id	sid	tid	token	lemma	pos
ejpam-2415	1	1	compile	compile	NOUN
ejpam-2415	1	2	/	/	SYM
ejpam-2415	1	3	output.dvi	output.dvi	NOUN
ejpam-2415	1	4	european	european	ADJ
ejpam-2415	1	5	journal	journal	NOUN
ejpam-2415	1	6	of	of	ADP
ejpam-2415	1	7	pure	pure	ADJ
ejpam-2415	1	8	and	and	CCONJ
ejpam-2415	1	9	applied	apply	VERB
ejpam-2415	1	10	mathematics	mathematic	NOUN
ejpam-2415	1	11	vol	vol	NOUN
ejpam-2415	1	12	.	.	PROPN
ejpam-2415	1	13	8	8	NUM
ejpam-2415	1	14	,	,	PUNCT
ejpam-2415	1	15	no	no	INTJ
ejpam-2415	1	16	.	.	NOUN
ejpam-2415	1	17	3	3	NUM
ejpam-2415	1	18	,	,	PUNCT
ejpam-2415	1	19	2015	2015	NUM
ejpam-2415	1	20	,	,	PUNCT
ejpam-2415	1	21	332	332	NUM
ejpam-2415	1	22	-	-	SYM
ejpam-2415	1	23	342	342	NUM
ejpam-2415	1	24	issn	issn	PROPN
ejpam-2415	1	25	1307	1307	NUM
ejpam-2415	1	26	-	-	SYM
ejpam-2415	1	27	5543	5543	NUM
ejpam-2415	1	28	–	–	PUNCT
ejpam-2415	1	29	www.ejpam.com	www.ejpam.com	X
ejpam-2415	1	30	baer	baer	PROPN
ejpam-2415	1	31	elements	element	NOUN
ejpam-2415	1	32	in	in	ADP
ejpam-2415	1	33	lattice	lattice	NOUN
ejpam-2415	1	34	modules	module	NOUN
ejpam-2415	2	1	c	c	PROPN
ejpam-2415	2	2	s	s	PART
ejpam-2415	2	3	manjarekar	manjarekar	NOUN
ejpam-2415	2	4	1	1	NUM
ejpam-2415	2	5	,	,	PUNCT
ejpam-2415	2	6	u	u	NOUN
ejpam-2415	2	7	n	n	PRON
ejpam-2415	2	8	kandale	kandale	NOUN
ejpam-2415	2	9	2,∗	2,∗	NUM
ejpam-2415	2	10	1	1	NUM
ejpam-2415	2	11	department	department	NOUN
ejpam-2415	2	12	of	of	ADP
ejpam-2415	2	13	mathematics	mathematics	PROPN
ejpam-2415	2	14	,	,	PUNCT
ejpam-2415	2	15	shivaji	shivaji	PROPN
ejpam-2415	2	16	university	university	PROPN
ejpam-2415	2	17	,	,	PUNCT
ejpam-2415	2	18	kolhapur	kolhapur	PROPN
ejpam-2415	2	19	,	,	PUNCT
ejpam-2415	2	20	india	india	PROPN
ejpam-2415	2	21	2	2	NUM
ejpam-2415	2	22	department	department	NOUN
ejpam-2415	2	23	of	of	ADP
ejpam-2415	2	24	general	general	ADJ
ejpam-2415	2	25	engineering	engineering	PROPN
ejpam-2415	2	26	,	,	PUNCT
ejpam-2415	2	27	sharad	sharad	PROPN
ejpam-2415	2	28	institute	institute	PROPN
ejpam-2415	2	29	,	,	PUNCT
ejpam-2415	2	30	shivaji	shivaji	PROPN
ejpam-2415	2	31	university	university	PROPN
ejpam-2415	2	32	,	,	PUNCT
ejpam-2415	2	33	kolhapur	kolhapur	PROPN
ejpam-2415	2	34	,	,	PUNCT
ejpam-2415	2	35	india	india	PROPN
ejpam-2415	2	36	abstract	abstract	NOUN
ejpam-2415	2	37	.	.	PUNCT
ejpam-2415	3	1	let	let	VERB
ejpam-2415	3	2	l	l	NOUN
ejpam-2415	3	3	be	be	AUX
ejpam-2415	3	4	a	a	DET
ejpam-2415	3	5	compactly	compactly	ADV
ejpam-2415	3	6	generated	generate	VERB
ejpam-2415	3	7	multiplicative	multiplicative	ADJ
ejpam-2415	3	8	lattice	lattice	NOUN
ejpam-2415	3	9	with	with	ADP
ejpam-2415	3	10	1	1	NUM
ejpam-2415	3	11	compact	compact	ADJ
ejpam-2415	3	12	in	in	ADP
ejpam-2415	3	13	which	which	PRON
ejpam-2415	3	14	every	every	DET
ejpam-2415	3	15	finite	finite	ADJ
ejpam-2415	3	16	product	product	NOUN
ejpam-2415	3	17	of	of	ADP
ejpam-2415	3	18	compact	compact	ADJ
ejpam-2415	3	19	elements	element	NOUN
ejpam-2415	3	20	is	be	AUX
ejpam-2415	3	21	compact	compact	ADJ
ejpam-2415	3	22	and	and	CCONJ
ejpam-2415	3	23	m	m	AUX
ejpam-2415	3	24	be	be	AUX
ejpam-2415	3	25	a	a	DET
ejpam-2415	3	26	module	module	NOUN
ejpam-2415	3	27	over	over	ADP
ejpam-2415	3	28	l.	l.	PROPN
ejpam-2415	3	29	in	in	ADP
ejpam-2415	3	30	this	this	DET
ejpam-2415	3	31	paper	paper	NOUN
ejpam-2415	3	32	we	we	PRON
ejpam-2415	3	33	generalize	generalize	VERB
ejpam-2415	3	34	the	the	DET
ejpam-2415	3	35	concepts	concept	NOUN
ejpam-2415	3	36	of	of	ADP
ejpam-2415	3	37	baer	baer	PROPN
ejpam-2415	3	38	elements,∗-elements	elements,∗-elements	PROPN
ejpam-2415	3	39	and	and	CCONJ
ejpam-2415	3	40	closed	closed	ADJ
ejpam-2415	3	41	elements	element	NOUN
ejpam-2415	3	42	and	and	CCONJ
ejpam-2415	3	43	obtain	obtain	VERB
ejpam-2415	3	44	the	the	DET
ejpam-2415	3	45	relation	relation	NOUN
ejpam-2415	3	46	between	between	ADP
ejpam-2415	3	47	∗-elements	∗-element	NOUN
ejpam-2415	3	48	and	and	CCONJ
ejpam-2415	3	49	baer	baer	PROPN
ejpam-2415	3	50	elements	element	NOUN
ejpam-2415	3	51	and	and	CCONJ
ejpam-2415	3	52	also	also	ADV
ejpam-2415	3	53	closed	close	VERB
ejpam-2415	3	54	elements	element	NOUN
ejpam-2415	3	55	and	and	CCONJ
ejpam-2415	3	56	baer	baer	PROPN
ejpam-2415	3	57	elements	element	NOUN
ejpam-2415	3	58	.	.	PUNCT
ejpam-2415	4	1	some	some	DET
ejpam-2415	4	2	characterization	characterization	NOUN
ejpam-2415	4	3	are	be	AUX
ejpam-2415	4	4	also	also	ADV
ejpam-2415	4	5	obtain	obtain	ADJ
ejpam-2415	4	6	for	for	ADP
ejpam-2415	4	7	closed	closed	ADJ
ejpam-2415	4	8	elements	element	NOUN
ejpam-2415	4	9	of	of	ADP
ejpam-2415	4	10	m	m	NOUN
ejpam-2415	4	11	and	and	CCONJ
ejpam-2415	4	12	minimal	minimal	ADJ
ejpam-2415	4	13	prime	prime	ADJ
ejpam-2415	4	14	elements	element	NOUN
ejpam-2415	4	15	of	of	ADP
ejpam-2415	4	16	m.	m.	NOUN
ejpam-2415	4	17	2010	2010	NUM
ejpam-2415	4	18	mathematics	mathematic	NOUN
ejpam-2415	4	19	subject	subject	NOUN
ejpam-2415	4	20	classifications	classification	NOUN
ejpam-2415	4	21	:	:	PUNCT
ejpam-2415	4	22	13a99	13a99	NUM
ejpam-2415	4	23	key	key	ADJ
ejpam-2415	4	24	words	word	NOUN
ejpam-2415	4	25	and	and	CCONJ
ejpam-2415	4	26	phrases	phrase	NOUN
ejpam-2415	4	27	:	:	PUNCT
ejpam-2415	4	28	prime	prime	ADJ
ejpam-2415	4	29	element	element	NOUN
ejpam-2415	4	30	,	,	PUNCT
ejpam-2415	4	31	primary	primary	ADJ
ejpam-2415	4	32	element	element	NOUN
ejpam-2415	4	33	,	,	PUNCT
ejpam-2415	4	34	lattice	lattice	NOUN
ejpam-2415	4	35	modules	module	NOUN
ejpam-2415	4	36	,	,	PUNCT
ejpam-2415	4	37	baer	baer	PROPN
ejpam-2415	4	38	element	element	NOUN
ejpam-2415	4	39	,	,	PUNCT
ejpam-2415	4	40	∗-element	∗-element	ADJ
ejpam-2415	4	41	,	,	PUNCT
ejpam-2415	4	42	closed	closed	ADJ
ejpam-2415	4	43	element	element	NOUN
ejpam-2415	4	44	.	.	PUNCT
ejpam-2415	5	1	1	1	X
ejpam-2415	5	2	.	.	X
ejpam-2415	5	3	introduction	introduction	NOUN
ejpam-2415	5	4	a	a	DET
ejpam-2415	5	5	multiplicative	multiplicative	ADJ
ejpam-2415	5	6	lattice	lattice	NOUN
ejpam-2415	5	7	l	l	NOUN
ejpam-2415	5	8	is	be	AUX
ejpam-2415	5	9	a	a	DET
ejpam-2415	5	10	complete	complete	ADJ
ejpam-2415	5	11	lattice	lattice	NOUN
ejpam-2415	5	12	provided	provide	VERB
ejpam-2415	5	13	with	with	ADP
ejpam-2415	5	14	commutative	commutative	ADJ
ejpam-2415	5	15	,	,	PUNCT
ejpam-2415	5	16	associative	associative	ADJ
ejpam-2415	5	17	and	and	CCONJ
ejpam-2415	5	18	join	join	VERB
ejpam-2415	5	19	distributive	distributive	ADJ
ejpam-2415	5	20	multiplication	multiplication	NOUN
ejpam-2415	5	21	in	in	ADP
ejpam-2415	5	22	which	which	PRON
ejpam-2415	5	23	the	the	DET
ejpam-2415	5	24	largest	large	ADJ
ejpam-2415	5	25	element	element	NOUN
ejpam-2415	5	26	1	1	NUM
ejpam-2415	5	27	acts	act	NOUN
ejpam-2415	5	28	as	as	ADP
ejpam-2415	5	29	a	a	DET
ejpam-2415	5	30	multiplicative	multiplicative	ADJ
ejpam-2415	5	31	identity	identity	NOUN
ejpam-2415	5	32	.	.	PUNCT
ejpam-2415	6	1	an	an	DET
ejpam-2415	6	2	element	element	NOUN
ejpam-2415	6	3	a	a	DET
ejpam-2415	6	4	∈	∈	PROPN
ejpam-2415	6	5	l	l	NOUN
ejpam-2415	6	6	is	be	AUX
ejpam-2415	6	7	called	call	VERB
ejpam-2415	6	8	proper	proper	ADJ
ejpam-2415	6	9	if	if	SCONJ
ejpam-2415	6	10	a	a	DET
ejpam-2415	6	11	<	<	X
ejpam-2415	6	12	1	1	NUM
ejpam-2415	6	13	.	.	PUNCT
ejpam-2415	7	1	a	a	DET
ejpam-2415	7	2	proper	proper	ADJ
ejpam-2415	7	3	element	element	NOUN
ejpam-2415	7	4	p	p	NOUN
ejpam-2415	7	5	of	of	ADP
ejpam-2415	7	6	l	l	NOUN
ejpam-2415	7	7	is	be	AUX
ejpam-2415	7	8	said	say	VERB
ejpam-2415	7	9	to	to	PART
ejpam-2415	7	10	be	be	AUX
ejpam-2415	7	11	prime	prime	ADJ
ejpam-2415	7	12	if	if	SCONJ
ejpam-2415	7	13	ab	ab	PROPN
ejpam-2415	7	14	≤	≤	PROPN
ejpam-2415	7	15	p	p	PROPN
ejpam-2415	7	16	implies	imply	VERB
ejpam-2415	7	17	a	a	DET
ejpam-2415	7	18	≤	≤	NUM
ejpam-2415	7	19	p	p	NOUN
ejpam-2415	7	20	or	or	CCONJ
ejpam-2415	7	21	b	b	NOUN
ejpam-2415	7	22	≤	≤	NOUN
ejpam-2415	8	1	p.	p.	NOUN
ejpam-2415	8	2	if	if	SCONJ
ejpam-2415	8	3	a	a	DET
ejpam-2415	8	4	∈	∈	PROPN
ejpam-2415	8	5	l	l	NOUN
ejpam-2415	8	6	,	,	PUNCT
ejpam-2415	8	7	b	b	PROPN
ejpam-2415	8	8	∈	∈	PROPN
ejpam-2415	8	9	l	l	NOUN
ejpam-2415	8	10	,	,	PUNCT
ejpam-2415	8	11	(	(	PUNCT
ejpam-2415	8	12	a	a	DET
ejpam-2415	8	13	:	:	PUNCT
ejpam-2415	8	14	b	b	X
ejpam-2415	8	15	)	)	PUNCT
ejpam-2415	8	16	is	be	AUX
ejpam-2415	8	17	the	the	DET
ejpam-2415	8	18	join	join	NOUN
ejpam-2415	8	19	of	of	ADP
ejpam-2415	8	20	all	all	DET
ejpam-2415	8	21	elements	element	NOUN
ejpam-2415	8	22	c	c	NOUN
ejpam-2415	8	23	in	in	ADP
ejpam-2415	8	24	l	l	NOUN
ejpam-2415	8	25	such	such	ADJ
ejpam-2415	8	26	that	that	SCONJ
ejpam-2415	8	27	cb	cb	PROPN
ejpam-2415	8	28	≤	≤	PROPN
ejpam-2415	8	29	a.	a.	NOUN
ejpam-2415	8	30	a	a	DET
ejpam-2415	8	31	proper	proper	ADJ
ejpam-2415	8	32	element	element	NOUN
ejpam-2415	8	33	p	p	NOUN
ejpam-2415	8	34	of	of	ADP
ejpam-2415	8	35	l	l	NOUN
ejpam-2415	8	36	is	be	AUX
ejpam-2415	8	37	said	say	VERB
ejpam-2415	8	38	to	to	PART
ejpam-2415	8	39	be	be	AUX
ejpam-2415	8	40	primary	primary	ADJ
ejpam-2415	8	41	if	if	SCONJ
ejpam-2415	8	42	ab	ab	PROPN
ejpam-2415	8	43	≤	≤	PROPN
ejpam-2415	8	44	p	p	PROPN
ejpam-2415	8	45	implies	imply	VERB
ejpam-2415	8	46	a	a	DET
ejpam-2415	8	47	≤	≤	NUM
ejpam-2415	8	48	p	p	NOUN
ejpam-2415	8	49	or	or	CCONJ
ejpam-2415	8	50	bn	bn	NOUN
ejpam-2415	8	51	≤	≤	NOUN
ejpam-2415	8	52	p	p	NOUN
ejpam-2415	8	53	for	for	ADP
ejpam-2415	8	54	some	some	DET
ejpam-2415	8	55	positive	positive	ADJ
ejpam-2415	8	56	integer	integer	NOUN
ejpam-2415	8	57	n.	n.	NOUN
ejpam-2415	8	58	if	if	SCONJ
ejpam-2415	8	59	a	a	DET
ejpam-2415	8	60	∈	∈	NOUN
ejpam-2415	8	61	l	l	NOUN
ejpam-2415	8	62	then	then	ADV
ejpam-2415	8	63	p	p	X
ejpam-2415	8	64	a	a	DET
ejpam-2415	8	65	=	=	SYM
ejpam-2415	8	66	∨{x	∨{x	NOUN
ejpam-2415	8	67	∈	∈	NOUN
ejpam-2415	8	68	l	l	NOUN
ejpam-2415	9	1	|	|	ADV
ejpam-2415	9	2	xn	xn	PROPN
ejpam-2415	9	3	¶	¶	PROPN
ejpam-2415	9	4	a	a	PROPN
ejpam-2415	9	5	,	,	PUNCT
ejpam-2415	9	6	n	n	NOUN
ejpam-2415	9	7	∈	∈	NOUN
ejpam-2415	9	8	z+	z+	NUM
ejpam-2415	9	9	}	}	PUNCT
ejpam-2415	9	10	.	.	PUNCT
ejpam-2415	10	1	an	an	DET
ejpam-2415	10	2	element	element	NOUN
ejpam-2415	10	3	a	a	DET
ejpam-2415	10	4	∈	∈	PROPN
ejpam-2415	10	5	l	l	NOUN
ejpam-2415	10	6	is	be	AUX
ejpam-2415	10	7	called	call	VERB
ejpam-2415	10	8	a	a	DET
ejpam-2415	10	9	radical	radical	ADJ
ejpam-2415	10	10	element	element	NOUN
ejpam-2415	10	11	if	if	SCONJ
ejpam-2415	10	12	a	a	PRON
ejpam-2415	10	13	=	=	X
ejpam-2415	10	14	p	p	NOUN
ejpam-2415	10	15	a.	a.	NOUN
ejpam-2415	10	16	an	an	DET
ejpam-2415	10	17	element	element	NOUN
ejpam-2415	10	18	a	a	DET
ejpam-2415	10	19	∈	∈	PROPN
ejpam-2415	10	20	l	l	NOUN
ejpam-2415	10	21	is	be	AUX
ejpam-2415	10	22	called	call	VERB
ejpam-2415	10	23	compact	compact	ADJ
ejpam-2415	10	24	if	if	SCONJ
ejpam-2415	10	25	a	a	DET
ejpam-2415	10	26	¶	¶	PROPN
ejpam-2415	10	27	∨	∨	NOUN
ejpam-2415	10	28	α	α	DET
ejpam-2415	10	29	bα	bα	PROPN
ejpam-2415	10	30	implies	imply	VERB
ejpam-2415	10	31	a	a	DET
ejpam-2415	10	32	¶	¶	ADJ
ejpam-2415	10	33	bα1	bα1	NOUN
ejpam-2415	10	34	∨	∨	NUM
ejpam-2415	10	35	bα2	bα2	NOUN
ejpam-2415	10	36	∨	∨	NOUN
ejpam-2415	10	37	.	.	PUNCT
ejpam-2415	11	1	.	.	PUNCT
ejpam-2415	12	1	.∨	.∨	PROPN
ejpam-2415	12	2	bαn	bαn	PROPN
ejpam-2415	12	3	for	for	ADP
ejpam-2415	12	4	some	some	DET
ejpam-2415	12	5	finite	finite	NOUN
ejpam-2415	12	6	subset	subset	NOUN
ejpam-2415	12	7	{	{	PUNCT
ejpam-2415	12	8	α1,α2	α1,α2	PROPN
ejpam-2415	12	9	,	,	PUNCT
ejpam-2415	12	10	.	.	PUNCT
ejpam-2415	12	11	.	.	PUNCT
ejpam-2415	12	12	.	.	PUNCT
ejpam-2415	13	1	,	,	PUNCT
ejpam-2415	13	2	αn	αn	NOUN
ejpam-2415	13	3	}	}	PUNCT
ejpam-2415	13	4	.	.	PUNCT
ejpam-2415	14	1	throughout	throughout	ADP
ejpam-2415	14	2	this	this	DET
ejpam-2415	14	3	paper	paper	NOUN
ejpam-2415	14	4	,	,	PUNCT
ejpam-2415	14	5	l	l	NOUN
ejpam-2415	14	6	denotes	denote	VERB
ejpam-2415	14	7	a	a	DET
ejpam-2415	14	8	compactly	compactly	ADV
ejpam-2415	14	9	generated	generate	VERB
ejpam-2415	14	10	multiplicative	multiplicative	ADJ
ejpam-2415	14	11	lattice	lattice	NOUN
ejpam-2415	14	12	with	with	ADP
ejpam-2415	14	13	1	1	NUM
ejpam-2415	14	14	compact	compact	ADJ
ejpam-2415	14	15	and	and	CCONJ
ejpam-2415	14	16	every	every	DET
ejpam-2415	14	17	finite	finite	ADJ
ejpam-2415	14	18	product	product	NOUN
ejpam-2415	14	19	of	of	ADP
ejpam-2415	14	20	compact	compact	ADJ
ejpam-2415	14	21	elements	element	NOUN
ejpam-2415	14	22	is	be	AUX
ejpam-2415	14	23	compact	compact	ADJ
ejpam-2415	14	24	.	.	PUNCT
ejpam-2415	15	1	we	we	PRON
ejpam-2415	15	2	shall	shall	AUX
ejpam-2415	15	3	denote	denote	VERB
ejpam-2415	15	4	by	by	ADP
ejpam-2415	15	5	l∗	l∗	PROPN
ejpam-2415	15	6	the	the	DET
ejpam-2415	15	7	set	set	ADJ
ejpam-2415	15	8	compact	compact	ADJ
ejpam-2415	15	9	elements	element	NOUN
ejpam-2415	15	10	of	of	ADP
ejpam-2415	15	11	l.	l.	PROPN
ejpam-2415	15	12	a	a	DET
ejpam-2415	15	13	nonempty	nonempty	NOUN
ejpam-2415	15	14	subset	subset	VERB
ejpam-2415	15	15	f	f	PROPN
ejpam-2415	15	16	of	of	ADP
ejpam-2415	15	17	l∗	l∗	PROPN
ejpam-2415	15	18	is	be	AUX
ejpam-2415	15	19	called	call	VERB
ejpam-2415	15	20	a	a	DET
ejpam-2415	15	21	filter	filter	NOUN
ejpam-2415	15	22	of	of	ADP
ejpam-2415	15	23	l∗	l∗	PROPN
ejpam-2415	15	24	if	if	SCONJ
ejpam-2415	15	25	the	the	DET
ejpam-2415	15	26	following	follow	VERB
ejpam-2415	15	27	conditions	condition	NOUN
ejpam-2415	15	28	are	be	AUX
ejpam-2415	15	29	satisfied	satisfied	ADJ
ejpam-2415	15	30	,	,	PUNCT
ejpam-2415	15	31	(	(	PUNCT
ejpam-2415	15	32	i	i	NOUN
ejpam-2415	15	33	)	)	PUNCT
ejpam-2415	15	34	x	x	SYM
ejpam-2415	15	35	,	,	PUNCT
ejpam-2415	15	36	y	y	PROPN
ejpam-2415	15	37	∈	∈	PROPN
ejpam-2415	15	38	f	f	PROPN
ejpam-2415	15	39	implies	imply	VERB
ejpam-2415	15	40	x	x	PUNCT
ejpam-2415	15	41	y	y	PROPN
ejpam-2415	15	42	∈	∈	PROPN
ejpam-2415	15	43	f	f	PROPN
ejpam-2415	15	44	(	(	PUNCT
ejpam-2415	15	45	ii	ii	PROPN
ejpam-2415	15	46	)	)	PUNCT
ejpam-2415	15	47	x	x	PUNCT
ejpam-2415	15	48	∈	∈	PROPN
ejpam-2415	15	49	f	f	X
ejpam-2415	15	50	,	,	PUNCT
ejpam-2415	15	51	x	x	PROPN
ejpam-2415	15	52	¶	¶	PROPN
ejpam-2415	15	53	y	y	PROPN
ejpam-2415	15	54	implies	imply	VERB
ejpam-2415	15	55	y	y	PROPN
ejpam-2415	15	56	∈	∈	PROPN
ejpam-2415	15	57	f	f	X
ejpam-2415	15	58	.	.	PUNCT
ejpam-2415	16	1	∗corresponding	∗corresponde	VERB
ejpam-2415	16	2	author	author	NOUN
ejpam-2415	16	3	.	.	PUNCT
ejpam-2415	17	1	email	email	NOUN
ejpam-2415	17	2	addresses	address	NOUN
ejpam-2415	17	3	:	:	PUNCT
ejpam-2415	17	4	csmanjrekar@yahoo.co.in	csmanjrekar@yahoo.co.in	X
ejpam-2415	17	5	(	(	PUNCT
ejpam-2415	17	6	c	c	NOUN
ejpam-2415	17	7	manjarekar	manjarekar	NOUN
ejpam-2415	17	8	)	)	PUNCT
ejpam-2415	17	9	,	,	PUNCT
ejpam-2415	17	10	ujwalabiraje@gmail.com	ujwalabiraje@gmail.com	X
ejpam-2415	17	11	(	(	PUNCT
ejpam-2415	17	12	u	u	NOUN
ejpam-2415	17	13	kandale	kandale	PROPN
ejpam-2415	17	14	)	)	PUNCT
ejpam-2415	17	15	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2415	18	1	332	332	NUM
ejpam-2415	18	2	c	c	X
ejpam-2415	18	3	©	©	PROPN
ejpam-2415	18	4	2015	2015	NUM
ejpam-2415	18	5	ejpam	ejpam	NOUN
ejpam-2415	18	6	all	all	DET
ejpam-2415	18	7	rights	right	NOUN
ejpam-2415	18	8	reserved	reserve	VERB
ejpam-2415	18	9	.	.	PUNCT
ejpam-2415	19	1	c	c	PROPN
ejpam-2415	19	2	manjarekar	manjarekar	PROPN
ejpam-2415	19	3	,	,	PUNCT
ejpam-2415	19	4	u	u	NOUN
ejpam-2415	19	5	kandale	kandale	PROPN
ejpam-2415	19	6	/	/	SYM
ejpam-2415	19	7	eur	eur	PROPN
ejpam-2415	19	8	.	.	PUNCT
ejpam-2415	20	1	j.	j.	PROPN
ejpam-2415	20	2	pure	pure	PROPN
ejpam-2415	20	3	appl	appl	PROPN
ejpam-2415	20	4	.	.	PROPN
ejpam-2415	20	5	math	math	PROPN
ejpam-2415	20	6	,	,	PUNCT
ejpam-2415	20	7	8	8	NUM
ejpam-2415	20	8	(	(	PUNCT
ejpam-2415	20	9	2015	2015	NUM
ejpam-2415	20	10	)	)	PUNCT
ejpam-2415	20	11	,	,	PUNCT
ejpam-2415	20	12	332	332	NUM
ejpam-2415	20	13	-	-	SYM
ejpam-2415	20	14	342	342	NUM
ejpam-2415	20	15	333	333	NUM
ejpam-2415	20	16	let	let	VERB
ejpam-2415	20	17	f(l∗	f(l∗	NOUN
ejpam-2415	20	18	)	)	PUNCT
ejpam-2415	20	19	denote	denote	VERB
ejpam-2415	20	20	the	the	DET
ejpam-2415	20	21	set	set	NOUN
ejpam-2415	20	22	of	of	ADP
ejpam-2415	20	23	all	all	DET
ejpam-2415	20	24	filters	filter	NOUN
ejpam-2415	20	25	of	of	ADP
ejpam-2415	20	26	l.	l.	NOUN
ejpam-2415	20	27	for	for	ADP
ejpam-2415	20	28	a	a	DET
ejpam-2415	20	29	nonempty	nonempty	ADJ
ejpam-2415	20	30	subset	subset	NOUN
ejpam-2415	20	31	{	{	PUNCT
ejpam-2415	20	32	fα	fα	NOUN
ejpam-2415	20	33	}	}	SYM
ejpam-2415	20	34	⊆	⊆	NUM
ejpam-2415	20	35	f(l∗	f(l∗	NUM
ejpam-2415	20	36	)	)	PUNCT
ejpam-2415	20	37	,	,	PUNCT
ejpam-2415	20	38	define	define	VERB
ejpam-2415	20	39	⋒fα	⋒fα	NOUN
ejpam-2415	20	40	=	=	PUNCT
ejpam-2415	20	41	{	{	PUNCT
ejpam-2415	20	42	x	x	PUNCT
ejpam-2415	20	43	∈	∈	PROPN
ejpam-2415	20	44	l∗	l∗	NOUN
ejpam-2415	21	1	|	|	ADV
ejpam-2415	21	2	x	x	NOUN
ejpam-2415	21	3	≥	≥	NOUN
ejpam-2415	21	4	f1	f1	NOUN
ejpam-2415	21	5	f2	f2	PROPN
ejpam-2415	21	6	·	·	PUNCT
ejpam-2415	21	7	·	·	PUNCT
ejpam-2415	21	8	·	·	PUNCT
ejpam-2415	22	1	fn	fn	X
ejpam-2415	22	2	∈	∈	PROPN
ejpam-2415	22	3	fαi	fαi	NOUN
ejpam-2415	22	4	,	,	PUNCT
ejpam-2415	22	5	for	for	ADP
ejpam-2415	22	6	some	some	DET
ejpam-2415	22	7	i	i	NOUN
ejpam-2415	22	8	=	=	NOUN
ejpam-2415	22	9	1,2	1,2	NUM
ejpam-2415	22	10	,	,	PUNCT
ejpam-2415	22	11	.	.	PUNCT
ejpam-2415	22	12	.	.	PUNCT
ejpam-2415	22	13	.	.	PUNCT
ejpam-2415	22	14	,	,	PUNCT
ejpam-2415	22	15	n	n	CCONJ
ejpam-2415	22	16	}	}	PUNCT
ejpam-2415	22	17	.	.	PUNCT
ejpam-2415	23	1	then	then	ADV
ejpam-2415	23	2	it	it	PRON
ejpam-2415	23	3	is	be	AUX
ejpam-2415	23	4	observed	observe	VERB
ejpam-2415	23	5	that	that	SCONJ
ejpam-2415	23	6	,	,	PUNCT
ejpam-2415	23	7	f(l∗	f(l∗	X
ejpam-2415	23	8	)	)	PUNCT
ejpam-2415	23	9	=	=	PUNCT
ejpam-2415	24	1	〈	〈	PRON
ejpam-2415	24	2	f(l∗),⋒,∩	f(l∗),⋒,∩	ADJ
ejpam-2415	24	3	〉	〉	NOUN
ejpam-2415	24	4	is	be	AUX
ejpam-2415	24	5	a	a	DET
ejpam-2415	24	6	complete	complete	ADJ
ejpam-2415	24	7	distributive	distributive	ADJ
ejpam-2415	24	8	lattice	lattice	NOUN
ejpam-2415	24	9	with	with	ADP
ejpam-2415	24	10	⋒	⋒	NOUN
ejpam-2415	24	11	as	as	ADP
ejpam-2415	24	12	the	the	DET
ejpam-2415	24	13	supremum	supremum	ADJ
ejpam-2415	24	14	and	and	CCONJ
ejpam-2415	24	15	the	the	DET
ejpam-2415	24	16	set	set	ADJ
ejpam-2415	24	17	theroretic	theroretic	ADJ
ejpam-2415	24	18	⋂	⋂	PROPN
ejpam-2415	24	19	as	as	ADP
ejpam-2415	24	20	the	the	DET
ejpam-2415	24	21	infimum	infimum	NOUN
ejpam-2415	24	22	.	.	PUNCT
ejpam-2415	25	1	for	for	ADP
ejpam-2415	25	2	a	a	DET
ejpam-2415	25	3	∈	∈	PROPN
ejpam-2415	25	4	l∗	l∗	NOUN
ejpam-2415	25	5	the	the	DET
ejpam-2415	25	6	smallest	small	ADJ
ejpam-2415	25	7	filter	filter	NOUN
ejpam-2415	25	8	containing	contain	VERB
ejpam-2415	25	9	a	a	PRON
ejpam-2415	25	10	is	be	AUX
ejpam-2415	25	11	denoted	denote	VERB
ejpam-2415	25	12	by	by	ADP
ejpam-2415	25	13	[	[	X
ejpam-2415	25	14	a	a	X
ejpam-2415	25	15	)	)	PUNCT
ejpam-2415	25	16	and	and	CCONJ
ejpam-2415	25	17	it	it	PRON
ejpam-2415	25	18	is	be	AUX
ejpam-2415	25	19	given	give	VERB
ejpam-2415	25	20	by	by	ADP
ejpam-2415	25	21	[	[	X
ejpam-2415	25	22	a	a	X
ejpam-2415	25	23	)	)	PUNCT
ejpam-2415	25	24	=	=	SYM
ejpam-2415	25	25	{	{	PUNCT
ejpam-2415	25	26	x	x	PUNCT
ejpam-2415	25	27	∈	∈	PROPN
ejpam-2415	25	28	l∗	l∗	NOUN
ejpam-2415	26	1	|	|	ADV
ejpam-2415	26	2	x	x	CCONJ
ejpam-2415	26	3	≥	≥	X
ejpam-2415	26	4	an	an	PRON
ejpam-2415	26	5	for	for	ADP
ejpam-2415	26	6	some	some	DET
ejpam-2415	26	7	nonnegative	nonnegative	ADJ
ejpam-2415	26	8	integer	integer	NOUN
ejpam-2415	26	9	n	n	CCONJ
ejpam-2415	26	10	}	}	PUNCT
ejpam-2415	26	11	.	.	PUNCT
ejpam-2415	27	1	for	for	ADP
ejpam-2415	27	2	a	a	DET
ejpam-2415	27	3	filter	filter	NOUN
ejpam-2415	27	4	f	f	PROPN
ejpam-2415	27	5	∈	∈	PROPN
ejpam-2415	27	6	f(l∗	f(l∗	NOUN
ejpam-2415	27	7	)	)	PUNCT
ejpam-2415	27	8	we	we	PRON
ejpam-2415	27	9	denote,0f	denote,0f	ADV
ejpam-2415	27	10	=	=	SYM
ejpam-2415	27	11	∨{x	∨{x	PROPN
ejpam-2415	27	12	∈	∈	PROPN
ejpam-2415	27	13	l∗	l∗	PROPN
ejpam-2415	27	14	|	|	ADV
ejpam-2415	27	15	xs	xs	PROPN
ejpam-2415	27	16	=	=	SYM
ejpam-2415	27	17	0	0	PROPN
ejpam-2415	27	18	,	,	PUNCT
ejpam-2415	27	19	for	for	ADP
ejpam-2415	27	20	s	s	PROPN
ejpam-2415	27	21	∈	∈	PROPN
ejpam-2415	27	22	f	f	X
ejpam-2415	27	23	}	}	PUNCT
ejpam-2415	27	24	.	.	PUNCT
ejpam-2415	28	1	let	let	VERB
ejpam-2415	28	2	m	m	PRON
ejpam-2415	28	3	be	be	AUX
ejpam-2415	28	4	a	a	DET
ejpam-2415	28	5	complete	complete	ADJ
ejpam-2415	28	6	lattice	lattice	NOUN
ejpam-2415	28	7	and	and	CCONJ
ejpam-2415	28	8	l	l	NOUN
ejpam-2415	28	9	be	be	AUX
ejpam-2415	28	10	a	a	DET
ejpam-2415	28	11	multiplicative	multiplicative	ADJ
ejpam-2415	28	12	lattice	lattice	NOUN
ejpam-2415	28	13	.	.	PUNCT
ejpam-2415	29	1	then	then	ADV
ejpam-2415	29	2	m	m	PROPN
ejpam-2415	29	3	is	be	AUX
ejpam-2415	29	4	called	call	VERB
ejpam-2415	29	5	l	l	NOUN
ejpam-2415	29	6	-	-	NOUN
ejpam-2415	29	7	module	module	NOUN
ejpam-2415	29	8	or	or	CCONJ
ejpam-2415	29	9	module	module	NOUN
ejpam-2415	29	10	over	over	ADP
ejpam-2415	29	11	l	l	NOUN
ejpam-2415	29	12	if	if	SCONJ
ejpam-2415	29	13	there	there	PRON
ejpam-2415	29	14	is	be	VERB
ejpam-2415	29	15	a	a	DET
ejpam-2415	29	16	multiplication	multiplication	NOUN
ejpam-2415	29	17	between	between	ADP
ejpam-2415	29	18	elements	element	NOUN
ejpam-2415	29	19	of	of	ADP
ejpam-2415	29	20	l	l	NOUN
ejpam-2415	29	21	and	and	CCONJ
ejpam-2415	29	22	m	m	AUX
ejpam-2415	29	23	written	write	VERB
ejpam-2415	29	24	as	as	ADP
ejpam-2415	29	25	ab	ab	NUM
ejpam-2415	29	26	where	where	SCONJ
ejpam-2415	29	27	a	a	DET
ejpam-2415	29	28	∈	∈	PROPN
ejpam-2415	29	29	l	l	NOUN
ejpam-2415	29	30	and	and	CCONJ
ejpam-2415	29	31	b	b	X
ejpam-2415	29	32	∈	∈	NOUN
ejpam-2415	29	33	m	m	VERB
ejpam-2415	29	34	which	which	PRON
ejpam-2415	29	35	satisfies	satisfy	VERB
ejpam-2415	29	36	the	the	DET
ejpam-2415	29	37	following	follow	VERB
ejpam-2415	29	38	properties	property	NOUN
ejpam-2415	29	39	,	,	PUNCT
ejpam-2415	29	40	(	(	PUNCT
ejpam-2415	29	41	i	i	NOUN
ejpam-2415	29	42	)	)	PUNCT
ejpam-2415	29	43	(	(	PUNCT
ejpam-2415	29	44	∨	∨	X
ejpam-2415	29	45	α	α	NOUN
ejpam-2415	29	46	aα)a=	aα)a=	ADP
ejpam-2415	29	47	∨	∨	NOUN
ejpam-2415	29	48	α	α	PROPN
ejpam-2415	29	49	aαa	aαa	VERB
ejpam-2415	29	50	∀aα	∀aα	NOUN
ejpam-2415	29	51	∈	∈	PROPN
ejpam-2415	29	52	l	l	NOUN
ejpam-2415	29	53	,	,	PUNCT
ejpam-2415	29	54	a∈	a∈	PROPN
ejpam-2415	29	55	m	m	PROPN
ejpam-2415	29	56	(	(	PUNCT
ejpam-2415	29	57	ii	ii	NOUN
ejpam-2415	29	58	)	)	PUNCT
ejpam-2415	29	59	a(∨	a(∨	PUNCT
ejpam-2415	30	1	α	α	DET
ejpam-2415	30	2	aα	aα	NOUN
ejpam-2415	30	3	)	)	PUNCT
ejpam-2415	30	4	=	=	PUNCT
ejpam-2415	31	1	∨	∨	NUM
ejpam-2415	31	2	α	α	PRON
ejpam-2415	31	3	aaα	aaα	PRON
ejpam-2415	31	4	∀a	∀a	NOUN
ejpam-2415	31	5	∈	∈	PROPN
ejpam-2415	31	6	l	l	NOUN
ejpam-2415	31	7	,	,	PUNCT
ejpam-2415	31	8	aα	aα	NOUN
ejpam-2415	31	9	∈	∈	PROPN
ejpam-2415	31	10	m	m	NOUN
ejpam-2415	31	11	(	(	PUNCT
ejpam-2415	31	12	iii	iii	NOUN
ejpam-2415	31	13	)	)	PUNCT
ejpam-2415	31	14	(	(	PUNCT
ejpam-2415	31	15	ab)a=	ab)a=	ADP
ejpam-2415	31	16	a(ba	a(ba	NOUN
ejpam-2415	31	17	)	)	PUNCT
ejpam-2415	31	18	∀a	∀a	NOUN
ejpam-2415	31	19	,	,	PUNCT
ejpam-2415	31	20	b	b	X
ejpam-2415	31	21	∈	∈	PROPN
ejpam-2415	31	22	l	l	NOUN
ejpam-2415	31	23	,	,	PUNCT
ejpam-2415	31	24	a∈	a∈	PROPN
ejpam-2415	31	25	m	m	PROPN
ejpam-2415	31	26	(	(	PUNCT
ejpam-2415	31	27	iv	iv	X
ejpam-2415	31	28	)	)	PUNCT
ejpam-2415	31	29	1b	1b	NOUN
ejpam-2415	31	30	=	=	SYM
ejpam-2415	31	31	b	b	PROPN
ejpam-2415	31	32	(	(	PUNCT
ejpam-2415	31	33	v	v	NOUN
ejpam-2415	31	34	)	)	PUNCT
ejpam-2415	31	35	0b	0b	NOUN
ejpam-2415	31	36	=	=	SYM
ejpam-2415	31	37	0	0	NUM
ejpam-2415	31	38	m	m	VERB
ejpam-2415	31	39	for	for	ADP
ejpam-2415	31	40	all	all	DET
ejpam-2415	31	41	a	a	DET
ejpam-2415	31	42	,	,	PUNCT
ejpam-2415	31	43	aα	aα	NOUN
ejpam-2415	31	44	,	,	PUNCT
ejpam-2415	31	45	b	b	PROPN
ejpam-2415	31	46	∈	∈	PROPN
ejpam-2415	31	47	l	l	NOUN
ejpam-2415	31	48	and	and	CCONJ
ejpam-2415	31	49	a	a	DET
ejpam-2415	31	50	,	,	PUNCT
ejpam-2415	31	51	aα	aα	NOUN
ejpam-2415	31	52	∈	∈	PROPN
ejpam-2415	31	53	m	m	NOUN
ejpam-2415	31	54	,	,	PUNCT
ejpam-2415	31	55	where	where	SCONJ
ejpam-2415	31	56	1	1	NUM
ejpam-2415	31	57	is	be	AUX
ejpam-2415	31	58	the	the	DET
ejpam-2415	31	59	supremum	supremum	NOUN
ejpam-2415	31	60	of	of	ADP
ejpam-2415	31	61	l	l	NOUN
ejpam-2415	31	62	and	and	CCONJ
ejpam-2415	31	63	0	0	NUM
ejpam-2415	31	64	is	be	AUX
ejpam-2415	31	65	the	the	DET
ejpam-2415	31	66	infimum	infimum	NOUN
ejpam-2415	31	67	of	of	ADP
ejpam-2415	31	68	l.	l.	NOUN
ejpam-2415	31	69	we	we	PRON
ejpam-2415	31	70	denote	denote	VERB
ejpam-2415	31	71	by	by	ADP
ejpam-2415	31	72	0	0	NUM
ejpam-2415	31	73	m	m	VERB
ejpam-2415	31	74	and	and	CCONJ
ejpam-2415	31	75	i	i	PRON
ejpam-2415	31	76	m	m	VERB
ejpam-2415	31	77	the	the	DET
ejpam-2415	31	78	least	least	ADJ
ejpam-2415	31	79	element	element	NOUN
ejpam-2415	31	80	and	and	CCONJ
ejpam-2415	31	81	the	the	DET
ejpam-2415	31	82	greatest	great	ADJ
ejpam-2415	31	83	element	element	NOUN
ejpam-2415	31	84	of	of	ADP
ejpam-2415	31	85	m.	m.	NOUN
ejpam-2415	31	86	elements	element	NOUN
ejpam-2415	31	87	of	of	ADP
ejpam-2415	31	88	l	l	NOUN
ejpam-2415	31	89	will	will	AUX
ejpam-2415	31	90	generally	generally	ADV
ejpam-2415	31	91	be	be	AUX
ejpam-2415	31	92	denoted	denote	VERB
ejpam-2415	31	93	by	by	ADP
ejpam-2415	31	94	a	a	DET
ejpam-2415	31	95	,	,	PUNCT
ejpam-2415	31	96	b	b	PROPN
ejpam-2415	31	97	,	,	PUNCT
ejpam-2415	31	98	c	c	NOUN
ejpam-2415	31	99	,	,	PUNCT
ejpam-2415	31	100	.	.	PUNCT
ejpam-2415	31	101	.	.	PUNCT
ejpam-2415	32	1	.	.	PUNCT
ejpam-2415	33	1	and	and	CCONJ
ejpam-2415	33	2	elements	element	NOUN
ejpam-2415	33	3	of	of	ADP
ejpam-2415	33	4	m	m	PROPN
ejpam-2415	33	5	will	will	AUX
ejpam-2415	33	6	generally	generally	ADV
ejpam-2415	33	7	be	be	AUX
ejpam-2415	33	8	denoted	denote	VERB
ejpam-2415	33	9	by	by	ADP
ejpam-2415	33	10	a	a	DET
ejpam-2415	33	11	,	,	PUNCT
ejpam-2415	33	12	b	b	NOUN
ejpam-2415	33	13	,	,	PUNCT
ejpam-2415	33	14	c	c	NOUN
ejpam-2415	33	15	.	.	PUNCT
ejpam-2415	33	16	.	.	PUNCT
ejpam-2415	34	1	..	..	PUNCT
ejpam-2415	34	2	let	let	VERB
ejpam-2415	34	3	m	m	PRON
ejpam-2415	34	4	be	be	AUX
ejpam-2415	34	5	a	a	DET
ejpam-2415	34	6	l	l	NOUN
ejpam-2415	34	7	-	-	NOUN
ejpam-2415	34	8	module	module	NOUN
ejpam-2415	34	9	.	.	PUNCT
ejpam-2415	35	1	if	if	SCONJ
ejpam-2415	35	2	n	n	PRON
ejpam-2415	35	3	∈	∈	VERB
ejpam-2415	35	4	m	m	VERB
ejpam-2415	35	5	and	and	CCONJ
ejpam-2415	35	6	a	a	DET
ejpam-2415	35	7	∈	∈	NOUN
ejpam-2415	35	8	l	l	NOUN
ejpam-2415	35	9	then	then	ADV
ejpam-2415	35	10	(	(	PUNCT
ejpam-2415	35	11	n	n	X
ejpam-2415	35	12	:	:	PUNCT
ejpam-2415	35	13	a	a	X
ejpam-2415	35	14	)	)	PUNCT
ejpam-2415	36	1	=	=	SYM
ejpam-2415	36	2	∨{x	∨{x	PROPN
ejpam-2415	37	1	∈	∈	NOUN
ejpam-2415	37	2	m	m	VERB
ejpam-2415	37	3	|	|	ADV
ejpam-2415	37	4	ax	ax	NOUN
ejpam-2415	37	5	¶	¶	PROPN
ejpam-2415	37	6	n	n	CCONJ
ejpam-2415	37	7	}	}	PUNCT
ejpam-2415	37	8	.	.	PUNCT
ejpam-2415	38	1	if	if	SCONJ
ejpam-2415	38	2	a	a	PRON
ejpam-2415	38	3	,	,	PUNCT
ejpam-2415	38	4	b	b	X
ejpam-2415	38	5	∈	∈	ADV
ejpam-2415	38	6	m	m	NOUN
ejpam-2415	38	7	,	,	PUNCT
ejpam-2415	38	8	then	then	ADV
ejpam-2415	38	9	(	(	PUNCT
ejpam-2415	38	10	a	a	DET
ejpam-2415	38	11	:	:	PUNCT
ejpam-2415	38	12	b	b	X
ejpam-2415	38	13	)	)	PUNCT
ejpam-2415	38	14	=	=	SYM
ejpam-2415	39	1	∨{x	∨{x	NOUN
ejpam-2415	39	2	∈	∈	NOUN
ejpam-2415	39	3	l	l	NOUN
ejpam-2415	40	1	|	|	ADV
ejpam-2415	40	2	xb	xb	PROPN
ejpam-2415	40	3	¶	¶	PROPN
ejpam-2415	40	4	a	a	PRON
ejpam-2415	40	5	}	}	PUNCT
ejpam-2415	40	6	.	.	PUNCT
ejpam-2415	41	1	an	an	DET
ejpam-2415	41	2	l	l	NOUN
ejpam-2415	41	3	-	-	NOUN
ejpam-2415	41	4	module	module	NOUN
ejpam-2415	41	5	m	m	NOUN
ejpam-2415	41	6	is	be	AUX
ejpam-2415	41	7	called	call	VERB
ejpam-2415	41	8	a	a	DET
ejpam-2415	41	9	multiplication	multiplication	NOUN
ejpam-2415	41	10	l	l	NOUN
ejpam-2415	41	11	-	-	NOUN
ejpam-2415	41	12	module	module	NOUN
ejpam-2415	41	13	if	if	SCONJ
ejpam-2415	41	14	for	for	ADP
ejpam-2415	41	15	every	every	DET
ejpam-2415	41	16	element	element	NOUN
ejpam-2415	41	17	n	n	PRON
ejpam-2415	41	18	∈	∈	NOUN
ejpam-2415	42	1	m	m	AUX
ejpam-2415	42	2	there	there	PRON
ejpam-2415	42	3	exists	exist	VERB
ejpam-2415	42	4	an	an	DET
ejpam-2415	42	5	element	element	NOUN
ejpam-2415	42	6	a	a	DET
ejpam-2415	42	7	∈	∈	NOUN
ejpam-2415	42	8	l	l	NOUN
ejpam-2415	42	9	such	such	ADJ
ejpam-2415	42	10	that	that	SCONJ
ejpam-2415	42	11	n	n	NOUN
ejpam-2415	42	12	=	=	NOUN
ejpam-2415	42	13	aim	aim	AUX
ejpam-2415	42	14	see	see	VERB
ejpam-2415	42	15	[	[	X
ejpam-2415	42	16	2	2	NUM
ejpam-2415	42	17	]	]	PUNCT
ejpam-2415	42	18	.	.	PUNCT
ejpam-2415	43	1	in	in	ADP
ejpam-2415	43	2	this	this	DET
ejpam-2415	43	3	paper	paper	NOUN
ejpam-2415	43	4	a	a	DET
ejpam-2415	43	5	lattice	lattice	NOUN
ejpam-2415	43	6	module	module	NOUN
ejpam-2415	43	7	m	m	VERB
ejpam-2415	43	8	will	will	AUX
ejpam-2415	43	9	be	be	AUX
ejpam-2415	43	10	a	a	DET
ejpam-2415	43	11	multiplication	multiplication	NOUN
ejpam-2415	43	12	lattice	lattice	NOUN
ejpam-2415	43	13	module	module	NOUN
ejpam-2415	43	14	,	,	PUNCT
ejpam-2415	43	15	which	which	PRON
ejpam-2415	43	16	is	be	AUX
ejpam-2415	43	17	compactly	compactly	ADV
ejpam-2415	43	18	generated	generate	VERB
ejpam-2415	43	19	with	with	ADP
ejpam-2415	43	20	the	the	DET
ejpam-2415	43	21	largest	large	ADJ
ejpam-2415	43	22	element	element	NOUN
ejpam-2415	43	23	i	i	NOUN
ejpam-2415	43	24	m	m	VERB
ejpam-2415	43	25	compact	compact	ADJ
ejpam-2415	43	26	.	.	PUNCT
ejpam-2415	44	1	a	a	DET
ejpam-2415	44	2	proper	proper	ADJ
ejpam-2415	44	3	element	element	NOUN
ejpam-2415	44	4	n	n	PROPN
ejpam-2415	44	5	of	of	ADP
ejpam-2415	44	6	m	m	PROPN
ejpam-2415	44	7	is	be	AUX
ejpam-2415	44	8	said	say	VERB
ejpam-2415	44	9	to	to	PART
ejpam-2415	44	10	be	be	AUX
ejpam-2415	44	11	prime	prime	ADJ
ejpam-2415	44	12	if	if	SCONJ
ejpam-2415	44	13	ax	ax	NOUN
ejpam-2415	44	14	¶	¶	PROPN
ejpam-2415	44	15	n	n	PRON
ejpam-2415	44	16	implies	imply	VERB
ejpam-2415	44	17	x	x	PROPN
ejpam-2415	44	18	¶	¶	NOUN
ejpam-2415	44	19	n	n	PRON
ejpam-2415	44	20	or	or	CCONJ
ejpam-2415	44	21	aim	aim	VERB
ejpam-2415	44	22	¶	¶	PROPN
ejpam-2415	44	23	n	n	CCONJ
ejpam-2415	44	24	that	that	PRON
ejpam-2415	44	25	is	be	AUX
ejpam-2415	44	26	a	a	DET
ejpam-2415	44	27	¶	¶	NOUN
ejpam-2415	44	28	(	(	PUNCT
ejpam-2415	44	29	n	n	NUM
ejpam-2415	44	30	:	:	PUNCT
ejpam-2415	44	31	i	i	PRON
ejpam-2415	44	32	m	m	VERB
ejpam-2415	44	33	)	)	PUNCT
ejpam-2415	44	34	for	for	ADP
ejpam-2415	44	35	every	every	DET
ejpam-2415	44	36	a	a	DET
ejpam-2415	44	37	∈	∈	PROPN
ejpam-2415	44	38	l	l	NOUN
ejpam-2415	44	39	,	,	PUNCT
ejpam-2415	44	40	x	x	SYM
ejpam-2415	44	41	∈	∈	PROPN
ejpam-2415	44	42	m	m	VERB
ejpam-2415	44	43	.	.	PUNCT
ejpam-2415	45	1	if	if	SCONJ
ejpam-2415	45	2	n	n	PRON
ejpam-2415	45	3	is	be	AUX
ejpam-2415	45	4	a	a	DET
ejpam-2415	45	5	prime	prime	ADJ
ejpam-2415	45	6	element	element	NOUN
ejpam-2415	45	7	of	of	ADP
ejpam-2415	45	8	m	m	PRON
ejpam-2415	45	9	then	then	ADV
ejpam-2415	45	10	(	(	PUNCT
ejpam-2415	45	11	n	n	X
ejpam-2415	45	12	:	:	PUNCT
ejpam-2415	45	13	i	i	PRON
ejpam-2415	45	14	m	m	PROPN
ejpam-2415	45	15	)	)	PUNCT
ejpam-2415	45	16	is	be	AUX
ejpam-2415	45	17	prime	prime	ADJ
ejpam-2415	45	18	element	element	NOUN
ejpam-2415	45	19	of	of	ADP
ejpam-2415	45	20	l	l	NOUN
ejpam-2415	46	1	[	[	X
ejpam-2415	46	2	4	4	NUM
ejpam-2415	46	3	]	]	PUNCT
ejpam-2415	46	4	.	.	PUNCT
ejpam-2415	47	1	an	an	DET
ejpam-2415	47	2	element	element	NOUN
ejpam-2415	47	3	n	n	CCONJ
ejpam-2415	47	4	<	<	X
ejpam-2415	47	5	i	i	X
ejpam-2415	47	6	m	m	VERB
ejpam-2415	47	7	in	in	ADP
ejpam-2415	47	8	m	m	PROPN
ejpam-2415	47	9	is	be	AUX
ejpam-2415	47	10	said	say	VERB
ejpam-2415	47	11	to	to	PART
ejpam-2415	47	12	be	be	AUX
ejpam-2415	47	13	primary	primary	ADJ
ejpam-2415	47	14	if	if	SCONJ
ejpam-2415	47	15	ax	ax	NOUN
ejpam-2415	47	16	¶	¶	PROPN
ejpam-2415	47	17	n	n	PRON
ejpam-2415	47	18	implies	imply	VERB
ejpam-2415	47	19	x	x	PROPN
ejpam-2415	47	20	¶	¶	NOUN
ejpam-2415	47	21	n	n	ADP
ejpam-2415	47	22	or	or	CCONJ
ejpam-2415	47	23	an	an	DET
ejpam-2415	47	24	i	i	NOUN
ejpam-2415	47	25	m	m	PROPN
ejpam-2415	47	26	¶	¶	PROPN
ejpam-2415	47	27	n	n	CCONJ
ejpam-2415	47	28	that	that	PRON
ejpam-2415	47	29	is	be	AUX
ejpam-2415	47	30	an	an	DET
ejpam-2415	47	31	¶	¶	NOUN
ejpam-2415	47	32	(	(	PUNCT
ejpam-2415	47	33	n	n	NUM
ejpam-2415	47	34	:	:	PUNCT
ejpam-2415	47	35	i	i	PRON
ejpam-2415	47	36	m	m	VERB
ejpam-2415	47	37	)	)	PUNCT
ejpam-2415	47	38	for	for	ADP
ejpam-2415	47	39	some	some	DET
ejpam-2415	47	40	integer	integer	NOUN
ejpam-2415	47	41	n.	n.	NOUN
ejpam-2415	47	42	an	an	DET
ejpam-2415	47	43	element	element	NOUN
ejpam-2415	47	44	n	n	PROPN
ejpam-2415	47	45	of	of	ADP
ejpam-2415	47	46	m	m	PROPN
ejpam-2415	47	47	is	be	AUX
ejpam-2415	47	48	called	call	VERB
ejpam-2415	47	49	a	a	DET
ejpam-2415	47	50	radical	radical	ADJ
ejpam-2415	47	51	element	element	NOUN
ejpam-2415	47	52	if	if	SCONJ
ejpam-2415	47	53	(	(	PUNCT
ejpam-2415	47	54	n	n	X
ejpam-2415	47	55	:	:	PUNCT
ejpam-2415	47	56	i	i	PRON
ejpam-2415	47	57	m	m	VERB
ejpam-2415	47	58	)	)	PUNCT
ejpam-2415	48	1	=	=	SYM
ejpam-2415	48	2	p	p	X
ejpam-2415	48	3	(	(	PUNCT
ejpam-2415	48	4	n	n	NOUN
ejpam-2415	48	5	:	:	PUNCT
ejpam-2415	48	6	i	i	PRON
ejpam-2415	48	7	m	m	PROPN
ejpam-2415	48	8	)	)	PUNCT
ejpam-2415	48	9	.	.	PUNCT
ejpam-2415	49	1	if	if	SCONJ
ejpam-2415	49	2	an	an	DET
ejpam-2415	49	3	=	=	NOUN
ejpam-2415	49	4	0	0	NUM
ejpam-2415	49	5	m	m	NOUN
ejpam-2415	49	6	implies	imply	VERB
ejpam-2415	49	7	a	a	DET
ejpam-2415	49	8	=	=	SYM
ejpam-2415	49	9	0	0	NUM
ejpam-2415	49	10	or	or	CCONJ
ejpam-2415	49	11	n	n	CCONJ
ejpam-2415	49	12	=	=	SYM
ejpam-2415	49	13	0	0	NUM
ejpam-2415	49	14	m	m	VERB
ejpam-2415	49	15	for	for	ADP
ejpam-2415	49	16	any	any	DET
ejpam-2415	49	17	a	a	DET
ejpam-2415	49	18	∈	∈	ADJ
ejpam-2415	49	19	l	l	NOUN
ejpam-2415	49	20	and	and	CCONJ
ejpam-2415	49	21	n	n	PRON
ejpam-2415	49	22	∈	∈	NOUN
ejpam-2415	49	23	m	m	VERB
ejpam-2415	49	24	then	then	ADV
ejpam-2415	49	25	m	m	VERB
ejpam-2415	49	26	is	be	AUX
ejpam-2415	49	27	called	call	VERB
ejpam-2415	49	28	a	a	DET
ejpam-2415	49	29	torsion	torsion	NOUN
ejpam-2415	49	30	free	free	ADJ
ejpam-2415	49	31	l	l	NOUN
ejpam-2415	49	32	-	-	NOUN
ejpam-2415	49	33	module	module	NOUN
ejpam-2415	49	34	.	.	PUNCT
ejpam-2415	50	1	2	2	X
ejpam-2415	50	2	.	.	NOUN
ejpam-2415	50	3	residuation	residuation	NOUN
ejpam-2415	50	4	properties	property	NOUN
ejpam-2415	50	5	we	we	PRON
ejpam-2415	50	6	state	state	VERB
ejpam-2415	50	7	some	some	DET
ejpam-2415	50	8	elementary	elementary	ADJ
ejpam-2415	50	9	properties	property	NOUN
ejpam-2415	50	10	of	of	ADP
ejpam-2415	50	11	residuation	residuation	NOUN
ejpam-2415	50	12	in	in	ADP
ejpam-2415	50	13	the	the	DET
ejpam-2415	50	14	following	follow	VERB
ejpam-2415	50	15	theorem	theorem	PROPN
ejpam-2415	50	16	.	.	PUNCT
ejpam-2415	51	1	theorem	theorem	NOUN
ejpam-2415	51	2	1	1	NUM
ejpam-2415	51	3	.	.	PUNCT
ejpam-2415	52	1	let	let	VERB
ejpam-2415	52	2	l	l	NOUN
ejpam-2415	52	3	be	be	AUX
ejpam-2415	52	4	a	a	DET
ejpam-2415	52	5	multiplicative	multiplicative	ADJ
ejpam-2415	52	6	lattice	lattice	NOUN
ejpam-2415	52	7	and	and	CCONJ
ejpam-2415	52	8	m	m	AUX
ejpam-2415	52	9	be	be	AUX
ejpam-2415	52	10	a	a	DET
ejpam-2415	52	11	multiplication	multiplication	NOUN
ejpam-2415	52	12	lattice	lattice	NOUN
ejpam-2415	52	13	module	module	NOUN
ejpam-2415	52	14	over	over	ADV
ejpam-2415	52	15	l.for	l.for	ADP
ejpam-2415	52	16	x	x	X
ejpam-2415	52	17	,	,	PUNCT
ejpam-2415	52	18	y	y	PROPN
ejpam-2415	52	19	∈	∈	PROPN
ejpam-2415	52	20	l	l	NOUN
ejpam-2415	52	21	and	and	CCONJ
ejpam-2415	52	22	z	z	NOUN
ejpam-2415	52	23	,	,	PUNCT
ejpam-2415	52	24	a	a	PRON
ejpam-2415	52	25	,	,	PUNCT
ejpam-2415	52	26	b	b	PROPN
ejpam-2415	52	27	∈	∈	PROPN
ejpam-2415	52	28	m	m	NOUN
ejpam-2415	52	29	,	,	PUNCT
ejpam-2415	52	30	where	where	SCONJ
ejpam-2415	52	31	(	(	PUNCT
ejpam-2415	52	32	0	0	NUM
ejpam-2415	52	33	m	m	AUX
ejpam-2415	52	34	:	:	PUNCT
ejpam-2415	52	35	i	i	PRON
ejpam-2415	52	36	m	m	PROPN
ejpam-2415	52	37	)	)	PUNCT
ejpam-2415	52	38	is	be	AUX
ejpam-2415	52	39	a	a	DET
ejpam-2415	52	40	radical	radical	ADJ
ejpam-2415	52	41	element	element	NOUN
ejpam-2415	52	42	.	.	PUNCT
ejpam-2415	53	1	we	we	PRON
ejpam-2415	53	2	have	have	VERB
ejpam-2415	53	3	the	the	DET
ejpam-2415	53	4	following	follow	VERB
ejpam-2415	53	5	identities	identity	NOUN
ejpam-2415	53	6	,	,	PUNCT
ejpam-2415	53	7	(	(	PUNCT
ejpam-2415	53	8	i	i	NOUN
ejpam-2415	53	9	)	)	PUNCT
ejpam-2415	53	10	x	x	SYM
ejpam-2415	53	11	¶	¶	PROPN
ejpam-2415	53	12	y	y	PROPN
ejpam-2415	53	13	implies	imply	VERB
ejpam-2415	53	14	(	(	PUNCT
ejpam-2415	53	15	0	0	NUM
ejpam-2415	53	16	m	m	VERB
ejpam-2415	53	17	:	:	PUNCT
ejpam-2415	53	18	y)¶	y)¶	X
ejpam-2415	53	19	(	(	PUNCT
ejpam-2415	53	20	0	0	NUM
ejpam-2415	53	21	m	m	VERB
ejpam-2415	53	22	:	:	PUNCT
ejpam-2415	53	23	x	x	X
ejpam-2415	53	24	)	)	PUNCT
ejpam-2415	53	25	and	and	CCONJ
ejpam-2415	53	26	0	0	NUM
ejpam-2415	53	27	m	m	VERB
ejpam-2415	53	28	:	:	PUNCT
ejpam-2415	53	29	(	(	PUNCT
ejpam-2415	53	30	0	0	NUM
ejpam-2415	53	31	m	m	VERB
ejpam-2415	53	32	:	:	PUNCT
ejpam-2415	53	33	x)¶	x)¶	PROPN
ejpam-2415	53	34	0	0	NUM
ejpam-2415	53	35	m	m	VERB
ejpam-2415	53	36	:	:	PUNCT
ejpam-2415	53	37	(	(	PUNCT
ejpam-2415	53	38	0	0	NUM
ejpam-2415	53	39	m	m	VERB
ejpam-2415	53	40	:	:	PUNCT
ejpam-2415	53	41	y	y	X
ejpam-2415	53	42	)	)	PUNCT
ejpam-2415	53	43	(	(	PUNCT
ejpam-2415	53	44	ii	ii	NOUN
ejpam-2415	53	45	)	)	PUNCT
ejpam-2415	53	46	x	x	SYM
ejpam-2415	54	1	¶	¶	PROPN
ejpam-2415	54	2	0	0	NUM
ejpam-2415	54	3	m	m	VERB
ejpam-2415	54	4	:	:	PUNCT
ejpam-2415	54	5	(	(	PUNCT
ejpam-2415	54	6	0	0	NUM
ejpam-2415	54	7	m	m	VERB
ejpam-2415	54	8	:	:	PUNCT
ejpam-2415	54	9	x	x	X
ejpam-2415	54	10	)	)	PUNCT
ejpam-2415	54	11	(	(	PUNCT
ejpam-2415	54	12	iii	iii	NOUN
ejpam-2415	54	13	)	)	PUNCT
ejpam-2415	54	14	0	0	NUM
ejpam-2415	54	15	m	m	VERB
ejpam-2415	54	16	:	:	PUNCT
ejpam-2415	55	1	[	[	X
ejpam-2415	55	2	0	0	NUM
ejpam-2415	55	3	m	m	VERB
ejpam-2415	55	4	:	:	PUNCT
ejpam-2415	55	5	(	(	PUNCT
ejpam-2415	55	6	0	0	NUM
ejpam-2415	55	7	m	m	VERB
ejpam-2415	55	8	:	:	PUNCT
ejpam-2415	55	9	x	x	X
ejpam-2415	55	10	)	)	PUNCT
ejpam-2415	55	11	]	]	PUNCT
ejpam-2415	56	1	=	=	PUNCT
ejpam-2415	56	2	(	(	PUNCT
ejpam-2415	56	3	0	0	NUM
ejpam-2415	56	4	m	m	VERB
ejpam-2415	56	5	:	:	PUNCT
ejpam-2415	56	6	x	x	X
ejpam-2415	56	7	)	)	PUNCT
ejpam-2415	56	8	c	c	PROPN
ejpam-2415	56	9	manjarekar	manjarekar	NOUN
ejpam-2415	56	10	,	,	PUNCT
ejpam-2415	56	11	u	u	NOUN
ejpam-2415	56	12	kandale	kandale	PROPN
ejpam-2415	56	13	/	/	SYM
ejpam-2415	56	14	eur	eur	PROPN
ejpam-2415	56	15	.	.	PUNCT
ejpam-2415	57	1	j.	j.	PROPN
ejpam-2415	57	2	pure	pure	PROPN
ejpam-2415	57	3	appl	appl	PROPN
ejpam-2415	57	4	.	.	PROPN
ejpam-2415	57	5	math	math	PROPN
ejpam-2415	57	6	,	,	PUNCT
ejpam-2415	57	7	8	8	NUM
ejpam-2415	57	8	(	(	PUNCT
ejpam-2415	57	9	2015	2015	NUM
ejpam-2415	57	10	)	)	PUNCT
ejpam-2415	57	11	,	,	PUNCT
ejpam-2415	57	12	332	332	NUM
ejpam-2415	57	13	-	-	SYM
ejpam-2415	57	14	342	342	NUM
ejpam-2415	57	15	334	334	NUM
ejpam-2415	57	16	(	(	PUNCT
ejpam-2415	57	17	iv	iv	X
ejpam-2415	57	18	)	)	PUNCT
ejpam-2415	57	19	(	(	PUNCT
ejpam-2415	57	20	0	0	NUM
ejpam-2415	57	21	m	m	VERB
ejpam-2415	57	22	:	:	PUNCT
ejpam-2415	57	23	x	x	X
ejpam-2415	57	24	)	)	PUNCT
ejpam-2415	57	25	=	=	SYM
ejpam-2415	57	26	(	(	PUNCT
ejpam-2415	57	27	0	0	NUM
ejpam-2415	57	28	m	m	VERB
ejpam-2415	57	29	:	:	PUNCT
ejpam-2415	57	30	xn	xn	X
ejpam-2415	57	31	)	)	PUNCT
ejpam-2415	57	32	for	for	ADP
ejpam-2415	57	33	every	every	DET
ejpam-2415	57	34	n	n	CCONJ
ejpam-2415	57	35	∈	∈	PROPN
ejpam-2415	57	36	z+	z+	NUM
ejpam-2415	57	37	(	(	PUNCT
ejpam-2415	57	38	v	v	NOUN
ejpam-2415	57	39	)	)	PUNCT
ejpam-2415	57	40	0	0	NUM
ejpam-2415	57	41	m	m	VERB
ejpam-2415	57	42	:	:	PUNCT
ejpam-2415	57	43	(	(	PUNCT
ejpam-2415	57	44	0	0	NUM
ejpam-2415	57	45	m	m	VERB
ejpam-2415	57	46	:	:	PUNCT
ejpam-2415	57	47	x)∧	x)∧	PUNCT
ejpam-2415	57	48	0	0	NUM
ejpam-2415	57	49	m	m	VERB
ejpam-2415	57	50	:	:	PUNCT
ejpam-2415	57	51	(	(	PUNCT
ejpam-2415	57	52	0	0	NUM
ejpam-2415	57	53	m	m	VERB
ejpam-2415	57	54	:	:	PUNCT
ejpam-2415	57	55	y	y	X
ejpam-2415	57	56	)	)	PUNCT
ejpam-2415	57	57	=	=	PUNCT
ejpam-2415	58	1	0	0	NUM
ejpam-2415	58	2	m	m	VERB
ejpam-2415	58	3	:	:	PUNCT
ejpam-2415	58	4	(	(	PUNCT
ejpam-2415	58	5	0	0	NUM
ejpam-2415	58	6	m	m	VERB
ejpam-2415	58	7	:	:	PUNCT
ejpam-2415	58	8	x	x	SYM
ejpam-2415	58	9	y	y	X
ejpam-2415	58	10	)	)	PUNCT
ejpam-2415	58	11	=	=	PUNCT
ejpam-2415	59	1	0	0	NUM
ejpam-2415	59	2	m	m	VERB
ejpam-2415	59	3	:	:	PUNCT
ejpam-2415	60	1	[	[	X
ejpam-2415	60	2	0	0	NUM
ejpam-2415	60	3	m	m	VERB
ejpam-2415	60	4	:	:	PUNCT
ejpam-2415	60	5	(	(	PUNCT
ejpam-2415	60	6	x	x	PUNCT
ejpam-2415	60	7	∧	∧	PROPN
ejpam-2415	60	8	y	y	PROPN
ejpam-2415	60	9	)	)	PUNCT
ejpam-2415	60	10	]	]	PUNCT
ejpam-2415	60	11	(	(	PUNCT
ejpam-2415	60	12	vi	vi	NOUN
ejpam-2415	60	13	)	)	PUNCT
ejpam-2415	60	14	(	(	PUNCT
ejpam-2415	60	15	0	0	NUM
ejpam-2415	60	16	m	m	VERB
ejpam-2415	60	17	:	:	PUNCT
ejpam-2415	60	18	a	a	X
ejpam-2415	60	19	)	)	PUNCT
ejpam-2415	61	1	=	=	SYM
ejpam-2415	61	2	0	0	NUM
ejpam-2415	61	3	m	m	NOUN
ejpam-2415	61	4	implies	imply	VERB
ejpam-2415	61	5	(	(	PUNCT
ejpam-2415	61	6	0	0	NUM
ejpam-2415	61	7	m	m	VERB
ejpam-2415	61	8	:	:	PUNCT
ejpam-2415	61	9	an	an	X
ejpam-2415	61	10	)	)	PUNCT
ejpam-2415	61	11	=	=	SYM
ejpam-2415	61	12	0	0	NUM
ejpam-2415	62	1	for	for	ADP
ejpam-2415	62	2	every	every	DET
ejpam-2415	62	3	n	n	PRON
ejpam-2415	62	4	∈	∈	PROPN
ejpam-2415	62	5	z+	z+	NUM
ejpam-2415	62	6	(	(	PUNCT
ejpam-2415	62	7	vii	vii	PROPN
ejpam-2415	62	8	)	)	PUNCT
ejpam-2415	62	9	x	x	PROPN
ejpam-2415	62	10	∨	∨	NUM
ejpam-2415	62	11	y	y	NOUN
ejpam-2415	62	12	=	=	SYM
ejpam-2415	62	13	1	1	NUM
ejpam-2415	62	14	implies	imply	VERB
ejpam-2415	62	15	(	(	PUNCT
ejpam-2415	62	16	0	0	NUM
ejpam-2415	62	17	m	m	VERB
ejpam-2415	62	18	:	:	PUNCT
ejpam-2415	62	19	x)∨	x)∨	PROPN
ejpam-2415	62	20	(	(	PUNCT
ejpam-2415	62	21	0	0	NUM
ejpam-2415	62	22	m	m	VERB
ejpam-2415	62	23	:	:	PUNCT
ejpam-2415	62	24	y	y	X
ejpam-2415	62	25	)	)	PUNCT
ejpam-2415	62	26	=	=	PUNCT
ejpam-2415	62	27	0	0	NUM
ejpam-2415	62	28	m	m	VERB
ejpam-2415	62	29	:	:	PUNCT
ejpam-2415	62	30	(	(	PUNCT
ejpam-2415	62	31	x	x	PUNCT
ejpam-2415	62	32	∧	∧	PROPN
ejpam-2415	62	33	y	y	NOUN
ejpam-2415	62	34	)	)	PUNCT
ejpam-2415	62	35	=	=	PUNCT
ejpam-2415	62	36	0	0	NUM
ejpam-2415	62	37	m	m	VERB
ejpam-2415	62	38	:	:	PUNCT
ejpam-2415	62	39	x	x	SYM
ejpam-2415	62	40	y	y	PROPN
ejpam-2415	62	41	(	(	PUNCT
ejpam-2415	62	42	viii	viii	PROPN
ejpam-2415	62	43	)	)	PUNCT
ejpam-2415	62	44	for	for	ADP
ejpam-2415	62	45	z	z	PROPN
ejpam-2415	62	46	in	in	ADP
ejpam-2415	62	47	m	m	PROPN
ejpam-2415	62	48	,	,	PUNCT
ejpam-2415	62	49	z	z	PROPN
ejpam-2415	62	50	¶	¶	PROPN
ejpam-2415	62	51	0	0	NUM
ejpam-2415	62	52	m	m	VERB
ejpam-2415	62	53	:	:	PUNCT
ejpam-2415	62	54	(	(	PUNCT
ejpam-2415	62	55	0	0	NUM
ejpam-2415	62	56	m	m	VERB
ejpam-2415	62	57	:	:	PUNCT
ejpam-2415	62	58	z	z	X
ejpam-2415	62	59	)	)	PUNCT
ejpam-2415	62	60	(	(	PUNCT
ejpam-2415	62	61	ix	ix	PROPN
ejpam-2415	62	62	)	)	PUNCT
ejpam-2415	62	63	a¶	a¶	PRON
ejpam-2415	62	64	b	b	PROPN
ejpam-2415	62	65	implies	imply	VERB
ejpam-2415	62	66	(	(	PUNCT
ejpam-2415	62	67	0	0	NUM
ejpam-2415	62	68	m	m	VERB
ejpam-2415	62	69	:	:	PUNCT
ejpam-2415	62	70	b)¶	b)¶	NOUN
ejpam-2415	62	71	(	(	PUNCT
ejpam-2415	62	72	0	0	NUM
ejpam-2415	62	73	m	m	VERB
ejpam-2415	62	74	:	:	PUNCT
ejpam-2415	62	75	a	a	X
ejpam-2415	62	76	)	)	PUNCT
ejpam-2415	62	77	(	(	PUNCT
ejpam-2415	62	78	x	x	X
ejpam-2415	62	79	)	)	PUNCT
ejpam-2415	62	80	0	0	NUM
ejpam-2415	62	81	m	m	VERB
ejpam-2415	62	82	:	:	PUNCT
ejpam-2415	63	1	[	[	X
ejpam-2415	63	2	0	0	NUM
ejpam-2415	63	3	m	m	VERB
ejpam-2415	63	4	:	:	PUNCT
ejpam-2415	63	5	(	(	PUNCT
ejpam-2415	63	6	0	0	NUM
ejpam-2415	63	7	m	m	VERB
ejpam-2415	63	8	:	:	PUNCT
ejpam-2415	63	9	a	a	X
ejpam-2415	63	10	)	)	PUNCT
ejpam-2415	63	11	]	]	PUNCT
ejpam-2415	64	1	=	=	PUNCT
ejpam-2415	64	2	0	0	NUM
ejpam-2415	64	3	m	m	VERB
ejpam-2415	64	4	:	:	PUNCT
ejpam-2415	64	5	a	a	DET
ejpam-2415	64	6	(	(	PUNCT
ejpam-2415	64	7	xi	xi	NOUN
ejpam-2415	64	8	)	)	PUNCT
ejpam-2415	64	9	0	0	NUM
ejpam-2415	64	10	m	m	VERB
ejpam-2415	64	11	:	:	PUNCT
ejpam-2415	64	12	x	x	VERB
ejpam-2415	65	1	i	i	PRON
ejpam-2415	65	2	m	m	VERB
ejpam-2415	65	3	=	=	ADJ
ejpam-2415	65	4	0	0	NUM
ejpam-2415	65	5	m	m	VERB
ejpam-2415	65	6	:	:	PUNCT
ejpam-2415	65	7	xn	xn	PUNCT
ejpam-2415	66	1	i	i	PRON
ejpam-2415	66	2	m	m	VERB
ejpam-2415	66	3	for	for	ADP
ejpam-2415	66	4	some	some	DET
ejpam-2415	66	5	positive	positive	ADJ
ejpam-2415	66	6	integer	integer	NOUN
ejpam-2415	66	7	n.	n.	NOUN
ejpam-2415	66	8	we	we	PRON
ejpam-2415	66	9	define	define	VERB
ejpam-2415	66	10	,	,	PUNCT
ejpam-2415	66	11	0f	0f	NOUN
ejpam-2415	66	12	m	m	NOUN
ejpam-2415	66	13	=	=	SYM
ejpam-2415	66	14	∨{x	∨{x	PROPN
ejpam-2415	66	15	∈	∈	PROPN
ejpam-2415	66	16	m∗	m∗	VERB
ejpam-2415	66	17	|	|	ADV
ejpam-2415	66	18	sx	sx	PROPN
ejpam-2415	66	19	=	=	PUNCT
ejpam-2415	66	20	0	0	NUM
ejpam-2415	66	21	m	m	VERB
ejpam-2415	66	22	for	for	ADP
ejpam-2415	66	23	some	some	PRON
ejpam-2415	66	24	s	s	NOUN
ejpam-2415	66	25	∈	∈	ADJ
ejpam-2415	66	26	f	f	X
ejpam-2415	66	27	}	}	PUNCT
ejpam-2415	66	28	,	,	PUNCT
ejpam-2415	66	29	where	where	SCONJ
ejpam-2415	66	30	m∗	m∗	PROPN
ejpam-2415	66	31	is	be	AUX
ejpam-2415	66	32	the	the	DET
ejpam-2415	66	33	set	set	NOUN
ejpam-2415	66	34	of	of	ADP
ejpam-2415	66	35	compact	compact	ADJ
ejpam-2415	66	36	elements	element	NOUN
ejpam-2415	66	37	of	of	ADP
ejpam-2415	66	38	m.	m.	NOUN
ejpam-2415	66	39	the	the	DET
ejpam-2415	66	40	proofs	proof	NOUN
ejpam-2415	66	41	of	of	ADP
ejpam-2415	66	42	the	the	DET
ejpam-2415	66	43	following	follow	VERB
ejpam-2415	66	44	theorems	theorem	NOUN
ejpam-2415	66	45	are	be	AUX
ejpam-2415	66	46	simple	simple	ADJ
ejpam-2415	66	47	theorem	theorem	NOUN
ejpam-2415	66	48	2	2	X
ejpam-2415	66	49	.	.	PUNCT
ejpam-2415	67	1	let	let	VERB
ejpam-2415	67	2	f	f	PROPN
ejpam-2415	67	3	⊆	⊆	NUM
ejpam-2415	67	4	l	l	NOUN
ejpam-2415	67	5	be	be	AUX
ejpam-2415	67	6	a	a	DET
ejpam-2415	67	7	filter	filter	NOUN
ejpam-2415	67	8	of	of	ADP
ejpam-2415	67	9	f(l∗	f(l∗	NOUN
ejpam-2415	67	10	)	)	PUNCT
ejpam-2415	67	11	and	and	CCONJ
ejpam-2415	67	12	let	let	VERB
ejpam-2415	67	13	x	x	PRON
ejpam-2415	67	14	be	be	AUX
ejpam-2415	67	15	a	a	DET
ejpam-2415	67	16	compact	compact	ADJ
ejpam-2415	67	17	element	element	NOUN
ejpam-2415	67	18	of	of	ADP
ejpam-2415	67	19	m.	m.	NOUN
ejpam-2415	67	20	then	then	ADV
ejpam-2415	67	21	x	x	PROPN
ejpam-2415	67	22	¶	¶	PROPN
ejpam-2415	67	23	0f	0f	PROPN
ejpam-2415	68	1	m	m	X
ejpam-2415	68	2	if	if	SCONJ
ejpam-2415	68	3	and	and	CCONJ
ejpam-2415	68	4	only	only	ADV
ejpam-2415	68	5	if	if	SCONJ
ejpam-2415	68	6	sx	sx	PROPN
ejpam-2415	68	7	=	=	NOUN
ejpam-2415	68	8	0	0	NUM
ejpam-2415	68	9	m	m	VERB
ejpam-2415	68	10	for	for	ADP
ejpam-2415	68	11	some	some	PRON
ejpam-2415	68	12	s	s	PROPN
ejpam-2415	68	13	∈	∈	PROPN
ejpam-2415	68	14	f.	f.	PROPN
ejpam-2415	68	15	theorem	theorem	VERB
ejpam-2415	68	16	3	3	X
ejpam-2415	68	17	.	.	X
ejpam-2415	69	1	for	for	ADP
ejpam-2415	69	2	f	f	PROPN
ejpam-2415	69	3	∈	∈	PROPN
ejpam-2415	69	4	f(l∗	f(l∗	NOUN
ejpam-2415	69	5	)	)	PUNCT
ejpam-2415	69	6	,	,	PUNCT
ejpam-2415	69	7	0f	0f	NOUN
ejpam-2415	69	8	m	m	NOUN
ejpam-2415	69	9	=	=	ADJ
ejpam-2415	69	10	∨{(0	∨{(0	ADJ
ejpam-2415	69	11	m	m	NOUN
ejpam-2415	69	12	:	:	PUNCT
ejpam-2415	69	13	x	x	X
ejpam-2415	69	14	)	)	PUNCT
ejpam-2415	70	1	|	|	ADV
ejpam-2415	70	2	x	x	SYM
ejpam-2415	70	3	∈	∈	PROPN
ejpam-2415	70	4	f	f	X
ejpam-2415	70	5	}	}	PUNCT
ejpam-2415	70	6	.	.	PUNCT
ejpam-2415	71	1	theorem	theorem	VERB
ejpam-2415	71	2	4	4	NUM
ejpam-2415	71	3	.	.	X
ejpam-2415	71	4	for	for	ADP
ejpam-2415	71	5	f1	f1	NOUN
ejpam-2415	71	6	,	,	PUNCT
ejpam-2415	71	7	f2	f2	PROPN
ejpam-2415	71	8	∈	∈	PROPN
ejpam-2415	71	9	f(l∗	f(l∗	NOUN
ejpam-2415	71	10	)	)	PUNCT
ejpam-2415	71	11	(	(	PUNCT
ejpam-2415	71	12	i	i	NOUN
ejpam-2415	71	13	)	)	PUNCT
ejpam-2415	71	14	f1	f1	PROPN
ejpam-2415	71	15	⊆	⊆	NUM
ejpam-2415	71	16	f2	f2	PROPN
ejpam-2415	71	17	implies	imply	VERB
ejpam-2415	71	18	0f1	0f1	NUM
ejpam-2415	71	19	m	m	PROPN
ejpam-2415	71	20	¶	¶	NOUN
ejpam-2415	71	21	0f2	0f2	PROPN
ejpam-2415	71	22	m	m	PROPN
ejpam-2415	71	23	.	.	PUNCT
ejpam-2415	72	1	(	(	PUNCT
ejpam-2415	72	2	ii	ii	NOUN
ejpam-2415	72	3	)	)	PUNCT
ejpam-2415	72	4	0f1	0f1	NUM
ejpam-2415	72	5	m	m	PROPN
ejpam-2415	72	6	∧	∧	NOUN
ejpam-2415	72	7	0f2	0f2	NOUN
ejpam-2415	72	8	m	m	PROPN
ejpam-2415	72	9	=	=	NOUN
ejpam-2415	73	1	0(f1	0(f1	ADJ
ejpam-2415	73	2	⋂	⋂	NUM
ejpam-2415	73	3	f2)m	f2)m	NOUN
ejpam-2415	73	4	3	3	NUM
ejpam-2415	73	5	.	.	PUNCT
ejpam-2415	74	1	baer	baer	PROPN
ejpam-2415	74	2	elements	element	VERB
ejpam-2415	74	3	a	a	DET
ejpam-2415	74	4	study	study	NOUN
ejpam-2415	74	5	of	of	ADP
ejpam-2415	74	6	baer	baer	PROPN
ejpam-2415	74	7	elements	element	NOUN
ejpam-2415	74	8	,	,	PUNCT
ejpam-2415	74	9	∗-elements	∗-element	NOUN
ejpam-2415	74	10	and	and	CCONJ
ejpam-2415	74	11	closed	closed	ADJ
ejpam-2415	74	12	elements	element	NOUN
ejpam-2415	74	13	carried	carry	VERB
ejpam-2415	74	14	out	out	ADP
ejpam-2415	74	15	by	by	ADP
ejpam-2415	74	16	d	d	PROPN
ejpam-2415	74	17	d	d	PROPN
ejpam-2415	74	18	anderson	anderson	PROPN
ejpam-2415	74	19	,	,	PUNCT
ejpam-2415	74	20	et	et	PROPN
ejpam-2415	74	21	al	al	PROPN
ejpam-2415	74	22	.	.	PUNCT
ejpam-2415	75	1	[	[	X
ejpam-2415	75	2	1	1	NUM
ejpam-2415	75	3	]	]	PUNCT
ejpam-2415	75	4	.	.	PUNCT
ejpam-2415	76	1	we	we	PRON
ejpam-2415	76	2	generalize	generalize	VERB
ejpam-2415	76	3	these	these	DET
ejpam-2415	76	4	concepts	concept	NOUN
ejpam-2415	76	5	for	for	ADP
ejpam-2415	76	6	lattice	lattice	NOUN
ejpam-2415	76	7	modules	module	NOUN
ejpam-2415	76	8	.	.	PUNCT
ejpam-2415	77	1	definition	definition	NOUN
ejpam-2415	77	2	1	1	NUM
ejpam-2415	77	3	.	.	PUNCT
ejpam-2415	78	1	an	an	DET
ejpam-2415	78	2	element	element	NOUN
ejpam-2415	78	3	a	a	DET
ejpam-2415	78	4	∈	∈	NOUN
ejpam-2415	78	5	m	m	VERB
ejpam-2415	78	6	is	be	AUX
ejpam-2415	78	7	said	say	VERB
ejpam-2415	78	8	to	to	PART
ejpam-2415	78	9	be	be	AUX
ejpam-2415	78	10	baer	baer	PROPN
ejpam-2415	78	11	element	element	NOUN
ejpam-2415	78	12	if	if	SCONJ
ejpam-2415	78	13	for	for	ADP
ejpam-2415	78	14	x	x	PROPN
ejpam-2415	78	15	∈	∈	PROPN
ejpam-2415	78	16	l∗	l∗	PROPN
ejpam-2415	78	17	,	,	PUNCT
ejpam-2415	78	18	x	x	PROPN
ejpam-2415	78	19	i	i	NOUN
ejpam-2415	78	20	m	m	VERB
ejpam-2415	78	21	¶	¶	PROPN
ejpam-2415	78	22	a	a	DET
ejpam-2415	78	23	implies	imply	VERB
ejpam-2415	78	24	0	0	NUM
ejpam-2415	78	25	m	m	VERB
ejpam-2415	78	26	:	:	PUNCT
ejpam-2415	78	27	(	(	PUNCT
ejpam-2415	78	28	0	0	NUM
ejpam-2415	78	29	m	m	VERB
ejpam-2415	78	30	:	:	PUNCT
ejpam-2415	78	31	x	x	PUNCT
ejpam-2415	79	1	i	i	NOUN
ejpam-2415	79	2	m	m	PROPN
ejpam-2415	79	3	)	)	PUNCT
ejpam-2415	79	4	¶	¶	PROPN
ejpam-2415	79	5	a.	a.	NOUN
ejpam-2415	79	6	definition	definition	NOUN
ejpam-2415	79	7	2	2	NUM
ejpam-2415	79	8	.	.	PUNCT
ejpam-2415	80	1	an	an	DET
ejpam-2415	80	2	element	element	NOUN
ejpam-2415	80	3	a	a	PRON
ejpam-2415	80	4	of	of	ADP
ejpam-2415	80	5	m	m	PROPN
ejpam-2415	80	6	is	be	AUX
ejpam-2415	80	7	said	say	VERB
ejpam-2415	80	8	to	to	PART
ejpam-2415	80	9	be	be	AUX
ejpam-2415	80	10	∗-element	∗-element	ADJ
ejpam-2415	80	11	if	if	SCONJ
ejpam-2415	80	12	a=	a=	NOUN
ejpam-2415	80	13	0f	0f	X
ejpam-2415	80	14	m	m	VERB
ejpam-2415	80	15	for	for	ADP
ejpam-2415	80	16	some	some	DET
ejpam-2415	80	17	filter	filter	NOUN
ejpam-2415	80	18	f	f	PROPN
ejpam-2415	80	19	∈	∈	PROPN
ejpam-2415	80	20	f(l∗	f(l∗	NOUN
ejpam-2415	80	21	)	)	PUNCT
ejpam-2415	80	22	such	such	ADJ
ejpam-2415	80	23	that	that	SCONJ
ejpam-2415	80	24	zero	zero	NUM
ejpam-2415	80	25	does	do	AUX
ejpam-2415	80	26	not	not	PART
ejpam-2415	80	27	belong	belong	VERB
ejpam-2415	80	28	to	to	ADP
ejpam-2415	80	29	f.	f.	PROPN
ejpam-2415	80	30	definition	definition	PROPN
ejpam-2415	80	31	3	3	NUM
ejpam-2415	80	32	.	.	PUNCT
ejpam-2415	81	1	an	an	DET
ejpam-2415	81	2	element	element	NOUN
ejpam-2415	81	3	a	a	PRON
ejpam-2415	81	4	of	of	ADP
ejpam-2415	81	5	m	m	PROPN
ejpam-2415	81	6	is	be	AUX
ejpam-2415	81	7	said	say	VERB
ejpam-2415	81	8	to	to	PART
ejpam-2415	81	9	be	be	AUX
ejpam-2415	81	10	closed	close	VERB
ejpam-2415	81	11	element	element	NOUN
ejpam-2415	81	12	if	if	SCONJ
ejpam-2415	81	13	a=	a=	PROPN
ejpam-2415	81	14	0	0	NOUN
ejpam-2415	81	15	m	m	VERB
ejpam-2415	81	16	:	:	PUNCT
ejpam-2415	81	17	(	(	PUNCT
ejpam-2415	81	18	0	0	NUM
ejpam-2415	81	19	m	m	VERB
ejpam-2415	81	20	:	:	PUNCT
ejpam-2415	81	21	a	a	X
ejpam-2415	81	22	)	)	PUNCT
ejpam-2415	81	23	.	.	PUNCT
ejpam-2415	82	1	the	the	DET
ejpam-2415	82	2	next	next	ADJ
ejpam-2415	82	3	result	result	NOUN
ejpam-2415	82	4	establishes	establish	VERB
ejpam-2415	82	5	the	the	DET
ejpam-2415	82	6	relation	relation	NOUN
ejpam-2415	82	7	between	between	ADP
ejpam-2415	82	8	closed	close	VERB
ejpam-2415	82	9	element	element	NOUN
ejpam-2415	82	10	and	and	CCONJ
ejpam-2415	82	11	baer	baer	PROPN
ejpam-2415	82	12	element	element	NOUN
ejpam-2415	82	13	.	.	PUNCT
ejpam-2415	83	1	theorem	theorem	VERB
ejpam-2415	83	2	5	5	NUM
ejpam-2415	83	3	.	.	PUNCT
ejpam-2415	84	1	every	every	DET
ejpam-2415	84	2	closed	closed	ADJ
ejpam-2415	84	3	element	element	NOUN
ejpam-2415	84	4	is	be	AUX
ejpam-2415	84	5	a	a	DET
ejpam-2415	84	6	baer	baer	PROPN
ejpam-2415	84	7	element	element	NOUN
ejpam-2415	84	8	.	.	PUNCT
ejpam-2415	85	1	proof	proof	NOUN
ejpam-2415	85	2	.	.	PUNCT
ejpam-2415	86	1	let	let	VERB
ejpam-2415	86	2	a	a	PRON
ejpam-2415	86	3	be	be	AUX
ejpam-2415	86	4	a	a	DET
ejpam-2415	86	5	closed	closed	ADJ
ejpam-2415	86	6	element	element	NOUN
ejpam-2415	86	7	of	of	ADP
ejpam-2415	86	8	m	m	PROPN
ejpam-2415	86	9	and	and	CCONJ
ejpam-2415	86	10	x	x	PART
ejpam-2415	86	11	be	be	AUX
ejpam-2415	86	12	a	a	DET
ejpam-2415	86	13	compact	compact	ADJ
ejpam-2415	86	14	element	element	NOUN
ejpam-2415	86	15	of	of	ADP
ejpam-2415	86	16	l∗	l∗	PROPN
ejpam-2415	86	17	such	such	ADJ
ejpam-2415	86	18	that	that	SCONJ
ejpam-2415	86	19	x	x	PUNCT
ejpam-2415	87	1	i	i	NOUN
ejpam-2415	87	2	m	m	VERB
ejpam-2415	87	3	¶	¶	NOUN
ejpam-2415	87	4	a.	a.	NOUN
ejpam-2415	87	5	then	then	ADV
ejpam-2415	87	6	0	0	NUM
ejpam-2415	87	7	m	m	VERB
ejpam-2415	87	8	:	:	PUNCT
ejpam-2415	87	9	(	(	PUNCT
ejpam-2415	87	10	0	0	NUM
ejpam-2415	87	11	m	m	VERB
ejpam-2415	87	12	:	:	PUNCT
ejpam-2415	87	13	x	x	PUNCT
ejpam-2415	88	1	i	i	NOUN
ejpam-2415	88	2	m	m	VERB
ejpam-2415	88	3	)	)	PUNCT
ejpam-2415	89	1	¶	¶	PROPN
ejpam-2415	89	2	0	0	NUM
ejpam-2415	89	3	m	m	VERB
ejpam-2415	89	4	:	:	PUNCT
ejpam-2415	89	5	(	(	PUNCT
ejpam-2415	89	6	0	0	NUM
ejpam-2415	89	7	m	m	VERB
ejpam-2415	89	8	:	:	PUNCT
ejpam-2415	89	9	a	a	X
ejpam-2415	89	10	)	)	PUNCT
ejpam-2415	89	11	=	=	PUNCT
ejpam-2415	89	12	a	a	PRON
ejpam-2415	89	13	as	as	ADP
ejpam-2415	89	14	a	a	PRON
ejpam-2415	89	15	is	be	AUX
ejpam-2415	89	16	a	a	DET
ejpam-2415	89	17	closed	closed	ADJ
ejpam-2415	89	18	.	.	PUNCT
ejpam-2415	90	1	this	this	PRON
ejpam-2415	90	2	shows	show	VERB
ejpam-2415	90	3	that	that	SCONJ
ejpam-2415	90	4	a	a	PRON
ejpam-2415	90	5	is	be	AUX
ejpam-2415	90	6	a	a	DET
ejpam-2415	90	7	baer	baer	PROPN
ejpam-2415	90	8	element	element	NOUN
ejpam-2415	90	9	.	.	PUNCT
ejpam-2415	91	1	c	c	PROPN
ejpam-2415	91	2	manjarekar	manjarekar	PROPN
ejpam-2415	91	3	,	,	PUNCT
ejpam-2415	91	4	u	u	NOUN
ejpam-2415	91	5	kandale	kandale	PROPN
ejpam-2415	91	6	/	/	SYM
ejpam-2415	91	7	eur	eur	PROPN
ejpam-2415	91	8	.	.	PUNCT
ejpam-2415	92	1	j.	j.	PROPN
ejpam-2415	92	2	pure	pure	PROPN
ejpam-2415	92	3	appl	appl	PROPN
ejpam-2415	92	4	.	.	PROPN
ejpam-2415	92	5	math	math	PROPN
ejpam-2415	92	6	,	,	PUNCT
ejpam-2415	92	7	8	8	NUM
ejpam-2415	92	8	(	(	PUNCT
ejpam-2415	92	9	2015	2015	NUM
ejpam-2415	92	10	)	)	PUNCT
ejpam-2415	92	11	,	,	PUNCT
ejpam-2415	92	12	332	332	NUM
ejpam-2415	92	13	-	-	SYM
ejpam-2415	92	14	342	342	NUM
ejpam-2415	92	15	335	335	NUM
ejpam-2415	92	16	definition	definition	NOUN
ejpam-2415	92	17	4	4	NUM
ejpam-2415	92	18	.	.	PUNCT
ejpam-2415	93	1	an	an	DET
ejpam-2415	93	2	element	element	NOUN
ejpam-2415	93	3	p	p	NOUN
ejpam-2415	93	4	of	of	ADP
ejpam-2415	93	5	m	m	PROPN
ejpam-2415	93	6	is	be	AUX
ejpam-2415	93	7	called	call	VERB
ejpam-2415	93	8	a	a	DET
ejpam-2415	93	9	minimal	minimal	ADJ
ejpam-2415	93	10	prime	prime	ADJ
ejpam-2415	93	11	element	element	NOUN
ejpam-2415	93	12	over	over	ADP
ejpam-2415	93	13	a∈	a∈	PROPN
ejpam-2415	93	14	m	m	VERB
ejpam-2415	93	15	if	if	SCONJ
ejpam-2415	93	16	a¶	a¶	PRON
ejpam-2415	93	17	p	p	NOUN
ejpam-2415	93	18	and	and	CCONJ
ejpam-2415	93	19	there	there	PRON
ejpam-2415	93	20	is	be	VERB
ejpam-2415	93	21	no	no	DET
ejpam-2415	93	22	other	other	ADJ
ejpam-2415	93	23	prime	prime	ADJ
ejpam-2415	93	24	element	element	NOUN
ejpam-2415	93	25	q	q	PROPN
ejpam-2415	93	26	of	of	ADP
ejpam-2415	93	27	m	m	PRON
ejpam-2415	93	28	such	such	ADJ
ejpam-2415	93	29	that	that	SCONJ
ejpam-2415	93	30	a¶q	a¶q	SCONJ
ejpam-2415	93	31	<	<	X
ejpam-2415	93	32	p.	p.	NOUN
ejpam-2415	93	33	the	the	DET
ejpam-2415	93	34	following	follow	VERB
ejpam-2415	93	35	result	result	NOUN
ejpam-2415	93	36	gives	give	VERB
ejpam-2415	93	37	the	the	DET
ejpam-2415	93	38	characterization	characterization	NOUN
ejpam-2415	93	39	of	of	ADP
ejpam-2415	93	40	a	a	DET
ejpam-2415	93	41	minimal	minimal	ADJ
ejpam-2415	93	42	prime	prime	ADJ
ejpam-2415	93	43	element	element	NOUN
ejpam-2415	93	44	over	over	ADP
ejpam-2415	93	45	an	an	DET
ejpam-2415	93	46	element	element	NOUN
ejpam-2415	93	47	.	.	PUNCT
ejpam-2415	94	1	theorem	theorem	NOUN
ejpam-2415	94	2	6	6	NUM
ejpam-2415	94	3	.	.	PUNCT
ejpam-2415	95	1	let	let	VERB
ejpam-2415	95	2	a	a	PRON
ejpam-2415	95	3	be	be	AUX
ejpam-2415	95	4	proper	proper	ADJ
ejpam-2415	95	5	element	element	NOUN
ejpam-2415	95	6	of	of	ADP
ejpam-2415	95	7	l	l	PROPN
ejpam-2415	95	8	and	and	CCONJ
ejpam-2415	95	9	p	p	NOUN
ejpam-2415	95	10	be	be	AUX
ejpam-2415	95	11	a	a	DET
ejpam-2415	95	12	prime	prime	ADJ
ejpam-2415	95	13	element	element	NOUN
ejpam-2415	95	14	of	of	ADP
ejpam-2415	95	15	m	m	PROPN
ejpam-2415	95	16	with	with	ADP
ejpam-2415	95	17	aim	aim	PROPN
ejpam-2415	95	18	¶	¶	PROPN
ejpam-2415	95	19	p.	p.	NOUN
ejpam-2415	95	20	then	then	ADV
ejpam-2415	95	21	the	the	DET
ejpam-2415	95	22	following	follow	VERB
ejpam-2415	95	23	statements	statement	NOUN
ejpam-2415	95	24	are	be	AUX
ejpam-2415	95	25	equivalent	equivalent	ADJ
ejpam-2415	95	26	,	,	PUNCT
ejpam-2415	95	27	(	(	PUNCT
ejpam-2415	95	28	i	i	NOUN
ejpam-2415	95	29	)	)	PUNCT
ejpam-2415	95	30	p	p	NOUN
ejpam-2415	95	31	is	be	AUX
ejpam-2415	95	32	minimal	minimal	ADJ
ejpam-2415	95	33	prime	prime	ADJ
ejpam-2415	95	34	element	element	NOUN
ejpam-2415	95	35	over	over	ADP
ejpam-2415	95	36	aim	aim	NOUN
ejpam-2415	95	37	.	.	PUNCT
ejpam-2415	96	1	(	(	PUNCT
ejpam-2415	96	2	ii	ii	NOUN
ejpam-2415	96	3	)	)	PUNCT
ejpam-2415	96	4	for	for	ADP
ejpam-2415	96	5	each	each	DET
ejpam-2415	96	6	compact	compact	ADJ
ejpam-2415	96	7	element	element	NOUN
ejpam-2415	96	8	x	x	PUNCT
ejpam-2415	96	9	in	in	ADP
ejpam-2415	96	10	l	l	NOUN
ejpam-2415	96	11	,	,	PUNCT
ejpam-2415	96	12	x	x	PROPN
ejpam-2415	97	1	i	i	NOUN
ejpam-2415	97	2	m	m	VERB
ejpam-2415	97	3	¶	¶	PROPN
ejpam-2415	97	4	p	p	X
ejpam-2415	97	5	,	,	PUNCT
ejpam-2415	97	6	there	there	PRON
ejpam-2415	97	7	is	be	VERB
ejpam-2415	97	8	compact	compact	ADJ
ejpam-2415	97	9	element	element	NOUN
ejpam-2415	97	10	y	y	PROPN
ejpam-2415	97	11	in	in	ADP
ejpam-2415	97	12	l	l	PROPN
ejpam-2415	97	13	such	such	ADJ
ejpam-2415	97	14	that	that	SCONJ
ejpam-2415	97	15	y	y	PROPN
ejpam-2415	98	1	i	i	NOUN
ejpam-2415	98	2	m	m	VERB
ejpam-2415	98	3	�	�	PROPN
ejpam-2415	98	4	p	p	PROPN
ejpam-2415	98	5	and	and	CCONJ
ejpam-2415	98	6	xn	xn	PROPN
ejpam-2415	98	7	y	y	PROPN
ejpam-2415	99	1	i	i	PRON
ejpam-2415	99	2	m	m	VERB
ejpam-2415	99	3	¶	¶	VERB
ejpam-2415	99	4	aim	aim	NOUN
ejpam-2415	99	5	=	=	PUNCT
ejpam-2415	99	6	a	a	PRON
ejpam-2415	99	7	for	for	ADP
ejpam-2415	99	8	some	some	DET
ejpam-2415	99	9	positive	positive	ADJ
ejpam-2415	99	10	integer	integer	NOUN
ejpam-2415	99	11	n.	n.	NOUN
ejpam-2415	99	12	proof	proof	NOUN
ejpam-2415	99	13	.	.	PUNCT
ejpam-2415	100	1	(	(	PUNCT
ejpam-2415	100	2	i)⇒	i)⇒	PROPN
ejpam-2415	100	3	(	(	PUNCT
ejpam-2415	100	4	ii	ii	NOUN
ejpam-2415	100	5	)	)	PUNCT
ejpam-2415	100	6	let	let	VERB
ejpam-2415	100	7	p	p	PRON
ejpam-2415	100	8	be	be	AUX
ejpam-2415	100	9	a	a	DET
ejpam-2415	100	10	minimal	minimal	ADJ
ejpam-2415	100	11	prime	prime	NOUN
ejpam-2415	100	12	over	over	ADP
ejpam-2415	100	13	aim	aim	NOUN
ejpam-2415	100	14	and	and	CCONJ
ejpam-2415	100	15	suppose	suppose	VERB
ejpam-2415	100	16	x	x	PUNCT
ejpam-2415	100	17	i	i	NOUN
ejpam-2415	100	18	m	m	VERB
ejpam-2415	100	19	¶	¶	PROPN
ejpam-2415	100	20	p.	p.	NOUN
ejpam-2415	100	21	let	let	VERB
ejpam-2415	100	22	s	s	AUX
ejpam-2415	100	23	=	=	PUNCT
ejpam-2415	100	24	{	{	PUNCT
ejpam-2415	100	25	xn	xn	PROPN
ejpam-2415	100	26	y	y	PROPN
ejpam-2415	100	27	|	|	ADV
ejpam-2415	100	28	y	y	PROPN
ejpam-2415	100	29	6¶	6¶	NUM
ejpam-2415	100	30	(	(	PUNCT
ejpam-2415	100	31	p	p	X
ejpam-2415	100	32	:	:	PUNCT
ejpam-2415	100	33	i	i	PRON
ejpam-2415	100	34	m	m	PROPN
ejpam-2415	100	35	)	)	PUNCT
ejpam-2415	100	36	and	and	CCONJ
ejpam-2415	100	37	n	n	PRON
ejpam-2415	100	38	is	be	AUX
ejpam-2415	100	39	a	a	DET
ejpam-2415	100	40	positive	positive	ADJ
ejpam-2415	100	41	integer	integer	NOUN
ejpam-2415	100	42	}	}	PUNCT
ejpam-2415	100	43	.	.	PUNCT
ejpam-2415	101	1	it	it	PRON
ejpam-2415	101	2	is	be	AUX
ejpam-2415	101	3	clear	clear	ADJ
ejpam-2415	101	4	that	that	SCONJ
ejpam-2415	101	5	,	,	PUNCT
ejpam-2415	101	6	s	s	VERB
ejpam-2415	101	7	is	be	AUX
ejpam-2415	101	8	a	a	DET
ejpam-2415	101	9	multiplicatively	multiplicatively	ADV
ejpam-2415	101	10	closed	close	VERB
ejpam-2415	101	11	set	set	NOUN
ejpam-2415	101	12	.	.	PUNCT
ejpam-2415	102	1	suppose	suppose	VERB
ejpam-2415	102	2	xn	xn	PROPN
ejpam-2415	103	1	y	y	PROPN
ejpam-2415	103	2	6¶	6¶	NUM
ejpam-2415	103	3	aim	aim	VERB
ejpam-2415	103	4	for	for	ADP
ejpam-2415	103	5	any	any	DET
ejpam-2415	103	6	integer	integer	NOUN
ejpam-2415	103	7	n	n	NOUN
ejpam-2415	103	8	and	and	CCONJ
ejpam-2415	103	9	for	for	ADP
ejpam-2415	103	10	any	any	DET
ejpam-2415	103	11	y	y	PROPN
ejpam-2415	103	12	i	i	PRON
ejpam-2415	103	13	m	m	VERB
ejpam-2415	103	14	�	�	PROPN
ejpam-2415	103	15	p	p	NOUN
ejpam-2415	103	16	,	,	PUNCT
ejpam-2415	103	17	where	where	SCONJ
ejpam-2415	103	18	y	y	PROPN
ejpam-2415	103	19	is	be	AUX
ejpam-2415	103	20	compact	compact	ADJ
ejpam-2415	103	21	in	in	ADP
ejpam-2415	103	22	l.	l.	NOUN
ejpam-2415	103	23	by	by	ADP
ejpam-2415	103	24	the	the	DET
ejpam-2415	103	25	separation	separation	NOUN
ejpam-2415	103	26	lemma	lemma	PROPN
ejpam-2415	103	27	(	(	PUNCT
ejpam-2415	103	28	see	see	VERB
ejpam-2415	103	29	[	[	X
ejpam-2415	103	30	5	5	NUM
ejpam-2415	103	31	]	]	NUM
ejpam-2415	103	32	)	)	PUNCT
ejpam-2415	103	33	,	,	PUNCT
ejpam-2415	103	34	there	there	PRON
ejpam-2415	103	35	is	be	VERB
ejpam-2415	103	36	a	a	DET
ejpam-2415	103	37	prime	prime	ADJ
ejpam-2415	103	38	element	element	NOUN
ejpam-2415	103	39	(	(	PUNCT
ejpam-2415	103	40	q	q	NOUN
ejpam-2415	103	41	:	:	PUNCT
ejpam-2415	103	42	i	i	PRON
ejpam-2415	103	43	m	m	VERB
ejpam-2415	103	44	)	)	PUNCT
ejpam-2415	103	45	of	of	ADP
ejpam-2415	103	46	l	l	NOUN
ejpam-2415	103	47	such	such	ADJ
ejpam-2415	103	48	that	that	SCONJ
ejpam-2415	103	49	(	(	PUNCT
ejpam-2415	103	50	p	p	X
ejpam-2415	103	51	:	:	PUNCT
ejpam-2415	103	52	i	i	PRON
ejpam-2415	103	53	m	m	VERB
ejpam-2415	103	54	)	)	PUNCT
ejpam-2415	103	55	¶	¶	PROPN
ejpam-2415	103	56	(	(	PUNCT
ejpam-2415	103	57	q	q	NOUN
ejpam-2415	103	58	:	:	PUNCT
ejpam-2415	103	59	i	i	PRON
ejpam-2415	103	60	m	m	PROPN
ejpam-2415	103	61	)	)	PUNCT
ejpam-2415	103	62	and	and	CCONJ
ejpam-2415	103	63	t	t	PROPN
ejpam-2415	103	64	6¶	6¶	NUM
ejpam-2415	103	65	(	(	PUNCT
ejpam-2415	103	66	q	q	NOUN
ejpam-2415	103	67	:	:	PUNCT
ejpam-2415	103	68	i	i	PRON
ejpam-2415	103	69	m	m	VERB
ejpam-2415	103	70	)	)	PUNCT
ejpam-2415	103	71	for	for	ADP
ejpam-2415	103	72	all	all	DET
ejpam-2415	103	73	t	t	PROPN
ejpam-2415	103	74	∈	∈	PROPN
ejpam-2415	103	75	s.	s.	PROPN
ejpam-2415	103	76	then	then	ADV
ejpam-2415	103	77	we	we	PRON
ejpam-2415	103	78	have	have	VERB
ejpam-2415	103	79	(	(	PUNCT
ejpam-2415	103	80	q	q	NOUN
ejpam-2415	103	81	:	:	PUNCT
ejpam-2415	103	82	i	i	PRON
ejpam-2415	103	83	m	m	VERB
ejpam-2415	103	84	)	)	PUNCT
ejpam-2415	104	1	¶	¶	PROPN
ejpam-2415	104	2	(	(	PUNCT
ejpam-2415	104	3	p	p	X
ejpam-2415	104	4	:	:	PUNCT
ejpam-2415	104	5	i	i	PRON
ejpam-2415	104	6	m	m	VERB
ejpam-2415	104	7	)	)	PUNCT
ejpam-2415	104	8	since	since	SCONJ
ejpam-2415	104	9	otherwise	otherwise	ADV
ejpam-2415	104	10	xn(q	xn(q	X
ejpam-2415	104	11	:	:	PUNCT
ejpam-2415	105	1	i	i	PRON
ejpam-2415	105	2	m	m	VERB
ejpam-2415	105	3	)	)	PUNCT
ejpam-2415	105	4	∈	∈	PROPN
ejpam-2415	105	5	s	s	PART
ejpam-2415	105	6	and	and	CCONJ
ejpam-2415	105	7	xn(q	xn(q	X
ejpam-2415	105	8	:	:	PUNCT
ejpam-2415	106	1	i	i	PRON
ejpam-2415	106	2	m	m	VERB
ejpam-2415	106	3	)	)	PUNCT
ejpam-2415	106	4	6¶	6¶	NUM
ejpam-2415	106	5	(	(	PUNCT
ejpam-2415	106	6	q	q	NOUN
ejpam-2415	106	7	:	:	PUNCT
ejpam-2415	106	8	i	i	PRON
ejpam-2415	106	9	m	m	VERB
ejpam-2415	106	10	)	)	PUNCT
ejpam-2415	106	11	a	a	DET
ejpam-2415	106	12	contradiction	contradiction	NOUN
ejpam-2415	106	13	.	.	PUNCT
ejpam-2415	107	1	hence	hence	ADV
ejpam-2415	107	2	(	(	PUNCT
ejpam-2415	107	3	p	p	X
ejpam-2415	107	4	:	:	PUNCT
ejpam-2415	107	5	i	i	PRON
ejpam-2415	107	6	m	m	VERB
ejpam-2415	107	7	)	)	PUNCT
ejpam-2415	108	1	=	=	PUNCT
ejpam-2415	109	1	(	(	PUNCT
ejpam-2415	109	2	q	q	NOUN
ejpam-2415	109	3	:	:	PUNCT
ejpam-2415	109	4	i	i	PRON
ejpam-2415	109	5	m	m	PROPN
ejpam-2415	109	6	)	)	PUNCT
ejpam-2415	109	7	.	.	PUNCT
ejpam-2415	110	1	it	it	PRON
ejpam-2415	110	2	follows	follow	VERB
ejpam-2415	110	3	that	that	SCONJ
ejpam-2415	110	4	p	p	PROPN
ejpam-2415	110	5	=	=	X
ejpam-2415	110	6	q	q	X
ejpam-2415	110	7	(	(	PUNCT
ejpam-2415	110	8	see	see	VERB
ejpam-2415	110	9	[	[	X
ejpam-2415	110	10	3	3	NUM
ejpam-2415	110	11	]	]	PUNCT
ejpam-2415	110	12	.	.	PUNCT
ejpam-2415	111	1	but	but	CCONJ
ejpam-2415	111	2	then	then	ADV
ejpam-2415	111	3	for	for	ADP
ejpam-2415	111	4	t	t	PROPN
ejpam-2415	111	5	∈	∈	PROPN
ejpam-2415	111	6	s	s	PROPN
ejpam-2415	111	7	,	,	PUNCT
ejpam-2415	111	8	t	t	PROPN
ejpam-2415	111	9	¶	¶	PROPN
ejpam-2415	111	10	x	x	SYM
ejpam-2415	111	11	¶	¶	PROPN
ejpam-2415	111	12	(	(	PUNCT
ejpam-2415	111	13	p	p	X
ejpam-2415	111	14	:	:	PUNCT
ejpam-2415	111	15	i	i	PRON
ejpam-2415	111	16	m	m	VERB
ejpam-2415	111	17	)	)	PUNCT
ejpam-2415	112	1	=	=	PUNCT
ejpam-2415	113	1	(	(	PUNCT
ejpam-2415	113	2	q	q	NOUN
ejpam-2415	113	3	:	:	PUNCT
ejpam-2415	113	4	i	i	PRON
ejpam-2415	113	5	m	m	VERB
ejpam-2415	113	6	)	)	PUNCT
ejpam-2415	113	7	a	a	DET
ejpam-2415	113	8	contraduction	contraduction	NOUN
ejpam-2415	113	9	.	.	PUNCT
ejpam-2415	114	1	(	(	PUNCT
ejpam-2415	114	2	ii)⇒	ii)⇒	PROPN
ejpam-2415	114	3	(	(	PUNCT
ejpam-2415	114	4	i	i	NOUN
ejpam-2415	114	5	)	)	PUNCT
ejpam-2415	114	6	suppose	suppose	VERB
ejpam-2415	114	7	for	for	ADP
ejpam-2415	114	8	any	any	DET
ejpam-2415	114	9	x	x	NOUN
ejpam-2415	114	10	in	in	ADP
ejpam-2415	114	11	l	l	NOUN
ejpam-2415	114	12	,	,	PUNCT
ejpam-2415	114	13	x	x	PROPN
ejpam-2415	115	1	i	i	NOUN
ejpam-2415	115	2	m	m	VERB
ejpam-2415	115	3	¶	¶	PROPN
ejpam-2415	115	4	p	p	X
ejpam-2415	115	5	,	,	PUNCT
ejpam-2415	115	6	there	there	PRON
ejpam-2415	115	7	is	be	VERB
ejpam-2415	115	8	y	y	PROPN
ejpam-2415	115	9	in	in	ADP
ejpam-2415	115	10	l	l	NOUN
ejpam-2415	115	11	such	such	ADJ
ejpam-2415	115	12	that	that	SCONJ
ejpam-2415	115	13	y	y	PROPN
ejpam-2415	115	14	i	i	PRON
ejpam-2415	115	15	m	m	VERB
ejpam-2415	115	16	6¶	6¶	NUM
ejpam-2415	115	17	p	p	NOUN
ejpam-2415	116	1	and	and	CCONJ
ejpam-2415	116	2	xn	xn	PROPN
ejpam-2415	117	1	y	y	PROPN
ejpam-2415	118	1	i	i	PRON
ejpam-2415	118	2	m	m	VERB
ejpam-2415	118	3	¶	¶	NOUN
ejpam-2415	118	4	aim	aim	NOUN
ejpam-2415	118	5	for	for	ADP
ejpam-2415	118	6	some	some	DET
ejpam-2415	118	7	positive	positive	ADJ
ejpam-2415	118	8	integer	integer	NOUN
ejpam-2415	118	9	n.	n.	NOUN
ejpam-2415	118	10	also	also	ADV
ejpam-2415	118	11	suppose	suppose	VERB
ejpam-2415	118	12	that	that	SCONJ
ejpam-2415	118	13	there	there	PRON
ejpam-2415	118	14	is	be	VERB
ejpam-2415	118	15	a	a	DET
ejpam-2415	118	16	prime	prime	ADJ
ejpam-2415	118	17	element	element	NOUN
ejpam-2415	118	18	q	q	PROPN
ejpam-2415	118	19	of	of	ADP
ejpam-2415	118	20	m	m	PROPN
ejpam-2415	118	21	with	with	ADP
ejpam-2415	118	22	aim	aim	NOUN
ejpam-2415	118	23	¶q	¶q	PROPN
ejpam-2415	118	24	<	<	X
ejpam-2415	118	25	p.	p.	NOUN
ejpam-2415	118	26	choose	choose	VERB
ejpam-2415	118	27	,	,	PUNCT
ejpam-2415	118	28	x	x	PROPN
ejpam-2415	118	29	i	i	NOUN
ejpam-2415	118	30	m	m	VERB
ejpam-2415	118	31	¶	¶	PROPN
ejpam-2415	118	32	p	p	NOUN
ejpam-2415	118	33	and	and	CCONJ
ejpam-2415	118	34	x	x	SYM
ejpam-2415	118	35	i	i	PRON
ejpam-2415	118	36	m	m	VERB
ejpam-2415	118	37	6¶	6¶	NUM
ejpam-2415	118	38	q.	q.	NOUN
ejpam-2415	118	39	by	by	ADP
ejpam-2415	118	40	hyphothesis	hyphothesis	NOUN
ejpam-2415	118	41	,	,	PUNCT
ejpam-2415	118	42	there	there	PRON
ejpam-2415	118	43	is	be	VERB
ejpam-2415	118	44	a	a	DET
ejpam-2415	118	45	compact	compact	ADJ
ejpam-2415	118	46	element	element	NOUN
ejpam-2415	118	47	y	y	PROPN
ejpam-2415	118	48	in	in	ADP
ejpam-2415	118	49	l	l	PROPN
ejpam-2415	118	50	such	such	ADJ
ejpam-2415	118	51	that	that	SCONJ
ejpam-2415	118	52	y	y	PROPN
ejpam-2415	118	53	i	i	PRON
ejpam-2415	118	54	m	m	VERB
ejpam-2415	118	55	6¶	6¶	NUM
ejpam-2415	118	56	p	p	NOUN
ejpam-2415	118	57	and	and	CCONJ
ejpam-2415	118	58	integer	integer	PROPN
ejpam-2415	118	59	n	n	CCONJ
ejpam-2415	118	60	such	such	ADJ
ejpam-2415	118	61	that	that	SCONJ
ejpam-2415	118	62	xn	xn	PROPN
ejpam-2415	119	1	y	y	PROPN
ejpam-2415	119	2	i	i	PRON
ejpam-2415	119	3	m	m	VERB
ejpam-2415	119	4	¶	¶	ADJ
ejpam-2415	119	5	aim	aim	PROPN
ejpam-2415	119	6	¶	¶	PROPN
ejpam-2415	119	7	q.	q.	PROPN
ejpam-2415	119	8	as	as	ADP
ejpam-2415	119	9	x	x	PROPN
ejpam-2415	119	10	i	i	PROPN
ejpam-2415	119	11	m	m	VERB
ejpam-2415	119	12	�	�	PROPN
ejpam-2415	119	13	q	q	PROPN
ejpam-2415	119	14	,	,	PUNCT
ejpam-2415	119	15	x	x	X
ejpam-2415	119	16	�	�	PROPN
ejpam-2415	119	17	(	(	PUNCT
ejpam-2415	119	18	q	q	NOUN
ejpam-2415	119	19	:	:	PUNCT
ejpam-2415	119	20	i	i	PRON
ejpam-2415	119	21	m	m	PROPN
ejpam-2415	119	22	)	)	PUNCT
ejpam-2415	119	23	.	.	PUNCT
ejpam-2415	120	1	since	since	SCONJ
ejpam-2415	120	2	q	q	PROPN
ejpam-2415	120	3	is	be	AUX
ejpam-2415	120	4	a	a	DET
ejpam-2415	120	5	prime	prime	ADJ
ejpam-2415	120	6	element	element	NOUN
ejpam-2415	120	7	of	of	ADP
ejpam-2415	120	8	m	m	PRON
ejpam-2415	120	9	,	,	PUNCT
ejpam-2415	120	10	(	(	PUNCT
ejpam-2415	120	11	q	q	NOUN
ejpam-2415	120	12	:	:	PUNCT
ejpam-2415	120	13	i	i	PRON
ejpam-2415	120	14	m	m	PROPN
ejpam-2415	120	15	)	)	PUNCT
ejpam-2415	120	16	is	be	AUX
ejpam-2415	120	17	also	also	ADV
ejpam-2415	120	18	prime	prime	ADJ
ejpam-2415	120	19	element	element	NOUN
ejpam-2415	120	20	of	of	ADP
ejpam-2415	120	21	l	l	NOUN
ejpam-2415	120	22	(	(	PUNCT
ejpam-2415	120	23	see	see	VERB
ejpam-2415	120	24	[	[	X
ejpam-2415	120	25	4	4	NUM
ejpam-2415	120	26	]	]	NUM
ejpam-2415	120	27	)	)	PUNCT
ejpam-2415	120	28	.	.	PUNCT
ejpam-2415	121	1	hence	hence	ADV
ejpam-2415	121	2	xn	xn	PROPN
ejpam-2415	121	3	�	�	PROPN
ejpam-2415	121	4	(	(	PUNCT
ejpam-2415	121	5	q	q	NOUN
ejpam-2415	121	6	:	:	PUNCT
ejpam-2415	121	7	i	i	PRON
ejpam-2415	121	8	m	m	PROPN
ejpam-2415	121	9	)	)	PUNCT
ejpam-2415	121	10	.	.	PUNCT
ejpam-2415	122	1	thus	thus	ADV
ejpam-2415	122	2	,	,	PUNCT
ejpam-2415	122	3	xn	xn	PROPN
ejpam-2415	122	4	6¶	6¶	NUM
ejpam-2415	122	5	(	(	PUNCT
ejpam-2415	122	6	q	q	NOUN
ejpam-2415	122	7	:	:	PUNCT
ejpam-2415	122	8	i	i	PRON
ejpam-2415	122	9	m	m	PROPN
ejpam-2415	122	10	)	)	PUNCT
ejpam-2415	122	11	and	and	CCONJ
ejpam-2415	122	12	y	y	PROPN
ejpam-2415	122	13	6¶	6¶	NUM
ejpam-2415	122	14	(	(	PUNCT
ejpam-2415	122	15	q	q	NOUN
ejpam-2415	122	16	:	:	PUNCT
ejpam-2415	122	17	i	i	PRON
ejpam-2415	122	18	m	m	VERB
ejpam-2415	122	19	)	)	PUNCT
ejpam-2415	122	20	where	where	SCONJ
ejpam-2415	122	21	(	(	PUNCT
ejpam-2415	122	22	q	q	NOUN
ejpam-2415	122	23	:	:	PUNCT
ejpam-2415	122	24	i	i	PRON
ejpam-2415	122	25	m	m	PROPN
ejpam-2415	122	26	)	)	PUNCT
ejpam-2415	122	27	is	be	AUX
ejpam-2415	122	28	a	a	DET
ejpam-2415	122	29	prime	prime	ADJ
ejpam-2415	122	30	element	element	NOUN
ejpam-2415	122	31	of	of	ADP
ejpam-2415	122	32	l	l	NOUN
ejpam-2415	122	33	,	,	PUNCT
ejpam-2415	122	34	which	which	PRON
ejpam-2415	122	35	is	be	AUX
ejpam-2415	122	36	a	a	DET
ejpam-2415	122	37	contradiction	contradiction	NOUN
ejpam-2415	122	38	.	.	PUNCT
ejpam-2415	123	1	in	in	ADP
ejpam-2415	123	2	the	the	DET
ejpam-2415	123	3	next	next	ADJ
ejpam-2415	123	4	result	result	NOUN
ejpam-2415	123	5	,	,	PUNCT
ejpam-2415	123	6	we	we	PRON
ejpam-2415	123	7	prove	prove	VERB
ejpam-2415	123	8	the	the	DET
ejpam-2415	123	9	important	important	ADJ
ejpam-2415	123	10	property	property	NOUN
ejpam-2415	123	11	of	of	ADP
ejpam-2415	123	12	a	a	DET
ejpam-2415	123	13	minimal	minimal	ADJ
ejpam-2415	123	14	prime	prime	ADJ
ejpam-2415	123	15	element	element	NOUN
ejpam-2415	123	16	.	.	PUNCT
ejpam-2415	124	1	theorem	theorem	VERB
ejpam-2415	124	2	7	7	NUM
ejpam-2415	124	3	.	.	PUNCT
ejpam-2415	125	1	let	let	VERB
ejpam-2415	125	2	m	m	PRON
ejpam-2415	125	3	be	be	AUX
ejpam-2415	125	4	an	an	DET
ejpam-2415	125	5	lattice	lattice	NOUN
ejpam-2415	125	6	module	module	NOUN
ejpam-2415	125	7	.	.	PUNCT
ejpam-2415	126	1	every	every	DET
ejpam-2415	126	2	minimal	minimal	ADJ
ejpam-2415	126	3	prime	prime	ADJ
ejpam-2415	126	4	element	element	NOUN
ejpam-2415	126	5	of	of	ADP
ejpam-2415	126	6	m	m	PROPN
ejpam-2415	126	7	is	be	AUX
ejpam-2415	126	8	a	a	DET
ejpam-2415	126	9	∗-element	∗-element	NUM
ejpam-2415	126	10	where	where	SCONJ
ejpam-2415	126	11	0f	0f	PROPN
ejpam-2415	126	12	m	m	NOUN
ejpam-2415	126	13	is	be	AUX
ejpam-2415	126	14	prime	prime	ADJ
ejpam-2415	126	15	element	element	NOUN
ejpam-2415	126	16	.	.	PUNCT
ejpam-2415	127	1	proof	proof	NOUN
ejpam-2415	127	2	.	.	PUNCT
ejpam-2415	128	1	let	let	VERB
ejpam-2415	128	2	p	p	PRON
ejpam-2415	128	3	be	be	AUX
ejpam-2415	128	4	a	a	DET
ejpam-2415	128	5	minimal	minimal	ADJ
ejpam-2415	128	6	prime	prime	ADJ
ejpam-2415	128	7	element	element	NOUN
ejpam-2415	128	8	of	of	ADP
ejpam-2415	128	9	m.	m.	NOUN
ejpam-2415	128	10	define	define	VERB
ejpam-2415	128	11	the	the	DET
ejpam-2415	128	12	set	set	NOUN
ejpam-2415	129	1	f	f	NOUN
ejpam-2415	129	2	=	=	PRON
ejpam-2415	129	3	{	{	PUNCT
ejpam-2415	129	4	x	x	PROPN
ejpam-2415	129	5	∈	∈	PROPN
ejpam-2415	129	6	l∗	l∗	NOUN
ejpam-2415	130	1	|	|	ADV
ejpam-2415	130	2	x	x	PROPN
ejpam-2415	131	1	i	i	NOUN
ejpam-2415	131	2	m	m	VERB
ejpam-2415	131	3	�	�	PROPN
ejpam-2415	131	4	p	p	X
ejpam-2415	131	5	}	}	PUNCT
ejpam-2415	131	6	.	.	PUNCT
ejpam-2415	132	1	we	we	PRON
ejpam-2415	132	2	first	first	ADV
ejpam-2415	132	3	show	show	VERB
ejpam-2415	132	4	that	that	SCONJ
ejpam-2415	132	5	f	f	PROPN
ejpam-2415	132	6	is	be	AUX
ejpam-2415	132	7	a	a	DET
ejpam-2415	132	8	filter	filter	NOUN
ejpam-2415	132	9	of	of	ADP
ejpam-2415	132	10	f(l∗	f(l∗	NOUN
ejpam-2415	132	11	)	)	PUNCT
ejpam-2415	132	12	.	.	PUNCT
ejpam-2415	133	1	let	let	VERB
ejpam-2415	133	2	x	x	PRON
ejpam-2415	133	3	and	and	CCONJ
ejpam-2415	133	4	y	y	PROPN
ejpam-2415	133	5	be	be	AUX
ejpam-2415	133	6	compact	compact	ADJ
ejpam-2415	133	7	element	element	NOUN
ejpam-2415	133	8	of	of	ADP
ejpam-2415	133	9	l	l	NOUN
ejpam-2415	134	1	such	such	ADJ
ejpam-2415	134	2	that	that	SCONJ
ejpam-2415	134	3	x	x	X
ejpam-2415	134	4	,	,	PUNCT
ejpam-2415	134	5	y	y	PROPN
ejpam-2415	134	6	∈	∈	PROPN
ejpam-2415	134	7	f	f	X
ejpam-2415	134	8	.	.	PUNCT
ejpam-2415	135	1	so	so	ADV
ejpam-2415	135	2	x	x	VERB
ejpam-2415	135	3	i	i	VERB
ejpam-2415	135	4	m	m	VERB
ejpam-2415	135	5	�	�	PROPN
ejpam-2415	135	6	p	p	NOUN
ejpam-2415	135	7	and	and	CCONJ
ejpam-2415	135	8	y	y	PROPN
ejpam-2415	136	1	i	i	PROPN
ejpam-2415	136	2	m	m	VERB
ejpam-2415	136	3	�	�	PROPN
ejpam-2415	136	4	p.	p.	NOUN
ejpam-2415	136	5	as	as	SCONJ
ejpam-2415	136	6	p	p	PROPN
ejpam-2415	136	7	is	be	AUX
ejpam-2415	136	8	prime	prime	ADJ
ejpam-2415	136	9	,	,	PUNCT
ejpam-2415	136	10	x	x	VERB
ejpam-2415	137	1	y	y	VERB
ejpam-2415	137	2	i	i	NOUN
ejpam-2415	137	3	m	m	VERB
ejpam-2415	137	4	�	�	PROPN
ejpam-2415	137	5	p.	p.	NOUN
ejpam-2415	137	6	this	this	PRON
ejpam-2415	137	7	shows	show	VERB
ejpam-2415	137	8	that	that	SCONJ
ejpam-2415	137	9	x	x	PUNCT
ejpam-2415	137	10	y	y	PROPN
ejpam-2415	137	11	∈	∈	PROPN
ejpam-2415	138	1	f	f	X
ejpam-2415	138	2	.	.	PUNCT
ejpam-2415	139	1	now	now	ADV
ejpam-2415	139	2	let	let	VERB
ejpam-2415	139	3	x	x	SYM
ejpam-2415	139	4	∈	∈	PROPN
ejpam-2415	139	5	f	f	PROPN
ejpam-2415	139	6	and	and	CCONJ
ejpam-2415	139	7	x	x	PROPN
ejpam-2415	139	8	¶	¶	PROPN
ejpam-2415	139	9	y	y	PROPN
ejpam-2415	139	10	.	.	PUNCT
ejpam-2415	140	1	hence	hence	ADV
ejpam-2415	140	2	x	x	VERB
ejpam-2415	140	3	i	i	PRON
ejpam-2415	140	4	m	m	VERB
ejpam-2415	140	5	�	�	PROPN
ejpam-2415	140	6	p	p	PROPN
ejpam-2415	140	7	implies	imply	VERB
ejpam-2415	140	8	y	y	PROPN
ejpam-2415	140	9	i	i	PROPN
ejpam-2415	140	10	m	m	VERB
ejpam-2415	140	11	�	�	PROPN
ejpam-2415	140	12	p	p	NOUN
ejpam-2415	140	13	and	and	CCONJ
ejpam-2415	140	14	y	y	PROPN
ejpam-2415	140	15	∈	∈	PROPN
ejpam-2415	141	1	f	f	X
ejpam-2415	141	2	.	.	PUNCT
ejpam-2415	142	1	if	if	SCONJ
ejpam-2415	142	2	0	0	NUM
ejpam-2415	142	3	∈	∈	PROPN
ejpam-2415	142	4	f	f	NOUN
ejpam-2415	142	5	then	then	ADV
ejpam-2415	142	6	we	we	PRON
ejpam-2415	142	7	have	have	VERB
ejpam-2415	142	8	0im	0im	PROPN
ejpam-2415	142	9	�	�	PROPN
ejpam-2415	143	1	p	p	NOUN
ejpam-2415	143	2	that	that	PRON
ejpam-2415	143	3	is	be	AUX
ejpam-2415	143	4	0	0	NUM
ejpam-2415	143	5	m	m	NOUN
ejpam-2415	143	6	�	�	NOUN
ejpam-2415	143	7	p	p	NOUN
ejpam-2415	143	8	a	a	DET
ejpam-2415	143	9	contradction	contradction	NOUN
ejpam-2415	143	10	.	.	PUNCT
ejpam-2415	144	1	thus	thus	ADV
ejpam-2415	144	2	f	f	PROPN
ejpam-2415	144	3	∈	∈	PROPN
ejpam-2415	144	4	f(l∗	f(l∗	NOUN
ejpam-2415	144	5	)	)	PUNCT
ejpam-2415	144	6	and	and	CCONJ
ejpam-2415	144	7	0	0	NUM
ejpam-2415	144	8	/∈	/∈	NUM
ejpam-2415	145	1	f	f	PROPN
ejpam-2415	145	2	.	.	PUNCT
ejpam-2415	146	1	now	now	ADV
ejpam-2415	146	2	we	we	PRON
ejpam-2415	146	3	show	show	VERB
ejpam-2415	146	4	that	that	SCONJ
ejpam-2415	146	5	p	p	X
ejpam-2415	146	6	=	=	SYM
ejpam-2415	146	7	0f	0f	NOUN
ejpam-2415	146	8	m	m	VERB
ejpam-2415	146	9	.	.	PUNCT
ejpam-2415	147	1	let	let	VERB
ejpam-2415	147	2	x	x	PRON
ejpam-2415	147	3	be	be	AUX
ejpam-2415	147	4	a	a	DET
ejpam-2415	147	5	compact	compact	ADJ
ejpam-2415	147	6	element	element	NOUN
ejpam-2415	147	7	of	of	ADP
ejpam-2415	147	8	l	l	NOUN
ejpam-2415	147	9	such	such	ADJ
ejpam-2415	147	10	that	that	SCONJ
ejpam-2415	147	11	x	x	PUNCT
ejpam-2415	148	1	i	i	NOUN
ejpam-2415	148	2	m	m	VERB
ejpam-2415	148	3	¶	¶	PROPN
ejpam-2415	148	4	p.	p.	NOUN
ejpam-2415	148	5	by	by	ADP
ejpam-2415	148	6	theorem	theorem	NOUN
ejpam-2415	148	7	6	6	NUM
ejpam-2415	148	8	it	it	PRON
ejpam-2415	148	9	follows	follow	VERB
ejpam-2415	148	10	that	that	SCONJ
ejpam-2415	148	11	there	there	PRON
ejpam-2415	148	12	exist	exist	VERB
ejpam-2415	148	13	a	a	DET
ejpam-2415	148	14	compact	compact	ADJ
ejpam-2415	148	15	element	element	NOUN
ejpam-2415	148	16	y	y	PROPN
ejpam-2415	148	17	∈	∈	PROPN
ejpam-2415	148	18	l	l	NOUN
ejpam-2415	148	19	such	such	ADJ
ejpam-2415	148	20	that	that	SCONJ
ejpam-2415	148	21	y	y	PROPN
ejpam-2415	149	1	i	i	NOUN
ejpam-2415	149	2	m	m	VERB
ejpam-2415	149	3	�	�	PROPN
ejpam-2415	149	4	p	p	PROPN
ejpam-2415	149	5	and	and	CCONJ
ejpam-2415	149	6	xn	xn	PROPN
ejpam-2415	149	7	y	y	PROPN
ejpam-2415	149	8	i	i	PRON
ejpam-2415	149	9	m	m	VERB
ejpam-2415	149	10	=	=	ADJ
ejpam-2415	149	11	0	0	NUM
ejpam-2415	149	12	m	m	VERB
ejpam-2415	149	13	for	for	ADP
ejpam-2415	149	14	some	some	DET
ejpam-2415	149	15	positive	positive	ADJ
ejpam-2415	149	16	integer	integer	NOUN
ejpam-2415	149	17	n.	n.	NOUN
ejpam-2415	149	18	we	we	PRON
ejpam-2415	149	19	have	have	VERB
ejpam-2415	149	20	y	y	PROPN
ejpam-2415	149	21	∈	∈	PROPN
ejpam-2415	149	22	f	f	PROPN
ejpam-2415	149	23	and	and	CCONJ
ejpam-2415	149	24	xn	xn	PROPN
ejpam-2415	150	1	i	i	PRON
ejpam-2415	150	2	m	m	VERB
ejpam-2415	150	3	¶	¶	PROPN
ejpam-2415	150	4	0f	0f	PROPN
ejpam-2415	150	5	m	m	X
ejpam-2415	150	6	.	.	PUNCT
ejpam-2415	151	1	as	as	SCONJ
ejpam-2415	151	2	0f	0f	PROPN
ejpam-2415	151	3	m	m	NOUN
ejpam-2415	151	4	is	be	AUX
ejpam-2415	151	5	prime	prime	ADJ
ejpam-2415	151	6	element	element	NOUN
ejpam-2415	151	7	,	,	PUNCT
ejpam-2415	151	8	so	so	SCONJ
ejpam-2415	151	9	x	x	VERB
ejpam-2415	152	1	i	i	NOUN
ejpam-2415	152	2	m	m	PROPN
ejpam-2415	152	3	¶	¶	PROPN
ejpam-2415	152	4	0f	0f	PROPN
ejpam-2415	152	5	m	m	PROPN
ejpam-2415	152	6	implies	imply	VERB
ejpam-2415	152	7	p	p	PROPN
ejpam-2415	152	8	¶	¶	PROPN
ejpam-2415	152	9	0f	0f	PROPN
ejpam-2415	152	10	m	m	PROPN
ejpam-2415	152	11	.	.	PUNCT
ejpam-2415	153	1	now	now	ADV
ejpam-2415	153	2	let	let	VERB
ejpam-2415	153	3	x	x	PRON
ejpam-2415	153	4	be	be	AUX
ejpam-2415	153	5	a	a	DET
ejpam-2415	153	6	c	c	NOUN
ejpam-2415	153	7	manjarekar	manjarekar	NOUN
ejpam-2415	153	8	,	,	PUNCT
ejpam-2415	153	9	u	u	NOUN
ejpam-2415	153	10	kandale	kandale	PROPN
ejpam-2415	153	11	/	/	SYM
ejpam-2415	153	12	eur	eur	PROPN
ejpam-2415	153	13	.	.	PUNCT
ejpam-2415	154	1	j.	j.	PROPN
ejpam-2415	154	2	pure	pure	PROPN
ejpam-2415	154	3	appl	appl	PROPN
ejpam-2415	154	4	.	.	PROPN
ejpam-2415	154	5	math	math	PROPN
ejpam-2415	154	6	,	,	PUNCT
ejpam-2415	154	7	8	8	NUM
ejpam-2415	154	8	(	(	PUNCT
ejpam-2415	154	9	2015	2015	NUM
ejpam-2415	154	10	)	)	PUNCT
ejpam-2415	154	11	,	,	PUNCT
ejpam-2415	154	12	332	332	NUM
ejpam-2415	154	13	-	-	SYM
ejpam-2415	154	14	342	342	NUM
ejpam-2415	154	15	336	336	NUM
ejpam-2415	154	16	compact	compact	ADJ
ejpam-2415	154	17	element	element	NOUN
ejpam-2415	154	18	of	of	ADP
ejpam-2415	154	19	l	l	NOUN
ejpam-2415	155	1	such	such	ADJ
ejpam-2415	155	2	that	that	SCONJ
ejpam-2415	155	3	x	x	PROPN
ejpam-2415	156	1	i	i	NOUN
ejpam-2415	156	2	m	m	PROPN
ejpam-2415	156	3	¶	¶	PROPN
ejpam-2415	156	4	0f	0f	PROPN
ejpam-2415	156	5	m	m	X
ejpam-2415	156	6	.	.	PUNCT
ejpam-2415	157	1	then	then	ADV
ejpam-2415	157	2	by	by	ADP
ejpam-2415	157	3	theorem	theorem	NOUN
ejpam-2415	157	4	2	2	NUM
ejpam-2415	157	5	,	,	PUNCT
ejpam-2415	157	6	r	r	NOUN
ejpam-2415	157	7	x	x	PUNCT
ejpam-2415	157	8	i	i	PRON
ejpam-2415	157	9	m	m	VERB
ejpam-2415	157	10	=	=	ADJ
ejpam-2415	157	11	0	0	NUM
ejpam-2415	157	12	m	m	VERB
ejpam-2415	157	13	for	for	ADP
ejpam-2415	157	14	some	some	DET
ejpam-2415	157	15	r	r	NOUN
ejpam-2415	157	16	∈	∈	PROPN
ejpam-2415	157	17	f	f	NOUN
ejpam-2415	157	18	.	.	PUNCT
ejpam-2415	158	1	so	so	ADV
ejpam-2415	158	2	we	we	PRON
ejpam-2415	158	3	have	have	VERB
ejpam-2415	158	4	r	r	NOUN
ejpam-2415	158	5	x	x	PUNCT
ejpam-2415	158	6	i	i	NOUN
ejpam-2415	158	7	m	m	VERB
ejpam-2415	158	8	¶	¶	PROPN
ejpam-2415	158	9	p	p	NOUN
ejpam-2415	158	10	and	and	CCONJ
ejpam-2415	158	11	r	r	NOUN
ejpam-2415	158	12	i	i	NOUN
ejpam-2415	158	13	m	m	PROPN
ejpam-2415	158	14	�	�	PROPN
ejpam-2415	158	15	p.	p.	NOUN
ejpam-2415	158	16	as	as	SCONJ
ejpam-2415	158	17	p	p	PROPN
ejpam-2415	158	18	is	be	AUX
ejpam-2415	158	19	prime	prime	ADJ
ejpam-2415	158	20	,	,	PUNCT
ejpam-2415	158	21	x	x	VERB
ejpam-2415	158	22	i	i	NOUN
ejpam-2415	158	23	m	m	VERB
ejpam-2415	158	24	¶	¶	PROPN
ejpam-2415	158	25	p	p	NOUN
ejpam-2415	158	26	and	and	CCONJ
ejpam-2415	158	27	0f	0f	PROPN
ejpam-2415	158	28	m	m	PROPN
ejpam-2415	158	29	¶	¶	PROPN
ejpam-2415	158	30	p	p	NOUN
ejpam-2415	158	31	which	which	PRON
ejpam-2415	158	32	shows	show	VERB
ejpam-2415	158	33	that	that	SCONJ
ejpam-2415	158	34	p	p	NOUN
ejpam-2415	158	35	=	=	SYM
ejpam-2415	158	36	0f	0f	NOUN
ejpam-2415	158	37	m	m	NOUN
ejpam-2415	158	38	.	.	PUNCT
ejpam-2415	159	1	thus	thus	ADV
ejpam-2415	159	2	every	every	DET
ejpam-2415	159	3	minimal	minimal	ADJ
ejpam-2415	159	4	prime	prime	ADJ
ejpam-2415	159	5	element	element	NOUN
ejpam-2415	159	6	of	of	ADP
ejpam-2415	159	7	m	m	PROPN
ejpam-2415	159	8	is	be	AUX
ejpam-2415	159	9	∗-element	∗-element	ADJ
ejpam-2415	159	10	.	.	PUNCT
ejpam-2415	160	1	the	the	DET
ejpam-2415	160	2	relation	relation	NOUN
ejpam-2415	160	3	between	between	ADP
ejpam-2415	160	4	∗-element	∗-element	NUM
ejpam-2415	160	5	and	and	CCONJ
ejpam-2415	160	6	baer	baer	PROPN
ejpam-2415	160	7	element	element	NOUN
ejpam-2415	160	8	is	be	AUX
ejpam-2415	160	9	proved	prove	VERB
ejpam-2415	160	10	in	in	ADP
ejpam-2415	160	11	the	the	DET
ejpam-2415	160	12	next	next	ADJ
ejpam-2415	160	13	result	result	NOUN
ejpam-2415	160	14	.	.	PUNCT
ejpam-2415	161	1	theorem	theorem	VERB
ejpam-2415	161	2	8	8	NUM
ejpam-2415	161	3	.	.	PUNCT
ejpam-2415	162	1	each	each	DET
ejpam-2415	162	2	∗-element	∗-element	NOUN
ejpam-2415	162	3	of	of	ADP
ejpam-2415	162	4	m	m	PROPN
ejpam-2415	162	5	is	be	AUX
ejpam-2415	162	6	a	a	DET
ejpam-2415	162	7	baer	baer	PROPN
ejpam-2415	162	8	element	element	NOUN
ejpam-2415	162	9	.	.	PUNCT
ejpam-2415	163	1	proof	proof	NOUN
ejpam-2415	163	2	.	.	PUNCT
ejpam-2415	164	1	suppose	suppose	VERB
ejpam-2415	164	2	an	an	DET
ejpam-2415	164	3	element	element	NOUN
ejpam-2415	164	4	a	a	PRON
ejpam-2415	164	5	of	of	ADP
ejpam-2415	164	6	m	m	PROPN
ejpam-2415	164	7	is	be	AUX
ejpam-2415	164	8	∗-element	∗-element	ADJ
ejpam-2415	164	9	.	.	PUNCT
ejpam-2415	165	1	hence	hence	ADV
ejpam-2415	165	2	a=	a=	VERB
ejpam-2415	165	3	0f	0f	PROPN
ejpam-2415	165	4	m	m	NOUN
ejpam-2415	165	5	for	for	ADP
ejpam-2415	165	6	some	some	DET
ejpam-2415	165	7	filter	filter	NOUN
ejpam-2415	165	8	f	f	PROPN
ejpam-2415	165	9	∈	∈	PROPN
ejpam-2415	165	10	f(l∗	f(l∗	NOUN
ejpam-2415	165	11	)	)	PUNCT
ejpam-2415	166	1	such	such	ADJ
ejpam-2415	166	2	that	that	DET
ejpam-2415	166	3	0	0	NUM
ejpam-2415	166	4	/∈	/∈	NUM
ejpam-2415	167	1	f	f	PROPN
ejpam-2415	167	2	.	.	PUNCT
ejpam-2415	168	1	let	let	VERB
ejpam-2415	168	2	x	x	PUNCT
ejpam-2415	168	3	∈	∈	PROPN
ejpam-2415	168	4	l∗	l∗	NOUN
ejpam-2415	168	5	such	such	ADJ
ejpam-2415	168	6	that	that	SCONJ
ejpam-2415	168	7	x	x	PUNCT
ejpam-2415	169	1	i	i	NOUN
ejpam-2415	169	2	m	m	VERB
ejpam-2415	169	3	¶	¶	NOUN
ejpam-2415	169	4	a.	a.	NOUN
ejpam-2415	169	5	then	then	ADV
ejpam-2415	169	6	we	we	PRON
ejpam-2415	169	7	have	have	VERB
ejpam-2415	169	8	r	r	NOUN
ejpam-2415	169	9	x	x	PUNCT
ejpam-2415	169	10	i	i	PRON
ejpam-2415	169	11	m	m	VERB
ejpam-2415	169	12	=	=	ADJ
ejpam-2415	169	13	0	0	NUM
ejpam-2415	169	14	m	m	NOUN
ejpam-2415	169	15	that	that	PRON
ejpam-2415	169	16	is	be	AUX
ejpam-2415	169	17	x	x	PUNCT
ejpam-2415	169	18	i	i	NOUN
ejpam-2415	169	19	m	m	VERB
ejpam-2415	169	20	¶	¶	NOUN
ejpam-2415	169	21	(	(	PUNCT
ejpam-2415	169	22	0	0	NUM
ejpam-2415	169	23	m	m	VERB
ejpam-2415	169	24	:	:	PUNCT
ejpam-2415	169	25	r	r	X
ejpam-2415	169	26	)	)	PUNCT
ejpam-2415	169	27	for	for	ADP
ejpam-2415	169	28	some	some	DET
ejpam-2415	169	29	r	r	NOUN
ejpam-2415	169	30	∈	∈	NOUN
ejpam-2415	169	31	f	f	X
ejpam-2415	169	32	by	by	ADP
ejpam-2415	169	33	theorem	theorem	NOUN
ejpam-2415	169	34	2	2	NUM
ejpam-2415	169	35	.	.	PUNCT
ejpam-2415	169	36	therefore	therefore	ADV
ejpam-2415	169	37	by	by	SCONJ
ejpam-2415	169	38	(	(	PUNCT
ejpam-2415	169	39	i	i	NOUN
ejpam-2415	169	40	)	)	PUNCT
ejpam-2415	169	41	and	and	CCONJ
ejpam-2415	169	42	(	(	PUNCT
ejpam-2415	169	43	iii	iii	NOUN
ejpam-2415	169	44	)	)	PUNCT
ejpam-2415	169	45	of	of	ADP
ejpam-2415	169	46	theorem	theorem	NOUN
ejpam-2415	169	47	1	1	NUM
ejpam-2415	169	48	we	we	PRON
ejpam-2415	169	49	get	get	VERB
ejpam-2415	169	50	0	0	NUM
ejpam-2415	169	51	m	m	VERB
ejpam-2415	169	52	:	:	PUNCT
ejpam-2415	169	53	(	(	PUNCT
ejpam-2415	169	54	0	0	NUM
ejpam-2415	169	55	m	m	VERB
ejpam-2415	169	56	:	:	PUNCT
ejpam-2415	169	57	x	x	PUNCT
ejpam-2415	169	58	i	i	NOUN
ejpam-2415	169	59	m	m	PROPN
ejpam-2415	169	60	)	)	PUNCT
ejpam-2415	169	61	¶	¶	PROPN
ejpam-2415	169	62	0	0	NUM
ejpam-2415	169	63	m	m	VERB
ejpam-2415	169	64	:	:	PUNCT
ejpam-2415	170	1	[	[	X
ejpam-2415	170	2	0	0	NUM
ejpam-2415	170	3	m	m	VERB
ejpam-2415	170	4	:	:	PUNCT
ejpam-2415	170	5	(	(	PUNCT
ejpam-2415	170	6	0	0	NUM
ejpam-2415	170	7	m	m	VERB
ejpam-2415	170	8	:	:	PUNCT
ejpam-2415	170	9	r	r	X
ejpam-2415	170	10	)	)	PUNCT
ejpam-2415	170	11	]	]	PUNCT
ejpam-2415	170	12	=	=	PUNCT
ejpam-2415	170	13	(	(	PUNCT
ejpam-2415	170	14	0	0	NUM
ejpam-2415	170	15	m	m	VERB
ejpam-2415	170	16	:	:	PUNCT
ejpam-2415	170	17	r	r	X
ejpam-2415	170	18	)	)	PUNCT
ejpam-2415	170	19	.	.	PUNCT
ejpam-2415	171	1	hence	hence	ADV
ejpam-2415	171	2	by	by	ADP
ejpam-2415	171	3	theorem	theorem	ADJ
ejpam-2415	171	4	3	3	NUM
ejpam-2415	171	5	,	,	PUNCT
ejpam-2415	171	6	0	0	NUM
ejpam-2415	171	7	m	m	VERB
ejpam-2415	171	8	:	:	PUNCT
ejpam-2415	171	9	(	(	PUNCT
ejpam-2415	171	10	0	0	NUM
ejpam-2415	171	11	m	m	VERB
ejpam-2415	171	12	:	:	PUNCT
ejpam-2415	171	13	x	x	PUNCT
ejpam-2415	171	14	i	i	NOUN
ejpam-2415	171	15	m	m	PROPN
ejpam-2415	171	16	)	)	PUNCT
ejpam-2415	171	17	¶	¶	PROPN
ejpam-2415	171	18	∨	∨	PROPN
ejpam-2415	171	19	s∈f	s∈f	PROPN
ejpam-2415	171	20	(	(	PUNCT
ejpam-2415	171	21	0	0	NUM
ejpam-2415	171	22	m	m	VERB
ejpam-2415	171	23	:	:	PUNCT
ejpam-2415	171	24	s	s	X
ejpam-2415	171	25	)	)	PUNCT
ejpam-2415	171	26	=	=	SYM
ejpam-2415	171	27	0f	0f	NOUN
ejpam-2415	171	28	m	m	NOUN
ejpam-2415	171	29	=	=	ADJ
ejpam-2415	171	30	a.	a.	NOUN
ejpam-2415	171	31	this	this	PRON
ejpam-2415	171	32	shows	show	VERB
ejpam-2415	171	33	that	that	SCONJ
ejpam-2415	171	34	a	a	PRON
ejpam-2415	171	35	is	be	AUX
ejpam-2415	171	36	a	a	DET
ejpam-2415	171	37	baer	baer	PROPN
ejpam-2415	171	38	element	element	NOUN
ejpam-2415	171	39	.	.	PUNCT
ejpam-2415	172	1	the	the	DET
ejpam-2415	172	2	next	next	ADJ
ejpam-2415	172	3	result	result	NOUN
ejpam-2415	172	4	we	we	PRON
ejpam-2415	172	5	prove	prove	VERB
ejpam-2415	172	6	the	the	DET
ejpam-2415	172	7	existence	existence	NOUN
ejpam-2415	172	8	of	of	ADP
ejpam-2415	172	9	closed	closed	ADJ
ejpam-2415	172	10	and	and	CCONJ
ejpam-2415	172	11	baer	baer	PROPN
ejpam-2415	172	12	elements	element	NOUN
ejpam-2415	172	13	.	.	PUNCT
ejpam-2415	173	1	theorem	theorem	VERB
ejpam-2415	173	2	9	9	NUM
ejpam-2415	173	3	.	.	PUNCT
ejpam-2415	174	1	let	let	VERB
ejpam-2415	174	2	m	m	PRON
ejpam-2415	174	3	be	be	AUX
ejpam-2415	174	4	multiplication	multiplication	NOUN
ejpam-2415	174	5	lattice	lattice	NOUN
ejpam-2415	174	6	module	module	NOUN
ejpam-2415	174	7	.	.	PUNCT
ejpam-2415	175	1	for	for	ADP
ejpam-2415	175	2	any	any	DET
ejpam-2415	175	3	x	x	SYM
ejpam-2415	175	4	∈	∈	PROPN
ejpam-2415	175	5	l	l	NOUN
ejpam-2415	175	6	,	,	PUNCT
ejpam-2415	175	7	(	(	PUNCT
ejpam-2415	175	8	0	0	NUM
ejpam-2415	175	9	m	m	VERB
ejpam-2415	175	10	:	:	PUNCT
ejpam-2415	175	11	x	x	X
ejpam-2415	175	12	)	)	PUNCT
ejpam-2415	175	13	is	be	AUX
ejpam-2415	175	14	both	both	DET
ejpam-2415	175	15	baer	baer	PROPN
ejpam-2415	175	16	and	and	CCONJ
ejpam-2415	175	17	closed	closed	ADJ
ejpam-2415	175	18	element	element	NOUN
ejpam-2415	175	19	.	.	PUNCT
ejpam-2415	176	1	proof	proof	NOUN
ejpam-2415	176	2	.	.	PUNCT
ejpam-2415	177	1	for	for	ADP
ejpam-2415	177	2	an	an	DET
ejpam-2415	177	3	element	element	NOUN
ejpam-2415	177	4	x	x	SYM
ejpam-2415	177	5	∈	∈	PROPN
ejpam-2415	177	6	l∗	l∗	PROPN
ejpam-2415	177	7	,	,	PUNCT
ejpam-2415	177	8	let	let	VERB
ejpam-2415	177	9	x	x	PUNCT
ejpam-2415	177	10	i	i	NOUN
ejpam-2415	177	11	m	m	VERB
ejpam-2415	177	12	¶	¶	NOUN
ejpam-2415	177	13	(	(	PUNCT
ejpam-2415	177	14	0	0	NUM
ejpam-2415	177	15	m	m	VERB
ejpam-2415	177	16	:	:	PUNCT
ejpam-2415	177	17	x	x	X
ejpam-2415	177	18	)	)	PUNCT
ejpam-2415	177	19	,	,	PUNCT
ejpam-2415	177	20	then	then	ADV
ejpam-2415	177	21	0	0	NUM
ejpam-2415	177	22	m	m	VERB
ejpam-2415	177	23	:	:	PUNCT
ejpam-2415	177	24	(	(	PUNCT
ejpam-2415	177	25	0	0	NUM
ejpam-2415	177	26	m	m	VERB
ejpam-2415	177	27	:	:	PUNCT
ejpam-2415	177	28	x	x	PUNCT
ejpam-2415	177	29	i	i	NOUN
ejpam-2415	177	30	m	m	PROPN
ejpam-2415	177	31	)	)	PUNCT
ejpam-2415	177	32	¶	¶	PROPN
ejpam-2415	177	33	0	0	NUM
ejpam-2415	177	34	m	m	VERB
ejpam-2415	177	35	:	:	PUNCT
ejpam-2415	178	1	[	[	X
ejpam-2415	178	2	0	0	NUM
ejpam-2415	178	3	m	m	VERB
ejpam-2415	178	4	:	:	PUNCT
ejpam-2415	178	5	(	(	PUNCT
ejpam-2415	178	6	0	0	NUM
ejpam-2415	178	7	m	m	VERB
ejpam-2415	178	8	:	:	PUNCT
ejpam-2415	178	9	x	x	X
ejpam-2415	178	10	)	)	PUNCT
ejpam-2415	178	11	]	]	PUNCT
ejpam-2415	179	1	=	=	PUNCT
ejpam-2415	179	2	(	(	PUNCT
ejpam-2415	179	3	0	0	NUM
ejpam-2415	179	4	m	m	VERB
ejpam-2415	179	5	:	:	PUNCT
ejpam-2415	179	6	x	x	X
ejpam-2415	179	7	)	)	PUNCT
ejpam-2415	179	8	by	by	ADP
ejpam-2415	179	9	(	(	PUNCT
ejpam-2415	179	10	i	i	NOUN
ejpam-2415	179	11	)	)	PUNCT
ejpam-2415	179	12	and	and	CCONJ
ejpam-2415	179	13	(	(	PUNCT
ejpam-2415	179	14	iii	iii	NOUN
ejpam-2415	179	15	)	)	PUNCT
ejpam-2415	179	16	of	of	ADP
ejpam-2415	179	17	theorem	theorem	NOUN
ejpam-2415	179	18	1	1	NUM
ejpam-2415	179	19	.	.	PUNCT
ejpam-2415	180	1	thus	thus	ADV
ejpam-2415	180	2	(	(	PUNCT
ejpam-2415	180	3	0	0	NUM
ejpam-2415	180	4	m	m	VERB
ejpam-2415	180	5	:	:	PUNCT
ejpam-2415	180	6	x	x	X
ejpam-2415	180	7	)	)	PUNCT
ejpam-2415	180	8	is	be	AUX
ejpam-2415	180	9	a	a	DET
ejpam-2415	180	10	baer	baer	PROPN
ejpam-2415	180	11	element	element	NOUN
ejpam-2415	180	12	.	.	PUNCT
ejpam-2415	181	1	again	again	ADV
ejpam-2415	181	2	from	from	ADP
ejpam-2415	181	3	(	(	PUNCT
ejpam-2415	181	4	iii	iii	NOUN
ejpam-2415	181	5	)	)	PUNCT
ejpam-2415	181	6	of	of	ADP
ejpam-2415	181	7	theorem	theorem	NOUN
ejpam-2415	181	8	1	1	NUM
ejpam-2415	181	9	,	,	PUNCT
ejpam-2415	181	10	(	(	PUNCT
ejpam-2415	181	11	0	0	NUM
ejpam-2415	181	12	m	m	VERB
ejpam-2415	181	13	:	:	PUNCT
ejpam-2415	181	14	x	x	X
ejpam-2415	181	15	)	)	PUNCT
ejpam-2415	181	16	=	=	PUNCT
ejpam-2415	182	1	0	0	NUM
ejpam-2415	182	2	m	m	VERB
ejpam-2415	182	3	:	:	PUNCT
ejpam-2415	182	4	(	(	PUNCT
ejpam-2415	182	5	0	0	NUM
ejpam-2415	182	6	m	m	VERB
ejpam-2415	182	7	:	:	PUNCT
ejpam-2415	182	8	(	(	PUNCT
ejpam-2415	182	9	0	0	NUM
ejpam-2415	182	10	m	m	VERB
ejpam-2415	182	11	:	:	PUNCT
ejpam-2415	182	12	x	x	X
ejpam-2415	182	13	)	)	PUNCT
ejpam-2415	182	14	)	)	PUNCT
ejpam-2415	182	15	.	.	PUNCT
ejpam-2415	183	1	this	this	PRON
ejpam-2415	183	2	shows	show	VERB
ejpam-2415	183	3	that	that	SCONJ
ejpam-2415	183	4	(	(	PUNCT
ejpam-2415	183	5	0	0	NUM
ejpam-2415	183	6	m	m	VERB
ejpam-2415	183	7	:	:	PUNCT
ejpam-2415	183	8	x	x	X
ejpam-2415	183	9	)	)	PUNCT
ejpam-2415	183	10	is	be	AUX
ejpam-2415	183	11	a	a	DET
ejpam-2415	183	12	closed	closed	ADJ
ejpam-2415	183	13	element	element	NOUN
ejpam-2415	183	14	.	.	PUNCT
ejpam-2415	184	1	in	in	ADP
ejpam-2415	184	2	the	the	DET
ejpam-2415	184	3	following	follow	VERB
ejpam-2415	184	4	theorem	theorem	NOUN
ejpam-2415	184	5	we	we	PRON
ejpam-2415	184	6	prove	prove	VERB
ejpam-2415	184	7	the	the	DET
ejpam-2415	184	8	characterization	characterization	NOUN
ejpam-2415	184	9	of	of	ADP
ejpam-2415	184	10	closed	closed	ADJ
ejpam-2415	184	11	element	element	NOUN
ejpam-2415	184	12	in	in	ADP
ejpam-2415	184	13	terms	term	NOUN
ejpam-2415	184	14	of	of	ADP
ejpam-2415	184	15	baer	baer	PROPN
ejpam-2415	184	16	element	element	NOUN
ejpam-2415	184	17	.	.	PUNCT
ejpam-2415	185	1	theorem	theorem	VERB
ejpam-2415	185	2	10	10	NUM
ejpam-2415	185	3	.	.	PUNCT
ejpam-2415	186	1	for	for	ADP
ejpam-2415	186	2	a	a	DET
ejpam-2415	186	3	∈	∈	PROPN
ejpam-2415	186	4	l∗	l∗	NOUN
ejpam-2415	186	5	,	,	PUNCT
ejpam-2415	186	6	aim	aim	NOUN
ejpam-2415	186	7	is	be	AUX
ejpam-2415	186	8	closed	close	VERB
ejpam-2415	186	9	if	if	SCONJ
ejpam-2415	186	10	and	and	CCONJ
ejpam-2415	186	11	only	only	ADV
ejpam-2415	186	12	if	if	SCONJ
ejpam-2415	186	13	aim	aim	NOUN
ejpam-2415	186	14	is	be	AUX
ejpam-2415	186	15	a	a	DET
ejpam-2415	186	16	baer	baer	PROPN
ejpam-2415	186	17	element	element	NOUN
ejpam-2415	186	18	.	.	PUNCT
ejpam-2415	187	1	proof	proof	NOUN
ejpam-2415	187	2	.	.	PUNCT
ejpam-2415	188	1	let	let	VERB
ejpam-2415	188	2	l∗	l∗	PROPN
ejpam-2415	188	3	be	be	AUX
ejpam-2415	188	4	the	the	DET
ejpam-2415	188	5	set	set	NOUN
ejpam-2415	188	6	of	of	ADP
ejpam-2415	188	7	all	all	DET
ejpam-2415	188	8	compact	compact	ADJ
ejpam-2415	188	9	element	element	NOUN
ejpam-2415	188	10	of	of	ADP
ejpam-2415	188	11	l	l	NOUN
ejpam-2415	188	12	and	and	CCONJ
ejpam-2415	188	13	aim	aim	VERB
ejpam-2415	188	14	be	be	AUX
ejpam-2415	188	15	a	a	DET
ejpam-2415	188	16	baer	baer	PROPN
ejpam-2415	188	17	element	element	NOUN
ejpam-2415	188	18	of	of	ADP
ejpam-2415	188	19	m.	m.	NOUN
ejpam-2415	188	20	we	we	PRON
ejpam-2415	188	21	show	show	VERB
ejpam-2415	188	22	that	that	SCONJ
ejpam-2415	188	23	aim	aim	NOUN
ejpam-2415	188	24	=	=	PUNCT
ejpam-2415	188	25	0	0	NUM
ejpam-2415	188	26	m	m	VERB
ejpam-2415	188	27	:	:	PUNCT
ejpam-2415	188	28	(	(	PUNCT
ejpam-2415	188	29	0	0	NUM
ejpam-2415	188	30	m	m	VERB
ejpam-2415	188	31	:	:	PUNCT
ejpam-2415	188	32	aim	aim	NOUN
ejpam-2415	188	33	)	)	PUNCT
ejpam-2415	188	34	.	.	PUNCT
ejpam-2415	189	1	as	as	SCONJ
ejpam-2415	189	2	aim	aim	NOUN
ejpam-2415	189	3	¶	¶	PROPN
ejpam-2415	189	4	aim	aim	NOUN
ejpam-2415	189	5	,	,	PUNCT
ejpam-2415	189	6	we	we	PRON
ejpam-2415	189	7	have	have	VERB
ejpam-2415	189	8	[	[	X
ejpam-2415	189	9	0	0	NUM
ejpam-2415	189	10	m	m	VERB
ejpam-2415	189	11	:	:	PUNCT
ejpam-2415	189	12	(	(	PUNCT
ejpam-2415	189	13	0	0	NUM
ejpam-2415	189	14	m	m	VERB
ejpam-2415	189	15	:	:	PUNCT
ejpam-2415	189	16	aim	aim	VERB
ejpam-2415	189	17	)	)	PUNCT
ejpam-2415	189	18	]	]	PUNCT
ejpam-2415	190	1	¶	¶	PROPN
ejpam-2415	190	2	aim	aim	NOUN
ejpam-2415	190	3	.	.	PUNCT
ejpam-2415	191	1	but	but	CCONJ
ejpam-2415	191	2	aim	aim	VERB
ejpam-2415	191	3	(	(	PUNCT
ejpam-2415	191	4	0	0	NUM
ejpam-2415	191	5	m	m	VERB
ejpam-2415	191	6	:	:	PUNCT
ejpam-2415	191	7	aim	aim	NOUN
ejpam-2415	191	8	)	)	PUNCT
ejpam-2415	192	1	¶	¶	ADP
ejpam-2415	192	2	0	0	NUM
ejpam-2415	192	3	m	m	PROPN
ejpam-2415	192	4	implies	imply	VERB
ejpam-2415	192	5	aim	aim	PROPN
ejpam-2415	192	6	¶	¶	PROPN
ejpam-2415	192	7	0	0	PROPN
ejpam-2415	192	8	m	m	VERB
ejpam-2415	192	9	:	:	PUNCT
ejpam-2415	192	10	(	(	PUNCT
ejpam-2415	192	11	0	0	NUM
ejpam-2415	192	12	m	m	VERB
ejpam-2415	192	13	:	:	PUNCT
ejpam-2415	192	14	aim	aim	NOUN
ejpam-2415	192	15	)	)	PUNCT
ejpam-2415	192	16	.	.	PUNCT
ejpam-2415	193	1	therefore	therefore	ADV
ejpam-2415	193	2	0	0	NUM
ejpam-2415	193	3	m	m	VERB
ejpam-2415	193	4	:	:	PUNCT
ejpam-2415	193	5	(	(	PUNCT
ejpam-2415	193	6	0	0	NUM
ejpam-2415	193	7	m	m	VERB
ejpam-2415	193	8	:	:	PUNCT
ejpam-2415	193	9	aim	aim	VERB
ejpam-2415	193	10	)	)	PUNCT
ejpam-2415	194	1	=	=	PRON
ejpam-2415	194	2	aim	aim	VERB
ejpam-2415	194	3	.	.	PUNCT
ejpam-2415	195	1	thus	thus	ADV
ejpam-2415	195	2	aim	aim	VERB
ejpam-2415	195	3	is	be	AUX
ejpam-2415	195	4	closed	close	VERB
ejpam-2415	195	5	.	.	PUNCT
ejpam-2415	196	1	the	the	DET
ejpam-2415	196	2	converse	converse	NOUN
ejpam-2415	196	3	is	be	AUX
ejpam-2415	196	4	proved	prove	VERB
ejpam-2415	196	5	in	in	ADP
ejpam-2415	196	6	theorem	theorem	ADJ
ejpam-2415	196	7	5	5	NUM
ejpam-2415	196	8	.	.	PUNCT
ejpam-2415	196	9	theorem	theorem	VERB
ejpam-2415	196	10	11	11	NUM
ejpam-2415	196	11	.	.	PUNCT
ejpam-2415	197	1	for	for	ADP
ejpam-2415	197	2	a	a	DET
ejpam-2415	197	3	nonzero	nonzero	ADJ
ejpam-2415	197	4	compact	compact	ADJ
ejpam-2415	197	5	element	element	NOUN
ejpam-2415	197	6	a	a	PRON
ejpam-2415	197	7	in	in	ADP
ejpam-2415	197	8	l	l	NOUN
ejpam-2415	197	9	,	,	PUNCT
ejpam-2415	197	10	0	0	NUM
ejpam-2415	197	11	m	m	VERB
ejpam-2415	197	12	:	:	PUNCT
ejpam-2415	197	13	a	a	DET
ejpam-2415	197	14	=	=	PUNCT
ejpam-2415	197	15	0[a	0[a	NOUN
ejpam-2415	197	16	)	)	PUNCT
ejpam-2415	197	17	.	.	PUNCT
ejpam-2415	198	1	proof	proof	NOUN
ejpam-2415	198	2	.	.	PUNCT
ejpam-2415	199	1	we	we	PRON
ejpam-2415	199	2	note	note	VERB
ejpam-2415	199	3	that	that	SCONJ
ejpam-2415	199	4	f	f	PROPN
ejpam-2415	200	1	=	=	PUNCT
ejpam-2415	201	1	[	[	X
ejpam-2415	201	2	a	a	X
ejpam-2415	201	3	)	)	PUNCT
ejpam-2415	201	4	=	=	SYM
ejpam-2415	201	5	{	{	PUNCT
ejpam-2415	201	6	z	z	NOUN
ejpam-2415	201	7	∈	∈	PROPN
ejpam-2415	201	8	l∗	l∗	NOUN
ejpam-2415	201	9	|	|	ADV
ejpam-2415	201	10	z	z	PROPN
ejpam-2415	201	11	≥	≥	NOUN
ejpam-2415	201	12	an	an	PRON
ejpam-2415	201	13	for	for	ADP
ejpam-2415	201	14	some	some	DET
ejpam-2415	201	15	n	n	PRON
ejpam-2415	201	16	∈	∈	NOUN
ejpam-2415	201	17	z+	z+	PRON
ejpam-2415	201	18	}	}	PUNCT
ejpam-2415	201	19	∈	∈	NOUN
ejpam-2415	201	20	f(l∗	f(l∗	NOUN
ejpam-2415	201	21	)	)	PUNCT
ejpam-2415	201	22	and	and	CCONJ
ejpam-2415	201	23	0f	0f	NOUN
ejpam-2415	201	24	m	m	NOUN
ejpam-2415	201	25	=	=	SYM
ejpam-2415	201	26	∨{x	∨{x	PROPN
ejpam-2415	201	27	∈	∈	PROPN
ejpam-2415	201	28	m∗	m∗	VERB
ejpam-2415	201	29	|	|	ADV
ejpam-2415	201	30	sx	sx	PROPN
ejpam-2415	201	31	=	=	PUNCT
ejpam-2415	201	32	0	0	NUM
ejpam-2415	201	33	m	m	VERB
ejpam-2415	201	34	for	for	ADP
ejpam-2415	201	35	some	some	DET
ejpam-2415	201	36	s	s	NOUN
ejpam-2415	201	37	∈	∈	NOUN
ejpam-2415	201	38	f	f	X
ejpam-2415	201	39	}	}	PUNCT
ejpam-2415	201	40	.	.	PUNCT
ejpam-2415	202	1	now	now	ADV
ejpam-2415	202	2	let	let	VERB
ejpam-2415	202	3	z	z	NOUN
ejpam-2415	202	4	be	be	AUX
ejpam-2415	202	5	compact	compact	ADJ
ejpam-2415	202	6	element	element	NOUN
ejpam-2415	202	7	of	of	ADP
ejpam-2415	202	8	l	l	NOUN
ejpam-2415	202	9	such	such	ADJ
ejpam-2415	202	10	that	that	SCONJ
ejpam-2415	202	11	z	z	PROPN
ejpam-2415	202	12	∈	∈	PROPN
ejpam-2415	202	13	f	f	X
ejpam-2415	202	14	∩{0	∩{0	NOUN
ejpam-2415	202	15	}	}	PUNCT
ejpam-2415	202	16	.	.	PUNCT
ejpam-2415	203	1	then	then	ADV
ejpam-2415	203	2	z	z	PROPN
ejpam-2415	203	3	∈	∈	PROPN
ejpam-2415	203	4	f	f	PROPN
ejpam-2415	203	5	and	and	CCONJ
ejpam-2415	203	6	z	z	NOUN
ejpam-2415	203	7	=	=	NOUN
ejpam-2415	203	8	0	0	X
ejpam-2415	203	9	.	.	PUNCT
ejpam-2415	204	1	as	as	ADP
ejpam-2415	204	2	z	z	PROPN
ejpam-2415	204	3	∈	∈	PROPN
ejpam-2415	204	4	f	f	PROPN
ejpam-2415	204	5	,	,	PUNCT
ejpam-2415	204	6	z	z	PROPN
ejpam-2415	204	7	≥	≥	NOUN
ejpam-2415	204	8	an	an	DET
ejpam-2415	204	9	for	for	ADP
ejpam-2415	204	10	some	some	DET
ejpam-2415	204	11	n	n	PRON
ejpam-2415	204	12	∈	∈	NOUN
ejpam-2415	204	13	z+	z+	NOUN
ejpam-2415	204	14	.	.	PUNCT
ejpam-2415	205	1	hence	hence	ADV
ejpam-2415	205	2	a	a	DET
ejpam-2415	205	3	¶	¶	NOUN
ejpam-2415	205	4	p	p	NOUN
ejpam-2415	205	5	z	z	PROPN
ejpam-2415	205	6	=	=	SYM
ejpam-2415	205	7	0	0	NUM
ejpam-2415	205	8	which	which	PRON
ejpam-2415	205	9	shows	show	VERB
ejpam-2415	205	10	that	that	SCONJ
ejpam-2415	205	11	a	a	DET
ejpam-2415	205	12	=	=	NOUN
ejpam-2415	205	13	0	0	NUM
ejpam-2415	205	14	.	.	PUNCT
ejpam-2415	206	1	this	this	DET
ejpam-2415	206	2	contradiction	contradiction	NOUN
ejpam-2415	206	3	implies	imply	VERB
ejpam-2415	206	4	that	that	SCONJ
ejpam-2415	206	5	0	0	NUM
ejpam-2415	207	1	/∈	/∈	NUM
ejpam-2415	208	1	f	f	PROPN
ejpam-2415	208	2	.	.	PUNCT
ejpam-2415	209	1	now	now	ADV
ejpam-2415	209	2	we	we	PRON
ejpam-2415	209	3	show	show	VERB
ejpam-2415	209	4	that	that	SCONJ
ejpam-2415	209	5	0	0	NUM
ejpam-2415	209	6	m	m	VERB
ejpam-2415	209	7	:	:	PUNCT
ejpam-2415	209	8	a	a	DET
ejpam-2415	209	9	=	=	SYM
ejpam-2415	209	10	0f	0f	NOUN
ejpam-2415	209	11	m	m	NOUN
ejpam-2415	209	12	.	.	PUNCT
ejpam-2415	210	1	as	as	SCONJ
ejpam-2415	210	2	a	a	PRON
ejpam-2415	210	3	is	be	AUX
ejpam-2415	210	4	a	a	DET
ejpam-2415	210	5	compact	compact	ADJ
ejpam-2415	210	6	element	element	NOUN
ejpam-2415	210	7	in	in	ADP
ejpam-2415	210	8	l	l	NOUN
ejpam-2415	210	9	,	,	PUNCT
ejpam-2415	210	10	a	a	DET
ejpam-2415	210	11	∈	∈	PROPN
ejpam-2415	210	12	f	f	X
ejpam-2415	210	13	.	.	PUNCT
ejpam-2415	211	1	so	so	ADV
ejpam-2415	211	2	we	we	PRON
ejpam-2415	211	3	have	have	VERB
ejpam-2415	211	4	0	0	NUM
ejpam-2415	211	5	m	m	VERB
ejpam-2415	211	6	:	:	PUNCT
ejpam-2415	211	7	a	a	DET
ejpam-2415	211	8	¶	¶	PROPN
ejpam-2415	211	9	0f	0f	NOUN
ejpam-2415	211	10	m	m	PROPN
ejpam-2415	211	11	=	=	ADJ
ejpam-2415	211	12	∨{(0	∨{(0	ADJ
ejpam-2415	211	13	m	m	NOUN
ejpam-2415	211	14	:	:	PUNCT
ejpam-2415	211	15	x	x	X
ejpam-2415	211	16	)	)	PUNCT
ejpam-2415	212	1	|	|	ADV
ejpam-2415	212	2	x	x	SYM
ejpam-2415	212	3	∈	∈	PROPN
ejpam-2415	212	4	f	f	X
ejpam-2415	212	5	}	}	PUNCT
ejpam-2415	212	6	.	.	PUNCT
ejpam-2415	213	1	let	let	VERB
ejpam-2415	213	2	z	z	PRON
ejpam-2415	213	3	be	be	AUX
ejpam-2415	213	4	a	a	DET
ejpam-2415	213	5	compact	compact	ADJ
ejpam-2415	213	6	element	element	NOUN
ejpam-2415	213	7	in	in	ADP
ejpam-2415	213	8	m	m	PROPN
ejpam-2415	213	9	and	and	CCONJ
ejpam-2415	213	10	z	z	PROPN
ejpam-2415	213	11	¶	¶	PROPN
ejpam-2415	213	12	0f	0f	PROPN
ejpam-2415	213	13	m	m	X
ejpam-2415	213	14	.	.	PUNCT
ejpam-2415	214	1	then	then	ADV
ejpam-2415	214	2	by	by	ADP
ejpam-2415	214	3	theorem	theorem	NOUN
ejpam-2415	214	4	2	2	NUM
ejpam-2415	214	5	sz	sz	NOUN
ejpam-2415	214	6	=	=	NOUN
ejpam-2415	214	7	0	0	NUM
ejpam-2415	214	8	m	m	VERB
ejpam-2415	214	9	for	for	ADP
ejpam-2415	214	10	some	some	DET
ejpam-2415	214	11	s	s	VERB
ejpam-2415	214	12	∈	∈	PROPN
ejpam-2415	214	13	f	f	X
ejpam-2415	214	14	.	.	PUNCT
ejpam-2415	215	1	so	so	ADV
ejpam-2415	215	2	s	s	VERB
ejpam-2415	215	3	≥	≥	NOUN
ejpam-2415	215	4	an	an	PRON
ejpam-2415	215	5	for	for	ADP
ejpam-2415	215	6	some	some	DET
ejpam-2415	215	7	n	n	PRON
ejpam-2415	215	8	∈	∈	NOUN
ejpam-2415	215	9	z+	z+	PUNCT
ejpam-2415	215	10	.	.	PUNCT
ejpam-2415	216	1	we	we	PRON
ejpam-2415	216	2	note	note	VERB
ejpam-2415	216	3	that	that	SCONJ
ejpam-2415	216	4	0	0	NUM
ejpam-2415	216	5	m	m	VERB
ejpam-2415	216	6	:	:	PUNCT
ejpam-2415	216	7	an	an	DET
ejpam-2415	216	8	=	=	NOUN
ejpam-2415	216	9	0	0	NUM
ejpam-2415	216	10	m	m	VERB
ejpam-2415	216	11	:	:	PUNCT
ejpam-2415	216	12	a.	a.	NOUN
ejpam-2415	216	13	consequently	consequently	ADV
ejpam-2415	216	14	,	,	PUNCT
ejpam-2415	216	15	we	we	PRON
ejpam-2415	216	16	have	have	VERB
ejpam-2415	216	17	anz	anz	PROPN
ejpam-2415	216	18	¶	¶	PROPN
ejpam-2415	216	19	sz	sz	PROPN
ejpam-2415	217	1	=	=	ADJ
ejpam-2415	217	2	0	0	NUM
ejpam-2415	217	3	m	m	NOUN
ejpam-2415	217	4	.	.	PUNCT
ejpam-2415	218	1	this	this	PRON
ejpam-2415	218	2	implies	imply	VERB
ejpam-2415	218	3	that	that	SCONJ
ejpam-2415	218	4	z	z	PROPN
ejpam-2415	218	5	¶	¶	PROPN
ejpam-2415	218	6	(	(	PUNCT
ejpam-2415	218	7	0	0	NUM
ejpam-2415	218	8	m	m	VERB
ejpam-2415	218	9	:	:	PUNCT
ejpam-2415	218	10	an	an	X
ejpam-2415	218	11	)	)	PUNCT
ejpam-2415	218	12	=	=	SYM
ejpam-2415	218	13	(	(	PUNCT
ejpam-2415	218	14	0	0	NUM
ejpam-2415	218	15	m	m	VERB
ejpam-2415	218	16	:	:	PUNCT
ejpam-2415	218	17	a	a	X
ejpam-2415	218	18	)	)	PUNCT
ejpam-2415	218	19	.	.	PUNCT
ejpam-2415	219	1	consequently	consequently	ADV
ejpam-2415	219	2	,	,	PUNCT
ejpam-2415	219	3	0f	0f	PROPN
ejpam-2415	219	4	¶	¶	PROPN
ejpam-2415	219	5	(	(	PUNCT
ejpam-2415	219	6	0	0	NUM
ejpam-2415	219	7	m	m	VERB
ejpam-2415	219	8	:	:	PUNCT
ejpam-2415	219	9	a	a	X
ejpam-2415	219	10	)	)	PUNCT
ejpam-2415	219	11	and	and	CCONJ
ejpam-2415	219	12	(	(	PUNCT
ejpam-2415	219	13	0	0	NUM
ejpam-2415	219	14	m	m	VERB
ejpam-2415	219	15	:	:	PUNCT
ejpam-2415	219	16	a	a	X
ejpam-2415	219	17	)	)	PUNCT
ejpam-2415	219	18	=	=	SYM
ejpam-2415	219	19	0f	0f	NOUN
ejpam-2415	219	20	.	.	PUNCT
ejpam-2415	220	1	the	the	DET
ejpam-2415	220	2	following	follow	VERB
ejpam-2415	220	3	theorem	theorem	NOUN
ejpam-2415	220	4	establishes	establish	VERB
ejpam-2415	220	5	the	the	DET
ejpam-2415	220	6	property	property	NOUN
ejpam-2415	220	7	of	of	ADP
ejpam-2415	220	8	baer	baer	PROPN
ejpam-2415	220	9	,	,	PUNCT
ejpam-2415	220	10	closed	closed	ADJ
ejpam-2415	220	11	and	and	CCONJ
ejpam-2415	220	12	∗-element	∗-element	ADJ
ejpam-2415	220	13	.	.	PUNCT
ejpam-2415	221	1	c	c	PROPN
ejpam-2415	221	2	manjarekar	manjarekar	PROPN
ejpam-2415	221	3	,	,	PUNCT
ejpam-2415	221	4	u	u	NOUN
ejpam-2415	221	5	kandale	kandale	PROPN
ejpam-2415	221	6	/	/	SYM
ejpam-2415	221	7	eur	eur	PROPN
ejpam-2415	221	8	.	.	PUNCT
ejpam-2415	222	1	j.	j.	PROPN
ejpam-2415	222	2	pure	pure	PROPN
ejpam-2415	222	3	appl	appl	PROPN
ejpam-2415	222	4	.	.	PROPN
ejpam-2415	222	5	math	math	PROPN
ejpam-2415	222	6	,	,	PUNCT
ejpam-2415	222	7	8	8	NUM
ejpam-2415	222	8	(	(	PUNCT
ejpam-2415	222	9	2015	2015	NUM
ejpam-2415	222	10	)	)	PUNCT
ejpam-2415	222	11	,	,	PUNCT
ejpam-2415	222	12	332	332	NUM
ejpam-2415	222	13	-	-	SYM
ejpam-2415	222	14	342	342	NUM
ejpam-2415	222	15	337	337	NUM
ejpam-2415	222	16	theorem	theorem	NOUN
ejpam-2415	222	17	12	12	NUM
ejpam-2415	222	18	.	.	PUNCT
ejpam-2415	223	1	suppose	suppose	VERB
ejpam-2415	223	2	l	l	NOUN
ejpam-2415	223	3	has	have	VERB
ejpam-2415	223	4	no	no	DET
ejpam-2415	223	5	divisors	divisor	NOUN
ejpam-2415	223	6	of	of	ADP
ejpam-2415	223	7	zero	zero	NUM
ejpam-2415	223	8	then	then	ADV
ejpam-2415	223	9	the	the	DET
ejpam-2415	223	10	element	element	NOUN
ejpam-2415	223	11	0	0	NUM
ejpam-2415	223	12	m	m	NOUN
ejpam-2415	223	13	is	be	AUX
ejpam-2415	223	14	always	always	ADV
ejpam-2415	223	15	a	a	DET
ejpam-2415	223	16	baer	baer	PROPN
ejpam-2415	223	17	,	,	PUNCT
ejpam-2415	223	18	closed	closed	ADJ
ejpam-2415	223	19	and	and	CCONJ
ejpam-2415	223	20	∗-element	∗-element	ADJ
ejpam-2415	224	1	whereas	whereas	SCONJ
ejpam-2415	224	2	1	1	NUM
ejpam-2415	224	3	m	m	NOUN
ejpam-2415	224	4	is	be	AUX
ejpam-2415	224	5	baer	baer	PROPN
ejpam-2415	224	6	and	and	CCONJ
ejpam-2415	224	7	closed	close	VERB
ejpam-2415	224	8	.	.	PUNCT
ejpam-2415	225	1	proof	proof	NOUN
ejpam-2415	225	2	.	.	PUNCT
ejpam-2415	226	1	let	let	VERB
ejpam-2415	226	2	x	x	PRON
ejpam-2415	226	3	be	be	AUX
ejpam-2415	226	4	a	a	DET
ejpam-2415	226	5	nonzero	nonzero	ADJ
ejpam-2415	226	6	element	element	NOUN
ejpam-2415	226	7	of	of	ADP
ejpam-2415	226	8	l.	l.	PROPN
ejpam-2415	226	9	from	from	ADP
ejpam-2415	226	10	theorem	theorem	NOUN
ejpam-2415	226	11	9,for	9,for	NUM
ejpam-2415	226	12	any	any	DET
ejpam-2415	226	13	x	x	SYM
ejpam-2415	226	14	∈	∈	PROPN
ejpam-2415	226	15	l	l	NOUN
ejpam-2415	226	16	,	,	PUNCT
ejpam-2415	226	17	0	0	NUM
ejpam-2415	226	18	m	m	VERB
ejpam-2415	226	19	:	:	PUNCT
ejpam-2415	226	20	x	x	X
ejpam-2415	226	21	is	be	AUX
ejpam-2415	226	22	both	both	DET
ejpam-2415	226	23	baer	baer	PROPN
ejpam-2415	226	24	and	and	CCONJ
ejpam-2415	226	25	closed	close	VERB
ejpam-2415	226	26	and	and	CCONJ
ejpam-2415	226	27	by	by	ADP
ejpam-2415	226	28	theorem	theorem	NOUN
ejpam-2415	226	29	11	11	NUM
ejpam-2415	226	30	for	for	ADP
ejpam-2415	226	31	a	a	DET
ejpam-2415	226	32	nonzero	nonzero	ADJ
ejpam-2415	226	33	compact	compact	ADJ
ejpam-2415	226	34	element	element	NOUN
ejpam-2415	226	35	x	x	PUNCT
ejpam-2415	226	36	of	of	ADP
ejpam-2415	226	37	l	l	NOUN
ejpam-2415	226	38	,	,	PUNCT
ejpam-2415	226	39	0	0	NUM
ejpam-2415	226	40	m	m	VERB
ejpam-2415	226	41	:	:	PUNCT
ejpam-2415	227	1	x	x	X
ejpam-2415	227	2	=	=	SYM
ejpam-2415	227	3	0[x	0[x	PROPN
ejpam-2415	227	4	)	)	PUNCT
ejpam-2415	227	5	.	.	PUNCT
ejpam-2415	228	1	to	to	PART
ejpam-2415	228	2	show	show	VERB
ejpam-2415	228	3	that	that	SCONJ
ejpam-2415	228	4	0	0	NUM
ejpam-2415	228	5	m	m	NOUN
ejpam-2415	228	6	a	a	PRON
ejpam-2415	228	7	is	be	AUX
ejpam-2415	228	8	baer	baer	PROPN
ejpam-2415	228	9	element	element	NOUN
ejpam-2415	228	10	,	,	PUNCT
ejpam-2415	228	11	take	take	VERB
ejpam-2415	228	12	x	x	PUNCT
ejpam-2415	228	13	∈	∈	PROPN
ejpam-2415	228	14	l∗	l∗	NOUN
ejpam-2415	228	15	such	such	ADJ
ejpam-2415	228	16	that	that	SCONJ
ejpam-2415	228	17	x	x	PROPN
ejpam-2415	229	1	i	i	NOUN
ejpam-2415	229	2	m	m	VERB
ejpam-2415	229	3	¶	¶	PROPN
ejpam-2415	229	4	0	0	NUM
ejpam-2415	229	5	m	m	VERB
ejpam-2415	229	6	.	.	PUNCT
ejpam-2415	230	1	we	we	PRON
ejpam-2415	230	2	have	have	VERB
ejpam-2415	230	3	0	0	NUM
ejpam-2415	230	4	m	m	VERB
ejpam-2415	230	5	:	:	PUNCT
ejpam-2415	230	6	(	(	PUNCT
ejpam-2415	230	7	0	0	NUM
ejpam-2415	230	8	m	m	VERB
ejpam-2415	230	9	:	:	PUNCT
ejpam-2415	230	10	x	x	PUNCT
ejpam-2415	230	11	i	i	NOUN
ejpam-2415	230	12	m	m	PROPN
ejpam-2415	230	13	)	)	PUNCT
ejpam-2415	230	14	¶	¶	ADV
ejpam-2415	230	15	om	om	PROPN
ejpam-2415	230	16	:	:	PUNCT
ejpam-2415	230	17	(	(	PUNCT
ejpam-2415	230	18	0	0	NUM
ejpam-2415	230	19	m	m	VERB
ejpam-2415	230	20	:	:	PUNCT
ejpam-2415	230	21	0	0	NUM
ejpam-2415	230	22	m	m	NOUN
ejpam-2415	230	23	)	)	PUNCT
ejpam-2415	231	1	=	=	PUNCT
ejpam-2415	231	2	0	0	NUM
ejpam-2415	231	3	m	m	NOUN
ejpam-2415	231	4	.	.	PUNCT
ejpam-2415	232	1	hence	hence	ADV
ejpam-2415	232	2	0	0	NUM
ejpam-2415	232	3	m	m	NOUN
ejpam-2415	232	4	is	be	AUX
ejpam-2415	232	5	a	a	DET
ejpam-2415	232	6	baer	baer	PROPN
ejpam-2415	232	7	element	element	NOUN
ejpam-2415	232	8	.	.	PUNCT
ejpam-2415	233	1	as	as	ADP
ejpam-2415	233	2	0	0	NUM
ejpam-2415	233	3	m	m	NOUN
ejpam-2415	233	4	=	=	NOUN
ejpam-2415	233	5	0	0	NUM
ejpam-2415	233	6	m	m	VERB
ejpam-2415	233	7	:	:	PUNCT
ejpam-2415	233	8	(	(	PUNCT
ejpam-2415	233	9	0	0	NUM
ejpam-2415	233	10	m	m	VERB
ejpam-2415	233	11	:	:	PUNCT
ejpam-2415	233	12	0	0	NUM
ejpam-2415	233	13	m	m	NOUN
ejpam-2415	233	14	)	)	PUNCT
ejpam-2415	233	15	,	,	PUNCT
ejpam-2415	233	16	0	0	NUM
ejpam-2415	233	17	m	m	NOUN
ejpam-2415	233	18	is	be	AUX
ejpam-2415	233	19	closed	closed	ADJ
ejpam-2415	233	20	.	.	PUNCT
ejpam-2415	234	1	every	every	DET
ejpam-2415	234	2	baer	baer	PROPN
ejpam-2415	234	3	element	element	NOUN
ejpam-2415	234	4	is	be	AUX
ejpam-2415	234	5	a	a	DET
ejpam-2415	234	6	∗-element	∗-element	NOUN
ejpam-2415	234	7	.	.	PUNCT
ejpam-2415	235	1	to	to	PART
ejpam-2415	235	2	show	show	VERB
ejpam-2415	235	3	that	that	SCONJ
ejpam-2415	235	4	1	1	NUM
ejpam-2415	235	5	m	m	NOUN
ejpam-2415	235	6	is	be	AUX
ejpam-2415	235	7	a	a	DET
ejpam-2415	235	8	baer	baer	PROPN
ejpam-2415	235	9	element	element	NOUN
ejpam-2415	235	10	.	.	PUNCT
ejpam-2415	236	1	take	take	VERB
ejpam-2415	236	2	any	any	DET
ejpam-2415	236	3	x	x	SYM
ejpam-2415	236	4	∈	∈	PROPN
ejpam-2415	236	5	l∗	l∗	NOUN
ejpam-2415	236	6	such	such	ADJ
ejpam-2415	236	7	that	that	SCONJ
ejpam-2415	236	8	x	x	PROPN
ejpam-2415	237	1	i	i	NOUN
ejpam-2415	237	2	m	m	VERB
ejpam-2415	237	3	¶	¶	PROPN
ejpam-2415	237	4	1	1	NUM
ejpam-2415	237	5	m	m	NOUN
ejpam-2415	237	6	.	.	PUNCT
ejpam-2415	238	1	we	we	PRON
ejpam-2415	238	2	have	have	VERB
ejpam-2415	238	3	0	0	NUM
ejpam-2415	238	4	m	m	VERB
ejpam-2415	238	5	:	:	PUNCT
ejpam-2415	238	6	(	(	PUNCT
ejpam-2415	238	7	0	0	NUM
ejpam-2415	238	8	m	m	VERB
ejpam-2415	238	9	:	:	PUNCT
ejpam-2415	238	10	x	x	PUNCT
ejpam-2415	238	11	i	i	NOUN
ejpam-2415	238	12	m	m	VERB
ejpam-2415	238	13	)	)	PUNCT
ejpam-2415	239	1	=	=	PUNCT
ejpam-2415	239	2	0	0	NUM
ejpam-2415	239	3	m	m	VERB
ejpam-2415	239	4	:	:	PUNCT
ejpam-2415	240	1	[	[	X
ejpam-2415	240	2	∨{a	∨{a	PROPN
ejpam-2415	240	3	∈	∈	PROPN
ejpam-2415	240	4	l	l	NOUN
ejpam-2415	241	1	|	|	ADV
ejpam-2415	241	2	ax	ax	INTJ
ejpam-2415	242	1	i	i	PRON
ejpam-2415	242	2	m	m	VERB
ejpam-2415	242	3	=	=	ADJ
ejpam-2415	242	4	0	0	NUM
ejpam-2415	242	5	m	m	NOUN
ejpam-2415	242	6	}	}	PUNCT
ejpam-2415	242	7	]	]	PUNCT
ejpam-2415	243	1	=	=	PUNCT
ejpam-2415	243	2	0	0	NUM
ejpam-2415	243	3	m	m	VERB
ejpam-2415	243	4	:	:	PUNCT
ejpam-2415	243	5	0	0	NUM
ejpam-2415	244	1	=	=	SYM
ejpam-2415	244	2	1	1	NUM
ejpam-2415	244	3	m	m	NOUN
ejpam-2415	244	4	.	.	PUNCT
ejpam-2415	245	1	so	so	ADV
ejpam-2415	245	2	1	1	NUM
ejpam-2415	245	3	m	m	NOUN
ejpam-2415	245	4	is	be	AUX
ejpam-2415	245	5	a	a	DET
ejpam-2415	245	6	baer	baer	PROPN
ejpam-2415	245	7	element	element	NOUN
ejpam-2415	245	8	.	.	PUNCT
ejpam-2415	246	1	now	now	ADV
ejpam-2415	246	2	0	0	NUM
ejpam-2415	246	3	m	m	VERB
ejpam-2415	246	4	:	:	PUNCT
ejpam-2415	246	5	(	(	PUNCT
ejpam-2415	246	6	0	0	NUM
ejpam-2415	246	7	m	m	VERB
ejpam-2415	246	8	:	:	PUNCT
ejpam-2415	246	9	1	1	NUM
ejpam-2415	246	10	m	m	NOUN
ejpam-2415	246	11	)	)	PUNCT
ejpam-2415	247	1	=	=	PUNCT
ejpam-2415	247	2	0	0	NUM
ejpam-2415	247	3	m	m	VERB
ejpam-2415	247	4	:	:	PUNCT
ejpam-2415	248	1	[	[	X
ejpam-2415	248	2	∨{a	∨{a	PROPN
ejpam-2415	248	3	∈	∈	PROPN
ejpam-2415	248	4	l	l	NOUN
ejpam-2415	248	5	|	|	ADV
ejpam-2415	248	6	aim	aim	VERB
ejpam-2415	248	7	=	=	SYM
ejpam-2415	248	8	0	0	NUM
ejpam-2415	248	9	m	m	NOUN
ejpam-2415	248	10	}	}	PUNCT
ejpam-2415	248	11	]	]	PUNCT
ejpam-2415	248	12	=	=	PUNCT
ejpam-2415	248	13	1	1	NUM
ejpam-2415	248	14	m	m	NOUN
ejpam-2415	248	15	and	and	CCONJ
ejpam-2415	248	16	1	1	NUM
ejpam-2415	248	17	m	m	NOUN
ejpam-2415	248	18	is	be	AUX
ejpam-2415	248	19	closed	closed	ADJ
ejpam-2415	248	20	.	.	PUNCT
ejpam-2415	249	1	remark	remark	NOUN
ejpam-2415	249	2	1	1	NUM
ejpam-2415	249	3	.	.	PUNCT
ejpam-2415	250	1	for	for	ADP
ejpam-2415	250	2	defining	define	VERB
ejpam-2415	250	3	the	the	DET
ejpam-2415	250	4	∗-element	∗-element	NOUN
ejpam-2415	250	5	,	,	PUNCT
ejpam-2415	250	6	the	the	DET
ejpam-2415	250	7	condition	condition	NOUN
ejpam-2415	250	8	0	0	NUM
ejpam-2415	250	9	/∈	/∈	PUNCT
ejpam-2415	251	1	f	f	PROPN
ejpam-2415	251	2	is	be	AUX
ejpam-2415	251	3	necessary	necessary	ADJ
ejpam-2415	251	4	.	.	PUNCT
ejpam-2415	252	1	suppose	suppose	VERB
ejpam-2415	252	2	if	if	SCONJ
ejpam-2415	252	3	possible	possible	ADJ
ejpam-2415	252	4	x	x	VERB
ejpam-2415	252	5	is	be	AUX
ejpam-2415	252	6	a	a	DET
ejpam-2415	252	7	∗-element	∗-element	NOUN
ejpam-2415	252	8	.	.	PUNCT
ejpam-2415	253	1	hence	hence	ADV
ejpam-2415	253	2	x	x	X
ejpam-2415	253	3	=	=	SYM
ejpam-2415	253	4	0f	0f	NOUN
ejpam-2415	253	5	m	m	VERB
ejpam-2415	253	6	,	,	PUNCT
ejpam-2415	253	7	for	for	ADP
ejpam-2415	253	8	some	some	DET
ejpam-2415	253	9	filter	filter	NOUN
ejpam-2415	253	10	f	f	NOUN
ejpam-2415	254	1	such	such	ADJ
ejpam-2415	254	2	that	that	PRON
ejpam-2415	254	3	0	0	NUM
ejpam-2415	254	4	/∈	/∈	PUNCT
ejpam-2415	255	1	f.	f.	PROPN
ejpam-2415	255	2	then	then	ADV
ejpam-2415	255	3	we	we	PRON
ejpam-2415	255	4	have	have	VERB
ejpam-2415	255	5	x	x	NOUN
ejpam-2415	255	6	=	=	SYM
ejpam-2415	255	7	∨{(0	∨{(0	ADJ
ejpam-2415	255	8	m	m	NOUN
ejpam-2415	255	9	:	:	PUNCT
ejpam-2415	256	1	r	r	X
ejpam-2415	256	2	)	)	PUNCT
ejpam-2415	256	3	|	|	ADV
ejpam-2415	256	4	r	r	NOUN
ejpam-2415	256	5	∈	∈	PROPN
ejpam-2415	256	6	f	f	X
ejpam-2415	256	7	}	}	PUNCT
ejpam-2415	256	8	.	.	PUNCT
ejpam-2415	257	1	now	now	ADV
ejpam-2415	257	2	0	0	NUM
ejpam-2415	257	3	m	m	VERB
ejpam-2415	257	4	:	:	PUNCT
ejpam-2415	257	5	0	0	NUM
ejpam-2415	258	1	=	=	PUNCT
ejpam-2415	258	2	∨{a	∨{a	PROPN
ejpam-2415	258	3	∈	∈	PROPN
ejpam-2415	258	4	m	m	VERB
ejpam-2415	258	5	|	|	ADV
ejpam-2415	258	6	0a=	0a=	NUM
ejpam-2415	258	7	0	0	NUM
ejpam-2415	258	8	m	m	VERB
ejpam-2415	258	9	}	}	PUNCT
ejpam-2415	258	10	=	=	PUNCT
ejpam-2415	258	11	1	1	NUM
ejpam-2415	258	12	m	m	NOUN
ejpam-2415	258	13	.	.	PUNCT
ejpam-2415	259	1	thus	thus	ADV
ejpam-2415	259	2	only	only	ADV
ejpam-2415	259	3	1	1	NUM
ejpam-2415	259	4	m	m	NOUN
ejpam-2415	259	5	will	will	AUX
ejpam-2415	259	6	be	be	AUX
ejpam-2415	259	7	a	a	DET
ejpam-2415	259	8	∗-element	∗-element	NOUN
ejpam-2415	259	9	.	.	PUNCT
ejpam-2415	260	1	hence	hence	ADV
ejpam-2415	260	2	,	,	PUNCT
ejpam-2415	260	3	for	for	ADP
ejpam-2415	260	4	defining	define	VERB
ejpam-2415	260	5	a	a	DET
ejpam-2415	260	6	∗-element	∗-element	NOUN
ejpam-2415	260	7	we	we	PRON
ejpam-2415	260	8	take	take	VERB
ejpam-2415	260	9	f	f	PRON
ejpam-2415	260	10	such	such	ADJ
ejpam-2415	260	11	that	that	DET
ejpam-2415	260	12	0	0	NUM
ejpam-2415	260	13	/∈	/∈	PROPN
ejpam-2415	261	1	f.	f.	PROPN
ejpam-2415	261	2	theorem	theorem	VERB
ejpam-2415	261	3	13	13	NUM
ejpam-2415	261	4	.	.	PUNCT
ejpam-2415	262	1	if	if	SCONJ
ejpam-2415	262	2	{	{	PUNCT
ejpam-2415	262	3	aα}α	aα}α	NOUN
ejpam-2415	262	4	is	be	AUX
ejpam-2415	262	5	a	a	DET
ejpam-2415	262	6	family	family	NOUN
ejpam-2415	262	7	of	of	ADP
ejpam-2415	262	8	baer	baer	PROPN
ejpam-2415	262	9	elements	element	NOUN
ejpam-2415	262	10	then	then	ADV
ejpam-2415	262	11	∧	∧	PROPN
ejpam-2415	262	12	α	α	PRON
ejpam-2415	262	13	aα	aα	NOUN
ejpam-2415	262	14	is	be	AUX
ejpam-2415	262	15	a	a	DET
ejpam-2415	262	16	baer	baer	PROPN
ejpam-2415	262	17	element	element	NOUN
ejpam-2415	262	18	.	.	PUNCT
ejpam-2415	263	1	proof	proof	NOUN
ejpam-2415	263	2	.	.	PUNCT
ejpam-2415	264	1	let	let	VERB
ejpam-2415	264	2	x	x	PRON
ejpam-2415	264	3	∈	∈	PROPN
ejpam-2415	264	4	l∗	l∗	NOUN
ejpam-2415	264	5	such	such	ADJ
ejpam-2415	264	6	that	that	SCONJ
ejpam-2415	264	7	x	x	PROPN
ejpam-2415	265	1	i	i	NOUN
ejpam-2415	265	2	m	m	VERB
ejpam-2415	265	3	¶	¶	NUM
ejpam-2415	265	4	∧	∧	PROPN
ejpam-2415	265	5	α	α	PROPN
ejpam-2415	265	6	aα	aα	NOUN
ejpam-2415	265	7	.	.	PUNCT
ejpam-2415	266	1	then	then	ADV
ejpam-2415	266	2	for	for	ADP
ejpam-2415	266	3	each	each	DET
ejpam-2415	266	4	α	α	NOUN
ejpam-2415	266	5	,	,	PUNCT
ejpam-2415	266	6	x	x	PROPN
ejpam-2415	266	7	i	i	NOUN
ejpam-2415	266	8	m	m	VERB
ejpam-2415	266	9	¶	¶	PROPN
ejpam-2415	266	10	aα	aα	PROPN
ejpam-2415	266	11	.	.	PUNCT
ejpam-2415	267	1	as	as	SCONJ
ejpam-2415	267	2	each	each	DET
ejpam-2415	267	3	aα	aα	NOUN
ejpam-2415	267	4	is	be	AUX
ejpam-2415	267	5	a	a	DET
ejpam-2415	267	6	baer	baer	PROPN
ejpam-2415	267	7	element	element	NOUN
ejpam-2415	267	8	,	,	PUNCT
ejpam-2415	267	9	0	0	NUM
ejpam-2415	267	10	m	m	VERB
ejpam-2415	267	11	:	:	PUNCT
ejpam-2415	267	12	(	(	PUNCT
ejpam-2415	267	13	0	0	NUM
ejpam-2415	267	14	m	m	VERB
ejpam-2415	267	15	:	:	PUNCT
ejpam-2415	267	16	x	x	PUNCT
ejpam-2415	267	17	i	i	NOUN
ejpam-2415	267	18	m	m	VERB
ejpam-2415	267	19	)	)	PUNCT
ejpam-2415	267	20	¶	¶	PROPN
ejpam-2415	267	21	aα	aα	NOUN
ejpam-2415	267	22	.	.	PUNCT
ejpam-2415	268	1	hence	hence	ADV
ejpam-2415	268	2	0	0	NUM
ejpam-2415	268	3	m	m	VERB
ejpam-2415	268	4	:	:	PUNCT
ejpam-2415	268	5	(	(	PUNCT
ejpam-2415	268	6	0	0	NUM
ejpam-2415	268	7	m	m	VERB
ejpam-2415	268	8	:	:	PUNCT
ejpam-2415	268	9	x	x	PUNCT
ejpam-2415	268	10	i	i	NOUN
ejpam-2415	268	11	m	m	PROPN
ejpam-2415	268	12	)	)	PUNCT
ejpam-2415	268	13	¶	¶	PROPN
ejpam-2415	268	14	∧	∧	PROPN
ejpam-2415	268	15	α	α	PROPN
ejpam-2415	268	16	aα	aα	NOUN
ejpam-2415	268	17	.	.	PUNCT
ejpam-2415	269	1	thus	thus	ADV
ejpam-2415	269	2	∧	∧	PROPN
ejpam-2415	269	3	α	α	PRON
ejpam-2415	269	4	aα	aα	NOUN
ejpam-2415	269	5	is	be	AUX
ejpam-2415	269	6	a	a	DET
ejpam-2415	269	7	baer	baer	PROPN
ejpam-2415	269	8	element	element	NOUN
ejpam-2415	269	9	.	.	PUNCT
ejpam-2415	270	1	the	the	DET
ejpam-2415	270	2	next	next	ADJ
ejpam-2415	270	3	result	result	NOUN
ejpam-2415	270	4	we	we	PRON
ejpam-2415	270	5	prove	prove	VERB
ejpam-2415	270	6	the	the	DET
ejpam-2415	270	7	relation	relation	NOUN
ejpam-2415	270	8	between	between	ADP
ejpam-2415	270	9	minimal	minimal	ADJ
ejpam-2415	270	10	prime	prime	ADJ
ejpam-2415	270	11	element	element	NOUN
ejpam-2415	270	12	and	and	CCONJ
ejpam-2415	270	13	baer	baer	PROPN
ejpam-2415	270	14	element	element	PROPN
ejpam-2415	270	15	.	.	PUNCT
ejpam-2415	271	1	theorem	theorem	VERB
ejpam-2415	271	2	14	14	NUM
ejpam-2415	271	3	.	.	PUNCT
ejpam-2415	272	1	if	if	SCONJ
ejpam-2415	272	2	a	a	PRON
ejpam-2415	272	3	is	be	AUX
ejpam-2415	272	4	a	a	DET
ejpam-2415	272	5	meet	meet	NOUN
ejpam-2415	272	6	of	of	ADP
ejpam-2415	272	7	minimal	minimal	ADJ
ejpam-2415	272	8	prime	prime	ADJ
ejpam-2415	272	9	elements	element	NOUN
ejpam-2415	272	10	then	then	ADV
ejpam-2415	272	11	a	a	PRON
ejpam-2415	272	12	is	be	AUX
ejpam-2415	272	13	a	a	DET
ejpam-2415	272	14	baer	baer	PROPN
ejpam-2415	272	15	element	element	NOUN
ejpam-2415	272	16	.	.	PUNCT
ejpam-2415	273	1	proof	proof	NOUN
ejpam-2415	273	2	.	.	PUNCT
ejpam-2415	274	1	from	from	ADP
ejpam-2415	274	2	theorem	theorem	ADJ
ejpam-2415	274	3	7	7	NUM
ejpam-2415	274	4	,	,	PUNCT
ejpam-2415	274	5	every	every	DET
ejpam-2415	274	6	minimal	minimal	ADJ
ejpam-2415	274	7	prime	prime	ADJ
ejpam-2415	274	8	element	element	NOUN
ejpam-2415	274	9	of	of	ADP
ejpam-2415	274	10	m	m	PROPN
ejpam-2415	274	11	is	be	AUX
ejpam-2415	274	12	a	a	DET
ejpam-2415	274	13	∗-element	∗-element	ADJ
ejpam-2415	274	14	and	and	CCONJ
ejpam-2415	274	15	by	by	ADP
ejpam-2415	274	16	theorem	theorem	NOUN
ejpam-2415	274	17	8	8	NUM
ejpam-2415	274	18	,	,	PUNCT
ejpam-2415	274	19	each	each	DET
ejpam-2415	274	20	∗-element	∗-element	NOUN
ejpam-2415	274	21	of	of	ADP
ejpam-2415	274	22	m	m	PROPN
ejpam-2415	274	23	is	be	AUX
ejpam-2415	274	24	a	a	DET
ejpam-2415	274	25	baer	baer	PROPN
ejpam-2415	274	26	element	element	NOUN
ejpam-2415	274	27	.	.	PUNCT
ejpam-2415	275	1	from	from	ADP
ejpam-2415	275	2	these	these	DET
ejpam-2415	275	3	two	two	NUM
ejpam-2415	275	4	results	result	NOUN
ejpam-2415	275	5	,	,	PUNCT
ejpam-2415	275	6	every	every	DET
ejpam-2415	275	7	minimal	minimal	ADJ
ejpam-2415	275	8	prime	prime	ADJ
ejpam-2415	275	9	element	element	NOUN
ejpam-2415	275	10	is	be	AUX
ejpam-2415	275	11	a	a	DET
ejpam-2415	275	12	baer	baer	PROPN
ejpam-2415	275	13	element	element	NOUN
ejpam-2415	275	14	.	.	PUNCT
ejpam-2415	276	1	so	so	ADV
ejpam-2415	276	2	meet	meet	VERB
ejpam-2415	276	3	of	of	ADP
ejpam-2415	276	4	all	all	DET
ejpam-2415	276	5	minimal	minimal	ADJ
ejpam-2415	276	6	prime	prime	ADJ
ejpam-2415	276	7	elements	element	NOUN
ejpam-2415	276	8	is	be	AUX
ejpam-2415	276	9	a	a	DET
ejpam-2415	276	10	baer	baer	PROPN
ejpam-2415	276	11	element	element	NOUN
ejpam-2415	276	12	,	,	PUNCT
ejpam-2415	276	13	by	by	ADP
ejpam-2415	276	14	theorem	theorem	NOUN
ejpam-2415	276	15	13	13	NUM
ejpam-2415	276	16	.	.	PUNCT
ejpam-2415	277	1	theorem	theorem	VERB
ejpam-2415	277	2	15	15	NUM
ejpam-2415	277	3	.	.	PUNCT
ejpam-2415	278	1	if	if	SCONJ
ejpam-2415	278	2	{	{	PUNCT
ejpam-2415	278	3	aα}α	aα}α	NOUN
ejpam-2415	278	4	is	be	AUX
ejpam-2415	278	5	a	a	DET
ejpam-2415	278	6	family	family	NOUN
ejpam-2415	278	7	of	of	ADP
ejpam-2415	278	8	closed	closed	ADJ
ejpam-2415	278	9	elements	element	NOUN
ejpam-2415	278	10	then	then	ADV
ejpam-2415	278	11	∧	∧	PROPN
ejpam-2415	278	12	α	α	PRON
ejpam-2415	278	13	aα	aα	NOUN
ejpam-2415	278	14	is	be	AUX
ejpam-2415	278	15	a	a	DET
ejpam-2415	278	16	closed	closed	ADJ
ejpam-2415	278	17	element	element	NOUN
ejpam-2415	278	18	.	.	PUNCT
ejpam-2415	279	1	proof	proof	NOUN
ejpam-2415	279	2	.	.	PUNCT
ejpam-2415	280	1	we	we	PRON
ejpam-2415	280	2	have	have	VERB
ejpam-2415	280	3	∧	∧	PROPN
ejpam-2415	280	4	α	α	PRON
ejpam-2415	280	5	aα	aα	NOUN
ejpam-2415	280	6	¶	¶	NUM
ejpam-2415	280	7	aα	aα	NOUN
ejpam-2415	280	8	for	for	ADP
ejpam-2415	280	9	each	each	DET
ejpam-2415	280	10	α	α	NOUN
ejpam-2415	280	11	.	.	PUNCT
ejpam-2415	281	1	as	as	SCONJ
ejpam-2415	281	2	each	each	DET
ejpam-2415	281	3	aα	aα	NOUN
ejpam-2415	281	4	is	be	AUX
ejpam-2415	281	5	a	a	DET
ejpam-2415	281	6	closed	closed	ADJ
ejpam-2415	281	7	element	element	NOUN
ejpam-2415	281	8	we	we	PRON
ejpam-2415	281	9	have	have	VERB
ejpam-2415	281	10	0	0	NUM
ejpam-2415	281	11	m	m	VERB
ejpam-2415	281	12	:	:	PUNCT
ejpam-2415	282	1	[	[	X
ejpam-2415	282	2	0	0	NUM
ejpam-2415	282	3	m	m	VERB
ejpam-2415	282	4	:	:	PUNCT
ejpam-2415	282	5	(	(	PUNCT
ejpam-2415	282	6	∧aα)]¶	∧aα)]¶	ADV
ejpam-2415	282	7	0	0	NUM
ejpam-2415	282	8	m	m	VERB
ejpam-2415	282	9	:	:	PUNCT
ejpam-2415	282	10	(	(	PUNCT
ejpam-2415	282	11	0	0	NUM
ejpam-2415	282	12	m	m	VERB
ejpam-2415	282	13	:	:	PUNCT
ejpam-2415	282	14	aα	aα	NOUN
ejpam-2415	282	15	)	)	PUNCT
ejpam-2415	282	16	=	=	SYM
ejpam-2415	282	17	aα	aα	NOUN
ejpam-2415	282	18	.	.	PUNCT
ejpam-2415	283	1	this	this	PRON
ejpam-2415	283	2	gives	give	VERB
ejpam-2415	283	3	0	0	NUM
ejpam-2415	283	4	m	m	VERB
ejpam-2415	283	5	:	:	PUNCT
ejpam-2415	284	1	[	[	X
ejpam-2415	284	2	0	0	NUM
ejpam-2415	284	3	m	m	VERB
ejpam-2415	284	4	:	:	PUNCT
ejpam-2415	284	5	(	(	PUNCT
ejpam-2415	284	6	∧	∧	NOUN
ejpam-2415	284	7	α	α	NOUN
ejpam-2415	284	8	aα)]¶	aα)]¶	PUNCT
ejpam-2415	284	9	∧	∧	PROPN
ejpam-2415	284	10	α	α	NOUN
ejpam-2415	284	11	aα	aα	NOUN
ejpam-2415	284	12	.	.	PUNCT
ejpam-2415	285	1	now	now	ADV
ejpam-2415	285	2	let	let	VERB
ejpam-2415	285	3	z	z	NOUN
ejpam-2415	285	4	be	be	AUX
ejpam-2415	285	5	an	an	DET
ejpam-2415	285	6	element	element	NOUN
ejpam-2415	285	7	of	of	ADP
ejpam-2415	285	8	m	m	PRON
ejpam-2415	285	9	such	such	ADJ
ejpam-2415	285	10	that	that	SCONJ
ejpam-2415	285	11	z	z	PROPN
ejpam-2415	285	12	¶	¶	NUM
ejpam-2415	285	13	∧	∧	PROPN
ejpam-2415	285	14	α	α	PROPN
ejpam-2415	285	15	aα	aα	NOUN
ejpam-2415	285	16	.	.	PUNCT
ejpam-2415	286	1	then	then	ADV
ejpam-2415	286	2	we	we	PRON
ejpam-2415	286	3	have	have	VERB
ejpam-2415	286	4	z	z	PROPN
ejpam-2415	286	5	¶	¶	PROPN
ejpam-2415	286	6	0	0	PROPN
ejpam-2415	286	7	m	m	VERB
ejpam-2415	286	8	:	:	PUNCT
ejpam-2415	286	9	(	(	PUNCT
ejpam-2415	286	10	0	0	NUM
ejpam-2415	286	11	m	m	VERB
ejpam-2415	286	12	:	:	PUNCT
ejpam-2415	286	13	z	z	X
ejpam-2415	286	14	)	)	PUNCT
ejpam-2415	286	15	¶	¶	PROPN
ejpam-2415	286	16	0	0	NUM
ejpam-2415	286	17	m	m	VERB
ejpam-2415	286	18	:	:	PUNCT
ejpam-2415	286	19	(	(	PUNCT
ejpam-2415	286	20	0	0	NUM
ejpam-2415	286	21	m	m	VERB
ejpam-2415	286	22	:	:	PUNCT
ejpam-2415	286	23	∧	∧	NOUN
ejpam-2415	286	24	α	α	NOUN
ejpam-2415	286	25	aα	aα	NOUN
ejpam-2415	286	26	)	)	PUNCT
ejpam-2415	286	27	,	,	PUNCT
ejpam-2415	286	28	by	by	ADP
ejpam-2415	286	29	(	(	PUNCT
ejpam-2415	286	30	ix	ix	INTJ
ejpam-2415	286	31	)	)	PUNCT
ejpam-2415	286	32	of	of	ADP
ejpam-2415	286	33	theorem	theorem	NOUN
ejpam-2415	286	34	1	1	X
ejpam-2415	286	35	.	.	PUNCT
ejpam-2415	287	1	this	this	PRON
ejpam-2415	287	2	gives	give	VERB
ejpam-2415	287	3	∧	∧	PROPN
ejpam-2415	287	4	α	α	PRON
ejpam-2415	287	5	aα	aα	NOUN
ejpam-2415	287	6	¶	¶	PROPN
ejpam-2415	287	7	0	0	NUM
ejpam-2415	287	8	m	m	VERB
ejpam-2415	287	9	:	:	PUNCT
ejpam-2415	288	1	[	[	X
ejpam-2415	288	2	0	0	NUM
ejpam-2415	288	3	m	m	VERB
ejpam-2415	288	4	:	:	PUNCT
ejpam-2415	288	5	(	(	PUNCT
ejpam-2415	288	6	∧	∧	NOUN
ejpam-2415	288	7	α	α	NOUN
ejpam-2415	288	8	aα	aα	NOUN
ejpam-2415	288	9	)	)	PUNCT
ejpam-2415	288	10	]	]	PUNCT
ejpam-2415	288	11	.	.	PUNCT
ejpam-2415	289	1	thus	thus	ADV
ejpam-2415	289	2	we	we	PRON
ejpam-2415	289	3	get	get	VERB
ejpam-2415	289	4	0	0	NUM
ejpam-2415	289	5	m	m	VERB
ejpam-2415	289	6	:	:	PUNCT
ejpam-2415	290	1	[	[	X
ejpam-2415	290	2	0	0	NUM
ejpam-2415	290	3	m	m	VERB
ejpam-2415	290	4	:	:	PUNCT
ejpam-2415	290	5	(	(	PUNCT
ejpam-2415	290	6	∧	∧	NOUN
ejpam-2415	290	7	α	α	NOUN
ejpam-2415	290	8	aα	aα	NOUN
ejpam-2415	290	9	)	)	PUNCT
ejpam-2415	290	10	]	]	PUNCT
ejpam-2415	291	1	=	=	PUNCT
ejpam-2415	291	2	∧	∧	NOUN
ejpam-2415	291	3	α	α	NOUN
ejpam-2415	291	4	aα	aα	NOUN
ejpam-2415	291	5	.	.	PUNCT
ejpam-2415	292	1	here	here	ADV
ejpam-2415	292	2	is	be	AUX
ejpam-2415	292	3	an	an	DET
ejpam-2415	292	4	important	important	ADJ
ejpam-2415	292	5	property	property	NOUN
ejpam-2415	292	6	of	of	ADP
ejpam-2415	292	7	largest	large	ADJ
ejpam-2415	292	8	element	element	NOUN
ejpam-2415	292	9	of	of	ADP
ejpam-2415	292	10	m	m	PRON
ejpam-2415	292	11	which	which	PRON
ejpam-2415	292	12	is	be	AUX
ejpam-2415	292	13	compact	compact	ADJ
ejpam-2415	292	14	.	.	PUNCT
ejpam-2415	293	1	theorem	theorem	VERB
ejpam-2415	293	2	16	16	NUM
ejpam-2415	293	3	.	.	NOUN
ejpam-2415	294	1	1	1	NUM
ejpam-2415	294	2	m	m	NOUN
ejpam-2415	294	3	is	be	AUX
ejpam-2415	294	4	never	never	ADV
ejpam-2415	294	5	a	a	DET
ejpam-2415	294	6	∗-element	∗-element	NOUN
ejpam-2415	294	7	where	where	SCONJ
ejpam-2415	294	8	1	1	NUM
ejpam-2415	294	9	m	m	NOUN
ejpam-2415	294	10	is	be	AUX
ejpam-2415	294	11	compact	compact	ADJ
ejpam-2415	294	12	and	and	CCONJ
ejpam-2415	294	13	m	m	VERB
ejpam-2415	294	14	is	be	AUX
ejpam-2415	294	15	torsion	torsion	NOUN
ejpam-2415	294	16	free	free	ADJ
ejpam-2415	294	17	l	l	NOUN
ejpam-2415	294	18	-	-	NOUN
ejpam-2415	294	19	module	module	NOUN
ejpam-2415	294	20	.	.	PUNCT
ejpam-2415	295	1	c	c	PROPN
ejpam-2415	295	2	manjarekar	manjarekar	PROPN
ejpam-2415	295	3	,	,	PUNCT
ejpam-2415	295	4	u	u	NOUN
ejpam-2415	295	5	kandale	kandale	PROPN
ejpam-2415	295	6	/	/	SYM
ejpam-2415	295	7	eur	eur	PROPN
ejpam-2415	295	8	.	.	PUNCT
ejpam-2415	296	1	j.	j.	PROPN
ejpam-2415	296	2	pure	pure	PROPN
ejpam-2415	296	3	appl	appl	PROPN
ejpam-2415	296	4	.	.	PROPN
ejpam-2415	296	5	math	math	PROPN
ejpam-2415	296	6	,	,	PUNCT
ejpam-2415	296	7	8	8	NUM
ejpam-2415	296	8	(	(	PUNCT
ejpam-2415	296	9	2015	2015	NUM
ejpam-2415	296	10	)	)	PUNCT
ejpam-2415	296	11	,	,	PUNCT
ejpam-2415	296	12	332	332	NUM
ejpam-2415	296	13	-	-	SYM
ejpam-2415	296	14	342	342	NUM
ejpam-2415	296	15	338	338	NUM
ejpam-2415	296	16	proof	proof	NOUN
ejpam-2415	296	17	.	.	PUNCT
ejpam-2415	296	18	suppose	suppose	VERB
ejpam-2415	296	19	that	that	SCONJ
ejpam-2415	296	20	1	1	NUM
ejpam-2415	296	21	m	m	NOUN
ejpam-2415	296	22	is	be	AUX
ejpam-2415	296	23	a	a	DET
ejpam-2415	296	24	∗-element	∗-element	NOUN
ejpam-2415	296	25	.	.	PUNCT
ejpam-2415	297	1	then	then	ADV
ejpam-2415	297	2	there	there	PRON
ejpam-2415	297	3	exist	exist	VERB
ejpam-2415	297	4	some	some	DET
ejpam-2415	297	5	filter	filter	NOUN
ejpam-2415	297	6	f	f	PROPN
ejpam-2415	297	7	∈	∈	PROPN
ejpam-2415	297	8	f(l∗	f(l∗	NOUN
ejpam-2415	297	9	)	)	PUNCT
ejpam-2415	297	10	such	such	ADJ
ejpam-2415	297	11	that	that	SCONJ
ejpam-2415	297	12	1	1	NUM
ejpam-2415	297	13	m	m	NOUN
ejpam-2415	297	14	=	=	NOUN
ejpam-2415	297	15	0f	0f	NOUN
ejpam-2415	297	16	m	m	NOUN
ejpam-2415	297	17	,	,	PUNCT
ejpam-2415	297	18	where	where	SCONJ
ejpam-2415	297	19	0	0	NUM
ejpam-2415	297	20	/∈	/∈	PROPN
ejpam-2415	298	1	f	f	PROPN
ejpam-2415	298	2	.	.	PUNCT
ejpam-2415	299	1	then	then	ADV
ejpam-2415	299	2	as	as	SCONJ
ejpam-2415	299	3	1	1	NUM
ejpam-2415	299	4	m	m	NOUN
ejpam-2415	299	5	is	be	AUX
ejpam-2415	299	6	compact	compact	ADJ
ejpam-2415	299	7	and	and	CCONJ
ejpam-2415	300	1	1	1	NUM
ejpam-2415	300	2	m	m	NOUN
ejpam-2415	300	3	=	=	NOUN
ejpam-2415	300	4	0f	0f	NOUN
ejpam-2415	300	5	m	m	NOUN
ejpam-2415	300	6	=	=	ADJ
ejpam-2415	300	7	∨{(0	∨{(0	ADJ
ejpam-2415	300	8	m	m	NOUN
ejpam-2415	300	9	:	:	PUNCT
ejpam-2415	300	10	x	x	X
ejpam-2415	300	11	)	)	PUNCT
ejpam-2415	301	1	|	|	ADV
ejpam-2415	301	2	x	x	SYM
ejpam-2415	301	3	∈	∈	PROPN
ejpam-2415	301	4	f	f	X
ejpam-2415	301	5	}	}	PUNCT
ejpam-2415	301	6	,	,	PUNCT
ejpam-2415	301	7	1	1	NUM
ejpam-2415	301	8	m	m	NOUN
ejpam-2415	301	9	=	=	PUNCT
ejpam-2415	301	10	(	(	PUNCT
ejpam-2415	301	11	0	0	NUM
ejpam-2415	301	12	m	m	VERB
ejpam-2415	301	13	:	:	PUNCT
ejpam-2415	301	14	x1)∨	x1)∨	PROPN
ejpam-2415	301	15	(	(	PUNCT
ejpam-2415	301	16	0	0	NUM
ejpam-2415	301	17	m	m	VERB
ejpam-2415	301	18	:	:	PUNCT
ejpam-2415	301	19	x2)∨	x2)∨	PROPN
ejpam-2415	301	20	.	.	PUNCT
ejpam-2415	301	21	.	.	PUNCT
ejpam-2415	302	1	.∨	.∨	PUNCT
ejpam-2415	303	1	(	(	PUNCT
ejpam-2415	303	2	0	0	NUM
ejpam-2415	303	3	m	m	VERB
ejpam-2415	303	4	:	:	PUNCT
ejpam-2415	303	5	xn	xn	X
ejpam-2415	303	6	)	)	PUNCT
ejpam-2415	303	7	for	for	ADP
ejpam-2415	303	8	some	some	DET
ejpam-2415	303	9	x1	x1	PROPN
ejpam-2415	303	10	,	,	PUNCT
ejpam-2415	303	11	x2	x2	PROPN
ejpam-2415	303	12	,	,	PUNCT
ejpam-2415	303	13	.	.	PUNCT
ejpam-2415	303	14	.	.	PUNCT
ejpam-2415	303	15	.	.	PUNCT
ejpam-2415	304	1	,	,	PUNCT
ejpam-2415	304	2	xn	xn	PROPN
ejpam-2415	304	3	∈	∈	PROPN
ejpam-2415	304	4	f	f	X
ejpam-2415	304	5	.	.	PUNCT
ejpam-2415	305	1	consequently	consequently	ADV
ejpam-2415	305	2	,	,	PUNCT
ejpam-2415	305	3	as	as	SCONJ
ejpam-2415	305	4	1	1	NUM
ejpam-2415	305	5	m	m	NOUN
ejpam-2415	305	6	is	be	AUX
ejpam-2415	305	7	closed	closed	ADJ
ejpam-2415	305	8	,	,	PUNCT
ejpam-2415	305	9	1	1	NUM
ejpam-2415	305	10	m	m	NOUN
ejpam-2415	305	11	=	=	NOUN
ejpam-2415	305	12	0	0	NUM
ejpam-2415	305	13	m	m	VERB
ejpam-2415	305	14	:	:	PUNCT
ejpam-2415	305	15	(	(	PUNCT
ejpam-2415	305	16	0	0	NUM
ejpam-2415	305	17	m	m	VERB
ejpam-2415	305	18	:	:	PUNCT
ejpam-2415	305	19	1	1	NUM
ejpam-2415	305	20	m	m	NOUN
ejpam-2415	305	21	)	)	PUNCT
ejpam-2415	306	1	=	=	PUNCT
ejpam-2415	306	2	0	0	NUM
ejpam-2415	306	3	m	m	VERB
ejpam-2415	306	4	:	:	PUNCT
ejpam-2415	307	1	[	[	X
ejpam-2415	307	2	0	0	NUM
ejpam-2415	307	3	m	m	VERB
ejpam-2415	307	4	:	:	PUNCT
ejpam-2415	307	5	(	(	PUNCT
ejpam-2415	307	6	(	(	PUNCT
ejpam-2415	307	7	0	0	NUM
ejpam-2415	307	8	m	m	VERB
ejpam-2415	307	9	:	:	PUNCT
ejpam-2415	307	10	x1)∨	x1)∨	PROPN
ejpam-2415	307	11	(	(	PUNCT
ejpam-2415	307	12	0	0	NUM
ejpam-2415	307	13	m	m	VERB
ejpam-2415	307	14	:	:	PUNCT
ejpam-2415	307	15	x2)∨	x2)∨	PROPN
ejpam-2415	307	16	.	.	PUNCT
ejpam-2415	307	17	.	.	PUNCT
ejpam-2415	308	1	.∨	.∨	PUNCT
ejpam-2415	309	1	(	(	PUNCT
ejpam-2415	309	2	0	0	NUM
ejpam-2415	309	3	m	m	VERB
ejpam-2415	309	4	:	:	PUNCT
ejpam-2415	309	5	xn	xn	NUM
ejpam-2415	309	6	)	)	PUNCT
ejpam-2415	309	7	)	)	PUNCT
ejpam-2415	309	8	]	]	PUNCT
ejpam-2415	310	1	=	=	PUNCT
ejpam-2415	310	2	0	0	NUM
ejpam-2415	310	3	m	m	VERB
ejpam-2415	310	4	:	:	PUNCT
ejpam-2415	311	1	[	[	X
ejpam-2415	311	2	0	0	NUM
ejpam-2415	311	3	m	m	VERB
ejpam-2415	311	4	:	:	PUNCT
ejpam-2415	311	5	(	(	PUNCT
ejpam-2415	311	6	0	0	NUM
ejpam-2415	311	7	m	m	VERB
ejpam-2415	311	8	:	:	PUNCT
ejpam-2415	311	9	x1)∧	x1)∧	PROPN
ejpam-2415	311	10	0	0	NUM
ejpam-2415	311	11	m	m	VERB
ejpam-2415	311	12	:	:	PUNCT
ejpam-2415	311	13	(	(	PUNCT
ejpam-2415	311	14	0	0	NUM
ejpam-2415	311	15	m	m	VERB
ejpam-2415	311	16	:	:	PUNCT
ejpam-2415	311	17	x2)∧	x2)∧	PROPN
ejpam-2415	311	18	.	.	PUNCT
ejpam-2415	311	19	.	.	PUNCT
ejpam-2415	312	1	.∧	.∧	PUNCT
ejpam-2415	313	1	0	0	NUM
ejpam-2415	313	2	m	m	VERB
ejpam-2415	313	3	:	:	PUNCT
ejpam-2415	313	4	(	(	PUNCT
ejpam-2415	313	5	0	0	NUM
ejpam-2415	313	6	m	m	VERB
ejpam-2415	313	7	:	:	PUNCT
ejpam-2415	313	8	xn	xn	X
ejpam-2415	313	9	)	)	PUNCT
ejpam-2415	313	10	]	]	PUNCT
ejpam-2415	313	11	.	.	PUNCT
ejpam-2415	314	1	therefore	therefore	ADV
ejpam-2415	314	2	1	1	NUM
ejpam-2415	314	3	m	m	VERB
ejpam-2415	314	4	=	=	NOUN
ejpam-2415	314	5	0	0	NUM
ejpam-2415	314	6	m	m	VERB
ejpam-2415	314	7	:	:	PUNCT
ejpam-2415	315	1	[	[	X
ejpam-2415	315	2	0	0	NUM
ejpam-2415	315	3	m	m	VERB
ejpam-2415	315	4	:	:	PUNCT
ejpam-2415	315	5	(	(	PUNCT
ejpam-2415	315	6	0	0	NUM
ejpam-2415	315	7	m	m	VERB
ejpam-2415	315	8	:	:	PUNCT
ejpam-2415	315	9	(	(	PUNCT
ejpam-2415	315	10	x1	x1	INTJ
ejpam-2415	315	11	x2	x2	INTJ
ejpam-2415	315	12	.	.	PUNCT
ejpam-2415	315	13	.	.	PUNCT
ejpam-2415	315	14	.	.	PUNCT
ejpam-2415	316	1	xn	xn	X
ejpam-2415	316	2	)	)	PUNCT
ejpam-2415	316	3	]	]	PUNCT
ejpam-2415	317	1	=	=	PUNCT
ejpam-2415	317	2	0	0	NUM
ejpam-2415	317	3	m	m	VERB
ejpam-2415	317	4	:	:	PUNCT
ejpam-2415	317	5	(	(	PUNCT
ejpam-2415	318	1	x1	x1	INTJ
ejpam-2415	318	2	x2	x2	INTJ
ejpam-2415	318	3	.	.	PUNCT
ejpam-2415	318	4	.	.	PUNCT
ejpam-2415	318	5	.	.	PUNCT
ejpam-2415	319	1	xn	xn	X
ejpam-2415	319	2	)	)	PUNCT
ejpam-2415	319	3	,	,	PUNCT
ejpam-2415	319	4	by	by	ADP
ejpam-2415	319	5	(	(	PUNCT
ejpam-2415	319	6	iii	iii	NOUN
ejpam-2415	319	7	)	)	PUNCT
ejpam-2415	319	8	and	and	CCONJ
ejpam-2415	319	9	(	(	PUNCT
ejpam-2415	319	10	v	v	NOUN
ejpam-2415	319	11	)	)	PUNCT
ejpam-2415	319	12	of	of	ADP
ejpam-2415	319	13	theorem	theorem	NOUN
ejpam-2415	319	14	1	1	X
ejpam-2415	319	15	.	.	PUNCT
ejpam-2415	320	1	this	this	PRON
ejpam-2415	320	2	implies	imply	VERB
ejpam-2415	320	3	that	that	SCONJ
ejpam-2415	320	4	x1	x1	PROPN
ejpam-2415	320	5	x2	x2	INTJ
ejpam-2415	320	6	.	.	PUNCT
ejpam-2415	320	7	.	.	PUNCT
ejpam-2415	320	8	.	.	PUNCT
ejpam-2415	321	1	xn	xn	X
ejpam-2415	322	1	=	=	SYM
ejpam-2415	322	2	0	0	X
ejpam-2415	322	3	.	.	PUNCT
ejpam-2415	323	1	since	since	SCONJ
ejpam-2415	323	2	x1	x1	PROPN
ejpam-2415	323	3	,	,	PUNCT
ejpam-2415	323	4	x2	x2	PROPN
ejpam-2415	323	5	,	,	PUNCT
ejpam-2415	323	6	.	.	PUNCT
ejpam-2415	323	7	.	.	PUNCT
ejpam-2415	323	8	.	.	PUNCT
ejpam-2415	324	1	,	,	PUNCT
ejpam-2415	324	2	xn	xn	PROPN
ejpam-2415	324	3	are	be	AUX
ejpam-2415	324	4	in	in	ADP
ejpam-2415	324	5	f.	f.	PROPN
ejpam-2415	324	6	we	we	PRON
ejpam-2415	324	7	have	have	VERB
ejpam-2415	324	8	0	0	NUM
ejpam-2415	325	1	=	=	SYM
ejpam-2415	325	2	x1	x1	NUM
ejpam-2415	326	1	x2	x2	INTJ
ejpam-2415	326	2	.	.	PUNCT
ejpam-2415	326	3	.	.	PUNCT
ejpam-2415	326	4	.	.	PUNCT
ejpam-2415	327	1	xn	xn	PROPN
ejpam-2415	328	1	∈	∈	PROPN
ejpam-2415	328	2	f	f	PROPN
ejpam-2415	328	3	.	.	PUNCT
ejpam-2415	329	1	which	which	PRON
ejpam-2415	329	2	is	be	AUX
ejpam-2415	329	3	a	a	DET
ejpam-2415	329	4	contradiction	contradiction	NOUN
ejpam-2415	329	5	as	as	ADP
ejpam-2415	329	6	0	0	NUM
ejpam-2415	329	7	/∈	/∈	PROPN
ejpam-2415	329	8	f	f	PROPN
ejpam-2415	329	9	.	.	PUNCT
ejpam-2415	330	1	the	the	DET
ejpam-2415	330	2	next	next	ADJ
ejpam-2415	330	3	result	result	NOUN
ejpam-2415	330	4	we	we	PRON
ejpam-2415	330	5	prove	prove	VERB
ejpam-2415	330	6	the	the	DET
ejpam-2415	330	7	characterization	characterization	NOUN
ejpam-2415	330	8	of	of	ADP
ejpam-2415	330	9	a	a	DET
ejpam-2415	330	10	baer	baer	PROPN
ejpam-2415	330	11	element	element	NOUN
ejpam-2415	330	12	.	.	PUNCT
ejpam-2415	331	1	theorem	theorem	VERB
ejpam-2415	331	2	17	17	NUM
ejpam-2415	331	3	.	.	PUNCT
ejpam-2415	332	1	the	the	DET
ejpam-2415	332	2	following	follow	VERB
ejpam-2415	332	3	statements	statement	NOUN
ejpam-2415	332	4	are	be	AUX
ejpam-2415	332	5	equivalent	equivalent	ADJ
ejpam-2415	332	6	,	,	PUNCT
ejpam-2415	332	7	(	(	PUNCT
ejpam-2415	332	8	i	i	NOUN
ejpam-2415	332	9	)	)	PUNCT
ejpam-2415	332	10	an	an	DET
ejpam-2415	332	11	element	element	NOUN
ejpam-2415	332	12	a∈	a∈	PROPN
ejpam-2415	332	13	m	m	VERB
ejpam-2415	332	14	is	be	AUX
ejpam-2415	332	15	a	a	DET
ejpam-2415	332	16	baer	baer	PROPN
ejpam-2415	332	17	element	element	NOUN
ejpam-2415	332	18	.	.	PUNCT
ejpam-2415	333	1	(	(	PUNCT
ejpam-2415	333	2	ii	ii	NOUN
ejpam-2415	333	3	)	)	PUNCT
ejpam-2415	333	4	for	for	ADP
ejpam-2415	333	5	any	any	DET
ejpam-2415	333	6	element	element	NOUN
ejpam-2415	333	7	x	x	X
ejpam-2415	333	8	,	,	PUNCT
ejpam-2415	333	9	y	y	PROPN
ejpam-2415	333	10	∈	∈	PROPN
ejpam-2415	333	11	l	l	NOUN
ejpam-2415	333	12	such	such	ADJ
ejpam-2415	333	13	that	that	SCONJ
ejpam-2415	333	14	x	x	PRON
ejpam-2415	333	15	is	be	AUX
ejpam-2415	333	16	compact	compact	ADJ
ejpam-2415	333	17	0	0	NUM
ejpam-2415	333	18	m	m	VERB
ejpam-2415	333	19	:	:	PUNCT
ejpam-2415	333	20	x	x	PUNCT
ejpam-2415	334	1	i	i	PRON
ejpam-2415	334	2	m	m	VERB
ejpam-2415	334	3	=	=	ADJ
ejpam-2415	334	4	0	0	NUM
ejpam-2415	334	5	m	m	VERB
ejpam-2415	334	6	:	:	PUNCT
ejpam-2415	335	1	y	y	PROPN
ejpam-2415	335	2	i	i	PRON
ejpam-2415	335	3	m	m	VERB
ejpam-2415	335	4	and	and	CCONJ
ejpam-2415	335	5	x	x	PUNCT
ejpam-2415	335	6	i	i	NOUN
ejpam-2415	335	7	m	m	VERB
ejpam-2415	335	8	¶	¶	PROPN
ejpam-2415	335	9	a	a	PRON
ejpam-2415	335	10	implies	imply	VERB
ejpam-2415	335	11	y	y	PROPN
ejpam-2415	335	12	i	i	PRON
ejpam-2415	335	13	m	m	VERB
ejpam-2415	335	14	¶	¶	PROPN
ejpam-2415	335	15	a.	a.	NOUN
ejpam-2415	335	16	(	(	PUNCT
ejpam-2415	335	17	iii	iii	NOUN
ejpam-2415	335	18	)	)	PUNCT
ejpam-2415	335	19	for	for	ADP
ejpam-2415	335	20	any	any	DET
ejpam-2415	335	21	element	element	NOUN
ejpam-2415	335	22	x	x	INTJ
ejpam-2415	335	23	,	,	PUNCT
ejpam-2415	335	24	y	y	PROPN
ejpam-2415	335	25	∈	∈	PROPN
ejpam-2415	335	26	l∗	l∗	PROPN
ejpam-2415	335	27	,	,	PUNCT
ejpam-2415	335	28	0	0	NUM
ejpam-2415	335	29	m	m	VERB
ejpam-2415	335	30	:	:	PUNCT
ejpam-2415	335	31	x	x	SYM
ejpam-2415	336	1	=	=	SYM
ejpam-2415	336	2	0	0	NUM
ejpam-2415	336	3	m	m	VERB
ejpam-2415	336	4	:	:	PUNCT
ejpam-2415	336	5	y	y	PROPN
ejpam-2415	336	6	and	and	CCONJ
ejpam-2415	336	7	x	x	PROPN
ejpam-2415	336	8	i	i	NOUN
ejpam-2415	336	9	m	m	VERB
ejpam-2415	336	10	¶	¶	PROPN
ejpam-2415	336	11	a	a	PRON
ejpam-2415	336	12	implies	imply	VERB
ejpam-2415	336	13	y	y	PROPN
ejpam-2415	336	14	i	i	PRON
ejpam-2415	336	15	m	m	VERB
ejpam-2415	336	16	¶	¶	ADJ
ejpam-2415	336	17	a.	a.	NOUN
ejpam-2415	336	18	proof	proof	NOUN
ejpam-2415	336	19	.	.	PUNCT
ejpam-2415	337	1	(	(	PUNCT
ejpam-2415	337	2	i)⇒	i)⇒	PROPN
ejpam-2415	337	3	(	(	PUNCT
ejpam-2415	337	4	ii	ii	NOUN
ejpam-2415	337	5	)	)	PUNCT
ejpam-2415	337	6	assume	assume	VERB
ejpam-2415	337	7	that	that	SCONJ
ejpam-2415	337	8	a	a	PRON
ejpam-2415	337	9	is	be	AUX
ejpam-2415	337	10	a	a	DET
ejpam-2415	337	11	baer	baer	PROPN
ejpam-2415	337	12	element	element	NOUN
ejpam-2415	337	13	of	of	ADP
ejpam-2415	337	14	m.	m.	NOUN
ejpam-2415	337	15	let	let	VERB
ejpam-2415	337	16	x	x	PRON
ejpam-2415	337	17	,	,	PUNCT
ejpam-2415	337	18	y	y	PROPN
ejpam-2415	337	19	∈	∈	PROPN
ejpam-2415	337	20	l	l	NOUN
ejpam-2415	337	21	be	be	AUX
ejpam-2415	337	22	such	such	ADJ
ejpam-2415	337	23	that	that	SCONJ
ejpam-2415	337	24	x	x	PRON
ejpam-2415	337	25	is	be	AUX
ejpam-2415	337	26	compact	compact	ADJ
ejpam-2415	337	27	,	,	PUNCT
ejpam-2415	337	28	x	x	VERB
ejpam-2415	338	1	i	i	NOUN
ejpam-2415	338	2	m	m	VERB
ejpam-2415	338	3	¶	¶	PROPN
ejpam-2415	338	4	a	a	NOUN
ejpam-2415	338	5	,	,	PUNCT
ejpam-2415	338	6	and	and	CCONJ
ejpam-2415	338	7	0	0	NUM
ejpam-2415	338	8	m	m	VERB
ejpam-2415	338	9	:	:	PUNCT
ejpam-2415	338	10	x	x	VERB
ejpam-2415	339	1	i	i	PRON
ejpam-2415	339	2	m	m	VERB
ejpam-2415	339	3	=	=	ADJ
ejpam-2415	339	4	0	0	NUM
ejpam-2415	339	5	m	m	VERB
ejpam-2415	339	6	:	:	PUNCT
ejpam-2415	340	1	y	y	PROPN
ejpam-2415	340	2	i	i	PRON
ejpam-2415	340	3	m	m	VERB
ejpam-2415	340	4	.	.	PUNCT
ejpam-2415	341	1	then	then	ADV
ejpam-2415	341	2	by	by	ADP
ejpam-2415	341	3	theorem	theorem	NOUN
ejpam-2415	341	4	1	1	NUM
ejpam-2415	341	5	,	,	PUNCT
ejpam-2415	341	6	y	y	PROPN
ejpam-2415	341	7	i	i	PRON
ejpam-2415	341	8	m	m	VERB
ejpam-2415	341	9	¶	¶	PROPN
ejpam-2415	341	10	0	0	NUM
ejpam-2415	341	11	m	m	VERB
ejpam-2415	341	12	:	:	PUNCT
ejpam-2415	341	13	(	(	PUNCT
ejpam-2415	341	14	0	0	NUM
ejpam-2415	341	15	m	m	VERB
ejpam-2415	341	16	:	:	PUNCT
ejpam-2415	342	1	y	y	PROPN
ejpam-2415	342	2	i	i	NOUN
ejpam-2415	342	3	m	m	VERB
ejpam-2415	342	4	)	)	PUNCT
ejpam-2415	343	1	=	=	PUNCT
ejpam-2415	343	2	0	0	NUM
ejpam-2415	343	3	m	m	VERB
ejpam-2415	343	4	:	:	PUNCT
ejpam-2415	343	5	(	(	PUNCT
ejpam-2415	343	6	0	0	NUM
ejpam-2415	343	7	m	m	VERB
ejpam-2415	343	8	:	:	PUNCT
ejpam-2415	343	9	x	x	PUNCT
ejpam-2415	343	10	i	i	NOUN
ejpam-2415	343	11	m	m	VERB
ejpam-2415	343	12	)	)	PUNCT
ejpam-2415	343	13	¶	¶	PROPN
ejpam-2415	343	14	a	a	X
ejpam-2415	343	15	,	,	PUNCT
ejpam-2415	343	16	since	since	SCONJ
ejpam-2415	343	17	a	a	PRON
ejpam-2415	343	18	is	be	AUX
ejpam-2415	343	19	a	a	DET
ejpam-2415	343	20	baer	baer	PROPN
ejpam-2415	343	21	element	element	NOUN
ejpam-2415	343	22	.	.	PUNCT
ejpam-2415	344	1	(	(	PUNCT
ejpam-2415	344	2	ii)⇒	ii)⇒	X
ejpam-2415	344	3	(	(	PUNCT
ejpam-2415	344	4	iii	iii	NOUN
ejpam-2415	344	5	)	)	PUNCT
ejpam-2415	344	6	obvious	obvious	ADJ
ejpam-2415	344	7	.	.	PUNCT
ejpam-2415	345	1	(	(	PUNCT
ejpam-2415	345	2	iii)⇒	iii)⇒	PROPN
ejpam-2415	345	3	(	(	PUNCT
ejpam-2415	345	4	i	i	NOUN
ejpam-2415	345	5	)	)	PUNCT
ejpam-2415	345	6	assume	assume	VERB
ejpam-2415	345	7	that	that	SCONJ
ejpam-2415	345	8	for	for	ADP
ejpam-2415	345	9	any	any	DET
ejpam-2415	345	10	element	element	NOUN
ejpam-2415	345	11	x	x	INTJ
ejpam-2415	345	12	,	,	PUNCT
ejpam-2415	345	13	y	y	PROPN
ejpam-2415	345	14	∈	∈	PROPN
ejpam-2415	345	15	l∗	l∗	PROPN
ejpam-2415	345	16	,	,	PUNCT
ejpam-2415	345	17	0	0	NUM
ejpam-2415	345	18	m	m	VERB
ejpam-2415	345	19	:	:	PUNCT
ejpam-2415	345	20	x	x	VERB
ejpam-2415	345	21	i	i	PRON
ejpam-2415	345	22	m	m	VERB
ejpam-2415	345	23	=	=	ADJ
ejpam-2415	345	24	0	0	NUM
ejpam-2415	345	25	m	m	VERB
ejpam-2415	345	26	:	:	PUNCT
ejpam-2415	346	1	y	y	PROPN
ejpam-2415	346	2	i	i	PRON
ejpam-2415	346	3	m	m	VERB
ejpam-2415	346	4	and	and	CCONJ
ejpam-2415	346	5	x	x	PUNCT
ejpam-2415	346	6	i	i	NOUN
ejpam-2415	346	7	m	m	VERB
ejpam-2415	346	8	¶	¶	PROPN
ejpam-2415	346	9	a	a	PRON
ejpam-2415	346	10	implies	imply	VERB
ejpam-2415	346	11	y	y	PROPN
ejpam-2415	346	12	i	i	PRON
ejpam-2415	346	13	m	m	VERB
ejpam-2415	346	14	¶	¶	NOUN
ejpam-2415	346	15	a.	a.	NOUN
ejpam-2415	346	16	we	we	PRON
ejpam-2415	346	17	show	show	VERB
ejpam-2415	346	18	that	that	SCONJ
ejpam-2415	346	19	a∈	a∈	PROPN
ejpam-2415	346	20	m	m	PROPN
ejpam-2415	346	21	is	be	AUX
ejpam-2415	346	22	a	a	DET
ejpam-2415	346	23	baer	baer	PROPN
ejpam-2415	346	24	element	element	NOUN
ejpam-2415	346	25	.	.	PUNCT
ejpam-2415	347	1	let	let	VERB
ejpam-2415	347	2	x	x	PRON
ejpam-2415	347	3	∈	∈	PROPN
ejpam-2415	347	4	l∗	l∗	NOUN
ejpam-2415	347	5	be	be	AUX
ejpam-2415	347	6	such	such	ADJ
ejpam-2415	347	7	that	that	SCONJ
ejpam-2415	347	8	x	x	PUNCT
ejpam-2415	348	1	i	i	NOUN
ejpam-2415	348	2	m	m	VERB
ejpam-2415	348	3	¶	¶	NOUN
ejpam-2415	348	4	a.	a.	NOUN
ejpam-2415	348	5	we	we	PRON
ejpam-2415	348	6	have	have	VERB
ejpam-2415	348	7	0	0	NUM
ejpam-2415	348	8	m	m	VERB
ejpam-2415	348	9	:	:	PUNCT
ejpam-2415	349	1	x	x	PUNCT
ejpam-2415	350	1	i	i	PRON
ejpam-2415	350	2	m	m	VERB
ejpam-2415	350	3	=	=	ADJ
ejpam-2415	350	4	0	0	NUM
ejpam-2415	350	5	m	m	VERB
ejpam-2415	350	6	:	:	PUNCT
ejpam-2415	351	1	[	[	X
ejpam-2415	351	2	0	0	NUM
ejpam-2415	351	3	m	m	VERB
ejpam-2415	351	4	:	:	PUNCT
ejpam-2415	351	5	(	(	PUNCT
ejpam-2415	351	6	0	0	NUM
ejpam-2415	351	7	m	m	VERB
ejpam-2415	351	8	:	:	PUNCT
ejpam-2415	351	9	x	x	PUNCT
ejpam-2415	351	10	i	i	NOUN
ejpam-2415	351	11	m	m	PROPN
ejpam-2415	351	12	)	)	PUNCT
ejpam-2415	351	13	]	]	PUNCT
ejpam-2415	351	14	.	.	PUNCT
ejpam-2415	352	1	hence	hence	ADV
ejpam-2415	352	2	by	by	ADP
ejpam-2415	352	3	(	(	PUNCT
ejpam-2415	352	4	iii	iii	NOUN
ejpam-2415	352	5	)	)	PUNCT
ejpam-2415	352	6	,	,	PUNCT
ejpam-2415	352	7	we	we	PRON
ejpam-2415	352	8	have	have	VERB
ejpam-2415	352	9	0	0	NUM
ejpam-2415	352	10	m	m	VERB
ejpam-2415	352	11	:	:	PUNCT
ejpam-2415	352	12	(	(	PUNCT
ejpam-2415	352	13	0	0	NUM
ejpam-2415	352	14	m	m	VERB
ejpam-2415	352	15	:	:	PUNCT
ejpam-2415	352	16	x	x	PUNCT
ejpam-2415	352	17	i	i	NOUN
ejpam-2415	352	18	m	m	VERB
ejpam-2415	352	19	)	)	PUNCT
ejpam-2415	352	20	¶	¶	PROPN
ejpam-2415	352	21	a.	a.	NOUN
ejpam-2415	352	22	hence	hence	ADV
ejpam-2415	352	23	,	,	PUNCT
ejpam-2415	352	24	a	a	PRON
ejpam-2415	352	25	is	be	AUX
ejpam-2415	352	26	a	a	DET
ejpam-2415	352	27	baer	baer	PROPN
ejpam-2415	352	28	element	element	NOUN
ejpam-2415	352	29	.	.	PUNCT
ejpam-2415	353	1	in	in	ADP
ejpam-2415	353	2	the	the	DET
ejpam-2415	353	3	following	follow	VERB
ejpam-2415	353	4	theorem	theorem	NOUN
ejpam-2415	353	5	we	we	PRON
ejpam-2415	353	6	prove	prove	VERB
ejpam-2415	353	7	the	the	DET
ejpam-2415	353	8	relation	relation	NOUN
ejpam-2415	353	9	between	between	ADP
ejpam-2415	353	10	baer	baer	PROPN
ejpam-2415	353	11	element	element	NOUN
ejpam-2415	353	12	of	of	ADP
ejpam-2415	353	13	a	a	DET
ejpam-2415	353	14	lattice	lattice	NOUN
ejpam-2415	353	15	module	module	NOUN
ejpam-2415	353	16	and	and	CCONJ
ejpam-2415	353	17	radical	radical	ADJ
ejpam-2415	353	18	element	element	NOUN
ejpam-2415	353	19	of	of	ADP
ejpam-2415	353	20	a	a	DET
ejpam-2415	353	21	multiplicative	multiplicative	ADJ
ejpam-2415	353	22	lattice	lattice	NOUN
ejpam-2415	353	23	.	.	PUNCT
ejpam-2415	354	1	theorem	theorem	VERB
ejpam-2415	354	2	18	18	NUM
ejpam-2415	354	3	.	.	PUNCT
ejpam-2415	355	1	if	if	SCONJ
ejpam-2415	355	2	a	a	PRON
ejpam-2415	355	3	is	be	AUX
ejpam-2415	355	4	baer	baer	PROPN
ejpam-2415	355	5	element	element	NOUN
ejpam-2415	355	6	of	of	ADP
ejpam-2415	355	7	m	m	PROPN
ejpam-2415	355	8	then	then	ADV
ejpam-2415	355	9	a	a	PRON
ejpam-2415	355	10	:	:	PUNCT
ejpam-2415	355	11	i	i	PRON
ejpam-2415	355	12	m	m	VERB
ejpam-2415	355	13	is	be	AUX
ejpam-2415	355	14	a	a	DET
ejpam-2415	355	15	radical	radical	ADJ
ejpam-2415	355	16	element	element	NOUN
ejpam-2415	355	17	.	.	PUNCT
ejpam-2415	356	1	proof	proof	NOUN
ejpam-2415	356	2	.	.	PUNCT
ejpam-2415	357	1	let	let	VERB
ejpam-2415	357	2	a	a	PRON
ejpam-2415	357	3	be	be	AUX
ejpam-2415	357	4	baer	baer	PROPN
ejpam-2415	357	5	element	element	NOUN
ejpam-2415	357	6	of	of	ADP
ejpam-2415	357	7	a	a	DET
ejpam-2415	357	8	lattice	lattice	NOUN
ejpam-2415	357	9	module	module	NOUN
ejpam-2415	357	10	m.	m.	NOUN
ejpam-2415	357	11	we	we	PRON
ejpam-2415	357	12	show	show	VERB
ejpam-2415	357	13	that	that	SCONJ
ejpam-2415	357	14	(	(	PUNCT
ejpam-2415	357	15	a	a	PRON
ejpam-2415	357	16	:	:	PUNCT
ejpam-2415	357	17	i	i	PRON
ejpam-2415	357	18	m	m	VERB
ejpam-2415	357	19	)	)	PUNCT
ejpam-2415	358	1	=	=	SYM
ejpam-2415	358	2	p	p	X
ejpam-2415	358	3	(	(	PUNCT
ejpam-2415	358	4	a	a	NOUN
ejpam-2415	358	5	:	:	PUNCT
ejpam-2415	358	6	i	i	PRON
ejpam-2415	358	7	m	m	PROPN
ejpam-2415	358	8	)	)	PUNCT
ejpam-2415	358	9	.	.	PUNCT
ejpam-2415	359	1	assume	assume	VERB
ejpam-2415	359	2	that	that	SCONJ
ejpam-2415	359	3	x	x	PRON
ejpam-2415	359	4	is	be	AUX
ejpam-2415	359	5	compact	compact	ADJ
ejpam-2415	359	6	element	element	NOUN
ejpam-2415	359	7	such	such	ADJ
ejpam-2415	359	8	that	that	SCONJ
ejpam-2415	359	9	xn	xn	PROPN
ejpam-2415	360	1	i	i	PRON
ejpam-2415	360	2	m	m	VERB
ejpam-2415	360	3	¶	¶	NOUN
ejpam-2415	360	4	a	a	PRON
ejpam-2415	360	5	for	for	ADP
ejpam-2415	360	6	some	some	DET
ejpam-2415	360	7	positive	positive	ADJ
ejpam-2415	360	8	integer	integer	NOUN
ejpam-2415	360	9	n.	n.	NOUN
ejpam-2415	360	10	we	we	PRON
ejpam-2415	360	11	have	have	VERB
ejpam-2415	360	12	0	0	NUM
ejpam-2415	360	13	m	m	VERB
ejpam-2415	360	14	:	:	PUNCT
ejpam-2415	361	1	x	x	PUNCT
ejpam-2415	362	1	i	i	PRON
ejpam-2415	362	2	m	m	VERB
ejpam-2415	362	3	=	=	ADJ
ejpam-2415	362	4	0	0	NUM
ejpam-2415	362	5	m	m	VERB
ejpam-2415	362	6	:	:	PUNCT
ejpam-2415	362	7	xn	xn	PROPN
ejpam-2415	363	1	i	i	VERB
ejpam-2415	363	2	m	m	VERB
ejpam-2415	363	3	,	,	PUNCT
ejpam-2415	363	4	by	by	ADP
ejpam-2415	363	5	(	(	PUNCT
ejpam-2415	363	6	xii	xii	NOUN
ejpam-2415	363	7	)	)	PUNCT
ejpam-2415	363	8	of	of	ADP
ejpam-2415	363	9	theorem	theorem	NOUN
ejpam-2415	363	10	1	1	NUM
ejpam-2415	363	11	and	and	CCONJ
ejpam-2415	363	12	hence	hence	ADV
ejpam-2415	363	13	by	by	ADP
ejpam-2415	363	14	above	above	ADP
ejpam-2415	363	15	theorem	theorem	NOUN
ejpam-2415	363	16	x	x	PUNCT
ejpam-2415	363	17	i	i	NOUN
ejpam-2415	363	18	m	m	VERB
ejpam-2415	363	19	¶	¶	NOUN
ejpam-2415	363	20	a	a	PRON
ejpam-2415	363	21	that	that	ADV
ejpam-2415	363	22	is	be	AUX
ejpam-2415	363	23	x	x	X
ejpam-2415	363	24	¶	¶	X
ejpam-2415	363	25	(	(	PUNCT
ejpam-2415	363	26	a	a	PRON
ejpam-2415	363	27	:	:	PUNCT
ejpam-2415	363	28	i	i	PRON
ejpam-2415	363	29	m	m	PROPN
ejpam-2415	363	30	)	)	PUNCT
ejpam-2415	363	31	.	.	PUNCT
ejpam-2415	364	1	hence	hence	ADV
ejpam-2415	364	2	p	p	X
ejpam-2415	364	3	(	(	PUNCT
ejpam-2415	364	4	a	a	NOUN
ejpam-2415	364	5	:	:	PUNCT
ejpam-2415	364	6	i	i	PRON
ejpam-2415	364	7	m	m	PROPN
ejpam-2415	364	8	)	)	PUNCT
ejpam-2415	364	9	¶	¶	PROPN
ejpam-2415	364	10	(	(	PUNCT
ejpam-2415	364	11	a	a	PRON
ejpam-2415	364	12	:	:	PUNCT
ejpam-2415	364	13	i	i	PRON
ejpam-2415	364	14	m	m	PROPN
ejpam-2415	364	15	)	)	PUNCT
ejpam-2415	364	16	and	and	CCONJ
ejpam-2415	364	17	we	we	PRON
ejpam-2415	364	18	have	have	VERB
ejpam-2415	364	19	p	p	NOUN
ejpam-2415	364	20	(	(	PUNCT
ejpam-2415	364	21	a	a	NOUN
ejpam-2415	364	22	:	:	PUNCT
ejpam-2415	364	23	i	i	PRON
ejpam-2415	364	24	m	m	VERB
ejpam-2415	364	25	)	)	PUNCT
ejpam-2415	365	1	=	=	SYM
ejpam-2415	365	2	(	(	PUNCT
ejpam-2415	365	3	a	a	X
ejpam-2415	365	4	:	:	PUNCT
ejpam-2415	365	5	i	i	PRON
ejpam-2415	365	6	m	m	VERB
ejpam-2415	365	7	)	)	PUNCT
ejpam-2415	365	8	i.e.(a	i.e.(a	PROPN
ejpam-2415	365	9	:	:	PUNCT
ejpam-2415	365	10	i	i	PRON
ejpam-2415	365	11	m	m	VERB
ejpam-2415	365	12	)	)	PUNCT
ejpam-2415	365	13	is	be	AUX
ejpam-2415	365	14	a	a	DET
ejpam-2415	365	15	radical	radical	ADJ
ejpam-2415	365	16	element	element	NOUN
ejpam-2415	365	17	.	.	PUNCT
ejpam-2415	366	1	theorem	theorem	NOUN
ejpam-2415	366	2	19	19	NUM
ejpam-2415	366	3	.	.	PUNCT
ejpam-2415	367	1	if	if	SCONJ
ejpam-2415	367	2	a	a	PRON
ejpam-2415	367	3	is	be	AUX
ejpam-2415	367	4	a	a	DET
ejpam-2415	367	5	baer	baer	PROPN
ejpam-2415	367	6	element	element	NOUN
ejpam-2415	367	7	then	then	ADV
ejpam-2415	367	8	every	every	DET
ejpam-2415	367	9	minimal	minimal	ADJ
ejpam-2415	367	10	prime	prime	ADJ
ejpam-2415	367	11	element	element	NOUN
ejpam-2415	367	12	over	over	ADP
ejpam-2415	367	13	a	a	PRON
ejpam-2415	367	14	is	be	AUX
ejpam-2415	367	15	a	a	DET
ejpam-2415	367	16	baer	baer	PROPN
ejpam-2415	367	17	element	element	NOUN
ejpam-2415	367	18	.	.	PUNCT
ejpam-2415	368	1	c	c	PROPN
ejpam-2415	368	2	manjarekar	manjarekar	PROPN
ejpam-2415	368	3	,	,	PUNCT
ejpam-2415	368	4	u	u	NOUN
ejpam-2415	368	5	kandale	kandale	PROPN
ejpam-2415	368	6	/	/	SYM
ejpam-2415	368	7	eur	eur	PROPN
ejpam-2415	368	8	.	.	PUNCT
ejpam-2415	369	1	j.	j.	PROPN
ejpam-2415	369	2	pure	pure	PROPN
ejpam-2415	369	3	appl	appl	PROPN
ejpam-2415	369	4	.	.	PROPN
ejpam-2415	369	5	math	math	PROPN
ejpam-2415	369	6	,	,	PUNCT
ejpam-2415	369	7	8	8	NUM
ejpam-2415	369	8	(	(	PUNCT
ejpam-2415	369	9	2015	2015	NUM
ejpam-2415	369	10	)	)	PUNCT
ejpam-2415	369	11	,	,	PUNCT
ejpam-2415	369	12	332	332	NUM
ejpam-2415	369	13	-	-	SYM
ejpam-2415	369	14	342	342	NUM
ejpam-2415	369	15	339	339	NUM
ejpam-2415	369	16	proof	proof	NOUN
ejpam-2415	369	17	.	.	PUNCT
ejpam-2415	370	1	let	let	VERB
ejpam-2415	370	2	a	a	PRON
ejpam-2415	370	3	be	be	AUX
ejpam-2415	370	4	a	a	DET
ejpam-2415	370	5	baer	baer	PROPN
ejpam-2415	370	6	element	element	NOUN
ejpam-2415	370	7	and	and	CCONJ
ejpam-2415	370	8	p	p	NOUN
ejpam-2415	370	9	be	be	AUX
ejpam-2415	370	10	a	a	DET
ejpam-2415	370	11	minimal	minimal	ADJ
ejpam-2415	370	12	prime	prime	NOUN
ejpam-2415	370	13	in	in	ADP
ejpam-2415	370	14	m	m	PROPN
ejpam-2415	370	15	over	over	ADP
ejpam-2415	370	16	a.	a.	NOUN
ejpam-2415	370	17	assume	assume	VERB
ejpam-2415	370	18	that	that	SCONJ
ejpam-2415	370	19	0	0	NUM
ejpam-2415	370	20	m	m	VERB
ejpam-2415	370	21	:	:	PUNCT
ejpam-2415	370	22	x	x	SYM
ejpam-2415	370	23	=	=	SYM
ejpam-2415	370	24	0	0	NUM
ejpam-2415	370	25	m	m	VERB
ejpam-2415	370	26	:	:	PUNCT
ejpam-2415	370	27	z	z	NOUN
ejpam-2415	370	28	for	for	ADP
ejpam-2415	370	29	some	some	DET
ejpam-2415	370	30	x	x	SYM
ejpam-2415	370	31	,	,	PUNCT
ejpam-2415	370	32	z	z	NOUN
ejpam-2415	370	33	∈	∈	PROPN
ejpam-2415	370	34	l	l	NOUN
ejpam-2415	370	35	such	such	ADJ
ejpam-2415	370	36	that	that	SCONJ
ejpam-2415	370	37	x	x	PRON
ejpam-2415	370	38	is	be	AUX
ejpam-2415	370	39	compact	compact	ADJ
ejpam-2415	370	40	and	and	CCONJ
ejpam-2415	370	41	x	x	PUNCT
ejpam-2415	370	42	i	i	NOUN
ejpam-2415	370	43	m	m	VERB
ejpam-2415	370	44	¶	¶	PROPN
ejpam-2415	370	45	p.	p.	NOUN
ejpam-2415	370	46	there	there	PRON
ejpam-2415	370	47	exists	exist	VERB
ejpam-2415	370	48	a	a	DET
ejpam-2415	370	49	compact	compact	ADJ
ejpam-2415	370	50	element	element	NOUN
ejpam-2415	370	51	y	y	PROPN
ejpam-2415	370	52	∈	∈	PROPN
ejpam-2415	370	53	l	l	NOUN
ejpam-2415	370	54	such	such	ADJ
ejpam-2415	370	55	that	that	SCONJ
ejpam-2415	370	56	y	y	PROPN
ejpam-2415	370	57	i	i	NOUN
ejpam-2415	370	58	m	m	VERB
ejpam-2415	370	59	�	�	PROPN
ejpam-2415	370	60	p	p	PROPN
ejpam-2415	370	61	and	and	CCONJ
ejpam-2415	370	62	xn	xn	PROPN
ejpam-2415	371	1	y	y	PROPN
ejpam-2415	372	1	i	i	PRON
ejpam-2415	372	2	m	m	VERB
ejpam-2415	372	3	¶	¶	VERB
ejpam-2415	372	4	a¶	a¶	X
ejpam-2415	372	5	p	p	NOUN
ejpam-2415	372	6	for	for	ADP
ejpam-2415	372	7	some	some	DET
ejpam-2415	372	8	positive	positive	ADJ
ejpam-2415	372	9	integer	integer	NOUN
ejpam-2415	372	10	n	n	CCONJ
ejpam-2415	372	11	,	,	PUNCT
ejpam-2415	372	12	by	by	ADP
ejpam-2415	372	13	theorem	theorem	NOUN
ejpam-2415	372	14	14	14	NUM
ejpam-2415	372	15	.	.	PUNCT
ejpam-2415	372	16	note	note	VERB
ejpam-2415	372	17	that	that	SCONJ
ejpam-2415	372	18	0	0	NUM
ejpam-2415	372	19	m	m	VERB
ejpam-2415	372	20	:	:	PUNCT
ejpam-2415	373	1	y	y	NOUN
ejpam-2415	373	2	x	x	PUNCT
ejpam-2415	373	3	=	=	PUNCT
ejpam-2415	373	4	(	(	PUNCT
ejpam-2415	373	5	0	0	NUM
ejpam-2415	373	6	m	m	VERB
ejpam-2415	373	7	:	:	PUNCT
ejpam-2415	373	8	x	x	X
ejpam-2415	373	9	)	)	PUNCT
ejpam-2415	373	10	:	:	PUNCT
ejpam-2415	374	1	y	y	PROPN
ejpam-2415	374	2	=	=	SYM
ejpam-2415	374	3	(	(	PUNCT
ejpam-2415	374	4	0	0	NUM
ejpam-2415	374	5	m	m	VERB
ejpam-2415	374	6	:	:	PUNCT
ejpam-2415	374	7	xn	xn	X
ejpam-2415	374	8	)	)	PUNCT
ejpam-2415	374	9	:	:	PUNCT
ejpam-2415	375	1	y	y	NOUN
ejpam-2415	375	2	=	=	PUNCT
ejpam-2415	375	3	0	0	NUM
ejpam-2415	375	4	m	m	VERB
ejpam-2415	375	5	:	:	PUNCT
ejpam-2415	375	6	xn	xn	PROPN
ejpam-2415	375	7	y	y	PROPN
ejpam-2415	375	8	=	=	PUNCT
ejpam-2415	375	9	0	0	NUM
ejpam-2415	375	10	m	m	VERB
ejpam-2415	375	11	:	:	PUNCT
ejpam-2415	375	12	y	y	NOUN
ejpam-2415	375	13	xn	xn	PUNCT
ejpam-2415	376	1	=	=	PUNCT
ejpam-2415	376	2	0	0	NUM
ejpam-2415	376	3	m	m	VERB
ejpam-2415	376	4	:	:	PUNCT
ejpam-2415	377	1	yz	yz	PROPN
ejpam-2415	377	2	.	.	PROPN
ejpam-2415	378	1	as	as	SCONJ
ejpam-2415	378	2	a	a	PRON
ejpam-2415	378	3	is	be	AUX
ejpam-2415	378	4	a	a	DET
ejpam-2415	378	5	baer	baer	PROPN
ejpam-2415	378	6	element	element	NOUN
ejpam-2415	378	7	.	.	PUNCT
ejpam-2415	379	1	by	by	ADP
ejpam-2415	379	2	theorem	theorem	NOUN
ejpam-2415	379	3	17	17	NUM
ejpam-2415	379	4	,	,	PUNCT
ejpam-2415	379	5	x	x	PROPN
ejpam-2415	379	6	y	y	VERB
ejpam-2415	379	7	i	i	NOUN
ejpam-2415	379	8	m	m	VERB
ejpam-2415	379	9	¶	¶	PROPN
ejpam-2415	379	10	a	a	PRON
ejpam-2415	379	11	implies	imply	VERB
ejpam-2415	379	12	yzim	yzim	PROPN
ejpam-2415	379	13	¶	¶	PROPN
ejpam-2415	379	14	a¶	a¶	X
ejpam-2415	380	1	p.	p.	NOUN
ejpam-2415	380	2	hence	hence	ADV
ejpam-2415	380	3	zim	zim	PROPN
ejpam-2415	380	4	¶	¶	PROPN
ejpam-2415	380	5	p	p	PROPN
ejpam-2415	380	6	as	as	SCONJ
ejpam-2415	380	7	p	p	PROPN
ejpam-2415	380	8	is	be	AUX
ejpam-2415	380	9	prime	prime	ADJ
ejpam-2415	380	10	.	.	PUNCT
ejpam-2415	381	1	so	so	ADV
ejpam-2415	381	2	again	again	ADV
ejpam-2415	381	3	by	by	ADP
ejpam-2415	381	4	theorem	theorem	NOUN
ejpam-2415	381	5	17	17	NUM
ejpam-2415	381	6	,	,	PUNCT
ejpam-2415	381	7	p	p	NOUN
ejpam-2415	381	8	is	be	AUX
ejpam-2415	381	9	a	a	DET
ejpam-2415	381	10	baer	baer	PROPN
ejpam-2415	381	11	element	element	NOUN
ejpam-2415	381	12	.	.	PUNCT
ejpam-2415	382	1	the	the	DET
ejpam-2415	382	2	characterization	characterization	NOUN
ejpam-2415	382	3	of	of	ADP
ejpam-2415	382	4	minimal	minimal	ADJ
ejpam-2415	382	5	prime	prime	ADJ
ejpam-2415	382	6	element	element	NOUN
ejpam-2415	382	7	of	of	ADP
ejpam-2415	382	8	m	m	PROPN
ejpam-2415	382	9	is	be	AUX
ejpam-2415	382	10	proved	prove	VERB
ejpam-2415	382	11	in	in	ADP
ejpam-2415	382	12	the	the	DET
ejpam-2415	382	13	next	next	ADJ
ejpam-2415	382	14	theorem	theorem	PROPN
ejpam-2415	382	15	.	.	PUNCT
ejpam-2415	382	16	theorem	theorem	PROPN
ejpam-2415	382	17	20	20	NUM
ejpam-2415	382	18	.	.	PUNCT
ejpam-2415	383	1	let	let	VERB
ejpam-2415	383	2	l	l	NOUN
ejpam-2415	383	3	be	be	AUX
ejpam-2415	383	4	a	a	DET
ejpam-2415	383	5	lattice	lattice	NOUN
ejpam-2415	383	6	module	module	NOUN
ejpam-2415	383	7	and	and	CCONJ
ejpam-2415	383	8	p	p	NOUN
ejpam-2415	383	9	be	be	AUX
ejpam-2415	383	10	a	a	DET
ejpam-2415	383	11	prime	prime	ADJ
ejpam-2415	383	12	element	element	NOUN
ejpam-2415	383	13	of	of	ADP
ejpam-2415	383	14	m.	m.	NOUN
ejpam-2415	383	15	then	then	ADV
ejpam-2415	383	16	p	p	NOUN
ejpam-2415	383	17	is	be	AUX
ejpam-2415	383	18	a	a	DET
ejpam-2415	383	19	minimal	minimal	ADJ
ejpam-2415	383	20	prime	prime	ADJ
ejpam-2415	383	21	element	element	NOUN
ejpam-2415	383	22	if	if	SCONJ
ejpam-2415	383	23	and	and	CCONJ
ejpam-2415	383	24	only	only	ADV
ejpam-2415	383	25	if	if	SCONJ
ejpam-2415	383	26	for	for	ADP
ejpam-2415	383	27	x	x	PROPN
ejpam-2415	383	28	∈	∈	PROPN
ejpam-2415	383	29	l∗	l∗	PROPN
ejpam-2415	383	30	,	,	PUNCT
ejpam-2415	383	31	p	p	NOUN
ejpam-2415	383	32	contains	contain	VERB
ejpam-2415	383	33	precisely	precisely	ADV
ejpam-2415	383	34	one	one	NUM
ejpam-2415	383	35	of	of	ADP
ejpam-2415	383	36	x	x	PUNCT
ejpam-2415	383	37	i	i	PRON
ejpam-2415	383	38	m	m	VERB
ejpam-2415	383	39	and	and	CCONJ
ejpam-2415	383	40	0	0	NUM
ejpam-2415	383	41	m	m	VERB
ejpam-2415	383	42	:	:	PUNCT
ejpam-2415	384	1	x.	x.	NOUN
ejpam-2415	384	2	proof	proof	NOUN
ejpam-2415	384	3	.	.	PUNCT
ejpam-2415	385	1	if	if	SCONJ
ejpam-2415	385	2	part	part	NOUN
ejpam-2415	385	3	:	:	PUNCT
ejpam-2415	385	4	assume	assume	VERB
ejpam-2415	385	5	that	that	SCONJ
ejpam-2415	385	6	for	for	ADP
ejpam-2415	385	7	x	x	SYM
ejpam-2415	385	8	∈	∈	PROPN
ejpam-2415	385	9	l∗,p	l∗,p	NOUN
ejpam-2415	385	10	contains	contain	VERB
ejpam-2415	385	11	precisely	precisely	ADV
ejpam-2415	385	12	one	one	NUM
ejpam-2415	385	13	of	of	ADP
ejpam-2415	385	14	x	x	PUNCT
ejpam-2415	385	15	i	i	PRON
ejpam-2415	385	16	m	m	VERB
ejpam-2415	385	17	and	and	CCONJ
ejpam-2415	385	18	0	0	NUM
ejpam-2415	385	19	m	m	VERB
ejpam-2415	385	20	:	:	PUNCT
ejpam-2415	386	1	x	x	X
ejpam-2415	386	2	.	.	PUNCT
ejpam-2415	387	1	first	first	ADV
ejpam-2415	387	2	assume	assume	VERB
ejpam-2415	387	3	that	that	SCONJ
ejpam-2415	387	4	p	p	NOUN
ejpam-2415	387	5	contains	contain	VERB
ejpam-2415	387	6	x	x	PUNCT
ejpam-2415	387	7	i	i	PRON
ejpam-2415	387	8	m	m	VERB
ejpam-2415	387	9	.	.	PUNCT
ejpam-2415	388	1	but	but	CCONJ
ejpam-2415	388	2	0	0	NUM
ejpam-2415	388	3	m	m	VERB
ejpam-2415	388	4	:	:	PUNCT
ejpam-2415	388	5	x	x	X
ejpam-2415	388	6	�	�	PROPN
ejpam-2415	388	7	p.	p.	NOUN
ejpam-2415	388	8	therefore	therefore	ADV
ejpam-2415	388	9	there	there	PRON
ejpam-2415	388	10	exists	exist	VERB
ejpam-2415	388	11	a	a	DET
ejpam-2415	388	12	compact	compact	ADJ
ejpam-2415	388	13	element	element	NOUN
ejpam-2415	388	14	y	y	PROPN
ejpam-2415	388	15	in	in	ADP
ejpam-2415	388	16	l	l	PROPN
ejpam-2415	388	17	such	such	ADJ
ejpam-2415	388	18	that	that	SCONJ
ejpam-2415	388	19	y	y	PROPN
ejpam-2415	389	1	i	i	PRON
ejpam-2415	389	2	m	m	VERB
ejpam-2415	389	3	¶	¶	PROPN
ejpam-2415	389	4	0	0	NUM
ejpam-2415	389	5	m	m	VERB
ejpam-2415	389	6	:	:	PUNCT
ejpam-2415	390	1	x	x	X
ejpam-2415	390	2	but	but	CCONJ
ejpam-2415	390	3	y	y	PROPN
ejpam-2415	391	1	i	i	PROPN
ejpam-2415	391	2	m	m	VERB
ejpam-2415	391	3	�	�	PROPN
ejpam-2415	391	4	p.	p.	NOUN
ejpam-2415	392	1	thus	thus	ADV
ejpam-2415	392	2	x	x	X
ejpam-2415	392	3	y	y	NOUN
ejpam-2415	393	1	i	i	PRON
ejpam-2415	393	2	m	m	VERB
ejpam-2415	393	3	¶	¶	PROPN
ejpam-2415	393	4	0	0	NUM
ejpam-2415	393	5	m	m	NOUN
ejpam-2415	393	6	.	.	PUNCT
ejpam-2415	394	1	this	this	PRON
ejpam-2415	394	2	shows	show	VERB
ejpam-2415	394	3	that	that	SCONJ
ejpam-2415	394	4	for	for	ADP
ejpam-2415	394	5	each	each	DET
ejpam-2415	394	6	compact	compact	ADJ
ejpam-2415	394	7	element	element	NOUN
ejpam-2415	394	8	x	x	PUNCT
ejpam-2415	394	9	in	in	ADP
ejpam-2415	394	10	l	l	NOUN
ejpam-2415	394	11	,	,	PUNCT
ejpam-2415	394	12	x	x	PROPN
ejpam-2415	394	13	i	i	NOUN
ejpam-2415	394	14	m	m	VERB
ejpam-2415	394	15	¶	¶	PROPN
ejpam-2415	394	16	p	p	X
ejpam-2415	394	17	,	,	PUNCT
ejpam-2415	394	18	there	there	PRON
ejpam-2415	394	19	exist	exist	VERB
ejpam-2415	394	20	a	a	DET
ejpam-2415	394	21	compact	compact	ADJ
ejpam-2415	394	22	element	element	NOUN
ejpam-2415	394	23	y	y	PROPN
ejpam-2415	394	24	in	in	ADP
ejpam-2415	394	25	l	l	PROPN
ejpam-2415	394	26	such	such	ADJ
ejpam-2415	394	27	that	that	SCONJ
ejpam-2415	394	28	y	y	PROPN
ejpam-2415	395	1	i	i	NOUN
ejpam-2415	395	2	m	m	VERB
ejpam-2415	395	3	�	�	PROPN
ejpam-2415	395	4	p	p	NOUN
ejpam-2415	395	5	and	and	CCONJ
ejpam-2415	395	6	x	x	SYM
ejpam-2415	395	7	y	y	PROPN
ejpam-2415	395	8	i	i	NOUN
ejpam-2415	395	9	m	m	VERB
ejpam-2415	395	10	¶	¶	PROPN
ejpam-2415	395	11	0	0	NUM
ejpam-2415	395	12	m	m	NOUN
ejpam-2415	395	13	.	.	PUNCT
ejpam-2415	396	1	by	by	ADP
ejpam-2415	396	2	theorem	theorem	NOUN
ejpam-2415	396	3	6	6	NUM
ejpam-2415	396	4	,	,	PUNCT
ejpam-2415	396	5	it	it	PRON
ejpam-2415	396	6	follows	follow	VERB
ejpam-2415	396	7	that	that	SCONJ
ejpam-2415	396	8	p	p	NOUN
ejpam-2415	396	9	is	be	AUX
ejpam-2415	396	10	a	a	DET
ejpam-2415	396	11	minimal	minimal	ADJ
ejpam-2415	396	12	prime	prime	ADJ
ejpam-2415	396	13	element	element	NOUN
ejpam-2415	396	14	of	of	ADP
ejpam-2415	396	15	m.	m.	NOUN
ejpam-2415	396	16	next	next	ADV
ejpam-2415	396	17	assume	assume	VERB
ejpam-2415	396	18	that	that	SCONJ
ejpam-2415	396	19	0	0	NUM
ejpam-2415	396	20	m	m	VERB
ejpam-2415	396	21	:	:	PUNCT
ejpam-2415	396	22	x	x	X
ejpam-2415	396	23	¶	¶	NOUN
ejpam-2415	396	24	p	p	NOUN
ejpam-2415	397	1	but	but	CCONJ
ejpam-2415	397	2	x	x	PROPN
ejpam-2415	397	3	i	i	NOUN
ejpam-2415	397	4	m	m	VERB
ejpam-2415	397	5	�	�	PROPN
ejpam-2415	397	6	p.	p.	NOUN
ejpam-2415	397	7	let	let	VERB
ejpam-2415	397	8	z	z	NOUN
ejpam-2415	397	9	be	be	AUX
ejpam-2415	397	10	a	a	DET
ejpam-2415	397	11	compact	compact	ADJ
ejpam-2415	397	12	element	element	NOUN
ejpam-2415	397	13	of	of	ADP
ejpam-2415	397	14	l	l	NOUN
ejpam-2415	397	15	such	such	ADJ
ejpam-2415	397	16	that	that	SCONJ
ejpam-2415	397	17	zim	zim	PROPN
ejpam-2415	397	18	¶	¶	PROPN
ejpam-2415	397	19	(	(	PUNCT
ejpam-2415	397	20	0	0	NUM
ejpam-2415	397	21	m	m	VERB
ejpam-2415	397	22	:	:	PUNCT
ejpam-2415	397	23	x	x	X
ejpam-2415	397	24	)	)	PUNCT
ejpam-2415	397	25	¶	¶	PROPN
ejpam-2415	397	26	p.	p.	NOUN
ejpam-2415	398	1	but	but	CCONJ
ejpam-2415	398	2	x	x	X
ejpam-2415	398	3	i	i	VERB
ejpam-2415	398	4	m	m	VERB
ejpam-2415	398	5	�	�	PROPN
ejpam-2415	398	6	p	p	PROPN
ejpam-2415	398	7	and	and	CCONJ
ejpam-2415	398	8	xzim	xzim	PROPN
ejpam-2415	398	9	¶	¶	PROPN
ejpam-2415	398	10	0	0	PROPN
ejpam-2415	398	11	m	m	VERB
ejpam-2415	398	12	.	.	PUNCT
ejpam-2415	399	1	consequently	consequently	ADV
ejpam-2415	399	2	,	,	PUNCT
ejpam-2415	399	3	by	by	ADP
ejpam-2415	399	4	theorem	theorem	NOUN
ejpam-2415	399	5	6	6	NUM
ejpam-2415	399	6	p	p	NOUN
ejpam-2415	399	7	is	be	AUX
ejpam-2415	399	8	a	a	DET
ejpam-2415	399	9	minimal	minimal	ADJ
ejpam-2415	399	10	prime	prime	ADJ
ejpam-2415	399	11	element	element	NOUN
ejpam-2415	399	12	.	.	PUNCT
ejpam-2415	400	1	thus	thus	ADV
ejpam-2415	400	2	the	the	DET
ejpam-2415	400	3	condition	condition	NOUN
ejpam-2415	400	4	is	be	AUX
ejpam-2415	400	5	sufficient	sufficient	ADJ
ejpam-2415	400	6	.	.	PUNCT
ejpam-2415	401	1	only	only	ADV
ejpam-2415	401	2	if	if	SCONJ
ejpam-2415	401	3	part	part	NOUN
ejpam-2415	401	4	:	:	PUNCT
ejpam-2415	401	5	assume	assume	VERB
ejpam-2415	401	6	that	that	SCONJ
ejpam-2415	401	7	p	p	NOUN
ejpam-2415	401	8	is	be	AUX
ejpam-2415	401	9	a	a	DET
ejpam-2415	401	10	minimal	minimal	ADJ
ejpam-2415	401	11	prime	prime	ADJ
ejpam-2415	401	12	element	element	NOUN
ejpam-2415	401	13	of	of	ADP
ejpam-2415	401	14	m.	m.	NOUN
ejpam-2415	401	15	let	let	VERB
ejpam-2415	401	16	x	x	PRON
ejpam-2415	401	17	be	be	AUX
ejpam-2415	401	18	a	a	DET
ejpam-2415	401	19	compact	compact	ADJ
ejpam-2415	401	20	element	element	NOUN
ejpam-2415	401	21	of	of	ADP
ejpam-2415	401	22	l.	l.	PROPN
ejpam-2415	401	23	suppose	suppose	VERB
ejpam-2415	401	24	if	if	SCONJ
ejpam-2415	401	25	possible	possible	ADJ
ejpam-2415	401	26	x	x	PUNCT
ejpam-2415	401	27	i	i	NOUN
ejpam-2415	401	28	m	m	VERB
ejpam-2415	401	29	¶	¶	PROPN
ejpam-2415	401	30	p.	p.	NOUN
ejpam-2415	401	31	then	then	ADV
ejpam-2415	401	32	by	by	ADP
ejpam-2415	401	33	theorem	theorem	NOUN
ejpam-2415	401	34	6	6	NUM
ejpam-2415	401	35	,	,	PUNCT
ejpam-2415	401	36	there	there	PRON
ejpam-2415	401	37	exist	exist	VERB
ejpam-2415	401	38	a	a	DET
ejpam-2415	401	39	compact	compact	ADJ
ejpam-2415	401	40	element	element	NOUN
ejpam-2415	401	41	y	y	PROPN
ejpam-2415	401	42	in	in	ADP
ejpam-2415	401	43	l	l	PROPN
ejpam-2415	401	44	such	such	ADJ
ejpam-2415	401	45	that	that	SCONJ
ejpam-2415	401	46	y	y	PROPN
ejpam-2415	402	1	i	i	NOUN
ejpam-2415	402	2	m	m	VERB
ejpam-2415	402	3	�	�	PROPN
ejpam-2415	402	4	p	p	PROPN
ejpam-2415	402	5	and	and	CCONJ
ejpam-2415	402	6	xn	xn	PROPN
ejpam-2415	402	7	y	y	PROPN
ejpam-2415	402	8	i	i	PRON
ejpam-2415	402	9	m	m	VERB
ejpam-2415	402	10	=	=	ADJ
ejpam-2415	402	11	0	0	NUM
ejpam-2415	402	12	m	m	VERB
ejpam-2415	402	13	for	for	ADP
ejpam-2415	402	14	some	some	DET
ejpam-2415	402	15	positive	positive	ADJ
ejpam-2415	402	16	integer	integer	NOUN
ejpam-2415	402	17	n.	n.	NOUN
ejpam-2415	402	18	consequently	consequently	ADV
ejpam-2415	402	19	,	,	PUNCT
ejpam-2415	402	20	y	y	PROPN
ejpam-2415	402	21	i	i	PRON
ejpam-2415	402	22	m	m	VERB
ejpam-2415	402	23	¶	¶	PROPN
ejpam-2415	402	24	0	0	NUM
ejpam-2415	402	25	m	m	VERB
ejpam-2415	402	26	:	:	PUNCT
ejpam-2415	402	27	xn	xn	PUNCT
ejpam-2415	403	1	=	=	SYM
ejpam-2415	403	2	0	0	NUM
ejpam-2415	403	3	m	m	VERB
ejpam-2415	403	4	:	:	PUNCT
ejpam-2415	403	5	x	x	X
ejpam-2415	403	6	.	.	PUNCT
ejpam-2415	404	1	this	this	PRON
ejpam-2415	404	2	implies	imply	VERB
ejpam-2415	404	3	that	that	SCONJ
ejpam-2415	404	4	0	0	NUM
ejpam-2415	404	5	m	m	VERB
ejpam-2415	404	6	:	:	PUNCT
ejpam-2415	404	7	x	x	X
ejpam-2415	404	8	�	�	PROPN
ejpam-2415	404	9	p.	p.	PROPN
ejpam-2415	404	10	now	now	ADV
ejpam-2415	404	11	suppose	suppose	VERB
ejpam-2415	404	12	if	if	SCONJ
ejpam-2415	404	13	possible	possible	ADJ
ejpam-2415	404	14	x	x	PUNCT
ejpam-2415	404	15	i	i	NOUN
ejpam-2415	404	16	m	m	VERB
ejpam-2415	404	17	�	�	PROPN
ejpam-2415	404	18	p	p	NOUN
ejpam-2415	404	19	and	and	CCONJ
ejpam-2415	404	20	0	0	NUM
ejpam-2415	404	21	m	m	VERB
ejpam-2415	404	22	:	:	PUNCT
ejpam-2415	404	23	x	x	X
ejpam-2415	404	24	�	�	PROPN
ejpam-2415	404	25	p.	p.	NOUN
ejpam-2415	404	26	then	then	ADV
ejpam-2415	404	27	there	there	PRON
ejpam-2415	404	28	exist	exist	VERB
ejpam-2415	404	29	a	a	DET
ejpam-2415	404	30	compact	compact	ADJ
ejpam-2415	404	31	element	element	NOUN
ejpam-2415	404	32	y	y	PROPN
ejpam-2415	404	33	in	in	ADP
ejpam-2415	404	34	l	l	PROPN
ejpam-2415	404	35	such	such	ADJ
ejpam-2415	404	36	that	that	SCONJ
ejpam-2415	404	37	y	y	PROPN
ejpam-2415	404	38	i	i	PRON
ejpam-2415	404	39	m	m	VERB
ejpam-2415	404	40	¶	¶	PROPN
ejpam-2415	404	41	0	0	NUM
ejpam-2415	404	42	m	m	VERB
ejpam-2415	404	43	:	:	PUNCT
ejpam-2415	405	1	x	x	X
ejpam-2415	405	2	but	but	CCONJ
ejpam-2415	405	3	y	y	PROPN
ejpam-2415	406	1	i	i	PROPN
ejpam-2415	406	2	m	m	VERB
ejpam-2415	406	3	�	�	PROPN
ejpam-2415	406	4	p.	p.	NOUN
ejpam-2415	406	5	hence	hence	ADV
ejpam-2415	406	6	we	we	PRON
ejpam-2415	406	7	have	have	VERB
ejpam-2415	406	8	x	x	X
ejpam-2415	406	9	y	y	VERB
ejpam-2415	406	10	i	i	PRON
ejpam-2415	406	11	m	m	VERB
ejpam-2415	406	12	¶	¶	PROPN
ejpam-2415	406	13	0	0	NUM
ejpam-2415	407	1	m	m	PROPN
ejpam-2415	408	1	and	and	CCONJ
ejpam-2415	408	2	so	so	ADV
ejpam-2415	408	3	x	x	VERB
ejpam-2415	408	4	y	y	NOUN
ejpam-2415	408	5	i	i	NOUN
ejpam-2415	408	6	m	m	VERB
ejpam-2415	408	7	¶	¶	NOUN
ejpam-2415	408	8	p.	p.	NOUN
ejpam-2415	409	1	but	but	CCONJ
ejpam-2415	409	2	x	x	X
ejpam-2415	409	3	i	i	VERB
ejpam-2415	409	4	m	m	VERB
ejpam-2415	409	5	�	�	PROPN
ejpam-2415	409	6	p	p	NOUN
ejpam-2415	409	7	and	and	CCONJ
ejpam-2415	409	8	y	y	PROPN
ejpam-2415	410	1	i	i	PROPN
ejpam-2415	410	2	m	m	VERB
ejpam-2415	410	3	�	�	PROPN
ejpam-2415	410	4	p	p	NOUN
ejpam-2415	410	5	which	which	PRON
ejpam-2415	410	6	contradicts	contradict	VERB
ejpam-2415	410	7	the	the	DET
ejpam-2415	410	8	fact	fact	NOUN
ejpam-2415	410	9	that	that	SCONJ
ejpam-2415	410	10	p	p	NOUN
ejpam-2415	410	11	is	be	AUX
ejpam-2415	410	12	prime	prime	ADJ
ejpam-2415	410	13	element	element	NOUN
ejpam-2415	410	14	of	of	ADP
ejpam-2415	410	15	m.	m.	NOUN
ejpam-2415	410	16	this	this	PRON
ejpam-2415	410	17	shows	show	VERB
ejpam-2415	410	18	that	that	SCONJ
ejpam-2415	410	19	p	p	NOUN
ejpam-2415	410	20	contains	contain	VERB
ejpam-2415	410	21	precisely	precisely	ADV
ejpam-2415	410	22	one	one	NUM
ejpam-2415	410	23	of	of	ADP
ejpam-2415	410	24	x	x	PUNCT
ejpam-2415	410	25	i	i	PRON
ejpam-2415	410	26	m	m	VERB
ejpam-2415	410	27	and	and	CCONJ
ejpam-2415	410	28	(	(	PUNCT
ejpam-2415	410	29	0	0	NUM
ejpam-2415	410	30	m	m	VERB
ejpam-2415	410	31	:	:	PUNCT
ejpam-2415	410	32	x	x	X
ejpam-2415	410	33	)	)	PUNCT
ejpam-2415	410	34	.	.	PUNCT
ejpam-2415	411	1	the	the	DET
ejpam-2415	411	2	relation	relation	NOUN
ejpam-2415	411	3	between	between	ADP
ejpam-2415	411	4	∗-element	∗-element	NOUN
ejpam-2415	411	5	of	of	ADP
ejpam-2415	411	6	m	m	PROPN
ejpam-2415	411	7	and	and	CCONJ
ejpam-2415	411	8	a	a	DET
ejpam-2415	411	9	minimal	minimal	ADJ
ejpam-2415	411	10	prime	prime	ADJ
ejpam-2415	411	11	element	element	NOUN
ejpam-2415	411	12	over	over	ADP
ejpam-2415	411	13	it	it	PRON
ejpam-2415	411	14	is	be	AUX
ejpam-2415	411	15	established	establish	VERB
ejpam-2415	411	16	in	in	ADP
ejpam-2415	411	17	the	the	DET
ejpam-2415	411	18	next	next	ADJ
ejpam-2415	411	19	theorem	theorem	PROPN
ejpam-2415	411	20	.	.	PUNCT
ejpam-2415	411	21	theorem	theorem	PROPN
ejpam-2415	411	22	21	21	NUM
ejpam-2415	411	23	.	.	PUNCT
ejpam-2415	412	1	if	if	SCONJ
ejpam-2415	412	2	a	a	PRON
ejpam-2415	412	3	is	be	AUX
ejpam-2415	412	4	a	a	DET
ejpam-2415	412	5	∗-element	∗-element	NOUN
ejpam-2415	412	6	of	of	ADP
ejpam-2415	412	7	m	m	PRON
ejpam-2415	412	8	then	then	ADV
ejpam-2415	412	9	every	every	DET
ejpam-2415	412	10	minimal	minimal	ADJ
ejpam-2415	412	11	prime	prime	NOUN
ejpam-2415	412	12	over	over	ADP
ejpam-2415	412	13	a	a	PRON
ejpam-2415	412	14	is	be	AUX
ejpam-2415	412	15	a	a	DET
ejpam-2415	412	16	minimal	minimal	ADJ
ejpam-2415	412	17	prime	prime	NOUN
ejpam-2415	412	18	.	.	PUNCT
ejpam-2415	413	1	proof	proof	NOUN
ejpam-2415	413	2	.	.	PUNCT
ejpam-2415	414	1	let	let	VERB
ejpam-2415	414	2	p	p	PRON
ejpam-2415	414	3	be	be	AUX
ejpam-2415	414	4	a	a	DET
ejpam-2415	414	5	minimal	minimal	ADJ
ejpam-2415	414	6	prime	prime	ADJ
ejpam-2415	414	7	element	element	NOUN
ejpam-2415	414	8	of	of	ADP
ejpam-2415	414	9	m	m	PROPN
ejpam-2415	414	10	over	over	ADP
ejpam-2415	414	11	a.	a.	NOUN
ejpam-2415	414	12	we	we	PRON
ejpam-2415	414	13	know	know	VERB
ejpam-2415	414	14	by	by	ADP
ejpam-2415	414	15	theorem	theorem	NOUN
ejpam-2415	414	16	8	8	NUM
ejpam-2415	414	17	and	and	CCONJ
ejpam-2415	414	18	theorem	theorem	VERB
ejpam-2415	414	19	18	18	NUM
ejpam-2415	414	20	,	,	PUNCT
ejpam-2415	414	21	a	a	DET
ejpam-2415	414	22	∗-element	∗-element	NOUN
ejpam-2415	414	23	a	a	PRON
ejpam-2415	414	24	is	be	AUX
ejpam-2415	414	25	a	a	DET
ejpam-2415	414	26	baer	baer	PROPN
ejpam-2415	414	27	element	element	NOUN
ejpam-2415	414	28	and	and	CCONJ
ejpam-2415	414	29	(	(	PUNCT
ejpam-2415	414	30	a	a	PRON
ejpam-2415	414	31	:	:	PUNCT
ejpam-2415	414	32	i	i	PRON
ejpam-2415	414	33	m	m	PROPN
ejpam-2415	414	34	)	)	PUNCT
ejpam-2415	414	35	is	be	AUX
ejpam-2415	414	36	a	a	DET
ejpam-2415	414	37	radical	radical	ADJ
ejpam-2415	414	38	element	element	NOUN
ejpam-2415	414	39	.	.	PUNCT
ejpam-2415	415	1	let	let	VERB
ejpam-2415	415	2	x	x	PRON
ejpam-2415	415	3	∈	∈	PROPN
ejpam-2415	415	4	l∗	l∗	NOUN
ejpam-2415	415	5	be	be	AUX
ejpam-2415	415	6	such	such	ADJ
ejpam-2415	415	7	that	that	SCONJ
ejpam-2415	415	8	x	x	PUNCT
ejpam-2415	415	9	i	i	NOUN
ejpam-2415	415	10	m	m	VERB
ejpam-2415	415	11	¶	¶	PROPN
ejpam-2415	415	12	p.	p.	NOUN
ejpam-2415	416	1	but	but	CCONJ
ejpam-2415	416	2	p	p	NOUN
ejpam-2415	416	3	is	be	AUX
ejpam-2415	416	4	a	a	DET
ejpam-2415	416	5	minimal	minimal	ADJ
ejpam-2415	416	6	prime	prime	NOUN
ejpam-2415	416	7	over	over	ADP
ejpam-2415	416	8	a.	a.	NOUN
ejpam-2415	416	9	then	then	ADV
ejpam-2415	416	10	by	by	ADP
ejpam-2415	416	11	theorem	theorem	NOUN
ejpam-2415	416	12	2	2	NUM
ejpam-2415	416	13	there	there	ADV
ejpam-2415	416	14	exists	exist	VERB
ejpam-2415	416	15	y	y	PROPN
ejpam-2415	416	16	∈	∈	PROPN
ejpam-2415	416	17	l∗	l∗	PROPN
ejpam-2415	416	18	such	such	ADJ
ejpam-2415	416	19	that	that	SCONJ
ejpam-2415	416	20	y	y	PROPN
ejpam-2415	417	1	i	i	NOUN
ejpam-2415	417	2	m	m	VERB
ejpam-2415	417	3	�	�	PROPN
ejpam-2415	417	4	p	p	PROPN
ejpam-2415	417	5	and	and	CCONJ
ejpam-2415	417	6	xn	xn	PROPN
ejpam-2415	417	7	y	y	PROPN
ejpam-2415	417	8	i	i	PRON
ejpam-2415	417	9	m	m	VERB
ejpam-2415	417	10	¶	¶	NOUN
ejpam-2415	417	11	a	a	PRON
ejpam-2415	417	12	i.e.	i.e.	X
ejpam-2415	417	13	xn	xn	PROPN
ejpam-2415	417	14	y	y	PROPN
ejpam-2415	417	15	¶	¶	PROPN
ejpam-2415	417	16	a	a	PRON
ejpam-2415	417	17	:	:	PUNCT
ejpam-2415	417	18	i	i	PRON
ejpam-2415	417	19	m	m	VERB
ejpam-2415	417	20	.	.	PUNCT
ejpam-2415	418	1	so	so	ADV
ejpam-2415	418	2	xn	xn	PROPN
ejpam-2415	419	1	yn	yn	PROPN
ejpam-2415	419	2	¶	¶	PROPN
ejpam-2415	419	3	a	a	PRON
ejpam-2415	419	4	:	:	PUNCT
ejpam-2415	419	5	i	i	PRON
ejpam-2415	419	6	m	m	VERB
ejpam-2415	419	7	i.e.	i.e.	X
ejpam-2415	419	8	x	x	VERB
ejpam-2415	419	9	y	y	PROPN
ejpam-2415	419	10	¶	¶	PROPN
ejpam-2415	419	11	p	p	PROPN
ejpam-2415	419	12	(	(	PUNCT
ejpam-2415	419	13	a	a	PRON
ejpam-2415	419	14	:	:	PUNCT
ejpam-2415	419	15	i	i	PRON
ejpam-2415	419	16	m	m	VERB
ejpam-2415	419	17	)	)	PUNCT
ejpam-2415	419	18	=	=	SYM
ejpam-2415	419	19	(	(	PUNCT
ejpam-2415	419	20	a	a	X
ejpam-2415	419	21	:	:	PUNCT
ejpam-2415	419	22	i	i	PRON
ejpam-2415	419	23	m	m	PROPN
ejpam-2415	419	24	)	)	PUNCT
ejpam-2415	419	25	.	.	PUNCT
ejpam-2415	420	1	by	by	ADP
ejpam-2415	420	2	hyphothesis	hyphothesis	NOUN
ejpam-2415	420	3	,	,	PUNCT
ejpam-2415	420	4	x	x	PROPN
ejpam-2415	420	5	y	y	PROPN
ejpam-2415	420	6	is	be	AUX
ejpam-2415	420	7	compact	compact	ADJ
ejpam-2415	420	8	and	and	CCONJ
ejpam-2415	420	9	x	x	SYM
ejpam-2415	420	10	y	y	PROPN
ejpam-2415	421	1	i	i	PRON
ejpam-2415	421	2	m	m	VERB
ejpam-2415	421	3	¶	¶	NUM
ejpam-2415	421	4	a=	a=	PROPN
ejpam-2415	421	5	0f	0f	PROPN
ejpam-2415	421	6	m	m	PROPN
ejpam-2415	421	7	,	,	PUNCT
ejpam-2415	421	8	for	for	ADP
ejpam-2415	421	9	some	some	DET
ejpam-2415	421	10	filter	filter	NOUN
ejpam-2415	421	11	f	f	NOUN
ejpam-2415	421	12	of	of	ADP
ejpam-2415	421	13	l∗	l∗	PROPN
ejpam-2415	422	1	such	such	ADJ
ejpam-2415	422	2	that	that	PRON
ejpam-2415	422	3	0	0	NUM
ejpam-2415	422	4	/∈	/∈	NUM
ejpam-2415	423	1	f	f	PROPN
ejpam-2415	423	2	.	.	PUNCT
ejpam-2415	424	1	hence	hence	ADV
ejpam-2415	424	2	x	x	PUNCT
ejpam-2415	424	3	y	y	NOUN
ejpam-2415	424	4	i	i	NOUN
ejpam-2415	424	5	m	m	VERB
ejpam-2415	424	6	d	d	NOUN
ejpam-2415	424	7	=	=	PUNCT
ejpam-2415	424	8	0	0	NUM
ejpam-2415	424	9	m	m	VERB
ejpam-2415	424	10	for	for	ADP
ejpam-2415	424	11	some	some	DET
ejpam-2415	424	12	d	d	PROPN
ejpam-2415	424	13	∈	∈	PROPN
ejpam-2415	424	14	f	f	X
ejpam-2415	424	15	.	.	PUNCT
ejpam-2415	425	1	we	we	PRON
ejpam-2415	425	2	show	show	VERB
ejpam-2415	425	3	that	that	SCONJ
ejpam-2415	425	4	there	there	PRON
ejpam-2415	425	5	is	be	VERB
ejpam-2415	425	6	no	no	DET
ejpam-2415	425	7	compact	compact	ADJ
ejpam-2415	425	8	element	element	NOUN
ejpam-2415	425	9	x	x	PUNCT
ejpam-2415	425	10	in	in	ADP
ejpam-2415	425	11	f	f	PROPN
ejpam-2415	425	12	such	such	ADJ
ejpam-2415	425	13	that	that	SCONJ
ejpam-2415	425	14	x	x	PROPN
ejpam-2415	426	1	i	i	NOUN
ejpam-2415	426	2	m	m	VERB
ejpam-2415	426	3	¶	¶	PROPN
ejpam-2415	426	4	p.	p.	NOUN
ejpam-2415	426	5	suppose	suppose	VERB
ejpam-2415	426	6	there	there	PRON
ejpam-2415	426	7	is	be	VERB
ejpam-2415	426	8	compact	compact	ADJ
ejpam-2415	426	9	element	element	NOUN
ejpam-2415	426	10	z	z	NOUN
ejpam-2415	426	11	in	in	ADP
ejpam-2415	426	12	l	l	PROPN
ejpam-2415	427	1	such	such	ADJ
ejpam-2415	427	2	that	that	SCONJ
ejpam-2415	427	3	zim	zim	PROPN
ejpam-2415	427	4	¶	¶	PROPN
ejpam-2415	427	5	p	p	PROPN
ejpam-2415	427	6	and	and	CCONJ
ejpam-2415	427	7	z	z	PROPN
ejpam-2415	427	8	∈	∈	PROPN
ejpam-2415	427	9	f	f	X
ejpam-2415	427	10	.	.	PUNCT
ejpam-2415	428	1	then	then	ADV
ejpam-2415	428	2	by	by	ADP
ejpam-2415	428	3	theorem	theorem	NOUN
ejpam-2415	428	4	3	3	NUM
ejpam-2415	428	5	,	,	PUNCT
ejpam-2415	428	6	0	0	NUM
ejpam-2415	428	7	m	m	AUX
ejpam-2415	428	8	:	:	PUNCT
ejpam-2415	428	9	z	z	PROPN
ejpam-2415	428	10	¶	¶	PROPN
ejpam-2415	428	11	0f	0f	PROPN
ejpam-2415	429	1	=	=	SYM
ejpam-2415	429	2	a¶	a¶	NOUN
ejpam-2415	429	3	p.	p.	NOUN
ejpam-2415	429	4	this	this	PRON
ejpam-2415	429	5	contradict	contradict	VERB
ejpam-2415	429	6	the	the	DET
ejpam-2415	429	7	fact	fact	NOUN
ejpam-2415	429	8	that	that	SCONJ
ejpam-2415	429	9	p	p	NOUN
ejpam-2415	429	10	contains	contain	VERB
ejpam-2415	429	11	precisely	precisely	ADV
ejpam-2415	429	12	one	one	NUM
ejpam-2415	429	13	of	of	ADP
ejpam-2415	429	14	zim	zim	PROPN
ejpam-2415	429	15	and	and	CCONJ
ejpam-2415	429	16	0	0	NUM
ejpam-2415	429	17	m	m	VERB
ejpam-2415	429	18	:	:	PUNCT
ejpam-2415	429	19	z	z	X
ejpam-2415	429	20	where	where	SCONJ
ejpam-2415	429	21	z	z	PROPN
ejpam-2415	429	22	∈	∈	PROPN
ejpam-2415	429	23	l∗.	l∗.	NOUN
ejpam-2415	429	24	hence	hence	ADV
ejpam-2415	429	25	there	there	PRON
ejpam-2415	429	26	is	be	VERB
ejpam-2415	429	27	no	no	DET
ejpam-2415	429	28	compact	compact	ADJ
ejpam-2415	429	29	element	element	NOUN
ejpam-2415	429	30	x	x	PUNCT
ejpam-2415	429	31	in	in	ADP
ejpam-2415	429	32	f	f	PROPN
ejpam-2415	429	33	such	such	ADJ
ejpam-2415	429	34	that	that	SCONJ
ejpam-2415	429	35	x	x	PROPN
ejpam-2415	430	1	i	i	NOUN
ejpam-2415	430	2	m	m	VERB
ejpam-2415	430	3	¶	¶	PROPN
ejpam-2415	430	4	p.	p.	NOUN
ejpam-2415	431	1	this	this	PRON
ejpam-2415	431	2	implies	imply	VERB
ejpam-2415	431	3	that	that	SCONJ
ejpam-2415	431	4	dim	dim	VERB
ejpam-2415	431	5	6¶	6¶	NUM
ejpam-2415	431	6	p.	p.	NOUN
ejpam-2415	431	7	as	as	SCONJ
ejpam-2415	431	8	p	p	PROPN
ejpam-2415	431	9	is	be	AUX
ejpam-2415	431	10	prime	prime	ADJ
ejpam-2415	431	11	,	,	PUNCT
ejpam-2415	431	12	dim	dim	ADJ
ejpam-2415	431	13	6¶	6¶	NUM
ejpam-2415	431	14	p	p	NOUN
ejpam-2415	432	1	and	and	CCONJ
ejpam-2415	432	2	y	y	PROPN
ejpam-2415	432	3	i	i	PRON
ejpam-2415	432	4	m	m	VERB
ejpam-2415	432	5	6¶	6¶	NUM
ejpam-2415	432	6	p	p	NOUN
ejpam-2415	432	7	implies	imply	VERB
ejpam-2415	432	8	yd	yd	ADP
ejpam-2415	433	1	i	i	PRON
ejpam-2415	433	2	m	m	VERB
ejpam-2415	433	3	6¶	6¶	NUM
ejpam-2415	434	1	p.	p.	NOUN
ejpam-2415	434	2	thus	thus	ADV
ejpam-2415	434	3	x	x	X
ejpam-2415	434	4	yd	yd	VERB
ejpam-2415	434	5	i	i	PRON
ejpam-2415	434	6	m	m	VERB
ejpam-2415	434	7	=	=	ADJ
ejpam-2415	434	8	0	0	NUM
ejpam-2415	434	9	m	m	NOUN
ejpam-2415	434	10	¶	¶	NOUN
ejpam-2415	434	11	p	p	NOUN
ejpam-2415	434	12	and	and	CCONJ
ejpam-2415	434	13	yd	yd	ADP
ejpam-2415	434	14	i	i	PRON
ejpam-2415	434	15	m	m	VERB
ejpam-2415	434	16	6¶	6¶	NUM
ejpam-2415	434	17	p.	p.	NOUN
ejpam-2415	434	18	therefore	therefore	ADV
ejpam-2415	434	19	by	by	ADP
ejpam-2415	434	20	theorem	theorem	NOUN
ejpam-2415	434	21	6	6	NUM
ejpam-2415	434	22	,	,	PUNCT
ejpam-2415	434	23	p	p	NOUN
ejpam-2415	434	24	is	be	AUX
ejpam-2415	434	25	minimal	minimal	ADJ
ejpam-2415	434	26	prime	prime	NOUN
ejpam-2415	434	27	.	.	PUNCT
ejpam-2415	435	1	c	c	PROPN
ejpam-2415	435	2	manjarekar	manjarekar	PROPN
ejpam-2415	435	3	,	,	PUNCT
ejpam-2415	435	4	u	u	NOUN
ejpam-2415	435	5	kandale	kandale	PROPN
ejpam-2415	435	6	/	/	SYM
ejpam-2415	435	7	eur	eur	PROPN
ejpam-2415	435	8	.	.	PUNCT
ejpam-2415	436	1	j.	j.	PROPN
ejpam-2415	436	2	pure	pure	PROPN
ejpam-2415	436	3	appl	appl	PROPN
ejpam-2415	436	4	.	.	PROPN
ejpam-2415	436	5	math	math	PROPN
ejpam-2415	436	6	,	,	PUNCT
ejpam-2415	436	7	8	8	NUM
ejpam-2415	436	8	(	(	PUNCT
ejpam-2415	436	9	2015	2015	NUM
ejpam-2415	436	10	)	)	PUNCT
ejpam-2415	436	11	,	,	PUNCT
ejpam-2415	436	12	332	332	NUM
ejpam-2415	436	13	-	-	SYM
ejpam-2415	436	14	342	342	NUM
ejpam-2415	436	15	340	340	NUM
ejpam-2415	436	16	remark	remark	NOUN
ejpam-2415	436	17	2	2	NUM
ejpam-2415	436	18	.	.	PUNCT
ejpam-2415	436	19	by	by	ADP
ejpam-2415	436	20	theorem	theorem	NOUN
ejpam-2415	436	21	7	7	NUM
ejpam-2415	437	1	,	,	PUNCT
ejpam-2415	437	2	we	we	PRON
ejpam-2415	437	3	infer	infer	VERB
ejpam-2415	437	4	that	that	SCONJ
ejpam-2415	437	5	every	every	DET
ejpam-2415	437	6	minimal	minimal	ADJ
ejpam-2415	437	7	prime	prime	ADJ
ejpam-2415	437	8	element	element	NOUN
ejpam-2415	437	9	is	be	AUX
ejpam-2415	437	10	a	a	DET
ejpam-2415	437	11	∗-element	∗-element	NOUN
ejpam-2415	437	12	and	and	CCONJ
ejpam-2415	437	13	it	it	PRON
ejpam-2415	437	14	is	be	AUX
ejpam-2415	437	15	a	a	DET
ejpam-2415	437	16	baer	baer	PROPN
ejpam-2415	437	17	element	element	NOUN
ejpam-2415	437	18	.	.	PUNCT
ejpam-2415	438	1	therefore	therefore	ADV
ejpam-2415	438	2	by	by	ADP
ejpam-2415	438	3	theorem	theorem	NOUN
ejpam-2415	438	4	21	21	NUM
ejpam-2415	438	5	,	,	PUNCT
ejpam-2415	438	6	if	if	SCONJ
ejpam-2415	438	7	a	a	PRON
ejpam-2415	438	8	is	be	AUX
ejpam-2415	438	9	the	the	DET
ejpam-2415	438	10	meet	meet	NOUN
ejpam-2415	438	11	of	of	ADP
ejpam-2415	438	12	all	all	DET
ejpam-2415	438	13	minimal	minimal	ADJ
ejpam-2415	438	14	prime	prime	ADJ
ejpam-2415	438	15	elements	element	NOUN
ejpam-2415	438	16	containing	contain	VERB
ejpam-2415	438	17	it	it	PRON
ejpam-2415	438	18	,	,	PUNCT
ejpam-2415	438	19	a	a	PRON
ejpam-2415	438	20	is	be	AUX
ejpam-2415	438	21	a	a	DET
ejpam-2415	438	22	baer	baer	PROPN
ejpam-2415	438	23	element	element	NOUN
ejpam-2415	438	24	.	.	PUNCT
ejpam-2415	439	1	notation	notation	NOUN
ejpam-2415	439	2	:	:	PUNCT
ejpam-2415	439	3	for	for	ADP
ejpam-2415	439	4	a	a	DET
ejpam-2415	439	5	family	family	NOUN
ejpam-2415	439	6	{	{	PUNCT
ejpam-2415	439	7	aα	aα	NOUN
ejpam-2415	439	8	}	}	PUNCT
ejpam-2415	439	9	of	of	ADP
ejpam-2415	439	10	baer	baer	PROPN
ejpam-2415	439	11	elements	element	NOUN
ejpam-2415	439	12	of	of	ADP
ejpam-2415	439	13	l	l	NOUN
ejpam-2415	439	14	we	we	PRON
ejpam-2415	439	15	define	define	VERB
ejpam-2415	439	16	,	,	PUNCT
ejpam-2415	439	17	⊻aα	⊻aα	PROPN
ejpam-2415	439	18	=	=	SYM
ejpam-2415	439	19	∨{x	∨{x	PROPN
ejpam-2415	440	1	i	i	PRON
ejpam-2415	440	2	m	m	VERB
ejpam-2415	440	3	,	,	PUNCT
ejpam-2415	440	4	x	x	SYM
ejpam-2415	440	5	∈	∈	PROPN
ejpam-2415	440	6	l∗	l∗	NOUN
ejpam-2415	440	7	|	|	ADV
ejpam-2415	440	8	0	0	NUM
ejpam-2415	440	9	m	m	VERB
ejpam-2415	440	10	:	:	PUNCT
ejpam-2415	440	11	(	(	PUNCT
ejpam-2415	440	12	x1	x1	PROPN
ejpam-2415	440	13	∨	∨	NUM
ejpam-2415	440	14	x2	x2	PROPN
ejpam-2415	440	15	.	.	PUNCT
ejpam-2415	440	16	.	.	PUNCT
ejpam-2415	441	1	.∨	.∨	PUNCT
ejpam-2415	442	1	xn)im	xn)im	PUNCT
ejpam-2415	442	2	¶	¶	PROPN
ejpam-2415	442	3	0	0	NUM
ejpam-2415	442	4	m	m	VERB
ejpam-2415	442	5	:	:	PUNCT
ejpam-2415	442	6	x	x	PUNCT
ejpam-2415	442	7	i	i	VERB
ejpam-2415	442	8	m	m	VERB
ejpam-2415	442	9	,	,	PUNCT
ejpam-2415	442	10	for	for	ADP
ejpam-2415	442	11	some	some	DET
ejpam-2415	442	12	compact	compact	ADJ
ejpam-2415	442	13	elements	element	NOUN
ejpam-2415	442	14	x	x	PUNCT
ejpam-2415	442	15	j	j	NOUN
ejpam-2415	442	16	i	i	NOUN
ejpam-2415	442	17	m	m	VERB
ejpam-2415	442	18	¶	¶	PROPN
ejpam-2415	442	19	aα	aα	PROPN
ejpam-2415	442	20	j	j	PROPN
ejpam-2415	442	21	and	and	CCONJ
ejpam-2415	442	22	some	some	DET
ejpam-2415	442	23	j	j	NOUN
ejpam-2415	442	24	=	=	SYM
ejpam-2415	442	25	1,2	1,2	NUM
ejpam-2415	442	26	,	,	PUNCT
ejpam-2415	442	27	.	.	PUNCT
ejpam-2415	442	28	.	.	PUNCT
ejpam-2415	442	29	.	.	PUNCT
ejpam-2415	442	30	,	,	PUNCT
ejpam-2415	442	31	n	n	CCONJ
ejpam-2415	442	32	}	}	PUNCT
ejpam-2415	442	33	.	.	PUNCT
ejpam-2415	443	1	the	the	DET
ejpam-2415	443	2	important	important	ADJ
ejpam-2415	443	3	property	property	NOUN
ejpam-2415	443	4	of	of	ADP
ejpam-2415	443	5	a	a	DET
ejpam-2415	443	6	family	family	NOUN
ejpam-2415	443	7	of	of	ADP
ejpam-2415	443	8	baer	baer	PROPN
ejpam-2415	443	9	elements	element	NOUN
ejpam-2415	443	10	is	be	AUX
ejpam-2415	443	11	established	establish	VERB
ejpam-2415	443	12	in	in	ADP
ejpam-2415	443	13	the	the	DET
ejpam-2415	443	14	next	next	ADJ
ejpam-2415	443	15	theorem	theorem	PROPN
ejpam-2415	443	16	.	.	PUNCT
ejpam-2415	443	17	theorem	theorem	VERB
ejpam-2415	443	18	22	22	NUM
ejpam-2415	443	19	.	.	PUNCT
ejpam-2415	444	1	if	if	SCONJ
ejpam-2415	444	2	{	{	PUNCT
ejpam-2415	444	3	aα	aα	NOUN
ejpam-2415	444	4	}	}	PUNCT
ejpam-2415	444	5	is	be	AUX
ejpam-2415	444	6	a	a	DET
ejpam-2415	444	7	family	family	NOUN
ejpam-2415	444	8	of	of	ADP
ejpam-2415	444	9	baer	baer	PROPN
ejpam-2415	444	10	elements	element	NOUN
ejpam-2415	444	11	of	of	ADP
ejpam-2415	444	12	l,⊻aα	l,⊻aα	NUM
ejpam-2415	444	13	is	be	AUX
ejpam-2415	444	14	the	the	DET
ejpam-2415	444	15	smallest	small	ADJ
ejpam-2415	444	16	baer	baer	PROPN
ejpam-2415	444	17	element	element	NOUN
ejpam-2415	444	18	greater	great	ADJ
ejpam-2415	444	19	than	than	ADP
ejpam-2415	444	20	each	each	DET
ejpam-2415	444	21	aα	aα	NOUN
ejpam-2415	444	22	.	.	PUNCT
ejpam-2415	445	1	proof	proof	NOUN
ejpam-2415	445	2	.	.	PUNCT
ejpam-2415	446	1	we	we	PRON
ejpam-2415	446	2	first	first	ADV
ejpam-2415	446	3	show	show	VERB
ejpam-2415	446	4	that	that	SCONJ
ejpam-2415	446	5	⊻aα	⊻aα	PROPN
ejpam-2415	446	6	is	be	AUX
ejpam-2415	446	7	a	a	DET
ejpam-2415	446	8	baer	baer	PROPN
ejpam-2415	446	9	element	element	NOUN
ejpam-2415	446	10	greater	great	ADJ
ejpam-2415	446	11	than	than	ADP
ejpam-2415	446	12	each	each	DET
ejpam-2415	446	13	aα	aα	NOUN
ejpam-2415	446	14	.	.	PUNCT
ejpam-2415	447	1	let	let	VERB
ejpam-2415	447	2	x	x	PRON
ejpam-2415	447	3	be	be	AUX
ejpam-2415	447	4	a	a	DET
ejpam-2415	447	5	compact	compact	ADJ
ejpam-2415	447	6	element	element	NOUN
ejpam-2415	447	7	of	of	ADP
ejpam-2415	447	8	l	l	NOUN
ejpam-2415	447	9	such	such	ADJ
ejpam-2415	447	10	that	that	SCONJ
ejpam-2415	447	11	x	x	PUNCT
ejpam-2415	448	1	i	i	NOUN
ejpam-2415	448	2	m	m	VERB
ejpam-2415	448	3	¶	¶	PROPN
ejpam-2415	448	4	⊻aα	⊻aα	PROPN
ejpam-2415	448	5	.	.	PUNCT
ejpam-2415	449	1	then	then	ADV
ejpam-2415	449	2	there	there	PRON
ejpam-2415	449	3	exist	exist	VERB
ejpam-2415	449	4	compact	compact	ADJ
ejpam-2415	449	5	elements	element	NOUN
ejpam-2415	449	6	x1	x1	PROPN
ejpam-2415	449	7	,	,	PUNCT
ejpam-2415	449	8	x2	x2	PROPN
ejpam-2415	449	9	,	,	PUNCT
ejpam-2415	449	10	.	.	PUNCT
ejpam-2415	449	11	.	.	PUNCT
ejpam-2415	450	1	.	.	PUNCT
ejpam-2415	451	1	,	,	PUNCT
ejpam-2415	451	2	xn	xn	PROPN
ejpam-2415	451	3	such	such	ADJ
ejpam-2415	451	4	that	that	SCONJ
ejpam-2415	451	5	0	0	NUM
ejpam-2415	451	6	m	m	VERB
ejpam-2415	451	7	:	:	PUNCT
ejpam-2415	451	8	(	(	PUNCT
ejpam-2415	451	9	x1	x1	PROPN
ejpam-2415	451	10	∨	∨	NUM
ejpam-2415	451	11	x2	x2	PROPN
ejpam-2415	451	12	∨	∨	PROPN
ejpam-2415	451	13	.	.	PUNCT
ejpam-2415	451	14	.	.	PUNCT
ejpam-2415	451	15	.	.	PUNCT
ejpam-2415	452	1	∨	∨	NOUN
ejpam-2415	452	2	xn)im	xn)im	X
ejpam-2415	452	3	¶	¶	PROPN
ejpam-2415	452	4	0	0	NUM
ejpam-2415	452	5	m	m	VERB
ejpam-2415	452	6	:	:	PUNCT
ejpam-2415	452	7	x	x	VERB
ejpam-2415	453	1	i	i	PRON
ejpam-2415	453	2	m	m	VERB
ejpam-2415	453	3	and	and	CCONJ
ejpam-2415	453	4	x	x	SYM
ejpam-2415	453	5	j	j	PROPN
ejpam-2415	453	6	i	i	NOUN
ejpam-2415	453	7	m	m	VERB
ejpam-2415	453	8	¶	¶	PROPN
ejpam-2415	453	9	aα	aα	PROPN
ejpam-2415	453	10	j	j	PROPN
ejpam-2415	453	11	j	j	PROPN
ejpam-2415	453	12	=	=	SYM
ejpam-2415	453	13	1,2	1,2	NUM
ejpam-2415	453	14	,	,	PUNCT
ejpam-2415	453	15	.	.	PUNCT
ejpam-2415	453	16	.	.	PUNCT
ejpam-2415	454	1	.	.	PUNCT
ejpam-2415	455	1	,	,	PUNCT
ejpam-2415	455	2	n.	n.	PROPN
ejpam-2415	455	3	next	next	ADV
ejpam-2415	455	4	we	we	PRON
ejpam-2415	455	5	show	show	VERB
ejpam-2415	455	6	that	that	SCONJ
ejpam-2415	455	7	0	0	NUM
ejpam-2415	455	8	m	m	VERB
ejpam-2415	455	9	:	:	PUNCT
ejpam-2415	455	10	(	(	PUNCT
ejpam-2415	455	11	0	0	NUM
ejpam-2415	455	12	m	m	VERB
ejpam-2415	455	13	:	:	PUNCT
ejpam-2415	455	14	x	x	PUNCT
ejpam-2415	455	15	i	i	NOUN
ejpam-2415	455	16	m	m	PROPN
ejpam-2415	455	17	)	)	PUNCT
ejpam-2415	455	18	¶	¶	PROPN
ejpam-2415	455	19	⊻aα	⊻aα	PROPN
ejpam-2415	455	20	.	.	PUNCT
ejpam-2415	456	1	let	let	VERB
ejpam-2415	456	2	z	z	PRON
ejpam-2415	456	3	be	be	AUX
ejpam-2415	456	4	compact	compact	ADJ
ejpam-2415	456	5	element	element	NOUN
ejpam-2415	456	6	in	in	ADP
ejpam-2415	456	7	l	l	NOUN
ejpam-2415	456	8	such	such	ADJ
ejpam-2415	456	9	that	that	SCONJ
ejpam-2415	456	10	zim	zim	PROPN
ejpam-2415	456	11	¶	¶	PROPN
ejpam-2415	456	12	0	0	PROPN
ejpam-2415	456	13	m	m	VERB
ejpam-2415	456	14	:	:	PUNCT
ejpam-2415	456	15	(	(	PUNCT
ejpam-2415	456	16	0	0	NUM
ejpam-2415	456	17	m	m	VERB
ejpam-2415	456	18	:	:	PUNCT
ejpam-2415	456	19	x	x	PUNCT
ejpam-2415	456	20	i	i	NOUN
ejpam-2415	456	21	m	m	PROPN
ejpam-2415	456	22	)	)	PUNCT
ejpam-2415	456	23	.	.	PUNCT
ejpam-2415	457	1	then	then	ADV
ejpam-2415	457	2	0	0	NUM
ejpam-2415	457	3	m	m	VERB
ejpam-2415	457	4	:	:	PUNCT
ejpam-2415	457	5	zim	zim	X
ejpam-2415	457	6	≥	≥	NUM
ejpam-2415	457	7	0	0	NUM
ejpam-2415	457	8	m	m	VERB
ejpam-2415	457	9	:	:	PUNCT
ejpam-2415	458	1	[	[	X
ejpam-2415	458	2	0	0	NUM
ejpam-2415	458	3	m	m	VERB
ejpam-2415	458	4	:	:	PUNCT
ejpam-2415	458	5	(	(	PUNCT
ejpam-2415	458	6	0	0	NUM
ejpam-2415	458	7	m	m	VERB
ejpam-2415	458	8	:	:	PUNCT
ejpam-2415	458	9	x	x	PUNCT
ejpam-2415	458	10	i	i	NOUN
ejpam-2415	458	11	m	m	PROPN
ejpam-2415	458	12	)	)	PUNCT
ejpam-2415	458	13	]	]	PUNCT
ejpam-2415	458	14	.	.	PUNCT
ejpam-2415	459	1	that	that	PRON
ejpam-2415	459	2	is	be	AUX
ejpam-2415	459	3	0	0	NUM
ejpam-2415	459	4	m	m	VERB
ejpam-2415	459	5	:	:	PUNCT
ejpam-2415	459	6	x	x	PUNCT
ejpam-2415	460	1	i	i	NOUN
ejpam-2415	460	2	m	m	VERB
ejpam-2415	460	3	¶	¶	PROPN
ejpam-2415	460	4	0	0	NUM
ejpam-2415	460	5	m	m	VERB
ejpam-2415	460	6	:	:	PUNCT
ejpam-2415	460	7	zim	zim	X
ejpam-2415	460	8	(	(	PUNCT
ejpam-2415	460	9	by	by	ADP
ejpam-2415	460	10	theorem	theorem	NOUN
ejpam-2415	460	11	1	1	NUM
ejpam-2415	460	12	,	,	PUNCT
ejpam-2415	460	13	(	(	PUNCT
ejpam-2415	460	14	x	x	X
ejpam-2415	460	15	)	)	PUNCT
ejpam-2415	460	16	and	and	CCONJ
ejpam-2415	460	17	(	(	PUNCT
ejpam-2415	460	18	xi	xi	NOUN
ejpam-2415	460	19	)	)	PUNCT
ejpam-2415	460	20	)	)	PUNCT
ejpam-2415	460	21	.	.	PUNCT
ejpam-2415	461	1	therefore	therefore	ADV
ejpam-2415	461	2	0	0	NUM
ejpam-2415	461	3	m	m	VERB
ejpam-2415	461	4	:	:	PUNCT
ejpam-2415	461	5	(	(	PUNCT
ejpam-2415	461	6	x1	x1	PROPN
ejpam-2415	461	7	∨	∨	NUM
ejpam-2415	461	8	x2	x2	PROPN
ejpam-2415	461	9	∨	∨	PROPN
ejpam-2415	461	10	.	.	PUNCT
ejpam-2415	461	11	.	.	PUNCT
ejpam-2415	461	12	.	.	PUNCT
ejpam-2415	462	1	∨	∨	NOUN
ejpam-2415	462	2	xn)im	xn)im	X
ejpam-2415	462	3	¶	¶	PROPN
ejpam-2415	462	4	0	0	NUM
ejpam-2415	462	5	m	m	VERB
ejpam-2415	462	6	:	:	PUNCT
ejpam-2415	462	7	zim	zim	X
ejpam-2415	462	8	.	.	PUNCT
ejpam-2415	463	1	this	this	PRON
ejpam-2415	463	2	implies	imply	VERB
ejpam-2415	463	3	that	that	SCONJ
ejpam-2415	463	4	zim	zim	PROPN
ejpam-2415	463	5	¶	¶	PROPN
ejpam-2415	463	6	⊻aα	⊻aα	PROPN
ejpam-2415	463	7	.	.	PUNCT
ejpam-2415	464	1	thus	thus	ADV
ejpam-2415	464	2	0	0	NUM
ejpam-2415	464	3	m	m	VERB
ejpam-2415	464	4	:	:	PUNCT
ejpam-2415	464	5	(	(	PUNCT
ejpam-2415	464	6	0	0	NUM
ejpam-2415	464	7	m	m	VERB
ejpam-2415	464	8	:	:	PUNCT
ejpam-2415	464	9	x	x	PUNCT
ejpam-2415	464	10	i	i	NOUN
ejpam-2415	464	11	m	m	VERB
ejpam-2415	464	12	)	)	PUNCT
ejpam-2415	464	13	¶	¶	PROPN
ejpam-2415	464	14	⊻aα	⊻aα	PROPN
ejpam-2415	464	15	.	.	PUNCT
ejpam-2415	465	1	this	this	PRON
ejpam-2415	465	2	shows	show	VERB
ejpam-2415	465	3	that	that	SCONJ
ejpam-2415	465	4	⊻aα	⊻aα	PROPN
ejpam-2415	465	5	is	be	AUX
ejpam-2415	465	6	a	a	DET
ejpam-2415	465	7	baer	baer	PROPN
ejpam-2415	465	8	element	element	NOUN
ejpam-2415	465	9	.	.	PUNCT
ejpam-2415	466	1	let	let	VERB
ejpam-2415	466	2	z	z	PRON
ejpam-2415	466	3	be	be	AUX
ejpam-2415	466	4	a	a	DET
ejpam-2415	466	5	compact	compact	ADJ
ejpam-2415	466	6	element	element	NOUN
ejpam-2415	466	7	in	in	ADP
ejpam-2415	466	8	l	l	NOUN
ejpam-2415	466	9	such	such	ADJ
ejpam-2415	466	10	that	that	SCONJ
ejpam-2415	466	11	zim	zim	PROPN
ejpam-2415	466	12	¶	¶	PROPN
ejpam-2415	466	13	aα	aα	NOUN
ejpam-2415	466	14	for	for	ADP
ejpam-2415	466	15	some	some	DET
ejpam-2415	466	16	α	α	NOUN
ejpam-2415	466	17	.	.	PUNCT
ejpam-2415	467	1	but	but	CCONJ
ejpam-2415	467	2	0	0	NUM
ejpam-2415	467	3	m	m	VERB
ejpam-2415	467	4	:	:	PUNCT
ejpam-2415	467	5	zim	zim	PROPN
ejpam-2415	467	6	¶	¶	PROPN
ejpam-2415	467	7	0	0	PROPN
ejpam-2415	467	8	m	m	VERB
ejpam-2415	467	9	:	:	PUNCT
ejpam-2415	468	1	zim	zim	X
ejpam-2415	468	2	.	.	PUNCT
ejpam-2415	469	1	thus	thus	ADV
ejpam-2415	469	2	zim	zim	PROPN
ejpam-2415	469	3	¶	¶	PROPN
ejpam-2415	469	4	⊻aα	⊻aα	PROPN
ejpam-2415	469	5	.	.	PUNCT
ejpam-2415	470	1	hence	hence	ADV
ejpam-2415	470	2	each	each	DET
ejpam-2415	470	3	aα	aα	NOUN
ejpam-2415	470	4	¶	¶	PROPN
ejpam-2415	470	5	⊻aα	⊻aα	PROPN
ejpam-2415	470	6	.	.	PUNCT
ejpam-2415	471	1	let	let	VERB
ejpam-2415	471	2	b	b	X
ejpam-2415	471	3	be	be	AUX
ejpam-2415	471	4	a	a	DET
ejpam-2415	471	5	baer	baer	PROPN
ejpam-2415	471	6	element	element	NOUN
ejpam-2415	471	7	such	such	ADJ
ejpam-2415	471	8	that	that	DET
ejpam-2415	471	9	aα	aα	PROPN
ejpam-2415	471	10	¶	¶	PROPN
ejpam-2415	471	11	b	b	PROPN
ejpam-2415	471	12	for	for	ADP
ejpam-2415	471	13	each	each	DET
ejpam-2415	471	14	α	α	NOUN
ejpam-2415	471	15	and	and	CCONJ
ejpam-2415	471	16	let	let	VERB
ejpam-2415	471	17	x	x	PRON
ejpam-2415	471	18	be	be	AUX
ejpam-2415	471	19	a	a	DET
ejpam-2415	471	20	compact	compact	ADJ
ejpam-2415	471	21	element	element	NOUN
ejpam-2415	471	22	in	in	ADP
ejpam-2415	471	23	l	l	NOUN
ejpam-2415	472	1	such	such	ADJ
ejpam-2415	472	2	that	that	DET
ejpam-2415	472	3	0	0	NUM
ejpam-2415	472	4	m	m	VERB
ejpam-2415	472	5	:	:	PUNCT
ejpam-2415	472	6	(	(	PUNCT
ejpam-2415	472	7	x1	x1	PROPN
ejpam-2415	472	8	∨	∨	NUM
ejpam-2415	472	9	x2	x2	PROPN
ejpam-2415	472	10	∨	∨	PROPN
ejpam-2415	472	11	.	.	PUNCT
ejpam-2415	472	12	.	.	PUNCT
ejpam-2415	473	1	.∨	.∨	PUNCT
ejpam-2415	474	1	xn)im	xn)im	PUNCT
ejpam-2415	474	2	¶	¶	PROPN
ejpam-2415	474	3	0	0	NUM
ejpam-2415	474	4	m	m	VERB
ejpam-2415	474	5	:	:	PUNCT
ejpam-2415	474	6	x	x	PUNCT
ejpam-2415	474	7	i	i	PRON
ejpam-2415	474	8	m	m	VERB
ejpam-2415	474	9	for	for	ADP
ejpam-2415	474	10	some	some	DET
ejpam-2415	474	11	compact	compact	ADJ
ejpam-2415	474	12	elements	element	NOUN
ejpam-2415	474	13	x	x	PUNCT
ejpam-2415	474	14	j	j	NOUN
ejpam-2415	474	15	i	i	NOUN
ejpam-2415	474	16	m	m	VERB
ejpam-2415	474	17	¶	¶	PROPN
ejpam-2415	474	18	aα	aα	PROPN
ejpam-2415	475	1	j	j	PROPN
ejpam-2415	475	2	,	,	PUNCT
ejpam-2415	475	3	j	j	PROPN
ejpam-2415	475	4	=	=	SYM
ejpam-2415	475	5	1,2	1,2	NUM
ejpam-2415	475	6	,	,	PUNCT
ejpam-2415	475	7	.	.	PUNCT
ejpam-2415	475	8	.	.	PUNCT
ejpam-2415	475	9	.	.	PUNCT
ejpam-2415	476	1	,	,	PUNCT
ejpam-2415	476	2	n	n	X
ejpam-2415	476	3	so	so	ADV
ejpam-2415	476	4	that	that	SCONJ
ejpam-2415	476	5	x	x	PUNCT
ejpam-2415	477	1	i	i	NOUN
ejpam-2415	477	2	m	m	VERB
ejpam-2415	477	3	¶	¶	PROPN
ejpam-2415	477	4	⊻aα	⊻aα	PROPN
ejpam-2415	477	5	.	.	PUNCT
ejpam-2415	478	1	note	note	VERB
ejpam-2415	478	2	that	that	SCONJ
ejpam-2415	478	3	b	b	NOUN
ejpam-2415	478	4	is	be	AUX
ejpam-2415	478	5	a	a	DET
ejpam-2415	478	6	baer	baer	PROPN
ejpam-2415	478	7	element	element	NOUN
ejpam-2415	478	8	and	and	CCONJ
ejpam-2415	478	9	the	the	DET
ejpam-2415	478	10	compact	compact	ADJ
ejpam-2415	478	11	element	element	NOUN
ejpam-2415	478	12	(	(	PUNCT
ejpam-2415	478	13	x1	x1	PROPN
ejpam-2415	478	14	∨	∨	NUM
ejpam-2415	478	15	x2	x2	PROPN
ejpam-2415	478	16	∨	∨	PROPN
ejpam-2415	478	17	.	.	PUNCT
ejpam-2415	478	18	.	.	PUNCT
ejpam-2415	478	19	.	.	PUNCT
ejpam-2415	479	1	∨	∨	NOUN
ejpam-2415	479	2	xn)im	xn)im	PROPN
ejpam-2415	479	3	¶	¶	PROPN
ejpam-2415	479	4	b.	b.	PROPN
ejpam-2415	480	1	hence	hence	ADV
ejpam-2415	480	2	0	0	NUM
ejpam-2415	480	3	m	m	VERB
ejpam-2415	480	4	:	:	PUNCT
ejpam-2415	481	1	[	[	X
ejpam-2415	481	2	0	0	NUM
ejpam-2415	481	3	m	m	VERB
ejpam-2415	481	4	:	:	PUNCT
ejpam-2415	481	5	(	(	PUNCT
ejpam-2415	481	6	x1	x1	PROPN
ejpam-2415	481	7	∨	∨	NUM
ejpam-2415	481	8	x2	x2	PROPN
ejpam-2415	481	9	∨	∨	PROPN
ejpam-2415	481	10	.	.	PUNCT
ejpam-2415	481	11	.	.	PUNCT
ejpam-2415	481	12	.	.	PUNCT
ejpam-2415	482	1	∨	∨	NOUN
ejpam-2415	482	2	xn)im	xn)im	PUNCT
ejpam-2415	482	3	]	]	PUNCT
ejpam-2415	482	4	¶	¶	PROPN
ejpam-2415	482	5	b.	b.	PROPN
ejpam-2415	482	6	again	again	ADV
ejpam-2415	482	7	note	note	VERB
ejpam-2415	482	8	that	that	SCONJ
ejpam-2415	482	9	0	0	NUM
ejpam-2415	482	10	m	m	VERB
ejpam-2415	482	11	:	:	PUNCT
ejpam-2415	482	12	(	(	PUNCT
ejpam-2415	482	13	0	0	NUM
ejpam-2415	482	14	m	m	VERB
ejpam-2415	482	15	:	:	PUNCT
ejpam-2415	482	16	x	x	PUNCT
ejpam-2415	482	17	i	i	NOUN
ejpam-2415	482	18	m	m	VERB
ejpam-2415	482	19	)	)	PUNCT
ejpam-2415	482	20	¶	¶	PROPN
ejpam-2415	482	21	0	0	NUM
ejpam-2415	482	22	m	m	VERB
ejpam-2415	482	23	:	:	PUNCT
ejpam-2415	483	1	[	[	X
ejpam-2415	483	2	0	0	NUM
ejpam-2415	483	3	m	m	VERB
ejpam-2415	483	4	:	:	PUNCT
ejpam-2415	483	5	(	(	PUNCT
ejpam-2415	483	6	x1	x1	PROPN
ejpam-2415	483	7	∨	∨	NUM
ejpam-2415	483	8	x2	x2	PROPN
ejpam-2415	483	9	∨	∨	PROPN
ejpam-2415	483	10	.	.	PUNCT
ejpam-2415	483	11	.	.	PUNCT
ejpam-2415	483	12	.	.	PUNCT
ejpam-2415	484	1	∨	∨	NOUN
ejpam-2415	484	2	xn)im	xn)im	PUNCT
ejpam-2415	484	3	]	]	PUNCT
ejpam-2415	485	1	and	and	CCONJ
ejpam-2415	485	2	x	x	PUNCT
ejpam-2415	486	1	i	i	NOUN
ejpam-2415	486	2	m	m	VERB
ejpam-2415	486	3	¶	¶	PROPN
ejpam-2415	486	4	0	0	NUM
ejpam-2415	486	5	m	m	VERB
ejpam-2415	486	6	:	:	PUNCT
ejpam-2415	486	7	(	(	PUNCT
ejpam-2415	486	8	0	0	NUM
ejpam-2415	486	9	m	m	VERB
ejpam-2415	486	10	:	:	PUNCT
ejpam-2415	486	11	x	x	PUNCT
ejpam-2415	486	12	i	i	NOUN
ejpam-2415	486	13	m	m	PROPN
ejpam-2415	486	14	)	)	PUNCT
ejpam-2415	486	15	.	.	PUNCT
ejpam-2415	487	1	therefore	therefore	ADV
ejpam-2415	487	2	x	x	VERB
ejpam-2415	487	3	i	i	NOUN
ejpam-2415	487	4	m	m	VERB
ejpam-2415	487	5	¶	¶	PROPN
ejpam-2415	487	6	b	b	PROPN
ejpam-2415	487	7	and	and	CCONJ
ejpam-2415	487	8	hence	hence	ADV
ejpam-2415	487	9	⊻aα	⊻aα	PROPN
ejpam-2415	487	10	¶	¶	PROPN
ejpam-2415	487	11	b.	b.	PROPN
ejpam-2415	488	1	consequently	consequently	ADV
ejpam-2415	488	2	⊻aα	⊻aα	PROPN
ejpam-2415	488	3	is	be	AUX
ejpam-2415	488	4	the	the	DET
ejpam-2415	488	5	smallest	small	ADJ
ejpam-2415	488	6	baer	baer	PROPN
ejpam-2415	488	7	element	element	NOUN
ejpam-2415	488	8	greater	great	ADJ
ejpam-2415	488	9	than	than	ADP
ejpam-2415	488	10	each	each	DET
ejpam-2415	488	11	aα	aα	NOUN
ejpam-2415	488	12	.	.	PUNCT
ejpam-2415	489	1	theorem	theorem	VERB
ejpam-2415	489	2	23	23	NUM
ejpam-2415	489	3	.	.	PUNCT
ejpam-2415	490	1	for	for	ADP
ejpam-2415	490	2	any	any	DET
ejpam-2415	490	3	proper	proper	ADJ
ejpam-2415	490	4	element	element	NOUN
ejpam-2415	490	5	a	a	DET
ejpam-2415	490	6	∈	∈	PROPN
ejpam-2415	490	7	m	m	NOUN
ejpam-2415	490	8	,	,	PUNCT
ejpam-2415	490	9	⊻{0	⊻{0	AUX
ejpam-2415	490	10	m	m	PRON
ejpam-2415	490	11	:	:	PUNCT
ejpam-2415	490	12	(	(	PUNCT
ejpam-2415	490	13	0	0	NUM
ejpam-2415	490	14	m	m	VERB
ejpam-2415	490	15	:	:	PUNCT
ejpam-2415	490	16	x	x	PUNCT
ejpam-2415	490	17	i	i	PRON
ejpam-2415	490	18	m	m	VERB
ejpam-2415	490	19	)	)	PUNCT
ejpam-2415	491	1	|	|	ADV
ejpam-2415	491	2	x	x	SYM
ejpam-2415	491	3	∈	∈	PROPN
ejpam-2415	491	4	l∗	l∗	NOUN
ejpam-2415	491	5	and	and	CCONJ
ejpam-2415	491	6	x	x	PUNCT
ejpam-2415	491	7	i	i	NOUN
ejpam-2415	491	8	m	m	VERB
ejpam-2415	491	9	¶	¶	PROPN
ejpam-2415	491	10	a	a	X
ejpam-2415	491	11	}	}	PUNCT
ejpam-2415	491	12	is	be	AUX
ejpam-2415	491	13	the	the	DET
ejpam-2415	491	14	smallest	small	ADJ
ejpam-2415	491	15	baer	baer	PROPN
ejpam-2415	491	16	element	element	NOUN
ejpam-2415	491	17	greater	great	ADJ
ejpam-2415	491	18	than	than	ADP
ejpam-2415	491	19	a.	a.	NOUN
ejpam-2415	491	20	proof	proof	NOUN
ejpam-2415	491	21	.	.	PUNCT
ejpam-2415	492	1	first	first	ADV
ejpam-2415	492	2	we	we	PRON
ejpam-2415	492	3	show	show	VERB
ejpam-2415	492	4	that	that	SCONJ
ejpam-2415	492	5	0	0	NUM
ejpam-2415	492	6	m	m	VERB
ejpam-2415	492	7	:	:	PUNCT
ejpam-2415	492	8	(	(	PUNCT
ejpam-2415	492	9	0	0	NUM
ejpam-2415	492	10	m	m	VERB
ejpam-2415	492	11	:	:	PUNCT
ejpam-2415	492	12	x	x	VERB
ejpam-2415	492	13	i	i	PRON
ejpam-2415	492	14	m	m	PROPN
ejpam-2415	492	15	)	)	PUNCT
ejpam-2415	492	16	is	be	AUX
ejpam-2415	492	17	a	a	DET
ejpam-2415	492	18	baer	baer	PROPN
ejpam-2415	492	19	element	element	NOUN
ejpam-2415	492	20	i.e.	i.e.	X
ejpam-2415	492	21	we	we	PRON
ejpam-2415	492	22	show	show	VERB
ejpam-2415	492	23	that	that	SCONJ
ejpam-2415	492	24	for	for	ADP
ejpam-2415	492	25	any	any	DET
ejpam-2415	492	26	x	x	SYM
ejpam-2415	492	27	∈	∈	PROPN
ejpam-2415	492	28	l∗	l∗	NOUN
ejpam-2415	492	29	,	,	PUNCT
ejpam-2415	492	30	x	x	PROPN
ejpam-2415	492	31	i	i	NOUN
ejpam-2415	492	32	m	m	VERB
ejpam-2415	492	33	¶	¶	PROPN
ejpam-2415	492	34	0	0	NUM
ejpam-2415	492	35	m	m	AUX
ejpam-2415	492	36	:	:	PUNCT
ejpam-2415	492	37	(	(	PUNCT
ejpam-2415	492	38	0	0	NUM
ejpam-2415	492	39	m	m	VERB
ejpam-2415	492	40	:	:	PUNCT
ejpam-2415	492	41	x	x	VERB
ejpam-2415	492	42	i	i	PRON
ejpam-2415	492	43	m	m	PROPN
ejpam-2415	492	44	)	)	PUNCT
ejpam-2415	492	45	implies	imply	VERB
ejpam-2415	492	46	0	0	NUM
ejpam-2415	492	47	m	m	VERB
ejpam-2415	492	48	:	:	PUNCT
ejpam-2415	492	49	(	(	PUNCT
ejpam-2415	492	50	0	0	NUM
ejpam-2415	492	51	m	m	VERB
ejpam-2415	492	52	:	:	PUNCT
ejpam-2415	492	53	x	x	PUNCT
ejpam-2415	492	54	i	i	NOUN
ejpam-2415	492	55	m	m	VERB
ejpam-2415	492	56	)	)	PUNCT
ejpam-2415	492	57	¶	¶	PROPN
ejpam-2415	492	58	0	0	NUM
ejpam-2415	492	59	m	m	VERB
ejpam-2415	492	60	:	:	PUNCT
ejpam-2415	492	61	(	(	PUNCT
ejpam-2415	492	62	0	0	NUM
ejpam-2415	492	63	m	m	VERB
ejpam-2415	492	64	:	:	PUNCT
ejpam-2415	492	65	x	x	PUNCT
ejpam-2415	492	66	i	i	NOUN
ejpam-2415	492	67	m	m	VERB
ejpam-2415	492	68	)	)	PUNCT
ejpam-2415	492	69	which	which	PRON
ejpam-2415	492	70	holds	hold	VERB
ejpam-2415	492	71	obviously	obviously	ADV
ejpam-2415	492	72	.	.	PUNCT
ejpam-2415	493	1	hence	hence	ADV
ejpam-2415	493	2	by	by	ADP
ejpam-2415	493	3	theorem	theorem	NOUN
ejpam-2415	493	4	22	22	NUM
ejpam-2415	493	5	,	,	PUNCT
ejpam-2415	493	6	b	b	X
ejpam-2415	493	7	=	=	PUNCT
ejpam-2415	493	8	⊻{0	⊻{0	ADP
ejpam-2415	493	9	m	m	VERB
ejpam-2415	493	10	:	:	PUNCT
ejpam-2415	493	11	(	(	PUNCT
ejpam-2415	493	12	0	0	NUM
ejpam-2415	493	13	m	m	VERB
ejpam-2415	493	14	:	:	PUNCT
ejpam-2415	493	15	x	x	PUNCT
ejpam-2415	493	16	i	i	PRON
ejpam-2415	493	17	m	m	VERB
ejpam-2415	493	18	)	)	PUNCT
ejpam-2415	494	1	|	|	ADV
ejpam-2415	494	2	x	x	SYM
ejpam-2415	494	3	∈	∈	PROPN
ejpam-2415	494	4	l∗	l∗	NOUN
ejpam-2415	494	5	and	and	CCONJ
ejpam-2415	494	6	x	x	PUNCT
ejpam-2415	494	7	i	i	NOUN
ejpam-2415	494	8	m	m	VERB
ejpam-2415	494	9	¶	¶	PROPN
ejpam-2415	494	10	a	a	X
ejpam-2415	494	11	}	}	PUNCT
ejpam-2415	494	12	is	be	AUX
ejpam-2415	494	13	the	the	DET
ejpam-2415	494	14	smallest	small	ADJ
ejpam-2415	494	15	baer	baer	PROPN
ejpam-2415	494	16	element	element	NOUN
ejpam-2415	494	17	containing	contain	VERB
ejpam-2415	494	18	each	each	DET
ejpam-2415	494	19	0	0	NUM
ejpam-2415	494	20	m	m	VERB
ejpam-2415	494	21	:	:	PUNCT
ejpam-2415	494	22	(	(	PUNCT
ejpam-2415	494	23	0	0	NUM
ejpam-2415	494	24	m	m	VERB
ejpam-2415	494	25	:	:	PUNCT
ejpam-2415	494	26	x	x	PUNCT
ejpam-2415	494	27	i	i	NOUN
ejpam-2415	494	28	m	m	VERB
ejpam-2415	494	29	)	)	PUNCT
ejpam-2415	494	30	for	for	ADP
ejpam-2415	494	31	x	x	PROPN
ejpam-2415	494	32	i	i	NOUN
ejpam-2415	494	33	m	m	PROPN
ejpam-2415	494	34	¶	¶	NOUN
ejpam-2415	494	35	a.	a.	NOUN
ejpam-2415	494	36	let	let	VERB
ejpam-2415	494	37	a	a	DET
ejpam-2415	494	38	compact	compact	ADJ
ejpam-2415	494	39	element	element	NOUN
ejpam-2415	494	40	x	x	PUNCT
ejpam-2415	494	41	in	in	ADP
ejpam-2415	494	42	l	l	NOUN
ejpam-2415	494	43	be	be	VERB
ejpam-2415	494	44	such	such	ADJ
ejpam-2415	494	45	that	that	SCONJ
ejpam-2415	494	46	x	x	PUNCT
ejpam-2415	494	47	i	i	NOUN
ejpam-2415	494	48	m	m	VERB
ejpam-2415	494	49	¶	¶	NOUN
ejpam-2415	494	50	a.	a.	NOUN
ejpam-2415	495	1	then	then	ADV
ejpam-2415	495	2	we	we	PRON
ejpam-2415	495	3	have	have	VERB
ejpam-2415	495	4	x	x	PROPN
ejpam-2415	495	5	i	i	PRON
ejpam-2415	495	6	m	m	VERB
ejpam-2415	495	7	¶	¶	PROPN
ejpam-2415	495	8	0	0	NUM
ejpam-2415	495	9	m	m	VERB
ejpam-2415	495	10	:	:	PUNCT
ejpam-2415	495	11	(	(	PUNCT
ejpam-2415	495	12	0	0	NUM
ejpam-2415	495	13	m	m	VERB
ejpam-2415	495	14	:	:	PUNCT
ejpam-2415	495	15	x	x	PUNCT
ejpam-2415	495	16	i	i	NOUN
ejpam-2415	495	17	m	m	PROPN
ejpam-2415	495	18	)	)	PUNCT
ejpam-2415	496	1	¶	¶	PROPN
ejpam-2415	496	2	b.	b.	PROPN
ejpam-2415	497	1	thus	thus	ADV
ejpam-2415	497	2	a¶	a¶	ADP
ejpam-2415	497	3	b.	b.	PROPN
ejpam-2415	497	4	let	let	VERB
ejpam-2415	497	5	zim	zim	PROPN
ejpam-2415	497	6	be	be	AUX
ejpam-2415	497	7	a	a	DET
ejpam-2415	497	8	baer	baer	PROPN
ejpam-2415	497	9	element	element	NOUN
ejpam-2415	497	10	in	in	ADP
ejpam-2415	497	11	m	m	PROPN
ejpam-2415	497	12	such	such	ADJ
ejpam-2415	497	13	that	that	SCONJ
ejpam-2415	497	14	a¶	a¶	ADP
ejpam-2415	497	15	zim	zim	PROPN
ejpam-2415	497	16	and	and	CCONJ
ejpam-2415	497	17	let	let	VERB
ejpam-2415	497	18	y	y	PRON
ejpam-2415	497	19	be	be	AUX
ejpam-2415	497	20	compact	compact	ADJ
ejpam-2415	497	21	element	element	NOUN
ejpam-2415	497	22	in	in	ADP
ejpam-2415	497	23	l	l	NOUN
ejpam-2415	497	24	such	such	ADJ
ejpam-2415	497	25	that	that	SCONJ
ejpam-2415	497	26	y	y	PROPN
ejpam-2415	498	1	i	i	PRON
ejpam-2415	498	2	m	m	PROPN
ejpam-2415	498	3	¶	¶	PROPN
ejpam-2415	498	4	b.	b.	PROPN
ejpam-2415	499	1	then	then	ADV
ejpam-2415	499	2	0	0	NUM
ejpam-2415	499	3	m	m	VERB
ejpam-2415	499	4	:	:	PUNCT
ejpam-2415	499	5	(	(	PUNCT
ejpam-2415	499	6	z1	z1	PROPN
ejpam-2415	499	7	∨	∨	PROPN
ejpam-2415	499	8	z2	z2	PROPN
ejpam-2415	499	9	∨	∨	NUM
ejpam-2415	499	10	.	.	PUNCT
ejpam-2415	499	11	.	.	PUNCT
ejpam-2415	499	12	.	.	PUNCT
ejpam-2415	500	1	∨	∨	PROPN
ejpam-2415	500	2	zn)im	zn)im	X
ejpam-2415	500	3	¶	¶	NOUN
ejpam-2415	500	4	0	0	NUM
ejpam-2415	500	5	m	m	VERB
ejpam-2415	500	6	:	:	PUNCT
ejpam-2415	500	7	y	y	PROPN
ejpam-2415	500	8	i	i	PRON
ejpam-2415	500	9	m	m	VERB
ejpam-2415	500	10	,	,	PUNCT
ejpam-2415	500	11	for	for	ADP
ejpam-2415	500	12	some	some	DET
ejpam-2415	500	13	compact	compact	ADJ
ejpam-2415	500	14	elements	element	NOUN
ejpam-2415	500	15	zi	zi	NOUN
ejpam-2415	501	1	i	i	PRON
ejpam-2415	501	2	m	m	VERB
ejpam-2415	501	3	¶	¶	PROPN
ejpam-2415	501	4	0	0	NUM
ejpam-2415	501	5	m	m	VERB
ejpam-2415	501	6	:	:	PUNCT
ejpam-2415	501	7	(	(	PUNCT
ejpam-2415	501	8	0	0	NUM
ejpam-2415	501	9	m	m	VERB
ejpam-2415	501	10	:	:	PUNCT
ejpam-2415	502	1	x	x	PUNCT
ejpam-2415	502	2	i	i	PRON
ejpam-2415	502	3	i	i	NOUN
ejpam-2415	502	4	m	m	VERB
ejpam-2415	502	5	)	)	PUNCT
ejpam-2415	502	6	,	,	PUNCT
ejpam-2415	502	7	where	where	SCONJ
ejpam-2415	502	8	i	i	PRON
ejpam-2415	502	9	=	=	SYM
ejpam-2415	502	10	1,2	1,2	NUM
ejpam-2415	502	11	,	,	PUNCT
ejpam-2415	502	12	.	.	PUNCT
ejpam-2415	502	13	.	.	PUNCT
ejpam-2415	502	14	.	.	PUNCT
ejpam-2415	503	1	,	,	PUNCT
ejpam-2415	503	2	n.	n.	NOUN
ejpam-2415	503	3	thus	thus	ADV
ejpam-2415	503	4	0	0	NUM
ejpam-2415	503	5	m	m	VERB
ejpam-2415	503	6	:	:	PUNCT
ejpam-2415	503	7	x	x	PUNCT
ejpam-2415	503	8	i	i	PRON
ejpam-2415	503	9	i	i	VERB
ejpam-2415	503	10	m	m	VERB
ejpam-2415	503	11	¶	¶	PROPN
ejpam-2415	503	12	0	0	NUM
ejpam-2415	503	13	m	m	VERB
ejpam-2415	503	14	:	:	PUNCT
ejpam-2415	503	15	zi	zi	VERB
ejpam-2415	504	1	i	i	PRON
ejpam-2415	504	2	m	m	VERB
ejpam-2415	504	3	for	for	ADP
ejpam-2415	504	4	each	each	DET
ejpam-2415	504	5	i.	i.	NOUN
ejpam-2415	504	6	this	this	PRON
ejpam-2415	504	7	gives	give	VERB
ejpam-2415	504	8	0	0	NUM
ejpam-2415	504	9	m	m	NUM
ejpam-2415	504	10	:(	:(	NOUN
ejpam-2415	505	1	x1	x1	PROPN
ejpam-2415	505	2	∨	∨	NUM
ejpam-2415	505	3	x2	x2	PROPN
ejpam-2415	505	4	∨	∨	PROPN
ejpam-2415	505	5	.	.	PUNCT
ejpam-2415	505	6	.	.	PUNCT
ejpam-2415	506	1	.∨	.∨	PUNCT
ejpam-2415	506	2	xn)im	xn)im	PUNCT
ejpam-2415	507	1	=	=	PUNCT
ejpam-2415	507	2	0	0	NUM
ejpam-2415	507	3	m	m	VERB
ejpam-2415	507	4	:	:	PUNCT
ejpam-2415	508	1	x1	x1	PROPN
ejpam-2415	509	1	i	i	PRON
ejpam-2415	509	2	m	m	VERB
ejpam-2415	509	3	∧	∧	NOUN
ejpam-2415	509	4	0	0	NUM
ejpam-2415	509	5	m	m	VERB
ejpam-2415	509	6	:	:	PUNCT
ejpam-2415	510	1	x2	x2	INTJ
ejpam-2415	511	1	i	i	PRON
ejpam-2415	511	2	m	m	VERB
ejpam-2415	511	3	∧	∧	NOUN
ejpam-2415	511	4	.	.	PUNCT
ejpam-2415	511	5	.	.	PUNCT
ejpam-2415	511	6	.	.	PUNCT
ejpam-2415	512	1	0	0	NUM
ejpam-2415	512	2	m	m	VERB
ejpam-2415	512	3	:	:	PUNCT
ejpam-2415	512	4	xn	xn	PROPN
ejpam-2415	513	1	i	i	PRON
ejpam-2415	513	2	m	m	VERB
ejpam-2415	513	3	¶0	¶0	PROPN
ejpam-2415	513	4	m	m	PROPN
ejpam-2415	513	5	:	:	PUNCT
ejpam-2415	513	6	z1	z1	VERB
ejpam-2415	513	7	i	i	PRON
ejpam-2415	513	8	m	m	VERB
ejpam-2415	513	9	∧	∧	PROPN
ejpam-2415	513	10	0	0	NUM
ejpam-2415	513	11	m	m	VERB
ejpam-2415	513	12	:	:	PUNCT
ejpam-2415	514	1	z2	z2	VERB
ejpam-2415	514	2	i	i	NOUN
ejpam-2415	514	3	m	m	PROPN
ejpam-2415	514	4	∧	∧	PROPN
ejpam-2415	514	5	.	.	PUNCT
ejpam-2415	514	6	.	.	PUNCT
ejpam-2415	515	1	.∧	.∧	PUNCT
ejpam-2415	516	1	0	0	NUM
ejpam-2415	516	2	m	m	VERB
ejpam-2415	516	3	:	:	PUNCT
ejpam-2415	516	4	zn	zn	PROPN
ejpam-2415	516	5	i	i	PRON
ejpam-2415	516	6	m	m	VERB
ejpam-2415	516	7	=	=	NOUN
ejpam-2415	516	8	0	0	NUM
ejpam-2415	516	9	m	m	VERB
ejpam-2415	516	10	:	:	PUNCT
ejpam-2415	516	11	(	(	PUNCT
ejpam-2415	516	12	z1	z1	PROPN
ejpam-2415	516	13	∨	∨	PROPN
ejpam-2415	516	14	z2	z2	PROPN
ejpam-2415	516	15	∨	∨	NUM
ejpam-2415	516	16	.	.	PUNCT
ejpam-2415	516	17	.	.	PUNCT
ejpam-2415	517	1	.∨	.∨	PUNCT
ejpam-2415	518	1	zn)im	zn)im	X
ejpam-2415	518	2	¶	¶	NOUN
ejpam-2415	518	3	0	0	NUM
ejpam-2415	518	4	m	m	VERB
ejpam-2415	518	5	:	:	PUNCT
ejpam-2415	519	1	y	y	PROPN
ejpam-2415	519	2	i	i	PRON
ejpam-2415	519	3	m	m	VERB
ejpam-2415	519	4	.	.	PUNCT
ejpam-2415	520	1	c	c	PROPN
ejpam-2415	520	2	manjarekar	manjarekar	PROPN
ejpam-2415	520	3	,	,	PUNCT
ejpam-2415	520	4	u	u	NOUN
ejpam-2415	520	5	kandale	kandale	PROPN
ejpam-2415	520	6	/	/	SYM
ejpam-2415	520	7	eur	eur	PROPN
ejpam-2415	520	8	.	.	PUNCT
ejpam-2415	521	1	j.	j.	PROPN
ejpam-2415	521	2	pure	pure	PROPN
ejpam-2415	521	3	appl	appl	PROPN
ejpam-2415	521	4	.	.	PROPN
ejpam-2415	521	5	math	math	PROPN
ejpam-2415	521	6	,	,	PUNCT
ejpam-2415	521	7	8	8	NUM
ejpam-2415	521	8	(	(	PUNCT
ejpam-2415	521	9	2015	2015	NUM
ejpam-2415	521	10	)	)	PUNCT
ejpam-2415	521	11	,	,	PUNCT
ejpam-2415	521	12	332	332	NUM
ejpam-2415	521	13	-	-	SYM
ejpam-2415	521	14	342	342	NUM
ejpam-2415	521	15	341	341	NUM
ejpam-2415	521	16	thus	thus	ADV
ejpam-2415	521	17	if	if	SCONJ
ejpam-2415	521	18	x	x	PROPN
ejpam-2415	521	19	=	=	X
ejpam-2415	521	20	x1∨x2∨.	x1∨x2∨.	PROPN
ejpam-2415	521	21	.	.	PUNCT
ejpam-2415	522	1	.∨xn	.∨xn	PUNCT
ejpam-2415	522	2	is	be	AUX
ejpam-2415	522	3	compact	compact	ADJ
ejpam-2415	522	4	element	element	NOUN
ejpam-2415	522	5	such	such	ADJ
ejpam-2415	522	6	that	that	SCONJ
ejpam-2415	522	7	x	x	PUNCT
ejpam-2415	523	1	i	i	PRON
ejpam-2415	523	2	m	m	VERB
ejpam-2415	523	3	=	=	PUNCT
ejpam-2415	523	4	(	(	PUNCT
ejpam-2415	523	5	x1∨x2∨.	x1∨x2∨.	PROPN
ejpam-2415	523	6	.	.	PUNCT
ejpam-2415	524	1	.∨xn)im	.∨xn)im	PROPN
ejpam-2415	524	2	¶	¶	INTJ
ejpam-2415	524	3	a¶	a¶	X
ejpam-2415	524	4	zim	zim	PROPN
ejpam-2415	524	5	,	,	PUNCT
ejpam-2415	524	6	we	we	PRON
ejpam-2415	524	7	get	get	VERB
ejpam-2415	524	8	0	0	NUM
ejpam-2415	524	9	m	m	VERB
ejpam-2415	524	10	:	:	PUNCT
ejpam-2415	524	11	x	x	PUNCT
ejpam-2415	525	1	i	i	NOUN
ejpam-2415	525	2	m	m	VERB
ejpam-2415	525	3	¶	¶	PROPN
ejpam-2415	525	4	0	0	NUM
ejpam-2415	525	5	m	m	VERB
ejpam-2415	525	6	:	:	PUNCT
ejpam-2415	526	1	y	y	PROPN
ejpam-2415	526	2	i	i	PRON
ejpam-2415	526	3	m	m	VERB
ejpam-2415	526	4	.	.	PUNCT
ejpam-2415	527	1	as	as	SCONJ
ejpam-2415	527	2	zim	zim	PROPN
ejpam-2415	527	3	is	be	AUX
ejpam-2415	527	4	a	a	DET
ejpam-2415	527	5	baer	baer	PROPN
ejpam-2415	527	6	element	element	NOUN
ejpam-2415	527	7	we	we	PRON
ejpam-2415	527	8	have	have	VERB
ejpam-2415	527	9	y	y	PROPN
ejpam-2415	527	10	i	i	PRON
ejpam-2415	527	11	m	m	VERB
ejpam-2415	527	12	¶	¶	PROPN
ejpam-2415	527	13	0	0	NUM
ejpam-2415	527	14	m	m	VERB
ejpam-2415	527	15	:	:	PUNCT
ejpam-2415	527	16	(	(	PUNCT
ejpam-2415	527	17	0	0	NUM
ejpam-2415	527	18	m	m	VERB
ejpam-2415	527	19	:	:	PUNCT
ejpam-2415	528	1	y	y	PROPN
ejpam-2415	528	2	i	i	PRON
ejpam-2415	528	3	m	m	VERB
ejpam-2415	528	4	)	)	PUNCT
ejpam-2415	528	5	¶	¶	PROPN
ejpam-2415	528	6	0	0	NUM
ejpam-2415	528	7	m	m	VERB
ejpam-2415	528	8	:	:	PUNCT
ejpam-2415	528	9	(	(	PUNCT
ejpam-2415	528	10	0	0	NUM
ejpam-2415	528	11	m	m	VERB
ejpam-2415	528	12	:	:	PUNCT
ejpam-2415	528	13	x	x	PUNCT
ejpam-2415	528	14	i	i	NOUN
ejpam-2415	528	15	m	m	PROPN
ejpam-2415	528	16	)	)	PUNCT
ejpam-2415	528	17	¶	¶	PROPN
ejpam-2415	528	18	zim	zim	PROPN
ejpam-2415	528	19	.	.	PUNCT
ejpam-2415	529	1	therefore	therefore	ADV
ejpam-2415	529	2	b	b	PROPN
ejpam-2415	529	3	¶	¶	PROPN
ejpam-2415	529	4	zim	zim	PROPN
ejpam-2415	529	5	.	.	PUNCT
ejpam-2415	530	1	this	this	PRON
ejpam-2415	530	2	shows	show	VERB
ejpam-2415	530	3	that	that	SCONJ
ejpam-2415	530	4	⊻{0	⊻{0	ADP
ejpam-2415	530	5	m	m	VERB
ejpam-2415	530	6	:	:	PUNCT
ejpam-2415	530	7	(	(	PUNCT
ejpam-2415	530	8	0	0	NUM
ejpam-2415	530	9	m	m	VERB
ejpam-2415	530	10	:	:	PUNCT
ejpam-2415	530	11	x	x	PUNCT
ejpam-2415	530	12	i	i	PRON
ejpam-2415	530	13	m	m	VERB
ejpam-2415	530	14	)	)	PUNCT
ejpam-2415	531	1	|	|	ADV
ejpam-2415	531	2	x	x	SYM
ejpam-2415	531	3	∈	∈	PROPN
ejpam-2415	531	4	l∗	l∗	NOUN
ejpam-2415	531	5	and	and	CCONJ
ejpam-2415	531	6	x	x	PUNCT
ejpam-2415	531	7	i	i	NOUN
ejpam-2415	531	8	m	m	VERB
ejpam-2415	531	9	¶	¶	PROPN
ejpam-2415	531	10	a	a	X
ejpam-2415	531	11	}	}	PUNCT
ejpam-2415	531	12	is	be	AUX
ejpam-2415	531	13	the	the	DET
ejpam-2415	531	14	smallest	small	ADJ
ejpam-2415	531	15	baer	baer	PROPN
ejpam-2415	531	16	element	element	NOUN
ejpam-2415	531	17	greater	great	ADJ
ejpam-2415	531	18	than	than	ADP
ejpam-2415	531	19	a.	a.	NOUN
ejpam-2415	531	20	notation	notation	NOUN
ejpam-2415	531	21	:	:	PUNCT
ejpam-2415	531	22	for	for	ADP
ejpam-2415	531	23	a	a	DET
ejpam-2415	531	24	family	family	NOUN
ejpam-2415	531	25	{	{	PUNCT
ejpam-2415	531	26	aα	aα	NOUN
ejpam-2415	531	27	}	}	PUNCT
ejpam-2415	531	28	of	of	ADP
ejpam-2415	531	29	closed	closed	ADJ
ejpam-2415	531	30	elements	element	NOUN
ejpam-2415	531	31	of	of	ADP
ejpam-2415	531	32	m	m	VERB
ejpam-2415	531	33	we	we	PRON
ejpam-2415	531	34	define	define	VERB
ejpam-2415	531	35	,	,	PUNCT
ejpam-2415	531	36	a	a	DET
ejpam-2415	531	37	▽	▽	NOUN
ejpam-2415	531	38	b	b	NOUN
ejpam-2415	531	39	=	=	SYM
ejpam-2415	531	40	∨{zim	∨{zim	NOUN
ejpam-2415	531	41	,	,	PUNCT
ejpam-2415	531	42	z	z	PROPN
ejpam-2415	531	43	∈	∈	PROPN
ejpam-2415	531	44	l∗	l∗	NOUN
ejpam-2415	531	45	|	|	ADV
ejpam-2415	531	46	0	0	NUM
ejpam-2415	531	47	m	m	VERB
ejpam-2415	531	48	:	:	PUNCT
ejpam-2415	531	49	(	(	PUNCT
ejpam-2415	531	50	x	x	SYM
ejpam-2415	531	51	∨	∨	NUM
ejpam-2415	531	52	y)im	y)im	PROPN
ejpam-2415	531	53	¶	¶	PROPN
ejpam-2415	531	54	0	0	PROPN
ejpam-2415	531	55	m	m	VERB
ejpam-2415	531	56	:	:	PUNCT
ejpam-2415	531	57	zim	zim	NOUN
ejpam-2415	531	58	for	for	ADP
ejpam-2415	531	59	some	some	PRON
ejpam-2415	531	60	x	x	PROPN
ejpam-2415	532	1	i	i	PRON
ejpam-2415	532	2	m	m	VERB
ejpam-2415	532	3	¶	¶	PROPN
ejpam-2415	532	4	a	a	PRON
ejpam-2415	532	5	and	and	CCONJ
ejpam-2415	532	6	y	y	NOUN
ejpam-2415	532	7	i	i	NOUN
ejpam-2415	532	8	m	m	VERB
ejpam-2415	532	9	¶	¶	PROPN
ejpam-2415	532	10	b	b	PROPN
ejpam-2415	532	11	}	}	PUNCT
ejpam-2415	532	12	.	.	PUNCT
ejpam-2415	533	1	then	then	ADV
ejpam-2415	533	2	we	we	PRON
ejpam-2415	533	3	have	have	VERB
ejpam-2415	533	4	the	the	DET
ejpam-2415	533	5	following	follow	VERB
ejpam-2415	533	6	important	important	ADJ
ejpam-2415	533	7	result	result	NOUN
ejpam-2415	533	8	.	.	PUNCT
ejpam-2415	534	1	the	the	DET
ejpam-2415	534	2	property	property	NOUN
ejpam-2415	534	3	of	of	ADP
ejpam-2415	534	4	closed	closed	ADJ
ejpam-2415	534	5	elements	element	NOUN
ejpam-2415	534	6	is	be	AUX
ejpam-2415	534	7	proved	prove	VERB
ejpam-2415	534	8	in	in	ADP
ejpam-2415	534	9	the	the	DET
ejpam-2415	534	10	next	next	ADJ
ejpam-2415	534	11	theorem	theorem	PROPN
ejpam-2415	534	12	.	.	PUNCT
ejpam-2415	534	13	theorem	theorem	PROPN
ejpam-2415	534	14	24	24	NUM
ejpam-2415	534	15	.	.	PUNCT
ejpam-2415	535	1	if	if	SCONJ
ejpam-2415	535	2	a	a	PRON
ejpam-2415	535	3	and	and	CCONJ
ejpam-2415	535	4	b	b	NOUN
ejpam-2415	535	5	are	be	AUX
ejpam-2415	535	6	closed	closed	ADJ
ejpam-2415	535	7	elements	element	NOUN
ejpam-2415	535	8	of	of	ADP
ejpam-2415	535	9	m	m	PROPN
ejpam-2415	535	10	a	a	DET
ejpam-2415	535	11	▽	▽	ADJ
ejpam-2415	535	12	b	b	NOUN
ejpam-2415	535	13	is	be	AUX
ejpam-2415	535	14	the	the	DET
ejpam-2415	535	15	smallest	small	ADJ
ejpam-2415	535	16	closed	closed	ADJ
ejpam-2415	535	17	element	element	NOUN
ejpam-2415	535	18	greater	great	ADJ
ejpam-2415	535	19	than	than	ADP
ejpam-2415	535	20	a	a	DET
ejpam-2415	535	21	as	as	ADV
ejpam-2415	535	22	well	well	ADV
ejpam-2415	535	23	as	as	ADP
ejpam-2415	535	24	b.	b.	PROPN
ejpam-2415	535	25	proof	proof	NOUN
ejpam-2415	535	26	.	.	PUNCT
ejpam-2415	536	1	we	we	PRON
ejpam-2415	536	2	show	show	VERB
ejpam-2415	536	3	that	that	SCONJ
ejpam-2415	536	4	a	a	DET
ejpam-2415	536	5	▽	▽	ADJ
ejpam-2415	536	6	b	b	NOUN
ejpam-2415	536	7	is	be	AUX
ejpam-2415	536	8	closed	close	VERB
ejpam-2415	536	9	greater	great	ADJ
ejpam-2415	536	10	than	than	ADP
ejpam-2415	536	11	a	a	PRON
ejpam-2415	536	12	as	as	ADV
ejpam-2415	536	13	well	well	ADV
ejpam-2415	536	14	as	as	ADP
ejpam-2415	536	15	b.	b.	PROPN
ejpam-2415	536	16	let	let	VERB
ejpam-2415	536	17	c	c	NOUN
ejpam-2415	536	18	=	=	VERB
ejpam-2415	536	19	a	a	DET
ejpam-2415	536	20	▽	▽	X
ejpam-2415	536	21	b.	b.	NOUN
ejpam-2415	536	22	we	we	PRON
ejpam-2415	536	23	always	always	ADV
ejpam-2415	536	24	have	have	VERB
ejpam-2415	536	25	c	c	PROPN
ejpam-2415	536	26	¶	¶	PROPN
ejpam-2415	536	27	0	0	NUM
ejpam-2415	536	28	m	m	VERB
ejpam-2415	536	29	:	:	PUNCT
ejpam-2415	536	30	(	(	PUNCT
ejpam-2415	536	31	0	0	NUM
ejpam-2415	536	32	m	m	VERB
ejpam-2415	536	33	:	:	PUNCT
ejpam-2415	536	34	c	c	X
ejpam-2415	536	35	)	)	PUNCT
ejpam-2415	536	36	where	where	SCONJ
ejpam-2415	536	37	c	c	PROPN
ejpam-2415	536	38	∈	∈	PROPN
ejpam-2415	536	39	m	m	VERB
ejpam-2415	536	40	.	.	PUNCT
ejpam-2415	537	1	let	let	VERB
ejpam-2415	537	2	x	x	PRON
ejpam-2415	537	3	be	be	AUX
ejpam-2415	537	4	compact	compact	ADJ
ejpam-2415	537	5	element	element	NOUN
ejpam-2415	537	6	in	in	ADP
ejpam-2415	537	7	l	l	NOUN
ejpam-2415	537	8	such	such	ADJ
ejpam-2415	537	9	that	that	SCONJ
ejpam-2415	537	10	x	x	PROPN
ejpam-2415	538	1	i	i	NOUN
ejpam-2415	538	2	m	m	VERB
ejpam-2415	538	3	¶	¶	PROPN
ejpam-2415	538	4	0	0	NUM
ejpam-2415	538	5	m	m	VERB
ejpam-2415	538	6	:	:	PUNCT
ejpam-2415	538	7	(	(	PUNCT
ejpam-2415	538	8	0	0	NUM
ejpam-2415	538	9	m	m	VERB
ejpam-2415	538	10	:	:	PUNCT
ejpam-2415	538	11	c	c	X
ejpam-2415	538	12	)	)	PUNCT
ejpam-2415	538	13	.	.	PUNCT
ejpam-2415	539	1	then	then	ADV
ejpam-2415	539	2	0	0	NUM
ejpam-2415	539	3	m	m	VERB
ejpam-2415	539	4	:	:	PUNCT
ejpam-2415	539	5	c	c	PROPN
ejpam-2415	539	6	¶	¶	PROPN
ejpam-2415	539	7	0	0	NUM
ejpam-2415	539	8	m	m	VERB
ejpam-2415	539	9	:	:	PUNCT
ejpam-2415	539	10	x	x	PUNCT
ejpam-2415	539	11	i	i	PRON
ejpam-2415	539	12	m	m	VERB
ejpam-2415	539	13	.	.	PUNCT
ejpam-2415	540	1	this	this	PRON
ejpam-2415	540	2	implies	imply	VERB
ejpam-2415	540	3	that	that	SCONJ
ejpam-2415	540	4	0	0	NUM
ejpam-2415	540	5	m	m	VERB
ejpam-2415	540	6	:	:	PUNCT
ejpam-2415	540	7	(	(	PUNCT
ejpam-2415	540	8	y	y	PROPN
ejpam-2415	540	9	∨	∨	PROPN
ejpam-2415	540	10	z)im	z)im	PROPN
ejpam-2415	540	11	¶	¶	PROPN
ejpam-2415	540	12	0	0	NUM
ejpam-2415	540	13	m	m	VERB
ejpam-2415	540	14	:	:	PUNCT
ejpam-2415	541	1	c	c	PROPN
ejpam-2415	541	2	¶	¶	PROPN
ejpam-2415	541	3	0	0	NUM
ejpam-2415	541	4	m	m	VERB
ejpam-2415	541	5	:	:	PUNCT
ejpam-2415	541	6	x	x	PUNCT
ejpam-2415	541	7	i	i	PRON
ejpam-2415	541	8	m	m	VERB
ejpam-2415	541	9	where	where	SCONJ
ejpam-2415	541	10	y	y	X
ejpam-2415	541	11	,	,	PUNCT
ejpam-2415	541	12	z	z	PROPN
ejpam-2415	541	13	∈	∈	PROPN
ejpam-2415	541	14	l∗	l∗	PROPN
ejpam-2415	541	15	,	,	PUNCT
ejpam-2415	541	16	y	y	PROPN
ejpam-2415	541	17	i	i	PROPN
ejpam-2415	541	18	m	m	VERB
ejpam-2415	541	19	¶	¶	PROPN
ejpam-2415	541	20	a	a	PRON
ejpam-2415	541	21	and	and	CCONJ
ejpam-2415	541	22	zim	zim	PROPN
ejpam-2415	541	23	¶	¶	PROPN
ejpam-2415	541	24	b.	b.	PROPN
ejpam-2415	542	1	but	but	CCONJ
ejpam-2415	542	2	y	y	PROPN
ejpam-2415	542	3	i	i	PRON
ejpam-2415	542	4	m	m	VERB
ejpam-2415	542	5	¶	¶	PROPN
ejpam-2415	542	6	a	a	DET
ejpam-2415	542	7	▽	▽	ADJ
ejpam-2415	542	8	b	b	NOUN
ejpam-2415	542	9	,	,	PUNCT
ejpam-2415	542	10	zim	zim	PROPN
ejpam-2415	542	11	¶	¶	PROPN
ejpam-2415	542	12	a	a	DET
ejpam-2415	542	13	▽	▽	X
ejpam-2415	542	14	b.	b.	NOUN
ejpam-2415	542	15	hence	hence	ADV
ejpam-2415	542	16	0	0	NUM
ejpam-2415	542	17	m	m	VERB
ejpam-2415	542	18	:	:	PUNCT
ejpam-2415	542	19	(	(	PUNCT
ejpam-2415	542	20	r∨s)im	r∨s)im	PROPN
ejpam-2415	542	21	¶	¶	PROPN
ejpam-2415	542	22	0	0	PROPN
ejpam-2415	542	23	m	m	VERB
ejpam-2415	542	24	:	:	PUNCT
ejpam-2415	543	1	y	y	PROPN
ejpam-2415	543	2	i	i	PRON
ejpam-2415	543	3	m	m	VERB
ejpam-2415	543	4	and	and	CCONJ
ejpam-2415	543	5	0	0	NUM
ejpam-2415	543	6	m	m	VERB
ejpam-2415	543	7	:	:	PUNCT
ejpam-2415	543	8	(	(	PUNCT
ejpam-2415	543	9	u∨v)im	u∨v)im	ADJ
ejpam-2415	543	10	¶	¶	PROPN
ejpam-2415	543	11	0	0	PROPN
ejpam-2415	543	12	m	m	VERB
ejpam-2415	543	13	:	:	PUNCT
ejpam-2415	543	14	zim	zim	X
ejpam-2415	543	15	where	where	SCONJ
ejpam-2415	543	16	r	r	NOUN
ejpam-2415	543	17	i	i	PRON
ejpam-2415	543	18	m	m	VERB
ejpam-2415	543	19	,	,	PUNCT
ejpam-2415	543	20	uim	uim	PROPN
ejpam-2415	543	21	¶	¶	PROPN
ejpam-2415	543	22	a	a	PRON
ejpam-2415	543	23	and	and	CCONJ
ejpam-2415	543	24	sim	sim	ADJ
ejpam-2415	543	25	,	,	PUNCT
ejpam-2415	543	26	vim	vim	PROPN
ejpam-2415	543	27	¶	¶	PROPN
ejpam-2415	543	28	b.	b.	PROPN
ejpam-2415	544	1	therefore	therefore	ADV
ejpam-2415	544	2	0	0	NUM
ejpam-2415	544	3	m	m	VERB
ejpam-2415	544	4	:	:	PUNCT
ejpam-2415	544	5	(	(	PUNCT
ejpam-2415	544	6	r	r	NOUN
ejpam-2415	544	7	∨	∨	NUM
ejpam-2415	544	8	s)im	s)im	PROPN
ejpam-2415	544	9	∧	∧	PROPN
ejpam-2415	544	10	0	0	NUM
ejpam-2415	544	11	m	m	VERB
ejpam-2415	544	12	:	:	PUNCT
ejpam-2415	544	13	(	(	PUNCT
ejpam-2415	544	14	u∨	u∨	PROPN
ejpam-2415	544	15	v)im	v)im	PROPN
ejpam-2415	544	16	¶	¶	PROPN
ejpam-2415	544	17	0	0	PROPN
ejpam-2415	544	18	m	m	VERB
ejpam-2415	544	19	:	:	PUNCT
ejpam-2415	545	1	y	y	PROPN
ejpam-2415	546	1	i	i	PRON
ejpam-2415	546	2	m	m	VERB
ejpam-2415	546	3	∧	∧	PROPN
ejpam-2415	546	4	0	0	NUM
ejpam-2415	546	5	m	m	VERB
ejpam-2415	546	6	:	:	PUNCT
ejpam-2415	546	7	zim	zim	X
ejpam-2415	546	8	.	.	PUNCT
ejpam-2415	547	1	consequently	consequently	ADV
ejpam-2415	547	2	0	0	NUM
ejpam-2415	547	3	m	m	VERB
ejpam-2415	547	4	:	:	PUNCT
ejpam-2415	547	5	(	(	PUNCT
ejpam-2415	547	6	r	r	NOUN
ejpam-2415	547	7	∨	∨	NUM
ejpam-2415	547	8	s	s	PART
ejpam-2415	547	9	∨	∨	NOUN
ejpam-2415	547	10	u∨	u∨	ADJ
ejpam-2415	547	11	v)im	v)im	PROPN
ejpam-2415	547	12	¶	¶	PROPN
ejpam-2415	547	13	0	0	PROPN
ejpam-2415	547	14	m	m	VERB
ejpam-2415	547	15	:	:	PUNCT
ejpam-2415	547	16	(	(	PUNCT
ejpam-2415	547	17	y	y	PROPN
ejpam-2415	547	18	∨	∨	PROPN
ejpam-2415	547	19	z)im	z)im	PROPN
ejpam-2415	547	20	¶	¶	PROPN
ejpam-2415	547	21	0	0	NUM
ejpam-2415	547	22	m	m	VERB
ejpam-2415	547	23	:	:	PUNCT
ejpam-2415	547	24	x	x	PUNCT
ejpam-2415	547	25	i	i	PRON
ejpam-2415	547	26	m	m	VERB
ejpam-2415	547	27	,	,	PUNCT
ejpam-2415	547	28	where	where	SCONJ
ejpam-2415	547	29	(	(	PUNCT
ejpam-2415	547	30	r	r	NOUN
ejpam-2415	547	31	∨	∨	NUM
ejpam-2415	547	32	u)im	u)im	PROPN
ejpam-2415	547	33	¶	¶	PROPN
ejpam-2415	547	34	a	a	PRON
ejpam-2415	547	35	and	and	CCONJ
ejpam-2415	547	36	(	(	PUNCT
ejpam-2415	547	37	s	s	NOUN
ejpam-2415	547	38	∨	∨	NUM
ejpam-2415	547	39	v)im	v)im	PROPN
ejpam-2415	547	40	¶	¶	PROPN
ejpam-2415	547	41	b.	b.	PROPN
ejpam-2415	548	1	this	this	PRON
ejpam-2415	548	2	implies	imply	VERB
ejpam-2415	548	3	that	that	SCONJ
ejpam-2415	548	4	x	x	PUNCT
ejpam-2415	548	5	i	i	NOUN
ejpam-2415	548	6	m	m	VERB
ejpam-2415	548	7	¶	¶	PROPN
ejpam-2415	548	8	c	c	NOUN
ejpam-2415	548	9	.	.	PUNCT
ejpam-2415	549	1	hence	hence	ADV
ejpam-2415	549	2	0	0	NUM
ejpam-2415	549	3	m	m	VERB
ejpam-2415	549	4	:	:	PUNCT
ejpam-2415	549	5	(	(	PUNCT
ejpam-2415	549	6	0	0	NUM
ejpam-2415	549	7	m	m	VERB
ejpam-2415	549	8	:	:	PUNCT
ejpam-2415	549	9	c	c	X
ejpam-2415	549	10	)	)	PUNCT
ejpam-2415	549	11	¶	¶	PROPN
ejpam-2415	549	12	c	c	PROPN
ejpam-2415	549	13	.	.	PUNCT
ejpam-2415	550	1	this	this	PRON
ejpam-2415	550	2	gives	give	VERB
ejpam-2415	550	3	0	0	NUM
ejpam-2415	550	4	m	m	VERB
ejpam-2415	550	5	:	:	PUNCT
ejpam-2415	550	6	(	(	PUNCT
ejpam-2415	550	7	0	0	NUM
ejpam-2415	550	8	m	m	VERB
ejpam-2415	550	9	:	:	PUNCT
ejpam-2415	551	1	c	c	X
ejpam-2415	551	2	)	)	PUNCT
ejpam-2415	551	3	=	=	SYM
ejpam-2415	552	1	c	c	NOUN
ejpam-2415	552	2	and	and	CCONJ
ejpam-2415	552	3	c	c	PROPN
ejpam-2415	552	4	is	be	AUX
ejpam-2415	552	5	closed	closed	ADJ
ejpam-2415	552	6	.	.	PUNCT
ejpam-2415	553	1	as	as	ADP
ejpam-2415	553	2	0	0	NUM
ejpam-2415	553	3	m	m	NOUN
ejpam-2415	553	4	;	;	PUNCT
ejpam-2415	553	5	sim	sim	ADJ
ejpam-2415	553	6	¶	¶	PROPN
ejpam-2415	553	7	0	0	PROPN
ejpam-2415	553	8	m	m	VERB
ejpam-2415	553	9	:	:	PUNCT
ejpam-2415	553	10	sim	sim	ADJ
ejpam-2415	553	11	for	for	ADP
ejpam-2415	553	12	any	any	DET
ejpam-2415	553	13	element	element	NOUN
ejpam-2415	553	14	s	s	PART
ejpam-2415	553	15	in	in	ADP
ejpam-2415	553	16	l	l	NOUN
ejpam-2415	553	17	,	,	PUNCT
ejpam-2415	553	18	it	it	PRON
ejpam-2415	553	19	follows	follow	VERB
ejpam-2415	553	20	that	that	SCONJ
ejpam-2415	553	21	a	a	DET
ejpam-2415	553	22	,	,	PUNCT
ejpam-2415	553	23	b	b	PROPN
ejpam-2415	553	24	¶	¶	PROPN
ejpam-2415	553	25	a	a	DET
ejpam-2415	553	26	▽	▽	X
ejpam-2415	553	27	b.	b.	PROPN
ejpam-2415	553	28	suppose	suppose	VERB
ejpam-2415	553	29	that	that	SCONJ
ejpam-2415	553	30	w	w	NOUN
ejpam-2415	553	31	is	be	AUX
ejpam-2415	553	32	closed	closed	ADJ
ejpam-2415	553	33	element	element	NOUN
ejpam-2415	553	34	such	such	ADJ
ejpam-2415	553	35	that	that	SCONJ
ejpam-2415	553	36	a	a	DET
ejpam-2415	553	37	,	,	PUNCT
ejpam-2415	553	38	b	b	NOUN
ejpam-2415	553	39	¶w	¶w	NOUN
ejpam-2415	553	40	and	and	CCONJ
ejpam-2415	553	41	let	let	VERB
ejpam-2415	553	42	x	x	X
ejpam-2415	553	43	∈	∈	PROPN
ejpam-2415	553	44	l∗	l∗	NOUN
ejpam-2415	553	45	be	be	AUX
ejpam-2415	553	46	such	such	ADJ
ejpam-2415	553	47	that	that	SCONJ
ejpam-2415	553	48	0	0	NUM
ejpam-2415	553	49	m	m	VERB
ejpam-2415	553	50	:	:	PUNCT
ejpam-2415	553	51	(	(	PUNCT
ejpam-2415	553	52	u∨	u∨	PROPN
ejpam-2415	553	53	v)im	v)im	PROPN
ejpam-2415	553	54	¶	¶	PROPN
ejpam-2415	553	55	0	0	PROPN
ejpam-2415	553	56	m	m	VERB
ejpam-2415	553	57	:	:	PUNCT
ejpam-2415	553	58	x	x	PUNCT
ejpam-2415	554	1	i	i	PRON
ejpam-2415	554	2	m	m	VERB
ejpam-2415	554	3	for	for	ADP
ejpam-2415	554	4	some	some	DET
ejpam-2415	554	5	uim	uim	NOUN
ejpam-2415	554	6	¶	¶	PROPN
ejpam-2415	554	7	a	a	PROPN
ejpam-2415	554	8	and	and	CCONJ
ejpam-2415	554	9	vim	vim	PROPN
ejpam-2415	554	10	¶	¶	PROPN
ejpam-2415	554	11	b.	b.	PROPN
ejpam-2415	554	12	note	note	VERB
ejpam-2415	554	13	that	that	SCONJ
ejpam-2415	554	14	w	w	NOUN
ejpam-2415	554	15	is	be	AUX
ejpam-2415	554	16	a	a	DET
ejpam-2415	554	17	closed	closed	ADJ
ejpam-2415	554	18	element	element	NOUN
ejpam-2415	554	19	and	and	CCONJ
ejpam-2415	554	20	(	(	PUNCT
ejpam-2415	554	21	u	u	NOUN
ejpam-2415	554	22	∨	∨	PROPN
ejpam-2415	554	23	v)im	v)im	PROPN
ejpam-2415	554	24	¶	¶	PROPN
ejpam-2415	554	25	w	w	PROPN
ejpam-2415	554	26	.	.	PUNCT
ejpam-2415	555	1	hence	hence	ADV
ejpam-2415	555	2	we	we	PRON
ejpam-2415	555	3	have	have	VERB
ejpam-2415	555	4	0	0	NUM
ejpam-2415	555	5	m	m	VERB
ejpam-2415	555	6	:	:	PUNCT
ejpam-2415	556	1	[	[	X
ejpam-2415	556	2	0	0	NUM
ejpam-2415	556	3	m	m	VERB
ejpam-2415	556	4	:	:	PUNCT
ejpam-2415	556	5	(	(	PUNCT
ejpam-2415	556	6	u	u	NOUN
ejpam-2415	556	7	∨	∨	NUM
ejpam-2415	556	8	v)im	v)im	PROPN
ejpam-2415	556	9	]	]	PUNCT
ejpam-2415	557	1	¶	¶	PROPN
ejpam-2415	557	2	0	0	NUM
ejpam-2415	557	3	m	m	VERB
ejpam-2415	557	4	:	:	PUNCT
ejpam-2415	557	5	(	(	PUNCT
ejpam-2415	557	6	0	0	NUM
ejpam-2415	557	7	m	m	VERB
ejpam-2415	557	8	:	:	PUNCT
ejpam-2415	557	9	w	w	X
ejpam-2415	557	10	)	)	PUNCT
ejpam-2415	558	1	=	=	PUNCT
ejpam-2415	558	2	w	w	X
ejpam-2415	558	3	.	.	PUNCT
ejpam-2415	558	4	again	again	ADV
ejpam-2415	558	5	note	note	VERB
ejpam-2415	558	6	that	that	SCONJ
ejpam-2415	558	7	0	0	NUM
ejpam-2415	558	8	m	m	VERB
ejpam-2415	558	9	:	:	PUNCT
ejpam-2415	558	10	(	(	PUNCT
ejpam-2415	558	11	0	0	NUM
ejpam-2415	558	12	m	m	VERB
ejpam-2415	558	13	:	:	PUNCT
ejpam-2415	558	14	x	x	PUNCT
ejpam-2415	558	15	i	i	NOUN
ejpam-2415	558	16	m	m	VERB
ejpam-2415	558	17	)	)	PUNCT
ejpam-2415	558	18	¶	¶	PROPN
ejpam-2415	558	19	0	0	NUM
ejpam-2415	558	20	m	m	VERB
ejpam-2415	558	21	:	:	PUNCT
ejpam-2415	559	1	[	[	X
ejpam-2415	559	2	0	0	NUM
ejpam-2415	559	3	m	m	VERB
ejpam-2415	559	4	:	:	PUNCT
ejpam-2415	559	5	(	(	PUNCT
ejpam-2415	559	6	u	u	NOUN
ejpam-2415	559	7	∨	∨	NUM
ejpam-2415	559	8	v)im	v)im	PROPN
ejpam-2415	559	9	]	]	PUNCT
ejpam-2415	560	1	¶	¶	PROPN
ejpam-2415	560	2	w	w	PROPN
ejpam-2415	561	1	and	and	CCONJ
ejpam-2415	561	2	x	x	PROPN
ejpam-2415	562	1	i	i	NOUN
ejpam-2415	562	2	m	m	VERB
ejpam-2415	562	3	¶	¶	PROPN
ejpam-2415	562	4	0	0	NUM
ejpam-2415	562	5	m	m	VERB
ejpam-2415	562	6	:	:	PUNCT
ejpam-2415	562	7	(	(	PUNCT
ejpam-2415	562	8	0	0	NUM
ejpam-2415	562	9	m	m	VERB
ejpam-2415	562	10	:	:	PUNCT
ejpam-2415	562	11	x	x	PUNCT
ejpam-2415	562	12	i	i	NOUN
ejpam-2415	562	13	m	m	PROPN
ejpam-2415	562	14	)	)	PUNCT
ejpam-2415	562	15	.	.	PUNCT
ejpam-2415	563	1	therefore	therefore	ADV
ejpam-2415	563	2	x	x	VERB
ejpam-2415	563	3	i	i	NOUN
ejpam-2415	563	4	m	m	VERB
ejpam-2415	563	5	¶w	¶w	NOUN
ejpam-2415	563	6	and	and	CCONJ
ejpam-2415	563	7	hence	hence	ADV
ejpam-2415	563	8	a	a	DET
ejpam-2415	563	9	▽	▽	ADJ
ejpam-2415	563	10	b	b	NOUN
ejpam-2415	563	11	¶w	¶w	NOUN
ejpam-2415	563	12	.	.	PUNCT
ejpam-2415	564	1	consequently	consequently	ADV
ejpam-2415	564	2	,	,	PUNCT
ejpam-2415	564	3	it	it	PRON
ejpam-2415	564	4	proves	prove	VERB
ejpam-2415	564	5	that	that	SCONJ
ejpam-2415	564	6	a	a	DET
ejpam-2415	564	7	▽	▽	ADJ
ejpam-2415	564	8	b	b	NOUN
ejpam-2415	564	9	is	be	AUX
ejpam-2415	564	10	the	the	DET
ejpam-2415	564	11	smallest	small	ADJ
ejpam-2415	564	12	closed	closed	ADJ
ejpam-2415	564	13	element	element	NOUN
ejpam-2415	564	14	greater	great	ADJ
ejpam-2415	564	15	than	than	ADP
ejpam-2415	564	16	a	a	PRON
ejpam-2415	564	17	as	as	ADV
ejpam-2415	564	18	well	well	ADV
ejpam-2415	564	19	as	as	ADP
ejpam-2415	564	20	b.	b.	PROPN
ejpam-2415	564	21	theorem	theorem	PROPN
ejpam-2415	564	22	25	25	NUM
ejpam-2415	564	23	.	.	PUNCT
ejpam-2415	565	1	if	if	SCONJ
ejpam-2415	565	2	a	a	PRON
ejpam-2415	565	3	and	and	CCONJ
ejpam-2415	565	4	b	b	NOUN
ejpam-2415	565	5	are	be	AUX
ejpam-2415	565	6	closed	closed	ADJ
ejpam-2415	565	7	elements	element	NOUN
ejpam-2415	565	8	of	of	ADP
ejpam-2415	565	9	m	m	PRON
ejpam-2415	565	10	then	then	ADV
ejpam-2415	565	11	a	a	DET
ejpam-2415	565	12	▽	▽	NOUN
ejpam-2415	565	13	b	b	NOUN
ejpam-2415	565	14	=	=	SYM
ejpam-2415	565	15	0	0	NUM
ejpam-2415	565	16	m	m	VERB
ejpam-2415	565	17	:	:	PUNCT
ejpam-2415	566	1	[	[	X
ejpam-2415	566	2	0	0	NUM
ejpam-2415	566	3	m	m	VERB
ejpam-2415	566	4	:	:	PUNCT
ejpam-2415	566	5	(	(	PUNCT
ejpam-2415	566	6	a∨	a∨	PROPN
ejpam-2415	566	7	b	b	PROPN
ejpam-2415	566	8	)	)	PUNCT
ejpam-2415	566	9	]	]	PUNCT
ejpam-2415	566	10	.	.	PUNCT
ejpam-2415	567	1	proof	proof	NOUN
ejpam-2415	567	2	.	.	PUNCT
ejpam-2415	568	1	by	by	ADP
ejpam-2415	568	2	theorem	theorem	NOUN
ejpam-2415	568	3	24	24	NUM
ejpam-2415	568	4	,	,	PUNCT
ejpam-2415	568	5	we	we	PRON
ejpam-2415	568	6	have	have	VERB
ejpam-2415	568	7	a∨b	a∨b	PROPN
ejpam-2415	568	8	¶	¶	PROPN
ejpam-2415	568	9	a	a	DET
ejpam-2415	568	10	▽	▽	X
ejpam-2415	568	11	b.	b.	NOUN
ejpam-2415	568	12	hence	hence	ADV
ejpam-2415	568	13	0	0	NUM
ejpam-2415	568	14	m	m	VERB
ejpam-2415	568	15	:	:	PUNCT
ejpam-2415	569	1	[	[	X
ejpam-2415	569	2	0	0	NUM
ejpam-2415	569	3	m	m	VERB
ejpam-2415	569	4	:	:	PUNCT
ejpam-2415	569	5	(	(	PUNCT
ejpam-2415	569	6	a∨b)]¶	a∨b)]¶	ADP
ejpam-2415	569	7	a	a	DET
ejpam-2415	569	8	▽	▽	NOUN
ejpam-2415	569	9	b	b	NOUN
ejpam-2415	569	10	as	as	ADP
ejpam-2415	569	11	a	a	DET
ejpam-2415	569	12	▽	▽	NOUN
ejpam-2415	569	13	b	b	NOUN
ejpam-2415	569	14	is	be	AUX
ejpam-2415	569	15	a	a	DET
ejpam-2415	569	16	closed	closed	ADJ
ejpam-2415	569	17	element	element	NOUN
ejpam-2415	569	18	.	.	PUNCT
ejpam-2415	570	1	let	let	VERB
ejpam-2415	570	2	x	x	PUNCT
ejpam-2415	571	1	i	i	PRON
ejpam-2415	571	2	m	m	VERB
ejpam-2415	571	3	¶	¶	PROPN
ejpam-2415	571	4	a	a	DET
ejpam-2415	571	5	▽	▽	PROPN
ejpam-2415	571	6	b	b	NOUN
ejpam-2415	571	7	,	,	PUNCT
ejpam-2415	571	8	x	x	SYM
ejpam-2415	571	9	∈	∈	PROPN
ejpam-2415	571	10	l∗.	l∗.	NOUN
ejpam-2415	571	11	then	then	ADV
ejpam-2415	571	12	0	0	NUM
ejpam-2415	571	13	m	m	VERB
ejpam-2415	571	14	:	:	PUNCT
ejpam-2415	571	15	(	(	PUNCT
ejpam-2415	571	16	u∨	u∨	PROPN
ejpam-2415	571	17	v)im	v)im	PROPN
ejpam-2415	571	18	¶	¶	PROPN
ejpam-2415	571	19	0	0	PROPN
ejpam-2415	571	20	m	m	VERB
ejpam-2415	571	21	:	:	PUNCT
ejpam-2415	571	22	x	x	PUNCT
ejpam-2415	572	1	i	i	VERB
ejpam-2415	572	2	m	m	VERB
ejpam-2415	572	3	,	,	PUNCT
ejpam-2415	572	4	for	for	ADP
ejpam-2415	572	5	some	some	DET
ejpam-2415	572	6	uim	uim	NOUN
ejpam-2415	572	7	¶	¶	PROPN
ejpam-2415	572	8	a	a	PROPN
ejpam-2415	572	9	and	and	CCONJ
ejpam-2415	572	10	vim	vim	PROPN
ejpam-2415	572	11	¶	¶	PROPN
ejpam-2415	572	12	b.	b.	PROPN
ejpam-2415	572	13	consequently	consequently	ADV
ejpam-2415	572	14	,	,	PUNCT
ejpam-2415	572	15	we	we	PRON
ejpam-2415	572	16	have	have	VERB
ejpam-2415	572	17	x	x	PROPN
ejpam-2415	572	18	i	i	PRON
ejpam-2415	572	19	m	m	VERB
ejpam-2415	572	20	¶	¶	PROPN
ejpam-2415	572	21	0	0	NUM
ejpam-2415	572	22	m	m	VERB
ejpam-2415	572	23	:	:	PUNCT
ejpam-2415	572	24	(	(	PUNCT
ejpam-2415	572	25	0	0	NUM
ejpam-2415	572	26	m	m	VERB
ejpam-2415	572	27	:	:	PUNCT
ejpam-2415	572	28	x	x	PUNCT
ejpam-2415	572	29	i	i	NOUN
ejpam-2415	572	30	m	m	PROPN
ejpam-2415	572	31	)	)	PUNCT
ejpam-2415	572	32	¶	¶	PROPN
ejpam-2415	572	33	0	0	NUM
ejpam-2415	572	34	m	m	VERB
ejpam-2415	572	35	:	:	PUNCT
ejpam-2415	573	1	[	[	X
ejpam-2415	573	2	0	0	NUM
ejpam-2415	573	3	m	m	VERB
ejpam-2415	573	4	:	:	PUNCT
ejpam-2415	573	5	(	(	PUNCT
ejpam-2415	573	6	u∨	u∨	PROPN
ejpam-2415	573	7	v)im	v)im	PROPN
ejpam-2415	573	8	]	]	SYM
ejpam-2415	573	9	¶	¶	PROPN
ejpam-2415	573	10	0	0	NUM
ejpam-2415	573	11	m	m	VERB
ejpam-2415	573	12	:	:	PUNCT
ejpam-2415	574	1	[	[	X
ejpam-2415	574	2	0	0	NUM
ejpam-2415	574	3	m	m	VERB
ejpam-2415	574	4	:	:	PUNCT
ejpam-2415	574	5	(	(	PUNCT
ejpam-2415	574	6	a∨	a∨	PROPN
ejpam-2415	574	7	b	b	PROPN
ejpam-2415	574	8	)	)	PUNCT
ejpam-2415	574	9	]	]	PUNCT
ejpam-2415	574	10	.	.	PUNCT
ejpam-2415	575	1	hence	hence	ADV
ejpam-2415	575	2	a	a	DET
ejpam-2415	575	3	▽	▽	NOUN
ejpam-2415	575	4	b	b	NOUN
ejpam-2415	575	5	¶	¶	X
ejpam-2415	575	6	(	(	PUNCT
ejpam-2415	575	7	0	0	NUM
ejpam-2415	575	8	m	m	VERB
ejpam-2415	575	9	:	:	PUNCT
ejpam-2415	575	10	0	0	NUM
ejpam-2415	575	11	m	m	VERB
ejpam-2415	575	12	:	:	PUNCT
ejpam-2415	575	13	(	(	PUNCT
ejpam-2415	575	14	a∨	a∨	PROPN
ejpam-2415	575	15	b	b	PROPN
ejpam-2415	575	16	)	)	PUNCT
ejpam-2415	575	17	)	)	PUNCT
ejpam-2415	575	18	.	.	PUNCT
ejpam-2415	576	1	thus	thus	ADV
ejpam-2415	576	2	a	a	DET
ejpam-2415	576	3	▽	▽	NOUN
ejpam-2415	576	4	b	b	NOUN
ejpam-2415	576	5	=	=	SYM
ejpam-2415	576	6	0	0	NUM
ejpam-2415	576	7	m	m	VERB
ejpam-2415	576	8	:	:	PUNCT
ejpam-2415	577	1	[	[	X
ejpam-2415	577	2	0	0	NUM
ejpam-2415	577	3	m	m	VERB
ejpam-2415	577	4	:	:	PUNCT
ejpam-2415	577	5	(	(	PUNCT
ejpam-2415	577	6	a∨	a∨	PROPN
ejpam-2415	577	7	b	b	PROPN
ejpam-2415	577	8	)	)	PUNCT
ejpam-2415	577	9	]	]	PUNCT
ejpam-2415	577	10	.	.	PUNCT
ejpam-2415	578	1	references	reference	NOUN
ejpam-2415	578	2	342	342	NUM
ejpam-2415	578	3	acknowledgements	acknowledgement	NOUN
ejpam-2415	578	4	the	the	DET
ejpam-2415	578	5	authors	author	NOUN
ejpam-2415	578	6	thank	thank	VERB
ejpam-2415	578	7	the	the	DET
ejpam-2415	578	8	readers	reader	NOUN
ejpam-2415	578	9	of	of	ADP
ejpam-2415	578	10	european	european	PROPN
ejpam-2415	578	11	journal	journal	PROPN
ejpam-2415	578	12	of	of	ADP
ejpam-2415	578	13	pure	pure	ADJ
ejpam-2415	578	14	and	and	CCONJ
ejpam-2415	578	15	applied	applied	ADJ
ejpam-2415	578	16	mathematics	mathematic	NOUN
ejpam-2415	578	17	,	,	PUNCT
ejpam-2415	578	18	for	for	ADP
ejpam-2415	578	19	making	make	VERB
ejpam-2415	578	20	our	our	PRON
ejpam-2415	578	21	journal	journal	NOUN
ejpam-2415	578	22	successful	successful	ADJ
ejpam-2415	578	23	.	.	PUNCT
ejpam-2415	579	1	we	we	PRON
ejpam-2415	579	2	dedicate	dedicate	VERB
ejpam-2415	579	3	this	this	DET
ejpam-2415	579	4	research	research	NOUN
ejpam-2415	579	5	article	article	NOUN
ejpam-2415	579	6	to	to	PART
ejpam-2415	579	7	prof	prof	PROPN
ejpam-2415	579	8	dr	dr	PROPN
ejpam-2415	579	9	u	u	PROPN
ejpam-2415	579	10	tekir	tekir	PROPN
ejpam-2415	579	11	&	&	CCONJ
ejpam-2415	579	12	prof	prof	PROPN
ejpam-2415	579	13	dr	dr	PROPN
ejpam-2415	579	14	c	c	PROPN
ejpam-2415	579	15	jayram	jayram	PROPN
ejpam-2415	579	16	.	.	PUNCT
ejpam-2415	580	1	references	reference	NOUN
ejpam-2415	580	2	[	[	X
ejpam-2415	580	3	1	1	NUM
ejpam-2415	580	4	]	]	X
ejpam-2415	580	5	d.d	d.d	PROPN
ejpam-2415	580	6	.	.	PROPN
ejpam-2415	580	7	anderson	anderson	PROPN
ejpam-2415	580	8	,	,	PUNCT
ejpam-2415	580	9	c.	c.	PROPN
ejpam-2415	580	10	jayaram	jayaram	PROPN
ejpam-2415	580	11	,	,	PUNCT
ejpam-2415	580	12	and	and	CCONJ
ejpam-2415	580	13	p.a	p.a	PROPN
ejpam-2415	580	14	.	.	PROPN
ejpam-2415	580	15	phiri	phiri	PROPN
ejpam-2415	580	16	.	.	PUNCT
ejpam-2415	581	1	baer	baer	PROPN
ejpam-2415	581	2	lattices	lattices	PROPN
ejpam-2415	581	3	.	.	PUNCT
ejpam-2415	582	1	acta	acta	PROPN
ejpam-2415	582	2	scientiarum	scientiarum	PROPN
ejpam-2415	582	3	mathematicarum	mathematicarum	PROPN
ejpam-2415	582	4	,	,	PUNCT
ejpam-2415	582	5	vol	vol	NOUN
ejpam-2415	582	6	59	59	NUM
ejpam-2415	582	7	.	.	PUNCT
ejpam-2415	582	8	pps	pps	PROPN
ejpam-2415	582	9	61	61	NUM
ejpam-2415	582	10	-	-	SYM
ejpam-2415	582	11	74	74	NUM
ejpam-2415	582	12	.	.	PUNCT
ejpam-2415	582	13	1994	1994	NUM
ejpam-2415	582	14	.	.	PUNCT
ejpam-2415	583	1	[	[	X
ejpam-2415	583	2	2	2	NUM
ejpam-2415	583	3	]	]	PUNCT
ejpam-2415	583	4	f.	f.	PROPN
ejpam-2415	583	5	callialp	callialp	PROPN
ejpam-2415	583	6	and	and	CCONJ
ejpam-2415	583	7	u.	u.	PROPN
ejpam-2415	583	8	tekir	tekir	PROPN
ejpam-2415	583	9	.	.	PUNCT
ejpam-2415	584	1	multiplication	multiplication	NOUN
ejpam-2415	584	2	lattice	lattice	PROPN
ejpam-2415	584	3	modules	module	NOUN
ejpam-2415	584	4	,	,	PUNCT
ejpam-2415	584	5	iranian	iranian	ADJ
ejpam-2415	584	6	journal	journal	PROPN
ejpam-2415	584	7	of	of	ADP
ejpam-2415	584	8	science	science	NOUN
ejpam-2415	584	9	and	and	CCONJ
ejpam-2415	584	10	technology	technology	NOUN
ejpam-2415	584	11	,	,	PUNCT
ejpam-2415	584	12	vol	vol	NOUN
ejpam-2415	584	13	a4	a4	NUM
ejpam-2415	584	14	.	.	PUNCT
ejpam-2415	585	1	pps	pps	NOUN
ejpam-2415	585	2	309	309	NUM
ejpam-2415	585	3	-	-	SYM
ejpam-2415	585	4	313	313	NUM
ejpam-2415	585	5	.	.	PUNCT
ejpam-2415	585	6	2011	2011	NUM
ejpam-2415	585	7	.	.	PUNCT
ejpam-2415	586	1	[	[	X
ejpam-2415	586	2	3	3	X
ejpam-2415	586	3	]	]	PUNCT
ejpam-2415	586	4	j.	j.	PROPN
ejpam-2415	586	5	a.	a.	PROPN
ejpam-2415	586	6	johnson	johnson	PROPN
ejpam-2415	586	7	.	.	PUNCT
ejpam-2415	587	1	a	a	DET
ejpam-2415	587	2	-	-	PUNCT
ejpam-2415	587	3	adic	adic	ADJ
ejpam-2415	587	4	completions	completion	NOUN
ejpam-2415	587	5	of	of	ADP
ejpam-2415	587	6	noetherian	noetherian	ADJ
ejpam-2415	587	7	lattice	lattice	NOUN
ejpam-2415	587	8	modules	module	NOUN
ejpam-2415	587	9	.	.	PUNCT
ejpam-2415	588	1	fundamenta	fundamenta	PROPN
ejpam-2415	588	2	mathematica	mathematica	PROPN
ejpam-2415	588	3	,	,	PUNCT
ejpam-2415	588	4	vol	vol	NOUN
ejpam-2415	588	5	66	66	NUM
ejpam-2415	588	6	.	.	PUNCT
ejpam-2415	589	1	pps	pps	PROPN
ejpam-2415	589	2	.	.	PUNCT
ejpam-2415	590	1	341	341	NUM
ejpam-2415	590	2	-	-	SYM
ejpam-2415	590	3	371	371	NUM
ejpam-2415	590	4	.	.	PUNCT
ejpam-2415	591	1	1970	1970	NUM
ejpam-2415	591	2	.	.	PUNCT
ejpam-2415	592	1	[	[	X
ejpam-2415	592	2	4	4	NUM
ejpam-2415	592	3	]	]	PUNCT
ejpam-2415	592	4	a.	a.	PROPN
ejpam-2415	592	5	kkhouja	kkhouja	PROPN
ejpam-2415	592	6	-	-	PUNCT
ejpam-2415	592	7	al	al	PROPN
ejpam-2415	592	8	eaman	eaman	NOUN
ejpam-2415	592	9	.	.	PUNCT
ejpam-2415	593	1	maximal	maximal	ADJ
ejpam-2415	593	2	elements	element	NOUN
ejpam-2415	593	3	and	and	CCONJ
ejpam-2415	593	4	prime	prime	ADJ
ejpam-2415	593	5	elements	element	NOUN
ejpam-2415	593	6	in	in	ADP
ejpam-2415	593	7	lattice	lattice	NOUN
ejpam-2415	593	8	modules	module	NOUN
ejpam-2415	593	9	.	.	PUNCT
ejpam-2415	594	1	damascus	damascus	PROPN
ejpam-2415	594	2	university	university	PROPN
ejpam-2415	594	3	journal	journal	NOUN
ejpam-2415	594	4	for	for	ADP
ejpam-2415	594	5	basic	basic	ADJ
ejpam-2415	594	6	sciences	science	NOUN
ejpam-2415	594	7	,	,	PUNCT
ejpam-2415	594	8	vol	vol	NOUN
ejpam-2415	594	9	19(2	19(2	NUM
ejpam-2415	594	10	)	)	PUNCT
ejpam-2415	594	11	.	.	PUNCT
ejpam-2415	595	1	2003	2003	NUM
ejpam-2415	595	2	.	.	PUNCT
ejpam-2415	596	1	[	[	X
ejpam-2415	596	2	5	5	NUM
ejpam-2415	596	3	]	]	X
ejpam-2415	596	4	n.k	n.k	PROPN
ejpam-2415	596	5	.	.	PROPN
ejpam-2415	596	6	thakare	thakare	PROPN
ejpam-2415	596	7	and	and	CCONJ
ejpam-2415	596	8	c.s	c.s	PROPN
ejpam-2415	596	9	.	.	PROPN
ejpam-2415	596	10	manjarekar	manjarekar	PROPN
ejpam-2415	596	11	.	.	PUNCT
ejpam-2415	597	1	abstract	abstract	ADJ
ejpam-2415	597	2	spectral	spectral	ADJ
ejpam-2415	597	3	theory	theory	NOUN
ejpam-2415	597	4	:	:	PUNCT
ejpam-2415	597	5	multiplicative	multiplicative	ADJ
ejpam-2415	597	6	lattices	lattice	NOUN
ejpam-2415	597	7	in	in	ADP
ejpam-2415	597	8	which	which	PRON
ejpam-2415	597	9	every	every	DET
ejpam-2415	597	10	character	character	NOUN
ejpam-2415	597	11	is	be	AUX
ejpam-2415	597	12	contained	contain	VERB
ejpam-2415	597	13	in	in	ADP
ejpam-2415	597	14	a	a	DET
ejpam-2415	597	15	unique	unique	ADJ
ejpam-2415	597	16	maximal	maximal	ADJ
ejpam-2415	597	17	character	character	NOUN
ejpam-2415	597	18	.	.	PUNCT
ejpam-2415	598	1	proceedings	proceeding	NOUN
ejpam-2415	598	2	of	of	ADP
ejpam-2415	598	3	the	the	DET
ejpam-2415	598	4	international	international	ADJ
ejpam-2415	598	5	symposium	symposium	NOUN
ejpam-2415	598	6	on	on	ADP
ejpam-2415	598	7	algebra	algebra	NOUN
ejpam-2415	598	8	and	and	CCONJ
ejpam-2415	598	9	its	its	PRON
ejpam-2415	598	10	applications	application	NOUN
ejpam-2415	598	11	,	,	PUNCT
ejpam-2415	598	12	marcel	marcel	PROPN
ejpam-2415	598	13	dekker	dekker	PROPN
ejpam-2415	598	14	and	and	CCONJ
ejpam-2415	598	15	bessel	bessel	NOUN
ejpam-2415	598	16	.	.	PUNCT
ejpam-2415	599	1	pps	pps	PROPN
ejpam-2415	599	2	265	265	NUM
ejpam-2415	599	3	-	-	SYM
ejpam-2415	599	4	276	276	NUM
ejpam-2415	599	5	.	.	PUNCT
ejpam-2415	599	6	1984	1984	NUM
ejpam-2415	599	7	.	.	PUNCT