id	sid	tid	token	lemma	pos
ejpam-3228	1	1	european	european	PROPN
ejpam-3228	1	2	journal	journal	PROPN
ejpam-3228	1	3	of	of	ADP
ejpam-3228	1	4	pure	pure	ADJ
ejpam-3228	1	5	and	and	CCONJ
ejpam-3228	1	6	applied	apply	VERB
ejpam-3228	1	7	mathematics	mathematic	NOUN
ejpam-3228	1	8	vol	vol	NOUN
ejpam-3228	1	9	.	.	PUNCT
ejpam-3228	2	1	11	11	NUM
ejpam-3228	2	2	,	,	PUNCT
ejpam-3228	2	3	no	no	INTJ
ejpam-3228	2	4	.	.	NOUN
ejpam-3228	2	5	2	2	NUM
ejpam-3228	2	6	,	,	PUNCT
ejpam-3228	2	7	2018	2018	NUM
ejpam-3228	2	8	,	,	PUNCT
ejpam-3228	2	9	517	517	NUM
ejpam-3228	2	10	-	-	SYM
ejpam-3228	2	11	536	536	NUM
ejpam-3228	2	12	issn	issn	PROPN
ejpam-3228	2	13	1307	1307	NUM
ejpam-3228	2	14	-	-	SYM
ejpam-3228	2	15	5543	5543	NUM
ejpam-3228	2	16	–	–	PUNCT
ejpam-3228	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3228	2	18	published	publish	VERB
ejpam-3228	2	19	by	by	ADP
ejpam-3228	2	20	new	new	PROPN
ejpam-3228	2	21	york	york	PROPN
ejpam-3228	2	22	business	business	PROPN
ejpam-3228	2	23	global	global	PROPN
ejpam-3228	2	24	soft	soft	ADJ
ejpam-3228	2	25	uni	uni	ADJ
ejpam-3228	2	26	-	-	PUNCT
ejpam-3228	2	27	abel	abel	NOUN
ejpam-3228	2	28	-	-	PUNCT
ejpam-3228	2	29	grassmann	grassmann	PROPN
ejpam-3228	2	30	’s	’s	PART
ejpam-3228	2	31	groups	group	NOUN
ejpam-3228	2	32	aman	aman	VERB
ejpam-3228	2	33	ullah1,∗	ullah1,∗	PROPN
ejpam-3228	2	34	,	,	PUNCT
ejpam-3228	2	35	faruk	faruk	PROPN
ejpam-3228	2	36	karaaslan2	karaaslan2	PROPN
ejpam-3228	2	37	,	,	PUNCT
ejpam-3228	2	38	imtiaz	imtiaz	PROPN
ejpam-3228	2	39	ahmad1	ahmad1	PROPN
ejpam-3228	3	1	1	1	NUM
ejpam-3228	3	2	department	department	NOUN
ejpam-3228	3	3	of	of	ADP
ejpam-3228	3	4	mathematics	mathematic	NOUN
ejpam-3228	3	5	,	,	PUNCT
ejpam-3228	3	6	faculty	faculty	NOUN
ejpam-3228	3	7	of	of	ADP
ejpam-3228	3	8	sciences	science	NOUN
ejpam-3228	3	9	,	,	PUNCT
ejpam-3228	3	10	university	university	NOUN
ejpam-3228	3	11	of	of	ADP
ejpam-3228	3	12	malakand	malakand	PROPN
ejpam-3228	3	13	,	,	PUNCT
ejpam-3228	3	14	chakdara	chakdara	NOUN
ejpam-3228	3	15	dir	dir	NOUN
ejpam-3228	3	16	lower	lower	ADV
ejpam-3228	3	17	,	,	PUNCT
ejpam-3228	3	18	pakistan	pakistan	PROPN
ejpam-3228	3	19	2	2	NUM
ejpam-3228	3	20	department	department	NOUN
ejpam-3228	3	21	of	of	ADP
ejpam-3228	3	22	mathematics	mathematic	NOUN
ejpam-3228	3	23	,	,	PUNCT
ejpam-3228	3	24	faculty	faculty	NOUN
ejpam-3228	3	25	of	of	ADP
ejpam-3228	3	26	sciences	science	NOUN
ejpam-3228	3	27	,	,	PUNCT
ejpam-3228	3	28	çankırı	çankırı	PROPN
ejpam-3228	3	29	karatekin	karatekin	PROPN
ejpam-3228	3	30	university	university	PROPN
ejpam-3228	3	31	,	,	PUNCT
ejpam-3228	3	32	18100	18100	NUM
ejpam-3228	3	33	,	,	PUNCT
ejpam-3228	3	34	çankırı	çankırı	PROPN
ejpam-3228	3	35	,	,	PUNCT
ejpam-3228	3	36	türkiye	türkiye	NOUN
ejpam-3228	3	37	abstract	abstract	NOUN
ejpam-3228	3	38	.	.	PUNCT
ejpam-3228	4	1	in	in	ADP
ejpam-3228	4	2	this	this	DET
ejpam-3228	4	3	paper	paper	NOUN
ejpam-3228	4	4	,	,	PUNCT
ejpam-3228	4	5	we	we	PRON
ejpam-3228	4	6	define	define	VERB
ejpam-3228	4	7	soft	soft	ADJ
ejpam-3228	4	8	union	union	NOUN
ejpam-3228	4	9	ag	ag	PROPN
ejpam-3228	4	10	-	-	PUNCT
ejpam-3228	4	11	group	group	NOUN
ejpam-3228	4	12	(	(	PUNCT
ejpam-3228	4	13	abbreviated	abbreviate	VERB
ejpam-3228	4	14	as	as	ADP
ejpam-3228	4	15	soft	soft	ADJ
ejpam-3228	4	16	uni	uni	ADJ
ejpam-3228	4	17	-	-	PUNCT
ejpam-3228	4	18	ag	ag	NOUN
ejpam-3228	4	19	-	-	PUNCT
ejpam-3228	4	20	group	group	NOUN
ejpam-3228	4	21	)	)	PUNCT
ejpam-3228	4	22	.	.	PUNCT
ejpam-3228	5	1	we	we	PRON
ejpam-3228	5	2	also	also	ADV
ejpam-3228	5	3	define	define	VERB
ejpam-3228	5	4	e	e	NOUN
ejpam-3228	5	5	-	-	NOUN
ejpam-3228	5	6	set	set	ADJ
ejpam-3228	5	7	and	and	CCONJ
ejpam-3228	5	8	α	α	NOUN
ejpam-3228	5	9	-	-	NOUN
ejpam-3228	5	10	inclusion	inclusion	NOUN
ejpam-3228	5	11	of	of	ADP
ejpam-3228	5	12	soft	soft	ADJ
ejpam-3228	5	13	uni	uni	ADJ
ejpam-3228	5	14	-	-	PUNCT
ejpam-3228	5	15	ag	ag	ADJ
ejpam-3228	5	16	-	-	PUNCT
ejpam-3228	5	17	groups	group	NOUN
ejpam-3228	5	18	,	,	PUNCT
ejpam-3228	5	19	normal	normal	ADJ
ejpam-3228	5	20	soft	soft	ADJ
ejpam-3228	5	21	uni	uni	ADJ
ejpam-3228	5	22	-	-	PUNCT
ejpam-3228	5	23	ag	ag	NOUN
ejpam-3228	5	24	-	-	PUNCT
ejpam-3228	5	25	subgroups	subgroup	NOUN
ejpam-3228	5	26	,	,	PUNCT
ejpam-3228	5	27	conjugate	conjugate	ADJ
ejpam-3228	5	28	of	of	ADP
ejpam-3228	5	29	soft	soft	ADJ
ejpam-3228	5	30	uni	uni	ADJ
ejpam-3228	5	31	-	-	PUNCT
ejpam-3228	5	32	ag	ag	ADJ
ejpam-3228	5	33	-	-	PUNCT
ejpam-3228	5	34	groups	group	NOUN
ejpam-3228	5	35	and	and	CCONJ
ejpam-3228	5	36	commutators	commutator	NOUN
ejpam-3228	5	37	of	of	ADP
ejpam-3228	5	38	ag	ag	PROPN
ejpam-3228	5	39	-	-	PUNCT
ejpam-3228	5	40	groups	group	NOUN
ejpam-3228	5	41	.	.	PUNCT
ejpam-3228	6	1	we	we	PRON
ejpam-3228	6	2	investigate	investigate	VERB
ejpam-3228	6	3	various	various	ADJ
ejpam-3228	6	4	properties	property	NOUN
ejpam-3228	6	5	of	of	ADP
ejpam-3228	6	6	these	these	DET
ejpam-3228	6	7	notions	notion	NOUN
ejpam-3228	6	8	and	and	CCONJ
ejpam-3228	6	9	provide	provide	VERB
ejpam-3228	6	10	a	a	DET
ejpam-3228	6	11	variety	variety	NOUN
ejpam-3228	6	12	of	of	ADP
ejpam-3228	6	13	relevant	relevant	ADJ
ejpam-3228	6	14	examples	example	NOUN
ejpam-3228	6	15	that	that	PRON
ejpam-3228	6	16	are	be	AUX
ejpam-3228	6	17	produced	produce	VERB
ejpam-3228	6	18	by	by	ADP
ejpam-3228	6	19	a	a	DET
ejpam-3228	6	20	computer	computer	NOUN
ejpam-3228	6	21	package	package	NOUN
ejpam-3228	6	22	gap	gap	NOUN
ejpam-3228	6	23	to	to	PART
ejpam-3228	6	24	illustrate	illustrate	VERB
ejpam-3228	6	25	these	these	DET
ejpam-3228	6	26	notations	notation	NOUN
ejpam-3228	6	27	.	.	PUNCT
ejpam-3228	7	1	2010	2010	NUM
ejpam-3228	7	2	mathematics	mathematic	NOUN
ejpam-3228	7	3	subject	subject	NOUN
ejpam-3228	7	4	classifications	classification	NOUN
ejpam-3228	7	5	:	:	PUNCT
ejpam-3228	7	6	03exx	03exx	PROPN
ejpam-3228	7	7	,	,	PUNCT
ejpam-3228	7	8	20bxx	20bxx	PROPN
ejpam-3228	7	9	,	,	PUNCT
ejpam-3228	7	10	03e20	03e20	NUM
ejpam-3228	7	11	key	key	ADJ
ejpam-3228	7	12	words	word	NOUN
ejpam-3228	7	13	and	and	CCONJ
ejpam-3228	7	14	phrases	phrase	NOUN
ejpam-3228	7	15	:	:	PUNCT
ejpam-3228	7	16	soft	soft	ADJ
ejpam-3228	7	17	set	set	NOUN
ejpam-3228	7	18	,	,	PUNCT
ejpam-3228	7	19	soft	soft	ADJ
ejpam-3228	7	20	uni	uni	ADJ
ejpam-3228	7	21	-	-	PUNCT
ejpam-3228	7	22	ag	ag	NOUN
ejpam-3228	7	23	-	-	PUNCT
ejpam-3228	7	24	group	group	NOUN
ejpam-3228	7	25	,	,	PUNCT
ejpam-3228	7	26	α	α	NOUN
ejpam-3228	7	27	-	-	NOUN
ejpam-3228	7	28	inclusion	inclusion	NOUN
ejpam-3228	7	29	,	,	PUNCT
ejpam-3228	7	30	conjugate	conjugate	VERB
ejpam-3228	7	31	normal	normal	ADJ
ejpam-3228	7	32	soft	soft	ADJ
ejpam-3228	7	33	uniag	uniag	NOUN
ejpam-3228	7	34	-	-	NOUN
ejpam-3228	7	35	group	group	NOUN
ejpam-3228	7	36	,	,	PUNCT
ejpam-3228	7	37	normal	normal	ADJ
ejpam-3228	7	38	soft	soft	ADJ
ejpam-3228	7	39	uni	uni	ADJ
ejpam-3228	7	40	-	-	PUNCT
ejpam-3228	7	41	ag	ag	NOUN
ejpam-3228	7	42	-	-	PUNCT
ejpam-3228	7	43	subgroup	subgroup	NOUN
ejpam-3228	7	44	.	.	PUNCT
ejpam-3228	8	1	1	1	X
ejpam-3228	8	2	.	.	X
ejpam-3228	8	3	introduction	introduction	NOUN
ejpam-3228	8	4	in	in	ADP
ejpam-3228	8	5	1999	1999	NUM
ejpam-3228	8	6	,	,	PUNCT
ejpam-3228	8	7	soft	soft	ADJ
ejpam-3228	8	8	set	set	NOUN
ejpam-3228	8	9	theory	theory	NOUN
ejpam-3228	8	10	was	be	AUX
ejpam-3228	8	11	proposed	propose	VERB
ejpam-3228	8	12	by	by	ADP
ejpam-3228	8	13	molodtsov	molodtsov	NOUN
ejpam-3228	8	14	[	[	X
ejpam-3228	8	15	1	1	NUM
ejpam-3228	8	16	]	]	PUNCT
ejpam-3228	8	17	as	as	ADP
ejpam-3228	8	18	an	an	DET
ejpam-3228	8	19	alternative	alternative	ADJ
ejpam-3228	8	20	approach	approach	NOUN
ejpam-3228	8	21	to	to	ADP
ejpam-3228	8	22	fuzzy	fuzzy	ADJ
ejpam-3228	8	23	set	set	ADJ
ejpam-3228	8	24	and	and	CCONJ
ejpam-3228	8	25	intuitionistic	intuitionistic	ADJ
ejpam-3228	8	26	fuzzy	fuzzy	ADJ
ejpam-3228	8	27	set	set	NOUN
ejpam-3228	8	28	theories	theory	NOUN
ejpam-3228	8	29	.	.	PUNCT
ejpam-3228	9	1	this	this	DET
ejpam-3228	9	2	study	study	NOUN
ejpam-3228	9	3	of	of	ADP
ejpam-3228	9	4	molodtsov	molodtsov	NOUN
ejpam-3228	9	5	provided	provide	VERB
ejpam-3228	9	6	a	a	DET
ejpam-3228	9	7	general	general	ADJ
ejpam-3228	9	8	skeleton	skeleton	NOUN
ejpam-3228	9	9	to	to	ADP
ejpam-3228	9	10	researchers	researcher	NOUN
ejpam-3228	9	11	that	that	PRON
ejpam-3228	9	12	naturally	naturally	ADV
ejpam-3228	9	13	requires	require	VERB
ejpam-3228	9	14	a	a	DET
ejpam-3228	9	15	study	study	NOUN
ejpam-3228	9	16	on	on	ADP
ejpam-3228	9	17	algebraic	algebraic	ADJ
ejpam-3228	9	18	structures	structure	NOUN
ejpam-3228	9	19	.	.	PUNCT
ejpam-3228	10	1	after	after	ADP
ejpam-3228	10	2	that	that	PRON
ejpam-3228	10	3	,	,	PUNCT
ejpam-3228	10	4	maji	maji	PROPN
ejpam-3228	10	5	et	et	PROPN
ejpam-3228	10	6	al	al	PROPN
ejpam-3228	10	7	.	.	PUNCT
ejpam-3228	11	1	[	[	X
ejpam-3228	11	2	2	2	NUM
ejpam-3228	11	3	]	]	PUNCT
ejpam-3228	11	4	defined	define	VERB
ejpam-3228	11	5	set	set	VERB
ejpam-3228	11	6	theoretical	theoretical	ADJ
ejpam-3228	11	7	operations	operation	NOUN
ejpam-3228	11	8	of	of	ADP
ejpam-3228	11	9	soft	soft	ADJ
ejpam-3228	11	10	sets	set	NOUN
ejpam-3228	11	11	.	.	PUNCT
ejpam-3228	12	1	in	in	ADP
ejpam-3228	12	2	2010	2010	NUM
ejpam-3228	12	3	,	,	PUNCT
ejpam-3228	12	4	çağman	çağman	NOUN
ejpam-3228	12	5	and	and	CCONJ
ejpam-3228	12	6	enginoğlu	enginoğlu	NOUN
ejpam-3228	13	1	[	[	X
ejpam-3228	13	2	3	3	NUM
ejpam-3228	13	3	]	]	PUNCT
ejpam-3228	13	4	redefined	redefine	VERB
ejpam-3228	13	5	soft	soft	ADJ
ejpam-3228	13	6	set	set	ADJ
ejpam-3228	13	7	operations	operation	NOUN
ejpam-3228	13	8	in	in	ADP
ejpam-3228	13	9	decision	decision	NOUN
ejpam-3228	13	10	making	make	VERB
ejpam-3228	13	11	problems	problem	NOUN
ejpam-3228	13	12	.	.	PUNCT
ejpam-3228	14	1	ali	ali	PROPN
ejpam-3228	14	2	et	et	PROPN
ejpam-3228	14	3	al	al	PROPN
ejpam-3228	14	4	.	.	PUNCT
ejpam-3228	15	1	[	[	X
ejpam-3228	15	2	4	4	NUM
ejpam-3228	15	3	]	]	PUNCT
ejpam-3228	15	4	,	,	PUNCT
ejpam-3228	15	5	sezgin	sezgin	VERB
ejpam-3228	15	6	and	and	CCONJ
ejpam-3228	15	7	atagün	atagün	NOUN
ejpam-3228	16	1	[	[	X
ejpam-3228	16	2	5	5	NUM
ejpam-3228	16	3	]	]	PUNCT
ejpam-3228	16	4	studied	study	VERB
ejpam-3228	16	5	some	some	DET
ejpam-3228	16	6	new	new	ADJ
ejpam-3228	16	7	operations	operation	NOUN
ejpam-3228	16	8	on	on	ADP
ejpam-3228	16	9	soft	soft	ADJ
ejpam-3228	16	10	sets	set	NOUN
ejpam-3228	16	11	.	.	PUNCT
ejpam-3228	17	1	the	the	DET
ejpam-3228	17	2	first	first	ADJ
ejpam-3228	17	3	study	study	NOUN
ejpam-3228	17	4	on	on	ADP
ejpam-3228	17	5	algebraic	algebraic	ADJ
ejpam-3228	17	6	structures	structure	NOUN
ejpam-3228	17	7	of	of	ADP
ejpam-3228	17	8	soft	soft	ADJ
ejpam-3228	17	9	sets	set	NOUN
ejpam-3228	17	10	was	be	AUX
ejpam-3228	17	11	made	make	VERB
ejpam-3228	17	12	by	by	ADP
ejpam-3228	17	13	aktaş	aktaş	PROPN
ejpam-3228	17	14	and	and	CCONJ
ejpam-3228	17	15	çağman	çağman	NOUN
ejpam-3228	18	1	[	[	X
ejpam-3228	18	2	6	6	NUM
ejpam-3228	18	3	]	]	PUNCT
ejpam-3228	18	4	in	in	ADP
ejpam-3228	18	5	2007	2007	NUM
ejpam-3228	18	6	.	.	PUNCT
ejpam-3228	19	1	they	they	PRON
ejpam-3228	19	2	defined	define	VERB
ejpam-3228	19	3	concept	concept	NOUN
ejpam-3228	19	4	of	of	ADP
ejpam-3228	19	5	soft	soft	ADJ
ejpam-3228	19	6	groups	group	NOUN
ejpam-3228	19	7	.	.	PUNCT
ejpam-3228	20	1	after	after	ADP
ejpam-3228	20	2	aktaş	aktaş	PROPN
ejpam-3228	20	3	and	and	CCONJ
ejpam-3228	20	4	çağman	çağman	NOUN
ejpam-3228	20	5	’s	’s	PART
ejpam-3228	20	6	study	study	NOUN
ejpam-3228	20	7	,	,	PUNCT
ejpam-3228	20	8	studies	study	NOUN
ejpam-3228	20	9	related	relate	VERB
ejpam-3228	20	10	to	to	ADP
ejpam-3228	20	11	algebraic	algebraic	ADJ
ejpam-3228	20	12	structures	structure	NOUN
ejpam-3228	20	13	of	of	ADP
ejpam-3228	20	14	soft	soft	ADJ
ejpam-3228	20	15	sets	set	NOUN
ejpam-3228	20	16	increased	increase	VERB
ejpam-3228	20	17	rapidly	rapidly	ADV
ejpam-3228	20	18	.	.	PUNCT
ejpam-3228	21	1	in	in	ADP
ejpam-3228	21	2	2010	2010	NUM
ejpam-3228	21	3	,	,	PUNCT
ejpam-3228	21	4	çağman	çağman	NOUN
ejpam-3228	21	5	et	et	NOUN
ejpam-3228	21	6	al	al	PROPN
ejpam-3228	21	7	.	.	PUNCT
ejpam-3228	22	1	[	[	X
ejpam-3228	22	2	7	7	X
ejpam-3228	22	3	]	]	SYM
ejpam-3228	22	4	defined	define	VERB
ejpam-3228	22	5	concept	concept	NOUN
ejpam-3228	22	6	of	of	ADP
ejpam-3228	22	7	soft	soft	ADJ
ejpam-3228	22	8	int	int	NOUN
ejpam-3228	22	9	-	-	PUNCT
ejpam-3228	22	10	groups	group	NOUN
ejpam-3228	22	11	with	with	ADP
ejpam-3228	22	12	a	a	DET
ejpam-3228	22	13	similar	similar	ADJ
ejpam-3228	22	14	approach	approach	NOUN
ejpam-3228	22	15	to	to	ADP
ejpam-3228	22	16	fuzzy	fuzzy	ADJ
ejpam-3228	22	17	group	group	NOUN
ejpam-3228	22	18	definition	definition	NOUN
ejpam-3228	22	19	of	of	ADP
ejpam-3228	22	20	rosenfeld	rosenfeld	PROPN
ejpam-3228	22	21	[	[	X
ejpam-3228	22	22	8	8	NUM
ejpam-3228	22	23	]	]	PUNCT
ejpam-3228	22	24	,	,	PUNCT
ejpam-3228	22	25	and	and	CCONJ
ejpam-3228	22	26	obtained	obtain	VERB
ejpam-3228	22	27	some	some	DET
ejpam-3228	22	28	properties	property	NOUN
ejpam-3228	22	29	of	of	ADP
ejpam-3228	22	30	soft	soft	ADJ
ejpam-3228	22	31	int	int	NOUN
ejpam-3228	22	32	-	-	PUNCT
ejpam-3228	22	33	groups	group	NOUN
ejpam-3228	22	34	.	.	PUNCT
ejpam-3228	23	1	kaygısız	kaygısız	PROPN
ejpam-3228	24	1	[	[	X
ejpam-3228	24	2	9	9	NUM
ejpam-3228	24	3	]	]	PUNCT
ejpam-3228	24	4	derived	derive	VERB
ejpam-3228	24	5	some	some	DET
ejpam-3228	24	6	new	new	ADJ
ejpam-3228	24	7	results	result	NOUN
ejpam-3228	24	8	on	on	ADP
ejpam-3228	24	9	soft	soft	ADJ
ejpam-3228	24	10	int	int	NOUN
ejpam-3228	24	11	-	-	PUNCT
ejpam-3228	24	12	groups	group	NOUN
ejpam-3228	24	13	.	.	PUNCT
ejpam-3228	25	1	sezgin	sezgin	VERB
ejpam-3228	25	2	[	[	X
ejpam-3228	25	3	10	10	NUM
ejpam-3228	25	4	]	]	PUNCT
ejpam-3228	25	5	made	make	VERB
ejpam-3228	25	6	some	some	DET
ejpam-3228	25	7	corrections	correction	NOUN
ejpam-3228	25	8	for	for	ADP
ejpam-3228	25	9	some	some	DET
ejpam-3228	25	10	problematic	problematic	ADJ
ejpam-3228	25	11	case	case	NOUN
ejpam-3228	25	12	related	relate	VERB
ejpam-3228	25	13	to	to	ADP
ejpam-3228	25	14	soft	soft	ADJ
ejpam-3228	25	15	groups	group	NOUN
ejpam-3228	25	16	defined	define	VERB
ejpam-3228	25	17	by	by	ADP
ejpam-3228	25	18	aktaş	aktaş	PROPN
ejpam-3228	25	19	and	and	CCONJ
ejpam-3228	25	20	çağman	çağman	NOUN
ejpam-3228	25	21	,	,	PUNCT
ejpam-3228	25	22	and	and	CCONJ
ejpam-3228	25	23	they	they	PRON
ejpam-3228	25	24	defined	define	VERB
ejpam-3228	25	25	concepts	concept	NOUN
ejpam-3228	25	26	of	of	ADP
ejpam-3228	25	27	normalistic	normalistic	ADJ
ejpam-3228	25	28	soft	soft	ADJ
ejpam-3228	25	29	group	group	NOUN
ejpam-3228	25	30	and	and	CCONJ
ejpam-3228	25	31	normalistic	normalistic	ADJ
ejpam-3228	25	32	soft	soft	ADJ
ejpam-3228	25	33	group	group	NOUN
ejpam-3228	25	34	homomorphism	homomorphism	NOUN
ejpam-3228	25	35	.	.	PUNCT
ejpam-3228	26	1	sezgin	sezgin	VERB
ejpam-3228	26	2	et	et	PROPN
ejpam-3228	26	3	al	al	PROPN
ejpam-3228	26	4	.	.	PUNCT
ejpam-3228	27	1	[	[	X
ejpam-3228	27	2	11	11	NUM
ejpam-3228	27	3	]	]	PUNCT
ejpam-3228	27	4	gave	give	VERB
ejpam-3228	27	5	definitions	definition	NOUN
ejpam-3228	27	6	of	of	ADP
ejpam-3228	27	7	∗corresponding	∗corresponde	VERB
ejpam-3228	27	8	author	author	NOUN
ejpam-3228	27	9	.	.	PUNCT
ejpam-3228	28	1	email	email	NOUN
ejpam-3228	28	2	addresses	address	NOUN
ejpam-3228	28	3	:	:	PUNCT
ejpam-3228	28	4	amanswt@uom.edu.pk	amanswt@uom.edu.pk	PROPN
ejpam-3228	28	5	(	(	PUNCT
ejpam-3228	28	6	a.	a.	NOUN
ejpam-3228	28	7	ullah∗	ullah∗	PROPN
ejpam-3228	28	8	)	)	PUNCT
ejpam-3228	28	9	,	,	PUNCT
ejpam-3228	28	10	fkaraaslan@karatekin.edu.tr	fkaraaslan@karatekin.edu.tr	PROPN
ejpam-3228	28	11	(	(	PUNCT
ejpam-3228	28	12	f.	f.	PROPN
ejpam-3228	28	13	karaaslan	karaaslan	PROPN
ejpam-3228	28	14	)	)	PUNCT
ejpam-3228	28	15	,	,	PUNCT
ejpam-3228	28	16	iahmad@uom.edu.pk	iahmad@uom.edu.pk	NOUN
ejpam-3228	28	17	(	(	PUNCT
ejpam-3228	28	18	i.	i.	PROPN
ejpam-3228	28	19	ahmad	ahmad	PROPN
ejpam-3228	28	20	)	)	PUNCT
ejpam-3228	28	21	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3228	29	1	517	517	NUM
ejpam-3228	29	2	c	c	X
ejpam-3228	29	3	©	©	PROPN
ejpam-3228	29	4	2018	2018	NUM
ejpam-3228	29	5	ejpam	ejpam	VERB
ejpam-3228	29	6	all	all	DET
ejpam-3228	29	7	rights	right	NOUN
ejpam-3228	29	8	reserved	reserve	VERB
ejpam-3228	29	9	.	.	PUNCT
ejpam-3228	30	1	a.	a.	PROPN
ejpam-3228	30	2	ullah	ullah	PROPN
ejpam-3228	30	3	,	,	PUNCT
ejpam-3228	30	4	f.	f.	PROPN
ejpam-3228	30	5	karaaslan	karaaslan	PROPN
ejpam-3228	30	6	,	,	PUNCT
ejpam-3228	30	7	i.	i.	PROPN
ejpam-3228	30	8	ahmad	ahmad	PROPN
ejpam-3228	30	9	/	/	SYM
ejpam-3228	30	10	eur	eur	PROPN
ejpam-3228	30	11	.	.	PUNCT
ejpam-3228	31	1	j.	j.	PROPN
ejpam-3228	31	2	pure	pure	PROPN
ejpam-3228	31	3	appl	appl	PROPN
ejpam-3228	31	4	.	.	PROPN
ejpam-3228	31	5	math	math	PROPN
ejpam-3228	31	6	,	,	PUNCT
ejpam-3228	31	7	11	11	NUM
ejpam-3228	31	8	(	(	PUNCT
ejpam-3228	31	9	2	2	NUM
ejpam-3228	31	10	)	)	PUNCT
ejpam-3228	31	11	(	(	PUNCT
ejpam-3228	31	12	2018	2018	NUM
ejpam-3228	31	13	)	)	PUNCT
ejpam-3228	31	14	,	,	PUNCT
ejpam-3228	31	15	517	517	NUM
ejpam-3228	31	16	-	-	SYM
ejpam-3228	31	17	536	536	NUM
ejpam-3228	31	18	518	518	NUM
ejpam-3228	31	19	soft	soft	ADJ
ejpam-3228	31	20	uni	uni	ADJ
ejpam-3228	31	21	-	-	PUNCT
ejpam-3228	31	22	groups	group	NOUN
ejpam-3228	31	23	and	and	CCONJ
ejpam-3228	31	24	uni	uni	ADJ
ejpam-3228	31	25	-	-	ADJ
ejpam-3228	31	26	soft	soft	ADJ
ejpam-3228	31	27	normal	normal	ADJ
ejpam-3228	31	28	subgroup	subgroup	NOUN
ejpam-3228	31	29	of	of	ADP
ejpam-3228	31	30	a	a	DET
ejpam-3228	31	31	group	group	NOUN
ejpam-3228	31	32	,	,	PUNCT
ejpam-3228	31	33	and	and	CCONJ
ejpam-3228	31	34	investigated	investigate	VERB
ejpam-3228	31	35	their	their	PRON
ejpam-3228	31	36	related	relate	VERB
ejpam-3228	31	37	properties	property	NOUN
ejpam-3228	31	38	especially	especially	ADV
ejpam-3228	31	39	with	with	ADP
ejpam-3228	31	40	respect	respect	NOUN
ejpam-3228	31	41	to	to	ADP
ejpam-3228	31	42	anti	anti	ADJ
ejpam-3228	31	43	-	-	NOUN
ejpam-3228	31	44	image	image	ADJ
ejpam-3228	31	45	,	,	PUNCT
ejpam-3228	31	46	α−inclusion	α−inclusion	NOUN
ejpam-3228	31	47	of	of	ADP
ejpam-3228	31	48	a	a	DET
ejpam-3228	31	49	soft	soft	ADJ
ejpam-3228	31	50	set	set	NOUN
ejpam-3228	31	51	.	.	PUNCT
ejpam-3228	32	1	sezgin	sezgin	VERB
ejpam-3228	32	2	[	[	X
ejpam-3228	32	3	12	12	NUM
ejpam-3228	32	4	]	]	PUNCT
ejpam-3228	32	5	introduced	introduce	VERB
ejpam-3228	32	6	the	the	DET
ejpam-3228	32	7	concept	concept	NOUN
ejpam-3228	32	8	of	of	ADP
ejpam-3228	32	9	soft	soft	ADJ
ejpam-3228	32	10	intersection	intersection	NOUN
ejpam-3228	32	11	la	la	NOUN
ejpam-3228	32	12	-	-	PUNCT
ejpam-3228	32	13	semigroups	semigroups	X
ejpam-3228	32	14	(	(	PUNCT
ejpam-3228	32	15	abel	abel	NOUN
ejpam-3228	32	16	-	-	PUNCT
ejpam-3228	32	17	grassman	grassman	NOUN
ejpam-3228	32	18	’s	’s	PART
ejpam-3228	32	19	groupoids	groupoid	NOUN
ejpam-3228	32	20	)	)	PUNCT
ejpam-3228	32	21	and	and	CCONJ
ejpam-3228	32	22	studied	study	VERB
ejpam-3228	32	23	various	various	ADJ
ejpam-3228	32	24	ideals	ideal	NOUN
ejpam-3228	32	25	in	in	ADP
ejpam-3228	32	26	la	la	NOUN
ejpam-3228	32	27	-	-	PUNCT
ejpam-3228	32	28	semigroups	semigroup	NOUN
ejpam-3228	32	29	such	such	ADJ
ejpam-3228	32	30	as	as	ADP
ejpam-3228	32	31	left	leave	VERB
ejpam-3228	32	32	(	(	PUNCT
ejpam-3228	32	33	right	right	ADJ
ejpam-3228	32	34	)	)	PUNCT
ejpam-3228	32	35	ideals	ideal	NOUN
ejpam-3228	32	36	,	,	PUNCT
ejpam-3228	32	37	bi	bi	NOUN
ejpam-3228	32	38	-	-	NOUN
ejpam-3228	32	39	ideals	ideal	NOUN
ejpam-3228	32	40	,	,	PUNCT
ejpam-3228	32	41	interior	interior	ADJ
ejpam-3228	32	42	ideals	ideal	NOUN
ejpam-3228	32	43	and	and	CCONJ
ejpam-3228	32	44	quasi	quasi	ADJ
ejpam-3228	32	45	ideals	ideal	NOUN
ejpam-3228	32	46	by	by	ADP
ejpam-3228	32	47	defining	define	VERB
ejpam-3228	32	48	soft	soft	ADJ
ejpam-3228	32	49	intersection	intersection	NOUN
ejpam-3228	32	50	product	product	NOUN
ejpam-3228	32	51	operations	operation	NOUN
ejpam-3228	32	52	.	.	PUNCT
ejpam-3228	33	1	the	the	DET
ejpam-3228	33	2	concept	concept	NOUN
ejpam-3228	33	3	of	of	ADP
ejpam-3228	33	4	soft	soft	ADJ
ejpam-3228	33	5	intersection	intersection	NOUN
ejpam-3228	33	6	abel	abel	NOUN
ejpam-3228	33	7	-	-	PUNCT
ejpam-3228	33	8	grassmann	grassmann	PROPN
ejpam-3228	33	9	’s	’s	PART
ejpam-3228	33	10	groups	group	NOUN
ejpam-3228	33	11	was	be	AUX
ejpam-3228	33	12	defined	define	VERB
ejpam-3228	33	13	by	by	ADP
ejpam-3228	33	14	ullah	ullah	PROPN
ejpam-3228	33	15	et	et	PROPN
ejpam-3228	33	16	al	al	PROPN
ejpam-3228	33	17	.	.	PUNCT
ejpam-3228	34	1	[	[	X
ejpam-3228	34	2	13	13	NUM
ejpam-3228	34	3	]	]	PUNCT
ejpam-3228	34	4	and	and	CCONJ
ejpam-3228	34	5	related	related	ADJ
ejpam-3228	34	6	properties	property	NOUN
ejpam-3228	34	7	were	be	AUX
ejpam-3228	34	8	investigated	investigate	VERB
ejpam-3228	34	9	.	.	PUNCT
ejpam-3228	35	1	there	there	PRON
ejpam-3228	35	2	are	be	VERB
ejpam-3228	35	3	many	many	ADJ
ejpam-3228	35	4	studies	study	NOUN
ejpam-3228	35	5	on	on	ADP
ejpam-3228	35	6	algebraic	algebraic	ADJ
ejpam-3228	35	7	structures	structure	NOUN
ejpam-3228	35	8	of	of	ADP
ejpam-3228	35	9	soft	soft	ADJ
ejpam-3228	35	10	sets	set	NOUN
ejpam-3228	35	11	,	,	PUNCT
ejpam-3228	35	12	some	some	PRON
ejpam-3228	35	13	of	of	ADP
ejpam-3228	35	14	them	they	PRON
ejpam-3228	35	15	are	be	AUX
ejpam-3228	35	16	as	as	ADP
ejpam-3228	35	17	in	in	ADP
ejpam-3228	35	18	following	follow	VERB
ejpam-3228	35	19	[	[	X
ejpam-3228	35	20	14–18	14–18	NUM
ejpam-3228	35	21	]	]	PUNCT
ejpam-3228	35	22	.	.	PUNCT
ejpam-3228	36	1	in	in	ADP
ejpam-3228	36	2	this	this	DET
ejpam-3228	36	3	study	study	NOUN
ejpam-3228	36	4	,	,	PUNCT
ejpam-3228	36	5	we	we	PRON
ejpam-3228	36	6	introduce	introduce	VERB
ejpam-3228	36	7	the	the	DET
ejpam-3228	36	8	notion	notion	NOUN
ejpam-3228	36	9	of	of	ADP
ejpam-3228	36	10	soft	soft	ADJ
ejpam-3228	36	11	uni	uni	ADJ
ejpam-3228	36	12	-	-	PUNCT
ejpam-3228	36	13	ag	ag	ADJ
ejpam-3228	36	14	-	-	PUNCT
ejpam-3228	36	15	groups	group	NOUN
ejpam-3228	36	16	,	,	PUNCT
ejpam-3228	36	17	and	and	CCONJ
ejpam-3228	36	18	define	define	VERB
ejpam-3228	36	19	some	some	DET
ejpam-3228	36	20	new	new	ADJ
ejpam-3228	36	21	concepts	concept	NOUN
ejpam-3228	36	22	related	relate	VERB
ejpam-3228	36	23	to	to	ADP
ejpam-3228	36	24	soft	soft	ADJ
ejpam-3228	36	25	uni	uni	ADJ
ejpam-3228	36	26	-	-	PUNCT
ejpam-3228	36	27	ag	ag	ADJ
ejpam-3228	36	28	-	-	PUNCT
ejpam-3228	36	29	groups	group	NOUN
ejpam-3228	36	30	such	such	ADJ
ejpam-3228	36	31	as	as	ADP
ejpam-3228	36	32	e	e	NOUN
ejpam-3228	36	33	-	-	NOUN
ejpam-3228	36	34	set	set	ADJ
ejpam-3228	36	35	and	and	CCONJ
ejpam-3228	36	36	α	α	NOUN
ejpam-3228	36	37	-	-	NOUN
ejpam-3228	36	38	inclusion	inclusion	NOUN
ejpam-3228	36	39	of	of	ADP
ejpam-3228	36	40	soft	soft	ADJ
ejpam-3228	36	41	uni	uni	ADJ
ejpam-3228	36	42	-	-	PUNCT
ejpam-3228	36	43	ag	ag	ADJ
ejpam-3228	36	44	-	-	PUNCT
ejpam-3228	36	45	groups	group	NOUN
ejpam-3228	36	46	,	,	PUNCT
ejpam-3228	36	47	normal	normal	ADJ
ejpam-3228	36	48	soft	soft	ADJ
ejpam-3228	36	49	uni	uni	ADJ
ejpam-3228	36	50	-	-	PUNCT
ejpam-3228	36	51	ag	ag	NOUN
ejpam-3228	36	52	-	-	PUNCT
ejpam-3228	36	53	subgroups	subgroup	NOUN
ejpam-3228	36	54	,	,	PUNCT
ejpam-3228	36	55	conjugate	conjugate	ADJ
ejpam-3228	36	56	of	of	ADP
ejpam-3228	36	57	soft	soft	ADJ
ejpam-3228	36	58	uni	uni	ADJ
ejpam-3228	36	59	-	-	PUNCT
ejpam-3228	36	60	ag	ag	ADJ
ejpam-3228	36	61	-	-	PUNCT
ejpam-3228	36	62	groups	group	NOUN
ejpam-3228	36	63	and	and	CCONJ
ejpam-3228	36	64	commutators	commutator	NOUN
ejpam-3228	36	65	of	of	ADP
ejpam-3228	36	66	aggroups	aggroup	NOUN
ejpam-3228	36	67	.	.	PUNCT
ejpam-3228	37	1	we	we	PRON
ejpam-3228	37	2	support	support	VERB
ejpam-3228	37	3	our	our	PRON
ejpam-3228	37	4	definitions	definition	NOUN
ejpam-3228	37	5	with	with	ADP
ejpam-3228	37	6	examples	example	NOUN
ejpam-3228	37	7	to	to	PART
ejpam-3228	37	8	be	be	AUX
ejpam-3228	37	9	more	more	ADV
ejpam-3228	37	10	understandable	understandable	ADJ
ejpam-3228	37	11	.	.	PUNCT
ejpam-3228	38	1	furthermore	furthermore	ADV
ejpam-3228	38	2	,	,	PUNCT
ejpam-3228	38	3	we	we	PRON
ejpam-3228	38	4	obtain	obtain	VERB
ejpam-3228	38	5	interrelations	interrelation	NOUN
ejpam-3228	38	6	of	of	ADP
ejpam-3228	38	7	these	these	DET
ejpam-3228	38	8	concepts	concept	NOUN
ejpam-3228	38	9	.	.	PUNCT
ejpam-3228	39	1	definition	definition	NOUN
ejpam-3228	39	2	1	1	NUM
ejpam-3228	39	3	.	.	PUNCT
ejpam-3228	40	1	[	[	X
ejpam-3228	40	2	1	1	X
ejpam-3228	40	3	]	]	PUNCT
ejpam-3228	40	4	let	let	VERB
ejpam-3228	40	5	u	u	PRON
ejpam-3228	40	6	be	be	AUX
ejpam-3228	40	7	the	the	DET
ejpam-3228	40	8	universal	universal	ADJ
ejpam-3228	40	9	set	set	NOUN
ejpam-3228	40	10	,	,	PUNCT
ejpam-3228	40	11	e	e	X
ejpam-3228	40	12	be	be	VERB
ejpam-3228	40	13	the	the	DET
ejpam-3228	40	14	set	set	NOUN
ejpam-3228	40	15	of	of	ADP
ejpam-3228	40	16	parameters	parameter	NOUN
ejpam-3228	40	17	and	and	CCONJ
ejpam-3228	40	18	p	p	X
ejpam-3228	40	19	(	(	PUNCT
ejpam-3228	40	20	u	u	NOUN
ejpam-3228	40	21	)	)	PUNCT
ejpam-3228	40	22	be	be	VERB
ejpam-3228	40	23	the	the	DET
ejpam-3228	40	24	power	power	NOUN
ejpam-3228	40	25	set	set	NOUN
ejpam-3228	40	26	of	of	ADP
ejpam-3228	40	27	u	u	PROPN
ejpam-3228	40	28	.	.	PUNCT
ejpam-3228	41	1	then	then	ADV
ejpam-3228	41	2	a	a	DET
ejpam-3228	41	3	soft	soft	ADJ
ejpam-3228	41	4	set	set	NOUN
ejpam-3228	41	5	,	,	PUNCT
ejpam-3228	41	6	a	a	PRON
ejpam-3228	41	7	is	be	AUX
ejpam-3228	41	8	a	a	DET
ejpam-3228	41	9	set	set	NOUN
ejpam-3228	41	10	of	of	ADP
ejpam-3228	41	11	ordered	order	VERB
ejpam-3228	41	12	pairs	pair	NOUN
ejpam-3228	41	13	a	a	PRON
ejpam-3228	41	14	=	=	X
ejpam-3228	41	15	{	{	PUNCT
ejpam-3228	41	16	(	(	PUNCT
ejpam-3228	41	17	ε	ε	PROPN
ejpam-3228	41	18	,	,	PUNCT
ejpam-3228	41	19	fa(ε	fa(ε	PUNCT
ejpam-3228	41	20	)	)	PUNCT
ejpam-3228	41	21	)	)	PUNCT
ejpam-3228	41	22	:	:	PUNCT
ejpam-3228	42	1	ε	ε	PROPN
ejpam-3228	42	2	∈	∈	PROPN
ejpam-3228	42	3	e	e	PROPN
ejpam-3228	42	4	}	}	PUNCT
ejpam-3228	42	5	,	,	PUNCT
ejpam-3228	42	6	where	where	SCONJ
ejpam-3228	42	7	fa	fa	PROPN
ejpam-3228	42	8	is	be	AUX
ejpam-3228	42	9	a	a	DET
ejpam-3228	42	10	set	set	NOUN
ejpam-3228	42	11	valued	value	VERB
ejpam-3228	42	12	function	function	NOUN
ejpam-3228	42	13	from	from	ADP
ejpam-3228	42	14	e	e	NOUN
ejpam-3228	42	15	to	to	ADP
ejpam-3228	42	16	p	p	PROPN
ejpam-3228	42	17	(	(	PUNCT
ejpam-3228	42	18	u	u	NOUN
ejpam-3228	42	19	)	)	PUNCT
ejpam-3228	42	20	i.e.	i.e.	X
ejpam-3228	42	21	fa	fa	X
ejpam-3228	42	22	:	:	PUNCT
ejpam-3228	42	23	e	e	X
ejpam-3228	42	24	→	→	SYM
ejpam-3228	42	25	p	p	X
ejpam-3228	42	26	(	(	PUNCT
ejpam-3228	42	27	u	u	NOUN
ejpam-3228	42	28	)	)	PUNCT
ejpam-3228	42	29	.	.	PUNCT
ejpam-3228	43	1	note	note	VERB
ejpam-3228	43	2	that	that	SCONJ
ejpam-3228	43	3	if	if	SCONJ
ejpam-3228	43	4	fa(ε	fa(ε	PUNCT
ejpam-3228	43	5	)	)	PUNCT
ejpam-3228	43	6	=	=	SYM
ejpam-3228	43	7	∅	∅	NOUN
ejpam-3228	43	8	,	,	PUNCT
ejpam-3228	43	9	where	where	SCONJ
ejpam-3228	43	10	ε	ε	PROPN
ejpam-3228	43	11	∈	∈	PROPN
ejpam-3228	43	12	e.	e.	PROPN
ejpam-3228	43	13	then	then	ADV
ejpam-3228	43	14	(	(	PUNCT
ejpam-3228	43	15	ε	ε	PROPN
ejpam-3228	43	16	,	,	PUNCT
ejpam-3228	43	17	fa(ε	fa(ε	PUNCT
ejpam-3228	43	18	)	)	PUNCT
ejpam-3228	43	19	)	)	PUNCT
ejpam-3228	43	20	is	be	AUX
ejpam-3228	43	21	not	not	PART
ejpam-3228	43	22	appeared	appear	VERB
ejpam-3228	43	23	in	in	ADP
ejpam-3228	43	24	the	the	DET
ejpam-3228	43	25	set	set	NOUN
ejpam-3228	43	26	a.	a.	NOUN
ejpam-3228	43	27	the	the	DET
ejpam-3228	43	28	set	set	NOUN
ejpam-3228	43	29	of	of	ADP
ejpam-3228	43	30	all	all	DET
ejpam-3228	43	31	soft	soft	ADJ
ejpam-3228	43	32	sets	set	NOUN
ejpam-3228	43	33	over	over	ADP
ejpam-3228	43	34	u	u	NOUN
ejpam-3228	43	35	is	be	AUX
ejpam-3228	43	36	denoted	denote	VERB
ejpam-3228	43	37	by	by	ADP
ejpam-3228	43	38	s(u	s(u	PROPN
ejpam-3228	43	39	)	)	PUNCT
ejpam-3228	43	40	.	.	PUNCT
ejpam-3228	44	1	definition	definition	NOUN
ejpam-3228	44	2	2	2	NUM
ejpam-3228	44	3	.	.	PUNCT
ejpam-3228	45	1	[	[	X
ejpam-3228	45	2	3	3	X
ejpam-3228	45	3	]	]	PUNCT
ejpam-3228	45	4	let	let	VERB
ejpam-3228	45	5	a	a	DET
ejpam-3228	45	6	,	,	PUNCT
ejpam-3228	45	7	b	b	PROPN
ejpam-3228	45	8	∈	∈	PROPN
ejpam-3228	45	9	s(u	s(u	PROPN
ejpam-3228	45	10	)	)	PUNCT
ejpam-3228	45	11	.	.	PUNCT
ejpam-3228	46	1	then	then	ADV
ejpam-3228	46	2	1	1	X
ejpam-3228	46	3	.	.	PUNCT
ejpam-3228	47	1	if	if	SCONJ
ejpam-3228	47	2	fa(ε	fa(ε	PUNCT
ejpam-3228	47	3	)	)	PUNCT
ejpam-3228	47	4	=	=	SYM
ejpam-3228	47	5	∅	∅	NOUN
ejpam-3228	47	6	for	for	ADP
ejpam-3228	47	7	all	all	DET
ejpam-3228	47	8	ε	ε	PROPN
ejpam-3228	47	9	∈	∈	PROPN
ejpam-3228	47	10	e	e	NOUN
ejpam-3228	47	11	,	,	PUNCT
ejpam-3228	47	12	a	a	PRON
ejpam-3228	47	13	is	be	AUX
ejpam-3228	47	14	said	say	VERB
ejpam-3228	47	15	to	to	PART
ejpam-3228	47	16	be	be	AUX
ejpam-3228	47	17	a	a	DET
ejpam-3228	47	18	null	null	ADJ
ejpam-3228	47	19	soft	soft	ADJ
ejpam-3228	47	20	set	set	NOUN
ejpam-3228	47	21	,	,	PUNCT
ejpam-3228	47	22	denoted	denote	VERB
ejpam-3228	47	23	by	by	ADP
ejpam-3228	47	24	φ	φ	PROPN
ejpam-3228	47	25	.	.	PROPN
ejpam-3228	48	1	2	2	NUM
ejpam-3228	48	2	.	.	X
ejpam-3228	49	1	if	if	SCONJ
ejpam-3228	49	2	fa(ε	fa(ε	PUNCT
ejpam-3228	49	3	)	)	PUNCT
ejpam-3228	49	4	=	=	SYM
ejpam-3228	49	5	u	u	NOUN
ejpam-3228	49	6	for	for	ADP
ejpam-3228	49	7	all	all	DET
ejpam-3228	49	8	ε	ε	PROPN
ejpam-3228	49	9	∈	∈	PROPN
ejpam-3228	49	10	e	e	NOUN
ejpam-3228	49	11	,	,	PUNCT
ejpam-3228	49	12	a	a	PRON
ejpam-3228	49	13	is	be	AUX
ejpam-3228	49	14	said	say	VERB
ejpam-3228	49	15	to	to	PART
ejpam-3228	49	16	be	be	AUX
ejpam-3228	49	17	absolute	absolute	ADJ
ejpam-3228	49	18	soft	soft	ADJ
ejpam-3228	49	19	set	set	NOUN
ejpam-3228	49	20	,	,	PUNCT
ejpam-3228	49	21	denoted	denote	VERB
ejpam-3228	49	22	by	by	ADP
ejpam-3228	49	23	û	û	NUM
ejpam-3228	49	24	.	.	PUNCT
ejpam-3228	50	1	3	3	X
ejpam-3228	50	2	.	.	X
ejpam-3228	50	3	a	a	PRON
ejpam-3228	50	4	is	be	AUX
ejpam-3228	50	5	soft	soft	ADJ
ejpam-3228	50	6	subset	subset	NOUN
ejpam-3228	50	7	of	of	ADP
ejpam-3228	50	8	b	b	NOUN
ejpam-3228	50	9	,	,	PUNCT
ejpam-3228	50	10	denoted	denote	VERB
ejpam-3228	50	11	by	by	ADP
ejpam-3228	50	12	a⊆̃b	a⊆̃b	ADJ
ejpam-3228	50	13	,	,	PUNCT
ejpam-3228	50	14	if	if	SCONJ
ejpam-3228	50	15	fa(ε	fa(ε	PUNCT
ejpam-3228	50	16	)	)	PUNCT
ejpam-3228	50	17	⊆	⊆	NUM
ejpam-3228	50	18	fb(ε	fb(ε	NUM
ejpam-3228	50	19	)	)	PUNCT
ejpam-3228	50	20	for	for	ADP
ejpam-3228	50	21	all	all	DET
ejpam-3228	50	22	ε	ε	PROPN
ejpam-3228	50	23	∈	∈	PROPN
ejpam-3228	50	24	e.	e.	PROPN
ejpam-3228	50	25	4	4	PROPN
ejpam-3228	50	26	.	.	PUNCT
ejpam-3228	51	1	a=̃b	a=̃b	ADJ
ejpam-3228	51	2	,	,	PUNCT
ejpam-3228	51	3	if	if	SCONJ
ejpam-3228	51	4	a⊆̃b	a⊆̃b	ADJ
ejpam-3228	51	5	and	and	CCONJ
ejpam-3228	51	6	b⊆̃a	b⊆̃a	NOUN
ejpam-3228	51	7	.	.	NOUN
ejpam-3228	52	1	5	5	NUM
ejpam-3228	52	2	.	.	NOUN
ejpam-3228	52	3	soft	soft	ADJ
ejpam-3228	52	4	union	union	NOUN
ejpam-3228	52	5	of	of	ADP
ejpam-3228	52	6	a	a	PRON
ejpam-3228	52	7	and	and	CCONJ
ejpam-3228	52	8	b	b	NOUN
ejpam-3228	52	9	,	,	PUNCT
ejpam-3228	52	10	denoted	denote	VERB
ejpam-3228	52	11	by	by	ADP
ejpam-3228	52	12	a∪̃b	a∪̃b	PROPN
ejpam-3228	52	13	,	,	PUNCT
ejpam-3228	52	14	is	be	AUX
ejpam-3228	52	15	a	a	DET
ejpam-3228	52	16	soft	soft	ADJ
ejpam-3228	52	17	set	set	NOUN
ejpam-3228	52	18	over	over	ADP
ejpam-3228	52	19	u	u	NOUN
ejpam-3228	52	20	and	and	CCONJ
ejpam-3228	52	21	defined	define	VERB
ejpam-3228	52	22	by	by	ADP
ejpam-3228	52	23	a∪̃b	a∪̃b	PROPN
ejpam-3228	52	24	=	=	SYM
ejpam-3228	52	25	{	{	PUNCT
ejpam-3228	52	26	(	(	PUNCT
ejpam-3228	52	27	ε	ε	PROPN
ejpam-3228	52	28	,	,	PUNCT
ejpam-3228	52	29	(	(	PUNCT
ejpam-3228	52	30	fa∪̃fb	fa∪̃fb	PROPN
ejpam-3228	52	31	)	)	PUNCT
ejpam-3228	52	32	(	(	PUNCT
ejpam-3228	52	33	ε	ε	PROPN
ejpam-3228	52	34	)	)	PUNCT
ejpam-3228	52	35	)	)	PUNCT
ejpam-3228	52	36	:	:	PUNCT
ejpam-3228	53	1	ε	ε	PROPN
ejpam-3228	53	2	∈	∈	PROPN
ejpam-3228	53	3	e	e	X
ejpam-3228	53	4	}	}	PUNCT
ejpam-3228	53	5	=	=	SYM
ejpam-3228	53	6	{	{	PUNCT
ejpam-3228	53	7	(	(	PUNCT
ejpam-3228	53	8	ε	ε	PROPN
ejpam-3228	53	9	,	,	PUNCT
ejpam-3228	53	10	(	(	PUNCT
ejpam-3228	53	11	fa(ε	fa(ε	PUNCT
ejpam-3228	53	12	)	)	PUNCT
ejpam-3228	53	13	∪	∪	ADP
ejpam-3228	53	14	fb(ε	fb(ε	NUM
ejpam-3228	53	15	)	)	PUNCT
ejpam-3228	53	16	)	)	PUNCT
ejpam-3228	53	17	)	)	PUNCT
ejpam-3228	53	18	:	:	PUNCT
ejpam-3228	54	1	ε	ε	PROPN
ejpam-3228	54	2	∈	∈	PROPN
ejpam-3228	54	3	e	e	X
ejpam-3228	54	4	}	}	PUNCT
ejpam-3228	54	5	.	.	PUNCT
ejpam-3228	55	1	6	6	X
ejpam-3228	55	2	.	.	X
ejpam-3228	55	3	soft	soft	ADJ
ejpam-3228	55	4	intersection	intersection	NOUN
ejpam-3228	55	5	of	of	ADP
ejpam-3228	55	6	a	a	PRON
ejpam-3228	55	7	and	and	CCONJ
ejpam-3228	55	8	b	b	NOUN
ejpam-3228	55	9	,	,	PUNCT
ejpam-3228	55	10	denoted	denote	VERB
ejpam-3228	55	11	by	by	ADP
ejpam-3228	55	12	a∩̃b	a∩̃b	NOUN
ejpam-3228	55	13	,	,	PUNCT
ejpam-3228	55	14	is	be	AUX
ejpam-3228	55	15	a	a	DET
ejpam-3228	55	16	soft	soft	ADJ
ejpam-3228	55	17	set	set	NOUN
ejpam-3228	55	18	over	over	ADP
ejpam-3228	55	19	u	u	NOUN
ejpam-3228	55	20	and	and	CCONJ
ejpam-3228	55	21	defined	define	VERB
ejpam-3228	55	22	by	by	ADP
ejpam-3228	55	23	a∩̃b	a∩̃b	NOUN
ejpam-3228	55	24	=	=	PUNCT
ejpam-3228	55	25	{	{	PUNCT
ejpam-3228	55	26	(	(	PUNCT
ejpam-3228	55	27	ε	ε	PROPN
ejpam-3228	55	28	,	,	PUNCT
ejpam-3228	55	29	(	(	PUNCT
ejpam-3228	55	30	fa∩̃fb	fa∩̃fb	PROPN
ejpam-3228	55	31	)	)	PUNCT
ejpam-3228	55	32	(	(	PUNCT
ejpam-3228	55	33	ε	ε	PROPN
ejpam-3228	55	34	)	)	PUNCT
ejpam-3228	55	35	)	)	PUNCT
ejpam-3228	55	36	:	:	PUNCT
ejpam-3228	56	1	ε	ε	PROPN
ejpam-3228	56	2	∈	∈	PROPN
ejpam-3228	56	3	e	e	X
ejpam-3228	56	4	}	}	PUNCT
ejpam-3228	56	5	=	=	SYM
ejpam-3228	56	6	{	{	PUNCT
ejpam-3228	56	7	(	(	PUNCT
ejpam-3228	56	8	ε	ε	PROPN
ejpam-3228	56	9	,	,	PUNCT
ejpam-3228	56	10	(	(	PUNCT
ejpam-3228	56	11	fa(ε	fa(ε	PUNCT
ejpam-3228	56	12	)	)	PUNCT
ejpam-3228	56	13	∩	∩	NOUN
ejpam-3228	56	14	fb(ε	fb(ε	NUM
ejpam-3228	56	15	)	)	PUNCT
ejpam-3228	56	16	)	)	PUNCT
ejpam-3228	56	17	)	)	PUNCT
ejpam-3228	56	18	:	:	PUNCT
ejpam-3228	57	1	ε	ε	PROPN
ejpam-3228	57	2	∈	∈	PROPN
ejpam-3228	57	3	e	e	PROPN
ejpam-3228	57	4	}	}	PUNCT
ejpam-3228	57	5	.	.	PUNCT
ejpam-3228	58	1	a.	a.	PROPN
ejpam-3228	58	2	ullah	ullah	PROPN
ejpam-3228	58	3	,	,	PUNCT
ejpam-3228	58	4	f.	f.	PROPN
ejpam-3228	58	5	karaaslan	karaaslan	PROPN
ejpam-3228	58	6	,	,	PUNCT
ejpam-3228	58	7	i.	i.	PROPN
ejpam-3228	58	8	ahmad	ahmad	PROPN
ejpam-3228	58	9	/	/	SYM
ejpam-3228	58	10	eur	eur	PROPN
ejpam-3228	58	11	.	.	PUNCT
ejpam-3228	59	1	j.	j.	PROPN
ejpam-3228	59	2	pure	pure	PROPN
ejpam-3228	59	3	appl	appl	PROPN
ejpam-3228	59	4	.	.	PROPN
ejpam-3228	59	5	math	math	PROPN
ejpam-3228	59	6	,	,	PUNCT
ejpam-3228	59	7	11	11	NUM
ejpam-3228	59	8	(	(	PUNCT
ejpam-3228	59	9	2	2	NUM
ejpam-3228	59	10	)	)	PUNCT
ejpam-3228	59	11	(	(	PUNCT
ejpam-3228	59	12	2018	2018	NUM
ejpam-3228	59	13	)	)	PUNCT
ejpam-3228	59	14	,	,	PUNCT
ejpam-3228	59	15	517	517	NUM
ejpam-3228	59	16	-	-	SYM
ejpam-3228	59	17	536	536	NUM
ejpam-3228	59	18	519	519	NUM
ejpam-3228	59	19	definition	definition	NOUN
ejpam-3228	59	20	3	3	NUM
ejpam-3228	59	21	.	.	PUNCT
ejpam-3228	60	1	[	[	X
ejpam-3228	60	2	3	3	X
ejpam-3228	60	3	]	]	PUNCT
ejpam-3228	60	4	let	let	VERB
ejpam-3228	60	5	a	a	DET
ejpam-3228	60	6	,	,	PUNCT
ejpam-3228	60	7	b	b	PROPN
ejpam-3228	60	8	∈	∈	PROPN
ejpam-3228	60	9	s(u	s(u	PROPN
ejpam-3228	60	10	)	)	PUNCT
ejpam-3228	60	11	.	.	PUNCT
ejpam-3228	61	1	then	then	ADV
ejpam-3228	61	2	,	,	PUNCT
ejpam-3228	61	3	and	and	CCONJ
ejpam-3228	61	4	and	and	CCONJ
ejpam-3228	61	5	or	or	CCONJ
ejpam-3228	61	6	operators	operator	NOUN
ejpam-3228	61	7	of	of	ADP
ejpam-3228	61	8	a	a	PRON
ejpam-3228	61	9	and	and	CCONJ
ejpam-3228	61	10	b	b	NOUN
ejpam-3228	61	11	is	be	AUX
ejpam-3228	61	12	represented	represent	VERB
ejpam-3228	61	13	by	by	ADP
ejpam-3228	61	14	a	a	DET
ejpam-3228	61	15	∧b	∧b	NOUN
ejpam-3228	61	16	and	and	CCONJ
ejpam-3228	61	17	a	a	DET
ejpam-3228	61	18	∨b	∨b	NOUN
ejpam-3228	61	19	respectively	respectively	ADV
ejpam-3228	61	20	,	,	PUNCT
ejpam-3228	61	21	defined	define	VERB
ejpam-3228	61	22	by	by	ADP
ejpam-3228	61	23	a	a	DET
ejpam-3228	61	24	∧b	∧b	NOUN
ejpam-3228	61	25	=	=	SYM
ejpam-3228	61	26	{	{	PUNCT
ejpam-3228	61	27	(	(	PUNCT
ejpam-3228	61	28	(	(	PUNCT
ejpam-3228	61	29	ε	ε	PROPN
ejpam-3228	61	30	,	,	PUNCT
ejpam-3228	61	31	ε′	ε′	NUM
ejpam-3228	61	32	)	)	PUNCT
ejpam-3228	61	33	,	,	PUNCT
ejpam-3228	61	34	fa∧b(ε	fa∧b(ε	NUM
ejpam-3228	61	35	,	,	PUNCT
ejpam-3228	61	36	ε′	ε′	NUM
ejpam-3228	61	37	)	)	PUNCT
ejpam-3228	61	38	)	)	PUNCT
ejpam-3228	62	1	:	:	PUNCT
ejpam-3228	62	2	ε	ε	PROPN
ejpam-3228	62	3	,	,	PUNCT
ejpam-3228	62	4	ε′	ε′	NOUN
ejpam-3228	62	5	∈	∈	ADJ
ejpam-3228	62	6	e	e	X
ejpam-3228	62	7	}	}	PUNCT
ejpam-3228	62	8	=	=	SYM
ejpam-3228	62	9	{	{	PUNCT
ejpam-3228	62	10	(	(	PUNCT
ejpam-3228	62	11	(	(	PUNCT
ejpam-3228	62	12	ε	ε	PROPN
ejpam-3228	62	13	,	,	PUNCT
ejpam-3228	62	14	ε′	ε′	NUM
ejpam-3228	62	15	)	)	PUNCT
ejpam-3228	62	16	,	,	PUNCT
ejpam-3228	62	17	fa(ε	fa(ε	PUNCT
ejpam-3228	62	18	)	)	PUNCT
ejpam-3228	62	19	∩	∩	X
ejpam-3228	62	20	fb(ε′	fb(ε′	NOUN
ejpam-3228	62	21	)	)	PUNCT
ejpam-3228	62	22	)	)	PUNCT
ejpam-3228	62	23	:	:	PUNCT
ejpam-3228	63	1	ε	ε	PROPN
ejpam-3228	63	2	,	,	PUNCT
ejpam-3228	63	3	ε′	ε′	NOUN
ejpam-3228	63	4	∈	∈	PROPN
ejpam-3228	63	5	e	e	X
ejpam-3228	63	6	}	}	PUNCT
ejpam-3228	63	7	,	,	PUNCT
ejpam-3228	63	8	and	and	CCONJ
ejpam-3228	63	9	a	a	DET
ejpam-3228	63	10	∨b	∨b	NOUN
ejpam-3228	63	11	=	=	PUNCT
ejpam-3228	63	12	{	{	PUNCT
ejpam-3228	63	13	(	(	PUNCT
ejpam-3228	63	14	(	(	PUNCT
ejpam-3228	63	15	ε	ε	PROPN
ejpam-3228	63	16	,	,	PUNCT
ejpam-3228	63	17	ε′	ε′	NUM
ejpam-3228	63	18	)	)	PUNCT
ejpam-3228	63	19	,	,	PUNCT
ejpam-3228	63	20	fa∨b(ε	fa∨b(ε	NOUN
ejpam-3228	63	21	,	,	PUNCT
ejpam-3228	63	22	ε′	ε′	NUM
ejpam-3228	63	23	)	)	PUNCT
ejpam-3228	63	24	)	)	PUNCT
ejpam-3228	63	25	:	:	PUNCT
ejpam-3228	64	1	ε	ε	PROPN
ejpam-3228	64	2	,	,	PUNCT
ejpam-3228	64	3	ε′	ε′	NOUN
ejpam-3228	64	4	∈	∈	ADJ
ejpam-3228	64	5	e	e	X
ejpam-3228	64	6	}	}	PUNCT
ejpam-3228	64	7	=	=	SYM
ejpam-3228	64	8	{	{	PUNCT
ejpam-3228	64	9	(	(	PUNCT
ejpam-3228	64	10	(	(	PUNCT
ejpam-3228	64	11	ε	ε	PROPN
ejpam-3228	64	12	,	,	PUNCT
ejpam-3228	64	13	ε′	ε′	NUM
ejpam-3228	64	14	)	)	PUNCT
ejpam-3228	64	15	,	,	PUNCT
ejpam-3228	64	16	fa(ε	fa(ε	PUNCT
ejpam-3228	64	17	)	)	PUNCT
ejpam-3228	64	18	∪	∪	ADP
ejpam-3228	64	19	fb(ε′	fb(ε′	PROPN
ejpam-3228	64	20	)	)	PUNCT
ejpam-3228	64	21	)	)	PUNCT
ejpam-3228	64	22	:	:	PUNCT
ejpam-3228	65	1	ε	ε	PROPN
ejpam-3228	65	2	,	,	PUNCT
ejpam-3228	65	3	ε′	ε′	NOUN
ejpam-3228	65	4	∈	∈	PROPN
ejpam-3228	65	5	e	e	X
ejpam-3228	65	6	}	}	PUNCT
ejpam-3228	65	7	.	.	PUNCT
ejpam-3228	66	1	in	in	ADP
ejpam-3228	66	2	the	the	DET
ejpam-3228	66	3	rest	rest	NOUN
ejpam-3228	66	4	of	of	ADP
ejpam-3228	66	5	this	this	DET
ejpam-3228	66	6	paper	paper	NOUN
ejpam-3228	66	7	,	,	PUNCT
ejpam-3228	66	8	g	g	PROPN
ejpam-3228	66	9	denotes	denote	VERB
ejpam-3228	66	10	an	an	DET
ejpam-3228	66	11	ag	ag	PROPN
ejpam-3228	66	12	-	-	PUNCT
ejpam-3228	66	13	group	group	NOUN
ejpam-3228	66	14	and	and	CCONJ
ejpam-3228	66	15	e	e	NOUN
ejpam-3228	66	16	denotes	denote	VERB
ejpam-3228	66	17	the	the	DET
ejpam-3228	66	18	left	left	ADJ
ejpam-3228	66	19	identity	identity	NOUN
ejpam-3228	66	20	of	of	ADP
ejpam-3228	66	21	g	g	NOUN
ejpam-3228	66	22	unless	unless	SCONJ
ejpam-3228	66	23	otherwise	otherwise	ADV
ejpam-3228	66	24	stated	state	VERB
ejpam-3228	66	25	.	.	PUNCT
ejpam-3228	67	1	an	an	DET
ejpam-3228	67	2	ag	ag	PROPN
ejpam-3228	67	3	-	-	PUNCT
ejpam-3228	67	4	group	group	NOUN
ejpam-3228	67	5	is	be	AUX
ejpam-3228	67	6	a	a	DET
ejpam-3228	67	7	non	non	ADJ
ejpam-3228	67	8	-	-	ADJ
ejpam-3228	67	9	associative	associative	ADJ
ejpam-3228	67	10	structure	structure	NOUN
ejpam-3228	67	11	,	,	PUNCT
ejpam-3228	67	12	in	in	ADP
ejpam-3228	67	13	which	which	PRON
ejpam-3228	67	14	commutativity	commutativity	NOUN
ejpam-3228	67	15	and	and	CCONJ
ejpam-3228	67	16	associativity	associativity	NOUN
ejpam-3228	67	17	imply	imply	VERB
ejpam-3228	67	18	each	each	DET
ejpam-3228	67	19	other	other	ADJ
ejpam-3228	67	20	and	and	CCONJ
ejpam-3228	67	21	thus	thus	ADV
ejpam-3228	67	22	ag	ag	PROPN
ejpam-3228	67	23	-	-	PUNCT
ejpam-3228	67	24	group	group	NOUN
ejpam-3228	67	25	become	become	VERB
ejpam-3228	67	26	an	an	DET
ejpam-3228	67	27	abelian	abelian	ADJ
ejpam-3228	67	28	group	group	NOUN
ejpam-3228	67	29	if	if	SCONJ
ejpam-3228	67	30	any	any	DET
ejpam-3228	67	31	one	one	NUM
ejpam-3228	67	32	of	of	ADP
ejpam-3228	67	33	the	the	DET
ejpam-3228	67	34	property	property	NOUN
ejpam-3228	67	35	is	be	AUX
ejpam-3228	67	36	allowed	allow	VERB
ejpam-3228	67	37	in	in	ADP
ejpam-3228	67	38	ag	ag	PROPN
ejpam-3228	67	39	-	-	NOUN
ejpam-3228	67	40	group	group	NOUN
ejpam-3228	67	41	.	.	PUNCT
ejpam-3228	68	1	ag	ag	PROPN
ejpam-3228	68	2	-	-	PUNCT
ejpam-3228	68	3	group	group	NOUN
ejpam-3228	68	4	is	be	AUX
ejpam-3228	68	5	a	a	DET
ejpam-3228	68	6	generalization	generalization	NOUN
ejpam-3228	68	7	of	of	ADP
ejpam-3228	68	8	abelian	abelian	PROPN
ejpam-3228	68	9	group	group	NOUN
ejpam-3228	68	10	and	and	CCONJ
ejpam-3228	68	11	a	a	DET
ejpam-3228	68	12	special	special	ADJ
ejpam-3228	68	13	case	case	NOUN
ejpam-3228	68	14	of	of	ADP
ejpam-3228	68	15	quasi	quasi	NOUN
ejpam-3228	68	16	-	-	NOUN
ejpam-3228	68	17	group	group	NOUN
ejpam-3228	68	18	.	.	PUNCT
ejpam-3228	69	1	an	an	DET
ejpam-3228	69	2	ag	ag	PROPN
ejpam-3228	69	3	-	-	NOUN
ejpam-3228	69	4	groupoid	groupoid	PROPN
ejpam-3228	69	5	(	(	PUNCT
ejpam-3228	69	6	or	or	CCONJ
ejpam-3228	69	7	la	la	ADJ
ejpam-3228	69	8	-	-	PUNCT
ejpam-3228	69	9	semigroup	semigroup	NOUN
ejpam-3228	69	10	)	)	PUNCT
ejpam-3228	69	11	is	be	AUX
ejpam-3228	69	12	a	a	DET
ejpam-3228	69	13	non	non	ADJ
ejpam-3228	69	14	-	-	ADJ
ejpam-3228	69	15	associative	associative	ADJ
ejpam-3228	69	16	groupoid	groupoid	NOUN
ejpam-3228	69	17	in	in	ADP
ejpam-3228	69	18	general	general	ADJ
ejpam-3228	69	19	,	,	PUNCT
ejpam-3228	69	20	in	in	ADP
ejpam-3228	69	21	which	which	PRON
ejpam-3228	69	22	the	the	DET
ejpam-3228	69	23	left	left	ADJ
ejpam-3228	69	24	invertive	invertive	ADJ
ejpam-3228	69	25	law	law	NOUN
ejpam-3228	69	26	:	:	PUNCT
ejpam-3228	69	27	(	(	PUNCT
ejpam-3228	69	28	ab)c	ab)c	PROPN
ejpam-3228	69	29	=	=	SYM
ejpam-3228	69	30	(	(	PUNCT
ejpam-3228	69	31	cb)a	cb)a	PROPN
ejpam-3228	69	32	holds	hold	VERB
ejpam-3228	69	33	for	for	ADP
ejpam-3228	69	34	all	all	DET
ejpam-3228	69	35	a	a	DET
ejpam-3228	69	36	,	,	PUNCT
ejpam-3228	69	37	b	b	NOUN
ejpam-3228	69	38	,	,	PUNCT
ejpam-3228	69	39	c	c	PROPN
ejpam-3228	69	40	∈	∈	PROPN
ejpam-3228	69	41	g.	g.	PROPN
ejpam-3228	69	42	an	an	DET
ejpam-3228	69	43	ag	ag	PROPN
ejpam-3228	69	44	-	-	PROPN
ejpam-3228	69	45	groupoid	groupoid	PROPN
ejpam-3228	69	46	g	g	PROPN
ejpam-3228	69	47	is	be	AUX
ejpam-3228	69	48	called	call	VERB
ejpam-3228	69	49	an	an	DET
ejpam-3228	69	50	ag	ag	PROPN
ejpam-3228	69	51	-	-	PUNCT
ejpam-3228	69	52	group	group	NOUN
ejpam-3228	69	53	or	or	CCONJ
ejpam-3228	69	54	left	leave	VERB
ejpam-3228	69	55	almost	almost	ADV
ejpam-3228	69	56	group	group	NOUN
ejpam-3228	69	57	(	(	PUNCT
ejpam-3228	69	58	la	la	NOUN
ejpam-3228	69	59	-	-	NOUN
ejpam-3228	69	60	group	group	NOUN
ejpam-3228	69	61	)	)	PUNCT
ejpam-3228	69	62	,	,	PUNCT
ejpam-3228	69	63	if	if	SCONJ
ejpam-3228	69	64	there	there	PRON
ejpam-3228	69	65	exists	exist	VERB
ejpam-3228	69	66	a	a	DET
ejpam-3228	69	67	unique	unique	ADJ
ejpam-3228	69	68	left	left	ADJ
ejpam-3228	69	69	identity	identity	NOUN
ejpam-3228	69	70	e	e	NOUN
ejpam-3228	69	71	in	in	ADP
ejpam-3228	69	72	g	g	PROPN
ejpam-3228	69	73	(	(	PUNCT
ejpam-3228	69	74	i.e.	i.e.	X
ejpam-3228	69	75	ea	ea	X
ejpam-3228	69	76	=	=	SYM
ejpam-3228	69	77	a	a	PRON
ejpam-3228	69	78	for	for	ADP
ejpam-3228	69	79	all	all	DET
ejpam-3228	69	80	a	a	DET
ejpam-3228	69	81	∈	∈	PROPN
ejpam-3228	69	82	g	g	NOUN
ejpam-3228	69	83	)	)	PUNCT
ejpam-3228	69	84	,	,	PUNCT
ejpam-3228	69	85	and	and	CCONJ
ejpam-3228	69	86	for	for	ADP
ejpam-3228	69	87	all	all	DET
ejpam-3228	69	88	a	a	DET
ejpam-3228	69	89	∈	∈	PROPN
ejpam-3228	69	90	g	g	NOUN
ejpam-3228	69	91	there	there	PRON
ejpam-3228	69	92	exists	exist	VERB
ejpam-3228	69	93	a−1	a−1	PROPN
ejpam-3228	69	94	∈	∈	PROPN
ejpam-3228	69	95	g	g	ADP
ejpam-3228	69	96	such	such	ADJ
ejpam-3228	69	97	that	that	DET
ejpam-3228	69	98	aa−1	aa−1	NOUN
ejpam-3228	70	1	=	=	PUNCT
ejpam-3228	70	2	a−1a	a−1a	PROPN
ejpam-3228	71	1	=	=	SYM
ejpam-3228	72	1	e.	e.	PROPN
ejpam-3228	73	1	nowadays	nowadays	ADV
ejpam-3228	73	2	,	,	PUNCT
ejpam-3228	73	3	many	many	ADJ
ejpam-3228	73	4	researchers	researcher	NOUN
ejpam-3228	73	5	take	take	VERB
ejpam-3228	73	6	keen	keen	ADJ
ejpam-3228	73	7	interest	interest	NOUN
ejpam-3228	73	8	to	to	PART
ejpam-3228	73	9	fuzzify	fuzzify	VERB
ejpam-3228	73	10	ag	ag	PROPN
ejpam-3228	73	11	-	-	PUNCT
ejpam-3228	73	12	groupoids	groupoid	NOUN
ejpam-3228	73	13	and	and	CCONJ
ejpam-3228	73	14	ag	ag	PROPN
ejpam-3228	73	15	-	-	PUNCT
ejpam-3228	73	16	groups	group	NOUN
ejpam-3228	73	17	;	;	PUNCT
ejpam-3228	73	18	also	also	ADV
ejpam-3228	73	19	they	they	PRON
ejpam-3228	73	20	develop	develop	VERB
ejpam-3228	73	21	soft	soft	ADJ
ejpam-3228	73	22	theory	theory	NOUN
ejpam-3228	73	23	of	of	ADP
ejpam-3228	73	24	ag	ag	PROPN
ejpam-3228	73	25	-	-	PUNCT
ejpam-3228	73	26	groupoids	groupoids	PROPN
ejpam-3228	73	27	and	and	CCONJ
ejpam-3228	73	28	ag	ag	NOUN
ejpam-3228	73	29	-	-	PUNCT
ejpam-3228	73	30	groups	group	NOUN
ejpam-3228	73	31	[	[	X
ejpam-3228	73	32	19–23	19–23	NUM
ejpam-3228	73	33	]	]	PUNCT
ejpam-3228	73	34	.	.	PUNCT
ejpam-3228	74	1	an	an	PRON
ejpam-3228	74	2	ag	ag	PROPN
ejpam-3228	74	3	-	-	PUNCT
ejpam-3228	74	4	group	group	NOUN
ejpam-3228	74	5	(	(	PUNCT
ejpam-3228	74	6	g	g	NOUN
ejpam-3228	74	7	,	,	PUNCT
ejpam-3228	74	8	∗	∗	NOUN
ejpam-3228	74	9	)	)	PUNCT
ejpam-3228	74	10	can	can	AUX
ejpam-3228	74	11	be	be	AUX
ejpam-3228	74	12	easily	easily	ADV
ejpam-3228	74	13	obtained	obtain	VERB
ejpam-3228	74	14	from	from	ADP
ejpam-3228	74	15	an	an	DET
ejpam-3228	74	16	abelian	abelian	ADJ
ejpam-3228	74	17	group	group	NOUN
ejpam-3228	74	18	(	(	PUNCT
ejpam-3228	74	19	g1	g1	PROPN
ejpam-3228	74	20	,	,	PUNCT
ejpam-3228	74	21	·	·	PUNCT
ejpam-3228	74	22	)	)	PUNCT
ejpam-3228	74	23	by	by	ADP
ejpam-3228	74	24	:	:	PUNCT
ejpam-3228	74	25	a	a	DET
ejpam-3228	74	26	∗	∗	NOUN
ejpam-3228	74	27	b	b	NOUN
ejpam-3228	74	28	=	=	SYM
ejpam-3228	74	29	a−1	a−1	PROPN
ejpam-3228	74	30	·	·	PUNCT
ejpam-3228	74	31	b	b	PROPN
ejpam-3228	74	32	or	or	CCONJ
ejpam-3228	74	33	a	a	DET
ejpam-3228	74	34	∗	∗	NOUN
ejpam-3228	75	1	b	b	NOUN
ejpam-3228	75	2	=	=	SYM
ejpam-3228	75	3	b	b	PROPN
ejpam-3228	75	4	·	·	PUNCT
ejpam-3228	75	5	a−1	a−1	NOUN
ejpam-3228	75	6	∀	∀	NOUN
ejpam-3228	75	7	a	a	PRON
ejpam-3228	75	8	,	,	PUNCT
ejpam-3228	75	9	b	b	PROPN
ejpam-3228	75	10	∈	∈	PROPN
ejpam-3228	75	11	g1	g1	NOUN
ejpam-3228	75	12	.	.	PUNCT
ejpam-3228	76	1	it	it	PRON
ejpam-3228	76	2	is	be	AUX
ejpam-3228	76	3	easy	easy	ADJ
ejpam-3228	76	4	to	to	PART
ejpam-3228	76	5	prove	prove	VERB
ejpam-3228	76	6	that	that	SCONJ
ejpam-3228	76	7	in	in	ADP
ejpam-3228	76	8	an	an	DET
ejpam-3228	76	9	ag	ag	PROPN
ejpam-3228	76	10	-	-	PUNCT
ejpam-3228	76	11	group	group	NOUN
ejpam-3228	76	12	g	g	PROPN
ejpam-3228	76	13	the	the	DET
ejpam-3228	76	14	right	right	ADJ
ejpam-3228	76	15	identity	identity	NOUN
ejpam-3228	76	16	become	become	VERB
ejpam-3228	76	17	the	the	DET
ejpam-3228	76	18	two	two	NUM
ejpam-3228	76	19	sided	sided	ADJ
ejpam-3228	76	20	identity	identity	NOUN
ejpam-3228	76	21	,	,	PUNCT
ejpam-3228	76	22	and	and	CCONJ
ejpam-3228	76	23	thus	thus	ADV
ejpam-3228	76	24	g	g	NOUN
ejpam-3228	76	25	with	with	ADP
ejpam-3228	76	26	right	right	ADJ
ejpam-3228	76	27	identity	identity	NOUN
ejpam-3228	76	28	become	become	VERB
ejpam-3228	76	29	an	an	DET
ejpam-3228	76	30	abelian	abelian	ADJ
ejpam-3228	76	31	group	group	NOUN
ejpam-3228	76	32	.	.	PUNCT
ejpam-3228	77	1	ag	ag	PROPN
ejpam-3228	77	2	-	-	PUNCT
ejpam-3228	77	3	group	group	NOUN
ejpam-3228	77	4	posses	posse	VERB
ejpam-3228	77	5	the	the	DET
ejpam-3228	77	6	property	property	NOUN
ejpam-3228	77	7	of	of	ADP
ejpam-3228	77	8	cancellativity	cancellativity	NOUN
ejpam-3228	77	9	like	like	ADP
ejpam-3228	77	10	groups	group	NOUN
ejpam-3228	77	11	.	.	PUNCT
ejpam-3228	78	1	a	a	DET
ejpam-3228	78	2	nonempty	nonempty	ADV
ejpam-3228	78	3	subset	subset	VERB
ejpam-3228	78	4	h	h	NOUN
ejpam-3228	78	5	of	of	ADP
ejpam-3228	78	6	g	g	PROPN
ejpam-3228	78	7	is	be	AUX
ejpam-3228	78	8	called	call	VERB
ejpam-3228	78	9	an	an	DET
ejpam-3228	78	10	ag	ag	PROPN
ejpam-3228	78	11	-	-	PUNCT
ejpam-3228	78	12	subgroup	subgroup	NOUN
ejpam-3228	78	13	of	of	ADP
ejpam-3228	78	14	g	g	PROPN
ejpam-3228	78	15	,	,	PUNCT
ejpam-3228	78	16	if	if	SCONJ
ejpam-3228	78	17	h	h	PRON
ejpam-3228	78	18	itself	itself	PRON
ejpam-3228	78	19	is	be	AUX
ejpam-3228	78	20	an	an	DET
ejpam-3228	78	21	ag	ag	PROPN
ejpam-3228	78	22	-	-	PUNCT
ejpam-3228	78	23	group	group	NOUN
ejpam-3228	78	24	under	under	ADP
ejpam-3228	78	25	the	the	DET
ejpam-3228	78	26	same	same	ADJ
ejpam-3228	78	27	binary	binary	ADJ
ejpam-3228	78	28	operation	operation	NOUN
ejpam-3228	78	29	defined	define	VERB
ejpam-3228	78	30	on	on	ADP
ejpam-3228	78	31	g.	g.	PROPN
ejpam-3228	78	32	various	various	ADJ
ejpam-3228	78	33	comparative	comparative	ADJ
ejpam-3228	78	34	properties	property	NOUN
ejpam-3228	78	35	of	of	ADP
ejpam-3228	78	36	ag	ag	NOUN
ejpam-3228	78	37	-	-	PUNCT
ejpam-3228	78	38	groups	group	NOUN
ejpam-3228	78	39	and	and	CCONJ
ejpam-3228	78	40	groups	group	NOUN
ejpam-3228	78	41	are	be	AUX
ejpam-3228	78	42	explored	explore	VERB
ejpam-3228	78	43	in	in	ADP
ejpam-3228	78	44	[	[	X
ejpam-3228	78	45	24–26	24–26	NUM
ejpam-3228	78	46	]	]	PUNCT
ejpam-3228	78	47	.	.	PUNCT
ejpam-3228	79	1	the	the	DET
ejpam-3228	79	2	following	follow	VERB
ejpam-3228	79	3	identities	identity	NOUN
ejpam-3228	79	4	can	can	AUX
ejpam-3228	79	5	be	be	AUX
ejpam-3228	79	6	easily	easily	ADV
ejpam-3228	79	7	proved	prove	VERB
ejpam-3228	79	8	in	in	ADP
ejpam-3228	79	9	an	an	DET
ejpam-3228	79	10	ag	ag	PROPN
ejpam-3228	79	11	-	-	PUNCT
ejpam-3228	79	12	group	group	NOUN
ejpam-3228	79	13	g.	g.	PROPN
ejpam-3228	79	14	lemma	lemma	PROPN
ejpam-3228	80	1	1	1	NUM
ejpam-3228	80	2	.	.	PUNCT
ejpam-3228	81	1	[	[	X
ejpam-3228	81	2	24	24	NUM
ejpam-3228	81	3	]	]	PUNCT
ejpam-3228	81	4	let	let	VERB
ejpam-3228	81	5	e	e	PROPN
ejpam-3228	81	6	∈	∈	PROPN
ejpam-3228	81	7	g	g	PROPN
ejpam-3228	81	8	,	,	PUNCT
ejpam-3228	81	9	and	and	CCONJ
ejpam-3228	81	10	a	a	DET
ejpam-3228	81	11	,	,	PUNCT
ejpam-3228	81	12	b	b	NOUN
ejpam-3228	81	13	,	,	PUNCT
ejpam-3228	81	14	c	c	NOUN
ejpam-3228	81	15	,	,	PUNCT
ejpam-3228	81	16	d	d	PROPN
ejpam-3228	81	17	∈	∈	PROPN
ejpam-3228	81	18	g	g	NOUN
ejpam-3228	81	19	,	,	PUNCT
ejpam-3228	81	20	then	then	ADV
ejpam-3228	81	21	1	1	X
ejpam-3228	81	22	.	.	PUNCT
ejpam-3228	81	23	(	(	PUNCT
ejpam-3228	81	24	ab)(cd	ab)(cd	PROPN
ejpam-3228	81	25	)	)	PUNCT
ejpam-3228	81	26	=	=	SYM
ejpam-3228	81	27	(	(	PUNCT
ejpam-3228	81	28	ac)(bd	ac)(bd	PROPN
ejpam-3228	81	29	)	)	PUNCT
ejpam-3228	81	30	(	(	PUNCT
ejpam-3228	81	31	medial	medial	ADJ
ejpam-3228	81	32	law	law	NOUN
ejpam-3228	81	33	)	)	PUNCT
ejpam-3228	81	34	.	.	PUNCT
ejpam-3228	82	1	2	2	X
ejpam-3228	82	2	.	.	X
ejpam-3228	82	3	a(bc	a(bc	NUM
ejpam-3228	82	4	)	)	PUNCT
ejpam-3228	83	1	=	=	SYM
ejpam-3228	83	2	b(ac	b(ac	PROPN
ejpam-3228	83	3	)	)	PUNCT
ejpam-3228	83	4	.	.	PUNCT
ejpam-3228	84	1	3	3	X
ejpam-3228	84	2	.	.	X
ejpam-3228	84	3	(	(	PUNCT
ejpam-3228	84	4	ab)(cd	ab)(cd	PROPN
ejpam-3228	84	5	)	)	PUNCT
ejpam-3228	84	6	=	=	SYM
ejpam-3228	84	7	(	(	PUNCT
ejpam-3228	84	8	db)(ca	db)(ca	PROPN
ejpam-3228	84	9	)	)	PUNCT
ejpam-3228	84	10	(	(	PUNCT
ejpam-3228	84	11	paramedial	paramedial	ADJ
ejpam-3228	84	12	law	law	NOUN
ejpam-3228	84	13	)	)	PUNCT
ejpam-3228	84	14	.	.	PUNCT
ejpam-3228	85	1	4	4	X
ejpam-3228	85	2	.	.	X
ejpam-3228	85	3	(	(	PUNCT
ejpam-3228	85	4	ab)(cd	ab)(cd	PROPN
ejpam-3228	85	5	)	)	PUNCT
ejpam-3228	85	6	=	=	SYM
ejpam-3228	85	7	(	(	PUNCT
ejpam-3228	85	8	dc)(ba	dc)(ba	PROPN
ejpam-3228	85	9	)	)	PUNCT
ejpam-3228	85	10	.	.	PUNCT
ejpam-3228	86	1	5	5	X
ejpam-3228	86	2	.	.	X
ejpam-3228	86	3	(	(	PUNCT
ejpam-3228	86	4	ab)−1	ab)−1	PROPN
ejpam-3228	86	5	=	=	SYM
ejpam-3228	86	6	a−1b−1	a−1b−1	PROPN
ejpam-3228	86	7	.	.	PROPN
ejpam-3228	86	8	a.	a.	PROPN
ejpam-3228	86	9	ullah	ullah	PROPN
ejpam-3228	86	10	,	,	PUNCT
ejpam-3228	86	11	f.	f.	PROPN
ejpam-3228	86	12	karaaslan	karaaslan	PROPN
ejpam-3228	86	13	,	,	PUNCT
ejpam-3228	86	14	i.	i.	PROPN
ejpam-3228	86	15	ahmad	ahmad	PROPN
ejpam-3228	86	16	/	/	SYM
ejpam-3228	86	17	eur	eur	PROPN
ejpam-3228	86	18	.	.	PUNCT
ejpam-3228	87	1	j.	j.	PROPN
ejpam-3228	87	2	pure	pure	PROPN
ejpam-3228	87	3	appl	appl	PROPN
ejpam-3228	87	4	.	.	PROPN
ejpam-3228	87	5	math	math	PROPN
ejpam-3228	87	6	,	,	PUNCT
ejpam-3228	87	7	11	11	NUM
ejpam-3228	87	8	(	(	PUNCT
ejpam-3228	87	9	2	2	NUM
ejpam-3228	87	10	)	)	PUNCT
ejpam-3228	87	11	(	(	PUNCT
ejpam-3228	87	12	2018	2018	NUM
ejpam-3228	87	13	)	)	PUNCT
ejpam-3228	87	14	,	,	PUNCT
ejpam-3228	87	15	517	517	NUM
ejpam-3228	87	16	-	-	SYM
ejpam-3228	87	17	536	536	NUM
ejpam-3228	87	18	520	520	NUM
ejpam-3228	87	19	2	2	NUM
ejpam-3228	87	20	.	.	PUNCT
ejpam-3228	87	21	soft	soft	ADJ
ejpam-3228	87	22	uni	uni	ADJ
ejpam-3228	87	23	-	-	PUNCT
ejpam-3228	87	24	ag	ag	NOUN
ejpam-3228	87	25	-	-	PUNCT
ejpam-3228	87	26	groups	group	NOUN
ejpam-3228	87	27	in	in	ADP
ejpam-3228	87	28	this	this	DET
ejpam-3228	87	29	section	section	NOUN
ejpam-3228	87	30	the	the	DET
ejpam-3228	87	31	basic	basic	ADJ
ejpam-3228	87	32	definition	definition	NOUN
ejpam-3228	87	33	of	of	ADP
ejpam-3228	87	34	soft	soft	ADJ
ejpam-3228	87	35	union	union	NOUN
ejpam-3228	87	36	ag	ag	PROPN
ejpam-3228	87	37	-	-	PUNCT
ejpam-3228	87	38	group	group	NOUN
ejpam-3228	87	39	(	(	PUNCT
ejpam-3228	87	40	soft	soft	ADJ
ejpam-3228	87	41	uni	uni	ADJ
ejpam-3228	87	42	-	-	PUNCT
ejpam-3228	87	43	ag	ag	NOUN
ejpam-3228	87	44	-	-	PUNCT
ejpam-3228	87	45	group	group	NOUN
ejpam-3228	87	46	)	)	PUNCT
ejpam-3228	87	47	is	be	AUX
ejpam-3228	87	48	given	give	VERB
ejpam-3228	87	49	,	,	PUNCT
ejpam-3228	87	50	some	some	PRON
ejpam-3228	87	51	of	of	ADP
ejpam-3228	87	52	the	the	DET
ejpam-3228	87	53	basic	basic	ADJ
ejpam-3228	87	54	results	result	NOUN
ejpam-3228	87	55	along	along	ADP
ejpam-3228	87	56	with	with	ADP
ejpam-3228	87	57	suitable	suitable	ADJ
ejpam-3228	87	58	examples	example	NOUN
ejpam-3228	87	59	are	be	AUX
ejpam-3228	87	60	provided	provide	VERB
ejpam-3228	87	61	.	.	PUNCT
ejpam-3228	88	1	definition	definition	NOUN
ejpam-3228	88	2	4	4	NUM
ejpam-3228	88	3	.	.	PUNCT
ejpam-3228	89	1	let	let	VERB
ejpam-3228	89	2	g	g	PRON
ejpam-3228	89	3	be	be	AUX
ejpam-3228	89	4	an	an	DET
ejpam-3228	89	5	ag	ag	PROPN
ejpam-3228	89	6	-	-	PUNCT
ejpam-3228	89	7	group	group	NOUN
ejpam-3228	89	8	and	and	CCONJ
ejpam-3228	89	9	a	a	DET
ejpam-3228	89	10	∈	∈	PROPN
ejpam-3228	89	11	s(u	s(u	PROPN
ejpam-3228	89	12	)	)	PUNCT
ejpam-3228	89	13	be	be	VERB
ejpam-3228	89	14	a	a	DET
ejpam-3228	89	15	soft	soft	ADJ
ejpam-3228	89	16	set	set	NOUN
ejpam-3228	89	17	.	.	PUNCT
ejpam-3228	90	1	then	then	ADV
ejpam-3228	90	2	,	,	PUNCT
ejpam-3228	90	3	a	a	PRON
ejpam-3228	90	4	is	be	AUX
ejpam-3228	90	5	called	call	VERB
ejpam-3228	90	6	soft	soft	ADJ
ejpam-3228	90	7	uni	uni	ADJ
ejpam-3228	90	8	-	-	PUNCT
ejpam-3228	90	9	ag	ag	NOUN
ejpam-3228	90	10	-	-	PUNCT
ejpam-3228	90	11	group	group	NOUN
ejpam-3228	90	12	over	over	ADP
ejpam-3228	90	13	u	u	NOUN
ejpam-3228	90	14	if	if	SCONJ
ejpam-3228	90	15	1	1	NUM
ejpam-3228	90	16	.	.	PUNCT
ejpam-3228	90	17	fa(ab	fa(ab	NOUN
ejpam-3228	90	18	)	)	PUNCT
ejpam-3228	90	19	⊆	⊆	NUM
ejpam-3228	90	20	fa(a	fa(a	NOUN
ejpam-3228	90	21	)	)	PUNCT
ejpam-3228	90	22	∪	∪	ADP
ejpam-3228	90	23	fa(b	fa(b	NOUN
ejpam-3228	90	24	)	)	PUNCT
ejpam-3228	90	25	∀	∀	X
ejpam-3228	90	26	a	a	PRON
ejpam-3228	90	27	,	,	PUNCT
ejpam-3228	90	28	b	b	PROPN
ejpam-3228	90	29	∈	∈	PROPN
ejpam-3228	90	30	g	g	PROPN
ejpam-3228	90	31	,	,	PUNCT
ejpam-3228	90	32	2	2	NUM
ejpam-3228	90	33	.	.	X
ejpam-3228	90	34	fa(a−1	fa(a−1	NOUN
ejpam-3228	90	35	)	)	PUNCT
ejpam-3228	90	36	=	=	PUNCT
ejpam-3228	90	37	fa(a	fa(a	NOUN
ejpam-3228	90	38	)	)	PUNCT
ejpam-3228	90	39	∀	∀	X
ejpam-3228	90	40	a	a	DET
ejpam-3228	90	41	∈	∈	PROPN
ejpam-3228	90	42	g.	g.	NOUN
ejpam-3228	90	43	the	the	DET
ejpam-3228	90	44	set	set	NOUN
ejpam-3228	90	45	of	of	ADP
ejpam-3228	90	46	all	all	DET
ejpam-3228	90	47	soft	soft	ADJ
ejpam-3228	90	48	uni	uni	ADJ
ejpam-3228	90	49	-	-	PUNCT
ejpam-3228	90	50	ag	ag	NOUN
ejpam-3228	90	51	-	-	PUNCT
ejpam-3228	90	52	group	group	NOUN
ejpam-3228	90	53	over	over	ADP
ejpam-3228	90	54	u	u	PROPN
ejpam-3228	90	55	is	be	AUX
ejpam-3228	90	56	symbolically	symbolically	ADV
ejpam-3228	90	57	represented	represent	VERB
ejpam-3228	90	58	by	by	ADP
ejpam-3228	90	59	s∪ag(u	s∪ag(u	NOUN
ejpam-3228	90	60	)	)	PUNCT
ejpam-3228	90	61	.	.	PUNCT
ejpam-3228	91	1	example	example	NOUN
ejpam-3228	92	1	1	1	X
ejpam-3228	92	2	.	.	X
ejpam-3228	92	3	consider	consider	VERB
ejpam-3228	92	4	a	a	DET
ejpam-3228	92	5	non	non	ADJ
ejpam-3228	92	6	-	-	ADJ
ejpam-3228	92	7	associative	associative	ADJ
ejpam-3228	92	8	ag	ag	PROPN
ejpam-3228	92	9	-	-	PUNCT
ejpam-3228	92	10	group	group	NOUN
ejpam-3228	92	11	g	g	NOUN
ejpam-3228	92	12	=	=	PUNCT
ejpam-3228	92	13	{	{	PUNCT
ejpam-3228	92	14	0	0	NUM
ejpam-3228	92	15	,	,	PUNCT
ejpam-3228	92	16	1	1	NUM
ejpam-3228	92	17	,	,	PUNCT
ejpam-3228	92	18	2	2	NUM
ejpam-3228	92	19	}	}	PUNCT
ejpam-3228	92	20	of	of	ADP
ejpam-3228	92	21	order	order	NOUN
ejpam-3228	92	22	3	3	NUM
ejpam-3228	92	23	with	with	ADP
ejpam-3228	92	24	left	left	ADJ
ejpam-3228	92	25	identity	identity	NOUN
ejpam-3228	92	26	0	0	NUM
ejpam-3228	92	27	,	,	PUNCT
ejpam-3228	92	28	defined	define	VERB
ejpam-3228	92	29	in	in	ADP
ejpam-3228	92	30	the	the	DET
ejpam-3228	92	31	following	follow	VERB
ejpam-3228	92	32	table	table	NOUN
ejpam-3228	92	33	:	:	PUNCT
ejpam-3228	92	34	.	.	PUNCT
ejpam-3228	93	1	0	0	NUM
ejpam-3228	93	2	1	1	NUM
ejpam-3228	93	3	2	2	NUM
ejpam-3228	93	4	0	0	NUM
ejpam-3228	93	5	0	0	NUM
ejpam-3228	93	6	1	1	NUM
ejpam-3228	93	7	2	2	NUM
ejpam-3228	93	8	1	1	NUM
ejpam-3228	93	9	2	2	NUM
ejpam-3228	93	10	0	0	NUM
ejpam-3228	93	11	1	1	NUM
ejpam-3228	93	12	2	2	NUM
ejpam-3228	93	13	1	1	NUM
ejpam-3228	93	14	2	2	NUM
ejpam-3228	93	15	0	0	NUM
ejpam-3228	93	16	let	let	VERB
ejpam-3228	93	17	a	a	PRON
ejpam-3228	93	18	be	be	AUX
ejpam-3228	93	19	a	a	DET
ejpam-3228	93	20	soft	soft	ADJ
ejpam-3228	93	21	set	set	NOUN
ejpam-3228	93	22	over	over	ADP
ejpam-3228	93	23	u	u	NOUN
ejpam-3228	93	24	=	=	NOUN
ejpam-3228	93	25	{	{	PUNCT
ejpam-3228	93	26	u1	u1	PROPN
ejpam-3228	93	27	,	,	PUNCT
ejpam-3228	93	28	u2	u2	NOUN
ejpam-3228	93	29	,	,	PUNCT
ejpam-3228	93	30	.	.	PUNCT
ejpam-3228	93	31	.	.	PUNCT
ejpam-3228	94	1	.	.	PUNCT
ejpam-3228	95	1	,	,	PUNCT
ejpam-3228	95	2	u10	u10	PROPN
ejpam-3228	95	3	}	}	PUNCT
ejpam-3228	95	4	,	,	PUNCT
ejpam-3228	95	5	defined	define	VERB
ejpam-3228	95	6	by	by	ADP
ejpam-3228	95	7	a	a	DET
ejpam-3228	95	8	=	=	X
ejpam-3228	95	9	{	{	PUNCT
ejpam-3228	95	10	(	(	PUNCT
ejpam-3228	95	11	0	0	NUM
ejpam-3228	95	12	,	,	PUNCT
ejpam-3228	95	13	fa(0	fa(0	NOUN
ejpam-3228	95	14	)	)	PUNCT
ejpam-3228	95	15	)	)	PUNCT
ejpam-3228	95	16	,	,	PUNCT
ejpam-3228	95	17	(	(	PUNCT
ejpam-3228	95	18	1	1	NUM
ejpam-3228	95	19	,	,	PUNCT
ejpam-3228	95	20	fa(1	fa(1	NOUN
ejpam-3228	95	21	)	)	PUNCT
ejpam-3228	95	22	)	)	PUNCT
ejpam-3228	95	23	,	,	PUNCT
ejpam-3228	95	24	(	(	PUNCT
ejpam-3228	95	25	2	2	NUM
ejpam-3228	95	26	,	,	PUNCT
ejpam-3228	95	27	fa(2	fa(2	NOUN
ejpam-3228	95	28	)	)	PUNCT
ejpam-3228	95	29	)	)	PUNCT
ejpam-3228	95	30	}	}	PUNCT
ejpam-3228	96	1	=	=	SYM
ejpam-3228	96	2	{	{	PUNCT
ejpam-3228	96	3	(	(	PUNCT
ejpam-3228	96	4	0	0	NUM
ejpam-3228	96	5	,	,	PUNCT
ejpam-3228	96	6	{	{	PUNCT
ejpam-3228	96	7	u1	u1	NOUN
ejpam-3228	96	8	,	,	PUNCT
ejpam-3228	96	9	u3	u3	NOUN
ejpam-3228	96	10	}	}	PUNCT
ejpam-3228	96	11	)	)	PUNCT
ejpam-3228	96	12	,	,	PUNCT
ejpam-3228	96	13	(	(	PUNCT
ejpam-3228	96	14	1	1	NUM
ejpam-3228	96	15	,	,	PUNCT
ejpam-3228	96	16	{	{	PUNCT
ejpam-3228	96	17	u1	u1	NOUN
ejpam-3228	96	18	,	,	PUNCT
ejpam-3228	96	19	u3	u3	PROPN
ejpam-3228	96	20	,	,	PUNCT
ejpam-3228	96	21	u5	u5	PROPN
ejpam-3228	96	22	}	}	PUNCT
ejpam-3228	96	23	)	)	PUNCT
ejpam-3228	96	24	,	,	PUNCT
ejpam-3228	96	25	(	(	PUNCT
ejpam-3228	96	26	2	2	NUM
ejpam-3228	96	27	,	,	PUNCT
ejpam-3228	96	28	{	{	PUNCT
ejpam-3228	96	29	u1	u1	NOUN
ejpam-3228	96	30	,	,	PUNCT
ejpam-3228	96	31	u3	u3	PROPN
ejpam-3228	96	32	,	,	PUNCT
ejpam-3228	96	33	u5	u5	PROPN
ejpam-3228	96	34	}	}	PUNCT
ejpam-3228	96	35	)	)	PUNCT
ejpam-3228	96	36	}	}	PUNCT
ejpam-3228	96	37	.	.	PUNCT
ejpam-3228	97	1	then	then	ADV
ejpam-3228	97	2	,	,	PUNCT
ejpam-3228	97	3	a	a	PRON
ejpam-3228	97	4	is	be	AUX
ejpam-3228	97	5	a	a	DET
ejpam-3228	97	6	soft	soft	ADJ
ejpam-3228	97	7	uni	uni	ADJ
ejpam-3228	97	8	-	-	PUNCT
ejpam-3228	97	9	ag	ag	NOUN
ejpam-3228	97	10	-	-	PUNCT
ejpam-3228	97	11	group	group	NOUN
ejpam-3228	97	12	.	.	PUNCT
ejpam-3228	97	13	example	example	NOUN
ejpam-3228	98	1	2	2	NUM
ejpam-3228	98	2	.	.	X
ejpam-3228	98	3	consider	consider	VERB
ejpam-3228	98	4	a	a	DET
ejpam-3228	98	5	non	non	ADJ
ejpam-3228	98	6	-	-	ADJ
ejpam-3228	98	7	associative	associative	ADJ
ejpam-3228	98	8	ag	ag	PROPN
ejpam-3228	98	9	-	-	PUNCT
ejpam-3228	98	10	group	group	NOUN
ejpam-3228	98	11	g	g	NOUN
ejpam-3228	98	12	=	=	PUNCT
ejpam-3228	98	13	{	{	PUNCT
ejpam-3228	98	14	0	0	NUM
ejpam-3228	98	15	,	,	PUNCT
ejpam-3228	98	16	1	1	NUM
ejpam-3228	98	17	,	,	PUNCT
ejpam-3228	98	18	2	2	NUM
ejpam-3228	98	19	,	,	PUNCT
ejpam-3228	98	20	3	3	NUM
ejpam-3228	98	21	}	}	PUNCT
ejpam-3228	98	22	of	of	ADP
ejpam-3228	98	23	order	order	NOUN
ejpam-3228	98	24	4	4	NUM
ejpam-3228	98	25	with	with	ADP
ejpam-3228	98	26	left	left	ADJ
ejpam-3228	98	27	identity	identity	NOUN
ejpam-3228	98	28	0	0	NUM
ejpam-3228	98	29	defined	define	VERB
ejpam-3228	98	30	by	by	ADP
ejpam-3228	98	31	:	:	PUNCT
ejpam-3228	98	32	.	.	PUNCT
ejpam-3228	99	1	0	0	NUM
ejpam-3228	100	1	1	1	NUM
ejpam-3228	100	2	2	2	NUM
ejpam-3228	100	3	3	3	NUM
ejpam-3228	100	4	0	0	NUM
ejpam-3228	100	5	0	0	NUM
ejpam-3228	100	6	1	1	NUM
ejpam-3228	100	7	2	2	NUM
ejpam-3228	100	8	3	3	NUM
ejpam-3228	100	9	1	1	NUM
ejpam-3228	100	10	3	3	NUM
ejpam-3228	100	11	0	0	NUM
ejpam-3228	100	12	1	1	NUM
ejpam-3228	100	13	2	2	NUM
ejpam-3228	100	14	2	2	NUM
ejpam-3228	100	15	2	2	NUM
ejpam-3228	100	16	3	3	NUM
ejpam-3228	100	17	0	0	NUM
ejpam-3228	100	18	1	1	NUM
ejpam-3228	100	19	3	3	NUM
ejpam-3228	100	20	1	1	NUM
ejpam-3228	100	21	2	2	NUM
ejpam-3228	100	22	3	3	NUM
ejpam-3228	100	23	0	0	NUM
ejpam-3228	100	24	let	let	VERB
ejpam-3228	100	25	a	a	PRON
ejpam-3228	100	26	be	be	AUX
ejpam-3228	100	27	a	a	DET
ejpam-3228	100	28	soft	soft	ADJ
ejpam-3228	100	29	set	set	NOUN
ejpam-3228	100	30	over	over	ADP
ejpam-3228	100	31	u	u	NOUN
ejpam-3228	100	32	=	=	PROPN
ejpam-3228	100	33	z	z	PROPN
ejpam-3228	100	34	,	,	PUNCT
ejpam-3228	100	35	defined	define	VERB
ejpam-3228	100	36	by	by	ADP
ejpam-3228	100	37	a	a	DET
ejpam-3228	100	38	=	=	X
ejpam-3228	100	39	{	{	PUNCT
ejpam-3228	100	40	(	(	PUNCT
ejpam-3228	100	41	0	0	NUM
ejpam-3228	100	42	,	,	PUNCT
ejpam-3228	100	43	fa(0	fa(0	NOUN
ejpam-3228	100	44	)	)	PUNCT
ejpam-3228	100	45	)	)	PUNCT
ejpam-3228	100	46	,	,	PUNCT
ejpam-3228	100	47	(	(	PUNCT
ejpam-3228	100	48	1	1	NUM
ejpam-3228	100	49	,	,	PUNCT
ejpam-3228	100	50	fa(1	fa(1	NOUN
ejpam-3228	100	51	)	)	PUNCT
ejpam-3228	100	52	)	)	PUNCT
ejpam-3228	100	53	,	,	PUNCT
ejpam-3228	100	54	(	(	PUNCT
ejpam-3228	100	55	3	3	NUM
ejpam-3228	100	56	,	,	PUNCT
ejpam-3228	100	57	fa(3	fa(3	NOUN
ejpam-3228	100	58	)	)	PUNCT
ejpam-3228	100	59	)	)	PUNCT
ejpam-3228	100	60	,	,	PUNCT
ejpam-3228	100	61	(	(	PUNCT
ejpam-3228	100	62	4	4	NUM
ejpam-3228	100	63	,	,	PUNCT
ejpam-3228	100	64	fa(4	fa(4	NOUN
ejpam-3228	100	65	)	)	PUNCT
ejpam-3228	100	66	)	)	PUNCT
ejpam-3228	100	67	}	}	PUNCT
ejpam-3228	101	1	=	=	SYM
ejpam-3228	101	2	{	{	PUNCT
ejpam-3228	101	3	(	(	PUNCT
ejpam-3228	101	4	0	0	NUM
ejpam-3228	101	5	,	,	PUNCT
ejpam-3228	101	6	{	{	PUNCT
ejpam-3228	101	7	1	1	NUM
ejpam-3228	101	8	,	,	PUNCT
ejpam-3228	101	9	3	3	NUM
ejpam-3228	101	10	}	}	PUNCT
ejpam-3228	101	11	)	)	PUNCT
ejpam-3228	101	12	,	,	PUNCT
ejpam-3228	101	13	(	(	PUNCT
ejpam-3228	101	14	1	1	NUM
ejpam-3228	101	15	,	,	PUNCT
ejpam-3228	101	16	{	{	PUNCT
ejpam-3228	101	17	1	1	NUM
ejpam-3228	101	18	,	,	PUNCT
ejpam-3228	101	19	3	3	NUM
ejpam-3228	101	20	,	,	PUNCT
ejpam-3228	101	21	5	5	NUM
ejpam-3228	101	22	,	,	PUNCT
ejpam-3228	101	23	7	7	NUM
ejpam-3228	101	24	}	}	PUNCT
ejpam-3228	101	25	)	)	PUNCT
ejpam-3228	101	26	,	,	PUNCT
ejpam-3228	101	27	(	(	PUNCT
ejpam-3228	101	28	2	2	NUM
ejpam-3228	101	29	,	,	PUNCT
ejpam-3228	101	30	{	{	PUNCT
ejpam-3228	101	31	1	1	NUM
ejpam-3228	101	32	,	,	PUNCT
ejpam-3228	101	33	3	3	NUM
ejpam-3228	101	34	,	,	PUNCT
ejpam-3228	101	35	5	5	NUM
ejpam-3228	101	36	,	,	PUNCT
ejpam-3228	101	37	7	7	NUM
ejpam-3228	101	38	}	}	PUNCT
ejpam-3228	101	39	)	)	PUNCT
ejpam-3228	101	40	,	,	PUNCT
ejpam-3228	101	41	(	(	PUNCT
ejpam-3228	101	42	3	3	X
ejpam-3228	101	43	,	,	PUNCT
ejpam-3228	101	44	{	{	PUNCT
ejpam-3228	101	45	1	1	NUM
ejpam-3228	101	46	,	,	PUNCT
ejpam-3228	101	47	3	3	NUM
ejpam-3228	101	48	,	,	PUNCT
ejpam-3228	101	49	5	5	NUM
ejpam-3228	101	50	,	,	PUNCT
ejpam-3228	101	51	7	7	NUM
ejpam-3228	101	52	}	}	PUNCT
ejpam-3228	101	53	)	)	PUNCT
ejpam-3228	101	54	}	}	PUNCT
ejpam-3228	101	55	.	.	PUNCT
ejpam-3228	102	1	then	then	ADV
ejpam-3228	102	2	,	,	PUNCT
ejpam-3228	102	3	one	one	PRON
ejpam-3228	102	4	can	can	AUX
ejpam-3228	102	5	easily	easily	ADV
ejpam-3228	102	6	show	show	VERB
ejpam-3228	102	7	that	that	SCONJ
ejpam-3228	102	8	a	a	DET
ejpam-3228	102	9	∈	∈	PROPN
ejpam-3228	102	10	s∪ag(u	s∪ag(u	NUM
ejpam-3228	102	11	)	)	PUNCT
ejpam-3228	102	12	.	.	PUNCT
ejpam-3228	103	1	lemma	lemma	PROPN
ejpam-3228	103	2	2	2	X
ejpam-3228	103	3	.	.	PUNCT
ejpam-3228	103	4	let	let	VERB
ejpam-3228	103	5	a	a	DET
ejpam-3228	103	6	∈	∈	NOUN
ejpam-3228	103	7	s∪ag(u	s∪ag(u	NUM
ejpam-3228	103	8	)	)	PUNCT
ejpam-3228	103	9	.	.	PUNCT
ejpam-3228	104	1	then	then	ADV
ejpam-3228	104	2	,	,	PUNCT
ejpam-3228	104	3	fa(e	fa(e	X
ejpam-3228	104	4	)	)	PUNCT
ejpam-3228	104	5	⊆	⊆	NUM
ejpam-3228	104	6	fa(a	fa(a	NOUN
ejpam-3228	104	7	)	)	PUNCT
ejpam-3228	104	8	for	for	ADP
ejpam-3228	104	9	all	all	DET
ejpam-3228	104	10	a	a	DET
ejpam-3228	104	11	∈	∈	PROPN
ejpam-3228	104	12	g.	g.	PROPN
ejpam-3228	104	13	a.	a.	PROPN
ejpam-3228	104	14	ullah	ullah	PROPN
ejpam-3228	104	15	,	,	PUNCT
ejpam-3228	104	16	f.	f.	PROPN
ejpam-3228	104	17	karaaslan	karaaslan	PROPN
ejpam-3228	104	18	,	,	PUNCT
ejpam-3228	104	19	i.	i.	PROPN
ejpam-3228	104	20	ahmad	ahmad	PROPN
ejpam-3228	104	21	/	/	SYM
ejpam-3228	104	22	eur	eur	PROPN
ejpam-3228	104	23	.	.	PUNCT
ejpam-3228	105	1	j.	j.	PROPN
ejpam-3228	105	2	pure	pure	PROPN
ejpam-3228	105	3	appl	appl	PROPN
ejpam-3228	105	4	.	.	PROPN
ejpam-3228	105	5	math	math	PROPN
ejpam-3228	105	6	,	,	PUNCT
ejpam-3228	105	7	11	11	NUM
ejpam-3228	105	8	(	(	PUNCT
ejpam-3228	105	9	2	2	NUM
ejpam-3228	105	10	)	)	PUNCT
ejpam-3228	105	11	(	(	PUNCT
ejpam-3228	105	12	2018	2018	NUM
ejpam-3228	105	13	)	)	PUNCT
ejpam-3228	105	14	,	,	PUNCT
ejpam-3228	105	15	517	517	NUM
ejpam-3228	105	16	-	-	SYM
ejpam-3228	105	17	536	536	NUM
ejpam-3228	105	18	521	521	NUM
ejpam-3228	105	19	proof	proof	NOUN
ejpam-3228	105	20	.	.	PUNCT
ejpam-3228	106	1	since	since	SCONJ
ejpam-3228	106	2	a	a	DET
ejpam-3228	106	3	∈	∈	PROPN
ejpam-3228	106	4	s∪ag(u	s∪ag(u	NUM
ejpam-3228	106	5	)	)	PUNCT
ejpam-3228	106	6	.	.	PUNCT
ejpam-3228	107	1	then	then	ADV
ejpam-3228	107	2	,	,	PUNCT
ejpam-3228	107	3	for	for	ADP
ejpam-3228	107	4	all	all	DET
ejpam-3228	107	5	a	a	DET
ejpam-3228	107	6	∈	∈	PROPN
ejpam-3228	107	7	g	g	NOUN
ejpam-3228	107	8	,	,	PUNCT
ejpam-3228	107	9	fa(e	fa(e	X
ejpam-3228	107	10	)	)	PUNCT
ejpam-3228	107	11	=	=	SYM
ejpam-3228	107	12	fa(aa−1	fa(aa−1	PROPN
ejpam-3228	107	13	)	)	PUNCT
ejpam-3228	107	14	⊆	⊆	NUM
ejpam-3228	107	15	fa(a	fa(a	NOUN
ejpam-3228	107	16	)	)	PUNCT
ejpam-3228	107	17	∪	∪	ADP
ejpam-3228	107	18	fa(a−1	fa(a−1	NOUN
ejpam-3228	107	19	)	)	PUNCT
ejpam-3228	107	20	=	=	PUNCT
ejpam-3228	107	21	fa(a	fa(a	NOUN
ejpam-3228	107	22	)	)	PUNCT
ejpam-3228	107	23	∪	∪	ADP
ejpam-3228	107	24	fa(a	fa(a	NOUN
ejpam-3228	107	25	)	)	PUNCT
ejpam-3228	107	26	=	=	SYM
ejpam-3228	107	27	fa(a	fa(a	NOUN
ejpam-3228	107	28	)	)	PUNCT
ejpam-3228	107	29	.	.	PUNCT
ejpam-3228	108	1	hence	hence	ADV
ejpam-3228	108	2	,	,	PUNCT
ejpam-3228	108	3	fa(e	fa(e	X
ejpam-3228	108	4	)	)	PUNCT
ejpam-3228	108	5	⊆	⊆	NUM
ejpam-3228	108	6	fa(a	fa(a	NOUN
ejpam-3228	108	7	)	)	PUNCT
ejpam-3228	108	8	for	for	ADP
ejpam-3228	108	9	all	all	DET
ejpam-3228	108	10	a	a	DET
ejpam-3228	108	11	∈	∈	PROPN
ejpam-3228	108	12	g.	g.	NOUN
ejpam-3228	108	13	lemma	lemma	PROPN
ejpam-3228	108	14	3	3	X
ejpam-3228	108	15	.	.	PUNCT
ejpam-3228	108	16	let	let	VERB
ejpam-3228	108	17	a	a	DET
ejpam-3228	108	18	∈	∈	NOUN
ejpam-3228	108	19	s∪ag(u	s∪ag(u	NUM
ejpam-3228	108	20	)	)	PUNCT
ejpam-3228	108	21	.	.	PUNCT
ejpam-3228	109	1	then	then	ADV
ejpam-3228	109	2	fa(ab	fa(ab	NOUN
ejpam-3228	109	3	)	)	PUNCT
ejpam-3228	109	4	=	=	SYM
ejpam-3228	109	5	fa(ba	fa(ba	PROPN
ejpam-3228	109	6	)	)	PUNCT
ejpam-3228	109	7	for	for	ADP
ejpam-3228	109	8	all	all	DET
ejpam-3228	109	9	a	a	DET
ejpam-3228	109	10	,	,	PUNCT
ejpam-3228	109	11	b	b	PROPN
ejpam-3228	109	12	∈	∈	PROPN
ejpam-3228	109	13	g.	g.	NOUN
ejpam-3228	109	14	proof	proof	NOUN
ejpam-3228	109	15	.	.	PUNCT
ejpam-3228	110	1	let	let	VERB
ejpam-3228	110	2	a	a	DET
ejpam-3228	110	3	∈	∈	NOUN
ejpam-3228	110	4	s∪ag(u	s∪ag(u	NUM
ejpam-3228	110	5	)	)	PUNCT
ejpam-3228	110	6	.	.	PUNCT
ejpam-3228	111	1	then	then	ADV
ejpam-3228	111	2	for	for	ADP
ejpam-3228	111	3	all	all	DET
ejpam-3228	111	4	a	a	PRON
ejpam-3228	111	5	,	,	PUNCT
ejpam-3228	111	6	b	b	PROPN
ejpam-3228	111	7	∈	∈	PROPN
ejpam-3228	111	8	g	g	NOUN
ejpam-3228	111	9	,	,	PUNCT
ejpam-3228	111	10	fa(ab	fa(ab	NOUN
ejpam-3228	111	11	)	)	PUNCT
ejpam-3228	111	12	=	=	SYM
ejpam-3228	111	13	fa((ea)b	fa((ea)b	NUM
ejpam-3228	111	14	)	)	PUNCT
ejpam-3228	111	15	=	=	SYM
ejpam-3228	111	16	fa	fa	INTJ
ejpam-3228	111	17	(	(	PUNCT
ejpam-3228	111	18	(	(	PUNCT
ejpam-3228	111	19	ba)e	ba)e	NOUN
ejpam-3228	111	20	)	)	PUNCT
ejpam-3228	111	21	(	(	PUNCT
ejpam-3228	111	22	by	by	ADP
ejpam-3228	111	23	the	the	DET
ejpam-3228	111	24	left	left	ADJ
ejpam-3228	111	25	invertive	invertive	ADJ
ejpam-3228	111	26	law	law	NOUN
ejpam-3228	111	27	)	)	PUNCT
ejpam-3228	111	28	⊆	⊆	NUM
ejpam-3228	111	29	fa(ba	fa(ba	NOUN
ejpam-3228	111	30	)	)	PUNCT
ejpam-3228	111	31	∪	∪	ADP
ejpam-3228	111	32	fa(e	fa(e	NUM
ejpam-3228	111	33	)	)	PUNCT
ejpam-3228	111	34	=	=	SYM
ejpam-3228	111	35	fa(ba	fa(ba	ADJ
ejpam-3228	111	36	)	)	PUNCT
ejpam-3228	111	37	(	(	PUNCT
ejpam-3228	111	38	by	by	ADP
ejpam-3228	111	39	lemma	lemma	PROPN
ejpam-3228	111	40	2	2	NUM
ejpam-3228	111	41	)	)	PUNCT
ejpam-3228	111	42	⇒	⇒	NOUN
ejpam-3228	111	43	fa(ab	fa(ab	NOUN
ejpam-3228	111	44	)	)	PUNCT
ejpam-3228	111	45	⊆	⊆	NUM
ejpam-3228	111	46	fa(ba	fa(ba	NOUN
ejpam-3228	111	47	)	)	PUNCT
ejpam-3228	111	48	.	.	PUNCT
ejpam-3228	112	1	similarly	similarly	ADV
ejpam-3228	112	2	,	,	PUNCT
ejpam-3228	112	3	it	it	PRON
ejpam-3228	112	4	can	can	AUX
ejpam-3228	112	5	be	be	AUX
ejpam-3228	112	6	shown	show	VERB
ejpam-3228	112	7	that	that	SCONJ
ejpam-3228	112	8	fa(ba	fa(ba	NOUN
ejpam-3228	112	9	)	)	PUNCT
ejpam-3228	112	10	⊆	⊆	NUM
ejpam-3228	112	11	fa(ab	fa(ab	NOUN
ejpam-3228	112	12	)	)	PUNCT
ejpam-3228	112	13	.	.	PUNCT
ejpam-3228	113	1	hence	hence	ADV
ejpam-3228	113	2	,	,	PUNCT
ejpam-3228	113	3	fa(ab	fa(ab	PROPN
ejpam-3228	113	4	)	)	PUNCT
ejpam-3228	113	5	=	=	SYM
ejpam-3228	113	6	fa(ba	fa(ba	PROPN
ejpam-3228	113	7	)	)	PUNCT
ejpam-3228	113	8	for	for	ADP
ejpam-3228	113	9	all	all	DET
ejpam-3228	113	10	a	a	PRON
ejpam-3228	113	11	,	,	PUNCT
ejpam-3228	113	12	b	b	PROPN
ejpam-3228	113	13	∈	∈	PROPN
ejpam-3228	113	14	g.	g.	NOUN
ejpam-3228	113	15	theorem	theorem	VERB
ejpam-3228	113	16	1	1	NUM
ejpam-3228	113	17	.	.	PUNCT
ejpam-3228	114	1	a	a	DET
ejpam-3228	114	2	soft	soft	ADJ
ejpam-3228	114	3	set	set	NOUN
ejpam-3228	114	4	a	a	PRON
ejpam-3228	114	5	over	over	ADP
ejpam-3228	114	6	u	u	NOUN
ejpam-3228	114	7	is	be	AUX
ejpam-3228	114	8	a	a	DET
ejpam-3228	114	9	soft	soft	ADJ
ejpam-3228	114	10	uni	uni	ADJ
ejpam-3228	114	11	-	-	PUNCT
ejpam-3228	114	12	ag	ag	NOUN
ejpam-3228	114	13	-	-	PUNCT
ejpam-3228	114	14	group	group	NOUN
ejpam-3228	114	15	over	over	ADP
ejpam-3228	114	16	u	u	NOUN
ejpam-3228	114	17	if	if	SCONJ
ejpam-3228	114	18	and	and	CCONJ
ejpam-3228	114	19	only	only	ADV
ejpam-3228	114	20	if	if	SCONJ
ejpam-3228	114	21	fa(ab−1	fa(ab−1	NOUN
ejpam-3228	114	22	)	)	PUNCT
ejpam-3228	114	23	⊆	⊆	NUM
ejpam-3228	114	24	fa(a	fa(a	NOUN
ejpam-3228	114	25	)	)	PUNCT
ejpam-3228	114	26	∪	∪	ADP
ejpam-3228	114	27	fa(b	fa(b	NOUN
ejpam-3228	114	28	)	)	PUNCT
ejpam-3228	114	29	for	for	ADP
ejpam-3228	114	30	all	all	DET
ejpam-3228	114	31	a	a	DET
ejpam-3228	114	32	,	,	PUNCT
ejpam-3228	114	33	b	b	PROPN
ejpam-3228	114	34	∈	∈	PROPN
ejpam-3228	114	35	g.	g.	NOUN
ejpam-3228	114	36	proof	proof	NOUN
ejpam-3228	114	37	.	.	PUNCT
ejpam-3228	115	1	suppose	suppose	VERB
ejpam-3228	115	2	a	a	DET
ejpam-3228	115	3	∈	∈	PROPN
ejpam-3228	115	4	s∪ag(u	s∪ag(u	NUM
ejpam-3228	115	5	)	)	PUNCT
ejpam-3228	115	6	.	.	PUNCT
ejpam-3228	116	1	then	then	ADV
ejpam-3228	116	2	,	,	PUNCT
ejpam-3228	116	3	for	for	ADP
ejpam-3228	116	4	all	all	DET
ejpam-3228	116	5	a	a	DET
ejpam-3228	116	6	,	,	PUNCT
ejpam-3228	116	7	b	b	PROPN
ejpam-3228	116	8	∈	∈	PROPN
ejpam-3228	116	9	g	g	PROPN
ejpam-3228	116	10	,	,	PUNCT
ejpam-3228	116	11	fa(ab−1	fa(ab−1	PROPN
ejpam-3228	116	12	)	)	PUNCT
ejpam-3228	116	13	⊆	⊆	NUM
ejpam-3228	116	14	fa(a	fa(a	NOUN
ejpam-3228	116	15	)	)	PUNCT
ejpam-3228	116	16	∪	∪	ADP
ejpam-3228	116	17	fa(b−1	fa(b−1	NOUN
ejpam-3228	116	18	)	)	PUNCT
ejpam-3228	116	19	=	=	SYM
ejpam-3228	116	20	fa(a	fa(a	NOUN
ejpam-3228	116	21	)	)	PUNCT
ejpam-3228	116	22	∪	∪	ADP
ejpam-3228	116	23	fa(b	fa(b	NOUN
ejpam-3228	116	24	)	)	PUNCT
ejpam-3228	116	25	⇒	⇒	NOUN
ejpam-3228	116	26	fa(ab−1	fa(ab−1	NOUN
ejpam-3228	116	27	)	)	PUNCT
ejpam-3228	116	28	⊆	⊆	NUM
ejpam-3228	116	29	fa(a	fa(a	NOUN
ejpam-3228	116	30	)	)	PUNCT
ejpam-3228	116	31	∪	∪	ADP
ejpam-3228	116	32	fa(b	fa(b	NOUN
ejpam-3228	116	33	)	)	PUNCT
ejpam-3228	116	34	.	.	PUNCT
ejpam-3228	117	1	conversely	conversely	ADV
ejpam-3228	117	2	,	,	PUNCT
ejpam-3228	117	3	suppose	suppose	VERB
ejpam-3228	117	4	that	that	SCONJ
ejpam-3228	117	5	for	for	ADP
ejpam-3228	117	6	all	all	DET
ejpam-3228	117	7	a	a	PRON
ejpam-3228	117	8	,	,	PUNCT
ejpam-3228	117	9	b	b	PROPN
ejpam-3228	117	10	∈	∈	PROPN
ejpam-3228	117	11	g	g	PROPN
ejpam-3228	117	12	,	,	PUNCT
ejpam-3228	117	13	fa(ab−1	fa(ab−1	PROPN
ejpam-3228	117	14	)	)	PUNCT
ejpam-3228	117	15	⊆	⊆	NUM
ejpam-3228	117	16	fa(a	fa(a	NOUN
ejpam-3228	117	17	)	)	PUNCT
ejpam-3228	117	18	∪	∪	ADP
ejpam-3228	117	19	fa(b	fa(b	NOUN
ejpam-3228	117	20	)	)	PUNCT
ejpam-3228	117	21	.	.	PUNCT
ejpam-3228	118	1	then	then	ADV
ejpam-3228	118	2	by	by	ADP
ejpam-3228	118	3	choosing	choose	VERB
ejpam-3228	118	4	a	a	DET
ejpam-3228	118	5	=	=	PUNCT
ejpam-3228	118	6	e	e	X
ejpam-3228	118	7	we	we	PRON
ejpam-3228	118	8	get	get	VERB
ejpam-3228	118	9	fa(b−1	fa(b−1	NOUN
ejpam-3228	118	10	)	)	PUNCT
ejpam-3228	118	11	⊆	⊆	NUM
ejpam-3228	118	12	fa(b	fa(b	NUM
ejpam-3228	118	13	)	)	PUNCT
ejpam-3228	118	14	.	.	PUNCT
ejpam-3228	119	1	(	(	PUNCT
ejpam-3228	119	2	by	by	ADP
ejpam-3228	119	3	lemma	lemma	PROPN
ejpam-3228	119	4	2	2	NUM
ejpam-3228	119	5	)	)	PUNCT
ejpam-3228	119	6	thus	thus	ADV
ejpam-3228	119	7	,	,	PUNCT
ejpam-3228	119	8	fa(b	fa(b	NOUN
ejpam-3228	119	9	)	)	PUNCT
ejpam-3228	119	10	=	=	SYM
ejpam-3228	119	11	fa((b−1)−1	fa((b−1)−1	NOUN
ejpam-3228	119	12	)	)	PUNCT
ejpam-3228	119	13	⊆	⊆	NUM
ejpam-3228	119	14	fa(b−1	fa(b−1	NOUN
ejpam-3228	119	15	)	)	PUNCT
ejpam-3228	119	16	.	.	PUNCT
ejpam-3228	120	1	consequently	consequently	ADV
ejpam-3228	120	2	,	,	PUNCT
ejpam-3228	120	3	fa(b	fa(b	NOUN
ejpam-3228	120	4	)	)	PUNCT
ejpam-3228	120	5	=	=	SYM
ejpam-3228	120	6	fa(b−1	fa(b−1	NOUN
ejpam-3228	120	7	)	)	PUNCT
ejpam-3228	120	8	∀	∀	PUNCT
ejpam-3228	121	1	b	b	X
ejpam-3228	121	2	∈	∈	PROPN
ejpam-3228	121	3	g.	g.	NOUN
ejpam-3228	121	4	now	now	ADV
ejpam-3228	121	5	,	,	PUNCT
ejpam-3228	121	6	fa(ab	fa(ab	PROPN
ejpam-3228	121	7	)	)	PUNCT
ejpam-3228	121	8	=	=	SYM
ejpam-3228	121	9	fa(a(b−1)−1	fa(a(b−1)−1	NOUN
ejpam-3228	121	10	)	)	PUNCT
ejpam-3228	121	11	⊆	⊆	NUM
ejpam-3228	121	12	fa(a	fa(a	NOUN
ejpam-3228	121	13	)	)	PUNCT
ejpam-3228	121	14	∪	∪	ADP
ejpam-3228	121	15	fa(b−1	fa(b−1	NOUN
ejpam-3228	121	16	)	)	PUNCT
ejpam-3228	121	17	=	=	SYM
ejpam-3228	121	18	fa(a	fa(a	NOUN
ejpam-3228	121	19	)	)	PUNCT
ejpam-3228	121	20	∪	∪	ADP
ejpam-3228	121	21	fa(b	fa(b	NOUN
ejpam-3228	121	22	)	)	PUNCT
ejpam-3228	121	23	.	.	PUNCT
ejpam-3228	122	1	hence	hence	ADV
ejpam-3228	122	2	,	,	PUNCT
ejpam-3228	122	3	a	a	DET
ejpam-3228	122	4	∈	∈	PROPN
ejpam-3228	122	5	s∪ag(u	s∪ag(u	NUM
ejpam-3228	122	6	)	)	PUNCT
ejpam-3228	122	7	.	.	PUNCT
ejpam-3228	123	1	a.	a.	PROPN
ejpam-3228	123	2	ullah	ullah	PROPN
ejpam-3228	123	3	,	,	PUNCT
ejpam-3228	123	4	f.	f.	PROPN
ejpam-3228	123	5	karaaslan	karaaslan	PROPN
ejpam-3228	123	6	,	,	PUNCT
ejpam-3228	123	7	i.	i.	PROPN
ejpam-3228	123	8	ahmad	ahmad	PROPN
ejpam-3228	123	9	/	/	SYM
ejpam-3228	123	10	eur	eur	PROPN
ejpam-3228	123	11	.	.	PUNCT
ejpam-3228	124	1	j.	j.	PROPN
ejpam-3228	124	2	pure	pure	PROPN
ejpam-3228	124	3	appl	appl	PROPN
ejpam-3228	124	4	.	.	PROPN
ejpam-3228	124	5	math	math	PROPN
ejpam-3228	124	6	,	,	PUNCT
ejpam-3228	124	7	11	11	NUM
ejpam-3228	124	8	(	(	PUNCT
ejpam-3228	124	9	2	2	NUM
ejpam-3228	124	10	)	)	PUNCT
ejpam-3228	124	11	(	(	PUNCT
ejpam-3228	124	12	2018	2018	NUM
ejpam-3228	124	13	)	)	PUNCT
ejpam-3228	124	14	,	,	PUNCT
ejpam-3228	124	15	517	517	NUM
ejpam-3228	124	16	-	-	SYM
ejpam-3228	124	17	536	536	NUM
ejpam-3228	124	18	522	522	NUM
ejpam-3228	124	19	lemma	lemma	PROPN
ejpam-3228	124	20	4	4	NUM
ejpam-3228	124	21	.	.	PUNCT
ejpam-3228	125	1	let	let	VERB
ejpam-3228	125	2	a	a	DET
ejpam-3228	125	3	∈	∈	NOUN
ejpam-3228	125	4	s∪ag(u	s∪ag(u	NUM
ejpam-3228	125	5	)	)	PUNCT
ejpam-3228	125	6	.	.	PUNCT
ejpam-3228	126	1	then	then	ADV
ejpam-3228	126	2	,	,	PUNCT
ejpam-3228	126	3	for	for	ADP
ejpam-3228	126	4	all	all	DET
ejpam-3228	126	5	a	a	DET
ejpam-3228	126	6	,	,	PUNCT
ejpam-3228	126	7	b	b	PROPN
ejpam-3228	126	8	∈	∈	PROPN
ejpam-3228	126	9	g	g	NOUN
ejpam-3228	126	10	,	,	PUNCT
ejpam-3228	126	11	fa(ab	fa(ab	NOUN
ejpam-3228	126	12	)	)	PUNCT
ejpam-3228	126	13	=	=	SYM
ejpam-3228	126	14	fa(b	fa(b	NOUN
ejpam-3228	126	15	)	)	PUNCT
ejpam-3228	126	16	if	if	SCONJ
ejpam-3228	126	17	and	and	CCONJ
ejpam-3228	126	18	only	only	ADV
ejpam-3228	126	19	if	if	SCONJ
ejpam-3228	126	20	fa(a	fa(a	VERB
ejpam-3228	126	21	)	)	PUNCT
ejpam-3228	126	22	=	=	SYM
ejpam-3228	126	23	fa(e	fa(e	X
ejpam-3228	126	24	)	)	PUNCT
ejpam-3228	126	25	.	.	PUNCT
ejpam-3228	127	1	proof	proof	NOUN
ejpam-3228	127	2	.	.	PUNCT
ejpam-3228	128	1	let	let	VERB
ejpam-3228	128	2	a	a	DET
ejpam-3228	128	3	∈	∈	PROPN
ejpam-3228	128	4	s∪ag(u	s∪ag(u	NUM
ejpam-3228	128	5	)	)	PUNCT
ejpam-3228	128	6	and	and	CCONJ
ejpam-3228	128	7	fa(ab	fa(ab	NOUN
ejpam-3228	128	8	)	)	PUNCT
ejpam-3228	128	9	=	=	SYM
ejpam-3228	128	10	fa(b	fa(b	NOUN
ejpam-3228	128	11	)	)	PUNCT
ejpam-3228	128	12	for	for	ADP
ejpam-3228	128	13	all	all	DET
ejpam-3228	128	14	a	a	DET
ejpam-3228	128	15	,	,	PUNCT
ejpam-3228	128	16	b	b	X
ejpam-3228	128	17	∈	∈	PROPN
ejpam-3228	128	18	g.	g.	NOUN
ejpam-3228	128	19	by	by	ADP
ejpam-3228	128	20	choosing	choose	VERB
ejpam-3228	128	21	b	b	NOUN
ejpam-3228	128	22	=	=	SYM
ejpam-3228	128	23	e	e	X
ejpam-3228	128	24	we	we	PRON
ejpam-3228	128	25	get	get	VERB
ejpam-3228	128	26	fa(ae	fa(ae	NOUN
ejpam-3228	128	27	)	)	PUNCT
ejpam-3228	129	1	=	=	SYM
ejpam-3228	129	2	fa(e	fa(e	X
ejpam-3228	129	3	)	)	PUNCT
ejpam-3228	129	4	⇒	⇒	PROPN
ejpam-3228	129	5	fa(ea	fa(ea	PROPN
ejpam-3228	129	6	)	)	PUNCT
ejpam-3228	129	7	=	=	SYM
ejpam-3228	129	8	fa(e	fa(e	X
ejpam-3228	129	9	)	)	PUNCT
ejpam-3228	129	10	(	(	PUNCT
ejpam-3228	129	11	by	by	ADP
ejpam-3228	129	12	lemma	lemma	PROPN
ejpam-3228	129	13	3	3	NUM
ejpam-3228	129	14	)	)	PUNCT
ejpam-3228	129	15	⇒	⇒	NOUN
ejpam-3228	129	16	fa(a	fa(a	PROPN
ejpam-3228	129	17	)	)	PUNCT
ejpam-3228	129	18	=	=	SYM
ejpam-3228	129	19	fa(e	fa(e	X
ejpam-3228	129	20	)	)	PUNCT
ejpam-3228	129	21	.	.	PUNCT
ejpam-3228	130	1	conversely	conversely	ADV
ejpam-3228	130	2	,	,	PUNCT
ejpam-3228	130	3	suppose	suppose	VERB
ejpam-3228	130	4	that	that	SCONJ
ejpam-3228	130	5	fa(a	fa(a	PRON
ejpam-3228	130	6	)	)	PUNCT
ejpam-3228	130	7	=	=	SYM
ejpam-3228	130	8	fa(e	fa(e	X
ejpam-3228	130	9	)	)	PUNCT
ejpam-3228	130	10	∀	∀	X
ejpam-3228	130	11	a	a	DET
ejpam-3228	130	12	∈	∈	PROPN
ejpam-3228	130	13	g.	g.	NOUN
ejpam-3228	130	14	then	then	ADV
ejpam-3228	130	15	,	,	PUNCT
ejpam-3228	130	16	fa(ab	fa(ab	NOUN
ejpam-3228	130	17	)	)	PUNCT
ejpam-3228	130	18	⊆	⊆	NUM
ejpam-3228	130	19	fa(a	fa(a	NOUN
ejpam-3228	130	20	)	)	PUNCT
ejpam-3228	130	21	∪	∪	ADP
ejpam-3228	130	22	fa(b	fa(b	NOUN
ejpam-3228	130	23	)	)	PUNCT
ejpam-3228	130	24	=	=	SYM
ejpam-3228	130	25	fa(e	fa(e	X
ejpam-3228	130	26	)	)	PUNCT
ejpam-3228	130	27	∪	∪	ADP
ejpam-3228	130	28	fa(b	fa(b	NOUN
ejpam-3228	130	29	)	)	PUNCT
ejpam-3228	130	30	=	=	SYM
ejpam-3228	130	31	fa(b	fa(b	X
ejpam-3228	130	32	)	)	PUNCT
ejpam-3228	130	33	(	(	PUNCT
ejpam-3228	130	34	by	by	ADP
ejpam-3228	130	35	lemma	lemma	PROPN
ejpam-3228	130	36	2	2	NUM
ejpam-3228	130	37	)	)	PUNCT
ejpam-3228	130	38	this	this	PRON
ejpam-3228	130	39	implies	imply	VERB
ejpam-3228	130	40	that	that	SCONJ
ejpam-3228	130	41	fa(ab	fa(ab	NOUN
ejpam-3228	130	42	)	)	PUNCT
ejpam-3228	130	43	⊆	⊆	NUM
ejpam-3228	130	44	fa(b	fa(b	NUM
ejpam-3228	130	45	)	)	PUNCT
ejpam-3228	130	46	.	.	PUNCT
ejpam-3228	131	1	(	(	PUNCT
ejpam-3228	131	2	1	1	X
ejpam-3228	131	3	)	)	PUNCT
ejpam-3228	131	4	also	also	ADV
ejpam-3228	131	5	,	,	PUNCT
ejpam-3228	131	6	fa(b	fa(b	NOUN
ejpam-3228	131	7	)	)	PUNCT
ejpam-3228	131	8	=	=	SYM
ejpam-3228	131	9	fa(eb	fa(eb	PROPN
ejpam-3228	131	10	)	)	PUNCT
ejpam-3228	131	11	=	=	SYM
ejpam-3228	132	1	fa((a−1a)b	fa((a−1a)b	X
ejpam-3228	132	2	)	)	PUNCT
ejpam-3228	132	3	=	=	SYM
ejpam-3228	132	4	fa	fa	INTJ
ejpam-3228	132	5	(	(	PUNCT
ejpam-3228	132	6	(	(	PUNCT
ejpam-3228	132	7	ba)a−1	ba)a−1	X
ejpam-3228	132	8	)	)	PUNCT
ejpam-3228	132	9	(	(	PUNCT
ejpam-3228	132	10	by	by	ADP
ejpam-3228	132	11	the	the	DET
ejpam-3228	132	12	left	left	ADJ
ejpam-3228	132	13	invertive	invertive	ADJ
ejpam-3228	132	14	law	law	NOUN
ejpam-3228	132	15	)	)	PUNCT
ejpam-3228	132	16	⊆	⊆	NUM
ejpam-3228	132	17	fa(ba	fa(ba	NOUN
ejpam-3228	132	18	)	)	PUNCT
ejpam-3228	132	19	∪	∪	NOUN
ejpam-3228	132	20	fa(a−1	fa(a−1	NOUN
ejpam-3228	132	21	)	)	PUNCT
ejpam-3228	132	22	=	=	SYM
ejpam-3228	132	23	fa(ab	fa(ab	PROPN
ejpam-3228	132	24	)	)	PUNCT
ejpam-3228	132	25	∪	∪	ADP
ejpam-3228	132	26	fa(a	fa(a	PROPN
ejpam-3228	132	27	)	)	PUNCT
ejpam-3228	132	28	(	(	PUNCT
ejpam-3228	132	29	by	by	ADP
ejpam-3228	132	30	lemma	lemma	PROPN
ejpam-3228	132	31	3	3	NUM
ejpam-3228	132	32	)	)	PUNCT
ejpam-3228	132	33	=	=	SYM
ejpam-3228	132	34	fa(ab	fa(ab	PROPN
ejpam-3228	132	35	)	)	PUNCT
ejpam-3228	132	36	∪	∪	NOUN
ejpam-3228	132	37	fa(e	fa(e	NUM
ejpam-3228	132	38	)	)	PUNCT
ejpam-3228	132	39	=	=	SYM
ejpam-3228	132	40	fa(ab	fa(ab	PROPN
ejpam-3228	132	41	)	)	PUNCT
ejpam-3228	132	42	.	.	PUNCT
ejpam-3228	133	1	(	(	PUNCT
ejpam-3228	133	2	by	by	ADP
ejpam-3228	133	3	lemma	lemma	PROPN
ejpam-3228	133	4	2	2	NUM
ejpam-3228	133	5	)	)	PUNCT
ejpam-3228	133	6	this	this	PRON
ejpam-3228	133	7	implies	imply	VERB
ejpam-3228	133	8	that	that	SCONJ
ejpam-3228	133	9	fa(b	fa(b	NUM
ejpam-3228	133	10	)	)	PUNCT
ejpam-3228	133	11	⊆	⊆	NUM
ejpam-3228	133	12	fa(ab	fa(ab	NOUN
ejpam-3228	133	13	)	)	PUNCT
ejpam-3228	133	14	.	.	PUNCT
ejpam-3228	134	1	(	(	PUNCT
ejpam-3228	134	2	2	2	X
ejpam-3228	134	3	)	)	PUNCT
ejpam-3228	134	4	consequently	consequently	ADV
ejpam-3228	134	5	,	,	PUNCT
ejpam-3228	134	6	from	from	ADP
ejpam-3228	134	7	equation	equation	NOUN
ejpam-3228	134	8	(	(	PUNCT
ejpam-3228	134	9	1	1	NUM
ejpam-3228	134	10	)	)	PUNCT
ejpam-3228	134	11	and	and	CCONJ
ejpam-3228	134	12	(	(	PUNCT
ejpam-3228	134	13	2	2	X
ejpam-3228	134	14	)	)	PUNCT
ejpam-3228	134	15	we	we	PRON
ejpam-3228	134	16	get	get	VERB
ejpam-3228	134	17	,	,	PUNCT
ejpam-3228	134	18	fa(ab	fa(ab	NOUN
ejpam-3228	134	19	)	)	PUNCT
ejpam-3228	134	20	=	=	SYM
ejpam-3228	134	21	fa(b	fa(b	NOUN
ejpam-3228	134	22	)	)	PUNCT
ejpam-3228	134	23	.	.	PUNCT
ejpam-3228	135	1	lemma	lemma	PROPN
ejpam-3228	135	2	5	5	X
ejpam-3228	135	3	.	.	PUNCT
ejpam-3228	136	1	let	let	VERB
ejpam-3228	136	2	a	a	DET
ejpam-3228	136	3	∈	∈	NOUN
ejpam-3228	136	4	s∪ag(u	s∪ag(u	NUM
ejpam-3228	136	5	)	)	PUNCT
ejpam-3228	136	6	.	.	PUNCT
ejpam-3228	137	1	then	then	ADV
ejpam-3228	137	2	fa(a	fa(a	NOUN
ejpam-3228	137	3	)	)	PUNCT
ejpam-3228	137	4	=	=	SYM
ejpam-3228	137	5	fa(b	fa(b	NUM
ejpam-3228	137	6	)	)	PUNCT
ejpam-3228	137	7	,	,	PUNCT
ejpam-3228	137	8	if	if	SCONJ
ejpam-3228	137	9	fa(ab−1	fa(ab−1	NOUN
ejpam-3228	137	10	)	)	PUNCT
ejpam-3228	137	11	=	=	SYM
ejpam-3228	137	12	fa(e	fa(e	X
ejpam-3228	137	13	)	)	PUNCT
ejpam-3228	137	14	for	for	ADP
ejpam-3228	137	15	all	all	DET
ejpam-3228	137	16	a	a	PRON
ejpam-3228	137	17	,	,	PUNCT
ejpam-3228	137	18	b	b	PROPN
ejpam-3228	137	19	∈	∈	PROPN
ejpam-3228	137	20	g.	g.	NOUN
ejpam-3228	137	21	proof	proof	NOUN
ejpam-3228	137	22	.	.	PUNCT
ejpam-3228	138	1	let	let	VERB
ejpam-3228	138	2	a	a	DET
ejpam-3228	138	3	∈	∈	PROPN
ejpam-3228	138	4	s∪ag(u	s∪ag(u	NOUN
ejpam-3228	138	5	)	)	PUNCT
ejpam-3228	138	6	such	such	ADJ
ejpam-3228	138	7	that	that	SCONJ
ejpam-3228	138	8	fa(ab−1	fa(ab−1	NOUN
ejpam-3228	138	9	)	)	PUNCT
ejpam-3228	138	10	=	=	SYM
ejpam-3228	138	11	fa(e	fa(e	X
ejpam-3228	138	12	)	)	PUNCT
ejpam-3228	138	13	.	.	PUNCT
ejpam-3228	139	1	then	then	ADV
ejpam-3228	139	2	,	,	PUNCT
ejpam-3228	139	3	for	for	SCONJ
ejpam-3228	139	4	all	all	DET
ejpam-3228	139	5	a	a	PRON
ejpam-3228	139	6	,	,	PUNCT
ejpam-3228	139	7	b	b	X
ejpam-3228	139	8	∈	∈	PROPN
ejpam-3228	139	9	g	g	PROPN
ejpam-3228	139	10	fa(a	fa(a	NOUN
ejpam-3228	139	11	)	)	PUNCT
ejpam-3228	139	12	=	=	SYM
ejpam-3228	139	13	fa(e	fa(e	X
ejpam-3228	139	14	·	·	PUNCT
ejpam-3228	139	15	a	a	X
ejpam-3228	139	16	)	)	PUNCT
ejpam-3228	139	17	=	=	SYM
ejpam-3228	139	18	fa((bb−1)a	fa((bb−1)a	VERB
ejpam-3228	139	19	)	)	PUNCT
ejpam-3228	140	1	=	=	SYM
ejpam-3228	140	2	fa	fa	INTJ
ejpam-3228	140	3	(	(	PUNCT
ejpam-3228	140	4	(	(	PUNCT
ejpam-3228	140	5	ab−1)b	ab−1)b	X
ejpam-3228	140	6	)	)	PUNCT
ejpam-3228	140	7	(	(	PUNCT
ejpam-3228	140	8	by	by	ADP
ejpam-3228	140	9	the	the	DET
ejpam-3228	140	10	left	left	ADJ
ejpam-3228	140	11	invertive	invertive	ADJ
ejpam-3228	140	12	law	law	NOUN
ejpam-3228	140	13	)	)	PUNCT
ejpam-3228	140	14	⊆	⊆	NUM
ejpam-3228	140	15	fa(ab−1	fa(ab−1	NOUN
ejpam-3228	140	16	)	)	PUNCT
ejpam-3228	140	17	∪	∪	ADP
ejpam-3228	140	18	fa(b	fa(b	NOUN
ejpam-3228	140	19	)	)	PUNCT
ejpam-3228	140	20	=	=	SYM
ejpam-3228	140	21	fa(e	fa(e	X
ejpam-3228	140	22	)	)	PUNCT
ejpam-3228	140	23	∪	∪	ADP
ejpam-3228	140	24	fa(b	fa(b	NOUN
ejpam-3228	140	25	)	)	PUNCT
ejpam-3228	140	26	=	=	SYM
ejpam-3228	140	27	fa(b	fa(b	NOUN
ejpam-3228	140	28	)	)	PUNCT
ejpam-3228	140	29	.	.	PUNCT
ejpam-3228	141	1	(	(	PUNCT
ejpam-3228	141	2	by	by	ADP
ejpam-3228	141	3	assumption	assumption	NOUN
ejpam-3228	141	4	and	and	CCONJ
ejpam-3228	141	5	lemma	lemma	PROPN
ejpam-3228	141	6	2	2	NUM
ejpam-3228	141	7	)	)	PUNCT
ejpam-3228	141	8	thus	thus	ADV
ejpam-3228	141	9	fa(a	fa(a	NOUN
ejpam-3228	141	10	)	)	PUNCT
ejpam-3228	141	11	⊆	⊆	NUM
ejpam-3228	141	12	fa(b	fa(b	NUM
ejpam-3228	141	13	)	)	PUNCT
ejpam-3228	141	14	.	.	PUNCT
ejpam-3228	142	1	(	(	PUNCT
ejpam-3228	142	2	3	3	X
ejpam-3228	142	3	)	)	PUNCT
ejpam-3228	142	4	a.	a.	NOUN
ejpam-3228	142	5	ullah	ullah	PROPN
ejpam-3228	142	6	,	,	PUNCT
ejpam-3228	142	7	f.	f.	PROPN
ejpam-3228	142	8	karaaslan	karaaslan	PROPN
ejpam-3228	142	9	,	,	PUNCT
ejpam-3228	142	10	i.	i.	PROPN
ejpam-3228	142	11	ahmad	ahmad	PROPN
ejpam-3228	142	12	/	/	SYM
ejpam-3228	142	13	eur	eur	PROPN
ejpam-3228	142	14	.	.	PUNCT
ejpam-3228	143	1	j.	j.	PROPN
ejpam-3228	143	2	pure	pure	PROPN
ejpam-3228	143	3	appl	appl	PROPN
ejpam-3228	143	4	.	.	PROPN
ejpam-3228	143	5	math	math	PROPN
ejpam-3228	143	6	,	,	PUNCT
ejpam-3228	143	7	11	11	NUM
ejpam-3228	143	8	(	(	PUNCT
ejpam-3228	143	9	2	2	NUM
ejpam-3228	143	10	)	)	PUNCT
ejpam-3228	143	11	(	(	PUNCT
ejpam-3228	143	12	2018	2018	NUM
ejpam-3228	143	13	)	)	PUNCT
ejpam-3228	143	14	,	,	PUNCT
ejpam-3228	143	15	517	517	NUM
ejpam-3228	143	16	-	-	SYM
ejpam-3228	143	17	536	536	NUM
ejpam-3228	143	18	523	523	NUM
ejpam-3228	143	19	and	and	CCONJ
ejpam-3228	143	20	fa(b	fa(b	NOUN
ejpam-3228	143	21	)	)	PUNCT
ejpam-3228	143	22	=	=	SYM
ejpam-3228	144	1	fa(b−1	fa(b−1	PROPN
ejpam-3228	144	2	)	)	PUNCT
ejpam-3228	144	3	=	=	SYM
ejpam-3228	144	4	fa(e	fa(e	X
ejpam-3228	144	5	·	·	PUNCT
ejpam-3228	144	6	b−1	b−1	NOUN
ejpam-3228	144	7	)	)	PUNCT
ejpam-3228	144	8	=	=	SYM
ejpam-3228	144	9	fa((a−1a)b−1	fa((a−1a)b−1	PROPN
ejpam-3228	144	10	)	)	PUNCT
ejpam-3228	144	11	=	=	SYM
ejpam-3228	144	12	fa	fa	INTJ
ejpam-3228	144	13	(	(	PUNCT
ejpam-3228	144	14	(	(	PUNCT
ejpam-3228	144	15	b−1a)a−1	b−1a)a−1	PROPN
ejpam-3228	144	16	)	)	PUNCT
ejpam-3228	144	17	(	(	PUNCT
ejpam-3228	144	18	by	by	ADP
ejpam-3228	144	19	the	the	DET
ejpam-3228	144	20	left	left	ADJ
ejpam-3228	144	21	invertive	invertive	ADJ
ejpam-3228	144	22	law	law	NOUN
ejpam-3228	144	23	)	)	PUNCT
ejpam-3228	144	24	⊆	⊆	NUM
ejpam-3228	144	25	fa(b−1a	fa(b−1a	X
ejpam-3228	144	26	)	)	PUNCT
ejpam-3228	144	27	∪	∪	NOUN
ejpam-3228	144	28	fa(a−1	fa(a−1	NOUN
ejpam-3228	144	29	)	)	PUNCT
ejpam-3228	144	30	=	=	SYM
ejpam-3228	144	31	fa(ab−1	fa(ab−1	NOUN
ejpam-3228	144	32	)	)	PUNCT
ejpam-3228	144	33	∪	∪	ADP
ejpam-3228	144	34	fa(a	fa(a	PROPN
ejpam-3228	144	35	)	)	PUNCT
ejpam-3228	144	36	(	(	PUNCT
ejpam-3228	144	37	by	by	ADP
ejpam-3228	144	38	lemma	lemma	PROPN
ejpam-3228	144	39	3	3	NUM
ejpam-3228	144	40	)	)	PUNCT
ejpam-3228	144	41	=	=	PRON
ejpam-3228	144	42	fa(a	fa(a	NOUN
ejpam-3228	144	43	)	)	PUNCT
ejpam-3228	144	44	.	.	PUNCT
ejpam-3228	145	1	(	(	PUNCT
ejpam-3228	145	2	by	by	ADP
ejpam-3228	145	3	lemma	lemma	PROPN
ejpam-3228	145	4	2	2	NUM
ejpam-3228	145	5	)	)	PUNCT
ejpam-3228	145	6	thus	thus	ADV
ejpam-3228	145	7	fa(b	fa(b	NUM
ejpam-3228	145	8	)	)	PUNCT
ejpam-3228	145	9	⊆	⊆	NUM
ejpam-3228	145	10	fa(a	fa(a	NOUN
ejpam-3228	145	11	)	)	PUNCT
ejpam-3228	145	12	.	.	PUNCT
ejpam-3228	146	1	(	(	PUNCT
ejpam-3228	146	2	4	4	X
ejpam-3228	146	3	)	)	PUNCT
ejpam-3228	146	4	hence	hence	ADV
ejpam-3228	146	5	,	,	PUNCT
ejpam-3228	146	6	fa(a	fa(a	NOUN
ejpam-3228	146	7	)	)	PUNCT
ejpam-3228	146	8	=	=	SYM
ejpam-3228	146	9	fa(b	fa(b	NOUN
ejpam-3228	146	10	)	)	PUNCT
ejpam-3228	146	11	for	for	ADP
ejpam-3228	146	12	all	all	DET
ejpam-3228	146	13	a	a	PRON
ejpam-3228	146	14	,	,	PUNCT
ejpam-3228	146	15	b	b	X
ejpam-3228	146	16	∈	∈	PROPN
ejpam-3228	146	17	g	g	NOUN
ejpam-3228	146	18	using	use	VERB
ejpam-3228	146	19	equations	equation	NOUN
ejpam-3228	146	20	(	(	PUNCT
ejpam-3228	146	21	3	3	NUM
ejpam-3228	146	22	)	)	PUNCT
ejpam-3228	146	23	and	and	CCONJ
ejpam-3228	146	24	(	(	PUNCT
ejpam-3228	146	25	4	4	NUM
ejpam-3228	146	26	)	)	PUNCT
ejpam-3228	146	27	.	.	PUNCT
ejpam-3228	147	1	theorem	theorem	NOUN
ejpam-3228	147	2	2	2	NUM
ejpam-3228	147	3	.	.	PUNCT
ejpam-3228	148	1	let	let	VERB
ejpam-3228	148	2	a	a	DET
ejpam-3228	148	3	,	,	PUNCT
ejpam-3228	148	4	b	b	PROPN
ejpam-3228	148	5	∈	∈	PROPN
ejpam-3228	148	6	s∪ag(u	s∪ag(u	NUM
ejpam-3228	148	7	)	)	PUNCT
ejpam-3228	148	8	.	.	PUNCT
ejpam-3228	149	1	then	then	ADV
ejpam-3228	149	2	,	,	PUNCT
ejpam-3228	149	3	a	a	DET
ejpam-3228	149	4	∨b	∨b	NOUN
ejpam-3228	149	5	∈	∈	PROPN
ejpam-3228	149	6	s∪ag(u	s∪ag(u	PROPN
ejpam-3228	149	7	)	)	PUNCT
ejpam-3228	149	8	.	.	PUNCT
ejpam-3228	150	1	proof	proof	NOUN
ejpam-3228	150	2	.	.	PUNCT
ejpam-3228	151	1	let	let	VERB
ejpam-3228	151	2	(	(	PUNCT
ejpam-3228	151	3	x1	x1	PROPN
ejpam-3228	151	4	,	,	PUNCT
ejpam-3228	151	5	y1	y1	PROPN
ejpam-3228	151	6	)	)	PUNCT
ejpam-3228	151	7	,	,	PUNCT
ejpam-3228	151	8	(	(	PUNCT
ejpam-3228	151	9	x2	x2	PROPN
ejpam-3228	151	10	,	,	PUNCT
ejpam-3228	151	11	y2	y2	PROPN
ejpam-3228	151	12	)	)	PUNCT
ejpam-3228	151	13	∈	∈	PROPN
ejpam-3228	151	14	g1	g1	PROPN
ejpam-3228	151	15	×g2	×g2	PROPN
ejpam-3228	151	16	.	.	PUNCT
ejpam-3228	152	1	then	then	ADV
ejpam-3228	152	2	,	,	PUNCT
ejpam-3228	152	3	by	by	ADP
ejpam-3228	152	4	definition	definition	NOUN
ejpam-3228	152	5	3	3	NUM
ejpam-3228	152	6	and	and	CCONJ
ejpam-3228	152	7	theorem	theorem	VERB
ejpam-3228	152	8	1	1	NUM
ejpam-3228	152	9	,	,	PUNCT
ejpam-3228	152	10	(	(	PUNCT
ejpam-3228	152	11	fa	fa	PROPN
ejpam-3228	152	12	∨	∨	NUM
ejpam-3228	152	13	fb	fb	NOUN
ejpam-3228	152	14	)	)	PUNCT
ejpam-3228	152	15	(	(	PUNCT
ejpam-3228	152	16	(	(	PUNCT
ejpam-3228	152	17	x1	x1	ADJ
ejpam-3228	152	18	,	,	PUNCT
ejpam-3228	152	19	y1	y1	PROPN
ejpam-3228	152	20	)	)	PUNCT
ejpam-3228	152	21	·	·	PUNCT
ejpam-3228	152	22	(	(	PUNCT
ejpam-3228	152	23	x2	x2	INTJ
ejpam-3228	152	24	,	,	PUNCT
ejpam-3228	152	25	y2)−1	y2)−1	NOUN
ejpam-3228	152	26	)	)	PUNCT
ejpam-3228	152	27	=	=	SYM
ejpam-3228	152	28	(	(	PUNCT
ejpam-3228	152	29	fa	fa	PROPN
ejpam-3228	152	30	∨	∨	NUM
ejpam-3228	152	31	fb	fb	NOUN
ejpam-3228	152	32	)	)	PUNCT
ejpam-3228	152	33	(	(	PUNCT
ejpam-3228	152	34	(	(	PUNCT
ejpam-3228	152	35	x1	x1	ADJ
ejpam-3228	152	36	,	,	PUNCT
ejpam-3228	152	37	y1	y1	PROPN
ejpam-3228	152	38	)	)	PUNCT
ejpam-3228	152	39	·	·	PUNCT
ejpam-3228	152	40	(	(	PUNCT
ejpam-3228	152	41	x−12	x−12	NOUN
ejpam-3228	152	42	,	,	PUNCT
ejpam-3228	152	43	y−12	y−12	NOUN
ejpam-3228	152	44	)	)	PUNCT
ejpam-3228	152	45	)	)	PUNCT
ejpam-3228	153	1	=	=	PUNCT
ejpam-3228	153	2	(	(	PUNCT
ejpam-3228	153	3	fa	fa	PROPN
ejpam-3228	153	4	∨	∨	NUM
ejpam-3228	153	5	fb	fb	NOUN
ejpam-3228	153	6	)	)	PUNCT
ejpam-3228	153	7	(	(	PUNCT
ejpam-3228	153	8	x1x	x1x	PROPN
ejpam-3228	153	9	−1	−1	NOUN
ejpam-3228	153	10	2	2	NUM
ejpam-3228	153	11	,	,	PUNCT
ejpam-3228	153	12	y1y	y1y	PROPN
ejpam-3228	153	13	−1	−1	NOUN
ejpam-3228	153	14	2	2	X
ejpam-3228	153	15	)	)	PUNCT
ejpam-3228	153	16	=	=	PUNCT
ejpam-3228	154	1	fa(x1x	fa(x1x	NOUN
ejpam-3228	154	2	−1	−1	NOUN
ejpam-3228	154	3	2	2	NUM
ejpam-3228	154	4	)	)	PUNCT
ejpam-3228	154	5	∪	∪	ADP
ejpam-3228	154	6	fb(y1y	fb(y1y	PROPN
ejpam-3228	154	7	−1	−1	NOUN
ejpam-3228	154	8	2	2	NUM
ejpam-3228	154	9	)	)	PUNCT
ejpam-3228	154	10	⊆	⊆	NUM
ejpam-3228	154	11	(	(	PUNCT
ejpam-3228	154	12	fa(x1	fa(x1	NOUN
ejpam-3228	154	13	)	)	PUNCT
ejpam-3228	154	14	∪	∪	NOUN
ejpam-3228	154	15	fa(x−12	fa(x−12	NOUN
ejpam-3228	154	16	)	)	PUNCT
ejpam-3228	154	17	)	)	PUNCT
ejpam-3228	154	18	∪	∪	NOUN
ejpam-3228	154	19	(	(	PUNCT
ejpam-3228	154	20	fb(y1	fb(y1	NOUN
ejpam-3228	154	21	)	)	PUNCT
ejpam-3228	154	22	∪	∪	ADJ
ejpam-3228	154	23	fb(y−12	fb(y−12	NOUN
ejpam-3228	154	24	)	)	PUNCT
ejpam-3228	154	25	)	)	PUNCT
ejpam-3228	155	1	=	=	SYM
ejpam-3228	155	2	(	(	PUNCT
ejpam-3228	155	3	fa(x1	fa(x1	NOUN
ejpam-3228	155	4	)	)	PUNCT
ejpam-3228	155	5	∪	∪	NOUN
ejpam-3228	155	6	fa(x2	fa(x2	NOUN
ejpam-3228	155	7	)	)	PUNCT
ejpam-3228	155	8	)	)	PUNCT
ejpam-3228	155	9	∪	∪	ADP
ejpam-3228	155	10	(	(	PUNCT
ejpam-3228	155	11	fb(y1	fb(y1	NOUN
ejpam-3228	155	12	)	)	PUNCT
ejpam-3228	155	13	∪	∪	ADP
ejpam-3228	155	14	fb(y2	fb(y2	NOUN
ejpam-3228	155	15	)	)	PUNCT
ejpam-3228	155	16	)	)	PUNCT
ejpam-3228	156	1	=	=	SYM
ejpam-3228	156	2	(	(	PUNCT
ejpam-3228	156	3	fa(x1	fa(x1	NOUN
ejpam-3228	156	4	)	)	PUNCT
ejpam-3228	156	5	∪	∪	ADJ
ejpam-3228	156	6	fb(y1	fb(y1	NOUN
ejpam-3228	156	7	)	)	PUNCT
ejpam-3228	156	8	)	)	PUNCT
ejpam-3228	156	9	∪	∪	NOUN
ejpam-3228	156	10	(	(	PUNCT
ejpam-3228	156	11	fa(x2	fa(x2	NOUN
ejpam-3228	156	12	)	)	PUNCT
ejpam-3228	156	13	∪	∪	ADP
ejpam-3228	156	14	fb(y2	fb(y2	NOUN
ejpam-3228	156	15	)	)	PUNCT
ejpam-3228	156	16	)	)	PUNCT
ejpam-3228	157	1	=	=	SYM
ejpam-3228	157	2	(	(	PUNCT
ejpam-3228	157	3	fa	fa	PROPN
ejpam-3228	157	4	∨	∨	NUM
ejpam-3228	157	5	fb	fb	NOUN
ejpam-3228	157	6	)	)	PUNCT
ejpam-3228	157	7	(	(	PUNCT
ejpam-3228	157	8	x1	x1	PROPN
ejpam-3228	157	9	,	,	PUNCT
ejpam-3228	157	10	y1	y1	NOUN
ejpam-3228	157	11	)	)	PUNCT
ejpam-3228	157	12	∪	∪	NOUN
ejpam-3228	157	13	(	(	PUNCT
ejpam-3228	157	14	fa	fa	PROPN
ejpam-3228	157	15	∨	∨	NUM
ejpam-3228	157	16	fb	fb	NOUN
ejpam-3228	157	17	)	)	PUNCT
ejpam-3228	157	18	(	(	PUNCT
ejpam-3228	157	19	x2	x2	PROPN
ejpam-3228	157	20	,	,	PUNCT
ejpam-3228	157	21	y2	y2	PROPN
ejpam-3228	157	22	)	)	PUNCT
ejpam-3228	157	23	.	.	PUNCT
ejpam-3228	158	1	therefore	therefore	ADV
ejpam-3228	158	2	,	,	PUNCT
ejpam-3228	158	3	a	a	DET
ejpam-3228	158	4	∨b	∨b	NOUN
ejpam-3228	158	5	∈	∈	PROPN
ejpam-3228	158	6	s∪ag(u	s∪ag(u	PROPN
ejpam-3228	158	7	)	)	PUNCT
ejpam-3228	158	8	.	.	PUNCT
ejpam-3228	159	1	the	the	DET
ejpam-3228	159	2	following	follow	VERB
ejpam-3228	159	3	counter	counter	PROPN
ejpam-3228	159	4	example	example	NOUN
ejpam-3228	159	5	shows	show	VERB
ejpam-3228	159	6	that	that	SCONJ
ejpam-3228	159	7	a	a	DET
ejpam-3228	159	8	∧	∧	PROPN
ejpam-3228	159	9	b	b	PROPN
ejpam-3228	159	10	of	of	ADP
ejpam-3228	159	11	any	any	DET
ejpam-3228	159	12	two	two	NUM
ejpam-3228	159	13	soft	soft	ADJ
ejpam-3228	159	14	sets	set	NOUN
ejpam-3228	159	15	a	a	PRON
ejpam-3228	159	16	and	and	CCONJ
ejpam-3228	159	17	b	b	NOUN
ejpam-3228	159	18	may	may	AUX
ejpam-3228	159	19	not	not	PART
ejpam-3228	159	20	be	be	AUX
ejpam-3228	159	21	a	a	DET
ejpam-3228	159	22	soft	soft	ADJ
ejpam-3228	159	23	uni	uni	ADJ
ejpam-3228	159	24	-	-	PUNCT
ejpam-3228	159	25	ag	ag	NOUN
ejpam-3228	159	26	-	-	PUNCT
ejpam-3228	159	27	group	group	NOUN
ejpam-3228	159	28	.	.	PUNCT
ejpam-3228	160	1	example	example	NOUN
ejpam-3228	161	1	3	3	X
ejpam-3228	161	2	.	.	X
ejpam-3228	161	3	consider	consider	VERB
ejpam-3228	161	4	a	a	DET
ejpam-3228	161	5	non	non	ADJ
ejpam-3228	161	6	-	-	ADJ
ejpam-3228	161	7	associative	associative	ADJ
ejpam-3228	161	8	ag	ag	PROPN
ejpam-3228	161	9	-	-	PUNCT
ejpam-3228	161	10	group	group	NOUN
ejpam-3228	161	11	g	g	NOUN
ejpam-3228	161	12	=	=	PUNCT
ejpam-3228	161	13	{	{	PUNCT
ejpam-3228	161	14	0	0	NUM
ejpam-3228	161	15	,	,	PUNCT
ejpam-3228	161	16	1	1	NUM
ejpam-3228	161	17	,	,	PUNCT
ejpam-3228	161	18	2	2	NUM
ejpam-3228	161	19	,	,	PUNCT
ejpam-3228	161	20	3	3	NUM
ejpam-3228	161	21	}	}	PUNCT
ejpam-3228	161	22	of	of	ADP
ejpam-3228	161	23	order	order	NOUN
ejpam-3228	161	24	4	4	NUM
ejpam-3228	161	25	with	with	ADP
ejpam-3228	161	26	left	left	ADJ
ejpam-3228	161	27	identity	identity	NOUN
ejpam-3228	161	28	0	0	NUM
ejpam-3228	161	29	defined	define	VERB
ejpam-3228	161	30	by	by	ADP
ejpam-3228	161	31	:	:	PUNCT
ejpam-3228	161	32	.	.	PUNCT
ejpam-3228	162	1	0	0	NUM
ejpam-3228	162	2	1	1	NUM
ejpam-3228	162	3	2	2	NUM
ejpam-3228	162	4	3	3	NUM
ejpam-3228	162	5	0	0	NUM
ejpam-3228	162	6	0	0	NUM
ejpam-3228	162	7	1	1	NUM
ejpam-3228	162	8	2	2	NUM
ejpam-3228	162	9	3	3	NUM
ejpam-3228	162	10	1	1	NUM
ejpam-3228	162	11	1	1	NUM
ejpam-3228	162	12	0	0	NUM
ejpam-3228	162	13	3	3	NUM
ejpam-3228	162	14	2	2	NUM
ejpam-3228	162	15	2	2	NUM
ejpam-3228	162	16	3	3	NUM
ejpam-3228	162	17	2	2	NUM
ejpam-3228	162	18	1	1	NUM
ejpam-3228	162	19	0	0	NUM
ejpam-3228	162	20	3	3	NUM
ejpam-3228	162	21	2	2	NUM
ejpam-3228	162	22	3	3	NUM
ejpam-3228	162	23	0	0	NUM
ejpam-3228	162	24	1	1	NUM
ejpam-3228	162	25	let	let	VERB
ejpam-3228	162	26	a	a	PRON
ejpam-3228	162	27	and	and	CCONJ
ejpam-3228	162	28	b	b	NOUN
ejpam-3228	162	29	be	be	AUX
ejpam-3228	162	30	any	any	DET
ejpam-3228	162	31	two	two	NUM
ejpam-3228	162	32	soft	soft	ADJ
ejpam-3228	162	33	sets	set	NOUN
ejpam-3228	162	34	over	over	ADP
ejpam-3228	162	35	u	u	NOUN
ejpam-3228	162	36	=	=	NOUN
ejpam-3228	162	37	z10	z10	NOUN
ejpam-3228	162	38	as	as	SCONJ
ejpam-3228	162	39	follow	follow	VERB
ejpam-3228	162	40	:	:	PUNCT
ejpam-3228	162	41	a	a	PRON
ejpam-3228	162	42	=	=	X
ejpam-3228	162	43	{	{	PUNCT
ejpam-3228	162	44	(	(	PUNCT
ejpam-3228	162	45	0	0	NUM
ejpam-3228	162	46	,	,	PUNCT
ejpam-3228	162	47	fa(0	fa(0	NOUN
ejpam-3228	162	48	)	)	PUNCT
ejpam-3228	162	49	)	)	PUNCT
ejpam-3228	162	50	,	,	PUNCT
ejpam-3228	162	51	(	(	PUNCT
ejpam-3228	162	52	1	1	NUM
ejpam-3228	162	53	,	,	PUNCT
ejpam-3228	162	54	fa(1	fa(1	NOUN
ejpam-3228	162	55	)	)	PUNCT
ejpam-3228	162	56	)	)	PUNCT
ejpam-3228	162	57	,	,	PUNCT
ejpam-3228	162	58	(	(	PUNCT
ejpam-3228	162	59	2	2	NUM
ejpam-3228	162	60	,	,	PUNCT
ejpam-3228	162	61	fa(3	fa(3	NOUN
ejpam-3228	162	62	)	)	PUNCT
ejpam-3228	162	63	)	)	PUNCT
ejpam-3228	162	64	,	,	PUNCT
ejpam-3228	162	65	(	(	PUNCT
ejpam-3228	162	66	3	3	NUM
ejpam-3228	162	67	,	,	PUNCT
ejpam-3228	162	68	fa(4	fa(4	NOUN
ejpam-3228	162	69	)	)	PUNCT
ejpam-3228	162	70	)	)	PUNCT
ejpam-3228	162	71	}	}	PUNCT
ejpam-3228	163	1	=	=	SYM
ejpam-3228	163	2	{	{	PUNCT
ejpam-3228	163	3	(	(	PUNCT
ejpam-3228	163	4	0	0	NUM
ejpam-3228	163	5	,	,	PUNCT
ejpam-3228	163	6	{	{	PUNCT
ejpam-3228	163	7	0	0	NUM
ejpam-3228	163	8	,	,	PUNCT
ejpam-3228	163	9	1	1	NUM
ejpam-3228	163	10	,	,	PUNCT
ejpam-3228	163	11	2	2	NUM
ejpam-3228	163	12	}	}	PUNCT
ejpam-3228	163	13	)	)	PUNCT
ejpam-3228	163	14	,	,	PUNCT
ejpam-3228	163	15	(	(	PUNCT
ejpam-3228	163	16	1	1	NUM
ejpam-3228	163	17	,	,	PUNCT
ejpam-3228	163	18	{	{	PUNCT
ejpam-3228	163	19	0	0	NUM
ejpam-3228	163	20	,	,	PUNCT
ejpam-3228	163	21	1	1	NUM
ejpam-3228	163	22	,	,	PUNCT
ejpam-3228	163	23	2	2	NUM
ejpam-3228	163	24	,	,	PUNCT
ejpam-3228	163	25	3	3	NUM
ejpam-3228	163	26	,	,	PUNCT
ejpam-3228	163	27	4	4	NUM
ejpam-3228	163	28	,	,	PUNCT
ejpam-3228	163	29	5	5	NUM
ejpam-3228	163	30	}	}	PUNCT
ejpam-3228	163	31	)	)	PUNCT
ejpam-3228	163	32	,	,	PUNCT
ejpam-3228	163	33	(	(	PUNCT
ejpam-3228	163	34	2	2	NUM
ejpam-3228	163	35	,	,	PUNCT
ejpam-3228	163	36	{	{	PUNCT
ejpam-3228	163	37	0	0	NUM
ejpam-3228	163	38	,	,	PUNCT
ejpam-3228	163	39	1	1	NUM
ejpam-3228	163	40	,	,	PUNCT
ejpam-3228	163	41	2	2	NUM
ejpam-3228	163	42	,	,	PUNCT
ejpam-3228	163	43	3	3	NUM
ejpam-3228	163	44	,	,	PUNCT
ejpam-3228	163	45	4	4	NUM
ejpam-3228	163	46	,	,	PUNCT
ejpam-3228	163	47	5	5	NUM
ejpam-3228	163	48	,	,	PUNCT
ejpam-3228	163	49	6	6	NUM
ejpam-3228	163	50	,	,	PUNCT
ejpam-3228	163	51	7	7	NUM
ejpam-3228	163	52	}	}	PUNCT
ejpam-3228	163	53	)	)	PUNCT
ejpam-3228	163	54	,	,	PUNCT
ejpam-3228	163	55	(	(	PUNCT
ejpam-3228	163	56	3	3	NUM
ejpam-3228	163	57	,	,	PUNCT
ejpam-3228	163	58	{	{	PUNCT
ejpam-3228	163	59	0	0	NUM
ejpam-3228	163	60	,	,	PUNCT
ejpam-3228	163	61	1	1	NUM
ejpam-3228	163	62	,	,	PUNCT
ejpam-3228	163	63	2	2	NUM
ejpam-3228	163	64	,	,	PUNCT
ejpam-3228	163	65	3	3	NUM
ejpam-3228	163	66	,	,	PUNCT
ejpam-3228	163	67	4	4	NUM
ejpam-3228	163	68	,	,	PUNCT
ejpam-3228	163	69	5	5	NUM
ejpam-3228	163	70	,	,	PUNCT
ejpam-3228	163	71	6	6	NUM
ejpam-3228	163	72	,	,	PUNCT
ejpam-3228	163	73	7	7	NUM
ejpam-3228	163	74	}	}	PUNCT
ejpam-3228	163	75	)	)	PUNCT
ejpam-3228	163	76	}	}	PUNCT
ejpam-3228	163	77	.	.	PUNCT
ejpam-3228	164	1	a.	a.	PROPN
ejpam-3228	164	2	ullah	ullah	PROPN
ejpam-3228	164	3	,	,	PUNCT
ejpam-3228	164	4	f.	f.	PROPN
ejpam-3228	164	5	karaaslan	karaaslan	PROPN
ejpam-3228	164	6	,	,	PUNCT
ejpam-3228	164	7	i.	i.	PROPN
ejpam-3228	164	8	ahmad	ahmad	PROPN
ejpam-3228	164	9	/	/	SYM
ejpam-3228	164	10	eur	eur	PROPN
ejpam-3228	164	11	.	.	PUNCT
ejpam-3228	165	1	j.	j.	PROPN
ejpam-3228	165	2	pure	pure	PROPN
ejpam-3228	165	3	appl	appl	PROPN
ejpam-3228	165	4	.	.	PROPN
ejpam-3228	165	5	math	math	PROPN
ejpam-3228	165	6	,	,	PUNCT
ejpam-3228	165	7	11	11	NUM
ejpam-3228	165	8	(	(	PUNCT
ejpam-3228	165	9	2	2	NUM
ejpam-3228	165	10	)	)	PUNCT
ejpam-3228	165	11	(	(	PUNCT
ejpam-3228	165	12	2018	2018	NUM
ejpam-3228	165	13	)	)	PUNCT
ejpam-3228	165	14	,	,	PUNCT
ejpam-3228	165	15	517	517	NUM
ejpam-3228	165	16	-	-	SYM
ejpam-3228	165	17	536	536	NUM
ejpam-3228	165	18	524	524	NUM
ejpam-3228	165	19	b	b	X
ejpam-3228	165	20	=	=	PRON
ejpam-3228	165	21	{	{	PUNCT
ejpam-3228	165	22	(	(	PUNCT
ejpam-3228	165	23	0	0	NUM
ejpam-3228	165	24	,	,	PUNCT
ejpam-3228	165	25	fb(0	fb(0	NOUN
ejpam-3228	165	26	)	)	PUNCT
ejpam-3228	165	27	)	)	PUNCT
ejpam-3228	165	28	,	,	PUNCT
ejpam-3228	165	29	(	(	PUNCT
ejpam-3228	165	30	1	1	NUM
ejpam-3228	165	31	,	,	PUNCT
ejpam-3228	165	32	fb(1	fb(1	PROPN
ejpam-3228	165	33	)	)	PUNCT
ejpam-3228	165	34	)	)	PUNCT
ejpam-3228	165	35	,	,	PUNCT
ejpam-3228	165	36	(	(	PUNCT
ejpam-3228	165	37	2	2	NUM
ejpam-3228	165	38	,	,	PUNCT
ejpam-3228	165	39	fb(3	fb(3	NOUN
ejpam-3228	165	40	)	)	PUNCT
ejpam-3228	165	41	)	)	PUNCT
ejpam-3228	165	42	,	,	PUNCT
ejpam-3228	165	43	(	(	PUNCT
ejpam-3228	165	44	3	3	NUM
ejpam-3228	165	45	,	,	PUNCT
ejpam-3228	165	46	fb(4	fb(4	PROPN
ejpam-3228	165	47	)	)	PUNCT
ejpam-3228	165	48	)	)	PUNCT
ejpam-3228	165	49	}	}	PUNCT
ejpam-3228	165	50	=	=	SYM
ejpam-3228	165	51	{	{	PUNCT
ejpam-3228	165	52	(	(	PUNCT
ejpam-3228	165	53	0	0	NUM
ejpam-3228	165	54	,	,	PUNCT
ejpam-3228	165	55	{	{	PUNCT
ejpam-3228	165	56	5	5	NUM
ejpam-3228	165	57	,	,	PUNCT
ejpam-3228	165	58	6	6	NUM
ejpam-3228	165	59	}	}	PUNCT
ejpam-3228	165	60	)	)	PUNCT
ejpam-3228	165	61	,	,	PUNCT
ejpam-3228	165	62	(	(	PUNCT
ejpam-3228	165	63	1	1	NUM
ejpam-3228	165	64	,	,	PUNCT
ejpam-3228	165	65	{	{	PUNCT
ejpam-3228	165	66	5	5	NUM
ejpam-3228	165	67	,	,	PUNCT
ejpam-3228	165	68	6	6	NUM
ejpam-3228	165	69	,	,	PUNCT
ejpam-3228	165	70	7	7	NUM
ejpam-3228	165	71	,	,	PUNCT
ejpam-3228	165	72	8	8	NUM
ejpam-3228	165	73	}	}	PUNCT
ejpam-3228	165	74	)	)	PUNCT
ejpam-3228	165	75	,	,	PUNCT
ejpam-3228	165	76	(	(	PUNCT
ejpam-3228	165	77	2	2	NUM
ejpam-3228	165	78	,	,	PUNCT
ejpam-3228	165	79	{	{	PUNCT
ejpam-3228	165	80	5	5	NUM
ejpam-3228	165	81	,	,	PUNCT
ejpam-3228	165	82	6	6	NUM
ejpam-3228	165	83	,	,	PUNCT
ejpam-3228	165	84	7	7	NUM
ejpam-3228	165	85	,	,	PUNCT
ejpam-3228	165	86	8	8	NUM
ejpam-3228	165	87	,	,	PUNCT
ejpam-3228	165	88	9	9	NUM
ejpam-3228	165	89	,	,	PUNCT
ejpam-3228	165	90	10	10	NUM
ejpam-3228	165	91	}	}	PUNCT
ejpam-3228	165	92	)	)	PUNCT
ejpam-3228	165	93	,	,	PUNCT
ejpam-3228	165	94	(	(	PUNCT
ejpam-3228	165	95	3	3	NUM
ejpam-3228	165	96	,	,	PUNCT
ejpam-3228	165	97	{	{	PUNCT
ejpam-3228	165	98	5	5	NUM
ejpam-3228	165	99	,	,	PUNCT
ejpam-3228	165	100	6	6	NUM
ejpam-3228	165	101	,	,	PUNCT
ejpam-3228	165	102	7	7	NUM
ejpam-3228	165	103	,	,	PUNCT
ejpam-3228	165	104	8	8	NUM
ejpam-3228	165	105	,	,	PUNCT
ejpam-3228	165	106	9	9	NUM
ejpam-3228	165	107	,	,	PUNCT
ejpam-3228	165	108	10	10	NUM
ejpam-3228	165	109	}	}	PUNCT
ejpam-3228	165	110	)	)	PUNCT
ejpam-3228	165	111	}	}	PUNCT
ejpam-3228	165	112	.	.	PUNCT
ejpam-3228	166	1	it	it	PRON
ejpam-3228	166	2	is	be	AUX
ejpam-3228	166	3	clear	clear	ADJ
ejpam-3228	166	4	that	that	SCONJ
ejpam-3228	166	5	both	both	CCONJ
ejpam-3228	166	6	a	a	DET
ejpam-3228	166	7	,	,	PUNCT
ejpam-3228	166	8	b	b	PROPN
ejpam-3228	166	9	∈	∈	PROPN
ejpam-3228	166	10	s∪ag(u	s∪ag(u	NUM
ejpam-3228	166	11	)	)	PUNCT
ejpam-3228	166	12	.	.	PUNCT
ejpam-3228	167	1	now	now	ADV
ejpam-3228	167	2	,	,	PUNCT
ejpam-3228	167	3	take	take	VERB
ejpam-3228	167	4	(	(	PUNCT
ejpam-3228	167	5	fa	fa	INTJ
ejpam-3228	167	6	∧	∧	PROPN
ejpam-3228	167	7	fb	fb	NOUN
ejpam-3228	167	8	)	)	PUNCT
ejpam-3228	167	9	(	(	PUNCT
ejpam-3228	167	10	(	(	PUNCT
ejpam-3228	167	11	1	1	NUM
ejpam-3228	167	12	,	,	PUNCT
ejpam-3228	167	13	1	1	NUM
ejpam-3228	167	14	)	)	PUNCT
ejpam-3228	167	15	·	·	PUNCT
ejpam-3228	168	1	(	(	PUNCT
ejpam-3228	168	2	0	0	NUM
ejpam-3228	168	3	,	,	PUNCT
ejpam-3228	168	4	2)−1	2)−1	NUM
ejpam-3228	168	5	)	)	PUNCT
ejpam-3228	168	6	=	=	SYM
ejpam-3228	169	1	(	(	PUNCT
ejpam-3228	169	2	fa	fa	INTJ
ejpam-3228	169	3	∧	∧	PROPN
ejpam-3228	169	4	fb	fb	PROPN
ejpam-3228	169	5	)	)	PUNCT
ejpam-3228	169	6	(	(	PUNCT
ejpam-3228	169	7	(	(	PUNCT
ejpam-3228	169	8	1	1	NUM
ejpam-3228	169	9	,	,	PUNCT
ejpam-3228	169	10	1	1	NUM
ejpam-3228	169	11	)	)	PUNCT
ejpam-3228	169	12	·	·	PUNCT
ejpam-3228	169	13	(	(	PUNCT
ejpam-3228	169	14	0	0	NUM
ejpam-3228	169	15	,	,	PUNCT
ejpam-3228	169	16	3	3	NUM
ejpam-3228	169	17	)	)	PUNCT
ejpam-3228	169	18	)	)	PUNCT
ejpam-3228	170	1	(	(	PUNCT
ejpam-3228	170	2	fa	fa	INTJ
ejpam-3228	170	3	∧	∧	PROPN
ejpam-3228	170	4	fb	fb	NOUN
ejpam-3228	170	5	)	)	PUNCT
ejpam-3228	170	6	(	(	PUNCT
ejpam-3228	170	7	1	1	NUM
ejpam-3228	170	8	·	·	SYM
ejpam-3228	170	9	0	0	NUM
ejpam-3228	170	10	,	,	PUNCT
ejpam-3228	170	11	1	1	NUM
ejpam-3228	170	12	·	·	SYM
ejpam-3228	170	13	3	3	X
ejpam-3228	170	14	)	)	PUNCT
ejpam-3228	170	15	=	=	SYM
ejpam-3228	170	16	(	(	PUNCT
ejpam-3228	170	17	fa	fa	INTJ
ejpam-3228	170	18	∧	∧	PROPN
ejpam-3228	170	19	fb	fb	NOUN
ejpam-3228	170	20	)	)	PUNCT
ejpam-3228	170	21	(	(	PUNCT
ejpam-3228	170	22	1	1	NUM
ejpam-3228	170	23	,	,	PUNCT
ejpam-3228	170	24	2	2	NUM
ejpam-3228	170	25	)	)	PUNCT
ejpam-3228	170	26	=	=	SYM
ejpam-3228	170	27	(	(	PUNCT
ejpam-3228	170	28	fa	fa	NOUN
ejpam-3228	170	29	)	)	PUNCT
ejpam-3228	170	30	(	(	PUNCT
ejpam-3228	170	31	1	1	X
ejpam-3228	170	32	)	)	PUNCT
ejpam-3228	170	33	∧	∧	NOUN
ejpam-3228	170	34	(	(	PUNCT
ejpam-3228	170	35	fb	fb	NOUN
ejpam-3228	170	36	)	)	PUNCT
ejpam-3228	170	37	(	(	PUNCT
ejpam-3228	170	38	2	2	X
ejpam-3228	170	39	)	)	PUNCT
ejpam-3228	170	40	=	=	NOUN
ejpam-3228	170	41	{	{	PUNCT
ejpam-3228	170	42	5	5	NUM
ejpam-3228	170	43	}	}	PUNCT
ejpam-3228	170	44	,	,	PUNCT
ejpam-3228	170	45	and	and	CCONJ
ejpam-3228	170	46	(	(	PUNCT
ejpam-3228	170	47	fa	fa	INTJ
ejpam-3228	170	48	∧	∧	PROPN
ejpam-3228	170	49	fb	fb	NOUN
ejpam-3228	170	50	)	)	PUNCT
ejpam-3228	170	51	(	(	PUNCT
ejpam-3228	170	52	1	1	NUM
ejpam-3228	170	53	,	,	PUNCT
ejpam-3228	170	54	1	1	NUM
ejpam-3228	170	55	)	)	PUNCT
ejpam-3228	170	56	∪	∪	NOUN
ejpam-3228	170	57	(	(	PUNCT
ejpam-3228	170	58	fa	fa	INTJ
ejpam-3228	170	59	∧	∧	PROPN
ejpam-3228	170	60	fb	fb	NOUN
ejpam-3228	170	61	)	)	PUNCT
ejpam-3228	170	62	(	(	PUNCT
ejpam-3228	170	63	0	0	NUM
ejpam-3228	170	64	,	,	PUNCT
ejpam-3228	170	65	2	2	NUM
ejpam-3228	170	66	)	)	PUNCT
ejpam-3228	170	67	=	=	PUNCT
ejpam-3228	170	68	φ	φ	PROPN
ejpam-3228	170	69	∪	∪	X
ejpam-3228	170	70	φ	φ	PROPN
ejpam-3228	170	71	=	=	SYM
ejpam-3228	170	72	φ	φ	PROPN
ejpam-3228	170	73	,	,	PUNCT
ejpam-3228	170	74	this	this	PRON
ejpam-3228	170	75	implies	imply	VERB
ejpam-3228	170	76	that	that	SCONJ
ejpam-3228	170	77	(	(	PUNCT
ejpam-3228	170	78	fa	fa	INTJ
ejpam-3228	170	79	∧	∧	PROPN
ejpam-3228	170	80	fb	fb	NOUN
ejpam-3228	170	81	)	)	PUNCT
ejpam-3228	170	82	(	(	PUNCT
ejpam-3228	170	83	(	(	PUNCT
ejpam-3228	170	84	1	1	NUM
ejpam-3228	170	85	,	,	PUNCT
ejpam-3228	170	86	1	1	NUM
ejpam-3228	170	87	)	)	PUNCT
ejpam-3228	170	88	·	·	PUNCT
ejpam-3228	170	89	(	(	PUNCT
ejpam-3228	170	90	0	0	NUM
ejpam-3228	170	91	,	,	PUNCT
ejpam-3228	170	92	2)−1	2)−1	NUM
ejpam-3228	170	93	)	)	PUNCT
ejpam-3228	170	94	(	(	PUNCT
ejpam-3228	170	95	fa	fa	INTJ
ejpam-3228	170	96	∧	∧	PROPN
ejpam-3228	170	97	fb	fb	NOUN
ejpam-3228	170	98	)	)	PUNCT
ejpam-3228	170	99	(	(	PUNCT
ejpam-3228	170	100	1	1	NUM
ejpam-3228	170	101	,	,	PUNCT
ejpam-3228	170	102	1	1	NUM
ejpam-3228	170	103	)	)	PUNCT
ejpam-3228	170	104	∩	∩	NOUN
ejpam-3228	170	105	(	(	PUNCT
ejpam-3228	170	106	fa	fa	PROPN
ejpam-3228	170	107	∧	∧	PROPN
ejpam-3228	170	108	fb	fb	NOUN
ejpam-3228	170	109	)	)	PUNCT
ejpam-3228	170	110	(	(	PUNCT
ejpam-3228	170	111	0	0	NUM
ejpam-3228	170	112	,	,	PUNCT
ejpam-3228	170	113	2	2	NUM
ejpam-3228	170	114	)	)	PUNCT
ejpam-3228	170	115	.	.	PUNCT
ejpam-3228	171	1	hence	hence	ADV
ejpam-3228	171	2	,	,	PUNCT
ejpam-3228	171	3	a	a	DET
ejpam-3228	171	4	∧b	∧b	NOUN
ejpam-3228	171	5	/∈	/∈	SYM
ejpam-3228	171	6	s∪ag(u	s∪ag(u	NOUN
ejpam-3228	171	7	)	)	PUNCT
ejpam-3228	171	8	.	.	PUNCT
ejpam-3228	172	1	definition	definition	NOUN
ejpam-3228	172	2	5	5	NUM
ejpam-3228	172	3	.	.	PUNCT
ejpam-3228	173	1	let	let	VERB
ejpam-3228	173	2	a	a	DET
ejpam-3228	173	3	,	,	PUNCT
ejpam-3228	173	4	b	b	PROPN
ejpam-3228	173	5	∈	∈	PROPN
ejpam-3228	173	6	s∪ag(u	s∪ag(u	PROPN
ejpam-3228	173	7	)	)	PUNCT
ejpam-3228	173	8	on	on	ADP
ejpam-3228	173	9	ag	ag	PROPN
ejpam-3228	173	10	-	-	PUNCT
ejpam-3228	173	11	groups	group	NOUN
ejpam-3228	173	12	g1	g1	NOUN
ejpam-3228	173	13	and	and	CCONJ
ejpam-3228	173	14	g2	g2	PROPN
ejpam-3228	173	15	respectively	respectively	ADV
ejpam-3228	173	16	.	.	PUNCT
ejpam-3228	174	1	then	then	ADV
ejpam-3228	174	2	,	,	PUNCT
ejpam-3228	174	3	the	the	DET
ejpam-3228	174	4	product	product	NOUN
ejpam-3228	174	5	of	of	ADP
ejpam-3228	174	6	a	a	PRON
ejpam-3228	174	7	and	and	CCONJ
ejpam-3228	174	8	b	b	NOUN
ejpam-3228	174	9	is	be	AUX
ejpam-3228	174	10	denoted	denote	VERB
ejpam-3228	174	11	by	by	ADP
ejpam-3228	174	12	a×b	a×b	PROPN
ejpam-3228	174	13	and	and	CCONJ
ejpam-3228	174	14	is	be	AUX
ejpam-3228	174	15	defined	define	VERB
ejpam-3228	174	16	by	by	ADP
ejpam-3228	174	17	a×b	a×b	PROPN
ejpam-3228	174	18	=	=	SYM
ejpam-3228	174	19	{	{	PUNCT
ejpam-3228	174	20	(	(	PUNCT
ejpam-3228	174	21	(	(	PUNCT
ejpam-3228	174	22	a	a	DET
ejpam-3228	174	23	,	,	PUNCT
ejpam-3228	174	24	b	b	NOUN
ejpam-3228	174	25	)	)	PUNCT
ejpam-3228	174	26	,	,	PUNCT
ejpam-3228	174	27	(	(	PUNCT
ejpam-3228	174	28	fa×b	fa×b	NOUN
ejpam-3228	174	29	)	)	PUNCT
ejpam-3228	174	30	(	(	PUNCT
ejpam-3228	174	31	a	a	DET
ejpam-3228	174	32	,	,	PUNCT
ejpam-3228	174	33	b	b	NOUN
ejpam-3228	174	34	)	)	PUNCT
ejpam-3228	174	35	)	)	PUNCT
ejpam-3228	174	36	∀	∀	X
ejpam-3228	175	1	(	(	PUNCT
ejpam-3228	175	2	a	a	PRON
ejpam-3228	175	3	,	,	PUNCT
ejpam-3228	175	4	b	b	NOUN
ejpam-3228	175	5	)	)	PUNCT
ejpam-3228	175	6	∈	∈	PROPN
ejpam-3228	175	7	g1	g1	PROPN
ejpam-3228	175	8	×g2	×g2	PROPN
ejpam-3228	175	9	}	}	PUNCT
ejpam-3228	175	10	=	=	SYM
ejpam-3228	175	11	{	{	PUNCT
ejpam-3228	175	12	(	(	PUNCT
ejpam-3228	175	13	(	(	PUNCT
ejpam-3228	175	14	a	a	DET
ejpam-3228	175	15	,	,	PUNCT
ejpam-3228	175	16	b	b	NOUN
ejpam-3228	175	17	)	)	PUNCT
ejpam-3228	175	18	,	,	PUNCT
ejpam-3228	175	19	(	(	PUNCT
ejpam-3228	175	20	fa(a)×	fa(a)×	PROPN
ejpam-3228	175	21	fb(b	fb(b	NOUN
ejpam-3228	175	22	)	)	PUNCT
ejpam-3228	175	23	)	)	PUNCT
ejpam-3228	175	24	)	)	PUNCT
ejpam-3228	175	25	∀	∀	X
ejpam-3228	176	1	(	(	PUNCT
ejpam-3228	176	2	a	a	PRON
ejpam-3228	176	3	,	,	PUNCT
ejpam-3228	176	4	b	b	NOUN
ejpam-3228	176	5	)	)	PUNCT
ejpam-3228	176	6	∈	∈	PROPN
ejpam-3228	176	7	g1	g1	PROPN
ejpam-3228	176	8	×g2	×g2	PROPN
ejpam-3228	176	9	}	}	PUNCT
ejpam-3228	176	10	.	.	PUNCT
ejpam-3228	177	1	example	example	NOUN
ejpam-3228	178	1	4	4	NUM
ejpam-3228	178	2	.	.	PUNCT
ejpam-3228	178	3	let	let	VERB
ejpam-3228	178	4	u	u	PRON
ejpam-3228	178	5	=	=	NOUN
ejpam-3228	178	6	z10	z10	NOUN
ejpam-3228	178	7	be	be	AUX
ejpam-3228	178	8	a	a	DET
ejpam-3228	178	9	universal	universal	ADJ
ejpam-3228	178	10	set	set	NOUN
ejpam-3228	178	11	,	,	PUNCT
ejpam-3228	178	12	and	and	CCONJ
ejpam-3228	178	13	g1	g1	PROPN
ejpam-3228	178	14	=	=	SYM
ejpam-3228	178	15	{	{	PUNCT
ejpam-3228	178	16	a	a	PRON
ejpam-3228	178	17	,	,	PUNCT
ejpam-3228	178	18	b	b	NOUN
ejpam-3228	178	19	,	,	PUNCT
ejpam-3228	178	20	c	c	NOUN
ejpam-3228	178	21	,	,	PUNCT
ejpam-3228	178	22	d	d	NOUN
ejpam-3228	178	23	}	}	PUNCT
ejpam-3228	178	24	and	and	CCONJ
ejpam-3228	178	25	g2	g2	PROPN
ejpam-3228	178	26	=	=	PUNCT
ejpam-3228	178	27	{	{	PUNCT
ejpam-3228	178	28	x	x	PROPN
ejpam-3228	178	29	,	,	PUNCT
ejpam-3228	178	30	y	y	PROPN
ejpam-3228	178	31	,	,	PUNCT
ejpam-3228	178	32	z	z	NOUN
ejpam-3228	178	33	}	}	PUNCT
ejpam-3228	178	34	are	be	AUX
ejpam-3228	178	35	ag	ag	NOUN
ejpam-3228	178	36	-	-	PUNCT
ejpam-3228	178	37	groups	group	NOUN
ejpam-3228	178	38	of	of	ADP
ejpam-3228	178	39	order	order	NOUN
ejpam-3228	178	40	4	4	NUM
ejpam-3228	178	41	and	and	CCONJ
ejpam-3228	178	42	3	3	NUM
ejpam-3228	178	43	defined	define	VERB
ejpam-3228	178	44	in	in	ADP
ejpam-3228	178	45	the	the	DET
ejpam-3228	178	46	following	follow	VERB
ejpam-3228	178	47	tables	table	NOUN
ejpam-3228	178	48	(	(	PUNCT
ejpam-3228	178	49	i	i	NOUN
ejpam-3228	178	50	)	)	PUNCT
ejpam-3228	178	51	and	and	CCONJ
ejpam-3228	178	52	(	(	PUNCT
ejpam-3228	178	53	ii	ii	NOUN
ejpam-3228	178	54	)	)	PUNCT
ejpam-3228	178	55	respectively	respectively	ADV
ejpam-3228	178	56	:	:	PUNCT
ejpam-3228	178	57	.	.	PUNCT
ejpam-3228	179	1	a	a	DET
ejpam-3228	179	2	b	b	X
ejpam-3228	179	3	c	c	NOUN
ejpam-3228	179	4	d	d	NOUN
ejpam-3228	179	5	.	.	PUNCT
ejpam-3228	180	1	x	x	PUNCT
ejpam-3228	180	2	y	y	PROPN
ejpam-3228	180	3	z	z	PROPN
ejpam-3228	180	4	a	a	PROPN
ejpam-3228	181	1	d	d	X
ejpam-3228	181	2	a	a	DET
ejpam-3228	181	3	b	b	NOUN
ejpam-3228	181	4	c	c	NOUN
ejpam-3228	181	5	x	x	SYM
ejpam-3228	181	6	x	x	PUNCT
ejpam-3228	181	7	y	y	PROPN
ejpam-3228	181	8	z	z	PROPN
ejpam-3228	181	9	b	b	PROPN
ejpam-3228	182	1	c	c	X
ejpam-3228	182	2	d	d	PROPN
ejpam-3228	182	3	a	a	PRON
ejpam-3228	182	4	b	b	X
ejpam-3228	182	5	y	y	PROPN
ejpam-3228	182	6	z	z	NOUN
ejpam-3228	182	7	x	x	PROPN
ejpam-3228	183	1	y	y	NOUN
ejpam-3228	183	2	c	c	NOUN
ejpam-3228	183	3	b	b	PROPN
ejpam-3228	183	4	c	c	PROPN
ejpam-3228	183	5	d	d	X
ejpam-3228	183	6	a	a	DET
ejpam-3228	183	7	z	z	NOUN
ejpam-3228	183	8	y	y	NOUN
ejpam-3228	183	9	z	z	NOUN
ejpam-3228	183	10	x	x	PROPN
ejpam-3228	184	1	d	d	X
ejpam-3228	184	2	a	a	DET
ejpam-3228	184	3	b	b	NOUN
ejpam-3228	184	4	c	c	X
ejpam-3228	184	5	d	d	X
ejpam-3228	184	6	(	(	PUNCT
ejpam-3228	184	7	i	i	NOUN
ejpam-3228	184	8	)	)	PUNCT
ejpam-3228	184	9	(	(	PUNCT
ejpam-3228	184	10	ii	ii	NOUN
ejpam-3228	184	11	)	)	PUNCT
ejpam-3228	184	12	let	let	VERB
ejpam-3228	184	13	a	a	DET
ejpam-3228	184	14	,	,	PUNCT
ejpam-3228	184	15	b	b	PROPN
ejpam-3228	184	16	∈	∈	PROPN
ejpam-3228	184	17	s∪ag(u	s∪ag(u	PROPN
ejpam-3228	184	18	)	)	PUNCT
ejpam-3228	184	19	on	on	ADP
ejpam-3228	184	20	ag	ag	PROPN
ejpam-3228	184	21	-	-	PUNCT
ejpam-3228	184	22	groups	group	NOUN
ejpam-3228	184	23	g1	g1	PROPN
ejpam-3228	184	24	and	and	CCONJ
ejpam-3228	184	25	g2	g2	PROPN
ejpam-3228	184	26	respectively	respectively	ADV
ejpam-3228	184	27	defined	define	VERB
ejpam-3228	184	28	by	by	ADP
ejpam-3228	184	29	:	:	PUNCT
ejpam-3228	184	30	fa(a	fa(a	NUM
ejpam-3228	184	31	)	)	PUNCT
ejpam-3228	185	1	=	=	PRON
ejpam-3228	185	2	{	{	PUNCT
ejpam-3228	185	3	0	0	NUM
ejpam-3228	185	4	,	,	PUNCT
ejpam-3228	185	5	1	1	NUM
ejpam-3228	185	6	,	,	PUNCT
ejpam-3228	185	7	2	2	NUM
ejpam-3228	185	8	}	}	PUNCT
ejpam-3228	185	9	=	=	PUNCT
ejpam-3228	185	10	fa(c	fa(c	X
ejpam-3228	185	11	)	)	PUNCT
ejpam-3228	185	12	,	,	PUNCT
ejpam-3228	185	13	fa(b	fa(b	NOUN
ejpam-3228	185	14	)	)	PUNCT
ejpam-3228	185	15	=	=	SYM
ejpam-3228	185	16	{	{	PUNCT
ejpam-3228	185	17	0	0	NUM
ejpam-3228	185	18	,	,	PUNCT
ejpam-3228	185	19	1	1	NUM
ejpam-3228	185	20	}	}	PUNCT
ejpam-3228	185	21	,	,	PUNCT
ejpam-3228	185	22	fa(d	fa(d	NUM
ejpam-3228	185	23	)	)	PUNCT
ejpam-3228	185	24	=	=	PRON
ejpam-3228	185	25	{	{	PUNCT
ejpam-3228	185	26	0	0	NUM
ejpam-3228	185	27	}	}	PUNCT
ejpam-3228	185	28	,	,	PUNCT
ejpam-3228	185	29	and	and	CCONJ
ejpam-3228	185	30	fb(x	fb(x	NUM
ejpam-3228	185	31	)	)	PUNCT
ejpam-3228	185	32	=	=	PRON
ejpam-3228	185	33	{	{	PUNCT
ejpam-3228	185	34	0	0	NUM
ejpam-3228	185	35	}	}	PUNCT
ejpam-3228	185	36	,	,	PUNCT
ejpam-3228	185	37	fb(y	fb(y	PROPN
ejpam-3228	185	38	)	)	PUNCT
ejpam-3228	185	39	=	=	PRON
ejpam-3228	185	40	{	{	PUNCT
ejpam-3228	185	41	0	0	NUM
ejpam-3228	185	42	,	,	PUNCT
ejpam-3228	185	43	1	1	NUM
ejpam-3228	185	44	}	}	PUNCT
ejpam-3228	185	45	=	=	PUNCT
ejpam-3228	185	46	fb(z	fb(z	X
ejpam-3228	185	47	)	)	PUNCT
ejpam-3228	185	48	.	.	PUNCT
ejpam-3228	186	1	a.	a.	PROPN
ejpam-3228	186	2	ullah	ullah	PROPN
ejpam-3228	186	3	,	,	PUNCT
ejpam-3228	186	4	f.	f.	PROPN
ejpam-3228	186	5	karaaslan	karaaslan	PROPN
ejpam-3228	186	6	,	,	PUNCT
ejpam-3228	186	7	i.	i.	PROPN
ejpam-3228	186	8	ahmad	ahmad	PROPN
ejpam-3228	186	9	/	/	SYM
ejpam-3228	186	10	eur	eur	PROPN
ejpam-3228	186	11	.	.	PUNCT
ejpam-3228	187	1	j.	j.	PROPN
ejpam-3228	187	2	pure	pure	PROPN
ejpam-3228	187	3	appl	appl	PROPN
ejpam-3228	187	4	.	.	PROPN
ejpam-3228	187	5	math	math	PROPN
ejpam-3228	187	6	,	,	PUNCT
ejpam-3228	187	7	11	11	NUM
ejpam-3228	187	8	(	(	PUNCT
ejpam-3228	187	9	2	2	NUM
ejpam-3228	187	10	)	)	PUNCT
ejpam-3228	187	11	(	(	PUNCT
ejpam-3228	187	12	2018	2018	NUM
ejpam-3228	187	13	)	)	PUNCT
ejpam-3228	187	14	,	,	PUNCT
ejpam-3228	187	15	517	517	NUM
ejpam-3228	187	16	-	-	SYM
ejpam-3228	187	17	536	536	NUM
ejpam-3228	187	18	525	525	NUM
ejpam-3228	187	19	then	then	ADV
ejpam-3228	187	20	a×b	a×b	PUNCT
ejpam-3228	187	21	=	=	PRON
ejpam-3228	187	22	{	{	PUNCT
ejpam-3228	187	23	(	(	PUNCT
ejpam-3228	187	24	a	a	DET
ejpam-3228	187	25	,	,	PUNCT
ejpam-3228	187	26	b	b	NOUN
ejpam-3228	187	27	)	)	PUNCT
ejpam-3228	187	28	,	,	PUNCT
ejpam-3228	187	29	(	(	PUNCT
ejpam-3228	187	30	fa(a)×	fa(a)×	PROPN
ejpam-3228	187	31	fb(b	fb(b	NOUN
ejpam-3228	187	32	)	)	PUNCT
ejpam-3228	187	33	)	)	PUNCT
ejpam-3228	187	34	∀	∀	X
ejpam-3228	188	1	(	(	PUNCT
ejpam-3228	188	2	a	a	PRON
ejpam-3228	188	3	,	,	PUNCT
ejpam-3228	188	4	b	b	NOUN
ejpam-3228	188	5	)	)	PUNCT
ejpam-3228	188	6	∈	∈	PROPN
ejpam-3228	188	7	g1	g1	PROPN
ejpam-3228	188	8	×g2	×g2	PROPN
ejpam-3228	188	9	}	}	PUNCT
ejpam-3228	188	10	,	,	PUNCT
ejpam-3228	188	11	=	=	PRON
ejpam-3228	188	12	{	{	PUNCT
ejpam-3228	188	13	{	{	PUNCT
ejpam-3228	188	14	(	(	PUNCT
ejpam-3228	188	15	a	a	PRON
ejpam-3228	188	16	,	,	PUNCT
ejpam-3228	188	17	x	x	NOUN
ejpam-3228	188	18	)	)	PUNCT
ejpam-3228	188	19	,	,	PUNCT
ejpam-3228	188	20	(	(	PUNCT
ejpam-3228	188	21	(	(	PUNCT
ejpam-3228	188	22	0	0	NUM
ejpam-3228	188	23	,	,	PUNCT
ejpam-3228	188	24	0	0	NUM
ejpam-3228	188	25	)	)	PUNCT
ejpam-3228	188	26	,	,	PUNCT
ejpam-3228	188	27	(	(	PUNCT
ejpam-3228	188	28	1	1	NUM
ejpam-3228	188	29	,	,	PUNCT
ejpam-3228	188	30	0	0	NUM
ejpam-3228	188	31	)	)	PUNCT
ejpam-3228	188	32	,	,	PUNCT
ejpam-3228	188	33	(	(	PUNCT
ejpam-3228	188	34	2	2	NUM
ejpam-3228	188	35	,	,	PUNCT
ejpam-3228	188	36	0	0	NUM
ejpam-3228	188	37	)	)	PUNCT
ejpam-3228	188	38	)	)	PUNCT
ejpam-3228	188	39	}	}	PUNCT
ejpam-3228	188	40	,	,	PUNCT
ejpam-3228	188	41	{	{	PUNCT
ejpam-3228	188	42	(	(	PUNCT
ejpam-3228	188	43	a	a	PROPN
ejpam-3228	188	44	,	,	PUNCT
ejpam-3228	188	45	y	y	PROPN
ejpam-3228	188	46	)	)	PUNCT
ejpam-3228	188	47	,	,	PUNCT
ejpam-3228	188	48	(	(	PUNCT
ejpam-3228	188	49	(	(	PUNCT
ejpam-3228	188	50	0	0	NUM
ejpam-3228	188	51	,	,	PUNCT
ejpam-3228	188	52	0	0	NUM
ejpam-3228	188	53	)	)	PUNCT
ejpam-3228	188	54	,	,	PUNCT
ejpam-3228	188	55	(	(	PUNCT
ejpam-3228	188	56	0	0	NUM
ejpam-3228	188	57	,	,	PUNCT
ejpam-3228	188	58	1	1	NUM
ejpam-3228	188	59	)	)	PUNCT
ejpam-3228	188	60	,	,	PUNCT
ejpam-3228	188	61	(	(	PUNCT
ejpam-3228	188	62	1	1	NUM
ejpam-3228	188	63	,	,	PUNCT
ejpam-3228	188	64	0	0	NUM
ejpam-3228	188	65	)	)	PUNCT
ejpam-3228	188	66	,	,	PUNCT
ejpam-3228	188	67	(	(	PUNCT
ejpam-3228	188	68	1	1	NUM
ejpam-3228	188	69	,	,	PUNCT
ejpam-3228	188	70	1	1	NUM
ejpam-3228	188	71	)	)	PUNCT
ejpam-3228	188	72	,	,	PUNCT
ejpam-3228	188	73	(	(	PUNCT
ejpam-3228	188	74	2	2	NUM
ejpam-3228	188	75	,	,	PUNCT
ejpam-3228	188	76	0	0	NUM
ejpam-3228	188	77	)	)	PUNCT
ejpam-3228	188	78	,	,	PUNCT
ejpam-3228	188	79	(	(	PUNCT
ejpam-3228	188	80	2	2	NUM
ejpam-3228	188	81	,	,	PUNCT
ejpam-3228	188	82	1	1	NUM
ejpam-3228	188	83	)	)	PUNCT
ejpam-3228	188	84	)	)	PUNCT
ejpam-3228	188	85	}	}	PUNCT
ejpam-3228	188	86	,	,	PUNCT
ejpam-3228	188	87	{	{	PUNCT
ejpam-3228	188	88	(	(	PUNCT
ejpam-3228	188	89	a	a	DET
ejpam-3228	188	90	,	,	PUNCT
ejpam-3228	188	91	z	z	NOUN
ejpam-3228	188	92	)	)	PUNCT
ejpam-3228	188	93	,	,	PUNCT
ejpam-3228	188	94	(	(	PUNCT
ejpam-3228	188	95	(	(	PUNCT
ejpam-3228	188	96	0	0	NUM
ejpam-3228	188	97	,	,	PUNCT
ejpam-3228	188	98	0	0	NUM
ejpam-3228	188	99	)	)	PUNCT
ejpam-3228	188	100	,	,	PUNCT
ejpam-3228	188	101	(	(	PUNCT
ejpam-3228	188	102	0	0	NUM
ejpam-3228	188	103	,	,	PUNCT
ejpam-3228	188	104	1	1	NUM
ejpam-3228	188	105	)	)	PUNCT
ejpam-3228	188	106	,	,	PUNCT
ejpam-3228	188	107	(	(	PUNCT
ejpam-3228	188	108	1	1	NUM
ejpam-3228	188	109	,	,	PUNCT
ejpam-3228	188	110	0	0	NUM
ejpam-3228	188	111	)	)	PUNCT
ejpam-3228	188	112	,	,	PUNCT
ejpam-3228	188	113	(	(	PUNCT
ejpam-3228	188	114	1	1	NUM
ejpam-3228	188	115	,	,	PUNCT
ejpam-3228	188	116	1	1	NUM
ejpam-3228	188	117	)	)	PUNCT
ejpam-3228	188	118	,	,	PUNCT
ejpam-3228	188	119	(	(	PUNCT
ejpam-3228	188	120	2	2	NUM
ejpam-3228	188	121	,	,	PUNCT
ejpam-3228	188	122	0	0	NUM
ejpam-3228	188	123	)	)	PUNCT
ejpam-3228	188	124	,	,	PUNCT
ejpam-3228	188	125	(	(	PUNCT
ejpam-3228	188	126	2	2	NUM
ejpam-3228	188	127	,	,	PUNCT
ejpam-3228	188	128	1	1	NUM
ejpam-3228	188	129	)	)	PUNCT
ejpam-3228	188	130	)	)	PUNCT
ejpam-3228	188	131	}	}	PUNCT
ejpam-3228	188	132	,	,	PUNCT
ejpam-3228	188	133	{	{	PUNCT
ejpam-3228	188	134	(	(	PUNCT
ejpam-3228	188	135	b	b	NOUN
ejpam-3228	188	136	,	,	PUNCT
ejpam-3228	188	137	x	x	NOUN
ejpam-3228	188	138	)	)	PUNCT
ejpam-3228	188	139	,	,	PUNCT
ejpam-3228	188	140	(	(	PUNCT
ejpam-3228	188	141	(	(	PUNCT
ejpam-3228	188	142	0	0	NUM
ejpam-3228	188	143	,	,	PUNCT
ejpam-3228	188	144	0	0	NUM
ejpam-3228	188	145	)	)	PUNCT
ejpam-3228	188	146	,	,	PUNCT
ejpam-3228	188	147	(	(	PUNCT
ejpam-3228	188	148	1	1	NUM
ejpam-3228	188	149	,	,	PUNCT
ejpam-3228	188	150	0	0	NUM
ejpam-3228	188	151	)	)	PUNCT
ejpam-3228	188	152	)	)	PUNCT
ejpam-3228	188	153	}	}	PUNCT
ejpam-3228	188	154	,	,	PUNCT
ejpam-3228	188	155	{	{	PUNCT
ejpam-3228	188	156	(	(	PUNCT
ejpam-3228	188	157	b	b	NOUN
ejpam-3228	188	158	,	,	PUNCT
ejpam-3228	188	159	y	y	PROPN
ejpam-3228	188	160	)	)	PUNCT
ejpam-3228	188	161	,	,	PUNCT
ejpam-3228	188	162	(	(	PUNCT
ejpam-3228	188	163	(	(	PUNCT
ejpam-3228	188	164	0	0	NUM
ejpam-3228	188	165	,	,	PUNCT
ejpam-3228	188	166	0	0	NUM
ejpam-3228	188	167	)	)	PUNCT
ejpam-3228	188	168	,	,	PUNCT
ejpam-3228	188	169	(	(	PUNCT
ejpam-3228	188	170	0	0	NUM
ejpam-3228	188	171	,	,	PUNCT
ejpam-3228	188	172	1	1	NUM
ejpam-3228	188	173	)	)	PUNCT
ejpam-3228	188	174	,	,	PUNCT
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ejpam-3228	188	176	1	1	NUM
ejpam-3228	188	177	,	,	PUNCT
ejpam-3228	188	178	0	0	NUM
ejpam-3228	188	179	)	)	PUNCT
ejpam-3228	188	180	,	,	PUNCT
ejpam-3228	188	181	(	(	PUNCT
ejpam-3228	188	182	1	1	NUM
ejpam-3228	188	183	,	,	PUNCT
ejpam-3228	188	184	1	1	NUM
ejpam-3228	188	185	)	)	PUNCT
ejpam-3228	188	186	)	)	PUNCT
ejpam-3228	188	187	}	}	PUNCT
ejpam-3228	188	188	,	,	PUNCT
ejpam-3228	188	189	{	{	PUNCT
ejpam-3228	188	190	(	(	PUNCT
ejpam-3228	188	191	b	b	NOUN
ejpam-3228	188	192	,	,	PUNCT
ejpam-3228	188	193	z	z	NOUN
ejpam-3228	188	194	)	)	PUNCT
ejpam-3228	188	195	,	,	PUNCT
ejpam-3228	188	196	(	(	PUNCT
ejpam-3228	188	197	(	(	PUNCT
ejpam-3228	188	198	0	0	NUM
ejpam-3228	188	199	,	,	PUNCT
ejpam-3228	188	200	0	0	NUM
ejpam-3228	188	201	)	)	PUNCT
ejpam-3228	188	202	,	,	PUNCT
ejpam-3228	188	203	(	(	PUNCT
ejpam-3228	188	204	0	0	NUM
ejpam-3228	188	205	,	,	PUNCT
ejpam-3228	188	206	1	1	NUM
ejpam-3228	188	207	)	)	PUNCT
ejpam-3228	188	208	,	,	PUNCT
ejpam-3228	188	209	(	(	PUNCT
ejpam-3228	188	210	1	1	NUM
ejpam-3228	188	211	,	,	PUNCT
ejpam-3228	188	212	0	0	NUM
ejpam-3228	188	213	)	)	PUNCT
ejpam-3228	188	214	,	,	PUNCT
ejpam-3228	188	215	(	(	PUNCT
ejpam-3228	188	216	1	1	NUM
ejpam-3228	188	217	,	,	PUNCT
ejpam-3228	188	218	1	1	NUM
ejpam-3228	188	219	)	)	PUNCT
ejpam-3228	188	220	)	)	PUNCT
ejpam-3228	188	221	}	}	PUNCT
ejpam-3228	188	222	,	,	PUNCT
ejpam-3228	188	223	{	{	PUNCT
ejpam-3228	188	224	{	{	PUNCT
ejpam-3228	188	225	(	(	PUNCT
ejpam-3228	188	226	c	c	NOUN
ejpam-3228	188	227	,	,	PUNCT
ejpam-3228	188	228	x	x	NOUN
ejpam-3228	188	229	)	)	PUNCT
ejpam-3228	188	230	,	,	PUNCT
ejpam-3228	188	231	(	(	PUNCT
ejpam-3228	188	232	(	(	PUNCT
ejpam-3228	188	233	0	0	NUM
ejpam-3228	188	234	,	,	PUNCT
ejpam-3228	188	235	0	0	NUM
ejpam-3228	188	236	)	)	PUNCT
ejpam-3228	188	237	,	,	PUNCT
ejpam-3228	188	238	(	(	PUNCT
ejpam-3228	188	239	1	1	NUM
ejpam-3228	188	240	,	,	PUNCT
ejpam-3228	188	241	0	0	NUM
ejpam-3228	188	242	)	)	PUNCT
ejpam-3228	188	243	,	,	PUNCT
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ejpam-3228	188	245	2	2	NUM
ejpam-3228	188	246	,	,	PUNCT
ejpam-3228	188	247	0	0	NUM
ejpam-3228	188	248	)	)	PUNCT
ejpam-3228	188	249	)	)	PUNCT
ejpam-3228	188	250	}	}	PUNCT
ejpam-3228	188	251	,	,	PUNCT
ejpam-3228	188	252	{	{	PUNCT
ejpam-3228	188	253	(	(	PUNCT
ejpam-3228	188	254	c	c	X
ejpam-3228	188	255	,	,	PUNCT
ejpam-3228	188	256	y	y	PROPN
ejpam-3228	188	257	)	)	PUNCT
ejpam-3228	188	258	,	,	PUNCT
ejpam-3228	188	259	(	(	PUNCT
ejpam-3228	188	260	(	(	PUNCT
ejpam-3228	188	261	0	0	NUM
ejpam-3228	188	262	,	,	PUNCT
ejpam-3228	188	263	0	0	NUM
ejpam-3228	188	264	)	)	PUNCT
ejpam-3228	188	265	,	,	PUNCT
ejpam-3228	188	266	(	(	PUNCT
ejpam-3228	188	267	0	0	NUM
ejpam-3228	188	268	,	,	PUNCT
ejpam-3228	188	269	1	1	NUM
ejpam-3228	188	270	)	)	PUNCT
ejpam-3228	188	271	,	,	PUNCT
ejpam-3228	188	272	(	(	PUNCT
ejpam-3228	188	273	1	1	NUM
ejpam-3228	188	274	,	,	PUNCT
ejpam-3228	188	275	0	0	NUM
ejpam-3228	188	276	)	)	PUNCT
ejpam-3228	188	277	,	,	PUNCT
ejpam-3228	188	278	(	(	PUNCT
ejpam-3228	188	279	1	1	NUM
ejpam-3228	188	280	,	,	PUNCT
ejpam-3228	188	281	1	1	NUM
ejpam-3228	188	282	)	)	PUNCT
ejpam-3228	188	283	,	,	PUNCT
ejpam-3228	188	284	(	(	PUNCT
ejpam-3228	188	285	2	2	NUM
ejpam-3228	188	286	,	,	PUNCT
ejpam-3228	188	287	0	0	NUM
ejpam-3228	188	288	)	)	PUNCT
ejpam-3228	188	289	,	,	PUNCT
ejpam-3228	188	290	(	(	PUNCT
ejpam-3228	188	291	2	2	NUM
ejpam-3228	188	292	,	,	PUNCT
ejpam-3228	188	293	1	1	NUM
ejpam-3228	188	294	)	)	PUNCT
ejpam-3228	188	295	)	)	PUNCT
ejpam-3228	188	296	}	}	PUNCT
ejpam-3228	188	297	,	,	PUNCT
ejpam-3228	188	298	{	{	PUNCT
ejpam-3228	188	299	(	(	PUNCT
ejpam-3228	188	300	c	c	X
ejpam-3228	188	301	,	,	PUNCT
ejpam-3228	188	302	z	z	NOUN
ejpam-3228	188	303	)	)	PUNCT
ejpam-3228	188	304	,	,	PUNCT
ejpam-3228	188	305	(	(	PUNCT
ejpam-3228	188	306	(	(	PUNCT
ejpam-3228	188	307	0	0	NUM
ejpam-3228	188	308	,	,	PUNCT
ejpam-3228	188	309	0	0	NUM
ejpam-3228	188	310	)	)	PUNCT
ejpam-3228	188	311	,	,	PUNCT
ejpam-3228	188	312	(	(	PUNCT
ejpam-3228	188	313	0	0	NUM
ejpam-3228	188	314	,	,	PUNCT
ejpam-3228	188	315	1	1	NUM
ejpam-3228	188	316	)	)	PUNCT
ejpam-3228	188	317	,	,	PUNCT
ejpam-3228	188	318	(	(	PUNCT
ejpam-3228	188	319	1	1	NUM
ejpam-3228	188	320	,	,	PUNCT
ejpam-3228	188	321	0	0	NUM
ejpam-3228	188	322	)	)	PUNCT
ejpam-3228	188	323	,	,	PUNCT
ejpam-3228	188	324	(	(	PUNCT
ejpam-3228	188	325	1	1	NUM
ejpam-3228	188	326	,	,	PUNCT
ejpam-3228	188	327	1	1	NUM
ejpam-3228	188	328	)	)	PUNCT
ejpam-3228	188	329	,	,	PUNCT
ejpam-3228	188	330	(	(	PUNCT
ejpam-3228	188	331	2	2	NUM
ejpam-3228	188	332	,	,	PUNCT
ejpam-3228	188	333	0	0	NUM
ejpam-3228	188	334	)	)	PUNCT
ejpam-3228	188	335	,	,	PUNCT
ejpam-3228	188	336	(	(	PUNCT
ejpam-3228	188	337	2	2	NUM
ejpam-3228	188	338	,	,	PUNCT
ejpam-3228	188	339	1	1	NUM
ejpam-3228	188	340	)	)	PUNCT
ejpam-3228	188	341	)	)	PUNCT
ejpam-3228	188	342	}	}	PUNCT
ejpam-3228	188	343	,	,	PUNCT
ejpam-3228	188	344	{	{	PUNCT
ejpam-3228	188	345	(	(	PUNCT
ejpam-3228	188	346	d	d	NOUN
ejpam-3228	188	347	,	,	PUNCT
ejpam-3228	188	348	x	x	NOUN
ejpam-3228	188	349	)	)	PUNCT
ejpam-3228	188	350	,	,	PUNCT
ejpam-3228	188	351	(	(	PUNCT
ejpam-3228	188	352	(	(	PUNCT
ejpam-3228	188	353	0	0	NUM
ejpam-3228	188	354	,	,	PUNCT
ejpam-3228	188	355	0	0	NUM
ejpam-3228	188	356	)	)	PUNCT
ejpam-3228	188	357	)	)	PUNCT
ejpam-3228	188	358	}	}	PUNCT
ejpam-3228	188	359	,	,	PUNCT
ejpam-3228	188	360	{	{	PUNCT
ejpam-3228	188	361	(	(	PUNCT
ejpam-3228	188	362	d	d	PROPN
ejpam-3228	188	363	,	,	PUNCT
ejpam-3228	188	364	y	y	PROPN
ejpam-3228	188	365	)	)	PUNCT
ejpam-3228	188	366	,	,	PUNCT
ejpam-3228	188	367	(	(	PUNCT
ejpam-3228	188	368	(	(	PUNCT
ejpam-3228	188	369	0	0	NUM
ejpam-3228	188	370	,	,	PUNCT
ejpam-3228	188	371	0	0	NUM
ejpam-3228	188	372	)	)	PUNCT
ejpam-3228	188	373	,	,	PUNCT
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ejpam-3228	188	375	0	0	NUM
ejpam-3228	188	376	,	,	PUNCT
ejpam-3228	188	377	1	1	NUM
ejpam-3228	188	378	)	)	PUNCT
ejpam-3228	188	379	)	)	PUNCT
ejpam-3228	188	380	}	}	PUNCT
ejpam-3228	188	381	,	,	PUNCT
ejpam-3228	188	382	{	{	PUNCT
ejpam-3228	188	383	(	(	PUNCT
ejpam-3228	188	384	d	d	NOUN
ejpam-3228	188	385	,	,	PUNCT
ejpam-3228	188	386	z	z	NOUN
ejpam-3228	188	387	)	)	PUNCT
ejpam-3228	188	388	,	,	PUNCT
ejpam-3228	188	389	(	(	PUNCT
ejpam-3228	188	390	(	(	PUNCT
ejpam-3228	188	391	0	0	NUM
ejpam-3228	188	392	,	,	PUNCT
ejpam-3228	188	393	0	0	NUM
ejpam-3228	188	394	)	)	PUNCT
ejpam-3228	188	395	,	,	PUNCT
ejpam-3228	188	396	(	(	PUNCT
ejpam-3228	188	397	0	0	NUM
ejpam-3228	188	398	,	,	PUNCT
ejpam-3228	188	399	1	1	NUM
ejpam-3228	188	400	)	)	PUNCT
ejpam-3228	188	401	)	)	PUNCT
ejpam-3228	188	402	}	}	PUNCT
ejpam-3228	188	403	}	}	PUNCT
ejpam-3228	188	404	.	.	PUNCT
ejpam-3228	189	1	theorem	theorem	NOUN
ejpam-3228	189	2	3	3	X
ejpam-3228	189	3	.	.	PUNCT
ejpam-3228	190	1	let	let	VERB
ejpam-3228	190	2	a	a	DET
ejpam-3228	190	3	,	,	PUNCT
ejpam-3228	190	4	b	b	PROPN
ejpam-3228	190	5	∈	∈	PROPN
ejpam-3228	190	6	s∪ag(u	s∪ag(u	PROPN
ejpam-3228	190	7	)	)	PUNCT
ejpam-3228	190	8	with	with	ADP
ejpam-3228	190	9	respect	respect	NOUN
ejpam-3228	190	10	to	to	ADP
ejpam-3228	190	11	ag	ag	PROPN
ejpam-3228	190	12	-	-	PUNCT
ejpam-3228	190	13	groups	group	NOUN
ejpam-3228	190	14	g1	g1	NOUN
ejpam-3228	190	15	and	and	CCONJ
ejpam-3228	190	16	g2	g2	PROPN
ejpam-3228	190	17	.	.	PUNCT
ejpam-3228	191	1	then	then	ADV
ejpam-3228	191	2	a×b	a×b	PUNCT
ejpam-3228	191	3	∈	∈	PROPN
ejpam-3228	191	4	s∪ag(u	s∪ag(u	PROPN
ejpam-3228	191	5	×	×	PROPN
ejpam-3228	191	6	u	u	NOUN
ejpam-3228	191	7	)	)	PUNCT
ejpam-3228	191	8	.	.	PUNCT
ejpam-3228	192	1	proof	proof	NOUN
ejpam-3228	192	2	.	.	PUNCT
ejpam-3228	193	1	for	for	ADP
ejpam-3228	193	2	any	any	DET
ejpam-3228	193	3	(	(	PUNCT
ejpam-3228	193	4	x1	x1	PROPN
ejpam-3228	193	5	,	,	PUNCT
ejpam-3228	193	6	y1	y1	PROPN
ejpam-3228	193	7	)	)	PUNCT
ejpam-3228	193	8	,	,	PUNCT
ejpam-3228	193	9	(	(	PUNCT
ejpam-3228	193	10	x2	x2	PROPN
ejpam-3228	193	11	,	,	PUNCT
ejpam-3228	193	12	y2	y2	PROPN
ejpam-3228	193	13	)	)	PUNCT
ejpam-3228	193	14	∈	∈	PROPN
ejpam-3228	193	15	g1	g1	PROPN
ejpam-3228	193	16	×g2	×g2	PROPN
ejpam-3228	193	17	,	,	PUNCT
ejpam-3228	193	18	(	(	PUNCT
ejpam-3228	193	19	fa×b	fa×b	NOUN
ejpam-3228	193	20	)	)	PUNCT
ejpam-3228	193	21	(	(	PUNCT
ejpam-3228	193	22	(	(	PUNCT
ejpam-3228	193	23	x1	x1	PROPN
ejpam-3228	193	24	,	,	PUNCT
ejpam-3228	193	25	y1	y1	PROPN
ejpam-3228	193	26	)	)	PUNCT
ejpam-3228	193	27	,	,	PUNCT
ejpam-3228	193	28	(	(	PUNCT
ejpam-3228	193	29	x2	x2	PROPN
ejpam-3228	193	30	,	,	PUNCT
ejpam-3228	193	31	y2	y2	NOUN
ejpam-3228	193	32	)	)	PUNCT
ejpam-3228	193	33	−1	−1	NOUN
ejpam-3228	193	34	)	)	PUNCT
ejpam-3228	193	35	=	=	PUNCT
ejpam-3228	193	36	(	(	PUNCT
ejpam-3228	193	37	fa×b	fa×b	PROPN
ejpam-3228	193	38	)	)	PUNCT
ejpam-3228	193	39	(	(	PUNCT
ejpam-3228	193	40	(	(	PUNCT
ejpam-3228	193	41	x1	x1	PROPN
ejpam-3228	193	42	,	,	PUNCT
ejpam-3228	193	43	y1	y1	PROPN
ejpam-3228	193	44	)	)	PUNCT
ejpam-3228	193	45	,	,	PUNCT
ejpam-3228	193	46	(	(	PUNCT
ejpam-3228	193	47	x	x	SYM
ejpam-3228	193	48	−1	−1	NOUN
ejpam-3228	193	49	2	2	NUM
ejpam-3228	193	50	,	,	PUNCT
ejpam-3228	193	51	y−12	y−12	NOUN
ejpam-3228	193	52	)	)	PUNCT
ejpam-3228	193	53	)	)	PUNCT
ejpam-3228	194	1	=	=	PRON
ejpam-3228	194	2	(	(	PUNCT
ejpam-3228	194	3	fa×b	fa×b	PROPN
ejpam-3228	194	4	)	)	PUNCT
ejpam-3228	194	5	(	(	PUNCT
ejpam-3228	194	6	(	(	PUNCT
ejpam-3228	194	7	x1x	x1x	PROPN
ejpam-3228	194	8	−1	−1	NOUN
ejpam-3228	194	9	2	2	NUM
ejpam-3228	194	10	,	,	PUNCT
ejpam-3228	194	11	y1y	y1y	PROPN
ejpam-3228	194	12	−1	−1	NOUN
ejpam-3228	194	13	2	2	X
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ejpam-3228	195	1	=	=	PUNCT
ejpam-3228	195	2	fa(x1x	fa(x1x	NOUN
ejpam-3228	195	3	−1	−1	NOUN
ejpam-3228	195	4	2	2	NUM
ejpam-3228	195	5	)	)	PUNCT
ejpam-3228	195	6	×	×	NOUN
ejpam-3228	195	7	fb(y1y	fb(y1y	PROPN
ejpam-3228	195	8	−1	−1	NOUN
ejpam-3228	195	9	2	2	NUM
ejpam-3228	195	10	)	)	PUNCT
ejpam-3228	195	11	(	(	PUNCT
ejpam-3228	195	12	by	by	ADP
ejpam-3228	195	13	definition	definition	NOUN
ejpam-3228	195	14	5	5	NUM
ejpam-3228	195	15	)	)	PUNCT
ejpam-3228	195	16	⊆	⊆	NUM
ejpam-3228	195	17	(	(	PUNCT
ejpam-3228	195	18	fa(x1	fa(x1	NOUN
ejpam-3228	195	19	)	)	PUNCT
ejpam-3228	195	20	∪	∪	ADP
ejpam-3228	195	21	fa(x2))×	fa(x2))×	PROPN
ejpam-3228	195	22	(	(	PUNCT
ejpam-3228	195	23	fb(y1	fb(y1	NOUN
ejpam-3228	195	24	)	)	PUNCT
ejpam-3228	195	25	∪	∪	ADP
ejpam-3228	195	26	fb(y2	fb(y2	NOUN
ejpam-3228	195	27	)	)	PUNCT
ejpam-3228	195	28	)	)	PUNCT
ejpam-3228	196	1	=	=	SYM
ejpam-3228	196	2	(	(	PUNCT
ejpam-3228	196	3	fa(x1)×	fa(x1)×	NOUN
ejpam-3228	196	4	fb(y1	fb(y1	NOUN
ejpam-3228	196	5	)	)	PUNCT
ejpam-3228	196	6	)	)	PUNCT
ejpam-3228	196	7	∪	∪	ADP
ejpam-3228	196	8	(	(	PUNCT
ejpam-3228	196	9	fa(x2)×	fa(x2)×	NOUN
ejpam-3228	196	10	fb(y2	fb(y2	ADJ
ejpam-3228	196	11	)	)	PUNCT
ejpam-3228	196	12	)	)	PUNCT
ejpam-3228	197	1	=	=	SYM
ejpam-3228	197	2	(	(	PUNCT
ejpam-3228	197	3	fa×b	fa×b	PROPN
ejpam-3228	197	4	)	)	PUNCT
ejpam-3228	197	5	(	(	PUNCT
ejpam-3228	197	6	x1	x1	PROPN
ejpam-3228	197	7	,	,	PUNCT
ejpam-3228	197	8	y1	y1	NOUN
ejpam-3228	197	9	)	)	PUNCT
ejpam-3228	197	10	∪	∪	NOUN
ejpam-3228	197	11	(	(	PUNCT
ejpam-3228	197	12	fa×b	fa×b	NOUN
ejpam-3228	197	13	)	)	PUNCT
ejpam-3228	197	14	(	(	PUNCT
ejpam-3228	197	15	x2	x2	PROPN
ejpam-3228	197	16	,	,	PUNCT
ejpam-3228	197	17	y2	y2	PROPN
ejpam-3228	197	18	)	)	PUNCT
ejpam-3228	197	19	.	.	PUNCT
ejpam-3228	198	1	hence	hence	ADV
ejpam-3228	198	2	,	,	PUNCT
ejpam-3228	198	3	a×b	a×b	PROPN
ejpam-3228	198	4	∈	∈	PROPN
ejpam-3228	198	5	s∪ag(u	s∪ag(u	PROPN
ejpam-3228	198	6	×	×	PROPN
ejpam-3228	198	7	u	u	NOUN
ejpam-3228	198	8	)	)	PUNCT
ejpam-3228	198	9	.	.	PUNCT
ejpam-3228	199	1	theorem	theorem	ADJ
ejpam-3228	199	2	4	4	NUM
ejpam-3228	199	3	.	.	PUNCT
ejpam-3228	200	1	let	let	VERB
ejpam-3228	200	2	a	a	DET
ejpam-3228	200	3	,	,	PUNCT
ejpam-3228	200	4	b	b	PROPN
ejpam-3228	200	5	∈	∈	PROPN
ejpam-3228	200	6	s∪ag(u	s∪ag(u	NUM
ejpam-3228	200	7	)	)	PUNCT
ejpam-3228	200	8	,	,	PUNCT
ejpam-3228	200	9	then	then	ADV
ejpam-3228	200	10	a∪̃b	a∪̃b	PROPN
ejpam-3228	200	11	∈	∈	PROPN
ejpam-3228	200	12	s∪ag(u	s∪ag(u	PROPN
ejpam-3228	200	13	)	)	PUNCT
ejpam-3228	200	14	.	.	PUNCT
ejpam-3228	201	1	proof	proof	NOUN
ejpam-3228	201	2	.	.	PUNCT
ejpam-3228	202	1	since	since	SCONJ
ejpam-3228	202	2	a	a	DET
ejpam-3228	202	3	,	,	PUNCT
ejpam-3228	202	4	b	b	PROPN
ejpam-3228	202	5	∈	∈	PROPN
ejpam-3228	202	6	s∪ag(u	s∪ag(u	PROPN
ejpam-3228	202	7	)	)	PUNCT
ejpam-3228	202	8	.	.	PUNCT
ejpam-3228	203	1	therefore	therefore	ADV
ejpam-3228	203	2	,	,	PUNCT
ejpam-3228	203	3	a∪̃b	a∪̃b	PROPN
ejpam-3228	203	4	6=	6=	ADP
ejpam-3228	203	5	∅.	∅.	VERB
ejpam-3228	203	6	for	for	ADP
ejpam-3228	203	7	any	any	DET
ejpam-3228	203	8	a	a	PRON
ejpam-3228	203	9	,	,	PUNCT
ejpam-3228	203	10	b	b	PROPN
ejpam-3228	203	11	∈	∈	PROPN
ejpam-3228	203	12	a∪̃b	a∪̃b	PROPN
ejpam-3228	203	13	,	,	PUNCT
ejpam-3228	203	14	we	we	PRON
ejpam-3228	203	15	have	have	AUX
ejpam-3228	203	16	(	(	PUNCT
ejpam-3228	203	17	fa∪̃fb	fa∪̃fb	PROPN
ejpam-3228	203	18	)	)	PUNCT
ejpam-3228	203	19	(	(	PUNCT
ejpam-3228	203	20	ab−1	ab−1	PROPN
ejpam-3228	203	21	)	)	PUNCT
ejpam-3228	203	22	=	=	SYM
ejpam-3228	204	1	fa(ab−1	fa(ab−1	NOUN
ejpam-3228	204	2	)	)	PUNCT
ejpam-3228	204	3	∪	∪	ADP
ejpam-3228	204	4	fb(ab−1	fb(ab−1	NOUN
ejpam-3228	204	5	)	)	PUNCT
ejpam-3228	204	6	(	(	PUNCT
ejpam-3228	204	7	by	by	ADP
ejpam-3228	204	8	definition	definition	NOUN
ejpam-3228	204	9	2-(v	2-(v	NUM
ejpam-3228	204	10	)	)	PUNCT
ejpam-3228	204	11	)	)	PUNCT
ejpam-3228	205	1	⊆	⊆	NUM
ejpam-3228	205	2	(	(	PUNCT
ejpam-3228	205	3	fa(a	fa(a	NOUN
ejpam-3228	205	4	)	)	PUNCT
ejpam-3228	205	5	∪	∪	ADP
ejpam-3228	205	6	fa(b	fa(b	NOUN
ejpam-3228	205	7	)	)	PUNCT
ejpam-3228	205	8	)	)	PUNCT
ejpam-3228	205	9	∪	∪	ADP
ejpam-3228	205	10	(	(	PUNCT
ejpam-3228	205	11	fb(a	fb(a	NOUN
ejpam-3228	205	12	)	)	PUNCT
ejpam-3228	205	13	∪	∪	ADP
ejpam-3228	205	14	fb(b	fb(b	NOUN
ejpam-3228	205	15	)	)	PUNCT
ejpam-3228	205	16	)	)	PUNCT
ejpam-3228	206	1	=	=	PRON
ejpam-3228	206	2	(	(	PUNCT
ejpam-3228	206	3	fa(a	fa(a	NOUN
ejpam-3228	206	4	)	)	PUNCT
ejpam-3228	206	5	∪	∪	ADP
ejpam-3228	206	6	fb(a	fb(a	NOUN
ejpam-3228	206	7	)	)	PUNCT
ejpam-3228	206	8	)	)	PUNCT
ejpam-3228	206	9	∪	∪	ADP
ejpam-3228	206	10	(	(	PUNCT
ejpam-3228	206	11	fa(b	fa(b	NOUN
ejpam-3228	206	12	)	)	PUNCT
ejpam-3228	206	13	∪	∪	ADP
ejpam-3228	206	14	fb(b	fb(b	NOUN
ejpam-3228	206	15	)	)	PUNCT
ejpam-3228	206	16	)	)	PUNCT
ejpam-3228	207	1	=	=	SYM
ejpam-3228	207	2	(	(	PUNCT
ejpam-3228	207	3	fa∪̃fb	fa∪̃fb	PROPN
ejpam-3228	207	4	)	)	PUNCT
ejpam-3228	207	5	(	(	PUNCT
ejpam-3228	207	6	a	a	X
ejpam-3228	207	7	)	)	PUNCT
ejpam-3228	207	8	∪	∪	NOUN
ejpam-3228	207	9	(	(	PUNCT
ejpam-3228	207	10	fa∪̃fb	fa∪̃fb	PROPN
ejpam-3228	207	11	)	)	PUNCT
ejpam-3228	207	12	(	(	PUNCT
ejpam-3228	207	13	b	b	NOUN
ejpam-3228	207	14	)	)	PUNCT
ejpam-3228	207	15	.	.	PUNCT
ejpam-3228	208	1	hence	hence	ADV
ejpam-3228	208	2	,	,	PUNCT
ejpam-3228	208	3	a∪̃b	a∪̃b	PROPN
ejpam-3228	208	4	∈	∈	PROPN
ejpam-3228	208	5	s∪ag(u	s∪ag(u	PROPN
ejpam-3228	208	6	)	)	PUNCT
ejpam-3228	208	7	.	.	PUNCT
ejpam-3228	209	1	the	the	DET
ejpam-3228	209	2	following	follow	VERB
ejpam-3228	209	3	counter	counter	NOUN
ejpam-3228	209	4	example	example	NOUN
ejpam-3228	209	5	,	,	PUNCT
ejpam-3228	209	6	depicts	depict	VERB
ejpam-3228	209	7	that	that	SCONJ
ejpam-3228	209	8	a∩̃b	a∩̃b	PRON
ejpam-3228	209	9	/∈	/∈	PUNCT
ejpam-3228	209	10	s∪ag(u	s∪ag(u	PROPN
ejpam-3228	209	11	)	)	PUNCT
ejpam-3228	209	12	for	for	ADP
ejpam-3228	209	13	any	any	DET
ejpam-3228	209	14	a	a	DET
ejpam-3228	209	15	,	,	PUNCT
ejpam-3228	209	16	b	b	PROPN
ejpam-3228	209	17	∈	∈	PROPN
ejpam-3228	209	18	s∪ag(u	s∪ag(u	PROPN
ejpam-3228	209	19	)	)	PUNCT
ejpam-3228	209	20	.	.	PUNCT
ejpam-3228	210	1	example	example	NOUN
ejpam-3228	211	1	5	5	NUM
ejpam-3228	211	2	.	.	PUNCT
ejpam-3228	212	1	let	let	VERB
ejpam-3228	212	2	g	g	NOUN
ejpam-3228	212	3	=	=	PUNCT
ejpam-3228	212	4	{	{	PUNCT
ejpam-3228	212	5	0	0	NUM
ejpam-3228	212	6	,	,	PUNCT
ejpam-3228	212	7	1	1	NUM
ejpam-3228	212	8	,	,	PUNCT
ejpam-3228	212	9	2	2	NUM
ejpam-3228	212	10	,	,	PUNCT
ejpam-3228	212	11	3	3	NUM
ejpam-3228	212	12	,	,	PUNCT
ejpam-3228	212	13	4	4	NUM
ejpam-3228	212	14	,	,	PUNCT
ejpam-3228	212	15	5	5	NUM
ejpam-3228	212	16	,	,	PUNCT
ejpam-3228	212	17	6	6	NUM
ejpam-3228	212	18	,	,	PUNCT
ejpam-3228	212	19	7	7	NUM
ejpam-3228	212	20	,	,	PUNCT
ejpam-3228	212	21	8	8	NUM
ejpam-3228	212	22	}	}	PUNCT
ejpam-3228	212	23	be	be	AUX
ejpam-3228	212	24	an	an	DET
ejpam-3228	212	25	ag	ag	PROPN
ejpam-3228	212	26	-	-	PUNCT
ejpam-3228	212	27	group	group	NOUN
ejpam-3228	212	28	of	of	ADP
ejpam-3228	212	29	order	order	NOUN
ejpam-3228	212	30	9	9	NUM
ejpam-3228	212	31	defined	define	VERB
ejpam-3228	212	32	in	in	ADP
ejpam-3228	212	33	the	the	DET
ejpam-3228	212	34	following	follow	VERB
ejpam-3228	212	35	table	table	NOUN
ejpam-3228	212	36	:	:	PUNCT
ejpam-3228	212	37	a.	a.	PROPN
ejpam-3228	212	38	ullah	ullah	PROPN
ejpam-3228	212	39	,	,	PUNCT
ejpam-3228	212	40	f.	f.	PROPN
ejpam-3228	212	41	karaaslan	karaaslan	PROPN
ejpam-3228	212	42	,	,	PUNCT
ejpam-3228	212	43	i.	i.	PROPN
ejpam-3228	212	44	ahmad	ahmad	PROPN
ejpam-3228	212	45	/	/	SYM
ejpam-3228	212	46	eur	eur	PROPN
ejpam-3228	212	47	.	.	PUNCT
ejpam-3228	213	1	j.	j.	PROPN
ejpam-3228	213	2	pure	pure	PROPN
ejpam-3228	213	3	appl	appl	PROPN
ejpam-3228	213	4	.	.	PROPN
ejpam-3228	213	5	math	math	PROPN
ejpam-3228	213	6	,	,	PUNCT
ejpam-3228	213	7	11	11	NUM
ejpam-3228	213	8	(	(	PUNCT
ejpam-3228	213	9	2	2	NUM
ejpam-3228	213	10	)	)	PUNCT
ejpam-3228	213	11	(	(	PUNCT
ejpam-3228	213	12	2018	2018	NUM
ejpam-3228	213	13	)	)	PUNCT
ejpam-3228	213	14	,	,	PUNCT
ejpam-3228	213	15	517	517	NUM
ejpam-3228	213	16	-	-	SYM
ejpam-3228	213	17	536	536	NUM
ejpam-3228	213	18	526	526	NUM
ejpam-3228	213	19	·	·	SYM
ejpam-3228	213	20	0	0	NUM
ejpam-3228	214	1	1	1	NUM
ejpam-3228	214	2	2	2	NUM
ejpam-3228	214	3	3	3	NUM
ejpam-3228	214	4	4	4	NUM
ejpam-3228	214	5	5	5	NUM
ejpam-3228	214	6	6	6	NUM
ejpam-3228	214	7	7	7	NUM
ejpam-3228	214	8	8	8	NUM
ejpam-3228	214	9	0	0	NUM
ejpam-3228	214	10	0	0	NUM
ejpam-3228	214	11	1	1	NUM
ejpam-3228	214	12	2	2	NUM
ejpam-3228	214	13	3	3	NUM
ejpam-3228	214	14	4	4	NUM
ejpam-3228	214	15	5	5	NUM
ejpam-3228	214	16	6	6	NUM
ejpam-3228	214	17	7	7	NUM
ejpam-3228	214	18	8	8	NUM
ejpam-3228	214	19	1	1	NUM
ejpam-3228	214	20	2	2	NUM
ejpam-3228	214	21	0	0	NUM
ejpam-3228	214	22	1	1	NUM
ejpam-3228	214	23	4	4	NUM
ejpam-3228	214	24	5	5	NUM
ejpam-3228	214	25	3	3	NUM
ejpam-3228	214	26	7	7	NUM
ejpam-3228	214	27	8	8	NUM
ejpam-3228	214	28	6	6	NUM
ejpam-3228	214	29	2	2	NUM
ejpam-3228	214	30	1	1	NUM
ejpam-3228	214	31	2	2	NUM
ejpam-3228	214	32	0	0	NUM
ejpam-3228	214	33	5	5	NUM
ejpam-3228	214	34	3	3	NUM
ejpam-3228	214	35	4	4	NUM
ejpam-3228	214	36	8	8	NUM
ejpam-3228	214	37	6	6	NUM
ejpam-3228	214	38	7	7	NUM
ejpam-3228	214	39	3	3	NUM
ejpam-3228	214	40	7	7	NUM
ejpam-3228	214	41	6	6	NUM
ejpam-3228	214	42	8	8	NUM
ejpam-3228	214	43	0	0	NUM
ejpam-3228	214	44	2	2	NUM
ejpam-3228	214	45	1	1	NUM
ejpam-3228	214	46	5	5	NUM
ejpam-3228	214	47	3	3	NUM
ejpam-3228	214	48	4	4	NUM
ejpam-3228	214	49	4	4	NUM
ejpam-3228	214	50	6	6	NUM
ejpam-3228	214	51	8	8	NUM
ejpam-3228	214	52	7	7	NUM
ejpam-3228	214	53	1	1	NUM
ejpam-3228	214	54	0	0	NUM
ejpam-3228	214	55	2	2	NUM
ejpam-3228	214	56	4	4	NUM
ejpam-3228	214	57	5	5	NUM
ejpam-3228	214	58	3	3	NUM
ejpam-3228	214	59	5	5	NUM
ejpam-3228	214	60	8	8	NUM
ejpam-3228	214	61	7	7	NUM
ejpam-3228	214	62	6	6	NUM
ejpam-3228	214	63	2	2	NUM
ejpam-3228	214	64	1	1	NUM
ejpam-3228	214	65	0	0	NUM
ejpam-3228	214	66	3	3	NUM
ejpam-3228	214	67	4	4	NUM
ejpam-3228	214	68	5	5	NUM
ejpam-3228	214	69	6	6	NUM
ejpam-3228	214	70	4	4	NUM
ejpam-3228	214	71	3	3	NUM
ejpam-3228	214	72	5	5	NUM
ejpam-3228	214	73	8	8	NUM
ejpam-3228	214	74	6	6	NUM
ejpam-3228	214	75	7	7	NUM
ejpam-3228	214	76	0	0	NUM
ejpam-3228	214	77	2	2	NUM
ejpam-3228	214	78	1	1	NUM
ejpam-3228	214	79	7	7	NUM
ejpam-3228	214	80	3	3	NUM
ejpam-3228	214	81	5	5	NUM
ejpam-3228	214	82	4	4	NUM
ejpam-3228	214	83	7	7	NUM
ejpam-3228	214	84	8	8	NUM
ejpam-3228	214	85	6	6	NUM
ejpam-3228	214	86	1	1	NUM
ejpam-3228	214	87	0	0	NUM
ejpam-3228	214	88	2	2	NUM
ejpam-3228	214	89	8	8	NUM
ejpam-3228	214	90	5	5	NUM
ejpam-3228	214	91	4	4	NUM
ejpam-3228	214	92	3	3	NUM
ejpam-3228	214	93	6	6	NUM
ejpam-3228	214	94	7	7	NUM
ejpam-3228	214	95	8	8	NUM
ejpam-3228	214	96	2	2	NUM
ejpam-3228	214	97	1	1	NUM
ejpam-3228	214	98	0	0	NUM
ejpam-3228	214	99	let	let	VERB
ejpam-3228	214	100	a	a	DET
ejpam-3228	214	101	,	,	PUNCT
ejpam-3228	214	102	b	b	PROPN
ejpam-3228	214	103	∈	∈	PROPN
ejpam-3228	214	104	s∪ag(z10	s∪ag(z10	PROPN
ejpam-3228	214	105	)	)	PUNCT
ejpam-3228	214	106	,	,	PUNCT
ejpam-3228	214	107	defined	define	VERB
ejpam-3228	214	108	by	by	ADP
ejpam-3228	214	109	fa(0	fa(0	NOUN
ejpam-3228	214	110	)	)	PUNCT
ejpam-3228	214	111	=	=	NOUN
ejpam-3228	214	112	∅	∅	NOUN
ejpam-3228	214	113	,	,	PUNCT
ejpam-3228	214	114	fa(1	fa(1	NOUN
ejpam-3228	214	115	)	)	PUNCT
ejpam-3228	214	116	=	=	PUNCT
ejpam-3228	214	117	{	{	PUNCT
ejpam-3228	214	118	0	0	NUM
ejpam-3228	214	119	,	,	PUNCT
ejpam-3228	214	120	1	1	NUM
ejpam-3228	214	121	}	}	PUNCT
ejpam-3228	214	122	=	=	SYM
ejpam-3228	214	123	fa(2	fa(2	NOUN
ejpam-3228	214	124	)	)	PUNCT
ejpam-3228	214	125	,	,	PUNCT
ejpam-3228	214	126	fa(3	fa(3	NOUN
ejpam-3228	214	127	)	)	PUNCT
ejpam-3228	214	128	=	=	PUNCT
ejpam-3228	214	129	{	{	PUNCT
ejpam-3228	214	130	0	0	NUM
ejpam-3228	214	131	,	,	PUNCT
ejpam-3228	214	132	1	1	NUM
ejpam-3228	214	133	,	,	PUNCT
ejpam-3228	214	134	2	2	NUM
ejpam-3228	214	135	,	,	PUNCT
ejpam-3228	214	136	3	3	NUM
ejpam-3228	214	137	,	,	PUNCT
ejpam-3228	214	138	4	4	NUM
ejpam-3228	214	139	,	,	PUNCT
ejpam-3228	214	140	5	5	NUM
ejpam-3228	214	141	,	,	PUNCT
ejpam-3228	214	142	6	6	NUM
ejpam-3228	214	143	}	}	PUNCT
ejpam-3228	214	144	=	=	SYM
ejpam-3228	214	145	fa(4	fa(4	NOUN
ejpam-3228	214	146	)	)	PUNCT
ejpam-3228	214	147	=	=	SYM
ejpam-3228	214	148	fa(5	fa(5	PROPN
ejpam-3228	214	149	)	)	PUNCT
ejpam-3228	214	150	=	=	SYM
ejpam-3228	214	151	fa(6	fa(6	PROPN
ejpam-3228	214	152	)	)	PUNCT
ejpam-3228	214	153	=	=	SYM
ejpam-3228	214	154	fa(7	fa(7	X
ejpam-3228	214	155	)	)	PUNCT
ejpam-3228	214	156	=	=	SYM
ejpam-3228	214	157	fa(8	fa(8	NOUN
ejpam-3228	214	158	)	)	PUNCT
ejpam-3228	214	159	,	,	PUNCT
ejpam-3228	214	160	and	and	CCONJ
ejpam-3228	214	161	fb(0	fb(0	NOUN
ejpam-3228	214	162	)	)	PUNCT
ejpam-3228	214	163	=	=	NOUN
ejpam-3228	214	164	∅	∅	NOUN
ejpam-3228	214	165	,	,	PUNCT
ejpam-3228	214	166	fb(3	fb(3	NOUN
ejpam-3228	214	167	)	)	PUNCT
ejpam-3228	214	168	=	=	PRON
ejpam-3228	214	169	{	{	PUNCT
ejpam-3228	214	170	0	0	NUM
ejpam-3228	214	171	,	,	PUNCT
ejpam-3228	214	172	1	1	NUM
ejpam-3228	214	173	,	,	PUNCT
ejpam-3228	214	174	2	2	NUM
ejpam-3228	214	175	,	,	PUNCT
ejpam-3228	214	176	3	3	NUM
ejpam-3228	214	177	}	}	PUNCT
ejpam-3228	214	178	=	=	SYM
ejpam-3228	214	179	fb(7	fb(7	NOUN
ejpam-3228	214	180	)	)	PUNCT
ejpam-3228	214	181	,	,	PUNCT
ejpam-3228	214	182	fb(1	fb(1	PROPN
ejpam-3228	214	183	)	)	PUNCT
ejpam-3228	214	184	=	=	PUNCT
ejpam-3228	214	185	{	{	PUNCT
ejpam-3228	214	186	0	0	NUM
ejpam-3228	214	187	,	,	PUNCT
ejpam-3228	214	188	1	1	NUM
ejpam-3228	214	189	,	,	PUNCT
ejpam-3228	214	190	2	2	NUM
ejpam-3228	214	191	,	,	PUNCT
ejpam-3228	214	192	3	3	NUM
ejpam-3228	214	193	,	,	PUNCT
ejpam-3228	214	194	4	4	NUM
ejpam-3228	214	195	,	,	PUNCT
ejpam-3228	214	196	5	5	NUM
ejpam-3228	214	197	,	,	PUNCT
ejpam-3228	214	198	6	6	NUM
ejpam-3228	214	199	,	,	PUNCT
ejpam-3228	214	200	7	7	NUM
ejpam-3228	214	201	,	,	PUNCT
ejpam-3228	214	202	8	8	NUM
ejpam-3228	214	203	}	}	PUNCT
ejpam-3228	214	204	=	=	SYM
ejpam-3228	214	205	fb(2	fb(2	PROPN
ejpam-3228	214	206	)	)	PUNCT
ejpam-3228	214	207	=	=	SYM
ejpam-3228	214	208	fb(4	fb(4	PROPN
ejpam-3228	214	209	)	)	PUNCT
ejpam-3228	214	210	=	=	SYM
ejpam-3228	214	211	fb(5	fb(5	PROPN
ejpam-3228	214	212	)	)	PUNCT
ejpam-3228	214	213	=	=	SYM
ejpam-3228	214	214	fb(6	fb(6	X
ejpam-3228	214	215	)	)	PUNCT
ejpam-3228	214	216	=	=	SYM
ejpam-3228	214	217	fb(7	fb(7	NOUN
ejpam-3228	214	218	)	)	PUNCT
ejpam-3228	214	219	=	=	SYM
ejpam-3228	214	220	fb(8	fb(8	PROPN
ejpam-3228	214	221	)	)	PUNCT
ejpam-3228	214	222	,	,	PUNCT
ejpam-3228	214	223	it	it	PRON
ejpam-3228	214	224	is	be	AUX
ejpam-3228	214	225	clear	clear	ADJ
ejpam-3228	214	226	that	that	SCONJ
ejpam-3228	214	227	(	(	PUNCT
ejpam-3228	214	228	fa∩̃fb	fa∩̃fb	PROPN
ejpam-3228	214	229	)	)	PUNCT
ejpam-3228	214	230	(	(	PUNCT
ejpam-3228	214	231	2	2	NUM
ejpam-3228	214	232	·	·	SYM
ejpam-3228	214	233	3−1	3−1	NUM
ejpam-3228	214	234	)	)	PUNCT
ejpam-3228	215	1	=	=	SYM
ejpam-3228	215	2	(	(	PUNCT
ejpam-3228	215	3	fa∩̃fb	fa∩̃fb	PROPN
ejpam-3228	215	4	)	)	PUNCT
ejpam-3228	215	5	(	(	PUNCT
ejpam-3228	215	6	5	5	X
ejpam-3228	215	7	)	)	PUNCT
ejpam-3228	215	8	=	=	SYM
ejpam-3228	215	9	fa(5	fa(5	PROPN
ejpam-3228	215	10	)	)	PUNCT
ejpam-3228	215	11	∩	∩	NOUN
ejpam-3228	215	12	fb(5	fb(5	PROPN
ejpam-3228	215	13	)	)	PUNCT
ejpam-3228	215	14	=	=	SYM
ejpam-3228	215	15	{	{	PUNCT
ejpam-3228	215	16	0	0	NUM
ejpam-3228	215	17	,	,	PUNCT
ejpam-3228	215	18	1	1	NUM
ejpam-3228	215	19	,	,	PUNCT
ejpam-3228	215	20	2	2	NUM
ejpam-3228	215	21	,	,	PUNCT
ejpam-3228	215	22	3	3	NUM
ejpam-3228	215	23	,	,	PUNCT
ejpam-3228	215	24	4	4	NUM
ejpam-3228	215	25	,	,	PUNCT
ejpam-3228	215	26	5	5	NUM
ejpam-3228	215	27	,	,	PUNCT
ejpam-3228	215	28	6	6	NUM
ejpam-3228	215	29	}	}	PUNCT
ejpam-3228	215	30	,	,	PUNCT
ejpam-3228	215	31	(	(	PUNCT
ejpam-3228	215	32	5	5	NUM
ejpam-3228	215	33	)	)	PUNCT
ejpam-3228	215	34	and	and	CCONJ
ejpam-3228	215	35	(	(	PUNCT
ejpam-3228	215	36	(	(	PUNCT
ejpam-3228	215	37	fa∩̃fb	fa∩̃fb	NOUN
ejpam-3228	215	38	)	)	PUNCT
ejpam-3228	215	39	(	(	PUNCT
ejpam-3228	215	40	2	2	NUM
ejpam-3228	215	41	)	)	PUNCT
ejpam-3228	215	42	)	)	PUNCT
ejpam-3228	215	43	∪	∪	X
ejpam-3228	215	44	(	(	PUNCT
ejpam-3228	215	45	(	(	PUNCT
ejpam-3228	215	46	fa∩̃fb	fa∩̃fb	NOUN
ejpam-3228	215	47	)	)	PUNCT
ejpam-3228	215	48	(	(	PUNCT
ejpam-3228	215	49	3	3	NUM
ejpam-3228	215	50	)	)	PUNCT
ejpam-3228	215	51	)	)	PUNCT
ejpam-3228	216	1	=	=	SYM
ejpam-3228	216	2	(	(	PUNCT
ejpam-3228	216	3	fa(2	fa(2	NOUN
ejpam-3228	216	4	)	)	PUNCT
ejpam-3228	216	5	∩	∩	NOUN
ejpam-3228	216	6	fb(2	fb(2	PROPN
ejpam-3228	216	7	)	)	PUNCT
ejpam-3228	216	8	)	)	PUNCT
ejpam-3228	216	9	∪	∪	ADP
ejpam-3228	216	10	(	(	PUNCT
ejpam-3228	216	11	fa(3	fa(3	NOUN
ejpam-3228	216	12	)	)	PUNCT
ejpam-3228	216	13	∩	∩	NOUN
ejpam-3228	216	14	fb(3	fb(3	NOUN
ejpam-3228	216	15	)	)	PUNCT
ejpam-3228	216	16	)	)	PUNCT
ejpam-3228	217	1	=	=	PUNCT
ejpam-3228	217	2	{	{	PUNCT
ejpam-3228	217	3	0	0	NUM
ejpam-3228	217	4	,	,	PUNCT
ejpam-3228	217	5	1	1	NUM
ejpam-3228	217	6	,	,	PUNCT
ejpam-3228	217	7	2	2	NUM
ejpam-3228	217	8	,	,	PUNCT
ejpam-3228	217	9	3	3	NUM
ejpam-3228	217	10	}	}	PUNCT
ejpam-3228	217	11	,	,	PUNCT
ejpam-3228	217	12	this	this	PRON
ejpam-3228	217	13	implies	imply	VERB
ejpam-3228	217	14	that	that	SCONJ
ejpam-3228	217	15	(	(	PUNCT
ejpam-3228	217	16	(	(	PUNCT
ejpam-3228	217	17	fa∩̃fb	fa∩̃fb	NOUN
ejpam-3228	217	18	)	)	PUNCT
ejpam-3228	217	19	(	(	PUNCT
ejpam-3228	217	20	2	2	NUM
ejpam-3228	217	21	)	)	PUNCT
ejpam-3228	217	22	)	)	PUNCT
ejpam-3228	217	23	∪	∪	X
ejpam-3228	217	24	(	(	PUNCT
ejpam-3228	217	25	(	(	PUNCT
ejpam-3228	217	26	fa∩̃fb	fa∩̃fb	NOUN
ejpam-3228	217	27	)	)	PUNCT
ejpam-3228	217	28	(	(	PUNCT
ejpam-3228	217	29	3	3	NUM
ejpam-3228	217	30	)	)	PUNCT
ejpam-3228	217	31	)	)	PUNCT
ejpam-3228	218	1	=	=	PRON
ejpam-3228	218	2	{	{	PUNCT
ejpam-3228	218	3	0	0	NUM
ejpam-3228	218	4	,	,	PUNCT
ejpam-3228	218	5	1	1	NUM
ejpam-3228	218	6	,	,	PUNCT
ejpam-3228	218	7	2	2	NUM
ejpam-3228	218	8	,	,	PUNCT
ejpam-3228	218	9	3	3	NUM
ejpam-3228	218	10	}	}	PUNCT
ejpam-3228	218	11	.	.	PUNCT
ejpam-3228	219	1	(	(	PUNCT
ejpam-3228	219	2	6	6	NUM
ejpam-3228	219	3	)	)	PUNCT
ejpam-3228	219	4	from	from	ADP
ejpam-3228	219	5	equations	equation	NOUN
ejpam-3228	219	6	(	(	PUNCT
ejpam-3228	219	7	5	5	NUM
ejpam-3228	219	8	)	)	PUNCT
ejpam-3228	219	9	and	and	CCONJ
ejpam-3228	219	10	(	(	PUNCT
ejpam-3228	219	11	6	6	X
ejpam-3228	219	12	)	)	PUNCT
ejpam-3228	219	13	it	it	PRON
ejpam-3228	219	14	is	be	AUX
ejpam-3228	219	15	clear	clear	ADJ
ejpam-3228	219	16	that	that	SCONJ
ejpam-3228	219	17	(	(	PUNCT
ejpam-3228	219	18	fa∩̃fb	fa∩̃fb	PROPN
ejpam-3228	219	19	)	)	PUNCT
ejpam-3228	219	20	(	(	PUNCT
ejpam-3228	219	21	2	2	NUM
ejpam-3228	219	22	·	·	SYM
ejpam-3228	219	23	3−1	3−1	NUM
ejpam-3228	219	24	)	)	PUNCT
ejpam-3228	220	1	*	*	PUNCT
ejpam-3228	220	2	(	(	PUNCT
ejpam-3228	220	3	(	(	PUNCT
ejpam-3228	220	4	fa∩̃fb	fa∩̃fb	NOUN
ejpam-3228	220	5	)	)	PUNCT
ejpam-3228	220	6	(	(	PUNCT
ejpam-3228	220	7	2	2	NUM
ejpam-3228	220	8	)	)	PUNCT
ejpam-3228	220	9	)	)	PUNCT
ejpam-3228	220	10	∪	∪	X
ejpam-3228	220	11	(	(	PUNCT
ejpam-3228	220	12	(	(	PUNCT
ejpam-3228	220	13	fa∩̃fb	fa∩̃fb	NOUN
ejpam-3228	220	14	)	)	PUNCT
ejpam-3228	220	15	(	(	PUNCT
ejpam-3228	220	16	3	3	NUM
ejpam-3228	220	17	)	)	PUNCT
ejpam-3228	220	18	)	)	PUNCT
ejpam-3228	220	19	.	.	PUNCT
ejpam-3228	221	1	hence	hence	ADV
ejpam-3228	221	2	,	,	PUNCT
ejpam-3228	221	3	a∩̃b	a∩̃b	PRON
ejpam-3228	221	4	/∈	/∈	PUNCT
ejpam-3228	221	5	s∪ag(u	s∪ag(u	PROPN
ejpam-3228	221	6	)	)	PUNCT
ejpam-3228	221	7	.	.	PUNCT
ejpam-3228	222	1	definition	definition	NOUN
ejpam-3228	222	2	6	6	NUM
ejpam-3228	222	3	.	.	PUNCT
ejpam-3228	223	1	let	let	VERB
ejpam-3228	223	2	h	h	PRON
ejpam-3228	223	3	be	be	AUX
ejpam-3228	223	4	an	an	DET
ejpam-3228	223	5	ag	ag	PROPN
ejpam-3228	223	6	-	-	PUNCT
ejpam-3228	223	7	subgroup	subgroup	NOUN
ejpam-3228	223	8	of	of	ADP
ejpam-3228	223	9	an	an	DET
ejpam-3228	223	10	ag	ag	PROPN
ejpam-3228	223	11	-	-	PUNCT
ejpam-3228	223	12	group	group	NOUN
ejpam-3228	223	13	g.	g.	PROPN
ejpam-3228	223	14	then	then	ADV
ejpam-3228	223	15	a	a	DET
ejpam-3228	223	16	soft	soft	ADJ
ejpam-3228	223	17	subset	subset	NOUN
ejpam-3228	223	18	b	b	NOUN
ejpam-3228	223	19	over	over	ADP
ejpam-3228	223	20	h	h	NOUN
ejpam-3228	223	21	is	be	AUX
ejpam-3228	223	22	called	call	VERB
ejpam-3228	223	23	a	a	DET
ejpam-3228	223	24	soft	soft	ADJ
ejpam-3228	223	25	uni	uni	ADJ
ejpam-3228	223	26	-	-	PUNCT
ejpam-3228	223	27	ag	ag	NOUN
ejpam-3228	223	28	-	-	PUNCT
ejpam-3228	223	29	subgroup	subgroup	NOUN
ejpam-3228	223	30	of	of	ADP
ejpam-3228	223	31	a	a	DET
ejpam-3228	223	32	soft	soft	ADJ
ejpam-3228	223	33	subset	subset	NOUN
ejpam-3228	223	34	a	a	DET
ejpam-3228	223	35	over	over	ADP
ejpam-3228	223	36	g	g	NOUN
ejpam-3228	223	37	if	if	SCONJ
ejpam-3228	223	38	b	b	PROPN
ejpam-3228	223	39	is	be	AUX
ejpam-3228	223	40	a	a	DET
ejpam-3228	223	41	nonempty	nonempty	ADJ
ejpam-3228	223	42	soft	soft	ADJ
ejpam-3228	223	43	subset	subset	NOUN
ejpam-3228	223	44	of	of	ADP
ejpam-3228	223	45	a.	a.	NOUN
ejpam-3228	223	46	we	we	PRON
ejpam-3228	223	47	denote	denote	VERB
ejpam-3228	223	48	this	this	PRON
ejpam-3228	223	49	by	by	ADP
ejpam-3228	223	50	b≤̃a	b≤̃a	PROPN
ejpam-3228	223	51	.	.	PUNCT
ejpam-3228	224	1	a.	a.	PROPN
ejpam-3228	224	2	ullah	ullah	PROPN
ejpam-3228	224	3	,	,	PUNCT
ejpam-3228	224	4	f.	f.	PROPN
ejpam-3228	224	5	karaaslan	karaaslan	PROPN
ejpam-3228	224	6	,	,	PUNCT
ejpam-3228	224	7	i.	i.	PROPN
ejpam-3228	224	8	ahmad	ahmad	PROPN
ejpam-3228	224	9	/	/	SYM
ejpam-3228	224	10	eur	eur	PROPN
ejpam-3228	224	11	.	.	PUNCT
ejpam-3228	225	1	j.	j.	PROPN
ejpam-3228	225	2	pure	pure	PROPN
ejpam-3228	225	3	appl	appl	PROPN
ejpam-3228	225	4	.	.	PROPN
ejpam-3228	225	5	math	math	PROPN
ejpam-3228	225	6	,	,	PUNCT
ejpam-3228	225	7	11	11	NUM
ejpam-3228	225	8	(	(	PUNCT
ejpam-3228	225	9	2	2	NUM
ejpam-3228	225	10	)	)	PUNCT
ejpam-3228	225	11	(	(	PUNCT
ejpam-3228	225	12	2018	2018	NUM
ejpam-3228	225	13	)	)	PUNCT
ejpam-3228	225	14	,	,	PUNCT
ejpam-3228	225	15	517	517	NUM
ejpam-3228	225	16	-	-	SYM
ejpam-3228	225	17	536	536	NUM
ejpam-3228	225	18	527	527	NUM
ejpam-3228	225	19	example	example	NOUN
ejpam-3228	225	20	6	6	NUM
ejpam-3228	225	21	.	.	PUNCT
ejpam-3228	226	1	let	let	VERB
ejpam-3228	226	2	u	u	PRON
ejpam-3228	226	3	=	=	NOUN
ejpam-3228	226	4	z10	z10	NOUN
ejpam-3228	226	5	be	be	AUX
ejpam-3228	226	6	the	the	DET
ejpam-3228	226	7	universal	universal	ADJ
ejpam-3228	226	8	set	set	NOUN
ejpam-3228	226	9	and	and	CCONJ
ejpam-3228	226	10	g	g	NOUN
ejpam-3228	226	11	be	be	AUX
ejpam-3228	226	12	any	any	DET
ejpam-3228	226	13	ag	ag	PROPN
ejpam-3228	226	14	-	-	PUNCT
ejpam-3228	226	15	group	group	NOUN
ejpam-3228	226	16	of	of	ADP
ejpam-3228	226	17	order	order	NOUN
ejpam-3228	226	18	9	9	NUM
ejpam-3228	226	19	defined	define	VERB
ejpam-3228	226	20	as	as	ADP
ejpam-3228	226	21	in	in	ADP
ejpam-3228	226	22	example	example	NOUN
ejpam-3228	226	23	5	5	NUM
ejpam-3228	226	24	.	.	PUNCT
ejpam-3228	226	25	define	define	VERB
ejpam-3228	226	26	a	a	DET
ejpam-3228	226	27	soft	soft	ADJ
ejpam-3228	226	28	uni	uni	ADJ
ejpam-3228	226	29	-	-	PUNCT
ejpam-3228	226	30	ag	ag	NOUN
ejpam-3228	226	31	-	-	NOUN
ejpam-3228	226	32	group	group	NOUN
ejpam-3228	226	33	a	a	PRON
ejpam-3228	226	34	as	as	SCONJ
ejpam-3228	226	35	follows	follow	VERB
ejpam-3228	226	36	:	:	PUNCT
ejpam-3228	226	37	fa(0	fa(0	X
ejpam-3228	226	38	)	)	PUNCT
ejpam-3228	226	39	=	=	SYM
ejpam-3228	226	40	{	{	PUNCT
ejpam-3228	226	41	0	0	NUM
ejpam-3228	226	42	,	,	PUNCT
ejpam-3228	226	43	1	1	NUM
ejpam-3228	226	44	,	,	PUNCT
ejpam-3228	226	45	2	2	NUM
ejpam-3228	226	46	}	}	PUNCT
ejpam-3228	226	47	,	,	PUNCT
ejpam-3228	226	48	fa(3	fa(3	NOUN
ejpam-3228	226	49	)	)	PUNCT
ejpam-3228	226	50	=	=	PUNCT
ejpam-3228	226	51	{	{	PUNCT
ejpam-3228	226	52	0	0	NUM
ejpam-3228	226	53	,	,	PUNCT
ejpam-3228	226	54	1	1	NUM
ejpam-3228	226	55	,	,	PUNCT
ejpam-3228	226	56	2	2	NUM
ejpam-3228	226	57	,	,	PUNCT
ejpam-3228	226	58	3	3	NUM
ejpam-3228	226	59	,	,	PUNCT
ejpam-3228	226	60	4	4	NUM
ejpam-3228	226	61	}	}	PUNCT
ejpam-3228	226	62	=	=	SYM
ejpam-3228	226	63	fa(7	fa(7	NOUN
ejpam-3228	226	64	)	)	PUNCT
ejpam-3228	226	65	,	,	PUNCT
ejpam-3228	226	66	fa(1	fa(1	NOUN
ejpam-3228	226	67	)	)	PUNCT
ejpam-3228	226	68	=	=	PUNCT
ejpam-3228	226	69	{	{	PUNCT
ejpam-3228	226	70	0	0	NUM
ejpam-3228	226	71	,	,	PUNCT
ejpam-3228	226	72	1	1	NUM
ejpam-3228	226	73	,	,	PUNCT
ejpam-3228	226	74	2	2	NUM
ejpam-3228	226	75	,	,	PUNCT
ejpam-3228	226	76	3	3	NUM
ejpam-3228	226	77	,	,	PUNCT
ejpam-3228	226	78	4	4	NUM
ejpam-3228	226	79	,	,	PUNCT
ejpam-3228	226	80	5	5	NUM
ejpam-3228	226	81	,	,	PUNCT
ejpam-3228	226	82	6	6	NUM
ejpam-3228	226	83	}	}	PUNCT
ejpam-3228	226	84	=	=	SYM
ejpam-3228	226	85	fa(2	fa(2	NOUN
ejpam-3228	226	86	)	)	PUNCT
ejpam-3228	226	87	=	=	SYM
ejpam-3228	226	88	fa(4	fa(4	NOUN
ejpam-3228	226	89	)	)	PUNCT
ejpam-3228	226	90	=	=	SYM
ejpam-3228	226	91	fa(5	fa(5	PROPN
ejpam-3228	227	1	)	)	PUNCT
ejpam-3228	227	2	=	=	SYM
ejpam-3228	227	3	fa(6	fa(6	PROPN
ejpam-3228	227	4	)	)	PUNCT
ejpam-3228	227	5	=	=	SYM
ejpam-3228	227	6	fa(8	fa(8	NOUN
ejpam-3228	227	7	)	)	PUNCT
ejpam-3228	227	8	.	.	PUNCT
ejpam-3228	228	1	let	let	VERB
ejpam-3228	228	2	h1	h1	VERB
ejpam-3228	228	3	=	=	PRON
ejpam-3228	228	4	{	{	PUNCT
ejpam-3228	228	5	0	0	NUM
ejpam-3228	228	6	,	,	PUNCT
ejpam-3228	228	7	3	3	NUM
ejpam-3228	228	8	,	,	PUNCT
ejpam-3228	228	9	7	7	NUM
ejpam-3228	228	10	}	}	PUNCT
ejpam-3228	228	11	and	and	CCONJ
ejpam-3228	228	12	h2	h2	NOUN
ejpam-3228	228	13	=	=	SYM
ejpam-3228	228	14	{	{	PUNCT
ejpam-3228	228	15	0	0	NUM
ejpam-3228	228	16	,	,	PUNCT
ejpam-3228	228	17	1	1	NUM
ejpam-3228	228	18	,	,	PUNCT
ejpam-3228	228	19	2	2	NUM
ejpam-3228	228	20	}	}	PUNCT
ejpam-3228	228	21	be	be	AUX
ejpam-3228	228	22	two	two	NUM
ejpam-3228	228	23	ag	ag	NOUN
ejpam-3228	228	24	-	-	PUNCT
ejpam-3228	228	25	subgroups	subgroup	NOUN
ejpam-3228	228	26	of	of	ADP
ejpam-3228	228	27	g.	g.	NOUN
ejpam-3228	228	28	define	define	VERB
ejpam-3228	228	29	soft	soft	ADJ
ejpam-3228	228	30	uni	uni	ADJ
ejpam-3228	228	31	-	-	PUNCT
ejpam-3228	228	32	aggroups	aggroups	PROPN
ejpam-3228	228	33	b	b	PROPN
ejpam-3228	228	34	and	and	CCONJ
ejpam-3228	228	35	c	c	PROPN
ejpam-3228	228	36	over	over	ADP
ejpam-3228	228	37	u	u	PROPN
ejpam-3228	228	38	,	,	PUNCT
ejpam-3228	228	39	w.	w.	PROPN
ejpam-3228	228	40	r.	r.	PROPN
ejpam-3228	228	41	t.	t.	PROPN
ejpam-3228	228	42	h1	h1	PROPN
ejpam-3228	228	43	and	and	CCONJ
ejpam-3228	228	44	h2	h2	NOUN
ejpam-3228	228	45	respectively	respectively	ADV
ejpam-3228	228	46	as	as	SCONJ
ejpam-3228	228	47	follow	follow	VERB
ejpam-3228	228	48	:	:	PUNCT
ejpam-3228	228	49	b	b	X
ejpam-3228	228	50	=	=	PRON
ejpam-3228	228	51	{	{	PUNCT
ejpam-3228	228	52	(	(	PUNCT
ejpam-3228	228	53	0	0	NUM
ejpam-3228	228	54	,	,	PUNCT
ejpam-3228	228	55	{	{	PUNCT
ejpam-3228	228	56	0	0	NUM
ejpam-3228	228	57	,	,	PUNCT
ejpam-3228	228	58	1	1	NUM
ejpam-3228	228	59	}	}	PUNCT
ejpam-3228	228	60	)	)	PUNCT
ejpam-3228	228	61	,	,	PUNCT
ejpam-3228	228	62	(	(	PUNCT
ejpam-3228	228	63	3	3	NUM
ejpam-3228	228	64	,	,	PUNCT
ejpam-3228	228	65	{	{	PUNCT
ejpam-3228	228	66	0	0	NUM
ejpam-3228	228	67	,	,	PUNCT
ejpam-3228	228	68	1	1	NUM
ejpam-3228	228	69	,	,	PUNCT
ejpam-3228	228	70	2	2	NUM
ejpam-3228	228	71	}	}	PUNCT
ejpam-3228	228	72	)	)	PUNCT
ejpam-3228	228	73	,	,	PUNCT
ejpam-3228	228	74	(	(	PUNCT
ejpam-3228	228	75	7	7	NUM
ejpam-3228	228	76	,	,	PUNCT
ejpam-3228	228	77	{	{	PUNCT
ejpam-3228	228	78	0	0	NUM
ejpam-3228	228	79	,	,	PUNCT
ejpam-3228	228	80	1	1	NUM
ejpam-3228	228	81	,	,	PUNCT
ejpam-3228	228	82	2	2	NUM
ejpam-3228	228	83	}	}	PUNCT
ejpam-3228	228	84	)	)	PUNCT
ejpam-3228	228	85	}	}	PUNCT
ejpam-3228	228	86	,	,	PUNCT
ejpam-3228	228	87	and	and	CCONJ
ejpam-3228	228	88	c	c	X
ejpam-3228	228	89	=	=	SYM
ejpam-3228	228	90	{	{	PUNCT
ejpam-3228	228	91	(	(	PUNCT
ejpam-3228	228	92	0	0	NUM
ejpam-3228	228	93	,	,	PUNCT
ejpam-3228	228	94	{	{	PUNCT
ejpam-3228	228	95	0	0	NUM
ejpam-3228	228	96	,	,	PUNCT
ejpam-3228	228	97	2	2	NUM
ejpam-3228	228	98	}	}	PUNCT
ejpam-3228	228	99	)	)	PUNCT
ejpam-3228	228	100	,	,	PUNCT
ejpam-3228	228	101	(	(	PUNCT
ejpam-3228	228	102	1	1	NUM
ejpam-3228	228	103	,	,	PUNCT
ejpam-3228	228	104	{	{	PUNCT
ejpam-3228	228	105	0	0	NUM
ejpam-3228	228	106	,	,	PUNCT
ejpam-3228	228	107	2	2	NUM
ejpam-3228	228	108	,	,	PUNCT
ejpam-3228	228	109	4	4	NUM
ejpam-3228	228	110	}	}	PUNCT
ejpam-3228	228	111	)	)	PUNCT
ejpam-3228	228	112	,	,	PUNCT
ejpam-3228	228	113	(	(	PUNCT
ejpam-3228	228	114	2	2	NUM
ejpam-3228	228	115	,	,	PUNCT
ejpam-3228	228	116	{	{	PUNCT
ejpam-3228	228	117	0	0	NUM
ejpam-3228	228	118	,	,	PUNCT
ejpam-3228	228	119	2	2	NUM
ejpam-3228	228	120	,	,	PUNCT
ejpam-3228	228	121	4	4	NUM
ejpam-3228	228	122	}	}	PUNCT
ejpam-3228	228	123	)	)	PUNCT
ejpam-3228	228	124	}	}	PUNCT
ejpam-3228	228	125	.	.	PUNCT
ejpam-3228	229	1	as	as	ADP
ejpam-3228	229	2	b⊆̃a	b⊆̃a	NOUN
ejpam-3228	229	3	and	and	CCONJ
ejpam-3228	229	4	c⊆̃a	c⊆̃a	NOUN
ejpam-3228	229	5	.	.	PUNCT
ejpam-3228	230	1	therefore	therefore	ADV
ejpam-3228	230	2	,	,	PUNCT
ejpam-3228	230	3	b≤̃a	b≤̃a	ADV
ejpam-3228	230	4	and	and	CCONJ
ejpam-3228	230	5	c≤̃a	c≤̃a	PROPN
ejpam-3228	230	6	.	.	PUNCT
ejpam-3228	231	1	theorem	theorem	NOUN
ejpam-3228	231	2	5	5	NUM
ejpam-3228	231	3	.	.	PUNCT
ejpam-3228	232	1	let	let	VERB
ejpam-3228	232	2	b≤̃a	b≤̃a	ADV
ejpam-3228	232	3	and	and	CCONJ
ejpam-3228	232	4	c≤̃a	c≤̃a	NOUN
ejpam-3228	232	5	.	.	PUNCT
ejpam-3228	233	1	then	then	ADV
ejpam-3228	233	2	,	,	PUNCT
ejpam-3228	233	3	b∪̃c≤̃a	b∪̃c≤̃a	PROPN
ejpam-3228	233	4	.	.	PUNCT
ejpam-3228	234	1	proof	proof	NOUN
ejpam-3228	234	2	.	.	PUNCT
ejpam-3228	235	1	since	since	SCONJ
ejpam-3228	235	2	,	,	PUNCT
ejpam-3228	235	3	b≤̃a	b≤̃a	ADV
ejpam-3228	235	4	and	and	CCONJ
ejpam-3228	235	5	c≤̃a	c≤̃a	PROPN
ejpam-3228	235	6	.	.	PUNCT
ejpam-3228	236	1	therefore	therefore	ADV
ejpam-3228	236	2	,	,	PUNCT
ejpam-3228	236	3	b∪̃c	b∪̃c	PROPN
ejpam-3228	236	4	6=	6=	AUX
ejpam-3228	236	5	∅.	∅.	ADV
ejpam-3228	236	6	let	let	VERB
ejpam-3228	236	7	x	x	PRON
ejpam-3228	236	8	,	,	PUNCT
ejpam-3228	236	9	y	y	PROPN
ejpam-3228	236	10	∈	∈	PROPN
ejpam-3228	236	11	b∪̃c	b∪̃c	NOUN
ejpam-3228	236	12	.	.	PUNCT
ejpam-3228	237	1	then	then	ADV
ejpam-3228	237	2	by	by	ADP
ejpam-3228	237	3	theorem	theorem	NOUN
ejpam-3228	237	4	1	1	NUM
ejpam-3228	237	5	(	(	PUNCT
ejpam-3228	237	6	fb∪̃fc	fb∪̃fc	NOUN
ejpam-3228	237	7	)	)	PUNCT
ejpam-3228	237	8	(	(	PUNCT
ejpam-3228	237	9	xy−1	xy−1	PROPN
ejpam-3228	237	10	)	)	PUNCT
ejpam-3228	237	11	=	=	PRON
ejpam-3228	238	1	(	(	PUNCT
ejpam-3228	238	2	(	(	PUNCT
ejpam-3228	238	3	fb∪̃c	fb∪̃c	X
ejpam-3228	238	4	)	)	PUNCT
ejpam-3228	238	5	(	(	PUNCT
ejpam-3228	238	6	xy−1	xy−1	PROPN
ejpam-3228	238	7	)	)	PUNCT
ejpam-3228	238	8	)	)	PUNCT
ejpam-3228	239	1	=	=	SYM
ejpam-3228	239	2	fb(xy−1	fb(xy−1	NUM
ejpam-3228	239	3	)	)	PUNCT
ejpam-3228	239	4	∪	∪	ADP
ejpam-3228	239	5	fc(xy−1	fc(xy−1	PROPN
ejpam-3228	239	6	)	)	PUNCT
ejpam-3228	239	7	⊆	⊆	NUM
ejpam-3228	239	8	(	(	PUNCT
ejpam-3228	239	9	fb(x	fb(x	NOUN
ejpam-3228	239	10	)	)	PUNCT
ejpam-3228	239	11	∪	∪	ADP
ejpam-3228	239	12	fb(y	fb(y	NUM
ejpam-3228	239	13	)	)	PUNCT
ejpam-3228	239	14	)	)	PUNCT
ejpam-3228	239	15	∪	∪	ADP
ejpam-3228	239	16	(	(	PUNCT
ejpam-3228	239	17	fc(x	fc(x	NOUN
ejpam-3228	239	18	)	)	PUNCT
ejpam-3228	239	19	∪	∪	ADP
ejpam-3228	239	20	fc(y	fc(y	NOUN
ejpam-3228	239	21	)	)	PUNCT
ejpam-3228	239	22	)	)	PUNCT
ejpam-3228	240	1	=	=	PRON
ejpam-3228	240	2	(	(	PUNCT
ejpam-3228	240	3	fb(x	fb(x	ADJ
ejpam-3228	240	4	)	)	PUNCT
ejpam-3228	240	5	∪	∪	ADP
ejpam-3228	240	6	fc(x	fc(x	NOUN
ejpam-3228	240	7	)	)	PUNCT
ejpam-3228	240	8	)	)	PUNCT
ejpam-3228	240	9	∪	∪	ADP
ejpam-3228	240	10	(	(	PUNCT
ejpam-3228	240	11	fb(y	fb(y	NUM
ejpam-3228	240	12	)	)	PUNCT
ejpam-3228	240	13	∪	∪	ADP
ejpam-3228	240	14	fc(y	fc(y	NOUN
ejpam-3228	240	15	)	)	PUNCT
ejpam-3228	240	16	)	)	PUNCT
ejpam-3228	241	1	=	=	SYM
ejpam-3228	241	2	fb∪̃c(x	fb∪̃c(x	NOUN
ejpam-3228	241	3	)	)	PUNCT
ejpam-3228	241	4	∪	∪	ADP
ejpam-3228	241	5	fb∪̃c(y	fb∪̃c(y	NOUN
ejpam-3228	241	6	)	)	PUNCT
ejpam-3228	241	7	=	=	PUNCT
ejpam-3228	241	8	(	(	PUNCT
ejpam-3228	241	9	fb∪̃fc)(x	fb∪̃fc)(x	PROPN
ejpam-3228	241	10	)	)	PUNCT
ejpam-3228	241	11	∪	∪	NOUN
ejpam-3228	241	12	(	(	PUNCT
ejpam-3228	241	13	fb∪̃fc)(y	fb∪̃fc)(y	NOUN
ejpam-3228	241	14	)	)	PUNCT
ejpam-3228	241	15	.	.	PUNCT
ejpam-3228	242	1	hence	hence	ADV
ejpam-3228	242	2	,	,	PUNCT
ejpam-3228	242	3	b∪̃c≤̃a	b∪̃c≤̃a	PROPN
ejpam-3228	242	4	.	.	PUNCT
ejpam-3228	243	1	theorem	theorem	VERB
ejpam-3228	243	2	6	6	NUM
ejpam-3228	243	3	.	.	PUNCT
ejpam-3228	244	1	let	let	VERB
ejpam-3228	244	2	{	{	PUNCT
ejpam-3228	244	3	bi	bi	NOUN
ejpam-3228	244	4	:	:	PUNCT
ejpam-3228	244	5	i	i	PRON
ejpam-3228	244	6	∈	∈	VERB
ejpam-3228	244	7	i	i	PRON
ejpam-3228	244	8	}	}	PUNCT
ejpam-3228	244	9	≤̃a	≤̃a	X
ejpam-3228	244	10	for	for	ADP
ejpam-3228	244	11	all	all	PRON
ejpam-3228	244	12	i	i	PRON
ejpam-3228	244	13	∈	∈	PROPN
ejpam-3228	244	14	i.	i.	NOUN
ejpam-3228	244	15	then	then	ADV
ejpam-3228	244	16	∪̃	∪̃	PROPN
ejpam-3228	244	17	i∈i	i∈i	ADJ
ejpam-3228	244	18	bi≤̃a	bi≤̃a	NOUN
ejpam-3228	244	19	.	.	PUNCT
ejpam-3228	245	1	proof	proof	NOUN
ejpam-3228	245	2	.	.	PUNCT
ejpam-3228	246	1	since	since	SCONJ
ejpam-3228	246	2	,	,	PUNCT
ejpam-3228	246	3	{	{	PUNCT
ejpam-3228	246	4	bi	bi	NOUN
ejpam-3228	246	5	:	:	PUNCT
ejpam-3228	246	6	i	i	PRON
ejpam-3228	246	7	∈	∈	VERB
ejpam-3228	246	8	i	i	PRON
ejpam-3228	246	9	}	}	PUNCT
ejpam-3228	246	10	≤̃a	≤̃a	X
ejpam-3228	246	11	for	for	ADP
ejpam-3228	246	12	all	all	DET
ejpam-3228	246	13	i	i	PRON
ejpam-3228	246	14	∈	∈	PROPN
ejpam-3228	246	15	i.	i.	NOUN
ejpam-3228	246	16	therefore	therefore	ADV
ejpam-3228	246	17	,	,	PUNCT
ejpam-3228	246	18	∪	∪	ADP
ejpam-3228	246	19	i∈i	i∈i	ADJ
ejpam-3228	246	20	bi	bi	NOUN
ejpam-3228	246	21	6=	6=	ADP
ejpam-3228	246	22	∅.	∅.	AUX
ejpam-3228	246	23	let	let	VERB
ejpam-3228	246	24	x	x	PRON
ejpam-3228	246	25	,	,	PUNCT
ejpam-3228	246	26	y	y	PROPN
ejpam-3228	246	27	∈	∈	PROPN
ejpam-3228	246	28	∪	∪	ADP
ejpam-3228	246	29	i∈i	i∈i	ADJ
ejpam-3228	246	30	bi	bi	NOUN
ejpam-3228	246	31	.	.	PUNCT
ejpam-3228	247	1	then	then	ADV
ejpam-3228	247	2	by	by	ADP
ejpam-3228	247	3	theorem	theorem	NOUN
ejpam-3228	247	4	1	1	NUM
ejpam-3228	247	5	we	we	PRON
ejpam-3228	247	6	get	get	VERB
ejpam-3228	247	7	(	(	PUNCT
ejpam-3228	247	8	∪̃	∪̃	PROPN
ejpam-3228	247	9	i∈i	i∈i	ADJ
ejpam-3228	247	10	fbi	fbi	PROPN
ejpam-3228	247	11	)	)	PUNCT
ejpam-3228	248	1	(	(	PUNCT
ejpam-3228	248	2	xy−1	xy−1	PROPN
ejpam-3228	248	3	)	)	PUNCT
ejpam-3228	248	4	=	=	PUNCT
ejpam-3228	249	1	(	(	PUNCT
ejpam-3228	249	2	(	(	PUNCT
ejpam-3228	249	3	f	f	PROPN
ejpam-3228	249	4	∪̃	∪̃	PROPN
ejpam-3228	249	5	i∈i	i∈i	ADJ
ejpam-3228	249	6	bi	bi	NOUN
ejpam-3228	249	7	)	)	PUNCT
ejpam-3228	249	8	(	(	PUNCT
ejpam-3228	249	9	xy−1	xy−1	PROPN
ejpam-3228	249	10	)	)	PUNCT
ejpam-3228	249	11	)	)	PUNCT
ejpam-3228	250	1	=	=	PUNCT
ejpam-3228	250	2	∪	∪	ADP
ejpam-3228	250	3	i∈i	i∈i	ADJ
ejpam-3228	250	4	(	(	PUNCT
ejpam-3228	250	5	fbi(xy	fbi(xy	NOUN
ejpam-3228	250	6	−1	−1	NOUN
ejpam-3228	250	7	)	)	PUNCT
ejpam-3228	250	8	:	:	PUNCT
ejpam-3228	251	1	i	i	PRON
ejpam-3228	251	2	∈	∈	VERB
ejpam-3228	251	3	i	i	X
ejpam-3228	251	4	)	)	PUNCT
ejpam-3228	252	1	⊆	⊆	X
ejpam-3228	252	2	∪	∪	ADP
ejpam-3228	252	3	i∈i	i∈i	NOUN
ejpam-3228	252	4	(	(	PUNCT
ejpam-3228	252	5	(	(	PUNCT
ejpam-3228	252	6	fbi(x	fbi(x	NOUN
ejpam-3228	252	7	)	)	PUNCT
ejpam-3228	252	8	∪	∪	ADJ
ejpam-3228	252	9	fbi(y	fbi(y	PROPN
ejpam-3228	252	10	)	)	PUNCT
ejpam-3228	252	11	)	)	PUNCT
ejpam-3228	252	12	:	:	PUNCT
ejpam-3228	253	1	i	i	PRON
ejpam-3228	253	2	∈	∈	VERB
ejpam-3228	253	3	i	i	X
ejpam-3228	253	4	)	)	PUNCT
ejpam-3228	253	5	=	=	PUNCT
ejpam-3228	254	1	(	(	PUNCT
ejpam-3228	254	2	∪	∪	X
ejpam-3228	254	3	i∈i	i∈i	ADJ
ejpam-3228	254	4	(	(	PUNCT
ejpam-3228	254	5	fbi(x	fbi(x	PROPN
ejpam-3228	254	6	)	)	PUNCT
ejpam-3228	254	7	:	:	PUNCT
ejpam-3228	255	1	i	i	PRON
ejpam-3228	255	2	∈	∈	PROPN
ejpam-3228	255	3	i	i	NOUN
ejpam-3228	255	4	)	)	PUNCT
ejpam-3228	255	5	)	)	PUNCT
ejpam-3228	255	6	∪	∪	ADV
ejpam-3228	255	7	(	(	PUNCT
ejpam-3228	255	8	∪	∪	ADJ
ejpam-3228	255	9	i∈i	i∈i	ADJ
ejpam-3228	255	10	(	(	PUNCT
ejpam-3228	255	11	fbi(y	fbi(y	PROPN
ejpam-3228	255	12	)	)	PUNCT
ejpam-3228	255	13	:	:	PUNCT
ejpam-3228	256	1	i	i	PRON
ejpam-3228	256	2	∈	∈	PROPN
ejpam-3228	256	3	i	i	NOUN
ejpam-3228	256	4	)	)	PUNCT
ejpam-3228	256	5	)	)	PUNCT
ejpam-3228	257	1	a.	a.	PROPN
ejpam-3228	257	2	ullah	ullah	PROPN
ejpam-3228	257	3	,	,	PUNCT
ejpam-3228	257	4	f.	f.	PROPN
ejpam-3228	257	5	karaaslan	karaaslan	PROPN
ejpam-3228	257	6	,	,	PUNCT
ejpam-3228	257	7	i.	i.	PROPN
ejpam-3228	257	8	ahmad	ahmad	PROPN
ejpam-3228	257	9	/	/	SYM
ejpam-3228	257	10	eur	eur	PROPN
ejpam-3228	257	11	.	.	PUNCT
ejpam-3228	258	1	j.	j.	PROPN
ejpam-3228	258	2	pure	pure	PROPN
ejpam-3228	258	3	appl	appl	PROPN
ejpam-3228	258	4	.	.	PROPN
ejpam-3228	258	5	math	math	PROPN
ejpam-3228	258	6	,	,	PUNCT
ejpam-3228	258	7	11	11	NUM
ejpam-3228	258	8	(	(	PUNCT
ejpam-3228	258	9	2	2	NUM
ejpam-3228	258	10	)	)	PUNCT
ejpam-3228	258	11	(	(	PUNCT
ejpam-3228	258	12	2018	2018	NUM
ejpam-3228	258	13	)	)	PUNCT
ejpam-3228	258	14	,	,	PUNCT
ejpam-3228	258	15	517	517	NUM
ejpam-3228	258	16	-	-	SYM
ejpam-3228	258	17	536	536	NUM
ejpam-3228	258	18	528	528	NUM
ejpam-3228	258	19	=	=	SYM
ejpam-3228	258	20	(	(	PUNCT
ejpam-3228	258	21	(	(	PUNCT
ejpam-3228	258	22	f	f	PROPN
ejpam-3228	258	23	∪̃	∪̃	PROPN
ejpam-3228	258	24	i∈i	i∈i	ADJ
ejpam-3228	258	25	bi	bi	NOUN
ejpam-3228	258	26	)	)	PUNCT
ejpam-3228	258	27	(	(	PUNCT
ejpam-3228	258	28	x	x	X
ejpam-3228	258	29	)	)	PUNCT
ejpam-3228	258	30	)	)	PUNCT
ejpam-3228	258	31	∪	∪	X
ejpam-3228	258	32	(	(	PUNCT
ejpam-3228	258	33	(	(	PUNCT
ejpam-3228	258	34	f	f	PROPN
ejpam-3228	258	35	∪̃	∪̃	PROPN
ejpam-3228	258	36	i∈i	i∈i	ADJ
ejpam-3228	258	37	bi	bi	NOUN
ejpam-3228	258	38	)	)	PUNCT
ejpam-3228	258	39	(	(	PUNCT
ejpam-3228	258	40	y	y	NOUN
ejpam-3228	258	41	)	)	PUNCT
ejpam-3228	258	42	)	)	PUNCT
ejpam-3228	258	43	.	.	PUNCT
ejpam-3228	259	1	hence	hence	ADV
ejpam-3228	259	2	,	,	PUNCT
ejpam-3228	259	3	∪̃	∪̃	PROPN
ejpam-3228	259	4	i∈i	i∈i	ADJ
ejpam-3228	259	5	bi≤̃a	bi≤̃a	PROPN
ejpam-3228	259	6	.	.	PUNCT
ejpam-3228	260	1	the	the	DET
ejpam-3228	260	2	following	follow	VERB
ejpam-3228	260	3	counter	counter	ADJ
ejpam-3228	260	4	example	example	NOUN
ejpam-3228	260	5	clearly	clearly	ADV
ejpam-3228	260	6	shows	show	VERB
ejpam-3228	260	7	that	that	SCONJ
ejpam-3228	260	8	b∩̃c	b∩̃c	NOUN
ejpam-3228	260	9	�	�	NOUN
ejpam-3228	260	10	̃a	̃a	PROPN
ejpam-3228	260	11	.	.	PUNCT
ejpam-3228	260	12	example	example	NOUN
ejpam-3228	261	1	7	7	NUM
ejpam-3228	261	2	.	.	PUNCT
ejpam-3228	262	1	from	from	ADP
ejpam-3228	262	2	,	,	PUNCT
ejpam-3228	262	3	example	example	NOUN
ejpam-3228	262	4	5	5	NUM
ejpam-3228	262	5	,	,	PUNCT
ejpam-3228	262	6	we	we	PRON
ejpam-3228	262	7	have	have	VERB
ejpam-3228	262	8	(	(	PUNCT
ejpam-3228	262	9	fb∩̃fc	fb∩̃fc	PROPN
ejpam-3228	262	10	)	)	PUNCT
ejpam-3228	262	11	(	(	PUNCT
ejpam-3228	262	12	4	4	NUM
ejpam-3228	262	13	·	·	SYM
ejpam-3228	262	14	4−1	4−1	NUM
ejpam-3228	262	15	)	)	PUNCT
ejpam-3228	262	16	=	=	SYM
ejpam-3228	262	17	(	(	PUNCT
ejpam-3228	262	18	fb∩̃c	fb∩̃c	PROPN
ejpam-3228	262	19	)	)	PUNCT
ejpam-3228	262	20	(	(	PUNCT
ejpam-3228	262	21	4	4	NUM
ejpam-3228	262	22	·	·	SYM
ejpam-3228	262	23	4	4	NUM
ejpam-3228	262	24	)	)	PUNCT
ejpam-3228	262	25	=	=	SYM
ejpam-3228	262	26	(	(	PUNCT
ejpam-3228	262	27	fb∩̃c	fb∩̃c	PROPN
ejpam-3228	262	28	)	)	PUNCT
ejpam-3228	262	29	(	(	PUNCT
ejpam-3228	262	30	0	0	NUM
ejpam-3228	262	31	)	)	PUNCT
ejpam-3228	262	32	=	=	SYM
ejpam-3228	262	33	fb(0	fb(0	NOUN
ejpam-3228	262	34	)	)	PUNCT
ejpam-3228	262	35	∩	∩	NOUN
ejpam-3228	262	36	fc(0	fc(0	PROPN
ejpam-3228	262	37	)	)	PUNCT
ejpam-3228	262	38	=	=	NOUN
ejpam-3228	262	39	{	{	PUNCT
ejpam-3228	262	40	0	0	NUM
ejpam-3228	262	41	}	}	PUNCT
ejpam-3228	262	42	,	,	PUNCT
ejpam-3228	262	43	(	(	PUNCT
ejpam-3228	262	44	7	7	X
ejpam-3228	262	45	)	)	PUNCT
ejpam-3228	262	46	and	and	CCONJ
ejpam-3228	262	47	(	(	PUNCT
ejpam-3228	262	48	(	(	PUNCT
ejpam-3228	262	49	fb∩̃fc	fb∩̃fc	NOUN
ejpam-3228	262	50	)	)	PUNCT
ejpam-3228	262	51	(	(	PUNCT
ejpam-3228	262	52	4	4	NUM
ejpam-3228	262	53	)	)	PUNCT
ejpam-3228	262	54	)	)	PUNCT
ejpam-3228	262	55	∪	∪	X
ejpam-3228	262	56	(	(	PUNCT
ejpam-3228	262	57	(	(	PUNCT
ejpam-3228	262	58	fb∩̃fc	fb∩̃fc	NOUN
ejpam-3228	262	59	)	)	PUNCT
ejpam-3228	262	60	(	(	PUNCT
ejpam-3228	262	61	4	4	NUM
ejpam-3228	262	62	)	)	PUNCT
ejpam-3228	262	63	)	)	PUNCT
ejpam-3228	263	1	=	=	SYM
ejpam-3228	263	2	(	(	PUNCT
ejpam-3228	263	3	fb(4	fb(4	NOUN
ejpam-3228	263	4	)	)	PUNCT
ejpam-3228	263	5	∩	∩	ADJ
ejpam-3228	263	6	fc(4	fc(4	NOUN
ejpam-3228	263	7	)	)	PUNCT
ejpam-3228	263	8	)	)	PUNCT
ejpam-3228	264	1	∪	∪	ADP
ejpam-3228	264	2	(	(	PUNCT
ejpam-3228	264	3	fb(4	fb(4	NOUN
ejpam-3228	264	4	)	)	PUNCT
ejpam-3228	264	5	∩	∩	ADJ
ejpam-3228	264	6	fc(4	fc(4	NOUN
ejpam-3228	264	7	)	)	PUNCT
ejpam-3228	264	8	)	)	PUNCT
ejpam-3228	265	1	=	=	NOUN
ejpam-3228	265	2	∅	∅	NOUN
ejpam-3228	265	3	,	,	PUNCT
ejpam-3228	265	4	this	this	PRON
ejpam-3228	265	5	implies	imply	VERB
ejpam-3228	265	6	that	that	SCONJ
ejpam-3228	265	7	(	(	PUNCT
ejpam-3228	265	8	(	(	PUNCT
ejpam-3228	265	9	fb∩̃fc	fb∩̃fc	NOUN
ejpam-3228	265	10	)	)	PUNCT
ejpam-3228	265	11	(	(	PUNCT
ejpam-3228	265	12	4	4	NUM
ejpam-3228	265	13	)	)	PUNCT
ejpam-3228	265	14	)	)	PUNCT
ejpam-3228	265	15	∪	∪	X
ejpam-3228	265	16	(	(	PUNCT
ejpam-3228	265	17	(	(	PUNCT
ejpam-3228	265	18	fb∩̃fc	fb∩̃fc	NOUN
ejpam-3228	265	19	)	)	PUNCT
ejpam-3228	265	20	(	(	PUNCT
ejpam-3228	265	21	4	4	NUM
ejpam-3228	265	22	)	)	PUNCT
ejpam-3228	265	23	)	)	PUNCT
ejpam-3228	266	1	=	=	SYM
ejpam-3228	266	2	∅.	∅.	X
ejpam-3228	266	3	(	(	PUNCT
ejpam-3228	266	4	8)	8)	NUM
ejpam-3228	266	5	by	by	ADP
ejpam-3228	266	6	equations	equation	NOUN
ejpam-3228	266	7	(	(	PUNCT
ejpam-3228	266	8	7	7	NUM
ejpam-3228	266	9	)	)	PUNCT
ejpam-3228	266	10	and	and	CCONJ
ejpam-3228	266	11	(	(	PUNCT
ejpam-3228	266	12	8)	8)	NUM
ejpam-3228	266	13	,	,	PUNCT
ejpam-3228	266	14	we	we	PRON
ejpam-3228	266	15	get	get	VERB
ejpam-3228	266	16	(	(	PUNCT
ejpam-3228	266	17	fb∩̃fc	fb∩̃fc	NOUN
ejpam-3228	266	18	)	)	PUNCT
ejpam-3228	266	19	(	(	PUNCT
ejpam-3228	266	20	4	4	NUM
ejpam-3228	266	21	·	·	SYM
ejpam-3228	266	22	4−1	4−1	NUM
ejpam-3228	266	23	)	)	PUNCT
ejpam-3228	266	24	(	(	PUNCT
ejpam-3228	266	25	(	(	PUNCT
ejpam-3228	266	26	fb∩̃fc	fb∩̃fc	NOUN
ejpam-3228	266	27	)	)	PUNCT
ejpam-3228	266	28	(	(	PUNCT
ejpam-3228	266	29	4	4	NUM
ejpam-3228	266	30	)	)	PUNCT
ejpam-3228	266	31	)	)	PUNCT
ejpam-3228	266	32	∪	∪	X
ejpam-3228	266	33	(	(	PUNCT
ejpam-3228	266	34	(	(	PUNCT
ejpam-3228	266	35	fb∩̃fc	fb∩̃fc	NOUN
ejpam-3228	266	36	)	)	PUNCT
ejpam-3228	266	37	(	(	PUNCT
ejpam-3228	266	38	4	4	NUM
ejpam-3228	266	39	)	)	PUNCT
ejpam-3228	266	40	)	)	PUNCT
ejpam-3228	266	41	.	.	PUNCT
ejpam-3228	267	1	hence	hence	ADV
ejpam-3228	267	2	,	,	PUNCT
ejpam-3228	267	3	b∩̃c	b∩̃c	X
ejpam-3228	267	4	�	�	NOUN
ejpam-3228	267	5	̃a	̃a	PROPN
ejpam-3228	267	6	.	.	PUNCT
ejpam-3228	268	1	3	3	NUM
ejpam-3228	268	2	.	.	NOUN
ejpam-3228	268	3	conjugate	conjugate	VERB
ejpam-3228	268	4	soft	soft	ADJ
ejpam-3228	268	5	uni	uni	ADJ
ejpam-3228	268	6	-	-	PUNCT
ejpam-3228	268	7	ag	ag	ADJ
ejpam-3228	268	8	-	-	PUNCT
ejpam-3228	268	9	groups	group	NOUN
ejpam-3228	268	10	definition	definition	NOUN
ejpam-3228	268	11	7	7	NUM
ejpam-3228	268	12	.	.	PUNCT
ejpam-3228	269	1	let	let	VERB
ejpam-3228	269	2	a	a	DET
ejpam-3228	269	3	∈	∈	PROPN
ejpam-3228	269	4	s∪ag(u	s∪ag(u	NUM
ejpam-3228	269	5	)	)	PUNCT
ejpam-3228	269	6	and	and	CCONJ
ejpam-3228	269	7	x	x	PUNCT
ejpam-3228	269	8	∈	∈	PROPN
ejpam-3228	269	9	g.	g.	NOUN
ejpam-3228	269	10	then	then	ADV
ejpam-3228	269	11	ax	ax	NOUN
ejpam-3228	269	12	is	be	AUX
ejpam-3228	269	13	called	call	VERB
ejpam-3228	269	14	conjugate	conjugate	ADJ
ejpam-3228	269	15	soft	soft	ADJ
ejpam-3228	269	16	uniag	uniag	NOUN
ejpam-3228	269	17	-	-	PUNCT
ejpam-3228	269	18	group	group	NOUN
ejpam-3228	269	19	of	of	ADP
ejpam-3228	269	20	a	a	PRON
ejpam-3228	269	21	(	(	PUNCT
ejpam-3228	269	22	with	with	ADP
ejpam-3228	269	23	respect	respect	NOUN
ejpam-3228	269	24	to	to	ADP
ejpam-3228	269	25	x	x	SYM
ejpam-3228	269	26	)	)	PUNCT
ejpam-3228	269	27	denoted	denote	VERB
ejpam-3228	269	28	by	by	ADP
ejpam-3228	269	29	ax	ax	NOUN
ejpam-3228	269	30	c∼	c∼	PROPN
ejpam-3228	269	31	a	a	NOUN
ejpam-3228	269	32	,	,	PUNCT
ejpam-3228	269	33	and	and	CCONJ
ejpam-3228	269	34	is	be	AUX
ejpam-3228	269	35	given	give	VERB
ejpam-3228	269	36	by	by	ADP
ejpam-3228	269	37	fax(g	fax(g	NOUN
ejpam-3228	270	1	)	)	PUNCT
ejpam-3228	270	2	=	=	SYM
ejpam-3228	270	3	fa	fa	INTJ
ejpam-3228	270	4	(	(	PUNCT
ejpam-3228	270	5	(	(	PUNCT
ejpam-3228	270	6	xg)x−1	xg)x−1	PROPN
ejpam-3228	270	7	)	)	PUNCT
ejpam-3228	270	8	,	,	PUNCT
ejpam-3228	270	9	for	for	ADP
ejpam-3228	270	10	all	all	DET
ejpam-3228	270	11	g	g	PROPN
ejpam-3228	270	12	∈	∈	PROPN
ejpam-3228	270	13	g.	g.	NOUN
ejpam-3228	270	14	remark	remark	NOUN
ejpam-3228	270	15	1	1	NUM
ejpam-3228	270	16	.	.	PUNCT
ejpam-3228	271	1	it	it	PRON
ejpam-3228	271	2	is	be	AUX
ejpam-3228	271	3	noted	note	VERB
ejpam-3228	271	4	that	that	SCONJ
ejpam-3228	271	5	a	a	DET
ejpam-3228	271	6	conjugate	conjugate	ADJ
ejpam-3228	271	7	soft	soft	ADJ
ejpam-3228	271	8	uni	uni	ADJ
ejpam-3228	271	9	-	-	PUNCT
ejpam-3228	271	10	ag	ag	NOUN
ejpam-3228	271	11	-	-	PUNCT
ejpam-3228	271	12	group	group	NOUN
ejpam-3228	271	13	may	may	AUX
ejpam-3228	271	14	or	or	CCONJ
ejpam-3228	271	15	may	may	AUX
ejpam-3228	271	16	not	not	PART
ejpam-3228	271	17	be	be	AUX
ejpam-3228	271	18	a	a	DET
ejpam-3228	271	19	soft	soft	ADJ
ejpam-3228	271	20	-	-	PUNCT
ejpam-3228	271	21	uniag	uniag	ADJ
ejpam-3228	271	22	-	-	NOUN
ejpam-3228	271	23	group	group	NOUN
ejpam-3228	271	24	.	.	PUNCT
ejpam-3228	272	1	example	example	NOUN
ejpam-3228	272	2	8	8	NUM
ejpam-3228	272	3	.	.	PUNCT
ejpam-3228	273	1	consider	consider	VERB
ejpam-3228	273	2	an	an	DET
ejpam-3228	273	3	ag	ag	PROPN
ejpam-3228	273	4	-	-	PUNCT
ejpam-3228	273	5	group	group	NOUN
ejpam-3228	273	6	g	g	NOUN
ejpam-3228	273	7	of	of	ADP
ejpam-3228	273	8	order	order	NOUN
ejpam-3228	273	9	6	6	NUM
ejpam-3228	273	10	defined	define	VERB
ejpam-3228	273	11	by	by	ADP
ejpam-3228	273	12	·	·	SYM
ejpam-3228	273	13	0	0	NUM
ejpam-3228	274	1	1	1	NUM
ejpam-3228	274	2	2	2	NUM
ejpam-3228	274	3	3	3	NUM
ejpam-3228	274	4	4	4	NUM
ejpam-3228	274	5	5	5	NUM
ejpam-3228	274	6	0	0	NUM
ejpam-3228	274	7	0	0	NUM
ejpam-3228	274	8	1	1	NUM
ejpam-3228	274	9	2	2	NUM
ejpam-3228	274	10	3	3	NUM
ejpam-3228	274	11	4	4	NUM
ejpam-3228	274	12	5	5	NUM
ejpam-3228	274	13	1	1	NUM
ejpam-3228	274	14	5	5	NUM
ejpam-3228	274	15	0	0	NUM
ejpam-3228	274	16	1	1	NUM
ejpam-3228	274	17	2	2	NUM
ejpam-3228	274	18	3	3	NUM
ejpam-3228	274	19	4	4	NUM
ejpam-3228	274	20	2	2	NUM
ejpam-3228	274	21	4	4	NUM
ejpam-3228	274	22	5	5	NUM
ejpam-3228	274	23	0	0	NUM
ejpam-3228	274	24	1	1	NUM
ejpam-3228	274	25	2	2	NUM
ejpam-3228	274	26	3	3	NUM
ejpam-3228	274	27	3	3	NUM
ejpam-3228	274	28	3	3	NUM
ejpam-3228	274	29	4	4	NUM
ejpam-3228	274	30	5	5	NUM
ejpam-3228	274	31	0	0	NUM
ejpam-3228	274	32	1	1	NUM
ejpam-3228	274	33	2	2	NUM
ejpam-3228	274	34	4	4	NUM
ejpam-3228	274	35	2	2	NUM
ejpam-3228	274	36	3	3	NUM
ejpam-3228	274	37	4	4	NUM
ejpam-3228	274	38	5	5	NUM
ejpam-3228	274	39	0	0	NUM
ejpam-3228	274	40	1	1	NUM
ejpam-3228	274	41	5	5	NUM
ejpam-3228	274	42	1	1	NUM
ejpam-3228	274	43	2	2	NUM
ejpam-3228	274	44	3	3	NUM
ejpam-3228	274	45	4	4	NUM
ejpam-3228	274	46	5	5	NUM
ejpam-3228	274	47	0	0	NUM
ejpam-3228	274	48	a.	a.	PROPN
ejpam-3228	274	49	ullah	ullah	PROPN
ejpam-3228	274	50	,	,	PUNCT
ejpam-3228	274	51	f.	f.	PROPN
ejpam-3228	274	52	karaaslan	karaaslan	PROPN
ejpam-3228	274	53	,	,	PUNCT
ejpam-3228	274	54	i.	i.	PROPN
ejpam-3228	274	55	ahmad	ahmad	PROPN
ejpam-3228	274	56	/	/	SYM
ejpam-3228	274	57	eur	eur	PROPN
ejpam-3228	274	58	.	.	PUNCT
ejpam-3228	275	1	j.	j.	PROPN
ejpam-3228	275	2	pure	pure	PROPN
ejpam-3228	275	3	appl	appl	PROPN
ejpam-3228	275	4	.	.	PROPN
ejpam-3228	275	5	math	math	PROPN
ejpam-3228	275	6	,	,	PUNCT
ejpam-3228	275	7	11	11	NUM
ejpam-3228	275	8	(	(	PUNCT
ejpam-3228	275	9	2	2	NUM
ejpam-3228	275	10	)	)	PUNCT
ejpam-3228	275	11	(	(	PUNCT
ejpam-3228	275	12	2018	2018	NUM
ejpam-3228	275	13	)	)	PUNCT
ejpam-3228	275	14	,	,	PUNCT
ejpam-3228	275	15	517	517	NUM
ejpam-3228	275	16	-	-	SYM
ejpam-3228	275	17	536	536	NUM
ejpam-3228	275	18	529	529	NUM
ejpam-3228	275	19	let	let	VERB
ejpam-3228	275	20	a	a	DET
ejpam-3228	275	21	∈	∈	PROPN
ejpam-3228	275	22	s∪ag(z	s∪ag(z	NOUN
ejpam-3228	275	23	)	)	PUNCT
ejpam-3228	275	24	,	,	PUNCT
ejpam-3228	275	25	defined	define	VERB
ejpam-3228	275	26	as	as	SCONJ
ejpam-3228	275	27	follows	follow	VERB
ejpam-3228	275	28	:	:	PUNCT
ejpam-3228	275	29	fa(0	fa(0	X
ejpam-3228	275	30	)	)	PUNCT
ejpam-3228	275	31	=	=	PRON
ejpam-3228	275	32	{	{	PUNCT
ejpam-3228	275	33	−1	−1	NOUN
ejpam-3228	275	34	,	,	PUNCT
ejpam-3228	275	35	0	0	NUM
ejpam-3228	275	36	,	,	PUNCT
ejpam-3228	275	37	1	1	NUM
ejpam-3228	275	38	}	}	PUNCT
ejpam-3228	275	39	,	,	PUNCT
ejpam-3228	275	40	fa(2	fa(2	NOUN
ejpam-3228	275	41	)	)	PUNCT
ejpam-3228	275	42	=	=	NOUN
ejpam-3228	275	43	{	{	PUNCT
ejpam-3228	275	44	−2,−1	−2,−1	PROPN
ejpam-3228	275	45	,	,	PUNCT
ejpam-3228	275	46	0	0	NUM
ejpam-3228	275	47	,	,	PUNCT
ejpam-3228	275	48	1	1	NUM
ejpam-3228	275	49	,	,	PUNCT
ejpam-3228	275	50	2	2	NUM
ejpam-3228	275	51	}	}	PUNCT
ejpam-3228	275	52	=	=	SYM
ejpam-3228	275	53	fa(4	fa(4	NOUN
ejpam-3228	275	54	)	)	PUNCT
ejpam-3228	275	55	,	,	PUNCT
ejpam-3228	275	56	fa(1	fa(1	NOUN
ejpam-3228	275	57	)	)	PUNCT
ejpam-3228	275	58	=	=	PRON
ejpam-3228	275	59	{	{	PUNCT
ejpam-3228	275	60	−3,−2,−1	−3,−2,−1	NOUN
ejpam-3228	275	61	,	,	PUNCT
ejpam-3228	275	62	0	0	NUM
ejpam-3228	275	63	,	,	PUNCT
ejpam-3228	275	64	1	1	NUM
ejpam-3228	275	65	,	,	PUNCT
ejpam-3228	275	66	2	2	NUM
ejpam-3228	275	67	,	,	PUNCT
ejpam-3228	275	68	3	3	NUM
ejpam-3228	275	69	}	}	PUNCT
ejpam-3228	275	70	=	=	SYM
ejpam-3228	275	71	fa(3	fa(3	NOUN
ejpam-3228	275	72	)	)	PUNCT
ejpam-3228	275	73	=	=	SYM
ejpam-3228	275	74	fa(5	fa(5	PROPN
ejpam-3228	275	75	)	)	PUNCT
ejpam-3228	275	76	.	.	PUNCT
ejpam-3228	276	1	the	the	DET
ejpam-3228	276	2	conjugates	conjugate	NOUN
ejpam-3228	276	3	soft	soft	ADJ
ejpam-3228	276	4	uni	uni	ADJ
ejpam-3228	276	5	-	-	PUNCT
ejpam-3228	276	6	ag	ag	NOUN
ejpam-3228	276	7	-	-	PUNCT
ejpam-3228	276	8	groups	group	NOUN
ejpam-3228	276	9	of	of	ADP
ejpam-3228	276	10	a	a	PRON
ejpam-3228	276	11	is	be	AUX
ejpam-3228	276	12	given	give	VERB
ejpam-3228	276	13	by	by	ADP
ejpam-3228	276	14	:	:	PUNCT
ejpam-3228	276	15	fa0(0	fa0(0	ADJ
ejpam-3228	276	16	)	)	PUNCT
ejpam-3228	276	17	=	=	SYM
ejpam-3228	276	18	fa3(0	fa3(0	NOUN
ejpam-3228	276	19	)	)	PUNCT
ejpam-3228	276	20	=	=	SYM
ejpam-3228	276	21	fa(0	fa(0	X
ejpam-3228	276	22	)	)	PUNCT
ejpam-3228	276	23	=	=	PRON
ejpam-3228	276	24	{	{	PUNCT
ejpam-3228	276	25	−1	−1	NOUN
ejpam-3228	276	26	,	,	PUNCT
ejpam-3228	276	27	0	0	NUM
ejpam-3228	276	28	,	,	PUNCT
ejpam-3228	276	29	1	1	NUM
ejpam-3228	276	30	}	}	PUNCT
ejpam-3228	276	31	,	,	PUNCT
ejpam-3228	276	32	fa0(1	fa0(1	X
ejpam-3228	276	33	)	)	PUNCT
ejpam-3228	276	34	=	=	SYM
ejpam-3228	276	35	fa3(1	fa3(1	ADJ
ejpam-3228	276	36	)	)	PUNCT
ejpam-3228	276	37	=	=	SYM
ejpam-3228	276	38	fa(5	fa(5	PROPN
ejpam-3228	276	39	)	)	PUNCT
ejpam-3228	276	40	=	=	PRON
ejpam-3228	276	41	{	{	PUNCT
ejpam-3228	276	42	−3,−2,−1	−3,−2,−1	NOUN
ejpam-3228	276	43	,	,	PUNCT
ejpam-3228	276	44	0	0	NUM
ejpam-3228	276	45	,	,	PUNCT
ejpam-3228	276	46	1	1	NUM
ejpam-3228	276	47	,	,	PUNCT
ejpam-3228	276	48	2	2	NUM
ejpam-3228	276	49	,	,	PUNCT
ejpam-3228	276	50	3	3	NUM
ejpam-3228	276	51	}	}	PUNCT
ejpam-3228	276	52	,	,	PUNCT
ejpam-3228	277	1	fa0(2	fa0(2	ADJ
ejpam-3228	277	2	)	)	PUNCT
ejpam-3228	277	3	=	=	SYM
ejpam-3228	277	4	fa3(2	fa3(2	NOUN
ejpam-3228	277	5	)	)	PUNCT
ejpam-3228	277	6	=	=	SYM
ejpam-3228	277	7	fa(4	fa(4	NOUN
ejpam-3228	277	8	)	)	PUNCT
ejpam-3228	277	9	=	=	NOUN
ejpam-3228	277	10	{	{	PUNCT
ejpam-3228	277	11	−2,−1	−2,−1	PROPN
ejpam-3228	277	12	,	,	PUNCT
ejpam-3228	277	13	0	0	NUM
ejpam-3228	277	14	,	,	PUNCT
ejpam-3228	277	15	1	1	NUM
ejpam-3228	277	16	,	,	PUNCT
ejpam-3228	277	17	2	2	NUM
ejpam-3228	277	18	}	}	PUNCT
ejpam-3228	277	19	,	,	PUNCT
ejpam-3228	277	20	fa0(3	fa0(3	NOUN
ejpam-3228	277	21	)	)	PUNCT
ejpam-3228	277	22	=	=	SYM
ejpam-3228	277	23	fa3(3	fa3(3	ADJ
ejpam-3228	277	24	)	)	PUNCT
ejpam-3228	277	25	=	=	SYM
ejpam-3228	277	26	fa(3	fa(3	NOUN
ejpam-3228	277	27	)	)	PUNCT
ejpam-3228	277	28	=	=	PRON
ejpam-3228	277	29	{	{	PUNCT
ejpam-3228	277	30	−3,−2,−1	−3,−2,−1	NOUN
ejpam-3228	277	31	,	,	PUNCT
ejpam-3228	277	32	0	0	NUM
ejpam-3228	277	33	,	,	PUNCT
ejpam-3228	277	34	1	1	NUM
ejpam-3228	277	35	,	,	PUNCT
ejpam-3228	277	36	2	2	NUM
ejpam-3228	277	37	,	,	PUNCT
ejpam-3228	277	38	3	3	NUM
ejpam-3228	277	39	}	}	PUNCT
ejpam-3228	277	40	,	,	PUNCT
ejpam-3228	277	41	fa0(4	fa0(4	ADJ
ejpam-3228	277	42	)	)	PUNCT
ejpam-3228	277	43	=	=	SYM
ejpam-3228	277	44	fa3(4	fa3(4	NOUN
ejpam-3228	277	45	)	)	PUNCT
ejpam-3228	277	46	=	=	SYM
ejpam-3228	277	47	fa(2	fa(2	NOUN
ejpam-3228	277	48	)	)	PUNCT
ejpam-3228	277	49	=	=	NOUN
ejpam-3228	277	50	{	{	PUNCT
ejpam-3228	277	51	−2,−1	−2,−1	PROPN
ejpam-3228	277	52	,	,	PUNCT
ejpam-3228	277	53	0	0	NUM
ejpam-3228	277	54	,	,	PUNCT
ejpam-3228	277	55	1	1	NUM
ejpam-3228	277	56	,	,	PUNCT
ejpam-3228	277	57	2	2	NUM
ejpam-3228	277	58	}	}	PUNCT
ejpam-3228	277	59	,	,	PUNCT
ejpam-3228	277	60	fa0(5	fa0(5	PROPN
ejpam-3228	277	61	)	)	PUNCT
ejpam-3228	277	62	=	=	SYM
ejpam-3228	277	63	fa3(5	fa3(5	X
ejpam-3228	277	64	)	)	PUNCT
ejpam-3228	277	65	=	=	SYM
ejpam-3228	278	1	fa(1	fa(1	NOUN
ejpam-3228	278	2	)	)	PUNCT
ejpam-3228	278	3	=	=	PRON
ejpam-3228	278	4	{	{	PUNCT
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ejpam-3228	278	6	,	,	PUNCT
ejpam-3228	278	7	0	0	NUM
ejpam-3228	278	8	,	,	PUNCT
ejpam-3228	278	9	1	1	NUM
ejpam-3228	278	10	,	,	PUNCT
ejpam-3228	278	11	2	2	NUM
ejpam-3228	278	12	,	,	PUNCT
ejpam-3228	278	13	3	3	NUM
ejpam-3228	278	14	}	}	PUNCT
ejpam-3228	278	15	.	.	PUNCT
ejpam-3228	279	1	fa1(0	fa1(0	X
ejpam-3228	279	2	)	)	PUNCT
ejpam-3228	279	3	=	=	SYM
ejpam-3228	279	4	fa4(0	fa4(0	NOUN
ejpam-3228	279	5	)	)	PUNCT
ejpam-3228	279	6	=	=	SYM
ejpam-3228	279	7	fa(2	fa(2	NOUN
ejpam-3228	279	8	)	)	PUNCT
ejpam-3228	279	9	=	=	NOUN
ejpam-3228	279	10	{	{	PUNCT
ejpam-3228	279	11	−2,−1	−2,−1	PROPN
ejpam-3228	279	12	,	,	PUNCT
ejpam-3228	279	13	0	0	NUM
ejpam-3228	279	14	,	,	PUNCT
ejpam-3228	279	15	1	1	NUM
ejpam-3228	279	16	,	,	PUNCT
ejpam-3228	279	17	2	2	NUM
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ejpam-3228	279	20	fa1(1	fa1(1	ADJ
ejpam-3228	279	21	)	)	PUNCT
ejpam-3228	279	22	=	=	SYM
ejpam-3228	279	23	fa4(1	fa4(1	X
ejpam-3228	279	24	)	)	PUNCT
ejpam-3228	279	25	=	=	SYM
ejpam-3228	280	1	fa(1	fa(1	NOUN
ejpam-3228	280	2	)	)	PUNCT
ejpam-3228	280	3	=	=	PRON
ejpam-3228	280	4	{	{	PUNCT
ejpam-3228	280	5	−3,−2,−1	−3,−2,−1	NOUN
ejpam-3228	280	6	,	,	PUNCT
ejpam-3228	280	7	0	0	NUM
ejpam-3228	280	8	,	,	PUNCT
ejpam-3228	280	9	1	1	NUM
ejpam-3228	280	10	,	,	PUNCT
ejpam-3228	280	11	2	2	NUM
ejpam-3228	280	12	,	,	PUNCT
ejpam-3228	280	13	3	3	NUM
ejpam-3228	280	14	}	}	PUNCT
ejpam-3228	280	15	,	,	PUNCT
ejpam-3228	280	16	fa1(2	fa1(2	ADJ
ejpam-3228	280	17	)	)	PUNCT
ejpam-3228	280	18	=	=	SYM
ejpam-3228	280	19	fa4(2	fa4(2	NOUN
ejpam-3228	280	20	)	)	PUNCT
ejpam-3228	280	21	=	=	SYM
ejpam-3228	281	1	fa(0	fa(0	X
ejpam-3228	281	2	)	)	PUNCT
ejpam-3228	281	3	=	=	PRON
ejpam-3228	281	4	{	{	PUNCT
ejpam-3228	281	5	−1	−1	NOUN
ejpam-3228	281	6	,	,	PUNCT
ejpam-3228	281	7	0	0	NUM
ejpam-3228	281	8	,	,	PUNCT
ejpam-3228	281	9	1	1	NUM
ejpam-3228	281	10	}	}	PUNCT
ejpam-3228	281	11	,	,	PUNCT
ejpam-3228	281	12	fa1(3	fa1(3	ADJ
ejpam-3228	281	13	)	)	PUNCT
ejpam-3228	281	14	=	=	SYM
ejpam-3228	281	15	fa4(3	fa4(3	NOUN
ejpam-3228	281	16	)	)	PUNCT
ejpam-3228	281	17	=	=	SYM
ejpam-3228	281	18	fa(5	fa(5	PROPN
ejpam-3228	281	19	)	)	PUNCT
ejpam-3228	281	20	=	=	PRON
ejpam-3228	281	21	{	{	PUNCT
ejpam-3228	281	22	−3,−2,−1	−3,−2,−1	NOUN
ejpam-3228	281	23	,	,	PUNCT
ejpam-3228	281	24	0	0	NUM
ejpam-3228	281	25	,	,	PUNCT
ejpam-3228	281	26	1	1	NUM
ejpam-3228	281	27	,	,	PUNCT
ejpam-3228	281	28	2	2	NUM
ejpam-3228	281	29	,	,	PUNCT
ejpam-3228	281	30	3	3	NUM
ejpam-3228	281	31	}	}	PUNCT
ejpam-3228	281	32	,	,	PUNCT
ejpam-3228	281	33	fa1(4	fa1(4	X
ejpam-3228	281	34	)	)	PUNCT
ejpam-3228	281	35	=	=	SYM
ejpam-3228	281	36	fa4(4	fa4(4	NOUN
ejpam-3228	281	37	)	)	PUNCT
ejpam-3228	281	38	=	=	SYM
ejpam-3228	281	39	fa(4	fa(4	NOUN
ejpam-3228	281	40	)	)	PUNCT
ejpam-3228	281	41	=	=	NOUN
ejpam-3228	281	42	{	{	PUNCT
ejpam-3228	281	43	−2,−1	−2,−1	PROPN
ejpam-3228	281	44	,	,	PUNCT
ejpam-3228	281	45	0	0	NUM
ejpam-3228	281	46	,	,	PUNCT
ejpam-3228	281	47	1	1	NUM
ejpam-3228	281	48	,	,	PUNCT
ejpam-3228	281	49	2	2	NUM
ejpam-3228	281	50	}	}	PUNCT
ejpam-3228	281	51	,	,	PUNCT
ejpam-3228	281	52	fa1(5	fa1(5	NUM
ejpam-3228	281	53	)	)	PUNCT
ejpam-3228	281	54	=	=	SYM
ejpam-3228	281	55	fa4(5	fa4(5	NUM
ejpam-3228	281	56	)	)	PUNCT
ejpam-3228	282	1	=	=	SYM
ejpam-3228	282	2	fa(3	fa(3	NOUN
ejpam-3228	282	3	)	)	PUNCT
ejpam-3228	282	4	=	=	PRON
ejpam-3228	282	5	{	{	PUNCT
ejpam-3228	282	6	−3,−2,−1	−3,−2,−1	NOUN
ejpam-3228	282	7	,	,	PUNCT
ejpam-3228	282	8	0	0	NUM
ejpam-3228	282	9	,	,	PUNCT
ejpam-3228	282	10	1	1	NUM
ejpam-3228	282	11	,	,	PUNCT
ejpam-3228	282	12	2	2	NUM
ejpam-3228	282	13	,	,	PUNCT
ejpam-3228	282	14	3	3	NUM
ejpam-3228	282	15	}	}	PUNCT
ejpam-3228	282	16	.	.	PUNCT
ejpam-3228	283	1	fa2(0	fa2(0	NOUN
ejpam-3228	283	2	)	)	PUNCT
ejpam-3228	283	3	=	=	SYM
ejpam-3228	283	4	fa5(0	fa5(0	X
ejpam-3228	283	5	)	)	PUNCT
ejpam-3228	283	6	=	=	SYM
ejpam-3228	283	7	fa(4	fa(4	NOUN
ejpam-3228	283	8	)	)	PUNCT
ejpam-3228	283	9	=	=	NOUN
ejpam-3228	283	10	{	{	PUNCT
ejpam-3228	283	11	−2,−1	−2,−1	PROPN
ejpam-3228	283	12	,	,	PUNCT
ejpam-3228	283	13	0	0	NUM
ejpam-3228	283	14	,	,	PUNCT
ejpam-3228	283	15	1	1	NUM
ejpam-3228	283	16	,	,	PUNCT
ejpam-3228	283	17	2	2	NUM
ejpam-3228	283	18	}	}	PUNCT
ejpam-3228	283	19	,	,	PUNCT
ejpam-3228	283	20	fa2(1	fa2(1	NOUN
ejpam-3228	283	21	)	)	PUNCT
ejpam-3228	283	22	=	=	SYM
ejpam-3228	283	23	fa5(1	fa5(1	NOUN
ejpam-3228	283	24	)	)	PUNCT
ejpam-3228	283	25	=	=	SYM
ejpam-3228	283	26	fa(3	fa(3	NOUN
ejpam-3228	283	27	)	)	PUNCT
ejpam-3228	283	28	=	=	PRON
ejpam-3228	283	29	{	{	PUNCT
ejpam-3228	283	30	−3,−2,−1	−3,−2,−1	NOUN
ejpam-3228	283	31	,	,	PUNCT
ejpam-3228	283	32	0	0	NUM
ejpam-3228	283	33	,	,	PUNCT
ejpam-3228	283	34	1	1	NUM
ejpam-3228	283	35	,	,	PUNCT
ejpam-3228	283	36	2	2	NUM
ejpam-3228	283	37	,	,	PUNCT
ejpam-3228	283	38	3	3	NUM
ejpam-3228	283	39	}	}	PUNCT
ejpam-3228	283	40	,	,	PUNCT
ejpam-3228	283	41	fa2(2	fa2(2	INTJ
ejpam-3228	283	42	)	)	PUNCT
ejpam-3228	283	43	=	=	SYM
ejpam-3228	283	44	fa5(2	fa5(2	NOUN
ejpam-3228	283	45	)	)	PUNCT
ejpam-3228	283	46	=	=	SYM
ejpam-3228	283	47	fa(2	fa(2	NOUN
ejpam-3228	283	48	)	)	PUNCT
ejpam-3228	283	49	=	=	NOUN
ejpam-3228	283	50	{	{	PUNCT
ejpam-3228	283	51	−2,−1	−2,−1	PROPN
ejpam-3228	283	52	,	,	PUNCT
ejpam-3228	283	53	0	0	NUM
ejpam-3228	283	54	,	,	PUNCT
ejpam-3228	283	55	1	1	NUM
ejpam-3228	283	56	,	,	PUNCT
ejpam-3228	283	57	2	2	NUM
ejpam-3228	283	58	}	}	PUNCT
ejpam-3228	283	59	,	,	PUNCT
ejpam-3228	283	60	fa2(3	fa2(3	NOUN
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ejpam-3228	283	62	=	=	PUNCT
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ejpam-3228	283	64	)	)	PUNCT
ejpam-3228	283	65	=	=	SYM
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ejpam-3228	284	2	)	)	PUNCT
ejpam-3228	284	3	=	=	PRON
ejpam-3228	284	4	{	{	PUNCT
ejpam-3228	284	5	−3,−2,−1	−3,−2,−1	NOUN
ejpam-3228	284	6	,	,	PUNCT
ejpam-3228	284	7	0	0	NUM
ejpam-3228	284	8	,	,	PUNCT
ejpam-3228	284	9	1	1	NUM
ejpam-3228	284	10	,	,	PUNCT
ejpam-3228	284	11	2	2	NUM
ejpam-3228	284	12	,	,	PUNCT
ejpam-3228	284	13	3	3	NUM
ejpam-3228	284	14	}	}	PUNCT
ejpam-3228	284	15	,	,	PUNCT
ejpam-3228	284	16	fa2(4	fa2(4	NOUN
ejpam-3228	284	17	)	)	PUNCT
ejpam-3228	284	18	=	=	SYM
ejpam-3228	284	19	fa5(4	fa5(4	NOUN
ejpam-3228	284	20	)	)	PUNCT
ejpam-3228	284	21	=	=	SYM
ejpam-3228	285	1	fa(0	fa(0	X
ejpam-3228	285	2	)	)	PUNCT
ejpam-3228	285	3	=	=	PRON
ejpam-3228	285	4	{	{	PUNCT
ejpam-3228	285	5	−1	−1	NOUN
ejpam-3228	285	6	,	,	PUNCT
ejpam-3228	285	7	0	0	NUM
ejpam-3228	285	8	,	,	PUNCT
ejpam-3228	285	9	1	1	NUM
ejpam-3228	285	10	}	}	PUNCT
ejpam-3228	285	11	,	,	PUNCT
ejpam-3228	285	12	fa2(5	fa2(5	NOUN
ejpam-3228	285	13	)	)	PUNCT
ejpam-3228	285	14	=	=	SYM
ejpam-3228	285	15	fa5(5	fa5(5	NOUN
ejpam-3228	285	16	)	)	PUNCT
ejpam-3228	285	17	=	=	SYM
ejpam-3228	285	18	fa(5	fa(5	PROPN
ejpam-3228	285	19	)	)	PUNCT
ejpam-3228	285	20	=	=	PRON
ejpam-3228	285	21	{	{	PUNCT
ejpam-3228	285	22	−3,−2,−1	−3,−2,−1	NOUN
ejpam-3228	285	23	,	,	PUNCT
ejpam-3228	285	24	0	0	NUM
ejpam-3228	285	25	,	,	PUNCT
ejpam-3228	285	26	1	1	NUM
ejpam-3228	285	27	,	,	PUNCT
ejpam-3228	285	28	2	2	NUM
ejpam-3228	285	29	,	,	PUNCT
ejpam-3228	285	30	3	3	NUM
ejpam-3228	285	31	}	}	PUNCT
ejpam-3228	285	32	.	.	PUNCT
ejpam-3228	286	1	a1	a1	NOUN
ejpam-3228	286	2	and	and	CCONJ
ejpam-3228	286	3	a2	a2	PROPN
ejpam-3228	286	4	are	be	AUX
ejpam-3228	286	5	conjugate	conjugate	ADJ
ejpam-3228	286	6	soft	soft	ADJ
ejpam-3228	286	7	uni	uni	ADJ
ejpam-3228	286	8	-	-	PUNCT
ejpam-3228	286	9	ag	ag	ADJ
ejpam-3228	286	10	-	-	PUNCT
ejpam-3228	286	11	groups	group	NOUN
ejpam-3228	286	12	but	but	CCONJ
ejpam-3228	286	13	are	be	AUX
ejpam-3228	286	14	not	not	PART
ejpam-3228	286	15	soft	soft	ADJ
ejpam-3228	286	16	uni	uni	ADJ
ejpam-3228	286	17	-	-	PUNCT
ejpam-3228	286	18	ag	ag	ADJ
ejpam-3228	286	19	-	-	PUNCT
ejpam-3228	286	20	groups	group	NOUN
ejpam-3228	286	21	over	over	ADP
ejpam-3228	286	22	z	z	PROPN
ejpam-3228	286	23	,	,	PUNCT
ejpam-3228	286	24	as	as	ADP
ejpam-3228	286	25	fa1(2	fa1(2	NOUN
ejpam-3228	286	26	·	·	SYM
ejpam-3228	286	27	2	2	X
ejpam-3228	286	28	)	)	PUNCT
ejpam-3228	286	29	=	=	SYM
ejpam-3228	286	30	fa1(0	fa1(0	X
ejpam-3228	286	31	)	)	PUNCT
ejpam-3228	286	32	=	=	PRON
ejpam-3228	287	1	{	{	PUNCT
ejpam-3228	287	2	−2,−1	−2,−1	PROPN
ejpam-3228	287	3	,	,	PUNCT
ejpam-3228	287	4	0	0	NUM
ejpam-3228	287	5	,	,	PUNCT
ejpam-3228	287	6	1	1	NUM
ejpam-3228	287	7	,	,	PUNCT
ejpam-3228	287	8	2	2	NUM
ejpam-3228	287	9	}	}	SYM
ejpam-3228	287	10	fa1(2	fa1(2	NOUN
ejpam-3228	287	11	)	)	PUNCT
ejpam-3228	287	12	∪	∪	ADP
ejpam-3228	287	13	fa1(2	fa1(2	NOUN
ejpam-3228	287	14	)	)	PUNCT
ejpam-3228	287	15	=	=	PRON
ejpam-3228	287	16	{	{	PUNCT
ejpam-3228	287	17	−1	−1	NOUN
ejpam-3228	287	18	,	,	PUNCT
ejpam-3228	287	19	0	0	NUM
ejpam-3228	287	20	,	,	PUNCT
ejpam-3228	287	21	1	1	NUM
ejpam-3228	287	22	}	}	PUNCT
ejpam-3228	287	23	,	,	PUNCT
ejpam-3228	287	24	and	and	CCONJ
ejpam-3228	287	25	fa2(4	fa2(4	VERB
ejpam-3228	287	26	·	·	PUNCT
ejpam-3228	287	27	4	4	X
ejpam-3228	287	28	)	)	PUNCT
ejpam-3228	287	29	=	=	SYM
ejpam-3228	287	30	fa2(0	fa2(0	NOUN
ejpam-3228	287	31	)	)	PUNCT
ejpam-3228	287	32	=	=	PRON
ejpam-3228	287	33	{	{	PUNCT
ejpam-3228	287	34	−2,−1	−2,−1	PROPN
ejpam-3228	287	35	,	,	PUNCT
ejpam-3228	287	36	0	0	NUM
ejpam-3228	287	37	,	,	PUNCT
ejpam-3228	287	38	1	1	NUM
ejpam-3228	287	39	,	,	PUNCT
ejpam-3228	287	40	2	2	NUM
ejpam-3228	287	41	}	}	PUNCT
ejpam-3228	287	42	fa2(4	fa2(4	NOUN
ejpam-3228	287	43	)	)	PUNCT
ejpam-3228	287	44	∪	∪	ADP
ejpam-3228	287	45	fa2(4	fa2(4	NOUN
ejpam-3228	287	46	)	)	PUNCT
ejpam-3228	287	47	=	=	PRON
ejpam-3228	287	48	{	{	PUNCT
ejpam-3228	287	49	−1	−1	NOUN
ejpam-3228	287	50	,	,	PUNCT
ejpam-3228	287	51	0	0	NUM
ejpam-3228	287	52	,	,	PUNCT
ejpam-3228	287	53	1	1	NUM
ejpam-3228	287	54	}	}	PUNCT
ejpam-3228	287	55	.	.	PUNCT
ejpam-3228	288	1	definition	definition	NOUN
ejpam-3228	288	2	8	8	NUM
ejpam-3228	288	3	.	.	PUNCT
ejpam-3228	289	1	let	let	VERB
ejpam-3228	289	2	a	a	DET
ejpam-3228	289	3	∈	∈	NOUN
ejpam-3228	289	4	s∪ag(u	s∪ag(u	NUM
ejpam-3228	289	5	)	)	PUNCT
ejpam-3228	289	6	.	.	PUNCT
ejpam-3228	290	1	then	then	ADV
ejpam-3228	290	2	a	a	PRON
ejpam-3228	290	3	is	be	AUX
ejpam-3228	290	4	called	call	VERB
ejpam-3228	290	5	a	a	DET
ejpam-3228	290	6	normal	normal	ADJ
ejpam-3228	290	7	soft	soft	ADJ
ejpam-3228	290	8	uni	uni	ADJ
ejpam-3228	290	9	-	-	PUNCT
ejpam-3228	290	10	ag	ag	NOUN
ejpam-3228	290	11	-	-	NOUN
ejpam-3228	290	12	subgroup	subgroup	NOUN
ejpam-3228	290	13	over	over	ADP
ejpam-3228	290	14	u	u	NOUN
ejpam-3228	290	15	if	if	SCONJ
ejpam-3228	290	16	fax(y	fax(y	PROPN
ejpam-3228	290	17	)	)	PUNCT
ejpam-3228	290	18	=	=	SYM
ejpam-3228	290	19	fa	fa	INTJ
ejpam-3228	290	20	(	(	PUNCT
ejpam-3228	290	21	(	(	PUNCT
ejpam-3228	290	22	xy)x−1	xy)x−1	NUM
ejpam-3228	290	23	)	)	PUNCT
ejpam-3228	290	24	=	=	SYM
ejpam-3228	290	25	fa(y	fa(y	NOUN
ejpam-3228	290	26	)	)	PUNCT
ejpam-3228	290	27	∀	∀	PUNCT
ejpam-3228	291	1	x	x	X
ejpam-3228	291	2	,	,	PUNCT
ejpam-3228	291	3	y	y	PROPN
ejpam-3228	291	4	∈	∈	PROPN
ejpam-3228	291	5	g.	g.	NOUN
ejpam-3228	291	6	in	in	ADP
ejpam-3228	291	7	other	other	ADJ
ejpam-3228	291	8	words	word	NOUN
ejpam-3228	291	9	a	a	PRON
ejpam-3228	291	10	is	be	AUX
ejpam-3228	291	11	a	a	DET
ejpam-3228	291	12	normal	normal	ADJ
ejpam-3228	291	13	soft	soft	ADJ
ejpam-3228	291	14	uni	uni	ADJ
ejpam-3228	291	15	-	-	PUNCT
ejpam-3228	291	16	ag	ag	NOUN
ejpam-3228	291	17	-	-	NOUN
ejpam-3228	291	18	subgroup	subgroup	NOUN
ejpam-3228	291	19	over	over	ADP
ejpam-3228	291	20	u	u	PROPN
ejpam-3228	291	21	,	,	PUNCT
ejpam-3228	291	22	if	if	SCONJ
ejpam-3228	291	23	a	a	PRON
ejpam-3228	291	24	is	be	AUX
ejpam-3228	291	25	self	self	NOUN
ejpam-3228	291	26	-	-	PUNCT
ejpam-3228	291	27	conjugate	conjugate	ADJ
ejpam-3228	291	28	soft	soft	ADJ
ejpam-3228	291	29	uni	uni	ADJ
ejpam-3228	291	30	-	-	PUNCT
ejpam-3228	291	31	ag	ag	NOUN
ejpam-3228	291	32	-	-	PUNCT
ejpam-3228	291	33	group	group	NOUN
ejpam-3228	291	34	.	.	PUNCT
ejpam-3228	292	1	a.	a.	PROPN
ejpam-3228	292	2	ullah	ullah	PROPN
ejpam-3228	292	3	,	,	PUNCT
ejpam-3228	292	4	f.	f.	PROPN
ejpam-3228	292	5	karaaslan	karaaslan	PROPN
ejpam-3228	292	6	,	,	PUNCT
ejpam-3228	292	7	i.	i.	PROPN
ejpam-3228	292	8	ahmad	ahmad	PROPN
ejpam-3228	292	9	/	/	SYM
ejpam-3228	292	10	eur	eur	PROPN
ejpam-3228	292	11	.	.	PUNCT
ejpam-3228	293	1	j.	j.	PROPN
ejpam-3228	293	2	pure	pure	PROPN
ejpam-3228	293	3	appl	appl	PROPN
ejpam-3228	293	4	.	.	PROPN
ejpam-3228	293	5	math	math	PROPN
ejpam-3228	293	6	,	,	PUNCT
ejpam-3228	293	7	11	11	NUM
ejpam-3228	293	8	(	(	PUNCT
ejpam-3228	293	9	2	2	NUM
ejpam-3228	293	10	)	)	PUNCT
ejpam-3228	293	11	(	(	PUNCT
ejpam-3228	293	12	2018	2018	NUM
ejpam-3228	293	13	)	)	PUNCT
ejpam-3228	293	14	,	,	PUNCT
ejpam-3228	293	15	517	517	NUM
ejpam-3228	293	16	-	-	SYM
ejpam-3228	293	17	536	536	NUM
ejpam-3228	293	18	530	530	NUM
ejpam-3228	293	19	the	the	DET
ejpam-3228	293	20	set	set	NOUN
ejpam-3228	293	21	of	of	ADP
ejpam-3228	293	22	all	all	DET
ejpam-3228	293	23	normal	normal	ADJ
ejpam-3228	293	24	soft	soft	ADJ
ejpam-3228	293	25	uni	uni	ADJ
ejpam-3228	293	26	-	-	PUNCT
ejpam-3228	293	27	ag	ag	NOUN
ejpam-3228	293	28	-	-	PUNCT
ejpam-3228	293	29	subgroups	subgroup	NOUN
ejpam-3228	293	30	over	over	ADP
ejpam-3228	293	31	u	u	NOUN
ejpam-3228	293	32	is	be	AUX
ejpam-3228	293	33	represented	represent	VERB
ejpam-3228	293	34	by	by	ADP
ejpam-3228	293	35	ns∪ag(u	ns∪ag(u	NUM
ejpam-3228	293	36	)	)	PUNCT
ejpam-3228	293	37	.	.	PUNCT
ejpam-3228	294	1	example	example	NOUN
ejpam-3228	295	1	9	9	NUM
ejpam-3228	295	2	.	.	PUNCT
ejpam-3228	296	1	let	let	VERB
ejpam-3228	296	2	g	g	PRON
ejpam-3228	296	3	be	be	AUX
ejpam-3228	296	4	an	an	DET
ejpam-3228	296	5	ag	ag	PROPN
ejpam-3228	296	6	-	-	PUNCT
ejpam-3228	296	7	group	group	NOUN
ejpam-3228	296	8	of	of	ADP
ejpam-3228	296	9	order	order	NOUN
ejpam-3228	296	10	6	6	NUM
ejpam-3228	296	11	defined	define	VERB
ejpam-3228	296	12	as	as	ADP
ejpam-3228	296	13	in	in	ADP
ejpam-3228	296	14	example	example	NOUN
ejpam-3228	296	15	8	8	NUM
ejpam-3228	296	16	.	.	PUNCT
ejpam-3228	297	1	let	let	VERB
ejpam-3228	297	2	a	a	DET
ejpam-3228	297	3	∈	∈	PROPN
ejpam-3228	297	4	s∪ag(z	s∪ag(z	NOUN
ejpam-3228	297	5	)	)	PUNCT
ejpam-3228	297	6	,	,	PUNCT
ejpam-3228	297	7	defined	define	VERB
ejpam-3228	297	8	by	by	ADP
ejpam-3228	297	9	fa(0	fa(0	NOUN
ejpam-3228	297	10	)	)	PUNCT
ejpam-3228	297	11	=	=	PRON
ejpam-3228	298	1	{	{	PUNCT
ejpam-3228	298	2	−1	−1	NOUN
ejpam-3228	298	3	,	,	PUNCT
ejpam-3228	298	4	0	0	NUM
ejpam-3228	298	5	,	,	PUNCT
ejpam-3228	298	6	1	1	NUM
ejpam-3228	298	7	}	}	PUNCT
ejpam-3228	298	8	=	=	SYM
ejpam-3228	298	9	fa(2	fa(2	NOUN
ejpam-3228	298	10	)	)	PUNCT
ejpam-3228	298	11	=	=	SYM
ejpam-3228	298	12	fa(4	fa(4	NOUN
ejpam-3228	298	13	)	)	PUNCT
ejpam-3228	298	14	,	,	PUNCT
ejpam-3228	298	15	fa(1	fa(1	NOUN
ejpam-3228	298	16	)	)	PUNCT
ejpam-3228	298	17	=	=	PRON
ejpam-3228	298	18	{	{	PUNCT
ejpam-3228	298	19	−2,−1	−2,−1	PROPN
ejpam-3228	298	20	,	,	PUNCT
ejpam-3228	298	21	0	0	NUM
ejpam-3228	298	22	,	,	PUNCT
ejpam-3228	298	23	1	1	NUM
ejpam-3228	298	24	,	,	PUNCT
ejpam-3228	298	25	2	2	NUM
ejpam-3228	298	26	}	}	PUNCT
ejpam-3228	298	27	=	=	SYM
ejpam-3228	298	28	fa(3	fa(3	NOUN
ejpam-3228	298	29	)	)	PUNCT
ejpam-3228	298	30	=	=	SYM
ejpam-3228	298	31	fa(5	fa(5	PROPN
ejpam-3228	298	32	)	)	PUNCT
ejpam-3228	298	33	.	.	PUNCT
ejpam-3228	299	1	the	the	DET
ejpam-3228	299	2	conjugates	conjugate	NOUN
ejpam-3228	299	3	soft	soft	ADJ
ejpam-3228	299	4	uni	uni	ADJ
ejpam-3228	299	5	-	-	PUNCT
ejpam-3228	299	6	ag	ag	NOUN
ejpam-3228	299	7	-	-	PUNCT
ejpam-3228	299	8	groups	group	NOUN
ejpam-3228	299	9	of	of	ADP
ejpam-3228	299	10	a	a	PRON
ejpam-3228	299	11	are	be	AUX
ejpam-3228	299	12	given	give	VERB
ejpam-3228	299	13	by	by	ADP
ejpam-3228	299	14	:	:	PUNCT
ejpam-3228	299	15	fa0(0	fa0(0	ADJ
ejpam-3228	299	16	)	)	PUNCT
ejpam-3228	299	17	=	=	SYM
ejpam-3228	299	18	fa3(0	fa3(0	NOUN
ejpam-3228	299	19	)	)	PUNCT
ejpam-3228	299	20	=	=	SYM
ejpam-3228	299	21	fa(0	fa(0	X
ejpam-3228	299	22	)	)	PUNCT
ejpam-3228	299	23	=	=	PRON
ejpam-3228	299	24	{	{	PUNCT
ejpam-3228	299	25	−1	−1	NOUN
ejpam-3228	299	26	,	,	PUNCT
ejpam-3228	299	27	0	0	NUM
ejpam-3228	299	28	,	,	PUNCT
ejpam-3228	299	29	1	1	NUM
ejpam-3228	299	30	}	}	PUNCT
ejpam-3228	299	31	,	,	PUNCT
ejpam-3228	299	32	fa0(1	fa0(1	X
ejpam-3228	299	33	)	)	PUNCT
ejpam-3228	299	34	=	=	SYM
ejpam-3228	299	35	fa3(1	fa3(1	ADJ
ejpam-3228	299	36	)	)	PUNCT
ejpam-3228	299	37	=	=	SYM
ejpam-3228	299	38	fa(5	fa(5	PROPN
ejpam-3228	299	39	)	)	PUNCT
ejpam-3228	299	40	=	=	NOUN
ejpam-3228	299	41	{	{	PUNCT
ejpam-3228	299	42	−2,−1	−2,−1	PROPN
ejpam-3228	299	43	,	,	PUNCT
ejpam-3228	299	44	0	0	NUM
ejpam-3228	299	45	,	,	PUNCT
ejpam-3228	299	46	1	1	NUM
ejpam-3228	299	47	,	,	PUNCT
ejpam-3228	299	48	2	2	NUM
ejpam-3228	299	49	}	}	PUNCT
ejpam-3228	299	50	,	,	PUNCT
ejpam-3228	299	51	fa0(2	fa0(2	ADJ
ejpam-3228	299	52	)	)	PUNCT
ejpam-3228	299	53	=	=	SYM
ejpam-3228	299	54	fa3(2	fa3(2	NOUN
ejpam-3228	299	55	)	)	PUNCT
ejpam-3228	299	56	=	=	SYM
ejpam-3228	299	57	fa(4	fa(4	NOUN
ejpam-3228	299	58	)	)	PUNCT
ejpam-3228	299	59	=	=	PRON
ejpam-3228	299	60	{	{	PUNCT
ejpam-3228	299	61	−1	−1	NOUN
ejpam-3228	299	62	,	,	PUNCT
ejpam-3228	299	63	0	0	NUM
ejpam-3228	299	64	,	,	PUNCT
ejpam-3228	299	65	1	1	NUM
ejpam-3228	299	66	}	}	PUNCT
ejpam-3228	299	67	,	,	PUNCT
ejpam-3228	299	68	fa0(3	fa0(3	NOUN
ejpam-3228	299	69	)	)	PUNCT
ejpam-3228	299	70	=	=	SYM
ejpam-3228	299	71	fa3(3	fa3(3	ADJ
ejpam-3228	299	72	)	)	PUNCT
ejpam-3228	299	73	=	=	SYM
ejpam-3228	299	74	fa(3	fa(3	NOUN
ejpam-3228	299	75	)	)	PUNCT
ejpam-3228	299	76	=	=	PRON
ejpam-3228	299	77	{	{	PUNCT
ejpam-3228	299	78	−2,−1	−2,−1	PROPN
ejpam-3228	299	79	,	,	PUNCT
ejpam-3228	299	80	0	0	NUM
ejpam-3228	299	81	,	,	PUNCT
ejpam-3228	299	82	1	1	NUM
ejpam-3228	299	83	,	,	PUNCT
ejpam-3228	299	84	2	2	NUM
ejpam-3228	299	85	}	}	PUNCT
ejpam-3228	299	86	,	,	PUNCT
ejpam-3228	299	87	fa0(4	fa0(4	ADJ
ejpam-3228	299	88	)	)	PUNCT
ejpam-3228	299	89	=	=	SYM
ejpam-3228	299	90	fa3(4	fa3(4	NOUN
ejpam-3228	299	91	)	)	PUNCT
ejpam-3228	299	92	=	=	SYM
ejpam-3228	299	93	fa(2	fa(2	NOUN
ejpam-3228	299	94	)	)	PUNCT
ejpam-3228	299	95	=	=	PRON
ejpam-3228	299	96	{	{	PUNCT
ejpam-3228	299	97	−1	−1	NOUN
ejpam-3228	299	98	,	,	PUNCT
ejpam-3228	299	99	0	0	NUM
ejpam-3228	299	100	,	,	PUNCT
ejpam-3228	299	101	1	1	NUM
ejpam-3228	299	102	}	}	PUNCT
ejpam-3228	299	103	,	,	PUNCT
ejpam-3228	299	104	fa0(5	fa0(5	PROPN
ejpam-3228	299	105	)	)	PUNCT
ejpam-3228	299	106	=	=	SYM
ejpam-3228	299	107	fa3(5	fa3(5	X
ejpam-3228	299	108	)	)	PUNCT
ejpam-3228	299	109	=	=	SYM
ejpam-3228	300	1	fa(1	fa(1	NOUN
ejpam-3228	300	2	)	)	PUNCT
ejpam-3228	300	3	=	=	PRON
ejpam-3228	300	4	{	{	PUNCT
ejpam-3228	300	5	−2,−1	−2,−1	PROPN
ejpam-3228	300	6	,	,	PUNCT
ejpam-3228	300	7	0	0	NUM
ejpam-3228	300	8	,	,	PUNCT
ejpam-3228	300	9	1	1	NUM
ejpam-3228	300	10	,	,	PUNCT
ejpam-3228	300	11	2	2	NUM
ejpam-3228	300	12	}	}	PUNCT
ejpam-3228	300	13	.	.	PUNCT
ejpam-3228	301	1	fa1(0	fa1(0	X
ejpam-3228	301	2	)	)	PUNCT
ejpam-3228	301	3	=	=	SYM
ejpam-3228	301	4	fa4(0	fa4(0	NOUN
ejpam-3228	301	5	)	)	PUNCT
ejpam-3228	301	6	=	=	SYM
ejpam-3228	301	7	fa(2	fa(2	NOUN
ejpam-3228	301	8	)	)	PUNCT
ejpam-3228	301	9	=	=	PRON
ejpam-3228	301	10	{	{	PUNCT
ejpam-3228	301	11	−1	−1	NOUN
ejpam-3228	301	12	,	,	PUNCT
ejpam-3228	301	13	0	0	NUM
ejpam-3228	301	14	,	,	PUNCT
ejpam-3228	301	15	1	1	NUM
ejpam-3228	301	16	}	}	PUNCT
ejpam-3228	301	17	,	,	PUNCT
ejpam-3228	301	18	fa1(1	fa1(1	ADJ
ejpam-3228	301	19	)	)	PUNCT
ejpam-3228	301	20	=	=	SYM
ejpam-3228	301	21	fa4(1	fa4(1	X
ejpam-3228	301	22	)	)	PUNCT
ejpam-3228	301	23	=	=	SYM
ejpam-3228	301	24	fa(1	fa(1	NOUN
ejpam-3228	301	25	)	)	PUNCT
ejpam-3228	301	26	=	=	PRON
ejpam-3228	301	27	{	{	PUNCT
ejpam-3228	301	28	−2,−1	−2,−1	PROPN
ejpam-3228	301	29	,	,	PUNCT
ejpam-3228	301	30	0	0	NUM
ejpam-3228	301	31	,	,	PUNCT
ejpam-3228	301	32	1	1	NUM
ejpam-3228	301	33	,	,	PUNCT
ejpam-3228	301	34	2	2	NUM
ejpam-3228	301	35	}	}	PUNCT
ejpam-3228	301	36	,	,	PUNCT
ejpam-3228	301	37	fa1(2	fa1(2	ADJ
ejpam-3228	301	38	)	)	PUNCT
ejpam-3228	301	39	=	=	SYM
ejpam-3228	301	40	fa4(2	fa4(2	NOUN
ejpam-3228	301	41	)	)	PUNCT
ejpam-3228	301	42	=	=	SYM
ejpam-3228	302	1	fa(0	fa(0	X
ejpam-3228	302	2	)	)	PUNCT
ejpam-3228	302	3	=	=	PRON
ejpam-3228	302	4	{	{	PUNCT
ejpam-3228	302	5	−1	−1	NOUN
ejpam-3228	302	6	,	,	PUNCT
ejpam-3228	302	7	0	0	NUM
ejpam-3228	302	8	,	,	PUNCT
ejpam-3228	302	9	1	1	NUM
ejpam-3228	302	10	}	}	PUNCT
ejpam-3228	302	11	,	,	PUNCT
ejpam-3228	302	12	fa1(3	fa1(3	ADJ
ejpam-3228	302	13	)	)	PUNCT
ejpam-3228	302	14	=	=	SYM
ejpam-3228	302	15	fa4(3	fa4(3	NOUN
ejpam-3228	302	16	)	)	PUNCT
ejpam-3228	302	17	=	=	SYM
ejpam-3228	302	18	fa(5	fa(5	PROPN
ejpam-3228	302	19	)	)	PUNCT
ejpam-3228	302	20	=	=	NOUN
ejpam-3228	302	21	{	{	PUNCT
ejpam-3228	302	22	−2,−1	−2,−1	PROPN
ejpam-3228	302	23	,	,	PUNCT
ejpam-3228	302	24	0	0	NUM
ejpam-3228	302	25	,	,	PUNCT
ejpam-3228	302	26	1	1	NUM
ejpam-3228	302	27	,	,	PUNCT
ejpam-3228	302	28	2	2	NUM
ejpam-3228	302	29	}	}	PUNCT
ejpam-3228	302	30	,	,	PUNCT
ejpam-3228	302	31	fa1(4	fa1(4	X
ejpam-3228	302	32	)	)	PUNCT
ejpam-3228	302	33	=	=	SYM
ejpam-3228	302	34	fa4(4	fa4(4	NOUN
ejpam-3228	302	35	)	)	PUNCT
ejpam-3228	302	36	=	=	SYM
ejpam-3228	302	37	fa(4	fa(4	NOUN
ejpam-3228	302	38	)	)	PUNCT
ejpam-3228	302	39	=	=	PRON
ejpam-3228	302	40	{	{	PUNCT
ejpam-3228	302	41	−1	−1	NOUN
ejpam-3228	302	42	,	,	PUNCT
ejpam-3228	302	43	0	0	NUM
ejpam-3228	302	44	,	,	PUNCT
ejpam-3228	302	45	1	1	NUM
ejpam-3228	302	46	}	}	PUNCT
ejpam-3228	302	47	,	,	PUNCT
ejpam-3228	302	48	fa1(5	fa1(5	NUM
ejpam-3228	302	49	)	)	PUNCT
ejpam-3228	302	50	=	=	SYM
ejpam-3228	302	51	fa4(5	fa4(5	NUM
ejpam-3228	302	52	)	)	PUNCT
ejpam-3228	303	1	=	=	SYM
ejpam-3228	303	2	fa(3	fa(3	NOUN
ejpam-3228	303	3	)	)	PUNCT
ejpam-3228	303	4	=	=	PRON
ejpam-3228	303	5	{	{	PUNCT
ejpam-3228	303	6	−2,−1	−2,−1	PROPN
ejpam-3228	303	7	,	,	PUNCT
ejpam-3228	303	8	0	0	NUM
ejpam-3228	303	9	,	,	PUNCT
ejpam-3228	303	10	1	1	NUM
ejpam-3228	303	11	,	,	PUNCT
ejpam-3228	303	12	2	2	NUM
ejpam-3228	303	13	}	}	PUNCT
ejpam-3228	303	14	.	.	PUNCT
ejpam-3228	304	1	fa2(0	fa2(0	NOUN
ejpam-3228	304	2	)	)	PUNCT
ejpam-3228	304	3	=	=	SYM
ejpam-3228	304	4	fa5(0	fa5(0	X
ejpam-3228	304	5	)	)	PUNCT
ejpam-3228	304	6	=	=	SYM
ejpam-3228	304	7	fa(4	fa(4	NOUN
ejpam-3228	304	8	)	)	PUNCT
ejpam-3228	304	9	=	=	PRON
ejpam-3228	304	10	{	{	PUNCT
ejpam-3228	304	11	−1	−1	NOUN
ejpam-3228	304	12	,	,	PUNCT
ejpam-3228	304	13	0	0	NUM
ejpam-3228	304	14	,	,	PUNCT
ejpam-3228	304	15	1	1	NUM
ejpam-3228	304	16	}	}	PUNCT
ejpam-3228	304	17	,	,	PUNCT
ejpam-3228	304	18	fa2(1	fa2(1	NOUN
ejpam-3228	304	19	)	)	PUNCT
ejpam-3228	304	20	=	=	SYM
ejpam-3228	304	21	fa5(1	fa5(1	NOUN
ejpam-3228	304	22	)	)	PUNCT
ejpam-3228	304	23	=	=	SYM
ejpam-3228	304	24	fa(3	fa(3	NOUN
ejpam-3228	304	25	)	)	PUNCT
ejpam-3228	304	26	=	=	PRON
ejpam-3228	304	27	{	{	PUNCT
ejpam-3228	304	28	−2,−1	−2,−1	PROPN
ejpam-3228	304	29	,	,	PUNCT
ejpam-3228	304	30	0	0	NUM
ejpam-3228	304	31	,	,	PUNCT
ejpam-3228	304	32	1	1	NUM
ejpam-3228	304	33	,	,	PUNCT
ejpam-3228	304	34	2	2	NUM
ejpam-3228	304	35	}	}	PUNCT
ejpam-3228	304	36	,	,	PUNCT
ejpam-3228	304	37	fa2(2	fa2(2	INTJ
ejpam-3228	304	38	)	)	PUNCT
ejpam-3228	304	39	=	=	SYM
ejpam-3228	304	40	fa5(2	fa5(2	NOUN
ejpam-3228	304	41	)	)	PUNCT
ejpam-3228	304	42	=	=	SYM
ejpam-3228	304	43	fa(2	fa(2	NOUN
ejpam-3228	304	44	)	)	PUNCT
ejpam-3228	304	45	=	=	PRON
ejpam-3228	304	46	{	{	PUNCT
ejpam-3228	304	47	−1	−1	NOUN
ejpam-3228	304	48	,	,	PUNCT
ejpam-3228	304	49	0	0	NUM
ejpam-3228	304	50	,	,	PUNCT
ejpam-3228	304	51	1	1	NUM
ejpam-3228	304	52	}	}	PUNCT
ejpam-3228	304	53	,	,	PUNCT
ejpam-3228	304	54	fa2(3	fa2(3	NOUN
ejpam-3228	304	55	)	)	PUNCT
ejpam-3228	304	56	=	=	PUNCT
ejpam-3228	304	57	fa5(3	fa5(3	NOUN
ejpam-3228	304	58	)	)	PUNCT
ejpam-3228	304	59	=	=	SYM
ejpam-3228	305	1	fa(1	fa(1	NOUN
ejpam-3228	305	2	)	)	PUNCT
ejpam-3228	305	3	=	=	PRON
ejpam-3228	305	4	{	{	PUNCT
ejpam-3228	305	5	−2,−1	−2,−1	PROPN
ejpam-3228	305	6	,	,	PUNCT
ejpam-3228	305	7	0	0	NUM
ejpam-3228	305	8	,	,	PUNCT
ejpam-3228	305	9	1	1	NUM
ejpam-3228	305	10	,	,	PUNCT
ejpam-3228	305	11	2	2	NUM
ejpam-3228	305	12	}	}	PUNCT
ejpam-3228	305	13	,	,	PUNCT
ejpam-3228	305	14	fa2(4	fa2(4	NOUN
ejpam-3228	305	15	)	)	PUNCT
ejpam-3228	305	16	=	=	SYM
ejpam-3228	305	17	fa5(4	fa5(4	NOUN
ejpam-3228	305	18	)	)	PUNCT
ejpam-3228	305	19	=	=	SYM
ejpam-3228	306	1	fa(0	fa(0	X
ejpam-3228	306	2	)	)	PUNCT
ejpam-3228	306	3	=	=	PRON
ejpam-3228	306	4	{	{	PUNCT
ejpam-3228	306	5	−1	−1	NOUN
ejpam-3228	306	6	,	,	PUNCT
ejpam-3228	306	7	0	0	NUM
ejpam-3228	306	8	,	,	PUNCT
ejpam-3228	306	9	1	1	NUM
ejpam-3228	306	10	}	}	PUNCT
ejpam-3228	306	11	,	,	PUNCT
ejpam-3228	306	12	fa2(5	fa2(5	NOUN
ejpam-3228	306	13	)	)	PUNCT
ejpam-3228	306	14	=	=	SYM
ejpam-3228	306	15	fa5(5	fa5(5	NOUN
ejpam-3228	306	16	)	)	PUNCT
ejpam-3228	306	17	=	=	SYM
ejpam-3228	306	18	fa(5	fa(5	PROPN
ejpam-3228	306	19	)	)	PUNCT
ejpam-3228	306	20	=	=	NOUN
ejpam-3228	306	21	{	{	PUNCT
ejpam-3228	306	22	−2,−1	−2,−1	PROPN
ejpam-3228	306	23	,	,	PUNCT
ejpam-3228	306	24	0	0	NUM
ejpam-3228	306	25	,	,	PUNCT
ejpam-3228	306	26	1	1	NUM
ejpam-3228	306	27	,	,	PUNCT
ejpam-3228	306	28	2	2	NUM
ejpam-3228	306	29	}	}	PUNCT
ejpam-3228	306	30	.	.	PUNCT
ejpam-3228	307	1	hence	hence	ADV
ejpam-3228	307	2	,	,	PUNCT
ejpam-3228	307	3	a	a	DET
ejpam-3228	307	4	∈	∈	PROPN
ejpam-3228	307	5	ns∪ag(z	ns∪ag(z	PROPN
ejpam-3228	307	6	)	)	PUNCT
ejpam-3228	307	7	,	,	PUNCT
ejpam-3228	307	8	as	as	SCONJ
ejpam-3228	307	9	a	a	PRON
ejpam-3228	307	10	is	be	AUX
ejpam-3228	307	11	self	self	NOUN
ejpam-3228	307	12	conjugate	conjugate	ADJ
ejpam-3228	307	13	soft	soft	ADJ
ejpam-3228	307	14	uni	uni	ADJ
ejpam-3228	307	15	-	-	PUNCT
ejpam-3228	307	16	ag	ag	ADJ
ejpam-3228	307	17	-	-	PUNCT
ejpam-3228	307	18	subgroup	subgroup	NOUN
ejpam-3228	307	19	.	.	PUNCT
ejpam-3228	308	1	lemma	lemma	PROPN
ejpam-3228	308	2	6	6	NUM
ejpam-3228	308	3	.	.	PUNCT
ejpam-3228	309	1	let	let	VERB
ejpam-3228	309	2	a	a	DET
ejpam-3228	309	3	∈	∈	PROPN
ejpam-3228	309	4	ns∪ag(u	ns∪ag(u	NUM
ejpam-3228	309	5	)	)	PUNCT
ejpam-3228	309	6	.	.	PUNCT
ejpam-3228	310	1	then	then	ADV
ejpam-3228	310	2	for	for	ADP
ejpam-3228	310	3	all	all	DET
ejpam-3228	310	4	x	x	NOUN
ejpam-3228	310	5	,	,	PUNCT
ejpam-3228	310	6	y	y	PROPN
ejpam-3228	310	7	∈	∈	PROPN
ejpam-3228	310	8	g	g	PROPN
ejpam-3228	310	9	,	,	PUNCT
ejpam-3228	310	10	the	the	DET
ejpam-3228	310	11	following	follow	VERB
ejpam-3228	310	12	assertions	assertion	NOUN
ejpam-3228	310	13	are	be	AUX
ejpam-3228	310	14	equivalent	equivalent	ADJ
ejpam-3228	310	15	:	:	PUNCT
ejpam-3228	310	16	1	1	X
ejpam-3228	310	17	.	.	X
ejpam-3228	310	18	fa	fa	INTJ
ejpam-3228	310	19	(	(	PUNCT
ejpam-3228	310	20	(	(	PUNCT
ejpam-3228	310	21	xy)x−1	xy)x−1	NUM
ejpam-3228	310	22	)	)	PUNCT
ejpam-3228	310	23	=	=	SYM
ejpam-3228	310	24	fa(y	fa(y	PROPN
ejpam-3228	310	25	)	)	PUNCT
ejpam-3228	310	26	,	,	PUNCT
ejpam-3228	311	1	2	2	X
ejpam-3228	311	2	.	.	X
ejpam-3228	311	3	fa	fa	INTJ
ejpam-3228	312	1	(	(	PUNCT
ejpam-3228	312	2	(	(	PUNCT
ejpam-3228	312	3	xy)x−1	xy)x−1	NUM
ejpam-3228	312	4	)	)	PUNCT
ejpam-3228	312	5	⊇	⊇	PROPN
ejpam-3228	312	6	fa(y	fa(y	PROPN
ejpam-3228	312	7	)	)	PUNCT
ejpam-3228	312	8	,	,	PUNCT
ejpam-3228	312	9	3	3	X
ejpam-3228	312	10	.	.	X
ejpam-3228	312	11	fa	fa	INTJ
ejpam-3228	313	1	(	(	PUNCT
ejpam-3228	313	2	(	(	PUNCT
ejpam-3228	313	3	xy)x−1	xy)x−1	NUM
ejpam-3228	313	4	)	)	PUNCT
ejpam-3228	313	5	⊆	⊆	NUM
ejpam-3228	313	6	fa(y	fa(y	NOUN
ejpam-3228	313	7	)	)	PUNCT
ejpam-3228	313	8	.	.	PUNCT
ejpam-3228	314	1	a.	a.	PROPN
ejpam-3228	314	2	ullah	ullah	PROPN
ejpam-3228	314	3	,	,	PUNCT
ejpam-3228	314	4	f.	f.	PROPN
ejpam-3228	314	5	karaaslan	karaaslan	PROPN
ejpam-3228	314	6	,	,	PUNCT
ejpam-3228	314	7	i.	i.	PROPN
ejpam-3228	314	8	ahmad	ahmad	PROPN
ejpam-3228	314	9	/	/	SYM
ejpam-3228	314	10	eur	eur	PROPN
ejpam-3228	314	11	.	.	PUNCT
ejpam-3228	315	1	j.	j.	PROPN
ejpam-3228	315	2	pure	pure	PROPN
ejpam-3228	315	3	appl	appl	PROPN
ejpam-3228	315	4	.	.	PROPN
ejpam-3228	315	5	math	math	PROPN
ejpam-3228	315	6	,	,	PUNCT
ejpam-3228	315	7	11	11	NUM
ejpam-3228	315	8	(	(	PUNCT
ejpam-3228	315	9	2	2	NUM
ejpam-3228	315	10	)	)	PUNCT
ejpam-3228	315	11	(	(	PUNCT
ejpam-3228	315	12	2018	2018	NUM
ejpam-3228	315	13	)	)	PUNCT
ejpam-3228	315	14	,	,	PUNCT
ejpam-3228	315	15	517	517	NUM
ejpam-3228	315	16	-	-	SYM
ejpam-3228	315	17	536	536	NUM
ejpam-3228	315	18	531	531	NUM
ejpam-3228	315	19	proof	proof	NOUN
ejpam-3228	315	20	.	.	PUNCT
ejpam-3228	316	1	(	(	PUNCT
ejpam-3228	316	2	i)⇒	i)⇒	PROPN
ejpam-3228	316	3	(	(	PUNCT
ejpam-3228	316	4	ii	ii	NOUN
ejpam-3228	316	5	):	):	PUNCT
ejpam-3228	316	6	obvious	obvious	ADJ
ejpam-3228	316	7	.	.	PUNCT
ejpam-3228	317	1	(	(	PUNCT
ejpam-3228	317	2	ii)⇒	ii)⇒	X
ejpam-3228	317	3	(	(	PUNCT
ejpam-3228	317	4	iii	iii	NOUN
ejpam-3228	317	5	):	):	PUNCT
ejpam-3228	317	6	assume	assume	VERB
ejpam-3228	317	7	that	that	SCONJ
ejpam-3228	317	8	(	(	PUNCT
ejpam-3228	317	9	ii	ii	NOUN
ejpam-3228	317	10	)	)	PUNCT
ejpam-3228	317	11	holds	hold	VERB
ejpam-3228	317	12	.	.	PUNCT
ejpam-3228	318	1	consider	consider	VERB
ejpam-3228	318	2	fa	fa	PROPN
ejpam-3228	318	3	(	(	PUNCT
ejpam-3228	318	4	(	(	PUNCT
ejpam-3228	318	5	xy)x−1	xy)x−1	X
ejpam-3228	318	6	)	)	PUNCT
ejpam-3228	319	1	⊆	⊆	NUM
ejpam-3228	319	2	fa	fa	INTJ
ejpam-3228	319	3	(	(	PUNCT
ejpam-3228	319	4	(	(	PUNCT
ejpam-3228	319	5	x−1	x−1	NOUN
ejpam-3228	319	6	(	(	PUNCT
ejpam-3228	319	7	(	(	PUNCT
ejpam-3228	319	8	xy)x−1	xy)x−1	NUM
ejpam-3228	319	9	)	)	PUNCT
ejpam-3228	319	10	)	)	PUNCT
ejpam-3228	319	11	(	(	PUNCT
ejpam-3228	319	12	(	(	PUNCT
ejpam-3228	319	13	x−1)−1	x−1)−1	NOUN
ejpam-3228	319	14	)	)	PUNCT
ejpam-3228	319	15	)	)	PUNCT
ejpam-3228	320	1	=	=	SYM
ejpam-3228	320	2	fa	fa	INTJ
ejpam-3228	320	3	(	(	PUNCT
ejpam-3228	320	4	(	(	PUNCT
ejpam-3228	320	5	x−1	x−1	X
ejpam-3228	320	6	(	(	PUNCT
ejpam-3228	320	7	(	(	PUNCT
ejpam-3228	320	8	xy)x−1	xy)x−1	NUM
ejpam-3228	320	9	)	)	PUNCT
ejpam-3228	320	10	)	)	PUNCT
ejpam-3228	320	11	x	x	X
ejpam-3228	320	12	)	)	PUNCT
ejpam-3228	321	1	=	=	SYM
ejpam-3228	321	2	fa	fa	INTJ
ejpam-3228	321	3	(	(	PUNCT
ejpam-3228	321	4	(	(	PUNCT
ejpam-3228	321	5	x	x	SYM
ejpam-3228	321	6	(	(	PUNCT
ejpam-3228	321	7	(	(	PUNCT
ejpam-3228	321	8	xy)x−1	xy)x−1	NUM
ejpam-3228	321	9	)	)	PUNCT
ejpam-3228	321	10	)	)	PUNCT
ejpam-3228	322	1	x−1	x−1	PROPN
ejpam-3228	322	2	)	)	PUNCT
ejpam-3228	322	3	(	(	PUNCT
ejpam-3228	322	4	by	by	ADP
ejpam-3228	322	5	the	the	DET
ejpam-3228	322	6	left	left	ADJ
ejpam-3228	322	7	invertive	invertive	ADJ
ejpam-3228	322	8	law	law	NOUN
ejpam-3228	322	9	)	)	PUNCT
ejpam-3228	322	10	=	=	SYM
ejpam-3228	322	11	fa	fa	INTJ
ejpam-3228	322	12	(	(	PUNCT
ejpam-3228	322	13	(	(	PUNCT
ejpam-3228	322	14	(	(	PUNCT
ejpam-3228	322	15	xy	xy	NOUN
ejpam-3228	322	16	)	)	PUNCT
ejpam-3228	322	17	(	(	PUNCT
ejpam-3228	322	18	xx−1	xx−1	PROPN
ejpam-3228	322	19	)	)	PUNCT
ejpam-3228	322	20	)	)	PUNCT
ejpam-3228	323	1	x−1	x−1	PROPN
ejpam-3228	323	2	)	)	PUNCT
ejpam-3228	323	3	(	(	PUNCT
ejpam-3228	323	4	by	by	ADP
ejpam-3228	323	5	lemma	lemma	PROPN
ejpam-3228	323	6	1-(ii	1-(ii	NUM
ejpam-3228	323	7	)	)	PUNCT
ejpam-3228	323	8	)	)	PUNCT
ejpam-3228	324	1	=	=	SYM
ejpam-3228	324	2	fa	fa	INTJ
ejpam-3228	324	3	(	(	PUNCT
ejpam-3228	324	4	(	(	PUNCT
ejpam-3228	324	5	(	(	PUNCT
ejpam-3228	324	6	xy	xy	NOUN
ejpam-3228	324	7	)	)	PUNCT
ejpam-3228	324	8	e)x−1	e)x−1	NOUN
ejpam-3228	324	9	)	)	PUNCT
ejpam-3228	325	1	=	=	SYM
ejpam-3228	325	2	fa	fa	INTJ
ejpam-3228	325	3	(	(	PUNCT
ejpam-3228	325	4	(	(	PUNCT
ejpam-3228	325	5	(	(	PUNCT
ejpam-3228	325	6	ey)x)x−1	ey)x)x−1	NOUN
ejpam-3228	325	7	)	)	PUNCT
ejpam-3228	325	8	(	(	PUNCT
ejpam-3228	325	9	by	by	ADP
ejpam-3228	325	10	the	the	DET
ejpam-3228	325	11	left	left	ADJ
ejpam-3228	325	12	invertive	invertive	ADJ
ejpam-3228	325	13	law	law	NOUN
ejpam-3228	325	14	)	)	PUNCT
ejpam-3228	326	1	=	=	SYM
ejpam-3228	326	2	fa	fa	INTJ
ejpam-3228	326	3	(	(	PUNCT
ejpam-3228	326	4	(	(	PUNCT
ejpam-3228	326	5	yx)x−1	yx)x−1	X
ejpam-3228	326	6	)	)	PUNCT
ejpam-3228	327	1	=	=	SYM
ejpam-3228	327	2	fa	fa	INTJ
ejpam-3228	327	3	(	(	PUNCT
ejpam-3228	327	4	(	(	PUNCT
ejpam-3228	327	5	x−1x	x−1x	NOUN
ejpam-3228	327	6	)	)	PUNCT
ejpam-3228	327	7	y	y	PROPN
ejpam-3228	327	8	)	)	PUNCT
ejpam-3228	327	9	(	(	PUNCT
ejpam-3228	327	10	by	by	ADP
ejpam-3228	327	11	the	the	DET
ejpam-3228	327	12	left	left	ADJ
ejpam-3228	327	13	invertive	invertive	ADJ
ejpam-3228	327	14	law	law	NOUN
ejpam-3228	327	15	)	)	PUNCT
ejpam-3228	328	1	=	=	SYM
ejpam-3228	328	2	fa	fa	X
ejpam-3228	328	3	(	(	PUNCT
ejpam-3228	328	4	ey	ey	PROPN
ejpam-3228	328	5	)	)	PUNCT
ejpam-3228	328	6	=	=	SYM
ejpam-3228	328	7	fa(y	fa(y	NOUN
ejpam-3228	328	8	)	)	PUNCT
ejpam-3228	328	9	⇒	⇒	NOUN
ejpam-3228	328	10	fa	fa	X
ejpam-3228	329	1	(	(	PUNCT
ejpam-3228	329	2	(	(	PUNCT
ejpam-3228	329	3	xy)x−1	xy)x−1	NUM
ejpam-3228	329	4	)	)	PUNCT
ejpam-3228	329	5	⊆	⊆	NUM
ejpam-3228	329	6	fa(y	fa(y	NOUN
ejpam-3228	329	7	)	)	PUNCT
ejpam-3228	329	8	∀	∀	PUNCT
ejpam-3228	330	1	x	x	X
ejpam-3228	330	2	,	,	PUNCT
ejpam-3228	330	3	y	y	PROPN
ejpam-3228	330	4	∈	∈	PROPN
ejpam-3228	330	5	g.	g.	NOUN
ejpam-3228	330	6	(	(	PUNCT
ejpam-3228	330	7	iii)⇒	iii)⇒	PROPN
ejpam-3228	330	8	(	(	PUNCT
ejpam-3228	330	9	i	i	NOUN
ejpam-3228	330	10	):	):	PUNCT
ejpam-3228	330	11	assume	assume	VERB
ejpam-3228	330	12	that	that	SCONJ
ejpam-3228	330	13	(	(	PUNCT
ejpam-3228	330	14	iii	iii	NOUN
ejpam-3228	330	15	)	)	PUNCT
ejpam-3228	330	16	holds	hold	VERB
ejpam-3228	330	17	.	.	PUNCT
ejpam-3228	331	1	consider	consider	VERB
ejpam-3228	331	2	,	,	PUNCT
ejpam-3228	331	3	fa	fa	INTJ
ejpam-3228	331	4	(	(	PUNCT
ejpam-3228	331	5	(	(	PUNCT
ejpam-3228	331	6	xy)x−1	xy)x−1	NUM
ejpam-3228	331	7	)	)	PUNCT
ejpam-3228	331	8	⊇	⊇	PROPN
ejpam-3228	331	9	fa	fa	PROPN
ejpam-3228	331	10	(	(	PUNCT
ejpam-3228	331	11	(	(	PUNCT
ejpam-3228	331	12	x−1	x−1	NOUN
ejpam-3228	331	13	(	(	PUNCT
ejpam-3228	331	14	(	(	PUNCT
ejpam-3228	331	15	xy)x−1	xy)x−1	NUM
ejpam-3228	331	16	)	)	PUNCT
ejpam-3228	331	17	)	)	PUNCT
ejpam-3228	331	18	(	(	PUNCT
ejpam-3228	331	19	(	(	PUNCT
ejpam-3228	331	20	x−1	x−1	NOUN
ejpam-3228	331	21	)	)	PUNCT
ejpam-3228	331	22	−1	−1	NOUN
ejpam-3228	331	23	)	)	PUNCT
ejpam-3228	331	24	)	)	PUNCT
ejpam-3228	332	1	=	=	SYM
ejpam-3228	332	2	fa(y	fa(y	PROPN
ejpam-3228	332	3	)	)	PUNCT
ejpam-3228	332	4	,	,	PUNCT
ejpam-3228	332	5	as	as	ADP
ejpam-3228	332	6	in	in	ADP
ejpam-3228	332	7	the	the	DET
ejpam-3228	332	8	proof	proof	NOUN
ejpam-3228	332	9	(	(	PUNCT
ejpam-3228	332	10	ii)⇒	ii)⇒	X
ejpam-3228	332	11	(	(	PUNCT
ejpam-3228	332	12	iii	iii	NOUN
ejpam-3228	332	13	)	)	PUNCT
ejpam-3228	332	14	⇒	⇒	NOUN
ejpam-3228	332	15	fa	fa	X
ejpam-3228	332	16	(	(	PUNCT
ejpam-3228	332	17	(	(	PUNCT
ejpam-3228	332	18	xy)x−1	xy)x−1	NUM
ejpam-3228	332	19	)	)	PUNCT
ejpam-3228	332	20	⊇	⊇	PROPN
ejpam-3228	332	21	fa(y	fa(y	PROPN
ejpam-3228	332	22	)	)	PUNCT
ejpam-3228	332	23	∀	∀	PUNCT
ejpam-3228	333	1	x	x	X
ejpam-3228	333	2	,	,	PUNCT
ejpam-3228	333	3	y	y	PROPN
ejpam-3228	333	4	∈	∈	PROPN
ejpam-3228	333	5	g.	g.	PROPN
ejpam-3228	333	6	consequently	consequently	ADV
ejpam-3228	333	7	,	,	PUNCT
ejpam-3228	333	8	fa	fa	PROPN
ejpam-3228	333	9	(	(	PUNCT
ejpam-3228	333	10	(	(	PUNCT
ejpam-3228	333	11	xy)x−1	xy)x−1	NUM
ejpam-3228	333	12	)	)	PUNCT
ejpam-3228	333	13	⊆	⊆	NUM
ejpam-3228	333	14	fa(y	fa(y	NOUN
ejpam-3228	333	15	)	)	PUNCT
ejpam-3228	333	16	⊆	⊆	NUM
ejpam-3228	333	17	fa	fa	INTJ
ejpam-3228	333	18	(	(	PUNCT
ejpam-3228	333	19	(	(	PUNCT
ejpam-3228	333	20	xy)x−1	xy)x−1	NUM
ejpam-3228	333	21	)	)	PUNCT
ejpam-3228	333	22	.	.	PUNCT
ejpam-3228	334	1	hence	hence	ADV
ejpam-3228	334	2	,	,	PUNCT
ejpam-3228	334	3	fa	fa	INTJ
ejpam-3228	334	4	(	(	PUNCT
ejpam-3228	334	5	(	(	PUNCT
ejpam-3228	334	6	xy)x−1	xy)x−1	X
ejpam-3228	334	7	)	)	PUNCT
ejpam-3228	334	8	=	=	SYM
ejpam-3228	334	9	fa(y	fa(y	PROPN
ejpam-3228	334	10	)	)	PUNCT
ejpam-3228	334	11	.	.	PUNCT
ejpam-3228	335	1	theorem	theorem	VERB
ejpam-3228	335	2	7	7	NUM
ejpam-3228	335	3	.	.	PUNCT
ejpam-3228	336	1	let	let	VERB
ejpam-3228	336	2	a	a	DET
ejpam-3228	336	3	∈	∈	NOUN
ejpam-3228	336	4	s∪ag(u	s∪ag(u	NUM
ejpam-3228	336	5	)	)	PUNCT
ejpam-3228	336	6	.	.	PUNCT
ejpam-3228	337	1	then	then	ADV
ejpam-3228	337	2	a	a	DET
ejpam-3228	337	3	∈	∈	PROPN
ejpam-3228	337	4	ns∪ag(u	ns∪ag(u	NUM
ejpam-3228	337	5	)	)	PUNCT
ejpam-3228	337	6	if	if	SCONJ
ejpam-3228	337	7	and	and	CCONJ
ejpam-3228	337	8	only	only	ADV
ejpam-3228	337	9	if	if	SCONJ
ejpam-3228	337	10	fa([x	fa([x	PROPN
ejpam-3228	337	11	,	,	PUNCT
ejpam-3228	337	12	y	y	NOUN
ejpam-3228	337	13	]	]	X
ejpam-3228	337	14	)	)	PUNCT
ejpam-3228	337	15	⊆	⊆	NUM
ejpam-3228	337	16	fa(x	fa(x	NOUN
ejpam-3228	337	17	)	)	PUNCT
ejpam-3228	337	18	∀	∀	PUNCT
ejpam-3228	338	1	x	x	NOUN
ejpam-3228	338	2	,	,	PUNCT
ejpam-3228	338	3	y	y	PROPN
ejpam-3228	338	4	∈	∈	PROPN
ejpam-3228	338	5	g	g	PROPN
ejpam-3228	338	6	,	,	PUNCT
ejpam-3228	338	7	where	where	SCONJ
ejpam-3228	338	8	[	[	X
ejpam-3228	338	9	x	x	X
ejpam-3228	338	10	,	,	PUNCT
ejpam-3228	338	11	y	y	PROPN
ejpam-3228	338	12	]	]	X
ejpam-3228	338	13	=	=	X
ejpam-3228	339	1	xy	xy	X
ejpam-3228	339	2	·	·	PUNCT
ejpam-3228	340	1	y−1x−1	y−1x−1	NOUN
ejpam-3228	340	2	is	be	AUX
ejpam-3228	340	3	a	a	DET
ejpam-3228	340	4	commutator	commutator	NOUN
ejpam-3228	340	5	of	of	ADP
ejpam-3228	340	6	x	x	PROPN
ejpam-3228	340	7	and	and	CCONJ
ejpam-3228	340	8	y	y	PROPN
ejpam-3228	340	9	in	in	ADP
ejpam-3228	340	10	ag	ag	PROPN
ejpam-3228	340	11	-	-	PUNCT
ejpam-3228	340	12	group	group	NOUN
ejpam-3228	340	13	g.	g.	NOUN
ejpam-3228	340	14	proof	proof	NOUN
ejpam-3228	340	15	.	.	PUNCT
ejpam-3228	341	1	let	let	VERB
ejpam-3228	341	2	a	a	DET
ejpam-3228	341	3	∈	∈	PROPN
ejpam-3228	341	4	ns∪ag(u	ns∪ag(u	NUM
ejpam-3228	341	5	)	)	PUNCT
ejpam-3228	341	6	.	.	PUNCT
ejpam-3228	342	1	then	then	ADV
ejpam-3228	342	2	,	,	PUNCT
ejpam-3228	342	3	fa([x	fa([x	PROPN
ejpam-3228	342	4	,	,	PUNCT
ejpam-3228	342	5	y	y	NOUN
ejpam-3228	342	6	]	]	X
ejpam-3228	342	7	)	)	PUNCT
ejpam-3228	342	8	=	=	SYM
ejpam-3228	342	9	fa	fa	INTJ
ejpam-3228	342	10	(	(	PUNCT
ejpam-3228	342	11	(	(	PUNCT
ejpam-3228	342	12	xy	xy	NOUN
ejpam-3228	342	13	)	)	PUNCT
ejpam-3228	342	14	(	(	PUNCT
ejpam-3228	342	15	y−1x−1	y−1x−1	PROPN
ejpam-3228	342	16	)	)	PUNCT
ejpam-3228	342	17	)	)	PUNCT
ejpam-3228	342	18	(	(	PUNCT
ejpam-3228	342	19	by	by	ADP
ejpam-3228	342	20	definition	definition	NOUN
ejpam-3228	342	21	of	of	ADP
ejpam-3228	342	22	commutator	commutator	NOUN
ejpam-3228	342	23	in	in	ADP
ejpam-3228	342	24	g	g	NOUN
ejpam-3228	342	25	)	)	PUNCT
ejpam-3228	342	26	=	=	SYM
ejpam-3228	343	1	fa	fa	INTJ
ejpam-3228	343	2	(	(	PUNCT
ejpam-3228	343	3	(	(	PUNCT
ejpam-3228	343	4	y−1x−1	y−1x−1	PROPN
ejpam-3228	343	5	)	)	PUNCT
ejpam-3228	343	6	(	(	PUNCT
ejpam-3228	343	7	xy	xy	NOUN
ejpam-3228	343	8	)	)	PUNCT
ejpam-3228	343	9	)	)	PUNCT
ejpam-3228	344	1	(	(	PUNCT
ejpam-3228	344	2	by	by	ADP
ejpam-3228	344	3	lemma	lemma	PROPN
ejpam-3228	344	4	3	3	NUM
ejpam-3228	344	5	)	)	PUNCT
ejpam-3228	344	6	=	=	SYM
ejpam-3228	344	7	fa	fa	INTJ
ejpam-3228	344	8	(	(	PUNCT
ejpam-3228	344	9	(	(	PUNCT
ejpam-3228	344	10	yx	yx	NOUN
ejpam-3228	344	11	)	)	PUNCT
ejpam-3228	344	12	(	(	PUNCT
ejpam-3228	344	13	x−1y−1	x−1y−1	PROPN
ejpam-3228	344	14	)	)	PUNCT
ejpam-3228	344	15	)	)	PUNCT
ejpam-3228	345	1	(	(	PUNCT
ejpam-3228	345	2	by	by	ADP
ejpam-3228	345	3	lemma	lemma	PROPN
ejpam-3228	345	4	1-(iv	1-(iv	NUM
ejpam-3228	345	5	)	)	PUNCT
ejpam-3228	345	6	)	)	PUNCT
ejpam-3228	346	1	=	=	SYM
ejpam-3228	346	2	fa	fa	INTJ
ejpam-3228	346	3	(	(	PUNCT
ejpam-3228	346	4	x−1	x−1	NOUN
ejpam-3228	346	5	(	(	PUNCT
ejpam-3228	346	6	(	(	PUNCT
ejpam-3228	346	7	yx	yx	NOUN
ejpam-3228	346	8	)	)	PUNCT
ejpam-3228	346	9	y−1	y−1	PROPN
ejpam-3228	346	10	)	)	PUNCT
ejpam-3228	346	11	)	)	PUNCT
ejpam-3228	346	12	(	(	PUNCT
ejpam-3228	346	13	by	by	ADP
ejpam-3228	346	14	lemma	lemma	PROPN
ejpam-3228	346	15	1-(ii	1-(ii	NUM
ejpam-3228	346	16	)	)	PUNCT
ejpam-3228	346	17	)	)	PUNCT
ejpam-3228	347	1	⊆	⊆	X
ejpam-3228	347	2	fa	fa	INTJ
ejpam-3228	347	3	(	(	PUNCT
ejpam-3228	347	4	x−1	x−1	PROPN
ejpam-3228	347	5	)	)	PUNCT
ejpam-3228	347	6	∪	∪	ADP
ejpam-3228	347	7	fa	fa	PROPN
ejpam-3228	347	8	(	(	PUNCT
ejpam-3228	347	9	(	(	PUNCT
ejpam-3228	347	10	yx	yx	NOUN
ejpam-3228	347	11	)	)	PUNCT
ejpam-3228	347	12	y−1	y−1	NOUN
ejpam-3228	347	13	)	)	PUNCT
ejpam-3228	347	14	=	=	SYM
ejpam-3228	347	15	fa(x	fa(x	NOUN
ejpam-3228	347	16	)	)	PUNCT
ejpam-3228	347	17	∪	∪	X
ejpam-3228	347	18	fa(x	fa(x	NOUN
ejpam-3228	347	19	)	)	PUNCT
ejpam-3228	347	20	(	(	PUNCT
ejpam-3228	347	21	as	as	ADP
ejpam-3228	347	22	a	a	DET
ejpam-3228	347	23	∈	∈	PROPN
ejpam-3228	347	24	ns∪ag(u	ns∪ag(u	NUM
ejpam-3228	347	25	)	)	PUNCT
ejpam-3228	347	26	)	)	PUNCT
ejpam-3228	347	27	=	=	SYM
ejpam-3228	347	28	fa(x	fa(x	NOUN
ejpam-3228	347	29	)	)	PUNCT
ejpam-3228	347	30	.	.	PUNCT
ejpam-3228	348	1	hence	hence	ADV
ejpam-3228	348	2	,	,	PUNCT
ejpam-3228	348	3	fa([x	fa([x	PROPN
ejpam-3228	348	4	,	,	PUNCT
ejpam-3228	348	5	y	y	NOUN
ejpam-3228	348	6	]	]	X
ejpam-3228	348	7	)	)	PUNCT
ejpam-3228	348	8	⊆	⊆	NUM
ejpam-3228	348	9	fa(x	fa(x	NOUN
ejpam-3228	348	10	)	)	PUNCT
ejpam-3228	348	11	∀	∀	PUNCT
ejpam-3228	349	1	x	x	NOUN
ejpam-3228	349	2	,	,	PUNCT
ejpam-3228	349	3	y	y	PROPN
ejpam-3228	349	4	∈	∈	PROPN
ejpam-3228	349	5	g.	g.	NOUN
ejpam-3228	349	6	conversely	conversely	ADV
ejpam-3228	349	7	,	,	PUNCT
ejpam-3228	349	8	assume	assume	VERB
ejpam-3228	349	9	that	that	SCONJ
ejpam-3228	349	10	fa([x	fa([x	PROPN
ejpam-3228	349	11	,	,	PUNCT
ejpam-3228	349	12	y	y	NOUN
ejpam-3228	349	13	]	]	X
ejpam-3228	349	14	)	)	PUNCT
ejpam-3228	349	15	⊆	⊆	NUM
ejpam-3228	349	16	fa(x	fa(x	NOUN
ejpam-3228	349	17	)	)	PUNCT
ejpam-3228	349	18	∀	∀	PUNCT
ejpam-3228	350	1	x	x	NOUN
ejpam-3228	350	2	,	,	PUNCT
ejpam-3228	350	3	y	y	PROPN
ejpam-3228	350	4	∈	∈	PROPN
ejpam-3228	350	5	g.	g.	NOUN
ejpam-3228	350	6	then	then	ADV
ejpam-3228	350	7	,	,	PUNCT
ejpam-3228	350	8	for	for	ADP
ejpam-3228	350	9	any	any	DET
ejpam-3228	350	10	z	z	NOUN
ejpam-3228	350	11	∈	∈	PROPN
ejpam-3228	350	12	g	g	PROPN
ejpam-3228	350	13	,	,	PUNCT
ejpam-3228	350	14	fa	fa	PROPN
ejpam-3228	350	15	(	(	PUNCT
ejpam-3228	350	16	(	(	PUNCT
ejpam-3228	350	17	xz)x−1	xz)x−1	X
ejpam-3228	350	18	)	)	PUNCT
ejpam-3228	351	1	=	=	SYM
ejpam-3228	351	2	fa	fa	INTJ
ejpam-3228	351	3	(	(	PUNCT
ejpam-3228	351	4	e	e	X
ejpam-3228	351	5	(	(	PUNCT
ejpam-3228	351	6	(	(	PUNCT
ejpam-3228	351	7	xz)x−1	xz)x−1	X
ejpam-3228	351	8	)	)	PUNCT
ejpam-3228	351	9	)	)	PUNCT
ejpam-3228	352	1	=	=	SYM
ejpam-3228	352	2	fa	fa	INTJ
ejpam-3228	352	3	(	(	PUNCT
ejpam-3228	352	4	(	(	PUNCT
ejpam-3228	352	5	zz−1	zz−1	PROPN
ejpam-3228	352	6	)	)	PUNCT
ejpam-3228	352	7	(	(	PUNCT
ejpam-3228	352	8	(	(	PUNCT
ejpam-3228	352	9	xz)x−1	xz)x−1	X
ejpam-3228	352	10	)	)	PUNCT
ejpam-3228	352	11	)	)	PUNCT
ejpam-3228	353	1	=	=	SYM
ejpam-3228	353	2	fa	fa	INTJ
ejpam-3228	353	3	(	(	PUNCT
ejpam-3228	353	4	(	(	PUNCT
ejpam-3228	353	5	(	(	PUNCT
ejpam-3228	353	6	(	(	PUNCT
ejpam-3228	353	7	xz)x−1	xz)x−1	X
ejpam-3228	353	8	)	)	PUNCT
ejpam-3228	353	9	z−1	z−1	NUM
ejpam-3228	353	10	)	)	PUNCT
ejpam-3228	353	11	z	z	NOUN
ejpam-3228	353	12	)	)	PUNCT
ejpam-3228	353	13	(	(	PUNCT
ejpam-3228	353	14	by	by	ADP
ejpam-3228	353	15	the	the	DET
ejpam-3228	353	16	left	left	ADJ
ejpam-3228	353	17	invertive	invertive	ADJ
ejpam-3228	353	18	law	law	NOUN
ejpam-3228	353	19	)	)	PUNCT
ejpam-3228	353	20	a.	a.	PROPN
ejpam-3228	353	21	ullah	ullah	PROPN
ejpam-3228	353	22	,	,	PUNCT
ejpam-3228	353	23	f.	f.	PROPN
ejpam-3228	353	24	karaaslan	karaaslan	PROPN
ejpam-3228	353	25	,	,	PUNCT
ejpam-3228	353	26	i.	i.	PROPN
ejpam-3228	353	27	ahmad	ahmad	PROPN
ejpam-3228	353	28	/	/	SYM
ejpam-3228	353	29	eur	eur	PROPN
ejpam-3228	353	30	.	.	PUNCT
ejpam-3228	354	1	j.	j.	PROPN
ejpam-3228	354	2	pure	pure	PROPN
ejpam-3228	354	3	appl	appl	PROPN
ejpam-3228	354	4	.	.	PROPN
ejpam-3228	354	5	math	math	PROPN
ejpam-3228	354	6	,	,	PUNCT
ejpam-3228	354	7	11	11	NUM
ejpam-3228	354	8	(	(	PUNCT
ejpam-3228	354	9	2	2	NUM
ejpam-3228	354	10	)	)	PUNCT
ejpam-3228	354	11	(	(	PUNCT
ejpam-3228	354	12	2018	2018	NUM
ejpam-3228	354	13	)	)	PUNCT
ejpam-3228	354	14	,	,	PUNCT
ejpam-3228	354	15	517	517	NUM
ejpam-3228	354	16	-	-	SYM
ejpam-3228	354	17	536	536	NUM
ejpam-3228	354	18	532	532	NUM
ejpam-3228	354	19	=	=	SYM
ejpam-3228	354	20	fa	fa	X
ejpam-3228	354	21	(	(	PUNCT
ejpam-3228	354	22	(	(	PUNCT
ejpam-3228	354	23	(	(	PUNCT
ejpam-3228	354	24	z−1x−1	z−1x−1	NOUN
ejpam-3228	354	25	)	)	PUNCT
ejpam-3228	354	26	(	(	PUNCT
ejpam-3228	354	27	xz	xz	PROPN
ejpam-3228	354	28	)	)	PUNCT
ejpam-3228	354	29	)	)	PUNCT
ejpam-3228	354	30	z	z	NOUN
ejpam-3228	354	31	)	)	PUNCT
ejpam-3228	354	32	(	(	PUNCT
ejpam-3228	354	33	by	by	ADP
ejpam-3228	354	34	the	the	DET
ejpam-3228	354	35	left	left	ADJ
ejpam-3228	354	36	invertive	invertive	ADJ
ejpam-3228	354	37	law	law	NOUN
ejpam-3228	354	38	)	)	PUNCT
ejpam-3228	355	1	=	=	SYM
ejpam-3228	355	2	fa	fa	INTJ
ejpam-3228	355	3	(	(	PUNCT
ejpam-3228	355	4	(	(	PUNCT
ejpam-3228	355	5	(	(	PUNCT
ejpam-3228	355	6	zx	zx	NUM
ejpam-3228	355	7	)	)	PUNCT
ejpam-3228	355	8	(	(	PUNCT
ejpam-3228	355	9	x−1z−1	x−1z−1	PROPN
ejpam-3228	355	10	)	)	PUNCT
ejpam-3228	355	11	)	)	PUNCT
ejpam-3228	356	1	z	z	NOUN
ejpam-3228	356	2	)	)	PUNCT
ejpam-3228	356	3	(	(	PUNCT
ejpam-3228	356	4	by	by	ADP
ejpam-3228	356	5	lemma	lemma	PROPN
ejpam-3228	356	6	1-(iv	1-(iv	NUM
ejpam-3228	356	7	)	)	PUNCT
ejpam-3228	356	8	)	)	PUNCT
ejpam-3228	357	1	=	=	SYM
ejpam-3228	357	2	fa	fa	INTJ
ejpam-3228	357	3	(	(	PUNCT
ejpam-3228	357	4	[	[	X
ejpam-3228	357	5	z	z	NOUN
ejpam-3228	357	6	,	,	PUNCT
ejpam-3228	357	7	x]z	x]z	NOUN
ejpam-3228	357	8	)	)	PUNCT
ejpam-3228	357	9	⊆	⊆	X
ejpam-3228	358	1	fa([z	fa([z	PROPN
ejpam-3228	358	2	,	,	PUNCT
ejpam-3228	358	3	x	x	NOUN
ejpam-3228	358	4	]	]	X
ejpam-3228	358	5	)	)	PUNCT
ejpam-3228	358	6	∪	∪	ADP
ejpam-3228	358	7	fa(z	fa(z	PUNCT
ejpam-3228	358	8	)	)	PUNCT
ejpam-3228	358	9	⊆	⊆	NUM
ejpam-3228	358	10	fa(z	fa(z	NOUN
ejpam-3228	358	11	)	)	PUNCT
ejpam-3228	358	12	∪	∪	ADP
ejpam-3228	358	13	fa(z	fa(z	PUNCT
ejpam-3228	358	14	)	)	PUNCT
ejpam-3228	358	15	=	=	PUNCT
ejpam-3228	358	16	fa(z	fa(z	PRON
ejpam-3228	358	17	)	)	PUNCT
ejpam-3228	358	18	.	.	PUNCT
ejpam-3228	359	1	this	this	PRON
ejpam-3228	359	2	implies	imply	VERB
ejpam-3228	359	3	that	that	SCONJ
ejpam-3228	359	4	fa	fa	INTJ
ejpam-3228	359	5	(	(	PUNCT
ejpam-3228	359	6	(	(	PUNCT
ejpam-3228	359	7	xz)x−1	xz)x−1	X
ejpam-3228	359	8	)	)	PUNCT
ejpam-3228	359	9	⊆	⊆	NUM
ejpam-3228	359	10	fa(z	fa(z	NOUN
ejpam-3228	359	11	)	)	PUNCT
ejpam-3228	359	12	∀	∀	X
ejpam-3228	360	1	x	x	SYM
ejpam-3228	360	2	∈	∈	PROPN
ejpam-3228	360	3	g.	g.	NOUN
ejpam-3228	360	4	now	now	ADV
ejpam-3228	360	5	by	by	ADP
ejpam-3228	360	6	theorem	theorem	NOUN
ejpam-3228	360	7	6	6	NUM
ejpam-3228	360	8	,	,	PUNCT
ejpam-3228	360	9	we	we	PRON
ejpam-3228	360	10	have	have	VERB
ejpam-3228	360	11	fa	fa	INTJ
ejpam-3228	360	12	(	(	PUNCT
ejpam-3228	360	13	(	(	PUNCT
ejpam-3228	360	14	xz)x−1	xz)x−1	X
ejpam-3228	360	15	)	)	PUNCT
ejpam-3228	360	16	=	=	SYM
ejpam-3228	361	1	fa(z	fa(z	PRON
ejpam-3228	361	2	)	)	PUNCT
ejpam-3228	361	3	∀	∀	X
ejpam-3228	362	1	x	x	SYM
ejpam-3228	362	2	∈	∈	NOUN
ejpam-3228	362	3	g.	g.	NOUN
ejpam-3228	362	4	hence	hence	ADV
ejpam-3228	362	5	,	,	PUNCT
ejpam-3228	362	6	a	a	DET
ejpam-3228	362	7	∈	∈	PROPN
ejpam-3228	362	8	ns∪ag(u	ns∪ag(u	NUM
ejpam-3228	362	9	)	)	PUNCT
ejpam-3228	362	10	.	.	PUNCT
ejpam-3228	363	1	proposition	proposition	NOUN
ejpam-3228	363	2	1	1	NUM
ejpam-3228	363	3	.	.	PUNCT
ejpam-3228	364	1	let	let	VERB
ejpam-3228	364	2	a	a	DET
ejpam-3228	364	3	∈	∈	NOUN
ejpam-3228	364	4	s∪ag(u	s∪ag(u	NUM
ejpam-3228	364	5	)	)	PUNCT
ejpam-3228	364	6	.	.	PUNCT
ejpam-3228	365	1	then	then	ADV
ejpam-3228	365	2	fa([x	fa([x	PROPN
ejpam-3228	365	3	,	,	PUNCT
ejpam-3228	365	4	y	y	NOUN
ejpam-3228	365	5	]	]	X
ejpam-3228	365	6	)	)	PUNCT
ejpam-3228	365	7	=	=	SYM
ejpam-3228	365	8	fa(e	fa(e	X
ejpam-3228	365	9	)	)	PUNCT
ejpam-3228	365	10	∀	∀	PUNCT
ejpam-3228	366	1	x	x	X
ejpam-3228	366	2	,	,	PUNCT
ejpam-3228	366	3	y	y	PROPN
ejpam-3228	366	4	∈	∈	PROPN
ejpam-3228	366	5	g	g	PROPN
ejpam-3228	367	1	if	if	SCONJ
ejpam-3228	367	2	and	and	CCONJ
ejpam-3228	367	3	only	only	ADV
ejpam-3228	367	4	if	if	SCONJ
ejpam-3228	367	5	a	a	DET
ejpam-3228	367	6	∈	∈	PROPN
ejpam-3228	367	7	ns∪ag(u	ns∪ag(u	NUM
ejpam-3228	367	8	)	)	PUNCT
ejpam-3228	367	9	.	.	PUNCT
ejpam-3228	368	1	proof	proof	NOUN
ejpam-3228	368	2	.	.	PUNCT
ejpam-3228	369	1	a	a	DET
ejpam-3228	369	2	∈	∈	PROPN
ejpam-3228	369	3	ns∪ag(u	ns∪ag(u	NUM
ejpam-3228	369	4	)	)	PUNCT
ejpam-3228	369	5	,	,	PUNCT
ejpam-3228	369	6	if	if	SCONJ
ejpam-3228	369	7	and	and	CCONJ
ejpam-3228	369	8	only	only	ADV
ejpam-3228	369	9	if	if	SCONJ
ejpam-3228	369	10	fa	fa	INTJ
ejpam-3228	369	11	(	(	PUNCT
ejpam-3228	369	12	(	(	PUNCT
ejpam-3228	369	13	yx	yx	NOUN
ejpam-3228	369	14	)	)	PUNCT
ejpam-3228	369	15	y−1	y−1	NOUN
ejpam-3228	369	16	)	)	PUNCT
ejpam-3228	369	17	=	=	SYM
ejpam-3228	369	18	fa(x	fa(x	X
ejpam-3228	369	19	)	)	PUNCT
ejpam-3228	369	20	∀	∀	PUNCT
ejpam-3228	369	21	x	x	NOUN
ejpam-3228	369	22	,	,	PUNCT
ejpam-3228	369	23	y	y	PROPN
ejpam-3228	369	24	∈	∈	PROPN
ejpam-3228	369	25	g	g	PROPN
ejpam-3228	369	26	⇔	⇔	PROPN
ejpam-3228	369	27	fa	fa	PROPN
ejpam-3228	369	28	(	(	PUNCT
ejpam-3228	369	29	e	e	X
ejpam-3228	369	30	(	(	PUNCT
ejpam-3228	369	31	(	(	PUNCT
ejpam-3228	369	32	yx	yx	NOUN
ejpam-3228	369	33	)	)	PUNCT
ejpam-3228	369	34	y−1	y−1	PROPN
ejpam-3228	369	35	)	)	PUNCT
ejpam-3228	369	36	)	)	PUNCT
ejpam-3228	370	1	=	=	PRON
ejpam-3228	370	2	fa(x	fa(x	PROPN
ejpam-3228	370	3	)	)	PUNCT
ejpam-3228	370	4	⇔	⇔	X
ejpam-3228	370	5	fa	fa	PROPN
ejpam-3228	370	6	(	(	PUNCT
ejpam-3228	370	7	(	(	PUNCT
ejpam-3228	370	8	xx−1	xx−1	PROPN
ejpam-3228	370	9	)	)	PUNCT
ejpam-3228	370	10	(	(	PUNCT
ejpam-3228	370	11	(	(	PUNCT
ejpam-3228	370	12	yx	yx	NOUN
ejpam-3228	370	13	)	)	PUNCT
ejpam-3228	370	14	y−1	y−1	PROPN
ejpam-3228	370	15	)	)	PUNCT
ejpam-3228	370	16	)	)	PUNCT
ejpam-3228	371	1	=	=	PRON
ejpam-3228	371	2	fa(x	fa(x	PROPN
ejpam-3228	371	3	)	)	PUNCT
ejpam-3228	371	4	⇔	⇔	X
ejpam-3228	371	5	fa	fa	X
ejpam-3228	371	6	(	(	PUNCT
ejpam-3228	371	7	(	(	PUNCT
ejpam-3228	371	8	(	(	PUNCT
ejpam-3228	371	9	(	(	PUNCT
ejpam-3228	371	10	yx	yx	NOUN
ejpam-3228	371	11	)	)	PUNCT
ejpam-3228	371	12	y−1	y−1	PROPN
ejpam-3228	371	13	)	)	PUNCT
ejpam-3228	372	1	x−1	x−1	PROPN
ejpam-3228	372	2	)	)	PUNCT
ejpam-3228	373	1	x	x	X
ejpam-3228	373	2	)	)	PUNCT
ejpam-3228	373	3	=	=	SYM
ejpam-3228	373	4	fa(x	fa(x	X
ejpam-3228	373	5	)	)	PUNCT
ejpam-3228	373	6	(	(	PUNCT
ejpam-3228	373	7	by	by	ADP
ejpam-3228	373	8	the	the	DET
ejpam-3228	373	9	left	left	ADJ
ejpam-3228	373	10	invertive	invertive	ADJ
ejpam-3228	373	11	law	law	NOUN
ejpam-3228	373	12	)	)	PUNCT
ejpam-3228	373	13	⇔	⇔	PROPN
ejpam-3228	373	14	fa	fa	X
ejpam-3228	373	15	(	(	PUNCT
ejpam-3228	373	16	(	(	PUNCT
ejpam-3228	373	17	(	(	PUNCT
ejpam-3228	373	18	x−1y−1	x−1y−1	PROPN
ejpam-3228	373	19	)	)	PUNCT
ejpam-3228	373	20	(	(	PUNCT
ejpam-3228	373	21	yx	yx	NOUN
ejpam-3228	373	22	)	)	PUNCT
ejpam-3228	373	23	)	)	PUNCT
ejpam-3228	373	24	x	x	X
ejpam-3228	373	25	)	)	PUNCT
ejpam-3228	373	26	=	=	SYM
ejpam-3228	374	1	fa(x	fa(x	X
ejpam-3228	374	2	)	)	PUNCT
ejpam-3228	374	3	(	(	PUNCT
ejpam-3228	374	4	by	by	ADP
ejpam-3228	374	5	the	the	DET
ejpam-3228	374	6	left	left	ADJ
ejpam-3228	374	7	invertive	invertive	ADJ
ejpam-3228	374	8	law	law	NOUN
ejpam-3228	374	9	)	)	PUNCT
ejpam-3228	374	10	⇔	⇔	PROPN
ejpam-3228	374	11	fa	fa	X
ejpam-3228	374	12	(	(	PUNCT
ejpam-3228	374	13	(	(	PUNCT
ejpam-3228	374	14	(	(	PUNCT
ejpam-3228	374	15	xy	xy	NOUN
ejpam-3228	374	16	)	)	PUNCT
ejpam-3228	374	17	(	(	PUNCT
ejpam-3228	374	18	y−1x−1	y−1x−1	PROPN
ejpam-3228	374	19	)	)	PUNCT
ejpam-3228	374	20	)	)	PUNCT
ejpam-3228	374	21	x	x	X
ejpam-3228	374	22	)	)	PUNCT
ejpam-3228	374	23	=	=	SYM
ejpam-3228	375	1	fa(x	fa(x	X
ejpam-3228	375	2	)	)	PUNCT
ejpam-3228	375	3	(	(	PUNCT
ejpam-3228	375	4	by	by	ADP
ejpam-3228	375	5	lemma	lemma	PROPN
ejpam-3228	375	6	1-(iv	1-(iv	NUM
ejpam-3228	375	7	)	)	PUNCT
ejpam-3228	375	8	)	)	PUNCT
ejpam-3228	376	1	⇔	⇔	PROPN
ejpam-3228	376	2	fa	fa	X
ejpam-3228	376	3	(	(	PUNCT
ejpam-3228	376	4	(	(	PUNCT
ejpam-3228	376	5	[	[	X
ejpam-3228	376	6	x	x	NOUN
ejpam-3228	376	7	,	,	PUNCT
ejpam-3228	376	8	y])x	y])x	NOUN
ejpam-3228	376	9	)	)	PUNCT
ejpam-3228	376	10	=	=	SYM
ejpam-3228	376	11	fa(x	fa(x	X
ejpam-3228	376	12	)	)	PUNCT
ejpam-3228	376	13	⇔	⇔	PROPN
ejpam-3228	376	14	fa([x	fa([x	PROPN
ejpam-3228	376	15	,	,	PUNCT
ejpam-3228	376	16	y	y	NOUN
ejpam-3228	376	17	]	]	X
ejpam-3228	376	18	)	)	PUNCT
ejpam-3228	376	19	=	=	SYM
ejpam-3228	376	20	fa(e	fa(e	X
ejpam-3228	376	21	)	)	PUNCT
ejpam-3228	376	22	.	.	PUNCT
ejpam-3228	377	1	(	(	PUNCT
ejpam-3228	377	2	by	by	ADP
ejpam-3228	377	3	lemma	lemma	PROPN
ejpam-3228	377	4	4	4	NUM
ejpam-3228	377	5	)	)	PUNCT
ejpam-3228	377	6	hence	hence	ADV
ejpam-3228	377	7	,	,	PUNCT
ejpam-3228	377	8	a	a	DET
ejpam-3228	377	9	∈	∈	PROPN
ejpam-3228	377	10	ns∪ag(g	ns∪ag(g	NUM
ejpam-3228	377	11	)	)	PUNCT
ejpam-3228	378	1	if	if	SCONJ
ejpam-3228	378	2	and	and	CCONJ
ejpam-3228	378	3	only	only	ADV
ejpam-3228	378	4	if	if	SCONJ
ejpam-3228	378	5	fa([x	fa([x	PROPN
ejpam-3228	378	6	,	,	PUNCT
ejpam-3228	378	7	y	y	NOUN
ejpam-3228	378	8	]	]	X
ejpam-3228	378	9	)	)	PUNCT
ejpam-3228	378	10	=	=	SYM
ejpam-3228	378	11	fa(e	fa(e	X
ejpam-3228	378	12	)	)	PUNCT
ejpam-3228	378	13	∀	∀	PUNCT
ejpam-3228	379	1	x	x	X
ejpam-3228	379	2	,	,	PUNCT
ejpam-3228	379	3	y	y	PROPN
ejpam-3228	379	4	∈	∈	PROPN
ejpam-3228	379	5	g.	g.	PROPN
ejpam-3228	379	6	4	4	NUM
ejpam-3228	379	7	.	.	X
ejpam-3228	380	1	α	α	X
ejpam-3228	380	2	-	-	NOUN
ejpam-3228	380	3	inclusion	inclusion	NOUN
ejpam-3228	380	4	of	of	ADP
ejpam-3228	380	5	soft	soft	ADJ
ejpam-3228	380	6	uni	uni	ADJ
ejpam-3228	380	7	-	-	PUNCT
ejpam-3228	380	8	ag	ag	ADJ
ejpam-3228	380	9	-	-	PUNCT
ejpam-3228	380	10	groups	group	NOUN
ejpam-3228	380	11	definition	definition	NOUN
ejpam-3228	380	12	9	9	NUM
ejpam-3228	380	13	.	.	PUNCT
ejpam-3228	381	1	let	let	VERB
ejpam-3228	381	2	a	a	DET
ejpam-3228	381	3	∈	∈	NOUN
ejpam-3228	381	4	s∪ag(u	s∪ag(u	NUM
ejpam-3228	381	5	)	)	PUNCT
ejpam-3228	381	6	.	.	PUNCT
ejpam-3228	382	1	then	then	ADV
ejpam-3228	382	2	,	,	PUNCT
ejpam-3228	382	3	e	e	X
ejpam-3228	382	4	-	-	NOUN
ejpam-3228	382	5	set	set	NOUN
ejpam-3228	382	6	of	of	ADP
ejpam-3228	382	7	a	a	PRON
ejpam-3228	382	8	is	be	AUX
ejpam-3228	382	9	denoted	denote	VERB
ejpam-3228	382	10	by	by	ADP
ejpam-3228	382	11	aẽ	aẽ	ADV
ejpam-3228	382	12	and	and	CCONJ
ejpam-3228	382	13	defined	define	VERB
ejpam-3228	382	14	as	as	ADP
ejpam-3228	382	15	aẽ	aẽ	ADV
ejpam-3228	382	16	=	=	SYM
ejpam-3228	382	17	{	{	PUNCT
ejpam-3228	382	18	x	x	PUNCT
ejpam-3228	382	19	∈	∈	PROPN
ejpam-3228	382	20	g	g	NOUN
ejpam-3228	382	21	:	:	PUNCT
ejpam-3228	382	22	fa(x	fa(x	X
ejpam-3228	382	23	)	)	PUNCT
ejpam-3228	382	24	=	=	SYM
ejpam-3228	382	25	fa(e	fa(e	NOUN
ejpam-3228	382	26	)	)	PUNCT
ejpam-3228	382	27	}	}	PUNCT
ejpam-3228	382	28	.	.	PUNCT
ejpam-3228	383	1	example	example	NOUN
ejpam-3228	384	1	10	10	NUM
ejpam-3228	384	2	.	.	PUNCT
ejpam-3228	385	1	in	in	ADP
ejpam-3228	385	2	example	example	NOUN
ejpam-3228	385	3	2	2	NUM
ejpam-3228	385	4	,	,	PUNCT
ejpam-3228	385	5	aẽ	aẽ	PUNCT
ejpam-3228	385	6	=	=	NOUN
ejpam-3228	385	7	{	{	PUNCT
ejpam-3228	385	8	0	0	NUM
ejpam-3228	385	9	}	}	PUNCT
ejpam-3228	385	10	.	.	PUNCT
ejpam-3228	386	1	theorem	theorem	ADJ
ejpam-3228	386	2	8	8	NUM
ejpam-3228	386	3	.	.	PUNCT
ejpam-3228	387	1	let	let	VERB
ejpam-3228	387	2	a	a	DET
ejpam-3228	387	3	∈	∈	NOUN
ejpam-3228	387	4	s∪ag(u	s∪ag(u	NUM
ejpam-3228	387	5	)	)	PUNCT
ejpam-3228	387	6	.	.	PUNCT
ejpam-3228	388	1	then	then	ADV
ejpam-3228	388	2	,	,	PUNCT
ejpam-3228	388	3	aẽ	aẽ	ADV
ejpam-3228	388	4	is	be	AUX
ejpam-3228	388	5	an	an	DET
ejpam-3228	388	6	ag	ag	PROPN
ejpam-3228	388	7	-	-	PUNCT
ejpam-3228	388	8	subgroup	subgroup	NOUN
ejpam-3228	388	9	of	of	ADP
ejpam-3228	388	10	g.	g.	PROPN
ejpam-3228	388	11	proof	proof	NOUN
ejpam-3228	388	12	.	.	PUNCT
ejpam-3228	389	1	by	by	ADP
ejpam-3228	389	2	definition	definition	NOUN
ejpam-3228	389	3	of	of	ADP
ejpam-3228	389	4	aẽ	aẽ	PROPN
ejpam-3228	389	5	,	,	PUNCT
ejpam-3228	389	6	it	it	PRON
ejpam-3228	389	7	is	be	AUX
ejpam-3228	389	8	obvious	obvious	ADJ
ejpam-3228	389	9	that	that	SCONJ
ejpam-3228	389	10	aẽ	aẽ	NOUN
ejpam-3228	389	11	6=	6=	ADP
ejpam-3228	389	12	∅.	∅.	AUX
ejpam-3228	389	13	let	let	VERB
ejpam-3228	389	14	x	x	PRON
ejpam-3228	389	15	,	,	PUNCT
ejpam-3228	389	16	y	y	PROPN
ejpam-3228	389	17	∈	∈	PROPN
ejpam-3228	390	1	aẽ.	aẽ.	PROPN
ejpam-3228	390	2	then	then	ADV
ejpam-3228	390	3	,	,	PUNCT
ejpam-3228	390	4	fa(x	fa(x	NOUN
ejpam-3228	390	5	)	)	PUNCT
ejpam-3228	390	6	=	=	SYM
ejpam-3228	390	7	fa(e	fa(e	X
ejpam-3228	390	8	)	)	PUNCT
ejpam-3228	390	9	=	=	SYM
ejpam-3228	391	1	fa(y	fa(y	PROPN
ejpam-3228	391	2	)	)	PUNCT
ejpam-3228	391	3	.	.	PUNCT
ejpam-3228	392	1	consider	consider	VERB
ejpam-3228	392	2	,	,	PUNCT
ejpam-3228	392	3	fa(xy−1	fa(xy−1	NUM
ejpam-3228	392	4	)	)	PUNCT
ejpam-3228	392	5	⊆	⊆	NUM
ejpam-3228	392	6	fa(x	fa(x	NOUN
ejpam-3228	392	7	)	)	PUNCT
ejpam-3228	392	8	∪	∪	ADP
ejpam-3228	392	9	fa(y	fa(y	PROPN
ejpam-3228	392	10	)	)	PUNCT
ejpam-3228	392	11	=	=	SYM
ejpam-3228	392	12	fa(e	fa(e	X
ejpam-3228	392	13	)	)	PUNCT
ejpam-3228	392	14	∪	∪	ADP
ejpam-3228	392	15	fa(e	fa(e	NUM
ejpam-3228	392	16	)	)	PUNCT
ejpam-3228	392	17	=	=	SYM
ejpam-3228	392	18	fa(e	fa(e	X
ejpam-3228	392	19	)	)	PUNCT
ejpam-3228	392	20	,	,	PUNCT
ejpam-3228	392	21	also	also	ADV
ejpam-3228	392	22	by	by	ADP
ejpam-3228	392	23	theorem	theorem	NOUN
ejpam-3228	392	24	2	2	NUM
ejpam-3228	392	25	,	,	PUNCT
ejpam-3228	392	26	fa(e	fa(e	NUM
ejpam-3228	392	27	)	)	PUNCT
ejpam-3228	392	28	⊆	⊆	NUM
ejpam-3228	392	29	fa(xy−1	fa(xy−1	NOUN
ejpam-3228	392	30	)	)	PUNCT
ejpam-3228	392	31	∀	∀	X
ejpam-3228	393	1	x	x	NOUN
ejpam-3228	393	2	,	,	PUNCT
ejpam-3228	393	3	y	y	PROPN
ejpam-3228	393	4	∈	∈	PROPN
ejpam-3228	393	5	g.	g.	PROPN
ejpam-3228	393	6	consequently	consequently	ADV
ejpam-3228	393	7	,	,	PUNCT
ejpam-3228	393	8	fa(xy−1	fa(xy−1	NUM
ejpam-3228	393	9	)	)	PUNCT
ejpam-3228	393	10	=	=	SYM
ejpam-3228	393	11	fa(e	fa(e	X
ejpam-3228	393	12	)	)	PUNCT
ejpam-3228	393	13	.	.	PUNCT
ejpam-3228	394	1	this	this	PRON
ejpam-3228	394	2	implies	imply	VERB
ejpam-3228	394	3	that	that	SCONJ
ejpam-3228	394	4	xy−1	xy−1	PROPN
ejpam-3228	394	5	∈	∈	PROPN
ejpam-3228	395	1	aẽ.	aẽ.	PROPN
ejpam-3228	395	2	hence	hence	ADV
ejpam-3228	395	3	aẽ	aẽ	ADV
ejpam-3228	395	4	is	be	AUX
ejpam-3228	395	5	an	an	DET
ejpam-3228	395	6	ag	ag	PROPN
ejpam-3228	395	7	-	-	PUNCT
ejpam-3228	395	8	subgroup	subgroup	NOUN
ejpam-3228	395	9	of	of	ADP
ejpam-3228	395	10	g.	g.	PROPN
ejpam-3228	395	11	a.	a.	PROPN
ejpam-3228	395	12	ullah	ullah	PROPN
ejpam-3228	395	13	,	,	PUNCT
ejpam-3228	395	14	f.	f.	PROPN
ejpam-3228	395	15	karaaslan	karaaslan	PROPN
ejpam-3228	395	16	,	,	PUNCT
ejpam-3228	395	17	i.	i.	PROPN
ejpam-3228	395	18	ahmad	ahmad	PROPN
ejpam-3228	395	19	/	/	SYM
ejpam-3228	395	20	eur	eur	PROPN
ejpam-3228	395	21	.	.	PUNCT
ejpam-3228	396	1	j.	j.	PROPN
ejpam-3228	396	2	pure	pure	PROPN
ejpam-3228	396	3	appl	appl	PROPN
ejpam-3228	396	4	.	.	PROPN
ejpam-3228	396	5	math	math	PROPN
ejpam-3228	396	6	,	,	PUNCT
ejpam-3228	396	7	11	11	NUM
ejpam-3228	396	8	(	(	PUNCT
ejpam-3228	396	9	2	2	NUM
ejpam-3228	396	10	)	)	PUNCT
ejpam-3228	396	11	(	(	PUNCT
ejpam-3228	396	12	2018	2018	NUM
ejpam-3228	396	13	)	)	PUNCT
ejpam-3228	396	14	,	,	PUNCT
ejpam-3228	396	15	517	517	NUM
ejpam-3228	396	16	-	-	SYM
ejpam-3228	396	17	536	536	NUM
ejpam-3228	396	18	533	533	NUM
ejpam-3228	396	19	definition	definition	NOUN
ejpam-3228	396	20	10	10	NUM
ejpam-3228	396	21	.	.	PUNCT
ejpam-3228	397	1	let	let	VERB
ejpam-3228	397	2	a	a	DET
ejpam-3228	397	3	∈	∈	PROPN
ejpam-3228	397	4	s∪ag(u	s∪ag(u	NUM
ejpam-3228	397	5	)	)	PUNCT
ejpam-3228	397	6	and	and	CCONJ
ejpam-3228	397	7	α	α	PRON
ejpam-3228	397	8	∈	∈	PROPN
ejpam-3228	397	9	p	p	X
ejpam-3228	397	10	(	(	PUNCT
ejpam-3228	397	11	u	u	NOUN
ejpam-3228	397	12	)	)	PUNCT
ejpam-3228	397	13	.	.	PUNCT
ejpam-3228	398	1	then	then	ADV
ejpam-3228	398	2	α	α	X
ejpam-3228	398	3	-	-	NOUN
ejpam-3228	398	4	inclusion	inclusion	NOUN
ejpam-3228	398	5	of	of	ADP
ejpam-3228	398	6	a	a	PRON
ejpam-3228	398	7	,	,	PUNCT
ejpam-3228	398	8	is	be	AUX
ejpam-3228	398	9	denoted	denote	VERB
ejpam-3228	398	10	by	by	ADP
ejpam-3228	398	11	aα̃	aα̃	PROPN
ejpam-3228	398	12	,	,	PUNCT
ejpam-3228	398	13	and	and	CCONJ
ejpam-3228	398	14	defined	define	VERB
ejpam-3228	398	15	by	by	ADP
ejpam-3228	398	16	aα̃	aα̃	PROPN
ejpam-3228	398	17	=	=	SYM
ejpam-3228	398	18	{	{	PUNCT
ejpam-3228	398	19	x	x	PUNCT
ejpam-3228	398	20	∈	∈	PROPN
ejpam-3228	398	21	g	g	NOUN
ejpam-3228	398	22	:	:	PUNCT
ejpam-3228	398	23	fa(x	fa(x	NOUN
ejpam-3228	398	24	)	)	PUNCT
ejpam-3228	398	25	⊆	⊆	NUM
ejpam-3228	398	26	α	α	NOUN
ejpam-3228	398	27	}	}	PUNCT
ejpam-3228	398	28	,	,	PUNCT
ejpam-3228	398	29	while	while	SCONJ
ejpam-3228	398	30	the	the	DET
ejpam-3228	398	31	set	set	NOUN
ejpam-3228	398	32	aα̃+	aα̃+	PUNCT
ejpam-3228	398	33	=	=	PRON
ejpam-3228	398	34	{	{	PUNCT
ejpam-3228	398	35	x	x	PROPN
ejpam-3228	398	36	∈	∈	PROPN
ejpam-3228	398	37	g	g	NOUN
ejpam-3228	398	38	:	:	PUNCT
ejpam-3228	398	39	fa(x	fa(x	PROPN
ejpam-3228	398	40	)	)	PUNCT
ejpam-3228	398	41	⊂	⊂	PROPN
ejpam-3228	398	42	α	α	X
ejpam-3228	398	43	}	}	PUNCT
ejpam-3228	398	44	,	,	PUNCT
ejpam-3228	398	45	is	be	AUX
ejpam-3228	398	46	called	call	VERB
ejpam-3228	398	47	the	the	DET
ejpam-3228	398	48	strong	strong	ADJ
ejpam-3228	398	49	α	α	NOUN
ejpam-3228	398	50	-	-	NOUN
ejpam-3228	398	51	inclusion	inclusion	NOUN
ejpam-3228	398	52	of	of	ADP
ejpam-3228	398	53	a.	a.	NOUN
ejpam-3228	398	54	note	note	NOUN
ejpam-3228	399	1	that	that	SCONJ
ejpam-3228	399	2	if	if	SCONJ
ejpam-3228	399	3	α	α	PROPN
ejpam-3228	399	4	=	=	SYM
ejpam-3228	399	5	u	u	PROPN
ejpam-3228	399	6	.	.	PUNCT
ejpam-3228	399	7	then	then	ADV
ejpam-3228	399	8	aα̃	aα̃	PUNCT
ejpam-3228	399	9	=	=	PRON
ejpam-3228	399	10	{	{	PUNCT
ejpam-3228	399	11	x	x	PUNCT
ejpam-3228	399	12	∈	∈	PROPN
ejpam-3228	399	13	g	g	NOUN
ejpam-3228	399	14	:	:	PUNCT
ejpam-3228	399	15	fa(x	fa(x	X
ejpam-3228	399	16	)	)	PUNCT
ejpam-3228	399	17	6=	6=	NUM
ejpam-3228	399	18	u	u	NOUN
ejpam-3228	399	19	}	}	PUNCT
ejpam-3228	399	20	,	,	PUNCT
ejpam-3228	399	21	and	and	CCONJ
ejpam-3228	399	22	is	be	AUX
ejpam-3228	399	23	called	call	VERB
ejpam-3228	399	24	support	support	NOUN
ejpam-3228	399	25	of	of	ADP
ejpam-3228	399	26	a	a	PRON
ejpam-3228	399	27	,	,	PUNCT
ejpam-3228	399	28	and	and	CCONJ
ejpam-3228	399	29	is	be	AUX
ejpam-3228	399	30	denoted	denote	VERB
ejpam-3228	399	31	by	by	ADP
ejpam-3228	399	32	supp(a	supp(a	NOUN
ejpam-3228	399	33	)	)	PUNCT
ejpam-3228	399	34	.	.	PUNCT
ejpam-3228	400	1	example	example	NOUN
ejpam-3228	401	1	11	11	NUM
ejpam-3228	401	2	.	.	PUNCT
ejpam-3228	402	1	let	let	VERB
ejpam-3228	402	2	u	u	PRON
ejpam-3228	402	3	=	=	NOUN
ejpam-3228	402	4	{	{	PUNCT
ejpam-3228	402	5	u1	u1	NOUN
ejpam-3228	402	6	,	,	PUNCT
ejpam-3228	402	7	u2	u2	NOUN
ejpam-3228	402	8	,	,	PUNCT
ejpam-3228	402	9	u3	u3	PROPN
ejpam-3228	402	10	,	,	PUNCT
ejpam-3228	402	11	u4	u4	PROPN
ejpam-3228	402	12	,	,	PUNCT
ejpam-3228	402	13	u5	u5	PROPN
ejpam-3228	402	14	,	,	PUNCT
ejpam-3228	402	15	u6	u6	PROPN
ejpam-3228	402	16	,	,	PUNCT
ejpam-3228	402	17	u7	u7	PROPN
ejpam-3228	402	18	}	}	PUNCT
ejpam-3228	402	19	be	be	VERB
ejpam-3228	402	20	the	the	DET
ejpam-3228	402	21	universal	universal	ADJ
ejpam-3228	402	22	set	set	NOUN
ejpam-3228	402	23	and	and	CCONJ
ejpam-3228	402	24	g	g	NOUN
ejpam-3228	402	25	=	=	PUNCT
ejpam-3228	402	26	{	{	PUNCT
ejpam-3228	402	27	0	0	NUM
ejpam-3228	402	28	,	,	PUNCT
ejpam-3228	402	29	1	1	NUM
ejpam-3228	402	30	,	,	PUNCT
ejpam-3228	402	31	2	2	NUM
ejpam-3228	402	32	,	,	PUNCT
ejpam-3228	402	33	3	3	NUM
ejpam-3228	402	34	,	,	PUNCT
ejpam-3228	402	35	4	4	NUM
ejpam-3228	402	36	,	,	PUNCT
ejpam-3228	402	37	5	5	NUM
ejpam-3228	402	38	}	}	PUNCT
ejpam-3228	402	39	be	be	AUX
ejpam-3228	402	40	an	an	DET
ejpam-3228	402	41	ag	ag	PROPN
ejpam-3228	402	42	-	-	PUNCT
ejpam-3228	402	43	group	group	NOUN
ejpam-3228	402	44	of	of	ADP
ejpam-3228	402	45	order	order	NOUN
ejpam-3228	402	46	6	6	NUM
ejpam-3228	402	47	defined	define	VERB
ejpam-3228	402	48	as	as	ADP
ejpam-3228	402	49	in	in	ADP
ejpam-3228	402	50	example	example	NOUN
ejpam-3228	402	51	8	8	NUM
ejpam-3228	402	52	.	.	PUNCT
ejpam-3228	403	1	if	if	SCONJ
ejpam-3228	403	2	we	we	PRON
ejpam-3228	403	3	define	define	VERB
ejpam-3228	403	4	soft	soft	ADJ
ejpam-3228	403	5	uni	uni	ADJ
ejpam-3228	403	6	-	-	PUNCT
ejpam-3228	403	7	ag	ag	NOUN
ejpam-3228	403	8	-	-	NOUN
ejpam-3228	403	9	group	group	NOUN
ejpam-3228	403	10	a	a	PRON
ejpam-3228	403	11	over	over	ADP
ejpam-3228	403	12	u	u	NOUN
ejpam-3228	403	13	by	by	ADP
ejpam-3228	403	14	fa(0	fa(0	NOUN
ejpam-3228	403	15	)	)	PUNCT
ejpam-3228	403	16	=	=	SYM
ejpam-3228	403	17	{	{	PUNCT
ejpam-3228	403	18	u1	u1	NOUN
ejpam-3228	403	19	,	,	PUNCT
ejpam-3228	403	20	u2	u2	NOUN
ejpam-3228	403	21	,	,	PUNCT
ejpam-3228	403	22	u3	u3	NOUN
ejpam-3228	403	23	}	}	PUNCT
ejpam-3228	403	24	,	,	PUNCT
ejpam-3228	403	25	fa(2	fa(2	NOUN
ejpam-3228	403	26	)	)	PUNCT
ejpam-3228	403	27	=	=	SYM
ejpam-3228	403	28	{	{	PUNCT
ejpam-3228	403	29	u1	u1	NOUN
ejpam-3228	403	30	,	,	PUNCT
ejpam-3228	403	31	u2	u2	NOUN
ejpam-3228	403	32	,	,	PUNCT
ejpam-3228	403	33	u3	u3	PROPN
ejpam-3228	403	34	,	,	PUNCT
ejpam-3228	403	35	u4	u4	PROPN
ejpam-3228	403	36	,	,	PUNCT
ejpam-3228	403	37	u5	u5	PROPN
ejpam-3228	403	38	}	}	PUNCT
ejpam-3228	403	39	=	=	SYM
ejpam-3228	403	40	fa(4	fa(4	NOUN
ejpam-3228	403	41	)	)	PUNCT
ejpam-3228	403	42	,	,	PUNCT
ejpam-3228	403	43	fa(1	fa(1	NOUN
ejpam-3228	403	44	)	)	PUNCT
ejpam-3228	403	45	=	=	SYM
ejpam-3228	403	46	{	{	PUNCT
ejpam-3228	403	47	u1	u1	NOUN
ejpam-3228	403	48	,	,	PUNCT
ejpam-3228	403	49	u2	u2	NOUN
ejpam-3228	403	50	,	,	PUNCT
ejpam-3228	403	51	u3	u3	PROPN
ejpam-3228	403	52	,	,	PUNCT
ejpam-3228	403	53	u4	u4	PROPN
ejpam-3228	403	54	,	,	PUNCT
ejpam-3228	403	55	u5	u5	PROPN
ejpam-3228	403	56	,	,	PUNCT
ejpam-3228	403	57	u6	u6	NOUN
ejpam-3228	403	58	}	}	PUNCT
ejpam-3228	403	59	=	=	SYM
ejpam-3228	403	60	fa(3	fa(3	NOUN
ejpam-3228	403	61	)	)	PUNCT
ejpam-3228	403	62	=	=	SYM
ejpam-3228	403	63	fa(5	fa(5	PROPN
ejpam-3228	403	64	)	)	PUNCT
ejpam-3228	403	65	let	let	VERB
ejpam-3228	403	66	α	α	NOUN
ejpam-3228	403	67	=	=	SYM
ejpam-3228	403	68	{	{	PUNCT
ejpam-3228	403	69	u1	u1	NOUN
ejpam-3228	403	70	,	,	PUNCT
ejpam-3228	403	71	u2	u2	NOUN
ejpam-3228	403	72	,	,	PUNCT
ejpam-3228	403	73	u3	u3	PROPN
ejpam-3228	403	74	,	,	PUNCT
ejpam-3228	403	75	u4	u4	PROPN
ejpam-3228	403	76	,	,	PUNCT
ejpam-3228	403	77	u5	u5	PROPN
ejpam-3228	403	78	}	}	PUNCT
ejpam-3228	403	79	,	,	PUNCT
ejpam-3228	403	80	then	then	ADV
ejpam-3228	403	81	aα̃	aα̃	PROPN
ejpam-3228	403	82	=	=	PUNCT
ejpam-3228	403	83	{	{	PUNCT
ejpam-3228	403	84	0	0	NUM
ejpam-3228	403	85	,	,	PUNCT
ejpam-3228	403	86	2	2	NUM
ejpam-3228	403	87	,	,	PUNCT
ejpam-3228	403	88	4	4	NUM
ejpam-3228	403	89	}	}	PUNCT
ejpam-3228	403	90	and	and	CCONJ
ejpam-3228	403	91	aα̃+	aα̃+	NOUN
ejpam-3228	403	92	=	=	PRON
ejpam-3228	403	93	{	{	PUNCT
ejpam-3228	403	94	0	0	NUM
ejpam-3228	403	95	}	}	PUNCT
ejpam-3228	403	96	.	.	PUNCT
ejpam-3228	404	1	corollary	corollary	ADJ
ejpam-3228	404	2	1	1	NUM
ejpam-3228	404	3	.	.	PUNCT
ejpam-3228	405	1	let	let	VERB
ejpam-3228	405	2	b≤̃a	b≤̃a	ADV
ejpam-3228	405	3	and	and	CCONJ
ejpam-3228	405	4	c≤̃a	c≤̃a	NOUN
ejpam-3228	405	5	.	.	PUNCT
ejpam-3228	406	1	then	then	ADV
ejpam-3228	406	2	,	,	PUNCT
ejpam-3228	406	3	the	the	DET
ejpam-3228	406	4	following	follow	VERB
ejpam-3228	406	5	assertions	assertion	NOUN
ejpam-3228	406	6	hold	hold	VERB
ejpam-3228	406	7	;	;	PUNCT
ejpam-3228	406	8	1	1	X
ejpam-3228	406	9	.	.	X
ejpam-3228	407	1	if	if	SCONJ
ejpam-3228	407	2	b⊆̃c	b⊆̃c	NOUN
ejpam-3228	407	3	,	,	PUNCT
ejpam-3228	407	4	α	α	PROPN
ejpam-3228	407	5	∈	∈	PROPN
ejpam-3228	408	1	p	p	X
ejpam-3228	408	2	(	(	PUNCT
ejpam-3228	408	3	u	u	NOUN
ejpam-3228	408	4	)	)	PUNCT
ejpam-3228	408	5	.	.	PUNCT
ejpam-3228	409	1	then	then	ADV
ejpam-3228	409	2	cα̃	cα̃	VERB
ejpam-3228	409	3	⊆	⊆	NUM
ejpam-3228	409	4	bα̃	bα̃	ADJ
ejpam-3228	409	5	,	,	PUNCT
ejpam-3228	409	6	2	2	NUM
ejpam-3228	409	7	.	.	PUNCT
ejpam-3228	409	8	let	let	VERB
ejpam-3228	409	9	α2	α2	PROPN
ejpam-3228	409	10	⊆	⊆	NUM
ejpam-3228	409	11	α1	α1	NOUN
ejpam-3228	409	12	,	,	PUNCT
ejpam-3228	409	13	with	with	ADP
ejpam-3228	409	14	α1	α1	PROPN
ejpam-3228	409	15	,	,	PUNCT
ejpam-3228	409	16	α2	α2	PROPN
ejpam-3228	409	17	∈	∈	PROPN
ejpam-3228	409	18	p	p	X
ejpam-3228	409	19	(	(	PUNCT
ejpam-3228	409	20	u	u	NOUN
ejpam-3228	409	21	)	)	PUNCT
ejpam-3228	409	22	.	.	PUNCT
ejpam-3228	410	1	then	then	ADV
ejpam-3228	410	2	bα̃2	bα̃2	NOUN
ejpam-3228	410	3	⊆	⊆	NUM
ejpam-3228	410	4	bα̃1	bα̃1	NOUN
ejpam-3228	410	5	,	,	PUNCT
ejpam-3228	410	6	3	3	NUM
ejpam-3228	410	7	.	.	X
ejpam-3228	411	1	b=̃c	b=̃c	PROPN
ejpam-3228	411	2	⇔	⇔	PROPN
ejpam-3228	411	3	bα̃	bα̃	PROPN
ejpam-3228	412	1	=	=	SYM
ejpam-3228	412	2	cα̃	cα̃	NOUN
ejpam-3228	412	3	,	,	PUNCT
ejpam-3228	412	4	for	for	ADP
ejpam-3228	412	5	all	all	DET
ejpam-3228	412	6	α	α	NOUN
ejpam-3228	412	7	∈	∈	NOUN
ejpam-3228	412	8	p	p	X
ejpam-3228	412	9	(	(	PUNCT
ejpam-3228	412	10	u	u	NOUN
ejpam-3228	412	11	)	)	PUNCT
ejpam-3228	412	12	.	.	PUNCT
ejpam-3228	413	1	proof	proof	NOUN
ejpam-3228	413	2	.	.	PUNCT
ejpam-3228	414	1	let	let	VERB
ejpam-3228	414	2	b≤̃a	b≤̃a	ADV
ejpam-3228	414	3	and	and	CCONJ
ejpam-3228	414	4	c≤̃a	c≤̃a	NOUN
ejpam-3228	414	5	.	.	PUNCT
ejpam-3228	415	1	1	1	X
ejpam-3228	415	2	.	.	X
ejpam-3228	415	3	let	let	VERB
ejpam-3228	415	4	x	x	SYM
ejpam-3228	415	5	∈	∈	PROPN
ejpam-3228	415	6	cα̃	cα̃	NOUN
ejpam-3228	415	7	,	,	PUNCT
ejpam-3228	415	8	then	then	ADV
ejpam-3228	415	9	,	,	PUNCT
ejpam-3228	415	10	fc(x	fc(x	NOUN
ejpam-3228	415	11	)	)	PUNCT
ejpam-3228	415	12	⊆	⊆	NUM
ejpam-3228	415	13	α	α	NOUN
ejpam-3228	415	14	.	.	PUNCT
ejpam-3228	416	1	since	since	SCONJ
ejpam-3228	416	2	b⊆̃c	b⊆̃c	NOUN
ejpam-3228	416	3	,	,	PUNCT
ejpam-3228	417	1	α	α	PROPN
ejpam-3228	417	2	∈	∈	PROPN
ejpam-3228	417	3	p	p	X
ejpam-3228	417	4	(	(	PUNCT
ejpam-3228	417	5	u	u	NOUN
ejpam-3228	417	6	)	)	PUNCT
ejpam-3228	417	7	.	.	PUNCT
ejpam-3228	418	1	this	this	PRON
ejpam-3228	418	2	implies	imply	VERB
ejpam-3228	418	3	that	that	SCONJ
ejpam-3228	418	4	fb(x	fb(x	VERB
ejpam-3228	418	5	)	)	PUNCT
ejpam-3228	418	6	⊆	⊆	NUM
ejpam-3228	418	7	fc(x	fc(x	NOUN
ejpam-3228	418	8	)	)	PUNCT
ejpam-3228	418	9	⊆	⊆	NUM
ejpam-3228	418	10	α⇒	α⇒	NUM
ejpam-3228	418	11	fb(x	fb(x	ADJ
ejpam-3228	418	12	)	)	PUNCT
ejpam-3228	418	13	⊆	⊆	NUM
ejpam-3228	418	14	α⇒	α⇒	SYM
ejpam-3228	418	15	x	x	SYM
ejpam-3228	418	16	∈	∈	NOUN
ejpam-3228	418	17	bα̃.	bα̃.	NOUN
ejpam-3228	418	18	hence	hence	ADV
ejpam-3228	418	19	cα̃	cα̃	VERB
ejpam-3228	418	20	⊆	⊆	NUM
ejpam-3228	418	21	bα̃.	bα̃.	ADP
ejpam-3228	418	22	2	2	NUM
ejpam-3228	418	23	.	.	PUNCT
ejpam-3228	419	1	let	let	VERB
ejpam-3228	419	2	α2	α2	PROPN
ejpam-3228	419	3	⊆	⊆	NUM
ejpam-3228	419	4	α1	α1	PROPN
ejpam-3228	419	5	,	,	PUNCT
ejpam-3228	419	6	α1	α1	PROPN
ejpam-3228	419	7	,	,	PUNCT
ejpam-3228	419	8	α2	α2	PROPN
ejpam-3228	419	9	∈	∈	PROPN
ejpam-3228	419	10	p	p	X
ejpam-3228	419	11	(	(	PUNCT
ejpam-3228	419	12	u	u	NOUN
ejpam-3228	419	13	)	)	PUNCT
ejpam-3228	419	14	,	,	PUNCT
ejpam-3228	419	15	and	and	CCONJ
ejpam-3228	419	16	x	x	PUNCT
ejpam-3228	419	17	∈	∈	PROPN
ejpam-3228	419	18	bα̃2	bα̃2	NOUN
ejpam-3228	419	19	.	.	PUNCT
ejpam-3228	420	1	then	then	ADV
ejpam-3228	420	2	fb(x	fb(x	NOUN
ejpam-3228	420	3	)	)	PUNCT
ejpam-3228	420	4	⊆	⊆	NUM
ejpam-3228	420	5	α2	α2	ADJ
ejpam-3228	420	6	.	.	PUNCT
ejpam-3228	421	1	since	since	ADV
ejpam-3228	421	2	,	,	PUNCT
ejpam-3228	421	3	α2	α2	PROPN
ejpam-3228	421	4	⊆	⊆	NUM
ejpam-3228	421	5	α1	α1	PROPN
ejpam-3228	421	6	implies	imply	VERB
ejpam-3228	421	7	that	that	SCONJ
ejpam-3228	421	8	fb(x	fb(x	VERB
ejpam-3228	421	9	)	)	PUNCT
ejpam-3228	421	10	⊆	⊆	NUM
ejpam-3228	421	11	α1	α1	PROPN
ejpam-3228	421	12	⇒	⇒	NOUN
ejpam-3228	421	13	x	x	SYM
ejpam-3228	421	14	∈	∈	PROPN
ejpam-3228	421	15	bα̃1	bα̃1	PROPN
ejpam-3228	421	16	.	.	PUNCT
ejpam-3228	422	1	therefore	therefore	ADV
ejpam-3228	422	2	,	,	PUNCT
ejpam-3228	422	3	bα̃2	bα̃2	NOUN
ejpam-3228	422	4	⊆	⊆	NUM
ejpam-3228	422	5	bα̃1	bα̃1	PROPN
ejpam-3228	422	6	.	.	PUNCT
ejpam-3228	423	1	proof	proof	NOUN
ejpam-3228	423	2	.	.	PUNCT
ejpam-3228	424	1	the	the	DET
ejpam-3228	424	2	proof	proof	NOUN
ejpam-3228	424	3	is	be	AUX
ejpam-3228	424	4	straight	straight	ADV
ejpam-3228	424	5	forward	forward	ADV
ejpam-3228	424	6	.	.	PUNCT
ejpam-3228	425	1	theorem	theorem	ADJ
ejpam-3228	425	2	9	9	NUM
ejpam-3228	425	3	.	.	PUNCT
ejpam-3228	426	1	let	let	VERB
ejpam-3228	426	2	b	b	X
ejpam-3228	426	3	,	,	PUNCT
ejpam-3228	426	4	c	c	PROPN
ejpam-3228	426	5	are	be	AUX
ejpam-3228	426	6	any	any	DET
ejpam-3228	426	7	two	two	NUM
ejpam-3228	426	8	soft	soft	ADJ
ejpam-3228	426	9	sets	set	NOUN
ejpam-3228	426	10	of	of	ADP
ejpam-3228	426	11	g	g	NOUN
ejpam-3228	426	12	over	over	ADP
ejpam-3228	426	13	u	u	PROPN
ejpam-3228	426	14	and	and	CCONJ
ejpam-3228	426	15	α	α	NOUN
ejpam-3228	426	16	∈	∈	PROPN
ejpam-3228	427	1	p	p	X
ejpam-3228	427	2	(	(	PUNCT
ejpam-3228	427	3	u	u	NOUN
ejpam-3228	427	4	)	)	PUNCT
ejpam-3228	427	5	.	.	PUNCT
ejpam-3228	428	1	then	then	ADV
ejpam-3228	428	2	,	,	PUNCT
ejpam-3228	428	3	1	1	X
ejpam-3228	428	4	.	.	X
ejpam-3228	428	5	bα̃	bα̃	PROPN
ejpam-3228	428	6	∪	∪	ADP
ejpam-3228	428	7	cα̃	cα̃	NOUN
ejpam-3228	428	8	⊆	⊆	NUM
ejpam-3228	428	9	(	(	PUNCT
ejpam-3228	428	10	b∪̃c)α̃	b∪̃c)α̃	ADJ
ejpam-3228	428	11	,	,	PUNCT
ejpam-3228	428	12	2	2	NUM
ejpam-3228	428	13	.	.	PUNCT
ejpam-3228	428	14	bα̃	bα̃	ADJ
ejpam-3228	428	15	∩	∩	NOUN
ejpam-3228	428	16	cα̃	cα̃	X
ejpam-3228	429	1	=	=	SYM
ejpam-3228	429	2	(	(	PUNCT
ejpam-3228	429	3	b∩̃c)α̃.	b∩̃c)α̃.	ADP
ejpam-3228	429	4	theorem	theorem	VERB
ejpam-3228	429	5	10	10	NUM
ejpam-3228	429	6	.	.	PUNCT
ejpam-3228	430	1	let	let	VERB
ejpam-3228	430	2	{	{	PUNCT
ejpam-3228	430	3	bi	bi	NOUN
ejpam-3228	430	4	:	:	PUNCT
ejpam-3228	430	5	i	i	PRON
ejpam-3228	430	6	∈	∈	VERB
ejpam-3228	431	1	i	i	PRON
ejpam-3228	431	2	}	}	PUNCT
ejpam-3228	431	3	be	be	VERB
ejpam-3228	431	4	the	the	DET
ejpam-3228	431	5	family	family	NOUN
ejpam-3228	431	6	of	of	ADP
ejpam-3228	431	7	soft	soft	ADJ
ejpam-3228	431	8	sets	set	NOUN
ejpam-3228	431	9	of	of	ADP
ejpam-3228	431	10	g	g	NOUN
ejpam-3228	431	11	over	over	ADP
ejpam-3228	431	12	u	u	PROPN
ejpam-3228	431	13	.	.	PUNCT
ejpam-3228	432	1	then	then	ADV
ejpam-3228	432	2	,	,	PUNCT
ejpam-3228	432	3	for	for	ADP
ejpam-3228	432	4	any	any	DET
ejpam-3228	432	5	α	α	NOUN
ejpam-3228	432	6	∈	∈	NOUN
ejpam-3228	432	7	p	p	X
ejpam-3228	432	8	(	(	PUNCT
ejpam-3228	432	9	u	u	NOUN
ejpam-3228	432	10	)	)	PUNCT
ejpam-3228	432	11	references	reference	VERB
ejpam-3228	432	12	534	534	NUM
ejpam-3228	432	13	1	1	NUM
ejpam-3228	432	14	.	.	PUNCT
ejpam-3228	433	1	⋃	⋃	VERB
ejpam-3228	433	2	i∈i	i∈i	ADJ
ejpam-3228	433	3	(	(	PUNCT
ejpam-3228	433	4	biα̃	biα̃	PROPN
ejpam-3228	433	5	)	)	PUNCT
ejpam-3228	433	6	⊆	⊆	NUM
ejpam-3228	433	7	(	(	PUNCT
ejpam-3228	433	8	∪̃	∪̃	PROPN
ejpam-3228	433	9	i∈i	i∈i	ADJ
ejpam-3228	433	10	bi	bi	NOUN
ejpam-3228	433	11	)	)	PUNCT
ejpam-3228	433	12	α̃	α̃	PROPN
ejpam-3228	433	13	,	,	PUNCT
ejpam-3228	433	14	2	2	X
ejpam-3228	433	15	.	.	PUNCT
ejpam-3228	434	1	∩	∩	NOUN
ejpam-3228	434	2	i∈i	i∈i	ADJ
ejpam-3228	434	3	(	(	PUNCT
ejpam-3228	434	4	biα̃	biα̃	PROPN
ejpam-3228	434	5	)	)	PUNCT
ejpam-3228	434	6	=	=	NOUN
ejpam-3228	434	7	(	(	PUNCT
ejpam-3228	434	8	∩̃	∩̃	NUM
ejpam-3228	434	9	i∈i	i∈i	ADJ
ejpam-3228	434	10	bi	bi	NOUN
ejpam-3228	434	11	)	)	PUNCT
ejpam-3228	434	12	α̃	α̃	PROPN
ejpam-3228	434	13	.	.	PUNCT
ejpam-3228	435	1	theorem	theorem	VERB
ejpam-3228	435	2	11	11	NUM
ejpam-3228	435	3	.	.	PUNCT
ejpam-3228	436	1	let	let	VERB
ejpam-3228	436	2	g	g	PRON
ejpam-3228	436	3	be	be	AUX
ejpam-3228	436	4	an	an	DET
ejpam-3228	436	5	ag	ag	PROPN
ejpam-3228	436	6	-	-	PUNCT
ejpam-3228	436	7	group	group	NOUN
ejpam-3228	436	8	and	and	CCONJ
ejpam-3228	436	9	α	α	NOUN
ejpam-3228	436	10	∈	∈	PROPN
ejpam-3228	437	1	p	p	X
ejpam-3228	437	2	(	(	PUNCT
ejpam-3228	437	3	u	u	NOUN
ejpam-3228	437	4	)	)	PUNCT
ejpam-3228	437	5	.	.	PUNCT
ejpam-3228	438	1	then	then	ADV
ejpam-3228	438	2	a	a	DET
ejpam-3228	438	3	∈	∈	PROPN
ejpam-3228	438	4	s∪ag(u	s∪ag(u	NOUN
ejpam-3228	438	5	)	)	PUNCT
ejpam-3228	438	6	if	if	SCONJ
ejpam-3228	438	7	and	and	CCONJ
ejpam-3228	438	8	only	only	ADV
ejpam-3228	438	9	if	if	SCONJ
ejpam-3228	438	10	aα̃	aα̃	PROPN
ejpam-3228	438	11	is	be	AUX
ejpam-3228	438	12	a	a	DET
ejpam-3228	438	13	subgroup	subgroup	NOUN
ejpam-3228	438	14	of	of	ADP
ejpam-3228	438	15	g	g	PROPN
ejpam-3228	438	16	,	,	PUNCT
ejpam-3228	438	17	where	where	SCONJ
ejpam-3228	438	18	aα̃	aα̃	PROPN
ejpam-3228	438	19	6=	6=	ADP
ejpam-3228	438	20	∅.	∅.	PRON
ejpam-3228	438	21	proof	proof	NOUN
ejpam-3228	438	22	.	.	PUNCT
ejpam-3228	439	1	let	let	VERB
ejpam-3228	439	2	a	a	DET
ejpam-3228	439	3	∈	∈	PROPN
ejpam-3228	439	4	s∪ag(u	s∪ag(u	NUM
ejpam-3228	439	5	)	)	PUNCT
ejpam-3228	439	6	and	and	CCONJ
ejpam-3228	439	7	aα̃	aα̃	PROPN
ejpam-3228	439	8	6=	6=	AUX
ejpam-3228	439	9	∅.	∅.	PROPN
ejpam-3228	439	10	suppose	suppose	VERB
ejpam-3228	439	11	that	that	SCONJ
ejpam-3228	439	12	x	x	NOUN
ejpam-3228	439	13	,	,	PUNCT
ejpam-3228	439	14	y	y	PROPN
ejpam-3228	439	15	∈	∈	PROPN
ejpam-3228	439	16	aα̃	aα̃	PROPN
ejpam-3228	439	17	,	,	PUNCT
ejpam-3228	439	18	then	then	ADV
ejpam-3228	439	19	fa(x	fa(x	NOUN
ejpam-3228	439	20	)	)	PUNCT
ejpam-3228	439	21	⊆	⊆	NUM
ejpam-3228	439	22	α	α	NOUN
ejpam-3228	439	23	and	and	CCONJ
ejpam-3228	439	24	fa(y	fa(y	NOUN
ejpam-3228	439	25	)	)	PUNCT
ejpam-3228	439	26	⊆	⊆	NUM
ejpam-3228	439	27	α	α	NOUN
ejpam-3228	439	28	.	.	PUNCT
ejpam-3228	440	1	therefore	therefore	ADV
ejpam-3228	440	2	,	,	PUNCT
ejpam-3228	440	3	fa(xy−1	fa(xy−1	NUM
ejpam-3228	440	4	)	)	PUNCT
ejpam-3228	440	5	⊆	⊆	NUM
ejpam-3228	440	6	fa(x	fa(x	NOUN
ejpam-3228	440	7	)	)	PUNCT
ejpam-3228	440	8	∪	∪	ADP
ejpam-3228	440	9	fa(y	fa(y	PROPN
ejpam-3228	440	10	)	)	PUNCT
ejpam-3228	440	11	⊆	⊆	NUM
ejpam-3228	440	12	α	α	NOUN
ejpam-3228	440	13	.	.	PUNCT
ejpam-3228	441	1	this	this	PRON
ejpam-3228	441	2	implies	imply	VERB
ejpam-3228	441	3	that	that	SCONJ
ejpam-3228	441	4	,	,	PUNCT
ejpam-3228	441	5	xy−1	xy−1	PROPN
ejpam-3228	441	6	∈	∈	PROPN
ejpam-3228	441	7	aα̃.	aα̃.	PUNCT
ejpam-3228	441	8	hence	hence	ADV
ejpam-3228	441	9	,	,	PUNCT
ejpam-3228	441	10	aα̃	aα̃	PROPN
ejpam-3228	441	11	is	be	AUX
ejpam-3228	441	12	a	a	DET
ejpam-3228	441	13	subgroup	subgroup	NOUN
ejpam-3228	441	14	of	of	ADP
ejpam-3228	441	15	g.	g.	PROPN
ejpam-3228	441	16	conversely	conversely	ADV
ejpam-3228	441	17	,	,	PUNCT
ejpam-3228	441	18	suppose	suppose	VERB
ejpam-3228	441	19	that	that	SCONJ
ejpam-3228	441	20	aα̃	aα̃	PROPN
ejpam-3228	441	21	is	be	AUX
ejpam-3228	441	22	a	a	DET
ejpam-3228	441	23	subgroup	subgroup	NOUN
ejpam-3228	441	24	of	of	ADP
ejpam-3228	441	25	g	g	NOUN
ejpam-3228	441	26	for	for	ADP
ejpam-3228	441	27	any	any	DET
ejpam-3228	441	28	aα̃	aα̃	PROPN
ejpam-3228	441	29	6=	6=	AUX
ejpam-3228	441	30	∅.	∅.	ADV
ejpam-3228	441	31	let	let	VERB
ejpam-3228	441	32	x	x	PRON
ejpam-3228	441	33	,	,	PUNCT
ejpam-3228	441	34	y	y	PROPN
ejpam-3228	441	35	∈	∈	PROPN
ejpam-3228	441	36	g	g	PROPN
ejpam-3228	441	37	such	such	ADJ
ejpam-3228	441	38	that	that	PRON
ejpam-3228	441	39	fa(x	fa(x	NOUN
ejpam-3228	441	40	)	)	PUNCT
ejpam-3228	441	41	=	=	SYM
ejpam-3228	441	42	β	β	X
ejpam-3228	441	43	and	and	CCONJ
ejpam-3228	441	44	fa(y	fa(y	PROPN
ejpam-3228	441	45	)	)	PUNCT
ejpam-3228	441	46	=	=	SYM
ejpam-3228	441	47	γ	γ	NOUN
ejpam-3228	441	48	and	and	CCONJ
ejpam-3228	441	49	let	let	VERB
ejpam-3228	441	50	δ	δ	PROPN
ejpam-3228	441	51	=	=	VERB
ejpam-3228	441	52	β	β	PROPN
ejpam-3228	441	53	∪	∪	ADP
ejpam-3228	441	54	γ	γ	PROPN
ejpam-3228	441	55	.	.	PROPN
ejpam-3228	441	56	then	then	ADV
ejpam-3228	441	57	x	x	X
ejpam-3228	441	58	,	,	PUNCT
ejpam-3228	441	59	y	y	PROPN
ejpam-3228	441	60	∈	∈	PROPN
ejpam-3228	441	61	aδ̃	aδ̃	X
ejpam-3228	441	62	and	and	CCONJ
ejpam-3228	441	63	aδ̃	aδ̃	PRON
ejpam-3228	441	64	≤	≤	NOUN
ejpam-3228	441	65	g	g	NOUN
ejpam-3228	441	66	by	by	ADP
ejpam-3228	441	67	hypothesis	hypothesis	NOUN
ejpam-3228	441	68	.	.	PUNCT
ejpam-3228	442	1	so	so	ADV
ejpam-3228	442	2	xy−1	xy−1	PROPN
ejpam-3228	442	3	∈	∈	PROPN
ejpam-3228	442	4	aδ̃.	aδ̃.	NOUN
ejpam-3228	442	5	therefore	therefore	ADV
ejpam-3228	442	6	,	,	PUNCT
ejpam-3228	442	7	fa(xy−1	fa(xy−1	NUM
ejpam-3228	442	8	)	)	PUNCT
ejpam-3228	442	9	⊆	⊆	NUM
ejpam-3228	442	10	δ	δ	X
ejpam-3228	442	11	=	=	PUNCT
ejpam-3228	442	12	β	β	X
ejpam-3228	442	13	∪	∪	VERB
ejpam-3228	442	14	γ	γ	X
ejpam-3228	442	15	=	=	SYM
ejpam-3228	442	16	fa(x	fa(x	PROPN
ejpam-3228	442	17	)	)	PUNCT
ejpam-3228	442	18	∪	∪	ADP
ejpam-3228	442	19	fa(y	fa(y	PROPN
ejpam-3228	442	20	)	)	PUNCT
ejpam-3228	442	21	.	.	PUNCT
ejpam-3228	443	1	hence	hence	ADV
ejpam-3228	443	2	,	,	PUNCT
ejpam-3228	443	3	a	a	DET
ejpam-3228	443	4	∈	∈	PROPN
ejpam-3228	443	5	s∪ag(u	s∪ag(u	NUM
ejpam-3228	443	6	)	)	PUNCT
ejpam-3228	443	7	.	.	PUNCT
ejpam-3228	444	1	theorem	theorem	NOUN
ejpam-3228	444	2	12	12	NUM
ejpam-3228	444	3	.	.	PUNCT
ejpam-3228	445	1	let	let	VERB
ejpam-3228	445	2	a	a	DET
ejpam-3228	445	3	∈	∈	PROPN
ejpam-3228	445	4	ns∪ag(u	ns∪ag(u	NUM
ejpam-3228	445	5	)	)	PUNCT
ejpam-3228	445	6	.	.	PUNCT
ejpam-3228	446	1	then	then	ADV
ejpam-3228	446	2	,	,	PUNCT
ejpam-3228	446	3	aẽ	aẽ	ADV
ejpam-3228	446	4	is	be	AUX
ejpam-3228	446	5	a	a	DET
ejpam-3228	446	6	normal	normal	ADJ
ejpam-3228	446	7	ag	ag	PROPN
ejpam-3228	446	8	-	-	PUNCT
ejpam-3228	446	9	subgroup	subgroup	NOUN
ejpam-3228	446	10	of	of	ADP
ejpam-3228	446	11	g.	g.	PROPN
ejpam-3228	446	12	proof	proof	NOUN
ejpam-3228	446	13	.	.	PUNCT
ejpam-3228	447	1	by	by	ADP
ejpam-3228	447	2	theorem	theorem	NOUN
ejpam-3228	447	3	8	8	NUM
ejpam-3228	447	4	,	,	PUNCT
ejpam-3228	447	5	aẽ	aẽ	ADV
ejpam-3228	447	6	≤	≤	NUM
ejpam-3228	447	7	g.	g.	NOUN
ejpam-3228	447	8	let	let	VERB
ejpam-3228	447	9	x	x	PUNCT
ejpam-3228	447	10	∈	∈	PROPN
ejpam-3228	447	11	aẽ	aẽ	NOUN
ejpam-3228	448	1	and	and	CCONJ
ejpam-3228	448	2	g	g	PROPN
ejpam-3228	448	3	∈	∈	PROPN
ejpam-3228	448	4	g.	g.	NOUN
ejpam-3228	448	5	then	then	ADV
ejpam-3228	448	6	,	,	PUNCT
ejpam-3228	448	7	by	by	ADP
ejpam-3228	448	8	definition	definition	NOUN
ejpam-3228	448	9	8	8	NUM
ejpam-3228	448	10	,	,	PUNCT
ejpam-3228	448	11	we	we	PRON
ejpam-3228	448	12	get	get	VERB
ejpam-3228	448	13	fa(gx	fa(gx	ADJ
ejpam-3228	448	14	·	·	PUNCT
ejpam-3228	448	15	g−1	g−1	X
ejpam-3228	448	16	)	)	PUNCT
ejpam-3228	448	17	=	=	SYM
ejpam-3228	449	1	fa(x	fa(x	X
ejpam-3228	449	2	)	)	PUNCT
ejpam-3228	449	3	=	=	SYM
ejpam-3228	449	4	fa(e	fa(e	X
ejpam-3228	449	5	)	)	PUNCT
ejpam-3228	449	6	this	this	PRON
ejpam-3228	449	7	implies	imply	VERB
ejpam-3228	449	8	that	that	SCONJ
ejpam-3228	449	9	gx	gx	PROPN
ejpam-3228	449	10	·	·	PUNCT
ejpam-3228	449	11	g−1	g−1	PROPN
ejpam-3228	449	12	∈	∈	PROPN
ejpam-3228	449	13	aẽ.	aẽ.	NOUN
ejpam-3228	449	14	hence	hence	ADV
ejpam-3228	449	15	,	,	PUNCT
ejpam-3228	449	16	aẽ	aẽ	ADV
ejpam-3228	449	17	is	be	AUX
ejpam-3228	449	18	a	a	DET
ejpam-3228	449	19	normal	normal	ADJ
ejpam-3228	449	20	ag	ag	PROPN
ejpam-3228	449	21	-	-	PUNCT
ejpam-3228	449	22	subgroup	subgroup	NOUN
ejpam-3228	449	23	of	of	ADP
ejpam-3228	449	24	g.	g.	PROPN
ejpam-3228	449	25	5	5	NUM
ejpam-3228	449	26	.	.	PUNCT
ejpam-3228	449	27	conclusion	conclusion	NOUN
ejpam-3228	449	28	in	in	ADP
ejpam-3228	449	29	this	this	DET
ejpam-3228	449	30	paper	paper	NOUN
ejpam-3228	449	31	,	,	PUNCT
ejpam-3228	449	32	the	the	DET
ejpam-3228	449	33	concepts	concept	NOUN
ejpam-3228	449	34	of	of	ADP
ejpam-3228	449	35	“	"	PUNCT
ejpam-3228	449	36	soft	soft	ADJ
ejpam-3228	449	37	uni	uni	ADJ
ejpam-3228	449	38	-	-	PUNCT
ejpam-3228	449	39	groups	group	NOUN
ejpam-3228	449	40	”	"	PUNCT
ejpam-3228	449	41	are	be	AUX
ejpam-3228	449	42	extended	extend	VERB
ejpam-3228	449	43	to	to	ADP
ejpam-3228	449	44	soft	soft	ADJ
ejpam-3228	449	45	uni	uni	ADJ
ejpam-3228	449	46	-	-	PUNCT
ejpam-3228	449	47	ag	ag	ADJ
ejpam-3228	449	48	-	-	PUNCT
ejpam-3228	449	49	groups	group	NOUN
ejpam-3228	449	50	.	.	PUNCT
ejpam-3228	450	1	the	the	DET
ejpam-3228	450	2	notion	notion	NOUN
ejpam-3228	450	3	of	of	ADP
ejpam-3228	450	4	conjugates	conjugate	NOUN
ejpam-3228	450	5	soft	soft	ADJ
ejpam-3228	450	6	uni	uni	ADJ
ejpam-3228	450	7	-	-	PUNCT
ejpam-3228	450	8	ag	ag	ADJ
ejpam-3228	450	9	-	-	PUNCT
ejpam-3228	450	10	groups	group	NOUN
ejpam-3228	450	11	,	,	PUNCT
ejpam-3228	450	12	normal	normal	ADJ
ejpam-3228	450	13	soft	soft	ADJ
ejpam-3228	450	14	uni	uni	ADJ
ejpam-3228	450	15	-	-	PUNCT
ejpam-3228	450	16	ag	ag	ADJ
ejpam-3228	450	17	-	-	PUNCT
ejpam-3228	450	18	groups	group	NOUN
ejpam-3228	450	19	,	,	PUNCT
ejpam-3228	450	20	e	e	NOUN
ejpam-3228	450	21	-	-	NOUN
ejpam-3228	450	22	set	set	VERB
ejpam-3228	450	23	and	and	CCONJ
ejpam-3228	450	24	αinclusion	αinclusion	NOUN
ejpam-3228	450	25	of	of	ADP
ejpam-3228	450	26	soft	soft	ADJ
ejpam-3228	450	27	uni	uni	ADJ
ejpam-3228	450	28	-	-	PUNCT
ejpam-3228	450	29	ag	ag	ADJ
ejpam-3228	450	30	-	-	PUNCT
ejpam-3228	450	31	groups	group	NOUN
ejpam-3228	450	32	are	be	AUX
ejpam-3228	450	33	presented	present	VERB
ejpam-3228	450	34	and	and	CCONJ
ejpam-3228	450	35	investigated	investigate	VERB
ejpam-3228	450	36	.	.	PUNCT
ejpam-3228	451	1	in	in	ADP
ejpam-3228	451	2	future	future	NOUN
ejpam-3228	451	3	,	,	PUNCT
ejpam-3228	451	4	these	these	DET
ejpam-3228	451	5	concepts	concept	NOUN
ejpam-3228	451	6	can	can	AUX
ejpam-3228	451	7	further	far	ADV
ejpam-3228	451	8	be	be	AUX
ejpam-3228	451	9	generalized	generalize	VERB
ejpam-3228	451	10	to	to	ADP
ejpam-3228	451	11	bipolar	bipolar	ADJ
ejpam-3228	451	12	soft	soft	ADJ
ejpam-3228	451	13	uni	uni	ADJ
ejpam-3228	451	14	-	-	PUNCT
ejpam-3228	451	15	ag	ag	ADJ
ejpam-3228	451	16	-	-	PUNCT
ejpam-3228	451	17	groups	group	NOUN
ejpam-3228	451	18	,	,	PUNCT
ejpam-3228	451	19	soft	soft	ADJ
ejpam-3228	451	20	uni	uni	ADJ
ejpam-3228	451	21	-	-	ADJ
ejpam-3228	451	22	la	la	ADJ
ejpam-3228	451	23	-	-	PUNCT
ejpam-3228	451	24	rings	ring	NOUN
ejpam-3228	451	25	and	and	CCONJ
ejpam-3228	451	26	soft	soft	ADJ
ejpam-3228	451	27	unila	unila	NOUN
ejpam-3228	451	28	-	-	PUNCT
ejpam-3228	451	29	near	near	ADP
ejpam-3228	451	30	-	-	PUNCT
ejpam-3228	451	31	rings	ring	NOUN
ejpam-3228	451	32	.	.	PUNCT
ejpam-3228	452	1	moreover	moreover	ADV
ejpam-3228	452	2	,	,	PUNCT
ejpam-3228	452	3	the	the	DET
ejpam-3228	452	4	study	study	NOUN
ejpam-3228	452	5	of	of	ADP
ejpam-3228	452	6	isomorphism	isomorphism	NOUN
ejpam-3228	452	7	theorems	theorem	NOUN
ejpam-3228	452	8	may	may	AUX
ejpam-3228	452	9	also	also	ADV
ejpam-3228	452	10	be	be	AUX
ejpam-3228	452	11	a	a	DET
ejpam-3228	452	12	nice	nice	ADJ
ejpam-3228	452	13	work	work	NOUN
ejpam-3228	452	14	in	in	ADP
ejpam-3228	452	15	this	this	DET
ejpam-3228	452	16	area	area	NOUN
ejpam-3228	452	17	.	.	PUNCT
ejpam-3228	453	1	acknowledgements	acknowledgement	NOUN
ejpam-3228	453	2	this	this	DET
ejpam-3228	453	3	research	research	NOUN
ejpam-3228	453	4	is	be	AUX
ejpam-3228	453	5	financially	financially	ADV
ejpam-3228	453	6	supported	support	VERB
ejpam-3228	453	7	by	by	ADP
ejpam-3228	453	8	hec	hec	PROPN
ejpam-3228	453	9	through	through	ADP
ejpam-3228	453	10	nrpu	nrpu	NOUN
ejpam-3228	453	11	project-3509	project-3509	NOUN
ejpam-3228	453	12	.	.	PUNCT
ejpam-3228	454	1	references	reference	NOUN
ejpam-3228	454	2	[	[	X
ejpam-3228	454	3	1	1	X
ejpam-3228	454	4	]	]	PUNCT
ejpam-3228	454	5	d.	d.	PROPN
ejpam-3228	454	6	a.	a.	PROPN
ejpam-3228	454	7	molodtsov	molodtsov	PROPN
ejpam-3228	454	8	,	,	PUNCT
ejpam-3228	454	9	soft	soft	ADJ
ejpam-3228	454	10	set	set	NOUN
ejpam-3228	454	11	theory	theory	NOUN
ejpam-3228	454	12	-	-	PUNCT
ejpam-3228	454	13	first	first	ADJ
ejpam-3228	454	14	results	result	NOUN
ejpam-3228	454	15	,	,	PUNCT
ejpam-3228	454	16	computer	computer	NOUN
ejpam-3228	454	17	and	and	CCONJ
ejpam-3228	454	18	mathematics	mathematic	NOUN
ejpam-3228	454	19	with	with	ADP
ejpam-3228	454	20	applications	application	NOUN
ejpam-3228	454	21	37	37	NUM
ejpam-3228	454	22	,	,	PUNCT
ejpam-3228	454	23	19	19	NUM
ejpam-3228	454	24	-	-	SYM
ejpam-3228	454	25	31	31	NUM
ejpam-3228	454	26	,	,	PUNCT
ejpam-3228	454	27	1999	1999	NUM
ejpam-3228	454	28	.	.	PUNCT
ejpam-3228	455	1	references	reference	NOUN
ejpam-3228	455	2	535	535	NUM
ejpam-3228	456	1	[	[	X
ejpam-3228	456	2	2	2	NUM
ejpam-3228	456	3	]	]	PUNCT
ejpam-3228	456	4	p.	p.	NOUN
ejpam-3228	456	5	k.	k.	PROPN
ejpam-3228	457	1	maji	maji	PROPN
ejpam-3228	457	2	,	,	PUNCT
ejpam-3228	457	3	r.	r.	PROPN
ejpam-3228	457	4	biswas	biswas	PROPN
ejpam-3228	457	5	and	and	CCONJ
ejpam-3228	457	6	a.	a.	PROPN
ejpam-3228	457	7	r.	r.	PROPN
ejpam-3228	457	8	roy	roy	PROPN
ejpam-3228	457	9	,	,	PUNCT
ejpam-3228	457	10	soft	soft	ADJ
ejpam-3228	457	11	set	set	NOUN
ejpam-3228	457	12	theory	theory	NOUN
ejpam-3228	457	13	,	,	PUNCT
ejpam-3228	457	14	computer	computer	NOUN
ejpam-3228	457	15	mathematics	mathematic	NOUN
ejpam-3228	457	16	with	with	ADP
ejpam-3228	457	17	applications	application	NOUN
ejpam-3228	457	18	,	,	PUNCT
ejpam-3228	457	19	45	45	NUM
ejpam-3228	457	20	,	,	PUNCT
ejpam-3228	457	21	555	555	NUM
ejpam-3228	457	22	-	-	SYM
ejpam-3228	457	23	562	562	NUM
ejpam-3228	457	24	,	,	PUNCT
ejpam-3228	457	25	2003	2003	NUM
ejpam-3228	457	26	.	.	PUNCT
ejpam-3228	458	1	[	[	X
ejpam-3228	458	2	3	3	X
ejpam-3228	458	3	]	]	X
ejpam-3228	458	4	n.	n.	PROPN
ejpam-3228	458	5	çağman	çağman	PROPN
ejpam-3228	458	6	and	and	CCONJ
ejpam-3228	458	7	s.	s.	PROPN
ejpam-3228	458	8	enginoğlu	enginoğlu	PROPN
ejpam-3228	458	9	,	,	PUNCT
ejpam-3228	458	10	soft	soft	ADJ
ejpam-3228	458	11	set	set	NOUN
ejpam-3228	458	12	theory	theory	NOUN
ejpam-3228	458	13	and	and	CCONJ
ejpam-3228	458	14	uni	uni	ADJ
ejpam-3228	458	15	-	-	ADJ
ejpam-3228	458	16	int	int	NOUN
ejpam-3228	458	17	decision	decision	NOUN
ejpam-3228	458	18	making	making	NOUN
ejpam-3228	458	19	,	,	PUNCT
ejpam-3228	458	20	eur	eur	PROPN
ejpam-3228	458	21	.	.	PUNCT
ejpam-3228	459	1	j.	j.	PROPN
ejpam-3228	459	2	oper	oper	PROPN
ejpam-3228	459	3	res	re	NOUN
ejpam-3228	459	4	207	207	NUM
ejpam-3228	459	5	,	,	PUNCT
ejpam-3228	459	6	848	848	NUM
ejpam-3228	459	7	-	-	SYM
ejpam-3228	459	8	855	855	NUM
ejpam-3228	459	9	,	,	PUNCT
ejpam-3228	459	10	2010	2010	NUM
ejpam-3228	459	11	.	.	PUNCT
ejpam-3228	460	1	[	[	X
ejpam-3228	460	2	4	4	X
ejpam-3228	460	3	]	]	PUNCT
ejpam-3228	460	4	m.	m.	PROPN
ejpam-3228	460	5	i.	i.	PROPN
ejpam-3228	460	6	ali	ali	PROPN
ejpam-3228	460	7	,	,	PUNCT
ejpam-3228	460	8	f.	f.	PROPN
ejpam-3228	460	9	feng	feng	PROPN
ejpam-3228	460	10	,	,	PUNCT
ejpam-3228	460	11	x.	x.	PROPN
ejpam-3228	460	12	liu	liu	PROPN
ejpam-3228	460	13	,	,	PUNCT
ejpam-3228	460	14	w.	w.	PROPN
ejpam-3228	460	15	k.	k.	PROPN
ejpam-3228	460	16	min	min	PROPN
ejpam-3228	460	17	and	and	CCONJ
ejpam-3228	460	18	m.	m.	NOUN
ejpam-3228	460	19	shabir	shabir	PROPN
ejpam-3228	460	20	,	,	PUNCT
ejpam-3228	460	21	on	on	ADP
ejpam-3228	460	22	some	some	DET
ejpam-3228	460	23	new	new	ADJ
ejpam-3228	460	24	operations	operation	NOUN
ejpam-3228	460	25	in	in	ADP
ejpam-3228	460	26	soft	soft	ADJ
ejpam-3228	460	27	set	set	NOUN
ejpam-3228	460	28	theory	theory	NOUN
ejpam-3228	460	29	.	.	PUNCT
ejpam-3228	461	1	computer	computer	NOUN
ejpam-3228	461	2	mathematics	mathematic	NOUN
ejpam-3228	461	3	with	with	ADP
ejpam-3228	461	4	application	application	NOUN
ejpam-3228	461	5	,	,	PUNCT
ejpam-3228	461	6	57	57	NUM
ejpam-3228	461	7	,	,	PUNCT
ejpam-3228	461	8	1547	1547	NUM
ejpam-3228	461	9	-	-	SYM
ejpam-3228	461	10	1553	1553	NUM
ejpam-3228	461	11	,	,	PUNCT
ejpam-3228	461	12	2009	2009	NUM
ejpam-3228	461	13	.	.	PUNCT
ejpam-3228	462	1	[	[	X
ejpam-3228	462	2	5	5	NUM
ejpam-3228	462	3	]	]	PUNCT
ejpam-3228	462	4	a.	a.	NOUN
ejpam-3228	462	5	sezgin	sezgin	NOUN
ejpam-3228	462	6	and	and	CCONJ
ejpam-3228	462	7	a.	a.	NOUN
ejpam-3228	462	8	o.	o.	PROPN
ejpam-3228	462	9	atagün	atagün	PROPN
ejpam-3228	462	10	,	,	PUNCT
ejpam-3228	462	11	on	on	ADP
ejpam-3228	462	12	operations	operation	NOUN
ejpam-3228	462	13	of	of	ADP
ejpam-3228	462	14	soft	soft	ADJ
ejpam-3228	462	15	sets	set	NOUN
ejpam-3228	462	16	,	,	PUNCT
ejpam-3228	462	17	computers	computer	NOUN
ejpam-3228	462	18	and	and	CCONJ
ejpam-3228	462	19	mathematics	mathematic	NOUN
ejpam-3228	462	20	with	with	ADP
ejpam-3228	462	21	applications	application	NOUN
ejpam-3228	462	22	,	,	PUNCT
ejpam-3228	462	23	61	61	NUM
ejpam-3228	462	24	,	,	PUNCT
ejpam-3228	462	25	1457	1457	NUM
ejpam-3228	462	26	-	-	SYM
ejpam-3228	462	27	1467	1467	NUM
ejpam-3228	462	28	,	,	PUNCT
ejpam-3228	462	29	2011	2011	NUM
ejpam-3228	462	30	.	.	PUNCT
ejpam-3228	463	1	[	[	X
ejpam-3228	463	2	6	6	NUM
ejpam-3228	463	3	]	]	PUNCT
ejpam-3228	463	4	h.	h.	PROPN
ejpam-3228	463	5	aktaş	aktaş	PROPN
ejpam-3228	463	6	and	and	CCONJ
ejpam-3228	463	7	n.	n.	PROPN
ejpam-3228	463	8	çağman	çağman	PROPN
ejpam-3228	463	9	,	,	PUNCT
ejpam-3228	463	10	soft	soft	ADJ
ejpam-3228	463	11	sets	set	NOUN
ejpam-3228	463	12	and	and	CCONJ
ejpam-3228	463	13	soft	soft	ADJ
ejpam-3228	463	14	groups	group	NOUN
ejpam-3228	463	15	,	,	PUNCT
ejpam-3228	463	16	information	information	NOUN
ejpam-3228	463	17	sciences	science	NOUN
ejpam-3228	463	18	177	177	NUM
ejpam-3228	463	19	,	,	PUNCT
ejpam-3228	463	20	27262735	27262735	NUM
ejpam-3228	463	21	,	,	PUNCT
ejpam-3228	463	22	2007	2007	NUM
ejpam-3228	463	23	.	.	PUNCT
ejpam-3228	464	1	[	[	X
ejpam-3228	464	2	7	7	X
ejpam-3228	464	3	]	]	X
ejpam-3228	464	4	n.	n.	NOUN
ejpam-3228	464	5	çağman	çağman	PROPN
ejpam-3228	464	6	,	,	PUNCT
ejpam-3228	464	7	f.	f.	PROPN
ejpam-3228	464	8	çıtak	çıtak	PROPN
ejpam-3228	464	9	and	and	CCONJ
ejpam-3228	464	10	h.	h.	PROPN
ejpam-3228	464	11	aktaş	aktaş	PROPN
ejpam-3228	464	12	,	,	PUNCT
ejpam-3228	464	13	soft	soft	ADJ
ejpam-3228	464	14	int	int	NOUN
ejpam-3228	464	15	-	-	PUNCT
ejpam-3228	464	16	group	group	NOUN
ejpam-3228	464	17	,	,	PUNCT
ejpam-3228	464	18	neural	neural	ADJ
ejpam-3228	464	19	computing	computing	NOUN
ejpam-3228	464	20	and	and	CCONJ
ejpam-3228	464	21	application	application	NOUN
ejpam-3228	464	22	,	,	PUNCT
ejpam-3228	464	23	21(1	21(1	NUM
ejpam-3228	464	24	)	)	PUNCT
ejpam-3228	464	25	,	,	PUNCT
ejpam-3228	464	26	151	151	NUM
ejpam-3228	464	27	-	-	SYM
ejpam-3228	464	28	158	158	NUM
ejpam-3228	464	29	,	,	PUNCT
ejpam-3228	464	30	2012	2012	NUM
ejpam-3228	464	31	.	.	PUNCT
ejpam-3228	465	1	[	[	X
ejpam-3228	465	2	8	8	NUM
ejpam-3228	465	3	]	]	PUNCT
ejpam-3228	465	4	a.	a.	NOUN
ejpam-3228	465	5	rosenfeld	rosenfeld	PROPN
ejpam-3228	465	6	,	,	PUNCT
ejpam-3228	465	7	fuzzy	fuzzy	ADJ
ejpam-3228	465	8	group	group	NOUN
ejpam-3228	465	9	,	,	PUNCT
ejpam-3228	465	10	journal	journal	NOUN
ejpam-3228	465	11	of	of	ADP
ejpam-3228	465	12	mathematical	mathematical	ADJ
ejpam-3228	465	13	analysis	analysis	NOUN
ejpam-3228	465	14	and	and	CCONJ
ejpam-3228	465	15	applications	application	NOUN
ejpam-3228	465	16	,	,	PUNCT
ejpam-3228	465	17	35	35	NUM
ejpam-3228	465	18	,	,	PUNCT
ejpam-3228	465	19	512	512	NUM
ejpam-3228	465	20	-	-	SYM
ejpam-3228	465	21	517	517	NUM
ejpam-3228	465	22	,	,	PUNCT
ejpam-3228	465	23	1971	1971	NUM
ejpam-3228	465	24	.	.	PUNCT
ejpam-3228	466	1	[	[	X
ejpam-3228	466	2	9	9	NUM
ejpam-3228	466	3	]	]	PUNCT
ejpam-3228	466	4	k.	k.	PROPN
ejpam-3228	466	5	kaygisiz	kaygisiz	PROPN
ejpam-3228	466	6	,	,	PUNCT
ejpam-3228	466	7	on	on	ADP
ejpam-3228	466	8	soft	soft	ADJ
ejpam-3228	466	9	int	int	NOUN
ejpam-3228	466	10	-	-	PUNCT
ejpam-3228	466	11	groups	group	NOUN
ejpam-3228	466	12	,	,	PUNCT
ejpam-3228	466	13	annals	annal	NOUN
ejpam-3228	466	14	of	of	ADP
ejpam-3228	466	15	fuzzy	fuzzy	ADJ
ejpam-3228	466	16	mathematics	mathematic	NOUN
ejpam-3228	466	17	and	and	CCONJ
ejpam-3228	466	18	informatics	informatic	NOUN
ejpam-3228	466	19	,	,	PUNCT
ejpam-3228	466	20	4(2	4(2	NUM
ejpam-3228	466	21	)	)	PUNCT
ejpam-3228	466	22	,	,	PUNCT
ejpam-3228	466	23	363	363	NUM
ejpam-3228	466	24	-	-	SYM
ejpam-3228	466	25	375	375	NUM
ejpam-3228	466	26	,	,	PUNCT
ejpam-3228	466	27	2012	2012	NUM
ejpam-3228	466	28	.	.	PUNCT
ejpam-3228	467	1	[	[	X
ejpam-3228	467	2	10	10	NUM
ejpam-3228	467	3	]	]	PUNCT
ejpam-3228	467	4	a.	a.	NOUN
ejpam-3228	467	5	sezer	sezer	PROPN
ejpam-3228	467	6	,	,	PUNCT
ejpam-3228	467	7	a.	a.	NOUN
ejpam-3228	467	8	o.	o.	NOUN
ejpam-3228	467	9	atagün	atagün	PROPN
ejpam-3228	467	10	,	,	PUNCT
ejpam-3228	467	11	soft	soft	ADJ
ejpam-3228	467	12	groups	group	NOUN
ejpam-3228	467	13	and	and	CCONJ
ejpam-3228	467	14	normalistic	normalistic	ADJ
ejpam-3228	467	15	soft	soft	ADJ
ejpam-3228	467	16	groups	group	NOUN
ejpam-3228	467	17	,	,	PUNCT
ejpam-3228	467	18	computers	computer	NOUN
ejpam-3228	467	19	and	and	CCONJ
ejpam-3228	467	20	mathematics	mathematic	NOUN
ejpam-3228	467	21	with	with	ADP
ejpam-3228	467	22	applications	application	NOUN
ejpam-3228	467	23	,	,	PUNCT
ejpam-3228	467	24	62(2	62(2	NOUN
ejpam-3228	467	25	)	)	PUNCT
ejpam-3228	467	26	,	,	PUNCT
ejpam-3228	467	27	685	685	NUM
ejpam-3228	467	28	-	-	SYM
ejpam-3228	467	29	698	698	NUM
ejpam-3228	467	30	,	,	PUNCT
ejpam-3228	467	31	2011	2011	NUM
ejpam-3228	467	32	.	.	PUNCT
ejpam-3228	468	1	[	[	X
ejpam-3228	468	2	11	11	NUM
ejpam-3228	468	3	]	]	PUNCT
ejpam-3228	468	4	a.	a.	NOUN
ejpam-3228	468	5	sezgin	sezgin	PROPN
ejpam-3228	468	6	sezer	sezer	PROPN
ejpam-3228	468	7	,	,	PUNCT
ejpam-3228	468	8	n.	n.	PROPN
ejpam-3228	468	9	çağman	çağman	PROPN
ejpam-3228	468	10	,	,	PUNCT
ejpam-3228	468	11	a.	a.	NOUN
ejpam-3228	468	12	o.	o.	PROPN
ejpam-3228	468	13	atagün	atagün	PROPN
ejpam-3228	468	14	,	,	PUNCT
ejpam-3228	468	15	uni	uni	ADJ
ejpam-3228	468	16	-	-	ADJ
ejpam-3228	468	17	soft	soft	ADJ
ejpam-3228	468	18	substructures	substructure	NOUN
ejpam-3228	468	19	of	of	ADP
ejpam-3228	468	20	groups	group	NOUN
ejpam-3228	468	21	,	,	PUNCT
ejpam-3228	468	22	ann	ann	PROPN
ejpam-3228	468	23	.	.	PROPN
ejpam-3228	468	24	fuzzy	fuzzy	ADJ
ejpam-3228	468	25	math	math	PROPN
ejpam-3228	468	26	.	.	PUNCT
ejpam-3228	469	1	inform	inform	NOUN
ejpam-3228	469	2	,	,	PUNCT
ejpam-3228	469	3	9(2	9(2	NUM
ejpam-3228	469	4	)	)	PUNCT
ejpam-3228	469	5	,	,	PUNCT
ejpam-3228	469	6	235	235	NUM
ejpam-3228	469	7	-	-	SYM
ejpam-3228	469	8	246	246	NUM
ejpam-3228	469	9	,	,	PUNCT
ejpam-3228	469	10	2015	2015	NUM
ejpam-3228	469	11	.	.	PUNCT
ejpam-3228	470	1	[	[	X
ejpam-3228	470	2	12	12	NUM
ejpam-3228	470	3	]	]	PUNCT
ejpam-3228	470	4	a.	a.	NOUN
ejpam-3228	470	5	sezgin	sezgin	PROPN
ejpam-3228	470	6	sezer	sezer	PROPN
ejpam-3228	470	7	,	,	PUNCT
ejpam-3228	470	8	a	a	DET
ejpam-3228	470	9	new	new	ADJ
ejpam-3228	470	10	approach	approach	NOUN
ejpam-3228	470	11	to	to	ADP
ejpam-3228	470	12	la	la	ADJ
ejpam-3228	470	13	-	-	PUNCT
ejpam-3228	470	14	semigroup	semigroup	PROPN
ejpam-3228	470	15	theory	theory	NOUN
ejpam-3228	470	16	via	via	ADP
ejpam-3228	470	17	the	the	DET
ejpam-3228	470	18	soft	soft	ADJ
ejpam-3228	470	19	sets	set	NOUN
ejpam-3228	470	20	,	,	PUNCT
ejpam-3228	470	21	journal	journal	NOUN
ejpam-3228	470	22	of	of	ADP
ejpam-3228	470	23	intelligent	intelligent	ADJ
ejpam-3228	470	24	fuzzy	fuzzy	ADJ
ejpam-3228	470	25	systems	system	NOUN
ejpam-3228	470	26	,	,	PUNCT
ejpam-3228	470	27	26	26	NUM
ejpam-3228	470	28	,	,	PUNCT
ejpam-3228	470	29	2483	2483	NUM
ejpam-3228	470	30	-	-	SYM
ejpam-3228	470	31	2495	2495	NUM
ejpam-3228	470	32	,	,	PUNCT
ejpam-3228	470	33	2014	2014	NUM
ejpam-3228	470	34	.	.	PUNCT
ejpam-3228	471	1	[	[	X
ejpam-3228	471	2	13	13	NUM
ejpam-3228	471	3	]	]	PUNCT
ejpam-3228	471	4	a.	a.	PROPN
ejpam-3228	471	5	ullah	ullah	PROPN
ejpam-3228	471	6	,	,	PUNCT
ejpam-3228	471	7	i.	i.	PROPN
ejpam-3228	471	8	ahmad	ahmad	PROPN
ejpam-3228	471	9	,	,	PUNCT
ejpam-3228	471	10	f.	f.	PROPN
ejpam-3228	471	11	hayat	hayat	PROPN
ejpam-3228	471	12	,	,	PUNCT
ejpam-3228	471	13	f.	f.	PROPN
ejpam-3228	471	14	karaaslan	karaaslan	PROPN
ejpam-3228	471	15	,	,	PUNCT
ejpam-3228	471	16	m.	m.	PROPN
ejpam-3228	471	17	rashad	rashad	PROPN
ejpam-3228	471	18	,	,	PUNCT
ejpam-3228	471	19	soft	soft	ADJ
ejpam-3228	471	20	intersection	intersection	NOUN
ejpam-3228	471	21	abelgrassmann	abelgrassmann	NOUN
ejpam-3228	471	22	’s	’s	PART
ejpam-3228	471	23	groups	group	NOUN
ejpam-3228	471	24	,	,	PUNCT
ejpam-3228	471	25	submitted	submit	VERB
ejpam-3228	471	26	.	.	PUNCT
ejpam-3228	472	1	[	[	X
ejpam-3228	472	2	14	14	NUM
ejpam-3228	472	3	]	]	X
ejpam-3228	472	4	u.	u.	NOUN
ejpam-3228	472	5	acar	acar	PROPN
ejpam-3228	472	6	,	,	PUNCT
ejpam-3228	472	7	f.	f.	PROPN
ejpam-3228	472	8	koyuncu	koyuncu	PROPN
ejpam-3228	472	9	and	and	CCONJ
ejpam-3228	472	10	b.	b.	PROPN
ejpam-3228	472	11	tanay	tanay	PROPN
ejpam-3228	472	12	,	,	PUNCT
ejpam-3228	472	13	soft	soft	ADJ
ejpam-3228	472	14	sets	set	NOUN
ejpam-3228	472	15	and	and	CCONJ
ejpam-3228	472	16	soft	soft	ADJ
ejpam-3228	472	17	rings	ring	NOUN
ejpam-3228	472	18	,	,	PUNCT
ejpam-3228	472	19	computer	computer	NOUN
ejpam-3228	472	20	and	and	CCONJ
ejpam-3228	472	21	mathemetics	mathemetic	NOUN
ejpam-3228	472	22	with	with	ADP
ejpam-3228	472	23	application	application	NOUN
ejpam-3228	472	24	,	,	PUNCT
ejpam-3228	472	25	59	59	NUM
ejpam-3228	472	26	,	,	PUNCT
ejpam-3228	472	27	3458	3458	NUM
ejpam-3228	472	28	-	-	SYM
ejpam-3228	472	29	3463	3463	NUM
ejpam-3228	472	30	,	,	PUNCT
ejpam-3228	472	31	2010	2010	NUM
ejpam-3228	472	32	.	.	PUNCT
ejpam-3228	473	1	[	[	X
ejpam-3228	473	2	15	15	NUM
ejpam-3228	473	3	]	]	X
ejpam-3228	473	4	y.	y.	PROPN
ejpam-3228	473	5	b.	b.	PROPN
ejpam-3228	473	6	jun	jun	PROPN
ejpam-3228	473	7	,	,	PUNCT
ejpam-3228	473	8	soft	soft	ADJ
ejpam-3228	473	9	bck	bck	NOUN
ejpam-3228	473	10	/	/	SYM
ejpam-3228	473	11	bci	bci	NOUN
ejpam-3228	473	12	-	-	PUNCT
ejpam-3228	473	13	algebras	algebra	NOUN
ejpam-3228	473	14	,	,	PUNCT
ejpam-3228	473	15	computer	computer	NOUN
ejpam-3228	473	16	mathematics	mathematic	NOUN
ejpam-3228	473	17	with	with	ADP
ejpam-3228	473	18	applications	application	NOUN
ejpam-3228	473	19	,	,	PUNCT
ejpam-3228	473	20	56	56	NUM
ejpam-3228	473	21	,	,	PUNCT
ejpam-3228	473	22	1408	1408	NUM
ejpam-3228	473	23	-	-	SYM
ejpam-3228	473	24	1413	1413	NUM
ejpam-3228	473	25	,	,	PUNCT
ejpam-3228	473	26	2008	2008	NUM
ejpam-3228	473	27	.	.	PUNCT
ejpam-3228	474	1	[	[	X
ejpam-3228	474	2	16	16	NUM
ejpam-3228	474	3	]	]	X
ejpam-3228	474	4	y.	y.	PROPN
ejpam-3228	474	5	b.	b.	PROPN
ejpam-3228	474	6	jun	jun	PROPN
ejpam-3228	474	7	,	,	PUNCT
ejpam-3228	474	8	k.	k.	PROPN
ejpam-3228	474	9	j.	j.	PROPN
ejpam-3228	474	10	lee	lee	PROPN
ejpam-3228	474	11	and	and	CCONJ
ejpam-3228	474	12	j.	j.	PROPN
ejpam-3228	474	13	zhan	zhan	PROPN
ejpam-3228	474	14	,	,	PUNCT
ejpam-3228	474	15	soft	soft	ADJ
ejpam-3228	474	16	p	p	NOUN
ejpam-3228	474	17	-	-	PUNCT
ejpam-3228	474	18	ideals	ideal	NOUN
ejpam-3228	474	19	of	of	ADP
ejpam-3228	474	20	soft	soft	ADJ
ejpam-3228	474	21	bci	bci	NOUN
ejpam-3228	474	22	-	-	PUNCT
ejpam-3228	474	23	algebras	algebra	NOUN
ejpam-3228	474	24	,	,	PUNCT
ejpam-3228	474	25	comput	comput	NOUN
ejpam-3228	474	26	.	.	PUNCT
ejpam-3228	475	1	math	math	NOUN
ejpam-3228	475	2	.	.	PUNCT
ejpam-3228	476	1	appl	appl	PROPN
ejpam-3228	476	2	.	.	PUNCT
ejpam-3228	477	1	58	58	NUM
ejpam-3228	477	2	,	,	PUNCT
ejpam-3228	477	3	2060	2060	NUM
ejpam-3228	477	4	-	-	SYM
ejpam-3228	477	5	2068	2068	NUM
ejpam-3228	477	6	,	,	PUNCT
ejpam-3228	477	7	2009	2009	NUM
ejpam-3228	477	8	.	.	PUNCT
ejpam-3228	478	1	[	[	X
ejpam-3228	478	2	17	17	NUM
ejpam-3228	478	3	]	]	X
ejpam-3228	478	4	f.	f.	PROPN
ejpam-3228	478	5	karaaslan	karaaslan	PROPN
ejpam-3228	478	6	,	,	PUNCT
ejpam-3228	478	7	i.	i.	PROPN
ejpam-3228	478	8	ahmad	ahmad	PROPN
ejpam-3228	478	9	and	and	CCONJ
ejpam-3228	478	10	a.	a.	PROPN
ejpam-3228	478	11	ullah	ullah	PROPN
ejpam-3228	478	12	,	,	PUNCT
ejpam-3228	478	13	bipolar	bipolar	ADJ
ejpam-3228	478	14	soft	soft	ADJ
ejpam-3228	478	15	groups	group	NOUN
ejpam-3228	478	16	,	,	PUNCT
ejpam-3228	478	17	journal	journal	NOUN
ejpam-3228	478	18	of	of	ADP
ejpam-3228	478	19	intelligent	intelligent	ADJ
ejpam-3228	478	20	and	and	CCONJ
ejpam-3228	478	21	fuzzy	fuzzy	ADJ
ejpam-3228	478	22	systems	system	NOUN
ejpam-3228	478	23	,	,	PUNCT
ejpam-3228	478	24	31	31	NUM
ejpam-3228	478	25	,	,	PUNCT
ejpam-3228	478	26	651	651	NUM
ejpam-3228	478	27	-	-	SYM
ejpam-3228	478	28	662	662	NUM
ejpam-3228	478	29	,	,	PUNCT
ejpam-3228	478	30	2016	2016	NUM
ejpam-3228	478	31	.	.	PUNCT
ejpam-3228	478	32	references	reference	NOUN
ejpam-3228	478	33	536	536	NUM
ejpam-3228	478	34	[	[	SYM
ejpam-3228	478	35	18	18	NUM
ejpam-3228	478	36	]	]	PUNCT
ejpam-3228	478	37	m.	m.	NOUN
ejpam-3228	478	38	tun7ay	tun7ay	PROPN
ejpam-3228	478	39	and	and	CCONJ
ejpam-3228	478	40	a.	a.	NOUN
ejpam-3228	478	41	sezgin	sezgin	PROPN
ejpam-3228	478	42	,	,	PUNCT
ejpam-3228	478	43	soft	soft	ADJ
ejpam-3228	478	44	union	union	NOUN
ejpam-3228	478	45	ring	ring	NOUN
ejpam-3228	478	46	and	and	CCONJ
ejpam-3228	478	47	its	its	PRON
ejpam-3228	478	48	application	application	NOUN
ejpam-3228	478	49	ring	ring	NOUN
ejpam-3228	478	50	theory	theory	NOUN
ejpam-3228	478	51	,	,	PUNCT
ejpam-3228	478	52	international	international	ADJ
ejpam-3228	478	53	journal	journal	NOUN
ejpam-3228	478	54	of	of	ADP
ejpam-3228	478	55	computer	computer	NOUN
ejpam-3228	478	56	applications	application	NOUN
ejpam-3228	478	57	,	,	PUNCT
ejpam-3228	478	58	151(9),7	151(9),7	NUM
ejpam-3228	478	59	-	-	SYM
ejpam-3228	478	60	13	13	NUM
ejpam-3228	478	61	,	,	PUNCT
ejpam-3228	478	62	2016	2016	NUM
ejpam-3228	478	63	.	.	PUNCT
ejpam-3228	479	1	[	[	X
ejpam-3228	479	2	19	19	NUM
ejpam-3228	479	3	]	]	PUNCT
ejpam-3228	479	4	amanullah	amanullah	PROPN
ejpam-3228	479	5	,	,	PUNCT
ejpam-3228	479	6	imtiaz	imtiaz	PROPN
ejpam-3228	479	7	ahmad	ahmad	PROPN
ejpam-3228	479	8	,	,	PUNCT
ejpam-3228	479	9	and	and	CCONJ
ejpam-3228	479	10	faruk	faruk	PROPN
ejpam-3228	479	11	karaaslan	karaaslan	PROPN
ejpam-3228	479	12	,	,	PUNCT
ejpam-3228	479	13	cubic	cubic	ADJ
ejpam-3228	479	14	abel	abel	PROPN
ejpam-3228	479	15	-	-	PUNCT
ejpam-3228	479	16	grassmann	grassmann	PROPN
ejpam-3228	479	17	’s	’s	PART
ejpam-3228	479	18	subgroups	subgroup	NOUN
ejpam-3228	479	19	,	,	PUNCT
ejpam-3228	479	20	journal	journal	NOUN
ejpam-3228	479	21	of	of	ADP
ejpam-3228	479	22	computational	computational	ADJ
ejpam-3228	479	23	and	and	CCONJ
ejpam-3228	479	24	theoretical	theoretical	ADJ
ejpam-3228	479	25	nanoscience	nanoscience	NOUN
ejpam-3228	479	26	,	,	PUNCT
ejpam-3228	479	27	13(1	13(1	NUM
ejpam-3228	479	28	)	)	PUNCT
ejpam-3228	479	29	,	,	PUNCT
ejpam-3228	479	30	628	628	NUM
ejpam-3228	479	31	-	-	SYM
ejpam-3228	479	32	635	635	NUM
ejpam-3228	479	33	,	,	PUNCT
ejpam-3228	479	34	2016	2016	NUM
ejpam-3228	479	35	.	.	PUNCT
ejpam-3228	480	1	[	[	X
ejpam-3228	480	2	20	20	NUM
ejpam-3228	480	3	]	]	X
ejpam-3228	480	4	i.	i.	PROPN
ejpam-3228	480	5	ahmad	ahmad	PROPN
ejpam-3228	480	6	,	,	PUNCT
ejpam-3228	480	7	amanullah	amanullah	PROPN
ejpam-3228	480	8	,	,	PUNCT
ejpam-3228	480	9	m.	m.	NOUN
ejpam-3228	480	10	shah	shah	NOUN
ejpam-3228	480	11	,	,	PUNCT
ejpam-3228	480	12	fuzzy	fuzzy	ADJ
ejpam-3228	480	13	ag	ag	PROPN
ejpam-3228	480	14	-	-	PUNCT
ejpam-3228	480	15	subgroups	subgroup	NOUN
ejpam-3228	480	16	,	,	PUNCT
ejpam-3228	480	17	life	life	NOUN
ejpam-3228	480	18	science	science	NOUN
ejpam-3228	480	19	journal	journal	PROPN
ejpam-3228	480	20	,	,	PUNCT
ejpam-3228	480	21	9(4	9(4	NUM
ejpam-3228	480	22	)	)	PUNCT
ejpam-3228	480	23	,	,	PUNCT
ejpam-3228	480	24	3931	3931	NUM
ejpam-3228	480	25	-	-	SYM
ejpam-3228	480	26	3936	3936	NUM
ejpam-3228	480	27	,	,	PUNCT
ejpam-3228	480	28	2012	2012	NUM
ejpam-3228	480	29	.	.	PUNCT
ejpam-3228	481	1	[	[	X
ejpam-3228	481	2	21	21	NUM
ejpam-3228	481	3	]	]	X
ejpam-3228	481	4	amanullah	amanullah	PROPN
ejpam-3228	481	5	,	,	PUNCT
ejpam-3228	481	6	i.	i.	PROPN
ejpam-3228	481	7	ahmad	ahmad	PROPN
ejpam-3228	481	8	,	,	PUNCT
ejpam-3228	481	9	m.	m.	NOUN
ejpam-3228	481	10	shah	shah	NOUN
ejpam-3228	481	11	,	,	PUNCT
ejpam-3228	481	12	on	on	ADP
ejpam-3228	481	13	the	the	DET
ejpam-3228	481	14	equal	equal	ADJ
ejpam-3228	481	15	-	-	PUNCT
ejpam-3228	481	16	height	height	NOUN
ejpam-3228	481	17	elements	element	NOUN
ejpam-3228	481	18	of	of	ADP
ejpam-3228	481	19	fuzzy	fuzzy	ADJ
ejpam-3228	481	20	ag	ag	PROPN
ejpam-3228	481	21	-	-	PUNCT
ejpam-3228	481	22	subgroups	subgroup	NOUN
ejpam-3228	481	23	,	,	PUNCT
ejpam-3228	481	24	life	life	NOUN
ejpam-3228	481	25	science	science	NOUN
ejpam-3228	481	26	journal	journal	PROPN
ejpam-3228	481	27	,	,	PUNCT
ejpam-3228	481	28	10(4	10(4	NUM
ejpam-3228	481	29	)	)	PUNCT
ejpam-3228	481	30	,	,	PUNCT
ejpam-3228	481	31	3143	3143	NUM
ejpam-3228	481	32	-	-	SYM
ejpam-3228	481	33	3146	3146	NUM
ejpam-3228	481	34	,	,	PUNCT
ejpam-3228	481	35	2013	2013	NUM
ejpam-3228	481	36	.	.	PUNCT
ejpam-3228	482	1	[	[	X
ejpam-3228	482	2	22	22	NUM
ejpam-3228	482	3	]	]	PUNCT
ejpam-3228	482	4	t.	t.	NOUN
ejpam-3228	482	5	shah	shah	PROPN
ejpam-3228	482	6	,	,	PUNCT
ejpam-3228	482	7	i.	i.	PROPN
ejpam-3228	482	8	rehman	rehman	PROPN
ejpam-3228	482	9	and	and	CCONJ
ejpam-3228	482	10	a.	a.	PROPN
ejpam-3228	482	11	razzaq	razzaq	PROPN
ejpam-3228	482	12	,	,	PUNCT
ejpam-3228	482	13	soft	soft	ADJ
ejpam-3228	482	14	ordered	order	VERB
ejpam-3228	482	15	abel	abel	NOUN
ejpam-3228	482	16	-	-	PUNCT
ejpam-3228	482	17	grassman	grassman	NOUN
ejpam-3228	482	18	’s	’s	PART
ejpam-3228	482	19	groupoid	groupoid	NOUN
ejpam-3228	482	20	(	(	PUNCT
ejpam-3228	482	21	aggroupoid	aggroupoid	ADJ
ejpam-3228	482	22	)	)	PUNCT
ejpam-3228	482	23	,	,	PUNCT
ejpam-3228	482	24	international	international	ADJ
ejpam-3228	482	25	journal	journal	NOUN
ejpam-3228	482	26	of	of	ADP
ejpam-3228	482	27	the	the	DET
ejpam-3228	482	28	physical	physical	ADJ
ejpam-3228	482	29	sciences	sciences	PROPN
ejpam-3228	482	30	,	,	PUNCT
ejpam-3228	482	31	6(25	6(25	PROPN
ejpam-3228	482	32	)	)	PUNCT
ejpam-3228	482	33	,	,	PUNCT
ejpam-3228	482	34	6118	6118	NUM
ejpam-3228	482	35	-	-	SYM
ejpam-3228	482	36	6126	6126	NUM
ejpam-3228	482	37	,	,	PUNCT
ejpam-3228	482	38	2011	2011	NUM
ejpam-3228	482	39	.	.	PUNCT
ejpam-3228	483	1	[	[	X
ejpam-3228	483	2	23	23	NUM
ejpam-3228	483	3	]	]	PUNCT
ejpam-3228	483	4	a.	a.	NOUN
ejpam-3228	483	5	s.	s.	PROPN
ejpam-3228	483	6	sezer	sezer	PROPN
ejpam-3228	483	7	,	,	PUNCT
ejpam-3228	483	8	a	a	DET
ejpam-3228	483	9	new	new	ADJ
ejpam-3228	483	10	approach	approach	NOUN
ejpam-3228	483	11	to	to	ADP
ejpam-3228	483	12	la	la	ADJ
ejpam-3228	483	13	-	-	PUNCT
ejpam-3228	483	14	semigroup	semigroup	PROPN
ejpam-3228	483	15	theory	theory	NOUN
ejpam-3228	483	16	via	via	ADP
ejpam-3228	483	17	the	the	DET
ejpam-3228	483	18	soft	soft	ADJ
ejpam-3228	483	19	sets	set	NOUN
ejpam-3228	483	20	,	,	PUNCT
ejpam-3228	483	21	journal	journal	NOUN
ejpam-3228	483	22	of	of	ADP
ejpam-3228	483	23	intelligent	intelligent	ADJ
ejpam-3228	483	24	and	and	CCONJ
ejpam-3228	483	25	fuzzy	fuzzy	ADJ
ejpam-3228	483	26	systems	system	NOUN
ejpam-3228	483	27	,	,	PUNCT
ejpam-3228	483	28	26	26	NUM
ejpam-3228	483	29	,	,	PUNCT
ejpam-3228	483	30	2483	2483	NUM
ejpam-3228	483	31	-	-	SYM
ejpam-3228	483	32	2495	2495	NUM
ejpam-3228	483	33	,	,	PUNCT
ejpam-3228	483	34	2014	2014	NUM
ejpam-3228	483	35	.	.	PUNCT
ejpam-3228	484	1	[	[	X
ejpam-3228	484	2	24	24	NUM
ejpam-3228	484	3	]	]	PUNCT
ejpam-3228	484	4	m.	m.	NOUN
ejpam-3228	484	5	shah	shah	NOUN
ejpam-3228	484	6	and	and	CCONJ
ejpam-3228	484	7	a.	a.	PROPN
ejpam-3228	484	8	ali	ali	PROPN
ejpam-3228	484	9	,	,	PUNCT
ejpam-3228	484	10	some	some	DET
ejpam-3228	484	11	structural	structural	ADJ
ejpam-3228	484	12	properties	property	NOUN
ejpam-3228	484	13	of	of	ADP
ejpam-3228	484	14	ag	ag	PROPN
ejpam-3228	484	15	-	-	PUNCT
ejpam-3228	484	16	groups	group	NOUN
ejpam-3228	484	17	,	,	PUNCT
ejpam-3228	484	18	international	international	PROPN
ejpam-3228	484	19	mathematical	mathematical	ADJ
ejpam-3228	484	20	forum	forum	PROPN
ejpam-3228	484	21	,	,	PUNCT
ejpam-3228	484	22	6(34	6(34	NUM
ejpam-3228	484	23	)	)	PUNCT
ejpam-3228	484	24	,	,	PUNCT
ejpam-3228	484	25	1661	1661	NUM
ejpam-3228	484	26	-	-	SYM
ejpam-3228	484	27	1667	1667	NUM
ejpam-3228	484	28	,	,	PUNCT
ejpam-3228	484	29	2011	2011	NUM
ejpam-3228	484	30	.	.	PUNCT
ejpam-3228	485	1	[	[	X
ejpam-3228	485	2	25	25	NUM
ejpam-3228	485	3	]	]	PUNCT
ejpam-3228	485	4	m.	m.	NOUN
ejpam-3228	485	5	shah	shah	NOUN
ejpam-3228	485	6	,	,	PUNCT
ejpam-3228	485	7	c.	c.	PROPN
ejpam-3228	485	8	gretton	gretton	PROPN
ejpam-3228	485	9	,	,	PUNCT
ejpam-3228	485	10	v.	v.	ADP
ejpam-3228	485	11	sorge	sorge	PROPN
ejpam-3228	485	12	,	,	PUNCT
ejpam-3228	485	13	enumerating	enumerate	VERB
ejpam-3228	485	14	ag	ag	PROPN
ejpam-3228	485	15	-	-	PUNCT
ejpam-3228	485	16	groups	group	NOUN
ejpam-3228	485	17	with	with	ADP
ejpam-3228	485	18	a	a	DET
ejpam-3228	485	19	study	study	NOUN
ejpam-3228	485	20	of	of	ADP
ejpam-3228	485	21	smarandache	smarandache	PROPN
ejpam-3228	485	22	ag	ag	PROPN
ejpam-3228	485	23	-	-	PUNCT
ejpam-3228	485	24	groups	group	NOUN
ejpam-3228	485	25	,	,	PUNCT
ejpam-3228	485	26	international	international	PROPN
ejpam-3228	485	27	mathematical	mathematical	ADJ
ejpam-3228	485	28	forum	forum	PROPN
ejpam-3228	485	29	,	,	PUNCT
ejpam-3228	485	30	6(62	6(62	NUM
ejpam-3228	485	31	)	)	PUNCT
ejpam-3228	485	32	,	,	PUNCT
ejpam-3228	485	33	3079	3079	NUM
ejpam-3228	485	34	-	-	SYM
ejpam-3228	485	35	3086	3086	NUM
ejpam-3228	485	36	,	,	PUNCT
ejpam-3228	485	37	2011	2011	NUM
ejpam-3228	485	38	.	.	PUNCT
ejpam-3228	486	1	[	[	X
ejpam-3228	486	2	26	26	NUM
ejpam-3228	486	3	]	]	PUNCT
ejpam-3228	486	4	m.	m.	NOUN
ejpam-3228	486	5	iqbal	iqbal	PROPN
ejpam-3228	486	6	,	,	PUNCT
ejpam-3228	486	7	i.	i.	PROPN
ejpam-3228	486	8	ahmad	ahmad	PROPN
ejpam-3228	486	9	,	,	PUNCT
ejpam-3228	486	10	ideals	ideal	NOUN
ejpam-3228	486	11	in	in	ADP
ejpam-3228	486	12	ca	ca	NOUN
ejpam-3228	486	13	-	-	PUNCT
ejpam-3228	486	14	ag	ag	NOUN
ejpam-3228	486	15	-	-	PUNCT
ejpam-3228	486	16	groupoids	groupoid	NOUN
ejpam-3228	486	17	,	,	PUNCT
ejpam-3228	486	18	indian	indian	ADJ
ejpam-3228	486	19	journal	journal	NOUN
ejpam-3228	486	20	of	of	ADP
ejpam-3228	486	21	pure	pure	ADJ
ejpam-3228	486	22	and	and	CCONJ
ejpam-3228	486	23	applied	applied	ADJ
ejpam-3228	486	24	mathematics	mathematic	NOUN
ejpam-3228	486	25	,	,	PUNCT
ejpam-3228	486	26	ms	ms	PROPN
ejpam-3228	486	27	.	.	PROPN
ejpam-3228	487	1	no	no	PROPN
ejpam-3228	487	2	.	.	PUNCT
ejpam-3228	488	1	ijpa	ijpa	NOUN
ejpam-3228	488	2	-	-	PUNCT
ejpam-3228	488	3	d-16	d-16	NOUN
ejpam-3228	488	4	-	-	PUNCT
ejpam-3228	488	5	01038	01038	NUM
ejpam-3228	488	6	,	,	PUNCT
ejpam-3228	488	7	2018	2018	NUM
ejpam-3228	488	8	.	.	PUNCT