id	sid	tid	token	lemma	pos
ejpam-6247	1	1	european	european	PROPN
ejpam-6247	1	2	journal	journal	PROPN
ejpam-6247	1	3	of	of	ADP
ejpam-6247	1	4	pure	pure	ADJ
ejpam-6247	1	5	and	and	CCONJ
ejpam-6247	1	6	applied	applied	ADJ
ejpam-6247	1	7	mathematics	mathematic	NOUN
ejpam-6247	1	8	2025	2025	NUM
ejpam-6247	1	9	,	,	PUNCT
ejpam-6247	1	10	vol	vol	NOUN
ejpam-6247	1	11	.	.	PROPN
ejpam-6247	1	12	18	18	NUM
ejpam-6247	1	13	,	,	PUNCT
ejpam-6247	1	14	issue	issue	NOUN
ejpam-6247	1	15	3	3	NUM
ejpam-6247	1	16	,	,	PUNCT
ejpam-6247	1	17	article	article	NOUN
ejpam-6247	1	18	number	number	NOUN
ejpam-6247	1	19	6247	6247	NUM
ejpam-6247	1	20	issn	issn	PROPN
ejpam-6247	1	21	1307	1307	NUM
ejpam-6247	1	22	-	-	SYM
ejpam-6247	1	23	5543	5543	NUM
ejpam-6247	1	24	–	–	PUNCT
ejpam-6247	1	25	ejpam.com	ejpam.com	X
ejpam-6247	1	26	published	publish	VERB
ejpam-6247	1	27	by	by	ADP
ejpam-6247	1	28	new	new	PROPN
ejpam-6247	1	29	york	york	PROPN
ejpam-6247	1	30	business	business	PROPN
ejpam-6247	1	31	global	global	PROPN
ejpam-6247	1	32	topological	topological	ADJ
ejpam-6247	1	33	characterization	characterization	NOUN
ejpam-6247	1	34	of	of	ADP
ejpam-6247	1	35	hemicomplemented	hemicomplemente	VERB
ejpam-6247	1	36	almost	almost	ADV
ejpam-6247	1	37	distributive	distributive	ADJ
ejpam-6247	1	38	lattices	lattice	NOUN
ejpam-6247	1	39	noorbhasha	noorbhasha	VERB
ejpam-6247	1	40	rafi1	rafi1	NOUN
ejpam-6247	1	41	,	,	PUNCT
ejpam-6247	1	42	ravikumar	ravikumar	PROPN
ejpam-6247	1	43	bandaru2	bandaru2	PROPN
ejpam-6247	1	44	,	,	PUNCT
ejpam-6247	1	45	ravi	ravi	PROPN
ejpam-6247	1	46	kumar	kumar	PROPN
ejpam-6247	1	47	davala2	davala2	PROPN
ejpam-6247	1	48	,	,	PUNCT
ejpam-6247	1	49	aiyared	aiyare	VERB
ejpam-6247	1	50	iampan3,∗	iampan3,∗	ADJ
ejpam-6247	1	51	1	1	NUM
ejpam-6247	1	52	department	department	NOUN
ejpam-6247	1	53	of	of	ADP
ejpam-6247	1	54	mathematics	mathematic	NOUN
ejpam-6247	1	55	,	,	PUNCT
ejpam-6247	1	56	bapatla	bapatla	VERB
ejpam-6247	1	57	engineering	engineering	NOUN
ejpam-6247	1	58	college	college	NOUN
ejpam-6247	1	59	,	,	PUNCT
ejpam-6247	1	60	bapatla-522102	bapatla-522102	NOUN
ejpam-6247	1	61	,	,	PUNCT
ejpam-6247	1	62	andhra	andhra	PROPN
ejpam-6247	1	63	pradesh	pradesh	PROPN
ejpam-6247	1	64	,	,	PUNCT
ejpam-6247	1	65	india	india	PROPN
ejpam-6247	1	66	2	2	NUM
ejpam-6247	1	67	department	department	NOUN
ejpam-6247	1	68	of	of	ADP
ejpam-6247	1	69	mathematics	mathematic	NOUN
ejpam-6247	1	70	,	,	PUNCT
ejpam-6247	1	71	school	school	NOUN
ejpam-6247	1	72	of	of	ADP
ejpam-6247	1	73	advanced	advanced	ADJ
ejpam-6247	1	74	sciences	science	NOUN
ejpam-6247	1	75	,	,	PUNCT
ejpam-6247	1	76	vit	vit	PROPN
ejpam-6247	1	77	-	-	PUNCT
ejpam-6247	1	78	ap	ap	PROPN
ejpam-6247	1	79	university	university	PROPN
ejpam-6247	1	80	,	,	PUNCT
ejpam-6247	1	81	amaravati522237	amaravati522237	PROPN
ejpam-6247	1	82	,	,	PUNCT
ejpam-6247	1	83	andhra	andhra	PROPN
ejpam-6247	1	84	pradesh	pradesh	PROPN
ejpam-6247	1	85	,	,	PUNCT
ejpam-6247	1	86	india	india	PROPN
ejpam-6247	1	87	3	3	PROPN
ejpam-6247	1	88	department	department	PROPN
ejpam-6247	1	89	of	of	ADP
ejpam-6247	1	90	mathematics	mathematic	NOUN
ejpam-6247	1	91	,	,	PUNCT
ejpam-6247	1	92	school	school	NOUN
ejpam-6247	1	93	of	of	ADP
ejpam-6247	1	94	science	science	NOUN
ejpam-6247	1	95	,	,	PUNCT
ejpam-6247	1	96	university	university	NOUN
ejpam-6247	1	97	of	of	ADP
ejpam-6247	1	98	phayao	phayao	NOUN
ejpam-6247	1	99	,	,	PUNCT
ejpam-6247	1	100	mae	mae	PROPN
ejpam-6247	1	101	ka	ka	PROPN
ejpam-6247	1	102	,	,	PUNCT
ejpam-6247	1	103	mueang	mueang	PROPN
ejpam-6247	1	104	,	,	PUNCT
ejpam-6247	1	105	phayao	phayao	NOUN
ejpam-6247	1	106	56000	56000	NUM
ejpam-6247	1	107	,	,	PUNCT
ejpam-6247	1	108	thailand	thailand	PROPN
ejpam-6247	1	109	abstract	abstract	NOUN
ejpam-6247	1	110	.	.	PUNCT
ejpam-6247	2	1	the	the	DET
ejpam-6247	2	2	notion	notion	NOUN
ejpam-6247	2	3	of	of	ADP
ejpam-6247	2	4	d	d	NOUN
ejpam-6247	2	5	-	-	NOUN
ejpam-6247	2	6	stone	stone	NOUN
ejpam-6247	2	7	adls	adls	NOUN
ejpam-6247	2	8	is	be	AUX
ejpam-6247	2	9	introduced	introduce	VERB
ejpam-6247	2	10	,	,	PUNCT
ejpam-6247	2	11	and	and	CCONJ
ejpam-6247	2	12	their	their	PRON
ejpam-6247	2	13	core	core	NOUN
ejpam-6247	2	14	properties	property	NOUN
ejpam-6247	2	15	are	be	AUX
ejpam-6247	2	16	explored	explore	VERB
ejpam-6247	2	17	.	.	PUNCT
ejpam-6247	3	1	it	it	PRON
ejpam-6247	3	2	is	be	AUX
ejpam-6247	3	3	shown	show	VERB
ejpam-6247	3	4	that	that	SCONJ
ejpam-6247	3	5	every	every	DET
ejpam-6247	3	6	d	d	NOUN
ejpam-6247	3	7	-	-	PUNCT
ejpam-6247	3	8	stone	stone	NOUN
ejpam-6247	3	9	adl	adl	NOUN
ejpam-6247	3	10	is	be	AUX
ejpam-6247	3	11	hemicomplemented	hemicomplemente	VERB
ejpam-6247	3	12	but	but	CCONJ
ejpam-6247	3	13	not	not	PART
ejpam-6247	3	14	vice	vice	ADV
ejpam-6247	3	15	versa	versa	ADV
ejpam-6247	3	16	.	.	PUNCT
ejpam-6247	4	1	several	several	ADJ
ejpam-6247	4	2	equivalent	equivalent	ADJ
ejpam-6247	4	3	conditions	condition	NOUN
ejpam-6247	4	4	are	be	AUX
ejpam-6247	4	5	given	give	VERB
ejpam-6247	4	6	for	for	ADP
ejpam-6247	4	7	when	when	SCONJ
ejpam-6247	4	8	a	a	DET
ejpam-6247	4	9	hemicomplemented	hemicomplemente	VERB
ejpam-6247	4	10	adl	adl	NOUN
ejpam-6247	4	11	becomes	become	VERB
ejpam-6247	4	12	d	d	NOUN
ejpam-6247	4	13	-	-	NOUN
ejpam-6247	4	14	stone	stone	NOUN
ejpam-6247	4	15	.	.	PUNCT
ejpam-6247	5	1	topological	topological	ADJ
ejpam-6247	5	2	characterizations	characterization	NOUN
ejpam-6247	5	3	are	be	AUX
ejpam-6247	5	4	provided	provide	VERB
ejpam-6247	5	5	via	via	ADP
ejpam-6247	5	6	minimal	minimal	ADJ
ejpam-6247	5	7	prime	prime	ADJ
ejpam-6247	5	8	d	d	NOUN
ejpam-6247	5	9	-	-	PUNCT
ejpam-6247	5	10	filters	filter	NOUN
ejpam-6247	5	11	and	and	CCONJ
ejpam-6247	5	12	their	their	PRON
ejpam-6247	5	13	prime	prime	ADJ
ejpam-6247	5	14	spectra	spectra	NOUN
ejpam-6247	5	15	.	.	PROPN
ejpam-6247	6	1	2020	2020	NUM
ejpam-6247	7	1	mathematics	mathematics	PROPN
ejpam-6247	7	2	subject	subject	NOUN
ejpam-6247	7	3	classifications	classification	NOUN
ejpam-6247	7	4	:	:	PUNCT
ejpam-6247	7	5	06d99	06d99	NUM
ejpam-6247	7	6	,	,	PUNCT
ejpam-6247	7	7	06d15	06d15	DET
ejpam-6247	7	8	key	key	ADJ
ejpam-6247	7	9	words	word	NOUN
ejpam-6247	7	10	and	and	CCONJ
ejpam-6247	7	11	phrases	phrase	NOUN
ejpam-6247	7	12	:	:	PUNCT
ejpam-6247	7	13	almost	almost	ADV
ejpam-6247	7	14	distributive	distributive	ADJ
ejpam-6247	7	15	lattice	lattice	NOUN
ejpam-6247	7	16	(	(	PUNCT
ejpam-6247	7	17	adl	adl	PROPN
ejpam-6247	7	18	)	)	PUNCT
ejpam-6247	7	19	,	,	PUNCT
ejpam-6247	7	20	hemicomplemented	hemicomplemente	VERB
ejpam-6247	7	21	adl	adl	PROPN
ejpam-6247	7	22	,	,	PUNCT
ejpam-6247	7	23	dfilter	dfilter	NOUN
ejpam-6247	7	24	,	,	PUNCT
ejpam-6247	7	25	d	d	X
ejpam-6247	7	26	-	-	PUNCT
ejpam-6247	7	27	stone	stone	NOUN
ejpam-6247	7	28	adl	adl	PROPN
ejpam-6247	7	29	,	,	PUNCT
ejpam-6247	7	30	hausdorff	hausdorff	NOUN
ejpam-6247	7	31	space	space	NOUN
ejpam-6247	7	32	1	1	NUM
ejpam-6247	7	33	.	.	PUNCT
ejpam-6247	8	1	introduction	introduction	NOUN
ejpam-6247	8	2	lattice	lattice	PROPN
ejpam-6247	8	3	theory	theory	NOUN
ejpam-6247	8	4	has	have	AUX
ejpam-6247	8	5	long	long	ADV
ejpam-6247	8	6	served	serve	VERB
ejpam-6247	8	7	as	as	ADP
ejpam-6247	8	8	a	a	DET
ejpam-6247	8	9	fundamental	fundamental	ADJ
ejpam-6247	8	10	framework	framework	NOUN
ejpam-6247	8	11	for	for	ADP
ejpam-6247	8	12	algebraic	algebraic	ADJ
ejpam-6247	8	13	structures	structure	NOUN
ejpam-6247	8	14	,	,	PUNCT
ejpam-6247	8	15	with	with	ADP
ejpam-6247	8	16	comprehensive	comprehensive	ADJ
ejpam-6247	8	17	treatments	treatment	NOUN
ejpam-6247	8	18	available	available	ADJ
ejpam-6247	8	19	in	in	ADP
ejpam-6247	8	20	birkhoff	birkhoff	NOUN
ejpam-6247	8	21	’s	’s	PART
ejpam-6247	8	22	work	work	NOUN
ejpam-6247	9	1	[	[	X
ejpam-6247	9	2	1	1	X
ejpam-6247	9	3	]	]	PUNCT
ejpam-6247	9	4	and	and	CCONJ
ejpam-6247	9	5	grätzer	grätzer	PROPN
ejpam-6247	9	6	’s	’s	PART
ejpam-6247	9	7	monograph	monograph	NOUN
ejpam-6247	10	1	[	[	X
ejpam-6247	10	2	2	2	NUM
ejpam-6247	10	3	]	]	PUNCT
ejpam-6247	10	4	.	.	PUNCT
ejpam-6247	11	1	several	several	ADJ
ejpam-6247	11	2	foundational	foundational	ADJ
ejpam-6247	11	3	results	result	NOUN
ejpam-6247	11	4	regarding	regard	VERB
ejpam-6247	11	5	prime	prime	ADJ
ejpam-6247	11	6	spectra	spectra	ADJ
ejpam-6247	11	7	and	and	CCONJ
ejpam-6247	11	8	congruence	congruence	NOUN
ejpam-6247	11	9	structures	structure	NOUN
ejpam-6247	11	10	of	of	ADP
ejpam-6247	11	11	lattices	lattice	NOUN
ejpam-6247	11	12	have	have	AUX
ejpam-6247	11	13	also	also	ADV
ejpam-6247	11	14	been	be	AUX
ejpam-6247	11	15	developed	develop	VERB
ejpam-6247	11	16	in	in	ADP
ejpam-6247	11	17	works	work	NOUN
ejpam-6247	11	18	by	by	ADP
ejpam-6247	11	19	crawley	crawley	NOUN
ejpam-6247	11	20	and	and	CCONJ
ejpam-6247	11	21	dilworth	dilworth	PROPN
ejpam-6247	11	22	[	[	X
ejpam-6247	11	23	3	3	NUM
ejpam-6247	11	24	]	]	PUNCT
ejpam-6247	11	25	and	and	CCONJ
ejpam-6247	11	26	grätzer	grätzer	NOUN
ejpam-6247	11	27	and	and	CCONJ
ejpam-6247	11	28	schmidt	schmidt	NOUN
ejpam-6247	11	29	[	[	X
ejpam-6247	11	30	4	4	NUM
ejpam-6247	11	31	]	]	PUNCT
ejpam-6247	11	32	.	.	PUNCT
ejpam-6247	12	1	building	build	VERB
ejpam-6247	12	2	upon	upon	SCONJ
ejpam-6247	12	3	this	this	DET
ejpam-6247	12	4	foundational	foundational	PROPN
ejpam-6247	12	5	lattice	lattice	PROPN
ejpam-6247	12	6	theory	theory	NOUN
ejpam-6247	12	7	,	,	PUNCT
ejpam-6247	12	8	swamy	swamy	NOUN
ejpam-6247	12	9	and	and	CCONJ
ejpam-6247	12	10	rao	rao	NOUN
ejpam-6247	13	1	[	[	X
ejpam-6247	13	2	5	5	NUM
ejpam-6247	13	3	]	]	PUNCT
ejpam-6247	13	4	introduced	introduce	VERB
ejpam-6247	13	5	the	the	DET
ejpam-6247	13	6	concept	concept	NOUN
ejpam-6247	13	7	of	of	ADP
ejpam-6247	13	8	almost	almost	ADV
ejpam-6247	13	9	distributive	distributive	ADJ
ejpam-6247	13	10	lattices	lattice	NOUN
ejpam-6247	13	11	(	(	PUNCT
ejpam-6247	13	12	adls	adls	PROPN
ejpam-6247	13	13	)	)	PUNCT
ejpam-6247	13	14	as	as	ADP
ejpam-6247	13	15	an	an	DET
ejpam-6247	13	16	abstraction	abstraction	NOUN
ejpam-6247	13	17	of	of	ADP
ejpam-6247	13	18	distributive	distributive	ADJ
ejpam-6247	13	19	lattices	lattice	NOUN
ejpam-6247	13	20	and	and	CCONJ
ejpam-6247	13	21	boolean	boolean	ADJ
ejpam-6247	13	22	algebras	algebra	NOUN
ejpam-6247	13	23	.	.	PUNCT
ejpam-6247	14	1	they	they	PRON
ejpam-6247	14	2	defined	define	VERB
ejpam-6247	14	3	ideals	ideal	NOUN
ejpam-6247	14	4	in	in	ADP
ejpam-6247	14	5	adls	adls	PROPN
ejpam-6247	14	6	analogous	analogous	ADJ
ejpam-6247	14	7	to	to	ADP
ejpam-6247	14	8	those	those	PRON
ejpam-6247	14	9	in	in	ADP
ejpam-6247	14	10	distributive	distributive	ADJ
ejpam-6247	14	11	lattices	lattice	NOUN
ejpam-6247	14	12	.	.	PUNCT
ejpam-6247	15	1	they	they	PRON
ejpam-6247	15	2	showed	show	VERB
ejpam-6247	15	3	that	that	SCONJ
ejpam-6247	15	4	the	the	DET
ejpam-6247	15	5	collection	collection	NOUN
ejpam-6247	15	6	of	of	ADP
ejpam-6247	15	7	principal	principal	ADJ
ejpam-6247	15	8	ideals	ideal	NOUN
ejpam-6247	15	9	constitutes	constitute	VERB
ejpam-6247	15	10	a	a	DET
ejpam-6247	15	11	distributive	distributive	ADJ
ejpam-6247	15	12	lattice	lattice	NOUN
ejpam-6247	15	13	,	,	PUNCT
ejpam-6247	15	14	thereby	thereby	ADV
ejpam-6247	15	15	facilitating	facilitate	VERB
ejpam-6247	15	16	the	the	DET
ejpam-6247	15	17	extension	extension	NOUN
ejpam-6247	15	18	of	of	ADP
ejpam-6247	15	19	lattice	lattice	NOUN
ejpam-6247	15	20	theory	theory	NOUN
ejpam-6247	15	21	concepts	concept	NOUN
ejpam-6247	15	22	to	to	ADP
ejpam-6247	15	23	adls	adls	PROPN
ejpam-6247	15	24	.	.	PUNCT
ejpam-6247	16	1	rafi	rafi	PROPN
ejpam-6247	16	2	et	et	PROPN
ejpam-6247	16	3	al	al	PROPN
ejpam-6247	16	4	.	.	PUNCT
ejpam-6247	17	1	[	[	X
ejpam-6247	17	2	6	6	NUM
ejpam-6247	17	3	]	]	PUNCT
ejpam-6247	17	4	introduced	introduce	VERB
ejpam-6247	17	5	the	the	DET
ejpam-6247	17	6	concept	concept	NOUN
ejpam-6247	17	7	of	of	ADP
ejpam-6247	17	8	d	d	NOUN
ejpam-6247	17	9	-	-	PUNCT
ejpam-6247	17	10	filters	filter	NOUN
ejpam-6247	17	11	in	in	ADP
ejpam-6247	17	12	adls	adls	PROPN
ejpam-6247	17	13	,	,	PUNCT
ejpam-6247	17	14	examining	examine	VERB
ejpam-6247	17	15	their	their	PRON
ejpam-6247	17	16	key	key	ADJ
ejpam-6247	17	17	properties	property	NOUN
ejpam-6247	17	18	.	.	PUNCT
ejpam-6247	18	1	rafi	rafi	PROPN
ejpam-6247	18	2	et	et	PROPN
ejpam-6247	18	3	al	al	PROPN
ejpam-6247	18	4	.	.	PUNCT
ejpam-6247	19	1	[	[	X
ejpam-6247	19	2	7	7	X
ejpam-6247	19	3	]	]	PUNCT
ejpam-6247	19	4	studied	study	VERB
ejpam-6247	19	5	prime	prime	ADJ
ejpam-6247	19	6	e	e	NOUN
ejpam-6247	19	7	-	-	NOUN
ejpam-6247	19	8	ideals	ideal	NOUN
ejpam-6247	19	9	in	in	ADP
ejpam-6247	19	10	almost	almost	ADV
ejpam-6247	19	11	distributive	distributive	ADJ
ejpam-6247	19	12	lattices	lattice	NOUN
ejpam-6247	19	13	,	,	PUNCT
ejpam-6247	19	14	establishing	establish	VERB
ejpam-6247	19	15	key	key	ADJ
ejpam-6247	19	16	properties	property	NOUN
ejpam-6247	19	17	that	that	SCONJ
ejpam-6247	19	18	∗corresponding	∗corresponde	VERB
ejpam-6247	19	19	author	author	NOUN
ejpam-6247	19	20	.	.	PUNCT
ejpam-6247	20	1	doi	doi	NOUN
ejpam-6247	20	2	:	:	PUNCT
ejpam-6247	20	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6247	https://doi.org/10.29020/nybg.ejpam.v18i3.6247	PROPN
ejpam-6247	20	4	email	email	NOUN
ejpam-6247	20	5	addresses	address	NOUN
ejpam-6247	20	6	:	:	PUNCT
ejpam-6247	20	7	rafimaths@gmail.com	rafimaths@gmail.com	X
ejpam-6247	20	8	(	(	PUNCT
ejpam-6247	20	9	n.	n.	PROPN
ejpam-6247	20	10	rafi	rafi	PROPN
ejpam-6247	20	11	)	)	PUNCT
ejpam-6247	20	12	,	,	PUNCT
ejpam-6247	20	13	ravimaths83@gmail.com	ravimaths83@gmail.com	PROPN
ejpam-6247	20	14	(	(	PUNCT
ejpam-6247	20	15	r.	r.	PROPN
ejpam-6247	20	16	bandaru	bandaru	PROPN
ejpam-6247	20	17	)	)	PUNCT
ejpam-6247	20	18	,	,	PUNCT
ejpam-6247	21	1	davalaravikumar@gmail.com	davalaravikumar@gmail.com	PROPN
ejpam-6247	21	2	(	(	PUNCT
ejpam-6247	21	3	r.	r.	PROPN
ejpam-6247	21	4	k.	k.	PROPN
ejpam-6247	21	5	davala	davala	PROPN
ejpam-6247	21	6	)	)	PUNCT
ejpam-6247	21	7	,	,	PUNCT
ejpam-6247	21	8	aiyared.ia@up.ac.th	aiyared.ia@up.ac.th	NOUN
ejpam-6247	21	9	(	(	PUNCT
ejpam-6247	21	10	a.	a.	NOUN
ejpam-6247	21	11	iampan	iampan	PROPN
ejpam-6247	21	12	)	)	PUNCT
ejpam-6247	21	13	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6247	22	1	1	1	NUM
ejpam-6247	22	2	copyright	copyright	NOUN
ejpam-6247	22	3	:	:	PUNCT
ejpam-6247	22	4	©	©	PROPN
ejpam-6247	22	5	2025	2025	NUM
ejpam-6247	22	6	the	the	DET
ejpam-6247	22	7	author(s	author(s	NOUN
ejpam-6247	22	8	)	)	PUNCT
ejpam-6247	22	9	.	.	PUNCT
ejpam-6247	23	1	(	(	PUNCT
ejpam-6247	23	2	cc	cc	NOUN
ejpam-6247	23	3	by	by	ADP
ejpam-6247	23	4	-	-	PUNCT
ejpam-6247	23	5	nc	nc	PROPN
ejpam-6247	23	6	4.0	4.0	NUM
ejpam-6247	23	7	)	)	PUNCT
ejpam-6247	23	8	n.	n.	NOUN
ejpam-6247	23	9	rafi	rafi	PROPN
ejpam-6247	23	10	et	et	PROPN
ejpam-6247	23	11	al	al	PROPN
ejpam-6247	23	12	.	.	PUNCT
ejpam-6247	23	13	/	/	SYM
ejpam-6247	23	14	eur	eur	PROPN
ejpam-6247	23	15	.	.	PUNCT
ejpam-6247	24	1	j.	j.	PROPN
ejpam-6247	24	2	pure	pure	PROPN
ejpam-6247	24	3	appl	appl	PROPN
ejpam-6247	24	4	.	.	PROPN
ejpam-6247	24	5	math	math	PROPN
ejpam-6247	24	6	,	,	PUNCT
ejpam-6247	24	7	18	18	NUM
ejpam-6247	24	8	(	(	PUNCT
ejpam-6247	24	9	3	3	NUM
ejpam-6247	24	10	)	)	PUNCT
ejpam-6247	24	11	(	(	PUNCT
ejpam-6247	24	12	2025	2025	NUM
ejpam-6247	24	13	)	)	PUNCT
ejpam-6247	24	14	,	,	PUNCT
ejpam-6247	24	15	6247	6247	NUM
ejpam-6247	24	16	2	2	NUM
ejpam-6247	24	17	of	of	ADP
ejpam-6247	24	18	15	15	NUM
ejpam-6247	24	19	parallel	parallel	ADJ
ejpam-6247	24	20	prime	prime	ADJ
ejpam-6247	24	21	structures	structure	NOUN
ejpam-6247	24	22	in	in	ADP
ejpam-6247	24	23	classical	classical	ADJ
ejpam-6247	24	24	lattice	lattice	NOUN
ejpam-6247	24	25	theory	theory	NOUN
ejpam-6247	24	26	and	and	CCONJ
ejpam-6247	24	27	contribute	contribute	VERB
ejpam-6247	24	28	to	to	ADP
ejpam-6247	24	29	the	the	DET
ejpam-6247	24	30	broader	broad	ADJ
ejpam-6247	24	31	understanding	understanding	NOUN
ejpam-6247	24	32	of	of	ADP
ejpam-6247	24	33	ideal	ideal	ADV
ejpam-6247	24	34	-	-	PUNCT
ejpam-6247	24	35	based	base	VERB
ejpam-6247	24	36	frameworks	framework	NOUN
ejpam-6247	24	37	in	in	ADP
ejpam-6247	24	38	adls	adls	PROPN
ejpam-6247	24	39	.	.	PUNCT
ejpam-6247	25	1	ramesh	ramesh	PROPN
ejpam-6247	25	2	et	et	PROPN
ejpam-6247	25	3	al	al	PROPN
ejpam-6247	25	4	.	.	PUNCT
ejpam-6247	26	1	[	[	X
ejpam-6247	26	2	8	8	NUM
ejpam-6247	26	3	]	]	PUNCT
ejpam-6247	26	4	examined	examine	VERB
ejpam-6247	26	5	hierarchical	hierarchical	ADJ
ejpam-6247	26	6	classifications	classification	NOUN
ejpam-6247	26	7	within	within	ADP
ejpam-6247	26	8	almost	almost	ADV
ejpam-6247	26	9	distributive	distributive	ADJ
ejpam-6247	26	10	lattices	lattice	NOUN
ejpam-6247	26	11	,	,	PUNCT
ejpam-6247	26	12	offering	offer	VERB
ejpam-6247	26	13	a	a	DET
ejpam-6247	26	14	refined	refined	ADJ
ejpam-6247	26	15	structural	structural	ADJ
ejpam-6247	26	16	perspective	perspective	NOUN
ejpam-6247	26	17	that	that	PRON
ejpam-6247	26	18	complements	complement	VERB
ejpam-6247	26	19	the	the	DET
ejpam-6247	26	20	development	development	NOUN
ejpam-6247	26	21	of	of	ADP
ejpam-6247	26	22	filter	filter	NOUN
ejpam-6247	26	23	-	-	PUNCT
ejpam-6247	26	24	based	base	VERB
ejpam-6247	26	25	approaches	approach	NOUN
ejpam-6247	26	26	in	in	ADP
ejpam-6247	26	27	adls	adls	PROPN
ejpam-6247	26	28	.	.	PUNCT
ejpam-6247	27	1	rafi	rafi	PROPN
ejpam-6247	27	2	et	et	PROPN
ejpam-6247	27	3	al	al	PROPN
ejpam-6247	27	4	.	.	PUNCT
ejpam-6247	28	1	[	[	X
ejpam-6247	28	2	9	9	NUM
ejpam-6247	28	3	]	]	PUNCT
ejpam-6247	28	4	introduced	introduce	VERB
ejpam-6247	28	5	the	the	DET
ejpam-6247	28	6	concept	concept	NOUN
ejpam-6247	28	7	of	of	ADP
ejpam-6247	28	8	w	w	NOUN
ejpam-6247	28	9	-	-	PUNCT
ejpam-6247	28	10	filters	filter	NOUN
ejpam-6247	28	11	in	in	ADP
ejpam-6247	28	12	almost	almost	ADV
ejpam-6247	28	13	distributive	distributive	ADJ
ejpam-6247	28	14	lattices	lattice	NOUN
ejpam-6247	28	15	,	,	PUNCT
ejpam-6247	28	16	thereby	thereby	ADV
ejpam-6247	28	17	expanding	expand	VERB
ejpam-6247	28	18	the	the	DET
ejpam-6247	28	19	theoretical	theoretical	ADJ
ejpam-6247	28	20	landscape	landscape	NOUN
ejpam-6247	28	21	of	of	ADP
ejpam-6247	28	22	generalized	generalized	ADJ
ejpam-6247	28	23	filter	filter	NOUN
ejpam-6247	28	24	structures	structure	NOUN
ejpam-6247	28	25	closely	closely	ADV
ejpam-6247	28	26	related	relate	VERB
ejpam-6247	28	27	to	to	ADP
ejpam-6247	28	28	the	the	DET
ejpam-6247	28	29	notion	notion	NOUN
ejpam-6247	28	30	ofd	ofd	VERB
ejpam-6247	28	31	-	-	PUNCT
ejpam-6247	28	32	filters	filter	NOUN
ejpam-6247	28	33	considered	consider	VERB
ejpam-6247	28	34	in	in	ADP
ejpam-6247	28	35	the	the	DET
ejpam-6247	28	36	present	present	ADJ
ejpam-6247	28	37	study	study	NOUN
ejpam-6247	28	38	.	.	PUNCT
ejpam-6247	29	1	rafi	rafi	PROPN
ejpam-6247	29	2	et	et	PROPN
ejpam-6247	29	3	al	al	PROPN
ejpam-6247	29	4	.	.	PUNCT
ejpam-6247	30	1	[	[	X
ejpam-6247	30	2	10	10	NUM
ejpam-6247	30	3	]	]	PUNCT
ejpam-6247	30	4	introduced	introduce	VERB
ejpam-6247	30	5	the	the	DET
ejpam-6247	30	6	concept	concept	NOUN
ejpam-6247	30	7	of	of	ADP
ejpam-6247	30	8	hemicomplemented	hemicomplemente	VERB
ejpam-6247	30	9	adl	adl	PROPN
ejpam-6247	30	10	and	and	CCONJ
ejpam-6247	30	11	studied	study	VERB
ejpam-6247	30	12	their	their	PRON
ejpam-6247	30	13	properties	property	NOUN
ejpam-6247	30	14	.	.	PUNCT
ejpam-6247	31	1	the	the	DET
ejpam-6247	31	2	concept	concept	NOUN
ejpam-6247	31	3	of	of	ADP
ejpam-6247	31	4	d	d	NOUN
ejpam-6247	31	5	-	-	NOUN
ejpam-6247	31	6	stone	stone	NOUN
ejpam-6247	31	7	adls	adls	NOUN
ejpam-6247	31	8	is	be	AUX
ejpam-6247	31	9	proposed	propose	VERB
ejpam-6247	31	10	,	,	PUNCT
ejpam-6247	31	11	and	and	CCONJ
ejpam-6247	31	12	their	their	PRON
ejpam-6247	31	13	defining	define	VERB
ejpam-6247	31	14	attributes	attribute	NOUN
ejpam-6247	31	15	are	be	AUX
ejpam-6247	31	16	investigated	investigate	VERB
ejpam-6247	31	17	.	.	PUNCT
ejpam-6247	32	1	it	it	PRON
ejpam-6247	32	2	is	be	AUX
ejpam-6247	32	3	found	find	VERB
ejpam-6247	32	4	that	that	SCONJ
ejpam-6247	32	5	while	while	SCONJ
ejpam-6247	32	6	every	every	DET
ejpam-6247	32	7	d	d	NOUN
ejpam-6247	32	8	-	-	PUNCT
ejpam-6247	32	9	stone	stone	NOUN
ejpam-6247	32	10	adl	adl	NOUN
ejpam-6247	32	11	is	be	AUX
ejpam-6247	32	12	necessarily	necessarily	ADV
ejpam-6247	32	13	hemicomplemented	hemicomplemente	VERB
ejpam-6247	32	14	,	,	PUNCT
ejpam-6247	32	15	the	the	DET
ejpam-6247	32	16	converse	converse	NOUN
ejpam-6247	32	17	does	do	AUX
ejpam-6247	32	18	not	not	PART
ejpam-6247	32	19	hold	hold	VERB
ejpam-6247	32	20	in	in	ADP
ejpam-6247	32	21	general	general	ADJ
ejpam-6247	32	22	.	.	PUNCT
ejpam-6247	33	1	several	several	ADJ
ejpam-6247	33	2	equivalent	equivalent	ADJ
ejpam-6247	33	3	conditions	condition	NOUN
ejpam-6247	33	4	are	be	AUX
ejpam-6247	33	5	presented	present	VERB
ejpam-6247	33	6	that	that	PRON
ejpam-6247	33	7	ensure	ensure	VERB
ejpam-6247	33	8	a	a	DET
ejpam-6247	33	9	hemicomplemented	hemicomplemente	VERB
ejpam-6247	33	10	adl	adl	NOUN
ejpam-6247	33	11	is	be	AUX
ejpam-6247	33	12	,	,	PUNCT
ejpam-6247	33	13	in	in	ADP
ejpam-6247	33	14	fact	fact	NOUN
ejpam-6247	33	15	,	,	PUNCT
ejpam-6247	33	16	a	a	DET
ejpam-6247	33	17	d	d	NOUN
ejpam-6247	33	18	-	-	NOUN
ejpam-6247	33	19	stone	stone	NOUN
ejpam-6247	33	20	adl	adl	PROPN
ejpam-6247	33	21	.	.	PUNCT
ejpam-6247	34	1	a	a	DET
ejpam-6247	34	2	condition	condition	NOUN
ejpam-6247	34	3	is	be	AUX
ejpam-6247	34	4	also	also	ADV
ejpam-6247	34	5	identified	identify	VERB
ejpam-6247	34	6	to	to	PART
ejpam-6247	34	7	determine	determine	VERB
ejpam-6247	34	8	when	when	SCONJ
ejpam-6247	34	9	the	the	DET
ejpam-6247	34	10	collection	collection	NOUN
ejpam-6247	34	11	of	of	ADP
ejpam-6247	34	12	all	all	DET
ejpam-6247	34	13	minimal	minimal	ADJ
ejpam-6247	34	14	prime	prime	ADJ
ejpam-6247	34	15	d	d	NOUN
ejpam-6247	34	16	-	-	PUNCT
ejpam-6247	34	17	filters	filter	NOUN
ejpam-6247	34	18	forms	form	VERB
ejpam-6247	34	19	a	a	DET
ejpam-6247	34	20	compact	compact	ADJ
ejpam-6247	34	21	topological	topological	ADJ
ejpam-6247	34	22	space	space	NOUN
ejpam-6247	34	23	.	.	PUNCT
ejpam-6247	35	1	finally	finally	ADV
ejpam-6247	35	2	,	,	PUNCT
ejpam-6247	35	3	topological	topological	ADJ
ejpam-6247	35	4	characterizations	characterization	NOUN
ejpam-6247	35	5	of	of	ADP
ejpam-6247	35	6	hemicomplemented	hemicomplemente	VERB
ejpam-6247	35	7	and	and	CCONJ
ejpam-6247	35	8	d	d	NOUN
ejpam-6247	35	9	-	-	NOUN
ejpam-6247	35	10	stone	stone	NOUN
ejpam-6247	35	11	adls	adls	PROPN
ejpam-6247	35	12	are	be	AUX
ejpam-6247	35	13	established	establish	VERB
ejpam-6247	35	14	,	,	PUNCT
ejpam-6247	35	15	involving	involve	VERB
ejpam-6247	35	16	both	both	CCONJ
ejpam-6247	35	17	the	the	DET
ejpam-6247	35	18	set	set	NOUN
ejpam-6247	35	19	of	of	ADP
ejpam-6247	35	20	minimal	minimal	ADJ
ejpam-6247	35	21	prime	prime	ADJ
ejpam-6247	35	22	d	d	NOUN
ejpam-6247	35	23	-	-	PUNCT
ejpam-6247	35	24	filters	filter	NOUN
ejpam-6247	35	25	and	and	CCONJ
ejpam-6247	35	26	the	the	DET
ejpam-6247	35	27	prime	prime	ADJ
ejpam-6247	35	28	spectrum	spectrum	NOUN
ejpam-6247	35	29	of	of	ADP
ejpam-6247	35	30	d	d	NOUN
ejpam-6247	35	31	-	-	PUNCT
ejpam-6247	35	32	filters	filter	NOUN
ejpam-6247	35	33	in	in	ADP
ejpam-6247	35	34	adls	adls	PROPN
ejpam-6247	35	35	.	.	PUNCT
ejpam-6247	36	1	2	2	X
ejpam-6247	36	2	.	.	X
ejpam-6247	36	3	preliminaries	preliminary	NOUN
ejpam-6247	36	4	this	this	DET
ejpam-6247	36	5	section	section	NOUN
ejpam-6247	36	6	presents	present	VERB
ejpam-6247	36	7	fundamental	fundamental	ADJ
ejpam-6247	36	8	definitions	definition	NOUN
ejpam-6247	36	9	and	and	CCONJ
ejpam-6247	36	10	key	key	ADJ
ejpam-6247	36	11	results	result	NOUN
ejpam-6247	36	12	from	from	ADP
ejpam-6247	36	13	[	[	X
ejpam-6247	36	14	5	5	NUM
ejpam-6247	36	15	,	,	PUNCT
ejpam-6247	36	16	11	11	NUM
ejpam-6247	36	17	]	]	PUNCT
ejpam-6247	36	18	,	,	PUNCT
ejpam-6247	36	19	which	which	PRON
ejpam-6247	36	20	will	will	AUX
ejpam-6247	36	21	be	be	AUX
ejpam-6247	36	22	referenced	reference	VERB
ejpam-6247	36	23	throughout	throughout	ADP
ejpam-6247	36	24	the	the	DET
ejpam-6247	36	25	paper	paper	NOUN
ejpam-6247	36	26	.	.	PUNCT
ejpam-6247	37	1	definition	definition	NOUN
ejpam-6247	37	2	1	1	NUM
ejpam-6247	37	3	.	.	PUNCT
ejpam-6247	38	1	[	[	X
ejpam-6247	38	2	5	5	NUM
ejpam-6247	38	3	]	]	PUNCT
ejpam-6247	38	4	a	a	DET
ejpam-6247	38	5	structure	structure	NOUN
ejpam-6247	38	6	(	(	PUNCT
ejpam-6247	38	7	l,∨,∧	l,∨,∧	NOUN
ejpam-6247	38	8	,	,	PUNCT
ejpam-6247	38	9	0	0	NUM
ejpam-6247	38	10	)	)	PUNCT
ejpam-6247	38	11	of	of	ADP
ejpam-6247	38	12	type	type	NOUN
ejpam-6247	38	13	(	(	PUNCT
ejpam-6247	38	14	2	2	NUM
ejpam-6247	38	15	,	,	PUNCT
ejpam-6247	38	16	2	2	NUM
ejpam-6247	38	17	,	,	PUNCT
ejpam-6247	38	18	0	0	NUM
ejpam-6247	38	19	)	)	PUNCT
ejpam-6247	38	20	is	be	AUX
ejpam-6247	38	21	called	call	VERB
ejpam-6247	38	22	an	an	DET
ejpam-6247	38	23	almost	almost	ADV
ejpam-6247	38	24	distributive	distributive	ADJ
ejpam-6247	38	25	lattice	lattice	NOUN
ejpam-6247	38	26	(	(	PUNCT
ejpam-6247	38	27	adl	adl	PROPN
ejpam-6247	38	28	)	)	PUNCT
ejpam-6247	38	29	with	with	ADP
ejpam-6247	38	30	zero	zero	NUM
ejpam-6247	38	31	if	if	SCONJ
ejpam-6247	38	32	it	it	PRON
ejpam-6247	38	33	fulfills	fulfill	VERB
ejpam-6247	38	34	the	the	DET
ejpam-6247	38	35	following	follow	VERB
ejpam-6247	38	36	conditions	condition	NOUN
ejpam-6247	38	37	:	:	PUNCT
ejpam-6247	38	38	(	(	PUNCT
ejpam-6247	38	39	1	1	X
ejpam-6247	38	40	)	)	PUNCT
ejpam-6247	38	41	(	(	PUNCT
ejpam-6247	38	42	θ	θ	PROPN
ejpam-6247	38	43	∨	∨	NUM
ejpam-6247	38	44	ϑ	ϑ	X
ejpam-6247	38	45	)	)	PUNCT
ejpam-6247	38	46	∧	∧	PROPN
ejpam-6247	38	47	σ	σ	NOUN
ejpam-6247	38	48	=	=	SYM
ejpam-6247	38	49	(	(	PUNCT
ejpam-6247	38	50	θ	θ	PROPN
ejpam-6247	38	51	∧	∧	PROPN
ejpam-6247	38	52	σ	σ	PROPN
ejpam-6247	38	53	)	)	PUNCT
ejpam-6247	38	54	∨	∨	NOUN
ejpam-6247	38	55	(	(	PUNCT
ejpam-6247	38	56	ϑ	ϑ	X
ejpam-6247	38	57	∧	∧	PROPN
ejpam-6247	38	58	σ	σ	PROPN
ejpam-6247	38	59	)	)	PUNCT
ejpam-6247	38	60	,	,	PUNCT
ejpam-6247	38	61	(	(	PUNCT
ejpam-6247	38	62	2	2	X
ejpam-6247	38	63	)	)	PUNCT
ejpam-6247	38	64	θ	θ	NOUN
ejpam-6247	38	65	∧	∧	PROPN
ejpam-6247	38	66	(	(	PUNCT
ejpam-6247	38	67	ϑ	ϑ	PROPN
ejpam-6247	38	68	∨	∨	PROPN
ejpam-6247	38	69	σ	σ	PROPN
ejpam-6247	38	70	)	)	PUNCT
ejpam-6247	38	71	=	=	PUNCT
ejpam-6247	38	72	(	(	PUNCT
ejpam-6247	38	73	θ	θ	PROPN
ejpam-6247	38	74	∧	∧	PROPN
ejpam-6247	38	75	ϑ	ϑ	X
ejpam-6247	38	76	)	)	PUNCT
ejpam-6247	38	77	∨	∨	PROPN
ejpam-6247	38	78	(	(	PUNCT
ejpam-6247	38	79	θ	θ	PROPN
ejpam-6247	38	80	∧	∧	PROPN
ejpam-6247	38	81	σ	σ	PROPN
ejpam-6247	38	82	)	)	PUNCT
ejpam-6247	38	83	,	,	PUNCT
ejpam-6247	38	84	(	(	PUNCT
ejpam-6247	38	85	3	3	X
ejpam-6247	38	86	)	)	PUNCT
ejpam-6247	38	87	θ	θ	NOUN
ejpam-6247	38	88	∨	∨	PROPN
ejpam-6247	38	89	(	(	PUNCT
ejpam-6247	38	90	ϑ	ϑ	X
ejpam-6247	38	91	∧	∧	PROPN
ejpam-6247	38	92	σ	σ	PROPN
ejpam-6247	38	93	)	)	PUNCT
ejpam-6247	38	94	=	=	PUNCT
ejpam-6247	38	95	(	(	PUNCT
ejpam-6247	38	96	θ	θ	PROPN
ejpam-6247	38	97	∨	∨	NUM
ejpam-6247	38	98	ϑ	ϑ	X
ejpam-6247	38	99	)	)	PUNCT
ejpam-6247	38	100	∧	∧	PROPN
ejpam-6247	38	101	(	(	PUNCT
ejpam-6247	38	102	θ	θ	PROPN
ejpam-6247	38	103	∨	∨	PROPN
ejpam-6247	38	104	σ	σ	PROPN
ejpam-6247	38	105	)	)	PUNCT
ejpam-6247	38	106	,	,	PUNCT
ejpam-6247	38	107	(	(	PUNCT
ejpam-6247	38	108	4	4	NUM
ejpam-6247	38	109	)	)	PUNCT
ejpam-6247	38	110	(	(	PUNCT
ejpam-6247	38	111	θ	θ	PROPN
ejpam-6247	38	112	∨	∨	NUM
ejpam-6247	38	113	ϑ	ϑ	X
ejpam-6247	38	114	)	)	PUNCT
ejpam-6247	38	115	∧	∧	PROPN
ejpam-6247	38	116	ϑ	ϑ	X
ejpam-6247	38	117	=	=	X
ejpam-6247	38	118	ϑ	ϑ	X
ejpam-6247	38	119	,	,	PUNCT
ejpam-6247	38	120	(	(	PUNCT
ejpam-6247	38	121	5	5	NUM
ejpam-6247	38	122	)	)	PUNCT
ejpam-6247	38	123	θ	θ	NOUN
ejpam-6247	38	124	∨	∨	NUM
ejpam-6247	38	125	0	0	X
ejpam-6247	38	126	=	=	SYM
ejpam-6247	38	127	θ	θ	PROPN
ejpam-6247	38	128	,	,	PUNCT
ejpam-6247	38	129	(	(	PUNCT
ejpam-6247	38	130	6	6	NUM
ejpam-6247	38	131	)	)	PUNCT
ejpam-6247	38	132	0	0	NUM
ejpam-6247	39	1	∧	∧	NOUN
ejpam-6247	39	2	θ	θ	NOUN
ejpam-6247	39	3	=	=	SYM
ejpam-6247	39	4	0	0	NUM
ejpam-6247	39	5	,	,	PUNCT
ejpam-6247	39	6	for	for	ADP
ejpam-6247	39	7	any	any	DET
ejpam-6247	39	8	θ	θ	PROPN
ejpam-6247	39	9	,	,	PUNCT
ejpam-6247	39	10	ϑ	ϑ	X
ejpam-6247	39	11	,	,	PUNCT
ejpam-6247	39	12	σ	σ	PROPN
ejpam-6247	39	13	∈	∈	PROPN
ejpam-6247	39	14	l.	l.	NOUN
ejpam-6247	39	15	to	to	PART
ejpam-6247	39	16	define	define	VERB
ejpam-6247	39	17	a	a	DET
ejpam-6247	39	18	partial	partial	ADJ
ejpam-6247	39	19	order	order	NOUN
ejpam-6247	39	20	≤	≤	NOUN
ejpam-6247	39	21	on	on	ADP
ejpam-6247	39	22	l	l	NOUN
ejpam-6247	39	23	,	,	PUNCT
ejpam-6247	39	24	consider	consider	VERB
ejpam-6247	39	25	the	the	DET
ejpam-6247	39	26	condition	condition	NOUN
ejpam-6247	39	27	θ	θ	NOUN
ejpam-6247	39	28	=	=	PUNCT
ejpam-6247	39	29	θ	θ	X
ejpam-6247	39	30	∧	∧	PROPN
ejpam-6247	39	31	ϑ	ϑ	X
ejpam-6247	39	32	or	or	CCONJ
ejpam-6247	39	33	equivalently	equivalently	ADV
ejpam-6247	39	34	θ∨ϑ	θ∨ϑ	PROPN
ejpam-6247	39	35	=	=	SYM
ejpam-6247	39	36	ϑ	ϑ	PROPN
ejpam-6247	39	37	for	for	ADP
ejpam-6247	39	38	every	every	DET
ejpam-6247	39	39	θ	θ	PROPN
ejpam-6247	39	40	,	,	PUNCT
ejpam-6247	39	41	ϑ	ϑ	X
ejpam-6247	39	42	∈	∈	PROPN
ejpam-6247	39	43	l.	l.	NOUN
ejpam-6247	39	44	this	this	DET
ejpam-6247	39	45	condition	condition	NOUN
ejpam-6247	39	46	ensures	ensure	VERB
ejpam-6247	39	47	that	that	SCONJ
ejpam-6247	39	48	θ	θ	PROPN
ejpam-6247	39	49	≤	≤	PROPN
ejpam-6247	39	50	ϑ	ϑ	VERB
ejpam-6247	39	51	,	,	PUNCT
ejpam-6247	39	52	establishing	establish	VERB
ejpam-6247	39	53	≤	≤	NUM
ejpam-6247	39	54	as	as	ADP
ejpam-6247	39	55	a	a	DET
ejpam-6247	39	56	partial	partial	ADJ
ejpam-6247	39	57	order	order	NOUN
ejpam-6247	39	58	on	on	ADP
ejpam-6247	39	59	l.	l.	NOUN
ejpam-6247	39	60	when	when	SCONJ
ejpam-6247	39	61	m	m	PROPN
ejpam-6247	39	62	∈	∈	NOUN
ejpam-6247	39	63	l	l	NOUN
ejpam-6247	39	64	is	be	AUX
ejpam-6247	39	65	maximal	maximal	ADJ
ejpam-6247	39	66	with	with	ADP
ejpam-6247	39	67	respect	respect	NOUN
ejpam-6247	39	68	to	to	ADP
ejpam-6247	39	69	this	this	DET
ejpam-6247	39	70	partial	partial	ADJ
ejpam-6247	39	71	order	order	NOUN
ejpam-6247	39	72	,	,	PUNCT
ejpam-6247	39	73	it	it	PRON
ejpam-6247	39	74	is	be	AUX
ejpam-6247	39	75	referred	refer	VERB
ejpam-6247	39	76	to	to	ADP
ejpam-6247	39	77	as	as	ADV
ejpam-6247	39	78	maximal	maximal	ADJ
ejpam-6247	39	79	.	.	PUNCT
ejpam-6247	40	1	the	the	DET
ejpam-6247	40	2	collection	collection	NOUN
ejpam-6247	40	3	of	of	ADP
ejpam-6247	40	4	all	all	DET
ejpam-6247	40	5	such	such	ADJ
ejpam-6247	40	6	maximal	maximal	ADJ
ejpam-6247	40	7	elements	element	NOUN
ejpam-6247	40	8	in	in	ADP
ejpam-6247	40	9	l	l	NOUN
ejpam-6247	40	10	is	be	AUX
ejpam-6247	40	11	indicated	indicate	VERB
ejpam-6247	40	12	by	by	ADP
ejpam-6247	40	13	m(l	m(l	NOUN
ejpam-6247	40	14	)	)	PUNCT
ejpam-6247	40	15	.	.	PUNCT
ejpam-6247	41	1	adl	adl	PROPN
ejpam-6247	41	2	l	l	NOUN
ejpam-6247	41	3	exhibits	exhibit	VERB
ejpam-6247	41	4	many	many	ADJ
ejpam-6247	41	5	properties	property	NOUN
ejpam-6247	41	6	of	of	ADP
ejpam-6247	41	7	a	a	DET
ejpam-6247	41	8	distributive	distributive	ADJ
ejpam-6247	41	9	lattice	lattice	NOUN
ejpam-6247	41	10	,	,	PUNCT
ejpam-6247	41	11	with	with	ADP
ejpam-6247	41	12	the	the	DET
ejpam-6247	41	13	exception	exception	NOUN
ejpam-6247	41	14	of	of	ADP
ejpam-6247	41	15	noncommutativity	noncommutativity	NOUN
ejpam-6247	41	16	of	of	ADP
ejpam-6247	41	17	∨	∨	NOUN
ejpam-6247	41	18	and	and	CCONJ
ejpam-6247	41	19	∧	∧	NOUN
ejpam-6247	41	20	and	and	CCONJ
ejpam-6247	41	21	lack	lack	NOUN
ejpam-6247	41	22	of	of	ADP
ejpam-6247	41	23	right	right	ADJ
ejpam-6247	41	24	distributivity	distributivity	NOUN
ejpam-6247	41	25	of	of	ADP
ejpam-6247	41	26	∨	∨	NUM
ejpam-6247	41	27	over	over	ADP
ejpam-6247	41	28	∧	∧	PROPN
ejpam-6247	41	29	,	,	PUNCT
ejpam-6247	41	30	as	as	SCONJ
ejpam-6247	41	31	highlighted	highlight	VERB
ejpam-6247	41	32	in	in	ADP
ejpam-6247	41	33	swamy	swamy	PROPN
ejpam-6247	41	34	’s	’s	PART
ejpam-6247	41	35	work	work	NOUN
ejpam-6247	41	36	[	[	X
ejpam-6247	41	37	5	5	NUM
ejpam-6247	41	38	]	]	PUNCT
ejpam-6247	41	39	.	.	PUNCT
ejpam-6247	42	1	if	if	SCONJ
ejpam-6247	42	2	either	either	PRON
ejpam-6247	42	3	of	of	ADP
ejpam-6247	42	4	these	these	DET
ejpam-6247	42	5	properties	property	NOUN
ejpam-6247	42	6	held	hold	VERB
ejpam-6247	42	7	,	,	PUNCT
ejpam-6247	42	8	l	l	PROPN
ejpam-6247	42	9	would	would	AUX
ejpam-6247	42	10	be	be	AUX
ejpam-6247	42	11	classified	classify	VERB
ejpam-6247	42	12	as	as	ADP
ejpam-6247	42	13	a	a	DET
ejpam-6247	42	14	distributive	distributive	ADJ
ejpam-6247	42	15	lattice	lattice	NOUN
ejpam-6247	42	16	.	.	PUNCT
ejpam-6247	43	1	we	we	PRON
ejpam-6247	43	2	define	define	VERB
ejpam-6247	43	3	a	a	DET
ejpam-6247	43	4	non	non	ADJ
ejpam-6247	43	5	-	-	ADJ
ejpam-6247	43	6	void	void	ADJ
ejpam-6247	43	7	subset	subset	VERB
ejpam-6247	43	8	i	i	PRON
ejpam-6247	43	9	of	of	ADP
ejpam-6247	43	10	l	l	NOUN
ejpam-6247	43	11	as	as	ADP
ejpam-6247	43	12	an	an	DET
ejpam-6247	43	13	ideal	ideal	NOUN
ejpam-6247	43	14	(	(	PUNCT
ejpam-6247	43	15	filter	filter	NOUN
ejpam-6247	43	16	)	)	PUNCT
ejpam-6247	43	17	if	if	SCONJ
ejpam-6247	43	18	it	it	PRON
ejpam-6247	43	19	satisfies	satisfy	VERB
ejpam-6247	43	20	that	that	SCONJ
ejpam-6247	43	21	for	for	ADP
ejpam-6247	43	22	any	any	DET
ejpam-6247	43	23	elements	element	NOUN
ejpam-6247	43	24	θ	θ	NOUN
ejpam-6247	43	25	,	,	PUNCT
ejpam-6247	43	26	ϑ	ϑ	X
ejpam-6247	43	27	∈	∈	X
ejpam-6247	43	28	i	i	PRON
ejpam-6247	43	29	and	and	CCONJ
ejpam-6247	43	30	µ	µ	PRON
ejpam-6247	43	31	∈	∈	PROPN
ejpam-6247	43	32	l	l	NOUN
ejpam-6247	43	33	,	,	PUNCT
ejpam-6247	43	34	the	the	DET
ejpam-6247	43	35	subset	subset	NOUN
ejpam-6247	43	36	i	i	PRON
ejpam-6247	43	37	must	must	AUX
ejpam-6247	43	38	include	include	VERB
ejpam-6247	43	39	θ	θ	PROPN
ejpam-6247	43	40	∧	∧	PROPN
ejpam-6247	43	41	µ	µ	X
ejpam-6247	43	42	and	and	CCONJ
ejpam-6247	43	43	θ	θ	PROPN
ejpam-6247	43	44	∨	∨	NUM
ejpam-6247	43	45	ϑ	ϑ	X
ejpam-6247	43	46	(	(	PUNCT
ejpam-6247	43	47	µ	µ	X
ejpam-6247	43	48	∨	∨	NUM
ejpam-6247	43	49	θ	θ	PROPN
ejpam-6247	43	50	and	and	CCONJ
ejpam-6247	43	51	θ∧ϑ	θ∧ϑ	PROPN
ejpam-6247	43	52	)	)	PUNCT
ejpam-6247	43	53	.	.	PUNCT
ejpam-6247	44	1	a	a	DET
ejpam-6247	44	2	maximal	maximal	ADJ
ejpam-6247	44	3	ideal	ideal	NOUN
ejpam-6247	44	4	(	(	PUNCT
ejpam-6247	44	5	filter	filter	NOUN
ejpam-6247	44	6	)	)	PUNCT
ejpam-6247	44	7	contains	contain	VERB
ejpam-6247	44	8	every	every	DET
ejpam-6247	44	9	proper	proper	ADJ
ejpam-6247	44	10	ideal	ideal	NOUN
ejpam-6247	44	11	(	(	PUNCT
ejpam-6247	44	12	filter	filter	NOUN
ejpam-6247	44	13	)	)	PUNCT
ejpam-6247	44	14	of	of	ADP
ejpam-6247	44	15	l.	l.	PROPN
ejpam-6247	44	16	the	the	DET
ejpam-6247	44	17	smallest	small	ADJ
ejpam-6247	44	18	ideal	ideal	ADJ
ejpam-6247	44	19	n.	n.	PROPN
ejpam-6247	44	20	rafi	rafi	PROPN
ejpam-6247	44	21	et	et	PROPN
ejpam-6247	44	22	al	al	PROPN
ejpam-6247	44	23	.	.	PUNCT
ejpam-6247	44	24	/	/	SYM
ejpam-6247	44	25	eur	eur	PROPN
ejpam-6247	44	26	.	.	PUNCT
ejpam-6247	45	1	j.	j.	PROPN
ejpam-6247	45	2	pure	pure	PROPN
ejpam-6247	45	3	appl	appl	PROPN
ejpam-6247	45	4	.	.	PROPN
ejpam-6247	45	5	math	math	PROPN
ejpam-6247	45	6	,	,	PUNCT
ejpam-6247	45	7	18	18	NUM
ejpam-6247	45	8	(	(	PUNCT
ejpam-6247	45	9	3	3	NUM
ejpam-6247	45	10	)	)	PUNCT
ejpam-6247	45	11	(	(	PUNCT
ejpam-6247	45	12	2025	2025	NUM
ejpam-6247	45	13	)	)	PUNCT
ejpam-6247	45	14	,	,	PUNCT
ejpam-6247	45	15	6247	6247	NUM
ejpam-6247	45	16	3	3	NUM
ejpam-6247	45	17	of	of	ADP
ejpam-6247	45	18	15	15	NUM
ejpam-6247	45	19	containing	contain	VERB
ejpam-6247	45	20	a	a	DET
ejpam-6247	45	21	subset	subset	NOUN
ejpam-6247	45	22	s	s	NOUN
ejpam-6247	45	23	of	of	ADP
ejpam-6247	45	24	l	l	NOUN
ejpam-6247	45	25	is	be	AUX
ejpam-6247	45	26	defined	define	VERB
ejpam-6247	45	27	as	as	ADP
ejpam-6247	45	28	(	(	PUNCT
ejpam-6247	45	29	s	s	X
ejpam-6247	45	30	]	]	X
ejpam-6247	45	31	:	:	PUNCT
ejpam-6247	45	32	=	=	SYM
ejpam-6247	45	33	{	{	PUNCT
ejpam-6247	45	34	(	(	PUNCT
ejpam-6247	45	35	n∨	n∨	PROPN
ejpam-6247	45	36	i=1	i=1	PROPN
ejpam-6247	45	37	θi	θi	PROPN
ejpam-6247	45	38	)	)	PUNCT
ejpam-6247	45	39	∧	∧	PROPN
ejpam-6247	45	40	µ	µ	PROPN
ejpam-6247	45	41	|	|	NOUN
ejpam-6247	45	42	θi	θi	ADP
ejpam-6247	45	43	∈	∈	PROPN
ejpam-6247	45	44	s	s	PROPN
ejpam-6247	45	45	,	,	PUNCT
ejpam-6247	45	46	µ	µ	X
ejpam-6247	45	47	∈	∈	PROPN
ejpam-6247	45	48	l	l	NOUN
ejpam-6247	45	49	,	,	PUNCT
ejpam-6247	45	50	n	n	PROPN
ejpam-6247	45	51	∈	∈	PROPN
ejpam-6247	45	52	n	n	CCONJ
ejpam-6247	45	53	}	}	PUNCT
ejpam-6247	45	54	.	.	PUNCT
ejpam-6247	46	1	a	a	DET
ejpam-6247	46	2	principal	principal	ADJ
ejpam-6247	46	3	ideal	ideal	NOUN
ejpam-6247	46	4	generated	generate	VERB
ejpam-6247	46	5	by	by	ADP
ejpam-6247	46	6	an	an	DET
ejpam-6247	46	7	element	element	NOUN
ejpam-6247	46	8	θ	θ	PROPN
ejpam-6247	46	9	is	be	AUX
ejpam-6247	46	10	denoted	denote	VERB
ejpam-6247	46	11	as	as	ADP
ejpam-6247	46	12	(	(	PUNCT
ejpam-6247	46	13	θ	θ	NOUN
ejpam-6247	46	14	]	]	PUNCT
ejpam-6247	46	15	.	.	PUNCT
ejpam-6247	47	1	similarly	similarly	ADV
ejpam-6247	47	2	,	,	PUNCT
ejpam-6247	47	3	for	for	ADP
ejpam-6247	47	4	each	each	DET
ejpam-6247	47	5	subset	subset	NOUN
ejpam-6247	47	6	s	s	PROPN
ejpam-6247	47	7	of	of	ADP
ejpam-6247	47	8	l	l	NOUN
ejpam-6247	47	9	,	,	PUNCT
ejpam-6247	47	10	the	the	DET
ejpam-6247	47	11	smallest	small	ADJ
ejpam-6247	47	12	filter	filter	NOUN
ejpam-6247	47	13	containing	contain	VERB
ejpam-6247	47	14	s	s	NOUN
ejpam-6247	47	15	is	be	AUX
ejpam-6247	47	16	defined	define	VERB
ejpam-6247	47	17	as	as	ADP
ejpam-6247	47	18	[	[	X
ejpam-6247	47	19	s	s	X
ejpam-6247	47	20	)	)	PUNCT
ejpam-6247	47	21	:	:	PUNCT
ejpam-6247	47	22	=	=	SYM
ejpam-6247	47	23	{	{	PUNCT
ejpam-6247	47	24	µ∨	µ∨	NOUN
ejpam-6247	47	25	(	(	PUNCT
ejpam-6247	47	26	n∧	n∧	NUM
ejpam-6247	47	27	i=1	i=1	PROPN
ejpam-6247	47	28	θi	θi	X
ejpam-6247	47	29	)	)	PUNCT
ejpam-6247	48	1	|	|	ADV
ejpam-6247	48	2	θi	θi	ADP
ejpam-6247	48	3	∈	∈	PROPN
ejpam-6247	48	4	s	s	PROPN
ejpam-6247	48	5	,	,	PUNCT
ejpam-6247	48	6	µ	µ	X
ejpam-6247	48	7	∈	∈	PROPN
ejpam-6247	48	8	l	l	NOUN
ejpam-6247	48	9	,	,	PUNCT
ejpam-6247	48	10	n	n	PROPN
ejpam-6247	48	11	∈	∈	PROPN
ejpam-6247	48	12	n	n	CCONJ
ejpam-6247	48	13	}	}	PUNCT
ejpam-6247	48	14	.	.	PUNCT
ejpam-6247	49	1	a	a	DET
ejpam-6247	49	2	principal	principal	ADJ
ejpam-6247	49	3	filter	filter	NOUN
ejpam-6247	49	4	generated	generate	VERB
ejpam-6247	49	5	by	by	ADP
ejpam-6247	49	6	an	an	DET
ejpam-6247	49	7	element	element	NOUN
ejpam-6247	49	8	θ	θ	PROPN
ejpam-6247	49	9	is	be	AUX
ejpam-6247	49	10	denoted	denote	VERB
ejpam-6247	49	11	as	as	ADP
ejpam-6247	49	12	[	[	X
ejpam-6247	49	13	θ	θ	NOUN
ejpam-6247	49	14	)	)	PUNCT
ejpam-6247	49	15	.	.	PUNCT
ejpam-6247	50	1	it	it	PRON
ejpam-6247	50	2	is	be	AUX
ejpam-6247	50	3	established	establish	VERB
ejpam-6247	50	4	that	that	SCONJ
ejpam-6247	50	5	(	(	PUNCT
ejpam-6247	50	6	θ	θ	X
ejpam-6247	50	7	]	]	X
ejpam-6247	50	8	∨	∨	X
ejpam-6247	50	9	(	(	PUNCT
ejpam-6247	50	10	ϑ	ϑ	X
ejpam-6247	50	11	]	]	X
ejpam-6247	50	12	=	=	SYM
ejpam-6247	50	13	(	(	PUNCT
ejpam-6247	50	14	θ	θ	PROPN
ejpam-6247	50	15	∨	∨	NUM
ejpam-6247	50	16	ϑ	ϑ	X
ejpam-6247	50	17	]	]	PUNCT
ejpam-6247	50	18	and	and	CCONJ
ejpam-6247	50	19	(	(	PUNCT
ejpam-6247	50	20	θ	θ	NOUN
ejpam-6247	50	21	]	]	X
ejpam-6247	50	22	∩	∩	NOUN
ejpam-6247	50	23	(	(	PUNCT
ejpam-6247	50	24	ϑ	ϑ	X
ejpam-6247	50	25	]	]	X
ejpam-6247	50	26	=	=	SYM
ejpam-6247	50	27	(	(	PUNCT
ejpam-6247	50	28	θ	θ	X
ejpam-6247	50	29	∧	∧	PROPN
ejpam-6247	50	30	ϑ	ϑ	X
ejpam-6247	50	31	]	]	X
ejpam-6247	50	32	for	for	ADP
ejpam-6247	50	33	any	any	DET
ejpam-6247	50	34	θ	θ	PROPN
ejpam-6247	50	35	,	,	PUNCT
ejpam-6247	50	36	ϑ	ϑ	X
ejpam-6247	50	37	∈	∈	PROPN
ejpam-6247	50	38	l.	l.	NOUN
ejpam-6247	50	39	represented	represent	VERB
ejpam-6247	50	40	all	all	DET
ejpam-6247	50	41	principal	principal	ADJ
ejpam-6247	50	42	ideals	ideal	NOUN
ejpam-6247	50	43	of	of	ADP
ejpam-6247	50	44	l	l	NOUN
ejpam-6247	50	45	by	by	ADP
ejpam-6247	50	46	the	the	DET
ejpam-6247	50	47	set	set	NOUN
ejpam-6247	50	48	(	(	PUNCT
ejpam-6247	50	49	pi(l),∨,∩	pi(l),∨,∩	NOUN
ejpam-6247	50	50	)	)	PUNCT
ejpam-6247	50	51	,	,	PUNCT
ejpam-6247	50	52	this	this	PRON
ejpam-6247	50	53	brings	bring	VERB
ejpam-6247	50	54	out	out	ADP
ejpam-6247	50	55	a	a	DET
ejpam-6247	50	56	sublattice	sublattice	NOUN
ejpam-6247	50	57	of	of	ADP
ejpam-6247	50	58	the	the	DET
ejpam-6247	50	59	distributive	distributive	ADJ
ejpam-6247	50	60	lattice	lattice	NOUN
ejpam-6247	50	61	(	(	PUNCT
ejpam-6247	50	62	i(l),∨,∩	i(l),∨,∩	NOUN
ejpam-6247	50	63	)	)	PUNCT
ejpam-6247	50	64	of	of	ADP
ejpam-6247	50	65	all	all	DET
ejpam-6247	50	66	ideals	ideal	NOUN
ejpam-6247	50	67	of	of	ADP
ejpam-6247	50	68	l.	l.	PROPN
ejpam-6247	50	69	furthermore	furthermore	ADV
ejpam-6247	50	70	,	,	PUNCT
ejpam-6247	50	71	the	the	DET
ejpam-6247	50	72	set	set	NOUN
ejpam-6247	50	73	(	(	PUNCT
ejpam-6247	50	74	f(l),∨,∩	f(l),∨,∩	NOUN
ejpam-6247	50	75	)	)	PUNCT
ejpam-6247	50	76	of	of	ADP
ejpam-6247	50	77	all	all	DET
ejpam-6247	50	78	filters	filter	NOUN
ejpam-6247	50	79	of	of	ADP
ejpam-6247	50	80	l	l	NOUN
ejpam-6247	50	81	forms	form	NOUN
ejpam-6247	50	82	a	a	DET
ejpam-6247	50	83	bounded	bounded	ADJ
ejpam-6247	50	84	distributive	distributive	ADJ
ejpam-6247	50	85	lattice	lattice	NOUN
ejpam-6247	50	86	.	.	PUNCT
ejpam-6247	51	1	in	in	ADP
ejpam-6247	51	2	an	an	DET
ejpam-6247	51	3	adl	adl	NOUN
ejpam-6247	51	4	[	[	X
ejpam-6247	51	5	12	12	NUM
ejpam-6247	51	6	]	]	X
ejpam-6247	51	7	,	,	PUNCT
ejpam-6247	51	8	a	a	DET
ejpam-6247	51	9	prime	prime	ADJ
ejpam-6247	51	10	ideal	ideal	NOUN
ejpam-6247	51	11	q	q	PROPN
ejpam-6247	51	12	of	of	ADP
ejpam-6247	51	13	l	l	NOUN
ejpam-6247	51	14	exists	exist	VERB
ejpam-6247	51	15	if	if	SCONJ
ejpam-6247	51	16	and	and	CCONJ
ejpam-6247	51	17	only	only	ADV
ejpam-6247	51	18	if	if	SCONJ
ejpam-6247	51	19	l	l	NOUN
ejpam-6247	51	20	\	\	PUNCT
ejpam-6247	51	21	q	q	X
ejpam-6247	51	22	is	be	AUX
ejpam-6247	51	23	a	a	DET
ejpam-6247	51	24	prime	prime	ADJ
ejpam-6247	51	25	filter	filter	NOUN
ejpam-6247	51	26	of	of	ADP
ejpam-6247	51	27	l.	l.	PROPN
ejpam-6247	51	28	a	a	DET
ejpam-6247	51	29	prime	prime	ADJ
ejpam-6247	51	30	ideal	ideal	NOUN
ejpam-6247	51	31	q	q	PROPN
ejpam-6247	51	32	of	of	ADP
ejpam-6247	51	33	an	an	DET
ejpam-6247	51	34	adl	adl	NOUN
ejpam-6247	51	35	is	be	AUX
ejpam-6247	51	36	a	a	DET
ejpam-6247	51	37	minimal	minimal	ADJ
ejpam-6247	51	38	prime	prime	ADJ
ejpam-6247	51	39	ideal	ideal	NOUN
ejpam-6247	52	1	if	if	SCONJ
ejpam-6247	52	2	and	and	CCONJ
ejpam-6247	52	3	only	only	ADV
ejpam-6247	52	4	if	if	SCONJ
ejpam-6247	52	5	to	to	ADP
ejpam-6247	52	6	each	each	DET
ejpam-6247	52	7	µ	µ	PROPN
ejpam-6247	52	8	∈	∈	NOUN
ejpam-6247	52	9	q	q	NOUN
ejpam-6247	52	10	there	there	PRON
ejpam-6247	52	11	exists	exist	VERB
ejpam-6247	52	12	π	π	PROPN
ejpam-6247	52	13	/∈	/∈	PUNCT
ejpam-6247	53	1	q	q	NOUN
ejpam-6247	54	1	such	such	ADJ
ejpam-6247	54	2	that	that	SCONJ
ejpam-6247	54	3	µ	µ	ADJ
ejpam-6247	54	4	∧	∧	PROPN
ejpam-6247	54	5	π	π	NOUN
ejpam-6247	54	6	=	=	SYM
ejpam-6247	54	7	0	0	PUNCT
ejpam-6247	54	8	(	(	PUNCT
ejpam-6247	54	9	or	or	CCONJ
ejpam-6247	54	10	equivalently	equivalently	ADV
ejpam-6247	54	11	,	,	PUNCT
ejpam-6247	54	12	for	for	ADP
ejpam-6247	54	13	any	any	DET
ejpam-6247	54	14	µ	µ	PROPN
ejpam-6247	54	15	∈	∈	PROPN
ejpam-6247	54	16	l	l	NOUN
ejpam-6247	54	17	,	,	PUNCT
ejpam-6247	54	18	µ	µ	X
ejpam-6247	54	19	/∈	/∈	NOUN
ejpam-6247	54	20	q	q	NOUN
ejpam-6247	55	1	if	if	SCONJ
ejpam-6247	55	2	and	and	CCONJ
ejpam-6247	55	3	only	only	ADV
ejpam-6247	55	4	if	if	SCONJ
ejpam-6247	55	5	(	(	PUNCT
ejpam-6247	55	6	µ)∗	µ)∗	PROPN
ejpam-6247	55	7	⊆	⊆	NUM
ejpam-6247	55	8	q	q	NOUN
ejpam-6247	55	9	)	)	PUNCT
ejpam-6247	55	10	.	.	PUNCT
ejpam-6247	56	1	for	for	ADP
ejpam-6247	56	2	each	each	DET
ejpam-6247	56	3	non	non	ADJ
ejpam-6247	56	4	-	-	ADJ
ejpam-6247	56	5	void	void	ADJ
ejpam-6247	56	6	subset	subset	NOUN
ejpam-6247	56	7	s	s	PROPN
ejpam-6247	56	8	of	of	ADP
ejpam-6247	56	9	l	l	NOUN
ejpam-6247	56	10	,	,	PUNCT
ejpam-6247	56	11	the	the	DET
ejpam-6247	56	12	set	set	NOUN
ejpam-6247	56	13	s∗	s∗	PROPN
ejpam-6247	56	14	=	=	SYM
ejpam-6247	56	15	{	{	PUNCT
ejpam-6247	56	16	µ	µ	X
ejpam-6247	56	17	∈	∈	X
ejpam-6247	56	18	l	l	NOUN
ejpam-6247	56	19	|	|	NOUN
ejpam-6247	56	20	θ	θ	X
ejpam-6247	56	21	∧	∧	PROPN
ejpam-6247	56	22	µ	µ	X
ejpam-6247	56	23	=	=	SYM
ejpam-6247	56	24	0	0	NUM
ejpam-6247	56	25	,	,	PUNCT
ejpam-6247	56	26	for	for	ADP
ejpam-6247	56	27	all	all	DET
ejpam-6247	56	28	θ	θ	NOUN
ejpam-6247	56	29	∈	∈	PROPN
ejpam-6247	56	30	s	s	VERB
ejpam-6247	56	31	}	}	PUNCT
ejpam-6247	56	32	is	be	AUX
ejpam-6247	56	33	an	an	DET
ejpam-6247	56	34	ideal	ideal	NOUN
ejpam-6247	56	35	of	of	ADP
ejpam-6247	56	36	l.	l.	PROPN
ejpam-6247	56	37	generally	generally	ADV
ejpam-6247	56	38	,	,	PUNCT
ejpam-6247	56	39	for	for	ADP
ejpam-6247	56	40	every	every	DET
ejpam-6247	56	41	θ	θ	PROPN
ejpam-6247	56	42	∈	∈	PROPN
ejpam-6247	56	43	l	l	NOUN
ejpam-6247	56	44	,	,	PUNCT
ejpam-6247	56	45	{	{	PUNCT
ejpam-6247	56	46	θ}∗	θ}∗	ADJ
ejpam-6247	56	47	=	=	SYM
ejpam-6247	56	48	(	(	PUNCT
ejpam-6247	56	49	θ)∗	θ)∗	NOUN
ejpam-6247	56	50	,	,	PUNCT
ejpam-6247	56	51	where	where	SCONJ
ejpam-6247	56	52	(	(	PUNCT
ejpam-6247	56	53	θ	θ	NOUN
ejpam-6247	56	54	)	)	PUNCT
ejpam-6247	56	55	=	=	SYM
ejpam-6247	56	56	(	(	PUNCT
ejpam-6247	56	57	θ	θ	NOUN
ejpam-6247	56	58	]	]	X
ejpam-6247	56	59	.	.	PUNCT
ejpam-6247	57	1	the	the	DET
ejpam-6247	57	2	annihilator	annihilator	NOUN
ejpam-6247	57	3	of	of	ADP
ejpam-6247	57	4	an	an	DET
ejpam-6247	57	5	element	element	NOUN
ejpam-6247	57	6	θ	θ	PROPN
ejpam-6247	57	7	∈	∈	PROPN
ejpam-6247	57	8	l	l	NOUN
ejpam-6247	57	9	is	be	AUX
ejpam-6247	57	10	defined	define	VERB
ejpam-6247	57	11	as	as	ADP
ejpam-6247	57	12	the	the	DET
ejpam-6247	57	13	set	set	NOUN
ejpam-6247	57	14	(	(	PUNCT
ejpam-6247	57	15	θ)∗	θ)∗	PROPN
ejpam-6247	57	16	=	=	PUNCT
ejpam-6247	57	17	{	{	PUNCT
ejpam-6247	57	18	µ	µ	X
ejpam-6247	57	19	∈	∈	X
ejpam-6247	57	20	l	l	NOUN
ejpam-6247	57	21	|	|	NOUN
ejpam-6247	57	22	µ	µ	X
ejpam-6247	57	23	∧	∧	NOUN
ejpam-6247	57	24	θ	θ	NOUN
ejpam-6247	57	25	=	=	PUNCT
ejpam-6247	57	26	0	0	NUM
ejpam-6247	57	27	}	}	PUNCT
ejpam-6247	57	28	.	.	PUNCT
ejpam-6247	58	1	if	if	SCONJ
ejpam-6247	58	2	(	(	PUNCT
ejpam-6247	58	3	e)∗	e)∗	PROPN
ejpam-6247	58	4	=	=	SYM
ejpam-6247	58	5	{	{	PUNCT
ejpam-6247	58	6	0	0	NUM
ejpam-6247	58	7	}	}	PUNCT
ejpam-6247	58	8	then	then	ADV
ejpam-6247	58	9	an	an	DET
ejpam-6247	58	10	element	element	NOUN
ejpam-6247	58	11	e	e	PART
ejpam-6247	58	12	∈	∈	PROPN
ejpam-6247	58	13	l	l	NOUN
ejpam-6247	58	14	is	be	AUX
ejpam-6247	58	15	considered	consider	VERB
ejpam-6247	58	16	dense	dense	ADJ
ejpam-6247	58	17	.	.	PUNCT
ejpam-6247	59	1	within	within	ADP
ejpam-6247	59	2	l	l	NOUN
ejpam-6247	59	3	,	,	PUNCT
ejpam-6247	59	4	the	the	DET
ejpam-6247	59	5	set	set	NOUN
ejpam-6247	59	6	d	d	NOUN
ejpam-6247	59	7	is	be	AUX
ejpam-6247	59	8	the	the	DET
ejpam-6247	59	9	set	set	NOUN
ejpam-6247	59	10	of	of	ADP
ejpam-6247	59	11	dense	dense	ADJ
ejpam-6247	59	12	elements	element	NOUN
ejpam-6247	59	13	.	.	PUNCT
ejpam-6247	60	1	a	a	DET
ejpam-6247	60	2	filter	filter	NOUN
ejpam-6247	60	3	of	of	ADP
ejpam-6247	60	4	an	an	DET
ejpam-6247	60	5	adl	adl	PROPN
ejpam-6247	60	6	l	l	NOUN
ejpam-6247	60	7	can	can	AUX
ejpam-6247	60	8	be	be	AUX
ejpam-6247	60	9	obtained	obtain	VERB
ejpam-6247	60	10	by	by	ADP
ejpam-6247	60	11	the	the	DET
ejpam-6247	60	12	set	set	NOUN
ejpam-6247	60	13	d.	d.	PROPN
ejpam-6247	60	14	the	the	DET
ejpam-6247	60	15	adl	adl	PROPN
ejpam-6247	60	16	l	l	PROPN
ejpam-6247	60	17	is	be	AUX
ejpam-6247	60	18	termed	term	VERB
ejpam-6247	60	19	a	a	DET
ejpam-6247	60	20	generalized	generalized	ADJ
ejpam-6247	60	21	stone	stone	NOUN
ejpam-6247	60	22	adl	adl	NOUN
ejpam-6247	61	1	[	[	X
ejpam-6247	61	2	13	13	NUM
ejpam-6247	61	3	]	]	PUNCT
ejpam-6247	61	4	when	when	SCONJ
ejpam-6247	61	5	it	it	PRON
ejpam-6247	61	6	satisfies	satisfy	VERB
ejpam-6247	61	7	the	the	DET
ejpam-6247	61	8	property	property	NOUN
ejpam-6247	61	9	(	(	PUNCT
ejpam-6247	61	10	µ)∗	µ)∗	PROPN
ejpam-6247	61	11	∨	∨	NUM
ejpam-6247	61	12	(	(	PUNCT
ejpam-6247	61	13	µ)∗∗	µ)∗∗	X
ejpam-6247	61	14	=	=	SYM
ejpam-6247	61	15	l	l	NOUN
ejpam-6247	61	16	for	for	ADP
ejpam-6247	61	17	all	all	DET
ejpam-6247	61	18	µ	µ	PRON
ejpam-6247	61	19	∈	∈	NOUN
ejpam-6247	61	20	l.	l.	NOUN
ejpam-6247	61	21	according	accord	VERB
ejpam-6247	61	22	to	to	ADP
ejpam-6247	61	23	[	[	X
ejpam-6247	61	24	6	6	NUM
ejpam-6247	61	25	]	]	PUNCT
ejpam-6247	61	26	,	,	PUNCT
ejpam-6247	61	27	a	a	DET
ejpam-6247	61	28	filter	filter	NOUN
ejpam-6247	61	29	g	g	NOUN
ejpam-6247	61	30	of	of	ADP
ejpam-6247	61	31	an	an	DET
ejpam-6247	61	32	adl	adl	PROPN
ejpam-6247	61	33	l	l	NOUN
ejpam-6247	61	34	is	be	AUX
ejpam-6247	61	35	known	know	VERB
ejpam-6247	61	36	as	as	ADP
ejpam-6247	61	37	a	a	DET
ejpam-6247	61	38	d	d	NOUN
ejpam-6247	61	39	-	-	NOUN
ejpam-6247	61	40	filter	filter	NOUN
ejpam-6247	61	41	if	if	SCONJ
ejpam-6247	61	42	d	d	PROPN
ejpam-6247	61	43	⊆	⊆	NUM
ejpam-6247	61	44	g.	g.	X
ejpam-6247	61	45	the	the	DET
ejpam-6247	61	46	smallest	small	ADJ
ejpam-6247	61	47	d	d	NOUN
ejpam-6247	61	48	-	-	NOUN
ejpam-6247	61	49	filter	filter	NOUN
ejpam-6247	61	50	is	be	AUX
ejpam-6247	61	51	d.	d.	NOUN
ejpam-6247	61	52	for	for	ADP
ejpam-6247	61	53	any	any	DET
ejpam-6247	61	54	nonempty	nonempty	NOUN
ejpam-6247	61	55	subset	subset	VERB
ejpam-6247	61	56	s	s	PROPN
ejpam-6247	61	57	of	of	ADP
ejpam-6247	61	58	l	l	NOUN
ejpam-6247	61	59	,	,	PUNCT
ejpam-6247	61	60	consider	consider	VERB
ejpam-6247	61	61	the	the	DET
ejpam-6247	61	62	set	set	NOUN
ejpam-6247	61	63	(	(	PUNCT
ejpam-6247	61	64	s	s	X
ejpam-6247	61	65	,	,	PUNCT
ejpam-6247	61	66	d	d	NOUN
ejpam-6247	61	67	)	)	PUNCT
ejpam-6247	61	68	=	=	SYM
ejpam-6247	61	69	{	{	PUNCT
ejpam-6247	61	70	µ	µ	X
ejpam-6247	61	71	∈	∈	X
ejpam-6247	61	72	l	l	NOUN
ejpam-6247	62	1	|	|	NOUN
ejpam-6247	62	2	θ	θ	X
ejpam-6247	62	3	∨	∨	X
ejpam-6247	62	4	µ	µ	X
ejpam-6247	62	5	∈	∈	PROPN
ejpam-6247	62	6	d	d	NOUN
ejpam-6247	62	7	for	for	ADP
ejpam-6247	62	8	all	all	DET
ejpam-6247	62	9	θ	θ	PRON
ejpam-6247	62	10	∈	∈	NOUN
ejpam-6247	62	11	s	s	PART
ejpam-6247	62	12	}	}	PUNCT
ejpam-6247	62	13	.	.	PUNCT
ejpam-6247	63	1	it	it	PRON
ejpam-6247	63	2	is	be	AUX
ejpam-6247	63	3	noted	note	VERB
ejpam-6247	63	4	that	that	SCONJ
ejpam-6247	63	5	(	(	PUNCT
ejpam-6247	63	6	l	l	NOUN
ejpam-6247	63	7	,	,	PUNCT
ejpam-6247	63	8	d	d	NOUN
ejpam-6247	63	9	)	)	PUNCT
ejpam-6247	63	10	=	=	SYM
ejpam-6247	64	1	d	d	PROPN
ejpam-6247	64	2	and	and	CCONJ
ejpam-6247	64	3	(	(	PUNCT
ejpam-6247	64	4	d	d	NOUN
ejpam-6247	64	5	,	,	PUNCT
ejpam-6247	64	6	d	d	NOUN
ejpam-6247	64	7	)	)	PUNCT
ejpam-6247	64	8	=	=	SYM
ejpam-6247	64	9	l.	l.	PROPN
ejpam-6247	64	10	furthermore	furthermore	ADV
ejpam-6247	64	11	,	,	PUNCT
ejpam-6247	64	12	for	for	ADP
ejpam-6247	64	13	any	any	DET
ejpam-6247	64	14	subset	subset	NOUN
ejpam-6247	64	15	s	s	PROPN
ejpam-6247	64	16	of	of	ADP
ejpam-6247	64	17	l	l	NOUN
ejpam-6247	64	18	,	,	PUNCT
ejpam-6247	64	19	d	d	PROPN
ejpam-6247	64	20	⊆	⊆	NUM
ejpam-6247	64	21	(	(	PUNCT
ejpam-6247	64	22	s	s	PROPN
ejpam-6247	64	23	,	,	PUNCT
ejpam-6247	64	24	d	d	NOUN
ejpam-6247	64	25	)	)	PUNCT
ejpam-6247	64	26	.	.	PUNCT
ejpam-6247	65	1	for	for	ADP
ejpam-6247	65	2	every	every	DET
ejpam-6247	65	3	θ	θ	PROPN
ejpam-6247	65	4	∈	∈	PROPN
ejpam-6247	65	5	l	l	NOUN
ejpam-6247	65	6	,	,	PUNCT
ejpam-6247	65	7	(	(	PUNCT
ejpam-6247	65	8	{	{	PUNCT
ejpam-6247	65	9	θ},d	θ},d	PROPN
ejpam-6247	65	10	)	)	PUNCT
ejpam-6247	65	11	is	be	AUX
ejpam-6247	65	12	denoted	denote	VERB
ejpam-6247	65	13	as	as	ADP
ejpam-6247	65	14	(	(	PUNCT
ejpam-6247	65	15	θ	θ	NOUN
ejpam-6247	65	16	,	,	PUNCT
ejpam-6247	65	17	d	d	NOUN
ejpam-6247	65	18	)	)	PUNCT
ejpam-6247	65	19	.	.	PUNCT
ejpam-6247	66	1	therefore	therefore	ADV
ejpam-6247	66	2	,	,	PUNCT
ejpam-6247	66	3	(	(	PUNCT
ejpam-6247	66	4	m	m	NOUN
ejpam-6247	66	5	,	,	PUNCT
ejpam-6247	66	6	d	d	NOUN
ejpam-6247	66	7	)	)	PUNCT
ejpam-6247	66	8	=	=	SYM
ejpam-6247	66	9	l	l	NOUN
ejpam-6247	66	10	for	for	ADP
ejpam-6247	66	11	any	any	DET
ejpam-6247	66	12	m	m	PROPN
ejpam-6247	66	13	∈	∈	PROPN
ejpam-6247	66	14	m(l	m(l	NOUN
ejpam-6247	66	15	)	)	PUNCT
ejpam-6247	66	16	.	.	PUNCT
ejpam-6247	67	1	(	(	PUNCT
ejpam-6247	67	2	s	s	X
ejpam-6247	67	3	,	,	PUNCT
ejpam-6247	67	4	d	d	NOUN
ejpam-6247	67	5	)	)	PUNCT
ejpam-6247	67	6	forms	form	VERB
ejpam-6247	67	7	a	a	DET
ejpam-6247	67	8	d	d	NOUN
ejpam-6247	67	9	-	-	NOUN
ejpam-6247	67	10	filter	filter	NOUN
ejpam-6247	67	11	in	in	ADP
ejpam-6247	67	12	l	l	NOUN
ejpam-6247	67	13	for	for	ADP
ejpam-6247	67	14	each	each	DET
ejpam-6247	67	15	subset	subset	NOUN
ejpam-6247	67	16	s	s	PROPN
ejpam-6247	67	17	in	in	ADP
ejpam-6247	67	18	l.	l.	PROPN
ejpam-6247	67	19	lemma	lemma	PROPN
ejpam-6247	68	1	1	1	NUM
ejpam-6247	68	2	.	.	PUNCT
ejpam-6247	69	1	[	[	X
ejpam-6247	69	2	6	6	NUM
ejpam-6247	69	3	]	]	PUNCT
ejpam-6247	69	4	given	give	VERB
ejpam-6247	69	5	two	two	NUM
ejpam-6247	69	6	subsets	subset	NOUN
ejpam-6247	69	7	s	s	PART
ejpam-6247	69	8	,	,	PUNCT
ejpam-6247	69	9	t	t	PROPN
ejpam-6247	69	10	of	of	ADP
ejpam-6247	69	11	an	an	DET
ejpam-6247	69	12	adl	adl	PROPN
ejpam-6247	69	13	l	l	PROPN
ejpam-6247	69	14	,	,	PUNCT
ejpam-6247	69	15	the	the	DET
ejpam-6247	69	16	following	follow	VERB
ejpam-6247	69	17	holds	hold	VERB
ejpam-6247	69	18	:	:	PUNCT
ejpam-6247	69	19	(	(	PUNCT
ejpam-6247	69	20	1	1	X
ejpam-6247	69	21	)	)	PUNCT
ejpam-6247	69	22	s	s	PART
ejpam-6247	69	23	⊆	⊆	NUM
ejpam-6247	69	24	t	t	NOUN
ejpam-6247	69	25	⇒	⇒	NOUN
ejpam-6247	69	26	(	(	PUNCT
ejpam-6247	69	27	t	t	PROPN
ejpam-6247	69	28	,	,	PUNCT
ejpam-6247	69	29	d	d	NOUN
ejpam-6247	69	30	)	)	PUNCT
ejpam-6247	69	31	⊆	⊆	NUM
ejpam-6247	69	32	(	(	PUNCT
ejpam-6247	69	33	s	s	X
ejpam-6247	69	34	,	,	PUNCT
ejpam-6247	69	35	d	d	NOUN
ejpam-6247	69	36	)	)	PUNCT
ejpam-6247	69	37	,	,	PUNCT
ejpam-6247	69	38	(	(	PUNCT
ejpam-6247	69	39	2	2	X
ejpam-6247	69	40	)	)	PUNCT
ejpam-6247	69	41	s	s	NOUN
ejpam-6247	69	42	⊆	⊆	NUM
ejpam-6247	69	43	(	(	PUNCT
ejpam-6247	69	44	(	(	PUNCT
ejpam-6247	69	45	s	s	X
ejpam-6247	69	46	,	,	PUNCT
ejpam-6247	69	47	d),d	d),d	PROPN
ejpam-6247	69	48	)	)	PUNCT
ejpam-6247	69	49	,	,	PUNCT
ejpam-6247	69	50	(	(	PUNCT
ejpam-6247	69	51	3	3	X
ejpam-6247	69	52	)	)	PUNCT
ejpam-6247	69	53	(	(	PUNCT
ejpam-6247	69	54	s	s	X
ejpam-6247	69	55	,	,	PUNCT
ejpam-6247	69	56	d	d	NOUN
ejpam-6247	69	57	)	)	PUNCT
ejpam-6247	69	58	=	=	SYM
ejpam-6247	69	59	(	(	PUNCT
ejpam-6247	69	60	(	(	PUNCT
ejpam-6247	69	61	(	(	PUNCT
ejpam-6247	69	62	s	s	X
ejpam-6247	69	63	,	,	PUNCT
ejpam-6247	69	64	d),d),d	d),d),d	NOUN
ejpam-6247	69	65	)	)	PUNCT
ejpam-6247	69	66	,	,	PUNCT
ejpam-6247	69	67	(	(	PUNCT
ejpam-6247	69	68	4	4	X
ejpam-6247	69	69	)	)	PUNCT
ejpam-6247	69	70	s	s	PART
ejpam-6247	69	71	⊆	⊆	NUM
ejpam-6247	69	72	d	d	SYM
ejpam-6247	69	73	⇔	⇔	X
ejpam-6247	69	74	(	(	PUNCT
ejpam-6247	69	75	s	s	PROPN
ejpam-6247	69	76	,	,	PUNCT
ejpam-6247	69	77	d	d	NOUN
ejpam-6247	69	78	)	)	PUNCT
ejpam-6247	69	79	=	=	PUNCT
ejpam-6247	69	80	l.	l.	NOUN
ejpam-6247	69	81	proposition	proposition	NOUN
ejpam-6247	69	82	1	1	NUM
ejpam-6247	69	83	.	.	PUNCT
ejpam-6247	70	1	[	[	X
ejpam-6247	70	2	6	6	NUM
ejpam-6247	70	3	]	]	PUNCT
ejpam-6247	70	4	given	give	VERB
ejpam-6247	70	5	filters	filter	NOUN
ejpam-6247	70	6	g	g	PROPN
ejpam-6247	70	7	,	,	PUNCT
ejpam-6247	70	8	u	u	NOUN
ejpam-6247	70	9	of	of	ADP
ejpam-6247	70	10	an	an	DET
ejpam-6247	70	11	adl	adl	PROPN
ejpam-6247	70	12	l	l	PROPN
ejpam-6247	70	13	,	,	PUNCT
ejpam-6247	70	14	the	the	DET
ejpam-6247	70	15	following	follow	VERB
ejpam-6247	70	16	holds	hold	VERB
ejpam-6247	70	17	:	:	PUNCT
ejpam-6247	70	18	(	(	PUNCT
ejpam-6247	70	19	1	1	X
ejpam-6247	70	20	)	)	PUNCT
ejpam-6247	70	21	(	(	PUNCT
ejpam-6247	70	22	g	g	NOUN
ejpam-6247	70	23	,	,	PUNCT
ejpam-6247	70	24	d	d	NOUN
ejpam-6247	70	25	)	)	PUNCT
ejpam-6247	70	26	∩	∩	NOUN
ejpam-6247	70	27	(	(	PUNCT
ejpam-6247	70	28	(	(	PUNCT
ejpam-6247	70	29	g	g	NOUN
ejpam-6247	70	30	,	,	PUNCT
ejpam-6247	70	31	d),d	d),d	PROPN
ejpam-6247	70	32	)	)	PUNCT
ejpam-6247	70	33	=	=	SYM
ejpam-6247	71	1	d	d	NOUN
ejpam-6247	71	2	,	,	PUNCT
ejpam-6247	71	3	(	(	PUNCT
ejpam-6247	71	4	2	2	X
ejpam-6247	71	5	)	)	PUNCT
ejpam-6247	71	6	g	g	NOUN
ejpam-6247	71	7	∩	∩	NOUN
ejpam-6247	71	8	u	u	NOUN
ejpam-6247	71	9	⊆	⊆	NUM
ejpam-6247	71	10	d	d	PROPN
ejpam-6247	71	11	⇒	⇒	NOUN
ejpam-6247	71	12	g	g	PROPN
ejpam-6247	71	13	⊆	⊆	NUM
ejpam-6247	71	14	(	(	PUNCT
ejpam-6247	71	15	u	u	NOUN
ejpam-6247	71	16	,	,	PUNCT
ejpam-6247	71	17	d	d	PROPN
ejpam-6247	71	18	)	)	PUNCT
ejpam-6247	71	19	,	,	PUNCT
ejpam-6247	71	20	(	(	PUNCT
ejpam-6247	71	21	3	3	X
ejpam-6247	71	22	)	)	PUNCT
ejpam-6247	71	23	(	(	PUNCT
ejpam-6247	71	24	(	(	PUNCT
ejpam-6247	71	25	g	g	PROPN
ejpam-6247	71	26	∨	∨	NUM
ejpam-6247	71	27	u),d	u),d	NOUN
ejpam-6247	71	28	)	)	PUNCT
ejpam-6247	72	1	=	=	SYM
ejpam-6247	72	2	(	(	PUNCT
ejpam-6247	72	3	g	g	NOUN
ejpam-6247	72	4	,	,	PUNCT
ejpam-6247	72	5	d	d	NOUN
ejpam-6247	72	6	)	)	PUNCT
ejpam-6247	72	7	∩	∩	NOUN
ejpam-6247	72	8	(	(	PUNCT
ejpam-6247	72	9	u	u	NOUN
ejpam-6247	72	10	,	,	PUNCT
ejpam-6247	72	11	d	d	PROPN
ejpam-6247	72	12	)	)	PUNCT
ejpam-6247	72	13	,	,	PUNCT
ejpam-6247	72	14	(	(	PUNCT
ejpam-6247	72	15	4	4	X
ejpam-6247	72	16	)	)	PUNCT
ejpam-6247	72	17	(	(	PUNCT
ejpam-6247	72	18	(	(	PUNCT
ejpam-6247	72	19	g	g	PROPN
ejpam-6247	72	20	∩	∩	ADJ
ejpam-6247	72	21	u	u	NOUN
ejpam-6247	72	22	,	,	PUNCT
ejpam-6247	72	23	d),d	d),d	PROPN
ejpam-6247	72	24	)	)	PUNCT
ejpam-6247	72	25	=	=	PRON
ejpam-6247	73	1	(	(	PUNCT
ejpam-6247	73	2	(	(	PUNCT
ejpam-6247	73	3	g	g	NOUN
ejpam-6247	73	4	,	,	PUNCT
ejpam-6247	73	5	d),d	d),d	NOUN
ejpam-6247	73	6	)	)	PUNCT
ejpam-6247	73	7	∩	∩	NOUN
ejpam-6247	73	8	(	(	PUNCT
ejpam-6247	73	9	(	(	PUNCT
ejpam-6247	73	10	u	u	NOUN
ejpam-6247	73	11	,	,	PUNCT
ejpam-6247	73	12	d),d	d),d	PROPN
ejpam-6247	73	13	)	)	PUNCT
ejpam-6247	73	14	.	.	PUNCT
ejpam-6247	74	1	the	the	DET
ejpam-6247	74	2	idea	idea	NOUN
ejpam-6247	74	3	that	that	SCONJ
ejpam-6247	74	4	(	(	PUNCT
ejpam-6247	74	5	[	[	X
ejpam-6247	74	6	µ),d	µ),d	NOUN
ejpam-6247	74	7	)	)	PUNCT
ejpam-6247	74	8	=	=	PUNCT
ejpam-6247	74	9	(	(	PUNCT
ejpam-6247	74	10	µ,d	µ,d	NOUN
ejpam-6247	74	11	)	)	PUNCT
ejpam-6247	74	12	is	be	AUX
ejpam-6247	74	13	obvious	obvious	ADJ
ejpam-6247	74	14	.	.	PUNCT
ejpam-6247	75	1	it	it	PRON
ejpam-6247	75	2	follows	follow	VERB
ejpam-6247	75	3	that	that	PRON
ejpam-6247	75	4	(	(	PUNCT
ejpam-6247	75	5	0,d	0,d	PUNCT
ejpam-6247	75	6	)	)	PUNCT
ejpam-6247	75	7	=	=	VERB
ejpam-6247	76	1	d.	d.	PROPN
ejpam-6247	76	2	the	the	DET
ejpam-6247	76	3	previously	previously	ADV
ejpam-6247	76	4	noted	note	VERB
ejpam-6247	76	5	observations	observation	NOUN
ejpam-6247	76	6	directly	directly	ADV
ejpam-6247	76	7	lead	lead	VERB
ejpam-6247	76	8	to	to	ADP
ejpam-6247	76	9	the	the	DET
ejpam-6247	76	10	corollary	corollary	NOUN
ejpam-6247	76	11	that	that	PRON
ejpam-6247	76	12	follows	follow	VERB
ejpam-6247	76	13	.	.	PUNCT
ejpam-6247	77	1	n.	n.	PROPN
ejpam-6247	77	2	rafi	rafi	PROPN
ejpam-6247	77	3	et	et	PROPN
ejpam-6247	77	4	al	al	PROPN
ejpam-6247	77	5	.	.	PUNCT
ejpam-6247	77	6	/	/	SYM
ejpam-6247	77	7	eur	eur	PROPN
ejpam-6247	77	8	.	.	PUNCT
ejpam-6247	78	1	j.	j.	PROPN
ejpam-6247	78	2	pure	pure	PROPN
ejpam-6247	78	3	appl	appl	PROPN
ejpam-6247	78	4	.	.	PROPN
ejpam-6247	78	5	math	math	PROPN
ejpam-6247	78	6	,	,	PUNCT
ejpam-6247	78	7	18	18	NUM
ejpam-6247	78	8	(	(	PUNCT
ejpam-6247	78	9	3	3	NUM
ejpam-6247	78	10	)	)	PUNCT
ejpam-6247	78	11	(	(	PUNCT
ejpam-6247	78	12	2025	2025	NUM
ejpam-6247	78	13	)	)	PUNCT
ejpam-6247	78	14	,	,	PUNCT
ejpam-6247	78	15	6247	6247	NUM
ejpam-6247	78	16	4	4	NUM
ejpam-6247	78	17	of	of	ADP
ejpam-6247	78	18	15	15	NUM
ejpam-6247	78	19	corollary	corollary	ADJ
ejpam-6247	78	20	1	1	NUM
ejpam-6247	78	21	.	.	PUNCT
ejpam-6247	79	1	[	[	X
ejpam-6247	79	2	6	6	NUM
ejpam-6247	79	3	]	]	PUNCT
ejpam-6247	79	4	for	for	ADP
ejpam-6247	79	5	any	any	DET
ejpam-6247	79	6	µ	µ	NOUN
ejpam-6247	79	7	,	,	PUNCT
ejpam-6247	79	8	π	π	PROPN
ejpam-6247	79	9	,	,	PUNCT
ejpam-6247	79	10	ψ	ψ	PROPN
ejpam-6247	79	11	∈	∈	PROPN
ejpam-6247	79	12	l	l	NOUN
ejpam-6247	79	13	,	,	PUNCT
ejpam-6247	79	14	we	we	PRON
ejpam-6247	79	15	have	have	VERB
ejpam-6247	79	16	the	the	DET
ejpam-6247	79	17	following	following	NOUN
ejpam-6247	79	18	:	:	PUNCT
ejpam-6247	79	19	(	(	PUNCT
ejpam-6247	79	20	1	1	X
ejpam-6247	79	21	)	)	PUNCT
ejpam-6247	79	22	(	(	PUNCT
ejpam-6247	79	23	[	[	X
ejpam-6247	79	24	µ),d	µ),d	NOUN
ejpam-6247	79	25	)	)	PUNCT
ejpam-6247	79	26	=	=	PUNCT
ejpam-6247	79	27	(	(	PUNCT
ejpam-6247	79	28	µ,d	µ,d	NOUN
ejpam-6247	79	29	)	)	PUNCT
ejpam-6247	79	30	,	,	PUNCT
ejpam-6247	79	31	(	(	PUNCT
ejpam-6247	79	32	2	2	X
ejpam-6247	79	33	)	)	PUNCT
ejpam-6247	79	34	µ	µ	PRON
ejpam-6247	79	35	≤	≤	PUNCT
ejpam-6247	79	36	π	π	PROPN
ejpam-6247	79	37	⇒	⇒	NOUN
ejpam-6247	79	38	(	(	PUNCT
ejpam-6247	79	39	µ,d	µ,d	NOUN
ejpam-6247	79	40	)	)	PUNCT
ejpam-6247	79	41	⊆	⊆	NUM
ejpam-6247	79	42	(	(	PUNCT
ejpam-6247	79	43	π	π	PROPN
ejpam-6247	79	44	,	,	PUNCT
ejpam-6247	79	45	d	d	NOUN
ejpam-6247	79	46	)	)	PUNCT
ejpam-6247	79	47	,	,	PUNCT
ejpam-6247	79	48	(	(	PUNCT
ejpam-6247	79	49	3	3	X
ejpam-6247	79	50	)	)	PUNCT
ejpam-6247	79	51	(	(	PUNCT
ejpam-6247	79	52	µ	µ	X
ejpam-6247	79	53	∧	∧	PROPN
ejpam-6247	79	54	π	π	PROPN
ejpam-6247	79	55	,	,	PUNCT
ejpam-6247	79	56	d	d	NOUN
ejpam-6247	79	57	)	)	PUNCT
ejpam-6247	79	58	=	=	SYM
ejpam-6247	79	59	(	(	PUNCT
ejpam-6247	79	60	µ,d	µ,d	NOUN
ejpam-6247	79	61	)	)	PUNCT
ejpam-6247	79	62	∩	∩	NOUN
ejpam-6247	79	63	(	(	PUNCT
ejpam-6247	79	64	π	π	X
ejpam-6247	79	65	,	,	PUNCT
ejpam-6247	79	66	d	d	NOUN
ejpam-6247	79	67	)	)	PUNCT
ejpam-6247	79	68	,	,	PUNCT
ejpam-6247	79	69	(	(	PUNCT
ejpam-6247	79	70	4	4	X
ejpam-6247	79	71	)	)	PUNCT
ejpam-6247	79	72	(	(	PUNCT
ejpam-6247	79	73	(	(	PUNCT
ejpam-6247	79	74	µ	µ	X
ejpam-6247	79	75	∨	∨	NUM
ejpam-6247	79	76	π	π	PROPN
ejpam-6247	79	77	,	,	PUNCT
ejpam-6247	79	78	d),d	d),d	PROPN
ejpam-6247	79	79	)	)	PUNCT
ejpam-6247	80	1	=	=	PRON
ejpam-6247	80	2	(	(	PUNCT
ejpam-6247	80	3	(	(	PUNCT
ejpam-6247	80	4	µ,d),d	µ,d),d	NOUN
ejpam-6247	80	5	)	)	PUNCT
ejpam-6247	80	6	∩	∩	NOUN
ejpam-6247	80	7	(	(	PUNCT
ejpam-6247	80	8	(	(	PUNCT
ejpam-6247	80	9	π	π	PROPN
ejpam-6247	80	10	,	,	PUNCT
ejpam-6247	80	11	d),d	d),d	PROPN
ejpam-6247	80	12	)	)	PUNCT
ejpam-6247	80	13	,	,	PUNCT
ejpam-6247	80	14	(	(	PUNCT
ejpam-6247	80	15	5	5	X
ejpam-6247	80	16	)	)	PUNCT
ejpam-6247	80	17	(	(	PUNCT
ejpam-6247	80	18	µ,d	µ,d	NOUN
ejpam-6247	80	19	)	)	PUNCT
ejpam-6247	80	20	=	=	SYM
ejpam-6247	80	21	l	l	PROPN
ejpam-6247	80	22	⇔	⇔	X
ejpam-6247	80	23	µ	µ	X
ejpam-6247	80	24	∈	∈	PROPN
ejpam-6247	80	25	d	d	PROPN
ejpam-6247	80	26	,	,	PUNCT
ejpam-6247	80	27	(	(	PUNCT
ejpam-6247	80	28	6	6	NUM
ejpam-6247	80	29	)	)	PUNCT
ejpam-6247	80	30	(	(	PUNCT
ejpam-6247	80	31	µ,d	µ,d	NOUN
ejpam-6247	80	32	)	)	PUNCT
ejpam-6247	80	33	=	=	SYM
ejpam-6247	80	34	(	(	PUNCT
ejpam-6247	80	35	π	π	PROPN
ejpam-6247	80	36	,	,	PUNCT
ejpam-6247	80	37	d	d	NOUN
ejpam-6247	80	38	)	)	PUNCT
ejpam-6247	80	39	⇔	⇔	X
ejpam-6247	80	40	(	(	PUNCT
ejpam-6247	80	41	µ	µ	X
ejpam-6247	80	42	∧	∧	PROPN
ejpam-6247	80	43	ψ	ψ	X
ejpam-6247	80	44	,	,	PUNCT
ejpam-6247	80	45	d	d	NOUN
ejpam-6247	80	46	)	)	PUNCT
ejpam-6247	80	47	=	=	SYM
ejpam-6247	80	48	(	(	PUNCT
ejpam-6247	80	49	π	π	PROPN
ejpam-6247	80	50	∧	∧	PROPN
ejpam-6247	80	51	ψ	ψ	PROPN
ejpam-6247	80	52	,	,	PUNCT
ejpam-6247	80	53	d	d	NOUN
ejpam-6247	80	54	)	)	PUNCT
ejpam-6247	80	55	,	,	PUNCT
ejpam-6247	80	56	(	(	PUNCT
ejpam-6247	80	57	7	7	X
ejpam-6247	80	58	)	)	PUNCT
ejpam-6247	80	59	(	(	PUNCT
ejpam-6247	80	60	µ,d	µ,d	NOUN
ejpam-6247	80	61	)	)	PUNCT
ejpam-6247	80	62	=	=	SYM
ejpam-6247	80	63	(	(	PUNCT
ejpam-6247	80	64	π	π	PROPN
ejpam-6247	80	65	,	,	PUNCT
ejpam-6247	80	66	d	d	NOUN
ejpam-6247	80	67	)	)	PUNCT
ejpam-6247	80	68	⇔	⇔	X
ejpam-6247	80	69	(	(	PUNCT
ejpam-6247	80	70	µ	µ	X
ejpam-6247	80	71	∨	∨	NUM
ejpam-6247	80	72	ψ	ψ	X
ejpam-6247	80	73	,	,	PUNCT
ejpam-6247	80	74	d	d	NOUN
ejpam-6247	80	75	)	)	PUNCT
ejpam-6247	80	76	=	=	SYM
ejpam-6247	80	77	(	(	PUNCT
ejpam-6247	80	78	π	π	PROPN
ejpam-6247	80	79	∨	∨	NUM
ejpam-6247	80	80	ψ	ψ	X
ejpam-6247	80	81	,	,	PUNCT
ejpam-6247	80	82	d	d	NOUN
ejpam-6247	80	83	)	)	PUNCT
ejpam-6247	80	84	.	.	PUNCT
ejpam-6247	81	1	definition	definition	NOUN
ejpam-6247	81	2	2	2	NUM
ejpam-6247	81	3	.	.	PUNCT
ejpam-6247	82	1	[	[	X
ejpam-6247	82	2	10	10	NUM
ejpam-6247	82	3	]	]	X
ejpam-6247	82	4	an	an	DET
ejpam-6247	82	5	element	element	NOUN
ejpam-6247	82	6	µ	µ	NOUN
ejpam-6247	82	7	in	in	ADP
ejpam-6247	82	8	an	an	DET
ejpam-6247	82	9	adl	adl	PROPN
ejpam-6247	82	10	l	l	NOUN
ejpam-6247	82	11	is	be	AUX
ejpam-6247	82	12	said	say	VERB
ejpam-6247	82	13	to	to	PART
ejpam-6247	82	14	be	be	AUX
ejpam-6247	82	15	condensed	condense	VERB
ejpam-6247	82	16	if	if	SCONJ
ejpam-6247	82	17	the	the	DET
ejpam-6247	82	18	filter	filter	NOUN
ejpam-6247	82	19	extension	extension	NOUN
ejpam-6247	82	20	(	(	PUNCT
ejpam-6247	82	21	µ,d	µ,d	NOUN
ejpam-6247	82	22	)	)	PUNCT
ejpam-6247	82	23	is	be	AUX
ejpam-6247	82	24	equal	equal	ADJ
ejpam-6247	82	25	to	to	ADP
ejpam-6247	82	26	d.	d.	PROPN
ejpam-6247	82	27	the	the	DET
ejpam-6247	82	28	zero	zero	NUM
ejpam-6247	82	29	element	element	NOUN
ejpam-6247	82	30	0	0	NUM
ejpam-6247	82	31	of	of	ADP
ejpam-6247	82	32	an	an	DET
ejpam-6247	82	33	adl	adl	PROPN
ejpam-6247	82	34	l	l	NOUN
ejpam-6247	82	35	is	be	AUX
ejpam-6247	82	36	always	always	ADV
ejpam-6247	82	37	condensed	condense	VERB
ejpam-6247	82	38	.	.	PUNCT
ejpam-6247	83	1	let	let	VERB
ejpam-6247	83	2	us	we	PRON
ejpam-6247	83	3	use	use	VERB
ejpam-6247	83	4	the	the	DET
ejpam-6247	83	5	notation	notation	NOUN
ejpam-6247	83	6	d∞	d∞	PROPN
ejpam-6247	83	7	to	to	PART
ejpam-6247	83	8	represent	represent	VERB
ejpam-6247	83	9	the	the	DET
ejpam-6247	83	10	collection	collection	NOUN
ejpam-6247	83	11	of	of	ADP
ejpam-6247	83	12	all	all	DET
ejpam-6247	83	13	condensed	condense	VERB
ejpam-6247	83	14	elements	element	NOUN
ejpam-6247	83	15	in	in	ADP
ejpam-6247	83	16	l.	l.	NOUN
ejpam-6247	83	17	with	with	ADP
ejpam-6247	83	18	this	this	DET
ejpam-6247	83	19	definition	definition	NOUN
ejpam-6247	83	20	,	,	PUNCT
ejpam-6247	83	21	we	we	PRON
ejpam-6247	83	22	arrive	arrive	VERB
ejpam-6247	83	23	at	at	ADP
ejpam-6247	83	24	the	the	DET
ejpam-6247	83	25	following	following	ADJ
ejpam-6247	83	26	result	result	NOUN
ejpam-6247	83	27	.	.	PUNCT
ejpam-6247	84	1	proposition	proposition	NOUN
ejpam-6247	84	2	2	2	NUM
ejpam-6247	84	3	.	.	PUNCT
ejpam-6247	85	1	[	[	X
ejpam-6247	85	2	10	10	NUM
ejpam-6247	85	3	]	]	X
ejpam-6247	85	4	the	the	DET
ejpam-6247	85	5	following	follow	VERB
ejpam-6247	85	6	statements	statement	NOUN
ejpam-6247	85	7	are	be	AUX
ejpam-6247	85	8	valid	valid	ADJ
ejpam-6247	85	9	in	in	ADP
ejpam-6247	85	10	an	an	DET
ejpam-6247	85	11	adl	adl	PROPN
ejpam-6247	85	12	l	l	NOUN
ejpam-6247	85	13	:	:	PUNCT
ejpam-6247	85	14	(	(	PUNCT
ejpam-6247	85	15	1	1	X
ejpam-6247	85	16	)	)	PUNCT
ejpam-6247	85	17	d	d	NOUN
ejpam-6247	85	18	∩d∞	∩d∞	NOUN
ejpam-6247	85	19	=	=	NOUN
ejpam-6247	85	20	∅	∅	NOUN
ejpam-6247	85	21	,	,	PUNCT
ejpam-6247	85	22	(	(	PUNCT
ejpam-6247	85	23	2	2	X
ejpam-6247	85	24	)	)	PUNCT
ejpam-6247	85	25	d∞	d∞	NOUN
ejpam-6247	85	26	is	be	AUX
ejpam-6247	85	27	an	an	DET
ejpam-6247	85	28	ideal	ideal	NOUN
ejpam-6247	85	29	in	in	ADP
ejpam-6247	85	30	l.	l.	PROPN
ejpam-6247	85	31	definition	definition	NOUN
ejpam-6247	85	32	3	3	NUM
ejpam-6247	85	33	.	.	PUNCT
ejpam-6247	86	1	[	[	X
ejpam-6247	86	2	10	10	NUM
ejpam-6247	86	3	]	]	X
ejpam-6247	86	4	an	an	DET
ejpam-6247	86	5	adl	adl	PROPN
ejpam-6247	86	6	l	l	NOUN
ejpam-6247	86	7	is	be	AUX
ejpam-6247	86	8	termed	term	VERB
ejpam-6247	86	9	hemicomplemented	hemicomplemente	VERB
ejpam-6247	86	10	if	if	SCONJ
ejpam-6247	86	11	for	for	ADP
ejpam-6247	86	12	every	every	DET
ejpam-6247	86	13	element	element	NOUN
ejpam-6247	86	14	µ	µ	NOUN
ejpam-6247	86	15	in	in	ADP
ejpam-6247	86	16	l	l	NOUN
ejpam-6247	86	17	,	,	PUNCT
ejpam-6247	86	18	there	there	PRON
ejpam-6247	86	19	is	be	VERB
ejpam-6247	86	20	an	an	DET
ejpam-6247	86	21	element	element	NOUN
ejpam-6247	86	22	π	π	PROPN
ejpam-6247	86	23	∈	∈	PROPN
ejpam-6247	86	24	l	l	NOUN
ejpam-6247	86	25	such	such	ADJ
ejpam-6247	86	26	that	that	SCONJ
ejpam-6247	86	27	µ	µ	ADJ
ejpam-6247	86	28	∧	∧	PROPN
ejpam-6247	86	29	π	π	X
ejpam-6247	86	30	∈	∈	PROPN
ejpam-6247	86	31	d∞	d∞	NOUN
ejpam-6247	86	32	and	and	CCONJ
ejpam-6247	86	33	µ	µ	PRON
ejpam-6247	86	34	∨	∨	NOUN
ejpam-6247	86	35	π	π	PROPN
ejpam-6247	86	36	∈	∈	PROPN
ejpam-6247	86	37	d.	d.	PROPN
ejpam-6247	86	38	3	3	NUM
ejpam-6247	86	39	.	.	PUNCT
ejpam-6247	87	1	d	d	X
ejpam-6247	87	2	-	-	PUNCT
ejpam-6247	87	3	stone	stone	NOUN
ejpam-6247	87	4	almost	almost	ADV
ejpam-6247	87	5	distributive	distributive	ADJ
ejpam-6247	87	6	lattices	lattice	NOUN
ejpam-6247	87	7	this	this	DET
ejpam-6247	87	8	section	section	NOUN
ejpam-6247	87	9	introduces	introduce	VERB
ejpam-6247	87	10	the	the	DET
ejpam-6247	87	11	concept	concept	NOUN
ejpam-6247	87	12	of	of	ADP
ejpam-6247	87	13	d	d	NOUN
ejpam-6247	87	14	-	-	NOUN
ejpam-6247	87	15	stone	stone	NOUN
ejpam-6247	87	16	adls	adls	PROPN
ejpam-6247	87	17	.	.	PUNCT
ejpam-6247	88	1	a	a	DET
ejpam-6247	88	2	collection	collection	NOUN
ejpam-6247	88	3	of	of	ADP
ejpam-6247	88	4	equivalent	equivalent	ADJ
ejpam-6247	88	5	criteria	criterion	NOUN
ejpam-6247	88	6	is	be	AUX
ejpam-6247	88	7	established	establish	VERB
ejpam-6247	88	8	,	,	PUNCT
ejpam-6247	88	9	characterizing	characterize	VERB
ejpam-6247	88	10	when	when	SCONJ
ejpam-6247	88	11	a	a	DET
ejpam-6247	88	12	hemicomplemented	hemicomplemente	VERB
ejpam-6247	88	13	adl	adl	NOUN
ejpam-6247	88	14	qualifies	qualifie	NOUN
ejpam-6247	88	15	as	as	ADP
ejpam-6247	88	16	a	a	DET
ejpam-6247	88	17	d	d	NOUN
ejpam-6247	88	18	-	-	NOUN
ejpam-6247	88	19	stone	stone	NOUN
ejpam-6247	88	20	adl	adl	PROPN
ejpam-6247	88	21	.	.	PUNCT
ejpam-6247	89	1	it	it	PRON
ejpam-6247	89	2	is	be	AUX
ejpam-6247	89	3	shown	show	VERB
ejpam-6247	89	4	that	that	SCONJ
ejpam-6247	89	5	a	a	DET
ejpam-6247	89	6	hemicomplemented	hemicomplemente	VERB
ejpam-6247	89	7	adl	adl	NOUN
ejpam-6247	89	8	is	be	AUX
ejpam-6247	89	9	d	d	NOUN
ejpam-6247	89	10	-	-	NOUN
ejpam-6247	89	11	stone	stone	NOUN
ejpam-6247	89	12	precisely	precisely	ADV
ejpam-6247	89	13	when	when	SCONJ
ejpam-6247	89	14	d	d	NOUN
ejpam-6247	89	15	◦	◦	NOUN
ejpam-6247	89	16	(l	(l	NUM
ejpam-6247	89	17	)	)	PUNCT
ejpam-6247	89	18	(	(	PUNCT
ejpam-6247	89	19	see	see	VERB
ejpam-6247	89	20	definition	definition	NOUN
ejpam-6247	89	21	5	5	NUM
ejpam-6247	89	22	)	)	PUNCT
ejpam-6247	89	23	forms	form	VERB
ejpam-6247	89	24	a	a	DET
ejpam-6247	89	25	boolean	boolean	ADJ
ejpam-6247	89	26	algebra	algebra	NOUN
ejpam-6247	89	27	.	.	PUNCT
ejpam-6247	90	1	lemma	lemma	PROPN
ejpam-6247	90	2	2	2	NUM
ejpam-6247	90	3	.	.	PUNCT
ejpam-6247	91	1	for	for	ADP
ejpam-6247	91	2	all	all	DET
ejpam-6247	91	3	elements	element	NOUN
ejpam-6247	91	4	a	a	PRON
ejpam-6247	91	5	,	,	PUNCT
ejpam-6247	91	6	b	b	PROPN
ejpam-6247	91	7	∈	∈	PROPN
ejpam-6247	91	8	l	l	NOUN
ejpam-6247	91	9	,	,	PUNCT
ejpam-6247	91	10	the	the	DET
ejpam-6247	91	11	conditions	condition	NOUN
ejpam-6247	91	12	below	below	ADV
ejpam-6247	91	13	are	be	AUX
ejpam-6247	91	14	equivalent	equivalent	ADJ
ejpam-6247	91	15	:	:	PUNCT
ejpam-6247	91	16	(	(	PUNCT
ejpam-6247	91	17	1	1	X
ejpam-6247	91	18	)	)	PUNCT
ejpam-6247	91	19	θ	θ	NOUN
ejpam-6247	91	20	∨	∨	NUM
ejpam-6247	91	21	ϑ	ϑ	X
ejpam-6247	91	22	∈	∈	PROPN
ejpam-6247	91	23	d	d	PROPN
ejpam-6247	91	24	,	,	PUNCT
ejpam-6247	91	25	(	(	PUNCT
ejpam-6247	91	26	2	2	NUM
ejpam-6247	91	27	)	)	PUNCT
ejpam-6247	91	28	(	(	PUNCT
ejpam-6247	91	29	(	(	PUNCT
ejpam-6247	91	30	θ	θ	NOUN
ejpam-6247	91	31	,	,	PUNCT
ejpam-6247	91	32	d),d	d),d	NOUN
ejpam-6247	91	33	)	)	PUNCT
ejpam-6247	91	34	∩	∩	NOUN
ejpam-6247	92	1	[	[	X
ejpam-6247	92	2	ϑ	ϑ	X
ejpam-6247	92	3	)	)	PUNCT
ejpam-6247	92	4	⊆	⊆	NUM
ejpam-6247	92	5	d	d	NOUN
ejpam-6247	92	6	,	,	PUNCT
ejpam-6247	92	7	(	(	PUNCT
ejpam-6247	92	8	3	3	NUM
ejpam-6247	92	9	)	)	PUNCT
ejpam-6247	92	10	(	(	PUNCT
ejpam-6247	92	11	(	(	PUNCT
ejpam-6247	92	12	θ	θ	NOUN
ejpam-6247	92	13	,	,	PUNCT
ejpam-6247	92	14	d),d	d),d	NOUN
ejpam-6247	92	15	)	)	PUNCT
ejpam-6247	92	16	∩	∩	NOUN
ejpam-6247	92	17	(	(	PUNCT
ejpam-6247	92	18	(	(	PUNCT
ejpam-6247	92	19	ϑ,d),d	ϑ,d),d	NOUN
ejpam-6247	92	20	)	)	PUNCT
ejpam-6247	92	21	⊆	⊆	PROPN
ejpam-6247	92	22	d.	d.	PROPN
ejpam-6247	92	23	n.	n.	PROPN
ejpam-6247	92	24	rafi	rafi	PROPN
ejpam-6247	92	25	et	et	PROPN
ejpam-6247	92	26	al	al	PROPN
ejpam-6247	92	27	.	.	PUNCT
ejpam-6247	92	28	/	/	SYM
ejpam-6247	92	29	eur	eur	PROPN
ejpam-6247	92	30	.	.	PUNCT
ejpam-6247	93	1	j.	j.	PROPN
ejpam-6247	93	2	pure	pure	PROPN
ejpam-6247	93	3	appl	appl	PROPN
ejpam-6247	93	4	.	.	PROPN
ejpam-6247	93	5	math	math	PROPN
ejpam-6247	93	6	,	,	PUNCT
ejpam-6247	93	7	18	18	NUM
ejpam-6247	93	8	(	(	PUNCT
ejpam-6247	93	9	3	3	NUM
ejpam-6247	93	10	)	)	PUNCT
ejpam-6247	93	11	(	(	PUNCT
ejpam-6247	93	12	2025	2025	NUM
ejpam-6247	93	13	)	)	PUNCT
ejpam-6247	93	14	,	,	PUNCT
ejpam-6247	93	15	6247	6247	NUM
ejpam-6247	93	16	5	5	NUM
ejpam-6247	93	17	of	of	ADP
ejpam-6247	93	18	15	15	NUM
ejpam-6247	93	19	proof	proof	NOUN
ejpam-6247	93	20	.	.	PUNCT
ejpam-6247	94	1	(	(	PUNCT
ejpam-6247	94	2	1	1	X
ejpam-6247	94	3	)	)	PUNCT
ejpam-6247	94	4	⇒	⇒	NOUN
ejpam-6247	94	5	(	(	PUNCT
ejpam-6247	94	6	2	2	NUM
ejpam-6247	94	7	)	)	PUNCT
ejpam-6247	94	8	:	:	PUNCT
ejpam-6247	94	9	assume	assume	VERB
ejpam-6247	94	10	(	(	PUNCT
ejpam-6247	94	11	1	1	NUM
ejpam-6247	94	12	)	)	PUNCT
ejpam-6247	94	13	.	.	PUNCT
ejpam-6247	95	1	let	let	VERB
ejpam-6247	95	2	θ	θ	NOUN
ejpam-6247	95	3	,	,	PUNCT
ejpam-6247	95	4	ϑ	ϑ	X
ejpam-6247	95	5	∈	∈	PROPN
ejpam-6247	95	6	l.	l.	NOUN
ejpam-6247	95	7	suppose	suppose	VERB
ejpam-6247	95	8	θ	θ	PROPN
ejpam-6247	95	9	∨	∨	X
ejpam-6247	95	10	ϑ	ϑ	X
ejpam-6247	95	11	∈	∈	PROPN
ejpam-6247	95	12	d.	d.	NOUN
ejpam-6247	95	13	then	then	ADV
ejpam-6247	95	14	ϑ	ϑ	PROPN
ejpam-6247	95	15	∈	∈	PROPN
ejpam-6247	95	16	(	(	PUNCT
ejpam-6247	95	17	θ	θ	PROPN
ejpam-6247	95	18	,	,	PUNCT
ejpam-6247	95	19	d	d	NOUN
ejpam-6247	95	20	)	)	PUNCT
ejpam-6247	95	21	,	,	PUNCT
ejpam-6247	95	22	this	this	PRON
ejpam-6247	95	23	gives	give	VERB
ejpam-6247	95	24	[	[	X
ejpam-6247	95	25	ϑ	ϑ	NOUN
ejpam-6247	95	26	)	)	PUNCT
ejpam-6247	95	27	⊆	⊆	NUM
ejpam-6247	95	28	(	(	PUNCT
ejpam-6247	95	29	θ	θ	NOUN
ejpam-6247	95	30	,	,	PUNCT
ejpam-6247	95	31	d	d	NOUN
ejpam-6247	95	32	)	)	PUNCT
ejpam-6247	95	33	.	.	PUNCT
ejpam-6247	96	1	therefore	therefore	ADV
ejpam-6247	96	2	,	,	PUNCT
ejpam-6247	96	3	(	(	PUNCT
ejpam-6247	96	4	(	(	PUNCT
ejpam-6247	96	5	θ	θ	NOUN
ejpam-6247	96	6	,	,	PUNCT
ejpam-6247	96	7	d),d	d),d	NOUN
ejpam-6247	96	8	)	)	PUNCT
ejpam-6247	96	9	∩	∩	NOUN
ejpam-6247	96	10	[	[	X
ejpam-6247	96	11	ϑ	ϑ	X
ejpam-6247	96	12	)	)	PUNCT
ejpam-6247	96	13	⊆	⊆	NUM
ejpam-6247	96	14	(	(	PUNCT
ejpam-6247	96	15	(	(	PUNCT
ejpam-6247	96	16	θ	θ	NOUN
ejpam-6247	96	17	,	,	PUNCT
ejpam-6247	96	18	d),d	d),d	NOUN
ejpam-6247	96	19	)	)	PUNCT
ejpam-6247	96	20	∩	∩	NOUN
ejpam-6247	96	21	(	(	PUNCT
ejpam-6247	96	22	θ	θ	NOUN
ejpam-6247	96	23	,	,	PUNCT
ejpam-6247	96	24	d	d	NOUN
ejpam-6247	96	25	)	)	PUNCT
ejpam-6247	96	26	=	=	SYM
ejpam-6247	96	27	d.	d.	NOUN
ejpam-6247	96	28	(	(	PUNCT
ejpam-6247	96	29	2	2	NUM
ejpam-6247	96	30	)	)	PUNCT
ejpam-6247	96	31	⇒	⇒	NOUN
ejpam-6247	96	32	(	(	PUNCT
ejpam-6247	96	33	3	3	NUM
ejpam-6247	96	34	)	)	PUNCT
ejpam-6247	96	35	:	:	PUNCT
ejpam-6247	96	36	assume	assume	VERB
ejpam-6247	96	37	(	(	PUNCT
ejpam-6247	96	38	(	(	PUNCT
ejpam-6247	96	39	θ	θ	NOUN
ejpam-6247	96	40	,	,	PUNCT
ejpam-6247	96	41	d),d)∩	d),d)∩	PROPN
ejpam-6247	96	42	[	[	X
ejpam-6247	96	43	ϑ	ϑ	X
ejpam-6247	96	44	)	)	PUNCT
ejpam-6247	96	45	⊆	⊆	NUM
ejpam-6247	96	46	d	d	NOUN
ejpam-6247	96	47	for	for	ADP
ejpam-6247	96	48	any	any	DET
ejpam-6247	96	49	θ	θ	NOUN
ejpam-6247	96	50	,	,	PUNCT
ejpam-6247	96	51	ϑ	ϑ	X
ejpam-6247	96	52	∈	∈	PROPN
ejpam-6247	96	53	l.	l.	NOUN
ejpam-6247	96	54	by	by	ADP
ejpam-6247	96	55	corollary	corollary	ADJ
ejpam-6247	96	56	1(2	1(2	NUM
ejpam-6247	96	57	)	)	PUNCT
ejpam-6247	96	58	,	,	PUNCT
ejpam-6247	96	59	we	we	PRON
ejpam-6247	96	60	obtain	obtain	VERB
ejpam-6247	96	61	(	(	PUNCT
ejpam-6247	96	62	(	(	PUNCT
ejpam-6247	96	63	θ	θ	NOUN
ejpam-6247	96	64	,	,	PUNCT
ejpam-6247	96	65	d),d	d),d	NOUN
ejpam-6247	96	66	)	)	PUNCT
ejpam-6247	97	1	⊆	⊆	NUM
ejpam-6247	97	2	(	(	PUNCT
ejpam-6247	97	3	ϑ,d	ϑ,d	NOUN
ejpam-6247	97	4	)	)	PUNCT
ejpam-6247	97	5	.	.	PUNCT
ejpam-6247	98	1	thus	thus	ADV
ejpam-6247	98	2	,	,	PUNCT
ejpam-6247	98	3	(	(	PUNCT
ejpam-6247	98	4	(	(	PUNCT
ejpam-6247	98	5	θ	θ	NOUN
ejpam-6247	98	6	,	,	PUNCT
ejpam-6247	98	7	d),d	d),d	NOUN
ejpam-6247	98	8	)	)	PUNCT
ejpam-6247	98	9	∩	∩	NOUN
ejpam-6247	98	10	(	(	PUNCT
ejpam-6247	98	11	(	(	PUNCT
ejpam-6247	98	12	ϑ,d),d	ϑ,d),d	NOUN
ejpam-6247	98	13	)	)	PUNCT
ejpam-6247	98	14	⊆	⊆	NUM
ejpam-6247	98	15	(	(	PUNCT
ejpam-6247	98	16	ϑ,d	ϑ,d	NOUN
ejpam-6247	98	17	)	)	PUNCT
ejpam-6247	98	18	∩	∩	NOUN
ejpam-6247	98	19	(	(	PUNCT
ejpam-6247	98	20	(	(	PUNCT
ejpam-6247	98	21	ϑ,d),d	ϑ,d),d	NOUN
ejpam-6247	98	22	)	)	PUNCT
ejpam-6247	98	23	⊆	⊆	PROPN
ejpam-6247	98	24	d.	d.	NOUN
ejpam-6247	98	25	(	(	PUNCT
ejpam-6247	98	26	3	3	NUM
ejpam-6247	98	27	)	)	PUNCT
ejpam-6247	98	28	⇒	⇒	NOUN
ejpam-6247	98	29	(	(	PUNCT
ejpam-6247	98	30	1	1	NUM
ejpam-6247	98	31	)	)	PUNCT
ejpam-6247	98	32	:	:	PUNCT
ejpam-6247	98	33	assume	assume	VERB
ejpam-6247	98	34	(	(	PUNCT
ejpam-6247	98	35	(	(	PUNCT
ejpam-6247	98	36	θ	θ	NOUN
ejpam-6247	98	37	,	,	PUNCT
ejpam-6247	98	38	d),d	d),d	NOUN
ejpam-6247	98	39	)	)	PUNCT
ejpam-6247	98	40	∩	∩	NOUN
ejpam-6247	98	41	(	(	PUNCT
ejpam-6247	98	42	(	(	PUNCT
ejpam-6247	98	43	ϑ,d),d	ϑ,d),d	NOUN
ejpam-6247	98	44	)	)	PUNCT
ejpam-6247	98	45	⊆	⊆	NUM
ejpam-6247	98	46	d	d	NOUN
ejpam-6247	98	47	for	for	ADP
ejpam-6247	98	48	every	every	DET
ejpam-6247	98	49	θ	θ	PROPN
ejpam-6247	98	50	,	,	PUNCT
ejpam-6247	98	51	ϑ	ϑ	X
ejpam-6247	98	52	∈	∈	PROPN
ejpam-6247	98	53	l.	l.	NOUN
ejpam-6247	98	54	by	by	ADP
ejpam-6247	98	55	corollary	corollary	ADJ
ejpam-6247	98	56	1(2	1(2	NUM
ejpam-6247	98	57	)	)	PUNCT
ejpam-6247	98	58	,	,	PUNCT
ejpam-6247	98	59	we	we	PRON
ejpam-6247	98	60	obtain	obtain	VERB
ejpam-6247	98	61	(	(	PUNCT
ejpam-6247	98	62	(	(	PUNCT
ejpam-6247	98	63	θ	θ	NOUN
ejpam-6247	98	64	,	,	PUNCT
ejpam-6247	98	65	d),d	d),d	NOUN
ejpam-6247	98	66	)	)	PUNCT
ejpam-6247	99	1	⊆	⊆	NUM
ejpam-6247	99	2	(	(	PUNCT
ejpam-6247	99	3	(	(	PUNCT
ejpam-6247	99	4	(	(	PUNCT
ejpam-6247	99	5	ϑ,d),d),d	ϑ,d),d),d	NOUN
ejpam-6247	99	6	)	)	PUNCT
ejpam-6247	99	7	=	=	PUNCT
ejpam-6247	99	8	(	(	PUNCT
ejpam-6247	99	9	ϑ,d	ϑ,d	NOUN
ejpam-6247	99	10	)	)	PUNCT
ejpam-6247	99	11	.	.	PUNCT
ejpam-6247	100	1	therefore	therefore	ADV
ejpam-6247	100	2	,	,	PUNCT
ejpam-6247	100	3	θ	θ	PROPN
ejpam-6247	100	4	∈	∈	PROPN
ejpam-6247	100	5	(	(	PUNCT
ejpam-6247	100	6	(	(	PUNCT
ejpam-6247	100	7	θ	θ	NOUN
ejpam-6247	100	8	,	,	PUNCT
ejpam-6247	100	9	d),d)∩	d),d)∩	PROPN
ejpam-6247	100	10	(	(	PUNCT
ejpam-6247	100	11	ϑ,d	ϑ,d	NOUN
ejpam-6247	100	12	)	)	PUNCT
ejpam-6247	100	13	,	,	PUNCT
ejpam-6247	100	14	which	which	PRON
ejpam-6247	100	15	gives	give	VERB
ejpam-6247	100	16	θ	θ	PROPN
ejpam-6247	100	17	∨	∨	X
ejpam-6247	100	18	ϑ	ϑ	X
ejpam-6247	100	19	∈	∈	PROPN
ejpam-6247	100	20	d.	d.	NOUN
ejpam-6247	100	21	proposition	proposition	NOUN
ejpam-6247	100	22	3	3	NUM
ejpam-6247	100	23	.	.	PUNCT
ejpam-6247	101	1	the	the	DET
ejpam-6247	101	2	intersection	intersection	NOUN
ejpam-6247	101	3	of	of	ADP
ejpam-6247	101	4	all	all	DET
ejpam-6247	101	5	minimal	minimal	ADJ
ejpam-6247	101	6	prime	prime	ADJ
ejpam-6247	101	7	d	d	NOUN
ejpam-6247	101	8	-	-	PUNCT
ejpam-6247	101	9	filters	filter	NOUN
ejpam-6247	101	10	is	be	AUX
ejpam-6247	101	11	d.	d.	NOUN
ejpam-6247	101	12	proof	proof	NOUN
ejpam-6247	101	13	.	.	PUNCT
ejpam-6247	102	1	it	it	PRON
ejpam-6247	102	2	is	be	AUX
ejpam-6247	102	3	easy	easy	ADJ
ejpam-6247	102	4	to	to	PART
ejpam-6247	102	5	verify	verify	VERB
ejpam-6247	102	6	that	that	SCONJ
ejpam-6247	102	7	d	d	PROPN
ejpam-6247	102	8	⊆	⊆	NUM
ejpam-6247	102	9	⋂	⋂	PROPN
ejpam-6247	102	10	{	{	PUNCT
ejpam-6247	102	11	q	q	NOUN
ejpam-6247	102	12	|	|	ADV
ejpam-6247	102	13	q	q	NOUN
ejpam-6247	102	14	is	be	AUX
ejpam-6247	102	15	a	a	DET
ejpam-6247	102	16	minimal	minimal	ADJ
ejpam-6247	102	17	prime	prime	ADJ
ejpam-6247	102	18	d	d	NOUN
ejpam-6247	102	19	-	-	NOUN
ejpam-6247	102	20	filter	filter	NOUN
ejpam-6247	102	21	}	}	PUNCT
ejpam-6247	102	22	.	.	PUNCT
ejpam-6247	103	1	let	let	VERB
ejpam-6247	103	2	µ	µ	X
ejpam-6247	103	3	/∈	/∈	PUNCT
ejpam-6247	103	4	d.	d.	PROPN
ejpam-6247	104	1	then	then	ADV
ejpam-6247	104	2	there	there	PRON
ejpam-6247	104	3	exists	exist	VERB
ejpam-6247	104	4	an	an	DET
ejpam-6247	104	5	ideal	ideal	NOUN
ejpam-6247	104	6	i	i	PRON
ejpam-6247	104	7	such	such	ADJ
ejpam-6247	104	8	that	that	SCONJ
ejpam-6247	104	9	µ	µ	NUM
ejpam-6247	104	10	∈	∈	NOUN
ejpam-6247	105	1	i	i	PRON
ejpam-6247	105	2	and	and	CCONJ
ejpam-6247	105	3	i	i	PRON
ejpam-6247	105	4	is	be	AUX
ejpam-6247	105	5	maximal	maximal	ADJ
ejpam-6247	105	6	with	with	ADP
ejpam-6247	105	7	i	i	PRON
ejpam-6247	105	8	∩	∩	ADJ
ejpam-6247	105	9	d	d	NOUN
ejpam-6247	105	10	=	=	PUNCT
ejpam-6247	105	11	∅.	∅.	VERB
ejpam-6247	105	12	clearly	clearly	ADV
ejpam-6247	105	13	,	,	PUNCT
ejpam-6247	105	14	l	l	NOUN
ejpam-6247	105	15	\	\	PROPN
ejpam-6247	106	1	i	i	PRON
ejpam-6247	106	2	is	be	AUX
ejpam-6247	106	3	a	a	DET
ejpam-6247	106	4	minimal	minimal	ADJ
ejpam-6247	106	5	prime	prime	ADJ
ejpam-6247	106	6	d	d	NOUN
ejpam-6247	106	7	-	-	NOUN
ejpam-6247	106	8	filter	filter	NOUN
ejpam-6247	106	9	and	and	CCONJ
ejpam-6247	106	10	µ	µ	NOUN
ejpam-6247	106	11	/∈	/∈	PUNCT
ejpam-6247	106	12	l	l	NOUN
ejpam-6247	106	13	\	\	PROPN
ejpam-6247	106	14	i.	i.	PROPN
ejpam-6247	106	15	thus	thus	ADV
ejpam-6247	106	16	,	,	PUNCT
ejpam-6247	106	17	µ	µ	X
ejpam-6247	106	18	/∈	/∈	NOUN
ejpam-6247	106	19	⋂	⋂	PROPN
ejpam-6247	106	20	{	{	PUNCT
ejpam-6247	106	21	q	q	PROPN
ejpam-6247	107	1	|	|	ADV
ejpam-6247	107	2	q	q	NOUN
ejpam-6247	107	3	is	be	AUX
ejpam-6247	107	4	a	a	DET
ejpam-6247	107	5	minimal	minimal	ADJ
ejpam-6247	107	6	prime	prime	ADJ
ejpam-6247	107	7	d	d	NOUN
ejpam-6247	107	8	-	-	NOUN
ejpam-6247	107	9	filter	filter	NOUN
ejpam-6247	107	10	}	}	PUNCT
ejpam-6247	107	11	.	.	PUNCT
ejpam-6247	108	1	therefore	therefore	ADV
ejpam-6247	108	2	,	,	PUNCT
ejpam-6247	108	3	⋂	⋂	PROPN
ejpam-6247	108	4	{	{	PUNCT
ejpam-6247	108	5	q	q	PROPN
ejpam-6247	108	6	|	|	ADV
ejpam-6247	108	7	q	q	NOUN
ejpam-6247	108	8	is	be	AUX
ejpam-6247	108	9	a	a	DET
ejpam-6247	108	10	minimal	minimal	ADJ
ejpam-6247	108	11	prime	prime	ADJ
ejpam-6247	108	12	d	d	NOUN
ejpam-6247	108	13	-	-	NOUN
ejpam-6247	108	14	filter	filter	NOUN
ejpam-6247	108	15	}	}	PUNCT
ejpam-6247	108	16	⊆	⊆	NUM
ejpam-6247	108	17	d.	d.	NOUN
ejpam-6247	108	18	hence	hence	ADV
ejpam-6247	108	19	,	,	PUNCT
ejpam-6247	108	20	d	d	PROPN
ejpam-6247	108	21	=	=	SYM
ejpam-6247	108	22	⋂	⋂	PROPN
ejpam-6247	108	23	{	{	PUNCT
ejpam-6247	108	24	q	q	NOUN
ejpam-6247	109	1	|	|	ADV
ejpam-6247	109	2	q	q	NOUN
ejpam-6247	109	3	is	be	AUX
ejpam-6247	109	4	a	a	DET
ejpam-6247	109	5	minimal	minimal	ADJ
ejpam-6247	109	6	prime	prime	ADJ
ejpam-6247	109	7	d	d	NOUN
ejpam-6247	109	8	-	-	NOUN
ejpam-6247	109	9	filter	filter	NOUN
ejpam-6247	109	10	}	}	PUNCT
ejpam-6247	109	11	.	.	PUNCT
ejpam-6247	110	1	corollary	corollary	ADJ
ejpam-6247	110	2	2	2	NUM
ejpam-6247	110	3	.	.	PUNCT
ejpam-6247	111	1	for	for	ADP
ejpam-6247	111	2	any	any	DET
ejpam-6247	111	3	µ	µ	PROPN
ejpam-6247	111	4	∈	∈	PROPN
ejpam-6247	111	5	l	l	NOUN
ejpam-6247	111	6	,	,	PUNCT
ejpam-6247	111	7	we	we	PRON
ejpam-6247	111	8	have	have	VERB
ejpam-6247	111	9	(	(	PUNCT
ejpam-6247	111	10	µ,d	µ,d	NOUN
ejpam-6247	111	11	)	)	PUNCT
ejpam-6247	111	12	=	=	SYM
ejpam-6247	111	13	⋂	⋂	PROPN
ejpam-6247	111	14	{	{	PUNCT
ejpam-6247	111	15	q	q	NOUN
ejpam-6247	112	1	|	|	ADV
ejpam-6247	112	2	q	q	NOUN
ejpam-6247	112	3	is	be	AUX
ejpam-6247	112	4	a	a	DET
ejpam-6247	112	5	minimal	minimal	ADJ
ejpam-6247	112	6	prime	prime	ADJ
ejpam-6247	112	7	d	d	NOUN
ejpam-6247	112	8	-	-	NOUN
ejpam-6247	112	9	filter	filter	NOUN
ejpam-6247	112	10	such	such	ADJ
ejpam-6247	112	11	that	that	PRON
ejpam-6247	112	12	µ	µ	NOUN
ejpam-6247	112	13	/∈	/∈	NOUN
ejpam-6247	112	14	q	q	NOUN
ejpam-6247	112	15	}	}	PUNCT
ejpam-6247	112	16	.	.	PUNCT
ejpam-6247	113	1	proof	proof	NOUN
ejpam-6247	113	2	.	.	PUNCT
ejpam-6247	114	1	let	let	VERB
ejpam-6247	114	2	θ	θ	PROPN
ejpam-6247	114	3	∈	∈	PROPN
ejpam-6247	114	4	(	(	PUNCT
ejpam-6247	114	5	µ,d	µ,d	NOUN
ejpam-6247	114	6	)	)	PUNCT
ejpam-6247	114	7	and	and	CCONJ
ejpam-6247	114	8	q	q	ADJ
ejpam-6247	114	9	a	a	DET
ejpam-6247	114	10	minimal	minimal	ADJ
ejpam-6247	114	11	prime	prime	ADJ
ejpam-6247	114	12	d	d	NOUN
ejpam-6247	114	13	-	-	NOUN
ejpam-6247	114	14	filter	filter	NOUN
ejpam-6247	114	15	with	with	ADP
ejpam-6247	114	16	µ	µ	PROPN
ejpam-6247	114	17	/∈	/∈	PUNCT
ejpam-6247	114	18	q.	q.	NOUN
ejpam-6247	114	19	then	then	ADV
ejpam-6247	114	20	µ∨θ	µ∨θ	VERB
ejpam-6247	114	21	∈	∈	PROPN
ejpam-6247	114	22	d	d	PROPN
ejpam-6247	114	23	⊆	⊆	NUM
ejpam-6247	114	24	q.	q.	NOUN
ejpam-6247	114	25	as	as	ADP
ejpam-6247	114	26	µ	µ	NOUN
ejpam-6247	114	27	/∈	/∈	PUNCT
ejpam-6247	115	1	q	q	X
ejpam-6247	115	2	,	,	PUNCT
ejpam-6247	115	3	we	we	PRON
ejpam-6247	115	4	obtain	obtain	VERB
ejpam-6247	115	5	θ	θ	PROPN
ejpam-6247	115	6	∈	∈	PROPN
ejpam-6247	115	7	q	q	NOUN
ejpam-6247	115	8	for	for	ADP
ejpam-6247	115	9	every	every	DET
ejpam-6247	115	10	minimal	minimal	ADJ
ejpam-6247	115	11	prime	prime	ADJ
ejpam-6247	115	12	d	d	NOUN
ejpam-6247	115	13	-	-	NOUN
ejpam-6247	115	14	filters	filter	NOUN
ejpam-6247	115	15	with	with	ADP
ejpam-6247	115	16	µ	µ	PROPN
ejpam-6247	115	17	/∈	/∈	PUNCT
ejpam-6247	115	18	q.	q.	PROPN
ejpam-6247	115	19	thus	thus	ADV
ejpam-6247	115	20	,	,	PUNCT
ejpam-6247	115	21	(	(	PUNCT
ejpam-6247	115	22	µ,d	µ,d	NOUN
ejpam-6247	115	23	)	)	PUNCT
ejpam-6247	115	24	⊆	⊆	PROPN
ejpam-6247	115	25	⋂	⋂	PROPN
ejpam-6247	115	26	{	{	PUNCT
ejpam-6247	115	27	q	q	NOUN
ejpam-6247	116	1	|	|	ADV
ejpam-6247	116	2	q	q	NOUN
ejpam-6247	116	3	is	be	AUX
ejpam-6247	116	4	a	a	DET
ejpam-6247	116	5	minimal	minimal	ADJ
ejpam-6247	116	6	prime	prime	ADJ
ejpam-6247	116	7	d	d	NOUN
ejpam-6247	116	8	-	-	NOUN
ejpam-6247	116	9	filter	filter	NOUN
ejpam-6247	116	10	such	such	ADJ
ejpam-6247	116	11	that	that	PRON
ejpam-6247	116	12	µ	µ	NOUN
ejpam-6247	116	13	/∈	/∈	NOUN
ejpam-6247	116	14	q	q	NOUN
ejpam-6247	116	15	}	}	PUNCT
ejpam-6247	116	16	.	.	PUNCT
ejpam-6247	117	1	conversely	conversely	ADV
ejpam-6247	117	2	,	,	PUNCT
ejpam-6247	117	3	assume	assume	VERB
ejpam-6247	117	4	that	that	SCONJ
ejpam-6247	117	5	ν	ν	NOUN
ejpam-6247	117	6	/∈	/∈	PUNCT
ejpam-6247	118	1	(	(	PUNCT
ejpam-6247	118	2	µ,d	µ,d	NOUN
ejpam-6247	118	3	)	)	PUNCT
ejpam-6247	118	4	.	.	PUNCT
ejpam-6247	119	1	then	then	ADV
ejpam-6247	119	2	ν	ν	X
ejpam-6247	119	3	∨	∨	X
ejpam-6247	119	4	µ	µ	X
ejpam-6247	119	5	/∈	/∈	PUNCT
ejpam-6247	119	6	d.	d.	NOUN
ejpam-6247	119	7	by	by	ADP
ejpam-6247	119	8	the	the	DET
ejpam-6247	119	9	above	above	ADJ
ejpam-6247	119	10	result	result	NOUN
ejpam-6247	119	11	,	,	PUNCT
ejpam-6247	119	12	there	there	PRON
ejpam-6247	119	13	is	be	VERB
ejpam-6247	119	14	a	a	DET
ejpam-6247	119	15	minimal	minimal	ADJ
ejpam-6247	119	16	prime	prime	ADJ
ejpam-6247	119	17	d	d	NOUN
ejpam-6247	119	18	-	-	NOUN
ejpam-6247	119	19	filter	filter	NOUN
ejpam-6247	119	20	q	q	NOUN
ejpam-6247	119	21	such	such	ADJ
ejpam-6247	119	22	that	that	SCONJ
ejpam-6247	119	23	ν	ν	PROPN
ejpam-6247	119	24	∨	∨	X
ejpam-6247	119	25	µ	µ	X
ejpam-6247	119	26	/∈	/∈	PUNCT
ejpam-6247	119	27	q.	q.	NOUN
ejpam-6247	119	28	hence	hence	ADV
ejpam-6247	119	29	,	,	PUNCT
ejpam-6247	119	30	ν	ν	PROPN
ejpam-6247	119	31	/∈	/∈	PUNCT
ejpam-6247	120	1	⋂	⋂	PROPN
ejpam-6247	120	2	{	{	PUNCT
ejpam-6247	120	3	q	q	PROPN
ejpam-6247	121	1	|	|	ADV
ejpam-6247	121	2	q	q	NOUN
ejpam-6247	121	3	is	be	AUX
ejpam-6247	121	4	a	a	DET
ejpam-6247	121	5	minimal	minimal	ADJ
ejpam-6247	121	6	prime	prime	ADJ
ejpam-6247	121	7	d	d	NOUN
ejpam-6247	121	8	-	-	NOUN
ejpam-6247	121	9	filter	filter	NOUN
ejpam-6247	121	10	such	such	ADJ
ejpam-6247	121	11	that	that	PRON
ejpam-6247	121	12	µ	µ	NOUN
ejpam-6247	121	13	/∈	/∈	NOUN
ejpam-6247	121	14	q	q	NOUN
ejpam-6247	121	15	}	}	PUNCT
ejpam-6247	121	16	.	.	PUNCT
ejpam-6247	122	1	hence	hence	ADV
ejpam-6247	122	2	,	,	PUNCT
ejpam-6247	122	3	⋂	⋂	PROPN
ejpam-6247	122	4	{	{	PUNCT
ejpam-6247	122	5	q	q	PROPN
ejpam-6247	122	6	|	|	ADV
ejpam-6247	122	7	q	q	NOUN
ejpam-6247	122	8	is	be	AUX
ejpam-6247	122	9	a	a	DET
ejpam-6247	122	10	minimal	minimal	ADJ
ejpam-6247	122	11	prime	prime	ADJ
ejpam-6247	122	12	d	d	NOUN
ejpam-6247	122	13	-	-	NOUN
ejpam-6247	122	14	filter	filter	NOUN
ejpam-6247	122	15	such	such	ADJ
ejpam-6247	122	16	that	that	PRON
ejpam-6247	122	17	µ	µ	ADJ
ejpam-6247	122	18	/∈	/∈	PUNCT
ejpam-6247	122	19	q	q	NOUN
ejpam-6247	122	20	}	}	PUNCT
ejpam-6247	122	21	⊆	⊆	NUM
ejpam-6247	122	22	(	(	PUNCT
ejpam-6247	122	23	µ,d	µ,d	NOUN
ejpam-6247	122	24	)	)	PUNCT
ejpam-6247	122	25	.	.	PUNCT
ejpam-6247	123	1	definition	definition	NOUN
ejpam-6247	123	2	4	4	NUM
ejpam-6247	123	3	.	.	PUNCT
ejpam-6247	124	1	an	an	DET
ejpam-6247	124	2	adl	adl	PROPN
ejpam-6247	124	3	l	l	NOUN
ejpam-6247	124	4	is	be	AUX
ejpam-6247	124	5	said	say	VERB
ejpam-6247	124	6	to	to	PART
ejpam-6247	124	7	be	be	AUX
ejpam-6247	124	8	a	a	DET
ejpam-6247	124	9	d	d	NOUN
ejpam-6247	124	10	-	-	NOUN
ejpam-6247	124	11	stone	stone	NOUN
ejpam-6247	124	12	adl	adl	NOUN
ejpam-6247	125	1	if	if	SCONJ
ejpam-6247	125	2	(	(	PUNCT
ejpam-6247	125	3	µ,d	µ,d	NOUN
ejpam-6247	125	4	)	)	PUNCT
ejpam-6247	125	5	∨	∨	NOUN
ejpam-6247	125	6	(	(	PUNCT
ejpam-6247	125	7	(	(	PUNCT
ejpam-6247	125	8	µ,d),d	µ,d),d	NOUN
ejpam-6247	125	9	)	)	PUNCT
ejpam-6247	125	10	=	=	SYM
ejpam-6247	125	11	l	l	NOUN
ejpam-6247	125	12	for	for	ADP
ejpam-6247	125	13	all	all	DET
ejpam-6247	125	14	µ	µ	PRON
ejpam-6247	125	15	∈	∈	PROPN
ejpam-6247	125	16	l.	l.	NOUN
ejpam-6247	125	17	example	example	NOUN
ejpam-6247	125	18	1	1	X
ejpam-6247	125	19	.	.	X
ejpam-6247	125	20	consider	consider	VERB
ejpam-6247	125	21	the	the	DET
ejpam-6247	125	22	set	set	NOUN
ejpam-6247	125	23	l	l	NOUN
ejpam-6247	125	24	=	=	PUNCT
ejpam-6247	125	25	{	{	PUNCT
ejpam-6247	125	26	0	0	NUM
ejpam-6247	125	27	,	,	PUNCT
ejpam-6247	125	28	θ	θ	PROPN
ejpam-6247	125	29	,	,	PUNCT
ejpam-6247	125	30	ϑ	ϑ	X
ejpam-6247	125	31	,	,	PUNCT
ejpam-6247	125	32	σ	σ	PROPN
ejpam-6247	125	33	,	,	PUNCT
ejpam-6247	125	34	e	e	PROPN
ejpam-6247	125	35	,	,	PUNCT
ejpam-6247	125	36	π	π	PROPN
ejpam-6247	125	37	,	,	PUNCT
ejpam-6247	125	38	ρ	ρ	PROPN
ejpam-6247	125	39	}	}	PUNCT
ejpam-6247	125	40	,	,	PUNCT
ejpam-6247	125	41	with	with	ADP
ejpam-6247	125	42	the	the	DET
ejpam-6247	125	43	operations	operation	NOUN
ejpam-6247	125	44	∨	∨	NOUN
ejpam-6247	125	45	(	(	PUNCT
ejpam-6247	125	46	join	join	NOUN
ejpam-6247	125	47	)	)	PUNCT
ejpam-6247	125	48	and	and	CCONJ
ejpam-6247	125	49	∧	∧	PROPN
ejpam-6247	125	50	(	(	PUNCT
ejpam-6247	125	51	meet	meet	NOUN
ejpam-6247	125	52	)	)	PUNCT
ejpam-6247	125	53	defined	define	VERB
ejpam-6247	125	54	on	on	ADP
ejpam-6247	125	55	l	l	NOUN
ejpam-6247	125	56	as	as	SCONJ
ejpam-6247	125	57	follows	follow	VERB
ejpam-6247	125	58	:	:	PUNCT
ejpam-6247	125	59	∧	∧	NOUN
ejpam-6247	125	60	0	0	NUM
ejpam-6247	125	61	θ	θ	PROPN
ejpam-6247	125	62	ϑ	ϑ	PROPN
ejpam-6247	125	63	σ	σ	X
ejpam-6247	125	64	e	e	PROPN
ejpam-6247	125	65	π	π	PROPN
ejpam-6247	125	66	ρ	ρ	PROPN
ejpam-6247	125	67	0	0	NUM
ejpam-6247	125	68	0	0	NUM
ejpam-6247	125	69	0	0	NUM
ejpam-6247	125	70	0	0	NUM
ejpam-6247	125	71	0	0	NUM
ejpam-6247	125	72	0	0	NUM
ejpam-6247	125	73	0	0	NUM
ejpam-6247	125	74	0	0	NUM
ejpam-6247	125	75	θ	θ	NOUN
ejpam-6247	125	76	0	0	PUNCT
ejpam-6247	125	77	θ	θ	X
ejpam-6247	125	78	ϑ	ϑ	PROPN
ejpam-6247	125	79	σ	σ	X
ejpam-6247	125	80	e	e	PROPN
ejpam-6247	125	81	π	π	PROPN
ejpam-6247	125	82	ρ	ρ	X
ejpam-6247	125	83	ϑ	ϑ	X
ejpam-6247	125	84	0	0	NUM
ejpam-6247	125	85	θ	θ	PROPN
ejpam-6247	125	86	ϑ	ϑ	PROPN
ejpam-6247	125	87	σ	σ	X
ejpam-6247	125	88	e	e	PROPN
ejpam-6247	125	89	π	π	PROPN
ejpam-6247	125	90	ρ	ρ	PROPN
ejpam-6247	125	91	σ	σ	PROPN
ejpam-6247	125	92	0	0	PUNCT
ejpam-6247	125	93	σ	σ	PROPN
ejpam-6247	125	94	σ	σ	PROPN
ejpam-6247	125	95	σ	σ	PROPN
ejpam-6247	125	96	0	0	PUNCT
ejpam-6247	125	97	σ	σ	PROPN
ejpam-6247	125	98	σ	σ	PROPN
ejpam-6247	125	99	e	e	NOUN
ejpam-6247	125	100	0	0	PUNCT
ejpam-6247	125	101	e	e	X
ejpam-6247	125	102	e	e	X
ejpam-6247	125	103	0	0	NUM
ejpam-6247	125	104	e	e	NOUN
ejpam-6247	125	105	e	e	X
ejpam-6247	125	106	e	e	X
ejpam-6247	125	107	π	π	X
ejpam-6247	125	108	0	0	PUNCT
ejpam-6247	126	1	π	π	X
ejpam-6247	126	2	π	π	X
ejpam-6247	126	3	σ	σ	PUNCT
ejpam-6247	126	4	e	e	PROPN
ejpam-6247	126	5	π	π	PROPN
ejpam-6247	126	6	π	π	PROPN
ejpam-6247	126	7	ρ	ρ	PROPN
ejpam-6247	126	8	0	0	NUM
ejpam-6247	126	9	ρ	ρ	PROPN
ejpam-6247	126	10	ρ	ρ	PROPN
ejpam-6247	126	11	σ	σ	PROPN
ejpam-6247	126	12	e	e	PROPN
ejpam-6247	126	13	π	π	PROPN
ejpam-6247	126	14	ρ	ρ	PROPN
ejpam-6247	126	15	∨	∨	PROPN
ejpam-6247	126	16	0	0	NUM
ejpam-6247	126	17	θ	θ	PROPN
ejpam-6247	126	18	ϑ	ϑ	PROPN
ejpam-6247	126	19	σ	σ	X
ejpam-6247	126	20	e	e	PROPN
ejpam-6247	126	21	π	π	PROPN
ejpam-6247	126	22	ρ	ρ	PROPN
ejpam-6247	126	23	0	0	NUM
ejpam-6247	126	24	0	0	NUM
ejpam-6247	126	25	θ	θ	PROPN
ejpam-6247	126	26	ϑ	ϑ	PROPN
ejpam-6247	126	27	σ	σ	X
ejpam-6247	126	28	e	e	PROPN
ejpam-6247	126	29	π	π	PROPN
ejpam-6247	126	30	ρ	ρ	NUM
ejpam-6247	126	31	θ	θ	NOUN
ejpam-6247	126	32	θ	θ	NOUN
ejpam-6247	126	33	θ	θ	NOUN
ejpam-6247	126	34	θ	θ	NOUN
ejpam-6247	126	35	θ	θ	X
ejpam-6247	126	36	θ	θ	X
ejpam-6247	126	37	θ	θ	X
ejpam-6247	126	38	θ	θ	X
ejpam-6247	126	39	ϑ	ϑ	X
ejpam-6247	126	40	ϑ	ϑ	X
ejpam-6247	126	41	ϑ	ϑ	X
ejpam-6247	126	42	ϑ	ϑ	X
ejpam-6247	126	43	ϑ	ϑ	X
ejpam-6247	126	44	ϑ	ϑ	X
ejpam-6247	126	45	ϑ	ϑ	X
ejpam-6247	126	46	ϑ	ϑ	X
ejpam-6247	126	47	σ	σ	PROPN
ejpam-6247	126	48	σ	σ	PROPN
ejpam-6247	126	49	θ	θ	PROPN
ejpam-6247	126	50	ϑ	ϑ	X
ejpam-6247	126	51	σ	σ	X
ejpam-6247	126	52	π	π	PROPN
ejpam-6247	126	53	π	π	PROPN
ejpam-6247	126	54	ρ	ρ	X
ejpam-6247	126	55	e	e	X
ejpam-6247	126	56	e	e	X
ejpam-6247	126	57	θ	θ	X
ejpam-6247	126	58	ϑ	ϑ	X
ejpam-6247	126	59	π	π	X
ejpam-6247	126	60	e	e	PROPN
ejpam-6247	126	61	π	π	PROPN
ejpam-6247	126	62	ρ	ρ	PROPN
ejpam-6247	126	63	π	π	PROPN
ejpam-6247	126	64	π	π	PUNCT
ejpam-6247	126	65	θ	θ	X
ejpam-6247	126	66	ϑ	ϑ	X
ejpam-6247	126	67	π	π	X
ejpam-6247	126	68	π	π	PROPN
ejpam-6247	126	69	π	π	PROPN
ejpam-6247	126	70	ρ	ρ	PROPN
ejpam-6247	126	71	ρ	ρ	PROPN
ejpam-6247	126	72	ρ	ρ	PROPN
ejpam-6247	126	73	θ	θ	PROPN
ejpam-6247	126	74	ϑ	ϑ	PROPN
ejpam-6247	126	75	ρ	ρ	PROPN
ejpam-6247	126	76	ρ	ρ	PROPN
ejpam-6247	126	77	ρ	ρ	PROPN
ejpam-6247	126	78	ρ	ρ	PROPN
ejpam-6247	126	79	thus	thus	ADV
ejpam-6247	126	80	,	,	PUNCT
ejpam-6247	126	81	(	(	PUNCT
ejpam-6247	126	82	l,∨,∧	l,∨,∧	NOUN
ejpam-6247	126	83	)	)	PUNCT
ejpam-6247	126	84	is	be	AUX
ejpam-6247	126	85	an	an	DET
ejpam-6247	126	86	adl	adl	PROPN
ejpam-6247	126	87	.	.	PUNCT
ejpam-6247	127	1	clearly	clearly	ADV
ejpam-6247	127	2	,	,	PUNCT
ejpam-6247	127	3	we	we	PRON
ejpam-6247	127	4	have	have	VERB
ejpam-6247	127	5	the	the	DET
ejpam-6247	127	6	dense	dense	ADJ
ejpam-6247	127	7	set	set	NOUN
ejpam-6247	127	8	d	d	NOUN
ejpam-6247	127	9	=	=	SYM
ejpam-6247	127	10	{	{	PUNCT
ejpam-6247	127	11	θ	θ	PROPN
ejpam-6247	127	12	,	,	PUNCT
ejpam-6247	127	13	ϑ	ϑ	X
ejpam-6247	127	14	,	,	PUNCT
ejpam-6247	127	15	π	π	PROPN
ejpam-6247	127	16	,	,	PUNCT
ejpam-6247	127	17	ρ	ρ	PROPN
ejpam-6247	127	18	}	}	PUNCT
ejpam-6247	127	19	.	.	PUNCT
ejpam-6247	128	1	it	it	PRON
ejpam-6247	128	2	is	be	AUX
ejpam-6247	128	3	evident	evident	ADJ
ejpam-6247	128	4	that	that	SCONJ
ejpam-6247	128	5	l	l	NOUN
ejpam-6247	128	6	is	be	AUX
ejpam-6247	128	7	a	a	DET
ejpam-6247	128	8	d	d	ADJ
ejpam-6247	128	9	-	-	PUNCT
ejpam-6247	128	10	stone	stone	NOUN
ejpam-6247	128	11	adl	adl	NOUN
ejpam-6247	128	12	,	,	PUNCT
ejpam-6247	128	13	because	because	SCONJ
ejpam-6247	128	14	(	(	PUNCT
ejpam-6247	128	15	µ,d	µ,d	NOUN
ejpam-6247	128	16	)	)	PUNCT
ejpam-6247	128	17	∨	∨	NOUN
ejpam-6247	128	18	(	(	PUNCT
ejpam-6247	128	19	(	(	PUNCT
ejpam-6247	128	20	µ,d)d	µ,d)d	NOUN
ejpam-6247	128	21	)	)	PUNCT
ejpam-6247	128	22	=	=	SYM
ejpam-6247	129	1	l	l	NOUN
ejpam-6247	129	2	,	,	PUNCT
ejpam-6247	129	3	for	for	ADP
ejpam-6247	129	4	all	all	DET
ejpam-6247	129	5	µ	µ	PRON
ejpam-6247	129	6	∈	∈	PROPN
ejpam-6247	129	7	l.	l.	PROPN
ejpam-6247	129	8	n.	n.	PROPN
ejpam-6247	129	9	rafi	rafi	PROPN
ejpam-6247	129	10	et	et	PROPN
ejpam-6247	129	11	al	al	PROPN
ejpam-6247	129	12	.	.	PUNCT
ejpam-6247	129	13	/	/	SYM
ejpam-6247	129	14	eur	eur	PROPN
ejpam-6247	129	15	.	.	PUNCT
ejpam-6247	130	1	j.	j.	PROPN
ejpam-6247	130	2	pure	pure	PROPN
ejpam-6247	130	3	appl	appl	PROPN
ejpam-6247	130	4	.	.	PROPN
ejpam-6247	130	5	math	math	PROPN
ejpam-6247	130	6	,	,	PUNCT
ejpam-6247	130	7	18	18	NUM
ejpam-6247	130	8	(	(	PUNCT
ejpam-6247	130	9	3	3	NUM
ejpam-6247	130	10	)	)	PUNCT
ejpam-6247	130	11	(	(	PUNCT
ejpam-6247	130	12	2025	2025	NUM
ejpam-6247	130	13	)	)	PUNCT
ejpam-6247	130	14	,	,	PUNCT
ejpam-6247	130	15	6247	6247	NUM
ejpam-6247	130	16	6	6	NUM
ejpam-6247	130	17	of	of	ADP
ejpam-6247	130	18	15	15	NUM
ejpam-6247	130	19	proposition	proposition	NOUN
ejpam-6247	130	20	4	4	NUM
ejpam-6247	130	21	.	.	X
ejpam-6247	131	1	for	for	ADP
ejpam-6247	131	2	any	any	DET
ejpam-6247	131	3	prime	prime	ADJ
ejpam-6247	131	4	d	d	NOUN
ejpam-6247	131	5	-	-	NOUN
ejpam-6247	131	6	filter	filter	NOUN
ejpam-6247	131	7	of	of	ADP
ejpam-6247	131	8	l	l	NOUN
ejpam-6247	131	9	is	be	AUX
ejpam-6247	131	10	minimal	minimal	ADJ
ejpam-6247	131	11	,	,	PUNCT
ejpam-6247	131	12	we	we	PRON
ejpam-6247	131	13	have	have	VERB
ejpam-6247	131	14	l	l	NOUN
ejpam-6247	131	15	is	be	AUX
ejpam-6247	131	16	a	a	DET
ejpam-6247	131	17	d	d	ADJ
ejpam-6247	131	18	-	-	PUNCT
ejpam-6247	131	19	stone	stone	NOUN
ejpam-6247	131	20	adl	adl	PROPN
ejpam-6247	131	21	.	.	PUNCT
ejpam-6247	131	22	proof	proof	NOUN
ejpam-6247	131	23	.	.	PUNCT
ejpam-6247	132	1	suppose	suppose	VERB
ejpam-6247	132	2	that	that	SCONJ
ejpam-6247	132	3	every	every	DET
ejpam-6247	132	4	prime	prime	ADJ
ejpam-6247	132	5	d	d	NOUN
ejpam-6247	132	6	-	-	NOUN
ejpam-6247	132	7	filter	filter	NOUN
ejpam-6247	132	8	of	of	ADP
ejpam-6247	132	9	l	l	NOUN
ejpam-6247	132	10	is	be	AUX
ejpam-6247	132	11	minimal	minimal	ADJ
ejpam-6247	132	12	.	.	PUNCT
ejpam-6247	133	1	let	let	VERB
ejpam-6247	133	2	µ	µ	X
ejpam-6247	133	3	∈	∈	NOUN
ejpam-6247	133	4	l.	l.	NOUN
ejpam-6247	134	1	if	if	SCONJ
ejpam-6247	134	2	(	(	PUNCT
ejpam-6247	134	3	µ,d	µ,d	NOUN
ejpam-6247	134	4	)	)	PUNCT
ejpam-6247	134	5	∨	∨	NOUN
ejpam-6247	134	6	(	(	PUNCT
ejpam-6247	134	7	(	(	PUNCT
ejpam-6247	134	8	µ,d),d	µ,d),d	NOUN
ejpam-6247	134	9	)	)	PUNCT
ejpam-6247	134	10	=	=	SYM
ejpam-6247	135	1	l	l	NOUN
ejpam-6247	135	2	,	,	PUNCT
ejpam-6247	135	3	then	then	ADV
ejpam-6247	135	4	there	there	PRON
ejpam-6247	135	5	is	be	VERB
ejpam-6247	135	6	a	a	DET
ejpam-6247	135	7	prime	prime	ADJ
ejpam-6247	135	8	d	d	NOUN
ejpam-6247	135	9	-	-	NOUN
ejpam-6247	135	10	filter	filter	NOUN
ejpam-6247	135	11	q	q	NOUN
ejpam-6247	135	12	such	such	ADJ
ejpam-6247	135	13	that	that	SCONJ
ejpam-6247	135	14	(	(	PUNCT
ejpam-6247	135	15	µ,d	µ,d	NOUN
ejpam-6247	135	16	)	)	PUNCT
ejpam-6247	135	17	∨	∨	NOUN
ejpam-6247	135	18	(	(	PUNCT
ejpam-6247	135	19	(	(	PUNCT
ejpam-6247	135	20	µ,d),d	µ,d),d	X
ejpam-6247	135	21	)	)	PUNCT
ejpam-6247	135	22	⊆	⊆	NUM
ejpam-6247	135	23	q.	q.	NOUN
ejpam-6247	135	24	therefore	therefore	ADV
ejpam-6247	135	25	(	(	PUNCT
ejpam-6247	135	26	µ,d	µ,d	NOUN
ejpam-6247	135	27	)	)	PUNCT
ejpam-6247	135	28	⊆	⊆	NUM
ejpam-6247	135	29	q	q	NOUN
ejpam-6247	135	30	and	and	CCONJ
ejpam-6247	135	31	(	(	PUNCT
ejpam-6247	135	32	(	(	PUNCT
ejpam-6247	135	33	µ,d),d	µ,d),d	X
ejpam-6247	135	34	)	)	PUNCT
ejpam-6247	135	35	⊆	⊆	NUM
ejpam-6247	135	36	q.	q.	NOUN
ejpam-6247	135	37	by	by	ADP
ejpam-6247	135	38	corollary	corollary	ADJ
ejpam-6247	135	39	2	2	NUM
ejpam-6247	135	40	,	,	PUNCT
ejpam-6247	135	41	we	we	PRON
ejpam-6247	135	42	obtain	obtain	VERB
ejpam-6247	135	43	µ	µ	PRON
ejpam-6247	135	44	/∈	/∈	PUNCT
ejpam-6247	135	45	q.	q.	NOUN
ejpam-6247	136	1	it	it	PRON
ejpam-6247	136	2	is	be	AUX
ejpam-6247	136	3	evident	evident	ADJ
ejpam-6247	136	4	that	that	SCONJ
ejpam-6247	136	5	µ	µ	X
ejpam-6247	136	6	∈	∈	NOUN
ejpam-6247	136	7	(	(	PUNCT
ejpam-6247	136	8	(	(	PUNCT
ejpam-6247	136	9	µ,d),d	µ,d),d	X
ejpam-6247	136	10	)	)	PUNCT
ejpam-6247	136	11	⊆	⊆	NUM
ejpam-6247	136	12	q.	q.	NOUN
ejpam-6247	136	13	thus	thus	ADV
ejpam-6247	136	14	,	,	PUNCT
ejpam-6247	136	15	µ	µ	PROPN
ejpam-6247	136	16	∈	∈	PROPN
ejpam-6247	136	17	q	q	NOUN
ejpam-6247	136	18	,	,	PUNCT
ejpam-6247	136	19	which	which	PRON
ejpam-6247	136	20	leads	lead	VERB
ejpam-6247	136	21	to	to	ADP
ejpam-6247	136	22	a	a	DET
ejpam-6247	136	23	contradiction	contradiction	NOUN
ejpam-6247	136	24	.	.	PUNCT
ejpam-6247	137	1	hence	hence	ADV
ejpam-6247	137	2	,	,	PUNCT
ejpam-6247	137	3	(	(	PUNCT
ejpam-6247	137	4	µ,d	µ,d	NOUN
ejpam-6247	137	5	)	)	PUNCT
ejpam-6247	137	6	∨	∨	NOUN
ejpam-6247	137	7	(	(	PUNCT
ejpam-6247	137	8	(	(	PUNCT
ejpam-6247	137	9	µ,d),d	µ,d),d	NOUN
ejpam-6247	137	10	)	)	PUNCT
ejpam-6247	138	1	=	=	PUNCT
ejpam-6247	138	2	l.	l.	PROPN
ejpam-6247	138	3	therefore	therefore	ADV
ejpam-6247	138	4	,	,	PUNCT
ejpam-6247	138	5	l	l	NOUN
ejpam-6247	138	6	is	be	AUX
ejpam-6247	138	7	a	a	DET
ejpam-6247	138	8	d	d	ADJ
ejpam-6247	138	9	-	-	PUNCT
ejpam-6247	138	10	stone	stone	NOUN
ejpam-6247	138	11	adl	adl	PROPN
ejpam-6247	138	12	.	.	PUNCT
ejpam-6247	138	13	proposition	proposition	NOUN
ejpam-6247	138	14	5	5	NUM
ejpam-6247	138	15	.	.	PUNCT
ejpam-6247	139	1	every	every	DET
ejpam-6247	139	2	d	d	NOUN
ejpam-6247	139	3	-	-	PUNCT
ejpam-6247	139	4	stone	stone	NOUN
ejpam-6247	139	5	adl	adl	NOUN
ejpam-6247	139	6	is	be	AUX
ejpam-6247	139	7	hemicomplemented	hemicomplemente	VERB
ejpam-6247	139	8	.	.	PUNCT
ejpam-6247	140	1	proof	proof	NOUN
ejpam-6247	140	2	.	.	PUNCT
ejpam-6247	141	1	assume	assume	VERB
ejpam-6247	141	2	that	that	SCONJ
ejpam-6247	141	3	l	l	NOUN
ejpam-6247	141	4	is	be	AUX
ejpam-6247	141	5	a	a	DET
ejpam-6247	141	6	d	d	ADJ
ejpam-6247	141	7	-	-	NOUN
ejpam-6247	141	8	stone	stone	NOUN
ejpam-6247	141	9	adl	adl	NOUN
ejpam-6247	141	10	and	and	CCONJ
ejpam-6247	141	11	let	let	VERB
ejpam-6247	141	12	µ	µ	X
ejpam-6247	141	13	∈	∈	X
ejpam-6247	141	14	l.	l.	NOUN
ejpam-6247	141	15	by	by	ADP
ejpam-6247	141	16	definition	definition	NOUN
ejpam-6247	141	17	,	,	PUNCT
ejpam-6247	141	18	we	we	PRON
ejpam-6247	141	19	have	have	VERB
ejpam-6247	141	20	(	(	PUNCT
ejpam-6247	141	21	µ,d)∨	µ,d)∨	PROPN
ejpam-6247	141	22	(	(	PUNCT
ejpam-6247	141	23	(	(	PUNCT
ejpam-6247	141	24	µ,d),d	µ,d),d	NOUN
ejpam-6247	141	25	)	)	PUNCT
ejpam-6247	141	26	=	=	VERB
ejpam-6247	142	1	l.	l.	NOUN
ejpam-6247	142	2	this	this	PRON
ejpam-6247	142	3	implies	imply	VERB
ejpam-6247	142	4	that	that	SCONJ
ejpam-6247	142	5	0	0	NUM
ejpam-6247	142	6	∈	∈	NOUN
ejpam-6247	142	7	(	(	PUNCT
ejpam-6247	142	8	µ,d)∨	µ,d)∨	PROPN
ejpam-6247	142	9	(	(	PUNCT
ejpam-6247	142	10	(	(	PUNCT
ejpam-6247	142	11	µ,d),d	µ,d),d	NOUN
ejpam-6247	142	12	)	)	PUNCT
ejpam-6247	142	13	,	,	PUNCT
ejpam-6247	142	14	so	so	SCONJ
ejpam-6247	142	15	there	there	PRON
ejpam-6247	142	16	exist	exist	VERB
ejpam-6247	142	17	elements	element	NOUN
ejpam-6247	142	18	θ	θ	PROPN
ejpam-6247	142	19	∈	∈	PROPN
ejpam-6247	142	20	(	(	PUNCT
ejpam-6247	142	21	µ,d	µ,d	NOUN
ejpam-6247	142	22	)	)	PUNCT
ejpam-6247	142	23	and	and	CCONJ
ejpam-6247	142	24	ϑ	ϑ	X
ejpam-6247	142	25	∈	∈	PROPN
ejpam-6247	142	26	(	(	PUNCT
ejpam-6247	142	27	(	(	PUNCT
ejpam-6247	142	28	µ,d),d	µ,d),d	NOUN
ejpam-6247	142	29	)	)	PUNCT
ejpam-6247	142	30	such	such	ADJ
ejpam-6247	142	31	that	that	SCONJ
ejpam-6247	142	32	θ	θ	PROPN
ejpam-6247	142	33	∧	∧	PROPN
ejpam-6247	142	34	ϑ	ϑ	X
ejpam-6247	142	35	=	=	NOUN
ejpam-6247	142	36	0	0	NUM
ejpam-6247	142	37	.	.	PUNCT
ejpam-6247	143	1	consequently	consequently	ADV
ejpam-6247	143	2	,	,	PUNCT
ejpam-6247	143	3	(	(	PUNCT
ejpam-6247	143	4	θ	θ	NOUN
ejpam-6247	143	5	,	,	PUNCT
ejpam-6247	143	6	d	d	NOUN
ejpam-6247	143	7	)	)	PUNCT
ejpam-6247	143	8	∩	∩	NOUN
ejpam-6247	143	9	(	(	PUNCT
ejpam-6247	143	10	ϑ,d	ϑ,d	NOUN
ejpam-6247	143	11	)	)	PUNCT
ejpam-6247	143	12	=	=	SYM
ejpam-6247	143	13	(	(	PUNCT
ejpam-6247	143	14	θ	θ	PROPN
ejpam-6247	143	15	∧	∧	PROPN
ejpam-6247	143	16	ϑ,d	ϑ,d	NOUN
ejpam-6247	143	17	)	)	PUNCT
ejpam-6247	143	18	=	=	SYM
ejpam-6247	143	19	(	(	PUNCT
ejpam-6247	143	20	0,d	0,d	PUNCT
ejpam-6247	143	21	)	)	PUNCT
ejpam-6247	143	22	=	=	VERB
ejpam-6247	144	1	d.	d.	NOUN
ejpam-6247	144	2	this	this	DET
ejpam-6247	144	3	inclusion	inclusion	NOUN
ejpam-6247	144	4	implies	imply	VERB
ejpam-6247	144	5	that	that	SCONJ
ejpam-6247	144	6	(	(	PUNCT
ejpam-6247	144	7	θ	θ	NOUN
ejpam-6247	144	8	,	,	PUNCT
ejpam-6247	144	9	d	d	NOUN
ejpam-6247	144	10	)	)	PUNCT
ejpam-6247	144	11	⊆	⊆	NUM
ejpam-6247	144	12	(	(	PUNCT
ejpam-6247	144	13	(	(	PUNCT
ejpam-6247	144	14	ϑ,d),d	ϑ,d),d	NOUN
ejpam-6247	144	15	)	)	PUNCT
ejpam-6247	144	16	,	,	PUNCT
ejpam-6247	144	17	and	and	CCONJ
ejpam-6247	144	18	since	since	SCONJ
ejpam-6247	144	19	θ	θ	PROPN
ejpam-6247	144	20	∈	∈	PROPN
ejpam-6247	144	21	(	(	PUNCT
ejpam-6247	144	22	µ,d	µ,d	NOUN
ejpam-6247	144	23	)	)	PUNCT
ejpam-6247	144	24	,	,	PUNCT
ejpam-6247	144	25	we	we	PRON
ejpam-6247	144	26	also	also	ADV
ejpam-6247	144	27	have	have	VERB
ejpam-6247	144	28	(	(	PUNCT
ejpam-6247	144	29	(	(	PUNCT
ejpam-6247	144	30	µ,d),d	µ,d),d	X
ejpam-6247	144	31	)	)	PUNCT
ejpam-6247	144	32	⊆	⊆	NUM
ejpam-6247	144	33	(	(	PUNCT
ejpam-6247	144	34	θ	θ	NOUN
ejpam-6247	144	35	,	,	PUNCT
ejpam-6247	144	36	d	d	NOUN
ejpam-6247	144	37	)	)	PUNCT
ejpam-6247	144	38	.	.	PUNCT
ejpam-6247	145	1	hence	hence	ADV
ejpam-6247	145	2	,	,	PUNCT
ejpam-6247	145	3	(	(	PUNCT
ejpam-6247	145	4	(	(	PUNCT
ejpam-6247	145	5	µ,d),d	µ,d),d	NOUN
ejpam-6247	145	6	)	)	PUNCT
ejpam-6247	145	7	=	=	SYM
ejpam-6247	145	8	(	(	PUNCT
ejpam-6247	145	9	θ	θ	PROPN
ejpam-6247	145	10	,	,	PUNCT
ejpam-6247	145	11	d	d	NOUN
ejpam-6247	145	12	)	)	PUNCT
ejpam-6247	145	13	.	.	PUNCT
ejpam-6247	146	1	therefore	therefore	ADV
ejpam-6247	146	2	,	,	PUNCT
ejpam-6247	146	3	l	l	NOUN
ejpam-6247	146	4	satisfies	satisfy	VERB
ejpam-6247	146	5	the	the	DET
ejpam-6247	146	6	condition	condition	NOUN
ejpam-6247	146	7	for	for	ADP
ejpam-6247	146	8	being	be	AUX
ejpam-6247	146	9	hemicomplemented	hemicomplemente	VERB
ejpam-6247	146	10	.	.	PUNCT
ejpam-6247	147	1	the	the	DET
ejpam-6247	147	2	converse	converse	NOUN
ejpam-6247	147	3	of	of	ADP
ejpam-6247	147	4	the	the	DET
ejpam-6247	147	5	preceding	precede	VERB
ejpam-6247	147	6	proposition	proposition	NOUN
ejpam-6247	147	7	does	do	AUX
ejpam-6247	147	8	not	not	PART
ejpam-6247	147	9	hold	hold	VERB
ejpam-6247	147	10	universally	universally	ADV
ejpam-6247	147	11	.	.	PUNCT
ejpam-6247	148	1	however	however	ADV
ejpam-6247	148	2	,	,	PUNCT
ejpam-6247	148	3	we	we	PRON
ejpam-6247	148	4	now	now	ADV
ejpam-6247	148	5	develop	develop	VERB
ejpam-6247	148	6	a	a	DET
ejpam-6247	148	7	set	set	NOUN
ejpam-6247	148	8	of	of	ADP
ejpam-6247	148	9	equivalent	equivalent	ADJ
ejpam-6247	148	10	conditions	condition	NOUN
ejpam-6247	148	11	under	under	ADP
ejpam-6247	148	12	which	which	PRON
ejpam-6247	148	13	a	a	DET
ejpam-6247	148	14	hemicomplemented	hemicomplemente	VERB
ejpam-6247	148	15	adl	adl	NOUN
ejpam-6247	148	16	becomes	become	VERB
ejpam-6247	148	17	a	a	DET
ejpam-6247	148	18	d	d	ADJ
ejpam-6247	148	19	-	-	NOUN
ejpam-6247	148	20	stone	stone	NOUN
ejpam-6247	148	21	adl	adl	PROPN
ejpam-6247	148	22	.	.	PUNCT
ejpam-6247	149	1	to	to	PART
ejpam-6247	149	2	aid	aid	VERB
ejpam-6247	149	3	this	this	DET
ejpam-6247	149	4	characterization	characterization	NOUN
ejpam-6247	149	5	,	,	PUNCT
ejpam-6247	149	6	we	we	PRON
ejpam-6247	149	7	introduce	introduce	VERB
ejpam-6247	149	8	the	the	DET
ejpam-6247	149	9	notion	notion	NOUN
ejpam-6247	149	10	of	of	ADP
ejpam-6247	149	11	a	a	DET
ejpam-6247	149	12	d	d	NOUN
ejpam-6247	149	13	-	-	NOUN
ejpam-6247	149	14	factor	factor	NOUN
ejpam-6247	149	15	in	in	ADP
ejpam-6247	149	16	an	an	DET
ejpam-6247	149	17	adl	adl	PROPN
ejpam-6247	149	18	l.	l.	PROPN
ejpam-6247	149	19	a	a	PRON
ejpam-6247	149	20	d	d	NOUN
ejpam-6247	149	21	-	-	NOUN
ejpam-6247	149	22	filter	filter	NOUN
ejpam-6247	149	23	g	g	NOUN
ejpam-6247	149	24	of	of	ADP
ejpam-6247	149	25	l	l	NOUN
ejpam-6247	149	26	is	be	AUX
ejpam-6247	149	27	said	say	VERB
ejpam-6247	149	28	to	to	PART
ejpam-6247	149	29	be	be	AUX
ejpam-6247	149	30	a	a	DET
ejpam-6247	149	31	d	d	NOUN
ejpam-6247	149	32	-	-	NOUN
ejpam-6247	149	33	factor	factor	NOUN
ejpam-6247	149	34	if	if	SCONJ
ejpam-6247	149	35	there	there	PRON
ejpam-6247	149	36	exists	exist	VERB
ejpam-6247	149	37	a	a	DET
ejpam-6247	149	38	proper	proper	ADJ
ejpam-6247	149	39	d	d	NOUN
ejpam-6247	149	40	-	-	ADJ
ejpam-6247	149	41	filter	filter	ADJ
ejpam-6247	149	42	u	u	NOUN
ejpam-6247	149	43	such	such	ADJ
ejpam-6247	149	44	that	that	SCONJ
ejpam-6247	149	45	g	g	PROPN
ejpam-6247	149	46	∩	∩	ADJ
ejpam-6247	149	47	u	u	NOUN
ejpam-6247	149	48	=	=	SYM
ejpam-6247	149	49	d	d	PROPN
ejpam-6247	149	50	and	and	CCONJ
ejpam-6247	149	51	g	g	PROPN
ejpam-6247	149	52	∨	∨	NUM
ejpam-6247	149	53	u	u	NOUN
ejpam-6247	149	54	=	=	PROPN
ejpam-6247	149	55	l.	l.	PROPN
ejpam-6247	149	56	before	before	ADP
ejpam-6247	149	57	proceeding	proceeding	NOUN
ejpam-6247	149	58	,	,	PUNCT
ejpam-6247	149	59	we	we	PRON
ejpam-6247	149	60	introduce	introduce	VERB
ejpam-6247	149	61	the	the	DET
ejpam-6247	149	62	following	following	ADJ
ejpam-6247	149	63	notation	notation	NOUN
ejpam-6247	149	64	.	.	PUNCT
ejpam-6247	150	1	definition	definition	NOUN
ejpam-6247	150	2	5	5	NUM
ejpam-6247	150	3	.	.	PUNCT
ejpam-6247	151	1	let	let	VERB
ejpam-6247	151	2	l	l	NOUN
ejpam-6247	151	3	be	be	AUX
ejpam-6247	151	4	an	an	DET
ejpam-6247	151	5	adl	adl	NOUN
ejpam-6247	151	6	.	.	PUNCT
ejpam-6247	152	1	we	we	PRON
ejpam-6247	152	2	define	define	VERB
ejpam-6247	152	3	d	d	PUNCT
ejpam-6247	152	4	◦	◦	NOUN
ejpam-6247	152	5	(l	(l	NUM
ejpam-6247	152	6	)	)	PUNCT
ejpam-6247	152	7	:	:	PUNCT
ejpam-6247	153	1	=	=	SYM
ejpam-6247	153	2	{	{	PUNCT
ejpam-6247	153	3	(	(	PUNCT
ejpam-6247	153	4	µ,d	µ,d	NOUN
ejpam-6247	153	5	)	)	PUNCT
ejpam-6247	153	6	|	|	ADV
ejpam-6247	153	7	µ	µ	X
ejpam-6247	153	8	∈	∈	NOUN
ejpam-6247	153	9	l	l	NOUN
ejpam-6247	153	10	}	}	PUNCT
ejpam-6247	153	11	,	,	PUNCT
ejpam-6247	153	12	the	the	DET
ejpam-6247	153	13	collection	collection	NOUN
ejpam-6247	153	14	of	of	ADP
ejpam-6247	153	15	all	all	DET
ejpam-6247	153	16	principal	principal	ADJ
ejpam-6247	153	17	d	d	NOUN
ejpam-6247	153	18	-	-	NOUN
ejpam-6247	153	19	filters	filter	NOUN
ejpam-6247	153	20	in	in	ADP
ejpam-6247	153	21	l.	l.	NOUN
ejpam-6247	153	22	when	when	SCONJ
ejpam-6247	153	23	equipped	equip	VERB
ejpam-6247	153	24	with	with	ADP
ejpam-6247	153	25	the	the	DET
ejpam-6247	153	26	operations	operation	NOUN
ejpam-6247	153	27	∨	∨	ADV
ejpam-6247	153	28	and	and	CCONJ
ejpam-6247	153	29	∩	∩	NOUN
ejpam-6247	153	30	inherited	inherit	VERB
ejpam-6247	153	31	from	from	ADP
ejpam-6247	153	32	the	the	DET
ejpam-6247	153	33	lattice	lattice	NOUN
ejpam-6247	153	34	of	of	ADP
ejpam-6247	153	35	filters	filter	NOUN
ejpam-6247	153	36	f(l	f(l	NOUN
ejpam-6247	153	37	)	)	PUNCT
ejpam-6247	153	38	,	,	PUNCT
ejpam-6247	153	39	d	d	PUNCT
ejpam-6247	153	40	◦	◦	NOUN
ejpam-6247	153	41	(l	(l	NOUN
ejpam-6247	153	42	)	)	PUNCT
ejpam-6247	153	43	forms	form	VERB
ejpam-6247	153	44	a	a	DET
ejpam-6247	153	45	substructure	substructure	NOUN
ejpam-6247	153	46	of	of	ADP
ejpam-6247	153	47	f	f	PROPN
ejpam-6247	153	48	(	(	PUNCT
ejpam-6247	153	49	l	l	NOUN
ejpam-6247	153	50	)	)	PUNCT
ejpam-6247	153	51	whose	whose	DET
ejpam-6247	153	52	properties	property	NOUN
ejpam-6247	153	53	will	will	AUX
ejpam-6247	153	54	be	be	AUX
ejpam-6247	153	55	explored	explore	VERB
ejpam-6247	153	56	in	in	ADP
ejpam-6247	153	57	the	the	DET
ejpam-6247	153	58	subsequent	subsequent	ADJ
ejpam-6247	153	59	results	result	NOUN
ejpam-6247	153	60	.	.	PUNCT
ejpam-6247	154	1	theorem	theorem	NOUN
ejpam-6247	154	2	1	1	NUM
ejpam-6247	154	3	.	.	PUNCT
ejpam-6247	155	1	the	the	DET
ejpam-6247	155	2	conditions	condition	NOUN
ejpam-6247	155	3	listed	list	VERB
ejpam-6247	155	4	below	below	ADV
ejpam-6247	155	5	are	be	AUX
ejpam-6247	155	6	equivalent	equivalent	ADJ
ejpam-6247	155	7	in	in	ADP
ejpam-6247	155	8	a	a	DET
ejpam-6247	155	9	hemicomplemented	hemicomplemente	VERB
ejpam-6247	155	10	adl	adl	NOUN
ejpam-6247	155	11	:	:	PUNCT
ejpam-6247	155	12	(	(	PUNCT
ejpam-6247	155	13	1	1	X
ejpam-6247	155	14	)	)	PUNCT
ejpam-6247	155	15	l	l	NOUN
ejpam-6247	155	16	is	be	AUX
ejpam-6247	155	17	a	a	DET
ejpam-6247	155	18	d	d	ADJ
ejpam-6247	155	19	-	-	PUNCT
ejpam-6247	155	20	stone	stone	NOUN
ejpam-6247	155	21	adl	adl	PROPN
ejpam-6247	155	22	,	,	PUNCT
ejpam-6247	155	23	(	(	PUNCT
ejpam-6247	155	24	2	2	X
ejpam-6247	155	25	)	)	PUNCT
ejpam-6247	155	26	each	each	DET
ejpam-6247	155	27	(	(	PUNCT
ejpam-6247	155	28	µ,d	µ,d	NOUN
ejpam-6247	155	29	)	)	PUNCT
ejpam-6247	155	30	is	be	AUX
ejpam-6247	155	31	a	a	DET
ejpam-6247	155	32	d	d	NOUN
ejpam-6247	155	33	-	-	NOUN
ejpam-6247	155	34	factor	factor	NOUN
ejpam-6247	155	35	of	of	ADP
ejpam-6247	155	36	l	l	NOUN
ejpam-6247	155	37	,	,	PUNCT
ejpam-6247	155	38	(	(	PUNCT
ejpam-6247	155	39	3	3	X
ejpam-6247	155	40	)	)	PUNCT
ejpam-6247	155	41	for	for	ADP
ejpam-6247	155	42	each	each	DET
ejpam-6247	155	43	µ	µ	PROPN
ejpam-6247	155	44	∈	∈	PROPN
ejpam-6247	155	45	l	l	NOUN
ejpam-6247	155	46	,	,	PUNCT
ejpam-6247	155	47	there	there	PRON
ejpam-6247	155	48	exists	exist	VERB
ejpam-6247	155	49	µ′	µ′	X
ejpam-6247	155	50	∈	∈	PROPN
ejpam-6247	155	51	l	l	NOUN
ejpam-6247	155	52	such	such	ADJ
ejpam-6247	155	53	that	that	SCONJ
ejpam-6247	155	54	(	(	PUNCT
ejpam-6247	155	55	µ,d	µ,d	NOUN
ejpam-6247	155	56	)	)	PUNCT
ejpam-6247	155	57	∨	∨	NOUN
ejpam-6247	155	58	(	(	PUNCT
ejpam-6247	155	59	µ′,d	µ′,d	NOUN
ejpam-6247	155	60	)	)	PUNCT
ejpam-6247	155	61	=	=	SYM
ejpam-6247	156	1	l	l	NOUN
ejpam-6247	156	2	,	,	PUNCT
ejpam-6247	156	3	(	(	PUNCT
ejpam-6247	156	4	4	4	NUM
ejpam-6247	156	5	)	)	PUNCT
ejpam-6247	156	6	for	for	ADP
ejpam-6247	156	7	µ	µ	NUM
ejpam-6247	156	8	,	,	PUNCT
ejpam-6247	156	9	π	π	PROPN
ejpam-6247	156	10	∈	∈	PROPN
ejpam-6247	156	11	l	l	NOUN
ejpam-6247	156	12	,	,	PUNCT
ejpam-6247	156	13	(	(	PUNCT
ejpam-6247	156	14	µ,d	µ,d	NOUN
ejpam-6247	156	15	)	)	PUNCT
ejpam-6247	156	16	∨	∨	NOUN
ejpam-6247	156	17	(	(	PUNCT
ejpam-6247	156	18	π	π	PROPN
ejpam-6247	156	19	,	,	PUNCT
ejpam-6247	156	20	d	d	NOUN
ejpam-6247	156	21	)	)	PUNCT
ejpam-6247	156	22	=	=	SYM
ejpam-6247	156	23	(	(	PUNCT
ejpam-6247	156	24	µ	µ	X
ejpam-6247	156	25	∨	∨	NUM
ejpam-6247	156	26	π	π	PROPN
ejpam-6247	156	27	,	,	PUNCT
ejpam-6247	156	28	d	d	NOUN
ejpam-6247	156	29	)	)	PUNCT
ejpam-6247	156	30	,	,	PUNCT
ejpam-6247	156	31	(	(	PUNCT
ejpam-6247	156	32	5	5	X
ejpam-6247	156	33	)	)	PUNCT
ejpam-6247	157	1	d	d	NOUN
ejpam-6247	157	2	◦	◦	NOUN
ejpam-6247	157	3	◦	◦	NOUN
ejpam-6247	157	4	(l	(l	NUM
ejpam-6247	158	1	)	)	PUNCT
ejpam-6247	158	2	=	=	PRON
ejpam-6247	158	3	{	{	PUNCT
ejpam-6247	158	4	(	(	PUNCT
ejpam-6247	158	5	(	(	PUNCT
ejpam-6247	158	6	µ,d),d	µ,d),d	NOUN
ejpam-6247	158	7	)	)	PUNCT
ejpam-6247	158	8	|	|	ADV
ejpam-6247	158	9	µ	µ	X
ejpam-6247	158	10	∈	∈	NOUN
ejpam-6247	158	11	l	l	NOUN
ejpam-6247	158	12	}	}	PUNCT
ejpam-6247	158	13	is	be	AUX
ejpam-6247	158	14	a	a	DET
ejpam-6247	158	15	sublattice	sublattice	NOUN
ejpam-6247	158	16	of	of	ADP
ejpam-6247	158	17	f(l	f(l	NOUN
ejpam-6247	158	18	)	)	PUNCT
ejpam-6247	158	19	,	,	PUNCT
ejpam-6247	158	20	where	where	SCONJ
ejpam-6247	158	21	f(l	f(l	NOUN
ejpam-6247	158	22	)	)	PUNCT
ejpam-6247	158	23	is	be	AUX
ejpam-6247	158	24	the	the	DET
ejpam-6247	158	25	set	set	NOUN
ejpam-6247	158	26	of	of	ADP
ejpam-6247	158	27	all	all	DET
ejpam-6247	158	28	filters	filter	NOUN
ejpam-6247	158	29	of	of	ADP
ejpam-6247	158	30	l.	l.	PROPN
ejpam-6247	158	31	proof	proof	PROPN
ejpam-6247	158	32	.	.	PUNCT
ejpam-6247	159	1	(	(	PUNCT
ejpam-6247	159	2	1	1	X
ejpam-6247	159	3	)	)	PUNCT
ejpam-6247	159	4	⇒	⇒	NOUN
ejpam-6247	159	5	(	(	PUNCT
ejpam-6247	159	6	2	2	NUM
ejpam-6247	159	7	)	)	PUNCT
ejpam-6247	159	8	:	:	PUNCT
ejpam-6247	159	9	assume	assume	VERB
ejpam-6247	159	10	(	(	PUNCT
ejpam-6247	159	11	1	1	NUM
ejpam-6247	159	12	)	)	PUNCT
ejpam-6247	159	13	.	.	PUNCT
ejpam-6247	160	1	let	let	VERB
ejpam-6247	160	2	µ	µ	X
ejpam-6247	160	3	∈	∈	NOUN
ejpam-6247	160	4	l.	l.	NOUN
ejpam-6247	160	5	it	it	PRON
ejpam-6247	160	6	can	can	AUX
ejpam-6247	160	7	be	be	AUX
ejpam-6247	160	8	seen	see	VERB
ejpam-6247	160	9	that	that	SCONJ
ejpam-6247	160	10	(	(	PUNCT
ejpam-6247	160	11	µ,d)∩((µ,d),d	µ,d)∩((µ,d),d	PROPN
ejpam-6247	160	12	)	)	PUNCT
ejpam-6247	161	1	=	=	PUNCT
ejpam-6247	161	2	d.	d.	NOUN
ejpam-6247	161	3	by	by	ADP
ejpam-6247	161	4	our	our	PRON
ejpam-6247	161	5	assumption	assumption	NOUN
ejpam-6247	161	6	(	(	PUNCT
ejpam-6247	161	7	1	1	NUM
ejpam-6247	161	8	)	)	PUNCT
ejpam-6247	161	9	,	,	PUNCT
ejpam-6247	161	10	we	we	PRON
ejpam-6247	161	11	obtain	obtain	VERB
ejpam-6247	161	12	(	(	PUNCT
ejpam-6247	161	13	µ,d	µ,d	NOUN
ejpam-6247	161	14	)	)	PUNCT
ejpam-6247	161	15	∨	∨	NOUN
ejpam-6247	161	16	(	(	PUNCT
ejpam-6247	161	17	(	(	PUNCT
ejpam-6247	161	18	µ,d),d	µ,d),d	NOUN
ejpam-6247	161	19	)	)	PUNCT
ejpam-6247	161	20	=	=	PUNCT
ejpam-6247	162	1	l.	l.	PROPN
ejpam-6247	162	2	thus	thus	ADV
ejpam-6247	162	3	,	,	PUNCT
ejpam-6247	162	4	(	(	PUNCT
ejpam-6247	162	5	µ,d	µ,d	NOUN
ejpam-6247	162	6	)	)	PUNCT
ejpam-6247	162	7	is	be	AUX
ejpam-6247	162	8	a	a	DET
ejpam-6247	162	9	d	d	NOUN
ejpam-6247	162	10	-	-	NOUN
ejpam-6247	162	11	factor	factor	NOUN
ejpam-6247	162	12	of	of	ADP
ejpam-6247	162	13	l.	l.	PROPN
ejpam-6247	162	14	n.	n.	PROPN
ejpam-6247	162	15	rafi	rafi	PROPN
ejpam-6247	162	16	et	et	PROPN
ejpam-6247	162	17	al	al	PROPN
ejpam-6247	162	18	.	.	PUNCT
ejpam-6247	162	19	/	/	SYM
ejpam-6247	162	20	eur	eur	PROPN
ejpam-6247	162	21	.	.	PUNCT
ejpam-6247	163	1	j.	j.	PROPN
ejpam-6247	163	2	pure	pure	PROPN
ejpam-6247	163	3	appl	appl	PROPN
ejpam-6247	163	4	.	.	PROPN
ejpam-6247	163	5	math	math	PROPN
ejpam-6247	163	6	,	,	PUNCT
ejpam-6247	163	7	18	18	NUM
ejpam-6247	163	8	(	(	PUNCT
ejpam-6247	163	9	3	3	NUM
ejpam-6247	163	10	)	)	PUNCT
ejpam-6247	163	11	(	(	PUNCT
ejpam-6247	163	12	2025	2025	NUM
ejpam-6247	163	13	)	)	PUNCT
ejpam-6247	163	14	,	,	PUNCT
ejpam-6247	163	15	6247	6247	NUM
ejpam-6247	163	16	7	7	NUM
ejpam-6247	163	17	of	of	ADP
ejpam-6247	163	18	15	15	NUM
ejpam-6247	163	19	(	(	PUNCT
ejpam-6247	163	20	2	2	NUM
ejpam-6247	163	21	)	)	PUNCT
ejpam-6247	163	22	⇒	⇒	NOUN
ejpam-6247	163	23	(	(	PUNCT
ejpam-6247	163	24	3	3	NUM
ejpam-6247	163	25	)	)	PUNCT
ejpam-6247	163	26	:	:	PUNCT
ejpam-6247	163	27	assume	assume	VERB
ejpam-6247	163	28	(	(	PUNCT
ejpam-6247	163	29	2	2	NUM
ejpam-6247	163	30	)	)	PUNCT
ejpam-6247	163	31	.	.	PUNCT
ejpam-6247	164	1	let	let	VERB
ejpam-6247	164	2	µ	µ	X
ejpam-6247	164	3	∈	∈	X
ejpam-6247	164	4	l.	l.	NOUN
ejpam-6247	164	5	as	as	SCONJ
ejpam-6247	164	6	l	l	PROPN
ejpam-6247	164	7	is	be	AUX
ejpam-6247	164	8	hemicomplemented	hemicomplemente	VERB
ejpam-6247	164	9	,	,	PUNCT
ejpam-6247	164	10	there	there	PRON
ejpam-6247	164	11	is	be	VERB
ejpam-6247	164	12	µ′	µ′	DET
ejpam-6247	164	13	∈	∈	PROPN
ejpam-6247	164	14	l	l	NOUN
ejpam-6247	165	1	such	such	ADJ
ejpam-6247	165	2	that	that	SCONJ
ejpam-6247	165	3	(	(	PUNCT
ejpam-6247	165	4	(	(	PUNCT
ejpam-6247	165	5	µ,d),d	µ,d),d	NOUN
ejpam-6247	165	6	)	)	PUNCT
ejpam-6247	165	7	=	=	SYM
ejpam-6247	166	1	(	(	PUNCT
ejpam-6247	166	2	µ′,d	µ′,d	NOUN
ejpam-6247	166	3	)	)	PUNCT
ejpam-6247	166	4	.	.	PUNCT
ejpam-6247	167	1	by	by	ADP
ejpam-6247	167	2	(	(	PUNCT
ejpam-6247	167	3	2	2	NUM
ejpam-6247	167	4	)	)	PUNCT
ejpam-6247	167	5	,	,	PUNCT
ejpam-6247	167	6	there	there	PRON
ejpam-6247	167	7	exists	exist	VERB
ejpam-6247	167	8	a	a	DET
ejpam-6247	167	9	d	d	ADJ
ejpam-6247	167	10	-	-	ADJ
ejpam-6247	167	11	filter	filter	NOUN
ejpam-6247	167	12	u	u	NOUN
ejpam-6247	167	13	such	such	ADJ
ejpam-6247	167	14	that	that	SCONJ
ejpam-6247	167	15	(	(	PUNCT
ejpam-6247	167	16	µ,d	µ,d	NOUN
ejpam-6247	167	17	)	)	PUNCT
ejpam-6247	167	18	∩	∩	NOUN
ejpam-6247	167	19	u	u	NOUN
ejpam-6247	167	20	=	=	PROPN
ejpam-6247	167	21	d	d	PROPN
ejpam-6247	167	22	and	and	CCONJ
ejpam-6247	167	23	(	(	PUNCT
ejpam-6247	167	24	µ,d	µ,d	NOUN
ejpam-6247	167	25	)	)	PUNCT
ejpam-6247	167	26	∨	∨	NOUN
ejpam-6247	167	27	u	u	NOUN
ejpam-6247	167	28	=	=	PUNCT
ejpam-6247	167	29	l.	l.	PROPN
ejpam-6247	167	30	since	since	SCONJ
ejpam-6247	167	31	(	(	PUNCT
ejpam-6247	167	32	µ,d	µ,d	NOUN
ejpam-6247	167	33	)	)	PUNCT
ejpam-6247	167	34	∩	∩	NOUN
ejpam-6247	167	35	u	u	NOUN
ejpam-6247	167	36	=	=	SYM
ejpam-6247	167	37	d	d	PROPN
ejpam-6247	167	38	,	,	PUNCT
ejpam-6247	167	39	we	we	PRON
ejpam-6247	167	40	have	have	VERB
ejpam-6247	167	41	u	u	PRON
ejpam-6247	167	42	⊆	⊆	NUM
ejpam-6247	167	43	(	(	PUNCT
ejpam-6247	167	44	(	(	PUNCT
ejpam-6247	167	45	µ,d),d	µ,d),d	NOUN
ejpam-6247	167	46	)	)	PUNCT
ejpam-6247	168	1	=	=	SYM
ejpam-6247	168	2	(	(	PUNCT
ejpam-6247	168	3	µ′,d	µ′,d	NOUN
ejpam-6247	168	4	)	)	PUNCT
ejpam-6247	168	5	hence	hence	ADV
ejpam-6247	168	6	,	,	PUNCT
ejpam-6247	168	7	l	l	NOUN
ejpam-6247	168	8	=	=	SYM
ejpam-6247	168	9	(	(	PUNCT
ejpam-6247	168	10	µ,d	µ,d	NOUN
ejpam-6247	168	11	)	)	PUNCT
ejpam-6247	168	12	∨	∨	NOUN
ejpam-6247	168	13	u	u	NOUN
ejpam-6247	168	14	⊆	⊆	NUM
ejpam-6247	168	15	(	(	PUNCT
ejpam-6247	168	16	µ,d	µ,d	NOUN
ejpam-6247	168	17	)	)	PUNCT
ejpam-6247	168	18	∨	∨	NOUN
ejpam-6247	168	19	(	(	PUNCT
ejpam-6247	168	20	µ′,d	µ′,d	NOUN
ejpam-6247	168	21	)	)	PUNCT
ejpam-6247	168	22	.	.	PUNCT
ejpam-6247	169	1	thus	thus	ADV
ejpam-6247	169	2	,	,	PUNCT
ejpam-6247	169	3	(	(	PUNCT
ejpam-6247	169	4	µ,d	µ,d	NOUN
ejpam-6247	169	5	)	)	PUNCT
ejpam-6247	169	6	∨	∨	NOUN
ejpam-6247	169	7	(	(	PUNCT
ejpam-6247	169	8	µ′,d	µ′,d	NOUN
ejpam-6247	169	9	)	)	PUNCT
ejpam-6247	169	10	=	=	SYM
ejpam-6247	169	11	l.	l.	NOUN
ejpam-6247	169	12	(	(	PUNCT
ejpam-6247	169	13	3	3	NUM
ejpam-6247	169	14	)	)	PUNCT
ejpam-6247	169	15	⇒	⇒	NOUN
ejpam-6247	169	16	(	(	PUNCT
ejpam-6247	169	17	4	4	NUM
ejpam-6247	169	18	)	)	PUNCT
ejpam-6247	169	19	:	:	PUNCT
ejpam-6247	169	20	assume	assume	VERB
ejpam-6247	169	21	(	(	PUNCT
ejpam-6247	169	22	3	3	NUM
ejpam-6247	169	23	)	)	PUNCT
ejpam-6247	169	24	.	.	PUNCT
ejpam-6247	170	1	let	let	VERB
ejpam-6247	170	2	µ	µ	NOUN
ejpam-6247	170	3	,	,	PUNCT
ejpam-6247	170	4	π	π	PROPN
ejpam-6247	170	5	∈	∈	PROPN
ejpam-6247	170	6	l.	l.	NOUN
ejpam-6247	170	7	by	by	ADP
ejpam-6247	170	8	(	(	PUNCT
ejpam-6247	170	9	3	3	NUM
ejpam-6247	170	10	)	)	PUNCT
ejpam-6247	170	11	,	,	PUNCT
ejpam-6247	170	12	there	there	PRON
ejpam-6247	170	13	is	be	VERB
ejpam-6247	170	14	µ′	µ′	DET
ejpam-6247	170	15	∈	∈	PROPN
ejpam-6247	170	16	l	l	NOUN
ejpam-6247	170	17	such	such	ADJ
ejpam-6247	170	18	that	that	SCONJ
ejpam-6247	170	19	(	(	PUNCT
ejpam-6247	170	20	µ,d)∨(µ′,d	µ,d)∨(µ′,d	NOUN
ejpam-6247	170	21	)	)	PUNCT
ejpam-6247	170	22	=	=	VERB
ejpam-6247	170	23	l.	l.	PROPN
ejpam-6247	171	1	clearly	clearly	ADV
ejpam-6247	171	2	we	we	PRON
ejpam-6247	171	3	have	have	VERB
ejpam-6247	171	4	(	(	PUNCT
ejpam-6247	171	5	µ,d	µ,d	NOUN
ejpam-6247	171	6	)	)	PUNCT
ejpam-6247	171	7	∨	∨	NOUN
ejpam-6247	171	8	(	(	PUNCT
ejpam-6247	171	9	π	π	PROPN
ejpam-6247	171	10	,	,	PUNCT
ejpam-6247	171	11	d	d	NOUN
ejpam-6247	171	12	)	)	PUNCT
ejpam-6247	171	13	⊆	⊆	NUM
ejpam-6247	171	14	(	(	PUNCT
ejpam-6247	171	15	µ	µ	X
ejpam-6247	171	16	∨	∨	NUM
ejpam-6247	171	17	π	π	PROPN
ejpam-6247	171	18	,	,	PUNCT
ejpam-6247	171	19	d	d	NOUN
ejpam-6247	171	20	)	)	PUNCT
ejpam-6247	171	21	.	.	PUNCT
ejpam-6247	172	1	conversely	conversely	ADV
ejpam-6247	172	2	,	,	PUNCT
ejpam-6247	172	3	let	let	VERB
ejpam-6247	172	4	θ	θ	PROPN
ejpam-6247	172	5	∈	∈	PROPN
ejpam-6247	172	6	(	(	PUNCT
ejpam-6247	172	7	µ	µ	X
ejpam-6247	172	8	∨	∨	NUM
ejpam-6247	172	9	π	π	PROPN
ejpam-6247	172	10	,	,	PUNCT
ejpam-6247	172	11	d	d	NOUN
ejpam-6247	172	12	)	)	PUNCT
ejpam-6247	172	13	.	.	PUNCT
ejpam-6247	173	1	then	then	ADV
ejpam-6247	173	2	θ	θ	PROPN
ejpam-6247	173	3	∨	∨	PROPN
ejpam-6247	173	4	µ	µ	X
ejpam-6247	173	5	∨	∨	NUM
ejpam-6247	174	1	π	π	PROPN
ejpam-6247	174	2	∈	∈	PROPN
ejpam-6247	174	3	d	d	NOUN
ejpam-6247	174	4	,	,	PUNCT
ejpam-6247	174	5	which	which	PRON
ejpam-6247	174	6	leads	lead	VERB
ejpam-6247	174	7	θ	θ	PROPN
ejpam-6247	174	8	∨	∨	NUM
ejpam-6247	174	9	π	π	PROPN
ejpam-6247	174	10	∈	∈	PROPN
ejpam-6247	174	11	(	(	PUNCT
ejpam-6247	174	12	µ,d	µ,d	NOUN
ejpam-6247	174	13	)	)	PUNCT
ejpam-6247	174	14	.	.	PUNCT
ejpam-6247	175	1	by	by	ADP
ejpam-6247	175	2	corollary	corollary	ADJ
ejpam-6247	175	3	1(2	1(2	NUM
ejpam-6247	175	4	)	)	PUNCT
ejpam-6247	175	5	and	and	CCONJ
ejpam-6247	175	6	lemma	lemma	PROPN
ejpam-6247	175	7	2	2	NUM
ejpam-6247	175	8	,	,	PUNCT
ejpam-6247	175	9	we	we	PRON
ejpam-6247	175	10	obtain	obtain	VERB
ejpam-6247	175	11	θ	θ	PROPN
ejpam-6247	175	12	∨	∨	NUM
ejpam-6247	175	13	π	π	PROPN
ejpam-6247	175	14	∈	∈	PROPN
ejpam-6247	175	15	(	(	PUNCT
ejpam-6247	175	16	µ,d	µ,d	NOUN
ejpam-6247	175	17	)	)	PUNCT
ejpam-6247	175	18	⇒	⇒	NOUN
ejpam-6247	175	19	(	(	PUNCT
ejpam-6247	175	20	(	(	PUNCT
ejpam-6247	175	21	µ,d),d	µ,d),d	X
ejpam-6247	175	22	)	)	PUNCT
ejpam-6247	175	23	⊆	⊆	NUM
ejpam-6247	175	24	(	(	PUNCT
ejpam-6247	175	25	θ	θ	PROPN
ejpam-6247	175	26	∨	∨	NUM
ejpam-6247	175	27	π	π	PROPN
ejpam-6247	175	28	,	,	PUNCT
ejpam-6247	175	29	d	d	NOUN
ejpam-6247	175	30	)	)	PUNCT
ejpam-6247	175	31	⇒	⇒	NOUN
ejpam-6247	175	32	(	(	PUNCT
ejpam-6247	175	33	(	(	PUNCT
ejpam-6247	175	34	µ,d),d	µ,d),d	NOUN
ejpam-6247	175	35	)	)	PUNCT
ejpam-6247	175	36	∩	∩	NOUN
ejpam-6247	176	1	[	[	X
ejpam-6247	176	2	θ	θ	PROPN
ejpam-6247	176	3	∨	∨	NUM
ejpam-6247	176	4	π	π	PROPN
ejpam-6247	176	5	)	)	PUNCT
ejpam-6247	176	6	⊆	⊆	NUM
ejpam-6247	176	7	d	d	NOUN
ejpam-6247	176	8	⇒	⇒	NOUN
ejpam-6247	176	9	(	(	PUNCT
ejpam-6247	176	10	(	(	PUNCT
ejpam-6247	176	11	µ,d),d	µ,d),d	NOUN
ejpam-6247	176	12	)	)	PUNCT
ejpam-6247	176	13	∩	∩	NOUN
ejpam-6247	176	14	{	{	PUNCT
ejpam-6247	176	15	[	[	X
ejpam-6247	176	16	θ	θ	NOUN
ejpam-6247	176	17	)	)	PUNCT
ejpam-6247	176	18	∩	∩	NOUN
ejpam-6247	176	19	[	[	X
ejpam-6247	176	20	π	π	NOUN
ejpam-6247	176	21	)	)	PUNCT
ejpam-6247	176	22	}	}	PUNCT
ejpam-6247	176	23	⊆	⊆	NUM
ejpam-6247	176	24	d	d	NOUN
ejpam-6247	176	25	⇒	⇒	NOUN
ejpam-6247	176	26	{	{	PUNCT
ejpam-6247	176	27	(	(	PUNCT
ejpam-6247	176	28	(	(	PUNCT
ejpam-6247	176	29	µ,d),d	µ,d),d	NOUN
ejpam-6247	176	30	)	)	PUNCT
ejpam-6247	176	31	∩	∩	NOUN
ejpam-6247	176	32	[	[	X
ejpam-6247	176	33	θ	θ	NOUN
ejpam-6247	176	34	)	)	PUNCT
ejpam-6247	176	35	}	}	PUNCT
ejpam-6247	176	36	∩	∩	NOUN
ejpam-6247	177	1	[	[	X
ejpam-6247	177	2	π	π	X
ejpam-6247	177	3	)	)	PUNCT
ejpam-6247	177	4	⊆	⊆	NUM
ejpam-6247	177	5	d	d	NOUN
ejpam-6247	177	6	⇒	⇒	NOUN
ejpam-6247	177	7	{	{	PUNCT
ejpam-6247	177	8	(	(	PUNCT
ejpam-6247	177	9	(	(	PUNCT
ejpam-6247	177	10	µ,d),d	µ,d),d	NOUN
ejpam-6247	177	11	)	)	PUNCT
ejpam-6247	177	12	∩	∩	NOUN
ejpam-6247	178	1	[	[	X
ejpam-6247	178	2	θ	θ	NOUN
ejpam-6247	178	3	)	)	PUNCT
ejpam-6247	178	4	}	}	PUNCT
ejpam-6247	178	5	⊆	⊆	NUM
ejpam-6247	178	6	(	(	PUNCT
ejpam-6247	178	7	π	π	PROPN
ejpam-6247	178	8	,	,	PUNCT
ejpam-6247	178	9	d	d	NOUN
ejpam-6247	178	10	)	)	PUNCT
ejpam-6247	178	11	⇒	⇒	NOUN
ejpam-6247	178	12	{	{	PUNCT
ejpam-6247	178	13	(	(	PUNCT
ejpam-6247	178	14	µ′,d	µ′,d	NOUN
ejpam-6247	178	15	)	)	PUNCT
ejpam-6247	178	16	∩	∩	NOUN
ejpam-6247	179	1	[	[	X
ejpam-6247	179	2	θ	θ	NOUN
ejpam-6247	179	3	)	)	PUNCT
ejpam-6247	179	4	}	}	PUNCT
ejpam-6247	179	5	⊆	⊆	NUM
ejpam-6247	179	6	(	(	PUNCT
ejpam-6247	179	7	π	π	PROPN
ejpam-6247	179	8	,	,	PUNCT
ejpam-6247	179	9	d	d	NOUN
ejpam-6247	179	10	)	)	PUNCT
ejpam-6247	179	11	.	.	PUNCT
ejpam-6247	180	1	clearly	clearly	ADV
ejpam-6247	180	2	,	,	PUNCT
ejpam-6247	180	3	(	(	PUNCT
ejpam-6247	180	4	µ,d	µ,d	NOUN
ejpam-6247	180	5	)	)	PUNCT
ejpam-6247	180	6	∩	∩	NOUN
ejpam-6247	180	7	[	[	X
ejpam-6247	180	8	θ	θ	X
ejpam-6247	180	9	)	)	PUNCT
ejpam-6247	180	10	⊆	⊆	NUM
ejpam-6247	180	11	(	(	PUNCT
ejpam-6247	180	12	µ,d	µ,d	NOUN
ejpam-6247	180	13	)	)	PUNCT
ejpam-6247	180	14	.	.	PUNCT
ejpam-6247	181	1	hence	hence	ADV
ejpam-6247	181	2	,	,	PUNCT
ejpam-6247	181	3	θ	θ	PROPN
ejpam-6247	181	4	∈	∈	PROPN
ejpam-6247	181	5	[	[	X
ejpam-6247	181	6	θ	θ	NOUN
ejpam-6247	181	7	)	)	PUNCT
ejpam-6247	181	8	=	=	SYM
ejpam-6247	181	9	l	l	NOUN
ejpam-6247	181	10	∩	∩	X
ejpam-6247	181	11	[	[	X
ejpam-6247	181	12	θ	θ	X
ejpam-6247	181	13	)	)	PUNCT
ejpam-6247	181	14	=	=	SYM
ejpam-6247	181	15	{	{	PUNCT
ejpam-6247	181	16	(	(	PUNCT
ejpam-6247	181	17	µ,d	µ,d	NOUN
ejpam-6247	181	18	)	)	PUNCT
ejpam-6247	181	19	∨	∨	NOUN
ejpam-6247	181	20	(	(	PUNCT
ejpam-6247	181	21	µ′,d	µ′,d	NOUN
ejpam-6247	181	22	)	)	PUNCT
ejpam-6247	181	23	}	}	PUNCT
ejpam-6247	181	24	∩	∩	NOUN
ejpam-6247	181	25	[	[	X
ejpam-6247	181	26	θ	θ	X
ejpam-6247	181	27	)	)	PUNCT
ejpam-6247	181	28	=	=	SYM
ejpam-6247	181	29	{	{	PUNCT
ejpam-6247	181	30	(	(	PUNCT
ejpam-6247	181	31	µ,d	µ,d	NOUN
ejpam-6247	181	32	)	)	PUNCT
ejpam-6247	181	33	∩	∩	NOUN
ejpam-6247	181	34	[	[	X
ejpam-6247	181	35	θ	θ	NOUN
ejpam-6247	181	36	)	)	PUNCT
ejpam-6247	181	37	}	}	PUNCT
ejpam-6247	181	38	∩	∩	NOUN
ejpam-6247	181	39	{	{	PUNCT
ejpam-6247	181	40	(	(	PUNCT
ejpam-6247	181	41	µ′,d	µ′,d	NOUN
ejpam-6247	181	42	)	)	PUNCT
ejpam-6247	181	43	∩	∩	NOUN
ejpam-6247	181	44	[	[	X
ejpam-6247	181	45	θ	θ	NOUN
ejpam-6247	181	46	)	)	PUNCT
ejpam-6247	181	47	}	}	PUNCT
ejpam-6247	181	48	⊆	⊆	NUM
ejpam-6247	181	49	(	(	PUNCT
ejpam-6247	181	50	µ,d	µ,d	NOUN
ejpam-6247	181	51	)	)	PUNCT
ejpam-6247	181	52	∨	∨	NOUN
ejpam-6247	181	53	(	(	PUNCT
ejpam-6247	181	54	π	π	PROPN
ejpam-6247	181	55	,	,	PUNCT
ejpam-6247	181	56	d	d	NOUN
ejpam-6247	181	57	)	)	PUNCT
ejpam-6247	181	58	.	.	PUNCT
ejpam-6247	182	1	hence	hence	ADV
ejpam-6247	182	2	,	,	PUNCT
ejpam-6247	182	3	(	(	PUNCT
ejpam-6247	182	4	µ	µ	X
ejpam-6247	182	5	∨	∨	NUM
ejpam-6247	182	6	π	π	PROPN
ejpam-6247	182	7	,	,	PUNCT
ejpam-6247	182	8	d	d	NOUN
ejpam-6247	182	9	)	)	PUNCT
ejpam-6247	182	10	⊆	⊆	NUM
ejpam-6247	182	11	(	(	PUNCT
ejpam-6247	182	12	µ,d	µ,d	NOUN
ejpam-6247	182	13	)	)	PUNCT
ejpam-6247	182	14	∨	∨	NOUN
ejpam-6247	182	15	(	(	PUNCT
ejpam-6247	182	16	π	π	PROPN
ejpam-6247	182	17	,	,	PUNCT
ejpam-6247	182	18	d	d	NOUN
ejpam-6247	182	19	)	)	PUNCT
ejpam-6247	182	20	.	.	PUNCT
ejpam-6247	183	1	(	(	PUNCT
ejpam-6247	183	2	4	4	X
ejpam-6247	183	3	)	)	PUNCT
ejpam-6247	183	4	⇒	⇒	NOUN
ejpam-6247	183	5	(	(	PUNCT
ejpam-6247	183	6	5	5	NUM
ejpam-6247	183	7	)	)	PUNCT
ejpam-6247	183	8	:	:	PUNCT
ejpam-6247	183	9	for	for	ADP
ejpam-6247	183	10	any	any	DET
ejpam-6247	183	11	µ	µ	NOUN
ejpam-6247	183	12	,	,	PUNCT
ejpam-6247	183	13	π	π	PROPN
ejpam-6247	183	14	∈	∈	PROPN
ejpam-6247	183	15	l	l	NOUN
ejpam-6247	183	16	,	,	PUNCT
ejpam-6247	183	17	it	it	PRON
ejpam-6247	183	18	is	be	AUX
ejpam-6247	183	19	clear	clear	ADJ
ejpam-6247	183	20	that	that	SCONJ
ejpam-6247	183	21	(	(	PUNCT
ejpam-6247	183	22	(	(	PUNCT
ejpam-6247	183	23	µ,d),d)∩	µ,d),d)∩	PROPN
ejpam-6247	183	24	(	(	PUNCT
ejpam-6247	183	25	(	(	PUNCT
ejpam-6247	183	26	π	π	PROPN
ejpam-6247	183	27	,	,	PUNCT
ejpam-6247	183	28	d),d	d),d	PROPN
ejpam-6247	183	29	)	)	PUNCT
ejpam-6247	183	30	=	=	SYM
ejpam-6247	183	31	(	(	PUNCT
ejpam-6247	183	32	(	(	PUNCT
ejpam-6247	183	33	µ∨	µ∨	PROPN
ejpam-6247	183	34	π	π	PROPN
ejpam-6247	183	35	,	,	PUNCT
ejpam-6247	183	36	d),d	d),d	PROPN
ejpam-6247	183	37	)	)	PUNCT
ejpam-6247	183	38	.	.	PUNCT
ejpam-6247	184	1	since	since	SCONJ
ejpam-6247	184	2	l	l	NOUN
ejpam-6247	184	3	is	be	AUX
ejpam-6247	184	4	hemicomplemented	hemicomplemente	VERB
ejpam-6247	184	5	,	,	PUNCT
ejpam-6247	184	6	there	there	PRON
ejpam-6247	184	7	is	be	VERB
ejpam-6247	184	8	µ′	µ′	NUM
ejpam-6247	184	9	,	,	PUNCT
ejpam-6247	184	10	π′	π′	NOUN
ejpam-6247	184	11	∈	∈	NOUN
ejpam-6247	184	12	l	l	NOUN
ejpam-6247	184	13	such	such	ADJ
ejpam-6247	184	14	that	that	SCONJ
ejpam-6247	184	15	(	(	PUNCT
ejpam-6247	184	16	(	(	PUNCT
ejpam-6247	184	17	µ,d),d	µ,d),d	NOUN
ejpam-6247	184	18	)	)	PUNCT
ejpam-6247	184	19	=	=	SYM
ejpam-6247	184	20	(	(	PUNCT
ejpam-6247	184	21	µ′,d	µ′,d	NOUN
ejpam-6247	184	22	)	)	PUNCT
ejpam-6247	184	23	and	and	CCONJ
ejpam-6247	184	24	(	(	PUNCT
ejpam-6247	184	25	(	(	PUNCT
ejpam-6247	184	26	π	π	PROPN
ejpam-6247	184	27	,	,	PUNCT
ejpam-6247	184	28	d),d	d),d	PROPN
ejpam-6247	184	29	)	)	PUNCT
ejpam-6247	184	30	=	=	PRON
ejpam-6247	184	31	(	(	PUNCT
ejpam-6247	184	32	π′,d	π′,d	NOUN
ejpam-6247	184	33	)	)	PUNCT
ejpam-6247	184	34	.	.	PUNCT
ejpam-6247	185	1	hence	hence	ADV
ejpam-6247	185	2	(	(	PUNCT
ejpam-6247	185	3	(	(	PUNCT
ejpam-6247	185	4	µ,d),d	µ,d),d	NOUN
ejpam-6247	185	5	)	)	PUNCT
ejpam-6247	185	6	∨	∨	NOUN
ejpam-6247	185	7	(	(	PUNCT
ejpam-6247	185	8	(	(	PUNCT
ejpam-6247	185	9	π	π	PROPN
ejpam-6247	185	10	,	,	PUNCT
ejpam-6247	185	11	d),d	d),d	PROPN
ejpam-6247	185	12	)	)	PUNCT
ejpam-6247	185	13	=	=	PRON
ejpam-6247	185	14	(	(	PUNCT
ejpam-6247	185	15	µ′,d	µ′,d	NOUN
ejpam-6247	185	16	)	)	PUNCT
ejpam-6247	185	17	∨	∨	NUM
ejpam-6247	185	18	(	(	PUNCT
ejpam-6247	185	19	π′,d	π′,d	NOUN
ejpam-6247	185	20	)	)	PUNCT
ejpam-6247	185	21	=	=	PUNCT
ejpam-6247	185	22	(	(	PUNCT
ejpam-6247	185	23	µ′	µ′	NOUN
ejpam-6247	185	24	∨	∨	NUM
ejpam-6247	185	25	π′,d	π′,d	NOUN
ejpam-6247	185	26	)	)	PUNCT
ejpam-6247	185	27	=	=	SYM
ejpam-6247	185	28	(	(	PUNCT
ejpam-6247	185	29	(	(	PUNCT
ejpam-6247	185	30	σ	σ	NOUN
ejpam-6247	185	31	,	,	PUNCT
ejpam-6247	185	32	d),d	d),d	PROPN
ejpam-6247	185	33	)	)	PUNCT
ejpam-6247	185	34	for	for	ADP
ejpam-6247	185	35	some	some	DET
ejpam-6247	185	36	σ	σ	NUM
ejpam-6247	185	37	∈	∈	PROPN
ejpam-6247	185	38	l	l	NOUN
ejpam-6247	185	39	,	,	PUNCT
ejpam-6247	185	40	as	as	SCONJ
ejpam-6247	185	41	l	l	NOUN
ejpam-6247	185	42	is	be	AUX
ejpam-6247	185	43	hemicomplemented	hemicomplemente	VERB
ejpam-6247	185	44	.	.	PUNCT
ejpam-6247	186	1	therefore	therefore	ADV
ejpam-6247	186	2	,	,	PUNCT
ejpam-6247	186	3	d	d	PUNCT
ejpam-6247	186	4	◦	◦	NOUN
ejpam-6247	186	5	◦	◦	NOUN
ejpam-6247	186	6	(l	(l	NUM
ejpam-6247	186	7	)	)	PUNCT
ejpam-6247	186	8	is	be	AUX
ejpam-6247	186	9	a	a	DET
ejpam-6247	186	10	sublattice	sublattice	NOUN
ejpam-6247	186	11	of	of	ADP
ejpam-6247	186	12	f(l	f(l	NOUN
ejpam-6247	186	13	)	)	PUNCT
ejpam-6247	186	14	.	.	PUNCT
ejpam-6247	187	1	(	(	PUNCT
ejpam-6247	187	2	5	5	X
ejpam-6247	187	3	)	)	PUNCT
ejpam-6247	187	4	⇒	⇒	NOUN
ejpam-6247	187	5	(	(	PUNCT
ejpam-6247	187	6	1	1	NUM
ejpam-6247	187	7	)	)	PUNCT
ejpam-6247	187	8	:	:	PUNCT
ejpam-6247	187	9	assume	assume	VERB
ejpam-6247	187	10	(	(	PUNCT
ejpam-6247	187	11	5	5	NUM
ejpam-6247	187	12	)	)	PUNCT
ejpam-6247	187	13	.	.	PUNCT
ejpam-6247	188	1	let	let	VERB
ejpam-6247	188	2	µ	µ	X
ejpam-6247	188	3	∈	∈	X
ejpam-6247	188	4	l.	l.	NOUN
ejpam-6247	188	5	since	since	SCONJ
ejpam-6247	188	6	l	l	PROPN
ejpam-6247	188	7	is	be	AUX
ejpam-6247	188	8	hemicomplemented	hemicomplemente	VERB
ejpam-6247	188	9	,	,	PUNCT
ejpam-6247	188	10	there	there	PRON
ejpam-6247	188	11	is	be	VERB
ejpam-6247	188	12	π	π	PROPN
ejpam-6247	188	13	∈	∈	PROPN
ejpam-6247	188	14	l	l	NOUN
ejpam-6247	188	15	such	such	ADJ
ejpam-6247	188	16	that	that	SCONJ
ejpam-6247	188	17	(	(	PUNCT
ejpam-6247	188	18	(	(	PUNCT
ejpam-6247	188	19	µ,d),d	µ,d),d	NOUN
ejpam-6247	188	20	)	)	PUNCT
ejpam-6247	188	21	=	=	SYM
ejpam-6247	189	1	(	(	PUNCT
ejpam-6247	189	2	π	π	X
ejpam-6247	189	3	,	,	PUNCT
ejpam-6247	189	4	d	d	NOUN
ejpam-6247	189	5	)	)	PUNCT
ejpam-6247	189	6	.	.	PUNCT
ejpam-6247	190	1	as	as	ADP
ejpam-6247	190	2	d	d	X
ejpam-6247	190	3	◦	◦	NOUN
ejpam-6247	190	4	◦	◦	NOUN
ejpam-6247	190	5	(l	(l	NUM
ejpam-6247	190	6	)	)	PUNCT
ejpam-6247	190	7	is	be	AUX
ejpam-6247	190	8	a	a	DET
ejpam-6247	190	9	sublattice	sublattice	NOUN
ejpam-6247	190	10	of	of	ADP
ejpam-6247	190	11	f(l	f(l	NOUN
ejpam-6247	190	12	)	)	PUNCT
ejpam-6247	190	13	,	,	PUNCT
ejpam-6247	190	14	we	we	PRON
ejpam-6247	190	15	obtain	obtain	VERB
ejpam-6247	190	16	(	(	PUNCT
ejpam-6247	190	17	(	(	PUNCT
ejpam-6247	190	18	µ,d),d)∨	µ,d),d)∨	X
ejpam-6247	190	19	(	(	PUNCT
ejpam-6247	190	20	(	(	PUNCT
ejpam-6247	190	21	π	π	PROPN
ejpam-6247	190	22	,	,	PUNCT
ejpam-6247	190	23	d),d	d),d	PROPN
ejpam-6247	190	24	)	)	PUNCT
ejpam-6247	190	25	=	=	SYM
ejpam-6247	191	1	(	(	PUNCT
ejpam-6247	191	2	(	(	PUNCT
ejpam-6247	191	3	ν	ν	NOUN
ejpam-6247	191	4	,	,	PUNCT
ejpam-6247	191	5	d),d	d),d	PROPN
ejpam-6247	191	6	)	)	PUNCT
ejpam-6247	191	7	for	for	ADP
ejpam-6247	191	8	some	some	DET
ejpam-6247	191	9	ν	ν	NOUN
ejpam-6247	191	10	∈	∈	PROPN
ejpam-6247	191	11	l.	l.	NOUN
ejpam-6247	191	12	hence	hence	ADV
ejpam-6247	191	13	,	,	PUNCT
ejpam-6247	191	14	µ	µ	X
ejpam-6247	191	15	∧	∧	PROPN
ejpam-6247	191	16	π	π	PROPN
ejpam-6247	191	17	∈	∈	PROPN
ejpam-6247	191	18	(	(	PUNCT
ejpam-6247	191	19	(	(	PUNCT
ejpam-6247	191	20	µ,d),d	µ,d),d	NOUN
ejpam-6247	191	21	)	)	PUNCT
ejpam-6247	191	22	∨	∨	NOUN
ejpam-6247	191	23	(	(	PUNCT
ejpam-6247	191	24	(	(	PUNCT
ejpam-6247	191	25	π	π	PROPN
ejpam-6247	191	26	,	,	PUNCT
ejpam-6247	191	27	d),d	d),d	PROPN
ejpam-6247	191	28	)	)	PUNCT
ejpam-6247	191	29	=	=	SYM
ejpam-6247	192	1	(	(	PUNCT
ejpam-6247	192	2	(	(	PUNCT
ejpam-6247	192	3	ν	ν	NOUN
ejpam-6247	192	4	,	,	PUNCT
ejpam-6247	192	5	d),d	d),d	PROPN
ejpam-6247	192	6	)	)	PUNCT
ejpam-6247	192	7	.	.	PUNCT
ejpam-6247	193	1	thus	thus	ADV
ejpam-6247	193	2	,	,	PUNCT
ejpam-6247	193	3	l	l	NOUN
ejpam-6247	193	4	is	be	AUX
ejpam-6247	193	5	a	a	DET
ejpam-6247	193	6	d	d	ADJ
ejpam-6247	193	7	-	-	PUNCT
ejpam-6247	193	8	stone	stone	NOUN
ejpam-6247	193	9	adl	adl	PROPN
ejpam-6247	193	10	.	.	PUNCT
ejpam-6247	193	11	corollary	corollary	ADJ
ejpam-6247	193	12	3	3	NUM
ejpam-6247	193	13	.	.	PUNCT
ejpam-6247	194	1	in	in	ADP
ejpam-6247	194	2	any	any	DET
ejpam-6247	194	3	d	d	NOUN
ejpam-6247	194	4	-	-	NOUN
ejpam-6247	194	5	stone	stone	NOUN
ejpam-6247	194	6	adl	adl	PROPN
ejpam-6247	194	7	l	l	PROPN
ejpam-6247	194	8	,	,	PUNCT
ejpam-6247	194	9	we	we	PRON
ejpam-6247	194	10	have	have	VERB
ejpam-6247	194	11	d	d	PUNCT
ejpam-6247	194	12	◦	◦	NOUN
ejpam-6247	194	13	(l	(l	NUM
ejpam-6247	194	14	)	)	PUNCT
ejpam-6247	194	15	is	be	AUX
ejpam-6247	194	16	a	a	DET
ejpam-6247	194	17	sublattice	sublattice	NOUN
ejpam-6247	194	18	of	of	ADP
ejpam-6247	194	19	f(l	f(l	NOUN
ejpam-6247	194	20	)	)	PUNCT
ejpam-6247	194	21	.	.	PUNCT
ejpam-6247	195	1	a	a	DET
ejpam-6247	195	2	property	property	NOUN
ejpam-6247	195	3	of	of	ADP
ejpam-6247	195	4	d	d	NOUN
ejpam-6247	195	5	-	-	NOUN
ejpam-6247	195	6	stone	stone	NOUN
ejpam-6247	195	7	adls	adls	PROPN
ejpam-6247	195	8	,	,	PUNCT
ejpam-6247	195	9	expressed	express	VERB
ejpam-6247	195	10	via	via	ADP
ejpam-6247	195	11	minimal	minimal	ADJ
ejpam-6247	195	12	prime	prime	ADJ
ejpam-6247	195	13	d	d	NOUN
ejpam-6247	195	14	-	-	PUNCT
ejpam-6247	195	15	filters	filter	NOUN
ejpam-6247	195	16	,	,	PUNCT
ejpam-6247	195	17	is	be	AUX
ejpam-6247	195	18	established	establish	VERB
ejpam-6247	195	19	in	in	ADP
ejpam-6247	195	20	the	the	DET
ejpam-6247	195	21	next	next	ADJ
ejpam-6247	195	22	corollary	corollary	NOUN
ejpam-6247	195	23	.	.	PUNCT
ejpam-6247	196	1	comaximality	comaximality	NOUN
ejpam-6247	196	2	of	of	ADP
ejpam-6247	196	3	two	two	NUM
ejpam-6247	196	4	d	d	NOUN
ejpam-6247	196	5	-	-	PUNCT
ejpam-6247	196	6	filters	filter	NOUN
ejpam-6247	196	7	g	g	NOUN
ejpam-6247	196	8	and	and	CCONJ
ejpam-6247	196	9	u	u	PROPN
ejpam-6247	196	10	in	in	ADP
ejpam-6247	196	11	an	an	DET
ejpam-6247	196	12	adl	adl	PROPN
ejpam-6247	196	13	l	l	NOUN
ejpam-6247	196	14	is	be	AUX
ejpam-6247	196	15	defined	define	VERB
ejpam-6247	196	16	by	by	ADP
ejpam-6247	196	17	the	the	DET
ejpam-6247	196	18	condition	condition	NOUN
ejpam-6247	196	19	g	g	PROPN
ejpam-6247	196	20	∨	∨	NUM
ejpam-6247	196	21	u	u	NOUN
ejpam-6247	196	22	=	=	PROPN
ejpam-6247	196	23	l.	l.	PROPN
ejpam-6247	196	24	corollary	corollary	PROPN
ejpam-6247	196	25	4	4	NUM
ejpam-6247	196	26	.	.	PUNCT
ejpam-6247	197	1	any	any	DET
ejpam-6247	197	2	two	two	NUM
ejpam-6247	197	3	distinct	distinct	ADJ
ejpam-6247	197	4	minimal	minimal	ADJ
ejpam-6247	197	5	prime	prime	ADJ
ejpam-6247	197	6	d	d	NOUN
ejpam-6247	197	7	-	-	NOUN
ejpam-6247	197	8	filters	filter	NOUN
ejpam-6247	197	9	of	of	ADP
ejpam-6247	197	10	a	a	DET
ejpam-6247	197	11	d	d	NOUN
ejpam-6247	197	12	-	-	NOUN
ejpam-6247	197	13	stone	stone	NOUN
ejpam-6247	197	14	adl	adl	PROPN
ejpam-6247	197	15	l	l	NOUN
ejpam-6247	197	16	are	be	AUX
ejpam-6247	197	17	comaximal	comaximal	ADJ
ejpam-6247	197	18	.	.	PUNCT
ejpam-6247	198	1	proof	proof	NOUN
ejpam-6247	198	2	.	.	PUNCT
ejpam-6247	199	1	suppose	suppose	VERB
ejpam-6247	199	2	that	that	SCONJ
ejpam-6247	199	3	l	l	NOUN
ejpam-6247	199	4	is	be	AUX
ejpam-6247	199	5	a	a	DET
ejpam-6247	199	6	d	d	ADJ
ejpam-6247	199	7	-	-	NOUN
ejpam-6247	199	8	stone	stone	NOUN
ejpam-6247	199	9	adl	adl	PROPN
ejpam-6247	199	10	.	.	PUNCT
ejpam-6247	200	1	according	accord	VERB
ejpam-6247	200	2	to	to	ADP
ejpam-6247	200	3	condition	condition	NOUN
ejpam-6247	200	4	(	(	PUNCT
ejpam-6247	200	5	2	2	NUM
ejpam-6247	200	6	)	)	PUNCT
ejpam-6247	200	7	of	of	ADP
ejpam-6247	200	8	the	the	DET
ejpam-6247	200	9	main	main	ADJ
ejpam-6247	200	10	theorem	theorem	NOUN
ejpam-6247	200	11	,	,	PUNCT
ejpam-6247	200	12	every	every	DET
ejpam-6247	200	13	(	(	PUNCT
ejpam-6247	200	14	µ,d	µ,d	NOUN
ejpam-6247	200	15	)	)	PUNCT
ejpam-6247	200	16	serves	serve	VERB
ejpam-6247	200	17	as	as	ADP
ejpam-6247	200	18	a	a	DET
ejpam-6247	200	19	d	d	NOUN
ejpam-6247	200	20	-	-	NOUN
ejpam-6247	200	21	factor	factor	NOUN
ejpam-6247	200	22	of	of	ADP
ejpam-6247	200	23	l.	l.	PROPN
ejpam-6247	200	24	let	let	VERB
ejpam-6247	200	25	q	q	NOUN
ejpam-6247	201	1	and	and	CCONJ
ejpam-6247	201	2	p	p	NOUN
ejpam-6247	201	3	be	be	AUX
ejpam-6247	201	4	two	two	NUM
ejpam-6247	201	5	distinct	distinct	ADJ
ejpam-6247	201	6	minimal	minimal	ADJ
ejpam-6247	201	7	prime	prime	ADJ
ejpam-6247	201	8	d	d	NOUN
ejpam-6247	201	9	-	-	NOUN
ejpam-6247	201	10	filters	filter	NOUN
ejpam-6247	201	11	in	in	ADP
ejpam-6247	201	12	l.	l.	PROPN
ejpam-6247	201	13	select	select	VERB
ejpam-6247	201	14	an	an	DET
ejpam-6247	201	15	element	element	NOUN
ejpam-6247	201	16	θ	θ	PROPN
ejpam-6247	201	17	∈	∈	PROPN
ejpam-6247	201	18	q	q	PUNCT
ejpam-6247	201	19	\	\	NOUN
ejpam-6247	202	1	p.	p.	NOUN
ejpam-6247	202	2	this	this	PRON
ejpam-6247	202	3	implies	imply	VERB
ejpam-6247	202	4	that	that	SCONJ
ejpam-6247	202	5	(	(	PUNCT
ejpam-6247	202	6	θ	θ	NOUN
ejpam-6247	202	7	,	,	PUNCT
ejpam-6247	202	8	d	d	NOUN
ejpam-6247	202	9	)	)	PUNCT
ejpam-6247	202	10	⊆	⊆	NUM
ejpam-6247	202	11	p.	p.	NOUN
ejpam-6247	202	12	since	since	SCONJ
ejpam-6247	202	13	q	q	PROPN
ejpam-6247	202	14	is	be	AUX
ejpam-6247	202	15	minimal	minimal	ADJ
ejpam-6247	202	16	,	,	PUNCT
ejpam-6247	202	17	it	it	PRON
ejpam-6247	202	18	follows	follow	VERB
ejpam-6247	202	19	that	that	SCONJ
ejpam-6247	202	20	(	(	PUNCT
ejpam-6247	202	21	(	(	PUNCT
ejpam-6247	202	22	θ	θ	NOUN
ejpam-6247	202	23	,	,	PUNCT
ejpam-6247	202	24	d),d	d),d	PROPN
ejpam-6247	202	25	)	)	PUNCT
ejpam-6247	202	26	⊆	⊆	NUM
ejpam-6247	202	27	q.	q.	NOUN
ejpam-6247	202	28	given	give	VERB
ejpam-6247	202	29	that	that	SCONJ
ejpam-6247	202	30	(	(	PUNCT
ejpam-6247	202	31	θ	θ	NOUN
ejpam-6247	202	32	,	,	PUNCT
ejpam-6247	202	33	d	d	NOUN
ejpam-6247	202	34	)	)	PUNCT
ejpam-6247	202	35	is	be	AUX
ejpam-6247	202	36	a	a	DET
ejpam-6247	202	37	d	d	NOUN
ejpam-6247	202	38	-	-	NOUN
ejpam-6247	202	39	factor	factor	NOUN
ejpam-6247	202	40	of	of	ADP
ejpam-6247	202	41	l	l	NOUN
ejpam-6247	202	42	,	,	PUNCT
ejpam-6247	202	43	there	there	PRON
ejpam-6247	202	44	exists	exist	VERB
ejpam-6247	202	45	a	a	DET
ejpam-6247	202	46	d	d	ADJ
ejpam-6247	202	47	-	-	ADJ
ejpam-6247	202	48	filter	filter	NOUN
ejpam-6247	202	49	u	u	NOUN
ejpam-6247	202	50	such	such	ADJ
ejpam-6247	202	51	that	that	SCONJ
ejpam-6247	202	52	(	(	PUNCT
ejpam-6247	202	53	θ	θ	PROPN
ejpam-6247	202	54	,	,	PUNCT
ejpam-6247	203	1	d)∩u	d)∩u	PROPN
ejpam-6247	203	2	=	=	SYM
ejpam-6247	203	3	d	d	PROPN
ejpam-6247	203	4	and	and	CCONJ
ejpam-6247	203	5	(	(	PUNCT
ejpam-6247	203	6	θ	θ	PROPN
ejpam-6247	203	7	,	,	PUNCT
ejpam-6247	203	8	d	d	NOUN
ejpam-6247	203	9	)	)	PUNCT
ejpam-6247	203	10	∨	∨	NUM
ejpam-6247	203	11	u	u	NOUN
ejpam-6247	203	12	=	=	PROPN
ejpam-6247	203	13	l.	l.	PROPN
ejpam-6247	203	14	this	this	DET
ejpam-6247	203	15	inclusion	inclusion	NOUN
ejpam-6247	203	16	implies	imply	VERB
ejpam-6247	203	17	that	that	SCONJ
ejpam-6247	203	18	u	u	PRON
ejpam-6247	203	19	⊆	⊆	NUM
ejpam-6247	203	20	(	(	PUNCT
ejpam-6247	203	21	(	(	PUNCT
ejpam-6247	203	22	θ	θ	NOUN
ejpam-6247	203	23	,	,	PUNCT
ejpam-6247	203	24	d),d	d),d	PROPN
ejpam-6247	203	25	)	)	PUNCT
ejpam-6247	203	26	⊆	⊆	NUM
ejpam-6247	203	27	q.	q.	NOUN
ejpam-6247	203	28	hence	hence	ADV
ejpam-6247	203	29	,	,	PUNCT
ejpam-6247	203	30	we	we	PRON
ejpam-6247	203	31	obtain	obtain	VERB
ejpam-6247	203	32	l	l	NOUN
ejpam-6247	203	33	=	=	SYM
ejpam-6247	203	34	(	(	PUNCT
ejpam-6247	203	35	θ	θ	PROPN
ejpam-6247	203	36	,	,	PUNCT
ejpam-6247	203	37	d	d	NOUN
ejpam-6247	203	38	)	)	PUNCT
ejpam-6247	203	39	∨	∨	NUM
ejpam-6247	203	40	u	u	NOUN
ejpam-6247	203	41	⊆	⊆	NUM
ejpam-6247	203	42	p	p	NOUN
ejpam-6247	203	43	∨q	∨q	NOUN
ejpam-6247	203	44	.	.	PUNCT
ejpam-6247	204	1	therefore	therefore	ADV
ejpam-6247	204	2	,	,	PUNCT
ejpam-6247	204	3	q	q	PUNCT
ejpam-6247	204	4	and	and	CCONJ
ejpam-6247	204	5	p	p	NOUN
ejpam-6247	204	6	are	be	AUX
ejpam-6247	204	7	comaximal	comaximal	ADJ
ejpam-6247	204	8	.	.	PUNCT
ejpam-6247	205	1	n.	n.	PROPN
ejpam-6247	205	2	rafi	rafi	PROPN
ejpam-6247	205	3	et	et	PROPN
ejpam-6247	205	4	al	al	PROPN
ejpam-6247	205	5	.	.	PUNCT
ejpam-6247	205	6	/	/	SYM
ejpam-6247	205	7	eur	eur	PROPN
ejpam-6247	205	8	.	.	PUNCT
ejpam-6247	206	1	j.	j.	PROPN
ejpam-6247	206	2	pure	pure	PROPN
ejpam-6247	206	3	appl	appl	PROPN
ejpam-6247	206	4	.	.	PROPN
ejpam-6247	206	5	math	math	PROPN
ejpam-6247	206	6	,	,	PUNCT
ejpam-6247	206	7	18	18	NUM
ejpam-6247	206	8	(	(	PUNCT
ejpam-6247	206	9	3	3	NUM
ejpam-6247	206	10	)	)	PUNCT
ejpam-6247	206	11	(	(	PUNCT
ejpam-6247	206	12	2025	2025	NUM
ejpam-6247	206	13	)	)	PUNCT
ejpam-6247	206	14	,	,	PUNCT
ejpam-6247	206	15	6247	6247	NUM
ejpam-6247	206	16	8	8	NUM
ejpam-6247	206	17	of	of	ADP
ejpam-6247	206	18	15	15	NUM
ejpam-6247	206	19	theorem	theorem	NOUN
ejpam-6247	206	20	2	2	NUM
ejpam-6247	206	21	.	.	PUNCT
ejpam-6247	207	1	in	in	ADP
ejpam-6247	207	2	a	a	DET
ejpam-6247	207	3	hemicomplemented	hemicomplemente	VERB
ejpam-6247	207	4	adl	adl	PROPN
ejpam-6247	207	5	l	l	PROPN
ejpam-6247	207	6	,	,	PUNCT
ejpam-6247	207	7	we	we	PRON
ejpam-6247	207	8	have	have	VERB
ejpam-6247	207	9	l	l	NOUN
ejpam-6247	207	10	is	be	AUX
ejpam-6247	207	11	d	d	NOUN
ejpam-6247	207	12	-	-	NOUN
ejpam-6247	207	13	stone	stone	NOUN
ejpam-6247	207	14	if	if	SCONJ
ejpam-6247	207	15	and	and	CCONJ
ejpam-6247	208	1	only	only	ADV
ejpam-6247	208	2	if	if	SCONJ
ejpam-6247	208	3	d	d	PROPN
ejpam-6247	208	4	◦	◦	NOUN
ejpam-6247	208	5	(l	(l	NUM
ejpam-6247	208	6	)	)	PUNCT
ejpam-6247	208	7	is	be	AUX
ejpam-6247	208	8	a	a	DET
ejpam-6247	208	9	boolean	boolean	ADJ
ejpam-6247	208	10	algebra	algebra	NOUN
ejpam-6247	208	11	.	.	PUNCT
ejpam-6247	209	1	proof	proof	NOUN
ejpam-6247	209	2	.	.	PUNCT
ejpam-6247	210	1	assume	assume	VERB
ejpam-6247	210	2	that	that	SCONJ
ejpam-6247	210	3	l	l	NOUN
ejpam-6247	210	4	is	be	AUX
ejpam-6247	210	5	a	a	DET
ejpam-6247	210	6	d	d	ADJ
ejpam-6247	210	7	-	-	NOUN
ejpam-6247	210	8	stone	stone	NOUN
ejpam-6247	210	9	adl	adl	PROPN
ejpam-6247	210	10	.	.	PUNCT
ejpam-6247	211	1	let	let	VERB
ejpam-6247	211	2	(	(	PUNCT
ejpam-6247	211	3	µ,d	µ,d	NOUN
ejpam-6247	211	4	)	)	PUNCT
ejpam-6247	211	5	and	and	CCONJ
ejpam-6247	211	6	(	(	PUNCT
ejpam-6247	211	7	π	π	PROPN
ejpam-6247	211	8	,	,	PUNCT
ejpam-6247	211	9	d	d	NOUN
ejpam-6247	211	10	)	)	PUNCT
ejpam-6247	211	11	be	be	AUX
ejpam-6247	211	12	elements	element	NOUN
ejpam-6247	211	13	in	in	ADP
ejpam-6247	211	14	d	d	NOUN
ejpam-6247	211	15	◦	◦	NOUN
ejpam-6247	211	16	(l	(l	NUM
ejpam-6247	211	17	)	)	PUNCT
ejpam-6247	211	18	.	.	PUNCT
ejpam-6247	212	1	it	it	PRON
ejpam-6247	212	2	is	be	AUX
ejpam-6247	212	3	straightforward	straightforward	ADJ
ejpam-6247	212	4	to	to	PART
ejpam-6247	212	5	see	see	VERB
ejpam-6247	212	6	that	that	PRON
ejpam-6247	212	7	(	(	PUNCT
ejpam-6247	212	8	µ,d	µ,d	NOUN
ejpam-6247	212	9	)	)	PUNCT
ejpam-6247	212	10	∩	∩	NOUN
ejpam-6247	212	11	(	(	PUNCT
ejpam-6247	212	12	π	π	X
ejpam-6247	212	13	,	,	PUNCT
ejpam-6247	212	14	d	d	NOUN
ejpam-6247	212	15	)	)	PUNCT
ejpam-6247	212	16	=	=	SYM
ejpam-6247	212	17	(	(	PUNCT
ejpam-6247	212	18	µ	µ	X
ejpam-6247	212	19	∧	∧	PROPN
ejpam-6247	212	20	π	π	PROPN
ejpam-6247	212	21	,	,	PUNCT
ejpam-6247	212	22	d	d	NOUN
ejpam-6247	212	23	)	)	PUNCT
ejpam-6247	212	24	.	.	PUNCT
ejpam-6247	213	1	since	since	SCONJ
ejpam-6247	213	2	l	l	NOUN
ejpam-6247	213	3	is	be	AUX
ejpam-6247	213	4	a	a	DET
ejpam-6247	213	5	d	d	ADJ
ejpam-6247	213	6	-	-	PUNCT
ejpam-6247	213	7	stone	stone	NOUN
ejpam-6247	213	8	adl	adl	PROPN
ejpam-6247	213	9	,	,	PUNCT
ejpam-6247	213	10	it	it	PRON
ejpam-6247	213	11	satisfies	satisfy	VERB
ejpam-6247	213	12	that	that	SCONJ
ejpam-6247	213	13	(	(	PUNCT
ejpam-6247	213	14	µ,d	µ,d	NOUN
ejpam-6247	213	15	)	)	PUNCT
ejpam-6247	213	16	∨	∨	NOUN
ejpam-6247	213	17	(	(	PUNCT
ejpam-6247	213	18	π	π	PROPN
ejpam-6247	213	19	,	,	PUNCT
ejpam-6247	213	20	d	d	NOUN
ejpam-6247	213	21	)	)	PUNCT
ejpam-6247	213	22	=	=	SYM
ejpam-6247	213	23	(	(	PUNCT
ejpam-6247	213	24	µ	µ	X
ejpam-6247	213	25	∨	∨	NUM
ejpam-6247	213	26	π	π	PROPN
ejpam-6247	213	27	,	,	PUNCT
ejpam-6247	213	28	d	d	NOUN
ejpam-6247	213	29	)	)	PUNCT
ejpam-6247	213	30	.	.	PUNCT
ejpam-6247	214	1	therefore	therefore	ADV
ejpam-6247	214	2	,	,	PUNCT
ejpam-6247	214	3	(	(	PUNCT
ejpam-6247	214	4	d	d	PUNCT
ejpam-6247	214	5	◦	◦	NOUN
ejpam-6247	214	6	(l),∨,∩	(l),∨,∩	NOUN
ejpam-6247	214	7	)	)	PUNCT
ejpam-6247	214	8	forms	form	VERB
ejpam-6247	214	9	a	a	DET
ejpam-6247	214	10	lattice	lattice	NOUN
ejpam-6247	214	11	.	.	PUNCT
ejpam-6247	215	1	moreover	moreover	ADV
ejpam-6247	215	2	,	,	PUNCT
ejpam-6247	215	3	observe	observe	VERB
ejpam-6247	215	4	that	that	SCONJ
ejpam-6247	215	5	for	for	ADP
ejpam-6247	215	6	every	every	DET
ejpam-6247	215	7	µ	µ	PRON
ejpam-6247	215	8	∈	∈	NOUN
ejpam-6247	215	9	d∞	d∞	NOUN
ejpam-6247	215	10	,	,	PUNCT
ejpam-6247	215	11	we	we	PRON
ejpam-6247	215	12	have	have	VERB
ejpam-6247	215	13	(	(	PUNCT
ejpam-6247	215	14	µ,d	µ,d	NOUN
ejpam-6247	215	15	)	)	PUNCT
ejpam-6247	216	1	=	=	SYM
ejpam-6247	216	2	d	d	NOUN
ejpam-6247	216	3	,	,	PUNCT
ejpam-6247	216	4	indicating	indicate	VERB
ejpam-6247	216	5	that	that	SCONJ
ejpam-6247	216	6	d	d	PROPN
ejpam-6247	216	7	is	be	AUX
ejpam-6247	216	8	the	the	DET
ejpam-6247	216	9	least	least	ADJ
ejpam-6247	216	10	element	element	NOUN
ejpam-6247	216	11	in	in	ADP
ejpam-6247	216	12	d	d	PROPN
ejpam-6247	216	13	◦	◦	NOUN
ejpam-6247	216	14	(l	(l	NUM
ejpam-6247	216	15	)	)	PUNCT
ejpam-6247	216	16	.	.	PUNCT
ejpam-6247	217	1	likewise	likewise	ADV
ejpam-6247	217	2	,	,	PUNCT
ejpam-6247	217	3	since	since	SCONJ
ejpam-6247	217	4	(	(	PUNCT
ejpam-6247	217	5	e	e	NOUN
ejpam-6247	217	6	,	,	PUNCT
ejpam-6247	217	7	d	d	NOUN
ejpam-6247	217	8	)	)	PUNCT
ejpam-6247	217	9	=	=	SYM
ejpam-6247	217	10	l	l	NOUN
ejpam-6247	217	11	for	for	ADP
ejpam-6247	217	12	all	all	DET
ejpam-6247	217	13	e	e	PROPN
ejpam-6247	217	14	∈	∈	PROPN
ejpam-6247	217	15	d	d	X
ejpam-6247	217	16	,	,	PUNCT
ejpam-6247	217	17	it	it	PRON
ejpam-6247	217	18	follows	follow	VERB
ejpam-6247	217	19	that	that	SCONJ
ejpam-6247	217	20	l	l	NOUN
ejpam-6247	217	21	serves	serve	VERB
ejpam-6247	217	22	as	as	ADP
ejpam-6247	217	23	the	the	DET
ejpam-6247	217	24	greatest	great	ADJ
ejpam-6247	217	25	element	element	NOUN
ejpam-6247	217	26	of	of	ADP
ejpam-6247	217	27	d∞.	d∞.	PROPN
ejpam-6247	217	28	thus	thus	ADV
ejpam-6247	217	29	,	,	PUNCT
ejpam-6247	217	30	the	the	DET
ejpam-6247	217	31	set	set	NOUN
ejpam-6247	217	32	d	d	PROPN
ejpam-6247	217	33	◦	◦	NOUN
ejpam-6247	217	34	(l	(l	NUM
ejpam-6247	217	35	)	)	PUNCT
ejpam-6247	217	36	,	,	PUNCT
ejpam-6247	217	37	equipped	equip	VERB
ejpam-6247	217	38	with	with	ADP
ejpam-6247	217	39	the	the	DET
ejpam-6247	217	40	operations	operation	NOUN
ejpam-6247	217	41	∨	∨	NOUN
ejpam-6247	217	42	and	and	CCONJ
ejpam-6247	217	43	∩	∩	NOUN
ejpam-6247	217	44	,	,	PUNCT
ejpam-6247	217	45	forms	form	VERB
ejpam-6247	217	46	a	a	DET
ejpam-6247	217	47	bounded	bounded	ADJ
ejpam-6247	217	48	distributive	distributive	ADJ
ejpam-6247	217	49	lattice	lattice	NOUN
ejpam-6247	217	50	.	.	PUNCT
ejpam-6247	218	1	next	next	ADV
ejpam-6247	218	2	,	,	PUNCT
ejpam-6247	218	3	consider	consider	VERB
ejpam-6247	218	4	(	(	PUNCT
ejpam-6247	218	5	µ,d	µ,d	NOUN
ejpam-6247	218	6	)	)	PUNCT
ejpam-6247	218	7	∈	∈	PROPN
ejpam-6247	219	1	d	d	PROPN
ejpam-6247	219	2	◦	◦	NOUN
ejpam-6247	219	3	(l	(l	NUM
ejpam-6247	219	4	)	)	PUNCT
ejpam-6247	219	5	with	with	ADP
ejpam-6247	219	6	µ	µ	PROPN
ejpam-6247	219	7	∈	∈	PRON
ejpam-6247	219	8	l.	l.	NOUN
ejpam-6247	219	9	since	since	SCONJ
ejpam-6247	219	10	l	l	PROPN
ejpam-6247	219	11	is	be	AUX
ejpam-6247	219	12	hemicomplemented	hemicomplemente	VERB
ejpam-6247	219	13	,	,	PUNCT
ejpam-6247	219	14	there	there	PRON
ejpam-6247	219	15	exists	exist	VERB
ejpam-6247	219	16	an	an	DET
ejpam-6247	219	17	element	element	NOUN
ejpam-6247	219	18	µ′	µ′	PUNCT
ejpam-6247	219	19	∈	∈	PROPN
ejpam-6247	219	20	l	l	NOUN
ejpam-6247	219	21	such	such	ADJ
ejpam-6247	219	22	that	that	SCONJ
ejpam-6247	219	23	(	(	PUNCT
ejpam-6247	219	24	(	(	PUNCT
ejpam-6247	219	25	µ,d),d	µ,d),d	NOUN
ejpam-6247	219	26	)	)	PUNCT
ejpam-6247	219	27	=	=	SYM
ejpam-6247	220	1	(	(	PUNCT
ejpam-6247	220	2	µ′,d	µ′,d	NOUN
ejpam-6247	220	3	)	)	PUNCT
ejpam-6247	220	4	.	.	PUNCT
ejpam-6247	221	1	this	this	PRON
ejpam-6247	221	2	implies	imply	VERB
ejpam-6247	221	3	that	that	SCONJ
ejpam-6247	221	4	(	(	PUNCT
ejpam-6247	221	5	µ,d	µ,d	NOUN
ejpam-6247	221	6	)	)	PUNCT
ejpam-6247	221	7	∩	∩	NOUN
ejpam-6247	221	8	(	(	PUNCT
ejpam-6247	221	9	µ′,d	µ′,d	NOUN
ejpam-6247	221	10	)	)	PUNCT
ejpam-6247	221	11	=	=	SYM
ejpam-6247	222	1	d	d	NOUN
ejpam-6247	222	2	,	,	PUNCT
ejpam-6247	222	3	and	and	CCONJ
ejpam-6247	222	4	as	as	SCONJ
ejpam-6247	222	5	l	l	NOUN
ejpam-6247	222	6	is	be	AUX
ejpam-6247	222	7	a	a	DET
ejpam-6247	222	8	d	d	ADJ
ejpam-6247	222	9	-	-	PUNCT
ejpam-6247	222	10	stone	stone	NOUN
ejpam-6247	222	11	adl	adl	PROPN
ejpam-6247	222	12	,	,	PUNCT
ejpam-6247	222	13	we	we	PRON
ejpam-6247	222	14	also	also	ADV
ejpam-6247	222	15	have	have	VERB
ejpam-6247	222	16	(	(	PUNCT
ejpam-6247	222	17	µ,d	µ,d	NOUN
ejpam-6247	222	18	)	)	PUNCT
ejpam-6247	222	19	∨	∨	NOUN
ejpam-6247	222	20	(	(	PUNCT
ejpam-6247	222	21	(	(	PUNCT
ejpam-6247	222	22	µ,d),d	µ,d),d	NOUN
ejpam-6247	222	23	)	)	PUNCT
ejpam-6247	223	1	=	=	SYM
ejpam-6247	223	2	l	l	NOUN
ejpam-6247	223	3	,	,	PUNCT
ejpam-6247	223	4	which	which	PRON
ejpam-6247	223	5	leads	lead	VERB
ejpam-6247	223	6	to	to	ADP
ejpam-6247	223	7	(	(	PUNCT
ejpam-6247	223	8	µ,d	µ,d	NOUN
ejpam-6247	223	9	)	)	PUNCT
ejpam-6247	223	10	∨	∨	NOUN
ejpam-6247	223	11	(	(	PUNCT
ejpam-6247	223	12	µ′,d	µ′,d	NOUN
ejpam-6247	223	13	)	)	PUNCT
ejpam-6247	223	14	=	=	SYM
ejpam-6247	224	1	l.	l.	PROPN
ejpam-6247	224	2	hence	hence	ADV
ejpam-6247	224	3	,	,	PUNCT
ejpam-6247	224	4	(	(	PUNCT
ejpam-6247	224	5	µ′,d	µ′,d	NOUN
ejpam-6247	224	6	)	)	PUNCT
ejpam-6247	224	7	serves	serve	VERB
ejpam-6247	224	8	as	as	ADP
ejpam-6247	224	9	the	the	DET
ejpam-6247	224	10	complement	complement	NOUN
ejpam-6247	224	11	of	of	ADP
ejpam-6247	224	12	(	(	PUNCT
ejpam-6247	224	13	µ,d	µ,d	NOUN
ejpam-6247	224	14	)	)	PUNCT
ejpam-6247	224	15	in	in	ADP
ejpam-6247	224	16	d	d	PROPN
ejpam-6247	224	17	◦	◦	NOUN
ejpam-6247	224	18	(l	(l	NUM
ejpam-6247	224	19	)	)	PUNCT
ejpam-6247	224	20	,	,	PUNCT
ejpam-6247	224	21	showing	show	VERB
ejpam-6247	224	22	that	that	SCONJ
ejpam-6247	224	23	d	d	PROPN
ejpam-6247	224	24	◦	◦	NOUN
ejpam-6247	224	25	(l	(l	NOUN
ejpam-6247	224	26	)	)	PUNCT
ejpam-6247	224	27	forms	form	VERB
ejpam-6247	224	28	a	a	DET
ejpam-6247	224	29	boolean	boolean	ADJ
ejpam-6247	224	30	algebra	algebra	NOUN
ejpam-6247	224	31	.	.	PUNCT
ejpam-6247	225	1	conversely	conversely	ADV
ejpam-6247	225	2	,	,	PUNCT
ejpam-6247	225	3	suppose	suppose	VERB
ejpam-6247	225	4	that	that	SCONJ
ejpam-6247	225	5	d	d	X
ejpam-6247	225	6	◦	◦	NOUN
ejpam-6247	225	7	(l	(l	NUM
ejpam-6247	225	8	)	)	PUNCT
ejpam-6247	225	9	is	be	AUX
ejpam-6247	225	10	a	a	DET
ejpam-6247	225	11	boolean	boolean	ADJ
ejpam-6247	225	12	algebra	algebra	NOUN
ejpam-6247	225	13	.	.	PUNCT
ejpam-6247	226	1	for	for	ADP
ejpam-6247	226	2	any	any	DET
ejpam-6247	226	3	µ	µ	PROPN
ejpam-6247	226	4	∈	∈	PROPN
ejpam-6247	226	5	l	l	NOUN
ejpam-6247	226	6	,	,	PUNCT
ejpam-6247	226	7	the	the	DET
ejpam-6247	226	8	element	element	NOUN
ejpam-6247	226	9	(	(	PUNCT
ejpam-6247	226	10	µ,d	µ,d	NOUN
ejpam-6247	226	11	)	)	PUNCT
ejpam-6247	226	12	belongs	belong	VERB
ejpam-6247	226	13	to	to	ADP
ejpam-6247	226	14	d	d	PUNCT
ejpam-6247	226	15	◦	◦	NOUN
ejpam-6247	226	16	(l	(l	NUM
ejpam-6247	226	17	)	)	PUNCT
ejpam-6247	226	18	.	.	PUNCT
ejpam-6247	227	1	then	then	ADV
ejpam-6247	227	2	there	there	PRON
ejpam-6247	227	3	exists	exist	VERB
ejpam-6247	227	4	an	an	DET
ejpam-6247	227	5	element	element	NOUN
ejpam-6247	227	6	(	(	PUNCT
ejpam-6247	227	7	µ′,d	µ′,d	NOUN
ejpam-6247	227	8	)	)	PUNCT
ejpam-6247	227	9	∈	∈	PROPN
ejpam-6247	228	1	d	d	PUNCT
ejpam-6247	228	2	◦	◦	NOUN
ejpam-6247	228	3	(l	(l	NOUN
ejpam-6247	228	4	)	)	PUNCT
ejpam-6247	228	5	such	such	ADJ
ejpam-6247	228	6	that	that	SCONJ
ejpam-6247	228	7	(	(	PUNCT
ejpam-6247	228	8	µ,d	µ,d	NOUN
ejpam-6247	228	9	)	)	PUNCT
ejpam-6247	228	10	∩	∩	NOUN
ejpam-6247	228	11	(	(	PUNCT
ejpam-6247	228	12	µ′,d	µ′,d	NOUN
ejpam-6247	228	13	)	)	PUNCT
ejpam-6247	228	14	=	=	SYM
ejpam-6247	229	1	d	d	PROPN
ejpam-6247	229	2	and	and	CCONJ
ejpam-6247	229	3	(	(	PUNCT
ejpam-6247	229	4	µ,d	µ,d	NOUN
ejpam-6247	229	5	)	)	PUNCT
ejpam-6247	229	6	∨	∨	NOUN
ejpam-6247	229	7	(	(	PUNCT
ejpam-6247	229	8	µ′,d	µ′,d	NOUN
ejpam-6247	229	9	)	)	PUNCT
ejpam-6247	229	10	=	=	VERB
ejpam-6247	230	1	l.	l.	PROPN
ejpam-6247	230	2	the	the	DET
ejpam-6247	230	3	former	former	ADJ
ejpam-6247	230	4	implies	imply	VERB
ejpam-6247	230	5	(	(	PUNCT
ejpam-6247	230	6	µ′,d	µ′,d	NOUN
ejpam-6247	230	7	)	)	PUNCT
ejpam-6247	230	8	⊆	⊆	NUM
ejpam-6247	230	9	(	(	PUNCT
ejpam-6247	230	10	(	(	PUNCT
ejpam-6247	230	11	µ,d),d	µ,d),d	NOUN
ejpam-6247	230	12	)	)	PUNCT
ejpam-6247	230	13	,	,	PUNCT
ejpam-6247	230	14	and	and	CCONJ
ejpam-6247	230	15	thus	thus	ADV
ejpam-6247	230	16	we	we	PRON
ejpam-6247	230	17	obtain	obtain	VERB
ejpam-6247	230	18	l	l	NOUN
ejpam-6247	230	19	=	=	SYM
ejpam-6247	230	20	(	(	PUNCT
ejpam-6247	230	21	µ,d	µ,d	NOUN
ejpam-6247	230	22	)	)	PUNCT
ejpam-6247	230	23	∨	∨	NOUN
ejpam-6247	230	24	(	(	PUNCT
ejpam-6247	230	25	µ′,d	µ′,d	NOUN
ejpam-6247	230	26	)	)	PUNCT
ejpam-6247	230	27	⊆	⊆	NUM
ejpam-6247	230	28	(	(	PUNCT
ejpam-6247	230	29	µ,d	µ,d	NOUN
ejpam-6247	230	30	)	)	PUNCT
ejpam-6247	230	31	∨	∨	NOUN
ejpam-6247	230	32	(	(	PUNCT
ejpam-6247	230	33	(	(	PUNCT
ejpam-6247	230	34	µ,d),d	µ,d),d	NOUN
ejpam-6247	230	35	)	)	PUNCT
ejpam-6247	230	36	,	,	PUNCT
ejpam-6247	230	37	which	which	PRON
ejpam-6247	230	38	shows	show	VERB
ejpam-6247	230	39	that	that	SCONJ
ejpam-6247	230	40	(	(	PUNCT
ejpam-6247	230	41	µ,d	µ,d	NOUN
ejpam-6247	230	42	)	)	PUNCT
ejpam-6247	230	43	∨	∨	NOUN
ejpam-6247	230	44	(	(	PUNCT
ejpam-6247	230	45	(	(	PUNCT
ejpam-6247	230	46	µ,d),d	µ,d),d	NOUN
ejpam-6247	230	47	)	)	PUNCT
ejpam-6247	230	48	=	=	PUNCT
ejpam-6247	230	49	l.	l.	PROPN
ejpam-6247	230	50	therefore	therefore	ADV
ejpam-6247	230	51	,	,	PUNCT
ejpam-6247	230	52	l	l	NOUN
ejpam-6247	230	53	satisfies	satisfy	VERB
ejpam-6247	230	54	the	the	DET
ejpam-6247	230	55	condition	condition	NOUN
ejpam-6247	230	56	to	to	PART
ejpam-6247	230	57	be	be	AUX
ejpam-6247	230	58	a	a	DET
ejpam-6247	230	59	d	d	ADJ
ejpam-6247	230	60	-	-	NOUN
ejpam-6247	230	61	stone	stone	NOUN
ejpam-6247	230	62	adl	adl	PROPN
ejpam-6247	230	63	.	.	PROPN
ejpam-6247	230	64	4	4	X
ejpam-6247	230	65	.	.	X
ejpam-6247	230	66	topological	topological	ADJ
ejpam-6247	230	67	characterizations	characterization	NOUN
ejpam-6247	230	68	in	in	ADP
ejpam-6247	230	69	this	this	DET
ejpam-6247	230	70	section	section	NOUN
ejpam-6247	230	71	,	,	PUNCT
ejpam-6247	230	72	we	we	PRON
ejpam-6247	230	73	provide	provide	VERB
ejpam-6247	230	74	a	a	DET
ejpam-6247	230	75	topological	topological	ADJ
ejpam-6247	230	76	characterization	characterization	NOUN
ejpam-6247	230	77	of	of	ADP
ejpam-6247	230	78	the	the	DET
ejpam-6247	230	79	classes	class	NOUN
ejpam-6247	230	80	of	of	ADP
ejpam-6247	230	81	hemicomplemented	hemicomplemente	VERB
ejpam-6247	230	82	adls	adls	NOUN
ejpam-6247	230	83	and	and	CCONJ
ejpam-6247	230	84	d	d	NOUN
ejpam-6247	230	85	-	-	NOUN
ejpam-6247	230	86	stone	stone	NOUN
ejpam-6247	230	87	adls	adls	PROPN
ejpam-6247	230	88	.	.	PUNCT
ejpam-6247	231	1	let	let	VERB
ejpam-6247	231	2	us	we	PRON
ejpam-6247	231	3	denote	denote	VERB
ejpam-6247	231	4	by	by	ADP
ejpam-6247	231	5	specdmf	specdmf	NOUN
ejpam-6247	231	6	(	(	PUNCT
ejpam-6247	231	7	l	l	NOUN
ejpam-6247	231	8	)	)	PUNCT
ejpam-6247	231	9	the	the	DET
ejpam-6247	231	10	collection	collection	NOUN
ejpam-6247	231	11	of	of	ADP
ejpam-6247	231	12	all	all	DET
ejpam-6247	231	13	minimal	minimal	ADJ
ejpam-6247	231	14	prime	prime	ADJ
ejpam-6247	231	15	d	d	NOUN
ejpam-6247	231	16	-	-	NOUN
ejpam-6247	231	17	filters	filter	NOUN
ejpam-6247	231	18	of	of	ADP
ejpam-6247	231	19	l.	l.	NOUN
ejpam-6247	231	20	for	for	ADP
ejpam-6247	231	21	any	any	DET
ejpam-6247	231	22	subset	subset	NOUN
ejpam-6247	231	23	h	h	NOUN
ejpam-6247	231	24	⊆	⊆	NUM
ejpam-6247	231	25	l	l	NOUN
ejpam-6247	231	26	,	,	PUNCT
ejpam-6247	231	27	define	define	VERB
ejpam-6247	231	28	the	the	DET
ejpam-6247	231	29	set	set	NOUN
ejpam-6247	231	30	jm(h	jm(h	NUM
ejpam-6247	231	31	)	)	PUNCT
ejpam-6247	231	32	=	=	NOUN
ejpam-6247	231	33	{	{	PUNCT
ejpam-6247	231	34	q	q	NOUN
ejpam-6247	231	35	∈	∈	PROPN
ejpam-6247	231	36	specdmf	specdmf	NOUN
ejpam-6247	231	37	(	(	PUNCT
ejpam-6247	231	38	l	l	NOUN
ejpam-6247	231	39	)	)	PUNCT
ejpam-6247	231	40	|	|	ADV
ejpam-6247	231	41	h	h	NOUN
ejpam-6247	231	42	⊈	⊈	PRON
ejpam-6247	231	43	q	q	X
ejpam-6247	231	44	}	}	PUNCT
ejpam-6247	231	45	.	.	PUNCT
ejpam-6247	232	1	in	in	ADP
ejpam-6247	232	2	particular	particular	ADJ
ejpam-6247	232	3	,	,	PUNCT
ejpam-6247	232	4	for	for	ADP
ejpam-6247	232	5	a	a	DET
ejpam-6247	232	6	set	set	NOUN
ejpam-6247	232	7	h	h	NOUN
ejpam-6247	232	8	=	=	PUNCT
ejpam-6247	232	9	{	{	PUNCT
ejpam-6247	232	10	µ	µ	NOUN
ejpam-6247	232	11	}	}	PUNCT
ejpam-6247	232	12	,	,	PUNCT
ejpam-6247	232	13	we	we	PRON
ejpam-6247	232	14	use	use	VERB
ejpam-6247	232	15	the	the	DET
ejpam-6247	232	16	notation	notation	NOUN
ejpam-6247	232	17	jm(µ	jm(µ	NOUN
ejpam-6247	232	18	)	)	PUNCT
ejpam-6247	232	19	in	in	ADP
ejpam-6247	232	20	place	place	NOUN
ejpam-6247	232	21	of	of	ADP
ejpam-6247	232	22	jm({µ	jm({µ	NOUN
ejpam-6247	232	23	}	}	PUNCT
ejpam-6247	232	24	)	)	PUNCT
ejpam-6247	232	25	,	,	PUNCT
ejpam-6247	232	26	which	which	PRON
ejpam-6247	232	27	explicitly	explicitly	ADV
ejpam-6247	232	28	becomes	become	VERB
ejpam-6247	232	29	jm(µ	jm(µ	NOUN
ejpam-6247	232	30	)	)	PUNCT
ejpam-6247	233	1	=	=	PRON
ejpam-6247	233	2	{	{	PUNCT
ejpam-6247	233	3	q	q	PUNCT
ejpam-6247	233	4	∈	∈	PROPN
ejpam-6247	233	5	specdmf	specdmf	NOUN
ejpam-6247	233	6	(	(	PUNCT
ejpam-6247	233	7	l	l	NOUN
ejpam-6247	233	8	)	)	PUNCT
ejpam-6247	233	9	|	|	ADV
ejpam-6247	233	10	µ	µ	X
ejpam-6247	233	11	/∈	/∈	NOUN
ejpam-6247	233	12	q	q	PUNCT
ejpam-6247	233	13	}	}	PUNCT
ejpam-6247	233	14	.	.	PUNCT
ejpam-6247	234	1	it	it	PRON
ejpam-6247	234	2	follows	follow	VERB
ejpam-6247	234	3	immediately	immediately	ADV
ejpam-6247	234	4	that	that	SCONJ
ejpam-6247	234	5	for	for	ADP
ejpam-6247	234	6	any	any	DET
ejpam-6247	234	7	subset	subset	ADJ
ejpam-6247	234	8	h	h	NOUN
ejpam-6247	234	9	of	of	ADP
ejpam-6247	234	10	l	l	PROPN
ejpam-6247	234	11	,	,	PUNCT
ejpam-6247	234	12	the	the	DET
ejpam-6247	234	13	corresponding	corresponding	NOUN
ejpam-6247	234	14	jm(h	jm(h	NUM
ejpam-6247	234	15	)	)	PUNCT
ejpam-6247	234	16	can	can	AUX
ejpam-6247	234	17	be	be	AUX
ejpam-6247	234	18	expressed	express	VERB
ejpam-6247	234	19	as	as	ADP
ejpam-6247	234	20	the	the	DET
ejpam-6247	234	21	union	union	NOUN
ejpam-6247	234	22	jm(h	jm(h	PUNCT
ejpam-6247	234	23	)	)	PUNCT
ejpam-6247	234	24	=	=	SYM
ejpam-6247	235	1	⋃	⋃	NOUN
ejpam-6247	235	2	µ∈h	µ∈h	ADJ
ejpam-6247	235	3	jm(µ	jm(µ	NOUN
ejpam-6247	235	4	)	)	PUNCT
ejpam-6247	235	5	.	.	PUNCT
ejpam-6247	236	1	lemma	lemma	PROPN
ejpam-6247	236	2	3	3	X
ejpam-6247	236	3	.	.	X
ejpam-6247	237	1	for	for	ADP
ejpam-6247	237	2	any	any	DET
ejpam-6247	237	3	elements	element	NOUN
ejpam-6247	237	4	µ	µ	NUM
ejpam-6247	237	5	,	,	PUNCT
ejpam-6247	237	6	π	π	PROPN
ejpam-6247	237	7	in	in	ADP
ejpam-6247	237	8	an	an	DET
ejpam-6247	237	9	adl	adl	PROPN
ejpam-6247	237	10	l	l	PROPN
ejpam-6247	237	11	,	,	PUNCT
ejpam-6247	237	12	the	the	DET
ejpam-6247	237	13	following	follow	VERB
ejpam-6247	237	14	properties	property	NOUN
ejpam-6247	237	15	are	be	AUX
ejpam-6247	237	16	satisfied	satisfied	ADJ
ejpam-6247	237	17	:	:	PUNCT
ejpam-6247	237	18	(	(	PUNCT
ejpam-6247	237	19	1	1	X
ejpam-6247	237	20	)	)	PUNCT
ejpam-6247	237	21	jm(µ	jm(µ	NOUN
ejpam-6247	237	22	)	)	PUNCT
ejpam-6247	237	23	∩	∩	NOUN
ejpam-6247	237	24	jm(π	jm(π	PUNCT
ejpam-6247	237	25	)	)	PUNCT
ejpam-6247	238	1	=	=	SYM
ejpam-6247	238	2	jm(µ	jm(µ	PUNCT
ejpam-6247	238	3	∨	∨	NUM
ejpam-6247	238	4	π	π	PROPN
ejpam-6247	238	5	)	)	PUNCT
ejpam-6247	238	6	,	,	PUNCT
ejpam-6247	238	7	(	(	PUNCT
ejpam-6247	238	8	2	2	NUM
ejpam-6247	238	9	)	)	PUNCT
ejpam-6247	238	10	jm(µ	jm(µ	NOUN
ejpam-6247	238	11	∧	∧	PROPN
ejpam-6247	238	12	π	π	PROPN
ejpam-6247	238	13	)	)	PUNCT
ejpam-6247	238	14	⊆	⊆	NUM
ejpam-6247	238	15	jm(µ	jm(µ	NOUN
ejpam-6247	238	16	)	)	PUNCT
ejpam-6247	238	17	∪	∪	ADP
ejpam-6247	238	18	jm(π	jm(π	NOUN
ejpam-6247	238	19	)	)	PUNCT
ejpam-6247	238	20	,	,	PUNCT
ejpam-6247	238	21	(	(	PUNCT
ejpam-6247	238	22	3	3	X
ejpam-6247	238	23	)	)	PUNCT
ejpam-6247	238	24	jm(µ	jm(µ	NOUN
ejpam-6247	238	25	)	)	PUNCT
ejpam-6247	238	26	=	=	SYM
ejpam-6247	238	27	km(((µ,d),d	km(((µ,d),d	NOUN
ejpam-6247	238	28	)	)	PUNCT
ejpam-6247	238	29	)	)	PUNCT
ejpam-6247	238	30	,	,	PUNCT
ejpam-6247	238	31	(	(	PUNCT
ejpam-6247	238	32	4	4	X
ejpam-6247	238	33	)	)	PUNCT
ejpam-6247	238	34	(	(	PUNCT
ejpam-6247	238	35	µ,d	µ,d	NOUN
ejpam-6247	238	36	)	)	PUNCT
ejpam-6247	238	37	⊆	⊆	NUM
ejpam-6247	238	38	(	(	PUNCT
ejpam-6247	238	39	π	π	PROPN
ejpam-6247	238	40	,	,	PUNCT
ejpam-6247	238	41	d	d	PROPN
ejpam-6247	238	42	)	)	PUNCT
ejpam-6247	238	43	⇔	⇔	NOUN
ejpam-6247	238	44	jm(π	jm(π	PROPN
ejpam-6247	238	45	)	)	PUNCT
ejpam-6247	238	46	⊆	⊆	NUM
ejpam-6247	238	47	jm(µ	jm(µ	NOUN
ejpam-6247	238	48	)	)	PUNCT
ejpam-6247	238	49	,	,	PUNCT
ejpam-6247	238	50	(	(	PUNCT
ejpam-6247	238	51	5	5	NUM
ejpam-6247	238	52	)	)	PUNCT
ejpam-6247	238	53	jm(µ	jm(µ	NOUN
ejpam-6247	238	54	)	)	PUNCT
ejpam-6247	238	55	=	=	NOUN
ejpam-6247	238	56	∅	∅	NOUN
ejpam-6247	238	57	⇔	⇔	PROPN
ejpam-6247	238	58	µ	µ	X
ejpam-6247	238	59	∈	∈	PROPN
ejpam-6247	238	60	d	d	PROPN
ejpam-6247	238	61	,	,	PUNCT
ejpam-6247	238	62	(	(	PUNCT
ejpam-6247	238	63	6	6	NUM
ejpam-6247	238	64	)	)	PUNCT
ejpam-6247	238	65	jm(µ	jm(µ	NOUN
ejpam-6247	238	66	)	)	PUNCT
ejpam-6247	239	1	=	=	X
ejpam-6247	239	2	specdmf	specdmf	NOUN
ejpam-6247	239	3	(	(	PUNCT
ejpam-6247	239	4	l	l	NOUN
ejpam-6247	239	5	)	)	PUNCT
ejpam-6247	239	6	⇔	⇔	PROPN
ejpam-6247	239	7	µ	µ	PROPN
ejpam-6247	239	8	is	be	AUX
ejpam-6247	239	9	condensed	condense	VERB
ejpam-6247	239	10	.	.	PUNCT
ejpam-6247	240	1	proof	proof	NOUN
ejpam-6247	240	2	.	.	PUNCT
ejpam-6247	241	1	the	the	DET
ejpam-6247	241	2	verifications	verification	NOUN
ejpam-6247	241	3	of	of	ADP
ejpam-6247	241	4	statements	statement	NOUN
ejpam-6247	241	5	(	(	PUNCT
ejpam-6247	241	6	1	1	NUM
ejpam-6247	241	7	)	)	PUNCT
ejpam-6247	241	8	and	and	CCONJ
ejpam-6247	241	9	(	(	PUNCT
ejpam-6247	241	10	2	2	X
ejpam-6247	241	11	)	)	PUNCT
ejpam-6247	241	12	follow	follow	VERB
ejpam-6247	241	13	directly	directly	ADV
ejpam-6247	241	14	from	from	ADP
ejpam-6247	241	15	the	the	DET
ejpam-6247	241	16	definitions	definition	NOUN
ejpam-6247	241	17	.	.	PUNCT
ejpam-6247	242	1	n.	n.	PROPN
ejpam-6247	242	2	rafi	rafi	PROPN
ejpam-6247	242	3	et	et	PROPN
ejpam-6247	242	4	al	al	PROPN
ejpam-6247	242	5	.	.	PUNCT
ejpam-6247	242	6	/	/	SYM
ejpam-6247	242	7	eur	eur	PROPN
ejpam-6247	242	8	.	.	PUNCT
ejpam-6247	243	1	j.	j.	PROPN
ejpam-6247	243	2	pure	pure	PROPN
ejpam-6247	243	3	appl	appl	PROPN
ejpam-6247	243	4	.	.	PROPN
ejpam-6247	243	5	math	math	PROPN
ejpam-6247	243	6	,	,	PUNCT
ejpam-6247	243	7	18	18	NUM
ejpam-6247	243	8	(	(	PUNCT
ejpam-6247	243	9	3	3	NUM
ejpam-6247	243	10	)	)	PUNCT
ejpam-6247	243	11	(	(	PUNCT
ejpam-6247	243	12	2025	2025	NUM
ejpam-6247	243	13	)	)	PUNCT
ejpam-6247	243	14	,	,	PUNCT
ejpam-6247	243	15	6247	6247	NUM
ejpam-6247	243	16	9	9	NUM
ejpam-6247	243	17	of	of	ADP
ejpam-6247	243	18	15	15	NUM
ejpam-6247	243	19	(	(	PUNCT
ejpam-6247	243	20	3	3	NUM
ejpam-6247	243	21	)	)	PUNCT
ejpam-6247	243	22	let	let	VERB
ejpam-6247	243	23	q	q	NOUN
ejpam-6247	243	24	∈	∈	PROPN
ejpam-6247	243	25	jm(µ	jm(µ	NOUN
ejpam-6247	243	26	)	)	PUNCT
ejpam-6247	243	27	.	.	PUNCT
ejpam-6247	244	1	this	this	PRON
ejpam-6247	244	2	implies	imply	VERB
ejpam-6247	244	3	that	that	SCONJ
ejpam-6247	244	4	µ	µ	X
ejpam-6247	244	5	/∈	/∈	PUNCT
ejpam-6247	244	6	q.	q.	PROPN
ejpam-6247	244	7	given	give	VERB
ejpam-6247	244	8	that	that	PRON
ejpam-6247	244	9	q	q	NOUN
ejpam-6247	244	10	is	be	AUX
ejpam-6247	244	11	a	a	DET
ejpam-6247	244	12	minimal	minimal	ADJ
ejpam-6247	244	13	prime	prime	ADJ
ejpam-6247	244	14	dfilter	dfilter	NOUN
ejpam-6247	244	15	,	,	PUNCT
ejpam-6247	244	16	it	it	PRON
ejpam-6247	244	17	follows	follow	VERB
ejpam-6247	244	18	that	that	SCONJ
ejpam-6247	244	19	(	(	PUNCT
ejpam-6247	244	20	(	(	PUNCT
ejpam-6247	244	21	µ,d),d	µ,d),d	NOUN
ejpam-6247	244	22	)	)	PUNCT
ejpam-6247	244	23	is	be	AUX
ejpam-6247	244	24	not	not	PART
ejpam-6247	244	25	entirely	entirely	ADV
ejpam-6247	244	26	contained	contain	VERB
ejpam-6247	244	27	in	in	ADP
ejpam-6247	244	28	q.	q.	PROPN
ejpam-6247	244	29	thus	thus	ADV
ejpam-6247	244	30	,	,	PUNCT
ejpam-6247	244	31	q	q	PROPN
ejpam-6247	244	32	∈	∈	PROPN
ejpam-6247	244	33	jm(((µ,d),d	jm(((µ,d),d	NOUN
ejpam-6247	244	34	)	)	PUNCT
ejpam-6247	244	35	)	)	PUNCT
ejpam-6247	244	36	,	,	PUNCT
ejpam-6247	244	37	and	and	CCONJ
ejpam-6247	244	38	we	we	PRON
ejpam-6247	244	39	obtain	obtain	VERB
ejpam-6247	244	40	the	the	DET
ejpam-6247	244	41	inclusion	inclusion	NOUN
ejpam-6247	244	42	jm(µ	jm(µ	NOUN
ejpam-6247	244	43	)	)	PUNCT
ejpam-6247	244	44	⊆	⊆	NUM
ejpam-6247	244	45	jm(((µ,d),d	jm(((µ,d),d	NOUN
ejpam-6247	244	46	)	)	PUNCT
ejpam-6247	244	47	)	)	PUNCT
ejpam-6247	244	48	.	.	PUNCT
ejpam-6247	245	1	for	for	ADP
ejpam-6247	245	2	the	the	DET
ejpam-6247	245	3	reverse	reverse	ADJ
ejpam-6247	245	4	inclusion	inclusion	NOUN
ejpam-6247	245	5	,	,	PUNCT
ejpam-6247	245	6	assume	assume	VERB
ejpam-6247	245	7	q	q	X
ejpam-6247	245	8	∈	∈	PROPN
ejpam-6247	245	9	jm(((µ,d),d	jm(((µ,d),d	NOUN
ejpam-6247	245	10	)	)	PUNCT
ejpam-6247	245	11	)	)	PUNCT
ejpam-6247	245	12	.	.	PUNCT
ejpam-6247	246	1	that	that	PRON
ejpam-6247	246	2	is	be	AUX
ejpam-6247	246	3	,	,	PUNCT
ejpam-6247	246	4	(	(	PUNCT
ejpam-6247	246	5	(	(	PUNCT
ejpam-6247	246	6	µ,d),d	µ,d),d	NOUN
ejpam-6247	246	7	)	)	PUNCT
ejpam-6247	246	8	⊈	⊈	PROPN
ejpam-6247	246	9	q.	q.	PROPN
ejpam-6247	246	10	suppose	suppose	VERB
ejpam-6247	246	11	,	,	PUNCT
ejpam-6247	246	12	for	for	ADP
ejpam-6247	246	13	contradiction	contradiction	NOUN
ejpam-6247	246	14	,	,	PUNCT
ejpam-6247	246	15	that	that	SCONJ
ejpam-6247	246	16	µ	µ	X
ejpam-6247	246	17	∈	∈	PROPN
ejpam-6247	246	18	q.	q.	NOUN
ejpam-6247	246	19	then	then	ADV
ejpam-6247	246	20	,	,	PUNCT
ejpam-6247	246	21	due	due	ADP
ejpam-6247	246	22	to	to	ADP
ejpam-6247	246	23	the	the	DET
ejpam-6247	246	24	minimality	minimality	NOUN
ejpam-6247	246	25	of	of	ADP
ejpam-6247	246	26	q	q	PROPN
ejpam-6247	246	27	,	,	PUNCT
ejpam-6247	246	28	we	we	PRON
ejpam-6247	246	29	must	must	AUX
ejpam-6247	246	30	have	have	VERB
ejpam-6247	246	31	(	(	PUNCT
ejpam-6247	246	32	(	(	PUNCT
ejpam-6247	246	33	µ,d),d	µ,d),d	X
ejpam-6247	246	34	)	)	PUNCT
ejpam-6247	246	35	⊆	⊆	NUM
ejpam-6247	246	36	q	q	NOUN
ejpam-6247	246	37	,	,	PUNCT
ejpam-6247	246	38	which	which	PRON
ejpam-6247	246	39	contradicts	contradict	VERB
ejpam-6247	246	40	our	our	PRON
ejpam-6247	246	41	assumption	assumption	NOUN
ejpam-6247	246	42	.	.	PUNCT
ejpam-6247	247	1	hence	hence	ADV
ejpam-6247	247	2	,	,	PUNCT
ejpam-6247	247	3	µ	µ	X
ejpam-6247	247	4	/∈	/∈	NOUN
ejpam-6247	247	5	q	q	NOUN
ejpam-6247	247	6	,	,	PUNCT
ejpam-6247	247	7	meaning	mean	VERB
ejpam-6247	247	8	q	q	X
ejpam-6247	247	9	∈	∈	PROPN
ejpam-6247	247	10	jm(µ	jm(µ	NOUN
ejpam-6247	247	11	)	)	PUNCT
ejpam-6247	247	12	.	.	PUNCT
ejpam-6247	248	1	therefore	therefore	ADV
ejpam-6247	248	2	,	,	PUNCT
ejpam-6247	248	3	we	we	PRON
ejpam-6247	248	4	conclude	conclude	VERB
ejpam-6247	248	5	that	that	PRON
ejpam-6247	248	6	jm(µ	jm(µ	NOUN
ejpam-6247	248	7	)	)	PUNCT
ejpam-6247	248	8	=	=	SYM
ejpam-6247	248	9	jm(((µ,d),d	jm(((µ,d),d	NOUN
ejpam-6247	248	10	)	)	PUNCT
ejpam-6247	248	11	)	)	PUNCT
ejpam-6247	248	12	.	.	PUNCT
ejpam-6247	249	1	(	(	PUNCT
ejpam-6247	249	2	4	4	X
ejpam-6247	249	3	)	)	PUNCT
ejpam-6247	249	4	suppose	suppose	VERB
ejpam-6247	249	5	that	that	SCONJ
ejpam-6247	249	6	(	(	PUNCT
ejpam-6247	249	7	µ,d	µ,d	NOUN
ejpam-6247	249	8	)	)	PUNCT
ejpam-6247	249	9	⊆	⊆	NUM
ejpam-6247	249	10	(	(	PUNCT
ejpam-6247	249	11	π	π	PROPN
ejpam-6247	249	12	,	,	PUNCT
ejpam-6247	249	13	d	d	NOUN
ejpam-6247	249	14	)	)	PUNCT
ejpam-6247	249	15	.	.	PUNCT
ejpam-6247	250	1	let	let	VERB
ejpam-6247	250	2	q	q	PROPN
ejpam-6247	250	3	∈	∈	PROPN
ejpam-6247	250	4	jm(π	jm(π	PROPN
ejpam-6247	250	5	)	)	PUNCT
ejpam-6247	250	6	.	.	PUNCT
ejpam-6247	251	1	then	then	ADV
ejpam-6247	251	2	π	π	X
ejpam-6247	251	3	/∈	/∈	PUNCT
ejpam-6247	252	1	q	q	X
ejpam-6247	252	2	,	,	PUNCT
ejpam-6247	253	1	which	which	PRON
ejpam-6247	253	2	,	,	PUNCT
ejpam-6247	253	3	together	together	ADV
ejpam-6247	253	4	with	with	ADP
ejpam-6247	253	5	the	the	DET
ejpam-6247	253	6	inclusion	inclusion	NOUN
ejpam-6247	253	7	(	(	PUNCT
ejpam-6247	253	8	µ,d	µ,d	NOUN
ejpam-6247	253	9	)	)	PUNCT
ejpam-6247	253	10	⊆	⊆	NUM
ejpam-6247	253	11	(	(	PUNCT
ejpam-6247	253	12	π	π	PROPN
ejpam-6247	253	13	,	,	PUNCT
ejpam-6247	253	14	d	d	PROPN
ejpam-6247	253	15	)	)	PUNCT
ejpam-6247	253	16	,	,	PUNCT
ejpam-6247	253	17	implies	imply	VERB
ejpam-6247	253	18	that	that	SCONJ
ejpam-6247	253	19	(	(	PUNCT
ejpam-6247	253	20	µ,d	µ,d	NOUN
ejpam-6247	253	21	)	)	PUNCT
ejpam-6247	253	22	⊆	⊆	NUM
ejpam-6247	253	23	q.	q.	NOUN
ejpam-6247	253	24	since	since	SCONJ
ejpam-6247	253	25	q	q	PROPN
ejpam-6247	253	26	is	be	AUX
ejpam-6247	253	27	a	a	DET
ejpam-6247	253	28	minimal	minimal	ADJ
ejpam-6247	253	29	prime	prime	ADJ
ejpam-6247	253	30	d	d	NOUN
ejpam-6247	253	31	-	-	NOUN
ejpam-6247	253	32	filter	filter	NOUN
ejpam-6247	253	33	,	,	PUNCT
ejpam-6247	253	34	this	this	PRON
ejpam-6247	253	35	leads	lead	VERB
ejpam-6247	253	36	to	to	ADP
ejpam-6247	253	37	µ	µ	PROPN
ejpam-6247	253	38	/∈	/∈	NOUN
ejpam-6247	254	1	q	q	NOUN
ejpam-6247	254	2	,	,	PUNCT
ejpam-6247	255	1	and	and	CCONJ
ejpam-6247	255	2	so	so	ADV
ejpam-6247	255	3	q	q	X
ejpam-6247	255	4	∈	∈	PROPN
ejpam-6247	255	5	jm(µ	jm(µ	NOUN
ejpam-6247	255	6	)	)	PUNCT
ejpam-6247	255	7	.	.	PUNCT
ejpam-6247	256	1	hence	hence	ADV
ejpam-6247	256	2	,	,	PUNCT
ejpam-6247	256	3	we	we	PRON
ejpam-6247	256	4	have	have	VERB
ejpam-6247	256	5	jm(π	jm(π	NOUN
ejpam-6247	256	6	)	)	PUNCT
ejpam-6247	256	7	⊆	⊆	NUM
ejpam-6247	256	8	jm(µ	jm(µ	NOUN
ejpam-6247	256	9	)	)	PUNCT
ejpam-6247	256	10	.	.	PUNCT
ejpam-6247	257	1	conversely	conversely	ADV
ejpam-6247	257	2	,	,	PUNCT
ejpam-6247	257	3	assume	assume	VERB
ejpam-6247	257	4	jm(π	jm(π	PUNCT
ejpam-6247	257	5	)	)	PUNCT
ejpam-6247	258	1	⊆	⊆	NUM
ejpam-6247	258	2	jm(µ	jm(µ	NOUN
ejpam-6247	258	3	)	)	PUNCT
ejpam-6247	258	4	.	.	PUNCT
ejpam-6247	259	1	take	take	VERB
ejpam-6247	259	2	any	any	DET
ejpam-6247	259	3	θ	θ	NOUN
ejpam-6247	259	4	∈	∈	PROPN
ejpam-6247	259	5	(	(	PUNCT
ejpam-6247	259	6	π	π	PROPN
ejpam-6247	259	7	,	,	PUNCT
ejpam-6247	259	8	d	d	NOUN
ejpam-6247	259	9	)	)	PUNCT
ejpam-6247	259	10	,	,	PUNCT
ejpam-6247	259	11	so	so	CCONJ
ejpam-6247	259	12	by	by	ADP
ejpam-6247	259	13	definition	definition	NOUN
ejpam-6247	259	14	,	,	PUNCT
ejpam-6247	259	15	θ	θ	PROPN
ejpam-6247	259	16	∨	∨	PROPN
ejpam-6247	259	17	π	π	PROPN
ejpam-6247	259	18	/∈	/∈	PUNCT
ejpam-6247	260	1	d.	d.	PROPN
ejpam-6247	260	2	by	by	ADP
ejpam-6247	260	3	proposition	proposition	NOUN
ejpam-6247	260	4	3	3	NUM
ejpam-6247	260	5	,	,	PUNCT
ejpam-6247	260	6	this	this	PRON
ejpam-6247	260	7	implies	imply	VERB
ejpam-6247	260	8	the	the	DET
ejpam-6247	260	9	existence	existence	NOUN
ejpam-6247	260	10	of	of	ADP
ejpam-6247	260	11	a	a	DET
ejpam-6247	260	12	minimal	minimal	ADJ
ejpam-6247	260	13	prime	prime	ADJ
ejpam-6247	260	14	d	d	NOUN
ejpam-6247	260	15	-	-	ADJ
ejpam-6247	260	16	filter	filter	NOUN
ejpam-6247	260	17	q0	q0	NOUN
ejpam-6247	260	18	such	such	ADJ
ejpam-6247	260	19	that	that	SCONJ
ejpam-6247	260	20	θ	θ	PROPN
ejpam-6247	260	21	∨	∨	PROPN
ejpam-6247	260	22	π	π	PROPN
ejpam-6247	260	23	/∈	/∈	PUNCT
ejpam-6247	261	1	q0	q0	PROPN
ejpam-6247	261	2	.	.	PUNCT
ejpam-6247	262	1	consequently	consequently	ADV
ejpam-6247	262	2	,	,	PUNCT
ejpam-6247	262	3	both	both	DET
ejpam-6247	262	4	θ	θ	PROPN
ejpam-6247	262	5	/∈	/∈	PUNCT
ejpam-6247	262	6	q0	q0	PROPN
ejpam-6247	262	7	and	and	CCONJ
ejpam-6247	262	8	π	π	PROPN
ejpam-6247	262	9	/∈	/∈	PROPN
ejpam-6247	263	1	q0	q0	PROPN
ejpam-6247	263	2	,	,	PUNCT
ejpam-6247	263	3	meaning	mean	VERB
ejpam-6247	263	4	q0	q0	PROPN
ejpam-6247	263	5	∈	∈	PROPN
ejpam-6247	263	6	jm(π	jm(π	X
ejpam-6247	263	7	)	)	PUNCT
ejpam-6247	264	1	⊆	⊆	NUM
ejpam-6247	264	2	jm(µ	jm(µ	NOUN
ejpam-6247	264	3	)	)	PUNCT
ejpam-6247	264	4	,	,	PUNCT
ejpam-6247	264	5	so	so	ADV
ejpam-6247	264	6	µ	µ	ADV
ejpam-6247	264	7	/∈	/∈	NOUN
ejpam-6247	264	8	q0	q0	PROPN
ejpam-6247	264	9	as	as	ADV
ejpam-6247	264	10	well	well	ADV
ejpam-6247	264	11	.	.	PUNCT
ejpam-6247	265	1	it	it	PRON
ejpam-6247	265	2	follows	follow	VERB
ejpam-6247	265	3	that	that	SCONJ
ejpam-6247	265	4	θ	θ	PROPN
ejpam-6247	265	5	∨	∨	PROPN
ejpam-6247	265	6	µ	µ	PRON
ejpam-6247	265	7	/∈	/∈	NOUN
ejpam-6247	265	8	q0	q0	ADJ
ejpam-6247	265	9	,	,	PUNCT
ejpam-6247	265	10	and	and	CCONJ
ejpam-6247	265	11	thus	thus	ADV
ejpam-6247	265	12	θ	θ	X
ejpam-6247	265	13	∨	∨	X
ejpam-6247	265	14	µ	µ	X
ejpam-6247	265	15	/∈	/∈	PUNCT
ejpam-6247	266	1	d	d	NOUN
ejpam-6247	266	2	,	,	PUNCT
ejpam-6247	266	3	which	which	PRON
ejpam-6247	266	4	means	mean	VERB
ejpam-6247	266	5	θ	θ	PROPN
ejpam-6247	266	6	/∈	/∈	PUNCT
ejpam-6247	267	1	(	(	PUNCT
ejpam-6247	267	2	µ,d	µ,d	NOUN
ejpam-6247	267	3	)	)	PUNCT
ejpam-6247	267	4	.	.	PUNCT
ejpam-6247	268	1	therefore	therefore	ADV
ejpam-6247	268	2	,	,	PUNCT
ejpam-6247	268	3	(	(	PUNCT
ejpam-6247	268	4	µ,d	µ,d	NOUN
ejpam-6247	268	5	)	)	PUNCT
ejpam-6247	268	6	⊆	⊆	NUM
ejpam-6247	268	7	(	(	PUNCT
ejpam-6247	268	8	π	π	PROPN
ejpam-6247	268	9	,	,	PUNCT
ejpam-6247	268	10	d	d	NOUN
ejpam-6247	268	11	)	)	PUNCT
ejpam-6247	268	12	.	.	PUNCT
ejpam-6247	269	1	(	(	PUNCT
ejpam-6247	269	2	5	5	X
ejpam-6247	269	3	)	)	PUNCT
ejpam-6247	269	4	this	this	PRON
ejpam-6247	269	5	follows	follow	VERB
ejpam-6247	269	6	directly	directly	ADV
ejpam-6247	269	7	from	from	ADP
ejpam-6247	269	8	proposition	proposition	NOUN
ejpam-6247	269	9	3	3	NUM
ejpam-6247	269	10	.	.	PUNCT
ejpam-6247	270	1	(	(	PUNCT
ejpam-6247	270	2	6	6	X
ejpam-6247	270	3	)	)	PUNCT
ejpam-6247	270	4	suppose	suppose	VERB
ejpam-6247	270	5	that	that	SCONJ
ejpam-6247	270	6	jm(µ	jm(µ	NOUN
ejpam-6247	270	7	)	)	PUNCT
ejpam-6247	270	8	=	=	X
ejpam-6247	270	9	specdmf	specdmf	NOUN
ejpam-6247	270	10	(	(	PUNCT
ejpam-6247	270	11	l	l	NOUN
ejpam-6247	270	12	)	)	PUNCT
ejpam-6247	270	13	.	.	PUNCT
ejpam-6247	271	1	then	then	ADV
ejpam-6247	271	2	,	,	PUNCT
ejpam-6247	271	3	we	we	PRON
ejpam-6247	271	4	have	have	VERB
ejpam-6247	271	5	(	(	PUNCT
ejpam-6247	271	6	µ,d	µ,d	NOUN
ejpam-6247	271	7	)	)	PUNCT
ejpam-6247	271	8	=	=	PUNCT
ejpam-6247	272	1	⋂	⋂	PROPN
ejpam-6247	272	2	q∈jm(l	q∈jm(l	PROPN
ejpam-6247	272	3	)	)	PUNCT
ejpam-6247	272	4	q	q	NOUN
ejpam-6247	273	1	=	=	SYM
ejpam-6247	273	2	⋂	⋂	PROPN
ejpam-6247	273	3	q∈specdmf	q∈specdmf	PROPN
ejpam-6247	273	4	(	(	PUNCT
ejpam-6247	273	5	l	l	NOUN
ejpam-6247	273	6	)	)	PUNCT
ejpam-6247	273	7	q	q	NOUN
ejpam-6247	274	1	=	=	PUNCT
ejpam-6247	274	2	d.	d.	PROPN
ejpam-6247	274	3	thus	thus	ADV
ejpam-6247	274	4	,	,	PUNCT
ejpam-6247	274	5	µ	µ	X
ejpam-6247	274	6	is	be	AUX
ejpam-6247	274	7	condensed	condense	VERB
ejpam-6247	274	8	.	.	PUNCT
ejpam-6247	275	1	conversely	conversely	ADV
ejpam-6247	275	2	,	,	PUNCT
ejpam-6247	275	3	assume	assume	VERB
ejpam-6247	275	4	that	that	SCONJ
ejpam-6247	275	5	µ	µ	NOUN
ejpam-6247	275	6	is	be	AUX
ejpam-6247	275	7	condensed	condense	VERB
ejpam-6247	275	8	,	,	PUNCT
ejpam-6247	275	9	i.e.	i.e.	X
ejpam-6247	275	10	,	,	PUNCT
ejpam-6247	275	11	(	(	PUNCT
ejpam-6247	275	12	µ,d	µ,d	NOUN
ejpam-6247	275	13	)	)	PUNCT
ejpam-6247	275	14	=	=	PUNCT
ejpam-6247	276	1	d.	d.	PROPN
ejpam-6247	276	2	this	this	PRON
ejpam-6247	276	3	implies	imply	VERB
ejpam-6247	276	4	that	that	SCONJ
ejpam-6247	276	5	(	(	PUNCT
ejpam-6247	276	6	µ,d	µ,d	NOUN
ejpam-6247	276	7	)	)	PUNCT
ejpam-6247	276	8	⊆	⊆	NUM
ejpam-6247	276	9	q	q	NOUN
ejpam-6247	276	10	for	for	ADP
ejpam-6247	276	11	every	every	DET
ejpam-6247	276	12	q	q	PROPN
ejpam-6247	276	13	∈	∈	PROPN
ejpam-6247	276	14	specdmf	specdmf	NOUN
ejpam-6247	276	15	(	(	PUNCT
ejpam-6247	276	16	l	l	NOUN
ejpam-6247	276	17	)	)	PUNCT
ejpam-6247	276	18	,	,	PUNCT
ejpam-6247	276	19	and	and	CCONJ
ejpam-6247	276	20	hence	hence	ADV
ejpam-6247	276	21	µ	µ	X
ejpam-6247	276	22	/∈	/∈	NOUN
ejpam-6247	276	23	q	q	NOUN
ejpam-6247	276	24	for	for	ADP
ejpam-6247	276	25	all	all	DET
ejpam-6247	276	26	such	such	ADJ
ejpam-6247	276	27	q.	q.	NOUN
ejpam-6247	276	28	therefore	therefore	ADV
ejpam-6247	276	29	,	,	PUNCT
ejpam-6247	276	30	q	q	PROPN
ejpam-6247	276	31	∈	∈	PROPN
ejpam-6247	276	32	jm(µ	jm(µ	NOUN
ejpam-6247	276	33	)	)	PUNCT
ejpam-6247	276	34	for	for	ADP
ejpam-6247	276	35	all	all	DET
ejpam-6247	276	36	q	q	PROPN
ejpam-6247	276	37	∈	∈	PROPN
ejpam-6247	276	38	specdmf	specdmf	NOUN
ejpam-6247	276	39	(	(	PUNCT
ejpam-6247	276	40	l	l	NOUN
ejpam-6247	276	41	)	)	PUNCT
ejpam-6247	276	42	,	,	PUNCT
ejpam-6247	276	43	which	which	PRON
ejpam-6247	276	44	yields	yield	VERB
ejpam-6247	276	45	jm(µ	jm(µ	NOUN
ejpam-6247	276	46	)	)	PUNCT
ejpam-6247	276	47	=	=	X
ejpam-6247	276	48	specdmf	specdmf	NOUN
ejpam-6247	276	49	(	(	PUNCT
ejpam-6247	276	50	l	l	NOUN
ejpam-6247	276	51	)	)	PUNCT
ejpam-6247	276	52	.	.	PUNCT
ejpam-6247	277	1	from	from	ADP
ejpam-6247	277	2	the	the	DET
ejpam-6247	277	3	previous	previous	ADJ
ejpam-6247	277	4	result	result	NOUN
ejpam-6247	277	5	,	,	PUNCT
ejpam-6247	277	6	it	it	PRON
ejpam-6247	277	7	follows	follow	VERB
ejpam-6247	277	8	that	that	SCONJ
ejpam-6247	277	9	the	the	DET
ejpam-6247	277	10	collection	collection	NOUN
ejpam-6247	277	11	{	{	PUNCT
ejpam-6247	277	12	jm(µ	jm(µ	NOUN
ejpam-6247	277	13	)	)	PUNCT
ejpam-6247	277	14	|	|	ADV
ejpam-6247	277	15	µ	µ	X
ejpam-6247	277	16	∈	∈	NOUN
ejpam-6247	277	17	l	l	NOUN
ejpam-6247	277	18	}	}	PUNCT
ejpam-6247	277	19	consists	consist	VERB
ejpam-6247	277	20	of	of	ADP
ejpam-6247	277	21	subsets	subset	NOUN
ejpam-6247	277	22	of	of	ADP
ejpam-6247	277	23	specdmf	specdmf	NOUN
ejpam-6247	277	24	(	(	PUNCT
ejpam-6247	277	25	l	l	NOUN
ejpam-6247	277	26	)	)	PUNCT
ejpam-6247	277	27	that	that	PRON
ejpam-6247	277	28	is	be	AUX
ejpam-6247	277	29	closed	close	VERB
ejpam-6247	277	30	under	under	ADP
ejpam-6247	277	31	finite	finite	ADJ
ejpam-6247	277	32	intersections	intersection	NOUN
ejpam-6247	277	33	.	.	PUNCT
ejpam-6247	278	1	moreover	moreover	ADV
ejpam-6247	278	2	,	,	PUNCT
ejpam-6247	278	3	since	since	SCONJ
ejpam-6247	278	4	every	every	DET
ejpam-6247	278	5	minimal	minimal	ADJ
ejpam-6247	278	6	prime	prime	ADJ
ejpam-6247	278	7	d	d	NOUN
ejpam-6247	278	8	-	-	NOUN
ejpam-6247	278	9	filter	filter	NOUN
ejpam-6247	278	10	is	be	AUX
ejpam-6247	278	11	proper	proper	ADJ
ejpam-6247	278	12	,	,	PUNCT
ejpam-6247	278	13	we	we	PRON
ejpam-6247	278	14	have⋃	have⋃	VERB
ejpam-6247	278	15	µ∈l	µ∈l	PRON
ejpam-6247	278	16	jm(µ	jm(µ	NOUN
ejpam-6247	278	17	)	)	PUNCT
ejpam-6247	279	1	=	=	X
ejpam-6247	279	2	specdmf	specdmf	NOUN
ejpam-6247	279	3	(	(	PUNCT
ejpam-6247	279	4	l	l	NOUN
ejpam-6247	279	5	)	)	PUNCT
ejpam-6247	279	6	.	.	PUNCT
ejpam-6247	280	1	thus	thus	ADV
ejpam-6247	280	2	,	,	PUNCT
ejpam-6247	280	3	this	this	DET
ejpam-6247	280	4	collection	collection	NOUN
ejpam-6247	280	5	forms	form	VERB
ejpam-6247	280	6	a	a	DET
ejpam-6247	280	7	basis	basis	NOUN
ejpam-6247	280	8	for	for	ADP
ejpam-6247	280	9	a	a	DET
ejpam-6247	280	10	topology	topology	NOUN
ejpam-6247	280	11	on	on	ADP
ejpam-6247	280	12	specdmf	specdmf	NOUN
ejpam-6247	280	13	(	(	PUNCT
ejpam-6247	280	14	l	l	NOUN
ejpam-6247	280	15	)	)	PUNCT
ejpam-6247	280	16	.	.	PUNCT
ejpam-6247	281	1	now	now	ADV
ejpam-6247	281	2	,	,	PUNCT
ejpam-6247	281	3	for	for	ADP
ejpam-6247	281	4	any	any	DET
ejpam-6247	281	5	subset	subset	NOUN
ejpam-6247	281	6	h	h	NOUN
ejpam-6247	281	7	⊆	⊆	NUM
ejpam-6247	281	8	l	l	NOUN
ejpam-6247	281	9	,	,	PUNCT
ejpam-6247	281	10	define	define	VERB
ejpam-6247	281	11	vm(h	vm(h	NUM
ejpam-6247	281	12	)	)	PUNCT
ejpam-6247	282	1	=	=	PRON
ejpam-6247	282	2	{	{	PUNCT
ejpam-6247	282	3	q	q	NOUN
ejpam-6247	282	4	∈	∈	PROPN
ejpam-6247	282	5	specdmf	specdmf	NOUN
ejpam-6247	282	6	(	(	PUNCT
ejpam-6247	282	7	l	l	NOUN
ejpam-6247	282	8	)	)	PUNCT
ejpam-6247	283	1	|	|	ADV
ejpam-6247	283	2	h	h	NOUN
ejpam-6247	283	3	⊆	⊆	NUM
ejpam-6247	283	4	q	q	NOUN
ejpam-6247	283	5	}	}	PUNCT
ejpam-6247	283	6	.	.	PUNCT
ejpam-6247	284	1	in	in	ADP
ejpam-6247	284	2	particular	particular	ADJ
ejpam-6247	284	3	,	,	PUNCT
ejpam-6247	284	4	for	for	ADP
ejpam-6247	284	5	a	a	DET
ejpam-6247	284	6	singleton	singleton	NOUN
ejpam-6247	284	7	h	h	NOUN
ejpam-6247	284	8	=	=	PUNCT
ejpam-6247	284	9	{	{	PUNCT
ejpam-6247	284	10	µ	µ	NOUN
ejpam-6247	284	11	}	}	PUNCT
ejpam-6247	284	12	,	,	PUNCT
ejpam-6247	284	13	we	we	PRON
ejpam-6247	284	14	write	write	VERB
ejpam-6247	284	15	vm(µ	vm(µ	NOUN
ejpam-6247	284	16	)	)	PUNCT
ejpam-6247	284	17	instead	instead	ADV
ejpam-6247	284	18	of	of	ADP
ejpam-6247	284	19	vm({µ	vm({µ	NOUN
ejpam-6247	284	20	}	}	PUNCT
ejpam-6247	284	21	)	)	PUNCT
ejpam-6247	284	22	,	,	PUNCT
ejpam-6247	285	1	where	where	SCONJ
ejpam-6247	285	2	vm(µ	vm(µ	NOUN
ejpam-6247	285	3	)	)	PUNCT
ejpam-6247	286	1	=	=	PUNCT
ejpam-6247	286	2	{	{	PUNCT
ejpam-6247	286	3	q	q	NOUN
ejpam-6247	286	4	∈	∈	PROPN
ejpam-6247	286	5	specdmf	specdmf	NOUN
ejpam-6247	286	6	(	(	PUNCT
ejpam-6247	286	7	l	l	NOUN
ejpam-6247	286	8	)	)	PUNCT
ejpam-6247	286	9	|	|	ADV
ejpam-6247	286	10	µ	µ	X
ejpam-6247	286	11	∈	∈	NOUN
ejpam-6247	286	12	q	q	X
ejpam-6247	286	13	}	}	PUNCT
ejpam-6247	286	14	.	.	PUNCT
ejpam-6247	287	1	with	with	ADP
ejpam-6247	287	2	these	these	DET
ejpam-6247	287	3	definitions	definition	NOUN
ejpam-6247	287	4	and	and	CCONJ
ejpam-6247	287	5	observations	observation	NOUN
ejpam-6247	287	6	in	in	ADP
ejpam-6247	287	7	place	place	NOUN
ejpam-6247	287	8	,	,	PUNCT
ejpam-6247	287	9	we	we	PRON
ejpam-6247	287	10	arrive	arrive	VERB
ejpam-6247	287	11	at	at	ADP
ejpam-6247	287	12	the	the	DET
ejpam-6247	287	13	following	following	ADJ
ejpam-6247	287	14	result	result	NOUN
ejpam-6247	287	15	:	:	PUNCT
ejpam-6247	287	16	lemma	lemma	PROPN
ejpam-6247	287	17	4	4	X
ejpam-6247	287	18	.	.	PUNCT
ejpam-6247	288	1	let	let	VERB
ejpam-6247	288	2	g	g	NOUN
ejpam-6247	288	3	and	and	CCONJ
ejpam-6247	288	4	u	u	NOUN
ejpam-6247	288	5	be	be	VERB
ejpam-6247	288	6	two	two	NUM
ejpam-6247	288	7	d	d	NOUN
ejpam-6247	288	8	-	-	PUNCT
ejpam-6247	288	9	filters	filter	NOUN
ejpam-6247	288	10	of	of	ADP
ejpam-6247	288	11	an	an	DET
ejpam-6247	288	12	adl	adl	PROPN
ejpam-6247	288	13	l.	l.	NOUN
ejpam-6247	288	14	then	then	ADV
ejpam-6247	288	15	the	the	DET
ejpam-6247	288	16	following	follow	VERB
ejpam-6247	288	17	properties	property	NOUN
ejpam-6247	288	18	hold	hold	VERB
ejpam-6247	288	19	:	:	PUNCT
ejpam-6247	289	1	n.	n.	PROPN
ejpam-6247	289	2	rafi	rafi	PROPN
ejpam-6247	289	3	et	et	PROPN
ejpam-6247	289	4	al	al	PROPN
ejpam-6247	289	5	.	.	PUNCT
ejpam-6247	289	6	/	/	SYM
ejpam-6247	289	7	eur	eur	PROPN
ejpam-6247	289	8	.	.	PUNCT
ejpam-6247	290	1	j.	j.	PROPN
ejpam-6247	290	2	pure	pure	PROPN
ejpam-6247	290	3	appl	appl	PROPN
ejpam-6247	290	4	.	.	PROPN
ejpam-6247	290	5	math	math	PROPN
ejpam-6247	290	6	,	,	PUNCT
ejpam-6247	290	7	18	18	NUM
ejpam-6247	290	8	(	(	PUNCT
ejpam-6247	290	9	3	3	NUM
ejpam-6247	290	10	)	)	PUNCT
ejpam-6247	290	11	(	(	PUNCT
ejpam-6247	290	12	2025	2025	NUM
ejpam-6247	290	13	)	)	PUNCT
ejpam-6247	290	14	,	,	PUNCT
ejpam-6247	290	15	6247	6247	NUM
ejpam-6247	290	16	10	10	NUM
ejpam-6247	290	17	of	of	ADP
ejpam-6247	290	18	15	15	NUM
ejpam-6247	290	19	(	(	PUNCT
ejpam-6247	290	20	1	1	NUM
ejpam-6247	290	21	)	)	PUNCT
ejpam-6247	290	22	vm(g	vm(g	NOUN
ejpam-6247	290	23	)	)	PUNCT
ejpam-6247	290	24	∩	∩	NOUN
ejpam-6247	290	25	vm(u	vm(u	NUM
ejpam-6247	290	26	)	)	PUNCT
ejpam-6247	290	27	=	=	SYM
ejpam-6247	290	28	vm(g	vm(g	PART
ejpam-6247	290	29	∨	∨	NUM
ejpam-6247	290	30	u	u	NOUN
ejpam-6247	290	31	)	)	PUNCT
ejpam-6247	290	32	,	,	PUNCT
ejpam-6247	290	33	(	(	PUNCT
ejpam-6247	290	34	2	2	X
ejpam-6247	290	35	)	)	PUNCT
ejpam-6247	290	36	vm(g	vm(g	NOUN
ejpam-6247	290	37	)	)	PUNCT
ejpam-6247	291	1	=	=	X
ejpam-6247	291	2	specdmf	specdmf	NOUN
ejpam-6247	291	3	(	(	PUNCT
ejpam-6247	291	4	l	l	NOUN
ejpam-6247	291	5	)	)	PUNCT
ejpam-6247	291	6	⇔	⇔	NOUN
ejpam-6247	291	7	g	g	PROPN
ejpam-6247	291	8	=	=	SYM
ejpam-6247	291	9	d	d	PROPN
ejpam-6247	291	10	,	,	PUNCT
ejpam-6247	291	11	(	(	PUNCT
ejpam-6247	291	12	3	3	NUM
ejpam-6247	291	13	)	)	PUNCT
ejpam-6247	291	14	jm(µ	jm(µ	NOUN
ejpam-6247	291	15	)	)	PUNCT
ejpam-6247	291	16	=	=	SYM
ejpam-6247	291	17	vm((µ,d	vm((µ,d	NOUN
ejpam-6247	291	18	)	)	PUNCT
ejpam-6247	291	19	)	)	PUNCT
ejpam-6247	291	20	,	,	PUNCT
ejpam-6247	291	21	for	for	ADP
ejpam-6247	291	22	all	all	DET
ejpam-6247	291	23	µ	µ	PRON
ejpam-6247	291	24	∈	∈	NOUN
ejpam-6247	291	25	l	l	NOUN
ejpam-6247	291	26	,	,	PUNCT
ejpam-6247	291	27	(	(	PUNCT
ejpam-6247	291	28	4	4	NUM
ejpam-6247	291	29	)	)	PUNCT
ejpam-6247	291	30	vm(µ	vm(µ	NOUN
ejpam-6247	291	31	)	)	PUNCT
ejpam-6247	291	32	=	=	SYM
ejpam-6247	291	33	jm((µ,d	jm((µ,d	NOUN
ejpam-6247	291	34	)	)	PUNCT
ejpam-6247	291	35	)	)	PUNCT
ejpam-6247	291	36	.	.	PUNCT
ejpam-6247	292	1	proof	proof	NOUN
ejpam-6247	292	2	.	.	PUNCT
ejpam-6247	293	1	(	(	PUNCT
ejpam-6247	293	2	1	1	X
ejpam-6247	293	3	)	)	PUNCT
ejpam-6247	293	4	clear	clear	ADJ
ejpam-6247	293	5	.	.	PUNCT
ejpam-6247	294	1	(	(	PUNCT
ejpam-6247	294	2	2	2	X
ejpam-6247	294	3	)	)	PUNCT
ejpam-6247	294	4	suppose	suppose	VERB
ejpam-6247	294	5	vm(g	vm(g	NOUN
ejpam-6247	294	6	)	)	PUNCT
ejpam-6247	294	7	=	=	X
ejpam-6247	294	8	specdmf	specdmf	NOUN
ejpam-6247	294	9	(	(	PUNCT
ejpam-6247	294	10	l	l	NOUN
ejpam-6247	294	11	)	)	PUNCT
ejpam-6247	294	12	.	.	PUNCT
ejpam-6247	295	1	this	this	PRON
ejpam-6247	295	2	means	mean	VERB
ejpam-6247	295	3	that	that	SCONJ
ejpam-6247	295	4	every	every	DET
ejpam-6247	295	5	minimal	minimal	ADJ
ejpam-6247	295	6	prime	prime	ADJ
ejpam-6247	295	7	d	d	NOUN
ejpam-6247	295	8	-	-	NOUN
ejpam-6247	295	9	filter	filter	ADJ
ejpam-6247	295	10	q	q	NOUN
ejpam-6247	295	11	contains	contain	VERB
ejpam-6247	295	12	g.	g.	PROPN
ejpam-6247	295	13	take	take	VERB
ejpam-6247	295	14	any	any	DET
ejpam-6247	295	15	element	element	NOUN
ejpam-6247	295	16	µ	µ	PROPN
ejpam-6247	295	17	∈	∈	PROPN
ejpam-6247	295	18	g.	g.	PROPN
ejpam-6247	295	19	assume	assume	VERB
ejpam-6247	295	20	,	,	PUNCT
ejpam-6247	295	21	contrary	contrary	ADJ
ejpam-6247	295	22	to	to	ADP
ejpam-6247	295	23	what	what	PRON
ejpam-6247	295	24	we	we	PRON
ejpam-6247	295	25	want	want	VERB
ejpam-6247	295	26	to	to	PART
ejpam-6247	295	27	prove	prove	VERB
ejpam-6247	295	28	,	,	PUNCT
ejpam-6247	295	29	that	that	DET
ejpam-6247	295	30	µ	µ	X
ejpam-6247	295	31	/∈	/∈	SYM
ejpam-6247	295	32	d.	d.	PROPN
ejpam-6247	295	33	then	then	ADV
ejpam-6247	295	34	,	,	PUNCT
ejpam-6247	295	35	according	accord	VERB
ejpam-6247	295	36	to	to	ADP
ejpam-6247	295	37	proposition	proposition	NOUN
ejpam-6247	295	38	3	3	NUM
ejpam-6247	295	39	,	,	PUNCT
ejpam-6247	295	40	there	there	PRON
ejpam-6247	295	41	exists	exist	VERB
ejpam-6247	295	42	some	some	DET
ejpam-6247	295	43	q	q	NOUN
ejpam-6247	295	44	∈	∈	PROPN
ejpam-6247	295	45	specdmf	specdmf	NOUN
ejpam-6247	295	46	(	(	PUNCT
ejpam-6247	295	47	l	l	NOUN
ejpam-6247	295	48	)	)	PUNCT
ejpam-6247	295	49	such	such	ADJ
ejpam-6247	295	50	that	that	SCONJ
ejpam-6247	295	51	µ	µ	PROPN
ejpam-6247	295	52	/∈	/∈	PUNCT
ejpam-6247	295	53	q.	q.	NOUN
ejpam-6247	295	54	as	as	ADP
ejpam-6247	295	55	a	a	DET
ejpam-6247	295	56	result	result	NOUN
ejpam-6247	295	57	,	,	PUNCT
ejpam-6247	295	58	g	g	PROPN
ejpam-6247	295	59	⊈	⊈	PROPN
ejpam-6247	295	60	q	q	X
ejpam-6247	295	61	,	,	PUNCT
ejpam-6247	295	62	which	which	PRON
ejpam-6247	295	63	contradicts	contradict	VERB
ejpam-6247	295	64	our	our	PRON
ejpam-6247	295	65	initial	initial	ADJ
ejpam-6247	295	66	assumption	assumption	NOUN
ejpam-6247	295	67	.	.	PUNCT
ejpam-6247	296	1	therefore	therefore	ADV
ejpam-6247	296	2	,	,	PUNCT
ejpam-6247	296	3	µ	µ	X
ejpam-6247	296	4	∈	∈	PROPN
ejpam-6247	296	5	d	d	NOUN
ejpam-6247	296	6	for	for	ADP
ejpam-6247	296	7	all	all	DET
ejpam-6247	296	8	µ	µ	PRON
ejpam-6247	296	9	∈	∈	NOUN
ejpam-6247	296	10	g	g	NOUN
ejpam-6247	296	11	,	,	PUNCT
ejpam-6247	296	12	and	and	CCONJ
ejpam-6247	296	13	thus	thus	ADV
ejpam-6247	296	14	g	g	PROPN
ejpam-6247	296	15	⊆	⊆	NUM
ejpam-6247	296	16	d.	d.	NOUN
ejpam-6247	296	17	since	since	SCONJ
ejpam-6247	296	18	g	g	PROPN
ejpam-6247	296	19	is	be	AUX
ejpam-6247	296	20	a	a	DET
ejpam-6247	296	21	d	d	NOUN
ejpam-6247	296	22	-	-	NOUN
ejpam-6247	296	23	filter	filter	NOUN
ejpam-6247	296	24	,	,	PUNCT
ejpam-6247	296	25	we	we	PRON
ejpam-6247	296	26	conclude	conclude	VERB
ejpam-6247	296	27	that	that	PRON
ejpam-6247	296	28	g	g	PROPN
ejpam-6247	296	29	=	=	PUNCT
ejpam-6247	296	30	d.	d.	PROPN
ejpam-6247	296	31	conversely	conversely	ADV
ejpam-6247	296	32	,	,	PUNCT
ejpam-6247	296	33	if	if	SCONJ
ejpam-6247	296	34	g	g	PROPN
ejpam-6247	296	35	=	=	SYM
ejpam-6247	296	36	d	d	PROPN
ejpam-6247	296	37	,	,	PUNCT
ejpam-6247	296	38	then	then	ADV
ejpam-6247	296	39	it	it	PRON
ejpam-6247	296	40	is	be	AUX
ejpam-6247	296	41	immediate	immediate	ADJ
ejpam-6247	296	42	that	that	SCONJ
ejpam-6247	296	43	g	g	PROPN
ejpam-6247	296	44	⊆	⊆	NUM
ejpam-6247	296	45	q	q	NOUN
ejpam-6247	296	46	for	for	ADP
ejpam-6247	296	47	all	all	DET
ejpam-6247	296	48	q	q	PROPN
ejpam-6247	296	49	∈	∈	PROPN
ejpam-6247	296	50	specdmf	specdmf	NOUN
ejpam-6247	296	51	(	(	PUNCT
ejpam-6247	296	52	l	l	NOUN
ejpam-6247	296	53	)	)	PUNCT
ejpam-6247	296	54	,	,	PUNCT
ejpam-6247	296	55	and	and	CCONJ
ejpam-6247	296	56	hence	hence	ADV
ejpam-6247	296	57	vm(g	vm(g	NUM
ejpam-6247	296	58	)	)	PUNCT
ejpam-6247	297	1	=	=	X
ejpam-6247	297	2	specdmf	specdmf	NOUN
ejpam-6247	297	3	(	(	PUNCT
ejpam-6247	297	4	l	l	NOUN
ejpam-6247	297	5	)	)	PUNCT
ejpam-6247	297	6	.	.	PUNCT
ejpam-6247	298	1	(	(	PUNCT
ejpam-6247	298	2	3	3	X
ejpam-6247	298	3	)	)	PUNCT
ejpam-6247	298	4	letq	letq	ADJ
ejpam-6247	298	5	∈	∈	PROPN
ejpam-6247	298	6	specdmf	specdmf	NOUN
ejpam-6247	298	7	(	(	PUNCT
ejpam-6247	298	8	l	l	NOUN
ejpam-6247	298	9	)	)	PUNCT
ejpam-6247	298	10	.	.	PUNCT
ejpam-6247	299	1	thenq	thenq	NOUN
ejpam-6247	299	2	∈	∈	PROPN
ejpam-6247	299	3	jm(µ	jm(µ	PROPN
ejpam-6247	299	4	)	)	PUNCT
ejpam-6247	300	1	⇔	⇔	PROPN
ejpam-6247	300	2	µ	µ	X
ejpam-6247	300	3	/∈	/∈	PUNCT
ejpam-6247	300	4	q	q	PROPN
ejpam-6247	300	5	⇔	⇔	X
ejpam-6247	300	6	(	(	PUNCT
ejpam-6247	300	7	µ,d	µ,d	NOUN
ejpam-6247	300	8	)	)	PUNCT
ejpam-6247	300	9	⊆	⊆	NUM
ejpam-6247	300	10	q	q	PROPN
ejpam-6247	300	11	⇔	⇔	PROPN
ejpam-6247	300	12	q	q	X
ejpam-6247	300	13	∈	∈	PROPN
ejpam-6247	300	14	vm((µ,d	vm((µ,d	NOUN
ejpam-6247	300	15	)	)	PUNCT
ejpam-6247	300	16	)	)	PUNCT
ejpam-6247	300	17	.	.	PUNCT
ejpam-6247	301	1	(	(	PUNCT
ejpam-6247	301	2	4	4	X
ejpam-6247	301	3	)	)	PUNCT
ejpam-6247	301	4	the	the	DET
ejpam-6247	301	5	proof	proof	NOUN
ejpam-6247	301	6	proceeds	proceed	VERB
ejpam-6247	301	7	similarly	similarly	ADV
ejpam-6247	301	8	.	.	PUNCT
ejpam-6247	302	1	the	the	DET
ejpam-6247	302	2	following	follow	VERB
ejpam-6247	302	3	two	two	NUM
ejpam-6247	302	4	theorems	theorem	NOUN
ejpam-6247	302	5	demonstrate	demonstrate	VERB
ejpam-6247	302	6	some	some	DET
ejpam-6247	302	7	topological	topological	ADJ
ejpam-6247	302	8	properties	property	NOUN
ejpam-6247	302	9	of	of	ADP
ejpam-6247	302	10	the	the	DET
ejpam-6247	302	11	space	space	NOUN
ejpam-6247	302	12	specdmf	specdmf	NOUN
ejpam-6247	302	13	(	(	PUNCT
ejpam-6247	302	14	l	l	NOUN
ejpam-6247	302	15	)	)	PUNCT
ejpam-6247	302	16	,	,	PUNCT
ejpam-6247	302	17	which	which	PRON
ejpam-6247	302	18	represents	represent	VERB
ejpam-6247	302	19	the	the	DET
ejpam-6247	302	20	collection	collection	NOUN
ejpam-6247	302	21	of	of	ADP
ejpam-6247	302	22	all	all	DET
ejpam-6247	302	23	minimal	minimal	ADJ
ejpam-6247	302	24	prime	prime	ADJ
ejpam-6247	302	25	d	d	NOUN
ejpam-6247	302	26	-	-	NOUN
ejpam-6247	302	27	filters	filter	NOUN
ejpam-6247	302	28	in	in	ADP
ejpam-6247	302	29	an	an	DET
ejpam-6247	302	30	adl	adl	PROPN
ejpam-6247	302	31	l.	l.	PROPN
ejpam-6247	302	32	theorem	theorem	PROPN
ejpam-6247	302	33	3	3	NUM
ejpam-6247	302	34	.	.	X
ejpam-6247	302	35	for	for	ADP
ejpam-6247	302	36	any	any	DET
ejpam-6247	302	37	adl	adl	PROPN
ejpam-6247	302	38	l	l	PROPN
ejpam-6247	302	39	,	,	PUNCT
ejpam-6247	302	40	the	the	DET
ejpam-6247	302	41	space	space	NOUN
ejpam-6247	302	42	specdmf	specdmf	NOUN
ejpam-6247	302	43	(	(	PUNCT
ejpam-6247	302	44	l	l	NOUN
ejpam-6247	302	45	)	)	PUNCT
ejpam-6247	302	46	is	be	AUX
ejpam-6247	302	47	compact	compact	ADJ
ejpam-6247	302	48	if	if	SCONJ
ejpam-6247	302	49	and	and	CCONJ
ejpam-6247	302	50	only	only	ADV
ejpam-6247	302	51	if	if	SCONJ
ejpam-6247	302	52	for	for	ADP
ejpam-6247	302	53	every	every	DET
ejpam-6247	302	54	filter	filter	NOUN
ejpam-6247	302	55	g	g	NOUN
ejpam-6247	302	56	of	of	ADP
ejpam-6247	302	57	l	l	PROPN
ejpam-6247	302	58	,	,	PUNCT
ejpam-6247	302	59	the	the	DET
ejpam-6247	302	60	condition	condition	NOUN
ejpam-6247	302	61	vm(g	vm(g	PART
ejpam-6247	302	62	)	)	PUNCT
ejpam-6247	303	1	=	=	NOUN
ejpam-6247	303	2	∅	∅	NOUN
ejpam-6247	303	3	implies	imply	VERB
ejpam-6247	303	4	that	that	SCONJ
ejpam-6247	303	5	g	g	PROPN
ejpam-6247	303	6	∩	∩	NOUN
ejpam-6247	303	7	d∞	d∞	PROPN
ejpam-6247	303	8	̸=	̸=	PROPN
ejpam-6247	303	9	∅.	∅.	ADP
ejpam-6247	303	10	proof	proof	NOUN
ejpam-6247	303	11	.	.	PUNCT
ejpam-6247	304	1	assume	assume	VERB
ejpam-6247	304	2	that	that	SCONJ
ejpam-6247	304	3	specdmf	specdmf	NOUN
ejpam-6247	304	4	(	(	PUNCT
ejpam-6247	304	5	l	l	NOUN
ejpam-6247	304	6	)	)	PUNCT
ejpam-6247	304	7	is	be	AUX
ejpam-6247	304	8	compact	compact	ADJ
ejpam-6247	304	9	.	.	PUNCT
ejpam-6247	305	1	let	let	VERB
ejpam-6247	305	2	g	g	PRON
ejpam-6247	305	3	be	be	AUX
ejpam-6247	305	4	a	a	DET
ejpam-6247	305	5	filter	filter	NOUN
ejpam-6247	305	6	of	of	ADP
ejpam-6247	305	7	l	l	NOUN
ejpam-6247	305	8	such	such	ADJ
ejpam-6247	305	9	that	that	SCONJ
ejpam-6247	305	10	vm(g	vm(g	VERB
ejpam-6247	305	11	)	)	PUNCT
ejpam-6247	306	1	=	=	PUNCT
ejpam-6247	306	2	∅.	∅.	NOUN
ejpam-6247	306	3	then	then	ADV
ejpam-6247	306	4	for	for	ADP
ejpam-6247	306	5	every	every	DET
ejpam-6247	306	6	q	q	PROPN
ejpam-6247	306	7	∈	∈	PROPN
ejpam-6247	306	8	specdmf	specdmf	NOUN
ejpam-6247	306	9	(	(	PUNCT
ejpam-6247	306	10	l	l	NOUN
ejpam-6247	306	11	)	)	PUNCT
ejpam-6247	306	12	,	,	PUNCT
ejpam-6247	306	13	g	g	PROPN
ejpam-6247	306	14	is	be	AUX
ejpam-6247	306	15	not	not	PART
ejpam-6247	306	16	a	a	DET
ejpam-6247	306	17	subset	subset	NOUN
ejpam-6247	306	18	of	of	ADP
ejpam-6247	306	19	q.	q.	PROPN
ejpam-6247	306	20	thus	thus	ADV
ejpam-6247	306	21	,	,	PUNCT
ejpam-6247	306	22	specdmf	specdmf	NOUN
ejpam-6247	306	23	(	(	PUNCT
ejpam-6247	306	24	l	l	NOUN
ejpam-6247	306	25	)	)	PUNCT
ejpam-6247	306	26	=	=	SYM
ejpam-6247	306	27	jm(g	jm(g	NOUN
ejpam-6247	306	28	)	)	PUNCT
ejpam-6247	307	1	=	=	NOUN
ejpam-6247	307	2	⋃	⋃	NOUN
ejpam-6247	307	3	µ∈g	µ∈g	ADJ
ejpam-6247	307	4	jm(µ	jm(µ	NOUN
ejpam-6247	307	5	)	)	PUNCT
ejpam-6247	307	6	.	.	PUNCT
ejpam-6247	308	1	since	since	SCONJ
ejpam-6247	308	2	specdmf	specdmf	NOUN
ejpam-6247	308	3	(	(	PUNCT
ejpam-6247	308	4	l	l	NOUN
ejpam-6247	308	5	)	)	PUNCT
ejpam-6247	308	6	is	be	AUX
ejpam-6247	308	7	compact	compact	ADJ
ejpam-6247	308	8	,	,	PUNCT
ejpam-6247	308	9	there	there	PRON
ejpam-6247	308	10	exists	exist	VERB
ejpam-6247	308	11	θ	θ	PROPN
ejpam-6247	308	12	∈	∈	PROPN
ejpam-6247	308	13	g	g	PROPN
ejpam-6247	308	14	such	such	ADJ
ejpam-6247	308	15	that	that	DET
ejpam-6247	308	16	specdmf	specdmf	NOUN
ejpam-6247	308	17	(	(	PUNCT
ejpam-6247	308	18	l	l	NOUN
ejpam-6247	308	19	)	)	PUNCT
ejpam-6247	308	20	=	=	SYM
ejpam-6247	308	21	jm(θ	jm(θ	NOUN
ejpam-6247	308	22	)	)	PUNCT
ejpam-6247	308	23	.	.	PUNCT
ejpam-6247	309	1	by	by	ADP
ejpam-6247	309	2	lemma	lemma	PROPN
ejpam-6247	309	3	3	3	NUM
ejpam-6247	309	4	(	(	PUNCT
ejpam-6247	309	5	6	6	NUM
ejpam-6247	309	6	)	)	PUNCT
ejpam-6247	309	7	,	,	PUNCT
ejpam-6247	309	8	we	we	PRON
ejpam-6247	309	9	deduce	deduce	VERB
ejpam-6247	309	10	that	that	SCONJ
ejpam-6247	309	11	θ	θ	PROPN
ejpam-6247	309	12	∈	∈	PROPN
ejpam-6247	310	1	d∞.	d∞.	INTJ
ejpam-6247	310	2	therefore	therefore	ADV
ejpam-6247	310	3	,	,	PUNCT
ejpam-6247	310	4	g	g	PROPN
ejpam-6247	310	5	∩	∩	NOUN
ejpam-6247	310	6	d∞	d∞	PROPN
ejpam-6247	310	7	̸=	̸=	PROPN
ejpam-6247	310	8	∅.	∅.	ADV
ejpam-6247	310	9	conversely	conversely	ADV
ejpam-6247	310	10	,	,	PUNCT
ejpam-6247	310	11	assume	assume	VERB
ejpam-6247	310	12	that	that	SCONJ
ejpam-6247	310	13	for	for	ADP
ejpam-6247	310	14	every	every	DET
ejpam-6247	310	15	d	d	NOUN
ejpam-6247	310	16	-	-	NOUN
ejpam-6247	310	17	filter	filter	NOUN
ejpam-6247	310	18	g	g	NOUN
ejpam-6247	310	19	of	of	ADP
ejpam-6247	310	20	l	l	NOUN
ejpam-6247	310	21	,	,	PUNCT
ejpam-6247	310	22	if	if	SCONJ
ejpam-6247	310	23	vm(g	vm(g	VERB
ejpam-6247	310	24	)	)	PUNCT
ejpam-6247	310	25	=	=	SYM
ejpam-6247	310	26	∅	∅	NOUN
ejpam-6247	310	27	,	,	PUNCT
ejpam-6247	310	28	then	then	ADV
ejpam-6247	310	29	g	g	NOUN
ejpam-6247	310	30	∩d∞	∩d∞	PUNCT
ejpam-6247	310	31	̸=	̸=	PROPN
ejpam-6247	310	32	∅.	∅.	ADV
ejpam-6247	310	33	let	let	VERB
ejpam-6247	310	34	h	h	PRON
ejpam-6247	310	35	⊆	⊆	NUM
ejpam-6247	310	36	l	l	NOUN
ejpam-6247	310	37	be	be	VERB
ejpam-6247	310	38	such	such	ADJ
ejpam-6247	310	39	that	that	DET
ejpam-6247	310	40	specdmf	specdmf	NOUN
ejpam-6247	310	41	(	(	PUNCT
ejpam-6247	310	42	l	l	NOUN
ejpam-6247	310	43	)	)	PUNCT
ejpam-6247	310	44	=	=	SYM
ejpam-6247	310	45	⋃	⋃	NOUN
ejpam-6247	310	46	θ∈h	θ∈h	ADJ
ejpam-6247	310	47	jm(θ	jm(θ	NOUN
ejpam-6247	310	48	)	)	PUNCT
ejpam-6247	310	49	=	=	SYM
ejpam-6247	310	50	jm(h	jm(h	NUM
ejpam-6247	310	51	)	)	PUNCT
ejpam-6247	310	52	=	=	SYM
ejpam-6247	310	53	jm(g	jm(g	PROPN
ejpam-6247	310	54	)	)	PUNCT
ejpam-6247	310	55	,	,	PUNCT
ejpam-6247	310	56	where	where	SCONJ
ejpam-6247	310	57	g	g	PROPN
ejpam-6247	310	58	is	be	AUX
ejpam-6247	310	59	the	the	DET
ejpam-6247	310	60	d	d	ADJ
ejpam-6247	310	61	-	-	NOUN
ejpam-6247	310	62	filter	filter	NOUN
ejpam-6247	310	63	generated	generate	VERB
ejpam-6247	310	64	by	by	ADP
ejpam-6247	310	65	h.	h.	PROPN
ejpam-6247	310	66	now	now	ADV
ejpam-6247	310	67	,	,	PUNCT
ejpam-6247	310	68	choose	choose	VERB
ejpam-6247	310	69	σ	σ	NUM
ejpam-6247	310	70	∈	∈	PROPN
ejpam-6247	310	71	g	g	PROPN
ejpam-6247	311	1	∩d∞.	∩d∞.	PROPN
ejpam-6247	311	2	then	then	ADV
ejpam-6247	311	3	,	,	PUNCT
ejpam-6247	311	4	we	we	PRON
ejpam-6247	311	5	can	can	AUX
ejpam-6247	311	6	express	express	VERB
ejpam-6247	311	7	σ	σ	X
ejpam-6247	311	8	=	=	PUNCT
ejpam-6247	311	9	n∧	n∧	PROPN
ejpam-6247	311	10	i=1	i=1	PROPN
ejpam-6247	311	11	θi	θi	NOUN
ejpam-6247	311	12	for	for	ADP
ejpam-6247	311	13	some	some	DET
ejpam-6247	311	14	θ1	θ1	NOUN
ejpam-6247	311	15	,	,	PUNCT
ejpam-6247	311	16	θ2	θ2	PROPN
ejpam-6247	311	17	,	,	PUNCT
ejpam-6247	311	18	.	.	PUNCT
ejpam-6247	311	19	.	.	PUNCT
ejpam-6247	311	20	.	.	PUNCT
ejpam-6247	312	1	,	,	PUNCT
ejpam-6247	312	2	θn	θn	PROPN
ejpam-6247	312	3	∈	∈	PROPN
ejpam-6247	312	4	h	h	NOUN
ejpam-6247	312	5	and	and	CCONJ
ejpam-6247	312	6	n	n	CCONJ
ejpam-6247	312	7	∈	∈	PROPN
ejpam-6247	312	8	n.	n.	NOUN
ejpam-6247	312	9	hence	hence	ADV
ejpam-6247	312	10	,	,	PUNCT
ejpam-6247	312	11	by	by	ADP
ejpam-6247	312	12	lemma	lemma	PROPN
ejpam-6247	312	13	3	3	NUM
ejpam-6247	312	14	(	(	PUNCT
ejpam-6247	312	15	6	6	NUM
ejpam-6247	312	16	)	)	PUNCT
ejpam-6247	312	17	,	,	PUNCT
ejpam-6247	312	18	we	we	PRON
ejpam-6247	312	19	obtain	obtain	VERB
ejpam-6247	312	20	specdmf	specdmf	NOUN
ejpam-6247	312	21	(	(	PUNCT
ejpam-6247	312	22	l	l	NOUN
ejpam-6247	312	23	)	)	PUNCT
ejpam-6247	312	24	=	=	PUNCT
ejpam-6247	312	25	jm(σ	jm(σ	PRON
ejpam-6247	312	26	)	)	PUNCT
ejpam-6247	313	1	=	=	PUNCT
ejpam-6247	314	1	jm	jm	PROPN
ejpam-6247	314	2	(	(	PUNCT
ejpam-6247	314	3	n∧	n∧	PROPN
ejpam-6247	314	4	i=1	i=1	PROPN
ejpam-6247	314	5	θi	θi	PROPN
ejpam-6247	314	6	)	)	PUNCT
ejpam-6247	314	7	⊆	⊆	NUM
ejpam-6247	314	8	n⋃	n⋃	X
ejpam-6247	314	9	i=1	i=1	PROPN
ejpam-6247	314	10	jm(θi	jm(θi	PROPN
ejpam-6247	314	11	)	)	PUNCT
ejpam-6247	314	12	.	.	PUNCT
ejpam-6247	315	1	this	this	PRON
ejpam-6247	315	2	proves	prove	VERB
ejpam-6247	315	3	that	that	PRON
ejpam-6247	315	4	specdmf	specdmf	NOUN
ejpam-6247	315	5	(	(	PUNCT
ejpam-6247	315	6	l	l	NOUN
ejpam-6247	315	7	)	)	PUNCT
ejpam-6247	315	8	is	be	AUX
ejpam-6247	315	9	compact	compact	ADJ
ejpam-6247	315	10	.	.	PUNCT
ejpam-6247	316	1	theorem	theorem	ADJ
ejpam-6247	316	2	4	4	NUM
ejpam-6247	316	3	.	.	X
ejpam-6247	317	1	for	for	ADP
ejpam-6247	317	2	any	any	DET
ejpam-6247	317	3	adl	adl	PROPN
ejpam-6247	317	4	l	l	PROPN
ejpam-6247	317	5	,	,	PUNCT
ejpam-6247	317	6	specdmf	specdmf	NOUN
ejpam-6247	317	7	(	(	PUNCT
ejpam-6247	317	8	l	l	NOUN
ejpam-6247	317	9	)	)	PUNCT
ejpam-6247	317	10	is	be	AUX
ejpam-6247	317	11	a	a	DET
ejpam-6247	317	12	hausdorff	hausdorff	NOUN
ejpam-6247	317	13	space	space	NOUN
ejpam-6247	317	14	.	.	PUNCT
ejpam-6247	318	1	proof	proof	NOUN
ejpam-6247	318	2	.	.	PUNCT
ejpam-6247	319	1	let	let	VERB
ejpam-6247	319	2	q	q	NOUN
ejpam-6247	320	1	and	and	CCONJ
ejpam-6247	320	2	p	p	NOUN
ejpam-6247	320	3	be	be	AUX
ejpam-6247	320	4	two	two	NUM
ejpam-6247	320	5	distinct	distinct	ADJ
ejpam-6247	320	6	elements	element	NOUN
ejpam-6247	320	7	of	of	ADP
ejpam-6247	320	8	specdmf	specdmf	NOUN
ejpam-6247	320	9	(	(	PUNCT
ejpam-6247	320	10	l	l	NOUN
ejpam-6247	320	11	)	)	PUNCT
ejpam-6247	320	12	.	.	PUNCT
ejpam-6247	321	1	choose	choose	VERB
ejpam-6247	321	2	µ	µ	PRON
ejpam-6247	321	3	∈	∈	NOUN
ejpam-6247	321	4	l	l	NOUN
ejpam-6247	321	5	such	such	ADJ
ejpam-6247	321	6	that	that	SCONJ
ejpam-6247	321	7	µ	µ	PROPN
ejpam-6247	321	8	∈	∈	X
ejpam-6247	321	9	q	q	NOUN
ejpam-6247	321	10	and	and	CCONJ
ejpam-6247	321	11	µ	µ	NOUN
ejpam-6247	321	12	/∈	/∈	PUNCT
ejpam-6247	322	1	p.	p.	NOUN
ejpam-6247	322	2	this	this	PRON
ejpam-6247	322	3	implies	imply	VERB
ejpam-6247	322	4	that	that	SCONJ
ejpam-6247	322	5	p	p	PROPN
ejpam-6247	322	6	∈	∈	PROPN
ejpam-6247	322	7	jm(µ	jm(µ	NOUN
ejpam-6247	322	8	)	)	PUNCT
ejpam-6247	322	9	.	.	PUNCT
ejpam-6247	323	1	since	since	SCONJ
ejpam-6247	323	2	µ	µ	NOUN
ejpam-6247	323	3	∈	∈	PROPN
ejpam-6247	323	4	q	q	NOUN
ejpam-6247	323	5	and	and	CCONJ
ejpam-6247	323	6	q	q	NOUN
ejpam-6247	323	7	is	be	AUX
ejpam-6247	323	8	minimal	minimal	ADJ
ejpam-6247	323	9	,	,	PUNCT
ejpam-6247	323	10	there	there	PRON
ejpam-6247	323	11	exists	exist	VERB
ejpam-6247	323	12	π	π	PROPN
ejpam-6247	323	13	/∈	/∈	PUNCT
ejpam-6247	324	1	q	q	NOUN
ejpam-6247	324	2	such	such	ADJ
ejpam-6247	324	3	that	that	SCONJ
ejpam-6247	324	4	µ	µ	PROPN
ejpam-6247	324	5	∨	∨	NOUN
ejpam-6247	324	6	π	π	PROPN
ejpam-6247	324	7	∈	∈	PROPN
ejpam-6247	324	8	d.	d.	PROPN
ejpam-6247	324	9	thus	thus	ADV
ejpam-6247	324	10	,	,	PUNCT
ejpam-6247	324	11	q	q	PROPN
ejpam-6247	324	12	∈	∈	PROPN
ejpam-6247	324	13	jm(π	jm(π	ADV
ejpam-6247	324	14	)	)	PUNCT
ejpam-6247	324	15	and	and	CCONJ
ejpam-6247	324	16	also	also	ADV
ejpam-6247	324	17	jm(µ	jm(µ	NOUN
ejpam-6247	324	18	)	)	PUNCT
ejpam-6247	324	19	∩	∩	NOUN
ejpam-6247	324	20	jm(π	jm(π	PUNCT
ejpam-6247	324	21	)	)	PUNCT
ejpam-6247	325	1	=	=	SYM
ejpam-6247	325	2	jm(µ	jm(µ	PUNCT
ejpam-6247	325	3	∨	∨	NUM
ejpam-6247	325	4	π	π	NOUN
ejpam-6247	325	5	)	)	PUNCT
ejpam-6247	325	6	=	=	PUNCT
ejpam-6247	325	7	∅	∅	NOUN
ejpam-6247	325	8	due	due	ADJ
ejpam-6247	325	9	to	to	ADP
ejpam-6247	325	10	lemma	lemma	PROPN
ejpam-6247	325	11	3	3	NUM
ejpam-6247	325	12	(	(	PUNCT
ejpam-6247	325	13	5	5	NUM
ejpam-6247	325	14	)	)	PUNCT
ejpam-6247	325	15	.	.	PUNCT
ejpam-6247	326	1	hence	hence	ADV
ejpam-6247	326	2	,	,	PUNCT
ejpam-6247	326	3	specdmf	specdmf	NOUN
ejpam-6247	326	4	(	(	PUNCT
ejpam-6247	326	5	l	l	NOUN
ejpam-6247	326	6	)	)	PUNCT
ejpam-6247	326	7	is	be	AUX
ejpam-6247	326	8	a	a	DET
ejpam-6247	326	9	hausdorff	hausdorff	NOUN
ejpam-6247	326	10	space	space	NOUN
ejpam-6247	326	11	.	.	PUNCT
ejpam-6247	327	1	n.	n.	PROPN
ejpam-6247	327	2	rafi	rafi	PROPN
ejpam-6247	327	3	et	et	PROPN
ejpam-6247	327	4	al	al	PROPN
ejpam-6247	327	5	.	.	PUNCT
ejpam-6247	327	6	/	/	SYM
ejpam-6247	327	7	eur	eur	PROPN
ejpam-6247	327	8	.	.	PUNCT
ejpam-6247	328	1	j.	j.	PROPN
ejpam-6247	328	2	pure	pure	PROPN
ejpam-6247	328	3	appl	appl	PROPN
ejpam-6247	328	4	.	.	PROPN
ejpam-6247	328	5	math	math	PROPN
ejpam-6247	328	6	,	,	PUNCT
ejpam-6247	328	7	18	18	NUM
ejpam-6247	328	8	(	(	PUNCT
ejpam-6247	328	9	3	3	NUM
ejpam-6247	328	10	)	)	PUNCT
ejpam-6247	328	11	(	(	PUNCT
ejpam-6247	328	12	2025	2025	NUM
ejpam-6247	328	13	)	)	PUNCT
ejpam-6247	328	14	,	,	PUNCT
ejpam-6247	328	15	6247	6247	NUM
ejpam-6247	328	16	11	11	NUM
ejpam-6247	328	17	of	of	ADP
ejpam-6247	328	18	15	15	NUM
ejpam-6247	328	19	in	in	ADP
ejpam-6247	328	20	the	the	DET
ejpam-6247	328	21	following	following	NOUN
ejpam-6247	328	22	theorem	theorem	NOUN
ejpam-6247	328	23	,	,	PUNCT
ejpam-6247	328	24	a	a	DET
ejpam-6247	328	25	set	set	NOUN
ejpam-6247	328	26	of	of	ADP
ejpam-6247	328	27	equivalent	equivalent	ADJ
ejpam-6247	328	28	conditions	condition	NOUN
ejpam-6247	328	29	is	be	AUX
ejpam-6247	328	30	derived	derive	VERB
ejpam-6247	328	31	for	for	SCONJ
ejpam-6247	328	32	an	an	DET
ejpam-6247	328	33	adl	adl	NOUN
ejpam-6247	328	34	to	to	PART
ejpam-6247	328	35	be	be	AUX
ejpam-6247	328	36	classified	classify	VERB
ejpam-6247	328	37	as	as	ADP
ejpam-6247	328	38	hemicomplemented	hemicomplemente	VERB
ejpam-6247	328	39	,	,	PUNCT
ejpam-6247	328	40	which	which	PRON
ejpam-6247	328	41	subsequently	subsequently	ADV
ejpam-6247	328	42	leads	lead	VERB
ejpam-6247	328	43	to	to	ADP
ejpam-6247	328	44	a	a	DET
ejpam-6247	328	45	topological	topological	ADJ
ejpam-6247	328	46	characterization	characterization	NOUN
ejpam-6247	328	47	.	.	PUNCT
ejpam-6247	329	1	theorem	theorem	NOUN
ejpam-6247	329	2	5	5	NUM
ejpam-6247	329	3	.	.	PUNCT
ejpam-6247	330	1	the	the	DET
ejpam-6247	330	2	equivalence	equivalence	NOUN
ejpam-6247	330	3	of	of	ADP
ejpam-6247	330	4	the	the	DET
ejpam-6247	330	5	following	follow	VERB
ejpam-6247	330	6	conditions	condition	NOUN
ejpam-6247	330	7	holds	hold	VERB
ejpam-6247	330	8	in	in	ADP
ejpam-6247	330	9	an	an	DET
ejpam-6247	330	10	adl	adl	NOUN
ejpam-6247	330	11	l	l	NOUN
ejpam-6247	330	12	:	:	PUNCT
ejpam-6247	330	13	(	(	PUNCT
ejpam-6247	330	14	1	1	X
ejpam-6247	330	15	)	)	PUNCT
ejpam-6247	330	16	l	l	NOUN
ejpam-6247	330	17	is	be	AUX
ejpam-6247	330	18	hemicomplemented	hemicomplemente	VERB
ejpam-6247	330	19	,	,	PUNCT
ejpam-6247	330	20	(	(	PUNCT
ejpam-6247	330	21	2	2	NUM
ejpam-6247	330	22	)	)	PUNCT
ejpam-6247	330	23	for	for	ADP
ejpam-6247	330	24	each	each	DET
ejpam-6247	330	25	µ	µ	PROPN
ejpam-6247	330	26	∈	∈	PROPN
ejpam-6247	330	27	l	l	NOUN
ejpam-6247	330	28	,	,	PUNCT
ejpam-6247	330	29	there	there	PRON
ejpam-6247	330	30	exists	exist	VERB
ejpam-6247	330	31	π	π	PROPN
ejpam-6247	330	32	∈	∈	PROPN
ejpam-6247	330	33	l	l	NOUN
ejpam-6247	330	34	such	such	ADJ
ejpam-6247	330	35	that	that	DET
ejpam-6247	330	36	vm(µ	vm(µ	NOUN
ejpam-6247	330	37	)	)	PUNCT
ejpam-6247	330	38	=	=	PUNCT
ejpam-6247	330	39	jm(π	jm(π	NOUN
ejpam-6247	330	40	)	)	PUNCT
ejpam-6247	330	41	,	,	PUNCT
ejpam-6247	330	42	(	(	PUNCT
ejpam-6247	330	43	3	3	X
ejpam-6247	330	44	)	)	PUNCT
ejpam-6247	330	45	for	for	ADP
ejpam-6247	330	46	each	each	DET
ejpam-6247	330	47	µ	µ	PROPN
ejpam-6247	330	48	∈	∈	PROPN
ejpam-6247	330	49	l	l	NOUN
ejpam-6247	330	50	,	,	PUNCT
ejpam-6247	330	51	there	there	PRON
ejpam-6247	330	52	exists	exist	VERB
ejpam-6247	330	53	π	π	PROPN
ejpam-6247	330	54	∈	∈	PROPN
ejpam-6247	330	55	l	l	NOUN
ejpam-6247	330	56	such	such	ADJ
ejpam-6247	330	57	that	that	DET
ejpam-6247	330	58	jm(µ	jm(µ	NOUN
ejpam-6247	330	59	)	)	PUNCT
ejpam-6247	331	1	=	=	SYM
ejpam-6247	331	2	jm((π	jm((π	PROPN
ejpam-6247	331	3	,	,	PUNCT
ejpam-6247	331	4	d	d	NOUN
ejpam-6247	331	5	)	)	PUNCT
ejpam-6247	331	6	)	)	PUNCT
ejpam-6247	331	7	.	.	PUNCT
ejpam-6247	332	1	proof	proof	NOUN
ejpam-6247	332	2	.	.	PUNCT
ejpam-6247	333	1	(	(	PUNCT
ejpam-6247	333	2	1	1	X
ejpam-6247	333	3	)	)	PUNCT
ejpam-6247	333	4	⇒	⇒	NOUN
ejpam-6247	333	5	(	(	PUNCT
ejpam-6247	333	6	2	2	NUM
ejpam-6247	333	7	)	)	PUNCT
ejpam-6247	333	8	:	:	PUNCT
ejpam-6247	333	9	assume	assume	VERB
ejpam-6247	333	10	(	(	PUNCT
ejpam-6247	333	11	1	1	NUM
ejpam-6247	333	12	)	)	PUNCT
ejpam-6247	333	13	.	.	PUNCT
ejpam-6247	334	1	let	let	VERB
ejpam-6247	334	2	µ	µ	X
ejpam-6247	334	3	∈	∈	PROPN
ejpam-6247	334	4	l.	l.	NOUN
ejpam-6247	334	5	then	then	ADV
ejpam-6247	334	6	there	there	PRON
ejpam-6247	334	7	is	be	VERB
ejpam-6247	334	8	π	π	PROPN
ejpam-6247	334	9	∈	∈	PROPN
ejpam-6247	334	10	l	l	NOUN
ejpam-6247	334	11	such	such	ADJ
ejpam-6247	334	12	that	that	SCONJ
ejpam-6247	334	13	(	(	PUNCT
ejpam-6247	334	14	µ,d	µ,d	NOUN
ejpam-6247	334	15	)	)	PUNCT
ejpam-6247	334	16	=	=	SYM
ejpam-6247	334	17	(	(	PUNCT
ejpam-6247	334	18	(	(	PUNCT
ejpam-6247	334	19	π	π	PROPN
ejpam-6247	334	20	,	,	PUNCT
ejpam-6247	334	21	d),d	d),d	PROPN
ejpam-6247	334	22	)	)	PUNCT
ejpam-6247	334	23	.	.	PUNCT
ejpam-6247	335	1	by	by	ADP
ejpam-6247	335	2	lemma	lemma	PROPN
ejpam-6247	335	3	3	3	NUM
ejpam-6247	335	4	(	(	PUNCT
ejpam-6247	335	5	6	6	NUM
ejpam-6247	335	6	)	)	PUNCT
ejpam-6247	335	7	and	and	CCONJ
ejpam-6247	335	8	lemma	lemma	PROPN
ejpam-6247	335	9	4	4	NUM
ejpam-6247	335	10	(	(	PUNCT
ejpam-6247	335	11	4	4	NUM
ejpam-6247	335	12	)	)	PUNCT
ejpam-6247	335	13	,	,	PUNCT
ejpam-6247	335	14	we	we	PRON
ejpam-6247	335	15	obtain	obtain	VERB
ejpam-6247	335	16	vm(µ	vm(µ	NOUN
ejpam-6247	335	17	)	)	PUNCT
ejpam-6247	335	18	=	=	SYM
ejpam-6247	335	19	jm((µ,d	jm((µ,d	NOUN
ejpam-6247	335	20	)	)	PUNCT
ejpam-6247	335	21	)	)	PUNCT
ejpam-6247	336	1	=	=	SYM
ejpam-6247	336	2	jm((π	jm((π	PROPN
ejpam-6247	336	3	,	,	PUNCT
ejpam-6247	336	4	d),d	d),d	PROPN
ejpam-6247	336	5	)	)	PUNCT
ejpam-6247	336	6	=	=	PUNCT
ejpam-6247	336	7	jm(π	jm(π	NUM
ejpam-6247	336	8	)	)	PUNCT
ejpam-6247	336	9	.	.	PUNCT
ejpam-6247	337	1	(	(	PUNCT
ejpam-6247	337	2	2	2	X
ejpam-6247	337	3	)	)	PUNCT
ejpam-6247	337	4	⇒	⇒	NOUN
ejpam-6247	337	5	(	(	PUNCT
ejpam-6247	337	6	3	3	NUM
ejpam-6247	337	7	)	)	PUNCT
ejpam-6247	337	8	:	:	PUNCT
ejpam-6247	337	9	assume	assume	VERB
ejpam-6247	337	10	(	(	PUNCT
ejpam-6247	337	11	2	2	NUM
ejpam-6247	337	12	)	)	PUNCT
ejpam-6247	337	13	.	.	PUNCT
ejpam-6247	338	1	let	let	VERB
ejpam-6247	338	2	µ	µ	X
ejpam-6247	338	3	∈	∈	PROPN
ejpam-6247	338	4	l.	l.	NOUN
ejpam-6247	338	5	then	then	ADV
ejpam-6247	338	6	there	there	PRON
ejpam-6247	338	7	is	be	VERB
ejpam-6247	338	8	π	π	PROPN
ejpam-6247	338	9	∈	∈	PROPN
ejpam-6247	338	10	l	l	NOUN
ejpam-6247	338	11	such	such	ADJ
ejpam-6247	338	12	that	that	DET
ejpam-6247	338	13	jm(µ	jm(µ	NOUN
ejpam-6247	338	14	)	)	PUNCT
ejpam-6247	338	15	=	=	PUNCT
ejpam-6247	338	16	vm(π	vm(π	NUM
ejpam-6247	338	17	)	)	PUNCT
ejpam-6247	338	18	.	.	PUNCT
ejpam-6247	339	1	by	by	ADP
ejpam-6247	339	2	lemma	lemma	PROPN
ejpam-6247	339	3	3	3	NUM
ejpam-6247	339	4	(	(	PUNCT
ejpam-6247	339	5	6	6	NUM
ejpam-6247	339	6	)	)	PUNCT
ejpam-6247	339	7	,	,	PUNCT
ejpam-6247	339	8	we	we	PRON
ejpam-6247	339	9	obtain	obtain	VERB
ejpam-6247	339	10	vm(π	vm(π	NOUN
ejpam-6247	339	11	)	)	PUNCT
ejpam-6247	340	1	=	=	SYM
ejpam-6247	340	2	jm((π	jm((π	PROPN
ejpam-6247	340	3	,	,	PUNCT
ejpam-6247	340	4	d	d	NOUN
ejpam-6247	340	5	)	)	PUNCT
ejpam-6247	340	6	)	)	PUNCT
ejpam-6247	340	7	.	.	PUNCT
ejpam-6247	341	1	thus	thus	ADV
ejpam-6247	341	2	,	,	PUNCT
ejpam-6247	341	3	jm(µ	jm(µ	NOUN
ejpam-6247	341	4	)	)	PUNCT
ejpam-6247	342	1	=	=	SYM
ejpam-6247	342	2	jm((π	jm((π	PROPN
ejpam-6247	342	3	,	,	PUNCT
ejpam-6247	342	4	d	d	NOUN
ejpam-6247	342	5	)	)	PUNCT
ejpam-6247	342	6	)	)	PUNCT
ejpam-6247	342	7	.	.	PUNCT
ejpam-6247	343	1	(	(	PUNCT
ejpam-6247	343	2	3	3	X
ejpam-6247	343	3	)	)	PUNCT
ejpam-6247	343	4	⇒	⇒	NOUN
ejpam-6247	343	5	(	(	PUNCT
ejpam-6247	343	6	1	1	NUM
ejpam-6247	343	7	)	)	PUNCT
ejpam-6247	343	8	:	:	PUNCT
ejpam-6247	343	9	assume	assume	VERB
ejpam-6247	343	10	(	(	PUNCT
ejpam-6247	343	11	3	3	NUM
ejpam-6247	343	12	)	)	PUNCT
ejpam-6247	343	13	.	.	PUNCT
ejpam-6247	344	1	let	let	VERB
ejpam-6247	344	2	µ	µ	X
ejpam-6247	344	3	∈	∈	X
ejpam-6247	344	4	l.	l.	NOUN
ejpam-6247	344	5	from	from	ADP
ejpam-6247	344	6	condition	condition	NOUN
ejpam-6247	344	7	(	(	PUNCT
ejpam-6247	344	8	3	3	NUM
ejpam-6247	344	9	)	)	PUNCT
ejpam-6247	344	10	,	,	PUNCT
ejpam-6247	344	11	there	there	PRON
ejpam-6247	344	12	exists	exist	VERB
ejpam-6247	344	13	a	a	DET
ejpam-6247	344	14	π	π	PROPN
ejpam-6247	344	15	∈	∈	PROPN
ejpam-6247	344	16	l	l	NOUN
ejpam-6247	344	17	such	such	ADJ
ejpam-6247	344	18	that	that	DET
ejpam-6247	344	19	jm(µ	jm(µ	NOUN
ejpam-6247	344	20	)	)	PUNCT
ejpam-6247	345	1	=	=	SYM
ejpam-6247	345	2	jm((π	jm((π	PROPN
ejpam-6247	345	3	,	,	PUNCT
ejpam-6247	345	4	d	d	NOUN
ejpam-6247	345	5	)	)	PUNCT
ejpam-6247	345	6	)	)	PUNCT
ejpam-6247	345	7	.	.	PUNCT
ejpam-6247	346	1	now	now	ADV
ejpam-6247	346	2	,	,	PUNCT
ejpam-6247	346	3	let	let	VERB
ejpam-6247	346	4	θ	θ	PROPN
ejpam-6247	346	5	/∈	/∈	PUNCT
ejpam-6247	347	1	(	(	PUNCT
ejpam-6247	347	2	π	π	X
ejpam-6247	347	3	,	,	PUNCT
ejpam-6247	347	4	d	d	NOUN
ejpam-6247	347	5	)	)	PUNCT
ejpam-6247	347	6	.	.	PUNCT
ejpam-6247	348	1	since	since	SCONJ
ejpam-6247	348	2	θ	θ	PROPN
ejpam-6247	348	3	∨	∨	PROPN
ejpam-6247	348	4	π	π	PROPN
ejpam-6247	348	5	/∈	/∈	PUNCT
ejpam-6247	349	1	d	d	NOUN
ejpam-6247	349	2	,	,	PUNCT
ejpam-6247	349	3	by	by	ADP
ejpam-6247	349	4	the	the	DET
ejpam-6247	349	5	properties	property	NOUN
ejpam-6247	349	6	of	of	ADP
ejpam-6247	349	7	minimal	minimal	ADJ
ejpam-6247	349	8	prime	prime	ADJ
ejpam-6247	349	9	d	d	NOUN
ejpam-6247	349	10	-	-	PUNCT
ejpam-6247	349	11	filters	filter	NOUN
ejpam-6247	349	12	,	,	PUNCT
ejpam-6247	349	13	there	there	PRON
ejpam-6247	349	14	exists	exist	VERB
ejpam-6247	349	15	a	a	DET
ejpam-6247	349	16	minimal	minimal	ADJ
ejpam-6247	349	17	prime	prime	ADJ
ejpam-6247	349	18	d	d	NOUN
ejpam-6247	349	19	-	-	NOUN
ejpam-6247	349	20	filter	filter	NOUN
ejpam-6247	349	21	q	q	NOUN
ejpam-6247	349	22	such	such	ADJ
ejpam-6247	349	23	that	that	SCONJ
ejpam-6247	349	24	θ	θ	PROPN
ejpam-6247	349	25	∨	∨	NUM
ejpam-6247	349	26	π	π	PROPN
ejpam-6247	349	27	/∈	/∈	PUNCT
ejpam-6247	350	1	q.	q.	PROPN
ejpam-6247	351	1	this	this	PRON
ejpam-6247	351	2	implies	imply	VERB
ejpam-6247	351	3	θ	θ	PROPN
ejpam-6247	351	4	/∈	/∈	PUNCT
ejpam-6247	351	5	q	q	NOUN
ejpam-6247	352	1	and	and	CCONJ
ejpam-6247	352	2	π	π	PROPN
ejpam-6247	352	3	/∈	/∈	PUNCT
ejpam-6247	352	4	q.	q.	PROPN
ejpam-6247	353	1	because	because	SCONJ
ejpam-6247	353	2	π	π	PROPN
ejpam-6247	353	3	/∈	/∈	PUNCT
ejpam-6247	354	1	q	q	INTJ
ejpam-6247	354	2	,	,	PUNCT
ejpam-6247	354	3	we	we	PRON
ejpam-6247	354	4	deduce	deduce	VERB
ejpam-6247	354	5	that	that	SCONJ
ejpam-6247	354	6	(	(	PUNCT
ejpam-6247	354	7	π	π	X
ejpam-6247	354	8	,	,	PUNCT
ejpam-6247	354	9	d	d	NOUN
ejpam-6247	354	10	)	)	PUNCT
ejpam-6247	354	11	⊆	⊆	NUM
ejpam-6247	354	12	q	q	NOUN
ejpam-6247	354	13	,	,	PUNCT
ejpam-6247	354	14	which	which	PRON
ejpam-6247	354	15	means	mean	VERB
ejpam-6247	354	16	q	q	X
ejpam-6247	354	17	/∈	/∈	PUNCT
ejpam-6247	355	1	jm((π	jm((π	PROPN
ejpam-6247	355	2	,	,	PUNCT
ejpam-6247	355	3	d	d	NOUN
ejpam-6247	355	4	)	)	PUNCT
ejpam-6247	355	5	)	)	PUNCT
ejpam-6247	355	6	=	=	SYM
ejpam-6247	355	7	jm(µ	jm(µ	NOUN
ejpam-6247	355	8	)	)	PUNCT
ejpam-6247	355	9	.	.	PUNCT
ejpam-6247	356	1	therefore	therefore	ADV
ejpam-6247	356	2	,	,	PUNCT
ejpam-6247	356	3	we	we	PRON
ejpam-6247	356	4	conclude	conclude	VERB
ejpam-6247	356	5	that	that	SCONJ
ejpam-6247	356	6	µ	µ	PROPN
ejpam-6247	356	7	∈	∈	PROPN
ejpam-6247	356	8	q.	q.	NOUN
ejpam-6247	356	9	since	since	SCONJ
ejpam-6247	356	10	q	q	PROPN
ejpam-6247	356	11	is	be	AUX
ejpam-6247	356	12	minimal	minimal	ADJ
ejpam-6247	356	13	,	,	PUNCT
ejpam-6247	356	14	we	we	PRON
ejpam-6247	356	15	get	get	VERB
ejpam-6247	356	16	(	(	PUNCT
ejpam-6247	356	17	(	(	PUNCT
ejpam-6247	356	18	µ,d),d	µ,d),d	X
ejpam-6247	356	19	)	)	PUNCT
ejpam-6247	356	20	⊆	⊆	NUM
ejpam-6247	356	21	q.	q.	NOUN
ejpam-6247	356	22	as	as	ADP
ejpam-6247	356	23	θ	θ	PROPN
ejpam-6247	356	24	/∈	/∈	PUNCT
ejpam-6247	357	1	q	q	X
ejpam-6247	357	2	,	,	PUNCT
ejpam-6247	357	3	it	it	PRON
ejpam-6247	357	4	follows	follow	VERB
ejpam-6247	357	5	that	that	PRON
ejpam-6247	357	6	θ	θ	PROPN
ejpam-6247	357	7	/∈	/∈	PUNCT
ejpam-6247	358	1	(	(	PUNCT
ejpam-6247	358	2	(	(	PUNCT
ejpam-6247	358	3	µ,d),d	µ,d),d	NOUN
ejpam-6247	358	4	)	)	PUNCT
ejpam-6247	358	5	,	,	PUNCT
ejpam-6247	358	6	so	so	ADV
ejpam-6247	358	7	we	we	PRON
ejpam-6247	358	8	conclude	conclude	VERB
ejpam-6247	358	9	(	(	PUNCT
ejpam-6247	358	10	(	(	PUNCT
ejpam-6247	358	11	µ,d),d	µ,d),d	X
ejpam-6247	358	12	)	)	PUNCT
ejpam-6247	359	1	⊆	⊆	NUM
ejpam-6247	359	2	(	(	PUNCT
ejpam-6247	359	3	π	π	PROPN
ejpam-6247	359	4	,	,	PUNCT
ejpam-6247	359	5	d	d	NOUN
ejpam-6247	359	6	)	)	PUNCT
ejpam-6247	359	7	.	.	PUNCT
ejpam-6247	360	1	by	by	ADP
ejpam-6247	360	2	similar	similar	ADJ
ejpam-6247	360	3	reasoning	reasoning	NOUN
ejpam-6247	360	4	,	,	PUNCT
ejpam-6247	360	5	we	we	PRON
ejpam-6247	360	6	can	can	AUX
ejpam-6247	360	7	also	also	ADV
ejpam-6247	360	8	obtain	obtain	VERB
ejpam-6247	360	9	(	(	PUNCT
ejpam-6247	360	10	π	π	X
ejpam-6247	360	11	,	,	PUNCT
ejpam-6247	360	12	d	d	NOUN
ejpam-6247	360	13	)	)	PUNCT
ejpam-6247	360	14	⊆	⊆	NUM
ejpam-6247	360	15	(	(	PUNCT
ejpam-6247	360	16	(	(	PUNCT
ejpam-6247	360	17	µ,d),d	µ,d),d	NOUN
ejpam-6247	360	18	)	)	PUNCT
ejpam-6247	360	19	.	.	PUNCT
ejpam-6247	361	1	hence	hence	ADV
ejpam-6247	361	2	,	,	PUNCT
ejpam-6247	361	3	we	we	PRON
ejpam-6247	361	4	establish	establish	VERB
ejpam-6247	361	5	that	that	SCONJ
ejpam-6247	361	6	l	l	NOUN
ejpam-6247	361	7	is	be	AUX
ejpam-6247	361	8	hemicomplemented	hemicomplemente	VERB
ejpam-6247	361	9	.	.	PUNCT
ejpam-6247	362	1	it	it	PRON
ejpam-6247	362	2	can	can	AUX
ejpam-6247	362	3	be	be	AUX
ejpam-6247	362	4	easily	easily	ADV
ejpam-6247	362	5	seen	see	VERB
ejpam-6247	362	6	that	that	SCONJ
ejpam-6247	362	7	the	the	DET
ejpam-6247	362	8	collection	collection	NOUN
ejpam-6247	362	9	j	j	PROPN
ejpam-6247	362	10	(	(	PUNCT
ejpam-6247	362	11	l	l	NOUN
ejpam-6247	362	12	)	)	PUNCT
ejpam-6247	362	13	=	=	SYM
ejpam-6247	362	14	{	{	PUNCT
ejpam-6247	362	15	jm(µ	jm(µ	NOUN
ejpam-6247	362	16	)	)	PUNCT
ejpam-6247	362	17	|	|	ADV
ejpam-6247	362	18	µ	µ	X
ejpam-6247	362	19	∈	∈	PROPN
ejpam-6247	362	20	l	l	NOUN
ejpam-6247	362	21	}	}	PUNCT
ejpam-6247	362	22	forms	form	VERB
ejpam-6247	362	23	a	a	DET
ejpam-6247	362	24	distributive	distributive	ADJ
ejpam-6247	362	25	lattice	lattice	NOUN
ejpam-6247	362	26	with	with	ADP
ejpam-6247	362	27	respect	respect	NOUN
ejpam-6247	362	28	to	to	ADP
ejpam-6247	362	29	the	the	DET
ejpam-6247	362	30	set	set	ADJ
ejpam-6247	362	31	operations	operation	NOUN
ejpam-6247	362	32	∩	∩	NOUN
ejpam-6247	362	33	and	and	CCONJ
ejpam-6247	362	34	∪.	∪.	NOUN
ejpam-6247	362	35	however	however	ADV
ejpam-6247	362	36	,	,	PUNCT
ejpam-6247	362	37	in	in	ADP
ejpam-6247	362	38	general	general	ADJ
ejpam-6247	362	39	,	,	PUNCT
ejpam-6247	362	40	⟨{jm(µ	⟨{jm(µ	PROPN
ejpam-6247	362	41	)	)	PUNCT
ejpam-6247	363	1	|	|	ADV
ejpam-6247	363	2	µ	µ	X
ejpam-6247	363	3	∈	∈	NOUN
ejpam-6247	363	4	l},∩,∪⟩	l},∩,∪⟩	NOUN
ejpam-6247	363	5	does	do	AUX
ejpam-6247	363	6	not	not	PART
ejpam-6247	363	7	form	form	VERB
ejpam-6247	363	8	a	a	DET
ejpam-6247	363	9	boolean	boolean	ADJ
ejpam-6247	363	10	algebra	algebra	NOUN
ejpam-6247	363	11	for	for	ADP
ejpam-6247	363	12	an	an	DET
ejpam-6247	363	13	adl	adl	PROPN
ejpam-6247	363	14	l.	l.	NOUN
ejpam-6247	363	15	the	the	DET
ejpam-6247	363	16	next	next	ADJ
ejpam-6247	363	17	theorem	theorem	NOUN
ejpam-6247	363	18	establishes	establish	VERB
ejpam-6247	363	19	a	a	DET
ejpam-6247	363	20	necessary	necessary	ADJ
ejpam-6247	363	21	and	and	CCONJ
ejpam-6247	363	22	sufficient	sufficient	ADJ
ejpam-6247	363	23	condition	condition	NOUN
ejpam-6247	363	24	for	for	ADP
ejpam-6247	363	25	this	this	DET
ejpam-6247	363	26	collection	collection	NOUN
ejpam-6247	363	27	to	to	PART
ejpam-6247	363	28	become	become	VERB
ejpam-6247	363	29	a	a	DET
ejpam-6247	363	30	boolean	boolean	ADJ
ejpam-6247	363	31	algebra	algebra	NOUN
ejpam-6247	363	32	.	.	PUNCT
ejpam-6247	364	1	theorem	theorem	VERB
ejpam-6247	364	2	6	6	NUM
ejpam-6247	364	3	.	.	PUNCT
ejpam-6247	365	1	an	an	DET
ejpam-6247	365	2	adl	adl	PROPN
ejpam-6247	365	3	l	l	NOUN
ejpam-6247	365	4	is	be	AUX
ejpam-6247	365	5	hemicomplemented	hemicomplemente	VERB
ejpam-6247	365	6	if	if	SCONJ
ejpam-6247	365	7	and	and	CCONJ
ejpam-6247	365	8	only	only	ADV
ejpam-6247	365	9	if	if	SCONJ
ejpam-6247	365	10	j	j	PROPN
ejpam-6247	365	11	(	(	PUNCT
ejpam-6247	365	12	l	l	NOUN
ejpam-6247	365	13	)	)	PUNCT
ejpam-6247	365	14	=	=	SYM
ejpam-6247	365	15	⟨{jm(µ	⟨{jm(µ	NOUN
ejpam-6247	365	16	)	)	PUNCT
ejpam-6247	365	17	|	|	ADV
ejpam-6247	365	18	µ	µ	X
ejpam-6247	365	19	∈	∈	NOUN
ejpam-6247	365	20	l},∩,∪⟩	l},∩,∪⟩	NOUN
ejpam-6247	365	21	is	be	AUX
ejpam-6247	365	22	a	a	DET
ejpam-6247	365	23	boolean	boolean	ADJ
ejpam-6247	365	24	algebra	algebra	NOUN
ejpam-6247	365	25	.	.	PUNCT
ejpam-6247	366	1	proof	proof	NOUN
ejpam-6247	366	2	.	.	PUNCT
ejpam-6247	367	1	assume	assume	VERB
ejpam-6247	367	2	l	l	NOUN
ejpam-6247	367	3	is	be	AUX
ejpam-6247	367	4	a	a	DET
ejpam-6247	367	5	hemicomplemented	hemicomplemente	VERB
ejpam-6247	367	6	adl	adl	NOUN
ejpam-6247	367	7	.	.	PUNCT
ejpam-6247	368	1	let	let	VERB
ejpam-6247	368	2	jm(µ	jm(µ	NOUN
ejpam-6247	368	3	)	)	PUNCT
ejpam-6247	369	1	∈	∈	PROPN
ejpam-6247	369	2	j	j	PROPN
ejpam-6247	369	3	(	(	PUNCT
ejpam-6247	369	4	l	l	NOUN
ejpam-6247	369	5	)	)	PUNCT
ejpam-6247	369	6	.	.	PUNCT
ejpam-6247	370	1	then	then	ADV
ejpam-6247	370	2	there	there	PRON
ejpam-6247	370	3	is	be	VERB
ejpam-6247	370	4	π	π	PROPN
ejpam-6247	370	5	∈	∈	PROPN
ejpam-6247	370	6	l	l	NOUN
ejpam-6247	370	7	such	such	ADJ
ejpam-6247	370	8	that	that	DET
ejpam-6247	370	9	µ∨π	µ∨π	NOUN
ejpam-6247	370	10	∈	∈	PROPN
ejpam-6247	370	11	d	d	NOUN
ejpam-6247	370	12	and	and	CCONJ
ejpam-6247	370	13	(	(	PUNCT
ejpam-6247	370	14	µ,d)∩	µ,d)∩	PROPN
ejpam-6247	370	15	(	(	PUNCT
ejpam-6247	370	16	π	π	PROPN
ejpam-6247	370	17	,	,	PUNCT
ejpam-6247	370	18	d	d	NOUN
ejpam-6247	370	19	)	)	PUNCT
ejpam-6247	370	20	=	=	SYM
ejpam-6247	370	21	(	(	PUNCT
ejpam-6247	370	22	µ∧π	µ∧π	PROPN
ejpam-6247	370	23	,	,	PUNCT
ejpam-6247	370	24	d	d	NOUN
ejpam-6247	370	25	)	)	PUNCT
ejpam-6247	370	26	=	=	SYM
ejpam-6247	370	27	d.	d.	PROPN
ejpam-6247	370	28	hence	hence	ADV
ejpam-6247	370	29	,	,	PUNCT
ejpam-6247	370	30	jm(µ)∩jm(π	jm(µ)∩jm(π	PROPN
ejpam-6247	370	31	)	)	PUNCT
ejpam-6247	371	1	=	=	SYM
ejpam-6247	371	2	jm(µ	jm(µ	PUNCT
ejpam-6247	371	3	∨	∨	NUM
ejpam-6247	371	4	π	π	X
ejpam-6247	371	5	)	)	PUNCT
ejpam-6247	372	1	=	=	PUNCT
ejpam-6247	372	2	∅.	∅.	NOUN
ejpam-6247	372	3	also	also	ADV
ejpam-6247	372	4	jm(µ	jm(µ	NOUN
ejpam-6247	372	5	)	)	PUNCT
ejpam-6247	372	6	∪	∪	ADP
ejpam-6247	372	7	jm(π	jm(π	NOUN
ejpam-6247	372	8	)	)	PUNCT
ejpam-6247	372	9	=	=	SYM
ejpam-6247	372	10	vm((µ,d	vm((µ,d	NOUN
ejpam-6247	372	11	)	)	PUNCT
ejpam-6247	372	12	)	)	PUNCT
ejpam-6247	372	13	∪	∪	ADP
ejpam-6247	372	14	vm((π	vm((π	NOUN
ejpam-6247	372	15	,	,	PUNCT
ejpam-6247	372	16	d	d	NOUN
ejpam-6247	372	17	)	)	PUNCT
ejpam-6247	372	18	)	)	PUNCT
ejpam-6247	373	1	=	=	SYM
ejpam-6247	373	2	vm((µ,d	vm((µ,d	ADJ
ejpam-6247	373	3	)	)	PUNCT
ejpam-6247	373	4	∩	∩	NOUN
ejpam-6247	373	5	(	(	PUNCT
ejpam-6247	373	6	π	π	X
ejpam-6247	373	7	,	,	PUNCT
ejpam-6247	373	8	d	d	NOUN
ejpam-6247	373	9	)	)	PUNCT
ejpam-6247	373	10	)	)	PUNCT
ejpam-6247	373	11	=	=	SYM
ejpam-6247	373	12	vm(d	vm(d	NUM
ejpam-6247	373	13	)	)	PUNCT
ejpam-6247	373	14	=	=	SYM
ejpam-6247	373	15	specdmf	specdmf	NOUN
ejpam-6247	373	16	(	(	PUNCT
ejpam-6247	373	17	l	l	NOUN
ejpam-6247	373	18	)	)	PUNCT
ejpam-6247	373	19	.	.	PUNCT
ejpam-6247	374	1	hence	hence	ADV
ejpam-6247	374	2	,	,	PUNCT
ejpam-6247	374	3	jm(π	jm(π	PROPN
ejpam-6247	374	4	)	)	PUNCT
ejpam-6247	374	5	is	be	AUX
ejpam-6247	374	6	the	the	DET
ejpam-6247	374	7	complement	complement	NOUN
ejpam-6247	374	8	of	of	ADP
ejpam-6247	374	9	jm(µ	jm(µ	NOUN
ejpam-6247	374	10	)	)	PUNCT
ejpam-6247	374	11	in	in	ADP
ejpam-6247	374	12	j	j	PROPN
ejpam-6247	374	13	(	(	PUNCT
ejpam-6247	374	14	l	l	NOUN
ejpam-6247	374	15	)	)	PUNCT
ejpam-6247	374	16	.	.	PUNCT
ejpam-6247	375	1	thus	thus	ADV
ejpam-6247	375	2	j	j	PROPN
ejpam-6247	375	3	(	(	PUNCT
ejpam-6247	375	4	l	l	NOUN
ejpam-6247	375	5	)	)	PUNCT
ejpam-6247	375	6	is	be	AUX
ejpam-6247	375	7	a	a	DET
ejpam-6247	375	8	boolean	boolean	ADJ
ejpam-6247	375	9	algebra	algebra	NOUN
ejpam-6247	375	10	.	.	PUNCT
ejpam-6247	376	1	conversely	conversely	ADV
ejpam-6247	376	2	,	,	PUNCT
ejpam-6247	376	3	assume	assume	VERB
ejpam-6247	376	4	that	that	SCONJ
ejpam-6247	376	5	j	j	PROPN
ejpam-6247	376	6	(	(	PUNCT
ejpam-6247	376	7	l	l	NOUN
ejpam-6247	376	8	)	)	PUNCT
ejpam-6247	376	9	is	be	AUX
ejpam-6247	376	10	a	a	DET
ejpam-6247	376	11	boolean	boolean	ADJ
ejpam-6247	376	12	algebra	algebra	NOUN
ejpam-6247	376	13	.	.	PUNCT
ejpam-6247	377	1	let	let	VERB
ejpam-6247	377	2	µ	µ	X
ejpam-6247	377	3	∈	∈	PROPN
ejpam-6247	377	4	l.	l.	NOUN
ejpam-6247	377	5	then	then	ADV
ejpam-6247	377	6	jm(µ	jm(µ	PUNCT
ejpam-6247	377	7	)	)	PUNCT
ejpam-6247	378	1	∈	∈	PROPN
ejpam-6247	378	2	j	j	PROPN
ejpam-6247	378	3	(	(	PUNCT
ejpam-6247	378	4	l	l	NOUN
ejpam-6247	378	5	)	)	PUNCT
ejpam-6247	378	6	.	.	PUNCT
ejpam-6247	379	1	then	then	ADV
ejpam-6247	379	2	there	there	PRON
ejpam-6247	379	3	exists	exist	VERB
ejpam-6247	379	4	jm(π	jm(π	NOUN
ejpam-6247	379	5	)	)	PUNCT
ejpam-6247	380	1	∈	∈	PROPN
ejpam-6247	380	2	j	j	PROPN
ejpam-6247	380	3	(	(	PUNCT
ejpam-6247	380	4	l	l	NOUN
ejpam-6247	380	5	)	)	PUNCT
ejpam-6247	380	6	such	such	ADJ
ejpam-6247	380	7	that	that	DET
ejpam-6247	380	8	jm(µ∧π	jm(µ∧π	NOUN
ejpam-6247	380	9	)	)	PUNCT
ejpam-6247	380	10	=	=	SYM
ejpam-6247	380	11	jm(µ)∩jm(π	jm(µ)∩jm(π	PROPN
ejpam-6247	380	12	)	)	PUNCT
ejpam-6247	380	13	=	=	NOUN
ejpam-6247	380	14	∅	∅	NOUN
ejpam-6247	380	15	and	and	CCONJ
ejpam-6247	380	16	jm(µ	jm(µ	NOUN
ejpam-6247	380	17	)	)	PUNCT
ejpam-6247	380	18	∪	∪	ADP
ejpam-6247	380	19	jm(π	jm(π	NOUN
ejpam-6247	380	20	)	)	PUNCT
ejpam-6247	380	21	=	=	PRON
ejpam-6247	380	22	specdmf	specdmf	NOUN
ejpam-6247	380	23	(	(	PUNCT
ejpam-6247	380	24	l	l	NOUN
ejpam-6247	380	25	)	)	PUNCT
ejpam-6247	380	26	.	.	PUNCT
ejpam-6247	381	1	therefore	therefore	ADV
ejpam-6247	381	2	,	,	PUNCT
ejpam-6247	381	3	µ	µ	X
ejpam-6247	381	4	∨	∨	NUM
ejpam-6247	381	5	π	π	PROPN
ejpam-6247	381	6	∈	∈	PROPN
ejpam-6247	381	7	d.	d.	PROPN
ejpam-6247	381	8	also	also	ADV
ejpam-6247	381	9	,	,	PUNCT
ejpam-6247	381	10	jm(µ	jm(µ	NOUN
ejpam-6247	381	11	)	)	PUNCT
ejpam-6247	381	12	∪	∪	ADP
ejpam-6247	381	13	jm(π	jm(π	NOUN
ejpam-6247	381	14	)	)	PUNCT
ejpam-6247	381	15	=	=	PRON
ejpam-6247	381	16	specdmf	specdmf	NOUN
ejpam-6247	381	17	(	(	PUNCT
ejpam-6247	381	18	l	l	NOUN
ejpam-6247	381	19	)	)	PUNCT
ejpam-6247	381	20	⇒	⇒	NOUN
ejpam-6247	381	21	vm((µ,d	vm((µ,d	NOUN
ejpam-6247	381	22	)	)	PUNCT
ejpam-6247	381	23	)	)	PUNCT
ejpam-6247	381	24	∪	∪	ADP
ejpam-6247	381	25	vm((π	vm((π	NOUN
ejpam-6247	381	26	,	,	PUNCT
ejpam-6247	381	27	d	d	NOUN
ejpam-6247	381	28	)	)	PUNCT
ejpam-6247	381	29	)	)	PUNCT
ejpam-6247	382	1	=	=	PRON
ejpam-6247	382	2	specdmf	specdmf	NOUN
ejpam-6247	382	3	(	(	PUNCT
ejpam-6247	382	4	l	l	NOUN
ejpam-6247	382	5	)	)	PUNCT
ejpam-6247	382	6	⇒	⇒	NOUN
ejpam-6247	382	7	vm((µ,d	vm((µ,d	NOUN
ejpam-6247	382	8	)	)	PUNCT
ejpam-6247	382	9	∩	∩	NOUN
ejpam-6247	382	10	(	(	PUNCT
ejpam-6247	382	11	π	π	X
ejpam-6247	382	12	,	,	PUNCT
ejpam-6247	382	13	d	d	NOUN
ejpam-6247	382	14	)	)	PUNCT
ejpam-6247	382	15	)	)	PUNCT
ejpam-6247	383	1	=	=	PRON
ejpam-6247	383	2	specdmf	specdmf	NOUN
ejpam-6247	383	3	(	(	PUNCT
ejpam-6247	383	4	l	l	NOUN
ejpam-6247	383	5	)	)	PUNCT
ejpam-6247	383	6	⇒	⇒	NOUN
ejpam-6247	383	7	(	(	PUNCT
ejpam-6247	383	8	µ,d	µ,d	NOUN
ejpam-6247	383	9	)	)	PUNCT
ejpam-6247	383	10	∩	∩	NOUN
ejpam-6247	383	11	(	(	PUNCT
ejpam-6247	383	12	π	π	X
ejpam-6247	383	13	,	,	PUNCT
ejpam-6247	383	14	d	d	NOUN
ejpam-6247	383	15	)	)	PUNCT
ejpam-6247	383	16	=	=	SYM
ejpam-6247	383	17	d.	d.	NOUN
ejpam-6247	383	18	(	(	PUNCT
ejpam-6247	383	19	by	by	ADP
ejpam-6247	383	20	lemma	lemma	PROPN
ejpam-6247	383	21	4(2	4(2	PROPN
ejpam-6247	383	22	)	)	PUNCT
ejpam-6247	383	23	)	)	PUNCT
ejpam-6247	384	1	therefore	therefore	ADV
ejpam-6247	384	2	,	,	PUNCT
ejpam-6247	384	3	l	l	NOUN
ejpam-6247	384	4	is	be	AUX
ejpam-6247	384	5	hemicomplemented	hemicomplemente	VERB
ejpam-6247	384	6	.	.	PUNCT
ejpam-6247	385	1	n.	n.	PROPN
ejpam-6247	385	2	rafi	rafi	PROPN
ejpam-6247	385	3	et	et	PROPN
ejpam-6247	385	4	al	al	PROPN
ejpam-6247	385	5	.	.	PUNCT
ejpam-6247	385	6	/	/	SYM
ejpam-6247	385	7	eur	eur	PROPN
ejpam-6247	385	8	.	.	PUNCT
ejpam-6247	386	1	j.	j.	PROPN
ejpam-6247	386	2	pure	pure	PROPN
ejpam-6247	386	3	appl	appl	PROPN
ejpam-6247	386	4	.	.	PROPN
ejpam-6247	386	5	math	math	PROPN
ejpam-6247	386	6	,	,	PUNCT
ejpam-6247	386	7	18	18	NUM
ejpam-6247	386	8	(	(	PUNCT
ejpam-6247	386	9	3	3	NUM
ejpam-6247	386	10	)	)	PUNCT
ejpam-6247	386	11	(	(	PUNCT
ejpam-6247	386	12	2025	2025	NUM
ejpam-6247	386	13	)	)	PUNCT
ejpam-6247	386	14	,	,	PUNCT
ejpam-6247	386	15	6247	6247	NUM
ejpam-6247	386	16	12	12	NUM
ejpam-6247	386	17	of	of	ADP
ejpam-6247	386	18	15	15	NUM
ejpam-6247	386	19	we	we	PRON
ejpam-6247	386	20	now	now	ADV
ejpam-6247	386	21	present	present	VERB
ejpam-6247	386	22	a	a	DET
ejpam-6247	386	23	topological	topological	ADJ
ejpam-6247	386	24	description	description	NOUN
ejpam-6247	386	25	of	of	ADP
ejpam-6247	386	26	d	d	NOUN
ejpam-6247	386	27	-	-	NOUN
ejpam-6247	386	28	stone	stone	NOUN
ejpam-6247	386	29	adls	adls	PROPN
ejpam-6247	386	30	.	.	PUNCT
ejpam-6247	387	1	let	let	AUX
ejpam-6247	387	2	specdg	specdg	PROPN
ejpam-6247	387	3	(	(	PUNCT
ejpam-6247	387	4	l	l	NOUN
ejpam-6247	387	5	)	)	PUNCT
ejpam-6247	387	6	represent	represent	VERB
ejpam-6247	387	7	the	the	DET
ejpam-6247	387	8	collection	collection	NOUN
ejpam-6247	387	9	of	of	ADP
ejpam-6247	387	10	all	all	DET
ejpam-6247	387	11	prime	prime	ADJ
ejpam-6247	387	12	d	d	NOUN
ejpam-6247	387	13	-	-	NOUN
ejpam-6247	387	14	filters	filter	NOUN
ejpam-6247	387	15	of	of	ADP
ejpam-6247	387	16	an	an	DET
ejpam-6247	387	17	adl	adl	NOUN
ejpam-6247	387	18	l.	l.	NOUN
ejpam-6247	387	19	for	for	ADP
ejpam-6247	387	20	any	any	DET
ejpam-6247	387	21	subset	subset	NOUN
ejpam-6247	387	22	s	s	VERB
ejpam-6247	387	23	⊆	⊆	NUM
ejpam-6247	387	24	l	l	NOUN
ejpam-6247	387	25	,	,	PUNCT
ejpam-6247	387	26	we	we	PRON
ejpam-6247	387	27	define	define	VERB
ejpam-6247	387	28	j	j	PROPN
ejpam-6247	387	29	(	(	PUNCT
ejpam-6247	387	30	s	s	PROPN
ejpam-6247	387	31	)	)	PUNCT
ejpam-6247	387	32	=	=	SYM
ejpam-6247	387	33	{	{	PUNCT
ejpam-6247	387	34	q	q	NOUN
ejpam-6247	387	35	∈	∈	PROPN
ejpam-6247	387	36	specdg	specdg	NOUN
ejpam-6247	387	37	(	(	PUNCT
ejpam-6247	387	38	l	l	NOUN
ejpam-6247	387	39	)	)	PUNCT
ejpam-6247	388	1	|	|	ADV
ejpam-6247	388	2	s	s	VERB
ejpam-6247	388	3	̸⊆	̸⊆	NOUN
ejpam-6247	388	4	q	q	NOUN
ejpam-6247	388	5	}	}	PUNCT
ejpam-6247	388	6	,	,	PUNCT
ejpam-6247	388	7	v(s	v(s	PROPN
ejpam-6247	388	8	)	)	PUNCT
ejpam-6247	388	9	=	=	PRON
ejpam-6247	389	1	{	{	PUNCT
ejpam-6247	389	2	q	q	NOUN
ejpam-6247	389	3	∈	∈	PROPN
ejpam-6247	389	4	specdg	specdg	NOUN
ejpam-6247	389	5	(	(	PUNCT
ejpam-6247	389	6	l	l	NOUN
ejpam-6247	389	7	)	)	PUNCT
ejpam-6247	389	8	|	|	ADV
ejpam-6247	389	9	s	s	VERB
ejpam-6247	389	10	⊆	⊆	NUM
ejpam-6247	389	11	q	q	NOUN
ejpam-6247	389	12	}	}	PUNCT
ejpam-6247	389	13	.	.	PUNCT
ejpam-6247	390	1	in	in	ADP
ejpam-6247	390	2	the	the	DET
ejpam-6247	390	3	case	case	NOUN
ejpam-6247	390	4	where	where	SCONJ
ejpam-6247	390	5	s	s	VERB
ejpam-6247	390	6	=	=	X
ejpam-6247	390	7	{	{	PUNCT
ejpam-6247	390	8	µ	µ	NOUN
ejpam-6247	390	9	}	}	PUNCT
ejpam-6247	390	10	,	,	PUNCT
ejpam-6247	390	11	we	we	PRON
ejpam-6247	390	12	use	use	VERB
ejpam-6247	390	13	the	the	DET
ejpam-6247	390	14	following	following	ADJ
ejpam-6247	390	15	simplified	simplified	ADJ
ejpam-6247	390	16	notations	notation	NOUN
ejpam-6247	390	17	:	:	PUNCT
ejpam-6247	390	18	j	j	PROPN
ejpam-6247	390	19	(	(	PUNCT
ejpam-6247	390	20	µ	µ	NOUN
ejpam-6247	390	21	)	)	PUNCT
ejpam-6247	390	22	=	=	PRON
ejpam-6247	390	23	{	{	PUNCT
ejpam-6247	390	24	q	q	NOUN
ejpam-6247	390	25	∈	∈	PROPN
ejpam-6247	390	26	specdg	specdg	NOUN
ejpam-6247	390	27	(	(	PUNCT
ejpam-6247	390	28	l	l	NOUN
ejpam-6247	390	29	)	)	PUNCT
ejpam-6247	390	30	|	|	ADV
ejpam-6247	390	31	µ	µ	X
ejpam-6247	390	32	/∈	/∈	NOUN
ejpam-6247	390	33	q	q	NOUN
ejpam-6247	390	34	}	}	PUNCT
ejpam-6247	390	35	,	,	PUNCT
ejpam-6247	390	36	v(µ	v(µ	PROPN
ejpam-6247	390	37	)	)	PUNCT
ejpam-6247	390	38	=	=	PRON
ejpam-6247	390	39	{	{	PUNCT
ejpam-6247	390	40	q	q	NOUN
ejpam-6247	390	41	∈	∈	PROPN
ejpam-6247	390	42	specdg	specdg	NOUN
ejpam-6247	390	43	(	(	PUNCT
ejpam-6247	390	44	l	l	NOUN
ejpam-6247	390	45	)	)	PUNCT
ejpam-6247	391	1	|	|	ADV
ejpam-6247	391	2	µ	µ	X
ejpam-6247	391	3	∈	∈	NOUN
ejpam-6247	391	4	q	q	X
ejpam-6247	391	5	}	}	PUNCT
ejpam-6247	391	6	.	.	PUNCT
ejpam-6247	392	1	lemma	lemma	PROPN
ejpam-6247	392	2	5	5	NUM
ejpam-6247	392	3	.	.	PUNCT
ejpam-6247	393	1	for	for	ADP
ejpam-6247	393	2	any	any	DET
ejpam-6247	393	3	pair	pair	NOUN
ejpam-6247	393	4	of	of	ADP
ejpam-6247	393	5	elements	element	NOUN
ejpam-6247	393	6	µ	µ	X
ejpam-6247	393	7	and	and	CCONJ
ejpam-6247	393	8	π	π	PROPN
ejpam-6247	393	9	in	in	ADP
ejpam-6247	393	10	l	l	PROPN
ejpam-6247	393	11	,	,	PUNCT
ejpam-6247	393	12	the	the	DET
ejpam-6247	393	13	following	follow	VERB
ejpam-6247	393	14	properties	property	NOUN
ejpam-6247	393	15	are	be	AUX
ejpam-6247	393	16	true	true	ADJ
ejpam-6247	393	17	:	:	PUNCT
ejpam-6247	393	18	(	(	PUNCT
ejpam-6247	393	19	1	1	X
ejpam-6247	393	20	)	)	PUNCT
ejpam-6247	393	21	⋃	⋃	NOUN
ejpam-6247	393	22	µ∈l	µ∈l	ADJ
ejpam-6247	393	23	j	j	PROPN
ejpam-6247	393	24	(	(	PUNCT
ejpam-6247	393	25	µ	µ	NOUN
ejpam-6247	393	26	)	)	PUNCT
ejpam-6247	394	1	=	=	SYM
ejpam-6247	394	2	specdg	specdg	PROPN
ejpam-6247	394	3	(	(	PUNCT
ejpam-6247	394	4	l	l	NOUN
ejpam-6247	394	5	)	)	PUNCT
ejpam-6247	394	6	,	,	PUNCT
ejpam-6247	394	7	(	(	PUNCT
ejpam-6247	394	8	2	2	X
ejpam-6247	394	9	)	)	PUNCT
ejpam-6247	394	10	j	j	NOUN
ejpam-6247	394	11	(	(	PUNCT
ejpam-6247	394	12	µ	µ	NOUN
ejpam-6247	394	13	)	)	PUNCT
ejpam-6247	394	14	∩	∩	ADJ
ejpam-6247	394	15	j	j	PROPN
ejpam-6247	394	16	(	(	PUNCT
ejpam-6247	394	17	π	π	PROPN
ejpam-6247	394	18	)	)	PUNCT
ejpam-6247	394	19	=	=	SYM
ejpam-6247	394	20	j	j	PROPN
ejpam-6247	394	21	(	(	PUNCT
ejpam-6247	394	22	µ	µ	X
ejpam-6247	394	23	∨	∨	NUM
ejpam-6247	394	24	π	π	PROPN
ejpam-6247	394	25	)	)	PUNCT
ejpam-6247	394	26	,	,	PUNCT
ejpam-6247	394	27	(	(	PUNCT
ejpam-6247	394	28	3	3	X
ejpam-6247	394	29	)	)	PUNCT
ejpam-6247	394	30	j	j	NOUN
ejpam-6247	394	31	(	(	PUNCT
ejpam-6247	394	32	µ	µ	NOUN
ejpam-6247	394	33	)	)	PUNCT
ejpam-6247	394	34	∪	∪	PROPN
ejpam-6247	394	35	j	j	PROPN
ejpam-6247	394	36	(	(	PUNCT
ejpam-6247	394	37	π	π	PROPN
ejpam-6247	394	38	)	)	PUNCT
ejpam-6247	394	39	=	=	SYM
ejpam-6247	394	40	j	j	PROPN
ejpam-6247	394	41	(	(	PUNCT
ejpam-6247	394	42	µ	µ	X
ejpam-6247	394	43	∧	∧	PROPN
ejpam-6247	394	44	π	π	PROPN
ejpam-6247	394	45	)	)	PUNCT
ejpam-6247	394	46	,	,	PUNCT
ejpam-6247	394	47	(	(	PUNCT
ejpam-6247	394	48	4	4	X
ejpam-6247	394	49	)	)	PUNCT
ejpam-6247	394	50	j	j	PROPN
ejpam-6247	394	51	(	(	PUNCT
ejpam-6247	394	52	µ	µ	NOUN
ejpam-6247	394	53	)	)	PUNCT
ejpam-6247	394	54	=	=	SYM
ejpam-6247	394	55	∅	∅	NOUN
ejpam-6247	394	56	⇔	⇔	PROPN
ejpam-6247	394	57	µ	µ	X
ejpam-6247	394	58	∈	∈	PROPN
ejpam-6247	394	59	d	d	PROPN
ejpam-6247	394	60	,	,	PUNCT
ejpam-6247	394	61	(	(	PUNCT
ejpam-6247	394	62	5	5	X
ejpam-6247	394	63	)	)	PUNCT
ejpam-6247	394	64	j	j	NOUN
ejpam-6247	394	65	(	(	PUNCT
ejpam-6247	394	66	0	0	NUM
ejpam-6247	394	67	)	)	PUNCT
ejpam-6247	394	68	=	=	SYM
ejpam-6247	394	69	specdg	specdg	PROPN
ejpam-6247	394	70	(	(	PUNCT
ejpam-6247	394	71	l	l	NOUN
ejpam-6247	394	72	)	)	PUNCT
ejpam-6247	394	73	.	.	PUNCT
ejpam-6247	395	1	proof	proof	NOUN
ejpam-6247	395	2	.	.	PUNCT
ejpam-6247	396	1	(	(	PUNCT
ejpam-6247	396	2	1	1	X
ejpam-6247	396	3	)	)	PUNCT
ejpam-6247	396	4	let	let	VERB
ejpam-6247	396	5	q	q	PROPN
ejpam-6247	396	6	∈	∈	PROPN
ejpam-6247	396	7	specdg	specdg	NOUN
ejpam-6247	396	8	(	(	PUNCT
ejpam-6247	396	9	l	l	NOUN
ejpam-6247	396	10	)	)	PUNCT
ejpam-6247	396	11	.	.	PUNCT
ejpam-6247	397	1	since	since	SCONJ
ejpam-6247	397	2	q	q	PROPN
ejpam-6247	397	3	is	be	AUX
ejpam-6247	397	4	a	a	DET
ejpam-6247	397	5	proper	proper	ADJ
ejpam-6247	397	6	prime	prime	ADJ
ejpam-6247	397	7	d	d	NOUN
ejpam-6247	397	8	-	-	NOUN
ejpam-6247	397	9	filter	filter	NOUN
ejpam-6247	397	10	,	,	PUNCT
ejpam-6247	397	11	it	it	PRON
ejpam-6247	397	12	omits	omit	VERB
ejpam-6247	397	13	at	at	ADV
ejpam-6247	397	14	least	least	ADV
ejpam-6247	397	15	one	one	NUM
ejpam-6247	397	16	element	element	NOUN
ejpam-6247	397	17	µ	µ	PROPN
ejpam-6247	397	18	∈	∈	PROPN
ejpam-6247	397	19	l	l	NOUN
ejpam-6247	397	20	,	,	PUNCT
ejpam-6247	397	21	so	so	ADV
ejpam-6247	397	22	µ	µ	PROPN
ejpam-6247	397	23	/∈	/∈	PUNCT
ejpam-6247	397	24	q.	q.	PROPN
ejpam-6247	397	25	thus	thus	ADV
ejpam-6247	397	26	,	,	PUNCT
ejpam-6247	397	27	q	q	PROPN
ejpam-6247	397	28	∈	∈	PROPN
ejpam-6247	397	29	j	j	PROPN
ejpam-6247	397	30	(	(	PUNCT
ejpam-6247	397	31	µ	µ	NOUN
ejpam-6247	397	32	)	)	PUNCT
ejpam-6247	397	33	and	and	CCONJ
ejpam-6247	397	34	therefore	therefore	ADV
ejpam-6247	397	35	q	q	X
ejpam-6247	397	36	∈	∈	PROPN
ejpam-6247	397	37	⋃	⋃	ADP
ejpam-6247	397	38	µ∈l	µ∈l	ADJ
ejpam-6247	397	39	j	j	NOUN
ejpam-6247	397	40	(	(	PUNCT
ejpam-6247	397	41	µ	µ	NOUN
ejpam-6247	397	42	)	)	PUNCT
ejpam-6247	397	43	.	.	PUNCT
ejpam-6247	398	1	conversely	conversely	ADV
ejpam-6247	398	2	,	,	PUNCT
ejpam-6247	398	3	any	any	DET
ejpam-6247	398	4	q	q	NOUN
ejpam-6247	398	5	in	in	ADP
ejpam-6247	398	6	⋃	⋃	NOUN
ejpam-6247	398	7	µ∈l	µ∈l	ADJ
ejpam-6247	398	8	j	j	NOUN
ejpam-6247	398	9	(	(	PUNCT
ejpam-6247	398	10	µ	µ	NOUN
ejpam-6247	398	11	)	)	PUNCT
ejpam-6247	398	12	belongs	belong	VERB
ejpam-6247	398	13	to	to	ADP
ejpam-6247	398	14	specdg	specdg	PROPN
ejpam-6247	398	15	(	(	PUNCT
ejpam-6247	398	16	l	l	NOUN
ejpam-6247	398	17	)	)	PUNCT
ejpam-6247	398	18	by	by	ADP
ejpam-6247	398	19	definition	definition	NOUN
ejpam-6247	398	20	.	.	PUNCT
ejpam-6247	399	1	hence,⋃	hence,⋃	ADP
ejpam-6247	399	2	µ∈l	µ∈l	ADJ
ejpam-6247	399	3	j	j	PROPN
ejpam-6247	399	4	(	(	PUNCT
ejpam-6247	399	5	µ	µ	NOUN
ejpam-6247	399	6	)	)	PUNCT
ejpam-6247	399	7	=	=	SYM
ejpam-6247	399	8	specdg	specdg	PROPN
ejpam-6247	399	9	(	(	PUNCT
ejpam-6247	399	10	l	l	NOUN
ejpam-6247	399	11	)	)	PUNCT
ejpam-6247	399	12	.	.	PUNCT
ejpam-6247	400	1	(	(	PUNCT
ejpam-6247	400	2	2	2	X
ejpam-6247	400	3	)	)	PUNCT
ejpam-6247	400	4	by	by	ADP
ejpam-6247	400	5	definition	definition	NOUN
ejpam-6247	400	6	,	,	PUNCT
ejpam-6247	400	7	j	j	PROPN
ejpam-6247	400	8	(	(	PUNCT
ejpam-6247	400	9	µ	µ	NOUN
ejpam-6247	400	10	)	)	PUNCT
ejpam-6247	400	11	=	=	PRON
ejpam-6247	400	12	{	{	PUNCT
ejpam-6247	400	13	q	q	NOUN
ejpam-6247	400	14	∈	∈	PROPN
ejpam-6247	400	15	specdg	specdg	NOUN
ejpam-6247	400	16	(	(	PUNCT
ejpam-6247	400	17	l	l	NOUN
ejpam-6247	400	18	)	)	PUNCT
ejpam-6247	400	19	|	|	ADV
ejpam-6247	400	20	µ	µ	X
ejpam-6247	400	21	/∈	/∈	PUNCT
ejpam-6247	400	22	q	q	NOUN
ejpam-6247	400	23	}	}	PUNCT
ejpam-6247	400	24	and	and	CCONJ
ejpam-6247	400	25	j	j	PROPN
ejpam-6247	400	26	(	(	PUNCT
ejpam-6247	400	27	π	π	PROPN
ejpam-6247	400	28	)	)	PUNCT
ejpam-6247	400	29	=	=	PRON
ejpam-6247	401	1	{	{	PUNCT
ejpam-6247	401	2	q	q	NOUN
ejpam-6247	401	3	∈	∈	PROPN
ejpam-6247	401	4	specdg	specdg	NOUN
ejpam-6247	401	5	(	(	PUNCT
ejpam-6247	401	6	l	l	NOUN
ejpam-6247	401	7	)	)	PUNCT
ejpam-6247	402	1	|	|	ADV
ejpam-6247	402	2	π	π	X
ejpam-6247	402	3	/∈	/∈	PUNCT
ejpam-6247	403	1	q	q	ADJ
ejpam-6247	403	2	}	}	PUNCT
ejpam-6247	403	3	.	.	PUNCT
ejpam-6247	404	1	thus	thus	ADV
ejpam-6247	404	2	,	,	PUNCT
ejpam-6247	404	3	j	j	PROPN
ejpam-6247	404	4	(	(	PUNCT
ejpam-6247	404	5	µ	µ	NOUN
ejpam-6247	404	6	)	)	PUNCT
ejpam-6247	404	7	∩	∩	ADJ
ejpam-6247	404	8	j	j	PROPN
ejpam-6247	404	9	(	(	PUNCT
ejpam-6247	404	10	π	π	PROPN
ejpam-6247	404	11	)	)	PUNCT
ejpam-6247	404	12	=	=	PRON
ejpam-6247	404	13	{	{	PUNCT
ejpam-6247	404	14	q	q	NOUN
ejpam-6247	404	15	∈	∈	PROPN
ejpam-6247	404	16	specdg	specdg	NOUN
ejpam-6247	404	17	(	(	PUNCT
ejpam-6247	404	18	l	l	NOUN
ejpam-6247	404	19	)	)	PUNCT
ejpam-6247	404	20	|	|	ADV
ejpam-6247	404	21	µ	µ	X
ejpam-6247	404	22	/∈	/∈	NOUN
ejpam-6247	404	23	q	q	NOUN
ejpam-6247	404	24	and	and	CCONJ
ejpam-6247	404	25	π	π	NOUN
ejpam-6247	404	26	/∈	/∈	PUNCT
ejpam-6247	404	27	q	q	ADJ
ejpam-6247	404	28	}	}	PUNCT
ejpam-6247	404	29	.	.	PUNCT
ejpam-6247	405	1	since	since	SCONJ
ejpam-6247	405	2	q	q	PROPN
ejpam-6247	405	3	is	be	AUX
ejpam-6247	405	4	a	a	DET
ejpam-6247	405	5	prime	prime	ADJ
ejpam-6247	405	6	d	d	NOUN
ejpam-6247	405	7	-	-	NOUN
ejpam-6247	405	8	filter	filter	NOUN
ejpam-6247	405	9	,	,	PUNCT
ejpam-6247	405	10	µ	µ	X
ejpam-6247	405	11	∨	∨	NOUN
ejpam-6247	405	12	π	π	PROPN
ejpam-6247	405	13	∈	∈	PROPN
ejpam-6247	405	14	q	q	PROPN
ejpam-6247	405	15	implies	imply	VERB
ejpam-6247	405	16	µ	µ	PRON
ejpam-6247	405	17	∈	∈	X
ejpam-6247	405	18	q	q	NOUN
ejpam-6247	405	19	or	or	CCONJ
ejpam-6247	405	20	π	π	PROPN
ejpam-6247	405	21	∈	∈	PROPN
ejpam-6247	405	22	q.	q.	PROPN
ejpam-6247	405	23	therefore	therefore	ADV
ejpam-6247	405	24	,	,	PUNCT
ejpam-6247	405	25	µ	µ	X
ejpam-6247	405	26	/∈	/∈	NOUN
ejpam-6247	405	27	q	q	NOUN
ejpam-6247	405	28	and	and	CCONJ
ejpam-6247	405	29	π	π	NOUN
ejpam-6247	405	30	/∈	/∈	PUNCT
ejpam-6247	405	31	q	q	PUNCT
ejpam-6247	405	32	together	together	ADV
ejpam-6247	405	33	imply	imply	AUX
ejpam-6247	405	34	µ∨π	µ∨π	VERB
ejpam-6247	405	35	/∈	/∈	PUNCT
ejpam-6247	406	1	q.	q.	PROPN
ejpam-6247	406	2	conversely	conversely	ADV
ejpam-6247	406	3	,	,	PUNCT
ejpam-6247	406	4	if	if	SCONJ
ejpam-6247	406	5	µ∨π	µ∨π	VERB
ejpam-6247	406	6	/∈	/∈	PUNCT
ejpam-6247	407	1	q	q	INTJ
ejpam-6247	407	2	,	,	PUNCT
ejpam-6247	407	3	then	then	ADV
ejpam-6247	407	4	µ	µ	X
ejpam-6247	407	5	/∈	/∈	NOUN
ejpam-6247	407	6	q	q	NOUN
ejpam-6247	408	1	and	and	CCONJ
ejpam-6247	409	1	π	π	PROPN
ejpam-6247	409	2	/∈	/∈	PUNCT
ejpam-6247	410	1	q.	q.	PROPN
ejpam-6247	410	2	hence	hence	ADV
ejpam-6247	410	3	,	,	PUNCT
ejpam-6247	410	4	j	j	PROPN
ejpam-6247	410	5	(	(	PUNCT
ejpam-6247	410	6	µ	µ	NOUN
ejpam-6247	410	7	)	)	PUNCT
ejpam-6247	410	8	∩	∩	ADJ
ejpam-6247	410	9	j	j	PROPN
ejpam-6247	410	10	(	(	PUNCT
ejpam-6247	410	11	π	π	PROPN
ejpam-6247	410	12	)	)	PUNCT
ejpam-6247	410	13	=	=	PRON
ejpam-6247	410	14	{	{	PUNCT
ejpam-6247	410	15	q	q	NOUN
ejpam-6247	410	16	∈	∈	PROPN
ejpam-6247	410	17	specdg	specdg	NOUN
ejpam-6247	410	18	(	(	PUNCT
ejpam-6247	410	19	l	l	NOUN
ejpam-6247	410	20	)	)	PUNCT
ejpam-6247	410	21	|	|	ADV
ejpam-6247	410	22	µ	µ	PRON
ejpam-6247	410	23	∨	∨	NUM
ejpam-6247	410	24	π	π	NOUN
ejpam-6247	410	25	/∈	/∈	PUNCT
ejpam-6247	410	26	q	q	NOUN
ejpam-6247	410	27	}	}	PUNCT
ejpam-6247	410	28	=	=	SYM
ejpam-6247	410	29	j	j	PROPN
ejpam-6247	410	30	(	(	PUNCT
ejpam-6247	410	31	µ	µ	X
ejpam-6247	410	32	∨	∨	NUM
ejpam-6247	410	33	π	π	PROPN
ejpam-6247	410	34	)	)	PUNCT
ejpam-6247	410	35	.	.	PUNCT
ejpam-6247	411	1	(	(	PUNCT
ejpam-6247	411	2	3	3	X
ejpam-6247	411	3	)	)	PUNCT
ejpam-6247	411	4	by	by	ADP
ejpam-6247	411	5	definition	definition	NOUN
ejpam-6247	411	6	,	,	PUNCT
ejpam-6247	411	7	j	j	PROPN
ejpam-6247	411	8	(	(	PUNCT
ejpam-6247	411	9	µ	µ	NOUN
ejpam-6247	411	10	)	)	PUNCT
ejpam-6247	411	11	∪	∪	PROPN
ejpam-6247	411	12	j	j	PROPN
ejpam-6247	411	13	(	(	PUNCT
ejpam-6247	411	14	π	π	PROPN
ejpam-6247	411	15	)	)	PUNCT
ejpam-6247	411	16	=	=	PRON
ejpam-6247	411	17	{	{	PUNCT
ejpam-6247	411	18	q	q	NOUN
ejpam-6247	411	19	∈	∈	PROPN
ejpam-6247	411	20	specdg	specdg	NOUN
ejpam-6247	411	21	(	(	PUNCT
ejpam-6247	411	22	l	l	NOUN
ejpam-6247	411	23	)	)	PUNCT
ejpam-6247	411	24	|	|	ADV
ejpam-6247	411	25	µ	µ	X
ejpam-6247	411	26	/∈	/∈	NOUN
ejpam-6247	411	27	q	q	NOUN
ejpam-6247	411	28	or	or	CCONJ
ejpam-6247	411	29	π	π	NOUN
ejpam-6247	411	30	/∈	/∈	PUNCT
ejpam-6247	412	1	q	q	ADJ
ejpam-6247	412	2	}	}	PUNCT
ejpam-6247	412	3	.	.	PUNCT
ejpam-6247	413	1	n.	n.	PROPN
ejpam-6247	413	2	rafi	rafi	PROPN
ejpam-6247	413	3	et	et	PROPN
ejpam-6247	413	4	al	al	PROPN
ejpam-6247	413	5	.	.	PUNCT
ejpam-6247	413	6	/	/	SYM
ejpam-6247	413	7	eur	eur	PROPN
ejpam-6247	413	8	.	.	PUNCT
ejpam-6247	414	1	j.	j.	PROPN
ejpam-6247	414	2	pure	pure	PROPN
ejpam-6247	414	3	appl	appl	PROPN
ejpam-6247	414	4	.	.	PROPN
ejpam-6247	414	5	math	math	PROPN
ejpam-6247	414	6	,	,	PUNCT
ejpam-6247	414	7	18	18	NUM
ejpam-6247	414	8	(	(	PUNCT
ejpam-6247	414	9	3	3	NUM
ejpam-6247	414	10	)	)	PUNCT
ejpam-6247	414	11	(	(	PUNCT
ejpam-6247	414	12	2025	2025	NUM
ejpam-6247	414	13	)	)	PUNCT
ejpam-6247	414	14	,	,	PUNCT
ejpam-6247	414	15	6247	6247	NUM
ejpam-6247	414	16	13	13	NUM
ejpam-6247	414	17	of	of	ADP
ejpam-6247	414	18	15	15	NUM
ejpam-6247	414	19	since	since	SCONJ
ejpam-6247	414	20	filters	filter	NOUN
ejpam-6247	414	21	are	be	AUX
ejpam-6247	414	22	upwards	upwards	ADV
ejpam-6247	414	23	closed	closed	ADJ
ejpam-6247	414	24	,	,	PUNCT
ejpam-6247	414	25	if	if	SCONJ
ejpam-6247	414	26	µ∧π	µ∧π	NOUN
ejpam-6247	414	27	∈	∈	PROPN
ejpam-6247	415	1	q	q	NOUN
ejpam-6247	415	2	,	,	PUNCT
ejpam-6247	415	3	then	then	ADV
ejpam-6247	415	4	both	both	DET
ejpam-6247	415	5	µ	µ	NOUN
ejpam-6247	415	6	,	,	PUNCT
ejpam-6247	415	7	π	π	PROPN
ejpam-6247	415	8	∈	∈	PROPN
ejpam-6247	415	9	q.	q.	NOUN
ejpam-6247	415	10	conversely	conversely	ADV
ejpam-6247	415	11	,	,	PUNCT
ejpam-6247	415	12	if	if	SCONJ
ejpam-6247	415	13	µ∧π	µ∧π	NOUN
ejpam-6247	415	14	/∈	/∈	PUNCT
ejpam-6247	416	1	q	q	INTJ
ejpam-6247	416	2	,	,	PUNCT
ejpam-6247	416	3	at	at	ADV
ejpam-6247	416	4	least	least	ADJ
ejpam-6247	416	5	one	one	NUM
ejpam-6247	416	6	of	of	ADP
ejpam-6247	416	7	µ	µ	NOUN
ejpam-6247	416	8	or	or	CCONJ
ejpam-6247	416	9	π	π	PROPN
ejpam-6247	416	10	is	be	AUX
ejpam-6247	416	11	not	not	PART
ejpam-6247	416	12	in	in	ADP
ejpam-6247	416	13	q.	q.	PROPN
ejpam-6247	416	14	thus	thus	ADV
ejpam-6247	416	15	,	,	PUNCT
ejpam-6247	416	16	j	j	PROPN
ejpam-6247	416	17	(	(	PUNCT
ejpam-6247	416	18	µ	µ	NOUN
ejpam-6247	416	19	)	)	PUNCT
ejpam-6247	416	20	∪	∪	PROPN
ejpam-6247	416	21	j	j	PROPN
ejpam-6247	416	22	(	(	PUNCT
ejpam-6247	416	23	π	π	PROPN
ejpam-6247	416	24	)	)	PUNCT
ejpam-6247	416	25	=	=	PRON
ejpam-6247	416	26	{	{	PUNCT
ejpam-6247	416	27	q	q	NOUN
ejpam-6247	416	28	∈	∈	PROPN
ejpam-6247	416	29	specdg	specdg	NOUN
ejpam-6247	416	30	(	(	PUNCT
ejpam-6247	416	31	l	l	NOUN
ejpam-6247	416	32	)	)	PUNCT
ejpam-6247	416	33	|	|	ADV
ejpam-6247	416	34	µ	µ	X
ejpam-6247	416	35	∧	∧	PROPN
ejpam-6247	416	36	π	π	X
ejpam-6247	416	37	/∈	/∈	PUNCT
ejpam-6247	417	1	q	q	NOUN
ejpam-6247	417	2	}	}	PUNCT
ejpam-6247	417	3	=	=	SYM
ejpam-6247	417	4	j	j	PROPN
ejpam-6247	417	5	(	(	PUNCT
ejpam-6247	417	6	µ	µ	X
ejpam-6247	417	7	∧	∧	PROPN
ejpam-6247	417	8	π	π	PROPN
ejpam-6247	417	9	)	)	PUNCT
ejpam-6247	417	10	.	.	PUNCT
ejpam-6247	418	1	(	(	PUNCT
ejpam-6247	418	2	4	4	X
ejpam-6247	418	3	)	)	PUNCT
ejpam-6247	418	4	if	if	SCONJ
ejpam-6247	418	5	µ	µ	PRON
ejpam-6247	418	6	∈	∈	NOUN
ejpam-6247	418	7	d	d	NOUN
ejpam-6247	418	8	,	,	PUNCT
ejpam-6247	418	9	then	then	ADV
ejpam-6247	418	10	µ	µ	X
ejpam-6247	418	11	∈	∈	NOUN
ejpam-6247	418	12	q	q	NOUN
ejpam-6247	418	13	for	for	ADP
ejpam-6247	418	14	all	all	DET
ejpam-6247	418	15	prime	prime	ADJ
ejpam-6247	418	16	d	d	NOUN
ejpam-6247	418	17	-	-	PUNCT
ejpam-6247	418	18	filters	filter	NOUN
ejpam-6247	418	19	q	q	NOUN
ejpam-6247	418	20	because	because	SCONJ
ejpam-6247	418	21	d	d	PROPN
ejpam-6247	418	22	⊆	⊆	NUM
ejpam-6247	418	23	q.	q.	NOUN
ejpam-6247	418	24	therefore	therefore	ADV
ejpam-6247	418	25	,	,	PUNCT
ejpam-6247	418	26	there	there	PRON
ejpam-6247	418	27	does	do	AUX
ejpam-6247	418	28	not	not	PART
ejpam-6247	418	29	exist	exist	VERB
ejpam-6247	418	30	any	any	DET
ejpam-6247	418	31	q	q	NOUN
ejpam-6247	418	32	with	with	ADP
ejpam-6247	418	33	µ	µ	NOUN
ejpam-6247	418	34	/∈	/∈	PUNCT
ejpam-6247	418	35	q	q	NOUN
ejpam-6247	418	36	,	,	PUNCT
ejpam-6247	418	37	so	so	ADV
ejpam-6247	418	38	j	j	PROPN
ejpam-6247	418	39	(	(	PUNCT
ejpam-6247	418	40	µ	µ	NOUN
ejpam-6247	418	41	)	)	PUNCT
ejpam-6247	418	42	=	=	NOUN
ejpam-6247	418	43	∅.	∅.	VERB
ejpam-6247	418	44	conversely	conversely	ADV
ejpam-6247	418	45	,	,	PUNCT
ejpam-6247	418	46	if	if	SCONJ
ejpam-6247	418	47	j	j	PROPN
ejpam-6247	418	48	(	(	PUNCT
ejpam-6247	418	49	µ	µ	NOUN
ejpam-6247	418	50	)	)	PUNCT
ejpam-6247	418	51	=	=	SYM
ejpam-6247	418	52	∅	∅	NOUN
ejpam-6247	418	53	,	,	PUNCT
ejpam-6247	418	54	there	there	PRON
ejpam-6247	418	55	is	be	VERB
ejpam-6247	418	56	no	no	DET
ejpam-6247	418	57	prime	prime	ADJ
ejpam-6247	418	58	d	d	NOUN
ejpam-6247	418	59	-	-	NOUN
ejpam-6247	418	60	filter	filter	NOUN
ejpam-6247	418	61	omitting	omit	VERB
ejpam-6247	418	62	µ	µ	NOUN
ejpam-6247	418	63	,	,	PUNCT
ejpam-6247	418	64	which	which	PRON
ejpam-6247	418	65	implies	imply	VERB
ejpam-6247	418	66	µ	µ	PRON
ejpam-6247	418	67	∈	∈	ADJ
ejpam-6247	418	68	q	q	NOUN
ejpam-6247	418	69	for	for	ADP
ejpam-6247	418	70	all	all	DET
ejpam-6247	418	71	prime	prime	ADJ
ejpam-6247	418	72	d	d	NOUN
ejpam-6247	418	73	-	-	PUNCT
ejpam-6247	418	74	filters	filter	NOUN
ejpam-6247	418	75	q.	q.	PROPN
ejpam-6247	418	76	thus	thus	ADV
ejpam-6247	418	77	,	,	PUNCT
ejpam-6247	418	78	µ	µ	PROPN
ejpam-6247	418	79	∈	∈	NOUN
ejpam-6247	418	80	⋂	⋂	X
ejpam-6247	418	81	q∈specdg	q∈specdg	INTJ
ejpam-6247	418	82	(	(	PUNCT
ejpam-6247	419	1	l)q	l)q	X
ejpam-6247	419	2	=	=	SYM
ejpam-6247	419	3	d	d	NOUN
ejpam-6247	419	4	,	,	PUNCT
ejpam-6247	419	5	confirming	confirm	VERB
ejpam-6247	419	6	that	that	SCONJ
ejpam-6247	419	7	µ	µ	PROPN
ejpam-6247	419	8	∈	∈	PROPN
ejpam-6247	419	9	d.	d.	NOUN
ejpam-6247	419	10	(	(	PUNCT
ejpam-6247	419	11	5	5	NUM
ejpam-6247	419	12	)	)	PUNCT
ejpam-6247	419	13	since	since	SCONJ
ejpam-6247	419	14	0	0	NUM
ejpam-6247	419	15	is	be	AUX
ejpam-6247	419	16	not	not	PART
ejpam-6247	419	17	contained	contain	VERB
ejpam-6247	419	18	in	in	ADP
ejpam-6247	419	19	any	any	DET
ejpam-6247	419	20	proper	proper	ADJ
ejpam-6247	419	21	filter	filter	NOUN
ejpam-6247	419	22	,	,	PUNCT
ejpam-6247	419	23	in	in	ADP
ejpam-6247	419	24	particular	particular	ADJ
ejpam-6247	419	25	,	,	PUNCT
ejpam-6247	419	26	no	no	DET
ejpam-6247	419	27	prime	prime	ADJ
ejpam-6247	419	28	d	d	NOUN
ejpam-6247	419	29	-	-	NOUN
ejpam-6247	419	30	filter	filter	NOUN
ejpam-6247	419	31	contains	contain	VERB
ejpam-6247	419	32	0	0	NUM
ejpam-6247	419	33	.	.	PUNCT
ejpam-6247	420	1	thus	thus	ADV
ejpam-6247	420	2	,	,	PUNCT
ejpam-6247	420	3	for	for	ADP
ejpam-6247	420	4	every	every	DET
ejpam-6247	420	5	q	q	PROPN
ejpam-6247	420	6	∈	∈	PROPN
ejpam-6247	420	7	specdg	specdg	NOUN
ejpam-6247	420	8	(	(	PUNCT
ejpam-6247	420	9	l	l	NOUN
ejpam-6247	420	10	)	)	PUNCT
ejpam-6247	420	11	,	,	PUNCT
ejpam-6247	420	12	0	0	NUM
ejpam-6247	420	13	/∈	/∈	CCONJ
ejpam-6247	420	14	q	q	NOUN
ejpam-6247	420	15	and	and	CCONJ
ejpam-6247	420	16	hence	hence	ADV
ejpam-6247	420	17	j	j	PROPN
ejpam-6247	420	18	(	(	PUNCT
ejpam-6247	420	19	0	0	NUM
ejpam-6247	420	20	)	)	PUNCT
ejpam-6247	420	21	=	=	PRON
ejpam-6247	420	22	{	{	PUNCT
ejpam-6247	420	23	q	q	NOUN
ejpam-6247	420	24	∈	∈	PROPN
ejpam-6247	420	25	specdg	specdg	NOUN
ejpam-6247	420	26	(	(	PUNCT
ejpam-6247	420	27	l	l	NOUN
ejpam-6247	420	28	)	)	PUNCT
ejpam-6247	420	29	|	|	ADV
ejpam-6247	420	30	0	0	NUM
ejpam-6247	420	31	/∈	/∈	PUNCT
ejpam-6247	421	1	q	q	NOUN
ejpam-6247	421	2	}	}	PUNCT
ejpam-6247	421	3	=	=	SYM
ejpam-6247	421	4	specdg	specdg	PROPN
ejpam-6247	421	5	(	(	PUNCT
ejpam-6247	421	6	l	l	NOUN
ejpam-6247	421	7	)	)	PUNCT
ejpam-6247	421	8	.	.	PUNCT
ejpam-6247	422	1	based	base	VERB
ejpam-6247	422	2	on	on	ADP
ejpam-6247	422	3	the	the	DET
ejpam-6247	422	4	previous	previous	ADJ
ejpam-6247	422	5	result	result	NOUN
ejpam-6247	422	6	,	,	PUNCT
ejpam-6247	422	7	it	it	PRON
ejpam-6247	422	8	is	be	AUX
ejpam-6247	422	9	evident	evident	ADJ
ejpam-6247	422	10	that	that	SCONJ
ejpam-6247	422	11	the	the	DET
ejpam-6247	422	12	collection	collection	NOUN
ejpam-6247	422	13	{	{	PUNCT
ejpam-6247	422	14	j	j	PROPN
ejpam-6247	422	15	(	(	PUNCT
ejpam-6247	422	16	µ	µ	NOUN
ejpam-6247	422	17	)	)	PUNCT
ejpam-6247	422	18	|	|	ADV
ejpam-6247	422	19	µ	µ	X
ejpam-6247	422	20	∈	∈	PROPN
ejpam-6247	422	21	l	l	NOUN
ejpam-6247	422	22	}	}	PUNCT
ejpam-6247	422	23	forms	form	VERB
ejpam-6247	422	24	a	a	DET
ejpam-6247	422	25	basis	basis	NOUN
ejpam-6247	422	26	for	for	ADP
ejpam-6247	422	27	a	a	DET
ejpam-6247	422	28	topology	topology	NOUN
ejpam-6247	422	29	on	on	ADP
ejpam-6247	422	30	specdg	specdg	PROPN
ejpam-6247	422	31	(	(	PUNCT
ejpam-6247	422	32	l	l	NOUN
ejpam-6247	422	33	)	)	PUNCT
ejpam-6247	422	34	.	.	PUNCT
ejpam-6247	423	1	in	in	ADP
ejpam-6247	423	2	the	the	DET
ejpam-6247	423	3	case	case	NOUN
ejpam-6247	423	4	of	of	ADP
ejpam-6247	423	5	the	the	DET
ejpam-6247	423	6	topology	topology	NOUN
ejpam-6247	423	7	on	on	ADP
ejpam-6247	423	8	specdmf	specdmf	NOUN
ejpam-6247	423	9	(	(	PUNCT
ejpam-6247	423	10	l	l	NOUN
ejpam-6247	423	11	)	)	PUNCT
ejpam-6247	423	12	,	,	PUNCT
ejpam-6247	423	13	the	the	DET
ejpam-6247	423	14	open	open	ADJ
ejpam-6247	423	15	set	set	NOUN
ejpam-6247	423	16	corresponding	correspond	VERB
ejpam-6247	423	17	to	to	ADP
ejpam-6247	423	18	any	any	DET
ejpam-6247	423	19	element	element	NOUN
ejpam-6247	423	20	µ	µ	PROPN
ejpam-6247	423	21	∈	∈	NOUN
ejpam-6247	423	22	l	l	NOUN
ejpam-6247	423	23	is	be	AUX
ejpam-6247	423	24	given	give	VERB
ejpam-6247	423	25	by	by	ADP
ejpam-6247	423	26	the	the	DET
ejpam-6247	423	27	intersection	intersection	NOUN
ejpam-6247	423	28	specdmf	specdmf	NOUN
ejpam-6247	423	29	(	(	PUNCT
ejpam-6247	423	30	l)∩j	l)∩j	PROPN
ejpam-6247	423	31	(	(	PUNCT
ejpam-6247	423	32	µ	µ	NOUN
ejpam-6247	423	33	)	)	PUNCT
ejpam-6247	423	34	,	,	PUNCT
ejpam-6247	423	35	which	which	PRON
ejpam-6247	423	36	is	be	AUX
ejpam-6247	423	37	denoted	denote	VERB
ejpam-6247	423	38	as	as	ADP
ejpam-6247	423	39	jm(µ	jm(µ	NOUN
ejpam-6247	423	40	)	)	PUNCT
ejpam-6247	423	41	.	.	PUNCT
ejpam-6247	424	1	this	this	DET
ejpam-6247	424	2	topology	topology	NOUN
ejpam-6247	424	3	on	on	ADP
ejpam-6247	424	4	specdg	specdg	PROPN
ejpam-6247	424	5	(	(	PUNCT
ejpam-6247	424	6	l	l	NOUN
ejpam-6247	424	7	)	)	PUNCT
ejpam-6247	424	8	is	be	AUX
ejpam-6247	424	9	referred	refer	VERB
ejpam-6247	424	10	to	to	ADP
ejpam-6247	424	11	as	as	ADP
ejpam-6247	424	12	the	the	DET
ejpam-6247	424	13	hull	hull	NOUN
ejpam-6247	424	14	-	-	PUNCT
ejpam-6247	424	15	kernel	kernel	NOUN
ejpam-6247	424	16	topology	topology	NOUN
ejpam-6247	424	17	,	,	PUNCT
ejpam-6247	424	18	where	where	SCONJ
ejpam-6247	424	19	{	{	PUNCT
ejpam-6247	424	20	v(µ	v(µ	NOUN
ejpam-6247	424	21	)	)	PUNCT
ejpam-6247	424	22	|	|	ADV
ejpam-6247	424	23	µ	µ	X
ejpam-6247	424	24	∈	∈	NOUN
ejpam-6247	424	25	l	l	NOUN
ejpam-6247	424	26	}	}	PUNCT
ejpam-6247	424	27	represents	represent	VERB
ejpam-6247	424	28	the	the	DET
ejpam-6247	424	29	hull	hull	NOUN
ejpam-6247	424	30	,	,	PUNCT
ejpam-6247	424	31	which	which	PRON
ejpam-6247	424	32	serves	serve	VERB
ejpam-6247	424	33	as	as	ADP
ejpam-6247	424	34	the	the	DET
ejpam-6247	424	35	basis	basis	NOUN
ejpam-6247	424	36	,	,	PUNCT
ejpam-6247	424	37	and	and	CCONJ
ejpam-6247	424	38	{	{	PUNCT
ejpam-6247	424	39	j	j	PROPN
ejpam-6247	424	40	(	(	PUNCT
ejpam-6247	424	41	µ	µ	NOUN
ejpam-6247	424	42	)	)	PUNCT
ejpam-6247	424	43	|	|	ADV
ejpam-6247	424	44	µ	µ	X
ejpam-6247	424	45	∈	∈	PROPN
ejpam-6247	424	46	l	l	NOUN
ejpam-6247	424	47	}	}	PUNCT
ejpam-6247	424	48	corresponds	correspond	VERB
ejpam-6247	424	49	to	to	ADP
ejpam-6247	424	50	the	the	DET
ejpam-6247	424	51	kernel	kernel	NOUN
ejpam-6247	424	52	.	.	PUNCT
ejpam-6247	425	1	lemma	lemma	PROPN
ejpam-6247	425	2	6	6	NUM
ejpam-6247	425	3	.	.	PUNCT
ejpam-6247	426	1	for	for	ADP
ejpam-6247	426	2	arbitrary	arbitrary	ADJ
ejpam-6247	426	3	d	d	NOUN
ejpam-6247	426	4	-	-	NOUN
ejpam-6247	426	5	filters	filter	NOUN
ejpam-6247	426	6	g	g	NOUN
ejpam-6247	426	7	and	and	CCONJ
ejpam-6247	426	8	u	u	PROPN
ejpam-6247	426	9	in	in	ADP
ejpam-6247	426	10	l	l	PROPN
ejpam-6247	426	11	,	,	PUNCT
ejpam-6247	426	12	we	we	PRON
ejpam-6247	426	13	have	have	VERB
ejpam-6247	426	14	the	the	DET
ejpam-6247	426	15	following	follow	VERB
ejpam-6247	426	16	conditions	condition	NOUN
ejpam-6247	426	17	:	:	PUNCT
ejpam-6247	426	18	(	(	PUNCT
ejpam-6247	426	19	1	1	X
ejpam-6247	426	20	)	)	PUNCT
ejpam-6247	426	21	v(g	v(g	ADJ
ejpam-6247	426	22	)	)	PUNCT
ejpam-6247	426	23	=	=	SYM
ejpam-6247	426	24	specdg	specdg	PROPN
ejpam-6247	426	25	(	(	PUNCT
ejpam-6247	426	26	l	l	NOUN
ejpam-6247	426	27	)	)	PUNCT
ejpam-6247	426	28	⇔	⇔	NOUN
ejpam-6247	426	29	g	g	PROPN
ejpam-6247	426	30	=	=	SYM
ejpam-6247	426	31	d	d	PROPN
ejpam-6247	426	32	,	,	PUNCT
ejpam-6247	426	33	(	(	PUNCT
ejpam-6247	426	34	2	2	NUM
ejpam-6247	426	35	)	)	PUNCT
ejpam-6247	426	36	v(g	v(g	ADJ
ejpam-6247	426	37	)	)	PUNCT
ejpam-6247	426	38	=	=	SYM
ejpam-6247	426	39	∅	∅	NOUN
ejpam-6247	426	40	⇔	⇔	X
ejpam-6247	426	41	g	g	PROPN
ejpam-6247	426	42	=	=	PROPN
ejpam-6247	426	43	l	l	PROPN
ejpam-6247	426	44	,	,	PUNCT
ejpam-6247	426	45	(	(	PUNCT
ejpam-6247	426	46	3	3	X
ejpam-6247	426	47	)	)	PUNCT
ejpam-6247	426	48	g	g	NOUN
ejpam-6247	426	49	⊆	⊆	NUM
ejpam-6247	426	50	u	u	NOUN
ejpam-6247	426	51	⇒	⇒	NOUN
ejpam-6247	426	52	v(u	v(u	PROPN
ejpam-6247	426	53	)	)	PUNCT
ejpam-6247	427	1	⊆	⊆	NUM
ejpam-6247	427	2	v(g	v(g	NUM
ejpam-6247	427	3	)	)	PUNCT
ejpam-6247	427	4	,	,	PUNCT
ejpam-6247	427	5	(	(	PUNCT
ejpam-6247	427	6	4	4	X
ejpam-6247	427	7	)	)	PUNCT
ejpam-6247	427	8	v(g	v(g	ADJ
ejpam-6247	427	9	)	)	PUNCT
ejpam-6247	427	10	∩	∩	NOUN
ejpam-6247	427	11	v(u	v(u	NOUN
ejpam-6247	427	12	)	)	PUNCT
ejpam-6247	427	13	=	=	SYM
ejpam-6247	428	1	v(g	v(g	PROPN
ejpam-6247	428	2	∨	∨	NUM
ejpam-6247	428	3	u	u	NOUN
ejpam-6247	428	4	)	)	PUNCT
ejpam-6247	428	5	,	,	PUNCT
ejpam-6247	428	6	(	(	PUNCT
ejpam-6247	428	7	5	5	X
ejpam-6247	428	8	)	)	PUNCT
ejpam-6247	428	9	v(g	v(g	ADJ
ejpam-6247	428	10	)	)	PUNCT
ejpam-6247	428	11	∪	∪	ADP
ejpam-6247	428	12	v(u	v(u	NOUN
ejpam-6247	428	13	)	)	PUNCT
ejpam-6247	428	14	=	=	SYM
ejpam-6247	428	15	v(g	v(g	ADJ
ejpam-6247	428	16	∩	∩	ADJ
ejpam-6247	428	17	u	u	NOUN
ejpam-6247	428	18	)	)	PUNCT
ejpam-6247	428	19	.	.	PUNCT
ejpam-6247	429	1	proof	proof	NOUN
ejpam-6247	429	2	.	.	PUNCT
ejpam-6247	430	1	(	(	PUNCT
ejpam-6247	430	2	1	1	X
ejpam-6247	430	3	)	)	PUNCT
ejpam-6247	430	4	since	since	SCONJ
ejpam-6247	430	5	g	g	PROPN
ejpam-6247	430	6	is	be	AUX
ejpam-6247	430	7	a	a	DET
ejpam-6247	430	8	d	d	NOUN
ejpam-6247	430	9	-	-	NOUN
ejpam-6247	430	10	filter	filter	NOUN
ejpam-6247	430	11	,	,	PUNCT
ejpam-6247	430	12	we	we	PRON
ejpam-6247	430	13	have	have	VERB
ejpam-6247	430	14	d	d	PROPN
ejpam-6247	430	15	⊆	⊆	NUM
ejpam-6247	430	16	g.	g.	NOUN
ejpam-6247	430	17	now	now	ADV
ejpam-6247	430	18	,	,	PUNCT
ejpam-6247	430	19	assume	assume	VERB
ejpam-6247	430	20	that	that	SCONJ
ejpam-6247	430	21	v(g	v(g	VERB
ejpam-6247	430	22	)	)	PUNCT
ejpam-6247	431	1	=	=	SYM
ejpam-6247	431	2	specdg	specdg	PROPN
ejpam-6247	431	3	(	(	PUNCT
ejpam-6247	431	4	l	l	NOUN
ejpam-6247	431	5	)	)	PUNCT
ejpam-6247	431	6	.	.	PUNCT
ejpam-6247	432	1	this	this	PRON
ejpam-6247	432	2	implies	imply	VERB
ejpam-6247	432	3	that	that	SCONJ
ejpam-6247	432	4	g	g	PROPN
ejpam-6247	432	5	⊆	⊆	NUM
ejpam-6247	432	6	q	q	NOUN
ejpam-6247	432	7	for	for	ADP
ejpam-6247	432	8	all	all	DET
ejpam-6247	432	9	q	q	PROPN
ejpam-6247	432	10	∈	∈	PROPN
ejpam-6247	432	11	specdg	specdg	NOUN
ejpam-6247	432	12	(	(	PUNCT
ejpam-6247	432	13	l	l	NOUN
ejpam-6247	432	14	)	)	PUNCT
ejpam-6247	432	15	.	.	PUNCT
ejpam-6247	433	1	therefore	therefore	ADV
ejpam-6247	433	2	,	,	PUNCT
ejpam-6247	433	3	we	we	PRON
ejpam-6247	433	4	can	can	AUX
ejpam-6247	433	5	conclude	conclude	VERB
ejpam-6247	433	6	that	that	SCONJ
ejpam-6247	433	7	g	g	PROPN
ejpam-6247	433	8	⊆⋂	⊆⋂	PROPN
ejpam-6247	433	9	q∈specdg	q∈specdg	INTJ
ejpam-6247	433	10	(	(	PUNCT
ejpam-6247	433	11	l)q	l)q	X
ejpam-6247	433	12	=	=	SYM
ejpam-6247	433	13	d.	d.	PROPN
ejpam-6247	433	14	thus	thus	ADV
ejpam-6247	433	15	,	,	PUNCT
ejpam-6247	433	16	we	we	PRON
ejpam-6247	433	17	deduce	deduce	VERB
ejpam-6247	433	18	that	that	PRON
ejpam-6247	433	19	g	g	NOUN
ejpam-6247	433	20	=	=	PUNCT
ejpam-6247	433	21	d.	d.	PROPN
ejpam-6247	433	22	conversely	conversely	ADV
ejpam-6247	433	23	,	,	PUNCT
ejpam-6247	433	24	suppose	suppose	VERB
ejpam-6247	433	25	that	that	SCONJ
ejpam-6247	433	26	g	g	PROPN
ejpam-6247	433	27	=	=	PROPN
ejpam-6247	433	28	d.	d.	PROPN
ejpam-6247	433	29	then	then	ADV
ejpam-6247	433	30	,	,	PUNCT
ejpam-6247	433	31	g	g	PROPN
ejpam-6247	433	32	=	=	SYM
ejpam-6247	433	33	d	d	NOUN
ejpam-6247	433	34	is	be	AUX
ejpam-6247	433	35	contained	contain	VERB
ejpam-6247	433	36	in	in	ADP
ejpam-6247	433	37	all	all	DET
ejpam-6247	433	38	q	q	PROPN
ejpam-6247	433	39	∈	∈	PROPN
ejpam-6247	433	40	specdg	specdg	NOUN
ejpam-6247	433	41	(	(	PUNCT
ejpam-6247	433	42	l	l	NOUN
ejpam-6247	433	43	)	)	PUNCT
ejpam-6247	433	44	,	,	PUNCT
ejpam-6247	433	45	which	which	PRON
ejpam-6247	433	46	implies	imply	VERB
ejpam-6247	433	47	that	that	SCONJ
ejpam-6247	433	48	v(g	v(g	ADJ
ejpam-6247	433	49	)	)	PUNCT
ejpam-6247	434	1	=	=	SYM
ejpam-6247	434	2	specdg	specdg	PROPN
ejpam-6247	434	3	(	(	PUNCT
ejpam-6247	434	4	l	l	NOUN
ejpam-6247	434	5	)	)	PUNCT
ejpam-6247	434	6	.	.	PUNCT
ejpam-6247	435	1	(	(	PUNCT
ejpam-6247	435	2	2	2	X
ejpam-6247	435	3	)	)	PUNCT
ejpam-6247	435	4	assume	assume	VERB
ejpam-6247	435	5	that	that	SCONJ
ejpam-6247	435	6	v(g	v(g	VERB
ejpam-6247	435	7	)	)	PUNCT
ejpam-6247	435	8	=	=	PUNCT
ejpam-6247	435	9	∅.	∅.	PROPN
ejpam-6247	435	10	suppose	suppose	VERB
ejpam-6247	435	11	,	,	PUNCT
ejpam-6247	435	12	for	for	ADP
ejpam-6247	435	13	the	the	DET
ejpam-6247	435	14	sake	sake	NOUN
ejpam-6247	435	15	of	of	ADP
ejpam-6247	435	16	contradiction	contradiction	NOUN
ejpam-6247	435	17	,	,	PUNCT
ejpam-6247	435	18	that	that	SCONJ
ejpam-6247	435	19	g	g	NOUN
ejpam-6247	435	20	=	=	NOUN
ejpam-6247	435	21	̸	̸	X
ejpam-6247	435	22	l.	l.	NOUN
ejpam-6247	435	23	in	in	ADP
ejpam-6247	435	24	this	this	DET
ejpam-6247	435	25	case	case	NOUN
ejpam-6247	435	26	,	,	PUNCT
ejpam-6247	435	27	there	there	PRON
ejpam-6247	435	28	exists	exist	VERB
ejpam-6247	435	29	a	a	DET
ejpam-6247	435	30	prime	prime	ADJ
ejpam-6247	435	31	d	d	NOUN
ejpam-6247	435	32	-	-	NOUN
ejpam-6247	435	33	filter	filter	NOUN
ejpam-6247	435	34	q	q	NOUN
ejpam-6247	436	1	such	such	ADJ
ejpam-6247	436	2	that	that	SCONJ
ejpam-6247	436	3	g	g	PROPN
ejpam-6247	436	4	⊆	⊆	NUM
ejpam-6247	436	5	q.	q.	NOUN
ejpam-6247	436	6	consequently	consequently	ADV
ejpam-6247	436	7	,	,	PUNCT
ejpam-6247	436	8	q	q	PROPN
ejpam-6247	436	9	∈	∈	PROPN
ejpam-6247	436	10	v(g	v(g	NOUN
ejpam-6247	436	11	)	)	PUNCT
ejpam-6247	436	12	,	,	PUNCT
ejpam-6247	436	13	but	but	CCONJ
ejpam-6247	436	14	since	since	SCONJ
ejpam-6247	436	15	v(g	v(g	ADJ
ejpam-6247	436	16	)	)	PUNCT
ejpam-6247	436	17	=	=	VERB
ejpam-6247	436	18	∅	∅	NOUN
ejpam-6247	436	19	,	,	PUNCT
ejpam-6247	436	20	this	this	PRON
ejpam-6247	436	21	leads	lead	VERB
ejpam-6247	436	22	to	to	ADP
ejpam-6247	436	23	a	a	DET
ejpam-6247	436	24	contradiction	contradiction	NOUN
ejpam-6247	436	25	.	.	PUNCT
ejpam-6247	437	1	therefore	therefore	ADV
ejpam-6247	437	2	,	,	PUNCT
ejpam-6247	437	3	we	we	PRON
ejpam-6247	437	4	conclude	conclude	VERB
ejpam-6247	437	5	that	that	PRON
ejpam-6247	437	6	g	g	PROPN
ejpam-6247	437	7	=	=	PUNCT
ejpam-6247	437	8	l.	l.	PROPN
ejpam-6247	437	9	conversely	conversely	ADV
ejpam-6247	437	10	,	,	PUNCT
ejpam-6247	437	11	let	let	VERB
ejpam-6247	437	12	g	g	PROPN
ejpam-6247	437	13	=	=	PUNCT
ejpam-6247	437	14	l.	l.	PROPN
ejpam-6247	437	15	since	since	SCONJ
ejpam-6247	437	16	there	there	PRON
ejpam-6247	437	17	is	be	VERB
ejpam-6247	437	18	no	no	DET
ejpam-6247	437	19	prime	prime	ADJ
ejpam-6247	437	20	d	d	NOUN
ejpam-6247	437	21	-	-	NOUN
ejpam-6247	437	22	filter	filter	NOUN
ejpam-6247	437	23	containing	contain	VERB
ejpam-6247	437	24	g	g	NOUN
ejpam-6247	437	25	,	,	PUNCT
ejpam-6247	437	26	we	we	PRON
ejpam-6247	437	27	get	get	VERB
ejpam-6247	437	28	v(g	v(g	ADJ
ejpam-6247	437	29	)	)	PUNCT
ejpam-6247	437	30	=	=	SYM
ejpam-6247	437	31	∅.	∅.	X
ejpam-6247	437	32	(	(	PUNCT
ejpam-6247	437	33	3	3	X
ejpam-6247	437	34	)	)	PUNCT
ejpam-6247	437	35	it	it	PRON
ejpam-6247	437	36	is	be	AUX
ejpam-6247	437	37	evident	evident	ADJ
ejpam-6247	437	38	that	that	SCONJ
ejpam-6247	437	39	,	,	PUNCT
ejpam-6247	437	40	since	since	SCONJ
ejpam-6247	437	41	q	q	NOUN
ejpam-6247	437	42	is	be	AUX
ejpam-6247	437	43	a	a	DET
ejpam-6247	437	44	prime	prime	ADJ
ejpam-6247	437	45	d	d	NOUN
ejpam-6247	437	46	-	-	NOUN
ejpam-6247	437	47	filter	filter	NOUN
ejpam-6247	437	48	,	,	PUNCT
ejpam-6247	437	49	properties	property	NOUN
ejpam-6247	437	50	(	(	PUNCT
ejpam-6247	437	51	4	4	NUM
ejpam-6247	437	52	)	)	PUNCT
ejpam-6247	437	53	and	and	CCONJ
ejpam-6247	437	54	(	(	PUNCT
ejpam-6247	437	55	5	5	X
ejpam-6247	437	56	)	)	PUNCT
ejpam-6247	437	57	follow	follow	VERB
ejpam-6247	437	58	directly	directly	ADV
ejpam-6247	437	59	.	.	PUNCT
ejpam-6247	438	1	from	from	ADP
ejpam-6247	438	2	the	the	DET
ejpam-6247	438	3	results	result	NOUN
ejpam-6247	438	4	above	above	ADV
ejpam-6247	438	5	,	,	PUNCT
ejpam-6247	438	6	it	it	PRON
ejpam-6247	438	7	is	be	AUX
ejpam-6247	438	8	evident	evident	ADJ
ejpam-6247	438	9	that	that	SCONJ
ejpam-6247	438	10	the	the	DET
ejpam-6247	438	11	collection	collection	NOUN
ejpam-6247	438	12	{	{	PUNCT
ejpam-6247	438	13	j	j	PROPN
ejpam-6247	438	14	(	(	PUNCT
ejpam-6247	438	15	g	g	NOUN
ejpam-6247	438	16	)	)	PUNCT
ejpam-6247	438	17	|	|	ADV
ejpam-6247	438	18	g	g	PROPN
ejpam-6247	438	19	∈	∈	PROPN
ejpam-6247	438	20	gd(l	gd(l	NOUN
ejpam-6247	438	21	)	)	PUNCT
ejpam-6247	438	22	}	}	PUNCT
ejpam-6247	438	23	forms	form	VERB
ejpam-6247	438	24	a	a	DET
ejpam-6247	438	25	basis	basis	NOUN
ejpam-6247	438	26	for	for	ADP
ejpam-6247	438	27	a	a	DET
ejpam-6247	438	28	topology	topology	NOUN
ejpam-6247	438	29	on	on	ADP
ejpam-6247	438	30	specdg	specdg	PROPN
ejpam-6247	438	31	(	(	PUNCT
ejpam-6247	438	32	l	l	NOUN
ejpam-6247	438	33	)	)	PUNCT
ejpam-6247	438	34	.	.	PUNCT
ejpam-6247	439	1	in	in	ADP
ejpam-6247	439	2	this	this	DET
ejpam-6247	439	3	hull	hull	NOUN
ejpam-6247	439	4	-	-	PUNCT
ejpam-6247	439	5	kernel	kernel	NOUN
ejpam-6247	439	6	topology	topology	NOUN
ejpam-6247	439	7	,	,	PUNCT
ejpam-6247	439	8	the	the	DET
ejpam-6247	439	9	open	open	ADJ
ejpam-6247	439	10	sets	set	NOUN
ejpam-6247	439	11	are	be	AUX
ejpam-6247	439	12	of	of	ADP
ejpam-6247	439	13	the	the	DET
ejpam-6247	439	14	form	form	NOUN
ejpam-6247	439	15	j	j	PROPN
ejpam-6247	439	16	(	(	PUNCT
ejpam-6247	439	17	g	g	NOUN
ejpam-6247	439	18	)	)	PUNCT
ejpam-6247	439	19	,	,	PUNCT
ejpam-6247	439	20	where	where	SCONJ
ejpam-6247	439	21	j	j	PROPN
ejpam-6247	439	22	(	(	PUNCT
ejpam-6247	439	23	g	g	NOUN
ejpam-6247	439	24	)	)	PUNCT
ejpam-6247	439	25	=	=	PRON
ejpam-6247	439	26	{	{	PUNCT
ejpam-6247	439	27	q	q	NOUN
ejpam-6247	439	28	∈	∈	PROPN
ejpam-6247	439	29	specdg	specdg	NOUN
ejpam-6247	439	30	(	(	PUNCT
ejpam-6247	439	31	l	l	NOUN
ejpam-6247	439	32	)	)	PUNCT
ejpam-6247	440	1	|	|	ADV
ejpam-6247	440	2	g	g	X
ejpam-6247	440	3	̸⊆	̸⊆	NOUN
ejpam-6247	440	4	q	q	NOUN
ejpam-6247	440	5	}	}	PUNCT
ejpam-6247	440	6	,	,	PUNCT
ejpam-6247	440	7	and	and	CCONJ
ejpam-6247	440	8	the	the	DET
ejpam-6247	440	9	closed	close	VERB
ejpam-6247	440	10	sets	set	NOUN
ejpam-6247	440	11	are	be	AUX
ejpam-6247	440	12	of	of	ADP
ejpam-6247	440	13	the	the	DET
ejpam-6247	440	14	form	form	NOUN
ejpam-6247	440	15	v(g	v(g	ADJ
ejpam-6247	440	16	)	)	PUNCT
ejpam-6247	440	17	=	=	SYM
ejpam-6247	441	1	specdg	specdg	PROPN
ejpam-6247	441	2	(	(	PUNCT
ejpam-6247	441	3	l	l	NOUN
ejpam-6247	441	4	)	)	PUNCT
ejpam-6247	441	5	\	\	PROPN
ejpam-6247	442	1	j	j	PROPN
ejpam-6247	442	2	(	(	PUNCT
ejpam-6247	442	3	g	g	NOUN
ejpam-6247	442	4	)	)	PUNCT
ejpam-6247	442	5	.	.	PUNCT
ejpam-6247	443	1	for	for	ADP
ejpam-6247	443	2	any	any	DET
ejpam-6247	443	3	subset	subset	NOUN
ejpam-6247	443	4	s	s	PROPN
ejpam-6247	443	5	of	of	ADP
ejpam-6247	443	6	specdg	specdg	PROPN
ejpam-6247	443	7	(	(	PUNCT
ejpam-6247	443	8	l	l	NOUN
ejpam-6247	443	9	)	)	PUNCT
ejpam-6247	443	10	,	,	PUNCT
ejpam-6247	443	11	the	the	DET
ejpam-6247	443	12	closure	closure	NOUN
ejpam-6247	443	13	s	s	X
ejpam-6247	443	14	of	of	ADP
ejpam-6247	443	15	s	s	PRON
ejpam-6247	443	16	in	in	ADP
ejpam-6247	443	17	the	the	DET
ejpam-6247	443	18	hull	hull	NOUN
ejpam-6247	443	19	-	-	PUNCT
ejpam-6247	443	20	kernel	kernel	NOUN
ejpam-6247	443	21	topology	topology	NOUN
ejpam-6247	443	22	is	be	AUX
ejpam-6247	443	23	given	give	VERB
ejpam-6247	443	24	by	by	ADP
ejpam-6247	443	25	s	s	NOUN
ejpam-6247	443	26	=	=	PUNCT
ejpam-6247	443	27	{	{	PUNCT
ejpam-6247	443	28	p	p	NOUN
ejpam-6247	443	29	∈	∈	PROPN
ejpam-6247	443	30	specdg	specdg	NOUN
ejpam-6247	443	31	(	(	PUNCT
ejpam-6247	443	32	l	l	NOUN
ejpam-6247	443	33	)	)	PUNCT
ejpam-6247	444	1	|	|	ADV
ejpam-6247	444	2	⋂	⋂	PROPN
ejpam-6247	444	3	q∈s	q∈s	NOUN
ejpam-6247	444	4	q	q	NOUN
ejpam-6247	445	1	⊆	⊆	NUM
ejpam-6247	445	2	p	p	X
ejpam-6247	445	3	}	}	PUNCT
ejpam-6247	445	4	.	.	PUNCT
ejpam-6247	446	1	n.	n.	PROPN
ejpam-6247	446	2	rafi	rafi	PROPN
ejpam-6247	446	3	et	et	PROPN
ejpam-6247	446	4	al	al	PROPN
ejpam-6247	446	5	.	.	PUNCT
ejpam-6247	446	6	/	/	SYM
ejpam-6247	446	7	eur	eur	PROPN
ejpam-6247	446	8	.	.	PUNCT
ejpam-6247	447	1	j.	j.	PROPN
ejpam-6247	447	2	pure	pure	PROPN
ejpam-6247	447	3	appl	appl	PROPN
ejpam-6247	447	4	.	.	PROPN
ejpam-6247	447	5	math	math	PROPN
ejpam-6247	447	6	,	,	PUNCT
ejpam-6247	447	7	18	18	NUM
ejpam-6247	447	8	(	(	PUNCT
ejpam-6247	447	9	3	3	NUM
ejpam-6247	447	10	)	)	PUNCT
ejpam-6247	447	11	(	(	PUNCT
ejpam-6247	447	12	2025	2025	NUM
ejpam-6247	447	13	)	)	PUNCT
ejpam-6247	447	14	,	,	PUNCT
ejpam-6247	447	15	6247	6247	NUM
ejpam-6247	447	16	14	14	NUM
ejpam-6247	447	17	of	of	ADP
ejpam-6247	447	18	15	15	NUM
ejpam-6247	447	19	lemma	lemma	PROPN
ejpam-6247	447	20	7	7	NUM
ejpam-6247	447	21	.	.	X
ejpam-6247	448	1	for	for	ADP
ejpam-6247	448	2	any	any	DET
ejpam-6247	448	3	element	element	NOUN
ejpam-6247	448	4	µ	µ	PROPN
ejpam-6247	448	5	∈	∈	PROPN
ejpam-6247	448	6	l	l	NOUN
ejpam-6247	448	7	,	,	PUNCT
ejpam-6247	448	8	we	we	PRON
ejpam-6247	448	9	have	have	VERB
ejpam-6247	448	10	j	j	PROPN
ejpam-6247	448	11	(	(	PUNCT
ejpam-6247	448	12	µ	µ	NOUN
ejpam-6247	448	13	)	)	PUNCT
ejpam-6247	448	14	=	=	SYM
ejpam-6247	448	15	v((µ,d	v((µ,d	NOUN
ejpam-6247	448	16	)	)	PUNCT
ejpam-6247	448	17	)	)	PUNCT
ejpam-6247	448	18	.	.	PUNCT
ejpam-6247	449	1	proof	proof	NOUN
ejpam-6247	449	2	.	.	PUNCT
ejpam-6247	450	1	j	j	PROPN
ejpam-6247	450	2	(	(	PUNCT
ejpam-6247	450	3	µ	µ	NOUN
ejpam-6247	450	4	)	)	PUNCT
ejpam-6247	450	5	=	=	PRON
ejpam-6247	450	6	{	{	PUNCT
ejpam-6247	450	7	p	p	NOUN
ejpam-6247	450	8	∈	∈	PROPN
ejpam-6247	450	9	specdg	specdg	NOUN
ejpam-6247	450	10	(	(	PUNCT
ejpam-6247	450	11	l	l	NOUN
ejpam-6247	450	12	)	)	PUNCT
ejpam-6247	451	1	|	|	ADV
ejpam-6247	451	2	⋂	⋂	PROPN
ejpam-6247	451	3	q∈j	q∈j	NOUN
ejpam-6247	451	4	(	(	PUNCT
ejpam-6247	451	5	µ	µ	NOUN
ejpam-6247	451	6	)	)	PUNCT
ejpam-6247	451	7	q	q	NOUN
ejpam-6247	452	1	⊆	⊆	NUM
ejpam-6247	452	2	p	p	NOUN
ejpam-6247	452	3	}	}	PUNCT
ejpam-6247	452	4	=	=	PUNCT
ejpam-6247	452	5	{	{	PUNCT
ejpam-6247	452	6	p	p	NOUN
ejpam-6247	452	7	∈	∈	PROPN
ejpam-6247	452	8	specdg	specdg	NOUN
ejpam-6247	452	9	(	(	PUNCT
ejpam-6247	452	10	l	l	NOUN
ejpam-6247	452	11	)	)	PUNCT
ejpam-6247	452	12	|	|	ADV
ejpam-6247	452	13	(	(	PUNCT
ejpam-6247	452	14	µ,d	µ,d	NOUN
ejpam-6247	452	15	)	)	PUNCT
ejpam-6247	452	16	⊆	⊆	NUM
ejpam-6247	452	17	p	p	X
ejpam-6247	452	18	}	}	PUNCT
ejpam-6247	452	19	=	=	SYM
ejpam-6247	452	20	v((µ,d	v((µ,d	NOUN
ejpam-6247	452	21	)	)	PUNCT
ejpam-6247	452	22	)	)	PUNCT
ejpam-6247	452	23	.	.	PUNCT
ejpam-6247	453	1	theorem	theorem	VERB
ejpam-6247	453	2	7	7	NUM
ejpam-6247	453	3	.	.	PUNCT
ejpam-6247	453	4	an	an	DET
ejpam-6247	453	5	adl	adl	PROPN
ejpam-6247	453	6	l	l	NOUN
ejpam-6247	453	7	is	be	AUX
ejpam-6247	453	8	d	d	NOUN
ejpam-6247	453	9	-	-	NOUN
ejpam-6247	453	10	stone	stone	NOUN
ejpam-6247	453	11	if	if	SCONJ
ejpam-6247	453	12	and	and	CCONJ
ejpam-6247	453	13	only	only	ADV
ejpam-6247	453	14	if	if	SCONJ
ejpam-6247	453	15	for	for	ADP
ejpam-6247	453	16	any	any	DET
ejpam-6247	453	17	µ	µ	PROPN
ejpam-6247	453	18	∈	∈	PROPN
ejpam-6247	453	19	l	l	NOUN
ejpam-6247	453	20	,	,	PUNCT
ejpam-6247	453	21	the	the	DET
ejpam-6247	453	22	closure	closure	NOUN
ejpam-6247	453	23	j	j	PROPN
ejpam-6247	453	24	(	(	PUNCT
ejpam-6247	453	25	µ	µ	NOUN
ejpam-6247	453	26	)	)	PUNCT
ejpam-6247	453	27	is	be	AUX
ejpam-6247	453	28	open	open	ADJ
ejpam-6247	453	29	in	in	ADP
ejpam-6247	453	30	the	the	DET
ejpam-6247	453	31	hull	hull	NOUN
ejpam-6247	453	32	-	-	PUNCT
ejpam-6247	453	33	kernel	kernel	NOUN
ejpam-6247	453	34	topology	topology	NOUN
ejpam-6247	453	35	on	on	ADP
ejpam-6247	453	36	specdg	specdg	PROPN
ejpam-6247	453	37	(	(	PUNCT
ejpam-6247	453	38	l	l	NOUN
ejpam-6247	453	39	)	)	PUNCT
ejpam-6247	453	40	.	.	PUNCT
ejpam-6247	454	1	proof	proof	NOUN
ejpam-6247	454	2	.	.	PUNCT
ejpam-6247	455	1	assume	assume	VERB
ejpam-6247	455	2	that	that	SCONJ
ejpam-6247	455	3	l	l	NOUN
ejpam-6247	455	4	is	be	AUX
ejpam-6247	455	5	d	d	NOUN
ejpam-6247	455	6	-	-	NOUN
ejpam-6247	455	7	stone	stone	NOUN
ejpam-6247	455	8	.	.	PUNCT
ejpam-6247	456	1	let	let	VERB
ejpam-6247	456	2	µ	µ	X
ejpam-6247	456	3	∈	∈	PROPN
ejpam-6247	456	4	l.	l.	NOUN
ejpam-6247	456	5	then	then	ADV
ejpam-6247	456	6	j	j	PROPN
ejpam-6247	456	7	(	(	PUNCT
ejpam-6247	456	8	µ	µ	NOUN
ejpam-6247	456	9	)	)	PUNCT
ejpam-6247	456	10	=	=	PRON
ejpam-6247	456	11	{	{	PUNCT
ejpam-6247	456	12	p	p	NOUN
ejpam-6247	456	13	∈	∈	PROPN
ejpam-6247	456	14	specdg	specdg	NOUN
ejpam-6247	456	15	(	(	PUNCT
ejpam-6247	456	16	l	l	NOUN
ejpam-6247	456	17	)	)	PUNCT
ejpam-6247	457	1	|	|	ADV
ejpam-6247	457	2	⋂	⋂	PROPN
ejpam-6247	457	3	q∈j	q∈j	NOUN
ejpam-6247	457	4	(	(	PUNCT
ejpam-6247	457	5	µ	µ	NOUN
ejpam-6247	457	6	)	)	PUNCT
ejpam-6247	457	7	q	q	NOUN
ejpam-6247	458	1	⊆	⊆	NUM
ejpam-6247	458	2	p	p	NOUN
ejpam-6247	458	3	}	}	PUNCT
ejpam-6247	458	4	=	=	PUNCT
ejpam-6247	458	5	{	{	PUNCT
ejpam-6247	458	6	p	p	NOUN
ejpam-6247	458	7	∈	∈	PROPN
ejpam-6247	458	8	specdg	specdg	NOUN
ejpam-6247	458	9	(	(	PUNCT
ejpam-6247	458	10	l	l	NOUN
ejpam-6247	458	11	)	)	PUNCT
ejpam-6247	458	12	|	|	ADV
ejpam-6247	458	13	(	(	PUNCT
ejpam-6247	458	14	µ,d	µ,d	NOUN
ejpam-6247	458	15	)	)	PUNCT
ejpam-6247	458	16	⊆	⊆	NUM
ejpam-6247	458	17	p	p	X
ejpam-6247	458	18	}	}	PUNCT
ejpam-6247	458	19	=	=	PUNCT
ejpam-6247	458	20	{	{	PUNCT
ejpam-6247	458	21	p	p	NOUN
ejpam-6247	458	22	∈	∈	PROPN
ejpam-6247	458	23	specdg	specdg	NOUN
ejpam-6247	458	24	(	(	PUNCT
ejpam-6247	458	25	l	l	NOUN
ejpam-6247	458	26	)	)	PUNCT
ejpam-6247	459	1	|	|	ADV
ejpam-6247	459	2	(	(	PUNCT
ejpam-6247	459	3	(	(	PUNCT
ejpam-6247	459	4	µ,d),d	µ,d),d	NOUN
ejpam-6247	459	5	)	)	PUNCT
ejpam-6247	459	6	⊈	⊈	PROPN
ejpam-6247	460	1	p	p	X
ejpam-6247	460	2	}	}	PUNCT
ejpam-6247	460	3	(	(	PUNCT
ejpam-6247	460	4	since	since	SCONJ
ejpam-6247	460	5	l	l	PROPN
ejpam-6247	460	6	is	be	AUX
ejpam-6247	460	7	d	d	NOUN
ejpam-6247	460	8	-	-	NOUN
ejpam-6247	460	9	stone	stone	NOUN
ejpam-6247	460	10	)	)	PUNCT
ejpam-6247	461	1	=	=	SYM
ejpam-6247	461	2	j	j	PROPN
ejpam-6247	461	3	(	(	PUNCT
ejpam-6247	461	4	(	(	PUNCT
ejpam-6247	461	5	(	(	PUNCT
ejpam-6247	461	6	µ,d),d	µ,d),d	NOUN
ejpam-6247	461	7	)	)	PUNCT
ejpam-6247	461	8	)	)	PUNCT
ejpam-6247	461	9	.	.	PUNCT
ejpam-6247	462	1	since	since	SCONJ
ejpam-6247	462	2	j	j	PROPN
ejpam-6247	462	3	(	(	PUNCT
ejpam-6247	462	4	(	(	PUNCT
ejpam-6247	462	5	(	(	PUNCT
ejpam-6247	462	6	µ,d),d	µ,d),d	NOUN
ejpam-6247	462	7	)	)	PUNCT
ejpam-6247	462	8	)	)	PUNCT
ejpam-6247	462	9	is	be	AUX
ejpam-6247	462	10	an	an	DET
ejpam-6247	462	11	open	open	ADJ
ejpam-6247	462	12	set	set	NOUN
ejpam-6247	462	13	in	in	ADP
ejpam-6247	462	14	specdg	specdg	PROPN
ejpam-6247	462	15	(	(	PUNCT
ejpam-6247	462	16	l	l	NOUN
ejpam-6247	462	17	)	)	PUNCT
ejpam-6247	462	18	,	,	PUNCT
ejpam-6247	462	19	it	it	PRON
ejpam-6247	462	20	follows	follow	VERB
ejpam-6247	462	21	that	that	SCONJ
ejpam-6247	462	22	j	j	PROPN
ejpam-6247	462	23	(	(	PUNCT
ejpam-6247	462	24	µ	µ	NOUN
ejpam-6247	462	25	)	)	PUNCT
ejpam-6247	462	26	must	must	AUX
ejpam-6247	462	27	be	be	AUX
ejpam-6247	462	28	open	open	ADJ
ejpam-6247	462	29	in	in	ADP
ejpam-6247	462	30	specdg	specdg	PROPN
ejpam-6247	462	31	(	(	PUNCT
ejpam-6247	462	32	l	l	NOUN
ejpam-6247	462	33	)	)	PUNCT
ejpam-6247	462	34	.	.	PUNCT
ejpam-6247	463	1	on	on	ADP
ejpam-6247	463	2	the	the	DET
ejpam-6247	463	3	other	other	ADJ
ejpam-6247	463	4	hand	hand	NOUN
ejpam-6247	463	5	,	,	PUNCT
ejpam-6247	463	6	suppose	suppose	VERB
ejpam-6247	463	7	j	j	PROPN
ejpam-6247	463	8	(	(	PUNCT
ejpam-6247	463	9	µ	µ	NOUN
ejpam-6247	463	10	)	)	PUNCT
ejpam-6247	463	11	is	be	AUX
ejpam-6247	463	12	open	open	ADJ
ejpam-6247	463	13	in	in	ADP
ejpam-6247	463	14	the	the	DET
ejpam-6247	463	15	hull	hull	NOUN
ejpam-6247	463	16	-	-	PUNCT
ejpam-6247	463	17	kernel	kernel	NOUN
ejpam-6247	463	18	topology	topology	NOUN
ejpam-6247	463	19	on	on	ADP
ejpam-6247	463	20	specdg	specdg	PROPN
ejpam-6247	463	21	(	(	PUNCT
ejpam-6247	463	22	l	l	NOUN
ejpam-6247	463	23	)	)	PUNCT
ejpam-6247	463	24	.	.	PUNCT
ejpam-6247	464	1	this	this	PRON
ejpam-6247	464	2	means	mean	VERB
ejpam-6247	464	3	that	that	SCONJ
ejpam-6247	464	4	specdg	specdg	PROPN
ejpam-6247	464	5	(	(	PUNCT
ejpam-6247	464	6	l)\j	l)\j	PROPN
ejpam-6247	464	7	(	(	PUNCT
ejpam-6247	464	8	µ	µ	NOUN
ejpam-6247	464	9	)	)	PUNCT
ejpam-6247	464	10	is	be	AUX
ejpam-6247	464	11	a	a	DET
ejpam-6247	464	12	closed	closed	ADJ
ejpam-6247	464	13	set	set	NOUN
ejpam-6247	464	14	in	in	ADP
ejpam-6247	464	15	specdg	specdg	PROPN
ejpam-6247	464	16	(	(	PUNCT
ejpam-6247	464	17	l	l	NOUN
ejpam-6247	464	18	)	)	PUNCT
ejpam-6247	464	19	.	.	PUNCT
ejpam-6247	465	1	therefore	therefore	ADV
ejpam-6247	465	2	,	,	PUNCT
ejpam-6247	465	3	there	there	PRON
ejpam-6247	465	4	must	must	AUX
ejpam-6247	465	5	exist	exist	VERB
ejpam-6247	465	6	a	a	DET
ejpam-6247	465	7	prime	prime	ADJ
ejpam-6247	465	8	d	d	NOUN
ejpam-6247	465	9	-	-	NOUN
ejpam-6247	465	10	filter	filter	NOUN
ejpam-6247	465	11	g	g	NOUN
ejpam-6247	465	12	of	of	ADP
ejpam-6247	465	13	l	l	NOUN
ejpam-6247	465	14	such	such	ADJ
ejpam-6247	465	15	that	that	DET
ejpam-6247	465	16	specdg	specdg	PROPN
ejpam-6247	465	17	(	(	PUNCT
ejpam-6247	465	18	l)\j	l)\j	PROPN
ejpam-6247	465	19	(	(	PUNCT
ejpam-6247	465	20	µ	µ	NOUN
ejpam-6247	465	21	)	)	PUNCT
ejpam-6247	465	22	=	=	SYM
ejpam-6247	465	23	v(g	v(g	ADJ
ejpam-6247	465	24	)	)	PUNCT
ejpam-6247	465	25	.	.	PUNCT
ejpam-6247	466	1	from	from	ADP
ejpam-6247	466	2	earlier	early	ADJ
ejpam-6247	466	3	results	result	NOUN
ejpam-6247	466	4	,	,	PUNCT
ejpam-6247	466	5	we	we	PRON
ejpam-6247	466	6	know	know	VERB
ejpam-6247	466	7	that	that	SCONJ
ejpam-6247	466	8	j	j	PROPN
ejpam-6247	466	9	(	(	PUNCT
ejpam-6247	466	10	µ	µ	NOUN
ejpam-6247	466	11	)	)	PUNCT
ejpam-6247	466	12	=	=	SYM
ejpam-6247	466	13	v((µ,d	v((µ,d	NOUN
ejpam-6247	466	14	)	)	PUNCT
ejpam-6247	466	15	)	)	PUNCT
ejpam-6247	466	16	.	.	PUNCT
ejpam-6247	467	1	as	as	ADP
ejpam-6247	467	2	a	a	DET
ejpam-6247	467	3	result	result	NOUN
ejpam-6247	467	4	,	,	PUNCT
ejpam-6247	467	5	v(g	v(g	ADJ
ejpam-6247	467	6	)	)	PUNCT
ejpam-6247	467	7	and	and	CCONJ
ejpam-6247	467	8	v((µ,d	v((µ,d	NOUN
ejpam-6247	467	9	)	)	PUNCT
ejpam-6247	467	10	)	)	PUNCT
ejpam-6247	467	11	are	be	AUX
ejpam-6247	467	12	complementary	complementary	ADJ
ejpam-6247	467	13	sets	set	NOUN
ejpam-6247	467	14	in	in	ADP
ejpam-6247	467	15	specdg	specdg	PROPN
ejpam-6247	467	16	(	(	PUNCT
ejpam-6247	467	17	l	l	NOUN
ejpam-6247	467	18	)	)	PUNCT
ejpam-6247	467	19	,	,	PUNCT
ejpam-6247	467	20	so	so	ADV
ejpam-6247	467	21	v((µ,d))∪v(g	v((µ,d))∪v(g	NOUN
ejpam-6247	467	22	)	)	PUNCT
ejpam-6247	468	1	=	=	SYM
ejpam-6247	468	2	specdg	specdg	PROPN
ejpam-6247	468	3	(	(	PUNCT
ejpam-6247	468	4	l	l	NOUN
ejpam-6247	468	5	)	)	PUNCT
ejpam-6247	468	6	and	and	CCONJ
ejpam-6247	468	7	v((µ,d))∩v(g	v((µ,d))∩v(g	ADJ
ejpam-6247	468	8	)	)	PUNCT
ejpam-6247	468	9	=	=	PUNCT
ejpam-6247	468	10	∅.	∅.	X
ejpam-6247	468	11	by	by	ADP
ejpam-6247	468	12	lemma	lemma	PROPN
ejpam-6247	468	13	5	5	NUM
ejpam-6247	468	14	(	(	PUNCT
ejpam-6247	468	15	4	4	NUM
ejpam-6247	468	16	)	)	PUNCT
ejpam-6247	468	17	and	and	CCONJ
ejpam-6247	468	18	(	(	PUNCT
ejpam-6247	468	19	6	6	NUM
ejpam-6247	468	20	)	)	PUNCT
ejpam-6247	468	21	,	,	PUNCT
ejpam-6247	468	22	it	it	PRON
ejpam-6247	468	23	follows	follow	VERB
ejpam-6247	468	24	that	that	SCONJ
ejpam-6247	468	25	v((µ,d)∩g	v((µ,d)∩g	NOUN
ejpam-6247	468	26	)	)	PUNCT
ejpam-6247	469	1	=	=	SYM
ejpam-6247	469	2	specdg	specdg	PROPN
ejpam-6247	469	3	(	(	PUNCT
ejpam-6247	469	4	l	l	NOUN
ejpam-6247	469	5	)	)	PUNCT
ejpam-6247	469	6	and	and	CCONJ
ejpam-6247	469	7	v((µ,d)∨g	v((µ,d)∨g	NOUN
ejpam-6247	469	8	)	)	PUNCT
ejpam-6247	470	1	=	=	PUNCT
ejpam-6247	470	2	∅.	∅.	ADP
ejpam-6247	470	3	applying	apply	VERB
ejpam-6247	470	4	lemma	lemma	PROPN
ejpam-6247	470	5	5	5	NUM
ejpam-6247	470	6	(	(	PUNCT
ejpam-6247	470	7	1	1	NUM
ejpam-6247	470	8	)	)	PUNCT
ejpam-6247	470	9	and	and	CCONJ
ejpam-6247	470	10	(	(	PUNCT
ejpam-6247	470	11	2	2	NUM
ejpam-6247	470	12	)	)	PUNCT
ejpam-6247	470	13	,	,	PUNCT
ejpam-6247	470	14	we	we	PRON
ejpam-6247	470	15	get	get	VERB
ejpam-6247	470	16	(	(	PUNCT
ejpam-6247	470	17	µ,d)∩g	µ,d)∩g	X
ejpam-6247	470	18	=	=	SYM
ejpam-6247	470	19	d	d	PROPN
ejpam-6247	470	20	and	and	CCONJ
ejpam-6247	470	21	(	(	PUNCT
ejpam-6247	470	22	µ,d)∨g	µ,d)∨g	X
ejpam-6247	470	23	=	=	PUNCT
ejpam-6247	470	24	l.	l.	PROPN
ejpam-6247	470	25	since	since	SCONJ
ejpam-6247	470	26	(	(	PUNCT
ejpam-6247	470	27	µ,d)∩g	µ,d)∩g	PROPN
ejpam-6247	470	28	=	=	SYM
ejpam-6247	470	29	d	d	NOUN
ejpam-6247	470	30	,	,	PUNCT
ejpam-6247	470	31	by	by	ADP
ejpam-6247	470	32	proposition	proposition	NOUN
ejpam-6247	470	33	1	1	NUM
ejpam-6247	470	34	(	(	PUNCT
ejpam-6247	470	35	2	2	NUM
ejpam-6247	470	36	)	)	PUNCT
ejpam-6247	470	37	,	,	PUNCT
ejpam-6247	470	38	we	we	PRON
ejpam-6247	470	39	conclude	conclude	VERB
ejpam-6247	470	40	g	g	PROPN
ejpam-6247	470	41	⊆	⊆	NUM
ejpam-6247	470	42	(	(	PUNCT
ejpam-6247	470	43	(	(	PUNCT
ejpam-6247	470	44	µ,d),d	µ,d),d	NOUN
ejpam-6247	470	45	)	)	PUNCT
ejpam-6247	470	46	.	.	PUNCT
ejpam-6247	471	1	hence	hence	ADV
ejpam-6247	471	2	,	,	PUNCT
ejpam-6247	471	3	we	we	PRON
ejpam-6247	471	4	have	have	VERB
ejpam-6247	471	5	l	l	NOUN
ejpam-6247	471	6	=	=	SYM
ejpam-6247	471	7	(	(	PUNCT
ejpam-6247	471	8	µ,d	µ,d	NOUN
ejpam-6247	471	9	)	)	PUNCT
ejpam-6247	471	10	∨	∨	NOUN
ejpam-6247	471	11	g	g	PROPN
ejpam-6247	471	12	⊆	⊆	NUM
ejpam-6247	471	13	(	(	PUNCT
ejpam-6247	471	14	µ,d	µ,d	NOUN
ejpam-6247	471	15	)	)	PUNCT
ejpam-6247	471	16	∨	∨	NOUN
ejpam-6247	471	17	(	(	PUNCT
ejpam-6247	471	18	(	(	PUNCT
ejpam-6247	471	19	µ,d),d	µ,d),d	NOUN
ejpam-6247	471	20	)	)	PUNCT
ejpam-6247	471	21	.	.	PUNCT
ejpam-6247	472	1	thus	thus	ADV
ejpam-6247	472	2	,	,	PUNCT
ejpam-6247	472	3	l	l	NOUN
ejpam-6247	472	4	is	be	AUX
ejpam-6247	472	5	a	a	DET
ejpam-6247	472	6	d	d	ADJ
ejpam-6247	472	7	-	-	NOUN
ejpam-6247	472	8	stone	stone	NOUN
ejpam-6247	472	9	adl	adl	PROPN
ejpam-6247	472	10	.	.	PROPN
ejpam-6247	472	11	5	5	NUM
ejpam-6247	472	12	.	.	X
ejpam-6247	472	13	conclusion	conclusion	NOUN
ejpam-6247	472	14	this	this	DET
ejpam-6247	472	15	article	article	NOUN
ejpam-6247	472	16	investigates	investigate	VERB
ejpam-6247	472	17	the	the	DET
ejpam-6247	472	18	structural	structural	ADJ
ejpam-6247	472	19	characteristics	characteristic	NOUN
ejpam-6247	472	20	of	of	ADP
ejpam-6247	472	21	hemicomplemented	hemicomplemente	VERB
ejpam-6247	472	22	adls	adls	NOUN
ejpam-6247	472	23	and	and	CCONJ
ejpam-6247	472	24	d	d	NOUN
ejpam-6247	472	25	-	-	NOUN
ejpam-6247	472	26	stone	stone	NOUN
ejpam-6247	472	27	adls	adls	PROPN
ejpam-6247	472	28	,	,	PUNCT
ejpam-6247	472	29	elucidating	elucidate	VERB
ejpam-6247	472	30	their	their	PRON
ejpam-6247	472	31	interrelationship	interrelationship	NOUN
ejpam-6247	472	32	and	and	CCONJ
ejpam-6247	472	33	providing	provide	VERB
ejpam-6247	472	34	a	a	DET
ejpam-6247	472	35	set	set	NOUN
ejpam-6247	472	36	of	of	ADP
ejpam-6247	472	37	equivalent	equivalent	ADJ
ejpam-6247	472	38	conditions	condition	NOUN
ejpam-6247	472	39	that	that	PRON
ejpam-6247	472	40	characterize	characterize	VERB
ejpam-6247	472	41	when	when	SCONJ
ejpam-6247	472	42	a	a	DET
ejpam-6247	472	43	hemicomplemented	hemicomplemente	VERB
ejpam-6247	472	44	adl	adl	NOUN
ejpam-6247	472	45	is	be	AUX
ejpam-6247	472	46	,	,	PUNCT
ejpam-6247	472	47	in	in	ADP
ejpam-6247	472	48	fact	fact	NOUN
ejpam-6247	472	49	,	,	PUNCT
ejpam-6247	472	50	a	a	DET
ejpam-6247	472	51	d	d	NOUN
ejpam-6247	472	52	-	-	NOUN
ejpam-6247	472	53	stone	stone	NOUN
ejpam-6247	472	54	adl	adl	PROPN
ejpam-6247	472	55	.	.	PUNCT
ejpam-6247	473	1	additionally	additionally	ADV
ejpam-6247	473	2	,	,	PUNCT
ejpam-6247	473	3	it	it	PRON
ejpam-6247	473	4	examines	examine	VERB
ejpam-6247	473	5	topological	topological	ADJ
ejpam-6247	473	6	characterizations	characterization	NOUN
ejpam-6247	473	7	of	of	ADP
ejpam-6247	473	8	these	these	DET
ejpam-6247	473	9	classes	class	NOUN
ejpam-6247	473	10	of	of	ADP
ejpam-6247	473	11	lattices	lattice	NOUN
ejpam-6247	473	12	,	,	PUNCT
ejpam-6247	473	13	particularly	particularly	ADV
ejpam-6247	473	14	through	through	ADP
ejpam-6247	473	15	the	the	DET
ejpam-6247	473	16	prime	prime	ADJ
ejpam-6247	473	17	spectrum	spectrum	NOUN
ejpam-6247	473	18	of	of	ADP
ejpam-6247	473	19	minimal	minimal	ADJ
ejpam-6247	473	20	prime	prime	ADJ
ejpam-6247	473	21	d	d	NOUN
ejpam-6247	473	22	-	-	NOUN
ejpam-6247	473	23	filters	filter	NOUN
ejpam-6247	473	24	.	.	PUNCT
ejpam-6247	474	1	these	these	DET
ejpam-6247	474	2	results	result	VERB
ejpam-6247	474	3	not	not	PART
ejpam-6247	474	4	only	only	ADV
ejpam-6247	474	5	extend	extend	VERB
ejpam-6247	474	6	the	the	DET
ejpam-6247	474	7	foundational	foundational	ADJ
ejpam-6247	474	8	understanding	understanding	NOUN
ejpam-6247	474	9	of	of	ADP
ejpam-6247	474	10	adls	adls	PROPN
ejpam-6247	474	11	but	but	CCONJ
ejpam-6247	474	12	also	also	ADV
ejpam-6247	474	13	reveal	reveal	VERB
ejpam-6247	474	14	intricate	intricate	ADJ
ejpam-6247	474	15	connections	connection	NOUN
ejpam-6247	474	16	between	between	ADP
ejpam-6247	474	17	algebraic	algebraic	ADJ
ejpam-6247	474	18	and	and	CCONJ
ejpam-6247	474	19	topological	topological	ADJ
ejpam-6247	474	20	properties	property	NOUN
ejpam-6247	474	21	.	.	PUNCT
ejpam-6247	475	1	as	as	ADP
ejpam-6247	475	2	a	a	DET
ejpam-6247	475	3	direction	direction	NOUN
ejpam-6247	475	4	for	for	ADP
ejpam-6247	475	5	future	future	ADJ
ejpam-6247	475	6	research	research	NOUN
ejpam-6247	475	7	,	,	PUNCT
ejpam-6247	475	8	the	the	DET
ejpam-6247	475	9	study	study	NOUN
ejpam-6247	475	10	proposes	propose	VERB
ejpam-6247	475	11	examining	examine	VERB
ejpam-6247	475	12	how	how	SCONJ
ejpam-6247	475	13	congruence	congruence	ADJ
ejpam-6247	475	14	relations	relation	NOUN
ejpam-6247	475	15	interact	interact	VERB
ejpam-6247	475	16	with	with	ADP
ejpam-6247	475	17	hemicomplemented	hemicomplemente	VERB
ejpam-6247	475	18	and	and	CCONJ
ejpam-6247	475	19	d	d	NOUN
ejpam-6247	475	20	-	-	ADJ
ejpam-6247	475	21	stone	stone	NOUN
ejpam-6247	475	22	structures	structure	NOUN
ejpam-6247	475	23	,	,	PUNCT
ejpam-6247	475	24	potentially	potentially	ADV
ejpam-6247	475	25	revealing	reveal	VERB
ejpam-6247	475	26	new	new	ADJ
ejpam-6247	475	27	topological	topological	ADJ
ejpam-6247	475	28	characterizations	characterization	NOUN
ejpam-6247	475	29	.	.	PUNCT
ejpam-6247	476	1	extending	extend	VERB
ejpam-6247	476	2	these	these	DET
ejpam-6247	476	3	results	result	NOUN
ejpam-6247	476	4	to	to	ADP
ejpam-6247	476	5	modular	modular	ADJ
ejpam-6247	476	6	and	and	CCONJ
ejpam-6247	476	7	non	non	ADJ
ejpam-6247	476	8	-	-	ADJ
ejpam-6247	476	9	modular	modular	ADJ
ejpam-6247	476	10	generalizations	generalization	NOUN
ejpam-6247	476	11	of	of	ADP
ejpam-6247	476	12	adls	adls	PROPN
ejpam-6247	476	13	is	be	AUX
ejpam-6247	476	14	also	also	ADV
ejpam-6247	476	15	anticipated	anticipate	VERB
ejpam-6247	476	16	to	to	PART
ejpam-6247	476	17	broaden	broaden	VERB
ejpam-6247	476	18	the	the	DET
ejpam-6247	476	19	understanding	understanding	NOUN
ejpam-6247	476	20	of	of	ADP
ejpam-6247	476	21	algebraic	algebraic	ADJ
ejpam-6247	476	22	-	-	PUNCT
ejpam-6247	476	23	topological	topological	ADJ
ejpam-6247	476	24	connections	connection	NOUN
ejpam-6247	476	25	in	in	ADP
ejpam-6247	476	26	these	these	DET
ejpam-6247	476	27	lattices	lattice	NOUN
ejpam-6247	476	28	.	.	PUNCT
ejpam-6247	477	1	n.	n.	PROPN
ejpam-6247	477	2	rafi	rafi	PROPN
ejpam-6247	477	3	et	et	PROPN
ejpam-6247	477	4	al	al	PROPN
ejpam-6247	477	5	.	.	PUNCT
ejpam-6247	477	6	/	/	SYM
ejpam-6247	477	7	eur	eur	PROPN
ejpam-6247	477	8	.	.	PUNCT
ejpam-6247	478	1	j.	j.	PROPN
ejpam-6247	478	2	pure	pure	PROPN
ejpam-6247	478	3	appl	appl	PROPN
ejpam-6247	478	4	.	.	PROPN
ejpam-6247	478	5	math	math	PROPN
ejpam-6247	478	6	,	,	PUNCT
ejpam-6247	478	7	18	18	NUM
ejpam-6247	478	8	(	(	PUNCT
ejpam-6247	478	9	3	3	NUM
ejpam-6247	478	10	)	)	PUNCT
ejpam-6247	478	11	(	(	PUNCT
ejpam-6247	478	12	2025	2025	NUM
ejpam-6247	478	13	)	)	PUNCT
ejpam-6247	478	14	,	,	PUNCT
ejpam-6247	478	15	6247	6247	NUM
ejpam-6247	478	16	15	15	NUM
ejpam-6247	478	17	of	of	ADP
ejpam-6247	478	18	15	15	NUM
ejpam-6247	478	19	acknowledgements	acknowledgement	NOUN
ejpam-6247	478	20	this	this	DET
ejpam-6247	478	21	research	research	NOUN
ejpam-6247	478	22	was	be	AUX
ejpam-6247	478	23	supported	support	VERB
ejpam-6247	478	24	by	by	ADP
ejpam-6247	478	25	university	university	NOUN
ejpam-6247	478	26	of	of	ADP
ejpam-6247	478	27	phayao	phayao	NOUN
ejpam-6247	478	28	and	and	CCONJ
ejpam-6247	478	29	thailand	thailand	PROPN
ejpam-6247	478	30	science	science	PROPN
ejpam-6247	478	31	research	research	PROPN
ejpam-6247	478	32	and	and	CCONJ
ejpam-6247	478	33	innovation	innovation	NOUN
ejpam-6247	478	34	fund	fund	NOUN
ejpam-6247	478	35	(	(	PUNCT
ejpam-6247	478	36	fundamental	fundamental	ADJ
ejpam-6247	478	37	fund	fund	NOUN
ejpam-6247	478	38	2025	2025	NUM
ejpam-6247	478	39	,	,	PUNCT
ejpam-6247	478	40	grant	grant	VERB
ejpam-6247	478	41	no	no	NOUN
ejpam-6247	478	42	.	.	PROPN
ejpam-6247	479	1	5027/2567	5027/2567	NUM
ejpam-6247	479	2	)	)	PUNCT
ejpam-6247	479	3	.	.	PUNCT
ejpam-6247	480	1	references	reference	NOUN
ejpam-6247	480	2	[	[	X
ejpam-6247	480	3	1	1	NUM
ejpam-6247	480	4	]	]	PUNCT
ejpam-6247	480	5	g.	g.	NOUN
ejpam-6247	480	6	birkhoff	birkhoff	PROPN
ejpam-6247	480	7	.	.	PUNCT
ejpam-6247	481	1	lattice	lattice	PROPN
ejpam-6247	481	2	theory	theory	PROPN
ejpam-6247	481	3	.	.	PUNCT
ejpam-6247	482	1	amer	amer	PROPN
ejpam-6247	482	2	.	.	PUNCT
ejpam-6247	482	3	math	math	PROPN
ejpam-6247	482	4	.	.	PUNCT
ejpam-6247	483	1	soc	soc	PROPN
ejpam-6247	483	2	.	.	PUNCT
ejpam-6247	484	1	colloq	colloq	PROPN
ejpam-6247	484	2	.	.	PUNCT
ejpam-6247	485	1	xxv	xxv	PROPN
ejpam-6247	485	2	,	,	PUNCT
ejpam-6247	485	3	providence	providence	NOUN
ejpam-6247	485	4	,	,	PUNCT
ejpam-6247	485	5	u.s.a	u.s.a	PROPN
ejpam-6247	485	6	.	.	PROPN
ejpam-6247	485	7	,	,	PUNCT
ejpam-6247	485	8	1967	1967	NUM
ejpam-6247	485	9	.	.	PUNCT
ejpam-6247	486	1	[	[	X
ejpam-6247	486	2	2	2	X
ejpam-6247	486	3	]	]	X
ejpam-6247	486	4	g.	g.	PROPN
ejpam-6247	486	5	grätzer	grätzer	PROPN
ejpam-6247	486	6	.	.	PUNCT
ejpam-6247	486	7	general	general	PROPN
ejpam-6247	486	8	lattice	lattice	PROPN
ejpam-6247	486	9	theory	theory	NOUN
ejpam-6247	486	10	.	.	PUNCT
ejpam-6247	487	1	academic	academic	ADJ
ejpam-6247	487	2	press	press	NOUN
ejpam-6247	487	3	,	,	PUNCT
ejpam-6247	487	4	new	new	PROPN
ejpam-6247	487	5	york	york	PROPN
ejpam-6247	487	6	,	,	PUNCT
ejpam-6247	487	7	san	san	PROPN
ejpam-6247	487	8	francisco	francisco	PROPN
ejpam-6247	487	9	,	,	PUNCT
ejpam-6247	487	10	1978	1978	NUM
ejpam-6247	487	11	.	.	PUNCT
ejpam-6247	488	1	[	[	X
ejpam-6247	488	2	3	3	X
ejpam-6247	488	3	]	]	X
ejpam-6247	488	4	p.	p.	NOUN
ejpam-6247	488	5	crawley	crawley	PROPN
ejpam-6247	488	6	and	and	CCONJ
ejpam-6247	488	7	r.	r.	PROPN
ejpam-6247	488	8	p.	p.	PROPN
ejpam-6247	488	9	dilworth	dilworth	PROPN
ejpam-6247	488	10	.	.	PUNCT
ejpam-6247	489	1	algebraic	algebraic	ADJ
ejpam-6247	489	2	theory	theory	NOUN
ejpam-6247	489	3	of	of	ADP
ejpam-6247	489	4	lattices	lattice	NOUN
ejpam-6247	489	5	.	.	PUNCT
ejpam-6247	490	1	prentice	prentice	NOUN
ejpam-6247	490	2	-	-	PUNCT
ejpam-6247	490	3	hall	hall	NOUN
ejpam-6247	490	4	,	,	PUNCT
ejpam-6247	490	5	1973	1973	NUM
ejpam-6247	490	6	.	.	PUNCT
ejpam-6247	491	1	[	[	X
ejpam-6247	491	2	4	4	X
ejpam-6247	491	3	]	]	X
ejpam-6247	491	4	g.	g.	PROPN
ejpam-6247	491	5	grätzer	grätzer	PROPN
ejpam-6247	491	6	and	and	CCONJ
ejpam-6247	491	7	e.	e.	PROPN
ejpam-6247	491	8	t.	t.	PROPN
ejpam-6247	491	9	schmidt	schmidt	PROPN
ejpam-6247	491	10	.	.	PUNCT
ejpam-6247	492	1	characterizations	characterization	NOUN
ejpam-6247	492	2	of	of	ADP
ejpam-6247	492	3	congruence	congruence	NOUN
ejpam-6247	492	4	lattices	lattice	NOUN
ejpam-6247	492	5	of	of	ADP
ejpam-6247	492	6	abstract	abstract	ADJ
ejpam-6247	492	7	algebras	algebra	NOUN
ejpam-6247	492	8	.	.	PUNCT
ejpam-6247	493	1	acta	acta	PROPN
ejpam-6247	493	2	sci	sci	PROPN
ejpam-6247	493	3	.	.	PROPN
ejpam-6247	493	4	math	math	PROPN
ejpam-6247	493	5	.	.	PUNCT
ejpam-6247	494	1	(	(	PUNCT
ejpam-6247	494	2	szeged	szeged	PROPN
ejpam-6247	494	3	)	)	PUNCT
ejpam-6247	494	4	,	,	PUNCT
ejpam-6247	494	5	24:34–59	24:34–59	PROPN
ejpam-6247	494	6	,	,	PUNCT
ejpam-6247	494	7	1963	1963	NUM
ejpam-6247	494	8	.	.	PUNCT
ejpam-6247	495	1	[	[	X
ejpam-6247	495	2	5	5	X
ejpam-6247	495	3	]	]	X
ejpam-6247	495	4	u.	u.	PROPN
ejpam-6247	495	5	m.	m.	PROPN
ejpam-6247	495	6	swamy	swamy	PROPN
ejpam-6247	495	7	and	and	CCONJ
ejpam-6247	495	8	g.	g.	PROPN
ejpam-6247	495	9	c.	c.	PROPN
ejpam-6247	495	10	rao	rao	PROPN
ejpam-6247	495	11	.	.	PUNCT
ejpam-6247	496	1	almost	almost	ADV
ejpam-6247	496	2	distributive	distributive	ADJ
ejpam-6247	496	3	lattices	lattice	NOUN
ejpam-6247	496	4	.	.	PUNCT
ejpam-6247	497	1	j.	j.	PROPN
ejpam-6247	497	2	aust	aust	PROPN
ejpam-6247	497	3	.	.	PUNCT
ejpam-6247	498	1	math	math	PROPN
ejpam-6247	498	2	.	.	PUNCT
ejpam-6247	499	1	soc	soc	PROPN
ejpam-6247	499	2	.	.	PUNCT
ejpam-6247	500	1	(	(	PUNCT
ejpam-6247	500	2	series	series	PROPN
ejpam-6247	500	3	a	a	PROPN
ejpam-6247	500	4	)	)	PUNCT
ejpam-6247	500	5	,	,	PUNCT
ejpam-6247	500	6	31:77–91	31:77–91	NUM
ejpam-6247	500	7	,	,	PUNCT
ejpam-6247	500	8	1981	1981	NUM
ejpam-6247	500	9	.	.	PUNCT
ejpam-6247	501	1	[	[	X
ejpam-6247	501	2	6	6	NUM
ejpam-6247	501	3	]	]	X
ejpam-6247	501	4	n.	n.	PROPN
ejpam-6247	501	5	rafi	rafi	PROPN
ejpam-6247	501	6	,	,	PUNCT
ejpam-6247	501	7	p.	p.	PROPN
ejpam-6247	501	8	vijaya	vijaya	PROPN
ejpam-6247	501	9	saradhi	saradhi	PROPN
ejpam-6247	501	10	,	,	PUNCT
ejpam-6247	501	11	and	and	CCONJ
ejpam-6247	501	12	m.	m.	NOUN
ejpam-6247	501	13	balaiah	balaiah	PROPN
ejpam-6247	501	14	.	.	PUNCT
ejpam-6247	502	1	the	the	DET
ejpam-6247	502	2	space	space	NOUN
ejpam-6247	502	3	of	of	ADP
ejpam-6247	502	4	minimal	minimal	ADJ
ejpam-6247	502	5	prime	prime	ADJ
ejpam-6247	502	6	d	d	NOUN
ejpam-6247	502	7	-	-	NOUN
ejpam-6247	502	8	filters	filter	NOUN
ejpam-6247	502	9	of	of	ADP
ejpam-6247	502	10	almost	almost	ADV
ejpam-6247	502	11	distributive	distributive	ADJ
ejpam-6247	502	12	lattices	lattice	NOUN
ejpam-6247	502	13	.	.	PUNCT
ejpam-6247	503	1	discuss	discuss	PROPN
ejpam-6247	503	2	.	.	PUNCT
ejpam-6247	503	3	math	math	PROPN
ejpam-6247	503	4	.	.	PUNCT
ejpam-6247	503	5	,	,	PUNCT
ejpam-6247	503	6	gen	gen	PROPN
ejpam-6247	503	7	.	.	PROPN
ejpam-6247	503	8	algebra	algebra	PROPN
ejpam-6247	503	9	appl	appl	PROPN
ejpam-6247	503	10	.	.	PROPN
ejpam-6247	503	11	,	,	PUNCT
ejpam-6247	503	12	44:343–368	44:343–368	PROPN
ejpam-6247	503	13	,	,	PUNCT
ejpam-6247	503	14	2024	2024	NUM
ejpam-6247	503	15	.	.	PUNCT
ejpam-6247	504	1	[	[	X
ejpam-6247	504	2	7	7	X
ejpam-6247	504	3	]	]	X
ejpam-6247	504	4	n.	n.	PROPN
ejpam-6247	504	5	rafi	rafi	PROPN
ejpam-6247	504	6	,	,	PUNCT
ejpam-6247	504	7	y.	y.	PROPN
ejpam-6247	504	8	monikarchana	monikarchana	PROPN
ejpam-6247	504	9	,	,	PUNCT
ejpam-6247	504	10	r.	r.	PROPN
ejpam-6247	504	11	bandaru	bandaru	PROPN
ejpam-6247	504	12	,	,	PUNCT
ejpam-6247	504	13	and	and	CCONJ
ejpam-6247	504	14	a.	a.	NOUN
ejpam-6247	504	15	iampan	iampan	PROPN
ejpam-6247	504	16	.	.	PUNCT
ejpam-6247	505	1	on	on	ADP
ejpam-6247	505	2	prime	prime	ADJ
ejpam-6247	505	3	e	e	NOUN
ejpam-6247	505	4	-	-	NOUN
ejpam-6247	505	5	ideals	ideal	NOUN
ejpam-6247	505	6	of	of	ADP
ejpam-6247	505	7	almost	almost	ADV
ejpam-6247	505	8	distributive	distributive	ADJ
ejpam-6247	505	9	lattices	lattice	NOUN
ejpam-6247	505	10	.	.	PUNCT
ejpam-6247	506	1	int	int	NOUN
ejpam-6247	506	2	.	.	PUNCT
ejpam-6247	507	1	j.	j.	PROPN
ejpam-6247	507	2	anal	anal	PROPN
ejpam-6247	507	3	.	.	PUNCT
ejpam-6247	508	1	appl	appl	PROPN
ejpam-6247	508	2	.	.	PROPN
ejpam-6247	508	3	,	,	PUNCT
ejpam-6247	508	4	11:85	11:85	NUM
ejpam-6247	508	5	,	,	PUNCT
ejpam-6247	508	6	2023	2023	NUM
ejpam-6247	508	7	.	.	PUNCT
ejpam-6247	509	1	[	[	X
ejpam-6247	509	2	8	8	NUM
ejpam-6247	509	3	]	]	X
ejpam-6247	509	4	s.	s.	PROPN
ejpam-6247	509	5	ramesh	ramesh	PROPN
ejpam-6247	509	6	,	,	PUNCT
ejpam-6247	509	7	g.	g.	PROPN
ejpam-6247	509	8	chinnayya	chinnayya	PROPN
ejpam-6247	509	9	,	,	PUNCT
ejpam-6247	509	10	g.	g.	PROPN
ejpam-6247	509	11	jogarao	jogarao	PROPN
ejpam-6247	509	12	,	,	PUNCT
ejpam-6247	509	13	r.	r.	PROPN
ejpam-6247	509	14	bandaru	bandaru	PROPN
ejpam-6247	509	15	,	,	PUNCT
ejpam-6247	509	16	and	and	CCONJ
ejpam-6247	509	17	a.	a.	NOUN
ejpam-6247	509	18	iampan	iampan	PROPN
ejpam-6247	509	19	.	.	PUNCT
ejpam-6247	510	1	hierarchy	hierarchy	NOUN
ejpam-6247	510	2	elements	element	NOUN
ejpam-6247	510	3	in	in	ADP
ejpam-6247	510	4	an	an	DET
ejpam-6247	510	5	almost	almost	ADV
ejpam-6247	510	6	distributive	distributive	ADJ
ejpam-6247	510	7	lattice	lattice	NOUN
ejpam-6247	510	8	.	.	PUNCT
ejpam-6247	511	1	eur	eur	PROPN
ejpam-6247	511	2	.	.	PUNCT
ejpam-6247	512	1	j.	j.	PROPN
ejpam-6247	512	2	pure	pure	PROPN
ejpam-6247	512	3	appl	appl	PROPN
ejpam-6247	512	4	.	.	PUNCT
ejpam-6247	512	5	math	math	PROPN
ejpam-6247	512	6	.	.	PUNCT
ejpam-6247	512	7	,	,	PUNCT
ejpam-6247	512	8	17(3):1691	17(3):1691	NUM
ejpam-6247	512	9	–	–	PUNCT
ejpam-6247	512	10	1704	1704	NUM
ejpam-6247	512	11	,	,	PUNCT
ejpam-6247	512	12	2024	2024	NUM
ejpam-6247	512	13	.	.	PUNCT
ejpam-6247	513	1	[	[	X
ejpam-6247	513	2	9	9	NUM
ejpam-6247	513	3	]	]	X
ejpam-6247	513	4	n.	n.	PROPN
ejpam-6247	513	5	rafi	rafi	PROPN
ejpam-6247	513	6	,	,	PUNCT
ejpam-6247	513	7	p.	p.	PROPN
ejpam-6247	513	8	vijaya	vijaya	PROPN
ejpam-6247	513	9	saradhi	saradhi	PROPN
ejpam-6247	513	10	,	,	PUNCT
ejpam-6247	513	11	and	and	CCONJ
ejpam-6247	513	12	m.	m.	NOUN
ejpam-6247	513	13	balaiah	balaiah	PROPN
ejpam-6247	513	14	.	.	PUNCT
ejpam-6247	514	1	w	w	NOUN
ejpam-6247	514	2	-	-	PUNCT
ejpam-6247	514	3	filters	filter	NOUN
ejpam-6247	514	4	of	of	ADP
ejpam-6247	514	5	almost	almost	ADV
ejpam-6247	514	6	distributive	distributive	ADJ
ejpam-6247	514	7	lattices	lattice	NOUN
ejpam-6247	514	8	.	.	PUNCT
ejpam-6247	515	1	j.	j.	PROPN
ejpam-6247	515	2	algebr	algebr	PROPN
ejpam-6247	515	3	.	.	PUNCT
ejpam-6247	516	1	syst	syst	PROPN
ejpam-6247	516	2	.	.	PROPN
ejpam-6247	516	3	,	,	PUNCT
ejpam-6247	516	4	13(2):37–52	13(2):37–52	NUM
ejpam-6247	516	5	,	,	PUNCT
ejpam-6247	516	6	2025	2025	NUM
ejpam-6247	516	7	.	.	PUNCT
ejpam-6247	517	1	[	[	X
ejpam-6247	517	2	10	10	NUM
ejpam-6247	517	3	]	]	X
ejpam-6247	517	4	n.	n.	PROPN
ejpam-6247	517	5	rafi	rafi	PROPN
ejpam-6247	517	6	and	and	CCONJ
ejpam-6247	517	7	r.	r.	PROPN
ejpam-6247	517	8	k.	k.	PROPN
ejpam-6247	517	9	bandaru	bandaru	PROPN
ejpam-6247	517	10	.	.	PUNCT
ejpam-6247	518	1	hemi	hemi	NOUN
ejpam-6247	518	2	-	-	PUNCT
ejpam-6247	518	3	complemented	complement	VERB
ejpam-6247	518	4	almost	almost	ADV
ejpam-6247	518	5	distributive	distributive	ADJ
ejpam-6247	518	6	lattices	lattice	NOUN
ejpam-6247	518	7	.	.	PUNCT
ejpam-6247	518	8	communicated	communicate	VERB
ejpam-6247	518	9	.	.	PUNCT
ejpam-6247	519	1	[	[	X
ejpam-6247	519	2	11	11	NUM
ejpam-6247	519	3	]	]	X
ejpam-6247	519	4	g.	g.	PROPN
ejpam-6247	519	5	c.	c.	PROPN
ejpam-6247	519	6	rao	rao	PROPN
ejpam-6247	519	7	.	.	PUNCT
ejpam-6247	520	1	almost	almost	ADV
ejpam-6247	520	2	distributive	distributive	ADJ
ejpam-6247	520	3	lattices	lattice	NOUN
ejpam-6247	520	4	,	,	PUNCT
ejpam-6247	520	5	doctoral	doctoral	ADJ
ejpam-6247	520	6	thesis	thesis	NOUN
ejpam-6247	520	7	.	.	PUNCT
ejpam-6247	521	1	department	department	NOUN
ejpam-6247	521	2	of	of	ADP
ejpam-6247	521	3	mathematics	mathematics	PROPN
ejpam-6247	521	4	,	,	PUNCT
ejpam-6247	521	5	andhra	andhra	PROPN
ejpam-6247	521	6	university	university	PROPN
ejpam-6247	521	7	,	,	PUNCT
ejpam-6247	521	8	visakhapatnam	visakhapatnam	PROPN
ejpam-6247	521	9	,	,	PUNCT
ejpam-6247	521	10	1980	1980	NUM
ejpam-6247	521	11	.	.	PUNCT
ejpam-6247	522	1	[	[	X
ejpam-6247	522	2	12	12	NUM
ejpam-6247	522	3	]	]	X
ejpam-6247	522	4	g.	g.	PROPN
ejpam-6247	522	5	c.	c.	PROPN
ejpam-6247	522	6	rao	rao	PROPN
ejpam-6247	522	7	and	and	CCONJ
ejpam-6247	522	8	s.	s.	PROPN
ejpam-6247	522	9	ravi	ravi	PROPN
ejpam-6247	522	10	kumar	kumar	PROPN
ejpam-6247	522	11	.	.	PROPN
ejpam-6247	522	12	minimal	minimal	ADJ
ejpam-6247	522	13	prime	prime	ADJ
ejpam-6247	522	14	ideals	ideal	NOUN
ejpam-6247	522	15	in	in	ADP
ejpam-6247	522	16	almost	almost	ADV
ejpam-6247	522	17	distributive	distributive	ADJ
ejpam-6247	522	18	lattices	lattice	NOUN
ejpam-6247	522	19	.	.	PUNCT
ejpam-6247	523	1	int	int	NOUN
ejpam-6247	523	2	.	.	PUNCT
ejpam-6247	524	1	j.	j.	PROPN
ejpam-6247	524	2	contemp	contemp	PROPN
ejpam-6247	524	3	.	.	PUNCT
ejpam-6247	525	1	math	math	NOUN
ejpam-6247	525	2	.	.	PUNCT
ejpam-6247	526	1	sci	sci	PROPN
ejpam-6247	526	2	.	.	PROPN
ejpam-6247	526	3	,	,	PUNCT
ejpam-6247	526	4	4(10):475–484	4(10):475–484	PROPN
ejpam-6247	526	5	,	,	PUNCT
ejpam-6247	526	6	2009	2009	NUM
ejpam-6247	526	7	.	.	PUNCT
ejpam-6247	527	1	[	[	X
ejpam-6247	527	2	13	13	NUM
ejpam-6247	527	3	]	]	SYM
ejpam-6247	527	4	g.	g.	PROPN
ejpam-6247	527	5	c.	c.	PROPN
ejpam-6247	527	6	rao	rao	PROPN
ejpam-6247	527	7	and	and	CCONJ
ejpam-6247	527	8	m.	m.	PROPN
ejpam-6247	527	9	sambasiva	sambasiva	PROPN
ejpam-6247	527	10	rao	rao	PROPN
ejpam-6247	527	11	.	.	PUNCT
ejpam-6247	528	1	exploring	explore	VERB
ejpam-6247	528	2	the	the	DET
ejpam-6247	528	3	boundaries	boundary	NOUN
ejpam-6247	528	4	of	of	ADP
ejpam-6247	528	5	uncertainty	uncertainty	NOUN
ejpam-6247	528	6	:	:	PUNCT
ejpam-6247	528	7	interval	interval	NOUN
ejpam-6247	528	8	valued	value	VERB
ejpam-6247	528	9	pythagorean	pythagorean	PROPN
ejpam-6247	528	10	neutrosophic	neutrosophic	PROPN
ejpam-6247	528	11	set	set	NOUN
ejpam-6247	528	12	and	and	CCONJ
ejpam-6247	528	13	their	their	PRON
ejpam-6247	528	14	properties	property	NOUN
ejpam-6247	528	15	.	.	PUNCT
ejpam-6247	529	1	eur	eur	PROPN
ejpam-6247	529	2	.	.	PUNCT
ejpam-6247	530	1	j.	j.	PROPN
ejpam-6247	530	2	pure	pure	PROPN
ejpam-6247	530	3	appl	appl	PROPN
ejpam-6247	530	4	.	.	PUNCT
ejpam-6247	530	5	math	math	PROPN
ejpam-6247	530	6	.	.	PUNCT
ejpam-6247	530	7	,	,	PUNCT
ejpam-6247	530	8	2(1):58–72	2(1):58–72	NUM
ejpam-6247	530	9	,	,	PUNCT
ejpam-6247	530	10	2009	2009	NUM
ejpam-6247	530	11	.	.	PUNCT