
ejpam-6798	200	34	.	.	PUNCT
ejpam-6798	201	1	⋆	⋆	VERB
ejpam-6798	201	2	0	0	NUM
ejpam-6798	201	3	s	s	PART
ejpam-6798	201	4	l	l	NOUN
ejpam-6798	201	5	z	z	PROPN
ejpam-6798	201	6	w	w	NOUN
ejpam-6798	201	7	0	0	NUM
ejpam-6798	201	8	0	0	NUM
ejpam-6798	201	9	0	0	NUM
ejpam-6798	201	10	w	w	NOUN
ejpam-6798	201	11	z	z	PROPN
ejpam-6798	201	12	l	l	NOUN
ejpam-6798	202	1	s	s	X
ejpam-6798	203	1	s	s	NOUN
ejpam-6798	203	2	0	0	NUM
ejpam-6798	203	3	w	w	PROPN
ejpam-6798	203	4	z	z	PROPN
ejpam-6798	203	5	l	l	NOUN
ejpam-6798	203	6	l	l	NOUN
ejpam-6798	203	7	l	l	NOUN
ejpam-6798	203	8	l	l	NOUN
ejpam-6798	203	9	0	0	PUNCT
ejpam-6798	203	10	l	l	NOUN
ejpam-6798	203	11	z	z	NOUN
ejpam-6798	203	12	z	z	NOUN
ejpam-6798	203	13	z	z	NOUN
ejpam-6798	203	14	z	z	NOUN
ejpam-6798	203	15	l	l	NOUN
ejpam-6798	203	16	0	0	PUNCT
ejpam-6798	204	1	w	w	PROPN
ejpam-6798	204	2	w	w	PROPN
ejpam-6798	204	3	w	w	PROPN
ejpam-6798	204	4	w	w	PROPN
ejpam-6798	204	5	z	z	PROPN
ejpam-6798	204	6	l	l	NOUN
ejpam-6798	204	7	0	0	NUM
ejpam-6798	205	1	the	the	DET
ejpam-6798	205	2	following	following	ADJ
ejpam-6798	205	3	result	result	NOUN
ejpam-6798	205	4	indicates	indicate	VERB
ejpam-6798	205	5	membership	membership	NOUN
ejpam-6798	205	6	degree	degree	NOUN
ejpam-6798	205	7	of	of	ADP
ejpam-6798	205	8	identity	identity	NOUN
ejpam-6798	205	9	element	element	NOUN
ejpam-6798	205	10	of	of	ADP
ejpam-6798	205	11	cifs	cif	NOUN
ejpam-6798	205	12	is	be	AUX
ejpam-6798	205	13	greater	great	ADJ
ejpam-6798	205	14	than	than	ADP
ejpam-6798	205	15	all	all	DET
ejpam-6798	205	16	other	other	ADJ
ejpam-6798	205	17	elements	element	NOUN
ejpam-6798	205	18	.	.	PUNCT
ejpam-6798	206	1	also	also	ADV
ejpam-6798	206	2	,	,	PUNCT
ejpam-6798	206	3	the	the	DET
ejpam-6798	206	4	non	non	ADJ
ejpam-6798	206	5	-	-	ADJ
ejpam-6798	206	6	membership	membership	ADJ
ejpam-6798	206	7	degree	degree	NOUN
ejpam-6798	206	8	of	of	ADP
ejpam-6798	206	9	identity	identity	NOUN
ejpam-6798	206	10	element	element	NOUN
ejpam-6798	206	11	is	be	AUX
ejpam-6798	206	12	less	less	ADJ
ejpam-6798	206	13	than	than	ADP
ejpam-6798	206	14	the	the	DET
ejpam-6798	206	15	non	non	NOUN
ejpam-6798	206	16	-	-	NOUN
ejpam-6798	206	17	membership	membership	NOUN
ejpam-6798	206	18	of	of	ADP
ejpam-6798	206	19	remaining	remain	VERB
ejpam-6798	206	20	elements	element	NOUN
ejpam-6798	206	21	of	of	ADP
ejpam-6798	206	22	cifs	cif	NOUN
ejpam-6798	206	23	.	.	PUNCT
ejpam-6798	207	1	theorem	theorem	NOUN
ejpam-6798	207	2	1	1	NUM
ejpam-6798	207	3	.	.	PUNCT
ejpam-6798	208	1	if	if	SCONJ
ejpam-6798	208	2	l	l	NOUN
ejpam-6798	208	3	is	be	AUX
ejpam-6798	208	4	a	a	DET
ejpam-6798	208	5	cifs	cif	NOUN
ejpam-6798	208	6	of	of	ADP
ejpam-6798	208	7	m	m	PRON
ejpam-6798	208	8	,	,	PUNCT
ejpam-6798	208	9	then	then	ADV
ejpam-6798	208	10	µl(0	µl(0	PROPN
ejpam-6798	208	11	)	)	PUNCT
ejpam-6798	208	12	≥	≥	NOUN
ejpam-6798	208	13	µl(s	µl(s	NUM
ejpam-6798	208	14	)	)	PUNCT
ejpam-6798	208	15	and	and	CCONJ
ejpam-6798	208	16	νl(0	νl(0	PROPN
ejpam-6798	208	17	)	)	PUNCT
ejpam-6798	208	18	≤	≤	NOUN
ejpam-6798	208	19	νl(s	νl(	NOUN
ejpam-6798	208	20	)	)	PUNCT
ejpam-6798	208	21	.	.	PUNCT
ejpam-6798	209	1	proof	proof	NOUN
ejpam-6798	209	2	.	.	PUNCT
ejpam-6798	210	1	let	let	VERB
ejpam-6798	210	2	l	l	NOUN
ejpam-6798	210	3	be	be	AUX
ejpam-6798	210	4	a	a	DET
ejpam-6798	210	5	cifs	cif	NOUN
ejpam-6798	210	6	of	of	ADP
ejpam-6798	210	7	m	m	PROPN
ejpam-6798	210	8	.	.	PUNCT
ejpam-6798	211	1	then	then	ADV
ejpam-6798	211	2	µl(0	µl(0	VERB
ejpam-6798	211	3	)	)	PUNCT
ejpam-6798	211	4	=	=	SYM
ejpam-6798	212	1	γl(0)e	γl(0)e	NOUN
ejpam-6798	212	2	ιθl(0	ιθl(0	NOUN
ejpam-6798	212	3	)	)	PUNCT
ejpam-6798	213	1	=	=	PRON
ejpam-6798	213	2	γl(s	γl(s	NUM
ejpam-6798	213	3	⋆	⋆	PUNCT
ejpam-6798	213	4	s)eιθl(s⋆s	s)eιθl(s⋆s	NOUN
ejpam-6798	213	5	)	)	PUNCT
ejpam-6798	213	6	≥	≥	NOUN
ejpam-6798	213	7	(	(	PUNCT
ejpam-6798	213	8	γl(s	γl(	NOUN
ejpam-6798	213	9	)	)	PUNCT
ejpam-6798	213	10	∧	∧	NOUN
ejpam-6798	213	11	γl(s))e	γl(s))e	PUNCT
ejpam-6798	213	12	ι(θl(s)∧θl(s	ι(θl(s)∧θl(s	NOUN
ejpam-6798	213	13	)	)	PUNCT
ejpam-6798	213	14	)	)	PUNCT
ejpam-6798	214	1	=	=	PUNCT
ejpam-6798	214	2	γl(s)e	γl(s)e	NUM
ejpam-6798	214	3	ιθl(s	ιθl(s	PROPN
ejpam-6798	214	4	)	)	PUNCT
ejpam-6798	214	5	≥	≥	NOUN
ejpam-6798	214	6	µl(s	µl(s	NUM
ejpam-6798	214	7	)	)	PUNCT
ejpam-6798	214	8	.	.	PUNCT
ejpam-6798	215	1	and	and	CCONJ
ejpam-6798	215	2	νl(0	νl(0	PROPN
ejpam-6798	215	3	)	)	PUNCT
ejpam-6798	216	1	=	=	SYM
ejpam-6798	216	2	γl(0)e	γl(0)e	NOUN
ejpam-6798	216	3	ιθl(0	ιθl(0	NOUN
ejpam-6798	216	4	)	)	PUNCT
ejpam-6798	217	1	=	=	PRON
ejpam-6798	217	2	γl(s	γl(s	NUM
ejpam-6798	217	3	⋆	⋆	PUNCT
ejpam-6798	217	4	s)eιθl(s⋆s	s)eιθl(s⋆s	NOUN
ejpam-6798	217	5	)	)	PUNCT
ejpam-6798	217	6	≤	≤	NOUN
ejpam-6798	217	7	(	(	PUNCT
ejpam-6798	217	8	γl(s	γl(	NOUN
ejpam-6798	217	9	)	)	PUNCT
ejpam-6798	217	10	∨	∨	NUM
ejpam-6798	217	11	γl(s))e	γl(s))e	X
ejpam-6798	217	12	ι(θl(s)∨θl(s	ι(θl(s)∨θl(s	NOUN
ejpam-6798	217	13	)	)	PUNCT
ejpam-6798	217	14	)	)	PUNCT
ejpam-6798	218	1	=	=	PUNCT
ejpam-6798	218	2	γl(s)e	γl(s)e	NUM
ejpam-6798	218	3	ιθl(s	ιθl(s	PROPN
ejpam-6798	218	4	)	)	PUNCT
ejpam-6798	218	5	≤	≤	NOUN
ejpam-6798	218	6	νl(s	νl(	NOUN
ejpam-6798	218	7	)	)	PUNCT
ejpam-6798	218	8	.	.	PUNCT
ejpam-6798	219	1	thus	thus	ADV
ejpam-6798	219	2	,	,	PUNCT
ejpam-6798	219	3	we	we	PRON
ejpam-6798	219	4	conclude	conclude	VERB
ejpam-6798	219	5	the	the	DET
ejpam-6798	219	6	required	require	VERB
ejpam-6798	219	7	result	result	NOUN
ejpam-6798	219	8	.	.	PUNCT
ejpam-6798	220	1	definition	definition	NOUN
ejpam-6798	220	2	9	9	NUM
ejpam-6798	220	3	.	.	PUNCT
ejpam-6798	221	1	let	let	VERB
ejpam-6798	221	2	l	l	NOUN
ejpam-6798	221	3	be	be	AUX
ejpam-6798	221	4	a	a	DET
ejpam-6798	221	5	cifs	cif	NOUN
ejpam-6798	221	6	of	of	ADP
ejpam-6798	221	7	m	m	PROPN
ejpam-6798	221	8	.	.	PUNCT
ejpam-6798	222	1	then	then	ADV
ejpam-6798	222	2	modal	modal	ADJ
ejpam-6798	222	3	operator	operator	NOUN
ejpam-6798	222	4	⊕l	⊕l	NOUN
ejpam-6798	222	5	is	be	AUX
ejpam-6798	222	6	defined	define	VERB
ejpam-6798	222	7	as	as	ADP
ejpam-6798	222	8	µ⊕l(s	µ⊕l(s	PROPN
ejpam-6798	222	9	)	)	PUNCT
ejpam-6798	222	10	=	=	SYM
ejpam-6798	223	1	γl(s	γl(	NOUN
ejpam-6798	223	2	)	)	PUNCT
ejpam-6798	223	3	2	2	NUM
ejpam-6798	223	4	eι	eι	NOUN
ejpam-6798	223	5	(	(	PUNCT
ejpam-6798	223	6	θl(s	θl(s	NOUN
ejpam-6798	223	7	)	)	PUNCT
ejpam-6798	223	8	2	2	NUM
ejpam-6798	223	9	)	)	PUNCT
ejpam-6798	223	10	,	,	PUNCT
ejpam-6798	223	11	ν⊕l(s	ν⊕l(s	PROPN
ejpam-6798	223	12	)	)	PUNCT
ejpam-6798	223	13	=	=	SYM
ejpam-6798	223	14	γl(s	γl(	NOUN
ejpam-6798	223	15	)	)	PUNCT
ejpam-6798	223	16	2	2	NUM
ejpam-6798	223	17	eι	eι	NOUN
ejpam-6798	223	18	(	(	PUNCT
ejpam-6798	223	19	θl(s	θl(s	NOUN
ejpam-6798	223	20	)	)	PUNCT
ejpam-6798	223	21	2	2	NUM
ejpam-6798	223	22	)	)	PUNCT
ejpam-6798	223	23	.	.	PUNCT
ejpam-6798	224	1	example	example	NOUN
ejpam-6798	225	1	3	3	X
ejpam-6798	225	2	.	.	PUNCT
ejpam-6798	226	1	let	let	VERB
ejpam-6798	226	2	(	(	PUNCT
ejpam-6798	226	3	µl(s	µl(	NOUN
ejpam-6798	226	4	)	)	PUNCT
ejpam-6798	226	5	,	,	PUNCT
ejpam-6798	226	6	νl(s	νl(	NOUN
ejpam-6798	226	7	)	)	PUNCT
ejpam-6798	226	8	)	)	PUNCT
ejpam-6798	227	1	=	=	PRON
ejpam-6798	227	2	{	{	PUNCT
ejpam-6798	227	3	(	(	PUNCT
ejpam-6798	227	4	0	0	NUM
ejpam-6798	227	5	,	,	PUNCT
ejpam-6798	227	6	0.4eι0.5π	0.4eι0.5π	PROPN
ejpam-6798	227	7	,	,	PUNCT
ejpam-6798	227	8	0.2eι0.3π	0.2eι0.3π	PROPN
ejpam-6798	227	9	)	)	PUNCT
ejpam-6798	227	10	,	,	PUNCT
ejpam-6798	227	11	(	(	PUNCT
ejpam-6798	227	12	s	s	X
ejpam-6798	227	13	,	,	PUNCT
ejpam-6798	227	14	0.8eι0.1π	0.8eι0.1π	PROPN
ejpam-6798	227	15	,	,	PUNCT
ejpam-6798	227	16	0.6eι0.01π	0.6eι0.01π	NUM
ejpam-6798	227	17	)	)	PUNCT
ejpam-6798	227	18	,	,	PUNCT
ejpam-6798	227	19	(	(	PUNCT
ejpam-6798	227	20	l	l	NOUN
ejpam-6798	227	21	,	,	PUNCT
ejpam-6798	227	22	0.6eι0.3π	0.6eι0.3π	PROPN
ejpam-6798	227	23	,	,	PUNCT
ejpam-6798	227	24	0.4eι0.1π	0.4eι0.1π	PROPN
ejpam-6798	227	25	)	)	PUNCT
ejpam-6798	227	26	}	}	PUNCT
ejpam-6798	227	27	be	be	AUX
ejpam-6798	227	28	a	a	DET
ejpam-6798	227	29	cifs	cif	NOUN
ejpam-6798	227	30	of	of	ADP
ejpam-6798	227	31	m	m	PROPN
ejpam-6798	227	32	.	.	PUNCT
ejpam-6798	228	1	then	then	ADV
ejpam-6798	228	2	(	(	PUNCT
ejpam-6798	228	3	µ⊕l(s	µ⊕l(s	PROPN
ejpam-6798	228	4	)	)	PUNCT
ejpam-6798	228	5	,	,	PUNCT
ejpam-6798	228	6	ν⊕l(s	ν⊕l(s	PROPN
ejpam-6798	228	7	)	)	PUNCT
ejpam-6798	228	8	)	)	PUNCT
ejpam-6798	229	1	=	=	PRON
ejpam-6798	229	2	{	{	PUNCT
ejpam-6798	229	3	(	(	PUNCT
ejpam-6798	229	4	0	0	NUM
ejpam-6798	229	5	,	,	PUNCT
ejpam-6798	229	6	0.2eι0.25π	0.2eι0.25π	NOUN
ejpam-6798	229	7	,	,	PUNCT
ejpam-6798	229	8	0.1eι0.15π	0.1eι0.15π	PROPN
ejpam-6798	229	9	)	)	PUNCT
ejpam-6798	229	10	,	,	PUNCT
ejpam-6798	229	11	(	(	PUNCT
ejpam-6798	229	12	s	s	X
ejpam-6798	229	13	,	,	PUNCT
ejpam-6798	229	14	0.4eι0.05π	0.4eι0.05π	NUM
ejpam-6798	229	15	,	,	PUNCT
ejpam-6798	229	16	0.3eι0.005π	0.3eι0.005π	NUM
ejpam-6798	229	17	)	)	PUNCT
ejpam-6798	229	18	,	,	PUNCT
ejpam-6798	229	19	(	(	PUNCT
ejpam-6798	229	20	l	l	NOUN
ejpam-6798	229	21	,	,	PUNCT
ejpam-6798	229	22	0.3eι0.15π	0.3eι0.15π	NOUN
ejpam-6798	229	23	,	,	PUNCT
ejpam-6798	229	24	0.2eι0.05π	0.2eι0.05π	NOUN
ejpam-6798	229	25	)	)	PUNCT
ejpam-6798	229	26	}	}	PUNCT
ejpam-6798	229	27	is	be	AUX
ejpam-6798	229	28	a	a	DET
ejpam-6798	229	29	cifs	cif	NOUN
ejpam-6798	229	30	of	of	ADP
ejpam-6798	229	31	m	m	PRON
ejpam-6798	229	32	.	.	PUNCT
ejpam-6798	230	1	the	the	DET
ejpam-6798	230	2	following	follow	VERB
ejpam-6798	230	3	result	result	NOUN
ejpam-6798	230	4	shows	show	VERB
ejpam-6798	230	5	that	that	SCONJ
ejpam-6798	230	6	the	the	DET
ejpam-6798	230	7	modal	modal	ADJ
ejpam-6798	230	8	operator	operator	NOUN
ejpam-6798	230	9	⊕	⊕	PROPN
ejpam-6798	230	10	of	of	ADP
ejpam-6798	230	11	cifi	cifi	NOUN
ejpam-6798	230	12	of	of	ADP
ejpam-6798	230	13	m	m	PROPN
ejpam-6798	230	14	is	be	AUX
ejpam-6798	230	15	also	also	ADV
ejpam-6798	230	16	cifi	cifi	NOUN
ejpam-6798	230	17	.	.	PUNCT
ejpam-6798	231	1	theorem	theorem	NOUN
ejpam-6798	231	2	2	2	NUM
ejpam-6798	231	3	.	.	PUNCT
ejpam-6798	232	1	if	if	SCONJ
ejpam-6798	232	2	l	l	NOUN
ejpam-6798	232	3	is	be	AUX
ejpam-6798	232	4	a	a	DET
ejpam-6798	232	5	cifs	cif	NOUN
ejpam-6798	232	6	of	of	ADP
ejpam-6798	232	7	m	m	PROPN
ejpam-6798	232	8	.	.	PUNCT
ejpam-6798	233	1	then	then	ADV
ejpam-6798	233	2	⊕l	⊕l	NOUN
ejpam-6798	233	3	is	be	AUX
ejpam-6798	233	4	a	a	DET
ejpam-6798	233	5	cifs	cifs	NOUN
ejpam-6798	233	6	l	l	NOUN
ejpam-6798	233	7	of	of	ADP
ejpam-6798	233	8	m	m	PROPN
ejpam-6798	233	9	.	.	PUNCT
ejpam-6798	234	1	proof	proof	NOUN
ejpam-6798	234	2	.	.	PUNCT
ejpam-6798	235	1	for	for	ADP
ejpam-6798	235	2	each	each	DET
ejpam-6798	235	3	s	s	X
ejpam-6798	235	4	∈	∈	PROPN
ejpam-6798	235	5	m	m	PRON
ejpam-6798	235	6	,	,	PUNCT
ejpam-6798	235	7	we	we	PRON
ejpam-6798	235	8	have	have	VERB
ejpam-6798	235	9	µ⊕l(0	µ⊕l(0	NOUN
ejpam-6798	235	10	)	)	PUNCT
ejpam-6798	236	1	=	=	SYM
ejpam-6798	236	2	γl(0	γl(0	NOUN
ejpam-6798	236	3	)	)	PUNCT
ejpam-6798	236	4	2	2	NUM
ejpam-6798	236	5	eι	eι	PROPN
ejpam-6798	236	6	(	(	PUNCT
ejpam-6798	236	7	θl(0	θl(0	PROPN
ejpam-6798	236	8	)	)	PUNCT
ejpam-6798	236	9	2	2	NUM
ejpam-6798	236	10	)	)	PUNCT
ejpam-6798	236	11	≥	≥	NOUN
ejpam-6798	236	12	γl(s	γl(	NOUN
ejpam-6798	236	13	)	)	PUNCT
ejpam-6798	236	14	2	2	NUM
ejpam-6798	236	15	eι	eι	NOUN
ejpam-6798	236	16	(	(	PUNCT
ejpam-6798	236	17	θl(s	θl(s	NOUN
ejpam-6798	236	18	)	)	PUNCT
ejpam-6798	236	19	2	2	NUM
ejpam-6798	236	20	)	)	PUNCT
ejpam-6798	236	21	=	=	SYM
ejpam-6798	236	22	µ⊕l(s	µ⊕l(s	PROPN
ejpam-6798	236	23	)	)	PUNCT
ejpam-6798	236	24	.	.	PUNCT
ejpam-6798	237	1	let	let	VERB
ejpam-6798	237	2	s	s	PRON
ejpam-6798	237	3	,	,	PUNCT
ejpam-6798	237	4	l	l	PROPN
ejpam-6798	237	5	∈	∈	PROPN
ejpam-6798	237	6	m	m	PRON
ejpam-6798	237	7	,	,	PUNCT
ejpam-6798	237	8	then	then	ADV
ejpam-6798	237	9	µ⊕l(s⋆l	µ⊕l(s⋆l	NUM
ejpam-6798	237	10	)	)	PUNCT
ejpam-6798	237	11	=	=	SYM
ejpam-6798	237	12	γl(s⋆l	γl(s⋆l	ADJ
ejpam-6798	237	13	)	)	PUNCT
ejpam-6798	237	14	2	2	NUM
ejpam-6798	237	15	eι	eι	NOUN
ejpam-6798	237	16	(	(	PUNCT
ejpam-6798	237	17	θl(s⋆l	θl(s⋆l	NOUN
ejpam-6798	237	18	)	)	PUNCT
ejpam-6798	237	19	2	2	NUM
ejpam-6798	237	20	)	)	PUNCT
ejpam-6798	237	21	≥	≥	NOUN
ejpam-6798	237	22	(	(	PUNCT
ejpam-6798	237	23	γl(s)2	γl(s)2	PROPN
ejpam-6798	237	24	∧	∧	PROPN
ejpam-6798	237	25	γl(l	γl(l	NUM
ejpam-6798	237	26	)	)	PUNCT
ejpam-6798	237	27	2	2	NUM
ejpam-6798	237	28	)	)	PUNCT
ejpam-6798	237	29	eι	eι	PROPN
ejpam-6798	237	30	(	(	PUNCT
ejpam-6798	237	31	θl(s	θl(s	X
ejpam-6798	237	32	)	)	PUNCT
ejpam-6798	237	33	2	2	NUM
ejpam-6798	237	34	∧	∧	NOUN
ejpam-6798	237	35	θl(l	θl(l	PUNCT
ejpam-6798	237	36	)	)	PUNCT
ejpam-6798	237	37	2	2	NUM
ejpam-6798	237	38	)	)	PUNCT
ejpam-6798	237	39	=	=	PUNCT
ejpam-6798	237	40	µ⊕l(s)∧µ⊕l(l	µ⊕l(s)∧µ⊕l(l	PROPN
ejpam-6798	237	41	)	)	PUNCT
ejpam-6798	237	42	.	.	PUNCT
ejpam-6798	238	1	for	for	ADP
ejpam-6798	238	2	each	each	DET
ejpam-6798	238	3	s	s	X
ejpam-6798	238	4	∈	∈	PROPN
ejpam-6798	238	5	m	m	PRON
ejpam-6798	238	6	,	,	PUNCT
ejpam-6798	238	7	we	we	PRON
ejpam-6798	238	8	have	have	VERB
ejpam-6798	238	9	ν⊕l(0	ν⊕l(0	NOUN
ejpam-6798	238	10	)	)	PUNCT
ejpam-6798	238	11	=	=	SYM
ejpam-6798	238	12	γl(0	γl(0	NOUN
ejpam-6798	238	13	)	)	PUNCT
ejpam-6798	238	14	2	2	NUM
ejpam-6798	238	15	eι	eι	PROPN
ejpam-6798	238	16	(	(	PUNCT
ejpam-6798	238	17	θl(0	θl(0	PROPN
ejpam-6798	238	18	)	)	PUNCT
ejpam-6798	238	19	2	2	NUM
ejpam-6798	238	20	)	)	PUNCT
ejpam-6798	238	21	≤	≤	NOUN
ejpam-6798	238	22	γl(s	γl(	NOUN
ejpam-6798	238	23	)	)	PUNCT
ejpam-6798	238	24	2	2	NUM
ejpam-6798	238	25	eι	eι	NOUN
ejpam-6798	238	26	(	(	PUNCT
ejpam-6798	238	27	θl(s	θl(s	NOUN
ejpam-6798	238	28	)	)	PUNCT
ejpam-6798	238	29	2	2	NUM
ejpam-6798	238	30	)	)	PUNCT
ejpam-6798	238	31	=	=	SYM
ejpam-6798	238	32	ν⊕l(s	ν⊕l(s	PROPN
ejpam-6798	238	33	)	)	PUNCT
ejpam-6798	238	34	.	.	PUNCT
ejpam-6798	239	1	suppose	suppose	VERB
ejpam-6798	239	2	that	that	SCONJ
ejpam-6798	239	3	s	s	SYM
ejpam-6798	239	4	,	,	PUNCT
ejpam-6798	239	5	l	l	PROPN
ejpam-6798	239	6	∈	∈	PROPN
ejpam-6798	239	7	m	m	NOUN
ejpam-6798	239	8	,	,	PUNCT
ejpam-6798	239	9	then	then	ADV
ejpam-6798	239	10	ν⊕l(s⋆l	ν⊕l(s⋆l	PROPN
ejpam-6798	239	11	)	)	PUNCT
ejpam-6798	239	12	=	=	SYM
ejpam-6798	239	13	γl(s⋆l	γl(s⋆l	ADJ
ejpam-6798	239	14	)	)	PUNCT
ejpam-6798	239	15	2	2	NUM
ejpam-6798	239	16	eι	eι	NOUN
ejpam-6798	239	17	(	(	PUNCT
ejpam-6798	239	18	θl(s⋆l	θl(s⋆l	NOUN
ejpam-6798	239	19	)	)	PUNCT
ejpam-6798	239	20	2	2	NUM
ejpam-6798	239	21	)	)	PUNCT
ejpam-6798	239	22	≤	≤	NOUN
ejpam-6798	239	23	(	(	PUNCT
ejpam-6798	239	24	γl(s	γl(	NOUN
ejpam-6798	239	25	)	)	PUNCT
ejpam-6798	239	26	2	2	NUM
ejpam-6798	239	27	∨	∨	NUM
ejpam-6798	239	28	γl(l	γl(l	NUM
ejpam-6798	239	29	)	)	PUNCT
ejpam-6798	239	30	2	2	NUM
ejpam-6798	239	31	)	)	PUNCT
ejpam-6798	239	32	eι	eι	PROPN
ejpam-6798	239	33	(	(	PUNCT
ejpam-6798	239	34	θl(s	θl(s	X
ejpam-6798	239	35	)	)	PUNCT
ejpam-6798	239	36	2	2	NUM
ejpam-6798	239	37	∨	∨	NOUN
ejpam-6798	239	38	θl(l	θl(l	NUM
ejpam-6798	239	39	)	)	PUNCT
ejpam-6798	239	40	2	2	NUM
ejpam-6798	239	41	)	)	PUNCT
ejpam-6798	239	42	=	=	SYM
ejpam-6798	239	43	ν⊕l(s)∨ν⊕l(l	ν⊕l(s)∨ν⊕l(l	PROPN
ejpam-6798	239	44	)	)	PUNCT
ejpam-6798	239	45	.	.	PUNCT
ejpam-6798	240	1	this	this	PRON
ejpam-6798	240	2	concludes	conclude	VERB
ejpam-6798	240	3	the	the	DET
ejpam-6798	240	4	proof	proof	NOUN
ejpam-6798	240	5	.	.	PUNCT
ejpam-6798	241	1	definition	definition	NOUN
ejpam-6798	241	2	10	10	NUM
ejpam-6798	241	3	.	.	PUNCT
ejpam-6798	242	1	let	let	VERB
ejpam-6798	242	2	l	l	NOUN
ejpam-6798	242	3	be	be	AUX
ejpam-6798	242	4	a	a	DET
ejpam-6798	242	5	cifs	cif	NOUN
ejpam-6798	242	6	of	of	ADP
ejpam-6798	242	7	m	m	PROPN
ejpam-6798	242	8	.	.	PUNCT
ejpam-6798	243	1	then	then	ADV
ejpam-6798	243	2	modal	modal	ADJ
ejpam-6798	243	3	operator	operator	NOUN
ejpam-6798	243	4	⊗l	⊗l	NOUN
ejpam-6798	243	5	is	be	AUX
ejpam-6798	243	6	describe	describe	NOUN
ejpam-6798	243	7	as	as	ADP
ejpam-6798	243	8	µ⊗l(s	µ⊗l(s	NOUN
ejpam-6798	243	9	)	)	PUNCT
ejpam-6798	244	1	=	=	PUNCT
ejpam-6798	244	2	γl(s)+1	γl(s)+1	NOUN
ejpam-6798	244	3	2	2	NUM
ejpam-6798	244	4	eι	eι	NOUN
ejpam-6798	244	5	(	(	PUNCT
ejpam-6798	244	6	θl(s)+1	θl(s)+1	NOUN
ejpam-6798	244	7	2	2	NUM
ejpam-6798	244	8	)	)	PUNCT
ejpam-6798	244	9	,	,	PUNCT
ejpam-6798	244	10	ν⊗l(s	ν⊗l(s	NOUN
ejpam-6798	244	11	)	)	PUNCT
ejpam-6798	244	12	=	=	SYM
ejpam-6798	245	1	γl(s)+1	γl(s)+1	NOUN
ejpam-6798	245	2	2	2	NUM
ejpam-6798	245	3	eι	eι	NOUN
ejpam-6798	245	4	(	(	PUNCT
ejpam-6798	245	5	θl(s)+1	θl(s)+1	NOUN
ejpam-6798	245	6	2	2	NUM
ejpam-6798	245	7	)	)	PUNCT
ejpam-6798	245	8	.	.	PUNCT
ejpam-6798	245	9	example	example	NOUN
ejpam-6798	246	1	4	4	X
ejpam-6798	246	2	.	.	PUNCT
ejpam-6798	247	1	let	let	VERB
ejpam-6798	247	2	(	(	PUNCT
ejpam-6798	247	3	µl(s	µl(	NOUN
ejpam-6798	247	4	)	)	PUNCT
ejpam-6798	247	5	,	,	PUNCT
ejpam-6798	247	6	νl(s	νl(	NOUN
ejpam-6798	247	7	)	)	PUNCT
ejpam-6798	247	8	)	)	PUNCT
ejpam-6798	248	1	=	=	PRON
ejpam-6798	248	2	{	{	PUNCT
ejpam-6798	248	3	(	(	PUNCT
ejpam-6798	248	4	s	s	X
ejpam-6798	248	5	,	,	PUNCT
ejpam-6798	248	6	0.3eι0.5π	0.3eι0.5π	PROPN
ejpam-6798	248	7	,	,	PUNCT
ejpam-6798	248	8	0.1eι0.3π	0.1eι0.3π	PROPN
ejpam-6798	248	9	)	)	PUNCT
ejpam-6798	248	10	,	,	PUNCT
ejpam-6798	248	11	(	(	PUNCT
ejpam-6798	248	12	l	l	NOUN
ejpam-6798	248	13	,	,	PUNCT
ejpam-6798	248	14	0.7eι0.2π	0.7eι0.2π	PROPN
ejpam-6798	248	15	,	,	PUNCT
ejpam-6798	248	16	0.5eι0.1π	0.5eι0.1π	PROPN
ejpam-6798	248	17	)	)	PUNCT
ejpam-6798	248	18	,	,	PUNCT
ejpam-6798	248	19	(	(	PUNCT
ejpam-6798	248	20	z	z	X
ejpam-6798	248	21	,	,	PUNCT
ejpam-6798	248	22	0.5eι0.4π	0.5eι0.4π	PROPN
ejpam-6798	248	23	,	,	PUNCT
ejpam-6798	248	24	0.3eι0.2π	0.3eι0.2π	NOUN
ejpam-6798	248	25	)	)	PUNCT
ejpam-6798	248	26	}	}	PUNCT
ejpam-6798	248	27	be	be	AUX
ejpam-6798	248	28	a	a	DET
ejpam-6798	248	29	cifs	cif	NOUN
ejpam-6798	248	30	of	of	ADP
ejpam-6798	248	31	m	m	PROPN
ejpam-6798	248	32	.	.	PUNCT
ejpam-6798	249	1	then	then	ADV
ejpam-6798	249	2	(	(	PUNCT
ejpam-6798	249	3	µ⊗l(s	µ⊗l(s	NOUN
ejpam-6798	249	4	)	)	PUNCT
ejpam-6798	249	5	,	,	PUNCT
ejpam-6798	249	6	ν⊗l(s	ν⊗l(s	NOUN
ejpam-6798	249	7	)	)	PUNCT
ejpam-6798	249	8	)	)	PUNCT
ejpam-6798	250	1	=	=	PRON
ejpam-6798	250	2	{	{	PUNCT
ejpam-6798	250	3	(	(	PUNCT
ejpam-6798	250	4	s	s	PROPN
ejpam-6798	250	5	,	,	PUNCT
ejpam-6798	250	6	0.65eι0.75π	0.65eι0.75π	NUM
ejpam-6798	250	7	,	,	PUNCT
ejpam-6798	250	8	0.55eι0.65π	0.55eι0.65π	PROPN
ejpam-6798	250	9	)	)	PUNCT
ejpam-6798	250	10	,	,	PUNCT
ejpam-6798	250	11	(	(	PUNCT
ejpam-6798	250	12	l	l	NOUN
ejpam-6798	250	13	,	,	PUNCT
ejpam-6798	250	14	0.85eι0.6π	0.85eι0.6π	NUM
ejpam-6798	250	15	,	,	PUNCT
ejpam-6798	250	16	0.75eι0.55π	0.75eι0.55π	NOUN
ejpam-6798	250	17	)	)	PUNCT
ejpam-6798	250	18	,	,	PUNCT
ejpam-6798	250	19	(	(	PUNCT
ejpam-6798	250	20	z	z	NOUN
ejpam-6798	250	21	,	,	PUNCT
ejpam-6798	250	22	0.75eι0.7π	0.75eι0.7π	NUM
ejpam-6798	250	23	,	,	PUNCT
ejpam-6798	250	24	0.65eι0.6π	0.65eι0.6π	NUM
ejpam-6798	250	25	)	)	PUNCT
ejpam-6798	250	26	}	}	PUNCT
ejpam-6798	250	27	is	be	AUX
ejpam-6798	250	28	a	a	DET
ejpam-6798	250	29	cifs	cif	NOUN
ejpam-6798	250	30	of	of	ADP
ejpam-6798	250	31	m	m	PROPN
ejpam-6798	250	32	.	.	PUNCT
ejpam-6798	251	1	m.	m.	PROPN
ejpam-6798	251	2	jawad	jawad	PROPN
ejpam-6798	251	3	et	et	PROPN
ejpam-6798	251	4	al	al	PROPN
ejpam-6798	251	5	.	.	PUNCT
ejpam-6798	251	6	/	/	SYM
ejpam-6798	251	7	eur	eur	PROPN
ejpam-6798	251	8	.	.	PUNCT
ejpam-6798	252	1	j.	j.	PROPN
ejpam-6798	252	2	pure	pure	PROPN
ejpam-6798	252	3	appl	appl	PROPN
ejpam-6798	252	4	.	.	PROPN
ejpam-6798	252	5	math	math	PROPN
ejpam-6798	252	6	,	,	PUNCT
ejpam-6798	252	7	18	18	NUM
ejpam-6798	252	8	(	(	PUNCT
ejpam-6798	252	9	4	4	NUM
ejpam-6798	252	10	)	)	PUNCT
ejpam-6798	252	11	(	(	PUNCT
ejpam-6798	252	12	2025	2025	NUM
ejpam-6798	252	13	)	)	PUNCT
ejpam-6798	252	14	,	,	PUNCT
ejpam-6798	252	15	6798	6798	NUM
ejpam-6798	252	16	9	9	NUM
ejpam-6798	252	17	of	of	ADP
ejpam-6798	252	18	22	22	NUM
ejpam-6798	252	19	the	the	DET
ejpam-6798	252	20	subsequent	subsequent	ADJ
ejpam-6798	252	21	result	result	NOUN
ejpam-6798	252	22	demonstrates	demonstrate	VERB
ejpam-6798	252	23	that	that	SCONJ
ejpam-6798	252	24	the	the	DET
ejpam-6798	252	25	modal	modal	ADJ
ejpam-6798	252	26	operator	operator	NOUN
ejpam-6798	252	27	⊗	⊗	PROPN
ejpam-6798	252	28	of	of	ADP
ejpam-6798	252	29	cifi	cifi	NOUN
ejpam-6798	252	30	of	of	ADP
ejpam-6798	252	31	m	m	PROPN
ejpam-6798	252	32	is	be	AUX
ejpam-6798	252	33	also	also	ADV
ejpam-6798	252	34	cifi	cifi	NOUN
ejpam-6798	252	35	.	.	PUNCT
ejpam-6798	253	1	theorem	theorem	NOUN
ejpam-6798	253	2	3	3	X
ejpam-6798	253	3	.	.	PUNCT
ejpam-6798	253	4	suppose	suppose	VERB
ejpam-6798	253	5	that	that	SCONJ
ejpam-6798	253	6	l	l	NOUN
ejpam-6798	253	7	is	be	AUX
ejpam-6798	253	8	a	a	DET
ejpam-6798	253	9	cifs	cif	NOUN
ejpam-6798	253	10	of	of	ADP
ejpam-6798	253	11	m	m	PROPN
ejpam-6798	253	12	.	.	PUNCT
ejpam-6798	254	1	then	then	ADV
ejpam-6798	254	2	⊗l	⊗l	PROPN
ejpam-6798	254	3	is	be	AUX
ejpam-6798	254	4	a	a	DET
ejpam-6798	254	5	cifs	cifs	NOUN
ejpam-6798	254	6	l	l	NOUN
ejpam-6798	254	7	of	of	ADP
ejpam-6798	254	8	m	m	PROPN
ejpam-6798	254	9	.	.	PUNCT
ejpam-6798	255	1	proof	proof	NOUN
ejpam-6798	255	2	.	.	PUNCT
ejpam-6798	256	1	for	for	ADP
ejpam-6798	256	2	each	each	DET
ejpam-6798	256	3	s	s	X
ejpam-6798	256	4	∈	∈	PROPN
ejpam-6798	256	5	m	m	PRON
ejpam-6798	256	6	,	,	PUNCT
ejpam-6798	256	7	we	we	PRON
ejpam-6798	256	8	have	have	VERB
ejpam-6798	256	9	µ⊗l(0	µ⊗l(0	NOUN
ejpam-6798	256	10	)	)	PUNCT
ejpam-6798	257	1	=	=	SYM
ejpam-6798	257	2	γl(0)+1	γl(0)+1	NOUN
ejpam-6798	257	3	2	2	NUM
ejpam-6798	257	4	eι	eι	NOUN
ejpam-6798	257	5	(	(	PUNCT
ejpam-6798	257	6	θl(0)+1	θl(0)+1	NOUN
ejpam-6798	257	7	2	2	NUM
ejpam-6798	257	8	)	)	PUNCT
ejpam-6798	257	9	≥	≥	NOUN
ejpam-6798	257	10	γl(s)+1	γl(s)+1	NOUN
ejpam-6798	257	11	2	2	NUM
ejpam-6798	257	12	eι	eι	NOUN
ejpam-6798	257	13	(	(	PUNCT
ejpam-6798	257	14	θl(s)+1	θl(s)+1	NOUN
ejpam-6798	257	15	2	2	NUM
ejpam-6798	257	16	)	)	PUNCT
ejpam-6798	257	17	=	=	SYM
ejpam-6798	257	18	µ⊕l(s	µ⊕l(s	PROPN
ejpam-6798	257	19	)	)	PUNCT
ejpam-6798	257	20	.	.	PUNCT
ejpam-6798	258	1	let	let	VERB
ejpam-6798	258	2	s	s	PRON
ejpam-6798	258	3	,	,	PUNCT
ejpam-6798	258	4	l	l	PROPN
ejpam-6798	258	5	∈	∈	PROPN
ejpam-6798	258	6	m	m	NOUN
ejpam-6798	258	7	,	,	PUNCT
ejpam-6798	258	8	then	then	ADV
ejpam-6798	258	9	µ⊗l(s⋆l	µ⊗l(s⋆l	ADV
ejpam-6798	258	10	)	)	PUNCT
ejpam-6798	258	11	=	=	SYM
ejpam-6798	259	1	γl(s⋆l)+1	γl(s⋆l)+1	PROPN
ejpam-6798	259	2	2	2	NUM
ejpam-6798	259	3	eι	eι	NOUN
ejpam-6798	259	4	(	(	PUNCT
ejpam-6798	259	5	θl(s⋆l)+1	θl(s⋆l)+1	PROPN
ejpam-6798	259	6	2	2	NUM
ejpam-6798	259	7	)	)	PUNCT
ejpam-6798	259	8	≥	≥	NOUN
ejpam-6798	259	9	(	(	PUNCT
ejpam-6798	259	10	γl(s)+1	γl(s)+1	NOUN
ejpam-6798	259	11	2	2	NUM
ejpam-6798	259	12	∧γl(l)+1	∧γl(l)+1	NOUN
ejpam-6798	259	13	2	2	NUM
ejpam-6798	259	14	)	)	PUNCT
ejpam-6798	259	15	eι	eι	PROPN
ejpam-6798	259	16	(	(	PUNCT
ejpam-6798	259	17	θl(s)+1	θl(s)+1	PROPN
ejpam-6798	259	18	2	2	NUM
ejpam-6798	259	19	∧	∧	PROPN
ejpam-6798	259	20	θl(l)+1	θl(l)+1	PROPN
ejpam-6798	259	21	2	2	NUM
ejpam-6798	259	22	)	)	PUNCT
ejpam-6798	259	23	=	=	SYM
ejpam-6798	259	24	µ⊗l(s)∧µ⊗l(l	µ⊗l(s)∧µ⊗l(l	PROPN
ejpam-6798	259	25	)	)	PUNCT
ejpam-6798	259	26	.	.	PUNCT
ejpam-6798	260	1	for	for	ADP
ejpam-6798	260	2	each	each	DET
ejpam-6798	260	3	s	s	X
ejpam-6798	260	4	∈	∈	PROPN
ejpam-6798	260	5	m	m	PRON
ejpam-6798	260	6	,	,	PUNCT
ejpam-6798	260	7	we	we	PRON
ejpam-6798	260	8	have	have	VERB
ejpam-6798	260	9	ν⊗l(0	ν⊗l(0	NOUN
ejpam-6798	260	10	)	)	PUNCT
ejpam-6798	261	1	=	=	SYM
ejpam-6798	261	2	γl(0)+1	γl(0)+1	NOUN
ejpam-6798	261	3	2	2	NUM
ejpam-6798	261	4	eι	eι	NOUN
ejpam-6798	261	5	(	(	PUNCT
ejpam-6798	261	6	θl(0)+1	θl(0)+1	NOUN
ejpam-6798	261	7	2	2	NUM
ejpam-6798	261	8	)	)	PUNCT
ejpam-6798	261	9	≤	≤	NOUN
ejpam-6798	261	10	γl(s)+1	γl(s)+1	ADP
ejpam-6798	261	11	2	2	NUM
ejpam-6798	261	12	eι	eι	NOUN
ejpam-6798	261	13	(	(	PUNCT
ejpam-6798	261	14	θl(s)+1	θl(s)+1	NOUN
ejpam-6798	261	15	2	2	NUM
ejpam-6798	261	16	)	)	PUNCT
ejpam-6798	261	17	=	=	SYM
ejpam-6798	261	18	ν⊕l(s	ν⊕l(s	PROPN
ejpam-6798	261	19	)	)	PUNCT
ejpam-6798	261	20	.	.	PUNCT
ejpam-6798	262	1	suppose	suppose	VERB
ejpam-6798	262	2	that	that	SCONJ
ejpam-6798	262	3	s	s	SYM
ejpam-6798	262	4	,	,	PUNCT
ejpam-6798	262	5	l	l	PROPN
ejpam-6798	262	6	∈	∈	PROPN
ejpam-6798	262	7	m	m	NOUN
ejpam-6798	262	8	,	,	PUNCT
ejpam-6798	262	9	then	then	ADV
ejpam-6798	262	10	ν⊗l(s⋆	ν⊗l(s⋆	PROPN
ejpam-6798	262	11	l	l	NOUN
ejpam-6798	262	12	)	)	PUNCT
ejpam-6798	262	13	=	=	SYM
ejpam-6798	263	1	γl(s⋆l)+1	γl(s⋆l)+1	PROPN
ejpam-6798	263	2	2	2	NUM
ejpam-6798	263	3	eι	eι	NOUN
ejpam-6798	263	4	(	(	PUNCT
ejpam-6798	263	5	θl(s⋆l)+1	θl(s⋆l)+1	PROPN
ejpam-6798	263	6	2	2	NUM
ejpam-6798	263	7	)	)	PUNCT
ejpam-6798	263	8	≤	≤	NOUN
ejpam-6798	263	9	(	(	PUNCT
ejpam-6798	263	10	γl(s)+1	γl(s)+1	NOUN
ejpam-6798	263	11	2	2	NUM
ejpam-6798	263	12	∨	∨	NOUN
ejpam-6798	263	13	γl(l)+1	γl(l)+1	X
ejpam-6798	263	14	2	2	NUM
ejpam-6798	263	15	)	)	PUNCT
ejpam-6798	263	16	eι	eι	PROPN
ejpam-6798	263	17	(	(	PUNCT
ejpam-6798	263	18	θl(s)+1	θl(s)+1	NOUN
ejpam-6798	263	19	2	2	NUM
ejpam-6798	263	20	∨	∨	NOUN
ejpam-6798	263	21	θl(l)+1	θl(l)+1	PROPN
ejpam-6798	263	22	2	2	NUM
ejpam-6798	263	23	)	)	PUNCT
ejpam-6798	263	24	=	=	SYM
ejpam-6798	263	25	ν⊗l(s	ν⊗l(s	NOUN
ejpam-6798	263	26	)	)	PUNCT
ejpam-6798	263	27	∨	∨	NUM
ejpam-6798	263	28	ν⊗l(l	ν⊗l(l	NUM
ejpam-6798	263	29	)	)	PUNCT
ejpam-6798	263	30	.	.	PUNCT
ejpam-6798	264	1	therefore	therefore	ADV
ejpam-6798	264	2	,	,	PUNCT
ejpam-6798	264	3	⊗l	⊗l	PROPN
ejpam-6798	264	4	is	be	AUX
ejpam-6798	264	5	a	a	DET
ejpam-6798	264	6	cifs	cifs	NOUN
ejpam-6798	264	7	l	l	NOUN
ejpam-6798	264	8	of	of	ADP
ejpam-6798	264	9	m	m	PROPN
ejpam-6798	264	10	.	.	PUNCT
ejpam-6798	265	1	definition	definition	NOUN
ejpam-6798	265	2	11	11	NUM
ejpam-6798	265	3	.	.	PUNCT
ejpam-6798	265	4	suppose	suppose	VERB
ejpam-6798	265	5	that	that	SCONJ
ejpam-6798	265	6	l	l	NOUN
ejpam-6798	265	7	is	be	AUX
ejpam-6798	265	8	a	a	DET
ejpam-6798	265	9	cifs	cif	NOUN
ejpam-6798	265	10	of	of	ADP
ejpam-6798	265	11	m	m	PROPN
ejpam-6798	265	12	.	.	PUNCT
ejpam-6798	266	1	then	then	ADV
ejpam-6798	266	2	level	level	NOUN
ejpam-6798	266	3	operator	operator	NOUN
ejpam-6798	266	4	†l	†l	NOUN
ejpam-6798	266	5	is	be	AUX
ejpam-6798	266	6	describe	describe	VERB
ejpam-6798	266	7	as	as	ADP
ejpam-6798	266	8	µ†l(s	µ†l(s	ADJ
ejpam-6798	266	9	)	)	PUNCT
ejpam-6798	266	10	=	=	PUNCT
ejpam-6798	267	1	(	(	PUNCT
ejpam-6798	267	2	12	12	NUM
ejpam-6798	267	3	∨	∨	NOUN
ejpam-6798	267	4	γl(s))e	γl(s))e	X
ejpam-6798	267	5	ι	ι	X
ejpam-6798	267	6	(	(	PUNCT
ejpam-6798	267	7	1	1	NUM
ejpam-6798	267	8	2	2	NUM
ejpam-6798	267	9	∨θl(s	∨θl(s	PROPN
ejpam-6798	267	10	)	)	PUNCT
ejpam-6798	267	11	)	)	PUNCT
ejpam-6798	267	12	,	,	PUNCT
ejpam-6798	267	13	ν†l(s	ν†l(s	NOUN
ejpam-6798	267	14	)	)	PUNCT
ejpam-6798	267	15	=	=	PUNCT
ejpam-6798	268	1	(	(	PUNCT
ejpam-6798	268	2	12	12	NUM
ejpam-6798	268	3	∧	∧	PROPN
ejpam-6798	268	4	γl(s))e	γl(s))e	X
ejpam-6798	268	5	ι	ι	X
ejpam-6798	268	6	(	(	PUNCT
ejpam-6798	268	7	1	1	NUM
ejpam-6798	268	8	2	2	NUM
ejpam-6798	268	9	∧θl(s	∧θl(s	ADJ
ejpam-6798	268	10	)	)	PUNCT
ejpam-6798	268	11	)	)	PUNCT
ejpam-6798	268	12	.	.	PUNCT
ejpam-6798	269	1	example	example	NOUN
ejpam-6798	270	1	5	5	NUM
ejpam-6798	270	2	.	.	PUNCT
ejpam-6798	271	1	let	let	VERB
ejpam-6798	271	2	(	(	PUNCT
ejpam-6798	271	3	µl(s	µl(	NOUN
ejpam-6798	271	4	)	)	PUNCT
ejpam-6798	271	5	,	,	PUNCT
ejpam-6798	271	6	νl(s	νl(	NOUN
ejpam-6798	271	7	)	)	PUNCT
ejpam-6798	271	8	)	)	PUNCT
ejpam-6798	272	1	=	=	PRON
ejpam-6798	272	2	{	{	PUNCT
ejpam-6798	272	3	(	(	PUNCT
ejpam-6798	272	4	s	s	X
ejpam-6798	272	5	,	,	PUNCT
ejpam-6798	272	6	0.4eι0.6π	0.4eι0.6π	PROPN
ejpam-6798	272	7	,	,	PUNCT
ejpam-6798	272	8	0.2eι0.4π	0.2eι0.4π	PROPN
ejpam-6798	272	9	)	)	PUNCT
ejpam-6798	272	10	,	,	PUNCT
ejpam-6798	272	11	(	(	PUNCT
ejpam-6798	272	12	l	l	NOUN
ejpam-6798	272	13	,	,	PUNCT
ejpam-6798	272	14	0.6eι0.2π	0.6eι0.2π	PROPN
ejpam-6798	272	15	,	,	PUNCT
ejpam-6798	272	16	0.4eι0.1π	0.4eι0.1π	PROPN
ejpam-6798	272	17	)	)	PUNCT
ejpam-6798	272	18	,	,	PUNCT
ejpam-6798	272	19	(	(	PUNCT
ejpam-6798	272	20	z	z	X
ejpam-6798	272	21	,	,	PUNCT
ejpam-6798	272	22	0.5eι0.7π	0.5eι0.7π	PROPN
ejpam-6798	272	23	,	,	PUNCT
ejpam-6798	272	24	0.3eι0.5π	0.3eι0.5π	PROPN
ejpam-6798	272	25	)	)	PUNCT
ejpam-6798	272	26	}	}	PUNCT
ejpam-6798	272	27	be	be	AUX
ejpam-6798	272	28	a	a	DET
ejpam-6798	272	29	cifs	cif	NOUN
ejpam-6798	272	30	of	of	ADP
ejpam-6798	272	31	m	m	PROPN
ejpam-6798	272	32	.	.	PUNCT
ejpam-6798	273	1	then	then	ADV
ejpam-6798	273	2	µ†l(s	µ†l(s	PROPN
ejpam-6798	273	3	)	)	PUNCT
ejpam-6798	273	4	,	,	PUNCT
ejpam-6798	273	5	ν†l(s	ν†l(s	NOUN
ejpam-6798	273	6	)	)	PUNCT
ejpam-6798	273	7	)	)	PUNCT
ejpam-6798	274	1	=	=	PRON
ejpam-6798	274	2	{	{	PUNCT
ejpam-6798	274	3	(	(	PUNCT
ejpam-6798	274	4	s	s	PROPN
ejpam-6798	274	5	,	,	PUNCT
ejpam-6798	274	6	0.5eι0.6π	0.5eι0.6π	PROPN
ejpam-6798	274	7	,	,	PUNCT
ejpam-6798	274	8	0.2eι0.4π	0.2eι0.4π	PROPN
ejpam-6798	274	9	)	)	PUNCT
ejpam-6798	274	10	,	,	PUNCT
ejpam-6798	274	11	(	(	PUNCT
ejpam-6798	274	12	l	l	NOUN
ejpam-6798	274	13	,	,	PUNCT
ejpam-6798	274	14	0.6eι0.5π	0.6eι0.5π	PROPN
ejpam-6798	274	15	,	,	PUNCT
ejpam-6798	274	16	0.4eι0.1π	0.4eι0.1π	PROPN
ejpam-6798	274	17	)	)	PUNCT
ejpam-6798	274	18	,	,	PUNCT
ejpam-6798	274	19	(	(	PUNCT
ejpam-6798	274	20	z	z	X
ejpam-6798	274	21	,	,	PUNCT
ejpam-6798	274	22	0.5eι0.6π	0.5eι0.6π	PROPN
ejpam-6798	274	23	,	,	PUNCT
ejpam-6798	274	24	0.3eι0.5π	0.3eι0.5π	PROPN
ejpam-6798	274	25	)	)	PUNCT
ejpam-6798	274	26	}	}	PUNCT
ejpam-6798	274	27	is	be	AUX
ejpam-6798	274	28	a	a	DET
ejpam-6798	274	29	cifs	cif	NOUN
ejpam-6798	274	30	of	of	ADP
ejpam-6798	274	31	m	m	PRON
ejpam-6798	274	32	.	.	PUNCT
ejpam-6798	275	1	the	the	DET
ejpam-6798	275	2	following	follow	VERB
ejpam-6798	275	3	outcome	outcome	NOUN
ejpam-6798	275	4	shows	show	VERB
ejpam-6798	275	5	that	that	SCONJ
ejpam-6798	275	6	the	the	DET
ejpam-6798	275	7	level	level	NOUN
ejpam-6798	275	8	operator	operator	NOUN
ejpam-6798	275	9	†	†	NOUN
ejpam-6798	275	10	of	of	ADP
ejpam-6798	275	11	the	the	DET
ejpam-6798	275	12	cifi	cifi	NOUN
ejpam-6798	275	13	of	of	ADP
ejpam-6798	275	14	m	m	PROPN
ejpam-6798	275	15	is	be	AUX
ejpam-6798	275	16	also	also	ADV
ejpam-6798	275	17	cifi	cifi	NOUN
ejpam-6798	275	18	.	.	PUNCT
ejpam-6798	276	1	theorem	theorem	NOUN
ejpam-6798	276	2	4	4	NUM
ejpam-6798	276	3	.	.	PUNCT
ejpam-6798	276	4	suppose	suppose	VERB
ejpam-6798	276	5	that	that	SCONJ
ejpam-6798	276	6	l	l	NOUN
ejpam-6798	276	7	is	be	AUX
ejpam-6798	276	8	a	a	DET
ejpam-6798	276	9	cifs	cif	NOUN
ejpam-6798	276	10	of	of	ADP
ejpam-6798	276	11	m	m	PROPN
ejpam-6798	276	12	.	.	PUNCT
ejpam-6798	277	1	then	then	ADV
ejpam-6798	277	2	†l	†l	NOUN
ejpam-6798	277	3	is	be	AUX
ejpam-6798	277	4	a	a	DET
ejpam-6798	277	5	cifs	cifs	NOUN
ejpam-6798	277	6	l	l	NOUN
ejpam-6798	277	7	of	of	ADP
ejpam-6798	277	8	m	m	PROPN
ejpam-6798	277	9	.	.	PUNCT
ejpam-6798	278	1	proof	proof	NOUN
ejpam-6798	278	2	.	.	PUNCT
ejpam-6798	279	1	for	for	ADP
ejpam-6798	279	2	each	each	DET
ejpam-6798	279	3	s	s	X
ejpam-6798	279	4	∈	∈	PROPN
ejpam-6798	279	5	m	m	PRON
ejpam-6798	279	6	,	,	PUNCT
ejpam-6798	279	7	we	we	PRON
ejpam-6798	279	8	have	have	VERB
ejpam-6798	279	9	µ†l(0	µ†l(0	NOUN
ejpam-6798	279	10	)	)	PUNCT
ejpam-6798	280	1	=	=	SYM
ejpam-6798	281	1	(	(	PUNCT
ejpam-6798	281	2	12∨γl(0))e	12∨γl(0))e	NUM
ejpam-6798	281	3	ι	ι	PROPN
ejpam-6798	281	4	(	(	PUNCT
ejpam-6798	281	5	1	1	NUM
ejpam-6798	281	6	2	2	NUM
ejpam-6798	281	7	∨θl(0	∨θl(0	NOUN
ejpam-6798	281	8	)	)	PUNCT
ejpam-6798	281	9	)	)	PUNCT
ejpam-6798	281	10	≥	≥	NOUN
ejpam-6798	281	11	(	(	PUNCT
ejpam-6798	281	12	12∨γl(s))e	12∨γl(s))e	NUM
ejpam-6798	281	13	ι	ι	PROPN
ejpam-6798	281	14	(	(	PUNCT
ejpam-6798	281	15	1	1	NUM
ejpam-6798	281	16	2	2	NUM
ejpam-6798	281	17	∨θl(s	∨θl(s	PROPN
ejpam-6798	281	18	)	)	PUNCT
ejpam-6798	281	19	)	)	PUNCT
ejpam-6798	282	1	=	=	SYM
ejpam-6798	282	2	µ†l(s	µ†l(s	NOUN
ejpam-6798	282	3	)	)	PUNCT
ejpam-6798	282	4	.	.	PUNCT
ejpam-6798	283	1	let	let	VERB
ejpam-6798	283	2	s	s	PRON
ejpam-6798	283	3	,	,	PUNCT
ejpam-6798	283	4	l	l	PROPN
ejpam-6798	283	5	∈	∈	PROPN
ejpam-6798	283	6	m	m	X
ejpam-6798	283	7	,	,	PUNCT
ejpam-6798	283	8	then	then	ADV
ejpam-6798	283	9	µ†l(s	µ†l(s	VERB
ejpam-6798	283	10	⋆	⋆	PUNCT
ejpam-6798	283	11	l	l	NOUN
ejpam-6798	283	12	)	)	PUNCT
ejpam-6798	283	13	=	=	PUNCT
ejpam-6798	284	1	(	(	PUNCT
ejpam-6798	284	2	12	12	NUM
ejpam-6798	284	3	∨	∨	NOUN
ejpam-6798	284	4	γl(s	γl(s	PUNCT
ejpam-6798	284	5	⋆	⋆	VERB
ejpam-6798	284	6	l))e	l))e	PROPN
ejpam-6798	284	7	ι	ι	PROPN
ejpam-6798	284	8	(	(	PUNCT
ejpam-6798	284	9	1	1	NUM
ejpam-6798	284	10	2	2	NUM
ejpam-6798	284	11	∨θl(s⋆l	∨θl(s⋆l	NOUN
ejpam-6798	284	12	)	)	PUNCT
ejpam-6798	284	13	)	)	PUNCT
ejpam-6798	284	14	≥	≥	NOUN
ejpam-6798	284	15	1	1	NUM
ejpam-6798	284	16	2	2	NUM
ejpam-6798	284	17	∨	∨	NUM
ejpam-6798	284	18	(	(	PUNCT
ejpam-6798	284	19	γl(s	γl(s	NOUN
ejpam-6798	284	20	)	)	PUNCT
ejpam-6798	284	21	∧	∧	NOUN
ejpam-6798	284	22	γl(l	γl(l	NUM
ejpam-6798	284	23	)	)	PUNCT
ejpam-6798	284	24	)	)	PUNCT
ejpam-6798	285	1	eι	eι	PROPN
ejpam-6798	285	2	(	(	PUNCT
ejpam-6798	285	3	1	1	NUM
ejpam-6798	285	4	2	2	NUM
ejpam-6798	285	5	∨(γl(s)∧γl(l	∨(γl(s)∧γl(l	NOUN
ejpam-6798	285	6	)	)	PUNCT
ejpam-6798	285	7	)	)	PUNCT
ejpam-6798	285	8	)	)	PUNCT
ejpam-6798	286	1	=	=	PUNCT
ejpam-6798	286	2	(	(	PUNCT
ejpam-6798	286	3	12	12	NUM
ejpam-6798	286	4	∨	∨	NOUN
ejpam-6798	286	5	(	(	PUNCT
ejpam-6798	286	6	γl(s))e	γl(s))e	X
ejpam-6798	286	7	ι	ι	X
ejpam-6798	286	8	(	(	PUNCT
ejpam-6798	286	9	1	1	NUM
ejpam-6798	286	10	2	2	NUM
ejpam-6798	286	11	∨(γl(s	∨(γl(s	NOUN
ejpam-6798	286	12	)	)	PUNCT
ejpam-6798	286	13	)	)	PUNCT
ejpam-6798	286	14	)	)	PUNCT
ejpam-6798	286	15	)	)	PUNCT
ejpam-6798	287	1	∧	∧	NOUN
ejpam-6798	287	2	(	(	PUNCT
ejpam-6798	287	3	12	12	NUM
ejpam-6798	287	4	∨	∨	NOUN
ejpam-6798	287	5	(	(	PUNCT
ejpam-6798	287	6	γl(l))e	γl(l))e	X
ejpam-6798	287	7	ι	ι	X
ejpam-6798	287	8	(	(	PUNCT
ejpam-6798	287	9	1	1	NUM
ejpam-6798	287	10	2	2	NUM
ejpam-6798	287	11	∨(γl(l	∨(γl(l	NUM
ejpam-6798	287	12	)	)	PUNCT
ejpam-6798	287	13	)	)	PUNCT
ejpam-6798	287	14	)	)	PUNCT
ejpam-6798	287	15	)	)	PUNCT
ejpam-6798	288	1	=	=	SYM
ejpam-6798	288	2	µ†l(s	µ†l(s	ADJ
ejpam-6798	288	3	)	)	PUNCT
ejpam-6798	288	4	∧	∧	NOUN
ejpam-6798	288	5	µ†l(l	µ†l(l	ADJ
ejpam-6798	288	6	)	)	PUNCT
ejpam-6798	288	7	.	.	PUNCT
ejpam-6798	289	1	for	for	ADP
ejpam-6798	289	2	each	each	DET
ejpam-6798	289	3	s	s	X
ejpam-6798	289	4	∈	∈	PROPN
ejpam-6798	289	5	m	m	PRON
ejpam-6798	289	6	,	,	PUNCT
ejpam-6798	289	7	we	we	PRON
ejpam-6798	289	8	have	have	VERB
ejpam-6798	289	9	ν†l(0	ν†l(0	PRON
ejpam-6798	289	10	)	)	PUNCT
ejpam-6798	290	1	=	=	SYM
ejpam-6798	290	2	(	(	PUNCT
ejpam-6798	290	3	12	12	NUM
ejpam-6798	290	4	∧	∧	PROPN
ejpam-6798	290	5	γl(0))e	γl(0))e	ADJ
ejpam-6798	290	6	ι	ι	X
ejpam-6798	290	7	(	(	PUNCT
ejpam-6798	290	8	1	1	NUM
ejpam-6798	290	9	2	2	NUM
ejpam-6798	290	10	∧θl(0	∧θl(0	NOUN
ejpam-6798	290	11	)	)	PUNCT
ejpam-6798	290	12	)	)	PUNCT
ejpam-6798	290	13	≤	≤	NOUN
ejpam-6798	290	14	(	(	PUNCT
ejpam-6798	290	15	12	12	NUM
ejpam-6798	290	16	∧	∧	PROPN
ejpam-6798	290	17	γl(s))e	γl(s))e	X
ejpam-6798	290	18	ι	ι	X
ejpam-6798	290	19	(	(	PUNCT
ejpam-6798	290	20	1	1	NUM
ejpam-6798	290	21	2	2	NUM
ejpam-6798	290	22	∧θl(s	∧θl(s	ADJ
ejpam-6798	290	23	)	)	PUNCT
ejpam-6798	290	24	)	)	PUNCT
ejpam-6798	290	25	=	=	SYM
ejpam-6798	290	26	ν†l(s	ν†l(s	NOUN
ejpam-6798	290	27	)	)	PUNCT
ejpam-6798	290	28	.	.	PUNCT
ejpam-6798	290	29	suppose	suppose	VERB
ejpam-6798	290	30	that	that	SCONJ
ejpam-6798	290	31	s	s	SYM
ejpam-6798	290	32	,	,	PUNCT
ejpam-6798	290	33	l	l	PROPN
ejpam-6798	290	34	∈	∈	PROPN
ejpam-6798	290	35	m	m	NOUN
ejpam-6798	290	36	,	,	PUNCT
ejpam-6798	290	37	then	then	ADV
ejpam-6798	290	38	ν†l(s	ν†l(s	NOUN
ejpam-6798	290	39	⋆	⋆	PROPN
ejpam-6798	290	40	l	l	NOUN
ejpam-6798	290	41	)	)	PUNCT
ejpam-6798	290	42	=	=	SYM
ejpam-6798	290	43	(	(	PUNCT
ejpam-6798	290	44	12	12	NUM
ejpam-6798	290	45	∧	∧	PROPN
ejpam-6798	290	46	γl(s	γl(s	PUNCT
ejpam-6798	290	47	⋆	⋆	VERB
ejpam-6798	290	48	l))eι	l))eι	PROPN
ejpam-6798	290	49	(	(	PUNCT
ejpam-6798	290	50	1	1	NUM
ejpam-6798	290	51	2	2	NUM
ejpam-6798	290	52	∧θl(s⋆l	∧θl(s⋆l	NUM
ejpam-6798	290	53	)	)	PUNCT
ejpam-6798	290	54	)	)	PUNCT
ejpam-6798	290	55	≤	≤	NUM
ejpam-6798	290	56	1	1	NUM
ejpam-6798	290	57	2	2	NUM
ejpam-6798	290	58	∧	∧	PROPN
ejpam-6798	290	59	(	(	PUNCT
ejpam-6798	290	60	γl(s	γl(s	NOUN
ejpam-6798	290	61	)	)	PUNCT
ejpam-6798	290	62	∨	∨	NUM
ejpam-6798	290	63	γl(l))e	γl(l))e	PUNCT
ejpam-6798	290	64	ι	ι	X
ejpam-6798	290	65	(	(	PUNCT
ejpam-6798	290	66	1	1	NUM
ejpam-6798	290	67	2	2	NUM
ejpam-6798	290	68	∧(γl(s)∨γl(l	∧(γl(s)∨γl(l	NUM
ejpam-6798	290	69	)	)	PUNCT
ejpam-6798	290	70	)	)	PUNCT
ejpam-6798	290	71	)	)	PUNCT
ejpam-6798	291	1	=	=	PUNCT
ejpam-6798	291	2	(	(	PUNCT
ejpam-6798	291	3	12	12	NUM
ejpam-6798	291	4	∧	∧	PROPN
ejpam-6798	291	5	(	(	PUNCT
ejpam-6798	291	6	γl(s))e	γl(s))e	X
ejpam-6798	291	7	ι	ι	X
ejpam-6798	291	8	(	(	PUNCT
ejpam-6798	291	9	1	1	NUM
ejpam-6798	291	10	2	2	NUM
ejpam-6798	291	11	∧(γl(s	∧(γl(s	NUM
ejpam-6798	291	12	)	)	PUNCT
ejpam-6798	291	13	)	)	PUNCT
ejpam-6798	291	14	)	)	PUNCT
ejpam-6798	291	15	)	)	PUNCT
ejpam-6798	292	1	∨	∨	NUM
ejpam-6798	292	2	(	(	PUNCT
ejpam-6798	292	3	12	12	NUM
ejpam-6798	292	4	∧	∧	PROPN
ejpam-6798	292	5	(	(	PUNCT
ejpam-6798	292	6	γl(l))e	γl(l))e	X
ejpam-6798	292	7	ι	ι	X
ejpam-6798	292	8	(	(	PUNCT
ejpam-6798	292	9	1	1	NUM
ejpam-6798	292	10	2	2	NUM
ejpam-6798	292	11	∧(γl(l	∧(γl(l	NOUN
ejpam-6798	292	12	)	)	PUNCT
ejpam-6798	292	13	)	)	PUNCT
ejpam-6798	292	14	)	)	PUNCT
ejpam-6798	292	15	)	)	PUNCT
ejpam-6798	292	16	=	=	SYM
ejpam-6798	292	17	ν†l(s	ν†l(s	NOUN
ejpam-6798	292	18	)	)	PUNCT
ejpam-6798	292	19	∨	∨	NUM
ejpam-6798	292	20	ν†l(l	ν†l(l	ADV
ejpam-6798	292	21	)	)	PUNCT
ejpam-6798	292	22	.	.	PUNCT
ejpam-6798	293	1	therefore	therefore	ADV
ejpam-6798	293	2	,	,	PUNCT
ejpam-6798	293	3	†l	†l	NOUN
ejpam-6798	293	4	is	be	AUX
ejpam-6798	293	5	a	a	DET
ejpam-6798	293	6	cifs	cifs	NOUN
ejpam-6798	293	7	l	l	NOUN
ejpam-6798	293	8	of	of	ADP
ejpam-6798	293	9	m	m	PROPN
ejpam-6798	293	10	.	.	PUNCT
ejpam-6798	294	1	definition	definition	NOUN
ejpam-6798	294	2	12	12	NUM
ejpam-6798	294	3	.	.	PUNCT
ejpam-6798	295	1	let	let	VERB
ejpam-6798	295	2	l	l	NOUN
ejpam-6798	295	3	be	be	AUX
ejpam-6798	295	4	a	a	DET
ejpam-6798	295	5	cifs	cif	NOUN
ejpam-6798	295	6	of	of	ADP
ejpam-6798	295	7	m	m	PROPN
ejpam-6798	295	8	.	.	PUNCT
ejpam-6798	296	1	then	then	ADV
ejpam-6798	296	2	level	level	NOUN
ejpam-6798	296	3	operator	operator	NOUN
ejpam-6798	296	4	‡l	‡l	NOUN
ejpam-6798	296	5	is	be	AUX
ejpam-6798	296	6	describe	describe	NOUN
ejpam-6798	296	7	as	as	ADP
ejpam-6798	296	8	µ‡l(s	µ‡l(s	ADJ
ejpam-6798	296	9	)	)	PUNCT
ejpam-6798	296	10	=	=	SYM
ejpam-6798	297	1	(	(	PUNCT
ejpam-6798	297	2	12	12	NUM
ejpam-6798	297	3	∧	∧	PROPN
ejpam-6798	297	4	γl(s))e	γl(s))e	X
ejpam-6798	297	5	ι	ι	X
ejpam-6798	297	6	(	(	PUNCT
ejpam-6798	297	7	1	1	NUM
ejpam-6798	297	8	2	2	NUM
ejpam-6798	297	9	∧θl(s	∧θl(s	ADJ
ejpam-6798	297	10	)	)	PUNCT
ejpam-6798	297	11	)	)	PUNCT
ejpam-6798	297	12	,	,	PUNCT
ejpam-6798	297	13	ν‡l(s	ν‡l(s	NOUN
ejpam-6798	297	14	)	)	PUNCT
ejpam-6798	297	15	=	=	PUNCT
ejpam-6798	298	1	(	(	PUNCT
ejpam-6798	298	2	12	12	NUM
ejpam-6798	298	3	∨	∨	NOUN
ejpam-6798	298	4	γl(s))e	γl(s))e	X
ejpam-6798	298	5	ι	ι	X
ejpam-6798	298	6	(	(	PUNCT
ejpam-6798	298	7	1	1	NUM
ejpam-6798	298	8	2	2	NUM
ejpam-6798	298	9	∨θl(s	∨θl(s	PROPN
ejpam-6798	298	10	)	)	PUNCT
ejpam-6798	298	11	)	)	PUNCT
ejpam-6798	298	12	.	.	PUNCT
ejpam-6798	299	1	example	example	NOUN
ejpam-6798	300	1	6	6	NUM
ejpam-6798	300	2	.	.	PUNCT
ejpam-6798	301	1	let	let	VERB
ejpam-6798	301	2	(	(	PUNCT
ejpam-6798	301	3	µl(s	µl(	NOUN
ejpam-6798	301	4	)	)	PUNCT
ejpam-6798	301	5	,	,	PUNCT
ejpam-6798	301	6	νl(s	νl(	NOUN
ejpam-6798	301	7	)	)	PUNCT
ejpam-6798	301	8	)	)	PUNCT
ejpam-6798	302	1	=	=	PRON
ejpam-6798	302	2	{	{	PUNCT
ejpam-6798	302	3	(	(	PUNCT
ejpam-6798	302	4	s	s	X
ejpam-6798	302	5	,	,	PUNCT
ejpam-6798	302	6	0.4eι0.6π	0.4eι0.6π	PROPN
ejpam-6798	302	7	,	,	PUNCT
ejpam-6798	302	8	0.2eι0.4π	0.2eι0.4π	PROPN
ejpam-6798	302	9	)	)	PUNCT
ejpam-6798	302	10	,	,	PUNCT
ejpam-6798	302	11	(	(	PUNCT
ejpam-6798	302	12	l	l	NOUN
ejpam-6798	302	13	,	,	PUNCT
ejpam-6798	302	14	0.6eι0.2π	0.6eι0.2π	PROPN
ejpam-6798	302	15	,	,	PUNCT
ejpam-6798	302	16	0.4eι0.1π	0.4eι0.1π	PROPN
ejpam-6798	302	17	)	)	PUNCT
ejpam-6798	302	18	,	,	PUNCT
ejpam-6798	302	19	(	(	PUNCT
ejpam-6798	302	20	z	z	X
ejpam-6798	302	21	,	,	PUNCT
ejpam-6798	302	22	0.5eι0.7π	0.5eι0.7π	PROPN
ejpam-6798	302	23	,	,	PUNCT
ejpam-6798	302	24	0.3eι0.5π	0.3eι0.5π	PROPN
ejpam-6798	302	25	)	)	PUNCT
ejpam-6798	302	26	}	}	PUNCT
ejpam-6798	302	27	be	be	AUX
ejpam-6798	302	28	a	a	DET
ejpam-6798	302	29	cifs	cif	NOUN
ejpam-6798	302	30	of	of	ADP
ejpam-6798	302	31	m	m	PROPN
ejpam-6798	302	32	.	.	PUNCT
ejpam-6798	303	1	then	then	ADV
ejpam-6798	303	2	(	(	PUNCT
ejpam-6798	303	3	µ‡l(s	µ‡l(s	NOUN
ejpam-6798	303	4	)	)	PUNCT
ejpam-6798	303	5	,	,	PUNCT
ejpam-6798	303	6	ν‡l(s	ν‡l(s	NOUN
ejpam-6798	303	7	)	)	PUNCT
ejpam-6798	303	8	)	)	PUNCT
ejpam-6798	304	1	=	=	PRON
ejpam-6798	304	2	{	{	PUNCT
ejpam-6798	304	3	(	(	PUNCT
ejpam-6798	304	4	s	s	PROPN
ejpam-6798	304	5	,	,	PUNCT
ejpam-6798	304	6	0.4eι0.5π	0.4eι0.5π	PROPN
ejpam-6798	304	7	,	,	PUNCT
ejpam-6798	304	8	0.5eι0.5π	0.5eι0.5π	PROPN
ejpam-6798	304	9	)	)	PUNCT
ejpam-6798	304	10	,	,	PUNCT
ejpam-6798	304	11	(	(	PUNCT
ejpam-6798	304	12	l	l	NOUN
ejpam-6798	304	13	,	,	PUNCT
ejpam-6798	304	14	0.5eι0.2π	0.5eι0.2π	PROPN
ejpam-6798	304	15	,	,	PUNCT
ejpam-6798	304	16	0.5eι0.5π	0.5eι0.5π	PROPN
ejpam-6798	304	17	)	)	PUNCT
ejpam-6798	304	18	,	,	PUNCT
ejpam-6798	304	19	(	(	PUNCT
ejpam-6798	304	20	z	z	X
ejpam-6798	304	21	,	,	PUNCT
ejpam-6798	304	22	0.5eι0.5π	0.5eι0.5π	PROPN
ejpam-6798	304	23	,	,	PUNCT
ejpam-6798	304	24	0.5eι0.5π	0.5eι0.5π	PROPN
ejpam-6798	304	25	)	)	PUNCT
ejpam-6798	304	26	}	}	PUNCT
ejpam-6798	304	27	is	be	AUX
ejpam-6798	304	28	a	a	DET
ejpam-6798	304	29	cifs	cif	NOUN
ejpam-6798	304	30	of	of	ADP
ejpam-6798	304	31	m	m	PRON
ejpam-6798	304	32	.	.	PUNCT
ejpam-6798	305	1	the	the	DET
ejpam-6798	305	2	following	follow	VERB
ejpam-6798	305	3	result	result	NOUN
ejpam-6798	305	4	shows	show	VERB
ejpam-6798	305	5	that	that	SCONJ
ejpam-6798	305	6	the	the	DET
ejpam-6798	305	7	level	level	NOUN
ejpam-6798	305	8	operator	operator	NOUN
ejpam-6798	305	9	‡	‡	NOUN
ejpam-6798	305	10	of	of	ADP
ejpam-6798	305	11	the	the	DET
ejpam-6798	305	12	cifi	cifi	NOUN
ejpam-6798	305	13	of	of	ADP
ejpam-6798	305	14	m	m	PROPN
ejpam-6798	305	15	is	be	AUX
ejpam-6798	305	16	also	also	ADV
ejpam-6798	305	17	cifi	cifi	NOUN
ejpam-6798	305	18	.	.	PUNCT
ejpam-6798	306	1	theorem	theorem	NOUN
ejpam-6798	306	2	5	5	NUM
ejpam-6798	306	3	.	.	PUNCT
ejpam-6798	306	4	suppose	suppose	VERB
ejpam-6798	306	5	that	that	SCONJ
ejpam-6798	306	6	l	l	NOUN
ejpam-6798	306	7	is	be	AUX
ejpam-6798	306	8	a	a	DET
ejpam-6798	306	9	cifs	cif	NOUN
ejpam-6798	306	10	of	of	ADP
ejpam-6798	306	11	m	m	PRON
ejpam-6798	306	12	.	.	PUNCT
ejpam-6798	307	1	then	then	ADV
ejpam-6798	307	2	‡l	‡l	PROPN
ejpam-6798	307	3	is	be	AUX
ejpam-6798	307	4	a	a	DET
ejpam-6798	307	5	cifs	cifs	NOUN
ejpam-6798	307	6	l	l	NOUN
ejpam-6798	307	7	of	of	ADP
ejpam-6798	307	8	m	m	PROPN
ejpam-6798	307	9	.	.	PUNCT
ejpam-6798	308	1	proof	proof	NOUN
ejpam-6798	308	2	.	.	PUNCT
ejpam-6798	309	1	for	for	ADP
ejpam-6798	309	2	each	each	DET
ejpam-6798	309	3	s	s	X
ejpam-6798	309	4	∈	∈	PROPN
ejpam-6798	309	5	m	m	PRON
ejpam-6798	309	6	,	,	PUNCT
ejpam-6798	309	7	we	we	PRON
ejpam-6798	309	8	have	have	VERB
ejpam-6798	309	9	µ‡l(0	µ‡l(0	NOUN
ejpam-6798	309	10	)	)	PUNCT
ejpam-6798	310	1	=	=	SYM
ejpam-6798	310	2	(	(	PUNCT
ejpam-6798	310	3	12∧γl(0))e	12∧γl(0))e	NUM
ejpam-6798	310	4	ι	ι	X
ejpam-6798	310	5	(	(	PUNCT
ejpam-6798	310	6	1	1	NUM
ejpam-6798	310	7	2	2	NUM
ejpam-6798	310	8	∧θl(0	∧θl(0	NOUN
ejpam-6798	310	9	)	)	PUNCT
ejpam-6798	310	10	)	)	PUNCT
ejpam-6798	310	11	≥	≥	X
ejpam-6798	310	12	(	(	PUNCT
ejpam-6798	310	13	12∧γl(s))e	12∧γl(s))e	NUM
ejpam-6798	310	14	ι	ι	X
ejpam-6798	310	15	(	(	PUNCT
ejpam-6798	310	16	1	1	NUM
ejpam-6798	310	17	2	2	NUM
ejpam-6798	310	18	∧θl(s	∧θl(s	ADJ
ejpam-6798	310	19	)	)	PUNCT
ejpam-6798	310	20	)	)	PUNCT
ejpam-6798	311	1	=	=	SYM
ejpam-6798	311	2	µ‡l(s	µ‡l(s	NOUN
ejpam-6798	311	3	)	)	PUNCT
ejpam-6798	311	4	.	.	PUNCT
ejpam-6798	312	1	let	let	VERB
ejpam-6798	312	2	s	s	PRON
ejpam-6798	312	3	,	,	PUNCT
ejpam-6798	312	4	l	l	PROPN
ejpam-6798	312	5	∈	∈	PROPN
ejpam-6798	312	6	m	m	X
ejpam-6798	312	7	,	,	PUNCT
ejpam-6798	312	8	then	then	ADV
ejpam-6798	312	9	µ‡l(s	µ‡l(s	ADJ
ejpam-6798	312	10	⋆	⋆	PROPN
ejpam-6798	312	11	l	l	NOUN
ejpam-6798	312	12	)	)	PUNCT
ejpam-6798	312	13	=	=	SYM
ejpam-6798	312	14	(	(	PUNCT
ejpam-6798	312	15	12	12	NUM
ejpam-6798	312	16	∧	∧	PROPN
ejpam-6798	312	17	γl(s	γl(s	PUNCT
ejpam-6798	312	18	⋆	⋆	VERB
ejpam-6798	312	19	l))e	l))e	PROPN
ejpam-6798	312	20	ι	ι	PROPN
ejpam-6798	312	21	(	(	PUNCT
ejpam-6798	312	22	1	1	NUM
ejpam-6798	312	23	2	2	NUM
ejpam-6798	312	24	∧θl(s⋆l	∧θl(s⋆l	NUM
ejpam-6798	312	25	)	)	PUNCT
ejpam-6798	312	26	)	)	PUNCT
ejpam-6798	312	27	≥	≥	NOUN
ejpam-6798	313	1	1	1	NUM
ejpam-6798	313	2	2	2	NUM
ejpam-6798	313	3	∧	∧	PROPN
ejpam-6798	313	4	(	(	PUNCT
ejpam-6798	313	5	γl(s	γl(s	NOUN
ejpam-6798	313	6	)	)	PUNCT
ejpam-6798	313	7	∧	∧	NOUN
ejpam-6798	313	8	γl(l	γl(l	NUM
ejpam-6798	313	9	)	)	PUNCT
ejpam-6798	313	10	)	)	PUNCT
ejpam-6798	313	11	m.	m.	NOUN
ejpam-6798	313	12	jawad	jawad	PROPN
ejpam-6798	313	13	et	et	PROPN
ejpam-6798	313	14	al	al	PROPN
ejpam-6798	313	15	.	.	PUNCT
ejpam-6798	313	16	/	/	SYM
ejpam-6798	313	17	eur	eur	PROPN
ejpam-6798	313	18	.	.	PUNCT
ejpam-6798	314	1	j.	j.	PROPN
ejpam-6798	314	2	pure	pure	PROPN
ejpam-6798	314	3	appl	appl	PROPN
ejpam-6798	314	4	.	.	PROPN
ejpam-6798	314	5	math	math	PROPN
ejpam-6798	314	6	,	,	PUNCT
ejpam-6798	314	7	18	18	NUM
ejpam-6798	314	8	(	(	PUNCT
ejpam-6798	314	9	4	4	NUM
ejpam-6798	314	10	)	)	PUNCT
ejpam-6798	314	11	(	(	PUNCT
ejpam-6798	314	12	2025	2025	NUM
ejpam-6798	314	13	)	)	PUNCT
ejpam-6798	314	14	,	,	PUNCT
ejpam-6798	314	15	6798	6798	NUM
ejpam-6798	314	16	10	10	NUM
ejpam-6798	314	17	of	of	ADP
ejpam-6798	314	18	22	22	NUM
ejpam-6798	314	19	eι	eι	NOUN
ejpam-6798	314	20	(	(	PUNCT
ejpam-6798	314	21	1	1	NUM
ejpam-6798	314	22	2	2	NUM
ejpam-6798	314	23	∧(γl(s)∧γl(l	∧(γl(s)∧γl(l	PROPN
ejpam-6798	314	24	)	)	PUNCT
ejpam-6798	314	25	)	)	PUNCT
ejpam-6798	314	26	)	)	PUNCT
ejpam-6798	315	1	=	=	PUNCT
ejpam-6798	315	2	(	(	PUNCT
ejpam-6798	315	3	12	12	NUM
ejpam-6798	315	4	∧	∧	PROPN
ejpam-6798	315	5	(	(	PUNCT
ejpam-6798	315	6	γl(s))e	γl(s))e	X
ejpam-6798	315	7	ι	ι	X
ejpam-6798	315	8	(	(	PUNCT
ejpam-6798	315	9	1	1	NUM
ejpam-6798	315	10	2	2	NUM
ejpam-6798	315	11	∧(γl(s	∧(γl(s	NUM
ejpam-6798	315	12	)	)	PUNCT
ejpam-6798	315	13	)	)	PUNCT
ejpam-6798	315	14	)	)	PUNCT
ejpam-6798	315	15	)	)	PUNCT
ejpam-6798	316	1	∧	∧	NOUN
ejpam-6798	316	2	(	(	PUNCT
ejpam-6798	316	3	12	12	NUM
ejpam-6798	316	4	∧	∧	PROPN
ejpam-6798	316	5	(	(	PUNCT
ejpam-6798	316	6	γl(l))e	γl(l))e	X
ejpam-6798	316	7	ι	ι	X
ejpam-6798	316	8	(	(	PUNCT
ejpam-6798	316	9	1	1	NUM
ejpam-6798	316	10	2	2	NUM
ejpam-6798	316	11	∧(γl(l	∧(γl(l	NOUN
ejpam-6798	316	12	)	)	PUNCT
ejpam-6798	316	13	)	)	PUNCT
ejpam-6798	316	14	)	)	PUNCT
ejpam-6798	316	15	)	)	PUNCT
ejpam-6798	317	1	=	=	SYM
ejpam-6798	317	2	µ‡l(s	µ‡l(s	NOUN
ejpam-6798	317	3	)	)	PUNCT
ejpam-6798	317	4	∧	∧	PROPN
ejpam-6798	317	5	µ‡l(l	µ‡l(l	VERB
ejpam-6798	317	6	)	)	PUNCT
ejpam-6798	317	7	.	.	PUNCT
ejpam-6798	318	1	for	for	ADP
ejpam-6798	318	2	each	each	DET
ejpam-6798	318	3	s	s	X
ejpam-6798	318	4	∈	∈	PROPN
ejpam-6798	318	5	m	m	PRON
ejpam-6798	318	6	,	,	PUNCT
ejpam-6798	318	7	we	we	PRON
ejpam-6798	318	8	have	have	VERB
ejpam-6798	318	9	ν‡l(0	ν‡l(0	NOUN
ejpam-6798	318	10	)	)	PUNCT
ejpam-6798	319	1	=	=	PUNCT
ejpam-6798	319	2	(	(	PUNCT
ejpam-6798	319	3	12	12	NUM
ejpam-6798	319	4	∨	∨	NOUN
ejpam-6798	319	5	γl(0))e	γl(0))e	PROPN
ejpam-6798	319	6	ι	ι	X
ejpam-6798	319	7	(	(	PUNCT
ejpam-6798	319	8	1	1	NUM
ejpam-6798	319	9	2	2	NUM
ejpam-6798	319	10	∨θl(0	∨θl(0	NOUN
ejpam-6798	319	11	)	)	PUNCT
ejpam-6798	319	12	)	)	PUNCT
ejpam-6798	319	13	≤	≤	NOUN
ejpam-6798	319	14	(	(	PUNCT
ejpam-6798	319	15	12	12	NUM
ejpam-6798	319	16	∨	∨	NUM
ejpam-6798	319	17	γl(s))e	γl(s))e	X
ejpam-6798	320	1	ι	ι	X
ejpam-6798	320	2	(	(	PUNCT
ejpam-6798	320	3	1	1	NUM
ejpam-6798	320	4	2	2	NUM
ejpam-6798	320	5	∨θl(s	∨θl(s	PROPN
ejpam-6798	320	6	)	)	PUNCT
ejpam-6798	320	7	)	)	PUNCT
ejpam-6798	321	1	=	=	SYM
ejpam-6798	321	2	ν‡l(s	ν‡l(s	NOUN
ejpam-6798	321	3	)	)	PUNCT
ejpam-6798	321	4	.	.	PUNCT
ejpam-6798	322	1	suppose	suppose	VERB
ejpam-6798	322	2	that	that	SCONJ
ejpam-6798	322	3	s	s	SYM
ejpam-6798	322	4	,	,	PUNCT
ejpam-6798	322	5	l	l	PROPN
ejpam-6798	322	6	∈	∈	PROPN
ejpam-6798	322	7	m	m	NOUN
ejpam-6798	322	8	,	,	PUNCT
ejpam-6798	322	9	then	then	ADV
ejpam-6798	322	10	ν‡l(s	ν‡l(s	PROPN
ejpam-6798	322	11	⋆	⋆	PROPN
ejpam-6798	322	12	l	l	NOUN
ejpam-6798	322	13	)	)	PUNCT
ejpam-6798	322	14	=	=	PUNCT
ejpam-6798	322	15	(	(	PUNCT
ejpam-6798	322	16	12	12	NUM
ejpam-6798	322	17	∨	∨	NOUN
ejpam-6798	322	18	γl(s	γl(s	PUNCT
ejpam-6798	322	19	⋆	⋆	X
ejpam-6798	322	20	l))eι	l))eι	PROPN
ejpam-6798	322	21	(	(	PUNCT
ejpam-6798	322	22	1	1	NUM
ejpam-6798	322	23	2	2	NUM
ejpam-6798	322	24	∨θl(s⋆l	∨θl(s⋆l	NOUN
ejpam-6798	322	25	)	)	PUNCT
ejpam-6798	322	26	)	)	PUNCT
ejpam-6798	322	27	≤	≤	NUM
ejpam-6798	322	28	1	1	NUM
ejpam-6798	322	29	2	2	NUM
ejpam-6798	322	30	∨	∨	NUM
ejpam-6798	322	31	(	(	PUNCT
ejpam-6798	322	32	γl(s	γl(	NOUN
ejpam-6798	322	33	)	)	PUNCT
ejpam-6798	322	34	∨	∨	NUM
ejpam-6798	322	35	γl(l))e	γl(l))e	PUNCT
ejpam-6798	322	36	ι	ι	X
ejpam-6798	322	37	(	(	PUNCT
ejpam-6798	322	38	1	1	NUM
ejpam-6798	322	39	2	2	NUM
ejpam-6798	322	40	∨(γl(s)∨γl(l	∨(γl(s)∨γl(l	NOUN
ejpam-6798	322	41	)	)	PUNCT
ejpam-6798	322	42	)	)	PUNCT
ejpam-6798	322	43	)	)	PUNCT
ejpam-6798	323	1	=	=	PUNCT
ejpam-6798	323	2	(	(	PUNCT
ejpam-6798	323	3	12	12	NUM
ejpam-6798	323	4	∨	∨	NOUN
ejpam-6798	323	5	(	(	PUNCT
ejpam-6798	323	6	γl(s))e	γl(s))e	X
ejpam-6798	323	7	ι	ι	X
ejpam-6798	323	8	(	(	PUNCT
ejpam-6798	323	9	1	1	NUM
ejpam-6798	323	10	2	2	NUM
ejpam-6798	323	11	∨(γl(s	∨(γl(s	NOUN
ejpam-6798	323	12	)	)	PUNCT
ejpam-6798	323	13	)	)	PUNCT
ejpam-6798	323	14	)	)	PUNCT
ejpam-6798	323	15	)	)	PUNCT
ejpam-6798	323	16	∨	∨	NUM
ejpam-6798	323	17	(	(	PUNCT
ejpam-6798	323	18	12	12	NUM
ejpam-6798	323	19	∨	∨	NOUN
ejpam-6798	323	20	(	(	PUNCT
ejpam-6798	323	21	γl(l))e	γl(l))e	X
ejpam-6798	323	22	ι	ι	X
ejpam-6798	323	23	(	(	PUNCT
ejpam-6798	323	24	1	1	NUM
ejpam-6798	323	25	2	2	NUM
ejpam-6798	323	26	∨(γl(l	∨(γl(l	NUM
ejpam-6798	323	27	)	)	PUNCT
ejpam-6798	323	28	)	)	PUNCT
ejpam-6798	323	29	)	)	PUNCT
ejpam-6798	323	30	)	)	PUNCT
ejpam-6798	324	1	=	=	SYM
ejpam-6798	324	2	ν‡l(s	ν‡l(s	PROPN
ejpam-6798	324	3	)	)	PUNCT
ejpam-6798	324	4	∨	∨	NUM
ejpam-6798	324	5	ν‡l(l	ν‡l(l	NOUN
ejpam-6798	324	6	)	)	PUNCT
ejpam-6798	324	7	.	.	PUNCT
ejpam-6798	325	1	therefore	therefore	ADV
ejpam-6798	325	2	,	,	PUNCT
ejpam-6798	325	3	‡l	‡l	PROPN
ejpam-6798	325	4	is	be	AUX
ejpam-6798	325	5	a	a	DET
ejpam-6798	325	6	cifs	cifs	NOUN
ejpam-6798	325	7	l	l	NOUN
ejpam-6798	325	8	of	of	ADP
ejpam-6798	325	9	m	m	PROPN
ejpam-6798	325	10	.	.	PUNCT
ejpam-6798	326	1	4	4	X
ejpam-6798	326	2	.	.	X
ejpam-6798	326	3	complex	complex	ADJ
ejpam-6798	326	4	intuitionistic	intuitionistic	ADJ
ejpam-6798	326	5	fuzzy	fuzzy	ADJ
ejpam-6798	326	6	ideals	ideal	NOUN
ejpam-6798	326	7	(	(	PUNCT
ejpam-6798	326	8	cifis	cifis	PROPN
ejpam-6798	326	9	)	)	PUNCT
ejpam-6798	326	10	of	of	ADP
ejpam-6798	326	11	bck	bck	PROPN
ejpam-6798	326	12	/	/	SYM
ejpam-6798	326	13	bci	bci	NOUN
ejpam-6798	326	14	-	-	PUNCT
ejpam-6798	326	15	algebras	algebra	NOUN
ejpam-6798	326	16	in	in	ADP
ejpam-6798	326	17	the	the	DET
ejpam-6798	326	18	following	following	ADJ
ejpam-6798	326	19	part	part	NOUN
ejpam-6798	326	20	,	,	PUNCT
ejpam-6798	326	21	we	we	PRON
ejpam-6798	326	22	will	will	AUX
ejpam-6798	326	23	examine	examine	VERB
ejpam-6798	326	24	fundamental	fundamental	ADJ
ejpam-6798	326	25	concepts	concept	NOUN
ejpam-6798	326	26	about	about	ADP
ejpam-6798	326	27	the	the	DET
ejpam-6798	326	28	cifis	cifis	NOUN
ejpam-6798	326	29	,	,	PUNCT
ejpam-6798	326	30	and	and	CCONJ
ejpam-6798	326	31	cifi	cifi	NOUN
ejpam-6798	326	32	over	over	ADP
ejpam-6798	326	33	the	the	DET
ejpam-6798	326	34	universal	universal	ADJ
ejpam-6798	326	35	set	set	NOUN
ejpam-6798	326	36	m	m	PROPN
ejpam-6798	326	37	.	.	PUNCT
ejpam-6798	327	1	definition	definition	NOUN
ejpam-6798	327	2	13	13	NUM
ejpam-6798	327	3	.	.	PUNCT
ejpam-6798	328	1	a	a	DET
ejpam-6798	328	2	cifs	cifs	NOUN
ejpam-6798	328	3	l	l	NOUN
ejpam-6798	328	4	=	=	SYM
ejpam-6798	328	5	(	(	PUNCT
ejpam-6798	328	6	s	s	X
ejpam-6798	328	7	,	,	PUNCT
ejpam-6798	328	8	µl(s	µl(s	NUM
ejpam-6798	328	9	)	)	PUNCT
ejpam-6798	328	10	,	,	PUNCT
ejpam-6798	328	11	νl(s	νl(	NOUN
ejpam-6798	328	12	)	)	PUNCT
ejpam-6798	328	13	)	)	PUNCT
ejpam-6798	328	14	is	be	AUX
ejpam-6798	328	15	considered	consider	VERB
ejpam-6798	328	16	a	a	DET
ejpam-6798	328	17	cifsa	cifsa	NOUN
ejpam-6798	328	18	of	of	ADP
ejpam-6798	328	19	m	m	PROPN
ejpam-6798	328	20	,	,	PUNCT
ejpam-6798	328	21	where	where	SCONJ
ejpam-6798	328	22	s	s	X
ejpam-6798	328	23	,	,	PUNCT
ejpam-6798	328	24	l	l	PROPN
ejpam-6798	328	25	∈	∈	PROPN
ejpam-6798	328	26	m	m	X
ejpam-6798	328	27	,	,	PUNCT
ejpam-6798	328	28	and	and	CCONJ
ejpam-6798	328	29	the	the	DET
ejpam-6798	328	30	following	follow	VERB
ejpam-6798	328	31	hold	hold	NOUN
ejpam-6798	328	32	:	:	PUNCT
ejpam-6798	328	33	µl(s)e	µl(s)e	X
ejpam-6798	328	34	ιθl(s	ιθl(s	PROPN
ejpam-6798	328	35	)	)	PUNCT
ejpam-6798	328	36	≥	≥	NOUN
ejpam-6798	328	37	µl(s	µl(	NOUN
ejpam-6798	328	38	⋆	⋆	VERB
ejpam-6798	328	39	l)eιθl(s⋆l	l)eιθl(s⋆l	ADJ
ejpam-6798	328	40	)	)	PUNCT
ejpam-6798	328	41	∧	∧	PROPN
ejpam-6798	328	42	µl(l)e	µl(l)e	X
ejpam-6798	328	43	ιθl(l	ιθl(l	PROPN
ejpam-6798	328	44	)	)	PUNCT
ejpam-6798	328	45	,	,	PUNCT
ejpam-6798	328	46	∀s	∀s	PROPN
ejpam-6798	328	47	,	,	PUNCT
ejpam-6798	329	1	l	l	PROPN
ejpam-6798	329	2	∈	∈	PROPN
ejpam-6798	329	3	m	m	NOUN
ejpam-6798	329	4	,	,	PUNCT
ejpam-6798	329	5	νl(s)e	νl(s)e	PROPN
ejpam-6798	329	6	ιθl(s	ιθl(s	PROPN
ejpam-6798	329	7	)	)	PUNCT
ejpam-6798	329	8	≤	≤	NOUN
ejpam-6798	329	9	νl(s	νl(s	PUNCT
ejpam-6798	329	10	⋆	⋆	X
ejpam-6798	329	11	l)e	l)e	X
ejpam-6798	329	12	ιθl(s⋆l	ιθl(s⋆l	NOUN
ejpam-6798	329	13	)	)	PUNCT
ejpam-6798	329	14	∨	∨	NOUN
ejpam-6798	329	15	νl(l)e	νl(l)e	X
ejpam-6798	329	16	ιθl(l	ιθl(l	PROPN
ejpam-6798	329	17	)	)	PUNCT
ejpam-6798	329	18	,	,	PUNCT
ejpam-6798	329	19	∀s	∀s	PROPN
ejpam-6798	329	20	,	,	PUNCT
ejpam-6798	329	21	l	l	PROPN
ejpam-6798	329	22	∈	∈	PROPN
ejpam-6798	329	23	m	m	NOUN
ejpam-6798	329	24	.	.	PUNCT
ejpam-6798	330	1	example	example	NOUN
ejpam-6798	331	1	7	7	NUM
ejpam-6798	331	2	.	.	X
ejpam-6798	331	3	take	take	VERB
ejpam-6798	331	4	a	a	DET
ejpam-6798	331	5	bck	bck	NOUN
ejpam-6798	331	6	-	-	PUNCT
ejpam-6798	331	7	algebra	algebra	NOUN
ejpam-6798	331	8	m	m	NOUN
ejpam-6798	331	9	=	=	SYM
ejpam-6798	331	10	{	{	PUNCT
ejpam-6798	331	11	0	0	NUM
ejpam-6798	331	12	,	,	PUNCT
ejpam-6798	331	13	s	s	X
ejpam-6798	331	14	,	,	PUNCT
ejpam-6798	331	15	l	l	NOUN
ejpam-6798	331	16	,	,	PUNCT
ejpam-6798	331	17	z	z	NOUN
ejpam-6798	331	18	}	}	PUNCT
ejpam-6798	331	19	,	,	PUNCT
ejpam-6798	331	20	where	where	SCONJ
ejpam-6798	331	21	the	the	DET
ejpam-6798	331	22	binary	binary	ADJ
ejpam-6798	331	23	operation	operation	NOUN
ejpam-6798	331	24	is	be	AUX
ejpam-6798	331	25	defined	define	VERB
ejpam-6798	331	26	by	by	ADP
ejpam-6798	331	27	the	the	DET
ejpam-6798	331	28	caley	caley	NOUN
ejpam-6798	331	29	table	table	NOUN
ejpam-6798	331	30	4	4	NUM
ejpam-6798	331	31	.	.	PUNCT
ejpam-6798	332	1	now	now	ADV
ejpam-6798	332	2	describe	describe	VERB
ejpam-6798	332	3	a	a	DET
ejpam-6798	332	4	cifs	cif	NOUN
ejpam-6798	332	5	on	on	ADP
ejpam-6798	332	6	m	m	NOUN
ejpam-6798	332	7	as	as	ADP
ejpam-6798	332	8	:	:	PUNCT
ejpam-6798	332	9	l	l	NOUN
ejpam-6798	332	10	=	=	SYM
ejpam-6798	332	11	{	{	PUNCT
ejpam-6798	332	12	(	(	PUNCT
ejpam-6798	332	13	0	0	NUM
ejpam-6798	332	14	,	,	PUNCT
ejpam-6798	332	15	0.67eι0.5π	0.67eι0.5π	NUM
ejpam-6798	332	16	,	,	PUNCT
ejpam-6798	332	17	0.47eι0.25π	0.47eι0.25π	NOUN
ejpam-6798	332	18	)	)	PUNCT
ejpam-6798	332	19	,	,	PUNCT
ejpam-6798	332	20	(	(	PUNCT
ejpam-6798	332	21	s	s	X
ejpam-6798	332	22	,	,	PUNCT
ejpam-6798	332	23	0.34eι0.43π	0.34eι0.43π	ADJ
ejpam-6798	332	24	,	,	PUNCT
ejpam-6798	332	25	0.14eι0.23π	0.14eι0.23π	NUM
ejpam-6798	332	26	)	)	PUNCT
ejpam-6798	332	27	,	,	PUNCT
ejpam-6798	332	28	(	(	PUNCT
ejpam-6798	332	29	l	l	NOUN
ejpam-6798	332	30	,	,	PUNCT
ejpam-6798	332	31	0.67eι0.05π	0.67eι0.05π	NUM
ejpam-6798	332	32	,	,	PUNCT
ejpam-6798	332	33	0.47eι0.025π	0.47eι0.025π	NUM
ejpam-6798	332	34	)	)	PUNCT
ejpam-6798	332	35	,	,	PUNCT
ejpam-6798	332	36	(	(	PUNCT
ejpam-6798	332	37	z	z	X
ejpam-6798	332	38	,	,	PUNCT
ejpam-6798	332	39	0.34eι0.43π	0.34eι0.43π	ADJ
ejpam-6798	332	40	,	,	PUNCT
ejpam-6798	332	41	0.14eι0.23π	0.14eι0.23π	NUM
ejpam-6798	332	42	)	)	PUNCT
ejpam-6798	332	43	,	,	PUNCT
ejpam-6798	332	44	(	(	PUNCT
ejpam-6798	332	45	w	w	NOUN
ejpam-6798	332	46	,	,	PUNCT
ejpam-6798	332	47	0.34eι0.43π	0.34eι0.43π	ADJ
ejpam-6798	332	48	,	,	PUNCT
ejpam-6798	332	49	0.14eι0.23π	0.14eι0.23π	NUM
ejpam-6798	332	50	)	)	PUNCT
ejpam-6798	332	51	}	}	PUNCT
ejpam-6798	332	52	.	.	PUNCT
ejpam-6798	333	1	it	it	PRON
ejpam-6798	333	2	is	be	AUX
ejpam-6798	333	3	straightforward	straightforward	ADJ
ejpam-6798	333	4	to	to	PART
ejpam-6798	333	5	prove	prove	VERB
ejpam-6798	333	6	that	that	SCONJ
ejpam-6798	333	7	l	l	NOUN
ejpam-6798	333	8	is	be	AUX
ejpam-6798	333	9	a	a	DET
ejpam-6798	333	10	cifi	cifi	NOUN
ejpam-6798	333	11	of	of	ADP
ejpam-6798	333	12	m	m	PROPN
ejpam-6798	333	13	.	.	PUNCT
ejpam-6798	334	1	table	table	NOUN
ejpam-6798	334	2	4	4	NUM
ejpam-6798	334	3	:	:	PUNCT
ejpam-6798	334	4	cayley	cayley	PROPN
ejpam-6798	334	5	’s	’s	PART
ejpam-6798	334	6	table	table	NOUN
ejpam-6798	334	7	describing	describe	VERB
ejpam-6798	334	8	the	the	DET
ejpam-6798	334	9	binary	binary	ADJ
ejpam-6798	334	10	operation	operation	NOUN
ejpam-6798	334	11	expressed	express	VERB
ejpam-6798	334	12	by	by	ADP
ejpam-6798	334	13	“	"	PUNCT
ejpam-6798	334	14	⋆	⋆	VERB
ejpam-6798	334	15	”	"	PUNCT
ejpam-6798	334	16	.	.	PUNCT
ejpam-6798	335	1	⋆	⋆	VERB
ejpam-6798	335	2	0	0	NUM
ejpam-6798	335	3	s	s	PART
ejpam-6798	335	4	l	l	NOUN
ejpam-6798	335	5	z	z	PROPN
ejpam-6798	335	6	w	w	NOUN
ejpam-6798	335	7	0	0	NUM
ejpam-6798	335	8	0	0	NUM
ejpam-6798	335	9	0	0	NUM
ejpam-6798	335	10	0	0	NUM
ejpam-6798	335	11	0	0	NUM
ejpam-6798	335	12	0	0	NUM
ejpam-6798	336	1	s	s	NOUN
ejpam-6798	336	2	s	s	NOUN
ejpam-6798	336	3	0	0	NUM
ejpam-6798	336	4	s	s	NOUN
ejpam-6798	336	5	0	0	NUM
ejpam-6798	336	6	0	0	NUM
ejpam-6798	336	7	l	l	NOUN
ejpam-6798	336	8	l	l	NOUN
ejpam-6798	336	9	l	l	NOUN
ejpam-6798	336	10	0	0	NUM
ejpam-6798	336	11	0	0	NUM
ejpam-6798	336	12	0	0	NUM
ejpam-6798	337	1	z	z	NOUN
ejpam-6798	337	2	z	z	NOUN
ejpam-6798	337	3	z	z	NOUN
ejpam-6798	337	4	z	z	NOUN
ejpam-6798	337	5	0	0	NUM
ejpam-6798	337	6	0	0	NUM
ejpam-6798	338	1	w	w	PROPN
ejpam-6798	338	2	w	w	PROPN
ejpam-6798	338	3	z	z	PROPN
ejpam-6798	338	4	w	w	PROPN
ejpam-6798	338	5	s	s	PROPN
ejpam-6798	338	6	0	0	NUM
ejpam-6798	339	1	the	the	DET
ejpam-6798	339	2	next	next	ADJ
ejpam-6798	339	3	theorem	theorem	NOUN
ejpam-6798	339	4	shows	show	VERB
ejpam-6798	339	5	that	that	SCONJ
ejpam-6798	339	6	every	every	DET
ejpam-6798	339	7	cifi	cifi	NOUN
ejpam-6798	339	8	of	of	ADP
ejpam-6798	339	9	m	m	PROPN
ejpam-6798	339	10	is	be	AUX
ejpam-6798	339	11	also	also	ADV
ejpam-6798	339	12	order	order	NOUN
ejpam-6798	339	13	preserving	preserve	VERB
ejpam-6798	339	14	.	.	PUNCT
ejpam-6798	340	1	theorem	theorem	ADJ
ejpam-6798	340	2	6	6	NUM
ejpam-6798	340	3	.	.	PUNCT
ejpam-6798	341	1	every	every	DET
ejpam-6798	341	2	cifi	cifi	NOUN
ejpam-6798	341	3	of	of	ADP
ejpam-6798	341	4	m	m	PROPN
ejpam-6798	341	5	is	be	AUX
ejpam-6798	341	6	order	order	NOUN
ejpam-6798	341	7	-	-	PUNCT
ejpam-6798	341	8	preserving	preserve	VERB
ejpam-6798	341	9	.	.	PUNCT
ejpam-6798	342	1	proof	proof	NOUN
ejpam-6798	342	2	.	.	PUNCT
ejpam-6798	343	1	assume	assume	VERB
ejpam-6798	343	2	that	that	SCONJ
ejpam-6798	343	3	l	l	NOUN
ejpam-6798	343	4	is	be	AUX
ejpam-6798	343	5	a	a	DET
ejpam-6798	343	6	cifsa	cifsa	NOUN
ejpam-6798	343	7	of	of	ADP
ejpam-6798	343	8	m	m	PRON
ejpam-6798	343	9	and	and	CCONJ
ejpam-6798	343	10	assume	assume	VERB
ejpam-6798	343	11	that	that	SCONJ
ejpam-6798	343	12	s	s	SYM
ejpam-6798	343	13	,	,	PUNCT
ejpam-6798	343	14	l	l	PROPN
ejpam-6798	343	15	∈	∈	PROPN
ejpam-6798	343	16	m	m	VERB
ejpam-6798	343	17	are	be	AUX
ejpam-6798	343	18	such	such	ADJ
ejpam-6798	343	19	that	that	PRON
ejpam-6798	343	20	s	s	VERB
ejpam-6798	343	21	≤	≤	PROPN
ejpam-6798	343	22	l.	l.	NOUN
ejpam-6798	343	23	then	then	ADV
ejpam-6798	343	24	µl(s	µl(	NOUN
ejpam-6798	343	25	)	)	PUNCT
ejpam-6798	344	1	=	=	SYM
ejpam-6798	344	2	γl(s)e	γl(s)e	NUM
ejpam-6798	344	3	ιθl(s	ιθl(s	PROPN
ejpam-6798	344	4	)	)	PUNCT
ejpam-6798	344	5	≥	≥	NOUN
ejpam-6798	344	6	γl(s	γl(s	PUNCT
ejpam-6798	344	7	⋆	⋆	X
ejpam-6798	344	8	l)e	l)e	X
ejpam-6798	344	9	ιθl(s⋆l	ιθl(s⋆l	NOUN
ejpam-6798	344	10	)	)	PUNCT
ejpam-6798	344	11	∧	∧	NOUN
ejpam-6798	344	12	γl(l)e	γl(l)e	NUM
ejpam-6798	344	13	ιθl(l	ιθl(l	PROPN
ejpam-6798	344	14	)	)	PUNCT
ejpam-6798	344	15	=	=	PUNCT
ejpam-6798	344	16	(	(	PUNCT
ejpam-6798	344	17	γl(s	γl(s	PUNCT
ejpam-6798	344	18	⋆	⋆	X
ejpam-6798	344	19	l	l	NOUN
ejpam-6798	344	20	)	)	PUNCT
ejpam-6798	344	21	∧	∧	PROPN
ejpam-6798	344	22	γl(l))e	γl(l))e	PUNCT
ejpam-6798	344	23	ι(θl(s⋆l)∧θl(l	ι(θl(s⋆l)∧θl(l	NOUN
ejpam-6798	344	24	)	)	PUNCT
ejpam-6798	344	25	)	)	PUNCT
ejpam-6798	345	1	=	=	SYM
ejpam-6798	345	2	(	(	PUNCT
ejpam-6798	345	3	γl(0	γl(0	PROPN
ejpam-6798	345	4	)	)	PUNCT
ejpam-6798	345	5	∧	∧	PROPN
ejpam-6798	345	6	γl(0))e	γl(0))e	NOUN
ejpam-6798	345	7	ι(θl(0)∧θl(0	ι(θl(0)∧θl(0	PROPN
ejpam-6798	345	8	)	)	PUNCT
ejpam-6798	345	9	)	)	PUNCT
ejpam-6798	346	1	=	=	SYM
ejpam-6798	346	2	γl(l)e	γl(l)e	NUM
ejpam-6798	346	3	ιθl(l	ιθl(l	PROPN
ejpam-6798	346	4	)	)	PUNCT
ejpam-6798	346	5	≥	≥	NOUN
ejpam-6798	346	6	µl(l	µl(l	NUM
ejpam-6798	346	7	)	)	PUNCT
ejpam-6798	346	8	.	.	PUNCT
ejpam-6798	347	1	and	and	CCONJ
ejpam-6798	347	2	νl(s	νl(	NOUN
ejpam-6798	347	3	)	)	PUNCT
ejpam-6798	347	4	=	=	SYM
ejpam-6798	347	5	γl(s)e	γl(s)e	NUM
ejpam-6798	347	6	ιθl(s	ιθl(s	PROPN
ejpam-6798	347	7	)	)	PUNCT
ejpam-6798	347	8	m.	m.	NOUN
ejpam-6798	347	9	jawad	jawad	PROPN
ejpam-6798	347	10	et	et	PROPN
ejpam-6798	347	11	al	al	PROPN
ejpam-6798	347	12	.	.	PUNCT
ejpam-6798	347	13	/	/	SYM
ejpam-6798	347	14	eur	eur	PROPN
ejpam-6798	347	15	.	.	PUNCT
ejpam-6798	348	1	j.	j.	PROPN
ejpam-6798	348	2	pure	pure	PROPN
ejpam-6798	348	3	appl	appl	PROPN
ejpam-6798	348	4	.	.	PROPN
ejpam-6798	348	5	math	math	PROPN
ejpam-6798	348	6	,	,	PUNCT
ejpam-6798	348	7	18	18	NUM
ejpam-6798	348	8	(	(	PUNCT
ejpam-6798	348	9	4	4	NUM
ejpam-6798	348	10	)	)	PUNCT
ejpam-6798	348	11	(	(	PUNCT
ejpam-6798	348	12	2025	2025	NUM
ejpam-6798	348	13	)	)	PUNCT
ejpam-6798	348	14	,	,	PUNCT
ejpam-6798	348	15	6798	6798	NUM
ejpam-6798	348	16	11	11	NUM
ejpam-6798	348	17	of	of	ADP
ejpam-6798	348	18	22	22	NUM
ejpam-6798	348	19	≤	≤	NOUN
ejpam-6798	348	20	γl(s	γl(s	PUNCT
ejpam-6798	348	21	⋆	⋆	X
ejpam-6798	348	22	l)e	l)e	X
ejpam-6798	348	23	ιθl(s⋆l	ιθl(s⋆l	NOUN
ejpam-6798	348	24	)	)	PUNCT
ejpam-6798	348	25	∨	∨	NUM
ejpam-6798	348	26	γl(l)e	γl(l)e	NUM
ejpam-6798	348	27	ιθl(l	ιθl(l	PROPN
ejpam-6798	348	28	)	)	PUNCT
ejpam-6798	348	29	=	=	PUNCT
ejpam-6798	348	30	(	(	PUNCT
ejpam-6798	348	31	γl(s	γl(s	PUNCT
ejpam-6798	348	32	⋆	⋆	X
ejpam-6798	348	33	l	l	NOUN
ejpam-6798	348	34	)	)	PUNCT
ejpam-6798	348	35	∨	∨	NUM
ejpam-6798	348	36	γl(l))e	γl(l))e	PUNCT
ejpam-6798	348	37	ι(θl(s⋆l)∨θl(l	ι(θl(s⋆l)∨θl(l	NOUN
ejpam-6798	348	38	)	)	PUNCT
ejpam-6798	348	39	)	)	PUNCT
ejpam-6798	349	1	=	=	SYM
ejpam-6798	349	2	(	(	PUNCT
ejpam-6798	349	3	γl(0	γl(0	PROPN
ejpam-6798	349	4	)	)	PUNCT
ejpam-6798	349	5	∨	∨	PROPN
ejpam-6798	349	6	γl(0))e	γl(0))e	PROPN
ejpam-6798	349	7	ι(θl(0)∨θl(0	ι(θl(0)∨θl(0	NOUN
ejpam-6798	349	8	)	)	PUNCT
ejpam-6798	349	9	)	)	PUNCT
ejpam-6798	350	1	=	=	SYM
ejpam-6798	350	2	γl(l)e	γl(l)e	NUM
ejpam-6798	350	3	ιθl(l	ιθl(l	PROPN
ejpam-6798	350	4	)	)	PUNCT
ejpam-6798	350	5	≤	≤	NOUN
ejpam-6798	350	6	νl(l	νl(l	NOUN
ejpam-6798	350	7	)	)	PUNCT
ejpam-6798	350	8	.	.	PUNCT
ejpam-6798	351	1	this	this	PRON
ejpam-6798	351	2	concludes	conclude	VERB
ejpam-6798	351	3	the	the	DET
ejpam-6798	351	4	proof	proof	NOUN
ejpam-6798	351	5	.	.	PUNCT
ejpam-6798	352	1	the	the	DET
ejpam-6798	352	2	next	next	ADJ
ejpam-6798	352	3	theorem	theorem	NOUN
ejpam-6798	352	4	shows	show	VERB
ejpam-6798	352	5	that	that	SCONJ
ejpam-6798	352	6	every	every	DET
ejpam-6798	352	7	cifi	cifi	NOUN
ejpam-6798	352	8	of	of	ADP
ejpam-6798	352	9	the	the	DET
ejpam-6798	352	10	set	set	NOUN
ejpam-6798	352	11	is	be	AUX
ejpam-6798	352	12	equal	equal	ADJ
ejpam-6798	352	13	to	to	ADP
ejpam-6798	352	14	a	a	DET
ejpam-6798	352	15	cifsa	cifsa	NOUN
ejpam-6798	352	16	.	.	PUNCT
ejpam-6798	353	1	theorem	theorem	VERB
ejpam-6798	353	2	7	7	NUM
ejpam-6798	353	3	.	.	PUNCT
ejpam-6798	354	1	every	every	DET
ejpam-6798	354	2	cifi	cifi	NOUN
ejpam-6798	354	3	of	of	ADP
ejpam-6798	354	4	m	m	PROPN
ejpam-6798	354	5	is	be	AUX
ejpam-6798	354	6	a	a	DET
ejpam-6798	354	7	cifsa	cifsa	NOUN
ejpam-6798	354	8	of	of	ADP
ejpam-6798	354	9	m	m	PROPN
ejpam-6798	354	10	.	.	PUNCT
ejpam-6798	355	1	proof	proof	NOUN
ejpam-6798	355	2	.	.	PUNCT
ejpam-6798	356	1	since	since	SCONJ
ejpam-6798	356	2	s	s	PRON
ejpam-6798	356	3	⋆	⋆	PUNCT
ejpam-6798	356	4	l	l	NOUN
ejpam-6798	356	5	≤	≤	PROPN
ejpam-6798	356	6	s	s	X
ejpam-6798	356	7	,	,	PUNCT
ejpam-6798	356	8	it	it	PRON
ejpam-6798	356	9	follows	follow	VERB
ejpam-6798	356	10	from	from	ADP
ejpam-6798	356	11	property	property	NOUN
ejpam-6798	356	12	2	2	NUM
ejpam-6798	356	13	that	that	PRON
ejpam-6798	356	14	µl(s	µl(s	NUM
ejpam-6798	356	15	⋆	⋆	X
ejpam-6798	356	16	l	l	NOUN
ejpam-6798	356	17	)	)	PUNCT
ejpam-6798	356	18	≥	≥	NOUN
ejpam-6798	356	19	µl(s	µl(s	NUM
ejpam-6798	356	20	)	)	PUNCT
ejpam-6798	356	21	and	and	CCONJ
ejpam-6798	356	22	νl(s	νl(s	PUNCT
ejpam-6798	356	23	⋆	⋆	X
ejpam-6798	356	24	l	l	NOUN
ejpam-6798	356	25	)	)	PUNCT
ejpam-6798	356	26	≤	≤	NOUN
ejpam-6798	356	27	νl(s	νl(	NOUN
ejpam-6798	356	28	)	)	PUNCT
ejpam-6798	356	29	.	.	PUNCT
ejpam-6798	357	1	hence	hence	ADV
ejpam-6798	357	2	by	by	ADP
ejpam-6798	357	3	definition	definition	NOUN
ejpam-6798	357	4	,	,	PUNCT
ejpam-6798	357	5	µl(s	µl(s	PUNCT
ejpam-6798	357	6	⋆	⋆	X
ejpam-6798	357	7	l	l	NOUN
ejpam-6798	357	8	)	)	PUNCT
ejpam-6798	357	9	≥	≥	NOUN
ejpam-6798	357	10	γl(s)e	γl(s)e	NUM
ejpam-6798	357	11	ιθl(s	ιθl(s	PROPN
ejpam-6798	357	12	)	)	PUNCT
ejpam-6798	357	13	=	=	PRON
ejpam-6798	357	14	(	(	PUNCT
ejpam-6798	357	15	γl(s	γl(s	PUNCT
ejpam-6798	357	16	⋆	⋆	X
ejpam-6798	357	17	l)e	l)e	X
ejpam-6798	357	18	ιθl(s⋆l	ιθl(s⋆l	NOUN
ejpam-6798	357	19	)	)	PUNCT
ejpam-6798	357	20	)	)	PUNCT
ejpam-6798	358	1	∧	∧	NOUN
ejpam-6798	358	2	γl(l)e	γl(l)e	NUM
ejpam-6798	358	3	ιθl(l	ιθl(l	PROPN
ejpam-6798	358	4	)	)	PUNCT
ejpam-6798	358	5	=	=	PUNCT
ejpam-6798	358	6	(	(	PUNCT
ejpam-6798	358	7	γl(s	γl(s	PUNCT
ejpam-6798	358	8	⋆	⋆	X
ejpam-6798	358	9	l	l	NOUN
ejpam-6798	358	10	)	)	PUNCT
ejpam-6798	358	11	∧	∧	PROPN
ejpam-6798	358	12	γl(l))e	γl(l))e	PUNCT
ejpam-6798	358	13	ι(θl(s⋆l)∧θl(l	ι(θl(s⋆l)∧θl(l	NOUN
ejpam-6798	358	14	)	)	PUNCT
ejpam-6798	358	15	)	)	PUNCT
ejpam-6798	359	1	=	=	SYM
ejpam-6798	359	2	(	(	PUNCT
ejpam-6798	359	3	γl(s	γl(s	NOUN
ejpam-6798	359	4	)	)	PUNCT
ejpam-6798	359	5	∧	∧	PROPN
ejpam-6798	359	6	γl(l))e	γl(l))e	PUNCT
ejpam-6798	359	7	ι(θl(s)∧θl(l	ι(θl(s)∧θl(l	PROPN
ejpam-6798	359	8	)	)	PUNCT
ejpam-6798	359	9	)	)	PUNCT
ejpam-6798	359	10	≥	≥	NOUN
ejpam-6798	359	11	µl(s	µl(	NOUN
ejpam-6798	359	12	)	)	PUNCT
ejpam-6798	359	13	∧	∧	PROPN
ejpam-6798	359	14	µl(l	µl(l	NUM
ejpam-6798	359	15	)	)	PUNCT
ejpam-6798	359	16	.	.	PUNCT
ejpam-6798	360	1	moreover	moreover	ADV
ejpam-6798	360	2	νl(s	νl(s	PUNCT
ejpam-6798	360	3	⋆	⋆	X
ejpam-6798	360	4	l	l	NOUN
ejpam-6798	360	5	)	)	PUNCT
ejpam-6798	360	6	≤	≤	NOUN
ejpam-6798	360	7	γl(s)e	γl(s)e	X
ejpam-6798	360	8	ιθl(s	ιθl(s	PROPN
ejpam-6798	360	9	)	)	PUNCT
ejpam-6798	360	10	=	=	SYM
ejpam-6798	360	11	(	(	PUNCT
ejpam-6798	360	12	γl(s	γl(s	PUNCT
ejpam-6798	360	13	⋆	⋆	X
ejpam-6798	360	14	l)e	l)e	X
ejpam-6798	360	15	ιθl(s⋆l	ιθl(s⋆l	NOUN
ejpam-6798	360	16	)	)	PUNCT
ejpam-6798	360	17	)	)	PUNCT
ejpam-6798	360	18	∨	∨	NUM
ejpam-6798	360	19	γl(l)e	γl(l)e	NUM
ejpam-6798	360	20	ιθl(l	ιθl(l	PROPN
ejpam-6798	360	21	)	)	PUNCT
ejpam-6798	360	22	=	=	PUNCT
ejpam-6798	360	23	(	(	PUNCT
ejpam-6798	360	24	γl(s	γl(s	PUNCT
ejpam-6798	360	25	⋆	⋆	X
ejpam-6798	360	26	l	l	NOUN
ejpam-6798	360	27	)	)	PUNCT
ejpam-6798	360	28	∨	∨	NUM
ejpam-6798	360	29	γl(l))e	γl(l))e	PUNCT
ejpam-6798	360	30	ι(θl(s⋆l)∨θl(l	ι(θl(s⋆l)∨θl(l	NOUN
ejpam-6798	360	31	)	)	PUNCT
ejpam-6798	360	32	)	)	PUNCT
ejpam-6798	361	1	=	=	SYM
ejpam-6798	361	2	(	(	PUNCT
ejpam-6798	361	3	γl(s	γl(s	NOUN
ejpam-6798	361	4	)	)	PUNCT
ejpam-6798	361	5	∨	∨	NUM
ejpam-6798	361	6	γl(l))e	γl(l))e	PUNCT
ejpam-6798	361	7	ι(θl(s)∨θl(l	ι(θl(s)∨θl(l	PROPN
ejpam-6798	361	8	)	)	PUNCT
ejpam-6798	361	9	)	)	PUNCT
ejpam-6798	361	10	≤	≤	NOUN
ejpam-6798	361	11	νl(s	νl(	NOUN
ejpam-6798	361	12	)	)	PUNCT
ejpam-6798	361	13	∨	∨	NUM
ejpam-6798	361	14	νl(l	νl(l	NUM
ejpam-6798	361	15	)	)	PUNCT
ejpam-6798	361	16	.	.	PUNCT
ejpam-6798	362	1	so	so	ADV
ejpam-6798	362	2	l	l	NOUN
ejpam-6798	362	3	is	be	AUX
ejpam-6798	362	4	a	a	DET
ejpam-6798	362	5	cifs	cifs	NOUN
ejpam-6798	362	6	l	l	NOUN
ejpam-6798	362	7	of	of	ADP
ejpam-6798	362	8	m	m	PROPN
ejpam-6798	362	9	.	.	PUNCT
ejpam-6798	363	1	the	the	DET
ejpam-6798	363	2	following	follow	VERB
ejpam-6798	363	3	result	result	NOUN
ejpam-6798	363	4	shows	show	VERB
ejpam-6798	363	5	that	that	SCONJ
ejpam-6798	363	6	if	if	SCONJ
ejpam-6798	363	7	s	s	PRON
ejpam-6798	363	8	⋆	⋆	VERB
ejpam-6798	363	9	l	l	NOUN
ejpam-6798	363	10	≤	≤	PROPN
ejpam-6798	363	11	z	z	NOUN
ejpam-6798	363	12	then	then	ADV
ejpam-6798	363	13	µl(s	µl(	NOUN
ejpam-6798	363	14	)	)	PUNCT
ejpam-6798	363	15	≥	≥	NOUN
ejpam-6798	363	16	µl(l	µl(l	ADV
ejpam-6798	363	17	)	)	PUNCT
ejpam-6798	363	18	∧	∧	NOUN
ejpam-6798	363	19	µl(z	µl(z	NOUN
ejpam-6798	363	20	)	)	PUNCT
ejpam-6798	363	21	and	and	CCONJ
ejpam-6798	363	22	νl(s	νl(	NOUN
ejpam-6798	363	23	)	)	PUNCT
ejpam-6798	363	24	≤	≤	NOUN
ejpam-6798	363	25	νl(l	νl(l	NOUN
ejpam-6798	363	26	)	)	PUNCT
ejpam-6798	363	27	∨	∨	NUM
ejpam-6798	363	28	νl(z	νl(z	NOUN
ejpam-6798	363	29	)	)	PUNCT
ejpam-6798	363	30	.	.	PUNCT
ejpam-6798	364	1	theorem	theorem	ADJ
ejpam-6798	364	2	8	8	NUM
ejpam-6798	364	3	.	.	PUNCT
ejpam-6798	365	1	let	let	VERB
ejpam-6798	365	2	l	l	NOUN
ejpam-6798	365	3	be	be	AUX
ejpam-6798	365	4	a	a	DET
ejpam-6798	365	5	cifi	cifi	NOUN
ejpam-6798	365	6	of	of	ADP
ejpam-6798	365	7	m	m	PROPN
ejpam-6798	365	8	.	.	PUNCT
ejpam-6798	366	1	if	if	SCONJ
ejpam-6798	366	2	the	the	DET
ejpam-6798	366	3	inequality	inequality	NOUN
ejpam-6798	366	4	s	s	PART
ejpam-6798	366	5	⋆	⋆	NOUN
ejpam-6798	366	6	l	l	NOUN
ejpam-6798	366	7	≤	≤	X
ejpam-6798	366	8	z	z	NOUN
ejpam-6798	366	9	holds	hold	VERB
ejpam-6798	366	10	in	in	ADP
ejpam-6798	366	11	m	m	PROPN
ejpam-6798	366	12	,	,	PUNCT
ejpam-6798	366	13	then	then	ADV
ejpam-6798	366	14	µl(s	µl(	NOUN
ejpam-6798	366	15	)	)	PUNCT
ejpam-6798	366	16	≥	≥	NOUN
ejpam-6798	366	17	µl(l	µl(l	ADV
ejpam-6798	366	18	)	)	PUNCT
ejpam-6798	367	1	∧	∧	NOUN
ejpam-6798	367	2	µl(z	µl(z	NOUN
ejpam-6798	367	3	)	)	PUNCT
ejpam-6798	367	4	and	and	CCONJ
ejpam-6798	367	5	νl(s	νl(	NOUN
ejpam-6798	367	6	)	)	PUNCT
ejpam-6798	367	7	≤	≤	NOUN
ejpam-6798	367	8	νl(l	νl(l	NOUN
ejpam-6798	367	9	)	)	PUNCT
ejpam-6798	367	10	∨	∨	NUM
ejpam-6798	367	11	νl(z	νl(z	NOUN
ejpam-6798	367	12	)	)	PUNCT
ejpam-6798	367	13	.	.	PUNCT
ejpam-6798	368	1	proof	proof	NOUN
ejpam-6798	368	2	.	.	PUNCT
ejpam-6798	369	1	suppose	suppose	VERB
ejpam-6798	369	2	that	that	SCONJ
ejpam-6798	369	3	l	l	NOUN
ejpam-6798	369	4	is	be	AUX
ejpam-6798	369	5	a	a	DET
ejpam-6798	369	6	cfsa	cfsa	NOUN
ejpam-6798	369	7	of	of	ADP
ejpam-6798	369	8	m	m	PRON
ejpam-6798	369	9	and	and	CCONJ
ejpam-6798	369	10	let	let	VERB
ejpam-6798	369	11	s	s	PRON
ejpam-6798	369	12	⋆	⋆	VERB
ejpam-6798	369	13	l	l	NOUN
ejpam-6798	369	14	≤	≤	X
ejpam-6798	369	15	z	z	NOUN
ejpam-6798	369	16	holds	hold	VERB
ejpam-6798	369	17	in	in	ADP
ejpam-6798	369	18	m	m	PROPN
ejpam-6798	369	19	.	.	PUNCT
ejpam-6798	370	1	then	then	ADV
ejpam-6798	370	2	µl(s	µl(s	PUNCT
ejpam-6798	370	3	⋆	⋆	VERB
ejpam-6798	370	4	l	l	NOUN
ejpam-6798	370	5	)	)	PUNCT
ejpam-6798	370	6	=	=	SYM
ejpam-6798	370	7	γl(s	γl(s	NUM
ejpam-6798	370	8	⋆	⋆	X
ejpam-6798	370	9	l)e	l)e	X
ejpam-6798	370	10	ιθl(s⋆l	ιθl(s⋆l	NOUN
ejpam-6798	370	11	)	)	PUNCT
ejpam-6798	370	12	≥	≥	PROPN
ejpam-6798	370	13	(	(	PUNCT
ejpam-6798	370	14	γl((s	γl((	VERB
ejpam-6798	370	15	⋆	⋆	X
ejpam-6798	370	16	l	l	NOUN
ejpam-6798	370	17	)	)	PUNCT
ejpam-6798	370	18	⋆	⋆	VERB
ejpam-6798	370	19	z	z	NOUN
ejpam-6798	370	20	)	)	PUNCT
ejpam-6798	370	21	∧	∧	PROPN
ejpam-6798	370	22	γl(z))e	γl(z))e	SYM
ejpam-6798	370	23	ι(θl((s⋆l)⋆z)∧θl(z	ι(θl((s⋆l)⋆z)∧θl(z	NOUN
ejpam-6798	370	24	)	)	PUNCT
ejpam-6798	370	25	)	)	PUNCT
ejpam-6798	371	1	=	=	SYM
ejpam-6798	371	2	(	(	PUNCT
ejpam-6798	371	3	γl(0	γl(0	PROPN
ejpam-6798	371	4	)	)	PUNCT
ejpam-6798	371	5	∧	∧	PROPN
ejpam-6798	371	6	γl(z))e	γl(z))e	PUNCT
ejpam-6798	371	7	ι(θl(0)∧θl(z	ι(θl(0)∧θl(z	NOUN
ejpam-6798	371	8	)	)	PUNCT
ejpam-6798	371	9	)	)	PUNCT
ejpam-6798	372	1	=	=	SYM
ejpam-6798	373	1	γl(z)e	γl(z)e	NUM
ejpam-6798	373	2	ιθl(z	ιθl(z	PROPN
ejpam-6798	373	3	)	)	PUNCT
ejpam-6798	373	4	≥	≥	NOUN
ejpam-6798	373	5	µl(z	µl(z	NOUN
ejpam-6798	373	6	)	)	PUNCT
ejpam-6798	373	7	.	.	PUNCT
ejpam-6798	374	1	it	it	PRON
ejpam-6798	374	2	follows	follow	VERB
ejpam-6798	374	3	that	that	SCONJ
ejpam-6798	374	4	µl(s	µl(s	NUM
ejpam-6798	374	5	)	)	PUNCT
ejpam-6798	374	6	≥	≥	NOUN
ejpam-6798	374	7	µl(l	µl(l	ADV
ejpam-6798	374	8	)	)	PUNCT
ejpam-6798	374	9	∧	∧	NOUN
ejpam-6798	374	10	µl(z	µl(z	NOUN
ejpam-6798	374	11	)	)	PUNCT
ejpam-6798	374	12	.	.	PUNCT
ejpam-6798	375	1	moreover	moreover	ADV
ejpam-6798	375	2	νl(s	νl(s	PUNCT
ejpam-6798	375	3	⋆	⋆	X
ejpam-6798	375	4	l	l	NOUN
ejpam-6798	375	5	)	)	PUNCT
ejpam-6798	375	6	=	=	SYM
ejpam-6798	375	7	γl(s	γl(s	NUM
ejpam-6798	375	8	⋆	⋆	X
ejpam-6798	375	9	l)e	l)e	X
ejpam-6798	375	10	ιθl(s⋆l	ιθl(s⋆l	NOUN
ejpam-6798	375	11	)	)	PUNCT
ejpam-6798	375	12	m.	m.	NOUN
ejpam-6798	375	13	jawad	jawad	PROPN
ejpam-6798	375	14	et	et	PROPN
ejpam-6798	375	15	al	al	PROPN
ejpam-6798	375	16	.	.	PUNCT
ejpam-6798	375	17	/	/	SYM
ejpam-6798	375	18	eur	eur	PROPN
ejpam-6798	375	19	.	.	PUNCT
ejpam-6798	376	1	j.	j.	PROPN
ejpam-6798	376	2	pure	pure	PROPN
ejpam-6798	376	3	appl	appl	PROPN
ejpam-6798	376	4	.	.	PROPN
ejpam-6798	376	5	math	math	PROPN
ejpam-6798	376	6	,	,	PUNCT
ejpam-6798	376	7	18	18	NUM
ejpam-6798	376	8	(	(	PUNCT
ejpam-6798	376	9	4	4	NUM
ejpam-6798	376	10	)	)	PUNCT
ejpam-6798	376	11	(	(	PUNCT
ejpam-6798	376	12	2025	2025	NUM
ejpam-6798	376	13	)	)	PUNCT
ejpam-6798	376	14	,	,	PUNCT
ejpam-6798	376	15	6798	6798	NUM
ejpam-6798	376	16	12	12	NUM
ejpam-6798	376	17	of	of	ADP
ejpam-6798	376	18	22	22	NUM
ejpam-6798	376	19	≤	≤	NOUN
ejpam-6798	376	20	(	(	PUNCT
ejpam-6798	376	21	γl((s	γl((	VERB
ejpam-6798	376	22	⋆	⋆	X
ejpam-6798	376	23	l	l	NOUN
ejpam-6798	376	24	)	)	PUNCT
ejpam-6798	376	25	⋆	⋆	VERB
ejpam-6798	376	26	z	z	NOUN
ejpam-6798	376	27	)	)	PUNCT
ejpam-6798	376	28	∨	∨	NUM
ejpam-6798	376	29	γl(z))e	γl(z))e	X
ejpam-6798	376	30	ι(θl((s⋆l)⋆z)∨θl(z	ι(θl((s⋆l)⋆z)∨θl(z	NOUN
ejpam-6798	376	31	)	)	PUNCT
ejpam-6798	376	32	)	)	PUNCT
ejpam-6798	377	1	=	=	SYM
ejpam-6798	377	2	(	(	PUNCT
ejpam-6798	377	3	γl(0	γl(0	PROPN
ejpam-6798	377	4	)	)	PUNCT
ejpam-6798	377	5	∨	∨	NUM
ejpam-6798	377	6	γl(z))e	γl(z))e	CCONJ
ejpam-6798	377	7	ι(θl(0)∨θl(z	ι(θl(0)∨θl(z	NOUN
ejpam-6798	377	8	)	)	PUNCT
ejpam-6798	377	9	)	)	PUNCT
ejpam-6798	378	1	=	=	SYM
ejpam-6798	378	2	γl(z)e	γl(z)e	NUM
ejpam-6798	378	3	ιθl(z	ιθl(z	PROPN
ejpam-6798	378	4	)	)	PUNCT
ejpam-6798	378	5	≤	≤	NOUN
ejpam-6798	378	6	νl(z	νl(z	NOUN
ejpam-6798	378	7	)	)	PUNCT
ejpam-6798	378	8	.	.	PUNCT
ejpam-6798	379	1	it	it	PRON
ejpam-6798	379	2	follows	follow	VERB
ejpam-6798	379	3	that	that	PRON
ejpam-6798	379	4	νl(s	νl(	NOUN
ejpam-6798	379	5	)	)	PUNCT
ejpam-6798	379	6	≤	≤	NOUN
ejpam-6798	379	7	νl(l	νl(l	NOUN
ejpam-6798	379	8	)	)	PUNCT
ejpam-6798	379	9	∨	∨	NUM
ejpam-6798	379	10	νl(z	νl(z	NOUN
ejpam-6798	379	11	)	)	PUNCT
ejpam-6798	379	12	.	.	PUNCT
ejpam-6798	380	1	definition	definition	NOUN
ejpam-6798	380	2	14	14	NUM
ejpam-6798	380	3	.	.	PUNCT
ejpam-6798	381	1	let	let	VERB
ejpam-6798	381	2	l	l	NOUN
ejpam-6798	381	3	be	be	AUX
ejpam-6798	381	4	a	a	DET
ejpam-6798	381	5	cifs	cif	NOUN
ejpam-6798	381	6	of	of	ADP
ejpam-6798	381	7	m	m	PRON
ejpam-6798	381	8	.	.	PUNCT
ejpam-6798	382	1	then	then	ADV
ejpam-6798	382	2	,	,	PUNCT
ejpam-6798	382	3	the	the	DET
ejpam-6798	382	4	complement	complement	NOUN
ejpam-6798	382	5	l	l	NOUN
ejpam-6798	382	6	is	be	AUX
ejpam-6798	382	7	described	describe	VERB
ejpam-6798	382	8	as	as	ADP
ejpam-6798	382	9	:	:	PUNCT
ejpam-6798	382	10	c(µl(s	c(µl(	NOUN
ejpam-6798	382	11	)	)	PUNCT
ejpam-6798	382	12	)	)	PUNCT
ejpam-6798	383	1	=	=	SYM
ejpam-6798	383	2	(	(	PUNCT
ejpam-6798	383	3	1−	1−	NUM
ejpam-6798	383	4	γl(s))e	γl(s))e	X
ejpam-6798	383	5	ι(2π−θl(s	ι(2π−θl(s	PROPN
ejpam-6798	383	6	)	)	PUNCT
ejpam-6798	383	7	)	)	PUNCT
ejpam-6798	383	8	,	,	PUNCT
ejpam-6798	383	9	c(νl(s	c(νl(s	PROPN
ejpam-6798	383	10	)	)	PUNCT
ejpam-6798	383	11	)	)	PUNCT
ejpam-6798	384	1	=	=	SYM
ejpam-6798	384	2	(	(	PUNCT
ejpam-6798	384	3	1−	1−	NUM
ejpam-6798	384	4	γl(s))e	γl(s))e	X
ejpam-6798	384	5	ι(2π−θl(s	ι(2π−θl(s	PROPN
ejpam-6798	384	6	)	)	PUNCT
ejpam-6798	384	7	)	)	PUNCT
ejpam-6798	384	8	.	.	PUNCT
ejpam-6798	385	1	example	example	NOUN
ejpam-6798	386	1	8	8	NUM
ejpam-6798	386	2	.	.	PUNCT
ejpam-6798	387	1	let	let	VERB
ejpam-6798	387	2	(	(	PUNCT
ejpam-6798	387	3	µl(s	µl(	NOUN
ejpam-6798	387	4	)	)	PUNCT
ejpam-6798	387	5	,	,	PUNCT
ejpam-6798	387	6	νl(s	νl(	NOUN
ejpam-6798	387	7	)	)	PUNCT
ejpam-6798	387	8	)	)	PUNCT
ejpam-6798	388	1	=	=	PRON
ejpam-6798	388	2	{	{	PUNCT
ejpam-6798	388	3	(	(	PUNCT
ejpam-6798	388	4	s1	s1	NOUN
ejpam-6798	388	5	,	,	PUNCT
ejpam-6798	388	6	0.3eι0.4π	0.3eι0.4π	PROPN
ejpam-6798	388	7	,	,	PUNCT
ejpam-6798	388	8	0.1eι0.24π	0.1eι0.24π	NUM
ejpam-6798	388	9	)	)	PUNCT
ejpam-6798	388	10	,	,	PUNCT
ejpam-6798	388	11	(	(	PUNCT
ejpam-6798	388	12	s2	s2	PROPN
ejpam-6798	388	13	,	,	PUNCT
ejpam-6798	388	14	0.6eι0.2π	0.6eι0.2π	PROPN
ejpam-6798	388	15	,	,	PUNCT
ejpam-6798	388	16	0.4eι0.12π	0.4eι0.12π	NOUN
ejpam-6798	388	17	)	)	PUNCT
ejpam-6798	388	18	,	,	PUNCT
ejpam-6798	388	19	(	(	PUNCT
ejpam-6798	388	20	s3	s3	PROPN
ejpam-6798	388	21	,	,	PUNCT
ejpam-6798	388	22	0.8eι0.1π	0.8eι0.1π	PROPN
ejpam-6798	388	23	,	,	PUNCT
ejpam-6798	388	24	0.6eι0.01π	0.6eι0.01π	NUM
ejpam-6798	388	25	)	)	PUNCT
ejpam-6798	388	26	,	,	PUNCT
ejpam-6798	388	27	(	(	PUNCT
ejpam-6798	388	28	s4	s4	PROPN
ejpam-6798	388	29	,	,	PUNCT
ejpam-6798	388	30	0.2e	0.2e	NOUN
ejpam-6798	388	31	ι0.3π	ι0.3π	PROPN
ejpam-6798	388	32	,	,	PUNCT
ejpam-6798	388	33	0.1eι0.13π	0.1eι0.13π	NOUN
ejpam-6798	388	34	)	)	PUNCT
ejpam-6798	388	35	,	,	PUNCT
ejpam-6798	388	36	(	(	PUNCT
ejpam-6798	388	37	s5	s5	PROPN
ejpam-6798	388	38	,	,	PUNCT
ejpam-6798	388	39	0.5e	0.5e	NUM
ejpam-6798	388	40	ιπ	ιπ	ADJ
ejpam-6798	388	41	,	,	PUNCT
ejpam-6798	388	42	0.3eι0.8π	0.3eι0.8π	PROPN
ejpam-6798	388	43	)	)	PUNCT
ejpam-6798	388	44	,	,	PUNCT
ejpam-6798	388	45	(	(	PUNCT
ejpam-6798	388	46	s6	s6	PROPN
ejpam-6798	388	47	,	,	PUNCT
ejpam-6798	388	48	0.9e	0.9e	ADJ
ejpam-6798	388	49	ι0.1π	ι0.1π	NOUN
ejpam-6798	388	50	,	,	PUNCT
ejpam-6798	388	51	0.7eι0.01π	0.7eι0.01π	NUM
ejpam-6798	388	52	)	)	PUNCT
ejpam-6798	388	53	}	}	PUNCT
ejpam-6798	388	54	be	be	AUX
ejpam-6798	388	55	a	a	DET
ejpam-6798	388	56	cifs	cif	NOUN
ejpam-6798	388	57	of	of	ADP
ejpam-6798	388	58	m	m	PROPN
ejpam-6798	388	59	.	.	PUNCT
ejpam-6798	389	1	then	then	ADV
ejpam-6798	389	2	c(µl(s	c(µl(	NOUN
ejpam-6798	389	3	)	)	PUNCT
ejpam-6798	389	4	,	,	PUNCT
ejpam-6798	389	5	νl(s	νl(	NOUN
ejpam-6798	389	6	)	)	PUNCT
ejpam-6798	389	7	)	)	PUNCT
ejpam-6798	390	1	=	=	PRON
ejpam-6798	390	2	{	{	PUNCT
ejpam-6798	390	3	(	(	PUNCT
ejpam-6798	390	4	s1	s1	NOUN
ejpam-6798	390	5	,	,	PUNCT
ejpam-6798	390	6	0.7eι1.6π	0.7eι1.6π	PROPN
ejpam-6798	390	7	,	,	PUNCT
ejpam-6798	390	8	0.9eι1.76π	0.9eι1.76π	NOUN
ejpam-6798	390	9	)	)	PUNCT
ejpam-6798	390	10	,	,	PUNCT
ejpam-6798	390	11	(	(	PUNCT
ejpam-6798	390	12	s2	s2	PROPN
ejpam-6798	390	13	,	,	PUNCT
ejpam-6798	390	14	0.4eι1.8π	0.4eι1.8π	PROPN
ejpam-6798	390	15	,	,	PUNCT
ejpam-6798	390	16	0.6eι1.88π	0.6eι1.88π	PROPN
ejpam-6798	390	17	)	)	PUNCT
ejpam-6798	390	18	,	,	PUNCT
ejpam-6798	390	19	(	(	PUNCT
ejpam-6798	390	20	s3	s3	PROPN
ejpam-6798	390	21	,	,	PUNCT
ejpam-6798	390	22	0.2eι1.9π	0.2eι1.9π	PROPN
ejpam-6798	390	23	,	,	PUNCT
ejpam-6798	390	24	0.4eι1.99π	0.4eι1.99π	NOUN
ejpam-6798	390	25	)	)	PUNCT
ejpam-6798	390	26	,	,	PUNCT
ejpam-6798	390	27	(	(	PUNCT
ejpam-6798	390	28	s4	s4	PROPN
ejpam-6798	390	29	,	,	PUNCT
ejpam-6798	390	30	0.8e	0.8e	PROPN
ejpam-6798	390	31	ι1.7π	ι1.7π	PROPN
ejpam-6798	390	32	,	,	PUNCT
ejpam-6798	390	33	0.9eι1.87π	0.9eι1.87π	NUM
ejpam-6798	390	34	)	)	PUNCT
ejpam-6798	390	35	,	,	PUNCT
ejpam-6798	390	36	(	(	PUNCT
ejpam-6798	390	37	s5	s5	PROPN
ejpam-6798	390	38	,	,	PUNCT
ejpam-6798	390	39	0.5e	0.5e	NUM
ejpam-6798	390	40	ιπ	ιπ	ADJ
ejpam-6798	390	41	,	,	PUNCT
ejpam-6798	390	42	0.7eι1.2π	0.7eι1.2π	PROPN
ejpam-6798	390	43	)	)	PUNCT
ejpam-6798	390	44	,	,	PUNCT
ejpam-6798	390	45	(	(	PUNCT
ejpam-6798	390	46	s6	s6	PROPN
ejpam-6798	390	47	,	,	PUNCT
ejpam-6798	390	48	0.1e	0.1e	PROPN
ejpam-6798	390	49	ι1.9π	ι1.9π	PROPN
ejpam-6798	390	50	,	,	PUNCT
ejpam-6798	390	51	0.3eι1.99π	0.3eι1.99π	NUM
ejpam-6798	390	52	)	)	PUNCT
ejpam-6798	390	53	}	}	PUNCT
ejpam-6798	390	54	is	be	AUX
ejpam-6798	390	55	a	a	DET
ejpam-6798	390	56	cifi	cifi	NOUN
ejpam-6798	390	57	of	of	ADP
ejpam-6798	390	58	m	m	PROPN
ejpam-6798	390	59	.	.	PUNCT
ejpam-6798	391	1	the	the	DET
ejpam-6798	391	2	following	follow	VERB
ejpam-6798	391	3	outcome	outcome	NOUN
ejpam-6798	391	4	shows	show	VERB
ejpam-6798	391	5	that	that	SCONJ
ejpam-6798	391	6	the	the	DET
ejpam-6798	391	7	complement	complement	NOUN
ejpam-6798	391	8	of	of	ADP
ejpam-6798	391	9	cifi	cifi	NOUN
ejpam-6798	391	10	of	of	ADP
ejpam-6798	391	11	m	m	PROPN
ejpam-6798	391	12	is	be	AUX
ejpam-6798	391	13	also	also	ADV
ejpam-6798	391	14	cifi	cifi	NOUN
ejpam-6798	391	15	.	.	PUNCT
ejpam-6798	392	1	theorem	theorem	VERB
ejpam-6798	392	2	9	9	NUM
ejpam-6798	392	3	.	.	PUNCT
ejpam-6798	393	1	a	a	DET
ejpam-6798	393	2	cifs	cif	NOUN
ejpam-6798	393	3	of	of	ADP
ejpam-6798	393	4	m	m	VERB
ejpam-6798	393	5	is	be	AUX
ejpam-6798	393	6	a	a	DET
ejpam-6798	393	7	cifi	cifi	NOUN
ejpam-6798	393	8	of	of	ADP
ejpam-6798	393	9	m	m	PROPN
ejpam-6798	393	10	iff	iff	NOUN
ejpam-6798	393	11	c(µl(s	c(µl(	NOUN
ejpam-6798	393	12	)	)	PUNCT
ejpam-6798	393	13	)	)	PUNCT
ejpam-6798	393	14	and	and	CCONJ
ejpam-6798	393	15	c(νl(s	c(νl(s	PROPN
ejpam-6798	393	16	)	)	PUNCT
ejpam-6798	393	17	)	)	PUNCT
ejpam-6798	394	1	is	be	AUX
ejpam-6798	394	2	a	a	DET
ejpam-6798	394	3	cifi	cifi	NOUN
ejpam-6798	394	4	of	of	ADP
ejpam-6798	394	5	m	m	PROPN
ejpam-6798	394	6	.	.	PUNCT
ejpam-6798	395	1	proof	proof	NOUN
ejpam-6798	395	2	.	.	PUNCT
ejpam-6798	396	1	suppose	suppose	VERB
ejpam-6798	396	2	that	that	SCONJ
ejpam-6798	396	3	l	l	NOUN
ejpam-6798	396	4	is	be	AUX
ejpam-6798	396	5	a	a	DET
ejpam-6798	396	6	cifsa	cifsa	NOUN
ejpam-6798	396	7	of	of	ADP
ejpam-6798	396	8	m	m	PRON
ejpam-6798	396	9	and	and	CCONJ
ejpam-6798	396	10	let	let	VERB
ejpam-6798	396	11	s	s	NOUN
ejpam-6798	396	12	,	,	PUNCT
ejpam-6798	396	13	l	l	PROPN
ejpam-6798	396	14	∈	∈	PROPN
ejpam-6798	396	15	m	m	VERB
ejpam-6798	396	16	.	.	PUNCT
ejpam-6798	397	1	then	then	ADV
ejpam-6798	397	2	c(µl(0	c(µl(0	PROPN
ejpam-6798	397	3	)	)	PUNCT
ejpam-6798	397	4	)	)	PUNCT
ejpam-6798	398	1	=	=	SYM
ejpam-6798	398	2	1−	1−	NUM
ejpam-6798	398	3	µl(0	µl(0	PROPN
ejpam-6798	398	4	)	)	PUNCT
ejpam-6798	398	5	=	=	PUNCT
ejpam-6798	398	6	(	(	PUNCT
ejpam-6798	398	7	1−	1−	NUM
ejpam-6798	398	8	γl(0))e	γl(0))e	PROPN
ejpam-6798	398	9	ι(2π−θl(0	ι(2π−θl(0	PROPN
ejpam-6798	398	10	)	)	PUNCT
ejpam-6798	398	11	)	)	PUNCT
ejpam-6798	398	12	≥	≥	NUM
ejpam-6798	398	13	(	(	PUNCT
ejpam-6798	398	14	1−	1−	NUM
ejpam-6798	398	15	γl(s))e	γl(s))e	X
ejpam-6798	398	16	ι(2π−θl(s	ι(2π−θl(s	PROPN
ejpam-6798	398	17	)	)	PUNCT
ejpam-6798	398	18	)	)	PUNCT
ejpam-6798	399	1	=	=	PUNCT
ejpam-6798	400	1	c(µl(s	c(µl(s	PROPN
ejpam-6798	400	2	)	)	PUNCT
ejpam-6798	400	3	)	)	PUNCT
ejpam-6798	400	4	.	.	PUNCT
ejpam-6798	401	1	and	and	CCONJ
ejpam-6798	401	2	c(µl(s	c(µl(	NOUN
ejpam-6798	401	3	)	)	PUNCT
ejpam-6798	401	4	)	)	PUNCT
ejpam-6798	402	1	=	=	SYM
ejpam-6798	402	2	1−	1−	NUM
ejpam-6798	402	3	µl(s	µl(s	NUM
ejpam-6798	402	4	)	)	PUNCT
ejpam-6798	402	5	≥	≥	NOUN
ejpam-6798	402	6	1−	1−	NUM
ejpam-6798	402	7	(	(	PUNCT
ejpam-6798	402	8	γl(s	γl(s	PUNCT
ejpam-6798	402	9	⋆	⋆	X
ejpam-6798	402	10	l)e	l)e	X
ejpam-6798	402	11	ι(2π−θl(s⋆l	ι(2π−θl(s⋆l	NUM
ejpam-6798	402	12	)	)	PUNCT
ejpam-6798	402	13	)	)	PUNCT
ejpam-6798	403	1	∧	∧	NOUN
ejpam-6798	403	2	γl(l)e	γl(l)e	NUM
ejpam-6798	403	3	ι(2π−θl(l	ι(2π−θl(l	ADJ
ejpam-6798	403	4	)	)	PUNCT
ejpam-6798	403	5	)	)	PUNCT
ejpam-6798	403	6	)	)	PUNCT
ejpam-6798	404	1	=	=	PUNCT
ejpam-6798	404	2	(	(	PUNCT
ejpam-6798	404	3	1−	1−	NUM
ejpam-6798	404	4	γl(s	γl(s	PUNCT
ejpam-6798	404	5	⋆	⋆	PUNCT
ejpam-6798	404	6	l))e	l))e	PROPN
ejpam-6798	404	7	ι(2π−θl(s⋆l	ι(2π−θl(s⋆l	PROPN
ejpam-6798	404	8	)	)	PUNCT
ejpam-6798	404	9	)	)	PUNCT
ejpam-6798	405	1	∧	∧	NOUN
ejpam-6798	405	2	(	(	PUNCT
ejpam-6798	405	3	1−	1−	NUM
ejpam-6798	405	4	γl(l))e	γl(l))e	NUM
ejpam-6798	405	5	ι(2π−θl(l	ι(2π−θl(l	ADJ
ejpam-6798	405	6	)	)	PUNCT
ejpam-6798	405	7	)	)	PUNCT
ejpam-6798	405	8	≥	≥	PRON
ejpam-6798	406	1	c(µl(s	c(µl(s	PRON
ejpam-6798	406	2	⋆	⋆	PROPN
ejpam-6798	406	3	l	l	NOUN
ejpam-6798	406	4	)	)	PUNCT
ejpam-6798	406	5	)	)	PUNCT
ejpam-6798	407	1	∧	∧	PROPN
ejpam-6798	407	2	c(µl(l	c(µl(l	PROPN
ejpam-6798	407	3	)	)	PUNCT
ejpam-6798	407	4	)	)	PUNCT
ejpam-6798	407	5	.	.	PUNCT
ejpam-6798	407	6	suppose	suppose	VERB
ejpam-6798	407	7	that	that	SCONJ
ejpam-6798	407	8	l	l	NOUN
ejpam-6798	407	9	is	be	AUX
ejpam-6798	407	10	a	a	DET
ejpam-6798	407	11	cifsa	cifsa	NOUN
ejpam-6798	407	12	of	of	ADP
ejpam-6798	407	13	m	m	PRON
ejpam-6798	407	14	and	and	CCONJ
ejpam-6798	407	15	let	let	VERB
ejpam-6798	407	16	s	s	NOUN
ejpam-6798	407	17	,	,	PUNCT
ejpam-6798	407	18	l	l	PROPN
ejpam-6798	407	19	∈	∈	PROPN
ejpam-6798	407	20	m	m	VERB
ejpam-6798	407	21	.	.	PUNCT
ejpam-6798	408	1	then	then	ADV
ejpam-6798	408	2	c(νl(0	c(νl(0	PROPN
ejpam-6798	408	3	)	)	PUNCT
ejpam-6798	408	4	)	)	PUNCT
ejpam-6798	409	1	=	=	SYM
ejpam-6798	409	2	1−	1−	NUM
ejpam-6798	409	3	νl(0	νl(0	PROPN
ejpam-6798	409	4	)	)	PUNCT
ejpam-6798	409	5	=	=	SYM
ejpam-6798	410	1	(	(	PUNCT
ejpam-6798	410	2	1−	1−	NUM
ejpam-6798	410	3	γl(0))e	γl(0))e	PROPN
ejpam-6798	410	4	ι(2π−θl(0	ι(2π−θl(0	PROPN
ejpam-6798	410	5	)	)	PUNCT
ejpam-6798	410	6	)	)	PUNCT
ejpam-6798	411	1	≤	≤	NOUN
ejpam-6798	411	2	(	(	PUNCT
ejpam-6798	411	3	1−	1−	NUM
ejpam-6798	411	4	γl(s))e	γl(s))e	X
ejpam-6798	411	5	ι(2π−θl(s	ι(2π−θl(s	PROPN
ejpam-6798	411	6	)	)	PUNCT
ejpam-6798	411	7	)	)	PUNCT
ejpam-6798	412	1	=	=	PUNCT
ejpam-6798	412	2	c(νl(s	c(νl(s	PROPN
ejpam-6798	412	3	)	)	PUNCT
ejpam-6798	412	4	)	)	PUNCT
ejpam-6798	412	5	.	.	PUNCT
ejpam-6798	413	1	and	and	CCONJ
ejpam-6798	413	2	c(νl(s	c(νl(	NOUN
ejpam-6798	413	3	)	)	PUNCT
ejpam-6798	413	4	)	)	PUNCT
ejpam-6798	414	1	=	=	SYM
ejpam-6798	414	2	1−	1−	NUM
ejpam-6798	414	3	νl(s	νl(	NOUN
ejpam-6798	414	4	)	)	PUNCT
ejpam-6798	414	5	≤	≤	NUM
ejpam-6798	414	6	1−	1−	NUM
ejpam-6798	414	7	(	(	PUNCT
ejpam-6798	414	8	γl(s	γl(s	PUNCT
ejpam-6798	414	9	⋆	⋆	X
ejpam-6798	414	10	l)e	l)e	X
ejpam-6798	414	11	ι(2π−θl(s⋆l	ι(2π−θl(s⋆l	NUM
ejpam-6798	414	12	)	)	PUNCT
ejpam-6798	414	13	)	)	PUNCT
ejpam-6798	415	1	∨	∨	NUM
ejpam-6798	415	2	γl(l)e	γl(l)e	NUM
ejpam-6798	415	3	ι(2π−θl(l	ι(2π−θl(l	ADJ
ejpam-6798	415	4	)	)	PUNCT
ejpam-6798	415	5	)	)	PUNCT
ejpam-6798	415	6	)	)	PUNCT
ejpam-6798	416	1	=	=	PUNCT
ejpam-6798	416	2	(	(	PUNCT
ejpam-6798	416	3	1−	1−	NUM
ejpam-6798	416	4	γl(s	γl(s	PUNCT
ejpam-6798	416	5	⋆	⋆	PUNCT
ejpam-6798	416	6	l))e	l))e	PROPN
ejpam-6798	416	7	ι(2π−θl(s⋆l	ι(2π−θl(s⋆l	PROPN
ejpam-6798	416	8	)	)	PUNCT
ejpam-6798	416	9	)	)	PUNCT
ejpam-6798	416	10	∨	∨	NUM
ejpam-6798	416	11	(	(	PUNCT
ejpam-6798	416	12	1−	1−	NUM
ejpam-6798	416	13	γl(l))e	γl(l))e	NUM
ejpam-6798	416	14	ι(2π−θl(l	ι(2π−θl(l	ADJ
ejpam-6798	416	15	)	)	PUNCT
ejpam-6798	416	16	)	)	PUNCT
ejpam-6798	416	17	≤	≤	NOUN
ejpam-6798	416	18	c(νl(s	c(νl(s	PRON
ejpam-6798	416	19	⋆	⋆	PROPN
ejpam-6798	416	20	l	l	NOUN
ejpam-6798	416	21	)	)	PUNCT
ejpam-6798	416	22	)	)	PUNCT
ejpam-6798	416	23	∨	∨	NUM
ejpam-6798	416	24	c(νl(l	c(νl(l	PROPN
ejpam-6798	416	25	)	)	PUNCT
ejpam-6798	416	26	)	)	PUNCT
ejpam-6798	416	27	.	.	PUNCT
ejpam-6798	417	1	thus	thus	ADV
ejpam-6798	417	2	,	,	PUNCT
ejpam-6798	417	3	the	the	DET
ejpam-6798	417	4	complement	complement	NOUN
ejpam-6798	417	5	of	of	ADP
ejpam-6798	417	6	membership	membership	NOUN
ejpam-6798	417	7	and	and	CCONJ
ejpam-6798	417	8	non	non	ADJ
ejpam-6798	417	9	-	-	ADJ
ejpam-6798	417	10	membership	membership	ADJ
ejpam-6798	417	11	l	l	NOUN
ejpam-6798	417	12	is	be	AUX
ejpam-6798	417	13	a	a	DET
ejpam-6798	417	14	cifi	cifi	NOUN
ejpam-6798	417	15	of	of	ADP
ejpam-6798	417	16	m	m	PROPN
ejpam-6798	417	17	.	.	PUNCT
ejpam-6798	418	1	m.	m.	PROPN
ejpam-6798	418	2	jawad	jawad	PROPN
ejpam-6798	418	3	et	et	PROPN
ejpam-6798	418	4	al	al	PROPN
ejpam-6798	418	5	.	.	PUNCT
ejpam-6798	418	6	/	/	SYM
ejpam-6798	418	7	eur	eur	PROPN
ejpam-6798	418	8	.	.	PUNCT
ejpam-6798	419	1	j.	j.	PROPN
ejpam-6798	419	2	pure	pure	PROPN
ejpam-6798	419	3	appl	appl	PROPN
ejpam-6798	419	4	.	.	PROPN
ejpam-6798	419	5	math	math	PROPN
ejpam-6798	419	6	,	,	PUNCT
ejpam-6798	419	7	18	18	NUM
ejpam-6798	419	8	(	(	PUNCT
ejpam-6798	419	9	4	4	NUM
ejpam-6798	419	10	)	)	PUNCT
ejpam-6798	419	11	(	(	PUNCT
ejpam-6798	419	12	2025	2025	NUM
ejpam-6798	419	13	)	)	PUNCT
ejpam-6798	419	14	,	,	PUNCT
ejpam-6798	419	15	6798	6798	NUM
ejpam-6798	419	16	13	13	NUM
ejpam-6798	419	17	of	of	ADP
ejpam-6798	419	18	22	22	NUM
ejpam-6798	419	19	definition	definition	NOUN
ejpam-6798	419	20	15	15	NUM
ejpam-6798	419	21	.	.	PUNCT
ejpam-6798	419	22	suppose	suppose	VERB
ejpam-6798	419	23	that	that	SCONJ
ejpam-6798	419	24	l1	l1	PROPN
ejpam-6798	419	25	and	and	CCONJ
ejpam-6798	419	26	l2	l2	NOUN
ejpam-6798	419	27	are	be	AUX
ejpam-6798	419	28	two	two	NUM
ejpam-6798	419	29	cifss	cifss	NOUN
ejpam-6798	419	30	of	of	ADP
ejpam-6798	419	31	m	m	PROPN
ejpam-6798	419	32	.	.	PUNCT
ejpam-6798	420	1	then	then	ADV
ejpam-6798	420	2	,	,	PUNCT
ejpam-6798	420	3	the	the	DET
ejpam-6798	420	4	union	union	NOUN
ejpam-6798	420	5	l1	l1	PROPN
ejpam-6798	420	6	∪	∪	PROPN
ejpam-6798	420	7	l2	l2	PROPN
ejpam-6798	420	8	is	be	AUX
ejpam-6798	420	9	defined	define	VERB
ejpam-6798	420	10	as	as	ADP
ejpam-6798	420	11	µl1∪l2(s	µl1∪l2(s	NOUN
ejpam-6798	420	12	)	)	PUNCT
ejpam-6798	420	13	=	=	SYM
ejpam-6798	421	1	(	(	PUNCT
ejpam-6798	421	2	γl1(s)∨γl2(s))e	γl1(s)∨γl2(s))e	VERB
ejpam-6798	421	3	ι(θl1	ι(θl1	PROPN
ejpam-6798	421	4	(	(	PUNCT
ejpam-6798	421	5	s)∨θl2	s)∨θl2	PROPN
ejpam-6798	421	6	(	(	PUNCT
ejpam-6798	421	7	s	s	NOUN
ejpam-6798	421	8	)	)	PUNCT
ejpam-6798	421	9	)	)	PUNCT
ejpam-6798	421	10	,	,	PUNCT
ejpam-6798	421	11	νl1∪l2(s	νl1∪l2(s	NOUN
ejpam-6798	421	12	)	)	PUNCT
ejpam-6798	421	13	=	=	SYM
ejpam-6798	421	14	(	(	PUNCT
ejpam-6798	421	15	γl1	γl1	X
ejpam-6798	421	16	(	(	PUNCT
ejpam-6798	421	17	s)∧γl2	s)∧γl2	NOUN
ejpam-6798	421	18	(	(	PUNCT
ejpam-6798	421	19	s))eι(θl1	s))eι(θl1	NOUN
ejpam-6798	421	20	(	(	PUNCT
ejpam-6798	421	21	s)∧θl2	s)∧θl2	PROPN
ejpam-6798	421	22	(	(	PUNCT
ejpam-6798	421	23	s	s	NOUN
ejpam-6798	421	24	)	)	PUNCT
ejpam-6798	421	25	)	)	PUNCT
ejpam-6798	421	26	.	.	PUNCT
ejpam-6798	422	1	example	example	NOUN
ejpam-6798	423	1	9	9	NUM
ejpam-6798	423	2	.	.	PUNCT
ejpam-6798	424	1	let	let	VERB
ejpam-6798	424	2	(	(	PUNCT
ejpam-6798	424	3	µl1(s	µl1(s	PROPN
ejpam-6798	424	4	)	)	PUNCT
ejpam-6798	424	5	,	,	PUNCT
ejpam-6798	424	6	νl1(s	νl1(s	PROPN
ejpam-6798	424	7	)	)	PUNCT
ejpam-6798	424	8	)	)	PUNCT
ejpam-6798	425	1	=	=	PRON
ejpam-6798	425	2	{	{	PUNCT
ejpam-6798	425	3	(	(	PUNCT
ejpam-6798	425	4	s1	s1	NOUN
ejpam-6798	425	5	,	,	PUNCT
ejpam-6798	425	6	0.6eι0.5π	0.6eι0.5π	PROPN
ejpam-6798	425	7	,	,	PUNCT
ejpam-6798	425	8	0.4eι0.25π	0.4eι0.25π	NOUN
ejpam-6798	425	9	)	)	PUNCT
ejpam-6798	425	10	,	,	PUNCT
ejpam-6798	425	11	(	(	PUNCT
ejpam-6798	425	12	s2	s2	PROPN
ejpam-6798	425	13	,	,	PUNCT
ejpam-6798	425	14	1eι0.5π	1eι0.5π	NUM
ejpam-6798	425	15	,	,	PUNCT
ejpam-6798	425	16	0.8eι0.25π	0.8eι0.25π	NOUN
ejpam-6798	425	17	)	)	PUNCT
ejpam-6798	425	18	,	,	PUNCT
ejpam-6798	425	19	(	(	PUNCT
ejpam-6798	425	20	s3	s3	PROPN
ejpam-6798	425	21	,	,	PUNCT
ejpam-6798	425	22	0.8eι2π	0.8eι2π	NUM
ejpam-6798	425	23	,	,	PUNCT
ejpam-6798	425	24	0.6eι1.5π	0.6eι1.5π	NUM
ejpam-6798	425	25	)	)	PUNCT
ejpam-6798	425	26	,	,	PUNCT
ejpam-6798	425	27	(	(	PUNCT
ejpam-6798	425	28	s4	s4	X
ejpam-6798	425	29	,	,	PUNCT
ejpam-6798	425	30	0.9e	0.9e	NOUN
ejpam-6798	425	31	ι0.4π	ι0.4π	NOUN
ejpam-6798	425	32	,	,	PUNCT
ejpam-6798	425	33	0.7eι0.24π	0.7eι0.24π	NOUN
ejpam-6798	425	34	)	)	PUNCT
ejpam-6798	425	35	,	,	PUNCT
ejpam-6798	425	36	(	(	PUNCT
ejpam-6798	425	37	s5	s5	PROPN
ejpam-6798	425	38	,	,	PUNCT
ejpam-6798	425	39	0.7e	0.7e	NOUN
ejpam-6798	425	40	ιπ	ιπ	ADJ
ejpam-6798	425	41	,	,	PUNCT
ejpam-6798	425	42	0.5eι0.8π	0.5eι0.8π	PROPN
ejpam-6798	425	43	)	)	PUNCT
ejpam-6798	425	44	,	,	PUNCT
ejpam-6798	425	45	(	(	PUNCT
ejpam-6798	425	46	s6	s6	PROPN
ejpam-6798	425	47	,	,	PUNCT
ejpam-6798	425	48	0.5e	0.5e	NUM
ejpam-6798	425	49	ι0.4π	ι0.4π	NOUN
ejpam-6798	425	50	,	,	PUNCT
ejpam-6798	425	51	0.3eι0.24π	0.3eι0.24π	NOUN
ejpam-6798	425	52	)	)	PUNCT
ejpam-6798	425	53	}	}	PUNCT
ejpam-6798	425	54	and	and	CCONJ
ejpam-6798	425	55	(	(	PUNCT
ejpam-6798	425	56	µl2(s	µl2(s	PROPN
ejpam-6798	425	57	)	)	PUNCT
ejpam-6798	425	58	,	,	PUNCT
ejpam-6798	425	59	νl2(s	νl2(s	PROPN
ejpam-6798	425	60	)	)	PUNCT
ejpam-6798	425	61	)	)	PUNCT
ejpam-6798	425	62	=	=	PRON
ejpam-6798	426	1	{	{	PUNCT
ejpam-6798	426	2	(	(	PUNCT
ejpam-6798	426	3	s1	s1	NOUN
ejpam-6798	426	4	,	,	PUNCT
ejpam-6798	426	5	0.2eιπ	0.2eιπ	NUM
ejpam-6798	426	6	,	,	PUNCT
ejpam-6798	426	7	0.1eι0.88π	0.1eι0.88π	NUM
ejpam-6798	426	8	)	)	PUNCT
ejpam-6798	426	9	,	,	PUNCT
ejpam-6798	426	10	(	(	PUNCT
ejpam-6798	426	11	s2	s2	PROPN
ejpam-6798	426	12	,	,	PUNCT
ejpam-6798	426	13	0.1eι0.8π	0.1eι0.8π	NOUN
ejpam-6798	426	14	,	,	PUNCT
ejpam-6798	426	15	0.01eι0.6π	0.01eι0.6π	NUM
ejpam-6798	426	16	)	)	PUNCT
ejpam-6798	426	17	,	,	PUNCT
ejpam-6798	426	18	(	(	PUNCT
ejpam-6798	426	19	s3	s3	PROPN
ejpam-6798	426	20	,	,	PUNCT
ejpam-6798	426	21	0.8eι0.8π	0.8eι0.8π	PROPN
ejpam-6798	426	22	,	,	PUNCT
ejpam-6798	426	23	0.6eι0.68π	0.6eι0.68π	NOUN
ejpam-6798	426	24	)	)	PUNCT
ejpam-6798	426	25	,	,	PUNCT
ejpam-6798	426	26	(	(	PUNCT
ejpam-6798	426	27	s4	s4	PROPN
ejpam-6798	426	28	,	,	PUNCT
ejpam-6798	426	29	0.2eιπ	0.2eιπ	NUM
ejpam-6798	426	30	,	,	PUNCT
ejpam-6798	426	31	0.1eι0.88π	0.1eι0.88π	NUM
ejpam-6798	426	32	)	)	PUNCT
ejpam-6798	426	33	,	,	PUNCT
ejpam-6798	426	34	(	(	PUNCT
ejpam-6798	426	35	s5	s5	PROPN
ejpam-6798	426	36	,	,	PUNCT
ejpam-6798	426	37	0.9e	0.9e	PROPN
ejpam-6798	426	38	ι0.9π	ι0.9π	PROPN
ejpam-6798	426	39	,	,	PUNCT
ejpam-6798	426	40	0.7eι0.7π	0.7eι0.7π	PROPN
ejpam-6798	426	41	)	)	PUNCT
ejpam-6798	426	42	,	,	PUNCT
ejpam-6798	426	43	(	(	PUNCT
ejpam-6798	426	44	s6	s6	PROPN
ejpam-6798	426	45	,	,	PUNCT
ejpam-6798	426	46	0.3e	0.3e	NOUN
ejpam-6798	426	47	ι2π	ι2π	NOUN
ejpam-6798	426	48	,	,	PUNCT
ejpam-6798	426	49	0.1eι1.88π	0.1eι1.88π	PROPN
ejpam-6798	426	50	)	)	PUNCT
ejpam-6798	426	51	}	}	PUNCT
ejpam-6798	426	52	be	be	AUX
ejpam-6798	426	53	a	a	DET
ejpam-6798	426	54	cifss	cifss	NOUN
ejpam-6798	426	55	.	.	PUNCT
ejpam-6798	427	1	then	then	ADV
ejpam-6798	427	2	,	,	PUNCT
ejpam-6798	427	3	(	(	PUNCT
ejpam-6798	427	4	µl1∪l2(s	µl1∪l2(s	NOUN
ejpam-6798	427	5	)	)	PUNCT
ejpam-6798	427	6	,	,	PUNCT
ejpam-6798	427	7	νl1∪l2(s	νl1∪l2(s	NOUN
ejpam-6798	427	8	)	)	PUNCT
ejpam-6798	427	9	)	)	PUNCT
ejpam-6798	428	1	=	=	PRON
ejpam-6798	428	2	{	{	PUNCT
ejpam-6798	428	3	(	(	PUNCT
ejpam-6798	428	4	s1	s1	NOUN
ejpam-6798	428	5	,	,	PUNCT
ejpam-6798	428	6	0.6eιπ	0.6eιπ	NUM
ejpam-6798	428	7	,	,	PUNCT
ejpam-6798	428	8	0.1eι0.25π	0.1eι0.25π	NOUN
ejpam-6798	428	9	)	)	PUNCT
ejpam-6798	428	10	,	,	PUNCT
ejpam-6798	428	11	(	(	PUNCT
ejpam-6798	428	12	s2	s2	PROPN
ejpam-6798	428	13	,	,	PUNCT
ejpam-6798	428	14	1eι0.8π	1eι0.8π	NUM
ejpam-6798	428	15	,	,	PUNCT
ejpam-6798	428	16	0.01eι0.25π	0.01eι0.25π	NOUN
ejpam-6798	428	17	)	)	PUNCT
ejpam-6798	428	18	,	,	PUNCT
ejpam-6798	428	19	(	(	PUNCT
ejpam-6798	428	20	s3	s3	PROPN
ejpam-6798	428	21	,	,	PUNCT
ejpam-6798	428	22	0.8eι2π	0.8eι2π	NUM
ejpam-6798	428	23	,	,	PUNCT
ejpam-6798	428	24	0.6eι0.68π	0.6eι0.68π	NOUN
ejpam-6798	428	25	)	)	PUNCT
ejpam-6798	428	26	,	,	PUNCT
ejpam-6798	428	27	(	(	PUNCT
ejpam-6798	428	28	s4	s4	PROPN
ejpam-6798	428	29	,	,	PUNCT
ejpam-6798	428	30	0.9eιπ	0.9eιπ	NUM
ejpam-6798	428	31	,	,	PUNCT
ejpam-6798	428	32	0.1eι0.24π	0.1eι0.24π	NUM
ejpam-6798	428	33	)	)	PUNCT
ejpam-6798	428	34	,	,	PUNCT
ejpam-6798	428	35	(	(	PUNCT
ejpam-6798	428	36	s5	s5	PROPN
ejpam-6798	428	37	,	,	PUNCT
ejpam-6798	428	38	0.9e	0.9e	PROPN
ejpam-6798	428	39	ιπ	ιπ	PROPN
ejpam-6798	428	40	,	,	PUNCT
ejpam-6798	428	41	0.5eι0.7π	0.5eι0.7π	PROPN
ejpam-6798	428	42	)	)	PUNCT
ejpam-6798	428	43	,	,	PUNCT
ejpam-6798	428	44	(	(	PUNCT
ejpam-6798	428	45	s6	s6	PROPN
ejpam-6798	428	46	,	,	PUNCT
ejpam-6798	428	47	0.5e	0.5e	NUM
ejpam-6798	428	48	ι2π	ι2π	NOUN
ejpam-6798	428	49	,	,	PUNCT
ejpam-6798	428	50	0.1eι0.24π	0.1eι0.24π	NUM
ejpam-6798	428	51	)	)	PUNCT
ejpam-6798	428	52	}	}	PUNCT
ejpam-6798	428	53	.	.	PUNCT
ejpam-6798	429	1	the	the	DET
ejpam-6798	429	2	subsequent	subsequent	ADJ
ejpam-6798	429	3	theorem	theorem	NOUN
ejpam-6798	429	4	demonstrates	demonstrate	VERB
ejpam-6798	429	5	that	that	SCONJ
ejpam-6798	429	6	the	the	DET
ejpam-6798	429	7	union	union	NOUN
ejpam-6798	429	8	∪	∪	NOUN
ejpam-6798	429	9	of	of	ADP
ejpam-6798	429	10	two	two	NUM
ejpam-6798	429	11	cifis	cifis	NOUN
ejpam-6798	429	12	of	of	ADP
ejpam-6798	429	13	m	m	PROPN
ejpam-6798	429	14	is	be	AUX
ejpam-6798	429	15	also	also	ADV
ejpam-6798	429	16	cifi	cifi	NOUN
ejpam-6798	429	17	.	.	PUNCT
ejpam-6798	430	1	theorem	theorem	ADJ
ejpam-6798	430	2	10	10	NUM
ejpam-6798	430	3	.	.	PUNCT
ejpam-6798	431	1	assume	assume	VERB
ejpam-6798	431	2	that	that	SCONJ
ejpam-6798	431	3	l1	l1	PROPN
ejpam-6798	431	4	and	and	CCONJ
ejpam-6798	431	5	l2	l2	NOUN
ejpam-6798	431	6	are	be	AUX
ejpam-6798	431	7	two	two	NUM
ejpam-6798	431	8	cifis	cifis	NOUN
ejpam-6798	431	9	of	of	ADP
ejpam-6798	431	10	m	m	PROPN
ejpam-6798	431	11	.	.	PUNCT
ejpam-6798	432	1	then	then	ADV
ejpam-6798	432	2	,	,	PUNCT
ejpam-6798	432	3	l1	l1	PROPN
ejpam-6798	432	4	∪	∪	PROPN
ejpam-6798	432	5	l2	l2	PROPN
ejpam-6798	432	6	is	be	AUX
ejpam-6798	432	7	a	a	DET
ejpam-6798	432	8	cifi	cifi	NOUN
ejpam-6798	432	9	of	of	ADP
ejpam-6798	432	10	m	m	PROPN
ejpam-6798	432	11	.	.	PUNCT
ejpam-6798	433	1	proof	proof	NOUN
ejpam-6798	433	2	.	.	PUNCT
ejpam-6798	434	1	let	let	VERB
ejpam-6798	434	2	l1	l1	PROPN
ejpam-6798	434	3	and	and	CCONJ
ejpam-6798	434	4	l2	l2	NOUN
ejpam-6798	434	5	be	be	AUX
ejpam-6798	434	6	two	two	NUM
ejpam-6798	434	7	cifis	cifis	NOUN
ejpam-6798	434	8	of	of	ADP
ejpam-6798	434	9	m	m	PRON
ejpam-6798	434	10	and	and	CCONJ
ejpam-6798	434	11	let	let	VERB
ejpam-6798	434	12	s	s	NOUN
ejpam-6798	434	13	,	,	PUNCT
ejpam-6798	434	14	l	l	PROPN
ejpam-6798	434	15	∈	∈	PROPN
ejpam-6798	434	16	m	m	VERB
ejpam-6798	434	17	.	.	PUNCT
ejpam-6798	435	1	then	then	ADV
ejpam-6798	435	2	µl1∪l2(0	µl1∪l2(0	NUM
ejpam-6798	435	3	)	)	PUNCT
ejpam-6798	435	4	=	=	SYM
ejpam-6798	435	5	(	(	PUNCT
ejpam-6798	435	6	γl1(0	γl1(0	NOUN
ejpam-6798	435	7	)	)	PUNCT
ejpam-6798	435	8	∨	∨	NUM
ejpam-6798	435	9	γl2(0))e	γl2(0))e	PROPN
ejpam-6798	435	10	ι(θl1	ι(θl1	PROPN
ejpam-6798	435	11	(	(	PUNCT
ejpam-6798	435	12	0)∨θl2	0)∨θl2	NUM
ejpam-6798	435	13	(	(	PUNCT
ejpam-6798	435	14	0	0	NUM
ejpam-6798	435	15	)	)	PUNCT
ejpam-6798	435	16	)	)	PUNCT
ejpam-6798	435	17	≥	≥	NOUN
ejpam-6798	435	18	(	(	PUNCT
ejpam-6798	435	19	γl1(s	γl1(s	PROPN
ejpam-6798	435	20	)	)	PUNCT
ejpam-6798	435	21	∨	∨	NOUN
ejpam-6798	435	22	γl2(s))e	γl2(s))e	PROPN
ejpam-6798	435	23	ι(θl1	ι(θl1	PROPN
ejpam-6798	435	24	(	(	PUNCT
ejpam-6798	435	25	s)∨θl2	s)∨θl2	PROPN
ejpam-6798	435	26	(	(	PUNCT
ejpam-6798	435	27	s	s	NOUN
ejpam-6798	435	28	)	)	PUNCT
ejpam-6798	435	29	)	)	PUNCT
ejpam-6798	435	30	=	=	SYM
ejpam-6798	435	31	µl1∪l2(s	µl1∪l2(s	NOUN
ejpam-6798	435	32	)	)	PUNCT
ejpam-6798	435	33	.	.	PUNCT
ejpam-6798	436	1	moreover	moreover	ADV
ejpam-6798	436	2	µl1∪l2(s	µl1∪l2(s	NOUN
ejpam-6798	436	3	)	)	PUNCT
ejpam-6798	436	4	=	=	SYM
ejpam-6798	436	5	(	(	PUNCT
ejpam-6798	436	6	γl1(s	γl1(s	PROPN
ejpam-6798	436	7	)	)	PUNCT
ejpam-6798	436	8	∨	∨	NOUN
ejpam-6798	436	9	γl2(s))e	γl2(s))e	PROPN
ejpam-6798	437	1	ι(θl1	ι(θl1	PROPN
ejpam-6798	437	2	(	(	PUNCT
ejpam-6798	437	3	s)∨θl2	s)∨θl2	PROPN
ejpam-6798	437	4	(	(	PUNCT
ejpam-6798	437	5	s	s	NOUN
ejpam-6798	437	6	)	)	PUNCT
ejpam-6798	437	7	)	)	PUNCT
ejpam-6798	437	8	≥	≥	NOUN
ejpam-6798	437	9	(	(	PUNCT
ejpam-6798	437	10	(	(	PUNCT
ejpam-6798	437	11	γl1(s	γl1(s	X
ejpam-6798	437	12	⋆	⋆	ADJ
ejpam-6798	437	13	l	l	NOUN
ejpam-6798	437	14	)	)	PUNCT
ejpam-6798	437	15	∧	∧	PROPN
ejpam-6798	437	16	γl1(l	γl1(l	PROPN
ejpam-6798	437	17	)	)	PUNCT
ejpam-6798	437	18	)	)	PUNCT
ejpam-6798	437	19	∨	∨	NUM
ejpam-6798	437	20	(	(	PUNCT
ejpam-6798	437	21	γl2(s	γl2(s	PROPN
ejpam-6798	437	22	⋆	⋆	NOUN
ejpam-6798	437	23	l	l	NOUN
ejpam-6798	437	24	)	)	PUNCT
ejpam-6798	437	25	∧	∧	PROPN
ejpam-6798	437	26	γl2(l	γl2(l	NOUN
ejpam-6798	437	27	)	)	PUNCT
ejpam-6798	437	28	)	)	PUNCT
ejpam-6798	437	29	)	)	PUNCT
ejpam-6798	438	1	eι((θl1	eι((θl1	NOUN
ejpam-6798	438	2	(	(	PUNCT
ejpam-6798	438	3	s⋆l)∧θl1	s⋆l)∧θl1	PROPN
ejpam-6798	438	4	(	(	PUNCT
ejpam-6798	438	5	l))∨(θl2	l))∨(θl2	PROPN
ejpam-6798	438	6	(	(	PUNCT
ejpam-6798	438	7	s⋆l)∧θl2	s⋆l)∧θl2	NOUN
ejpam-6798	438	8	(	(	PUNCT
ejpam-6798	438	9	l	l	NOUN
ejpam-6798	438	10	)	)	PUNCT
ejpam-6798	438	11	)	)	PUNCT
ejpam-6798	438	12	)	)	PUNCT
ejpam-6798	438	13	≥	≥	X
ejpam-6798	438	14	(	(	PUNCT
ejpam-6798	438	15	(	(	PUNCT
ejpam-6798	438	16	γl1(s	γl1(s	X
ejpam-6798	438	17	⋆	⋆	PROPN
ejpam-6798	438	18	l	l	NOUN
ejpam-6798	438	19	)	)	PUNCT
ejpam-6798	438	20	∨	∨	NUM
ejpam-6798	438	21	γl2(s	γl2(s	PROPN
ejpam-6798	438	22	⋆	⋆	VERB
ejpam-6798	438	23	l	l	NOUN
ejpam-6798	438	24	)	)	PUNCT
ejpam-6798	438	25	)	)	PUNCT
ejpam-6798	439	1	∧	∧	PROPN
ejpam-6798	439	2	(	(	PUNCT
ejpam-6798	439	3	γl1(l	γl1(l	PROPN
ejpam-6798	439	4	)	)	PUNCT
ejpam-6798	439	5	∨	∨	NUM
ejpam-6798	439	6	γl2(l	γl2(l	PROPN
ejpam-6798	439	7	)	)	PUNCT
ejpam-6798	439	8	)	)	PUNCT
ejpam-6798	439	9	)	)	PUNCT
ejpam-6798	440	1	eι((θl1	eι((θl1	NOUN
ejpam-6798	440	2	(	(	PUNCT
ejpam-6798	440	3	s⋆l)∨θl2	s⋆l)∨θl2	NOUN
ejpam-6798	440	4	(	(	PUNCT
ejpam-6798	440	5	s⋆l))∧(θl1	s⋆l))∧(θl1	PROPN
ejpam-6798	440	6	(	(	PUNCT
ejpam-6798	440	7	l)∨θl2	l)∨θl2	NOUN
ejpam-6798	440	8	(	(	PUNCT
ejpam-6798	440	9	l	l	NOUN
ejpam-6798	440	10	)	)	PUNCT
ejpam-6798	440	11	)	)	PUNCT
ejpam-6798	440	12	)	)	PUNCT
ejpam-6798	441	1	=	=	PUNCT
ejpam-6798	441	2	(	(	PUNCT
ejpam-6798	441	3	γl1(s	γl1(s	X
ejpam-6798	441	4	⋆	⋆	PROPN
ejpam-6798	441	5	l	l	NOUN
ejpam-6798	441	6	)	)	PUNCT
ejpam-6798	441	7	∨	∨	NUM
ejpam-6798	441	8	γl2(s	γl2(s	PROPN
ejpam-6798	441	9	⋆	⋆	VERB
ejpam-6798	441	10	l))e	l))e	PROPN
ejpam-6798	441	11	ι(θl1	ι(θl1	PROPN
ejpam-6798	441	12	(	(	PUNCT
ejpam-6798	441	13	s⋆l)∨θl2	s⋆l)∨θl2	NOUN
ejpam-6798	441	14	(	(	PUNCT
ejpam-6798	441	15	s⋆l	s⋆l	NOUN
ejpam-6798	441	16	)	)	PUNCT
ejpam-6798	441	17	)	)	PUNCT
ejpam-6798	442	1	∧	∧	PROPN
ejpam-6798	442	2	(	(	PUNCT
ejpam-6798	442	3	γl1(l	γl1(l	PROPN
ejpam-6798	442	4	)	)	PUNCT
ejpam-6798	442	5	∨	∨	NUM
ejpam-6798	442	6	γl2(l))e	γl2(l))e	PROPN
ejpam-6798	442	7	ι(θl1	ι(θl1	PROPN
ejpam-6798	442	8	(	(	PUNCT
ejpam-6798	442	9	l)∨θl2	l)∨θl2	NOUN
ejpam-6798	442	10	(	(	PUNCT
ejpam-6798	442	11	l	l	NOUN
ejpam-6798	442	12	)	)	PUNCT
ejpam-6798	442	13	)	)	PUNCT
ejpam-6798	442	14	≥	≥	PROPN
ejpam-6798	442	15	µl1∪l2(s	µl1∪l2(s	NOUN
ejpam-6798	442	16	⋆	⋆	NOUN
ejpam-6798	442	17	l	l	NOUN
ejpam-6798	442	18	)	)	PUNCT
ejpam-6798	442	19	∧	∧	PROPN
ejpam-6798	442	20	µl1∪l2(l	µl1∪l2(l	NOUN
ejpam-6798	442	21	)	)	PUNCT
ejpam-6798	442	22	.	.	PUNCT
ejpam-6798	442	23	suppose	suppose	VERB
ejpam-6798	442	24	that	that	SCONJ
ejpam-6798	442	25	l1	l1	PROPN
ejpam-6798	442	26	and	and	CCONJ
ejpam-6798	442	27	l2	l2	NOUN
ejpam-6798	442	28	are	be	AUX
ejpam-6798	442	29	two	two	NUM
ejpam-6798	442	30	cifis	cifis	NOUN
ejpam-6798	442	31	of	of	ADP
ejpam-6798	442	32	m	m	PRON
ejpam-6798	442	33	and	and	CCONJ
ejpam-6798	442	34	let	let	VERB
ejpam-6798	442	35	s	s	NOUN
ejpam-6798	442	36	,	,	PUNCT
ejpam-6798	442	37	l	l	PROPN
ejpam-6798	442	38	∈	∈	PROPN
ejpam-6798	442	39	m	m	VERB
ejpam-6798	442	40	.	.	PUNCT
ejpam-6798	443	1	then	then	ADV
ejpam-6798	443	2	νl1∪l2(0	νl1∪l2(0	PROPN
ejpam-6798	443	3	)	)	PUNCT
ejpam-6798	444	1	=	=	PUNCT
ejpam-6798	444	2	(	(	PUNCT
ejpam-6798	444	3	γl1	γl1	NOUN
ejpam-6798	444	4	(	(	PUNCT
ejpam-6798	444	5	0	0	NUM
ejpam-6798	444	6	)	)	PUNCT
ejpam-6798	444	7	∧	∧	NOUN
ejpam-6798	444	8	γl2	γl2	PROPN
ejpam-6798	444	9	(	(	PUNCT
ejpam-6798	444	10	0))eι(θl1	0))eι(θl1	NUM
ejpam-6798	444	11	(	(	PUNCT
ejpam-6798	444	12	0)∧θl2	0)∧θl2	NOUN
ejpam-6798	444	13	(	(	PUNCT
ejpam-6798	444	14	0	0	NUM
ejpam-6798	444	15	)	)	PUNCT
ejpam-6798	444	16	)	)	PUNCT
ejpam-6798	444	17	≤	≤	NOUN
ejpam-6798	444	18	(	(	PUNCT
ejpam-6798	444	19	γl1	γl1	NOUN
ejpam-6798	444	20	(	(	PUNCT
ejpam-6798	444	21	s	s	NOUN
ejpam-6798	444	22	)	)	PUNCT
ejpam-6798	444	23	∧	∧	NOUN
ejpam-6798	444	24	γl2	γl2	NOUN
ejpam-6798	444	25	(	(	PUNCT
ejpam-6798	444	26	s))eι(θl1	s))eι(θl1	NOUN
ejpam-6798	444	27	(	(	PUNCT
ejpam-6798	444	28	s)∧θl2	s)∧θl2	PROPN
ejpam-6798	444	29	(	(	PUNCT
ejpam-6798	444	30	s	s	NOUN
ejpam-6798	444	31	)	)	PUNCT
ejpam-6798	444	32	)	)	PUNCT
ejpam-6798	444	33	=	=	SYM
ejpam-6798	444	34	νl1∪l2(s	νl1∪l2(s	NOUN
ejpam-6798	444	35	)	)	PUNCT
ejpam-6798	444	36	.	.	PUNCT
ejpam-6798	445	1	moreover	moreover	ADV
ejpam-6798	445	2	νl1∪l2(s	νl1∪l2(s	NOUN
ejpam-6798	445	3	)	)	PUNCT
ejpam-6798	445	4	=	=	SYM
ejpam-6798	445	5	(	(	PUNCT
ejpam-6798	445	6	γl1	γl1	X
ejpam-6798	445	7	(	(	PUNCT
ejpam-6798	445	8	s	s	NOUN
ejpam-6798	445	9	)	)	PUNCT
ejpam-6798	445	10	∧	∧	NOUN
ejpam-6798	445	11	γl2	γl2	NOUN
ejpam-6798	445	12	(	(	PUNCT
ejpam-6798	445	13	s))eι(θl1	s))eι(θl1	NOUN
ejpam-6798	445	14	(	(	PUNCT
ejpam-6798	445	15	s)∧θl2	s)∧θl2	PROPN
ejpam-6798	445	16	(	(	PUNCT
ejpam-6798	445	17	s	s	NOUN
ejpam-6798	445	18	)	)	PUNCT
ejpam-6798	445	19	)	)	PUNCT
ejpam-6798	445	20	≤	≤	NOUN
ejpam-6798	445	21	(	(	PUNCT
ejpam-6798	445	22	(	(	PUNCT
ejpam-6798	445	23	γl1	γl1	NOUN
ejpam-6798	445	24	(	(	PUNCT
ejpam-6798	445	25	s	s	X
ejpam-6798	445	26	⋆	⋆	NOUN
ejpam-6798	445	27	l	l	NOUN
ejpam-6798	445	28	)	)	PUNCT
ejpam-6798	445	29	∨	∨	NUM
ejpam-6798	445	30	γl1	γl1	NOUN
ejpam-6798	445	31	(	(	PUNCT
ejpam-6798	445	32	l	l	NOUN
ejpam-6798	445	33	)	)	PUNCT
ejpam-6798	445	34	)	)	PUNCT
ejpam-6798	445	35	∧	∧	NOUN
ejpam-6798	445	36	(	(	PUNCT
ejpam-6798	445	37	γl2	γl2	PROPN
ejpam-6798	445	38	(	(	PUNCT
ejpam-6798	445	39	s	s	X
ejpam-6798	445	40	⋆	⋆	NOUN
ejpam-6798	445	41	l	l	NOUN
ejpam-6798	445	42	)	)	PUNCT
ejpam-6798	445	43	∨	∨	NUM
ejpam-6798	445	44	γl2	γl2	PROPN
ejpam-6798	445	45	(	(	PUNCT
ejpam-6798	445	46	l	l	NOUN
ejpam-6798	445	47	)	)	PUNCT
ejpam-6798	445	48	)	)	PUNCT
ejpam-6798	445	49	)	)	PUNCT
ejpam-6798	446	1	m.	m.	NOUN
ejpam-6798	446	2	jawad	jawad	PROPN
ejpam-6798	446	3	et	et	PROPN
ejpam-6798	446	4	al	al	PROPN
ejpam-6798	446	5	.	.	PUNCT
ejpam-6798	446	6	/	/	SYM
ejpam-6798	446	7	eur	eur	PROPN
ejpam-6798	446	8	.	.	PUNCT
ejpam-6798	447	1	j.	j.	PROPN
ejpam-6798	447	2	pure	pure	PROPN
ejpam-6798	447	3	appl	appl	PROPN
ejpam-6798	447	4	.	.	PROPN
ejpam-6798	447	5	math	math	PROPN
ejpam-6798	447	6	,	,	PUNCT
ejpam-6798	447	7	18	18	NUM
ejpam-6798	447	8	(	(	PUNCT
ejpam-6798	447	9	4	4	NUM
ejpam-6798	447	10	)	)	PUNCT
ejpam-6798	447	11	(	(	PUNCT
ejpam-6798	447	12	2025	2025	NUM
ejpam-6798	447	13	)	)	PUNCT
ejpam-6798	447	14	,	,	PUNCT
ejpam-6798	447	15	6798	6798	NUM
ejpam-6798	447	16	14	14	NUM
ejpam-6798	447	17	of	of	ADP
ejpam-6798	447	18	22	22	NUM
ejpam-6798	447	19	eι((θl1	eι((θl1	NOUN
ejpam-6798	447	20	(	(	PUNCT
ejpam-6798	447	21	s⋆l)∨θl1	s⋆l)∨θl1	NOUN
ejpam-6798	447	22	(	(	PUNCT
ejpam-6798	447	23	l))∧(θl2	l))∧(θl2	X
ejpam-6798	447	24	(	(	PUNCT
ejpam-6798	447	25	s⋆l)∨θl2	s⋆l)∨θl2	NOUN
ejpam-6798	447	26	(	(	PUNCT
ejpam-6798	447	27	l	l	NOUN
ejpam-6798	447	28	)	)	PUNCT
ejpam-6798	447	29	)	)	PUNCT
ejpam-6798	447	30	)	)	PUNCT
ejpam-6798	447	31	≤	≤	NOUN
ejpam-6798	448	1	(	(	PUNCT
ejpam-6798	448	2	(	(	PUNCT
ejpam-6798	448	3	γl1	γl1	NOUN
ejpam-6798	448	4	(	(	PUNCT
ejpam-6798	448	5	s	s	X
ejpam-6798	448	6	⋆	⋆	NOUN
ejpam-6798	448	7	l	l	NOUN
ejpam-6798	448	8	)	)	PUNCT
ejpam-6798	448	9	∧	∧	NOUN
ejpam-6798	448	10	γl2	γl2	NOUN
ejpam-6798	448	11	(	(	PUNCT
ejpam-6798	448	12	s	s	X
ejpam-6798	448	13	⋆	⋆	NOUN
ejpam-6798	448	14	l	l	NOUN
ejpam-6798	448	15	)	)	PUNCT
ejpam-6798	448	16	)	)	PUNCT
ejpam-6798	448	17	∨	∨	NUM
ejpam-6798	448	18	(	(	PUNCT
ejpam-6798	448	19	γl1	γl1	NOUN
ejpam-6798	448	20	(	(	PUNCT
ejpam-6798	448	21	l	l	NOUN
ejpam-6798	448	22	)	)	PUNCT
ejpam-6798	448	23	∧	∧	NOUN
ejpam-6798	448	24	γl2	γl2	PROPN
ejpam-6798	448	25	(	(	PUNCT
ejpam-6798	448	26	l	l	NOUN
ejpam-6798	448	27	)	)	PUNCT
ejpam-6798	448	28	)	)	PUNCT
ejpam-6798	448	29	)	)	PUNCT
ejpam-6798	448	30	eι((θl1	eι((θl1	NOUN
ejpam-6798	448	31	(	(	PUNCT
ejpam-6798	448	32	s⋆l)∧θl2	s⋆l)∧θl2	NOUN
ejpam-6798	448	33	(	(	PUNCT
ejpam-6798	448	34	s⋆l))∨(θl1	s⋆l))∨(θl1	VERB
ejpam-6798	448	35	(	(	PUNCT
ejpam-6798	448	36	l)∧θl2	l)∧θl2	PROPN
ejpam-6798	448	37	(	(	PUNCT
ejpam-6798	448	38	l	l	NOUN
ejpam-6798	448	39	)	)	PUNCT
ejpam-6798	448	40	)	)	PUNCT
ejpam-6798	448	41	)	)	PUNCT
ejpam-6798	449	1	=	=	PRON
ejpam-6798	449	2	(	(	PUNCT
ejpam-6798	449	3	γl1	γl1	NOUN
ejpam-6798	449	4	(	(	PUNCT
ejpam-6798	449	5	s	s	X
ejpam-6798	449	6	⋆	⋆	NOUN
ejpam-6798	449	7	l	l	NOUN
ejpam-6798	449	8	)	)	PUNCT
ejpam-6798	449	9	∧	∧	NOUN
ejpam-6798	449	10	γl2	γl2	NOUN
ejpam-6798	449	11	(	(	PUNCT
ejpam-6798	449	12	s	s	X
ejpam-6798	449	13	⋆	⋆	X
ejpam-6798	449	14	l))eι(θl1	l))eι(θl1	NOUN
ejpam-6798	449	15	(	(	PUNCT
ejpam-6798	449	16	s⋆l)∧θl2	s⋆l)∧θl2	NOUN
ejpam-6798	449	17	(	(	PUNCT
ejpam-6798	449	18	s⋆l	s⋆l	NOUN
ejpam-6798	449	19	)	)	PUNCT
ejpam-6798	449	20	)	)	PUNCT
ejpam-6798	449	21	∨	∨	NUM
ejpam-6798	449	22	(	(	PUNCT
ejpam-6798	449	23	γl1	γl1	NOUN
ejpam-6798	449	24	(	(	PUNCT
ejpam-6798	449	25	l	l	NOUN
ejpam-6798	449	26	)	)	PUNCT
ejpam-6798	449	27	∧	∧	NOUN
ejpam-6798	449	28	γl2	γl2	NOUN
ejpam-6798	449	29	(	(	PUNCT
ejpam-6798	449	30	l))eι(θl1	l))eι(θl1	X
ejpam-6798	449	31	(	(	PUNCT
ejpam-6798	449	32	l)∧θl2	l)∧θl2	PROPN
ejpam-6798	449	33	(	(	PUNCT
ejpam-6798	449	34	l	l	NOUN
ejpam-6798	449	35	)	)	PUNCT
ejpam-6798	449	36	)	)	PUNCT
ejpam-6798	449	37	≤	≤	NUM
ejpam-6798	449	38	νl1∪l2(s	νl1∪l2(s	VERB
ejpam-6798	449	39	⋆	⋆	ADJ
ejpam-6798	449	40	l	l	NOUN
ejpam-6798	449	41	)	)	PUNCT
ejpam-6798	449	42	∨	∨	NUM
ejpam-6798	449	43	νl1∪l2(l	νl1∪l2(l	NOUN
ejpam-6798	449	44	)	)	PUNCT
ejpam-6798	449	45	.	.	PUNCT
ejpam-6798	450	1	therefore	therefore	ADV
ejpam-6798	450	2	,	,	PUNCT
ejpam-6798	450	3	l1	l1	PROPN
ejpam-6798	450	4	∪	∪	PROPN
ejpam-6798	450	5	l2	l2	PROPN
ejpam-6798	450	6	is	be	AUX
ejpam-6798	450	7	a	a	DET
ejpam-6798	450	8	cifi	cifi	NOUN
ejpam-6798	450	9	of	of	ADP
ejpam-6798	450	10	m	m	PROPN
ejpam-6798	450	11	.	.	PUNCT
ejpam-6798	451	1	example	example	NOUN
ejpam-6798	451	2	10	10	NUM
ejpam-6798	451	3	.	.	PUNCT
ejpam-6798	452	1	take	take	VERB
ejpam-6798	452	2	a	a	DET
ejpam-6798	452	3	bck	bck	NOUN
ejpam-6798	452	4	-	-	PUNCT
ejpam-6798	452	5	algebra	algebra	NOUN
ejpam-6798	452	6	m	m	NOUN
ejpam-6798	452	7	=	=	SYM
ejpam-6798	452	8	{	{	PUNCT
ejpam-6798	452	9	0	0	NUM
ejpam-6798	452	10	,	,	PUNCT
ejpam-6798	452	11	s	s	X
ejpam-6798	452	12	,	,	PUNCT
ejpam-6798	452	13	l	l	NOUN
ejpam-6798	452	14	,	,	PUNCT
ejpam-6798	452	15	z	z	NOUN
ejpam-6798	452	16	,	,	PUNCT
ejpam-6798	452	17	w	w	PROPN
ejpam-6798	452	18	}	}	PUNCT
ejpam-6798	452	19	,	,	PUNCT
ejpam-6798	452	20	where	where	SCONJ
ejpam-6798	452	21	the	the	DET
ejpam-6798	452	22	binary	binary	ADJ
ejpam-6798	452	23	operation	operation	NOUN
ejpam-6798	452	24	is	be	AUX
ejpam-6798	452	25	defined	define	VERB
ejpam-6798	452	26	by	by	ADP
ejpam-6798	452	27	the	the	DET
ejpam-6798	452	28	caley	caley	NOUN
ejpam-6798	452	29	table	table	NOUN
ejpam-6798	452	30	5	5	NUM
ejpam-6798	452	31	.	.	PUNCT
ejpam-6798	452	32	now	now	ADV
ejpam-6798	452	33	define	define	VERB
ejpam-6798	452	34	a	a	DET
ejpam-6798	452	35	cifs	cifs	NOUN
ejpam-6798	452	36	l1	l1	NOUN
ejpam-6798	452	37	on	on	ADP
ejpam-6798	452	38	m	m	NOUN
ejpam-6798	452	39	as	as	ADP
ejpam-6798	452	40	:	:	PUNCT
ejpam-6798	452	41	l1	l1	PROPN
ejpam-6798	452	42	=	=	SYM
ejpam-6798	452	43	{	{	PUNCT
ejpam-6798	452	44	(	(	PUNCT
ejpam-6798	452	45	0	0	NUM
ejpam-6798	452	46	,	,	PUNCT
ejpam-6798	452	47	0.9eι0.7π	0.9eι0.7π	PROPN
ejpam-6798	452	48	,	,	PUNCT
ejpam-6798	452	49	0.7eι0.5π	0.7eι0.5π	PROPN
ejpam-6798	452	50	)	)	PUNCT
ejpam-6798	452	51	,	,	PUNCT
ejpam-6798	452	52	(	(	PUNCT
ejpam-6798	452	53	s	s	X
ejpam-6798	452	54	,	,	PUNCT
ejpam-6798	452	55	0.7eι0.5π	0.7eι0.5π	PROPN
ejpam-6798	452	56	,	,	PUNCT
ejpam-6798	452	57	0.5eι0.3π	0.5eι0.3π	PROPN
ejpam-6798	452	58	)	)	PUNCT
ejpam-6798	452	59	,	,	PUNCT
ejpam-6798	452	60	(	(	PUNCT
ejpam-6798	452	61	l	l	NOUN
ejpam-6798	452	62	,	,	PUNCT
ejpam-6798	452	63	0.5eι0.3π	0.5eι0.3π	NOUN
ejpam-6798	452	64	,	,	PUNCT
ejpam-6798	452	65	0.3eι0.1π	0.3eι0.1π	PROPN
ejpam-6798	452	66	)	)	PUNCT
ejpam-6798	452	67	,	,	PUNCT
ejpam-6798	452	68	(	(	PUNCT
ejpam-6798	452	69	z	z	NOUN
ejpam-6798	452	70	,	,	PUNCT
ejpam-6798	452	71	0.3eι0.1π	0.3eι0.1π	PROPN
ejpam-6798	452	72	,	,	PUNCT
ejpam-6798	452	73	0.1eι0.01π	0.1eι0.01π	NOUN
ejpam-6798	452	74	)	)	PUNCT
ejpam-6798	452	75	,	,	PUNCT
ejpam-6798	452	76	(	(	PUNCT
ejpam-6798	452	77	w	w	NOUN
ejpam-6798	452	78	,	,	PUNCT
ejpam-6798	452	79	0.3eι0.1π	0.3eι0.1π	PROPN
ejpam-6798	452	80	,	,	PUNCT
ejpam-6798	452	81	0.1eι0.01π	0.1eι0.01π	NOUN
ejpam-6798	452	82	)	)	PUNCT
ejpam-6798	452	83	}	}	PUNCT
ejpam-6798	452	84	.	.	PUNCT
ejpam-6798	453	1	it	it	PRON
ejpam-6798	453	2	is	be	AUX
ejpam-6798	453	3	easy	easy	ADJ
ejpam-6798	453	4	to	to	PART
ejpam-6798	453	5	show	show	VERB
ejpam-6798	453	6	that	that	SCONJ
ejpam-6798	453	7	l1	l1	PROPN
ejpam-6798	453	8	is	be	AUX
ejpam-6798	453	9	a	a	DET
ejpam-6798	453	10	cifi	cifi	NOUN
ejpam-6798	453	11	of	of	ADP
ejpam-6798	453	12	m	m	PROPN
ejpam-6798	453	13	.	.	PUNCT
ejpam-6798	454	1	now	now	ADV
ejpam-6798	454	2	define	define	VERB
ejpam-6798	454	3	a	a	DET
ejpam-6798	454	4	cifs	cifs	NOUN
ejpam-6798	454	5	l2	l2	NOUN
ejpam-6798	454	6	on	on	ADP
ejpam-6798	454	7	m	m	NOUN
ejpam-6798	454	8	as	as	ADP
ejpam-6798	454	9	:	:	PUNCT
ejpam-6798	454	10	l2	l2	NOUN
ejpam-6798	454	11	=	=	SYM
ejpam-6798	454	12	{	{	PUNCT
ejpam-6798	454	13	(	(	PUNCT
ejpam-6798	454	14	0	0	NUM
ejpam-6798	454	15	,	,	PUNCT
ejpam-6798	454	16	0.6eι0.5π	0.6eι0.5π	PROPN
ejpam-6798	454	17	,	,	PUNCT
ejpam-6798	454	18	0.4eι0.3π	0.4eι0.3π	PROPN
ejpam-6798	454	19	)	)	PUNCT
ejpam-6798	454	20	,	,	PUNCT
ejpam-6798	454	21	(	(	PUNCT
ejpam-6798	454	22	s	s	X
ejpam-6798	454	23	,	,	PUNCT
ejpam-6798	454	24	0.4eι0.6π	0.4eι0.6π	PROPN
ejpam-6798	454	25	,	,	PUNCT
ejpam-6798	454	26	0.2eι0.4π	0.2eι0.4π	PROPN
ejpam-6798	454	27	)	)	PUNCT
ejpam-6798	454	28	,	,	PUNCT
ejpam-6798	454	29	(	(	PUNCT
ejpam-6798	454	30	l	l	NOUN
ejpam-6798	454	31	,	,	PUNCT
ejpam-6798	454	32	0.6eι0.5π	0.6eι0.5π	PROPN
ejpam-6798	454	33	,	,	PUNCT
ejpam-6798	454	34	0.4eι0.3π	0.4eι0.3π	PROPN
ejpam-6798	454	35	)	)	PUNCT
ejpam-6798	454	36	,	,	PUNCT
ejpam-6798	454	37	(	(	PUNCT
ejpam-6798	454	38	z	z	X
ejpam-6798	454	39	,	,	PUNCT
ejpam-6798	454	40	0.4eι0.6π	0.4eι0.6π	PROPN
ejpam-6798	454	41	,	,	PUNCT
ejpam-6798	454	42	0.2eι0.4π	0.2eι0.4π	PROPN
ejpam-6798	454	43	)	)	PUNCT
ejpam-6798	454	44	,	,	PUNCT
ejpam-6798	454	45	(	(	PUNCT
ejpam-6798	454	46	w	w	X
ejpam-6798	454	47	,	,	PUNCT
ejpam-6798	454	48	0.4eι0.6π	0.4eι0.6π	PROPN
ejpam-6798	454	49	,	,	PUNCT
ejpam-6798	454	50	0.2eι0.4π	0.2eι0.4π	NOUN
ejpam-6798	454	51	)	)	PUNCT
ejpam-6798	454	52	}	}	PUNCT
ejpam-6798	454	53	.	.	PUNCT
ejpam-6798	455	1	it	it	PRON
ejpam-6798	455	2	is	be	AUX
ejpam-6798	455	3	easy	easy	ADJ
ejpam-6798	455	4	to	to	PART
ejpam-6798	455	5	show	show	VERB
ejpam-6798	455	6	that	that	SCONJ
ejpam-6798	455	7	l2	l2	NOUN
ejpam-6798	455	8	is	be	AUX
ejpam-6798	455	9	a	a	DET
ejpam-6798	455	10	cifi	cifi	NOUN
ejpam-6798	455	11	of	of	ADP
ejpam-6798	455	12	m	m	PROPN
ejpam-6798	455	13	.	.	PUNCT
ejpam-6798	456	1	now	now	ADV
ejpam-6798	456	2	define	define	VERB
ejpam-6798	456	3	a	a	DET
ejpam-6798	456	4	cifs	cifs	NOUN
ejpam-6798	456	5	l1∪l2	l1∪l2	PROPN
ejpam-6798	456	6	on	on	ADP
ejpam-6798	456	7	m	m	NOUN
ejpam-6798	456	8	as	as	ADP
ejpam-6798	456	9	:	:	PUNCT
ejpam-6798	456	10	l1∪l2	l1∪l2	PROPN
ejpam-6798	456	11	=	=	X
ejpam-6798	456	12	{	{	PUNCT
ejpam-6798	456	13	(	(	PUNCT
ejpam-6798	456	14	0	0	NUM
ejpam-6798	456	15	,	,	PUNCT
ejpam-6798	456	16	0.9eι0.7π	0.9eι0.7π	PROPN
ejpam-6798	456	17	,	,	PUNCT
ejpam-6798	456	18	0.4eι0.3π	0.4eι0.3π	NOUN
ejpam-6798	456	19	)	)	PUNCT
ejpam-6798	456	20	,	,	PUNCT
ejpam-6798	456	21	(	(	PUNCT
ejpam-6798	456	22	s	s	X
ejpam-6798	456	23	,	,	PUNCT
ejpam-6798	456	24	0.7eι0.6π	0.7eι0.6π	PROPN
ejpam-6798	456	25	,	,	PUNCT
ejpam-6798	456	26	0.2eι0.3π	0.2eι0.3π	PROPN
ejpam-6798	456	27	)	)	PUNCT
ejpam-6798	456	28	,	,	PUNCT
ejpam-6798	456	29	(	(	PUNCT
ejpam-6798	456	30	l	l	NOUN
ejpam-6798	456	31	,	,	PUNCT
ejpam-6798	456	32	0.6eι0.5π	0.6eι0.5π	PROPN
ejpam-6798	456	33	,	,	PUNCT
ejpam-6798	456	34	0.3eι0.1π	0.3eι0.1π	PROPN
ejpam-6798	456	35	)	)	PUNCT
ejpam-6798	456	36	,	,	PUNCT
ejpam-6798	456	37	(	(	PUNCT
ejpam-6798	456	38	z	z	X
ejpam-6798	456	39	,	,	PUNCT
ejpam-6798	456	40	0.4eι0.6π	0.4eι0.6π	PROPN
ejpam-6798	456	41	,	,	PUNCT
ejpam-6798	456	42	0.1eι0.01π	0.1eι0.01π	NOUN
ejpam-6798	456	43	)	)	PUNCT
ejpam-6798	456	44	,	,	PUNCT
ejpam-6798	456	45	(	(	PUNCT
ejpam-6798	456	46	w	w	X
ejpam-6798	456	47	,	,	PUNCT
ejpam-6798	456	48	0.4eι0.6π	0.4eι0.6π	PROPN
ejpam-6798	456	49	,	,	PUNCT
ejpam-6798	456	50	0.1eι0.01π	0.1eι0.01π	NOUN
ejpam-6798	456	51	)	)	PUNCT
ejpam-6798	456	52	}	}	PUNCT
ejpam-6798	456	53	.	.	PUNCT
ejpam-6798	457	1	it	it	PRON
ejpam-6798	457	2	is	be	AUX
ejpam-6798	457	3	straightforward	straightforward	ADJ
ejpam-6798	457	4	to	to	PART
ejpam-6798	457	5	prove	prove	VERB
ejpam-6798	457	6	that	that	SCONJ
ejpam-6798	457	7	l1	l1	PROPN
ejpam-6798	457	8	∪l2	∪l2	NOUN
ejpam-6798	457	9	is	be	AUX
ejpam-6798	457	10	a	a	DET
ejpam-6798	457	11	cifi	cifi	NOUN
ejpam-6798	457	12	of	of	ADP
ejpam-6798	457	13	m	m	PROPN
ejpam-6798	457	14	.	.	PUNCT
ejpam-6798	458	1	table	table	NOUN
ejpam-6798	458	2	5	5	NUM
ejpam-6798	458	3	:	:	PUNCT
ejpam-6798	458	4	cayley	cayley	PROPN
ejpam-6798	458	5	’s	’s	PART
ejpam-6798	458	6	table	table	NOUN
ejpam-6798	458	7	describing	describe	VERB
ejpam-6798	458	8	the	the	DET
ejpam-6798	458	9	binary	binary	ADJ
ejpam-6798	458	10	operation	operation	NOUN
ejpam-6798	458	11	expressed	express	VERB
ejpam-6798	458	12	by	by	ADP
ejpam-6798	458	13	“	"	PUNCT
ejpam-6798	458	14	⋆	⋆	VERB
ejpam-6798	458	15	”	"	PUNCT
ejpam-6798	458	16	.	.	PUNCT
ejpam-6798	459	1	⋆	⋆	VERB
ejpam-6798	459	2	0	0	NUM
ejpam-6798	459	3	s	s	PART
ejpam-6798	459	4	l	l	NOUN
ejpam-6798	459	5	z	z	PROPN
ejpam-6798	459	6	w	w	NOUN
ejpam-6798	459	7	0	0	NUM
ejpam-6798	459	8	0	0	NUM
ejpam-6798	459	9	0	0	NUM
ejpam-6798	459	10	0	0	NUM
ejpam-6798	459	11	0	0	NUM
ejpam-6798	459	12	0	0	NUM
ejpam-6798	460	1	s	s	NOUN
ejpam-6798	460	2	s	s	NOUN
ejpam-6798	460	3	0	0	NUM
ejpam-6798	460	4	s	s	NOUN
ejpam-6798	460	5	0	0	NUM
ejpam-6798	460	6	0	0	NUM
ejpam-6798	460	7	l	l	NOUN
ejpam-6798	460	8	l	l	NOUN
ejpam-6798	460	9	l	l	NOUN
ejpam-6798	460	10	0	0	NUM
ejpam-6798	460	11	0	0	NUM
ejpam-6798	460	12	0	0	NUM
ejpam-6798	461	1	z	z	NOUN
ejpam-6798	461	2	z	z	NOUN
ejpam-6798	461	3	z	z	NOUN
ejpam-6798	461	4	z	z	NOUN
ejpam-6798	461	5	0	0	NUM
ejpam-6798	461	6	0	0	NUM
ejpam-6798	462	1	w	w	PROPN
ejpam-6798	462	2	w	w	PROPN
ejpam-6798	462	3	z	z	PROPN
ejpam-6798	462	4	w	w	PROPN
ejpam-6798	462	5	z	z	PROPN
ejpam-6798	462	6	0	0	NUM
ejpam-6798	462	7	definition	definition	NOUN
ejpam-6798	462	8	16	16	NUM
ejpam-6798	462	9	.	.	PUNCT
ejpam-6798	463	1	assume	assume	VERB
ejpam-6798	463	2	that	that	SCONJ
ejpam-6798	463	3	l1	l1	PROPN
ejpam-6798	463	4	and	and	CCONJ
ejpam-6798	463	5	l2	l2	NOUN
ejpam-6798	463	6	are	be	AUX
ejpam-6798	463	7	two	two	NUM
ejpam-6798	463	8	cifss	cifss	NOUN
ejpam-6798	463	9	of	of	ADP
ejpam-6798	463	10	m	m	PROPN
ejpam-6798	463	11	.	.	PUNCT
ejpam-6798	464	1	then	then	ADV
ejpam-6798	464	2	,	,	PUNCT
ejpam-6798	464	3	the	the	DET
ejpam-6798	464	4	intersection	intersection	NOUN
ejpam-6798	464	5	l1	l1	PROPN
ejpam-6798	464	6	∩	∩	ADJ
ejpam-6798	464	7	l2	l2	NOUN
ejpam-6798	464	8	is	be	AUX
ejpam-6798	464	9	defined	define	VERB
ejpam-6798	464	10	as	as	ADP
ejpam-6798	464	11	µl1∩l2(s	µl1∩l2(s	NOUN
ejpam-6798	464	12	)	)	PUNCT
ejpam-6798	464	13	=	=	PUNCT
ejpam-6798	465	1	(	(	PUNCT
ejpam-6798	465	2	γl1(s)∧γl2(s))e	γl1(s)∧γl2(s))e	PROPN
ejpam-6798	465	3	ι(θl1	ι(θl1	PROPN
ejpam-6798	465	4	(	(	PUNCT
ejpam-6798	465	5	s)∧θl2	s)∧θl2	PROPN
ejpam-6798	465	6	(	(	PUNCT
ejpam-6798	465	7	s	s	NOUN
ejpam-6798	465	8	)	)	PUNCT
ejpam-6798	465	9	)	)	PUNCT
ejpam-6798	465	10	,	,	PUNCT
ejpam-6798	465	11	νl1∩l2(s	νl1∩l2(s	NOUN
ejpam-6798	465	12	)	)	PUNCT
ejpam-6798	465	13	=	=	SYM
ejpam-6798	465	14	(	(	PUNCT
ejpam-6798	465	15	γl1	γl1	X
ejpam-6798	465	16	(	(	PUNCT
ejpam-6798	465	17	s)∨γl2	s)∨γl2	NOUN
ejpam-6798	465	18	(	(	PUNCT
ejpam-6798	465	19	s))eι(θl1	s))eι(θl1	NOUN
ejpam-6798	465	20	(	(	PUNCT
ejpam-6798	465	21	s)∨θl2	s)∨θl2	PROPN
ejpam-6798	465	22	(	(	PUNCT
ejpam-6798	465	23	s	s	NOUN
ejpam-6798	465	24	)	)	PUNCT
ejpam-6798	465	25	)	)	PUNCT
ejpam-6798	465	26	.	.	PUNCT
ejpam-6798	465	27	example	example	NOUN
ejpam-6798	466	1	11	11	NUM
ejpam-6798	466	2	.	.	PUNCT
ejpam-6798	467	1	let	let	VERB
ejpam-6798	467	2	(	(	PUNCT
ejpam-6798	467	3	µl1(s	µl1(s	PROPN
ejpam-6798	467	4	)	)	PUNCT
ejpam-6798	467	5	,	,	PUNCT
ejpam-6798	467	6	νl1(s	νl1(s	PROPN
ejpam-6798	467	7	)	)	PUNCT
ejpam-6798	467	8	)	)	PUNCT
ejpam-6798	468	1	=	=	PRON
ejpam-6798	468	2	{	{	PUNCT
ejpam-6798	468	3	(	(	PUNCT
ejpam-6798	468	4	s1	s1	NOUN
ejpam-6798	468	5	,	,	PUNCT
ejpam-6798	468	6	0.6eι0.5π	0.6eι0.5π	PROPN
ejpam-6798	468	7	,	,	PUNCT
ejpam-6798	468	8	0.4eι0.25π	0.4eι0.25π	NOUN
ejpam-6798	468	9	)	)	PUNCT
ejpam-6798	468	10	,	,	PUNCT
ejpam-6798	468	11	(	(	PUNCT
ejpam-6798	468	12	s2	s2	PROPN
ejpam-6798	468	13	,	,	PUNCT
ejpam-6798	468	14	1eι0.5π	1eι0.5π	NUM
ejpam-6798	468	15	,	,	PUNCT
ejpam-6798	468	16	0.8eι0.25π	0.8eι0.25π	NOUN
ejpam-6798	468	17	)	)	PUNCT
ejpam-6798	468	18	,	,	PUNCT
ejpam-6798	468	19	(	(	PUNCT
ejpam-6798	468	20	s3	s3	PROPN
ejpam-6798	468	21	,	,	PUNCT
ejpam-6798	468	22	0.8eι2π	0.8eι2π	NUM
ejpam-6798	468	23	,	,	PUNCT
ejpam-6798	468	24	0.6eι1.5π	0.6eι1.5π	NUM
ejpam-6798	468	25	)	)	PUNCT
ejpam-6798	468	26	,	,	PUNCT
ejpam-6798	468	27	(	(	PUNCT
ejpam-6798	468	28	s4	s4	X
ejpam-6798	468	29	,	,	PUNCT
ejpam-6798	468	30	0.9e	0.9e	NOUN
ejpam-6798	468	31	ι0.4π	ι0.4π	NOUN
ejpam-6798	468	32	,	,	PUNCT
ejpam-6798	468	33	0.7eι0.24π	0.7eι0.24π	NOUN
ejpam-6798	468	34	)	)	PUNCT
ejpam-6798	468	35	,	,	PUNCT
ejpam-6798	468	36	(	(	PUNCT
ejpam-6798	468	37	s5	s5	PROPN
ejpam-6798	468	38	,	,	PUNCT
ejpam-6798	468	39	0.7e	0.7e	NOUN
ejpam-6798	468	40	ιπ	ιπ	ADJ
ejpam-6798	468	41	,	,	PUNCT
ejpam-6798	468	42	0.5eι0.8π	0.5eι0.8π	PROPN
ejpam-6798	468	43	)	)	PUNCT
ejpam-6798	468	44	,	,	PUNCT
ejpam-6798	468	45	(	(	PUNCT
ejpam-6798	468	46	s6	s6	PROPN
ejpam-6798	468	47	,	,	PUNCT
ejpam-6798	468	48	0.5e	0.5e	NUM
ejpam-6798	468	49	ι0.4π	ι0.4π	NOUN
ejpam-6798	468	50	,	,	PUNCT
ejpam-6798	468	51	0.3eι0.24π	0.3eι0.24π	NOUN
ejpam-6798	468	52	)	)	PUNCT
ejpam-6798	468	53	}	}	PUNCT
ejpam-6798	468	54	and	and	CCONJ
ejpam-6798	468	55	(	(	PUNCT
ejpam-6798	468	56	µl2(s	µl2(s	PROPN
ejpam-6798	468	57	)	)	PUNCT
ejpam-6798	468	58	,	,	PUNCT
ejpam-6798	468	59	νl2(s	νl2(s	PROPN
ejpam-6798	468	60	)	)	PUNCT
ejpam-6798	468	61	)	)	PUNCT
ejpam-6798	468	62	=	=	PRON
ejpam-6798	469	1	{	{	PUNCT
ejpam-6798	469	2	(	(	PUNCT
ejpam-6798	469	3	s1	s1	NOUN
ejpam-6798	469	4	,	,	PUNCT
ejpam-6798	469	5	0.2eιπ	0.2eιπ	NUM
ejpam-6798	469	6	,	,	PUNCT
ejpam-6798	469	7	0.1eι0.88π	0.1eι0.88π	NUM
ejpam-6798	469	8	)	)	PUNCT
ejpam-6798	469	9	,	,	PUNCT
ejpam-6798	469	10	(	(	PUNCT
ejpam-6798	469	11	s2	s2	PROPN
ejpam-6798	469	12	,	,	PUNCT
ejpam-6798	469	13	0.1eι0.8π	0.1eι0.8π	NOUN
ejpam-6798	469	14	,	,	PUNCT
ejpam-6798	469	15	0.01eι0.6π	0.01eι0.6π	NUM
ejpam-6798	469	16	)	)	PUNCT
ejpam-6798	469	17	,	,	PUNCT
ejpam-6798	469	18	(	(	PUNCT
ejpam-6798	469	19	s3	s3	PROPN
ejpam-6798	469	20	,	,	PUNCT
ejpam-6798	469	21	0.8eι0.8π	0.8eι0.8π	PROPN
ejpam-6798	469	22	,	,	PUNCT
ejpam-6798	469	23	0.6eι0.68π	0.6eι0.68π	NOUN
ejpam-6798	469	24	)	)	PUNCT
ejpam-6798	469	25	,	,	PUNCT
ejpam-6798	469	26	(	(	PUNCT
ejpam-6798	469	27	s4	s4	PROPN
ejpam-6798	469	28	,	,	PUNCT
ejpam-6798	469	29	0.2eιπ	0.2eιπ	NUM
ejpam-6798	469	30	,	,	PUNCT
ejpam-6798	469	31	0.1eι0.88π	0.1eι0.88π	NUM
ejpam-6798	469	32	)	)	PUNCT
ejpam-6798	469	33	,	,	PUNCT
ejpam-6798	469	34	(	(	PUNCT
ejpam-6798	469	35	s5	s5	PROPN
ejpam-6798	469	36	,	,	PUNCT
ejpam-6798	469	37	0.9e	0.9e	PROPN
ejpam-6798	469	38	ι0.9π	ι0.9π	PROPN
ejpam-6798	469	39	,	,	PUNCT
ejpam-6798	469	40	0.7eι0.7π	0.7eι0.7π	PROPN
ejpam-6798	469	41	)	)	PUNCT
ejpam-6798	469	42	,	,	PUNCT
ejpam-6798	469	43	(	(	PUNCT
ejpam-6798	469	44	s6	s6	PROPN
ejpam-6798	469	45	,	,	PUNCT
ejpam-6798	469	46	0.3e	0.3e	NOUN
ejpam-6798	469	47	ι2π	ι2π	NOUN
ejpam-6798	469	48	,	,	PUNCT
ejpam-6798	469	49	0.1eι1.88π	0.1eι1.88π	PROPN
ejpam-6798	469	50	)	)	PUNCT
ejpam-6798	469	51	}	}	PUNCT
ejpam-6798	469	52	be	be	AUX
ejpam-6798	469	53	a	a	DET
ejpam-6798	469	54	cifss	cifss	NOUN
ejpam-6798	469	55	.	.	PUNCT
ejpam-6798	470	1	then	then	ADV
ejpam-6798	470	2	,	,	PUNCT
ejpam-6798	470	3	µl1∩l2(s	µl1∩l2(s	PROPN
ejpam-6798	470	4	)	)	PUNCT
ejpam-6798	470	5	=	=	SYM
ejpam-6798	470	6	{	{	PUNCT
ejpam-6798	470	7	(	(	PUNCT
ejpam-6798	470	8	s1	s1	NOUN
ejpam-6798	470	9	,	,	PUNCT
ejpam-6798	470	10	0.2eι0.5π	0.2eι0.5π	PROPN
ejpam-6798	470	11	,	,	PUNCT
ejpam-6798	470	12	0.4eι0.88π	0.4eι0.88π	PROPN
ejpam-6798	470	13	)	)	PUNCT
ejpam-6798	470	14	,	,	PUNCT
ejpam-6798	470	15	(	(	PUNCT
ejpam-6798	470	16	s2	s2	PROPN
ejpam-6798	470	17	,	,	PUNCT
ejpam-6798	470	18	0.1eι0.5π	0.1eι0.5π	PROPN
ejpam-6798	470	19	,	,	PUNCT
ejpam-6798	470	20	0.8eι0.6π	0.8eι0.6π	PROPN
ejpam-6798	470	21	)	)	PUNCT
ejpam-6798	470	22	,	,	PUNCT
ejpam-6798	470	23	(	(	PUNCT
ejpam-6798	470	24	s3	s3	PROPN
ejpam-6798	470	25	,	,	PUNCT
ejpam-6798	470	26	0.8eι0.8π	0.8eι0.8π	PROPN
ejpam-6798	470	27	,	,	PUNCT
ejpam-6798	470	28	0.6eι1.5π	0.6eι1.5π	PROPN
ejpam-6798	470	29	)	)	PUNCT
ejpam-6798	470	30	,	,	PUNCT
ejpam-6798	470	31	(	(	PUNCT
ejpam-6798	470	32	s4	s4	PROPN
ejpam-6798	470	33	,	,	PUNCT
ejpam-6798	470	34	0.2eι0.4π	0.2eι0.4π	NOUN
ejpam-6798	470	35	,	,	PUNCT
ejpam-6798	470	36	0.7eι0.88π	0.7eι0.88π	NOUN
ejpam-6798	470	37	)	)	PUNCT
ejpam-6798	470	38	,	,	PUNCT
ejpam-6798	470	39	(	(	PUNCT
ejpam-6798	470	40	s5	s5	X
ejpam-6798	470	41	,	,	PUNCT
ejpam-6798	470	42	0.7e	0.7e	NOUN
ejpam-6798	470	43	ι0.9π	ι0.9π	PROPN
ejpam-6798	470	44	,	,	PUNCT
ejpam-6798	470	45	0.7eι0.8π	0.7eι0.8π	PROPN
ejpam-6798	470	46	)	)	PUNCT
ejpam-6798	470	47	,	,	PUNCT
ejpam-6798	470	48	(	(	PUNCT
ejpam-6798	470	49	s6	s6	PROPN
ejpam-6798	470	50	,	,	PUNCT
ejpam-6798	470	51	0.3e	0.3e	NOUN
ejpam-6798	470	52	ι0.4π	ι0.4π	NOUN
ejpam-6798	470	53	,	,	PUNCT
ejpam-6798	470	54	0.3eι1.88π	0.3eι1.88π	NOUN
ejpam-6798	470	55	)	)	PUNCT
ejpam-6798	470	56	}	}	PUNCT
ejpam-6798	470	57	.	.	PUNCT
ejpam-6798	471	1	the	the	DET
ejpam-6798	471	2	subsequent	subsequent	ADJ
ejpam-6798	471	3	theorem	theorem	NOUN
ejpam-6798	471	4	demonstrates	demonstrate	VERB
ejpam-6798	471	5	that	that	SCONJ
ejpam-6798	471	6	the	the	DET
ejpam-6798	471	7	intersection	intersection	NOUN
ejpam-6798	471	8	∩	∩	NOUN
ejpam-6798	471	9	of	of	ADP
ejpam-6798	471	10	two	two	NUM
ejpam-6798	471	11	cifis	cifis	NOUN
ejpam-6798	471	12	of	of	ADP
ejpam-6798	471	13	m	m	PROPN
ejpam-6798	471	14	is	be	AUX
ejpam-6798	471	15	also	also	ADV
ejpam-6798	471	16	a	a	DET
ejpam-6798	471	17	cifi	cifi	NOUN
ejpam-6798	471	18	.	.	PUNCT
ejpam-6798	472	1	theorem	theorem	NOUN
ejpam-6798	472	2	11	11	NUM
ejpam-6798	472	3	.	.	PUNCT
ejpam-6798	473	1	assume	assume	VERB
ejpam-6798	473	2	that	that	SCONJ
ejpam-6798	473	3	l1	l1	PROPN
ejpam-6798	473	4	and	and	CCONJ
ejpam-6798	473	5	l2	l2	NOUN
ejpam-6798	473	6	are	be	AUX
ejpam-6798	473	7	two	two	NUM
ejpam-6798	473	8	cifis	cifis	NOUN
ejpam-6798	473	9	of	of	ADP
ejpam-6798	473	10	m	m	PROPN
ejpam-6798	473	11	.	.	PUNCT
ejpam-6798	474	1	then	then	ADV
ejpam-6798	474	2	l1	l1	PROPN
ejpam-6798	474	3	∩	∩	ADJ
ejpam-6798	474	4	l2	l2	NOUN
ejpam-6798	474	5	is	be	AUX
ejpam-6798	474	6	a	a	DET
ejpam-6798	474	7	cifi	cifi	NOUN
ejpam-6798	474	8	of	of	ADP
ejpam-6798	474	9	m	m	PROPN
ejpam-6798	474	10	.	.	PUNCT
ejpam-6798	475	1	m.	m.	PROPN
ejpam-6798	475	2	jawad	jawad	PROPN
ejpam-6798	475	3	et	et	PROPN
ejpam-6798	475	4	al	al	PROPN
ejpam-6798	475	5	.	.	PUNCT
ejpam-6798	475	6	/	/	SYM
ejpam-6798	475	7	eur	eur	PROPN
ejpam-6798	475	8	.	.	PUNCT
ejpam-6798	476	1	j.	j.	PROPN
ejpam-6798	476	2	pure	pure	PROPN
ejpam-6798	476	3	appl	appl	PROPN
ejpam-6798	476	4	.	.	PROPN
ejpam-6798	476	5	math	math	PROPN
ejpam-6798	476	6	,	,	PUNCT
ejpam-6798	476	7	18	18	NUM
ejpam-6798	476	8	(	(	PUNCT
ejpam-6798	476	9	4	4	NUM
ejpam-6798	476	10	)	)	PUNCT
ejpam-6798	476	11	(	(	PUNCT
ejpam-6798	476	12	2025	2025	NUM
ejpam-6798	476	13	)	)	PUNCT
ejpam-6798	476	14	,	,	PUNCT
ejpam-6798	476	15	6798	6798	NUM
ejpam-6798	476	16	15	15	NUM
ejpam-6798	476	17	of	of	ADP
ejpam-6798	476	18	22	22	NUM
ejpam-6798	476	19	proof	proof	NOUN
ejpam-6798	476	20	.	.	PUNCT
ejpam-6798	477	1	let	let	VERB
ejpam-6798	477	2	l1	l1	PROPN
ejpam-6798	477	3	and	and	CCONJ
ejpam-6798	477	4	l2	l2	NOUN
ejpam-6798	477	5	be	be	AUX
ejpam-6798	477	6	two	two	NUM
ejpam-6798	477	7	cifis	cifis	NOUN
ejpam-6798	477	8	of	of	ADP
ejpam-6798	477	9	m	m	PRON
ejpam-6798	477	10	and	and	CCONJ
ejpam-6798	477	11	let	let	VERB
ejpam-6798	477	12	s	s	NOUN
ejpam-6798	477	13	,	,	PUNCT
ejpam-6798	477	14	l	l	PROPN
ejpam-6798	477	15	∈	∈	PROPN
ejpam-6798	477	16	m	m	VERB
ejpam-6798	477	17	.	.	PUNCT
ejpam-6798	478	1	then	then	ADV
ejpam-6798	478	2	µl1∩l2(0	µl1∩l2(0	PUNCT
ejpam-6798	478	3	)	)	PUNCT
ejpam-6798	479	1	=	=	PRON
ejpam-6798	479	2	(	(	PUNCT
ejpam-6798	479	3	γl1(0	γl1(0	NOUN
ejpam-6798	479	4	)	)	PUNCT
ejpam-6798	479	5	∧	∧	PROPN
ejpam-6798	479	6	γl2(0))e	γl2(0))e	PROPN
ejpam-6798	479	7	ι(θl1	ι(θl1	PROPN
ejpam-6798	479	8	(	(	PUNCT
ejpam-6798	479	9	0)∧θl2	0)∧θl2	NOUN
ejpam-6798	479	10	(	(	PUNCT
ejpam-6798	479	11	0	0	NUM
ejpam-6798	479	12	)	)	PUNCT
ejpam-6798	479	13	)	)	PUNCT
ejpam-6798	479	14	≥	≥	NOUN
ejpam-6798	479	15	(	(	PUNCT
ejpam-6798	479	16	γl1(s	γl1(s	PROPN
ejpam-6798	479	17	)	)	PUNCT
ejpam-6798	479	18	∧	∧	NOUN
ejpam-6798	479	19	γl2(s))e	γl2(s))e	PROPN
ejpam-6798	479	20	ι(θl1	ι(θl1	INTJ
ejpam-6798	479	21	(	(	PUNCT
ejpam-6798	479	22	s)∧θl2	s)∧θl2	PROPN
ejpam-6798	479	23	(	(	PUNCT
ejpam-6798	479	24	s	s	NOUN
ejpam-6798	479	25	)	)	PUNCT
ejpam-6798	479	26	)	)	PUNCT
ejpam-6798	480	1	=	=	SYM
ejpam-6798	480	2	µl1∩l2(s	µl1∩l2(s	PROPN
ejpam-6798	480	3	)	)	PUNCT
ejpam-6798	480	4	.	.	PUNCT
ejpam-6798	481	1	moreover	moreover	ADV
ejpam-6798	481	2	µl1∩l2(s	µl1∩l2(s	NOUN
ejpam-6798	481	3	)	)	PUNCT
ejpam-6798	481	4	=	=	PUNCT
ejpam-6798	481	5	(	(	PUNCT
ejpam-6798	481	6	γl1(s	γl1(s	PROPN
ejpam-6798	481	7	)	)	PUNCT
ejpam-6798	481	8	∧	∧	NOUN
ejpam-6798	481	9	γl2(s))e	γl2(s))e	PROPN
ejpam-6798	481	10	ι(θl1	ι(θl1	INTJ
ejpam-6798	481	11	(	(	PUNCT
ejpam-6798	481	12	s)∧θl2	s)∧θl2	PROPN
ejpam-6798	481	13	(	(	PUNCT
ejpam-6798	481	14	s	s	NOUN
ejpam-6798	481	15	)	)	PUNCT
ejpam-6798	481	16	)	)	PUNCT
ejpam-6798	481	17	≥	≥	NOUN
ejpam-6798	481	18	(	(	PUNCT
ejpam-6798	481	19	(	(	PUNCT
ejpam-6798	481	20	γl1(s	γl1(s	X
ejpam-6798	481	21	⋆	⋆	ADJ
ejpam-6798	481	22	l	l	NOUN
ejpam-6798	481	23	)	)	PUNCT
ejpam-6798	481	24	∧	∧	PROPN
ejpam-6798	481	25	γl1(l	γl1(l	PROPN
ejpam-6798	481	26	)	)	PUNCT
ejpam-6798	481	27	)	)	PUNCT
ejpam-6798	482	1	∧	∧	NOUN
ejpam-6798	482	2	(	(	PUNCT
ejpam-6798	482	3	γl2(s	γl2(s	PROPN
ejpam-6798	482	4	⋆	⋆	NOUN
ejpam-6798	482	5	l	l	NOUN
ejpam-6798	482	6	)	)	PUNCT
ejpam-6798	482	7	∧	∧	PROPN
ejpam-6798	482	8	γl2(l	γl2(l	NOUN
ejpam-6798	482	9	)	)	PUNCT
ejpam-6798	482	10	)	)	PUNCT
ejpam-6798	482	11	)	)	PUNCT
ejpam-6798	483	1	eι((θl1	eι((θl1	NOUN
ejpam-6798	483	2	(	(	PUNCT
ejpam-6798	483	3	s⋆l)∧θl1	s⋆l)∧θl1	PROPN
ejpam-6798	483	4	(	(	PUNCT
ejpam-6798	483	5	l))∧(θl2	l))∧(θl2	X
ejpam-6798	483	6	(	(	PUNCT
ejpam-6798	483	7	s⋆l)∧θl2	s⋆l)∧θl2	NOUN
ejpam-6798	483	8	(	(	PUNCT
ejpam-6798	483	9	l	l	NOUN
ejpam-6798	483	10	)	)	PUNCT
ejpam-6798	483	11	)	)	PUNCT
ejpam-6798	483	12	)	)	PUNCT
ejpam-6798	483	13	≥	≥	X
ejpam-6798	483	14	(	(	PUNCT
ejpam-6798	483	15	(	(	PUNCT
ejpam-6798	483	16	γl1(s	γl1(s	X
ejpam-6798	483	17	⋆	⋆	NOUN
ejpam-6798	483	18	l	l	NOUN
ejpam-6798	483	19	)	)	PUNCT
ejpam-6798	483	20	∧	∧	PROPN
ejpam-6798	483	21	γl2(s	γl2(s	PROPN
ejpam-6798	483	22	⋆	⋆	ADJ
ejpam-6798	483	23	l	l	NOUN
ejpam-6798	483	24	)	)	PUNCT
ejpam-6798	483	25	)	)	PUNCT
ejpam-6798	484	1	∧	∧	PROPN
ejpam-6798	484	2	(	(	PUNCT
ejpam-6798	484	3	γl1(l	γl1(l	PROPN
ejpam-6798	484	4	)	)	PUNCT
ejpam-6798	484	5	∧	∧	PROPN
ejpam-6798	484	6	γl2(l	γl2(l	NOUN
ejpam-6798	484	7	)	)	PUNCT
ejpam-6798	484	8	)	)	PUNCT
ejpam-6798	484	9	)	)	PUNCT
ejpam-6798	485	1	eι((θl1	eι((θl1	NOUN
ejpam-6798	485	2	(	(	PUNCT
ejpam-6798	485	3	s⋆l)∧θl2	s⋆l)∧θl2	PROPN
ejpam-6798	485	4	(	(	PUNCT
ejpam-6798	485	5	s⋆l))∧(θl1	s⋆l))∧(θl1	VERB
ejpam-6798	485	6	(	(	PUNCT
ejpam-6798	485	7	l)∧θl2	l)∧θl2	PROPN
ejpam-6798	485	8	(	(	PUNCT
ejpam-6798	485	9	l	l	NOUN
ejpam-6798	485	10	)	)	PUNCT
ejpam-6798	485	11	)	)	PUNCT
ejpam-6798	485	12	)	)	PUNCT
ejpam-6798	486	1	=	=	PUNCT
ejpam-6798	486	2	(	(	PUNCT
ejpam-6798	486	3	γl1(s	γl1(s	X
ejpam-6798	486	4	⋆	⋆	NOUN
ejpam-6798	486	5	l	l	NOUN
ejpam-6798	486	6	)	)	PUNCT
ejpam-6798	486	7	∧	∧	PROPN
ejpam-6798	486	8	γl2(s	γl2(s	PROPN
ejpam-6798	486	9	⋆	⋆	VERB
ejpam-6798	486	10	l))e	l))e	PROPN
ejpam-6798	486	11	ι(θl1	ι(θl1	PROPN
ejpam-6798	486	12	(	(	PUNCT
ejpam-6798	486	13	s⋆l)∧θl2	s⋆l)∧θl2	NOUN
ejpam-6798	486	14	(	(	PUNCT
ejpam-6798	486	15	s⋆l	s⋆l	NOUN
ejpam-6798	486	16	)	)	PUNCT
ejpam-6798	486	17	)	)	PUNCT
ejpam-6798	487	1	∧	∧	PROPN
ejpam-6798	487	2	(	(	PUNCT
ejpam-6798	487	3	γl1(l	γl1(l	PROPN
ejpam-6798	487	4	)	)	PUNCT
ejpam-6798	487	5	∧	∧	PROPN
ejpam-6798	487	6	γl2(l))e	γl2(l))e	PROPN
ejpam-6798	487	7	ι(θl1	ι(θl1	NUM
ejpam-6798	487	8	(	(	PUNCT
ejpam-6798	487	9	l)∧θl2	l)∧θl2	PROPN
ejpam-6798	487	10	(	(	PUNCT
ejpam-6798	487	11	l	l	NOUN
ejpam-6798	487	12	)	)	PUNCT
ejpam-6798	487	13	)	)	PUNCT
ejpam-6798	487	14	≥	≥	X
ejpam-6798	487	15	µl1∩l2(s	µl1∩l2(s	PROPN
ejpam-6798	487	16	⋆	⋆	PROPN
ejpam-6798	487	17	l	l	NOUN
ejpam-6798	487	18	)	)	PUNCT
ejpam-6798	487	19	∧	∧	NOUN
ejpam-6798	487	20	µl1∩l2(l	µl1∩l2(l	NOUN
ejpam-6798	487	21	)	)	PUNCT
ejpam-6798	487	22	.	.	PUNCT
ejpam-6798	487	23	suppose	suppose	VERB
ejpam-6798	487	24	that	that	SCONJ
ejpam-6798	487	25	l1	l1	PROPN
ejpam-6798	487	26	and	and	CCONJ
ejpam-6798	487	27	l2	l2	NOUN
ejpam-6798	487	28	are	be	AUX
ejpam-6798	487	29	two	two	NUM
ejpam-6798	487	30	cifis	cifis	NOUN
ejpam-6798	487	31	of	of	ADP
ejpam-6798	487	32	m	m	PRON
ejpam-6798	487	33	and	and	CCONJ
ejpam-6798	487	34	let	let	VERB
ejpam-6798	487	35	s	s	NOUN
ejpam-6798	487	36	,	,	PUNCT
ejpam-6798	487	37	l	l	PROPN
ejpam-6798	487	38	∈	∈	PROPN
ejpam-6798	487	39	m	m	VERB
ejpam-6798	487	40	.	.	PUNCT
ejpam-6798	488	1	then	then	ADV
ejpam-6798	488	2	νl1∩l2(0	νl1∩l2(0	PUNCT
ejpam-6798	488	3	)	)	PUNCT
ejpam-6798	489	1	=	=	PRON
ejpam-6798	489	2	(	(	PUNCT
ejpam-6798	489	3	γl1	γl1	NOUN
ejpam-6798	489	4	(	(	PUNCT
ejpam-6798	489	5	0	0	NUM
ejpam-6798	489	6	)	)	PUNCT
ejpam-6798	489	7	∨	∨	NUM
ejpam-6798	489	8	γl2	γl2	NOUN
ejpam-6798	489	9	(	(	PUNCT
ejpam-6798	489	10	0))eι(θl1	0))eι(θl1	NUM
ejpam-6798	489	11	(	(	PUNCT
ejpam-6798	489	12	0)∨θl2	0)∨θl2	NUM
ejpam-6798	489	13	(	(	PUNCT
ejpam-6798	489	14	0	0	NUM
ejpam-6798	489	15	)	)	PUNCT
ejpam-6798	489	16	)	)	PUNCT
ejpam-6798	489	17	≤	≤	NOUN
ejpam-6798	489	18	(	(	PUNCT
ejpam-6798	489	19	γl1	γl1	NOUN
ejpam-6798	489	20	(	(	PUNCT
ejpam-6798	489	21	s	s	NOUN
ejpam-6798	489	22	)	)	PUNCT
ejpam-6798	489	23	∨	∨	NUM
ejpam-6798	490	1	γl2	γl2	PROPN
ejpam-6798	490	2	(	(	PUNCT
ejpam-6798	490	3	s))eι(θl1	s))eι(θl1	NOUN
ejpam-6798	490	4	(	(	PUNCT
ejpam-6798	490	5	s)∨θl2	s)∨θl2	PROPN
ejpam-6798	490	6	(	(	PUNCT
ejpam-6798	490	7	s	s	NOUN
ejpam-6798	490	8	)	)	PUNCT
ejpam-6798	490	9	)	)	PUNCT
ejpam-6798	491	1	=	=	SYM
ejpam-6798	491	2	νl1∩l2(s	νl1∩l2(s	NOUN
ejpam-6798	491	3	)	)	PUNCT
ejpam-6798	491	4	.	.	PUNCT
ejpam-6798	492	1	and	and	CCONJ
ejpam-6798	492	2	νl1∩l2(s	νl1∩l2(s	NOUN
ejpam-6798	492	3	)	)	PUNCT
ejpam-6798	492	4	=	=	PUNCT
ejpam-6798	492	5	(	(	PUNCT
ejpam-6798	492	6	γl1	γl1	X
ejpam-6798	492	7	(	(	PUNCT
ejpam-6798	492	8	s	s	NOUN
ejpam-6798	492	9	)	)	PUNCT
ejpam-6798	492	10	∨	∨	NUM
ejpam-6798	492	11	γl2	γl2	PROPN
ejpam-6798	492	12	(	(	PUNCT
ejpam-6798	492	13	s))eι(θl1	s))eι(θl1	NOUN
ejpam-6798	492	14	(	(	PUNCT
ejpam-6798	492	15	s)∨θl2	s)∨θl2	PROPN
ejpam-6798	492	16	(	(	PUNCT
ejpam-6798	492	17	s	s	NOUN
ejpam-6798	492	18	)	)	PUNCT
ejpam-6798	492	19	)	)	PUNCT
ejpam-6798	492	20	≤	≤	NOUN
ejpam-6798	492	21	(	(	PUNCT
ejpam-6798	492	22	(	(	PUNCT
ejpam-6798	492	23	γl1	γl1	NOUN
ejpam-6798	492	24	(	(	PUNCT
ejpam-6798	492	25	s	s	X
ejpam-6798	492	26	⋆	⋆	NOUN
ejpam-6798	492	27	l	l	NOUN
ejpam-6798	492	28	)	)	PUNCT
ejpam-6798	492	29	∨	∨	NUM
ejpam-6798	492	30	γl1	γl1	NOUN
ejpam-6798	492	31	(	(	PUNCT
ejpam-6798	492	32	l	l	NOUN
ejpam-6798	492	33	)	)	PUNCT
ejpam-6798	492	34	)	)	PUNCT
ejpam-6798	492	35	∨	∨	NUM
ejpam-6798	492	36	(	(	PUNCT
ejpam-6798	492	37	γl2	γl2	PROPN
ejpam-6798	492	38	(	(	PUNCT
ejpam-6798	492	39	s	s	X
ejpam-6798	492	40	⋆	⋆	NOUN
ejpam-6798	492	41	l	l	NOUN
ejpam-6798	492	42	)	)	PUNCT
ejpam-6798	492	43	∨	∨	NUM
ejpam-6798	493	1	γl2	γl2	PROPN
ejpam-6798	493	2	(	(	PUNCT
ejpam-6798	493	3	l	l	NOUN
ejpam-6798	493	4	)	)	PUNCT
ejpam-6798	493	5	)	)	PUNCT
ejpam-6798	493	6	)	)	PUNCT
ejpam-6798	494	1	eι((θl1	eι((θl1	NOUN
ejpam-6798	494	2	(	(	PUNCT
ejpam-6798	494	3	s⋆l)∨θl1	s⋆l)∨θl1	NOUN
ejpam-6798	494	4	(	(	PUNCT
ejpam-6798	494	5	l))∨(θl2	l))∨(θl2	PROPN
ejpam-6798	494	6	(	(	PUNCT
ejpam-6798	494	7	s⋆l)∨θl2	s⋆l)∨θl2	NOUN
ejpam-6798	494	8	(	(	PUNCT
ejpam-6798	494	9	l	l	NOUN
ejpam-6798	494	10	)	)	PUNCT
ejpam-6798	494	11	)	)	PUNCT
ejpam-6798	494	12	)	)	PUNCT
ejpam-6798	494	13	≤	≤	NOUN
ejpam-6798	494	14	(	(	PUNCT
ejpam-6798	494	15	(	(	PUNCT
ejpam-6798	494	16	γl1	γl1	NOUN
ejpam-6798	494	17	(	(	PUNCT
ejpam-6798	494	18	s	s	X
ejpam-6798	494	19	⋆	⋆	NOUN
ejpam-6798	494	20	l	l	NOUN
ejpam-6798	494	21	)	)	PUNCT
ejpam-6798	494	22	∨	∨	NUM
ejpam-6798	494	23	γl2	γl2	NOUN
ejpam-6798	494	24	(	(	PUNCT
ejpam-6798	494	25	s	s	X
ejpam-6798	494	26	⋆	⋆	NOUN
ejpam-6798	494	27	l	l	NOUN
ejpam-6798	494	28	)	)	PUNCT
ejpam-6798	494	29	)	)	PUNCT
ejpam-6798	494	30	∨	∨	NUM
ejpam-6798	494	31	(	(	PUNCT
ejpam-6798	494	32	γl1	γl1	NOUN
ejpam-6798	494	33	(	(	PUNCT
ejpam-6798	494	34	l	l	NOUN
ejpam-6798	494	35	)	)	PUNCT
ejpam-6798	494	36	∨	∨	NUM
ejpam-6798	494	37	γl2	γl2	PROPN
ejpam-6798	494	38	(	(	PUNCT
ejpam-6798	494	39	l	l	NOUN
ejpam-6798	494	40	)	)	PUNCT
ejpam-6798	494	41	)	)	PUNCT
ejpam-6798	494	42	)	)	PUNCT
ejpam-6798	495	1	eι((θl1	eι((θl1	NOUN
ejpam-6798	495	2	(	(	PUNCT
ejpam-6798	495	3	s⋆l)∨θl2	s⋆l)∨θl2	NOUN
ejpam-6798	495	4	(	(	PUNCT
ejpam-6798	495	5	s⋆l))∨(θl1	s⋆l))∨(θl1	NOUN
ejpam-6798	495	6	(	(	PUNCT
ejpam-6798	495	7	l)∨θl2	l)∨θl2	NOUN
ejpam-6798	495	8	(	(	PUNCT
ejpam-6798	495	9	l	l	NOUN
ejpam-6798	495	10	)	)	PUNCT
ejpam-6798	495	11	)	)	PUNCT
ejpam-6798	495	12	)	)	PUNCT
ejpam-6798	496	1	=	=	PRON
ejpam-6798	496	2	(	(	PUNCT
ejpam-6798	496	3	γl1	γl1	NOUN
ejpam-6798	496	4	(	(	PUNCT
ejpam-6798	496	5	s	s	X
ejpam-6798	496	6	⋆	⋆	NOUN
ejpam-6798	496	7	l	l	NOUN
ejpam-6798	496	8	)	)	PUNCT
ejpam-6798	496	9	∨	∨	NUM
ejpam-6798	496	10	γl2	γl2	NOUN
ejpam-6798	496	11	(	(	PUNCT
ejpam-6798	496	12	s	s	X
ejpam-6798	496	13	⋆	⋆	X
ejpam-6798	496	14	l))eι(θl1	l))eι(θl1	NOUN
ejpam-6798	496	15	(	(	PUNCT
ejpam-6798	496	16	s⋆l)∨θl2	s⋆l)∨θl2	NOUN
ejpam-6798	496	17	(	(	PUNCT
ejpam-6798	496	18	s⋆l	s⋆l	NOUN
ejpam-6798	496	19	)	)	PUNCT
ejpam-6798	496	20	)	)	PUNCT
ejpam-6798	496	21	∨	∨	NUM
ejpam-6798	496	22	(	(	PUNCT
ejpam-6798	496	23	γl1	γl1	NOUN
ejpam-6798	496	24	(	(	PUNCT
ejpam-6798	496	25	l	l	NOUN
ejpam-6798	496	26	)	)	PUNCT
ejpam-6798	496	27	∨	∨	NUM
ejpam-6798	497	1	γl2	γl2	NOUN
ejpam-6798	497	2	(	(	PUNCT
ejpam-6798	497	3	l))eι(θl1	l))eι(θl1	X
ejpam-6798	497	4	(	(	PUNCT
ejpam-6798	497	5	l)∨θl2	l)∨θl2	NOUN
ejpam-6798	497	6	(	(	PUNCT
ejpam-6798	497	7	l	l	NOUN
ejpam-6798	497	8	)	)	PUNCT
ejpam-6798	497	9	)	)	PUNCT
ejpam-6798	497	10	≤	≤	NUM
ejpam-6798	497	11	νl1∩l2(s	νl1∩l2(s	PROPN
ejpam-6798	497	12	⋆	⋆	PUNCT
ejpam-6798	497	13	l	l	NOUN
ejpam-6798	497	14	)	)	PUNCT
ejpam-6798	497	15	∨	∨	NUM
ejpam-6798	497	16	νl1∩l2(l	νl1∩l2(l	NOUN
ejpam-6798	497	17	)	)	PUNCT
ejpam-6798	497	18	.	.	PUNCT
ejpam-6798	498	1	therefore	therefore	ADV
ejpam-6798	498	2	,	,	PUNCT
ejpam-6798	498	3	l1	l1	PROPN
ejpam-6798	498	4	∩	∩	ADJ
ejpam-6798	498	5	l2	l2	NOUN
ejpam-6798	498	6	is	be	AUX
ejpam-6798	498	7	a	a	DET
ejpam-6798	498	8	cifi	cifi	NOUN
ejpam-6798	498	9	of	of	ADP
ejpam-6798	498	10	m	m	PROPN
ejpam-6798	498	11	.	.	PUNCT
ejpam-6798	498	12	example	example	NOUN
ejpam-6798	499	1	12	12	NUM
ejpam-6798	499	2	.	.	PUNCT
ejpam-6798	500	1	take	take	VERB
ejpam-6798	500	2	a	a	DET
ejpam-6798	500	3	bck	bck	NOUN
ejpam-6798	500	4	-	-	PUNCT
ejpam-6798	500	5	algebra	algebra	NOUN
ejpam-6798	500	6	m	m	NOUN
ejpam-6798	500	7	=	=	SYM
ejpam-6798	500	8	{	{	PUNCT
ejpam-6798	500	9	0	0	NUM
ejpam-6798	500	10	,	,	PUNCT
ejpam-6798	500	11	s	s	X
ejpam-6798	500	12	,	,	PUNCT
ejpam-6798	500	13	l	l	NOUN
ejpam-6798	500	14	,	,	PUNCT
ejpam-6798	500	15	z	z	NOUN
ejpam-6798	500	16	,	,	PUNCT
ejpam-6798	500	17	w	w	PROPN
ejpam-6798	500	18	}	}	PUNCT
ejpam-6798	500	19	,	,	PUNCT
ejpam-6798	500	20	where	where	SCONJ
ejpam-6798	500	21	the	the	DET
ejpam-6798	500	22	binary	binary	ADJ
ejpam-6798	500	23	operation	operation	NOUN
ejpam-6798	500	24	is	be	AUX
ejpam-6798	500	25	defined	define	VERB
ejpam-6798	500	26	by	by	ADP
ejpam-6798	500	27	the	the	DET
ejpam-6798	500	28	caley	caley	NOUN
ejpam-6798	500	29	table	table	NOUN
ejpam-6798	500	30	6	6	NUM
ejpam-6798	500	31	.	.	PUNCT
ejpam-6798	501	1	now	now	ADV
ejpam-6798	501	2	,	,	PUNCT
ejpam-6798	501	3	define	define	VERB
ejpam-6798	501	4	a	a	DET
ejpam-6798	501	5	cifs	cifs	NOUN
ejpam-6798	501	6	l1	l1	NOUN
ejpam-6798	501	7	on	on	ADP
ejpam-6798	501	8	m	m	NOUN
ejpam-6798	501	9	as	as	ADP
ejpam-6798	501	10	:	:	PUNCT
ejpam-6798	501	11	l1	l1	PROPN
ejpam-6798	501	12	=	=	SYM
ejpam-6798	501	13	{	{	PUNCT
ejpam-6798	501	14	(	(	PUNCT
ejpam-6798	501	15	0	0	NUM
ejpam-6798	501	16	,	,	PUNCT
ejpam-6798	501	17	0.9eι0.7π	0.9eι0.7π	PROPN
ejpam-6798	501	18	,	,	PUNCT
ejpam-6798	501	19	0.7eι0.5π	0.7eι0.5π	PROPN
ejpam-6798	501	20	)	)	PUNCT
ejpam-6798	501	21	,	,	PUNCT
ejpam-6798	501	22	(	(	PUNCT
ejpam-6798	501	23	s	s	X
ejpam-6798	501	24	,	,	PUNCT
ejpam-6798	501	25	0.7eι0.5π	0.7eι0.5π	PROPN
ejpam-6798	501	26	,	,	PUNCT
ejpam-6798	501	27	0.5eι0.3π	0.5eι0.3π	PROPN
ejpam-6798	501	28	)	)	PUNCT
ejpam-6798	501	29	,	,	PUNCT
ejpam-6798	501	30	(	(	PUNCT
ejpam-6798	501	31	l	l	NOUN
ejpam-6798	501	32	,	,	PUNCT
ejpam-6798	501	33	0.5eι0.3π	0.5eι0.3π	NOUN
ejpam-6798	501	34	,	,	PUNCT
ejpam-6798	501	35	0.3eι0.1π	0.3eι0.1π	PROPN
ejpam-6798	501	36	)	)	PUNCT
ejpam-6798	501	37	,	,	PUNCT
ejpam-6798	501	38	(	(	PUNCT
ejpam-6798	501	39	z	z	NOUN
ejpam-6798	501	40	,	,	PUNCT
ejpam-6798	501	41	0.3eι0.1π	0.3eι0.1π	PROPN
ejpam-6798	501	42	,	,	PUNCT
ejpam-6798	501	43	0.1eι0.01π	0.1eι0.01π	NOUN
ejpam-6798	501	44	)	)	PUNCT
ejpam-6798	501	45	,	,	PUNCT
ejpam-6798	501	46	(	(	PUNCT
ejpam-6798	501	47	w	w	NOUN
ejpam-6798	501	48	,	,	PUNCT
ejpam-6798	501	49	0.3eι0.1π	0.3eι0.1π	PROPN
ejpam-6798	501	50	,	,	PUNCT
ejpam-6798	501	51	0.1eι0.01π	0.1eι0.01π	NOUN
ejpam-6798	501	52	)	)	PUNCT
ejpam-6798	501	53	}	}	PUNCT
ejpam-6798	501	54	.	.	PUNCT
ejpam-6798	502	1	it	it	PRON
ejpam-6798	502	2	is	be	AUX
ejpam-6798	502	3	easy	easy	ADJ
ejpam-6798	502	4	to	to	PART
ejpam-6798	502	5	show	show	VERB
ejpam-6798	502	6	that	that	SCONJ
ejpam-6798	502	7	l1	l1	PROPN
ejpam-6798	502	8	is	be	AUX
ejpam-6798	502	9	a	a	DET
ejpam-6798	502	10	cifi	cifi	NOUN
ejpam-6798	502	11	of	of	ADP
ejpam-6798	502	12	m	m	PROPN
ejpam-6798	502	13	.	.	PUNCT
ejpam-6798	503	1	now	now	ADV
ejpam-6798	503	2	,	,	PUNCT
ejpam-6798	503	3	define	define	VERB
ejpam-6798	503	4	a	a	DET
ejpam-6798	503	5	cifs	cifs	NOUN
ejpam-6798	503	6	l2	l2	NOUN
ejpam-6798	503	7	on	on	ADP
ejpam-6798	503	8	m	m	NOUN
ejpam-6798	503	9	as	as	ADP
ejpam-6798	503	10	:	:	PUNCT
ejpam-6798	503	11	l2	l2	NOUN
ejpam-6798	503	12	=	=	SYM
ejpam-6798	503	13	m.	m.	NOUN
ejpam-6798	503	14	jawad	jawad	PROPN
ejpam-6798	503	15	et	et	PROPN
ejpam-6798	503	16	al	al	PROPN
ejpam-6798	503	17	.	.	PUNCT
ejpam-6798	503	18	/	/	SYM
ejpam-6798	503	19	eur	eur	PROPN
ejpam-6798	503	20	.	.	PUNCT
ejpam-6798	504	1	j.	j.	PROPN
ejpam-6798	504	2	pure	pure	PROPN
ejpam-6798	504	3	appl	appl	PROPN
ejpam-6798	504	4	.	.	PROPN
ejpam-6798	504	5	math	math	PROPN
ejpam-6798	504	6	,	,	PUNCT
ejpam-6798	504	7	18	18	NUM
ejpam-6798	504	8	(	(	PUNCT
ejpam-6798	504	9	4	4	NUM
ejpam-6798	504	10	)	)	PUNCT
ejpam-6798	504	11	(	(	PUNCT
ejpam-6798	504	12	2025	2025	NUM
ejpam-6798	504	13	)	)	PUNCT
ejpam-6798	504	14	,	,	PUNCT
ejpam-6798	504	15	6798	6798	NUM
ejpam-6798	504	16	16	16	NUM
ejpam-6798	504	17	of	of	ADP
ejpam-6798	504	18	22	22	NUM
ejpam-6798	504	19	{	{	PUNCT
ejpam-6798	504	20	(	(	PUNCT
ejpam-6798	504	21	0	0	NUM
ejpam-6798	504	22	,	,	PUNCT
ejpam-6798	504	23	0.6eι0.5π	0.6eι0.5π	PROPN
ejpam-6798	504	24	,	,	PUNCT
ejpam-6798	504	25	0.4eι0.3π	0.4eι0.3π	PROPN
ejpam-6798	504	26	)	)	PUNCT
ejpam-6798	504	27	,	,	PUNCT
ejpam-6798	504	28	(	(	PUNCT
ejpam-6798	504	29	s	s	X
ejpam-6798	504	30	,	,	PUNCT
ejpam-6798	504	31	0.4eι0.6π	0.4eι0.6π	PROPN
ejpam-6798	504	32	,	,	PUNCT
ejpam-6798	504	33	0.2eι0.4π	0.2eι0.4π	PROPN
ejpam-6798	504	34	)	)	PUNCT
ejpam-6798	504	35	,	,	PUNCT
ejpam-6798	504	36	(	(	PUNCT
ejpam-6798	504	37	l	l	NOUN
ejpam-6798	504	38	,	,	PUNCT
ejpam-6798	504	39	0.6eι0.5π	0.6eι0.5π	PROPN
ejpam-6798	504	40	,	,	PUNCT
ejpam-6798	504	41	0.4eι0.3π	0.4eι0.3π	PROPN
ejpam-6798	504	42	)	)	PUNCT
ejpam-6798	504	43	,	,	PUNCT
ejpam-6798	504	44	(	(	PUNCT
ejpam-6798	504	45	z	z	X
ejpam-6798	504	46	,	,	PUNCT
ejpam-6798	504	47	0.4eι0.6π	0.4eι0.6π	PROPN
ejpam-6798	504	48	,	,	PUNCT
ejpam-6798	504	49	0.2eι0.4π	0.2eι0.4π	PROPN
ejpam-6798	504	50	)	)	PUNCT
ejpam-6798	504	51	,	,	PUNCT
ejpam-6798	504	52	(	(	PUNCT
ejpam-6798	504	53	w	w	X
ejpam-6798	504	54	,	,	PUNCT
ejpam-6798	504	55	0.4eι0.6π	0.4eι0.6π	PROPN
ejpam-6798	504	56	,	,	PUNCT
ejpam-6798	504	57	0.2eι0.4π	0.2eι0.4π	NOUN
ejpam-6798	504	58	)	)	PUNCT
ejpam-6798	504	59	}	}	PUNCT
ejpam-6798	504	60	.	.	PUNCT
ejpam-6798	505	1	it	it	PRON
ejpam-6798	505	2	is	be	AUX
ejpam-6798	505	3	easy	easy	ADJ
ejpam-6798	505	4	to	to	PART
ejpam-6798	505	5	show	show	VERB
ejpam-6798	505	6	that	that	SCONJ
ejpam-6798	505	7	l2	l2	NOUN
ejpam-6798	505	8	is	be	AUX
ejpam-6798	505	9	a	a	DET
ejpam-6798	505	10	cifi	cifi	NOUN
ejpam-6798	505	11	of	of	ADP
ejpam-6798	505	12	m	m	PROPN
ejpam-6798	505	13	.	.	PUNCT
ejpam-6798	506	1	now	now	ADV
ejpam-6798	506	2	,	,	PUNCT
ejpam-6798	506	3	define	define	VERB
ejpam-6798	506	4	a	a	DET
ejpam-6798	506	5	cifs	cifs	NOUN
ejpam-6798	506	6	l1∩l2	l1∩l2	NOUN
ejpam-6798	506	7	on	on	ADP
ejpam-6798	506	8	m	m	NOUN
ejpam-6798	506	9	as	as	ADP
ejpam-6798	506	10	:	:	PUNCT
ejpam-6798	506	11	l1∩l2	l1∩l2	PROPN
ejpam-6798	506	12	=	=	SYM
ejpam-6798	506	13	{	{	PUNCT
ejpam-6798	506	14	(	(	PUNCT
ejpam-6798	506	15	0	0	NUM
ejpam-6798	506	16	,	,	PUNCT
ejpam-6798	506	17	0.6eι0.5π	0.6eι0.5π	PROPN
ejpam-6798	506	18	,	,	PUNCT
ejpam-6798	506	19	0.7eι0.5π	0.7eι0.5π	PROPN
ejpam-6798	506	20	)	)	PUNCT
ejpam-6798	506	21	,	,	PUNCT
ejpam-6798	506	22	(	(	PUNCT
ejpam-6798	506	23	s	s	X
ejpam-6798	506	24	,	,	PUNCT
ejpam-6798	506	25	0.4eι0.5π	0.4eι0.5π	PROPN
ejpam-6798	506	26	,	,	PUNCT
ejpam-6798	506	27	0.5eι0.4π	0.5eι0.4π	PROPN
ejpam-6798	506	28	)	)	PUNCT
ejpam-6798	506	29	,	,	PUNCT
ejpam-6798	506	30	(	(	PUNCT
ejpam-6798	506	31	l	l	NOUN
ejpam-6798	506	32	,	,	PUNCT
ejpam-6798	506	33	0.5eι0.3π	0.5eι0.3π	PROPN
ejpam-6798	506	34	,	,	PUNCT
ejpam-6798	506	35	0.4eι0.3π	0.4eι0.3π	PROPN
ejpam-6798	506	36	)	)	PUNCT
ejpam-6798	506	37	,	,	PUNCT
ejpam-6798	506	38	(	(	PUNCT
ejpam-6798	506	39	z	z	NOUN
ejpam-6798	506	40	,	,	PUNCT
ejpam-6798	506	41	0.3eι0.1π	0.3eι0.1π	PROPN
ejpam-6798	506	42	,	,	PUNCT
ejpam-6798	506	43	0.2eι0.4π	0.2eι0.4π	PROPN
ejpam-6798	506	44	)	)	PUNCT
ejpam-6798	506	45	,	,	PUNCT
ejpam-6798	506	46	(	(	PUNCT
ejpam-6798	506	47	w	w	NOUN
ejpam-6798	506	48	,	,	PUNCT
ejpam-6798	506	49	0.3eι0.1π	0.3eι0.1π	PROPN
ejpam-6798	506	50	,	,	PUNCT
ejpam-6798	506	51	0.2eι0.4π	0.2eι0.4π	NOUN
ejpam-6798	506	52	)	)	PUNCT
ejpam-6798	506	53	}	}	PUNCT
ejpam-6798	506	54	.	.	PUNCT
ejpam-6798	507	1	it	it	PRON
ejpam-6798	507	2	is	be	AUX
ejpam-6798	507	3	straightforward	straightforward	ADJ
ejpam-6798	507	4	to	to	PART
ejpam-6798	507	5	prove	prove	VERB
ejpam-6798	507	6	that	that	SCONJ
ejpam-6798	507	7	l1	l1	PROPN
ejpam-6798	507	8	∩l2	∩l2	PROPN
ejpam-6798	507	9	is	be	AUX
ejpam-6798	507	10	a	a	DET
ejpam-6798	507	11	cifi	cifi	NOUN
ejpam-6798	507	12	of	of	ADP
ejpam-6798	507	13	m	m	PROPN
ejpam-6798	507	14	.	.	PUNCT
ejpam-6798	508	1	table	table	NOUN
ejpam-6798	508	2	6	6	NUM
ejpam-6798	508	3	:	:	PUNCT
ejpam-6798	508	4	cayley	cayley	PROPN
ejpam-6798	508	5	’s	’s	PART
ejpam-6798	508	6	table	table	NOUN
ejpam-6798	508	7	describing	describe	VERB
ejpam-6798	508	8	the	the	DET
ejpam-6798	508	9	binary	binary	ADJ
ejpam-6798	508	10	operation	operation	NOUN
ejpam-6798	508	11	expressed	express	VERB
ejpam-6798	508	12	by	by	ADP
ejpam-6798	508	13	“	"	PUNCT
ejpam-6798	508	14	⋆	⋆	VERB
ejpam-6798	508	15	”	"	PUNCT
ejpam-6798	508	16	.	.	PUNCT
ejpam-6798	509	1	⋆	⋆	VERB
ejpam-6798	509	2	0	0	NUM
ejpam-6798	509	3	s	s	PART
ejpam-6798	509	4	l	l	NOUN
ejpam-6798	509	5	z	z	PROPN
ejpam-6798	509	6	w	w	NOUN
ejpam-6798	509	7	0	0	NUM
ejpam-6798	509	8	0	0	NUM
ejpam-6798	509	9	0	0	NUM
ejpam-6798	509	10	0	0	NUM
ejpam-6798	509	11	0	0	NUM
ejpam-6798	509	12	0	0	NUM
ejpam-6798	510	1	s	s	NOUN
ejpam-6798	510	2	s	s	NOUN
ejpam-6798	510	3	0	0	NUM
ejpam-6798	510	4	s	s	NOUN
ejpam-6798	510	5	0	0	NUM
ejpam-6798	510	6	0	0	NUM
ejpam-6798	510	7	l	l	NOUN
ejpam-6798	510	8	l	l	NOUN
ejpam-6798	510	9	l	l	NOUN
ejpam-6798	510	10	0	0	NUM
ejpam-6798	510	11	0	0	NUM
ejpam-6798	510	12	0	0	NUM
ejpam-6798	511	1	z	z	NOUN
ejpam-6798	511	2	z	z	NOUN
ejpam-6798	511	3	z	z	NOUN
ejpam-6798	511	4	z	z	NOUN
ejpam-6798	511	5	0	0	NUM
ejpam-6798	511	6	0	0	NUM
ejpam-6798	512	1	w	w	PROPN
ejpam-6798	512	2	w	w	PROPN
ejpam-6798	512	3	w	w	PROPN
ejpam-6798	512	4	z	z	PROPN
ejpam-6798	512	5	l	l	NOUN
ejpam-6798	512	6	0	0	NUM
ejpam-6798	512	7	definition	definition	NOUN
ejpam-6798	512	8	17	17	NUM
ejpam-6798	512	9	.	.	PUNCT
ejpam-6798	513	1	let	let	VERB
ejpam-6798	513	2	l1	l1	PROPN
ejpam-6798	513	3	and	and	CCONJ
ejpam-6798	513	4	l2	l2	NOUN
ejpam-6798	513	5	be	be	AUX
ejpam-6798	513	6	two	two	NUM
ejpam-6798	513	7	cifss	cifss	NOUN
ejpam-6798	513	8	of	of	ADP
ejpam-6798	513	9	m	m	PROPN
ejpam-6798	513	10	.	.	PUNCT
ejpam-6798	514	1	then	then	ADV
ejpam-6798	514	2	,	,	PUNCT
ejpam-6798	514	3	the	the	DET
ejpam-6798	514	4	simple	simple	ADJ
ejpam-6798	514	5	difference	difference	NOUN
ejpam-6798	514	6	l1\l2	l1\l2	PUNCT
ejpam-6798	514	7	is	be	AUX
ejpam-6798	514	8	defined	define	VERB
ejpam-6798	514	9	as	as	ADP
ejpam-6798	514	10	µl1\l2	µl1\l2	ADV
ejpam-6798	514	11	(	(	PUNCT
ejpam-6798	514	12	s	s	NOUN
ejpam-6798	514	13	)	)	PUNCT
ejpam-6798	514	14	=	=	SYM
ejpam-6798	515	1	(	(	PUNCT
ejpam-6798	515	2	γl1(s)∧γl2(s))e	γl1(s)∧γl2(s))e	PROPN
ejpam-6798	515	3	ι(θl1	ι(θl1	PROPN
ejpam-6798	515	4	(	(	PUNCT
ejpam-6798	515	5	s)∧θl2	s)∧θl2	PROPN
ejpam-6798	515	6	(	(	PUNCT
ejpam-6798	515	7	s	s	NOUN
ejpam-6798	515	8	)	)	PUNCT
ejpam-6798	515	9	)	)	PUNCT
ejpam-6798	515	10	,	,	PUNCT
ejpam-6798	515	11	νl1\l2	νl1\l2	X
ejpam-6798	515	12	(	(	PUNCT
ejpam-6798	515	13	s	s	X
ejpam-6798	515	14	)	)	PUNCT
ejpam-6798	515	15	=	=	SYM
ejpam-6798	515	16	(	(	PUNCT
ejpam-6798	515	17	γl1	γl1	X
ejpam-6798	515	18	(	(	PUNCT
ejpam-6798	515	19	s)∨γl2	s)∨γl2	NOUN
ejpam-6798	515	20	(	(	PUNCT
ejpam-6798	515	21	s))eι(θl1	s))eι(θl1	NOUN
ejpam-6798	515	22	(	(	PUNCT
ejpam-6798	515	23	s)∨θl2	s)∨θl2	PROPN
ejpam-6798	515	24	(	(	PUNCT
ejpam-6798	515	25	s	s	NOUN
ejpam-6798	515	26	)	)	PUNCT
ejpam-6798	515	27	)	)	PUNCT
ejpam-6798	515	28	.	.	PUNCT
ejpam-6798	516	1	example	example	NOUN
ejpam-6798	517	1	13	13	NUM
ejpam-6798	517	2	.	.	PUNCT
ejpam-6798	518	1	let	let	VERB
ejpam-6798	518	2	(	(	PUNCT
ejpam-6798	518	3	µl1(s	µl1(s	PROPN
ejpam-6798	518	4	)	)	PUNCT
ejpam-6798	518	5	,	,	PUNCT
ejpam-6798	518	6	νl1(s	νl1(s	PROPN
ejpam-6798	518	7	)	)	PUNCT
ejpam-6798	518	8	)	)	PUNCT
ejpam-6798	519	1	=	=	PRON
ejpam-6798	519	2	{	{	PUNCT
ejpam-6798	519	3	(	(	PUNCT
ejpam-6798	519	4	s1	s1	NOUN
ejpam-6798	519	5	,	,	PUNCT
ejpam-6798	519	6	0.6eι0.5π	0.6eι0.5π	PROPN
ejpam-6798	519	7	,	,	PUNCT
ejpam-6798	519	8	0.4eι0.25π	0.4eι0.25π	NOUN
ejpam-6798	519	9	)	)	PUNCT
ejpam-6798	519	10	,	,	PUNCT
ejpam-6798	519	11	(	(	PUNCT
ejpam-6798	519	12	s2	s2	PROPN
ejpam-6798	519	13	,	,	PUNCT
ejpam-6798	519	14	1eι0.5π	1eι0.5π	NUM
ejpam-6798	519	15	,	,	PUNCT
ejpam-6798	519	16	0.8eι0.25π	0.8eι0.25π	NOUN
ejpam-6798	519	17	)	)	PUNCT
ejpam-6798	519	18	,	,	PUNCT
ejpam-6798	519	19	(	(	PUNCT
ejpam-6798	519	20	s3	s3	PROPN
ejpam-6798	519	21	,	,	PUNCT
ejpam-6798	519	22	0.8eι2π	0.8eι2π	NUM
ejpam-6798	519	23	,	,	PUNCT
ejpam-6798	519	24	0.6eι1.5π	0.6eι1.5π	NUM
ejpam-6798	519	25	)	)	PUNCT
ejpam-6798	519	26	,	,	PUNCT
ejpam-6798	519	27	(	(	PUNCT
ejpam-6798	519	28	s4	s4	X
ejpam-6798	519	29	,	,	PUNCT
ejpam-6798	519	30	0.9e	0.9e	NOUN
ejpam-6798	519	31	ι0.4π	ι0.4π	NOUN
ejpam-6798	519	32	,	,	PUNCT
ejpam-6798	519	33	0.7eι0.24π	0.7eι0.24π	NOUN
ejpam-6798	519	34	)	)	PUNCT
ejpam-6798	519	35	,	,	PUNCT
ejpam-6798	519	36	(	(	PUNCT
ejpam-6798	519	37	s5	s5	PROPN
ejpam-6798	519	38	,	,	PUNCT
ejpam-6798	519	39	0.7e	0.7e	NOUN
ejpam-6798	519	40	ιπ	ιπ	ADJ
ejpam-6798	519	41	,	,	PUNCT
ejpam-6798	519	42	0.5eι0.8π	0.5eι0.8π	PROPN
ejpam-6798	519	43	)	)	PUNCT
ejpam-6798	519	44	,	,	PUNCT
ejpam-6798	519	45	(	(	PUNCT
ejpam-6798	519	46	s6	s6	PROPN
ejpam-6798	519	47	,	,	PUNCT
ejpam-6798	519	48	0.5e	0.5e	NUM
ejpam-6798	519	49	ι0.4π	ι0.4π	NOUN
ejpam-6798	519	50	,	,	PUNCT
ejpam-6798	519	51	0.3eι0.24π	0.3eι0.24π	NOUN
ejpam-6798	519	52	)	)	PUNCT
ejpam-6798	519	53	}	}	PUNCT
ejpam-6798	519	54	and	and	CCONJ
ejpam-6798	519	55	(	(	PUNCT
ejpam-6798	519	56	µl2(s	µl2(s	PROPN
ejpam-6798	519	57	)	)	PUNCT
ejpam-6798	519	58	,	,	PUNCT
ejpam-6798	519	59	νl2(s	νl2(s	PROPN
ejpam-6798	519	60	)	)	PUNCT
ejpam-6798	519	61	)	)	PUNCT
ejpam-6798	519	62	=	=	PRON
ejpam-6798	520	1	{	{	PUNCT
ejpam-6798	520	2	(	(	PUNCT
ejpam-6798	520	3	s1	s1	NOUN
ejpam-6798	520	4	,	,	PUNCT
ejpam-6798	520	5	0.2eιπ	0.2eιπ	NUM
ejpam-6798	520	6	,	,	PUNCT
ejpam-6798	520	7	0.1eι0.88π	0.1eι0.88π	NUM
ejpam-6798	520	8	)	)	PUNCT
ejpam-6798	520	9	,	,	PUNCT
ejpam-6798	520	10	(	(	PUNCT
ejpam-6798	520	11	s2	s2	PROPN
ejpam-6798	520	12	,	,	PUNCT
ejpam-6798	520	13	0.1eι0.8π	0.1eι0.8π	NOUN
ejpam-6798	520	14	,	,	PUNCT
ejpam-6798	520	15	0.01eι0.6π	0.01eι0.6π	NUM
ejpam-6798	520	16	)	)	PUNCT
ejpam-6798	520	17	,	,	PUNCT
ejpam-6798	520	18	(	(	PUNCT
ejpam-6798	520	19	s3	s3	PROPN
ejpam-6798	520	20	,	,	PUNCT
ejpam-6798	520	21	0.8eι0.8π	0.8eι0.8π	PROPN
ejpam-6798	520	22	,	,	PUNCT
ejpam-6798	520	23	0.6eι0.68π	0.6eι0.68π	NOUN
ejpam-6798	520	24	)	)	PUNCT
ejpam-6798	520	25	,	,	PUNCT
ejpam-6798	520	26	(	(	PUNCT
ejpam-6798	520	27	s4	s4	PROPN
ejpam-6798	520	28	,	,	PUNCT
ejpam-6798	520	29	0.2eιπ	0.2eιπ	NUM
ejpam-6798	520	30	,	,	PUNCT
ejpam-6798	520	31	0.1eι0.88π	0.1eι0.88π	NUM
ejpam-6798	520	32	)	)	PUNCT
ejpam-6798	520	33	,	,	PUNCT
ejpam-6798	520	34	(	(	PUNCT
ejpam-6798	520	35	s5	s5	PROPN
ejpam-6798	520	36	,	,	PUNCT
ejpam-6798	520	37	0.9e	0.9e	PROPN
ejpam-6798	520	38	ι0.9π	ι0.9π	PROPN
ejpam-6798	520	39	,	,	PUNCT
ejpam-6798	520	40	0.7eι0.7π	0.7eι0.7π	PROPN
ejpam-6798	520	41	)	)	PUNCT
ejpam-6798	520	42	,	,	PUNCT
ejpam-6798	520	43	(	(	PUNCT
ejpam-6798	520	44	s6	s6	PROPN
ejpam-6798	520	45	,	,	PUNCT
ejpam-6798	520	46	0.3e	0.3e	NOUN
ejpam-6798	520	47	ι2π	ι2π	NOUN
ejpam-6798	520	48	,	,	PUNCT
ejpam-6798	520	49	0.1eι1.88π	0.1eι1.88π	PROPN
ejpam-6798	520	50	)	)	PUNCT
ejpam-6798	520	51	}	}	PUNCT
ejpam-6798	520	52	be	be	AUX
ejpam-6798	520	53	a	a	DET
ejpam-6798	520	54	cifss	cifss	NOUN
ejpam-6798	520	55	.	.	PUNCT
ejpam-6798	521	1	then	then	ADV
ejpam-6798	521	2	,	,	PUNCT
ejpam-6798	521	3	µl1\l2	µl1\l2	ADV
ejpam-6798	521	4	(	(	PUNCT
ejpam-6798	521	5	s	s	X
ejpam-6798	521	6	)	)	PUNCT
ejpam-6798	521	7	=	=	SYM
ejpam-6798	521	8	{	{	PUNCT
ejpam-6798	521	9	(	(	PUNCT
ejpam-6798	521	10	s1	s1	NOUN
ejpam-6798	521	11	,	,	PUNCT
ejpam-6798	521	12	0.2eι0.5π	0.2eι0.5π	PROPN
ejpam-6798	521	13	,	,	PUNCT
ejpam-6798	521	14	0.4eι0.88π	0.4eι0.88π	PROPN
ejpam-6798	521	15	)	)	PUNCT
ejpam-6798	521	16	,	,	PUNCT
ejpam-6798	521	17	(	(	PUNCT
ejpam-6798	521	18	s2	s2	PROPN
ejpam-6798	521	19	,	,	PUNCT
ejpam-6798	521	20	0.1eι0.5π	0.1eι0.5π	PROPN
ejpam-6798	521	21	,	,	PUNCT
ejpam-6798	521	22	0.8eι0.6π	0.8eι0.6π	PROPN
ejpam-6798	521	23	)	)	PUNCT
ejpam-6798	521	24	,	,	PUNCT
ejpam-6798	521	25	(	(	PUNCT
ejpam-6798	521	26	s3	s3	PROPN
ejpam-6798	521	27	,	,	PUNCT
ejpam-6798	521	28	0.8eι0.8π	0.8eι0.8π	PROPN
ejpam-6798	521	29	,	,	PUNCT
ejpam-6798	521	30	0.6eι1.5π	0.6eι1.5π	PROPN
ejpam-6798	521	31	)	)	PUNCT
ejpam-6798	521	32	,	,	PUNCT
ejpam-6798	521	33	(	(	PUNCT
ejpam-6798	521	34	s4	s4	PROPN
ejpam-6798	521	35	,	,	PUNCT
ejpam-6798	521	36	0.2eι0.4π	0.2eι0.4π	NOUN
ejpam-6798	521	37	,	,	PUNCT
ejpam-6798	521	38	0.7eι0.88π	0.7eι0.88π	NOUN
ejpam-6798	521	39	)	)	PUNCT
ejpam-6798	521	40	,	,	PUNCT
ejpam-6798	521	41	(	(	PUNCT
ejpam-6798	521	42	s5	s5	X
ejpam-6798	521	43	,	,	PUNCT
ejpam-6798	521	44	0.7e	0.7e	NOUN
ejpam-6798	521	45	ι0.9π	ι0.9π	PROPN
ejpam-6798	521	46	,	,	PUNCT
ejpam-6798	521	47	0.7eι0.8π	0.7eι0.8π	PROPN
ejpam-6798	521	48	)	)	PUNCT
ejpam-6798	521	49	,	,	PUNCT
ejpam-6798	521	50	(	(	PUNCT
ejpam-6798	521	51	s6	s6	PROPN
ejpam-6798	521	52	,	,	PUNCT
ejpam-6798	521	53	0.3e	0.3e	NOUN
ejpam-6798	521	54	ι0.4π	ι0.4π	NOUN
ejpam-6798	521	55	,	,	PUNCT
ejpam-6798	521	56	0.3eι1.88π	0.3eι1.88π	NOUN
ejpam-6798	521	57	)	)	PUNCT
ejpam-6798	521	58	}	}	PUNCT
ejpam-6798	521	59	.	.	PUNCT
ejpam-6798	522	1	it	it	PRON
ejpam-6798	522	2	is	be	AUX
ejpam-6798	522	3	straightforward	straightforward	ADJ
ejpam-6798	522	4	to	to	PART
ejpam-6798	522	5	prove	prove	VERB
ejpam-6798	522	6	that	that	SCONJ
ejpam-6798	522	7	l1\l2	l1\l2	PROPN
ejpam-6798	522	8	is	be	AUX
ejpam-6798	522	9	a	a	DET
ejpam-6798	522	10	cifi	cifi	NOUN
ejpam-6798	522	11	of	of	ADP
ejpam-6798	522	12	m	m	PROPN
ejpam-6798	522	13	.	.	PUNCT
ejpam-6798	523	1	the	the	DET
ejpam-6798	523	2	subsequent	subsequent	ADJ
ejpam-6798	523	3	theorem	theorem	NOUN
ejpam-6798	523	4	demonstrates	demonstrate	VERB
ejpam-6798	523	5	that	that	SCONJ
ejpam-6798	523	6	the	the	DET
ejpam-6798	523	7	simple	simple	ADJ
ejpam-6798	523	8	difference	difference	NOUN
ejpam-6798	523	9	\	\	PUNCT
ejpam-6798	523	10	of	of	ADP
ejpam-6798	523	11	two	two	NUM
ejpam-6798	523	12	cifis	cifis	NOUN
ejpam-6798	523	13	of	of	ADP
ejpam-6798	523	14	m	m	PROPN
ejpam-6798	523	15	is	be	AUX
ejpam-6798	523	16	also	also	ADV
ejpam-6798	523	17	cifi	cifi	NOUN
ejpam-6798	523	18	.	.	PUNCT
ejpam-6798	524	1	theorem	theorem	PROPN
ejpam-6798	524	2	12	12	NUM
ejpam-6798	524	3	.	.	PUNCT
ejpam-6798	525	1	assume	assume	VERB
ejpam-6798	525	2	that	that	SCONJ
ejpam-6798	525	3	l1	l1	PROPN
ejpam-6798	525	4	and	and	CCONJ
ejpam-6798	525	5	l2	l2	NOUN
ejpam-6798	525	6	are	be	AUX
ejpam-6798	525	7	two	two	NUM
ejpam-6798	525	8	cifis	cifis	NOUN
ejpam-6798	525	9	of	of	ADP
ejpam-6798	525	10	m	m	PROPN
ejpam-6798	525	11	.	.	PUNCT
ejpam-6798	526	1	then	then	ADV
ejpam-6798	526	2	,	,	PUNCT
ejpam-6798	526	3	l1\l2	l1\l2	ADV
ejpam-6798	526	4	is	be	AUX
ejpam-6798	526	5	a	a	DET
ejpam-6798	526	6	cifi	cifi	NOUN
ejpam-6798	526	7	of	of	ADP
ejpam-6798	526	8	m	m	PROPN
ejpam-6798	526	9	.	.	PUNCT
ejpam-6798	527	1	proof	proof	NOUN
ejpam-6798	527	2	.	.	PUNCT
ejpam-6798	528	1	let	let	VERB
ejpam-6798	528	2	l1	l1	PROPN
ejpam-6798	528	3	and	and	CCONJ
ejpam-6798	528	4	l2	l2	NOUN
ejpam-6798	528	5	be	be	AUX
ejpam-6798	528	6	two	two	NUM
ejpam-6798	528	7	cifis	cifis	NOUN
ejpam-6798	528	8	of	of	ADP
ejpam-6798	528	9	m	m	PRON
ejpam-6798	528	10	and	and	CCONJ
ejpam-6798	528	11	let	let	VERB
ejpam-6798	528	12	s	s	NOUN
ejpam-6798	528	13	,	,	PUNCT
ejpam-6798	528	14	l	l	PROPN
ejpam-6798	528	15	∈	∈	PROPN
ejpam-6798	528	16	m	m	VERB
ejpam-6798	528	17	.	.	PUNCT
ejpam-6798	529	1	then	then	ADV
ejpam-6798	529	2	µl1\l2	µl1\l2	ADV
ejpam-6798	529	3	(	(	PUNCT
ejpam-6798	529	4	0	0	NUM
ejpam-6798	529	5	)	)	PUNCT
ejpam-6798	529	6	=	=	SYM
ejpam-6798	529	7	(	(	PUNCT
ejpam-6798	529	8	γl1(0	γl1(0	NOUN
ejpam-6798	529	9	)	)	PUNCT
ejpam-6798	529	10	∧	∧	PROPN
ejpam-6798	529	11	γl2(0))e	γl2(0))e	PROPN
ejpam-6798	529	12	ι(θl1	ι(θl1	PROPN
ejpam-6798	529	13	(	(	PUNCT
ejpam-6798	529	14	0)∧θl2	0)∧θl2	NOUN
ejpam-6798	529	15	(	(	PUNCT
ejpam-6798	529	16	0	0	NUM
ejpam-6798	529	17	)	)	PUNCT
ejpam-6798	529	18	)	)	PUNCT
ejpam-6798	529	19	≥	≥	NOUN
ejpam-6798	529	20	(	(	PUNCT
ejpam-6798	529	21	γl1(s	γl1(s	PROPN
ejpam-6798	529	22	)	)	PUNCT
ejpam-6798	529	23	∧	∧	NOUN
ejpam-6798	529	24	γl2(s))e	γl2(s))e	PROPN
ejpam-6798	529	25	ι(θl1	ι(θl1	INTJ
ejpam-6798	529	26	(	(	PUNCT
ejpam-6798	529	27	s)∧θl2	s)∧θl2	PROPN
ejpam-6798	529	28	(	(	PUNCT
ejpam-6798	529	29	s	s	NOUN
ejpam-6798	529	30	)	)	PUNCT
ejpam-6798	529	31	)	)	PUNCT
ejpam-6798	530	1	=	=	PRON
ejpam-6798	530	2	µl1\l2	µl1\l2	X
ejpam-6798	530	3	(	(	PUNCT
ejpam-6798	530	4	s	s	NOUN
ejpam-6798	530	5	)	)	PUNCT
ejpam-6798	530	6	.	.	PUNCT
ejpam-6798	531	1	moreover	moreover	ADV
ejpam-6798	531	2	µl1\l2	µl1\l2	ADV
ejpam-6798	531	3	(	(	PUNCT
ejpam-6798	531	4	s	s	X
ejpam-6798	531	5	)	)	PUNCT
ejpam-6798	531	6	=	=	SYM
ejpam-6798	531	7	(	(	PUNCT
ejpam-6798	531	8	γl1(s	γl1(s	PROPN
ejpam-6798	531	9	)	)	PUNCT
ejpam-6798	531	10	∧	∧	NOUN
ejpam-6798	531	11	γl2(s))e	γl2(s))e	PROPN
ejpam-6798	531	12	ι(θl1	ι(θl1	INTJ
ejpam-6798	531	13	(	(	PUNCT
ejpam-6798	531	14	s)∧θl2	s)∧θl2	PROPN
ejpam-6798	531	15	(	(	PUNCT
ejpam-6798	531	16	s	s	NOUN
ejpam-6798	531	17	)	)	PUNCT
ejpam-6798	531	18	)	)	PUNCT
ejpam-6798	531	19	≥	≥	NOUN
ejpam-6798	531	20	(	(	PUNCT
ejpam-6798	531	21	(	(	PUNCT
ejpam-6798	531	22	γl1(s	γl1(s	X
ejpam-6798	531	23	⋆	⋆	ADJ
ejpam-6798	531	24	l	l	NOUN
ejpam-6798	531	25	)	)	PUNCT
ejpam-6798	531	26	∧	∧	PROPN
ejpam-6798	531	27	γl1(l	γl1(l	PROPN
ejpam-6798	531	28	)	)	PUNCT
ejpam-6798	531	29	)	)	PUNCT
ejpam-6798	532	1	∧	∧	NOUN
ejpam-6798	532	2	(	(	PUNCT
ejpam-6798	532	3	γl2(s	γl2(s	PROPN
ejpam-6798	532	4	⋆	⋆	NOUN
ejpam-6798	532	5	l	l	NOUN
ejpam-6798	532	6	)	)	PUNCT
ejpam-6798	532	7	∧	∧	PROPN
ejpam-6798	532	8	γl2(l	γl2(l	NOUN
ejpam-6798	532	9	)	)	PUNCT
ejpam-6798	532	10	)	)	PUNCT
ejpam-6798	532	11	)	)	PUNCT
ejpam-6798	533	1	eι((θl1	eι((θl1	NOUN
ejpam-6798	533	2	(	(	PUNCT
ejpam-6798	533	3	s⋆l)∧θl1	s⋆l)∧θl1	PROPN
ejpam-6798	533	4	(	(	PUNCT
ejpam-6798	533	5	l))∧(θl2	l))∧(θl2	X
ejpam-6798	533	6	(	(	PUNCT
ejpam-6798	533	7	s⋆l)∧θl2	s⋆l)∧θl2	NOUN
ejpam-6798	533	8	(	(	PUNCT
ejpam-6798	533	9	l	l	NOUN
ejpam-6798	533	10	)	)	PUNCT
ejpam-6798	533	11	)	)	PUNCT
ejpam-6798	533	12	)	)	PUNCT
ejpam-6798	533	13	m.	m.	NOUN
ejpam-6798	533	14	jawad	jawad	PROPN
ejpam-6798	533	15	et	et	PROPN
ejpam-6798	533	16	al	al	PROPN
ejpam-6798	533	17	.	.	PUNCT
ejpam-6798	533	18	/	/	SYM
ejpam-6798	533	19	eur	eur	PROPN
ejpam-6798	533	20	.	.	PUNCT
ejpam-6798	534	1	j.	j.	PROPN
ejpam-6798	534	2	pure	pure	PROPN
ejpam-6798	534	3	appl	appl	PROPN
ejpam-6798	534	4	.	.	PROPN
ejpam-6798	534	5	math	math	PROPN
ejpam-6798	534	6	,	,	PUNCT
ejpam-6798	534	7	18	18	NUM
ejpam-6798	534	8	(	(	PUNCT
ejpam-6798	534	9	4	4	NUM
ejpam-6798	534	10	)	)	PUNCT
ejpam-6798	534	11	(	(	PUNCT
ejpam-6798	534	12	2025	2025	NUM
ejpam-6798	534	13	)	)	PUNCT
ejpam-6798	534	14	,	,	PUNCT
ejpam-6798	534	15	6798	6798	NUM
ejpam-6798	534	16	17	17	NUM
ejpam-6798	534	17	of	of	ADP
ejpam-6798	534	18	22	22	NUM
ejpam-6798	534	19	≥	≥	NOUN
ejpam-6798	534	20	(	(	PUNCT
ejpam-6798	534	21	(	(	PUNCT
ejpam-6798	534	22	γl1(s	γl1(s	X
ejpam-6798	534	23	⋆	⋆	NOUN
ejpam-6798	534	24	l	l	NOUN
ejpam-6798	534	25	)	)	PUNCT
ejpam-6798	534	26	∧	∧	PROPN
ejpam-6798	534	27	γl2(s	γl2(s	PROPN
ejpam-6798	534	28	⋆	⋆	ADJ
ejpam-6798	534	29	l	l	NOUN
ejpam-6798	534	30	)	)	PUNCT
ejpam-6798	534	31	)	)	PUNCT
ejpam-6798	535	1	∧	∧	PROPN
ejpam-6798	535	2	(	(	PUNCT
ejpam-6798	535	3	γl1(l	γl1(l	PROPN
ejpam-6798	535	4	)	)	PUNCT
ejpam-6798	535	5	∧	∧	PROPN
ejpam-6798	535	6	γl2(l	γl2(l	NOUN
ejpam-6798	535	7	)	)	PUNCT
ejpam-6798	535	8	)	)	PUNCT
ejpam-6798	535	9	)	)	PUNCT
ejpam-6798	536	1	eι((θl1	eι((θl1	NOUN
ejpam-6798	536	2	(	(	PUNCT
ejpam-6798	536	3	s⋆l)∧θl2	s⋆l)∧θl2	PROPN
ejpam-6798	536	4	(	(	PUNCT
ejpam-6798	536	5	s⋆l))∧(θl1	s⋆l))∧(θl1	VERB
ejpam-6798	536	6	(	(	PUNCT
ejpam-6798	536	7	l)∧θl2	l)∧θl2	PROPN
ejpam-6798	536	8	(	(	PUNCT
ejpam-6798	536	9	l	l	NOUN
ejpam-6798	536	10	)	)	PUNCT
ejpam-6798	536	11	)	)	PUNCT
ejpam-6798	536	12	)	)	PUNCT
ejpam-6798	537	1	=	=	PUNCT
ejpam-6798	537	2	(	(	PUNCT
ejpam-6798	537	3	γl1(s	γl1(s	X
ejpam-6798	537	4	⋆	⋆	NOUN
ejpam-6798	537	5	l	l	NOUN
ejpam-6798	537	6	)	)	PUNCT
ejpam-6798	537	7	∧	∧	PROPN
ejpam-6798	537	8	γl2(s	γl2(s	PROPN
ejpam-6798	537	9	⋆	⋆	VERB
ejpam-6798	537	10	l))e	l))e	PROPN
ejpam-6798	537	11	ι(θl1	ι(θl1	PROPN
ejpam-6798	537	12	(	(	PUNCT
ejpam-6798	537	13	s⋆l)∧θl2	s⋆l)∧θl2	NOUN
ejpam-6798	537	14	(	(	PUNCT
ejpam-6798	537	15	s⋆l	s⋆l	NOUN
ejpam-6798	537	16	)	)	PUNCT
ejpam-6798	537	17	)	)	PUNCT
ejpam-6798	538	1	∧	∧	PROPN
ejpam-6798	538	2	(	(	PUNCT
ejpam-6798	538	3	γl1(l	γl1(l	PROPN
ejpam-6798	538	4	)	)	PUNCT
ejpam-6798	538	5	∧	∧	PROPN
ejpam-6798	538	6	γl2(l))e	γl2(l))e	PROPN
ejpam-6798	538	7	ι(θl1	ι(θl1	NUM
ejpam-6798	538	8	(	(	PUNCT
ejpam-6798	538	9	l)∧θl2	l)∧θl2	PROPN
ejpam-6798	538	10	(	(	PUNCT
ejpam-6798	538	11	l	l	NOUN
ejpam-6798	538	12	)	)	PUNCT
ejpam-6798	538	13	)	)	PUNCT
ejpam-6798	538	14	≥	≥	PROPN
ejpam-6798	538	15	µl1\l2	µl1\l2	ADV
ejpam-6798	538	16	(	(	PUNCT
ejpam-6798	538	17	s	s	X
ejpam-6798	538	18	⋆	⋆	NOUN
ejpam-6798	538	19	l	l	NOUN
ejpam-6798	538	20	)	)	PUNCT
ejpam-6798	538	21	∧	∧	PROPN
ejpam-6798	538	22	µl1\l2	µl1\l2	ADV
ejpam-6798	538	23	(	(	PUNCT
ejpam-6798	538	24	l	l	NOUN
ejpam-6798	538	25	)	)	PUNCT
ejpam-6798	538	26	.	.	PUNCT
ejpam-6798	539	1	suppose	suppose	VERB
ejpam-6798	539	2	that	that	SCONJ
ejpam-6798	539	3	l1	l1	PROPN
ejpam-6798	539	4	and	and	CCONJ
ejpam-6798	539	5	l2	l2	NOUN
ejpam-6798	539	6	are	be	AUX
ejpam-6798	539	7	two	two	NUM
ejpam-6798	539	8	cifis	cifis	NOUN
ejpam-6798	539	9	of	of	ADP
ejpam-6798	539	10	m	m	PRON
ejpam-6798	539	11	and	and	CCONJ
ejpam-6798	539	12	let	let	VERB
ejpam-6798	539	13	s	s	NOUN
ejpam-6798	539	14	,	,	PUNCT
ejpam-6798	539	15	l	l	PROPN
ejpam-6798	539	16	∈	∈	PROPN
ejpam-6798	539	17	m	m	VERB
ejpam-6798	539	18	.	.	PUNCT
ejpam-6798	540	1	then	then	ADV
ejpam-6798	540	2	νl1\l2	νl1\l2	X
ejpam-6798	540	3	(	(	PUNCT
ejpam-6798	540	4	0	0	NUM
ejpam-6798	540	5	)	)	PUNCT
ejpam-6798	540	6	=	=	SYM
ejpam-6798	540	7	(	(	PUNCT
ejpam-6798	540	8	γl1	γl1	NOUN
ejpam-6798	540	9	(	(	PUNCT
ejpam-6798	540	10	0	0	NUM
ejpam-6798	540	11	)	)	PUNCT
ejpam-6798	540	12	∨	∨	NUM
ejpam-6798	540	13	γl2	γl2	NOUN
ejpam-6798	540	14	(	(	PUNCT
ejpam-6798	540	15	0))eι(θl1	0))eι(θl1	NUM
ejpam-6798	540	16	(	(	PUNCT
ejpam-6798	540	17	0)∨θl2	0)∨θl2	NUM
ejpam-6798	540	18	(	(	PUNCT
ejpam-6798	540	19	0	0	NUM
ejpam-6798	540	20	)	)	PUNCT
ejpam-6798	540	21	)	)	PUNCT
ejpam-6798	540	22	≤	≤	NOUN
ejpam-6798	540	23	(	(	PUNCT
ejpam-6798	540	24	γl1	γl1	NOUN
ejpam-6798	540	25	(	(	PUNCT
ejpam-6798	540	26	s	s	NOUN
ejpam-6798	540	27	)	)	PUNCT
ejpam-6798	540	28	∨	∨	NUM
ejpam-6798	540	29	γl2	γl2	PROPN
ejpam-6798	540	30	(	(	PUNCT
ejpam-6798	540	31	s))eι(θl1	s))eι(θl1	NOUN
ejpam-6798	540	32	(	(	PUNCT
ejpam-6798	540	33	s)∨θl2	s)∨θl2	PROPN
ejpam-6798	540	34	(	(	PUNCT
ejpam-6798	540	35	s	s	NOUN
ejpam-6798	540	36	)	)	PUNCT
ejpam-6798	540	37	)	)	PUNCT
ejpam-6798	541	1	=	=	PRON
ejpam-6798	541	2	νl1\l2	νl1\l2	X
ejpam-6798	541	3	(	(	PUNCT
ejpam-6798	541	4	s	s	NOUN
ejpam-6798	541	5	)	)	PUNCT
ejpam-6798	541	6	.	.	PUNCT
ejpam-6798	542	1	and	and	CCONJ
ejpam-6798	542	2	νl1\l2	νl1\l2	ADV
ejpam-6798	542	3	(	(	PUNCT
ejpam-6798	542	4	s	s	X
ejpam-6798	542	5	)	)	PUNCT
ejpam-6798	542	6	=	=	SYM
ejpam-6798	542	7	(	(	PUNCT
ejpam-6798	542	8	γl1	γl1	X
ejpam-6798	542	9	(	(	PUNCT
ejpam-6798	542	10	s	s	NOUN
ejpam-6798	542	11	)	)	PUNCT
ejpam-6798	542	12	∨	∨	NUM
ejpam-6798	542	13	γl2	γl2	PROPN
ejpam-6798	542	14	(	(	PUNCT
ejpam-6798	542	15	s))eι(θl1	s))eι(θl1	NOUN
ejpam-6798	542	16	(	(	PUNCT
ejpam-6798	542	17	s)∨θl2	s)∨θl2	PROPN
ejpam-6798	542	18	(	(	PUNCT
ejpam-6798	542	19	s	s	NOUN
ejpam-6798	542	20	)	)	PUNCT
ejpam-6798	542	21	)	)	PUNCT
ejpam-6798	542	22	≤	≤	NOUN
ejpam-6798	542	23	(	(	PUNCT
ejpam-6798	542	24	(	(	PUNCT
ejpam-6798	542	25	γl1	γl1	NOUN
ejpam-6798	542	26	(	(	PUNCT
ejpam-6798	542	27	s	s	X
ejpam-6798	542	28	⋆	⋆	NOUN
ejpam-6798	542	29	l	l	NOUN
ejpam-6798	542	30	)	)	PUNCT
ejpam-6798	542	31	∨	∨	NUM
ejpam-6798	542	32	γl1	γl1	NOUN
ejpam-6798	542	33	(	(	PUNCT
ejpam-6798	542	34	l	l	NOUN
ejpam-6798	542	35	)	)	PUNCT
ejpam-6798	542	36	)	)	PUNCT
ejpam-6798	542	37	∨	∨	NUM
ejpam-6798	542	38	(	(	PUNCT
ejpam-6798	542	39	γl2	γl2	PROPN
ejpam-6798	542	40	(	(	PUNCT
ejpam-6798	542	41	s	s	X
ejpam-6798	542	42	⋆	⋆	NOUN
ejpam-6798	542	43	l	l	NOUN
ejpam-6798	542	44	)	)	PUNCT
ejpam-6798	542	45	∨	∨	NUM
ejpam-6798	542	46	γl2	γl2	PROPN
ejpam-6798	542	47	(	(	PUNCT
ejpam-6798	542	48	l	l	NOUN
ejpam-6798	542	49	)	)	PUNCT
ejpam-6798	542	50	)	)	PUNCT
ejpam-6798	542	51	)	)	PUNCT
ejpam-6798	542	52	eι((θl1	eι((θl1	NOUN
ejpam-6798	542	53	(	(	PUNCT
ejpam-6798	542	54	s⋆l)∨θl1	s⋆l)∨θl1	NOUN
ejpam-6798	542	55	(	(	PUNCT
ejpam-6798	542	56	l))∨(θl2	l))∨(θl2	PROPN
ejpam-6798	542	57	(	(	PUNCT
ejpam-6798	542	58	s⋆l)∨θl2	s⋆l)∨θl2	NOUN
ejpam-6798	542	59	(	(	PUNCT
ejpam-6798	542	60	l	l	NOUN
ejpam-6798	542	61	)	)	PUNCT
ejpam-6798	542	62	)	)	PUNCT
ejpam-6798	542	63	)	)	PUNCT
ejpam-6798	542	64	≤	≤	NOUN
ejpam-6798	542	65	(	(	PUNCT
ejpam-6798	542	66	(	(	PUNCT
ejpam-6798	542	67	γl1	γl1	NOUN
ejpam-6798	542	68	(	(	PUNCT
ejpam-6798	542	69	s	s	X
ejpam-6798	542	70	⋆	⋆	NOUN
ejpam-6798	542	71	l	l	NOUN
ejpam-6798	542	72	)	)	PUNCT
ejpam-6798	542	73	∨	∨	NUM
ejpam-6798	542	74	γl2	γl2	NOUN
ejpam-6798	542	75	(	(	PUNCT
ejpam-6798	542	76	s	s	X
ejpam-6798	542	77	⋆	⋆	NOUN
ejpam-6798	542	78	l	l	NOUN
ejpam-6798	542	79	)	)	PUNCT
ejpam-6798	542	80	)	)	PUNCT
ejpam-6798	542	81	∨	∨	NUM
ejpam-6798	542	82	(	(	PUNCT
ejpam-6798	542	83	γl1	γl1	NOUN
ejpam-6798	542	84	(	(	PUNCT
ejpam-6798	542	85	l	l	NOUN
ejpam-6798	542	86	)	)	PUNCT
ejpam-6798	542	87	∨	∨	NUM
ejpam-6798	542	88	γl2	γl2	PROPN
ejpam-6798	542	89	(	(	PUNCT
ejpam-6798	542	90	l	l	NOUN
ejpam-6798	542	91	)	)	PUNCT
ejpam-6798	542	92	)	)	PUNCT
ejpam-6798	542	93	)	)	PUNCT
ejpam-6798	543	1	eι((θl1	eι((θl1	NOUN
ejpam-6798	543	2	(	(	PUNCT
ejpam-6798	543	3	s⋆l)∨θl2	s⋆l)∨θl2	NOUN
ejpam-6798	543	4	(	(	PUNCT
ejpam-6798	543	5	s⋆l))∨(θl1	s⋆l))∨(θl1	NOUN
ejpam-6798	543	6	(	(	PUNCT
ejpam-6798	543	7	l)∨θl2	l)∨θl2	NOUN
ejpam-6798	543	8	(	(	PUNCT
ejpam-6798	543	9	l	l	NOUN
ejpam-6798	543	10	)	)	PUNCT
ejpam-6798	543	11	)	)	PUNCT
ejpam-6798	543	12	)	)	PUNCT
ejpam-6798	544	1	=	=	PRON
ejpam-6798	544	2	(	(	PUNCT
ejpam-6798	544	3	γl1	γl1	NOUN
ejpam-6798	544	4	(	(	PUNCT
ejpam-6798	544	5	s	s	X
ejpam-6798	544	6	⋆	⋆	NOUN
ejpam-6798	544	7	l	l	NOUN
ejpam-6798	544	8	)	)	PUNCT
ejpam-6798	544	9	∨	∨	NUM
ejpam-6798	544	10	γl2	γl2	NOUN
ejpam-6798	544	11	(	(	PUNCT
ejpam-6798	544	12	s	s	X
ejpam-6798	544	13	⋆	⋆	X
ejpam-6798	544	14	l))eι(θl1	l))eι(θl1	NOUN
ejpam-6798	544	15	(	(	PUNCT
ejpam-6798	544	16	s⋆l)∨θl2	s⋆l)∨θl2	NOUN
ejpam-6798	544	17	(	(	PUNCT
ejpam-6798	544	18	s⋆l	s⋆l	NOUN
ejpam-6798	544	19	)	)	PUNCT
ejpam-6798	544	20	)	)	PUNCT
ejpam-6798	544	21	∨	∨	NUM
ejpam-6798	544	22	(	(	PUNCT
ejpam-6798	544	23	γl1	γl1	NOUN
ejpam-6798	544	24	(	(	PUNCT
ejpam-6798	544	25	l	l	NOUN
ejpam-6798	544	26	)	)	PUNCT
ejpam-6798	544	27	∨	∨	NUM
ejpam-6798	545	1	γl2	γl2	NOUN
ejpam-6798	545	2	(	(	PUNCT
ejpam-6798	545	3	l))eι(θl1	l))eι(θl1	X
ejpam-6798	545	4	(	(	PUNCT
ejpam-6798	545	5	l)∨θl2	l)∨θl2	NOUN
ejpam-6798	545	6	(	(	PUNCT
ejpam-6798	545	7	l	l	NOUN
ejpam-6798	545	8	)	)	PUNCT
ejpam-6798	545	9	)	)	PUNCT
ejpam-6798	545	10	≤	≤	NOUN
ejpam-6798	546	1	νl1\l2	νl1\l2	ADV
ejpam-6798	546	2	(	(	PUNCT
ejpam-6798	546	3	s	s	X
ejpam-6798	546	4	⋆	⋆	NOUN
ejpam-6798	546	5	l	l	NOUN
ejpam-6798	546	6	)	)	PUNCT
ejpam-6798	546	7	∨	∨	NUM
ejpam-6798	546	8	νl1\l2	νl1\l2	X
ejpam-6798	546	9	(	(	PUNCT
ejpam-6798	546	10	l	l	NOUN
ejpam-6798	546	11	)	)	PUNCT
ejpam-6798	546	12	.	.	PUNCT
ejpam-6798	547	1	therefore	therefore	ADV
ejpam-6798	547	2	,	,	PUNCT
ejpam-6798	547	3	l1\l2	l1\l2	ADV
ejpam-6798	547	4	is	be	AUX
ejpam-6798	547	5	a	a	DET
ejpam-6798	547	6	cifi	cifi	NOUN
ejpam-6798	547	7	of	of	ADP
ejpam-6798	547	8	m	m	PROPN
ejpam-6798	547	9	.	.	PUNCT
ejpam-6798	547	10	example	example	NOUN
ejpam-6798	548	1	14	14	NUM
ejpam-6798	548	2	.	.	PUNCT
ejpam-6798	549	1	take	take	VERB
ejpam-6798	549	2	a	a	DET
ejpam-6798	549	3	bck	bck	NOUN
ejpam-6798	549	4	-	-	PUNCT
ejpam-6798	549	5	algebra	algebra	NOUN
ejpam-6798	549	6	m	m	NOUN
ejpam-6798	549	7	=	=	SYM
ejpam-6798	549	8	{	{	PUNCT
ejpam-6798	549	9	0	0	NUM
ejpam-6798	549	10	,	,	PUNCT
ejpam-6798	549	11	s	s	X
ejpam-6798	549	12	,	,	PUNCT
ejpam-6798	549	13	l	l	NOUN
ejpam-6798	549	14	,	,	PUNCT
ejpam-6798	549	15	z	z	NOUN
ejpam-6798	549	16	,	,	PUNCT
ejpam-6798	549	17	w	w	PROPN
ejpam-6798	549	18	}	}	PUNCT
ejpam-6798	549	19	,	,	PUNCT
ejpam-6798	549	20	where	where	SCONJ
ejpam-6798	549	21	the	the	DET
ejpam-6798	549	22	binary	binary	ADJ
ejpam-6798	549	23	operation	operation	NOUN
ejpam-6798	549	24	is	be	AUX
ejpam-6798	549	25	defined	define	VERB
ejpam-6798	549	26	by	by	ADP
ejpam-6798	549	27	the	the	DET
ejpam-6798	549	28	caley	caley	NOUN
ejpam-6798	549	29	table	table	NOUN
ejpam-6798	549	30	7	7	NUM
ejpam-6798	549	31	.	.	PUNCT
ejpam-6798	550	1	now	now	ADV
ejpam-6798	550	2	,	,	PUNCT
ejpam-6798	550	3	define	define	VERB
ejpam-6798	550	4	a	a	DET
ejpam-6798	550	5	cifs	cifs	NOUN
ejpam-6798	550	6	l1	l1	NOUN
ejpam-6798	550	7	on	on	ADP
ejpam-6798	550	8	m	m	NOUN
ejpam-6798	550	9	as	as	ADP
ejpam-6798	550	10	:	:	PUNCT
ejpam-6798	550	11	l1	l1	PROPN
ejpam-6798	550	12	=	=	SYM
ejpam-6798	550	13	{	{	PUNCT
ejpam-6798	550	14	(	(	PUNCT
ejpam-6798	550	15	0	0	NUM
ejpam-6798	550	16	,	,	PUNCT
ejpam-6798	550	17	0.9eι0.7π	0.9eι0.7π	PROPN
ejpam-6798	550	18	,	,	PUNCT
ejpam-6798	550	19	0.7eι0.5π	0.7eι0.5π	PROPN
ejpam-6798	550	20	)	)	PUNCT
ejpam-6798	550	21	,	,	PUNCT
ejpam-6798	550	22	(	(	PUNCT
ejpam-6798	550	23	s	s	X
ejpam-6798	550	24	,	,	PUNCT
ejpam-6798	550	25	0.7eι0.5π	0.7eι0.5π	PROPN
ejpam-6798	550	26	,	,	PUNCT
ejpam-6798	550	27	0.5eι0.3π	0.5eι0.3π	PROPN
ejpam-6798	550	28	)	)	PUNCT
ejpam-6798	550	29	,	,	PUNCT
ejpam-6798	550	30	(	(	PUNCT
ejpam-6798	550	31	l	l	NOUN
ejpam-6798	550	32	,	,	PUNCT
ejpam-6798	550	33	0.5eι0.3π	0.5eι0.3π	NOUN
ejpam-6798	550	34	,	,	PUNCT
ejpam-6798	550	35	0.3eι0.1π	0.3eι0.1π	PROPN
ejpam-6798	550	36	)	)	PUNCT
ejpam-6798	550	37	,	,	PUNCT
ejpam-6798	550	38	(	(	PUNCT
ejpam-6798	550	39	z	z	NOUN
ejpam-6798	550	40	,	,	PUNCT
ejpam-6798	550	41	0.3eι0.1π	0.3eι0.1π	PROPN
ejpam-6798	550	42	,	,	PUNCT
ejpam-6798	550	43	0.1eι0.01π	0.1eι0.01π	NOUN
ejpam-6798	550	44	)	)	PUNCT
ejpam-6798	550	45	,	,	PUNCT
ejpam-6798	550	46	(	(	PUNCT
ejpam-6798	550	47	w	w	NOUN
ejpam-6798	550	48	,	,	PUNCT
ejpam-6798	550	49	0.3eι0.1π	0.3eι0.1π	PROPN
ejpam-6798	550	50	,	,	PUNCT
ejpam-6798	550	51	0.1eι0.01π	0.1eι0.01π	NOUN
ejpam-6798	550	52	)	)	PUNCT
ejpam-6798	550	53	}	}	PUNCT
ejpam-6798	550	54	.	.	PUNCT
ejpam-6798	551	1	it	it	PRON
ejpam-6798	551	2	is	be	AUX
ejpam-6798	551	3	easy	easy	ADJ
ejpam-6798	551	4	to	to	PART
ejpam-6798	551	5	show	show	VERB
ejpam-6798	551	6	that	that	SCONJ
ejpam-6798	551	7	l1	l1	PROPN
ejpam-6798	551	8	is	be	AUX
ejpam-6798	551	9	a	a	DET
ejpam-6798	551	10	cifi	cifi	NOUN
ejpam-6798	551	11	of	of	ADP
ejpam-6798	551	12	m	m	PROPN
ejpam-6798	551	13	.	.	PUNCT
ejpam-6798	552	1	now	now	ADV
ejpam-6798	552	2	define	define	VERB
ejpam-6798	552	3	a	a	DET
ejpam-6798	552	4	cifs	cifs	NOUN
ejpam-6798	552	5	l2	l2	NOUN
ejpam-6798	552	6	on	on	ADP
ejpam-6798	552	7	m	m	NOUN
ejpam-6798	552	8	as	as	ADP
ejpam-6798	552	9	:	:	PUNCT
ejpam-6798	552	10	l2	l2	NOUN
ejpam-6798	552	11	=	=	SYM
ejpam-6798	552	12	{	{	PUNCT
ejpam-6798	552	13	(	(	PUNCT
ejpam-6798	552	14	0	0	NUM
ejpam-6798	552	15	,	,	PUNCT
ejpam-6798	552	16	0.6eι0.5π	0.6eι0.5π	PROPN
ejpam-6798	552	17	,	,	PUNCT
ejpam-6798	552	18	0.4eι0.3π	0.4eι0.3π	PROPN
ejpam-6798	552	19	)	)	PUNCT
ejpam-6798	552	20	,	,	PUNCT
ejpam-6798	552	21	(	(	PUNCT
ejpam-6798	552	22	s	s	X
ejpam-6798	552	23	,	,	PUNCT
ejpam-6798	552	24	0.4eι0.6π	0.4eι0.6π	PROPN
ejpam-6798	552	25	,	,	PUNCT
ejpam-6798	552	26	0.2eι0.4π	0.2eι0.4π	PROPN
ejpam-6798	552	27	)	)	PUNCT
ejpam-6798	552	28	,	,	PUNCT
ejpam-6798	552	29	(	(	PUNCT
ejpam-6798	552	30	l	l	NOUN
ejpam-6798	552	31	,	,	PUNCT
ejpam-6798	552	32	0.6eι0.5π	0.6eι0.5π	PROPN
ejpam-6798	552	33	,	,	PUNCT
ejpam-6798	552	34	0.4eι0.3π	0.4eι0.3π	PROPN
ejpam-6798	552	35	)	)	PUNCT
ejpam-6798	552	36	,	,	PUNCT
ejpam-6798	552	37	(	(	PUNCT
ejpam-6798	552	38	z	z	X
ejpam-6798	552	39	,	,	PUNCT
ejpam-6798	552	40	0.4eι0.6π	0.4eι0.6π	PROPN
ejpam-6798	552	41	,	,	PUNCT
ejpam-6798	552	42	0.2eι0.4π	0.2eι0.4π	PROPN
ejpam-6798	552	43	)	)	PUNCT
ejpam-6798	552	44	,	,	PUNCT
ejpam-6798	552	45	(	(	PUNCT
ejpam-6798	552	46	w	w	X
ejpam-6798	552	47	,	,	PUNCT
ejpam-6798	552	48	0.4eι0.6π	0.4eι0.6π	PROPN
ejpam-6798	552	49	,	,	PUNCT
ejpam-6798	552	50	0.2eι0.4π	0.2eι0.4π	NOUN
ejpam-6798	552	51	)	)	PUNCT
ejpam-6798	552	52	}	}	PUNCT
ejpam-6798	552	53	.	.	PUNCT
ejpam-6798	553	1	it	it	PRON
ejpam-6798	553	2	is	be	AUX
ejpam-6798	553	3	easy	easy	ADJ
ejpam-6798	553	4	to	to	PART
ejpam-6798	553	5	show	show	VERB
ejpam-6798	553	6	that	that	SCONJ
ejpam-6798	553	7	l2	l2	NOUN
ejpam-6798	553	8	is	be	AUX
ejpam-6798	553	9	a	a	DET
ejpam-6798	553	10	cifi	cifi	NOUN
ejpam-6798	553	11	of	of	ADP
ejpam-6798	553	12	m	m	PROPN
ejpam-6798	553	13	.	.	PUNCT
ejpam-6798	554	1	now	now	ADV
ejpam-6798	554	2	define	define	VERB
ejpam-6798	554	3	a	a	DET
ejpam-6798	554	4	cifs	cif	NOUN
ejpam-6798	554	5	l1\l2	l1\l2	ADV
ejpam-6798	554	6	on	on	ADP
ejpam-6798	554	7	m	m	NOUN
ejpam-6798	554	8	as	as	ADP
ejpam-6798	554	9	:	:	PUNCT
ejpam-6798	554	10	l1\l2	l1\l2	PROPN
ejpam-6798	554	11	=	=	SYM
ejpam-6798	554	12	{	{	PUNCT
ejpam-6798	554	13	(	(	PUNCT
ejpam-6798	554	14	0	0	NUM
ejpam-6798	554	15	,	,	PUNCT
ejpam-6798	554	16	0.6eι0.5π	0.6eι0.5π	PROPN
ejpam-6798	554	17	,	,	PUNCT
ejpam-6798	554	18	0.7eι0.5π	0.7eι0.5π	PROPN
ejpam-6798	554	19	)	)	PUNCT
ejpam-6798	554	20	,	,	PUNCT
ejpam-6798	554	21	(	(	PUNCT
ejpam-6798	554	22	s	s	X
ejpam-6798	554	23	,	,	PUNCT
ejpam-6798	554	24	0.4eι0.5π	0.4eι0.5π	PROPN
ejpam-6798	554	25	,	,	PUNCT
ejpam-6798	554	26	0.5eι0.4π	0.5eι0.4π	PROPN
ejpam-6798	554	27	)	)	PUNCT
ejpam-6798	554	28	,	,	PUNCT
ejpam-6798	554	29	(	(	PUNCT
ejpam-6798	554	30	l	l	NOUN
ejpam-6798	554	31	,	,	PUNCT
ejpam-6798	554	32	0.5eι0.3π	0.5eι0.3π	PROPN
ejpam-6798	554	33	,	,	PUNCT
ejpam-6798	554	34	0.4eι0.3π	0.4eι0.3π	PROPN
ejpam-6798	554	35	)	)	PUNCT
ejpam-6798	554	36	,	,	PUNCT
ejpam-6798	554	37	(	(	PUNCT
ejpam-6798	554	38	z	z	NOUN
ejpam-6798	554	39	,	,	PUNCT
ejpam-6798	554	40	0.3eι0.1π	0.3eι0.1π	PROPN
ejpam-6798	554	41	,	,	PUNCT
ejpam-6798	554	42	0.2eι0.4π	0.2eι0.4π	PROPN
ejpam-6798	554	43	)	)	PUNCT
ejpam-6798	554	44	,	,	PUNCT
ejpam-6798	554	45	(	(	PUNCT
ejpam-6798	554	46	w	w	NOUN
ejpam-6798	554	47	,	,	PUNCT
ejpam-6798	554	48	0.3eι0.1π	0.3eι0.1π	PROPN
ejpam-6798	554	49	,	,	PUNCT
ejpam-6798	554	50	0.2eι0.4π	0.2eι0.4π	NOUN
ejpam-6798	554	51	)	)	PUNCT
ejpam-6798	554	52	}	}	PUNCT
ejpam-6798	554	53	.	.	PUNCT
ejpam-6798	555	1	it	it	PRON
ejpam-6798	555	2	is	be	AUX
ejpam-6798	555	3	straightforward	straightforward	ADJ
ejpam-6798	555	4	to	to	PART
ejpam-6798	555	5	prove	prove	VERB
ejpam-6798	555	6	that	that	SCONJ
ejpam-6798	555	7	l1\l2	l1\l2	PROPN
ejpam-6798	555	8	is	be	AUX
ejpam-6798	555	9	a	a	DET
ejpam-6798	555	10	cifi	cifi	NOUN
ejpam-6798	555	11	of	of	ADP
ejpam-6798	555	12	m	m	PROPN
ejpam-6798	555	13	.	.	PUNCT
ejpam-6798	556	1	m.	m.	PROPN
ejpam-6798	556	2	jawad	jawad	PROPN
ejpam-6798	556	3	et	et	PROPN
ejpam-6798	556	4	al	al	PROPN
ejpam-6798	556	5	.	.	PUNCT
ejpam-6798	556	6	/	/	SYM
ejpam-6798	556	7	eur	eur	PROPN
ejpam-6798	556	8	.	.	PUNCT
ejpam-6798	557	1	j.	j.	PROPN
ejpam-6798	557	2	pure	pure	PROPN
ejpam-6798	557	3	appl	appl	PROPN
ejpam-6798	557	4	.	.	PROPN
ejpam-6798	557	5	math	math	PROPN
ejpam-6798	557	6	,	,	PUNCT
ejpam-6798	557	7	18	18	NUM
ejpam-6798	557	8	(	(	PUNCT
ejpam-6798	557	9	4	4	NUM
ejpam-6798	557	10	)	)	PUNCT
ejpam-6798	557	11	(	(	PUNCT
ejpam-6798	557	12	2025	2025	NUM
ejpam-6798	557	13	)	)	PUNCT
ejpam-6798	557	14	,	,	PUNCT
ejpam-6798	557	15	6798	6798	NUM
ejpam-6798	557	16	18	18	NUM
ejpam-6798	557	17	of	of	ADP
ejpam-6798	557	18	22	22	NUM
ejpam-6798	557	19	table	table	NOUN
ejpam-6798	557	20	7	7	NUM
ejpam-6798	557	21	:	:	PUNCT
ejpam-6798	557	22	cayley	cayley	PROPN
ejpam-6798	557	23	’s	’s	PART
ejpam-6798	557	24	table	table	NOUN
ejpam-6798	557	25	describing	describe	VERB
ejpam-6798	557	26	the	the	DET
ejpam-6798	557	27	binary	binary	ADJ
ejpam-6798	557	28	operation	operation	NOUN
ejpam-6798	557	29	expressed	express	VERB
ejpam-6798	557	30	by	by	ADP
ejpam-6798	557	31	“	"	PUNCT
ejpam-6798	557	32	⋆	⋆	VERB
ejpam-6798	557	33	”	"	PUNCT
ejpam-6798	557	34	.	.	PUNCT
ejpam-6798	558	1	⋆	⋆	VERB
ejpam-6798	558	2	0	0	NUM
ejpam-6798	558	3	s	s	PART
ejpam-6798	558	4	l	l	NOUN
ejpam-6798	558	5	z	z	PROPN
ejpam-6798	558	6	w	w	NOUN
ejpam-6798	558	7	0	0	NUM
ejpam-6798	558	8	0	0	NUM
ejpam-6798	558	9	0	0	NUM
ejpam-6798	558	10	0	0	NUM
ejpam-6798	558	11	0	0	NUM
ejpam-6798	558	12	0	0	NUM
ejpam-6798	559	1	s	s	NOUN
ejpam-6798	559	2	s	s	NOUN
ejpam-6798	559	3	0	0	NUM
ejpam-6798	559	4	s	s	NOUN
ejpam-6798	559	5	0	0	NUM
ejpam-6798	559	6	0	0	NUM
ejpam-6798	559	7	l	l	NOUN
ejpam-6798	559	8	l	l	NOUN
ejpam-6798	559	9	l	l	NOUN
ejpam-6798	559	10	0	0	NUM
ejpam-6798	559	11	0	0	NUM
ejpam-6798	559	12	0	0	NUM
ejpam-6798	560	1	z	z	NOUN
ejpam-6798	560	2	z	z	NOUN
ejpam-6798	560	3	z	z	NOUN
ejpam-6798	560	4	z	z	NOUN
ejpam-6798	560	5	0	0	NUM
ejpam-6798	560	6	0	0	NUM
ejpam-6798	561	1	w	w	PROPN
ejpam-6798	561	2	w	w	PROPN
ejpam-6798	561	3	w	w	PROPN
ejpam-6798	561	4	z	z	PROPN
ejpam-6798	561	5	l	l	NOUN
ejpam-6798	561	6	0	0	NUM
ejpam-6798	561	7	definition	definition	NOUN
ejpam-6798	561	8	18	18	NUM
ejpam-6798	561	9	.	.	PUNCT
ejpam-6798	562	1	let	let	VERB
ejpam-6798	562	2	l1	l1	PROPN
ejpam-6798	562	3	and	and	CCONJ
ejpam-6798	562	4	l2	l2	NOUN
ejpam-6798	562	5	be	be	AUX
ejpam-6798	562	6	two	two	NUM
ejpam-6798	562	7	cifss	cifss	NOUN
ejpam-6798	562	8	of	of	ADP
ejpam-6798	562	9	m	m	PROPN
ejpam-6798	562	10	.	.	PUNCT
ejpam-6798	563	1	then	then	ADV
ejpam-6798	563	2	,	,	PUNCT
ejpam-6798	563	3	the	the	DET
ejpam-6798	563	4	bounded	bounded	ADJ
ejpam-6798	563	5	difference	difference	NOUN
ejpam-6798	563	6	l1⊖l2	l1⊖l2	NOUN
ejpam-6798	563	7	is	be	AUX
ejpam-6798	563	8	defined	define	VERB
ejpam-6798	563	9	as	as	ADP
ejpam-6798	563	10	µl1⊖l2(s	µl1⊖l2(s	NOUN
ejpam-6798	563	11	)	)	PUNCT
ejpam-6798	563	12	=	=	SYM
ejpam-6798	564	1	(	(	PUNCT
ejpam-6798	564	2	0∨(γl1(s)−γl2(s)))e	0∨(γl1(s)−γl2(s)))e	NOUN
ejpam-6798	564	3	ι(θl1	ι(θl1	PROPN
ejpam-6798	564	4	(	(	PUNCT
ejpam-6798	564	5	s)∨θl2	s)∨θl2	PROPN
ejpam-6798	564	6	(	(	PUNCT
ejpam-6798	564	7	s	s	NOUN
ejpam-6798	564	8	)	)	PUNCT
ejpam-6798	564	9	)	)	PUNCT
ejpam-6798	564	10	,	,	PUNCT
ejpam-6798	564	11	νl1⊖l2(s	νl1⊖l2(s	NOUN
ejpam-6798	564	12	)	)	PUNCT
ejpam-6798	564	13	=	=	SYM
ejpam-6798	564	14	(	(	PUNCT
ejpam-6798	564	15	0∧(γl1	0∧(γl1	NUM
ejpam-6798	564	16	(	(	PUNCT
ejpam-6798	564	17	s)−	s)−	PROPN
ejpam-6798	564	18	γl2	γl2	PROPN
ejpam-6798	564	19	(	(	PUNCT
ejpam-6798	564	20	s)))eι(θl1	s)))eι(θl1	PROPN
ejpam-6798	564	21	(	(	PUNCT
ejpam-6798	564	22	s)∧θl2	s)∧θl2	PROPN
ejpam-6798	564	23	(	(	PUNCT
ejpam-6798	564	24	s	s	NOUN
ejpam-6798	564	25	)	)	PUNCT
ejpam-6798	564	26	)	)	PUNCT
ejpam-6798	564	27	.	.	PUNCT
ejpam-6798	565	1	example	example	NOUN
ejpam-6798	566	1	15	15	NUM
ejpam-6798	566	2	.	.	PUNCT
ejpam-6798	567	1	let	let	VERB
ejpam-6798	567	2	(	(	PUNCT
ejpam-6798	567	3	µl1(s	µl1(s	PROPN
ejpam-6798	567	4	)	)	PUNCT
ejpam-6798	567	5	,	,	PUNCT
ejpam-6798	567	6	νl1(s	νl1(s	PROPN
ejpam-6798	567	7	)	)	PUNCT
ejpam-6798	567	8	)	)	PUNCT
ejpam-6798	568	1	=	=	PRON
ejpam-6798	568	2	{	{	PUNCT
ejpam-6798	568	3	(	(	PUNCT
ejpam-6798	568	4	s1	s1	NOUN
ejpam-6798	568	5	,	,	PUNCT
ejpam-6798	568	6	0.6eι0.5π	0.6eι0.5π	PROPN
ejpam-6798	568	7	,	,	PUNCT
ejpam-6798	568	8	0.4eι0.25π	0.4eι0.25π	NOUN
ejpam-6798	568	9	)	)	PUNCT
ejpam-6798	568	10	,	,	PUNCT
ejpam-6798	568	11	(	(	PUNCT
ejpam-6798	568	12	s2	s2	PROPN
ejpam-6798	568	13	,	,	PUNCT
ejpam-6798	568	14	1eι0.5π	1eι0.5π	NUM
ejpam-6798	568	15	,	,	PUNCT
ejpam-6798	568	16	0.8eι0.25π	0.8eι0.25π	NOUN
ejpam-6798	568	17	)	)	PUNCT
ejpam-6798	568	18	,	,	PUNCT
ejpam-6798	568	19	(	(	PUNCT
ejpam-6798	568	20	s3	s3	PROPN
ejpam-6798	568	21	,	,	PUNCT
ejpam-6798	568	22	0.8eι2π	0.8eι2π	NUM
ejpam-6798	568	23	,	,	PUNCT
ejpam-6798	568	24	0.6eι1.5π	0.6eι1.5π	NUM
ejpam-6798	568	25	)	)	PUNCT
ejpam-6798	568	26	,	,	PUNCT
ejpam-6798	568	27	(	(	PUNCT
ejpam-6798	568	28	s4	s4	X
ejpam-6798	568	29	,	,	PUNCT
ejpam-6798	568	30	0.9e	0.9e	NOUN
ejpam-6798	568	31	ι0.4π	ι0.4π	NOUN
ejpam-6798	568	32	,	,	PUNCT
ejpam-6798	568	33	0.7eι0.24π	0.7eι0.24π	NOUN
ejpam-6798	568	34	)	)	PUNCT
ejpam-6798	568	35	,	,	PUNCT
ejpam-6798	568	36	(	(	PUNCT
ejpam-6798	568	37	s5	s5	PROPN
ejpam-6798	568	38	,	,	PUNCT
ejpam-6798	568	39	0.7e	0.7e	NOUN
ejpam-6798	568	40	ιπ	ιπ	ADJ
ejpam-6798	568	41	,	,	PUNCT
ejpam-6798	568	42	0.5eι0.8π	0.5eι0.8π	PROPN
ejpam-6798	568	43	)	)	PUNCT
ejpam-6798	568	44	,	,	PUNCT
ejpam-6798	568	45	(	(	PUNCT
ejpam-6798	568	46	s6	s6	PROPN
ejpam-6798	568	47	,	,	PUNCT
ejpam-6798	568	48	0.5e	0.5e	NUM
ejpam-6798	568	49	ι0.4π	ι0.4π	NOUN
ejpam-6798	568	50	,	,	PUNCT
ejpam-6798	568	51	0.3eι0.24π	0.3eι0.24π	NOUN
ejpam-6798	568	52	)	)	PUNCT
ejpam-6798	568	53	}	}	PUNCT
ejpam-6798	568	54	and	and	CCONJ
ejpam-6798	568	55	(	(	PUNCT
ejpam-6798	568	56	µl2(s	µl2(s	PROPN
ejpam-6798	568	57	)	)	PUNCT
ejpam-6798	568	58	,	,	PUNCT
ejpam-6798	568	59	νl2(s	νl2(s	PROPN
ejpam-6798	568	60	)	)	PUNCT
ejpam-6798	568	61	)	)	PUNCT
ejpam-6798	568	62	=	=	PRON
ejpam-6798	569	1	{	{	PUNCT
ejpam-6798	569	2	(	(	PUNCT
ejpam-6798	569	3	s1	s1	NOUN
ejpam-6798	569	4	,	,	PUNCT
ejpam-6798	569	5	0.2eιπ	0.2eιπ	NUM
ejpam-6798	569	6	,	,	PUNCT
ejpam-6798	569	7	0.1eι0.88π	0.1eι0.88π	NUM
ejpam-6798	569	8	)	)	PUNCT
ejpam-6798	569	9	,	,	PUNCT
ejpam-6798	569	10	(	(	PUNCT
ejpam-6798	569	11	s2	s2	PROPN
ejpam-6798	569	12	,	,	PUNCT
ejpam-6798	569	13	0.1eι0.8π	0.1eι0.8π	NOUN
ejpam-6798	569	14	,	,	PUNCT
ejpam-6798	569	15	0.01eι0.6π	0.01eι0.6π	NUM
ejpam-6798	569	16	)	)	PUNCT
ejpam-6798	569	17	,	,	PUNCT
ejpam-6798	569	18	(	(	PUNCT
ejpam-6798	569	19	s3	s3	PROPN
ejpam-6798	569	20	,	,	PUNCT
ejpam-6798	569	21	0.8eι0.8π	0.8eι0.8π	PROPN
ejpam-6798	569	22	,	,	PUNCT
ejpam-6798	569	23	0.6eι0.68π	0.6eι0.68π	NOUN
ejpam-6798	569	24	)	)	PUNCT
ejpam-6798	569	25	,	,	PUNCT
ejpam-6798	569	26	(	(	PUNCT
ejpam-6798	569	27	s4	s4	PROPN
ejpam-6798	569	28	,	,	PUNCT
ejpam-6798	569	29	0.2eιπ	0.2eιπ	NUM
ejpam-6798	569	30	,	,	PUNCT
ejpam-6798	569	31	0.1eι0.88π	0.1eι0.88π	NUM
ejpam-6798	569	32	)	)	PUNCT
ejpam-6798	569	33	,	,	PUNCT
ejpam-6798	569	34	(	(	PUNCT
ejpam-6798	569	35	s5	s5	PROPN
ejpam-6798	569	36	,	,	PUNCT
ejpam-6798	569	37	0.5e	0.5e	NUM
ejpam-6798	569	38	ι0.9π	ι0.9π	PROPN
ejpam-6798	569	39	,	,	PUNCT
ejpam-6798	569	40	0.3eι0.7π	0.3eι0.7π	PROPN
ejpam-6798	569	41	)	)	PUNCT
ejpam-6798	569	42	,	,	PUNCT
ejpam-6798	569	43	(	(	PUNCT
ejpam-6798	569	44	s6	s6	PROPN
ejpam-6798	569	45	,	,	PUNCT
ejpam-6798	569	46	0.3e	0.3e	NOUN
ejpam-6798	569	47	ι2π	ι2π	NOUN
ejpam-6798	569	48	,	,	PUNCT
ejpam-6798	569	49	0.1eι1.88π	0.1eι1.88π	PROPN
ejpam-6798	569	50	)	)	PUNCT
ejpam-6798	569	51	}	}	PUNCT
ejpam-6798	569	52	be	be	AUX
ejpam-6798	569	53	a	a	DET
ejpam-6798	569	54	cifss	cifss	NOUN
ejpam-6798	569	55	.	.	PUNCT
ejpam-6798	570	1	then	then	ADV
ejpam-6798	570	2	,	,	PUNCT
ejpam-6798	570	3	µl1⊖l2(s	µl1⊖l2(s	NOUN
ejpam-6798	570	4	)	)	PUNCT
ejpam-6798	570	5	=	=	PRON
ejpam-6798	570	6	{	{	PUNCT
ejpam-6798	570	7	(	(	PUNCT
ejpam-6798	570	8	s1	s1	NOUN
ejpam-6798	570	9	,	,	PUNCT
ejpam-6798	570	10	0.4eιπ	0.4eιπ	NUM
ejpam-6798	570	11	,	,	PUNCT
ejpam-6798	570	12	0.3eι0.25π	0.3eι0.25π	NOUN
ejpam-6798	570	13	)	)	PUNCT
ejpam-6798	570	14	,	,	PUNCT
ejpam-6798	570	15	(	(	PUNCT
ejpam-6798	570	16	s2	s2	PROPN
ejpam-6798	570	17	,	,	PUNCT
ejpam-6798	570	18	0.9eι0.8π	0.9eι0.8π	PROPN
ejpam-6798	570	19	,	,	PUNCT
ejpam-6798	570	20	0.79eι0.25π	0.79eι0.25π	NOUN
ejpam-6798	570	21	)	)	PUNCT
ejpam-6798	570	22	,	,	PUNCT
ejpam-6798	570	23	(	(	PUNCT
ejpam-6798	570	24	s3	s3	PROPN
ejpam-6798	570	25	,	,	PUNCT
ejpam-6798	570	26	0eι2π	0eι2π	PROPN
ejpam-6798	570	27	,	,	PUNCT
ejpam-6798	570	28	0eι0.68π	0eι0.68π	NOUN
ejpam-6798	570	29	)	)	PUNCT
ejpam-6798	570	30	,	,	PUNCT
ejpam-6798	570	31	(	(	PUNCT
ejpam-6798	570	32	s4	s4	PROPN
ejpam-6798	570	33	,	,	PUNCT
ejpam-6798	570	34	0.7eιπ	0.7eιπ	NUM
ejpam-6798	570	35	,	,	PUNCT
ejpam-6798	570	36	0.6eι0.24π	0.6eι0.24π	NOUN
ejpam-6798	570	37	)	)	PUNCT
ejpam-6798	570	38	,	,	PUNCT
ejpam-6798	570	39	(	(	PUNCT
ejpam-6798	570	40	s5	s5	PROPN
ejpam-6798	570	41	,	,	PUNCT
ejpam-6798	570	42	0.5e	0.5e	NUM
ejpam-6798	570	43	ιπ	ιπ	ADJ
ejpam-6798	570	44	,	,	PUNCT
ejpam-6798	570	45	0.2eι0.7π	0.2eι0.7π	PROPN
ejpam-6798	570	46	)	)	PUNCT
ejpam-6798	570	47	,	,	PUNCT
ejpam-6798	570	48	(	(	PUNCT
ejpam-6798	570	49	s6	s6	PROPN
ejpam-6798	570	50	,	,	PUNCT
ejpam-6798	570	51	0.2e	0.2e	NOUN
ejpam-6798	570	52	ι2π	ι2π	NOUN
ejpam-6798	570	53	,	,	PUNCT
ejpam-6798	570	54	0.2eι0.24π	0.2eι0.24π	PROPN
ejpam-6798	570	55	)	)	PUNCT
ejpam-6798	570	56	}	}	PUNCT
ejpam-6798	570	57	.	.	PUNCT
ejpam-6798	571	1	the	the	DET
ejpam-6798	571	2	following	follow	VERB
ejpam-6798	571	3	outcome	outcome	NOUN
ejpam-6798	571	4	shows	show	VERB
ejpam-6798	571	5	that	that	SCONJ
ejpam-6798	571	6	the	the	DET
ejpam-6798	571	7	bounded	bounded	ADJ
ejpam-6798	571	8	difference	difference	NOUN
ejpam-6798	571	9	⊖	⊖	NOUN
ejpam-6798	571	10	of	of	ADP
ejpam-6798	571	11	two	two	NUM
ejpam-6798	571	12	cifis	cifis	NOUN
ejpam-6798	571	13	of	of	ADP
ejpam-6798	571	14	m	m	PROPN
ejpam-6798	571	15	is	be	AUX
ejpam-6798	571	16	also	also	ADV
ejpam-6798	571	17	cifi	cifi	NOUN
ejpam-6798	571	18	.	.	PUNCT
ejpam-6798	572	1	theorem	theorem	PROPN
ejpam-6798	572	2	13	13	NUM
ejpam-6798	572	3	.	.	PUNCT
ejpam-6798	573	1	assume	assume	VERB
ejpam-6798	573	2	that	that	SCONJ
ejpam-6798	573	3	l1	l1	PROPN
ejpam-6798	573	4	and	and	CCONJ
ejpam-6798	573	5	l2	l2	NOUN
ejpam-6798	573	6	are	be	AUX
ejpam-6798	573	7	two	two	NUM
ejpam-6798	573	8	cifis	cifis	NOUN
ejpam-6798	573	9	of	of	ADP
ejpam-6798	573	10	m	m	PROPN
ejpam-6798	573	11	.	.	PUNCT
ejpam-6798	574	1	then	then	ADV
ejpam-6798	574	2	l1	l1	PROPN
ejpam-6798	574	3	⊖	⊖	AUX
ejpam-6798	574	4	l2	l2	NOUN
ejpam-6798	574	5	is	be	AUX
ejpam-6798	574	6	a	a	DET
ejpam-6798	574	7	cifi	cifi	NOUN
ejpam-6798	574	8	of	of	ADP
ejpam-6798	574	9	m	m	PROPN
ejpam-6798	574	10	.	.	PUNCT
ejpam-6798	575	1	proof	proof	NOUN
ejpam-6798	575	2	.	.	PUNCT
ejpam-6798	576	1	let	let	VERB
ejpam-6798	576	2	l1	l1	PROPN
ejpam-6798	576	3	and	and	CCONJ
ejpam-6798	576	4	l2	l2	NOUN
ejpam-6798	576	5	be	be	AUX
ejpam-6798	576	6	two	two	NUM
ejpam-6798	576	7	cifis	cifis	NOUN
ejpam-6798	576	8	of	of	ADP
ejpam-6798	576	9	m	m	PRON
ejpam-6798	576	10	and	and	CCONJ
ejpam-6798	576	11	let	let	VERB
ejpam-6798	576	12	s	s	NOUN
ejpam-6798	576	13	,	,	PUNCT
ejpam-6798	576	14	l	l	PROPN
ejpam-6798	576	15	∈	∈	PROPN
ejpam-6798	576	16	m	m	VERB
ejpam-6798	576	17	.	.	PUNCT
ejpam-6798	577	1	then	then	ADV
ejpam-6798	577	2	µl1⊖l2(0	µl1⊖l2(0	ADJ
ejpam-6798	577	3	)	)	PUNCT
ejpam-6798	577	4	=	=	PUNCT
ejpam-6798	578	1	(	(	PUNCT
ejpam-6798	578	2	0	0	NUM
ejpam-6798	578	3	∨	∨	NUM
ejpam-6798	578	4	(	(	PUNCT
ejpam-6798	578	5	γl1(0)−	γl1(0)−	PROPN
ejpam-6798	578	6	γl2(0)))e	γl2(0)))e	PROPN
ejpam-6798	578	7	ι(θl1	ι(θl1	PROPN
ejpam-6798	578	8	(	(	PUNCT
ejpam-6798	578	9	0)∨θl2	0)∨θl2	NUM
ejpam-6798	578	10	(	(	PUNCT
ejpam-6798	578	11	0	0	NUM
ejpam-6798	578	12	)	)	PUNCT
ejpam-6798	578	13	)	)	PUNCT
ejpam-6798	578	14	≥	≥	NOUN
ejpam-6798	578	15	(	(	PUNCT
ejpam-6798	578	16	0	0	NUM
ejpam-6798	578	17	∨	∨	NUM
ejpam-6798	578	18	(	(	PUNCT
ejpam-6798	578	19	γl1(s)−	γl1(s)−	PROPN
ejpam-6798	578	20	γl2(s)))e	γl2(s)))e	PROPN
ejpam-6798	578	21	ι(θl1	ι(θl1	PROPN
ejpam-6798	578	22	(	(	PUNCT
ejpam-6798	578	23	s)∨θl2	s)∨θl2	PROPN
ejpam-6798	578	24	(	(	PUNCT
ejpam-6798	578	25	s	s	NOUN
ejpam-6798	578	26	)	)	PUNCT
ejpam-6798	578	27	)	)	PUNCT
ejpam-6798	579	1	=	=	SYM
ejpam-6798	579	2	µl1⊖l2(s	µl1⊖l2(s	NOUN
ejpam-6798	579	3	)	)	PUNCT
ejpam-6798	579	4	.	.	PUNCT
ejpam-6798	580	1	moreover	moreover	ADV
ejpam-6798	580	2	µl1⊖l2(s	µl1⊖l2(s	NOUN
ejpam-6798	580	3	)	)	PUNCT
ejpam-6798	580	4	=	=	SYM
ejpam-6798	580	5	(	(	PUNCT
ejpam-6798	580	6	0	0	NUM
ejpam-6798	580	7	∨	∨	NUM
ejpam-6798	580	8	(	(	PUNCT
ejpam-6798	580	9	γl1(s)−	γl1(s)−	PROPN
ejpam-6798	580	10	γl2(s)))e	γl2(s)))e	PROPN
ejpam-6798	581	1	ι(θl1	ι(θl1	PROPN
ejpam-6798	581	2	(	(	PUNCT
ejpam-6798	581	3	s)∨θl2	s)∨θl2	PROPN
ejpam-6798	581	4	(	(	PUNCT
ejpam-6798	581	5	s	s	NOUN
ejpam-6798	581	6	)	)	PUNCT
ejpam-6798	581	7	)	)	PUNCT
ejpam-6798	581	8	≥	≥	NOUN
ejpam-6798	581	9	(	(	PUNCT
ejpam-6798	581	10	0	0	NUM
ejpam-6798	581	11	∨	∨	NUM
ejpam-6798	581	12	(	(	PUNCT
ejpam-6798	581	13	γl1(s	γl1(s	PROPN
ejpam-6798	581	14	⋆	⋆	VERB
ejpam-6798	581	15	l)−	l)−	PROPN
ejpam-6798	581	16	γl1(l	γl1(l	PROPN
ejpam-6798	581	17	)	)	PUNCT
ejpam-6798	581	18	)	)	PUNCT
ejpam-6798	581	19	)	)	PUNCT
ejpam-6798	582	1	∨	∨	NUM
ejpam-6798	582	2	(	(	PUNCT
ejpam-6798	582	3	γl2(s	γl2(s	PROPN
ejpam-6798	582	4	⋆	⋆	VERB
ejpam-6798	582	5	l)−	l)−	PROPN
ejpam-6798	582	6	γl2(l	γl2(l	NOUN
ejpam-6798	582	7	)	)	PUNCT
ejpam-6798	582	8	)	)	PUNCT
ejpam-6798	582	9	)	)	PUNCT
ejpam-6798	583	1	eι((θl1	eι((θl1	NOUN
ejpam-6798	583	2	(	(	PUNCT
ejpam-6798	583	3	s⋆l)∧θl1	s⋆l)∧θl1	PROPN
ejpam-6798	583	4	(	(	PUNCT
ejpam-6798	583	5	l))∨(θl2	l))∨(θl2	PROPN
ejpam-6798	583	6	(	(	PUNCT
ejpam-6798	583	7	s⋆l)∧θl2	s⋆l)∧θl2	NOUN
ejpam-6798	583	8	(	(	PUNCT
ejpam-6798	583	9	l	l	NOUN
ejpam-6798	583	10	)	)	PUNCT
ejpam-6798	583	11	)	)	PUNCT
ejpam-6798	583	12	)	)	PUNCT
ejpam-6798	584	1	=	=	PUNCT
ejpam-6798	584	2	(	(	PUNCT
ejpam-6798	584	3	(	(	PUNCT
ejpam-6798	584	4	0	0	NUM
ejpam-6798	584	5	∨	∨	NUM
ejpam-6798	584	6	(	(	PUNCT
ejpam-6798	584	7	γl1(s	γl1(s	PROPN
ejpam-6798	584	8	⋆	⋆	VERB
ejpam-6798	584	9	l)−	l)−	PROPN
ejpam-6798	584	10	γl2(s	γl2(s	PROPN
ejpam-6798	584	11	⋆	⋆	PUNCT
ejpam-6798	584	12	l	l	NOUN
ejpam-6798	584	13	)	)	PUNCT
ejpam-6798	584	14	)	)	PUNCT
ejpam-6798	584	15	)	)	PUNCT
ejpam-6798	585	1	∧	∧	NOUN
ejpam-6798	585	2	(	(	PUNCT
ejpam-6798	585	3	0	0	NUM
ejpam-6798	585	4	∨	∨	NUM
ejpam-6798	585	5	γl1(l)−	γl1(l)−	PROPN
ejpam-6798	585	6	γl2(l	γl2(l	NOUN
ejpam-6798	585	7	)	)	PUNCT
ejpam-6798	585	8	)	)	PUNCT
ejpam-6798	585	9	)	)	PUNCT
ejpam-6798	585	10	eι((θl1	eι((θl1	NOUN
ejpam-6798	585	11	(	(	PUNCT
ejpam-6798	585	12	s⋆l)∨θl2	s⋆l)∨θl2	NOUN
ejpam-6798	585	13	(	(	PUNCT
ejpam-6798	585	14	s⋆l))∧(θl1	s⋆l))∧(θl1	PROPN
ejpam-6798	585	15	(	(	PUNCT
ejpam-6798	585	16	l)∨θl2	l)∨θl2	NOUN
ejpam-6798	585	17	(	(	PUNCT
ejpam-6798	585	18	l	l	NOUN
ejpam-6798	585	19	)	)	PUNCT
ejpam-6798	585	20	)	)	PUNCT
ejpam-6798	585	21	)	)	PUNCT
ejpam-6798	586	1	=	=	PUNCT
ejpam-6798	586	2	(	(	PUNCT
ejpam-6798	586	3	0	0	NUM
ejpam-6798	586	4	∨	∨	NUM
ejpam-6798	586	5	(	(	PUNCT
ejpam-6798	586	6	γl1(s	γl1(s	PROPN
ejpam-6798	586	7	⋆	⋆	VERB
ejpam-6798	586	8	l)−	l)−	PROPN
ejpam-6798	586	9	γl2(s	γl2(s	PROPN
ejpam-6798	586	10	⋆	⋆	VERB
ejpam-6798	586	11	l)))e	l)))e	PROPN
ejpam-6798	586	12	ι(θl1	ι(θl1	PROPN
ejpam-6798	586	13	(	(	PUNCT
ejpam-6798	586	14	s⋆l)∨θl2	s⋆l)∨θl2	NOUN
ejpam-6798	586	15	(	(	PUNCT
ejpam-6798	586	16	s⋆l	s⋆l	NOUN
ejpam-6798	586	17	)	)	PUNCT
ejpam-6798	586	18	)	)	PUNCT
ejpam-6798	587	1	∧	∧	NOUN
ejpam-6798	587	2	(	(	PUNCT
ejpam-6798	587	3	0	0	NUM
ejpam-6798	587	4	∨	∨	NUM
ejpam-6798	587	5	(	(	PUNCT
ejpam-6798	587	6	γl1(l)−	γl1(l)−	PROPN
ejpam-6798	587	7	γl2(l)))e	γl2(l)))e	PROPN
ejpam-6798	587	8	ι(θl1	ι(θl1	PROPN
ejpam-6798	587	9	(	(	PUNCT
ejpam-6798	587	10	l)∨θl2	l)∨θl2	NOUN
ejpam-6798	587	11	(	(	PUNCT
ejpam-6798	587	12	l	l	NOUN
ejpam-6798	587	13	)	)	PUNCT
ejpam-6798	587	14	)	)	PUNCT
ejpam-6798	587	15	≥	≥	NOUN
ejpam-6798	587	16	µl1⊖l2(s	µl1⊖l2(s	NUM
ejpam-6798	587	17	⋆	⋆	X
ejpam-6798	587	18	l	l	NOUN
ejpam-6798	587	19	)	)	PUNCT
ejpam-6798	587	20	∧	∧	PROPN
ejpam-6798	587	21	µl1⊖l2(l	µl1⊖l2(l	NOUN
ejpam-6798	587	22	)	)	PUNCT
ejpam-6798	587	23	.	.	PUNCT
ejpam-6798	588	1	m.	m.	PROPN
ejpam-6798	588	2	jawad	jawad	PROPN
ejpam-6798	588	3	et	et	PROPN
ejpam-6798	588	4	al	al	PROPN
ejpam-6798	588	5	.	.	PUNCT
ejpam-6798	588	6	/	/	SYM
ejpam-6798	588	7	eur	eur	PROPN
ejpam-6798	588	8	.	.	PUNCT
ejpam-6798	589	1	j.	j.	PROPN
ejpam-6798	589	2	pure	pure	PROPN
ejpam-6798	589	3	appl	appl	PROPN
ejpam-6798	589	4	.	.	PROPN
ejpam-6798	589	5	math	math	PROPN
ejpam-6798	589	6	,	,	PUNCT
ejpam-6798	589	7	18	18	NUM
ejpam-6798	589	8	(	(	PUNCT
ejpam-6798	589	9	4	4	NUM
ejpam-6798	589	10	)	)	PUNCT
ejpam-6798	589	11	(	(	PUNCT
ejpam-6798	589	12	2025	2025	NUM
ejpam-6798	589	13	)	)	PUNCT
ejpam-6798	589	14	,	,	PUNCT
ejpam-6798	589	15	6798	6798	NUM
ejpam-6798	589	16	19	19	NUM
ejpam-6798	589	17	of	of	ADP
ejpam-6798	589	18	22	22	NUM
ejpam-6798	589	19	suppose	suppose	VERB
ejpam-6798	589	20	that	that	SCONJ
ejpam-6798	589	21	l1	l1	PROPN
ejpam-6798	589	22	and	and	CCONJ
ejpam-6798	589	23	l2	l2	NOUN
ejpam-6798	589	24	are	be	AUX
ejpam-6798	589	25	two	two	NUM
ejpam-6798	589	26	cifis	cifis	NOUN
ejpam-6798	589	27	of	of	ADP
ejpam-6798	589	28	m	m	PRON
ejpam-6798	589	29	and	and	CCONJ
ejpam-6798	589	30	let	let	VERB
ejpam-6798	589	31	s	s	NOUN
ejpam-6798	589	32	,	,	PUNCT
ejpam-6798	589	33	l	l	PROPN
ejpam-6798	589	34	∈	∈	PROPN
ejpam-6798	589	35	m	m	VERB
ejpam-6798	589	36	.	.	PUNCT
ejpam-6798	590	1	then	then	ADV
ejpam-6798	590	2	νl1⊖l2(0	νl1⊖l2(0	VERB
ejpam-6798	590	3	)	)	PUNCT
ejpam-6798	591	1	=	=	PUNCT
ejpam-6798	591	2	(	(	PUNCT
ejpam-6798	591	3	0	0	NUM
ejpam-6798	591	4	∧	∧	PROPN
ejpam-6798	591	5	(	(	PUNCT
ejpam-6798	591	6	γl1	γl1	NOUN
ejpam-6798	591	7	(	(	PUNCT
ejpam-6798	591	8	0)−	0)−	NUM
ejpam-6798	591	9	γl2	γl2	PROPN
ejpam-6798	591	10	(	(	PUNCT
ejpam-6798	591	11	0)))eι(θl1	0)))eι(θl1	NUM
ejpam-6798	591	12	(	(	PUNCT
ejpam-6798	591	13	0)∧θl2	0)∧θl2	NOUN
ejpam-6798	591	14	(	(	PUNCT
ejpam-6798	591	15	0	0	NUM
ejpam-6798	591	16	)	)	PUNCT
ejpam-6798	591	17	)	)	PUNCT
ejpam-6798	591	18	≤	≤	NOUN
ejpam-6798	591	19	(	(	PUNCT
ejpam-6798	591	20	0	0	NUM
ejpam-6798	591	21	∧	∧	PROPN
ejpam-6798	591	22	(	(	PUNCT
ejpam-6798	591	23	γl1	γl1	NOUN
ejpam-6798	591	24	(	(	PUNCT
ejpam-6798	591	25	s)−	s)−	PROPN
ejpam-6798	591	26	γl2	γl2	PROPN
ejpam-6798	591	27	(	(	PUNCT
ejpam-6798	591	28	s)))eι(θl1	s)))eι(θl1	PROPN
ejpam-6798	591	29	(	(	PUNCT
ejpam-6798	591	30	s)∧θl2	s)∧θl2	PROPN
ejpam-6798	591	31	(	(	PUNCT
ejpam-6798	591	32	s	s	NOUN
ejpam-6798	591	33	)	)	PUNCT
ejpam-6798	591	34	)	)	PUNCT
ejpam-6798	591	35	=	=	SYM
ejpam-6798	591	36	νl1⊖l2(s	νl1⊖l2(s	NOUN
ejpam-6798	591	37	)	)	PUNCT
ejpam-6798	591	38	.	.	PUNCT
ejpam-6798	591	39	and	and	CCONJ
ejpam-6798	591	40	νl1⊖l2(s	νl1⊖l2(s	NOUN
ejpam-6798	591	41	)	)	PUNCT
ejpam-6798	591	42	=	=	SYM
ejpam-6798	591	43	(	(	PUNCT
ejpam-6798	591	44	0	0	NUM
ejpam-6798	591	45	∧	∧	PROPN
ejpam-6798	591	46	(	(	PUNCT
ejpam-6798	591	47	γl1	γl1	NOUN
ejpam-6798	591	48	(	(	PUNCT
ejpam-6798	591	49	s)−	s)−	PROPN
ejpam-6798	591	50	γl2	γl2	PROPN
ejpam-6798	591	51	(	(	PUNCT
ejpam-6798	591	52	s)))eι(θl1	s)))eι(θl1	PROPN
ejpam-6798	591	53	(	(	PUNCT
ejpam-6798	591	54	s)∧θl2	s)∧θl2	PROPN
ejpam-6798	591	55	(	(	PUNCT
ejpam-6798	591	56	s	s	NOUN
ejpam-6798	591	57	)	)	PUNCT
ejpam-6798	591	58	)	)	PUNCT
ejpam-6798	591	59	≤	≤	NOUN
ejpam-6798	591	60	(	(	PUNCT
ejpam-6798	591	61	0	0	NUM
ejpam-6798	591	62	∧	∧	PROPN
ejpam-6798	591	63	(	(	PUNCT
ejpam-6798	591	64	γl1	γl1	NOUN
ejpam-6798	591	65	(	(	PUNCT
ejpam-6798	591	66	s	s	AUX
ejpam-6798	591	67	⋆	⋆	VERB
ejpam-6798	591	68	l)−	l)−	PROPN
ejpam-6798	591	69	γl1	γl1	NOUN
ejpam-6798	591	70	(	(	PUNCT
ejpam-6798	591	71	l	l	NOUN
ejpam-6798	591	72	)	)	PUNCT
ejpam-6798	591	73	)	)	PUNCT
ejpam-6798	591	74	)	)	PUNCT
ejpam-6798	591	75	∨	∨	NUM
ejpam-6798	591	76	(	(	PUNCT
ejpam-6798	591	77	γl2	γl2	PROPN
ejpam-6798	591	78	(	(	PUNCT
ejpam-6798	591	79	s	s	AUX
ejpam-6798	591	80	⋆	⋆	VERB
ejpam-6798	591	81	l)−	l)−	PROPN
ejpam-6798	591	82	γl2	γl2	PROPN
ejpam-6798	591	83	(	(	PUNCT
ejpam-6798	591	84	l	l	NOUN
ejpam-6798	591	85	)	)	PUNCT
ejpam-6798	591	86	)	)	PUNCT
ejpam-6798	591	87	)	)	PUNCT
ejpam-6798	592	1	eι((θl1	eι((θl1	NOUN
ejpam-6798	592	2	(	(	PUNCT
ejpam-6798	592	3	s⋆l)∧θl1	s⋆l)∧θl1	PROPN
ejpam-6798	592	4	(	(	PUNCT
ejpam-6798	592	5	l))∧(θl2	l))∧(θl2	X
ejpam-6798	592	6	(	(	PUNCT
ejpam-6798	592	7	s⋆l)∧θl2	s⋆l)∧θl2	NOUN
ejpam-6798	592	8	(	(	PUNCT
ejpam-6798	592	9	l	l	NOUN
ejpam-6798	592	10	)	)	PUNCT
ejpam-6798	592	11	)	)	PUNCT
ejpam-6798	592	12	)	)	PUNCT
ejpam-6798	593	1	=	=	PUNCT
ejpam-6798	593	2	(	(	PUNCT
ejpam-6798	593	3	(	(	PUNCT
ejpam-6798	593	4	0	0	NUM
ejpam-6798	593	5	∧	∧	PROPN
ejpam-6798	593	6	(	(	PUNCT
ejpam-6798	593	7	γl1	γl1	NOUN
ejpam-6798	593	8	(	(	PUNCT
ejpam-6798	593	9	s	s	X
ejpam-6798	593	10	⋆	⋆	VERB
ejpam-6798	593	11	l)−	l)−	PROPN
ejpam-6798	593	12	γl2	γl2	PROPN
ejpam-6798	593	13	(	(	PUNCT
ejpam-6798	593	14	s	s	X
ejpam-6798	593	15	⋆	⋆	NOUN
ejpam-6798	593	16	l	l	NOUN
ejpam-6798	593	17	)	)	PUNCT
ejpam-6798	593	18	)	)	PUNCT
ejpam-6798	593	19	)	)	PUNCT
ejpam-6798	593	20	∨	∨	NUM
ejpam-6798	593	21	(	(	PUNCT
ejpam-6798	593	22	0	0	NUM
ejpam-6798	593	23	∧	∧	PROPN
ejpam-6798	593	24	γl1	γl1	NOUN
ejpam-6798	593	25	(	(	PUNCT
ejpam-6798	593	26	l)−	l)−	PROPN
ejpam-6798	593	27	γl2	γl2	PROPN
ejpam-6798	593	28	(	(	PUNCT
ejpam-6798	593	29	l	l	NOUN
ejpam-6798	593	30	)	)	PUNCT
ejpam-6798	593	31	)	)	PUNCT
ejpam-6798	593	32	)	)	PUNCT
ejpam-6798	594	1	eι((θl1	eι((θl1	NOUN
ejpam-6798	594	2	(	(	PUNCT
ejpam-6798	594	3	s⋆l)∧θl2	s⋆l)∧θl2	PROPN
ejpam-6798	594	4	(	(	PUNCT
ejpam-6798	594	5	s⋆l))∧(θl1	s⋆l))∧(θl1	VERB
ejpam-6798	594	6	(	(	PUNCT
ejpam-6798	594	7	l)∧θl2	l)∧θl2	PROPN
ejpam-6798	594	8	(	(	PUNCT
ejpam-6798	594	9	l	l	NOUN
ejpam-6798	594	10	)	)	PUNCT
ejpam-6798	594	11	)	)	PUNCT
ejpam-6798	594	12	)	)	PUNCT
ejpam-6798	595	1	=	=	PUNCT
ejpam-6798	595	2	(	(	PUNCT
ejpam-6798	595	3	0	0	NUM
ejpam-6798	595	4	∧	∧	PROPN
ejpam-6798	595	5	(	(	PUNCT
ejpam-6798	595	6	γl1	γl1	NOUN
ejpam-6798	595	7	(	(	PUNCT
ejpam-6798	595	8	s	s	X
ejpam-6798	595	9	⋆	⋆	VERB
ejpam-6798	595	10	l)−	l)−	PROPN
ejpam-6798	595	11	γl2	γl2	PROPN
ejpam-6798	595	12	(	(	PUNCT
ejpam-6798	595	13	s	s	X
ejpam-6798	595	14	⋆	⋆	X
ejpam-6798	595	15	l)))eι(θl1	l)))eι(θl1	NOUN
ejpam-6798	595	16	(	(	PUNCT
ejpam-6798	595	17	s⋆l)∧θl2	s⋆l)∧θl2	NOUN
ejpam-6798	595	18	(	(	PUNCT
ejpam-6798	595	19	s⋆l	s⋆l	NOUN
ejpam-6798	595	20	)	)	PUNCT
ejpam-6798	595	21	)	)	PUNCT
ejpam-6798	595	22	∨	∨	NUM
ejpam-6798	595	23	(	(	PUNCT
ejpam-6798	595	24	0	0	NUM
ejpam-6798	595	25	∧	∧	PROPN
ejpam-6798	595	26	(	(	PUNCT
ejpam-6798	595	27	γl1	γl1	NOUN
ejpam-6798	595	28	(	(	PUNCT
ejpam-6798	595	29	l)−	l)−	PROPN
ejpam-6798	595	30	γl2	γl2	PROPN
ejpam-6798	595	31	(	(	PUNCT
ejpam-6798	595	32	l)))eι(θl1	l)))eι(θl1	NOUN
ejpam-6798	595	33	(	(	PUNCT
ejpam-6798	595	34	l)∧θl2	l)∧θl2	PROPN
ejpam-6798	595	35	(	(	PUNCT
ejpam-6798	595	36	l	l	NOUN
ejpam-6798	595	37	)	)	PUNCT
ejpam-6798	595	38	)	)	PUNCT
ejpam-6798	596	1	≤	≤	NUM
ejpam-6798	596	2	νl1⊖l2(s	νl1⊖l2(s	NOUN
ejpam-6798	596	3	⋆	⋆	X
ejpam-6798	596	4	l	l	NOUN
ejpam-6798	596	5	)	)	PUNCT
ejpam-6798	596	6	∨	∨	NUM
ejpam-6798	596	7	νl1⊖l2(l	νl1⊖l2(l	NOUN
ejpam-6798	596	8	)	)	PUNCT
ejpam-6798	596	9	.	.	PUNCT
ejpam-6798	597	1	therefore	therefore	ADV
ejpam-6798	597	2	,	,	PUNCT
ejpam-6798	597	3	l1	l1	PROPN
ejpam-6798	597	4	⊖	⊖	AUX
ejpam-6798	597	5	l2	l2	NOUN
ejpam-6798	597	6	is	be	AUX
ejpam-6798	597	7	a	a	DET
ejpam-6798	597	8	cfi	cfi	NOUN
ejpam-6798	597	9	of	of	ADP
ejpam-6798	597	10	m	m	PROPN
ejpam-6798	597	11	.	.	PUNCT
ejpam-6798	597	12	example	example	NOUN
ejpam-6798	598	1	16	16	NUM
ejpam-6798	598	2	.	.	PUNCT
ejpam-6798	599	1	take	take	VERB
ejpam-6798	599	2	a	a	DET
ejpam-6798	599	3	bck	bck	NOUN
ejpam-6798	599	4	-	-	PUNCT
ejpam-6798	599	5	algebra	algebra	NOUN
ejpam-6798	599	6	m	m	NOUN
ejpam-6798	599	7	=	=	SYM
ejpam-6798	599	8	{	{	PUNCT
ejpam-6798	599	9	0	0	NUM
ejpam-6798	599	10	,	,	PUNCT
ejpam-6798	599	11	s	s	X
ejpam-6798	599	12	,	,	PUNCT
ejpam-6798	599	13	l	l	NOUN
ejpam-6798	599	14	,	,	PUNCT
ejpam-6798	599	15	z	z	NOUN
ejpam-6798	599	16	,	,	PUNCT
ejpam-6798	599	17	w	w	NOUN
ejpam-6798	599	18	}	}	PUNCT
ejpam-6798	599	19	with	with	ADP
ejpam-6798	599	20	table	table	NOUN
ejpam-6798	599	21	8	8	NUM
ejpam-6798	599	22	.	.	PUNCT
ejpam-6798	600	1	now	now	ADV
ejpam-6798	600	2	,	,	PUNCT
ejpam-6798	600	3	define	define	VERB
ejpam-6798	600	4	a	a	DET
ejpam-6798	600	5	cifs	cifs	NOUN
ejpam-6798	600	6	l1	l1	NOUN
ejpam-6798	600	7	on	on	ADP
ejpam-6798	600	8	m	m	NOUN
ejpam-6798	600	9	as	as	ADP
ejpam-6798	600	10	:	:	PUNCT
ejpam-6798	600	11	l1	l1	PROPN
ejpam-6798	600	12	=	=	SYM
ejpam-6798	600	13	{	{	PUNCT
ejpam-6798	600	14	(	(	PUNCT
ejpam-6798	600	15	0	0	NUM
ejpam-6798	600	16	,	,	PUNCT
ejpam-6798	600	17	0.9eι0.7π	0.9eι0.7π	PROPN
ejpam-6798	600	18	,	,	PUNCT
ejpam-6798	600	19	0.7eι0.5π	0.7eι0.5π	PROPN
ejpam-6798	600	20	)	)	PUNCT
ejpam-6798	600	21	,	,	PUNCT
ejpam-6798	600	22	(	(	PUNCT
ejpam-6798	600	23	s	s	X
ejpam-6798	600	24	,	,	PUNCT
ejpam-6798	600	25	0.7eι0.5π	0.7eι0.5π	PROPN
ejpam-6798	600	26	,	,	PUNCT
ejpam-6798	600	27	0.5eι0.3π	0.5eι0.3π	PROPN
ejpam-6798	600	28	)	)	PUNCT
ejpam-6798	600	29	,	,	PUNCT
ejpam-6798	600	30	(	(	PUNCT
ejpam-6798	600	31	l	l	NOUN
ejpam-6798	600	32	,	,	PUNCT
ejpam-6798	600	33	0.7eι0.3π	0.7eι0.3π	PROPN
ejpam-6798	600	34	,	,	PUNCT
ejpam-6798	600	35	0.5eι0.1π	0.5eι0.1π	PROPN
ejpam-6798	600	36	)	)	PUNCT
ejpam-6798	600	37	,	,	PUNCT
ejpam-6798	600	38	(	(	PUNCT
ejpam-6798	600	39	z	z	X
ejpam-6798	600	40	,	,	PUNCT
ejpam-6798	600	41	0.5eι0.1π	0.5eι0.1π	ADJ
ejpam-6798	600	42	,	,	PUNCT
ejpam-6798	600	43	0.4eι0.01π	0.4eι0.01π	NOUN
ejpam-6798	600	44	)	)	PUNCT
ejpam-6798	600	45	,	,	PUNCT
ejpam-6798	600	46	(	(	PUNCT
ejpam-6798	600	47	w	w	NOUN
ejpam-6798	600	48	,	,	PUNCT
ejpam-6798	600	49	0.7eι0.1π	0.7eι0.1π	PROPN
ejpam-6798	600	50	,	,	PUNCT
ejpam-6798	600	51	0.5eι0.01π	0.5eι0.01π	NUM
ejpam-6798	600	52	)	)	PUNCT
ejpam-6798	600	53	}	}	PUNCT
ejpam-6798	600	54	.	.	PUNCT
ejpam-6798	601	1	it	it	PRON
ejpam-6798	601	2	is	be	AUX
ejpam-6798	601	3	easy	easy	ADJ
ejpam-6798	601	4	to	to	PART
ejpam-6798	601	5	show	show	VERB
ejpam-6798	601	6	that	that	SCONJ
ejpam-6798	601	7	l1	l1	PROPN
ejpam-6798	601	8	is	be	AUX
ejpam-6798	601	9	a	a	DET
ejpam-6798	601	10	cifi	cifi	NOUN
ejpam-6798	601	11	of	of	ADP
ejpam-6798	601	12	m	m	PROPN
ejpam-6798	601	13	.	.	PUNCT
ejpam-6798	602	1	now	now	ADV
ejpam-6798	602	2	,	,	PUNCT
ejpam-6798	602	3	define	define	VERB
ejpam-6798	602	4	a	a	DET
ejpam-6798	602	5	cifs	cifs	NOUN
ejpam-6798	602	6	l2	l2	NOUN
ejpam-6798	602	7	on	on	ADP
ejpam-6798	602	8	m	m	NOUN
ejpam-6798	602	9	as	as	ADP
ejpam-6798	602	10	:	:	PUNCT
ejpam-6798	602	11	l2	l2	NOUN
ejpam-6798	602	12	=	=	SYM
ejpam-6798	602	13	{	{	PUNCT
ejpam-6798	602	14	(	(	PUNCT
ejpam-6798	602	15	0	0	NUM
ejpam-6798	602	16	,	,	PUNCT
ejpam-6798	602	17	0.6eι0.5π	0.6eι0.5π	PROPN
ejpam-6798	602	18	,	,	PUNCT
ejpam-6798	602	19	0.4eι0.3π	0.4eι0.3π	PROPN
ejpam-6798	602	20	)	)	PUNCT
ejpam-6798	602	21	,	,	PUNCT
ejpam-6798	602	22	(	(	PUNCT
ejpam-6798	602	23	s	s	X
ejpam-6798	602	24	,	,	PUNCT
ejpam-6798	602	25	0.4eι0.6π	0.4eι0.6π	PROPN
ejpam-6798	602	26	,	,	PUNCT
ejpam-6798	602	27	0.2eι0.4π	0.2eι0.4π	PROPN
ejpam-6798	602	28	)	)	PUNCT
ejpam-6798	602	29	,	,	PUNCT
ejpam-6798	602	30	(	(	PUNCT
ejpam-6798	602	31	l	l	NOUN
ejpam-6798	602	32	,	,	PUNCT
ejpam-6798	602	33	0.6eι0.5π	0.6eι0.5π	PROPN
ejpam-6798	602	34	,	,	PUNCT
ejpam-6798	602	35	0.4eι0.3π	0.4eι0.3π	PROPN
ejpam-6798	602	36	)	)	PUNCT
ejpam-6798	602	37	,	,	PUNCT
ejpam-6798	602	38	(	(	PUNCT
ejpam-6798	602	39	z	z	X
ejpam-6798	602	40	,	,	PUNCT
ejpam-6798	602	41	0.4eι0.6π	0.4eι0.6π	PROPN
ejpam-6798	602	42	,	,	PUNCT
ejpam-6798	602	43	0.2eι0.4π	0.2eι0.4π	PROPN
ejpam-6798	602	44	)	)	PUNCT
ejpam-6798	602	45	,	,	PUNCT
ejpam-6798	602	46	(	(	PUNCT
ejpam-6798	602	47	w	w	X
ejpam-6798	602	48	,	,	PUNCT
ejpam-6798	602	49	0.4eι0.6π	0.4eι0.6π	PROPN
ejpam-6798	602	50	,	,	PUNCT
ejpam-6798	602	51	0.2eι0.4π	0.2eι0.4π	NOUN
ejpam-6798	602	52	)	)	PUNCT
ejpam-6798	602	53	}	}	PUNCT
ejpam-6798	602	54	.	.	PUNCT
ejpam-6798	603	1	it	it	PRON
ejpam-6798	603	2	is	be	AUX
ejpam-6798	603	3	easy	easy	ADJ
ejpam-6798	603	4	to	to	PART
ejpam-6798	603	5	show	show	VERB
ejpam-6798	603	6	that	that	SCONJ
ejpam-6798	603	7	l2	l2	NOUN
ejpam-6798	603	8	is	be	AUX
ejpam-6798	603	9	a	a	DET
ejpam-6798	603	10	cifi	cifi	NOUN
ejpam-6798	603	11	of	of	ADP
ejpam-6798	603	12	m	m	PROPN
ejpam-6798	603	13	.	.	PUNCT
ejpam-6798	604	1	now	now	ADV
ejpam-6798	604	2	define	define	VERB
ejpam-6798	604	3	a	a	DET
ejpam-6798	604	4	cifs	cif	NOUN
ejpam-6798	604	5	l1⊖l2	l1⊖l2	NOUN
ejpam-6798	604	6	on	on	ADP
ejpam-6798	604	7	m	m	NOUN
ejpam-6798	604	8	as	as	ADP
ejpam-6798	604	9	:	:	PUNCT
ejpam-6798	604	10	l1⊖l2	l1⊖l2	X
ejpam-6798	604	11	=	=	SYM
ejpam-6798	604	12	{	{	PUNCT
ejpam-6798	604	13	(	(	PUNCT
ejpam-6798	604	14	0	0	NUM
ejpam-6798	604	15	,	,	PUNCT
ejpam-6798	604	16	0.3eι0.7π	0.3eι0.7π	PROPN
ejpam-6798	604	17	,	,	PUNCT
ejpam-6798	604	18	0.3eι0.3π	0.3eι0.3π	PROPN
ejpam-6798	604	19	)	)	PUNCT
ejpam-6798	604	20	,	,	PUNCT
ejpam-6798	604	21	(	(	PUNCT
ejpam-6798	604	22	s	s	X
ejpam-6798	604	23	,	,	PUNCT
ejpam-6798	604	24	0.3eι0.6π	0.3eι0.6π	NUM
ejpam-6798	604	25	,	,	PUNCT
ejpam-6798	604	26	0.3eι0.3π	0.3eι0.3π	NOUN
ejpam-6798	604	27	)	)	PUNCT
ejpam-6798	604	28	,	,	PUNCT
ejpam-6798	604	29	(	(	PUNCT
ejpam-6798	604	30	l	l	NOUN
ejpam-6798	604	31	,	,	PUNCT
ejpam-6798	604	32	0.1eι0.5π	0.1eι0.5π	PROPN
ejpam-6798	604	33	,	,	PUNCT
ejpam-6798	604	34	0.1eι0.1π	0.1eι0.1π	ADJ
ejpam-6798	604	35	)	)	PUNCT
ejpam-6798	604	36	,	,	PUNCT
ejpam-6798	604	37	(	(	PUNCT
ejpam-6798	604	38	z	z	X
ejpam-6798	604	39	,	,	PUNCT
ejpam-6798	604	40	0.1eι0.6π	0.1eι0.6π	PROPN
ejpam-6798	604	41	,	,	PUNCT
ejpam-6798	604	42	0.2eι0.01π	0.2eι0.01π	NOUN
ejpam-6798	604	43	)	)	PUNCT
ejpam-6798	604	44	,	,	PUNCT
ejpam-6798	604	45	(	(	PUNCT
ejpam-6798	604	46	w	w	NOUN
ejpam-6798	604	47	,	,	PUNCT
ejpam-6798	604	48	0.3eι0.6π	0.3eι0.6π	PROPN
ejpam-6798	604	49	,	,	PUNCT
ejpam-6798	604	50	0.3eι0.01π	0.3eι0.01π	NUM
ejpam-6798	604	51	)	)	PUNCT
ejpam-6798	604	52	}	}	PUNCT
ejpam-6798	604	53	.	.	PUNCT
ejpam-6798	605	1	it	it	PRON
ejpam-6798	605	2	is	be	AUX
ejpam-6798	605	3	straightforward	straightforward	ADJ
ejpam-6798	605	4	to	to	PART
ejpam-6798	605	5	prove	prove	VERB
ejpam-6798	605	6	that	that	SCONJ
ejpam-6798	605	7	l1	l1	PROPN
ejpam-6798	605	8	⊖	⊖	AUX
ejpam-6798	605	9	l2	l2	NOUN
ejpam-6798	605	10	is	be	AUX
ejpam-6798	605	11	a	a	DET
ejpam-6798	605	12	cifi	cifi	NOUN
ejpam-6798	605	13	of	of	ADP
ejpam-6798	605	14	m	m	PROPN
ejpam-6798	605	15	.	.	PUNCT
ejpam-6798	606	1	table	table	NOUN
ejpam-6798	606	2	8	8	NUM
ejpam-6798	606	3	:	:	PUNCT
ejpam-6798	606	4	cayley	cayley	PROPN
ejpam-6798	606	5	’s	’s	PART
ejpam-6798	606	6	table	table	NOUN
ejpam-6798	606	7	describing	describe	VERB
ejpam-6798	606	8	the	the	DET
ejpam-6798	606	9	binary	binary	ADJ
ejpam-6798	606	10	operation	operation	NOUN
ejpam-6798	606	11	expressed	express	VERB
ejpam-6798	606	12	by	by	ADP
ejpam-6798	606	13	“	"	PUNCT
ejpam-6798	606	14	⋆	⋆	VERB
ejpam-6798	606	15	”	"	PUNCT
ejpam-6798	606	16	.	.	PUNCT
ejpam-6798	607	1	⋆	⋆	VERB
ejpam-6798	607	2	0	0	NUM
ejpam-6798	607	3	s	s	PART
ejpam-6798	607	4	l	l	NOUN
ejpam-6798	607	5	z	z	PROPN
ejpam-6798	607	6	w	w	NOUN
ejpam-6798	607	7	0	0	NUM
ejpam-6798	607	8	0	0	NUM
ejpam-6798	607	9	0	0	NUM
ejpam-6798	607	10	0	0	NUM
ejpam-6798	607	11	0	0	NUM
ejpam-6798	607	12	0	0	NUM
ejpam-6798	608	1	s	s	NOUN
ejpam-6798	608	2	s	s	NOUN
ejpam-6798	608	3	0	0	NUM
ejpam-6798	608	4	s	s	NOUN
ejpam-6798	608	5	0	0	NUM
ejpam-6798	608	6	0	0	NUM
ejpam-6798	608	7	l	l	NOUN
ejpam-6798	608	8	l	l	NOUN
ejpam-6798	608	9	l	l	NOUN
ejpam-6798	608	10	0	0	NUM
ejpam-6798	608	11	0	0	NUM
ejpam-6798	608	12	0	0	NUM
ejpam-6798	609	1	z	z	NOUN
ejpam-6798	609	2	z	z	NOUN
ejpam-6798	609	3	z	z	NOUN
ejpam-6798	609	4	z	z	NOUN
ejpam-6798	609	5	0	0	NUM
ejpam-6798	609	6	0	0	NUM
ejpam-6798	610	1	w	w	PROPN
ejpam-6798	610	2	w	w	PROPN
ejpam-6798	610	3	z	z	PROPN
ejpam-6798	610	4	w	w	PROPN
ejpam-6798	610	5	z	z	NOUN
ejpam-6798	610	6	0	0	NUM
ejpam-6798	610	7	conclusion	conclusion	NOUN
ejpam-6798	610	8	we	we	PRON
ejpam-6798	610	9	have	have	AUX
ejpam-6798	610	10	used	use	VERB
ejpam-6798	610	11	cifss	cifss	NOUN
ejpam-6798	610	12	in	in	ADP
ejpam-6798	610	13	the	the	DET
ejpam-6798	610	14	context	context	NOUN
ejpam-6798	610	15	of	of	ADP
ejpam-6798	610	16	bck	bck	PROPN
ejpam-6798	610	17	/	/	SYM
ejpam-6798	610	18	bci	bci	NOUN
ejpam-6798	610	19	-	-	PUNCT
ejpam-6798	610	20	algebras	algebra	NOUN
ejpam-6798	610	21	in	in	ADP
ejpam-6798	610	22	this	this	DET
ejpam-6798	610	23	paper	paper	NOUN
ejpam-6798	610	24	;	;	PUNCT
ejpam-6798	610	25	also	also	ADV
ejpam-6798	610	26	,	,	PUNCT
ejpam-6798	610	27	the	the	DET
ejpam-6798	610	28	cifi	cifi	NOUN
ejpam-6798	610	29	have	have	AUX
ejpam-6798	610	30	been	be	AUX
ejpam-6798	610	31	defined	define	VERB
ejpam-6798	610	32	,	,	PUNCT
ejpam-6798	610	33	and	and	CCONJ
ejpam-6798	610	34	its	its	PRON
ejpam-6798	610	35	features	feature	NOUN
ejpam-6798	610	36	have	have	AUX
ejpam-6798	610	37	been	be	AUX
ejpam-6798	610	38	investigated	investigate	VERB
ejpam-6798	610	39	.	.	PUNCT
ejpam-6798	611	1	this	this	PRON
ejpam-6798	611	2	adds	add	VERB
ejpam-6798	611	3	a	a	DET
ejpam-6798	611	4	lot	lot	NOUN
ejpam-6798	611	5	to	to	ADP
ejpam-6798	611	6	the	the	DET
ejpam-6798	611	7	field	field	NOUN
ejpam-6798	611	8	of	of	ADP
ejpam-6798	611	9	m.	m.	NOUN
ejpam-6798	611	10	jawad	jawad	PROPN
ejpam-6798	611	11	et	et	PROPN
ejpam-6798	611	12	al	al	PROPN
ejpam-6798	611	13	.	.	PUNCT
ejpam-6798	611	14	/	/	SYM
ejpam-6798	611	15	eur	eur	PROPN
ejpam-6798	611	16	.	.	PUNCT
ejpam-6798	612	1	j.	j.	PROPN
ejpam-6798	612	2	pure	pure	PROPN
ejpam-6798	612	3	appl	appl	PROPN
ejpam-6798	612	4	.	.	PROPN
ejpam-6798	612	5	math	math	PROPN
ejpam-6798	612	6	,	,	PUNCT
ejpam-6798	612	7	18	18	NUM
ejpam-6798	612	8	(	(	PUNCT
ejpam-6798	612	9	4	4	NUM
ejpam-6798	612	10	)	)	PUNCT
ejpam-6798	612	11	(	(	PUNCT
ejpam-6798	612	12	2025	2025	NUM
ejpam-6798	612	13	)	)	PUNCT
ejpam-6798	612	14	,	,	PUNCT
ejpam-6798	612	15	6798	6798	NUM
ejpam-6798	612	16	20	20	NUM
ejpam-6798	612	17	of	of	ADP
ejpam-6798	612	18	22	22	NUM
ejpam-6798	612	19	classical	classical	ADJ
ejpam-6798	612	20	fuzzy	fuzzy	ADJ
ejpam-6798	612	21	set	set	NOUN
ejpam-6798	612	22	theory	theory	NOUN
ejpam-6798	612	23	.	.	PUNCT
ejpam-6798	613	1	in	in	ADP
ejpam-6798	613	2	cifs	cifs	PROPN
ejpam-6798	613	3	,	,	PUNCT
ejpam-6798	613	4	both	both	DET
ejpam-6798	613	5	non	non	ADJ
ejpam-6798	613	6	-	-	ADJ
ejpam-6798	613	7	membership	membership	ADJ
ejpam-6798	613	8	and	and	CCONJ
ejpam-6798	613	9	membership	membership	NOUN
ejpam-6798	613	10	functions	function	NOUN
ejpam-6798	613	11	with	with	ADP
ejpam-6798	613	12	complex	complex	ADJ
ejpam-6798	613	13	degrees	degree	NOUN
ejpam-6798	613	14	have	have	AUX
ejpam-6798	613	15	been	be	AUX
ejpam-6798	613	16	used	use	VERB
ejpam-6798	613	17	to	to	PART
ejpam-6798	613	18	improve	improve	VERB
ejpam-6798	613	19	the	the	DET
ejpam-6798	613	20	algebraic	algebraic	ADJ
ejpam-6798	613	21	structure	structure	NOUN
ejpam-6798	613	22	and	and	CCONJ
ejpam-6798	613	23	decision	decision	NOUN
ejpam-6798	613	24	-	-	PUNCT
ejpam-6798	613	25	making	make	VERB
ejpam-6798	613	26	processes	process	NOUN
ejpam-6798	613	27	within	within	ADP
ejpam-6798	613	28	bck	bck	PROPN
ejpam-6798	613	29	/	/	SYM
ejpam-6798	613	30	bci	bci	NOUN
ejpam-6798	613	31	-	-	PUNCT
ejpam-6798	613	32	algebras	algebras	X
ejpam-6798	613	33	.	.	PUNCT
ejpam-6798	614	1	in	in	ADP
ejpam-6798	614	2	bck	bck	PROPN
ejpam-6798	614	3	/	/	SYM
ejpam-6798	614	4	bci	bci	PROPN
ejpam-6798	614	5	-	-	PUNCT
ejpam-6798	614	6	algebras	algebra	NOUN
ejpam-6798	614	7	,	,	PUNCT
ejpam-6798	614	8	level	level	NOUN
ejpam-6798	614	9	operators	operator	NOUN
ejpam-6798	614	10	and	and	CCONJ
ejpam-6798	614	11	model	model	NOUN
ejpam-6798	614	12	operators	operator	NOUN
ejpam-6798	614	13	have	have	AUX
ejpam-6798	614	14	been	be	AUX
ejpam-6798	614	15	used	use	VERB
ejpam-6798	614	16	to	to	PART
ejpam-6798	614	17	explain	explain	VERB
ejpam-6798	614	18	what	what	PRON
ejpam-6798	614	19	a	a	DET
ejpam-6798	614	20	cifsa	cifsa	NOUN
ejpam-6798	614	21	is	be	AUX
ejpam-6798	614	22	,	,	PUNCT
ejpam-6798	614	23	and	and	CCONJ
ejpam-6798	614	24	then	then	ADV
ejpam-6798	614	25	its	its	PRON
ejpam-6798	614	26	basic	basic	ADJ
ejpam-6798	614	27	properties	property	NOUN
ejpam-6798	614	28	have	have	AUX
ejpam-6798	614	29	been	be	AUX
ejpam-6798	614	30	looked	look	VERB
ejpam-6798	614	31	at	at	ADP
ejpam-6798	614	32	.	.	PUNCT
ejpam-6798	615	1	we	we	PRON
ejpam-6798	615	2	have	have	AUX
ejpam-6798	615	3	also	also	ADV
ejpam-6798	615	4	studied	study	VERB
ejpam-6798	615	5	various	various	ADJ
ejpam-6798	615	6	operations	operation	NOUN
ejpam-6798	615	7	,	,	PUNCT
ejpam-6798	615	8	including	include	VERB
ejpam-6798	615	9	complement	complement	NOUN
ejpam-6798	615	10	,	,	PUNCT
ejpam-6798	615	11	intersection	intersection	NOUN
ejpam-6798	615	12	,	,	PUNCT
ejpam-6798	615	13	union	union	NOUN
ejpam-6798	615	14	,	,	PUNCT
ejpam-6798	615	15	and	and	CCONJ
ejpam-6798	615	16	differences	difference	NOUN
ejpam-6798	615	17	.	.	PUNCT
ejpam-6798	616	1	we	we	PRON
ejpam-6798	616	2	plan	plan	VERB
ejpam-6798	616	3	to	to	PART
ejpam-6798	616	4	investigate	investigate	VERB
ejpam-6798	616	5	the	the	DET
ejpam-6798	616	6	more	more	ADV
ejpam-6798	616	7	complex	complex	ADJ
ejpam-6798	616	8	features	feature	NOUN
ejpam-6798	616	9	of	of	ADP
ejpam-6798	616	10	the	the	DET
ejpam-6798	616	11	bck	bck	PROPN
ejpam-6798	616	12	/	/	SYM
ejpam-6798	616	13	bci	bci	NOUN
ejpam-6798	616	14	-	-	PUNCT
ejpam-6798	616	15	algebras	algebra	NOUN
ejpam-6798	616	16	under	under	ADP
ejpam-6798	616	17	the	the	DET
ejpam-6798	616	18	influence	influence	NOUN
ejpam-6798	616	19	of	of	ADP
ejpam-6798	616	20	cifs	cif	NOUN
ejpam-6798	616	21	.	.	PUNCT
ejpam-6798	617	1	furthermore	furthermore	ADV
ejpam-6798	617	2	,	,	PUNCT
ejpam-6798	617	3	we	we	PRON
ejpam-6798	617	4	want	want	VERB
ejpam-6798	617	5	to	to	PART
ejpam-6798	617	6	apply	apply	VERB
ejpam-6798	617	7	complex	complex	ADJ
ejpam-6798	617	8	spherical	spherical	ADJ
ejpam-6798	617	9	fuzzy	fuzzy	ADJ
ejpam-6798	617	10	set	set	NOUN
ejpam-6798	617	11	and	and	CCONJ
ejpam-6798	617	12	complex	complex	ADJ
ejpam-6798	617	13	linear	linear	ADJ
ejpam-6798	617	14	diophantine	diophantine	NOUN
ejpam-6798	617	15	fuzzy	fuzzy	ADJ
ejpam-6798	617	16	set	set	VERB
ejpam-6798	617	17	on	on	ADP
ejpam-6798	617	18	bck	bck	PROPN
ejpam-6798	617	19	/	/	SYM
ejpam-6798	617	20	bci	bci	NOUN
ejpam-6798	617	21	-	-	PUNCT
ejpam-6798	617	22	algebras	algebras	X
ejpam-6798	617	23	.	.	PUNCT
ejpam-6798	618	1	in	in	ADP
ejpam-6798	618	2	the	the	DET
ejpam-6798	618	3	future	future	NOUN
ejpam-6798	618	4	,	,	PUNCT
ejpam-6798	618	5	we	we	PRON
ejpam-6798	618	6	focus	focus	VERB
ejpam-6798	618	7	on	on	ADP
ejpam-6798	618	8	characterising	characterise	VERB
ejpam-6798	618	9	cifsas	cifsa	NOUN
ejpam-6798	618	10	under	under	ADP
ejpam-6798	618	11	algebraic	algebraic	PROPN
ejpam-6798	618	12	homomorphisms	homomorphism	NOUN
ejpam-6798	618	13	and	and	CCONJ
ejpam-6798	618	14	isomorphisms	isomorphism	NOUN
ejpam-6798	618	15	.	.	PUNCT
ejpam-6798	619	1	this	this	PRON
ejpam-6798	619	2	will	will	AUX
ejpam-6798	619	3	provide	provide	VERB
ejpam-6798	619	4	a	a	DET
ejpam-6798	619	5	better	well	ADJ
ejpam-6798	619	6	understanding	understanding	NOUN
ejpam-6798	619	7	of	of	ADP
ejpam-6798	619	8	how	how	SCONJ
ejpam-6798	619	9	complex	complex	ADJ
ejpam-6798	619	10	intuitionistic	intuitionistic	ADJ
ejpam-6798	619	11	fuzziness	fuzziness	NOUN
ejpam-6798	619	12	interacts	interact	VERB
ejpam-6798	619	13	with	with	ADP
ejpam-6798	619	14	structure	structure	NOUN
ejpam-6798	619	15	preservation	preservation	NOUN
ejpam-6798	619	16	between	between	ADP
ejpam-6798	619	17	algebras	algebras	PROPN
ejpam-6798	619	18	.	.	PUNCT
ejpam-6798	620	1	also	also	ADV
ejpam-6798	620	2	,	,	PUNCT
ejpam-6798	620	3	complex	complex	ADJ
ejpam-6798	620	4	intuitionistic	intuitionistic	ADJ
ejpam-6798	620	5	fuzzy	fuzzy	ADJ
ejpam-6798	620	6	sub	sub	NOUN
ejpam-6798	620	7	-	-	ADJ
ejpam-6798	620	8	algebra	algebra	ADJ
ejpam-6798	620	9	provide	provide	VERB
ejpam-6798	620	10	richer	rich	ADJ
ejpam-6798	620	11	modelling	modelling	NOUN
ejpam-6798	620	12	tools	tool	NOUN
ejpam-6798	620	13	for	for	ADP
ejpam-6798	620	14	uncertainty	uncertainty	NOUN
ejpam-6798	620	15	;	;	PUNCT
ejpam-6798	620	16	future	future	ADJ
ejpam-6798	620	17	research	research	NOUN
ejpam-6798	620	18	will	will	AUX
ejpam-6798	620	19	explore	explore	VERB
ejpam-6798	620	20	their	their	PRON
ejpam-6798	620	21	applications	application	NOUN
ejpam-6798	620	22	in	in	ADP
ejpam-6798	620	23	multi	multi	ADJ
ejpam-6798	620	24	-	-	ADJ
ejpam-6798	620	25	criteria	criterion	NOUN
ejpam-6798	620	26	decision	decision	NOUN
ejpam-6798	620	27	-	-	PUNCT
ejpam-6798	620	28	making	making	NOUN
ejpam-6798	620	29	,	,	PUNCT
ejpam-6798	620	30	artificial	artificial	ADJ
ejpam-6798	620	31	intelligence	intelligence	NOUN
ejpam-6798	620	32	,	,	PUNCT
ejpam-6798	620	33	and	and	CCONJ
ejpam-6798	620	34	information	information	NOUN
ejpam-6798	620	35	systems	system	NOUN
ejpam-6798	620	36	.	.	PUNCT
ejpam-6798	621	1	acknowledgements	acknowledgement	NOUN
ejpam-6798	621	2	the	the	DET
ejpam-6798	621	3	second	second	ADJ
ejpam-6798	621	4	author	author	NOUN
ejpam-6798	621	5	thanks	thank	NOUN
ejpam-6798	621	6	the	the	DET
ejpam-6798	621	7	ministry	ministry	PROPN
ejpam-6798	621	8	of	of	ADP
ejpam-6798	621	9	defence	defence	PROPN
ejpam-6798	621	10	of	of	ADP
ejpam-6798	621	11	the	the	DET
ejpam-6798	621	12	czech	czech	PROPN
ejpam-6798	621	13	republic	republic	NOUN
ejpam-6798	621	14	for	for	ADP
ejpam-6798	621	15	the	the	DET
ejpam-6798	621	16	support	support	NOUN
ejpam-6798	621	17	via	via	ADP
ejpam-6798	621	18	grant	grant	NOUN
ejpam-6798	621	19	varops	varop	NOUN
ejpam-6798	621	20	.	.	PUNCT
ejpam-6798	622	1	conflict	conflict	NOUN
ejpam-6798	622	2	of	of	ADP
ejpam-6798	622	3	interest	interest	NOUN
ejpam-6798	622	4	:	:	PUNCT
ejpam-6798	622	5	the	the	DET
ejpam-6798	622	6	authors	author	NOUN
ejpam-6798	622	7	state	state	VERB
ejpam-6798	622	8	that	that	SCONJ
ejpam-6798	622	9	they	they	PRON
ejpam-6798	622	10	do	do	AUX
ejpam-6798	622	11	not	not	PART
ejpam-6798	622	12	have	have	VERB
ejpam-6798	622	13	a	a	DET
ejpam-6798	622	14	conflict	conflict	NOUN
ejpam-6798	622	15	of	of	ADP
ejpam-6798	622	16	interest	interest	NOUN
ejpam-6798	622	17	in	in	ADP
ejpam-6798	622	18	relation	relation	NOUN
ejpam-6798	622	19	to	to	ADP
ejpam-6798	622	20	the	the	DET
ejpam-6798	622	21	publication	publication	NOUN
ejpam-6798	622	22	of	of	ADP
ejpam-6798	622	23	this	this	DET
ejpam-6798	622	24	research	research	NOUN
ejpam-6798	622	25	article	article	NOUN
ejpam-6798	622	26	.	.	PUNCT
ejpam-6798	623	1	references	reference	NOUN
ejpam-6798	623	2	[	[	X
ejpam-6798	623	3	1	1	NUM
ejpam-6798	623	4	]	]	PUNCT
ejpam-6798	623	5	k.	k.	PROPN
ejpam-6798	623	6	l.	l.	PROPN
ejpam-6798	623	7	zhang	zhang	PROPN
ejpam-6798	623	8	and	and	CCONJ
ejpam-6798	623	9	l.	l.	PROPN
ejpam-6798	623	10	x.	x.	PROPN
ejpam-6798	623	11	song	song	PROPN
ejpam-6798	623	12	.	.	PUNCT
ejpam-6798	624	1	definitions	definition	NOUN
ejpam-6798	624	2	of	of	ADP
ejpam-6798	624	3	bck	bck	PROPN
ejpam-6798	624	4	algebras	algebra	NOUN
ejpam-6798	624	5	and	and	CCONJ
ejpam-6798	624	6	bci	bci	PROPN
ejpam-6798	624	7	algebras	algebra	NOUN
ejpam-6798	624	8	.	.	PUNCT
ejpam-6798	625	1	in	in	ADP
ejpam-6798	625	2	2015	2015	NUM
ejpam-6798	625	3	international	international	ADJ
ejpam-6798	625	4	conference	conference	NOUN
ejpam-6798	625	5	on	on	ADP
ejpam-6798	625	6	intelligent	intelligent	ADJ
ejpam-6798	625	7	systems	system	NOUN
ejpam-6798	625	8	research	research	NOUN
ejpam-6798	625	9	and	and	CCONJ
ejpam-6798	625	10	mechatronics	mechatronic	NOUN
ejpam-6798	625	11	engineering	engineering	NOUN
ejpam-6798	625	12	,	,	PUNCT
ejpam-6798	625	13	pages	page	NOUN
ejpam-6798	625	14	1085–1089	1085–1089	NUM
ejpam-6798	625	15	,	,	PUNCT
ejpam-6798	625	16	2015	2015	NUM
ejpam-6798	625	17	.	.	PUNCT
ejpam-6798	626	1	[	[	X
ejpam-6798	626	2	2	2	X
ejpam-6798	626	3	]	]	X
ejpam-6798	626	4	y.	y.	PROPN
ejpam-6798	626	5	l.	l.	PROPN
ejpam-6798	626	6	liu	liu	PROPN
ejpam-6798	626	7	and	and	CCONJ
ejpam-6798	626	8	j.	j.	PROPN
ejpam-6798	626	9	meng	meng	PROPN
ejpam-6798	626	10	.	.	PUNCT
ejpam-6798	627	1	fuzzy	fuzzy	ADJ
ejpam-6798	627	2	ideals	ideal	NOUN
ejpam-6798	627	3	in	in	ADP
ejpam-6798	627	4	bci	bci	NOUN
ejpam-6798	627	5	-	-	PUNCT
ejpam-6798	627	6	algebras	algebras	X
ejpam-6798	627	7	.	.	PUNCT
ejpam-6798	627	8	fuzzy	fuzzy	ADJ
ejpam-6798	627	9	sets	set	NOUN
ejpam-6798	627	10	and	and	CCONJ
ejpam-6798	627	11	systems	system	NOUN
ejpam-6798	627	12	,	,	PUNCT
ejpam-6798	627	13	123(2):227–237	123(2):227–237	NUM
ejpam-6798	627	14	,	,	PUNCT
ejpam-6798	627	15	2001	2001	NUM
ejpam-6798	627	16	.	.	PUNCT
ejpam-6798	628	1	[	[	X
ejpam-6798	628	2	3	3	X
ejpam-6798	628	3	]	]	PUNCT
ejpam-6798	628	4	j.	j.	PROPN
ejpam-6798	628	5	meng	meng	PROPN
ejpam-6798	628	6	,	,	PUNCT
ejpam-6798	628	7	y.	y.	PROPN
ejpam-6798	628	8	b.	b.	PROPN
ejpam-6798	628	9	jun	jun	PROPN
ejpam-6798	628	10	,	,	PUNCT
ejpam-6798	628	11	and	and	CCONJ
ejpam-6798	628	12	h.	h.	PROPN
ejpam-6798	628	13	s.	s.	PROPN
ejpam-6798	628	14	kim	kim	PROPN
ejpam-6798	628	15	.	.	PUNCT
ejpam-6798	629	1	fuzzy	fuzzy	ADJ
ejpam-6798	629	2	implicative	implicative	ADJ
ejpam-6798	629	3	ideals	ideal	NOUN
ejpam-6798	629	4	of	of	ADP
ejpam-6798	629	5	bck	bck	NOUN
ejpam-6798	629	6	-	-	PUNCT
ejpam-6798	629	7	algebras	algebras	PROPN
ejpam-6798	629	8	.	.	PUNCT
ejpam-6798	630	1	fuzzy	fuzzy	ADJ
ejpam-6798	630	2	sets	set	NOUN
ejpam-6798	630	3	and	and	CCONJ
ejpam-6798	630	4	systems	system	NOUN
ejpam-6798	630	5	,	,	PUNCT
ejpam-6798	630	6	89(2):243–248	89(2):243–248	PROPN
ejpam-6798	630	7	,	,	PUNCT
ejpam-6798	630	8	1997	1997	NUM
ejpam-6798	630	9	.	.	PUNCT
ejpam-6798	631	1	[	[	X
ejpam-6798	631	2	4	4	X
ejpam-6798	631	3	]	]	X
ejpam-6798	631	4	y.	y.	PROPN
ejpam-6798	631	5	b.	b.	PROPN
ejpam-6798	631	6	jun	jun	PROPN
ejpam-6798	631	7	.	.	PROPN
ejpam-6798	631	8	soft	soft	ADJ
ejpam-6798	631	9	bck	bck	PROPN
ejpam-6798	631	10	/	/	SYM
ejpam-6798	631	11	bci	bci	NOUN
ejpam-6798	631	12	-	-	PUNCT
ejpam-6798	631	13	algebras	algebra	NOUN
ejpam-6798	631	14	.	.	PUNCT
ejpam-6798	632	1	computers	computer	NOUN
ejpam-6798	632	2	and	and	CCONJ
ejpam-6798	632	3	mathematics	mathematic	NOUN
ejpam-6798	632	4	with	with	ADP
ejpam-6798	632	5	applications	application	NOUN
ejpam-6798	632	6	,	,	PUNCT
ejpam-6798	632	7	56(5):1408–1413	56(5):1408–1413	NUM
ejpam-6798	632	8	,	,	PUNCT
ejpam-6798	632	9	2008	2008	NUM
ejpam-6798	632	10	.	.	PUNCT
ejpam-6798	633	1	[	[	X
ejpam-6798	633	2	5	5	NUM
ejpam-6798	633	3	]	]	PUNCT
ejpam-6798	633	4	m.	m.	NOUN
ejpam-6798	633	5	senapati	senapati	PROPN
ejpam-6798	633	6	and	and	CCONJ
ejpam-6798	633	7	k.	k.	PROPN
ejpam-6798	633	8	p.	p.	PROPN
ejpam-6798	633	9	shum	shum	PROPN
ejpam-6798	633	10	.	.	PUNCT
ejpam-6798	634	1	cubic	cubic	ADJ
ejpam-6798	634	2	set	set	VERB
ejpam-6798	634	3	notion	notion	NOUN
ejpam-6798	634	4	to	to	ADP
ejpam-6798	634	5	implicative	implicative	ADJ
ejpam-6798	634	6	ideals	ideal	NOUN
ejpam-6798	634	7	of	of	ADP
ejpam-6798	634	8	bck	bck	NOUN
ejpam-6798	634	9	-	-	PUNCT
ejpam-6798	634	10	algebras	algebra	NOUN
ejpam-6798	634	11	and	and	CCONJ
ejpam-6798	634	12	characterisation	characterisation	NOUN
ejpam-6798	634	13	of	of	ADP
ejpam-6798	634	14	their	their	PRON
ejpam-6798	634	15	basic	basic	ADJ
ejpam-6798	634	16	attributes	attribute	NOUN
ejpam-6798	634	17	.	.	PUNCT
ejpam-6798	635	1	concept	concept	NOUN
ejpam-6798	635	2	introduction	introduction	NOUN
ejpam-6798	635	3	;	;	PUNCT
ejpam-6798	635	4	source	source	NOUN
ejpam-6798	635	5	summary	summary	NOUN
ejpam-6798	635	6	without	without	ADP
ejpam-6798	635	7	formal	formal	ADJ
ejpam-6798	635	8	publication	publication	NOUN
ejpam-6798	635	9	.	.	PUNCT
ejpam-6798	636	1	[	[	X
ejpam-6798	636	2	6	6	NUM
ejpam-6798	636	3	]	]	PUNCT
ejpam-6798	636	4	j.	j.	PROPN
ejpam-6798	636	5	de	de	PROPN
ejpam-6798	636	6	andrés	andrés	PROPN
ejpam-6798	636	7	-	-	PUNCT
ejpam-6798	636	8	sánchez	sánchez	NOUN
ejpam-6798	636	9	.	.	PUNCT
ejpam-6798	637	1	a	a	DET
ejpam-6798	637	2	systematic	systematic	ADJ
ejpam-6798	637	3	review	review	NOUN
ejpam-6798	637	4	of	of	ADP
ejpam-6798	637	5	the	the	DET
ejpam-6798	637	6	interactions	interaction	NOUN
ejpam-6798	637	7	of	of	ADP
ejpam-6798	637	8	fuzzy	fuzzy	ADJ
ejpam-6798	637	9	set	set	NOUN
ejpam-6798	637	10	theory	theory	NOUN
ejpam-6798	637	11	and	and	CCONJ
ejpam-6798	637	12	option	option	NOUN
ejpam-6798	637	13	pricing	pricing	NOUN
ejpam-6798	637	14	.	.	PUNCT
ejpam-6798	638	1	expert	expert	NOUN
ejpam-6798	638	2	systems	system	NOUN
ejpam-6798	638	3	with	with	ADP
ejpam-6798	638	4	applications	application	NOUN
ejpam-6798	638	5	,	,	PUNCT
ejpam-6798	638	6	223(1):119868	223(1):119868	NOUN
ejpam-6798	638	7	,	,	PUNCT
ejpam-6798	638	8	2023	2023	NUM
ejpam-6798	638	9	.	.	PUNCT
ejpam-6798	639	1	[	[	X
ejpam-6798	639	2	7	7	NUM
ejpam-6798	639	3	]	]	PUNCT
ejpam-6798	639	4	a.	a.	NOUN
ejpam-6798	639	5	mardani	mardani	PROPN
ejpam-6798	639	6	,	,	PUNCT
ejpam-6798	639	7	r.	r.	PROPN
ejpam-6798	639	8	e.	e.	PROPN
ejpam-6798	639	9	hooker	hooker	PROPN
ejpam-6798	639	10	,	,	PUNCT
ejpam-6798	639	11	s.	s.	PROPN
ejpam-6798	639	12	ozkul	ozkul	PROPN
ejpam-6798	639	13	,	,	PUNCT
ejpam-6798	639	14	s.	s.	PROPN
ejpam-6798	639	15	yifan	yifan	PROPN
ejpam-6798	639	16	,	,	PUNCT
ejpam-6798	639	17	m.	m.	PROPN
ejpam-6798	639	18	nilashi	nilashi	PROPN
ejpam-6798	639	19	,	,	PUNCT
ejpam-6798	639	20	h.	h.	PROPN
ejpam-6798	639	21	z.	z.	PROPN
ejpam-6798	639	22	sabzi	sabzi	PROPN
ejpam-6798	639	23	,	,	PUNCT
ejpam-6798	639	24	and	and	CCONJ
ejpam-6798	639	25	g.	g.	PROPN
ejpam-6798	639	26	c.	c.	PROPN
ejpam-6798	639	27	fei	fei	PROPN
ejpam-6798	639	28	.	.	PUNCT
ejpam-6798	640	1	application	application	NOUN
ejpam-6798	640	2	of	of	ADP
ejpam-6798	640	3	decision	decision	NOUN
ejpam-6798	640	4	-	-	PUNCT
ejpam-6798	640	5	making	make	VERB
ejpam-6798	640	6	and	and	CCONJ
ejpam-6798	640	7	fuzzy	fuzzy	ADJ
ejpam-6798	640	8	sets	set	NOUN
ejpam-6798	640	9	theory	theory	NOUN
ejpam-6798	640	10	to	to	PART
ejpam-6798	640	11	evaluate	evaluate	VERB
ejpam-6798	640	12	the	the	DET
ejpam-6798	640	13	healthcare	healthcare	NOUN
ejpam-6798	640	14	and	and	CCONJ
ejpam-6798	640	15	medical	medical	ADJ
ejpam-6798	640	16	problems	problem	NOUN
ejpam-6798	640	17	:	:	PUNCT
ejpam-6798	640	18	a	a	DET
ejpam-6798	640	19	review	review	NOUN
ejpam-6798	640	20	of	of	ADP
ejpam-6798	640	21	three	three	NUM
ejpam-6798	640	22	decades	decade	NOUN
ejpam-6798	640	23	of	of	ADP
ejpam-6798	640	24	research	research	NOUN
ejpam-6798	640	25	with	with	ADP
ejpam-6798	640	26	recent	recent	ADJ
ejpam-6798	640	27	developments	development	NOUN
ejpam-6798	640	28	.	.	PUNCT
ejpam-6798	641	1	expert	expert	NOUN
ejpam-6798	641	2	systems	system	NOUN
ejpam-6798	641	3	with	with	ADP
ejpam-6798	641	4	applications	application	NOUN
ejpam-6798	641	5	,	,	PUNCT
ejpam-6798	641	6	137(1):202–231	137(1):202–231	NUM
ejpam-6798	641	7	,	,	PUNCT
ejpam-6798	641	8	2019	2019	NUM
ejpam-6798	641	9	.	.	PUNCT
ejpam-6798	642	1	m.	m.	NOUN
ejpam-6798	642	2	jawad	jawad	PROPN
ejpam-6798	642	3	et	et	PROPN
ejpam-6798	642	4	al	al	PROPN
ejpam-6798	642	5	.	.	PUNCT
ejpam-6798	642	6	/	/	SYM
ejpam-6798	642	7	eur	eur	PROPN
ejpam-6798	642	8	.	.	PUNCT
ejpam-6798	643	1	j.	j.	PROPN
ejpam-6798	643	2	pure	pure	PROPN
ejpam-6798	643	3	appl	appl	PROPN
ejpam-6798	643	4	.	.	PROPN
ejpam-6798	643	5	math	math	PROPN
ejpam-6798	643	6	,	,	PUNCT
ejpam-6798	643	7	18	18	NUM
ejpam-6798	643	8	(	(	PUNCT
ejpam-6798	643	9	4	4	NUM
ejpam-6798	643	10	)	)	PUNCT
ejpam-6798	643	11	(	(	PUNCT
ejpam-6798	643	12	2025	2025	NUM
ejpam-6798	643	13	)	)	PUNCT
ejpam-6798	643	14	,	,	PUNCT
ejpam-6798	643	15	6798	6798	NUM
ejpam-6798	643	16	21	21	NUM
ejpam-6798	643	17	of	of	ADP
ejpam-6798	643	18	22	22	NUM
ejpam-6798	644	1	[	[	NOUN
ejpam-6798	644	2	8	8	NUM
ejpam-6798	644	3	]	]	PUNCT
ejpam-6798	644	4	m.	m.	NOUN
ejpam-6798	644	5	luo	luo	PROPN
ejpam-6798	644	6	and	and	CCONJ
ejpam-6798	644	7	r.	r.	PROPN
ejpam-6798	644	8	zhao	zhao	PROPN
ejpam-6798	644	9	.	.	PUNCT
ejpam-6798	645	1	a	a	DET
ejpam-6798	645	2	distance	distance	NOUN
ejpam-6798	645	3	measure	measure	NOUN
ejpam-6798	645	4	between	between	ADP
ejpam-6798	645	5	intuitionistic	intuitionistic	ADJ
ejpam-6798	645	6	fuzzy	fuzzy	ADJ
ejpam-6798	645	7	sets	set	NOUN
ejpam-6798	645	8	and	and	CCONJ
ejpam-6798	645	9	its	its	PRON
ejpam-6798	645	10	application	application	NOUN
ejpam-6798	645	11	in	in	ADP
ejpam-6798	645	12	medical	medical	ADJ
ejpam-6798	645	13	diagnosis	diagnosis	NOUN
ejpam-6798	645	14	.	.	PUNCT
ejpam-6798	646	1	artificial	artificial	ADJ
ejpam-6798	646	2	intelligence	intelligence	NOUN
ejpam-6798	646	3	in	in	ADP
ejpam-6798	646	4	medicine	medicine	NOUN
ejpam-6798	646	5	,	,	PUNCT
ejpam-6798	646	6	89(1):34–39	89(1):34–39	NUM
ejpam-6798	646	7	,	,	PUNCT
ejpam-6798	646	8	2018	2018	NUM
ejpam-6798	646	9	.	.	PUNCT
ejpam-6798	647	1	[	[	X
ejpam-6798	647	2	9	9	X
ejpam-6798	647	3	]	]	X
ejpam-6798	647	4	y.	y.	PROPN
ejpam-6798	647	5	fan	fan	PROPN
ejpam-6798	647	6	and	and	CCONJ
ejpam-6798	647	7	f.	f.	PROPN
ejpam-6798	647	8	xiao	xiao	PROPN
ejpam-6798	647	9	.	.	PROPN
ejpam-6798	647	10	tdifs	tdifs	PROPN
ejpam-6798	647	11	:	:	PUNCT
ejpam-6798	647	12	two	two	NUM
ejpam-6798	647	13	dimensional	dimensional	ADJ
ejpam-6798	647	14	intuitionistic	intuitionistic	ADJ
ejpam-6798	647	15	fuzzy	fuzzy	ADJ
ejpam-6798	647	16	sets	set	NOUN
ejpam-6798	647	17	.	.	PUNCT
ejpam-6798	648	1	engineering	engineering	NOUN
ejpam-6798	648	2	applications	application	NOUN
ejpam-6798	648	3	of	of	ADP
ejpam-6798	648	4	artificial	artificial	ADJ
ejpam-6798	648	5	intelligence	intelligence	NOUN
ejpam-6798	648	6	,	,	PUNCT
ejpam-6798	648	7	95(1):103882	95(1):103882	NUM
ejpam-6798	648	8	,	,	PUNCT
ejpam-6798	648	9	2020	2020	NUM
ejpam-6798	648	10	.	.	PUNCT
ejpam-6798	649	1	[	[	X
ejpam-6798	649	2	10	10	NUM
ejpam-6798	649	3	]	]	X
ejpam-6798	649	4	b.	b.	PROPN
ejpam-6798	649	5	gohain	gohain	PROPN
ejpam-6798	649	6	,	,	PUNCT
ejpam-6798	649	7	r.	r.	PROPN
ejpam-6798	649	8	chutia	chutia	PROPN
ejpam-6798	649	9	,	,	PUNCT
ejpam-6798	649	10	and	and	CCONJ
ejpam-6798	649	11	p.	p.	PROPN
ejpam-6798	649	12	dutta	dutta	PROPN
ejpam-6798	649	13	.	.	PUNCT
ejpam-6798	650	1	distance	distance	NOUN
ejpam-6798	650	2	measure	measure	NOUN
ejpam-6798	650	3	on	on	ADP
ejpam-6798	650	4	intuitionistic	intuitionistic	ADJ
ejpam-6798	650	5	fuzzy	fuzzy	ADJ
ejpam-6798	650	6	sets	set	NOUN
ejpam-6798	650	7	and	and	CCONJ
ejpam-6798	650	8	its	its	PRON
ejpam-6798	650	9	application	application	NOUN
ejpam-6798	650	10	in	in	ADP
ejpam-6798	650	11	decision	decision	NOUN
ejpam-6798	650	12	-	-	PUNCT
ejpam-6798	650	13	making	making	NOUN
ejpam-6798	650	14	,	,	PUNCT
ejpam-6798	650	15	pattern	pattern	NOUN
ejpam-6798	650	16	recognition	recognition	NOUN
ejpam-6798	650	17	,	,	PUNCT
ejpam-6798	650	18	and	and	CCONJ
ejpam-6798	650	19	clustering	cluster	VERB
ejpam-6798	650	20	problems	problem	NOUN
ejpam-6798	650	21	.	.	PUNCT
ejpam-6798	651	1	international	international	ADJ
ejpam-6798	651	2	journal	journal	NOUN
ejpam-6798	651	3	of	of	ADP
ejpam-6798	651	4	intelligent	intelligent	ADJ
ejpam-6798	651	5	systems	system	NOUN
ejpam-6798	651	6	,	,	PUNCT
ejpam-6798	651	7	37(3):2458–2501	37(3):2458–2501	NUM
ejpam-6798	651	8	,	,	PUNCT
ejpam-6798	651	9	2022	2022	NUM
ejpam-6798	651	10	.	.	PUNCT
ejpam-6798	652	1	[	[	X
ejpam-6798	652	2	11	11	NUM
ejpam-6798	652	3	]	]	PUNCT
ejpam-6798	652	4	d.	d.	PROPN
ejpam-6798	652	5	k.	k.	PROPN
ejpam-6798	652	6	kushwaha	kushwaha	PROPN
ejpam-6798	652	7	,	,	PUNCT
ejpam-6798	652	8	d.	d.	PROPN
ejpam-6798	652	9	panchal	panchal	PROPN
ejpam-6798	652	10	,	,	PUNCT
ejpam-6798	652	11	and	and	CCONJ
ejpam-6798	652	12	a.	a.	PROPN
ejpam-6798	652	13	sachdeva	sachdeva	PROPN
ejpam-6798	652	14	.	.	PUNCT
ejpam-6798	653	1	risk	risk	VERB
ejpam-6798	653	2	analysis	analysis	NOUN
ejpam-6798	653	3	of	of	ADP
ejpam-6798	653	4	cutting	cut	VERB
ejpam-6798	653	5	system	system	NOUN
ejpam-6798	653	6	under	under	ADP
ejpam-6798	653	7	intuitionistic	intuitionistic	ADJ
ejpam-6798	653	8	fuzzy	fuzzy	ADJ
ejpam-6798	653	9	environment	environment	NOUN
ejpam-6798	653	10	.	.	PUNCT
ejpam-6798	654	1	reports	report	NOUN
ejpam-6798	654	2	in	in	ADP
ejpam-6798	654	3	mechanical	mechanical	ADJ
ejpam-6798	654	4	engineering	engineering	NOUN
ejpam-6798	654	5	,	,	PUNCT
ejpam-6798	654	6	1(1):162–173	1(1):162–173	NUM
ejpam-6798	654	7	,	,	PUNCT
ejpam-6798	654	8	2020	2020	NUM
ejpam-6798	654	9	.	.	PUNCT
ejpam-6798	655	1	[	[	X
ejpam-6798	655	2	12	12	NUM
ejpam-6798	655	3	]	]	PUNCT
ejpam-6798	655	4	j.	j.	PROPN
ejpam-6798	655	5	gao	gao	PROPN
ejpam-6798	655	6	,	,	PUNCT
ejpam-6798	655	7	f.	f.	PROPN
ejpam-6798	655	8	guo	guo	PROPN
ejpam-6798	655	9	,	,	PUNCT
ejpam-6798	655	10	z.	z.	PROPN
ejpam-6798	655	11	ma	ma	PROPN
ejpam-6798	655	12	,	,	PUNCT
ejpam-6798	655	13	and	and	CCONJ
ejpam-6798	655	14	x.	x.	PROPN
ejpam-6798	655	15	huang	huang	PROPN
ejpam-6798	655	16	.	.	PUNCT
ejpam-6798	656	1	multi	multi	ADJ
ejpam-6798	656	2	-	-	NOUN
ejpam-6798	656	3	criteria	criterion	NOUN
ejpam-6798	656	4	decision	decision	NOUN
ejpam-6798	656	5	-	-	PUNCT
ejpam-6798	656	6	making	make	VERB
ejpam-6798	656	7	framework	framework	NOUN
ejpam-6798	656	8	for	for	ADP
ejpam-6798	656	9	large	large	ADJ
ejpam-6798	656	10	-	-	PUNCT
ejpam-6798	656	11	scale	scale	NOUN
ejpam-6798	656	12	rooftop	rooftop	NOUN
ejpam-6798	656	13	photovoltaic	photovoltaic	NOUN
ejpam-6798	656	14	project	project	NOUN
ejpam-6798	656	15	site	site	NOUN
ejpam-6798	656	16	selection	selection	NOUN
ejpam-6798	656	17	based	base	VERB
ejpam-6798	656	18	on	on	ADP
ejpam-6798	656	19	intuitionistic	intuitionistic	ADJ
ejpam-6798	656	20	fuzzy	fuzzy	ADJ
ejpam-6798	656	21	sets	set	NOUN
ejpam-6798	656	22	.	.	PUNCT
ejpam-6798	657	1	applied	apply	VERB
ejpam-6798	657	2	soft	soft	ADJ
ejpam-6798	657	3	computing	computing	NOUN
ejpam-6798	657	4	,	,	PUNCT
ejpam-6798	657	5	102(1):107098–107117	102(1):107098–107117	NUM
ejpam-6798	657	6	,	,	PUNCT
ejpam-6798	657	7	2021	2021	NUM
ejpam-6798	657	8	.	.	PUNCT
ejpam-6798	658	1	[	[	X
ejpam-6798	658	2	13	13	NUM
ejpam-6798	658	3	]	]	PUNCT
ejpam-6798	658	4	l.	l.	PROPN
ejpam-6798	658	5	a.	a.	PROPN
ejpam-6798	658	6	zadeh	zadeh	PROPN
ejpam-6798	658	7	.	.	PUNCT
ejpam-6798	658	8	fuzzy	fuzzy	ADJ
ejpam-6798	658	9	sets	set	NOUN
ejpam-6798	658	10	.	.	PUNCT
ejpam-6798	659	1	information	information	NOUN
ejpam-6798	659	2	and	and	CCONJ
ejpam-6798	659	3	control	control	NOUN
ejpam-6798	659	4	,	,	PUNCT
ejpam-6798	659	5	1965	1965	NUM
ejpam-6798	659	6	.	.	PUNCT
ejpam-6798	660	1	[	[	X
ejpam-6798	660	2	14	14	NUM
ejpam-6798	660	3	]	]	PUNCT
ejpam-6798	660	4	a.	a.	PROPN
ejpam-6798	660	5	rosenfeld	rosenfeld	PROPN
ejpam-6798	660	6	.	.	PUNCT
ejpam-6798	661	1	fuzzy	fuzzy	ADJ
ejpam-6798	661	2	groups	group	NOUN
ejpam-6798	661	3	.	.	PUNCT
ejpam-6798	662	1	journal	journal	PROPN
ejpam-6798	662	2	of	of	ADP
ejpam-6798	662	3	mathematical	mathematical	ADJ
ejpam-6798	662	4	analysis	analysis	NOUN
ejpam-6798	662	5	and	and	CCONJ
ejpam-6798	662	6	applications	application	NOUN
ejpam-6798	662	7	,	,	PUNCT
ejpam-6798	662	8	35(3):512–517	35(3):512–517	PROPN
ejpam-6798	662	9	,	,	PUNCT
ejpam-6798	662	10	1971	1971	NUM
ejpam-6798	662	11	.	.	PUNCT
ejpam-6798	663	1	[	[	X
ejpam-6798	663	2	15	15	NUM
ejpam-6798	663	3	]	]	X
ejpam-6798	664	1	p.	p.	NOUN
ejpam-6798	664	2	s.	s.	PROPN
ejpam-6798	664	3	das	das	PROPN
ejpam-6798	664	4	.	.	PROPN
ejpam-6798	665	1	fuzzy	fuzzy	ADJ
ejpam-6798	665	2	groups	group	NOUN
ejpam-6798	665	3	and	and	CCONJ
ejpam-6798	665	4	level	level	NOUN
ejpam-6798	665	5	subgroups	subgroup	NOUN
ejpam-6798	665	6	.	.	PUNCT
ejpam-6798	666	1	journal	journal	PROPN
ejpam-6798	666	2	of	of	ADP
ejpam-6798	666	3	mathematical	mathematical	ADJ
ejpam-6798	666	4	analysis	analysis	NOUN
ejpam-6798	666	5	and	and	CCONJ
ejpam-6798	666	6	applications	application	NOUN
ejpam-6798	666	7	,	,	PUNCT
ejpam-6798	666	8	84(1):264–269	84(1):264–269	PROPN
ejpam-6798	666	9	,	,	PUNCT
ejpam-6798	666	10	1981	1981	NUM
ejpam-6798	666	11	.	.	PUNCT
ejpam-6798	667	1	[	[	X
ejpam-6798	667	2	16	16	NUM
ejpam-6798	667	3	]	]	PUNCT
ejpam-6798	667	4	j.	j.	PROPN
ejpam-6798	667	5	meng	meng	PROPN
ejpam-6798	667	6	and	and	CCONJ
ejpam-6798	667	7	x.	x.	PROPN
ejpam-6798	667	8	e.	e.	PROPN
ejpam-6798	667	9	guo	guo	PROPN
ejpam-6798	667	10	.	.	PUNCT
ejpam-6798	668	1	on	on	ADP
ejpam-6798	668	2	fuzzy	fuzzy	ADJ
ejpam-6798	668	3	ideals	ideal	NOUN
ejpam-6798	668	4	in	in	ADP
ejpam-6798	668	5	bck	bck	PROPN
ejpam-6798	668	6	/	/	SYM
ejpam-6798	668	7	bci	bci	NOUN
ejpam-6798	668	8	-	-	PUNCT
ejpam-6798	668	9	algebras	algebras	X
ejpam-6798	668	10	.	.	PUNCT
ejpam-6798	669	1	fuzzy	fuzzy	ADJ
ejpam-6798	669	2	sets	set	NOUN
ejpam-6798	669	3	and	and	CCONJ
ejpam-6798	669	4	systems	system	NOUN
ejpam-6798	669	5	,	,	PUNCT
ejpam-6798	669	6	149(3):509–525	149(3):509–525	NUM
ejpam-6798	669	7	,	,	PUNCT
ejpam-6798	669	8	2005	2005	NUM
ejpam-6798	669	9	.	.	PUNCT
ejpam-6798	670	1	[	[	X
ejpam-6798	670	2	17	17	NUM
ejpam-6798	670	3	]	]	PUNCT
ejpam-6798	670	4	k.	k.	PROPN
ejpam-6798	670	5	atanassov	atanassov	PROPN
ejpam-6798	670	6	.	.	PUNCT
ejpam-6798	671	1	intuitionistic	intuitionistic	ADJ
ejpam-6798	671	2	fuzzy	fuzzy	ADJ
ejpam-6798	671	3	sets	set	NOUN
ejpam-6798	671	4	.	.	PUNCT
ejpam-6798	672	1	international	international	ADJ
ejpam-6798	672	2	journal	journal	PROPN
ejpam-6798	672	3	bioautomation	bioautomation	NOUN
ejpam-6798	672	4	,	,	PUNCT
ejpam-6798	672	5	20(1):87–96	20(1):87–96	NUM
ejpam-6798	672	6	,	,	PUNCT
ejpam-6798	672	7	2016	2016	NUM
ejpam-6798	672	8	.	.	PUNCT
ejpam-6798	673	1	[	[	X
ejpam-6798	673	2	18	18	NUM
ejpam-6798	673	3	]	]	PUNCT
ejpam-6798	673	4	m.	m.	NOUN
ejpam-6798	673	5	akram	akram	PROPN
ejpam-6798	673	6	.	.	PUNCT
ejpam-6798	674	1	intuitionistic	intuitionistic	ADJ
ejpam-6798	674	2	fuzzy	fuzzy	ADJ
ejpam-6798	674	3	closed	closed	ADJ
ejpam-6798	674	4	ideals	ideal	NOUN
ejpam-6798	674	5	in	in	ADP
ejpam-6798	674	6	bci	bci	NOUN
ejpam-6798	674	7	-	-	PUNCT
ejpam-6798	674	8	algebras	algebras	PROPN
ejpam-6798	674	9	.	.	PUNCT
ejpam-6798	675	1	in	in	ADP
ejpam-6798	675	2	international	international	PROPN
ejpam-6798	675	3	mathematical	mathematical	ADJ
ejpam-6798	675	4	forum	forum	PROPN
ejpam-6798	675	5	,	,	PUNCT
ejpam-6798	675	6	volume	volume	NOUN
ejpam-6798	675	7	1	1	NUM
ejpam-6798	675	8	,	,	PUNCT
ejpam-6798	675	9	pages	page	NOUN
ejpam-6798	675	10	445–453	445–453	NUM
ejpam-6798	675	11	,	,	PUNCT
ejpam-6798	675	12	2006	2006	NUM
ejpam-6798	675	13	.	.	PUNCT
ejpam-6798	676	1	[	[	X
ejpam-6798	676	2	19	19	NUM
ejpam-6798	676	3	]	]	X
ejpam-6798	676	4	g.	g.	PROPN
ejpam-6798	676	5	muhiuddin	muhiuddin	PROPN
ejpam-6798	676	6	,	,	PUNCT
ejpam-6798	676	7	d.	d.	PROPN
ejpam-6798	676	8	al	al	PROPN
ejpam-6798	676	9	-	-	PUNCT
ejpam-6798	676	10	kadi	kadi	PROPN
ejpam-6798	676	11	,	,	PUNCT
ejpam-6798	676	12	k.	k.	PROPN
ejpam-6798	676	13	p.	p.	PROPN
ejpam-6798	676	14	shum	shum	PROPN
ejpam-6798	676	15	,	,	PUNCT
ejpam-6798	676	16	and	and	CCONJ
ejpam-6798	676	17	a.	a.	NOUN
ejpam-6798	676	18	m.	m.	NOUN
ejpam-6798	676	19	alanazi	alanazi	PROPN
ejpam-6798	676	20	.	.	PUNCT
ejpam-6798	677	1	generalized	generalized	ADJ
ejpam-6798	677	2	ideals	ideal	NOUN
ejpam-6798	677	3	of	of	ADP
ejpam-6798	677	4	bck	bck	PROPN
ejpam-6798	677	5	/	/	SYM
ejpam-6798	677	6	bci	bci	NOUN
ejpam-6798	677	7	-	-	PUNCT
ejpam-6798	677	8	algebras	algebras	PROPN
ejpam-6798	677	9	based	base	VERB
ejpam-6798	677	10	on	on	ADP
ejpam-6798	677	11	fuzzy	fuzzy	ADJ
ejpam-6798	677	12	soft	soft	ADJ
ejpam-6798	677	13	set	set	NOUN
ejpam-6798	677	14	theory	theory	NOUN
ejpam-6798	677	15	.	.	PUNCT
ejpam-6798	678	1	advances	advance	NOUN
ejpam-6798	678	2	in	in	ADP
ejpam-6798	678	3	fuzzy	fuzzy	ADJ
ejpam-6798	678	4	systems	system	NOUN
ejpam-6798	678	5	,	,	PUNCT
ejpam-6798	678	6	2021(1):8869931–8869941	2021(1):8869931–8869941	NUM
ejpam-6798	678	7	,	,	PUNCT
ejpam-6798	678	8	2021	2021	NUM
ejpam-6798	678	9	.	.	PUNCT
ejpam-6798	679	1	[	[	X
ejpam-6798	679	2	20	20	NUM
ejpam-6798	679	3	]	]	PUNCT
ejpam-6798	679	4	t.	t.	NOUN
ejpam-6798	679	5	senapati	senapati	PROPN
ejpam-6798	679	6	,	,	PUNCT
ejpam-6798	679	7	m.	m.	NOUN
ejpam-6798	679	8	bhowmik	bhowmik	ADJ
ejpam-6798	679	9	,	,	PUNCT
ejpam-6798	679	10	m.	m.	NOUN
ejpam-6798	679	11	pal	pal	NOUN
ejpam-6798	679	12	,	,	PUNCT
ejpam-6798	679	13	and	and	CCONJ
ejpam-6798	679	14	b.	b.	PROPN
ejpam-6798	679	15	davvaz	davvaz	PROPN
ejpam-6798	679	16	.	.	PUNCT
ejpam-6798	680	1	atanassov	atanassov	PROPN
ejpam-6798	680	2	’s	’s	PART
ejpam-6798	680	3	intuitionistic	intuitionistic	ADJ
ejpam-6798	680	4	fuzzy	fuzzy	ADJ
ejpam-6798	680	5	translations	translation	NOUN
ejpam-6798	680	6	of	of	ADP
ejpam-6798	680	7	intuitionistic	intuitionistic	ADJ
ejpam-6798	680	8	fuzzy	fuzzy	ADJ
ejpam-6798	680	9	subalgebras	subalgebra	NOUN
ejpam-6798	680	10	and	and	CCONJ
ejpam-6798	680	11	ideals	ideal	NOUN
ejpam-6798	680	12	in	in	ADP
ejpam-6798	680	13	bck	bck	PROPN
ejpam-6798	680	14	/	/	SYM
ejpam-6798	680	15	bci	bci	NOUN
ejpam-6798	680	16	-	-	PUNCT
ejpam-6798	680	17	algebras	algebra	NOUN
ejpam-6798	680	18	.	.	PUNCT
ejpam-6798	681	1	eurasian	eurasian	ADJ
ejpam-6798	681	2	mathematical	mathematical	PROPN
ejpam-6798	681	3	journal	journal	PROPN
ejpam-6798	681	4	,	,	PUNCT
ejpam-6798	681	5	6(1):96–114	6(1):96–114	NOUN
ejpam-6798	681	6	,	,	PUNCT
ejpam-6798	681	7	2015	2015	NUM
ejpam-6798	681	8	.	.	PUNCT
ejpam-6798	682	1	[	[	X
ejpam-6798	682	2	21	21	NUM
ejpam-6798	682	3	]	]	PUNCT
ejpam-6798	682	4	t.	t.	NOUN
ejpam-6798	682	5	senapati	senapati	PROPN
ejpam-6798	682	6	,	,	PUNCT
ejpam-6798	682	7	y.	y.	PROPN
ejpam-6798	682	8	b.	b.	PROPN
ejpam-6798	682	9	jun	jun	PROPN
ejpam-6798	682	10	,	,	PUNCT
ejpam-6798	682	11	and	and	CCONJ
ejpam-6798	682	12	k.	k.	PROPN
ejpam-6798	682	13	p.	p.	PROPN
ejpam-6798	682	14	shum	shum	PROPN
ejpam-6798	682	15	.	.	PUNCT
ejpam-6798	683	1	cubic	cubic	ADJ
ejpam-6798	683	2	intuitionistic	intuitionistic	ADJ
ejpam-6798	683	3	implicative	implicative	ADJ
ejpam-6798	683	4	ideals	ideal	NOUN
ejpam-6798	683	5	of	of	ADP
ejpam-6798	683	6	bck	bck	NOUN
ejpam-6798	683	7	-	-	PUNCT
ejpam-6798	683	8	algebras	algebra	NOUN
ejpam-6798	683	9	.	.	PUNCT
ejpam-6798	684	1	proceedings	proceeding	NOUN
ejpam-6798	684	2	of	of	ADP
ejpam-6798	684	3	the	the	DET
ejpam-6798	684	4	national	national	PROPN
ejpam-6798	684	5	academy	academy	PROPN
ejpam-6798	684	6	of	of	ADP
ejpam-6798	684	7	sciences	sciences	PROPN
ejpam-6798	684	8	,	,	PUNCT
ejpam-6798	684	9	india	india	PROPN
ejpam-6798	684	10	section	section	PROPN
ejpam-6798	684	11	a	a	PRON
ejpam-6798	684	12	:	:	PUNCT
ejpam-6798	684	13	physical	physical	ADJ
ejpam-6798	684	14	sciences	science	NOUN
ejpam-6798	684	15	,	,	PUNCT
ejpam-6798	684	16	91(2):273–282	91(2):273–282	PROPN
ejpam-6798	684	17	,	,	PUNCT
ejpam-6798	684	18	2021	2021	NUM
ejpam-6798	684	19	.	.	PUNCT
ejpam-6798	685	1	[	[	X
ejpam-6798	685	2	22	22	NUM
ejpam-6798	685	3	]	]	X
ejpam-6798	685	4	d.	d.	PROPN
ejpam-6798	685	5	ramot	ramot	PROPN
ejpam-6798	685	6	,	,	PUNCT
ejpam-6798	685	7	m.	m.	NOUN
ejpam-6798	685	8	friedman	friedman	PROPN
ejpam-6798	685	9	,	,	PUNCT
ejpam-6798	685	10	g.	g.	PROPN
ejpam-6798	685	11	langholz	langholz	PROPN
ejpam-6798	685	12	,	,	PUNCT
ejpam-6798	685	13	and	and	CCONJ
ejpam-6798	685	14	a.	a.	NOUN
ejpam-6798	685	15	kandel	kandel	PROPN
ejpam-6798	685	16	.	.	PUNCT
ejpam-6798	686	1	complex	complex	ADJ
ejpam-6798	686	2	fuzzy	fuzzy	ADJ
ejpam-6798	686	3	logic	logic	NOUN
ejpam-6798	686	4	.	.	PUNCT
ejpam-6798	687	1	ieee	ieee	NOUN
ejpam-6798	687	2	transactions	transaction	NOUN
ejpam-6798	687	3	on	on	ADP
ejpam-6798	687	4	fuzzy	fuzzy	ADJ
ejpam-6798	687	5	systems	system	NOUN
ejpam-6798	687	6	,	,	PUNCT
ejpam-6798	687	7	11(4):450–461	11(4):450–461	NUM
ejpam-6798	687	8	,	,	PUNCT
ejpam-6798	687	9	2003	2003	NUM
ejpam-6798	687	10	.	.	PUNCT
ejpam-6798	688	1	[	[	X
ejpam-6798	688	2	23	23	NUM
ejpam-6798	688	3	]	]	X
ejpam-6798	688	4	y.	y.	PROPN
ejpam-6798	688	5	b.	b.	PROPN
ejpam-6798	688	6	jun	jun	PROPN
ejpam-6798	688	7	.	.	PROPN
ejpam-6798	688	8	soft	soft	ADJ
ejpam-6798	688	9	bck	bck	PROPN
ejpam-6798	688	10	/	/	SYM
ejpam-6798	688	11	bci	bci	NOUN
ejpam-6798	688	12	-	-	PUNCT
ejpam-6798	688	13	algebras	algebra	NOUN
ejpam-6798	688	14	.	.	PUNCT
ejpam-6798	689	1	computers	computer	NOUN
ejpam-6798	689	2	and	and	CCONJ
ejpam-6798	689	3	mathematics	mathematic	NOUN
ejpam-6798	689	4	with	with	ADP
ejpam-6798	689	5	applications	application	NOUN
ejpam-6798	689	6	,	,	PUNCT
ejpam-6798	689	7	56(5):1408–1413	56(5):1408–1413	NUM
ejpam-6798	689	8	,	,	PUNCT
ejpam-6798	689	9	2008	2008	NUM
ejpam-6798	689	10	.	.	PUNCT
ejpam-6798	690	1	[	[	X
ejpam-6798	690	2	24	24	NUM
ejpam-6798	690	3	]	]	PUNCT
ejpam-6798	690	4	m.	m.	NOUN
ejpam-6798	690	5	balamurugan	balamurugan	NOUN
ejpam-6798	690	6	,	,	PUNCT
ejpam-6798	690	7	t.	t.	PROPN
ejpam-6798	690	8	ramesh	ramesh	PROPN
ejpam-6798	690	9	,	,	PUNCT
ejpam-6798	690	10	a.	a.	PROPN
ejpam-6798	690	11	al	al	PROPN
ejpam-6798	690	12	-	-	PROPN
ejpam-6798	690	13	masarwah	masarwah	PROPN
ejpam-6798	690	14	,	,	PUNCT
ejpam-6798	690	15	and	and	CCONJ
ejpam-6798	690	16	k.	k.	PROPN
ejpam-6798	690	17	alsager	alsager	PROPN
ejpam-6798	690	18	.	.	PUNCT
ejpam-6798	691	1	a	a	DET
ejpam-6798	691	2	new	new	ADJ
ejpam-6798	691	3	approach	approach	NOUN
ejpam-6798	691	4	of	of	ADP
ejpam-6798	691	5	complex	complex	ADJ
ejpam-6798	691	6	fuzzy	fuzzy	ADJ
ejpam-6798	691	7	ideals	ideal	NOUN
ejpam-6798	691	8	in	in	ADP
ejpam-6798	691	9	bck	bck	PROPN
ejpam-6798	691	10	/	/	SYM
ejpam-6798	691	11	bci	bci	NOUN
ejpam-6798	691	12	-	-	PUNCT
ejpam-6798	691	13	algebras	algebra	NOUN
ejpam-6798	691	14	.	.	PUNCT
ejpam-6798	692	1	mathematics	mathematic	NOUN
ejpam-6798	692	2	,	,	PUNCT
ejpam-6798	692	3	12(10):1583–1601	12(10):1583–1601	NUM
ejpam-6798	692	4	,	,	PUNCT
ejpam-6798	692	5	2024	2024	NUM
ejpam-6798	692	6	.	.	PUNCT
ejpam-6798	693	1	[	[	X
ejpam-6798	693	2	25	25	NUM
ejpam-6798	693	3	]	]	X
ejpam-6798	693	4	h.	h.	PROPN
ejpam-6798	693	5	alolaiyan	alolaiyan	PROPN
ejpam-6798	693	6	,	,	PUNCT
ejpam-6798	693	7	h.	h.	PROPN
ejpam-6798	693	8	a.	a.	PROPN
ejpam-6798	693	9	alshehri	alshehri	PROPN
ejpam-6798	693	10	,	,	PUNCT
ejpam-6798	693	11	m.	m.	PROPN
ejpam-6798	693	12	h.	h.	PROPN
ejpam-6798	693	13	mateen	mateen	PROPN
ejpam-6798	693	14	,	,	PUNCT
ejpam-6798	693	15	d.	d.	PROPN
ejpam-6798	693	16	pamucar	pamucar	PROPN
ejpam-6798	693	17	,	,	PUNCT
ejpam-6798	693	18	and	and	CCONJ
ejpam-6798	693	19	m.	m.	PROPN
ejpam-6798	693	20	gulzar	gulzar	PROPN
ejpam-6798	693	21	.	.	PUNCT
ejpam-6798	694	1	a	a	DET
ejpam-6798	694	2	novel	novel	ADJ
ejpam-6798	694	3	algebraic	algebraic	ADJ
ejpam-6798	694	4	structure	structure	NOUN
ejpam-6798	694	5	of	of	ADP
ejpam-6798	694	6	(	(	PUNCT
ejpam-6798	694	7	α	α	X
ejpam-6798	694	8	,	,	PUNCT
ejpam-6798	694	9	β)-complex	β)-complex	ADJ
ejpam-6798	694	10	fuzzy	fuzzy	ADJ
ejpam-6798	694	11	subgroups	subgroup	NOUN
ejpam-6798	694	12	.	.	PUNCT
ejpam-6798	695	1	entropy	entropy	PROPN
ejpam-6798	695	2	,	,	PUNCT
ejpam-6798	695	3	23(8):992–1008	23(8):992–1008	NUM
ejpam-6798	695	4	,	,	PUNCT
ejpam-6798	695	5	2021	2021	NUM
ejpam-6798	695	6	.	.	PUNCT
ejpam-6798	696	1	[	[	X
ejpam-6798	696	2	26	26	NUM
ejpam-6798	696	3	]	]	PUNCT
ejpam-6798	696	4	z.	z.	PROPN
ejpam-6798	696	5	gong	gong	PROPN
ejpam-6798	696	6	and	and	CCONJ
ejpam-6798	696	7	f.	f.	PROPN
ejpam-6798	696	8	wang	wang	PROPN
ejpam-6798	696	9	.	.	PUNCT
ejpam-6798	697	1	operation	operation	NOUN
ejpam-6798	697	2	properties	property	NOUN
ejpam-6798	697	3	and	and	CCONJ
ejpam-6798	697	4	(	(	PUNCT
ejpam-6798	697	5	α	α	NOUN
ejpam-6798	697	6	,	,	PUNCT
ejpam-6798	697	7	β)-equalities	β)-equalities	PUNCT
ejpam-6798	697	8	of	of	ADP
ejpam-6798	697	9	complex	complex	ADJ
ejpam-6798	697	10	intum	intum	NOUN
ejpam-6798	697	11	.	.	PUNCT
ejpam-6798	698	1	jawad	jawad	PROPN
ejpam-6798	698	2	et	et	PROPN
ejpam-6798	698	3	al	al	PROPN
ejpam-6798	698	4	.	.	PUNCT
ejpam-6798	698	5	/	/	SYM
ejpam-6798	698	6	eur	eur	PROPN
ejpam-6798	698	7	.	.	PUNCT
ejpam-6798	699	1	j.	j.	PROPN
ejpam-6798	699	2	pure	pure	PROPN
ejpam-6798	699	3	appl	appl	PROPN
ejpam-6798	699	4	.	.	PROPN
ejpam-6798	699	5	math	math	PROPN
ejpam-6798	699	6	,	,	PUNCT
ejpam-6798	699	7	18	18	NUM
ejpam-6798	699	8	(	(	PUNCT
ejpam-6798	699	9	4	4	NUM
ejpam-6798	699	10	)	)	PUNCT
ejpam-6798	699	11	(	(	PUNCT
ejpam-6798	699	12	2025	2025	NUM
ejpam-6798	699	13	)	)	PUNCT
ejpam-6798	699	14	,	,	PUNCT
ejpam-6798	699	15	6798	6798	NUM
ejpam-6798	699	16	22	22	NUM
ejpam-6798	699	17	of	of	ADP
ejpam-6798	699	18	22	22	NUM
ejpam-6798	699	19	itionistic	itionistic	ADJ
ejpam-6798	699	20	fuzzy	fuzzy	ADJ
ejpam-6798	699	21	sets	set	NOUN
ejpam-6798	699	22	.	.	PUNCT
ejpam-6798	700	1	soft	soft	ADJ
ejpam-6798	700	2	computing	computing	NOUN
ejpam-6798	700	3	,	,	PUNCT
ejpam-6798	700	4	27(8):4369–4391	27(8):4369–4391	NUM
ejpam-6798	700	5	,	,	PUNCT
ejpam-6798	700	6	2023	2023	NUM
ejpam-6798	700	7	.	.	PUNCT
ejpam-6798	701	1	[	[	X
ejpam-6798	701	2	27	27	NUM
ejpam-6798	701	3	]	]	PUNCT
ejpam-6798	701	4	m.	m.	NOUN
ejpam-6798	701	5	gulzar	gulzar	PROPN
ejpam-6798	701	6	,	,	PUNCT
ejpam-6798	701	7	m.	m.	PROPN
ejpam-6798	701	8	h.	h.	PROPN
ejpam-6798	701	9	mateen	mateen	PROPN
ejpam-6798	701	10	,	,	PUNCT
ejpam-6798	701	11	y.	y.	PROPN
ejpam-6798	701	12	m.	m.	PROPN
ejpam-6798	701	13	chu	chu	PROPN
ejpam-6798	701	14	,	,	PUNCT
ejpam-6798	701	15	d.	d.	PROPN
ejpam-6798	701	16	alghazzawi	alghazzawi	PROPN
ejpam-6798	701	17	,	,	PUNCT
ejpam-6798	701	18	and	and	CCONJ
ejpam-6798	701	19	g.	g.	PROPN
ejpam-6798	701	20	abbas	abbas	PROPN
ejpam-6798	701	21	.	.	PUNCT
ejpam-6798	702	1	generalized	generalize	VERB
ejpam-6798	702	2	direct	direct	ADJ
ejpam-6798	702	3	product	product	NOUN
ejpam-6798	702	4	of	of	ADP
ejpam-6798	702	5	complex	complex	ADJ
ejpam-6798	702	6	intuitionistic	intuitionistic	ADJ
ejpam-6798	702	7	fuzzy	fuzzy	ADJ
ejpam-6798	702	8	subrings	subring	NOUN
ejpam-6798	702	9	.	.	PUNCT
ejpam-6798	703	1	international	international	ADJ
ejpam-6798	703	2	journal	journal	PROPN
ejpam-6798	703	3	of	of	ADP
ejpam-6798	703	4	computational	computational	ADJ
ejpam-6798	703	5	intelligence	intelligence	NOUN
ejpam-6798	703	6	systems	system	NOUN
ejpam-6798	703	7	,	,	PUNCT
ejpam-6798	703	8	14(1):582–593	14(1):582–593	NUM
ejpam-6798	703	9	,	,	PUNCT
ejpam-6798	703	10	2021	2021	NUM
ejpam-6798	703	11	.	.	PUNCT
ejpam-6798	704	1	[	[	X
ejpam-6798	704	2	28	28	NUM
ejpam-6798	704	3	]	]	X
ejpam-6798	704	4	l.	l.	PROPN
ejpam-6798	704	5	latif	latif	PROPN
ejpam-6798	704	6	and	and	CCONJ
ejpam-6798	704	7	u.	u.	PROPN
ejpam-6798	704	8	shuaib	shuaib	PROPN
ejpam-6798	704	9	.	.	PUNCT
ejpam-6798	704	10	application	application	NOUN
ejpam-6798	704	11	of	of	ADP
ejpam-6798	704	12	t	t	PROPN
ejpam-6798	704	13	-	-	PUNCT
ejpam-6798	704	14	intuitionistic	intuitionistic	ADJ
ejpam-6798	704	15	fuzzy	fuzzy	ADJ
ejpam-6798	704	16	sub	sub	NOUN
ejpam-6798	704	17	-	-	NOUN
ejpam-6798	704	18	group	group	NOUN
ejpam-6798	704	19	to	to	PART
ejpam-6798	704	20	sylow	sylow	VERB
ejpam-6798	704	21	theory	theory	NOUN
ejpam-6798	704	22	.	.	PUNCT
ejpam-6798	705	1	heliyon	heliyon	NOUN
ejpam-6798	705	2	,	,	PUNCT
ejpam-6798	705	3	9(9):19822–19843	9(9):19822–19843	NUM
ejpam-6798	705	4	,	,	PUNCT
ejpam-6798	705	5	2023	2023	NUM
ejpam-6798	705	6	.	.	PUNCT
ejpam-6798	706	1	[	[	X
ejpam-6798	706	2	29	29	NUM
ejpam-6798	706	3	]	]	PUNCT
ejpam-6798	706	4	m.	m.	NOUN
ejpam-6798	706	5	gulzar	gulzar	PROPN
ejpam-6798	706	6	,	,	PUNCT
ejpam-6798	706	7	d.	d.	PROPN
ejpam-6798	706	8	alghazzawi	alghazzawi	PROPN
ejpam-6798	706	9	,	,	PUNCT
ejpam-6798	706	10	m.	m.	PROPN
ejpam-6798	706	11	h.	h.	PROPN
ejpam-6798	706	12	mateen	mateen	PROPN
ejpam-6798	706	13	,	,	PUNCT
ejpam-6798	706	14	and	and	CCONJ
ejpam-6798	706	15	n.	n.	PROPN
ejpam-6798	706	16	kausar	kausar	PROPN
ejpam-6798	706	17	.	.	PUNCT
ejpam-6798	707	1	a	a	DET
ejpam-6798	707	2	certain	certain	ADJ
ejpam-6798	707	3	class	class	NOUN
ejpam-6798	707	4	of	of	ADP
ejpam-6798	707	5	tintuitionistic	tintuitionistic	ADJ
ejpam-6798	707	6	fuzzy	fuzzy	ADJ
ejpam-6798	707	7	subgroups	subgroup	NOUN
ejpam-6798	707	8	.	.	PUNCT
ejpam-6798	708	1	ieee	ieee	NOUN
ejpam-6798	708	2	access	access	NOUN
ejpam-6798	708	3	,	,	PUNCT
ejpam-6798	708	4	8(1):163260–163268	8(1):163260–163268	NUM
ejpam-6798	708	5	,	,	PUNCT
ejpam-6798	708	6	2020	2020	NUM
ejpam-6798	708	7	.	.	PUNCT
ejpam-6798	709	1	[	[	X
ejpam-6798	709	2	30	30	NUM
ejpam-6798	709	3	]	]	PUNCT
ejpam-6798	709	4	a.	a.	PROPN
ejpam-6798	709	5	al	al	PROPN
ejpam-6798	709	6	-	-	PROPN
ejpam-6798	709	7	husban	husban	PROPN
ejpam-6798	709	8	and	and	CCONJ
ejpam-6798	709	9	a.	a.	PROPN
ejpam-6798	709	10	r.	r.	PROPN
ejpam-6798	709	11	salleh	salleh	PROPN
ejpam-6798	709	12	.	.	PUNCT
ejpam-6798	710	1	complex	complex	ADJ
ejpam-6798	710	2	fuzzy	fuzzy	ADJ
ejpam-6798	710	3	group	group	NOUN
ejpam-6798	710	4	based	base	VERB
ejpam-6798	710	5	on	on	ADP
ejpam-6798	710	6	complex	complex	ADJ
ejpam-6798	710	7	fuzzy	fuzzy	ADJ
ejpam-6798	710	8	space	space	NOUN
ejpam-6798	710	9	.	.	PUNCT
ejpam-6798	711	1	global	global	ADJ
ejpam-6798	711	2	journal	journal	PROPN
ejpam-6798	711	3	of	of	ADP
ejpam-6798	711	4	pure	pure	ADJ
ejpam-6798	711	5	and	and	CCONJ
ejpam-6798	711	6	applied	applied	ADJ
ejpam-6798	711	7	mathematics	mathematic	NOUN
ejpam-6798	711	8	,	,	PUNCT
ejpam-6798	711	9	12(1):1433–1450	12(1):1433–1450	NUM
ejpam-6798	711	10	,	,	PUNCT
ejpam-6798	711	11	2016	2016	NUM
ejpam-6798	711	12	.	.	PUNCT
ejpam-6798	712	1	[	[	X
ejpam-6798	712	2	31	31	NUM
ejpam-6798	712	3	]	]	PUNCT
ejpam-6798	712	4	a.	a.	PROPN
ejpam-6798	712	5	ali	ali	PROPN
ejpam-6798	712	6	,	,	PUNCT
ejpam-6798	712	7	m.	m.	PROPN
ejpam-6798	712	8	h.	h.	PROPN
ejpam-6798	712	9	mateen	mateen	PROPN
ejpam-6798	712	10	,	,	PUNCT
ejpam-6798	712	11	q.	q.	PROPN
ejpam-6798	712	12	xin	xin	PROPN
ejpam-6798	712	13	,	,	PUNCT
ejpam-6798	712	14	t.	t.	PROPN
ejpam-6798	712	15	alsuraiheed	alsuraiheed	NOUN
ejpam-6798	712	16	,	,	PUNCT
ejpam-6798	712	17	and	and	CCONJ
ejpam-6798	712	18	g.	g.	PROPN
ejpam-6798	712	19	alhamzi	alhamzi	PROPN
ejpam-6798	712	20	.	.	PUNCT
ejpam-6798	713	1	(	(	PUNCT
ejpam-6798	713	2	ϵ	ϵ	X
ejpam-6798	713	3	,	,	PUNCT
ejpam-6798	713	4	δ)-complex	δ)-complex	X
ejpam-6798	713	5	anti	anti	X
ejpam-6798	713	6	fuzzy	fuzzy	ADJ
ejpam-6798	713	7	subgroups	subgroup	NOUN
ejpam-6798	713	8	and	and	CCONJ
ejpam-6798	713	9	their	their	PRON
ejpam-6798	713	10	applications	application	NOUN
ejpam-6798	713	11	.	.	PUNCT
ejpam-6798	714	1	aims	aim	VERB
ejpam-6798	714	2	mathematics	mathematic	NOUN
ejpam-6798	714	3	,	,	PUNCT
ejpam-6798	714	4	9(5):11580–11595	9(5):11580–11595	NUM
ejpam-6798	714	5	,	,	PUNCT
ejpam-6798	714	6	2024	2024	NUM
ejpam-6798	714	7	.	.	PUNCT
ejpam-6798	715	1	[	[	X
ejpam-6798	715	2	32	32	NUM
ejpam-6798	715	3	]	]	PUNCT
ejpam-6798	715	4	m.	m.	NOUN
ejpam-6798	715	5	gulzar	gulzar	PROPN
ejpam-6798	715	6	,	,	PUNCT
ejpam-6798	715	7	m.	m.	PROPN
ejpam-6798	715	8	h.	h.	PROPN
ejpam-6798	715	9	mateen	mateen	PROPN
ejpam-6798	715	10	,	,	PUNCT
ejpam-6798	715	11	d.	d.	PROPN
ejpam-6798	715	12	alghazzawi	alghazzawi	PROPN
ejpam-6798	715	13	,	,	PUNCT
ejpam-6798	715	14	and	and	CCONJ
ejpam-6798	715	15	n.	n.	PROPN
ejpam-6798	715	16	kausar	kausar	PROPN
ejpam-6798	715	17	.	.	PUNCT
ejpam-6798	716	1	a	a	DET
ejpam-6798	716	2	novel	novel	ADJ
ejpam-6798	716	3	applications	application	NOUN
ejpam-6798	716	4	of	of	ADP
ejpam-6798	716	5	complex	complex	ADJ
ejpam-6798	716	6	intuitionistic	intuitionistic	ADJ
ejpam-6798	716	7	fuzzy	fuzzy	ADJ
ejpam-6798	716	8	sets	set	NOUN
ejpam-6798	716	9	in	in	ADP
ejpam-6798	716	10	group	group	NOUN
ejpam-6798	716	11	theory	theory	NOUN
ejpam-6798	716	12	.	.	PUNCT
ejpam-6798	717	1	ieee	ieee	NOUN
ejpam-6798	717	2	access	access	NOUN
ejpam-6798	717	3	,	,	PUNCT
ejpam-6798	717	4	8(1):196075–196085	8(1):196075–196085	NUM
ejpam-6798	717	5	,	,	PUNCT
ejpam-6798	717	6	2020	2020	NUM
ejpam-6798	717	7	.	.	PUNCT
ejpam-6798	718	1	[	[	X
ejpam-6798	718	2	33	33	NUM
ejpam-6798	718	3	]	]	PUNCT
ejpam-6798	718	4	m.	m.	PROPN
ejpam-6798	718	5	jawad	jawad	PROPN
ejpam-6798	718	6	,	,	PUNCT
ejpam-6798	718	7	n.	n.	PROPN
ejpam-6798	718	8	nigar	nigar	PROPN
ejpam-6798	718	9	,	,	PUNCT
ejpam-6798	718	10	s.	s.	PROPN
ejpam-6798	718	11	hoskova	hoskova	PROPN
ejpam-6798	718	12	-	-	PUNCT
ejpam-6798	718	13	mayerova	mayerova	PROPN
ejpam-6798	718	14	,	,	PUNCT
ejpam-6798	718	15	b.	b.	PROPN
ejpam-6798	718	16	davvaz	davvaz	PROPN
ejpam-6798	718	17	,	,	PUNCT
ejpam-6798	718	18	and	and	CCONJ
ejpam-6798	718	19	m.	m.	PROPN
ejpam-6798	718	20	h.	h.	PROPN
ejpam-6798	718	21	mateen	mateen	PROPN
ejpam-6798	718	22	.	.	PUNCT
ejpam-6798	719	1	fundamental	fundamental	ADJ
ejpam-6798	719	2	theorems	theorem	NOUN
ejpam-6798	719	3	of	of	ADP
ejpam-6798	719	4	group	group	NOUN
ejpam-6798	719	5	isomorphism	isomorphism	NOUN
ejpam-6798	719	6	under	under	ADP
ejpam-6798	719	7	the	the	DET
ejpam-6798	719	8	framework	framework	NOUN
ejpam-6798	719	9	of	of	ADP
ejpam-6798	719	10	complex	complex	ADJ
ejpam-6798	719	11	intuitionistic	intuitionistic	ADJ
ejpam-6798	719	12	fuzzy	fuzzy	ADJ
ejpam-6798	719	13	set	set	NOUN
ejpam-6798	719	14	.	.	PUNCT
ejpam-6798	720	1	aims	aim	VERB
ejpam-6798	720	2	mathematics	mathematic	NOUN
ejpam-6798	720	3	,	,	PUNCT
ejpam-6798	720	4	10(1):1900–1920	10(1):1900–1920	NUM
ejpam-6798	720	5	,	,	PUNCT
ejpam-6798	720	6	2025	2025	NUM
ejpam-6798	720	7	.	.	PUNCT
ejpam-6798	721	1	[	[	X
ejpam-6798	721	2	34	34	NUM
ejpam-6798	721	3	]	]	X
ejpam-6798	721	4	y.	y.	PROPN
ejpam-6798	721	5	b.	b.	PROPN
ejpam-6798	721	6	jun	jun	PROPN
ejpam-6798	721	7	and	and	CCONJ
ejpam-6798	721	8	x.	x.	PROPN
ejpam-6798	721	9	l.	l.	PROPN
ejpam-6798	721	10	xin	xin	PROPN
ejpam-6798	721	11	.	.	PUNCT
ejpam-6798	722	1	complex	complex	ADJ
ejpam-6798	722	2	fuzzy	fuzzy	ADJ
ejpam-6798	722	3	sets	set	NOUN
ejpam-6798	722	4	with	with	ADP
ejpam-6798	722	5	application	application	NOUN
ejpam-6798	722	6	in	in	ADP
ejpam-6798	722	7	bck	bck	PROPN
ejpam-6798	722	8	/	/	SYM
ejpam-6798	722	9	bci	bci	NOUN
ejpam-6798	722	10	-	-	PUNCT
ejpam-6798	722	11	algebras	algebra	NOUN
ejpam-6798	722	12	.	.	PUNCT
ejpam-6798	723	1	bulletin	bulletin	NOUN
ejpam-6798	723	2	of	of	ADP
ejpam-6798	723	3	the	the	DET
ejpam-6798	723	4	section	section	NOUN
ejpam-6798	723	5	of	of	ADP
ejpam-6798	723	6	logic	logic	NOUN
ejpam-6798	723	7	,	,	PUNCT
ejpam-6798	723	8	48(3):173–185	48(3):173–185	ADJ
ejpam-6798	723	9	,	,	PUNCT
ejpam-6798	723	10	2019	2019	NUM
ejpam-6798	723	11	.	.	PUNCT
ejpam-6798	724	1	[	[	X
ejpam-6798	724	2	35	35	NUM
ejpam-6798	724	3	]	]	PUNCT
ejpam-6798	724	4	t.	t.	NOUN
ejpam-6798	724	5	senapati	senapati	PROPN
ejpam-6798	724	6	,	,	PUNCT
ejpam-6798	724	7	m.	m.	NOUN
ejpam-6798	724	8	bhowmik	bhowmik	ADJ
ejpam-6798	724	9	,	,	PUNCT
ejpam-6798	724	10	and	and	CCONJ
ejpam-6798	724	11	m.	m.	NOUN
ejpam-6798	724	12	pal	pal	NOUN
ejpam-6798	724	13	.	.	PUNCT
ejpam-6798	725	1	intuitionistic	intuitionistic	ADJ
ejpam-6798	725	2	fuzzifications	fuzzification	NOUN
ejpam-6798	725	3	of	of	ADP
ejpam-6798	725	4	ideals	ideal	NOUN
ejpam-6798	725	5	in	in	ADP
ejpam-6798	725	6	bgalgebras	bgalgebras	PROPN
ejpam-6798	725	7	.	.	PUNCT
ejpam-6798	726	1	mathematica	mathematica	PROPN
ejpam-6798	726	2	aeterna	aeterna	PROPN
ejpam-6798	726	3	,	,	PUNCT
ejpam-6798	726	4	2(9):761–778	2(9):761–778	NUM
ejpam-6798	726	5	,	,	PUNCT
ejpam-6798	726	6	2012	2012	NUM
ejpam-6798	726	7	.	.	PUNCT
ejpam-6798	727	1	[	[	X
ejpam-6798	727	2	36	36	NUM
ejpam-6798	727	3	]	]	PUNCT
ejpam-6798	727	4	k.	k.	PROPN
ejpam-6798	727	5	hur	hur	PROPN
ejpam-6798	727	6	,	,	PUNCT
ejpam-6798	727	7	h.	h.	PROPN
ejpam-6798	727	8	w.	w.	PROPN
ejpam-6798	727	9	kang	kang	PROPN
ejpam-6798	727	10	,	,	PUNCT
ejpam-6798	727	11	and	and	CCONJ
ejpam-6798	727	12	h.	h.	PROPN
ejpam-6798	727	13	k.	k.	PROPN
ejpam-6798	727	14	song	song	PROPN
ejpam-6798	727	15	.	.	PUNCT
ejpam-6798	728	1	intuitionistic	intuitionistic	ADJ
ejpam-6798	728	2	fuzzy	fuzzy	ADJ
ejpam-6798	728	3	subgroups	subgroup	NOUN
ejpam-6798	728	4	and	and	CCONJ
ejpam-6798	728	5	subrings	subring	NOUN
ejpam-6798	728	6	.	.	PUNCT
ejpam-6798	729	1	honam	honam	PROPN
ejpam-6798	729	2	mathematical	mathematical	PROPN
ejpam-6798	729	3	journal	journal	PROPN
ejpam-6798	729	4	,	,	PUNCT
ejpam-6798	729	5	25(1):19–41	25(1):19–41	NUM
ejpam-6798	729	6	,	,	PUNCT
ejpam-6798	729	7	2003	2003	NUM
ejpam-6798	729	8	.	.	PUNCT
ejpam-6798	730	1	[	[	X
ejpam-6798	730	2	37	37	NUM
ejpam-6798	730	3	]	]	PUNCT
ejpam-6798	730	4	a.	a.	NOUN
ejpam-6798	730	5	m.	m.	PROPN
ejpam-6798	730	6	d.	d.	PROPN
ejpam-6798	730	7	j.	j.	PROPN
ejpam-6798	730	8	s.	s.	PROPN
ejpam-6798	730	9	alkouri	alkouri	PROPN
ejpam-6798	730	10	and	and	CCONJ
ejpam-6798	730	11	a.	a.	PROPN
ejpam-6798	730	12	r.	r.	PROPN
ejpam-6798	730	13	salleh	salleh	PROPN
ejpam-6798	730	14	.	.	PUNCT
ejpam-6798	731	1	complex	complex	ADJ
ejpam-6798	731	2	intuitionistic	intuitionistic	ADJ
ejpam-6798	731	3	fuzzy	fuzzy	ADJ
ejpam-6798	731	4	sets	set	NOUN
ejpam-6798	731	5	.	.	PUNCT
ejpam-6798	732	1	in	in	ADP
ejpam-6798	732	2	aip	aip	PROPN
ejpam-6798	732	3	conference	conference	NOUN
ejpam-6798	732	4	proceedings	proceeding	NOUN
ejpam-6798	732	5	,	,	PUNCT
ejpam-6798	732	6	volume	volume	NOUN
ejpam-6798	732	7	1482	1482	NUM
ejpam-6798	732	8	,	,	PUNCT
ejpam-6798	732	9	pages	page	NOUN
ejpam-6798	732	10	464–470	464–470	NUM
ejpam-6798	732	11	.	.	PUNCT
ejpam-6798	733	1	american	american	PROPN
ejpam-6798	733	2	institute	institute	PROPN
ejpam-6798	733	3	of	of	ADP
ejpam-6798	733	4	physics	physics	PROPN
ejpam-6798	733	5	,	,	PUNCT
ejpam-6798	733	6	2012	2012	NUM
ejpam-6798	733	7	.	.	PUNCT
ejpam-6798	734	1	[	[	X
ejpam-6798	734	2	38	38	NUM
ejpam-6798	734	3	]	]	PUNCT
ejpam-6798	734	4	m.	m.	NOUN
ejpam-6798	734	5	gulzar	gulzar	PROPN
ejpam-6798	734	6	,	,	PUNCT
ejpam-6798	734	7	d.	d.	PROPN
ejpam-6798	734	8	alghazzawi	alghazzawi	PROPN
ejpam-6798	734	9	,	,	PUNCT
ejpam-6798	734	10	m.	m.	PROPN
ejpam-6798	734	11	h.	h.	PROPN
ejpam-6798	734	12	mateen	mateen	PROPN
ejpam-6798	734	13	,	,	PUNCT
ejpam-6798	734	14	and	and	CCONJ
ejpam-6798	734	15	m.	m.	PROPN
ejpam-6798	734	16	premkumar	premkumar	PROPN
ejpam-6798	734	17	.	.	PUNCT
ejpam-6798	735	1	on	on	ADP
ejpam-6798	735	2	some	some	DET
ejpam-6798	735	3	characterization	characterization	NOUN
ejpam-6798	735	4	of	of	ADP
ejpam-6798	735	5	q	q	ADJ
ejpam-6798	735	6	-	-	PUNCT
ejpam-6798	735	7	complex	complex	ADJ
ejpam-6798	735	8	fuzzy	fuzzy	ADJ
ejpam-6798	735	9	sub	sub	NOUN
ejpam-6798	735	10	-	-	NOUN
ejpam-6798	735	11	rings	ring	NOUN
ejpam-6798	735	12	.	.	PUNCT
ejpam-6798	735	13	journal	journal	PROPN
ejpam-6798	735	14	of	of	ADP
ejpam-6798	735	15	mathematics	mathematics	PROPN
ejpam-6798	735	16	and	and	CCONJ
ejpam-6798	735	17	computer	computer	NOUN
ejpam-6798	735	18	science	science	NOUN
ejpam-6798	735	19	,	,	PUNCT
ejpam-6798	735	20	22(1):295–305	22(1):295–305	NOUN
ejpam-6798	735	21	,	,	PUNCT
ejpam-6798	735	22	2021	2021	NUM
ejpam-6798	735	23	.	.	PUNCT