id	sid	tid	token	lemma	pos
ejpam-855	1	1	6_kilicman.dvi	6_kilicman.dvi	NUM
ejpam-855	1	2	european	european	ADJ
ejpam-855	1	3	journal	journal	NOUN
ejpam-855	1	4	of	of	ADP
ejpam-855	1	5	pure	pure	ADJ
ejpam-855	1	6	and	and	CCONJ
ejpam-855	1	7	applied	apply	VERB
ejpam-855	1	8	mathematics	mathematic	NOUN
ejpam-855	1	9	vol	vol	NOUN
ejpam-855	1	10	.	.	PROPN
ejpam-855	1	11	5	5	NUM
ejpam-855	1	12	,	,	PUNCT
ejpam-855	1	13	no	no	INTJ
ejpam-855	1	14	.	.	NOUN
ejpam-855	1	15	3	3	NUM
ejpam-855	1	16	,	,	PUNCT
ejpam-855	1	17	2012	2012	NUM
ejpam-855	1	18	,	,	PUNCT
ejpam-855	1	19	357	357	NUM
ejpam-855	1	20	-	-	SYM
ejpam-855	1	21	364	364	NUM
ejpam-855	1	22	issn	issn	PROPN
ejpam-855	1	23	1307	1307	NUM
ejpam-855	1	24	-	-	SYM
ejpam-855	1	25	5543	5543	NUM
ejpam-855	1	26	–	–	PUNCT
ejpam-855	1	27	www.ejpam.com	www.ejpam.com	X
ejpam-855	1	28	on	on	ADP
ejpam-855	1	29	characterizations	characterization	NOUN
ejpam-855	1	30	of	of	ADP
ejpam-855	1	31	new	new	ADJ
ejpam-855	1	32	separation	separation	NOUN
ejpam-855	1	33	axioms	axiom	NOUN
ejpam-855	1	34	and	and	CCONJ
ejpam-855	1	35	topological	topological	ADJ
ejpam-855	1	36	properties	property	NOUN
ejpam-855	1	37	s.	s.	PROPN
ejpam-855	1	38	pious	pious	ADJ
ejpam-855	1	39	missier1	missier1	NOUN
ejpam-855	1	40	,	,	PUNCT
ejpam-855	1	41	m.	m.	NOUN
ejpam-855	1	42	j.	j.	PROPN
ejpam-855	1	43	jeyanthi2	jeyanthi2	PROPN
ejpam-855	1	44	,	,	PUNCT
ejpam-855	1	45	adem	adem	PROPN
ejpam-855	1	46	kılıçman3,∗	kılıçman3,∗	PROPN
ejpam-855	1	47	1	1	NUM
ejpam-855	1	48	department	department	NOUN
ejpam-855	1	49	of	of	ADP
ejpam-855	1	50	mathematics	mathematic	NOUN
ejpam-855	1	51	,	,	PUNCT
ejpam-855	1	52	v.	v.	ADP
ejpam-855	1	53	o.	o.	PROPN
ejpam-855	1	54	chidambaram	chidambaram	PROPN
ejpam-855	1	55	college	college	PROPN
ejpam-855	1	56	,	,	PUNCT
ejpam-855	1	57	thoothukudi-628	thoothukudi-628	PROPN
ejpam-855	1	58	008	008	NUM
ejpam-855	1	59	(	(	PUNCT
ejpam-855	1	60	t.n	t.n	PROPN
ejpam-855	1	61	.	.	PROPN
ejpam-855	1	62	)	)	PUNCT
ejpam-855	1	63	,	,	PUNCT
ejpam-855	1	64	india	india	PROPN
ejpam-855	1	65	2	2	NUM
ejpam-855	1	66	aditanar	aditanar	PROPN
ejpam-855	1	67	college	college	NOUN
ejpam-855	1	68	of	of	ADP
ejpam-855	1	69	arts	art	NOUN
ejpam-855	1	70	and	and	CCONJ
ejpam-855	1	71	science	science	NOUN
ejpam-855	1	72	,	,	PUNCT
ejpam-855	1	73	tiruchendur(t.n	tiruchendur(t.n	PROPN
ejpam-855	1	74	.	.	PROPN
ejpam-855	1	75	)	)	PUNCT
ejpam-855	1	76	,	,	PUNCT
ejpam-855	1	77	india	india	PROPN
ejpam-855	1	78	3	3	PROPN
ejpam-855	1	79	institute	institute	PROPN
ejpam-855	1	80	of	of	ADP
ejpam-855	1	81	mathematical	mathematical	ADJ
ejpam-855	1	82	research	research	NOUN
ejpam-855	1	83	(	(	PUNCT
ejpam-855	1	84	inspem	inspem	NOUN
ejpam-855	1	85	)	)	PUNCT
ejpam-855	1	86	and	and	CCONJ
ejpam-855	1	87	department	department	NOUN
ejpam-855	1	88	of	of	ADP
ejpam-855	1	89	mathematics	mathematics	PROPN
ejpam-855	1	90	,	,	PUNCT
ejpam-855	1	91	university	university	NOUN
ejpam-855	1	92	putra	putra	PROPN
ejpam-855	1	93	malaysia	malaysia	PROPN
ejpam-855	1	94	,	,	PUNCT
ejpam-855	1	95	43400	43400	NUM
ejpam-855	1	96	upm	upm	PROPN
ejpam-855	1	97	,	,	PUNCT
ejpam-855	1	98	serdang	serdang	PROPN
ejpam-855	1	99	,	,	PUNCT
ejpam-855	1	100	selangor	selangor	PROPN
ejpam-855	1	101	,	,	PUNCT
ejpam-855	1	102	malaysia	malaysia	PROPN
ejpam-855	1	103	abstract	abstract	NOUN
ejpam-855	1	104	.	.	PUNCT
ejpam-855	2	1	in	in	ADP
ejpam-855	2	2	this	this	DET
ejpam-855	2	3	paper	paper	NOUN
ejpam-855	2	4	,	,	PUNCT
ejpam-855	2	5	we	we	PRON
ejpam-855	2	6	introduce	introduce	VERB
ejpam-855	2	7	new	new	ADJ
ejpam-855	2	8	separations	separation	NOUN
ejpam-855	2	9	axioms	axiom	VERB
ejpam-855	2	10	λr−r0	λr−r0	NOUN
ejpam-855	2	11	,	,	PUNCT
ejpam-855	2	12	λr	λr	ADP
ejpam-855	2	13	−r1	−r1	PROPN
ejpam-855	2	14	and	and	CCONJ
ejpam-855	2	15	λr	λr	ADP
ejpam-855	2	16	−dk	−dk	PROPN
ejpam-855	2	17	,	,	PUNCT
ejpam-855	2	18	and	and	CCONJ
ejpam-855	2	19	study	study	VERB
ejpam-855	2	20	their	their	PRON
ejpam-855	2	21	properties	property	NOUN
ejpam-855	2	22	.	.	PUNCT
ejpam-855	3	1	2010	2010	NUM
ejpam-855	3	2	mathematics	mathematic	NOUN
ejpam-855	3	3	subject	subject	NOUN
ejpam-855	3	4	classifications	classification	NOUN
ejpam-855	3	5	:	:	PUNCT
ejpam-855	3	6	54d10	54d10	NUM
ejpam-855	3	7	,	,	PUNCT
ejpam-855	3	8	54d15	54d15	NUM
ejpam-855	3	9	key	key	ADJ
ejpam-855	3	10	words	word	NOUN
ejpam-855	3	11	and	and	CCONJ
ejpam-855	3	12	phrases	phrase	NOUN
ejpam-855	3	13	:	:	PUNCT
ejpam-855	3	14	λr	λr	ADP
ejpam-855	3	15	−	−	PROPN
ejpam-855	3	16	r0	r0	NOUN
ejpam-855	3	17	,	,	PUNCT
ejpam-855	3	18	λr	λr	ADP
ejpam-855	3	19	−	−	PROPN
ejpam-855	3	20	r1	r1	NOUN
ejpam-855	3	21	and	and	CCONJ
ejpam-855	4	1	λr	λr	NOUN
ejpam-855	4	2	−	−	PROPN
ejpam-855	5	1	dk	dk	PROPN
ejpam-855	5	2	,	,	PUNCT
ejpam-855	5	3	k	k	PROPN
ejpam-855	6	1	=	=	PUNCT
ejpam-855	6	2	0,1,2	0,1,2	NUM
ejpam-855	6	3	1	1	NUM
ejpam-855	6	4	.	.	PUNCT
ejpam-855	7	1	introduction	introduction	NOUN
ejpam-855	7	2	caldas	caldas	PROPN
ejpam-855	7	3	and	and	CCONJ
ejpam-855	7	4	jafari	jafari	PROPN
ejpam-855	8	1	[	[	X
ejpam-855	8	2	1	1	X
ejpam-855	8	3	]	]	PUNCT
ejpam-855	8	4	introduced	introduce	VERB
ejpam-855	8	5	the	the	DET
ejpam-855	8	6	notions	notion	NOUN
ejpam-855	8	7	of	of	ADP
ejpam-855	8	8	λδ	λδ	PRON
ejpam-855	8	9	−	−	PROPN
ejpam-855	8	10	r0	r0	NOUN
ejpam-855	8	11	and	and	CCONJ
ejpam-855	8	12	λδ	λδ	PRON
ejpam-855	8	13	−	−	PROPN
ejpam-855	8	14	r1	r1	PROPN
ejpam-855	8	15	topological	topological	ADJ
ejpam-855	8	16	spaces	space	NOUN
ejpam-855	8	17	.	.	PUNCT
ejpam-855	9	1	in	in	ADP
ejpam-855	9	2	this	this	DET
ejpam-855	9	3	paper	paper	NOUN
ejpam-855	9	4	,	,	PUNCT
ejpam-855	9	5	we	we	PRON
ejpam-855	9	6	define	define	VERB
ejpam-855	9	7	λr	λr	NOUN
ejpam-855	9	8	-open	-open	ADJ
ejpam-855	9	9	sets	set	NOUN
ejpam-855	9	10	,	,	PUNCT
ejpam-855	9	11	that	that	ADV
ejpam-855	9	12	is	is	ADV
ejpam-855	9	13	,	,	PUNCT
ejpam-855	9	14	if	if	SCONJ
ejpam-855	9	15	(	(	PUNCT
ejpam-855	9	16	x	x	X
ejpam-855	9	17	,	,	PUNCT
ejpam-855	9	18	τ	τ	X
ejpam-855	9	19	)	)	PUNCT
ejpam-855	9	20	is	be	AUX
ejpam-855	9	21	a	a	DET
ejpam-855	9	22	topological	topological	ADJ
ejpam-855	9	23	space	space	NOUN
ejpam-855	9	24	and	and	CCONJ
ejpam-855	9	25	a	a	DET
ejpam-855	9	26	⊂	⊂	PROPN
ejpam-855	9	27	x	x	X
ejpam-855	9	28	.	.	PUNCT
ejpam-855	10	1	then	then	ADV
ejpam-855	10	2	λr	λr	VERB
ejpam-855	10	3	-kernel	-kernel	NOUN
ejpam-855	10	4	of	of	ADP
ejpam-855	10	5	a	a	PRON
ejpam-855	10	6	is	be	AUX
ejpam-855	10	7	defined	define	VERB
ejpam-855	10	8	by	by	ADP
ejpam-855	10	9	λr	λr	NOUN
ejpam-855	10	10	−	−	PROPN
ejpam-855	10	11	ker(a	ker(a	PROPN
ejpam-855	10	12	)	)	PUNCT
ejpam-855	10	13	=	=	NOUN
ejpam-855	10	14	∩	∩	X
ejpam-855	10	15	�	�	PROPN
ejpam-855	10	16	g	g	NOUN
ejpam-855	10	17	/	/	SYM
ejpam-855	10	18	g	g	NOUN
ejpam-855	10	19	∈	∈	PROPN
ejpam-855	10	20	λro(x	λro(x	PROPN
ejpam-855	10	21	,	,	PUNCT
ejpam-855	10	22	τ	τ	PROPN
ejpam-855	10	23	)	)	PUNCT
ejpam-855	10	24	and	and	CCONJ
ejpam-855	10	25	a⊂	a⊂	VERB
ejpam-855	10	26	g	g	PROPN
ejpam-855	10	27	�	�	PROPN
ejpam-855	10	28	.	.	PUNCT
ejpam-855	11	1	then	then	ADV
ejpam-855	11	2	we	we	PRON
ejpam-855	11	3	introduce	introduce	VERB
ejpam-855	11	4	some	some	PRON
ejpam-855	11	5	λr	λr	NOUN
ejpam-855	11	6	-separation	-separation	PROPN
ejpam-855	11	7	axioms	axiom	NOUN
ejpam-855	11	8	,	,	PUNCT
ejpam-855	11	9	we	we	PRON
ejpam-855	11	10	call	call	VERB
ejpam-855	11	11	these	these	DET
ejpam-855	11	12	axioms	axiom	NOUN
ejpam-855	11	13	as	as	SCONJ
ejpam-855	11	14	λr	λr	NOUN
ejpam-855	11	15	−	−	PROPN
ejpam-855	11	16	r0,λr	r0,λr	VERB
ejpam-855	11	17	−	−	PROPN
ejpam-855	11	18	r1	r1	NOUN
ejpam-855	11	19	and	and	CCONJ
ejpam-855	11	20	study	study	VERB
ejpam-855	11	21	the	the	DET
ejpam-855	11	22	properties	property	NOUN
ejpam-855	11	23	of	of	ADP
ejpam-855	11	24	these	these	DET
ejpam-855	11	25	axioms	axiom	NOUN
ejpam-855	11	26	.	.	PUNCT
ejpam-855	12	1	we	we	PRON
ejpam-855	12	2	also	also	ADV
ejpam-855	12	3	define	define	VERB
ejpam-855	12	4	λr	λr	NOUN
ejpam-855	12	5	-difference	-difference	NOUN
ejpam-855	12	6	sets	set	NOUN
ejpam-855	12	7	and	and	CCONJ
ejpam-855	12	8	utilize	utilize	VERB
ejpam-855	12	9	them	they	PRON
ejpam-855	12	10	to	to	PART
ejpam-855	12	11	define	define	VERB
ejpam-855	12	12	the	the	DET
ejpam-855	12	13	λr	λr	NOUN
ejpam-855	12	14	−	−	PROPN
ejpam-855	13	1	dk	dk	PROPN
ejpam-855	13	2	,	,	PUNCT
ejpam-855	13	3	k	k	PROPN
ejpam-855	13	4	=	=	SYM
ejpam-855	13	5	0,1,2	0,1,2	NUM
ejpam-855	13	6	axioms	axiom	NOUN
ejpam-855	13	7	.	.	PUNCT
ejpam-855	14	1	throughout	throughout	ADP
ejpam-855	14	2	the	the	DET
ejpam-855	14	3	paper	paper	NOUN
ejpam-855	14	4	(	(	PUNCT
ejpam-855	14	5	x	x	X
ejpam-855	14	6	,	,	PUNCT
ejpam-855	14	7	τ	τ	X
ejpam-855	14	8	)	)	PUNCT
ejpam-855	14	9	(	(	PUNCT
ejpam-855	14	10	or	or	CCONJ
ejpam-855	14	11	simply	simply	ADV
ejpam-855	14	12	x	x	X
ejpam-855	14	13	)	)	PUNCT
ejpam-855	14	14	will	will	AUX
ejpam-855	14	15	always	always	ADV
ejpam-855	14	16	denote	denote	VERB
ejpam-855	14	17	a	a	DET
ejpam-855	14	18	topological	topological	ADJ
ejpam-855	14	19	space	space	NOUN
ejpam-855	14	20	.	.	PUNCT
ejpam-855	15	1	let	let	VERB
ejpam-855	15	2	(	(	PUNCT
ejpam-855	15	3	x	x	X
ejpam-855	15	4	,	,	PUNCT
ejpam-855	15	5	τ	τ	X
ejpam-855	15	6	)	)	PUNCT
ejpam-855	15	7	be	be	VERB
ejpam-855	15	8	a	a	DET
ejpam-855	15	9	topological	topological	ADJ
ejpam-855	15	10	space	space	NOUN
ejpam-855	15	11	and	and	CCONJ
ejpam-855	15	12	s	s	NOUN
ejpam-855	15	13	⊂	⊂	PROPN
ejpam-855	15	14	x	x	X
ejpam-855	15	15	.	.	PUNCT
ejpam-855	16	1	then	then	ADV
ejpam-855	16	2	s	s	VERB
ejpam-855	16	3	is	be	AUX
ejpam-855	16	4	called	call	VERB
ejpam-855	16	5	regularly	regularly	ADV
ejpam-855	16	6	-	-	PUNCT
ejpam-855	16	7	open	open	ADJ
ejpam-855	16	8	if	if	SCONJ
ejpam-855	16	9	s	s	NOUN
ejpam-855	16	10	=	=	ADJ
ejpam-855	16	11	int(cls	int(cls	NOUN
ejpam-855	16	12	)	)	PUNCT
ejpam-855	16	13	.	.	PUNCT
ejpam-855	17	1	the	the	DET
ejpam-855	17	2	complement	complement	NOUN
ejpam-855	17	3	sc(=	sc(=	NOUN
ejpam-855	17	4	x	x	PUNCT
ejpam-855	17	5	\	\	PROPN
ejpam-855	17	6	s	s	X
ejpam-855	17	7	)	)	PUNCT
ejpam-855	17	8	of	of	ADP
ejpam-855	17	9	a	a	DET
ejpam-855	17	10	regularly	regularly	ADV
ejpam-855	17	11	-	-	PUNCT
ejpam-855	17	12	open	open	NOUN
ejpam-855	17	13	set	set	NOUN
ejpam-855	17	14	s	s	PART
ejpam-855	17	15	is	be	AUX
ejpam-855	17	16	called	call	VERB
ejpam-855	17	17	the	the	DET
ejpam-855	17	18	regularly	regularly	ADV
ejpam-855	17	19	-	-	PUNCT
ejpam-855	17	20	closed	close	VERB
ejpam-855	17	21	set	set	NOUN
ejpam-855	17	22	.	.	PUNCT
ejpam-855	18	1	the	the	DET
ejpam-855	18	2	family	family	NOUN
ejpam-855	18	3	of	of	ADP
ejpam-855	18	4	all	all	DET
ejpam-855	18	5	regularly	regularly	ADV
ejpam-855	18	6	-	-	PUNCT
ejpam-855	18	7	open	open	NOUN
ejpam-855	18	8	sets(resp	sets(resp	PROPN
ejpam-855	18	9	.	.	PUNCT
ejpam-855	19	1	regularly	regularly	ADV
ejpam-855	19	2	-	-	PUNCT
ejpam-855	19	3	closed	close	VERB
ejpam-855	19	4	sets	set	NOUN
ejpam-855	19	5	)	)	PUNCT
ejpam-855	19	6	will	will	AUX
ejpam-855	19	7	be	be	AUX
ejpam-855	19	8	denoted	denote	VERB
ejpam-855	19	9	by	by	ADP
ejpam-855	19	10	ro(x	ro(x	PUNCT
ejpam-855	19	11	,	,	PUNCT
ejpam-855	19	12	τ	τ	X
ejpam-855	19	13	)	)	PUNCT
ejpam-855	19	14	(	(	PUNCT
ejpam-855	19	15	resp	resp	NOUN
ejpam-855	19	16	.	.	PUNCT
ejpam-855	19	17	rc(x	rc(x	PROPN
ejpam-855	19	18	,	,	PUNCT
ejpam-855	19	19	τ	τ	PROPN
ejpam-855	19	20	)	)	PUNCT
ejpam-855	19	21	)	)	PUNCT
ejpam-855	19	22	.	.	PUNCT
ejpam-855	20	1	a	a	DET
ejpam-855	20	2	subset	subset	NOUN
ejpam-855	20	3	s	s	NOUN
ejpam-855	20	4	of	of	ADP
ejpam-855	20	5	a	a	DET
ejpam-855	20	6	topological	topological	ADJ
ejpam-855	20	7	space	space	NOUN
ejpam-855	20	8	(	(	PUNCT
ejpam-855	20	9	x	x	X
ejpam-855	20	10	,	,	PUNCT
ejpam-855	20	11	τ	τ	X
ejpam-855	20	12	)	)	PUNCT
ejpam-855	20	13	is	be	AUX
ejpam-855	20	14	called	call	VERB
ejpam-855	20	15	λr	λr	NOUN
ejpam-855	20	16	-set	-set	PUNCT
ejpam-855	20	17	if	if	SCONJ
ejpam-855	20	18	s	s	PART
ejpam-855	20	19	=	=	NOUN
ejpam-855	20	20	λr(s	λr(s	X
ejpam-855	20	21	)	)	PUNCT
ejpam-855	20	22	where	where	SCONJ
ejpam-855	20	23	λr(s	λr(	VERB
ejpam-855	20	24	)	)	PUNCT
ejpam-855	20	25	=	=	SYM
ejpam-855	20	26	∩{g	∩{g	PROPN
ejpam-855	20	27	/	/	SYM
ejpam-855	20	28	g	g	PROPN
ejpam-855	20	29	∈	∈	PROPN
ejpam-855	20	30	ro(x	ro(x	PUNCT
ejpam-855	20	31	,	,	PUNCT
ejpam-855	20	32	τ	τ	X
ejpam-855	20	33	)	)	PUNCT
ejpam-855	20	34	and	and	CCONJ
ejpam-855	20	35	s	s	VERB
ejpam-855	20	36	⊆	⊆	NUM
ejpam-855	20	37	g	g	NOUN
ejpam-855	20	38	}	}	PUNCT
ejpam-855	20	39	.	.	PUNCT
ejpam-855	21	1	∗corresponding	∗corresponde	VERB
ejpam-855	21	2	author	author	NOUN
ejpam-855	21	3	.	.	PUNCT
ejpam-855	22	1	email	email	NOUN
ejpam-855	22	2	addresses	address	NOUN
ejpam-855	22	3	:	:	PUNCT
ejpam-855	22	4	spmissier	spmissier	PROPN
ejpam-855	22	5	�	�	PROPN
ejpam-855	22	6	yahoo	yahoo	PROPN
ejpam-855	22	7	.	.	PUNCT
ejpam-855	23	1	om	om	PROPN
ejpam-855	23	2	(	(	PUNCT
ejpam-855	23	3	s.	s.	PROPN
ejpam-855	23	4	missier	missier	PROPN
ejpam-855	23	5	)	)	PUNCT
ejpam-855	23	6	,	,	PUNCT
ejpam-855	23	7	jeyanthimani	jeyanthimani	PROPN
ejpam-855	23	8	karaj	karaj	PROPN
ejpam-855	23	9	�	�	PROPN
ejpam-855	23	10	gmail	gmail	NOUN
ejpam-855	23	11	.	.	PUNCT
ejpam-855	24	1	om	om	PROPN
ejpam-855	24	2	(	(	PUNCT
ejpam-855	24	3	m.	m.	NOUN
ejpam-855	24	4	jeyanthi	jeyanthi	PROPN
ejpam-855	24	5	)	)	PUNCT
ejpam-855	24	6	,	,	PUNCT
ejpam-855	24	7	akili	akili	NOUN
ejpam-855	24	8	man�putra.upm.edu.my	man�putra.upm.edu.my	NOUN
ejpam-855	24	9	(	(	PUNCT
ejpam-855	24	10	a.	a.	NOUN
ejpam-855	24	11	kılıçman	kılıçman	PROPN
ejpam-855	24	12	)	)	PUNCT
ejpam-855	24	13	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-855	25	1	357	357	NUM
ejpam-855	25	2	c	c	NOUN
ejpam-855	25	3	©	©	PROPN
ejpam-855	25	4	2012	2012	NUM
ejpam-855	25	5	ejpam	ejpam	VERB
ejpam-855	25	6	all	all	DET
ejpam-855	25	7	rights	right	NOUN
ejpam-855	25	8	reserved	reserve	VERB
ejpam-855	25	9	.	.	PUNCT
ejpam-855	26	1	s.	s.	PROPN
ejpam-855	26	2	missier	missier	PROPN
ejpam-855	26	3	,	,	PUNCT
ejpam-855	26	4	m.	m.	NOUN
ejpam-855	26	5	jeyanthi	jeyanthi	PROPN
ejpam-855	26	6	,	,	PUNCT
ejpam-855	26	7	a.	a.	PROPN
ejpam-855	26	8	kılıçman	kılıçman	PROPN
ejpam-855	26	9	/	/	SYM
ejpam-855	26	10	eur	eur	PROPN
ejpam-855	26	11	.	.	PUNCT
ejpam-855	27	1	j.	j.	PROPN
ejpam-855	27	2	pure	pure	PROPN
ejpam-855	27	3	appl	appl	PROPN
ejpam-855	27	4	.	.	PROPN
ejpam-855	27	5	math	math	PROPN
ejpam-855	27	6	,	,	PUNCT
ejpam-855	27	7	5	5	NUM
ejpam-855	27	8	(	(	PUNCT
ejpam-855	27	9	2012	2012	NUM
ejpam-855	27	10	)	)	PUNCT
ejpam-855	27	11	,	,	PUNCT
ejpam-855	27	12	357	357	NUM
ejpam-855	27	13	-	-	SYM
ejpam-855	27	14	364	364	NUM
ejpam-855	27	15	358	358	NUM
ejpam-855	27	16	the	the	DET
ejpam-855	27	17	collection	collection	NOUN
ejpam-855	27	18	of	of	ADP
ejpam-855	27	19	all	all	PRON
ejpam-855	27	20	λr	λr	ADP
ejpam-855	27	21	-sets	-set	NOUN
ejpam-855	27	22	is	be	AUX
ejpam-855	27	23	denoted	denote	VERB
ejpam-855	27	24	by	by	ADP
ejpam-855	27	25	λr(x	λr(x	X
ejpam-855	27	26	,	,	PUNCT
ejpam-855	27	27	τ	τ	PROPN
ejpam-855	27	28	)	)	PUNCT
ejpam-855	27	29	.	.	PUNCT
ejpam-855	28	1	throughout	throughout	ADP
ejpam-855	28	2	this	this	DET
ejpam-855	28	3	paper	paper	NOUN
ejpam-855	28	4	,	,	PUNCT
ejpam-855	28	5	we	we	PRON
ejpam-855	28	6	let	let	VERB
ejpam-855	28	7	a	a	DET
ejpam-855	28	8	be	be	AUX
ejpam-855	28	9	a	a	DET
ejpam-855	28	10	subset	subset	NOUN
ejpam-855	28	11	of	of	ADP
ejpam-855	28	12	a	a	DET
ejpam-855	28	13	space	space	NOUN
ejpam-855	28	14	(	(	PUNCT
ejpam-855	28	15	x	x	X
ejpam-855	28	16	,	,	PUNCT
ejpam-855	28	17	τ	τ	PROPN
ejpam-855	28	18	)	)	PUNCT
ejpam-855	28	19	.	.	PUNCT
ejpam-855	29	1	then	then	ADV
ejpam-855	29	2	a	a	PRON
ejpam-855	29	3	is	be	AUX
ejpam-855	29	4	called	call	VERB
ejpam-855	29	5	a	a	DET
ejpam-855	29	6	λr	λr	NOUN
ejpam-855	29	7	-closed	-close	VERB
ejpam-855	29	8	set	set	NOUN
ejpam-855	29	9	if	if	SCONJ
ejpam-855	29	10	a=	a=	PROPN
ejpam-855	29	11	t	t	NOUN
ejpam-855	29	12	∩	∩	NOUN
ejpam-855	29	13	c	c	X
ejpam-855	29	14	where	where	SCONJ
ejpam-855	29	15	t	t	PROPN
ejpam-855	29	16	is	be	AUX
ejpam-855	29	17	a	a	DET
ejpam-855	29	18	λr	λr	NOUN
ejpam-855	29	19	-set	-set	ADJ
ejpam-855	29	20	and	and	CCONJ
ejpam-855	29	21	c	c	PROPN
ejpam-855	29	22	is	be	AUX
ejpam-855	29	23	a	a	DET
ejpam-855	29	24	closed	closed	ADJ
ejpam-855	29	25	set	set	NOUN
ejpam-855	29	26	.	.	PUNCT
ejpam-855	30	1	the	the	DET
ejpam-855	30	2	complement	complement	NOUN
ejpam-855	30	3	of	of	ADP
ejpam-855	30	4	a	a	DET
ejpam-855	30	5	λr	λr	NOUN
ejpam-855	30	6	-closed	-close	VERB
ejpam-855	30	7	set	set	NOUN
ejpam-855	30	8	is	be	AUX
ejpam-855	30	9	called	call	VERB
ejpam-855	30	10	λr	λr	ADP
ejpam-855	30	11	-open	-open	ADJ
ejpam-855	30	12	.	.	PUNCT
ejpam-855	31	1	the	the	DET
ejpam-855	31	2	collection	collection	NOUN
ejpam-855	31	3	of	of	ADP
ejpam-855	31	4	all	all	DET
ejpam-855	31	5	λr	λr	NOUN
ejpam-855	31	6	-open	-open	ADJ
ejpam-855	31	7	sets	set	NOUN
ejpam-855	31	8	is	be	AUX
ejpam-855	31	9	denoted	denote	VERB
ejpam-855	31	10	by	by	ADP
ejpam-855	31	11	λro(x	λro(x	PROPN
ejpam-855	31	12	,	,	PUNCT
ejpam-855	31	13	τ	τ	PROPN
ejpam-855	31	14	)	)	PUNCT
ejpam-855	31	15	.	.	PUNCT
ejpam-855	32	1	the	the	DET
ejpam-855	32	2	collection	collection	NOUN
ejpam-855	32	3	of	of	ADP
ejpam-855	32	4	all	all	DET
ejpam-855	32	5	λr	λr	NOUN
ejpam-855	32	6	-closed	-closed	ADJ
ejpam-855	32	7	sets	set	NOUN
ejpam-855	32	8	is	be	AUX
ejpam-855	32	9	denoted	denote	VERB
ejpam-855	32	10	by	by	ADP
ejpam-855	32	11	λr	λr	ADP
ejpam-855	32	12	c(x	c(x	PROPN
ejpam-855	32	13	,	,	PUNCT
ejpam-855	32	14	τ	τ	PROPN
ejpam-855	32	15	)	)	PUNCT
ejpam-855	32	16	.	.	PUNCT
ejpam-855	33	1	a	a	DET
ejpam-855	33	2	point	point	NOUN
ejpam-855	33	3	x	x	X
ejpam-855	33	4	∈	∈	NOUN
ejpam-855	33	5	x	x	PUNCT
ejpam-855	33	6	is	be	AUX
ejpam-855	33	7	called	call	VERB
ejpam-855	33	8	a	a	DET
ejpam-855	33	9	λr	λr	NOUN
ejpam-855	33	10	-cluster	-cluster	NOUN
ejpam-855	33	11	point	point	NOUN
ejpam-855	33	12	of	of	ADP
ejpam-855	33	13	a	a	DET
ejpam-855	33	14	if	if	NOUN
ejpam-855	33	15	for	for	ADP
ejpam-855	33	16	every	every	DET
ejpam-855	33	17	λr	λr	NOUN
ejpam-855	33	18	-open	-open	ADJ
ejpam-855	33	19	set	set	VERB
ejpam-855	33	20	u	u	NOUN
ejpam-855	33	21	containing	contain	VERB
ejpam-855	33	22	x	x	PUNCT
ejpam-855	33	23	,	,	PUNCT
ejpam-855	33	24	a∩	a∩	PROPN
ejpam-855	33	25	u	u	PROPN
ejpam-855	33	26	6=	6=	PROPN
ejpam-855	33	27	;	;	PUNCT
ejpam-855	33	28	.	.	PUNCT
ejpam-855	34	1	the	the	DET
ejpam-855	34	2	set	set	NOUN
ejpam-855	34	3	of	of	ADP
ejpam-855	34	4	all	all	DET
ejpam-855	34	5	λr	λr	NOUN
ejpam-855	34	6	-cluster	-cluster	NOUN
ejpam-855	34	7	points	point	NOUN
ejpam-855	34	8	of	of	ADP
ejpam-855	34	9	a	a	PRON
ejpam-855	34	10	is	be	AUX
ejpam-855	34	11	called	call	VERB
ejpam-855	34	12	the	the	DET
ejpam-855	34	13	λr	λr	NOUN
ejpam-855	34	14	-closure	-closure	NOUN
ejpam-855	34	15	of	of	ADP
ejpam-855	34	16	a	a	PRON
ejpam-855	34	17	and	and	CCONJ
ejpam-855	34	18	is	be	AUX
ejpam-855	34	19	denoted	denote	VERB
ejpam-855	34	20	by	by	ADP
ejpam-855	34	21	λr	λr	ADP
ejpam-855	34	22	−	−	PROPN
ejpam-855	34	23	cl(a	cl(a	NUM
ejpam-855	34	24	)	)	PUNCT
ejpam-855	34	25	.	.	PUNCT
ejpam-855	35	1	2	2	X
ejpam-855	35	2	.	.	X
ejpam-855	35	3	λr	λr	NOUN
ejpam-855	35	4	−	−	PROPN
ejpam-855	35	5	r0	r0	NOUN
ejpam-855	35	6	spaces	space	VERB
ejpam-855	35	7	definition	definition	NOUN
ejpam-855	35	8	1	1	NUM
ejpam-855	35	9	.	.	PUNCT
ejpam-855	36	1	the	the	DET
ejpam-855	36	2	topological	topological	ADJ
ejpam-855	36	3	space	space	NOUN
ejpam-855	36	4	(	(	PUNCT
ejpam-855	36	5	x	x	X
ejpam-855	36	6	,	,	PUNCT
ejpam-855	36	7	τ	τ	X
ejpam-855	36	8	)	)	PUNCT
ejpam-855	36	9	is	be	AUX
ejpam-855	36	10	said	say	VERB
ejpam-855	36	11	to	to	PART
ejpam-855	36	12	be	be	AUX
ejpam-855	36	13	λr	λr	ADP
ejpam-855	36	14	−	−	NOUN
ejpam-855	36	15	r0	r0	NOUN
ejpam-855	36	16	if	if	SCONJ
ejpam-855	36	17	for	for	SCONJ
ejpam-855	36	18	each	each	DET
ejpam-855	36	19	λr	λr	NOUN
ejpam-855	36	20	-open	-open	ADJ
ejpam-855	36	21	set	set	VERB
ejpam-855	36	22	g	g	NOUN
ejpam-855	36	23	,	,	PUNCT
ejpam-855	36	24	x	x	SYM
ejpam-855	36	25	∈	∈	PROPN
ejpam-855	36	26	g⇒	g⇒	PROPN
ejpam-855	36	27	λr	λr	VERB
ejpam-855	36	28	−	−	PROPN
ejpam-855	36	29	cl({x	cl({x	NOUN
ejpam-855	36	30	}	}	PUNCT
ejpam-855	36	31	)	)	PUNCT
ejpam-855	37	1	⊆	⊆	NUM
ejpam-855	37	2	g.	g.	NOUN
ejpam-855	37	3	theorem	theorem	VERB
ejpam-855	37	4	1	1	NUM
ejpam-855	37	5	.	.	X
ejpam-855	37	6	for	for	ADP
ejpam-855	37	7	a	a	DET
ejpam-855	37	8	topological	topological	ADJ
ejpam-855	37	9	space	space	NOUN
ejpam-855	37	10	(	(	PUNCT
ejpam-855	37	11	x	x	X
ejpam-855	37	12	,	,	PUNCT
ejpam-855	37	13	τ	τ	PROPN
ejpam-855	37	14	)	)	PUNCT
ejpam-855	37	15	,	,	PUNCT
ejpam-855	37	16	the	the	DET
ejpam-855	37	17	following	follow	VERB
ejpam-855	37	18	statements	statement	NOUN
ejpam-855	37	19	are	be	AUX
ejpam-855	37	20	equivalent	equivalent	ADJ
ejpam-855	37	21	:	:	PUNCT
ejpam-855	37	22	(	(	PUNCT
ejpam-855	37	23	1	1	X
ejpam-855	37	24	)	)	PUNCT
ejpam-855	37	25	(	(	PUNCT
ejpam-855	37	26	x	x	X
ejpam-855	37	27	,	,	PUNCT
ejpam-855	37	28	τ	τ	X
ejpam-855	37	29	)	)	PUNCT
ejpam-855	37	30	is	be	AUX
ejpam-855	37	31	λr	λr	ADP
ejpam-855	37	32	−	−	PROPN
ejpam-855	37	33	r0	r0	NOUN
ejpam-855	37	34	,	,	PUNCT
ejpam-855	37	35	(	(	PUNCT
ejpam-855	37	36	2	2	X
ejpam-855	37	37	)	)	PUNCT
ejpam-855	37	38	for	for	ADP
ejpam-855	37	39	any	any	DET
ejpam-855	37	40	λr	λr	NOUN
ejpam-855	37	41	-closed	-close	VERB
ejpam-855	37	42	set	set	VERB
ejpam-855	37	43	f	f	NOUN
ejpam-855	37	44	and	and	CCONJ
ejpam-855	37	45	a	a	DET
ejpam-855	37	46	point	point	NOUN
ejpam-855	37	47	x	x	X
ejpam-855	37	48	/∈	/∈	PUNCT
ejpam-855	38	1	f	f	X
ejpam-855	38	2	,	,	PUNCT
ejpam-855	38	3	∃u	∃u	PROPN
ejpam-855	38	4	∈	∈	PROPN
ejpam-855	38	5	λro(x	λro(x	PROPN
ejpam-855	38	6	,	,	PUNCT
ejpam-855	38	7	τ	τ	PROPN
ejpam-855	38	8	)	)	PUNCT
ejpam-855	38	9	such	such	ADJ
ejpam-855	38	10	that	that	SCONJ
ejpam-855	38	11	x	x	X
ejpam-855	38	12	/∈	/∈	PUNCT
ejpam-855	38	13	u	u	NOUN
ejpam-855	38	14	and	and	CCONJ
ejpam-855	38	15	f	f	PROPN
ejpam-855	38	16	⊆	⊆	NUM
ejpam-855	38	17	u	u	NOUN
ejpam-855	38	18	,	,	PUNCT
ejpam-855	38	19	(	(	PUNCT
ejpam-855	38	20	3	3	X
ejpam-855	38	21	)	)	PUNCT
ejpam-855	38	22	for	for	ADP
ejpam-855	38	23	any	any	DET
ejpam-855	38	24	λr	λr	NOUN
ejpam-855	38	25	-closed	-close	VERB
ejpam-855	38	26	set	set	VERB
ejpam-855	38	27	f	f	NOUN
ejpam-855	38	28	and	and	CCONJ
ejpam-855	38	29	a	a	DET
ejpam-855	38	30	point	point	NOUN
ejpam-855	38	31	x	x	X
ejpam-855	38	32	/∈	/∈	PUNCT
ejpam-855	39	1	f	f	X
ejpam-855	39	2	,	,	PUNCT
ejpam-855	39	3	λr	λr	VERB
ejpam-855	39	4	−	−	PROPN
ejpam-855	39	5	cl({x})∩	cl({x})∩	NOUN
ejpam-855	39	6	f	f	PROPN
ejpam-855	39	7	=	=	PUNCT
ejpam-855	39	8	;	;	PUNCT
ejpam-855	39	9	.	.	PUNCT
ejpam-855	40	1	proof	proof	NOUN
ejpam-855	40	2	.	.	PUNCT
ejpam-855	41	1	(	(	PUNCT
ejpam-855	41	2	1)⇒	1)⇒	NUM
ejpam-855	41	3	(	(	PUNCT
ejpam-855	41	4	2	2	NUM
ejpam-855	41	5	)	)	PUNCT
ejpam-855	41	6	let	let	VERB
ejpam-855	41	7	f	f	PRON
ejpam-855	41	8	be	be	AUX
ejpam-855	41	9	a	a	DET
ejpam-855	41	10	λr	λr	NOUN
ejpam-855	41	11	-closed	-close	VERB
ejpam-855	41	12	set	set	NOUN
ejpam-855	41	13	and	and	CCONJ
ejpam-855	41	14	x	x	SYM
ejpam-855	41	15	/∈	/∈	PROPN
ejpam-855	42	1	f	f	PROPN
ejpam-855	42	2	.	.	PUNCT
ejpam-855	43	1	then	then	ADV
ejpam-855	43	2	f	f	PROPN
ejpam-855	43	3	c	c	PROPN
ejpam-855	43	4	is	be	AUX
ejpam-855	43	5	λr	λr	INTJ
ejpam-855	43	6	-open	-open	ADJ
ejpam-855	43	7	and	and	CCONJ
ejpam-855	43	8	x	x	SYM
ejpam-855	43	9	∈	∈	PROPN
ejpam-855	43	10	f	f	NOUN
ejpam-855	43	11	c	c	PROPN
ejpam-855	43	12	.	.	PUNCT
ejpam-855	44	1	since	since	SCONJ
ejpam-855	44	2	x	x	PRON
ejpam-855	44	3	is	be	AUX
ejpam-855	44	4	λr	λr	ADP
ejpam-855	44	5	−r0	−r0	ADJ
ejpam-855	44	6	,	,	PUNCT
ejpam-855	44	7	λr	λr	VERB
ejpam-855	44	8	−	−	NOUN
ejpam-855	44	9	cl({x	cl({x	NOUN
ejpam-855	44	10	}	}	PUNCT
ejpam-855	44	11	)	)	PUNCT
ejpam-855	45	1	⊆	⊆	NUM
ejpam-855	45	2	f	f	X
ejpam-855	45	3	c	c	NOUN
ejpam-855	45	4	and	and	CCONJ
ejpam-855	45	5	hence	hence	ADV
ejpam-855	45	6	f	f	PROPN
ejpam-855	45	7	⊆	⊆	NUM
ejpam-855	45	8	x	x	SYM
ejpam-855	45	9	−	−	PROPN
ejpam-855	45	10	(	(	PUNCT
ejpam-855	45	11	λr	λr	NOUN
ejpam-855	45	12	−	−	PROPN
ejpam-855	45	13	cl({x	cl({x	NOUN
ejpam-855	45	14	}	}	PUNCT
ejpam-855	45	15	)	)	PUNCT
ejpam-855	45	16	)	)	PUNCT
ejpam-855	45	17	.	.	PUNCT
ejpam-855	46	1	thus	thus	ADV
ejpam-855	46	2	x	x	X
ejpam-855	46	3	−	−	PROPN
ejpam-855	46	4	(	(	PUNCT
ejpam-855	46	5	λr	λr	NOUN
ejpam-855	46	6	−	−	PROPN
ejpam-855	46	7	cl({x	cl({x	NOUN
ejpam-855	46	8	}	}	PUNCT
ejpam-855	46	9	)	)	PUNCT
ejpam-855	46	10	)	)	PUNCT
ejpam-855	46	11	is	be	AUX
ejpam-855	46	12	a	a	DET
ejpam-855	46	13	λr	λr	NOUN
ejpam-855	46	14	-open	-open	ADJ
ejpam-855	46	15	set	set	NOUN
ejpam-855	46	16	containing	contain	VERB
ejpam-855	46	17	f	f	PROPN
ejpam-855	46	18	and	and	CCONJ
ejpam-855	46	19	x	x	SYM
ejpam-855	46	20	/∈	/∈	PUNCT
ejpam-855	47	1	x	x	INTJ
ejpam-855	47	2	−	−	PROPN
ejpam-855	47	3	(	(	PUNCT
ejpam-855	47	4	λr	λr	NOUN
ejpam-855	47	5	−	−	PROPN
ejpam-855	47	6	cl({x	cl({x	NOUN
ejpam-855	47	7	}	}	PUNCT
ejpam-855	47	8	)	)	PUNCT
ejpam-855	47	9	)	)	PUNCT
ejpam-855	47	10	.	.	PUNCT
ejpam-855	48	1	(	(	PUNCT
ejpam-855	48	2	2	2	X
ejpam-855	48	3	)	)	PUNCT
ejpam-855	48	4	⇒	⇒	NOUN
ejpam-855	48	5	(	(	PUNCT
ejpam-855	48	6	3	3	X
ejpam-855	48	7	)	)	PUNCT
ejpam-855	48	8	let	let	VERB
ejpam-855	48	9	f	f	PRON
ejpam-855	48	10	be	be	AUX
ejpam-855	48	11	a	a	DET
ejpam-855	48	12	λr	λr	NOUN
ejpam-855	48	13	-closed	-close	VERB
ejpam-855	48	14	set	set	NOUN
ejpam-855	48	15	and	and	CCONJ
ejpam-855	48	16	x	x	SYM
ejpam-855	48	17	/∈	/∈	PROPN
ejpam-855	49	1	f	f	PROPN
ejpam-855	49	2	.	.	PUNCT
ejpam-855	50	1	then	then	ADV
ejpam-855	50	2	∃u	∃u	PROPN
ejpam-855	50	3	∈	∈	PROPN
ejpam-855	50	4	λro(x	λro(x	PROPN
ejpam-855	50	5	,	,	PUNCT
ejpam-855	50	6	τ	τ	PROPN
ejpam-855	50	7	)	)	PUNCT
ejpam-855	50	8	such	such	ADJ
ejpam-855	50	9	that	that	SCONJ
ejpam-855	50	10	x	x	X
ejpam-855	50	11	/∈	/∈	PUNCT
ejpam-855	50	12	u	u	NOUN
ejpam-855	50	13	and	and	CCONJ
ejpam-855	50	14	f	f	PROPN
ejpam-855	50	15	⊆	⊆	NUM
ejpam-855	50	16	u	u	PROPN
ejpam-855	50	17	.	.	PUNCT
ejpam-855	51	1	claim	claim	NOUN
ejpam-855	51	2	:	:	PUNCT
ejpam-855	51	3	u	u	NOUN
ejpam-855	51	4	∩	∩	NOUN
ejpam-855	51	5	λr	λr	VERB
ejpam-855	51	6	−	−	NOUN
ejpam-855	51	7	cl({x	cl({x	NUM
ejpam-855	51	8	}	}	PUNCT
ejpam-855	51	9	)	)	PUNCT
ejpam-855	51	10	=	=	SYM
ejpam-855	51	11	;	;	PUNCT
ejpam-855	51	12	.	.	PUNCT
ejpam-855	52	1	for	for	ADP
ejpam-855	52	2	,	,	PUNCT
ejpam-855	52	3	if	if	SCONJ
ejpam-855	52	4	u	u	PROPN
ejpam-855	52	5	∩	∩	NOUN
ejpam-855	52	6	λr	λr	VERB
ejpam-855	52	7	−	−	NOUN
ejpam-855	52	8	cl({x	cl({x	NUM
ejpam-855	52	9	}	}	PUNCT
ejpam-855	52	10	)	)	PUNCT
ejpam-855	52	11	6=	6=	NUM
ejpam-855	52	12	;	;	PUNCT
ejpam-855	52	13	,	,	PUNCT
ejpam-855	52	14	then	then	ADV
ejpam-855	52	15	∃	∃	PROPN
ejpam-855	52	16	a	a	DET
ejpam-855	52	17	point	point	NOUN
ejpam-855	52	18	y	y	PROPN
ejpam-855	52	19	in	in	ADP
ejpam-855	52	20	x	x	PUNCT
ejpam-855	52	21	such	such	ADJ
ejpam-855	52	22	that	that	SCONJ
ejpam-855	52	23	y	y	PROPN
ejpam-855	52	24	∈	∈	PROPN
ejpam-855	52	25	u	u	PROPN
ejpam-855	52	26	and	and	CCONJ
ejpam-855	52	27	y	y	PROPN
ejpam-855	52	28	∈	∈	PROPN
ejpam-855	52	29	λr	λr	VERB
ejpam-855	52	30	−	−	PROPN
ejpam-855	52	31	cl({x	cl({x	NOUN
ejpam-855	52	32	}	}	PUNCT
ejpam-855	52	33	)	)	PUNCT
ejpam-855	52	34	.	.	PUNCT
ejpam-855	53	1	that	that	PRON
ejpam-855	53	2	implies	imply	VERB
ejpam-855	53	3	y	y	PROPN
ejpam-855	53	4	is	be	AUX
ejpam-855	53	5	a	a	DET
ejpam-855	53	6	λr	λr	NOUN
ejpam-855	53	7	-cluster	-cluster	NOUN
ejpam-855	53	8	point	point	NOUN
ejpam-855	53	9	of	of	ADP
ejpam-855	53	10	{	{	PUNCT
ejpam-855	53	11	x	x	NOUN
ejpam-855	53	12	}	}	PUNCT
ejpam-855	53	13	.	.	PUNCT
ejpam-855	54	1	that	that	PRON
ejpam-855	54	2	implies	imply	VERB
ejpam-855	54	3	for	for	SCONJ
ejpam-855	54	4	every	every	DET
ejpam-855	54	5	λr	λr	NOUN
ejpam-855	54	6	-open	-open	ADJ
ejpam-855	54	7	set	set	VERB
ejpam-855	54	8	g	g	NOUN
ejpam-855	54	9	containing	contain	VERB
ejpam-855	54	10	y	y	PROPN
ejpam-855	54	11	,	,	PUNCT
ejpam-855	54	12	g	g	PROPN
ejpam-855	54	13	∩	∩	NOUN
ejpam-855	54	14	{	{	PUNCT
ejpam-855	54	15	x	x	X
ejpam-855	54	16	}	}	PUNCT
ejpam-855	54	17	6=	6=	NUM
ejpam-855	54	18	;	;	PUNCT
ejpam-855	54	19	.	.	PUNCT
ejpam-855	55	1	that	that	PRON
ejpam-855	55	2	is	be	AUX
ejpam-855	55	3	,	,	PUNCT
ejpam-855	55	4	x	x	SYM
ejpam-855	55	5	∈	∈	PROPN
ejpam-855	55	6	g.	g.	NOUN
ejpam-855	55	7	here	here	ADV
ejpam-855	55	8	u	u	NOUN
ejpam-855	55	9	is	be	AUX
ejpam-855	55	10	a	a	DET
ejpam-855	55	11	λr	λr	NOUN
ejpam-855	55	12	-open	-open	ADJ
ejpam-855	55	13	set	set	NOUN
ejpam-855	55	14	containing	contain	VERB
ejpam-855	55	15	y.	y.	NOUN
ejpam-855	55	16	hence	hence	ADV
ejpam-855	55	17	x	x	SYM
ejpam-855	55	18	∈	∈	PROPN
ejpam-855	55	19	u	u	NOUN
ejpam-855	55	20	,	,	PUNCT
ejpam-855	55	21	which	which	PRON
ejpam-855	55	22	is	be	AUX
ejpam-855	55	23	a	a	DET
ejpam-855	55	24	contradiction	contradiction	NOUN
ejpam-855	55	25	.	.	PUNCT
ejpam-855	56	1	therefore	therefore	ADV
ejpam-855	56	2	u	u	PROPN
ejpam-855	56	3	∩	∩	NOUN
ejpam-855	56	4	λr	λr	VERB
ejpam-855	56	5	−	−	NOUN
ejpam-855	56	6	cl({x	cl({x	NUM
ejpam-855	56	7	}	}	PUNCT
ejpam-855	56	8	)	)	PUNCT
ejpam-855	57	1	=	=	SYM
ejpam-855	57	2	;	;	PUNCT
ejpam-855	57	3	and	and	CCONJ
ejpam-855	57	4	hence	hence	ADV
ejpam-855	57	5	f	f	PROPN
ejpam-855	57	6	∩λr	∩λr	VERB
ejpam-855	57	7	−	−	PROPN
ejpam-855	57	8	cl({x	cl({x	NOUN
ejpam-855	57	9	}	}	PUNCT
ejpam-855	57	10	)	)	PUNCT
ejpam-855	57	11	=	=	SYM
ejpam-855	57	12	;	;	PUNCT
ejpam-855	57	13	.	.	PUNCT
ejpam-855	58	1	(	(	PUNCT
ejpam-855	58	2	3	3	X
ejpam-855	58	3	)	)	PUNCT
ejpam-855	58	4	⇒	⇒	NOUN
ejpam-855	58	5	(	(	PUNCT
ejpam-855	58	6	1	1	X
ejpam-855	58	7	)	)	PUNCT
ejpam-855	58	8	let	let	VERB
ejpam-855	58	9	g	g	NOUN
ejpam-855	58	10	be	be	AUX
ejpam-855	58	11	a	a	DET
ejpam-855	58	12	λr	λr	NOUN
ejpam-855	58	13	-open	-open	NOUN
ejpam-855	58	14	set	set	VERB
ejpam-855	59	1	and	and	CCONJ
ejpam-855	59	2	x	x	SYM
ejpam-855	59	3	∈	∈	PROPN
ejpam-855	59	4	g.	g.	NOUN
ejpam-855	59	5	then	then	ADV
ejpam-855	59	6	gc	gc	PROPN
ejpam-855	59	7	is	be	AUX
ejpam-855	59	8	λr	λr	ADP
ejpam-855	59	9	-closed	-close	VERB
ejpam-855	59	10	and	and	CCONJ
ejpam-855	59	11	x	x	ADJ
ejpam-855	59	12	/∈	/∈	PROPN
ejpam-855	59	13	gc	gc	PROPN
ejpam-855	59	14	.	.	PROPN
ejpam-855	60	1	by	by	ADP
ejpam-855	60	2	(	(	PUNCT
ejpam-855	60	3	3	3	NUM
ejpam-855	60	4	)	)	PUNCT
ejpam-855	60	5	,	,	PUNCT
ejpam-855	60	6	λr	λr	VERB
ejpam-855	60	7	−	−	PROPN
ejpam-855	60	8	cl({x})∩	cl({x})∩	PROPN
ejpam-855	60	9	gc	gc	PROPN
ejpam-855	60	10	=	=	PUNCT
ejpam-855	60	11	;	;	PUNCT
ejpam-855	60	12	and	and	CCONJ
ejpam-855	60	13	hence	hence	ADV
ejpam-855	60	14	λr	λr	ADP
ejpam-855	60	15	−	−	NOUN
ejpam-855	60	16	cl({x	cl({x	NOUN
ejpam-855	60	17	}	}	PUNCT
ejpam-855	60	18	)	)	PUNCT
ejpam-855	61	1	⊆	⊆	NUM
ejpam-855	61	2	g.	g.	NOUN
ejpam-855	61	3	therefore	therefore	ADV
ejpam-855	61	4	(	(	PUNCT
ejpam-855	61	5	x	x	X
ejpam-855	61	6	,	,	PUNCT
ejpam-855	61	7	τ	τ	X
ejpam-855	61	8	)	)	PUNCT
ejpam-855	61	9	is	be	AUX
ejpam-855	61	10	λr	λr	ADP
ejpam-855	61	11	−	−	PROPN
ejpam-855	61	12	r0	r0	NOUN
ejpam-855	61	13	.	.	PUNCT
ejpam-855	62	1	theorem	theorem	NOUN
ejpam-855	62	2	2	2	NUM
ejpam-855	62	3	.	.	PUNCT
ejpam-855	62	4	a	a	DET
ejpam-855	62	5	space	space	NOUN
ejpam-855	62	6	(	(	PUNCT
ejpam-855	62	7	x	x	X
ejpam-855	62	8	,	,	PUNCT
ejpam-855	62	9	τ	τ	X
ejpam-855	62	10	)	)	PUNCT
ejpam-855	62	11	is	be	AUX
ejpam-855	62	12	λr	λr	ADP
ejpam-855	62	13	−	−	PROPN
ejpam-855	62	14	r0	r0	NOUN
ejpam-855	62	15	iff	iff	PROPN
ejpam-855	62	16	for	for	ADP
ejpam-855	62	17	each	each	DET
ejpam-855	62	18	pair	pair	NOUN
ejpam-855	62	19	x	x	SYM
ejpam-855	62	20	,	,	PUNCT
ejpam-855	62	21	y	y	PROPN
ejpam-855	62	22	of	of	ADP
ejpam-855	62	23	distinct	distinct	ADJ
ejpam-855	62	24	points	point	NOUN
ejpam-855	62	25	in	in	ADP
ejpam-855	62	26	x	x	X
ejpam-855	62	27	,	,	PUNCT
ejpam-855	62	28	λr	λr	ADP
ejpam-855	62	29	−	−	NOUN
ejpam-855	62	30	cl({x})∩λr	cl({x})∩λr	NOUN
ejpam-855	62	31	−	−	NOUN
ejpam-855	62	32	cl({y	cl({y	X
ejpam-855	62	33	}	}	PUNCT
ejpam-855	62	34	)	)	PUNCT
ejpam-855	62	35	=	=	SYM
ejpam-855	62	36	;	;	PUNCT
ejpam-855	62	37	or	or	CCONJ
ejpam-855	62	38	{	{	PUNCT
ejpam-855	62	39	x	x	X
ejpam-855	62	40	,	,	PUNCT
ejpam-855	62	41	y	y	PROPN
ejpam-855	62	42	}	}	PUNCT
ejpam-855	62	43	⊆	⊆	NUM
ejpam-855	62	44	λr	λr	NOUN
ejpam-855	62	45	−	−	NOUN
ejpam-855	62	46	cl({x})∩λr	cl({x})∩λr	NOUN
ejpam-855	62	47	−	−	NOUN
ejpam-855	62	48	cl({y	cl({y	X
ejpam-855	62	49	}	}	PUNCT
ejpam-855	62	50	)	)	PUNCT
ejpam-855	62	51	.	.	PUNCT
ejpam-855	63	1	proof	proof	NOUN
ejpam-855	63	2	.	.	PUNCT
ejpam-855	64	1	let	let	VERB
ejpam-855	64	2	(	(	PUNCT
ejpam-855	64	3	x	x	X
ejpam-855	64	4	,	,	PUNCT
ejpam-855	64	5	τ	τ	X
ejpam-855	64	6	)	)	PUNCT
ejpam-855	64	7	be	be	VERB
ejpam-855	64	8	a	a	DET
ejpam-855	64	9	λr	λr	NOUN
ejpam-855	64	10	−	−	NOUN
ejpam-855	64	11	r0	r0	NOUN
ejpam-855	64	12	space	space	NOUN
ejpam-855	64	13	.	.	PUNCT
ejpam-855	65	1	let	let	VERB
ejpam-855	65	2	x	x	PRON
ejpam-855	65	3	,	,	PUNCT
ejpam-855	65	4	y	y	PROPN
ejpam-855	65	5	∈	∈	PROPN
ejpam-855	65	6	x	x	PUNCT
ejpam-855	65	7	such	such	ADJ
ejpam-855	65	8	that	that	SCONJ
ejpam-855	65	9	x	x	PRON
ejpam-855	65	10	6=	6=	X
ejpam-855	65	11	y.	y.	NOUN
ejpam-855	65	12	then	then	ADV
ejpam-855	65	13	we	we	PRON
ejpam-855	65	14	have	have	VERB
ejpam-855	65	15	case(i	case(i	NOUN
ejpam-855	65	16	):	):	PUNCT
ejpam-855	65	17	suppose	suppose	VERB
ejpam-855	65	18	λr	λr	ADP
ejpam-855	65	19	−	−	NOUN
ejpam-855	65	20	cl({x})∩λr	cl({x})∩λr	NOUN
ejpam-855	65	21	−	−	NOUN
ejpam-855	65	22	cl({y	cl({y	X
ejpam-855	65	23	}	}	PUNCT
ejpam-855	65	24	)	)	PUNCT
ejpam-855	65	25	6=	6=	NUM
ejpam-855	65	26	;	;	PUNCT
ejpam-855	65	27	.	.	PUNCT
ejpam-855	66	1	if	if	SCONJ
ejpam-855	66	2	{	{	PUNCT
ejpam-855	66	3	x	x	INTJ
ejpam-855	66	4	,	,	PUNCT
ejpam-855	66	5	y	y	PROPN
ejpam-855	66	6	}	}	PUNCT
ejpam-855	66	7	is	be	AUX
ejpam-855	66	8	not	not	PART
ejpam-855	66	9	a	a	DET
ejpam-855	66	10	subset	subset	NOUN
ejpam-855	66	11	of	of	ADP
ejpam-855	66	12	λr	λr	NOUN
ejpam-855	66	13	−	−	PROPN
ejpam-855	66	14	cl({x})∩λr	cl({x})∩λr	NOUN
ejpam-855	66	15	−	−	NOUN
ejpam-855	66	16	cl({y	cl({y	X
ejpam-855	66	17	}	}	PUNCT
ejpam-855	66	18	)	)	PUNCT
ejpam-855	67	1	and	and	CCONJ
ejpam-855	67	2	x	x	X
ejpam-855	67	3	/∈	/∈	INTJ
ejpam-855	68	1	λr	λr	INTJ
ejpam-855	68	2	−	−	PROPN
ejpam-855	68	3	cl({y	cl({y	X
ejpam-855	68	4	}	}	PUNCT
ejpam-855	68	5	)	)	PUNCT
ejpam-855	68	6	,	,	PUNCT
ejpam-855	68	7	then	then	ADV
ejpam-855	68	8	x	x	SYM
ejpam-855	68	9	∈	∈	PROPN
ejpam-855	68	10	x	x	X
ejpam-855	68	11	−	−	PROPN
ejpam-855	68	12	(	(	PUNCT
ejpam-855	68	13	λr	λr	INTJ
ejpam-855	68	14	−	−	PROPN
ejpam-855	68	15	cl({y	cl({y	NOUN
ejpam-855	68	16	}	}	PUNCT
ejpam-855	68	17	)	)	PUNCT
ejpam-855	68	18	)	)	PUNCT
ejpam-855	68	19	and	and	CCONJ
ejpam-855	68	20	s.	s.	PROPN
ejpam-855	68	21	missier	missier	PROPN
ejpam-855	68	22	,	,	PUNCT
ejpam-855	68	23	m.	m.	NOUN
ejpam-855	68	24	jeyanthi	jeyanthi	PROPN
ejpam-855	68	25	,	,	PUNCT
ejpam-855	68	26	a.	a.	PROPN
ejpam-855	68	27	kılıçman	kılıçman	PROPN
ejpam-855	68	28	/	/	SYM
ejpam-855	68	29	eur	eur	PROPN
ejpam-855	68	30	.	.	PUNCT
ejpam-855	69	1	j.	j.	PROPN
ejpam-855	69	2	pure	pure	PROPN
ejpam-855	69	3	appl	appl	PROPN
ejpam-855	69	4	.	.	PROPN
ejpam-855	69	5	math	math	PROPN
ejpam-855	69	6	,	,	PUNCT
ejpam-855	69	7	5	5	NUM
ejpam-855	69	8	(	(	PUNCT
ejpam-855	69	9	2012	2012	NUM
ejpam-855	69	10	)	)	PUNCT
ejpam-855	69	11	,	,	PUNCT
ejpam-855	69	12	357	357	NUM
ejpam-855	69	13	-	-	SYM
ejpam-855	69	14	364	364	NUM
ejpam-855	69	15	359	359	NUM
ejpam-855	69	16	x	x	NOUN
ejpam-855	69	17	−	−	PROPN
ejpam-855	70	1	(	(	PUNCT
ejpam-855	70	2	λr	λr	INTJ
ejpam-855	70	3	−	−	PROPN
ejpam-855	70	4	cl({y	cl({y	X
ejpam-855	70	5	}	}	PUNCT
ejpam-855	70	6	)	)	PUNCT
ejpam-855	70	7	)	)	PUNCT
ejpam-855	70	8	is	be	AUX
ejpam-855	70	9	λr	λr	NOUN
ejpam-855	70	10	-open	-open	ADJ
ejpam-855	70	11	.	.	PUNCT
ejpam-855	71	1	since	since	SCONJ
ejpam-855	71	2	(	(	PUNCT
ejpam-855	71	3	x	x	X
ejpam-855	71	4	,	,	PUNCT
ejpam-855	71	5	τ	τ	X
ejpam-855	71	6	)	)	PUNCT
ejpam-855	71	7	is	be	AUX
ejpam-855	71	8	λr	λr	ADP
ejpam-855	71	9	−	−	PROPN
ejpam-855	71	10	r0	r0	NOUN
ejpam-855	71	11	,	,	PUNCT
ejpam-855	71	12	λr	λr	VERB
ejpam-855	71	13	−	−	NOUN
ejpam-855	71	14	cl({x	cl({x	NOUN
ejpam-855	71	15	}	}	PUNCT
ejpam-855	71	16	)	)	PUNCT
ejpam-855	72	1	⊆	⊆	NUM
ejpam-855	72	2	x	x	SYM
ejpam-855	72	3	−	−	PROPN
ejpam-855	72	4	(	(	PUNCT
ejpam-855	72	5	λr	λr	INTJ
ejpam-855	72	6	−	−	PROPN
ejpam-855	72	7	cl({y	cl({y	NOUN
ejpam-855	72	8	}	}	PUNCT
ejpam-855	72	9	)	)	PUNCT
ejpam-855	72	10	)	)	PUNCT
ejpam-855	72	11	.	.	PUNCT
ejpam-855	73	1	therefore	therefore	ADV
ejpam-855	73	2	λr	λr	ADP
ejpam-855	73	3	−	−	NOUN
ejpam-855	73	4	cl({x})∩λr	cl({x})∩λr	NOUN
ejpam-855	73	5	−	−	NOUN
ejpam-855	73	6	cl({y	cl({y	X
ejpam-855	73	7	}	}	PUNCT
ejpam-855	73	8	)	)	PUNCT
ejpam-855	73	9	=	=	SYM
ejpam-855	73	10	;	;	PUNCT
ejpam-855	73	11	.	.	PUNCT
ejpam-855	74	1	this	this	PRON
ejpam-855	74	2	is	be	AUX
ejpam-855	74	3	a	a	DET
ejpam-855	74	4	contradiction	contradiction	NOUN
ejpam-855	74	5	.	.	PUNCT
ejpam-855	75	1	hence	hence	ADV
ejpam-855	75	2	{	{	PUNCT
ejpam-855	75	3	x	x	INTJ
ejpam-855	75	4	,	,	PUNCT
ejpam-855	75	5	y	y	PROPN
ejpam-855	75	6	}	}	PUNCT
ejpam-855	75	7	⊆	⊆	NUM
ejpam-855	75	8	λr	λr	NOUN
ejpam-855	75	9	−	−	NOUN
ejpam-855	75	10	cl({x})∩λr	cl({x})∩λr	NOUN
ejpam-855	75	11	−	−	NOUN
ejpam-855	75	12	cl({y	cl({y	X
ejpam-855	75	13	}	}	PUNCT
ejpam-855	75	14	)	)	PUNCT
ejpam-855	75	15	.	.	PUNCT
ejpam-855	76	1	case(ii	case(ii	ADJ
ejpam-855	76	2	):	):	PUNCT
ejpam-855	76	3	suppose	suppose	VERB
ejpam-855	76	4	{	{	PUNCT
ejpam-855	76	5	x	x	X
ejpam-855	76	6	,	,	PUNCT
ejpam-855	76	7	y	y	PROPN
ejpam-855	76	8	}	}	PUNCT
ejpam-855	76	9	is	be	AUX
ejpam-855	76	10	not	not	PART
ejpam-855	76	11	a	a	DET
ejpam-855	76	12	subset	subset	NOUN
ejpam-855	76	13	of	of	ADP
ejpam-855	76	14	λr−	λr−	PROPN
ejpam-855	76	15	cl({x})∩λr−	cl({x})∩λr−	NOUN
ejpam-855	76	16	cl({y	cl({y	X
ejpam-855	76	17	}	}	PUNCT
ejpam-855	76	18	)	)	PUNCT
ejpam-855	76	19	and	and	CCONJ
ejpam-855	76	20	let	let	VERB
ejpam-855	76	21	x	x	X
ejpam-855	76	22	/∈	/∈	PUNCT
ejpam-855	76	23	λr−	λr−	PUNCT
ejpam-855	76	24	cl({y	cl({y	NOUN
ejpam-855	76	25	}	}	PUNCT
ejpam-855	76	26	)	)	PUNCT
ejpam-855	76	27	.	.	PUNCT
ejpam-855	77	1	then	then	ADV
ejpam-855	77	2	x	x	SYM
ejpam-855	77	3	∈	∈	PROPN
ejpam-855	77	4	x	x	X
ejpam-855	77	5	−	−	PROPN
ejpam-855	77	6	(	(	PUNCT
ejpam-855	77	7	λr	λr	INTJ
ejpam-855	77	8	−	−	PROPN
ejpam-855	77	9	cl({y	cl({y	NOUN
ejpam-855	77	10	}	}	PUNCT
ejpam-855	77	11	)	)	PUNCT
ejpam-855	77	12	)	)	PUNCT
ejpam-855	78	1	and	and	CCONJ
ejpam-855	78	2	x	x	SYM
ejpam-855	78	3	−	−	PROPN
ejpam-855	78	4	(	(	PUNCT
ejpam-855	78	5	λr	λr	INTJ
ejpam-855	78	6	−	−	PROPN
ejpam-855	78	7	cl({y	cl({y	X
ejpam-855	78	8	}	}	PUNCT
ejpam-855	78	9	)	)	PUNCT
ejpam-855	78	10	)	)	PUNCT
ejpam-855	78	11	is	be	AUX
ejpam-855	78	12	λr	λr	NOUN
ejpam-855	78	13	-open	-open	ADJ
ejpam-855	78	14	.	.	PUNCT
ejpam-855	79	1	since	since	SCONJ
ejpam-855	79	2	(	(	PUNCT
ejpam-855	79	3	x	x	X
ejpam-855	79	4	,	,	PUNCT
ejpam-855	79	5	τ	τ	X
ejpam-855	79	6	)	)	PUNCT
ejpam-855	79	7	is	be	AUX
ejpam-855	79	8	λr	λr	ADP
ejpam-855	79	9	−	−	PROPN
ejpam-855	79	10	r0	r0	NOUN
ejpam-855	79	11	,	,	PUNCT
ejpam-855	79	12	λr	λr	VERB
ejpam-855	79	13	−	−	NOUN
ejpam-855	79	14	cl({x	cl({x	NOUN
ejpam-855	79	15	}	}	PUNCT
ejpam-855	79	16	)	)	PUNCT
ejpam-855	80	1	⊆	⊆	NUM
ejpam-855	80	2	x	x	SYM
ejpam-855	80	3	−	−	PROPN
ejpam-855	80	4	(	(	PUNCT
ejpam-855	80	5	λr	λr	INTJ
ejpam-855	80	6	−	−	PROPN
ejpam-855	80	7	cl({y	cl({y	NOUN
ejpam-855	80	8	}	}	PUNCT
ejpam-855	80	9	)	)	PUNCT
ejpam-855	80	10	)	)	PUNCT
ejpam-855	80	11	and	and	CCONJ
ejpam-855	80	12	hence	hence	ADV
ejpam-855	80	13	λr	λr	ADP
ejpam-855	80	14	−	−	NOUN
ejpam-855	80	15	cl({x})∩λr	cl({x})∩λr	NOUN
ejpam-855	80	16	−	−	NOUN
ejpam-855	80	17	cl({y	cl({y	X
ejpam-855	80	18	}	}	PUNCT
ejpam-855	80	19	)	)	PUNCT
ejpam-855	80	20	=	=	SYM
ejpam-855	80	21	;	;	PUNCT
ejpam-855	80	22	.	.	PUNCT
ejpam-855	81	1	conversely	conversely	ADV
ejpam-855	81	2	,	,	PUNCT
ejpam-855	81	3	let	let	VERB
ejpam-855	81	4	u	u	PRON
ejpam-855	81	5	be	be	AUX
ejpam-855	81	6	a	a	DET
ejpam-855	81	7	λr	λr	NOUN
ejpam-855	81	8	-open	-open	NOUN
ejpam-855	81	9	set	set	VERB
ejpam-855	81	10	and	and	CCONJ
ejpam-855	81	11	x	x	SYM
ejpam-855	81	12	∈	∈	PROPN
ejpam-855	81	13	u	u	PROPN
ejpam-855	81	14	.	.	PUNCT
ejpam-855	81	15	suppose	suppose	VERB
ejpam-855	82	1	λr	λr	ADP
ejpam-855	82	2	−	−	PROPN
ejpam-855	82	3	cl({x	cl({x	NOUN
ejpam-855	82	4	}	}	PUNCT
ejpam-855	82	5	)	)	PUNCT
ejpam-855	82	6	is	be	AUX
ejpam-855	82	7	not	not	PART
ejpam-855	82	8	a	a	DET
ejpam-855	82	9	subset	subset	NOUN
ejpam-855	82	10	of	of	ADP
ejpam-855	82	11	u	u	PROPN
ejpam-855	82	12	.	.	PUNCT
ejpam-855	83	1	then	then	ADV
ejpam-855	83	2	∃	∃	PROPN
ejpam-855	83	3	a	a	DET
ejpam-855	83	4	point	point	NOUN
ejpam-855	83	5	y	y	PROPN
ejpam-855	83	6	∈	∈	PROPN
ejpam-855	83	7	λr	λr	VERB
ejpam-855	83	8	−	−	PROPN
ejpam-855	83	9	cl({x	cl({x	NOUN
ejpam-855	83	10	}	}	PUNCT
ejpam-855	83	11	)	)	PUNCT
ejpam-855	84	1	such	such	ADJ
ejpam-855	84	2	that	that	SCONJ
ejpam-855	84	3	y	y	PROPN
ejpam-855	84	4	/∈	/∈	PUNCT
ejpam-855	84	5	u	u	PROPN
ejpam-855	84	6	.	.	PUNCT
ejpam-855	85	1	that	that	PRON
ejpam-855	85	2	implies	imply	VERB
ejpam-855	85	3	y	y	PROPN
ejpam-855	85	4	∈	∈	PROPN
ejpam-855	85	5	x	x	PUNCT
ejpam-855	85	6	−	−	NOUN
ejpam-855	85	7	u	u	NOUN
ejpam-855	85	8	and	and	CCONJ
ejpam-855	85	9	x	x	SYM
ejpam-855	85	10	−	−	NOUN
ejpam-855	85	11	u	u	NOUN
ejpam-855	85	12	is	be	AUX
ejpam-855	85	13	λr	λr	ADP
ejpam-855	85	14	-closed	-close	VERB
ejpam-855	85	15	.	.	PUNCT
ejpam-855	86	1	since	since	SCONJ
ejpam-855	86	2	λr−	λr−	PROPN
ejpam-855	86	3	cl({y	cl({y	X
ejpam-855	86	4	}	}	PUNCT
ejpam-855	86	5	)	)	PUNCT
ejpam-855	86	6	is	be	AUX
ejpam-855	86	7	the	the	DET
ejpam-855	86	8	smallest	small	ADJ
ejpam-855	86	9	λr	λr	NOUN
ejpam-855	86	10	-closed	-close	VERB
ejpam-855	86	11	set	set	NOUN
ejpam-855	86	12	containing	contain	VERB
ejpam-855	86	13	y	y	PROPN
ejpam-855	86	14	,	,	PUNCT
ejpam-855	86	15	λr−	λr−	PROPN
ejpam-855	86	16	cl({y	cl({y	X
ejpam-855	86	17	}	}	PUNCT
ejpam-855	86	18	)	)	PUNCT
ejpam-855	87	1	⊆	⊆	NUM
ejpam-855	87	2	x	x	X
ejpam-855	87	3	−u	−u	NOUN
ejpam-855	87	4	and	and	CCONJ
ejpam-855	87	5	hence	hence	ADV
ejpam-855	87	6	λr	λr	ADP
ejpam-855	87	7	−	−	PROPN
ejpam-855	87	8	cl({y	cl({y	X
ejpam-855	87	9	}	}	PUNCT
ejpam-855	87	10	)	)	PUNCT
ejpam-855	87	11	∩	∩	NOUN
ejpam-855	87	12	u	u	NOUN
ejpam-855	87	13	=	=	PUNCT
ejpam-855	87	14	;	;	PUNCT
ejpam-855	87	15	.	.	PUNCT
ejpam-855	88	1	since	since	SCONJ
ejpam-855	88	2	x	x	PROPN
ejpam-855	88	3	∈	∈	PROPN
ejpam-855	88	4	u	u	NOUN
ejpam-855	88	5	,	,	PUNCT
ejpam-855	88	6	x	x	PROPN
ejpam-855	88	7	/∈	/∈	PUNCT
ejpam-855	88	8	λr	λr	INTJ
ejpam-855	88	9	−	−	PROPN
ejpam-855	88	10	cl({y	cl({y	X
ejpam-855	88	11	}	}	PUNCT
ejpam-855	88	12	)	)	PUNCT
ejpam-855	88	13	and	and	CCONJ
ejpam-855	88	14	hence	hence	ADV
ejpam-855	88	15	{	{	PUNCT
ejpam-855	88	16	x	x	SYM
ejpam-855	88	17	,	,	PUNCT
ejpam-855	88	18	y	y	PROPN
ejpam-855	88	19	}	}	PUNCT
ejpam-855	88	20	is	be	AUX
ejpam-855	88	21	not	not	PART
ejpam-855	88	22	a	a	DET
ejpam-855	88	23	subset	subset	NOUN
ejpam-855	88	24	of	of	ADP
ejpam-855	88	25	λr	λr	ADP
ejpam-855	88	26	−	−	PROPN
ejpam-855	88	27	cl({x	cl({x	NUM
ejpam-855	88	28	}	}	PUNCT
ejpam-855	88	29	)	)	PUNCT
ejpam-855	88	30	∩	∩	NOUN
ejpam-855	88	31	λr	λr	ADP
ejpam-855	88	32	−	−	PROPN
ejpam-855	88	33	cl({y	cl({y	NOUN
ejpam-855	88	34	}	}	PUNCT
ejpam-855	88	35	)	)	PUNCT
ejpam-855	88	36	.	.	PUNCT
ejpam-855	89	1	also	also	ADV
ejpam-855	89	2	y	y	PROPN
ejpam-855	89	3	∈	∈	PROPN
ejpam-855	89	4	λr	λr	VERB
ejpam-855	89	5	−	−	PROPN
ejpam-855	89	6	cl({x	cl({x	NOUN
ejpam-855	89	7	}	}	PUNCT
ejpam-855	89	8	)	)	PUNCT
ejpam-855	89	9	∩	∩	NOUN
ejpam-855	89	10	λr	λr	ADP
ejpam-855	89	11	−	−	PROPN
ejpam-855	89	12	cl({y	cl({y	NOUN
ejpam-855	89	13	}	}	PUNCT
ejpam-855	89	14	)	)	PUNCT
ejpam-855	89	15	.	.	PUNCT
ejpam-855	90	1	that	that	PRON
ejpam-855	90	2	implies	imply	VERB
ejpam-855	90	3	λr	λr	ADP
ejpam-855	90	4	−	−	NOUN
ejpam-855	90	5	cl({x})∩λr	cl({x})∩λr	NOUN
ejpam-855	90	6	−	−	NOUN
ejpam-855	90	7	cl({y	cl({y	X
ejpam-855	90	8	}	}	PUNCT
ejpam-855	90	9	)	)	PUNCT
ejpam-855	90	10	6=	6=	NUM
ejpam-855	90	11	;	;	PUNCT
ejpam-855	90	12	.	.	PUNCT
ejpam-855	91	1	so	so	ADV
ejpam-855	91	2	by	by	ADP
ejpam-855	91	3	this	this	DET
ejpam-855	91	4	contradiction	contradiction	NOUN
ejpam-855	91	5	,	,	PUNCT
ejpam-855	91	6	λr	λr	ADP
ejpam-855	91	7	−	−	NOUN
ejpam-855	91	8	cl({x	cl({x	NOUN
ejpam-855	91	9	}	}	PUNCT
ejpam-855	91	10	)	)	PUNCT
ejpam-855	92	1	⊆	⊆	NUM
ejpam-855	92	2	u	u	NOUN
ejpam-855	92	3	and	and	CCONJ
ejpam-855	92	4	hence	hence	ADV
ejpam-855	92	5	(	(	PUNCT
ejpam-855	92	6	x	x	X
ejpam-855	92	7	,	,	PUNCT
ejpam-855	92	8	τ	τ	X
ejpam-855	92	9	)	)	PUNCT
ejpam-855	92	10	is	be	AUX
ejpam-855	92	11	λr	λr	ADP
ejpam-855	92	12	−	−	PROPN
ejpam-855	92	13	r0	r0	NOUN
ejpam-855	92	14	.	.	PUNCT
ejpam-855	93	1	theorem	theorem	NOUN
ejpam-855	93	2	3	3	NUM
ejpam-855	93	3	.	.	X
ejpam-855	93	4	for	for	ADP
ejpam-855	93	5	any	any	DET
ejpam-855	93	6	points	point	NOUN
ejpam-855	93	7	x	x	PUNCT
ejpam-855	93	8	and	and	CCONJ
ejpam-855	93	9	y	y	PROPN
ejpam-855	93	10	in	in	ADP
ejpam-855	93	11	a	a	DET
ejpam-855	93	12	topological	topological	ADJ
ejpam-855	93	13	space	space	NOUN
ejpam-855	93	14	(	(	PUNCT
ejpam-855	93	15	x	x	X
ejpam-855	93	16	,	,	PUNCT
ejpam-855	93	17	τ	τ	PROPN
ejpam-855	93	18	)	)	PUNCT
ejpam-855	93	19	,	,	PUNCT
ejpam-855	93	20	the	the	DET
ejpam-855	93	21	following	follow	VERB
ejpam-855	93	22	are	be	AUX
ejpam-855	93	23	equivalent	equivalent	ADJ
ejpam-855	93	24	:	:	PUNCT
ejpam-855	93	25	(	(	PUNCT
ejpam-855	93	26	1	1	X
ejpam-855	93	27	)	)	PUNCT
ejpam-855	93	28	λr	λr	VERB
ejpam-855	93	29	−	−	PROPN
ejpam-855	93	30	ker({x	ker({x	NOUN
ejpam-855	93	31	}	}	PUNCT
ejpam-855	93	32	)	)	PUNCT
ejpam-855	94	1	6=	6=	ADP
ejpam-855	94	2	λr	λr	ADP
ejpam-855	94	3	−	−	PROPN
ejpam-855	94	4	ker({y	ker({y	PROPN
ejpam-855	94	5	}	}	PUNCT
ejpam-855	94	6	)	)	PUNCT
ejpam-855	94	7	,	,	PUNCT
ejpam-855	94	8	(	(	PUNCT
ejpam-855	94	9	2	2	X
ejpam-855	94	10	)	)	PUNCT
ejpam-855	94	11	λr	λr	ADP
ejpam-855	94	12	−	−	PROPN
ejpam-855	94	13	cl({x	cl({x	NOUN
ejpam-855	94	14	}	}	PUNCT
ejpam-855	94	15	)	)	PUNCT
ejpam-855	94	16	6=	6=	ADP
ejpam-855	94	17	λr	λr	ADP
ejpam-855	94	18	−	−	PROPN
ejpam-855	94	19	cl({y	cl({y	NOUN
ejpam-855	94	20	}	}	PUNCT
ejpam-855	94	21	)	)	PUNCT
ejpam-855	94	22	.	.	PUNCT
ejpam-855	95	1	proof	proof	NOUN
ejpam-855	95	2	.	.	PUNCT
ejpam-855	96	1	(	(	PUNCT
ejpam-855	96	2	1)⇒	1)⇒	NUM
ejpam-855	96	3	(	(	PUNCT
ejpam-855	96	4	2	2	NUM
ejpam-855	96	5	)	)	PUNCT
ejpam-855	96	6	suppose	suppose	VERB
ejpam-855	96	7	λr	λr	INTJ
ejpam-855	96	8	−	−	NOUN
ejpam-855	96	9	ker({x	ker({x	NOUN
ejpam-855	96	10	}	}	PUNCT
ejpam-855	96	11	)	)	PUNCT
ejpam-855	97	1	6=	6=	ADP
ejpam-855	97	2	λr	λr	ADP
ejpam-855	97	3	−	−	PROPN
ejpam-855	97	4	ker({y	ker({y	PROPN
ejpam-855	97	5	}	}	PUNCT
ejpam-855	97	6	)	)	PUNCT
ejpam-855	97	7	.	.	PUNCT
ejpam-855	98	1	then	then	ADV
ejpam-855	98	2	∃	∃	PROPN
ejpam-855	98	3	a	a	DET
ejpam-855	98	4	point	point	NOUN
ejpam-855	98	5	z	z	NOUN
ejpam-855	98	6	in	in	ADP
ejpam-855	98	7	x	x	PUNCT
ejpam-855	98	8	such	such	ADJ
ejpam-855	98	9	that	that	SCONJ
ejpam-855	98	10	z	z	PROPN
ejpam-855	98	11	∈	∈	PROPN
ejpam-855	98	12	λr	λr	VERB
ejpam-855	98	13	−	−	PROPN
ejpam-855	98	14	ker({x	ker({x	NOUN
ejpam-855	98	15	}	}	PUNCT
ejpam-855	98	16	)	)	PUNCT
ejpam-855	98	17	and	and	CCONJ
ejpam-855	98	18	z	z	NOUN
ejpam-855	98	19	/∈	/∈	PUNCT
ejpam-855	98	20	λr	λr	NOUN
ejpam-855	98	21	−	−	PROPN
ejpam-855	98	22	ker({y})⇒	ker({y})⇒	PROPN
ejpam-855	98	23	λr	λr	ADP
ejpam-855	98	24	−	−	NOUN
ejpam-855	98	25	cl({z	cl({z	ADJ
ejpam-855	98	26	}	}	PUNCT
ejpam-855	98	27	)	)	PUNCT
ejpam-855	98	28	∩	∩	NOUN
ejpam-855	98	29	{	{	PUNCT
ejpam-855	98	30	x	x	X
ejpam-855	98	31	}	}	PUNCT
ejpam-855	98	32	6=	6=	NUM
ejpam-855	98	33	;	;	PUNCT
ejpam-855	98	34	and	and	CCONJ
ejpam-855	98	35	λr	λr	ADP
ejpam-855	98	36	−	−	PROPN
ejpam-855	98	37	cl({z})∩{y	cl({z})∩{y	NOUN
ejpam-855	98	38	}	}	PUNCT
ejpam-855	98	39	=	=	SYM
ejpam-855	98	40	;	;	PUNCT
ejpam-855	98	41	⇒	⇒	NOUN
ejpam-855	98	42	x	x	PUNCT
ejpam-855	98	43	∈	∈	NOUN
ejpam-855	98	44	λr	λr	VERB
ejpam-855	98	45	−	−	NOUN
ejpam-855	98	46	cl({z	cl({z	NOUN
ejpam-855	98	47	}	}	PUNCT
ejpam-855	98	48	)	)	PUNCT
ejpam-855	98	49	and	and	CCONJ
ejpam-855	98	50	y	y	PROPN
ejpam-855	98	51	/∈	/∈	PUNCT
ejpam-855	99	1	λr	λr	NOUN
ejpam-855	99	2	−	−	PROPN
ejpam-855	99	3	cl({z})⇒	cl({z})⇒	NOUN
ejpam-855	99	4	λr	λr	ADP
ejpam-855	99	5	−	−	PROPN
ejpam-855	99	6	cl({x	cl({x	NOUN
ejpam-855	99	7	}	}	PUNCT
ejpam-855	99	8	)	)	PUNCT
ejpam-855	100	1	⊆	⊆	NUM
ejpam-855	100	2	λr	λr	NOUN
ejpam-855	100	3	−	−	NOUN
ejpam-855	100	4	cl({z	cl({z	NOUN
ejpam-855	100	5	}	}	PUNCT
ejpam-855	100	6	)	)	PUNCT
ejpam-855	100	7	and	and	CCONJ
ejpam-855	100	8	y	y	PROPN
ejpam-855	100	9	/∈	/∈	PUNCT
ejpam-855	101	1	λr	λr	INTJ
ejpam-855	101	2	−	−	PROPN
ejpam-855	101	3	cl({z})⇒	cl({z})⇒	NOUN
ejpam-855	101	4	y	y	PROPN
ejpam-855	101	5	/∈	/∈	PUNCT
ejpam-855	102	1	λr	λr	NOUN
ejpam-855	102	2	−	−	PROPN
ejpam-855	102	3	cl({x})⇒	cl({x})⇒	NOUN
ejpam-855	102	4	λr	λr	ADP
ejpam-855	102	5	−	−	PROPN
ejpam-855	102	6	cl({x	cl({x	NOUN
ejpam-855	102	7	}	}	PUNCT
ejpam-855	102	8	)	)	PUNCT
ejpam-855	102	9	6=	6=	ADP
ejpam-855	102	10	λr	λr	ADP
ejpam-855	102	11	−	−	PROPN
ejpam-855	102	12	cl({y	cl({y	NOUN
ejpam-855	102	13	}	}	PUNCT
ejpam-855	102	14	)	)	PUNCT
ejpam-855	102	15	.	.	PUNCT
ejpam-855	103	1	(	(	PUNCT
ejpam-855	103	2	2)⇒	2)⇒	NUM
ejpam-855	103	3	(	(	PUNCT
ejpam-855	103	4	1	1	X
ejpam-855	103	5	)	)	PUNCT
ejpam-855	103	6	suppose	suppose	VERB
ejpam-855	103	7	λr−cl({x	λr−cl({x	NOUN
ejpam-855	103	8	}	}	PUNCT
ejpam-855	103	9	)	)	PUNCT
ejpam-855	103	10	6=	6=	PUNCT
ejpam-855	104	1	λr−cl({y	λr−cl({y	SYM
ejpam-855	104	2	}	}	PUNCT
ejpam-855	104	3	)	)	PUNCT
ejpam-855	104	4	.	.	PUNCT
ejpam-855	105	1	then	then	ADV
ejpam-855	105	2	∃	∃	PROPN
ejpam-855	105	3	a	a	DET
ejpam-855	105	4	point	point	NOUN
ejpam-855	105	5	z	z	NOUN
ejpam-855	105	6	in	in	ADP
ejpam-855	105	7	x	x	PUNCT
ejpam-855	105	8	such	such	ADJ
ejpam-855	105	9	that	that	SCONJ
ejpam-855	105	10	z	z	PROPN
ejpam-855	105	11	∈	∈	PROPN
ejpam-855	105	12	λr−cl({x	λr−cl({x	NOUN
ejpam-855	105	13	}	}	PUNCT
ejpam-855	105	14	)	)	PUNCT
ejpam-855	105	15	and	and	CCONJ
ejpam-855	105	16	z	z	NOUN
ejpam-855	105	17	/∈	/∈	PUNCT
ejpam-855	105	18	λr−cl({y	λr−cl({y	PROPN
ejpam-855	105	19	}	}	PUNCT
ejpam-855	105	20	)	)	PUNCT
ejpam-855	105	21	.	.	PUNCT
ejpam-855	106	1	that	that	PRON
ejpam-855	106	2	implies	imply	VERB
ejpam-855	106	3	∃	∃	PROPN
ejpam-855	106	4	a	a	DET
ejpam-855	106	5	λr	λr	NOUN
ejpam-855	106	6	-open	-open	ADJ
ejpam-855	106	7	set	set	VERB
ejpam-855	106	8	v	v	NOUN
ejpam-855	106	9	containing	contain	VERB
ejpam-855	106	10	z	z	NOUN
ejpam-855	106	11	such	such	ADJ
ejpam-855	106	12	that	that	SCONJ
ejpam-855	106	13	x	x	SYM
ejpam-855	106	14	v	v	ADP
ejpam-855	106	15	∈	∈	NUM
ejpam-855	106	16	v	v	NOUN
ejpam-855	106	17	and	and	CCONJ
ejpam-855	106	18	y	y	PROPN
ejpam-855	106	19	/∈	/∈	PUNCT
ejpam-855	107	1	v	v	INTJ
ejpam-855	107	2	.	.	PUNCT
ejpam-855	108	1	that	that	PRON
ejpam-855	108	2	is	is	ADV
ejpam-855	108	3	,	,	PUNCT
ejpam-855	108	4	v	v	NOUN
ejpam-855	108	5	is	be	AUX
ejpam-855	108	6	a	a	DET
ejpam-855	108	7	λr	λr	NOUN
ejpam-855	108	8	-open	-open	ADJ
ejpam-855	108	9	set	set	NOUN
ejpam-855	108	10	containing	contain	VERB
ejpam-855	108	11	x	x	PUNCT
ejpam-855	108	12	but	but	CCONJ
ejpam-855	108	13	not	not	PART
ejpam-855	108	14	y.	y.	NOUN
ejpam-855	108	15	if	if	SCONJ
ejpam-855	108	16	y	y	PROPN
ejpam-855	108	17	∈	∈	PROPN
ejpam-855	108	18	λr−ker({x	λr−ker({x	PROPN
ejpam-855	108	19	}	}	PUNCT
ejpam-855	108	20	)	)	PUNCT
ejpam-855	108	21	,	,	PUNCT
ejpam-855	108	22	then	then	ADV
ejpam-855	108	23	x	x	X
ejpam-855	108	24	∈	∈	NOUN
ejpam-855	108	25	λr−cl({y	λr−cl({y	PROPN
ejpam-855	108	26	}	}	PUNCT
ejpam-855	108	27	)	)	PUNCT
ejpam-855	108	28	.	.	PUNCT
ejpam-855	109	1	that	that	PRON
ejpam-855	109	2	implies	imply	VERB
ejpam-855	109	3	for	for	SCONJ
ejpam-855	109	4	every	every	DET
ejpam-855	109	5	λr	λr	NOUN
ejpam-855	109	6	-open	-open	ADJ
ejpam-855	109	7	set	set	VERB
ejpam-855	109	8	g	g	NOUN
ejpam-855	109	9	containing	contain	VERB
ejpam-855	109	10	x	x	SYM
ejpam-855	109	11	,	,	PUNCT
ejpam-855	109	12	g	g	PROPN
ejpam-855	109	13	∩	∩	X
ejpam-855	109	14	{	{	PUNCT
ejpam-855	109	15	y	y	NOUN
ejpam-855	109	16	}	}	PUNCT
ejpam-855	109	17	6=	6=	NUM
ejpam-855	109	18	;	;	PUNCT
ejpam-855	109	19	.	.	PUNCT
ejpam-855	110	1	that	that	PRON
ejpam-855	110	2	is	be	AUX
ejpam-855	110	3	,	,	PUNCT
ejpam-855	110	4	y	y	PROPN
ejpam-855	110	5	∈	∈	PROPN
ejpam-855	110	6	g.	g.	NOUN
ejpam-855	110	7	by	by	ADP
ejpam-855	110	8	this	this	DET
ejpam-855	110	9	contradiction	contradiction	NOUN
ejpam-855	110	10	,	,	PUNCT
ejpam-855	110	11	y	y	PROPN
ejpam-855	110	12	/∈	/∈	PUNCT
ejpam-855	111	1	λr	λr	INTJ
ejpam-855	111	2	−	−	PROPN
ejpam-855	111	3	ker({x	ker({x	NOUN
ejpam-855	111	4	}	}	PUNCT
ejpam-855	111	5	)	)	PUNCT
ejpam-855	111	6	and	and	CCONJ
ejpam-855	111	7	hence	hence	ADV
ejpam-855	111	8	λr	λr	ADP
ejpam-855	111	9	−	−	PROPN
ejpam-855	111	10	ker({x	ker({x	NOUN
ejpam-855	111	11	}	}	PUNCT
ejpam-855	111	12	)	)	PUNCT
ejpam-855	112	1	6=	6=	ADP
ejpam-855	112	2	λr	λr	ADP
ejpam-855	112	3	−	−	PROPN
ejpam-855	112	4	ker({y	ker({y	PROPN
ejpam-855	112	5	}	}	PUNCT
ejpam-855	112	6	)	)	PUNCT
ejpam-855	112	7	.	.	PUNCT
ejpam-855	113	1	theorem	theorem	ADJ
ejpam-855	113	2	4	4	NUM
ejpam-855	113	3	.	.	X
ejpam-855	114	1	for	for	ADP
ejpam-855	114	2	a	a	DET
ejpam-855	114	3	topological	topological	ADJ
ejpam-855	114	4	space	space	NOUN
ejpam-855	114	5	(	(	PUNCT
ejpam-855	114	6	x	x	X
ejpam-855	114	7	,	,	PUNCT
ejpam-855	114	8	τ	τ	PROPN
ejpam-855	114	9	)	)	PUNCT
ejpam-855	114	10	,	,	PUNCT
ejpam-855	114	11	the	the	DET
ejpam-855	114	12	following	follow	VERB
ejpam-855	114	13	are	be	AUX
ejpam-855	114	14	equivalent	equivalent	ADJ
ejpam-855	114	15	:	:	PUNCT
ejpam-855	114	16	(	(	PUNCT
ejpam-855	114	17	1	1	X
ejpam-855	114	18	)	)	PUNCT
ejpam-855	114	19	(	(	PUNCT
ejpam-855	114	20	x	x	X
ejpam-855	114	21	,	,	PUNCT
ejpam-855	114	22	τ	τ	X
ejpam-855	114	23	)	)	PUNCT
ejpam-855	114	24	is	be	AUX
ejpam-855	114	25	λr	λr	ADP
ejpam-855	114	26	−	−	PROPN
ejpam-855	114	27	r0	r0	NOUN
ejpam-855	114	28	,	,	PUNCT
ejpam-855	114	29	(	(	PUNCT
ejpam-855	114	30	2	2	X
ejpam-855	114	31	)	)	PUNCT
ejpam-855	114	32	for	for	ADP
ejpam-855	114	33	any	any	DET
ejpam-855	114	34	non	non	ADJ
ejpam-855	114	35	-	-	ADJ
ejpam-855	114	36	empty	empty	ADJ
ejpam-855	114	37	set	set	NOUN
ejpam-855	114	38	a	a	PRON
ejpam-855	114	39	and	and	CCONJ
ejpam-855	114	40	g	g	PROPN
ejpam-855	114	41	∈	∈	PROPN
ejpam-855	115	1	λro(x	λro(x	PROPN
ejpam-855	115	2	,	,	PUNCT
ejpam-855	115	3	τ	τ	PROPN
ejpam-855	115	4	)	)	PUNCT
ejpam-855	115	5	such	such	ADJ
ejpam-855	115	6	that	that	SCONJ
ejpam-855	115	7	a∩	a∩	PROPN
ejpam-855	115	8	g	g	PROPN
ejpam-855	115	9	6=	6=	PROPN
ejpam-855	115	10	;	;	PUNCT
ejpam-855	115	11	,	,	PUNCT
ejpam-855	115	12	∃f	∃f	PROPN
ejpam-855	115	13	∈	∈	PROPN
ejpam-855	115	14	λr	λr	ADP
ejpam-855	115	15	c(x	c(x	NOUN
ejpam-855	115	16	,	,	PUNCT
ejpam-855	115	17	τ	τ	PROPN
ejpam-855	115	18	)	)	PUNCT
ejpam-855	115	19	such	such	ADJ
ejpam-855	115	20	that	that	SCONJ
ejpam-855	115	21	a∩	a∩	PROPN
ejpam-855	115	22	f	f	PROPN
ejpam-855	115	23	6=	6=	PROPN
ejpam-855	115	24	;	;	PUNCT
ejpam-855	115	25	and	and	CCONJ
ejpam-855	115	26	f	f	PROPN
ejpam-855	115	27	⊆	⊆	NUM
ejpam-855	115	28	g	g	NOUN
ejpam-855	115	29	,	,	PUNCT
ejpam-855	115	30	(	(	PUNCT
ejpam-855	115	31	3	3	X
ejpam-855	115	32	)	)	PUNCT
ejpam-855	115	33	for	for	ADP
ejpam-855	115	34	any	any	DET
ejpam-855	115	35	g	g	PROPN
ejpam-855	115	36	∈	∈	PROPN
ejpam-855	115	37	λro(x	λro(x	PROPN
ejpam-855	115	38	,	,	PUNCT
ejpam-855	115	39	τ	τ	PROPN
ejpam-855	115	40	)	)	PUNCT
ejpam-855	115	41	,	,	PUNCT
ejpam-855	115	42	g	g	PROPN
ejpam-855	115	43	=	=	SYM
ejpam-855	115	44	∪{f	∪{f	PROPN
ejpam-855	115	45	/	/	SYM
ejpam-855	115	46	f	f	PROPN
ejpam-855	115	47	∈	∈	PROPN
ejpam-855	115	48	λr	λr	ADP
ejpam-855	115	49	c(x	c(x	NOUN
ejpam-855	115	50	,	,	PUNCT
ejpam-855	115	51	τ	τ	PROPN
ejpam-855	115	52	)	)	PUNCT
ejpam-855	115	53	and	and	CCONJ
ejpam-855	115	54	f	f	PROPN
ejpam-855	115	55	⊆	⊆	NUM
ejpam-855	115	56	g	g	NOUN
ejpam-855	115	57	}	}	PUNCT
ejpam-855	115	58	,	,	PUNCT
ejpam-855	115	59	(	(	PUNCT
ejpam-855	115	60	4	4	X
ejpam-855	115	61	)	)	PUNCT
ejpam-855	115	62	for	for	ADP
ejpam-855	115	63	any	any	DET
ejpam-855	115	64	f	f	PROPN
ejpam-855	115	65	∈	∈	PROPN
ejpam-855	115	66	λr	λr	ADP
ejpam-855	115	67	c(x	c(x	NOUN
ejpam-855	115	68	,	,	PUNCT
ejpam-855	115	69	τ	τ	PROPN
ejpam-855	115	70	)	)	PUNCT
ejpam-855	115	71	,	,	PUNCT
ejpam-855	115	72	f	f	PROPN
ejpam-855	116	1	=	=	PUNCT
ejpam-855	116	2	∩{g	∩{g	PROPN
ejpam-855	116	3	/	/	SYM
ejpam-855	116	4	g	g	NOUN
ejpam-855	116	5	∈	∈	PROPN
ejpam-855	116	6	λro(x	λro(x	PROPN
ejpam-855	116	7	,	,	PUNCT
ejpam-855	116	8	τ	τ	PROPN
ejpam-855	116	9	)	)	PUNCT
ejpam-855	116	10	and	and	CCONJ
ejpam-855	116	11	f	f	PROPN
ejpam-855	117	1	⊆	⊆	NUM
ejpam-855	117	2	g	g	NOUN
ejpam-855	117	3	}	}	PUNCT
ejpam-855	117	4	,	,	PUNCT
ejpam-855	117	5	(	(	PUNCT
ejpam-855	117	6	5	5	NUM
ejpam-855	117	7	)	)	PUNCT
ejpam-855	117	8	for	for	ADP
ejpam-855	117	9	any	any	DET
ejpam-855	117	10	x	x	SYM
ejpam-855	117	11	∈	∈	PROPN
ejpam-855	117	12	x	x	X
ejpam-855	117	13	,	,	PUNCT
ejpam-855	117	14	λr	λr	ADP
ejpam-855	117	15	−	−	NOUN
ejpam-855	117	16	cl({x	cl({x	NOUN
ejpam-855	117	17	}	}	PUNCT
ejpam-855	117	18	)	)	PUNCT
ejpam-855	117	19	⊆	⊆	NUM
ejpam-855	117	20	λr	λr	NOUN
ejpam-855	117	21	−	−	NOUN
ejpam-855	117	22	ker({x	ker({x	NOUN
ejpam-855	117	23	}	}	PUNCT
ejpam-855	117	24	)	)	PUNCT
ejpam-855	117	25	,	,	PUNCT
ejpam-855	117	26	s.	s.	PROPN
ejpam-855	117	27	missier	missier	PROPN
ejpam-855	117	28	,	,	PUNCT
ejpam-855	117	29	m.	m.	NOUN
ejpam-855	117	30	jeyanthi	jeyanthi	PROPN
ejpam-855	117	31	,	,	PUNCT
ejpam-855	117	32	a.	a.	PROPN
ejpam-855	117	33	kılıçman	kılıçman	PROPN
ejpam-855	117	34	/	/	SYM
ejpam-855	117	35	eur	eur	PROPN
ejpam-855	117	36	.	.	PUNCT
ejpam-855	118	1	j.	j.	PROPN
ejpam-855	118	2	pure	pure	PROPN
ejpam-855	118	3	appl	appl	PROPN
ejpam-855	118	4	.	.	PROPN
ejpam-855	118	5	math	math	PROPN
ejpam-855	118	6	,	,	PUNCT
ejpam-855	118	7	5	5	NUM
ejpam-855	118	8	(	(	PUNCT
ejpam-855	118	9	2012	2012	NUM
ejpam-855	118	10	)	)	PUNCT
ejpam-855	118	11	,	,	PUNCT
ejpam-855	118	12	357	357	NUM
ejpam-855	118	13	-	-	SYM
ejpam-855	118	14	364	364	NUM
ejpam-855	118	15	360	360	NUM
ejpam-855	118	16	(	(	PUNCT
ejpam-855	118	17	6	6	NUM
ejpam-855	118	18	)	)	PUNCT
ejpam-855	118	19	for	for	ADP
ejpam-855	118	20	any	any	DET
ejpam-855	118	21	x	x	SYM
ejpam-855	118	22	,	,	PUNCT
ejpam-855	118	23	y	y	PROPN
ejpam-855	118	24	∈	∈	PROPN
ejpam-855	118	25	x	x	X
ejpam-855	118	26	,	,	PUNCT
ejpam-855	118	27	y	y	PROPN
ejpam-855	118	28	∈	∈	PROPN
ejpam-855	118	29	λr	λr	VERB
ejpam-855	118	30	−	−	PROPN
ejpam-855	118	31	cl({x})⇔	cl({x})⇔	PROPN
ejpam-855	119	1	x	x	SYM
ejpam-855	119	2	∈	∈	PROPN
ejpam-855	119	3	λr	λr	VERB
ejpam-855	119	4	−	−	PROPN
ejpam-855	119	5	cl({y	cl({y	X
ejpam-855	119	6	}	}	PUNCT
ejpam-855	119	7	)	)	PUNCT
ejpam-855	119	8	.	.	PUNCT
ejpam-855	120	1	proof	proof	NOUN
ejpam-855	120	2	.	.	PUNCT
ejpam-855	121	1	(	(	PUNCT
ejpam-855	121	2	1	1	X
ejpam-855	121	3	)	)	PUNCT
ejpam-855	121	4	⇒	⇒	NOUN
ejpam-855	121	5	(	(	PUNCT
ejpam-855	121	6	2	2	X
ejpam-855	121	7	)	)	PUNCT
ejpam-855	121	8	let	let	VERB
ejpam-855	121	9	a	a	DET
ejpam-855	121	10	be	be	AUX
ejpam-855	121	11	any	any	DET
ejpam-855	121	12	nonempty	nonempty	NOUN
ejpam-855	121	13	subset	subset	NOUN
ejpam-855	121	14	of	of	ADP
ejpam-855	121	15	x	x	X
ejpam-855	121	16	and	and	CCONJ
ejpam-855	121	17	g	g	PROPN
ejpam-855	121	18	be	be	VERB
ejpam-855	121	19	a	a	DET
ejpam-855	121	20	λr	λr	NOUN
ejpam-855	121	21	-open	-open	NOUN
ejpam-855	121	22	set	set	VERB
ejpam-855	121	23	such	such	ADJ
ejpam-855	121	24	that	that	SCONJ
ejpam-855	121	25	a∩	a∩	PROPN
ejpam-855	121	26	g	g	PROPN
ejpam-855	121	27	6=	6=	PROPN
ejpam-855	121	28	;	;	PUNCT
ejpam-855	121	29	.	.	PUNCT
ejpam-855	122	1	let	let	VERB
ejpam-855	122	2	x	x	SYM
ejpam-855	122	3	∈	∈	PROPN
ejpam-855	122	4	a∩	a∩	PROPN
ejpam-855	122	5	g.	g.	PROPN
ejpam-855	122	6	since	since	SCONJ
ejpam-855	122	7	(	(	PUNCT
ejpam-855	122	8	x	x	X
ejpam-855	122	9	,	,	PUNCT
ejpam-855	122	10	τ	τ	X
ejpam-855	122	11	)	)	PUNCT
ejpam-855	122	12	is	be	AUX
ejpam-855	122	13	λr	λr	ADP
ejpam-855	122	14	−	−	PROPN
ejpam-855	122	15	r0	r0	NOUN
ejpam-855	122	16	,	,	PUNCT
ejpam-855	122	17	x	x	SYM
ejpam-855	122	18	∈	∈	PROPN
ejpam-855	122	19	g	g	PROPN
ejpam-855	122	20	⇒	⇒	NOUN
ejpam-855	122	21	λr	λr	ADP
ejpam-855	122	22	−	−	PROPN
ejpam-855	122	23	cl({x	cl({x	NUM
ejpam-855	122	24	}	}	PUNCT
ejpam-855	122	25	)	)	PUNCT
ejpam-855	123	1	⊆	⊆	NUM
ejpam-855	123	2	g.	g.	NOUN
ejpam-855	123	3	since	since	SCONJ
ejpam-855	123	4	x	x	PROPN
ejpam-855	123	5	∈	∈	PROPN
ejpam-855	123	6	a	a	PRON
ejpam-855	123	7	,	,	PUNCT
ejpam-855	123	8	λr−cl({x})∩a	λr−cl({x})∩a	PROPN
ejpam-855	123	9	6=	6=	NUM
ejpam-855	123	10	;	;	PUNCT
ejpam-855	123	11	.	.	PUNCT
ejpam-855	124	1	thusλr−cl({x	thusλr−cl({x	NOUN
ejpam-855	124	2	}	}	PUNCT
ejpam-855	124	3	)	)	PUNCT
ejpam-855	124	4	is	be	AUX
ejpam-855	124	5	a	a	DET
ejpam-855	124	6	λr	λr	ADV
ejpam-855	124	7	-closed	-close	VERB
ejpam-855	124	8	set	set	NOUN
ejpam-855	124	9	contained	contain	VERB
ejpam-855	124	10	in	in	ADP
ejpam-855	124	11	g	g	PROPN
ejpam-855	124	12	and	and	CCONJ
ejpam-855	124	13	a∩λr−cl({x	a∩λr−cl({x	NOUN
ejpam-855	124	14	}	}	PUNCT
ejpam-855	124	15	)	)	PUNCT
ejpam-855	124	16	6=	6=	NUM
ejpam-855	124	17	;	;	PUNCT
ejpam-855	124	18	.	.	PUNCT
ejpam-855	125	1	(	(	PUNCT
ejpam-855	125	2	2)⇒	2)⇒	NUM
ejpam-855	125	3	(	(	PUNCT
ejpam-855	125	4	3	3	X
ejpam-855	125	5	)	)	PUNCT
ejpam-855	125	6	let	let	VERB
ejpam-855	125	7	g	g	PROPN
ejpam-855	125	8	∈	∈	PROPN
ejpam-855	125	9	λro(x	λro(x	PROPN
ejpam-855	125	10	,	,	PUNCT
ejpam-855	125	11	τ	τ	PROPN
ejpam-855	125	12	)	)	PUNCT
ejpam-855	125	13	and	and	CCONJ
ejpam-855	125	14	x	x	PUNCT
ejpam-855	125	15	∈	∈	PROPN
ejpam-855	125	16	g.	g.	NOUN
ejpam-855	125	17	then	then	ADV
ejpam-855	125	18	by	by	ADP
ejpam-855	125	19	(	(	PUNCT
ejpam-855	125	20	2	2	NUM
ejpam-855	125	21	)	)	PUNCT
ejpam-855	125	22	,	,	PUNCT
ejpam-855	125	23	∃f	∃f	PROPN
ejpam-855	125	24	∈	∈	PROPN
ejpam-855	125	25	λr	λr	ADP
ejpam-855	125	26	c(x	c(x	NOUN
ejpam-855	125	27	,	,	PUNCT
ejpam-855	125	28	τ	τ	PROPN
ejpam-855	125	29	)	)	PUNCT
ejpam-855	125	30	such	such	ADJ
ejpam-855	125	31	that	that	SCONJ
ejpam-855	125	32	{	{	PUNCT
ejpam-855	125	33	x	x	NOUN
ejpam-855	125	34	}	}	PUNCT
ejpam-855	125	35	∩	∩	X
ejpam-855	125	36	f	f	PROPN
ejpam-855	125	37	6=	6=	NUM
ejpam-855	125	38	;	;	PUNCT
ejpam-855	125	39	and	and	CCONJ
ejpam-855	125	40	f	f	PROPN
ejpam-855	125	41	⊆	⊆	NUM
ejpam-855	125	42	g.	g.	NOUN
ejpam-855	125	43	that	that	PRON
ejpam-855	125	44	implies	imply	VERB
ejpam-855	125	45	x	x	PUNCT
ejpam-855	125	46	∈	∈	PROPN
ejpam-855	125	47	f	f	X
ejpam-855	125	48	where	where	SCONJ
ejpam-855	125	49	f	f	PROPN
ejpam-855	125	50	∈	∈	PROPN
ejpam-855	125	51	λr	λr	ADP
ejpam-855	125	52	c(x	c(x	NOUN
ejpam-855	125	53	,	,	PUNCT
ejpam-855	125	54	τ	τ	PROPN
ejpam-855	125	55	)	)	PUNCT
ejpam-855	125	56	and	and	CCONJ
ejpam-855	125	57	f	f	PROPN
ejpam-855	125	58	⊆	⊆	NUM
ejpam-855	125	59	g	g	NOUN
ejpam-855	125	60	and	and	CCONJ
ejpam-855	125	61	hence	hence	ADV
ejpam-855	125	62	x	x	X
ejpam-855	125	63	∈	∈	PROPN
ejpam-855	125	64	∪{f	∪{f	PROPN
ejpam-855	125	65	/	/	SYM
ejpam-855	125	66	f	f	PROPN
ejpam-855	125	67	∈	∈	PROPN
ejpam-855	125	68	λr	λr	ADP
ejpam-855	125	69	c(x	c(x	NOUN
ejpam-855	125	70	,	,	PUNCT
ejpam-855	125	71	τ	τ	PROPN
ejpam-855	125	72	)	)	PUNCT
ejpam-855	125	73	and	and	CCONJ
ejpam-855	125	74	f	f	PROPN
ejpam-855	126	1	⊆	⊆	NUM
ejpam-855	126	2	g	g	NOUN
ejpam-855	126	3	}	}	PUNCT
ejpam-855	126	4	.	.	PUNCT
ejpam-855	127	1	therefore	therefore	ADV
ejpam-855	127	2	g	g	PROPN
ejpam-855	127	3	⊆	⊆	NUM
ejpam-855	127	4	∪{f	∪{f	PROPN
ejpam-855	127	5	/	/	SYM
ejpam-855	127	6	f	f	PROPN
ejpam-855	127	7	∈	∈	PROPN
ejpam-855	127	8	λr	λr	ADP
ejpam-855	127	9	c(x	c(x	NOUN
ejpam-855	127	10	,	,	PUNCT
ejpam-855	127	11	τ	τ	PROPN
ejpam-855	127	12	)	)	PUNCT
ejpam-855	127	13	and	and	CCONJ
ejpam-855	127	14	f	f	PROPN
ejpam-855	127	15	⊆	⊆	NUM
ejpam-855	127	16	g	g	NOUN
ejpam-855	127	17	}	}	PUNCT
ejpam-855	127	18	.	.	PUNCT
ejpam-855	128	1	also	also	ADV
ejpam-855	128	2	∪{f	∪{f	PROPN
ejpam-855	128	3	/	/	SYM
ejpam-855	128	4	f	f	PROPN
ejpam-855	128	5	∈	∈	PROPN
ejpam-855	128	6	λr	λr	ADP
ejpam-855	128	7	c(x	c(x	NOUN
ejpam-855	128	8	,	,	PUNCT
ejpam-855	128	9	τ	τ	PROPN
ejpam-855	128	10	)	)	PUNCT
ejpam-855	128	11	and	and	CCONJ
ejpam-855	128	12	f	f	PROPN
ejpam-855	129	1	⊆	⊆	NUM
ejpam-855	129	2	g	g	NOUN
ejpam-855	129	3	}	}	PUNCT
ejpam-855	129	4	⊆	⊆	NUM
ejpam-855	129	5	g.	g.	NOUN
ejpam-855	129	6	hence	hence	ADV
ejpam-855	129	7	g	g	PROPN
ejpam-855	129	8	=	=	PUNCT
ejpam-855	129	9	∪{f	∪{f	PROPN
ejpam-855	129	10	/	/	SYM
ejpam-855	129	11	f	f	PROPN
ejpam-855	129	12	∈	∈	PROPN
ejpam-855	129	13	λr	λr	ADP
ejpam-855	129	14	c(x	c(x	NOUN
ejpam-855	129	15	,	,	PUNCT
ejpam-855	129	16	τ	τ	PROPN
ejpam-855	129	17	)	)	PUNCT
ejpam-855	129	18	and	and	CCONJ
ejpam-855	129	19	f	f	PROPN
ejpam-855	129	20	⊆	⊆	NUM
ejpam-855	129	21	g	g	NOUN
ejpam-855	129	22	}	}	PUNCT
ejpam-855	129	23	.	.	PUNCT
ejpam-855	130	1	(	(	PUNCT
ejpam-855	130	2	3)⇒	3)⇒	NUM
ejpam-855	130	3	(	(	PUNCT
ejpam-855	130	4	4	4	NUM
ejpam-855	130	5	)	)	PUNCT
ejpam-855	130	6	let	let	VERB
ejpam-855	130	7	f	f	PROPN
ejpam-855	130	8	∈	∈	PROPN
ejpam-855	130	9	λr	λr	ADP
ejpam-855	130	10	c(x	c(x	NOUN
ejpam-855	130	11	,	,	PUNCT
ejpam-855	130	12	τ	τ	PROPN
ejpam-855	130	13	)	)	PUNCT
ejpam-855	130	14	.	.	PUNCT
ejpam-855	131	1	then	then	ADV
ejpam-855	131	2	f	f	PROPN
ejpam-855	131	3	c	c	PROPN
ejpam-855	131	4	∈	∈	PROPN
ejpam-855	132	1	λro(x	λro(x	PROPN
ejpam-855	132	2	,	,	PUNCT
ejpam-855	132	3	τ	τ	PROPN
ejpam-855	132	4	)	)	PUNCT
ejpam-855	132	5	.	.	PUNCT
ejpam-855	133	1	by	by	ADP
ejpam-855	133	2	(	(	PUNCT
ejpam-855	133	3	3	3	NUM
ejpam-855	133	4	)	)	PUNCT
ejpam-855	133	5	,	,	PUNCT
ejpam-855	133	6	f	f	PROPN
ejpam-855	133	7	c	c	NOUN
ejpam-855	133	8	=	=	SYM
ejpam-855	133	9	∪{gc	∪{gc	PROPN
ejpam-855	133	10	/	/	SYM
ejpam-855	133	11	gc	gc	PROPN
ejpam-855	133	12	∈	∈	PROPN
ejpam-855	133	13	λr	λr	ADP
ejpam-855	133	14	c(x	c(x	NOUN
ejpam-855	133	15	,	,	PUNCT
ejpam-855	133	16	τ	τ	PROPN
ejpam-855	133	17	)	)	PUNCT
ejpam-855	133	18	and	and	CCONJ
ejpam-855	133	19	gc	gc	PROPN
ejpam-855	133	20	⊆	⊆	NUM
ejpam-855	133	21	f	f	PROPN
ejpam-855	133	22	c	c	NOUN
ejpam-855	133	23	}	}	PUNCT
ejpam-855	133	24	.	.	PUNCT
ejpam-855	134	1	that	that	PRON
ejpam-855	134	2	implies	imply	VERB
ejpam-855	134	3	f	f	PROPN
ejpam-855	134	4	=	=	PUNCT
ejpam-855	134	5	∩{g	∩{g	PROPN
ejpam-855	134	6	/	/	SYM
ejpam-855	134	7	g	g	NOUN
ejpam-855	134	8	∈	∈	PROPN
ejpam-855	134	9	λro(x	λro(x	PROPN
ejpam-855	134	10	,	,	PUNCT
ejpam-855	134	11	τ	τ	PROPN
ejpam-855	134	12	)	)	PUNCT
ejpam-855	134	13	and	and	CCONJ
ejpam-855	134	14	f	f	PROPN
ejpam-855	135	1	⊆	⊆	NUM
ejpam-855	135	2	g	g	NOUN
ejpam-855	135	3	}	}	PUNCT
ejpam-855	135	4	.	.	PUNCT
ejpam-855	136	1	(	(	PUNCT
ejpam-855	136	2	4	4	X
ejpam-855	136	3	)	)	PUNCT
ejpam-855	136	4	⇒	⇒	NOUN
ejpam-855	136	5	(	(	PUNCT
ejpam-855	136	6	5	5	X
ejpam-855	136	7	)	)	PUNCT
ejpam-855	136	8	let	let	VERB
ejpam-855	136	9	y	y	PROPN
ejpam-855	136	10	/∈	/∈	PUNCT
ejpam-855	137	1	λr	λr	INTJ
ejpam-855	137	2	−	−	PROPN
ejpam-855	137	3	ker({x	ker({x	NOUN
ejpam-855	137	4	}	}	PUNCT
ejpam-855	137	5	)	)	PUNCT
ejpam-855	137	6	.	.	PUNCT
ejpam-855	138	1	then	then	ADV
ejpam-855	138	2	x	x	X
ejpam-855	138	3	/∈	/∈	INTJ
ejpam-855	139	1	λr	λr	INTJ
ejpam-855	139	2	−	−	PROPN
ejpam-855	139	3	cl({y	cl({y	X
ejpam-855	139	4	}	}	PUNCT
ejpam-855	139	5	)	)	PUNCT
ejpam-855	139	6	.	.	PUNCT
ejpam-855	140	1	that	that	PRON
ejpam-855	140	2	implies	imply	VERB
ejpam-855	140	3	∃	∃	PROPN
ejpam-855	140	4	a	a	DET
ejpam-855	140	5	λr	λr	NOUN
ejpam-855	140	6	-open	-open	ADJ
ejpam-855	140	7	set	set	VERB
ejpam-855	140	8	v	v	NOUN
ejpam-855	140	9	containing	contain	VERB
ejpam-855	140	10	x	x	PUNCT
ejpam-855	141	1	such	such	ADJ
ejpam-855	141	2	that	that	PRON
ejpam-855	141	3	v	v	NOUN
ejpam-855	141	4	∩	∩	NOUN
ejpam-855	141	5	{	{	PUNCT
ejpam-855	141	6	y	y	NOUN
ejpam-855	141	7	}	}	PUNCT
ejpam-855	141	8	=	=	SYM
ejpam-855	141	9	;	;	PUNCT
ejpam-855	141	10	and	and	CCONJ
ejpam-855	141	11	hence	hence	ADV
ejpam-855	141	12	λr	λr	ADP
ejpam-855	141	13	−	−	PROPN
ejpam-855	141	14	cl({y	cl({y	X
ejpam-855	141	15	}	}	PUNCT
ejpam-855	141	16	)	)	PUNCT
ejpam-855	141	17	∩	∩	NOUN
ejpam-855	141	18	v	v	NOUN
ejpam-855	141	19	=	=	PUNCT
ejpam-855	141	20	;	;	PUNCT
ejpam-855	141	21	.	.	PUNCT
ejpam-855	142	1	by	by	ADP
ejpam-855	142	2	(	(	PUNCT
ejpam-855	142	3	4	4	NUM
ejpam-855	142	4	)	)	PUNCT
ejpam-855	142	5	,	,	PUNCT
ejpam-855	142	6	λr−	λr−	PROPN
ejpam-855	142	7	cl({y	cl({y	X
ejpam-855	142	8	}	}	PUNCT
ejpam-855	142	9	)	)	PUNCT
ejpam-855	142	10	=	=	PUNCT
ejpam-855	142	11	∩{g	∩{g	PROPN
ejpam-855	142	12	/	/	SYM
ejpam-855	142	13	g	g	NOUN
ejpam-855	142	14	∈	∈	PROPN
ejpam-855	142	15	λro(x	λro(x	PROPN
ejpam-855	142	16	,	,	PUNCT
ejpam-855	142	17	τ	τ	PROPN
ejpam-855	142	18	)	)	PUNCT
ejpam-855	142	19	and	and	CCONJ
ejpam-855	142	20	λr−	λr−	PROPN
ejpam-855	142	21	cl({y	cl({y	X
ejpam-855	142	22	}	}	PUNCT
ejpam-855	142	23	)	)	PUNCT
ejpam-855	142	24	⊆	⊆	NUM
ejpam-855	142	25	g	g	NOUN
ejpam-855	142	26	}	}	PUNCT
ejpam-855	142	27	.	.	PUNCT
ejpam-855	143	1	since	since	SCONJ
ejpam-855	143	2	x	x	PROPN
ejpam-855	143	3	∈	∈	PROPN
ejpam-855	143	4	v	v	NOUN
ejpam-855	143	5	,	,	PUNCT
ejpam-855	143	6	x	x	PROPN
ejpam-855	143	7	/∈	/∈	PUNCT
ejpam-855	143	8	λr−	λr−	PUNCT
ejpam-855	143	9	cl({y	cl({y	NOUN
ejpam-855	143	10	}	}	PUNCT
ejpam-855	143	11	)	)	PUNCT
ejpam-855	143	12	and	and	CCONJ
ejpam-855	143	13	hence	hence	ADV
ejpam-855	143	14	∃g	∃g	PROPN
ejpam-855	143	15	∈	∈	PROPN
ejpam-855	143	16	λro(x	λro(x	PROPN
ejpam-855	143	17	,	,	PUNCT
ejpam-855	143	18	τ	τ	PROPN
ejpam-855	143	19	)	)	PUNCT
ejpam-855	143	20	such	such	ADJ
ejpam-855	143	21	that	that	SCONJ
ejpam-855	143	22	λr	λr	INTJ
ejpam-855	143	23	−	−	PROPN
ejpam-855	143	24	cl({y	cl({y	X
ejpam-855	143	25	}	}	PUNCT
ejpam-855	143	26	)	)	PUNCT
ejpam-855	144	1	⊆	⊆	NUM
ejpam-855	144	2	g	g	NOUN
ejpam-855	144	3	and	and	CCONJ
ejpam-855	144	4	x	x	PROPN
ejpam-855	144	5	/∈	/∈	PROPN
ejpam-855	145	1	g.	g.	PROPN
ejpam-855	145	2	therefore	therefore	ADV
ejpam-855	145	3	λr	λr	ADP
ejpam-855	145	4	−	−	PROPN
ejpam-855	145	5	cl({x})∩g	cl({x})∩g	X
ejpam-855	145	6	=	=	SYM
ejpam-855	145	7	;	;	PUNCT
ejpam-855	145	8	and	and	CCONJ
ejpam-855	145	9	hence	hence	ADV
ejpam-855	145	10	y	y	PROPN
ejpam-855	145	11	/∈	/∈	PUNCT
ejpam-855	146	1	λr	λr	ADP
ejpam-855	146	2	−	−	PROPN
ejpam-855	146	3	cl({x	cl({x	NOUN
ejpam-855	146	4	}	}	PUNCT
ejpam-855	146	5	)	)	PUNCT
ejpam-855	146	6	.	.	PUNCT
ejpam-855	147	1	therefore	therefore	ADV
ejpam-855	147	2	λr	λr	VERB
ejpam-855	147	3	−	−	PROPN
ejpam-855	147	4	cl({x	cl({x	NOUN
ejpam-855	147	5	}	}	PUNCT
ejpam-855	147	6	)	)	PUNCT
ejpam-855	147	7	⊆	⊆	NUM
ejpam-855	147	8	λr	λr	NOUN
ejpam-855	147	9	−	−	NOUN
ejpam-855	147	10	ker({x	ker({x	NOUN
ejpam-855	147	11	}	}	PUNCT
ejpam-855	147	12	)	)	PUNCT
ejpam-855	147	13	.	.	PUNCT
ejpam-855	148	1	(	(	PUNCT
ejpam-855	148	2	5)⇒	5)⇒	NUM
ejpam-855	148	3	(	(	PUNCT
ejpam-855	148	4	6	6	NUM
ejpam-855	148	5	)	)	PUNCT
ejpam-855	148	6	if	if	SCONJ
ejpam-855	148	7	y	y	PROPN
ejpam-855	148	8	∈	∈	PROPN
ejpam-855	148	9	λr	λr	VERB
ejpam-855	148	10	−	−	PROPN
ejpam-855	148	11	cl({x	cl({x	NOUN
ejpam-855	148	12	}	}	PUNCT
ejpam-855	148	13	)	)	PUNCT
ejpam-855	148	14	,	,	PUNCT
ejpam-855	148	15	then	then	ADV
ejpam-855	148	16	y	y	PROPN
ejpam-855	148	17	∈	∈	PROPN
ejpam-855	148	18	λr	λr	VERB
ejpam-855	148	19	−	−	PROPN
ejpam-855	148	20	ker({x	ker({x	NOUN
ejpam-855	148	21	}	}	PUNCT
ejpam-855	148	22	)	)	PUNCT
ejpam-855	148	23	by	by	ADP
ejpam-855	148	24	(	(	PUNCT
ejpam-855	148	25	5	5	NUM
ejpam-855	148	26	)	)	PUNCT
ejpam-855	148	27	.	.	PUNCT
ejpam-855	149	1	that	that	PRON
ejpam-855	149	2	implies	imply	VERB
ejpam-855	149	3	x	x	SYM
ejpam-855	149	4	∈	∈	NOUN
ejpam-855	149	5	λr	λr	VERB
ejpam-855	149	6	−	−	PROPN
ejpam-855	149	7	cl({y	cl({y	X
ejpam-855	149	8	}	}	PUNCT
ejpam-855	149	9	)	)	PUNCT
ejpam-855	149	10	.	.	PUNCT
ejpam-855	150	1	similarly	similarly	ADV
ejpam-855	150	2	,	,	PUNCT
ejpam-855	150	3	if	if	SCONJ
ejpam-855	150	4	x	x	SYM
ejpam-855	150	5	∈	∈	NOUN
ejpam-855	150	6	λr	λr	VERB
ejpam-855	150	7	−	−	PROPN
ejpam-855	150	8	cl({y	cl({y	X
ejpam-855	150	9	}	}	PUNCT
ejpam-855	150	10	)	)	PUNCT
ejpam-855	150	11	,	,	PUNCT
ejpam-855	150	12	then	then	ADV
ejpam-855	150	13	by	by	ADP
ejpam-855	150	14	(	(	PUNCT
ejpam-855	150	15	5	5	NUM
ejpam-855	150	16	)	)	PUNCT
ejpam-855	150	17	,	,	PUNCT
ejpam-855	150	18	x	x	PUNCT
ejpam-855	150	19	∈	∈	NOUN
ejpam-855	150	20	λr	λr	VERB
ejpam-855	150	21	−	−	PROPN
ejpam-855	150	22	ker({y	ker({y	PROPN
ejpam-855	150	23	}	}	PUNCT
ejpam-855	150	24	)	)	PUNCT
ejpam-855	150	25	and	and	CCONJ
ejpam-855	150	26	hence	hence	ADV
ejpam-855	150	27	y	y	PROPN
ejpam-855	150	28	∈	∈	PROPN
ejpam-855	150	29	λr	λr	VERB
ejpam-855	150	30	−	−	PROPN
ejpam-855	150	31	cl({x	cl({x	NOUN
ejpam-855	150	32	}	}	PUNCT
ejpam-855	150	33	)	)	PUNCT
ejpam-855	150	34	.	.	PUNCT
ejpam-855	151	1	thus	thus	ADV
ejpam-855	151	2	x	x	SYM
ejpam-855	151	3	∈	∈	NOUN
ejpam-855	151	4	λr	λr	VERB
ejpam-855	151	5	−	−	NOUN
ejpam-855	151	6	cl({y})⇔	cl({y})⇔	INTJ
ejpam-855	152	1	y	y	PROPN
ejpam-855	152	2	∈	∈	PROPN
ejpam-855	152	3	λr	λr	VERB
ejpam-855	152	4	−	−	PROPN
ejpam-855	152	5	cl({x	cl({x	NOUN
ejpam-855	152	6	}	}	PUNCT
ejpam-855	152	7	)	)	PUNCT
ejpam-855	152	8	.	.	PUNCT
ejpam-855	153	1	(	(	PUNCT
ejpam-855	153	2	6)⇒	6)⇒	NUM
ejpam-855	153	3	(	(	PUNCT
ejpam-855	153	4	1	1	X
ejpam-855	153	5	)	)	PUNCT
ejpam-855	153	6	let	let	VERB
ejpam-855	153	7	g	g	PROPN
ejpam-855	153	8	∈	∈	PROPN
ejpam-855	153	9	λro(x	λro(x	PROPN
ejpam-855	153	10	,	,	PUNCT
ejpam-855	153	11	τ	τ	PROPN
ejpam-855	153	12	)	)	PUNCT
ejpam-855	153	13	and	and	CCONJ
ejpam-855	153	14	x	x	PUNCT
ejpam-855	153	15	∈	∈	PROPN
ejpam-855	154	1	g.	g.	NOUN
ejpam-855	155	1	if	if	SCONJ
ejpam-855	155	2	y	y	PROPN
ejpam-855	155	3	/∈	/∈	VERB
ejpam-855	156	1	g	g	PROPN
ejpam-855	156	2	,	,	PUNCT
ejpam-855	156	3	then	then	ADV
ejpam-855	156	4	y	y	PROPN
ejpam-855	156	5	∈	∈	PROPN
ejpam-855	156	6	x	x	PUNCT
ejpam-855	156	7	−	−	NOUN
ejpam-855	156	8	g	g	NOUN
ejpam-855	156	9	and	and	CCONJ
ejpam-855	156	10	hence	hence	ADV
ejpam-855	156	11	λr	λr	ADP
ejpam-855	156	12	−	−	PROPN
ejpam-855	156	13	cl({y	cl({y	X
ejpam-855	156	14	}	}	PUNCT
ejpam-855	156	15	)	)	PUNCT
ejpam-855	157	1	⊆	⊆	NUM
ejpam-855	157	2	x	x	SYM
ejpam-855	157	3	−g	−g	NOUN
ejpam-855	157	4	since	since	SCONJ
ejpam-855	157	5	λr	λr	ADP
ejpam-855	157	6	−	−	PROPN
ejpam-855	157	7	cl({y	cl({y	X
ejpam-855	157	8	}	}	PUNCT
ejpam-855	157	9	)	)	PUNCT
ejpam-855	157	10	is	be	AUX
ejpam-855	157	11	the	the	DET
ejpam-855	157	12	smallest	small	ADJ
ejpam-855	157	13	λr	λr	NOUN
ejpam-855	157	14	-closed	-close	VERB
ejpam-855	157	15	set	set	NOUN
ejpam-855	157	16	containing	contain	VERB
ejpam-855	157	17	y.	y.	NOUN
ejpam-855	157	18	therefore	therefore	ADV
ejpam-855	157	19	λr	λr	ADP
ejpam-855	157	20	−	−	PROPN
ejpam-855	157	21	cl({y	cl({y	X
ejpam-855	157	22	}	}	PUNCT
ejpam-855	157	23	)	)	PUNCT
ejpam-855	157	24	∩	∩	PROPN
ejpam-855	157	25	g	g	NOUN
ejpam-855	157	26	=	=	PUNCT
ejpam-855	157	27	;	;	PUNCT
ejpam-855	157	28	and	and	CCONJ
ejpam-855	157	29	hence	hence	ADV
ejpam-855	157	30	x	x	X
ejpam-855	157	31	/∈	/∈	INTJ
ejpam-855	158	1	λr	λr	INTJ
ejpam-855	158	2	−	−	PROPN
ejpam-855	158	3	cl({y	cl({y	X
ejpam-855	158	4	}	}	PUNCT
ejpam-855	158	5	)	)	PUNCT
ejpam-855	158	6	.	.	PUNCT
ejpam-855	159	1	by	by	ADP
ejpam-855	159	2	(	(	PUNCT
ejpam-855	159	3	6	6	NUM
ejpam-855	159	4	)	)	PUNCT
ejpam-855	159	5	,	,	PUNCT
ejpam-855	159	6	y	y	PROPN
ejpam-855	159	7	/∈	/∈	PUNCT
ejpam-855	159	8	λr	λr	ADP
ejpam-855	159	9	−	−	PROPN
ejpam-855	159	10	cl({x	cl({x	NOUN
ejpam-855	159	11	}	}	PUNCT
ejpam-855	159	12	)	)	PUNCT
ejpam-855	159	13	.	.	PUNCT
ejpam-855	160	1	therefore	therefore	ADV
ejpam-855	160	2	λr	λr	VERB
ejpam-855	160	3	−	−	PROPN
ejpam-855	160	4	cl({x	cl({x	NOUN
ejpam-855	160	5	}	}	PUNCT
ejpam-855	160	6	)	)	PUNCT
ejpam-855	160	7	⊆	⊆	NUM
ejpam-855	160	8	g	g	NOUN
ejpam-855	160	9	and	and	CCONJ
ejpam-855	160	10	hence	hence	ADV
ejpam-855	160	11	(	(	PUNCT
ejpam-855	160	12	x	x	X
ejpam-855	160	13	,	,	PUNCT
ejpam-855	160	14	τ	τ	X
ejpam-855	160	15	)	)	PUNCT
ejpam-855	160	16	is	be	AUX
ejpam-855	160	17	λr	λr	ADP
ejpam-855	160	18	−	−	PROPN
ejpam-855	160	19	r0	r0	NOUN
ejpam-855	160	20	.	.	PUNCT
ejpam-855	161	1	corollary	corollary	ADJ
ejpam-855	161	2	1	1	NUM
ejpam-855	161	3	.	.	PUNCT
ejpam-855	162	1	for	for	ADP
ejpam-855	162	2	a	a	DET
ejpam-855	162	3	topological	topological	ADJ
ejpam-855	162	4	space	space	NOUN
ejpam-855	162	5	(	(	PUNCT
ejpam-855	162	6	x	x	X
ejpam-855	162	7	,	,	PUNCT
ejpam-855	162	8	τ	τ	PROPN
ejpam-855	162	9	)	)	PUNCT
ejpam-855	162	10	,	,	PUNCT
ejpam-855	162	11	the	the	DET
ejpam-855	162	12	following	follow	VERB
ejpam-855	162	13	properties	property	NOUN
ejpam-855	162	14	are	be	AUX
ejpam-855	162	15	equivalent	equivalent	ADJ
ejpam-855	162	16	:	:	PUNCT
ejpam-855	162	17	(	(	PUNCT
ejpam-855	162	18	1	1	X
ejpam-855	162	19	)	)	PUNCT
ejpam-855	162	20	(	(	PUNCT
ejpam-855	162	21	x	x	X
ejpam-855	162	22	,	,	PUNCT
ejpam-855	162	23	τ	τ	X
ejpam-855	162	24	)	)	PUNCT
ejpam-855	162	25	is	be	AUX
ejpam-855	162	26	λr	λr	ADP
ejpam-855	162	27	−	−	PROPN
ejpam-855	162	28	r0	r0	NOUN
ejpam-855	162	29	,	,	PUNCT
ejpam-855	162	30	(	(	PUNCT
ejpam-855	162	31	2	2	X
ejpam-855	162	32	)	)	PUNCT
ejpam-855	162	33	for	for	ADP
ejpam-855	162	34	any	any	DET
ejpam-855	162	35	x	x	SYM
ejpam-855	162	36	∈	∈	PROPN
ejpam-855	162	37	x	x	X
ejpam-855	162	38	,	,	PUNCT
ejpam-855	162	39	λr	λr	ADP
ejpam-855	162	40	−	−	NOUN
ejpam-855	162	41	cl({x	cl({x	NOUN
ejpam-855	162	42	}	}	PUNCT
ejpam-855	162	43	)	)	PUNCT
ejpam-855	163	1	=	=	PRON
ejpam-855	163	2	λr	λr	NOUN
ejpam-855	163	3	−	−	NOUN
ejpam-855	163	4	ker({x	ker({x	NOUN
ejpam-855	163	5	}	}	PUNCT
ejpam-855	163	6	)	)	PUNCT
ejpam-855	163	7	.	.	PUNCT
ejpam-855	164	1	theorem	theorem	NOUN
ejpam-855	164	2	5	5	NUM
ejpam-855	164	3	.	.	X
ejpam-855	164	4	for	for	ADP
ejpam-855	164	5	a	a	DET
ejpam-855	164	6	topological	topological	ADJ
ejpam-855	164	7	space	space	NOUN
ejpam-855	164	8	(	(	PUNCT
ejpam-855	164	9	x	x	X
ejpam-855	164	10	,	,	PUNCT
ejpam-855	164	11	τ	τ	PROPN
ejpam-855	164	12	)	)	PUNCT
ejpam-855	164	13	,	,	PUNCT
ejpam-855	164	14	the	the	DET
ejpam-855	164	15	following	follow	VERB
ejpam-855	164	16	properties	property	NOUN
ejpam-855	164	17	are	be	AUX
ejpam-855	164	18	equivalent	equivalent	ADJ
ejpam-855	164	19	:	:	PUNCT
ejpam-855	164	20	(	(	PUNCT
ejpam-855	164	21	1	1	X
ejpam-855	164	22	)	)	PUNCT
ejpam-855	164	23	(	(	PUNCT
ejpam-855	164	24	x	x	X
ejpam-855	164	25	,	,	PUNCT
ejpam-855	164	26	τ	τ	X
ejpam-855	164	27	)	)	PUNCT
ejpam-855	164	28	is	be	AUX
ejpam-855	164	29	λr	λr	ADP
ejpam-855	164	30	−	−	PROPN
ejpam-855	164	31	r0	r0	NOUN
ejpam-855	164	32	(	(	PUNCT
ejpam-855	164	33	2	2	NUM
ejpam-855	164	34	)	)	PUNCT
ejpam-855	164	35	if	if	SCONJ
ejpam-855	164	36	f	f	PROPN
ejpam-855	164	37	is	be	AUX
ejpam-855	164	38	λr	λr	ADV
ejpam-855	164	39	-closed	-close	VERB
ejpam-855	164	40	,	,	PUNCT
ejpam-855	164	41	then	then	ADV
ejpam-855	164	42	f	f	PROPN
ejpam-855	164	43	=	=	PRON
ejpam-855	164	44	λr	λr	NOUN
ejpam-855	164	45	−	−	PROPN
ejpam-855	164	46	ker(f	ker(f	PROPN
ejpam-855	164	47	)	)	PUNCT
ejpam-855	164	48	(	(	PUNCT
ejpam-855	164	49	3	3	X
ejpam-855	164	50	)	)	PUNCT
ejpam-855	164	51	if	if	SCONJ
ejpam-855	164	52	f	f	PROPN
ejpam-855	164	53	is	be	AUX
ejpam-855	164	54	λr	λr	PRON
ejpam-855	164	55	-closed	-close	VERB
ejpam-855	164	56	and	and	CCONJ
ejpam-855	164	57	x	x	SYM
ejpam-855	164	58	∈	∈	PROPN
ejpam-855	164	59	f	f	X
ejpam-855	164	60	,	,	PUNCT
ejpam-855	164	61	then	then	ADV
ejpam-855	164	62	λr	λr	ADP
ejpam-855	164	63	−	−	PROPN
ejpam-855	164	64	ker({x})⊆	ker({x})⊆	NOUN
ejpam-855	164	65	f	f	X
ejpam-855	164	66	(	(	PUNCT
ejpam-855	164	67	4	4	NUM
ejpam-855	164	68	)	)	PUNCT
ejpam-855	164	69	if	if	SCONJ
ejpam-855	164	70	x	x	PUNCT
ejpam-855	164	71	∈	∈	PROPN
ejpam-855	164	72	x	x	X
ejpam-855	164	73	,	,	PUNCT
ejpam-855	164	74	then	then	ADV
ejpam-855	164	75	λr	λr	ADP
ejpam-855	164	76	−	−	PROPN
ejpam-855	164	77	ker({x})⊆	ker({x})⊆	NOUN
ejpam-855	164	78	λr	λr	ADP
ejpam-855	164	79	−	−	NOUN
ejpam-855	164	80	cl({x	cl({x	NOUN
ejpam-855	164	81	}	}	PUNCT
ejpam-855	164	82	)	)	PUNCT
ejpam-855	164	83	.	.	PUNCT
ejpam-855	165	1	s.	s.	PROPN
ejpam-855	165	2	missier	missier	PROPN
ejpam-855	165	3	,	,	PUNCT
ejpam-855	165	4	m.	m.	NOUN
ejpam-855	165	5	jeyanthi	jeyanthi	PROPN
ejpam-855	165	6	,	,	PUNCT
ejpam-855	165	7	a.	a.	PROPN
ejpam-855	165	8	kılıçman	kılıçman	PROPN
ejpam-855	165	9	/	/	SYM
ejpam-855	165	10	eur	eur	PROPN
ejpam-855	165	11	.	.	PUNCT
ejpam-855	166	1	j.	j.	PROPN
ejpam-855	166	2	pure	pure	PROPN
ejpam-855	166	3	appl	appl	PROPN
ejpam-855	166	4	.	.	PROPN
ejpam-855	166	5	math	math	PROPN
ejpam-855	166	6	,	,	PUNCT
ejpam-855	166	7	5	5	NUM
ejpam-855	166	8	(	(	PUNCT
ejpam-855	166	9	2012	2012	NUM
ejpam-855	166	10	)	)	PUNCT
ejpam-855	166	11	,	,	PUNCT
ejpam-855	166	12	357	357	NUM
ejpam-855	166	13	-	-	SYM
ejpam-855	166	14	364	364	NUM
ejpam-855	166	15	361	361	NUM
ejpam-855	166	16	proof	proof	NOUN
ejpam-855	166	17	.	.	PUNCT
ejpam-855	167	1	(	(	PUNCT
ejpam-855	167	2	1)⇒	1)⇒	NUM
ejpam-855	167	3	(	(	PUNCT
ejpam-855	167	4	2	2	NUM
ejpam-855	167	5	)	)	PUNCT
ejpam-855	167	6	let	let	VERB
ejpam-855	167	7	f	f	PRON
ejpam-855	167	8	be	be	AUX
ejpam-855	167	9	a	a	DET
ejpam-855	167	10	λr	λr	NOUN
ejpam-855	167	11	-closed	-close	VERB
ejpam-855	167	12	set	set	NOUN
ejpam-855	167	13	and	and	CCONJ
ejpam-855	167	14	x	x	SYM
ejpam-855	167	15	/∈	/∈	PROPN
ejpam-855	168	1	f	f	PROPN
ejpam-855	168	2	.	.	PUNCT
ejpam-855	169	1	then	then	ADV
ejpam-855	169	2	x	x	X
ejpam-855	169	3	−	−	PROPN
ejpam-855	169	4	f	f	PROPN
ejpam-855	169	5	is	be	AUX
ejpam-855	169	6	λr	λr	INTJ
ejpam-855	169	7	-open	-open	ADJ
ejpam-855	169	8	and	and	CCONJ
ejpam-855	169	9	x	x	SYM
ejpam-855	169	10	∈	∈	NOUN
ejpam-855	169	11	x	x	X
ejpam-855	169	12	−	−	PROPN
ejpam-855	169	13	f	f	X
ejpam-855	169	14	.	.	PUNCT
ejpam-855	170	1	by	by	ADP
ejpam-855	170	2	(	(	PUNCT
ejpam-855	170	3	1	1	NUM
ejpam-855	170	4	)	)	PUNCT
ejpam-855	170	5	,	,	PUNCT
ejpam-855	170	6	λr	λr	ADP
ejpam-855	170	7	−	−	PROPN
ejpam-855	170	8	cl({x	cl({x	NOUN
ejpam-855	170	9	}	}	PUNCT
ejpam-855	170	10	)	)	PUNCT
ejpam-855	171	1	⊆	⊆	NUM
ejpam-855	171	2	x	x	SYM
ejpam-855	171	3	−	−	PROPN
ejpam-855	171	4	f	f	NOUN
ejpam-855	171	5	and	and	CCONJ
ejpam-855	171	6	hence	hence	ADV
ejpam-855	171	7	λr	λr	ADP
ejpam-855	171	8	−	−	NOUN
ejpam-855	171	9	cl({x	cl({x	NUM
ejpam-855	171	10	}	}	PUNCT
ejpam-855	171	11	)	)	PUNCT
ejpam-855	171	12	∩	∩	NOUN
ejpam-855	171	13	f	f	PROPN
ejpam-855	171	14	=	=	PUNCT
ejpam-855	171	15	;	;	PUNCT
ejpam-855	171	16	.	.	PUNCT
ejpam-855	172	1	that	that	PRON
ejpam-855	172	2	implies	imply	VERB
ejpam-855	172	3	x	x	X
ejpam-855	172	4	/∈	/∈	INTJ
ejpam-855	173	1	λr	λr	INTJ
ejpam-855	173	2	−	−	PROPN
ejpam-855	173	3	ker(f	ker(f	PROPN
ejpam-855	173	4	)	)	PUNCT
ejpam-855	173	5	.	.	PUNCT
ejpam-855	174	1	therefore	therefore	ADV
ejpam-855	174	2	λr	λr	INTJ
ejpam-855	174	3	−	−	PROPN
ejpam-855	174	4	ker(f	ker(f	PROPN
ejpam-855	174	5	)	)	PUNCT
ejpam-855	174	6	⊆	⊆	NUM
ejpam-855	174	7	f	f	NOUN
ejpam-855	174	8	.	.	PUNCT
ejpam-855	175	1	also	also	ADV
ejpam-855	175	2	f	f	PROPN
ejpam-855	175	3	⊂	⊂	PROPN
ejpam-855	175	4	λr	λr	VERB
ejpam-855	175	5	−	−	PROPN
ejpam-855	175	6	ker(f	ker(f	PROPN
ejpam-855	175	7	)	)	PUNCT
ejpam-855	175	8	.	.	PUNCT
ejpam-855	176	1	hence	hence	ADV
ejpam-855	176	2	f	f	PROPN
ejpam-855	176	3	=	=	PRON
ejpam-855	176	4	λr	λr	NOUN
ejpam-855	176	5	−	−	PROPN
ejpam-855	176	6	ker(f	ker(f	PROPN
ejpam-855	176	7	)	)	PUNCT
ejpam-855	176	8	.	.	PUNCT
ejpam-855	177	1	(	(	PUNCT
ejpam-855	177	2	2)⇒	2)⇒	NUM
ejpam-855	177	3	(	(	PUNCT
ejpam-855	177	4	3	3	X
ejpam-855	177	5	)	)	PUNCT
ejpam-855	177	6	let	let	VERB
ejpam-855	177	7	f	f	PRON
ejpam-855	177	8	be	be	AUX
ejpam-855	177	9	a	a	DET
ejpam-855	177	10	λr	λr	NOUN
ejpam-855	177	11	-closed	-close	VERB
ejpam-855	177	12	set	set	NOUN
ejpam-855	177	13	and	and	CCONJ
ejpam-855	178	1	x	x	SYM
ejpam-855	178	2	∈	∈	PROPN
ejpam-855	178	3	f	f	X
ejpam-855	178	4	.	.	PUNCT
ejpam-855	179	1	thenλr	thenλr	NOUN
ejpam-855	180	1	−	−	PROPN
ejpam-855	180	2	ker({x})⊆	ker({x})⊆	NOUN
ejpam-855	180	3	λr	λr	ADP
ejpam-855	180	4	−	−	PROPN
ejpam-855	180	5	ker(f	ker(f	PROPN
ejpam-855	180	6	)	)	PUNCT
ejpam-855	181	1	=	=	SYM
ejpam-855	181	2	f	f	PROPN
ejpam-855	181	3	.	.	PUNCT
ejpam-855	182	1	(	(	PUNCT
ejpam-855	182	2	3)⇒	3)⇒	NUM
ejpam-855	182	3	(	(	PUNCT
ejpam-855	182	4	4	4	NUM
ejpam-855	182	5	)	)	PUNCT
ejpam-855	182	6	since	since	SCONJ
ejpam-855	182	7	x	x	SYM
ejpam-855	182	8	∈	∈	PROPN
ejpam-855	182	9	λr	λr	VERB
ejpam-855	182	10	−	−	PROPN
ejpam-855	182	11	cl({x	cl({x	NOUN
ejpam-855	182	12	}	}	PUNCT
ejpam-855	182	13	)	)	PUNCT
ejpam-855	182	14	and	and	CCONJ
ejpam-855	182	15	λr	λr	ADP
ejpam-855	182	16	−	−	PROPN
ejpam-855	182	17	cl({x	cl({x	NUM
ejpam-855	182	18	}	}	PUNCT
ejpam-855	182	19	)	)	PUNCT
ejpam-855	182	20	is	be	AUX
ejpam-855	182	21	λr	λr	NOUN
ejpam-855	182	22	-closed	-close	VERB
ejpam-855	182	23	,	,	PUNCT
ejpam-855	182	24	by	by	ADP
ejpam-855	182	25	(	(	PUNCT
ejpam-855	182	26	3	3	NUM
ejpam-855	182	27	)	)	PUNCT
ejpam-855	182	28	,	,	PUNCT
ejpam-855	182	29	λr	λr	ADP
ejpam-855	182	30	−	−	PROPN
ejpam-855	182	31	ker({x})⊆	ker({x})⊆	NOUN
ejpam-855	182	32	λr	λr	ADP
ejpam-855	182	33	−	−	NOUN
ejpam-855	182	34	cl({x	cl({x	NOUN
ejpam-855	182	35	}	}	PUNCT
ejpam-855	182	36	)	)	PUNCT
ejpam-855	182	37	.	.	PUNCT
ejpam-855	183	1	(	(	PUNCT
ejpam-855	183	2	4)⇒	4)⇒	X
ejpam-855	183	3	(	(	PUNCT
ejpam-855	183	4	1	1	NUM
ejpam-855	183	5	)	)	PUNCT
ejpam-855	183	6	since	since	SCONJ
ejpam-855	183	7	x	x	SYM
ejpam-855	183	8	∈	∈	PROPN
ejpam-855	183	9	λr	λr	VERB
ejpam-855	183	10	−	−	NOUN
ejpam-855	183	11	cl({y})⇔	cl({y})⇔	INTJ
ejpam-855	183	12	y	y	PROPN
ejpam-855	183	13	∈	∈	PROPN
ejpam-855	183	14	λr	λr	VERB
ejpam-855	183	15	−	−	PROPN
ejpam-855	183	16	cl({x	cl({x	NOUN
ejpam-855	183	17	}	}	PUNCT
ejpam-855	183	18	)	)	PUNCT
ejpam-855	183	19	,	,	PUNCT
ejpam-855	183	20	(	(	PUNCT
ejpam-855	183	21	x	x	X
ejpam-855	183	22	,	,	PUNCT
ejpam-855	183	23	τ	τ	X
ejpam-855	183	24	)	)	PUNCT
ejpam-855	183	25	is	be	AUX
ejpam-855	183	26	λr	λr	ADP
ejpam-855	183	27	−	−	PROPN
ejpam-855	183	28	r0	r0	NOUN
ejpam-855	183	29	.	.	PUNCT
ejpam-855	184	1	the	the	DET
ejpam-855	184	2	following	follow	VERB
ejpam-855	184	3	examples	example	NOUN
ejpam-855	184	4	1	1	NUM
ejpam-855	184	5	and	and	CCONJ
ejpam-855	184	6	2	2	NUM
ejpam-855	184	7	show	show	VERB
ejpam-855	184	8	that	that	SCONJ
ejpam-855	184	9	λr	λr	VERB
ejpam-855	184	10	−	−	PROPN
ejpam-855	184	11	t0	t0	PROPN
ejpam-855	184	12	and	and	CCONJ
ejpam-855	184	13	λr	λr	INTJ
ejpam-855	184	14	−	−	PROPN
ejpam-855	184	15	r0	r0	NOUN
ejpam-855	184	16	are	be	AUX
ejpam-855	184	17	independent	independent	ADJ
ejpam-855	184	18	.	.	PUNCT
ejpam-855	184	19	example	example	NOUN
ejpam-855	185	1	1	1	NUM
ejpam-855	185	2	.	.	PUNCT
ejpam-855	185	3	let	let	VERB
ejpam-855	185	4	x	x	PUNCT
ejpam-855	185	5	=	=	PRON
ejpam-855	185	6	{	{	PUNCT
ejpam-855	185	7	a	a	PRON
ejpam-855	185	8	,	,	PUNCT
ejpam-855	185	9	b	b	NOUN
ejpam-855	185	10	,	,	PUNCT
ejpam-855	185	11	c	c	NOUN
ejpam-855	185	12	}	}	PUNCT
ejpam-855	185	13	and	and	CCONJ
ejpam-855	185	14	τ	τ	PROPN
ejpam-855	185	15	=	=	PUNCT
ejpam-855	185	16	{	{	PUNCT
ejpam-855	185	17	x	x	X
ejpam-855	185	18	,	,	PUNCT
ejpam-855	185	19	;	;	PUNCT
ejpam-855	185	20	,	,	PUNCT
ejpam-855	185	21	{	{	PUNCT
ejpam-855	185	22	a	a	X
ejpam-855	185	23	}	}	PUNCT
ejpam-855	185	24	,	,	PUNCT
ejpam-855	185	25	{	{	PUNCT
ejpam-855	185	26	b	b	X
ejpam-855	185	27	,	,	PUNCT
ejpam-855	185	28	c	c	NOUN
ejpam-855	185	29	}	}	PUNCT
ejpam-855	185	30	}	}	PUNCT
ejpam-855	185	31	.	.	PUNCT
ejpam-855	186	1	then	then	ADV
ejpam-855	186	2	λro(x	λro(x	PROPN
ejpam-855	186	3	,	,	PUNCT
ejpam-855	186	4	τ	τ	PROPN
ejpam-855	186	5	)	)	PUNCT
ejpam-855	186	6	=	=	PRON
ejpam-855	186	7	{	{	PUNCT
ejpam-855	186	8	x	x	X
ejpam-855	186	9	,	,	PUNCT
ejpam-855	186	10	;	;	PUNCT
ejpam-855	186	11	,	,	PUNCT
ejpam-855	186	12	{	{	PUNCT
ejpam-855	186	13	a	a	X
ejpam-855	186	14	}	}	PUNCT
ejpam-855	186	15	,	,	PUNCT
ejpam-855	186	16	{	{	PUNCT
ejpam-855	186	17	b	b	X
ejpam-855	186	18	,	,	PUNCT
ejpam-855	186	19	c	c	NOUN
ejpam-855	186	20	}	}	PUNCT
ejpam-855	186	21	}	}	PUNCT
ejpam-855	186	22	.	.	PUNCT
ejpam-855	187	1	here	here	ADV
ejpam-855	187	2	(	(	PUNCT
ejpam-855	187	3	x	x	X
ejpam-855	187	4	,	,	PUNCT
ejpam-855	187	5	τ	τ	X
ejpam-855	187	6	)	)	PUNCT
ejpam-855	187	7	is	be	AUX
ejpam-855	187	8	λr	λr	ADP
ejpam-855	187	9	−	−	NOUN
ejpam-855	187	10	r0	r0	NOUN
ejpam-855	188	1	but	but	CCONJ
ejpam-855	188	2	it	it	PRON
ejpam-855	188	3	is	be	AUX
ejpam-855	188	4	not	not	PART
ejpam-855	188	5	λr	λr	ADP
ejpam-855	188	6	−	−	PROPN
ejpam-855	188	7	t0	t0	PROPN
ejpam-855	188	8	.	.	PUNCT
ejpam-855	188	9	example	example	NOUN
ejpam-855	189	1	2	2	NUM
ejpam-855	189	2	.	.	PUNCT
ejpam-855	189	3	let	let	VERB
ejpam-855	189	4	x	x	PUNCT
ejpam-855	189	5	=	=	PRON
ejpam-855	189	6	{	{	PUNCT
ejpam-855	189	7	a	a	PRON
ejpam-855	189	8	,	,	PUNCT
ejpam-855	189	9	b	b	NOUN
ejpam-855	189	10	,	,	PUNCT
ejpam-855	189	11	c	c	NOUN
ejpam-855	189	12	}	}	PUNCT
ejpam-855	189	13	and	and	CCONJ
ejpam-855	189	14	τ	τ	PROPN
ejpam-855	189	15	=	=	PUNCT
ejpam-855	189	16	{	{	PUNCT
ejpam-855	189	17	x	x	X
ejpam-855	189	18	,	,	PUNCT
ejpam-855	189	19	;	;	PUNCT
ejpam-855	189	20	,	,	PUNCT
ejpam-855	189	21	{	{	PUNCT
ejpam-855	189	22	a	a	X
ejpam-855	189	23	}	}	PUNCT
ejpam-855	189	24	,	,	PUNCT
ejpam-855	189	25	{	{	PUNCT
ejpam-855	189	26	a	a	DET
ejpam-855	189	27	,	,	PUNCT
ejpam-855	189	28	b	b	NOUN
ejpam-855	189	29	}	}	PUNCT
ejpam-855	189	30	}	}	PUNCT
ejpam-855	189	31	.	.	PUNCT
ejpam-855	190	1	then	then	ADV
ejpam-855	190	2	λro(x	λro(x	PROPN
ejpam-855	190	3	,	,	PUNCT
ejpam-855	190	4	τ	τ	PROPN
ejpam-855	190	5	)	)	PUNCT
ejpam-855	190	6	=	=	PRON
ejpam-855	190	7	{	{	PUNCT
ejpam-855	190	8	x	x	X
ejpam-855	190	9	,	,	PUNCT
ejpam-855	190	10	;	;	PUNCT
ejpam-855	190	11	,	,	PUNCT
ejpam-855	190	12	{	{	PUNCT
ejpam-855	190	13	a	a	X
ejpam-855	190	14	}	}	PUNCT
ejpam-855	190	15	,	,	PUNCT
ejpam-855	190	16	{	{	PUNCT
ejpam-855	190	17	a	a	DET
ejpam-855	190	18	,	,	PUNCT
ejpam-855	190	19	b	b	NOUN
ejpam-855	190	20	}	}	PUNCT
ejpam-855	190	21	}	}	PUNCT
ejpam-855	190	22	.	.	PUNCT
ejpam-855	191	1	here	here	ADV
ejpam-855	191	2	(	(	PUNCT
ejpam-855	191	3	x	x	X
ejpam-855	191	4	,	,	PUNCT
ejpam-855	191	5	τ	τ	X
ejpam-855	191	6	)	)	PUNCT
ejpam-855	191	7	is	be	AUX
ejpam-855	191	8	λr	λr	ADP
ejpam-855	191	9	−	−	PROPN
ejpam-855	191	10	t0	t0	NOUN
ejpam-855	192	1	but	but	CCONJ
ejpam-855	192	2	it	it	PRON
ejpam-855	192	3	is	be	AUX
ejpam-855	192	4	not	not	PART
ejpam-855	192	5	λr	λr	ADP
ejpam-855	192	6	−	−	NOUN
ejpam-855	192	7	r0	r0	NOUN
ejpam-855	192	8	.	.	PUNCT
ejpam-855	193	1	3	3	X
ejpam-855	193	2	.	.	X
ejpam-855	193	3	λr	λr	NOUN
ejpam-855	193	4	−	−	PROPN
ejpam-855	193	5	r1	r1	PROPN
ejpam-855	193	6	spaces	space	VERB
ejpam-855	193	7	definition	definition	NOUN
ejpam-855	193	8	2	2	NUM
ejpam-855	193	9	.	.	PUNCT
ejpam-855	194	1	a	a	DET
ejpam-855	194	2	space	space	NOUN
ejpam-855	194	3	(	(	PUNCT
ejpam-855	194	4	x	x	X
ejpam-855	194	5	,	,	PUNCT
ejpam-855	194	6	τ	τ	X
ejpam-855	194	7	)	)	PUNCT
ejpam-855	194	8	is	be	AUX
ejpam-855	194	9	λr	λr	ADP
ejpam-855	194	10	−	−	PROPN
ejpam-855	194	11	r1	r1	PROPN
ejpam-855	194	12	if	if	SCONJ
ejpam-855	194	13	for	for	ADP
ejpam-855	194	14	each	each	DET
ejpam-855	194	15	x	x	X
ejpam-855	194	16	,	,	PUNCT
ejpam-855	194	17	y	y	PROPN
ejpam-855	194	18	∈	∈	PROPN
ejpam-855	194	19	x	x	PUNCT
ejpam-855	194	20	with	with	ADP
ejpam-855	194	21	λr	λr	ADP
ejpam-855	194	22	−	−	PROPN
ejpam-855	194	23	cl({x	cl({x	NOUN
ejpam-855	194	24	}	}	PUNCT
ejpam-855	194	25	)	)	PUNCT
ejpam-855	195	1	6=	6=	ADP
ejpam-855	195	2	λr	λr	ADP
ejpam-855	195	3	−	−	PROPN
ejpam-855	195	4	cl({y	cl({y	NOUN
ejpam-855	195	5	}	}	PUNCT
ejpam-855	195	6	)	)	PUNCT
ejpam-855	195	7	,	,	PUNCT
ejpam-855	195	8	∃λr	∃λr	NOUN
ejpam-855	195	9	-open	-open	PROPN
ejpam-855	195	10	sets	set	VERB
ejpam-855	195	11	u	u	NOUN
ejpam-855	195	12	and	and	CCONJ
ejpam-855	195	13	v	v	ADP
ejpam-855	195	14	such	such	ADJ
ejpam-855	195	15	that	that	PRON
ejpam-855	195	16	λr	λr	ADP
ejpam-855	195	17	−	−	PROPN
ejpam-855	195	18	cl({x	cl({x	NOUN
ejpam-855	195	19	}	}	PUNCT
ejpam-855	195	20	)	)	PUNCT
ejpam-855	196	1	⊆	⊆	NUM
ejpam-855	196	2	u	u	NOUN
ejpam-855	196	3	,	,	PUNCT
ejpam-855	196	4	λr	λr	ADP
ejpam-855	196	5	−	−	PROPN
ejpam-855	196	6	cl({y	cl({y	NOUN
ejpam-855	196	7	}	}	PUNCT
ejpam-855	196	8	)	)	PUNCT
ejpam-855	196	9	⊆	⊆	NUM
ejpam-855	196	10	v	v	NOUN
ejpam-855	196	11	and	and	CCONJ
ejpam-855	196	12	u	u	NOUN
ejpam-855	196	13	∩	∩	NOUN
ejpam-855	196	14	v	v	NOUN
ejpam-855	196	15	=	=	PUNCT
ejpam-855	196	16	;	;	PUNCT
ejpam-855	196	17	.	.	PUNCT
ejpam-855	197	1	proposition	proposition	NOUN
ejpam-855	197	2	1	1	NUM
ejpam-855	197	3	.	.	PUNCT
ejpam-855	198	1	if	if	SCONJ
ejpam-855	198	2	(	(	PUNCT
ejpam-855	198	3	x	x	X
ejpam-855	198	4	,	,	PUNCT
ejpam-855	198	5	τ	τ	X
ejpam-855	198	6	)	)	PUNCT
ejpam-855	198	7	is	be	AUX
ejpam-855	198	8	λr	λr	ADP
ejpam-855	198	9	−	−	PROPN
ejpam-855	198	10	r1	r1	NOUN
ejpam-855	198	11	,	,	PUNCT
ejpam-855	198	12	then	then	ADV
ejpam-855	198	13	(	(	PUNCT
ejpam-855	198	14	x	x	X
ejpam-855	198	15	,	,	PUNCT
ejpam-855	198	16	τ	τ	X
ejpam-855	198	17	)	)	PUNCT
ejpam-855	198	18	is	be	AUX
ejpam-855	198	19	λr	λr	ADP
ejpam-855	198	20	−	−	PROPN
ejpam-855	198	21	r0	r0	NOUN
ejpam-855	198	22	.	.	PUNCT
ejpam-855	199	1	proof	proof	NOUN
ejpam-855	199	2	.	.	PUNCT
ejpam-855	200	1	let	let	VERB
ejpam-855	200	2	(	(	PUNCT
ejpam-855	200	3	x	x	X
ejpam-855	200	4	,	,	PUNCT
ejpam-855	200	5	τ	τ	PROPN
ejpam-855	200	6	)	)	PUNCT
ejpam-855	200	7	be	be	AUX
ejpam-855	200	8	λr	λr	ADP
ejpam-855	200	9	−	−	PROPN
ejpam-855	200	10	r1	r1	PROPN
ejpam-855	200	11	.	.	PUNCT
ejpam-855	201	1	let	let	VERB
ejpam-855	201	2	u	u	PRON
ejpam-855	201	3	be	be	AUX
ejpam-855	201	4	λr	λr	ADP
ejpam-855	201	5	-open	-open	ADJ
ejpam-855	201	6	in	in	ADP
ejpam-855	201	7	x	x	X
ejpam-855	201	8	and	and	CCONJ
ejpam-855	201	9	x	x	SYM
ejpam-855	201	10	∈	∈	PROPN
ejpam-855	201	11	u	u	NOUN
ejpam-855	201	12	.	.	PUNCT
ejpam-855	202	1	for	for	ADP
ejpam-855	202	2	each	each	DET
ejpam-855	202	3	y	y	PROPN
ejpam-855	202	4	∈	∈	PROPN
ejpam-855	202	5	x	x	PUNCT
ejpam-855	202	6	−	−	PROPN
ejpam-855	202	7	u	u	NOUN
ejpam-855	202	8	,	,	PUNCT
ejpam-855	202	9	λr	λr	ADP
ejpam-855	202	10	−	−	NOUN
ejpam-855	202	11	cl({x	cl({x	NOUN
ejpam-855	202	12	}	}	PUNCT
ejpam-855	202	13	)	)	PUNCT
ejpam-855	202	14	6=	6=	ADP
ejpam-855	202	15	λr	λr	ADP
ejpam-855	202	16	−	−	PROPN
ejpam-855	202	17	cl({y	cl({y	NOUN
ejpam-855	202	18	}	}	PUNCT
ejpam-855	202	19	)	)	PUNCT
ejpam-855	202	20	.	.	PUNCT
ejpam-855	203	1	then	then	ADV
ejpam-855	203	2	∃	∃	PROPN
ejpam-855	203	3	disjoint	disjoint	NOUN
ejpam-855	203	4	λr	λr	ADP
ejpam-855	203	5	-open	-open	ADJ
ejpam-855	203	6	sets	set	NOUN
ejpam-855	203	7	uy	uy	NOUN
ejpam-855	203	8	and	and	CCONJ
ejpam-855	203	9	vy	vy	ADP
ejpam-855	203	10	such	such	ADJ
ejpam-855	203	11	that	that	SCONJ
ejpam-855	203	12	λr	λr	ADP
ejpam-855	203	13	−	−	PROPN
ejpam-855	203	14	cl({x	cl({x	NOUN
ejpam-855	203	15	}	}	PUNCT
ejpam-855	203	16	)	)	PUNCT
ejpam-855	204	1	⊆	⊆	NUM
ejpam-855	204	2	uy	uy	NOUN
ejpam-855	204	3	and	and	CCONJ
ejpam-855	204	4	λr	λr	INTJ
ejpam-855	204	5	−	−	PROPN
ejpam-855	204	6	cl({y	cl({y	NOUN
ejpam-855	204	7	}	}	PUNCT
ejpam-855	204	8	)	)	PUNCT
ejpam-855	204	9	⊆	⊆	NUM
ejpam-855	204	10	vy	vy	X
ejpam-855	204	11	.	.	PUNCT
ejpam-855	205	1	take	take	VERB
ejpam-855	205	2	v	v	NOUN
ejpam-855	205	3	=	=	SYM
ejpam-855	205	4	∪{vy	∪{vy	PROPN
ejpam-855	205	5	/	/	SYM
ejpam-855	205	6	y	y	PROPN
ejpam-855	205	7	∈	∈	PROPN
ejpam-855	205	8	x	x	PUNCT
ejpam-855	205	9	−	−	PUNCT
ejpam-855	205	10	u	u	NOUN
ejpam-855	205	11	}	}	PUNCT
ejpam-855	205	12	.	.	PUNCT
ejpam-855	206	1	then	then	ADV
ejpam-855	206	2	v	v	NOUN
ejpam-855	206	3	is	be	AUX
ejpam-855	206	4	λr	λr	NOUN
ejpam-855	206	5	-open	-open	ADJ
ejpam-855	206	6	,	,	PUNCT
ejpam-855	206	7	x	x	X
ejpam-855	206	8	−	−	NOUN
ejpam-855	206	9	u	u	NOUN
ejpam-855	206	10	⊆	⊆	NUM
ejpam-855	206	11	v	v	NOUN
ejpam-855	206	12	and	and	CCONJ
ejpam-855	206	13	x	x	NOUN
ejpam-855	206	14	/∈	/∈	NOUN
ejpam-855	206	15	v	v	INTJ
ejpam-855	206	16	.	.	PUNCT
ejpam-855	207	1	therefore	therefore	ADV
ejpam-855	207	2	λr	λr	ADP
ejpam-855	207	3	−	−	PROPN
ejpam-855	207	4	cl({x	cl({x	NOUN
ejpam-855	207	5	}	}	PUNCT
ejpam-855	207	6	)	)	PUNCT
ejpam-855	208	1	⊆	⊆	NUM
ejpam-855	208	2	x	x	SYM
ejpam-855	208	3	−	−	NOUN
ejpam-855	208	4	v	v	NUM
ejpam-855	208	5	⊆	⊆	NUM
ejpam-855	208	6	u	u	NOUN
ejpam-855	208	7	and	and	CCONJ
ejpam-855	208	8	hence	hence	ADV
ejpam-855	208	9	(	(	PUNCT
ejpam-855	208	10	x	x	X
ejpam-855	208	11	,	,	PUNCT
ejpam-855	208	12	τ	τ	X
ejpam-855	208	13	)	)	PUNCT
ejpam-855	208	14	is	be	AUX
ejpam-855	208	15	λr	λr	ADP
ejpam-855	208	16	−	−	PROPN
ejpam-855	208	17	r0	r0	NOUN
ejpam-855	208	18	.	.	PUNCT
ejpam-855	209	1	theorem	theorem	VERB
ejpam-855	209	2	6	6	NUM
ejpam-855	209	3	.	.	PUNCT
ejpam-855	210	1	if	if	SCONJ
ejpam-855	210	2	(	(	PUNCT
ejpam-855	210	3	x	x	X
ejpam-855	210	4	,	,	PUNCT
ejpam-855	210	5	τ	τ	X
ejpam-855	210	6	)	)	PUNCT
ejpam-855	210	7	is	be	AUX
ejpam-855	210	8	λr	λr	ADP
ejpam-855	210	9	−	−	PROPN
ejpam-855	210	10	t2	t2	NOUN
ejpam-855	210	11	,	,	PUNCT
ejpam-855	210	12	then	then	ADV
ejpam-855	210	13	(	(	PUNCT
ejpam-855	210	14	x	x	X
ejpam-855	210	15	,	,	PUNCT
ejpam-855	210	16	τ	τ	X
ejpam-855	210	17	)	)	PUNCT
ejpam-855	210	18	is	be	AUX
ejpam-855	210	19	λr	λr	ADP
ejpam-855	210	20	−	−	PROPN
ejpam-855	210	21	r1	r1	NOUN
ejpam-855	210	22	.	.	PUNCT
ejpam-855	211	1	proof	proof	NOUN
ejpam-855	211	2	.	.	PUNCT
ejpam-855	212	1	let	let	VERB
ejpam-855	212	2	x	x	PRON
ejpam-855	212	3	,	,	PUNCT
ejpam-855	212	4	y	y	PROPN
ejpam-855	212	5	∈	∈	PROPN
ejpam-855	212	6	x	x	PUNCT
ejpam-855	212	7	such	such	ADJ
ejpam-855	212	8	that	that	SCONJ
ejpam-855	212	9	x	x	SYM
ejpam-855	212	10	6=	6=	NUM
ejpam-855	212	11	y	y	PROPN
ejpam-855	212	12	and	and	CCONJ
ejpam-855	212	13	λr	λr	ADP
ejpam-855	212	14	−	−	PROPN
ejpam-855	212	15	cl({x	cl({x	NUM
ejpam-855	212	16	}	}	PUNCT
ejpam-855	212	17	)	)	PUNCT
ejpam-855	212	18	6=	6=	ADP
ejpam-855	212	19	λr	λr	ADP
ejpam-855	212	20	−	−	PROPN
ejpam-855	212	21	cl({y	cl({y	NOUN
ejpam-855	212	22	}	}	PUNCT
ejpam-855	212	23	)	)	PUNCT
ejpam-855	212	24	.	.	PUNCT
ejpam-855	213	1	since	since	SCONJ
ejpam-855	213	2	(	(	PUNCT
ejpam-855	213	3	x	x	X
ejpam-855	213	4	,	,	PUNCT
ejpam-855	213	5	τ	τ	X
ejpam-855	213	6	)	)	PUNCT
ejpam-855	213	7	is	be	AUX
ejpam-855	213	8	λr	λr	ADP
ejpam-855	213	9	−	−	PROPN
ejpam-855	213	10	t2	t2	NOUN
ejpam-855	213	11	,	,	PUNCT
ejpam-855	213	12	∃λr	∃λr	NOUN
ejpam-855	213	13	-open	-open	PROPN
ejpam-855	213	14	sets	set	VERB
ejpam-855	213	15	u	u	NOUN
ejpam-855	213	16	and	and	CCONJ
ejpam-855	213	17	v	v	ADP
ejpam-855	213	18	such	such	ADJ
ejpam-855	213	19	that	that	SCONJ
ejpam-855	213	20	x	x	SYM
ejpam-855	213	21	∈	∈	PROPN
ejpam-855	213	22	u	u	NOUN
ejpam-855	213	23	,	,	PUNCT
ejpam-855	213	24	y	y	PROPN
ejpam-855	213	25	∈	∈	PROPN
ejpam-855	213	26	v	v	NOUN
ejpam-855	213	27	and	and	CCONJ
ejpam-855	213	28	u	u	NOUN
ejpam-855	213	29	∩	∩	NOUN
ejpam-855	213	30	v	v	NOUN
ejpam-855	213	31	=	=	PUNCT
ejpam-855	213	32	;	;	PUNCT
ejpam-855	213	33	.	.	PUNCT
ejpam-855	214	1	that	that	PRON
ejpam-855	214	2	is	is	ADV
ejpam-855	214	3	,	,	PUNCT
ejpam-855	214	4	{	{	PUNCT
ejpam-855	214	5	x	x	NOUN
ejpam-855	214	6	}	}	PUNCT
ejpam-855	214	7	⊆	⊆	NUM
ejpam-855	214	8	u	u	NOUN
ejpam-855	214	9	and	and	CCONJ
ejpam-855	214	10	{	{	PUNCT
ejpam-855	214	11	y	y	NOUN
ejpam-855	214	12	}	}	PUNCT
ejpam-855	214	13	⊆	⊆	NUM
ejpam-855	214	14	v	v	NOUN
ejpam-855	214	15	.	.	PUNCT
ejpam-855	215	1	since	since	SCONJ
ejpam-855	215	2	(	(	PUNCT
ejpam-855	215	3	x	x	X
ejpam-855	215	4	,	,	PUNCT
ejpam-855	215	5	τ	τ	X
ejpam-855	215	6	)	)	PUNCT
ejpam-855	215	7	is	be	AUX
ejpam-855	215	8	λr	λr	ADP
ejpam-855	215	9	−	−	PROPN
ejpam-855	215	10	t2	t2	NOUN
ejpam-855	215	11	,	,	PUNCT
ejpam-855	215	12	it	it	PRON
ejpam-855	215	13	is	be	AUX
ejpam-855	215	14	λr	λr	ADP
ejpam-855	215	15	−	−	PROPN
ejpam-855	215	16	t1	t1	NOUN
ejpam-855	215	17	.	.	PUNCT
ejpam-855	216	1	therefore	therefore	ADV
ejpam-855	216	2	for	for	ADP
ejpam-855	216	3	every	every	DET
ejpam-855	216	4	x	x	SYM
ejpam-855	216	5	∈	∈	PROPN
ejpam-855	216	6	x	x	X
ejpam-855	216	7	,	,	PUNCT
ejpam-855	216	8	{	{	PUNCT
ejpam-855	216	9	x	x	NOUN
ejpam-855	216	10	}	}	PUNCT
ejpam-855	216	11	=	=	SYM
ejpam-855	216	12	λr	λr	ADP
ejpam-855	216	13	−	−	NOUN
ejpam-855	216	14	cl({x	cl({x	NOUN
ejpam-855	216	15	}	}	PUNCT
ejpam-855	216	16	)	)	PUNCT
ejpam-855	216	17	.	.	PUNCT
ejpam-855	217	1	thus	thus	ADV
ejpam-855	217	2	λr	λr	ADP
ejpam-855	217	3	−	−	NOUN
ejpam-855	217	4	cl({x	cl({x	NUM
ejpam-855	217	5	}	}	PUNCT
ejpam-855	217	6	)	)	PUNCT
ejpam-855	218	1	⊆	⊆	NUM
ejpam-855	218	2	u	u	NOUN
ejpam-855	218	3	,	,	PUNCT
ejpam-855	218	4	λr	λr	ADP
ejpam-855	218	5	−	−	PROPN
ejpam-855	218	6	cl({y	cl({y	NOUN
ejpam-855	218	7	}	}	PUNCT
ejpam-855	218	8	)	)	PUNCT
ejpam-855	218	9	⊆	⊆	NUM
ejpam-855	218	10	v	v	NOUN
ejpam-855	218	11	and	and	CCONJ
ejpam-855	218	12	u	u	NOUN
ejpam-855	218	13	∩	∩	NOUN
ejpam-855	218	14	v	v	NOUN
ejpam-855	218	15	=	=	PUNCT
ejpam-855	218	16	;	;	PUNCT
ejpam-855	218	17	.	.	PUNCT
ejpam-855	219	1	hence	hence	ADV
ejpam-855	219	2	(	(	PUNCT
ejpam-855	219	3	x	x	X
ejpam-855	219	4	,	,	PUNCT
ejpam-855	219	5	τ	τ	X
ejpam-855	219	6	)	)	PUNCT
ejpam-855	219	7	is	be	AUX
ejpam-855	219	8	λr	λr	ADP
ejpam-855	219	9	−	−	PROPN
ejpam-855	219	10	r1	r1	PROPN
ejpam-855	219	11	.	.	PUNCT
ejpam-855	220	1	remark	remark	PROPN
ejpam-855	220	2	1	1	NUM
ejpam-855	220	3	.	.	PUNCT
ejpam-855	221	1	the	the	DET
ejpam-855	221	2	converse	converse	NOUN
ejpam-855	221	3	of	of	ADP
ejpam-855	221	4	the	the	DET
ejpam-855	221	5	above	above	ADJ
ejpam-855	221	6	theorem	theorem	NOUN
ejpam-855	221	7	need	need	AUX
ejpam-855	221	8	not	not	PART
ejpam-855	221	9	be	be	AUX
ejpam-855	221	10	true	true	ADJ
ejpam-855	221	11	.	.	PUNCT
ejpam-855	222	1	for	for	ADP
ejpam-855	222	2	example	example	NOUN
ejpam-855	222	3	,	,	PUNCT
ejpam-855	222	4	let	let	VERB
ejpam-855	222	5	x	x	PUNCT
ejpam-855	222	6	=	=	PRON
ejpam-855	222	7	{	{	PUNCT
ejpam-855	222	8	a	a	PRON
ejpam-855	222	9	,	,	PUNCT
ejpam-855	222	10	b	b	NOUN
ejpam-855	222	11	,	,	PUNCT
ejpam-855	222	12	c	c	NOUN
ejpam-855	222	13	,	,	PUNCT
ejpam-855	222	14	d	d	NOUN
ejpam-855	222	15	}	}	PUNCT
ejpam-855	222	16	and	and	CCONJ
ejpam-855	222	17	τ	τ	PROPN
ejpam-855	222	18	=	=	PUNCT
ejpam-855	222	19	{	{	PUNCT
ejpam-855	222	20	x	x	X
ejpam-855	222	21	,	,	PUNCT
ejpam-855	222	22	;	;	PUNCT
ejpam-855	222	23	,	,	PUNCT
ejpam-855	222	24	{	{	PUNCT
ejpam-855	222	25	a	a	X
ejpam-855	222	26	}	}	PUNCT
ejpam-855	222	27	,	,	PUNCT
ejpam-855	222	28	{	{	PUNCT
ejpam-855	222	29	b	b	NOUN
ejpam-855	222	30	,	,	PUNCT
ejpam-855	222	31	c	c	NOUN
ejpam-855	222	32	}	}	PUNCT
ejpam-855	222	33	,	,	PUNCT
ejpam-855	222	34	{	{	PUNCT
ejpam-855	222	35	a	a	PRON
ejpam-855	222	36	,	,	PUNCT
ejpam-855	222	37	b	b	NOUN
ejpam-855	222	38	,	,	PUNCT
ejpam-855	222	39	c	c	NOUN
ejpam-855	222	40	}	}	PUNCT
ejpam-855	222	41	}	}	PUNCT
ejpam-855	222	42	.	.	PUNCT
ejpam-855	223	1	then	then	ADV
ejpam-855	223	2	λro(x	λro(x	PROPN
ejpam-855	223	3	,	,	PUNCT
ejpam-855	223	4	τ	τ	PROPN
ejpam-855	223	5	)	)	PUNCT
ejpam-855	223	6	=	=	PRON
ejpam-855	223	7	{	{	PUNCT
ejpam-855	223	8	x	x	X
ejpam-855	223	9	,	,	PUNCT
ejpam-855	223	10	;	;	PUNCT
ejpam-855	223	11	,	,	PUNCT
ejpam-855	223	12	{	{	PUNCT
ejpam-855	223	13	a	a	X
ejpam-855	223	14	}	}	PUNCT
ejpam-855	223	15	,	,	PUNCT
ejpam-855	223	16	{	{	PUNCT
ejpam-855	223	17	b	b	NOUN
ejpam-855	223	18	,	,	PUNCT
ejpam-855	223	19	c	c	NOUN
ejpam-855	223	20	}	}	PUNCT
ejpam-855	223	21	,	,	PUNCT
ejpam-855	223	22	{	{	PUNCT
ejpam-855	223	23	a	a	PRON
ejpam-855	223	24	,	,	PUNCT
ejpam-855	223	25	b	b	NOUN
ejpam-855	223	26	,	,	PUNCT
ejpam-855	223	27	c}{b	c}{b	PROPN
ejpam-855	223	28	,	,	PUNCT
ejpam-855	223	29	c	c	X
ejpam-855	223	30	,	,	PUNCT
ejpam-855	223	31	d	d	NOUN
ejpam-855	223	32	}	}	PUNCT
ejpam-855	223	33	,	,	PUNCT
ejpam-855	223	34	{	{	PUNCT
ejpam-855	223	35	a	a	PRON
ejpam-855	223	36	,	,	PUNCT
ejpam-855	223	37	d	d	NOUN
ejpam-855	223	38	}	}	PUNCT
ejpam-855	223	39	}	}	PUNCT
ejpam-855	223	40	.	.	PUNCT
ejpam-855	224	1	here	here	ADV
ejpam-855	224	2	(	(	PUNCT
ejpam-855	224	3	x	x	X
ejpam-855	224	4	,	,	PUNCT
ejpam-855	224	5	τ	τ	X
ejpam-855	224	6	)	)	PUNCT
ejpam-855	224	7	is	be	AUX
ejpam-855	224	8	λr	λr	ADP
ejpam-855	224	9	−	−	PROPN
ejpam-855	224	10	r1	r1	NOUN
ejpam-855	224	11	but	but	CCONJ
ejpam-855	224	12	not	not	PART
ejpam-855	224	13	λr	λr	VERB
ejpam-855	224	14	−	−	PROPN
ejpam-855	224	15	t2	t2	NOUN
ejpam-855	224	16	.	.	PUNCT
ejpam-855	225	1	note	note	VERB
ejpam-855	225	2	that	that	SCONJ
ejpam-855	225	3	λr	λr	VERB
ejpam-855	225	4	−	−	PROPN
ejpam-855	225	5	t0	t0	PROPN
ejpam-855	225	6	and	and	CCONJ
ejpam-855	225	7	λr	λr	NOUN
ejpam-855	225	8	−	−	PROPN
ejpam-855	225	9	r1	r1	PROPN
ejpam-855	225	10	are	be	AUX
ejpam-855	225	11	independent	independent	ADJ
ejpam-855	225	12	as	as	ADP
ejpam-855	225	13	in	in	ADP
ejpam-855	225	14	the	the	DET
ejpam-855	225	15	following	follow	VERB
ejpam-855	225	16	examples	example	NOUN
ejpam-855	225	17	3	3	NUM
ejpam-855	225	18	and	and	CCONJ
ejpam-855	225	19	4	4	NUM
ejpam-855	225	20	.	.	PUNCT
ejpam-855	226	1	s.	s.	PROPN
ejpam-855	226	2	missier	missier	PROPN
ejpam-855	226	3	,	,	PUNCT
ejpam-855	226	4	m.	m.	NOUN
ejpam-855	226	5	jeyanthi	jeyanthi	PROPN
ejpam-855	226	6	,	,	PUNCT
ejpam-855	226	7	a.	a.	PROPN
ejpam-855	226	8	kılıçman	kılıçman	PROPN
ejpam-855	226	9	/	/	SYM
ejpam-855	226	10	eur	eur	PROPN
ejpam-855	226	11	.	.	PUNCT
ejpam-855	227	1	j.	j.	PROPN
ejpam-855	227	2	pure	pure	PROPN
ejpam-855	227	3	appl	appl	PROPN
ejpam-855	227	4	.	.	PROPN
ejpam-855	227	5	math	math	PROPN
ejpam-855	227	6	,	,	PUNCT
ejpam-855	227	7	5	5	NUM
ejpam-855	227	8	(	(	PUNCT
ejpam-855	227	9	2012	2012	NUM
ejpam-855	227	10	)	)	PUNCT
ejpam-855	227	11	,	,	PUNCT
ejpam-855	227	12	357	357	NUM
ejpam-855	227	13	-	-	SYM
ejpam-855	227	14	364	364	NUM
ejpam-855	227	15	362	362	NUM
ejpam-855	227	16	example	example	NOUN
ejpam-855	227	17	3	3	NUM
ejpam-855	227	18	.	.	PUNCT
ejpam-855	228	1	let	let	VERB
ejpam-855	228	2	x	x	PUNCT
ejpam-855	228	3	=	=	PRON
ejpam-855	228	4	{	{	PUNCT
ejpam-855	228	5	a	a	PRON
ejpam-855	228	6	,	,	PUNCT
ejpam-855	228	7	b	b	NOUN
ejpam-855	228	8	,	,	PUNCT
ejpam-855	228	9	c	c	NOUN
ejpam-855	228	10	}	}	PUNCT
ejpam-855	228	11	and	and	CCONJ
ejpam-855	228	12	τ	τ	PROPN
ejpam-855	228	13	=	=	PUNCT
ejpam-855	228	14	{	{	PUNCT
ejpam-855	228	15	x	x	X
ejpam-855	228	16	,	,	PUNCT
ejpam-855	228	17	;	;	PUNCT
ejpam-855	228	18	,	,	PUNCT
ejpam-855	228	19	{	{	PUNCT
ejpam-855	228	20	c	c	NOUN
ejpam-855	228	21	}	}	PUNCT
ejpam-855	228	22	,	,	PUNCT
ejpam-855	228	23	{	{	PUNCT
ejpam-855	228	24	a	a	X
ejpam-855	228	25	,	,	PUNCT
ejpam-855	228	26	c	c	NOUN
ejpam-855	228	27	}	}	PUNCT
ejpam-855	228	28	,	,	PUNCT
ejpam-855	228	29	{	{	PUNCT
ejpam-855	228	30	b	b	X
ejpam-855	228	31	,	,	PUNCT
ejpam-855	228	32	c	c	NOUN
ejpam-855	228	33	}	}	PUNCT
ejpam-855	228	34	}	}	PUNCT
ejpam-855	228	35	.	.	PUNCT
ejpam-855	229	1	then	then	ADV
ejpam-855	229	2	λro(x	λro(x	PROPN
ejpam-855	229	3	,	,	PUNCT
ejpam-855	229	4	τ	τ	PROPN
ejpam-855	229	5	)	)	PUNCT
ejpam-855	229	6	=	=	PRON
ejpam-855	229	7	{	{	PUNCT
ejpam-855	229	8	x	x	X
ejpam-855	229	9	,	,	PUNCT
ejpam-855	229	10	;	;	PUNCT
ejpam-855	229	11	,	,	PUNCT
ejpam-855	229	12	{	{	PUNCT
ejpam-855	229	13	c	c	NOUN
ejpam-855	229	14	}	}	PUNCT
ejpam-855	229	15	,	,	PUNCT
ejpam-855	229	16	{	{	PUNCT
ejpam-855	229	17	a	a	X
ejpam-855	229	18	,	,	PUNCT
ejpam-855	229	19	c	c	NOUN
ejpam-855	229	20	}	}	PUNCT
ejpam-855	229	21	,	,	PUNCT
ejpam-855	229	22	{	{	PUNCT
ejpam-855	229	23	b	b	X
ejpam-855	229	24	,	,	PUNCT
ejpam-855	229	25	c	c	NOUN
ejpam-855	229	26	}	}	PUNCT
ejpam-855	229	27	}	}	PUNCT
ejpam-855	229	28	.	.	PUNCT
ejpam-855	230	1	here	here	ADV
ejpam-855	230	2	(	(	PUNCT
ejpam-855	230	3	x	x	X
ejpam-855	230	4	,	,	PUNCT
ejpam-855	230	5	τ	τ	X
ejpam-855	230	6	)	)	PUNCT
ejpam-855	230	7	is	be	AUX
ejpam-855	230	8	λr	λr	ADP
ejpam-855	230	9	−	−	PROPN
ejpam-855	230	10	t0	t0	NOUN
ejpam-855	231	1	but	but	CCONJ
ejpam-855	231	2	it	it	PRON
ejpam-855	231	3	is	be	AUX
ejpam-855	231	4	not	not	PART
ejpam-855	231	5	λr	λr	ADP
ejpam-855	231	6	−	−	PROPN
ejpam-855	231	7	r1	r1	PROPN
ejpam-855	231	8	.	.	PUNCT
ejpam-855	231	9	example	example	NOUN
ejpam-855	232	1	4	4	X
ejpam-855	232	2	.	.	PUNCT
ejpam-855	232	3	let	let	VERB
ejpam-855	232	4	x	x	PUNCT
ejpam-855	232	5	=	=	PRON
ejpam-855	232	6	{	{	PUNCT
ejpam-855	232	7	a	a	PRON
ejpam-855	232	8	,	,	PUNCT
ejpam-855	232	9	b	b	NOUN
ejpam-855	232	10	,	,	PUNCT
ejpam-855	232	11	c	c	NOUN
ejpam-855	232	12	,	,	PUNCT
ejpam-855	232	13	d	d	NOUN
ejpam-855	232	14	}	}	PUNCT
ejpam-855	232	15	and	and	CCONJ
ejpam-855	232	16	τ	τ	PROPN
ejpam-855	232	17	=	=	PUNCT
ejpam-855	232	18	{	{	PUNCT
ejpam-855	232	19	x	x	X
ejpam-855	232	20	,	,	PUNCT
ejpam-855	232	21	;	;	PUNCT
ejpam-855	232	22	,	,	PUNCT
ejpam-855	232	23	{	{	PUNCT
ejpam-855	232	24	a	a	X
ejpam-855	232	25	}	}	PUNCT
ejpam-855	232	26	,	,	PUNCT
ejpam-855	232	27	{	{	PUNCT
ejpam-855	232	28	b	b	NOUN
ejpam-855	232	29	,	,	PUNCT
ejpam-855	232	30	c	c	NOUN
ejpam-855	232	31	}	}	PUNCT
ejpam-855	232	32	,	,	PUNCT
ejpam-855	232	33	{	{	PUNCT
ejpam-855	232	34	a	a	PRON
ejpam-855	232	35	,	,	PUNCT
ejpam-855	232	36	b	b	NOUN
ejpam-855	232	37	,	,	PUNCT
ejpam-855	232	38	c	c	NOUN
ejpam-855	232	39	}	}	PUNCT
ejpam-855	232	40	}	}	PUNCT
ejpam-855	232	41	.	.	PUNCT
ejpam-855	233	1	then	then	ADV
ejpam-855	233	2	λro(x	λro(x	PROPN
ejpam-855	233	3	,	,	PUNCT
ejpam-855	233	4	τ	τ	PROPN
ejpam-855	233	5	)	)	PUNCT
ejpam-855	233	6	=	=	PRON
ejpam-855	233	7	{	{	PUNCT
ejpam-855	233	8	x	x	X
ejpam-855	233	9	,	,	PUNCT
ejpam-855	233	10	;	;	PUNCT
ejpam-855	233	11	,	,	PUNCT
ejpam-855	233	12	{	{	PUNCT
ejpam-855	233	13	a	a	X
ejpam-855	233	14	}	}	PUNCT
ejpam-855	233	15	,	,	PUNCT
ejpam-855	233	16	{	{	PUNCT
ejpam-855	233	17	a	a	PRON
ejpam-855	233	18	,	,	PUNCT
ejpam-855	233	19	d	d	NOUN
ejpam-855	233	20	}	}	PUNCT
ejpam-855	233	21	,	,	PUNCT
ejpam-855	233	22	{	{	PUNCT
ejpam-855	233	23	b	b	X
ejpam-855	233	24	,	,	PUNCT
ejpam-855	233	25	c	c	NOUN
ejpam-855	233	26	}	}	PUNCT
ejpam-855	233	27	,	,	PUNCT
ejpam-855	233	28	{	{	PUNCT
ejpam-855	233	29	a	a	DET
ejpam-855	233	30	,	,	PUNCT
ejpam-855	233	31	b	b	NOUN
ejpam-855	233	32	,	,	PUNCT
ejpam-855	233	33	c	c	NOUN
ejpam-855	233	34	}	}	PUNCT
ejpam-855	233	35	,	,	PUNCT
ejpam-855	233	36	{	{	PUNCT
ejpam-855	233	37	b	b	X
ejpam-855	233	38	,	,	PUNCT
ejpam-855	233	39	c	c	NOUN
ejpam-855	233	40	,	,	PUNCT
ejpam-855	233	41	d	d	NOUN
ejpam-855	233	42	}	}	PUNCT
ejpam-855	233	43	}	}	PUNCT
ejpam-855	233	44	.	.	PUNCT
ejpam-855	234	1	here	here	ADV
ejpam-855	234	2	(	(	PUNCT
ejpam-855	234	3	x	x	X
ejpam-855	234	4	,	,	PUNCT
ejpam-855	234	5	τ	τ	X
ejpam-855	234	6	)	)	PUNCT
ejpam-855	234	7	is	be	AUX
ejpam-855	234	8	λr	λr	ADP
ejpam-855	234	9	−	−	PROPN
ejpam-855	234	10	r1	r1	NOUN
ejpam-855	235	1	but	but	CCONJ
ejpam-855	235	2	it	it	PRON
ejpam-855	235	3	is	be	AUX
ejpam-855	235	4	not	not	PART
ejpam-855	235	5	λr	λr	ADP
ejpam-855	235	6	−	−	PROPN
ejpam-855	235	7	t0	t0	PROPN
ejpam-855	235	8	.	.	PUNCT
ejpam-855	236	1	theorem	theorem	VERB
ejpam-855	236	2	7	7	NUM
ejpam-855	236	3	.	.	X
ejpam-855	236	4	for	for	ADP
ejpam-855	236	5	a	a	DET
ejpam-855	236	6	space	space	NOUN
ejpam-855	236	7	(	(	PUNCT
ejpam-855	236	8	x	x	X
ejpam-855	236	9	,	,	PUNCT
ejpam-855	236	10	τ	τ	PROPN
ejpam-855	236	11	)	)	PUNCT
ejpam-855	236	12	,	,	PUNCT
ejpam-855	236	13	the	the	DET
ejpam-855	236	14	following	follow	VERB
ejpam-855	236	15	statements	statement	NOUN
ejpam-855	236	16	are	be	AUX
ejpam-855	236	17	equivalent	equivalent	ADJ
ejpam-855	236	18	:	:	PUNCT
ejpam-855	236	19	(	(	PUNCT
ejpam-855	236	20	1	1	X
ejpam-855	236	21	)	)	PUNCT
ejpam-855	236	22	(	(	PUNCT
ejpam-855	236	23	x	x	X
ejpam-855	236	24	,	,	PUNCT
ejpam-855	236	25	τ	τ	X
ejpam-855	236	26	)	)	PUNCT
ejpam-855	236	27	is	be	AUX
ejpam-855	236	28	λr	λr	ADP
ejpam-855	236	29	−	−	PROPN
ejpam-855	236	30	r1	r1	NOUN
ejpam-855	236	31	,	,	PUNCT
ejpam-855	236	32	(	(	PUNCT
ejpam-855	236	33	2	2	X
ejpam-855	236	34	)	)	PUNCT
ejpam-855	236	35	if	if	SCONJ
ejpam-855	236	36	x	x	PRON
ejpam-855	236	37	,	,	PUNCT
ejpam-855	236	38	y	y	PROPN
ejpam-855	236	39	∈	∈	PROPN
ejpam-855	236	40	x	x	PUNCT
ejpam-855	236	41	such	such	ADJ
ejpam-855	236	42	that	that	PRON
ejpam-855	236	43	λr	λr	ADP
ejpam-855	236	44	−	−	PROPN
ejpam-855	236	45	cl({x	cl({x	NOUN
ejpam-855	236	46	}	}	PUNCT
ejpam-855	236	47	)	)	PUNCT
ejpam-855	237	1	6=	6=	ADP
ejpam-855	237	2	λr	λr	ADP
ejpam-855	237	3	−	−	PROPN
ejpam-855	237	4	cl({y	cl({y	NOUN
ejpam-855	237	5	}	}	PUNCT
ejpam-855	237	6	)	)	PUNCT
ejpam-855	237	7	,	,	PUNCT
ejpam-855	237	8	then	then	ADV
ejpam-855	237	9	∃λr	∃λr	NOUN
ejpam-855	237	10	-closed	-close	VERB
ejpam-855	237	11	sets	set	NOUN
ejpam-855	237	12	f1	f1	NOUN
ejpam-855	237	13	and	and	CCONJ
ejpam-855	237	14	f2	f2	NOUN
ejpam-855	237	15	such	such	ADJ
ejpam-855	237	16	that	that	SCONJ
ejpam-855	237	17	x	x	SYM
ejpam-855	237	18	∈	∈	PROPN
ejpam-855	237	19	f1	f1	NOUN
ejpam-855	237	20	,	,	PUNCT
ejpam-855	237	21	y	y	PROPN
ejpam-855	237	22	/∈	/∈	PUNCT
ejpam-855	237	23	f1	f1	PROPN
ejpam-855	237	24	,	,	PUNCT
ejpam-855	237	25	x	x	PROPN
ejpam-855	237	26	/∈	/∈	PUNCT
ejpam-855	237	27	f2	f2	PROPN
ejpam-855	237	28	,	,	PUNCT
ejpam-855	237	29	y	y	PROPN
ejpam-855	237	30	∈	∈	PROPN
ejpam-855	237	31	f2	f2	PROPN
ejpam-855	237	32	and	and	CCONJ
ejpam-855	237	33	x	x	X
ejpam-855	237	34	=	=	PUNCT
ejpam-855	237	35	f1	f1	NOUN
ejpam-855	237	36	∪	∪	NOUN
ejpam-855	237	37	f2	f2	PROPN
ejpam-855	237	38	.	.	PUNCT
ejpam-855	238	1	proof	proof	NOUN
ejpam-855	238	2	.	.	PUNCT
ejpam-855	239	1	(	(	PUNCT
ejpam-855	239	2	1)⇒	1)⇒	NUM
ejpam-855	239	3	(	(	PUNCT
ejpam-855	239	4	2	2	NUM
ejpam-855	239	5	)	)	PUNCT
ejpam-855	239	6	let	let	VERB
ejpam-855	239	7	x	x	PRON
ejpam-855	239	8	,	,	PUNCT
ejpam-855	239	9	y	y	PROPN
ejpam-855	239	10	∈	∈	PROPN
ejpam-855	239	11	x	x	PUNCT
ejpam-855	239	12	such	such	ADJ
ejpam-855	239	13	that	that	SCONJ
ejpam-855	239	14	λr−cl({x	λr−cl({x	NOUN
ejpam-855	239	15	}	}	PUNCT
ejpam-855	239	16	)	)	PUNCT
ejpam-855	239	17	6=	6=	PUNCT
ejpam-855	240	1	λr−cl({y	λr−cl({y	SYM
ejpam-855	240	2	}	}	PUNCT
ejpam-855	240	3	)	)	PUNCT
ejpam-855	240	4	.	.	PUNCT
ejpam-855	241	1	then	then	ADV
ejpam-855	241	2	by	by	ADP
ejpam-855	241	3	(	(	PUNCT
ejpam-855	241	4	1	1	NUM
ejpam-855	241	5	)	)	PUNCT
ejpam-855	241	6	,	,	PUNCT
ejpam-855	241	7	∃	∃	PROPN
ejpam-855	241	8	disjoint	disjoint	NOUN
ejpam-855	241	9	λr	λr	ADP
ejpam-855	241	10	-open	-open	PROPN
ejpam-855	241	11	sets	set	NOUN
ejpam-855	241	12	u	u	NOUN
ejpam-855	241	13	and	and	CCONJ
ejpam-855	241	14	v	v	ADP
ejpam-855	241	15	such	such	ADJ
ejpam-855	241	16	that	that	PRON
ejpam-855	241	17	λr	λr	NOUN
ejpam-855	241	18	−	−	PROPN
ejpam-855	241	19	cl({x})⊆	cl({x})⊆	NOUN
ejpam-855	241	20	u	u	NOUN
ejpam-855	241	21	and	and	CCONJ
ejpam-855	241	22	λr	λr	INTJ
ejpam-855	241	23	−	−	PROPN
ejpam-855	241	24	cl({y	cl({y	NOUN
ejpam-855	241	25	}	}	PUNCT
ejpam-855	241	26	)	)	PUNCT
ejpam-855	241	27	⊆	⊆	NUM
ejpam-855	241	28	v	v	NOUN
ejpam-855	241	29	.	.	PUNCT
ejpam-855	242	1	take	take	VERB
ejpam-855	242	2	f1	f1	NOUN
ejpam-855	242	3	=	=	PUNCT
ejpam-855	242	4	x	x	PUNCT
ejpam-855	242	5	−	−	PROPN
ejpam-855	242	6	v	v	NOUN
ejpam-855	242	7	and	and	CCONJ
ejpam-855	242	8	f2	f2	ADV
ejpam-855	242	9	=	=	PUNCT
ejpam-855	242	10	x	x	SYM
ejpam-855	243	1	−	−	PROPN
ejpam-855	243	2	u	u	NOUN
ejpam-855	243	3	.	.	PUNCT
ejpam-855	244	1	then	then	ADV
ejpam-855	244	2	f1	f1	PROPN
ejpam-855	244	3	and	and	CCONJ
ejpam-855	244	4	f2	f2	PROPN
ejpam-855	244	5	are	be	AUX
ejpam-855	244	6	λr	λr	ADP
ejpam-855	244	7	-closed	-closed	ADJ
ejpam-855	244	8	sets	set	NOUN
ejpam-855	244	9	such	such	ADJ
ejpam-855	244	10	that	that	SCONJ
ejpam-855	244	11	x	x	SYM
ejpam-855	244	12	∈	∈	PROPN
ejpam-855	244	13	f1	f1	NOUN
ejpam-855	244	14	,	,	PUNCT
ejpam-855	244	15	y	y	PROPN
ejpam-855	244	16	/∈	/∈	PUNCT
ejpam-855	244	17	f1	f1	PROPN
ejpam-855	244	18	,	,	PUNCT
ejpam-855	244	19	x	x	PROPN
ejpam-855	244	20	/∈	/∈	PUNCT
ejpam-855	244	21	f2	f2	PROPN
ejpam-855	244	22	,	,	PUNCT
ejpam-855	244	23	y	y	PROPN
ejpam-855	244	24	∈	∈	PROPN
ejpam-855	244	25	f2	f2	PROPN
ejpam-855	244	26	and	and	CCONJ
ejpam-855	244	27	x	x	X
ejpam-855	244	28	=	=	PUNCT
ejpam-855	244	29	f1	f1	NOUN
ejpam-855	244	30	∪	∪	NOUN
ejpam-855	244	31	f2	f2	PROPN
ejpam-855	244	32	.	.	PUNCT
ejpam-855	245	1	(	(	PUNCT
ejpam-855	245	2	2)→	2)→	NUM
ejpam-855	245	3	(	(	PUNCT
ejpam-855	245	4	1	1	NUM
ejpam-855	245	5	)	)	PUNCT
ejpam-855	245	6	let	let	VERB
ejpam-855	245	7	x	x	PRON
ejpam-855	245	8	,	,	PUNCT
ejpam-855	245	9	y	y	PROPN
ejpam-855	245	10	∈	∈	PROPN
ejpam-855	245	11	x	x	PUNCT
ejpam-855	245	12	such	such	ADJ
ejpam-855	245	13	that	that	PRON
ejpam-855	245	14	λr	λr	ADP
ejpam-855	245	15	−	−	PROPN
ejpam-855	245	16	cl({x	cl({x	NOUN
ejpam-855	245	17	}	}	PUNCT
ejpam-855	245	18	)	)	PUNCT
ejpam-855	245	19	6=	6=	ADP
ejpam-855	245	20	λr	λr	ADP
ejpam-855	245	21	−	−	PROPN
ejpam-855	245	22	cl({y	cl({y	NOUN
ejpam-855	245	23	}	}	PUNCT
ejpam-855	245	24	)	)	PUNCT
ejpam-855	245	25	.	.	PUNCT
ejpam-855	246	1	then	then	ADV
ejpam-855	246	2	by	by	ADP
ejpam-855	246	3	(	(	PUNCT
ejpam-855	246	4	2	2	X
ejpam-855	246	5	)	)	PUNCT
ejpam-855	246	6	∃λr	∃λr	NOUN
ejpam-855	246	7	-closed	-close	VERB
ejpam-855	246	8	sets	set	NOUN
ejpam-855	246	9	f1	f1	NOUN
ejpam-855	246	10	and	and	CCONJ
ejpam-855	246	11	f2	f2	NOUN
ejpam-855	246	12	such	such	ADJ
ejpam-855	246	13	that	that	SCONJ
ejpam-855	246	14	x	x	SYM
ejpam-855	246	15	∈	∈	PROPN
ejpam-855	246	16	f1	f1	NOUN
ejpam-855	246	17	,	,	PUNCT
ejpam-855	246	18	y	y	PROPN
ejpam-855	246	19	/∈	/∈	PUNCT
ejpam-855	246	20	f1	f1	PROPN
ejpam-855	246	21	,	,	PUNCT
ejpam-855	246	22	x	x	PROPN
ejpam-855	246	23	/∈	/∈	PUNCT
ejpam-855	246	24	f2	f2	PROPN
ejpam-855	246	25	,	,	PUNCT
ejpam-855	246	26	y	y	PROPN
ejpam-855	246	27	∈	∈	PROPN
ejpam-855	246	28	f2	f2	PROPN
ejpam-855	246	29	and	and	CCONJ
ejpam-855	246	30	x	x	X
ejpam-855	246	31	=	=	PUNCT
ejpam-855	246	32	f1	f1	PROPN
ejpam-855	246	33	∪	∪	NOUN
ejpam-855	246	34	f2	f2	PROPN
ejpam-855	246	35	.	.	PUNCT
ejpam-855	247	1	take	take	VERB
ejpam-855	247	2	u	u	NOUN
ejpam-855	247	3	=	=	NOUN
ejpam-855	247	4	x	x	SYM
ejpam-855	247	5	−	−	X
ejpam-855	247	6	f2	f2	ADJ
ejpam-855	247	7	and	and	CCONJ
ejpam-855	247	8	v	v	NOUN
ejpam-855	247	9	=	=	NOUN
ejpam-855	247	10	x	x	NOUN
ejpam-855	248	1	−	−	PROPN
ejpam-855	248	2	f1	f1	NOUN
ejpam-855	248	3	.	.	PUNCT
ejpam-855	249	1	then	then	ADV
ejpam-855	249	2	u	u	PROPN
ejpam-855	249	3	and	and	CCONJ
ejpam-855	249	4	v	v	NOUN
ejpam-855	249	5	are	be	AUX
ejpam-855	249	6	λr	λr	ADP
ejpam-855	249	7	-open	-open	ADJ
ejpam-855	249	8	sets	set	NOUN
ejpam-855	249	9	,	,	PUNCT
ejpam-855	249	10	x	x	X
ejpam-855	249	11	∈	∈	PROPN
ejpam-855	249	12	u	u	NOUN
ejpam-855	249	13	,	,	PUNCT
ejpam-855	249	14	y	y	PROPN
ejpam-855	249	15	∈	∈	PROPN
ejpam-855	249	16	v	v	NOUN
ejpam-855	249	17	and	and	CCONJ
ejpam-855	249	18	u	u	NOUN
ejpam-855	249	19	∩	∩	NOUN
ejpam-855	249	20	v	v	NOUN
ejpam-855	249	21	=	=	PUNCT
ejpam-855	249	22	;	;	PUNCT
ejpam-855	249	23	.	.	PUNCT
ejpam-855	250	1	therefore	therefore	ADV
ejpam-855	250	2	(	(	PUNCT
ejpam-855	250	3	x	x	X
ejpam-855	250	4	,	,	PUNCT
ejpam-855	250	5	τ	τ	X
ejpam-855	250	6	)	)	PUNCT
ejpam-855	250	7	is	be	AUX
ejpam-855	250	8	λr	λr	ADP
ejpam-855	250	9	−	−	PROPN
ejpam-855	250	10	t2	t2	NOUN
ejpam-855	250	11	and	and	CCONJ
ejpam-855	250	12	hence	hence	ADV
ejpam-855	250	13	(	(	PUNCT
ejpam-855	250	14	x	x	X
ejpam-855	250	15	,	,	PUNCT
ejpam-855	250	16	τ	τ	X
ejpam-855	250	17	)	)	PUNCT
ejpam-855	250	18	is	be	AUX
ejpam-855	250	19	λr	λr	ADP
ejpam-855	250	20	−	−	PROPN
ejpam-855	250	21	r1	r1	PROPN
ejpam-855	250	22	.	.	PUNCT
ejpam-855	251	1	4	4	X
ejpam-855	251	2	.	.	X
ejpam-855	252	1	λr	λr	NOUN
ejpam-855	252	2	−	−	NOUN
ejpam-855	253	1	dk	dk	PROPN
ejpam-855	253	2	spaces	space	VERB
ejpam-855	253	3	definition	definition	NOUN
ejpam-855	253	4	3	3	X
ejpam-855	253	5	.	.	PUNCT
ejpam-855	254	1	let	let	AUX
ejpam-855	254	2	(	(	PUNCT
ejpam-855	254	3	x	x	X
ejpam-855	254	4	,	,	PUNCT
ejpam-855	254	5	τ	τ	X
ejpam-855	254	6	)	)	PUNCT
ejpam-855	254	7	be	be	VERB
ejpam-855	254	8	a	a	DET
ejpam-855	254	9	topological	topological	ADJ
ejpam-855	254	10	space	space	NOUN
ejpam-855	254	11	and	and	CCONJ
ejpam-855	254	12	a	a	DET
ejpam-855	254	13	be	be	AUX
ejpam-855	254	14	a	a	DET
ejpam-855	254	15	subset	subset	NOUN
ejpam-855	254	16	of	of	ADP
ejpam-855	254	17	x	x	X
ejpam-855	254	18	.	.	PUNCT
ejpam-855	255	1	then	then	ADV
ejpam-855	255	2	a	a	PRON
ejpam-855	255	3	is	be	AUX
ejpam-855	255	4	called	call	VERB
ejpam-855	255	5	λr	λr	ADP
ejpam-855	255	6	difference	difference	NOUN
ejpam-855	255	7	set	set	NOUN
ejpam-855	255	8	(	(	PUNCT
ejpam-855	255	9	shortly	shortly	ADV
ejpam-855	255	10	λr	λr	ADP
ejpam-855	255	11	-d	-d	DET
ejpam-855	255	12	set	set	NOUN
ejpam-855	255	13	)	)	PUNCT
ejpam-855	255	14	if	if	SCONJ
ejpam-855	255	15	∃u	∃u	NOUN
ejpam-855	255	16	,	,	PUNCT
ejpam-855	255	17	v	v	NUM
ejpam-855	255	18	∈	∈	NOUN
ejpam-855	256	1	λro(x	λro(x	X
ejpam-855	256	2	,	,	PUNCT
ejpam-855	256	3	τ	τ	PROPN
ejpam-855	256	4	)	)	PUNCT
ejpam-855	256	5	such	such	ADJ
ejpam-855	256	6	that	that	DET
ejpam-855	256	7	u	u	PROPN
ejpam-855	256	8	6=	6=	PROPN
ejpam-855	256	9	x	x	PROPN
ejpam-855	256	10	and	and	CCONJ
ejpam-855	256	11	a	a	DET
ejpam-855	256	12	=	=	X
ejpam-855	256	13	u	u	NOUN
ejpam-855	256	14	−	−	PROPN
ejpam-855	256	15	v	v	NOUN
ejpam-855	256	16	.	.	PUNCT
ejpam-855	257	1	the	the	DET
ejpam-855	257	2	collection	collection	NOUN
ejpam-855	257	3	of	of	ADP
ejpam-855	257	4	all	all	DET
ejpam-855	257	5	λr	λr	NOUN
ejpam-855	257	6	-difference	-difference	NOUN
ejpam-855	257	7	sets	set	NOUN
ejpam-855	257	8	of	of	ADP
ejpam-855	257	9	(	(	PUNCT
ejpam-855	257	10	x	x	INTJ
ejpam-855	257	11	,	,	PUNCT
ejpam-855	257	12	τ	τ	X
ejpam-855	257	13	)	)	PUNCT
ejpam-855	257	14	is	be	AUX
ejpam-855	257	15	denoted	denote	VERB
ejpam-855	257	16	by	by	ADP
ejpam-855	257	17	λr	λr	NOUN
ejpam-855	257	18	d(x	d(x	PROPN
ejpam-855	257	19	,	,	PUNCT
ejpam-855	257	20	τ	τ	PROPN
ejpam-855	257	21	)	)	PUNCT
ejpam-855	257	22	.	.	PUNCT
ejpam-855	258	1	remark	remark	NOUN
ejpam-855	258	2	2	2	NUM
ejpam-855	258	3	.	.	PUNCT
ejpam-855	259	1	every	every	DET
ejpam-855	259	2	λr	λr	NOUN
ejpam-855	259	3	-open	-open	PROPN
ejpam-855	259	4	set	set	VERB
ejpam-855	259	5	a	a	DET
ejpam-855	259	6	different	different	ADJ
ejpam-855	259	7	from	from	ADP
ejpam-855	259	8	x	x	VERB
ejpam-855	259	9	is	be	AUX
ejpam-855	259	10	a	a	DET
ejpam-855	259	11	λr	λr	NOUN
ejpam-855	259	12	-d	-d	PUNCT
ejpam-855	259	13	set	set	NOUN
ejpam-855	259	14	if	if	SCONJ
ejpam-855	259	15	u	u	NOUN
ejpam-855	259	16	=	=	PROPN
ejpam-855	259	17	a	a	PROPN
ejpam-855	259	18	and	and	CCONJ
ejpam-855	259	19	v	v	NOUN
ejpam-855	259	20	=	=	PUNCT
ejpam-855	259	21	;	;	PUNCT
ejpam-855	259	22	.	.	PUNCT
ejpam-855	260	1	but	but	CCONJ
ejpam-855	260	2	the	the	DET
ejpam-855	260	3	converse	converse	NOUN
ejpam-855	260	4	need	need	AUX
ejpam-855	260	5	not	not	PART
ejpam-855	260	6	be	be	AUX
ejpam-855	260	7	true	true	ADJ
ejpam-855	260	8	.	.	PUNCT
ejpam-855	261	1	for	for	ADP
ejpam-855	261	2	example	example	NOUN
ejpam-855	261	3	,	,	PUNCT
ejpam-855	261	4	let	let	VERB
ejpam-855	261	5	x	x	PUNCT
ejpam-855	261	6	=	=	PRON
ejpam-855	261	7	{	{	PUNCT
ejpam-855	261	8	a	a	PRON
ejpam-855	261	9	,	,	PUNCT
ejpam-855	261	10	b	b	NOUN
ejpam-855	261	11	,	,	PUNCT
ejpam-855	261	12	c	c	NOUN
ejpam-855	261	13	,	,	PUNCT
ejpam-855	261	14	d	d	NOUN
ejpam-855	261	15	}	}	PUNCT
ejpam-855	261	16	and	and	CCONJ
ejpam-855	261	17	τ	τ	PROPN
ejpam-855	261	18	=	=	PUNCT
ejpam-855	261	19	{	{	PUNCT
ejpam-855	261	20	x	x	X
ejpam-855	261	21	,	,	PUNCT
ejpam-855	261	22	;	;	PUNCT
ejpam-855	261	23	,	,	PUNCT
ejpam-855	261	24	{	{	PUNCT
ejpam-855	261	25	b	b	NOUN
ejpam-855	261	26	,	,	PUNCT
ejpam-855	261	27	d	d	NOUN
ejpam-855	261	28	}	}	PUNCT
ejpam-855	261	29	,	,	PUNCT
ejpam-855	261	30	{	{	PUNCT
ejpam-855	261	31	b	b	X
ejpam-855	261	32	,	,	PUNCT
ejpam-855	261	33	c	c	NOUN
ejpam-855	261	34	,	,	PUNCT
ejpam-855	261	35	d	d	NOUN
ejpam-855	261	36	}	}	PUNCT
ejpam-855	261	37	,	,	PUNCT
ejpam-855	261	38	{	{	PUNCT
ejpam-855	261	39	a	a	DET
ejpam-855	261	40	,	,	PUNCT
ejpam-855	261	41	b	b	NOUN
ejpam-855	261	42	,	,	PUNCT
ejpam-855	261	43	d	d	NOUN
ejpam-855	261	44	}	}	PUNCT
ejpam-855	261	45	}	}	PUNCT
ejpam-855	261	46	.	.	PUNCT
ejpam-855	262	1	then	then	ADV
ejpam-855	262	2	λro(x	λro(x	PROPN
ejpam-855	262	3	,	,	PUNCT
ejpam-855	262	4	τ	τ	PROPN
ejpam-855	262	5	)	)	PUNCT
ejpam-855	262	6	=	=	PRON
ejpam-855	262	7	{	{	PUNCT
ejpam-855	262	8	x	x	X
ejpam-855	262	9	,	,	PUNCT
ejpam-855	262	10	;	;	PUNCT
ejpam-855	262	11	,	,	PUNCT
ejpam-855	262	12	{	{	PUNCT
ejpam-855	262	13	b	b	NOUN
ejpam-855	262	14	,	,	PUNCT
ejpam-855	262	15	d	d	NOUN
ejpam-855	262	16	}	}	PUNCT
ejpam-855	262	17	,	,	PUNCT
ejpam-855	262	18	{	{	PUNCT
ejpam-855	262	19	b	b	X
ejpam-855	262	20	,	,	PUNCT
ejpam-855	262	21	c	c	NOUN
ejpam-855	262	22	,	,	PUNCT
ejpam-855	262	23	d	d	NOUN
ejpam-855	262	24	}	}	PUNCT
ejpam-855	262	25	,	,	PUNCT
ejpam-855	262	26	{	{	PUNCT
ejpam-855	262	27	a	a	PRON
ejpam-855	262	28	,	,	PUNCT
ejpam-855	262	29	b	b	NOUN
ejpam-855	262	30	,	,	PUNCT
ejpam-855	262	31	d	d	NOUN
ejpam-855	262	32	}	}	PUNCT
ejpam-855	262	33	}	}	PUNCT
ejpam-855	262	34	and	and	CCONJ
ejpam-855	262	35	λr	λr	INTJ
ejpam-855	262	36	d(x	d(x	PROPN
ejpam-855	262	37	,	,	PUNCT
ejpam-855	262	38	τ	τ	X
ejpam-855	262	39	)	)	PUNCT
ejpam-855	262	40	=	=	PRON
ejpam-855	262	41	{	{	PUNCT
ejpam-855	262	42	;	;	PUNCT
ejpam-855	262	43	,	,	PUNCT
ejpam-855	262	44	{	{	PUNCT
ejpam-855	262	45	b	b	NOUN
ejpam-855	262	46	,	,	PUNCT
ejpam-855	262	47	d	d	NOUN
ejpam-855	262	48	}	}	PUNCT
ejpam-855	262	49	,	,	PUNCT
ejpam-855	262	50	{	{	PUNCT
ejpam-855	262	51	b	b	X
ejpam-855	262	52	,	,	PUNCT
ejpam-855	262	53	c	c	NOUN
ejpam-855	262	54	,	,	PUNCT
ejpam-855	262	55	d	d	NOUN
ejpam-855	262	56	}	}	PUNCT
ejpam-855	262	57	,	,	PUNCT
ejpam-855	262	58	{	{	PUNCT
ejpam-855	262	59	a	a	DET
ejpam-855	262	60	,	,	PUNCT
ejpam-855	262	61	b	b	NOUN
ejpam-855	262	62	,	,	PUNCT
ejpam-855	262	63	d	d	NOUN
ejpam-855	262	64	}	}	PUNCT
ejpam-855	262	65	,	,	PUNCT
ejpam-855	262	66	{	{	PUNCT
ejpam-855	262	67	c	c	X
ejpam-855	262	68	}	}	PUNCT
ejpam-855	262	69	,	,	PUNCT
ejpam-855	262	70	{	{	PUNCT
ejpam-855	262	71	a	a	X
ejpam-855	262	72	}	}	PUNCT
ejpam-855	262	73	}	}	PUNCT
ejpam-855	262	74	.	.	PUNCT
ejpam-855	263	1	here	here	ADV
ejpam-855	263	2	{	{	PUNCT
ejpam-855	263	3	a	a	PRON
ejpam-855	263	4	}	}	PUNCT
ejpam-855	263	5	is	be	AUX
ejpam-855	263	6	a	a	DET
ejpam-855	263	7	λr	λr	NOUN
ejpam-855	263	8	-d	-d	PRON
ejpam-855	263	9	set	set	NOUN
ejpam-855	263	10	but	but	CCONJ
ejpam-855	263	11	not	not	PART
ejpam-855	263	12	λr	λr	ADP
ejpam-855	263	13	-open	-open	ADJ
ejpam-855	263	14	set	set	NOUN
ejpam-855	263	15	.	.	PUNCT
ejpam-855	264	1	definition	definition	NOUN
ejpam-855	264	2	4	4	NUM
ejpam-855	264	3	.	.	PUNCT
ejpam-855	265	1	a	a	DET
ejpam-855	265	2	space	space	NOUN
ejpam-855	265	3	(	(	PUNCT
ejpam-855	265	4	x	x	X
ejpam-855	265	5	,	,	PUNCT
ejpam-855	265	6	τ	τ	X
ejpam-855	265	7	)	)	PUNCT
ejpam-855	265	8	is	be	AUX
ejpam-855	265	9	called	call	VERB
ejpam-855	265	10	(	(	PUNCT
ejpam-855	265	11	1	1	NUM
ejpam-855	265	12	)	)	PUNCT
ejpam-855	265	13	λr	λr	VERB
ejpam-855	265	14	−	−	PROPN
ejpam-855	265	15	d0	d0	NOUN
ejpam-855	265	16	if	if	SCONJ
ejpam-855	265	17	for	for	ADP
ejpam-855	265	18	x	x	X
ejpam-855	265	19	,	,	PUNCT
ejpam-855	265	20	y	y	PROPN
ejpam-855	265	21	∈	∈	PROPN
ejpam-855	265	22	x	x	X
ejpam-855	265	23	,	,	PUNCT
ejpam-855	265	24	x	x	PROPN
ejpam-855	265	25	6=	6=	PROPN
ejpam-855	265	26	y	y	PROPN
ejpam-855	265	27	,	,	PUNCT
ejpam-855	265	28	∃	∃	PROPN
ejpam-855	265	29	a	a	DET
ejpam-855	265	30	λr	λr	X
ejpam-855	265	31	-d	-d	PRON
ejpam-855	265	32	set	set	NOUN
ejpam-855	265	33	containing	contain	VERB
ejpam-855	265	34	one	one	NUM
ejpam-855	265	35	of	of	ADP
ejpam-855	265	36	x	x	PUNCT
ejpam-855	265	37	and	and	CCONJ
ejpam-855	265	38	y	y	PROPN
ejpam-855	265	39	but	but	CCONJ
ejpam-855	265	40	not	not	PART
ejpam-855	265	41	the	the	DET
ejpam-855	265	42	other	other	ADJ
ejpam-855	265	43	(	(	PUNCT
ejpam-855	265	44	2	2	NUM
ejpam-855	265	45	)	)	PUNCT
ejpam-855	265	46	λr	λr	VERB
ejpam-855	265	47	−	−	PROPN
ejpam-855	265	48	d1	d1	PROPN
ejpam-855	265	49	if	if	SCONJ
ejpam-855	265	50	for	for	ADP
ejpam-855	265	51	x	x	X
ejpam-855	265	52	,	,	PUNCT
ejpam-855	265	53	y	y	PROPN
ejpam-855	265	54	∈	∈	PROPN
ejpam-855	265	55	x	x	X
ejpam-855	265	56	,	,	PUNCT
ejpam-855	265	57	x	x	PROPN
ejpam-855	265	58	6=	6=	PROPN
ejpam-855	265	59	y	y	PROPN
ejpam-855	265	60	,	,	PUNCT
ejpam-855	265	61	∃λr	∃λr	NOUN
ejpam-855	265	62	-d	-d	PUNCT
ejpam-855	265	63	sets	set	VERB
ejpam-855	265	64	u	u	NOUN
ejpam-855	265	65	and	and	CCONJ
ejpam-855	265	66	v	v	NOUN
ejpam-855	265	67	in	in	ADP
ejpam-855	265	68	x	x	PUNCT
ejpam-855	265	69	such	such	ADJ
ejpam-855	265	70	that	that	SCONJ
ejpam-855	265	71	x	x	SYM
ejpam-855	265	72	∈	∈	PROPN
ejpam-855	265	73	u	u	NOUN
ejpam-855	265	74	,	,	PUNCT
ejpam-855	265	75	y	y	PROPN
ejpam-855	265	76	/∈	/∈	PUNCT
ejpam-855	265	77	u	u	PROPN
ejpam-855	265	78	and	and	CCONJ
ejpam-855	265	79	y	y	PROPN
ejpam-855	265	80	∈	∈	PROPN
ejpam-855	265	81	v	v	NOUN
ejpam-855	265	82	,	,	PUNCT
ejpam-855	265	83	x	x	PROPN
ejpam-855	265	84	/∈	/∈	PUNCT
ejpam-855	266	1	v	v	INTJ
ejpam-855	266	2	(	(	PUNCT
ejpam-855	266	3	3	3	NUM
ejpam-855	266	4	)	)	PUNCT
ejpam-855	266	5	λr	λr	VERB
ejpam-855	266	6	−	−	PROPN
ejpam-855	266	7	d2	d2	PROPN
ejpam-855	266	8	if	if	SCONJ
ejpam-855	266	9	for	for	ADP
ejpam-855	266	10	x	x	X
ejpam-855	266	11	,	,	PUNCT
ejpam-855	266	12	y	y	PROPN
ejpam-855	266	13	∈	∈	PROPN
ejpam-855	266	14	x	x	X
ejpam-855	266	15	,	,	PUNCT
ejpam-855	266	16	x	x	PROPN
ejpam-855	266	17	6=	6=	PROPN
ejpam-855	266	18	y	y	PROPN
ejpam-855	266	19	,	,	PUNCT
ejpam-855	266	20	∃λr	∃λr	NOUN
ejpam-855	266	21	−	−	PROPN
ejpam-855	266	22	d	d	NOUN
ejpam-855	266	23	sets	set	VERB
ejpam-855	266	24	u	u	NOUN
ejpam-855	266	25	and	and	CCONJ
ejpam-855	266	26	v	v	NOUN
ejpam-855	266	27	in	in	ADP
ejpam-855	266	28	x	x	PUNCT
ejpam-855	266	29	such	such	ADJ
ejpam-855	266	30	that	that	SCONJ
ejpam-855	266	31	x	x	SYM
ejpam-855	266	32	∈	∈	PROPN
ejpam-855	266	33	u	u	NOUN
ejpam-855	266	34	,	,	PUNCT
ejpam-855	266	35	y	y	PROPN
ejpam-855	266	36	∈	∈	PROPN
ejpam-855	266	37	v	v	NOUN
ejpam-855	266	38	and	and	CCONJ
ejpam-855	266	39	u	u	NOUN
ejpam-855	266	40	∩	∩	NOUN
ejpam-855	266	41	v	v	NOUN
ejpam-855	266	42	=	=	PUNCT
ejpam-855	266	43	;	;	PUNCT
ejpam-855	266	44	.	.	PUNCT
ejpam-855	267	1	theorem	theorem	VERB
ejpam-855	267	2	8	8	NUM
ejpam-855	267	3	.	.	PUNCT
ejpam-855	268	1	a	a	DET
ejpam-855	268	2	space	space	NOUN
ejpam-855	268	3	(	(	PUNCT
ejpam-855	268	4	x	x	X
ejpam-855	268	5	,	,	PUNCT
ejpam-855	268	6	τ	τ	X
ejpam-855	268	7	)	)	PUNCT
ejpam-855	268	8	is	be	AUX
ejpam-855	268	9	λr	λr	ADP
ejpam-855	268	10	−	−	PROPN
ejpam-855	268	11	d0	d0	PROPN
ejpam-855	268	12	iff	iff	VERB
ejpam-855	268	13	it	it	PRON
ejpam-855	268	14	is	be	AUX
ejpam-855	268	15	λr	λr	ADP
ejpam-855	268	16	−	−	PROPN
ejpam-855	268	17	t0	t0	PROPN
ejpam-855	268	18	.	.	PUNCT
ejpam-855	269	1	s.	s.	PROPN
ejpam-855	269	2	missier	missier	PROPN
ejpam-855	269	3	,	,	PUNCT
ejpam-855	269	4	m.	m.	NOUN
ejpam-855	269	5	jeyanthi	jeyanthi	PROPN
ejpam-855	269	6	,	,	PUNCT
ejpam-855	269	7	a.	a.	PROPN
ejpam-855	269	8	kılıçman	kılıçman	PROPN
ejpam-855	269	9	/	/	SYM
ejpam-855	269	10	eur	eur	PROPN
ejpam-855	269	11	.	.	PUNCT
ejpam-855	270	1	j.	j.	PROPN
ejpam-855	270	2	pure	pure	PROPN
ejpam-855	270	3	appl	appl	PROPN
ejpam-855	270	4	.	.	PROPN
ejpam-855	270	5	math	math	PROPN
ejpam-855	270	6	,	,	PUNCT
ejpam-855	270	7	5	5	NUM
ejpam-855	270	8	(	(	PUNCT
ejpam-855	270	9	2012	2012	NUM
ejpam-855	270	10	)	)	PUNCT
ejpam-855	270	11	,	,	PUNCT
ejpam-855	270	12	357	357	NUM
ejpam-855	270	13	-	-	SYM
ejpam-855	270	14	364	364	NUM
ejpam-855	270	15	363	363	NUM
ejpam-855	270	16	proof	proof	NOUN
ejpam-855	270	17	.	.	PUNCT
ejpam-855	271	1	suppose	suppose	VERB
ejpam-855	271	2	(	(	PUNCT
ejpam-855	271	3	x	x	X
ejpam-855	271	4	,	,	PUNCT
ejpam-855	271	5	τ	τ	X
ejpam-855	271	6	)	)	PUNCT
ejpam-855	271	7	is	be	AUX
ejpam-855	271	8	λr	λr	ADP
ejpam-855	271	9	−	−	NOUN
ejpam-855	271	10	d0	d0	NOUN
ejpam-855	271	11	.	.	PUNCT
ejpam-855	272	1	let	let	VERB
ejpam-855	272	2	x	x	PRON
ejpam-855	272	3	,	,	PUNCT
ejpam-855	272	4	y	y	PROPN
ejpam-855	272	5	∈	∈	PROPN
ejpam-855	272	6	x	x	PUNCT
ejpam-855	272	7	such	such	ADJ
ejpam-855	272	8	that	that	SCONJ
ejpam-855	272	9	x	x	PRON
ejpam-855	272	10	6=	6=	X
ejpam-855	272	11	y.	y.	PROPN
ejpam-855	272	12	then	then	ADV
ejpam-855	272	13	∃	∃	PROPN
ejpam-855	272	14	an	an	DET
ejpam-855	272	15	λr	λr	X
ejpam-855	272	16	-d	-d	PRON
ejpam-855	272	17	set	set	VERB
ejpam-855	272	18	a	a	DET
ejpam-855	272	19	containing	contain	VERB
ejpam-855	272	20	one	one	NUM
ejpam-855	272	21	of	of	ADP
ejpam-855	272	22	x	x	PUNCT
ejpam-855	272	23	and	and	CCONJ
ejpam-855	272	24	y	y	PROPN
ejpam-855	272	25	but	but	CCONJ
ejpam-855	272	26	not	not	PART
ejpam-855	272	27	the	the	DET
ejpam-855	272	28	other	other	ADJ
ejpam-855	272	29	,	,	PUNCT
ejpam-855	272	30	say	say	VERB
ejpam-855	272	31	x	x	X
ejpam-855	272	32	∈	∈	PROPN
ejpam-855	272	33	a	a	PRON
ejpam-855	273	1	but	but	CCONJ
ejpam-855	273	2	y	y	PROPN
ejpam-855	273	3	/∈	/∈	PUNCT
ejpam-855	273	4	a.	a.	NOUN
ejpam-855	273	5	since	since	SCONJ
ejpam-855	273	6	a	a	PRON
ejpam-855	273	7	is	be	AUX
ejpam-855	273	8	a	a	DET
ejpam-855	273	9	λr	λr	ADP
ejpam-855	273	10	-d	-d	DET
ejpam-855	273	11	set	set	NOUN
ejpam-855	273	12	,	,	PUNCT
ejpam-855	273	13	a=	a=	VERB
ejpam-855	273	14	u	u	NOUN
ejpam-855	273	15	−	−	NOUN
ejpam-855	273	16	v	v	ADP
ejpam-855	273	17	where	where	SCONJ
ejpam-855	273	18	u	u	PROPN
ejpam-855	273	19	6=	6=	PROPN
ejpam-855	273	20	x	x	NOUN
ejpam-855	273	21	and	and	CCONJ
ejpam-855	273	22	u	u	NOUN
ejpam-855	273	23	,	,	PUNCT
ejpam-855	273	24	v	v	NOUN
ejpam-855	273	25	∈	∈	X
ejpam-855	274	1	λro(x	λro(x	X
ejpam-855	274	2	,	,	PUNCT
ejpam-855	274	3	τ	τ	PROPN
ejpam-855	274	4	)	)	PUNCT
ejpam-855	274	5	.	.	PUNCT
ejpam-855	275	1	since	since	SCONJ
ejpam-855	275	2	x	x	PROPN
ejpam-855	275	3	∈	∈	PROPN
ejpam-855	275	4	a	a	DET
ejpam-855	275	5	,	,	PUNCT
ejpam-855	275	6	x	x	SYM
ejpam-855	275	7	∈	∈	NOUN
ejpam-855	275	8	u	u	NOUN
ejpam-855	275	9	and	and	CCONJ
ejpam-855	275	10	x	x	NOUN
ejpam-855	275	11	/∈	/∈	NOUN
ejpam-855	275	12	v	v	INTJ
ejpam-855	275	13	.	.	PUNCT
ejpam-855	276	1	for	for	ADP
ejpam-855	276	2	y	y	PROPN
ejpam-855	276	3	/∈	/∈	PROPN
ejpam-855	277	1	a	a	INTJ
ejpam-855	277	2	,	,	PUNCT
ejpam-855	277	3	we	we	PRON
ejpam-855	277	4	have	have	VERB
ejpam-855	277	5	two	two	NUM
ejpam-855	277	6	cases	case	NOUN
ejpam-855	277	7	(	(	PUNCT
ejpam-855	277	8	a	a	X
ejpam-855	277	9	)	)	PUNCT
ejpam-855	277	10	y	y	PROPN
ejpam-855	277	11	/∈	/∈	PUNCT
ejpam-855	277	12	u	u	NOUN
ejpam-855	277	13	(	(	PUNCT
ejpam-855	277	14	b	b	NOUN
ejpam-855	277	15	)	)	PUNCT
ejpam-855	277	16	y	y	PROPN
ejpam-855	277	17	∈	∈	PROPN
ejpam-855	277	18	u	u	NOUN
ejpam-855	277	19	and	and	CCONJ
ejpam-855	277	20	y	y	PROPN
ejpam-855	277	21	∈	∈	PROPN
ejpam-855	277	22	v	v	NOUN
ejpam-855	277	23	.	.	PUNCT
ejpam-855	278	1	in	in	ADP
ejpam-855	278	2	case	case	NOUN
ejpam-855	278	3	(	(	PUNCT
ejpam-855	278	4	a	a	X
ejpam-855	278	5	)	)	PUNCT
ejpam-855	278	6	,	,	PUNCT
ejpam-855	278	7	x	x	PUNCT
ejpam-855	278	8	∈	∈	NOUN
ejpam-855	278	9	u	u	NOUN
ejpam-855	278	10	but	but	CCONJ
ejpam-855	278	11	y	y	PROPN
ejpam-855	278	12	/∈	/∈	PUNCT
ejpam-855	278	13	u	u	PROPN
ejpam-855	278	14	.	.	PUNCT
ejpam-855	279	1	in	in	ADP
ejpam-855	279	2	case	case	NOUN
ejpam-855	279	3	(	(	PUNCT
ejpam-855	279	4	b	b	NOUN
ejpam-855	279	5	)	)	PUNCT
ejpam-855	279	6	,	,	PUNCT
ejpam-855	279	7	y	y	PROPN
ejpam-855	279	8	∈	∈	PROPN
ejpam-855	279	9	v	v	NOUN
ejpam-855	279	10	but	but	CCONJ
ejpam-855	279	11	x	x	SYM
ejpam-855	279	12	/∈	/∈	NOUN
ejpam-855	279	13	v	v	INTJ
ejpam-855	279	14	.	.	PUNCT
ejpam-855	280	1	hence	hence	ADV
ejpam-855	280	2	(	(	PUNCT
ejpam-855	280	3	x	x	X
ejpam-855	280	4	,	,	PUNCT
ejpam-855	280	5	τ	τ	X
ejpam-855	280	6	)	)	PUNCT
ejpam-855	280	7	is	be	AUX
ejpam-855	280	8	λr	λr	ADP
ejpam-855	280	9	−	−	PROPN
ejpam-855	280	10	t0	t0	PROPN
ejpam-855	280	11	.	.	PUNCT
ejpam-855	281	1	conversely	conversely	ADV
ejpam-855	281	2	,	,	PUNCT
ejpam-855	281	3	suppose	suppose	VERB
ejpam-855	281	4	(	(	PUNCT
ejpam-855	281	5	x	x	X
ejpam-855	281	6	,	,	PUNCT
ejpam-855	281	7	τ	τ	X
ejpam-855	281	8	)	)	PUNCT
ejpam-855	281	9	is	be	AUX
ejpam-855	281	10	λr	λr	ADP
ejpam-855	281	11	−	−	PROPN
ejpam-855	281	12	t0	t0	PROPN
ejpam-855	281	13	.	.	PUNCT
ejpam-855	282	1	let	let	VERB
ejpam-855	282	2	x	x	PRON
ejpam-855	282	3	,	,	PUNCT
ejpam-855	282	4	y	y	PROPN
ejpam-855	282	5	∈	∈	PROPN
ejpam-855	282	6	x	x	PUNCT
ejpam-855	282	7	such	such	ADJ
ejpam-855	282	8	that	that	SCONJ
ejpam-855	282	9	x	x	PRON
ejpam-855	282	10	6=	6=	X
ejpam-855	282	11	y.	y.	PROPN
ejpam-855	282	12	then	then	ADV
ejpam-855	282	13	∃	∃	PROPN
ejpam-855	282	14	an	an	DET
ejpam-855	282	15	λr	λr	NOUN
ejpam-855	282	16	-open	-open	ADJ
ejpam-855	282	17	set	set	VERB
ejpam-855	282	18	u	u	NOUN
ejpam-855	282	19	containing	contain	VERB
ejpam-855	282	20	one	one	NUM
ejpam-855	282	21	of	of	ADP
ejpam-855	282	22	x	x	PUNCT
ejpam-855	282	23	and	and	CCONJ
ejpam-855	282	24	y	y	PROPN
ejpam-855	282	25	but	but	CCONJ
ejpam-855	282	26	not	not	PART
ejpam-855	282	27	the	the	DET
ejpam-855	282	28	other	other	ADJ
ejpam-855	282	29	,	,	PUNCT
ejpam-855	282	30	say	say	VERB
ejpam-855	282	31	x	x	X
ejpam-855	282	32	∈	∈	NOUN
ejpam-855	282	33	u	u	NOUN
ejpam-855	282	34	but	but	CCONJ
ejpam-855	282	35	y	y	PROPN
ejpam-855	282	36	/∈	/∈	PUNCT
ejpam-855	283	1	u	u	PROPN
ejpam-855	283	2	.	.	PUNCT
ejpam-855	284	1	then	then	ADV
ejpam-855	284	2	u	u	X
ejpam-855	284	3	6=	6=	PROPN
ejpam-855	284	4	x	x	X
ejpam-855	284	5	and	and	CCONJ
ejpam-855	284	6	hence	hence	ADV
ejpam-855	284	7	u	u	NOUN
ejpam-855	284	8	is	be	AUX
ejpam-855	284	9	a	a	DET
ejpam-855	284	10	λr	λr	ADP
ejpam-855	284	11	-d	-d	PRON
ejpam-855	284	12	set	set	NOUN
ejpam-855	284	13	.	.	PUNCT
ejpam-855	285	1	therefore	therefore	ADV
ejpam-855	285	2	u	u	PROPN
ejpam-855	285	3	is	be	AUX
ejpam-855	285	4	a	a	DET
ejpam-855	285	5	λr	λr	ADP
ejpam-855	285	6	-d	-d	PRON
ejpam-855	285	7	set	set	NOUN
ejpam-855	285	8	containing	contain	VERB
ejpam-855	285	9	x	x	PUNCT
ejpam-855	285	10	but	but	CCONJ
ejpam-855	285	11	not	not	PART
ejpam-855	285	12	y.	y.	NOUN
ejpam-855	285	13	hence	hence	ADV
ejpam-855	285	14	(	(	PUNCT
ejpam-855	285	15	x	x	X
ejpam-855	285	16	,	,	PUNCT
ejpam-855	285	17	τ	τ	X
ejpam-855	285	18	)	)	PUNCT
ejpam-855	285	19	is	be	AUX
ejpam-855	285	20	λr	λr	ADP
ejpam-855	285	21	−	−	NOUN
ejpam-855	285	22	d0	d0	NOUN
ejpam-855	285	23	.	.	PUNCT
ejpam-855	286	1	the	the	DET
ejpam-855	286	2	following	follow	VERB
ejpam-855	286	3	examples	example	NOUN
ejpam-855	286	4	5	5	NUM
ejpam-855	286	5	and	and	CCONJ
ejpam-855	286	6	6	6	NUM
ejpam-855	286	7	show	show	VERB
ejpam-855	286	8	that	that	SCONJ
ejpam-855	286	9	λr	λr	VERB
ejpam-855	286	10	−	−	NOUN
ejpam-855	286	11	r0	r0	NOUN
ejpam-855	286	12	and	and	CCONJ
ejpam-855	286	13	λr	λr	NOUN
ejpam-855	286	14	−	−	PROPN
ejpam-855	286	15	d0	d0	NOUN
ejpam-855	286	16	are	be	AUX
ejpam-855	286	17	independent	independent	ADJ
ejpam-855	286	18	.	.	PUNCT
ejpam-855	286	19	example	example	NOUN
ejpam-855	287	1	5	5	NUM
ejpam-855	287	2	.	.	PUNCT
ejpam-855	287	3	let	let	VERB
ejpam-855	287	4	x	x	PUNCT
ejpam-855	287	5	=	=	PRON
ejpam-855	287	6	{	{	PUNCT
ejpam-855	287	7	a	a	PRON
ejpam-855	287	8	,	,	PUNCT
ejpam-855	287	9	b	b	NOUN
ejpam-855	287	10	,	,	PUNCT
ejpam-855	287	11	c	c	NOUN
ejpam-855	287	12	}	}	PUNCT
ejpam-855	287	13	and	and	CCONJ
ejpam-855	287	14	τ	τ	PROPN
ejpam-855	287	15	=	=	PUNCT
ejpam-855	287	16	{	{	PUNCT
ejpam-855	287	17	x	x	X
ejpam-855	287	18	,	,	PUNCT
ejpam-855	287	19	;	;	PUNCT
ejpam-855	287	20	,	,	PUNCT
ejpam-855	287	21	{	{	PUNCT
ejpam-855	287	22	b	b	NOUN
ejpam-855	287	23	}	}	PUNCT
ejpam-855	287	24	,	,	PUNCT
ejpam-855	287	25	{	{	PUNCT
ejpam-855	287	26	a	a	PRON
ejpam-855	287	27	,	,	PUNCT
ejpam-855	287	28	c	c	NOUN
ejpam-855	287	29	}	}	PUNCT
ejpam-855	287	30	}	}	PUNCT
ejpam-855	287	31	.	.	PUNCT
ejpam-855	288	1	then	then	ADV
ejpam-855	288	2	λro(x	λro(x	PROPN
ejpam-855	288	3	,	,	PUNCT
ejpam-855	288	4	τ	τ	PROPN
ejpam-855	288	5	)	)	PUNCT
ejpam-855	288	6	=	=	PRON
ejpam-855	288	7	{	{	PUNCT
ejpam-855	288	8	x	x	X
ejpam-855	288	9	,	,	PUNCT
ejpam-855	288	10	;	;	PUNCT
ejpam-855	288	11	,	,	PUNCT
ejpam-855	288	12	{	{	PUNCT
ejpam-855	288	13	b	b	NOUN
ejpam-855	288	14	}	}	PUNCT
ejpam-855	288	15	,	,	PUNCT
ejpam-855	288	16	{	{	PUNCT
ejpam-855	288	17	a	a	PRON
ejpam-855	288	18	,	,	PUNCT
ejpam-855	288	19	c	c	NOUN
ejpam-855	288	20	}	}	PUNCT
ejpam-855	288	21	}	}	PUNCT
ejpam-855	288	22	.	.	PUNCT
ejpam-855	289	1	here	here	ADV
ejpam-855	289	2	(	(	PUNCT
ejpam-855	289	3	x	x	X
ejpam-855	289	4	,	,	PUNCT
ejpam-855	289	5	τ	τ	X
ejpam-855	289	6	)	)	PUNCT
ejpam-855	289	7	is	be	AUX
ejpam-855	289	8	λr	λr	ADP
ejpam-855	289	9	−	−	NOUN
ejpam-855	289	10	r0	r0	NOUN
ejpam-855	290	1	but	but	CCONJ
ejpam-855	290	2	it	it	PRON
ejpam-855	290	3	is	be	AUX
ejpam-855	290	4	not	not	PART
ejpam-855	290	5	λr	λr	ADP
ejpam-855	290	6	−	−	NOUN
ejpam-855	290	7	d0	d0	NOUN
ejpam-855	290	8	.	.	PUNCT
ejpam-855	290	9	example	example	NOUN
ejpam-855	291	1	6	6	NUM
ejpam-855	291	2	.	.	PUNCT
ejpam-855	292	1	let	let	VERB
ejpam-855	292	2	x	x	PUNCT
ejpam-855	292	3	=	=	PRON
ejpam-855	292	4	{	{	PUNCT
ejpam-855	292	5	a	a	DET
ejpam-855	292	6	,	,	PUNCT
ejpam-855	292	7	b	b	NOUN
ejpam-855	292	8	}	}	PUNCT
ejpam-855	292	9	and	and	CCONJ
ejpam-855	292	10	τ	τ	PROPN
ejpam-855	292	11	=	=	PUNCT
ejpam-855	292	12	{	{	PUNCT
ejpam-855	292	13	x	x	X
ejpam-855	292	14	,	,	PUNCT
ejpam-855	292	15	;	;	PUNCT
ejpam-855	292	16	,	,	PUNCT
ejpam-855	292	17	{	{	PUNCT
ejpam-855	292	18	a	a	X
ejpam-855	292	19	}	}	PUNCT
ejpam-855	292	20	}	}	PUNCT
ejpam-855	292	21	.	.	PUNCT
ejpam-855	293	1	then	then	ADV
ejpam-855	293	2	λro(x	λro(x	PROPN
ejpam-855	293	3	,	,	PUNCT
ejpam-855	293	4	τ	τ	PROPN
ejpam-855	293	5	)	)	PUNCT
ejpam-855	293	6	=	=	PRON
ejpam-855	293	7	{	{	PUNCT
ejpam-855	293	8	x	x	X
ejpam-855	293	9	,	,	PUNCT
ejpam-855	293	10	;	;	PUNCT
ejpam-855	293	11	,	,	PUNCT
ejpam-855	293	12	{	{	PUNCT
ejpam-855	293	13	a	a	X
ejpam-855	293	14	}	}	PUNCT
ejpam-855	293	15	}	}	PUNCT
ejpam-855	293	16	.	.	PUNCT
ejpam-855	294	1	here	here	ADV
ejpam-855	294	2	(	(	PUNCT
ejpam-855	294	3	x	x	X
ejpam-855	294	4	,	,	PUNCT
ejpam-855	294	5	τ	τ	X
ejpam-855	294	6	)	)	PUNCT
ejpam-855	294	7	is	be	AUX
ejpam-855	294	8	λr	λr	ADP
ejpam-855	294	9	−	−	NOUN
ejpam-855	294	10	d0	d0	NOUN
ejpam-855	295	1	but	but	CCONJ
ejpam-855	295	2	it	it	PRON
ejpam-855	295	3	is	be	AUX
ejpam-855	295	4	not	not	PART
ejpam-855	295	5	λr	λr	ADP
ejpam-855	295	6	−	−	PROPN
ejpam-855	295	7	r0	r0	NOUN
ejpam-855	295	8	.	.	PUNCT
ejpam-855	296	1	remark	remark	PROPN
ejpam-855	296	2	3	3	NUM
ejpam-855	296	3	.	.	PUNCT
ejpam-855	297	1	examples	example	NOUN
ejpam-855	297	2	7	7	NUM
ejpam-855	297	3	and	and	CCONJ
ejpam-855	297	4	8	8	NUM
ejpam-855	297	5	below	below	ADP
ejpam-855	297	6	show	show	VERB
ejpam-855	297	7	that	that	SCONJ
ejpam-855	297	8	λr	λr	VERB
ejpam-855	297	9	−	−	PROPN
ejpam-855	297	10	r1	r1	NOUN
ejpam-855	297	11	and	and	CCONJ
ejpam-855	297	12	λr	λr	NOUN
ejpam-855	297	13	−	−	PROPN
ejpam-855	297	14	d0	d0	NOUN
ejpam-855	297	15	are	be	AUX
ejpam-855	297	16	independent	independent	ADJ
ejpam-855	297	17	.	.	PUNCT
ejpam-855	297	18	example	example	NOUN
ejpam-855	298	1	7	7	X
ejpam-855	298	2	.	.	PUNCT
ejpam-855	299	1	let	let	VERB
ejpam-855	299	2	x	x	PUNCT
ejpam-855	299	3	=	=	PRON
ejpam-855	299	4	{	{	PUNCT
ejpam-855	299	5	a	a	PRON
ejpam-855	299	6	,	,	PUNCT
ejpam-855	299	7	b	b	NOUN
ejpam-855	299	8	,	,	PUNCT
ejpam-855	299	9	c	c	NOUN
ejpam-855	299	10	,	,	PUNCT
ejpam-855	299	11	d	d	NOUN
ejpam-855	299	12	}	}	PUNCT
ejpam-855	299	13	and	and	CCONJ
ejpam-855	299	14	τ=	τ=	PRON
ejpam-855	299	15	{	{	PUNCT
ejpam-855	299	16	x	x	X
ejpam-855	299	17	,	,	PUNCT
ejpam-855	299	18	;	;	PUNCT
ejpam-855	299	19	,	,	PUNCT
ejpam-855	299	20	{	{	PUNCT
ejpam-855	299	21	a	a	X
ejpam-855	299	22	}	}	PUNCT
ejpam-855	299	23	,	,	PUNCT
ejpam-855	299	24	{	{	PUNCT
ejpam-855	299	25	b	b	X
ejpam-855	299	26	,	,	PUNCT
ejpam-855	299	27	c	c	NOUN
ejpam-855	299	28	,	,	PUNCT
ejpam-855	299	29	d	d	NOUN
ejpam-855	299	30	}	}	PUNCT
ejpam-855	299	31	}	}	PUNCT
ejpam-855	299	32	.	.	PUNCT
ejpam-855	300	1	then	then	ADV
ejpam-855	300	2	λro(x	λro(x	PROPN
ejpam-855	300	3	,	,	PUNCT
ejpam-855	300	4	τ	τ	PROPN
ejpam-855	300	5	)	)	PUNCT
ejpam-855	300	6	=	=	PRON
ejpam-855	300	7	{	{	PUNCT
ejpam-855	300	8	x	x	X
ejpam-855	300	9	,	,	PUNCT
ejpam-855	300	10	;	;	PUNCT
ejpam-855	300	11	,	,	PUNCT
ejpam-855	300	12	{	{	PUNCT
ejpam-855	300	13	a	a	X
ejpam-855	300	14	}	}	PUNCT
ejpam-855	300	15	,	,	PUNCT
ejpam-855	300	16	{	{	PUNCT
ejpam-855	300	17	b	b	X
ejpam-855	300	18	,	,	PUNCT
ejpam-855	300	19	c	c	NOUN
ejpam-855	300	20	,	,	PUNCT
ejpam-855	300	21	d	d	NOUN
ejpam-855	300	22	}	}	PUNCT
ejpam-855	300	23	}	}	PUNCT
ejpam-855	300	24	.	.	PUNCT
ejpam-855	301	1	here	here	ADV
ejpam-855	301	2	(	(	PUNCT
ejpam-855	301	3	x	x	X
ejpam-855	301	4	,	,	PUNCT
ejpam-855	301	5	τ	τ	X
ejpam-855	301	6	)	)	PUNCT
ejpam-855	301	7	is	be	AUX
ejpam-855	301	8	λr	λr	ADP
ejpam-855	301	9	−	−	PROPN
ejpam-855	301	10	r1	r1	NOUN
ejpam-855	302	1	but	but	CCONJ
ejpam-855	302	2	it	it	PRON
ejpam-855	302	3	is	be	AUX
ejpam-855	302	4	not	not	PART
ejpam-855	302	5	λr	λr	ADP
ejpam-855	302	6	−	−	NOUN
ejpam-855	302	7	d0	d0	NOUN
ejpam-855	302	8	.	.	PUNCT
ejpam-855	302	9	example	example	NOUN
ejpam-855	303	1	8	8	NUM
ejpam-855	303	2	.	.	PUNCT
ejpam-855	304	1	let	let	VERB
ejpam-855	304	2	x	x	PUNCT
ejpam-855	304	3	=	=	PRON
ejpam-855	304	4	{	{	PUNCT
ejpam-855	304	5	a	a	PRON
ejpam-855	304	6	,	,	PUNCT
ejpam-855	304	7	b	b	NOUN
ejpam-855	304	8	,	,	PUNCT
ejpam-855	304	9	c	c	NOUN
ejpam-855	304	10	}	}	PUNCT
ejpam-855	304	11	and	and	CCONJ
ejpam-855	304	12	τ	τ	PROPN
ejpam-855	304	13	=	=	PUNCT
ejpam-855	304	14	{	{	PUNCT
ejpam-855	304	15	x	x	X
ejpam-855	304	16	,	,	PUNCT
ejpam-855	304	17	;	;	PUNCT
ejpam-855	304	18	,	,	PUNCT
ejpam-855	304	19	{	{	PUNCT
ejpam-855	304	20	b	b	NOUN
ejpam-855	304	21	}	}	PUNCT
ejpam-855	304	22	,	,	PUNCT
ejpam-855	304	23	{	{	PUNCT
ejpam-855	304	24	a	a	PRON
ejpam-855	304	25	,	,	PUNCT
ejpam-855	304	26	b	b	NOUN
ejpam-855	304	27	}	}	PUNCT
ejpam-855	304	28	}	}	PUNCT
ejpam-855	304	29	.	.	PUNCT
ejpam-855	305	1	then	then	ADV
ejpam-855	305	2	λro(x	λro(x	PROPN
ejpam-855	305	3	,	,	PUNCT
ejpam-855	305	4	τ	τ	PROPN
ejpam-855	305	5	)	)	PUNCT
ejpam-855	305	6	=	=	PRON
ejpam-855	305	7	{	{	PUNCT
ejpam-855	305	8	x	x	X
ejpam-855	305	9	,	,	PUNCT
ejpam-855	305	10	;	;	PUNCT
ejpam-855	305	11	,	,	PUNCT
ejpam-855	305	12	{	{	PUNCT
ejpam-855	305	13	b	b	NOUN
ejpam-855	305	14	}	}	PUNCT
ejpam-855	305	15	,	,	PUNCT
ejpam-855	305	16	{	{	PUNCT
ejpam-855	305	17	a	a	PRON
ejpam-855	305	18	,	,	PUNCT
ejpam-855	305	19	b	b	NOUN
ejpam-855	305	20	}	}	PUNCT
ejpam-855	305	21	}	}	PUNCT
ejpam-855	305	22	.	.	PUNCT
ejpam-855	306	1	here	here	ADV
ejpam-855	306	2	(	(	PUNCT
ejpam-855	306	3	x	x	X
ejpam-855	306	4	,	,	PUNCT
ejpam-855	306	5	τ	τ	X
ejpam-855	306	6	)	)	PUNCT
ejpam-855	306	7	is	be	AUX
ejpam-855	306	8	λr	λr	ADP
ejpam-855	306	9	−	−	NOUN
ejpam-855	306	10	d0	d0	NOUN
ejpam-855	307	1	but	but	CCONJ
ejpam-855	307	2	it	it	PRON
ejpam-855	307	3	is	be	AUX
ejpam-855	307	4	not	not	PART
ejpam-855	307	5	λr	λr	ADP
ejpam-855	307	6	−	−	PROPN
ejpam-855	307	7	r1	r1	PROPN
ejpam-855	307	8	.	.	PUNCT
ejpam-855	308	1	theorem	theorem	VERB
ejpam-855	308	2	9	9	NUM
ejpam-855	308	3	.	.	PUNCT
ejpam-855	309	1	a	a	DET
ejpam-855	309	2	space	space	NOUN
ejpam-855	309	3	(	(	PUNCT
ejpam-855	309	4	x	x	X
ejpam-855	309	5	,	,	PUNCT
ejpam-855	309	6	τ	τ	X
ejpam-855	309	7	)	)	PUNCT
ejpam-855	309	8	is	be	AUX
ejpam-855	309	9	λr	λr	ADP
ejpam-855	309	10	−	−	NOUN
ejpam-855	309	11	d1	d1	PROPN
ejpam-855	309	12	iff	iff	VERB
ejpam-855	309	13	it	it	PRON
ejpam-855	309	14	is	be	AUX
ejpam-855	309	15	λr	λr	ADP
ejpam-855	309	16	−	−	PROPN
ejpam-855	309	17	d2	d2	PROPN
ejpam-855	309	18	.	.	PUNCT
ejpam-855	310	1	proof	proof	NOUN
ejpam-855	310	2	.	.	PUNCT
ejpam-855	311	1	suppose	suppose	VERB
ejpam-855	311	2	(	(	PUNCT
ejpam-855	311	3	x	x	X
ejpam-855	311	4	,	,	PUNCT
ejpam-855	311	5	τ	τ	X
ejpam-855	311	6	)	)	PUNCT
ejpam-855	311	7	is	be	AUX
ejpam-855	311	8	λr	λr	ADP
ejpam-855	311	9	−	−	NOUN
ejpam-855	311	10	d1	d1	PROPN
ejpam-855	311	11	.	.	PUNCT
ejpam-855	312	1	then	then	ADV
ejpam-855	312	2	for	for	ADP
ejpam-855	312	3	each	each	DET
ejpam-855	312	4	pair	pair	NOUN
ejpam-855	312	5	of	of	ADP
ejpam-855	312	6	distinct	distinct	ADJ
ejpam-855	312	7	points	point	NOUN
ejpam-855	312	8	x	x	X
ejpam-855	312	9	,	,	PUNCT
ejpam-855	312	10	y	y	PROPN
ejpam-855	312	11	∈	∈	PROPN
ejpam-855	312	12	x	x	INTJ
ejpam-855	312	13	,	,	PUNCT
ejpam-855	312	14	we	we	PRON
ejpam-855	312	15	have	have	VERB
ejpam-855	312	16	λr	λr	INTJ
ejpam-855	312	17	-d	-d	PRON
ejpam-855	312	18	sets	set	VERB
ejpam-855	312	19	a	a	DET
ejpam-855	312	20	and	and	CCONJ
ejpam-855	312	21	b	b	NOUN
ejpam-855	312	22	such	such	ADJ
ejpam-855	312	23	that	that	SCONJ
ejpam-855	312	24	x	x	SYM
ejpam-855	312	25	∈	∈	PROPN
ejpam-855	312	26	a	a	X
ejpam-855	312	27	,	,	PUNCT
ejpam-855	312	28	y	y	PROPN
ejpam-855	312	29	/∈	/∈	PROPN
ejpam-855	313	1	a	a	PRON
ejpam-855	313	2	and	and	CCONJ
ejpam-855	313	3	y	y	PROPN
ejpam-855	313	4	∈	∈	PROPN
ejpam-855	313	5	b	b	PROPN
ejpam-855	313	6	,	,	PUNCT
ejpam-855	313	7	x	x	PROPN
ejpam-855	313	8	/∈	/∈	PROPN
ejpam-855	313	9	b.	b.	PROPN
ejpam-855	313	10	let	let	VERB
ejpam-855	313	11	a=	a=	ADV
ejpam-855	313	12	u1	u1	VERB
ejpam-855	313	13	−	−	PROPN
ejpam-855	313	14	v1	v1	NOUN
ejpam-855	313	15	and	and	CCONJ
ejpam-855	313	16	b	b	NOUN
ejpam-855	313	17	=	=	PROPN
ejpam-855	313	18	u2	u2	PROPN
ejpam-855	313	19	−	−	PROPN
ejpam-855	313	20	v2	v2	PROPN
ejpam-855	313	21	.	.	PUNCT
ejpam-855	314	1	then	then	ADV
ejpam-855	314	2	u1	u1	PROPN
ejpam-855	314	3	,	,	PUNCT
ejpam-855	314	4	v1	v1	NOUN
ejpam-855	314	5	,	,	PUNCT
ejpam-855	314	6	u2	u2	NOUN
ejpam-855	314	7	and	and	CCONJ
ejpam-855	314	8	v2	v2	PROPN
ejpam-855	314	9	are	be	AUX
ejpam-855	314	10	λr	λr	ADP
ejpam-855	314	11	-open	-open	ADJ
ejpam-855	314	12	sets	set	NOUN
ejpam-855	314	13	,	,	PUNCT
ejpam-855	314	14	u1	u1	NOUN
ejpam-855	314	15	6=	6=	NUM
ejpam-855	314	16	x	x	NOUN
ejpam-855	314	17	and	and	CCONJ
ejpam-855	314	18	u2	u2	PROPN
ejpam-855	314	19	6=	6=	PROPN
ejpam-855	314	20	x	x	X
ejpam-855	314	21	.	.	PUNCT
ejpam-855	315	1	for	for	ADP
ejpam-855	315	2	x	x	PROPN
ejpam-855	315	3	/∈	/∈	PROPN
ejpam-855	316	1	b	b	NOUN
ejpam-855	316	2	,	,	PUNCT
ejpam-855	316	3	we	we	PRON
ejpam-855	316	4	have	have	VERB
ejpam-855	316	5	two	two	NUM
ejpam-855	316	6	cases	case	NOUN
ejpam-855	316	7	(	(	PUNCT
ejpam-855	316	8	i	i	NOUN
ejpam-855	316	9	)	)	PUNCT
ejpam-855	316	10	x	x	PROPN
ejpam-855	316	11	/∈	/∈	PUNCT
ejpam-855	317	1	u2	u2	PROPN
ejpam-855	317	2	(	(	PUNCT
ejpam-855	317	3	ii	ii	PROPN
ejpam-855	317	4	)	)	PUNCT
ejpam-855	317	5	x	x	SYM
ejpam-855	317	6	∈	∈	PROPN
ejpam-855	317	7	u2	u2	NOUN
ejpam-855	317	8	and	and	CCONJ
ejpam-855	317	9	x	x	PUNCT
ejpam-855	317	10	∈	∈	PROPN
ejpam-855	317	11	v2	v2	PROPN
ejpam-855	317	12	.	.	PUNCT
ejpam-855	318	1	case(i	case(i	PROPN
ejpam-855	318	2	)	)	PUNCT
ejpam-855	318	3	x	x	PROPN
ejpam-855	318	4	/∈	/∈	PUNCT
ejpam-855	319	1	u2	u2	NOUN
ejpam-855	319	2	then	then	ADV
ejpam-855	319	3	since	since	SCONJ
ejpam-855	319	4	y	y	PROPN
ejpam-855	319	5	/∈	/∈	PROPN
ejpam-855	320	1	a	a	INTJ
ejpam-855	320	2	,	,	PUNCT
ejpam-855	320	3	either	either	CCONJ
ejpam-855	320	4	y	y	PROPN
ejpam-855	320	5	/∈	/∈	PUNCT
ejpam-855	320	6	u1	u1	PROPN
ejpam-855	320	7	or	or	CCONJ
ejpam-855	320	8	(	(	PUNCT
ejpam-855	320	9	y	y	PROPN
ejpam-855	320	10	∈	∈	PROPN
ejpam-855	320	11	u1	u1	NOUN
ejpam-855	320	12	and	and	CCONJ
ejpam-855	320	13	y	y	PROPN
ejpam-855	320	14	∈	∈	PROPN
ejpam-855	320	15	v1	v1	PROPN
ejpam-855	320	16	)	)	PUNCT
ejpam-855	320	17	.	.	PUNCT
ejpam-855	321	1	if	if	SCONJ
ejpam-855	321	2	y	y	PROPN
ejpam-855	321	3	/∈	/∈	PUNCT
ejpam-855	321	4	u1	u1	PROPN
ejpam-855	321	5	,	,	PUNCT
ejpam-855	321	6	from	from	ADP
ejpam-855	321	7	y	y	PROPN
ejpam-855	321	8	∈	∈	PROPN
ejpam-855	321	9	b	b	PROPN
ejpam-855	321	10	=	=	SYM
ejpam-855	321	11	u2−	u2−	NOUN
ejpam-855	321	12	v2	v2	NOUN
ejpam-855	321	13	,	,	PUNCT
ejpam-855	321	14	it	it	PRON
ejpam-855	321	15	follows	follow	VERB
ejpam-855	321	16	that	that	SCONJ
ejpam-855	321	17	y	y	PROPN
ejpam-855	321	18	∈	∈	PROPN
ejpam-855	321	19	u2−	u2−	NOUN
ejpam-855	321	20	(	(	PUNCT
ejpam-855	321	21	v2	v2	NOUN
ejpam-855	321	22	∪u1	∪u1	NOUN
ejpam-855	321	23	)	)	PUNCT
ejpam-855	321	24	.	.	PUNCT
ejpam-855	322	1	from	from	ADP
ejpam-855	322	2	x	x	SYM
ejpam-855	322	3	∈	∈	PROPN
ejpam-855	322	4	a=	a=	ADV
ejpam-855	322	5	u1−	u1−	NUM
ejpam-855	322	6	v1	v1	NOUN
ejpam-855	322	7	and	and	CCONJ
ejpam-855	322	8	x	x	NOUN
ejpam-855	322	9	/∈	/∈	PROPN
ejpam-855	322	10	u2	u2	PROPN
ejpam-855	322	11	,	,	PUNCT
ejpam-855	322	12	x	x	SYM
ejpam-855	322	13	∈	∈	NOUN
ejpam-855	322	14	u1−	u1−	PROPN
ejpam-855	322	15	(	(	PUNCT
ejpam-855	322	16	v1	v1	NOUN
ejpam-855	322	17	∪u2	∪u2	ADV
ejpam-855	322	18	)	)	PUNCT
ejpam-855	322	19	.	.	PUNCT
ejpam-855	323	1	also	also	ADV
ejpam-855	323	2	(	(	PUNCT
ejpam-855	323	3	u2−	u2−	NOUN
ejpam-855	323	4	(	(	PUNCT
ejpam-855	323	5	v2∪u1))∩	v2∪u1))∩	NOUN
ejpam-855	323	6	(	(	PUNCT
ejpam-855	323	7	u1−	u1−	PROPN
ejpam-855	323	8	(	(	PUNCT
ejpam-855	323	9	v1∪u2	v1∪u2	NUM
ejpam-855	323	10	)	)	PUNCT
ejpam-855	323	11	)	)	PUNCT
ejpam-855	324	1	=	=	PUNCT
ejpam-855	324	2	;	;	PUNCT
ejpam-855	324	3	.	.	PUNCT
ejpam-855	325	1	if	if	SCONJ
ejpam-855	325	2	y	y	PROPN
ejpam-855	325	3	∈	∈	PROPN
ejpam-855	325	4	u1	u1	NOUN
ejpam-855	325	5	and	and	CCONJ
ejpam-855	325	6	y	y	PROPN
ejpam-855	325	7	∈	∈	PROPN
ejpam-855	325	8	v1	v1	NOUN
ejpam-855	325	9	,	,	PUNCT
ejpam-855	325	10	then	then	ADV
ejpam-855	325	11	x	x	PART
ejpam-855	325	12	∈	∈	PROPN
ejpam-855	325	13	u1	u1	NOUN
ejpam-855	325	14	−	−	PROPN
ejpam-855	325	15	v1	v1	NOUN
ejpam-855	325	16	.	.	PUNCT
ejpam-855	326	1	that	that	PRON
ejpam-855	326	2	implies	imply	VERB
ejpam-855	326	3	(	(	PUNCT
ejpam-855	326	4	u1	u1	NOUN
ejpam-855	326	5	−	−	PROPN
ejpam-855	326	6	v1)∩	v1)∩	NOUN
ejpam-855	326	7	v1	v1	NOUN
ejpam-855	326	8	=	=	PUNCT
ejpam-855	326	9	;	;	PUNCT
ejpam-855	326	10	.	.	PUNCT
ejpam-855	327	1	case(ii	case(ii	X
ejpam-855	327	2	)	)	PUNCT
ejpam-855	327	3	x	x	SYM
ejpam-855	327	4	∈	∈	PROPN
ejpam-855	327	5	u2	u2	NOUN
ejpam-855	327	6	and	and	CCONJ
ejpam-855	327	7	x	x	PUNCT
ejpam-855	327	8	∈	∈	PROPN
ejpam-855	327	9	v2	v2	NOUN
ejpam-855	328	1	then	then	ADV
ejpam-855	328	2	we	we	PRON
ejpam-855	328	3	have	have	VERB
ejpam-855	328	4	y	y	PROPN
ejpam-855	328	5	∈	∈	PROPN
ejpam-855	328	6	b	b	PROPN
ejpam-855	328	7	=	=	PROPN
ejpam-855	328	8	u2	u2	PROPN
ejpam-855	328	9	−	−	PROPN
ejpam-855	328	10	v2	v2	PROPN
ejpam-855	328	11	,	,	PUNCT
ejpam-855	328	12	x	x	PUNCT
ejpam-855	328	13	∈	∈	NOUN
ejpam-855	328	14	v2	v2	NOUN
ejpam-855	328	15	and	and	CCONJ
ejpam-855	328	16	(	(	PUNCT
ejpam-855	328	17	u2	u2	PROPN
ejpam-855	328	18	−	−	PROPN
ejpam-855	328	19	v2	v2	PROPN
ejpam-855	328	20	)	)	PUNCT
ejpam-855	328	21	∩	∩	NOUN
ejpam-855	328	22	v2	v2	NOUN
ejpam-855	328	23	=	=	SYM
ejpam-855	328	24	;	;	PUNCT
ejpam-855	328	25	.	.	PUNCT
ejpam-855	329	1	hence	hence	ADV
ejpam-855	329	2	(	(	PUNCT
ejpam-855	329	3	x	x	X
ejpam-855	329	4	,	,	PUNCT
ejpam-855	329	5	τ	τ	X
ejpam-855	329	6	)	)	PUNCT
ejpam-855	329	7	is	be	AUX
ejpam-855	329	8	λr	λr	ADP
ejpam-855	329	9	−	−	PROPN
ejpam-855	329	10	d2	d2	PROPN
ejpam-855	329	11	.	.	PUNCT
ejpam-855	330	1	conversely	conversely	ADV
ejpam-855	330	2	,	,	PUNCT
ejpam-855	330	3	suppose	suppose	VERB
ejpam-855	330	4	(	(	PUNCT
ejpam-855	330	5	x	x	X
ejpam-855	330	6	,	,	PUNCT
ejpam-855	330	7	τ	τ	X
ejpam-855	330	8	)	)	PUNCT
ejpam-855	330	9	is	be	AUX
ejpam-855	330	10	λr	λr	ADP
ejpam-855	330	11	−	−	PROPN
ejpam-855	330	12	d2	d2	PROPN
ejpam-855	330	13	.	.	PUNCT
ejpam-855	331	1	let	let	VERB
ejpam-855	331	2	x	x	PRON
ejpam-855	331	3	,	,	PUNCT
ejpam-855	331	4	y	y	PROPN
ejpam-855	331	5	∈	∈	PROPN
ejpam-855	331	6	x	x	PUNCT
ejpam-855	331	7	such	such	ADJ
ejpam-855	331	8	that	that	SCONJ
ejpam-855	331	9	x	x	PRON
ejpam-855	331	10	6=	6=	X
ejpam-855	331	11	y.	y.	NOUN
ejpam-855	331	12	then	then	ADV
ejpam-855	331	13	∃λr	∃λr	NOUN
ejpam-855	331	14	−	−	PROPN
ejpam-855	331	15	d	d	NOUN
ejpam-855	331	16	sets	set	VERB
ejpam-855	331	17	a	a	PRON
ejpam-855	331	18	and	and	CCONJ
ejpam-855	331	19	b	b	NOUN
ejpam-855	331	20	such	such	ADJ
ejpam-855	331	21	that	that	SCONJ
ejpam-855	331	22	x	x	SYM
ejpam-855	331	23	∈	∈	PROPN
ejpam-855	331	24	a	a	X
ejpam-855	331	25	,	,	PUNCT
ejpam-855	331	26	y	y	PROPN
ejpam-855	331	27	∈	∈	PROPN
ejpam-855	331	28	b	b	PROPN
ejpam-855	331	29	and	and	CCONJ
ejpam-855	331	30	a∩	a∩	PROPN
ejpam-855	331	31	b	b	PROPN
ejpam-855	331	32	=	=	PUNCT
ejpam-855	331	33	;	;	PUNCT
ejpam-855	331	34	.	.	PUNCT
ejpam-855	332	1	therefore	therefore	ADV
ejpam-855	332	2	x	x	X
ejpam-855	332	3	∈	∈	PROPN
ejpam-855	332	4	a	a	X
ejpam-855	332	5	,	,	PUNCT
ejpam-855	332	6	y	y	PROPN
ejpam-855	332	7	/∈	/∈	PROPN
ejpam-855	333	1	a	a	DET
ejpam-855	333	2	and	and	CCONJ
ejpam-855	333	3	y	y	PROPN
ejpam-855	333	4	∈	∈	PROPN
ejpam-855	333	5	b	b	PROPN
ejpam-855	333	6	,	,	PUNCT
ejpam-855	333	7	x	x	PROPN
ejpam-855	333	8	/∈	/∈	PROPN
ejpam-855	333	9	b.	b.	PROPN
ejpam-855	334	1	hence	hence	ADV
ejpam-855	334	2	(	(	PUNCT
ejpam-855	334	3	x	x	X
ejpam-855	334	4	,	,	PUNCT
ejpam-855	334	5	τ	τ	X
ejpam-855	334	6	)	)	PUNCT
ejpam-855	334	7	is	be	AUX
ejpam-855	334	8	λr	λr	ADP
ejpam-855	334	9	−	−	NOUN
ejpam-855	334	10	d1	d1	PROPN
ejpam-855	334	11	.	.	PUNCT
ejpam-855	335	1	references	reference	VERB
ejpam-855	335	2	364	364	NUM
ejpam-855	335	3	corollary	corollary	ADJ
ejpam-855	335	4	2	2	NUM
ejpam-855	335	5	.	.	PUNCT
ejpam-855	336	1	if	if	SCONJ
ejpam-855	336	2	(	(	PUNCT
ejpam-855	336	3	x	x	X
ejpam-855	336	4	,	,	PUNCT
ejpam-855	336	5	τ	τ	X
ejpam-855	336	6	)	)	PUNCT
ejpam-855	336	7	is	be	AUX
ejpam-855	336	8	λr	λr	ADP
ejpam-855	336	9	−	−	NOUN
ejpam-855	336	10	d1	d1	PROPN
ejpam-855	336	11	,	,	PUNCT
ejpam-855	336	12	then	then	ADV
ejpam-855	336	13	it	it	PRON
ejpam-855	336	14	is	be	AUX
ejpam-855	336	15	λr	λr	ADP
ejpam-855	336	16	−	−	PROPN
ejpam-855	336	17	t0	t0	PROPN
ejpam-855	336	18	.	.	PUNCT
ejpam-855	337	1	remark	remark	PROPN
ejpam-855	337	2	4	4	NUM
ejpam-855	337	3	.	.	PUNCT
ejpam-855	338	1	the	the	DET
ejpam-855	338	2	converse	converse	NOUN
ejpam-855	338	3	of	of	ADP
ejpam-855	338	4	the	the	DET
ejpam-855	338	5	above	above	ADJ
ejpam-855	338	6	corollary	corollary	ADJ
ejpam-855	338	7	need	need	NOUN
ejpam-855	338	8	not	not	PART
ejpam-855	338	9	be	be	AUX
ejpam-855	338	10	true	true	ADJ
ejpam-855	338	11	.	.	PUNCT
ejpam-855	339	1	for	for	ADP
ejpam-855	339	2	example	example	NOUN
ejpam-855	339	3	,	,	PUNCT
ejpam-855	339	4	let	let	VERB
ejpam-855	339	5	x	x	PUNCT
ejpam-855	339	6	=	=	PRON
ejpam-855	339	7	{	{	PUNCT
ejpam-855	339	8	a	a	PRON
ejpam-855	339	9	,	,	PUNCT
ejpam-855	339	10	b	b	NOUN
ejpam-855	339	11	,	,	PUNCT
ejpam-855	339	12	c	c	NOUN
ejpam-855	339	13	}	}	PUNCT
ejpam-855	339	14	and	and	CCONJ
ejpam-855	339	15	τ	τ	PROPN
ejpam-855	339	16	=	=	PUNCT
ejpam-855	339	17	{	{	PUNCT
ejpam-855	339	18	x	x	X
ejpam-855	339	19	,	,	PUNCT
ejpam-855	339	20	;	;	PUNCT
ejpam-855	339	21	,	,	PUNCT
ejpam-855	339	22	{	{	PUNCT
ejpam-855	339	23	c	c	NOUN
ejpam-855	339	24	}	}	PUNCT
ejpam-855	339	25	,	,	PUNCT
ejpam-855	339	26	{	{	PUNCT
ejpam-855	339	27	a	a	PRON
ejpam-855	339	28	,	,	PUNCT
ejpam-855	339	29	c	c	NOUN
ejpam-855	339	30	}	}	PUNCT
ejpam-855	339	31	}	}	PUNCT
ejpam-855	339	32	.	.	PUNCT
ejpam-855	340	1	then	then	ADV
ejpam-855	340	2	λro(x	λro(x	PROPN
ejpam-855	340	3	,	,	PUNCT
ejpam-855	340	4	τ	τ	PROPN
ejpam-855	340	5	)	)	PUNCT
ejpam-855	340	6	=	=	PRON
ejpam-855	340	7	{	{	PUNCT
ejpam-855	340	8	x	x	X
ejpam-855	340	9	,	,	PUNCT
ejpam-855	340	10	;	;	PUNCT
ejpam-855	340	11	,	,	PUNCT
ejpam-855	340	12	{	{	PUNCT
ejpam-855	340	13	c	c	NOUN
ejpam-855	340	14	}	}	PUNCT
ejpam-855	340	15	,	,	PUNCT
ejpam-855	340	16	{	{	PUNCT
ejpam-855	340	17	a	a	PRON
ejpam-855	340	18	,	,	PUNCT
ejpam-855	340	19	c	c	NOUN
ejpam-855	340	20	}	}	PUNCT
ejpam-855	340	21	}	}	PUNCT
ejpam-855	340	22	and	and	CCONJ
ejpam-855	340	23	λr	λr	INTJ
ejpam-855	340	24	d(x	d(x	PROPN
ejpam-855	340	25	,	,	PUNCT
ejpam-855	340	26	τ	τ	X
ejpam-855	340	27	)	)	PUNCT
ejpam-855	340	28	=	=	PRON
ejpam-855	340	29	{	{	PUNCT
ejpam-855	340	30	;	;	PUNCT
ejpam-855	340	31	,	,	PUNCT
ejpam-855	340	32	{	{	PUNCT
ejpam-855	340	33	a	a	X
ejpam-855	340	34	}	}	PUNCT
ejpam-855	340	35	,	,	PUNCT
ejpam-855	340	36	{	{	PUNCT
ejpam-855	340	37	c	c	X
ejpam-855	340	38	}	}	PUNCT
ejpam-855	340	39	,	,	PUNCT
ejpam-855	340	40	{	{	PUNCT
ejpam-855	340	41	a	a	PRON
ejpam-855	340	42	,	,	PUNCT
ejpam-855	340	43	c	c	NOUN
ejpam-855	340	44	}	}	PUNCT
ejpam-855	340	45	}	}	PUNCT
ejpam-855	340	46	.	.	PUNCT
ejpam-855	341	1	here	here	ADV
ejpam-855	341	2	(	(	PUNCT
ejpam-855	341	3	x	x	X
ejpam-855	341	4	,	,	PUNCT
ejpam-855	341	5	τ	τ	X
ejpam-855	341	6	)	)	PUNCT
ejpam-855	341	7	is	be	AUX
ejpam-855	341	8	λr	λr	ADP
ejpam-855	341	9	−	−	PROPN
ejpam-855	341	10	t0	t0	NOUN
ejpam-855	341	11	but	but	CCONJ
ejpam-855	341	12	not	not	PART
ejpam-855	341	13	λr	λr	VERB
ejpam-855	341	14	−	−	PROPN
ejpam-855	341	15	d1	d1	PROPN
ejpam-855	341	16	.	.	PUNCT
ejpam-855	342	1	remark	remark	PROPN
ejpam-855	342	2	5	5	NUM
ejpam-855	342	3	.	.	PUNCT
ejpam-855	342	4	examples	example	NOUN
ejpam-855	342	5	9	9	NUM
ejpam-855	342	6	and	and	CCONJ
ejpam-855	342	7	10	10	NUM
ejpam-855	342	8	below	below	ADP
ejpam-855	342	9	show	show	VERB
ejpam-855	342	10	that	that	SCONJ
ejpam-855	342	11	λr	λr	VERB
ejpam-855	342	12	−	−	NOUN
ejpam-855	342	13	r0	r0	NOUN
ejpam-855	342	14	and	and	CCONJ
ejpam-855	342	15	λr	λr	NOUN
ejpam-855	342	16	−	−	PROPN
ejpam-855	342	17	d2	d2	PROPN
ejpam-855	342	18	are	be	AUX
ejpam-855	342	19	independent	independent	ADJ
ejpam-855	342	20	.	.	PUNCT
ejpam-855	342	21	example	example	NOUN
ejpam-855	343	1	9	9	NUM
ejpam-855	343	2	.	.	PUNCT
ejpam-855	344	1	let	let	VERB
ejpam-855	344	2	x	x	PUNCT
ejpam-855	344	3	=	=	PRON
ejpam-855	344	4	{	{	PUNCT
ejpam-855	344	5	a	a	PRON
ejpam-855	344	6	,	,	PUNCT
ejpam-855	344	7	b	b	NOUN
ejpam-855	344	8	,	,	PUNCT
ejpam-855	344	9	c	c	NOUN
ejpam-855	344	10	,	,	PUNCT
ejpam-855	344	11	d	d	NOUN
ejpam-855	344	12	}	}	PUNCT
ejpam-855	344	13	and	and	CCONJ
ejpam-855	344	14	τ	τ	PROPN
ejpam-855	344	15	=	=	PUNCT
ejpam-855	344	16	{	{	PUNCT
ejpam-855	344	17	x	x	X
ejpam-855	344	18	,	,	PUNCT
ejpam-855	344	19	;	;	PUNCT
ejpam-855	344	20	,	,	PUNCT
ejpam-855	344	21	{	{	PUNCT
ejpam-855	344	22	a	a	X
ejpam-855	344	23	}	}	PUNCT
ejpam-855	344	24	,	,	PUNCT
ejpam-855	344	25	{	{	PUNCT
ejpam-855	344	26	b	b	NOUN
ejpam-855	344	27	,	,	PUNCT
ejpam-855	344	28	c	c	NOUN
ejpam-855	344	29	}	}	PUNCT
ejpam-855	344	30	,	,	PUNCT
ejpam-855	344	31	{	{	PUNCT
ejpam-855	344	32	a	a	PRON
ejpam-855	344	33	,	,	PUNCT
ejpam-855	344	34	b	b	NOUN
ejpam-855	344	35	,	,	PUNCT
ejpam-855	344	36	c	c	NOUN
ejpam-855	344	37	}	}	PUNCT
ejpam-855	344	38	}	}	PUNCT
ejpam-855	344	39	.	.	PUNCT
ejpam-855	345	1	then	then	ADV
ejpam-855	345	2	λro(x	λro(x	PROPN
ejpam-855	345	3	,	,	PUNCT
ejpam-855	345	4	τ	τ	PROPN
ejpam-855	345	5	)	)	PUNCT
ejpam-855	345	6	=	=	PRON
ejpam-855	345	7	{	{	PUNCT
ejpam-855	345	8	x	x	X
ejpam-855	345	9	,	,	PUNCT
ejpam-855	345	10	;	;	PUNCT
ejpam-855	345	11	,	,	PUNCT
ejpam-855	345	12	{	{	PUNCT
ejpam-855	345	13	a	a	X
ejpam-855	345	14	}	}	PUNCT
ejpam-855	345	15	,	,	PUNCT
ejpam-855	345	16	{	{	PUNCT
ejpam-855	345	17	a	a	PRON
ejpam-855	345	18	,	,	PUNCT
ejpam-855	345	19	d	d	NOUN
ejpam-855	345	20	}	}	PUNCT
ejpam-855	345	21	,	,	PUNCT
ejpam-855	345	22	{	{	PUNCT
ejpam-855	345	23	b	b	X
ejpam-855	345	24	,	,	PUNCT
ejpam-855	345	25	c	c	NOUN
ejpam-855	345	26	}	}	PUNCT
ejpam-855	345	27	,	,	PUNCT
ejpam-855	345	28	{	{	PUNCT
ejpam-855	345	29	a	a	DET
ejpam-855	345	30	,	,	PUNCT
ejpam-855	345	31	b	b	NOUN
ejpam-855	345	32	,	,	PUNCT
ejpam-855	345	33	c	c	NOUN
ejpam-855	345	34	}	}	PUNCT
ejpam-855	345	35	,	,	PUNCT
ejpam-855	345	36	{	{	PUNCT
ejpam-855	345	37	b	b	X
ejpam-855	345	38	,	,	PUNCT
ejpam-855	345	39	c	c	NOUN
ejpam-855	345	40	,	,	PUNCT
ejpam-855	345	41	d	d	NOUN
ejpam-855	345	42	}	}	PUNCT
ejpam-855	345	43	}	}	PUNCT
ejpam-855	345	44	.	.	PUNCT
ejpam-855	346	1	here	here	ADV
ejpam-855	346	2	(	(	PUNCT
ejpam-855	346	3	x	x	X
ejpam-855	346	4	,	,	PUNCT
ejpam-855	346	5	τ	τ	X
ejpam-855	346	6	)	)	PUNCT
ejpam-855	346	7	is	be	AUX
ejpam-855	346	8	λr	λr	ADP
ejpam-855	346	9	−	−	NOUN
ejpam-855	346	10	r0	r0	NOUN
ejpam-855	347	1	but	but	CCONJ
ejpam-855	347	2	it	it	PRON
ejpam-855	347	3	is	be	AUX
ejpam-855	347	4	not	not	PART
ejpam-855	347	5	λr	λr	ADP
ejpam-855	347	6	−	−	PROPN
ejpam-855	347	7	d2	d2	PROPN
ejpam-855	347	8	.	.	PROPN
ejpam-855	347	9	example	example	NOUN
ejpam-855	347	10	10	10	NUM
ejpam-855	347	11	.	.	PUNCT
ejpam-855	348	1	let	let	VERB
ejpam-855	348	2	x	x	PUNCT
ejpam-855	348	3	=	=	PRON
ejpam-855	348	4	{	{	PUNCT
ejpam-855	348	5	a	a	PRON
ejpam-855	348	6	,	,	PUNCT
ejpam-855	348	7	b	b	NOUN
ejpam-855	348	8	,	,	PUNCT
ejpam-855	348	9	c	c	NOUN
ejpam-855	348	10	}	}	PUNCT
ejpam-855	348	11	and	and	CCONJ
ejpam-855	348	12	τ	τ	PROPN
ejpam-855	348	13	=	=	PUNCT
ejpam-855	348	14	{	{	PUNCT
ejpam-855	348	15	x	x	X
ejpam-855	348	16	,	,	PUNCT
ejpam-855	348	17	;	;	PUNCT
ejpam-855	348	18	,	,	PUNCT
ejpam-855	348	19	{	{	PUNCT
ejpam-855	348	20	b	b	NOUN
ejpam-855	348	21	}	}	PUNCT
ejpam-855	348	22	,	,	PUNCT
ejpam-855	348	23	{	{	PUNCT
ejpam-855	348	24	c	c	X
ejpam-855	348	25	}	}	PUNCT
ejpam-855	348	26	,	,	PUNCT
ejpam-855	348	27	{	{	PUNCT
ejpam-855	348	28	b	b	X
ejpam-855	348	29	,	,	PUNCT
ejpam-855	348	30	c	c	NOUN
ejpam-855	348	31	}	}	PUNCT
ejpam-855	348	32	,	,	PUNCT
ejpam-855	348	33	{	{	PUNCT
ejpam-855	348	34	a	a	PRON
ejpam-855	348	35	,	,	PUNCT
ejpam-855	348	36	c	c	NOUN
ejpam-855	348	37	}	}	PUNCT
ejpam-855	348	38	}	}	PUNCT
ejpam-855	348	39	.	.	PUNCT
ejpam-855	349	1	then	then	ADV
ejpam-855	349	2	λro(x	λro(x	PROPN
ejpam-855	349	3	,	,	PUNCT
ejpam-855	349	4	τ	τ	PROPN
ejpam-855	349	5	)	)	PUNCT
ejpam-855	349	6	=	=	PRON
ejpam-855	349	7	{	{	PUNCT
ejpam-855	349	8	x	x	X
ejpam-855	349	9	,	,	PUNCT
ejpam-855	349	10	;	;	PUNCT
ejpam-855	349	11	,	,	PUNCT
ejpam-855	349	12	{	{	PUNCT
ejpam-855	349	13	b	b	NOUN
ejpam-855	349	14	}	}	PUNCT
ejpam-855	349	15	,	,	PUNCT
ejpam-855	349	16	{	{	PUNCT
ejpam-855	349	17	c	c	X
ejpam-855	349	18	}	}	PUNCT
ejpam-855	349	19	,	,	PUNCT
ejpam-855	349	20	{	{	PUNCT
ejpam-855	349	21	b	b	X
ejpam-855	349	22	,	,	PUNCT
ejpam-855	349	23	c	c	NOUN
ejpam-855	349	24	}	}	PUNCT
ejpam-855	349	25	,	,	PUNCT
ejpam-855	349	26	{	{	PUNCT
ejpam-855	349	27	a	a	PRON
ejpam-855	349	28	,	,	PUNCT
ejpam-855	349	29	c	c	NOUN
ejpam-855	349	30	}	}	PUNCT
ejpam-855	349	31	}	}	PUNCT
ejpam-855	349	32	.	.	PUNCT
ejpam-855	350	1	here	here	ADV
ejpam-855	350	2	(	(	PUNCT
ejpam-855	350	3	x	x	X
ejpam-855	350	4	,	,	PUNCT
ejpam-855	350	5	τ	τ	X
ejpam-855	350	6	)	)	PUNCT
ejpam-855	350	7	is	be	AUX
ejpam-855	350	8	λr	λr	ADP
ejpam-855	350	9	−	−	PROPN
ejpam-855	350	10	d2	d2	PROPN
ejpam-855	351	1	but	but	CCONJ
ejpam-855	351	2	it	it	PRON
ejpam-855	351	3	is	be	AUX
ejpam-855	351	4	not	not	PART
ejpam-855	351	5	λr	λr	ADP
ejpam-855	351	6	−	−	PROPN
ejpam-855	351	7	r1	r1	PROPN
ejpam-855	351	8	.	.	PUNCT
ejpam-855	352	1	similar	similar	ADJ
ejpam-855	352	2	to	to	ADP
ejpam-855	352	3	the	the	DET
ejpam-855	352	4	previous	previous	ADJ
ejpam-855	352	5	cases	case	NOUN
ejpam-855	352	6	the	the	DET
ejpam-855	352	7	examples	example	NOUN
ejpam-855	352	8	11	11	NUM
ejpam-855	352	9	and	and	CCONJ
ejpam-855	352	10	12	12	NUM
ejpam-855	352	11	show	show	NOUN
ejpam-855	352	12	that	that	SCONJ
ejpam-855	352	13	λr	λr	VERB
ejpam-855	352	14	−	−	PROPN
ejpam-855	352	15	r1	r1	NOUN
ejpam-855	352	16	and	and	CCONJ
ejpam-855	352	17	λr	λr	NOUN
ejpam-855	352	18	−	−	PROPN
ejpam-855	352	19	d1	d1	PROPN
ejpam-855	352	20	are	be	AUX
ejpam-855	352	21	independent	independent	ADJ
ejpam-855	352	22	.	.	PUNCT
ejpam-855	352	23	example	example	NOUN
ejpam-855	353	1	11	11	NUM
ejpam-855	353	2	.	.	PUNCT
ejpam-855	354	1	let	let	VERB
ejpam-855	354	2	x	x	PUNCT
ejpam-855	354	3	=	=	PRON
ejpam-855	354	4	{	{	PUNCT
ejpam-855	354	5	a	a	PRON
ejpam-855	354	6	,	,	PUNCT
ejpam-855	354	7	b	b	NOUN
ejpam-855	354	8	,	,	PUNCT
ejpam-855	354	9	c	c	NOUN
ejpam-855	354	10	,	,	PUNCT
ejpam-855	354	11	d	d	NOUN
ejpam-855	354	12	}	}	PUNCT
ejpam-855	354	13	and	and	CCONJ
ejpam-855	354	14	τ	τ	PROPN
ejpam-855	354	15	=	=	PUNCT
ejpam-855	354	16	{	{	PUNCT
ejpam-855	354	17	x	x	X
ejpam-855	354	18	,	,	PUNCT
ejpam-855	354	19	;	;	PUNCT
ejpam-855	354	20	,	,	PUNCT
ejpam-855	354	21	{	{	PUNCT
ejpam-855	354	22	a	a	X
ejpam-855	354	23	}	}	PUNCT
ejpam-855	354	24	,	,	PUNCT
ejpam-855	354	25	{	{	PUNCT
ejpam-855	354	26	b	b	NOUN
ejpam-855	354	27	,	,	PUNCT
ejpam-855	354	28	c	c	NOUN
ejpam-855	354	29	}	}	PUNCT
ejpam-855	354	30	,	,	PUNCT
ejpam-855	354	31	{	{	PUNCT
ejpam-855	354	32	a	a	PRON
ejpam-855	354	33	,	,	PUNCT
ejpam-855	354	34	b	b	NOUN
ejpam-855	354	35	,	,	PUNCT
ejpam-855	354	36	c	c	NOUN
ejpam-855	354	37	}	}	PUNCT
ejpam-855	354	38	}	}	PUNCT
ejpam-855	354	39	.	.	PUNCT
ejpam-855	355	1	then	then	ADV
ejpam-855	355	2	λro(x	λro(x	PROPN
ejpam-855	355	3	,	,	PUNCT
ejpam-855	355	4	τ	τ	PROPN
ejpam-855	355	5	)	)	PUNCT
ejpam-855	355	6	=	=	PRON
ejpam-855	355	7	{	{	PUNCT
ejpam-855	355	8	x	x	X
ejpam-855	355	9	,	,	PUNCT
ejpam-855	355	10	;	;	PUNCT
ejpam-855	355	11	,	,	PUNCT
ejpam-855	355	12	{	{	PUNCT
ejpam-855	355	13	a	a	X
ejpam-855	355	14	}	}	PUNCT
ejpam-855	355	15	,	,	PUNCT
ejpam-855	355	16	{	{	PUNCT
ejpam-855	355	17	a	a	PRON
ejpam-855	355	18	,	,	PUNCT
ejpam-855	355	19	d	d	NOUN
ejpam-855	355	20	}	}	PUNCT
ejpam-855	355	21	,	,	PUNCT
ejpam-855	355	22	{	{	PUNCT
ejpam-855	355	23	b	b	X
ejpam-855	355	24	,	,	PUNCT
ejpam-855	355	25	c	c	NOUN
ejpam-855	355	26	}	}	PUNCT
ejpam-855	355	27	,	,	PUNCT
ejpam-855	355	28	{	{	PUNCT
ejpam-855	355	29	a	a	DET
ejpam-855	355	30	,	,	PUNCT
ejpam-855	355	31	b	b	NOUN
ejpam-855	355	32	,	,	PUNCT
ejpam-855	355	33	c	c	NOUN
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ejpam-855	355	35	,	,	PUNCT
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ejpam-855	355	38	,	,	PUNCT
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ejpam-855	355	40	,	,	PUNCT
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ejpam-855	355	44	.	.	PUNCT
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ejpam-855	356	2	(	(	PUNCT
ejpam-855	356	3	x	x	X
ejpam-855	356	4	,	,	PUNCT
ejpam-855	356	5	τ	τ	X
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ejpam-855	356	8	λr	λr	ADP
ejpam-855	356	9	−	−	PROPN
ejpam-855	356	10	r1	r1	NOUN
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ejpam-855	357	2	it	it	PRON
ejpam-855	357	3	is	be	AUX
ejpam-855	357	4	not	not	PART
ejpam-855	357	5	λr	λr	ADP
ejpam-855	357	6	−	−	NOUN
ejpam-855	357	7	d1	d1	PROPN
ejpam-855	357	8	.	.	PUNCT
ejpam-855	357	9	example	example	NOUN
ejpam-855	358	1	12	12	NUM
ejpam-855	358	2	.	.	PUNCT
ejpam-855	359	1	let	let	VERB
ejpam-855	359	2	x	x	PUNCT
ejpam-855	359	3	=	=	PRON
ejpam-855	359	4	{	{	PUNCT
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ejpam-855	359	6	,	,	PUNCT
ejpam-855	359	7	b	b	NOUN
ejpam-855	359	8	,	,	PUNCT
ejpam-855	359	9	c	c	NOUN
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ejpam-855	359	11	and	and	CCONJ
ejpam-855	359	12	τ	τ	PROPN
ejpam-855	359	13	=	=	PUNCT
ejpam-855	359	14	{	{	PUNCT
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ejpam-855	359	16	,	,	PUNCT
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ejpam-855	359	19	{	{	PUNCT
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ejpam-855	359	22	,	,	PUNCT
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ejpam-855	359	26	,	,	PUNCT
ejpam-855	359	27	{	{	PUNCT
ejpam-855	359	28	a	a	X
ejpam-855	359	29	,	,	PUNCT
ejpam-855	359	30	c	c	NOUN
ejpam-855	359	31	}	}	PUNCT
ejpam-855	359	32	,	,	PUNCT
ejpam-855	359	33	{	{	PUNCT
ejpam-855	359	34	b	b	X
ejpam-855	359	35	,	,	PUNCT
ejpam-855	359	36	c	c	NOUN
ejpam-855	359	37	}	}	PUNCT
ejpam-855	359	38	}	}	PUNCT
ejpam-855	359	39	.	.	PUNCT
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ejpam-855	360	2	λro(x	λro(x	PROPN
ejpam-855	360	3	,	,	PUNCT
ejpam-855	360	4	τ	τ	PROPN
ejpam-855	360	5	)	)	PUNCT
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ejpam-855	360	7	{	{	PUNCT
ejpam-855	360	8	x	x	X
ejpam-855	360	9	,	,	PUNCT
ejpam-855	360	10	;	;	PUNCT
ejpam-855	360	11	,	,	PUNCT
ejpam-855	360	12	{	{	PUNCT
ejpam-855	360	13	a	a	X
ejpam-855	360	14	}	}	PUNCT
ejpam-855	360	15	,	,	PUNCT
ejpam-855	360	16	{	{	PUNCT
ejpam-855	360	17	c	c	X
ejpam-855	360	18	}	}	PUNCT
ejpam-855	360	19	,	,	PUNCT
ejpam-855	360	20	{	{	PUNCT
ejpam-855	360	21	a	a	X
ejpam-855	360	22	,	,	PUNCT
ejpam-855	360	23	c	c	NOUN
ejpam-855	360	24	}	}	PUNCT
ejpam-855	360	25	,	,	PUNCT
ejpam-855	360	26	{	{	PUNCT
ejpam-855	360	27	b	b	X
ejpam-855	360	28	,	,	PUNCT
ejpam-855	360	29	c	c	NOUN
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ejpam-855	360	31	}	}	PUNCT
ejpam-855	360	32	.	.	PUNCT
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ejpam-855	361	2	(	(	PUNCT
ejpam-855	361	3	x	x	X
ejpam-855	361	4	,	,	PUNCT
ejpam-855	361	5	τ	τ	X
ejpam-855	361	6	)	)	PUNCT
ejpam-855	361	7	is	be	AUX
ejpam-855	361	8	λr	λr	NOUN
ejpam-855	361	9	−	−	NOUN
ejpam-855	361	10	d1	d1	NOUN
ejpam-855	362	1	but	but	CCONJ
ejpam-855	362	2	it	it	PRON
ejpam-855	362	3	is	be	AUX
ejpam-855	362	4	not	not	PART
ejpam-855	362	5	λr	λr	ADP
ejpam-855	362	6	−	−	PROPN
ejpam-855	362	7	r1	r1	PROPN
ejpam-855	362	8	.	.	PUNCT
ejpam-855	363	1	references	reference	NOUN
ejpam-855	363	2	[	[	X
ejpam-855	363	3	1	1	NUM
ejpam-855	363	4	]	]	PUNCT
ejpam-855	363	5	m.	m.	NOUN
ejpam-855	363	6	caldas	caldas	PROPN
ejpam-855	363	7	and	and	CCONJ
ejpam-855	363	8	s.	s.	PROPN
ejpam-855	363	9	jafar	jafar	PROPN
ejpam-855	363	10	.	.	PUNCT
ejpam-855	364	1	on	on	ADP
ejpam-855	364	2	some	some	DET
ejpam-855	364	3	low	low	ADJ
ejpam-855	364	4	separation	separation	NOUN
ejpam-855	364	5	axioms	axiom	NOUN
ejpam-855	364	6	in	in	ADP
ejpam-855	364	7	topological	topological	ADJ
ejpam-855	364	8	space	space	NOUN
ejpam-855	364	9	.	.	PUNCT
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ejpam-855	365	2	journal	journal	PROPN
ejpam-855	365	3	of	of	ADP
ejpam-855	365	4	math	math	NOUN
ejpam-855	365	5	,	,	PUNCT
ejpam-855	365	6	29:93–104	29:93–104	PROPN
ejpam-855	365	7	,	,	PUNCT
ejpam-855	365	8	2003	2003	NUM
ejpam-855	365	9	.	.	PUNCT