id	sid	tid	token	lemma	pos
ejpam-5563	1	1	european	european	PROPN
ejpam-5563	1	2	journal	journal	PROPN
ejpam-5563	1	3	of	of	ADP
ejpam-5563	1	4	pure	pure	ADJ
ejpam-5563	1	5	and	and	CCONJ
ejpam-5563	1	6	applied	apply	VERB
ejpam-5563	1	7	mathematics	mathematic	NOUN
ejpam-5563	1	8	vol	vol	NOUN
ejpam-5563	1	9	.	.	PROPN
ejpam-5563	2	1	17	17	NUM
ejpam-5563	2	2	,	,	PUNCT
ejpam-5563	2	3	no	no	INTJ
ejpam-5563	2	4	.	.	NOUN
ejpam-5563	2	5	4	4	NUM
ejpam-5563	2	6	,	,	PUNCT
ejpam-5563	2	7	2024	2024	NUM
ejpam-5563	2	8	,	,	PUNCT
ejpam-5563	2	9	3517	3517	NUM
ejpam-5563	2	10	-	-	SYM
ejpam-5563	2	11	3538	3538	NUM
ejpam-5563	2	12	issn	issn	PROPN
ejpam-5563	2	13	1307	1307	NUM
ejpam-5563	2	14	-	-	SYM
ejpam-5563	2	15	5543	5543	NUM
ejpam-5563	2	16	–	–	PUNCT
ejpam-5563	2	17	ejpam.com	ejpam.com	X
ejpam-5563	2	18	published	publish	VERB
ejpam-5563	2	19	by	by	ADP
ejpam-5563	2	20	new	new	PROPN
ejpam-5563	2	21	york	york	PROPN
ejpam-5563	2	22	business	business	PROPN
ejpam-5563	2	23	global	global	ADJ
ejpam-5563	2	24	further	further	ADJ
ejpam-5563	2	25	new	new	ADJ
ejpam-5563	2	26	operators	operator	NOUN
ejpam-5563	2	27	in	in	ADP
ejpam-5563	2	28	primal	primal	ADJ
ejpam-5563	2	29	spaces	space	NOUN
ejpam-5563	2	30	ohud	ohud	PROPN
ejpam-5563	2	31	alghamdi	alghamdi	PROPN
ejpam-5563	2	32	department	department	PROPN
ejpam-5563	2	33	of	of	ADP
ejpam-5563	2	34	mathematics	mathematic	NOUN
ejpam-5563	2	35	,	,	PUNCT
ejpam-5563	2	36	faculty	faculty	NOUN
ejpam-5563	2	37	of	of	ADP
ejpam-5563	2	38	science	science	NOUN
ejpam-5563	2	39	,	,	PUNCT
ejpam-5563	2	40	al	al	PROPN
ejpam-5563	2	41	-	-	PUNCT
ejpam-5563	2	42	baha	baha	PROPN
ejpam-5563	2	43	university	university	PROPN
ejpam-5563	2	44	,	,	PUNCT
ejpam-5563	2	45	al	al	PROPN
ejpam-5563	2	46	-	-	PUNCT
ejpam-5563	2	47	baha	baha	PROPN
ejpam-5563	2	48	,	,	PUNCT
ejpam-5563	2	49	saudi	saudi	PROPN
ejpam-5563	2	50	arabia	arabia	PROPN
ejpam-5563	2	51	abstract	abstract	NOUN
ejpam-5563	2	52	.	.	PUNCT
ejpam-5563	3	1	in	in	ADP
ejpam-5563	3	2	this	this	DET
ejpam-5563	3	3	paper	paper	NOUN
ejpam-5563	3	4	,	,	PUNCT
ejpam-5563	3	5	we	we	PRON
ejpam-5563	3	6	introduce	introduce	VERB
ejpam-5563	3	7	new	new	ADJ
ejpam-5563	3	8	operators	operator	NOUN
ejpam-5563	3	9	depending	depend	VERB
ejpam-5563	3	10	on	on	ADP
ejpam-5563	3	11	the	the	DET
ejpam-5563	3	12	definitions	definition	NOUN
ejpam-5563	3	13	of	of	ADP
ejpam-5563	3	14	γ	γ	NOUN
ejpam-5563	3	15	and	and	CCONJ
ejpam-5563	3	16	γ∗operators	γ∗operator	NOUN
ejpam-5563	3	17	that	that	PRON
ejpam-5563	3	18	were	be	AUX
ejpam-5563	3	19	defined	define	VERB
ejpam-5563	3	20	in	in	ADP
ejpam-5563	3	21	[	[	X
ejpam-5563	3	22	7	7	NUM
ejpam-5563	3	23	]	]	PUNCT
ejpam-5563	3	24	using	use	VERB
ejpam-5563	3	25	the	the	DET
ejpam-5563	3	26	structure	structure	NOUN
ejpam-5563	3	27	of	of	ADP
ejpam-5563	3	28	primal	primal	ADJ
ejpam-5563	3	29	topological	topological	ADJ
ejpam-5563	3	30	spaces	space	NOUN
ejpam-5563	3	31	.	.	PUNCT
ejpam-5563	4	1	we	we	PRON
ejpam-5563	4	2	provide	provide	VERB
ejpam-5563	4	3	some	some	DET
ejpam-5563	4	4	examples	example	NOUN
ejpam-5563	4	5	to	to	PART
ejpam-5563	4	6	illustrate	illustrate	VERB
ejpam-5563	4	7	the	the	DET
ejpam-5563	4	8	relation	relation	NOUN
ejpam-5563	4	9	between	between	ADP
ejpam-5563	4	10	these	these	DET
ejpam-5563	4	11	new	new	ADJ
ejpam-5563	4	12	operators	operator	NOUN
ejpam-5563	4	13	,	,	PUNCT
ejpam-5563	4	14	additionally	additionally	ADV
ejpam-5563	4	15	,	,	PUNCT
ejpam-5563	4	16	we	we	PRON
ejpam-5563	4	17	give	give	VERB
ejpam-5563	4	18	more	more	ADJ
ejpam-5563	4	19	results	result	NOUN
ejpam-5563	4	20	regarding	regard	VERB
ejpam-5563	4	21	to	to	ADP
ejpam-5563	4	22	γ	γ	ADJ
ejpam-5563	4	23	-	-	PUNCT
ejpam-5563	4	24	diamond	diamond	NOUN
ejpam-5563	4	25	operator	operator	NOUN
ejpam-5563	4	26	.	.	PUNCT
ejpam-5563	5	1	2020	2020	NUM
ejpam-5563	5	2	mathematics	mathematics	PROPN
ejpam-5563	5	3	subject	subject	NOUN
ejpam-5563	5	4	classifications	classification	NOUN
ejpam-5563	5	5	:	:	PUNCT
ejpam-5563	5	6	54a05	54a05	NUM
ejpam-5563	5	7	,	,	PUNCT
ejpam-5563	5	8	54a10	54a10	NUM
ejpam-5563	5	9	key	key	ADJ
ejpam-5563	5	10	words	word	NOUN
ejpam-5563	5	11	and	and	CCONJ
ejpam-5563	5	12	phrases	phrase	NOUN
ejpam-5563	5	13	:	:	PUNCT
ejpam-5563	5	14	primal	primal	ADJ
ejpam-5563	5	15	,	,	PUNCT
ejpam-5563	5	16	primal	primal	ADJ
ejpam-5563	5	17	topological	topological	ADJ
ejpam-5563	5	18	space	space	NOUN
ejpam-5563	5	19	,	,	PUNCT
ejpam-5563	5	20	λ	λ	NOUN
ejpam-5563	5	21	operator	operator	NOUN
ejpam-5563	5	22	,	,	PUNCT
ejpam-5563	5	23	λ⋄	λ⋄	NUM
ejpam-5563	5	24	operator	operator	NOUN
ejpam-5563	5	25	,	,	PUNCT
ejpam-5563	5	26	λ̃	λ̃	PROPN
ejpam-5563	5	27	operator	operator	NOUN
ejpam-5563	5	28	1	1	NUM
ejpam-5563	5	29	.	.	PUNCT
ejpam-5563	6	1	introduction	introduction	NOUN
ejpam-5563	6	2	recently	recently	ADV
ejpam-5563	6	3	,	,	PUNCT
ejpam-5563	6	4	there	there	PRON
ejpam-5563	6	5	are	be	VERB
ejpam-5563	6	6	several	several	ADJ
ejpam-5563	6	7	topological	topological	ADJ
ejpam-5563	6	8	structures	structure	NOUN
ejpam-5563	6	9	have	have	AUX
ejpam-5563	6	10	emerged	emerge	VERB
ejpam-5563	6	11	and	and	CCONJ
ejpam-5563	6	12	gained	gain	VERB
ejpam-5563	6	13	prominence	prominence	NOUN
ejpam-5563	6	14	in	in	ADP
ejpam-5563	6	15	a	a	DET
ejpam-5563	6	16	wide	wide	ADJ
ejpam-5563	6	17	array	array	NOUN
ejpam-5563	6	18	of	of	ADP
ejpam-5563	6	19	research	research	NOUN
ejpam-5563	6	20	studies	study	NOUN
ejpam-5563	6	21	.	.	PUNCT
ejpam-5563	7	1	one	one	NUM
ejpam-5563	7	2	of	of	ADP
ejpam-5563	7	3	these	these	DET
ejpam-5563	7	4	structures	structure	NOUN
ejpam-5563	7	5	was	be	AUX
ejpam-5563	7	6	named	name	VERB
ejpam-5563	7	7	grill	grill	NOUN
ejpam-5563	7	8	introduced	introduce	VERB
ejpam-5563	7	9	in	in	ADP
ejpam-5563	7	10	[	[	X
ejpam-5563	7	11	9	9	NUM
ejpam-5563	7	12	]	]	PUNCT
ejpam-5563	7	13	.	.	PUNCT
ejpam-5563	8	1	moreover	moreover	ADV
ejpam-5563	8	2	,	,	PUNCT
ejpam-5563	8	3	the	the	DET
ejpam-5563	8	4	concept	concept	NOUN
ejpam-5563	8	5	of	of	ADP
ejpam-5563	8	6	ideal	ideal	NOUN
ejpam-5563	8	7	[	[	X
ejpam-5563	8	8	10	10	NUM
ejpam-5563	8	9	,	,	PUNCT
ejpam-5563	8	10	11	11	NUM
ejpam-5563	8	11	]	]	PUNCT
ejpam-5563	8	12	and	and	CCONJ
ejpam-5563	8	13	filter	filter	NOUN
ejpam-5563	9	1	[	[	X
ejpam-5563	9	2	9	9	NUM
ejpam-5563	9	3	]	]	PUNCT
ejpam-5563	9	4	are	be	AUX
ejpam-5563	9	5	examples	example	NOUN
ejpam-5563	9	6	of	of	ADP
ejpam-5563	9	7	other	other	ADJ
ejpam-5563	9	8	topological	topological	ADJ
ejpam-5563	9	9	structures	structure	NOUN
ejpam-5563	9	10	.	.	PUNCT
ejpam-5563	10	1	in	in	ADP
ejpam-5563	10	2	addition	addition	NOUN
ejpam-5563	10	3	,	,	PUNCT
ejpam-5563	10	4	the	the	DET
ejpam-5563	10	5	primal	primal	ADJ
ejpam-5563	10	6	structure	structure	NOUN
ejpam-5563	10	7	is	be	AUX
ejpam-5563	10	8	among	among	ADP
ejpam-5563	10	9	these	these	DET
ejpam-5563	10	10	topological	topological	ADJ
ejpam-5563	10	11	structures	structure	NOUN
ejpam-5563	10	12	that	that	PRON
ejpam-5563	10	13	have	have	AUX
ejpam-5563	10	14	been	be	AUX
ejpam-5563	10	15	defined	define	VERB
ejpam-5563	10	16	by	by	ADP
ejpam-5563	10	17	acharjee	acharjee	NOUN
ejpam-5563	10	18	et	et	PROPN
ejpam-5563	10	19	al	al	PROPN
ejpam-5563	10	20	.	.	PUNCT
ejpam-5563	11	1	[	[	X
ejpam-5563	11	2	1	1	NUM
ejpam-5563	11	3	]	]	PUNCT
ejpam-5563	11	4	.	.	PUNCT
ejpam-5563	12	1	it	it	PRON
ejpam-5563	12	2	is	be	AUX
ejpam-5563	12	3	known	know	VERB
ejpam-5563	12	4	that	that	SCONJ
ejpam-5563	12	5	the	the	DET
ejpam-5563	12	6	primal	primal	ADJ
ejpam-5563	12	7	structure	structure	NOUN
ejpam-5563	12	8	was	be	AUX
ejpam-5563	12	9	studied	study	VERB
ejpam-5563	12	10	in	in	ADP
ejpam-5563	12	11	the	the	DET
ejpam-5563	12	12	framework	framework	NOUN
ejpam-5563	12	13	of	of	ADP
ejpam-5563	12	14	both	both	CCONJ
ejpam-5563	12	15	soft	soft	ADJ
ejpam-5563	12	16	and	and	CCONJ
ejpam-5563	12	17	fuzzy	fuzzy	ADJ
ejpam-5563	12	18	set	set	NOUN
ejpam-5563	12	19	theory	theory	NOUN
ejpam-5563	12	20	in	in	ADP
ejpam-5563	12	21	[	[	X
ejpam-5563	12	22	6	6	NUM
ejpam-5563	12	23	,	,	PUNCT
ejpam-5563	12	24	8	8	NUM
ejpam-5563	12	25	]	]	PUNCT
ejpam-5563	12	26	.	.	PUNCT
ejpam-5563	13	1	al	al	PROPN
ejpam-5563	13	2	-	-	PUNCT
ejpam-5563	13	3	omari	omari	PROPN
ejpam-5563	13	4	and	and	CCONJ
ejpam-5563	13	5	alqahtani	alqahtani	PROPN
ejpam-5563	13	6	defined	define	VERB
ejpam-5563	13	7	closure	closure	NOUN
ejpam-5563	13	8	operators	operator	NOUN
ejpam-5563	13	9	using	use	VERB
ejpam-5563	13	10	the	the	DET
ejpam-5563	13	11	concept	concept	NOUN
ejpam-5563	13	12	of	of	ADP
ejpam-5563	13	13	primal	primal	ADJ
ejpam-5563	13	14	spaces	space	NOUN
ejpam-5563	13	15	in	in	ADP
ejpam-5563	13	16	[	[	X
ejpam-5563	13	17	4	4	NUM
ejpam-5563	13	18	]	]	PUNCT
ejpam-5563	13	19	.	.	PUNCT
ejpam-5563	14	1	furthermore	furthermore	ADV
ejpam-5563	14	2	,	,	PUNCT
ejpam-5563	14	3	more	more	ADJ
ejpam-5563	14	4	operators	operator	NOUN
ejpam-5563	14	5	were	be	AUX
ejpam-5563	14	6	defined	define	VERB
ejpam-5563	14	7	using	use	VERB
ejpam-5563	14	8	the	the	DET
ejpam-5563	14	9	structure	structure	NOUN
ejpam-5563	14	10	of	of	ADP
ejpam-5563	14	11	primal	primal	ADJ
ejpam-5563	14	12	spaces	space	NOUN
ejpam-5563	14	13	and	and	CCONJ
ejpam-5563	14	14	soft	soft	ADJ
ejpam-5563	14	15	primal	primal	ADJ
ejpam-5563	14	16	space	space	NOUN
ejpam-5563	14	17	in	in	ADP
ejpam-5563	14	18	[	[	X
ejpam-5563	14	19	2	2	NUM
ejpam-5563	14	20	,	,	PUNCT
ejpam-5563	14	21	5	5	NUM
ejpam-5563	14	22	]	]	PUNCT
ejpam-5563	14	23	.	.	PUNCT
ejpam-5563	15	1	moreover	moreover	ADV
ejpam-5563	15	2	,	,	PUNCT
ejpam-5563	15	3	regularity	regularity	NOUN
ejpam-5563	15	4	and	and	CCONJ
ejpam-5563	15	5	normality	normality	NOUN
ejpam-5563	15	6	in	in	ADP
ejpam-5563	15	7	primal	primal	ADJ
ejpam-5563	15	8	spaces	space	NOUN
ejpam-5563	15	9	was	be	AUX
ejpam-5563	15	10	discussed	discuss	VERB
ejpam-5563	15	11	in	in	ADP
ejpam-5563	15	12	[	[	X
ejpam-5563	15	13	3	3	NUM
ejpam-5563	15	14	]	]	PUNCT
ejpam-5563	15	15	.	.	PUNCT
ejpam-5563	16	1	additionally	additionally	ADV
ejpam-5563	16	2	,	,	PUNCT
ejpam-5563	16	3	alghamdi	alghamdi	PROPN
ejpam-5563	16	4	et	et	PROPN
ejpam-5563	16	5	al	al	PROPN
ejpam-5563	16	6	.	.	PROPN
ejpam-5563	16	7	have	have	AUX
ejpam-5563	16	8	defined	define	VERB
ejpam-5563	16	9	new	new	ADJ
ejpam-5563	16	10	operators	operator	NOUN
ejpam-5563	16	11	using	use	VERB
ejpam-5563	16	12	the	the	DET
ejpam-5563	16	13	structure	structure	NOUN
ejpam-5563	16	14	of	of	ADP
ejpam-5563	16	15	primal	primal	ADJ
ejpam-5563	16	16	spaces	space	NOUN
ejpam-5563	16	17	in	in	ADP
ejpam-5563	16	18	[	[	X
ejpam-5563	16	19	7	7	NUM
ejpam-5563	16	20	]	]	PUNCT
ejpam-5563	16	21	.	.	PUNCT
ejpam-5563	17	1	in	in	ADP
ejpam-5563	17	2	this	this	DET
ejpam-5563	17	3	work	work	NOUN
ejpam-5563	17	4	,	,	PUNCT
ejpam-5563	17	5	we	we	PRON
ejpam-5563	17	6	will	will	AUX
ejpam-5563	17	7	continue	continue	VERB
ejpam-5563	17	8	present	present	ADJ
ejpam-5563	17	9	new	new	ADJ
ejpam-5563	17	10	results	result	NOUN
ejpam-5563	17	11	regarding	regard	VERB
ejpam-5563	17	12	to	to	ADP
ejpam-5563	17	13	diamond	diamond	NOUN
ejpam-5563	17	14	operators	operator	NOUN
ejpam-5563	17	15	that	that	PRON
ejpam-5563	17	16	were	be	AUX
ejpam-5563	17	17	defined	define	VERB
ejpam-5563	17	18	in	in	ADP
ejpam-5563	17	19	[	[	X
ejpam-5563	17	20	7	7	NUM
ejpam-5563	17	21	]	]	PUNCT
ejpam-5563	17	22	.	.	PUNCT
ejpam-5563	18	1	then	then	ADV
ejpam-5563	18	2	,	,	PUNCT
ejpam-5563	18	3	we	we	PRON
ejpam-5563	18	4	provide	provide	VERB
ejpam-5563	18	5	definitions	definition	NOUN
ejpam-5563	18	6	of	of	ADP
ejpam-5563	18	7	new	new	ADJ
ejpam-5563	18	8	operators	operator	NOUN
ejpam-5563	18	9	called	call	VERB
ejpam-5563	18	10	λ	λ	PROPN
ejpam-5563	18	11	,	,	PUNCT
ejpam-5563	18	12	λ⋄	λ⋄	X
ejpam-5563	18	13	and	and	CCONJ
ejpam-5563	18	14	λ̃.	λ̃.	ADV
ejpam-5563	18	15	finally	finally	ADV
ejpam-5563	18	16	,	,	PUNCT
ejpam-5563	18	17	we	we	PRON
ejpam-5563	18	18	present	present	VERB
ejpam-5563	18	19	some	some	DET
ejpam-5563	18	20	examples	example	NOUN
ejpam-5563	18	21	to	to	PART
ejpam-5563	18	22	clarify	clarify	VERB
ejpam-5563	18	23	the	the	DET
ejpam-5563	18	24	relations	relation	NOUN
ejpam-5563	18	25	between	between	ADP
ejpam-5563	18	26	them	they	PRON
ejpam-5563	18	27	under	under	ADP
ejpam-5563	18	28	different	different	ADJ
ejpam-5563	18	29	definitions	definition	NOUN
ejpam-5563	18	30	of	of	ADP
ejpam-5563	18	31	primal	primal	ADJ
ejpam-5563	18	32	spaces	space	NOUN
ejpam-5563	18	33	.	.	PUNCT
ejpam-5563	19	1	we	we	PRON
ejpam-5563	19	2	are	be	AUX
ejpam-5563	19	3	going	go	VERB
ejpam-5563	19	4	now	now	ADV
ejpam-5563	19	5	to	to	PART
ejpam-5563	19	6	present	present	VERB
ejpam-5563	19	7	some	some	DET
ejpam-5563	19	8	definitions	definition	NOUN
ejpam-5563	19	9	and	and	CCONJ
ejpam-5563	19	10	results	result	NOUN
ejpam-5563	19	11	that	that	SCONJ
ejpam-5563	19	12	we	we	PRON
ejpam-5563	19	13	use	use	VERB
ejpam-5563	19	14	through	through	ADP
ejpam-5563	19	15	the	the	DET
ejpam-5563	19	16	paper	paper	NOUN
ejpam-5563	19	17	.	.	PUNCT
ejpam-5563	20	1	definition	definition	NOUN
ejpam-5563	20	2	1	1	NUM
ejpam-5563	20	3	.	.	PUNCT
ejpam-5563	21	1	[	[	X
ejpam-5563	21	2	1	1	X
ejpam-5563	21	3	]	]	PUNCT
ejpam-5563	21	4	let	let	VERB
ejpam-5563	21	5	b	b	PRON
ejpam-5563	21	6	be	be	AUX
ejpam-5563	21	7	a	a	DET
ejpam-5563	21	8	nonempty	nonempty	ADJ
ejpam-5563	21	9	set	set	VERB
ejpam-5563	21	10	.	.	PUNCT
ejpam-5563	22	1	we	we	PRON
ejpam-5563	22	2	say	say	VERB
ejpam-5563	22	3	that	that	SCONJ
ejpam-5563	22	4	p	p	VERB
ejpam-5563	22	5	⊆	⊆	NUM
ejpam-5563	22	6	p(b	p(b	NOUN
ejpam-5563	22	7	)	)	PUNCT
ejpam-5563	22	8	,	,	PUNCT
ejpam-5563	22	9	where	where	SCONJ
ejpam-5563	22	10	p(b	p(b	NOUN
ejpam-5563	22	11	)	)	PUNCT
ejpam-5563	22	12	is	be	AUX
ejpam-5563	22	13	the	the	DET
ejpam-5563	22	14	power	power	NOUN
ejpam-5563	22	15	set	set	NOUN
ejpam-5563	22	16	of	of	ADP
ejpam-5563	22	17	b	b	PROPN
ejpam-5563	22	18	,	,	PUNCT
ejpam-5563	22	19	is	be	AUX
ejpam-5563	22	20	a	a	DET
ejpam-5563	22	21	primal	primal	NOUN
ejpam-5563	22	22	on	on	ADP
ejpam-5563	22	23	b	b	NOUN
ejpam-5563	22	24	if	if	SCONJ
ejpam-5563	22	25	the	the	DET
ejpam-5563	22	26	following	follow	VERB
ejpam-5563	22	27	conditions	condition	NOUN
ejpam-5563	22	28	hold	hold	VERB
ejpam-5563	22	29	:	:	PUNCT
ejpam-5563	23	1	1	1	NUM
ejpam-5563	23	2	.	.	X
ejpam-5563	23	3	b	b	PROPN
ejpam-5563	23	4	/∈	/∈	PUNCT
ejpam-5563	24	1	p.	p.	NOUN
ejpam-5563	24	2	doi	doi	NOUN
ejpam-5563	24	3	:	:	PUNCT
ejpam-5563	24	4	https://doi.org/10.29020/nybg.ejpam.v17i4.5563	https://doi.org/10.29020/nybg.ejpam.v17i4.5563	PROPN
ejpam-5563	24	5	email	email	NOUN
ejpam-5563	24	6	address	address	NOUN
ejpam-5563	24	7	:	:	PUNCT
ejpam-5563	25	1	ofalghamdi@bu.edu.sa	ofalghamdi@bu.edu.sa	PROPN
ejpam-5563	25	2	(	(	PUNCT
ejpam-5563	25	3	o.	o.	NOUN
ejpam-5563	25	4	alghamdi	alghamdi	PROPN
ejpam-5563	25	5	)	)	PUNCT
ejpam-5563	25	6	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5563	26	1	3517	3517	NUM
ejpam-5563	26	2	copyright	copyright	NOUN
ejpam-5563	26	3	:	:	PUNCT
ejpam-5563	26	4	©	©	PROPN
ejpam-5563	26	5	2024	2024	NUM
ejpam-5563	26	6	the	the	DET
ejpam-5563	26	7	author(s	author(s	NOUN
ejpam-5563	26	8	)	)	PUNCT
ejpam-5563	26	9	.	.	PUNCT
ejpam-5563	27	1	(	(	PUNCT
ejpam-5563	27	2	cc	cc	NOUN
ejpam-5563	27	3	by	by	ADP
ejpam-5563	27	4	-	-	PUNCT
ejpam-5563	27	5	nc	nc	PROPN
ejpam-5563	27	6	4.0	4.0	NUM
ejpam-5563	27	7	)	)	PUNCT
ejpam-5563	27	8	o.	o.	NOUN
ejpam-5563	27	9	alghamdi	alghamdi	PROPN
ejpam-5563	27	10	/	/	SYM
ejpam-5563	27	11	eur	eur	PROPN
ejpam-5563	27	12	.	.	PUNCT
ejpam-5563	28	1	j.	j.	PROPN
ejpam-5563	28	2	pure	pure	PROPN
ejpam-5563	28	3	appl	appl	PROPN
ejpam-5563	28	4	.	.	PROPN
ejpam-5563	28	5	math	math	PROPN
ejpam-5563	28	6	,	,	PUNCT
ejpam-5563	28	7	17	17	NUM
ejpam-5563	28	8	(	(	PUNCT
ejpam-5563	28	9	4	4	NUM
ejpam-5563	28	10	)	)	PUNCT
ejpam-5563	28	11	(	(	PUNCT
ejpam-5563	28	12	2024	2024	NUM
ejpam-5563	28	13	)	)	PUNCT
ejpam-5563	28	14	,	,	PUNCT
ejpam-5563	28	15	3517	3517	NUM
ejpam-5563	28	16	-	-	SYM
ejpam-5563	28	17	3538	3538	NUM
ejpam-5563	28	18	3518	3518	NUM
ejpam-5563	28	19	2	2	NUM
ejpam-5563	28	20	.	.	PUNCT
ejpam-5563	29	1	if	if	SCONJ
ejpam-5563	29	2	c	c	PROPN
ejpam-5563	29	3	⊆	⊆	NUM
ejpam-5563	29	4	q	q	NOUN
ejpam-5563	29	5	and	and	CCONJ
ejpam-5563	29	6	q	q	ADJ
ejpam-5563	29	7	∈	∈	PROPN
ejpam-5563	29	8	p	p	NOUN
ejpam-5563	29	9	,	,	PUNCT
ejpam-5563	29	10	then	then	ADV
ejpam-5563	29	11	c	c	PROPN
ejpam-5563	29	12	∈	∈	PROPN
ejpam-5563	29	13	p	p	PROPN
ejpam-5563	29	14	⇔	⇔	PROPN
ejpam-5563	29	15	if	if	SCONJ
ejpam-5563	29	16	c	c	PROPN
ejpam-5563	29	17	⊆	⊆	NUM
ejpam-5563	29	18	q	q	NOUN
ejpam-5563	29	19	and	and	CCONJ
ejpam-5563	29	20	c	c	NOUN
ejpam-5563	29	21	/∈	/∈	PUNCT
ejpam-5563	30	1	p	p	X
ejpam-5563	30	2	,	,	PUNCT
ejpam-5563	30	3	then	then	ADV
ejpam-5563	30	4	q	q	X
ejpam-5563	30	5	/∈	/∈	PUNCT
ejpam-5563	31	1	p.	p.	NOUN
ejpam-5563	31	2	3	3	NUM
ejpam-5563	31	3	.	.	PUNCT
ejpam-5563	32	1	if	if	SCONJ
ejpam-5563	32	2	c	c	PROPN
ejpam-5563	32	3	∩q	∩q	PROPN
ejpam-5563	32	4	∈	∈	PROPN
ejpam-5563	32	5	p	p	X
ejpam-5563	32	6	,	,	PUNCT
ejpam-5563	32	7	then	then	ADV
ejpam-5563	32	8	either	either	CCONJ
ejpam-5563	32	9	c	c	PROPN
ejpam-5563	32	10	∈	∈	PROPN
ejpam-5563	32	11	p	p	NOUN
ejpam-5563	32	12	or	or	CCONJ
ejpam-5563	32	13	q	q	NOUN
ejpam-5563	32	14	∈	∈	PROPN
ejpam-5563	32	15	p	p	NOUN
ejpam-5563	32	16	⇔	⇔	PROPN
ejpam-5563	32	17	if	if	SCONJ
ejpam-5563	32	18	c	c	PROPN
ejpam-5563	32	19	/∈	/∈	PUNCT
ejpam-5563	33	1	p	p	NOUN
ejpam-5563	33	2	and	and	CCONJ
ejpam-5563	33	3	q	q	NOUN
ejpam-5563	33	4	/∈	/∈	PUNCT
ejpam-5563	34	1	p	p	X
ejpam-5563	34	2	,	,	PUNCT
ejpam-5563	34	3	then	then	ADV
ejpam-5563	34	4	c	c	PROPN
ejpam-5563	34	5	∩q	∩q	PROPN
ejpam-5563	34	6	/∈	/∈	PUNCT
ejpam-5563	35	1	p.	p.	NOUN
ejpam-5563	35	2	we	we	PRON
ejpam-5563	35	3	say	say	VERB
ejpam-5563	35	4	that	that	SCONJ
ejpam-5563	35	5	(	(	PUNCT
ejpam-5563	35	6	b	b	X
ejpam-5563	35	7	,	,	PUNCT
ejpam-5563	35	8	γ	γ	PROPN
ejpam-5563	35	9	,	,	PUNCT
ejpam-5563	35	10	p	p	NOUN
ejpam-5563	35	11	)	)	PUNCT
ejpam-5563	35	12	is	be	AUX
ejpam-5563	35	13	a	a	DET
ejpam-5563	35	14	primal	primal	ADJ
ejpam-5563	35	15	topological	topological	ADJ
ejpam-5563	35	16	space	space	NOUN
ejpam-5563	35	17	(	(	PUNCT
ejpam-5563	35	18	ps	ps	NOUN
ejpam-5563	35	19	)	)	PUNCT
ejpam-5563	35	20	,	,	PUNCT
ejpam-5563	35	21	where	where	SCONJ
ejpam-5563	35	22	γ	γ	PROPN
ejpam-5563	35	23	is	be	AUX
ejpam-5563	35	24	a	a	DET
ejpam-5563	35	25	topology	topology	NOUN
ejpam-5563	35	26	on	on	ADP
ejpam-5563	35	27	b.	b.	PROPN
ejpam-5563	35	28	definition	definition	NOUN
ejpam-5563	35	29	2	2	NUM
ejpam-5563	35	30	.	.	PUNCT
ejpam-5563	36	1	[	[	X
ejpam-5563	36	2	1	1	X
ejpam-5563	36	3	]	]	X
ejpam-5563	36	4	let	let	VERB
ejpam-5563	36	5	(	(	PUNCT
ejpam-5563	36	6	b	b	X
ejpam-5563	36	7	,	,	PUNCT
ejpam-5563	36	8	γ	γ	PROPN
ejpam-5563	36	9	,	,	PUNCT
ejpam-5563	36	10	p	p	NOUN
ejpam-5563	36	11	)	)	PUNCT
ejpam-5563	36	12	be	be	AUX
ejpam-5563	36	13	a	a	DET
ejpam-5563	36	14	ps	ps	NOUN
ejpam-5563	36	15	.	.	PUNCT
ejpam-5563	37	1	for	for	ADP
ejpam-5563	37	2	any	any	DET
ejpam-5563	37	3	set	set	NOUN
ejpam-5563	37	4	q	q	NOUN
ejpam-5563	37	5	⊆	⊆	NUM
ejpam-5563	37	6	b	b	NOUN
ejpam-5563	37	7	,	,	PUNCT
ejpam-5563	37	8	the	the	DET
ejpam-5563	37	9	function	function	NOUN
ejpam-5563	37	10	(	(	PUNCT
ejpam-5563	37	11	·	·	PUNCT
ejpam-5563	37	12	)	)	PUNCT
ejpam-5563	37	13	⋄	⋄	NOUN
ejpam-5563	37	14	:	:	PUNCT
ejpam-5563	37	15	p(b	p(b	NOUN
ejpam-5563	37	16	)	)	PUNCT
ejpam-5563	37	17	→	→	SYM
ejpam-5563	37	18	p(b	p(b	PROPN
ejpam-5563	37	19	)	)	PUNCT
ejpam-5563	37	20	is	be	AUX
ejpam-5563	37	21	defined	define	VERB
ejpam-5563	37	22	as	as	ADP
ejpam-5563	37	23	:	:	PUNCT
ejpam-5563	37	24	q⋄	q⋄	X
ejpam-5563	37	25	=	=	SYM
ejpam-5563	37	26	q⋄(b	q⋄(b	PROPN
ejpam-5563	37	27	,	,	PUNCT
ejpam-5563	37	28	γ	γ	X
ejpam-5563	37	29	,	,	PUNCT
ejpam-5563	37	30	p	p	NOUN
ejpam-5563	37	31	)	)	PUNCT
ejpam-5563	37	32	=	=	SYM
ejpam-5563	38	1	{	{	PUNCT
ejpam-5563	38	2	r	r	NOUN
ejpam-5563	38	3	∈	∈	PROPN
ejpam-5563	38	4	b	b	PROPN
ejpam-5563	38	5	:	:	PUNCT
ejpam-5563	38	6	qc	qc	PROPN
ejpam-5563	38	7	∪oc	∪oc	PROPN
ejpam-5563	38	8	∈	∈	PROPN
ejpam-5563	38	9	p	p	PROPN
ejpam-5563	38	10	for	for	ADP
ejpam-5563	38	11	all	all	PRON
ejpam-5563	38	12	o	o	NOUN
ejpam-5563	38	13	∈	∈	PROPN
ejpam-5563	38	14	γ(r	γ(r	PROPN
ejpam-5563	38	15	)	)	PUNCT
ejpam-5563	38	16	}	}	PUNCT
ejpam-5563	38	17	.	.	PUNCT
ejpam-5563	39	1	from	from	ADP
ejpam-5563	39	2	the	the	DET
ejpam-5563	39	3	definition	definition	NOUN
ejpam-5563	39	4	,	,	PUNCT
ejpam-5563	39	5	it	it	PRON
ejpam-5563	39	6	is	be	AUX
ejpam-5563	39	7	clear	clear	ADJ
ejpam-5563	39	8	that	that	SCONJ
ejpam-5563	39	9	∀	∀	AUX
ejpam-5563	39	10	r	r	NOUN
ejpam-5563	39	11	∈	∈	PROPN
ejpam-5563	39	12	q⋄	q⋄	AUX
ejpam-5563	39	13	,	,	PUNCT
ejpam-5563	39	14	we	we	PRON
ejpam-5563	39	15	have	have	VERB
ejpam-5563	39	16	w	w	NOUN
ejpam-5563	39	17	∩	∩	ADJ
ejpam-5563	40	1	q	q	PROPN
ejpam-5563	40	2	̸=	̸=	PROPN
ejpam-5563	40	3	∅	∅	NOUN
ejpam-5563	40	4	for	for	ADP
ejpam-5563	40	5	every	every	DET
ejpam-5563	40	6	w	w	PROPN
ejpam-5563	40	7	∈	∈	PROPN
ejpam-5563	40	8	γ(r	γ(r	PROPN
ejpam-5563	40	9	)	)	PUNCT
ejpam-5563	40	10	;	;	PUNCT
ejpam-5563	40	11	hence	hence	ADV
ejpam-5563	40	12	,	,	PUNCT
ejpam-5563	40	13	q⋄	q⋄	X
ejpam-5563	40	14	⊆	⊆	NUM
ejpam-5563	40	15	cl(q	cl(q	NUM
ejpam-5563	40	16	)	)	PUNCT
ejpam-5563	40	17	.	.	PUNCT
ejpam-5563	41	1	definition	definition	NOUN
ejpam-5563	41	2	3	3	NUM
ejpam-5563	41	3	.	.	PUNCT
ejpam-5563	42	1	[	[	X
ejpam-5563	42	2	7	7	X
ejpam-5563	42	3	]	]	X
ejpam-5563	42	4	let	let	NOUN
ejpam-5563	42	5	(	(	PUNCT
ejpam-5563	42	6	b	b	X
ejpam-5563	42	7	,	,	PUNCT
ejpam-5563	42	8	γ	γ	PROPN
ejpam-5563	42	9	,	,	PUNCT
ejpam-5563	42	10	p	p	NOUN
ejpam-5563	42	11	)	)	PUNCT
ejpam-5563	42	12	be	be	AUX
ejpam-5563	42	13	a	a	DET
ejpam-5563	42	14	ps	ps	NOUN
ejpam-5563	42	15	and	and	CCONJ
ejpam-5563	42	16	let	let	VERB
ejpam-5563	42	17	o	o	NOUN
ejpam-5563	42	18	⊆	⊆	NUM
ejpam-5563	42	19	b	b	NOUN
ejpam-5563	42	20	be	be	AUX
ejpam-5563	42	21	any	any	DET
ejpam-5563	42	22	set	set	NOUN
ejpam-5563	42	23	.	.	PUNCT
ejpam-5563	43	1	then	then	ADV
ejpam-5563	43	2	,	,	PUNCT
ejpam-5563	43	3	the	the	DET
ejpam-5563	43	4	function	function	NOUN
ejpam-5563	43	5	γ	γ	X
ejpam-5563	43	6	:	:	PUNCT
ejpam-5563	43	7	p(b	p(b	NUM
ejpam-5563	43	8	)	)	PUNCT
ejpam-5563	43	9	→	→	SYM
ejpam-5563	43	10	p(b	p(b	PROPN
ejpam-5563	43	11	)	)	PUNCT
ejpam-5563	43	12	is	be	AUX
ejpam-5563	43	13	defined	define	VERB
ejpam-5563	43	14	as	as	ADP
ejpam-5563	43	15	:	:	PUNCT
ejpam-5563	43	16	γ(o	γ(o	X
ejpam-5563	43	17	)	)	PUNCT
ejpam-5563	43	18	=	=	PRON
ejpam-5563	44	1	{	{	PUNCT
ejpam-5563	44	2	r	r	NOUN
ejpam-5563	44	3	∈	∈	PROPN
ejpam-5563	44	4	b	b	NOUN
ejpam-5563	44	5	:	:	PUNCT
ejpam-5563	44	6	oc	oc	X
ejpam-5563	44	7	∪	∪	X
ejpam-5563	44	8	(	(	PUNCT
ejpam-5563	44	9	w	w	PROPN
ejpam-5563	44	10	⋄)c	⋄)c	PROPN
ejpam-5563	44	11	∈	∈	PROPN
ejpam-5563	44	12	p	p	NOUN
ejpam-5563	44	13	for	for	ADP
ejpam-5563	44	14	all	all	DET
ejpam-5563	44	15	w	w	PROPN
ejpam-5563	44	16	∈	∈	PROPN
ejpam-5563	44	17	γ(r	γ(r	PROPN
ejpam-5563	44	18	)	)	PUNCT
ejpam-5563	44	19	}	}	PUNCT
ejpam-5563	44	20	.	.	PUNCT
ejpam-5563	45	1	definition	definition	NOUN
ejpam-5563	45	2	4	4	NUM
ejpam-5563	45	3	.	.	PUNCT
ejpam-5563	46	1	[	[	X
ejpam-5563	46	2	7	7	X
ejpam-5563	46	3	]	]	X
ejpam-5563	46	4	let	let	NOUN
ejpam-5563	46	5	(	(	PUNCT
ejpam-5563	46	6	b	b	X
ejpam-5563	46	7	,	,	PUNCT
ejpam-5563	46	8	γ	γ	PROPN
ejpam-5563	46	9	,	,	PUNCT
ejpam-5563	46	10	p	p	NOUN
ejpam-5563	46	11	)	)	PUNCT
ejpam-5563	46	12	be	be	AUX
ejpam-5563	46	13	a	a	DET
ejpam-5563	46	14	ps	ps	NOUN
ejpam-5563	46	15	.	.	PUNCT
ejpam-5563	47	1	the	the	DET
ejpam-5563	47	2	operator	operator	NOUN
ejpam-5563	47	3	γ∗	γ∗	NOUN
ejpam-5563	47	4	:	:	PUNCT
ejpam-5563	47	5	p(b	p(b	NUM
ejpam-5563	47	6	)	)	PUNCT
ejpam-5563	47	7	→	→	SYM
ejpam-5563	47	8	p(b	p(b	PROPN
ejpam-5563	47	9	)	)	PUNCT
ejpam-5563	47	10	is	be	AUX
ejpam-5563	47	11	defined	define	VERB
ejpam-5563	47	12	as	as	ADP
ejpam-5563	47	13	:	:	PUNCT
ejpam-5563	47	14	γ∗(o	γ∗(o	PROPN
ejpam-5563	47	15	)	)	PUNCT
ejpam-5563	47	16	=	=	PRON
ejpam-5563	48	1	{	{	PUNCT
ejpam-5563	48	2	r	r	NOUN
ejpam-5563	48	3	∈	∈	PROPN
ejpam-5563	48	4	b	b	PROPN
ejpam-5563	48	5	:	:	PUNCT
ejpam-5563	48	6	∃	∃	PROPN
ejpam-5563	48	7	w	w	PROPN
ejpam-5563	48	8	∈	∈	PROPN
ejpam-5563	48	9	γ(r	γ(r	PROPN
ejpam-5563	48	10	)	)	PUNCT
ejpam-5563	48	11	such	such	ADJ
ejpam-5563	48	12	that	that	SCONJ
ejpam-5563	48	13	(	(	PUNCT
ejpam-5563	48	14	w	w	PROPN
ejpam-5563	48	15	⋄	⋄	PROPN
ejpam-5563	48	16	−o)c	−o)c	NOUN
ejpam-5563	48	17	/∈	/∈	PUNCT
ejpam-5563	49	1	p	p	X
ejpam-5563	49	2	}	}	PUNCT
ejpam-5563	49	3	for	for	ADP
ejpam-5563	49	4	every	every	DET
ejpam-5563	49	5	o	o	PROPN
ejpam-5563	49	6	⊆	⊆	NUM
ejpam-5563	49	7	b.	b.	NOUN
ejpam-5563	49	8	definition	definition	NOUN
ejpam-5563	49	9	5	5	NUM
ejpam-5563	49	10	.	.	PUNCT
ejpam-5563	50	1	[	[	X
ejpam-5563	50	2	7	7	X
ejpam-5563	50	3	]	]	X
ejpam-5563	50	4	if	if	SCONJ
ejpam-5563	50	5	(	(	PUNCT
ejpam-5563	50	6	b	b	NOUN
ejpam-5563	50	7	,	,	PUNCT
ejpam-5563	50	8	γ	γ	PROPN
ejpam-5563	50	9	,	,	PUNCT
ejpam-5563	50	10	p	p	NOUN
ejpam-5563	50	11	)	)	PUNCT
ejpam-5563	50	12	is	be	AUX
ejpam-5563	50	13	a	a	DET
ejpam-5563	50	14	ps	ps	NOUN
ejpam-5563	50	15	,	,	PUNCT
ejpam-5563	50	16	then	then	ADV
ejpam-5563	50	17	the	the	DET
ejpam-5563	50	18	topology	topology	NOUN
ejpam-5563	50	19	produced	produce	VERB
ejpam-5563	50	20	by	by	ADP
ejpam-5563	50	21	the	the	DET
ejpam-5563	50	22	operator	operator	NOUN
ejpam-5563	50	23	γ∗	γ∗	NOUN
ejpam-5563	50	24	is	be	AUX
ejpam-5563	50	25	defined	define	VERB
ejpam-5563	50	26	as	as	SCONJ
ejpam-5563	50	27	follows	follow	VERB
ejpam-5563	50	28	:	:	PUNCT
ejpam-5563	50	29	γγ∗	γγ∗	NOUN
ejpam-5563	50	30	=	=	PUNCT
ejpam-5563	50	31	{	{	PUNCT
ejpam-5563	50	32	u	u	NOUN
ejpam-5563	50	33	⊆	⊆	NUM
ejpam-5563	50	34	b	b	NOUN
ejpam-5563	50	35	|	|	CCONJ
ejpam-5563	50	36	u	u	NOUN
ejpam-5563	50	37	⊆	⊆	NUM
ejpam-5563	50	38	γ∗(u	γ∗(u	PROPN
ejpam-5563	50	39	)	)	PUNCT
ejpam-5563	50	40	}	}	PUNCT
ejpam-5563	50	41	and	and	CCONJ
ejpam-5563	50	42	clγ∗(s	clγ∗(s	NOUN
ejpam-5563	50	43	)	)	PUNCT
ejpam-5563	50	44	=	=	SYM
ejpam-5563	50	45	s	s	NOUN
ejpam-5563	50	46	∪	∪	ADJ
ejpam-5563	50	47	γ(s	γ(	NOUN
ejpam-5563	50	48	)	)	PUNCT
ejpam-5563	50	49	.	.	PUNCT
ejpam-5563	51	1	definition	definition	NOUN
ejpam-5563	51	2	6	6	NUM
ejpam-5563	51	3	.	.	PUNCT
ejpam-5563	52	1	[	[	X
ejpam-5563	52	2	12	12	NUM
ejpam-5563	52	3	]	]	X
ejpam-5563	52	4	if	if	SCONJ
ejpam-5563	52	5	(	(	PUNCT
ejpam-5563	52	6	b	b	NOUN
ejpam-5563	52	7	,	,	PUNCT
ejpam-5563	52	8	γ	γ	PROPN
ejpam-5563	52	9	,	,	PUNCT
ejpam-5563	52	10	p	p	NOUN
ejpam-5563	52	11	)	)	PUNCT
ejpam-5563	52	12	is	be	AUX
ejpam-5563	52	13	a	a	DET
ejpam-5563	52	14	ps	ps	NOUN
ejpam-5563	52	15	,	,	PUNCT
ejpam-5563	52	16	then	then	ADV
ejpam-5563	52	17	γθ	γθ	PROPN
ejpam-5563	52	18	is	be	AUX
ejpam-5563	52	19	defined	define	VERB
ejpam-5563	52	20	as	as	SCONJ
ejpam-5563	52	21	follows	follow	VERB
ejpam-5563	52	22	:	:	PUNCT
ejpam-5563	52	23	γθ	γθ	PROPN
ejpam-5563	52	24	=	=	PUNCT
ejpam-5563	52	25	{	{	PUNCT
ejpam-5563	52	26	w	w	PROPN
ejpam-5563	52	27	∈	∈	PROPN
ejpam-5563	52	28	γ	γ	NOUN
ejpam-5563	52	29	|	|	NOUN
ejpam-5563	52	30	∀	∀	NOUN
ejpam-5563	52	31	r	r	NOUN
ejpam-5563	52	32	∈	∈	PROPN
ejpam-5563	52	33	w	w	PROPN
ejpam-5563	52	34	∃	∃	PROPN
ejpam-5563	52	35	h	h	PROPN
ejpam-5563	52	36	∈	∈	PROPN
ejpam-5563	52	37	γ(r	γ(r	PROPN
ejpam-5563	52	38	)	)	PUNCT
ejpam-5563	52	39	such	such	ADJ
ejpam-5563	52	40	that	that	SCONJ
ejpam-5563	52	41	r	r	NOUN
ejpam-5563	52	42	∈	∈	PROPN
ejpam-5563	52	43	h	h	NOUN
ejpam-5563	52	44	⊆	⊆	NUM
ejpam-5563	52	45	cl(h	cl(h	NUM
ejpam-5563	52	46	)	)	PUNCT
ejpam-5563	52	47	⊆	⊆	NUM
ejpam-5563	52	48	w	w	NOUN
ejpam-5563	52	49	}	}	PUNCT
ejpam-5563	52	50	.	.	PUNCT
ejpam-5563	53	1	observe	observe	VERB
ejpam-5563	53	2	that	that	SCONJ
ejpam-5563	53	3	γθ	γθ	PROPN
ejpam-5563	53	4	⊆	⊆	NUM
ejpam-5563	53	5	γ	γ	X
ejpam-5563	53	6	.	.	PUNCT
ejpam-5563	54	1	moreover	moreover	ADV
ejpam-5563	54	2	,	,	PUNCT
ejpam-5563	54	3	clθ(k	clθ(k	ADJ
ejpam-5563	54	4	)	)	PUNCT
ejpam-5563	54	5	=	=	SYM
ejpam-5563	54	6	{	{	PUNCT
ejpam-5563	54	7	r	r	NOUN
ejpam-5563	54	8	∈	∈	PROPN
ejpam-5563	54	9	b	b	NOUN
ejpam-5563	55	1	|	|	ADV
ejpam-5563	55	2	k	k	PROPN
ejpam-5563	55	3	∩	∩	X
ejpam-5563	55	4	cl(o	cl(o	X
ejpam-5563	55	5	)	)	PUNCT
ejpam-5563	55	6	̸=	̸=	PROPN
ejpam-5563	55	7	∅	∅	NOUN
ejpam-5563	55	8	∀	∀	NOUN
ejpam-5563	55	9	o	o	X
ejpam-5563	55	10	∈	∈	PROPN
ejpam-5563	55	11	γ(r	γ(r	PROPN
ejpam-5563	55	12	)	)	PUNCT
ejpam-5563	55	13	}	}	PUNCT
ejpam-5563	55	14	and	and	CCONJ
ejpam-5563	55	15	intθ(k	intθ(k	ADJ
ejpam-5563	55	16	)	)	PUNCT
ejpam-5563	55	17	=	=	PRON
ejpam-5563	55	18	{	{	PUNCT
ejpam-5563	55	19	⋃	⋃	NOUN
ejpam-5563	55	20	α∈λ	α∈λ	NOUN
ejpam-5563	55	21	uα	uα	ADP
ejpam-5563	55	22	such	such	ADJ
ejpam-5563	55	23	that	that	PRON
ejpam-5563	55	24	uα	uα	PROPN
ejpam-5563	55	25	⊆	⊆	NUM
ejpam-5563	55	26	k	k	PROPN
ejpam-5563	55	27	and	and	CCONJ
ejpam-5563	55	28	uα	uα	PROPN
ejpam-5563	55	29	∈	∈	PROPN
ejpam-5563	55	30	γθ	γθ	PROPN
ejpam-5563	55	31	}	}	PUNCT
ejpam-5563	55	32	.	.	PUNCT
ejpam-5563	56	1	theorem	theorem	NOUN
ejpam-5563	56	2	1	1	NUM
ejpam-5563	56	3	.	.	PUNCT
ejpam-5563	57	1	[	[	X
ejpam-5563	57	2	7	7	X
ejpam-5563	57	3	]	]	X
ejpam-5563	57	4	let	let	NOUN
ejpam-5563	57	5	(	(	PUNCT
ejpam-5563	57	6	b	b	X
ejpam-5563	57	7	,	,	PUNCT
ejpam-5563	57	8	γ	γ	PROPN
ejpam-5563	57	9	,	,	PUNCT
ejpam-5563	57	10	p	p	NOUN
ejpam-5563	57	11	)	)	PUNCT
ejpam-5563	57	12	be	be	AUX
ejpam-5563	57	13	a	a	DET
ejpam-5563	57	14	ps	ps	NOUN
ejpam-5563	57	15	and	and	CCONJ
ejpam-5563	57	16	let	let	VERB
ejpam-5563	57	17	o	o	NOUN
ejpam-5563	57	18	,	,	PUNCT
ejpam-5563	57	19	o1,o2	o1,o2	PROPN
ejpam-5563	57	20	⊆	⊆	NUM
ejpam-5563	57	21	b.	b.	NOUN
ejpam-5563	57	22	the	the	DET
ejpam-5563	57	23	following	follow	VERB
ejpam-5563	57	24	properties	property	NOUN
ejpam-5563	57	25	hold	hold	VERB
ejpam-5563	57	26	:	:	PUNCT
ejpam-5563	57	27	(	(	PUNCT
ejpam-5563	57	28	i	i	NOUN
ejpam-5563	57	29	)	)	PUNCT
ejpam-5563	57	30	γ(∅	γ(∅	PROPN
ejpam-5563	57	31	)	)	PUNCT
ejpam-5563	57	32	=	=	SYM
ejpam-5563	57	33	∅.	∅.	PRON
ejpam-5563	57	34	(	(	PUNCT
ejpam-5563	57	35	ii	ii	NOUN
ejpam-5563	57	36	)	)	PUNCT
ejpam-5563	57	37	if	if	SCONJ
ejpam-5563	57	38	o1	o1	NOUN
ejpam-5563	57	39	⊆	⊆	NUM
ejpam-5563	57	40	o2	o2	PROPN
ejpam-5563	57	41	,	,	PUNCT
ejpam-5563	57	42	then	then	ADV
ejpam-5563	57	43	γ(o1	γ(o1	VERB
ejpam-5563	57	44	)	)	PUNCT
ejpam-5563	57	45	⊆	⊆	NUM
ejpam-5563	57	46	γ(o2	γ(o2	NUM
ejpam-5563	57	47	)	)	PUNCT
ejpam-5563	57	48	.	.	PUNCT
ejpam-5563	58	1	(	(	PUNCT
ejpam-5563	58	2	iii	iii	NOUN
ejpam-5563	58	3	)	)	PUNCT
ejpam-5563	58	4	γ(o	γ(o	PROPN
ejpam-5563	58	5	)	)	PUNCT
ejpam-5563	58	6	is	be	AUX
ejpam-5563	58	7	closed	closed	ADJ
ejpam-5563	58	8	.	.	PUNCT
ejpam-5563	59	1	(	(	PUNCT
ejpam-5563	59	2	iv	iv	X
ejpam-5563	59	3	)	)	PUNCT
ejpam-5563	59	4	γ(o	γ(o	PROPN
ejpam-5563	59	5	)	)	PUNCT
ejpam-5563	60	1	⊆	⊆	NUM
ejpam-5563	60	2	clθ(o	clθ(o	PROPN
ejpam-5563	60	3	)	)	PUNCT
ejpam-5563	60	4	.	.	PUNCT
ejpam-5563	61	1	(	(	PUNCT
ejpam-5563	61	2	v	v	NOUN
ejpam-5563	61	3	)	)	PUNCT
ejpam-5563	61	4	if	if	SCONJ
ejpam-5563	61	5	o	o	PROPN
ejpam-5563	61	6	⊆	⊆	NUM
ejpam-5563	61	7	γ(o	γ(o	NUM
ejpam-5563	61	8	)	)	PUNCT
ejpam-5563	61	9	and	and	CCONJ
ejpam-5563	61	10	γ(o	γ(o	NOUN
ejpam-5563	61	11	)	)	PUNCT
ejpam-5563	61	12	is	be	AUX
ejpam-5563	61	13	open	open	ADJ
ejpam-5563	61	14	,	,	PUNCT
ejpam-5563	61	15	then	then	ADV
ejpam-5563	61	16	γ(o	γ(o	ADJ
ejpam-5563	61	17	)	)	PUNCT
ejpam-5563	62	1	=	=	SYM
ejpam-5563	62	2	clθ(o	clθ(o	PROPN
ejpam-5563	62	3	)	)	PUNCT
ejpam-5563	62	4	.	.	PUNCT
ejpam-5563	63	1	o.	o.	PROPN
ejpam-5563	63	2	alghamdi	alghamdi	PROPN
ejpam-5563	63	3	/	/	SYM
ejpam-5563	63	4	eur	eur	PROPN
ejpam-5563	63	5	.	.	PUNCT
ejpam-5563	64	1	j.	j.	PROPN
ejpam-5563	64	2	pure	pure	PROPN
ejpam-5563	64	3	appl	appl	PROPN
ejpam-5563	64	4	.	.	PROPN
ejpam-5563	64	5	math	math	PROPN
ejpam-5563	64	6	,	,	PUNCT
ejpam-5563	64	7	17	17	NUM
ejpam-5563	64	8	(	(	PUNCT
ejpam-5563	64	9	4	4	NUM
ejpam-5563	64	10	)	)	PUNCT
ejpam-5563	64	11	(	(	PUNCT
ejpam-5563	64	12	2024	2024	NUM
ejpam-5563	64	13	)	)	PUNCT
ejpam-5563	64	14	,	,	PUNCT
ejpam-5563	64	15	3517	3517	NUM
ejpam-5563	64	16	-	-	SYM
ejpam-5563	64	17	3538	3538	NUM
ejpam-5563	64	18	3519	3519	NUM
ejpam-5563	64	19	(	(	PUNCT
ejpam-5563	64	20	vi	vi	NOUN
ejpam-5563	64	21	)	)	PUNCT
ejpam-5563	64	22	if	if	SCONJ
ejpam-5563	64	23	oc	oc	PART
ejpam-5563	64	24	/∈	/∈	PUNCT
ejpam-5563	65	1	p	p	X
ejpam-5563	65	2	,	,	PUNCT
ejpam-5563	65	3	then	then	ADV
ejpam-5563	65	4	γ(o	γ(o	ADJ
ejpam-5563	65	5	)	)	PUNCT
ejpam-5563	66	1	=	=	PUNCT
ejpam-5563	66	2	∅.	∅.	X
ejpam-5563	66	3	(	(	PUNCT
ejpam-5563	66	4	vii	vii	PROPN
ejpam-5563	66	5	)	)	PUNCT
ejpam-5563	66	6	γ(o1	γ(o1	VERB
ejpam-5563	66	7	∪	∪	ADJ
ejpam-5563	66	8	o2	o2	PROPN
ejpam-5563	66	9	)	)	PUNCT
ejpam-5563	66	10	=	=	SYM
ejpam-5563	66	11	γ(o1	γ(o1	NOUN
ejpam-5563	66	12	)	)	PUNCT
ejpam-5563	66	13	∪	∪	ADP
ejpam-5563	66	14	γ(o2	γ(o2	NUM
ejpam-5563	66	15	)	)	PUNCT
ejpam-5563	66	16	.	.	PUNCT
ejpam-5563	67	1	theorem	theorem	NOUN
ejpam-5563	67	2	2	2	NUM
ejpam-5563	67	3	.	.	PUNCT
ejpam-5563	68	1	[	[	X
ejpam-5563	68	2	7	7	X
ejpam-5563	68	3	]	]	X
ejpam-5563	68	4	let	let	NOUN
ejpam-5563	68	5	(	(	PUNCT
ejpam-5563	68	6	b	b	X
ejpam-5563	68	7	,	,	PUNCT
ejpam-5563	68	8	γ	γ	PROPN
ejpam-5563	68	9	,	,	PUNCT
ejpam-5563	68	10	p	p	NOUN
ejpam-5563	68	11	)	)	PUNCT
ejpam-5563	68	12	be	be	AUX
ejpam-5563	68	13	a	a	DET
ejpam-5563	68	14	ps	ps	NOUN
ejpam-5563	68	15	and	and	CCONJ
ejpam-5563	68	16	let	let	VERB
ejpam-5563	68	17	o	o	NOUN
ejpam-5563	68	18	,	,	PUNCT
ejpam-5563	68	19	o1,o2	o1,o2	PROPN
ejpam-5563	68	20	⊆	⊆	NUM
ejpam-5563	68	21	b.	b.	NOUN
ejpam-5563	68	22	then	then	ADV
ejpam-5563	68	23	,	,	PUNCT
ejpam-5563	68	24	(	(	PUNCT
ejpam-5563	68	25	i	i	NOUN
ejpam-5563	68	26	)	)	PUNCT
ejpam-5563	68	27	γ∗(o	γ∗(o	PROPN
ejpam-5563	68	28	)	)	PUNCT
ejpam-5563	69	1	=	=	NOUN
ejpam-5563	70	1	[	[	X
ejpam-5563	70	2	γ(oc)]c	γ(oc)]c	PROPN
ejpam-5563	70	3	.	.	PUNCT
ejpam-5563	70	4	(	(	PUNCT
ejpam-5563	70	5	ii	ii	NOUN
ejpam-5563	70	6	)	)	PUNCT
ejpam-5563	70	7	γ∗(o	γ∗(o	PROPN
ejpam-5563	70	8	)	)	PUNCT
ejpam-5563	70	9	is	be	AUX
ejpam-5563	70	10	open	open	ADJ
ejpam-5563	70	11	.	.	PUNCT
ejpam-5563	71	1	(	(	PUNCT
ejpam-5563	71	2	iii	iii	X
ejpam-5563	71	3	)	)	PUNCT
ejpam-5563	71	4	if	if	SCONJ
ejpam-5563	71	5	o1	o1	NOUN
ejpam-5563	71	6	⊆	⊆	NUM
ejpam-5563	71	7	o2	o2	PROPN
ejpam-5563	71	8	,	,	PUNCT
ejpam-5563	71	9	then	then	ADV
ejpam-5563	71	10	γ∗(o1	γ∗(o1	PROPN
ejpam-5563	71	11	)	)	PUNCT
ejpam-5563	71	12	⊆	⊆	NUM
ejpam-5563	71	13	γ∗(o2	γ∗(o2	PROPN
ejpam-5563	71	14	)	)	PUNCT
ejpam-5563	71	15	.	.	PUNCT
ejpam-5563	72	1	(	(	PUNCT
ejpam-5563	72	2	iv	iv	X
ejpam-5563	72	3	)	)	PUNCT
ejpam-5563	72	4	γ∗(o1	γ∗(o1	PROPN
ejpam-5563	72	5	∩	∩	ADJ
ejpam-5563	72	6	o2	o2	NOUN
ejpam-5563	72	7	)	)	PUNCT
ejpam-5563	72	8	=	=	SYM
ejpam-5563	72	9	γ∗(o1	γ∗(o1	ADJ
ejpam-5563	72	10	)	)	PUNCT
ejpam-5563	72	11	∩	∩	ADJ
ejpam-5563	72	12	γ∗(o2	γ∗(o2	PROPN
ejpam-5563	72	13	)	)	PUNCT
ejpam-5563	72	14	.	.	PUNCT
ejpam-5563	73	1	(	(	PUNCT
ejpam-5563	73	2	v	v	NOUN
ejpam-5563	73	3	)	)	PUNCT
ejpam-5563	73	4	γ∗(o	γ∗(o	PROPN
ejpam-5563	73	5	)	)	PUNCT
ejpam-5563	73	6	=	=	SYM
ejpam-5563	73	7	γ∗(γ∗(o	γ∗(γ∗(o	PROPN
ejpam-5563	73	8	)	)	PUNCT
ejpam-5563	73	9	)	)	PUNCT
ejpam-5563	74	1	⇔	⇔	PROPN
ejpam-5563	74	2	γ(oc	γ(oc	PROPN
ejpam-5563	74	3	)	)	PUNCT
ejpam-5563	74	4	=	=	SYM
ejpam-5563	74	5	γ(γ(oc	γ(γ(oc	NOUN
ejpam-5563	74	6	)	)	PUNCT
ejpam-5563	74	7	)	)	PUNCT
ejpam-5563	74	8	.	.	PUNCT
ejpam-5563	75	1	(	(	PUNCT
ejpam-5563	75	2	vi	vi	X
ejpam-5563	75	3	)	)	PUNCT
ejpam-5563	75	4	if	if	SCONJ
ejpam-5563	75	5	oc	oc	PART
ejpam-5563	75	6	/∈	/∈	PUNCT
ejpam-5563	76	1	p	p	X
ejpam-5563	76	2	,	,	PUNCT
ejpam-5563	76	3	then	then	ADV
ejpam-5563	76	4	γ∗(o	γ∗(o	PROPN
ejpam-5563	76	5	)	)	PUNCT
ejpam-5563	77	1	=	=	PUNCT
ejpam-5563	78	1	[	[	X
ejpam-5563	78	2	γ(b)]c	γ(b)]c	NOUN
ejpam-5563	78	3	.	.	PUNCT
ejpam-5563	79	1	(	(	PUNCT
ejpam-5563	79	2	vii	vii	PROPN
ejpam-5563	79	3	)	)	PUNCT
ejpam-5563	79	4	if	if	SCONJ
ejpam-5563	79	5	[	[	X
ejpam-5563	79	6	(	(	PUNCT
ejpam-5563	79	7	o1	o1	NOUN
ejpam-5563	79	8	−o2	−o2	NOUN
ejpam-5563	79	9	)	)	PUNCT
ejpam-5563	79	10	∪	∪	NOUN
ejpam-5563	79	11	(	(	PUNCT
ejpam-5563	79	12	o2	o2	PROPN
ejpam-5563	79	13	−o1	−o1	NOUN
ejpam-5563	79	14	)	)	PUNCT
ejpam-5563	79	15	]	]	PUNCT
ejpam-5563	80	1	c	c	X
ejpam-5563	80	2	/∈	/∈	PUNCT
ejpam-5563	81	1	p	p	X
ejpam-5563	81	2	,	,	PUNCT
ejpam-5563	81	3	then	then	ADV
ejpam-5563	81	4	γ∗(o1	γ∗(o1	ADJ
ejpam-5563	81	5	)	)	PUNCT
ejpam-5563	81	6	=	=	SYM
ejpam-5563	81	7	γ∗(o2	γ∗(o2	NOUN
ejpam-5563	81	8	)	)	PUNCT
ejpam-5563	81	9	.	.	PUNCT
ejpam-5563	82	1	(	(	PUNCT
ejpam-5563	82	2	viii	viii	NOUN
ejpam-5563	82	3	)	)	PUNCT
ejpam-5563	82	4	a	a	DET
ejpam-5563	82	5	subset	subset	NOUN
ejpam-5563	82	6	o	o	NOUN
ejpam-5563	82	7	is	be	AUX
ejpam-5563	82	8	a	a	DET
ejpam-5563	82	9	diamond	diamond	NOUN
ejpam-5563	82	10	-	-	PUNCT
ejpam-5563	82	11	closed	close	VERB
ejpam-5563	82	12	if	if	SCONJ
ejpam-5563	82	13	and	and	CCONJ
ejpam-5563	82	14	only	only	ADV
ejpam-5563	82	15	if	if	SCONJ
ejpam-5563	82	16	γ(o	γ(o	NOUN
ejpam-5563	82	17	)	)	PUNCT
ejpam-5563	82	18	⊆	⊆	NUM
ejpam-5563	82	19	o.	o.	NOUN
ejpam-5563	82	20	corollary	corollary	NOUN
ejpam-5563	82	21	1	1	NUM
ejpam-5563	82	22	.	.	PUNCT
ejpam-5563	83	1	[	[	X
ejpam-5563	83	2	7	7	X
ejpam-5563	83	3	]	]	X
ejpam-5563	83	4	let	let	NOUN
ejpam-5563	83	5	(	(	PUNCT
ejpam-5563	83	6	b	b	X
ejpam-5563	83	7	,	,	PUNCT
ejpam-5563	83	8	γ	γ	PROPN
ejpam-5563	83	9	,	,	PUNCT
ejpam-5563	83	10	p	p	NOUN
ejpam-5563	83	11	)	)	PUNCT
ejpam-5563	83	12	be	be	AUX
ejpam-5563	83	13	a	a	DET
ejpam-5563	83	14	ps	ps	NOUN
ejpam-5563	83	15	and	and	CCONJ
ejpam-5563	83	16	o	o	NOUN
ejpam-5563	83	17	,	,	PUNCT
ejpam-5563	83	18	m	m	VERB
ejpam-5563	83	19	⊆	⊆	NUM
ejpam-5563	83	20	b	b	NOUN
ejpam-5563	83	21	such	such	ADJ
ejpam-5563	83	22	that	that	DET
ejpam-5563	83	23	oc	oc	NOUN
ejpam-5563	83	24	/∈	/∈	PUNCT
ejpam-5563	84	1	p.	p.	NOUN
ejpam-5563	84	2	then	then	ADV
ejpam-5563	84	3	,	,	PUNCT
ejpam-5563	84	4	γ(o	γ(o	PROPN
ejpam-5563	84	5	∪m	∪m	NUM
ejpam-5563	84	6	)	)	PUNCT
ejpam-5563	84	7	=	=	PUNCT
ejpam-5563	84	8	γ(o	γ(o	VERB
ejpam-5563	84	9	)	)	PUNCT
ejpam-5563	84	10	=	=	SYM
ejpam-5563	84	11	γ(m	γ(m	PROPN
ejpam-5563	84	12	−o	−o	NOUN
ejpam-5563	84	13	)	)	PUNCT
ejpam-5563	84	14	.	.	PUNCT
ejpam-5563	85	1	theorem	theorem	NOUN
ejpam-5563	85	2	3	3	NUM
ejpam-5563	85	3	.	.	PUNCT
ejpam-5563	86	1	[	[	X
ejpam-5563	86	2	7	7	X
ejpam-5563	86	3	]	]	X
ejpam-5563	86	4	let	let	NOUN
ejpam-5563	86	5	(	(	PUNCT
ejpam-5563	86	6	b	b	X
ejpam-5563	86	7	,	,	PUNCT
ejpam-5563	86	8	γ	γ	PROPN
ejpam-5563	86	9	,	,	PUNCT
ejpam-5563	86	10	p	p	NOUN
ejpam-5563	86	11	)	)	PUNCT
ejpam-5563	86	12	be	be	AUX
ejpam-5563	86	13	a	a	DET
ejpam-5563	86	14	ps	ps	NOUN
ejpam-5563	86	15	.	.	PUNCT
ejpam-5563	87	1	then	then	ADV
ejpam-5563	87	2	,	,	PUNCT
ejpam-5563	87	3	γ(b	γ(b	X
ejpam-5563	87	4	)	)	PUNCT
ejpam-5563	88	1	=	=	SYM
ejpam-5563	88	2	b	b	NOUN
ejpam-5563	89	1	if	if	SCONJ
ejpam-5563	89	2	and	and	CCONJ
ejpam-5563	89	3	only	only	ADV
ejpam-5563	89	4	if	if	SCONJ
ejpam-5563	89	5	γ−	γ−	PROPN
ejpam-5563	89	6	{	{	PUNCT
ejpam-5563	89	7	b	b	NOUN
ejpam-5563	89	8	}	}	PUNCT
ejpam-5563	89	9	⊆	⊆	NUM
ejpam-5563	89	10	p	p	NOUN
ejpam-5563	89	11	and	and	CCONJ
ejpam-5563	89	12	△	△	NOUN
ejpam-5563	89	13	=	=	SYM
ejpam-5563	89	14	{	{	PUNCT
ejpam-5563	89	15	k	k	PROPN
ejpam-5563	89	16	∈	∈	PROPN
ejpam-5563	89	17	γ	γ	PROPN
ejpam-5563	89	18	|	|	NOUN
ejpam-5563	89	19	k⋄	k⋄	NOUN
ejpam-5563	89	20	=	=	NOUN
ejpam-5563	89	21	∅	∅	NOUN
ejpam-5563	89	22	}	}	PUNCT
ejpam-5563	89	23	=	=	SYM
ejpam-5563	89	24	{	{	PUNCT
ejpam-5563	89	25	∅	∅	NOUN
ejpam-5563	89	26	}	}	PUNCT
ejpam-5563	89	27	.	.	PUNCT
ejpam-5563	90	1	definition	definition	NOUN
ejpam-5563	90	2	7	7	NUM
ejpam-5563	90	3	.	.	PUNCT
ejpam-5563	91	1	[	[	X
ejpam-5563	91	2	7	7	X
ejpam-5563	91	3	]	]	X
ejpam-5563	91	4	let	let	NOUN
ejpam-5563	91	5	(	(	PUNCT
ejpam-5563	91	6	b	b	X
ejpam-5563	91	7	,	,	PUNCT
ejpam-5563	91	8	γ	γ	PROPN
ejpam-5563	91	9	,	,	PUNCT
ejpam-5563	91	10	p	p	NOUN
ejpam-5563	91	11	)	)	PUNCT
ejpam-5563	91	12	be	be	AUX
ejpam-5563	91	13	a	a	DET
ejpam-5563	91	14	ps	ps	NOUN
ejpam-5563	91	15	and	and	CCONJ
ejpam-5563	91	16	let	let	VERB
ejpam-5563	91	17	o	o	PROPN
ejpam-5563	91	18	⊆	⊆	NUM
ejpam-5563	91	19	b.	b.	PROPN
ejpam-5563	91	20	then	then	ADV
ejpam-5563	91	21	,	,	PUNCT
ejpam-5563	91	22	γ	γ	X
ejpam-5563	91	23	is	be	AUX
ejpam-5563	91	24	compatible	compatible	ADJ
ejpam-5563	91	25	with	with	ADP
ejpam-5563	91	26	p	p	PRON
ejpam-5563	91	27	if	if	SCONJ
ejpam-5563	91	28	for	for	ADP
ejpam-5563	91	29	every	every	DET
ejpam-5563	91	30	r	r	NOUN
ejpam-5563	91	31	∈	∈	NOUN
ejpam-5563	91	32	o	o	NOUN
ejpam-5563	91	33	there	there	PRON
ejpam-5563	91	34	exists	exist	VERB
ejpam-5563	91	35	w	w	PROPN
ejpam-5563	91	36	∈	∈	PROPN
ejpam-5563	91	37	γ(r	γ(r	PROPN
ejpam-5563	91	38	)	)	PUNCT
ejpam-5563	91	39	such	such	ADJ
ejpam-5563	91	40	that	that	SCONJ
ejpam-5563	91	41	(	(	PUNCT
ejpam-5563	91	42	w	w	NOUN
ejpam-5563	91	43	⋄)c	⋄)c	NOUN
ejpam-5563	91	44	∪	∪	NOUN
ejpam-5563	91	45	oc	oc	NOUN
ejpam-5563	91	46	/∈	/∈	PUNCT
ejpam-5563	92	1	p	p	X
ejpam-5563	92	2	,	,	PUNCT
ejpam-5563	92	3	then	then	ADV
ejpam-5563	92	4	oc	oc	X
ejpam-5563	92	5	/∈	/∈	PUNCT
ejpam-5563	93	1	p.	p.	NOUN
ejpam-5563	93	2	theorem	theorem	VERB
ejpam-5563	93	3	4	4	NUM
ejpam-5563	93	4	.	.	PUNCT
ejpam-5563	94	1	[	[	X
ejpam-5563	94	2	7	7	X
ejpam-5563	94	3	]	]	X
ejpam-5563	94	4	let	let	NOUN
ejpam-5563	94	5	(	(	PUNCT
ejpam-5563	94	6	b	b	X
ejpam-5563	94	7	,	,	PUNCT
ejpam-5563	94	8	γ	γ	PROPN
ejpam-5563	94	9	,	,	PUNCT
ejpam-5563	94	10	p	p	NOUN
ejpam-5563	94	11	)	)	PUNCT
ejpam-5563	94	12	be	be	AUX
ejpam-5563	94	13	a	a	DET
ejpam-5563	94	14	ps	ps	NOUN
ejpam-5563	94	15	and	and	CCONJ
ejpam-5563	94	16	let	let	VERB
ejpam-5563	94	17	o	o	PROPN
ejpam-5563	94	18	⊆	⊆	NUM
ejpam-5563	94	19	b.	b.	PROPN
ejpam-5563	94	20	then	then	ADV
ejpam-5563	94	21	,	,	PUNCT
ejpam-5563	94	22	γ	γ	X
ejpam-5563	94	23	is	be	AUX
ejpam-5563	94	24	compatible	compatible	ADJ
ejpam-5563	94	25	with	with	ADP
ejpam-5563	94	26	p	p	PROPN
ejpam-5563	94	27	⇐	⇐	ADJ
ejpam-5563	94	28	⇒	⇒	NOUN
ejpam-5563	94	29	[	[	X
ejpam-5563	94	30	o	o	X
ejpam-5563	94	31	−	−	X
ejpam-5563	94	32	γ(o)]c	γ(o)]c	PROPN
ejpam-5563	94	33	/∈	/∈	PUNCT
ejpam-5563	95	1	p.	p.	NOUN
ejpam-5563	95	2	lemma	lemma	PROPN
ejpam-5563	96	1	1	1	NUM
ejpam-5563	96	2	.	.	PUNCT
ejpam-5563	97	1	[	[	X
ejpam-5563	97	2	7	7	X
ejpam-5563	97	3	]	]	X
ejpam-5563	97	4	let	let	NOUN
ejpam-5563	97	5	(	(	PUNCT
ejpam-5563	97	6	b	b	X
ejpam-5563	97	7	,	,	PUNCT
ejpam-5563	97	8	γ	γ	PROPN
ejpam-5563	97	9	,	,	PUNCT
ejpam-5563	97	10	p	p	NOUN
ejpam-5563	97	11	)	)	PUNCT
ejpam-5563	97	12	be	be	AUX
ejpam-5563	97	13	a	a	DET
ejpam-5563	97	14	ps	ps	NOUN
ejpam-5563	97	15	.	.	PUNCT
ejpam-5563	98	1	if	if	SCONJ
ejpam-5563	98	2	g	g	PROPN
ejpam-5563	98	3	∈	∈	PROPN
ejpam-5563	98	4	γθ	γθ	PROPN
ejpam-5563	98	5	,	,	PUNCT
ejpam-5563	98	6	then	then	ADV
ejpam-5563	98	7	g	g	PROPN
ejpam-5563	98	8	∈	∈	PROPN
ejpam-5563	98	9	γγ∗.	γγ∗.	PROPN
ejpam-5563	98	10	lemma	lemma	PROPN
ejpam-5563	98	11	2	2	NUM
ejpam-5563	98	12	.	.	PUNCT
ejpam-5563	99	1	[	[	X
ejpam-5563	99	2	2	2	NUM
ejpam-5563	99	3	]	]	X
ejpam-5563	99	4	let	let	VERB
ejpam-5563	99	5	(	(	PUNCT
ejpam-5563	99	6	b	b	X
ejpam-5563	99	7	,	,	PUNCT
ejpam-5563	99	8	γ	γ	PROPN
ejpam-5563	99	9	,	,	PUNCT
ejpam-5563	99	10	p	p	NOUN
ejpam-5563	99	11	)	)	PUNCT
ejpam-5563	99	12	be	be	AUX
ejpam-5563	99	13	a	a	DET
ejpam-5563	99	14	ps	ps	NOUN
ejpam-5563	99	15	such	such	ADJ
ejpam-5563	99	16	that	that	DET
ejpam-5563	99	17	c(b)−	c(b)−	PROPN
ejpam-5563	99	18	{	{	PUNCT
ejpam-5563	99	19	b	b	NOUN
ejpam-5563	99	20	}	}	PUNCT
ejpam-5563	99	21	⊆	⊆	NUM
ejpam-5563	99	22	p	p	NOUN
ejpam-5563	99	23	,	,	PUNCT
ejpam-5563	99	24	where	where	SCONJ
ejpam-5563	99	25	c(b	c(b	PROPN
ejpam-5563	99	26	)	)	PUNCT
ejpam-5563	100	1	=	=	PRON
ejpam-5563	101	1	{	{	PUNCT
ejpam-5563	101	2	f	f	NOUN
ejpam-5563	101	3	:	:	PUNCT
ejpam-5563	101	4	f	f	PROPN
ejpam-5563	101	5	⊆	⊆	NUM
ejpam-5563	101	6	b	b	PROPN
ejpam-5563	101	7	is	be	AUX
ejpam-5563	101	8	a	a	DET
ejpam-5563	101	9	closed	closed	ADJ
ejpam-5563	101	10	set	set	NOUN
ejpam-5563	101	11	}	}	PUNCT
ejpam-5563	101	12	.	.	PUNCT
ejpam-5563	102	1	then	then	ADV
ejpam-5563	102	2	,	,	PUNCT
ejpam-5563	102	3	o	o	PROPN
ejpam-5563	102	4	⊆	⊆	NUM
ejpam-5563	102	5	o⋄	o⋄	X
ejpam-5563	102	6	for	for	ADP
ejpam-5563	102	7	all	all	DET
ejpam-5563	102	8	o	o	NOUN
ejpam-5563	102	9	∈	∈	PROPN
ejpam-5563	102	10	γ	γ	X
ejpam-5563	102	11	.	.	PROPN
ejpam-5563	102	12	2	2	NUM
ejpam-5563	102	13	.	.	X
ejpam-5563	102	14	more	more	ADJ
ejpam-5563	102	15	results	result	NOUN
ejpam-5563	102	16	about	about	ADP
ejpam-5563	102	17	γ	γ	NOUN
ejpam-5563	102	18	and	and	CCONJ
ejpam-5563	102	19	γ∗	γ∗	NOUN
ejpam-5563	102	20	in	in	ADP
ejpam-5563	102	21	this	this	DET
ejpam-5563	102	22	section	section	NOUN
ejpam-5563	102	23	,	,	PUNCT
ejpam-5563	102	24	we	we	PRON
ejpam-5563	102	25	present	present	VERB
ejpam-5563	102	26	further	further	ADJ
ejpam-5563	102	27	results	result	NOUN
ejpam-5563	102	28	pertaining	pertain	VERB
ejpam-5563	102	29	to	to	ADP
ejpam-5563	102	30	the	the	DET
ejpam-5563	102	31	operators	operator	NOUN
ejpam-5563	102	32	γ	γ	X
ejpam-5563	102	33	and	and	CCONJ
ejpam-5563	102	34	γ∗.	γ∗.	ADV
ejpam-5563	102	35	theorem	theorem	NOUN
ejpam-5563	102	36	5	5	NUM
ejpam-5563	102	37	.	.	PUNCT
ejpam-5563	103	1	let	let	VERB
ejpam-5563	103	2	(	(	PUNCT
ejpam-5563	103	3	b	b	X
ejpam-5563	103	4	,	,	PUNCT
ejpam-5563	103	5	γ	γ	PROPN
ejpam-5563	103	6	,	,	PUNCT
ejpam-5563	103	7	p	p	NOUN
ejpam-5563	103	8	)	)	PUNCT
ejpam-5563	103	9	be	be	AUX
ejpam-5563	103	10	a	a	DET
ejpam-5563	103	11	ps	ps	NOUN
ejpam-5563	103	12	.	.	PUNCT
ejpam-5563	104	1	then	then	ADV
ejpam-5563	104	2	,	,	PUNCT
ejpam-5563	104	3	intθ(o	intθ(o	ADP
ejpam-5563	104	4	)	)	PUNCT
ejpam-5563	104	5	⊆	⊆	NUM
ejpam-5563	104	6	γ∗(o	γ∗(o	PROPN
ejpam-5563	104	7	)	)	PUNCT
ejpam-5563	104	8	for	for	ADP
ejpam-5563	104	9	any	any	DET
ejpam-5563	104	10	set	set	NOUN
ejpam-5563	104	11	o	o	NOUN
ejpam-5563	104	12	⊆	⊆	NUM
ejpam-5563	104	13	b.	b.	NOUN
ejpam-5563	104	14	proof	proof	NOUN
ejpam-5563	104	15	.	.	PUNCT
ejpam-5563	105	1	let	let	VERB
ejpam-5563	105	2	r	r	PRON
ejpam-5563	105	3	/∈	/∈	PUNCT
ejpam-5563	105	4	γ∗(o	γ∗(o	PROPN
ejpam-5563	105	5	)	)	PUNCT
ejpam-5563	105	6	and	and	CCONJ
ejpam-5563	105	7	let	let	VERB
ejpam-5563	105	8	w	w	NOUN
ejpam-5563	105	9	∈	∈	PROPN
ejpam-5563	105	10	γ(r	γ(r	PROPN
ejpam-5563	105	11	)	)	PUNCT
ejpam-5563	105	12	.	.	PUNCT
ejpam-5563	106	1	then	then	ADV
ejpam-5563	106	2	,	,	PUNCT
ejpam-5563	106	3	r	r	NOUN
ejpam-5563	106	4	∈	∈	PROPN
ejpam-5563	106	5	γ(oc	γ(oc	PROPN
ejpam-5563	106	6	)	)	PUNCT
ejpam-5563	106	7	;	;	PUNCT
ejpam-5563	106	8	hence	hence	ADV
ejpam-5563	106	9	(	(	PUNCT
ejpam-5563	106	10	w	w	PROPN
ejpam-5563	106	11	⋄	⋄	PROPN
ejpam-5563	106	12	∩	∩	NOUN
ejpam-5563	106	13	oc)c	oc)c	PROPN
ejpam-5563	106	14	∈	∈	PROPN
ejpam-5563	106	15	p	p	NOUN
ejpam-5563	106	16	which	which	PRON
ejpam-5563	106	17	implies	imply	VERB
ejpam-5563	106	18	that	that	SCONJ
ejpam-5563	106	19	w	w	PROPN
ejpam-5563	106	20	⋄	⋄	PROPN
ejpam-5563	106	21	∩	∩	NOUN
ejpam-5563	106	22	oc	oc	ADP
ejpam-5563	106	23	̸=	̸=	PROPN
ejpam-5563	106	24	∅.	∅.	NOUN
ejpam-5563	106	25	then	then	ADV
ejpam-5563	106	26	,	,	PUNCT
ejpam-5563	106	27	cl(w	cl(w	NOUN
ejpam-5563	106	28	)	)	PUNCT
ejpam-5563	106	29	∩	∩	NOUN
ejpam-5563	106	30	oc	oc	ADP
ejpam-5563	106	31	̸=	̸=	PROPN
ejpam-5563	106	32	∅.	∅.	PRON
ejpam-5563	106	33	hence	hence	ADV
ejpam-5563	106	34	,	,	PUNCT
ejpam-5563	106	35	cl(w	cl(w	NOUN
ejpam-5563	106	36	)	)	PUNCT
ejpam-5563	106	37	̸⊆	̸⊆	NOUN
ejpam-5563	107	1	o.	o.	NOUN
ejpam-5563	107	2	then	then	ADV
ejpam-5563	107	3	,	,	PUNCT
ejpam-5563	107	4	r	r	NOUN
ejpam-5563	107	5	/∈	/∈	PUNCT
ejpam-5563	107	6	intθ(o	intθ(o	PROPN
ejpam-5563	107	7	)	)	PUNCT
ejpam-5563	107	8	.	.	PUNCT
ejpam-5563	108	1	o.	o.	PROPN
ejpam-5563	108	2	alghamdi	alghamdi	PROPN
ejpam-5563	108	3	/	/	SYM
ejpam-5563	108	4	eur	eur	PROPN
ejpam-5563	108	5	.	.	PUNCT
ejpam-5563	109	1	j.	j.	PROPN
ejpam-5563	109	2	pure	pure	PROPN
ejpam-5563	109	3	appl	appl	PROPN
ejpam-5563	109	4	.	.	PROPN
ejpam-5563	109	5	math	math	PROPN
ejpam-5563	109	6	,	,	PUNCT
ejpam-5563	109	7	17	17	NUM
ejpam-5563	109	8	(	(	PUNCT
ejpam-5563	109	9	4	4	NUM
ejpam-5563	109	10	)	)	PUNCT
ejpam-5563	109	11	(	(	PUNCT
ejpam-5563	109	12	2024	2024	NUM
ejpam-5563	109	13	)	)	PUNCT
ejpam-5563	109	14	,	,	PUNCT
ejpam-5563	109	15	3517	3517	NUM
ejpam-5563	109	16	-	-	SYM
ejpam-5563	109	17	3538	3538	NUM
ejpam-5563	109	18	3520	3520	NUM
ejpam-5563	109	19	theorem	theorem	NOUN
ejpam-5563	109	20	6	6	NUM
ejpam-5563	109	21	.	.	PUNCT
ejpam-5563	110	1	let	let	VERB
ejpam-5563	110	2	(	(	PUNCT
ejpam-5563	110	3	b	b	X
ejpam-5563	110	4	,	,	PUNCT
ejpam-5563	110	5	γ	γ	PROPN
ejpam-5563	110	6	,	,	PUNCT
ejpam-5563	110	7	p	p	NOUN
ejpam-5563	110	8	)	)	PUNCT
ejpam-5563	110	9	be	be	AUX
ejpam-5563	110	10	a	a	DET
ejpam-5563	110	11	ps	ps	NOUN
ejpam-5563	110	12	.	.	PUNCT
ejpam-5563	111	1	if	if	SCONJ
ejpam-5563	111	2	γ−	γ−	PROPN
ejpam-5563	111	3	{	{	PUNCT
ejpam-5563	111	4	b	b	NOUN
ejpam-5563	111	5	}	}	PUNCT
ejpam-5563	111	6	⊆	⊆	NUM
ejpam-5563	111	7	p	p	NOUN
ejpam-5563	111	8	and	and	CCONJ
ejpam-5563	111	9	△	△	NOUN
ejpam-5563	111	10	=	=	SYM
ejpam-5563	111	11	{	{	PUNCT
ejpam-5563	111	12	∅	∅	NOUN
ejpam-5563	111	13	}	}	PUNCT
ejpam-5563	111	14	,	,	PUNCT
ejpam-5563	111	15	then	then	ADV
ejpam-5563	111	16	γ∗(k	γ∗(k	NOUN
ejpam-5563	111	17	)	)	PUNCT
ejpam-5563	111	18	⊆	⊆	NUM
ejpam-5563	111	19	γ(k	γ(k	PROPN
ejpam-5563	111	20	)	)	PUNCT
ejpam-5563	111	21	for	for	ADP
ejpam-5563	111	22	every	every	DET
ejpam-5563	111	23	k	k	PROPN
ejpam-5563	111	24	⊆	⊆	NUM
ejpam-5563	111	25	b.	b.	NOUN
ejpam-5563	111	26	proof	proof	NOUN
ejpam-5563	111	27	.	.	PUNCT
ejpam-5563	112	1	since	since	SCONJ
ejpam-5563	112	2	γ	γ	PROPN
ejpam-5563	112	3	−	−	PROPN
ejpam-5563	112	4	{	{	PUNCT
ejpam-5563	112	5	b	b	NOUN
ejpam-5563	112	6	}	}	PUNCT
ejpam-5563	112	7	⊆	⊆	NUM
ejpam-5563	112	8	p	p	NOUN
ejpam-5563	112	9	and	and	CCONJ
ejpam-5563	112	10	△	△	NOUN
ejpam-5563	112	11	=	=	SYM
ejpam-5563	112	12	{	{	PUNCT
ejpam-5563	112	13	∅	∅	NOUN
ejpam-5563	112	14	}	}	PUNCT
ejpam-5563	112	15	,	,	PUNCT
ejpam-5563	112	16	then	then	ADV
ejpam-5563	112	17	b	b	X
ejpam-5563	112	18	=	=	PUNCT
ejpam-5563	112	19	γ(b	γ(b	X
ejpam-5563	112	20	)	)	PUNCT
ejpam-5563	112	21	by	by	ADP
ejpam-5563	112	22	using	use	VERB
ejpam-5563	112	23	theorem	theorem	NOUN
ejpam-5563	112	24	3	3	X
ejpam-5563	112	25	.	.	PUNCT
ejpam-5563	112	26	let	let	VERB
ejpam-5563	112	27	r	r	NOUN
ejpam-5563	112	28	∈	∈	PROPN
ejpam-5563	112	29	γ∗(k	γ∗(k	PROPN
ejpam-5563	112	30	)	)	PUNCT
ejpam-5563	112	31	.	.	PUNCT
ejpam-5563	113	1	then	then	ADV
ejpam-5563	113	2	,	,	PUNCT
ejpam-5563	113	3	[	[	X
ejpam-5563	113	4	w	w	PROPN
ejpam-5563	113	5	⋄	⋄	NOUN
ejpam-5563	113	6	−	−	PROPN
ejpam-5563	114	1	k]c	k]c	NOUN
ejpam-5563	114	2	/∈	/∈	PUNCT
ejpam-5563	115	1	p	p	NOUN
ejpam-5563	115	2	for	for	ADP
ejpam-5563	115	3	some	some	DET
ejpam-5563	115	4	w	w	PROPN
ejpam-5563	115	5	∈	∈	PROPN
ejpam-5563	115	6	γ(r	γ(r	PROPN
ejpam-5563	115	7	)	)	PUNCT
ejpam-5563	115	8	which	which	PRON
ejpam-5563	115	9	implies	imply	VERB
ejpam-5563	115	10	that	that	SCONJ
ejpam-5563	115	11	(	(	PUNCT
ejpam-5563	115	12	w	w	NOUN
ejpam-5563	115	13	⋄)c	⋄)c	PROPN
ejpam-5563	115	14	∪	∪	PROPN
ejpam-5563	115	15	k	k	PROPN
ejpam-5563	115	16	/∈	/∈	PUNCT
ejpam-5563	116	1	p.	p.	NOUN
ejpam-5563	116	2	thus	thus	ADV
ejpam-5563	116	3	,	,	PUNCT
ejpam-5563	116	4	r	r	NOUN
ejpam-5563	116	5	/∈	/∈	PUNCT
ejpam-5563	116	6	γ(kc	γ(kc	PROPN
ejpam-5563	116	7	)	)	PUNCT
ejpam-5563	116	8	.	.	PUNCT
ejpam-5563	117	1	since	since	SCONJ
ejpam-5563	117	2	r	r	NOUN
ejpam-5563	117	3	∈	∈	PROPN
ejpam-5563	117	4	b	b	NOUN
ejpam-5563	117	5	=	=	PUNCT
ejpam-5563	117	6	γ(b	γ(b	X
ejpam-5563	117	7	)	)	PUNCT
ejpam-5563	117	8	=	=	PUNCT
ejpam-5563	117	9	γ(k	γ(k	VERB
ejpam-5563	117	10	∪	∪	ADJ
ejpam-5563	117	11	kc	kc	PROPN
ejpam-5563	117	12	)	)	PUNCT
ejpam-5563	117	13	=	=	SYM
ejpam-5563	117	14	γ(k	γ(k	PROPN
ejpam-5563	117	15	)	)	PUNCT
ejpam-5563	117	16	∪	∪	X
ejpam-5563	117	17	γ(kc	γ(kc	PROPN
ejpam-5563	117	18	)	)	PUNCT
ejpam-5563	117	19	,	,	PUNCT
ejpam-5563	117	20	then	then	ADV
ejpam-5563	117	21	r	r	PROPN
ejpam-5563	117	22	∈	∈	PROPN
ejpam-5563	117	23	γ(k	γ(k	PROPN
ejpam-5563	117	24	)	)	PUNCT
ejpam-5563	117	25	.	.	PUNCT
ejpam-5563	118	1	theorem	theorem	VERB
ejpam-5563	118	2	7	7	NUM
ejpam-5563	118	3	.	.	PUNCT
ejpam-5563	119	1	let	let	VERB
ejpam-5563	119	2	(	(	PUNCT
ejpam-5563	119	3	b	b	X
ejpam-5563	119	4	,	,	PUNCT
ejpam-5563	119	5	γ	γ	PROPN
ejpam-5563	119	6	,	,	PUNCT
ejpam-5563	119	7	p	p	NOUN
ejpam-5563	119	8	)	)	PUNCT
ejpam-5563	119	9	be	be	AUX
ejpam-5563	119	10	a	a	DET
ejpam-5563	119	11	ps	ps	NOUN
ejpam-5563	119	12	.	.	PUNCT
ejpam-5563	120	1	then	then	ADV
ejpam-5563	120	2	,	,	PUNCT
ejpam-5563	120	3	(	(	PUNCT
ejpam-5563	120	4	i	i	NOUN
ejpam-5563	120	5	)	)	PUNCT
ejpam-5563	120	6	if	if	SCONJ
ejpam-5563	120	7	γ−	γ−	PROPN
ejpam-5563	120	8	{	{	PUNCT
ejpam-5563	120	9	b	b	NOUN
ejpam-5563	120	10	}	}	PUNCT
ejpam-5563	120	11	⊆	⊆	NUM
ejpam-5563	120	12	p	p	NOUN
ejpam-5563	120	13	and	and	CCONJ
ejpam-5563	120	14	△	△	NOUN
ejpam-5563	120	15	=	=	SYM
ejpam-5563	120	16	{	{	PUNCT
ejpam-5563	120	17	∅	∅	NOUN
ejpam-5563	120	18	}	}	PUNCT
ejpam-5563	120	19	,	,	PUNCT
ejpam-5563	120	20	then	then	ADV
ejpam-5563	120	21	γ∗(b	γ∗(b	NUM
ejpam-5563	120	22	)	)	PUNCT
ejpam-5563	120	23	=	=	PUNCT
ejpam-5563	120	24	γ(b	γ(b	NOUN
ejpam-5563	120	25	)	)	PUNCT
ejpam-5563	120	26	.	.	PUNCT
ejpam-5563	121	1	(	(	PUNCT
ejpam-5563	121	2	ii	ii	NOUN
ejpam-5563	121	3	)	)	PUNCT
ejpam-5563	121	4	if	if	SCONJ
ejpam-5563	121	5	γ∗(k	γ∗(k	NOUN
ejpam-5563	121	6	)	)	PUNCT
ejpam-5563	121	7	=	=	PUNCT
ejpam-5563	121	8	γ(k	γ(k	PROPN
ejpam-5563	121	9	)	)	PUNCT
ejpam-5563	121	10	for	for	ADP
ejpam-5563	121	11	any	any	DET
ejpam-5563	121	12	k	k	PROPN
ejpam-5563	121	13	⊆	⊆	NUM
ejpam-5563	121	14	b	b	NOUN
ejpam-5563	121	15	,	,	PUNCT
ejpam-5563	121	16	then	then	ADV
ejpam-5563	121	17	γ−	γ−	PROPN
ejpam-5563	121	18	{	{	PUNCT
ejpam-5563	121	19	b	b	NOUN
ejpam-5563	121	20	}	}	PUNCT
ejpam-5563	121	21	⊆	⊆	NUM
ejpam-5563	121	22	p	p	NOUN
ejpam-5563	121	23	and	and	CCONJ
ejpam-5563	121	24	△	△	NOUN
ejpam-5563	121	25	=	=	SYM
ejpam-5563	121	26	{	{	PUNCT
ejpam-5563	121	27	∅	∅	NOUN
ejpam-5563	121	28	}	}	PUNCT
ejpam-5563	121	29	.	.	PUNCT
ejpam-5563	122	1	proof	proof	NOUN
ejpam-5563	122	2	.	.	PUNCT
ejpam-5563	123	1	(	(	PUNCT
ejpam-5563	123	2	i	i	NOUN
ejpam-5563	123	3	)	)	PUNCT
ejpam-5563	123	4	γ∗(b	γ∗(b	PUNCT
ejpam-5563	123	5	)	)	PUNCT
ejpam-5563	123	6	=	=	PUNCT
ejpam-5563	124	1	[	[	X
ejpam-5563	124	2	γ(∅)]c	γ(∅)]c	NOUN
ejpam-5563	124	3	=	=	SYM
ejpam-5563	124	4	b	b	NOUN
ejpam-5563	124	5	=	=	PUNCT
ejpam-5563	124	6	γ(b	γ(b	X
ejpam-5563	124	7	)	)	PUNCT
ejpam-5563	124	8	by	by	ADP
ejpam-5563	124	9	theorem	theorem	NOUN
ejpam-5563	124	10	3	3	NUM
ejpam-5563	124	11	.	.	PUNCT
ejpam-5563	124	12	(	(	PUNCT
ejpam-5563	124	13	ii	ii	NOUN
ejpam-5563	124	14	)	)	PUNCT
ejpam-5563	124	15	we	we	PRON
ejpam-5563	124	16	know	know	VERB
ejpam-5563	124	17	that	that	SCONJ
ejpam-5563	124	18	γ∗(k	γ∗(k	NOUN
ejpam-5563	124	19	)	)	PUNCT
ejpam-5563	124	20	=	=	PUNCT
ejpam-5563	125	1	[	[	X
ejpam-5563	125	2	γ(kc)]c	γ(kc)]c	PROPN
ejpam-5563	125	3	.	.	PUNCT
ejpam-5563	125	4	then	then	ADV
ejpam-5563	125	5	,	,	PUNCT
ejpam-5563	125	6	γ(b	γ(b	X
ejpam-5563	125	7	)	)	PUNCT
ejpam-5563	125	8	=	=	SYM
ejpam-5563	125	9	γ(kc	γ(kc	PROPN
ejpam-5563	125	10	∪	∪	X
ejpam-5563	125	11	k	k	PROPN
ejpam-5563	125	12	)	)	PUNCT
ejpam-5563	125	13	=	=	SYM
ejpam-5563	125	14	γ(kc	γ(kc	PROPN
ejpam-5563	125	15	)	)	PUNCT
ejpam-5563	125	16	∪	∪	ADP
ejpam-5563	125	17	γ(k	γ(k	PROPN
ejpam-5563	125	18	)	)	PUNCT
ejpam-5563	125	19	=	=	PUNCT
ejpam-5563	126	1	γ(kc)∪	γ(kc)∪	ADJ
ejpam-5563	126	2	[	[	X
ejpam-5563	126	3	γ(kc)]c	γ(kc)]c	PROPN
ejpam-5563	126	4	=	=	SYM
ejpam-5563	126	5	b.	b.	PROPN
ejpam-5563	126	6	by	by	ADP
ejpam-5563	126	7	using	use	VERB
ejpam-5563	126	8	the	the	DET
ejpam-5563	126	9	result	result	NOUN
ejpam-5563	126	10	from	from	ADP
ejpam-5563	126	11	theorem	theorem	ADJ
ejpam-5563	126	12	3	3	NUM
ejpam-5563	126	13	,	,	PUNCT
ejpam-5563	126	14	we	we	PRON
ejpam-5563	126	15	get	get	VERB
ejpam-5563	126	16	that	that	PRON
ejpam-5563	126	17	γ−{b	γ−{b	PROPN
ejpam-5563	126	18	}	}	PUNCT
ejpam-5563	126	19	⊆	⊆	NUM
ejpam-5563	126	20	p	p	NOUN
ejpam-5563	126	21	and	and	CCONJ
ejpam-5563	126	22	△	△	NOUN
ejpam-5563	126	23	=	=	SYM
ejpam-5563	126	24	{	{	PUNCT
ejpam-5563	126	25	∅	∅	NOUN
ejpam-5563	126	26	}	}	PUNCT
ejpam-5563	126	27	.	.	PUNCT
ejpam-5563	127	1	theorem	theorem	ADJ
ejpam-5563	127	2	8	8	NUM
ejpam-5563	127	3	.	.	PUNCT
ejpam-5563	128	1	let	let	VERB
ejpam-5563	128	2	(	(	PUNCT
ejpam-5563	128	3	b	b	X
ejpam-5563	128	4	,	,	PUNCT
ejpam-5563	128	5	γ	γ	PROPN
ejpam-5563	128	6	,	,	PUNCT
ejpam-5563	128	7	p	p	NOUN
ejpam-5563	128	8	)	)	PUNCT
ejpam-5563	128	9	be	be	AUX
ejpam-5563	128	10	a	a	DET
ejpam-5563	128	11	ps	ps	NOUN
ejpam-5563	128	12	.	.	PUNCT
ejpam-5563	129	1	if	if	SCONJ
ejpam-5563	129	2	there	there	PRON
ejpam-5563	129	3	exists	exist	VERB
ejpam-5563	129	4	a	a	DET
ejpam-5563	129	5	set	set	NOUN
ejpam-5563	129	6	k	k	PROPN
ejpam-5563	129	7	⊆	⊆	NUM
ejpam-5563	129	8	b	b	NUM
ejpam-5563	129	9	such	such	ADJ
ejpam-5563	129	10	that	that	DET
ejpam-5563	129	11	γ∗(k	γ∗(k	NOUN
ejpam-5563	129	12	)	)	PUNCT
ejpam-5563	129	13	̸=	̸=	PROPN
ejpam-5563	129	14	γ(k	γ(k	PROPN
ejpam-5563	129	15	)	)	PUNCT
ejpam-5563	129	16	.	.	PUNCT
ejpam-5563	130	1	then	then	ADV
ejpam-5563	130	2	,	,	PUNCT
ejpam-5563	130	3	one	one	NUM
ejpam-5563	130	4	of	of	ADP
ejpam-5563	130	5	the	the	DET
ejpam-5563	130	6	following	follow	VERB
ejpam-5563	130	7	holds	hold	VERB
ejpam-5563	130	8	:	:	PUNCT
ejpam-5563	130	9	(	(	PUNCT
ejpam-5563	130	10	i	i	NOUN
ejpam-5563	130	11	)	)	PUNCT
ejpam-5563	130	12	there	there	PRON
ejpam-5563	130	13	exists	exist	VERB
ejpam-5563	130	14	r	r	NOUN
ejpam-5563	130	15	∈	∈	PROPN
ejpam-5563	130	16	b	b	PROPN
ejpam-5563	130	17	and	and	CCONJ
ejpam-5563	130	18	g	g	PROPN
ejpam-5563	130	19	∈	∈	PROPN
ejpam-5563	130	20	γ(r	γ(r	PROPN
ejpam-5563	130	21	)	)	PUNCT
ejpam-5563	130	22	such	such	ADJ
ejpam-5563	130	23	that	that	DET
ejpam-5563	130	24	b	b	NOUN
ejpam-5563	130	25	−g⋄	−g⋄	PUNCT
ejpam-5563	130	26	=	=	NOUN
ejpam-5563	130	27	(	(	PUNCT
ejpam-5563	130	28	g⋄)c	g⋄)c	VERB
ejpam-5563	130	29	∈	∈	PROPN
ejpam-5563	130	30	γ−	γ−	PROPN
ejpam-5563	130	31	{	{	PUNCT
ejpam-5563	130	32	p	p	X
ejpam-5563	130	33	}	}	PUNCT
ejpam-5563	130	34	.	.	PUNCT
ejpam-5563	131	1	(	(	PUNCT
ejpam-5563	131	2	ii	ii	NOUN
ejpam-5563	131	3	)	)	PUNCT
ejpam-5563	131	4	there	there	PRON
ejpam-5563	131	5	exists	exist	VERB
ejpam-5563	131	6	r	r	NOUN
ejpam-5563	131	7	∈	∈	PROPN
ejpam-5563	131	8	b	b	PROPN
ejpam-5563	131	9	and	and	CCONJ
ejpam-5563	131	10	g	g	PROPN
ejpam-5563	131	11	∈	∈	PROPN
ejpam-5563	131	12	γ(r	γ(r	PROPN
ejpam-5563	131	13	)	)	PUNCT
ejpam-5563	131	14	such	such	ADJ
ejpam-5563	131	15	that	that	SCONJ
ejpam-5563	131	16	int(gc	int(gc	NOUN
ejpam-5563	131	17	)	)	PUNCT
ejpam-5563	131	18	∈	∈	PROPN
ejpam-5563	131	19	p	p	NOUN
ejpam-5563	131	20	for	for	ADP
ejpam-5563	131	21	every	every	DET
ejpam-5563	131	22	g	g	PROPN
ejpam-5563	131	23	∈	∈	PROPN
ejpam-5563	131	24	γ(r	γ(r	PROPN
ejpam-5563	131	25	)	)	PUNCT
ejpam-5563	131	26	.	.	PUNCT
ejpam-5563	132	1	proof	proof	NOUN
ejpam-5563	132	2	.	.	PUNCT
ejpam-5563	133	1	we	we	PRON
ejpam-5563	133	2	know	know	VERB
ejpam-5563	133	3	that	that	SCONJ
ejpam-5563	133	4	γ∗(k	γ∗(k	NOUN
ejpam-5563	133	5	)	)	PUNCT
ejpam-5563	133	6	=	=	PUNCT
ejpam-5563	134	1	[	[	X
ejpam-5563	134	2	γ(kc)]c	γ(kc)]c	PROPN
ejpam-5563	134	3	.	.	PROPN
ejpam-5563	135	1	if	if	SCONJ
ejpam-5563	135	2	γ∗(k	γ∗(k	NOUN
ejpam-5563	135	3	)	)	PUNCT
ejpam-5563	135	4	̸=	̸=	PROPN
ejpam-5563	135	5	γ(k	γ(k	PROPN
ejpam-5563	135	6	)	)	PUNCT
ejpam-5563	135	7	,	,	PUNCT
ejpam-5563	135	8	we	we	PRON
ejpam-5563	135	9	have	have	VERB
ejpam-5563	135	10	two	two	NUM
ejpam-5563	135	11	cases	case	NOUN
ejpam-5563	135	12	:	:	PUNCT
ejpam-5563	135	13	(	(	PUNCT
ejpam-5563	135	14	i	i	NOUN
ejpam-5563	135	15	)	)	PUNCT
ejpam-5563	135	16	∃	∃	PROPN
ejpam-5563	135	17	r	r	PROPN
ejpam-5563	135	18	∈	∈	PROPN
ejpam-5563	135	19	γ∗(k	γ∗(k	NOUN
ejpam-5563	135	20	)	)	PUNCT
ejpam-5563	135	21	−	−	PROPN
ejpam-5563	135	22	γ(k	γ(k	PROPN
ejpam-5563	135	23	)	)	PUNCT
ejpam-5563	135	24	which	which	PRON
ejpam-5563	135	25	implies	imply	VERB
ejpam-5563	135	26	that	that	SCONJ
ejpam-5563	135	27	r	r	NOUN
ejpam-5563	135	28	/∈	/∈	PUNCT
ejpam-5563	135	29	γ(kc	γ(kc	NOUN
ejpam-5563	135	30	)	)	PUNCT
ejpam-5563	135	31	∪	∪	ADP
ejpam-5563	135	32	γ(k	γ(k	PROPN
ejpam-5563	135	33	)	)	PUNCT
ejpam-5563	135	34	.	.	PUNCT
ejpam-5563	136	1	hence	hence	ADV
ejpam-5563	136	2	,	,	PUNCT
ejpam-5563	136	3	there	there	PRON
ejpam-5563	136	4	exist	exist	VERB
ejpam-5563	136	5	l	l	NOUN
ejpam-5563	136	6	,	,	PUNCT
ejpam-5563	136	7	o	o	PROPN
ejpam-5563	136	8	∈	∈	PROPN
ejpam-5563	136	9	γ(r	γ(r	PROPN
ejpam-5563	136	10	)	)	PUNCT
ejpam-5563	136	11	such	such	ADJ
ejpam-5563	136	12	that	that	SCONJ
ejpam-5563	136	13	[	[	X
ejpam-5563	136	14	l⋄	l⋄	X
ejpam-5563	136	15	∩	∩	ADJ
ejpam-5563	136	16	k]c	k]c	NOUN
ejpam-5563	136	17	/∈	/∈	PUNCT
ejpam-5563	136	18	p	p	NOUN
ejpam-5563	136	19	and	and	CCONJ
ejpam-5563	136	20	[	[	X
ejpam-5563	136	21	o⋄	o⋄	X
ejpam-5563	136	22	∩	∩	ADJ
ejpam-5563	136	23	kc]c	kc]c	NOUN
ejpam-5563	136	24	/∈	/∈	PUNCT
ejpam-5563	136	25	p.	p.	NOUN
ejpam-5563	136	26	let	let	VERB
ejpam-5563	136	27	g	g	NOUN
ejpam-5563	136	28	=	=	SYM
ejpam-5563	136	29	l	l	NOUN
ejpam-5563	136	30	∩	∩	X
ejpam-5563	136	31	o.	o.	NOUN
ejpam-5563	136	32	then	then	ADV
ejpam-5563	136	33	,	,	PUNCT
ejpam-5563	136	34	as	as	ADP
ejpam-5563	136	35	[	[	X
ejpam-5563	136	36	l⋄	l⋄	X
ejpam-5563	136	37	∩	∩	NOUN
ejpam-5563	136	38	k]c	k]c	NOUN
ejpam-5563	136	39	⊆	⊆	NUM
ejpam-5563	136	40	[	[	X
ejpam-5563	136	41	g⋄	g⋄	X
ejpam-5563	136	42	∩	∩	ADJ
ejpam-5563	136	43	k]c	k]c	NOUN
ejpam-5563	136	44	and	and	CCONJ
ejpam-5563	136	45	[	[	X
ejpam-5563	136	46	o⋄	o⋄	X
ejpam-5563	136	47	∩	∩	ADJ
ejpam-5563	136	48	kc]c	kc]c	NOUN
ejpam-5563	136	49	⊆	⊆	NUM
ejpam-5563	136	50	[	[	X
ejpam-5563	136	51	g⋄	g⋄	X
ejpam-5563	136	52	∩	∩	ADJ
ejpam-5563	136	53	kc]c	kc]c	PROPN
ejpam-5563	136	54	,	,	PUNCT
ejpam-5563	136	55	we	we	PRON
ejpam-5563	136	56	have	have	VERB
ejpam-5563	136	57	[	[	X
ejpam-5563	136	58	g⋄	g⋄	ADJ
ejpam-5563	136	59	∩	∩	NOUN
ejpam-5563	136	60	k]c	k]c	NOUN
ejpam-5563	136	61	/∈	/∈	PUNCT
ejpam-5563	137	1	p	p	NOUN
ejpam-5563	137	2	and	and	CCONJ
ejpam-5563	137	3	[	[	X
ejpam-5563	137	4	g⋄	g⋄	ADJ
ejpam-5563	137	5	∩	∩	ADJ
ejpam-5563	137	6	kc]c	kc]c	NOUN
ejpam-5563	137	7	/∈	/∈	PUNCT
ejpam-5563	138	1	p.	p.	NOUN
ejpam-5563	138	2	hence	hence	ADV
ejpam-5563	138	3	,	,	PUNCT
ejpam-5563	138	4	(	(	PUNCT
ejpam-5563	138	5	g⋄)c	g⋄)c	X
ejpam-5563	138	6	=	=	PUNCT
ejpam-5563	139	1	[	[	X
ejpam-5563	139	2	g⋄	g⋄	X
ejpam-5563	139	3	∩	∩	NOUN
ejpam-5563	139	4	b]c	b]c	ADP
ejpam-5563	139	5	=[	=[	NOUN
ejpam-5563	139	6	g⋄	g⋄	NOUN
ejpam-5563	139	7	∩	∩	NOUN
ejpam-5563	139	8	(	(	PUNCT
ejpam-5563	139	9	k	k	X
ejpam-5563	139	10	∪	∪	ADJ
ejpam-5563	139	11	kc)]c	kc)]c	NOUN
ejpam-5563	139	12	=[	=[	NOUN
ejpam-5563	139	13	(	(	PUNCT
ejpam-5563	139	14	g⋄	g⋄	X
ejpam-5563	139	15	∩	∩	ADJ
ejpam-5563	139	16	k	k	NOUN
ejpam-5563	139	17	)	)	PUNCT
ejpam-5563	139	18	∪	∪	X
ejpam-5563	139	19	(	(	PUNCT
ejpam-5563	139	20	g⋄	g⋄	X
ejpam-5563	139	21	∩	∩	ADJ
ejpam-5563	139	22	kc)]c	kc)]c	NOUN
ejpam-5563	139	23	=(	=(	X
ejpam-5563	139	24	g⋄	g⋄	X
ejpam-5563	139	25	∩	∩	NOUN
ejpam-5563	139	26	k)c	k)c	NOUN
ejpam-5563	139	27	∩	∩	NOUN
ejpam-5563	139	28	(	(	PUNCT
ejpam-5563	139	29	g⋄	g⋄	X
ejpam-5563	139	30	∩	∩	NOUN
ejpam-5563	139	31	kc)c	kc)c	NOUN
ejpam-5563	139	32	/∈	/∈	PUNCT
ejpam-5563	140	1	p.	p.	NOUN
ejpam-5563	140	2	since	since	SCONJ
ejpam-5563	140	3	g⋄	g⋄	X
ejpam-5563	140	4	is	be	AUX
ejpam-5563	140	5	a	a	DET
ejpam-5563	140	6	closed	closed	ADJ
ejpam-5563	140	7	set	set	NOUN
ejpam-5563	140	8	,	,	PUNCT
ejpam-5563	140	9	then	then	ADV
ejpam-5563	140	10	(	(	PUNCT
ejpam-5563	140	11	g⋄)c	g⋄)c	PROPN
ejpam-5563	140	12	∈	∈	PROPN
ejpam-5563	140	13	γ	γ	X
ejpam-5563	140	14	.	.	PROPN
ejpam-5563	140	15	(	(	PUNCT
ejpam-5563	140	16	ii	ii	NOUN
ejpam-5563	140	17	)	)	PUNCT
ejpam-5563	140	18	∃	∃	PROPN
ejpam-5563	140	19	r	r	PROPN
ejpam-5563	140	20	∈	∈	PROPN
ejpam-5563	140	21	γ(k	γ(k	PROPN
ejpam-5563	140	22	)	)	PUNCT
ejpam-5563	140	23	−	−	PROPN
ejpam-5563	140	24	γ∗(k	γ∗(k	NOUN
ejpam-5563	140	25	)	)	PUNCT
ejpam-5563	140	26	which	which	PRON
ejpam-5563	140	27	implies	imply	VERB
ejpam-5563	140	28	that	that	SCONJ
ejpam-5563	140	29	r	r	PROPN
ejpam-5563	140	30	∈	∈	PROPN
ejpam-5563	140	31	γ(k	γ(k	PROPN
ejpam-5563	140	32	)	)	PUNCT
ejpam-5563	140	33	and	and	CCONJ
ejpam-5563	140	34	r	r	NOUN
ejpam-5563	140	35	∈	∈	PROPN
ejpam-5563	140	36	γ(kc	γ(kc	PROPN
ejpam-5563	140	37	)	)	PUNCT
ejpam-5563	140	38	.	.	PUNCT
ejpam-5563	141	1	let	let	VERB
ejpam-5563	141	2	g	g	PROPN
ejpam-5563	141	3	∈	∈	PROPN
ejpam-5563	141	4	γ(r	γ(r	PROPN
ejpam-5563	141	5	)	)	PUNCT
ejpam-5563	141	6	.	.	PUNCT
ejpam-5563	142	1	then	then	ADV
ejpam-5563	142	2	,	,	PUNCT
ejpam-5563	142	3	(	(	PUNCT
ejpam-5563	142	4	g⋄)c	g⋄)c	NOUN
ejpam-5563	142	5	∪	∪	VERB
ejpam-5563	142	6	kc	kc	PROPN
ejpam-5563	142	7	∈	∈	PROPN
ejpam-5563	142	8	p	p	X
ejpam-5563	142	9	;	;	PUNCT
ejpam-5563	142	10	hence	hence	ADV
ejpam-5563	142	11	(	(	PUNCT
ejpam-5563	142	12	cl(g))c	cl(g))c	PROPN
ejpam-5563	142	13	⊆	⊆	NUM
ejpam-5563	142	14	(	(	PUNCT
ejpam-5563	142	15	g⋄)c	g⋄)c	X
ejpam-5563	142	16	∪	∪	ADP
ejpam-5563	142	17	kc	kc	PROPN
ejpam-5563	142	18	=	=	PUNCT
ejpam-5563	142	19	⇒	⇒	NOUN
ejpam-5563	142	20	(	(	PUNCT
ejpam-5563	142	21	cl(g))c	cl(g))c	X
ejpam-5563	142	22	=	=	SYM
ejpam-5563	142	23	int(gc	int(gc	NOUN
ejpam-5563	142	24	)	)	PUNCT
ejpam-5563	142	25	∈	∈	PROPN
ejpam-5563	142	26	p.	p.	NOUN
ejpam-5563	142	27	theorem	theorem	VERB
ejpam-5563	142	28	9	9	NUM
ejpam-5563	142	29	.	.	PUNCT
ejpam-5563	143	1	let	let	VERB
ejpam-5563	143	2	(	(	PUNCT
ejpam-5563	143	3	b	b	X
ejpam-5563	143	4	,	,	PUNCT
ejpam-5563	143	5	γ	γ	PROPN
ejpam-5563	143	6	,	,	PUNCT
ejpam-5563	143	7	p	p	NOUN
ejpam-5563	143	8	)	)	PUNCT
ejpam-5563	143	9	be	be	AUX
ejpam-5563	143	10	a	a	DET
ejpam-5563	143	11	ps	ps	NOUN
ejpam-5563	143	12	and	and	CCONJ
ejpam-5563	143	13	k	k	NOUN
ejpam-5563	143	14	,	,	PUNCT
ejpam-5563	143	15	o	o	PROPN
ejpam-5563	143	16	⊆	⊆	NUM
ejpam-5563	143	17	b.	b.	NOUN
ejpam-5563	143	18	then	then	ADV
ejpam-5563	143	19	,	,	PUNCT
ejpam-5563	143	20	intθ(k	intθ(k	ADJ
ejpam-5563	143	21	)	)	PUNCT
ejpam-5563	143	22	∩	∩	NOUN
ejpam-5563	143	23	γ(o	γ(o	PROPN
ejpam-5563	143	24	)	)	PUNCT
ejpam-5563	143	25	⊆	⊆	NUM
ejpam-5563	143	26	γ(k	γ(k	PROPN
ejpam-5563	143	27	∩o	∩o	NOUN
ejpam-5563	143	28	)	)	PUNCT
ejpam-5563	143	29	.	.	PUNCT
ejpam-5563	144	1	o.	o.	PROPN
ejpam-5563	144	2	alghamdi	alghamdi	PROPN
ejpam-5563	144	3	/	/	SYM
ejpam-5563	144	4	eur	eur	PROPN
ejpam-5563	144	5	.	.	PUNCT
ejpam-5563	145	1	j.	j.	PROPN
ejpam-5563	145	2	pure	pure	PROPN
ejpam-5563	145	3	appl	appl	PROPN
ejpam-5563	145	4	.	.	PROPN
ejpam-5563	145	5	math	math	PROPN
ejpam-5563	145	6	,	,	PUNCT
ejpam-5563	145	7	17	17	NUM
ejpam-5563	145	8	(	(	PUNCT
ejpam-5563	145	9	4	4	NUM
ejpam-5563	145	10	)	)	PUNCT
ejpam-5563	145	11	(	(	PUNCT
ejpam-5563	145	12	2024	2024	NUM
ejpam-5563	145	13	)	)	PUNCT
ejpam-5563	145	14	,	,	PUNCT
ejpam-5563	145	15	3517	3517	NUM
ejpam-5563	145	16	-	-	SYM
ejpam-5563	145	17	3538	3538	NUM
ejpam-5563	145	18	3521	3521	NUM
ejpam-5563	145	19	proof	proof	NOUN
ejpam-5563	145	20	.	.	PUNCT
ejpam-5563	146	1	let	let	VERB
ejpam-5563	146	2	r	r	NOUN
ejpam-5563	146	3	∈	∈	PROPN
ejpam-5563	146	4	intθ(k	intθ(k	ADJ
ejpam-5563	146	5	)	)	PUNCT
ejpam-5563	146	6	∩	∩	NOUN
ejpam-5563	146	7	γ(o	γ(o	PROPN
ejpam-5563	146	8	)	)	PUNCT
ejpam-5563	146	9	.	.	PUNCT
ejpam-5563	147	1	then	then	ADV
ejpam-5563	147	2	,	,	PUNCT
ejpam-5563	147	3	there	there	PRON
ejpam-5563	147	4	exists	exist	VERB
ejpam-5563	147	5	h	h	NOUN
ejpam-5563	147	6	∈	∈	PROPN
ejpam-5563	147	7	γ(r	γ(r	PROPN
ejpam-5563	147	8	)	)	PUNCT
ejpam-5563	147	9	such	such	ADJ
ejpam-5563	147	10	that	that	SCONJ
ejpam-5563	147	11	r	r	NOUN
ejpam-5563	147	12	∈	∈	PROPN
ejpam-5563	147	13	h	h	NOUN
ejpam-5563	147	14	⊆	⊆	NUM
ejpam-5563	147	15	cl(h	cl(h	NUM
ejpam-5563	147	16	)	)	PUNCT
ejpam-5563	147	17	⊆	⊆	NUM
ejpam-5563	147	18	k.	k.	NOUN
ejpam-5563	147	19	since	since	SCONJ
ejpam-5563	147	20	r	r	PROPN
ejpam-5563	147	21	∈	∈	PROPN
ejpam-5563	147	22	γ(o	γ(o	PROPN
ejpam-5563	147	23	)	)	PUNCT
ejpam-5563	147	24	,	,	PUNCT
ejpam-5563	147	25	then	then	ADV
ejpam-5563	147	26	for	for	ADP
ejpam-5563	147	27	any	any	DET
ejpam-5563	147	28	d	d	PROPN
ejpam-5563	147	29	∈	∈	PROPN
ejpam-5563	147	30	γ(r	γ(r	PROPN
ejpam-5563	147	31	)	)	PUNCT
ejpam-5563	147	32	,	,	PUNCT
ejpam-5563	147	33	we	we	PRON
ejpam-5563	147	34	have	have	AUX
ejpam-5563	147	35	(	(	PUNCT
ejpam-5563	147	36	d⋄)c	d⋄)c	VERB
ejpam-5563	147	37	∪	∪	ADJ
ejpam-5563	147	38	oc	oc	ADP
ejpam-5563	147	39	∈	∈	PROPN
ejpam-5563	147	40	p.	p.	NOUN
ejpam-5563	148	1	[	[	X
ejpam-5563	148	2	d⋄	d⋄	X
ejpam-5563	148	3	∩	∩	NOUN
ejpam-5563	148	4	(	(	PUNCT
ejpam-5563	148	5	k	k	X
ejpam-5563	148	6	∩o)]c	∩o)]c	X
ejpam-5563	148	7	⊆[d⋄	⊆[d⋄	NOUN
ejpam-5563	148	8	∩	∩	X
ejpam-5563	148	9	(	(	PUNCT
ejpam-5563	148	10	cl(h	cl(h	NUM
ejpam-5563	148	11	)	)	PUNCT
ejpam-5563	148	12	∩	∩	ADJ
ejpam-5563	148	13	o)]c	o)]c	NOUN
ejpam-5563	148	14	⊆[(d⋄	⊆[(d⋄	NOUN
ejpam-5563	148	15	∩h⋄	∩h⋄	NOUN
ejpam-5563	148	16	)	)	PUNCT
ejpam-5563	148	17	∩	∩	NOUN
ejpam-5563	148	18	o]c	o]c	NOUN
ejpam-5563	148	19	using	use	VERB
ejpam-5563	148	20	the	the	DET
ejpam-5563	148	21	relation	relation	NOUN
ejpam-5563	148	22	h⋄	h⋄	NOUN
ejpam-5563	148	23	⊆	⊆	NUM
ejpam-5563	148	24	cl(h	cl(h	NUM
ejpam-5563	148	25	)	)	PUNCT
ejpam-5563	148	26	.	.	PUNCT
ejpam-5563	149	1	⊆[(d	⊆[(d	NOUN
ejpam-5563	149	2	∩h)⋄	∩h)⋄	SYM
ejpam-5563	149	3	∩	∩	NOUN
ejpam-5563	149	4	o]c	o]c	NOUN
ejpam-5563	149	5	since	since	SCONJ
ejpam-5563	149	6	(	(	PUNCT
ejpam-5563	149	7	d	d	X
ejpam-5563	149	8	∩h)⋄	∩h)⋄	PUNCT
ejpam-5563	149	9	⊆	⊆	NUM
ejpam-5563	149	10	d⋄	d⋄	NOUN
ejpam-5563	149	11	∩h⋄	∩h⋄	VERB
ejpam-5563	149	12	by	by	ADP
ejpam-5563	149	13	[	[	X
ejpam-5563	149	14	1	1	NUM
ejpam-5563	149	15	]	]	PUNCT
ejpam-5563	149	16	.	.	PUNCT
ejpam-5563	150	1	=[	=[	NOUN
ejpam-5563	150	2	(	(	PUNCT
ejpam-5563	150	3	d	d	PROPN
ejpam-5563	150	4	∩h)⋄	∩h)⋄	PUNCT
ejpam-5563	150	5	∩	∩	ADJ
ejpam-5563	150	6	o]c	o]c	PROPN
ejpam-5563	150	7	∈	∈	PROPN
ejpam-5563	150	8	p	p	NOUN
ejpam-5563	150	9	since	since	SCONJ
ejpam-5563	150	10	r	r	PROPN
ejpam-5563	150	11	∈	∈	PROPN
ejpam-5563	150	12	γ(o	γ(o	PROPN
ejpam-5563	150	13	)	)	PUNCT
ejpam-5563	150	14	.	.	PUNCT
ejpam-5563	151	1	hence	hence	ADV
ejpam-5563	151	2	,	,	PUNCT
ejpam-5563	151	3	r	r	PROPN
ejpam-5563	151	4	∈	∈	PROPN
ejpam-5563	151	5	γ(k	γ(k	PROPN
ejpam-5563	151	6	∩o	∩o	NOUN
ejpam-5563	151	7	)	)	PUNCT
ejpam-5563	151	8	.	.	PUNCT
ejpam-5563	152	1	theorem	theorem	ADJ
ejpam-5563	152	2	10	10	NUM
ejpam-5563	152	3	.	.	PUNCT
ejpam-5563	153	1	let	let	VERB
ejpam-5563	153	2	(	(	PUNCT
ejpam-5563	153	3	b	b	X
ejpam-5563	153	4	,	,	PUNCT
ejpam-5563	153	5	γ	γ	PROPN
ejpam-5563	153	6	,	,	PUNCT
ejpam-5563	153	7	p	p	NOUN
ejpam-5563	153	8	)	)	PUNCT
ejpam-5563	153	9	be	be	AUX
ejpam-5563	153	10	a	a	DET
ejpam-5563	153	11	ps	ps	NOUN
ejpam-5563	153	12	and	and	CCONJ
ejpam-5563	153	13	k	k	NOUN
ejpam-5563	153	14	,	,	PUNCT
ejpam-5563	153	15	o	o	PROPN
ejpam-5563	153	16	⊆	⊆	NUM
ejpam-5563	153	17	b.	b.	NOUN
ejpam-5563	153	18	then	then	ADV
ejpam-5563	153	19	,	,	PUNCT
ejpam-5563	153	20	intθ(k	intθ(k	ADJ
ejpam-5563	153	21	)	)	PUNCT
ejpam-5563	153	22	∩	∩	NOUN
ejpam-5563	153	23	int(γ(o	int(γ(o	VERB
ejpam-5563	153	24	)	)	PUNCT
ejpam-5563	153	25	)	)	PUNCT
ejpam-5563	154	1	⊆	⊆	NUM
ejpam-5563	154	2	int(γ(k	int(γ(k	NOUN
ejpam-5563	154	3	∩o	∩o	PROPN
ejpam-5563	154	4	)	)	PUNCT
ejpam-5563	154	5	)	)	PUNCT
ejpam-5563	154	6	.	.	PUNCT
ejpam-5563	155	1	proof	proof	NOUN
ejpam-5563	155	2	.	.	PUNCT
ejpam-5563	156	1	by	by	ADP
ejpam-5563	156	2	using	use	VERB
ejpam-5563	156	3	theorem	theorem	ADJ
ejpam-5563	156	4	9	9	NUM
ejpam-5563	156	5	,	,	PUNCT
ejpam-5563	156	6	intθ(k	intθ(k	ADJ
ejpam-5563	156	7	)	)	PUNCT
ejpam-5563	156	8	∩	∩	NOUN
ejpam-5563	156	9	int(γ(o	int(γ(o	VERB
ejpam-5563	156	10	)	)	PUNCT
ejpam-5563	156	11	)	)	PUNCT
ejpam-5563	157	1	=	=	SYM
ejpam-5563	157	2	int[intθ(k	int[intθ(k	ADJ
ejpam-5563	157	3	)	)	PUNCT
ejpam-5563	157	4	∩	∩	NOUN
ejpam-5563	157	5	γ(o	γ(o	PROPN
ejpam-5563	157	6	)	)	PUNCT
ejpam-5563	157	7	]	]	PUNCT
ejpam-5563	157	8	⊆int(γ(k	⊆int(γ(k	NUM
ejpam-5563	157	9	∩o	∩o	NOUN
ejpam-5563	157	10	)	)	PUNCT
ejpam-5563	157	11	)	)	PUNCT
ejpam-5563	157	12	.	.	PUNCT
ejpam-5563	158	1	definition	definition	NOUN
ejpam-5563	158	2	8	8	NUM
ejpam-5563	158	3	.	.	PUNCT
ejpam-5563	159	1	let	let	VERB
ejpam-5563	159	2	(	(	PUNCT
ejpam-5563	159	3	b	b	X
ejpam-5563	159	4	,	,	PUNCT
ejpam-5563	159	5	γ	γ	PROPN
ejpam-5563	159	6	,	,	PUNCT
ejpam-5563	159	7	p	p	NOUN
ejpam-5563	159	8	)	)	PUNCT
ejpam-5563	159	9	be	be	AUX
ejpam-5563	159	10	a	a	DET
ejpam-5563	159	11	ps	ps	NOUN
ejpam-5563	159	12	.	.	PUNCT
ejpam-5563	160	1	then	then	ADV
ejpam-5563	160	2	,	,	PUNCT
ejpam-5563	160	3	(	(	PUNCT
ejpam-5563	160	4	b	b	X
ejpam-5563	160	5	,	,	PUNCT
ejpam-5563	160	6	γ	γ	PROPN
ejpam-5563	160	7	,	,	PUNCT
ejpam-5563	160	8	p	p	NOUN
ejpam-5563	160	9	)	)	PUNCT
ejpam-5563	160	10	is	be	AUX
ejpam-5563	160	11	a	a	DET
ejpam-5563	160	12	⋄-extremally	⋄-extremally	ADV
ejpam-5563	160	13	disconnected	disconnected	ADJ
ejpam-5563	160	14	if	if	SCONJ
ejpam-5563	160	15	u⋄	u⋄	VERB
ejpam-5563	160	16	∈	∈	PROPN
ejpam-5563	160	17	γ	γ	NOUN
ejpam-5563	160	18	for	for	ADP
ejpam-5563	160	19	every	every	DET
ejpam-5563	160	20	u	u	PROPN
ejpam-5563	160	21	∈	∈	PROPN
ejpam-5563	160	22	γ	γ	X
ejpam-5563	160	23	.	.	PUNCT
ejpam-5563	161	1	the	the	DET
ejpam-5563	161	2	following	follow	VERB
ejpam-5563	161	3	example	example	NOUN
ejpam-5563	161	4	is	be	AUX
ejpam-5563	161	5	an	an	DET
ejpam-5563	161	6	example	example	NOUN
ejpam-5563	161	7	of	of	ADP
ejpam-5563	161	8	⋄-extremally	⋄-extremally	ADV
ejpam-5563	161	9	disconnected	disconnect	VERB
ejpam-5563	161	10	primal	primal	ADJ
ejpam-5563	161	11	topological	topological	ADJ
ejpam-5563	161	12	space	space	NOUN
ejpam-5563	161	13	.	.	PUNCT
ejpam-5563	162	1	example	example	NOUN
ejpam-5563	163	1	1	1	NUM
ejpam-5563	163	2	.	.	X
ejpam-5563	163	3	define	define	VERB
ejpam-5563	163	4	(	(	PUNCT
ejpam-5563	163	5	r	r	NOUN
ejpam-5563	163	6	,	,	PUNCT
ejpam-5563	163	7	γ0,p0	γ0,p0	PROPN
ejpam-5563	163	8	)	)	PUNCT
ejpam-5563	163	9	as	as	SCONJ
ejpam-5563	163	10	follows	follow	VERB
ejpam-5563	163	11	:	:	PUNCT
ejpam-5563	163	12	t	t	PROPN
ejpam-5563	163	13	∈	∈	PROPN
ejpam-5563	163	14	p0	p0	NOUN
ejpam-5563	163	15	⇐	⇐	ADJ
ejpam-5563	163	16	⇒	⇒	PROPN
ejpam-5563	163	17	0	0	NUM
ejpam-5563	163	18	/∈	/∈	PUNCT
ejpam-5563	163	19	t	t	PROPN
ejpam-5563	163	20	and	and	CCONJ
ejpam-5563	163	21	u	u	PROPN
ejpam-5563	163	22	∈	∈	PROPN
ejpam-5563	163	23	γ0	γ0	NOUN
ejpam-5563	163	24	⇐	⇐	ADJ
ejpam-5563	163	25	⇒	⇒	PROPN
ejpam-5563	163	26	u	u	NOUN
ejpam-5563	163	27	=	=	NOUN
ejpam-5563	163	28	∅	∅	NOUN
ejpam-5563	163	29	or	or	CCONJ
ejpam-5563	163	30	0	0	NUM
ejpam-5563	163	31	∈	∈	PROPN
ejpam-5563	163	32	u	u	NOUN
ejpam-5563	163	33	.	.	PUNCT
ejpam-5563	164	1	let	let	VERB
ejpam-5563	164	2	u	u	PRON
ejpam-5563	164	3	∈	∈	PROPN
ejpam-5563	164	4	γ0	γ0	NOUN
ejpam-5563	164	5	.	.	PUNCT
ejpam-5563	165	1	then	then	ADV
ejpam-5563	165	2	,	,	PUNCT
ejpam-5563	165	3	u⋄	u⋄	VERB
ejpam-5563	165	4	=	=	PRON
ejpam-5563	165	5	{	{	PUNCT
ejpam-5563	165	6	∅	∅	NOUN
ejpam-5563	165	7	if	if	SCONJ
ejpam-5563	165	8	u	u	NOUN
ejpam-5563	165	9	=	=	NOUN
ejpam-5563	165	10	∅	∅	NOUN
ejpam-5563	165	11	r	r	NOUN
ejpam-5563	165	12	if	if	SCONJ
ejpam-5563	165	13	u	u	NOUN
ejpam-5563	165	14	̸=	̸=	PROPN
ejpam-5563	165	15	∅	∅	NOUN
ejpam-5563	165	16	hence	hence	ADV
ejpam-5563	165	17	,	,	PUNCT
ejpam-5563	165	18	(	(	PUNCT
ejpam-5563	165	19	r	r	NOUN
ejpam-5563	165	20	,	,	PUNCT
ejpam-5563	165	21	γ0,p0	γ0,p0	PROPN
ejpam-5563	165	22	)	)	PUNCT
ejpam-5563	165	23	is	be	AUX
ejpam-5563	165	24	⋄-extremally	⋄-extremally	ADV
ejpam-5563	165	25	disconnected	disconnect	VERB
ejpam-5563	165	26	.	.	PUNCT
ejpam-5563	166	1	theorem	theorem	ADJ
ejpam-5563	166	2	11	11	NUM
ejpam-5563	166	3	.	.	PUNCT
ejpam-5563	167	1	let	let	VERB
ejpam-5563	167	2	(	(	PUNCT
ejpam-5563	167	3	b	b	X
ejpam-5563	167	4	,	,	PUNCT
ejpam-5563	167	5	γ	γ	PROPN
ejpam-5563	167	6	,	,	PUNCT
ejpam-5563	167	7	p	p	NOUN
ejpam-5563	167	8	)	)	PUNCT
ejpam-5563	167	9	be	be	AUX
ejpam-5563	167	10	⋄-extremally	⋄-extremally	ADV
ejpam-5563	167	11	disconnected	disconnect	VERB
ejpam-5563	167	12	.	.	PUNCT
ejpam-5563	168	1	then	then	ADV
ejpam-5563	168	2	,	,	PUNCT
ejpam-5563	168	3	for	for	ADP
ejpam-5563	168	4	any	any	DET
ejpam-5563	168	5	c	c	NOUN
ejpam-5563	168	6	⊆	⊆	NUM
ejpam-5563	168	7	b	b	NOUN
ejpam-5563	168	8	,	,	PUNCT
ejpam-5563	168	9	γ(γ(c	γ(γ(c	NOUN
ejpam-5563	168	10	)	)	PUNCT
ejpam-5563	168	11	)	)	PUNCT
ejpam-5563	169	1	⊆	⊆	NUM
ejpam-5563	169	2	γ(c	γ(c	NUM
ejpam-5563	169	3	)	)	PUNCT
ejpam-5563	169	4	.	.	PUNCT
ejpam-5563	170	1	proof	proof	NOUN
ejpam-5563	170	2	.	.	PUNCT
ejpam-5563	171	1	let	let	VERB
ejpam-5563	171	2	r	r	NOUN
ejpam-5563	171	3	∈	∈	PROPN
ejpam-5563	171	4	γ(γ(c	γ(γ(c	NOUN
ejpam-5563	171	5	)	)	PUNCT
ejpam-5563	171	6	)	)	PUNCT
ejpam-5563	171	7	.	.	PUNCT
ejpam-5563	172	1	then	then	ADV
ejpam-5563	172	2	,	,	PUNCT
ejpam-5563	172	3	[	[	X
ejpam-5563	172	4	o⋄∩γ(c)]c	o⋄∩γ(c)]c	X
ejpam-5563	172	5	∈	∈	PROPN
ejpam-5563	172	6	p	p	NOUN
ejpam-5563	172	7	for	for	ADP
ejpam-5563	172	8	each	each	DET
ejpam-5563	172	9	o	o	NOUN
ejpam-5563	172	10	∈	∈	PROPN
ejpam-5563	172	11	γ(r	γ(r	PROPN
ejpam-5563	172	12	)	)	PUNCT
ejpam-5563	172	13	.	.	PUNCT
ejpam-5563	173	1	hence	hence	ADV
ejpam-5563	173	2	,	,	PUNCT
ejpam-5563	173	3	o⋄∩γ(c	o⋄∩γ(c	NOUN
ejpam-5563	173	4	)	)	PUNCT
ejpam-5563	173	5	̸=	̸=	PROPN
ejpam-5563	173	6	∅.	∅.	ADV
ejpam-5563	173	7	let	let	VERB
ejpam-5563	173	8	t	t	PROPN
ejpam-5563	173	9	∈	∈	PROPN
ejpam-5563	173	10	o⋄	o⋄	X
ejpam-5563	173	11	∩	∩	NOUN
ejpam-5563	173	12	γ(c	γ(c	NUM
ejpam-5563	173	13	)	)	PUNCT
ejpam-5563	173	14	.	.	PUNCT
ejpam-5563	174	1	therefore	therefore	ADV
ejpam-5563	174	2	,	,	PUNCT
ejpam-5563	174	3	since	since	SCONJ
ejpam-5563	174	4	o⋄	o⋄	NUM
ejpam-5563	174	5	∈	∈	PROPN
ejpam-5563	174	6	γ(t	γ(t	NOUN
ejpam-5563	174	7	)	)	PUNCT
ejpam-5563	174	8	and	and	CCONJ
ejpam-5563	174	9	t	t	PROPN
ejpam-5563	174	10	∈	∈	PROPN
ejpam-5563	174	11	γ(c	γ(c	PROPN
ejpam-5563	174	12	)	)	PUNCT
ejpam-5563	174	13	,	,	PUNCT
ejpam-5563	174	14	then	then	ADV
ejpam-5563	174	15	[	[	X
ejpam-5563	174	16	c	c	NOUN
ejpam-5563	174	17	∩	∩	X
ejpam-5563	174	18	(	(	PUNCT
ejpam-5563	174	19	o⋄)⋄]c	o⋄)⋄]c	NOUN
ejpam-5563	174	20	∈	∈	PROPN
ejpam-5563	174	21	p.	p.	NOUN
ejpam-5563	174	22	as	as	ADP
ejpam-5563	174	23	[	[	X
ejpam-5563	174	24	c	c	X
ejpam-5563	174	25	∩	∩	NOUN
ejpam-5563	174	26	o⋄]c	o⋄]c	PRON
ejpam-5563	174	27	⊆	⊆	NUM
ejpam-5563	174	28	[	[	X
ejpam-5563	174	29	c	c	NOUN
ejpam-5563	174	30	∩	∩	X
ejpam-5563	174	31	(	(	PUNCT
ejpam-5563	174	32	o⋄)⋄]c	o⋄)⋄]c	NOUN
ejpam-5563	174	33	∈	∈	PROPN
ejpam-5563	174	34	p	p	NOUN
ejpam-5563	174	35	,	,	PUNCT
ejpam-5563	174	36	then	then	ADV
ejpam-5563	174	37	[	[	X
ejpam-5563	174	38	c	c	NOUN
ejpam-5563	174	39	∩	∩	VERB
ejpam-5563	174	40	o⋄]c	o⋄]c	NOUN
ejpam-5563	174	41	∈	∈	PROPN
ejpam-5563	174	42	p	p	X
ejpam-5563	174	43	which	which	PRON
ejpam-5563	174	44	implies	imply	VERB
ejpam-5563	174	45	that	that	SCONJ
ejpam-5563	174	46	r	r	PROPN
ejpam-5563	174	47	∈	∈	PROPN
ejpam-5563	174	48	γ(c	γ(c	PROPN
ejpam-5563	174	49	)	)	PUNCT
ejpam-5563	174	50	.	.	PUNCT
ejpam-5563	175	1	theorem	theorem	NOUN
ejpam-5563	175	2	12	12	NUM
ejpam-5563	175	3	.	.	PUNCT
ejpam-5563	176	1	let	let	VERB
ejpam-5563	176	2	(	(	PUNCT
ejpam-5563	176	3	b	b	X
ejpam-5563	176	4	,	,	PUNCT
ejpam-5563	176	5	γ	γ	PROPN
ejpam-5563	176	6	,	,	PUNCT
ejpam-5563	176	7	p	p	NOUN
ejpam-5563	176	8	)	)	PUNCT
ejpam-5563	176	9	be	be	AUX
ejpam-5563	176	10	a	a	DET
ejpam-5563	176	11	⋄-extremally	⋄-extremally	ADV
ejpam-5563	176	12	disconnected	disconnected	ADJ
ejpam-5563	176	13	and	and	CCONJ
ejpam-5563	176	14	c	c	NOUN
ejpam-5563	176	15	⊆	⊆	NUM
ejpam-5563	176	16	int(γ(c	int(γ(c	NOUN
ejpam-5563	176	17	)	)	PUNCT
ejpam-5563	176	18	)	)	PUNCT
ejpam-5563	176	19	.	.	PUNCT
ejpam-5563	177	1	then	then	ADV
ejpam-5563	177	2	,	,	PUNCT
ejpam-5563	177	3	γ(c	γ(c	PROPN
ejpam-5563	177	4	)	)	PUNCT
ejpam-5563	177	5	=	=	SYM
ejpam-5563	177	6	γ(γ(c	γ(γ(c	NOUN
ejpam-5563	177	7	)	)	PUNCT
ejpam-5563	177	8	)	)	PUNCT
ejpam-5563	177	9	.	.	PUNCT
ejpam-5563	178	1	proof	proof	NOUN
ejpam-5563	178	2	.	.	PUNCT
ejpam-5563	179	1	since	since	SCONJ
ejpam-5563	179	2	γ(γ(c	γ(γ(c	PROPN
ejpam-5563	179	3	)	)	PUNCT
ejpam-5563	179	4	)	)	PUNCT
ejpam-5563	180	1	⊆	⊆	NUM
ejpam-5563	180	2	γ(c	γ(c	NUM
ejpam-5563	180	3	)	)	PUNCT
ejpam-5563	180	4	by	by	ADP
ejpam-5563	180	5	theorem	theorem	NOUN
ejpam-5563	180	6	11	11	NUM
ejpam-5563	180	7	,	,	PUNCT
ejpam-5563	180	8	then	then	ADV
ejpam-5563	180	9	it	it	PRON
ejpam-5563	180	10	remains	remain	VERB
ejpam-5563	180	11	to	to	PART
ejpam-5563	180	12	show	show	VERB
ejpam-5563	180	13	that	that	PRON
ejpam-5563	180	14	γ(c	γ(c	PROPN
ejpam-5563	180	15	)	)	PUNCT
ejpam-5563	180	16	⊆	⊆	NUM
ejpam-5563	180	17	γ(γ(c	γ(γ(c	NOUN
ejpam-5563	180	18	)	)	PUNCT
ejpam-5563	180	19	)	)	PUNCT
ejpam-5563	180	20	.	.	PUNCT
ejpam-5563	181	1	indeed	indeed	ADV
ejpam-5563	181	2	,	,	PUNCT
ejpam-5563	181	3	since	since	SCONJ
ejpam-5563	181	4	c	c	NOUN
ejpam-5563	181	5	⊆	⊆	NUM
ejpam-5563	181	6	int(γ(c	int(γ(c	NOUN
ejpam-5563	181	7	)	)	PUNCT
ejpam-5563	181	8	)	)	PUNCT
ejpam-5563	181	9	,	,	PUNCT
ejpam-5563	181	10	then	then	ADV
ejpam-5563	181	11	γ(c	γ(c	PROPN
ejpam-5563	181	12	)	)	PUNCT
ejpam-5563	181	13	⊆	⊆	NUM
ejpam-5563	181	14	γ(int(γ(c	γ(int(γ(c	NUM
ejpam-5563	181	15	)	)	PUNCT
ejpam-5563	181	16	)	)	PUNCT
ejpam-5563	182	1	⊆	⊆	NUM
ejpam-5563	182	2	γ(γ(c	γ(γ(c	NOUN
ejpam-5563	182	3	)	)	PUNCT
ejpam-5563	182	4	)	)	PUNCT
ejpam-5563	182	5	.	.	PUNCT
ejpam-5563	183	1	o.	o.	PROPN
ejpam-5563	183	2	alghamdi	alghamdi	PROPN
ejpam-5563	183	3	/	/	SYM
ejpam-5563	183	4	eur	eur	PROPN
ejpam-5563	183	5	.	.	PUNCT
ejpam-5563	184	1	j.	j.	PROPN
ejpam-5563	184	2	pure	pure	PROPN
ejpam-5563	184	3	appl	appl	PROPN
ejpam-5563	184	4	.	.	PROPN
ejpam-5563	184	5	math	math	PROPN
ejpam-5563	184	6	,	,	PUNCT
ejpam-5563	184	7	17	17	NUM
ejpam-5563	184	8	(	(	PUNCT
ejpam-5563	184	9	4	4	NUM
ejpam-5563	184	10	)	)	PUNCT
ejpam-5563	184	11	(	(	PUNCT
ejpam-5563	184	12	2024	2024	NUM
ejpam-5563	184	13	)	)	PUNCT
ejpam-5563	184	14	,	,	PUNCT
ejpam-5563	184	15	3517	3517	NUM
ejpam-5563	184	16	-	-	SYM
ejpam-5563	184	17	3538	3538	NUM
ejpam-5563	184	18	3522	3522	NUM
ejpam-5563	184	19	3	3	NOUN
ejpam-5563	184	20	.	.	PUNCT
ejpam-5563	185	1	on	on	ADP
ejpam-5563	185	2	λ	λ	PROPN
ejpam-5563	185	3	operator	operator	NOUN
ejpam-5563	185	4	in	in	ADP
ejpam-5563	185	5	this	this	DET
ejpam-5563	185	6	part	part	NOUN
ejpam-5563	185	7	,	,	PUNCT
ejpam-5563	185	8	a	a	DET
ejpam-5563	185	9	new	new	ADJ
ejpam-5563	185	10	operator	operator	NOUN
ejpam-5563	185	11	called	call	VERB
ejpam-5563	185	12	the	the	DET
ejpam-5563	185	13	λ	λ	NOUN
ejpam-5563	185	14	operator	operator	NOUN
ejpam-5563	185	15	is	be	AUX
ejpam-5563	185	16	defined	define	VERB
ejpam-5563	185	17	.	.	PUNCT
ejpam-5563	186	1	we	we	PRON
ejpam-5563	186	2	provide	provide	VERB
ejpam-5563	186	3	some	some	DET
ejpam-5563	186	4	results	result	NOUN
ejpam-5563	186	5	and	and	CCONJ
ejpam-5563	186	6	examples	example	NOUN
ejpam-5563	186	7	to	to	PART
ejpam-5563	186	8	illustrate	illustrate	VERB
ejpam-5563	186	9	the	the	DET
ejpam-5563	186	10	relationship	relationship	NOUN
ejpam-5563	186	11	between	between	ADP
ejpam-5563	186	12	this	this	DET
ejpam-5563	186	13	operator	operator	NOUN
ejpam-5563	186	14	and	and	CCONJ
ejpam-5563	186	15	others	other	NOUN
ejpam-5563	186	16	.	.	PUNCT
ejpam-5563	187	1	definition	definition	NOUN
ejpam-5563	187	2	9	9	NUM
ejpam-5563	187	3	.	.	PUNCT
ejpam-5563	188	1	let	let	VERB
ejpam-5563	188	2	(	(	PUNCT
ejpam-5563	188	3	b	b	X
ejpam-5563	188	4	,	,	PUNCT
ejpam-5563	188	5	γ	γ	PROPN
ejpam-5563	188	6	,	,	PUNCT
ejpam-5563	188	7	p	p	NOUN
ejpam-5563	188	8	)	)	PUNCT
ejpam-5563	188	9	be	be	AUX
ejpam-5563	188	10	a	a	DET
ejpam-5563	188	11	ps	ps	NOUN
ejpam-5563	188	12	.	.	PUNCT
ejpam-5563	189	1	then	then	ADV
ejpam-5563	189	2	,	,	PUNCT
ejpam-5563	189	3	λ	λ	INTJ
ejpam-5563	189	4	:	:	PUNCT
ejpam-5563	189	5	p(b	p(b	NUM
ejpam-5563	189	6	)	)	PUNCT
ejpam-5563	189	7	→	→	SYM
ejpam-5563	189	8	p(b	p(b	PROPN
ejpam-5563	189	9	)	)	PUNCT
ejpam-5563	189	10	is	be	AUX
ejpam-5563	189	11	defined	define	VERB
ejpam-5563	189	12	as	as	ADP
ejpam-5563	189	13	:	:	PUNCT
ejpam-5563	189	14	λ(k	λ(k	X
ejpam-5563	189	15	)	)	PUNCT
ejpam-5563	189	16	=	=	PUNCT
ejpam-5563	190	1	γ∗(k)−k	γ∗(k)−k	PROPN
ejpam-5563	190	2	for	for	ADP
ejpam-5563	190	3	every	every	DET
ejpam-5563	190	4	k	k	PROPN
ejpam-5563	190	5	⊆	⊆	PROPN
ejpam-5563	190	6	b.	b.	PROPN
ejpam-5563	190	7	remark	remark	NOUN
ejpam-5563	190	8	1	1	NUM
ejpam-5563	190	9	.	.	PUNCT
ejpam-5563	191	1	let	let	VERB
ejpam-5563	191	2	(	(	PUNCT
ejpam-5563	191	3	b	b	X
ejpam-5563	191	4	,	,	PUNCT
ejpam-5563	191	5	γ	γ	PROPN
ejpam-5563	191	6	,	,	PUNCT
ejpam-5563	191	7	p	p	NOUN
ejpam-5563	191	8	)	)	PUNCT
ejpam-5563	191	9	be	be	AUX
ejpam-5563	191	10	a	a	DET
ejpam-5563	191	11	ps	ps	NOUN
ejpam-5563	191	12	such	such	ADJ
ejpam-5563	191	13	that	that	SCONJ
ejpam-5563	191	14	p	p	PROPN
ejpam-5563	191	15	=	=	SYM
ejpam-5563	191	16	p(b	p(b	PROPN
ejpam-5563	191	17	)	)	PUNCT
ejpam-5563	192	1	−	−	PROPN
ejpam-5563	192	2	{	{	PUNCT
ejpam-5563	192	3	b	b	NOUN
ejpam-5563	192	4	}	}	PUNCT
ejpam-5563	192	5	.	.	PUNCT
ejpam-5563	193	1	then	then	ADV
ejpam-5563	193	2	,	,	PUNCT
ejpam-5563	193	3	γ(o	γ(o	PROPN
ejpam-5563	193	4	)	)	PUNCT
ejpam-5563	193	5	=	=	SYM
ejpam-5563	193	6	clθ(o	clθ(o	PROPN
ejpam-5563	193	7	)	)	PUNCT
ejpam-5563	193	8	for	for	ADP
ejpam-5563	193	9	all	all	DET
ejpam-5563	193	10	o	o	NOUN
ejpam-5563	193	11	⊆	⊆	NUM
ejpam-5563	193	12	b.	b.	NOUN
ejpam-5563	193	13	proof	proof	NOUN
ejpam-5563	193	14	.	.	PUNCT
ejpam-5563	194	1	we	we	PRON
ejpam-5563	194	2	know	know	VERB
ejpam-5563	194	3	from	from	ADP
ejpam-5563	194	4	(	(	PUNCT
ejpam-5563	194	5	iv	iv	X
ejpam-5563	194	6	)	)	PUNCT
ejpam-5563	194	7	in	in	ADP
ejpam-5563	194	8	theorem	theorem	NOUN
ejpam-5563	194	9	1	1	NUM
ejpam-5563	194	10	that	that	SCONJ
ejpam-5563	194	11	γ(o	γ(o	NOUN
ejpam-5563	194	12	)	)	PUNCT
ejpam-5563	194	13	⊆	⊆	NUM
ejpam-5563	194	14	clθ(o	clθ(o	PROPN
ejpam-5563	194	15	)	)	PUNCT
ejpam-5563	194	16	.	.	PUNCT
ejpam-5563	195	1	for	for	ADP
ejpam-5563	195	2	the	the	DET
ejpam-5563	195	3	converse	converse	NOUN
ejpam-5563	195	4	,	,	PUNCT
ejpam-5563	195	5	let	let	VERB
ejpam-5563	195	6	r	r	PRON
ejpam-5563	195	7	/∈	/∈	PUNCT
ejpam-5563	195	8	γ(o	γ(o	PROPN
ejpam-5563	195	9	)	)	PUNCT
ejpam-5563	195	10	.	.	PUNCT
ejpam-5563	196	1	then	then	ADV
ejpam-5563	196	2	,	,	PUNCT
ejpam-5563	196	3	[	[	X
ejpam-5563	196	4	w	w	PROPN
ejpam-5563	196	5	⋄	⋄	PROPN
ejpam-5563	196	6	∩	∩	ADJ
ejpam-5563	196	7	o]c	o]c	PROPN
ejpam-5563	196	8	/∈	/∈	PUNCT
ejpam-5563	197	1	p	p	NOUN
ejpam-5563	197	2	for	for	ADP
ejpam-5563	197	3	some	some	DET
ejpam-5563	197	4	w	w	PROPN
ejpam-5563	197	5	∈	∈	PROPN
ejpam-5563	197	6	γ(r	γ(r	PROPN
ejpam-5563	197	7	)	)	PUNCT
ejpam-5563	197	8	.	.	PUNCT
ejpam-5563	198	1	hence	hence	ADV
ejpam-5563	198	2	,	,	PUNCT
ejpam-5563	198	3	w	w	PROPN
ejpam-5563	198	4	⋄	⋄	PROPN
ejpam-5563	198	5	∩	∩	ADJ
ejpam-5563	198	6	o	o	NOUN
ejpam-5563	198	7	=	=	PUNCT
ejpam-5563	198	8	∅.	∅.	VERB
ejpam-5563	198	9	thus	thus	ADV
ejpam-5563	198	10	,	,	PUNCT
ejpam-5563	198	11	if	if	SCONJ
ejpam-5563	198	12	t	t	PROPN
ejpam-5563	198	13	∈	∈	PROPN
ejpam-5563	198	14	o	o	NOUN
ejpam-5563	198	15	,	,	PUNCT
ejpam-5563	198	16	we	we	PRON
ejpam-5563	198	17	have	have	VERB
ejpam-5563	198	18	that	that	DET
ejpam-5563	198	19	u	u	PROPN
ejpam-5563	198	20	∩	∩	PROPN
ejpam-5563	198	21	w	w	NOUN
ejpam-5563	198	22	=	=	NOUN
ejpam-5563	198	23	∅	∅	NOUN
ejpam-5563	198	24	for	for	ADP
ejpam-5563	198	25	some	some	DET
ejpam-5563	198	26	u	u	NOUN
ejpam-5563	198	27	∈	∈	PROPN
ejpam-5563	198	28	γ(t	γ(t	NOUN
ejpam-5563	198	29	)	)	PUNCT
ejpam-5563	198	30	.	.	PUNCT
ejpam-5563	199	1	thus	thus	ADV
ejpam-5563	199	2	,	,	PUNCT
ejpam-5563	199	3	t	t	PROPN
ejpam-5563	199	4	/∈	/∈	PUNCT
ejpam-5563	199	5	cl(w	cl(w	PROPN
ejpam-5563	199	6	)	)	PUNCT
ejpam-5563	199	7	;	;	PUNCT
ejpam-5563	199	8	hence	hence	ADV
ejpam-5563	199	9	o	o	NOUN
ejpam-5563	199	10	∩	∩	NOUN
ejpam-5563	199	11	cl(w	cl(w	NOUN
ejpam-5563	199	12	)	)	PUNCT
ejpam-5563	200	1	=	=	NOUN
ejpam-5563	200	2	∅	∅	NOUN
ejpam-5563	200	3	which	which	PRON
ejpam-5563	200	4	implies	imply	VERB
ejpam-5563	200	5	that	that	SCONJ
ejpam-5563	200	6	r	r	NOUN
ejpam-5563	200	7	/∈	/∈	PUNCT
ejpam-5563	200	8	clθ(o	clθ(o	PROPN
ejpam-5563	200	9	)	)	PUNCT
ejpam-5563	200	10	.	.	PUNCT
ejpam-5563	201	1	therefore	therefore	ADV
ejpam-5563	201	2	,	,	PUNCT
ejpam-5563	201	3	clθ(o	clθ(o	PROPN
ejpam-5563	201	4	)	)	PUNCT
ejpam-5563	201	5	=	=	PUNCT
ejpam-5563	201	6	γ(o	γ(o	VERB
ejpam-5563	201	7	)	)	PUNCT
ejpam-5563	201	8	.	.	PUNCT
ejpam-5563	202	1	remark	remark	NOUN
ejpam-5563	202	2	2	2	NUM
ejpam-5563	202	3	.	.	PUNCT
ejpam-5563	203	1	let	let	VERB
ejpam-5563	203	2	(	(	PUNCT
ejpam-5563	203	3	b	b	X
ejpam-5563	203	4	,	,	PUNCT
ejpam-5563	203	5	γ	γ	PROPN
ejpam-5563	203	6	,	,	PUNCT
ejpam-5563	203	7	p	p	NOUN
ejpam-5563	203	8	)	)	PUNCT
ejpam-5563	203	9	be	be	AUX
ejpam-5563	203	10	a	a	DET
ejpam-5563	203	11	ps	ps	NOUN
ejpam-5563	203	12	.	.	PUNCT
ejpam-5563	204	1	then	then	ADV
ejpam-5563	204	2	,	,	PUNCT
ejpam-5563	204	3	1	1	X
ejpam-5563	204	4	.	.	PUNCT
ejpam-5563	205	1	if	if	SCONJ
ejpam-5563	205	2	p	p	NOUN
ejpam-5563	205	3	=	=	NOUN
ejpam-5563	205	4	∅	∅	NOUN
ejpam-5563	205	5	and	and	CCONJ
ejpam-5563	205	6	k	k	PROPN
ejpam-5563	205	7	is	be	AUX
ejpam-5563	205	8	any	any	DET
ejpam-5563	205	9	nonempty	nonempty	ADJ
ejpam-5563	205	10	proper	proper	ADJ
ejpam-5563	205	11	subset	subset	NOUN
ejpam-5563	205	12	of	of	ADP
ejpam-5563	205	13	b	b	PROPN
ejpam-5563	205	14	,	,	PUNCT
ejpam-5563	205	15	then	then	ADV
ejpam-5563	205	16	λ(k	λ(k	ADJ
ejpam-5563	205	17	)	)	PUNCT
ejpam-5563	205	18	=	=	SYM
ejpam-5563	205	19	kc	kc	PROPN
ejpam-5563	205	20	.	.	PUNCT
ejpam-5563	206	1	to	to	PART
ejpam-5563	206	2	show	show	VERB
ejpam-5563	206	3	that	that	SCONJ
ejpam-5563	206	4	,	,	PUNCT
ejpam-5563	206	5	we	we	PRON
ejpam-5563	206	6	have	have	VERB
ejpam-5563	206	7	λ(k	λ(k	ADJ
ejpam-5563	206	8	)	)	PUNCT
ejpam-5563	206	9	=	=	SYM
ejpam-5563	206	10	γ∗(k	γ∗(k	NOUN
ejpam-5563	206	11	)	)	PUNCT
ejpam-5563	206	12	−	−	NOUN
ejpam-5563	207	1	k	k	NOUN
ejpam-5563	207	2	=	=	PUNCT
ejpam-5563	208	1	[	[	X
ejpam-5563	208	2	γ(kc)]c	γ(kc)]c	PROPN
ejpam-5563	208	3	−	−	PROPN
ejpam-5563	208	4	k.	k.	NOUN
ejpam-5563	208	5	since	since	SCONJ
ejpam-5563	208	6	k	k	PROPN
ejpam-5563	208	7	=	=	NOUN
ejpam-5563	208	8	̸	̸	ADJ
ejpam-5563	208	9	∅	∅	NOUN
ejpam-5563	208	10	,	,	PUNCT
ejpam-5563	208	11	then	then	ADV
ejpam-5563	208	12	we	we	PRON
ejpam-5563	208	13	have	have	VERB
ejpam-5563	208	14	γ(kc	γ(kc	NOUN
ejpam-5563	208	15	)	)	PUNCT
ejpam-5563	208	16	=	=	NOUN
ejpam-5563	208	17	∅	∅	NOUN
ejpam-5563	208	18	by	by	ADP
ejpam-5563	208	19	(	(	PUNCT
ejpam-5563	208	20	vi	vi	NOUN
ejpam-5563	208	21	)	)	PUNCT
ejpam-5563	208	22	in	in	ADP
ejpam-5563	208	23	theorem	theorem	NOUN
ejpam-5563	208	24	1	1	NUM
ejpam-5563	208	25	.	.	PUNCT
ejpam-5563	208	26	hence	hence	ADV
ejpam-5563	208	27	,	,	PUNCT
ejpam-5563	208	28	λ(k	λ(k	PROPN
ejpam-5563	208	29	)	)	PUNCT
ejpam-5563	208	30	=	=	SYM
ejpam-5563	208	31	kc	kc	PROPN
ejpam-5563	208	32	.	.	PROPN
ejpam-5563	209	1	2	2	NUM
ejpam-5563	209	2	.	.	X
ejpam-5563	210	1	if	if	SCONJ
ejpam-5563	210	2	p	p	NOUN
ejpam-5563	210	3	=	=	VERB
ejpam-5563	210	4	p(b)−	p(b)−	PROPN
ejpam-5563	210	5	{	{	PUNCT
ejpam-5563	210	6	b	b	NOUN
ejpam-5563	210	7	}	}	PUNCT
ejpam-5563	210	8	and	and	CCONJ
ejpam-5563	210	9	k	k	PROPN
ejpam-5563	210	10	is	be	AUX
ejpam-5563	210	11	any	any	PRON
ejpam-5563	210	12	nonempty	nonempty	ADJ
ejpam-5563	210	13	proper	proper	ADJ
ejpam-5563	210	14	subset	subset	NOUN
ejpam-5563	210	15	of	of	ADP
ejpam-5563	210	16	b	b	PROPN
ejpam-5563	210	17	,	,	PUNCT
ejpam-5563	210	18	then	then	ADV
ejpam-5563	210	19	λ(k	λ(k	ADJ
ejpam-5563	210	20	)	)	PUNCT
ejpam-5563	210	21	=	=	PUNCT
ejpam-5563	210	22	∅.	∅.	NOUN
ejpam-5563	210	23	since	since	SCONJ
ejpam-5563	210	24	γ(s	γ(	NOUN
ejpam-5563	210	25	)	)	PUNCT
ejpam-5563	211	1	=	=	SYM
ejpam-5563	211	2	clθ(s	clθ(s	PROPN
ejpam-5563	211	3	)	)	PUNCT
ejpam-5563	211	4	for	for	ADP
ejpam-5563	211	5	every	every	PRON
ejpam-5563	211	6	s	s	PROPN
ejpam-5563	211	7	⊆	⊆	NUM
ejpam-5563	211	8	b	b	NOUN
ejpam-5563	211	9	,	,	PUNCT
ejpam-5563	211	10	then	then	ADV
ejpam-5563	211	11	λ(k	λ(k	ADJ
ejpam-5563	211	12	)	)	PUNCT
ejpam-5563	211	13	=	=	SYM
ejpam-5563	211	14	γ∗(k	γ∗(k	NOUN
ejpam-5563	211	15	)	)	PUNCT
ejpam-5563	211	16	−	−	NOUN
ejpam-5563	212	1	k	k	NOUN
ejpam-5563	212	2	=	=	PUNCT
ejpam-5563	213	1	[	[	X
ejpam-5563	213	2	γ(kc)]c	γ(kc)]c	PROPN
ejpam-5563	213	3	−	−	PROPN
ejpam-5563	213	4	k	k	NOUN
ejpam-5563	214	1	=	=	PUNCT
ejpam-5563	215	1	[	[	X
ejpam-5563	215	2	clθ(kc)]c	clθ(kc)]c	NOUN
ejpam-5563	215	3	−k	−k	NOUN
ejpam-5563	215	4	=	=	PUNCT
ejpam-5563	215	5	intθ(k)−k	intθ(k)−k	VERB
ejpam-5563	215	6	=	=	PUNCT
ejpam-5563	215	7	∅.	∅.	NOUN
ejpam-5563	215	8	example	example	NOUN
ejpam-5563	215	9	2	2	NUM
ejpam-5563	215	10	.	.	PUNCT
ejpam-5563	216	1	let	let	VERB
ejpam-5563	216	2	(	(	PUNCT
ejpam-5563	216	3	b	b	X
ejpam-5563	216	4	=	=	SYM
ejpam-5563	216	5	r	r	NOUN
ejpam-5563	216	6	,	,	PUNCT
ejpam-5563	216	7	τ√2,p	τ√2,p	NUM
ejpam-5563	216	8	)	)	PUNCT
ejpam-5563	216	9	be	be	AUX
ejpam-5563	216	10	defined	define	VERB
ejpam-5563	216	11	as	as	SCONJ
ejpam-5563	216	12	follows	follow	VERB
ejpam-5563	216	13	:	:	PUNCT
ejpam-5563	216	14	w	w	PROPN
ejpam-5563	216	15	∈	∈	PROPN
ejpam-5563	216	16	τ√2	τ√2	PUNCT
ejpam-5563	217	1	⇐	⇐	ADJ
ejpam-5563	217	2	⇒	⇒	NOUN
ejpam-5563	217	3	√	√	VERB
ejpam-5563	217	4	2	2	NUM
ejpam-5563	217	5	∈	∈	NOUN
ejpam-5563	217	6	w	w	NOUN
ejpam-5563	217	7	or	or	CCONJ
ejpam-5563	217	8	w	w	NOUN
ejpam-5563	217	9	=	=	PUNCT
ejpam-5563	217	10	∅	∅	NOUN
ejpam-5563	217	11	,	,	PUNCT
ejpam-5563	217	12	l	l	NOUN
ejpam-5563	217	13	∈	∈	PROPN
ejpam-5563	218	1	p	p	X
ejpam-5563	218	2	⇐	⇐	ADJ
ejpam-5563	218	3	⇒	⇒	PROPN
ejpam-5563	218	4	lc	lc	PROPN
ejpam-5563	218	5	is	be	AUX
ejpam-5563	218	6	an	an	DET
ejpam-5563	218	7	infinite	infinite	ADJ
ejpam-5563	218	8	subset	subset	NOUN
ejpam-5563	218	9	of	of	ADP
ejpam-5563	218	10	r.	r.	PROPN
ejpam-5563	218	11	let	let	VERB
ejpam-5563	218	12	k	k	PROPN
ejpam-5563	218	13	⊆	⊆	NUM
ejpam-5563	218	14	r	r	NOUN
ejpam-5563	218	15	be	be	VERB
ejpam-5563	218	16	any	any	DET
ejpam-5563	218	17	set	set	NOUN
ejpam-5563	218	18	.	.	PUNCT
ejpam-5563	219	1	then	then	ADV
ejpam-5563	219	2	,	,	PUNCT
ejpam-5563	219	3	since	since	SCONJ
ejpam-5563	219	4	w	w	PROPN
ejpam-5563	219	5	=	=	NOUN
ejpam-5563	219	6	{	{	PUNCT
ejpam-5563	219	7	√	√	ADP
ejpam-5563	219	8	2	2	NUM
ejpam-5563	219	9	}	}	PUNCT
ejpam-5563	219	10	is	be	AUX
ejpam-5563	219	11	an	an	DET
ejpam-5563	219	12	open	open	ADJ
ejpam-5563	219	13	neighborhood	neighborhood	NOUN
ejpam-5563	219	14	of	of	ADP
ejpam-5563	219	15	√	√	NOUN
ejpam-5563	219	16	2	2	NUM
ejpam-5563	219	17	such	such	ADJ
ejpam-5563	219	18	that	that	PRON
ejpam-5563	219	19	w	w	PROPN
ejpam-5563	219	20	c	c	NOUN
ejpam-5563	219	21	/∈	/∈	PUNCT
ejpam-5563	220	1	p	p	NOUN
ejpam-5563	220	2	because	because	SCONJ
ejpam-5563	220	3	w	w	PROPN
ejpam-5563	220	4	is	be	AUX
ejpam-5563	220	5	finite	finite	ADJ
ejpam-5563	220	6	,	,	PUNCT
ejpam-5563	220	7	we	we	PRON
ejpam-5563	220	8	have	have	VERB
ejpam-5563	220	9	√	√	NUM
ejpam-5563	220	10	2	2	NUM
ejpam-5563	220	11	/∈	/∈	PUNCT
ejpam-5563	220	12	k⋄.	k⋄.	VERB
ejpam-5563	220	13	moreover	moreover	ADV
ejpam-5563	220	14	,	,	PUNCT
ejpam-5563	220	15	if	if	SCONJ
ejpam-5563	220	16	r	r	NOUN
ejpam-5563	220	17	is	be	AUX
ejpam-5563	220	18	any	any	DET
ejpam-5563	220	19	real	real	ADJ
ejpam-5563	220	20	number	number	NOUN
ejpam-5563	220	21	different	different	ADJ
ejpam-5563	220	22	from	from	ADP
ejpam-5563	220	23	√	√	PROPN
ejpam-5563	220	24	2	2	NUM
ejpam-5563	220	25	,	,	PUNCT
ejpam-5563	220	26	then	then	ADV
ejpam-5563	220	27	w	w	X
ejpam-5563	220	28	=	=	SYM
ejpam-5563	220	29	{	{	PUNCT
ejpam-5563	220	30	r	r	NOUN
ejpam-5563	220	31	,	,	PUNCT
ejpam-5563	220	32	√	√	NOUN
ejpam-5563	220	33	2	2	NUM
ejpam-5563	220	34	}	}	PUNCT
ejpam-5563	220	35	is	be	AUX
ejpam-5563	220	36	an	an	DET
ejpam-5563	220	37	open	open	ADJ
ejpam-5563	220	38	neighborhood	neighborhood	NOUN
ejpam-5563	220	39	of	of	ADP
ejpam-5563	220	40	r	r	NOUN
ejpam-5563	220	41	such	such	ADJ
ejpam-5563	220	42	that	that	DET
ejpam-5563	220	43	w	w	PROPN
ejpam-5563	220	44	c	c	PROPN
ejpam-5563	220	45	/∈	/∈	PUNCT
ejpam-5563	221	1	p.	p.	NOUN
ejpam-5563	221	2	hence	hence	ADV
ejpam-5563	221	3	,	,	PUNCT
ejpam-5563	221	4	r	r	NOUN
ejpam-5563	221	5	/∈	/∈	PUNCT
ejpam-5563	221	6	k⋄	k⋄	PROPN
ejpam-5563	221	7	which	which	PRON
ejpam-5563	221	8	implies	imply	VERB
ejpam-5563	221	9	that	that	DET
ejpam-5563	221	10	k⋄	k⋄	PROPN
ejpam-5563	221	11	=	=	PUNCT
ejpam-5563	221	12	∅.	∅.	ADP
ejpam-5563	221	13	thus	thus	ADV
ejpam-5563	221	14	,	,	PUNCT
ejpam-5563	221	15	γ∗(k	γ∗(k	NOUN
ejpam-5563	221	16	)	)	PUNCT
ejpam-5563	221	17	=	=	PUNCT
ejpam-5563	221	18	r.	r.	PROPN
ejpam-5563	221	19	therefore	therefore	ADV
ejpam-5563	221	20	,	,	PUNCT
ejpam-5563	221	21	λ(k	λ(k	PROPN
ejpam-5563	221	22	)	)	PUNCT
ejpam-5563	221	23	=	=	SYM
ejpam-5563	221	24	kc	kc	PROPN
ejpam-5563	221	25	.	.	PUNCT
ejpam-5563	221	26	theorem	theorem	PROPN
ejpam-5563	221	27	13	13	NUM
ejpam-5563	221	28	.	.	PUNCT
ejpam-5563	222	1	let	let	VERB
ejpam-5563	222	2	(	(	PUNCT
ejpam-5563	222	3	b	b	X
ejpam-5563	222	4	,	,	PUNCT
ejpam-5563	222	5	γ	γ	PROPN
ejpam-5563	222	6	,	,	PUNCT
ejpam-5563	222	7	p	p	NOUN
ejpam-5563	222	8	)	)	PUNCT
ejpam-5563	222	9	be	be	AUX
ejpam-5563	222	10	a	a	DET
ejpam-5563	222	11	ps	ps	NOUN
ejpam-5563	222	12	and	and	CCONJ
ejpam-5563	222	13	let	let	VERB
ejpam-5563	222	14	k	k	NOUN
ejpam-5563	222	15	,	,	PUNCT
ejpam-5563	222	16	o	o	PROPN
ejpam-5563	222	17	⊆	⊆	NUM
ejpam-5563	222	18	b.	b.	NOUN
ejpam-5563	222	19	the	the	DET
ejpam-5563	222	20	following	follow	VERB
ejpam-5563	222	21	properties	property	NOUN
ejpam-5563	222	22	hold	hold	VERB
ejpam-5563	222	23	:	:	PUNCT
ejpam-5563	222	24	(	(	PUNCT
ejpam-5563	222	25	i	i	NOUN
ejpam-5563	222	26	)	)	PUNCT
ejpam-5563	222	27	λ(∅	λ(∅	PROPN
ejpam-5563	222	28	)	)	PUNCT
ejpam-5563	223	1	=	=	PUNCT
ejpam-5563	224	1	[	[	X
ejpam-5563	224	2	γ(b)]c	γ(b)]c	NOUN
ejpam-5563	224	3	.	.	PUNCT
ejpam-5563	224	4	(	(	PUNCT
ejpam-5563	224	5	ii	ii	NOUN
ejpam-5563	224	6	)	)	PUNCT
ejpam-5563	224	7	λ(b	λ(b	PROPN
ejpam-5563	224	8	)	)	PUNCT
ejpam-5563	224	9	=	=	PUNCT
ejpam-5563	224	10	∅.	∅.	PRON
ejpam-5563	224	11	(	(	PUNCT
ejpam-5563	224	12	iii	iii	NOUN
ejpam-5563	224	13	)	)	PUNCT
ejpam-5563	224	14	if	if	SCONJ
ejpam-5563	224	15	γ−	γ−	PROPN
ejpam-5563	224	16	{	{	PUNCT
ejpam-5563	224	17	b	b	NOUN
ejpam-5563	224	18	}	}	PUNCT
ejpam-5563	224	19	⊆	⊆	NUM
ejpam-5563	224	20	p	p	NOUN
ejpam-5563	224	21	with	with	ADP
ejpam-5563	224	22	△	△	NOUN
ejpam-5563	224	23	=	=	SYM
ejpam-5563	224	24	{	{	PUNCT
ejpam-5563	224	25	∅	∅	NOUN
ejpam-5563	224	26	}	}	PUNCT
ejpam-5563	224	27	and	and	CCONJ
ejpam-5563	224	28	kc	kc	PROPN
ejpam-5563	224	29	/∈	/∈	PUNCT
ejpam-5563	225	1	p	p	X
ejpam-5563	225	2	,	,	PUNCT
ejpam-5563	225	3	then	then	ADV
ejpam-5563	225	4	λ(k	λ(k	ADJ
ejpam-5563	225	5	)	)	PUNCT
ejpam-5563	225	6	=	=	SYM
ejpam-5563	225	7	∅.	∅.	X
ejpam-5563	225	8	(	(	PUNCT
ejpam-5563	225	9	iv	iv	X
ejpam-5563	225	10	)	)	PUNCT
ejpam-5563	225	11	λ(k	λ(k	PROPN
ejpam-5563	225	12	)	)	PUNCT
ejpam-5563	225	13	=	=	SYM
ejpam-5563	225	14	kc	kc	PROPN
ejpam-5563	225	15	−	−	PROPN
ejpam-5563	225	16	γ(kc	γ(kc	PROPN
ejpam-5563	225	17	)	)	PUNCT
ejpam-5563	225	18	.	.	PUNCT
ejpam-5563	226	1	(	(	PUNCT
ejpam-5563	226	2	v	v	NOUN
ejpam-5563	226	3	)	)	PUNCT
ejpam-5563	226	4	λ(k	λ(k	ADJ
ejpam-5563	226	5	)	)	PUNCT
ejpam-5563	227	1	∩	∩	NOUN
ejpam-5563	227	2	λ(o	λ(o	NOUN
ejpam-5563	227	3	)	)	PUNCT
ejpam-5563	227	4	⊆	⊆	NUM
ejpam-5563	227	5	λ(k	λ(k	NOUN
ejpam-5563	227	6	∪o	∪o	NUM
ejpam-5563	227	7	)	)	PUNCT
ejpam-5563	227	8	.	.	PUNCT
ejpam-5563	228	1	o.	o.	PROPN
ejpam-5563	228	2	alghamdi	alghamdi	PROPN
ejpam-5563	228	3	/	/	SYM
ejpam-5563	228	4	eur	eur	PROPN
ejpam-5563	228	5	.	.	PUNCT
ejpam-5563	229	1	j.	j.	PROPN
ejpam-5563	229	2	pure	pure	PROPN
ejpam-5563	229	3	appl	appl	PROPN
ejpam-5563	229	4	.	.	PROPN
ejpam-5563	229	5	math	math	PROPN
ejpam-5563	229	6	,	,	PUNCT
ejpam-5563	229	7	17	17	NUM
ejpam-5563	229	8	(	(	PUNCT
ejpam-5563	229	9	4	4	NUM
ejpam-5563	229	10	)	)	PUNCT
ejpam-5563	229	11	(	(	PUNCT
ejpam-5563	229	12	2024	2024	NUM
ejpam-5563	229	13	)	)	PUNCT
ejpam-5563	229	14	,	,	PUNCT
ejpam-5563	229	15	3517	3517	NUM
ejpam-5563	229	16	-	-	SYM
ejpam-5563	229	17	3538	3538	NUM
ejpam-5563	229	18	3523	3523	NUM
ejpam-5563	229	19	(	(	PUNCT
ejpam-5563	229	20	vi	vi	NOUN
ejpam-5563	229	21	)	)	PUNCT
ejpam-5563	229	22	λ(k	λ(k	ADJ
ejpam-5563	229	23	∩o	∩o	NOUN
ejpam-5563	229	24	)	)	PUNCT
ejpam-5563	229	25	=	=	SYM
ejpam-5563	229	26	(	(	PUNCT
ejpam-5563	229	27	λ(k	λ(k	ADJ
ejpam-5563	229	28	)	)	PUNCT
ejpam-5563	229	29	∩	∩	ADJ
ejpam-5563	229	30	γ∗(o	γ∗(o	PROPN
ejpam-5563	229	31	)	)	PUNCT
ejpam-5563	229	32	)	)	PUNCT
ejpam-5563	230	1	∪	∪	ADP
ejpam-5563	230	2	(	(	PUNCT
ejpam-5563	230	3	λ(o	λ(o	PROPN
ejpam-5563	230	4	)	)	PUNCT
ejpam-5563	230	5	∩	∩	ADJ
ejpam-5563	230	6	γ∗(k	γ∗(k	NOUN
ejpam-5563	230	7	)	)	PUNCT
ejpam-5563	230	8	)	)	PUNCT
ejpam-5563	231	1	⊆	⊆	NUM
ejpam-5563	231	2	λ(k	λ(k	NOUN
ejpam-5563	231	3	)	)	PUNCT
ejpam-5563	231	4	∪	∪	ADP
ejpam-5563	231	5	λ(o	λ(o	PROPN
ejpam-5563	231	6	)	)	PUNCT
ejpam-5563	231	7	.	.	PUNCT
ejpam-5563	232	1	(	(	PUNCT
ejpam-5563	232	2	vii	vii	PROPN
ejpam-5563	232	3	)	)	PUNCT
ejpam-5563	232	4	λ(λ(k	λ(λ(k	NOUN
ejpam-5563	232	5	)	)	PUNCT
ejpam-5563	232	6	)	)	PUNCT
ejpam-5563	233	1	⊆	⊆	NUM
ejpam-5563	233	2	λ(γ∗(k	λ(γ∗(k	NUM
ejpam-5563	233	3	)	)	PUNCT
ejpam-5563	233	4	)	)	PUNCT
ejpam-5563	233	5	∪	∪	ADP
ejpam-5563	233	6	γ∗(γ∗(k	γ∗(γ∗(k	NOUN
ejpam-5563	233	7	)	)	PUNCT
ejpam-5563	233	8	)	)	PUNCT
ejpam-5563	233	9	.	.	PUNCT
ejpam-5563	234	1	(	(	PUNCT
ejpam-5563	234	2	viii	viii	NOUN
ejpam-5563	234	3	)	)	PUNCT
ejpam-5563	234	4	γ(λ(k	γ(λ(k	NOUN
ejpam-5563	234	5	)	)	PUNCT
ejpam-5563	234	6	)	)	PUNCT
ejpam-5563	235	1	⊆	⊆	NUM
ejpam-5563	235	2	γ(γ∗(k	γ(γ∗(k	NOUN
ejpam-5563	235	3	)	)	PUNCT
ejpam-5563	235	4	)	)	PUNCT
ejpam-5563	235	5	.	.	PUNCT
ejpam-5563	236	1	(	(	PUNCT
ejpam-5563	236	2	ix	ix	ADJ
ejpam-5563	236	3	)	)	PUNCT
ejpam-5563	236	4	λ(k	λ(k	ADJ
ejpam-5563	236	5	)	)	PUNCT
ejpam-5563	236	6	∩	∩	NOUN
ejpam-5563	236	7	k	k	NOUN
ejpam-5563	236	8	=	=	PUNCT
ejpam-5563	236	9	∅	∅	NOUN
ejpam-5563	236	10	;	;	PUNCT
ejpam-5563	236	11	thus	thus	ADV
ejpam-5563	236	12	λ(k	λ(k	X
ejpam-5563	236	13	)	)	PUNCT
ejpam-5563	236	14	⊆	⊆	NUM
ejpam-5563	236	15	kc	kc	PROPN
ejpam-5563	236	16	.	.	PUNCT
ejpam-5563	237	1	(	(	PUNCT
ejpam-5563	237	2	x	x	X
ejpam-5563	237	3	)	)	PUNCT
ejpam-5563	237	4	λ(k	λ(k	ADJ
ejpam-5563	237	5	)	)	PUNCT
ejpam-5563	237	6	∪	∪	ADP
ejpam-5563	237	7	λ(o	λ(o	NOUN
ejpam-5563	237	8	)	)	PUNCT
ejpam-5563	238	1	⊆	⊆	NUM
ejpam-5563	238	2	(	(	PUNCT
ejpam-5563	238	3	k	k	X
ejpam-5563	238	4	∩	∩	NOUN
ejpam-5563	238	5	λ(o	λ(o	NOUN
ejpam-5563	238	6	)	)	PUNCT
ejpam-5563	238	7	)	)	PUNCT
ejpam-5563	238	8	∪	∪	ADP
ejpam-5563	238	9	(	(	PUNCT
ejpam-5563	238	10	λ(k	λ(k	ADJ
ejpam-5563	238	11	)	)	PUNCT
ejpam-5563	238	12	∩	∩	ADJ
ejpam-5563	238	13	o	o	NOUN
ejpam-5563	238	14	)	)	PUNCT
ejpam-5563	238	15	∪	∪	ADP
ejpam-5563	238	16	λ(k	λ(k	PROPN
ejpam-5563	238	17	∪o	∪o	NUM
ejpam-5563	238	18	)	)	PUNCT
ejpam-5563	238	19	.	.	PUNCT
ejpam-5563	239	1	proof	proof	NOUN
ejpam-5563	239	2	.	.	PUNCT
ejpam-5563	240	1	(	(	PUNCT
ejpam-5563	240	2	i	i	NOUN
ejpam-5563	240	3	)	)	PUNCT
ejpam-5563	240	4	λ(∅	λ(∅	PROPN
ejpam-5563	240	5	)	)	PUNCT
ejpam-5563	241	1	=	=	PRON
ejpam-5563	241	2	γ∗(∅)−	γ∗(∅)−	ADP
ejpam-5563	241	3	∅	∅	NOUN
ejpam-5563	241	4	=	=	PUNCT
ejpam-5563	242	1	[	[	X
ejpam-5563	242	2	γ(∅c)]c	γ(∅c)]c	X
ejpam-5563	242	3	=	=	PUNCT
ejpam-5563	243	1	[	[	X
ejpam-5563	243	2	γ(b)]c	γ(b)]c	ADP
ejpam-5563	243	3	by	by	ADP
ejpam-5563	243	4	using	use	VERB
ejpam-5563	243	5	(	(	PUNCT
ejpam-5563	243	6	i	i	NOUN
ejpam-5563	243	7	)	)	PUNCT
ejpam-5563	243	8	in	in	ADP
ejpam-5563	243	9	theorem	theorem	NOUN
ejpam-5563	243	10	2	2	NUM
ejpam-5563	243	11	.	.	PUNCT
ejpam-5563	243	12	(	(	PUNCT
ejpam-5563	243	13	ii	ii	NOUN
ejpam-5563	243	14	)	)	PUNCT
ejpam-5563	243	15	λ(b	λ(b	PROPN
ejpam-5563	243	16	)	)	PUNCT
ejpam-5563	243	17	=	=	PUNCT
ejpam-5563	244	1	γ∗(b)−	γ∗(b)−	PROPN
ejpam-5563	244	2	b	b	NOUN
ejpam-5563	245	1	=	=	PUNCT
ejpam-5563	246	1	[	[	X
ejpam-5563	246	2	γ(bc)]c	γ(bc)]c	PROPN
ejpam-5563	246	3	−	−	PROPN
ejpam-5563	246	4	b	b	NOUN
ejpam-5563	246	5	=	=	NOUN
ejpam-5563	246	6	∅	∅	NOUN
ejpam-5563	246	7	since	since	SCONJ
ejpam-5563	246	8	γ(∅	γ(∅	PROPN
ejpam-5563	246	9	)	)	PUNCT
ejpam-5563	246	10	=	=	PUNCT
ejpam-5563	246	11	∅.	∅.	PRON
ejpam-5563	246	12	(	(	PUNCT
ejpam-5563	246	13	iii	iii	NOUN
ejpam-5563	246	14	)	)	PUNCT
ejpam-5563	246	15	λ(k	λ(k	ADJ
ejpam-5563	246	16	)	)	PUNCT
ejpam-5563	246	17	=	=	SYM
ejpam-5563	247	1	γ∗(k)−k	γ∗(k)−k	PROPN
ejpam-5563	247	2	=	=	PUNCT
ejpam-5563	248	1	[	[	X
ejpam-5563	248	2	γ(kc)]c	γ(kc)]c	PROPN
ejpam-5563	248	3	−k	−k	VERB
ejpam-5563	248	4	.	.	PUNCT
ejpam-5563	249	1	since	since	SCONJ
ejpam-5563	249	2	kc	kc	PROPN
ejpam-5563	249	3	/∈	/∈	PROPN
ejpam-5563	250	1	p	p	X
ejpam-5563	250	2	,	,	PUNCT
ejpam-5563	250	3	then	then	ADV
ejpam-5563	250	4	γ(k	γ(k	PROPN
ejpam-5563	250	5	)	)	PUNCT
ejpam-5563	251	1	=	=	PUNCT
ejpam-5563	251	2	∅	∅	NOUN
ejpam-5563	251	3	by	by	ADP
ejpam-5563	251	4	(	(	PUNCT
ejpam-5563	251	5	vi	vi	NOUN
ejpam-5563	251	6	)	)	PUNCT
ejpam-5563	251	7	in	in	ADP
ejpam-5563	251	8	theorem	theorem	NOUN
ejpam-5563	251	9	1	1	NUM
ejpam-5563	251	10	.	.	PUNCT
ejpam-5563	251	11	by	by	ADP
ejpam-5563	251	12	using	use	VERB
ejpam-5563	251	13	theorem	theorem	ADJ
ejpam-5563	251	14	3	3	NUM
ejpam-5563	251	15	and	and	CCONJ
ejpam-5563	251	16	(	(	PUNCT
ejpam-5563	251	17	vii	vii	PROPN
ejpam-5563	251	18	)	)	PUNCT
ejpam-5563	251	19	in	in	ADP
ejpam-5563	251	20	theorem	theorem	NOUN
ejpam-5563	251	21	1	1	NUM
ejpam-5563	251	22	,	,	PUNCT
ejpam-5563	251	23	we	we	PRON
ejpam-5563	251	24	have	have	VERB
ejpam-5563	251	25	:	:	PUNCT
ejpam-5563	251	26	b	b	X
ejpam-5563	251	27	=	=	PUNCT
ejpam-5563	251	28	γ(b	γ(b	X
ejpam-5563	251	29	)	)	PUNCT
ejpam-5563	251	30	=	=	PUNCT
ejpam-5563	252	1	γ(k	γ(k	VERB
ejpam-5563	252	2	∪	∪	ADJ
ejpam-5563	252	3	kc	kc	PROPN
ejpam-5563	252	4	)	)	PUNCT
ejpam-5563	252	5	=	=	SYM
ejpam-5563	252	6	γ(k	γ(k	PROPN
ejpam-5563	252	7	)	)	PUNCT
ejpam-5563	252	8	∪	∪	X
ejpam-5563	252	9	γ(kc	γ(kc	PROPN
ejpam-5563	252	10	)	)	PUNCT
ejpam-5563	252	11	=	=	SYM
ejpam-5563	252	12	γ(kc	γ(kc	PROPN
ejpam-5563	252	13	)	)	PUNCT
ejpam-5563	252	14	.	.	PUNCT
ejpam-5563	253	1	then	then	ADV
ejpam-5563	253	2	,	,	PUNCT
ejpam-5563	253	3	λ(k	λ(k	PROPN
ejpam-5563	253	4	)	)	PUNCT
ejpam-5563	253	5	=	=	SYM
ejpam-5563	253	6	∅.	∅.	X
ejpam-5563	253	7	(	(	PUNCT
ejpam-5563	253	8	iv	iv	X
ejpam-5563	253	9	)	)	PUNCT
ejpam-5563	253	10	λ(k	λ(k	PROPN
ejpam-5563	253	11	)	)	PUNCT
ejpam-5563	254	1	=	=	SYM
ejpam-5563	254	2	γ∗(k)−k	γ∗(k)−k	PROPN
ejpam-5563	255	1	=	=	PUNCT
ejpam-5563	255	2	[	[	PUNCT
ejpam-5563	255	3	γ(kc)]c	γ(kc)]c	PROPN
ejpam-5563	255	4	∩	∩	ADJ
ejpam-5563	255	5	kc	kc	PROPN
ejpam-5563	255	6	=	=	PROPN
ejpam-5563	255	7	kc	kc	PROPN
ejpam-5563	255	8	−	−	PROPN
ejpam-5563	255	9	γ(kc	γ(kc	PROPN
ejpam-5563	255	10	)	)	PUNCT
ejpam-5563	255	11	.	.	PUNCT
ejpam-5563	256	1	(	(	PUNCT
ejpam-5563	256	2	v	v	X
ejpam-5563	256	3	)	)	PUNCT
ejpam-5563	256	4	r	r	NOUN
ejpam-5563	256	5	∈	∈	PROPN
ejpam-5563	256	6	λ(k	λ(k	NOUN
ejpam-5563	256	7	)	)	PUNCT
ejpam-5563	256	8	∩	∩	NOUN
ejpam-5563	256	9	λ(o	λ(o	NOUN
ejpam-5563	256	10	)	)	PUNCT
ejpam-5563	256	11	⇐	⇐	ADJ
ejpam-5563	256	12	⇒r	⇒r	NOUN
ejpam-5563	256	13	∈	∈	PROPN
ejpam-5563	256	14	λ(k	λ(k	PROPN
ejpam-5563	256	15	)	)	PUNCT
ejpam-5563	256	16	and	and	CCONJ
ejpam-5563	256	17	r	r	NOUN
ejpam-5563	256	18	∈	∈	PROPN
ejpam-5563	256	19	λ(o	λ(o	PROPN
ejpam-5563	256	20	)	)	PUNCT
ejpam-5563	256	21	⇐	⇐	ADJ
ejpam-5563	256	22	⇒r	⇒r	NOUN
ejpam-5563	256	23	∈	∈	PROPN
ejpam-5563	256	24	γ∗(k	γ∗(k	PROPN
ejpam-5563	256	25	)	)	PUNCT
ejpam-5563	256	26	∩	∩	NOUN
ejpam-5563	256	27	γ∗(o	γ∗(o	PROPN
ejpam-5563	256	28	)	)	PUNCT
ejpam-5563	256	29	and	and	CCONJ
ejpam-5563	256	30	r	r	NOUN
ejpam-5563	256	31	/∈	/∈	PUNCT
ejpam-5563	257	1	k	k	NOUN
ejpam-5563	257	2	∪	∪	ADP
ejpam-5563	257	3	o	o	PROPN
ejpam-5563	257	4	⇐	⇐	ADJ
ejpam-5563	257	5	⇒r	⇒r	ADJ
ejpam-5563	257	6	∈	∈	PROPN
ejpam-5563	257	7	γ∗(k	γ∗(k	NOUN
ejpam-5563	257	8	∩o	∩o	NOUN
ejpam-5563	257	9	)	)	PUNCT
ejpam-5563	257	10	and	and	CCONJ
ejpam-5563	257	11	r	r	NOUN
ejpam-5563	257	12	/∈	/∈	PUNCT
ejpam-5563	258	1	k	k	NOUN
ejpam-5563	258	2	∪	∪	ADP
ejpam-5563	258	3	o	o	NOUN
ejpam-5563	258	4	using	use	VERB
ejpam-5563	258	5	(	(	PUNCT
ejpam-5563	258	6	iv	iv	X
ejpam-5563	258	7	)	)	PUNCT
ejpam-5563	258	8	in	in	ADP
ejpam-5563	258	9	theorem	theorem	ADJ
ejpam-5563	258	10	2	2	NUM
ejpam-5563	258	11	⇐	⇐	ADJ
ejpam-5563	258	12	⇒r	⇒r	NOUN
ejpam-5563	258	13	∈	∈	PROPN
ejpam-5563	258	14	γ∗(k	γ∗(k	NOUN
ejpam-5563	258	15	∪o	∪o	ADV
ejpam-5563	258	16	)	)	PUNCT
ejpam-5563	258	17	and	and	CCONJ
ejpam-5563	258	18	r	r	NOUN
ejpam-5563	258	19	/∈	/∈	PUNCT
ejpam-5563	259	1	k	k	NOUN
ejpam-5563	259	2	∪	∪	ADP
ejpam-5563	259	3	o	o	NOUN
ejpam-5563	259	4	by	by	ADP
ejpam-5563	259	5	(	(	PUNCT
ejpam-5563	259	6	iii	iii	NOUN
ejpam-5563	259	7	)	)	PUNCT
ejpam-5563	259	8	in	in	ADP
ejpam-5563	259	9	theorem	theorem	ADJ
ejpam-5563	259	10	2	2	NUM
ejpam-5563	259	11	⇐	⇐	ADJ
ejpam-5563	259	12	⇒r	⇒r	NOUN
ejpam-5563	259	13	∈	∈	PROPN
ejpam-5563	259	14	γ∗(k	γ∗(k	NOUN
ejpam-5563	259	15	∪o)−	∪o)−	NOUN
ejpam-5563	259	16	(	(	PUNCT
ejpam-5563	259	17	k	k	NOUN
ejpam-5563	259	18	∪o	∪o	ADP
ejpam-5563	259	19	)	)	PUNCT
ejpam-5563	260	1	=	=	PUNCT
ejpam-5563	261	1	λ(k	λ(k	X
ejpam-5563	261	2	∪o	∪o	NUM
ejpam-5563	261	3	)	)	PUNCT
ejpam-5563	261	4	.	.	PUNCT
ejpam-5563	262	1	(	(	PUNCT
ejpam-5563	262	2	vi	vi	X
ejpam-5563	262	3	)	)	PUNCT
ejpam-5563	262	4	by	by	ADP
ejpam-5563	262	5	item	item	NOUN
ejpam-5563	262	6	(	(	PUNCT
ejpam-5563	262	7	iv	iv	NOUN
ejpam-5563	262	8	)	)	PUNCT
ejpam-5563	262	9	of	of	ADP
ejpam-5563	262	10	theorem	theorem	NOUN
ejpam-5563	262	11	2	2	NUM
ejpam-5563	262	12	,	,	PUNCT
ejpam-5563	262	13	we	we	PRON
ejpam-5563	262	14	have	have	VERB
ejpam-5563	262	15	r	r	NOUN
ejpam-5563	262	16	∈	∈	PROPN
ejpam-5563	263	1	λ(k	λ(k	PROPN
ejpam-5563	263	2	∩o	∩o	NOUN
ejpam-5563	263	3	)	)	PUNCT
ejpam-5563	263	4	⇐	⇐	ADJ
ejpam-5563	263	5	⇒r	⇒r	NOUN
ejpam-5563	263	6	∈	∈	PROPN
ejpam-5563	263	7	γ∗(k	γ∗(k	NOUN
ejpam-5563	263	8	∩o	∩o	NOUN
ejpam-5563	263	9	)	)	PUNCT
ejpam-5563	263	10	and	and	CCONJ
ejpam-5563	263	11	r	r	NOUN
ejpam-5563	263	12	/∈	/∈	PUNCT
ejpam-5563	264	1	(	(	PUNCT
ejpam-5563	264	2	k	k	PROPN
ejpam-5563	264	3	∩o	∩o	PROPN
ejpam-5563	264	4	)	)	PUNCT
ejpam-5563	265	1	⇐	⇐	ADJ
ejpam-5563	265	2	⇒r	⇒r	NOUN
ejpam-5563	265	3	∈	∈	PROPN
ejpam-5563	266	1	[	[	X
ejpam-5563	266	2	γ∗(k	γ∗(k	NOUN
ejpam-5563	266	3	)	)	PUNCT
ejpam-5563	266	4	∩	∩	NOUN
ejpam-5563	266	5	γ∗(o	γ∗(o	PROPN
ejpam-5563	266	6	)	)	PUNCT
ejpam-5563	266	7	]	]	PUNCT
ejpam-5563	266	8	and	and	CCONJ
ejpam-5563	266	9	r	r	NOUN
ejpam-5563	266	10	/∈	/∈	PUNCT
ejpam-5563	267	1	k	k	NOUN
ejpam-5563	267	2	or	or	CCONJ
ejpam-5563	267	3	r	r	NOUN
ejpam-5563	267	4	/∈	/∈	PUNCT
ejpam-5563	268	1	o.	o.	PROPN
ejpam-5563	268	2	suppose	suppose	VERB
ejpam-5563	268	3	that	that	SCONJ
ejpam-5563	268	4	r	r	NOUN
ejpam-5563	268	5	/∈	/∈	PUNCT
ejpam-5563	269	1	k.	k.	PROPN
ejpam-5563	270	1	then	then	ADV
ejpam-5563	270	2	,	,	PUNCT
ejpam-5563	270	3	r	r	NOUN
ejpam-5563	270	4	∈	∈	PROPN
ejpam-5563	270	5	[	[	X
ejpam-5563	270	6	γ∗(k	γ∗(k	NOUN
ejpam-5563	270	7	)	)	PUNCT
ejpam-5563	270	8	∩	∩	NOUN
ejpam-5563	270	9	γ∗(o	γ∗(o	PROPN
ejpam-5563	270	10	)	)	PUNCT
ejpam-5563	270	11	]	]	PUNCT
ejpam-5563	270	12	and	and	CCONJ
ejpam-5563	270	13	r	r	NOUN
ejpam-5563	270	14	/∈	/∈	PUNCT
ejpam-5563	270	15	k	k	X
ejpam-5563	271	1	=	=	NOUN
ejpam-5563	271	2	⇒r	⇒r	NOUN
ejpam-5563	271	3	∈	∈	PROPN
ejpam-5563	271	4	λ(k	λ(k	PROPN
ejpam-5563	271	5	)	)	PUNCT
ejpam-5563	271	6	∩	∩	NOUN
ejpam-5563	271	7	γ∗(o	γ∗(o	PROPN
ejpam-5563	271	8	)	)	PUNCT
ejpam-5563	271	9	.	.	PUNCT
ejpam-5563	272	1	now	now	ADV
ejpam-5563	272	2	,	,	PUNCT
ejpam-5563	272	3	suppose	suppose	VERB
ejpam-5563	272	4	that	that	SCONJ
ejpam-5563	272	5	r	r	NOUN
ejpam-5563	272	6	/∈	/∈	PUNCT
ejpam-5563	273	1	o.	o.	INTJ
ejpam-5563	273	2	then	then	ADV
ejpam-5563	273	3	,	,	PUNCT
ejpam-5563	273	4	r	r	NOUN
ejpam-5563	273	5	∈	∈	PROPN
ejpam-5563	273	6	[	[	X
ejpam-5563	273	7	γ∗(k	γ∗(k	NOUN
ejpam-5563	273	8	)	)	PUNCT
ejpam-5563	273	9	∩	∩	NOUN
ejpam-5563	273	10	γ∗(o	γ∗(o	PROPN
ejpam-5563	273	11	)	)	PUNCT
ejpam-5563	273	12	]	]	PUNCT
ejpam-5563	273	13	and	and	CCONJ
ejpam-5563	273	14	r	r	NOUN
ejpam-5563	273	15	/∈	/∈	NOUN
ejpam-5563	273	16	o	o	NOUN
ejpam-5563	274	1	=	=	NOUN
ejpam-5563	274	2	⇒r	⇒r	NOUN
ejpam-5563	274	3	∈	∈	PROPN
ejpam-5563	274	4	λ(o	λ(o	PROPN
ejpam-5563	274	5	)	)	PUNCT
ejpam-5563	274	6	∩	∩	ADJ
ejpam-5563	274	7	γ∗(k	γ∗(k	NOUN
ejpam-5563	274	8	)	)	PUNCT
ejpam-5563	275	1	=	=	NOUN
ejpam-5563	275	2	⇒r	⇒r	PRON
ejpam-5563	275	3	∈	∈	PROPN
ejpam-5563	276	1	[	[	X
ejpam-5563	276	2	λ(k	λ(k	X
ejpam-5563	276	3	)	)	PUNCT
ejpam-5563	276	4	∩	∩	NOUN
ejpam-5563	276	5	γ∗(o	γ∗(o	PROPN
ejpam-5563	276	6	)	)	PUNCT
ejpam-5563	276	7	]	]	PUNCT
ejpam-5563	276	8	∪	∪	ADP
ejpam-5563	276	9	[	[	X
ejpam-5563	276	10	λ(o	λ(o	X
ejpam-5563	276	11	)	)	PUNCT
ejpam-5563	276	12	∩	∩	ADJ
ejpam-5563	276	13	γ∗(k	γ∗(k	NOUN
ejpam-5563	276	14	)	)	PUNCT
ejpam-5563	276	15	]	]	PUNCT
ejpam-5563	277	1	⊆	⊆	NUM
ejpam-5563	277	2	λ(k	λ(k	NOUN
ejpam-5563	277	3	)	)	PUNCT
ejpam-5563	277	4	∪	∪	ADP
ejpam-5563	277	5	λ(o	λ(o	PROPN
ejpam-5563	277	6	)	)	PUNCT
ejpam-5563	277	7	.	.	PUNCT
ejpam-5563	278	1	o.	o.	PROPN
ejpam-5563	278	2	alghamdi	alghamdi	PROPN
ejpam-5563	278	3	/	/	SYM
ejpam-5563	278	4	eur	eur	PROPN
ejpam-5563	278	5	.	.	PUNCT
ejpam-5563	279	1	j.	j.	PROPN
ejpam-5563	279	2	pure	pure	PROPN
ejpam-5563	279	3	appl	appl	PROPN
ejpam-5563	279	4	.	.	PROPN
ejpam-5563	279	5	math	math	PROPN
ejpam-5563	279	6	,	,	PUNCT
ejpam-5563	279	7	17	17	NUM
ejpam-5563	279	8	(	(	PUNCT
ejpam-5563	279	9	4	4	NUM
ejpam-5563	279	10	)	)	PUNCT
ejpam-5563	279	11	(	(	PUNCT
ejpam-5563	279	12	2024	2024	NUM
ejpam-5563	279	13	)	)	PUNCT
ejpam-5563	279	14	,	,	PUNCT
ejpam-5563	279	15	3517	3517	NUM
ejpam-5563	279	16	-	-	SYM
ejpam-5563	279	17	3538	3538	NUM
ejpam-5563	279	18	3524	3524	NUM
ejpam-5563	279	19	(	(	PUNCT
ejpam-5563	279	20	vii	vii	PROPN
ejpam-5563	279	21	)	)	PUNCT
ejpam-5563	279	22	λ(λ(k	λ(λ(k	NOUN
ejpam-5563	279	23	)	)	PUNCT
ejpam-5563	279	24	)	)	PUNCT
ejpam-5563	280	1	=	=	NOUN
ejpam-5563	280	2	γ∗(λ(k))−	γ∗(λ(k))−	NOUN
ejpam-5563	280	3	λ(k	λ(k	X
ejpam-5563	280	4	)	)	PUNCT
ejpam-5563	281	1	=	=	X
ejpam-5563	281	2	γ∗(γ∗(k)−k)−	γ∗(γ∗(k)−k)−	PROPN
ejpam-5563	281	3	[	[	X
ejpam-5563	281	4	γ∗(k)−k	γ∗(k)−k	PROPN
ejpam-5563	281	5	]	]	X
ejpam-5563	281	6	=	=	SYM
ejpam-5563	281	7	γ∗[γ∗(k	γ∗[γ∗(k	NOUN
ejpam-5563	281	8	)	)	PUNCT
ejpam-5563	281	9	∩	∩	NOUN
ejpam-5563	281	10	kc]−	kc]−	X
ejpam-5563	282	1	[	[	X
ejpam-5563	282	2	γ∗(k	γ∗(k	NOUN
ejpam-5563	282	3	)	)	PUNCT
ejpam-5563	282	4	∩	∩	NOUN
ejpam-5563	282	5	kc	kc	X
ejpam-5563	282	6	]	]	X
ejpam-5563	282	7	=	=	NOUN
ejpam-5563	282	8	γ∗(γ∗(k	γ∗(γ∗(k	NOUN
ejpam-5563	282	9	)	)	PUNCT
ejpam-5563	282	10	)	)	PUNCT
ejpam-5563	283	1	∩	∩	ADJ
ejpam-5563	283	2	γ∗(kc	γ∗(kc	NOUN
ejpam-5563	283	3	)	)	PUNCT
ejpam-5563	283	4	∩	∩	NOUN
ejpam-5563	284	1	[	[	X
ejpam-5563	284	2	γ∗(k	γ∗(k	NOUN
ejpam-5563	284	3	)	)	PUNCT
ejpam-5563	284	4	∩	∩	NOUN
ejpam-5563	284	5	kc]c	kc]c	NOUN
ejpam-5563	284	6	=	=	NOUN
ejpam-5563	284	7	γ∗(γ∗(k	γ∗(γ∗(k	NOUN
ejpam-5563	284	8	)	)	PUNCT
ejpam-5563	284	9	)	)	PUNCT
ejpam-5563	284	10	∩	∩	ADJ
ejpam-5563	284	11	γ∗(kc	γ∗(kc	NOUN
ejpam-5563	284	12	)	)	PUNCT
ejpam-5563	284	13	∩	∩	NOUN
ejpam-5563	284	14	[	[	X
ejpam-5563	284	15	(	(	PUNCT
ejpam-5563	284	16	γ∗(k))c	γ∗(k))c	PROPN
ejpam-5563	284	17	∪	∪	VERB
ejpam-5563	284	18	k	k	X
ejpam-5563	284	19	]	]	X
ejpam-5563	284	20	⊆γ∗(γ∗(k	⊆γ∗(γ∗(k	NUM
ejpam-5563	284	21	)	)	PUNCT
ejpam-5563	284	22	)	)	PUNCT
ejpam-5563	284	23	∩	∩	NOUN
ejpam-5563	285	1	[	[	X
ejpam-5563	285	2	(	(	PUNCT
ejpam-5563	285	3	γ∗(k))c	γ∗(k))c	PROPN
ejpam-5563	285	4	∪	∪	VERB
ejpam-5563	285	5	k	k	X
ejpam-5563	285	6	]	]	X
ejpam-5563	285	7	=	=	NOUN
ejpam-5563	285	8	[	[	X
ejpam-5563	285	9	γ∗(γ∗(k	γ∗(γ∗(k	NOUN
ejpam-5563	285	10	)	)	PUNCT
ejpam-5563	285	11	)	)	PUNCT
ejpam-5563	285	12	∩	∩	NOUN
ejpam-5563	285	13	(	(	PUNCT
ejpam-5563	285	14	γ∗(k))c	γ∗(k))c	PROPN
ejpam-5563	285	15	]	]	PUNCT
ejpam-5563	285	16	∪	∪	ADP
ejpam-5563	285	17	[	[	X
ejpam-5563	285	18	γ∗(γ∗(k	γ∗(γ∗(k	NOUN
ejpam-5563	285	19	)	)	PUNCT
ejpam-5563	285	20	)	)	PUNCT
ejpam-5563	285	21	∩	∩	NOUN
ejpam-5563	286	1	k	k	X
ejpam-5563	286	2	]	]	X
ejpam-5563	286	3	=	=	NOUN
ejpam-5563	286	4	[	[	X
ejpam-5563	286	5	γ∗(γ∗(k))−	γ∗(γ∗(k))−	PROPN
ejpam-5563	286	6	γ∗(k	γ∗(k	NOUN
ejpam-5563	286	7	)	)	PUNCT
ejpam-5563	286	8	]	]	PUNCT
ejpam-5563	286	9	∪	∪	ADP
ejpam-5563	286	10	[	[	X
ejpam-5563	286	11	γ∗(γ∗(k	γ∗(γ∗(k	NOUN
ejpam-5563	286	12	)	)	PUNCT
ejpam-5563	286	13	)	)	PUNCT
ejpam-5563	287	1	∩	∩	X
ejpam-5563	287	2	k	k	X
ejpam-5563	287	3	]	]	X
ejpam-5563	287	4	⊆λ(γ∗(k	⊆λ(γ∗(k	NOUN
ejpam-5563	287	5	)	)	PUNCT
ejpam-5563	287	6	)	)	PUNCT
ejpam-5563	287	7	∪	∪	ADP
ejpam-5563	287	8	γ∗(γ∗(k	γ∗(γ∗(k	NOUN
ejpam-5563	287	9	)	)	PUNCT
ejpam-5563	287	10	)	)	PUNCT
ejpam-5563	287	11	.	.	PUNCT
ejpam-5563	288	1	(	(	PUNCT
ejpam-5563	288	2	viii	viii	NOUN
ejpam-5563	288	3	)	)	PUNCT
ejpam-5563	288	4	γ(λ(k	γ(λ(k	NOUN
ejpam-5563	288	5	)	)	PUNCT
ejpam-5563	288	6	)	)	PUNCT
ejpam-5563	289	1	=	=	PUNCT
ejpam-5563	289	2	γ[γ∗(k)−k	γ[γ∗(k)−k	VERB
ejpam-5563	289	3	]	]	PUNCT
ejpam-5563	289	4	⊆	⊆	NUM
ejpam-5563	289	5	γ(γ∗(k	γ(γ∗(k	NOUN
ejpam-5563	289	6	)	)	PUNCT
ejpam-5563	289	7	)	)	PUNCT
ejpam-5563	289	8	by	by	ADP
ejpam-5563	289	9	using	use	VERB
ejpam-5563	289	10	(	(	PUNCT
ejpam-5563	289	11	ii	ii	NOUN
ejpam-5563	289	12	)	)	PUNCT
ejpam-5563	289	13	in	in	ADP
ejpam-5563	289	14	theorem	theorem	NOUN
ejpam-5563	289	15	1	1	NUM
ejpam-5563	289	16	.	.	PUNCT
ejpam-5563	289	17	(	(	PUNCT
ejpam-5563	289	18	ix	ix	ADP
ejpam-5563	289	19	)	)	PUNCT
ejpam-5563	289	20	since	since	SCONJ
ejpam-5563	289	21	λ(k	λ(k	PROPN
ejpam-5563	289	22	)	)	PUNCT
ejpam-5563	289	23	=	=	SYM
ejpam-5563	290	1	γ∗(k)−k	γ∗(k)−k	ADJ
ejpam-5563	290	2	,	,	PUNCT
ejpam-5563	290	3	then	then	ADV
ejpam-5563	290	4	λ(k	λ(k	ADJ
ejpam-5563	290	5	)	)	PUNCT
ejpam-5563	290	6	∩	∩	NOUN
ejpam-5563	290	7	k	k	NOUN
ejpam-5563	290	8	=	=	PUNCT
ejpam-5563	290	9	∅.	∅.	VERB
ejpam-5563	290	10	hence	hence	ADV
ejpam-5563	290	11	,	,	PUNCT
ejpam-5563	290	12	λ(k	λ(k	PROPN
ejpam-5563	290	13	)	)	PUNCT
ejpam-5563	290	14	⊆	⊆	NUM
ejpam-5563	290	15	kc	kc	PROPN
ejpam-5563	290	16	.	.	PUNCT
ejpam-5563	291	1	(	(	PUNCT
ejpam-5563	291	2	x	x	X
ejpam-5563	291	3	)	)	PUNCT
ejpam-5563	291	4	let	let	VERB
ejpam-5563	291	5	r	r	NOUN
ejpam-5563	291	6	∈	∈	PROPN
ejpam-5563	291	7	λ(k	λ(k	NOUN
ejpam-5563	291	8	)	)	PUNCT
ejpam-5563	291	9	∪	∪	ADP
ejpam-5563	291	10	λ(o	λ(o	PROPN
ejpam-5563	291	11	)	)	PUNCT
ejpam-5563	291	12	.	.	PUNCT
ejpam-5563	292	1	then	then	ADV
ejpam-5563	292	2	,	,	PUNCT
ejpam-5563	292	3	we	we	PRON
ejpam-5563	292	4	have	have	VERB
ejpam-5563	292	5	two	two	NUM
ejpam-5563	292	6	cases	case	NOUN
ejpam-5563	292	7	:	:	PUNCT
ejpam-5563	292	8	case	case	NOUN
ejpam-5563	292	9	1	1	NUM
ejpam-5563	292	10	.	.	PUNCT
ejpam-5563	292	11	r	r	NOUN
ejpam-5563	292	12	∈	∈	PROPN
ejpam-5563	292	13	λ(k	λ(k	NOUN
ejpam-5563	292	14	)	)	PUNCT
ejpam-5563	292	15	=	=	NOUN
ejpam-5563	292	16	⇒	⇒	NOUN
ejpam-5563	292	17	r	r	NOUN
ejpam-5563	292	18	∈	∈	PROPN
ejpam-5563	292	19	γ∗(k	γ∗(k	NOUN
ejpam-5563	292	20	)	)	PUNCT
ejpam-5563	292	21	and	and	CCONJ
ejpam-5563	292	22	r	r	NOUN
ejpam-5563	292	23	/∈	/∈	PUNCT
ejpam-5563	292	24	k.	k.	PROPN
ejpam-5563	292	25	subcase	subcase	PROPN
ejpam-5563	292	26	1.1	1.1	NUM
ejpam-5563	292	27	.	.	PUNCT
ejpam-5563	293	1	if	if	SCONJ
ejpam-5563	293	2	r	r	PRON
ejpam-5563	293	3	/∈	/∈	PUNCT
ejpam-5563	294	1	o	o	NOUN
ejpam-5563	294	2	,	,	PUNCT
ejpam-5563	294	3	then	then	ADV
ejpam-5563	294	4	r	r	PROPN
ejpam-5563	294	5	/∈	/∈	PUNCT
ejpam-5563	294	6	k∪o	k∪o	PROPN
ejpam-5563	294	7	.	.	PUNCT
ejpam-5563	295	1	since	since	SCONJ
ejpam-5563	295	2	r	r	PROPN
ejpam-5563	295	3	∈	∈	PROPN
ejpam-5563	295	4	γ∗(k	γ∗(k	NOUN
ejpam-5563	295	5	)	)	PUNCT
ejpam-5563	295	6	⊆	⊆	NUM
ejpam-5563	295	7	γ∗(k∪o	γ∗(k∪o	NOUN
ejpam-5563	295	8	)	)	PUNCT
ejpam-5563	295	9	,	,	PUNCT
ejpam-5563	295	10	then	then	ADV
ejpam-5563	295	11	r	r	PROPN
ejpam-5563	295	12	∈	∈	PROPN
ejpam-5563	295	13	λ(k∪o	λ(k∪o	PROPN
ejpam-5563	295	14	)	)	PUNCT
ejpam-5563	295	15	.	.	PUNCT
ejpam-5563	296	1	subcase	subcase	PROPN
ejpam-5563	296	2	1.2	1.2	NUM
ejpam-5563	296	3	.	.	PUNCT
ejpam-5563	297	1	if	if	SCONJ
ejpam-5563	297	2	r	r	NOUN
ejpam-5563	297	3	∈	∈	PROPN
ejpam-5563	297	4	o	o	NOUN
ejpam-5563	297	5	,	,	PUNCT
ejpam-5563	297	6	then	then	ADV
ejpam-5563	297	7	r	r	NOUN
ejpam-5563	297	8	∈	∈	PROPN
ejpam-5563	297	9	λ(k	λ(k	NOUN
ejpam-5563	297	10	)	)	PUNCT
ejpam-5563	297	11	∩	∩	ADJ
ejpam-5563	297	12	o.	o.	NOUN
ejpam-5563	297	13	case	case	NOUN
ejpam-5563	297	14	2	2	NUM
ejpam-5563	297	15	.	.	PUNCT
ejpam-5563	297	16	r	r	NOUN
ejpam-5563	297	17	∈	∈	PROPN
ejpam-5563	297	18	λ(o	λ(o	PROPN
ejpam-5563	297	19	)	)	PUNCT
ejpam-5563	298	1	=	=	VERB
ejpam-5563	298	2	⇒	⇒	NOUN
ejpam-5563	298	3	r	r	NOUN
ejpam-5563	298	4	∈	∈	PROPN
ejpam-5563	298	5	γ∗(o	γ∗(o	PROPN
ejpam-5563	298	6	)	)	PUNCT
ejpam-5563	298	7	and	and	CCONJ
ejpam-5563	298	8	r	r	NOUN
ejpam-5563	298	9	/∈	/∈	PUNCT
ejpam-5563	298	10	o.	o.	PROPN
ejpam-5563	298	11	subcase	subcase	PROPN
ejpam-5563	298	12	2.1	2.1	NUM
ejpam-5563	298	13	.	.	PUNCT
ejpam-5563	299	1	if	if	SCONJ
ejpam-5563	299	2	r	r	NOUN
ejpam-5563	299	3	/∈	/∈	PUNCT
ejpam-5563	300	1	k	k	NOUN
ejpam-5563	300	2	,	,	PUNCT
ejpam-5563	300	3	then	then	ADV
ejpam-5563	300	4	r	r	NOUN
ejpam-5563	300	5	∈	∈	PROPN
ejpam-5563	300	6	λ(k	λ(k	X
ejpam-5563	300	7	∪o	∪o	NOUN
ejpam-5563	300	8	)	)	PUNCT
ejpam-5563	300	9	.	.	PUNCT
ejpam-5563	301	1	subcase	subcase	PROPN
ejpam-5563	301	2	2.2	2.2	NUM
ejpam-5563	301	3	.	.	PUNCT
ejpam-5563	302	1	if	if	SCONJ
ejpam-5563	302	2	r	r	NOUN
ejpam-5563	302	3	∈	∈	PROPN
ejpam-5563	302	4	k	k	NOUN
ejpam-5563	302	5	,	,	PUNCT
ejpam-5563	302	6	then	then	ADV
ejpam-5563	302	7	r	r	NOUN
ejpam-5563	302	8	∈	∈	PROPN
ejpam-5563	302	9	λ(o	λ(o	PROPN
ejpam-5563	302	10	)	)	PUNCT
ejpam-5563	302	11	∩	∩	PROPN
ejpam-5563	302	12	k.	k.	PROPN
ejpam-5563	302	13	hence	hence	ADV
ejpam-5563	302	14	,	,	PUNCT
ejpam-5563	302	15	λ(k	λ(k	PROPN
ejpam-5563	302	16	)	)	PUNCT
ejpam-5563	302	17	∪	∪	ADP
ejpam-5563	302	18	λ(o	λ(o	NOUN
ejpam-5563	302	19	)	)	PUNCT
ejpam-5563	302	20	⊆	⊆	NUM
ejpam-5563	302	21	λ(k	λ(k	NOUN
ejpam-5563	302	22	∪o	∪o	NOUN
ejpam-5563	302	23	)	)	PUNCT
ejpam-5563	302	24	∪	∪	ADP
ejpam-5563	302	25	[	[	X
ejpam-5563	302	26	λ(k	λ(k	ADJ
ejpam-5563	302	27	)	)	PUNCT
ejpam-5563	302	28	∩	∩	ADJ
ejpam-5563	302	29	o	o	X
ejpam-5563	302	30	]	]	X
ejpam-5563	302	31	∪	∪	ADP
ejpam-5563	302	32	[	[	X
ejpam-5563	302	33	λ(o	λ(o	NOUN
ejpam-5563	302	34	)	)	PUNCT
ejpam-5563	302	35	∩	∩	NOUN
ejpam-5563	302	36	k	k	X
ejpam-5563	302	37	]	]	X
ejpam-5563	302	38	.	.	PUNCT
ejpam-5563	303	1	the	the	DET
ejpam-5563	303	2	equality	equality	NOUN
ejpam-5563	303	3	in	in	ADP
ejpam-5563	303	4	the	the	DET
ejpam-5563	303	5	properties	property	NOUN
ejpam-5563	303	6	(	(	PUNCT
ejpam-5563	303	7	vii	vii	PROPN
ejpam-5563	303	8	)	)	PUNCT
ejpam-5563	303	9	and	and	CCONJ
ejpam-5563	303	10	(	(	PUNCT
ejpam-5563	303	11	viii	viii	NOUN
ejpam-5563	303	12	)	)	PUNCT
ejpam-5563	303	13	of	of	ADP
ejpam-5563	303	14	theorem	theorem	NOUN
ejpam-5563	303	15	13	13	NUM
ejpam-5563	303	16	may	may	AUX
ejpam-5563	303	17	not	not	PART
ejpam-5563	303	18	be	be	AUX
ejpam-5563	303	19	true	true	ADJ
ejpam-5563	303	20	in	in	ADP
ejpam-5563	303	21	general	general	ADJ
ejpam-5563	303	22	as	as	SCONJ
ejpam-5563	303	23	shown	show	VERB
ejpam-5563	303	24	in	in	ADP
ejpam-5563	303	25	example	example	NOUN
ejpam-5563	303	26	below	below	ADV
ejpam-5563	303	27	.	.	PUNCT
ejpam-5563	304	1	example	example	NOUN
ejpam-5563	305	1	3	3	X
ejpam-5563	305	2	.	.	X
ejpam-5563	306	1	let	let	VERB
ejpam-5563	306	2	(	(	PUNCT
ejpam-5563	306	3	r	r	NOUN
ejpam-5563	306	4	,	,	PUNCT
ejpam-5563	306	5	γ0,p0	γ0,p0	PROPN
ejpam-5563	306	6	)	)	PUNCT
ejpam-5563	306	7	be	be	AUX
ejpam-5563	306	8	defined	define	VERB
ejpam-5563	306	9	as	as	ADP
ejpam-5563	306	10	in	in	ADP
ejpam-5563	306	11	example	example	NOUN
ejpam-5563	306	12	1	1	NUM
ejpam-5563	306	13	.	.	PUNCT
ejpam-5563	306	14	consider	consider	VERB
ejpam-5563	306	15	the	the	DET
ejpam-5563	306	16	set	set	NOUN
ejpam-5563	306	17	w	w	NOUN
ejpam-5563	306	18	=	=	PUNCT
ejpam-5563	306	19	{	{	PUNCT
ejpam-5563	306	20	0	0	NUM
ejpam-5563	306	21	,	,	PUNCT
ejpam-5563	306	22	1	1	NUM
ejpam-5563	306	23	,	,	PUNCT
ejpam-5563	306	24	2	2	NUM
ejpam-5563	306	25	,	,	PUNCT
ejpam-5563	306	26	...	...	PUNCT
ejpam-5563	306	27	}	}	PUNCT
ejpam-5563	306	28	.	.	PUNCT
ejpam-5563	307	1	let	let	VERB
ejpam-5563	307	2	r	r	NOUN
ejpam-5563	307	3	∈	∈	NOUN
ejpam-5563	307	4	r	r	NOUN
ejpam-5563	307	5	and	and	CCONJ
ejpam-5563	307	6	let	let	VERB
ejpam-5563	307	7	o	o	PROPN
ejpam-5563	307	8	∈	∈	PROPN
ejpam-5563	307	9	γ0(r	γ0(r	PROPN
ejpam-5563	307	10	)	)	PUNCT
ejpam-5563	307	11	.	.	PUNCT
ejpam-5563	308	1	then	then	ADV
ejpam-5563	308	2	,	,	PUNCT
ejpam-5563	308	3	o⋄	o⋄	PROPN
ejpam-5563	308	4	=	=	SYM
ejpam-5563	308	5	r.	r.	PROPN
ejpam-5563	308	6	hence	hence	ADV
ejpam-5563	308	7	,	,	PUNCT
ejpam-5563	308	8	(	(	PUNCT
ejpam-5563	308	9	o⋄	o⋄	X
ejpam-5563	308	10	−w)c	−w)c	NOUN
ejpam-5563	308	11	=	=	NOUN
ejpam-5563	308	12	(	(	PUNCT
ejpam-5563	308	13	r	r	NOUN
ejpam-5563	308	14	−w)c	−w)c	NOUN
ejpam-5563	308	15	=	=	PROPN
ejpam-5563	308	16	w	w	PROPN
ejpam-5563	308	17	/∈	/∈	PROPN
ejpam-5563	308	18	p0	p0	NOUN
ejpam-5563	308	19	;	;	PUNCT
ejpam-5563	308	20	thus	thus	ADV
ejpam-5563	308	21	,	,	PUNCT
ejpam-5563	308	22	γ∗(w	γ∗(w	NUM
ejpam-5563	308	23	)	)	PUNCT
ejpam-5563	308	24	=	=	SYM
ejpam-5563	308	25	r.	r.	PROPN
ejpam-5563	308	26	therefore	therefore	ADV
ejpam-5563	308	27	,	,	PUNCT
ejpam-5563	308	28	λ(w	λ(w	X
ejpam-5563	308	29	)	)	PUNCT
ejpam-5563	308	30	=	=	SYM
ejpam-5563	308	31	wc	wc	PROPN
ejpam-5563	308	32	.	.	PUNCT
ejpam-5563	309	1	now	now	ADV
ejpam-5563	309	2	,	,	PUNCT
ejpam-5563	309	3	let	let	VERB
ejpam-5563	309	4	a	a	DET
ejpam-5563	309	5	be	be	AUX
ejpam-5563	309	6	any	any	DET
ejpam-5563	309	7	set	set	NOUN
ejpam-5563	310	1	such	such	ADJ
ejpam-5563	310	2	that	that	DET
ejpam-5563	310	3	0	0	NUM
ejpam-5563	310	4	/∈	/∈	PUNCT
ejpam-5563	310	5	a	a	PRON
ejpam-5563	310	6	and	and	CCONJ
ejpam-5563	310	7	let	let	VERB
ejpam-5563	310	8	r	r	PRON
ejpam-5563	310	9	∈	∈	PROPN
ejpam-5563	310	10	r.	r.	NOUN
ejpam-5563	310	11	then	then	ADV
ejpam-5563	310	12	,	,	PUNCT
ejpam-5563	310	13	if	if	SCONJ
ejpam-5563	310	14	o	o	NOUN
ejpam-5563	310	15	is	be	AUX
ejpam-5563	310	16	any	any	DET
ejpam-5563	310	17	arbitrary	arbitrary	ADJ
ejpam-5563	310	18	open	open	ADJ
ejpam-5563	310	19	set	set	VERB
ejpam-5563	310	20	with	with	ADP
ejpam-5563	310	21	r	r	NOUN
ejpam-5563	310	22	∈	∈	PROPN
ejpam-5563	310	23	o	o	NOUN
ejpam-5563	310	24	,	,	PUNCT
ejpam-5563	310	25	we	we	PRON
ejpam-5563	310	26	have	have	VERB
ejpam-5563	310	27	o⋄	o⋄	NUM
ejpam-5563	310	28	=	=	SYM
ejpam-5563	310	29	r.	r.	PROPN
ejpam-5563	310	30	thus	thus	ADV
ejpam-5563	310	31	,	,	PUNCT
ejpam-5563	310	32	(	(	PUNCT
ejpam-5563	310	33	o⋄	o⋄	NUM
ejpam-5563	310	34	−	−	ADP
ejpam-5563	310	35	a)c	a)c	X
ejpam-5563	310	36	∈	∈	PROPN
ejpam-5563	310	37	p0	p0	NOUN
ejpam-5563	310	38	.	.	PUNCT
ejpam-5563	311	1	therefore	therefore	ADV
ejpam-5563	311	2	,	,	PUNCT
ejpam-5563	311	3	γ∗(a	γ∗(a	PROPN
ejpam-5563	311	4	)	)	PUNCT
ejpam-5563	311	5	=	=	NOUN
ejpam-5563	311	6	∅	∅	NOUN
ejpam-5563	311	7	which	which	PRON
ejpam-5563	311	8	leads	lead	VERB
ejpam-5563	311	9	to	to	ADP
ejpam-5563	311	10	that	that	DET
ejpam-5563	311	11	λ(a	λ(a	NOUN
ejpam-5563	311	12	)	)	PUNCT
ejpam-5563	312	1	=	=	PUNCT
ejpam-5563	312	2	∅.	∅.	ADP
ejpam-5563	312	3	then	then	ADV
ejpam-5563	312	4	,	,	PUNCT
ejpam-5563	312	5	λ(λ(w	λ(λ(w	PROPN
ejpam-5563	312	6	)	)	PUNCT
ejpam-5563	312	7	)	)	PUNCT
ejpam-5563	313	1	=	=	NOUN
ejpam-5563	313	2	∅	∅	NOUN
ejpam-5563	313	3	and	and	CCONJ
ejpam-5563	313	4	γ∗(γ∗(w	γ∗(γ∗(w	NOUN
ejpam-5563	313	5	)	)	PUNCT
ejpam-5563	313	6	)	)	PUNCT
ejpam-5563	314	1	=	=	PUNCT
ejpam-5563	314	2	r.	r.	NOUN
ejpam-5563	314	3	on	on	ADP
ejpam-5563	314	4	the	the	DET
ejpam-5563	314	5	other	other	ADJ
ejpam-5563	314	6	hand	hand	NOUN
ejpam-5563	314	7	,	,	PUNCT
ejpam-5563	314	8	γ(γ∗(w	γ(γ∗(w	NOUN
ejpam-5563	314	9	)	)	PUNCT
ejpam-5563	314	10	)	)	PUNCT
ejpam-5563	315	1	=	=	PUNCT
ejpam-5563	315	2	r.	r.	PROPN
ejpam-5563	315	3	indeed	indeed	ADV
ejpam-5563	315	4	,	,	PUNCT
ejpam-5563	315	5	let	let	VERB
ejpam-5563	315	6	r	r	NOUN
ejpam-5563	315	7	∈	∈	NOUN
ejpam-5563	315	8	r	r	NOUN
ejpam-5563	315	9	and	and	CCONJ
ejpam-5563	315	10	let	let	VERB
ejpam-5563	315	11	o	o	PROPN
ejpam-5563	315	12	∈	∈	PROPN
ejpam-5563	315	13	γ0(r	γ0(r	PROPN
ejpam-5563	315	14	)	)	PUNCT
ejpam-5563	315	15	.	.	PUNCT
ejpam-5563	316	1	then	then	ADV
ejpam-5563	316	2	,	,	PUNCT
ejpam-5563	316	3	since	since	SCONJ
ejpam-5563	316	4	(	(	PUNCT
ejpam-5563	316	5	o⋄)c	o⋄)c	PROPN
ejpam-5563	316	6	∪	∪	VERB
ejpam-5563	316	7	u	u	PROPN
ejpam-5563	316	8	c	c	PROPN
ejpam-5563	316	9	∈	∈	PROPN
ejpam-5563	316	10	p0	p0	NOUN
ejpam-5563	316	11	for	for	ADP
ejpam-5563	316	12	all	all	DET
ejpam-5563	316	13	u	u	PROPN
ejpam-5563	316	14	∈	∈	PROPN
ejpam-5563	316	15	γ0(r	γ0(r	PROPN
ejpam-5563	316	16	)	)	PUNCT
ejpam-5563	316	17	,	,	PUNCT
ejpam-5563	316	18	we	we	PRON
ejpam-5563	316	19	have	have	VERB
ejpam-5563	316	20	γ(r	γ(r	NOUN
ejpam-5563	316	21	)	)	PUNCT
ejpam-5563	317	1	=	=	VERB
ejpam-5563	317	2	r.	r.	PROPN
ejpam-5563	317	3	moreover	moreover	ADV
ejpam-5563	317	4	,	,	PUNCT
ejpam-5563	317	5	γ(λ(w	γ(λ(w	ADJ
ejpam-5563	317	6	)	)	PUNCT
ejpam-5563	317	7	)	)	PUNCT
ejpam-5563	318	1	=	=	SYM
ejpam-5563	318	2	γ(wc	γ(wc	NOUN
ejpam-5563	318	3	)	)	PUNCT
ejpam-5563	318	4	=	=	NOUN
ejpam-5563	318	5	∅	∅	NOUN
ejpam-5563	318	6	because	because	SCONJ
ejpam-5563	318	7	0	0	NUM
ejpam-5563	318	8	∈	∈	PROPN
ejpam-5563	318	9	w	w	NOUN
ejpam-5563	318	10	which	which	PRON
ejpam-5563	318	11	implies	imply	VERB
ejpam-5563	318	12	that	that	DET
ejpam-5563	318	13	w	w	PROPN
ejpam-5563	318	14	/∈	/∈	PUNCT
ejpam-5563	318	15	p0	p0	NOUN
ejpam-5563	318	16	.	.	PUNCT
ejpam-5563	319	1	corollary	corollary	ADJ
ejpam-5563	319	2	2	2	NUM
ejpam-5563	319	3	.	.	PUNCT
ejpam-5563	320	1	let	let	VERB
ejpam-5563	320	2	(	(	PUNCT
ejpam-5563	320	3	b	b	X
ejpam-5563	320	4	,	,	PUNCT
ejpam-5563	320	5	γ	γ	PROPN
ejpam-5563	320	6	,	,	PUNCT
ejpam-5563	320	7	p	p	NOUN
ejpam-5563	320	8	)	)	PUNCT
ejpam-5563	320	9	be	be	AUX
ejpam-5563	320	10	a	a	DET
ejpam-5563	320	11	ps	ps	NOUN
ejpam-5563	320	12	.	.	PUNCT
ejpam-5563	321	1	then	then	ADV
ejpam-5563	321	2	,	,	PUNCT
ejpam-5563	321	3	γ	γ	PROPN
ejpam-5563	321	4	−	−	PROPN
ejpam-5563	321	5	{	{	PUNCT
ejpam-5563	321	6	b	b	NOUN
ejpam-5563	321	7	}	}	PUNCT
ejpam-5563	321	8	⊆	⊆	NUM
ejpam-5563	321	9	p	p	NOUN
ejpam-5563	321	10	and	and	CCONJ
ejpam-5563	321	11	△	△	NOUN
ejpam-5563	321	12	=	=	SYM
ejpam-5563	321	13	{	{	PUNCT
ejpam-5563	321	14	∅	∅	NOUN
ejpam-5563	321	15	}	}	PUNCT
ejpam-5563	321	16	if	if	SCONJ
ejpam-5563	321	17	and	and	CCONJ
ejpam-5563	321	18	only	only	ADV
ejpam-5563	321	19	if	if	SCONJ
ejpam-5563	321	20	λ(∅	λ(∅	NOUN
ejpam-5563	321	21	)	)	PUNCT
ejpam-5563	321	22	=	=	PUNCT
ejpam-5563	321	23	∅.	∅.	PROPN
ejpam-5563	321	24	o.	o.	PROPN
ejpam-5563	321	25	alghamdi	alghamdi	PROPN
ejpam-5563	321	26	/	/	SYM
ejpam-5563	321	27	eur	eur	PROPN
ejpam-5563	321	28	.	.	PUNCT
ejpam-5563	322	1	j.	j.	PROPN
ejpam-5563	322	2	pure	pure	PROPN
ejpam-5563	322	3	appl	appl	PROPN
ejpam-5563	322	4	.	.	PROPN
ejpam-5563	322	5	math	math	PROPN
ejpam-5563	322	6	,	,	PUNCT
ejpam-5563	322	7	17	17	NUM
ejpam-5563	322	8	(	(	PUNCT
ejpam-5563	322	9	4	4	NUM
ejpam-5563	322	10	)	)	PUNCT
ejpam-5563	322	11	(	(	PUNCT
ejpam-5563	322	12	2024	2024	NUM
ejpam-5563	322	13	)	)	PUNCT
ejpam-5563	322	14	,	,	PUNCT
ejpam-5563	322	15	3517	3517	NUM
ejpam-5563	322	16	-	-	SYM
ejpam-5563	322	17	3538	3538	NUM
ejpam-5563	322	18	3525	3525	NUM
ejpam-5563	322	19	proof	proof	NOUN
ejpam-5563	322	20	.	.	PUNCT
ejpam-5563	323	1	it	it	PRON
ejpam-5563	323	2	is	be	AUX
ejpam-5563	323	3	obvious	obvious	ADJ
ejpam-5563	323	4	by	by	ADP
ejpam-5563	323	5	theorem	theorem	ADJ
ejpam-5563	323	6	3	3	NUM
ejpam-5563	323	7	and	and	CCONJ
ejpam-5563	323	8	property	property	NOUN
ejpam-5563	323	9	(	(	PUNCT
ejpam-5563	323	10	i	i	NOUN
ejpam-5563	323	11	)	)	PUNCT
ejpam-5563	323	12	of	of	ADP
ejpam-5563	323	13	theorem	theorem	ADJ
ejpam-5563	323	14	13	13	NUM
ejpam-5563	323	15	.	.	PUNCT
ejpam-5563	324	1	theorem	theorem	NOUN
ejpam-5563	324	2	14	14	NUM
ejpam-5563	324	3	.	.	PUNCT
ejpam-5563	325	1	let	let	VERB
ejpam-5563	325	2	(	(	PUNCT
ejpam-5563	325	3	b	b	X
ejpam-5563	325	4	,	,	PUNCT
ejpam-5563	325	5	γ	γ	PROPN
ejpam-5563	325	6	,	,	PUNCT
ejpam-5563	325	7	p	p	NOUN
ejpam-5563	325	8	)	)	PUNCT
ejpam-5563	325	9	be	be	AUX
ejpam-5563	325	10	a	a	DET
ejpam-5563	325	11	ps	ps	NOUN
ejpam-5563	325	12	.	.	PUNCT
ejpam-5563	326	1	then	then	ADV
ejpam-5563	326	2	,	,	PUNCT
ejpam-5563	326	3	λ(oc	λ(oc	PROPN
ejpam-5563	326	4	)	)	PUNCT
ejpam-5563	327	1	=	=	SYM
ejpam-5563	327	2	o	o	NOUN
ejpam-5563	328	1	if	if	SCONJ
ejpam-5563	328	2	and	and	CCONJ
ejpam-5563	328	3	only	only	ADV
ejpam-5563	328	4	if	if	SCONJ
ejpam-5563	328	5	o	o	PROPN
ejpam-5563	328	6	∩	∩	X
ejpam-5563	328	7	γ(o	γ(o	ADJ
ejpam-5563	328	8	)	)	PUNCT
ejpam-5563	328	9	=	=	NOUN
ejpam-5563	328	10	∅	∅	NOUN
ejpam-5563	328	11	for	for	ADP
ejpam-5563	328	12	any	any	DET
ejpam-5563	328	13	o	o	NOUN
ejpam-5563	328	14	⊆	⊆	NUM
ejpam-5563	328	15	b.	b.	NOUN
ejpam-5563	328	16	proof	proof	NOUN
ejpam-5563	328	17	.	.	PUNCT
ejpam-5563	329	1	let	let	VERB
ejpam-5563	329	2	o	o	PROPN
ejpam-5563	329	3	⊆	⊆	NUM
ejpam-5563	329	4	b.	b.	PROPN
ejpam-5563	329	5	then	then	ADV
ejpam-5563	329	6	,	,	PUNCT
ejpam-5563	329	7	λ(oc	λ(oc	PROPN
ejpam-5563	329	8	)	)	PUNCT
ejpam-5563	330	1	=	=	NOUN
ejpam-5563	330	2	o	o	X
ejpam-5563	330	3	⇐	⇐	ADJ
ejpam-5563	330	4	⇒	⇒	PROPN
ejpam-5563	330	5	γ∗(oc)−oc	γ∗(oc)−oc	NOUN
ejpam-5563	330	6	=	=	SYM
ejpam-5563	330	7	γ∗(oc	γ∗(oc	PROPN
ejpam-5563	330	8	)	)	PUNCT
ejpam-5563	330	9	∩	∩	NOUN
ejpam-5563	330	10	o	o	NOUN
ejpam-5563	331	1	=	=	PUNCT
ejpam-5563	331	2	o	o	X
ejpam-5563	331	3	⇐	⇐	ADJ
ejpam-5563	331	4	⇒	⇒	NOUN
ejpam-5563	331	5	o	o	NOUN
ejpam-5563	331	6	⊆	⊆	NUM
ejpam-5563	331	7	γ∗(oc	γ∗(oc	NOUN
ejpam-5563	331	8	)	)	PUNCT
ejpam-5563	331	9	=	=	PUNCT
ejpam-5563	332	1	[	[	X
ejpam-5563	332	2	γ(o)]c	γ(o)]c	NOUN
ejpam-5563	332	3	⇐	⇐	ADJ
ejpam-5563	332	4	⇒	⇒	NOUN
ejpam-5563	332	5	o	o	NOUN
ejpam-5563	332	6	∩	∩	ADJ
ejpam-5563	332	7	γ(o	γ(o	ADJ
ejpam-5563	332	8	)	)	PUNCT
ejpam-5563	332	9	=	=	PUNCT
ejpam-5563	332	10	∅.	∅.	NOUN
ejpam-5563	332	11	theorem	theorem	VERB
ejpam-5563	332	12	15	15	NUM
ejpam-5563	332	13	.	.	PUNCT
ejpam-5563	333	1	let	let	VERB
ejpam-5563	333	2	(	(	PUNCT
ejpam-5563	333	3	b	b	X
ejpam-5563	333	4	,	,	PUNCT
ejpam-5563	333	5	γ	γ	PROPN
ejpam-5563	333	6	,	,	PUNCT
ejpam-5563	333	7	p	p	NOUN
ejpam-5563	333	8	)	)	PUNCT
ejpam-5563	333	9	be	be	AUX
ejpam-5563	333	10	a	a	DET
ejpam-5563	333	11	ps	ps	NOUN
ejpam-5563	333	12	.	.	PUNCT
ejpam-5563	334	1	then	then	ADV
ejpam-5563	334	2	,	,	PUNCT
ejpam-5563	334	3	γ	γ	X
ejpam-5563	334	4	is	be	AUX
ejpam-5563	334	5	compatible	compatible	ADJ
ejpam-5563	334	6	with	with	ADP
ejpam-5563	334	7	p	p	PRON
ejpam-5563	334	8	if	if	SCONJ
ejpam-5563	335	1	and	and	CCONJ
ejpam-5563	335	2	only	only	ADV
ejpam-5563	335	3	if	if	SCONJ
ejpam-5563	335	4	[	[	X
ejpam-5563	335	5	λ(o)]c	λ(o)]c	X
ejpam-5563	335	6	/∈	/∈	NOUN
ejpam-5563	335	7	p	p	NOUN
ejpam-5563	335	8	for	for	ADP
ejpam-5563	335	9	all	all	DET
ejpam-5563	335	10	o	o	NOUN
ejpam-5563	335	11	⊆	⊆	NUM
ejpam-5563	335	12	b.	b.	NOUN
ejpam-5563	335	13	proof	proof	NOUN
ejpam-5563	335	14	.	.	PUNCT
ejpam-5563	336	1	by	by	ADP
ejpam-5563	336	2	theorem	theorem	NOUN
ejpam-5563	336	3	4	4	NUM
ejpam-5563	336	4	,	,	PUNCT
ejpam-5563	336	5	we	we	PRON
ejpam-5563	336	6	have	have	VERB
ejpam-5563	336	7	:	:	PUNCT
ejpam-5563	336	8	γ	γ	X
ejpam-5563	336	9	is	be	AUX
ejpam-5563	336	10	compatible	compatible	ADJ
ejpam-5563	336	11	with	with	ADP
ejpam-5563	336	12	p	p	PROPN
ejpam-5563	336	13	⇐	⇐	ADJ
ejpam-5563	336	14	⇒	⇒	NOUN
ejpam-5563	337	1	[	[	X
ejpam-5563	337	2	o	o	X
ejpam-5563	337	3	−	−	X
ejpam-5563	337	4	γ(o)]c	γ(o)]c	PROPN
ejpam-5563	337	5	/∈	/∈	NOUN
ejpam-5563	337	6	p	p	NOUN
ejpam-5563	337	7	for	for	ADP
ejpam-5563	337	8	all	all	DET
ejpam-5563	337	9	o	o	NOUN
ejpam-5563	337	10	⊆	⊆	NUM
ejpam-5563	337	11	b.	b.	NOUN
ejpam-5563	337	12	hence	hence	ADV
ejpam-5563	337	13	,	,	PUNCT
ejpam-5563	337	14	γ	γ	X
ejpam-5563	337	15	is	be	AUX
ejpam-5563	337	16	compatible	compatible	ADJ
ejpam-5563	337	17	with	with	ADP
ejpam-5563	337	18	p	p	PROPN
ejpam-5563	337	19	⇐	⇐	ADJ
ejpam-5563	337	20	⇒	⇒	NOUN
ejpam-5563	337	21	[	[	X
ejpam-5563	337	22	oc	oc	X
ejpam-5563	337	23	−	−	PROPN
ejpam-5563	337	24	γ(oc)]c	γ(oc)]c	PROPN
ejpam-5563	337	25	/∈	/∈	PUNCT
ejpam-5563	338	1	p	p	X
ejpam-5563	338	2	⇐	⇐	ADJ
ejpam-5563	338	3	⇒	⇒	PROPN
ejpam-5563	338	4	[	[	X
ejpam-5563	338	5	(	(	PUNCT
ejpam-5563	338	6	γ(oc))c	γ(oc))c	PROPN
ejpam-5563	338	7	−o]c	−o]c	PROPN
ejpam-5563	338	8	/∈	/∈	PUNCT
ejpam-5563	339	1	p	p	X
ejpam-5563	339	2	⇐	⇐	ADJ
ejpam-5563	339	3	⇒	⇒	NOUN
ejpam-5563	339	4	[	[	X
ejpam-5563	339	5	γ∗(o)−o]c	γ∗(o)−o]c	PROPN
ejpam-5563	339	6	/∈	/∈	PUNCT
ejpam-5563	340	1	p	p	X
ejpam-5563	340	2	⇐	⇐	ADJ
ejpam-5563	340	3	⇒	⇒	NOUN
ejpam-5563	340	4	[	[	X
ejpam-5563	340	5	λ(o)]c	λ(o)]c	PROPN
ejpam-5563	340	6	/∈	/∈	PROPN
ejpam-5563	341	1	p.	p.	NOUN
ejpam-5563	341	2	theorem	theorem	VERB
ejpam-5563	341	3	16	16	NUM
ejpam-5563	341	4	.	.	PUNCT
ejpam-5563	342	1	let	let	VERB
ejpam-5563	342	2	(	(	PUNCT
ejpam-5563	342	3	b	b	X
ejpam-5563	342	4	,	,	PUNCT
ejpam-5563	342	5	γ	γ	PROPN
ejpam-5563	342	6	,	,	PUNCT
ejpam-5563	342	7	p	p	NOUN
ejpam-5563	342	8	)	)	PUNCT
ejpam-5563	342	9	be	be	AUX
ejpam-5563	342	10	a	a	DET
ejpam-5563	342	11	ps	ps	NOUN
ejpam-5563	342	12	and	and	CCONJ
ejpam-5563	342	13	o	o	NOUN
ejpam-5563	342	14	be	be	AUX
ejpam-5563	342	15	a	a	DET
ejpam-5563	342	16	diamond	diamond	NOUN
ejpam-5563	342	17	-	-	PUNCT
ejpam-5563	342	18	closed	close	VERB
ejpam-5563	342	19	subset	subset	NOUN
ejpam-5563	342	20	of	of	ADP
ejpam-5563	342	21	b.	b.	PROPN
ejpam-5563	342	22	then	then	ADV
ejpam-5563	342	23	,	,	PUNCT
ejpam-5563	342	24	λ(o	λ(o	PROPN
ejpam-5563	342	25	)	)	PUNCT
ejpam-5563	343	1	⊆	⊆	NUM
ejpam-5563	344	1	[	[	X
ejpam-5563	344	2	γ(b)]c	γ(b)]c	NOUN
ejpam-5563	344	3	.	.	PUNCT
ejpam-5563	345	1	proof	proof	NOUN
ejpam-5563	345	2	.	.	PUNCT
ejpam-5563	346	1	if	if	SCONJ
ejpam-5563	346	2	o	o	NOUN
ejpam-5563	346	3	is	be	AUX
ejpam-5563	346	4	a	a	DET
ejpam-5563	346	5	diamond	diamond	NOUN
ejpam-5563	346	6	-	-	PUNCT
ejpam-5563	346	7	closed	closed	ADJ
ejpam-5563	346	8	,	,	PUNCT
ejpam-5563	346	9	then	then	ADV
ejpam-5563	346	10	γ(o	γ(o	PROPN
ejpam-5563	346	11	)	)	PUNCT
ejpam-5563	346	12	⊆	⊆	NUM
ejpam-5563	346	13	o	o	NOUN
ejpam-5563	346	14	by	by	ADP
ejpam-5563	346	15	using	use	VERB
ejpam-5563	346	16	(	(	PUNCT
ejpam-5563	346	17	viii	viii	NOUN
ejpam-5563	346	18	)	)	PUNCT
ejpam-5563	346	19	in	in	ADP
ejpam-5563	346	20	theorem	theorem	NOUN
ejpam-5563	346	21	2	2	NUM
ejpam-5563	346	22	.	.	PUNCT
ejpam-5563	346	23	hence	hence	ADV
ejpam-5563	346	24	,	,	PUNCT
ejpam-5563	346	25	λ(o	λ(o	PROPN
ejpam-5563	346	26	)	)	PUNCT
ejpam-5563	346	27	=	=	SYM
ejpam-5563	346	28	γ∗(o)−o	γ∗(o)−o	PRON
ejpam-5563	346	29	⊆γ∗(o)−	⊆γ∗(o)−	ADJ
ejpam-5563	346	30	γ(o	γ(o	PROPN
ejpam-5563	346	31	)	)	PUNCT
ejpam-5563	346	32	=	=	SYM
ejpam-5563	346	33	γ∗(o	γ∗(o	PROPN
ejpam-5563	346	34	)	)	PUNCT
ejpam-5563	346	35	∩	∩	NOUN
ejpam-5563	346	36	[	[	X
ejpam-5563	346	37	γ(o)]c	γ(o)]c	NOUN
ejpam-5563	346	38	=	=	SYM
ejpam-5563	346	39	γ∗(o	γ∗(o	PROPN
ejpam-5563	346	40	)	)	PUNCT
ejpam-5563	346	41	∩	∩	ADJ
ejpam-5563	346	42	γ∗(oc	γ∗(oc	NOUN
ejpam-5563	346	43	)	)	PUNCT
ejpam-5563	346	44	=	=	NOUN
ejpam-5563	346	45	γ∗(o	γ∗(o	NUM
ejpam-5563	346	46	∩oc	∩oc	NOUN
ejpam-5563	346	47	)	)	PUNCT
ejpam-5563	346	48	by	by	ADP
ejpam-5563	346	49	using	use	VERB
ejpam-5563	346	50	(	(	PUNCT
ejpam-5563	346	51	iv	iv	NOUN
ejpam-5563	346	52	)	)	PUNCT
ejpam-5563	346	53	in	in	ADP
ejpam-5563	346	54	theorem	theorem	ADJ
ejpam-5563	346	55	2	2	NUM
ejpam-5563	346	56	=	=	SYM
ejpam-5563	346	57	γ∗(∅	γ∗(∅	X
ejpam-5563	346	58	)	)	PUNCT
ejpam-5563	347	1	=	=	PUNCT
ejpam-5563	348	1	[	[	X
ejpam-5563	348	2	γ(b)]c	γ(b)]c	NOUN
ejpam-5563	348	3	.	.	PUNCT
ejpam-5563	348	4	corollary	corollary	ADJ
ejpam-5563	348	5	3	3	X
ejpam-5563	348	6	.	.	PUNCT
ejpam-5563	349	1	let	let	VERB
ejpam-5563	349	2	(	(	PUNCT
ejpam-5563	349	3	b	b	X
ejpam-5563	349	4	,	,	PUNCT
ejpam-5563	349	5	γ	γ	PROPN
ejpam-5563	349	6	,	,	PUNCT
ejpam-5563	349	7	p	p	NOUN
ejpam-5563	349	8	)	)	PUNCT
ejpam-5563	349	9	be	be	AUX
ejpam-5563	349	10	a	a	DET
ejpam-5563	349	11	ps	ps	NOUN
ejpam-5563	349	12	.	.	PUNCT
ejpam-5563	350	1	(	(	PUNCT
ejpam-5563	350	2	i	i	NOUN
ejpam-5563	350	3	)	)	PUNCT
ejpam-5563	350	4	if	if	SCONJ
ejpam-5563	350	5	o	o	NOUN
ejpam-5563	350	6	is	be	AUX
ejpam-5563	350	7	a	a	DET
ejpam-5563	350	8	closed	closed	ADJ
ejpam-5563	350	9	subset	subset	NOUN
ejpam-5563	350	10	of	of	ADP
ejpam-5563	350	11	b	b	PROPN
ejpam-5563	350	12	,	,	PUNCT
ejpam-5563	350	13	then	then	ADV
ejpam-5563	350	14	λ(o	λ(o	PROPN
ejpam-5563	350	15	)	)	PUNCT
ejpam-5563	350	16	∈	∈	PROPN
ejpam-5563	350	17	γ	γ	X
ejpam-5563	350	18	.	.	PROPN
ejpam-5563	350	19	o.	o.	PROPN
ejpam-5563	350	20	alghamdi	alghamdi	PROPN
ejpam-5563	350	21	/	/	SYM
ejpam-5563	350	22	eur	eur	PROPN
ejpam-5563	350	23	.	.	PUNCT
ejpam-5563	351	1	j.	j.	PROPN
ejpam-5563	351	2	pure	pure	PROPN
ejpam-5563	351	3	appl	appl	PROPN
ejpam-5563	351	4	.	.	PROPN
ejpam-5563	351	5	math	math	PROPN
ejpam-5563	351	6	,	,	PUNCT
ejpam-5563	351	7	17	17	NUM
ejpam-5563	351	8	(	(	PUNCT
ejpam-5563	351	9	4	4	NUM
ejpam-5563	351	10	)	)	PUNCT
ejpam-5563	351	11	(	(	PUNCT
ejpam-5563	351	12	2024	2024	NUM
ejpam-5563	351	13	)	)	PUNCT
ejpam-5563	351	14	,	,	PUNCT
ejpam-5563	351	15	3517	3517	NUM
ejpam-5563	351	16	-	-	SYM
ejpam-5563	351	17	3538	3538	NUM
ejpam-5563	351	18	3526	3526	NUM
ejpam-5563	351	19	(	(	PUNCT
ejpam-5563	351	20	ii	ii	NOUN
ejpam-5563	351	21	)	)	PUNCT
ejpam-5563	351	22	if	if	SCONJ
ejpam-5563	351	23	o	o	NOUN
ejpam-5563	351	24	is	be	AUX
ejpam-5563	351	25	a	a	DET
ejpam-5563	351	26	diamond	diamond	NOUN
ejpam-5563	351	27	-	-	PUNCT
ejpam-5563	351	28	closed	close	VERB
ejpam-5563	351	29	subset	subset	NOUN
ejpam-5563	351	30	of	of	ADP
ejpam-5563	351	31	b	b	PROPN
ejpam-5563	351	32	and	and	CCONJ
ejpam-5563	351	33	γ−{b	γ−{b	PROPN
ejpam-5563	351	34	}	}	PUNCT
ejpam-5563	351	35	⊆	⊆	NUM
ejpam-5563	351	36	p	p	NOUN
ejpam-5563	351	37	and	and	CCONJ
ejpam-5563	351	38	△	△	NOUN
ejpam-5563	351	39	=	=	SYM
ejpam-5563	351	40	{	{	PUNCT
ejpam-5563	351	41	∅	∅	NOUN
ejpam-5563	351	42	}	}	PUNCT
ejpam-5563	351	43	,	,	PUNCT
ejpam-5563	351	44	then	then	ADV
ejpam-5563	351	45	λ(o	λ(o	PROPN
ejpam-5563	351	46	)	)	PUNCT
ejpam-5563	351	47	=	=	PUNCT
ejpam-5563	351	48	∅.	∅.	NOUN
ejpam-5563	351	49	proof	proof	NOUN
ejpam-5563	351	50	.	.	PUNCT
ejpam-5563	352	1	(	(	PUNCT
ejpam-5563	352	2	i	i	NOUN
ejpam-5563	352	3	)	)	PUNCT
ejpam-5563	352	4	λ(o	λ(o	PROPN
ejpam-5563	352	5	)	)	PUNCT
ejpam-5563	353	1	=	=	SYM
ejpam-5563	353	2	γ∗(o)−o	γ∗(o)−o	NOUN
ejpam-5563	353	3	is	be	AUX
ejpam-5563	353	4	an	an	DET
ejpam-5563	353	5	open	open	ADJ
ejpam-5563	353	6	set	set	VERB
ejpam-5563	353	7	by	by	ADP
ejpam-5563	353	8	(	(	PUNCT
ejpam-5563	353	9	ii	ii	NOUN
ejpam-5563	353	10	)	)	PUNCT
ejpam-5563	353	11	in	in	ADP
ejpam-5563	353	12	theorem	theorem	NOUN
ejpam-5563	353	13	2	2	NUM
ejpam-5563	353	14	.	.	PUNCT
ejpam-5563	353	15	(	(	PUNCT
ejpam-5563	353	16	ii	ii	NOUN
ejpam-5563	353	17	)	)	PUNCT
ejpam-5563	353	18	let	let	VERB
ejpam-5563	353	19	o	o	NOUN
ejpam-5563	353	20	be	be	AUX
ejpam-5563	353	21	a	a	DET
ejpam-5563	353	22	diamond	diamond	NOUN
ejpam-5563	353	23	-	-	PUNCT
ejpam-5563	353	24	closed	close	VERB
ejpam-5563	353	25	subset	subset	NOUN
ejpam-5563	353	26	of	of	ADP
ejpam-5563	353	27	b	b	PROPN
ejpam-5563	353	28	,	,	PUNCT
ejpam-5563	353	29	γ	γ	NOUN
ejpam-5563	353	30	−	−	PROPN
ejpam-5563	353	31	{	{	PUNCT
ejpam-5563	353	32	b	b	NOUN
ejpam-5563	353	33	}	}	PUNCT
ejpam-5563	353	34	⊆	⊆	NUM
ejpam-5563	353	35	p	p	NOUN
ejpam-5563	353	36	and	and	CCONJ
ejpam-5563	353	37	△	△	NOUN
ejpam-5563	353	38	=	=	SYM
ejpam-5563	353	39	{	{	PUNCT
ejpam-5563	353	40	∅	∅	NOUN
ejpam-5563	353	41	}	}	PUNCT
ejpam-5563	353	42	.	.	PUNCT
ejpam-5563	354	1	then	then	ADV
ejpam-5563	354	2	,	,	PUNCT
ejpam-5563	354	3	by	by	ADP
ejpam-5563	354	4	theorem	theorem	NOUN
ejpam-5563	354	5	3	3	NUM
ejpam-5563	354	6	,	,	PUNCT
ejpam-5563	354	7	we	we	PRON
ejpam-5563	354	8	have	have	VERB
ejpam-5563	354	9	γ(b	γ(b	NOUN
ejpam-5563	354	10	)	)	PUNCT
ejpam-5563	355	1	=	=	SYM
ejpam-5563	355	2	b.	b.	PROPN
ejpam-5563	355	3	hence	hence	ADV
ejpam-5563	355	4	,	,	PUNCT
ejpam-5563	355	5	λ(o	λ(o	PROPN
ejpam-5563	355	6	)	)	PUNCT
ejpam-5563	355	7	=	=	SYM
ejpam-5563	355	8	γ∗(o	γ∗(o	PROPN
ejpam-5563	355	9	)	)	PUNCT
ejpam-5563	356	1	−	−	NOUN
ejpam-5563	356	2	o	o	NOUN
ejpam-5563	356	3	⊆	⊆	NUM
ejpam-5563	356	4	γ∗(o	γ∗(o	PROPN
ejpam-5563	356	5	)	)	PUNCT
ejpam-5563	356	6	−	−	ADP
ejpam-5563	356	7	γ(o	γ(o	PROPN
ejpam-5563	356	8	)	)	PUNCT
ejpam-5563	356	9	=	=	SYM
ejpam-5563	356	10	γ∗(∅	γ∗(∅	ADJ
ejpam-5563	356	11	)	)	PUNCT
ejpam-5563	356	12	=	=	PUNCT
ejpam-5563	357	1	[	[	X
ejpam-5563	357	2	γ(b)]c	γ(b)]c	ADP
ejpam-5563	357	3	=	=	SYM
ejpam-5563	357	4	bc	bc	PROPN
ejpam-5563	357	5	=	=	PUNCT
ejpam-5563	357	6	∅.	∅.	VERB
ejpam-5563	357	7	4	4	NUM
ejpam-5563	357	8	.	.	PUNCT
ejpam-5563	358	1	on	on	ADP
ejpam-5563	358	2	λ⋄	λ⋄	NUM
ejpam-5563	358	3	operator	operator	NOUN
ejpam-5563	358	4	definition	definition	NOUN
ejpam-5563	358	5	10	10	NUM
ejpam-5563	358	6	.	.	PUNCT
ejpam-5563	359	1	let	let	VERB
ejpam-5563	359	2	(	(	PUNCT
ejpam-5563	359	3	b	b	X
ejpam-5563	359	4	,	,	PUNCT
ejpam-5563	359	5	γ	γ	PROPN
ejpam-5563	359	6	,	,	PUNCT
ejpam-5563	359	7	p	p	NOUN
ejpam-5563	359	8	)	)	PUNCT
ejpam-5563	359	9	be	be	AUX
ejpam-5563	359	10	a	a	DET
ejpam-5563	359	11	ps	ps	NOUN
ejpam-5563	359	12	.	.	PUNCT
ejpam-5563	360	1	then	then	ADV
ejpam-5563	360	2	,	,	PUNCT
ejpam-5563	360	3	the	the	DET
ejpam-5563	360	4	operator	operator	NOUN
ejpam-5563	360	5	λ⋄	λ⋄	X
ejpam-5563	360	6	:	:	PUNCT
ejpam-5563	360	7	p(b	p(b	NUM
ejpam-5563	360	8	)	)	PUNCT
ejpam-5563	360	9	→	→	SYM
ejpam-5563	360	10	p(b	p(b	PROPN
ejpam-5563	360	11	)	)	PUNCT
ejpam-5563	360	12	is	be	AUX
ejpam-5563	360	13	defined	define	VERB
ejpam-5563	360	14	as	as	SCONJ
ejpam-5563	360	15	follows	follow	VERB
ejpam-5563	360	16	:	:	PUNCT
ejpam-5563	360	17	λ⋄(o	λ⋄(o	NOUN
ejpam-5563	360	18	)	)	PUNCT
ejpam-5563	360	19	=	=	PUNCT
ejpam-5563	361	1	γ∗(o)−	γ∗(o)−	ADP
ejpam-5563	361	2	γ(o	γ(o	PROPN
ejpam-5563	361	3	)	)	PUNCT
ejpam-5563	361	4	for	for	ADP
ejpam-5563	361	5	any	any	DET
ejpam-5563	361	6	set	set	NOUN
ejpam-5563	361	7	o	o	NOUN
ejpam-5563	361	8	⊆	⊆	NUM
ejpam-5563	361	9	b.	b.	PROPN
ejpam-5563	361	10	remark	remark	NOUN
ejpam-5563	361	11	3	3	X
ejpam-5563	361	12	.	.	PUNCT
ejpam-5563	362	1	let	let	VERB
ejpam-5563	362	2	(	(	PUNCT
ejpam-5563	362	3	b	b	X
ejpam-5563	362	4	,	,	PUNCT
ejpam-5563	362	5	γ	γ	PROPN
ejpam-5563	362	6	,	,	PUNCT
ejpam-5563	362	7	p	p	NOUN
ejpam-5563	362	8	)	)	PUNCT
ejpam-5563	362	9	be	be	AUX
ejpam-5563	362	10	a	a	DET
ejpam-5563	362	11	ps	ps	NOUN
ejpam-5563	362	12	and	and	CCONJ
ejpam-5563	362	13	let	let	VERB
ejpam-5563	362	14	o	o	NOUN
ejpam-5563	362	15	⊆	⊆	NUM
ejpam-5563	362	16	b	b	PUNCT
ejpam-5563	362	17	be	be	AUX
ejpam-5563	362	18	a	a	DET
ejpam-5563	362	19	nonempty	nonempty	ADJ
ejpam-5563	362	20	proper	proper	ADJ
ejpam-5563	362	21	subset	subset	NOUN
ejpam-5563	362	22	of	of	ADP
ejpam-5563	362	23	b.	b.	PROPN
ejpam-5563	362	24	(	(	PUNCT
ejpam-5563	362	25	i	i	NOUN
ejpam-5563	362	26	)	)	PUNCT
ejpam-5563	362	27	λ⋄(o	λ⋄(o	PROPN
ejpam-5563	362	28	)	)	PUNCT
ejpam-5563	362	29	=	=	PUNCT
ejpam-5563	363	1	[	[	X
ejpam-5563	363	2	γ(b)]c	γ(b)]c	NOUN
ejpam-5563	363	3	.	.	PUNCT
ejpam-5563	363	4	(	(	PUNCT
ejpam-5563	363	5	ii	ii	NOUN
ejpam-5563	363	6	)	)	PUNCT
ejpam-5563	364	1	if	if	SCONJ
ejpam-5563	364	2	p	p	NOUN
ejpam-5563	364	3	=	=	NOUN
ejpam-5563	364	4	∅	∅	NOUN
ejpam-5563	364	5	,	,	PUNCT
ejpam-5563	364	6	then	then	ADV
ejpam-5563	364	7	λ⋄(o	λ⋄(o	PROPN
ejpam-5563	364	8	)	)	PUNCT
ejpam-5563	364	9	=	=	SYM
ejpam-5563	364	10	b.	b.	PROPN
ejpam-5563	364	11	(	(	PUNCT
ejpam-5563	364	12	iii	iii	NOUN
ejpam-5563	364	13	)	)	PUNCT
ejpam-5563	364	14	if	if	SCONJ
ejpam-5563	364	15	p	p	NOUN
ejpam-5563	364	16	=	=	VERB
ejpam-5563	364	17	p(b)−	p(b)−	PROPN
ejpam-5563	364	18	{	{	PUNCT
ejpam-5563	364	19	b	b	NOUN
ejpam-5563	364	20	}	}	PUNCT
ejpam-5563	364	21	,	,	PUNCT
ejpam-5563	364	22	then	then	ADV
ejpam-5563	364	23	λ⋄(o	λ⋄(o	PROPN
ejpam-5563	364	24	)	)	PUNCT
ejpam-5563	364	25	=	=	PUNCT
ejpam-5563	364	26	∅.	∅.	NOUN
ejpam-5563	364	27	proof	proof	NOUN
ejpam-5563	364	28	.	.	PUNCT
ejpam-5563	365	1	let	let	VERB
ejpam-5563	365	2	o	o	NOUN
ejpam-5563	365	3	be	be	AUX
ejpam-5563	365	4	any	any	PRON
ejpam-5563	365	5	nonempty	nonempty	ADJ
ejpam-5563	365	6	proper	proper	ADJ
ejpam-5563	365	7	subset	subset	NOUN
ejpam-5563	365	8	of	of	ADP
ejpam-5563	365	9	b.	b.	PROPN
ejpam-5563	365	10	then	then	ADV
ejpam-5563	365	11	,	,	PUNCT
ejpam-5563	365	12	(	(	PUNCT
ejpam-5563	365	13	i	i	NOUN
ejpam-5563	365	14	)	)	PUNCT
ejpam-5563	365	15	λ⋄(o	λ⋄(o	NOUN
ejpam-5563	365	16	)	)	PUNCT
ejpam-5563	366	1	=	=	VERB
ejpam-5563	366	2	γ∗(o)−	γ∗(o)−	ADP
ejpam-5563	366	3	γ(o	γ(o	NUM
ejpam-5563	366	4	)	)	PUNCT
ejpam-5563	367	1	=	=	SYM
ejpam-5563	367	2	γ∗(o	γ∗(o	PROPN
ejpam-5563	367	3	)	)	PUNCT
ejpam-5563	367	4	∩	∩	NOUN
ejpam-5563	367	5	[	[	X
ejpam-5563	367	6	γ(o)]c	γ(o)]c	NOUN
ejpam-5563	367	7	=	=	SYM
ejpam-5563	367	8	γ∗(o	γ∗(o	PROPN
ejpam-5563	367	9	)	)	PUNCT
ejpam-5563	367	10	∩	∩	ADJ
ejpam-5563	367	11	γ∗(oc	γ∗(oc	NOUN
ejpam-5563	367	12	)	)	PUNCT
ejpam-5563	367	13	=	=	NOUN
ejpam-5563	367	14	γ∗(o	γ∗(o	PROPN
ejpam-5563	367	15	∩oc	∩oc	NOUN
ejpam-5563	367	16	)	)	PUNCT
ejpam-5563	367	17	=	=	SYM
ejpam-5563	367	18	γ∗(∅	γ∗(∅	ADJ
ejpam-5563	367	19	)	)	PUNCT
ejpam-5563	367	20	=	=	PUNCT
ejpam-5563	368	1	[	[	X
ejpam-5563	368	2	γ(b)]c	γ(b)]c	NOUN
ejpam-5563	368	3	.	.	PUNCT
ejpam-5563	368	4	(	(	PUNCT
ejpam-5563	368	5	ii	ii	NOUN
ejpam-5563	368	6	)	)	PUNCT
ejpam-5563	368	7	if	if	SCONJ
ejpam-5563	368	8	p	p	NOUN
ejpam-5563	368	9	=	=	NOUN
ejpam-5563	368	10	∅	∅	NOUN
ejpam-5563	368	11	,	,	PUNCT
ejpam-5563	368	12	then	then	ADV
ejpam-5563	368	13	oc	oc	VERB
ejpam-5563	368	14	/∈	/∈	PUNCT
ejpam-5563	369	1	p	p	NOUN
ejpam-5563	369	2	since	since	SCONJ
ejpam-5563	369	3	it	it	PRON
ejpam-5563	369	4	is	be	AUX
ejpam-5563	369	5	a	a	DET
ejpam-5563	369	6	proper	proper	ADJ
ejpam-5563	369	7	subset	subset	NOUN
ejpam-5563	369	8	of	of	ADP
ejpam-5563	369	9	b	b	NOUN
ejpam-5563	369	10	;	;	PUNCT
ejpam-5563	369	11	hence	hence	ADV
ejpam-5563	369	12	γ(o	γ(o	ADJ
ejpam-5563	369	13	)	)	PUNCT
ejpam-5563	370	1	=	=	PUNCT
ejpam-5563	370	2	∅	∅	NOUN
ejpam-5563	370	3	by	by	ADP
ejpam-5563	370	4	(	(	PUNCT
ejpam-5563	370	5	vi	vi	NOUN
ejpam-5563	370	6	)	)	PUNCT
ejpam-5563	370	7	in	in	ADP
ejpam-5563	370	8	theorem	theorem	NOUN
ejpam-5563	370	9	1	1	NUM
ejpam-5563	370	10	.	.	PUNCT
ejpam-5563	371	1	thus	thus	ADV
ejpam-5563	371	2	,	,	PUNCT
ejpam-5563	371	3	since	since	SCONJ
ejpam-5563	371	4	o	o	NOUN
ejpam-5563	371	5	=	=	NOUN
ejpam-5563	371	6	̸	̸	ADJ
ejpam-5563	371	7	∅	∅	NOUN
ejpam-5563	371	8	,	,	PUNCT
ejpam-5563	371	9	λ⋄(o	λ⋄(o	NOUN
ejpam-5563	371	10	)	)	PUNCT
ejpam-5563	371	11	=	=	SYM
ejpam-5563	371	12	γ∗(o	γ∗(o	PROPN
ejpam-5563	371	13	)	)	PUNCT
ejpam-5563	371	14	=	=	SYM
ejpam-5563	371	15	b.	b.	PROPN
ejpam-5563	371	16	(	(	PUNCT
ejpam-5563	371	17	iii	iii	NOUN
ejpam-5563	371	18	)	)	PUNCT
ejpam-5563	371	19	suppose	suppose	VERB
ejpam-5563	371	20	that	that	SCONJ
ejpam-5563	371	21	p	p	X
ejpam-5563	371	22	=	=	PUNCT
ejpam-5563	371	23	p(b)−{b	p(b)−{b	PROPN
ejpam-5563	371	24	}	}	PUNCT
ejpam-5563	371	25	.	.	PUNCT
ejpam-5563	372	1	then	then	ADV
ejpam-5563	372	2	,	,	PUNCT
ejpam-5563	372	3	we	we	PRON
ejpam-5563	372	4	have	have	VERB
ejpam-5563	372	5	r	r	NOUN
ejpam-5563	372	6	∈	∈	PROPN
ejpam-5563	372	7	γ(b	γ(b	NOUN
ejpam-5563	372	8	)	)	PUNCT
ejpam-5563	372	9	for	for	ADP
ejpam-5563	372	10	every	every	DET
ejpam-5563	372	11	r	r	NOUN
ejpam-5563	372	12	∈	∈	PROPN
ejpam-5563	372	13	b	b	NOUN
ejpam-5563	372	14	since	since	SCONJ
ejpam-5563	372	15	u	u	PROPN
ejpam-5563	372	16	c	c	PROPN
ejpam-5563	372	17	∈	∈	PROPN
ejpam-5563	372	18	p	p	NOUN
ejpam-5563	372	19	for	for	ADP
ejpam-5563	372	20	each	each	DET
ejpam-5563	372	21	u	u	PROPN
ejpam-5563	372	22	∈	∈	PROPN
ejpam-5563	372	23	γ(r	γ(r	PROPN
ejpam-5563	372	24	)	)	PUNCT
ejpam-5563	372	25	.	.	PUNCT
ejpam-5563	373	1	∴	∴	PROPN
ejpam-5563	373	2	λ⋄(o	λ⋄(o	PROPN
ejpam-5563	373	3	)	)	PUNCT
ejpam-5563	373	4	=	=	PUNCT
ejpam-5563	374	1	[	[	X
ejpam-5563	374	2	γ(b)]c	γ(b)]c	ADP
ejpam-5563	374	3	=	=	SYM
ejpam-5563	375	1	[	[	X
ejpam-5563	375	2	b]c	b]c	NOUN
ejpam-5563	375	3	=	=	PUNCT
ejpam-5563	375	4	∅.	∅.	NOUN
ejpam-5563	375	5	example	example	NOUN
ejpam-5563	375	6	4	4	NUM
ejpam-5563	375	7	.	.	PUNCT
ejpam-5563	376	1	let	let	VERB
ejpam-5563	376	2	(	(	PUNCT
ejpam-5563	376	3	r	r	NOUN
ejpam-5563	376	4	,	,	PUNCT
ejpam-5563	376	5	τ√2,p	τ√2,p	NUM
ejpam-5563	376	6	)	)	PUNCT
ejpam-5563	376	7	be	be	AUX
ejpam-5563	376	8	defined	define	VERB
ejpam-5563	376	9	as	as	ADP
ejpam-5563	376	10	in	in	ADP
ejpam-5563	376	11	example	example	NOUN
ejpam-5563	376	12	2	2	NUM
ejpam-5563	376	13	and	and	CCONJ
ejpam-5563	376	14	let	let	VERB
ejpam-5563	376	15	k	k	PROPN
ejpam-5563	376	16	⊆	⊆	PROPN
ejpam-5563	376	17	r.	r.	PROPN
ejpam-5563	376	18	then	then	ADV
ejpam-5563	376	19	,	,	PUNCT
ejpam-5563	376	20	we	we	PRON
ejpam-5563	376	21	have	have	VERB
ejpam-5563	376	22	λ⋄(k	λ⋄(k	NOUN
ejpam-5563	376	23	)	)	PUNCT
ejpam-5563	376	24	=	=	PUNCT
ejpam-5563	377	1	[	[	X
ejpam-5563	377	2	γ(r)]c	γ(r)]c	X
ejpam-5563	377	3	=	=	SYM
ejpam-5563	377	4	r.	r.	PROPN
ejpam-5563	377	5	o.	o.	PROPN
ejpam-5563	377	6	alghamdi	alghamdi	PROPN
ejpam-5563	377	7	/	/	SYM
ejpam-5563	377	8	eur	eur	PROPN
ejpam-5563	377	9	.	.	PUNCT
ejpam-5563	378	1	j.	j.	PROPN
ejpam-5563	378	2	pure	pure	PROPN
ejpam-5563	378	3	appl	appl	PROPN
ejpam-5563	378	4	.	.	PROPN
ejpam-5563	378	5	math	math	PROPN
ejpam-5563	378	6	,	,	PUNCT
ejpam-5563	378	7	17	17	NUM
ejpam-5563	378	8	(	(	PUNCT
ejpam-5563	378	9	4	4	NUM
ejpam-5563	378	10	)	)	PUNCT
ejpam-5563	378	11	(	(	PUNCT
ejpam-5563	378	12	2024	2024	NUM
ejpam-5563	378	13	)	)	PUNCT
ejpam-5563	378	14	,	,	PUNCT
ejpam-5563	378	15	3517	3517	NUM
ejpam-5563	378	16	-	-	SYM
ejpam-5563	378	17	3538	3538	NUM
ejpam-5563	378	18	3527	3527	NUM
ejpam-5563	378	19	lemma	lemma	PROPN
ejpam-5563	378	20	3	3	X
ejpam-5563	378	21	.	.	PUNCT
ejpam-5563	379	1	let	let	VERB
ejpam-5563	379	2	(	(	PUNCT
ejpam-5563	379	3	b	b	X
ejpam-5563	379	4	,	,	PUNCT
ejpam-5563	379	5	γ	γ	PROPN
ejpam-5563	379	6	,	,	PUNCT
ejpam-5563	379	7	p	p	NOUN
ejpam-5563	379	8	)	)	PUNCT
ejpam-5563	379	9	be	be	AUX
ejpam-5563	379	10	a	a	DET
ejpam-5563	379	11	ps	ps	NOUN
ejpam-5563	379	12	and	and	CCONJ
ejpam-5563	379	13	o	o	PROPN
ejpam-5563	379	14	⊆	⊆	NUM
ejpam-5563	379	15	b.	b.	NOUN
ejpam-5563	379	16	then	then	ADV
ejpam-5563	379	17	,	,	PUNCT
ejpam-5563	379	18	(	(	PUNCT
ejpam-5563	379	19	i	i	NOUN
ejpam-5563	379	20	)	)	PUNCT
ejpam-5563	379	21	λ⋄(o	λ⋄(o	PROPN
ejpam-5563	379	22	)	)	PUNCT
ejpam-5563	379	23	∈	∈	PROPN
ejpam-5563	379	24	γ	γ	X
ejpam-5563	379	25	.	.	PROPN
ejpam-5563	379	26	(	(	PUNCT
ejpam-5563	379	27	ii	ii	NOUN
ejpam-5563	379	28	)	)	PUNCT
ejpam-5563	379	29	λ⋄(o	λ⋄(o	NOUN
ejpam-5563	379	30	)	)	PUNCT
ejpam-5563	379	31	=	=	PUNCT
ejpam-5563	379	32	∅	∅	NOUN
ejpam-5563	380	1	if	if	SCONJ
ejpam-5563	380	2	and	and	CCONJ
ejpam-5563	380	3	only	only	ADV
ejpam-5563	380	4	if	if	SCONJ
ejpam-5563	380	5	γ∗(o	γ∗(o	PROPN
ejpam-5563	380	6	)	)	PUNCT
ejpam-5563	380	7	⊆	⊆	NUM
ejpam-5563	380	8	γ(o	γ(o	NUM
ejpam-5563	380	9	)	)	PUNCT
ejpam-5563	380	10	.	.	PUNCT
ejpam-5563	381	1	proof	proof	NOUN
ejpam-5563	381	2	.	.	PUNCT
ejpam-5563	382	1	(	(	PUNCT
ejpam-5563	382	2	i	i	NOUN
ejpam-5563	382	3	)	)	PUNCT
ejpam-5563	382	4	since	since	SCONJ
ejpam-5563	382	5	λ⋄(o	λ⋄(o	NOUN
ejpam-5563	382	6	)	)	PUNCT
ejpam-5563	382	7	=	=	PUNCT
ejpam-5563	383	1	[	[	X
ejpam-5563	383	2	γ(b)]c	γ(b)]c	ADP
ejpam-5563	383	3	,	,	PUNCT
ejpam-5563	383	4	then	then	ADV
ejpam-5563	383	5	λ⋄(o	λ⋄(o	PROPN
ejpam-5563	383	6	)	)	PUNCT
ejpam-5563	383	7	∈	∈	PROPN
ejpam-5563	383	8	γ	γ	X
ejpam-5563	383	9	by	by	ADP
ejpam-5563	383	10	(	(	PUNCT
ejpam-5563	383	11	iii	iii	NOUN
ejpam-5563	383	12	)	)	PUNCT
ejpam-5563	383	13	in	in	ADP
ejpam-5563	383	14	theorem	theorem	NOUN
ejpam-5563	383	15	1	1	NUM
ejpam-5563	383	16	.	.	PUNCT
ejpam-5563	383	17	(	(	PUNCT
ejpam-5563	383	18	ii	ii	NOUN
ejpam-5563	383	19	)	)	PUNCT
ejpam-5563	383	20	it	it	PRON
ejpam-5563	383	21	is	be	AUX
ejpam-5563	383	22	obvious	obvious	ADJ
ejpam-5563	383	23	by	by	ADP
ejpam-5563	383	24	the	the	DET
ejpam-5563	383	25	definition	definition	NOUN
ejpam-5563	383	26	of	of	ADP
ejpam-5563	383	27	λ⋄	λ⋄	NUM
ejpam-5563	383	28	operator	operator	NOUN
ejpam-5563	383	29	.	.	PUNCT
ejpam-5563	384	1	corollary	corollary	ADJ
ejpam-5563	384	2	4	4	NUM
ejpam-5563	384	3	.	.	PUNCT
ejpam-5563	385	1	let	let	VERB
ejpam-5563	385	2	(	(	PUNCT
ejpam-5563	385	3	b	b	X
ejpam-5563	385	4	,	,	PUNCT
ejpam-5563	385	5	γ	γ	PROPN
ejpam-5563	385	6	,	,	PUNCT
ejpam-5563	385	7	p	p	NOUN
ejpam-5563	385	8	)	)	PUNCT
ejpam-5563	385	9	be	be	AUX
ejpam-5563	385	10	a	a	DET
ejpam-5563	385	11	ps	ps	NOUN
ejpam-5563	385	12	and	and	CCONJ
ejpam-5563	385	13	o	o	PROPN
ejpam-5563	385	14	⊆	⊆	NUM
ejpam-5563	385	15	b.	b.	PROPN
ejpam-5563	385	16	then	then	ADV
ejpam-5563	385	17	,	,	PUNCT
ejpam-5563	385	18	γ−	γ−	PROPN
ejpam-5563	385	19	{	{	PUNCT
ejpam-5563	385	20	b	b	NOUN
ejpam-5563	385	21	}	}	PUNCT
ejpam-5563	385	22	⊆	⊆	NUM
ejpam-5563	385	23	p	p	NOUN
ejpam-5563	385	24	and	and	CCONJ
ejpam-5563	385	25	△	△	NOUN
ejpam-5563	385	26	=	=	SYM
ejpam-5563	385	27	{	{	PUNCT
ejpam-5563	385	28	∅	∅	NOUN
ejpam-5563	385	29	}	}	PUNCT
ejpam-5563	385	30	⇔	⇔	PROPN
ejpam-5563	385	31	λ⋄(o	λ⋄(o	NOUN
ejpam-5563	385	32	)	)	PUNCT
ejpam-5563	385	33	=	=	PUNCT
ejpam-5563	385	34	∅.	∅.	NOUN
ejpam-5563	385	35	proof	proof	NOUN
ejpam-5563	385	36	.	.	PUNCT
ejpam-5563	386	1	let	let	VERB
ejpam-5563	386	2	o	o	NOUN
ejpam-5563	386	3	⊆	⊆	NUM
ejpam-5563	386	4	b	b	PROPN
ejpam-5563	386	5	and	and	CCONJ
ejpam-5563	386	6	γ−{b	γ−{b	PROPN
ejpam-5563	386	7	}	}	PUNCT
ejpam-5563	386	8	⊆	⊆	NUM
ejpam-5563	386	9	p	p	NOUN
ejpam-5563	386	10	such	such	ADJ
ejpam-5563	386	11	that	that	PRON
ejpam-5563	386	12	△	△	NOUN
ejpam-5563	386	13	=	=	SYM
ejpam-5563	386	14	{	{	PUNCT
ejpam-5563	386	15	∅	∅	NOUN
ejpam-5563	386	16	}	}	PUNCT
ejpam-5563	386	17	.	.	PUNCT
ejpam-5563	387	1	then	then	ADV
ejpam-5563	387	2	,	,	PUNCT
ejpam-5563	387	3	by	by	ADP
ejpam-5563	387	4	theorem	theorem	NOUN
ejpam-5563	387	5	3	3	NUM
ejpam-5563	387	6	,	,	PUNCT
ejpam-5563	387	7	γ(b	γ(b	X
ejpam-5563	387	8	)	)	PUNCT
ejpam-5563	387	9	=	=	SYM
ejpam-5563	387	10	b	b	NOUN
ejpam-5563	387	11	which	which	PRON
ejpam-5563	387	12	implies	imply	VERB
ejpam-5563	387	13	that	that	DET
ejpam-5563	387	14	λ⋄(o	λ⋄(o	NOUN
ejpam-5563	387	15	)	)	PUNCT
ejpam-5563	387	16	=	=	PUNCT
ejpam-5563	387	17	∅.	∅.	NOUN
ejpam-5563	387	18	for	for	ADP
ejpam-5563	387	19	the	the	DET
ejpam-5563	387	20	converse	converse	NOUN
ejpam-5563	387	21	,	,	PUNCT
ejpam-5563	387	22	if	if	SCONJ
ejpam-5563	387	23	λ⋄(o	λ⋄(o	NOUN
ejpam-5563	387	24	)	)	PUNCT
ejpam-5563	387	25	=	=	NOUN
ejpam-5563	387	26	∅	∅	NOUN
ejpam-5563	387	27	=	=	PUNCT
ejpam-5563	388	1	[	[	X
ejpam-5563	388	2	γ(b)]c	γ(b)]c	ADP
ejpam-5563	388	3	,	,	PUNCT
ejpam-5563	388	4	then	then	ADV
ejpam-5563	388	5	γ(b	γ(b	X
ejpam-5563	388	6	)	)	PUNCT
ejpam-5563	388	7	=	=	SYM
ejpam-5563	388	8	b	b	NOUN
ejpam-5563	388	9	which	which	PRON
ejpam-5563	388	10	implies	imply	VERB
ejpam-5563	388	11	that	that	SCONJ
ejpam-5563	388	12	γ−	γ−	PROPN
ejpam-5563	388	13	{	{	PUNCT
ejpam-5563	388	14	b	b	NOUN
ejpam-5563	388	15	}	}	PUNCT
ejpam-5563	388	16	⊆	⊆	NUM
ejpam-5563	388	17	p	p	NOUN
ejpam-5563	388	18	and	and	CCONJ
ejpam-5563	388	19	△	△	NOUN
ejpam-5563	388	20	=	=	SYM
ejpam-5563	388	21	{	{	PUNCT
ejpam-5563	388	22	∅	∅	NOUN
ejpam-5563	388	23	}	}	PUNCT
ejpam-5563	388	24	by	by	ADP
ejpam-5563	388	25	theorem	theorem	ADJ
ejpam-5563	388	26	3	3	NUM
ejpam-5563	388	27	.	.	PUNCT
ejpam-5563	388	28	theorem	theorem	NOUN
ejpam-5563	388	29	17	17	NUM
ejpam-5563	388	30	.	.	PUNCT
ejpam-5563	389	1	let	let	VERB
ejpam-5563	389	2	(	(	PUNCT
ejpam-5563	389	3	b	b	X
ejpam-5563	389	4	,	,	PUNCT
ejpam-5563	389	5	γ	γ	PROPN
ejpam-5563	389	6	,	,	PUNCT
ejpam-5563	389	7	p	p	NOUN
ejpam-5563	389	8	)	)	PUNCT
ejpam-5563	389	9	be	be	AUX
ejpam-5563	389	10	a	a	DET
ejpam-5563	389	11	ps	ps	NOUN
ejpam-5563	389	12	and	and	CCONJ
ejpam-5563	389	13	let	let	VERB
ejpam-5563	389	14	∅	∅	NOUN
ejpam-5563	389	15	=	=	NOUN
ejpam-5563	389	16	̸	̸	NUM
ejpam-5563	389	17	o	o	NOUN
ejpam-5563	390	1	⊆	⊆	NUM
ejpam-5563	390	2	b.	b.	NOUN
ejpam-5563	390	3	then	then	ADV
ejpam-5563	390	4	,	,	PUNCT
ejpam-5563	390	5	the	the	DET
ejpam-5563	390	6	following	follow	VERB
ejpam-5563	390	7	properties	property	NOUN
ejpam-5563	390	8	hold	hold	VERB
ejpam-5563	390	9	:	:	PUNCT
ejpam-5563	390	10	(	(	PUNCT
ejpam-5563	390	11	i	i	NOUN
ejpam-5563	390	12	)	)	PUNCT
ejpam-5563	390	13	λ⋄(o	λ⋄(o	NOUN
ejpam-5563	390	14	)	)	PUNCT
ejpam-5563	390	15	=	=	SYM
ejpam-5563	391	1	b	b	NOUN
ejpam-5563	392	1	if	if	SCONJ
ejpam-5563	392	2	and	and	CCONJ
ejpam-5563	392	3	only	only	ADV
ejpam-5563	392	4	if	if	SCONJ
ejpam-5563	392	5	for	for	ADP
ejpam-5563	392	6	every	every	DET
ejpam-5563	392	7	r	r	NOUN
ejpam-5563	392	8	∈	∈	PROPN
ejpam-5563	392	9	b	b	NOUN
ejpam-5563	392	10	,	,	PUNCT
ejpam-5563	392	11	there	there	PRON
ejpam-5563	392	12	exists	exist	VERB
ejpam-5563	392	13	r	r	NOUN
ejpam-5563	392	14	∈	∈	PROPN
ejpam-5563	392	15	γ(r	γ(r	PROPN
ejpam-5563	392	16	)	)	PUNCT
ejpam-5563	392	17	such	such	ADJ
ejpam-5563	392	18	that	that	SCONJ
ejpam-5563	392	19	(	(	PUNCT
ejpam-5563	392	20	r⋄)c	r⋄)c	PROPN
ejpam-5563	392	21	/∈	/∈	PUNCT
ejpam-5563	393	1	p.	p.	NOUN
ejpam-5563	393	2	(	(	PUNCT
ejpam-5563	393	3	ii	ii	PROPN
ejpam-5563	393	4	)	)	PUNCT
ejpam-5563	393	5	if	if	SCONJ
ejpam-5563	393	6	λ⋄(o	λ⋄(o	NOUN
ejpam-5563	393	7	)	)	PUNCT
ejpam-5563	394	1	=	=	SYM
ejpam-5563	394	2	o	o	NOUN
ejpam-5563	394	3	,	,	PUNCT
ejpam-5563	394	4	then	then	ADV
ejpam-5563	394	5	γ(b	γ(b	X
ejpam-5563	394	6	)	)	PUNCT
ejpam-5563	394	7	̸=	̸=	PROPN
ejpam-5563	394	8	b.	b.	PROPN
ejpam-5563	394	9	(	(	PUNCT
ejpam-5563	394	10	iii	iii	NOUN
ejpam-5563	394	11	)	)	PUNCT
ejpam-5563	394	12	λ⋄(o	λ⋄(o	NOUN
ejpam-5563	394	13	)	)	PUNCT
ejpam-5563	394	14	=	=	SYM
ejpam-5563	394	15	γ∗(oc	γ∗(oc	NOUN
ejpam-5563	394	16	)	)	PUNCT
ejpam-5563	395	1	if	if	SCONJ
ejpam-5563	395	2	and	and	CCONJ
ejpam-5563	395	3	only	only	ADV
ejpam-5563	395	4	if	if	SCONJ
ejpam-5563	395	5	[	[	X
ejpam-5563	395	6	γ(o)]c	γ(o)]c	NOUN
ejpam-5563	395	7	⊆	⊆	NUM
ejpam-5563	395	8	γ∗(o	γ∗(o	PROPN
ejpam-5563	395	9	)	)	PUNCT
ejpam-5563	395	10	.	.	PUNCT
ejpam-5563	396	1	(	(	PUNCT
ejpam-5563	396	2	iv	iv	X
ejpam-5563	396	3	)	)	PUNCT
ejpam-5563	396	4	if	if	SCONJ
ejpam-5563	396	5	o	o	NOUN
ejpam-5563	396	6	is	be	AUX
ejpam-5563	396	7	a	a	DET
ejpam-5563	396	8	diamond	diamond	NOUN
ejpam-5563	396	9	-	-	PUNCT
ejpam-5563	396	10	open	open	NOUN
ejpam-5563	396	11	set	set	NOUN
ejpam-5563	396	12	,	,	PUNCT
ejpam-5563	396	13	then	then	ADV
ejpam-5563	396	14	o	o	X
ejpam-5563	396	15	−	−	PROPN
ejpam-5563	396	16	γ(o	γ(o	PROPN
ejpam-5563	396	17	)	)	PUNCT
ejpam-5563	396	18	⊆	⊆	NUM
ejpam-5563	396	19	λ⋄(o	λ⋄(o	NOUN
ejpam-5563	396	20	)	)	PUNCT
ejpam-5563	396	21	.	.	PUNCT
ejpam-5563	397	1	(	(	PUNCT
ejpam-5563	397	2	v	v	NOUN
ejpam-5563	397	3	)	)	PUNCT
ejpam-5563	397	4	λ⋄(o	λ⋄(o	NOUN
ejpam-5563	397	5	)	)	PUNCT
ejpam-5563	397	6	⊆	⊆	NUM
ejpam-5563	397	7	γ∗(λ⋄(o	γ∗(λ⋄(o	NOUN
ejpam-5563	397	8	)	)	PUNCT
ejpam-5563	397	9	)	)	PUNCT
ejpam-5563	397	10	.	.	PUNCT
ejpam-5563	398	1	(	(	PUNCT
ejpam-5563	398	2	vi	vi	X
ejpam-5563	398	3	)	)	PUNCT
ejpam-5563	398	4	if	if	SCONJ
ejpam-5563	398	5	oc	oc	PART
ejpam-5563	398	6	/∈	/∈	PUNCT
ejpam-5563	399	1	p	p	X
ejpam-5563	399	2	,	,	PUNCT
ejpam-5563	399	3	then	then	ADV
ejpam-5563	399	4	λ⋄(o	λ⋄(o	PROPN
ejpam-5563	399	5	)	)	PUNCT
ejpam-5563	399	6	=	=	SYM
ejpam-5563	399	7	γ∗(o	γ∗(o	PROPN
ejpam-5563	399	8	)	)	PUNCT
ejpam-5563	399	9	.	.	PUNCT
ejpam-5563	400	1	proof	proof	NOUN
ejpam-5563	400	2	.	.	PUNCT
ejpam-5563	401	1	(	(	PUNCT
ejpam-5563	401	2	i	i	NOUN
ejpam-5563	401	3	)	)	PUNCT
ejpam-5563	401	4	λ⋄(o	λ⋄(o	NOUN
ejpam-5563	401	5	)	)	PUNCT
ejpam-5563	401	6	=	=	PUNCT
ejpam-5563	402	1	[	[	X
ejpam-5563	402	2	γ(b)]c	γ(b)]c	ADP
ejpam-5563	402	3	=	=	SYM
ejpam-5563	402	4	b	b	X
ejpam-5563	402	5	⇐	⇐	ADJ
ejpam-5563	402	6	⇒	⇒	NOUN
ejpam-5563	402	7	γ(b	γ(b	X
ejpam-5563	402	8	)	)	PUNCT
ejpam-5563	402	9	=	=	PUNCT
ejpam-5563	402	10	∅.	∅.	VERB
ejpam-5563	402	11	hence	hence	ADV
ejpam-5563	402	12	,	,	PUNCT
ejpam-5563	402	13	for	for	ADP
ejpam-5563	402	14	every	every	DET
ejpam-5563	402	15	r	r	NOUN
ejpam-5563	402	16	∈	∈	PROPN
ejpam-5563	402	17	b	b	NOUN
ejpam-5563	402	18	,	,	PUNCT
ejpam-5563	402	19	there	there	PRON
ejpam-5563	402	20	exists	exist	VERB
ejpam-5563	402	21	r	r	NOUN
ejpam-5563	402	22	∈	∈	PROPN
ejpam-5563	402	23	γ(r	γ(r	PROPN
ejpam-5563	402	24	)	)	PUNCT
ejpam-5563	402	25	such	such	ADJ
ejpam-5563	402	26	that	that	SCONJ
ejpam-5563	402	27	(	(	PUNCT
ejpam-5563	402	28	r⋄	r⋄	NOUN
ejpam-5563	402	29	∩	∩	X
ejpam-5563	402	30	b)c	b)c	X
ejpam-5563	402	31	=	=	SYM
ejpam-5563	402	32	(	(	PUNCT
ejpam-5563	402	33	r⋄)c	r⋄)c	VERB
ejpam-5563	402	34	/∈	/∈	PUNCT
ejpam-5563	403	1	p.	p.	NOUN
ejpam-5563	403	2	conversely	conversely	ADV
ejpam-5563	403	3	,	,	PUNCT
ejpam-5563	403	4	suppose	suppose	VERB
ejpam-5563	403	5	that	that	SCONJ
ejpam-5563	403	6	for	for	ADP
ejpam-5563	403	7	every	every	DET
ejpam-5563	403	8	r	r	NOUN
ejpam-5563	403	9	∈	∈	PROPN
ejpam-5563	403	10	b	b	NOUN
ejpam-5563	403	11	,	,	PUNCT
ejpam-5563	403	12	there	there	PRON
ejpam-5563	403	13	exists	exist	VERB
ejpam-5563	403	14	r	r	NOUN
ejpam-5563	403	15	∈	∈	PROPN
ejpam-5563	403	16	γ(r	γ(r	PROPN
ejpam-5563	403	17	)	)	PUNCT
ejpam-5563	404	1	such	such	ADJ
ejpam-5563	404	2	that	that	SCONJ
ejpam-5563	404	3	(	(	PUNCT
ejpam-5563	404	4	r⋄)c	r⋄)c	PROPN
ejpam-5563	404	5	/∈	/∈	PUNCT
ejpam-5563	405	1	p.	p.	NOUN
ejpam-5563	405	2	then	then	ADV
ejpam-5563	405	3	,	,	PUNCT
ejpam-5563	405	4	γ(b	γ(b	X
ejpam-5563	405	5	)	)	PUNCT
ejpam-5563	405	6	=	=	SYM
ejpam-5563	405	7	∅	∅	NOUN
ejpam-5563	405	8	;	;	PUNCT
ejpam-5563	405	9	hence	hence	ADV
ejpam-5563	405	10	,	,	PUNCT
ejpam-5563	405	11	λ⋄(o	λ⋄(o	NOUN
ejpam-5563	405	12	)	)	PUNCT
ejpam-5563	405	13	=	=	SYM
ejpam-5563	406	1	b	b	PROPN
ejpam-5563	406	2	for	for	ADP
ejpam-5563	406	3	any	any	PRON
ejpam-5563	406	4	o	o	NOUN
ejpam-5563	406	5	⊆	⊆	NUM
ejpam-5563	406	6	b.	b.	PROPN
ejpam-5563	406	7	(	(	PUNCT
ejpam-5563	406	8	ii	ii	NOUN
ejpam-5563	406	9	)	)	PUNCT
ejpam-5563	406	10	suppose	suppose	VERB
ejpam-5563	406	11	that	that	SCONJ
ejpam-5563	406	12	λ⋄(o	λ⋄(o	NOUN
ejpam-5563	406	13	)	)	PUNCT
ejpam-5563	406	14	=	=	SYM
ejpam-5563	407	1	o.	o.	NOUN
ejpam-5563	407	2	then	then	ADV
ejpam-5563	407	3	,	,	PUNCT
ejpam-5563	408	1	[	[	X
ejpam-5563	408	2	γ(b)]c	γ(b)]c	ADP
ejpam-5563	408	3	=	=	SYM
ejpam-5563	408	4	o	o	X
ejpam-5563	408	5	which	which	PRON
ejpam-5563	408	6	implies	imply	VERB
ejpam-5563	408	7	that	that	SCONJ
ejpam-5563	408	8	γ(b	γ(b	NOUN
ejpam-5563	408	9	)	)	PUNCT
ejpam-5563	408	10	=	=	SYM
ejpam-5563	408	11	oc	oc	ADP
ejpam-5563	408	12	̸=	̸=	PROPN
ejpam-5563	408	13	b	b	PROPN
ejpam-5563	408	14	since	since	SCONJ
ejpam-5563	408	15	o	o	NOUN
ejpam-5563	408	16	=	=	NOUN
ejpam-5563	408	17	̸	̸	ADV
ejpam-5563	408	18	∅.	∅.	VERB
ejpam-5563	408	19	o.	o.	PROPN
ejpam-5563	408	20	alghamdi	alghamdi	PROPN
ejpam-5563	408	21	/	/	SYM
ejpam-5563	408	22	eur	eur	PROPN
ejpam-5563	408	23	.	.	PUNCT
ejpam-5563	409	1	j.	j.	PROPN
ejpam-5563	409	2	pure	pure	PROPN
ejpam-5563	409	3	appl	appl	PROPN
ejpam-5563	409	4	.	.	PROPN
ejpam-5563	409	5	math	math	PROPN
ejpam-5563	409	6	,	,	PUNCT
ejpam-5563	409	7	17	17	NUM
ejpam-5563	409	8	(	(	PUNCT
ejpam-5563	409	9	4	4	NUM
ejpam-5563	409	10	)	)	PUNCT
ejpam-5563	409	11	(	(	PUNCT
ejpam-5563	409	12	2024	2024	NUM
ejpam-5563	409	13	)	)	PUNCT
ejpam-5563	409	14	,	,	PUNCT
ejpam-5563	409	15	3517	3517	NUM
ejpam-5563	409	16	-	-	SYM
ejpam-5563	409	17	3538	3538	NUM
ejpam-5563	409	18	3528	3528	NUM
ejpam-5563	409	19	(	(	PUNCT
ejpam-5563	409	20	iii	iii	NOUN
ejpam-5563	409	21	)	)	PUNCT
ejpam-5563	409	22	λ⋄(o	λ⋄(o	NOUN
ejpam-5563	409	23	)	)	PUNCT
ejpam-5563	410	1	=	=	VERB
ejpam-5563	410	2	γ∗(o)−	γ∗(o)−	ADP
ejpam-5563	410	3	γ(o	γ(o	NUM
ejpam-5563	410	4	)	)	PUNCT
ejpam-5563	410	5	=	=	SYM
ejpam-5563	410	6	γ∗(oc	γ∗(oc	NOUN
ejpam-5563	410	7	)	)	PUNCT
ejpam-5563	410	8	=	=	SYM
ejpam-5563	410	9	γ∗(o	γ∗(o	PROPN
ejpam-5563	410	10	)	)	PUNCT
ejpam-5563	410	11	∩	∩	NOUN
ejpam-5563	410	12	[	[	X
ejpam-5563	410	13	γ(o)]c	γ(o)]c	NOUN
ejpam-5563	410	14	=	=	SYM
ejpam-5563	410	15	γ∗(oc	γ∗(oc	PROPN
ejpam-5563	410	16	)	)	PUNCT
ejpam-5563	410	17	=	=	SYM
ejpam-5563	410	18	γ∗(o	γ∗(o	PROPN
ejpam-5563	410	19	)	)	PUNCT
ejpam-5563	410	20	∩	∩	ADJ
ejpam-5563	410	21	γ∗(oc	γ∗(oc	NOUN
ejpam-5563	410	22	)	)	PUNCT
ejpam-5563	410	23	=	=	SYM
ejpam-5563	410	24	γ∗(oc	γ∗(oc	NOUN
ejpam-5563	410	25	)	)	PUNCT
ejpam-5563	410	26	⇔γ∗(oc	⇔γ∗(oc	NOUN
ejpam-5563	410	27	)	)	PUNCT
ejpam-5563	410	28	=	=	NOUN
ejpam-5563	411	1	[	[	X
ejpam-5563	411	2	γ(o)]c	γ(o)]c	NOUN
ejpam-5563	411	3	⊆	⊆	NUM
ejpam-5563	411	4	γ∗(o	γ∗(o	PROPN
ejpam-5563	411	5	)	)	PUNCT
ejpam-5563	411	6	.	.	PUNCT
ejpam-5563	412	1	(	(	PUNCT
ejpam-5563	412	2	iv	iv	X
ejpam-5563	412	3	)	)	PUNCT
ejpam-5563	412	4	let	let	VERB
ejpam-5563	412	5	r	r	NOUN
ejpam-5563	412	6	∈	∈	PROPN
ejpam-5563	412	7	o	o	NOUN
ejpam-5563	412	8	−	−	PROPN
ejpam-5563	412	9	γ(o	γ(o	PROPN
ejpam-5563	412	10	)	)	PUNCT
ejpam-5563	412	11	.	.	PUNCT
ejpam-5563	413	1	then	then	ADV
ejpam-5563	413	2	,	,	PUNCT
ejpam-5563	413	3	r	r	NOUN
ejpam-5563	413	4	∈	∈	PROPN
ejpam-5563	413	5	o	o	NOUN
ejpam-5563	413	6	and	and	CCONJ
ejpam-5563	413	7	r	r	NOUN
ejpam-5563	413	8	/∈	/∈	PUNCT
ejpam-5563	413	9	γ(o	γ(o	PROPN
ejpam-5563	413	10	)	)	PUNCT
ejpam-5563	413	11	.	.	PUNCT
ejpam-5563	414	1	since	since	SCONJ
ejpam-5563	414	2	o	o	PROPN
ejpam-5563	414	3	is	be	AUX
ejpam-5563	414	4	a	a	DET
ejpam-5563	414	5	diamond	diamond	NOUN
ejpam-5563	414	6	open	open	NOUN
ejpam-5563	414	7	,	,	PUNCT
ejpam-5563	414	8	then	then	ADV
ejpam-5563	414	9	o	o	PROPN
ejpam-5563	414	10	⊆	⊆	NUM
ejpam-5563	414	11	γ∗(o	γ∗(o	PROPN
ejpam-5563	414	12	)	)	PUNCT
ejpam-5563	414	13	which	which	PRON
ejpam-5563	414	14	implies	imply	VERB
ejpam-5563	414	15	that	that	SCONJ
ejpam-5563	414	16	r	r	NOUN
ejpam-5563	414	17	∈	∈	PROPN
ejpam-5563	414	18	γ∗(o	γ∗(o	PROPN
ejpam-5563	414	19	)	)	PUNCT
ejpam-5563	414	20	;	;	PUNCT
ejpam-5563	414	21	hence	hence	ADV
ejpam-5563	414	22	,	,	PUNCT
ejpam-5563	414	23	r	r	NOUN
ejpam-5563	414	24	∈	∈	PROPN
ejpam-5563	414	25	λ⋄(o	λ⋄(o	NOUN
ejpam-5563	414	26	)	)	PUNCT
ejpam-5563	414	27	.	.	PUNCT
ejpam-5563	415	1	(	(	PUNCT
ejpam-5563	415	2	v	v	X
ejpam-5563	415	3	)	)	PUNCT
ejpam-5563	415	4	let	let	VERB
ejpam-5563	415	5	o	o	NOUN
ejpam-5563	415	6	⊆	⊆	NUM
ejpam-5563	415	7	b.	b.	PROPN
ejpam-5563	415	8	by	by	ADP
ejpam-5563	415	9	(	(	PUNCT
ejpam-5563	415	10	iii	iii	NOUN
ejpam-5563	415	11	)	)	PUNCT
ejpam-5563	415	12	in	in	ADP
ejpam-5563	415	13	theorem	theorem	NOUN
ejpam-5563	415	14	2	2	NUM
ejpam-5563	415	15	,	,	PUNCT
ejpam-5563	415	16	we	we	PRON
ejpam-5563	415	17	have	have	VERB
ejpam-5563	415	18	γ∗(∅	γ∗(∅	PROPN
ejpam-5563	415	19	)	)	PUNCT
ejpam-5563	415	20	⊆	⊆	NUM
ejpam-5563	415	21	γ∗(λ⋄(o	γ∗(λ⋄(o	NOUN
ejpam-5563	415	22	)	)	PUNCT
ejpam-5563	415	23	)	)	PUNCT
ejpam-5563	415	24	.	.	PUNCT
ejpam-5563	416	1	then	then	ADV
ejpam-5563	416	2	,	,	PUNCT
ejpam-5563	416	3	λ⋄(o	λ⋄(o	PROPN
ejpam-5563	416	4	)	)	PUNCT
ejpam-5563	416	5	=	=	PUNCT
ejpam-5563	417	1	[	[	X
ejpam-5563	417	2	γ(b)]c	γ(b)]c	ADP
ejpam-5563	417	3	=	=	SYM
ejpam-5563	417	4	γ∗(∅	γ∗(∅	PROPN
ejpam-5563	417	5	)	)	PUNCT
ejpam-5563	417	6	⊆	⊆	NUM
ejpam-5563	417	7	γ∗(λ⋄(o	γ∗(λ⋄(o	NOUN
ejpam-5563	417	8	)	)	PUNCT
ejpam-5563	417	9	)	)	PUNCT
ejpam-5563	417	10	.	.	PUNCT
ejpam-5563	418	1	(	(	PUNCT
ejpam-5563	418	2	vi	vi	X
ejpam-5563	418	3	)	)	PUNCT
ejpam-5563	418	4	since	since	SCONJ
ejpam-5563	418	5	oc	oc	PROPN
ejpam-5563	418	6	/∈	/∈	PUNCT
ejpam-5563	419	1	p	p	X
ejpam-5563	419	2	,	,	PUNCT
ejpam-5563	419	3	then	then	ADV
ejpam-5563	419	4	γ(o	γ(o	ADJ
ejpam-5563	419	5	)	)	PUNCT
ejpam-5563	420	1	=	=	PUNCT
ejpam-5563	420	2	∅	∅	NOUN
ejpam-5563	420	3	by	by	ADP
ejpam-5563	420	4	(	(	PUNCT
ejpam-5563	420	5	vi	vi	NOUN
ejpam-5563	420	6	)	)	PUNCT
ejpam-5563	420	7	in	in	ADP
ejpam-5563	420	8	theorem	theorem	NOUN
ejpam-5563	420	9	1	1	NUM
ejpam-5563	420	10	.	.	PUNCT
ejpam-5563	420	11	hence	hence	ADV
ejpam-5563	420	12	,	,	PUNCT
ejpam-5563	420	13	λ⋄(o	λ⋄(o	NOUN
ejpam-5563	420	14	)	)	PUNCT
ejpam-5563	420	15	=	=	SYM
ejpam-5563	420	16	γ∗(o	γ∗(o	PROPN
ejpam-5563	420	17	)	)	PUNCT
ejpam-5563	420	18	.	.	PUNCT
ejpam-5563	421	1	theorem	theorem	VERB
ejpam-5563	421	2	18	18	NUM
ejpam-5563	421	3	.	.	PUNCT
ejpam-5563	422	1	let	let	VERB
ejpam-5563	422	2	(	(	PUNCT
ejpam-5563	422	3	b	b	X
ejpam-5563	422	4	,	,	PUNCT
ejpam-5563	422	5	γ	γ	PROPN
ejpam-5563	422	6	,	,	PUNCT
ejpam-5563	422	7	p	p	NOUN
ejpam-5563	422	8	)	)	PUNCT
ejpam-5563	422	9	be	be	AUX
ejpam-5563	422	10	a	a	DET
ejpam-5563	422	11	ps	ps	NOUN
ejpam-5563	422	12	and	and	CCONJ
ejpam-5563	422	13	let	let	VERB
ejpam-5563	422	14	o	o	PROPN
ejpam-5563	422	15	⊆	⊆	NUM
ejpam-5563	422	16	b.	b.	PROPN
ejpam-5563	422	17	then	then	ADV
ejpam-5563	422	18	,	,	PUNCT
ejpam-5563	422	19	the	the	DET
ejpam-5563	422	20	following	follow	VERB
ejpam-5563	422	21	properties	property	NOUN
ejpam-5563	422	22	hold	hold	VERB
ejpam-5563	422	23	:	:	PUNCT
ejpam-5563	422	24	(	(	PUNCT
ejpam-5563	422	25	i	i	NOUN
ejpam-5563	422	26	)	)	PUNCT
ejpam-5563	422	27	λ(o	λ(o	PROPN
ejpam-5563	422	28	)	)	PUNCT
ejpam-5563	422	29	∩	∩	ADJ
ejpam-5563	422	30	λ⋄(o	λ⋄(o	NOUN
ejpam-5563	422	31	)	)	PUNCT
ejpam-5563	422	32	=	=	PUNCT
ejpam-5563	423	1	λ⋄(o)−o	λ⋄(o)−o	ADJ
ejpam-5563	423	2	.	.	PUNCT
ejpam-5563	424	1	(	(	PUNCT
ejpam-5563	424	2	ii	ii	NOUN
ejpam-5563	424	3	)	)	PUNCT
ejpam-5563	424	4	λ⋄(o)−	λ⋄(o)−	PROPN
ejpam-5563	424	5	λ(o	λ(o	PROPN
ejpam-5563	424	6	)	)	PUNCT
ejpam-5563	424	7	=	=	SYM
ejpam-5563	424	8	λ⋄(o	λ⋄(o	NOUN
ejpam-5563	424	9	)	)	PUNCT
ejpam-5563	424	10	∩	∩	ADJ
ejpam-5563	424	11	o.	o.	PROPN
ejpam-5563	424	12	(	(	PUNCT
ejpam-5563	424	13	iii	iii	NOUN
ejpam-5563	424	14	)	)	PUNCT
ejpam-5563	424	15	λ(o	λ(o	PROPN
ejpam-5563	424	16	)	)	PUNCT
ejpam-5563	424	17	∪	∪	PROPN
ejpam-5563	424	18	λ⋄(o	λ⋄(o	NOUN
ejpam-5563	424	19	)	)	PUNCT
ejpam-5563	424	20	=	=	PUNCT
ejpam-5563	425	1	γ∗(o)−	γ∗(o)−	ADV
ejpam-5563	425	2	(	(	PUNCT
ejpam-5563	425	3	o	o	X
ejpam-5563	425	4	∩	∩	X
ejpam-5563	425	5	γ(o	γ(o	PROPN
ejpam-5563	425	6	)	)	PUNCT
ejpam-5563	425	7	)	)	PUNCT
ejpam-5563	425	8	.	.	PUNCT
ejpam-5563	426	1	(	(	PUNCT
ejpam-5563	426	2	iv	iv	X
ejpam-5563	426	3	)	)	PUNCT
ejpam-5563	426	4	λ(λ⋄(o	λ(λ⋄(o	NUM
ejpam-5563	426	5	)	)	PUNCT
ejpam-5563	426	6	)	)	PUNCT
ejpam-5563	427	1	=	=	SYM
ejpam-5563	427	2	γ(b)−	γ(b)−	PROPN
ejpam-5563	427	3	γ(γ(b	γ(γ(b	PROPN
ejpam-5563	427	4	)	)	PUNCT
ejpam-5563	427	5	)	)	PUNCT
ejpam-5563	427	6	.	.	PUNCT
ejpam-5563	428	1	(	(	PUNCT
ejpam-5563	428	2	v	v	NOUN
ejpam-5563	428	3	)	)	PUNCT
ejpam-5563	428	4	λ⋄(o	λ⋄(o	NOUN
ejpam-5563	428	5	)	)	PUNCT
ejpam-5563	429	1	⊆	⊆	NUM
ejpam-5563	429	2	γ∗(λ(o	γ∗(λ(o	NUM
ejpam-5563	429	3	)	)	PUNCT
ejpam-5563	429	4	)	)	PUNCT
ejpam-5563	429	5	.	.	PUNCT
ejpam-5563	430	1	o.	o.	PROPN
ejpam-5563	430	2	alghamdi	alghamdi	PROPN
ejpam-5563	430	3	/	/	SYM
ejpam-5563	430	4	eur	eur	PROPN
ejpam-5563	430	5	.	.	PUNCT
ejpam-5563	431	1	j.	j.	PROPN
ejpam-5563	431	2	pure	pure	PROPN
ejpam-5563	431	3	appl	appl	PROPN
ejpam-5563	431	4	.	.	PROPN
ejpam-5563	431	5	math	math	PROPN
ejpam-5563	431	6	,	,	PUNCT
ejpam-5563	431	7	17	17	NUM
ejpam-5563	431	8	(	(	PUNCT
ejpam-5563	431	9	4	4	NUM
ejpam-5563	431	10	)	)	PUNCT
ejpam-5563	431	11	(	(	PUNCT
ejpam-5563	431	12	2024	2024	NUM
ejpam-5563	431	13	)	)	PUNCT
ejpam-5563	431	14	,	,	PUNCT
ejpam-5563	431	15	3517	3517	NUM
ejpam-5563	431	16	-	-	SYM
ejpam-5563	431	17	3538	3538	NUM
ejpam-5563	431	18	3529	3529	NUM
ejpam-5563	431	19	proof	proof	NOUN
ejpam-5563	431	20	.	.	PUNCT
ejpam-5563	432	1	(	(	PUNCT
ejpam-5563	432	2	i	i	NOUN
ejpam-5563	432	3	)	)	PUNCT
ejpam-5563	432	4	λ(o	λ(o	PROPN
ejpam-5563	432	5	)	)	PUNCT
ejpam-5563	432	6	∩	∩	ADJ
ejpam-5563	432	7	λ⋄(o	λ⋄(o	NOUN
ejpam-5563	432	8	)	)	PUNCT
ejpam-5563	432	9	=[	=[	NOUN
ejpam-5563	432	10	γ∗(o)−o	γ∗(o)−o	NOUN
ejpam-5563	432	11	]	]	PUNCT
ejpam-5563	432	12	∩	∩	NOUN
ejpam-5563	432	13	[	[	X
ejpam-5563	432	14	γ∗(o)−	γ∗(o)−	ADV
ejpam-5563	432	15	γ(o	γ(o	ADJ
ejpam-5563	432	16	)	)	PUNCT
ejpam-5563	432	17	]	]	PUNCT
ejpam-5563	433	1	=	=	PUNCT
ejpam-5563	433	2	[	[	X
ejpam-5563	433	3	γ∗(o	γ∗(o	PROPN
ejpam-5563	433	4	)	)	PUNCT
ejpam-5563	433	5	∩	∩	NOUN
ejpam-5563	433	6	oc	oc	ADP
ejpam-5563	433	7	]	]	X
ejpam-5563	433	8	∩	∩	NOUN
ejpam-5563	433	9	[	[	X
ejpam-5563	433	10	γ∗(o	γ∗(o	PROPN
ejpam-5563	433	11	)	)	PUNCT
ejpam-5563	433	12	∩	∩	NOUN
ejpam-5563	433	13	(	(	PUNCT
ejpam-5563	433	14	γ(o))c	γ(o))c	PROPN
ejpam-5563	433	15	]	]	PUNCT
ejpam-5563	433	16	=	=	SYM
ejpam-5563	433	17	[	[	X
ejpam-5563	433	18	γ∗(o	γ∗(o	PROPN
ejpam-5563	433	19	)	)	PUNCT
ejpam-5563	433	20	∩	∩	NOUN
ejpam-5563	433	21	oc	oc	ADP
ejpam-5563	433	22	]	]	X
ejpam-5563	433	23	∩	∩	NOUN
ejpam-5563	433	24	[	[	X
ejpam-5563	433	25	γ∗(o	γ∗(o	PROPN
ejpam-5563	433	26	)	)	PUNCT
ejpam-5563	433	27	∩	∩	ADJ
ejpam-5563	433	28	γ∗(oc	γ∗(oc	NOUN
ejpam-5563	433	29	)	)	PUNCT
ejpam-5563	433	30	]	]	PUNCT
ejpam-5563	434	1	=	=	X
ejpam-5563	434	2	γ∗(o	γ∗(o	PROPN
ejpam-5563	434	3	)	)	PUNCT
ejpam-5563	434	4	∩	∩	NOUN
ejpam-5563	434	5	[	[	X
ejpam-5563	434	6	oc	oc	ADP
ejpam-5563	434	7	∩	∩	ADJ
ejpam-5563	434	8	γ∗(oc	γ∗(oc	NOUN
ejpam-5563	434	9	)	)	PUNCT
ejpam-5563	434	10	]	]	PUNCT
ejpam-5563	435	1	=	=	PUNCT
ejpam-5563	435	2	[	[	X
ejpam-5563	435	3	γ∗(o	γ∗(o	PROPN
ejpam-5563	435	4	)	)	PUNCT
ejpam-5563	435	5	∩	∩	ADJ
ejpam-5563	435	6	γ∗(oc	γ∗(oc	NOUN
ejpam-5563	435	7	)	)	PUNCT
ejpam-5563	435	8	]	]	PUNCT
ejpam-5563	435	9	∩	∩	NOUN
ejpam-5563	435	10	oc	oc	ADP
ejpam-5563	435	11	=	=	NOUN
ejpam-5563	435	12	λ⋄(o)−o	λ⋄(o)−o	ADJ
ejpam-5563	435	13	.	.	PUNCT
ejpam-5563	436	1	(	(	PUNCT
ejpam-5563	436	2	ii	ii	NOUN
ejpam-5563	436	3	)	)	PUNCT
ejpam-5563	436	4	λ⋄(o)−	λ⋄(o)−	PROPN
ejpam-5563	436	5	λ(o	λ(o	PROPN
ejpam-5563	436	6	)	)	PUNCT
ejpam-5563	436	7	=[	=[	NOUN
ejpam-5563	436	8	γ∗(o)−	γ∗(o)−	ADV
ejpam-5563	436	9	γ(o)]−	γ(o)]−	NOUN
ejpam-5563	437	1	[	[	X
ejpam-5563	437	2	γ∗(o)−o	γ∗(o)−o	X
ejpam-5563	437	3	]	]	X
ejpam-5563	437	4	=	=	SYM
ejpam-5563	437	5	[	[	X
ejpam-5563	437	6	γ∗(o	γ∗(o	PROPN
ejpam-5563	437	7	)	)	PUNCT
ejpam-5563	437	8	∩	∩	ADJ
ejpam-5563	437	9	γ∗(oc	γ∗(oc	NOUN
ejpam-5563	437	10	)	)	PUNCT
ejpam-5563	437	11	]	]	PUNCT
ejpam-5563	438	1	∩	∩	NOUN
ejpam-5563	438	2	[	[	X
ejpam-5563	438	3	γ∗(o	γ∗(o	PROPN
ejpam-5563	438	4	)	)	PUNCT
ejpam-5563	438	5	∩	∩	NOUN
ejpam-5563	438	6	oc]c	oc]c	PROPN
ejpam-5563	438	7	=[	=[	NOUN
ejpam-5563	438	8	γ∗(o	γ∗(o	PROPN
ejpam-5563	438	9	)	)	PUNCT
ejpam-5563	438	10	∩	∩	ADJ
ejpam-5563	438	11	γ∗(oc	γ∗(oc	NOUN
ejpam-5563	438	12	)	)	PUNCT
ejpam-5563	438	13	]	]	PUNCT
ejpam-5563	439	1	∩	∩	NOUN
ejpam-5563	439	2	[	[	X
ejpam-5563	439	3	(	(	PUNCT
ejpam-5563	439	4	γ∗(o))c	γ∗(o))c	PROPN
ejpam-5563	439	5	∪	∪	ADP
ejpam-5563	439	6	o	o	NOUN
ejpam-5563	439	7	]	]	X
ejpam-5563	439	8	=	=	SYM
ejpam-5563	439	9	[	[	X
ejpam-5563	439	10	γ∗(o	γ∗(o	PROPN
ejpam-5563	439	11	)	)	PUNCT
ejpam-5563	439	12	∩	∩	ADJ
ejpam-5563	439	13	γ∗(oc	γ∗(oc	NOUN
ejpam-5563	439	14	)	)	PUNCT
ejpam-5563	439	15	∩	∩	NOUN
ejpam-5563	439	16	(	(	PUNCT
ejpam-5563	439	17	γ∗(o))c	γ∗(o))c	NUM
ejpam-5563	439	18	]	]	PUNCT
ejpam-5563	439	19	∪	∪	ADP
ejpam-5563	439	20	[	[	X
ejpam-5563	439	21	γ∗(o	γ∗(o	PROPN
ejpam-5563	439	22	)	)	PUNCT
ejpam-5563	439	23	∩	∩	ADJ
ejpam-5563	439	24	γ∗(oc	γ∗(oc	NOUN
ejpam-5563	439	25	)	)	PUNCT
ejpam-5563	439	26	∩	∩	NOUN
ejpam-5563	439	27	o	o	NOUN
ejpam-5563	439	28	]	]	X
ejpam-5563	439	29	=	=	NOUN
ejpam-5563	439	30	[	[	X
ejpam-5563	439	31	γ∗(oc	γ∗(oc	NOUN
ejpam-5563	439	32	)	)	PUNCT
ejpam-5563	439	33	∩	∩	NOUN
ejpam-5563	439	34	∅	∅	NOUN
ejpam-5563	439	35	]	]	PUNCT
ejpam-5563	439	36	∪	∪	ADP
ejpam-5563	439	37	[	[	X
ejpam-5563	439	38	λ⋄(o	λ⋄(o	NOUN
ejpam-5563	439	39	)	)	PUNCT
ejpam-5563	439	40	∩	∩	ADJ
ejpam-5563	439	41	o	o	X
ejpam-5563	439	42	]	]	X
ejpam-5563	439	43	=	=	ADJ
ejpam-5563	439	44	λ⋄(o	λ⋄(o	NOUN
ejpam-5563	439	45	)	)	PUNCT
ejpam-5563	439	46	∩	∩	ADJ
ejpam-5563	439	47	o.	o.	PROPN
ejpam-5563	439	48	(	(	PUNCT
ejpam-5563	439	49	iii	iii	NOUN
ejpam-5563	439	50	)	)	PUNCT
ejpam-5563	439	51	λ(o	λ(o	PROPN
ejpam-5563	439	52	)	)	PUNCT
ejpam-5563	439	53	∪	∪	PROPN
ejpam-5563	439	54	λ⋄(o	λ⋄(o	NOUN
ejpam-5563	439	55	)	)	PUNCT
ejpam-5563	439	56	=[	=[	NOUN
ejpam-5563	439	57	γ∗(o)−o	γ∗(o)−o	NOUN
ejpam-5563	439	58	]	]	PUNCT
ejpam-5563	439	59	∪	∪	ADP
ejpam-5563	439	60	[	[	X
ejpam-5563	439	61	γ∗(o)−	γ∗(o)−	ADV
ejpam-5563	439	62	γ(o	γ(o	NOUN
ejpam-5563	439	63	)	)	PUNCT
ejpam-5563	439	64	]	]	PUNCT
ejpam-5563	440	1	=	=	PUNCT
ejpam-5563	440	2	[	[	X
ejpam-5563	440	3	γ∗(o	γ∗(o	PROPN
ejpam-5563	440	4	)	)	PUNCT
ejpam-5563	440	5	∩	∩	NOUN
ejpam-5563	440	6	oc	oc	X
ejpam-5563	440	7	]	]	X
ejpam-5563	440	8	∪	∪	ADP
ejpam-5563	440	9	[	[	X
ejpam-5563	440	10	γ∗(o	γ∗(o	PROPN
ejpam-5563	440	11	)	)	PUNCT
ejpam-5563	440	12	∩	∩	NOUN
ejpam-5563	440	13	(	(	PUNCT
ejpam-5563	440	14	γ(o))c	γ(o))c	PROPN
ejpam-5563	440	15	]	]	PUNCT
ejpam-5563	440	16	=	=	SYM
ejpam-5563	440	17	[	[	X
ejpam-5563	440	18	γ∗(o	γ∗(o	PROPN
ejpam-5563	440	19	)	)	PUNCT
ejpam-5563	440	20	∩	∩	NOUN
ejpam-5563	440	21	oc	oc	X
ejpam-5563	440	22	]	]	X
ejpam-5563	440	23	∪	∪	ADP
ejpam-5563	440	24	[	[	X
ejpam-5563	440	25	γ∗(o	γ∗(o	PROPN
ejpam-5563	440	26	)	)	PUNCT
ejpam-5563	440	27	∩	∩	ADJ
ejpam-5563	440	28	γ∗(oc	γ∗(oc	NOUN
ejpam-5563	440	29	)	)	PUNCT
ejpam-5563	440	30	]	]	PUNCT
ejpam-5563	441	1	=	=	X
ejpam-5563	441	2	γ∗(o	γ∗(o	PROPN
ejpam-5563	441	3	)	)	PUNCT
ejpam-5563	441	4	∩	∩	NOUN
ejpam-5563	441	5	[	[	X
ejpam-5563	441	6	oc	oc	AUX
ejpam-5563	441	7	∪	∪	ADJ
ejpam-5563	441	8	γ∗(oc	γ∗(oc	NOUN
ejpam-5563	441	9	)	)	PUNCT
ejpam-5563	441	10	]	]	PUNCT
ejpam-5563	442	1	=	=	X
ejpam-5563	442	2	γ∗(o	γ∗(o	PROPN
ejpam-5563	442	3	)	)	PUNCT
ejpam-5563	442	4	∩	∩	NOUN
ejpam-5563	442	5	[	[	X
ejpam-5563	442	6	oc	oc	X
ejpam-5563	442	7	∪	∪	X
ejpam-5563	442	8	(	(	PUNCT
ejpam-5563	442	9	γ(o))c	γ(o))c	PROPN
ejpam-5563	442	10	]	]	PUNCT
ejpam-5563	442	11	=	=	NOUN
ejpam-5563	442	12	γ∗(o	γ∗(o	PROPN
ejpam-5563	442	13	)	)	PUNCT
ejpam-5563	442	14	∩	∩	NOUN
ejpam-5563	443	1	[	[	X
ejpam-5563	443	2	o	o	X
ejpam-5563	443	3	∩	∩	NOUN
ejpam-5563	443	4	γ(o)]c	γ(o)]c	NOUN
ejpam-5563	443	5	=	=	PRON
ejpam-5563	443	6	γ∗(o)−	γ∗(o)−	VERB
ejpam-5563	443	7	[	[	X
ejpam-5563	443	8	o	o	X
ejpam-5563	443	9	∩	∩	ADJ
ejpam-5563	443	10	γ(o	γ(o	PROPN
ejpam-5563	443	11	)	)	PUNCT
ejpam-5563	443	12	]	]	PUNCT
ejpam-5563	443	13	.	.	PUNCT
ejpam-5563	444	1	(	(	PUNCT
ejpam-5563	444	2	iv	iv	X
ejpam-5563	444	3	)	)	PUNCT
ejpam-5563	444	4	we	we	PRON
ejpam-5563	444	5	know	know	VERB
ejpam-5563	444	6	that	that	PRON
ejpam-5563	444	7	λ(λ⋄(o	λ(λ⋄(o	PUNCT
ejpam-5563	444	8	)	)	PUNCT
ejpam-5563	444	9	)	)	PUNCT
ejpam-5563	445	1	=	=	PUNCT
ejpam-5563	445	2	λ	λ	X
ejpam-5563	445	3	(	(	PUNCT
ejpam-5563	445	4	[	[	X
ejpam-5563	445	5	γ(b)]c	γ(b)]c	NOUN
ejpam-5563	445	6	)	)	PUNCT
ejpam-5563	445	7	.	.	PUNCT
ejpam-5563	446	1	then	then	ADV
ejpam-5563	446	2	,	,	PUNCT
ejpam-5563	446	3	λ(λ⋄(o	λ(λ⋄(o	NUM
ejpam-5563	446	4	)	)	PUNCT
ejpam-5563	446	5	)	)	PUNCT
ejpam-5563	447	1	=	=	PUNCT
ejpam-5563	447	2	λ	λ	X
ejpam-5563	447	3	(	(	PUNCT
ejpam-5563	447	4	[	[	X
ejpam-5563	447	5	γ(b)]c	γ(b)]c	NOUN
ejpam-5563	447	6	)	)	PUNCT
ejpam-5563	447	7	=	=	SYM
ejpam-5563	447	8	γ(b)−	γ(b)−	PROPN
ejpam-5563	447	9	[	[	X
ejpam-5563	447	10	γ(γ(b	γ(γ(b	NOUN
ejpam-5563	447	11	)	)	PUNCT
ejpam-5563	447	12	)	)	PUNCT
ejpam-5563	447	13	]	]	PUNCT
ejpam-5563	447	14	by	by	ADP
ejpam-5563	447	15	(	(	PUNCT
ejpam-5563	447	16	iv	iv	X
ejpam-5563	447	17	)	)	PUNCT
ejpam-5563	447	18	in	in	ADP
ejpam-5563	447	19	theorem	theorem	NOUN
ejpam-5563	447	20	13	13	NUM
ejpam-5563	447	21	.	.	PUNCT
ejpam-5563	448	1	(	(	PUNCT
ejpam-5563	448	2	v	v	NOUN
ejpam-5563	448	3	)	)	PUNCT
ejpam-5563	448	4	clearly	clearly	ADV
ejpam-5563	448	5	,	,	PUNCT
ejpam-5563	448	6	for	for	ADP
ejpam-5563	448	7	any	any	DET
ejpam-5563	448	8	o	o	NOUN
ejpam-5563	448	9	⊆	⊆	NUM
ejpam-5563	448	10	b	b	NOUN
ejpam-5563	448	11	,	,	PUNCT
ejpam-5563	448	12	we	we	PRON
ejpam-5563	448	13	have	have	VERB
ejpam-5563	448	14	λ⋄(o	λ⋄(o	NOUN
ejpam-5563	448	15	)	)	PUNCT
ejpam-5563	449	1	=	=	SYM
ejpam-5563	449	2	γ∗(∅	γ∗(∅	ADJ
ejpam-5563	449	3	)	)	PUNCT
ejpam-5563	449	4	⊆	⊆	NUM
ejpam-5563	449	5	γ∗(λ(o	γ∗(λ(o	NUM
ejpam-5563	449	6	)	)	PUNCT
ejpam-5563	449	7	)	)	PUNCT
ejpam-5563	449	8	.	.	PUNCT
ejpam-5563	450	1	o.	o.	PROPN
ejpam-5563	450	2	alghamdi	alghamdi	PROPN
ejpam-5563	450	3	/	/	SYM
ejpam-5563	450	4	eur	eur	PROPN
ejpam-5563	450	5	.	.	PUNCT
ejpam-5563	451	1	j.	j.	PROPN
ejpam-5563	451	2	pure	pure	PROPN
ejpam-5563	451	3	appl	appl	PROPN
ejpam-5563	451	4	.	.	PROPN
ejpam-5563	451	5	math	math	PROPN
ejpam-5563	451	6	,	,	PUNCT
ejpam-5563	451	7	17	17	NUM
ejpam-5563	451	8	(	(	PUNCT
ejpam-5563	451	9	4	4	NUM
ejpam-5563	451	10	)	)	PUNCT
ejpam-5563	451	11	(	(	PUNCT
ejpam-5563	451	12	2024	2024	NUM
ejpam-5563	451	13	)	)	PUNCT
ejpam-5563	451	14	,	,	PUNCT
ejpam-5563	451	15	3517	3517	NUM
ejpam-5563	451	16	-	-	SYM
ejpam-5563	451	17	3538	3538	NUM
ejpam-5563	451	18	3530	3530	NUM
ejpam-5563	451	19	5	5	NUM
ejpam-5563	451	20	.	.	PUNCT
ejpam-5563	452	1	on	on	ADP
ejpam-5563	452	2	λ̃	λ̃	PROPN
ejpam-5563	452	3	operator	operator	NOUN
ejpam-5563	452	4	in	in	ADP
ejpam-5563	452	5	this	this	DET
ejpam-5563	452	6	section	section	NOUN
ejpam-5563	452	7	,	,	PUNCT
ejpam-5563	452	8	we	we	PRON
ejpam-5563	452	9	introduce	introduce	VERB
ejpam-5563	452	10	an	an	DET
ejpam-5563	452	11	operator	operator	NOUN
ejpam-5563	452	12	,	,	PUNCT
ejpam-5563	452	13	denoted	denote	VERB
ejpam-5563	452	14	as	as	ADP
ejpam-5563	452	15	the	the	DET
ejpam-5563	452	16	λ̃	λ̃	PROPN
ejpam-5563	452	17	operator	operator	NOUN
ejpam-5563	452	18	.	.	PUNCT
ejpam-5563	453	1	we	we	PRON
ejpam-5563	453	2	will	will	AUX
ejpam-5563	453	3	present	present	VERB
ejpam-5563	453	4	a	a	DET
ejpam-5563	453	5	definition	definition	NOUN
ejpam-5563	453	6	of	of	ADP
ejpam-5563	453	7	this	this	DET
ejpam-5563	453	8	operator	operator	NOUN
ejpam-5563	453	9	and	and	CCONJ
ejpam-5563	453	10	explore	explore	VERB
ejpam-5563	453	11	its	its	PRON
ejpam-5563	453	12	properties	property	NOUN
ejpam-5563	453	13	.	.	PUNCT
ejpam-5563	454	1	additionally	additionally	ADV
ejpam-5563	454	2	,	,	PUNCT
ejpam-5563	454	3	we	we	PRON
ejpam-5563	454	4	will	will	AUX
ejpam-5563	454	5	discuss	discuss	VERB
ejpam-5563	454	6	various	various	ADJ
ejpam-5563	454	7	results	result	NOUN
ejpam-5563	454	8	that	that	SCONJ
ejpam-5563	454	9	connecting	connect	VERB
ejpam-5563	454	10	this	this	DET
ejpam-5563	454	11	operator	operator	NOUN
ejpam-5563	454	12	with	with	ADP
ejpam-5563	454	13	other	other	ADJ
ejpam-5563	454	14	operators	operator	NOUN
ejpam-5563	454	15	introduced	introduce	VERB
ejpam-5563	454	16	in	in	ADP
ejpam-5563	454	17	this	this	DET
ejpam-5563	454	18	paper	paper	NOUN
ejpam-5563	454	19	.	.	PUNCT
ejpam-5563	455	1	definition	definition	NOUN
ejpam-5563	455	2	11	11	NUM
ejpam-5563	455	3	.	.	PUNCT
ejpam-5563	456	1	let	let	VERB
ejpam-5563	456	2	(	(	PUNCT
ejpam-5563	456	3	b	b	X
ejpam-5563	456	4	,	,	PUNCT
ejpam-5563	456	5	γ	γ	PROPN
ejpam-5563	456	6	,	,	PUNCT
ejpam-5563	456	7	p	p	NOUN
ejpam-5563	456	8	)	)	PUNCT
ejpam-5563	456	9	be	be	AUX
ejpam-5563	456	10	a	a	DET
ejpam-5563	456	11	ps	ps	NOUN
ejpam-5563	456	12	.	.	PUNCT
ejpam-5563	457	1	then	then	ADV
ejpam-5563	457	2	,	,	PUNCT
ejpam-5563	457	3	we	we	PRON
ejpam-5563	457	4	define	define	VERB
ejpam-5563	457	5	the	the	DET
ejpam-5563	457	6	operator	operator	NOUN
ejpam-5563	457	7	λ̃	λ̃	PROPN
ejpam-5563	457	8	:	:	PUNCT
ejpam-5563	457	9	p(b	p(b	NUM
ejpam-5563	457	10	)	)	PUNCT
ejpam-5563	457	11	→	→	SYM
ejpam-5563	457	12	p(b	p(b	NUM
ejpam-5563	457	13	)	)	PUNCT
ejpam-5563	457	14	as	as	SCONJ
ejpam-5563	457	15	follows	follow	VERB
ejpam-5563	457	16	:	:	PUNCT
ejpam-5563	457	17	λ̃(o	λ̃(o	ADJ
ejpam-5563	457	18	)	)	PUNCT
ejpam-5563	458	1	=	=	SYM
ejpam-5563	458	2	o	o	NOUN
ejpam-5563	458	3	−	−	PROPN
ejpam-5563	458	4	γ(o	γ(o	PROPN
ejpam-5563	458	5	)	)	PUNCT
ejpam-5563	458	6	for	for	ADP
ejpam-5563	458	7	every	every	DET
ejpam-5563	458	8	o	o	PROPN
ejpam-5563	458	9	⊆	⊆	NUM
ejpam-5563	458	10	b.	b.	PROPN
ejpam-5563	458	11	example	example	NOUN
ejpam-5563	458	12	5	5	X
ejpam-5563	458	13	.	.	PUNCT
ejpam-5563	459	1	let	let	VERB
ejpam-5563	459	2	(	(	PUNCT
ejpam-5563	459	3	r	r	NOUN
ejpam-5563	459	4	,	,	PUNCT
ejpam-5563	459	5	τ√2,p	τ√2,p	NUM
ejpam-5563	459	6	)	)	PUNCT
ejpam-5563	459	7	be	be	AUX
ejpam-5563	459	8	defined	define	VERB
ejpam-5563	459	9	as	as	ADP
ejpam-5563	459	10	in	in	ADP
ejpam-5563	459	11	example	example	NOUN
ejpam-5563	459	12	2	2	NUM
ejpam-5563	459	13	and	and	CCONJ
ejpam-5563	459	14	let	let	VERB
ejpam-5563	459	15	k	k	PROPN
ejpam-5563	459	16	⊆	⊆	PROPN
ejpam-5563	459	17	r.	r.	PROPN
ejpam-5563	460	1	then	then	ADV
ejpam-5563	460	2	,	,	PUNCT
ejpam-5563	460	3	we	we	PRON
ejpam-5563	460	4	have	have	VERB
ejpam-5563	460	5	λ̃(k	λ̃(k	NOUN
ejpam-5563	460	6	)	)	PUNCT
ejpam-5563	460	7	=	=	SYM
ejpam-5563	460	8	k.	k.	PROPN
ejpam-5563	460	9	lemma	lemma	PROPN
ejpam-5563	460	10	4	4	X
ejpam-5563	460	11	.	.	PUNCT
ejpam-5563	461	1	let	let	VERB
ejpam-5563	461	2	(	(	PUNCT
ejpam-5563	461	3	b	b	X
ejpam-5563	461	4	,	,	PUNCT
ejpam-5563	461	5	γ	γ	PROPN
ejpam-5563	461	6	,	,	PUNCT
ejpam-5563	461	7	p	p	NOUN
ejpam-5563	461	8	)	)	PUNCT
ejpam-5563	461	9	be	be	AUX
ejpam-5563	461	10	a	a	DET
ejpam-5563	461	11	ps	ps	NOUN
ejpam-5563	461	12	and	and	CCONJ
ejpam-5563	461	13	o	o	PROPN
ejpam-5563	462	1	⊆	⊆	NUM
ejpam-5563	462	2	b.	b.	PROPN
ejpam-5563	462	3	then	then	ADV
ejpam-5563	462	4	,	,	PUNCT
ejpam-5563	462	5	we	we	PRON
ejpam-5563	462	6	have	have	VERB
ejpam-5563	462	7	:	:	PUNCT
ejpam-5563	462	8	(	(	PUNCT
ejpam-5563	462	9	i	i	NOUN
ejpam-5563	462	10	)	)	PUNCT
ejpam-5563	462	11	λ̃(o	λ̃(o	ADJ
ejpam-5563	462	12	)	)	PUNCT
ejpam-5563	462	13	=	=	SYM
ejpam-5563	462	14	λ(oc	λ(oc	PROPN
ejpam-5563	462	15	)	)	PUNCT
ejpam-5563	462	16	.	.	PUNCT
ejpam-5563	463	1	(	(	PUNCT
ejpam-5563	463	2	ii	ii	NOUN
ejpam-5563	463	3	)	)	PUNCT
ejpam-5563	463	4	λ(o	λ(o	PROPN
ejpam-5563	463	5	)	)	PUNCT
ejpam-5563	463	6	∩	∩	NOUN
ejpam-5563	463	7	λ̃(o	λ̃(o	ADJ
ejpam-5563	463	8	)	)	PUNCT
ejpam-5563	463	9	=	=	SYM
ejpam-5563	463	10	∅.	∅.	PRON
ejpam-5563	463	11	(	(	PUNCT
ejpam-5563	463	12	iii	iii	NOUN
ejpam-5563	463	13	)	)	PUNCT
ejpam-5563	463	14	λ(o	λ(o	NOUN
ejpam-5563	463	15	)	)	PUNCT
ejpam-5563	463	16	∩	∩	ADJ
ejpam-5563	463	17	λ(oc	λ(oc	X
ejpam-5563	463	18	)	)	PUNCT
ejpam-5563	463	19	=	=	PUNCT
ejpam-5563	463	20	∅.	∅.	X
ejpam-5563	463	21	(	(	PUNCT
ejpam-5563	463	22	iv	iv	X
ejpam-5563	463	23	)	)	PUNCT
ejpam-5563	463	24	if	if	SCONJ
ejpam-5563	463	25	o	o	PROPN
ejpam-5563	463	26	∈	∈	PROPN
ejpam-5563	463	27	γ	γ	X
ejpam-5563	463	28	,	,	PUNCT
ejpam-5563	463	29	then	then	ADV
ejpam-5563	463	30	λ̃(o	λ̃(o	PROPN
ejpam-5563	463	31	)	)	PUNCT
ejpam-5563	463	32	∈	∈	PROPN
ejpam-5563	463	33	γ	γ	X
ejpam-5563	463	34	.	.	PUNCT
ejpam-5563	463	35	proof	proof	NOUN
ejpam-5563	463	36	.	.	PUNCT
ejpam-5563	464	1	let	let	VERB
ejpam-5563	464	2	o	o	PROPN
ejpam-5563	464	3	⊆	⊆	NUM
ejpam-5563	464	4	b.	b.	NOUN
ejpam-5563	464	5	then	then	ADV
ejpam-5563	464	6	,	,	PUNCT
ejpam-5563	464	7	(	(	PUNCT
ejpam-5563	464	8	i	i	NOUN
ejpam-5563	464	9	)	)	PUNCT
ejpam-5563	464	10	λ(oc	λ(oc	PROPN
ejpam-5563	464	11	)	)	PUNCT
ejpam-5563	464	12	=	=	PUNCT
ejpam-5563	464	13	γ∗(oc)−oc	γ∗(oc)−oc	X
ejpam-5563	465	1	=	=	PUNCT
ejpam-5563	466	1	[	[	X
ejpam-5563	466	2	γ(o)]c	γ(o)]c	NOUN
ejpam-5563	466	3	∩	∩	ADJ
ejpam-5563	466	4	o	o	NOUN
ejpam-5563	466	5	=	=	PUNCT
ejpam-5563	466	6	o	o	X
ejpam-5563	466	7	−	−	X
ejpam-5563	466	8	γ(o	γ(o	PROPN
ejpam-5563	466	9	)	)	PUNCT
ejpam-5563	466	10	=	=	PUNCT
ejpam-5563	467	1	λ̃(o	λ̃(o	PROPN
ejpam-5563	467	2	)	)	PUNCT
ejpam-5563	467	3	.	.	PUNCT
ejpam-5563	468	1	(	(	PUNCT
ejpam-5563	468	2	ii	ii	NOUN
ejpam-5563	468	3	)	)	PUNCT
ejpam-5563	468	4	λ(o	λ(o	PROPN
ejpam-5563	468	5	)	)	PUNCT
ejpam-5563	468	6	∩	∩	NOUN
ejpam-5563	468	7	λ̃(o	λ̃(o	ADJ
ejpam-5563	468	8	)	)	PUNCT
ejpam-5563	468	9	=	=	PUNCT
ejpam-5563	469	1	[	[	X
ejpam-5563	469	2	γ∗(o	γ∗(o	PROPN
ejpam-5563	469	3	)	)	PUNCT
ejpam-5563	469	4	∩	∩	NOUN
ejpam-5563	469	5	oc	oc	ADP
ejpam-5563	469	6	]	]	X
ejpam-5563	469	7	∩	∩	NOUN
ejpam-5563	469	8	[	[	X
ejpam-5563	469	9	o	o	X
ejpam-5563	469	10	∩	∩	NOUN
ejpam-5563	469	11	[	[	X
ejpam-5563	469	12	γ(o)]c	γ(o)]c	X
ejpam-5563	469	13	]	]	X
ejpam-5563	469	14	=	=	SYM
ejpam-5563	469	15	∅.	∅.	X
ejpam-5563	469	16	(	(	PUNCT
ejpam-5563	469	17	iii	iii	NOUN
ejpam-5563	469	18	)	)	PUNCT
ejpam-5563	469	19	by	by	ADP
ejpam-5563	469	20	(	(	PUNCT
ejpam-5563	469	21	i	i	NOUN
ejpam-5563	469	22	)	)	PUNCT
ejpam-5563	469	23	and	and	CCONJ
ejpam-5563	469	24	(	(	PUNCT
ejpam-5563	469	25	ii	ii	NOUN
ejpam-5563	469	26	)	)	PUNCT
ejpam-5563	469	27	,	,	PUNCT
ejpam-5563	469	28	we	we	PRON
ejpam-5563	469	29	have	have	VERB
ejpam-5563	469	30	λ(o	λ(o	NOUN
ejpam-5563	469	31	)	)	PUNCT
ejpam-5563	469	32	∩	∩	ADJ
ejpam-5563	469	33	λ(oc	λ(oc	X
ejpam-5563	469	34	)	)	PUNCT
ejpam-5563	469	35	=	=	SYM
ejpam-5563	469	36	λ(o	λ(o	X
ejpam-5563	469	37	)	)	PUNCT
ejpam-5563	469	38	∩	∩	NOUN
ejpam-5563	469	39	λ̃(o	λ̃(o	ADJ
ejpam-5563	469	40	)	)	PUNCT
ejpam-5563	469	41	=	=	SYM
ejpam-5563	469	42	∅.	∅.	X
ejpam-5563	469	43	(	(	PUNCT
ejpam-5563	469	44	iv	iv	X
ejpam-5563	469	45	)	)	PUNCT
ejpam-5563	469	46	let	let	VERB
ejpam-5563	469	47	r	r	NOUN
ejpam-5563	469	48	∈	∈	NOUN
ejpam-5563	469	49	λ̃(o	λ̃(o	PROPN
ejpam-5563	469	50	)	)	PUNCT
ejpam-5563	470	1	=	=	SYM
ejpam-5563	470	2	o	o	NOUN
ejpam-5563	470	3	−	−	PROPN
ejpam-5563	470	4	γ(o	γ(o	PROPN
ejpam-5563	470	5	)	)	PUNCT
ejpam-5563	470	6	.	.	PUNCT
ejpam-5563	471	1	then	then	ADV
ejpam-5563	471	2	,	,	PUNCT
ejpam-5563	471	3	r	r	NOUN
ejpam-5563	471	4	∈	∈	PROPN
ejpam-5563	471	5	o	o	NOUN
ejpam-5563	471	6	and	and	CCONJ
ejpam-5563	471	7	r	r	NOUN
ejpam-5563	471	8	/∈	/∈	PUNCT
ejpam-5563	471	9	γ(o	γ(o	PROPN
ejpam-5563	471	10	)	)	PUNCT
ejpam-5563	471	11	.	.	PUNCT
ejpam-5563	472	1	hence	hence	ADV
ejpam-5563	472	2	,	,	PUNCT
ejpam-5563	472	3	r	r	NOUN
ejpam-5563	472	4	∈	∈	PROPN
ejpam-5563	472	5	[	[	X
ejpam-5563	472	6	γ(o)]c	γ(o)]c	NOUN
ejpam-5563	472	7	.	.	PUNCT
ejpam-5563	472	8	since	since	SCONJ
ejpam-5563	472	9	γ(o	γ(o	PROPN
ejpam-5563	472	10	)	)	PUNCT
ejpam-5563	472	11	is	be	AUX
ejpam-5563	472	12	a	a	DET
ejpam-5563	472	13	closed	closed	ADJ
ejpam-5563	472	14	set	set	VERB
ejpam-5563	472	15	by	by	ADP
ejpam-5563	472	16	(	(	PUNCT
ejpam-5563	472	17	iii	iii	NOUN
ejpam-5563	472	18	)	)	PUNCT
ejpam-5563	472	19	in	in	ADP
ejpam-5563	472	20	theorem	theorem	NOUN
ejpam-5563	472	21	1	1	NUM
ejpam-5563	472	22	,	,	PUNCT
ejpam-5563	472	23	then	then	ADV
ejpam-5563	472	24	there	there	PRON
ejpam-5563	472	25	exists	exist	VERB
ejpam-5563	472	26	h	h	NOUN
ejpam-5563	472	27	∈	∈	PROPN
ejpam-5563	472	28	γ	γ	NOUN
ejpam-5563	472	29	such	such	ADJ
ejpam-5563	472	30	that	that	SCONJ
ejpam-5563	472	31	r	r	NOUN
ejpam-5563	472	32	∈	∈	PROPN
ejpam-5563	472	33	h	h	NOUN
ejpam-5563	472	34	⊆	⊆	NUM
ejpam-5563	472	35	[	[	X
ejpam-5563	472	36	γ(o)]c	γ(o)]c	NOUN
ejpam-5563	472	37	.	.	PUNCT
ejpam-5563	473	1	thus	thus	ADV
ejpam-5563	473	2	,	,	PUNCT
ejpam-5563	473	3	r	r	NOUN
ejpam-5563	473	4	∈	∈	PROPN
ejpam-5563	473	5	h	h	NOUN
ejpam-5563	473	6	∩	∩	NOUN
ejpam-5563	473	7	o	o	NOUN
ejpam-5563	473	8	⊆	⊆	NUM
ejpam-5563	473	9	[	[	X
ejpam-5563	473	10	γ(o)]c	γ(o)]c	NOUN
ejpam-5563	473	11	∩	∩	ADJ
ejpam-5563	473	12	o	o	NOUN
ejpam-5563	473	13	=	=	PUNCT
ejpam-5563	473	14	o	o	X
ejpam-5563	473	15	−	−	PROPN
ejpam-5563	473	16	γ(o	γ(o	PROPN
ejpam-5563	473	17	)	)	PUNCT
ejpam-5563	473	18	.	.	PUNCT
ejpam-5563	474	1	then	then	ADV
ejpam-5563	474	2	,	,	PUNCT
ejpam-5563	474	3	λ̃(o	λ̃(o	PROPN
ejpam-5563	474	4	)	)	PUNCT
ejpam-5563	474	5	∈	∈	PROPN
ejpam-5563	474	6	γ	γ	X
ejpam-5563	474	7	.	.	PROPN
ejpam-5563	474	8	corollary	corollary	ADJ
ejpam-5563	474	9	5	5	NUM
ejpam-5563	474	10	.	.	PUNCT
ejpam-5563	475	1	let	let	VERB
ejpam-5563	475	2	(	(	PUNCT
ejpam-5563	475	3	b	b	X
ejpam-5563	475	4	,	,	PUNCT
ejpam-5563	475	5	γ	γ	PROPN
ejpam-5563	475	6	,	,	PUNCT
ejpam-5563	475	7	p	p	NOUN
ejpam-5563	475	8	)	)	PUNCT
ejpam-5563	475	9	be	be	AUX
ejpam-5563	475	10	a	a	DET
ejpam-5563	475	11	ps	ps	NOUN
ejpam-5563	475	12	and	and	CCONJ
ejpam-5563	475	13	let	let	VERB
ejpam-5563	475	14	o	o	PROPN
ejpam-5563	475	15	⊆	⊆	NUM
ejpam-5563	475	16	b.	b.	NOUN
ejpam-5563	475	17	then	then	ADV
ejpam-5563	475	18	,	,	PUNCT
ejpam-5563	475	19	λ̃(o	λ̃(o	PROPN
ejpam-5563	475	20	)	)	PUNCT
ejpam-5563	476	1	=	=	SYM
ejpam-5563	476	2	o	o	NOUN
ejpam-5563	476	3	if	if	SCONJ
ejpam-5563	476	4	and	and	CCONJ
ejpam-5563	476	5	only	only	ADV
ejpam-5563	476	6	if	if	SCONJ
ejpam-5563	476	7	o	o	PROPN
ejpam-5563	476	8	∩	∩	X
ejpam-5563	476	9	γ(o	γ(o	ADJ
ejpam-5563	476	10	)	)	PUNCT
ejpam-5563	476	11	=	=	PUNCT
ejpam-5563	476	12	∅.	∅.	PRON
ejpam-5563	476	13	remark	remark	NOUN
ejpam-5563	476	14	4	4	NUM
ejpam-5563	476	15	.	.	PUNCT
ejpam-5563	477	1	let	let	VERB
ejpam-5563	477	2	(	(	PUNCT
ejpam-5563	477	3	b	b	X
ejpam-5563	477	4	,	,	PUNCT
ejpam-5563	477	5	γ	γ	PROPN
ejpam-5563	477	6	,	,	PUNCT
ejpam-5563	477	7	p	p	NOUN
ejpam-5563	477	8	)	)	PUNCT
ejpam-5563	477	9	be	be	AUX
ejpam-5563	477	10	a	a	DET
ejpam-5563	477	11	ps	ps	NOUN
ejpam-5563	477	12	and	and	CCONJ
ejpam-5563	477	13	let	let	VERB
ejpam-5563	477	14	o	o	NOUN
ejpam-5563	477	15	be	be	AUX
ejpam-5563	477	16	a	a	DET
ejpam-5563	477	17	proper	proper	ADJ
ejpam-5563	477	18	subset	subset	NOUN
ejpam-5563	477	19	of	of	ADP
ejpam-5563	477	20	b.	b.	PROPN
ejpam-5563	477	21	then	then	ADV
ejpam-5563	477	22	,	,	PUNCT
ejpam-5563	477	23	(	(	PUNCT
ejpam-5563	477	24	i	i	NOUN
ejpam-5563	477	25	)	)	PUNCT
ejpam-5563	478	1	if	if	SCONJ
ejpam-5563	478	2	p	p	NOUN
ejpam-5563	478	3	=	=	NOUN
ejpam-5563	478	4	∅	∅	NOUN
ejpam-5563	478	5	,	,	PUNCT
ejpam-5563	478	6	then	then	ADV
ejpam-5563	478	7	λ̃(o	λ̃(o	ADJ
ejpam-5563	478	8	)	)	PUNCT
ejpam-5563	478	9	=	=	SYM
ejpam-5563	478	10	o.	o.	NOUN
ejpam-5563	478	11	(	(	PUNCT
ejpam-5563	478	12	ii	ii	NOUN
ejpam-5563	478	13	)	)	PUNCT
ejpam-5563	478	14	if	if	SCONJ
ejpam-5563	478	15	p	p	NOUN
ejpam-5563	478	16	=	=	VERB
ejpam-5563	478	17	p(b)−	p(b)−	PROPN
ejpam-5563	478	18	{	{	PUNCT
ejpam-5563	478	19	b	b	NOUN
ejpam-5563	478	20	}	}	PUNCT
ejpam-5563	478	21	,	,	PUNCT
ejpam-5563	478	22	then	then	ADV
ejpam-5563	478	23	λ̃(o	λ̃(o	PROPN
ejpam-5563	478	24	)	)	PUNCT
ejpam-5563	478	25	=	=	PUNCT
ejpam-5563	478	26	∅.	∅.	NOUN
ejpam-5563	478	27	proof	proof	NOUN
ejpam-5563	478	28	.	.	PUNCT
ejpam-5563	479	1	(	(	PUNCT
ejpam-5563	479	2	i	i	NOUN
ejpam-5563	479	3	)	)	PUNCT
ejpam-5563	479	4	since	since	SCONJ
ejpam-5563	479	5	o	o	NOUN
ejpam-5563	479	6	is	be	AUX
ejpam-5563	479	7	a	a	DET
ejpam-5563	479	8	proper	proper	ADJ
ejpam-5563	479	9	subset	subset	NOUN
ejpam-5563	479	10	of	of	ADP
ejpam-5563	479	11	b	b	NOUN
ejpam-5563	479	12	,	,	PUNCT
ejpam-5563	479	13	then	then	ADV
ejpam-5563	479	14	oc	oc	ADP
ejpam-5563	479	15	̸=	̸=	PROPN
ejpam-5563	479	16	∅	∅	NOUN
ejpam-5563	479	17	which	which	PRON
ejpam-5563	479	18	implies	imply	VERB
ejpam-5563	479	19	that	that	PRON
ejpam-5563	479	20	oc	oc	PART
ejpam-5563	479	21	/∈	/∈	PUNCT
ejpam-5563	480	1	p	p	X
ejpam-5563	480	2	;	;	PUNCT
ejpam-5563	480	3	hence	hence	ADV
ejpam-5563	480	4	,	,	PUNCT
ejpam-5563	480	5	γ(o	γ(o	PROPN
ejpam-5563	480	6	)	)	PUNCT
ejpam-5563	480	7	=	=	PUNCT
ejpam-5563	480	8	∅	∅	NOUN
ejpam-5563	480	9	by	by	ADP
ejpam-5563	480	10	(	(	PUNCT
ejpam-5563	480	11	vi	vi	NOUN
ejpam-5563	480	12	)	)	PUNCT
ejpam-5563	480	13	in	in	ADP
ejpam-5563	480	14	theorem	theorem	NOUN
ejpam-5563	480	15	1	1	NUM
ejpam-5563	480	16	.	.	PUNCT
ejpam-5563	480	17	thus	thus	ADV
ejpam-5563	480	18	,	,	PUNCT
ejpam-5563	480	19	λ̃(o	λ̃(o	PROPN
ejpam-5563	480	20	)	)	PUNCT
ejpam-5563	480	21	=	=	SYM
ejpam-5563	480	22	o.	o.	NOUN
ejpam-5563	480	23	o.	o.	PROPN
ejpam-5563	480	24	alghamdi	alghamdi	PROPN
ejpam-5563	480	25	/	/	SYM
ejpam-5563	480	26	eur	eur	PROPN
ejpam-5563	480	27	.	.	PUNCT
ejpam-5563	481	1	j.	j.	PROPN
ejpam-5563	481	2	pure	pure	PROPN
ejpam-5563	481	3	appl	appl	PROPN
ejpam-5563	481	4	.	.	PROPN
ejpam-5563	481	5	math	math	PROPN
ejpam-5563	481	6	,	,	PUNCT
ejpam-5563	481	7	17	17	NUM
ejpam-5563	481	8	(	(	PUNCT
ejpam-5563	481	9	4	4	NUM
ejpam-5563	481	10	)	)	PUNCT
ejpam-5563	481	11	(	(	PUNCT
ejpam-5563	481	12	2024	2024	NUM
ejpam-5563	481	13	)	)	PUNCT
ejpam-5563	481	14	,	,	PUNCT
ejpam-5563	481	15	3517	3517	NUM
ejpam-5563	481	16	-	-	SYM
ejpam-5563	481	17	3538	3538	NUM
ejpam-5563	481	18	3531	3531	NUM
ejpam-5563	481	19	(	(	PUNCT
ejpam-5563	481	20	ii	ii	NOUN
ejpam-5563	481	21	)	)	PUNCT
ejpam-5563	481	22	since	since	SCONJ
ejpam-5563	481	23	p	p	NOUN
ejpam-5563	481	24	=	=	VERB
ejpam-5563	481	25	p(b)−	p(b)−	PROPN
ejpam-5563	481	26	{	{	PUNCT
ejpam-5563	481	27	b	b	NOUN
ejpam-5563	481	28	}	}	PUNCT
ejpam-5563	481	29	,	,	PUNCT
ejpam-5563	481	30	then	then	ADV
ejpam-5563	481	31	λ̃(o	λ̃(o	ADJ
ejpam-5563	481	32	)	)	PUNCT
ejpam-5563	482	1	=	=	SYM
ejpam-5563	482	2	o	o	NOUN
ejpam-5563	482	3	−	−	X
ejpam-5563	482	4	γ(o	γ(o	PROPN
ejpam-5563	482	5	)	)	PUNCT
ejpam-5563	483	1	=	=	SYM
ejpam-5563	484	1	o	o	NOUN
ejpam-5563	484	2	−	−	X
ejpam-5563	484	3	clθ(o	clθ(o	PROPN
ejpam-5563	484	4	)	)	PUNCT
ejpam-5563	485	1	=	=	PUNCT
ejpam-5563	485	2	∅.	∅.	NOUN
ejpam-5563	485	3	theorem	theorem	VERB
ejpam-5563	485	4	19	19	NUM
ejpam-5563	485	5	.	.	PUNCT
ejpam-5563	486	1	let	let	VERB
ejpam-5563	486	2	(	(	PUNCT
ejpam-5563	486	3	b	b	X
ejpam-5563	486	4	,	,	PUNCT
ejpam-5563	486	5	γ	γ	PROPN
ejpam-5563	486	6	,	,	PUNCT
ejpam-5563	486	7	p	p	NOUN
ejpam-5563	486	8	)	)	PUNCT
ejpam-5563	486	9	be	be	AUX
ejpam-5563	486	10	a	a	DET
ejpam-5563	486	11	ps	ps	NOUN
ejpam-5563	486	12	and	and	CCONJ
ejpam-5563	486	13	o	o	NOUN
ejpam-5563	486	14	,	,	PUNCT
ejpam-5563	486	15	k	k	PROPN
ejpam-5563	486	16	⊆	⊆	NUM
ejpam-5563	486	17	b.	b.	PROPN
ejpam-5563	486	18	then	then	ADV
ejpam-5563	486	19	,	,	PUNCT
ejpam-5563	486	20	we	we	PRON
ejpam-5563	486	21	have	have	VERB
ejpam-5563	486	22	:	:	PUNCT
ejpam-5563	486	23	(	(	PUNCT
ejpam-5563	486	24	i	i	NOUN
ejpam-5563	486	25	)	)	PUNCT
ejpam-5563	487	1	λ̃(∅	λ̃(∅	ADJ
ejpam-5563	487	2	)	)	PUNCT
ejpam-5563	487	3	=	=	SYM
ejpam-5563	487	4	∅.	∅.	PRON
ejpam-5563	487	5	(	(	PUNCT
ejpam-5563	487	6	ii	ii	NOUN
ejpam-5563	487	7	)	)	PUNCT
ejpam-5563	487	8	λ̃(λ̃(k	λ̃(λ̃(k	NOUN
ejpam-5563	487	9	)	)	PUNCT
ejpam-5563	487	10	)	)	PUNCT
ejpam-5563	488	1	⊆	⊆	NUM
ejpam-5563	488	2	λ̃(k	λ̃(k	NOUN
ejpam-5563	488	3	)	)	PUNCT
ejpam-5563	488	4	⊆	⊆	NUM
ejpam-5563	488	5	k.	k.	NOUN
ejpam-5563	488	6	(	(	PUNCT
ejpam-5563	488	7	iii	iii	NOUN
ejpam-5563	488	8	)	)	PUNCT
ejpam-5563	488	9	λ̃(k	λ̃(k	NOUN
ejpam-5563	488	10	)	)	PUNCT
ejpam-5563	488	11	∩	∩	NOUN
ejpam-5563	488	12	γ(k	γ(k	PROPN
ejpam-5563	488	13	)	)	PUNCT
ejpam-5563	488	14	=	=	PUNCT
ejpam-5563	488	15	∅.	∅.	X
ejpam-5563	488	16	(	(	PUNCT
ejpam-5563	488	17	iv	iv	X
ejpam-5563	488	18	)	)	PUNCT
ejpam-5563	488	19	if	if	SCONJ
ejpam-5563	488	20	kc	kc	PROPN
ejpam-5563	488	21	/∈	/∈	PUNCT
ejpam-5563	489	1	p	p	X
ejpam-5563	489	2	,	,	PUNCT
ejpam-5563	489	3	then	then	ADV
ejpam-5563	489	4	λ̃(k	λ̃(k	NOUN
ejpam-5563	489	5	)	)	PUNCT
ejpam-5563	489	6	=	=	SYM
ejpam-5563	489	7	k.	k.	PROPN
ejpam-5563	489	8	(	(	PUNCT
ejpam-5563	489	9	v	v	NOUN
ejpam-5563	489	10	)	)	PUNCT
ejpam-5563	489	11	λ̃(k	λ̃(k	NOUN
ejpam-5563	489	12	∪o	∪o	NUM
ejpam-5563	489	13	)	)	PUNCT
ejpam-5563	490	1	=	=	PUNCT
ejpam-5563	491	1	[	[	X
ejpam-5563	491	2	λ̃(k)−	λ̃(k)−	PROPN
ejpam-5563	491	3	γ(o	γ(o	PROPN
ejpam-5563	491	4	)	)	PUNCT
ejpam-5563	491	5	]	]	PUNCT
ejpam-5563	491	6	∪	∪	X
ejpam-5563	491	7	[	[	PUNCT
ejpam-5563	491	8	λ̃(o)−	λ̃(o)−	PROPN
ejpam-5563	491	9	γ(k	γ(k	PROPN
ejpam-5563	491	10	)	)	PUNCT
ejpam-5563	491	11	]	]	PUNCT
ejpam-5563	491	12	.	.	PUNCT
ejpam-5563	492	1	(	(	PUNCT
ejpam-5563	492	2	vi	vi	NOUN
ejpam-5563	492	3	)	)	PUNCT
ejpam-5563	492	4	λ̃(k	λ̃(k	NOUN
ejpam-5563	492	5	)	)	PUNCT
ejpam-5563	492	6	∩	∩	NOUN
ejpam-5563	492	7	λ̃(o	λ̃(o	ADJ
ejpam-5563	492	8	)	)	PUNCT
ejpam-5563	492	9	=	=	PRON
ejpam-5563	492	10	(	(	PUNCT
ejpam-5563	492	11	k	k	X
ejpam-5563	492	12	∩o)−	∩o)−	PROPN
ejpam-5563	492	13	γ(k	γ(k	PROPN
ejpam-5563	492	14	∪o	∪o	ADP
ejpam-5563	492	15	)	)	PUNCT
ejpam-5563	492	16	.	.	PUNCT
ejpam-5563	493	1	proof	proof	NOUN
ejpam-5563	493	2	.	.	PUNCT
ejpam-5563	494	1	let	let	VERB
ejpam-5563	494	2	k	k	NOUN
ejpam-5563	494	3	,	,	PUNCT
ejpam-5563	494	4	o	o	PROPN
ejpam-5563	494	5	⊆	⊆	NUM
ejpam-5563	494	6	b.	b.	NOUN
ejpam-5563	494	7	then	then	ADV
ejpam-5563	494	8	,	,	PUNCT
ejpam-5563	494	9	(	(	PUNCT
ejpam-5563	494	10	i	i	NOUN
ejpam-5563	494	11	)	)	PUNCT
ejpam-5563	494	12	λ̃(∅	λ̃(∅	X
ejpam-5563	494	13	)	)	PUNCT
ejpam-5563	494	14	=	=	NOUN
ejpam-5563	494	15	∅	∅	NOUN
ejpam-5563	494	16	−	−	PROPN
ejpam-5563	494	17	γ(∅	γ(∅	NOUN
ejpam-5563	494	18	)	)	PUNCT
ejpam-5563	494	19	=	=	PUNCT
ejpam-5563	494	20	∅.	∅.	PROPN
ejpam-5563	494	21	(	(	PUNCT
ejpam-5563	494	22	ii	ii	NOUN
ejpam-5563	494	23	)	)	PUNCT
ejpam-5563	494	24	λ̃(λ̃(k	λ̃(λ̃(k	NOUN
ejpam-5563	494	25	)	)	PUNCT
ejpam-5563	494	26	)	)	PUNCT
ejpam-5563	495	1	=	=	SYM
ejpam-5563	495	2	λ̃(k)−	λ̃(k)−	PROPN
ejpam-5563	495	3	(	(	PUNCT
ejpam-5563	495	4	γ(λ̃(k	γ(λ̃(k	NOUN
ejpam-5563	495	5	)	)	PUNCT
ejpam-5563	495	6	)	)	PUNCT
ejpam-5563	495	7	⊆	⊆	NUM
ejpam-5563	495	8	λ̃(k	λ̃(k	NOUN
ejpam-5563	495	9	)	)	PUNCT
ejpam-5563	495	10	⊆	⊆	NUM
ejpam-5563	495	11	k.	k.	NOUN
ejpam-5563	495	12	(	(	PUNCT
ejpam-5563	495	13	iii	iii	NOUN
ejpam-5563	495	14	)	)	PUNCT
ejpam-5563	495	15	λ̃(k	λ̃(k	NOUN
ejpam-5563	495	16	)	)	PUNCT
ejpam-5563	495	17	∩	∩	NOUN
ejpam-5563	495	18	γ(k	γ(k	PROPN
ejpam-5563	495	19	)	)	PUNCT
ejpam-5563	495	20	=	=	PUNCT
ejpam-5563	496	1	[	[	X
ejpam-5563	496	2	k	k	X
ejpam-5563	496	3	−	−	PROPN
ejpam-5563	496	4	γ(k	γ(k	PROPN
ejpam-5563	496	5	)	)	PUNCT
ejpam-5563	496	6	]	]	PUNCT
ejpam-5563	497	1	∩	∩	X
ejpam-5563	497	2	γ(k	γ(k	PROPN
ejpam-5563	497	3	)	)	PUNCT
ejpam-5563	497	4	=	=	PUNCT
ejpam-5563	497	5	∅.	∅.	X
ejpam-5563	497	6	(	(	PUNCT
ejpam-5563	497	7	iv	iv	X
ejpam-5563	497	8	)	)	PUNCT
ejpam-5563	497	9	if	if	SCONJ
ejpam-5563	497	10	kc	kc	PROPN
ejpam-5563	497	11	/∈	/∈	PUNCT
ejpam-5563	498	1	p	p	X
ejpam-5563	498	2	,	,	PUNCT
ejpam-5563	498	3	then	then	ADV
ejpam-5563	498	4	by	by	ADP
ejpam-5563	498	5	(	(	PUNCT
ejpam-5563	498	6	vi	vi	NOUN
ejpam-5563	498	7	)	)	PUNCT
ejpam-5563	498	8	of	of	ADP
ejpam-5563	498	9	theorem	theorem	NOUN
ejpam-5563	498	10	1	1	NUM
ejpam-5563	498	11	,	,	PUNCT
ejpam-5563	498	12	we	we	PRON
ejpam-5563	498	13	have	have	VERB
ejpam-5563	498	14	γ(k	γ(k	PROPN
ejpam-5563	498	15	)	)	PUNCT
ejpam-5563	499	1	=	=	PUNCT
ejpam-5563	499	2	∅.	∅.	VERB
ejpam-5563	499	3	then	then	ADV
ejpam-5563	499	4	,	,	PUNCT
ejpam-5563	499	5	λ̃(k	λ̃(k	NOUN
ejpam-5563	499	6	)	)	PUNCT
ejpam-5563	499	7	=	=	SYM
ejpam-5563	499	8	k.	k.	PROPN
ejpam-5563	499	9	(	(	PUNCT
ejpam-5563	499	10	v	v	NOUN
ejpam-5563	499	11	)	)	PUNCT
ejpam-5563	499	12	λ̃(k	λ̃(k	NOUN
ejpam-5563	499	13	∪o	∪o	NUM
ejpam-5563	499	14	)	)	PUNCT
ejpam-5563	499	15	=(	=(	NOUN
ejpam-5563	499	16	k	k	PROPN
ejpam-5563	499	17	∪o)−	∪o)−	NOUN
ejpam-5563	499	18	γ(k	γ(k	VERB
ejpam-5563	499	19	∪o	∪o	ADP
ejpam-5563	499	20	)	)	PUNCT
ejpam-5563	500	1	=(	=(	NOUN
ejpam-5563	500	2	k	k	NOUN
ejpam-5563	500	3	∪o)−	∪o)−	PRON
ejpam-5563	501	1	[	[	X
ejpam-5563	501	2	γ(k	γ(k	NOUN
ejpam-5563	501	3	)	)	PUNCT
ejpam-5563	501	4	∪	∪	ADP
ejpam-5563	501	5	γ(o	γ(o	PROPN
ejpam-5563	501	6	)	)	PUNCT
ejpam-5563	501	7	]	]	PUNCT
ejpam-5563	502	1	=	=	X
ejpam-5563	502	2	(	(	PUNCT
ejpam-5563	502	3	k	k	X
ejpam-5563	502	4	∪o	∪o	PROPN
ejpam-5563	502	5	)	)	PUNCT
ejpam-5563	502	6	∩	∩	NOUN
ejpam-5563	503	1	[	[	X
ejpam-5563	503	2	(	(	PUNCT
ejpam-5563	503	3	γ(k))c	γ(k))c	PROPN
ejpam-5563	503	4	∩	∩	NOUN
ejpam-5563	503	5	(	(	PUNCT
ejpam-5563	503	6	γ(o))c	γ(o))c	PROPN
ejpam-5563	503	7	]	]	PUNCT
ejpam-5563	503	8	=	=	NOUN
ejpam-5563	503	9	[	[	X
ejpam-5563	503	10	k	k	X
ejpam-5563	503	11	∩	∩	X
ejpam-5563	503	12	(	(	PUNCT
ejpam-5563	503	13	γ(k))c	γ(k))c	PROPN
ejpam-5563	503	14	∩	∩	NOUN
ejpam-5563	503	15	(	(	PUNCT
ejpam-5563	503	16	γ(o))c	γ(o))c	PROPN
ejpam-5563	503	17	]	]	PUNCT
ejpam-5563	503	18	∪	∪	ADP
ejpam-5563	503	19	[	[	X
ejpam-5563	503	20	o	o	X
ejpam-5563	503	21	∩	∩	NOUN
ejpam-5563	503	22	(	(	PUNCT
ejpam-5563	503	23	γ(k))c	γ(k))c	PROPN
ejpam-5563	503	24	∩	∩	NOUN
ejpam-5563	503	25	(	(	PUNCT
ejpam-5563	503	26	γ(o))c	γ(o))c	PROPN
ejpam-5563	503	27	]	]	PUNCT
ejpam-5563	503	28	=	=	NOUN
ejpam-5563	503	29	[	[	X
ejpam-5563	503	30	λ̃(k	λ̃(k	NOUN
ejpam-5563	503	31	)	)	PUNCT
ejpam-5563	503	32	∩	∩	NOUN
ejpam-5563	503	33	(	(	PUNCT
ejpam-5563	503	34	γ(o))c	γ(o))c	PROPN
ejpam-5563	503	35	]	]	PUNCT
ejpam-5563	503	36	∪	∪	ADP
ejpam-5563	503	37	[	[	X
ejpam-5563	503	38	λ̃(o	λ̃(o	ADJ
ejpam-5563	503	39	)	)	PUNCT
ejpam-5563	503	40	∩	∩	NOUN
ejpam-5563	503	41	(	(	PUNCT
ejpam-5563	503	42	γ(k))c	γ(k))c	PROPN
ejpam-5563	503	43	]	]	X
ejpam-5563	503	44	=	=	NOUN
ejpam-5563	503	45	[	[	X
ejpam-5563	503	46	λ̃(k)−	λ̃(k)−	PROPN
ejpam-5563	503	47	γ(o	γ(o	PROPN
ejpam-5563	503	48	)	)	PUNCT
ejpam-5563	503	49	]	]	PUNCT
ejpam-5563	503	50	∪	∪	X
ejpam-5563	503	51	[	[	PUNCT
ejpam-5563	503	52	λ̃(o)−	λ̃(o)−	PROPN
ejpam-5563	503	53	γ(k	γ(k	PROPN
ejpam-5563	503	54	)	)	PUNCT
ejpam-5563	503	55	]	]	PUNCT
ejpam-5563	503	56	.	.	PUNCT
ejpam-5563	504	1	(	(	PUNCT
ejpam-5563	504	2	vi	vi	NOUN
ejpam-5563	504	3	)	)	PUNCT
ejpam-5563	504	4	λ̃(k	λ̃(k	NOUN
ejpam-5563	504	5	)	)	PUNCT
ejpam-5563	504	6	∩	∩	NOUN
ejpam-5563	504	7	λ̃(o	λ̃(o	ADJ
ejpam-5563	504	8	)	)	PUNCT
ejpam-5563	504	9	=(	=(	NOUN
ejpam-5563	504	10	k	k	PROPN
ejpam-5563	505	1	−	−	PROPN
ejpam-5563	505	2	γ(k	γ(k	PROPN
ejpam-5563	505	3	)	)	PUNCT
ejpam-5563	505	4	)	)	PUNCT
ejpam-5563	506	1	∩	∩	NOUN
ejpam-5563	506	2	(	(	PUNCT
ejpam-5563	506	3	o	o	NOUN
ejpam-5563	506	4	−	−	PROPN
ejpam-5563	506	5	γ(o	γ(o	PROPN
ejpam-5563	506	6	)	)	PUNCT
ejpam-5563	506	7	)	)	PUNCT
ejpam-5563	506	8	=(	=(	PROPN
ejpam-5563	506	9	k	k	PROPN
ejpam-5563	506	10	∩o	∩o	PROPN
ejpam-5563	506	11	)	)	PUNCT
ejpam-5563	506	12	∩	∩	NOUN
ejpam-5563	506	13	[	[	X
ejpam-5563	506	14	(	(	PUNCT
ejpam-5563	506	15	γ(k))c	γ(k))c	PROPN
ejpam-5563	506	16	∩	∩	NOUN
ejpam-5563	506	17	(	(	PUNCT
ejpam-5563	506	18	γ(o))c	γ(o))c	PROPN
ejpam-5563	506	19	]	]	PUNCT
ejpam-5563	506	20	=	=	PROPN
ejpam-5563	506	21	(	(	PUNCT
ejpam-5563	506	22	k	k	PROPN
ejpam-5563	506	23	∩o	∩o	PROPN
ejpam-5563	506	24	)	)	PUNCT
ejpam-5563	506	25	∩	∩	NOUN
ejpam-5563	507	1	[	[	X
ejpam-5563	507	2	(	(	PUNCT
ejpam-5563	507	3	γ(k	γ(k	NOUN
ejpam-5563	507	4	)	)	PUNCT
ejpam-5563	507	5	∪	∪	ADP
ejpam-5563	507	6	γ(o))]c	γ(o))]c	PROPN
ejpam-5563	507	7	=(	=(	NOUN
ejpam-5563	507	8	k	k	PROPN
ejpam-5563	507	9	∩o	∩o	PROPN
ejpam-5563	507	10	)	)	PUNCT
ejpam-5563	507	11	∩	∩	NOUN
ejpam-5563	508	1	[	[	X
ejpam-5563	508	2	γ(k	γ(k	PROPN
ejpam-5563	508	3	∪o)]c	∪o)]c	NOUN
ejpam-5563	508	4	=(	=(	NOUN
ejpam-5563	508	5	k	k	PROPN
ejpam-5563	508	6	∩o)−	∩o)−	PROPN
ejpam-5563	508	7	γ(k	γ(k	PROPN
ejpam-5563	508	8	∪o	∪o	ADP
ejpam-5563	508	9	)	)	PUNCT
ejpam-5563	508	10	.	.	PUNCT
ejpam-5563	509	1	o.	o.	PROPN
ejpam-5563	509	2	alghamdi	alghamdi	PROPN
ejpam-5563	509	3	/	/	SYM
ejpam-5563	509	4	eur	eur	PROPN
ejpam-5563	509	5	.	.	PUNCT
ejpam-5563	510	1	j.	j.	PROPN
ejpam-5563	510	2	pure	pure	PROPN
ejpam-5563	510	3	appl	appl	PROPN
ejpam-5563	510	4	.	.	PROPN
ejpam-5563	510	5	math	math	PROPN
ejpam-5563	510	6	,	,	PUNCT
ejpam-5563	510	7	17	17	NUM
ejpam-5563	510	8	(	(	PUNCT
ejpam-5563	510	9	4	4	NUM
ejpam-5563	510	10	)	)	PUNCT
ejpam-5563	510	11	(	(	PUNCT
ejpam-5563	510	12	2024	2024	NUM
ejpam-5563	510	13	)	)	PUNCT
ejpam-5563	510	14	,	,	PUNCT
ejpam-5563	510	15	3517	3517	NUM
ejpam-5563	510	16	-	-	SYM
ejpam-5563	510	17	3538	3538	NUM
ejpam-5563	510	18	3532	3532	NUM
ejpam-5563	510	19	lemma	lemma	PROPN
ejpam-5563	510	20	5	5	NUM
ejpam-5563	510	21	.	.	PUNCT
ejpam-5563	511	1	let	let	VERB
ejpam-5563	511	2	(	(	PUNCT
ejpam-5563	511	3	b	b	X
ejpam-5563	511	4	,	,	PUNCT
ejpam-5563	511	5	γ	γ	PROPN
ejpam-5563	511	6	,	,	PUNCT
ejpam-5563	511	7	p	p	NOUN
ejpam-5563	511	8	)	)	PUNCT
ejpam-5563	511	9	be	be	AUX
ejpam-5563	511	10	a	a	DET
ejpam-5563	511	11	ps	ps	NOUN
ejpam-5563	511	12	and	and	CCONJ
ejpam-5563	511	13	let	let	VERB
ejpam-5563	511	14	o	o	PROPN
ejpam-5563	511	15	⊆	⊆	NUM
ejpam-5563	511	16	b.	b.	NOUN
ejpam-5563	511	17	if	if	SCONJ
ejpam-5563	511	18	c(b)−	c(b)−	PROPN
ejpam-5563	511	19	{	{	PUNCT
ejpam-5563	511	20	b	b	NOUN
ejpam-5563	511	21	}	}	PUNCT
ejpam-5563	511	22	⊆	⊆	PROPN
ejpam-5563	511	23	p	p	NOUN
ejpam-5563	511	24	and	and	CCONJ
ejpam-5563	511	25	r	r	NOUN
ejpam-5563	511	26	∈	∈	PROPN
ejpam-5563	511	27	λ̃(o	λ̃(o	PROPN
ejpam-5563	511	28	)	)	PUNCT
ejpam-5563	511	29	,	,	PUNCT
ejpam-5563	511	30	then	then	ADV
ejpam-5563	511	31	(	(	PUNCT
ejpam-5563	511	32	{	{	PUNCT
ejpam-5563	511	33	r})c	r})c	NOUN
ejpam-5563	511	34	/∈	/∈	PUNCT
ejpam-5563	512	1	p.	p.	NOUN
ejpam-5563	512	2	proof	proof	NOUN
ejpam-5563	512	3	.	.	PUNCT
ejpam-5563	513	1	since	since	SCONJ
ejpam-5563	513	2	r	r	NOUN
ejpam-5563	513	3	∈	∈	NOUN
ejpam-5563	513	4	λ̃(o	λ̃(o	PROPN
ejpam-5563	513	5	)	)	PUNCT
ejpam-5563	513	6	,	,	PUNCT
ejpam-5563	513	7	then	then	ADV
ejpam-5563	513	8	r	r	NOUN
ejpam-5563	513	9	∈	∈	PROPN
ejpam-5563	513	10	o	o	NOUN
ejpam-5563	513	11	and	and	CCONJ
ejpam-5563	513	12	r	r	NOUN
ejpam-5563	513	13	/∈	/∈	PUNCT
ejpam-5563	513	14	γ(o	γ(o	PROPN
ejpam-5563	513	15	)	)	PUNCT
ejpam-5563	513	16	which	which	PRON
ejpam-5563	513	17	implies	imply	VERB
ejpam-5563	513	18	that	that	SCONJ
ejpam-5563	513	19	there	there	PRON
ejpam-5563	513	20	exists	exist	VERB
ejpam-5563	513	21	q	q	PROPN
ejpam-5563	513	22	∈	∈	PROPN
ejpam-5563	513	23	γ(r	γ(r	PROPN
ejpam-5563	513	24	)	)	PUNCT
ejpam-5563	514	1	such	such	ADJ
ejpam-5563	514	2	that	that	SCONJ
ejpam-5563	514	3	[	[	X
ejpam-5563	514	4	q⋄∩o]c	q⋄∩o]c	PROPN
ejpam-5563	514	5	/∈	/∈	PUNCT
ejpam-5563	514	6	p.	p.	NOUN
ejpam-5563	514	7	by	by	ADP
ejpam-5563	514	8	lemma	lemma	PROPN
ejpam-5563	514	9	2	2	NUM
ejpam-5563	514	10	,	,	PUNCT
ejpam-5563	514	11	we	we	PRON
ejpam-5563	514	12	know	know	VERB
ejpam-5563	514	13	that	that	SCONJ
ejpam-5563	514	14	q	q	PROPN
ejpam-5563	514	15	⊆	⊆	NUM
ejpam-5563	514	16	q⋄	q⋄	NOUN
ejpam-5563	514	17	;	;	PUNCT
ejpam-5563	514	18	hence	hence	ADV
ejpam-5563	514	19	,	,	PUNCT
ejpam-5563	514	20	[	[	X
ejpam-5563	514	21	q⋄∩o]c	q⋄∩o]c	NOUN
ejpam-5563	514	22	⊆	⊆	NUM
ejpam-5563	514	23	[	[	X
ejpam-5563	514	24	q	q	X
ejpam-5563	514	25	∩	∩	ADJ
ejpam-5563	514	26	o]c	o]c	NOUN
ejpam-5563	514	27	.	.	PUNCT
ejpam-5563	515	1	thus	thus	ADV
ejpam-5563	515	2	,	,	PUNCT
ejpam-5563	515	3	[	[	X
ejpam-5563	515	4	q	q	X
ejpam-5563	515	5	∩	∩	ADJ
ejpam-5563	515	6	o]c	o]c	NOUN
ejpam-5563	515	7	/∈	/∈	PROPN
ejpam-5563	516	1	p	p	NOUN
ejpam-5563	517	1	and	and	CCONJ
ejpam-5563	517	2	since	since	SCONJ
ejpam-5563	517	3	r	r	NOUN
ejpam-5563	517	4	/∈	/∈	PUNCT
ejpam-5563	518	1	[	[	X
ejpam-5563	518	2	q	q	X
ejpam-5563	518	3	∩	∩	ADJ
ejpam-5563	518	4	o]c	o]c	NOUN
ejpam-5563	518	5	,	,	PUNCT
ejpam-5563	518	6	then	then	ADV
ejpam-5563	518	7	(	(	PUNCT
ejpam-5563	518	8	{	{	PUNCT
ejpam-5563	518	9	r})c	r})c	NOUN
ejpam-5563	518	10	/∈	/∈	PUNCT
ejpam-5563	519	1	p.	p.	NOUN
ejpam-5563	519	2	theorem	theorem	VERB
ejpam-5563	519	3	20	20	NUM
ejpam-5563	519	4	.	.	PUNCT
ejpam-5563	520	1	let	let	VERB
ejpam-5563	520	2	(	(	PUNCT
ejpam-5563	520	3	b	b	X
ejpam-5563	520	4	,	,	PUNCT
ejpam-5563	520	5	γ	γ	PROPN
ejpam-5563	520	6	,	,	PUNCT
ejpam-5563	520	7	p	p	NOUN
ejpam-5563	520	8	)	)	PUNCT
ejpam-5563	520	9	be	be	AUX
ejpam-5563	520	10	a	a	DET
ejpam-5563	520	11	ps	ps	NOUN
ejpam-5563	520	12	and	and	CCONJ
ejpam-5563	520	13	c(b	c(b	PROPN
ejpam-5563	520	14	)	)	PUNCT
ejpam-5563	521	1	−	−	PROPN
ejpam-5563	521	2	{	{	PUNCT
ejpam-5563	521	3	b	b	NOUN
ejpam-5563	521	4	}	}	PUNCT
ejpam-5563	521	5	⊆	⊆	NUM
ejpam-5563	521	6	p.	p.	NOUN
ejpam-5563	521	7	then	then	ADV
ejpam-5563	521	8	,	,	PUNCT
ejpam-5563	521	9	r	r	NOUN
ejpam-5563	521	10	∈	∈	PROPN
ejpam-5563	521	11	λ̃({r	λ̃({r	NOUN
ejpam-5563	521	12	}	}	PUNCT
ejpam-5563	521	13	)	)	PUNCT
ejpam-5563	522	1	if	if	SCONJ
ejpam-5563	522	2	and	and	CCONJ
ejpam-5563	522	3	only	only	ADV
ejpam-5563	522	4	if	if	SCONJ
ejpam-5563	522	5	(	(	PUNCT
ejpam-5563	522	6	{	{	PUNCT
ejpam-5563	522	7	r})c	r})c	NOUN
ejpam-5563	522	8	/∈	/∈	PUNCT
ejpam-5563	522	9	p.	p.	NOUN
ejpam-5563	522	10	proof	proof	NOUN
ejpam-5563	522	11	.	.	PUNCT
ejpam-5563	523	1	(	(	PUNCT
ejpam-5563	523	2	⇒	⇒	NOUN
ejpam-5563	523	3	):	):	PUNCT
ejpam-5563	523	4	it	it	PRON
ejpam-5563	523	5	is	be	AUX
ejpam-5563	523	6	obvious	obvious	ADJ
ejpam-5563	523	7	by	by	ADP
ejpam-5563	523	8	lemma	lemma	PROPN
ejpam-5563	523	9	5	5	NUM
ejpam-5563	523	10	.	.	PUNCT
ejpam-5563	524	1	(	(	PUNCT
ejpam-5563	524	2	⇐	⇐	ADJ
ejpam-5563	524	3	):	):	PUNCT
ejpam-5563	524	4	suppose	suppose	VERB
ejpam-5563	524	5	that	that	SCONJ
ejpam-5563	524	6	(	(	PUNCT
ejpam-5563	524	7	{	{	PUNCT
ejpam-5563	524	8	r})c	r})c	NOUN
ejpam-5563	524	9	/∈	/∈	PUNCT
ejpam-5563	525	1	p.	p.	NOUN
ejpam-5563	525	2	we	we	PRON
ejpam-5563	525	3	want	want	VERB
ejpam-5563	525	4	to	to	PART
ejpam-5563	525	5	show	show	VERB
ejpam-5563	525	6	that	that	SCONJ
ejpam-5563	525	7	r	r	NOUN
ejpam-5563	525	8	∈	∈	PROPN
ejpam-5563	525	9	λ̃({r	λ̃({r	NOUN
ejpam-5563	525	10	}	}	PUNCT
ejpam-5563	525	11	)	)	PUNCT
ejpam-5563	525	12	which	which	PRON
ejpam-5563	525	13	is	be	AUX
ejpam-5563	525	14	equivalent	equivalent	ADJ
ejpam-5563	525	15	to	to	PART
ejpam-5563	525	16	show	show	VERB
ejpam-5563	525	17	that	that	SCONJ
ejpam-5563	525	18	r	r	NOUN
ejpam-5563	525	19	/∈	/∈	PUNCT
ejpam-5563	525	20	γ({r	γ({r	PROPN
ejpam-5563	525	21	}	}	PUNCT
ejpam-5563	525	22	)	)	PUNCT
ejpam-5563	525	23	.	.	PUNCT
ejpam-5563	526	1	since	since	SCONJ
ejpam-5563	526	2	b	b	PROPN
ejpam-5563	526	3	∈	∈	PROPN
ejpam-5563	526	4	γ(r	γ(r	PROPN
ejpam-5563	526	5	)	)	PUNCT
ejpam-5563	526	6	and	and	CCONJ
ejpam-5563	526	7	bc	bc	PROPN
ejpam-5563	526	8	∪	∪	ADV
ejpam-5563	526	9	(	(	PUNCT
ejpam-5563	526	10	{	{	PUNCT
ejpam-5563	526	11	r})c	r})c	NOUN
ejpam-5563	526	12	=	=	PUNCT
ejpam-5563	526	13	(	(	PUNCT
ejpam-5563	526	14	{	{	PUNCT
ejpam-5563	526	15	r})c	r})c	NOUN
ejpam-5563	526	16	/∈	/∈	PUNCT
ejpam-5563	527	1	p	p	X
ejpam-5563	527	2	,	,	PUNCT
ejpam-5563	527	3	we	we	PRON
ejpam-5563	527	4	get	get	VERB
ejpam-5563	527	5	the	the	DET
ejpam-5563	527	6	desired	desire	VERB
ejpam-5563	527	7	result	result	NOUN
ejpam-5563	527	8	.	.	PUNCT
ejpam-5563	528	1	theorem	theorem	NOUN
ejpam-5563	528	2	21	21	NUM
ejpam-5563	528	3	.	.	PUNCT
ejpam-5563	529	1	let	let	VERB
ejpam-5563	529	2	(	(	PUNCT
ejpam-5563	529	3	b	b	X
ejpam-5563	529	4	,	,	PUNCT
ejpam-5563	529	5	γ	γ	PROPN
ejpam-5563	529	6	,	,	PUNCT
ejpam-5563	529	7	p	p	NOUN
ejpam-5563	529	8	)	)	PUNCT
ejpam-5563	529	9	be	be	AUX
ejpam-5563	529	10	a	a	DET
ejpam-5563	529	11	ps	ps	NOUN
ejpam-5563	529	12	and	and	CCONJ
ejpam-5563	529	13	let	let	VERB
ejpam-5563	529	14	o	o	PROPN
ejpam-5563	529	15	⊆	⊆	NUM
ejpam-5563	529	16	b.	b.	NOUN
ejpam-5563	529	17	then	then	ADV
ejpam-5563	529	18	,	,	PUNCT
ejpam-5563	529	19	(	(	PUNCT
ejpam-5563	529	20	i	i	NOUN
ejpam-5563	529	21	)	)	PUNCT
ejpam-5563	529	22	λ⋄(o	λ⋄(o	NOUN
ejpam-5563	529	23	)	)	PUNCT
ejpam-5563	529	24	∩	∩	NOUN
ejpam-5563	529	25	λ̃(o	λ̃(o	ADJ
ejpam-5563	529	26	)	)	PUNCT
ejpam-5563	529	27	=	=	SYM
ejpam-5563	529	28	γ∗(o	γ∗(o	PROPN
ejpam-5563	529	29	)	)	PUNCT
ejpam-5563	529	30	∩	∩	NOUN
ejpam-5563	529	31	λ̃(o	λ̃(o	PROPN
ejpam-5563	529	32	)	)	PUNCT
ejpam-5563	529	33	.	.	PUNCT
ejpam-5563	530	1	(	(	PUNCT
ejpam-5563	530	2	ii	ii	NOUN
ejpam-5563	530	3	)	)	PUNCT
ejpam-5563	530	4	λ⋄(o)−	λ⋄(o)−	PROPN
ejpam-5563	530	5	λ̃(o	λ̃(o	PROPN
ejpam-5563	530	6	)	)	PUNCT
ejpam-5563	531	1	=	=	PUNCT
ejpam-5563	531	2	λ⋄(o)−o	λ⋄(o)−o	ADJ
ejpam-5563	531	3	.	.	PUNCT
ejpam-5563	532	1	(	(	PUNCT
ejpam-5563	532	2	iii	iii	X
ejpam-5563	532	3	)	)	PUNCT
ejpam-5563	532	4	λ̃(o)−	λ̃(o)−	PROPN
ejpam-5563	532	5	λ⋄(o	λ⋄(o	NOUN
ejpam-5563	532	6	)	)	PUNCT
ejpam-5563	533	1	=	=	PRON
ejpam-5563	533	2	λ̃(o)−	λ̃(o)−	PROPN
ejpam-5563	533	3	γ∗(o	γ∗(o	PROPN
ejpam-5563	533	4	)	)	PUNCT
ejpam-5563	533	5	.	.	PUNCT
ejpam-5563	534	1	(	(	PUNCT
ejpam-5563	534	2	iv	iv	X
ejpam-5563	534	3	)	)	PUNCT
ejpam-5563	534	4	λ⋄(o	λ⋄(o	NOUN
ejpam-5563	534	5	)	)	PUNCT
ejpam-5563	534	6	∪	∪	ADP
ejpam-5563	534	7	λ̃(o	λ̃(o	PROPN
ejpam-5563	534	8	)	)	PUNCT
ejpam-5563	535	1	=	=	PUNCT
ejpam-5563	536	1	[	[	X
ejpam-5563	536	2	γ∗(o	γ∗(o	X
ejpam-5563	536	3	)	)	PUNCT
ejpam-5563	536	4	∪	∪	ADP
ejpam-5563	536	5	o]−	o]−	ADJ
ejpam-5563	536	6	γ(o	γ(o	NOUN
ejpam-5563	536	7	)	)	PUNCT
ejpam-5563	536	8	.	.	PUNCT
ejpam-5563	537	1	(	(	PUNCT
ejpam-5563	537	2	v	v	NOUN
ejpam-5563	537	3	)	)	PUNCT
ejpam-5563	537	4	λ̃(λ⋄(o	λ̃(λ⋄(o	PROPN
ejpam-5563	537	5	)	)	PUNCT
ejpam-5563	537	6	)	)	PUNCT
ejpam-5563	538	1	=	=	PUNCT
ejpam-5563	539	1	[	[	X
ejpam-5563	539	2	γ(b)]c	γ(b)]c	NOUN
ejpam-5563	539	3	.	.	PUNCT
ejpam-5563	539	4	(	(	PUNCT
ejpam-5563	539	5	vi	vi	NOUN
ejpam-5563	539	6	)	)	PUNCT
ejpam-5563	539	7	λ̃(λ(o	λ̃(λ(o	NOUN
ejpam-5563	539	8	)	)	PUNCT
ejpam-5563	539	9	)	)	PUNCT
ejpam-5563	539	10	=	=	SYM
ejpam-5563	539	11	λ(o	λ(o	PROPN
ejpam-5563	539	12	)	)	PUNCT
ejpam-5563	539	13	.	.	PUNCT
ejpam-5563	540	1	proof	proof	NOUN
ejpam-5563	540	2	.	.	PUNCT
ejpam-5563	541	1	let	let	VERB
ejpam-5563	541	2	o	o	PROPN
ejpam-5563	541	3	⊆	⊆	NUM
ejpam-5563	541	4	b.	b.	NOUN
ejpam-5563	541	5	then	then	ADV
ejpam-5563	541	6	,	,	PUNCT
ejpam-5563	541	7	(	(	PUNCT
ejpam-5563	541	8	i	i	NOUN
ejpam-5563	541	9	)	)	PUNCT
ejpam-5563	541	10	λ⋄(o	λ⋄(o	NOUN
ejpam-5563	541	11	)	)	PUNCT
ejpam-5563	541	12	∩	∩	NOUN
ejpam-5563	541	13	λ̃(o	λ̃(o	PROPN
ejpam-5563	541	14	)	)	PUNCT
ejpam-5563	541	15	=[	=[	NOUN
ejpam-5563	541	16	γ∗(o	γ∗(o	PROPN
ejpam-5563	541	17	)	)	PUNCT
ejpam-5563	541	18	∩	∩	NOUN
ejpam-5563	541	19	(	(	PUNCT
ejpam-5563	541	20	γ(o))c	γ(o))c	PROPN
ejpam-5563	541	21	]	]	PUNCT
ejpam-5563	541	22	∩	∩	NOUN
ejpam-5563	542	1	[	[	X
ejpam-5563	542	2	o	o	X
ejpam-5563	542	3	∩	∩	X
ejpam-5563	542	4	(	(	PUNCT
ejpam-5563	542	5	γ(o))c	γ(o))c	PROPN
ejpam-5563	542	6	]	]	PUNCT
ejpam-5563	542	7	=	=	PUNCT
ejpam-5563	542	8	[	[	X
ejpam-5563	542	9	γ(o)]c	γ(o)]c	NOUN
ejpam-5563	542	10	∩	∩	NOUN
ejpam-5563	542	11	[	[	X
ejpam-5563	542	12	o	o	X
ejpam-5563	542	13	∩	∩	NOUN
ejpam-5563	542	14	γ∗(o	γ∗(o	PROPN
ejpam-5563	542	15	)	)	PUNCT
ejpam-5563	542	16	]	]	PUNCT
ejpam-5563	543	1	=	=	X
ejpam-5563	543	2	γ∗(o	γ∗(o	PROPN
ejpam-5563	543	3	)	)	PUNCT
ejpam-5563	543	4	∩	∩	NOUN
ejpam-5563	543	5	[	[	X
ejpam-5563	543	6	o	o	X
ejpam-5563	543	7	∩	∩	X
ejpam-5563	543	8	(	(	PUNCT
ejpam-5563	543	9	γ(o))c	γ(o))c	PROPN
ejpam-5563	543	10	)	)	PUNCT
ejpam-5563	543	11	]	]	PUNCT
ejpam-5563	544	1	=	=	X
ejpam-5563	544	2	γ∗(o	γ∗(o	PROPN
ejpam-5563	544	3	)	)	PUNCT
ejpam-5563	544	4	∩	∩	NOUN
ejpam-5563	544	5	λ̃(o	λ̃(o	PROPN
ejpam-5563	544	6	)	)	PUNCT
ejpam-5563	544	7	.	.	PUNCT
ejpam-5563	545	1	(	(	PUNCT
ejpam-5563	545	2	ii	ii	NOUN
ejpam-5563	545	3	)	)	PUNCT
ejpam-5563	545	4	λ⋄(o)−	λ⋄(o)−	PROPN
ejpam-5563	545	5	λ̃(o	λ̃(o	ADJ
ejpam-5563	545	6	)	)	PUNCT
ejpam-5563	545	7	=	=	SYM
ejpam-5563	545	8	λ⋄(o	λ⋄(o	NOUN
ejpam-5563	545	9	)	)	PUNCT
ejpam-5563	545	10	∩	∩	NOUN
ejpam-5563	545	11	[	[	X
ejpam-5563	545	12	λ̃(o)]c	λ̃(o)]c	PROPN
ejpam-5563	545	13	=	=	SYM
ejpam-5563	545	14	λ⋄(o	λ⋄(o	NOUN
ejpam-5563	545	15	)	)	PUNCT
ejpam-5563	545	16	∩	∩	NOUN
ejpam-5563	545	17	[	[	X
ejpam-5563	545	18	o	o	X
ejpam-5563	545	19	−	−	PROPN
ejpam-5563	545	20	(	(	PUNCT
ejpam-5563	545	21	γ(o))]c	γ(o))]c	PROPN
ejpam-5563	545	22	=	=	SYM
ejpam-5563	545	23	λ⋄(o	λ⋄(o	NOUN
ejpam-5563	545	24	)	)	PUNCT
ejpam-5563	545	25	∩	∩	NOUN
ejpam-5563	546	1	[	[	X
ejpam-5563	546	2	o	o	X
ejpam-5563	546	3	∩	∩	NOUN
ejpam-5563	546	4	(	(	PUNCT
ejpam-5563	546	5	γ(o))c]c	γ(o))c]c	NOUN
ejpam-5563	546	6	=	=	SYM
ejpam-5563	546	7	λ⋄(o	λ⋄(o	NOUN
ejpam-5563	546	8	)	)	PUNCT
ejpam-5563	546	9	∩	∩	NOUN
ejpam-5563	546	10	[	[	X
ejpam-5563	546	11	oc	oc	AUX
ejpam-5563	546	12	∪	∪	ADP
ejpam-5563	546	13	γ(o	γ(o	PROPN
ejpam-5563	546	14	)	)	PUNCT
ejpam-5563	546	15	]	]	PUNCT
ejpam-5563	547	1	=	=	PUNCT
ejpam-5563	547	2	[	[	X
ejpam-5563	547	3	λ⋄(o	λ⋄(o	NOUN
ejpam-5563	547	4	)	)	PUNCT
ejpam-5563	547	5	∩	∩	NOUN
ejpam-5563	547	6	oc	oc	ADP
ejpam-5563	547	7	]	]	X
ejpam-5563	547	8	∪	∪	ADP
ejpam-5563	547	9	[	[	X
ejpam-5563	547	10	λ⋄(o	λ⋄(o	NOUN
ejpam-5563	547	11	)	)	PUNCT
ejpam-5563	547	12	∩	∩	NOUN
ejpam-5563	547	13	γ(o	γ(o	PROPN
ejpam-5563	547	14	)	)	PUNCT
ejpam-5563	547	15	]	]	PUNCT
ejpam-5563	548	1	=	=	PUNCT
ejpam-5563	548	2	[	[	X
ejpam-5563	548	3	λ⋄(o)−o	λ⋄(o)−o	X
ejpam-5563	548	4	]	]	X
ejpam-5563	548	5	∪	∪	X
ejpam-5563	548	6	[	[	X
ejpam-5563	548	7	(	(	PUNCT
ejpam-5563	548	8	γ∗(o)−	γ∗(o)−	ADV
ejpam-5563	548	9	γ(o	γ(o	ADJ
ejpam-5563	548	10	)	)	PUNCT
ejpam-5563	548	11	)	)	PUNCT
ejpam-5563	548	12	∩	∩	NOUN
ejpam-5563	548	13	γ(o	γ(o	PROPN
ejpam-5563	548	14	)	)	PUNCT
ejpam-5563	548	15	]	]	PUNCT
ejpam-5563	549	1	=	=	PUNCT
ejpam-5563	549	2	λ⋄(o)−o	λ⋄(o)−o	ADJ
ejpam-5563	549	3	.	.	PUNCT
ejpam-5563	550	1	o.	o.	PROPN
ejpam-5563	550	2	alghamdi	alghamdi	PROPN
ejpam-5563	550	3	/	/	SYM
ejpam-5563	550	4	eur	eur	PROPN
ejpam-5563	550	5	.	.	PUNCT
ejpam-5563	551	1	j.	j.	PROPN
ejpam-5563	551	2	pure	pure	PROPN
ejpam-5563	551	3	appl	appl	PROPN
ejpam-5563	551	4	.	.	PROPN
ejpam-5563	551	5	math	math	PROPN
ejpam-5563	551	6	,	,	PUNCT
ejpam-5563	551	7	17	17	NUM
ejpam-5563	551	8	(	(	PUNCT
ejpam-5563	551	9	4	4	NUM
ejpam-5563	551	10	)	)	PUNCT
ejpam-5563	551	11	(	(	PUNCT
ejpam-5563	551	12	2024	2024	NUM
ejpam-5563	551	13	)	)	PUNCT
ejpam-5563	551	14	,	,	PUNCT
ejpam-5563	551	15	3517	3517	NUM
ejpam-5563	551	16	-	-	SYM
ejpam-5563	551	17	3538	3538	NUM
ejpam-5563	551	18	3533	3533	NUM
ejpam-5563	551	19	(	(	PUNCT
ejpam-5563	551	20	iii	iii	NOUN
ejpam-5563	551	21	)	)	PUNCT
ejpam-5563	551	22	λ̃(o)−	λ̃(o)−	PROPN
ejpam-5563	551	23	λ⋄(o	λ⋄(o	NOUN
ejpam-5563	551	24	)	)	PUNCT
ejpam-5563	552	1	=	=	SYM
ejpam-5563	552	2	λ̃(o	λ̃(o	ADJ
ejpam-5563	552	3	)	)	PUNCT
ejpam-5563	552	4	∩	∩	NOUN
ejpam-5563	553	1	[	[	X
ejpam-5563	553	2	λ⋄(o)]c	λ⋄(o)]c	X
ejpam-5563	553	3	=	=	SYM
ejpam-5563	553	4	λ̃(o	λ̃(o	ADJ
ejpam-5563	553	5	)	)	PUNCT
ejpam-5563	553	6	∩	∩	NOUN
ejpam-5563	553	7	[	[	X
ejpam-5563	553	8	γ∗(o	γ∗(o	PROPN
ejpam-5563	553	9	)	)	PUNCT
ejpam-5563	553	10	∩	∩	ADJ
ejpam-5563	553	11	γ∗(oc)]c	γ∗(oc)]c	NOUN
ejpam-5563	553	12	=	=	SYM
ejpam-5563	553	13	λ̃(o	λ̃(o	ADJ
ejpam-5563	553	14	)	)	PUNCT
ejpam-5563	553	15	∩	∩	NOUN
ejpam-5563	553	16	[	[	X
ejpam-5563	553	17	(	(	PUNCT
ejpam-5563	553	18	γ∗(o))c	γ∗(o))c	PROPN
ejpam-5563	553	19	∪	∪	ADJ
ejpam-5563	553	20	(	(	PUNCT
ejpam-5563	553	21	γ∗(oc))c	γ∗(oc))c	VERB
ejpam-5563	553	22	]	]	PUNCT
ejpam-5563	554	1	=	=	NOUN
ejpam-5563	554	2	[	[	X
ejpam-5563	554	3	λ̃(o	λ̃(o	ADJ
ejpam-5563	554	4	)	)	PUNCT
ejpam-5563	554	5	∩	∩	NOUN
ejpam-5563	554	6	(	(	PUNCT
ejpam-5563	554	7	γ∗(o))c	γ∗(o))c	NUM
ejpam-5563	554	8	]	]	PUNCT
ejpam-5563	554	9	∪	∪	ADP
ejpam-5563	554	10	[	[	X
ejpam-5563	554	11	λ̃(o	λ̃(o	ADJ
ejpam-5563	554	12	)	)	PUNCT
ejpam-5563	554	13	∩	∩	NOUN
ejpam-5563	554	14	(	(	PUNCT
ejpam-5563	554	15	γ∗(oc))c	γ∗(oc))c	X
ejpam-5563	554	16	]	]	X
ejpam-5563	555	1	=	=	PUNCT
ejpam-5563	555	2	[	[	X
ejpam-5563	555	3	λ̃(o)−	λ̃(o)−	PROPN
ejpam-5563	555	4	γ∗(o	γ∗(o	PROPN
ejpam-5563	555	5	)	)	PUNCT
ejpam-5563	555	6	]	]	PUNCT
ejpam-5563	555	7	∪	∪	X
ejpam-5563	555	8	[	[	X
ejpam-5563	555	9	o	o	X
ejpam-5563	555	10	∩	∩	NOUN
ejpam-5563	555	11	(	(	PUNCT
ejpam-5563	555	12	γ(o))c	γ(o))c	PROPN
ejpam-5563	555	13	∩	∩	NOUN
ejpam-5563	555	14	(	(	PUNCT
ejpam-5563	555	15	γ∗(oc))c	γ∗(oc))c	X
ejpam-5563	555	16	]	]	X
ejpam-5563	556	1	=	=	PUNCT
ejpam-5563	556	2	[	[	X
ejpam-5563	556	3	λ̃(o)−	λ̃(o)−	PROPN
ejpam-5563	556	4	γ∗(o	γ∗(o	PROPN
ejpam-5563	556	5	)	)	PUNCT
ejpam-5563	556	6	]	]	PUNCT
ejpam-5563	556	7	∪	∪	X
ejpam-5563	556	8	[	[	X
ejpam-5563	556	9	o	o	NOUN
ejpam-5563	556	10	∩	∩	ADJ
ejpam-5563	556	11	γ∗(oc	γ∗(oc	NOUN
ejpam-5563	556	12	)	)	PUNCT
ejpam-5563	556	13	∩	∩	NOUN
ejpam-5563	556	14	(	(	PUNCT
ejpam-5563	556	15	γ∗(oc))c	γ∗(oc))c	X
ejpam-5563	556	16	]	]	X
ejpam-5563	556	17	=	=	NOUN
ejpam-5563	556	18	λ̃(o)−	λ̃(o)−	PROPN
ejpam-5563	556	19	γ∗(o	γ∗(o	PROPN
ejpam-5563	556	20	)	)	PUNCT
ejpam-5563	556	21	.	.	PUNCT
ejpam-5563	557	1	(	(	PUNCT
ejpam-5563	557	2	iv	iv	X
ejpam-5563	557	3	)	)	PUNCT
ejpam-5563	557	4	λ⋄(o	λ⋄(o	NOUN
ejpam-5563	557	5	)	)	PUNCT
ejpam-5563	557	6	∪	∪	ADP
ejpam-5563	557	7	λ̃(o	λ̃(o	PROPN
ejpam-5563	557	8	)	)	PUNCT
ejpam-5563	557	9	=[	=[	NOUN
ejpam-5563	557	10	γ∗(o)−	γ∗(o)−	ADV
ejpam-5563	557	11	γ(o	γ(o	PROPN
ejpam-5563	557	12	)	)	PUNCT
ejpam-5563	557	13	]	]	PUNCT
ejpam-5563	557	14	∪	∪	ADP
ejpam-5563	558	1	[	[	X
ejpam-5563	558	2	o	o	X
ejpam-5563	558	3	−	−	X
ejpam-5563	558	4	γ(o	γ(o	PROPN
ejpam-5563	558	5	)	)	PUNCT
ejpam-5563	558	6	]	]	PUNCT
ejpam-5563	559	1	=	=	PUNCT
ejpam-5563	559	2	[	[	X
ejpam-5563	559	3	γ∗(o	γ∗(o	PROPN
ejpam-5563	559	4	)	)	PUNCT
ejpam-5563	559	5	∩	∩	NOUN
ejpam-5563	559	6	(	(	PUNCT
ejpam-5563	559	7	γ(o))c	γ(o))c	PROPN
ejpam-5563	559	8	]	]	PUNCT
ejpam-5563	559	9	∪	∪	ADP
ejpam-5563	559	10	[	[	X
ejpam-5563	559	11	o	o	X
ejpam-5563	559	12	∩	∩	NOUN
ejpam-5563	559	13	(	(	PUNCT
ejpam-5563	559	14	γ(o))c	γ(o))c	PROPN
ejpam-5563	559	15	]	]	PUNCT
ejpam-5563	559	16	=	=	PROPN
ejpam-5563	559	17	[	[	X
ejpam-5563	559	18	γ∗(o	γ∗(o	PROPN
ejpam-5563	559	19	)	)	PUNCT
ejpam-5563	559	20	∪	∪	ADP
ejpam-5563	559	21	o	o	NOUN
ejpam-5563	559	22	]	]	X
ejpam-5563	559	23	∩	∩	NOUN
ejpam-5563	559	24	(	(	PUNCT
ejpam-5563	559	25	γ(o))c	γ(o))c	PROPN
ejpam-5563	559	26	=[	=[	NOUN
ejpam-5563	559	27	γ∗(o	γ∗(o	PROPN
ejpam-5563	559	28	)	)	PUNCT
ejpam-5563	559	29	∪	∪	ADP
ejpam-5563	559	30	o]−	o]−	ADJ
ejpam-5563	559	31	γ(o	γ(o	NOUN
ejpam-5563	559	32	)	)	PUNCT
ejpam-5563	559	33	.	.	PUNCT
ejpam-5563	560	1	(	(	PUNCT
ejpam-5563	560	2	v	v	NOUN
ejpam-5563	560	3	)	)	PUNCT
ejpam-5563	560	4	λ̃(λ⋄(o	λ̃(λ⋄(o	PROPN
ejpam-5563	560	5	)	)	PUNCT
ejpam-5563	560	6	)	)	PUNCT
ejpam-5563	561	1	=	=	PUNCT
ejpam-5563	561	2	λ̃[(γ(b))c	λ̃[(γ(b))c	X
ejpam-5563	561	3	]	]	X
ejpam-5563	561	4	=	=	X
ejpam-5563	561	5	(	(	PUNCT
ejpam-5563	561	6	γ(b))c	γ(b))c	PROPN
ejpam-5563	561	7	−	−	PROPN
ejpam-5563	561	8	γ((γ(b))c	γ((γ(b))c	NOUN
ejpam-5563	561	9	)	)	PUNCT
ejpam-5563	561	10	=(	=(	NOUN
ejpam-5563	561	11	γ(b))c	γ(b))c	PROPN
ejpam-5563	561	12	∩	∩	PROPN
ejpam-5563	561	13	[	[	X
ejpam-5563	561	14	γ(γ(b))c]]c	γ(γ(b))c]]c	INTJ
ejpam-5563	561	15	=[	=[	NOUN
ejpam-5563	561	16	γ(b	γ(b	NOUN
ejpam-5563	561	17	)	)	PUNCT
ejpam-5563	561	18	∪	∪	ADP
ejpam-5563	561	19	γ(γ(b))c]c	γ(γ(b))c]c	NOUN
ejpam-5563	561	20	.	.	PUNCT
ejpam-5563	562	1	now	now	ADV
ejpam-5563	562	2	,	,	PUNCT
ejpam-5563	562	3	by	by	ADP
ejpam-5563	562	4	(	(	PUNCT
ejpam-5563	562	5	vii	vii	PROPN
ejpam-5563	562	6	)	)	PUNCT
ejpam-5563	562	7	in	in	ADP
ejpam-5563	562	8	theorem	theorem	NOUN
ejpam-5563	562	9	1	1	NUM
ejpam-5563	562	10	,	,	PUNCT
ejpam-5563	562	11	we	we	PRON
ejpam-5563	562	12	have	have	VERB
ejpam-5563	562	13	[	[	X
ejpam-5563	562	14	γ(b)∪γ(γ(b))c]c	γ(b)∪γ(γ(b))c]c	X
ejpam-5563	562	15	=	=	SYM
ejpam-5563	563	1	[	[	X
ejpam-5563	563	2	γ(b∪(γ(b))c)]c	γ(b∪(γ(b))c)]c	PROPN
ejpam-5563	563	3	=	=	PUNCT
ejpam-5563	564	1	[	[	X
ejpam-5563	564	2	γ(b)]c	γ(b)]c	NOUN
ejpam-5563	564	3	.	.	PUNCT
ejpam-5563	565	1	hence	hence	ADV
ejpam-5563	565	2	,	,	PUNCT
ejpam-5563	565	3	λ̃(λ⋄(o	λ̃(λ⋄(o	PROPN
ejpam-5563	565	4	)	)	PUNCT
ejpam-5563	565	5	)	)	PUNCT
ejpam-5563	566	1	=	=	PUNCT
ejpam-5563	567	1	[	[	X
ejpam-5563	567	2	γ(b)]c	γ(b)]c	NOUN
ejpam-5563	567	3	.	.	PUNCT
ejpam-5563	567	4	(	(	PUNCT
ejpam-5563	567	5	vi	vi	NOUN
ejpam-5563	567	6	)	)	PUNCT
ejpam-5563	567	7	λ̃(λ(o	λ̃(λ(o	NOUN
ejpam-5563	567	8	)	)	PUNCT
ejpam-5563	567	9	)	)	PUNCT
ejpam-5563	568	1	=	=	NOUN
ejpam-5563	568	2	λ(o)−	λ(o)−	NOUN
ejpam-5563	568	3	γ(λ(o	γ(λ(o	NOUN
ejpam-5563	568	4	)	)	PUNCT
ejpam-5563	568	5	)	)	PUNCT
ejpam-5563	569	1	=[	=[	NOUN
ejpam-5563	569	2	γ∗(o)−o]−	γ∗(o)−o]−	NOUN
ejpam-5563	569	3	γ[γ∗(o)−o	γ[γ∗(o)−o	PROPN
ejpam-5563	569	4	]	]	X
ejpam-5563	570	1	=	=	SYM
ejpam-5563	570	2	[	[	X
ejpam-5563	570	3	γ∗(o	γ∗(o	PROPN
ejpam-5563	570	4	)	)	PUNCT
ejpam-5563	570	5	∩	∩	NOUN
ejpam-5563	570	6	oc	oc	ADP
ejpam-5563	570	7	]	]	X
ejpam-5563	570	8	∩	∩	NOUN
ejpam-5563	570	9	[	[	X
ejpam-5563	570	10	γ[γ∗(o	γ[γ∗(o	NOUN
ejpam-5563	570	11	)	)	PUNCT
ejpam-5563	570	12	∩	∩	NOUN
ejpam-5563	570	13	oc]]c	oc]]c	PROPN
ejpam-5563	571	1	=	=	PRON
ejpam-5563	571	2	oc	oc	ADP
ejpam-5563	571	3	∩	∩	NOUN
ejpam-5563	571	4	[	[	X
ejpam-5563	571	5	γ∗(o	γ∗(o	PROPN
ejpam-5563	571	6	)	)	PUNCT
ejpam-5563	571	7	∩	∩	NOUN
ejpam-5563	571	8	[	[	X
ejpam-5563	571	9	γ[γ∗(o	γ[γ∗(o	NOUN
ejpam-5563	571	10	)	)	PUNCT
ejpam-5563	571	11	∩	∩	NOUN
ejpam-5563	571	12	oc]]c	oc]]c	PROPN
ejpam-5563	571	13	]	]	X
ejpam-5563	572	1	=	=	NOUN
ejpam-5563	572	2	oc	oc	ADP
ejpam-5563	572	3	∩	∩	NOUN
ejpam-5563	572	4	[	[	X
ejpam-5563	572	5	(	(	PUNCT
ejpam-5563	572	6	γ(oc))c	γ(oc))c	VERB
ejpam-5563	572	7	∩	∩	NOUN
ejpam-5563	572	8	[	[	X
ejpam-5563	572	9	γ[(γ(oc))c	γ[(γ(oc))c	PROPN
ejpam-5563	572	10	∩	∩	ADJ
ejpam-5563	572	11	oc]]c	oc]]c	PROPN
ejpam-5563	572	12	]	]	X
ejpam-5563	572	13	=	=	NOUN
ejpam-5563	572	14	oc	oc	ADP
ejpam-5563	572	15	∩	∩	NOUN
ejpam-5563	572	16	[	[	X
ejpam-5563	572	17	γ(oc	γ(oc	NOUN
ejpam-5563	572	18	)	)	PUNCT
ejpam-5563	572	19	∪	∪	ADP
ejpam-5563	572	20	γ[(γ(oc))c	γ[(γ(oc))c	PRON
ejpam-5563	572	21	∩	∩	ADJ
ejpam-5563	572	22	oc]]c	oc]]c	PROPN
ejpam-5563	572	23	=	=	PRON
ejpam-5563	572	24	oc	oc	ADP
ejpam-5563	572	25	∩	∩	NOUN
ejpam-5563	572	26	[	[	X
ejpam-5563	572	27	γ(oc	γ(oc	NOUN
ejpam-5563	572	28	∪	∪	VERB
ejpam-5563	572	29	γ∗(o	γ∗(o	PROPN
ejpam-5563	572	30	)	)	PUNCT
ejpam-5563	572	31	∩	∩	ADJ
ejpam-5563	572	32	oc)]c	oc)]c	NOUN
ejpam-5563	572	33	=	=	PRON
ejpam-5563	572	34	oc	oc	ADP
ejpam-5563	572	35	∩	∩	NOUN
ejpam-5563	572	36	[	[	X
ejpam-5563	572	37	γ(oc)]c	γ(oc)]c	PROPN
ejpam-5563	572	38	=	=	NOUN
ejpam-5563	572	39	γ∗(o)−o	γ∗(o)−o	PRON
ejpam-5563	572	40	=	=	SYM
ejpam-5563	572	41	λ(o	λ(o	NUM
ejpam-5563	572	42	)	)	PUNCT
ejpam-5563	572	43	.	.	PUNCT
ejpam-5563	573	1	o.	o.	PROPN
ejpam-5563	573	2	alghamdi	alghamdi	PROPN
ejpam-5563	573	3	/	/	SYM
ejpam-5563	573	4	eur	eur	PROPN
ejpam-5563	573	5	.	.	PUNCT
ejpam-5563	574	1	j.	j.	PROPN
ejpam-5563	574	2	pure	pure	PROPN
ejpam-5563	574	3	appl	appl	PROPN
ejpam-5563	574	4	.	.	PROPN
ejpam-5563	574	5	math	math	PROPN
ejpam-5563	574	6	,	,	PUNCT
ejpam-5563	574	7	17	17	NUM
ejpam-5563	574	8	(	(	PUNCT
ejpam-5563	574	9	4	4	NUM
ejpam-5563	574	10	)	)	PUNCT
ejpam-5563	574	11	(	(	PUNCT
ejpam-5563	574	12	2024	2024	NUM
ejpam-5563	574	13	)	)	PUNCT
ejpam-5563	574	14	,	,	PUNCT
ejpam-5563	574	15	3517	3517	NUM
ejpam-5563	574	16	-	-	SYM
ejpam-5563	574	17	3538	3538	NUM
ejpam-5563	574	18	3534	3534	NUM
ejpam-5563	574	19	corollary	corollary	NOUN
ejpam-5563	574	20	6	6	NUM
ejpam-5563	574	21	.	.	PUNCT
ejpam-5563	575	1	let	let	VERB
ejpam-5563	575	2	(	(	PUNCT
ejpam-5563	575	3	b	b	X
ejpam-5563	575	4	,	,	PUNCT
ejpam-5563	575	5	γ	γ	PROPN
ejpam-5563	575	6	,	,	PUNCT
ejpam-5563	575	7	p	p	NOUN
ejpam-5563	575	8	)	)	PUNCT
ejpam-5563	575	9	be	be	AUX
ejpam-5563	575	10	a	a	DET
ejpam-5563	575	11	ps	ps	NOUN
ejpam-5563	575	12	.	.	PUNCT
ejpam-5563	576	1	then	then	ADV
ejpam-5563	576	2	,	,	PUNCT
ejpam-5563	576	3	γ	γ	X
ejpam-5563	576	4	is	be	AUX
ejpam-5563	576	5	a	a	DET
ejpam-5563	576	6	compatible	compatible	ADJ
ejpam-5563	576	7	with	with	ADP
ejpam-5563	576	8	p	p	PRON
ejpam-5563	576	9	if	if	SCONJ
ejpam-5563	577	1	and	and	CCONJ
ejpam-5563	577	2	only	only	ADV
ejpam-5563	577	3	if	if	SCONJ
ejpam-5563	577	4	[	[	X
ejpam-5563	577	5	λ̃(o)]c	λ̃(o)]c	PROPN
ejpam-5563	577	6	/∈	/∈	PUNCT
ejpam-5563	577	7	p	p	NOUN
ejpam-5563	577	8	for	for	ADP
ejpam-5563	577	9	every	every	DET
ejpam-5563	577	10	o	o	PROPN
ejpam-5563	577	11	⊆	⊆	PROPN
ejpam-5563	577	12	b.	b.	PROPN
ejpam-5563	577	13	theorem	theorem	NOUN
ejpam-5563	577	14	22	22	NUM
ejpam-5563	577	15	.	.	PUNCT
ejpam-5563	578	1	let	let	VERB
ejpam-5563	578	2	(	(	PUNCT
ejpam-5563	578	3	b	b	X
ejpam-5563	578	4	,	,	PUNCT
ejpam-5563	578	5	γ	γ	PROPN
ejpam-5563	578	6	,	,	PUNCT
ejpam-5563	578	7	p	p	NOUN
ejpam-5563	578	8	)	)	PUNCT
ejpam-5563	578	9	be	be	AUX
ejpam-5563	578	10	a	a	DET
ejpam-5563	578	11	ps	ps	NOUN
ejpam-5563	578	12	and	and	CCONJ
ejpam-5563	578	13	o	o	PROPN
ejpam-5563	578	14	⊆	⊆	NUM
ejpam-5563	578	15	b.	b.	PROPN
ejpam-5563	578	16	then	then	ADV
ejpam-5563	578	17	,	,	PUNCT
ejpam-5563	578	18	the	the	DET
ejpam-5563	578	19	following	follow	VERB
ejpam-5563	578	20	holds	hold	VERB
ejpam-5563	578	21	:	:	PUNCT
ejpam-5563	578	22	(	(	PUNCT
ejpam-5563	578	23	i	i	NOUN
ejpam-5563	578	24	)	)	PUNCT
ejpam-5563	578	25	λ̃(λ⋄(λ(o	λ̃(λ⋄(λ(o	NUM
ejpam-5563	578	26	)	)	PUNCT
ejpam-5563	578	27	)	)	PUNCT
ejpam-5563	578	28	)	)	PUNCT
ejpam-5563	579	1	=	=	PUNCT
ejpam-5563	580	1	[	[	X
ejpam-5563	580	2	γ(b)]c	γ(b)]c	NOUN
ejpam-5563	580	3	.	.	PUNCT
ejpam-5563	580	4	(	(	PUNCT
ejpam-5563	580	5	ii	ii	NOUN
ejpam-5563	580	6	)	)	PUNCT
ejpam-5563	580	7	λ̃(λ(λ⋄(o	λ̃(λ(λ⋄(o	PROPN
ejpam-5563	580	8	)	)	PUNCT
ejpam-5563	580	9	)	)	PUNCT
ejpam-5563	580	10	)	)	PUNCT
ejpam-5563	581	1	=	=	SYM
ejpam-5563	581	2	γ(b)−	γ(b)−	PROPN
ejpam-5563	581	3	γ(γ(b	γ(γ(b	PROPN
ejpam-5563	581	4	)	)	PUNCT
ejpam-5563	581	5	)	)	PUNCT
ejpam-5563	581	6	.	.	PUNCT
ejpam-5563	582	1	proof	proof	NOUN
ejpam-5563	582	2	.	.	PUNCT
ejpam-5563	583	1	(	(	PUNCT
ejpam-5563	583	2	i	i	NOUN
ejpam-5563	583	3	)	)	PUNCT
ejpam-5563	583	4	let	let	VERB
ejpam-5563	583	5	o	o	PROPN
ejpam-5563	583	6	⊆	⊆	NUM
ejpam-5563	583	7	b.	b.	NOUN
ejpam-5563	583	8	then	then	ADV
ejpam-5563	583	9	,	,	PUNCT
ejpam-5563	583	10	λ̃(λ⋄(λ(o	λ̃(λ⋄(λ(o	NUM
ejpam-5563	583	11	)	)	PUNCT
ejpam-5563	583	12	)	)	PUNCT
ejpam-5563	583	13	)	)	PUNCT
ejpam-5563	584	1	=	=	PUNCT
ejpam-5563	584	2	λ̃[γ(b)]c	λ̃[γ(b)]c	NOUN
ejpam-5563	584	3	.	.	PUNCT
ejpam-5563	585	1	moreover	moreover	ADV
ejpam-5563	585	2	,	,	PUNCT
ejpam-5563	585	3	the	the	DET
ejpam-5563	585	4	property	property	NOUN
ejpam-5563	585	5	(	(	PUNCT
ejpam-5563	585	6	v	v	NOUN
ejpam-5563	585	7	)	)	PUNCT
ejpam-5563	585	8	in	in	ADP
ejpam-5563	585	9	theorem	theorem	ADJ
ejpam-5563	585	10	21	21	NUM
ejpam-5563	585	11	leads	lead	VERB
ejpam-5563	585	12	to	to	ADP
ejpam-5563	585	13	λ̃(λ⋄(λ(o	λ̃(λ⋄(λ(o	NUM
ejpam-5563	585	14	)	)	PUNCT
ejpam-5563	585	15	)	)	PUNCT
ejpam-5563	585	16	)	)	PUNCT
ejpam-5563	586	1	=	=	PUNCT
ejpam-5563	587	1	[	[	X
ejpam-5563	587	2	γ(b)]c	γ(b)]c	NOUN
ejpam-5563	587	3	.	.	PUNCT
ejpam-5563	587	4	(	(	PUNCT
ejpam-5563	587	5	ii	ii	NOUN
ejpam-5563	587	6	)	)	PUNCT
ejpam-5563	587	7	by	by	ADP
ejpam-5563	587	8	the	the	DET
ejpam-5563	587	9	property	property	NOUN
ejpam-5563	587	10	(	(	PUNCT
ejpam-5563	587	11	vi	vi	NOUN
ejpam-5563	587	12	)	)	PUNCT
ejpam-5563	587	13	in	in	ADP
ejpam-5563	587	14	theorem	theorem	NOUN
ejpam-5563	587	15	21	21	NUM
ejpam-5563	587	16	,	,	PUNCT
ejpam-5563	587	17	we	we	PRON
ejpam-5563	587	18	know	know	VERB
ejpam-5563	587	19	that	that	PRON
ejpam-5563	587	20	λ̃(λ(λ⋄(o	λ̃(λ(λ⋄(o	PROPN
ejpam-5563	587	21	)	)	PUNCT
ejpam-5563	587	22	)	)	PUNCT
ejpam-5563	587	23	)	)	PUNCT
ejpam-5563	588	1	=	=	SYM
ejpam-5563	588	2	λ(λ⋄(o	λ(λ⋄(o	NUM
ejpam-5563	588	3	)	)	PUNCT
ejpam-5563	588	4	)	)	PUNCT
ejpam-5563	588	5	.	.	PUNCT
ejpam-5563	589	1	additionally	additionally	ADV
ejpam-5563	589	2	,	,	PUNCT
ejpam-5563	589	3	we	we	PRON
ejpam-5563	589	4	use	use	VERB
ejpam-5563	589	5	property	property	NOUN
ejpam-5563	589	6	(	(	PUNCT
ejpam-5563	589	7	iv	iv	X
ejpam-5563	589	8	)	)	PUNCT
ejpam-5563	589	9	in	in	ADP
ejpam-5563	589	10	theorem	theorem	NOUN
ejpam-5563	589	11	18	18	NUM
ejpam-5563	589	12	to	to	PART
ejpam-5563	589	13	get	get	VERB
ejpam-5563	589	14	λ(λ⋄(o	λ(λ⋄(o	PUNCT
ejpam-5563	589	15	)	)	PUNCT
ejpam-5563	589	16	)	)	PUNCT
ejpam-5563	590	1	=	=	SYM
ejpam-5563	590	2	γ(b)−	γ(b)−	PROPN
ejpam-5563	590	3	γ(γ(b	γ(γ(b	PROPN
ejpam-5563	590	4	)	)	PUNCT
ejpam-5563	590	5	)	)	PUNCT
ejpam-5563	590	6	.	.	PUNCT
ejpam-5563	591	1	corollary	corollary	ADJ
ejpam-5563	591	2	7	7	NUM
ejpam-5563	591	3	.	.	PUNCT
ejpam-5563	592	1	let	let	VERB
ejpam-5563	592	2	(	(	PUNCT
ejpam-5563	592	3	b	b	X
ejpam-5563	592	4	,	,	PUNCT
ejpam-5563	592	5	γ	γ	PROPN
ejpam-5563	592	6	,	,	PUNCT
ejpam-5563	592	7	p	p	NOUN
ejpam-5563	592	8	)	)	PUNCT
ejpam-5563	592	9	be	be	AUX
ejpam-5563	592	10	a	a	DET
ejpam-5563	592	11	ps	ps	NOUN
ejpam-5563	592	12	and	and	CCONJ
ejpam-5563	592	13	o	o	NOUN
ejpam-5563	593	1	⊆	⊆	NUM
ejpam-5563	593	2	b	b	NOUN
ejpam-5563	593	3	such	such	ADJ
ejpam-5563	593	4	that	that	SCONJ
ejpam-5563	593	5	γ	γ	PROPN
ejpam-5563	593	6	−	−	PROPN
ejpam-5563	593	7	{	{	PUNCT
ejpam-5563	593	8	b	b	NOUN
ejpam-5563	593	9	}	}	PUNCT
ejpam-5563	593	10	⊆	⊆	NUM
ejpam-5563	593	11	p	p	NOUN
ejpam-5563	593	12	and	and	CCONJ
ejpam-5563	593	13	△	△	NOUN
ejpam-5563	593	14	=	=	SYM
ejpam-5563	593	15	{	{	PUNCT
ejpam-5563	593	16	∅	∅	NOUN
ejpam-5563	593	17	}	}	PUNCT
ejpam-5563	593	18	.	.	PUNCT
ejpam-5563	594	1	then	then	ADV
ejpam-5563	594	2	,	,	PUNCT
ejpam-5563	594	3	we	we	PRON
ejpam-5563	594	4	have	have	VERB
ejpam-5563	594	5	:	:	PUNCT
ejpam-5563	594	6	(	(	PUNCT
ejpam-5563	594	7	i	i	NOUN
ejpam-5563	594	8	)	)	PUNCT
ejpam-5563	594	9	λ⋄(λ(λ⋄(o	λ⋄(λ(λ⋄(o	PROPN
ejpam-5563	594	10	)	)	PUNCT
ejpam-5563	594	11	)	)	PUNCT
ejpam-5563	594	12	)	)	PUNCT
ejpam-5563	595	1	=	=	SYM
ejpam-5563	595	2	∅.	∅.	PRON
ejpam-5563	595	3	(	(	PUNCT
ejpam-5563	595	4	ii	ii	NOUN
ejpam-5563	595	5	)	)	PUNCT
ejpam-5563	595	6	λ⋄(λ(o	λ⋄(λ(o	NOUN
ejpam-5563	595	7	)	)	PUNCT
ejpam-5563	595	8	)	)	PUNCT
ejpam-5563	596	1	=	=	SYM
ejpam-5563	596	2	∅.	∅.	PRON
ejpam-5563	596	3	(	(	PUNCT
ejpam-5563	596	4	iii	iii	NOUN
ejpam-5563	596	5	)	)	PUNCT
ejpam-5563	596	6	λ⋄(λ̃(λ(o	λ⋄(λ̃(λ(o	PROPN
ejpam-5563	596	7	)	)	PUNCT
ejpam-5563	596	8	)	)	PUNCT
ejpam-5563	596	9	)	)	PUNCT
ejpam-5563	597	1	=	=	PUNCT
ejpam-5563	597	2	∅.	∅.	X
ejpam-5563	597	3	(	(	PUNCT
ejpam-5563	597	4	iv	iv	X
ejpam-5563	597	5	)	)	PUNCT
ejpam-5563	597	6	λ⋄(λ(λ̃(o	λ⋄(λ(λ̃(o	PROPN
ejpam-5563	597	7	)	)	PUNCT
ejpam-5563	597	8	)	)	PUNCT
ejpam-5563	597	9	)	)	PUNCT
ejpam-5563	598	1	=	=	PUNCT
ejpam-5563	598	2	∅.	∅.	X
ejpam-5563	598	3	(	(	PUNCT
ejpam-5563	598	4	v	v	NOUN
ejpam-5563	598	5	)	)	PUNCT
ejpam-5563	598	6	λ̃(λ⋄(λ(o	λ̃(λ⋄(λ(o	NUM
ejpam-5563	598	7	)	)	PUNCT
ejpam-5563	598	8	)	)	PUNCT
ejpam-5563	598	9	)	)	PUNCT
ejpam-5563	599	1	=	=	PUNCT
ejpam-5563	599	2	∅.	∅.	X
ejpam-5563	599	3	(	(	PUNCT
ejpam-5563	599	4	vi	vi	NOUN
ejpam-5563	599	5	)	)	PUNCT
ejpam-5563	599	6	λ̃[(γ(b))c	λ̃[(γ(b))c	X
ejpam-5563	599	7	]	]	X
ejpam-5563	599	8	=	=	SYM
ejpam-5563	599	9	∅.	∅.	X
ejpam-5563	599	10	(	(	PUNCT
ejpam-5563	599	11	vii	vii	PROPN
ejpam-5563	599	12	)	)	PUNCT
ejpam-5563	599	13	λ⋄(o	λ⋄(o	PROPN
ejpam-5563	599	14	)	)	PUNCT
ejpam-5563	599	15	=	=	PUNCT
ejpam-5563	599	16	∅.	∅.	X
ejpam-5563	599	17	(	(	PUNCT
ejpam-5563	599	18	viii	viii	NOUN
ejpam-5563	599	19	)	)	PUNCT
ejpam-5563	599	20	λ̃(λ(λ⋄(o	λ̃(λ(λ⋄(o	PROPN
ejpam-5563	599	21	)	)	PUNCT
ejpam-5563	599	22	)	)	PUNCT
ejpam-5563	599	23	)	)	PUNCT
ejpam-5563	600	1	=	=	PUNCT
ejpam-5563	600	2	∅.	∅.	X
ejpam-5563	600	3	(	(	PUNCT
ejpam-5563	600	4	ix	ix	ADJ
ejpam-5563	600	5	)	)	PUNCT
ejpam-5563	600	6	λ(λ⋄(λ̃(o	λ(λ⋄(λ̃(o	PROPN
ejpam-5563	600	7	)	)	PUNCT
ejpam-5563	600	8	)	)	PUNCT
ejpam-5563	600	9	)	)	PUNCT
ejpam-5563	601	1	=	=	PUNCT
ejpam-5563	601	2	∅.	∅.	X
ejpam-5563	601	3	(	(	PUNCT
ejpam-5563	601	4	x	x	NOUN
ejpam-5563	601	5	)	)	PUNCT
ejpam-5563	601	6	λ(λ̃(λ⋄(o	λ(λ̃(λ⋄(o	NUM
ejpam-5563	601	7	)	)	PUNCT
ejpam-5563	601	8	)	)	PUNCT
ejpam-5563	601	9	)	)	PUNCT
ejpam-5563	602	1	=	=	PUNCT
ejpam-5563	602	2	∅.	∅.	X
ejpam-5563	602	3	(	(	PUNCT
ejpam-5563	602	4	xi	xi	NOUN
ejpam-5563	602	5	)	)	PUNCT
ejpam-5563	602	6	γ(b)−	γ(b)−	PROPN
ejpam-5563	602	7	γ(γ(b	γ(γ(b	PROPN
ejpam-5563	602	8	)	)	PUNCT
ejpam-5563	602	9	)	)	PUNCT
ejpam-5563	603	1	=	=	PUNCT
ejpam-5563	603	2	∅.	∅.	PRON
ejpam-5563	603	3	o.	o.	PROPN
ejpam-5563	603	4	alghamdi	alghamdi	PROPN
ejpam-5563	603	5	/	/	SYM
ejpam-5563	603	6	eur	eur	PROPN
ejpam-5563	603	7	.	.	PUNCT
ejpam-5563	604	1	j.	j.	PROPN
ejpam-5563	604	2	pure	pure	PROPN
ejpam-5563	604	3	appl	appl	PROPN
ejpam-5563	604	4	.	.	PROPN
ejpam-5563	604	5	math	math	PROPN
ejpam-5563	604	6	,	,	PUNCT
ejpam-5563	604	7	17	17	NUM
ejpam-5563	604	8	(	(	PUNCT
ejpam-5563	604	9	4	4	NUM
ejpam-5563	604	10	)	)	PUNCT
ejpam-5563	604	11	(	(	PUNCT
ejpam-5563	604	12	2024	2024	NUM
ejpam-5563	604	13	)	)	PUNCT
ejpam-5563	604	14	,	,	PUNCT
ejpam-5563	604	15	3517	3517	NUM
ejpam-5563	604	16	-	-	SYM
ejpam-5563	604	17	3538	3538	NUM
ejpam-5563	604	18	3535	3535	NUM
ejpam-5563	604	19	6	6	NUM
ejpam-5563	604	20	.	.	PUNCT
ejpam-5563	605	1	examples	example	NOUN
ejpam-5563	605	2	we	we	PRON
ejpam-5563	605	3	provide	provide	VERB
ejpam-5563	605	4	illustrative	illustrative	ADJ
ejpam-5563	605	5	examples	example	NOUN
ejpam-5563	605	6	that	that	PRON
ejpam-5563	605	7	demonstrate	demonstrate	VERB
ejpam-5563	605	8	the	the	DET
ejpam-5563	605	9	relationships	relationship	NOUN
ejpam-5563	605	10	between	between	ADP
ejpam-5563	605	11	the	the	DET
ejpam-5563	605	12	λ̃	λ̃	PROPN
ejpam-5563	605	13	operator	operator	NOUN
ejpam-5563	605	14	and	and	CCONJ
ejpam-5563	605	15	other	other	ADJ
ejpam-5563	605	16	operators	operator	NOUN
ejpam-5563	605	17	.	.	PUNCT
ejpam-5563	606	1	example	example	NOUN
ejpam-5563	606	2	6	6	NUM
ejpam-5563	606	3	.	.	PUNCT
ejpam-5563	607	1	let	let	VERB
ejpam-5563	607	2	b	b	NOUN
ejpam-5563	607	3	=	=	PRON
ejpam-5563	607	4	{	{	PUNCT
ejpam-5563	607	5	e	e	NOUN
ejpam-5563	607	6	,	,	PUNCT
ejpam-5563	607	7	r	r	NOUN
ejpam-5563	607	8	,	,	PUNCT
ejpam-5563	607	9	t	t	PROPN
ejpam-5563	607	10	}	}	PUNCT
ejpam-5563	607	11	.	.	PUNCT
ejpam-5563	608	1	define	define	VERB
ejpam-5563	608	2	γ	γ	X
ejpam-5563	608	3	=	=	X
ejpam-5563	608	4	{	{	PUNCT
ejpam-5563	608	5	∅,b	∅,b	ADP
ejpam-5563	608	6	,	,	PUNCT
ejpam-5563	608	7	{	{	PUNCT
ejpam-5563	608	8	e	e	NOUN
ejpam-5563	608	9	}	}	PUNCT
ejpam-5563	608	10	,	,	PUNCT
ejpam-5563	608	11	{	{	PUNCT
ejpam-5563	608	12	r	r	NOUN
ejpam-5563	608	13	}	}	PUNCT
ejpam-5563	608	14	,	,	PUNCT
ejpam-5563	608	15	{	{	PUNCT
ejpam-5563	608	16	e	e	NOUN
ejpam-5563	608	17	,	,	PUNCT
ejpam-5563	608	18	r	r	NOUN
ejpam-5563	608	19	}	}	PUNCT
ejpam-5563	608	20	}	}	PUNCT
ejpam-5563	608	21	and	and	CCONJ
ejpam-5563	608	22	p	p	NOUN
ejpam-5563	608	23	=	=	PUNCT
ejpam-5563	608	24	{	{	PUNCT
ejpam-5563	608	25	∅	∅	NOUN
ejpam-5563	608	26	,	,	PUNCT
ejpam-5563	608	27	{	{	PUNCT
ejpam-5563	608	28	e	e	NOUN
ejpam-5563	608	29	}	}	PUNCT
ejpam-5563	608	30	,	,	PUNCT
ejpam-5563	608	31	{	{	PUNCT
ejpam-5563	608	32	r	r	NOUN
ejpam-5563	608	33	}	}	PUNCT
ejpam-5563	608	34	,	,	PUNCT
ejpam-5563	608	35	{	{	PUNCT
ejpam-5563	608	36	e	e	NOUN
ejpam-5563	608	37	,	,	PUNCT
ejpam-5563	608	38	r	r	NOUN
ejpam-5563	608	39	}	}	PUNCT
ejpam-5563	608	40	}	}	PUNCT
ejpam-5563	608	41	.	.	PUNCT
ejpam-5563	609	1	then	then	ADV
ejpam-5563	609	2	,	,	PUNCT
ejpam-5563	609	3	(	(	PUNCT
ejpam-5563	609	4	b	b	X
ejpam-5563	609	5	,	,	PUNCT
ejpam-5563	609	6	γ	γ	PROPN
ejpam-5563	609	7	,	,	PUNCT
ejpam-5563	609	8	p	p	NOUN
ejpam-5563	609	9	)	)	PUNCT
ejpam-5563	609	10	is	be	AUX
ejpam-5563	609	11	a	a	DET
ejpam-5563	609	12	ps	ps	NOUN
ejpam-5563	609	13	.	.	PUNCT
ejpam-5563	610	1	if	if	SCONJ
ejpam-5563	610	2	k	k	PROPN
ejpam-5563	610	3	⊆	⊆	NUM
ejpam-5563	610	4	b	b	NOUN
ejpam-5563	610	5	,	,	PUNCT
ejpam-5563	610	6	then	then	ADV
ejpam-5563	610	7	we	we	PRON
ejpam-5563	610	8	have	have	VERB
ejpam-5563	610	9	the	the	DET
ejpam-5563	610	10	following	follow	VERB
ejpam-5563	610	11	table	table	NOUN
ejpam-5563	610	12	.	.	PUNCT
ejpam-5563	611	1	k	k	PROPN
ejpam-5563	611	2	k⋄	k⋄	PROPN
ejpam-5563	611	3	γ(k	γ(k	PROPN
ejpam-5563	611	4	)	)	PUNCT
ejpam-5563	611	5	γ⋆(k	γ⋆(k	NOUN
ejpam-5563	611	6	)	)	PUNCT
ejpam-5563	612	1	λ(k	λ(k	ADJ
ejpam-5563	612	2	)	)	PUNCT
ejpam-5563	612	3	λ⋄(k	λ⋄(k	NOUN
ejpam-5563	612	4	)	)	PUNCT
ejpam-5563	612	5	λ̃(k	λ̃(k	NOUN
ejpam-5563	612	6	)	)	PUNCT
ejpam-5563	612	7	∅	∅	NOUN
ejpam-5563	612	8	∅	∅	NOUN
ejpam-5563	612	9	∅	∅	NOUN
ejpam-5563	612	10	{	{	PUNCT
ejpam-5563	612	11	e	e	NOUN
ejpam-5563	612	12	,	,	PUNCT
ejpam-5563	612	13	r	r	NOUN
ejpam-5563	612	14	}	}	PUNCT
ejpam-5563	612	15	{	{	PUNCT
ejpam-5563	612	16	e	e	NOUN
ejpam-5563	612	17	,	,	PUNCT
ejpam-5563	612	18	r	r	NOUN
ejpam-5563	612	19	}	}	PUNCT
ejpam-5563	612	20	{	{	PUNCT
ejpam-5563	612	21	e	e	NOUN
ejpam-5563	612	22	,	,	PUNCT
ejpam-5563	612	23	r	r	NOUN
ejpam-5563	612	24	}	}	PUNCT
ejpam-5563	612	25	∅	∅	NOUN
ejpam-5563	612	26	b	b	NOUN
ejpam-5563	612	27	{	{	PUNCT
ejpam-5563	612	28	t	t	PROPN
ejpam-5563	612	29	}	}	PUNCT
ejpam-5563	612	30	{	{	PUNCT
ejpam-5563	612	31	t	t	PROPN
ejpam-5563	612	32	}	}	PUNCT
ejpam-5563	612	33	b	b	PROPN
ejpam-5563	612	34	∅	∅	NOUN
ejpam-5563	612	35	{	{	PUNCT
ejpam-5563	612	36	e	e	NOUN
ejpam-5563	612	37	,	,	PUNCT
ejpam-5563	612	38	r	r	NOUN
ejpam-5563	612	39	}	}	PUNCT
ejpam-5563	612	40	{	{	PUNCT
ejpam-5563	612	41	e	e	NOUN
ejpam-5563	612	42	,	,	PUNCT
ejpam-5563	612	43	r	r	NOUN
ejpam-5563	612	44	}	}	PUNCT
ejpam-5563	612	45	{	{	PUNCT
ejpam-5563	612	46	e	e	NOUN
ejpam-5563	612	47	}	}	PUNCT
ejpam-5563	612	48	∅	∅	NOUN
ejpam-5563	612	49	∅	∅	NOUN
ejpam-5563	612	50	{	{	PUNCT
ejpam-5563	612	51	e	e	NOUN
ejpam-5563	612	52	,	,	PUNCT
ejpam-5563	612	53	r	r	NOUN
ejpam-5563	612	54	}	}	PUNCT
ejpam-5563	612	55	{	{	PUNCT
ejpam-5563	612	56	r	r	NOUN
ejpam-5563	612	57	}	}	PUNCT
ejpam-5563	612	58	{	{	PUNCT
ejpam-5563	612	59	e	e	NOUN
ejpam-5563	612	60	,	,	PUNCT
ejpam-5563	612	61	r	r	NOUN
ejpam-5563	612	62	}	}	PUNCT
ejpam-5563	612	63	{	{	PUNCT
ejpam-5563	612	64	e	e	NOUN
ejpam-5563	612	65	}	}	PUNCT
ejpam-5563	612	66	{	{	PUNCT
ejpam-5563	612	67	r	r	NOUN
ejpam-5563	612	68	}	}	PUNCT
ejpam-5563	612	69	∅	∅	NOUN
ejpam-5563	612	70	∅	∅	NOUN
ejpam-5563	612	71	{	{	PUNCT
ejpam-5563	612	72	e	e	NOUN
ejpam-5563	612	73	,	,	PUNCT
ejpam-5563	612	74	r	r	NOUN
ejpam-5563	612	75	}	}	PUNCT
ejpam-5563	612	76	{	{	PUNCT
ejpam-5563	612	77	e	e	NOUN
ejpam-5563	612	78	}	}	PUNCT
ejpam-5563	612	79	{	{	PUNCT
ejpam-5563	612	80	e	e	NOUN
ejpam-5563	612	81	,	,	PUNCT
ejpam-5563	612	82	r	r	NOUN
ejpam-5563	612	83	}	}	PUNCT
ejpam-5563	612	84	{	{	PUNCT
ejpam-5563	612	85	r	r	NOUN
ejpam-5563	612	86	}	}	PUNCT
ejpam-5563	612	87	{	{	PUNCT
ejpam-5563	612	88	t	t	NOUN
ejpam-5563	612	89	}	}	PUNCT
ejpam-5563	612	90	{	{	PUNCT
ejpam-5563	612	91	t	t	PROPN
ejpam-5563	612	92	}	}	PUNCT
ejpam-5563	612	93	{	{	PUNCT
ejpam-5563	612	94	t	t	PROPN
ejpam-5563	612	95	}	}	PUNCT
ejpam-5563	612	96	b	b	PROPN
ejpam-5563	612	97	{	{	PUNCT
ejpam-5563	612	98	e	e	NOUN
ejpam-5563	612	99	,	,	PUNCT
ejpam-5563	612	100	r	r	NOUN
ejpam-5563	612	101	}	}	PUNCT
ejpam-5563	612	102	{	{	PUNCT
ejpam-5563	612	103	e	e	NOUN
ejpam-5563	612	104	,	,	PUNCT
ejpam-5563	612	105	r	r	NOUN
ejpam-5563	612	106	}	}	PUNCT
ejpam-5563	612	107	∅	∅	NOUN
ejpam-5563	612	108	{	{	PUNCT
ejpam-5563	612	109	e	e	NOUN
ejpam-5563	612	110	,	,	PUNCT
ejpam-5563	612	111	r	r	NOUN
ejpam-5563	612	112	}	}	PUNCT
ejpam-5563	612	113	∅	∅	NOUN
ejpam-5563	612	114	∅	∅	NOUN
ejpam-5563	612	115	{	{	PUNCT
ejpam-5563	612	116	e	e	NOUN
ejpam-5563	612	117	,	,	PUNCT
ejpam-5563	612	118	r	r	NOUN
ejpam-5563	612	119	}	}	PUNCT
ejpam-5563	612	120	∅	∅	NOUN
ejpam-5563	612	121	{	{	PUNCT
ejpam-5563	612	122	e	e	NOUN
ejpam-5563	612	123	,	,	PUNCT
ejpam-5563	612	124	r	r	NOUN
ejpam-5563	612	125	}	}	PUNCT
ejpam-5563	612	126	{	{	PUNCT
ejpam-5563	612	127	e	e	NOUN
ejpam-5563	612	128	,	,	PUNCT
ejpam-5563	612	129	r	r	NOUN
ejpam-5563	612	130	}	}	PUNCT
ejpam-5563	612	131	{	{	PUNCT
ejpam-5563	612	132	e	e	NOUN
ejpam-5563	612	133	,	,	PUNCT
ejpam-5563	612	134	t	t	PROPN
ejpam-5563	612	135	}	}	PUNCT
ejpam-5563	612	136	{	{	PUNCT
ejpam-5563	612	137	t	t	PROPN
ejpam-5563	612	138	}	}	PUNCT
ejpam-5563	612	139	{	{	PUNCT
ejpam-5563	612	140	t	t	PROPN
ejpam-5563	612	141	}	}	PUNCT
ejpam-5563	612	142	b	b	PROPN
ejpam-5563	612	143	{	{	PUNCT
ejpam-5563	612	144	r	r	NOUN
ejpam-5563	612	145	}	}	PUNCT
ejpam-5563	612	146	{	{	PUNCT
ejpam-5563	612	147	e	e	NOUN
ejpam-5563	612	148	,	,	PUNCT
ejpam-5563	612	149	r	r	NOUN
ejpam-5563	612	150	}	}	PUNCT
ejpam-5563	612	151	{	{	PUNCT
ejpam-5563	612	152	e	e	NOUN
ejpam-5563	612	153	}	}	PUNCT
ejpam-5563	612	154	{	{	PUNCT
ejpam-5563	612	155	r	r	NOUN
ejpam-5563	612	156	,	,	PUNCT
ejpam-5563	612	157	t	t	PROPN
ejpam-5563	612	158	}	}	PUNCT
ejpam-5563	612	159	{	{	PUNCT
ejpam-5563	612	160	t	t	PROPN
ejpam-5563	612	161	}	}	PUNCT
ejpam-5563	612	162	{	{	PUNCT
ejpam-5563	612	163	t	t	PROPN
ejpam-5563	612	164	}	}	PUNCT
ejpam-5563	612	165	b	b	PROPN
ejpam-5563	612	166	{	{	PUNCT
ejpam-5563	612	167	e	e	NOUN
ejpam-5563	612	168	}	}	PUNCT
ejpam-5563	612	169	{	{	PUNCT
ejpam-5563	612	170	e	e	NOUN
ejpam-5563	612	171	,	,	PUNCT
ejpam-5563	612	172	r	r	NOUN
ejpam-5563	612	173	}	}	PUNCT
ejpam-5563	612	174	{	{	PUNCT
ejpam-5563	612	175	r	r	NOUN
ejpam-5563	612	176	}	}	PUNCT
ejpam-5563	612	177	example	example	NOUN
ejpam-5563	612	178	7	7	NUM
ejpam-5563	612	179	.	.	PUNCT
ejpam-5563	613	1	let	let	VERB
ejpam-5563	613	2	b	b	NOUN
ejpam-5563	613	3	=	=	PRON
ejpam-5563	613	4	{	{	PUNCT
ejpam-5563	613	5	e	e	NOUN
ejpam-5563	613	6	,	,	PUNCT
ejpam-5563	613	7	r	r	NOUN
ejpam-5563	613	8	,	,	PUNCT
ejpam-5563	613	9	t	t	PROPN
ejpam-5563	613	10	}	}	PUNCT
ejpam-5563	613	11	.	.	PUNCT
ejpam-5563	614	1	define	define	VERB
ejpam-5563	614	2	γ	γ	X
ejpam-5563	614	3	=	=	X
ejpam-5563	614	4	{	{	PUNCT
ejpam-5563	614	5	∅,b	∅,b	ADP
ejpam-5563	614	6	,	,	PUNCT
ejpam-5563	614	7	{	{	PUNCT
ejpam-5563	614	8	e	e	NOUN
ejpam-5563	614	9	}	}	PUNCT
ejpam-5563	614	10	,	,	PUNCT
ejpam-5563	614	11	{	{	PUNCT
ejpam-5563	614	12	r	r	NOUN
ejpam-5563	614	13	}	}	PUNCT
ejpam-5563	614	14	,	,	PUNCT
ejpam-5563	614	15	{	{	PUNCT
ejpam-5563	614	16	e	e	NOUN
ejpam-5563	614	17	,	,	PUNCT
ejpam-5563	614	18	r	r	NOUN
ejpam-5563	614	19	}	}	PUNCT
ejpam-5563	614	20	}	}	PUNCT
ejpam-5563	614	21	and	and	CCONJ
ejpam-5563	614	22	p	p	X
ejpam-5563	614	23	=	=	PUNCT
ejpam-5563	614	24	∅.	∅.	VERB
ejpam-5563	614	25	if	if	SCONJ
ejpam-5563	614	26	k	k	PROPN
ejpam-5563	614	27	⊆	⊆	NUM
ejpam-5563	614	28	b	b	NOUN
ejpam-5563	614	29	,	,	PUNCT
ejpam-5563	614	30	then	then	ADV
ejpam-5563	614	31	we	we	PRON
ejpam-5563	614	32	have	have	VERB
ejpam-5563	614	33	the	the	DET
ejpam-5563	614	34	following	follow	VERB
ejpam-5563	614	35	results	result	NOUN
ejpam-5563	614	36	.	.	PUNCT
ejpam-5563	615	1	k	k	PROPN
ejpam-5563	615	2	k⋄	k⋄	PROPN
ejpam-5563	615	3	γ(k	γ(k	PROPN
ejpam-5563	615	4	)	)	PUNCT
ejpam-5563	615	5	γ⋆(k	γ⋆(k	NOUN
ejpam-5563	615	6	)	)	PUNCT
ejpam-5563	616	1	λ(k	λ(k	ADJ
ejpam-5563	616	2	)	)	PUNCT
ejpam-5563	616	3	λ⋄(k	λ⋄(k	NOUN
ejpam-5563	616	4	)	)	PUNCT
ejpam-5563	616	5	λ̃(k	λ̃(k	NOUN
ejpam-5563	616	6	)	)	PUNCT
ejpam-5563	616	7	∅	∅	NOUN
ejpam-5563	616	8	∅	∅	NOUN
ejpam-5563	616	9	∅	∅	NOUN
ejpam-5563	616	10	b	b	PROPN
ejpam-5563	616	11	b	b	PROPN
ejpam-5563	616	12	b	b	PROPN
ejpam-5563	616	13	∅	∅	NOUN
ejpam-5563	616	14	b	b	NOUN
ejpam-5563	616	15	∅	∅	NOUN
ejpam-5563	616	16	∅	∅	NOUN
ejpam-5563	616	17	b	b	PROPN
ejpam-5563	616	18	∅	∅	NOUN
ejpam-5563	616	19	b	b	PROPN
ejpam-5563	616	20	b	b	X
ejpam-5563	616	21	{	{	PUNCT
ejpam-5563	616	22	e	e	NOUN
ejpam-5563	616	23	}	}	PUNCT
ejpam-5563	616	24	∅	∅	NOUN
ejpam-5563	616	25	∅	∅	NOUN
ejpam-5563	616	26	b	b	X
ejpam-5563	616	27	{	{	PUNCT
ejpam-5563	616	28	r	r	NOUN
ejpam-5563	616	29	,	,	PUNCT
ejpam-5563	616	30	t	t	PROPN
ejpam-5563	616	31	}	}	PUNCT
ejpam-5563	616	32	b	b	PROPN
ejpam-5563	616	33	{	{	PUNCT
ejpam-5563	616	34	e	e	NOUN
ejpam-5563	616	35	}	}	PUNCT
ejpam-5563	616	36	{	{	PUNCT
ejpam-5563	616	37	r	r	NOUN
ejpam-5563	616	38	}	}	PUNCT
ejpam-5563	616	39	∅	∅	NOUN
ejpam-5563	616	40	∅	∅	NOUN
ejpam-5563	616	41	b	b	X
ejpam-5563	616	42	{	{	PUNCT
ejpam-5563	616	43	e	e	NOUN
ejpam-5563	616	44	,	,	PUNCT
ejpam-5563	616	45	t	t	PROPN
ejpam-5563	616	46	}	}	PUNCT
ejpam-5563	616	47	b	b	PROPN
ejpam-5563	616	48	{	{	PUNCT
ejpam-5563	616	49	r	r	NOUN
ejpam-5563	616	50	}	}	PUNCT
ejpam-5563	616	51	{	{	PUNCT
ejpam-5563	616	52	t	t	NOUN
ejpam-5563	616	53	}	}	PUNCT
ejpam-5563	616	54	∅	∅	NOUN
ejpam-5563	616	55	∅	∅	NOUN
ejpam-5563	616	56	b	b	X
ejpam-5563	616	57	{	{	PUNCT
ejpam-5563	616	58	e	e	NOUN
ejpam-5563	616	59	,	,	PUNCT
ejpam-5563	616	60	r	r	NOUN
ejpam-5563	616	61	}	}	PUNCT
ejpam-5563	616	62	b	b	PROPN
ejpam-5563	616	63	{	{	PUNCT
ejpam-5563	616	64	t	t	PROPN
ejpam-5563	616	65	}	}	PUNCT
ejpam-5563	616	66	{	{	PUNCT
ejpam-5563	616	67	e	e	NOUN
ejpam-5563	616	68	,	,	PUNCT
ejpam-5563	616	69	r	r	NOUN
ejpam-5563	616	70	}	}	PUNCT
ejpam-5563	616	71	∅	∅	NOUN
ejpam-5563	616	72	∅	∅	NOUN
ejpam-5563	616	73	b	b	X
ejpam-5563	616	74	{	{	PUNCT
ejpam-5563	616	75	c	c	NOUN
ejpam-5563	616	76	}	}	PUNCT
ejpam-5563	616	77	b	b	PROPN
ejpam-5563	616	78	{	{	PUNCT
ejpam-5563	616	79	e	e	NOUN
ejpam-5563	616	80	,	,	PUNCT
ejpam-5563	616	81	r	r	NOUN
ejpam-5563	616	82	}	}	PUNCT
ejpam-5563	616	83	{	{	PUNCT
ejpam-5563	616	84	e	e	NOUN
ejpam-5563	616	85	,	,	PUNCT
ejpam-5563	616	86	t	t	PROPN
ejpam-5563	616	87	}	}	PUNCT
ejpam-5563	616	88	∅	∅	NOUN
ejpam-5563	616	89	∅	∅	NOUN
ejpam-5563	616	90	b	b	X
ejpam-5563	616	91	{	{	PUNCT
ejpam-5563	616	92	r	r	NOUN
ejpam-5563	616	93	}	}	PUNCT
ejpam-5563	616	94	b	b	PROPN
ejpam-5563	616	95	{	{	PUNCT
ejpam-5563	616	96	e	e	NOUN
ejpam-5563	616	97	,	,	PUNCT
ejpam-5563	616	98	t	t	PROPN
ejpam-5563	616	99	}	}	PUNCT
ejpam-5563	616	100	{	{	PUNCT
ejpam-5563	616	101	r	r	NOUN
ejpam-5563	616	102	,	,	PUNCT
ejpam-5563	616	103	t	t	PROPN
ejpam-5563	616	104	}	}	PUNCT
ejpam-5563	616	105	∅	∅	NOUN
ejpam-5563	616	106	∅	∅	NOUN
ejpam-5563	616	107	b	b	X
ejpam-5563	616	108	{	{	PUNCT
ejpam-5563	616	109	e	e	NOUN
ejpam-5563	616	110	}	}	PUNCT
ejpam-5563	616	111	b	b	PROPN
ejpam-5563	616	112	{	{	PUNCT
ejpam-5563	616	113	r	r	NOUN
ejpam-5563	616	114	,	,	PUNCT
ejpam-5563	616	115	t	t	NOUN
ejpam-5563	616	116	}	}	PUNCT
ejpam-5563	616	117	form	form	NOUN
ejpam-5563	616	118	example	example	NOUN
ejpam-5563	616	119	7	7	NUM
ejpam-5563	616	120	,	,	PUNCT
ejpam-5563	616	121	we	we	PRON
ejpam-5563	616	122	conclude	conclude	VERB
ejpam-5563	616	123	that	that	PRON
ejpam-5563	616	124	λ(k	λ(k	PROPN
ejpam-5563	616	125	)	)	PUNCT
ejpam-5563	616	126	=	=	SYM
ejpam-5563	616	127	kc	kc	PROPN
ejpam-5563	616	128	,	,	PUNCT
ejpam-5563	616	129	λ⋄(k	λ⋄(k	NOUN
ejpam-5563	616	130	)	)	PUNCT
ejpam-5563	616	131	=	=	SYM
ejpam-5563	616	132	b	b	PROPN
ejpam-5563	616	133	and	and	CCONJ
ejpam-5563	616	134	λ̃(k	λ̃(k	PROPN
ejpam-5563	616	135	)	)	PUNCT
ejpam-5563	616	136	=	=	SYM
ejpam-5563	616	137	k	k	PROPN
ejpam-5563	616	138	since	since	SCONJ
ejpam-5563	616	139	γ(k	γ(k	PROPN
ejpam-5563	616	140	)	)	PUNCT
ejpam-5563	617	1	=	=	NOUN
ejpam-5563	617	2	∅	∅	NOUN
ejpam-5563	617	3	for	for	ADP
ejpam-5563	617	4	every	every	DET
ejpam-5563	617	5	k	k	PROPN
ejpam-5563	617	6	⊆	⊆	PROPN
ejpam-5563	617	7	b.	b.	PROPN
ejpam-5563	617	8	observe	observe	VERB
ejpam-5563	617	9	that	that	SCONJ
ejpam-5563	617	10	p	p	X
ejpam-5563	617	11	=	=	PUNCT
ejpam-5563	617	12	∅.	∅.	X
ejpam-5563	617	13	o.	o.	PROPN
ejpam-5563	617	14	alghamdi	alghamdi	PROPN
ejpam-5563	617	15	/	/	SYM
ejpam-5563	617	16	eur	eur	PROPN
ejpam-5563	617	17	.	.	PUNCT
ejpam-5563	618	1	j.	j.	PROPN
ejpam-5563	618	2	pure	pure	PROPN
ejpam-5563	618	3	appl	appl	PROPN
ejpam-5563	618	4	.	.	PROPN
ejpam-5563	618	5	math	math	PROPN
ejpam-5563	618	6	,	,	PUNCT
ejpam-5563	618	7	17	17	NUM
ejpam-5563	618	8	(	(	PUNCT
ejpam-5563	618	9	4	4	NUM
ejpam-5563	618	10	)	)	PUNCT
ejpam-5563	618	11	(	(	PUNCT
ejpam-5563	618	12	2024	2024	NUM
ejpam-5563	618	13	)	)	PUNCT
ejpam-5563	618	14	,	,	PUNCT
ejpam-5563	618	15	3517	3517	NUM
ejpam-5563	618	16	-	-	SYM
ejpam-5563	618	17	3538	3538	NUM
ejpam-5563	618	18	3536	3536	NUM
ejpam-5563	618	19	example	example	NOUN
ejpam-5563	618	20	8	8	NUM
ejpam-5563	618	21	.	.	PUNCT
ejpam-5563	619	1	let	let	VERB
ejpam-5563	619	2	b	b	NOUN
ejpam-5563	619	3	=	=	PRON
ejpam-5563	619	4	{	{	PUNCT
ejpam-5563	619	5	e	e	NOUN
ejpam-5563	619	6	,	,	PUNCT
ejpam-5563	619	7	r	r	NOUN
ejpam-5563	619	8	,	,	PUNCT
ejpam-5563	619	9	t	t	PROPN
ejpam-5563	619	10	}	}	PUNCT
ejpam-5563	619	11	with	with	ADP
ejpam-5563	619	12	topology	topology	NOUN
ejpam-5563	619	13	τ	τ	X
ejpam-5563	619	14	=	=	PUNCT
ejpam-5563	619	15	{	{	PUNCT
ejpam-5563	619	16	∅,b	∅,b	ADP
ejpam-5563	619	17	,	,	PUNCT
ejpam-5563	619	18	{	{	PUNCT
ejpam-5563	619	19	e	e	NOUN
ejpam-5563	619	20	}	}	PUNCT
ejpam-5563	619	21	,	,	PUNCT
ejpam-5563	619	22	{	{	PUNCT
ejpam-5563	619	23	t	t	NOUN
ejpam-5563	619	24	}	}	PUNCT
ejpam-5563	619	25	,	,	PUNCT
ejpam-5563	619	26	{	{	PUNCT
ejpam-5563	619	27	r	r	NOUN
ejpam-5563	619	28	,	,	PUNCT
ejpam-5563	619	29	t	t	PROPN
ejpam-5563	619	30	}	}	PUNCT
ejpam-5563	619	31	,	,	PUNCT
ejpam-5563	619	32	{	{	PUNCT
ejpam-5563	619	33	e	e	NOUN
ejpam-5563	619	34	,	,	PUNCT
ejpam-5563	619	35	t	t	PROPN
ejpam-5563	619	36	}	}	PUNCT
ejpam-5563	619	37	}	}	PUNCT
ejpam-5563	619	38	and	and	CCONJ
ejpam-5563	619	39	the	the	DET
ejpam-5563	619	40	primal	primal	ADJ
ejpam-5563	619	41	p	p	X
ejpam-5563	619	42	=	=	SYM
ejpam-5563	619	43	p	p	X
ejpam-5563	619	44	(	(	PUNCT
ejpam-5563	619	45	b)−	b)−	PROPN
ejpam-5563	619	46	{	{	PUNCT
ejpam-5563	619	47	b}.if	b}.if	PROPN
ejpam-5563	619	48	k	k	PROPN
ejpam-5563	620	1	⊆	⊆	NUM
ejpam-5563	620	2	b	b	NOUN
ejpam-5563	620	3	,	,	PUNCT
ejpam-5563	620	4	then	then	ADV
ejpam-5563	620	5	:	:	PUNCT
ejpam-5563	620	6	k	k	PROPN
ejpam-5563	620	7	k⋄	k⋄	PROPN
ejpam-5563	620	8	γ(k	γ(k	PROPN
ejpam-5563	620	9	)	)	PUNCT
ejpam-5563	620	10	γ∗(k	γ∗(k	NOUN
ejpam-5563	620	11	)	)	PUNCT
ejpam-5563	620	12	λ(k	λ(k	ADJ
ejpam-5563	620	13	)	)	PUNCT
ejpam-5563	620	14	λ⋄(k	λ⋄(k	NOUN
ejpam-5563	620	15	)	)	PUNCT
ejpam-5563	620	16	λ̃(k	λ̃(k	NOUN
ejpam-5563	620	17	)	)	PUNCT
ejpam-5563	620	18	∅	∅	NOUN
ejpam-5563	620	19	∅	∅	NOUN
ejpam-5563	620	20	∅	∅	NOUN
ejpam-5563	620	21	∅	∅	NOUN
ejpam-5563	620	22	∅	∅	NOUN
ejpam-5563	620	23	∅	∅	NOUN
ejpam-5563	620	24	∅	∅	NOUN
ejpam-5563	620	25	b	b	PROPN
ejpam-5563	620	26	b	b	PROPN
ejpam-5563	620	27	b	b	PROPN
ejpam-5563	620	28	b	b	PROPN
ejpam-5563	620	29	∅	∅	NOUN
ejpam-5563	620	30	∅	∅	NOUN
ejpam-5563	620	31	∅	∅	NOUN
ejpam-5563	620	32	{	{	PUNCT
ejpam-5563	620	33	e	e	NOUN
ejpam-5563	620	34	}	}	PUNCT
ejpam-5563	620	35	{	{	PUNCT
ejpam-5563	620	36	e	e	NOUN
ejpam-5563	620	37	}	}	PUNCT
ejpam-5563	620	38	{	{	PUNCT
ejpam-5563	620	39	e	e	NOUN
ejpam-5563	620	40	}	}	PUNCT
ejpam-5563	620	41	{	{	PUNCT
ejpam-5563	620	42	e	e	NOUN
ejpam-5563	620	43	}	}	PUNCT
ejpam-5563	620	44	∅	∅	NOUN
ejpam-5563	620	45	∅	∅	NOUN
ejpam-5563	620	46	∅	∅	NOUN
ejpam-5563	620	47	{	{	PUNCT
ejpam-5563	620	48	r	r	NOUN
ejpam-5563	620	49	}	}	PUNCT
ejpam-5563	620	50	{	{	PUNCT
ejpam-5563	620	51	r	r	NOUN
ejpam-5563	620	52	}	}	PUNCT
ejpam-5563	620	53	{	{	PUNCT
ejpam-5563	620	54	r	r	NOUN
ejpam-5563	620	55	}	}	PUNCT
ejpam-5563	620	56	∅	∅	NOUN
ejpam-5563	620	57	∅	∅	NOUN
ejpam-5563	620	58	∅	∅	NOUN
ejpam-5563	620	59	∅	∅	NOUN
ejpam-5563	620	60	{	{	PUNCT
ejpam-5563	620	61	t	t	NOUN
ejpam-5563	620	62	}	}	PUNCT
ejpam-5563	620	63	{	{	PUNCT
ejpam-5563	620	64	r	r	NOUN
ejpam-5563	620	65	,	,	PUNCT
ejpam-5563	620	66	t	t	PROPN
ejpam-5563	620	67	}	}	PUNCT
ejpam-5563	620	68	{	{	PUNCT
ejpam-5563	620	69	r	r	NOUN
ejpam-5563	620	70	,	,	PUNCT
ejpam-5563	620	71	t	t	NOUN
ejpam-5563	620	72	}	}	PUNCT
ejpam-5563	620	73	∅	∅	NOUN
ejpam-5563	620	74	∅	∅	NOUN
ejpam-5563	620	75	∅	∅	NOUN
ejpam-5563	620	76	∅	∅	NOUN
ejpam-5563	620	77	{	{	PUNCT
ejpam-5563	620	78	e	e	NOUN
ejpam-5563	620	79	,	,	PUNCT
ejpam-5563	620	80	r	r	NOUN
ejpam-5563	620	81	}	}	PUNCT
ejpam-5563	620	82	{	{	PUNCT
ejpam-5563	620	83	e	e	NOUN
ejpam-5563	620	84	,	,	PUNCT
ejpam-5563	620	85	r	r	NOUN
ejpam-5563	620	86	}	}	PUNCT
ejpam-5563	620	87	b	b	PROPN
ejpam-5563	620	88	{	{	PUNCT
ejpam-5563	620	89	e	e	NOUN
ejpam-5563	620	90	}	}	PUNCT
ejpam-5563	620	91	∅	∅	NOUN
ejpam-5563	620	92	∅	∅	NOUN
ejpam-5563	620	93	∅	∅	NOUN
ejpam-5563	620	94	{	{	PUNCT
ejpam-5563	620	95	e	e	NOUN
ejpam-5563	620	96	,	,	PUNCT
ejpam-5563	620	97	t	t	PROPN
ejpam-5563	620	98	}	}	PUNCT
ejpam-5563	620	99	{	{	PUNCT
ejpam-5563	620	100	e	e	NOUN
ejpam-5563	620	101	,	,	PUNCT
ejpam-5563	620	102	t	t	PROPN
ejpam-5563	620	103	}	}	PUNCT
ejpam-5563	620	104	b	b	PROPN
ejpam-5563	620	105	{	{	PUNCT
ejpam-5563	620	106	e	e	NOUN
ejpam-5563	620	107	,	,	PUNCT
ejpam-5563	620	108	t	t	PROPN
ejpam-5563	620	109	}	}	PUNCT
ejpam-5563	620	110	∅	∅	NOUN
ejpam-5563	620	111	∅	∅	NOUN
ejpam-5563	620	112	∅	∅	NOUN
ejpam-5563	620	113	{	{	PUNCT
ejpam-5563	620	114	r	r	NOUN
ejpam-5563	620	115	,	,	PUNCT
ejpam-5563	620	116	t	t	PROPN
ejpam-5563	620	117	}	}	PUNCT
ejpam-5563	620	118	{	{	PUNCT
ejpam-5563	620	119	r	r	NOUN
ejpam-5563	620	120	,	,	PUNCT
ejpam-5563	620	121	t	t	PROPN
ejpam-5563	620	122	}	}	PUNCT
ejpam-5563	620	123	{	{	PUNCT
ejpam-5563	620	124	r	r	NOUN
ejpam-5563	620	125	,	,	PUNCT
ejpam-5563	620	126	t	t	PROPN
ejpam-5563	620	127	}	}	PUNCT
ejpam-5563	620	128	{	{	PUNCT
ejpam-5563	620	129	r	r	NOUN
ejpam-5563	620	130	,	,	PUNCT
ejpam-5563	620	131	t	t	NOUN
ejpam-5563	620	132	}	}	PUNCT
ejpam-5563	620	133	∅	∅	NOUN
ejpam-5563	620	134	∅	∅	NOUN
ejpam-5563	620	135	∅	∅	NOUN
ejpam-5563	620	136	form	form	NOUN
ejpam-5563	620	137	example	example	NOUN
ejpam-5563	620	138	8	8	NUM
ejpam-5563	620	139	,	,	PUNCT
ejpam-5563	620	140	we	we	PRON
ejpam-5563	620	141	conclude	conclude	VERB
ejpam-5563	620	142	that	that	PRON
ejpam-5563	620	143	λ(k	λ(k	X
ejpam-5563	620	144	)	)	PUNCT
ejpam-5563	620	145	=	=	SYM
ejpam-5563	620	146	λ⋄(k	λ⋄(k	NOUN
ejpam-5563	620	147	)	)	PUNCT
ejpam-5563	620	148	=	=	SYM
ejpam-5563	620	149	λ̃(k	λ̃(k	VERB
ejpam-5563	620	150	)	)	PUNCT
ejpam-5563	620	151	=	=	NOUN
ejpam-5563	620	152	∅	∅	NOUN
ejpam-5563	620	153	since	since	SCONJ
ejpam-5563	620	154	k	k	PROPN
ejpam-5563	620	155	⊆	⊆	NUM
ejpam-5563	620	156	γ(k	γ(k	PROPN
ejpam-5563	620	157	)	)	PUNCT
ejpam-5563	620	158	for	for	ADP
ejpam-5563	620	159	every	every	DET
ejpam-5563	620	160	k	k	PROPN
ejpam-5563	620	161	⊆	⊆	PROPN
ejpam-5563	620	162	b.	b.	PROPN
ejpam-5563	620	163	observe	observe	VERB
ejpam-5563	620	164	that	that	SCONJ
ejpam-5563	620	165	p	p	NOUN
ejpam-5563	620	166	=	=	X
ejpam-5563	620	167	p	p	X
ejpam-5563	620	168	(	(	PUNCT
ejpam-5563	620	169	b)−	b)−	PROPN
ejpam-5563	620	170	{	{	PUNCT
ejpam-5563	620	171	b	b	NOUN
ejpam-5563	620	172	}	}	PUNCT
ejpam-5563	620	173	.	.	PUNCT
ejpam-5563	621	1	example	example	NOUN
ejpam-5563	622	1	9	9	NUM
ejpam-5563	622	2	.	.	PUNCT
ejpam-5563	623	1	let	let	VERB
ejpam-5563	623	2	(	(	PUNCT
ejpam-5563	623	3	r	r	NOUN
ejpam-5563	623	4	,	,	PUNCT
ejpam-5563	623	5	f	f	PROPN
ejpam-5563	623	6	,	,	PUNCT
ejpam-5563	623	7	p	p	X
ejpam-5563	623	8	)	)	PUNCT
ejpam-5563	623	9	be	be	AUX
ejpam-5563	623	10	defined	define	VERB
ejpam-5563	623	11	as	as	SCONJ
ejpam-5563	623	12	follows	follow	VERB
ejpam-5563	623	13	:	:	PUNCT
ejpam-5563	623	14	o	o	X
ejpam-5563	623	15	∈	∈	PROPN
ejpam-5563	624	1	f	f	X
ejpam-5563	625	1	if	if	SCONJ
ejpam-5563	625	2	and	and	CCONJ
ejpam-5563	625	3	only	only	ADV
ejpam-5563	625	4	if	if	SCONJ
ejpam-5563	625	5	0	0	NUM
ejpam-5563	625	6	∈	∈	PROPN
ejpam-5563	625	7	oc	oc	NOUN
ejpam-5563	625	8	or	or	CCONJ
ejpam-5563	625	9	oc	oc	VERB
ejpam-5563	625	10	is	be	AUX
ejpam-5563	625	11	a	a	DET
ejpam-5563	625	12	finite	finite	NOUN
ejpam-5563	625	13	subset	subset	NOUN
ejpam-5563	625	14	of	of	ADP
ejpam-5563	625	15	r.	r.	PROPN
ejpam-5563	625	16	moreover	moreover	ADV
ejpam-5563	625	17	,	,	PUNCT
ejpam-5563	625	18	l	l	PROPN
ejpam-5563	625	19	∈	∈	PROPN
ejpam-5563	626	1	p	p	NOUN
ejpam-5563	626	2	if	if	SCONJ
ejpam-5563	626	3	and	and	CCONJ
ejpam-5563	626	4	only	only	ADV
ejpam-5563	626	5	if	if	SCONJ
ejpam-5563	626	6	lcis	lcis	PROPN
ejpam-5563	626	7	an	an	DET
ejpam-5563	626	8	infinite	infinite	ADJ
ejpam-5563	626	9	subset	subset	NOUN
ejpam-5563	626	10	of	of	ADP
ejpam-5563	626	11	r.	r.	PROPN
ejpam-5563	626	12	then	then	ADV
ejpam-5563	626	13	,	,	PUNCT
ejpam-5563	626	14	if	if	SCONJ
ejpam-5563	626	15	d	d	PROPN
ejpam-5563	626	16	⊆	⊆	NUM
ejpam-5563	626	17	r	r	NOUN
ejpam-5563	626	18	,	,	PUNCT
ejpam-5563	626	19	we	we	PRON
ejpam-5563	626	20	have	have	VERB
ejpam-5563	626	21	two	two	NUM
ejpam-5563	626	22	cases	case	NOUN
ejpam-5563	626	23	:	:	PUNCT
ejpam-5563	626	24	case	case	NOUN
ejpam-5563	626	25	1	1	NUM
ejpam-5563	626	26	.	.	PUNCT
ejpam-5563	627	1	d	d	NOUN
ejpam-5563	627	2	is	be	AUX
ejpam-5563	627	3	a	a	DET
ejpam-5563	627	4	finite	finite	NOUN
ejpam-5563	627	5	subset	subset	NOUN
ejpam-5563	627	6	of	of	ADP
ejpam-5563	627	7	r.	r.	PROPN
ejpam-5563	627	8	then	then	ADV
ejpam-5563	627	9	,	,	PUNCT
ejpam-5563	627	10	as	as	ADP
ejpam-5563	627	11	dc	dc	PROPN
ejpam-5563	627	12	/∈	/∈	PUNCT
ejpam-5563	628	1	p	p	X
ejpam-5563	628	2	,	,	PUNCT
ejpam-5563	628	3	we	we	PRON
ejpam-5563	628	4	have	have	VERB
ejpam-5563	628	5	d⋄	d⋄	NOUN
ejpam-5563	628	6	=	=	SYM
ejpam-5563	628	7	γ(d	γ(d	PROPN
ejpam-5563	628	8	)	)	PUNCT
ejpam-5563	628	9	=	=	PUNCT
ejpam-5563	628	10	∅.	∅.	PRON
ejpam-5563	628	11	case	case	NOUN
ejpam-5563	628	12	2	2	NUM
ejpam-5563	628	13	.	.	X
ejpam-5563	629	1	d	d	NOUN
ejpam-5563	629	2	is	be	AUX
ejpam-5563	629	3	an	an	DET
ejpam-5563	629	4	infinite	infinite	ADJ
ejpam-5563	629	5	subset	subset	NOUN
ejpam-5563	629	6	of	of	ADP
ejpam-5563	629	7	r.	r.	PROPN
ejpam-5563	629	8	then	then	ADV
ejpam-5563	629	9	,	,	PUNCT
ejpam-5563	629	10	let	let	VERB
ejpam-5563	629	11	r	r	PRON
ejpam-5563	629	12	∈	∈	PROPN
ejpam-5563	629	13	r.	r.	NOUN
ejpam-5563	629	14	we	we	PRON
ejpam-5563	629	15	have	have	VERB
ejpam-5563	629	16	two	two	NUM
ejpam-5563	629	17	cases	case	NOUN
ejpam-5563	629	18	:	:	PUNCT
ejpam-5563	629	19	subcase	subcase	NOUN
ejpam-5563	629	20	2.1	2.1	NUM
ejpam-5563	629	21	.	.	PUNCT
ejpam-5563	630	1	r	r	NOUN
ejpam-5563	630	2	̸=	̸=	PROPN
ejpam-5563	630	3	0	0	NUM
ejpam-5563	630	4	.	.	PUNCT
ejpam-5563	631	1	then	then	ADV
ejpam-5563	631	2	,	,	PUNCT
ejpam-5563	631	3	w	w	NOUN
ejpam-5563	631	4	=	=	SYM
ejpam-5563	631	5	{	{	PUNCT
ejpam-5563	631	6	r	r	NOUN
ejpam-5563	631	7	}	}	PUNCT
ejpam-5563	631	8	∈	∈	NOUN
ejpam-5563	631	9	f(r	f(r	NOUN
ejpam-5563	631	10	)	)	PUNCT
ejpam-5563	631	11	and	and	CCONJ
ejpam-5563	631	12	since	since	SCONJ
ejpam-5563	631	13	w	w	PROPN
ejpam-5563	631	14	c	c	PROPN
ejpam-5563	631	15	̸∈	̸∈	PROPN
ejpam-5563	631	16	p	p	PROPN
ejpam-5563	631	17	,	,	PUNCT
ejpam-5563	631	18	r	r	PROPN
ejpam-5563	631	19	̸∈	̸∈	PROPN
ejpam-5563	631	20	d⋄.	d⋄.	PROPN
ejpam-5563	631	21	subcase	subcase	PROPN
ejpam-5563	631	22	2.2	2.2	NUM
ejpam-5563	631	23	.	.	PUNCT
ejpam-5563	632	1	r	r	NOUN
ejpam-5563	632	2	=	=	SYM
ejpam-5563	632	3	0	0	X
ejpam-5563	632	4	.	.	PUNCT
ejpam-5563	633	1	let	let	VERB
ejpam-5563	633	2	w	w	PROPN
ejpam-5563	633	3	∈	∈	PROPN
ejpam-5563	633	4	f(0	f(0	NOUN
ejpam-5563	633	5	)	)	PUNCT
ejpam-5563	633	6	.	.	PUNCT
ejpam-5563	634	1	then	then	ADV
ejpam-5563	634	2	,	,	PUNCT
ejpam-5563	634	3	w	w	PROPN
ejpam-5563	634	4	c	c	PROPN
ejpam-5563	634	5	is	be	AUX
ejpam-5563	634	6	finite	finite	ADJ
ejpam-5563	634	7	;	;	PUNCT
ejpam-5563	634	8	hence	hence	ADV
ejpam-5563	634	9	d	d	ADP
ejpam-5563	634	10	∩w	∩w	NOUN
ejpam-5563	634	11	is	be	AUX
ejpam-5563	634	12	an	an	DET
ejpam-5563	634	13	infinite	infinite	ADJ
ejpam-5563	634	14	subset	subset	NOUN
ejpam-5563	634	15	of	of	ADP
ejpam-5563	634	16	r	r	NOUN
ejpam-5563	634	17	which	which	PRON
ejpam-5563	634	18	implies	imply	VERB
ejpam-5563	634	19	that	that	SCONJ
ejpam-5563	634	20	(	(	PUNCT
ejpam-5563	634	21	d	d	NOUN
ejpam-5563	634	22	∩w	∩w	NOUN
ejpam-5563	634	23	)	)	PUNCT
ejpam-5563	635	1	c	c	PROPN
ejpam-5563	635	2	∈	∈	PROPN
ejpam-5563	635	3	p.	p.	NOUN
ejpam-5563	635	4	thus	thus	ADV
ejpam-5563	635	5	,	,	PUNCT
ejpam-5563	635	6	d⋄	d⋄	X
ejpam-5563	635	7	=	=	PUNCT
ejpam-5563	635	8	{	{	PUNCT
ejpam-5563	635	9	0	0	NUM
ejpam-5563	635	10	}	}	PUNCT
ejpam-5563	635	11	.	.	PUNCT
ejpam-5563	636	1	since	since	SCONJ
ejpam-5563	636	2	w	w	PROPN
ejpam-5563	636	3	⋄	⋄	PROPN
ejpam-5563	636	4	is	be	AUX
ejpam-5563	636	5	a	a	DET
ejpam-5563	636	6	finite	finite	NOUN
ejpam-5563	636	7	subset	subset	NOUN
ejpam-5563	636	8	,	,	PUNCT
ejpam-5563	636	9	then	then	ADV
ejpam-5563	636	10	γ(d	γ(d	PROPN
ejpam-5563	636	11	)	)	PUNCT
ejpam-5563	636	12	=	=	NOUN
ejpam-5563	636	13	∅	∅	NOUN
ejpam-5563	636	14	for	for	ADP
ejpam-5563	636	15	all	all	DET
ejpam-5563	636	16	d	d	PROPN
ejpam-5563	636	17	⊆	⊆	PROPN
ejpam-5563	636	18	r.	r.	PROPN
ejpam-5563	636	19	therefore	therefore	ADV
ejpam-5563	636	20	,	,	PUNCT
ejpam-5563	636	21	γ∗(d	γ∗(d	PROPN
ejpam-5563	636	22	)	)	PUNCT
ejpam-5563	636	23	=	=	PUNCT
ejpam-5563	637	1	r.	r.	PROPN
ejpam-5563	637	2	consequently	consequently	ADV
ejpam-5563	637	3	,	,	PUNCT
ejpam-5563	637	4	for	for	ADP
ejpam-5563	637	5	any	any	DET
ejpam-5563	637	6	d	d	NOUN
ejpam-5563	637	7	⊆	⊆	NUM
ejpam-5563	637	8	r	r	NOUN
ejpam-5563	637	9	,	,	PUNCT
ejpam-5563	637	10	we	we	PRON
ejpam-5563	637	11	have	have	VERB
ejpam-5563	637	12	:	:	PUNCT
ejpam-5563	637	13	(	(	PUNCT
ejpam-5563	637	14	i	i	NOUN
ejpam-5563	637	15	)	)	PUNCT
ejpam-5563	637	16	λ(d	λ(d	PROPN
ejpam-5563	637	17	)	)	PUNCT
ejpam-5563	637	18	=	=	SYM
ejpam-5563	638	1	dc	dc	PROPN
ejpam-5563	638	2	.	.	PUNCT
ejpam-5563	638	3	(	(	PUNCT
ejpam-5563	638	4	ii	ii	NOUN
ejpam-5563	638	5	)	)	PUNCT
ejpam-5563	638	6	λ⋄(d	λ⋄(d	NOUN
ejpam-5563	638	7	)	)	PUNCT
ejpam-5563	638	8	=	=	SYM
ejpam-5563	638	9	r.	r.	PROPN
ejpam-5563	638	10	(	(	PUNCT
ejpam-5563	638	11	iii	iii	NOUN
ejpam-5563	638	12	)	)	PUNCT
ejpam-5563	638	13	λ̃(d	λ̃(d	NOUN
ejpam-5563	638	14	)	)	PUNCT
ejpam-5563	638	15	=	=	SYM
ejpam-5563	638	16	d.	d.	PROPN
ejpam-5563	638	17	references	reference	VERB
ejpam-5563	638	18	3537	3537	NUM
ejpam-5563	638	19	example	example	NOUN
ejpam-5563	638	20	10	10	NUM
ejpam-5563	638	21	.	.	PUNCT
ejpam-5563	639	1	let	let	VERB
ejpam-5563	639	2	(	(	PUNCT
ejpam-5563	639	3	r	r	NOUN
ejpam-5563	639	4	,	,	PUNCT
ejpam-5563	639	5	γ0,p0	γ0,p0	PROPN
ejpam-5563	639	6	)	)	PUNCT
ejpam-5563	639	7	be	be	AUX
ejpam-5563	639	8	defined	define	VERB
ejpam-5563	639	9	as	as	ADP
ejpam-5563	639	10	in	in	ADP
ejpam-5563	639	11	example	example	NOUN
ejpam-5563	640	1	1	1	X
ejpam-5563	640	2	.	.	PUNCT
ejpam-5563	641	1	then	then	ADV
ejpam-5563	641	2	,	,	PUNCT
ejpam-5563	641	3	if	if	SCONJ
ejpam-5563	641	4	d	d	PROPN
ejpam-5563	641	5	⊆	⊆	NUM
ejpam-5563	641	6	r	r	NOUN
ejpam-5563	641	7	,	,	PUNCT
ejpam-5563	641	8	we	we	PRON
ejpam-5563	641	9	have	have	VERB
ejpam-5563	641	10	two	two	NUM
ejpam-5563	641	11	cases	case	NOUN
ejpam-5563	641	12	:	:	PUNCT
ejpam-5563	641	13	case	case	NOUN
ejpam-5563	641	14	1	1	NUM
ejpam-5563	641	15	.	.	SYM
ejpam-5563	641	16	0	0	NUM
ejpam-5563	641	17	/∈	/∈	PUNCT
ejpam-5563	642	1	d.	d.	PROPN
ejpam-5563	642	2	then	then	ADV
ejpam-5563	642	3	,	,	PUNCT
ejpam-5563	642	4	dc	dc	PROPN
ejpam-5563	642	5	/∈	/∈	PUNCT
ejpam-5563	642	6	p0	p0	PROPN
ejpam-5563	642	7	since	since	SCONJ
ejpam-5563	642	8	0	0	NUM
ejpam-5563	642	9	∈	∈	PROPN
ejpam-5563	642	10	dc	dc	PROPN
ejpam-5563	642	11	.	.	PUNCT
ejpam-5563	643	1	therefore	therefore	ADV
ejpam-5563	643	2	,	,	PUNCT
ejpam-5563	643	3	d⋄	d⋄	X
ejpam-5563	643	4	=	=	SYM
ejpam-5563	643	5	γ(d	γ(d	PROPN
ejpam-5563	643	6	)	)	PUNCT
ejpam-5563	643	7	=	=	PUNCT
ejpam-5563	643	8	∅.	∅.	PRON
ejpam-5563	643	9	case	case	NOUN
ejpam-5563	643	10	2	2	NUM
ejpam-5563	643	11	.	.	NOUN
ejpam-5563	643	12	0	0	NUM
ejpam-5563	644	1	∈	∈	PROPN
ejpam-5563	644	2	d.	d.	NOUN
ejpam-5563	644	3	let	let	VERB
ejpam-5563	644	4	r	r	NOUN
ejpam-5563	644	5	∈	∈	NOUN
ejpam-5563	644	6	r	r	NOUN
ejpam-5563	644	7	and	and	CCONJ
ejpam-5563	644	8	let	let	VERB
ejpam-5563	644	9	w	w	PROPN
ejpam-5563	644	10	∈	∈	PROPN
ejpam-5563	644	11	γ0(r	γ0(r	PROPN
ejpam-5563	644	12	)	)	PUNCT
ejpam-5563	644	13	.	.	PUNCT
ejpam-5563	645	1	then	then	ADV
ejpam-5563	645	2	,	,	PUNCT
ejpam-5563	645	3	0	0	NUM
ejpam-5563	645	4	∈	∈	PROPN
ejpam-5563	645	5	w	w	NOUN
ejpam-5563	645	6	which	which	PRON
ejpam-5563	645	7	implies	imply	VERB
ejpam-5563	645	8	that	that	SCONJ
ejpam-5563	645	9	0	0	NUM
ejpam-5563	645	10	/∈	/∈	PUNCT
ejpam-5563	646	1	w	w	PROPN
ejpam-5563	646	2	c	c	NOUN
ejpam-5563	646	3	∪dc	∪dc	NOUN
ejpam-5563	646	4	.	.	PUNCT
ejpam-5563	647	1	hence	hence	ADV
ejpam-5563	647	2	,	,	PUNCT
ejpam-5563	647	3	d⋄	d⋄	X
ejpam-5563	647	4	=	=	PUNCT
ejpam-5563	647	5	r.	r.	NOUN
ejpam-5563	647	6	since	since	SCONJ
ejpam-5563	647	7	we	we	PRON
ejpam-5563	647	8	have	have	VERB
ejpam-5563	647	9	w	w	NOUN
ejpam-5563	647	10	⋄	⋄	NOUN
ejpam-5563	647	11	=	=	PUNCT
ejpam-5563	647	12	r	r	NOUN
ejpam-5563	647	13	for	for	ADP
ejpam-5563	647	14	every	every	DET
ejpam-5563	647	15	w	w	PROPN
ejpam-5563	647	16	∈	∈	PROPN
ejpam-5563	647	17	γ0(r	γ0(r	PROPN
ejpam-5563	647	18	)	)	PUNCT
ejpam-5563	647	19	,	,	PUNCT
ejpam-5563	647	20	we	we	PRON
ejpam-5563	647	21	get	get	VERB
ejpam-5563	647	22	that	that	PRON
ejpam-5563	647	23	γ(d	γ(d	NOUN
ejpam-5563	647	24	)	)	PUNCT
ejpam-5563	647	25	=	=	SYM
ejpam-5563	647	26	r.	r.	PROPN
ejpam-5563	647	27	note	note	VERB
ejpam-5563	647	28	that	that	SCONJ
ejpam-5563	647	29	:	:	PUNCT
ejpam-5563	647	30	γ∗(d	γ∗(d	ADJ
ejpam-5563	647	31	)	)	PUNCT
ejpam-5563	647	32	=	=	PRON
ejpam-5563	647	33	{	{	PUNCT
ejpam-5563	647	34	∅	∅	NOUN
ejpam-5563	647	35	if	if	SCONJ
ejpam-5563	647	36	0	0	NUM
ejpam-5563	647	37	/∈	/∈	PUNCT
ejpam-5563	648	1	d	d	NOUN
ejpam-5563	648	2	r	r	NOUN
ejpam-5563	648	3	if	if	SCONJ
ejpam-5563	648	4	0	0	NUM
ejpam-5563	648	5	∈	∈	PROPN
ejpam-5563	648	6	d	d	X
ejpam-5563	648	7	consequently	consequently	ADV
ejpam-5563	648	8	,	,	PUNCT
ejpam-5563	648	9	for	for	ADP
ejpam-5563	648	10	any	any	DET
ejpam-5563	648	11	o	o	NOUN
ejpam-5563	648	12	⊆	⊆	NUM
ejpam-5563	648	13	r	r	NOUN
ejpam-5563	648	14	,	,	PUNCT
ejpam-5563	648	15	we	we	PRON
ejpam-5563	648	16	have	have	VERB
ejpam-5563	648	17	:	:	PUNCT
ejpam-5563	648	18	(	(	PUNCT
ejpam-5563	648	19	i	i	NOUN
ejpam-5563	648	20	)	)	PUNCT
ejpam-5563	648	21	λ(d	λ(d	PROPN
ejpam-5563	648	22	)	)	PUNCT
ejpam-5563	649	1	=	=	PRON
ejpam-5563	649	2	{	{	PUNCT
ejpam-5563	649	3	∅	∅	NOUN
ejpam-5563	649	4	if	if	SCONJ
ejpam-5563	649	5	0	0	NUM
ejpam-5563	649	6	/∈	/∈	PUNCT
ejpam-5563	650	1	d	d	X
ejpam-5563	650	2	dc	dc	PROPN
ejpam-5563	650	3	if	if	SCONJ
ejpam-5563	650	4	0	0	NUM
ejpam-5563	650	5	∈	∈	PROPN
ejpam-5563	650	6	d	d	X
ejpam-5563	650	7	(	(	PUNCT
ejpam-5563	650	8	ii	ii	NOUN
ejpam-5563	650	9	)	)	PUNCT
ejpam-5563	650	10	λ⋄(d	λ⋄(d	NOUN
ejpam-5563	650	11	)	)	PUNCT
ejpam-5563	650	12	=	=	SYM
ejpam-5563	650	13	∅.	∅.	PRON
ejpam-5563	650	14	(	(	PUNCT
ejpam-5563	650	15	iii	iii	NOUN
ejpam-5563	650	16	)	)	PUNCT
ejpam-5563	650	17	λ̃(d	λ̃(d	NOUN
ejpam-5563	650	18	)	)	PUNCT
ejpam-5563	650	19	=	=	PRON
ejpam-5563	651	1	{	{	PUNCT
ejpam-5563	651	2	d	d	NOUN
ejpam-5563	651	3	if	if	SCONJ
ejpam-5563	651	4	0	0	NUM
ejpam-5563	651	5	/∈	/∈	NOUN
ejpam-5563	652	1	d	d	NOUN
ejpam-5563	652	2	∅	∅	NOUN
ejpam-5563	652	3	if	if	SCONJ
ejpam-5563	652	4	0	0	NUM
ejpam-5563	652	5	∈	∈	PROPN
ejpam-5563	652	6	d	d	NOUN
ejpam-5563	652	7	7	7	X
ejpam-5563	652	8	.	.	PUNCT
ejpam-5563	652	9	conclusion	conclusion	NOUN
ejpam-5563	652	10	our	our	PRON
ejpam-5563	652	11	work	work	NOUN
ejpam-5563	652	12	is	be	AUX
ejpam-5563	652	13	a	a	DET
ejpam-5563	652	14	continuation	continuation	NOUN
ejpam-5563	652	15	of	of	ADP
ejpam-5563	652	16	the	the	DET
ejpam-5563	652	17	paper	paper	NOUN
ejpam-5563	653	1	[	[	X
ejpam-5563	653	2	7	7	X
ejpam-5563	653	3	]	]	PUNCT
ejpam-5563	653	4	which	which	PRON
ejpam-5563	653	5	discussed	discuss	VERB
ejpam-5563	653	6	γ	γ	NOUN
ejpam-5563	653	7	and	and	CCONJ
ejpam-5563	653	8	γ∗-operators	γ∗-operator	NOUN
ejpam-5563	653	9	.	.	PUNCT
ejpam-5563	654	1	in	in	ADP
ejpam-5563	654	2	this	this	DET
ejpam-5563	654	3	paper	paper	NOUN
ejpam-5563	654	4	,	,	PUNCT
ejpam-5563	654	5	we	we	PRON
ejpam-5563	654	6	provide	provide	VERB
ejpam-5563	654	7	more	more	ADJ
ejpam-5563	654	8	results	result	NOUN
ejpam-5563	654	9	have	have	AUX
ejpam-5563	654	10	n’t	not	PART
ejpam-5563	654	11	been	be	AUX
ejpam-5563	654	12	discussed	discuss	VERB
ejpam-5563	654	13	in	in	ADP
ejpam-5563	654	14	[	[	X
ejpam-5563	654	15	7	7	NUM
ejpam-5563	654	16	]	]	PUNCT
ejpam-5563	654	17	.	.	PUNCT
ejpam-5563	655	1	moreover	moreover	ADV
ejpam-5563	655	2	,	,	PUNCT
ejpam-5563	655	3	we	we	PRON
ejpam-5563	655	4	define	define	VERB
ejpam-5563	655	5	an	an	DET
ejpam-5563	655	6	operator	operator	NOUN
ejpam-5563	655	7	called	call	VERB
ejpam-5563	655	8	λ	λ	NOUN
ejpam-5563	655	9	-	-	NOUN
ejpam-5563	655	10	operator	operator	NOUN
ejpam-5563	655	11	.	.	PUNCT
ejpam-5563	656	1	after	after	ADP
ejpam-5563	656	2	that	that	PRON
ejpam-5563	656	3	,	,	PUNCT
ejpam-5563	656	4	we	we	PRON
ejpam-5563	656	5	define	define	VERB
ejpam-5563	656	6	another	another	DET
ejpam-5563	656	7	operator	operator	NOUN
ejpam-5563	656	8	named	name	VERB
ejpam-5563	656	9	λ⋄-operator	λ⋄-operator	NOUN
ejpam-5563	656	10	and	and	CCONJ
ejpam-5563	656	11	we	we	PRON
ejpam-5563	656	12	show	show	VERB
ejpam-5563	656	13	that	that	SCONJ
ejpam-5563	656	14	λ⋄(o	λ⋄(o	NOUN
ejpam-5563	656	15	)	)	PUNCT
ejpam-5563	656	16	=	=	PUNCT
ejpam-5563	657	1	[	[	X
ejpam-5563	657	2	γ(b)]c	γ(b)]c	ADP
ejpam-5563	657	3	for	for	ADP
ejpam-5563	657	4	every	every	DET
ejpam-5563	657	5	o	o	NOUN
ejpam-5563	657	6	⊆	⊆	NUM
ejpam-5563	657	7	b	b	NOUN
ejpam-5563	657	8	in	in	ADP
ejpam-5563	657	9	a	a	DET
ejpam-5563	657	10	primal	primal	ADJ
ejpam-5563	657	11	topological	topological	ADJ
ejpam-5563	657	12	space	space	NOUN
ejpam-5563	657	13	(	(	PUNCT
ejpam-5563	657	14	b	b	NOUN
ejpam-5563	657	15	,	,	PUNCT
ejpam-5563	657	16	γ	γ	X
ejpam-5563	657	17	,	,	PUNCT
ejpam-5563	657	18	p	p	NOUN
ejpam-5563	657	19	)	)	PUNCT
ejpam-5563	657	20	.	.	PUNCT
ejpam-5563	657	21	additionally	additionally	ADV
ejpam-5563	657	22	,	,	PUNCT
ejpam-5563	657	23	we	we	PRON
ejpam-5563	657	24	define	define	VERB
ejpam-5563	657	25	an	an	DET
ejpam-5563	657	26	operator	operator	NOUN
ejpam-5563	657	27	called	call	VERB
ejpam-5563	657	28	λ̃-operator	λ̃-operator	PROPN
ejpam-5563	657	29	.	.	PUNCT
ejpam-5563	658	1	finally	finally	ADV
ejpam-5563	658	2	,	,	PUNCT
ejpam-5563	658	3	we	we	PRON
ejpam-5563	658	4	discuss	discuss	VERB
ejpam-5563	658	5	some	some	DET
ejpam-5563	658	6	examples	example	NOUN
ejpam-5563	658	7	illustrating	illustrate	VERB
ejpam-5563	658	8	the	the	DET
ejpam-5563	658	9	differences	difference	NOUN
ejpam-5563	658	10	between	between	ADP
ejpam-5563	658	11	these	these	DET
ejpam-5563	658	12	operators	operator	NOUN
ejpam-5563	658	13	.	.	PUNCT
ejpam-5563	659	1	acknowledgements	acknowledgement	NOUN
ejpam-5563	659	2	the	the	DET
ejpam-5563	659	3	author	author	NOUN
ejpam-5563	659	4	extends	extend	VERB
ejpam-5563	659	5	sincere	sincere	ADJ
ejpam-5563	659	6	gratitude	gratitude	NOUN
ejpam-5563	659	7	to	to	ADP
ejpam-5563	659	8	the	the	DET
ejpam-5563	659	9	editor	editor	NOUN
ejpam-5563	659	10	and	and	CCONJ
ejpam-5563	659	11	reviewers	reviewer	NOUN
ejpam-5563	659	12	for	for	ADP
ejpam-5563	659	13	their	their	PRON
ejpam-5563	659	14	valuable	valuable	ADJ
ejpam-5563	659	15	time	time	NOUN
ejpam-5563	659	16	and	and	CCONJ
ejpam-5563	659	17	insightful	insightful	ADJ
ejpam-5563	659	18	comments	comment	NOUN
ejpam-5563	659	19	.	.	PUNCT
ejpam-5563	660	1	references	reference	NOUN
ejpam-5563	660	2	[	[	X
ejpam-5563	660	3	1	1	NUM
ejpam-5563	660	4	]	]	PUNCT
ejpam-5563	660	5	santanu	santanu	ADJ
ejpam-5563	660	6	acharjee	acharjee	NOUN
ejpam-5563	660	7	,	,	PUNCT
ejpam-5563	660	8	murad	murad	NOUN
ejpam-5563	660	9	özkoç	özkoç	PROPN
ejpam-5563	660	10	,	,	PUNCT
ejpam-5563	660	11	and	and	CCONJ
ejpam-5563	660	12	faical	faical	ADJ
ejpam-5563	660	13	yacine	yacine	PROPN
ejpam-5563	660	14	issaka	issaka	PROPN
ejpam-5563	660	15	.	.	PUNCT
ejpam-5563	661	1	primal	primal	ADJ
ejpam-5563	661	2	topological	topological	ADJ
ejpam-5563	661	3	spaces	space	NOUN
ejpam-5563	661	4	.	.	PUNCT
ejpam-5563	662	1	arxiv	arxiv	PROPN
ejpam-5563	662	2	preprint	preprint	PROPN
ejpam-5563	662	3	arxiv:2209.12676	arxiv:2209.12676	NUM
ejpam-5563	662	4	,	,	PUNCT
ejpam-5563	662	5	2022	2022	NUM
ejpam-5563	662	6	.	.	PUNCT
ejpam-5563	663	1	[	[	X
ejpam-5563	663	2	2	2	X
ejpam-5563	663	3	]	]	X
ejpam-5563	663	4	ahmad	ahmad	PROPN
ejpam-5563	663	5	al	al	PROPN
ejpam-5563	663	6	-	-	PUNCT
ejpam-5563	663	7	omari	omari	PROPN
ejpam-5563	663	8	,	,	PUNCT
ejpam-5563	663	9	santanu	santanu	ADJ
ejpam-5563	663	10	acharjee	acharjee	NOUN
ejpam-5563	663	11	,	,	PUNCT
ejpam-5563	663	12	and	and	CCONJ
ejpam-5563	663	13	murad	murad	NOUN
ejpam-5563	663	14	özkoç.	özkoç.	NOUN
ejpam-5563	663	15	a	a	DET
ejpam-5563	663	16	new	new	ADJ
ejpam-5563	663	17	operator	operator	NOUN
ejpam-5563	663	18	of	of	ADP
ejpam-5563	663	19	primal	primal	ADJ
ejpam-5563	663	20	topological	topological	ADJ
ejpam-5563	663	21	spaces	space	NOUN
ejpam-5563	663	22	.	.	PUNCT
ejpam-5563	664	1	mathematica	mathematica	PROPN
ejpam-5563	664	2	,	,	PUNCT
ejpam-5563	664	3	65(1):175–183	65(1):175–183	NUM
ejpam-5563	664	4	,	,	PUNCT
ejpam-5563	664	5	2023	2023	NUM
ejpam-5563	664	6	.	.	PUNCT
ejpam-5563	665	1	references	reference	NOUN
ejpam-5563	665	2	3538	3538	NUM
ejpam-5563	665	3	[	[	X
ejpam-5563	665	4	3	3	NUM
ejpam-5563	665	5	]	]	X
ejpam-5563	665	6	ahmad	ahmad	PROPN
ejpam-5563	665	7	al	al	PROPN
ejpam-5563	665	8	-	-	PUNCT
ejpam-5563	665	9	omari	omari	PROPN
ejpam-5563	665	10	and	and	CCONJ
ejpam-5563	665	11	ohud	ohud	ADJ
ejpam-5563	665	12	alghamdi	alghamdi	NOUN
ejpam-5563	665	13	.	.	PUNCT
ejpam-5563	666	1	regularity	regularity	NOUN
ejpam-5563	666	2	and	and	CCONJ
ejpam-5563	666	3	normality	normality	NOUN
ejpam-5563	666	4	on	on	ADP
ejpam-5563	666	5	primal	primal	ADJ
ejpam-5563	666	6	spaces	space	NOUN
ejpam-5563	666	7	.	.	PUNCT
ejpam-5563	667	1	aims	aim	VERB
ejpam-5563	667	2	mathematics	mathematic	NOUN
ejpam-5563	667	3	,	,	PUNCT
ejpam-5563	667	4	9(3):7662–7672	9(3):7662–7672	NUM
ejpam-5563	667	5	,	,	PUNCT
ejpam-5563	667	6	2024	2024	NUM
ejpam-5563	667	7	.	.	PUNCT
ejpam-5563	668	1	[	[	X
ejpam-5563	668	2	4	4	X
ejpam-5563	668	3	]	]	X
ejpam-5563	668	4	ahmad	ahmad	PROPN
ejpam-5563	668	5	al	al	PROPN
ejpam-5563	668	6	-	-	PUNCT
ejpam-5563	668	7	omari	omari	PROPN
ejpam-5563	668	8	and	and	CCONJ
ejpam-5563	668	9	mesfer	mesfer	VERB
ejpam-5563	668	10	h	h	PROPN
ejpam-5563	668	11	alqahtani	alqahtani	ADJ
ejpam-5563	668	12	.	.	PUNCT
ejpam-5563	669	1	primal	primal	ADJ
ejpam-5563	669	2	structure	structure	NOUN
ejpam-5563	669	3	with	with	ADP
ejpam-5563	669	4	closure	closure	NOUN
ejpam-5563	669	5	operators	operator	NOUN
ejpam-5563	669	6	and	and	CCONJ
ejpam-5563	669	7	their	their	PRON
ejpam-5563	669	8	applications	application	NOUN
ejpam-5563	669	9	.	.	PUNCT
ejpam-5563	670	1	mathematics	mathematic	NOUN
ejpam-5563	670	2	,	,	PUNCT
ejpam-5563	670	3	11(24):4946	11(24):4946	NUM
ejpam-5563	670	4	,	,	PUNCT
ejpam-5563	670	5	2023	2023	NUM
ejpam-5563	670	6	.	.	PUNCT
ejpam-5563	671	1	[	[	X
ejpam-5563	671	2	5	5	X
ejpam-5563	671	3	]	]	X
ejpam-5563	671	4	ahmad	ahmad	PROPN
ejpam-5563	671	5	al	al	PROPN
ejpam-5563	671	6	-	-	PUNCT
ejpam-5563	671	7	omari	omari	PROPN
ejpam-5563	671	8	and	and	CCONJ
ejpam-5563	671	9	mesfer	mesfer	VERB
ejpam-5563	671	10	h	h	PROPN
ejpam-5563	671	11	alqahtani	alqahtani	ADJ
ejpam-5563	671	12	.	.	PUNCT
ejpam-5563	672	1	some	some	DET
ejpam-5563	672	2	operators	operator	NOUN
ejpam-5563	672	3	in	in	ADP
ejpam-5563	672	4	soft	soft	ADJ
ejpam-5563	672	5	primal	primal	ADJ
ejpam-5563	672	6	spaces	space	NOUN
ejpam-5563	672	7	.	.	PUNCT
ejpam-5563	673	1	aims	aim	VERB
ejpam-5563	673	2	mathematics	mathematic	NOUN
ejpam-5563	673	3	,	,	PUNCT
ejpam-5563	673	4	9(5):10756–10774	9(5):10756–10774	PROPN
ejpam-5563	673	5	,	,	PUNCT
ejpam-5563	673	6	2024	2024	NUM
ejpam-5563	673	7	.	.	PUNCT
ejpam-5563	674	1	[	[	X
ejpam-5563	674	2	6	6	NUM
ejpam-5563	674	3	]	]	X
ejpam-5563	674	4	tareq	tareq	PROPN
ejpam-5563	674	5	m	m	PROPN
ejpam-5563	674	6	al	al	PROPN
ejpam-5563	674	7	-	-	PUNCT
ejpam-5563	674	8	shami	shami	PROPN
ejpam-5563	674	9	,	,	PUNCT
ejpam-5563	674	10	zanyar	zanyar	PROPN
ejpam-5563	674	11	a	a	DET
ejpam-5563	674	12	ameen	ameen	NOUN
ejpam-5563	674	13	,	,	PUNCT
ejpam-5563	674	14	radwan	radwan	VERB
ejpam-5563	674	15	abu	abu	PROPN
ejpam-5563	674	16	-	-	PUNCT
ejpam-5563	674	17	gdairi	gdairi	PROPN
ejpam-5563	674	18	,	,	PUNCT
ejpam-5563	674	19	and	and	CCONJ
ejpam-5563	674	20	abdelwaheb	abdelwaheb	PROPN
ejpam-5563	674	21	mhemdi	mhemdi	PROPN
ejpam-5563	674	22	.	.	PUNCT
ejpam-5563	675	1	on	on	ADP
ejpam-5563	675	2	primal	primal	ADJ
ejpam-5563	675	3	soft	soft	ADJ
ejpam-5563	675	4	topology	topology	NOUN
ejpam-5563	675	5	.	.	PUNCT
ejpam-5563	676	1	mathematics	mathematic	NOUN
ejpam-5563	676	2	,	,	PUNCT
ejpam-5563	676	3	11(10):2329	11(10):2329	NUM
ejpam-5563	676	4	,	,	PUNCT
ejpam-5563	676	5	2023	2023	NUM
ejpam-5563	676	6	.	.	PUNCT
ejpam-5563	677	1	[	[	X
ejpam-5563	677	2	7	7	X
ejpam-5563	677	3	]	]	X
ejpam-5563	677	4	ohud	ohud	ADJ
ejpam-5563	677	5	alghamdi	alghamdi	NOUN
ejpam-5563	677	6	,	,	PUNCT
ejpam-5563	677	7	ahmad	ahmad	PROPN
ejpam-5563	677	8	al	al	PROPN
ejpam-5563	677	9	-	-	PUNCT
ejpam-5563	677	10	omari	omari	PROPN
ejpam-5563	677	11	,	,	PUNCT
ejpam-5563	677	12	and	and	CCONJ
ejpam-5563	677	13	mesfer	mesfer	VERB
ejpam-5563	677	14	h	h	PROPN
ejpam-5563	677	15	alqahtani	alqahtani	ADJ
ejpam-5563	677	16	.	.	PUNCT
ejpam-5563	678	1	novel	novel	ADJ
ejpam-5563	678	2	operators	operator	NOUN
ejpam-5563	678	3	in	in	ADP
ejpam-5563	678	4	the	the	DET
ejpam-5563	678	5	frame	frame	NOUN
ejpam-5563	678	6	of	of	ADP
ejpam-5563	678	7	primal	primal	ADJ
ejpam-5563	678	8	topological	topological	ADJ
ejpam-5563	678	9	spaces	space	NOUN
ejpam-5563	678	10	.	.	PUNCT
ejpam-5563	679	1	aims	aim	VERB
ejpam-5563	679	2	mathematics	mathematic	NOUN
ejpam-5563	679	3	,	,	PUNCT
ejpam-5563	679	4	9(9):25792–25808	9(9):25792–25808	NUM
ejpam-5563	679	5	,	,	PUNCT
ejpam-5563	679	6	2024	2024	NUM
ejpam-5563	679	7	.	.	PUNCT
ejpam-5563	680	1	[	[	X
ejpam-5563	680	2	8	8	NUM
ejpam-5563	680	3	]	]	PUNCT
ejpam-5563	680	4	zanyar	zanyar	PROPN
ejpam-5563	680	5	a	a	DET
ejpam-5563	680	6	ameen	ameen	NOUN
ejpam-5563	680	7	,	,	PUNCT
ejpam-5563	680	8	ramadhan	ramadhan	VERB
ejpam-5563	680	9	a	a	DET
ejpam-5563	680	10	mohammed	mohammed	PROPN
ejpam-5563	680	11	,	,	PUNCT
ejpam-5563	680	12	tareq	tareq	PROPN
ejpam-5563	680	13	m	m	PROPN
ejpam-5563	680	14	al	al	PROPN
ejpam-5563	680	15	-	-	PUNCT
ejpam-5563	680	16	shami	shami	PROPN
ejpam-5563	680	17	,	,	PUNCT
ejpam-5563	680	18	and	and	CCONJ
ejpam-5563	680	19	baravan	baravan	VERB
ejpam-5563	680	20	a	a	DET
ejpam-5563	680	21	asaad	asaad	NOUN
ejpam-5563	680	22	.	.	PUNCT
ejpam-5563	681	1	novel	novel	ADJ
ejpam-5563	681	2	fuzzy	fuzzy	ADJ
ejpam-5563	681	3	topologies	topology	NOUN
ejpam-5563	681	4	formed	form	VERB
ejpam-5563	681	5	by	by	ADP
ejpam-5563	681	6	fuzzy	fuzzy	ADJ
ejpam-5563	681	7	primal	primal	ADJ
ejpam-5563	681	8	frameworks	framework	NOUN
ejpam-5563	681	9	.	.	PUNCT
ejpam-5563	682	1	journal	journal	NOUN
ejpam-5563	682	2	of	of	ADP
ejpam-5563	682	3	intelligent	intelligent	ADJ
ejpam-5563	682	4	&	&	CCONJ
ejpam-5563	682	5	fuzzy	fuzzy	ADJ
ejpam-5563	682	6	systems	system	NOUN
ejpam-5563	682	7	,	,	PUNCT
ejpam-5563	682	8	(	(	PUNCT
ejpam-5563	682	9	preprint):1–10	preprint):1–10	NOUN
ejpam-5563	682	10	,	,	PUNCT
ejpam-5563	682	11	2024	2024	NUM
ejpam-5563	682	12	.	.	PUNCT
ejpam-5563	683	1	[	[	X
ejpam-5563	683	2	9	9	NUM
ejpam-5563	683	3	]	]	X
ejpam-5563	683	4	gustave	gustave	NOUN
ejpam-5563	683	5	choquet	choquet	NOUN
ejpam-5563	683	6	.	.	PUNCT
ejpam-5563	684	1	sur	sur	PROPN
ejpam-5563	684	2	les	les	PROPN
ejpam-5563	684	3	notions	notion	NOUN
ejpam-5563	684	4	de	de	X
ejpam-5563	684	5	filtre	filtre	NOUN
ejpam-5563	684	6	et	et	NOUN
ejpam-5563	684	7	de	de	NOUN
ejpam-5563	684	8	grille	grille	NOUN
ejpam-5563	684	9	.	.	PUNCT
ejpam-5563	685	1	comptes	compte	VERB
ejpam-5563	685	2	rendus	rendus	PROPN
ejpam-5563	685	3	acad	acad	PROPN
ejpam-5563	685	4	.	.	PUNCT
ejpam-5563	686	1	sci	sci	PROPN
ejpam-5563	686	2	.	.	PROPN
ejpam-5563	686	3	paris	paris	PROPN
ejpam-5563	686	4	,	,	PUNCT
ejpam-5563	686	5	224:171–173	224:171–173	NUM
ejpam-5563	686	6	,	,	PUNCT
ejpam-5563	686	7	1947	1947	NUM
ejpam-5563	686	8	.	.	PUNCT
ejpam-5563	687	1	[	[	X
ejpam-5563	687	2	10	10	NUM
ejpam-5563	687	3	]	]	X
ejpam-5563	687	4	dragan	dragan	NOUN
ejpam-5563	687	5	janković	janković	PROPN
ejpam-5563	687	6	and	and	CCONJ
ejpam-5563	687	7	tr	tr	VERB
ejpam-5563	687	8	hamlett	hamlett	PROPN
ejpam-5563	687	9	.	.	PUNCT
ejpam-5563	688	1	new	new	ADJ
ejpam-5563	688	2	topologies	topology	NOUN
ejpam-5563	688	3	from	from	ADP
ejpam-5563	688	4	old	old	ADJ
ejpam-5563	688	5	via	via	ADP
ejpam-5563	688	6	ideals	ideal	NOUN
ejpam-5563	688	7	.	.	PUNCT
ejpam-5563	689	1	the	the	DET
ejpam-5563	689	2	american	american	PROPN
ejpam-5563	689	3	mathematical	mathematical	PROPN
ejpam-5563	689	4	monthly	monthly	PROPN
ejpam-5563	689	5	,	,	PUNCT
ejpam-5563	689	6	97(4):295–310	97(4):295–310	PROPN
ejpam-5563	689	7	,	,	PUNCT
ejpam-5563	689	8	1990	1990	NUM
ejpam-5563	689	9	.	.	PUNCT
ejpam-5563	690	1	[	[	X
ejpam-5563	690	2	11	11	NUM
ejpam-5563	690	3	]	]	X
ejpam-5563	690	4	kazimierz	kazimierz	PROPN
ejpam-5563	690	5	kuratowski	kuratowski	PROPN
ejpam-5563	690	6	.	.	PUNCT
ejpam-5563	690	7	topology	topology	NOUN
ejpam-5563	690	8	:	:	PUNCT
ejpam-5563	690	9	volume	volume	NOUN
ejpam-5563	690	10	i	i	PRON
ejpam-5563	690	11	,	,	PUNCT
ejpam-5563	690	12	volume	volume	NOUN
ejpam-5563	690	13	1	1	NUM
ejpam-5563	690	14	.	.	PUNCT
ejpam-5563	691	1	elsevier	elsevier	NOUN
ejpam-5563	691	2	,	,	PUNCT
ejpam-5563	691	3	2014	2014	NUM
ejpam-5563	691	4	.	.	PUNCT
ejpam-5563	692	1	[	[	X
ejpam-5563	692	2	12	12	NUM
ejpam-5563	692	3	]	]	PUNCT
ejpam-5563	692	4	nv	nv	PROPN
ejpam-5563	692	5	velicko	velicko	NOUN
ejpam-5563	692	6	.	.	PUNCT
ejpam-5563	693	1	h	h	NOUN
ejpam-5563	693	2	-	-	PUNCT
ejpam-5563	693	3	closed	close	VERB
ejpam-5563	693	4	topological	topological	ADJ
ejpam-5563	693	5	spaces	space	NOUN
ejpam-5563	693	6	.	.	PUNCT
ejpam-5563	694	1	amer	amer	PROPN
ejpam-5563	694	2	.	.	PUNCT
ejpam-5563	694	3	math	math	PROPN
ejpam-5563	694	4	.	.	PUNCT
ejpam-5563	695	1	soc	soc	PROPN
ejpam-5563	695	2	.	.	PUNCT
ejpam-5563	696	1	transl	transl	PROPN
ejpam-5563	696	2	.	.	PUNCT
ejpam-5563	696	3	,	,	PUNCT
ejpam-5563	696	4	78(20):103–118	78(20):103–118	NUM
ejpam-5563	696	5	,	,	PUNCT
ejpam-5563	696	6	1967	1967	NUM
ejpam-5563	696	7	.	.	PUNCT