id	sid	tid	token	lemma	pos
ejpam-6249	1	1	european	european	PROPN
ejpam-6249	1	2	journal	journal	PROPN
ejpam-6249	1	3	of	of	ADP
ejpam-6249	1	4	pure	pure	ADJ
ejpam-6249	1	5	and	and	CCONJ
ejpam-6249	1	6	applied	applied	ADJ
ejpam-6249	1	7	mathematics	mathematic	NOUN
ejpam-6249	1	8	2025	2025	NUM
ejpam-6249	1	9	,	,	PUNCT
ejpam-6249	1	10	vol	vol	NOUN
ejpam-6249	1	11	.	.	PROPN
ejpam-6249	1	12	18	18	NUM
ejpam-6249	1	13	,	,	PUNCT
ejpam-6249	1	14	issue	issue	NOUN
ejpam-6249	1	15	4	4	NUM
ejpam-6249	1	16	,	,	PUNCT
ejpam-6249	1	17	article	article	NOUN
ejpam-6249	1	18	number	number	NOUN
ejpam-6249	1	19	6249	6249	NUM
ejpam-6249	1	20	issn	issn	PROPN
ejpam-6249	1	21	1307	1307	NUM
ejpam-6249	1	22	-	-	SYM
ejpam-6249	1	23	5543	5543	NUM
ejpam-6249	1	24	–	–	PUNCT
ejpam-6249	1	25	ejpam.com	ejpam.com	X
ejpam-6249	1	26	published	publish	VERB
ejpam-6249	1	27	by	by	ADP
ejpam-6249	1	28	new	new	PROPN
ejpam-6249	1	29	york	york	PROPN
ejpam-6249	1	30	business	business	PROPN
ejpam-6249	1	31	global	global	PROPN
ejpam-6249	1	32	hemicomplemented	hemicomplemente	VERB
ejpam-6249	1	33	almost	almost	ADV
ejpam-6249	1	34	distributive	distributive	ADJ
ejpam-6249	1	35	lattices	lattice	NOUN
ejpam-6249	1	36	noorbhasha	noorbhasha	VERB
ejpam-6249	1	37	rafi1	rafi1	PROPN
ejpam-6249	1	38	,	,	PUNCT
ejpam-6249	1	39	prashant	prashant	PROPN
ejpam-6249	1	40	patel2	patel2	PROPN
ejpam-6249	1	41	,	,	PUNCT
ejpam-6249	1	42	ravi	ravi	PROPN
ejpam-6249	1	43	kumar	kumar	PROPN
ejpam-6249	1	44	davala2	davala2	PROPN
ejpam-6249	1	45	,	,	PUNCT
ejpam-6249	1	46	rahul	rahul	PROPN
ejpam-6249	1	47	shukla3,∗	shukla3,∗	PROPN
ejpam-6249	1	48	1	1	NUM
ejpam-6249	1	49	department	department	NOUN
ejpam-6249	1	50	of	of	ADP
ejpam-6249	1	51	mathematics	mathematics	PROPN
ejpam-6249	1	52	,	,	PUNCT
ejpam-6249	1	53	siddhartha	siddhartha	PROPN
ejpam-6249	1	54	academy	academy	PROPN
ejpam-6249	1	55	of	of	ADP
ejpam-6249	1	56	higher	high	ADJ
ejpam-6249	1	57	education	education	NOUN
ejpam-6249	1	58	,	,	PUNCT
ejpam-6249	1	59	deemed	deem	VERB
ejpam-6249	1	60	to	to	PART
ejpam-6249	1	61	be	be	AUX
ejpam-6249	1	62	university	university	NOUN
ejpam-6249	1	63	,	,	PUNCT
ejpam-6249	1	64	vijayawada-520007	vijayawada-520007	ADJ
ejpam-6249	1	65	,	,	PUNCT
ejpam-6249	1	66	andhra	andhra	PROPN
ejpam-6249	1	67	pradesh	pradesh	PROPN
ejpam-6249	1	68	,	,	PUNCT
ejpam-6249	1	69	india	india	PROPN
ejpam-6249	1	70	2	2	NUM
ejpam-6249	1	71	department	department	NOUN
ejpam-6249	1	72	of	of	ADP
ejpam-6249	1	73	mathematics	mathematic	NOUN
ejpam-6249	1	74	,	,	PUNCT
ejpam-6249	1	75	school	school	NOUN
ejpam-6249	1	76	of	of	ADP
ejpam-6249	1	77	advanced	advanced	ADJ
ejpam-6249	1	78	sciences	science	NOUN
ejpam-6249	1	79	,	,	PUNCT
ejpam-6249	1	80	vit	vit	PROPN
ejpam-6249	1	81	-	-	PUNCT
ejpam-6249	1	82	ap	ap	PROPN
ejpam-6249	1	83	university	university	PROPN
ejpam-6249	1	84	,	,	PUNCT
ejpam-6249	1	85	andhra	andhra	PROPN
ejpam-6249	1	86	pradesh	pradesh	PROPN
ejpam-6249	1	87	,	,	PUNCT
ejpam-6249	1	88	india-522	india-522	VERB
ejpam-6249	1	89	237	237	NUM
ejpam-6249	1	90	3	3	NUM
ejpam-6249	1	91	department	department	NOUN
ejpam-6249	1	92	of	of	ADP
ejpam-6249	1	93	mathematical	mathematical	ADJ
ejpam-6249	1	94	sciences	sciences	PROPN
ejpam-6249	1	95	and	and	CCONJ
ejpam-6249	1	96	computing	computing	NOUN
ejpam-6249	1	97	,	,	PUNCT
ejpam-6249	1	98	walter	walter	PROPN
ejpam-6249	1	99	sisulu	sisulu	PROPN
ejpam-6249	1	100	university	university	PROPN
ejpam-6249	1	101	,	,	PUNCT
ejpam-6249	1	102	mthatha	mthatha	NOUN
ejpam-6249	1	103	5117	5117	NUM
ejpam-6249	1	104	,	,	PUNCT
ejpam-6249	1	105	south	south	PROPN
ejpam-6249	1	106	africa	africa	PROPN
ejpam-6249	1	107	abstract	abstract	PROPN
ejpam-6249	1	108	.	.	PUNCT
ejpam-6249	2	1	this	this	DET
ejpam-6249	2	2	paper	paper	NOUN
ejpam-6249	2	3	introduces	introduce	VERB
ejpam-6249	2	4	the	the	DET
ejpam-6249	2	5	concept	concept	NOUN
ejpam-6249	2	6	of	of	ADP
ejpam-6249	2	7	condensed	condense	VERB
ejpam-6249	2	8	elements	element	NOUN
ejpam-6249	2	9	in	in	ADP
ejpam-6249	2	10	an	an	DET
ejpam-6249	2	11	almost	almost	ADV
ejpam-6249	2	12	distributive	distributive	ADJ
ejpam-6249	2	13	lattice(adl	lattice(adl	NOUN
ejpam-6249	2	14	)	)	PUNCT
ejpam-6249	2	15	and	and	CCONJ
ejpam-6249	2	16	explores	explore	VERB
ejpam-6249	2	17	their	their	PRON
ejpam-6249	2	18	fundamental	fundamental	ADJ
ejpam-6249	2	19	properties	property	NOUN
ejpam-6249	2	20	.	.	PUNCT
ejpam-6249	3	1	it	it	PRON
ejpam-6249	3	2	also	also	ADV
ejpam-6249	3	3	presents	present	VERB
ejpam-6249	3	4	the	the	DET
ejpam-6249	3	5	concept	concept	NOUN
ejpam-6249	3	6	of	of	ADP
ejpam-6249	3	7	hemicomplemented	hemicomplemente	VERB
ejpam-6249	3	8	adl	adl	NOUN
ejpam-6249	3	9	and	and	CCONJ
ejpam-6249	3	10	characterizes	characterize	VERB
ejpam-6249	3	11	these	these	DET
ejpam-6249	3	12	adls	adls	NOUN
ejpam-6249	3	13	using	use	VERB
ejpam-6249	3	14	ideals	ideal	NOUN
ejpam-6249	3	15	,	,	PUNCT
ejpam-6249	3	16	congruences	congruence	NOUN
ejpam-6249	3	17	,	,	PUNCT
ejpam-6249	3	18	and	and	CCONJ
ejpam-6249	3	19	minimal	minimal	ADJ
ejpam-6249	3	20	prime	prime	ADJ
ejpam-6249	3	21	d	d	NOUN
ejpam-6249	3	22	-	-	NOUN
ejpam-6249	3	23	filters	filter	NOUN
ejpam-6249	3	24	.	.	PUNCT
ejpam-6249	4	1	furthermore	furthermore	ADV
ejpam-6249	4	2	,	,	PUNCT
ejpam-6249	4	3	a	a	DET
ejpam-6249	4	4	collection	collection	NOUN
ejpam-6249	4	5	of	of	ADP
ejpam-6249	4	6	equivalent	equivalent	ADJ
ejpam-6249	4	7	criteria	criterion	NOUN
ejpam-6249	4	8	is	be	AUX
ejpam-6249	4	9	established	establish	VERB
ejpam-6249	4	10	to	to	PART
ejpam-6249	4	11	determine	determine	VERB
ejpam-6249	4	12	when	when	SCONJ
ejpam-6249	4	13	a	a	DET
ejpam-6249	4	14	hemicomplemented	hemicomplemente	VERB
ejpam-6249	4	15	adl	adl	NOUN
ejpam-6249	4	16	qualifies	qualifie	NOUN
ejpam-6249	4	17	as	as	ADP
ejpam-6249	4	18	a	a	DET
ejpam-6249	4	19	quasicomplemented	quasicomplemented	ADJ
ejpam-6249	4	20	adl	adl	PROPN
ejpam-6249	4	21	.	.	PROPN
ejpam-6249	4	22	2020	2020	NUM
ejpam-6249	4	23	mathematics	mathematic	NOUN
ejpam-6249	4	24	subject	subject	NOUN
ejpam-6249	4	25	classifications	classification	NOUN
ejpam-6249	4	26	:	:	PUNCT
ejpam-6249	4	27	06d99	06d99	NUM
ejpam-6249	4	28	,	,	PUNCT
ejpam-6249	4	29	06d15	06d15	DET
ejpam-6249	4	30	key	key	ADJ
ejpam-6249	4	31	words	word	NOUN
ejpam-6249	4	32	and	and	CCONJ
ejpam-6249	4	33	phrases	phrase	NOUN
ejpam-6249	4	34	:	:	PUNCT
ejpam-6249	4	35	almost	almost	ADV
ejpam-6249	4	36	distributive	distributive	ADJ
ejpam-6249	4	37	lattice	lattice	NOUN
ejpam-6249	4	38	,	,	PUNCT
ejpam-6249	4	39	hemicomplemented	hemicomplemente	VERB
ejpam-6249	4	40	adl	adl	PROPN
ejpam-6249	4	41	,	,	PUNCT
ejpam-6249	4	42	d	d	NOUN
ejpam-6249	4	43	-	-	NOUN
ejpam-6249	4	44	filter	filter	NOUN
ejpam-6249	4	45	,	,	PUNCT
ejpam-6249	4	46	condensed	condense	VERB
ejpam-6249	4	47	element	element	NOUN
ejpam-6249	4	48	1	1	NUM
ejpam-6249	4	49	.	.	PUNCT
ejpam-6249	5	1	introduction	introduction	NOUN
ejpam-6249	5	2	swamy	swamy	PROPN
ejpam-6249	5	3	u.m	u.m	PROPN
ejpam-6249	5	4	.	.	PROPN
ejpam-6249	6	1	and	and	CCONJ
ejpam-6249	6	2	rao	rao	PROPN
ejpam-6249	6	3	g.c	g.c	PROPN
ejpam-6249	6	4	.	.	PROPN
ejpam-6249	6	5	defined	define	VERB
ejpam-6249	6	6	the	the	DET
ejpam-6249	6	7	concept	concept	NOUN
ejpam-6249	6	8	of	of	ADP
ejpam-6249	6	9	an	an	DET
ejpam-6249	6	10	almost	almost	ADV
ejpam-6249	6	11	distributive	distributive	ADJ
ejpam-6249	6	12	lattice(adl	lattice(adl	NOUN
ejpam-6249	6	13	)	)	PUNCT
ejpam-6249	6	14	as	as	ADP
ejpam-6249	6	15	a	a	DET
ejpam-6249	6	16	common	common	ADJ
ejpam-6249	6	17	abstraction	abstraction	NOUN
ejpam-6249	6	18	that	that	PRON
ejpam-6249	6	19	includes	include	VERB
ejpam-6249	6	20	various	various	ADJ
ejpam-6249	6	21	ring	ring	NOUN
ejpam-6249	6	22	-	-	PUNCT
ejpam-6249	6	23	theoretic	theoretic	NOUN
ejpam-6249	6	24	generalizations	generalization	NOUN
ejpam-6249	6	25	of	of	ADP
ejpam-6249	6	26	boolean	boolean	ADJ
ejpam-6249	6	27	algebras	algebra	NOUN
ejpam-6249	6	28	and	and	CCONJ
ejpam-6249	6	29	distributive	distributive	ADJ
ejpam-6249	6	30	lattices	lattice	NOUN
ejpam-6249	6	31	[	[	X
ejpam-6249	6	32	1	1	NUM
ejpam-6249	6	33	]	]	PUNCT
ejpam-6249	6	34	.	.	PUNCT
ejpam-6249	7	1	they	they	PRON
ejpam-6249	7	2	defined	define	VERB
ejpam-6249	7	3	ideals	ideal	NOUN
ejpam-6249	7	4	in	in	ADP
ejpam-6249	7	5	adls	adls	PROPN
ejpam-6249	7	6	analogous	analogous	ADJ
ejpam-6249	7	7	to	to	ADP
ejpam-6249	7	8	those	those	PRON
ejpam-6249	7	9	in	in	ADP
ejpam-6249	7	10	distributive	distributive	ADJ
ejpam-6249	7	11	lattices	lattice	NOUN
ejpam-6249	7	12	and	and	CCONJ
ejpam-6249	7	13	showed	show	VERB
ejpam-6249	7	14	that	that	SCONJ
ejpam-6249	7	15	the	the	DET
ejpam-6249	7	16	collection	collection	NOUN
ejpam-6249	7	17	of	of	ADP
ejpam-6249	7	18	principal	principal	ADJ
ejpam-6249	7	19	ideals	ideal	NOUN
ejpam-6249	7	20	constitutes	constitute	VERB
ejpam-6249	7	21	a	a	DET
ejpam-6249	7	22	distributive	distributive	ADJ
ejpam-6249	7	23	lattice	lattice	NOUN
ejpam-6249	7	24	,	,	PUNCT
ejpam-6249	7	25	thereby	thereby	ADV
ejpam-6249	7	26	facilitating	facilitate	VERB
ejpam-6249	7	27	the	the	DET
ejpam-6249	7	28	extension	extension	NOUN
ejpam-6249	7	29	of	of	ADP
ejpam-6249	7	30	lattice	lattice	NOUN
ejpam-6249	7	31	theory	theory	NOUN
ejpam-6249	7	32	concepts	concept	NOUN
ejpam-6249	7	33	to	to	ADP
ejpam-6249	7	34	adls	adls	PROPN
ejpam-6249	7	35	.	.	PUNCT
ejpam-6249	8	1	in	in	ADP
ejpam-6249	8	2	[	[	X
ejpam-6249	8	3	2	2	NUM
ejpam-6249	8	4	]	]	PUNCT
ejpam-6249	8	5	presented	present	VERB
ejpam-6249	8	6	the	the	DET
ejpam-6249	8	7	concept	concept	NOUN
ejpam-6249	8	8	ofd	ofd	NOUN
ejpam-6249	8	9	-	-	PUNCT
ejpam-6249	8	10	filters	filter	NOUN
ejpam-6249	8	11	in	in	ADP
ejpam-6249	8	12	adls	adls	PROPN
ejpam-6249	8	13	,	,	PUNCT
ejpam-6249	8	14	examining	examine	VERB
ejpam-6249	8	15	their	their	PRON
ejpam-6249	8	16	important	important	ADJ
ejpam-6249	8	17	properties	property	NOUN
ejpam-6249	8	18	.	.	PUNCT
ejpam-6249	9	1	in	in	ADP
ejpam-6249	9	2	[	[	X
ejpam-6249	9	3	3	3	NUM
ejpam-6249	9	4	]	]	PUNCT
ejpam-6249	9	5	,	,	PUNCT
ejpam-6249	9	6	introduced	introduce	VERB
ejpam-6249	9	7	the	the	DET
ejpam-6249	9	8	concept	concept	NOUN
ejpam-6249	9	9	of	of	ADP
ejpam-6249	9	10	a	a	DET
ejpam-6249	9	11	hemicomplemented	hemicomplemente	VERB
ejpam-6249	9	12	lattice	lattice	NOUN
ejpam-6249	9	13	and	and	CCONJ
ejpam-6249	9	14	studied	study	VERB
ejpam-6249	9	15	their	their	PRON
ejpam-6249	9	16	properties	property	NOUN
ejpam-6249	9	17	.	.	PUNCT
ejpam-6249	10	1	in	in	ADP
ejpam-6249	10	2	this	this	DET
ejpam-6249	10	3	article	article	NOUN
ejpam-6249	10	4	,	,	PUNCT
ejpam-6249	10	5	a	a	DET
ejpam-6249	10	6	new	new	ADJ
ejpam-6249	10	7	type	type	NOUN
ejpam-6249	10	8	of	of	ADP
ejpam-6249	10	9	element	element	NOUN
ejpam-6249	10	10	,	,	PUNCT
ejpam-6249	10	11	termed	term	VERB
ejpam-6249	10	12	condensed	condensed	ADJ
ejpam-6249	10	13	elements	element	NOUN
ejpam-6249	10	14	,	,	PUNCT
ejpam-6249	10	15	is	be	AUX
ejpam-6249	10	16	defined	define	VERB
ejpam-6249	10	17	within	within	ADP
ejpam-6249	10	18	adls	adls	PROPN
ejpam-6249	10	19	,	,	PUNCT
ejpam-6249	10	20	and	and	CCONJ
ejpam-6249	10	21	several	several	ADJ
ejpam-6249	10	22	of	of	ADP
ejpam-6249	10	23	their	their	PRON
ejpam-6249	10	24	essential	essential	ADJ
ejpam-6249	10	25	characteristics	characteristic	NOUN
ejpam-6249	10	26	are	be	AUX
ejpam-6249	10	27	examined	examine	VERB
ejpam-6249	10	28	.	.	PUNCT
ejpam-6249	11	1	the	the	DET
ejpam-6249	11	2	concept	concept	NOUN
ejpam-6249	11	3	of	of	ADP
ejpam-6249	11	4	hemicomplemented	hemicomplemente	VERB
ejpam-6249	11	5	adl	adl	PROPN
ejpam-6249	11	6	is	be	AUX
ejpam-6249	11	7	also	also	ADV
ejpam-6249	11	8	introduced	introduce	VERB
ejpam-6249	11	9	,	,	PUNCT
ejpam-6249	11	10	along	along	ADP
ejpam-6249	11	11	with	with	ADP
ejpam-6249	11	12	the	the	DET
ejpam-6249	11	13	derivation	derivation	NOUN
ejpam-6249	11	14	of	of	ADP
ejpam-6249	11	15	a	a	DET
ejpam-6249	11	16	number	number	NOUN
ejpam-6249	11	17	of	of	ADP
ejpam-6249	11	18	equivalent	equivalent	ADJ
ejpam-6249	11	19	statements	statement	NOUN
ejpam-6249	11	20	∗corresponding	∗corresponde	VERB
ejpam-6249	11	21	author	author	NOUN
ejpam-6249	11	22	.	.	PUNCT
ejpam-6249	12	1	doi	doi	PROPN
ejpam-6249	12	2	:	:	PUNCT
ejpam-6249	12	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6249	https://doi.org/10.29020/nybg.ejpam.v18i4.6249	PROPN
ejpam-6249	12	4	email	email	NOUN
ejpam-6249	12	5	addresses	address	VERB
ejpam-6249	12	6	:	:	PUNCT
ejpam-6249	12	7	rafimaths@gmail.com	rafimaths@gmail.com	X
ejpam-6249	12	8	(	(	PUNCT
ejpam-6249	12	9	n.	n.	PROPN
ejpam-6249	12	10	rafi	rafi	PROPN
ejpam-6249	12	11	)	)	PUNCT
ejpam-6249	12	12	,	,	PUNCT
ejpam-6249	12	13	prashant.patel9999@gmail.com	prashant.patel9999@gmail.com	PROPN
ejpam-6249	12	14	(	(	PUNCT
ejpam-6249	12	15	p.	p.	NOUN
ejpam-6249	12	16	patel	patel	PROPN
ejpam-6249	12	17	)	)	PUNCT
ejpam-6249	12	18	,	,	PUNCT
ejpam-6249	12	19	davalaravikumar@gmail.com	davalaravikumar@gmail.com	PROPN
ejpam-6249	12	20	(	(	PUNCT
ejpam-6249	12	21	r.	r.	PROPN
ejpam-6249	12	22	k.	k.	PROPN
ejpam-6249	12	23	davala	davala	PROPN
ejpam-6249	12	24	)	)	PUNCT
ejpam-6249	12	25	,	,	PUNCT
ejpam-6249	12	26	rshukla@wsu.ac.za	rshukla@wsu.ac.za	NOUN
ejpam-6249	12	27	(	(	PUNCT
ejpam-6249	12	28	r.	r.	NOUN
ejpam-6249	12	29	shukla	shukla	PROPN
ejpam-6249	12	30	)	)	PUNCT
ejpam-6249	12	31	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6249	12	32	1	1	NUM
ejpam-6249	12	33	copyright	copyright	NOUN
ejpam-6249	12	34	:	:	PUNCT
ejpam-6249	13	1	©	©	PROPN
ejpam-6249	13	2	2025	2025	NUM
ejpam-6249	13	3	the	the	DET
ejpam-6249	13	4	author(s	author(s	NOUN
ejpam-6249	13	5	)	)	PUNCT
ejpam-6249	13	6	.	.	PUNCT
ejpam-6249	14	1	(	(	PUNCT
ejpam-6249	14	2	cc	cc	NOUN
ejpam-6249	14	3	by	by	ADP
ejpam-6249	14	4	-	-	PUNCT
ejpam-6249	14	5	nc	nc	PROPN
ejpam-6249	14	6	4.0	4.0	NUM
ejpam-6249	14	7	)	)	PUNCT
ejpam-6249	14	8	n.	n.	NOUN
ejpam-6249	14	9	rafi	rafi	PROPN
ejpam-6249	14	10	et	et	PROPN
ejpam-6249	14	11	al	al	PROPN
ejpam-6249	14	12	.	.	PUNCT
ejpam-6249	14	13	/	/	SYM
ejpam-6249	14	14	eur	eur	PROPN
ejpam-6249	14	15	.	.	PUNCT
ejpam-6249	15	1	j.	j.	PROPN
ejpam-6249	15	2	pure	pure	PROPN
ejpam-6249	15	3	appl	appl	PROPN
ejpam-6249	15	4	.	.	PROPN
ejpam-6249	15	5	math	math	PROPN
ejpam-6249	15	6	,	,	PUNCT
ejpam-6249	15	7	18	18	NUM
ejpam-6249	15	8	(	(	PUNCT
ejpam-6249	15	9	4	4	NUM
ejpam-6249	15	10	)	)	PUNCT
ejpam-6249	15	11	(	(	PUNCT
ejpam-6249	15	12	2025	2025	NUM
ejpam-6249	15	13	)	)	PUNCT
ejpam-6249	15	14	,	,	PUNCT
ejpam-6249	15	15	6249	6249	NUM
ejpam-6249	15	16	2	2	NUM
ejpam-6249	15	17	of	of	ADP
ejpam-6249	15	18	11	11	NUM
ejpam-6249	15	19	determining	determine	VERB
ejpam-6249	15	20	when	when	SCONJ
ejpam-6249	15	21	such	such	ADJ
ejpam-6249	15	22	adls	adls	NOUN
ejpam-6249	15	23	can	can	AUX
ejpam-6249	15	24	be	be	AUX
ejpam-6249	15	25	regarded	regard	VERB
ejpam-6249	15	26	as	as	SCONJ
ejpam-6249	15	27	quasicomplemented	quasicomplemente	VERB
ejpam-6249	15	28	.	.	PUNCT
ejpam-6249	16	1	additionally	additionally	ADV
ejpam-6249	16	2	,	,	PUNCT
ejpam-6249	16	3	established	establish	VERB
ejpam-6249	16	4	a	a	DET
ejpam-6249	16	5	criterion	criterion	NOUN
ejpam-6249	16	6	that	that	PRON
ejpam-6249	16	7	is	be	AUX
ejpam-6249	16	8	both	both	PRON
ejpam-6249	16	9	necessary	necessary	ADJ
ejpam-6249	16	10	and	and	CCONJ
ejpam-6249	16	11	sufficient	sufficient	ADJ
ejpam-6249	16	12	for	for	SCONJ
ejpam-6249	16	13	a	a	DET
ejpam-6249	16	14	hemicomplemented	hemicomplemente	VERB
ejpam-6249	16	15	adl	adl	NOUN
ejpam-6249	16	16	to	to	PART
ejpam-6249	16	17	satisfy	satisfy	VERB
ejpam-6249	16	18	the	the	DET
ejpam-6249	16	19	conditions	condition	NOUN
ejpam-6249	16	20	of	of	ADP
ejpam-6249	16	21	a	a	DET
ejpam-6249	16	22	boolean	boolean	ADJ
ejpam-6249	16	23	algebra	algebra	NOUN
ejpam-6249	16	24	.	.	PUNCT
ejpam-6249	17	1	providing	provide	VERB
ejpam-6249	17	2	a	a	DET
ejpam-6249	17	3	characterization	characterization	NOUN
ejpam-6249	17	4	of	of	ADP
ejpam-6249	17	5	hemicomplemented	hemicomplemente	VERB
ejpam-6249	17	6	adls	adls	NOUN
ejpam-6249	17	7	is	be	AUX
ejpam-6249	17	8	proven	prove	VERB
ejpam-6249	17	9	using	use	VERB
ejpam-6249	17	10	d	d	NOUN
ejpam-6249	17	11	-	-	PUNCT
ejpam-6249	17	12	filters	filter	NOUN
ejpam-6249	17	13	and	and	CCONJ
ejpam-6249	17	14	minimal	minimal	ADJ
ejpam-6249	17	15	prime	prime	ADJ
ejpam-6249	17	16	d	d	NOUN
ejpam-6249	17	17	-	-	NOUN
ejpam-6249	17	18	filters	filter	NOUN
ejpam-6249	17	19	.	.	PUNCT
ejpam-6249	18	1	this	this	DET
ejpam-6249	18	2	particular	particular	ADJ
ejpam-6249	18	3	class	class	NOUN
ejpam-6249	18	4	of	of	ADP
ejpam-6249	18	5	adls	adls	PROPN
ejpam-6249	18	6	was	be	AUX
ejpam-6249	18	7	further	far	ADV
ejpam-6249	18	8	described	describe	VERB
ejpam-6249	18	9	through	through	ADP
ejpam-6249	18	10	the	the	DET
ejpam-6249	18	11	ideals	ideal	NOUN
ejpam-6249	18	12	and	and	CCONJ
ejpam-6249	18	13	congruences	congruence	NOUN
ejpam-6249	18	14	.	.	PUNCT
ejpam-6249	19	1	2	2	X
ejpam-6249	19	2	.	.	X
ejpam-6249	19	3	preliminaries	preliminary	NOUN
ejpam-6249	19	4	this	this	DET
ejpam-6249	19	5	section	section	NOUN
ejpam-6249	19	6	presents	present	VERB
ejpam-6249	19	7	fundamental	fundamental	ADJ
ejpam-6249	19	8	definitions	definition	NOUN
ejpam-6249	19	9	and	and	CCONJ
ejpam-6249	19	10	key	key	ADJ
ejpam-6249	19	11	results	result	NOUN
ejpam-6249	19	12	from	from	ADP
ejpam-6249	19	13	[	[	X
ejpam-6249	19	14	1	1	NUM
ejpam-6249	19	15	,	,	PUNCT
ejpam-6249	19	16	4	4	NUM
ejpam-6249	19	17	]	]	PUNCT
ejpam-6249	19	18	,	,	PUNCT
ejpam-6249	19	19	which	which	PRON
ejpam-6249	19	20	will	will	AUX
ejpam-6249	19	21	be	be	AUX
ejpam-6249	19	22	referenced	reference	VERB
ejpam-6249	19	23	throughout	throughout	ADP
ejpam-6249	19	24	the	the	DET
ejpam-6249	19	25	document	document	NOUN
ejpam-6249	19	26	.	.	PUNCT
ejpam-6249	20	1	definition	definition	NOUN
ejpam-6249	20	2	1	1	NUM
ejpam-6249	20	3	.	.	PUNCT
ejpam-6249	21	1	[	[	X
ejpam-6249	21	2	1	1	X
ejpam-6249	21	3	]	]	PUNCT
ejpam-6249	21	4	a	a	DET
ejpam-6249	21	5	structure	structure	NOUN
ejpam-6249	21	6	(	(	PUNCT
ejpam-6249	21	7	l,∨,∧	l,∨,∧	NOUN
ejpam-6249	21	8	,	,	PUNCT
ejpam-6249	21	9	0	0	NUM
ejpam-6249	21	10	)	)	PUNCT
ejpam-6249	21	11	of	of	ADP
ejpam-6249	21	12	type	type	NOUN
ejpam-6249	21	13	(	(	PUNCT
ejpam-6249	21	14	2	2	NUM
ejpam-6249	21	15	,	,	PUNCT
ejpam-6249	21	16	2	2	NUM
ejpam-6249	21	17	,	,	PUNCT
ejpam-6249	21	18	0	0	NUM
ejpam-6249	21	19	)	)	PUNCT
ejpam-6249	21	20	is	be	AUX
ejpam-6249	21	21	called	call	VERB
ejpam-6249	21	22	an	an	DET
ejpam-6249	21	23	almost	almost	ADV
ejpam-6249	21	24	distributive	distributive	ADJ
ejpam-6249	21	25	lattice(adl	lattice(adl	NOUN
ejpam-6249	21	26	)	)	PUNCT
ejpam-6249	21	27	with	with	ADP
ejpam-6249	21	28	zero	zero	NUM
ejpam-6249	21	29	if	if	SCONJ
ejpam-6249	21	30	it	it	PRON
ejpam-6249	21	31	fulfills	fulfill	VERB
ejpam-6249	21	32	the	the	DET
ejpam-6249	21	33	following	follow	VERB
ejpam-6249	21	34	conditions	condition	NOUN
ejpam-6249	21	35	:	:	PUNCT
ejpam-6249	21	36	(	(	PUNCT
ejpam-6249	21	37	1	1	X
ejpam-6249	21	38	)	)	PUNCT
ejpam-6249	21	39	(	(	PUNCT
ejpam-6249	21	40	θ	θ	PROPN
ejpam-6249	21	41	∨	∨	NUM
ejpam-6249	21	42	ϑ	ϑ	X
ejpam-6249	21	43	)	)	PUNCT
ejpam-6249	21	44	∧	∧	PROPN
ejpam-6249	21	45	σ	σ	NOUN
ejpam-6249	21	46	=	=	SYM
ejpam-6249	21	47	(	(	PUNCT
ejpam-6249	21	48	θ	θ	PROPN
ejpam-6249	21	49	∧	∧	PROPN
ejpam-6249	21	50	σ	σ	PROPN
ejpam-6249	21	51	)	)	PUNCT
ejpam-6249	21	52	∨	∨	NOUN
ejpam-6249	21	53	(	(	PUNCT
ejpam-6249	21	54	ϑ	ϑ	X
ejpam-6249	21	55	∧	∧	PROPN
ejpam-6249	21	56	σ	σ	PROPN
ejpam-6249	21	57	)	)	PUNCT
ejpam-6249	21	58	;	;	PUNCT
ejpam-6249	21	59	(	(	PUNCT
ejpam-6249	21	60	2	2	X
ejpam-6249	21	61	)	)	PUNCT
ejpam-6249	21	62	θ	θ	PROPN
ejpam-6249	21	63	∧	∧	PROPN
ejpam-6249	21	64	(	(	PUNCT
ejpam-6249	21	65	ϑ	ϑ	PROPN
ejpam-6249	21	66	∨	∨	PROPN
ejpam-6249	21	67	σ	σ	PROPN
ejpam-6249	21	68	)	)	PUNCT
ejpam-6249	21	69	=	=	PUNCT
ejpam-6249	21	70	(	(	PUNCT
ejpam-6249	21	71	θ	θ	PROPN
ejpam-6249	21	72	∧	∧	PROPN
ejpam-6249	21	73	ϑ	ϑ	X
ejpam-6249	21	74	)	)	PUNCT
ejpam-6249	21	75	∨	∨	PROPN
ejpam-6249	21	76	(	(	PUNCT
ejpam-6249	21	77	θ	θ	PROPN
ejpam-6249	21	78	∧	∧	PROPN
ejpam-6249	21	79	σ	σ	PROPN
ejpam-6249	21	80	)	)	PUNCT
ejpam-6249	21	81	;	;	PUNCT
ejpam-6249	21	82	(	(	PUNCT
ejpam-6249	21	83	3	3	X
ejpam-6249	21	84	)	)	PUNCT
ejpam-6249	21	85	(	(	PUNCT
ejpam-6249	21	86	θ	θ	PROPN
ejpam-6249	21	87	∨	∨	NUM
ejpam-6249	21	88	ϑ	ϑ	X
ejpam-6249	21	89	)	)	PUNCT
ejpam-6249	21	90	∧	∧	PROPN
ejpam-6249	21	91	ϑ	ϑ	X
ejpam-6249	21	92	=	=	X
ejpam-6249	21	93	ϑ	ϑ	X
ejpam-6249	21	94	;	;	PUNCT
ejpam-6249	21	95	(	(	PUNCT
ejpam-6249	21	96	4	4	NUM
ejpam-6249	21	97	)	)	PUNCT
ejpam-6249	21	98	(	(	PUNCT
ejpam-6249	21	99	θ	θ	PROPN
ejpam-6249	21	100	∨	∨	NUM
ejpam-6249	21	101	ϑ	ϑ	X
ejpam-6249	21	102	)	)	PUNCT
ejpam-6249	21	103	∧	∧	PROPN
ejpam-6249	21	104	θ	θ	NOUN
ejpam-6249	21	105	=	=	SYM
ejpam-6249	21	106	θ	θ	PROPN
ejpam-6249	21	107	;	;	PUNCT
ejpam-6249	21	108	(	(	PUNCT
ejpam-6249	21	109	5	5	X
ejpam-6249	21	110	)	)	PUNCT
ejpam-6249	21	111	θ	θ	NOUN
ejpam-6249	21	112	∨	∨	PROPN
ejpam-6249	21	113	(	(	PUNCT
ejpam-6249	21	114	θ	θ	PROPN
ejpam-6249	21	115	∧	∧	PROPN
ejpam-6249	21	116	ϑ	ϑ	X
ejpam-6249	21	117	)	)	PUNCT
ejpam-6249	21	118	=	=	SYM
ejpam-6249	21	119	θ	θ	PROPN
ejpam-6249	21	120	;	;	PUNCT
ejpam-6249	21	121	(	(	PUNCT
ejpam-6249	21	122	6	6	NUM
ejpam-6249	21	123	)	)	PUNCT
ejpam-6249	21	124	0	0	NUM
ejpam-6249	22	1	∧	∧	NOUN
ejpam-6249	22	2	θ	θ	NOUN
ejpam-6249	22	3	=	=	SYM
ejpam-6249	22	4	0	0	NUM
ejpam-6249	22	5	,	,	PUNCT
ejpam-6249	22	6	for	for	ADP
ejpam-6249	22	7	any	any	DET
ejpam-6249	22	8	θ	θ	PROPN
ejpam-6249	22	9	,	,	PUNCT
ejpam-6249	22	10	ϑ	ϑ	X
ejpam-6249	22	11	,	,	PUNCT
ejpam-6249	22	12	σ	σ	PROPN
ejpam-6249	22	13	∈	∈	PROPN
ejpam-6249	22	14	l.	l.	NOUN
ejpam-6249	22	15	to	to	PART
ejpam-6249	22	16	define	define	VERB
ejpam-6249	22	17	a	a	DET
ejpam-6249	22	18	partial	partial	ADJ
ejpam-6249	22	19	order	order	NOUN
ejpam-6249	22	20	≤	≤	NOUN
ejpam-6249	22	21	on	on	ADP
ejpam-6249	22	22	l	l	NOUN
ejpam-6249	22	23	,	,	PUNCT
ejpam-6249	22	24	consider	consider	VERB
ejpam-6249	22	25	the	the	DET
ejpam-6249	22	26	condition	condition	NOUN
ejpam-6249	22	27	θ	θ	NOUN
ejpam-6249	22	28	=	=	PUNCT
ejpam-6249	22	29	θ	θ	X
ejpam-6249	22	30	∧	∧	PROPN
ejpam-6249	22	31	ϑ	ϑ	X
ejpam-6249	22	32	or	or	CCONJ
ejpam-6249	22	33	equivalently	equivalently	ADV
ejpam-6249	22	34	θ∨ϑ	θ∨ϑ	PROPN
ejpam-6249	22	35	=	=	SYM
ejpam-6249	22	36	ϑ	ϑ	PROPN
ejpam-6249	22	37	for	for	ADP
ejpam-6249	22	38	every	every	DET
ejpam-6249	22	39	θ	θ	PROPN
ejpam-6249	22	40	,	,	PUNCT
ejpam-6249	22	41	ϑ	ϑ	X
ejpam-6249	22	42	∈	∈	PROPN
ejpam-6249	22	43	l.	l.	NOUN
ejpam-6249	22	44	this	this	DET
ejpam-6249	22	45	condition	condition	NOUN
ejpam-6249	22	46	ensures	ensure	VERB
ejpam-6249	22	47	that	that	SCONJ
ejpam-6249	22	48	θ	θ	PROPN
ejpam-6249	22	49	≤	≤	PROPN
ejpam-6249	22	50	ϑ	ϑ	VERB
ejpam-6249	22	51	,	,	PUNCT
ejpam-6249	22	52	establishing	establish	VERB
ejpam-6249	22	53	≤	≤	NUM
ejpam-6249	22	54	as	as	ADP
ejpam-6249	22	55	a	a	DET
ejpam-6249	22	56	partial	partial	ADJ
ejpam-6249	22	57	order	order	NOUN
ejpam-6249	22	58	on	on	ADP
ejpam-6249	22	59	l.	l.	NOUN
ejpam-6249	22	60	when	when	SCONJ
ejpam-6249	22	61	m	m	PROPN
ejpam-6249	22	62	∈	∈	NOUN
ejpam-6249	22	63	l	l	NOUN
ejpam-6249	22	64	is	be	AUX
ejpam-6249	22	65	maximal	maximal	ADJ
ejpam-6249	22	66	with	with	ADP
ejpam-6249	22	67	respect	respect	NOUN
ejpam-6249	22	68	to	to	ADP
ejpam-6249	22	69	this	this	DET
ejpam-6249	22	70	partial	partial	ADJ
ejpam-6249	22	71	order	order	NOUN
ejpam-6249	22	72	,	,	PUNCT
ejpam-6249	22	73	it	it	PRON
ejpam-6249	22	74	is	be	AUX
ejpam-6249	22	75	referred	refer	VERB
ejpam-6249	22	76	to	to	ADP
ejpam-6249	22	77	as	as	ADV
ejpam-6249	22	78	maximal	maximal	ADJ
ejpam-6249	22	79	.	.	PUNCT
ejpam-6249	23	1	the	the	DET
ejpam-6249	23	2	collection	collection	NOUN
ejpam-6249	23	3	of	of	ADP
ejpam-6249	23	4	all	all	DET
ejpam-6249	23	5	such	such	ADJ
ejpam-6249	23	6	maximal	maximal	ADJ
ejpam-6249	23	7	elements	element	NOUN
ejpam-6249	23	8	in	in	ADP
ejpam-6249	23	9	l	l	NOUN
ejpam-6249	23	10	is	be	AUX
ejpam-6249	23	11	indicated	indicate	VERB
ejpam-6249	23	12	by	by	ADP
ejpam-6249	23	13	m(l	m(l	NOUN
ejpam-6249	23	14	)	)	PUNCT
ejpam-6249	23	15	.	.	PUNCT
ejpam-6249	24	1	adl	adl	PROPN
ejpam-6249	24	2	l	l	NOUN
ejpam-6249	24	3	exhibits	exhibit	VERB
ejpam-6249	24	4	many	many	ADJ
ejpam-6249	24	5	properties	property	NOUN
ejpam-6249	24	6	of	of	ADP
ejpam-6249	24	7	a	a	DET
ejpam-6249	24	8	distributive	distributive	ADJ
ejpam-6249	24	9	lattice[5	lattice[5	NOUN
ejpam-6249	24	10	,	,	PUNCT
ejpam-6249	24	11	6	6	NUM
ejpam-6249	24	12	]	]	PUNCT
ejpam-6249	24	13	,	,	PUNCT
ejpam-6249	24	14	with	with	ADP
ejpam-6249	24	15	the	the	DET
ejpam-6249	24	16	exception	exception	NOUN
ejpam-6249	24	17	of	of	ADP
ejpam-6249	24	18	non	non	ADJ
ejpam-6249	24	19	-	-	NOUN
ejpam-6249	24	20	commutativity	commutativity	NOUN
ejpam-6249	24	21	of	of	ADP
ejpam-6249	24	22	∨	∨	NUM
ejpam-6249	24	23	and	and	CCONJ
ejpam-6249	24	24	∧	∧	NOUN
ejpam-6249	24	25	and	and	CCONJ
ejpam-6249	24	26	lack	lack	NOUN
ejpam-6249	24	27	of	of	ADP
ejpam-6249	24	28	right	right	ADJ
ejpam-6249	24	29	distributivity	distributivity	NOUN
ejpam-6249	24	30	of	of	ADP
ejpam-6249	24	31	∨	∨	NUM
ejpam-6249	24	32	over	over	ADP
ejpam-6249	24	33	∧	∧	PROPN
ejpam-6249	24	34	,	,	PUNCT
ejpam-6249	24	35	as	as	SCONJ
ejpam-6249	24	36	highlighted	highlight	VERB
ejpam-6249	24	37	in	in	ADP
ejpam-6249	24	38	swamy	swamy	PROPN
ejpam-6249	24	39	’s	’s	PART
ejpam-6249	24	40	work[1	work[1	PROPN
ejpam-6249	24	41	]	]	X
ejpam-6249	24	42	.	.	PUNCT
ejpam-6249	25	1	if	if	SCONJ
ejpam-6249	25	2	either	either	PRON
ejpam-6249	25	3	of	of	ADP
ejpam-6249	25	4	these	these	DET
ejpam-6249	25	5	properties	property	NOUN
ejpam-6249	25	6	held	hold	VERB
ejpam-6249	25	7	,	,	PUNCT
ejpam-6249	25	8	l	l	PROPN
ejpam-6249	25	9	would	would	AUX
ejpam-6249	25	10	be	be	AUX
ejpam-6249	25	11	classified	classify	VERB
ejpam-6249	25	12	as	as	ADP
ejpam-6249	25	13	a	a	DET
ejpam-6249	25	14	distributive	distributive	ADJ
ejpam-6249	25	15	lattice	lattice	NOUN
ejpam-6249	25	16	.	.	PUNCT
ejpam-6249	26	1	we	we	PRON
ejpam-6249	26	2	define	define	VERB
ejpam-6249	26	3	a	a	DET
ejpam-6249	26	4	non	non	ADJ
ejpam-6249	26	5	-	-	ADJ
ejpam-6249	26	6	void	void	ADJ
ejpam-6249	26	7	subset	subset	VERB
ejpam-6249	26	8	i	i	PRON
ejpam-6249	26	9	of	of	ADP
ejpam-6249	26	10	l	l	NOUN
ejpam-6249	26	11	as	as	ADP
ejpam-6249	26	12	an	an	DET
ejpam-6249	26	13	ideal(a	ideal(a	ADJ
ejpam-6249	26	14	filter	filter	NOUN
ejpam-6249	26	15	)	)	PUNCT
ejpam-6249	26	16	if	if	SCONJ
ejpam-6249	26	17	it	it	PRON
ejpam-6249	26	18	satisfies	satisfy	VERB
ejpam-6249	26	19	that	that	SCONJ
ejpam-6249	26	20	for	for	ADP
ejpam-6249	26	21	any	any	DET
ejpam-6249	26	22	elements	element	NOUN
ejpam-6249	26	23	θ	θ	NOUN
ejpam-6249	26	24	,	,	PUNCT
ejpam-6249	26	25	ϑ	ϑ	X
ejpam-6249	26	26	∈	∈	X
ejpam-6249	26	27	i	i	PRON
ejpam-6249	26	28	and	and	CCONJ
ejpam-6249	26	29	µ	µ	PRON
ejpam-6249	26	30	∈	∈	PROPN
ejpam-6249	26	31	l	l	NOUN
ejpam-6249	26	32	,	,	PUNCT
ejpam-6249	26	33	the	the	DET
ejpam-6249	26	34	subset	subset	NOUN
ejpam-6249	26	35	i	i	PRON
ejpam-6249	26	36	must	must	AUX
ejpam-6249	26	37	include	include	VERB
ejpam-6249	26	38	θ	θ	PROPN
ejpam-6249	26	39	∧	∧	PROPN
ejpam-6249	26	40	µ	µ	X
ejpam-6249	26	41	and	and	CCONJ
ejpam-6249	26	42	θ	θ	PROPN
ejpam-6249	26	43	∨	∨	NUM
ejpam-6249	26	44	ϑ	ϑ	X
ejpam-6249	26	45	(	(	PUNCT
ejpam-6249	26	46	µ	µ	X
ejpam-6249	26	47	∨	∨	NUM
ejpam-6249	26	48	θ	θ	PROPN
ejpam-6249	26	49	and	and	CCONJ
ejpam-6249	26	50	θ∧ϑ	θ∧ϑ	PROPN
ejpam-6249	26	51	)	)	PUNCT
ejpam-6249	26	52	.	.	PUNCT
ejpam-6249	27	1	a	a	DET
ejpam-6249	27	2	maximal	maximal	ADJ
ejpam-6249	27	3	ideal	ideal	NOUN
ejpam-6249	27	4	(	(	PUNCT
ejpam-6249	27	5	filter	filter	NOUN
ejpam-6249	27	6	)	)	PUNCT
ejpam-6249	27	7	contains	contain	VERB
ejpam-6249	27	8	every	every	DET
ejpam-6249	27	9	proper	proper	ADJ
ejpam-6249	27	10	ideal	ideal	NOUN
ejpam-6249	27	11	(	(	PUNCT
ejpam-6249	27	12	filter	filter	NOUN
ejpam-6249	27	13	)	)	PUNCT
ejpam-6249	27	14	of	of	ADP
ejpam-6249	27	15	l.	l.	PROPN
ejpam-6249	27	16	the	the	DET
ejpam-6249	27	17	smallest	small	ADJ
ejpam-6249	27	18	ideal	ideal	NOUN
ejpam-6249	27	19	containing	contain	VERB
ejpam-6249	27	20	a	a	DET
ejpam-6249	27	21	subset	subset	NOUN
ejpam-6249	27	22	s	s	NOUN
ejpam-6249	27	23	of	of	ADP
ejpam-6249	27	24	l	l	NOUN
ejpam-6249	27	25	is	be	AUX
ejpam-6249	27	26	defined	define	VERB
ejpam-6249	27	27	as	as	ADP
ejpam-6249	27	28	(	(	PUNCT
ejpam-6249	27	29	s	s	X
ejpam-6249	27	30	]	]	X
ejpam-6249	27	31	:	:	PUNCT
ejpam-6249	27	32	=	=	SYM
ejpam-6249	27	33	{	{	PUNCT
ejpam-6249	27	34	(	(	PUNCT
ejpam-6249	27	35	n∨	n∨	PROPN
ejpam-6249	27	36	i=1	i=1	PROPN
ejpam-6249	27	37	θi	θi	PROPN
ejpam-6249	27	38	)	)	PUNCT
ejpam-6249	27	39	∧	∧	PROPN
ejpam-6249	27	40	µ	µ	PROPN
ejpam-6249	27	41	|	|	NOUN
ejpam-6249	27	42	θi	θi	ADP
ejpam-6249	27	43	∈	∈	PROPN
ejpam-6249	27	44	s	s	PROPN
ejpam-6249	27	45	,	,	PUNCT
ejpam-6249	27	46	µ	µ	X
ejpam-6249	27	47	∈	∈	PROPN
ejpam-6249	27	48	l	l	NOUN
ejpam-6249	27	49	,	,	PUNCT
ejpam-6249	27	50	n	n	PROPN
ejpam-6249	27	51	∈	∈	PROPN
ejpam-6249	27	52	n	n	CCONJ
ejpam-6249	27	53	}	}	PUNCT
ejpam-6249	27	54	.	.	PUNCT
ejpam-6249	28	1	a	a	DET
ejpam-6249	28	2	principal	principal	ADJ
ejpam-6249	28	3	ideal	ideal	NOUN
ejpam-6249	28	4	generated	generate	VERB
ejpam-6249	28	5	by	by	ADP
ejpam-6249	28	6	an	an	DET
ejpam-6249	28	7	element	element	NOUN
ejpam-6249	28	8	θ	θ	PROPN
ejpam-6249	28	9	is	be	AUX
ejpam-6249	28	10	denoted	denote	VERB
ejpam-6249	28	11	as	as	ADP
ejpam-6249	28	12	(	(	PUNCT
ejpam-6249	28	13	θ	θ	NOUN
ejpam-6249	28	14	]	]	PUNCT
ejpam-6249	28	15	.	.	PUNCT
ejpam-6249	29	1	similarly	similarly	ADV
ejpam-6249	29	2	,	,	PUNCT
ejpam-6249	29	3	for	for	ADP
ejpam-6249	29	4	each	each	DET
ejpam-6249	29	5	subset	subset	NOUN
ejpam-6249	29	6	s	s	PROPN
ejpam-6249	29	7	of	of	ADP
ejpam-6249	29	8	l	l	NOUN
ejpam-6249	29	9	,	,	PUNCT
ejpam-6249	29	10	the	the	DET
ejpam-6249	29	11	smallest	small	ADJ
ejpam-6249	29	12	filter	filter	NOUN
ejpam-6249	29	13	containing	contain	VERB
ejpam-6249	29	14	s	s	NOUN
ejpam-6249	29	15	is	be	AUX
ejpam-6249	29	16	defined	define	VERB
ejpam-6249	29	17	as	as	ADP
ejpam-6249	29	18	[	[	X
ejpam-6249	29	19	s	s	X
ejpam-6249	29	20	)	)	PUNCT
ejpam-6249	29	21	:	:	PUNCT
ejpam-6249	29	22	=	=	SYM
ejpam-6249	29	23	{	{	PUNCT
ejpam-6249	29	24	µ∨	µ∨	NOUN
ejpam-6249	29	25	(	(	PUNCT
ejpam-6249	29	26	n∧	n∧	NUM
ejpam-6249	29	27	i=1	i=1	PROPN
ejpam-6249	29	28	θi	θi	X
ejpam-6249	29	29	)	)	PUNCT
ejpam-6249	30	1	|	|	ADV
ejpam-6249	30	2	θi	θi	ADP
ejpam-6249	30	3	∈	∈	PROPN
ejpam-6249	30	4	s	s	PROPN
ejpam-6249	30	5	,	,	PUNCT
ejpam-6249	30	6	µ	µ	X
ejpam-6249	30	7	∈	∈	PROPN
ejpam-6249	30	8	l	l	NOUN
ejpam-6249	30	9	,	,	PUNCT
ejpam-6249	30	10	n	n	PROPN
ejpam-6249	30	11	∈	∈	PROPN
ejpam-6249	30	12	n	n	CCONJ
ejpam-6249	30	13	}	}	PUNCT
ejpam-6249	30	14	.	.	PUNCT
ejpam-6249	31	1	a	a	DET
ejpam-6249	31	2	principal	principal	ADJ
ejpam-6249	31	3	filter	filter	NOUN
ejpam-6249	31	4	generated	generate	VERB
ejpam-6249	31	5	by	by	ADP
ejpam-6249	31	6	an	an	DET
ejpam-6249	31	7	element	element	NOUN
ejpam-6249	31	8	θ	θ	PROPN
ejpam-6249	31	9	is	be	AUX
ejpam-6249	31	10	denoted	denote	VERB
ejpam-6249	31	11	as	as	ADP
ejpam-6249	31	12	[	[	X
ejpam-6249	31	13	θ	θ	NOUN
ejpam-6249	31	14	)	)	PUNCT
ejpam-6249	31	15	.	.	PUNCT
ejpam-6249	32	1	it	it	PRON
ejpam-6249	32	2	is	be	AUX
ejpam-6249	32	3	established	establish	VERB
ejpam-6249	32	4	that	that	SCONJ
ejpam-6249	32	5	(	(	PUNCT
ejpam-6249	32	6	θ	θ	X
ejpam-6249	32	7	]	]	X
ejpam-6249	32	8	∨	∨	X
ejpam-6249	32	9	(	(	PUNCT
ejpam-6249	32	10	ϑ	ϑ	X
ejpam-6249	32	11	]	]	X
ejpam-6249	32	12	=	=	SYM
ejpam-6249	32	13	(	(	PUNCT
ejpam-6249	32	14	θ	θ	PROPN
ejpam-6249	32	15	∨	∨	NUM
ejpam-6249	32	16	ϑ	ϑ	X
ejpam-6249	32	17	]	]	PUNCT
ejpam-6249	32	18	and	and	CCONJ
ejpam-6249	32	19	(	(	PUNCT
ejpam-6249	32	20	θ	θ	NOUN
ejpam-6249	32	21	]	]	X
ejpam-6249	32	22	∩	∩	NOUN
ejpam-6249	32	23	(	(	PUNCT
ejpam-6249	32	24	ϑ	ϑ	X
ejpam-6249	32	25	]	]	X
ejpam-6249	32	26	=	=	SYM
ejpam-6249	32	27	(	(	PUNCT
ejpam-6249	32	28	θ	θ	X
ejpam-6249	32	29	∧	∧	PROPN
ejpam-6249	32	30	ϑ	ϑ	X
ejpam-6249	32	31	]	]	X
ejpam-6249	32	32	for	for	ADP
ejpam-6249	32	33	any	any	DET
ejpam-6249	32	34	θ	θ	PROPN
ejpam-6249	32	35	,	,	PUNCT
ejpam-6249	32	36	ϑ	ϑ	X
ejpam-6249	32	37	∈	∈	PROPN
ejpam-6249	32	38	l.	l.	NOUN
ejpam-6249	32	39	represented	represent	VERB
ejpam-6249	32	40	all	all	DET
ejpam-6249	32	41	principal	principal	ADJ
ejpam-6249	32	42	ideals	ideal	NOUN
ejpam-6249	32	43	of	of	ADP
ejpam-6249	32	44	l	l	NOUN
ejpam-6249	32	45	by	by	ADP
ejpam-6249	32	46	the	the	DET
ejpam-6249	32	47	set	set	NOUN
ejpam-6249	32	48	(	(	PUNCT
ejpam-6249	32	49	pi(l),∨,∩	pi(l),∨,∩	NOUN
ejpam-6249	32	50	)	)	PUNCT
ejpam-6249	32	51	,	,	PUNCT
ejpam-6249	32	52	this	this	PRON
ejpam-6249	32	53	brings	bring	VERB
ejpam-6249	32	54	out	out	ADP
ejpam-6249	32	55	a	a	DET
ejpam-6249	32	56	sublattice	sublattice	NOUN
ejpam-6249	32	57	of	of	ADP
ejpam-6249	32	58	the	the	DET
ejpam-6249	32	59	distributive	distributive	ADJ
ejpam-6249	32	60	lattice	lattice	NOUN
ejpam-6249	32	61	(	(	PUNCT
ejpam-6249	32	62	i(l),∨,∩	i(l),∨,∩	NOUN
ejpam-6249	32	63	)	)	PUNCT
ejpam-6249	32	64	of	of	ADP
ejpam-6249	32	65	all	all	DET
ejpam-6249	32	66	ideals	ideal	NOUN
ejpam-6249	32	67	of	of	ADP
ejpam-6249	32	68	l.	l.	PROPN
ejpam-6249	32	69	furthermore	furthermore	ADV
ejpam-6249	32	70	,	,	PUNCT
ejpam-6249	32	71	the	the	DET
ejpam-6249	32	72	set	set	NOUN
ejpam-6249	32	73	(	(	PUNCT
ejpam-6249	32	74	f(l),∨,∩	f(l),∨,∩	NOUN
ejpam-6249	32	75	)	)	PUNCT
ejpam-6249	32	76	of	of	ADP
ejpam-6249	32	77	all	all	DET
ejpam-6249	32	78	filters	filter	NOUN
ejpam-6249	32	79	of	of	ADP
ejpam-6249	32	80	l	l	NOUN
ejpam-6249	32	81	forms	form	NOUN
ejpam-6249	32	82	a	a	DET
ejpam-6249	32	83	bounded	bounded	ADJ
ejpam-6249	32	84	distributive	distributive	ADJ
ejpam-6249	32	85	lattice	lattice	NOUN
ejpam-6249	32	86	.	.	PUNCT
ejpam-6249	33	1	in	in	ADP
ejpam-6249	33	2	an	an	DET
ejpam-6249	33	3	adl[7	adl[7	NOUN
ejpam-6249	33	4	]	]	PUNCT
ejpam-6249	33	5	,	,	PUNCT
ejpam-6249	33	6	a	a	DET
ejpam-6249	33	7	prime	prime	ADJ
ejpam-6249	33	8	ideal	ideal	NOUN
ejpam-6249	33	9	q	q	PROPN
ejpam-6249	33	10	of	of	ADP
ejpam-6249	33	11	l	l	NOUN
ejpam-6249	33	12	exists	exist	VERB
ejpam-6249	33	13	if	if	SCONJ
ejpam-6249	33	14	and	and	CCONJ
ejpam-6249	33	15	only	only	ADV
ejpam-6249	33	16	if	if	SCONJ
ejpam-6249	33	17	l	l	NOUN
ejpam-6249	33	18	\	\	PUNCT
ejpam-6249	33	19	q	q	X
ejpam-6249	33	20	is	be	AUX
ejpam-6249	33	21	a	a	DET
ejpam-6249	33	22	prime	prime	ADJ
ejpam-6249	33	23	filter	filter	NOUN
ejpam-6249	33	24	of	of	ADP
ejpam-6249	33	25	l.	l.	PROPN
ejpam-6249	33	26	a	a	DET
ejpam-6249	33	27	prime	prime	ADJ
ejpam-6249	33	28	ideal	ideal	NOUN
ejpam-6249	33	29	q	q	PROPN
ejpam-6249	33	30	of	of	ADP
ejpam-6249	33	31	an	an	DET
ejpam-6249	33	32	adl	adl	NOUN
ejpam-6249	33	33	is	be	AUX
ejpam-6249	33	34	a	a	DET
ejpam-6249	33	35	minimal	minimal	ADJ
ejpam-6249	33	36	prime	prime	ADJ
ejpam-6249	33	37	ideal	ideal	NOUN
ejpam-6249	34	1	if	if	SCONJ
ejpam-6249	34	2	and	and	CCONJ
ejpam-6249	34	3	only	only	ADV
ejpam-6249	34	4	if	if	SCONJ
ejpam-6249	34	5	to	to	ADP
ejpam-6249	34	6	each	each	DET
ejpam-6249	34	7	µ	µ	PROPN
ejpam-6249	34	8	∈	∈	NOUN
ejpam-6249	34	9	q	q	NOUN
ejpam-6249	34	10	there	there	PRON
ejpam-6249	34	11	exists	exist	VERB
ejpam-6249	34	12	π	π	PROPN
ejpam-6249	34	13	/∈	/∈	PUNCT
ejpam-6249	35	1	q	q	NOUN
ejpam-6249	36	1	such	such	ADJ
ejpam-6249	36	2	that	that	SCONJ
ejpam-6249	36	3	µ	µ	ADJ
ejpam-6249	36	4	∧	∧	PROPN
ejpam-6249	36	5	π	π	NOUN
ejpam-6249	36	6	=	=	SYM
ejpam-6249	36	7	0	0	PUNCT
ejpam-6249	36	8	(	(	PUNCT
ejpam-6249	36	9	or	or	CCONJ
ejpam-6249	36	10	equivalently	equivalently	ADV
ejpam-6249	36	11	,	,	PUNCT
ejpam-6249	36	12	for	for	ADP
ejpam-6249	36	13	any	any	DET
ejpam-6249	36	14	µ	µ	PROPN
ejpam-6249	36	15	∈	∈	PROPN
ejpam-6249	36	16	l	l	NOUN
ejpam-6249	36	17	,	,	PUNCT
ejpam-6249	36	18	µ	µ	X
ejpam-6249	36	19	/∈	/∈	NOUN
ejpam-6249	36	20	q	q	NOUN
ejpam-6249	37	1	if	if	SCONJ
ejpam-6249	37	2	and	and	CCONJ
ejpam-6249	37	3	only	only	ADV
ejpam-6249	37	4	if	if	SCONJ
ejpam-6249	37	5	(	(	PUNCT
ejpam-6249	37	6	µ)∗	µ)∗	PROPN
ejpam-6249	37	7	⊆	⊆	NUM
ejpam-6249	37	8	q	q	NOUN
ejpam-6249	37	9	)	)	PUNCT
ejpam-6249	37	10	.	.	PUNCT
ejpam-6249	38	1	for	for	ADP
ejpam-6249	38	2	each	each	DET
ejpam-6249	38	3	non	non	ADJ
ejpam-6249	38	4	-	-	ADJ
ejpam-6249	38	5	void	void	ADJ
ejpam-6249	38	6	subset	subset	NOUN
ejpam-6249	38	7	s	s	PROPN
ejpam-6249	38	8	of	of	ADP
ejpam-6249	38	9	l	l	NOUN
ejpam-6249	38	10	,	,	PUNCT
ejpam-6249	38	11	the	the	DET
ejpam-6249	38	12	set	set	NOUN
ejpam-6249	38	13	n.	n.	PROPN
ejpam-6249	38	14	rafi	rafi	PROPN
ejpam-6249	38	15	et	et	PROPN
ejpam-6249	38	16	al	al	PROPN
ejpam-6249	38	17	.	.	PUNCT
ejpam-6249	38	18	/	/	SYM
ejpam-6249	38	19	eur	eur	PROPN
ejpam-6249	38	20	.	.	PUNCT
ejpam-6249	39	1	j.	j.	PROPN
ejpam-6249	39	2	pure	pure	PROPN
ejpam-6249	39	3	appl	appl	PROPN
ejpam-6249	39	4	.	.	PROPN
ejpam-6249	39	5	math	math	PROPN
ejpam-6249	39	6	,	,	PUNCT
ejpam-6249	39	7	18	18	NUM
ejpam-6249	39	8	(	(	PUNCT
ejpam-6249	39	9	4	4	NUM
ejpam-6249	39	10	)	)	PUNCT
ejpam-6249	39	11	(	(	PUNCT
ejpam-6249	39	12	2025	2025	NUM
ejpam-6249	39	13	)	)	PUNCT
ejpam-6249	39	14	,	,	PUNCT
ejpam-6249	39	15	6249	6249	NUM
ejpam-6249	39	16	3	3	NUM
ejpam-6249	39	17	of	of	ADP
ejpam-6249	39	18	11	11	NUM
ejpam-6249	39	19	s∗	s∗	NOUN
ejpam-6249	39	20	=	=	SYM
ejpam-6249	39	21	{	{	PUNCT
ejpam-6249	39	22	µ	µ	X
ejpam-6249	39	23	∈	∈	X
ejpam-6249	39	24	l	l	NOUN
ejpam-6249	39	25	|	|	NOUN
ejpam-6249	39	26	θ	θ	X
ejpam-6249	39	27	∧	∧	PROPN
ejpam-6249	39	28	µ	µ	X
ejpam-6249	39	29	=	=	SYM
ejpam-6249	39	30	0	0	NUM
ejpam-6249	39	31	,	,	PUNCT
ejpam-6249	39	32	for	for	ADP
ejpam-6249	39	33	all	all	DET
ejpam-6249	39	34	θ	θ	NOUN
ejpam-6249	39	35	∈	∈	PROPN
ejpam-6249	39	36	s	s	VERB
ejpam-6249	39	37	}	}	PUNCT
ejpam-6249	39	38	is	be	AUX
ejpam-6249	39	39	an	an	DET
ejpam-6249	39	40	ideal	ideal	NOUN
ejpam-6249	39	41	of	of	ADP
ejpam-6249	39	42	l.	l.	PROPN
ejpam-6249	39	43	generally	generally	ADV
ejpam-6249	39	44	,	,	PUNCT
ejpam-6249	39	45	for	for	ADP
ejpam-6249	39	46	every	every	DET
ejpam-6249	39	47	θ	θ	PROPN
ejpam-6249	39	48	∈	∈	PROPN
ejpam-6249	39	49	l	l	NOUN
ejpam-6249	39	50	,	,	PUNCT
ejpam-6249	39	51	{	{	PUNCT
ejpam-6249	39	52	θ}∗	θ}∗	ADJ
ejpam-6249	39	53	=	=	SYM
ejpam-6249	39	54	(	(	PUNCT
ejpam-6249	39	55	θ)∗	θ)∗	NOUN
ejpam-6249	39	56	,	,	PUNCT
ejpam-6249	39	57	where	where	SCONJ
ejpam-6249	39	58	(	(	PUNCT
ejpam-6249	39	59	θ	θ	NOUN
ejpam-6249	39	60	)	)	PUNCT
ejpam-6249	39	61	=	=	SYM
ejpam-6249	39	62	(	(	PUNCT
ejpam-6249	39	63	θ	θ	NOUN
ejpam-6249	39	64	]	]	X
ejpam-6249	39	65	.	.	PUNCT
ejpam-6249	40	1	the	the	DET
ejpam-6249	40	2	annihilator	annihilator	NOUN
ejpam-6249	40	3	of	of	ADP
ejpam-6249	40	4	an	an	DET
ejpam-6249	40	5	element	element	NOUN
ejpam-6249	40	6	θ	θ	PROPN
ejpam-6249	40	7	∈	∈	PROPN
ejpam-6249	40	8	l	l	NOUN
ejpam-6249	40	9	is	be	AUX
ejpam-6249	40	10	defined	define	VERB
ejpam-6249	40	11	as	as	ADP
ejpam-6249	40	12	the	the	DET
ejpam-6249	40	13	set	set	NOUN
ejpam-6249	40	14	(	(	PUNCT
ejpam-6249	40	15	θ)∗	θ)∗	PROPN
ejpam-6249	40	16	=	=	PUNCT
ejpam-6249	40	17	{	{	PUNCT
ejpam-6249	40	18	µ	µ	X
ejpam-6249	40	19	∈	∈	X
ejpam-6249	40	20	l	l	NOUN
ejpam-6249	40	21	|	|	NOUN
ejpam-6249	40	22	µ	µ	X
ejpam-6249	40	23	∧	∧	NOUN
ejpam-6249	40	24	θ	θ	NOUN
ejpam-6249	40	25	=	=	PUNCT
ejpam-6249	40	26	0	0	NUM
ejpam-6249	40	27	}	}	PUNCT
ejpam-6249	40	28	.	.	PUNCT
ejpam-6249	41	1	if	if	SCONJ
ejpam-6249	41	2	(	(	PUNCT
ejpam-6249	41	3	e)∗	e)∗	PROPN
ejpam-6249	41	4	=	=	SYM
ejpam-6249	41	5	{	{	PUNCT
ejpam-6249	41	6	0	0	NUM
ejpam-6249	41	7	}	}	PUNCT
ejpam-6249	41	8	then	then	ADV
ejpam-6249	41	9	an	an	DET
ejpam-6249	41	10	element	element	NOUN
ejpam-6249	41	11	e	e	PART
ejpam-6249	41	12	∈	∈	PROPN
ejpam-6249	41	13	l	l	NOUN
ejpam-6249	41	14	is	be	AUX
ejpam-6249	41	15	considered	consider	VERB
ejpam-6249	41	16	dense	dense	ADJ
ejpam-6249	41	17	.	.	PUNCT
ejpam-6249	42	1	within	within	ADP
ejpam-6249	42	2	l	l	NOUN
ejpam-6249	42	3	,	,	PUNCT
ejpam-6249	42	4	the	the	DET
ejpam-6249	42	5	set	set	NOUN
ejpam-6249	42	6	d	d	NOUN
ejpam-6249	42	7	is	be	AUX
ejpam-6249	42	8	the	the	DET
ejpam-6249	42	9	set	set	NOUN
ejpam-6249	42	10	of	of	ADP
ejpam-6249	42	11	dense	dense	ADJ
ejpam-6249	42	12	elements	element	NOUN
ejpam-6249	42	13	.	.	PUNCT
ejpam-6249	43	1	a	a	DET
ejpam-6249	43	2	filter	filter	NOUN
ejpam-6249	43	3	of	of	ADP
ejpam-6249	43	4	an	an	DET
ejpam-6249	43	5	adl	adl	PROPN
ejpam-6249	43	6	l	l	NOUN
ejpam-6249	43	7	can	can	AUX
ejpam-6249	43	8	be	be	AUX
ejpam-6249	43	9	obtained	obtain	VERB
ejpam-6249	43	10	by	by	ADP
ejpam-6249	43	11	the	the	DET
ejpam-6249	43	12	set	set	NOUN
ejpam-6249	43	13	d.	d.	PROPN
ejpam-6249	43	14	a	a	DET
ejpam-6249	43	15	adl	adl	PROPN
ejpam-6249	43	16	l	l	PROPN
ejpam-6249	43	17	is	be	AUX
ejpam-6249	43	18	called	call	VERB
ejpam-6249	43	19	normal	normal	ADJ
ejpam-6249	43	20	[	[	X
ejpam-6249	43	21	8	8	NUM
ejpam-6249	43	22	]	]	X
ejpam-6249	43	23	if	if	SCONJ
ejpam-6249	43	24	every	every	DET
ejpam-6249	43	25	prime	prime	ADJ
ejpam-6249	43	26	ideal	ideal	NOUN
ejpam-6249	43	27	contains	contain	VERB
ejpam-6249	43	28	a	a	DET
ejpam-6249	43	29	unique	unique	ADJ
ejpam-6249	43	30	minimal	minimal	ADJ
ejpam-6249	43	31	prime	prime	ADJ
ejpam-6249	43	32	ideal	ideal	NOUN
ejpam-6249	43	33	.	.	PUNCT
ejpam-6249	44	1	an	an	DET
ejpam-6249	44	2	adl	adl	PROPN
ejpam-6249	44	3	l	l	NOUN
ejpam-6249	44	4	is	be	AUX
ejpam-6249	44	5	called	call	VERB
ejpam-6249	44	6	quasi	quasi	ADJ
ejpam-6249	44	7	-	-	VERB
ejpam-6249	44	8	complemented	complemented	ADJ
ejpam-6249	44	9	[	[	X
ejpam-6249	44	10	9	9	NUM
ejpam-6249	44	11	]	]	X
ejpam-6249	44	12	if	if	SCONJ
ejpam-6249	44	13	to	to	ADP
ejpam-6249	44	14	each	each	DET
ejpam-6249	44	15	θ	θ	NOUN
ejpam-6249	44	16	∈	∈	PROPN
ejpam-6249	44	17	l	l	NOUN
ejpam-6249	44	18	,	,	PUNCT
ejpam-6249	44	19	θ	θ	NOUN
ejpam-6249	44	20	∧	∧	NOUN
ejpam-6249	44	21	θ′	θ′	PUNCT
ejpam-6249	44	22	=	=	SYM
ejpam-6249	44	23	0	0	NUM
ejpam-6249	44	24	and	and	CCONJ
ejpam-6249	44	25	θ	θ	PROPN
ejpam-6249	44	26	∨	∨	NOUN
ejpam-6249	44	27	θ′	θ′	NOUN
ejpam-6249	44	28	∈	∈	NOUN
ejpam-6249	44	29	d	d	NOUN
ejpam-6249	44	30	,	,	PUNCT
ejpam-6249	44	31	for	for	ADP
ejpam-6249	44	32	some	some	DET
ejpam-6249	44	33	θ′	θ′	NUM
ejpam-6249	44	34	∈	∈	PROPN
ejpam-6249	44	35	l.	l.	NOUN
ejpam-6249	44	36	an	an	DET
ejpam-6249	44	37	adl	adl	NOUN
ejpam-6249	44	38	with	with	ADP
ejpam-6249	44	39	dense	dense	ADJ
ejpam-6249	44	40	elements	element	NOUN
ejpam-6249	44	41	is	be	AUX
ejpam-6249	44	42	considered	consider	VERB
ejpam-6249	44	43	quasi	quasi	ADJ
ejpam-6249	44	44	-	-	VERB
ejpam-6249	44	45	complemented	complemented	ADJ
ejpam-6249	44	46	if	if	SCONJ
ejpam-6249	45	1	and	and	CCONJ
ejpam-6249	45	2	only	only	ADV
ejpam-6249	45	3	if	if	SCONJ
ejpam-6249	45	4	,	,	PUNCT
ejpam-6249	45	5	for	for	ADP
ejpam-6249	45	6	every	every	DET
ejpam-6249	45	7	µ	µ	PROPN
ejpam-6249	45	8	∈	∈	PROPN
ejpam-6249	45	9	l	l	NOUN
ejpam-6249	45	10	,	,	PUNCT
ejpam-6249	45	11	there	there	PRON
ejpam-6249	45	12	exists	exist	VERB
ejpam-6249	45	13	some	some	DET
ejpam-6249	45	14	µ′	µ′	PUNCT
ejpam-6249	45	15	∈	∈	PROPN
ejpam-6249	45	16	l	l	NOUN
ejpam-6249	45	17	such	such	ADJ
ejpam-6249	45	18	that	that	SCONJ
ejpam-6249	45	19	(	(	PUNCT
ejpam-6249	45	20	µ)∗∗	µ)∗∗	X
ejpam-6249	45	21	=	=	SYM
ejpam-6249	45	22	(	(	PUNCT
ejpam-6249	45	23	µ′)∗.	µ′)∗.	ADV
ejpam-6249	45	24	the	the	DET
ejpam-6249	45	25	adl	adl	PROPN
ejpam-6249	45	26	l	l	PROPN
ejpam-6249	45	27	is	be	AUX
ejpam-6249	45	28	termed	term	VERB
ejpam-6249	45	29	a	a	DET
ejpam-6249	45	30	generalized	generalized	ADJ
ejpam-6249	45	31	stone	stone	NOUN
ejpam-6249	45	32	adl	adl	NOUN
ejpam-6249	46	1	[	[	X
ejpam-6249	46	2	10	10	NUM
ejpam-6249	46	3	]	]	PUNCT
ejpam-6249	46	4	when	when	SCONJ
ejpam-6249	46	5	it	it	PRON
ejpam-6249	46	6	satisfies	satisfy	VERB
ejpam-6249	46	7	the	the	DET
ejpam-6249	46	8	property	property	NOUN
ejpam-6249	46	9	(	(	PUNCT
ejpam-6249	46	10	µ)∗∨	µ)∗∨	NOUN
ejpam-6249	46	11	(	(	PUNCT
ejpam-6249	46	12	µ)∗∗	µ)∗∗	X
ejpam-6249	46	13	=	=	SYM
ejpam-6249	46	14	l	l	NOUN
ejpam-6249	46	15	for	for	ADP
ejpam-6249	46	16	all	all	DET
ejpam-6249	46	17	µ	µ	PRON
ejpam-6249	46	18	∈	∈	NOUN
ejpam-6249	46	19	l.	l.	NOUN
ejpam-6249	46	20	a	a	DET
ejpam-6249	46	21	unary	unary	ADJ
ejpam-6249	46	22	operation	operation	NOUN
ejpam-6249	46	23	θ	θ	PROPN
ejpam-6249	46	24	7→	7→	NUM
ejpam-6249	46	25	θ∗	θ∗	NOUN
ejpam-6249	46	26	on	on	ADP
ejpam-6249	46	27	an	an	DET
ejpam-6249	46	28	adl	adl	PROPN
ejpam-6249	46	29	l	l	NOUN
ejpam-6249	46	30	is	be	AUX
ejpam-6249	46	31	said	say	VERB
ejpam-6249	46	32	to	to	PART
ejpam-6249	46	33	be	be	AUX
ejpam-6249	46	34	pseudo	pseudo	NOUN
ejpam-6249	46	35	-	-	NOUN
ejpam-6249	46	36	complementation[11	complementation[11	X
ejpam-6249	46	37	]	]	PUNCT
ejpam-6249	46	38	on	on	ADP
ejpam-6249	46	39	l	l	NOUN
ejpam-6249	46	40	if	if	SCONJ
ejpam-6249	46	41	,	,	PUNCT
ejpam-6249	46	42	for	for	ADP
ejpam-6249	46	43	any	any	DET
ejpam-6249	46	44	θ	θ	PROPN
ejpam-6249	46	45	,	,	PUNCT
ejpam-6249	46	46	ϑ	ϑ	X
ejpam-6249	46	47	∈	∈	PROPN
ejpam-6249	46	48	l	l	NOUN
ejpam-6249	46	49	,	,	PUNCT
ejpam-6249	46	50	(	(	PUNCT
ejpam-6249	46	51	1	1	X
ejpam-6249	46	52	)	)	PUNCT
ejpam-6249	46	53	θ∧ϑ	θ∧ϑ	NOUN
ejpam-6249	46	54	=	=	SYM
ejpam-6249	46	55	0	0	NUM
ejpam-6249	46	56	implies	imply	VERB
ejpam-6249	46	57	θ∗	θ∗	NOUN
ejpam-6249	46	58	∧ϑ	∧ϑ	NOUN
ejpam-6249	46	59	=	=	SYM
ejpam-6249	46	60	ϑ	ϑ	X
ejpam-6249	46	61	;	;	PUNCT
ejpam-6249	46	62	(	(	PUNCT
ejpam-6249	46	63	2	2	X
ejpam-6249	46	64	)	)	PUNCT
ejpam-6249	46	65	θ∧	θ∧	NOUN
ejpam-6249	46	66	θ∗	θ∗	NOUN
ejpam-6249	46	67	=	=	SYM
ejpam-6249	46	68	0	0	NUM
ejpam-6249	46	69	;	;	PUNCT
ejpam-6249	46	70	(	(	PUNCT
ejpam-6249	46	71	3	3	X
ejpam-6249	46	72	)	)	PUNCT
ejpam-6249	46	73	(	(	PUNCT
ejpam-6249	46	74	θ∨ϑ)∗	θ∨ϑ)∗	NUM
ejpam-6249	46	75	=	=	SYM
ejpam-6249	46	76	θ∗	θ∗	PROPN
ejpam-6249	46	77	∧ϑ∗.	∧ϑ∗.	PROPN
ejpam-6249	46	78	it	it	PRON
ejpam-6249	46	79	becomes	become	VERB
ejpam-6249	46	80	clear	clear	ADJ
ejpam-6249	46	81	that	that	SCONJ
ejpam-6249	46	82	every	every	DET
ejpam-6249	46	83	pseudo	pseudo	NOUN
ejpam-6249	46	84	-	-	ADJ
ejpam-6249	46	85	complemented	complemented	ADJ
ejpam-6249	46	86	adl	adl	NOUN
ejpam-6249	46	87	is	be	AUX
ejpam-6249	46	88	quasi	quasi	ADJ
ejpam-6249	46	89	-	-	VERB
ejpam-6249	46	90	complemented	complemented	ADJ
ejpam-6249	46	91	.	.	PUNCT
ejpam-6249	47	1	according	accord	VERB
ejpam-6249	47	2	to	to	ADP
ejpam-6249	47	3	[	[	X
ejpam-6249	47	4	2	2	NUM
ejpam-6249	47	5	]	]	PUNCT
ejpam-6249	47	6	,	,	PUNCT
ejpam-6249	47	7	a	a	DET
ejpam-6249	47	8	filter	filter	NOUN
ejpam-6249	47	9	g	g	NOUN
ejpam-6249	47	10	of	of	ADP
ejpam-6249	47	11	an	an	DET
ejpam-6249	47	12	adl	adl	PROPN
ejpam-6249	47	13	l	l	NOUN
ejpam-6249	47	14	is	be	AUX
ejpam-6249	47	15	known	know	VERB
ejpam-6249	47	16	as	as	ADP
ejpam-6249	47	17	a	a	DET
ejpam-6249	47	18	d	d	NOUN
ejpam-6249	47	19	-	-	NOUN
ejpam-6249	47	20	filter	filter	NOUN
ejpam-6249	47	21	if	if	SCONJ
ejpam-6249	47	22	d	d	PROPN
ejpam-6249	47	23	⊆	⊆	NUM
ejpam-6249	47	24	g.	g.	X
ejpam-6249	47	25	the	the	DET
ejpam-6249	47	26	smallest	small	ADJ
ejpam-6249	47	27	d	d	NOUN
ejpam-6249	47	28	-	-	NOUN
ejpam-6249	47	29	filter	filter	NOUN
ejpam-6249	47	30	is	be	AUX
ejpam-6249	47	31	d.	d.	NOUN
ejpam-6249	47	32	for	for	ADP
ejpam-6249	47	33	any	any	DET
ejpam-6249	47	34	non	non	ADJ
ejpam-6249	47	35	empty	empty	ADJ
ejpam-6249	47	36	subset	subset	NOUN
ejpam-6249	47	37	s	s	PROPN
ejpam-6249	47	38	of	of	ADP
ejpam-6249	47	39	l	l	NOUN
ejpam-6249	47	40	,	,	PUNCT
ejpam-6249	47	41	consider	consider	VERB
ejpam-6249	47	42	the	the	DET
ejpam-6249	47	43	set	set	NOUN
ejpam-6249	47	44	(	(	PUNCT
ejpam-6249	47	45	s	s	X
ejpam-6249	47	46	,	,	PUNCT
ejpam-6249	47	47	d	d	NOUN
ejpam-6249	47	48	)	)	PUNCT
ejpam-6249	47	49	=	=	SYM
ejpam-6249	47	50	{	{	PUNCT
ejpam-6249	47	51	µ	µ	X
ejpam-6249	47	52	∈	∈	X
ejpam-6249	47	53	l	l	NOUN
ejpam-6249	48	1	|	|	NOUN
ejpam-6249	48	2	θ∨µ	θ∨µ	VERB
ejpam-6249	48	3	∈	∈	PROPN
ejpam-6249	48	4	d	d	PROPN
ejpam-6249	48	5	for	for	ADP
ejpam-6249	48	6	all	all	DET
ejpam-6249	48	7	θ	θ	PRON
ejpam-6249	48	8	∈	∈	NOUN
ejpam-6249	48	9	s	s	PART
ejpam-6249	48	10	}	}	PUNCT
ejpam-6249	48	11	.	.	PUNCT
ejpam-6249	49	1	it	it	PRON
ejpam-6249	49	2	is	be	AUX
ejpam-6249	49	3	noted	note	VERB
ejpam-6249	49	4	that	that	SCONJ
ejpam-6249	49	5	(	(	PUNCT
ejpam-6249	49	6	l	l	NOUN
ejpam-6249	49	7	,	,	PUNCT
ejpam-6249	49	8	d	d	NOUN
ejpam-6249	49	9	)	)	PUNCT
ejpam-6249	49	10	=	=	SYM
ejpam-6249	50	1	d	d	PROPN
ejpam-6249	50	2	and	and	CCONJ
ejpam-6249	50	3	(	(	PUNCT
ejpam-6249	50	4	d	d	NOUN
ejpam-6249	50	5	,	,	PUNCT
ejpam-6249	50	6	d	d	NOUN
ejpam-6249	50	7	)	)	PUNCT
ejpam-6249	50	8	=	=	SYM
ejpam-6249	50	9	l.	l.	PROPN
ejpam-6249	50	10	furthermore	furthermore	ADV
ejpam-6249	50	11	,	,	PUNCT
ejpam-6249	50	12	for	for	ADP
ejpam-6249	50	13	any	any	DET
ejpam-6249	50	14	subset	subset	NOUN
ejpam-6249	50	15	s	s	PROPN
ejpam-6249	50	16	of	of	ADP
ejpam-6249	50	17	l	l	NOUN
ejpam-6249	50	18	,	,	PUNCT
ejpam-6249	50	19	d	d	PROPN
ejpam-6249	50	20	⊆	⊆	NUM
ejpam-6249	50	21	(	(	PUNCT
ejpam-6249	50	22	s	s	PROPN
ejpam-6249	50	23	,	,	PUNCT
ejpam-6249	50	24	d	d	NOUN
ejpam-6249	50	25	)	)	PUNCT
ejpam-6249	50	26	.	.	PUNCT
ejpam-6249	51	1	for	for	ADP
ejpam-6249	51	2	every	every	DET
ejpam-6249	51	3	θ	θ	PROPN
ejpam-6249	51	4	∈	∈	PROPN
ejpam-6249	51	5	l	l	NOUN
ejpam-6249	51	6	,	,	PUNCT
ejpam-6249	51	7	(	(	PUNCT
ejpam-6249	51	8	{	{	PUNCT
ejpam-6249	51	9	θ},d	θ},d	PROPN
ejpam-6249	51	10	)	)	PUNCT
ejpam-6249	51	11	is	be	AUX
ejpam-6249	51	12	denoted	denote	VERB
ejpam-6249	51	13	as	as	ADP
ejpam-6249	51	14	(	(	PUNCT
ejpam-6249	51	15	θ	θ	NOUN
ejpam-6249	51	16	,	,	PUNCT
ejpam-6249	51	17	d	d	NOUN
ejpam-6249	51	18	)	)	PUNCT
ejpam-6249	51	19	.	.	PUNCT
ejpam-6249	52	1	therefore	therefore	ADV
ejpam-6249	52	2	,	,	PUNCT
ejpam-6249	52	3	(	(	PUNCT
ejpam-6249	52	4	m	m	NOUN
ejpam-6249	52	5	,	,	PUNCT
ejpam-6249	52	6	d	d	NOUN
ejpam-6249	52	7	)	)	PUNCT
ejpam-6249	52	8	=	=	SYM
ejpam-6249	52	9	l	l	NOUN
ejpam-6249	52	10	for	for	ADP
ejpam-6249	52	11	any	any	DET
ejpam-6249	52	12	m	m	PROPN
ejpam-6249	52	13	∈	∈	PROPN
ejpam-6249	52	14	m(l	m(l	NOUN
ejpam-6249	52	15	)	)	PUNCT
ejpam-6249	52	16	.	.	PUNCT
ejpam-6249	53	1	(	(	PUNCT
ejpam-6249	53	2	s	s	X
ejpam-6249	53	3	,	,	PUNCT
ejpam-6249	53	4	d	d	NOUN
ejpam-6249	53	5	)	)	PUNCT
ejpam-6249	53	6	forms	form	VERB
ejpam-6249	53	7	a	a	DET
ejpam-6249	53	8	d	d	NOUN
ejpam-6249	53	9	-	-	NOUN
ejpam-6249	53	10	filter	filter	NOUN
ejpam-6249	53	11	in	in	ADP
ejpam-6249	53	12	l	l	NOUN
ejpam-6249	53	13	for	for	ADP
ejpam-6249	53	14	each	each	DET
ejpam-6249	53	15	subset	subset	NOUN
ejpam-6249	53	16	s	s	PROPN
ejpam-6249	53	17	in	in	ADP
ejpam-6249	53	18	l.	l.	PROPN
ejpam-6249	53	19	lemma	lemma	PROPN
ejpam-6249	54	1	1	1	NUM
ejpam-6249	54	2	.	.	PUNCT
ejpam-6249	55	1	[	[	X
ejpam-6249	55	2	2	2	NUM
ejpam-6249	55	3	]	]	PUNCT
ejpam-6249	55	4	given	give	VERB
ejpam-6249	55	5	two	two	NUM
ejpam-6249	55	6	subsets	subset	NOUN
ejpam-6249	55	7	s	s	PART
ejpam-6249	55	8	,	,	PUNCT
ejpam-6249	55	9	t	t	PROPN
ejpam-6249	55	10	of	of	ADP
ejpam-6249	55	11	an	an	DET
ejpam-6249	55	12	adl	adl	PROPN
ejpam-6249	55	13	l	l	PROPN
ejpam-6249	55	14	,	,	PUNCT
ejpam-6249	55	15	the	the	DET
ejpam-6249	55	16	following	follow	VERB
ejpam-6249	55	17	holds	hold	VERB
ejpam-6249	55	18	(	(	PUNCT
ejpam-6249	55	19	1	1	NUM
ejpam-6249	55	20	)	)	PUNCT
ejpam-6249	55	21	s	s	PART
ejpam-6249	55	22	⊆	⊆	NUM
ejpam-6249	55	23	t	t	NOUN
ejpam-6249	55	24	⇒	⇒	NOUN
ejpam-6249	55	25	(	(	PUNCT
ejpam-6249	55	26	t	t	PROPN
ejpam-6249	55	27	,	,	PUNCT
ejpam-6249	55	28	d	d	NOUN
ejpam-6249	55	29	)	)	PUNCT
ejpam-6249	55	30	⊆	⊆	NUM
ejpam-6249	55	31	(	(	PUNCT
ejpam-6249	55	32	s	s	X
ejpam-6249	55	33	,	,	PUNCT
ejpam-6249	55	34	d	d	NOUN
ejpam-6249	55	35	)	)	PUNCT
ejpam-6249	55	36	;	;	PUNCT
ejpam-6249	55	37	(	(	PUNCT
ejpam-6249	55	38	2	2	X
ejpam-6249	55	39	)	)	PUNCT
ejpam-6249	55	40	s	s	NOUN
ejpam-6249	55	41	⊆	⊆	NUM
ejpam-6249	55	42	(	(	PUNCT
ejpam-6249	55	43	(	(	PUNCT
ejpam-6249	55	44	s	s	X
ejpam-6249	55	45	,	,	PUNCT
ejpam-6249	55	46	d),d	d),d	PROPN
ejpam-6249	55	47	)	)	PUNCT
ejpam-6249	55	48	;	;	PUNCT
ejpam-6249	55	49	(	(	PUNCT
ejpam-6249	55	50	3	3	X
ejpam-6249	55	51	)	)	PUNCT
ejpam-6249	55	52	(	(	PUNCT
ejpam-6249	55	53	s	s	X
ejpam-6249	55	54	,	,	PUNCT
ejpam-6249	55	55	d	d	NOUN
ejpam-6249	55	56	)	)	PUNCT
ejpam-6249	55	57	=	=	SYM
ejpam-6249	55	58	(	(	PUNCT
ejpam-6249	55	59	(	(	PUNCT
ejpam-6249	55	60	(	(	PUNCT
ejpam-6249	55	61	s	s	X
ejpam-6249	55	62	,	,	PUNCT
ejpam-6249	55	63	d),d),d	d),d),d	NOUN
ejpam-6249	55	64	)	)	PUNCT
ejpam-6249	55	65	;	;	PUNCT
ejpam-6249	55	66	(	(	PUNCT
ejpam-6249	55	67	4	4	X
ejpam-6249	55	68	)	)	PUNCT
ejpam-6249	55	69	s	s	PART
ejpam-6249	55	70	⊆	⊆	NUM
ejpam-6249	55	71	d	d	SYM
ejpam-6249	55	72	⇔	⇔	X
ejpam-6249	55	73	(	(	PUNCT
ejpam-6249	55	74	s	s	PROPN
ejpam-6249	55	75	,	,	PUNCT
ejpam-6249	55	76	d	d	NOUN
ejpam-6249	55	77	)	)	PUNCT
ejpam-6249	55	78	=	=	PUNCT
ejpam-6249	55	79	l.	l.	NOUN
ejpam-6249	55	80	proposition	proposition	NOUN
ejpam-6249	55	81	1	1	NUM
ejpam-6249	55	82	.	.	PUNCT
ejpam-6249	56	1	[	[	X
ejpam-6249	56	2	2	2	NUM
ejpam-6249	56	3	]	]	PUNCT
ejpam-6249	56	4	given	give	VERB
ejpam-6249	56	5	filters	filter	NOUN
ejpam-6249	56	6	g	g	PROPN
ejpam-6249	56	7	,	,	PUNCT
ejpam-6249	56	8	u	u	NOUN
ejpam-6249	56	9	of	of	ADP
ejpam-6249	56	10	an	an	DET
ejpam-6249	56	11	adl	adl	PROPN
ejpam-6249	56	12	l	l	PROPN
ejpam-6249	56	13	,	,	PUNCT
ejpam-6249	56	14	the	the	DET
ejpam-6249	56	15	following	follow	VERB
ejpam-6249	56	16	holds	hold	VERB
ejpam-6249	56	17	(	(	PUNCT
ejpam-6249	56	18	1	1	NUM
ejpam-6249	56	19	)	)	PUNCT
ejpam-6249	56	20	(	(	PUNCT
ejpam-6249	56	21	g	g	NOUN
ejpam-6249	56	22	,	,	PUNCT
ejpam-6249	56	23	d	d	NOUN
ejpam-6249	56	24	)	)	PUNCT
ejpam-6249	56	25	∩	∩	NOUN
ejpam-6249	56	26	(	(	PUNCT
ejpam-6249	56	27	(	(	PUNCT
ejpam-6249	56	28	g	g	NOUN
ejpam-6249	56	29	,	,	PUNCT
ejpam-6249	56	30	d),d	d),d	NOUN
ejpam-6249	56	31	)	)	PUNCT
ejpam-6249	56	32	=	=	SYM
ejpam-6249	57	1	d	d	NOUN
ejpam-6249	57	2	;	;	PUNCT
ejpam-6249	57	3	(	(	PUNCT
ejpam-6249	57	4	2	2	X
ejpam-6249	57	5	)	)	PUNCT
ejpam-6249	57	6	g	g	NOUN
ejpam-6249	57	7	∩	∩	NOUN
ejpam-6249	57	8	u	u	NOUN
ejpam-6249	57	9	⊆	⊆	NUM
ejpam-6249	57	10	d	d	PROPN
ejpam-6249	57	11	⇒	⇒	NOUN
ejpam-6249	57	12	g	g	PROPN
ejpam-6249	57	13	⊆	⊆	NUM
ejpam-6249	57	14	(	(	PUNCT
ejpam-6249	57	15	u	u	NOUN
ejpam-6249	57	16	,	,	PUNCT
ejpam-6249	57	17	d	d	PROPN
ejpam-6249	57	18	)	)	PUNCT
ejpam-6249	57	19	;	;	PUNCT
ejpam-6249	57	20	(	(	PUNCT
ejpam-6249	57	21	3	3	X
ejpam-6249	57	22	)	)	PUNCT
ejpam-6249	57	23	(	(	PUNCT
ejpam-6249	57	24	(	(	PUNCT
ejpam-6249	57	25	g	g	PROPN
ejpam-6249	57	26	∨	∨	NUM
ejpam-6249	57	27	u),d	u),d	NOUN
ejpam-6249	57	28	)	)	PUNCT
ejpam-6249	57	29	=	=	SYM
ejpam-6249	58	1	(	(	PUNCT
ejpam-6249	58	2	g	g	NOUN
ejpam-6249	58	3	,	,	PUNCT
ejpam-6249	58	4	d	d	NOUN
ejpam-6249	58	5	)	)	PUNCT
ejpam-6249	58	6	∩	∩	NOUN
ejpam-6249	58	7	(	(	PUNCT
ejpam-6249	58	8	u	u	NOUN
ejpam-6249	58	9	,	,	PUNCT
ejpam-6249	58	10	d	d	PROPN
ejpam-6249	58	11	)	)	PUNCT
ejpam-6249	58	12	;	;	PUNCT
ejpam-6249	58	13	(	(	PUNCT
ejpam-6249	58	14	4	4	X
ejpam-6249	58	15	)	)	PUNCT
ejpam-6249	58	16	(	(	PUNCT
ejpam-6249	58	17	(	(	PUNCT
ejpam-6249	58	18	g	g	PROPN
ejpam-6249	58	19	∩	∩	ADJ
ejpam-6249	58	20	u	u	NOUN
ejpam-6249	58	21	,	,	PUNCT
ejpam-6249	58	22	d),d	d),d	PROPN
ejpam-6249	58	23	)	)	PUNCT
ejpam-6249	58	24	=	=	PRON
ejpam-6249	59	1	(	(	PUNCT
ejpam-6249	59	2	(	(	PUNCT
ejpam-6249	59	3	g	g	NOUN
ejpam-6249	59	4	,	,	PUNCT
ejpam-6249	59	5	d),d	d),d	NOUN
ejpam-6249	59	6	)	)	PUNCT
ejpam-6249	59	7	∩	∩	NOUN
ejpam-6249	59	8	(	(	PUNCT
ejpam-6249	59	9	(	(	PUNCT
ejpam-6249	59	10	u	u	NOUN
ejpam-6249	59	11	,	,	PUNCT
ejpam-6249	59	12	d),d	d),d	PROPN
ejpam-6249	59	13	)	)	PUNCT
ejpam-6249	59	14	.	.	PUNCT
ejpam-6249	60	1	the	the	DET
ejpam-6249	60	2	idea	idea	NOUN
ejpam-6249	60	3	that	that	SCONJ
ejpam-6249	60	4	(	(	PUNCT
ejpam-6249	60	5	[	[	X
ejpam-6249	60	6	µ),d	µ),d	NOUN
ejpam-6249	60	7	)	)	PUNCT
ejpam-6249	60	8	=	=	PUNCT
ejpam-6249	60	9	(	(	PUNCT
ejpam-6249	60	10	µ,d	µ,d	NOUN
ejpam-6249	60	11	)	)	PUNCT
ejpam-6249	60	12	is	be	AUX
ejpam-6249	60	13	obvious	obvious	ADJ
ejpam-6249	60	14	.	.	PUNCT
ejpam-6249	61	1	it	it	PRON
ejpam-6249	61	2	follows	follow	VERB
ejpam-6249	61	3	that	that	PRON
ejpam-6249	61	4	(	(	PUNCT
ejpam-6249	61	5	0,d	0,d	PUNCT
ejpam-6249	61	6	)	)	PUNCT
ejpam-6249	61	7	=	=	VERB
ejpam-6249	62	1	d.	d.	PROPN
ejpam-6249	62	2	the	the	DET
ejpam-6249	62	3	previously	previously	ADV
ejpam-6249	62	4	noted	note	VERB
ejpam-6249	62	5	observations	observation	NOUN
ejpam-6249	62	6	directly	directly	ADV
ejpam-6249	62	7	lead	lead	VERB
ejpam-6249	62	8	to	to	ADP
ejpam-6249	62	9	the	the	DET
ejpam-6249	62	10	corollary	corollary	NOUN
ejpam-6249	62	11	that	that	PRON
ejpam-6249	62	12	follows	follow	VERB
ejpam-6249	62	13	.	.	PUNCT
ejpam-6249	63	1	corollary	corollary	ADJ
ejpam-6249	63	2	1	1	NUM
ejpam-6249	63	3	.	.	PUNCT
ejpam-6249	64	1	[	[	X
ejpam-6249	64	2	2	2	NUM
ejpam-6249	64	3	]	]	PUNCT
ejpam-6249	64	4	for	for	ADP
ejpam-6249	64	5	any	any	DET
ejpam-6249	64	6	µ	µ	NOUN
ejpam-6249	64	7	,	,	PUNCT
ejpam-6249	64	8	π	π	PROPN
ejpam-6249	64	9	,	,	PUNCT
ejpam-6249	64	10	ψ	ψ	X
ejpam-6249	64	11	∈	∈	NOUN
ejpam-6249	64	12	l	l	NOUN
ejpam-6249	64	13	we	we	PRON
ejpam-6249	64	14	have	have	VERB
ejpam-6249	64	15	the	the	DET
ejpam-6249	64	16	following	follow	VERB
ejpam-6249	64	17	(	(	PUNCT
ejpam-6249	64	18	1	1	NUM
ejpam-6249	64	19	)	)	PUNCT
ejpam-6249	64	20	(	(	PUNCT
ejpam-6249	64	21	[	[	X
ejpam-6249	64	22	µ),d	µ),d	NOUN
ejpam-6249	64	23	)	)	PUNCT
ejpam-6249	64	24	=	=	PUNCT
ejpam-6249	64	25	(	(	PUNCT
ejpam-6249	64	26	µ,d	µ,d	NOUN
ejpam-6249	64	27	)	)	PUNCT
ejpam-6249	64	28	;	;	PUNCT
ejpam-6249	65	1	(	(	PUNCT
ejpam-6249	65	2	2	2	X
ejpam-6249	65	3	)	)	PUNCT
ejpam-6249	65	4	µ	µ	PRON
ejpam-6249	65	5	≤	≤	PUNCT
ejpam-6249	65	6	π	π	PROPN
ejpam-6249	65	7	⇒	⇒	NOUN
ejpam-6249	65	8	(	(	PUNCT
ejpam-6249	65	9	µ,d	µ,d	NOUN
ejpam-6249	65	10	)	)	PUNCT
ejpam-6249	65	11	⊆	⊆	NUM
ejpam-6249	65	12	(	(	PUNCT
ejpam-6249	65	13	π	π	PROPN
ejpam-6249	65	14	,	,	PUNCT
ejpam-6249	65	15	d	d	PROPN
ejpam-6249	65	16	)	)	PUNCT
ejpam-6249	65	17	;	;	PUNCT
ejpam-6249	65	18	(	(	PUNCT
ejpam-6249	65	19	3	3	X
ejpam-6249	65	20	)	)	PUNCT
ejpam-6249	65	21	(	(	PUNCT
ejpam-6249	65	22	µ	µ	X
ejpam-6249	65	23	∧	∧	PROPN
ejpam-6249	65	24	π	π	PROPN
ejpam-6249	65	25	,	,	PUNCT
ejpam-6249	65	26	d	d	NOUN
ejpam-6249	65	27	)	)	PUNCT
ejpam-6249	65	28	=	=	SYM
ejpam-6249	65	29	(	(	PUNCT
ejpam-6249	65	30	µ,d	µ,d	NOUN
ejpam-6249	65	31	)	)	PUNCT
ejpam-6249	65	32	∩	∩	NOUN
ejpam-6249	65	33	(	(	PUNCT
ejpam-6249	65	34	π	π	X
ejpam-6249	65	35	,	,	PUNCT
ejpam-6249	65	36	d	d	PROPN
ejpam-6249	65	37	)	)	PUNCT
ejpam-6249	65	38	;	;	PUNCT
ejpam-6249	65	39	(	(	PUNCT
ejpam-6249	65	40	4	4	X
ejpam-6249	65	41	)	)	PUNCT
ejpam-6249	65	42	(	(	PUNCT
ejpam-6249	65	43	(	(	PUNCT
ejpam-6249	65	44	µ	µ	X
ejpam-6249	65	45	∨	∨	NUM
ejpam-6249	65	46	π	π	PROPN
ejpam-6249	65	47	,	,	PUNCT
ejpam-6249	65	48	d),d	d),d	PROPN
ejpam-6249	65	49	)	)	PUNCT
ejpam-6249	65	50	=	=	PRON
ejpam-6249	65	51	(	(	PUNCT
ejpam-6249	65	52	(	(	PUNCT
ejpam-6249	65	53	µ,d),d	µ,d),d	NOUN
ejpam-6249	65	54	)	)	PUNCT
ejpam-6249	65	55	∩	∩	NOUN
ejpam-6249	65	56	(	(	PUNCT
ejpam-6249	65	57	(	(	PUNCT
ejpam-6249	65	58	π	π	PROPN
ejpam-6249	65	59	,	,	PUNCT
ejpam-6249	65	60	d),d	d),d	PROPN
ejpam-6249	65	61	)	)	PUNCT
ejpam-6249	65	62	;	;	PUNCT
ejpam-6249	65	63	(	(	PUNCT
ejpam-6249	65	64	5	5	X
ejpam-6249	65	65	)	)	PUNCT
ejpam-6249	65	66	(	(	PUNCT
ejpam-6249	65	67	µ,d	µ,d	NOUN
ejpam-6249	65	68	)	)	PUNCT
ejpam-6249	65	69	=	=	SYM
ejpam-6249	65	70	l	l	PROPN
ejpam-6249	65	71	⇔	⇔	X
ejpam-6249	65	72	µ	µ	X
ejpam-6249	65	73	∈	∈	PROPN
ejpam-6249	65	74	d	d	NOUN
ejpam-6249	65	75	;	;	PUNCT
ejpam-6249	65	76	(	(	PUNCT
ejpam-6249	65	77	6	6	NUM
ejpam-6249	65	78	)	)	PUNCT
ejpam-6249	65	79	(	(	PUNCT
ejpam-6249	65	80	µ,d	µ,d	NOUN
ejpam-6249	65	81	)	)	PUNCT
ejpam-6249	65	82	=	=	SYM
ejpam-6249	65	83	(	(	PUNCT
ejpam-6249	65	84	π	π	PROPN
ejpam-6249	65	85	,	,	PUNCT
ejpam-6249	65	86	d	d	NOUN
ejpam-6249	65	87	)	)	PUNCT
ejpam-6249	65	88	⇔	⇔	X
ejpam-6249	65	89	(	(	PUNCT
ejpam-6249	65	90	µ	µ	X
ejpam-6249	65	91	∧	∧	PROPN
ejpam-6249	65	92	ψ	ψ	X
ejpam-6249	65	93	,	,	PUNCT
ejpam-6249	65	94	d	d	NOUN
ejpam-6249	65	95	)	)	PUNCT
ejpam-6249	65	96	=	=	SYM
ejpam-6249	65	97	(	(	PUNCT
ejpam-6249	65	98	π	π	PROPN
ejpam-6249	65	99	∧	∧	PROPN
ejpam-6249	65	100	ψ	ψ	PROPN
ejpam-6249	65	101	,	,	PUNCT
ejpam-6249	65	102	d	d	PROPN
ejpam-6249	65	103	)	)	PUNCT
ejpam-6249	65	104	;	;	PUNCT
ejpam-6249	65	105	n.	n.	PROPN
ejpam-6249	65	106	rafi	rafi	PROPN
ejpam-6249	65	107	et	et	PROPN
ejpam-6249	65	108	al	al	PROPN
ejpam-6249	65	109	.	.	PUNCT
ejpam-6249	65	110	/	/	SYM
ejpam-6249	65	111	eur	eur	PROPN
ejpam-6249	65	112	.	.	PUNCT
ejpam-6249	66	1	j.	j.	PROPN
ejpam-6249	66	2	pure	pure	PROPN
ejpam-6249	66	3	appl	appl	PROPN
ejpam-6249	66	4	.	.	PROPN
ejpam-6249	66	5	math	math	PROPN
ejpam-6249	66	6	,	,	PUNCT
ejpam-6249	66	7	18	18	NUM
ejpam-6249	66	8	(	(	PUNCT
ejpam-6249	66	9	4	4	NUM
ejpam-6249	66	10	)	)	PUNCT
ejpam-6249	66	11	(	(	PUNCT
ejpam-6249	66	12	2025	2025	NUM
ejpam-6249	66	13	)	)	PUNCT
ejpam-6249	66	14	,	,	PUNCT
ejpam-6249	66	15	6249	6249	NUM
ejpam-6249	66	16	4	4	NUM
ejpam-6249	66	17	of	of	ADP
ejpam-6249	66	18	11	11	NUM
ejpam-6249	66	19	(	(	PUNCT
ejpam-6249	66	20	7	7	NUM
ejpam-6249	66	21	)	)	PUNCT
ejpam-6249	66	22	(	(	PUNCT
ejpam-6249	66	23	µ,d	µ,d	NOUN
ejpam-6249	66	24	)	)	PUNCT
ejpam-6249	66	25	=	=	SYM
ejpam-6249	66	26	(	(	PUNCT
ejpam-6249	66	27	π	π	PROPN
ejpam-6249	66	28	,	,	PUNCT
ejpam-6249	66	29	d	d	NOUN
ejpam-6249	66	30	)	)	PUNCT
ejpam-6249	66	31	⇔	⇔	X
ejpam-6249	66	32	(	(	PUNCT
ejpam-6249	66	33	µ	µ	X
ejpam-6249	66	34	∨	∨	NUM
ejpam-6249	66	35	ψ	ψ	X
ejpam-6249	66	36	,	,	PUNCT
ejpam-6249	66	37	d	d	NOUN
ejpam-6249	66	38	)	)	PUNCT
ejpam-6249	66	39	=	=	SYM
ejpam-6249	66	40	(	(	PUNCT
ejpam-6249	66	41	π	π	PROPN
ejpam-6249	66	42	∨	∨	NUM
ejpam-6249	66	43	ψ	ψ	X
ejpam-6249	66	44	,	,	PUNCT
ejpam-6249	66	45	d	d	NOUN
ejpam-6249	66	46	)	)	PUNCT
ejpam-6249	66	47	.	.	PUNCT
ejpam-6249	67	1	3	3	X
ejpam-6249	67	2	.	.	NUM
ejpam-6249	67	3	hemicomplemented	hemicomplemente	VERB
ejpam-6249	67	4	adls	adls	NOUN
ejpam-6249	67	5	in	in	ADP
ejpam-6249	67	6	this	this	DET
ejpam-6249	67	7	paper	paper	NOUN
ejpam-6249	67	8	,	,	PUNCT
ejpam-6249	67	9	the	the	DET
ejpam-6249	67	10	concept	concept	NOUN
ejpam-6249	67	11	of	of	ADP
ejpam-6249	67	12	hemicomplemented	hemicomplemente	VERB
ejpam-6249	67	13	adls	adls	PROPN
ejpam-6249	67	14	is	be	AUX
ejpam-6249	67	15	presented	present	VERB
ejpam-6249	67	16	,	,	PUNCT
ejpam-6249	67	17	and	and	CCONJ
ejpam-6249	67	18	these	these	DET
ejpam-6249	67	19	particular	particular	ADJ
ejpam-6249	67	20	types	type	NOUN
ejpam-6249	67	21	of	of	ADP
ejpam-6249	67	22	adls	adls	PROPN
ejpam-6249	67	23	are	be	AUX
ejpam-6249	67	24	described	describe	VERB
ejpam-6249	67	25	through	through	ADP
ejpam-6249	67	26	the	the	DET
ejpam-6249	67	27	ideals	ideal	NOUN
ejpam-6249	67	28	,	,	PUNCT
ejpam-6249	68	1	d	d	NOUN
ejpam-6249	68	2	-	-	PUNCT
ejpam-6249	68	3	filters	filter	NOUN
ejpam-6249	68	4	,	,	PUNCT
ejpam-6249	68	5	congruence	congruence	NOUN
ejpam-6249	68	6	relations	relation	NOUN
ejpam-6249	68	7	,	,	PUNCT
ejpam-6249	68	8	and	and	CCONJ
ejpam-6249	68	9	minimal	minimal	ADJ
ejpam-6249	68	10	prime	prime	ADJ
ejpam-6249	68	11	d	d	NOUN
ejpam-6249	68	12	-	-	NOUN
ejpam-6249	68	13	filters	filter	NOUN
ejpam-6249	68	14	.	.	PUNCT
ejpam-6249	69	1	a	a	DET
ejpam-6249	69	2	group	group	NOUN
ejpam-6249	69	3	of	of	ADP
ejpam-6249	69	4	equivalent	equivalent	ADJ
ejpam-6249	69	5	conditions	condition	NOUN
ejpam-6249	69	6	is	be	AUX
ejpam-6249	69	7	also	also	ADV
ejpam-6249	69	8	formulated	formulate	VERB
ejpam-6249	69	9	to	to	PART
ejpam-6249	69	10	identify	identify	VERB
ejpam-6249	69	11	when	when	SCONJ
ejpam-6249	69	12	a	a	DET
ejpam-6249	69	13	hemicomplemented	hemicomplemente	VERB
ejpam-6249	69	14	adl	adl	NOUN
ejpam-6249	69	15	can	can	AUX
ejpam-6249	69	16	be	be	AUX
ejpam-6249	69	17	converted	convert	VERB
ejpam-6249	69	18	as	as	ADP
ejpam-6249	69	19	a	a	DET
ejpam-6249	69	20	quasicomplemented	quasicomplemented	ADJ
ejpam-6249	69	21	adl	adl	PROPN
ejpam-6249	69	22	.	.	PUNCT
ejpam-6249	70	1	now	now	ADV
ejpam-6249	70	2	we	we	PRON
ejpam-6249	70	3	begin	begin	VERB
ejpam-6249	70	4	with	with	ADP
ejpam-6249	70	5	the	the	DET
ejpam-6249	70	6	following	follow	VERB
ejpam-6249	70	7	definition	definition	NOUN
ejpam-6249	70	8	.	.	PUNCT
ejpam-6249	71	1	definition	definition	NOUN
ejpam-6249	71	2	2	2	NUM
ejpam-6249	71	3	.	.	PUNCT
ejpam-6249	72	1	an	an	DET
ejpam-6249	72	2	element	element	NOUN
ejpam-6249	72	3	µ	µ	NOUN
ejpam-6249	72	4	in	in	ADP
ejpam-6249	72	5	an	an	DET
ejpam-6249	72	6	adl	adl	PROPN
ejpam-6249	72	7	l	l	NOUN
ejpam-6249	72	8	is	be	AUX
ejpam-6249	72	9	said	say	VERB
ejpam-6249	72	10	to	to	PART
ejpam-6249	72	11	be	be	AUX
ejpam-6249	72	12	condensed	condense	VERB
ejpam-6249	72	13	if	if	SCONJ
ejpam-6249	72	14	the	the	DET
ejpam-6249	72	15	filter	filter	NOUN
ejpam-6249	72	16	extension	extension	NOUN
ejpam-6249	72	17	(	(	PUNCT
ejpam-6249	72	18	µ,d	µ,d	NOUN
ejpam-6249	72	19	)	)	PUNCT
ejpam-6249	72	20	is	be	AUX
ejpam-6249	72	21	equal	equal	ADJ
ejpam-6249	72	22	to	to	ADP
ejpam-6249	72	23	d.	d.	PROPN
ejpam-6249	72	24	it	it	PRON
ejpam-6249	72	25	is	be	AUX
ejpam-6249	72	26	evident	evident	ADJ
ejpam-6249	72	27	that	that	SCONJ
ejpam-6249	72	28	the	the	DET
ejpam-6249	72	29	zero	zero	NUM
ejpam-6249	72	30	element	element	NOUN
ejpam-6249	72	31	0	0	NUM
ejpam-6249	72	32	of	of	ADP
ejpam-6249	72	33	an	an	DET
ejpam-6249	72	34	adl	adl	PROPN
ejpam-6249	72	35	l	l	NOUN
ejpam-6249	72	36	is	be	AUX
ejpam-6249	72	37	always	always	ADV
ejpam-6249	72	38	a	a	DET
ejpam-6249	72	39	condensed	condense	VERB
ejpam-6249	72	40	element	element	NOUN
ejpam-6249	72	41	.	.	PUNCT
ejpam-6249	73	1	let	let	VERB
ejpam-6249	73	2	us	we	PRON
ejpam-6249	73	3	use	use	VERB
ejpam-6249	73	4	the	the	DET
ejpam-6249	73	5	notation	notation	NOUN
ejpam-6249	73	6	d∞	d∞	PROPN
ejpam-6249	73	7	to	to	PART
ejpam-6249	73	8	represent	represent	VERB
ejpam-6249	73	9	the	the	DET
ejpam-6249	73	10	collection	collection	NOUN
ejpam-6249	73	11	of	of	ADP
ejpam-6249	73	12	all	all	DET
ejpam-6249	73	13	condensed	condense	VERB
ejpam-6249	73	14	elements	element	NOUN
ejpam-6249	73	15	in	in	ADP
ejpam-6249	73	16	l.	l.	NOUN
ejpam-6249	73	17	with	with	ADP
ejpam-6249	73	18	this	this	DET
ejpam-6249	73	19	definition	definition	NOUN
ejpam-6249	73	20	,	,	PUNCT
ejpam-6249	73	21	we	we	PRON
ejpam-6249	73	22	arrive	arrive	VERB
ejpam-6249	73	23	at	at	ADP
ejpam-6249	73	24	the	the	DET
ejpam-6249	73	25	following	following	ADJ
ejpam-6249	73	26	result	result	NOUN
ejpam-6249	73	27	.	.	PUNCT
ejpam-6249	74	1	proposition	proposition	NOUN
ejpam-6249	74	2	2	2	NUM
ejpam-6249	74	3	.	.	PUNCT
ejpam-6249	75	1	the	the	DET
ejpam-6249	75	2	following	follow	VERB
ejpam-6249	75	3	statements	statement	NOUN
ejpam-6249	75	4	are	be	AUX
ejpam-6249	75	5	valid	valid	ADJ
ejpam-6249	75	6	in	in	ADP
ejpam-6249	75	7	an	an	DET
ejpam-6249	75	8	adl	adl	PROPN
ejpam-6249	75	9	l	l	NOUN
ejpam-6249	75	10	(	(	PUNCT
ejpam-6249	75	11	1	1	NUM
ejpam-6249	75	12	)	)	PUNCT
ejpam-6249	75	13	d	d	NOUN
ejpam-6249	75	14	∩d∞	∩d∞	NOUN
ejpam-6249	75	15	=	=	NOUN
ejpam-6249	75	16	∅	∅	NOUN
ejpam-6249	75	17	;	;	PUNCT
ejpam-6249	75	18	(	(	PUNCT
ejpam-6249	75	19	2	2	X
ejpam-6249	75	20	)	)	PUNCT
ejpam-6249	75	21	d∞	d∞	NOUN
ejpam-6249	75	22	is	be	AUX
ejpam-6249	75	23	an	an	DET
ejpam-6249	75	24	ideal	ideal	NOUN
ejpam-6249	75	25	in	in	ADP
ejpam-6249	75	26	l.	l.	PROPN
ejpam-6249	75	27	proof	proof	PROPN
ejpam-6249	75	28	.	.	PUNCT
ejpam-6249	76	1	(	(	PUNCT
ejpam-6249	76	2	1	1	X
ejpam-6249	76	3	)	)	PUNCT
ejpam-6249	76	4	assume	assume	VERB
ejpam-6249	76	5	that	that	SCONJ
ejpam-6249	76	6	µ	µ	X
ejpam-6249	76	7	∈	∈	PROPN
ejpam-6249	76	8	d	d	NOUN
ejpam-6249	76	9	∩	∩	X
ejpam-6249	76	10	d∞.	d∞.	PROPN
ejpam-6249	76	11	by	by	ADP
ejpam-6249	76	12	the	the	DET
ejpam-6249	76	13	definition	definition	NOUN
ejpam-6249	76	14	of	of	ADP
ejpam-6249	76	15	condensed	condense	VERB
ejpam-6249	76	16	elements	element	NOUN
ejpam-6249	76	17	,	,	PUNCT
ejpam-6249	76	18	this	this	PRON
ejpam-6249	76	19	implies	imply	VERB
ejpam-6249	76	20	that	that	SCONJ
ejpam-6249	76	21	(	(	PUNCT
ejpam-6249	76	22	µ,d	µ,d	NOUN
ejpam-6249	76	23	)	)	PUNCT
ejpam-6249	77	1	=	=	SYM
ejpam-6249	77	2	d.	d.	NOUN
ejpam-6249	77	3	since	since	SCONJ
ejpam-6249	77	4	µ	µ	PROPN
ejpam-6249	77	5	also	also	ADV
ejpam-6249	77	6	belongs	belong	VERB
ejpam-6249	77	7	to	to	ADP
ejpam-6249	77	8	d	d	PROPN
ejpam-6249	77	9	,	,	PUNCT
ejpam-6249	77	10	it	it	PRON
ejpam-6249	77	11	follows	follow	VERB
ejpam-6249	77	12	that	that	SCONJ
ejpam-6249	77	13	l	l	NOUN
ejpam-6249	77	14	=	=	SYM
ejpam-6249	77	15	(	(	PUNCT
ejpam-6249	77	16	µ,d	µ,d	NOUN
ejpam-6249	77	17	)	)	PUNCT
ejpam-6249	77	18	=	=	SYM
ejpam-6249	78	1	d.	d.	PROPN
ejpam-6249	78	2	consequently	consequently	ADV
ejpam-6249	78	3	,	,	PUNCT
ejpam-6249	78	4	the	the	DET
ejpam-6249	78	5	zero	zero	NUM
ejpam-6249	78	6	element	element	NOUN
ejpam-6249	78	7	0	0	NUM
ejpam-6249	78	8	must	must	AUX
ejpam-6249	78	9	be	be	AUX
ejpam-6249	78	10	in	in	ADP
ejpam-6249	78	11	d	d	PROPN
ejpam-6249	78	12	,	,	PUNCT
ejpam-6249	78	13	which	which	PRON
ejpam-6249	78	14	contradicts	contradict	VERB
ejpam-6249	78	15	the	the	DET
ejpam-6249	78	16	assumption	assumption	NOUN
ejpam-6249	78	17	that	that	SCONJ
ejpam-6249	78	18	d	d	NOUN
ejpam-6249	78	19	is	be	AUX
ejpam-6249	78	20	a	a	DET
ejpam-6249	78	21	proper	proper	ADJ
ejpam-6249	78	22	filter	filter	NOUN
ejpam-6249	78	23	.	.	PUNCT
ejpam-6249	79	1	thus	thus	ADV
ejpam-6249	79	2	,	,	PUNCT
ejpam-6249	79	3	we	we	PRON
ejpam-6249	79	4	conclude	conclude	VERB
ejpam-6249	79	5	that	that	SCONJ
ejpam-6249	79	6	d	d	ADP
ejpam-6249	79	7	∩d∞	∩d∞	PRON
ejpam-6249	79	8	=	=	PUNCT
ejpam-6249	79	9	∅.	∅.	X
ejpam-6249	79	10	(	(	PUNCT
ejpam-6249	79	11	2	2	X
ejpam-6249	79	12	)	)	PUNCT
ejpam-6249	79	13	it	it	PRON
ejpam-6249	79	14	is	be	AUX
ejpam-6249	79	15	clear	clear	ADJ
ejpam-6249	79	16	that	that	SCONJ
ejpam-6249	79	17	0	0	NUM
ejpam-6249	79	18	belongs	belong	VERB
ejpam-6249	79	19	to	to	AUX
ejpam-6249	79	20	d∞.	d∞.	INTJ
ejpam-6249	79	21	suppose	suppose	VERB
ejpam-6249	79	22	µ	µ	X
ejpam-6249	79	23	,	,	PUNCT
ejpam-6249	79	24	π	π	PROPN
ejpam-6249	79	25	∈	∈	PROPN
ejpam-6249	79	26	d∞.	d∞.	INTJ
ejpam-6249	79	27	by	by	ADP
ejpam-6249	79	28	the	the	DET
ejpam-6249	79	29	definition	definition	NOUN
ejpam-6249	79	30	of	of	ADP
ejpam-6249	79	31	condensed	condense	VERB
ejpam-6249	79	32	elements	element	NOUN
ejpam-6249	79	33	,	,	PUNCT
ejpam-6249	79	34	we	we	PRON
ejpam-6249	79	35	have	have	VERB
ejpam-6249	79	36	(	(	PUNCT
ejpam-6249	79	37	µ,d	µ,d	NOUN
ejpam-6249	79	38	)	)	PUNCT
ejpam-6249	79	39	=	=	SYM
ejpam-6249	80	1	d	d	PROPN
ejpam-6249	80	2	and	and	CCONJ
ejpam-6249	80	3	(	(	PUNCT
ejpam-6249	80	4	π	π	PROPN
ejpam-6249	80	5	,	,	PUNCT
ejpam-6249	80	6	d	d	NOUN
ejpam-6249	80	7	)	)	PUNCT
ejpam-6249	80	8	=	=	SYM
ejpam-6249	80	9	d	d	NOUN
ejpam-6249	80	10	,	,	PUNCT
ejpam-6249	80	11	which	which	PRON
ejpam-6249	80	12	implies	imply	VERB
ejpam-6249	80	13	that	that	SCONJ
ejpam-6249	80	14	(	(	PUNCT
ejpam-6249	80	15	(	(	PUNCT
ejpam-6249	80	16	µ,d),d	µ,d),d	NOUN
ejpam-6249	80	17	)	)	PUNCT
ejpam-6249	80	18	=	=	SYM
ejpam-6249	81	1	l	l	NOUN
ejpam-6249	81	2	and	and	CCONJ
ejpam-6249	81	3	(	(	PUNCT
ejpam-6249	81	4	(	(	PUNCT
ejpam-6249	81	5	π	π	PROPN
ejpam-6249	81	6	,	,	PUNCT
ejpam-6249	81	7	d),d	d),d	NOUN
ejpam-6249	81	8	)	)	PUNCT
ejpam-6249	81	9	=	=	PUNCT
ejpam-6249	82	1	l.	l.	PROPN
ejpam-6249	82	2	therefore,((µ	therefore,((µ	PROPN
ejpam-6249	82	3	∨	∨	ADV
ejpam-6249	82	4	π),d),d	π),d),d	PROPN
ejpam-6249	82	5	)	)	PUNCT
ejpam-6249	82	6	=	=	SYM
ejpam-6249	82	7	(	(	PUNCT
ejpam-6249	82	8	(	(	PUNCT
ejpam-6249	82	9	µ,d),d	µ,d),d	NOUN
ejpam-6249	82	10	)	)	PUNCT
ejpam-6249	82	11	∩	∩	NOUN
ejpam-6249	82	12	(	(	PUNCT
ejpam-6249	82	13	(	(	PUNCT
ejpam-6249	82	14	π	π	PROPN
ejpam-6249	82	15	,	,	PUNCT
ejpam-6249	82	16	d),d	d),d	NOUN
ejpam-6249	82	17	)	)	PUNCT
ejpam-6249	82	18	=	=	VERB
ejpam-6249	83	1	l.	l.	NOUN
ejpam-6249	83	2	this	this	PRON
ejpam-6249	83	3	leads	lead	VERB
ejpam-6249	83	4	to	to	ADP
ejpam-6249	83	5	(	(	PUNCT
ejpam-6249	83	6	(	(	PUNCT
ejpam-6249	83	7	µ∨π),d	µ∨π),d	PROPN
ejpam-6249	83	8	)	)	PUNCT
ejpam-6249	84	1	=	=	PUNCT
ejpam-6249	84	2	(	(	PUNCT
ejpam-6249	84	3	l	l	NOUN
ejpam-6249	84	4	,	,	PUNCT
ejpam-6249	84	5	d	d	NOUN
ejpam-6249	84	6	)	)	PUNCT
ejpam-6249	84	7	=	=	SYM
ejpam-6249	84	8	d	d	NOUN
ejpam-6249	84	9	,	,	PUNCT
ejpam-6249	84	10	showing	show	VERB
ejpam-6249	84	11	that	that	DET
ejpam-6249	84	12	µ∨π	µ∨π	NOUN
ejpam-6249	84	13	∈	∈	PROPN
ejpam-6249	84	14	d∞.	d∞.	INTJ
ejpam-6249	84	15	now	now	ADV
ejpam-6249	84	16	,	,	PUNCT
ejpam-6249	84	17	let	let	VERB
ejpam-6249	84	18	µ	µ	X
ejpam-6249	84	19	∈	∈	NOUN
ejpam-6249	84	20	d∞.	d∞.	PROPN
ejpam-6249	84	21	then	then	ADV
ejpam-6249	84	22	(	(	PUNCT
ejpam-6249	84	23	µ,d	µ,d	NOUN
ejpam-6249	84	24	)	)	PUNCT
ejpam-6249	84	25	=	=	SYM
ejpam-6249	84	26	d.	d.	NOUN
ejpam-6249	84	27	for	for	ADP
ejpam-6249	84	28	any	any	DET
ejpam-6249	84	29	π	π	PROPN
ejpam-6249	84	30	∈	∈	PROPN
ejpam-6249	84	31	l	l	NOUN
ejpam-6249	84	32	,	,	PUNCT
ejpam-6249	84	33	we	we	PRON
ejpam-6249	84	34	have	have	AUX
ejpam-6249	84	35	(	(	PUNCT
ejpam-6249	84	36	π∧µ,d	π∧µ,d	NOUN
ejpam-6249	84	37	)	)	PUNCT
ejpam-6249	84	38	⊆	⊆	NUM
ejpam-6249	84	39	(	(	PUNCT
ejpam-6249	84	40	µ,d	µ,d	NOUN
ejpam-6249	84	41	)	)	PUNCT
ejpam-6249	84	42	=	=	SYM
ejpam-6249	85	1	d.	d.	NOUN
ejpam-6249	85	2	since	since	SCONJ
ejpam-6249	85	3	d	d	PROPN
ejpam-6249	85	4	is	be	AUX
ejpam-6249	85	5	always	always	ADV
ejpam-6249	85	6	contained	contain	VERB
ejpam-6249	85	7	in	in	ADP
ejpam-6249	85	8	(	(	PUNCT
ejpam-6249	85	9	π∧µ,d	π∧µ,d	NOUN
ejpam-6249	85	10	)	)	PUNCT
ejpam-6249	85	11	,	,	PUNCT
ejpam-6249	85	12	it	it	PRON
ejpam-6249	85	13	follows	follow	VERB
ejpam-6249	85	14	that	that	SCONJ
ejpam-6249	85	15	(	(	PUNCT
ejpam-6249	85	16	π	π	PROPN
ejpam-6249	85	17	∧	∧	PROPN
ejpam-6249	85	18	µ,d	µ,d	PROPN
ejpam-6249	85	19	)	)	PUNCT
ejpam-6249	86	1	=	=	SYM
ejpam-6249	86	2	d	d	NOUN
ejpam-6249	86	3	,	,	PUNCT
ejpam-6249	86	4	so	so	ADV
ejpam-6249	86	5	π	π	X
ejpam-6249	86	6	∧	∧	PROPN
ejpam-6249	86	7	µ	µ	PROPN
ejpam-6249	86	8	∈	∈	NOUN
ejpam-6249	87	1	d∞.	d∞.	NOUN
ejpam-6249	87	2	hence	hence	ADV
ejpam-6249	87	3	,	,	PUNCT
ejpam-6249	87	4	d∞	d∞	PROPN
ejpam-6249	87	5	is	be	AUX
ejpam-6249	87	6	an	an	DET
ejpam-6249	87	7	ideal	ideal	NOUN
ejpam-6249	87	8	in	in	ADP
ejpam-6249	87	9	l.	l.	PROPN
ejpam-6249	87	10	proposition	proposition	PROPN
ejpam-6249	87	11	3	3	NUM
ejpam-6249	87	12	.	.	NOUN
ejpam-6249	87	13	0	0	NUM
ejpam-6249	87	14	is	be	AUX
ejpam-6249	87	15	the	the	DET
ejpam-6249	87	16	unique	unique	ADJ
ejpam-6249	87	17	condensed	condense	VERB
ejpam-6249	87	18	element	element	NOUN
ejpam-6249	87	19	in	in	ADP
ejpam-6249	87	20	any	any	DET
ejpam-6249	87	21	dense	dense	ADJ
ejpam-6249	87	22	adl	adl	PROPN
ejpam-6249	87	23	.	.	PUNCT
ejpam-6249	87	24	proof	proof	NOUN
ejpam-6249	87	25	.	.	PUNCT
ejpam-6249	88	1	consider	consider	VERB
ejpam-6249	88	2	a	a	DET
ejpam-6249	88	3	dense	dense	ADJ
ejpam-6249	88	4	adl	adl	PROPN
ejpam-6249	88	5	l.	l.	NOUN
ejpam-6249	88	6	in	in	ADP
ejpam-6249	88	7	such	such	ADJ
ejpam-6249	88	8	adls	adls	NOUN
ejpam-6249	88	9	,	,	PUNCT
ejpam-6249	88	10	all	all	DET
ejpam-6249	88	11	elements	element	NOUN
ejpam-6249	88	12	except	except	SCONJ
ejpam-6249	88	13	zero	zero	NUM
ejpam-6249	88	14	are	be	AUX
ejpam-6249	88	15	dense	dense	ADJ
ejpam-6249	88	16	.	.	PUNCT
ejpam-6249	89	1	suppose	suppose	VERB
ejpam-6249	89	2	that	that	SCONJ
ejpam-6249	89	3	µ	µ	NOUN
ejpam-6249	89	4	is	be	AUX
ejpam-6249	89	5	a	a	DET
ejpam-6249	89	6	condensed	condense	VERB
ejpam-6249	89	7	element	element	NOUN
ejpam-6249	89	8	in	in	ADP
ejpam-6249	89	9	l	l	NOUN
ejpam-6249	89	10	,	,	PUNCT
ejpam-6249	89	11	meaning	mean	VERB
ejpam-6249	89	12	that	that	SCONJ
ejpam-6249	89	13	(	(	PUNCT
ejpam-6249	89	14	µ,d	µ,d	NOUN
ejpam-6249	89	15	)	)	PUNCT
ejpam-6249	89	16	=	=	SYM
ejpam-6249	90	1	d.	d.	PROPN
ejpam-6249	90	2	assume	assume	VERB
ejpam-6249	90	3	,	,	PUNCT
ejpam-6249	90	4	contrary	contrary	ADJ
ejpam-6249	90	5	to	to	ADP
ejpam-6249	90	6	what	what	PRON
ejpam-6249	90	7	we	we	PRON
ejpam-6249	90	8	aim	aim	VERB
ejpam-6249	90	9	to	to	PART
ejpam-6249	90	10	prove	prove	VERB
ejpam-6249	90	11	,	,	PUNCT
ejpam-6249	90	12	that	that	SCONJ
ejpam-6249	90	13	µ	µ	X
ejpam-6249	90	14	̸=	̸=	PROPN
ejpam-6249	90	15	0	0	NUM
ejpam-6249	90	16	.	.	PUNCT
ejpam-6249	91	1	since	since	SCONJ
ejpam-6249	91	2	l	l	NOUN
ejpam-6249	91	3	is	be	AUX
ejpam-6249	91	4	dense	dense	ADJ
ejpam-6249	91	5	,	,	PUNCT
ejpam-6249	91	6	this	this	PRON
ejpam-6249	91	7	implies	imply	VERB
ejpam-6249	91	8	that	that	SCONJ
ejpam-6249	91	9	µ	µ	NOUN
ejpam-6249	91	10	belongs	belong	VERB
ejpam-6249	91	11	to	to	ADP
ejpam-6249	91	12	d.	d.	NOUN
ejpam-6249	91	13	applying	apply	VERB
ejpam-6249	91	14	corollary	corollary	ADJ
ejpam-6249	91	15	1(5	1(5	NUM
ejpam-6249	91	16	)	)	PUNCT
ejpam-6249	91	17	,	,	PUNCT
ejpam-6249	91	18	we	we	PRON
ejpam-6249	91	19	then	then	ADV
ejpam-6249	91	20	obtain	obtain	VERB
ejpam-6249	91	21	(	(	PUNCT
ejpam-6249	91	22	µ,d	µ,d	NOUN
ejpam-6249	91	23	)	)	PUNCT
ejpam-6249	91	24	=	=	SYM
ejpam-6249	91	25	l	l	NOUN
ejpam-6249	91	26	,	,	PUNCT
ejpam-6249	91	27	which	which	PRON
ejpam-6249	91	28	contradicts	contradict	VERB
ejpam-6249	91	29	the	the	DET
ejpam-6249	91	30	earlier	early	ADJ
ejpam-6249	91	31	conclusion	conclusion	NOUN
ejpam-6249	91	32	that	that	SCONJ
ejpam-6249	91	33	(	(	PUNCT
ejpam-6249	91	34	µ,d	µ,d	NOUN
ejpam-6249	91	35	)	)	PUNCT
ejpam-6249	91	36	=	=	VERB
ejpam-6249	92	1	d.	d.	NOUN
ejpam-6249	92	2	this	this	DET
ejpam-6249	92	3	contradiction	contradiction	NOUN
ejpam-6249	92	4	forces	force	VERB
ejpam-6249	92	5	us	we	PRON
ejpam-6249	92	6	to	to	PART
ejpam-6249	92	7	reject	reject	VERB
ejpam-6249	92	8	the	the	DET
ejpam-6249	92	9	assumption	assumption	NOUN
ejpam-6249	92	10	that	that	SCONJ
ejpam-6249	92	11	µ	µ	X
ejpam-6249	92	12	̸=	̸=	PROPN
ejpam-6249	92	13	0	0	NUM
ejpam-6249	92	14	,	,	PUNCT
ejpam-6249	92	15	so	so	SCONJ
ejpam-6249	92	16	we	we	PRON
ejpam-6249	92	17	conclude	conclude	VERB
ejpam-6249	92	18	that	that	SCONJ
ejpam-6249	92	19	µ	µ	X
ejpam-6249	92	20	=	=	SYM
ejpam-6249	92	21	0	0	NUM
ejpam-6249	92	22	.	.	PUNCT
ejpam-6249	93	1	therefore	therefore	ADV
ejpam-6249	93	2	,	,	PUNCT
ejpam-6249	93	3	the	the	DET
ejpam-6249	93	4	only	only	ADJ
ejpam-6249	93	5	condensed	condense	VERB
ejpam-6249	93	6	element	element	NOUN
ejpam-6249	93	7	in	in	ADP
ejpam-6249	93	8	a	a	DET
ejpam-6249	93	9	dense	dense	ADJ
ejpam-6249	93	10	adl	adl	NOUN
ejpam-6249	93	11	is	be	AUX
ejpam-6249	93	12	the	the	DET
ejpam-6249	93	13	zero	zero	NUM
ejpam-6249	93	14	element	element	NOUN
ejpam-6249	93	15	,	,	PUNCT
ejpam-6249	93	16	or	or	CCONJ
ejpam-6249	93	17	equivalently	equivalently	ADV
ejpam-6249	93	18	,	,	PUNCT
ejpam-6249	93	19	d∞	d∞	PROPN
ejpam-6249	93	20	=	=	PUNCT
ejpam-6249	93	21	{	{	PUNCT
ejpam-6249	93	22	0	0	NUM
ejpam-6249	93	23	}	}	PUNCT
ejpam-6249	93	24	.	.	PUNCT
ejpam-6249	94	1	the	the	DET
ejpam-6249	94	2	following	follow	VERB
ejpam-6249	94	3	example	example	NOUN
ejpam-6249	94	4	illustrates	illustrate	VERB
ejpam-6249	94	5	that	that	SCONJ
ejpam-6249	94	6	an	an	DET
ejpam-6249	94	7	adl	adl	NOUN
ejpam-6249	94	8	with	with	ADP
ejpam-6249	94	9	a	a	DET
ejpam-6249	94	10	unique	unique	ADJ
ejpam-6249	94	11	condensed	condense	VERB
ejpam-6249	94	12	element	element	NOUN
ejpam-6249	94	13	0	0	NUM
ejpam-6249	94	14	does	do	AUX
ejpam-6249	94	15	not	not	PART
ejpam-6249	94	16	necessarily	necessarily	ADV
ejpam-6249	94	17	become	become	VERB
ejpam-6249	94	18	as	as	ADP
ejpam-6249	94	19	a	a	DET
ejpam-6249	94	20	dense	dense	ADJ
ejpam-6249	94	21	adl	adl	PROPN
ejpam-6249	94	22	.	.	PUNCT
ejpam-6249	94	23	n.	n.	PROPN
ejpam-6249	94	24	rafi	rafi	PROPN
ejpam-6249	94	25	et	et	PROPN
ejpam-6249	94	26	al	al	PROPN
ejpam-6249	94	27	.	.	PUNCT
ejpam-6249	94	28	/	/	SYM
ejpam-6249	94	29	eur	eur	PROPN
ejpam-6249	94	30	.	.	PUNCT
ejpam-6249	95	1	j.	j.	PROPN
ejpam-6249	95	2	pure	pure	PROPN
ejpam-6249	95	3	appl	appl	PROPN
ejpam-6249	95	4	.	.	PROPN
ejpam-6249	95	5	math	math	PROPN
ejpam-6249	95	6	,	,	PUNCT
ejpam-6249	95	7	18	18	NUM
ejpam-6249	95	8	(	(	PUNCT
ejpam-6249	95	9	4	4	NUM
ejpam-6249	95	10	)	)	PUNCT
ejpam-6249	95	11	(	(	PUNCT
ejpam-6249	95	12	2025	2025	NUM
ejpam-6249	95	13	)	)	PUNCT
ejpam-6249	95	14	,	,	PUNCT
ejpam-6249	95	15	6249	6249	NUM
ejpam-6249	95	16	5	5	NUM
ejpam-6249	95	17	of	of	ADP
ejpam-6249	95	18	11	11	NUM
ejpam-6249	95	19	example	example	NOUN
ejpam-6249	95	20	1	1	NUM
ejpam-6249	95	21	.	.	X
ejpam-6249	95	22	consider	consider	VERB
ejpam-6249	95	23	the	the	DET
ejpam-6249	95	24	set	set	NOUN
ejpam-6249	95	25	l	l	NOUN
ejpam-6249	95	26	=	=	PUNCT
ejpam-6249	95	27	{	{	PUNCT
ejpam-6249	95	28	0	0	NUM
ejpam-6249	95	29	,	,	PUNCT
ejpam-6249	95	30	1	1	NUM
ejpam-6249	95	31	,	,	PUNCT
ejpam-6249	95	32	2	2	NUM
ejpam-6249	95	33	,	,	PUNCT
ejpam-6249	95	34	3	3	NUM
ejpam-6249	95	35	,	,	PUNCT
ejpam-6249	95	36	4	4	NUM
ejpam-6249	95	37	,	,	PUNCT
ejpam-6249	95	38	5	5	NUM
ejpam-6249	95	39	,	,	PUNCT
ejpam-6249	95	40	6	6	NUM
ejpam-6249	95	41	}	}	PUNCT
ejpam-6249	95	42	,	,	PUNCT
ejpam-6249	95	43	with	with	ADP
ejpam-6249	95	44	the	the	DET
ejpam-6249	95	45	operations	operation	NOUN
ejpam-6249	95	46	∨	∨	NOUN
ejpam-6249	95	47	(	(	PUNCT
ejpam-6249	95	48	join	join	NOUN
ejpam-6249	95	49	)	)	PUNCT
ejpam-6249	95	50	and	and	CCONJ
ejpam-6249	95	51	∧	∧	PROPN
ejpam-6249	95	52	(	(	PUNCT
ejpam-6249	95	53	meet	meet	NOUN
ejpam-6249	95	54	)	)	PUNCT
ejpam-6249	95	55	defined	define	VERB
ejpam-6249	95	56	on	on	ADP
ejpam-6249	95	57	l	l	NOUN
ejpam-6249	95	58	as	as	SCONJ
ejpam-6249	95	59	follows	follow	VERB
ejpam-6249	95	60	:	:	PUNCT
ejpam-6249	95	61	∧	∧	NOUN
ejpam-6249	95	62	0	0	NUM
ejpam-6249	95	63	1	1	NUM
ejpam-6249	95	64	2	2	NUM
ejpam-6249	95	65	3	3	NUM
ejpam-6249	95	66	4	4	NUM
ejpam-6249	95	67	5	5	NUM
ejpam-6249	95	68	6	6	NUM
ejpam-6249	95	69	0	0	NUM
ejpam-6249	95	70	0	0	NUM
ejpam-6249	95	71	0	0	NUM
ejpam-6249	95	72	0	0	NUM
ejpam-6249	95	73	0	0	NUM
ejpam-6249	95	74	0	0	NUM
ejpam-6249	95	75	0	0	NUM
ejpam-6249	95	76	0	0	NUM
ejpam-6249	95	77	1	1	NUM
ejpam-6249	95	78	0	0	NUM
ejpam-6249	95	79	1	1	NUM
ejpam-6249	95	80	2	2	NUM
ejpam-6249	95	81	3	3	NUM
ejpam-6249	95	82	4	4	NUM
ejpam-6249	95	83	5	5	NUM
ejpam-6249	95	84	6	6	NUM
ejpam-6249	95	85	2	2	NUM
ejpam-6249	95	86	0	0	NUM
ejpam-6249	95	87	1	1	NUM
ejpam-6249	95	88	2	2	NUM
ejpam-6249	95	89	3	3	NUM
ejpam-6249	95	90	4	4	NUM
ejpam-6249	95	91	5	5	NUM
ejpam-6249	95	92	6	6	NUM
ejpam-6249	95	93	3	3	NUM
ejpam-6249	95	94	0	0	NUM
ejpam-6249	95	95	3	3	NUM
ejpam-6249	95	96	3	3	NUM
ejpam-6249	95	97	3	3	NUM
ejpam-6249	95	98	0	0	NUM
ejpam-6249	95	99	3	3	NUM
ejpam-6249	95	100	3	3	NUM
ejpam-6249	95	101	4	4	NUM
ejpam-6249	95	102	0	0	NUM
ejpam-6249	95	103	4	4	NUM
ejpam-6249	95	104	4	4	NUM
ejpam-6249	95	105	0	0	NUM
ejpam-6249	95	106	4	4	NUM
ejpam-6249	95	107	4	4	NUM
ejpam-6249	95	108	4	4	NUM
ejpam-6249	95	109	5	5	NUM
ejpam-6249	95	110	0	0	NUM
ejpam-6249	95	111	5	5	NUM
ejpam-6249	95	112	5	5	NUM
ejpam-6249	95	113	3	3	NUM
ejpam-6249	95	114	4	4	NUM
ejpam-6249	95	115	5	5	NUM
ejpam-6249	95	116	5	5	NUM
ejpam-6249	95	117	6	6	NUM
ejpam-6249	95	118	0	0	NUM
ejpam-6249	95	119	6	6	NUM
ejpam-6249	95	120	6	6	NUM
ejpam-6249	95	121	3	3	NUM
ejpam-6249	95	122	4	4	NUM
ejpam-6249	95	123	5	5	NUM
ejpam-6249	95	124	6	6	NUM
ejpam-6249	95	125	∨	∨	NUM
ejpam-6249	95	126	0	0	NUM
ejpam-6249	95	127	1	1	NUM
ejpam-6249	95	128	2	2	NUM
ejpam-6249	95	129	3	3	NUM
ejpam-6249	95	130	4	4	NUM
ejpam-6249	95	131	5	5	NUM
ejpam-6249	95	132	6	6	NUM
ejpam-6249	95	133	0	0	NUM
ejpam-6249	95	134	0	0	NUM
ejpam-6249	95	135	1	1	NUM
ejpam-6249	95	136	2	2	NUM
ejpam-6249	95	137	3	3	NUM
ejpam-6249	95	138	4	4	NUM
ejpam-6249	95	139	5	5	NUM
ejpam-6249	95	140	6	6	NUM
ejpam-6249	95	141	1	1	NUM
ejpam-6249	95	142	1	1	NUM
ejpam-6249	95	143	1	1	NUM
ejpam-6249	95	144	1	1	NUM
ejpam-6249	95	145	1	1	NUM
ejpam-6249	95	146	1	1	NUM
ejpam-6249	95	147	1	1	NUM
ejpam-6249	95	148	1	1	NUM
ejpam-6249	95	149	2	2	NUM
ejpam-6249	95	150	2	2	NUM
ejpam-6249	95	151	2	2	NUM
ejpam-6249	95	152	2	2	NUM
ejpam-6249	95	153	2	2	NUM
ejpam-6249	95	154	2	2	NUM
ejpam-6249	95	155	2	2	NUM
ejpam-6249	95	156	2	2	NUM
ejpam-6249	95	157	3	3	NUM
ejpam-6249	95	158	3	3	NUM
ejpam-6249	95	159	1	1	NUM
ejpam-6249	95	160	2	2	NUM
ejpam-6249	95	161	3	3	NUM
ejpam-6249	95	162	5	5	NUM
ejpam-6249	95	163	5	5	NUM
ejpam-6249	95	164	6	6	NUM
ejpam-6249	95	165	4	4	NUM
ejpam-6249	95	166	4	4	NUM
ejpam-6249	95	167	1	1	NUM
ejpam-6249	95	168	2	2	NUM
ejpam-6249	95	169	5	5	NUM
ejpam-6249	95	170	4	4	NUM
ejpam-6249	95	171	5	5	NUM
ejpam-6249	95	172	6	6	NUM
ejpam-6249	95	173	5	5	NUM
ejpam-6249	95	174	5	5	NUM
ejpam-6249	95	175	1	1	NUM
ejpam-6249	95	176	2	2	NUM
ejpam-6249	95	177	5	5	NUM
ejpam-6249	95	178	5	5	NUM
ejpam-6249	95	179	5	5	NUM
ejpam-6249	95	180	6	6	NUM
ejpam-6249	95	181	6	6	NUM
ejpam-6249	95	182	6	6	NUM
ejpam-6249	95	183	1	1	NUM
ejpam-6249	95	184	2	2	NUM
ejpam-6249	95	185	6	6	NUM
ejpam-6249	95	186	6	6	NUM
ejpam-6249	95	187	6	6	NUM
ejpam-6249	95	188	6	6	NUM
ejpam-6249	95	189	thus	thus	ADV
ejpam-6249	95	190	,	,	PUNCT
ejpam-6249	95	191	(	(	PUNCT
ejpam-6249	95	192	l,∨,∧	l,∨,∧	NOUN
ejpam-6249	95	193	)	)	PUNCT
ejpam-6249	95	194	is	be	AUX
ejpam-6249	95	195	an	an	DET
ejpam-6249	95	196	adl	adl	PROPN
ejpam-6249	95	197	.	.	PUNCT
ejpam-6249	96	1	clearly	clearly	ADV
ejpam-6249	96	2	,	,	PUNCT
ejpam-6249	96	3	we	we	PRON
ejpam-6249	96	4	have	have	VERB
ejpam-6249	96	5	the	the	DET
ejpam-6249	96	6	dense	dense	ADJ
ejpam-6249	96	7	set	set	NOUN
ejpam-6249	96	8	d	d	NOUN
ejpam-6249	96	9	=	=	SYM
ejpam-6249	96	10	{	{	PUNCT
ejpam-6249	96	11	1	1	NUM
ejpam-6249	96	12	,	,	PUNCT
ejpam-6249	96	13	2	2	NUM
ejpam-6249	96	14	,	,	PUNCT
ejpam-6249	96	15	5	5	NUM
ejpam-6249	96	16	,	,	PUNCT
ejpam-6249	96	17	6	6	NUM
ejpam-6249	96	18	}	}	PUNCT
ejpam-6249	96	19	.	.	PUNCT
ejpam-6249	97	1	it	it	PRON
ejpam-6249	97	2	is	be	AUX
ejpam-6249	97	3	evident	evident	ADJ
ejpam-6249	97	4	that	that	SCONJ
ejpam-6249	97	5	(	(	PUNCT
ejpam-6249	97	6	0,d	0,d	PUNCT
ejpam-6249	97	7	)	)	PUNCT
ejpam-6249	97	8	=	=	SYM
ejpam-6249	97	9	d	d	NOUN
ejpam-6249	97	10	,	,	PUNCT
ejpam-6249	97	11	and	and	CCONJ
ejpam-6249	97	12	l	l	NOUN
ejpam-6249	97	13	is	be	AUX
ejpam-6249	97	14	not	not	PART
ejpam-6249	97	15	a	a	DET
ejpam-6249	97	16	dense	dense	ADJ
ejpam-6249	97	17	adl	adl	NOUN
ejpam-6249	97	18	because	because	SCONJ
ejpam-6249	97	19	non	non	ADJ
ejpam-6249	97	20	zero	zero	NUM
ejpam-6249	97	21	elements	element	NOUN
ejpam-6249	97	22	3	3	NUM
ejpam-6249	97	23	,	,	PUNCT
ejpam-6249	97	24	4	4	NUM
ejpam-6249	97	25	are	be	AUX
ejpam-6249	97	26	not	not	PART
ejpam-6249	97	27	dense	dense	ADJ
ejpam-6249	97	28	.	.	PUNCT
ejpam-6249	98	1	proposition	proposition	NOUN
ejpam-6249	98	2	4	4	NUM
ejpam-6249	98	3	.	.	PUNCT
ejpam-6249	98	4	consider	consider	VERB
ejpam-6249	98	5	an	an	DET
ejpam-6249	98	6	almost	almost	ADV
ejpam-6249	98	7	distributive	distributive	ADJ
ejpam-6249	98	8	lattice	lattice	NOUN
ejpam-6249	98	9	(	(	PUNCT
ejpam-6249	98	10	adl	adl	PROPN
ejpam-6249	98	11	)	)	PUNCT
ejpam-6249	98	12	l	l	NOUN
ejpam-6249	98	13	,	,	PUNCT
ejpam-6249	98	14	and	and	CCONJ
ejpam-6249	98	15	introduce	introduce	VERB
ejpam-6249	98	16	a	a	DET
ejpam-6249	98	17	binary	binary	ADJ
ejpam-6249	98	18	relation	relation	NOUN
ejpam-6249	98	19	ψ	ψ	X
ejpam-6249	98	20	on	on	ADP
ejpam-6249	98	21	l	l	NOUN
ejpam-6249	98	22	defined	define	VERB
ejpam-6249	98	23	as	as	SCONJ
ejpam-6249	98	24	follows	follow	VERB
ejpam-6249	98	25	:	:	PUNCT
ejpam-6249	98	26	(	(	PUNCT
ejpam-6249	98	27	θ	θ	NOUN
ejpam-6249	98	28	,	,	PUNCT
ejpam-6249	98	29	ϑ	ϑ	NOUN
ejpam-6249	98	30	)	)	PUNCT
ejpam-6249	98	31	∈	∈	NOUN
ejpam-6249	98	32	ψ	ψ	NOUN
ejpam-6249	98	33	if	if	SCONJ
ejpam-6249	99	1	and	and	CCONJ
ejpam-6249	99	2	only	only	ADV
ejpam-6249	99	3	if	if	SCONJ
ejpam-6249	99	4	(	(	PUNCT
ejpam-6249	99	5	θ	θ	NOUN
ejpam-6249	99	6	,	,	PUNCT
ejpam-6249	99	7	d	d	NOUN
ejpam-6249	99	8	)	)	PUNCT
ejpam-6249	99	9	=	=	SYM
ejpam-6249	99	10	(	(	PUNCT
ejpam-6249	99	11	ϑ,d	ϑ,d	NOUN
ejpam-6249	99	12	)	)	PUNCT
ejpam-6249	99	13	,	,	PUNCT
ejpam-6249	99	14	for	for	SCONJ
ejpam-6249	99	15	every	every	DET
ejpam-6249	99	16	pair	pair	NOUN
ejpam-6249	99	17	of	of	ADP
ejpam-6249	99	18	elements	element	NOUN
ejpam-6249	99	19	θ	θ	PROPN
ejpam-6249	99	20	,	,	PUNCT
ejpam-6249	99	21	ϑ	ϑ	X
ejpam-6249	99	22	∈	∈	PROPN
ejpam-6249	99	23	l.	l.	NOUN
ejpam-6249	99	24	this	this	DET
ejpam-6249	99	25	relation	relation	NOUN
ejpam-6249	99	26	ψ	ψ	PROPN
ejpam-6249	99	27	constitutes	constitute	VERB
ejpam-6249	99	28	a	a	DET
ejpam-6249	99	29	congruence	congruence	NOUN
ejpam-6249	99	30	on	on	ADP
ejpam-6249	99	31	adl	adl	PROPN
ejpam-6249	99	32	l.	l.	PROPN
ejpam-6249	99	33	under	under	ADP
ejpam-6249	99	34	this	this	DET
ejpam-6249	99	35	congruence	congruence	NOUN
ejpam-6249	99	36	,	,	PUNCT
ejpam-6249	99	37	the	the	DET
ejpam-6249	99	38	set	set	ADJ
ejpam-6249	99	39	d∞	d∞	NOUN
ejpam-6249	99	40	forms	form	VERB
ejpam-6249	99	41	the	the	DET
ejpam-6249	99	42	least	least	ADJ
ejpam-6249	99	43	congruence	congruence	NOUN
ejpam-6249	99	44	class	class	NOUN
ejpam-6249	99	45	,	,	PUNCT
ejpam-6249	99	46	while	while	SCONJ
ejpam-6249	99	47	the	the	DET
ejpam-6249	99	48	class	class	NOUN
ejpam-6249	99	49	corresponding	correspond	VERB
ejpam-6249	99	50	to	to	ADP
ejpam-6249	99	51	the	the	DET
ejpam-6249	99	52	greatest	great	ADJ
ejpam-6249	99	53	element	element	NOUN
ejpam-6249	99	54	is	be	AUX
ejpam-6249	99	55	given	give	VERB
ejpam-6249	99	56	by	by	ADP
ejpam-6249	99	57	d.	d.	PROPN
ejpam-6249	99	58	proof	proof	NOUN
ejpam-6249	99	59	.	.	PUNCT
ejpam-6249	100	1	it	it	PRON
ejpam-6249	100	2	is	be	AUX
ejpam-6249	100	3	straightforward	straightforward	ADJ
ejpam-6249	100	4	to	to	PART
ejpam-6249	100	5	verify	verify	VERB
ejpam-6249	100	6	that	that	SCONJ
ejpam-6249	100	7	the	the	DET
ejpam-6249	100	8	relation	relation	NOUN
ejpam-6249	100	9	ψ	ψ	NOUN
ejpam-6249	100	10	defines	define	VERB
ejpam-6249	100	11	an	an	DET
ejpam-6249	100	12	equivalence	equivalence	NOUN
ejpam-6249	100	13	on	on	ADP
ejpam-6249	100	14	the	the	DET
ejpam-6249	100	15	set	set	NOUN
ejpam-6249	100	16	l.	l.	PROPN
ejpam-6249	100	17	moreover	moreover	ADV
ejpam-6249	100	18	,	,	PUNCT
ejpam-6249	100	19	using	use	VERB
ejpam-6249	100	20	items	item	NOUN
ejpam-6249	100	21	(	(	PUNCT
ejpam-6249	100	22	6	6	NUM
ejpam-6249	100	23	)	)	PUNCT
ejpam-6249	100	24	and	and	CCONJ
ejpam-6249	100	25	(	(	PUNCT
ejpam-6249	100	26	7	7	NUM
ejpam-6249	100	27	)	)	PUNCT
ejpam-6249	100	28	from	from	ADP
ejpam-6249	100	29	corollary	corollary	ADJ
ejpam-6249	100	30	1	1	NUM
ejpam-6249	100	31	,	,	PUNCT
ejpam-6249	100	32	we	we	PRON
ejpam-6249	100	33	conclude	conclude	VERB
ejpam-6249	100	34	that	that	SCONJ
ejpam-6249	100	35	ψ	ψ	NOUN
ejpam-6249	100	36	indeed	indeed	ADV
ejpam-6249	100	37	satisfies	satisfy	VERB
ejpam-6249	100	38	the	the	DET
ejpam-6249	100	39	necessary	necessary	ADJ
ejpam-6249	100	40	conditions	condition	NOUN
ejpam-6249	100	41	to	to	PART
ejpam-6249	100	42	be	be	AUX
ejpam-6249	100	43	a	a	DET
ejpam-6249	100	44	congruence	congruence	NOUN
ejpam-6249	100	45	relation	relation	NOUN
ejpam-6249	100	46	on	on	ADP
ejpam-6249	100	47	adl	adl	PROPN
ejpam-6249	100	48	l.	l.	PROPN
ejpam-6249	100	49	now	now	ADV
ejpam-6249	100	50	,	,	PUNCT
ejpam-6249	100	51	suppose	suppose	VERB
ejpam-6249	100	52	µ	µ	X
ejpam-6249	100	53	,	,	PUNCT
ejpam-6249	100	54	π	π	PROPN
ejpam-6249	100	55	∈	∈	PROPN
ejpam-6249	100	56	d∞.	d∞.	PROPN
ejpam-6249	100	57	since	since	SCONJ
ejpam-6249	100	58	both	both	DET
ejpam-6249	100	59	elements	element	NOUN
ejpam-6249	100	60	generate	generate	VERB
ejpam-6249	100	61	the	the	DET
ejpam-6249	100	62	same	same	ADJ
ejpam-6249	100	63	extension	extension	NOUN
ejpam-6249	100	64	filter	filter	NOUN
ejpam-6249	100	65	,	,	PUNCT
ejpam-6249	100	66	we	we	PRON
ejpam-6249	100	67	have	have	VERB
ejpam-6249	100	68	(	(	PUNCT
ejpam-6249	100	69	µ	µ	NUM
ejpam-6249	100	70	,	,	PUNCT
ejpam-6249	100	71	π	π	NOUN
ejpam-6249	100	72	)	)	PUNCT
ejpam-6249	100	73	∈	∈	PROPN
ejpam-6249	100	74	ψ	ψ	NOUN
ejpam-6249	100	75	,	,	PUNCT
ejpam-6249	100	76	which	which	PRON
ejpam-6249	100	77	implies	imply	VERB
ejpam-6249	100	78	that	that	SCONJ
ejpam-6249	100	79	d∞	d∞	PROPN
ejpam-6249	100	80	forms	form	VERB
ejpam-6249	100	81	a	a	DET
ejpam-6249	100	82	congruence	congruence	ADJ
ejpam-6249	100	83	class	class	NOUN
ejpam-6249	100	84	under	under	ADP
ejpam-6249	100	85	this	this	DET
ejpam-6249	100	86	relation	relation	NOUN
ejpam-6249	100	87	.	.	PUNCT
ejpam-6249	101	1	let	let	VERB
ejpam-6249	101	2	θ	θ	NOUN
ejpam-6249	101	3	be	be	AUX
ejpam-6249	101	4	any	any	DET
ejpam-6249	101	5	element	element	NOUN
ejpam-6249	101	6	in	in	ADP
ejpam-6249	101	7	d∞.	d∞.	PROPN
ejpam-6249	101	8	given	give	VERB
ejpam-6249	101	9	that	that	SCONJ
ejpam-6249	101	10	d∞	d∞	NOUN
ejpam-6249	101	11	is	be	AUX
ejpam-6249	101	12	an	an	DET
ejpam-6249	101	13	ideal	ideal	NOUN
ejpam-6249	101	14	,	,	PUNCT
ejpam-6249	101	15	the	the	DET
ejpam-6249	101	16	meet	meet	NOUN
ejpam-6249	101	17	θ	θ	PROPN
ejpam-6249	101	18	∧	∧	PROPN
ejpam-6249	101	19	µ	µ	X
ejpam-6249	101	20	must	must	AUX
ejpam-6249	101	21	also	also	ADV
ejpam-6249	101	22	lie	lie	VERB
ejpam-6249	101	23	in	in	ADP
ejpam-6249	101	24	d∞	d∞	NOUN
ejpam-6249	101	25	for	for	ADP
ejpam-6249	101	26	every	every	DET
ejpam-6249	101	27	µ	µ	PROPN
ejpam-6249	101	28	∈	∈	NOUN
ejpam-6249	101	29	l.	l.	NOUN
ejpam-6249	101	30	this	this	PRON
ejpam-6249	101	31	implies	imply	VERB
ejpam-6249	101	32	that	that	SCONJ
ejpam-6249	101	33	the	the	DET
ejpam-6249	101	34	intersection	intersection	NOUN
ejpam-6249	101	35	[	[	X
ejpam-6249	101	36	θ]ψ	θ]ψ	NOUN
ejpam-6249	101	37	∩	∩	NOUN
ejpam-6249	101	38	[	[	X
ejpam-6249	101	39	µ]ψ	µ]ψ	NOUN
ejpam-6249	101	40	=	=	PUNCT
ejpam-6249	101	41	[	[	X
ejpam-6249	101	42	θ	θ	X
ejpam-6249	101	43	∧	∧	NOUN
ejpam-6249	101	44	µ]ψ	µ]ψ	NOUN
ejpam-6249	101	45	=	=	SYM
ejpam-6249	102	1	[	[	X
ejpam-6249	102	2	θ]ψ	θ]ψ	NOUN
ejpam-6249	102	3	,	,	PUNCT
ejpam-6249	102	4	since	since	SCONJ
ejpam-6249	102	5	both	both	DET
ejpam-6249	102	6	θ	θ	PROPN
ejpam-6249	102	7	and	and	CCONJ
ejpam-6249	102	8	θ	θ	PROPN
ejpam-6249	102	9	∧	∧	PROPN
ejpam-6249	102	10	µ	µ	PROPN
ejpam-6249	102	11	belong	belong	VERB
ejpam-6249	102	12	to	to	ADP
ejpam-6249	102	13	d∞.	d∞.	PROPN
ejpam-6249	102	14	therefore	therefore	ADV
ejpam-6249	102	15	,	,	PUNCT
ejpam-6249	102	16	the	the	DET
ejpam-6249	102	17	equivalence	equivalence	NOUN
ejpam-6249	102	18	class	class	NOUN
ejpam-6249	103	1	[	[	X
ejpam-6249	103	2	θ]ψ	θ]ψ	NOUN
ejpam-6249	103	3	is	be	AUX
ejpam-6249	103	4	precisely	precisely	ADV
ejpam-6249	103	5	d∞	d∞	PROPN
ejpam-6249	103	6	,	,	PUNCT
ejpam-6249	103	7	confirming	confirm	VERB
ejpam-6249	103	8	that	that	SCONJ
ejpam-6249	103	9	this	this	PRON
ejpam-6249	103	10	is	be	AUX
ejpam-6249	103	11	the	the	DET
ejpam-6249	103	12	minimal	minimal	ADJ
ejpam-6249	103	13	congruence	congruence	NOUN
ejpam-6249	103	14	class	class	NOUN
ejpam-6249	103	15	under	under	ADP
ejpam-6249	103	16	ψ	ψ	NOUN
ejpam-6249	103	17	.	.	PUNCT
ejpam-6249	104	1	conversely	conversely	ADV
ejpam-6249	104	2	,	,	PUNCT
ejpam-6249	104	3	since	since	SCONJ
ejpam-6249	104	4	d	d	NOUN
ejpam-6249	104	5	is	be	AUX
ejpam-6249	104	6	a	a	DET
ejpam-6249	104	7	filter	filter	NOUN
ejpam-6249	104	8	,	,	PUNCT
ejpam-6249	104	9	a	a	DET
ejpam-6249	104	10	dual	dual	ADJ
ejpam-6249	104	11	argument	argument	NOUN
ejpam-6249	104	12	reveals	reveal	VERB
ejpam-6249	104	13	that	that	SCONJ
ejpam-6249	104	14	d	d	NOUN
ejpam-6249	104	15	corresponds	correspond	VERB
ejpam-6249	104	16	to	to	ADP
ejpam-6249	104	17	the	the	DET
ejpam-6249	104	18	greatest	great	ADJ
ejpam-6249	104	19	congruence	congruence	NOUN
ejpam-6249	104	20	class	class	NOUN
ejpam-6249	104	21	with	with	ADP
ejpam-6249	104	22	respect	respect	NOUN
ejpam-6249	104	23	to	to	ADP
ejpam-6249	104	24	the	the	DET
ejpam-6249	104	25	congruence	congruence	NOUN
ejpam-6249	104	26	ψ	ψ	PROPN
ejpam-6249	104	27	.	.	PUNCT
ejpam-6249	105	1	we	we	PRON
ejpam-6249	105	2	now	now	ADV
ejpam-6249	105	3	define	define	VERB
ejpam-6249	105	4	the	the	DET
ejpam-6249	105	5	concept	concept	NOUN
ejpam-6249	105	6	of	of	ADP
ejpam-6249	105	7	a	a	DET
ejpam-6249	105	8	hemicomplemented	hemicomplemente	VERB
ejpam-6249	105	9	adl	adl	PROPN
ejpam-6249	105	10	.	.	PUNCT
ejpam-6249	105	11	definition	definition	NOUN
ejpam-6249	105	12	3	3	NUM
ejpam-6249	105	13	.	.	PUNCT
ejpam-6249	106	1	an	an	DET
ejpam-6249	106	2	adl	adl	PROPN
ejpam-6249	106	3	l	l	NOUN
ejpam-6249	106	4	is	be	AUX
ejpam-6249	106	5	termed	term	VERB
ejpam-6249	106	6	hemicomplemented	hemicomplemente	VERB
ejpam-6249	106	7	if	if	SCONJ
ejpam-6249	106	8	for	for	ADP
ejpam-6249	106	9	every	every	DET
ejpam-6249	106	10	element	element	NOUN
ejpam-6249	106	11	µ	µ	NOUN
ejpam-6249	106	12	in	in	ADP
ejpam-6249	106	13	l	l	NOUN
ejpam-6249	106	14	,	,	PUNCT
ejpam-6249	106	15	there	there	PRON
ejpam-6249	106	16	is	be	VERB
ejpam-6249	106	17	an	an	DET
ejpam-6249	106	18	element	element	NOUN
ejpam-6249	106	19	π	π	PROPN
ejpam-6249	106	20	∈	∈	PROPN
ejpam-6249	106	21	l	l	NOUN
ejpam-6249	106	22	such	such	ADJ
ejpam-6249	106	23	that	that	SCONJ
ejpam-6249	106	24	µ	µ	ADJ
ejpam-6249	106	25	∧	∧	PROPN
ejpam-6249	106	26	π	π	X
ejpam-6249	106	27	∈	∈	PROPN
ejpam-6249	106	28	d∞	d∞	NOUN
ejpam-6249	106	29	and	and	CCONJ
ejpam-6249	106	30	µ	µ	PRON
ejpam-6249	106	31	∨	∨	NOUN
ejpam-6249	106	32	π	π	PROPN
ejpam-6249	106	33	∈	∈	PROPN
ejpam-6249	106	34	d.	d.	PROPN
ejpam-6249	106	35	it	it	PRON
ejpam-6249	106	36	can	can	AUX
ejpam-6249	106	37	be	be	AUX
ejpam-6249	106	38	observed	observe	VERB
ejpam-6249	106	39	that	that	SCONJ
ejpam-6249	106	40	every	every	DET
ejpam-6249	106	41	pseudocomplemented	pseudocomplemente	VERB
ejpam-6249	106	42	adl	adl	PROPN
ejpam-6249	106	43	is	be	AUX
ejpam-6249	106	44	also	also	ADV
ejpam-6249	106	45	hemicomplemented	hemicomplemente	VERB
ejpam-6249	106	46	.	.	PUNCT
ejpam-6249	107	1	to	to	PART
ejpam-6249	107	2	see	see	VERB
ejpam-6249	107	3	this	this	PRON
ejpam-6249	107	4	,	,	PUNCT
ejpam-6249	107	5	let	let	VERB
ejpam-6249	107	6	l	l	NOUN
ejpam-6249	107	7	be	be	AUX
ejpam-6249	107	8	a	a	DET
ejpam-6249	107	9	pseudocomplemented	pseudocomplemented	ADJ
ejpam-6249	107	10	adl	adl	NOUN
ejpam-6249	107	11	.	.	PUNCT
ejpam-6249	108	1	then	then	ADV
ejpam-6249	108	2	,	,	PUNCT
ejpam-6249	108	3	for	for	ADP
ejpam-6249	108	4	any	any	DET
ejpam-6249	108	5	µ	µ	PROPN
ejpam-6249	108	6	∈	∈	PROPN
ejpam-6249	108	7	l	l	NOUN
ejpam-6249	108	8	,	,	PUNCT
ejpam-6249	108	9	there	there	PRON
ejpam-6249	108	10	exists	exist	VERB
ejpam-6249	108	11	an	an	DET
ejpam-6249	108	12	element	element	NOUN
ejpam-6249	108	13	µ∗	µ∗	NOUN
ejpam-6249	108	14	∈	∈	PROPN
ejpam-6249	108	15	l	l	NOUN
ejpam-6249	108	16	such	such	ADJ
ejpam-6249	108	17	that	that	SCONJ
ejpam-6249	108	18	µ	µ	PRON
ejpam-6249	108	19	∧	∧	NOUN
ejpam-6249	108	20	µ∗	µ∗	NOUN
ejpam-6249	108	21	=	=	SYM
ejpam-6249	108	22	0	0	NUM
ejpam-6249	108	23	,	,	PUNCT
ejpam-6249	108	24	where	where	SCONJ
ejpam-6249	108	25	0	0	NUM
ejpam-6249	108	26	∈	∈	PROPN
ejpam-6249	108	27	d∞.	d∞.	PROPN
ejpam-6249	108	28	additionally	additionally	ADV
ejpam-6249	108	29	,	,	PUNCT
ejpam-6249	108	30	it	it	PRON
ejpam-6249	108	31	is	be	AUX
ejpam-6249	108	32	clear	clear	ADJ
ejpam-6249	108	33	that	that	SCONJ
ejpam-6249	108	34	µ	µ	X
ejpam-6249	108	35	∨	∨	NUM
ejpam-6249	108	36	µ∗	µ∗	PROPN
ejpam-6249	108	37	∈	∈	PROPN
ejpam-6249	108	38	d.	d.	PROPN
ejpam-6249	108	39	thus	thus	ADV
ejpam-6249	108	40	,	,	PUNCT
ejpam-6249	108	41	l	l	NOUN
ejpam-6249	108	42	satisfies	satisfy	VERB
ejpam-6249	108	43	the	the	DET
ejpam-6249	108	44	condition	condition	NOUN
ejpam-6249	108	45	for	for	ADP
ejpam-6249	108	46	being	be	AUX
ejpam-6249	108	47	hemicomplemented	hemicomplemente	VERB
ejpam-6249	108	48	.	.	PUNCT
ejpam-6249	109	1	in	in	ADP
ejpam-6249	109	2	the	the	DET
ejpam-6249	109	3	same	same	ADJ
ejpam-6249	109	4	way	way	NOUN
ejpam-6249	109	5	,	,	PUNCT
ejpam-6249	109	6	it	it	PRON
ejpam-6249	109	7	follows	follow	VERB
ejpam-6249	109	8	that	that	SCONJ
ejpam-6249	109	9	every	every	DET
ejpam-6249	109	10	quasicomplemented	quasicomplemente	VERB
ejpam-6249	109	11	adl	adl	PROPN
ejpam-6249	109	12	also	also	ADV
ejpam-6249	109	13	possesses	possess	VERB
ejpam-6249	109	14	the	the	DET
ejpam-6249	109	15	hemicomplemented	hemicomplemente	VERB
ejpam-6249	109	16	property	property	NOUN
ejpam-6249	109	17	.	.	PUNCT
ejpam-6249	110	1	in	in	ADP
ejpam-6249	110	2	the	the	DET
ejpam-6249	110	3	upcoming	upcoming	NOUN
ejpam-6249	110	4	theorem	theorem	NOUN
ejpam-6249	110	5	,	,	PUNCT
ejpam-6249	110	6	we	we	PRON
ejpam-6249	110	7	present	present	VERB
ejpam-6249	110	8	a	a	DET
ejpam-6249	110	9	collection	collection	NOUN
ejpam-6249	110	10	of	of	ADP
ejpam-6249	110	11	equivalent	equivalent	ADJ
ejpam-6249	110	12	statements	statement	NOUN
ejpam-6249	110	13	that	that	PRON
ejpam-6249	110	14	characterize	characterize	VERB
ejpam-6249	110	15	when	when	SCONJ
ejpam-6249	110	16	a	a	DET
ejpam-6249	110	17	hemicomplemented	hemicomplemente	VERB
ejpam-6249	110	18	adl	adl	NOUN
ejpam-6249	110	19	qualifies	qualifie	NOUN
ejpam-6249	110	20	as	as	ADP
ejpam-6249	110	21	a	a	DET
ejpam-6249	110	22	quasicomplemented	quasicomplemented	ADJ
ejpam-6249	110	23	adl	adl	PROPN
ejpam-6249	110	24	.	.	PUNCT
ejpam-6249	110	25	n.	n.	PROPN
ejpam-6249	110	26	rafi	rafi	PROPN
ejpam-6249	110	27	et	et	PROPN
ejpam-6249	110	28	al	al	PROPN
ejpam-6249	110	29	.	.	PUNCT
ejpam-6249	110	30	/	/	SYM
ejpam-6249	110	31	eur	eur	PROPN
ejpam-6249	110	32	.	.	PUNCT
ejpam-6249	111	1	j.	j.	PROPN
ejpam-6249	111	2	pure	pure	PROPN
ejpam-6249	111	3	appl	appl	PROPN
ejpam-6249	111	4	.	.	PROPN
ejpam-6249	111	5	math	math	PROPN
ejpam-6249	111	6	,	,	PUNCT
ejpam-6249	111	7	18	18	NUM
ejpam-6249	111	8	(	(	PUNCT
ejpam-6249	111	9	4	4	NUM
ejpam-6249	111	10	)	)	PUNCT
ejpam-6249	111	11	(	(	PUNCT
ejpam-6249	111	12	2025	2025	NUM
ejpam-6249	111	13	)	)	PUNCT
ejpam-6249	111	14	,	,	PUNCT
ejpam-6249	111	15	6249	6249	NUM
ejpam-6249	111	16	6	6	NUM
ejpam-6249	111	17	of	of	ADP
ejpam-6249	111	18	11	11	NUM
ejpam-6249	111	19	theorem	theorem	NOUN
ejpam-6249	111	20	1	1	NUM
ejpam-6249	111	21	.	.	X
ejpam-6249	112	1	for	for	ADP
ejpam-6249	112	2	a	a	DET
ejpam-6249	112	3	hemicomplemented	hemicomplemente	VERB
ejpam-6249	112	4	adl	adl	PROPN
ejpam-6249	112	5	l	l	PROPN
ejpam-6249	112	6	,	,	PUNCT
ejpam-6249	112	7	the	the	DET
ejpam-6249	112	8	following	follow	VERB
ejpam-6249	112	9	conditions	condition	NOUN
ejpam-6249	112	10	are	be	AUX
ejpam-6249	112	11	all	all	ADV
ejpam-6249	112	12	equivalent	equivalent	ADJ
ejpam-6249	112	13	.	.	PUNCT
ejpam-6249	113	1	(	(	PUNCT
ejpam-6249	113	2	1	1	X
ejpam-6249	113	3	)	)	PUNCT
ejpam-6249	113	4	l	l	NOUN
ejpam-6249	113	5	is	be	AUX
ejpam-6249	113	6	quasicomplemented	quasicomplemente	VERB
ejpam-6249	113	7	;	;	PUNCT
ejpam-6249	113	8	(	(	PUNCT
ejpam-6249	113	9	2	2	X
ejpam-6249	113	10	)	)	PUNCT
ejpam-6249	113	11	for	for	ADP
ejpam-6249	113	12	any	any	DET
ejpam-6249	113	13	µ	µ	NOUN
ejpam-6249	113	14	,	,	PUNCT
ejpam-6249	113	15	π	π	PROPN
ejpam-6249	113	16	∈	∈	PROPN
ejpam-6249	113	17	l	l	NOUN
ejpam-6249	113	18	\	\	X
ejpam-6249	114	1	d	d	X
ejpam-6249	114	2	,	,	PUNCT
ejpam-6249	114	3	(	(	PUNCT
ejpam-6249	114	4	µ,d	µ,d	NOUN
ejpam-6249	114	5	)	)	PUNCT
ejpam-6249	114	6	=	=	SYM
ejpam-6249	114	7	(	(	PUNCT
ejpam-6249	114	8	π	π	PROPN
ejpam-6249	114	9	,	,	PUNCT
ejpam-6249	114	10	d	d	PROPN
ejpam-6249	114	11	)	)	PUNCT
ejpam-6249	114	12	implies	imply	VERB
ejpam-6249	114	13	µ	µ	X
ejpam-6249	114	14	=	=	SYM
ejpam-6249	114	15	π	π	PROPN
ejpam-6249	114	16	;	;	PUNCT
ejpam-6249	114	17	(	(	PUNCT
ejpam-6249	114	18	3	3	X
ejpam-6249	114	19	)	)	PUNCT
ejpam-6249	114	20	l	l	NOUN
ejpam-6249	114	21	has	have	VERB
ejpam-6249	114	22	a	a	DET
ejpam-6249	114	23	unique	unique	ADJ
ejpam-6249	114	24	condensed	condense	VERB
ejpam-6249	114	25	element	element	NOUN
ejpam-6249	114	26	.	.	PUNCT
ejpam-6249	115	1	proof	proof	NOUN
ejpam-6249	115	2	.	.	PUNCT
ejpam-6249	116	1	(	(	PUNCT
ejpam-6249	116	2	1	1	X
ejpam-6249	116	3	)	)	PUNCT
ejpam-6249	116	4	⇒	⇒	NOUN
ejpam-6249	116	5	(	(	PUNCT
ejpam-6249	116	6	2	2	NUM
ejpam-6249	116	7	)	)	PUNCT
ejpam-6249	116	8	:	:	PUNCT
ejpam-6249	116	9	assume	assume	VERB
ejpam-6249	116	10	(	(	PUNCT
ejpam-6249	116	11	1	1	NUM
ejpam-6249	116	12	)	)	PUNCT
ejpam-6249	116	13	.	.	PUNCT
ejpam-6249	117	1	let	let	VERB
ejpam-6249	117	2	µ	µ	NOUN
ejpam-6249	117	3	,	,	PUNCT
ejpam-6249	117	4	π	π	PROPN
ejpam-6249	117	5	∈	∈	PROPN
ejpam-6249	117	6	l	l	NOUN
ejpam-6249	117	7	\	\	PUNCT
ejpam-6249	118	1	d	d	NOUN
ejpam-6249	118	2	with	with	ADP
ejpam-6249	118	3	(	(	PUNCT
ejpam-6249	118	4	µ,d	µ,d	NOUN
ejpam-6249	118	5	)	)	PUNCT
ejpam-6249	118	6	=	=	SYM
ejpam-6249	118	7	(	(	PUNCT
ejpam-6249	118	8	π	π	PROPN
ejpam-6249	118	9	,	,	PUNCT
ejpam-6249	118	10	d	d	NOUN
ejpam-6249	118	11	)	)	PUNCT
ejpam-6249	118	12	.	.	PUNCT
ejpam-6249	119	1	assume	assume	VERB
ejpam-6249	119	2	,	,	PUNCT
ejpam-6249	119	3	for	for	ADP
ejpam-6249	119	4	contradiction	contradiction	NOUN
ejpam-6249	119	5	,	,	PUNCT
ejpam-6249	119	6	that	that	SCONJ
ejpam-6249	119	7	µ	µ	X
ejpam-6249	119	8	̸=	̸=	PROPN
ejpam-6249	119	9	π	π	X
ejpam-6249	119	10	.	.	PUNCT
ejpam-6249	120	1	then	then	ADV
ejpam-6249	120	2	either	either	CCONJ
ejpam-6249	120	3	(	(	PUNCT
ejpam-6249	120	4	µ]∩	µ]∩	NOUN
ejpam-6249	120	5	(	(	PUNCT
ejpam-6249	120	6	[	[	X
ejpam-6249	120	7	π)∨d	π)∨d	ADJ
ejpam-6249	120	8	)	)	PUNCT
ejpam-6249	120	9	=	=	NOUN
ejpam-6249	120	10	∅	∅	NOUN
ejpam-6249	120	11	or	or	CCONJ
ejpam-6249	120	12	(	(	PUNCT
ejpam-6249	120	13	π]∩	π]∩	X
ejpam-6249	120	14	(	(	PUNCT
ejpam-6249	120	15	[	[	X
ejpam-6249	120	16	µ)∨d	µ)∨d	NOUN
ejpam-6249	120	17	)	)	PUNCT
ejpam-6249	120	18	=	=	VERB
ejpam-6249	120	19	∅.	∅.	AUX
ejpam-6249	120	20	suppose	suppose	VERB
ejpam-6249	120	21	(	(	PUNCT
ejpam-6249	120	22	π	π	X
ejpam-6249	120	23	]	]	X
ejpam-6249	120	24	∩	∩	NOUN
ejpam-6249	120	25	(	(	PUNCT
ejpam-6249	120	26	[	[	X
ejpam-6249	120	27	µ	µ	X
ejpam-6249	120	28	)	)	PUNCT
ejpam-6249	120	29	∨	∨	NUM
ejpam-6249	120	30	d	d	NOUN
ejpam-6249	120	31	)	)	PUNCT
ejpam-6249	120	32	=	=	PUNCT
ejpam-6249	120	33	∅.	∅.	NOUN
ejpam-6249	120	34	in	in	ADP
ejpam-6249	120	35	this	this	DET
ejpam-6249	120	36	case	case	NOUN
ejpam-6249	120	37	,	,	PUNCT
ejpam-6249	120	38	there	there	PRON
ejpam-6249	120	39	exists	exist	VERB
ejpam-6249	120	40	a	a	DET
ejpam-6249	120	41	prime	prime	ADJ
ejpam-6249	120	42	filter	filter	NOUN
ejpam-6249	120	43	q	q	NOUN
ejpam-6249	120	44	containing	contain	VERB
ejpam-6249	120	45	(	(	PUNCT
ejpam-6249	120	46	[	[	X
ejpam-6249	120	47	µ	µ	X
ejpam-6249	120	48	)	)	PUNCT
ejpam-6249	120	49	∨	∨	NUM
ejpam-6249	120	50	d	d	NOUN
ejpam-6249	120	51	)	)	PUNCT
ejpam-6249	120	52	but	but	CCONJ
ejpam-6249	120	53	disjoint	disjoint	VERB
ejpam-6249	120	54	from	from	ADP
ejpam-6249	120	55	the	the	DET
ejpam-6249	120	56	principal	principal	ADJ
ejpam-6249	120	57	ideal	ideal	NOUN
ejpam-6249	120	58	(	(	PUNCT
ejpam-6249	120	59	π	π	X
ejpam-6249	120	60	]	]	X
ejpam-6249	120	61	.	.	PUNCT
ejpam-6249	121	1	this	this	PRON
ejpam-6249	121	2	gives	give	VERB
ejpam-6249	121	3	µ	µ	PRON
ejpam-6249	121	4	∈	∈	NOUN
ejpam-6249	121	5	q	q	X
ejpam-6249	121	6	(	(	PUNCT
ejpam-6249	121	7	since	since	SCONJ
ejpam-6249	121	8	µ	µ	X
ejpam-6249	121	9	∈	∈	NOUN
ejpam-6249	121	10	(	(	PUNCT
ejpam-6249	121	11	[	[	X
ejpam-6249	121	12	µ	µ	X
ejpam-6249	121	13	)	)	PUNCT
ejpam-6249	121	14	∨	∨	NUM
ejpam-6249	121	15	d	d	NOUN
ejpam-6249	121	16	)	)	PUNCT
ejpam-6249	121	17	)	)	PUNCT
ejpam-6249	122	1	and	and	CCONJ
ejpam-6249	122	2	π	π	PROPN
ejpam-6249	122	3	/∈	/∈	PUNCT
ejpam-6249	122	4	q.	q.	PROPN
ejpam-6249	122	5	now	now	ADV
ejpam-6249	122	6	,	,	PUNCT
ejpam-6249	122	7	as	as	SCONJ
ejpam-6249	122	8	l	l	NOUN
ejpam-6249	122	9	is	be	AUX
ejpam-6249	122	10	quasicomplemented	quasicomplemente	VERB
ejpam-6249	122	11	,	,	PUNCT
ejpam-6249	122	12	there	there	PRON
ejpam-6249	122	13	exists	exist	VERB
ejpam-6249	122	14	an	an	DET
ejpam-6249	122	15	element	element	NOUN
ejpam-6249	122	16	µ′	µ′	PUNCT
ejpam-6249	122	17	∈	∈	PROPN
ejpam-6249	122	18	l	l	NOUN
ejpam-6249	122	19	such	such	ADJ
ejpam-6249	122	20	that	that	DET
ejpam-6249	122	21	µ∧	µ∧	NOUN
ejpam-6249	122	22	µ′	µ′	PUNCT
ejpam-6249	122	23	=	=	SYM
ejpam-6249	122	24	0	0	NUM
ejpam-6249	122	25	and	and	CCONJ
ejpam-6249	122	26	µ∨	µ∨	ADJ
ejpam-6249	122	27	µ′	µ′	PUNCT
ejpam-6249	122	28	∈	∈	PROPN
ejpam-6249	122	29	d.	d.	NOUN
ejpam-6249	122	30	since	since	SCONJ
ejpam-6249	122	31	(	(	PUNCT
ejpam-6249	122	32	µ,d	µ,d	NOUN
ejpam-6249	122	33	)	)	PUNCT
ejpam-6249	122	34	=	=	SYM
ejpam-6249	122	35	(	(	PUNCT
ejpam-6249	122	36	π	π	PROPN
ejpam-6249	122	37	,	,	PUNCT
ejpam-6249	122	38	d	d	PROPN
ejpam-6249	122	39	)	)	PUNCT
ejpam-6249	122	40	,	,	PUNCT
ejpam-6249	122	41	we	we	PRON
ejpam-6249	122	42	conclude	conclude	VERB
ejpam-6249	122	43	µ′	µ′	PROPN
ejpam-6249	122	44	∈	∈	PROPN
ejpam-6249	122	45	(	(	PUNCT
ejpam-6249	122	46	π	π	PROPN
ejpam-6249	122	47	,	,	PUNCT
ejpam-6249	122	48	d	d	NOUN
ejpam-6249	122	49	)	)	PUNCT
ejpam-6249	122	50	,	,	PUNCT
ejpam-6249	122	51	and	and	CCONJ
ejpam-6249	122	52	therefore	therefore	ADV
ejpam-6249	122	53	µ′	µ′	PUNCT
ejpam-6249	122	54	∨	∨	PROPN
ejpam-6249	122	55	π	π	PROPN
ejpam-6249	122	56	∈	∈	PROPN
ejpam-6249	122	57	d	d	PROPN
ejpam-6249	122	58	⊆	⊆	NUM
ejpam-6249	122	59	q.	q.	NOUN
ejpam-6249	122	60	because	because	SCONJ
ejpam-6249	122	61	q	q	PROPN
ejpam-6249	122	62	is	be	AUX
ejpam-6249	122	63	a	a	DET
ejpam-6249	122	64	prime	prime	ADJ
ejpam-6249	122	65	filter	filter	NOUN
ejpam-6249	122	66	and	and	CCONJ
ejpam-6249	122	67	µ′	µ′	NOUN
ejpam-6249	122	68	∨	∨	NUM
ejpam-6249	122	69	π	π	PROPN
ejpam-6249	122	70	∈	∈	PROPN
ejpam-6249	122	71	q	q	NOUN
ejpam-6249	122	72	while	while	SCONJ
ejpam-6249	122	73	π	π	X
ejpam-6249	122	74	/∈	/∈	PUNCT
ejpam-6249	123	1	q	q	X
ejpam-6249	123	2	,	,	PUNCT
ejpam-6249	123	3	it	it	PRON
ejpam-6249	123	4	must	must	AUX
ejpam-6249	123	5	be	be	AUX
ejpam-6249	123	6	that	that	SCONJ
ejpam-6249	123	7	µ′	µ′	PUNCT
ejpam-6249	123	8	∈	∈	PROPN
ejpam-6249	123	9	q.	q.	NOUN
ejpam-6249	123	10	but	but	CCONJ
ejpam-6249	123	11	this	this	PRON
ejpam-6249	123	12	implies	imply	VERB
ejpam-6249	123	13	that	that	SCONJ
ejpam-6249	123	14	µ	µ	DET
ejpam-6249	123	15	∧	∧	NOUN
ejpam-6249	123	16	µ′	µ′	PUNCT
ejpam-6249	123	17	=	=	SYM
ejpam-6249	123	18	0	0	NUM
ejpam-6249	123	19	∈	∈	PROPN
ejpam-6249	123	20	q	q	NOUN
ejpam-6249	123	21	,	,	PUNCT
ejpam-6249	123	22	which	which	PRON
ejpam-6249	123	23	contradicts	contradict	VERB
ejpam-6249	123	24	the	the	DET
ejpam-6249	123	25	definition	definition	NOUN
ejpam-6249	123	26	of	of	ADP
ejpam-6249	123	27	a	a	DET
ejpam-6249	123	28	proper	proper	ADJ
ejpam-6249	123	29	filter	filter	NOUN
ejpam-6249	123	30	.	.	PUNCT
ejpam-6249	124	1	thus	thus	ADV
ejpam-6249	124	2	,	,	PUNCT
ejpam-6249	124	3	our	our	PRON
ejpam-6249	124	4	initial	initial	ADJ
ejpam-6249	124	5	assumption	assumption	NOUN
ejpam-6249	124	6	that	that	SCONJ
ejpam-6249	124	7	µ	µ	X
ejpam-6249	124	8	̸=	̸=	PROPN
ejpam-6249	124	9	π	π	PROPN
ejpam-6249	124	10	is	be	AUX
ejpam-6249	124	11	incorrect	incorrect	ADJ
ejpam-6249	124	12	.	.	PUNCT
ejpam-6249	125	1	therefore	therefore	ADV
ejpam-6249	125	2	,	,	PUNCT
ejpam-6249	125	3	µ	µ	X
ejpam-6249	125	4	=	=	SYM
ejpam-6249	125	5	π	π	X
ejpam-6249	125	6	.	.	PUNCT
ejpam-6249	125	7	(	(	PUNCT
ejpam-6249	125	8	2	2	X
ejpam-6249	125	9	)	)	PUNCT
ejpam-6249	125	10	⇒	⇒	NOUN
ejpam-6249	125	11	(	(	PUNCT
ejpam-6249	125	12	3	3	NUM
ejpam-6249	125	13	)	)	PUNCT
ejpam-6249	125	14	:	:	PUNCT
ejpam-6249	125	15	suppose	suppose	VERB
ejpam-6249	125	16	that	that	SCONJ
ejpam-6249	125	17	the	the	DET
ejpam-6249	125	18	second	second	ADJ
ejpam-6249	125	19	condition	condition	NOUN
ejpam-6249	125	20	is	be	AUX
ejpam-6249	125	21	valid	valid	ADJ
ejpam-6249	125	22	.	.	PUNCT
ejpam-6249	126	1	assume	assume	VERB
ejpam-6249	126	2	,	,	PUNCT
ejpam-6249	126	3	for	for	ADP
ejpam-6249	126	4	contradiction	contradiction	NOUN
ejpam-6249	126	5	,	,	PUNCT
ejpam-6249	126	6	that	that	SCONJ
ejpam-6249	126	7	there	there	PRON
ejpam-6249	126	8	exist	exist	VERB
ejpam-6249	126	9	two	two	NUM
ejpam-6249	126	10	different	different	ADJ
ejpam-6249	126	11	condensed	condense	VERB
ejpam-6249	126	12	elements	element	NOUN
ejpam-6249	126	13	in	in	ADP
ejpam-6249	126	14	l	l	NOUN
ejpam-6249	126	15	,	,	PUNCT
ejpam-6249	126	16	denoted	denote	VERB
ejpam-6249	126	17	by	by	ADP
ejpam-6249	126	18	µ	µ	PROPN
ejpam-6249	126	19	and	and	CCONJ
ejpam-6249	126	20	π	π	PROPN
ejpam-6249	126	21	.	.	PUNCT
ejpam-6249	127	1	since	since	SCONJ
ejpam-6249	127	2	both	both	PRON
ejpam-6249	127	3	are	be	AUX
ejpam-6249	127	4	condensed	condense	VERB
ejpam-6249	127	5	,	,	PUNCT
ejpam-6249	127	6	it	it	PRON
ejpam-6249	127	7	follows	follow	VERB
ejpam-6249	127	8	that	that	SCONJ
ejpam-6249	127	9	(	(	PUNCT
ejpam-6249	127	10	µ,d	µ,d	NOUN
ejpam-6249	127	11	)	)	PUNCT
ejpam-6249	127	12	=	=	SYM
ejpam-6249	128	1	d	d	NOUN
ejpam-6249	128	2	=	=	SYM
ejpam-6249	128	3	(	(	PUNCT
ejpam-6249	128	4	π	π	PROPN
ejpam-6249	128	5	,	,	PUNCT
ejpam-6249	128	6	d	d	NOUN
ejpam-6249	128	7	)	)	PUNCT
ejpam-6249	128	8	.	.	PUNCT
ejpam-6249	129	1	according	accord	VERB
ejpam-6249	129	2	to	to	ADP
ejpam-6249	129	3	condition	condition	NOUN
ejpam-6249	129	4	(	(	PUNCT
ejpam-6249	129	5	2	2	NUM
ejpam-6249	129	6	)	)	PUNCT
ejpam-6249	129	7	,	,	PUNCT
ejpam-6249	129	8	this	this	PRON
ejpam-6249	129	9	implies	imply	VERB
ejpam-6249	129	10	that	that	SCONJ
ejpam-6249	129	11	µ	µ	NOUN
ejpam-6249	129	12	and	and	CCONJ
ejpam-6249	129	13	π	π	PROPN
ejpam-6249	129	14	must	must	AUX
ejpam-6249	129	15	be	be	AUX
ejpam-6249	129	16	equal	equal	ADJ
ejpam-6249	129	17	,	,	PUNCT
ejpam-6249	129	18	contradicting	contradict	VERB
ejpam-6249	129	19	our	our	PRON
ejpam-6249	129	20	assumption	assumption	NOUN
ejpam-6249	129	21	that	that	SCONJ
ejpam-6249	129	22	they	they	PRON
ejpam-6249	129	23	are	be	AUX
ejpam-6249	129	24	distinct	distinct	ADJ
ejpam-6249	129	25	.	.	PUNCT
ejpam-6249	130	1	thus	thus	ADV
ejpam-6249	130	2	,	,	PUNCT
ejpam-6249	130	3	it	it	PRON
ejpam-6249	130	4	follows	follow	VERB
ejpam-6249	130	5	that	that	SCONJ
ejpam-6249	130	6	l	l	NOUN
ejpam-6249	130	7	contains	contain	VERB
ejpam-6249	130	8	exactly	exactly	ADV
ejpam-6249	130	9	one	one	NUM
ejpam-6249	130	10	condensed	condense	VERB
ejpam-6249	130	11	element	element	NOUN
ejpam-6249	130	12	.	.	PUNCT
ejpam-6249	131	1	(	(	PUNCT
ejpam-6249	131	2	3	3	X
ejpam-6249	131	3	)	)	PUNCT
ejpam-6249	131	4	⇒	⇒	NOUN
ejpam-6249	131	5	(	(	PUNCT
ejpam-6249	131	6	1	1	NUM
ejpam-6249	131	7	)	)	PUNCT
ejpam-6249	131	8	:	:	PUNCT
ejpam-6249	131	9	let	let	VERB
ejpam-6249	131	10	us	we	PRON
ejpam-6249	131	11	assume	assume	VERB
ejpam-6249	131	12	that	that	SCONJ
ejpam-6249	131	13	the	the	DET
ejpam-6249	131	14	only	only	ADJ
ejpam-6249	131	15	condensed	condensed	ADJ
ejpam-6249	131	16	element	element	NOUN
ejpam-6249	131	17	in	in	ADP
ejpam-6249	131	18	l	l	PROPN
ejpam-6249	131	19	is	be	AUX
ejpam-6249	131	20	0	0	NUM
ejpam-6249	131	21	.	.	PUNCT
ejpam-6249	131	22	consider	consider	VERB
ejpam-6249	131	23	any	any	DET
ejpam-6249	131	24	element	element	NOUN
ejpam-6249	131	25	µ	µ	X
ejpam-6249	131	26	in	in	ADP
ejpam-6249	131	27	l.	l.	PROPN
ejpam-6249	131	28	since	since	SCONJ
ejpam-6249	131	29	l	l	PROPN
ejpam-6249	131	30	is	be	AUX
ejpam-6249	131	31	hemicomplemented	hemicomplemente	VERB
ejpam-6249	131	32	,	,	PUNCT
ejpam-6249	131	33	there	there	PRON
ejpam-6249	131	34	exists	exist	VERB
ejpam-6249	131	35	an	an	DET
ejpam-6249	131	36	element	element	NOUN
ejpam-6249	131	37	µ′	µ′	PUNCT
ejpam-6249	131	38	∈	∈	PROPN
ejpam-6249	131	39	l	l	NOUN
ejpam-6249	131	40	such	such	ADJ
ejpam-6249	131	41	that	that	SCONJ
ejpam-6249	131	42	µ	µ	PROPN
ejpam-6249	131	43	∧	∧	PROPN
ejpam-6249	131	44	µ′	µ′	PUNCT
ejpam-6249	131	45	belongs	belong	VERB
ejpam-6249	131	46	to	to	ADP
ejpam-6249	131	47	d∞	d∞	PROPN
ejpam-6249	131	48	and	and	CCONJ
ejpam-6249	131	49	µ	µ	PRON
ejpam-6249	131	50	∨	∨	NOUN
ejpam-6249	131	51	µ′	µ′	NOUN
ejpam-6249	131	52	lies	lie	VERB
ejpam-6249	131	53	in	in	ADP
ejpam-6249	131	54	d.	d.	NOUN
ejpam-6249	131	55	given	give	VERB
ejpam-6249	131	56	that	that	SCONJ
ejpam-6249	131	57	d∞	d∞	NOUN
ejpam-6249	131	58	=	=	SYM
ejpam-6249	131	59	0	0	NUM
ejpam-6249	131	60	,	,	PUNCT
ejpam-6249	131	61	we	we	PRON
ejpam-6249	131	62	conclude	conclude	VERB
ejpam-6249	131	63	that	that	SCONJ
ejpam-6249	131	64	µ	µ	X
ejpam-6249	131	65	∧	∧	NOUN
ejpam-6249	131	66	µ′	µ′	PUNCT
ejpam-6249	131	67	=	=	NOUN
ejpam-6249	131	68	0	0	X
ejpam-6249	131	69	.	.	PUNCT
ejpam-6249	132	1	this	this	PRON
ejpam-6249	132	2	confirms	confirm	VERB
ejpam-6249	132	3	that	that	SCONJ
ejpam-6249	132	4	l	l	NOUN
ejpam-6249	132	5	is	be	AUX
ejpam-6249	132	6	a	a	DET
ejpam-6249	132	7	quasicomplemented	quasicomplemented	ADJ
ejpam-6249	132	8	adl	adl	PROPN
ejpam-6249	132	9	.	.	PUNCT
ejpam-6249	132	10	corollary	corollary	ADJ
ejpam-6249	132	11	2	2	NUM
ejpam-6249	132	12	.	.	PUNCT
ejpam-6249	132	13	a	a	DET
ejpam-6249	132	14	hemicomplemented	hemicomplemente	VERB
ejpam-6249	132	15	adl	adl	PROPN
ejpam-6249	132	16	l	l	NOUN
ejpam-6249	132	17	is	be	AUX
ejpam-6249	132	18	a	a	DET
ejpam-6249	132	19	boolean	boolean	ADJ
ejpam-6249	132	20	algebra	algebra	NOUN
ejpam-6249	132	21	precisely	precisely	ADV
ejpam-6249	132	22	when	when	SCONJ
ejpam-6249	132	23	it	it	PRON
ejpam-6249	132	24	has	have	VERB
ejpam-6249	132	25	exactly	exactly	ADV
ejpam-6249	132	26	one	one	NUM
ejpam-6249	132	27	condensed	condense	VERB
ejpam-6249	132	28	element	element	NOUN
ejpam-6249	132	29	and	and	CCONJ
ejpam-6249	132	30	exactly	exactly	ADV
ejpam-6249	132	31	one	one	NUM
ejpam-6249	132	32	dense	dense	ADJ
ejpam-6249	132	33	element	element	NOUN
ejpam-6249	132	34	.	.	PUNCT
ejpam-6249	133	1	based	base	VERB
ejpam-6249	133	2	on	on	ADP
ejpam-6249	133	3	lemma	lemma	PROPN
ejpam-6249	133	4	1	1	NUM
ejpam-6249	133	5	,	,	PUNCT
ejpam-6249	133	6	one	one	PRON
ejpam-6249	133	7	can	can	AUX
ejpam-6249	133	8	readily	readily	ADV
ejpam-6249	133	9	establish	establish	VERB
ejpam-6249	133	10	that	that	SCONJ
ejpam-6249	133	11	the	the	DET
ejpam-6249	133	12	collection	collection	NOUN
ejpam-6249	133	13	d	d	X
ejpam-6249	133	14	◦	◦	NOUN
ejpam-6249	133	15	(l)—comprising	(l)—comprising	PUNCT
ejpam-6249	133	16	all	all	DET
ejpam-6249	133	17	filters	filter	NOUN
ejpam-6249	133	18	of	of	ADP
ejpam-6249	133	19	the	the	DET
ejpam-6249	133	20	form	form	NOUN
ejpam-6249	133	21	(	(	PUNCT
ejpam-6249	133	22	µ,d	µ,d	NOUN
ejpam-6249	133	23	)	)	PUNCT
ejpam-6249	133	24	for	for	ADP
ejpam-6249	133	25	elements	element	NOUN
ejpam-6249	133	26	µ	µ	X
ejpam-6249	133	27	∈	∈	NOUN
ejpam-6249	133	28	l	l	NOUN
ejpam-6249	133	29	constitutes	constitute	VERB
ejpam-6249	133	30	an	an	DET
ejpam-6249	133	31	almost	almost	ADV
ejpam-6249	133	32	distributive	distributive	ADJ
ejpam-6249	133	33	lattice	lattice	NOUN
ejpam-6249	133	34	(	(	PUNCT
ejpam-6249	133	35	adl	adl	PROPN
ejpam-6249	133	36	)	)	PUNCT
ejpam-6249	133	37	under	under	ADP
ejpam-6249	133	38	the	the	DET
ejpam-6249	133	39	binary	binary	ADJ
ejpam-6249	133	40	operations	operation	NOUN
ejpam-6249	133	41	:	:	PUNCT
ejpam-6249	133	42	(	(	PUNCT
ejpam-6249	133	43	µ,d	µ,d	NOUN
ejpam-6249	133	44	)	)	PUNCT
ejpam-6249	133	45	∩	∩	NOUN
ejpam-6249	133	46	(	(	PUNCT
ejpam-6249	133	47	π	π	X
ejpam-6249	133	48	,	,	PUNCT
ejpam-6249	133	49	d	d	NOUN
ejpam-6249	133	50	)	)	PUNCT
ejpam-6249	133	51	=	=	SYM
ejpam-6249	133	52	(	(	PUNCT
ejpam-6249	133	53	µ	µ	X
ejpam-6249	133	54	∧	∧	PROPN
ejpam-6249	133	55	π	π	PROPN
ejpam-6249	133	56	,	,	PUNCT
ejpam-6249	133	57	d	d	NOUN
ejpam-6249	133	58	)	)	PUNCT
ejpam-6249	133	59	and	and	CCONJ
ejpam-6249	133	60	(	(	PUNCT
ejpam-6249	133	61	µ,d	µ,d	NOUN
ejpam-6249	133	62	)	)	PUNCT
ejpam-6249	133	63	⊔	⊔	NOUN
ejpam-6249	133	64	(	(	PUNCT
ejpam-6249	133	65	π	π	X
ejpam-6249	133	66	,	,	PUNCT
ejpam-6249	133	67	d	d	NOUN
ejpam-6249	133	68	)	)	PUNCT
ejpam-6249	133	69	=	=	SYM
ejpam-6249	133	70	(	(	PUNCT
ejpam-6249	133	71	µ	µ	X
ejpam-6249	133	72	∨	∨	NUM
ejpam-6249	133	73	π	π	PROPN
ejpam-6249	133	74	,	,	PUNCT
ejpam-6249	133	75	d	d	PROPN
ejpam-6249	133	76	)	)	PUNCT
ejpam-6249	133	77	,	,	PUNCT
ejpam-6249	133	78	for	for	ADP
ejpam-6249	133	79	every	every	DET
ejpam-6249	133	80	µ	µ	NOUN
ejpam-6249	133	81	,	,	PUNCT
ejpam-6249	133	82	π	π	PROPN
ejpam-6249	133	83	∈	∈	PROPN
ejpam-6249	133	84	l.	l.	NOUN
ejpam-6249	133	85	in	in	ADP
ejpam-6249	133	86	the	the	DET
ejpam-6249	133	87	subsequent	subsequent	ADJ
ejpam-6249	133	88	theorem	theorem	NOUN
ejpam-6249	133	89	,	,	PUNCT
ejpam-6249	133	90	a	a	DET
ejpam-6249	133	91	collection	collection	NOUN
ejpam-6249	133	92	of	of	ADP
ejpam-6249	133	93	equivalent	equivalent	ADJ
ejpam-6249	133	94	criteria	criterion	NOUN
ejpam-6249	133	95	is	be	AUX
ejpam-6249	133	96	provided	provide	VERB
ejpam-6249	133	97	that	that	DET
ejpam-6249	133	98	determine	determine	NOUN
ejpam-6249	133	99	when	when	SCONJ
ejpam-6249	133	100	the	the	DET
ejpam-6249	133	101	lattice	lattice	NOUN
ejpam-6249	133	102	(	(	PUNCT
ejpam-6249	133	103	d	d	NOUN
ejpam-6249	133	104	◦	◦	NOUN
ejpam-6249	133	105	(l),⊔,∩	(l),⊔,∩	NOUN
ejpam-6249	133	106	)	)	PUNCT
ejpam-6249	133	107	becomes	become	VERB
ejpam-6249	133	108	a	a	DET
ejpam-6249	133	109	boolean	boolean	ADJ
ejpam-6249	133	110	algebra	algebra	NOUN
ejpam-6249	133	111	resulting	result	VERB
ejpam-6249	133	112	in	in	ADP
ejpam-6249	133	113	a	a	DET
ejpam-6249	133	114	characterization	characterization	NOUN
ejpam-6249	133	115	of	of	ADP
ejpam-6249	133	116	hemicomplemented	hemicomplemente	VERB
ejpam-6249	133	117	adls	adls	PROPN
ejpam-6249	133	118	.	.	PUNCT
ejpam-6249	134	1	theorem	theorem	NOUN
ejpam-6249	134	2	2	2	NUM
ejpam-6249	134	3	.	.	PUNCT
ejpam-6249	135	1	the	the	DET
ejpam-6249	135	2	following	follow	VERB
ejpam-6249	135	3	assertions	assertion	NOUN
ejpam-6249	135	4	are	be	AUX
ejpam-6249	135	5	equivalent	equivalent	ADJ
ejpam-6249	135	6	in	in	ADP
ejpam-6249	135	7	an	an	DET
ejpam-6249	135	8	adl	adl	PROPN
ejpam-6249	135	9	l	l	NOUN
ejpam-6249	135	10	:	:	PUNCT
ejpam-6249	135	11	(	(	PUNCT
ejpam-6249	135	12	1	1	X
ejpam-6249	135	13	)	)	PUNCT
ejpam-6249	135	14	l	l	NOUN
ejpam-6249	135	15	is	be	AUX
ejpam-6249	135	16	hemicomplemented	hemicomplemente	VERB
ejpam-6249	135	17	;	;	PUNCT
ejpam-6249	135	18	(	(	PUNCT
ejpam-6249	135	19	2	2	X
ejpam-6249	135	20	)	)	PUNCT
ejpam-6249	135	21	(	(	PUNCT
ejpam-6249	135	22	d	d	PUNCT
ejpam-6249	135	23	◦	◦	NOUN
ejpam-6249	135	24	(l),⊔,∩	(l),⊔,∩	NOUN
ejpam-6249	135	25	)	)	PUNCT
ejpam-6249	135	26	is	be	AUX
ejpam-6249	135	27	a	a	DET
ejpam-6249	135	28	boolean	boolean	ADJ
ejpam-6249	135	29	algebra	algebra	NOUN
ejpam-6249	135	30	;	;	PUNCT
ejpam-6249	135	31	(	(	PUNCT
ejpam-6249	135	32	3	3	X
ejpam-6249	135	33	)	)	PUNCT
ejpam-6249	135	34	l	l	NOUN
ejpam-6249	135	35	/	/	SYM
ejpam-6249	135	36	ψ	ψ	NOUN
ejpam-6249	135	37	is	be	AUX
ejpam-6249	135	38	a	a	DET
ejpam-6249	135	39	boolean	boolean	ADJ
ejpam-6249	135	40	algebra	algebra	NOUN
ejpam-6249	135	41	;	;	PUNCT
ejpam-6249	135	42	n.	n.	PROPN
ejpam-6249	135	43	rafi	rafi	PROPN
ejpam-6249	135	44	et	et	PROPN
ejpam-6249	135	45	al	al	PROPN
ejpam-6249	135	46	.	.	PUNCT
ejpam-6249	135	47	/	/	SYM
ejpam-6249	135	48	eur	eur	PROPN
ejpam-6249	135	49	.	.	PUNCT
ejpam-6249	136	1	j.	j.	PROPN
ejpam-6249	136	2	pure	pure	PROPN
ejpam-6249	136	3	appl	appl	PROPN
ejpam-6249	136	4	.	.	PROPN
ejpam-6249	136	5	math	math	PROPN
ejpam-6249	136	6	,	,	PUNCT
ejpam-6249	136	7	18	18	NUM
ejpam-6249	136	8	(	(	PUNCT
ejpam-6249	136	9	4	4	NUM
ejpam-6249	136	10	)	)	PUNCT
ejpam-6249	136	11	(	(	PUNCT
ejpam-6249	136	12	2025	2025	NUM
ejpam-6249	136	13	)	)	PUNCT
ejpam-6249	136	14	,	,	PUNCT
ejpam-6249	136	15	6249	6249	NUM
ejpam-6249	136	16	7	7	NUM
ejpam-6249	136	17	of	of	ADP
ejpam-6249	136	18	11	11	NUM
ejpam-6249	136	19	(	(	PUNCT
ejpam-6249	136	20	4	4	NUM
ejpam-6249	136	21	)	)	PUNCT
ejpam-6249	136	22	for	for	ADP
ejpam-6249	136	23	each	each	DET
ejpam-6249	136	24	µ	µ	PROPN
ejpam-6249	136	25	∈	∈	PROPN
ejpam-6249	136	26	l	l	NOUN
ejpam-6249	136	27	,	,	PUNCT
ejpam-6249	136	28	there	there	PRON
ejpam-6249	136	29	exists	exist	VERB
ejpam-6249	136	30	π	π	PROPN
ejpam-6249	136	31	∈	∈	PROPN
ejpam-6249	136	32	l	l	NOUN
ejpam-6249	136	33	such	such	ADJ
ejpam-6249	136	34	that	that	SCONJ
ejpam-6249	136	35	(	(	PUNCT
ejpam-6249	136	36	(	(	PUNCT
ejpam-6249	136	37	µ,d),d	µ,d),d	NOUN
ejpam-6249	136	38	)	)	PUNCT
ejpam-6249	136	39	=	=	SYM
ejpam-6249	137	1	(	(	PUNCT
ejpam-6249	137	2	π	π	PROPN
ejpam-6249	137	3	,	,	PUNCT
ejpam-6249	137	4	d	d	PROPN
ejpam-6249	137	5	)	)	PUNCT
ejpam-6249	137	6	;	;	PUNCT
ejpam-6249	137	7	(	(	PUNCT
ejpam-6249	137	8	5	5	X
ejpam-6249	137	9	)	)	PUNCT
ejpam-6249	137	10	for	for	ADP
ejpam-6249	137	11	any	any	DET
ejpam-6249	137	12	d	d	NOUN
ejpam-6249	137	13	-	-	NOUN
ejpam-6249	137	14	filter	filter	NOUN
ejpam-6249	137	15	g	g	NOUN
ejpam-6249	137	16	of	of	ADP
ejpam-6249	137	17	l	l	NOUN
ejpam-6249	137	18	with	with	ADP
ejpam-6249	137	19	g	g	NOUN
ejpam-6249	137	20	∩	∩	ADJ
ejpam-6249	137	21	d∞	d∞	NOUN
ejpam-6249	137	22	=	=	SYM
ejpam-6249	137	23	∅	∅	NOUN
ejpam-6249	137	24	,	,	PUNCT
ejpam-6249	137	25	there	there	PRON
ejpam-6249	137	26	exists	exist	VERB
ejpam-6249	137	27	a	a	DET
ejpam-6249	137	28	minimal	minimal	ADJ
ejpam-6249	137	29	prime	prime	ADJ
ejpam-6249	137	30	d	d	NOUN
ejpam-6249	137	31	-	-	NOUN
ejpam-6249	137	32	filter	filter	ADJ
ejpam-6249	137	33	q	q	NOUN
ejpam-6249	137	34	of	of	ADP
ejpam-6249	137	35	l	l	NOUN
ejpam-6249	137	36	such	such	ADJ
ejpam-6249	137	37	that	that	SCONJ
ejpam-6249	137	38	g	g	PROPN
ejpam-6249	137	39	⊆	⊆	NUM
ejpam-6249	137	40	q.	q.	NOUN
ejpam-6249	137	41	proof	proof	NOUN
ejpam-6249	137	42	.	.	PUNCT
ejpam-6249	138	1	(	(	PUNCT
ejpam-6249	138	2	1	1	X
ejpam-6249	138	3	)	)	PUNCT
ejpam-6249	138	4	⇒	⇒	NOUN
ejpam-6249	138	5	(	(	PUNCT
ejpam-6249	138	6	2	2	NUM
ejpam-6249	138	7	)	)	PUNCT
ejpam-6249	138	8	:	:	PUNCT
ejpam-6249	138	9	assume	assume	VERB
ejpam-6249	138	10	(	(	PUNCT
ejpam-6249	138	11	1	1	NUM
ejpam-6249	138	12	)	)	PUNCT
ejpam-6249	138	13	.	.	PUNCT
ejpam-6249	139	1	let	let	VERB
ejpam-6249	139	2	(	(	PUNCT
ejpam-6249	139	3	µ,d	µ,d	NOUN
ejpam-6249	139	4	)	)	PUNCT
ejpam-6249	139	5	∈	∈	PROPN
ejpam-6249	140	1	d	d	PROPN
ejpam-6249	140	2	◦	◦	NOUN
ejpam-6249	140	3	(l	(l	NUM
ejpam-6249	140	4	)	)	PUNCT
ejpam-6249	140	5	.	.	PUNCT
ejpam-6249	141	1	then	then	ADV
ejpam-6249	141	2	there	there	PRON
ejpam-6249	141	3	exists	exist	VERB
ejpam-6249	141	4	π	π	PROPN
ejpam-6249	141	5	∈	∈	PROPN
ejpam-6249	141	6	l	l	NOUN
ejpam-6249	141	7	such	such	ADJ
ejpam-6249	141	8	that	that	SCONJ
ejpam-6249	141	9	µ	µ	ADJ
ejpam-6249	141	10	∧	∧	PROPN
ejpam-6249	141	11	π	π	X
ejpam-6249	141	12	∈	∈	PROPN
ejpam-6249	141	13	d∞	d∞	NOUN
ejpam-6249	141	14	and	and	CCONJ
ejpam-6249	141	15	µ	µ	PRON
ejpam-6249	141	16	∨	∨	NOUN
ejpam-6249	141	17	π	π	PROPN
ejpam-6249	141	18	∈	∈	PROPN
ejpam-6249	141	19	d.	d.	PROPN
ejpam-6249	141	20	hence	hence	ADV
ejpam-6249	141	21	(	(	PUNCT
ejpam-6249	141	22	µ,d	µ,d	NOUN
ejpam-6249	141	23	)	)	PUNCT
ejpam-6249	141	24	∩	∩	NOUN
ejpam-6249	141	25	(	(	PUNCT
ejpam-6249	141	26	π	π	X
ejpam-6249	141	27	,	,	PUNCT
ejpam-6249	141	28	d	d	NOUN
ejpam-6249	141	29	)	)	PUNCT
ejpam-6249	141	30	=	=	SYM
ejpam-6249	141	31	(	(	PUNCT
ejpam-6249	141	32	µ	µ	X
ejpam-6249	141	33	∧	∧	PROPN
ejpam-6249	141	34	π	π	PROPN
ejpam-6249	141	35	,	,	PUNCT
ejpam-6249	141	36	d	d	NOUN
ejpam-6249	141	37	)	)	PUNCT
ejpam-6249	142	1	=	=	SYM
ejpam-6249	142	2	d	d	PROPN
ejpam-6249	142	3	and	and	CCONJ
ejpam-6249	142	4	(	(	PUNCT
ejpam-6249	142	5	µ,d	µ,d	NOUN
ejpam-6249	142	6	)	)	PUNCT
ejpam-6249	142	7	⊔	⊔	NOUN
ejpam-6249	142	8	(	(	PUNCT
ejpam-6249	142	9	π	π	X
ejpam-6249	142	10	,	,	PUNCT
ejpam-6249	142	11	d	d	NOUN
ejpam-6249	142	12	)	)	PUNCT
ejpam-6249	142	13	=	=	SYM
ejpam-6249	142	14	(	(	PUNCT
ejpam-6249	142	15	µ	µ	X
ejpam-6249	142	16	∨	∨	NUM
ejpam-6249	142	17	π	π	PROPN
ejpam-6249	142	18	,	,	PUNCT
ejpam-6249	142	19	d	d	NOUN
ejpam-6249	142	20	)	)	PUNCT
ejpam-6249	142	21	=	=	SYM
ejpam-6249	143	1	l.	l.	NOUN
ejpam-6249	143	2	hence	hence	ADV
ejpam-6249	143	3	(	(	PUNCT
ejpam-6249	143	4	d	d	PUNCT
ejpam-6249	143	5	◦	◦	NOUN
ejpam-6249	143	6	(l),⊔,∩	(l),⊔,∩	NOUN
ejpam-6249	143	7	)	)	PUNCT
ejpam-6249	143	8	is	be	AUX
ejpam-6249	143	9	a	a	DET
ejpam-6249	143	10	boolean	boolean	ADJ
ejpam-6249	143	11	algebra	algebra	NOUN
ejpam-6249	143	12	.	.	PUNCT
ejpam-6249	144	1	(	(	PUNCT
ejpam-6249	144	2	2	2	X
ejpam-6249	144	3	)	)	PUNCT
ejpam-6249	144	4	⇒	⇒	NOUN
ejpam-6249	144	5	(	(	PUNCT
ejpam-6249	144	6	3	3	NUM
ejpam-6249	144	7	)	)	PUNCT
ejpam-6249	144	8	:	:	PUNCT
ejpam-6249	144	9	assume	assume	VERB
ejpam-6249	144	10	(	(	PUNCT
ejpam-6249	144	11	2	2	NUM
ejpam-6249	144	12	)	)	PUNCT
ejpam-6249	144	13	.	.	PUNCT
ejpam-6249	145	1	consider	consider	VERB
ejpam-6249	145	2	any	any	DET
ejpam-6249	145	3	element	element	NOUN
ejpam-6249	145	4	[	[	X
ejpam-6249	145	5	µ]ψ	µ]ψ	NOUN
ejpam-6249	145	6	in	in	ADP
ejpam-6249	145	7	l	l	PROPN
ejpam-6249	145	8	/	/	SYM
ejpam-6249	145	9	ψ	ψ	NOUN
ejpam-6249	145	10	.	.	PUNCT
ejpam-6249	146	1	given	give	VERB
ejpam-6249	146	2	that	that	PRON
ejpam-6249	146	3	d	d	PROPN
ejpam-6249	146	4	◦	◦	NOUN
ejpam-6249	146	5	(l	(l	NOUN
ejpam-6249	146	6	)	)	PUNCT
ejpam-6249	146	7	forms	form	VERB
ejpam-6249	146	8	a	a	DET
ejpam-6249	146	9	boolean	boolean	ADJ
ejpam-6249	146	10	algebras	algebra	NOUN
ejpam-6249	146	11	,	,	PUNCT
ejpam-6249	146	12	there	there	PRON
ejpam-6249	146	13	exists	exist	VERB
ejpam-6249	146	14	some	some	DET
ejpam-6249	146	15	π	π	PROPN
ejpam-6249	146	16	∈	∈	PROPN
ejpam-6249	146	17	l	l	NOUN
ejpam-6249	146	18	such	such	ADJ
ejpam-6249	146	19	that	that	SCONJ
ejpam-6249	146	20	(	(	PUNCT
ejpam-6249	146	21	µ∧π	µ∧π	NOUN
ejpam-6249	146	22	,	,	PUNCT
ejpam-6249	146	23	d	d	NOUN
ejpam-6249	146	24	)	)	PUNCT
ejpam-6249	146	25	=	=	SYM
ejpam-6249	146	26	(	(	PUNCT
ejpam-6249	146	27	µ,d)∩	µ,d)∩	PROPN
ejpam-6249	146	28	(	(	PUNCT
ejpam-6249	146	29	π	π	PROPN
ejpam-6249	146	30	,	,	PUNCT
ejpam-6249	146	31	d	d	NOUN
ejpam-6249	146	32	)	)	PUNCT
ejpam-6249	147	1	=	=	SYM
ejpam-6249	147	2	d	d	NOUN
ejpam-6249	147	3	,	,	PUNCT
ejpam-6249	147	4	and	and	CCONJ
ejpam-6249	147	5	(	(	PUNCT
ejpam-6249	147	6	µ∨	µ∨	PROPN
ejpam-6249	147	7	π	π	PROPN
ejpam-6249	147	8	,	,	PUNCT
ejpam-6249	147	9	d	d	NOUN
ejpam-6249	147	10	)	)	PUNCT
ejpam-6249	147	11	=	=	SYM
ejpam-6249	147	12	(	(	PUNCT
ejpam-6249	147	13	µ,d)⊔	µ,d)⊔	PROPN
ejpam-6249	147	14	(	(	PUNCT
ejpam-6249	147	15	π	π	PROPN
ejpam-6249	147	16	,	,	PUNCT
ejpam-6249	147	17	d	d	NOUN
ejpam-6249	147	18	)	)	PUNCT
ejpam-6249	147	19	=	=	VERB
ejpam-6249	148	1	l.	l.	NOUN
ejpam-6249	148	2	this	this	PRON
ejpam-6249	148	3	leads	lead	VERB
ejpam-6249	148	4	to	to	ADP
ejpam-6249	148	5	µ∧	µ∧	PROPN
ejpam-6249	148	6	π	π	PROPN
ejpam-6249	148	7	∈	∈	PROPN
ejpam-6249	148	8	d∞	d∞	NOUN
ejpam-6249	148	9	and	and	CCONJ
ejpam-6249	148	10	µ∨	µ∨	PROPN
ejpam-6249	148	11	π	π	X
ejpam-6249	148	12	∈	∈	PROPN
ejpam-6249	148	13	d.	d.	PROPN
ejpam-6249	148	14	consequently	consequently	ADV
ejpam-6249	148	15	,	,	PUNCT
ejpam-6249	148	16	we	we	PRON
ejpam-6249	148	17	obtain	obtain	VERB
ejpam-6249	148	18	[	[	X
ejpam-6249	148	19	µ]ψ	µ]ψ	NOUN
ejpam-6249	148	20	∩	∩	NOUN
ejpam-6249	148	21	[	[	X
ejpam-6249	148	22	π]ψ	π]ψ	X
ejpam-6249	148	23	=	=	PUNCT
ejpam-6249	149	1	[	[	X
ejpam-6249	149	2	µ	µ	X
ejpam-6249	149	3	∧	∧	NOUN
ejpam-6249	149	4	π]ψ	π]ψ	NOUN
ejpam-6249	149	5	=	=	NOUN
ejpam-6249	149	6	d∞	d∞	NOUN
ejpam-6249	149	7	and	and	CCONJ
ejpam-6249	149	8	[	[	X
ejpam-6249	149	9	µ]ψ	µ]ψ	NOUN
ejpam-6249	149	10	∨	∨	NOUN
ejpam-6249	149	11	[	[	X
ejpam-6249	149	12	π]ψ	π]ψ	X
ejpam-6249	149	13	=	=	PUNCT
ejpam-6249	150	1	[	[	X
ejpam-6249	150	2	µ	µ	X
ejpam-6249	150	3	∨	∨	NUM
ejpam-6249	150	4	π]ψ	π]ψ	NOUN
ejpam-6249	150	5	=	=	SYM
ejpam-6249	150	6	d.	d.	PROPN
ejpam-6249	150	7	therefore	therefore	ADV
ejpam-6249	150	8	,	,	PUNCT
ejpam-6249	150	9	l	l	X
ejpam-6249	150	10	/	/	SYM
ejpam-6249	150	11	ψ	ψ	NOUN
ejpam-6249	150	12	satisfies	satisfie	NOUN
ejpam-6249	150	13	all	all	DET
ejpam-6249	150	14	the	the	DET
ejpam-6249	150	15	condition	condition	NOUN
ejpam-6249	150	16	for	for	ADP
ejpam-6249	150	17	being	be	AUX
ejpam-6249	150	18	a	a	DET
ejpam-6249	150	19	boolean	boolean	ADJ
ejpam-6249	150	20	algebra	algebra	NOUN
ejpam-6249	150	21	.	.	PUNCT
ejpam-6249	151	1	(	(	PUNCT
ejpam-6249	151	2	3	3	X
ejpam-6249	151	3	)	)	PUNCT
ejpam-6249	151	4	⇒	⇒	NOUN
ejpam-6249	151	5	(	(	PUNCT
ejpam-6249	151	6	4	4	NUM
ejpam-6249	151	7	)	)	PUNCT
ejpam-6249	152	1	:	:	PUNCT
ejpam-6249	152	2	assume	assume	VERB
ejpam-6249	152	3	(	(	PUNCT
ejpam-6249	152	4	3	3	NUM
ejpam-6249	152	5	)	)	PUNCT
ejpam-6249	152	6	.	.	PUNCT
ejpam-6249	153	1	let	let	VERB
ejpam-6249	153	2	µ	µ	X
ejpam-6249	153	3	∈	∈	PROPN
ejpam-6249	153	4	l.	l.	NOUN
ejpam-6249	153	5	then	then	ADV
ejpam-6249	153	6	there	there	PRON
ejpam-6249	153	7	is	be	VERB
ejpam-6249	153	8	[	[	X
ejpam-6249	153	9	π]ψ	π]ψ	NOUN
ejpam-6249	153	10	∈	∈	NOUN
ejpam-6249	153	11	l	l	NOUN
ejpam-6249	153	12	/	/	SYM
ejpam-6249	153	13	ψ	ψ	NOUN
ejpam-6249	153	14	such	such	ADJ
ejpam-6249	153	15	that	that	SCONJ
ejpam-6249	153	16	[	[	X
ejpam-6249	153	17	µ	µ	X
ejpam-6249	153	18	∧	∧	NOUN
ejpam-6249	153	19	π]ψ	π]ψ	NOUN
ejpam-6249	153	20	=	=	PUNCT
ejpam-6249	154	1	[	[	X
ejpam-6249	154	2	µ]ψ	µ]ψ	NOUN
ejpam-6249	154	3	∩	∩	NOUN
ejpam-6249	154	4	[	[	X
ejpam-6249	154	5	π]ψ	π]ψ	X
ejpam-6249	154	6	=	=	SYM
ejpam-6249	154	7	d∞	d∞	NOUN
ejpam-6249	154	8	and	and	CCONJ
ejpam-6249	154	9	[	[	X
ejpam-6249	154	10	µ	µ	X
ejpam-6249	154	11	∨	∨	NUM
ejpam-6249	154	12	π]ψ	π]ψ	NOUN
ejpam-6249	154	13	=	=	PUNCT
ejpam-6249	155	1	[	[	X
ejpam-6249	155	2	µ]ψ	µ]ψ	NOUN
ejpam-6249	155	3	∨	∨	NOUN
ejpam-6249	155	4	[	[	X
ejpam-6249	155	5	π]ψ	π]ψ	X
ejpam-6249	155	6	=	=	SYM
ejpam-6249	155	7	d.	d.	NOUN
ejpam-6249	155	8	therefore	therefore	ADV
ejpam-6249	155	9	µ	µ	PROPN
ejpam-6249	155	10	∧	∧	PROPN
ejpam-6249	155	11	π	π	X
ejpam-6249	155	12	∈	∈	PROPN
ejpam-6249	155	13	d∞	d∞	NOUN
ejpam-6249	155	14	and	and	CCONJ
ejpam-6249	155	15	µ	µ	PRON
ejpam-6249	155	16	∨	∨	NOUN
ejpam-6249	155	17	π	π	PROPN
ejpam-6249	155	18	∈	∈	PROPN
ejpam-6249	155	19	d.	d.	PROPN
ejpam-6249	155	20	now	now	ADV
ejpam-6249	155	21	,	,	PUNCT
ejpam-6249	155	22	µ	µ	X
ejpam-6249	155	23	∧	∧	PROPN
ejpam-6249	155	24	π	π	X
ejpam-6249	155	25	∈	∈	PROPN
ejpam-6249	155	26	d∞	d∞	NOUN
ejpam-6249	155	27	⇒	⇒	NOUN
ejpam-6249	155	28	(	(	PUNCT
ejpam-6249	155	29	µ	µ	X
ejpam-6249	155	30	∧	∧	PROPN
ejpam-6249	155	31	π	π	PROPN
ejpam-6249	155	32	,	,	PUNCT
ejpam-6249	155	33	d	d	NOUN
ejpam-6249	155	34	)	)	PUNCT
ejpam-6249	155	35	=	=	SYM
ejpam-6249	155	36	d	d	NOUN
ejpam-6249	155	37	⇒	⇒	NOUN
ejpam-6249	155	38	(	(	PUNCT
ejpam-6249	155	39	µ,d	µ,d	NOUN
ejpam-6249	155	40	)	)	PUNCT
ejpam-6249	155	41	∩	∩	NOUN
ejpam-6249	155	42	(	(	PUNCT
ejpam-6249	155	43	π	π	X
ejpam-6249	155	44	,	,	PUNCT
ejpam-6249	155	45	d	d	NOUN
ejpam-6249	155	46	)	)	PUNCT
ejpam-6249	155	47	=	=	SYM
ejpam-6249	155	48	d	d	NOUN
ejpam-6249	155	49	⇒	⇒	NOUN
ejpam-6249	155	50	(	(	PUNCT
ejpam-6249	155	51	π	π	X
ejpam-6249	155	52	,	,	PUNCT
ejpam-6249	155	53	d	d	NOUN
ejpam-6249	155	54	)	)	PUNCT
ejpam-6249	155	55	⊆	⊆	NUM
ejpam-6249	155	56	(	(	PUNCT
ejpam-6249	155	57	(	(	PUNCT
ejpam-6249	155	58	µ,d),d	µ,d),d	NOUN
ejpam-6249	155	59	)	)	PUNCT
ejpam-6249	155	60	µ	µ	NOUN
ejpam-6249	155	61	∨	∨	NOUN
ejpam-6249	155	62	π	π	PROPN
ejpam-6249	155	63	∈	∈	PROPN
ejpam-6249	155	64	d	d	X
ejpam-6249	155	65	⇒	⇒	PROPN
ejpam-6249	155	66	µ	µ	PROPN
ejpam-6249	155	67	∈	∈	PROPN
ejpam-6249	155	68	(	(	PUNCT
ejpam-6249	155	69	π	π	PROPN
ejpam-6249	155	70	,	,	PUNCT
ejpam-6249	155	71	d	d	NOUN
ejpam-6249	155	72	)	)	PUNCT
ejpam-6249	155	73	⇒	⇒	NOUN
ejpam-6249	155	74	[	[	X
ejpam-6249	155	75	µ	µ	X
ejpam-6249	155	76	)	)	PUNCT
ejpam-6249	155	77	⊆	⊆	NUM
ejpam-6249	155	78	(	(	PUNCT
ejpam-6249	155	79	π	π	PROPN
ejpam-6249	155	80	,	,	PUNCT
ejpam-6249	155	81	d	d	NOUN
ejpam-6249	155	82	)	)	PUNCT
ejpam-6249	155	83	⇒	⇒	NOUN
ejpam-6249	155	84	(	(	PUNCT
ejpam-6249	155	85	(	(	PUNCT
ejpam-6249	155	86	µ,d),d	µ,d),d	X
ejpam-6249	155	87	)	)	PUNCT
ejpam-6249	155	88	⊆	⊆	NUM
ejpam-6249	155	89	(	(	PUNCT
ejpam-6249	155	90	π	π	PROPN
ejpam-6249	155	91	,	,	PUNCT
ejpam-6249	155	92	d	d	NOUN
ejpam-6249	155	93	)	)	PUNCT
ejpam-6249	155	94	.	.	PUNCT
ejpam-6249	156	1	hence	hence	ADV
ejpam-6249	156	2	,	,	PUNCT
ejpam-6249	156	3	to	to	ADP
ejpam-6249	156	4	every	every	DET
ejpam-6249	156	5	µ	µ	PROPN
ejpam-6249	156	6	∈	∈	PROPN
ejpam-6249	156	7	l	l	NOUN
ejpam-6249	156	8	,	,	PUNCT
ejpam-6249	156	9	there	there	PRON
ejpam-6249	156	10	exists	exist	VERB
ejpam-6249	156	11	π	π	PROPN
ejpam-6249	156	12	∈	∈	PROPN
ejpam-6249	156	13	l	l	NOUN
ejpam-6249	156	14	such	such	ADJ
ejpam-6249	156	15	that	that	SCONJ
ejpam-6249	156	16	(	(	PUNCT
ejpam-6249	156	17	(	(	PUNCT
ejpam-6249	156	18	µ,d),d	µ,d),d	NOUN
ejpam-6249	156	19	)	)	PUNCT
ejpam-6249	156	20	=	=	SYM
ejpam-6249	157	1	(	(	PUNCT
ejpam-6249	157	2	π	π	X
ejpam-6249	157	3	,	,	PUNCT
ejpam-6249	157	4	d	d	NOUN
ejpam-6249	157	5	)	)	PUNCT
ejpam-6249	157	6	.	.	PUNCT
ejpam-6249	158	1	(	(	PUNCT
ejpam-6249	158	2	4	4	X
ejpam-6249	158	3	)	)	PUNCT
ejpam-6249	158	4	⇒	⇒	NOUN
ejpam-6249	158	5	(	(	PUNCT
ejpam-6249	158	6	5	5	NUM
ejpam-6249	158	7	)	)	PUNCT
ejpam-6249	158	8	:	:	PUNCT
ejpam-6249	158	9	assume	assume	VERB
ejpam-6249	158	10	(	(	PUNCT
ejpam-6249	158	11	4	4	NUM
ejpam-6249	158	12	)	)	PUNCT
ejpam-6249	158	13	.	.	PUNCT
ejpam-6249	159	1	let	let	VERB
ejpam-6249	159	2	f	f	PRON
ejpam-6249	159	3	be	be	AUX
ejpam-6249	159	4	a	a	DET
ejpam-6249	159	5	d	d	NOUN
ejpam-6249	159	6	-	-	NOUN
ejpam-6249	159	7	filter	filter	NOUN
ejpam-6249	159	8	in	in	ADP
ejpam-6249	159	9	the	the	DET
ejpam-6249	159	10	adl	adl	PROPN
ejpam-6249	159	11	l	l	NOUN
ejpam-6249	159	12	such	such	ADJ
ejpam-6249	159	13	that	that	SCONJ
ejpam-6249	159	14	f	f	PROPN
ejpam-6249	159	15	∩	∩	NOUN
ejpam-6249	159	16	d∞	d∞	NOUN
ejpam-6249	159	17	=	=	PUNCT
ejpam-6249	159	18	∅.	∅.	NOUN
ejpam-6249	159	19	then	then	ADV
ejpam-6249	159	20	,	,	PUNCT
ejpam-6249	159	21	there	there	PRON
ejpam-6249	159	22	exists	exist	VERB
ejpam-6249	159	23	a	a	DET
ejpam-6249	159	24	prime	prime	ADJ
ejpam-6249	159	25	filter	filter	NOUN
ejpam-6249	159	26	p	p	NOUN
ejpam-6249	159	27	in	in	ADP
ejpam-6249	159	28	l	l	NOUN
ejpam-6249	159	29	that	that	PRON
ejpam-6249	159	30	contains	contain	VERB
ejpam-6249	159	31	f	f	PROPN
ejpam-6249	159	32	and	and	CCONJ
ejpam-6249	159	33	also	also	ADV
ejpam-6249	159	34	remains	remain	VERB
ejpam-6249	159	35	disjoint	disjoint	NOUN
ejpam-6249	159	36	from	from	ADP
ejpam-6249	159	37	d∞	d∞	PROPN
ejpam-6249	159	38	,	,	PUNCT
ejpam-6249	159	39	i.e.	i.e.	X
ejpam-6249	159	40	,	,	PUNCT
ejpam-6249	159	41	f	f	PROPN
ejpam-6249	159	42	⊆	⊆	NUM
ejpam-6249	159	43	p	p	NOUN
ejpam-6249	159	44	and	and	CCONJ
ejpam-6249	159	45	p∩d∞	p∩d∞	VERB
ejpam-6249	159	46	=	=	PUNCT
ejpam-6249	160	1	∅.	∅.	NOUN
ejpam-6249	160	2	it	it	PRON
ejpam-6249	160	3	is	be	AUX
ejpam-6249	160	4	clear	clear	ADJ
ejpam-6249	160	5	that	that	SCONJ
ejpam-6249	160	6	such	such	DET
ejpam-6249	160	7	a	a	DET
ejpam-6249	160	8	p	p	NOUN
ejpam-6249	160	9	qualifies	qualifie	NOUN
ejpam-6249	160	10	as	as	ADP
ejpam-6249	160	11	a	a	DET
ejpam-6249	160	12	d	d	NOUN
ejpam-6249	160	13	-	-	NOUN
ejpam-6249	160	14	filter	filter	NOUN
ejpam-6249	160	15	.	.	PUNCT
ejpam-6249	161	1	our	our	PRON
ejpam-6249	161	2	next	next	ADJ
ejpam-6249	161	3	objective	objective	NOUN
ejpam-6249	161	4	is	be	AUX
ejpam-6249	161	5	to	to	PART
ejpam-6249	161	6	show	show	VERB
ejpam-6249	161	7	that	that	SCONJ
ejpam-6249	161	8	p	p	NOUN
ejpam-6249	161	9	is	be	AUX
ejpam-6249	161	10	minimal	minimal	ADJ
ejpam-6249	161	11	with	with	ADP
ejpam-6249	161	12	this	this	DET
ejpam-6249	161	13	property	property	NOUN
ejpam-6249	161	14	.	.	PUNCT
ejpam-6249	162	1	take	take	VERB
ejpam-6249	162	2	any	any	DET
ejpam-6249	162	3	element	element	NOUN
ejpam-6249	162	4	µ	µ	PRON
ejpam-6249	162	5	∈	∈	PROPN
ejpam-6249	162	6	p.	p.	NOUN
ejpam-6249	162	7	by	by	ADP
ejpam-6249	162	8	assumption	assumption	NOUN
ejpam-6249	162	9	(	(	PUNCT
ejpam-6249	162	10	specifically	specifically	ADV
ejpam-6249	162	11	,	,	PUNCT
ejpam-6249	162	12	condition	condition	NOUN
ejpam-6249	162	13	(	(	PUNCT
ejpam-6249	162	14	4	4	NUM
ejpam-6249	162	15	)	)	PUNCT
ejpam-6249	162	16	)	)	PUNCT
ejpam-6249	162	17	,	,	PUNCT
ejpam-6249	162	18	there	there	PRON
ejpam-6249	162	19	exists	exist	VERB
ejpam-6249	162	20	some	some	DET
ejpam-6249	162	21	π	π	PROPN
ejpam-6249	162	22	∈	∈	NOUN
ejpam-6249	162	23	l	l	NOUN
ejpam-6249	162	24	satisfying	satisfying	NOUN
ejpam-6249	162	25	(	(	PUNCT
ejpam-6249	162	26	(	(	PUNCT
ejpam-6249	162	27	µ,d),d	µ,d),d	NOUN
ejpam-6249	162	28	)	)	PUNCT
ejpam-6249	162	29	=	=	SYM
ejpam-6249	162	30	(	(	PUNCT
ejpam-6249	162	31	π	π	X
ejpam-6249	162	32	,	,	PUNCT
ejpam-6249	162	33	d	d	NOUN
ejpam-6249	162	34	)	)	PUNCT
ejpam-6249	162	35	.	.	PUNCT
ejpam-6249	163	1	since	since	SCONJ
ejpam-6249	163	2	µ	µ	X
ejpam-6249	163	3	belongs	belong	VERB
ejpam-6249	163	4	to	to	ADP
ejpam-6249	163	5	(	(	PUNCT
ejpam-6249	163	6	(	(	PUNCT
ejpam-6249	163	7	µ,d),d	µ,d),d	NOUN
ejpam-6249	163	8	)	)	PUNCT
ejpam-6249	163	9	,	,	PUNCT
ejpam-6249	163	10	we	we	PRON
ejpam-6249	163	11	get	get	VERB
ejpam-6249	163	12	µ	µ	PRON
ejpam-6249	163	13	∈	∈	NOUN
ejpam-6249	163	14	(	(	PUNCT
ejpam-6249	163	15	π	π	PROPN
ejpam-6249	163	16	,	,	PUNCT
ejpam-6249	163	17	d	d	PROPN
ejpam-6249	163	18	)	)	PUNCT
ejpam-6249	163	19	,	,	PUNCT
ejpam-6249	163	20	which	which	PRON
ejpam-6249	163	21	implies	imply	VERB
ejpam-6249	163	22	µ	µ	NUM
ejpam-6249	163	23	∨	∨	PROPN
ejpam-6249	163	24	π	π	PROPN
ejpam-6249	163	25	∈	∈	PROPN
ejpam-6249	163	26	d.	d.	PROPN
ejpam-6249	163	27	now	now	ADV
ejpam-6249	163	28	consider	consider	VERB
ejpam-6249	163	29	the	the	DET
ejpam-6249	163	30	meet	meet	NOUN
ejpam-6249	163	31	µ	µ	PRON
ejpam-6249	163	32	∧	∧	PROPN
ejpam-6249	163	33	π	π	PROPN
ejpam-6249	163	34	.	.	PUNCT
ejpam-6249	164	1	using	use	VERB
ejpam-6249	164	2	the	the	DET
ejpam-6249	164	3	properties	property	NOUN
ejpam-6249	164	4	of	of	ADP
ejpam-6249	164	5	filters	filter	NOUN
ejpam-6249	164	6	,	,	PUNCT
ejpam-6249	164	7	we	we	PRON
ejpam-6249	164	8	have	have	VERB
ejpam-6249	164	9	:	:	PUNCT
ejpam-6249	164	10	(	(	PUNCT
ejpam-6249	164	11	µ	µ	X
ejpam-6249	164	12	∧	∧	PROPN
ejpam-6249	164	13	π	π	PROPN
ejpam-6249	164	14	,	,	PUNCT
ejpam-6249	164	15	d	d	NOUN
ejpam-6249	164	16	)	)	PUNCT
ejpam-6249	164	17	=	=	SYM
ejpam-6249	164	18	(	(	PUNCT
ejpam-6249	164	19	µ,d	µ,d	NOUN
ejpam-6249	164	20	)	)	PUNCT
ejpam-6249	164	21	∩	∩	NOUN
ejpam-6249	164	22	(	(	PUNCT
ejpam-6249	164	23	π	π	X
ejpam-6249	164	24	,	,	PUNCT
ejpam-6249	164	25	d	d	NOUN
ejpam-6249	164	26	)	)	PUNCT
ejpam-6249	165	1	=	=	SYM
ejpam-6249	165	2	(	(	PUNCT
ejpam-6249	165	3	µ,d	µ,d	NOUN
ejpam-6249	165	4	)	)	PUNCT
ejpam-6249	165	5	∩	∩	NOUN
ejpam-6249	165	6	(	(	PUNCT
ejpam-6249	165	7	(	(	PUNCT
ejpam-6249	165	8	µ,d),d	µ,d),d	NOUN
ejpam-6249	165	9	)	)	PUNCT
ejpam-6249	165	10	=	=	SYM
ejpam-6249	166	1	d	d	NOUN
ejpam-6249	166	2	,	,	PUNCT
ejpam-6249	166	3	which	which	PRON
ejpam-6249	166	4	leads	lead	VERB
ejpam-6249	166	5	to	to	ADP
ejpam-6249	166	6	µ	µ	PRON
ejpam-6249	166	7	∧	∧	PROPN
ejpam-6249	166	8	π	π	X
ejpam-6249	166	9	∈	∈	PROPN
ejpam-6249	167	1	d∞.	d∞.	INTJ
ejpam-6249	167	2	however	however	ADV
ejpam-6249	167	3	,	,	PUNCT
ejpam-6249	167	4	since	since	SCONJ
ejpam-6249	167	5	p	p	NOUN
ejpam-6249	167	6	is	be	AUX
ejpam-6249	167	7	disjoint	disjoint	NOUN
ejpam-6249	167	8	from	from	ADP
ejpam-6249	167	9	d∞	d∞	PROPN
ejpam-6249	167	10	,	,	PUNCT
ejpam-6249	167	11	we	we	PRON
ejpam-6249	167	12	conclude	conclude	VERB
ejpam-6249	167	13	that	that	PRON
ejpam-6249	167	14	µ∧π	µ∧π	NOUN
ejpam-6249	167	15	/∈	/∈	PUNCT
ejpam-6249	168	1	p.	p.	NOUN
ejpam-6249	168	2	suppose	suppose	VERB
ejpam-6249	168	3	now	now	ADV
ejpam-6249	168	4	that	that	SCONJ
ejpam-6249	169	1	π	π	PROPN
ejpam-6249	169	2	∈	∈	PROPN
ejpam-6249	169	3	p.	p.	NOUN
ejpam-6249	169	4	then	then	ADV
ejpam-6249	170	1	x∧y	x∧y	PROPN
ejpam-6249	170	2	∈	∈	PROPN
ejpam-6249	170	3	p	p	X
ejpam-6249	170	4	,	,	PUNCT
ejpam-6249	170	5	contradicting	contradict	VERB
ejpam-6249	170	6	our	our	PRON
ejpam-6249	170	7	earlier	early	ADJ
ejpam-6249	170	8	conclusion	conclusion	NOUN
ejpam-6249	170	9	.	.	PUNCT
ejpam-6249	171	1	hence	hence	ADV
ejpam-6249	171	2	,	,	PUNCT
ejpam-6249	171	3	π	π	PROPN
ejpam-6249	171	4	/∈	/∈	PUNCT
ejpam-6249	171	5	p.	p.	NOUN
ejpam-6249	171	6	thus	thus	ADV
ejpam-6249	171	7	,	,	PUNCT
ejpam-6249	171	8	p	p	PROPN
ejpam-6249	171	9	is	be	AUX
ejpam-6249	171	10	a	a	DET
ejpam-6249	171	11	minimal	minimal	ADJ
ejpam-6249	171	12	prime	prime	ADJ
ejpam-6249	171	13	d	d	NOUN
ejpam-6249	171	14	-	-	NOUN
ejpam-6249	171	15	filter	filter	NOUN
ejpam-6249	171	16	of	of	ADP
ejpam-6249	171	17	l.	l.	PROPN
ejpam-6249	171	18	(	(	PUNCT
ejpam-6249	171	19	5	5	NUM
ejpam-6249	171	20	)	)	PUNCT
ejpam-6249	171	21	⇒	⇒	NOUN
ejpam-6249	171	22	(	(	PUNCT
ejpam-6249	171	23	1	1	NUM
ejpam-6249	171	24	)	)	PUNCT
ejpam-6249	171	25	:	:	PUNCT
ejpam-6249	171	26	assume	assume	VERB
ejpam-6249	171	27	(	(	PUNCT
ejpam-6249	171	28	5	5	NUM
ejpam-6249	171	29	)	)	PUNCT
ejpam-6249	171	30	.	.	PUNCT
ejpam-6249	172	1	let	let	VERB
ejpam-6249	172	2	µ	µ	X
ejpam-6249	172	3	∈	∈	PROPN
ejpam-6249	172	4	l.	l.	NOUN
ejpam-6249	172	5	it	it	PRON
ejpam-6249	172	6	is	be	AUX
ejpam-6249	172	7	evident	evident	ADJ
ejpam-6249	172	8	that	that	SCONJ
ejpam-6249	172	9	(	(	PUNCT
ejpam-6249	172	10	µ,d	µ,d	NOUN
ejpam-6249	172	11	)	)	PUNCT
ejpam-6249	172	12	∨	∨	NOUN
ejpam-6249	172	13	(	(	PUNCT
ejpam-6249	172	14	(	(	PUNCT
ejpam-6249	172	15	µ,d),d	µ,d),d	NOUN
ejpam-6249	172	16	)	)	PUNCT
ejpam-6249	172	17	forms	form	VERB
ejpam-6249	172	18	a	a	DET
ejpam-6249	172	19	d	d	NOUN
ejpam-6249	172	20	-	-	NOUN
ejpam-6249	172	21	filter	filter	NOUN
ejpam-6249	172	22	within	within	ADP
ejpam-6249	172	23	l.	l.	PROPN
ejpam-6249	172	24	suppose	suppose	VERB
ejpam-6249	172	25	there	there	PRON
ejpam-6249	172	26	exists	exist	VERB
ejpam-6249	172	27	a	a	DET
ejpam-6249	172	28	minimal	minimal	ADJ
ejpam-6249	172	29	prime	prime	ADJ
ejpam-6249	172	30	d	d	NOUN
ejpam-6249	172	31	-	-	NOUN
ejpam-6249	172	32	filter	filter	NOUN
ejpam-6249	172	33	q	q	NOUN
ejpam-6249	172	34	such	such	ADJ
ejpam-6249	172	35	that	that	SCONJ
ejpam-6249	172	36	(	(	PUNCT
ejpam-6249	172	37	µ,d)∨((µ,d),d	µ,d)∨((µ,d),d	PROPN
ejpam-6249	172	38	)	)	PUNCT
ejpam-6249	172	39	⊆	⊆	NUM
ejpam-6249	172	40	q.	q.	NOUN
ejpam-6249	172	41	then	then	ADV
ejpam-6249	172	42	,	,	PUNCT
ejpam-6249	172	43	since	since	SCONJ
ejpam-6249	172	44	µ	µ	NOUN
ejpam-6249	172	45	∈	∈	X
ejpam-6249	172	46	(	(	PUNCT
ejpam-6249	172	47	(	(	PUNCT
ejpam-6249	172	48	µ,d),d	µ,d),d	NOUN
ejpam-6249	172	49	)	)	PUNCT
ejpam-6249	172	50	⊆	⊆	NUM
ejpam-6249	172	51	q	q	NOUN
ejpam-6249	172	52	,	,	PUNCT
ejpam-6249	172	53	and	and	CCONJ
ejpam-6249	172	54	also	also	ADV
ejpam-6249	172	55	(	(	PUNCT
ejpam-6249	172	56	µ,d	µ,d	NOUN
ejpam-6249	172	57	)	)	PUNCT
ejpam-6249	172	58	⊆	⊆	NUM
ejpam-6249	172	59	q	q	NOUN
ejpam-6249	172	60	,	,	PUNCT
ejpam-6249	172	61	the	the	DET
ejpam-6249	172	62	minimality	minimality	NOUN
ejpam-6249	172	63	of	of	ADP
ejpam-6249	172	64	q	q	PROPN
ejpam-6249	172	65	implies	imply	VERB
ejpam-6249	172	66	that	that	SCONJ
ejpam-6249	172	67	µ	µ	X
ejpam-6249	172	68	/∈	/∈	PUNCT
ejpam-6249	172	69	q	q	NOUN
ejpam-6249	172	70	,	,	PUNCT
ejpam-6249	172	71	which	which	PRON
ejpam-6249	172	72	results	result	VERB
ejpam-6249	172	73	in	in	ADP
ejpam-6249	172	74	a	a	DET
ejpam-6249	172	75	contradiction	contradiction	NOUN
ejpam-6249	172	76	.	.	PUNCT
ejpam-6249	173	1	therefore	therefore	ADV
ejpam-6249	173	2	,	,	PUNCT
ejpam-6249	173	3	the	the	DET
ejpam-6249	173	4	filter	filter	NOUN
ejpam-6249	173	5	(	(	PUNCT
ejpam-6249	173	6	µ,d	µ,d	NOUN
ejpam-6249	173	7	)	)	PUNCT
ejpam-6249	173	8	∨	∨	NOUN
ejpam-6249	173	9	(	(	PUNCT
ejpam-6249	173	10	(	(	PUNCT
ejpam-6249	173	11	µ,d),d	µ,d),d	NOUN
ejpam-6249	173	12	)	)	PUNCT
ejpam-6249	173	13	n.	n.	PROPN
ejpam-6249	173	14	rafi	rafi	PROPN
ejpam-6249	173	15	et	et	PROPN
ejpam-6249	173	16	al	al	PROPN
ejpam-6249	173	17	.	.	PUNCT
ejpam-6249	173	18	/	/	SYM
ejpam-6249	173	19	eur	eur	PROPN
ejpam-6249	173	20	.	.	PUNCT
ejpam-6249	174	1	j.	j.	PROPN
ejpam-6249	174	2	pure	pure	PROPN
ejpam-6249	174	3	appl	appl	PROPN
ejpam-6249	174	4	.	.	PROPN
ejpam-6249	174	5	math	math	PROPN
ejpam-6249	174	6	,	,	PUNCT
ejpam-6249	174	7	18	18	NUM
ejpam-6249	174	8	(	(	PUNCT
ejpam-6249	174	9	4	4	NUM
ejpam-6249	174	10	)	)	PUNCT
ejpam-6249	174	11	(	(	PUNCT
ejpam-6249	174	12	2025	2025	NUM
ejpam-6249	174	13	)	)	PUNCT
ejpam-6249	174	14	,	,	PUNCT
ejpam-6249	174	15	6249	6249	NUM
ejpam-6249	174	16	8	8	NUM
ejpam-6249	174	17	of	of	ADP
ejpam-6249	174	18	11	11	NUM
ejpam-6249	174	19	can	can	AUX
ejpam-6249	174	20	not	not	PART
ejpam-6249	174	21	be	be	AUX
ejpam-6249	174	22	contained	contain	VERB
ejpam-6249	174	23	in	in	ADP
ejpam-6249	174	24	any	any	DET
ejpam-6249	174	25	minimal	minimal	ADJ
ejpam-6249	174	26	prime	prime	ADJ
ejpam-6249	174	27	d	d	NOUN
ejpam-6249	174	28	-	-	NOUN
ejpam-6249	174	29	filter	filter	NOUN
ejpam-6249	174	30	.	.	PUNCT
ejpam-6249	175	1	applying	apply	VERB
ejpam-6249	175	2	hypothesis	hypothesis	NOUN
ejpam-6249	175	3	(	(	PUNCT
ejpam-6249	175	4	5	5	NUM
ejpam-6249	175	5	)	)	PUNCT
ejpam-6249	175	6	,	,	PUNCT
ejpam-6249	175	7	it	it	PRON
ejpam-6249	175	8	gives	give	VERB
ejpam-6249	175	9	that	that	SCONJ
ejpam-6249	175	10	{	{	PUNCT
ejpam-6249	175	11	(	(	PUNCT
ejpam-6249	175	12	µ,d)∨	µ,d)∨	PROPN
ejpam-6249	175	13	(	(	PUNCT
ejpam-6249	175	14	(	(	PUNCT
ejpam-6249	175	15	µ,d),d)}∩d∞	µ,d),d)}∩d∞	ADP
ejpam-6249	175	16	̸=	̸=	PROPN
ejpam-6249	175	17	∅.	∅.	ADV
ejpam-6249	175	18	let	let	VERB
ejpam-6249	175	19	us	we	PRON
ejpam-6249	175	20	select	select	VERB
ejpam-6249	175	21	an	an	DET
ejpam-6249	175	22	element	element	NOUN
ejpam-6249	175	23	σ	σ	PROPN
ejpam-6249	175	24	in	in	ADP
ejpam-6249	175	25	{	{	PUNCT
ejpam-6249	175	26	(	(	PUNCT
ejpam-6249	175	27	µ,d)∨	µ,d)∨	PROPN
ejpam-6249	175	28	(	(	PUNCT
ejpam-6249	175	29	(	(	PUNCT
ejpam-6249	176	1	µ,d),d)}∩d∞.	µ,d),d)}∩d∞.	ADV
ejpam-6249	176	2	then	then	ADV
ejpam-6249	176	3	(	(	PUNCT
ejpam-6249	176	4	σ	σ	PROPN
ejpam-6249	176	5	,	,	PUNCT
ejpam-6249	176	6	d	d	NOUN
ejpam-6249	176	7	)	)	PUNCT
ejpam-6249	176	8	=	=	SYM
ejpam-6249	176	9	d	d	NOUN
ejpam-6249	176	10	,	,	PUNCT
ejpam-6249	176	11	and	and	CCONJ
ejpam-6249	176	12	there	there	PRON
ejpam-6249	176	13	exist	exist	VERB
ejpam-6249	176	14	elements	element	NOUN
ejpam-6249	176	15	θ	θ	PROPN
ejpam-6249	176	16	∈	∈	PROPN
ejpam-6249	176	17	(	(	PUNCT
ejpam-6249	176	18	µ,d	µ,d	NOUN
ejpam-6249	176	19	)	)	PUNCT
ejpam-6249	176	20	and	and	CCONJ
ejpam-6249	176	21	ϑ	ϑ	X
ejpam-6249	176	22	∈	∈	PROPN
ejpam-6249	176	23	(	(	PUNCT
ejpam-6249	176	24	(	(	PUNCT
ejpam-6249	176	25	µ,d),d	µ,d),d	NOUN
ejpam-6249	176	26	)	)	PUNCT
ejpam-6249	176	27	such	such	ADJ
ejpam-6249	176	28	that	that	SCONJ
ejpam-6249	176	29	σ	σ	NOUN
ejpam-6249	176	30	=	=	SYM
ejpam-6249	176	31	θ	θ	PROPN
ejpam-6249	176	32	∧	∧	PROPN
ejpam-6249	176	33	ϑ.	ϑ.	NOUN
ejpam-6249	176	34	since	since	SCONJ
ejpam-6249	176	35	θ	θ	PROPN
ejpam-6249	176	36	∈	∈	PROPN
ejpam-6249	176	37	(	(	PUNCT
ejpam-6249	176	38	µ,d	µ,d	NOUN
ejpam-6249	176	39	)	)	PUNCT
ejpam-6249	176	40	,	,	PUNCT
ejpam-6249	176	41	it	it	PRON
ejpam-6249	176	42	immediately	immediately	ADV
ejpam-6249	176	43	follows	follow	VERB
ejpam-6249	176	44	that	that	SCONJ
ejpam-6249	176	45	θ	θ	PROPN
ejpam-6249	176	46	∨	∨	NUM
ejpam-6249	176	47	µ	µ	PROPN
ejpam-6249	176	48	∈	∈	PROPN
ejpam-6249	176	49	d.	d.	NOUN
ejpam-6249	176	50	moreover	moreover	ADV
ejpam-6249	176	51	,	,	PUNCT
ejpam-6249	176	52	as	as	ADP
ejpam-6249	176	53	ϑ	ϑ	X
ejpam-6249	176	54	∈	∈	PROPN
ejpam-6249	176	55	(	(	PUNCT
ejpam-6249	176	56	(	(	PUNCT
ejpam-6249	176	57	µ,d),d	µ,d),d	NOUN
ejpam-6249	176	58	)	)	PUNCT
ejpam-6249	176	59	,	,	PUNCT
ejpam-6249	176	60	we	we	PRON
ejpam-6249	176	61	deduce	deduce	VERB
ejpam-6249	176	62	that	that	SCONJ
ejpam-6249	176	63	(	(	PUNCT
ejpam-6249	176	64	µ,d	µ,d	NOUN
ejpam-6249	176	65	)	)	PUNCT
ejpam-6249	176	66	⊆	⊆	NUM
ejpam-6249	176	67	(	(	PUNCT
ejpam-6249	176	68	ϑ,d	ϑ,d	NOUN
ejpam-6249	176	69	)	)	PUNCT
ejpam-6249	176	70	.	.	PUNCT
ejpam-6249	177	1	from	from	ADP
ejpam-6249	177	2	this	this	PRON
ejpam-6249	177	3	,	,	PUNCT
ejpam-6249	177	4	we	we	PRON
ejpam-6249	177	5	have	have	VERB
ejpam-6249	177	6	the	the	DET
ejpam-6249	177	7	following	follow	VERB
ejpam-6249	177	8	:	:	PUNCT
ejpam-6249	178	1	σ	σ	NOUN
ejpam-6249	178	2	=	=	PUNCT
ejpam-6249	178	3	θ	θ	X
ejpam-6249	178	4	∧	∧	PROPN
ejpam-6249	178	5	ϑ	ϑ	PRON
ejpam-6249	178	6	⇒	⇒	NOUN
ejpam-6249	178	7	(	(	PUNCT
ejpam-6249	178	8	θ	θ	PROPN
ejpam-6249	178	9	∧	∧	PROPN
ejpam-6249	178	10	ϑ,d	ϑ,d	NOUN
ejpam-6249	178	11	)	)	PUNCT
ejpam-6249	178	12	=	=	SYM
ejpam-6249	178	13	(	(	PUNCT
ejpam-6249	178	14	σ	σ	PROPN
ejpam-6249	178	15	,	,	PUNCT
ejpam-6249	178	16	d	d	NOUN
ejpam-6249	178	17	)	)	PUNCT
ejpam-6249	178	18	=	=	SYM
ejpam-6249	179	1	d	d	X
ejpam-6249	179	2	⇒	⇒	NOUN
ejpam-6249	179	3	(	(	PUNCT
ejpam-6249	179	4	θ	θ	PROPN
ejpam-6249	179	5	,	,	PUNCT
ejpam-6249	179	6	d	d	NOUN
ejpam-6249	179	7	)	)	PUNCT
ejpam-6249	179	8	∩	∩	NOUN
ejpam-6249	179	9	(	(	PUNCT
ejpam-6249	179	10	ϑ,d	ϑ,d	NOUN
ejpam-6249	179	11	)	)	PUNCT
ejpam-6249	179	12	=	=	SYM
ejpam-6249	180	1	d	d	X
ejpam-6249	180	2	⇒	⇒	NOUN
ejpam-6249	180	3	(	(	PUNCT
ejpam-6249	180	4	θ	θ	PROPN
ejpam-6249	180	5	,	,	PUNCT
ejpam-6249	180	6	d	d	NOUN
ejpam-6249	180	7	)	)	PUNCT
ejpam-6249	180	8	∩	∩	NOUN
ejpam-6249	180	9	(	(	PUNCT
ejpam-6249	180	10	µ,d	µ,d	NOUN
ejpam-6249	180	11	)	)	PUNCT
ejpam-6249	180	12	since	since	SCONJ
ejpam-6249	180	13	(	(	PUNCT
ejpam-6249	180	14	µ,d	µ,d	NOUN
ejpam-6249	180	15	)	)	PUNCT
ejpam-6249	180	16	⊆	⊆	NUM
ejpam-6249	180	17	(	(	PUNCT
ejpam-6249	180	18	ϑ,d	ϑ,d	NOUN
ejpam-6249	180	19	)	)	PUNCT
ejpam-6249	180	20	=	=	SYM
ejpam-6249	181	1	d	d	X
ejpam-6249	181	2	⇒	⇒	NOUN
ejpam-6249	181	3	(	(	PUNCT
ejpam-6249	181	4	θ	θ	PROPN
ejpam-6249	181	5	∧	∧	PROPN
ejpam-6249	181	6	µ,d	µ,d	NOUN
ejpam-6249	181	7	)	)	PUNCT
ejpam-6249	181	8	=	=	SYM
ejpam-6249	182	1	d	d	NOUN
ejpam-6249	182	2	⇒	⇒	NOUN
ejpam-6249	182	3	θ	θ	PROPN
ejpam-6249	182	4	∧	∧	PROPN
ejpam-6249	182	5	µ	µ	PRON
ejpam-6249	182	6	∈	∈	NOUN
ejpam-6249	182	7	d∞.	d∞.	PROPN
ejpam-6249	182	8	thus	thus	ADV
ejpam-6249	182	9	l	l	NOUN
ejpam-6249	182	10	is	be	AUX
ejpam-6249	182	11	hemicomplented	hemicomplente	VERB
ejpam-6249	182	12	.	.	PUNCT
ejpam-6249	183	1	in	in	ADP
ejpam-6249	183	2	the	the	DET
ejpam-6249	183	3	following	following	NOUN
ejpam-6249	183	4	,	,	PUNCT
ejpam-6249	183	5	another	another	DET
ejpam-6249	183	6	characterization	characterization	NOUN
ejpam-6249	183	7	is	be	AUX
ejpam-6249	183	8	given	give	VERB
ejpam-6249	183	9	for	for	ADP
ejpam-6249	183	10	the	the	DET
ejpam-6249	183	11	congruence	congruence	NOUN
ejpam-6249	183	12	ψ	ψ	NOUN
ejpam-6249	183	13	in	in	ADP
ejpam-6249	183	14	a	a	DET
ejpam-6249	183	15	hemicomplemented	hemicomplemente	VERB
ejpam-6249	183	16	adl	adl	NOUN
ejpam-6249	183	17	.	.	PUNCT
ejpam-6249	184	1	for	for	ADP
ejpam-6249	184	2	this	this	PRON
ejpam-6249	184	3	,	,	PUNCT
ejpam-6249	184	4	we	we	PRON
ejpam-6249	184	5	observe	observe	VERB
ejpam-6249	184	6	another	another	DET
ejpam-6249	184	7	congruence	congruence	NOUN
ejpam-6249	184	8	defined	define	VERB
ejpam-6249	184	9	in	in	ADP
ejpam-6249	184	10	terms	term	NOUN
ejpam-6249	184	11	of	of	ADP
ejpam-6249	184	12	d∞.	d∞.	ADP
ejpam-6249	184	13	definition	definition	NOUN
ejpam-6249	184	14	4	4	NUM
ejpam-6249	184	15	.	.	PUNCT
ejpam-6249	185	1	for	for	ADP
ejpam-6249	185	2	every	every	DET
ejpam-6249	185	3	θ	θ	PROPN
ejpam-6249	185	4	∈	∈	PROPN
ejpam-6249	185	5	l	l	NOUN
ejpam-6249	185	6	,	,	PUNCT
ejpam-6249	185	7	defined	define	VERB
ejpam-6249	185	8	⟨θ	⟨θ	NOUN
ejpam-6249	185	9	,	,	PUNCT
ejpam-6249	185	10	d∞⟩	d∞⟩	NOUN
ejpam-6249	185	11	=	=	SYM
ejpam-6249	185	12	{	{	PUNCT
ejpam-6249	185	13	µ	µ	X
ejpam-6249	185	14	∈	∈	X
ejpam-6249	185	15	l	l	NOUN
ejpam-6249	186	1	|	|	NOUN
ejpam-6249	186	2	µ	µ	X
ejpam-6249	186	3	∧	∧	PROPN
ejpam-6249	186	4	θ	θ	X
ejpam-6249	186	5	∈	∈	NOUN
ejpam-6249	186	6	d∞	d∞	NOUN
ejpam-6249	186	7	}	}	PUNCT
ejpam-6249	186	8	.	.	PUNCT
ejpam-6249	187	1	lemma	lemma	PROPN
ejpam-6249	187	2	2	2	NUM
ejpam-6249	187	3	.	.	X
ejpam-6249	187	4	for	for	ADP
ejpam-6249	187	5	any	any	DET
ejpam-6249	187	6	θ	θ	PROPN
ejpam-6249	187	7	,	,	PUNCT
ejpam-6249	187	8	ϑ	ϑ	X
ejpam-6249	187	9	∈	∈	PROPN
ejpam-6249	187	10	l	l	NOUN
ejpam-6249	187	11	,	,	PUNCT
ejpam-6249	187	12	we	we	PRON
ejpam-6249	187	13	obtain	obtain	VERB
ejpam-6249	187	14	the	the	DET
ejpam-6249	187	15	following	following	NOUN
ejpam-6249	187	16	:	:	PUNCT
ejpam-6249	187	17	(	(	PUNCT
ejpam-6249	187	18	1	1	X
ejpam-6249	187	19	)	)	PUNCT
ejpam-6249	187	20	⟨θ	⟨θ	NOUN
ejpam-6249	187	21	,	,	PUNCT
ejpam-6249	187	22	d∞⟩	d∞⟩	X
ejpam-6249	187	23	is	be	AUX
ejpam-6249	187	24	an	an	DET
ejpam-6249	187	25	ideal	ideal	NOUN
ejpam-6249	187	26	in	in	ADP
ejpam-6249	187	27	l	l	NOUN
ejpam-6249	187	28	;	;	PUNCT
ejpam-6249	187	29	(	(	PUNCT
ejpam-6249	187	30	2	2	X
ejpam-6249	187	31	)	)	PUNCT
ejpam-6249	187	32	d∞	d∞	NOUN
ejpam-6249	187	33	⊆	⊆	NUM
ejpam-6249	187	34	⟨θ	⟨θ	PUNCT
ejpam-6249	187	35	,	,	PUNCT
ejpam-6249	187	36	d∞⟩	d∞⟩	NOUN
ejpam-6249	187	37	;	;	PUNCT
ejpam-6249	187	38	(	(	PUNCT
ejpam-6249	187	39	3	3	X
ejpam-6249	187	40	)	)	PUNCT
ejpam-6249	187	41	θ	θ	NOUN
ejpam-6249	187	42	≤	≤	NOUN
ejpam-6249	187	43	ϑ	ϑ	X
ejpam-6249	187	44	implies	imply	VERB
ejpam-6249	187	45	⟨ϑ,d∞⟩	⟨ϑ,d∞⟩	NUM
ejpam-6249	187	46	⊆	⊆	NUM
ejpam-6249	187	47	⟨a	⟨a	NOUN
ejpam-6249	187	48	,	,	PUNCT
ejpam-6249	187	49	d∞⟩	d∞⟩	NOUN
ejpam-6249	187	50	;	;	PUNCT
ejpam-6249	187	51	(	(	PUNCT
ejpam-6249	187	52	4	4	X
ejpam-6249	187	53	)	)	PUNCT
ejpam-6249	187	54	⟨θ	⟨θ	X
ejpam-6249	187	55	∨	∨	X
ejpam-6249	187	56	ϑ,d∞⟩	ϑ,d∞⟩	PROPN
ejpam-6249	187	57	=	=	SYM
ejpam-6249	188	1	⟨θ	⟨θ	X
ejpam-6249	188	2	,	,	PUNCT
ejpam-6249	188	3	d∞⟩	d∞⟩	NOUN
ejpam-6249	188	4	∩	∩	NOUN
ejpam-6249	188	5	⟨ϑ,d∞⟩	⟨ϑ,d∞⟩	NUM
ejpam-6249	188	6	;	;	PUNCT
ejpam-6249	188	7	(	(	PUNCT
ejpam-6249	188	8	5	5	X
ejpam-6249	188	9	)	)	PUNCT
ejpam-6249	188	10	θ	θ	PROPN
ejpam-6249	188	11	∈	∈	PROPN
ejpam-6249	189	1	d∞	d∞	PROPN
ejpam-6249	189	2	iff	iff	NOUN
ejpam-6249	189	3	⟨θ	⟨θ	PUNCT
ejpam-6249	189	4	,	,	PUNCT
ejpam-6249	189	5	d∞⟩	d∞⟩	NOUN
ejpam-6249	189	6	=	=	SYM
ejpam-6249	189	7	l.	l.	PROPN
ejpam-6249	189	8	proof	proof	NOUN
ejpam-6249	189	9	.	.	PUNCT
ejpam-6249	190	1	(	(	PUNCT
ejpam-6249	190	2	1	1	X
ejpam-6249	190	3	)	)	PUNCT
ejpam-6249	190	4	it	it	PRON
ejpam-6249	190	5	is	be	AUX
ejpam-6249	190	6	evident	evident	ADJ
ejpam-6249	190	7	that	that	SCONJ
ejpam-6249	190	8	0	0	NUM
ejpam-6249	190	9	∈	∈	NOUN
ejpam-6249	190	10	⟨θ	⟨θ	NOUN
ejpam-6249	190	11	,	,	PUNCT
ejpam-6249	190	12	d∞⟩.	d∞⟩.	PROPN
ejpam-6249	190	13	let	let	VERB
ejpam-6249	190	14	µ	µ	NUM
ejpam-6249	190	15	,	,	PUNCT
ejpam-6249	190	16	π	π	PROPN
ejpam-6249	190	17	∈	∈	PROPN
ejpam-6249	190	18	⟨θ	⟨θ	NOUN
ejpam-6249	190	19	,	,	PUNCT
ejpam-6249	190	20	d∞⟩.	d∞⟩.	PROPN
ejpam-6249	190	21	then	then	ADV
ejpam-6249	190	22	θ	θ	PROPN
ejpam-6249	190	23	∧	∧	PROPN
ejpam-6249	190	24	µ	µ	PRON
ejpam-6249	190	25	∈	∈	NOUN
ejpam-6249	190	26	d∞	d∞	NOUN
ejpam-6249	190	27	and	and	CCONJ
ejpam-6249	191	1	θ	θ	NOUN
ejpam-6249	191	2	∧	∧	PROPN
ejpam-6249	192	1	π	π	X
ejpam-6249	192	2	∈	∈	PROPN
ejpam-6249	193	1	d∞.	d∞.	INTJ
ejpam-6249	193	2	hence	hence	ADV
ejpam-6249	193	3	(	(	PUNCT
ejpam-6249	193	4	(	(	PUNCT
ejpam-6249	193	5	θ	θ	PROPN
ejpam-6249	193	6	∧	∧	PROPN
ejpam-6249	193	7	(	(	PUNCT
ejpam-6249	193	8	µ	µ	X
ejpam-6249	193	9	∨	∨	X
ejpam-6249	193	10	π),d),d	π),d),d	NOUN
ejpam-6249	193	11	)	)	PUNCT
ejpam-6249	193	12	=	=	SYM
ejpam-6249	193	13	(	(	PUNCT
ejpam-6249	193	14	(	(	PUNCT
ejpam-6249	193	15	(	(	PUNCT
ejpam-6249	193	16	θ	θ	PROPN
ejpam-6249	193	17	∧	∧	PROPN
ejpam-6249	193	18	µ	µ	X
ejpam-6249	193	19	)	)	PUNCT
ejpam-6249	193	20	∨	∨	NOUN
ejpam-6249	193	21	(	(	PUNCT
ejpam-6249	193	22	θ	θ	PROPN
ejpam-6249	193	23	∧	∧	PROPN
ejpam-6249	193	24	π),d),d	π),d),d	PROPN
ejpam-6249	193	25	)	)	PUNCT
ejpam-6249	193	26	=	=	SYM
ejpam-6249	193	27	(	(	PUNCT
ejpam-6249	193	28	(	(	PUNCT
ejpam-6249	193	29	(	(	PUNCT
ejpam-6249	193	30	θ	θ	PROPN
ejpam-6249	193	31	∧	∧	PROPN
ejpam-6249	193	32	µ),d),d	µ),d),d	NOUN
ejpam-6249	193	33	)	)	PUNCT
ejpam-6249	193	34	∩	∩	NOUN
ejpam-6249	193	35	(	(	PUNCT
ejpam-6249	193	36	(	(	PUNCT
ejpam-6249	193	37	(	(	PUNCT
ejpam-6249	193	38	θ	θ	PROPN
ejpam-6249	193	39	∧	∧	PROPN
ejpam-6249	193	40	π),d),d	π),d),d	PROPN
ejpam-6249	193	41	)	)	PUNCT
ejpam-6249	193	42	=	=	SYM
ejpam-6249	194	1	l	l	NOUN
ejpam-6249	194	2	∩	∩	X
ejpam-6249	194	3	l	l	NOUN
ejpam-6249	194	4	=	=	PUNCT
ejpam-6249	194	5	l.	l.	PROPN
ejpam-6249	194	6	hence	hence	ADV
ejpam-6249	194	7	(	(	PUNCT
ejpam-6249	194	8	θ	θ	PROPN
ejpam-6249	194	9	∧	∧	PROPN
ejpam-6249	194	10	(	(	PUNCT
ejpam-6249	194	11	µ	µ	X
ejpam-6249	194	12	∨	∨	NUM
ejpam-6249	194	13	π),d	π),d	NOUN
ejpam-6249	194	14	)	)	PUNCT
ejpam-6249	194	15	=	=	SYM
ejpam-6249	194	16	(	(	PUNCT
ejpam-6249	194	17	l	l	NOUN
ejpam-6249	194	18	,	,	PUNCT
ejpam-6249	194	19	d	d	NOUN
ejpam-6249	194	20	)	)	PUNCT
ejpam-6249	194	21	=	=	SYM
ejpam-6249	195	1	d	d	NOUN
ejpam-6249	195	2	,	,	PUNCT
ejpam-6249	195	3	which	which	PRON
ejpam-6249	195	4	gives	give	VERB
ejpam-6249	195	5	that	that	PRON
ejpam-6249	195	6	θ	θ	PROPN
ejpam-6249	195	7	∧	∧	PROPN
ejpam-6249	195	8	(	(	PUNCT
ejpam-6249	195	9	µ	µ	X
ejpam-6249	195	10	∨	∨	NUM
ejpam-6249	195	11	π	π	NOUN
ejpam-6249	195	12	)	)	PUNCT
ejpam-6249	195	13	∈	∈	PROPN
ejpam-6249	195	14	d∞.	d∞.	PROPN
ejpam-6249	195	15	thus	thus	ADV
ejpam-6249	195	16	µ	µ	X
ejpam-6249	195	17	∨	∨	NUM
ejpam-6249	195	18	π	π	PROPN
ejpam-6249	195	19	∈	∈	PROPN
ejpam-6249	195	20	⟨θ	⟨θ	X
ejpam-6249	195	21	,	,	PUNCT
ejpam-6249	195	22	d∞⟩.	d∞⟩.	PROPN
ejpam-6249	195	23	let	let	VERB
ejpam-6249	195	24	µ	µ	PRON
ejpam-6249	195	25	∈	∈	NOUN
ejpam-6249	195	26	⟨θ	⟨θ	X
ejpam-6249	195	27	,	,	PUNCT
ejpam-6249	195	28	d∞⟩	d∞⟩	NOUN
ejpam-6249	195	29	and	and	CCONJ
ejpam-6249	195	30	π	π	PROPN
ejpam-6249	195	31	≤	≤	PROPN
ejpam-6249	195	32	µ.	µ.	NOUN
ejpam-6249	195	33	then	then	ADV
ejpam-6249	195	34	π	π	PROPN
ejpam-6249	195	35	∧	∧	PROPN
ejpam-6249	195	36	θ	θ	PROPN
ejpam-6249	195	37	≤	≤	NOUN
ejpam-6249	195	38	µ	µ	PRON
ejpam-6249	195	39	∧	∧	NOUN
ejpam-6249	195	40	θ	θ	PROPN
ejpam-6249	195	41	∈	∈	PROPN
ejpam-6249	196	1	d∞.	d∞.	INTJ
ejpam-6249	196	2	hence	hence	ADV
ejpam-6249	196	3	π	π	PROPN
ejpam-6249	196	4	∈	∈	PROPN
ejpam-6249	196	5	⟨θ	⟨θ	PUNCT
ejpam-6249	196	6	,	,	PUNCT
ejpam-6249	196	7	d∞⟩	d∞⟩	NOUN
ejpam-6249	196	8	,	,	PUNCT
ejpam-6249	196	9	which	which	PRON
ejpam-6249	196	10	leads	lead	VERB
ejpam-6249	196	11	that	that	SCONJ
ejpam-6249	196	12	⟨θ	⟨θ	PROPN
ejpam-6249	196	13	,	,	PUNCT
ejpam-6249	196	14	d∞⟩	d∞⟩	PROPN
ejpam-6249	196	15	is	be	AUX
ejpam-6249	196	16	an	an	DET
ejpam-6249	196	17	ideal	ideal	NOUN
ejpam-6249	196	18	in	in	ADP
ejpam-6249	196	19	l.	l.	PROPN
ejpam-6249	196	20	(	(	PUNCT
ejpam-6249	196	21	2	2	X
ejpam-6249	196	22	)	)	PUNCT
ejpam-6249	196	23	it	it	PRON
ejpam-6249	196	24	follows	follow	VERB
ejpam-6249	196	25	directly	directly	ADV
ejpam-6249	196	26	.	.	PUNCT
ejpam-6249	197	1	(	(	PUNCT
ejpam-6249	197	2	3	3	X
ejpam-6249	197	3	)	)	PUNCT
ejpam-6249	197	4	it	it	PRON
ejpam-6249	197	5	follows	follow	VERB
ejpam-6249	197	6	directly	directly	ADV
ejpam-6249	197	7	.	.	PUNCT
ejpam-6249	198	1	(	(	PUNCT
ejpam-6249	198	2	4	4	X
ejpam-6249	198	3	)	)	PUNCT
ejpam-6249	198	4	it	it	PRON
ejpam-6249	198	5	can	can	AUX
ejpam-6249	198	6	be	be	AUX
ejpam-6249	198	7	seen	see	VERB
ejpam-6249	198	8	that	that	SCONJ
ejpam-6249	198	9	⟨θ	⟨θ	PRON
ejpam-6249	198	10	∨ϑ,d∞⟩	∨ϑ,d∞⟩	NUM
ejpam-6249	198	11	⊆	⊆	NUM
ejpam-6249	198	12	⟨θ	⟨θ	NUM
ejpam-6249	198	13	,	,	PUNCT
ejpam-6249	198	14	d∞⟩	d∞⟩	ADJ
ejpam-6249	198	15	∩	∩	ADJ
ejpam-6249	198	16	⟨ϑ,d∞⟩.	⟨ϑ,d∞⟩.	NOUN
ejpam-6249	198	17	let	let	VERB
ejpam-6249	198	18	µ	µ	X
ejpam-6249	198	19	∈	∈	NOUN
ejpam-6249	198	20	⟨θ	⟨θ	X
ejpam-6249	198	21	,	,	PUNCT
ejpam-6249	198	22	d∞⟩	d∞⟩	ADJ
ejpam-6249	198	23	∩	∩	ADJ
ejpam-6249	198	24	⟨ϑ,d∞⟩.	⟨ϑ,d∞⟩.	PROPN
ejpam-6249	198	25	then	then	ADV
ejpam-6249	198	26	θ∧µ	θ∧µ	VERB
ejpam-6249	198	27	∈	∈	PROPN
ejpam-6249	198	28	d∞	d∞	NOUN
ejpam-6249	198	29	and	and	CCONJ
ejpam-6249	198	30	ϑ∧µ	ϑ∧µ	NOUN
ejpam-6249	198	31	∈	∈	PROPN
ejpam-6249	198	32	d∞.	d∞.	PROPN
ejpam-6249	198	33	as	as	SCONJ
ejpam-6249	198	34	d∞	d∞	PROPN
ejpam-6249	198	35	forms	form	VERB
ejpam-6249	198	36	an	an	DET
ejpam-6249	198	37	ideal	ideal	NOUN
ejpam-6249	198	38	,	,	PUNCT
ejpam-6249	198	39	we	we	PRON
ejpam-6249	198	40	obtain	obtain	VERB
ejpam-6249	199	1	(	(	PUNCT
ejpam-6249	199	2	θ∨ϑ)∧µ	θ∨ϑ)∧µ	PROPN
ejpam-6249	199	3	=	=	SYM
ejpam-6249	199	4	(	(	PUNCT
ejpam-6249	199	5	θ∧µ)∨(ϑ∧µ	θ∧µ)∨(ϑ∧µ	PROPN
ejpam-6249	199	6	)	)	PUNCT
ejpam-6249	199	7	∈	∈	PROPN
ejpam-6249	199	8	d∞.	d∞.	PROPN
ejpam-6249	200	1	thus	thus	ADV
ejpam-6249	200	2	µ	µ	X
ejpam-6249	200	3	∈	∈	NOUN
ejpam-6249	200	4	⟨θ	⟨θ	X
ejpam-6249	200	5	∨	∨	X
ejpam-6249	200	6	ϑ,d∞⟩.	ϑ,d∞⟩.	ADV
ejpam-6249	200	7	(	(	PUNCT
ejpam-6249	200	8	5	5	NUM
ejpam-6249	200	9	)	)	PUNCT
ejpam-6249	200	10	assume	assume	VERB
ejpam-6249	200	11	that	that	SCONJ
ejpam-6249	200	12	θ	θ	PROPN
ejpam-6249	200	13	∈	∈	PROPN
ejpam-6249	200	14	d∞.	d∞.	PROPN
ejpam-6249	200	15	as	as	SCONJ
ejpam-6249	200	16	d∞	d∞	PROPN
ejpam-6249	200	17	forms	form	VERB
ejpam-6249	200	18	an	an	DET
ejpam-6249	200	19	ideal	ideal	NOUN
ejpam-6249	200	20	,	,	PUNCT
ejpam-6249	200	21	we	we	PRON
ejpam-6249	200	22	obtain	obtain	VERB
ejpam-6249	200	23	θ	θ	PROPN
ejpam-6249	200	24	∧	∧	PROPN
ejpam-6249	200	25	µ	µ	PRON
ejpam-6249	200	26	∈	∈	NOUN
ejpam-6249	200	27	d∞	d∞	NOUN
ejpam-6249	200	28	for	for	ADP
ejpam-6249	200	29	each	each	DET
ejpam-6249	200	30	µ	µ	PRON
ejpam-6249	200	31	∈	∈	PROPN
ejpam-6249	200	32	l.	l.	NOUN
ejpam-6249	200	33	hence	hence	ADV
ejpam-6249	200	34	⟨θ	⟨θ	PROPN
ejpam-6249	200	35	,	,	PUNCT
ejpam-6249	200	36	d∞⟩	d∞⟩	NOUN
ejpam-6249	200	37	=	=	SYM
ejpam-6249	200	38	l.	l.	PROPN
ejpam-6249	200	39	on	on	ADP
ejpam-6249	200	40	the	the	DET
ejpam-6249	200	41	other	other	ADJ
ejpam-6249	200	42	hand	hand	NOUN
ejpam-6249	200	43	,	,	PUNCT
ejpam-6249	200	44	suppose	suppose	VERB
ejpam-6249	200	45	that	that	SCONJ
ejpam-6249	200	46	⟨θ	⟨θ	PROPN
ejpam-6249	200	47	,	,	PUNCT
ejpam-6249	200	48	d∞⟩	d∞⟩	NOUN
ejpam-6249	200	49	=	=	SYM
ejpam-6249	200	50	l.	l.	PROPN
ejpam-6249	200	51	then	then	ADV
ejpam-6249	200	52	m	m	VERB
ejpam-6249	200	53	∈	∈	PROPN
ejpam-6249	200	54	⟨θ	⟨θ	X
ejpam-6249	200	55	,	,	PUNCT
ejpam-6249	200	56	d∞⟩	d∞⟩	NOUN
ejpam-6249	200	57	,	,	PUNCT
ejpam-6249	200	58	for	for	ADP
ejpam-6249	200	59	all	all	DET
ejpam-6249	200	60	maximal	maximal	ADJ
ejpam-6249	200	61	elements	element	NOUN
ejpam-6249	200	62	m	m	VERB
ejpam-6249	200	63	in	in	ADP
ejpam-6249	200	64	l.	l.	PROPN
ejpam-6249	200	65	hence	hence	ADV
ejpam-6249	200	66	θ	θ	PROPN
ejpam-6249	201	1	=	=	PUNCT
ejpam-6249	201	2	m	m	VERB
ejpam-6249	202	1	∧	∧	NOUN
ejpam-6249	202	2	θ	θ	PROPN
ejpam-6249	202	3	∈	∈	PROPN
ejpam-6249	202	4	d∞.	d∞.	PROPN
ejpam-6249	202	5	n.	n.	PROPN
ejpam-6249	202	6	rafi	rafi	PROPN
ejpam-6249	202	7	et	et	PROPN
ejpam-6249	202	8	al	al	PROPN
ejpam-6249	202	9	.	.	PUNCT
ejpam-6249	202	10	/	/	SYM
ejpam-6249	202	11	eur	eur	PROPN
ejpam-6249	202	12	.	.	PUNCT
ejpam-6249	203	1	j.	j.	PROPN
ejpam-6249	203	2	pure	pure	PROPN
ejpam-6249	203	3	appl	appl	PROPN
ejpam-6249	203	4	.	.	PROPN
ejpam-6249	203	5	math	math	PROPN
ejpam-6249	203	6	,	,	PUNCT
ejpam-6249	203	7	18	18	NUM
ejpam-6249	203	8	(	(	PUNCT
ejpam-6249	203	9	4	4	NUM
ejpam-6249	203	10	)	)	PUNCT
ejpam-6249	203	11	(	(	PUNCT
ejpam-6249	203	12	2025	2025	NUM
ejpam-6249	203	13	)	)	PUNCT
ejpam-6249	203	14	,	,	PUNCT
ejpam-6249	203	15	6249	6249	NUM
ejpam-6249	203	16	9	9	NUM
ejpam-6249	203	17	of	of	ADP
ejpam-6249	203	18	11	11	NUM
ejpam-6249	203	19	proposition	proposition	NOUN
ejpam-6249	203	20	5	5	NUM
ejpam-6249	203	21	.	.	PUNCT
ejpam-6249	203	22	define	define	VERB
ejpam-6249	203	23	a	a	DET
ejpam-6249	203	24	relation	relation	NOUN
ejpam-6249	203	25	ψd∞	ψd∞	PROPN
ejpam-6249	203	26	on	on	ADP
ejpam-6249	203	27	l	l	PROPN
ejpam-6249	203	28	as	as	SCONJ
ejpam-6249	203	29	follows	follow	VERB
ejpam-6249	203	30	:	:	PUNCT
ejpam-6249	203	31	(	(	PUNCT
ejpam-6249	203	32	θ	θ	NOUN
ejpam-6249	203	33	,	,	PUNCT
ejpam-6249	203	34	ϑ	ϑ	NOUN
ejpam-6249	203	35	)	)	PUNCT
ejpam-6249	203	36	∈	∈	PROPN
ejpam-6249	203	37	ψd∞	ψd∞	PROPN
ejpam-6249	204	1	if	if	SCONJ
ejpam-6249	204	2	and	and	CCONJ
ejpam-6249	204	3	only	only	ADV
ejpam-6249	204	4	if	if	SCONJ
ejpam-6249	204	5	⟨θ	⟨θ	NUM
ejpam-6249	204	6	,	,	PUNCT
ejpam-6249	204	7	d∞⟩	d∞⟩	NOUN
ejpam-6249	204	8	=	=	SYM
ejpam-6249	204	9	⟨ϑ,d∞⟩	⟨ϑ,d∞⟩	NUM
ejpam-6249	204	10	for	for	ADP
ejpam-6249	204	11	all	all	DET
ejpam-6249	204	12	θ	θ	PROPN
ejpam-6249	204	13	,	,	PUNCT
ejpam-6249	204	14	ϑ	ϑ	X
ejpam-6249	204	15	∈	∈	PROPN
ejpam-6249	204	16	l.	l.	NOUN
ejpam-6249	204	17	then	then	ADV
ejpam-6249	204	18	ψd∞	ψd∞	PROPN
ejpam-6249	204	19	is	be	AUX
ejpam-6249	204	20	congruence	congruence	NOUN
ejpam-6249	204	21	on	on	ADP
ejpam-6249	204	22	l.	l.	PROPN
ejpam-6249	204	23	proof	proof	PROPN
ejpam-6249	204	24	.	.	PUNCT
ejpam-6249	205	1	it	it	PRON
ejpam-6249	205	2	is	be	AUX
ejpam-6249	205	3	evident	evident	ADJ
ejpam-6249	205	4	that	that	SCONJ
ejpam-6249	205	5	ψd∞	ψd∞	PROPN
ejpam-6249	205	6	is	be	AUX
ejpam-6249	205	7	an	an	DET
ejpam-6249	205	8	equivalence	equivalence	NOUN
ejpam-6249	205	9	relation	relation	NOUN
ejpam-6249	205	10	on	on	ADP
ejpam-6249	205	11	l.	l.	PROPN
ejpam-6249	205	12	let	let	PROPN
ejpam-6249	205	13	(	(	PUNCT
ejpam-6249	205	14	µ	µ	NUM
ejpam-6249	205	15	,	,	PUNCT
ejpam-6249	205	16	π	π	NOUN
ejpam-6249	205	17	)	)	PUNCT
ejpam-6249	205	18	∈	∈	PROPN
ejpam-6249	205	19	ψd∞	ψd∞	PROPN
ejpam-6249	205	20	.	.	PUNCT
ejpam-6249	206	1	for	for	ADP
ejpam-6249	206	2	each	each	DET
ejpam-6249	206	3	σ	σ	PROPN
ejpam-6249	206	4	∈	∈	PROPN
ejpam-6249	206	5	l	l	NOUN
ejpam-6249	206	6	,	,	PUNCT
ejpam-6249	206	7	we	we	PRON
ejpam-6249	206	8	obtain	obtain	VERB
ejpam-6249	206	9	⟨µ∨σ	⟨µ∨σ	NOUN
ejpam-6249	206	10	,	,	PUNCT
ejpam-6249	206	11	d∞⟩	d∞⟩	NOUN
ejpam-6249	207	1	=	=	SYM
ejpam-6249	207	2	⟨µ,d∞⟩∩⟨σ	⟨µ,d∞⟩∩⟨σ	PROPN
ejpam-6249	207	3	,	,	PUNCT
ejpam-6249	207	4	d∞⟩	d∞⟩	NOUN
ejpam-6249	207	5	=	=	SYM
ejpam-6249	207	6	⟨π	⟨π	X
ejpam-6249	207	7	,	,	PUNCT
ejpam-6249	207	8	d∞⟩∩⟨σ	d∞⟩∩⟨σ	NUM
ejpam-6249	207	9	,	,	PUNCT
ejpam-6249	207	10	d∞⟩	d∞⟩	NOUN
ejpam-6249	207	11	=	=	SYM
ejpam-6249	207	12	⟨π∨σ	⟨π∨σ	NOUN
ejpam-6249	207	13	,	,	PUNCT
ejpam-6249	207	14	d∞⟩.	d∞⟩.	PROPN
ejpam-6249	207	15	thus	thus	ADV
ejpam-6249	207	16	(	(	PUNCT
ejpam-6249	207	17	µ∨σ	µ∨σ	ADJ
ejpam-6249	207	18	,	,	PUNCT
ejpam-6249	207	19	π∨σ	π∨σ	PROPN
ejpam-6249	207	20	)	)	PUNCT
ejpam-6249	207	21	∈	∈	PROPN
ejpam-6249	207	22	ψd∞	ψd∞	PROPN
ejpam-6249	207	23	.	.	PUNCT
ejpam-6249	208	1	for	for	ADP
ejpam-6249	208	2	any	any	DET
ejpam-6249	208	3	ν	ν	NOUN
ejpam-6249	208	4	∈	∈	PROPN
ejpam-6249	208	5	l	l	NOUN
ejpam-6249	208	6	,	,	PUNCT
ejpam-6249	208	7	we	we	PRON
ejpam-6249	208	8	get	get	VERB
ejpam-6249	208	9	ν	ν	PRON
ejpam-6249	208	10	∈	∈	PROPN
ejpam-6249	208	11	⟨µ∧σ	⟨µ∧σ	X
ejpam-6249	208	12	,	,	PUNCT
ejpam-6249	208	13	d∞⟩	d∞⟩	PROPN
ejpam-6249	208	14	⇔	⇔	PROPN
ejpam-6249	208	15	ν∧µ∧σ	ν∧µ∧σ	PROPN
ejpam-6249	208	16	∈	∈	PROPN
ejpam-6249	208	17	d∞	d∞	PROPN
ejpam-6249	208	18	⇔	⇔	X
ejpam-6249	208	19	ν∧σ	ν∧σ	PROPN
ejpam-6249	208	20	∈	∈	PROPN
ejpam-6249	208	21	⟨µ,d∞⟩	⟨µ,d∞⟩	NUM
ejpam-6249	208	22	=	=	SYM
ejpam-6249	208	23	⟨π	⟨π	X
ejpam-6249	208	24	,	,	PUNCT
ejpam-6249	208	25	d∞⟩	d∞⟩	NOUN
ejpam-6249	208	26	⇔	⇔	PROPN
ejpam-6249	208	27	ν∧σ∧π	ν∧σ∧π	PROPN
ejpam-6249	208	28	∈	∈	PROPN
ejpam-6249	208	29	d∞	d∞	NOUN
ejpam-6249	208	30	⇔	⇔	X
ejpam-6249	208	31	ν	ν	X
ejpam-6249	208	32	∈	∈	PROPN
ejpam-6249	208	33	⟨π∧σ	⟨π∧σ	NOUN
ejpam-6249	208	34	,	,	PUNCT
ejpam-6249	208	35	d∞⟩.	d∞⟩.	PROPN
ejpam-6249	208	36	thus	thus	ADV
ejpam-6249	208	37	⟨µ∧σ	⟨µ∧σ	NOUN
ejpam-6249	208	38	,	,	PUNCT
ejpam-6249	208	39	d∞⟩	d∞⟩	NOUN
ejpam-6249	208	40	=	=	SYM
ejpam-6249	208	41	⟨π∧σ	⟨π∧σ	NOUN
ejpam-6249	208	42	,	,	PUNCT
ejpam-6249	208	43	d∞⟩.	d∞⟩.	PROPN
ejpam-6249	208	44	therefore	therefore	ADV
ejpam-6249	208	45	(	(	PUNCT
ejpam-6249	208	46	µ	µ	X
ejpam-6249	208	47	∧	∧	PROPN
ejpam-6249	208	48	σ	σ	PROPN
ejpam-6249	208	49	,	,	PUNCT
ejpam-6249	208	50	π	π	PROPN
ejpam-6249	208	51	∧	∧	PROPN
ejpam-6249	208	52	σ	σ	PROPN
ejpam-6249	208	53	)	)	PUNCT
ejpam-6249	208	54	∈	∈	PROPN
ejpam-6249	208	55	ψd∞	ψd∞	PROPN
ejpam-6249	208	56	.	.	PUNCT
ejpam-6249	209	1	thus	thus	ADV
ejpam-6249	209	2	ψd∞	ψd∞	PROPN
ejpam-6249	209	3	is	be	AUX
ejpam-6249	209	4	a	a	DET
ejpam-6249	209	5	congruence	congruence	NOUN
ejpam-6249	209	6	.	.	PUNCT
ejpam-6249	210	1	theorem	theorem	NOUN
ejpam-6249	210	2	3	3	NUM
ejpam-6249	210	3	.	.	PUNCT
ejpam-6249	211	1	in	in	ADP
ejpam-6249	211	2	a	a	DET
ejpam-6249	211	3	hemicomplemented	hemicomplemente	VERB
ejpam-6249	211	4	adl	adl	PROPN
ejpam-6249	211	5	l	l	PROPN
ejpam-6249	211	6	,	,	PUNCT
ejpam-6249	211	7	we	we	PRON
ejpam-6249	211	8	have	have	VERB
ejpam-6249	211	9	θ	θ	PROPN
ejpam-6249	211	10	=	=	SYM
ejpam-6249	211	11	ψd∞	ψd∞	PROPN
ejpam-6249	211	12	.	.	PUNCT
ejpam-6249	212	1	proof	proof	NOUN
ejpam-6249	212	2	.	.	PUNCT
ejpam-6249	213	1	let	let	VERB
ejpam-6249	213	2	(	(	PUNCT
ejpam-6249	213	3	µ	µ	NUM
ejpam-6249	213	4	,	,	PUNCT
ejpam-6249	213	5	π	π	NOUN
ejpam-6249	213	6	)	)	PUNCT
ejpam-6249	213	7	∈	∈	PROPN
ejpam-6249	213	8	θ	θ	PROPN
ejpam-6249	213	9	.	.	PUNCT
ejpam-6249	214	1	then	then	ADV
ejpam-6249	214	2	we	we	PRON
ejpam-6249	214	3	obtain	obtain	VERB
ejpam-6249	214	4	(	(	PUNCT
ejpam-6249	214	5	µ,d	µ,d	NOUN
ejpam-6249	214	6	)	)	PUNCT
ejpam-6249	214	7	=	=	SYM
ejpam-6249	214	8	(	(	PUNCT
ejpam-6249	214	9	π	π	PROPN
ejpam-6249	214	10	,	,	PUNCT
ejpam-6249	214	11	d	d	NOUN
ejpam-6249	214	12	)	)	PUNCT
ejpam-6249	214	13	.	.	PUNCT
ejpam-6249	215	1	for	for	ADP
ejpam-6249	215	2	any	any	DET
ejpam-6249	215	3	ν	ν	NOUN
ejpam-6249	215	4	∈	∈	PROPN
ejpam-6249	215	5	l	l	NOUN
ejpam-6249	215	6	,	,	PUNCT
ejpam-6249	215	7	we	we	PRON
ejpam-6249	215	8	have	have	VERB
ejpam-6249	215	9	the	the	DET
ejpam-6249	215	10	following	following	NOUN
ejpam-6249	215	11	:	:	PUNCT
ejpam-6249	215	12	ν	ν	PROPN
ejpam-6249	215	13	∈	∈	PROPN
ejpam-6249	215	14	⟨µ,d∞⟩	⟨µ,d∞⟩	PUNCT
ejpam-6249	215	15	⇔	⇔	X
ejpam-6249	215	16	µ	µ	PROPN
ejpam-6249	215	17	∧	∧	PROPN
ejpam-6249	215	18	ν	ν	NOUN
ejpam-6249	215	19	∈	∈	PROPN
ejpam-6249	215	20	d∞	d∞	PROPN
ejpam-6249	215	21	⇔	⇔	X
ejpam-6249	215	22	(	(	PUNCT
ejpam-6249	215	23	µ,d	µ,d	NOUN
ejpam-6249	215	24	)	)	PUNCT
ejpam-6249	215	25	∩	∩	NOUN
ejpam-6249	215	26	(	(	PUNCT
ejpam-6249	215	27	ν	ν	NOUN
ejpam-6249	215	28	,	,	PUNCT
ejpam-6249	215	29	d	d	NOUN
ejpam-6249	215	30	)	)	PUNCT
ejpam-6249	215	31	=	=	SYM
ejpam-6249	215	32	(	(	PUNCT
ejpam-6249	215	33	µ	µ	X
ejpam-6249	215	34	∧	∧	NOUN
ejpam-6249	215	35	ν	ν	NOUN
ejpam-6249	215	36	,	,	PUNCT
ejpam-6249	215	37	d	d	NOUN
ejpam-6249	215	38	)	)	PUNCT
ejpam-6249	215	39	=	=	SYM
ejpam-6249	215	40	d	d	X
ejpam-6249	215	41	⇔	⇔	X
ejpam-6249	215	42	(	(	PUNCT
ejpam-6249	215	43	π	π	PROPN
ejpam-6249	215	44	∧	∧	PROPN
ejpam-6249	215	45	ν	ν	PROPN
ejpam-6249	215	46	,	,	PUNCT
ejpam-6249	215	47	d	d	NOUN
ejpam-6249	215	48	)	)	PUNCT
ejpam-6249	215	49	=	=	SYM
ejpam-6249	215	50	(	(	PUNCT
ejpam-6249	215	51	π	π	PROPN
ejpam-6249	215	52	,	,	PUNCT
ejpam-6249	215	53	d	d	NOUN
ejpam-6249	215	54	)	)	PUNCT
ejpam-6249	215	55	∩	∩	NOUN
ejpam-6249	215	56	(	(	PUNCT
ejpam-6249	215	57	ν	ν	NOUN
ejpam-6249	215	58	,	,	PUNCT
ejpam-6249	215	59	d	d	NOUN
ejpam-6249	215	60	)	)	PUNCT
ejpam-6249	215	61	=	=	SYM
ejpam-6249	216	1	d	d	X
ejpam-6249	216	2	⇔	⇔	PROPN
ejpam-6249	216	3	π	π	PROPN
ejpam-6249	216	4	∧	∧	PROPN
ejpam-6249	216	5	ν	ν	PROPN
ejpam-6249	216	6	∈	∈	PROPN
ejpam-6249	216	7	d∞	d∞	PROPN
ejpam-6249	216	8	⇔	⇔	X
ejpam-6249	216	9	ν	ν	X
ejpam-6249	216	10	∈	∈	PROPN
ejpam-6249	216	11	⟨π	⟨π	NOUN
ejpam-6249	216	12	,	,	PUNCT
ejpam-6249	216	13	d∞⟩.	d∞⟩.	PROPN
ejpam-6249	216	14	hence	hence	ADV
ejpam-6249	216	15	⟨µ,d∞⟩	⟨µ,d∞⟩	NUM
ejpam-6249	216	16	=	=	SYM
ejpam-6249	216	17	⟨π	⟨π	NOUN
ejpam-6249	216	18	,	,	PUNCT
ejpam-6249	216	19	d∞⟩.	d∞⟩.	PROPN
ejpam-6249	216	20	thus	thus	ADV
ejpam-6249	216	21	(	(	PUNCT
ejpam-6249	216	22	µ	µ	X
ejpam-6249	216	23	,	,	PUNCT
ejpam-6249	216	24	π	π	NOUN
ejpam-6249	216	25	)	)	PUNCT
ejpam-6249	216	26	∈	∈	PROPN
ejpam-6249	216	27	ψd∞	ψd∞	PROPN
ejpam-6249	216	28	.	.	PUNCT
ejpam-6249	217	1	therefore	therefore	ADV
ejpam-6249	217	2	θ	θ	PROPN
ejpam-6249	217	3	⊆	⊆	NUM
ejpam-6249	217	4	ψd∞	ψd∞	PROPN
ejpam-6249	217	5	.	.	PUNCT
ejpam-6249	218	1	conversely	conversely	ADV
ejpam-6249	218	2	,	,	PUNCT
ejpam-6249	218	3	let	let	VERB
ejpam-6249	218	4	(	(	PUNCT
ejpam-6249	218	5	µ	µ	NUM
ejpam-6249	218	6	,	,	PUNCT
ejpam-6249	218	7	π	π	NOUN
ejpam-6249	218	8	)	)	PUNCT
ejpam-6249	218	9	∈	∈	PROPN
ejpam-6249	218	10	ψd∞	ψd∞	PROPN
ejpam-6249	218	11	for	for	ADP
ejpam-6249	218	12	µ	µ	NUM
ejpam-6249	218	13	,	,	PUNCT
ejpam-6249	218	14	π	π	PROPN
ejpam-6249	218	15	∈	∈	PROPN
ejpam-6249	218	16	l.	l.	PROPN
ejpam-6249	218	17	then	then	ADV
ejpam-6249	218	18	⟨µ,d∞⟩	⟨µ,d∞⟩	NUM
ejpam-6249	218	19	=	=	SYM
ejpam-6249	218	20	⟨π	⟨π	NOUN
ejpam-6249	218	21	,	,	PUNCT
ejpam-6249	218	22	d∞⟩.	d∞⟩.	PROPN
ejpam-6249	218	23	since	since	SCONJ
ejpam-6249	218	24	l	l	NOUN
ejpam-6249	218	25	is	be	AUX
ejpam-6249	218	26	hemicomplemented	hemicomplemente	VERB
ejpam-6249	218	27	,	,	PUNCT
ejpam-6249	218	28	there	there	PRON
ejpam-6249	218	29	exists	exist	VERB
ejpam-6249	218	30	µ′	µ′	X
ejpam-6249	218	31	∈	∈	PROPN
ejpam-6249	218	32	l	l	NOUN
ejpam-6249	218	33	such	such	ADJ
ejpam-6249	218	34	that	that	PRON
ejpam-6249	218	35	µ∧µ′	µ∧µ′	VERB
ejpam-6249	218	36	∈	∈	NOUN
ejpam-6249	218	37	d∞	d∞	NOUN
ejpam-6249	218	38	and	and	CCONJ
ejpam-6249	218	39	µ∨µ′	µ∨µ′	PROPN
ejpam-6249	218	40	∈	∈	PROPN
ejpam-6249	218	41	d.	d.	PROPN
ejpam-6249	218	42	hence	hence	ADV
ejpam-6249	218	43	µ′	µ′	PROPN
ejpam-6249	218	44	∈	∈	PROPN
ejpam-6249	218	45	⟨µ,d∞⟩	⟨µ,d∞⟩	NUM
ejpam-6249	218	46	=	=	SYM
ejpam-6249	218	47	⟨π	⟨π	NOUN
ejpam-6249	218	48	,	,	PUNCT
ejpam-6249	218	49	d∞⟩.	d∞⟩.	PROPN
ejpam-6249	218	50	hence	hence	ADV
ejpam-6249	218	51	µ′	µ′	PUNCT
ejpam-6249	218	52	∧	∧	PROPN
ejpam-6249	218	53	π	π	X
ejpam-6249	218	54	∈	∈	PROPN
ejpam-6249	219	1	d∞.	d∞.	INTJ
ejpam-6249	219	2	hence	hence	ADV
ejpam-6249	219	3	(	(	PUNCT
ejpam-6249	219	4	µ′,d	µ′,d	NOUN
ejpam-6249	219	5	)	)	PUNCT
ejpam-6249	219	6	∩	∩	NOUN
ejpam-6249	219	7	(	(	PUNCT
ejpam-6249	219	8	π	π	X
ejpam-6249	219	9	,	,	PUNCT
ejpam-6249	219	10	d	d	NOUN
ejpam-6249	219	11	)	)	PUNCT
ejpam-6249	219	12	=	=	SYM
ejpam-6249	219	13	d.	d.	PROPN
ejpam-6249	219	14	let	let	VERB
ejpam-6249	219	15	ν	ν	X
ejpam-6249	219	16	∈	∈	PROPN
ejpam-6249	219	17	(	(	PUNCT
ejpam-6249	219	18	π	π	PROPN
ejpam-6249	219	19	,	,	PUNCT
ejpam-6249	219	20	d	d	NOUN
ejpam-6249	219	21	)	)	PUNCT
ejpam-6249	219	22	.	.	PUNCT
ejpam-6249	220	1	since	since	SCONJ
ejpam-6249	220	2	(	(	PUNCT
ejpam-6249	220	3	π	π	PROPN
ejpam-6249	220	4	,	,	PUNCT
ejpam-6249	220	5	d	d	NOUN
ejpam-6249	220	6	)	)	PUNCT
ejpam-6249	220	7	is	be	AUX
ejpam-6249	220	8	a	a	DET
ejpam-6249	220	9	filter	filter	NOUN
ejpam-6249	220	10	,	,	PUNCT
ejpam-6249	220	11	which	which	PRON
ejpam-6249	220	12	gives	give	VERB
ejpam-6249	220	13	ν	ν	ADP
ejpam-6249	220	14	∨	∨	NUM
ejpam-6249	220	15	µ	µ	X
ejpam-6249	220	16	∈	∈	PROPN
ejpam-6249	220	17	(	(	PUNCT
ejpam-6249	220	18	π	π	PROPN
ejpam-6249	220	19	,	,	PUNCT
ejpam-6249	220	20	d	d	NOUN
ejpam-6249	220	21	)	)	PUNCT
ejpam-6249	220	22	.	.	PUNCT
ejpam-6249	221	1	as	as	SCONJ
ejpam-6249	221	2	µ	µ	X
ejpam-6249	221	3	∨	∨	NOUN
ejpam-6249	221	4	µ′	µ′	NOUN
ejpam-6249	221	5	∈	∈	PROPN
ejpam-6249	221	6	d	d	X
ejpam-6249	221	7	,	,	PUNCT
ejpam-6249	221	8	we	we	PRON
ejpam-6249	221	9	obtain	obtain	VERB
ejpam-6249	221	10	µ	µ	PRON
ejpam-6249	221	11	∈	∈	NOUN
ejpam-6249	221	12	(	(	PUNCT
ejpam-6249	221	13	µ′,d	µ′,d	NOUN
ejpam-6249	221	14	)	)	PUNCT
ejpam-6249	221	15	.	.	PUNCT
ejpam-6249	222	1	hence	hence	ADV
ejpam-6249	222	2	ν	ν	X
ejpam-6249	222	3	∨	∨	NUM
ejpam-6249	222	4	µ	µ	X
ejpam-6249	222	5	∈	∈	NOUN
ejpam-6249	222	6	(	(	PUNCT
ejpam-6249	222	7	µ′,d	µ′,d	NOUN
ejpam-6249	222	8	)	)	PUNCT
ejpam-6249	222	9	.	.	PUNCT
ejpam-6249	223	1	thus	thus	ADV
ejpam-6249	223	2	ν	ν	X
ejpam-6249	223	3	∨	∨	NUM
ejpam-6249	223	4	µ	µ	X
ejpam-6249	223	5	∈	∈	NOUN
ejpam-6249	223	6	(	(	PUNCT
ejpam-6249	223	7	µ′,d	µ′,d	NOUN
ejpam-6249	223	8	)	)	PUNCT
ejpam-6249	223	9	∩	∩	NOUN
ejpam-6249	223	10	(	(	PUNCT
ejpam-6249	223	11	π	π	X
ejpam-6249	223	12	,	,	PUNCT
ejpam-6249	223	13	d	d	NOUN
ejpam-6249	223	14	)	)	PUNCT
ejpam-6249	223	15	=	=	SYM
ejpam-6249	223	16	d.	d.	NOUN
ejpam-6249	223	17	hence	hence	ADV
ejpam-6249	223	18	ν	ν	X
ejpam-6249	223	19	∈	∈	PROPN
ejpam-6249	223	20	(	(	PUNCT
ejpam-6249	223	21	µ,d	µ,d	NOUN
ejpam-6249	223	22	)	)	PUNCT
ejpam-6249	223	23	.	.	PUNCT
ejpam-6249	224	1	therefore	therefore	ADV
ejpam-6249	224	2	(	(	PUNCT
ejpam-6249	224	3	π	π	X
ejpam-6249	224	4	,	,	PUNCT
ejpam-6249	224	5	d	d	NOUN
ejpam-6249	224	6	)	)	PUNCT
ejpam-6249	224	7	⊆	⊆	NUM
ejpam-6249	224	8	(	(	PUNCT
ejpam-6249	224	9	µ,d	µ,d	NOUN
ejpam-6249	224	10	)	)	PUNCT
ejpam-6249	224	11	.	.	PUNCT
ejpam-6249	224	12	with	with	ADP
ejpam-6249	224	13	a	a	DET
ejpam-6249	224	14	similar	similar	ADJ
ejpam-6249	224	15	approach	approach	NOUN
ejpam-6249	224	16	,	,	PUNCT
ejpam-6249	224	17	we	we	PRON
ejpam-6249	224	18	get	get	VERB
ejpam-6249	224	19	(	(	PUNCT
ejpam-6249	224	20	µ,d	µ,d	NOUN
ejpam-6249	224	21	)	)	PUNCT
ejpam-6249	224	22	⊆	⊆	NUM
ejpam-6249	224	23	(	(	PUNCT
ejpam-6249	224	24	π	π	PROPN
ejpam-6249	224	25	,	,	PUNCT
ejpam-6249	224	26	d	d	NOUN
ejpam-6249	224	27	)	)	PUNCT
ejpam-6249	224	28	.	.	PUNCT
ejpam-6249	225	1	hence	hence	ADV
ejpam-6249	225	2	(	(	PUNCT
ejpam-6249	225	3	µ	µ	X
ejpam-6249	225	4	,	,	PUNCT
ejpam-6249	225	5	π	π	NOUN
ejpam-6249	225	6	)	)	PUNCT
ejpam-6249	225	7	∈	∈	PROPN
ejpam-6249	225	8	θ	θ	PROPN
ejpam-6249	225	9	.	.	PUNCT
ejpam-6249	225	10	therefore	therefore	ADV
ejpam-6249	225	11	ψd∞	ψd∞	PROPN
ejpam-6249	225	12	⊆	⊆	NUM
ejpam-6249	225	13	θ	θ	PROPN
ejpam-6249	225	14	.	.	PUNCT
ejpam-6249	225	15	to	to	PART
ejpam-6249	225	16	characterize	characterize	VERB
ejpam-6249	225	17	hemicomplemented	hemicomplemente	VERB
ejpam-6249	225	18	adls	adls	PROPN
ejpam-6249	225	19	,	,	PUNCT
ejpam-6249	225	20	we	we	PRON
ejpam-6249	225	21	begin	begin	VERB
ejpam-6249	225	22	with	with	ADP
ejpam-6249	225	23	the	the	DET
ejpam-6249	225	24	following	follow	VERB
ejpam-6249	225	25	lemma	lemma	PROPN
ejpam-6249	225	26	.	.	PUNCT
ejpam-6249	226	1	lemma	lemma	PROPN
ejpam-6249	226	2	3	3	NUM
ejpam-6249	226	3	.	.	X
ejpam-6249	227	1	for	for	ADP
ejpam-6249	227	2	any	any	DET
ejpam-6249	227	3	ideal	ideal	ADJ
ejpam-6249	227	4	k	k	PROPN
ejpam-6249	227	5	of	of	ADP
ejpam-6249	227	6	l	l	PROPN
ejpam-6249	227	7	,	,	PUNCT
ejpam-6249	227	8	the	the	DET
ejpam-6249	227	9	set	set	NOUN
ejpam-6249	227	10	d(k	d(k	PROPN
ejpam-6249	227	11	)	)	PUNCT
ejpam-6249	227	12	=	=	PRON
ejpam-6249	227	13	{	{	PUNCT
ejpam-6249	227	14	µ	µ	X
ejpam-6249	227	15	∈	∈	X
ejpam-6249	227	16	l	l	NOUN
ejpam-6249	227	17	|	|	NOUN
ejpam-6249	227	18	µ	µ	X
ejpam-6249	227	19	∨	∨	NUM
ejpam-6249	227	20	θ	θ	X
ejpam-6249	227	21	∈	∈	PROPN
ejpam-6249	227	22	d	d	NOUN
ejpam-6249	227	23	,	,	PUNCT
ejpam-6249	227	24	for	for	ADP
ejpam-6249	227	25	some	some	DET
ejpam-6249	227	26	θ	θ	PROPN
ejpam-6249	227	27	∈	∈	PROPN
ejpam-6249	227	28	k	k	VERB
ejpam-6249	227	29	}	}	PUNCT
ejpam-6249	227	30	is	be	AUX
ejpam-6249	227	31	a	a	DET
ejpam-6249	227	32	filter	filter	NOUN
ejpam-6249	227	33	of	of	ADP
ejpam-6249	227	34	l.	l.	PROPN
ejpam-6249	227	35	proof	proof	PROPN
ejpam-6249	227	36	.	.	PUNCT
ejpam-6249	228	1	it	it	PRON
ejpam-6249	228	2	is	be	AUX
ejpam-6249	228	3	evident	evident	ADJ
ejpam-6249	228	4	that	that	SCONJ
ejpam-6249	228	5	d	d	PROPN
ejpam-6249	228	6	⊆	⊆	NUM
ejpam-6249	228	7	d(k	d(k	PROPN
ejpam-6249	228	8	)	)	PUNCT
ejpam-6249	228	9	.	.	PUNCT
ejpam-6249	229	1	let	let	VERB
ejpam-6249	229	2	µ	µ	NUM
ejpam-6249	229	3	,	,	PUNCT
ejpam-6249	229	4	π	π	PROPN
ejpam-6249	229	5	∈	∈	PROPN
ejpam-6249	229	6	d(k	d(k	PROPN
ejpam-6249	229	7	)	)	PUNCT
ejpam-6249	229	8	.	.	PUNCT
ejpam-6249	230	1	then	then	ADV
ejpam-6249	230	2	µ	µ	PROPN
ejpam-6249	230	3	∨	∨	PROPN
ejpam-6249	230	4	θ	θ	PROPN
ejpam-6249	230	5	,	,	PUNCT
ejpam-6249	230	6	π	π	PROPN
ejpam-6249	230	7	∨	∨	X
ejpam-6249	230	8	ϑ	ϑ	X
ejpam-6249	230	9	∈	∈	PROPN
ejpam-6249	230	10	d	d	NOUN
ejpam-6249	230	11	,	,	PUNCT
ejpam-6249	230	12	for	for	ADP
ejpam-6249	230	13	some	some	DET
ejpam-6249	230	14	θ	θ	PROPN
ejpam-6249	230	15	,	,	PUNCT
ejpam-6249	230	16	ϑ	ϑ	X
ejpam-6249	230	17	∈	∈	X
ejpam-6249	230	18	k.	k.	NOUN
ejpam-6249	230	19	hence	hence	ADV
ejpam-6249	230	20	(	(	PUNCT
ejpam-6249	230	21	µ∧π)∨	µ∧π)∨	NOUN
ejpam-6249	230	22	(	(	PUNCT
ejpam-6249	230	23	θ∨ϑ	θ∨ϑ	X
ejpam-6249	230	24	)	)	PUNCT
ejpam-6249	230	25	=	=	SYM
ejpam-6249	230	26	(	(	PUNCT
ejpam-6249	230	27	µ∨θ∨ϑ)∧	µ∨θ∨ϑ)∧	PROPN
ejpam-6249	230	28	(	(	PUNCT
ejpam-6249	230	29	π∨θ∨ϑ	π∨θ∨ϑ	PROPN
ejpam-6249	230	30	)	)	PUNCT
ejpam-6249	230	31	∈	∈	PROPN
ejpam-6249	230	32	d.	d.	PROPN
ejpam-6249	230	33	as	as	SCONJ
ejpam-6249	230	34	k	k	PROPN
ejpam-6249	230	35	is	be	AUX
ejpam-6249	230	36	an	an	DET
ejpam-6249	230	37	ideal	ideal	NOUN
ejpam-6249	230	38	,	,	PUNCT
ejpam-6249	230	39	we	we	PRON
ejpam-6249	230	40	obtain	obtain	VERB
ejpam-6249	230	41	µ	µ	PRON
ejpam-6249	230	42	∧	∧	PROPN
ejpam-6249	230	43	π	π	PROPN
ejpam-6249	230	44	∈	∈	PROPN
ejpam-6249	230	45	d(k	d(k	PROPN
ejpam-6249	230	46	)	)	PUNCT
ejpam-6249	230	47	.	.	PUNCT
ejpam-6249	231	1	let	let	VERB
ejpam-6249	231	2	µ	µ	PRON
ejpam-6249	231	3	∈	∈	PROPN
ejpam-6249	231	4	d(k	d(k	PROPN
ejpam-6249	231	5	)	)	PUNCT
ejpam-6249	231	6	and	and	CCONJ
ejpam-6249	231	7	µ	µ	PRON
ejpam-6249	231	8	≤	≤	NUM
ejpam-6249	231	9	π	π	X
ejpam-6249	231	10	.	.	PUNCT
ejpam-6249	232	1	then	then	ADV
ejpam-6249	232	2	µ	µ	X
ejpam-6249	232	3	∨	∨	NUM
ejpam-6249	232	4	θ	θ	X
ejpam-6249	232	5	∈	∈	PROPN
ejpam-6249	232	6	d	d	NOUN
ejpam-6249	232	7	,	,	PUNCT
ejpam-6249	232	8	for	for	ADP
ejpam-6249	232	9	all	all	DET
ejpam-6249	232	10	θ	θ	PROPN
ejpam-6249	232	11	∈	∈	PROPN
ejpam-6249	232	12	k.	k.	NOUN
ejpam-6249	232	13	hence	hence	ADV
ejpam-6249	232	14	π	π	PROPN
ejpam-6249	232	15	∨	∨	NUM
ejpam-6249	232	16	θ	θ	X
ejpam-6249	232	17	∈	∈	PROPN
ejpam-6249	233	1	d	d	NOUN
ejpam-6249	233	2	,	,	PUNCT
ejpam-6249	233	3	which	which	PRON
ejpam-6249	233	4	gives	give	VERB
ejpam-6249	233	5	that	that	PRON
ejpam-6249	233	6	π	π	PROPN
ejpam-6249	233	7	∈	∈	PROPN
ejpam-6249	233	8	d(k	d(k	PROPN
ejpam-6249	233	9	)	)	PUNCT
ejpam-6249	233	10	.	.	PUNCT
ejpam-6249	234	1	thus	thus	ADV
ejpam-6249	234	2	d(k	d(k	PROPN
ejpam-6249	234	3	)	)	PUNCT
ejpam-6249	234	4	is	be	AUX
ejpam-6249	234	5	a	a	DET
ejpam-6249	234	6	filter	filter	NOUN
ejpam-6249	234	7	of	of	ADP
ejpam-6249	234	8	l.	l.	PROPN
ejpam-6249	234	9	theorem	theorem	PROPN
ejpam-6249	234	10	4	4	NUM
ejpam-6249	234	11	.	.	X
ejpam-6249	234	12	for	for	ADP
ejpam-6249	234	13	an	an	DET
ejpam-6249	234	14	adl	adl	PROPN
ejpam-6249	234	15	l	l	PROPN
ejpam-6249	234	16	,	,	PUNCT
ejpam-6249	234	17	the	the	DET
ejpam-6249	234	18	following	follow	VERB
ejpam-6249	234	19	properties	property	NOUN
ejpam-6249	234	20	hold	hold	VERB
ejpam-6249	234	21	equivalently	equivalently	ADV
ejpam-6249	234	22	(	(	PUNCT
ejpam-6249	234	23	1	1	X
ejpam-6249	234	24	)	)	PUNCT
ejpam-6249	234	25	l	l	NOUN
ejpam-6249	234	26	is	be	AUX
ejpam-6249	234	27	hemicomplemented	hemicomplemente	VERB
ejpam-6249	234	28	;	;	PUNCT
ejpam-6249	234	29	(	(	PUNCT
ejpam-6249	234	30	2	2	X
ejpam-6249	234	31	)	)	PUNCT
ejpam-6249	234	32	for	for	ADP
ejpam-6249	234	33	every	every	DET
ejpam-6249	234	34	filter	filter	NOUN
ejpam-6249	234	35	g	g	NOUN
ejpam-6249	234	36	,	,	PUNCT
ejpam-6249	234	37	there	there	PRON
ejpam-6249	234	38	exists	exist	VERB
ejpam-6249	234	39	an	an	DET
ejpam-6249	234	40	ideal	ideal	NOUN
ejpam-6249	234	41	k	k	ADP
ejpam-6249	234	42	such	such	ADJ
ejpam-6249	234	43	that	that	PRON
ejpam-6249	234	44	(	(	PUNCT
ejpam-6249	234	45	(	(	PUNCT
ejpam-6249	234	46	g	g	NOUN
ejpam-6249	234	47	,	,	PUNCT
ejpam-6249	234	48	d),d	d),d	PROPN
ejpam-6249	234	49	)	)	PUNCT
ejpam-6249	234	50	=	=	SYM
ejpam-6249	234	51	d(k	d(k	PROPN
ejpam-6249	234	52	)	)	PUNCT
ejpam-6249	234	53	;	;	PUNCT
ejpam-6249	234	54	n.	n.	PROPN
ejpam-6249	234	55	rafi	rafi	PROPN
ejpam-6249	234	56	et	et	PROPN
ejpam-6249	234	57	al	al	PROPN
ejpam-6249	234	58	.	.	PUNCT
ejpam-6249	234	59	/	/	SYM
ejpam-6249	234	60	eur	eur	PROPN
ejpam-6249	234	61	.	.	PUNCT
ejpam-6249	235	1	j.	j.	PROPN
ejpam-6249	235	2	pure	pure	PROPN
ejpam-6249	235	3	appl	appl	PROPN
ejpam-6249	235	4	.	.	PROPN
ejpam-6249	235	5	math	math	PROPN
ejpam-6249	235	6	,	,	PUNCT
ejpam-6249	235	7	18	18	NUM
ejpam-6249	235	8	(	(	PUNCT
ejpam-6249	235	9	4	4	NUM
ejpam-6249	235	10	)	)	PUNCT
ejpam-6249	235	11	(	(	PUNCT
ejpam-6249	235	12	2025	2025	NUM
ejpam-6249	235	13	)	)	PUNCT
ejpam-6249	235	14	,	,	PUNCT
ejpam-6249	235	15	6249	6249	NUM
ejpam-6249	235	16	10	10	NUM
ejpam-6249	235	17	of	of	ADP
ejpam-6249	235	18	11	11	NUM
ejpam-6249	235	19	(	(	PUNCT
ejpam-6249	235	20	3	3	NUM
ejpam-6249	235	21	)	)	PUNCT
ejpam-6249	235	22	for	for	ADP
ejpam-6249	235	23	every	every	DET
ejpam-6249	235	24	filter	filter	NOUN
ejpam-6249	235	25	g	g	NOUN
ejpam-6249	235	26	,	,	PUNCT
ejpam-6249	235	27	(	(	PUNCT
ejpam-6249	235	28	(	(	PUNCT
ejpam-6249	235	29	g	g	NOUN
ejpam-6249	235	30	,	,	PUNCT
ejpam-6249	235	31	d),d	d),d	PROPN
ejpam-6249	235	32	)	)	PUNCT
ejpam-6249	235	33	=	=	SYM
ejpam-6249	236	1	d(k((g	d(k((g	ADJ
ejpam-6249	236	2	,	,	PUNCT
ejpam-6249	236	3	d),d	d),d	NOUN
ejpam-6249	236	4	)	)	PUNCT
ejpam-6249	236	5	)	)	PUNCT
ejpam-6249	236	6	,	,	PUNCT
ejpam-6249	236	7	where	where	SCONJ
ejpam-6249	236	8	k((g	k((g	ADJ
ejpam-6249	236	9	,	,	PUNCT
ejpam-6249	236	10	d),d	d),d	PROPN
ejpam-6249	236	11	)	)	PUNCT
ejpam-6249	236	12	is	be	AUX
ejpam-6249	236	13	the	the	DET
ejpam-6249	236	14	ideal	ideal	NOUN
ejpam-6249	236	15	defined	define	VERB
ejpam-6249	236	16	as	as	ADP
ejpam-6249	236	17	k((g	k((g	NOUN
ejpam-6249	236	18	,	,	PUNCT
ejpam-6249	236	19	d),d	d),d	PROPN
ejpam-6249	236	20	)	)	PUNCT
ejpam-6249	237	1	=	=	PRON
ejpam-6249	237	2	{	{	PUNCT
ejpam-6249	237	3	µ	µ	X
ejpam-6249	237	4	∈	∈	X
ejpam-6249	237	5	l	l	NOUN
ejpam-6249	238	1	|	|	NOUN
ejpam-6249	238	2	(	(	PUNCT
ejpam-6249	238	3	θ	θ	NOUN
ejpam-6249	238	4	,	,	PUNCT
ejpam-6249	238	5	d	d	NOUN
ejpam-6249	238	6	)	)	PUNCT
ejpam-6249	238	7	⊆	⊆	NUM
ejpam-6249	238	8	(	(	PUNCT
ejpam-6249	238	9	(	(	PUNCT
ejpam-6249	238	10	µ,d),d	µ,d),d	NOUN
ejpam-6249	238	11	)	)	PUNCT
ejpam-6249	238	12	,	,	PUNCT
ejpam-6249	238	13	for	for	ADP
ejpam-6249	238	14	some	some	DET
ejpam-6249	238	15	θ	θ	NOUN
ejpam-6249	238	16	∈	∈	PROPN
ejpam-6249	238	17	(	(	PUNCT
ejpam-6249	238	18	(	(	PUNCT
ejpam-6249	238	19	g	g	NOUN
ejpam-6249	238	20	,	,	PUNCT
ejpam-6249	238	21	d),d	d),d	NOUN
ejpam-6249	238	22	)	)	PUNCT
ejpam-6249	238	23	}	}	PUNCT
ejpam-6249	238	24	.	.	PUNCT
ejpam-6249	239	1	proof	proof	NOUN
ejpam-6249	239	2	.	.	PUNCT
ejpam-6249	240	1	(	(	PUNCT
ejpam-6249	240	2	1	1	X
ejpam-6249	240	3	)	)	PUNCT
ejpam-6249	240	4	⇒	⇒	NOUN
ejpam-6249	240	5	(	(	PUNCT
ejpam-6249	240	6	3	3	NUM
ejpam-6249	240	7	)	)	PUNCT
ejpam-6249	240	8	:	:	PUNCT
ejpam-6249	240	9	assume	assume	VERB
ejpam-6249	240	10	(	(	PUNCT
ejpam-6249	240	11	1	1	NUM
ejpam-6249	240	12	)	)	PUNCT
ejpam-6249	240	13	.	.	PUNCT
ejpam-6249	241	1	definek((g	definek((g	ADJ
ejpam-6249	241	2	,	,	PUNCT
ejpam-6249	241	3	d),d	d),d	PROPN
ejpam-6249	241	4	)	)	PUNCT
ejpam-6249	241	5	=	=	PRON
ejpam-6249	241	6	{	{	PUNCT
ejpam-6249	241	7	µ	µ	X
ejpam-6249	241	8	∈	∈	X
ejpam-6249	241	9	l	l	NOUN
ejpam-6249	242	1	|	|	NOUN
ejpam-6249	242	2	(	(	PUNCT
ejpam-6249	242	3	θ	θ	NOUN
ejpam-6249	242	4	,	,	PUNCT
ejpam-6249	242	5	d	d	NOUN
ejpam-6249	242	6	)	)	PUNCT
ejpam-6249	242	7	⊆	⊆	NUM
ejpam-6249	242	8	(	(	PUNCT
ejpam-6249	242	9	(	(	PUNCT
ejpam-6249	242	10	µ,d),d	µ,d),d	NOUN
ejpam-6249	242	11	)	)	PUNCT
ejpam-6249	242	12	,	,	PUNCT
ejpam-6249	242	13	for	for	ADP
ejpam-6249	242	14	some	some	DET
ejpam-6249	242	15	θ	θ	NOUN
ejpam-6249	242	16	∈	∈	PROPN
ejpam-6249	242	17	(	(	PUNCT
ejpam-6249	242	18	(	(	PUNCT
ejpam-6249	242	19	g	g	NOUN
ejpam-6249	242	20	,	,	PUNCT
ejpam-6249	242	21	d),d	d),d	NOUN
ejpam-6249	242	22	)	)	PUNCT
ejpam-6249	242	23	}	}	PUNCT
ejpam-6249	242	24	.	.	PUNCT
ejpam-6249	243	1	it	it	PRON
ejpam-6249	243	2	can	can	AUX
ejpam-6249	243	3	be	be	AUX
ejpam-6249	243	4	seen	see	VERB
ejpam-6249	243	5	that	that	SCONJ
ejpam-6249	243	6	0	0	NUM
ejpam-6249	243	7	∈	∈	PROPN
ejpam-6249	243	8	k((g	k((g	PROPN
ejpam-6249	243	9	,	,	PUNCT
ejpam-6249	243	10	d),d	d),d	PROPN
ejpam-6249	243	11	)	)	PUNCT
ejpam-6249	243	12	.	.	PUNCT
ejpam-6249	244	1	let	let	VERB
ejpam-6249	244	2	µ	µ	NOUN
ejpam-6249	244	3	,	,	PUNCT
ejpam-6249	244	4	π	π	PROPN
ejpam-6249	244	5	∈	∈	PROPN
ejpam-6249	244	6	k((g	k((g	PROPN
ejpam-6249	244	7	,	,	PUNCT
ejpam-6249	244	8	d),d	d),d	PROPN
ejpam-6249	244	9	)	)	PUNCT
ejpam-6249	244	10	.	.	PUNCT
ejpam-6249	245	1	then	then	ADV
ejpam-6249	245	2	(	(	PUNCT
ejpam-6249	245	3	θ	θ	NOUN
ejpam-6249	245	4	,	,	PUNCT
ejpam-6249	245	5	d	d	NOUN
ejpam-6249	245	6	)	)	PUNCT
ejpam-6249	245	7	⊆	⊆	NUM
ejpam-6249	245	8	(	(	PUNCT
ejpam-6249	245	9	(	(	PUNCT
ejpam-6249	245	10	µ,d),d	µ,d),d	NOUN
ejpam-6249	245	11	)	)	PUNCT
ejpam-6249	245	12	and	and	CCONJ
ejpam-6249	245	13	(	(	PUNCT
ejpam-6249	245	14	ϑ,d	ϑ,d	NOUN
ejpam-6249	245	15	)	)	PUNCT
ejpam-6249	245	16	⊆	⊆	NUM
ejpam-6249	245	17	(	(	PUNCT
ejpam-6249	245	18	(	(	PUNCT
ejpam-6249	245	19	π	π	PROPN
ejpam-6249	245	20	,	,	PUNCT
ejpam-6249	245	21	d),d	d),d	PROPN
ejpam-6249	245	22	)	)	PUNCT
ejpam-6249	245	23	,	,	PUNCT
ejpam-6249	245	24	for	for	ADP
ejpam-6249	245	25	some	some	DET
ejpam-6249	245	26	θ	θ	PROPN
ejpam-6249	245	27	,	,	PUNCT
ejpam-6249	245	28	ϑ	ϑ	X
ejpam-6249	245	29	∈	∈	PROPN
ejpam-6249	245	30	(	(	PUNCT
ejpam-6249	245	31	(	(	PUNCT
ejpam-6249	245	32	g	g	NOUN
ejpam-6249	245	33	,	,	PUNCT
ejpam-6249	245	34	d),d	d),d	PROPN
ejpam-6249	245	35	)	)	PUNCT
ejpam-6249	245	36	.	.	PUNCT
ejpam-6249	246	1	now	now	ADV
ejpam-6249	246	2	(	(	PUNCT
ejpam-6249	246	3	θ	θ	PROPN
ejpam-6249	246	4	∧	∧	PROPN
ejpam-6249	246	5	ϑ,d	ϑ,d	NOUN
ejpam-6249	246	6	)	)	PUNCT
ejpam-6249	246	7	=	=	SYM
ejpam-6249	246	8	(	(	PUNCT
ejpam-6249	246	9	θ	θ	PROPN
ejpam-6249	246	10	,	,	PUNCT
ejpam-6249	246	11	d	d	NOUN
ejpam-6249	246	12	)	)	PUNCT
ejpam-6249	246	13	∩	∩	NOUN
ejpam-6249	246	14	(	(	PUNCT
ejpam-6249	246	15	ϑ,d	ϑ,d	NOUN
ejpam-6249	246	16	)	)	PUNCT
ejpam-6249	246	17	⊆	⊆	NUM
ejpam-6249	246	18	(	(	PUNCT
ejpam-6249	246	19	(	(	PUNCT
ejpam-6249	246	20	µ,d),d	µ,d),d	NOUN
ejpam-6249	246	21	)	)	PUNCT
ejpam-6249	246	22	∩	∩	NOUN
ejpam-6249	246	23	(	(	PUNCT
ejpam-6249	246	24	(	(	PUNCT
ejpam-6249	246	25	π	π	PROPN
ejpam-6249	246	26	,	,	PUNCT
ejpam-6249	246	27	d),d	d),d	PROPN
ejpam-6249	246	28	)	)	PUNCT
ejpam-6249	246	29	=	=	SYM
ejpam-6249	247	1	(	(	PUNCT
ejpam-6249	247	2	(	(	PUNCT
ejpam-6249	247	3	µ	µ	X
ejpam-6249	247	4	∨	∨	NUM
ejpam-6249	247	5	π	π	PROPN
ejpam-6249	247	6	,	,	PUNCT
ejpam-6249	247	7	d),d	d),d	PROPN
ejpam-6249	247	8	)	)	PUNCT
ejpam-6249	247	9	and	and	CCONJ
ejpam-6249	247	10	θ	θ	PROPN
ejpam-6249	247	11	∧	∧	PROPN
ejpam-6249	247	12	ϑ	ϑ	PROPN
ejpam-6249	247	13	∈	∈	PROPN
ejpam-6249	247	14	(	(	PUNCT
ejpam-6249	247	15	(	(	PUNCT
ejpam-6249	247	16	g	g	NOUN
ejpam-6249	247	17	,	,	PUNCT
ejpam-6249	247	18	d),d	d),d	PROPN
ejpam-6249	247	19	)	)	PUNCT
ejpam-6249	247	20	.	.	PUNCT
ejpam-6249	248	1	hence	hence	ADV
ejpam-6249	248	2	µ	µ	X
ejpam-6249	248	3	∨	∨	NUM
ejpam-6249	248	4	π	π	PROPN
ejpam-6249	248	5	∈	∈	PROPN
ejpam-6249	248	6	k((g	k((g	PROPN
ejpam-6249	248	7	,	,	PUNCT
ejpam-6249	248	8	d),d	d),d	PROPN
ejpam-6249	248	9	)	)	PUNCT
ejpam-6249	248	10	.	.	PUNCT
ejpam-6249	249	1	let	let	VERB
ejpam-6249	249	2	µ	µ	PRON
ejpam-6249	249	3	∈	∈	PROPN
ejpam-6249	249	4	k((g	k((g	PROPN
ejpam-6249	249	5	,	,	PUNCT
ejpam-6249	249	6	d),d	d),d	PROPN
ejpam-6249	249	7	)	)	PUNCT
ejpam-6249	249	8	and	and	CCONJ
ejpam-6249	249	9	τ	τ	PROPN
ejpam-6249	249	10	∈	∈	PROPN
ejpam-6249	249	11	l.	l.	NOUN
ejpam-6249	249	12	then	then	ADV
ejpam-6249	249	13	(	(	PUNCT
ejpam-6249	249	14	θ	θ	PROPN
ejpam-6249	249	15	,	,	PUNCT
ejpam-6249	249	16	d	d	NOUN
ejpam-6249	249	17	)	)	PUNCT
ejpam-6249	249	18	⊆	⊆	NUM
ejpam-6249	249	19	(	(	PUNCT
ejpam-6249	249	20	(	(	PUNCT
ejpam-6249	249	21	µ,d),d	µ,d),d	NOUN
ejpam-6249	249	22	)	)	PUNCT
ejpam-6249	249	23	,	,	PUNCT
ejpam-6249	249	24	for	for	ADP
ejpam-6249	249	25	some	some	DET
ejpam-6249	249	26	θ	θ	NOUN
ejpam-6249	249	27	∈	∈	PROPN
ejpam-6249	249	28	(	(	PUNCT
ejpam-6249	249	29	(	(	PUNCT
ejpam-6249	249	30	g	g	NOUN
ejpam-6249	249	31	,	,	PUNCT
ejpam-6249	249	32	d),d	d),d	PROPN
ejpam-6249	249	33	)	)	PUNCT
ejpam-6249	249	34	.	.	PUNCT
ejpam-6249	250	1	now	now	ADV
ejpam-6249	250	2	(	(	PUNCT
ejpam-6249	250	3	θ	θ	NOUN
ejpam-6249	250	4	,	,	PUNCT
ejpam-6249	250	5	d	d	NOUN
ejpam-6249	250	6	)	)	PUNCT
ejpam-6249	250	7	⊆	⊆	NUM
ejpam-6249	250	8	(	(	PUNCT
ejpam-6249	250	9	(	(	PUNCT
ejpam-6249	250	10	µ,d),d	µ,d),d	X
ejpam-6249	250	11	)	)	PUNCT
ejpam-6249	250	12	⊆	⊆	NUM
ejpam-6249	250	13	(	(	PUNCT
ejpam-6249	250	14	(	(	PUNCT
ejpam-6249	250	15	µ	µ	X
ejpam-6249	250	16	∧	∧	PROPN
ejpam-6249	250	17	τ	τ	PROPN
ejpam-6249	250	18	,	,	PUNCT
ejpam-6249	250	19	d),d	d),d	PROPN
ejpam-6249	250	20	)	)	PUNCT
ejpam-6249	250	21	.	.	PUNCT
ejpam-6249	251	1	thus	thus	ADV
ejpam-6249	251	2	µ	µ	X
ejpam-6249	251	3	∧	∧	PROPN
ejpam-6249	251	4	τ	τ	PROPN
ejpam-6249	251	5	∈	∈	PROPN
ejpam-6249	251	6	k((g	k((g	PROPN
ejpam-6249	251	7	,	,	PUNCT
ejpam-6249	251	8	d),d	d),d	PROPN
ejpam-6249	251	9	)	)	PUNCT
ejpam-6249	251	10	.	.	PUNCT
ejpam-6249	252	1	therefore	therefore	ADV
ejpam-6249	252	2	k((g	k((g	PROPN
ejpam-6249	252	3	,	,	PUNCT
ejpam-6249	252	4	d),d	d),d	PROPN
ejpam-6249	252	5	)	)	PUNCT
ejpam-6249	252	6	is	be	AUX
ejpam-6249	252	7	an	an	DET
ejpam-6249	252	8	ideal	ideal	NOUN
ejpam-6249	252	9	of	of	ADP
ejpam-6249	252	10	l.	l.	PROPN
ejpam-6249	252	11	next	next	ADV
ejpam-6249	252	12	,	,	PUNCT
ejpam-6249	252	13	we	we	PRON
ejpam-6249	252	14	show	show	VERB
ejpam-6249	252	15	that	that	SCONJ
ejpam-6249	252	16	(	(	PUNCT
ejpam-6249	252	17	(	(	PUNCT
ejpam-6249	252	18	g	g	NOUN
ejpam-6249	252	19	,	,	PUNCT
ejpam-6249	252	20	d),d	d),d	PROPN
ejpam-6249	252	21	)	)	PUNCT
ejpam-6249	252	22	=	=	SYM
ejpam-6249	252	23	d(k((g	d(k((g	ADJ
ejpam-6249	252	24	,	,	PUNCT
ejpam-6249	252	25	d),d	d),d	NOUN
ejpam-6249	252	26	)	)	PUNCT
ejpam-6249	252	27	)	)	PUNCT
ejpam-6249	252	28	.	.	PUNCT
ejpam-6249	253	1	let	let	VERB
ejpam-6249	253	2	µ	µ	X
ejpam-6249	253	3	∈	∈	X
ejpam-6249	253	4	(	(	PUNCT
ejpam-6249	253	5	(	(	PUNCT
ejpam-6249	253	6	g	g	NOUN
ejpam-6249	253	7	,	,	PUNCT
ejpam-6249	253	8	d),d	d),d	PROPN
ejpam-6249	253	9	)	)	PUNCT
ejpam-6249	253	10	.	.	PUNCT
ejpam-6249	254	1	since	since	SCONJ
ejpam-6249	254	2	l	l	NOUN
ejpam-6249	254	3	is	be	AUX
ejpam-6249	254	4	hemicomplemented	hemicomplemente	VERB
ejpam-6249	254	5	,	,	PUNCT
ejpam-6249	254	6	there	there	PRON
ejpam-6249	254	7	exists	exist	VERB
ejpam-6249	254	8	π	π	PROPN
ejpam-6249	254	9	∈	∈	PROPN
ejpam-6249	254	10	l	l	NOUN
ejpam-6249	254	11	such	such	ADJ
ejpam-6249	254	12	that	that	SCONJ
ejpam-6249	254	13	(	(	PUNCT
ejpam-6249	254	14	(	(	PUNCT
ejpam-6249	254	15	µ,d),d	µ,d),d	NOUN
ejpam-6249	254	16	)	)	PUNCT
ejpam-6249	254	17	=	=	SYM
ejpam-6249	255	1	(	(	PUNCT
ejpam-6249	255	2	π	π	X
ejpam-6249	255	3	,	,	PUNCT
ejpam-6249	255	4	d	d	NOUN
ejpam-6249	255	5	)	)	PUNCT
ejpam-6249	255	6	.	.	PUNCT
ejpam-6249	256	1	as	as	ADP
ejpam-6249	256	2	µ	µ	X
ejpam-6249	256	3	∈	∈	NOUN
ejpam-6249	256	4	(	(	PUNCT
ejpam-6249	256	5	(	(	PUNCT
ejpam-6249	256	6	g	g	NOUN
ejpam-6249	256	7	,	,	PUNCT
ejpam-6249	256	8	d),d	d),d	PROPN
ejpam-6249	256	9	)	)	PUNCT
ejpam-6249	256	10	,	,	PUNCT
ejpam-6249	256	11	we	we	PRON
ejpam-6249	256	12	gives	give	VERB
ejpam-6249	256	13	that	that	PRON
ejpam-6249	256	14	π	π	PROPN
ejpam-6249	256	15	∈	∈	PROPN
ejpam-6249	256	16	k((g	k((g	PROPN
ejpam-6249	256	17	,	,	PUNCT
ejpam-6249	256	18	d),d	d),d	PROPN
ejpam-6249	256	19	)	)	PUNCT
ejpam-6249	256	20	.	.	PUNCT
ejpam-6249	257	1	now	now	ADV
ejpam-6249	257	2	,	,	PUNCT
ejpam-6249	257	3	µ	µ	X
ejpam-6249	257	4	∈	∈	X
ejpam-6249	257	5	(	(	PUNCT
ejpam-6249	257	6	(	(	PUNCT
ejpam-6249	257	7	µ,d),d	µ,d),d	NOUN
ejpam-6249	257	8	)	)	PUNCT
ejpam-6249	257	9	=	=	SYM
ejpam-6249	257	10	(	(	PUNCT
ejpam-6249	257	11	π	π	PROPN
ejpam-6249	257	12	,	,	PUNCT
ejpam-6249	257	13	d	d	NOUN
ejpam-6249	257	14	)	)	PUNCT
ejpam-6249	257	15	gives	give	VERB
ejpam-6249	257	16	that	that	PRON
ejpam-6249	257	17	µ	µ	NOUN
ejpam-6249	257	18	∨	∨	NOUN
ejpam-6249	257	19	π	π	PROPN
ejpam-6249	257	20	∈	∈	PROPN
ejpam-6249	257	21	d	d	NOUN
ejpam-6249	257	22	for	for	ADP
ejpam-6249	257	23	some	some	DET
ejpam-6249	257	24	π	π	PROPN
ejpam-6249	257	25	∈	∈	PROPN
ejpam-6249	257	26	k((g	k((g	PROPN
ejpam-6249	257	27	,	,	PUNCT
ejpam-6249	257	28	d),d	d),d	PROPN
ejpam-6249	257	29	)	)	PUNCT
ejpam-6249	257	30	.	.	PUNCT
ejpam-6249	258	1	therefore	therefore	ADV
ejpam-6249	258	2	(	(	PUNCT
ejpam-6249	258	3	(	(	PUNCT
ejpam-6249	258	4	g	g	NOUN
ejpam-6249	258	5	,	,	PUNCT
ejpam-6249	258	6	d),d	d),d	PROPN
ejpam-6249	258	7	)	)	PUNCT
ejpam-6249	258	8	⊆	⊆	NUM
ejpam-6249	258	9	d(k((g	d(k((g	ADJ
ejpam-6249	258	10	,	,	PUNCT
ejpam-6249	258	11	d),d	d),d	NOUN
ejpam-6249	258	12	)	)	PUNCT
ejpam-6249	258	13	)	)	PUNCT
ejpam-6249	258	14	.	.	PUNCT
ejpam-6249	259	1	let	let	VERB
ejpam-6249	259	2	µ	µ	PRON
ejpam-6249	259	3	∈	∈	ADJ
ejpam-6249	259	4	d(k((g	d(k((g	ADJ
ejpam-6249	259	5	,	,	PUNCT
ejpam-6249	259	6	d),d	d),d	NOUN
ejpam-6249	259	7	)	)	PUNCT
ejpam-6249	259	8	)	)	PUNCT
ejpam-6249	259	9	.	.	PUNCT
ejpam-6249	260	1	then	then	ADV
ejpam-6249	260	2	µ	µ	X
ejpam-6249	260	3	∨	∨	NUM
ejpam-6249	260	4	ρ	ρ	NOUN
ejpam-6249	260	5	∈	∈	PROPN
ejpam-6249	260	6	d	d	NOUN
ejpam-6249	260	7	for	for	ADP
ejpam-6249	260	8	some	some	DET
ejpam-6249	260	9	ρ	ρ	PROPN
ejpam-6249	260	10	∈	∈	PROPN
ejpam-6249	260	11	k((g	k((g	PROPN
ejpam-6249	260	12	,	,	PUNCT
ejpam-6249	260	13	d),d	d),d	PROPN
ejpam-6249	260	14	)	)	PUNCT
ejpam-6249	260	15	.	.	PUNCT
ejpam-6249	261	1	hence	hence	ADV
ejpam-6249	261	2	µ	µ	X
ejpam-6249	261	3	∈	∈	PROPN
ejpam-6249	261	4	(	(	PUNCT
ejpam-6249	261	5	ρ	ρ	PROPN
ejpam-6249	261	6	,	,	PUNCT
ejpam-6249	261	7	d	d	NOUN
ejpam-6249	261	8	)	)	PUNCT
ejpam-6249	261	9	for	for	ADP
ejpam-6249	261	10	some	some	DET
ejpam-6249	261	11	ρ	ρ	PROPN
ejpam-6249	261	12	∈	∈	PROPN
ejpam-6249	261	13	k((g	k((g	PROPN
ejpam-6249	261	14	,	,	PUNCT
ejpam-6249	261	15	d),d	d),d	PROPN
ejpam-6249	261	16	)	)	PUNCT
ejpam-6249	261	17	.	.	PUNCT
ejpam-6249	262	1	now	now	ADV
ejpam-6249	262	2	we	we	PRON
ejpam-6249	262	3	obtain	obtain	VERB
ejpam-6249	262	4	ρ	ρ	PRON
ejpam-6249	262	5	∈	∈	PROPN
ejpam-6249	262	6	k((g	k((g	PROPN
ejpam-6249	262	7	,	,	PUNCT
ejpam-6249	262	8	d),d	d),d	PROPN
ejpam-6249	262	9	)	)	PUNCT
ejpam-6249	262	10	⇒	⇒	NOUN
ejpam-6249	262	11	(	(	PUNCT
ejpam-6249	262	12	θ	θ	NOUN
ejpam-6249	262	13	,	,	PUNCT
ejpam-6249	262	14	d	d	NOUN
ejpam-6249	262	15	)	)	PUNCT
ejpam-6249	262	16	⊆	⊆	NUM
ejpam-6249	262	17	(	(	PUNCT
ejpam-6249	262	18	(	(	PUNCT
ejpam-6249	262	19	ρ	ρ	NOUN
ejpam-6249	262	20	,	,	PUNCT
ejpam-6249	262	21	d),d	d),d	PROPN
ejpam-6249	262	22	)	)	PUNCT
ejpam-6249	262	23	for	for	ADP
ejpam-6249	262	24	some	some	DET
ejpam-6249	262	25	θ	θ	NOUN
ejpam-6249	262	26	∈	∈	PROPN
ejpam-6249	262	27	(	(	PUNCT
ejpam-6249	262	28	(	(	PUNCT
ejpam-6249	262	29	g	g	NOUN
ejpam-6249	262	30	,	,	PUNCT
ejpam-6249	262	31	d),d	d),d	PROPN
ejpam-6249	262	32	)	)	PUNCT
ejpam-6249	262	33	⇒	⇒	NOUN
ejpam-6249	262	34	(	(	PUNCT
ejpam-6249	262	35	ρ	ρ	PROPN
ejpam-6249	262	36	,	,	PUNCT
ejpam-6249	262	37	d	d	NOUN
ejpam-6249	262	38	)	)	PUNCT
ejpam-6249	262	39	⊆	⊆	NUM
ejpam-6249	262	40	(	(	PUNCT
ejpam-6249	262	41	(	(	PUNCT
ejpam-6249	262	42	θ	θ	NOUN
ejpam-6249	262	43	,	,	PUNCT
ejpam-6249	262	44	d),d	d),d	NOUN
ejpam-6249	262	45	)	)	PUNCT
ejpam-6249	262	46	for	for	ADP
ejpam-6249	262	47	some	some	DET
ejpam-6249	262	48	θ	θ	NOUN
ejpam-6249	262	49	∈	∈	PROPN
ejpam-6249	262	50	(	(	PUNCT
ejpam-6249	262	51	(	(	PUNCT
ejpam-6249	262	52	g	g	NOUN
ejpam-6249	262	53	,	,	PUNCT
ejpam-6249	262	54	d),d	d),d	PROPN
ejpam-6249	262	55	)	)	PUNCT
ejpam-6249	262	56	⇒	⇒	NOUN
ejpam-6249	262	57	θ	θ	PROPN
ejpam-6249	262	58	∈	∈	PROPN
ejpam-6249	262	59	(	(	PUNCT
ejpam-6249	262	60	(	(	PUNCT
ejpam-6249	262	61	θ	θ	NOUN
ejpam-6249	262	62	,	,	PUNCT
ejpam-6249	262	63	d),d	d),d	NOUN
ejpam-6249	262	64	)	)	PUNCT
ejpam-6249	263	1	⊆	⊆	NUM
ejpam-6249	263	2	(	(	PUNCT
ejpam-6249	263	3	(	(	PUNCT
ejpam-6249	263	4	g	g	NOUN
ejpam-6249	263	5	,	,	PUNCT
ejpam-6249	263	6	d),d	d),d	PROPN
ejpam-6249	263	7	)	)	PUNCT
ejpam-6249	263	8	.	.	PUNCT
ejpam-6249	264	1	hence	hence	ADV
ejpam-6249	264	2	d(k((g	d(k((g	ADJ
ejpam-6249	264	3	,	,	PUNCT
ejpam-6249	264	4	d),d	d),d	NOUN
ejpam-6249	264	5	)	)	PUNCT
ejpam-6249	264	6	)	)	PUNCT
ejpam-6249	265	1	⊆	⊆	NUM
ejpam-6249	265	2	(	(	PUNCT
ejpam-6249	265	3	(	(	PUNCT
ejpam-6249	265	4	g	g	NOUN
ejpam-6249	265	5	,	,	PUNCT
ejpam-6249	265	6	d),d	d),d	PROPN
ejpam-6249	265	7	)	)	PUNCT
ejpam-6249	265	8	.	.	PUNCT
ejpam-6249	266	1	therefore	therefore	ADV
ejpam-6249	266	2	(	(	PUNCT
ejpam-6249	266	3	(	(	PUNCT
ejpam-6249	266	4	g	g	NOUN
ejpam-6249	266	5	,	,	PUNCT
ejpam-6249	266	6	d),d	d),d	PROPN
ejpam-6249	266	7	)	)	PUNCT
ejpam-6249	266	8	=	=	SYM
ejpam-6249	266	9	d(k((g	d(k((g	ADJ
ejpam-6249	266	10	,	,	PUNCT
ejpam-6249	266	11	d),d	d),d	NOUN
ejpam-6249	266	12	)	)	PUNCT
ejpam-6249	266	13	)	)	PUNCT
ejpam-6249	266	14	.	.	PUNCT
ejpam-6249	267	1	(	(	PUNCT
ejpam-6249	267	2	3	3	X
ejpam-6249	267	3	)	)	PUNCT
ejpam-6249	267	4	⇒	⇒	NOUN
ejpam-6249	267	5	(	(	PUNCT
ejpam-6249	267	6	2	2	NUM
ejpam-6249	267	7	)	)	PUNCT
ejpam-6249	267	8	:	:	PUNCT
ejpam-6249	267	9	it	it	PRON
ejpam-6249	267	10	is	be	AUX
ejpam-6249	267	11	clear	clear	ADJ
ejpam-6249	267	12	.	.	PUNCT
ejpam-6249	268	1	(	(	PUNCT
ejpam-6249	268	2	2	2	X
ejpam-6249	268	3	)	)	PUNCT
ejpam-6249	268	4	⇒	⇒	NOUN
ejpam-6249	268	5	(	(	PUNCT
ejpam-6249	268	6	1	1	NUM
ejpam-6249	268	7	)	)	PUNCT
ejpam-6249	268	8	:	:	PUNCT
ejpam-6249	268	9	assume	assume	VERB
ejpam-6249	268	10	(	(	PUNCT
ejpam-6249	268	11	2	2	NUM
ejpam-6249	268	12	)	)	PUNCT
ejpam-6249	268	13	.	.	PUNCT
ejpam-6249	269	1	let	let	VERB
ejpam-6249	269	2	µ	µ	X
ejpam-6249	269	3	∈	∈	PROPN
ejpam-6249	269	4	l.	l.	NOUN
ejpam-6249	269	5	then	then	ADV
ejpam-6249	269	6	there	there	PRON
ejpam-6249	269	7	is	be	VERB
ejpam-6249	269	8	an	an	DET
ejpam-6249	269	9	ideal	ideal	NOUN
ejpam-6249	269	10	k	k	ADP
ejpam-6249	269	11	such	such	ADJ
ejpam-6249	269	12	that	that	PRON
ejpam-6249	269	13	(	(	PUNCT
ejpam-6249	269	14	(	(	PUNCT
ejpam-6249	269	15	µ,d),d	µ,d),d	NOUN
ejpam-6249	269	16	)	)	PUNCT
ejpam-6249	269	17	=	=	SYM
ejpam-6249	269	18	d(k	d(k	PROPN
ejpam-6249	269	19	)	)	PUNCT
ejpam-6249	269	20	.	.	PUNCT
ejpam-6249	270	1	µ	µ	PROPN
ejpam-6249	270	2	∈	∈	PROPN
ejpam-6249	270	3	d(k	d(k	PROPN
ejpam-6249	270	4	)	)	PUNCT
ejpam-6249	270	5	⇒	⇒	VERB
ejpam-6249	270	6	µ	µ	PROPN
ejpam-6249	270	7	∨	∨	NUM
ejpam-6249	270	8	i	i	NOUN
ejpam-6249	270	9	∈	∈	PROPN
ejpam-6249	270	10	d	d	NOUN
ejpam-6249	270	11	for	for	ADP
ejpam-6249	270	12	some	some	DET
ejpam-6249	270	13	i	i	PRON
ejpam-6249	270	14	∈	∈	PROPN
ejpam-6249	270	15	k	k	PROPN
ejpam-6249	270	16	⇒	⇒	PROPN
ejpam-6249	270	17	[	[	X
ejpam-6249	270	18	µ	µ	X
ejpam-6249	270	19	)	)	PUNCT
ejpam-6249	270	20	⊆	⊆	NUM
ejpam-6249	270	21	(	(	PUNCT
ejpam-6249	270	22	i	i	PRON
ejpam-6249	270	23	,	,	PUNCT
ejpam-6249	270	24	d	d	NOUN
ejpam-6249	270	25	)	)	PUNCT
ejpam-6249	270	26	⇒	⇒	NOUN
ejpam-6249	270	27	(	(	PUNCT
ejpam-6249	270	28	(	(	PUNCT
ejpam-6249	270	29	µ,d),d	µ,d),d	X
ejpam-6249	270	30	)	)	PUNCT
ejpam-6249	270	31	⊆	⊆	NUM
ejpam-6249	270	32	(	(	PUNCT
ejpam-6249	270	33	(	(	PUNCT
ejpam-6249	270	34	(	(	PUNCT
ejpam-6249	270	35	i	i	NOUN
ejpam-6249	270	36	,	,	PUNCT
ejpam-6249	270	37	d),d),d	d),d),d	NOUN
ejpam-6249	270	38	)	)	PUNCT
ejpam-6249	270	39	=	=	PUNCT
ejpam-6249	271	1	(	(	PUNCT
ejpam-6249	271	2	i	i	PRON
ejpam-6249	271	3	,	,	PUNCT
ejpam-6249	271	4	d	d	NOUN
ejpam-6249	271	5	)	)	PUNCT
ejpam-6249	271	6	.	.	PUNCT
ejpam-6249	272	1	let	let	VERB
ejpam-6249	272	2	θ	θ	PROPN
ejpam-6249	272	3	∈	∈	PROPN
ejpam-6249	272	4	(	(	PUNCT
ejpam-6249	272	5	i	i	NOUN
ejpam-6249	272	6	,	,	PUNCT
ejpam-6249	272	7	d	d	NOUN
ejpam-6249	272	8	)	)	PUNCT
ejpam-6249	272	9	.	.	PUNCT
ejpam-6249	273	1	then	then	ADV
ejpam-6249	273	2	θ	θ	PROPN
ejpam-6249	273	3	∨	∨	NUM
ejpam-6249	274	1	i	i	NOUN
ejpam-6249	274	2	∈	∈	PROPN
ejpam-6249	275	1	d	d	NOUN
ejpam-6249	275	2	and	and	CCONJ
ejpam-6249	275	3	i	i	PROPN
ejpam-6249	275	4	∈	∈	PROPN
ejpam-6249	275	5	k.	k.	NOUN
ejpam-6249	276	1	thus	thus	ADV
ejpam-6249	276	2	θ	θ	PROPN
ejpam-6249	276	3	∈	∈	PROPN
ejpam-6249	276	4	d(k	d(k	PROPN
ejpam-6249	276	5	)	)	PUNCT
ejpam-6249	276	6	=	=	PRON
ejpam-6249	277	1	(	(	PUNCT
ejpam-6249	277	2	(	(	PUNCT
ejpam-6249	277	3	µ,d),d	µ,d),d	NOUN
ejpam-6249	277	4	)	)	PUNCT
ejpam-6249	277	5	.	.	PUNCT
ejpam-6249	278	1	thus	thus	ADV
ejpam-6249	278	2	(	(	PUNCT
ejpam-6249	278	3	i	i	PRON
ejpam-6249	278	4	,	,	PUNCT
ejpam-6249	278	5	d	d	PROPN
ejpam-6249	278	6	)	)	PUNCT
ejpam-6249	278	7	⊆	⊆	NUM
ejpam-6249	278	8	(	(	PUNCT
ejpam-6249	278	9	(	(	PUNCT
ejpam-6249	278	10	µ,d),d	µ,d),d	NOUN
ejpam-6249	278	11	)	)	PUNCT
ejpam-6249	278	12	.	.	PUNCT
ejpam-6249	279	1	therefore	therefore	ADV
ejpam-6249	279	2	(	(	PUNCT
ejpam-6249	279	3	(	(	PUNCT
ejpam-6249	279	4	µ,d),d	µ,d),d	NOUN
ejpam-6249	279	5	)	)	PUNCT
ejpam-6249	279	6	=	=	PUNCT
ejpam-6249	280	1	(	(	PUNCT
ejpam-6249	280	2	i	i	PRON
ejpam-6249	280	3	,	,	PUNCT
ejpam-6249	280	4	d	d	NOUN
ejpam-6249	280	5	)	)	PUNCT
ejpam-6249	280	6	.	.	PUNCT
ejpam-6249	281	1	hence	hence	ADV
ejpam-6249	281	2	l	l	NOUN
ejpam-6249	281	3	is	be	AUX
ejpam-6249	281	4	hemicomplemented	hemicomplemente	VERB
ejpam-6249	281	5	.	.	PUNCT
ejpam-6249	282	1	4	4	X
ejpam-6249	282	2	.	.	X
ejpam-6249	282	3	conclusions	conclusion	NOUN
ejpam-6249	282	4	this	this	DET
ejpam-6249	282	5	paper	paper	NOUN
ejpam-6249	282	6	introduces	introduce	VERB
ejpam-6249	282	7	the	the	DET
ejpam-6249	282	8	concept	concept	NOUN
ejpam-6249	282	9	of	of	ADP
ejpam-6249	282	10	condensed	condense	VERB
ejpam-6249	282	11	elements	element	NOUN
ejpam-6249	282	12	in	in	ADP
ejpam-6249	282	13	an	an	DET
ejpam-6249	282	14	almost	almost	ADV
ejpam-6249	282	15	distributive	distributive	ADJ
ejpam-6249	282	16	lattice(adl	lattice(adl	NOUN
ejpam-6249	282	17	)	)	PUNCT
ejpam-6249	282	18	and	and	CCONJ
ejpam-6249	282	19	explores	explore	VERB
ejpam-6249	282	20	their	their	PRON
ejpam-6249	282	21	fundamental	fundamental	ADJ
ejpam-6249	282	22	properties	property	NOUN
ejpam-6249	282	23	.	.	PUNCT
ejpam-6249	283	1	it	it	PRON
ejpam-6249	283	2	also	also	ADV
ejpam-6249	283	3	presents	present	VERB
ejpam-6249	283	4	the	the	DET
ejpam-6249	283	5	concept	concept	NOUN
ejpam-6249	283	6	of	of	ADP
ejpam-6249	283	7	hemicomplemented	hemicomplemente	VERB
ejpam-6249	283	8	adl	adl	NOUN
ejpam-6249	283	9	and	and	CCONJ
ejpam-6249	283	10	characterizes	characterize	VERB
ejpam-6249	283	11	these	these	DET
ejpam-6249	283	12	adls	adls	NOUN
ejpam-6249	283	13	using	use	VERB
ejpam-6249	283	14	ideals	ideal	NOUN
ejpam-6249	283	15	,	,	PUNCT
ejpam-6249	283	16	congruences	congruence	NOUN
ejpam-6249	283	17	,	,	PUNCT
ejpam-6249	283	18	and	and	CCONJ
ejpam-6249	283	19	minimal	minimal	ADJ
ejpam-6249	283	20	prime	prime	ADJ
ejpam-6249	283	21	d	d	NOUN
ejpam-6249	283	22	-	-	NOUN
ejpam-6249	283	23	filters	filter	NOUN
ejpam-6249	283	24	.	.	PUNCT
ejpam-6249	284	1	furthermore	furthermore	ADV
ejpam-6249	284	2	,	,	PUNCT
ejpam-6249	284	3	a	a	DET
ejpam-6249	284	4	collection	collection	NOUN
ejpam-6249	284	5	of	of	ADP
ejpam-6249	284	6	equivalent	equivalent	ADJ
ejpam-6249	284	7	criteria	criterion	NOUN
ejpam-6249	284	8	is	be	AUX
ejpam-6249	284	9	established	establish	VERB
ejpam-6249	284	10	to	to	PART
ejpam-6249	284	11	determine	determine	VERB
ejpam-6249	284	12	when	when	SCONJ
ejpam-6249	284	13	a	a	DET
ejpam-6249	284	14	hemicomplemented	hemicomplemente	VERB
ejpam-6249	284	15	adl	adl	NOUN
ejpam-6249	284	16	qualifies	qualifie	NOUN
ejpam-6249	284	17	as	as	ADP
ejpam-6249	284	18	a	a	DET
ejpam-6249	284	19	quasicomplemented	quasicomplemented	ADJ
ejpam-6249	284	20	adl	adl	PROPN
ejpam-6249	284	21	.	.	PUNCT
ejpam-6249	285	1	in	in	ADP
ejpam-6249	285	2	future	future	ADJ
ejpam-6249	285	3	work	work	NOUN
ejpam-6249	285	4	,	,	PUNCT
ejpam-6249	285	5	we	we	PRON
ejpam-6249	285	6	plan	plan	VERB
ejpam-6249	285	7	to	to	PART
ejpam-6249	285	8	study	study	VERB
ejpam-6249	285	9	the	the	DET
ejpam-6249	285	10	properties	property	NOUN
ejpam-6249	285	11	of	of	ADP
ejpam-6249	285	12	hemi	hemi	NOUN
ejpam-6249	285	13	-	-	PUNCT
ejpam-6249	285	14	complemented	complement	VERB
ejpam-6249	285	15	adls	adls	NOUN
ejpam-6249	285	16	and	and	CCONJ
ejpam-6249	285	17	d	d	NOUN
ejpam-6249	285	18	-	-	NOUN
ejpam-6249	285	19	stone	stone	NOUN
ejpam-6249	285	20	adls	adls	NOUN
ejpam-6249	285	21	using	use	VERB
ejpam-6249	285	22	congruences	congruence	NOUN
ejpam-6249	285	23	,	,	PUNCT
ejpam-6249	285	24	which	which	PRON
ejpam-6249	285	25	may	may	AUX
ejpam-6249	285	26	help	help	VERB
ejpam-6249	285	27	in	in	ADP
ejpam-6249	285	28	understanding	understand	VERB
ejpam-6249	285	29	different	different	ADJ
ejpam-6249	285	30	structures	structure	NOUN
ejpam-6249	285	31	of	of	ADP
ejpam-6249	285	32	adls	adls	PROPN
ejpam-6249	285	33	.	.	PUNCT
ejpam-6249	286	1	conflicts	conflict	NOUN
ejpam-6249	286	2	of	of	ADP
ejpam-6249	286	3	interest	interest	NOUN
ejpam-6249	286	4	or	or	CCONJ
ejpam-6249	286	5	competing	compete	VERB
ejpam-6249	286	6	interests	interest	NOUN
ejpam-6249	286	7	the	the	DET
ejpam-6249	286	8	authors	author	NOUN
ejpam-6249	286	9	declare	declare	VERB
ejpam-6249	286	10	that	that	SCONJ
ejpam-6249	286	11	they	they	PRON
ejpam-6249	286	12	have	have	VERB
ejpam-6249	286	13	no	no	DET
ejpam-6249	286	14	conflicts	conflict	NOUN
ejpam-6249	286	15	of	of	ADP
ejpam-6249	286	16	interest	interest	NOUN
ejpam-6249	286	17	.	.	PUNCT
ejpam-6249	287	1	n.	n.	PROPN
ejpam-6249	287	2	rafi	rafi	PROPN
ejpam-6249	287	3	et	et	PROPN
ejpam-6249	287	4	al	al	PROPN
ejpam-6249	287	5	.	.	PUNCT
ejpam-6249	287	6	/	/	SYM
ejpam-6249	287	7	eur	eur	PROPN
ejpam-6249	287	8	.	.	PUNCT
ejpam-6249	288	1	j.	j.	PROPN
ejpam-6249	288	2	pure	pure	PROPN
ejpam-6249	288	3	appl	appl	PROPN
ejpam-6249	288	4	.	.	PROPN
ejpam-6249	288	5	math	math	PROPN
ejpam-6249	288	6	,	,	PUNCT
ejpam-6249	288	7	18	18	NUM
ejpam-6249	288	8	(	(	PUNCT
ejpam-6249	288	9	4	4	NUM
ejpam-6249	288	10	)	)	PUNCT
ejpam-6249	288	11	(	(	PUNCT
ejpam-6249	288	12	2025	2025	NUM
ejpam-6249	288	13	)	)	PUNCT
ejpam-6249	288	14	,	,	PUNCT
ejpam-6249	288	15	6249	6249	NUM
ejpam-6249	288	16	11	11	NUM
ejpam-6249	288	17	of	of	ADP
ejpam-6249	288	18	11	11	NUM
ejpam-6249	288	19	acknowledgements	acknowledgement	NOUN
ejpam-6249	288	20	the	the	DET
ejpam-6249	288	21	authors	author	NOUN
ejpam-6249	288	22	wish	wish	VERB
ejpam-6249	288	23	to	to	PART
ejpam-6249	288	24	thank	thank	VERB
ejpam-6249	288	25	the	the	DET
ejpam-6249	288	26	anonymous	anonymous	ADJ
ejpam-6249	288	27	reviewers	reviewer	NOUN
ejpam-6249	288	28	for	for	ADP
ejpam-6249	288	29	their	their	PRON
ejpam-6249	288	30	valuable	valuable	ADJ
ejpam-6249	288	31	suggestions	suggestion	NOUN
ejpam-6249	288	32	.	.	PUNCT
ejpam-6249	289	1	funding	fund	VERB
ejpam-6249	289	2	this	this	DET
ejpam-6249	289	3	work	work	NOUN
ejpam-6249	289	4	was	be	AUX
ejpam-6249	289	5	supported	support	VERB
ejpam-6249	289	6	by	by	ADP
ejpam-6249	289	7	the	the	DET
ejpam-6249	289	8	directorate	directorate	NOUN
ejpam-6249	289	9	of	of	ADP
ejpam-6249	289	10	research	research	NOUN
ejpam-6249	289	11	and	and	CCONJ
ejpam-6249	289	12	innovation	innovation	NOUN
ejpam-6249	289	13	,	,	PUNCT
ejpam-6249	289	14	walter	walter	PROPN
ejpam-6249	289	15	sisulu	sisulu	PROPN
ejpam-6249	289	16	university	university	PROPN
ejpam-6249	289	17	.	.	PUNCT
ejpam-6249	290	1	references	reference	NOUN
ejpam-6249	290	2	[	[	X
ejpam-6249	290	3	1	1	NUM
ejpam-6249	290	4	]	]	X
ejpam-6249	290	5	u.	u.	PROPN
ejpam-6249	290	6	m.	m.	PROPN
ejpam-6249	290	7	swamy	swamy	PROPN
ejpam-6249	290	8	and	and	CCONJ
ejpam-6249	290	9	g.	g.	PROPN
ejpam-6249	290	10	c.	c.	PROPN
ejpam-6249	290	11	rao	rao	PROPN
ejpam-6249	290	12	.	.	PUNCT
ejpam-6249	291	1	almost	almost	ADV
ejpam-6249	291	2	distributive	distributive	ADJ
ejpam-6249	291	3	lattices	lattice	NOUN
ejpam-6249	291	4	.	.	PUNCT
ejpam-6249	292	1	journal	journal	NOUN
ejpam-6249	292	2	of	of	ADP
ejpam-6249	292	3	the	the	DET
ejpam-6249	292	4	australian	australian	ADJ
ejpam-6249	292	5	mathematical	mathematical	ADJ
ejpam-6249	292	6	society	society	NOUN
ejpam-6249	292	7	(	(	PUNCT
ejpam-6249	292	8	series	series	PROPN
ejpam-6249	292	9	a	a	PROPN
ejpam-6249	292	10	)	)	PUNCT
ejpam-6249	292	11	,	,	PUNCT
ejpam-6249	292	12	31:77–91	31:77–91	NUM
ejpam-6249	292	13	,	,	PUNCT
ejpam-6249	292	14	1981	1981	NUM
ejpam-6249	292	15	.	.	PUNCT
ejpam-6249	293	1	[	[	X
ejpam-6249	293	2	2	2	NUM
ejpam-6249	293	3	]	]	X
ejpam-6249	293	4	n.	n.	PROPN
ejpam-6249	293	5	rafi	rafi	PROPN
ejpam-6249	293	6	,	,	PUNCT
ejpam-6249	293	7	p.	p.	PROPN
ejpam-6249	293	8	vijaya	vijaya	PROPN
ejpam-6249	293	9	saradhi	saradhi	PROPN
ejpam-6249	293	10	,	,	PUNCT
ejpam-6249	293	11	and	and	CCONJ
ejpam-6249	293	12	m.	m.	NOUN
ejpam-6249	293	13	balaiah	balaiah	PROPN
ejpam-6249	293	14	.	.	PUNCT
ejpam-6249	294	1	the	the	DET
ejpam-6249	294	2	space	space	NOUN
ejpam-6249	294	3	of	of	ADP
ejpam-6249	294	4	minimal	minimal	ADJ
ejpam-6249	294	5	prime	prime	ADJ
ejpam-6249	294	6	d	d	NOUN
ejpam-6249	294	7	-	-	NOUN
ejpam-6249	294	8	filters	filter	NOUN
ejpam-6249	294	9	of	of	ADP
ejpam-6249	294	10	almost	almost	ADV
ejpam-6249	294	11	distributive	distributive	ADJ
ejpam-6249	294	12	lattices	lattice	NOUN
ejpam-6249	294	13	.	.	PUNCT
ejpam-6249	295	1	discussiones	discussione	NOUN
ejpam-6249	295	2	mathematicae	mathematicae	VERB
ejpam-6249	295	3	general	general	ADJ
ejpam-6249	295	4	algebra	algebra	PROPN
ejpam-6249	295	5	and	and	CCONJ
ejpam-6249	295	6	applications	application	NOUN
ejpam-6249	295	7	,	,	PUNCT
ejpam-6249	295	8	44:343–368	44:343–368	PROPN
ejpam-6249	295	9	,	,	PUNCT
ejpam-6249	295	10	2024	2024	NUM
ejpam-6249	295	11	.	.	PUNCT
ejpam-6249	296	1	[	[	X
ejpam-6249	296	2	3	3	NUM
ejpam-6249	296	3	]	]	PUNCT
ejpam-6249	296	4	a.	a.	NOUN
ejpam-6249	296	5	p.	p.	PROPN
ejpam-6249	296	6	p.	p.	PROPN
ejpam-6249	296	7	kumar	kumar	PROPN
ejpam-6249	296	8	and	and	CCONJ
ejpam-6249	296	9	m.	m.	PROPN
ejpam-6249	296	10	sambasiva	sambasiva	PROPN
ejpam-6249	296	11	rao	rao	PROPN
ejpam-6249	296	12	.	.	PUNCT
ejpam-6249	297	1	hemi	hemi	NOUN
ejpam-6249	297	2	-	-	PUNCT
ejpam-6249	297	3	complemented	complement	VERB
ejpam-6249	297	4	lattices	lattice	NOUN
ejpam-6249	297	5	.	.	PUNCT
ejpam-6249	298	1	journal	journal	NOUN
ejpam-6249	298	2	of	of	ADP
ejpam-6249	298	3	algebraic	algebraic	PROPN
ejpam-6249	298	4	systems	system	NOUN
ejpam-6249	298	5	,	,	PUNCT
ejpam-6249	298	6	13(2):13–35	13(2):13–35	NUM
ejpam-6249	298	7	,	,	PUNCT
ejpam-6249	298	8	2025	2025	NUM
ejpam-6249	298	9	.	.	PUNCT
ejpam-6249	299	1	[	[	X
ejpam-6249	299	2	4	4	X
ejpam-6249	299	3	]	]	X
ejpam-6249	299	4	g.	g.	PROPN
ejpam-6249	299	5	c.	c.	PROPN
ejpam-6249	299	6	rao	rao	PROPN
ejpam-6249	299	7	.	.	PUNCT
ejpam-6249	300	1	almost	almost	ADV
ejpam-6249	300	2	distributive	distributive	ADJ
ejpam-6249	300	3	lattices	lattice	NOUN
ejpam-6249	300	4	.	.	PUNCT
ejpam-6249	301	1	phd	phd	NOUN
ejpam-6249	301	2	thesis	thesis	PROPN
ejpam-6249	301	3	,	,	PUNCT
ejpam-6249	301	4	department	department	NOUN
ejpam-6249	301	5	of	of	ADP
ejpam-6249	301	6	mathematics	mathematics	PROPN
ejpam-6249	301	7	,	,	PUNCT
ejpam-6249	301	8	andhra	andhra	PROPN
ejpam-6249	301	9	university	university	PROPN
ejpam-6249	301	10	,	,	PUNCT
ejpam-6249	301	11	visakhapatnam	visakhapatnam	PROPN
ejpam-6249	301	12	,	,	PUNCT
ejpam-6249	301	13	india	india	PROPN
ejpam-6249	301	14	,	,	PUNCT
ejpam-6249	301	15	1980	1980	NUM
ejpam-6249	301	16	.	.	PUNCT
ejpam-6249	302	1	[	[	X
ejpam-6249	302	2	5	5	X
ejpam-6249	302	3	]	]	PUNCT
ejpam-6249	302	4	g.	g.	NOUN
ejpam-6249	302	5	birkhoff	birkhoff	PROPN
ejpam-6249	302	6	.	.	PUNCT
ejpam-6249	303	1	lattice	lattice	PROPN
ejpam-6249	303	2	theory	theory	PROPN
ejpam-6249	303	3	,	,	PUNCT
ejpam-6249	303	4	volume	volume	NOUN
ejpam-6249	303	5	25	25	NUM
ejpam-6249	303	6	of	of	ADP
ejpam-6249	303	7	american	american	PROPN
ejpam-6249	303	8	mathematical	mathematical	PROPN
ejpam-6249	303	9	society	society	NOUN
ejpam-6249	303	10	colloquium	colloquium	NOUN
ejpam-6249	303	11	publications	publication	NOUN
ejpam-6249	303	12	.	.	PUNCT
ejpam-6249	304	1	american	american	PROPN
ejpam-6249	304	2	mathematical	mathematical	PROPN
ejpam-6249	304	3	society	society	NOUN
ejpam-6249	304	4	,	,	PUNCT
ejpam-6249	304	5	providence	providence	NOUN
ejpam-6249	304	6	,	,	PUNCT
ejpam-6249	304	7	ri	ri	PROPN
ejpam-6249	304	8	,	,	PUNCT
ejpam-6249	304	9	usa	usa	PROPN
ejpam-6249	304	10	,	,	PUNCT
ejpam-6249	304	11	1967	1967	NUM
ejpam-6249	304	12	.	.	PUNCT
ejpam-6249	305	1	[	[	X
ejpam-6249	305	2	6	6	NUM
ejpam-6249	305	3	]	]	X
ejpam-6249	305	4	g.	g.	PROPN
ejpam-6249	305	5	grätzer	grätzer	PROPN
ejpam-6249	305	6	.	.	PUNCT
ejpam-6249	305	7	general	general	PROPN
ejpam-6249	305	8	lattice	lattice	PROPN
ejpam-6249	305	9	theory	theory	NOUN
ejpam-6249	305	10	.	.	PUNCT
ejpam-6249	306	1	academic	academic	ADJ
ejpam-6249	306	2	press	press	NOUN
ejpam-6249	306	3	,	,	PUNCT
ejpam-6249	306	4	new	new	PROPN
ejpam-6249	306	5	york	york	PROPN
ejpam-6249	306	6	,	,	PUNCT
ejpam-6249	306	7	1978	1978	NUM
ejpam-6249	306	8	.	.	PUNCT
ejpam-6249	307	1	[	[	X
ejpam-6249	307	2	7	7	X
ejpam-6249	307	3	]	]	X
ejpam-6249	307	4	g.	g.	PROPN
ejpam-6249	307	5	c.	c.	PROPN
ejpam-6249	307	6	rao	rao	PROPN
ejpam-6249	307	7	and	and	CCONJ
ejpam-6249	307	8	s.	s.	PROPN
ejpam-6249	307	9	ravi	ravi	PROPN
ejpam-6249	307	10	kumar	kumar	PROPN
ejpam-6249	307	11	.	.	PROPN
ejpam-6249	307	12	minimal	minimal	ADJ
ejpam-6249	307	13	prime	prime	ADJ
ejpam-6249	307	14	ideals	ideal	NOUN
ejpam-6249	307	15	in	in	ADP
ejpam-6249	307	16	an	an	DET
ejpam-6249	307	17	adl	adl	PROPN
ejpam-6249	307	18	.	.	PUNCT
ejpam-6249	307	19	international	international	ADJ
ejpam-6249	307	20	journal	journal	PROPN
ejpam-6249	307	21	of	of	ADP
ejpam-6249	307	22	contemporary	contemporary	PROPN
ejpam-6249	307	23	mathematical	mathematical	PROPN
ejpam-6249	307	24	sciences	sciences	PROPN
ejpam-6249	307	25	,	,	PUNCT
ejpam-6249	307	26	4:475–484	4:475–484	PROPN
ejpam-6249	307	27	,	,	PUNCT
ejpam-6249	307	28	2009	2009	NUM
ejpam-6249	307	29	.	.	PUNCT
ejpam-6249	308	1	[	[	X
ejpam-6249	308	2	8	8	NUM
ejpam-6249	308	3	]	]	X
ejpam-6249	308	4	g.	g.	PROPN
ejpam-6249	308	5	c.	c.	PROPN
ejpam-6249	308	6	rao	rao	PROPN
ejpam-6249	308	7	and	and	CCONJ
ejpam-6249	308	8	s.	s.	PROPN
ejpam-6249	308	9	ravi	ravi	PROPN
ejpam-6249	308	10	kumar	kumar	PROPN
ejpam-6249	308	11	.	.	PUNCT
ejpam-6249	309	1	normal	normal	ADJ
ejpam-6249	309	2	almost	almost	ADV
ejpam-6249	309	3	distributive	distributive	ADJ
ejpam-6249	309	4	lattices	lattice	NOUN
ejpam-6249	309	5	.	.	PUNCT
ejpam-6249	310	1	southeast	southeast	ADJ
ejpam-6249	310	2	asian	asian	ADJ
ejpam-6249	310	3	bulletin	bulletin	NOUN
ejpam-6249	310	4	of	of	ADP
ejpam-6249	310	5	mathematics	mathematic	NOUN
ejpam-6249	310	6	,	,	PUNCT
ejpam-6249	310	7	32:831–841	32:831–841	PROPN
ejpam-6249	310	8	,	,	PUNCT
ejpam-6249	310	9	2008	2008	NUM
ejpam-6249	310	10	.	.	PUNCT
ejpam-6249	311	1	[	[	X
ejpam-6249	311	2	9	9	NUM
ejpam-6249	311	3	]	]	X
ejpam-6249	311	4	g.	g.	PROPN
ejpam-6249	311	5	c.	c.	PROPN
ejpam-6249	311	6	rao	rao	PROPN
ejpam-6249	311	7	,	,	PUNCT
ejpam-6249	311	8	g.	g.	PROPN
ejpam-6249	311	9	n.	n.	PROPN
ejpam-6249	311	10	rao	rao	PROPN
ejpam-6249	311	11	,	,	PUNCT
ejpam-6249	311	12	and	and	CCONJ
ejpam-6249	311	13	a.	a.	PROPN
ejpam-6249	311	14	lakshmana	lakshmana	PROPN
ejpam-6249	311	15	.	.	PUNCT
ejpam-6249	312	1	quasi	quasi	ADJ
ejpam-6249	312	2	-	-	VERB
ejpam-6249	312	3	complemented	complemented	ADJ
ejpam-6249	312	4	almost	almost	ADV
ejpam-6249	312	5	distributive	distributive	ADJ
ejpam-6249	312	6	lattices	lattice	NOUN
ejpam-6249	312	7	.	.	PUNCT
ejpam-6249	313	1	southeast	southeast	ADJ
ejpam-6249	313	2	asian	asian	ADJ
ejpam-6249	313	3	bulletin	bulletin	NOUN
ejpam-6249	313	4	of	of	ADP
ejpam-6249	313	5	mathematics	mathematic	NOUN
ejpam-6249	313	6	,	,	PUNCT
ejpam-6249	313	7	39(3):311–319	39(3):311–319	PROPN
ejpam-6249	313	8	,	,	PUNCT
ejpam-6249	313	9	2015	2015	NUM
ejpam-6249	313	10	.	.	PUNCT
ejpam-6249	314	1	[	[	X
ejpam-6249	314	2	10	10	NUM
ejpam-6249	314	3	]	]	X
ejpam-6249	314	4	g.	g.	PROPN
ejpam-6249	314	5	c.	c.	PROPN
ejpam-6249	314	6	rao	rao	PROPN
ejpam-6249	314	7	and	and	CCONJ
ejpam-6249	314	8	m.	m.	PROPN
ejpam-6249	314	9	sambasiva	sambasiva	PROPN
ejpam-6249	314	10	rao	rao	PROPN
ejpam-6249	314	11	.	.	PUNCT
ejpam-6249	315	1	annulets	annulet	NOUN
ejpam-6249	315	2	in	in	ADP
ejpam-6249	315	3	almost	almost	ADV
ejpam-6249	315	4	distributive	distributive	ADJ
ejpam-6249	315	5	lattices	lattice	NOUN
ejpam-6249	315	6	.	.	PUNCT
ejpam-6249	316	1	european	european	ADJ
ejpam-6249	316	2	journal	journal	PROPN
ejpam-6249	316	3	of	of	ADP
ejpam-6249	316	4	pure	pure	ADJ
ejpam-6249	316	5	and	and	CCONJ
ejpam-6249	316	6	applied	applied	ADJ
ejpam-6249	316	7	mathematics	mathematic	NOUN
ejpam-6249	316	8	,	,	PUNCT
ejpam-6249	316	9	2(1):58–72	2(1):58–72	NUM
ejpam-6249	316	10	,	,	PUNCT
ejpam-6249	316	11	2009	2009	NUM
ejpam-6249	316	12	.	.	PUNCT
ejpam-6249	317	1	[	[	X
ejpam-6249	317	2	11	11	NUM
ejpam-6249	317	3	]	]	X
ejpam-6249	317	4	u.	u.	PROPN
ejpam-6249	317	5	m.	m.	PROPN
ejpam-6249	317	6	swamy	swamy	PROPN
ejpam-6249	317	7	,	,	PUNCT
ejpam-6249	317	8	g.	g.	PROPN
ejpam-6249	317	9	c.	c.	PROPN
ejpam-6249	317	10	rao	rao	PROPN
ejpam-6249	317	11	,	,	PUNCT
ejpam-6249	317	12	and	and	CCONJ
ejpam-6249	317	13	g.	g.	PROPN
ejpam-6249	317	14	nanaji	nanaji	PROPN
ejpam-6249	317	15	rao	rao	PROPN
ejpam-6249	317	16	.	.	PUNCT
ejpam-6249	318	1	pseudo	pseudo	NOUN
ejpam-6249	318	2	-	-	NOUN
ejpam-6249	318	3	complementation	complementation	NOUN
ejpam-6249	318	4	on	on	ADP
ejpam-6249	318	5	almost	almost	ADV
ejpam-6249	318	6	distributive	distributive	ADJ
ejpam-6249	318	7	lattices	lattice	NOUN
ejpam-6249	318	8	.	.	PUNCT
ejpam-6249	319	1	southeast	southeast	ADJ
ejpam-6249	319	2	asian	asian	ADJ
ejpam-6249	319	3	bulletin	bulletin	NOUN
ejpam-6249	319	4	of	of	ADP
ejpam-6249	319	5	mathematics	mathematic	NOUN
ejpam-6249	319	6	,	,	PUNCT
ejpam-6249	319	7	24:95–104	24:95–104	NUM
ejpam-6249	319	8	,	,	PUNCT
ejpam-6249	319	9	2000	2000	NUM
ejpam-6249	319	10	.	.	PUNCT
ejpam-6249	320	1	introduction	introduction	NOUN
ejpam-6249	320	2	preliminaries	preliminary	NOUN
ejpam-6249	320	3	hemicomplemented	hemicomplemente	VERB
ejpam-6249	320	4	adls	adls	PROPN
ejpam-6249	320	5	conclusions	conclusion	NOUN