id	sid	tid	token	lemma	pos
ejpam-5490	1	1	european	european	PROPN
ejpam-5490	1	2	journal	journal	PROPN
ejpam-5490	1	3	of	of	ADP
ejpam-5490	1	4	pure	pure	ADJ
ejpam-5490	1	5	and	and	CCONJ
ejpam-5490	1	6	applied	applied	ADJ
ejpam-5490	1	7	mathematics	mathematic	NOUN
ejpam-5490	1	8	2025	2025	NUM
ejpam-5490	1	9	,	,	PUNCT
ejpam-5490	1	10	vol	vol	NOUN
ejpam-5490	1	11	.	.	PROPN
ejpam-5490	1	12	18	18	NUM
ejpam-5490	1	13	,	,	PUNCT
ejpam-5490	1	14	issue	issue	NOUN
ejpam-5490	1	15	1	1	NUM
ejpam-5490	1	16	,	,	PUNCT
ejpam-5490	1	17	article	article	NOUN
ejpam-5490	1	18	number	number	NOUN
ejpam-5490	1	19	5490	5490	NUM
ejpam-5490	1	20	issn	issn	PROPN
ejpam-5490	1	21	1307	1307	NUM
ejpam-5490	1	22	-	-	SYM
ejpam-5490	1	23	5543	5543	NUM
ejpam-5490	1	24	–	–	PUNCT
ejpam-5490	1	25	ejpam.com	ejpam.com	X
ejpam-5490	1	26	published	publish	VERB
ejpam-5490	1	27	by	by	ADP
ejpam-5490	1	28	new	new	PROPN
ejpam-5490	1	29	york	york	PROPN
ejpam-5490	1	30	business	business	PROPN
ejpam-5490	1	31	global	global	ADJ
ejpam-5490	1	32	g	g	NOUN
ejpam-5490	1	33	-	-	PUNCT
ejpam-5490	1	34	filters	filter	NOUN
ejpam-5490	1	35	and	and	CCONJ
ejpam-5490	1	36	generalized	generalize	VERB
ejpam-5490	1	37	complemented	complemented	ADJ
ejpam-5490	1	38	distributive	distributive	ADJ
ejpam-5490	1	39	lattices	lattice	NOUN
ejpam-5490	1	40	jogarao	jogarao	PROPN
ejpam-5490	1	41	gunda1	gunda1	PROPN
ejpam-5490	1	42	,	,	PUNCT
ejpam-5490	1	43	ramesh	ramesh	PROPN
ejpam-5490	1	44	sirisetti2	sirisetti2	PROPN
ejpam-5490	1	45	,	,	PUNCT
ejpam-5490	1	46	ravikumar	ravikumar	PROPN
ejpam-5490	1	47	bandaru3	bandaru3	ADJ
ejpam-5490	1	48	,	,	PUNCT
ejpam-5490	1	49	rahul	rahul	PROPN
ejpam-5490	1	50	shukla4,∗	shukla4,∗	NOUN
ejpam-5490	1	51	1	1	NUM
ejpam-5490	1	52	department	department	NOUN
ejpam-5490	1	53	of	of	ADP
ejpam-5490	1	54	bs	bs	PROPN
ejpam-5490	1	55	&	&	CCONJ
ejpam-5490	1	56	h	h	PROPN
ejpam-5490	1	57	,	,	PUNCT
ejpam-5490	1	58	aditya	aditya	PROPN
ejpam-5490	1	59	institute	institute	PROPN
ejpam-5490	1	60	of	of	ADP
ejpam-5490	1	61	technology	technology	NOUN
ejpam-5490	1	62	and	and	CCONJ
ejpam-5490	1	63	management	management	NOUN
ejpam-5490	1	64	,	,	PUNCT
ejpam-5490	1	65	tekkali	tekkali	PROPN
ejpam-5490	1	66	,	,	PUNCT
ejpam-5490	1	67	srikakulam	srikakulam	PROPN
ejpam-5490	1	68	,	,	PUNCT
ejpam-5490	1	69	andhra	andhra	PROPN
ejpam-5490	1	70	pradesh-530021	pradesh-530021	PROPN
ejpam-5490	1	71	,	,	PUNCT
ejpam-5490	1	72	india	india	PROPN
ejpam-5490	1	73	2	2	NUM
ejpam-5490	1	74	department	department	NOUN
ejpam-5490	1	75	of	of	ADP
ejpam-5490	1	76	mathematics	mathematic	NOUN
ejpam-5490	1	77	,	,	PUNCT
ejpam-5490	1	78	gitam	gitam	NOUN
ejpam-5490	1	79	school	school	NOUN
ejpam-5490	1	80	of	of	ADP
ejpam-5490	1	81	science	science	NOUN
ejpam-5490	1	82	,	,	PUNCT
ejpam-5490	1	83	gitam	gitam	NOUN
ejpam-5490	1	84	(	(	PUNCT
ejpam-5490	1	85	deemed	deem	VERB
ejpam-5490	1	86	to	to	PART
ejpam-5490	1	87	be	be	AUX
ejpam-5490	1	88	university	university	NOUN
ejpam-5490	1	89	)	)	PUNCT
ejpam-5490	1	90	,	,	PUNCT
ejpam-5490	1	91	visakhapatnam	visakhapatnam	PROPN
ejpam-5490	1	92	,	,	PUNCT
ejpam-5490	1	93	andhra	andhra	PROPN
ejpam-5490	1	94	pradesh-530045	pradesh-530045	NOUN
ejpam-5490	1	95	,	,	PUNCT
ejpam-5490	1	96	india	india	PROPN
ejpam-5490	1	97	3	3	NUM
ejpam-5490	1	98	department	department	NOUN
ejpam-5490	1	99	of	of	ADP
ejpam-5490	1	100	mathematics	mathematic	NOUN
ejpam-5490	1	101	,	,	PUNCT
ejpam-5490	1	102	school	school	NOUN
ejpam-5490	1	103	of	of	ADP
ejpam-5490	1	104	advanced	advanced	ADJ
ejpam-5490	1	105	sciences	science	NOUN
ejpam-5490	1	106	,	,	PUNCT
ejpam-5490	1	107	vit	vit	PROPN
ejpam-5490	1	108	-	-	PUNCT
ejpam-5490	1	109	ap	ap	PROPN
ejpam-5490	1	110	university	university	PROPN
ejpam-5490	1	111	,	,	PUNCT
ejpam-5490	1	112	andhra	andhra	PROPN
ejpam-5490	1	113	pradesh-522237	pradesh-522237	NOUN
ejpam-5490	1	114	,	,	PUNCT
ejpam-5490	1	115	india	india	PROPN
ejpam-5490	1	116	4	4	NUM
ejpam-5490	1	117	department	department	PROPN
ejpam-5490	1	118	of	of	ADP
ejpam-5490	1	119	mathematical	mathematical	ADJ
ejpam-5490	1	120	sciences	sciences	PROPN
ejpam-5490	1	121	and	and	CCONJ
ejpam-5490	1	122	computing	computing	NOUN
ejpam-5490	1	123	,	,	PUNCT
ejpam-5490	1	124	walter	walter	PROPN
ejpam-5490	1	125	sisulu	sisulu	PROPN
ejpam-5490	1	126	university	university	PROPN
ejpam-5490	1	127	,	,	PUNCT
ejpam-5490	1	128	mthatha	mthatha	NOUN
ejpam-5490	1	129	5117	5117	NUM
ejpam-5490	1	130	,	,	PUNCT
ejpam-5490	1	131	south	south	PROPN
ejpam-5490	1	132	africa	africa	PROPN
ejpam-5490	1	133	abstract	abstract	PROPN
ejpam-5490	1	134	.	.	PUNCT
ejpam-5490	2	1	in	in	ADP
ejpam-5490	2	2	this	this	DET
ejpam-5490	2	3	work	work	NOUN
ejpam-5490	2	4	,	,	PUNCT
ejpam-5490	2	5	we	we	PRON
ejpam-5490	2	6	derive	derive	VERB
ejpam-5490	2	7	a	a	DET
ejpam-5490	2	8	class	class	NOUN
ejpam-5490	2	9	of	of	ADP
ejpam-5490	2	10	filters	filter	NOUN
ejpam-5490	2	11	(	(	PUNCT
ejpam-5490	2	12	g	g	NOUN
ejpam-5490	2	13	-	-	PUNCT
ejpam-5490	2	14	filters	filter	NOUN
ejpam-5490	2	15	,	,	PUNCT
ejpam-5490	2	16	normal	normal	ADJ
ejpam-5490	2	17	g	g	NOUN
ejpam-5490	2	18	-	-	PUNCT
ejpam-5490	2	19	filters	filter	NOUN
ejpam-5490	2	20	,	,	PUNCT
ejpam-5490	2	21	and	and	CCONJ
ejpam-5490	2	22	co	co	ADJ
ejpam-5490	2	23	-	-	ADJ
ejpam-5490	2	24	dense	dense	ADJ
ejpam-5490	2	25	filters	filter	NOUN
ejpam-5490	2	26	)	)	PUNCT
ejpam-5490	2	27	in	in	ADP
ejpam-5490	2	28	a	a	DET
ejpam-5490	2	29	distributive	distributive	ADJ
ejpam-5490	2	30	lattice	lattice	NOUN
ejpam-5490	2	31	(	(	PUNCT
ejpam-5490	2	32	with	with	ADP
ejpam-5490	2	33	dense	dense	ADJ
ejpam-5490	2	34	elements	element	NOUN
ejpam-5490	2	35	)	)	PUNCT
ejpam-5490	2	36	.	.	PUNCT
ejpam-5490	3	1	we	we	PRON
ejpam-5490	3	2	also	also	ADV
ejpam-5490	3	3	verify	verify	VERB
ejpam-5490	3	4	the	the	DET
ejpam-5490	3	5	various	various	ADJ
ejpam-5490	3	6	algebraic	algebraic	ADJ
ejpam-5490	3	7	properties	property	NOUN
ejpam-5490	3	8	of	of	ADP
ejpam-5490	3	9	these	these	DET
ejpam-5490	3	10	filters	filter	NOUN
ejpam-5490	3	11	.	.	PUNCT
ejpam-5490	4	1	it	it	PRON
ejpam-5490	4	2	is	be	AUX
ejpam-5490	4	3	observed	observe	VERB
ejpam-5490	4	4	that	that	SCONJ
ejpam-5490	4	5	the	the	DET
ejpam-5490	4	6	set	set	NOUN
ejpam-5490	4	7	of	of	ADP
ejpam-5490	4	8	co	co	ADJ
ejpam-5490	4	9	-	-	ADJ
ejpam-5490	4	10	dense	dense	ADJ
ejpam-5490	4	11	filters	filter	NOUN
ejpam-5490	4	12	forms	form	VERB
ejpam-5490	4	13	an	an	DET
ejpam-5490	4	14	uninduced	uninduced	ADJ
ejpam-5490	4	15	distributive	distributive	ADJ
ejpam-5490	4	16	lattice	lattice	NOUN
ejpam-5490	4	17	,	,	PUNCT
ejpam-5490	4	18	and	and	CCONJ
ejpam-5490	4	19	the	the	DET
ejpam-5490	4	20	set	set	NOUN
ejpam-5490	4	21	of	of	ADP
ejpam-5490	4	22	g	g	NOUN
ejpam-5490	4	23	-	-	PUNCT
ejpam-5490	4	24	filters	filter	NOUN
ejpam-5490	4	25	forms	form	VERB
ejpam-5490	4	26	a	a	DET
ejpam-5490	4	27	boolean	boolean	ADJ
ejpam-5490	4	28	algebra	algebra	NOUN
ejpam-5490	4	29	.	.	PUNCT
ejpam-5490	5	1	we	we	PRON
ejpam-5490	5	2	characterize	characterize	VERB
ejpam-5490	5	3	quasi	quasi	ADJ
ejpam-5490	5	4	-	-	ADJ
ejpam-5490	5	5	complemented	complemented	ADJ
ejpam-5490	5	6	distributive	distributive	ADJ
ejpam-5490	5	7	lattices	lattice	NOUN
ejpam-5490	5	8	using	use	VERB
ejpam-5490	5	9	g	g	NOUN
ejpam-5490	5	10	-	-	PUNCT
ejpam-5490	5	11	filters	filter	NOUN
ejpam-5490	5	12	and	and	CCONJ
ejpam-5490	5	13	normal	normal	ADJ
ejpam-5490	5	14	g	g	NOUN
ejpam-5490	5	15	-	-	PUNCT
ejpam-5490	5	16	filters	filter	NOUN
ejpam-5490	5	17	.	.	PUNCT
ejpam-5490	6	1	using	use	VERB
ejpam-5490	6	2	normal	normal	ADJ
ejpam-5490	6	3	g	g	NOUN
ejpam-5490	6	4	-	-	PUNCT
ejpam-5490	6	5	filters	filter	NOUN
ejpam-5490	6	6	,	,	PUNCT
ejpam-5490	6	7	we	we	PRON
ejpam-5490	6	8	demonstrate	demonstrate	VERB
ejpam-5490	6	9	several	several	ADJ
ejpam-5490	6	10	necessary	necessary	ADJ
ejpam-5490	6	11	and	and	CCONJ
ejpam-5490	6	12	sufficient	sufficient	ADJ
ejpam-5490	6	13	requirements	requirement	NOUN
ejpam-5490	6	14	for	for	ADP
ejpam-5490	6	15	a	a	DET
ejpam-5490	6	16	distributive	distributive	ADJ
ejpam-5490	6	17	lattice	lattice	NOUN
ejpam-5490	6	18	to	to	PART
ejpam-5490	6	19	become	become	VERB
ejpam-5490	6	20	quasi	quasi	ADJ
ejpam-5490	6	21	-	-	VERB
ejpam-5490	6	22	complemented	complemented	ADJ
ejpam-5490	6	23	.	.	PUNCT
ejpam-5490	7	1	also	also	ADV
ejpam-5490	7	2	,	,	PUNCT
ejpam-5490	7	3	we	we	PRON
ejpam-5490	7	4	introduce	introduce	VERB
ejpam-5490	7	5	generalized	generalized	ADJ
ejpam-5490	7	6	complementation	complementation	NOUN
ejpam-5490	7	7	on	on	ADP
ejpam-5490	7	8	a	a	DET
ejpam-5490	7	9	distributive	distributive	ADJ
ejpam-5490	7	10	lattice	lattice	NOUN
ejpam-5490	7	11	and	and	CCONJ
ejpam-5490	7	12	characterize	characterize	VERB
ejpam-5490	7	13	it	it	PRON
ejpam-5490	7	14	in	in	ADP
ejpam-5490	7	15	terms	term	NOUN
ejpam-5490	7	16	of	of	ADP
ejpam-5490	7	17	quasi	quasi	ADJ
ejpam-5490	7	18	-	-	ADJ
ejpam-5490	7	19	complemented	complemented	ADJ
ejpam-5490	7	20	distributive	distributive	ADJ
ejpam-5490	7	21	lattices	lattice	NOUN
ejpam-5490	7	22	.	.	PUNCT
ejpam-5490	8	1	2020	2020	NUM
ejpam-5490	8	2	mathematics	mathematic	NOUN
ejpam-5490	8	3	subject	subject	NOUN
ejpam-5490	8	4	classifications	classification	NOUN
ejpam-5490	8	5	:	:	PUNCT
ejpam-5490	8	6	06d05	06d05	NUM
ejpam-5490	8	7	,	,	PUNCT
ejpam-5490	8	8	06d15	06d15	DET
ejpam-5490	8	9	key	key	ADJ
ejpam-5490	8	10	words	word	NOUN
ejpam-5490	8	11	and	and	CCONJ
ejpam-5490	8	12	phrases	phrase	NOUN
ejpam-5490	8	13	:	:	PUNCT
ejpam-5490	8	14	dense	dense	ADJ
ejpam-5490	8	15	elements	element	NOUN
ejpam-5490	8	16	,	,	PUNCT
ejpam-5490	8	17	filters	filter	NOUN
ejpam-5490	8	18	,	,	PUNCT
ejpam-5490	8	19	g	g	NOUN
ejpam-5490	8	20	-	-	PUNCT
ejpam-5490	8	21	filters	filter	NOUN
ejpam-5490	8	22	,	,	PUNCT
ejpam-5490	8	23	normal	normal	ADJ
ejpam-5490	8	24	g	g	NOUN
ejpam-5490	8	25	-	-	PUNCT
ejpam-5490	8	26	filters	filter	NOUN
ejpam-5490	8	27	,	,	PUNCT
ejpam-5490	8	28	quasi	quasi	ADJ
ejpam-5490	8	29	-	-	ADJ
ejpam-5490	8	30	complemented	complemented	ADJ
ejpam-5490	8	31	distributive	distributive	ADJ
ejpam-5490	8	32	lattices	lattice	NOUN
ejpam-5490	8	33	and	and	CCONJ
ejpam-5490	8	34	generalized	generalize	VERB
ejpam-5490	8	35	complemented	complemented	ADJ
ejpam-5490	8	36	distributive	distributive	ADJ
ejpam-5490	8	37	lattices	lattice	NOUN
ejpam-5490	8	38	1	1	NUM
ejpam-5490	8	39	.	.	PUNCT
ejpam-5490	8	40	introduction	introduction	NOUN
ejpam-5490	8	41	in	in	ADP
ejpam-5490	8	42	the	the	DET
ejpam-5490	8	43	order	order	NOUN
ejpam-5490	8	44	(	(	PUNCT
ejpam-5490	8	45	lattice	lattice	NOUN
ejpam-5490	8	46	)	)	PUNCT
ejpam-5490	8	47	theory	theory	NOUN
ejpam-5490	8	48	,	,	PUNCT
ejpam-5490	8	49	distributive	distributive	ADJ
ejpam-5490	8	50	lattices	lattice	NOUN
ejpam-5490	8	51	are	be	AUX
ejpam-5490	8	52	foundational	foundational	ADJ
ejpam-5490	8	53	structures	structure	NOUN
ejpam-5490	8	54	,	,	PUNCT
ejpam-5490	8	55	embodying	embody	VERB
ejpam-5490	8	56	a	a	DET
ejpam-5490	8	57	delicate	delicate	ADJ
ejpam-5490	8	58	balance	balance	NOUN
ejpam-5490	8	59	between	between	ADP
ejpam-5490	8	60	order	order	NOUN
ejpam-5490	8	61	and	and	CCONJ
ejpam-5490	8	62	algebraic	algebraic	ADJ
ejpam-5490	8	63	properties	property	NOUN
ejpam-5490	8	64	.	.	PUNCT
ejpam-5490	9	1	within	within	ADP
ejpam-5490	9	2	these	these	DET
ejpam-5490	9	3	lattices	lattice	NOUN
ejpam-5490	9	4	,	,	PUNCT
ejpam-5490	9	5	filters	filter	NOUN
ejpam-5490	9	6	emerge	emerge	VERB
ejpam-5490	9	7	as	as	ADP
ejpam-5490	9	8	essential	essential	ADJ
ejpam-5490	9	9	constructs	construct	NOUN
ejpam-5490	9	10	,	,	PUNCT
ejpam-5490	9	11	offering	offer	VERB
ejpam-5490	9	12	insights	insight	NOUN
ejpam-5490	9	13	into	into	ADP
ejpam-5490	9	14	the	the	DET
ejpam-5490	9	15	dynamics	dynamic	NOUN
ejpam-5490	9	16	of	of	ADP
ejpam-5490	9	17	subsets	subset	NOUN
ejpam-5490	9	18	and	and	CCONJ
ejpam-5490	9	19	their	their	PRON
ejpam-5490	9	20	interactions	interaction	NOUN
ejpam-5490	9	21	.	.	PUNCT
ejpam-5490	10	1	in	in	ADP
ejpam-5490	10	2	this	this	DET
ejpam-5490	10	3	regard	regard	NOUN
ejpam-5490	10	4	,	,	PUNCT
ejpam-5490	10	5	the	the	DET
ejpam-5490	10	6	classification	classification	NOUN
ejpam-5490	10	7	of	of	ADP
ejpam-5490	10	8	filters	filter	NOUN
ejpam-5490	10	9	in	in	ADP
ejpam-5490	10	10	a	a	DET
ejpam-5490	10	11	distributive	distributive	ADJ
ejpam-5490	10	12	lattice	lattice	NOUN
ejpam-5490	10	13	was	be	AUX
ejpam-5490	10	14	studied	study	VERB
ejpam-5490	10	15	extensively	extensively	ADV
ejpam-5490	10	16	by	by	ADP
ejpam-5490	10	17	several	several	ADJ
ejpam-5490	10	18	authors	author	NOUN
ejpam-5490	10	19	[	[	X
ejpam-5490	10	20	5–7	5–7	X
ejpam-5490	10	21	]	]	PUNCT
ejpam-5490	10	22	and	and	CCONJ
ejpam-5490	10	23	then	then	ADV
ejpam-5490	10	24	introduced	introduce	VERB
ejpam-5490	10	25	µ-filters	µ-filter	NOUN
ejpam-5490	10	26	,	,	PUNCT
ejpam-5490	10	27	ω	ω	PROPN
ejpam-5490	10	28	–	–	PUNCT
ejpam-5490	10	29	filters	filter	NOUN
ejpam-5490	10	30	and	and	CCONJ
ejpam-5490	10	31	dfilters	dfilter	NOUN
ejpam-5490	10	32	,	,	PUNCT
ejpam-5490	10	33	etc	etc	X
ejpam-5490	10	34	.	.	X
ejpam-5490	11	1	at	at	ADP
ejpam-5490	11	2	the	the	DET
ejpam-5490	11	3	same	same	ADJ
ejpam-5490	11	4	time	time	NOUN
ejpam-5490	11	5	,	,	PUNCT
ejpam-5490	11	6	within	within	ADP
ejpam-5490	11	7	these	these	DET
ejpam-5490	11	8	lattices	lattice	NOUN
ejpam-5490	11	9	,	,	PUNCT
ejpam-5490	11	10	complements	complement	NOUN
ejpam-5490	11	11	emerge	emerge	VERB
ejpam-5490	11	12	as	as	ADP
ejpam-5490	11	13	fundamental	fundamental	ADJ
ejpam-5490	11	14	∗corresponding	∗corresponding	NOUN
ejpam-5490	11	15	author	author	NOUN
ejpam-5490	11	16	.	.	PUNCT
ejpam-5490	12	1	doi	doi	NOUN
ejpam-5490	12	2	:	:	PUNCT
ejpam-5490	12	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5490	https://doi.org/10.29020/nybg.ejpam.v18i1.5490	PROPN
ejpam-5490	12	4	email	email	NOUN
ejpam-5490	12	5	addresses	address	VERB
ejpam-5490	12	6	:	:	PUNCT
ejpam-5490	12	7	jogarao.gunda@gmail.com	jogarao.gunda@gmail.com	PROPN
ejpam-5490	12	8	(	(	PUNCT
ejpam-5490	12	9	j.	j.	PROPN
ejpam-5490	12	10	gunda	gunda	PROPN
ejpam-5490	12	11	)	)	PUNCT
ejpam-5490	12	12	,	,	PUNCT
ejpam-5490	12	13	ramesh.sirisetti@gmail.com	ramesh.sirisetti@gmail.com	X
ejpam-5490	12	14	(	(	PUNCT
ejpam-5490	12	15	r.	r.	PROPN
ejpam-5490	12	16	sirisetti	sirisetti	PROPN
ejpam-5490	12	17	)	)	PUNCT
ejpam-5490	12	18	,	,	PUNCT
ejpam-5490	12	19	ravimaths83@gmail.com	ravimaths83@gmail.com	PROPN
ejpam-5490	12	20	(	(	PUNCT
ejpam-5490	12	21	r.	r.	PROPN
ejpam-5490	12	22	bandaru	bandaru	PROPN
ejpam-5490	12	23	)	)	PUNCT
ejpam-5490	12	24	,	,	PUNCT
ejpam-5490	12	25	rshukla@wsu.ac.za	rshukla@wsu.ac.za	NOUN
ejpam-5490	12	26	(	(	PUNCT
ejpam-5490	12	27	r.	r.	NOUN
ejpam-5490	12	28	shukla	shukla	PROPN
ejpam-5490	12	29	)	)	PUNCT
ejpam-5490	12	30	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5490	12	31	1	1	NUM
ejpam-5490	12	32	copyright	copyright	NOUN
ejpam-5490	12	33	:	:	PUNCT
ejpam-5490	13	1	©	©	PROPN
ejpam-5490	13	2	2025	2025	NUM
ejpam-5490	13	3	the	the	DET
ejpam-5490	13	4	author(s	author(s	NOUN
ejpam-5490	13	5	)	)	PUNCT
ejpam-5490	13	6	.	.	PUNCT
ejpam-5490	14	1	(	(	PUNCT
ejpam-5490	14	2	cc	cc	NOUN
ejpam-5490	14	3	by	by	ADP
ejpam-5490	14	4	-	-	PUNCT
ejpam-5490	14	5	nc	nc	PROPN
ejpam-5490	14	6	4.0	4.0	NUM
ejpam-5490	14	7	)	)	PUNCT
ejpam-5490	14	8	j.	j.	PROPN
ejpam-5490	14	9	gunda	gunda	PROPN
ejpam-5490	14	10	et	et	PROPN
ejpam-5490	14	11	al	al	PROPN
ejpam-5490	14	12	.	.	PUNCT
ejpam-5490	14	13	/	/	SYM
ejpam-5490	14	14	eur	eur	PROPN
ejpam-5490	14	15	.	.	PUNCT
ejpam-5490	15	1	j.	j.	PROPN
ejpam-5490	15	2	pure	pure	PROPN
ejpam-5490	15	3	appl	appl	PROPN
ejpam-5490	15	4	.	.	PROPN
ejpam-5490	15	5	math	math	PROPN
ejpam-5490	15	6	,	,	PUNCT
ejpam-5490	15	7	18	18	NUM
ejpam-5490	15	8	(	(	PUNCT
ejpam-5490	15	9	1	1	NUM
ejpam-5490	15	10	)	)	PUNCT
ejpam-5490	15	11	(	(	PUNCT
ejpam-5490	15	12	2025	2025	NUM
ejpam-5490	15	13	)	)	PUNCT
ejpam-5490	15	14	,	,	PUNCT
ejpam-5490	15	15	5490	5490	NUM
ejpam-5490	15	16	2	2	NUM
ejpam-5490	15	17	of	of	ADP
ejpam-5490	15	18	11	11	NUM
ejpam-5490	15	19	constructs	construct	NOUN
ejpam-5490	15	20	,	,	PUNCT
ejpam-5490	15	21	offering	offer	VERB
ejpam-5490	15	22	profound	profound	ADJ
ejpam-5490	15	23	insights	insight	NOUN
ejpam-5490	15	24	into	into	ADP
ejpam-5490	15	25	the	the	DET
ejpam-5490	15	26	nature	nature	NOUN
ejpam-5490	15	27	of	of	ADP
ejpam-5490	15	28	duality	duality	NOUN
ejpam-5490	15	29	,	,	PUNCT
ejpam-5490	15	30	negation	negation	NOUN
ejpam-5490	15	31	,	,	PUNCT
ejpam-5490	15	32	and	and	CCONJ
ejpam-5490	15	33	complementation	complementation	NOUN
ejpam-5490	15	34	within	within	ADP
ejpam-5490	15	35	the	the	DET
ejpam-5490	15	36	lattice	lattice	NOUN
ejpam-5490	15	37	framework	framework	NOUN
ejpam-5490	15	38	.	.	PUNCT
ejpam-5490	16	1	thus	thus	ADV
ejpam-5490	16	2	,	,	PUNCT
ejpam-5490	16	3	the	the	DET
ejpam-5490	16	4	class	class	NOUN
ejpam-5490	16	5	of	of	ADP
ejpam-5490	16	6	complementations	complementation	NOUN
ejpam-5490	16	7	classified	classify	VERB
ejpam-5490	16	8	by	by	ADP
ejpam-5490	16	9	many	many	ADJ
ejpam-5490	16	10	authors	author	NOUN
ejpam-5490	16	11	[	[	X
ejpam-5490	16	12	[	[	X
ejpam-5490	16	13	1	1	NUM
ejpam-5490	16	14	]	]	PUNCT
ejpam-5490	16	15	,	,	PUNCT
ejpam-5490	16	16	[	[	X
ejpam-5490	16	17	8	8	NUM
ejpam-5490	16	18	]	]	PUNCT
ejpam-5490	16	19	,	,	PUNCT
ejpam-5490	16	20	[	[	X
ejpam-5490	16	21	3	3	NUM
ejpam-5490	16	22	]	]	X
ejpam-5490	16	23	]	]	PUNCT
ejpam-5490	16	24	is	be	AUX
ejpam-5490	16	25	called	call	VERB
ejpam-5490	16	26	ortho	ortho	NOUN
ejpam-5490	16	27	-	-	PUNCT
ejpam-5490	16	28	complementation	complementation	NOUN
ejpam-5490	16	29	,	,	PUNCT
ejpam-5490	16	30	pseudo	pseudo	NOUN
ejpam-5490	16	31	-	-	NOUN
ejpam-5490	16	32	complementation	complementation	NOUN
ejpam-5490	16	33	,	,	PUNCT
ejpam-5490	16	34	and	and	CCONJ
ejpam-5490	16	35	quasi	quasi	NOUN
ejpam-5490	16	36	-	-	NOUN
ejpam-5490	16	37	complementation	complementation	NOUN
ejpam-5490	16	38	,	,	PUNCT
ejpam-5490	16	39	etc	etc	X
ejpam-5490	16	40	.	.	X
ejpam-5490	17	1	the	the	DET
ejpam-5490	17	2	class	class	NOUN
ejpam-5490	17	3	of	of	ADP
ejpam-5490	17	4	maximal	maximal	ADJ
ejpam-5490	17	5	elements	element	NOUN
ejpam-5490	17	6	is	be	AUX
ejpam-5490	17	7	a	a	DET
ejpam-5490	17	8	proper	proper	ADJ
ejpam-5490	17	9	sub	sub	NOUN
ejpam-5490	17	10	-	-	NOUN
ejpam-5490	17	11	collection	collection	NOUN
ejpam-5490	17	12	of	of	ADP
ejpam-5490	17	13	the	the	DET
ejpam-5490	17	14	class	class	NOUN
ejpam-5490	17	15	of	of	ADP
ejpam-5490	17	16	dense	dense	ADJ
ejpam-5490	17	17	elements	element	NOUN
ejpam-5490	17	18	in	in	ADP
ejpam-5490	17	19	lattices	lattice	NOUN
ejpam-5490	17	20	.	.	PUNCT
ejpam-5490	18	1	we	we	PRON
ejpam-5490	18	2	start	start	VERB
ejpam-5490	18	3	working	work	VERB
ejpam-5490	18	4	on	on	ADP
ejpam-5490	18	5	a	a	DET
ejpam-5490	18	6	distributive	distributive	ADJ
ejpam-5490	18	7	lattice	lattice	NOUN
ejpam-5490	18	8	with	with	ADP
ejpam-5490	18	9	dense	dense	ADJ
ejpam-5490	18	10	elements	element	NOUN
ejpam-5490	18	11	with	with	ADP
ejpam-5490	18	12	this	this	DET
ejpam-5490	18	13	initiation	initiation	NOUN
ejpam-5490	18	14	.	.	PUNCT
ejpam-5490	19	1	this	this	DET
ejpam-5490	19	2	paper	paper	NOUN
ejpam-5490	19	3	introduces	introduce	VERB
ejpam-5490	19	4	g	g	NOUN
ejpam-5490	19	5	-	-	PUNCT
ejpam-5490	19	6	filters	filter	NOUN
ejpam-5490	19	7	,	,	PUNCT
ejpam-5490	19	8	normal	normal	ADJ
ejpam-5490	19	9	g	g	NOUN
ejpam-5490	19	10	-	-	PUNCT
ejpam-5490	19	11	filters	filter	NOUN
ejpam-5490	19	12	,	,	PUNCT
ejpam-5490	19	13	and	and	CCONJ
ejpam-5490	19	14	co	co	ADJ
ejpam-5490	19	15	-	-	ADJ
ejpam-5490	19	16	dense	dense	ADJ
ejpam-5490	19	17	filters	filter	NOUN
ejpam-5490	19	18	in	in	ADP
ejpam-5490	19	19	a	a	DET
ejpam-5490	19	20	distributive	distributive	ADJ
ejpam-5490	19	21	lattice	lattice	NOUN
ejpam-5490	19	22	with	with	ADP
ejpam-5490	19	23	dense	dense	ADJ
ejpam-5490	19	24	elements	element	NOUN
ejpam-5490	19	25	.	.	PUNCT
ejpam-5490	20	1	we	we	PRON
ejpam-5490	20	2	derive	derive	VERB
ejpam-5490	20	3	some	some	DET
ejpam-5490	20	4	algebraic	algebraic	ADJ
ejpam-5490	20	5	properties	property	NOUN
ejpam-5490	20	6	from	from	ADP
ejpam-5490	20	7	them	they	PRON
ejpam-5490	20	8	and	and	CCONJ
ejpam-5490	20	9	obtain	obtain	VERB
ejpam-5490	20	10	the	the	DET
ejpam-5490	20	11	necessary	necessary	ADJ
ejpam-5490	20	12	and	and	CCONJ
ejpam-5490	20	13	sufficient	sufficient	ADJ
ejpam-5490	20	14	conditions	condition	NOUN
ejpam-5490	20	15	for	for	SCONJ
ejpam-5490	20	16	a	a	DET
ejpam-5490	20	17	filter	filter	NOUN
ejpam-5490	20	18	to	to	PART
ejpam-5490	20	19	become	become	VERB
ejpam-5490	20	20	a	a	DET
ejpam-5490	20	21	g	g	NOUN
ejpam-5490	20	22	-	-	PUNCT
ejpam-5490	20	23	filter	filter	NOUN
ejpam-5490	20	24	(	(	PUNCT
ejpam-5490	20	25	normal	normal	ADJ
ejpam-5490	20	26	g	g	NOUN
ejpam-5490	20	27	-	-	PUNCT
ejpam-5490	20	28	filter	filter	NOUN
ejpam-5490	20	29	)	)	PUNCT
ejpam-5490	20	30	.	.	PUNCT
ejpam-5490	21	1	also	also	ADV
ejpam-5490	21	2	,	,	PUNCT
ejpam-5490	21	3	we	we	PRON
ejpam-5490	21	4	characterize	characterize	VERB
ejpam-5490	21	5	quasi	quasi	ADJ
ejpam-5490	21	6	-	-	ADJ
ejpam-5490	21	7	complemented	complemented	ADJ
ejpam-5490	21	8	distributive	distributive	ADJ
ejpam-5490	21	9	lattices	lattice	NOUN
ejpam-5490	21	10	using	use	VERB
ejpam-5490	21	11	g	g	NOUN
ejpam-5490	21	12	-	-	PUNCT
ejpam-5490	21	13	filters	filter	NOUN
ejpam-5490	21	14	and	and	CCONJ
ejpam-5490	21	15	normal	normal	ADJ
ejpam-5490	21	16	g	g	NOUN
ejpam-5490	21	17	-	-	PUNCT
ejpam-5490	21	18	filters	filter	NOUN
ejpam-5490	21	19	.	.	PUNCT
ejpam-5490	22	1	mainly	mainly	ADV
ejpam-5490	22	2	,	,	PUNCT
ejpam-5490	22	3	we	we	PRON
ejpam-5490	22	4	introduce	introduce	VERB
ejpam-5490	22	5	g	g	NOUN
ejpam-5490	22	6	-	-	PUNCT
ejpam-5490	22	7	complementation	complementation	NOUN
ejpam-5490	22	8	on	on	ADP
ejpam-5490	22	9	a	a	DET
ejpam-5490	22	10	distributive	distributive	ADJ
ejpam-5490	22	11	lattice	lattice	NOUN
ejpam-5490	22	12	(	(	PUNCT
ejpam-5490	22	13	which	which	PRON
ejpam-5490	22	14	may	may	AUX
ejpam-5490	22	15	or	or	CCONJ
ejpam-5490	22	16	may	may	AUX
ejpam-5490	22	17	not	not	PART
ejpam-5490	22	18	contain	contain	VERB
ejpam-5490	22	19	the	the	DET
ejpam-5490	22	20	zero	zero	NUM
ejpam-5490	22	21	element	element	NOUN
ejpam-5490	22	22	)	)	PUNCT
ejpam-5490	22	23	and	and	CCONJ
ejpam-5490	22	24	prove	prove	VERB
ejpam-5490	22	25	several	several	ADJ
ejpam-5490	22	26	algebraic	algebraic	ADJ
ejpam-5490	22	27	properties	property	NOUN
ejpam-5490	22	28	.	.	PUNCT
ejpam-5490	23	1	every	every	DET
ejpam-5490	23	2	finite	finite	PROPN
ejpam-5490	23	3	distributive	distributive	ADJ
ejpam-5490	23	4	lattice	lattice	NOUN
ejpam-5490	23	5	is	be	AUX
ejpam-5490	23	6	g	g	NOUN
ejpam-5490	23	7	-	-	PUNCT
ejpam-5490	23	8	complemented	complement	VERB
ejpam-5490	23	9	,	,	PUNCT
ejpam-5490	23	10	as	as	SCONJ
ejpam-5490	23	11	we	we	PRON
ejpam-5490	23	12	have	have	AUX
ejpam-5490	23	13	seen	see	VERB
ejpam-5490	23	14	.	.	PUNCT
ejpam-5490	24	1	ultimately	ultimately	ADV
ejpam-5490	24	2	,	,	PUNCT
ejpam-5490	24	3	we	we	PRON
ejpam-5490	24	4	derive	derive	VERB
ejpam-5490	24	5	certain	certain	ADJ
ejpam-5490	24	6	sufficient	sufficient	ADJ
ejpam-5490	24	7	and	and	CCONJ
ejpam-5490	24	8	necessary	necessary	ADJ
ejpam-5490	24	9	conditions	condition	NOUN
ejpam-5490	24	10	under	under	ADP
ejpam-5490	24	11	which	which	PRON
ejpam-5490	24	12	a	a	DET
ejpam-5490	24	13	distributive	distributive	ADJ
ejpam-5490	24	14	lattice	lattice	NOUN
ejpam-5490	24	15	becomes	become	VERB
ejpam-5490	24	16	g	g	NOUN
ejpam-5490	24	17	-	-	PUNCT
ejpam-5490	24	18	complemented	complement	VERB
ejpam-5490	24	19	.	.	PUNCT
ejpam-5490	25	1	2	2	X
ejpam-5490	25	2	.	.	X
ejpam-5490	25	3	g	g	NOUN
ejpam-5490	25	4	-	-	PUNCT
ejpam-5490	25	5	filters	filter	NOUN
ejpam-5490	25	6	in	in	ADP
ejpam-5490	25	7	this	this	DET
ejpam-5490	25	8	section	section	NOUN
ejpam-5490	25	9	,	,	PUNCT
ejpam-5490	25	10	we	we	PRON
ejpam-5490	25	11	introduce	introduce	VERB
ejpam-5490	25	12	g	g	NOUN
ejpam-5490	25	13	-	-	PUNCT
ejpam-5490	25	14	filters	filter	NOUN
ejpam-5490	25	15	and	and	CCONJ
ejpam-5490	25	16	co	co	ADJ
ejpam-5490	25	17	-	-	ADJ
ejpam-5490	25	18	dense	dense	ADJ
ejpam-5490	25	19	filters	filter	NOUN
ejpam-5490	25	20	in	in	ADP
ejpam-5490	25	21	a	a	DET
ejpam-5490	25	22	distributive	distributive	ADJ
ejpam-5490	25	23	lattice	lattice	NOUN
ejpam-5490	25	24	and	and	CCONJ
ejpam-5490	25	25	prove	prove	VERB
ejpam-5490	25	26	several	several	ADJ
ejpam-5490	25	27	algebraic	algebraic	ADJ
ejpam-5490	25	28	properties	property	NOUN
ejpam-5490	25	29	of	of	ADP
ejpam-5490	25	30	this	this	DET
ejpam-5490	25	31	class	class	NOUN
ejpam-5490	25	32	of	of	ADP
ejpam-5490	25	33	filters	filter	NOUN
ejpam-5490	25	34	.	.	PUNCT
ejpam-5490	26	1	we	we	PRON
ejpam-5490	26	2	prove	prove	VERB
ejpam-5490	26	3	the	the	DET
ejpam-5490	26	4	set	set	NOUN
ejpam-5490	26	5	of	of	ADP
ejpam-5490	26	6	g	g	NOUN
ejpam-5490	26	7	-	-	PUNCT
ejpam-5490	26	8	filters	filter	NOUN
ejpam-5490	26	9	forms	form	VERB
ejpam-5490	26	10	a	a	DET
ejpam-5490	26	11	boolean	boolean	ADJ
ejpam-5490	26	12	algebra	algebra	NOUN
ejpam-5490	26	13	,	,	PUNCT
ejpam-5490	26	14	and	and	CCONJ
ejpam-5490	26	15	the	the	DET
ejpam-5490	26	16	set	set	NOUN
ejpam-5490	26	17	of	of	ADP
ejpam-5490	26	18	co	co	ADJ
ejpam-5490	26	19	-	-	ADJ
ejpam-5490	26	20	dense	dense	ADJ
ejpam-5490	26	21	filters	filter	NOUN
ejpam-5490	26	22	forms	form	VERB
ejpam-5490	26	23	a	a	DET
ejpam-5490	26	24	distributive	distributive	ADJ
ejpam-5490	26	25	lattice	lattice	NOUN
ejpam-5490	26	26	.	.	PUNCT
ejpam-5490	27	1	finally	finally	ADV
ejpam-5490	27	2	,	,	PUNCT
ejpam-5490	27	3	we	we	PRON
ejpam-5490	27	4	observe	observe	VERB
ejpam-5490	27	5	that	that	SCONJ
ejpam-5490	27	6	every	every	DET
ejpam-5490	27	7	maximal	maximal	ADJ
ejpam-5490	27	8	filter	filter	NOUN
ejpam-5490	27	9	is	be	AUX
ejpam-5490	27	10	either	either	CCONJ
ejpam-5490	27	11	g	g	NOUN
ejpam-5490	27	12	-	-	PUNCT
ejpam-5490	27	13	filter	filter	NOUN
ejpam-5490	27	14	or	or	CCONJ
ejpam-5490	27	15	a	a	DET
ejpam-5490	27	16	co	co	ADJ
ejpam-5490	27	17	-	-	ADJ
ejpam-5490	27	18	dense	dense	ADJ
ejpam-5490	27	19	filter	filter	NOUN
ejpam-5490	27	20	.	.	PUNCT
ejpam-5490	28	1	in	in	ADP
ejpam-5490	28	2	this	this	DET
ejpam-5490	28	3	article	article	NOUN
ejpam-5490	28	4	,	,	PUNCT
ejpam-5490	28	5	a	a	DET
ejpam-5490	28	6	distributive	distributive	ADJ
ejpam-5490	28	7	lattice	lattice	NOUN
ejpam-5490	28	8	with	with	ADP
ejpam-5490	28	9	dense	dense	ADJ
ejpam-5490	28	10	elements	element	NOUN
ejpam-5490	28	11	is	be	AUX
ejpam-5490	28	12	denoted	denote	VERB
ejpam-5490	28	13	by	by	ADP
ejpam-5490	28	14	a.	a.	NOUN
ejpam-5490	28	15	in	in	ADP
ejpam-5490	28	16	[	[	X
ejpam-5490	28	17	4	4	NUM
ejpam-5490	28	18	]	]	PUNCT
ejpam-5490	28	19	,	,	PUNCT
ejpam-5490	28	20	kumar	kumar	PROPN
ejpam-5490	28	21	and	and	CCONJ
ejpam-5490	28	22	rao	rao	PROPN
ejpam-5490	28	23	introduced	introduce	VERB
ejpam-5490	28	24	a	a	DET
ejpam-5490	28	25	class	class	NOUN
ejpam-5490	28	26	{	{	PUNCT
ejpam-5490	28	27	sd	sd	NOUN
ejpam-5490	29	1	|	|	ADV
ejpam-5490	29	2	s	s	VERB
ejpam-5490	29	3	is	be	AUX
ejpam-5490	29	4	non	non	ADJ
ejpam-5490	29	5	-	-	ADJ
ejpam-5490	29	6	empty	empty	ADJ
ejpam-5490	29	7	subset	subset	NOUN
ejpam-5490	29	8	of	of	ADP
ejpam-5490	29	9	a	a	PRON
ejpam-5490	29	10	}	}	PUNCT
ejpam-5490	29	11	of	of	ADP
ejpam-5490	29	12	filters	filter	NOUN
ejpam-5490	29	13	,	,	PUNCT
ejpam-5490	29	14	where	where	SCONJ
ejpam-5490	29	15	sd	sd	ADV
ejpam-5490	29	16	=	=	SYM
ejpam-5490	29	17	{	{	PUNCT
ejpam-5490	29	18	v	v	NOUN
ejpam-5490	29	19	∈	∈	PROPN
ejpam-5490	29	20	a	a	DET
ejpam-5490	29	21	|	|	NOUN
ejpam-5490	29	22	s	s	VERB
ejpam-5490	29	23	∨∗	∨∗	NOUN
ejpam-5490	29	24	v	v	NOUN
ejpam-5490	29	25	is	be	AUX
ejpam-5490	29	26	dense	dense	ADJ
ejpam-5490	29	27	,	,	PUNCT
ejpam-5490	29	28	for	for	ADP
ejpam-5490	29	29	all	all	PRON
ejpam-5490	29	30	s	s	PART
ejpam-5490	29	31	∈	∈	NOUN
ejpam-5490	29	32	s	s	PART
ejpam-5490	29	33	}	}	PUNCT
ejpam-5490	29	34	.	.	PUNCT
ejpam-5490	30	1	definition	definition	NOUN
ejpam-5490	30	2	1	1	NUM
ejpam-5490	30	3	.	.	PUNCT
ejpam-5490	31	1	in	in	ADP
ejpam-5490	31	2	a	a	DET
ejpam-5490	31	3	distributive	distributive	ADJ
ejpam-5490	31	4	lattice	lattice	NOUN
ejpam-5490	31	5	a	a	PRON
ejpam-5490	31	6	,	,	PUNCT
ejpam-5490	31	7	filter	filter	NOUN
ejpam-5490	31	8	k	k	PROPN
ejpam-5490	31	9	is	be	AUX
ejpam-5490	31	10	said	say	VERB
ejpam-5490	31	11	to	to	PART
ejpam-5490	31	12	be	be	AUX
ejpam-5490	31	13	a	a	DET
ejpam-5490	31	14	g	g	NOUN
ejpam-5490	31	15	-	-	PUNCT
ejpam-5490	31	16	filter	filter	NOUN
ejpam-5490	31	17	,	,	PUNCT
ejpam-5490	31	18	if	if	SCONJ
ejpam-5490	31	19	kdd	kdd	PROPN
ejpam-5490	31	20	=	=	PROPN
ejpam-5490	31	21	k.	k.	PROPN
ejpam-5490	31	22	lemma	lemma	PROPN
ejpam-5490	32	1	1	1	NUM
ejpam-5490	32	2	.	.	PUNCT
ejpam-5490	33	1	for	for	ADP
ejpam-5490	33	2	any	any	DET
ejpam-5490	33	3	filter	filter	NOUN
ejpam-5490	33	4	k	k	NOUN
ejpam-5490	33	5	of	of	ADP
ejpam-5490	33	6	a	a	PRON
ejpam-5490	33	7	,	,	PUNCT
ejpam-5490	33	8	(	(	PUNCT
ejpam-5490	33	9	i	i	NOUN
ejpam-5490	33	10	)	)	PUNCT
ejpam-5490	33	11	kd	kd	PROPN
ejpam-5490	33	12	and	and	CCONJ
ejpam-5490	33	13	kdd	kdd	PROPN
ejpam-5490	33	14	are	be	AUX
ejpam-5490	33	15	g	g	NOUN
ejpam-5490	33	16	-	-	PUNCT
ejpam-5490	33	17	filters	filter	NOUN
ejpam-5490	33	18	.	.	PUNCT
ejpam-5490	34	1	(	(	PUNCT
ejpam-5490	34	2	ii	ii	X
ejpam-5490	34	3	)	)	PUNCT
ejpam-5490	34	4	kdd	kdd	PROPN
ejpam-5490	34	5	is	be	AUX
ejpam-5490	34	6	the	the	DET
ejpam-5490	34	7	smallest	small	ADJ
ejpam-5490	34	8	g	g	NOUN
ejpam-5490	34	9	-	-	PUNCT
ejpam-5490	34	10	filter	filter	NOUN
ejpam-5490	34	11	containing	contain	VERB
ejpam-5490	34	12	k.	k.	PROPN
ejpam-5490	34	13	lemma	lemma	PROPN
ejpam-5490	35	1	2	2	X
ejpam-5490	35	2	.	.	PUNCT
ejpam-5490	35	3	let	let	VERB
ejpam-5490	35	4	k	k	PRON
ejpam-5490	35	5	be	be	AUX
ejpam-5490	35	6	a	a	DET
ejpam-5490	35	7	proper	proper	ADJ
ejpam-5490	35	8	filter	filter	NOUN
ejpam-5490	35	9	containing	contain	VERB
ejpam-5490	35	10	a	a	DET
ejpam-5490	35	11	non	non	ADJ
ejpam-5490	35	12	-	-	ADJ
ejpam-5490	35	13	dense	dense	ADJ
ejpam-5490	35	14	element	element	NOUN
ejpam-5490	35	15	in	in	ADP
ejpam-5490	35	16	a.	a.	NOUN
ejpam-5490	35	17	then	then	ADV
ejpam-5490	35	18	kd	kd	PROPN
ejpam-5490	35	19	is	be	AUX
ejpam-5490	35	20	proper	proper	ADJ
ejpam-5490	35	21	.	.	PUNCT
ejpam-5490	36	1	proof	proof	NOUN
ejpam-5490	36	2	.	.	PUNCT
ejpam-5490	37	1	suppose	suppose	VERB
ejpam-5490	37	2	that	that	SCONJ
ejpam-5490	37	3	kd	kd	PROPN
ejpam-5490	37	4	=	=	PUNCT
ejpam-5490	37	5	a	a	PROPN
ejpam-5490	37	6	and	and	CCONJ
ejpam-5490	37	7	v	v	NOUN
ejpam-5490	37	8	is	be	AUX
ejpam-5490	37	9	a	a	DET
ejpam-5490	37	10	non	non	ADJ
ejpam-5490	37	11	-	-	ADJ
ejpam-5490	37	12	dense	dense	ADJ
ejpam-5490	37	13	element	element	NOUN
ejpam-5490	37	14	in	in	ADP
ejpam-5490	37	15	k.	k.	PROPN
ejpam-5490	37	16	since	since	SCONJ
ejpam-5490	37	17	0	0	NUM
ejpam-5490	37	18	∈	∈	PROPN
ejpam-5490	37	19	a	a	DET
ejpam-5490	37	20	=	=	X
ejpam-5490	37	21	kd	kd	PROPN
ejpam-5490	37	22	,	,	PUNCT
ejpam-5490	37	23	0	0	NUM
ejpam-5490	37	24	∨∗	∨∗	NOUN
ejpam-5490	37	25	f	f	PROPN
ejpam-5490	37	26	∈	∈	PROPN
ejpam-5490	37	27	d	d	PROPN
ejpam-5490	37	28	,	,	PUNCT
ejpam-5490	37	29	for	for	ADP
ejpam-5490	37	30	all	all	DET
ejpam-5490	37	31	f	f	PROPN
ejpam-5490	37	32	∈	∈	PROPN
ejpam-5490	37	33	k.	k.	PROPN
ejpam-5490	37	34	in	in	ADP
ejpam-5490	37	35	particular	particular	ADJ
ejpam-5490	37	36	,	,	PUNCT
ejpam-5490	37	37	for	for	ADP
ejpam-5490	37	38	v	v	ADP
ejpam-5490	37	39	∈	∈	PROPN
ejpam-5490	37	40	k	k	NOUN
ejpam-5490	37	41	,	,	PUNCT
ejpam-5490	37	42	we	we	PRON
ejpam-5490	37	43	have	have	VERB
ejpam-5490	37	44	0	0	NUM
ejpam-5490	37	45	∨∗	∨∗	CCONJ
ejpam-5490	37	46	v	v	NOUN
ejpam-5490	37	47	=	=	SYM
ejpam-5490	37	48	v	v	PROPN
ejpam-5490	37	49	∈	∈	PROPN
ejpam-5490	37	50	d.	d.	NOUN
ejpam-5490	37	51	which	which	PRON
ejpam-5490	37	52	is	be	AUX
ejpam-5490	37	53	contradiction	contradiction	NOUN
ejpam-5490	37	54	to	to	ADP
ejpam-5490	37	55	v	v	NOUN
ejpam-5490	37	56	is	be	AUX
ejpam-5490	37	57	non	non	ADJ
ejpam-5490	37	58	-	-	ADJ
ejpam-5490	37	59	dense	dense	ADJ
ejpam-5490	37	60	.	.	PUNCT
ejpam-5490	38	1	thus	thus	ADV
ejpam-5490	38	2	kd	kd	PROPN
ejpam-5490	38	3	is	be	AUX
ejpam-5490	38	4	proper	proper	ADJ
ejpam-5490	38	5	.	.	PUNCT
ejpam-5490	39	1	let	let	VERB
ejpam-5490	39	2	gf	gf	X
ejpam-5490	39	3	(	(	PUNCT
ejpam-5490	39	4	a	a	X
ejpam-5490	39	5	)	)	PUNCT
ejpam-5490	39	6	represent	represent	VERB
ejpam-5490	39	7	the	the	DET
ejpam-5490	39	8	set	set	NOUN
ejpam-5490	39	9	of	of	ADP
ejpam-5490	39	10	g	g	NOUN
ejpam-5490	39	11	-	-	PUNCT
ejpam-5490	39	12	filters	filter	NOUN
ejpam-5490	39	13	of	of	ADP
ejpam-5490	39	14	a	a	DET
ejpam-5490	39	15	..	..	PUNCT
ejpam-5490	39	16	theorem	theorem	NOUN
ejpam-5490	39	17	1	1	NUM
ejpam-5490	39	18	.	.	PUNCT
ejpam-5490	40	1	gf	gf	X
ejpam-5490	40	2	(	(	PUNCT
ejpam-5490	40	3	a	a	X
ejpam-5490	40	4	)	)	PUNCT
ejpam-5490	40	5	forms	form	VERB
ejpam-5490	40	6	a	a	DET
ejpam-5490	40	7	boolean	boolean	ADJ
ejpam-5490	40	8	algebra	algebra	NOUN
ejpam-5490	40	9	with	with	ADP
ejpam-5490	40	10	the	the	DET
ejpam-5490	40	11	operations	operation	NOUN
ejpam-5490	41	1	k	k	NOUN
ejpam-5490	41	2	⊔	⊔	NOUN
ejpam-5490	41	3	g	g	NOUN
ejpam-5490	41	4	=	=	PUNCT
ejpam-5490	41	5	(	(	PUNCT
ejpam-5490	41	6	k	k	X
ejpam-5490	41	7	∨∗	∨∗	PROPN
ejpam-5490	41	8	g	g	NOUN
ejpam-5490	41	9	)	)	PUNCT
ejpam-5490	41	10	dd	dd	NOUN
ejpam-5490	41	11	and	and	CCONJ
ejpam-5490	41	12	k	k	PROPN
ejpam-5490	41	13	∧∗	∧∗	PROPN
ejpam-5490	41	14	g	g	PROPN
ejpam-5490	41	15	=	=	PUNCT
ejpam-5490	41	16	kd	kd	PROPN
ejpam-5490	41	17	∩gd	∩gd	NOUN
ejpam-5490	41	18	,	,	PUNCT
ejpam-5490	41	19	where	where	SCONJ
ejpam-5490	41	20	k	k	X
ejpam-5490	41	21	,	,	PUNCT
ejpam-5490	41	22	g	g	PROPN
ejpam-5490	41	23	∈	∈	PROPN
ejpam-5490	41	24	gf	gf	X
ejpam-5490	41	25	(	(	PUNCT
ejpam-5490	41	26	a	a	NOUN
ejpam-5490	41	27	)	)	PUNCT
ejpam-5490	41	28	and	and	CCONJ
ejpam-5490	41	29	the	the	DET
ejpam-5490	41	30	complement	complement	NOUN
ejpam-5490	41	31	of	of	ADP
ejpam-5490	41	32	k	k	PROPN
ejpam-5490	41	33	is	be	AUX
ejpam-5490	41	34	kd	kd	PROPN
ejpam-5490	41	35	.	.	PUNCT
ejpam-5490	42	1	j.	j.	PROPN
ejpam-5490	42	2	gunda	gunda	PROPN
ejpam-5490	42	3	et	et	PROPN
ejpam-5490	42	4	al	al	PROPN
ejpam-5490	42	5	.	.	PUNCT
ejpam-5490	42	6	/	/	SYM
ejpam-5490	42	7	eur	eur	PROPN
ejpam-5490	42	8	.	.	PUNCT
ejpam-5490	43	1	j.	j.	PROPN
ejpam-5490	43	2	pure	pure	PROPN
ejpam-5490	43	3	appl	appl	PROPN
ejpam-5490	43	4	.	.	PROPN
ejpam-5490	43	5	math	math	PROPN
ejpam-5490	43	6	,	,	PUNCT
ejpam-5490	43	7	18	18	NUM
ejpam-5490	43	8	(	(	PUNCT
ejpam-5490	43	9	1	1	NUM
ejpam-5490	43	10	)	)	PUNCT
ejpam-5490	43	11	(	(	PUNCT
ejpam-5490	43	12	2025	2025	NUM
ejpam-5490	43	13	)	)	PUNCT
ejpam-5490	43	14	,	,	PUNCT
ejpam-5490	43	15	5490	5490	NUM
ejpam-5490	43	16	3	3	NUM
ejpam-5490	43	17	of	of	ADP
ejpam-5490	43	18	11	11	NUM
ejpam-5490	43	19	definition	definition	NOUN
ejpam-5490	43	20	2	2	NUM
ejpam-5490	43	21	.	.	PUNCT
ejpam-5490	44	1	for	for	ADP
ejpam-5490	44	2	each	each	DET
ejpam-5490	44	3	v	v	NOUN
ejpam-5490	44	4	,	,	PUNCT
ejpam-5490	44	5	w	w	PROPN
ejpam-5490	44	6	∈	∈	PROPN
ejpam-5490	44	7	a	a	PRON
ejpam-5490	44	8	,	,	PUNCT
ejpam-5490	44	9	v	v	NOUN
ejpam-5490	44	10	∧∗	∧∗	ADJ
ejpam-5490	44	11	w	w	PROPN
ejpam-5490	44	12	∈	∈	PROPN
ejpam-5490	44	13	k	k	PROPN
ejpam-5490	44	14	implies	imply	VERB
ejpam-5490	44	15	v	v	NUM
ejpam-5490	44	16	∈	∈	PROPN
ejpam-5490	44	17	k	k	NOUN
ejpam-5490	44	18	or	or	CCONJ
ejpam-5490	44	19	w	w	PROPN
ejpam-5490	44	20	∈	∈	PROPN
ejpam-5490	44	21	k.	k.	NOUN
ejpam-5490	45	1	this	this	PRON
ejpam-5490	45	2	indicates	indicate	VERB
ejpam-5490	45	3	that	that	SCONJ
ejpam-5490	45	4	k	k	PROPN
ejpam-5490	45	5	is	be	AUX
ejpam-5490	45	6	a	a	DET
ejpam-5490	45	7	prime	prime	ADJ
ejpam-5490	45	8	g	g	NOUN
ejpam-5490	45	9	-	-	PUNCT
ejpam-5490	45	10	filter	filter	NOUN
ejpam-5490	45	11	whenever	whenever	SCONJ
ejpam-5490	45	12	k	k	PROPN
ejpam-5490	45	13	is	be	AUX
ejpam-5490	45	14	a	a	DET
ejpam-5490	45	15	proper	proper	ADJ
ejpam-5490	45	16	g	g	NOUN
ejpam-5490	45	17	-	-	PUNCT
ejpam-5490	45	18	filter	filter	NOUN
ejpam-5490	45	19	of	of	ADP
ejpam-5490	45	20	a.	a.	NOUN
ejpam-5490	45	21	theorem	theorem	NOUN
ejpam-5490	45	22	2	2	X
ejpam-5490	45	23	.	.	PUNCT
ejpam-5490	46	1	let	let	VERB
ejpam-5490	46	2	i	i	PRON
ejpam-5490	46	3	be	be	AUX
ejpam-5490	46	4	an	an	DET
ejpam-5490	46	5	ideal	ideal	NOUN
ejpam-5490	46	6	in	in	ADP
ejpam-5490	46	7	a	a	DET
ejpam-5490	46	8	such	such	ADJ
ejpam-5490	46	9	that	that	SCONJ
ejpam-5490	46	10	k	k	PROPN
ejpam-5490	46	11	∩	∩	PROPN
ejpam-5490	46	12	i	i	NOUN
ejpam-5490	46	13	=	=	SYM
ejpam-5490	46	14	∅	∅	NOUN
ejpam-5490	46	15	,	,	PUNCT
ejpam-5490	46	16	where	where	SCONJ
ejpam-5490	46	17	k	k	PROPN
ejpam-5490	46	18	be	be	AUX
ejpam-5490	46	19	a	a	DET
ejpam-5490	46	20	g	g	NOUN
ejpam-5490	46	21	-	-	PUNCT
ejpam-5490	46	22	filter	filter	NOUN
ejpam-5490	46	23	.	.	PUNCT
ejpam-5490	47	1	then	then	ADV
ejpam-5490	47	2	,	,	PUNCT
ejpam-5490	47	3	u	u	NOUN
ejpam-5490	47	4	is	be	AUX
ejpam-5490	47	5	a	a	DET
ejpam-5490	47	6	prime	prime	ADJ
ejpam-5490	47	7	g	g	NOUN
ejpam-5490	47	8	-	-	NOUN
ejpam-5490	47	9	filter	filter	NOUN
ejpam-5490	47	10	in	in	ADP
ejpam-5490	47	11	a	a	DET
ejpam-5490	47	12	such	such	ADJ
ejpam-5490	47	13	that	that	SCONJ
ejpam-5490	47	14	k	k	PROPN
ejpam-5490	47	15	⊆	⊆	NUM
ejpam-5490	47	16	u	u	NOUN
ejpam-5490	47	17	and	and	CCONJ
ejpam-5490	47	18	u	u	NOUN
ejpam-5490	47	19	∩	∩	NOUN
ejpam-5490	47	20	i	i	NOUN
ejpam-5490	47	21	=	=	PUNCT
ejpam-5490	47	22	∅.	∅.	NOUN
ejpam-5490	47	23	proof	proof	NOUN
ejpam-5490	47	24	.	.	PUNCT
ejpam-5490	48	1	consider	consider	VERB
ejpam-5490	48	2	a	a	DET
ejpam-5490	48	3	set	set	NOUN
ejpam-5490	48	4	q	q	NOUN
ejpam-5490	49	1	=	=	PUNCT
ejpam-5490	49	2	{	{	PUNCT
ejpam-5490	49	3	g	g	PROPN
ejpam-5490	49	4	∈	∈	PROPN
ejpam-5490	49	5	gf	gf	X
ejpam-5490	49	6	(	(	PUNCT
ejpam-5490	49	7	a	a	X
ejpam-5490	49	8	)	)	PUNCT
ejpam-5490	49	9	|	|	ADV
ejpam-5490	49	10	g	g	NOUN
ejpam-5490	49	11	containing	contain	VERB
ejpam-5490	49	12	k	k	PROPN
ejpam-5490	49	13	and	and	CCONJ
ejpam-5490	49	14	g	g	PROPN
ejpam-5490	49	15	∩	∩	NOUN
ejpam-5490	49	16	i	i	NOUN
ejpam-5490	49	17	=	=	SYM
ejpam-5490	49	18	∅	∅	NOUN
ejpam-5490	49	19	}	}	PUNCT
ejpam-5490	49	20	,	,	PUNCT
ejpam-5490	49	21	which	which	PRON
ejpam-5490	49	22	is	be	AUX
ejpam-5490	49	23	a	a	DET
ejpam-5490	49	24	non	non	ADJ
ejpam-5490	49	25	-	-	ADJ
ejpam-5490	49	26	empty	empty	ADJ
ejpam-5490	49	27	set	set	NOUN
ejpam-5490	49	28	(	(	PUNCT
ejpam-5490	49	29	since	since	SCONJ
ejpam-5490	49	30	k	k	PROPN
ejpam-5490	49	31	∈	∈	PROPN
ejpam-5490	49	32	q	q	PROPN
ejpam-5490	49	33	)	)	PUNCT
ejpam-5490	49	34	.	.	PUNCT
ejpam-5490	49	35	suppose	suppose	VERB
ejpam-5490	49	36	that	that	SCONJ
ejpam-5490	49	37	g1	g1	PROPN
ejpam-5490	49	38	⊆	⊆	NUM
ejpam-5490	49	39	g2	g2	PROPN
ejpam-5490	49	40	⊆	⊆	NUM
ejpam-5490	49	41	g3	g3	PROPN
ejpam-5490	49	42	⊆	⊆	NUM
ejpam-5490	49	43	·	·	PUNCT
ejpam-5490	49	44	·	·	PUNCT
ejpam-5490	49	45	·	·	PUNCT
ejpam-5490	49	46	is	be	AUX
ejpam-5490	49	47	an	an	DET
ejpam-5490	49	48	increasing	increase	VERB
ejpam-5490	49	49	chain	chain	NOUN
ejpam-5490	49	50	in	in	ADP
ejpam-5490	49	51	q.	q.	PROPN
ejpam-5490	49	52	take	take	VERB
ejpam-5490	49	53	m	m	VERB
ejpam-5490	49	54	=	=	PUNCT
ejpam-5490	49	55	⊔gi	⊔gi	NOUN
ejpam-5490	49	56	for	for	ADP
ejpam-5490	49	57	i	i	PRON
ejpam-5490	49	58	=	=	NOUN
ejpam-5490	49	59	1	1	NUM
ejpam-5490	49	60	,	,	PUNCT
ejpam-5490	49	61	2	2	NUM
ejpam-5490	49	62	,	,	PUNCT
ejpam-5490	49	63	3	3	NUM
ejpam-5490	49	64	,	,	PUNCT
ejpam-5490	49	65	....	....	PUNCT
ejpam-5490	50	1	then	then	ADV
ejpam-5490	50	2	m	m	VERB
ejpam-5490	50	3	∈	∈	ADJ
ejpam-5490	50	4	gf	gf	X
ejpam-5490	50	5	(	(	PUNCT
ejpam-5490	50	6	a	a	NOUN
ejpam-5490	50	7	)	)	PUNCT
ejpam-5490	50	8	(	(	PUNCT
ejpam-5490	50	9	since	since	SCONJ
ejpam-5490	50	10	gf	gf	PROPN
ejpam-5490	50	11	(	(	PUNCT
ejpam-5490	50	12	a	a	PRON
ejpam-5490	50	13	)	)	PUNCT
ejpam-5490	50	14	is	be	AUX
ejpam-5490	50	15	a	a	DET
ejpam-5490	50	16	distributive	distributive	ADJ
ejpam-5490	50	17	lattice	lattice	NOUN
ejpam-5490	50	18	)	)	PUNCT
ejpam-5490	51	1	and	and	CCONJ
ejpam-5490	51	2	i	i	PRON
ejpam-5490	51	3	∩m	∩m	PUNCT
ejpam-5490	52	1	=	=	PUNCT
ejpam-5490	52	2	i	i	PRON
ejpam-5490	52	3	∩	∩	X
ejpam-5490	52	4	(	(	PUNCT
ejpam-5490	52	5	⊔gi	⊔gi	NOUN
ejpam-5490	52	6	)	)	PUNCT
ejpam-5490	52	7	=	=	SYM
ejpam-5490	52	8	⊔(i	⊔(i	PROPN
ejpam-5490	52	9	∩	∩	NOUN
ejpam-5490	52	10	(	(	PUNCT
ejpam-5490	52	11	gi	gi	NOUN
ejpam-5490	52	12	)	)	PUNCT
ejpam-5490	52	13	=	=	NOUN
ejpam-5490	52	14	∅	∅	NOUN
ejpam-5490	52	15	(	(	PUNCT
ejpam-5490	52	16	since	since	SCONJ
ejpam-5490	52	17	i	i	PRON
ejpam-5490	52	18	∩	∩	VERB
ejpam-5490	52	19	gi	gi	NOUN
ejpam-5490	52	20	=	=	NOUN
ejpam-5490	52	21	∅	∅	NOUN
ejpam-5490	52	22	for	for	ADP
ejpam-5490	52	23	all	all	DET
ejpam-5490	52	24	i	i	NOUN
ejpam-5490	52	25	)	)	PUNCT
ejpam-5490	52	26	.	.	PUNCT
ejpam-5490	53	1	therefore	therefore	ADV
ejpam-5490	53	2	m	m	VERB
ejpam-5490	53	3	∈	∈	PROPN
ejpam-5490	53	4	q.	q.	NOUN
ejpam-5490	53	5	in	in	ADP
ejpam-5490	53	6	this	this	DET
ejpam-5490	53	7	case	case	NOUN
ejpam-5490	53	8	,	,	PUNCT
ejpam-5490	53	9	the	the	DET
ejpam-5490	53	10	chain	chain	NOUN
ejpam-5490	53	11	’s	’s	PART
ejpam-5490	53	12	upper	upper	ADJ
ejpam-5490	53	13	bound	bind	VERB
ejpam-5490	53	14	in	in	ADP
ejpam-5490	53	15	q	q	PROPN
ejpam-5490	53	16	is	be	AUX
ejpam-5490	53	17	m	m	PRON
ejpam-5490	53	18	.	.	PUNCT
ejpam-5490	54	1	zorn	zorn	PROPN
ejpam-5490	54	2	’s	’s	PART
ejpam-5490	54	3	lemma	lemma	PROPN
ejpam-5490	54	4	states	states	PROPN
ejpam-5490	54	5	that	that	SCONJ
ejpam-5490	54	6	q	q	PROPN
ejpam-5490	54	7	has	have	VERB
ejpam-5490	54	8	a	a	DET
ejpam-5490	54	9	maximal	maximal	ADJ
ejpam-5490	54	10	element	element	NOUN
ejpam-5490	54	11	,	,	PUNCT
ejpam-5490	54	12	let	let	VERB
ejpam-5490	54	13	’s	’s	PRON
ejpam-5490	54	14	say	say	VERB
ejpam-5490	54	15	u	u	PROPN
ejpam-5490	54	16	,	,	PUNCT
ejpam-5490	54	17	such	such	ADJ
ejpam-5490	54	18	that	that	SCONJ
ejpam-5490	54	19	u	u	PROPN
ejpam-5490	54	20	∩	∩	NOUN
ejpam-5490	54	21	i	i	NOUN
ejpam-5490	54	22	=	=	NOUN
ejpam-5490	54	23	∅	∅	NOUN
ejpam-5490	54	24	and	and	CCONJ
ejpam-5490	54	25	k	k	PROPN
ejpam-5490	54	26	⊆	⊆	NUM
ejpam-5490	54	27	u	u	NOUN
ejpam-5490	54	28	.	.	PUNCT
ejpam-5490	55	1	choose	choose	VERB
ejpam-5490	55	2	v	v	NOUN
ejpam-5490	55	3	,	,	PUNCT
ejpam-5490	55	4	w	w	PROPN
ejpam-5490	55	5	∈	∈	PROPN
ejpam-5490	55	6	a	a	DET
ejpam-5490	55	7	such	such	ADJ
ejpam-5490	55	8	that	that	DET
ejpam-5490	55	9	v	v	NOUN
ejpam-5490	55	10	/∈	/∈	PUNCT
ejpam-5490	55	11	u	u	NOUN
ejpam-5490	55	12	and	and	CCONJ
ejpam-5490	55	13	w	w	PROPN
ejpam-5490	55	14	/∈	/∈	PROPN
ejpam-5490	55	15	u	u	PROPN
ejpam-5490	55	16	.	.	PUNCT
ejpam-5490	56	1	then	then	ADV
ejpam-5490	56	2	u	u	PRON
ejpam-5490	56	3	⊆	⊆	NUM
ejpam-5490	56	4	u	u	NOUN
ejpam-5490	56	5	⊔	⊔	NOUN
ejpam-5490	57	1	[	[	X
ejpam-5490	58	1	v)dd	v)dd	PROPN
ejpam-5490	58	2	=	=	SYM
ejpam-5490	58	3	{	{	PUNCT
ejpam-5490	58	4	ud	ud	INTJ
ejpam-5490	58	5	∧∗	∧∗	ADJ
ejpam-5490	59	1	[	[	X
ejpam-5490	59	2	v	v	NOUN
ejpam-5490	59	3	)	)	PUNCT
ejpam-5490	59	4	d}d	d}d	NOUN
ejpam-5490	59	5	=	=	PUNCT
ejpam-5490	60	1	[	[	X
ejpam-5490	60	2	u	u	X
ejpam-5490	60	3	∨∗	∨∗	PROPN
ejpam-5490	60	4	[	[	X
ejpam-5490	60	5	v	v	NOUN
ejpam-5490	60	6	)	)	PUNCT
ejpam-5490	60	7	]	]	PUNCT
ejpam-5490	60	8	dd	dd	NOUN
ejpam-5490	60	9	and	and	CCONJ
ejpam-5490	60	10	u	u	PRON
ejpam-5490	60	11	⊆	⊆	NUM
ejpam-5490	60	12	u	u	NOUN
ejpam-5490	60	13	⊔	⊔	NOUN
ejpam-5490	61	1	[	[	X
ejpam-5490	62	1	w)dd	w)dd	PROPN
ejpam-5490	62	2	=	=	PUNCT
ejpam-5490	62	3	{	{	PUNCT
ejpam-5490	62	4	ud∧∗	ud∧∗	PROPN
ejpam-5490	62	5	[	[	X
ejpam-5490	62	6	w	w	NOUN
ejpam-5490	62	7	)	)	PUNCT
ejpam-5490	62	8	d}d	d}d	NOUN
ejpam-5490	62	9	=	=	PUNCT
ejpam-5490	63	1	[	[	X
ejpam-5490	63	2	u	u	X
ejpam-5490	63	3	∨∗	∨∗	PROPN
ejpam-5490	63	4	[	[	X
ejpam-5490	63	5	w	w	NOUN
ejpam-5490	63	6	)	)	PUNCT
ejpam-5490	63	7	]	]	PUNCT
ejpam-5490	64	1	dd	dd	PROPN
ejpam-5490	64	2	.	.	PUNCT
ejpam-5490	65	1	since	since	SCONJ
ejpam-5490	65	2	u	u	NOUN
ejpam-5490	65	3	is	be	AUX
ejpam-5490	65	4	maximal	maximal	ADJ
ejpam-5490	65	5	,	,	PUNCT
ejpam-5490	65	6	[	[	X
ejpam-5490	65	7	u	u	X
ejpam-5490	65	8	∨∗	∨∗	PROPN
ejpam-5490	65	9	[	[	X
ejpam-5490	65	10	v	v	NOUN
ejpam-5490	65	11	)	)	PUNCT
ejpam-5490	65	12	]	]	PUNCT
ejpam-5490	65	13	dd∩i	dd∩i	VERB
ejpam-5490	65	14	̸=	̸=	PROPN
ejpam-5490	65	15	∅	∅	NOUN
ejpam-5490	65	16	and	and	CCONJ
ejpam-5490	65	17	[	[	X
ejpam-5490	65	18	u∨∗[w	u∨∗[w	PROPN
ejpam-5490	65	19	)	)	PUNCT
ejpam-5490	65	20	]	]	PUNCT
ejpam-5490	65	21	dd∩i	dd∩i	VERB
ejpam-5490	65	22	̸=	̸=	PROPN
ejpam-5490	65	23	∅.	∅.	VERB
ejpam-5490	65	24	therefore	therefore	ADV
ejpam-5490	65	25	{	{	PUNCT
ejpam-5490	65	26	[	[	NOUN
ejpam-5490	65	27	u∨∗[v	u∨∗[v	NOUN
ejpam-5490	65	28	)	)	PUNCT
ejpam-5490	65	29	]	]	PUNCT
ejpam-5490	66	1	dd∩i}∩{u∨∗[w	dd∩i}∩{u∨∗[w	PROPN
ejpam-5490	66	2	)	)	PUNCT
ejpam-5490	66	3	]	]	PUNCT
ejpam-5490	67	1	dd}∩i	dd}∩i	NOUN
ejpam-5490	67	2	=	=	PUNCT
ejpam-5490	67	3	{	{	PUNCT
ejpam-5490	67	4	u∨∗[[v	u∨∗[[v	PROPN
ejpam-5490	67	5	)	)	PUNCT
ejpam-5490	67	6	dd∩[w)dd]}∩i	dd∩[w)dd]}∩i	NOUN
ejpam-5490	67	7	=	=	SYM
ejpam-5490	67	8	{	{	PUNCT
ejpam-5490	67	9	u	u	NOUN
ejpam-5490	67	10	∨∗	∨∗	NOUN
ejpam-5490	67	11	[	[	X
ejpam-5490	67	12	[	[	X
ejpam-5490	67	13	v	v	NOUN
ejpam-5490	67	14	)	)	PUNCT
ejpam-5490	67	15	∩	∩	NOUN
ejpam-5490	67	16	[	[	X
ejpam-5490	67	17	w)]}dd	w)]}dd	X
ejpam-5490	67	18	∩	∩	NOUN
ejpam-5490	67	19	i	i	PRON
ejpam-5490	67	20	=	=	SYM
ejpam-5490	67	21	{	{	PUNCT
ejpam-5490	67	22	u	u	NOUN
ejpam-5490	67	23	∨∗	∨∗	PROPN
ejpam-5490	67	24	[	[	X
ejpam-5490	67	25	v	v	X
ejpam-5490	67	26	∨∗	∨∗	NOUN
ejpam-5490	67	27	w)}dd	w)}dd	PROPN
ejpam-5490	67	28	∩	∩	PROPN
ejpam-5490	67	29	i.	i.	NOUN
ejpam-5490	68	1	if	if	SCONJ
ejpam-5490	68	2	v	v	NUM
ejpam-5490	68	3	∨∗	∨∗	PROPN
ejpam-5490	68	4	w	w	PROPN
ejpam-5490	68	5	∈	∈	PROPN
ejpam-5490	68	6	u	u	NOUN
ejpam-5490	68	7	,	,	PUNCT
ejpam-5490	68	8	then	then	ADV
ejpam-5490	68	9	v	v	ADP
ejpam-5490	69	1	∨∗	∨∗	PROPN
ejpam-5490	69	2	w	w	PROPN
ejpam-5490	69	3	∈	∈	PROPN
ejpam-5490	69	4	udd	udd	PROPN
ejpam-5490	69	5	=	=	SYM
ejpam-5490	69	6	u	u	PROPN
ejpam-5490	69	7	(	(	PUNCT
ejpam-5490	69	8	since	since	SCONJ
ejpam-5490	69	9	u	u	NOUN
ejpam-5490	69	10	is	be	AUX
ejpam-5490	69	11	a	a	DET
ejpam-5490	69	12	g	g	NOUN
ejpam-5490	69	13	-	-	PUNCT
ejpam-5490	69	14	filter	filter	NOUN
ejpam-5490	69	15	)	)	PUNCT
ejpam-5490	69	16	and	and	CCONJ
ejpam-5490	69	17	v	v	ADP
ejpam-5490	69	18	∨∗	∨∗	NOUN
ejpam-5490	69	19	w	w	PROPN
ejpam-5490	69	20	∈	∈	PROPN
ejpam-5490	69	21	i.	i.	NOUN
ejpam-5490	69	22	therefore	therefore	ADV
ejpam-5490	69	23	u	u	PROPN
ejpam-5490	69	24	∩	∩	PROPN
ejpam-5490	69	25	i	i	PRON
ejpam-5490	69	26	̸=	̸=	PROPN
ejpam-5490	69	27	∅.	∅.	ADV
ejpam-5490	69	28	which	which	PRON
ejpam-5490	69	29	contradicts	contradict	VERB
ejpam-5490	69	30	itself	itself	PRON
ejpam-5490	69	31	.	.	PUNCT
ejpam-5490	70	1	so	so	ADV
ejpam-5490	70	2	that	that	DET
ejpam-5490	70	3	v	v	ADP
ejpam-5490	70	4	∈	∈	PROPN
ejpam-5490	70	5	u	u	NOUN
ejpam-5490	70	6	or	or	CCONJ
ejpam-5490	70	7	w	w	PROPN
ejpam-5490	70	8	∈	∈	PROPN
ejpam-5490	70	9	u	u	NOUN
ejpam-5490	70	10	.	.	PUNCT
ejpam-5490	71	1	for	for	ADP
ejpam-5490	71	2	this	this	DET
ejpam-5490	71	3	reason	reason	NOUN
ejpam-5490	71	4	,	,	PUNCT
ejpam-5490	71	5	u	u	NOUN
ejpam-5490	71	6	is	be	AUX
ejpam-5490	71	7	prime	prime	ADJ
ejpam-5490	71	8	.	.	PUNCT
ejpam-5490	72	1	corollary	corollary	ADJ
ejpam-5490	72	2	1	1	NUM
ejpam-5490	72	3	.	.	PUNCT
ejpam-5490	73	1	let	let	VERB
ejpam-5490	73	2	v	v	NOUN
ejpam-5490	73	3	/∈	/∈	PUNCT
ejpam-5490	74	1	k	k	PROPN
ejpam-5490	75	1	and	and	CCONJ
ejpam-5490	75	2	k	k	PROPN
ejpam-5490	75	3	be	be	AUX
ejpam-5490	75	4	a	a	DET
ejpam-5490	75	5	g	g	NOUN
ejpam-5490	75	6	-	-	NOUN
ejpam-5490	75	7	filter	filter	NOUN
ejpam-5490	75	8	in	in	ADP
ejpam-5490	75	9	a.	a.	NOUN
ejpam-5490	75	10	after	after	ADP
ejpam-5490	75	11	that	that	PRON
ejpam-5490	75	12	,	,	PUNCT
ejpam-5490	75	13	a	a	DET
ejpam-5490	75	14	prime	prime	ADJ
ejpam-5490	75	15	g	g	NOUN
ejpam-5490	75	16	-	-	PUNCT
ejpam-5490	75	17	filter	filter	NOUN
ejpam-5490	75	18	u	u	NOUN
ejpam-5490	75	19	exists	exist	VERB
ejpam-5490	75	20	such	such	ADJ
ejpam-5490	75	21	that	that	SCONJ
ejpam-5490	75	22	k	k	PROPN
ejpam-5490	75	23	⊆	⊆	NUM
ejpam-5490	75	24	u	u	NOUN
ejpam-5490	75	25	and	and	CCONJ
ejpam-5490	75	26	v	v	NOUN
ejpam-5490	75	27	/∈	/∈	NOUN
ejpam-5490	75	28	u	u	PROPN
ejpam-5490	75	29	.	.	PUNCT
ejpam-5490	76	1	theorem	theorem	NOUN
ejpam-5490	76	2	3	3	NUM
ejpam-5490	76	3	.	.	X
ejpam-5490	76	4	for	for	ADP
ejpam-5490	76	5	every	every	DET
ejpam-5490	76	6	filter	filter	NOUN
ejpam-5490	76	7	k	k	PROPN
ejpam-5490	76	8	of	of	ADP
ejpam-5490	76	9	a	a	PRON
ejpam-5490	76	10	,	,	PUNCT
ejpam-5490	76	11	kdd	kdd	PROPN
ejpam-5490	76	12	is	be	AUX
ejpam-5490	76	13	the	the	DET
ejpam-5490	76	14	intersection	intersection	NOUN
ejpam-5490	76	15	of	of	ADP
ejpam-5490	76	16	all	all	DET
ejpam-5490	76	17	prime	prime	ADJ
ejpam-5490	76	18	g	g	NOUN
ejpam-5490	76	19	-	-	PUNCT
ejpam-5490	76	20	filters	filter	NOUN
ejpam-5490	76	21	containing	contain	VERB
ejpam-5490	76	22	k.	k.	PROPN
ejpam-5490	76	23	proof	proof	NOUN
ejpam-5490	76	24	.	.	PUNCT
ejpam-5490	77	1	suppose	suppose	VERB
ejpam-5490	77	2	there	there	PRON
ejpam-5490	77	3	is	be	VERB
ejpam-5490	77	4	an	an	DET
ejpam-5490	77	5	element	element	NOUN
ejpam-5490	77	6	v	v	NOUN
ejpam-5490	77	7	in	in	ADP
ejpam-5490	77	8	a	a	DET
ejpam-5490	77	9	,	,	PUNCT
ejpam-5490	77	10	v	v	NOUN
ejpam-5490	77	11	/∈	/∈	PUNCT
ejpam-5490	77	12	kdd	kdd	PROPN
ejpam-5490	77	13	,	,	PUNCT
ejpam-5490	77	14	and	and	CCONJ
ejpam-5490	77	15	k	k	PROPN
ejpam-5490	77	16	is	be	AUX
ejpam-5490	77	17	a	a	DET
ejpam-5490	77	18	filter	filter	NOUN
ejpam-5490	77	19	.	.	PUNCT
ejpam-5490	78	1	consider	consider	VERB
ejpam-5490	78	2	u	u	PRON
ejpam-5490	78	3	=	=	PUNCT
ejpam-5490	78	4	{	{	PUNCT
ejpam-5490	78	5	g	g	NOUN
ejpam-5490	78	6	|	|	ADV
ejpam-5490	78	7	g	g	PROPN
ejpam-5490	78	8	is	be	AUX
ejpam-5490	78	9	a	a	DET
ejpam-5490	78	10	g	g	NOUN
ejpam-5490	78	11	-	-	PUNCT
ejpam-5490	78	12	filter	filter	NOUN
ejpam-5490	78	13	of	of	ADP
ejpam-5490	78	14	a	a	PRON
ejpam-5490	78	15	and	and	CCONJ
ejpam-5490	78	16	v	v	NOUN
ejpam-5490	78	17	/∈	/∈	PROPN
ejpam-5490	79	1	g	g	PROPN
ejpam-5490	79	2	and	and	CCONJ
ejpam-5490	79	3	k	k	PROPN
ejpam-5490	79	4	⊆	⊆	NUM
ejpam-5490	79	5	g	g	NOUN
ejpam-5490	79	6	}	}	PUNCT
ejpam-5490	79	7	.	.	PUNCT
ejpam-5490	80	1	then	then	ADV
ejpam-5490	80	2	u	u	PROPN
ejpam-5490	80	3	̸=	̸=	PROPN
ejpam-5490	80	4	ϕ	ϕ	PROPN
ejpam-5490	80	5	(	(	PUNCT
ejpam-5490	80	6	since	since	SCONJ
ejpam-5490	80	7	kdd	kdd	PROPN
ejpam-5490	80	8	∈	∈	PROPN
ejpam-5490	80	9	u	u	NOUN
ejpam-5490	80	10	)	)	PUNCT
ejpam-5490	80	11	.	.	PUNCT
ejpam-5490	81	1	let	let	VERB
ejpam-5490	81	2	k1	k1	PROPN
ejpam-5490	81	3	⊆	⊆	NUM
ejpam-5490	81	4	k2	k2	PROPN
ejpam-5490	81	5	⊆	⊆	NUM
ejpam-5490	81	6	·	·	PUNCT
ejpam-5490	81	7	·	·	PUNCT
ejpam-5490	81	8	·	·	PUNCT
ejpam-5490	81	9	be	be	AUX
ejpam-5490	81	10	a	a	DET
ejpam-5490	81	11	chain	chain	NOUN
ejpam-5490	81	12	in	in	ADP
ejpam-5490	81	13	u.	u.	PROPN
ejpam-5490	81	14	then	then	ADV
ejpam-5490	81	15	(	(	PUNCT
ejpam-5490	81	16	⊔ki	⊔ki	PROPN
ejpam-5490	81	17	)	)	PUNCT
ejpam-5490	81	18	dd	dd	NOUN
ejpam-5490	82	1	=	=	SYM
ejpam-5490	82	2	[	[	X
ejpam-5490	82	3	(	(	PUNCT
ejpam-5490	82	4	∨∗ki	∨∗ki	NOUN
ejpam-5490	82	5	)	)	PUNCT
ejpam-5490	82	6	dd]dd	dd]dd	NOUN
ejpam-5490	82	7	=	=	SYM
ejpam-5490	82	8	(	(	PUNCT
ejpam-5490	82	9	∨∗ki	∨∗ki	NOUN
ejpam-5490	82	10	)	)	PUNCT
ejpam-5490	82	11	dd	dd	NOUN
ejpam-5490	83	1	=	=	SYM
ejpam-5490	83	2	⊔ki	⊔ki	PROPN
ejpam-5490	83	3	(	(	PUNCT
ejpam-5490	83	4	since	since	SCONJ
ejpam-5490	83	5	gf	gf	PROPN
ejpam-5490	83	6	(	(	PUNCT
ejpam-5490	83	7	a	a	PRON
ejpam-5490	83	8	)	)	PUNCT
ejpam-5490	83	9	is	be	AUX
ejpam-5490	83	10	a	a	DET
ejpam-5490	83	11	distributive	distributive	ADJ
ejpam-5490	83	12	lattice	lattice	NOUN
ejpam-5490	83	13	)	)	PUNCT
ejpam-5490	83	14	.	.	PUNCT
ejpam-5490	84	1	therefore	therefore	ADV
ejpam-5490	84	2	⊔ki	⊔ki	PROPN
ejpam-5490	84	3	is	be	AUX
ejpam-5490	84	4	a	a	DET
ejpam-5490	84	5	g	g	NOUN
ejpam-5490	84	6	-	-	PUNCT
ejpam-5490	84	7	filter	filter	NOUN
ejpam-5490	84	8	and	and	CCONJ
ejpam-5490	84	9	k	k	NOUN
ejpam-5490	84	10	⊆	⊆	NUM
ejpam-5490	84	11	⊔ki	⊔ki	PROPN
ejpam-5490	84	12	and	and	CCONJ
ejpam-5490	84	13	(	(	PUNCT
ejpam-5490	84	14	⊔ki)∩	⊔ki)∩	NOUN
ejpam-5490	84	15	(	(	PUNCT
ejpam-5490	84	16	v	v	NOUN
ejpam-5490	84	17	]	]	X
ejpam-5490	84	18	=	=	PUNCT
ejpam-5490	84	19	⊔(ki	⊔(ki	ADP
ejpam-5490	84	20	∩	∩	NOUN
ejpam-5490	84	21	(	(	PUNCT
ejpam-5490	84	22	v	v	NOUN
ejpam-5490	84	23	]	]	X
ejpam-5490	84	24	)	)	PUNCT
ejpam-5490	85	1	=	=	SYM
ejpam-5490	85	2	ϕ.	ϕ.	NOUN
ejpam-5490	85	3	consequently	consequently	ADV
ejpam-5490	85	4	,	,	PUNCT
ejpam-5490	85	5	⊔ki	⊔ki	PROPN
ejpam-5490	85	6	∈	∈	PROPN
ejpam-5490	85	7	u	u	NOUN
ejpam-5490	85	8	,	,	PUNCT
ejpam-5490	85	9	and	and	CCONJ
ejpam-5490	85	10	an	an	DET
ejpam-5490	85	11	upper	upper	ADJ
ejpam-5490	85	12	bound	bind	VERB
ejpam-5490	85	13	of	of	ADP
ejpam-5490	85	14	the	the	DET
ejpam-5490	85	15	chain	chain	NOUN
ejpam-5490	85	16	in	in	ADP
ejpam-5490	85	17	u	u	PROPN
ejpam-5490	85	18	is	be	AUX
ejpam-5490	85	19	⊔ki	⊔ki	PROPN
ejpam-5490	85	20	.	.	PUNCT
ejpam-5490	86	1	zorn	zorn	PROPN
ejpam-5490	86	2	’s	’s	PART
ejpam-5490	86	3	lemma	lemma	PROPN
ejpam-5490	86	4	states	states	PROPN
ejpam-5490	86	5	that	that	SCONJ
ejpam-5490	86	6	,	,	PUNCT
ejpam-5490	86	7	the	the	DET
ejpam-5490	86	8	set	set	NOUN
ejpam-5490	86	9	u	u	NOUN
ejpam-5490	86	10	has	have	VERB
ejpam-5490	86	11	a	a	DET
ejpam-5490	86	12	maximal	maximal	ADJ
ejpam-5490	86	13	element	element	NOUN
ejpam-5490	86	14	,	,	PUNCT
ejpam-5490	86	15	say	say	VERB
ejpam-5490	86	16	that	that	SCONJ
ejpam-5490	86	17	the	the	DET
ejpam-5490	86	18	maximal	maximal	ADJ
ejpam-5490	86	19	,	,	PUNCT
ejpam-5490	86	20	element	element	NOUN
ejpam-5490	86	21	is	be	AUX
ejpam-5490	86	22	u	u	NOUN
ejpam-5490	86	23	.	.	PUNCT
ejpam-5490	87	1	in	in	ADP
ejpam-5490	87	2	the	the	DET
ejpam-5490	87	3	case	case	NOUN
ejpam-5490	87	4	where	where	SCONJ
ejpam-5490	87	5	v	v	NOUN
ejpam-5490	87	6	,	,	PUNCT
ejpam-5490	87	7	w	w	PROPN
ejpam-5490	87	8	∈	∈	PROPN
ejpam-5490	87	9	a	a	PRON
ejpam-5490	87	10	,	,	PUNCT
ejpam-5490	87	11	and	and	CCONJ
ejpam-5490	87	12	v	v	NOUN
ejpam-5490	87	13	/∈	/∈	CCONJ
ejpam-5490	87	14	u	u	NOUN
ejpam-5490	87	15	and	and	CCONJ
ejpam-5490	87	16	w	w	PROPN
ejpam-5490	87	17	/∈	/∈	PUNCT
ejpam-5490	87	18	u	u	NOUN
ejpam-5490	87	19	,	,	PUNCT
ejpam-5490	87	20	v	v	PROPN
ejpam-5490	87	21	∈	∈	NOUN
ejpam-5490	87	22	{	{	PUNCT
ejpam-5490	87	23	(	(	PUNCT
ejpam-5490	87	24	u	u	NOUN
ejpam-5490	87	25	⊔	⊔	PROPN
ejpam-5490	87	26	[	[	X
ejpam-5490	87	27	v)dd	v)dd	PROPN
ejpam-5490	87	28	)	)	PUNCT
ejpam-5490	87	29	∩	∩	NOUN
ejpam-5490	87	30	(	(	PUNCT
ejpam-5490	87	31	u	u	NOUN
ejpam-5490	87	32	⊔	⊔	PROPN
ejpam-5490	87	33	[	[	X
ejpam-5490	87	34	w)dd	w)dd	PROPN
ejpam-5490	87	35	)	)	PUNCT
ejpam-5490	87	36	}	}	PUNCT
ejpam-5490	87	37	⇒	⇒	VERB
ejpam-5490	87	38	v	v	ADP
ejpam-5490	87	39	∈	∈	PROPN
ejpam-5490	87	40	{	{	PUNCT
ejpam-5490	87	41	u	u	NOUN
ejpam-5490	87	42	⊔	⊔	PROPN
ejpam-5490	87	43	(	(	PUNCT
ejpam-5490	87	44	[	[	X
ejpam-5490	87	45	v)dd	v)dd	PROPN
ejpam-5490	87	46	∩	∩	NOUN
ejpam-5490	87	47	[	[	X
ejpam-5490	87	48	w)dd	w)dd	PROPN
ejpam-5490	87	49	)	)	PUNCT
ejpam-5490	87	50	}	}	PUNCT
ejpam-5490	87	51	⇒	⇒	VERB
ejpam-5490	87	52	v	v	ADP
ejpam-5490	87	53	∈	∈	PROPN
ejpam-5490	87	54	{	{	PUNCT
ejpam-5490	87	55	u	u	NOUN
ejpam-5490	87	56	⊔	⊔	PROPN
ejpam-5490	87	57	(	(	PUNCT
ejpam-5490	87	58	[	[	NOUN
ejpam-5490	87	59	v	v	NOUN
ejpam-5490	87	60	)	)	PUNCT
ejpam-5490	87	61	∩	∩	NOUN
ejpam-5490	87	62	[	[	X
ejpam-5490	87	63	w))dd	w))dd	NOUN
ejpam-5490	87	64	}	}	PUNCT
ejpam-5490	87	65	⇒	⇒	VERB
ejpam-5490	87	66	v	v	ADP
ejpam-5490	87	67	∈	∈	PROPN
ejpam-5490	87	68	{	{	PUNCT
ejpam-5490	87	69	u	u	NOUN
ejpam-5490	87	70	⊔	⊔	PROPN
ejpam-5490	87	71	(	(	PUNCT
ejpam-5490	87	72	[	[	X
ejpam-5490	87	73	v	v	ADP
ejpam-5490	87	74	∨∗	∨∗	NOUN
ejpam-5490	87	75	w	w	NOUN
ejpam-5490	87	76	)	)	PUNCT
ejpam-5490	87	77	dd	dd	NOUN
ejpam-5490	87	78	)	)	PUNCT
ejpam-5490	87	79	}	}	PUNCT
ejpam-5490	87	80	⇒	⇒	VERB
ejpam-5490	87	81	v	v	ADP
ejpam-5490	87	82	∈	∈	PROPN
ejpam-5490	87	83	{	{	PUNCT
ejpam-5490	87	84	u	u	NOUN
ejpam-5490	87	85	∨∗	∨∗	PROPN
ejpam-5490	87	86	[	[	X
ejpam-5490	87	87	v	v	X
ejpam-5490	87	88	∨∗	∨∗	NOUN
ejpam-5490	87	89	w	w	NOUN
ejpam-5490	87	90	)	)	PUNCT
ejpam-5490	87	91	dd}dd	dd}dd	PROPN
ejpam-5490	87	92	.	.	PUNCT
ejpam-5490	88	1	if	if	SCONJ
ejpam-5490	88	2	v∨∗w	v∨∗w	NOUN
ejpam-5490	88	3	∈	∈	PROPN
ejpam-5490	88	4	u	u	NOUN
ejpam-5490	88	5	,	,	PUNCT
ejpam-5490	88	6	then	then	ADV
ejpam-5490	88	7	[	[	X
ejpam-5490	88	8	v∨∗w	v∨∗w	NOUN
ejpam-5490	88	9	)	)	PUNCT
ejpam-5490	88	10	⊆	⊆	NUM
ejpam-5490	88	11	u	u	NOUN
ejpam-5490	88	12	and	and	CCONJ
ejpam-5490	88	13	[	[	X
ejpam-5490	88	14	v∨∗w	v∨∗w	NOUN
ejpam-5490	88	15	)	)	PUNCT
ejpam-5490	88	16	dd	dd	VERB
ejpam-5490	88	17	⊆	⊆	NUM
ejpam-5490	88	18	udd	udd	PROPN
ejpam-5490	88	19	=	=	SYM
ejpam-5490	88	20	u	u	PROPN
ejpam-5490	88	21	(	(	PUNCT
ejpam-5490	88	22	since	since	SCONJ
ejpam-5490	88	23	u	u	NOUN
ejpam-5490	88	24	is	be	AUX
ejpam-5490	88	25	g	g	NOUN
ejpam-5490	88	26	-	-	PUNCT
ejpam-5490	88	27	filter	filter	NOUN
ejpam-5490	88	28	)	)	PUNCT
ejpam-5490	88	29	.	.	PUNCT
ejpam-5490	89	1	therefore	therefore	ADV
ejpam-5490	89	2	v	v	ADP
ejpam-5490	89	3	∈	∈	PROPN
ejpam-5490	89	4	u	u	NOUN
ejpam-5490	89	5	.	.	PUNCT
ejpam-5490	90	1	which	which	PRON
ejpam-5490	90	2	is	be	AUX
ejpam-5490	90	3	a	a	DET
ejpam-5490	90	4	contradiction	contradiction	NOUN
ejpam-5490	90	5	.	.	PUNCT
ejpam-5490	91	1	thus	thus	ADV
ejpam-5490	91	2	u	u	NOUN
ejpam-5490	91	3	is	be	AUX
ejpam-5490	91	4	prime	prime	ADJ
ejpam-5490	91	5	and	and	CCONJ
ejpam-5490	91	6	v	v	NOUN
ejpam-5490	91	7	/∈	/∈	CCONJ
ejpam-5490	91	8	u	u	NOUN
ejpam-5490	91	9	.	.	PUNCT
ejpam-5490	92	1	corollary	corollary	ADJ
ejpam-5490	92	2	2	2	NUM
ejpam-5490	92	3	.	.	PUNCT
ejpam-5490	93	1	the	the	DET
ejpam-5490	93	2	intersection	intersection	NOUN
ejpam-5490	93	3	of	of	ADP
ejpam-5490	93	4	prime	prime	ADJ
ejpam-5490	93	5	g	g	NOUN
ejpam-5490	93	6	-	-	PUNCT
ejpam-5490	93	7	filters	filter	NOUN
ejpam-5490	93	8	is	be	AUX
ejpam-5490	93	9	equal	equal	ADJ
ejpam-5490	93	10	to	to	ADP
ejpam-5490	93	11	d.	d.	PROPN
ejpam-5490	93	12	definition	definition	NOUN
ejpam-5490	93	13	3	3	NUM
ejpam-5490	93	14	.	.	PUNCT
ejpam-5490	94	1	a	a	DET
ejpam-5490	94	2	filter	filter	NOUN
ejpam-5490	94	3	k	k	PROPN
ejpam-5490	94	4	in	in	ADP
ejpam-5490	94	5	a	a	PRON
ejpam-5490	94	6	is	be	AUX
ejpam-5490	94	7	said	say	VERB
ejpam-5490	94	8	to	to	PART
ejpam-5490	94	9	be	be	AUX
ejpam-5490	94	10	co	co	ADJ
ejpam-5490	94	11	-	-	ADJ
ejpam-5490	94	12	dense	dense	ADJ
ejpam-5490	94	13	,	,	PUNCT
ejpam-5490	94	14	if	if	SCONJ
ejpam-5490	94	15	kd	kd	PROPN
ejpam-5490	94	16	=	=	PROPN
ejpam-5490	94	17	d.	d.	PROPN
ejpam-5490	94	18	lemma	lemma	PROPN
ejpam-5490	94	19	3	3	X
ejpam-5490	94	20	.	.	PUNCT
ejpam-5490	95	1	every	every	DET
ejpam-5490	95	2	co	co	ADJ
ejpam-5490	95	3	-	-	ADJ
ejpam-5490	95	4	dense	dense	ADJ
ejpam-5490	95	5	filter	filter	NOUN
ejpam-5490	95	6	contains	contain	VERB
ejpam-5490	95	7	at	at	ADV
ejpam-5490	95	8	least	least	ADV
ejpam-5490	95	9	one	one	NUM
ejpam-5490	95	10	dense	dense	ADJ
ejpam-5490	95	11	element	element	NOUN
ejpam-5490	95	12	.	.	PUNCT
ejpam-5490	96	1	j.	j.	PROPN
ejpam-5490	96	2	gunda	gunda	PROPN
ejpam-5490	96	3	et	et	PROPN
ejpam-5490	96	4	al	al	PROPN
ejpam-5490	96	5	.	.	PUNCT
ejpam-5490	96	6	/	/	SYM
ejpam-5490	96	7	eur	eur	PROPN
ejpam-5490	96	8	.	.	PUNCT
ejpam-5490	97	1	j.	j.	PROPN
ejpam-5490	97	2	pure	pure	PROPN
ejpam-5490	97	3	appl	appl	PROPN
ejpam-5490	97	4	.	.	PROPN
ejpam-5490	97	5	math	math	PROPN
ejpam-5490	97	6	,	,	PUNCT
ejpam-5490	97	7	18	18	NUM
ejpam-5490	97	8	(	(	PUNCT
ejpam-5490	97	9	1	1	NUM
ejpam-5490	97	10	)	)	PUNCT
ejpam-5490	97	11	(	(	PUNCT
ejpam-5490	97	12	2025	2025	NUM
ejpam-5490	97	13	)	)	PUNCT
ejpam-5490	97	14	,	,	PUNCT
ejpam-5490	97	15	5490	5490	NUM
ejpam-5490	97	16	4	4	NUM
ejpam-5490	97	17	of	of	ADP
ejpam-5490	97	18	11	11	NUM
ejpam-5490	97	19	theorem	theorem	NOUN
ejpam-5490	97	20	4	4	NUM
ejpam-5490	97	21	.	.	PUNCT
ejpam-5490	97	22	with	with	ADP
ejpam-5490	97	23	the	the	DET
ejpam-5490	97	24	operations	operation	NOUN
ejpam-5490	98	1	k	k	PROPN
ejpam-5490	98	2	⊔g	⊔g	PROPN
ejpam-5490	99	1	=	=	SYM
ejpam-5490	99	2	(	(	PUNCT
ejpam-5490	99	3	k	k	PROPN
ejpam-5490	99	4	∨∗g	∨∗g	ADV
ejpam-5490	99	5	)	)	PUNCT
ejpam-5490	99	6	dd	dd	NOUN
ejpam-5490	99	7	and	and	CCONJ
ejpam-5490	99	8	k	k	PROPN
ejpam-5490	99	9	∧∗g	∧∗g	PUNCT
ejpam-5490	100	1	=	=	NOUN
ejpam-5490	100	2	kd	kd	PROPN
ejpam-5490	100	3	∩gd	∩gd	PROPN
ejpam-5490	100	4	,	,	PUNCT
ejpam-5490	100	5	the	the	DET
ejpam-5490	100	6	set	set	NOUN
ejpam-5490	100	7	of	of	ADP
ejpam-5490	100	8	co	co	ADJ
ejpam-5490	100	9	-	-	ADJ
ejpam-5490	100	10	dense	dense	ADJ
ejpam-5490	100	11	filters	filter	NOUN
ejpam-5490	100	12	forms	form	VERB
ejpam-5490	100	13	a	a	DET
ejpam-5490	100	14	distributive	distributive	ADJ
ejpam-5490	100	15	lattice	lattice	NOUN
ejpam-5490	100	16	,	,	PUNCT
ejpam-5490	100	17	where	where	SCONJ
ejpam-5490	100	18	k	k	PROPN
ejpam-5490	100	19	and	and	CCONJ
ejpam-5490	100	20	g	g	PROPN
ejpam-5490	100	21	are	be	AUX
ejpam-5490	100	22	co	co	ADJ
ejpam-5490	100	23	-	-	ADJ
ejpam-5490	100	24	dense	dense	ADJ
ejpam-5490	100	25	filters	filter	NOUN
ejpam-5490	100	26	in	in	ADP
ejpam-5490	100	27	a	a	PRON
ejpam-5490	100	28	with	with	ADP
ejpam-5490	100	29	the	the	DET
ejpam-5490	100	30	largest	large	ADJ
ejpam-5490	100	31	element	element	NOUN
ejpam-5490	100	32	a	a	PRON
ejpam-5490	100	33	and	and	CCONJ
ejpam-5490	100	34	the	the	DET
ejpam-5490	100	35	least	least	ADJ
ejpam-5490	100	36	element	element	ADJ
ejpam-5490	100	37	d.	d.	PROPN
ejpam-5490	100	38	theorem	theorem	VERB
ejpam-5490	100	39	5	5	NUM
ejpam-5490	100	40	.	.	PUNCT
ejpam-5490	101	1	every	every	DET
ejpam-5490	101	2	maximal	maximal	ADJ
ejpam-5490	101	3	filter	filter	NOUN
ejpam-5490	101	4	is	be	AUX
ejpam-5490	101	5	a	a	DET
ejpam-5490	101	6	g	g	NOUN
ejpam-5490	101	7	-	-	PUNCT
ejpam-5490	101	8	filter	filter	NOUN
ejpam-5490	101	9	or	or	CCONJ
ejpam-5490	101	10	co	co	NOUN
ejpam-5490	101	11	-	-	ADJ
ejpam-5490	101	12	dense	dense	ADJ
ejpam-5490	101	13	.	.	PUNCT
ejpam-5490	102	1	proof	proof	NOUN
ejpam-5490	102	2	.	.	PUNCT
ejpam-5490	103	1	consider	consider	VERB
ejpam-5490	103	2	a	a	DET
ejpam-5490	103	3	maximal	maximal	ADJ
ejpam-5490	103	4	filter	filter	NOUN
ejpam-5490	103	5	of	of	ADP
ejpam-5490	103	6	a	a	PRON
ejpam-5490	103	7	to	to	PART
ejpam-5490	103	8	be	be	AUX
ejpam-5490	103	9	k.	k.	PROPN
ejpam-5490	103	10	thus	thus	ADV
ejpam-5490	103	11	,	,	PUNCT
ejpam-5490	103	12	k	k	PROPN
ejpam-5490	103	13	⊆	⊆	NUM
ejpam-5490	103	14	kdd	kdd	PROPN
ejpam-5490	103	15	is	be	AUX
ejpam-5490	103	16	known	know	VERB
ejpam-5490	103	17	.	.	PUNCT
ejpam-5490	104	1	thus	thus	ADV
ejpam-5490	104	2	,	,	PUNCT
ejpam-5490	104	3	either	either	CCONJ
ejpam-5490	104	4	kdd	kdd	PROPN
ejpam-5490	104	5	=	=	PROPN
ejpam-5490	104	6	a	a	PROPN
ejpam-5490	104	7	or	or	CCONJ
ejpam-5490	104	8	k	k	PROPN
ejpam-5490	104	9	=	=	SYM
ejpam-5490	104	10	kdd	kdd	PROPN
ejpam-5490	104	11	.	.	PROPN
ejpam-5490	105	1	if	if	SCONJ
ejpam-5490	105	2	kdd	kdd	PROPN
ejpam-5490	105	3	=	=	PROPN
ejpam-5490	105	4	a	a	PROPN
ejpam-5490	105	5	,	,	PUNCT
ejpam-5490	105	6	then	then	ADV
ejpam-5490	105	7	kd	kd	PROPN
ejpam-5490	105	8	=	=	SYM
ejpam-5490	105	9	kddd	kddd	PROPN
ejpam-5490	105	10	=	=	SYM
ejpam-5490	105	11	ad	ad	NOUN
ejpam-5490	105	12	=	=	PUNCT
ejpam-5490	105	13	d.	d.	PROPN
ejpam-5490	105	14	therefore	therefore	ADV
ejpam-5490	105	15	k	k	PROPN
ejpam-5490	105	16	is	be	AUX
ejpam-5490	105	17	co	co	ADJ
ejpam-5490	105	18	-	-	ADJ
ejpam-5490	105	19	dense	dense	ADJ
ejpam-5490	105	20	.	.	PUNCT
ejpam-5490	106	1	otherwise	otherwise	ADV
ejpam-5490	106	2	k	k	PROPN
ejpam-5490	106	3	=	=	SYM
ejpam-5490	106	4	kdd	kdd	PROPN
ejpam-5490	106	5	,	,	PUNCT
ejpam-5490	106	6	and	and	CCONJ
ejpam-5490	106	7	then	then	ADV
ejpam-5490	106	8	k	k	PROPN
ejpam-5490	106	9	is	be	AUX
ejpam-5490	106	10	a	a	DET
ejpam-5490	106	11	g	g	NOUN
ejpam-5490	106	12	-	-	PUNCT
ejpam-5490	106	13	filter	filter	NOUN
ejpam-5490	106	14	.	.	PUNCT
ejpam-5490	107	1	3	3	X
ejpam-5490	107	2	.	.	X
ejpam-5490	107	3	normal	normal	ADJ
ejpam-5490	107	4	g	g	NOUN
ejpam-5490	107	5	-	-	PUNCT
ejpam-5490	107	6	filters	filter	NOUN
ejpam-5490	107	7	in	in	ADP
ejpam-5490	107	8	this	this	DET
ejpam-5490	107	9	section	section	NOUN
ejpam-5490	107	10	,	,	PUNCT
ejpam-5490	107	11	we	we	PRON
ejpam-5490	107	12	introduce	introduce	VERB
ejpam-5490	107	13	normal	normal	ADJ
ejpam-5490	107	14	g	g	NOUN
ejpam-5490	107	15	-	-	PUNCT
ejpam-5490	107	16	filters	filter	NOUN
ejpam-5490	107	17	and	and	CCONJ
ejpam-5490	107	18	obtain	obtain	VERB
ejpam-5490	107	19	several	several	ADJ
ejpam-5490	107	20	algebraic	algebraic	ADJ
ejpam-5490	107	21	properties	property	NOUN
ejpam-5490	107	22	.	.	PUNCT
ejpam-5490	108	1	we	we	PRON
ejpam-5490	108	2	prove	prove	VERB
ejpam-5490	108	3	that	that	SCONJ
ejpam-5490	108	4	several	several	ADJ
ejpam-5490	108	5	necessary	necessary	ADJ
ejpam-5490	108	6	and	and	CCONJ
ejpam-5490	108	7	sufficient	sufficient	ADJ
ejpam-5490	108	8	conditions	condition	NOUN
ejpam-5490	108	9	to	to	PART
ejpam-5490	108	10	become	become	VERB
ejpam-5490	108	11	the	the	DET
ejpam-5490	108	12	set	set	NOUN
ejpam-5490	108	13	of	of	ADP
ejpam-5490	108	14	normal	normal	ADJ
ejpam-5490	108	15	g	g	NOUN
ejpam-5490	108	16	-	-	PUNCT
ejpam-5490	108	17	filters	filter	NOUN
ejpam-5490	108	18	is	be	AUX
ejpam-5490	108	19	a	a	DET
ejpam-5490	108	20	boolean	boolean	ADJ
ejpam-5490	108	21	algebra	algebra	NOUN
ejpam-5490	108	22	.	.	PUNCT
ejpam-5490	109	1	now	now	ADV
ejpam-5490	109	2	,	,	PUNCT
ejpam-5490	109	3	let	let	VERB
ejpam-5490	109	4	us	we	PRON
ejpam-5490	109	5	denote	denote	VERB
ejpam-5490	109	6	(	(	PUNCT
ejpam-5490	109	7	w)d	w)d	ADJ
ejpam-5490	109	8	:	:	PUNCT
ejpam-5490	109	9	=	=	SYM
ejpam-5490	109	10	{	{	PUNCT
ejpam-5490	109	11	v	v	NUM
ejpam-5490	109	12	∈	∈	PROPN
ejpam-5490	110	1	a	a	DET
ejpam-5490	110	2	|	|	NOUN
ejpam-5490	110	3	w∨∗	w∨∗	ADJ
ejpam-5490	110	4	v	v	NOUN
ejpam-5490	110	5	is	be	AUX
ejpam-5490	110	6	dense	dense	ADJ
ejpam-5490	110	7	}	}	PUNCT
ejpam-5490	110	8	,	,	PUNCT
ejpam-5490	110	9	where	where	SCONJ
ejpam-5490	110	10	w	w	PROPN
ejpam-5490	110	11	∈	∈	PROPN
ejpam-5490	110	12	a.	a.	NOUN
ejpam-5490	110	13	lemma	lemma	PROPN
ejpam-5490	110	14	4	4	X
ejpam-5490	110	15	.	.	X
ejpam-5490	110	16	for	for	ADP
ejpam-5490	110	17	any	any	DET
ejpam-5490	110	18	v	v	NOUN
ejpam-5490	110	19	∈	∈	PROPN
ejpam-5490	110	20	a	a	PRON
ejpam-5490	110	21	,	,	PUNCT
ejpam-5490	110	22	(	(	PUNCT
ejpam-5490	110	23	i	i	NOUN
ejpam-5490	110	24	)	)	PUNCT
ejpam-5490	110	25	(	(	PUNCT
ejpam-5490	110	26	v)d	v)d	X
ejpam-5490	110	27	is	be	AUX
ejpam-5490	110	28	a	a	DET
ejpam-5490	110	29	filter	filter	NOUN
ejpam-5490	110	30	(	(	PUNCT
ejpam-5490	110	31	ii	ii	NOUN
ejpam-5490	110	32	)	)	PUNCT
ejpam-5490	110	33	(	(	PUNCT
ejpam-5490	111	1	0)d	0)d	NUM
ejpam-5490	111	2	=	=	SYM
ejpam-5490	111	3	d	d	PROPN
ejpam-5490	111	4	(	(	PUNCT
ejpam-5490	111	5	iii	iii	NOUN
ejpam-5490	111	6	)	)	PUNCT
ejpam-5490	112	1	[	[	X
ejpam-5490	112	2	v	v	NOUN
ejpam-5490	112	3	)	)	PUNCT
ejpam-5490	112	4	∩	∩	NOUN
ejpam-5490	112	5	[	[	X
ejpam-5490	112	6	v)d	v)d	NOUN
ejpam-5490	112	7	is	be	AUX
ejpam-5490	112	8	a	a	DET
ejpam-5490	112	9	subset	subset	NOUN
ejpam-5490	112	10	of	of	ADP
ejpam-5490	112	11	d	d	PROPN
ejpam-5490	112	12	(	(	PUNCT
ejpam-5490	112	13	iv	iv	X
ejpam-5490	112	14	)	)	PUNCT
ejpam-5490	112	15	(	(	PUNCT
ejpam-5490	112	16	v)ddd	v)ddd	NOUN
ejpam-5490	112	17	=	=	SYM
ejpam-5490	112	18	(	(	PUNCT
ejpam-5490	112	19	v)d	v)d	X
ejpam-5490	112	20	(	(	PUNCT
ejpam-5490	112	21	v	v	NOUN
ejpam-5490	112	22	)	)	PUNCT
ejpam-5490	112	23	v	v	NOUN
ejpam-5490	112	24	∈	∈	NOUN
ejpam-5490	112	25	(	(	PUNCT
ejpam-5490	112	26	v)dd	v)dd	PROPN
ejpam-5490	112	27	(	(	PUNCT
ejpam-5490	112	28	vi	vi	NOUN
ejpam-5490	112	29	)	)	PUNCT
ejpam-5490	112	30	(	(	PUNCT
ejpam-5490	112	31	v)d	v)d	X
ejpam-5490	112	32	=	=	PUNCT
ejpam-5490	112	33	a⇔	a⇔	NOUN
ejpam-5490	112	34	v	v	ADP
ejpam-5490	112	35	∈	∈	PROPN
ejpam-5490	112	36	d	d	X
ejpam-5490	112	37	(	(	PUNCT
ejpam-5490	112	38	vii	vii	PROPN
ejpam-5490	112	39	)	)	PUNCT
ejpam-5490	112	40	d	d	NOUN
ejpam-5490	112	41	is	be	AUX
ejpam-5490	112	42	a	a	DET
ejpam-5490	112	43	subset	subset	NOUN
ejpam-5490	112	44	of	of	ADP
ejpam-5490	112	45	(	(	PUNCT
ejpam-5490	112	46	v)d	v)d	X
ejpam-5490	112	47	lemma	lemma	PROPN
ejpam-5490	112	48	5	5	NUM
ejpam-5490	112	49	.	.	PUNCT
ejpam-5490	112	50	for	for	ADP
ejpam-5490	112	51	any	any	DET
ejpam-5490	112	52	w	w	NOUN
ejpam-5490	112	53	,	,	PUNCT
ejpam-5490	112	54	x	x	SYM
ejpam-5490	112	55	∈	∈	PROPN
ejpam-5490	112	56	a	a	DET
ejpam-5490	112	57	,	,	PUNCT
ejpam-5490	112	58	(	(	PUNCT
ejpam-5490	112	59	1	1	X
ejpam-5490	112	60	)	)	PUNCT
ejpam-5490	112	61	w	w	NOUN
ejpam-5490	112	62	≤	≤	NUM
ejpam-5490	112	63	x	x	X
ejpam-5490	113	1	=	=	NOUN
ejpam-5490	113	2	⇒	⇒	NOUN
ejpam-5490	113	3	(	(	PUNCT
ejpam-5490	113	4	w)d	w)d	ADJ
ejpam-5490	113	5	⊆	⊆	NUM
ejpam-5490	113	6	(	(	PUNCT
ejpam-5490	113	7	x)d	x)d	X
ejpam-5490	113	8	(	(	PUNCT
ejpam-5490	113	9	2	2	NUM
ejpam-5490	113	10	)	)	PUNCT
ejpam-5490	113	11	(	(	PUNCT
ejpam-5490	113	12	w)d	w)d	ADJ
ejpam-5490	113	13	⊆	⊆	NUM
ejpam-5490	113	14	(	(	PUNCT
ejpam-5490	113	15	x)d	x)d	NOUN
ejpam-5490	113	16	=	=	NOUN
ejpam-5490	113	17	⇒	⇒	NOUN
ejpam-5490	113	18	(	(	PUNCT
ejpam-5490	113	19	x)dd	x)dd	PROPN
ejpam-5490	113	20	⊆	⊆	NUM
ejpam-5490	113	21	(	(	PUNCT
ejpam-5490	113	22	w)dd	w)dd	PROPN
ejpam-5490	113	23	(	(	PUNCT
ejpam-5490	113	24	3	3	NUM
ejpam-5490	113	25	)	)	PUNCT
ejpam-5490	113	26	(	(	PUNCT
ejpam-5490	113	27	w)d	w)d	X
ejpam-5490	113	28	∩	∩	NOUN
ejpam-5490	113	29	(	(	PUNCT
ejpam-5490	113	30	x)d	x)d	NOUN
ejpam-5490	113	31	=	=	SYM
ejpam-5490	113	32	(	(	PUNCT
ejpam-5490	113	33	w	w	ADP
ejpam-5490	113	34	∧∗	∧∗	ADJ
ejpam-5490	113	35	x	x	X
ejpam-5490	113	36	)	)	PUNCT
ejpam-5490	113	37	d	d	NOUN
ejpam-5490	113	38	(	(	PUNCT
ejpam-5490	113	39	4	4	NUM
ejpam-5490	113	40	)	)	PUNCT
ejpam-5490	113	41	(	(	PUNCT
ejpam-5490	113	42	w	w	ADP
ejpam-5490	113	43	∨∗	∨∗	NOUN
ejpam-5490	113	44	x	x	X
ejpam-5490	113	45	)	)	PUNCT
ejpam-5490	113	46	d	d	NOUN
ejpam-5490	113	47	=	=	PUNCT
ejpam-5490	113	48	(	(	PUNCT
ejpam-5490	113	49	w)d	w)d	X
ejpam-5490	113	50	⊔	⊔	X
ejpam-5490	113	51	(	(	PUNCT
ejpam-5490	113	52	x)d	x)d	NOUN
ejpam-5490	113	53	remark	remark	NOUN
ejpam-5490	113	54	1	1	NUM
ejpam-5490	113	55	.	.	PUNCT
ejpam-5490	114	1	if	if	SCONJ
ejpam-5490	114	2	v	v	NOUN
ejpam-5490	114	3	,	,	PUNCT
ejpam-5490	114	4	w	w	PROPN
ejpam-5490	114	5	∈	∈	PROPN
ejpam-5490	115	1	a	a	PRON
ejpam-5490	115	2	,	,	PUNCT
ejpam-5490	115	3	then	then	ADV
ejpam-5490	115	4	(	(	PUNCT
ejpam-5490	115	5	v)d	v)d	X
ejpam-5490	115	6	=	=	SYM
ejpam-5490	115	7	(	(	PUNCT
ejpam-5490	115	8	w)d	w)d	ADJ
ejpam-5490	115	9	dose	dose	VERB
ejpam-5490	115	10	not	not	PART
ejpam-5490	115	11	implies	imply	VERB
ejpam-5490	115	12	v	v	ADP
ejpam-5490	115	13	=	=	SYM
ejpam-5490	115	14	w.	w.	PROPN
ejpam-5490	115	15	regarding	regard	VERB
ejpam-5490	115	16	,	,	PUNCT
ejpam-5490	115	17	have	have	VERB
ejpam-5490	115	18	a	a	DET
ejpam-5490	115	19	look	look	NOUN
ejpam-5490	115	20	at	at	ADP
ejpam-5490	115	21	this	this	DET
ejpam-5490	115	22	instance	instance	NOUN
ejpam-5490	115	23	:	:	PUNCT
ejpam-5490	115	24	example	example	NOUN
ejpam-5490	115	25	1	1	NUM
ejpam-5490	115	26	.	.	PUNCT
ejpam-5490	116	1	given	give	VERB
ejpam-5490	116	2	a	a	DET
ejpam-5490	116	3	lattice	lattice	NOUN
ejpam-5490	116	4	a	a	DET
ejpam-5490	116	5	=	=	PUNCT
ejpam-5490	116	6	{	{	PUNCT
ejpam-5490	116	7	0	0	NUM
ejpam-5490	116	8	,	,	PUNCT
ejpam-5490	116	9	v	v	NOUN
ejpam-5490	116	10	,	,	PUNCT
ejpam-5490	116	11	w	w	PROPN
ejpam-5490	116	12	,	,	PUNCT
ejpam-5490	116	13	x	x	NOUN
ejpam-5490	116	14	,	,	PUNCT
ejpam-5490	116	15	1	1	NUM
ejpam-5490	116	16	}	}	PUNCT
ejpam-5490	116	17	,	,	PUNCT
ejpam-5490	116	18	its	its	PRON
ejpam-5490	116	19	hasse	hasse	NOUN
ejpam-5490	116	20	-	-	PUNCT
ejpam-5490	116	21	diagram	diagram	NOUN
ejpam-5490	116	22	is	be	AUX
ejpam-5490	116	23	j.	j.	PROPN
ejpam-5490	116	24	gunda	gunda	PROPN
ejpam-5490	116	25	et	et	PROPN
ejpam-5490	116	26	al	al	PROPN
ejpam-5490	116	27	.	.	PUNCT
ejpam-5490	116	28	/	/	SYM
ejpam-5490	116	29	eur	eur	PROPN
ejpam-5490	116	30	.	.	PUNCT
ejpam-5490	117	1	j.	j.	PROPN
ejpam-5490	117	2	pure	pure	PROPN
ejpam-5490	117	3	appl	appl	PROPN
ejpam-5490	117	4	.	.	PROPN
ejpam-5490	117	5	math	math	PROPN
ejpam-5490	117	6	,	,	PUNCT
ejpam-5490	117	7	18	18	NUM
ejpam-5490	117	8	(	(	PUNCT
ejpam-5490	117	9	1	1	NUM
ejpam-5490	117	10	)	)	PUNCT
ejpam-5490	117	11	(	(	PUNCT
ejpam-5490	117	12	2025	2025	NUM
ejpam-5490	117	13	)	)	PUNCT
ejpam-5490	117	14	,	,	PUNCT
ejpam-5490	117	15	5490	5490	NUM
ejpam-5490	117	16	5	5	NUM
ejpam-5490	117	17	of	of	ADP
ejpam-5490	117	18	11	11	NUM
ejpam-5490	117	19	x	x	SYM
ejpam-5490	117	20	v	v	ADP
ejpam-5490	117	21	0	0	NUM
ejpam-5490	117	22	w	w	NOUN
ejpam-5490	117	23	1	1	NUM
ejpam-5490	117	24	then	then	ADV
ejpam-5490	117	25	(	(	PUNCT
ejpam-5490	117	26	1)d	1)d	NUM
ejpam-5490	117	27	=	=	SYM
ejpam-5490	117	28	a	a	PROPN
ejpam-5490	117	29	and	and	CCONJ
ejpam-5490	117	30	(	(	PUNCT
ejpam-5490	117	31	x)d	x)d	NOUN
ejpam-5490	117	32	=	=	SYM
ejpam-5490	117	33	a	a	NOUN
ejpam-5490	117	34	,	,	PUNCT
ejpam-5490	117	35	but	but	CCONJ
ejpam-5490	117	36	1	1	NUM
ejpam-5490	117	37	̸=	̸=	PROPN
ejpam-5490	117	38	x.	x.	NOUN
ejpam-5490	117	39	theorem	theorem	VERB
ejpam-5490	117	40	6	6	NUM
ejpam-5490	117	41	.	.	PUNCT
ejpam-5490	118	1	the	the	DET
ejpam-5490	118	2	class	class	NOUN
ejpam-5490	118	3	of	of	ADP
ejpam-5490	118	4	filters	filter	NOUN
ejpam-5490	118	5	ad	ad	NOUN
ejpam-5490	118	6	=	=	SYM
ejpam-5490	118	7	{	{	PUNCT
ejpam-5490	118	8	(	(	PUNCT
ejpam-5490	118	9	x)d	x)d	NOUN
ejpam-5490	118	10	|	|	NOUN
ejpam-5490	118	11	x	x	SYM
ejpam-5490	118	12	∈	∈	PROPN
ejpam-5490	118	13	l	l	NOUN
ejpam-5490	118	14	}	}	PUNCT
ejpam-5490	118	15	with	with	ADP
ejpam-5490	118	16	the	the	DET
ejpam-5490	118	17	operations	operation	NOUN
ejpam-5490	118	18	(	(	PUNCT
ejpam-5490	118	19	x)d	x)d	X
ejpam-5490	118	20	⊔	⊔	PROPN
ejpam-5490	118	21	(	(	PUNCT
ejpam-5490	118	22	y)d	y)d	NOUN
ejpam-5490	118	23	=	=	PUNCT
ejpam-5490	118	24	(	(	PUNCT
ejpam-5490	118	25	x	x	X
ejpam-5490	118	26	∨∗	∨∗	NOUN
ejpam-5490	118	27	y	y	X
ejpam-5490	118	28	)	)	PUNCT
ejpam-5490	118	29	d	d	NOUN
ejpam-5490	118	30	and	and	CCONJ
ejpam-5490	118	31	(	(	PUNCT
ejpam-5490	118	32	x)d	x)d	NOUN
ejpam-5490	118	33	∩	∩	X
ejpam-5490	118	34	(	(	PUNCT
ejpam-5490	118	35	y)d	y)d	SYM
ejpam-5490	118	36	=	=	SYM
ejpam-5490	118	37	(	(	PUNCT
ejpam-5490	118	38	x	x	X
ejpam-5490	118	39	∧∗	∧∗	PROPN
ejpam-5490	118	40	y	y	X
ejpam-5490	118	41	)	)	PUNCT
ejpam-5490	118	42	d	d	NOUN
ejpam-5490	118	43	forms	form	VERB
ejpam-5490	118	44	a	a	DET
ejpam-5490	118	45	distributive	distributive	ADJ
ejpam-5490	118	46	lattice	lattice	NOUN
ejpam-5490	118	47	.	.	PUNCT
ejpam-5490	119	1	a	a	PRON
ejpam-5490	119	2	is	be	AUX
ejpam-5490	119	3	said	say	VERB
ejpam-5490	119	4	to	to	PART
ejpam-5490	119	5	be	be	AUX
ejpam-5490	119	6	quasi	quasi	ADJ
ejpam-5490	119	7	-	-	VERB
ejpam-5490	119	8	complemented	complemented	ADJ
ejpam-5490	119	9	[	[	X
ejpam-5490	119	10	2	2	NUM
ejpam-5490	119	11	]	]	PUNCT
ejpam-5490	119	12	,	,	PUNCT
ejpam-5490	119	13	if	if	SCONJ
ejpam-5490	119	14	for	for	ADP
ejpam-5490	119	15	each	each	PRON
ejpam-5490	119	16	v	v	ADP
ejpam-5490	119	17	∈	∈	PRON
ejpam-5490	119	18	a	a	PRON
ejpam-5490	119	19	,	,	PUNCT
ejpam-5490	119	20	there	there	PRON
ejpam-5490	119	21	exists	exist	VERB
ejpam-5490	119	22	x	x	X
ejpam-5490	119	23	∈	∈	PROPN
ejpam-5490	119	24	a	a	DET
ejpam-5490	119	25	such	such	ADJ
ejpam-5490	119	26	that	that	DET
ejpam-5490	119	27	v	v	NOUN
ejpam-5490	119	28	∧∗	∧∗	ADJ
ejpam-5490	119	29	x	x	PUNCT
ejpam-5490	119	30	=	=	SYM
ejpam-5490	119	31	0	0	NUM
ejpam-5490	120	1	and	and	CCONJ
ejpam-5490	120	2	x	x	SYM
ejpam-5490	121	1	∨∗	∨∗	PRON
ejpam-5490	121	2	v	v	NOUN
ejpam-5490	121	3	is	be	AUX
ejpam-5490	121	4	dense	dense	ADJ
ejpam-5490	121	5	.	.	PUNCT
ejpam-5490	122	1	theorem	theorem	ADJ
ejpam-5490	122	2	7	7	NUM
ejpam-5490	122	3	.	.	PUNCT
ejpam-5490	123	1	if	if	SCONJ
ejpam-5490	123	2	a	a	PRON
ejpam-5490	123	3	is	be	AUX
ejpam-5490	123	4	quasi	quasi	ADJ
ejpam-5490	123	5	-	-	VERB
ejpam-5490	123	6	complemented	complemented	ADJ
ejpam-5490	123	7	,	,	PUNCT
ejpam-5490	123	8	then	then	ADV
ejpam-5490	123	9	(	(	PUNCT
ejpam-5490	123	10	ad,∩,⊔	ad,∩,⊔	X
ejpam-5490	123	11	,	,	PUNCT
ejpam-5490	123	12	d	d	NOUN
ejpam-5490	123	13	,	,	PUNCT
ejpam-5490	123	14	a	a	PRON
ejpam-5490	123	15	)	)	PUNCT
ejpam-5490	123	16	is	be	AUX
ejpam-5490	123	17	a	a	DET
ejpam-5490	123	18	boolean	boolean	ADJ
ejpam-5490	123	19	algebra	algebra	NOUN
ejpam-5490	123	20	.	.	PUNCT
ejpam-5490	124	1	proof	proof	NOUN
ejpam-5490	124	2	.	.	PUNCT
ejpam-5490	125	1	suppose	suppose	VERB
ejpam-5490	125	2	that	that	SCONJ
ejpam-5490	125	3	a	a	PRON
ejpam-5490	125	4	is	be	AUX
ejpam-5490	125	5	quasi	quasi	ADJ
ejpam-5490	125	6	-	-	VERB
ejpam-5490	125	7	complemented	complemented	ADJ
ejpam-5490	125	8	.	.	PUNCT
ejpam-5490	126	1	let	let	VERB
ejpam-5490	126	2	(	(	PUNCT
ejpam-5490	126	3	v)d	v)d	X
ejpam-5490	126	4	∈	∈	PROPN
ejpam-5490	126	5	ad	ad	NOUN
ejpam-5490	126	6	,	,	PUNCT
ejpam-5490	126	7	where	where	SCONJ
ejpam-5490	126	8	v	v	X
ejpam-5490	126	9	∈	∈	PROPN
ejpam-5490	126	10	a.	a.	NOUN
ejpam-5490	126	11	now	now	ADV
ejpam-5490	126	12	,	,	PUNCT
ejpam-5490	126	13	for	for	ADP
ejpam-5490	126	14	this	this	DET
ejpam-5490	126	15	v	v	ADP
ejpam-5490	126	16	∈	∈	PROPN
ejpam-5490	126	17	a	a	PRON
ejpam-5490	126	18	,	,	PUNCT
ejpam-5490	126	19	by	by	ADP
ejpam-5490	126	20	our	our	PRON
ejpam-5490	126	21	assumption	assumption	NOUN
ejpam-5490	126	22	,	,	PUNCT
ejpam-5490	126	23	there	there	PRON
ejpam-5490	126	24	exists	exist	VERB
ejpam-5490	126	25	x	x	X
ejpam-5490	126	26	∈	∈	PROPN
ejpam-5490	126	27	a	a	DET
ejpam-5490	126	28	such	such	ADJ
ejpam-5490	126	29	that	that	SCONJ
ejpam-5490	126	30	v∧∗	v∧∗	NOUN
ejpam-5490	126	31	x	x	PUNCT
ejpam-5490	126	32	=	=	SYM
ejpam-5490	126	33	0	0	NUM
ejpam-5490	126	34	and	and	CCONJ
ejpam-5490	126	35	v∨∗	v∨∗	NOUN
ejpam-5490	126	36	x	x	VERB
ejpam-5490	126	37	is	be	AUX
ejpam-5490	126	38	dense	dense	ADJ
ejpam-5490	126	39	.	.	PUNCT
ejpam-5490	127	1	therefore	therefore	ADV
ejpam-5490	127	2	(	(	PUNCT
ejpam-5490	127	3	v)d	v)d	X
ejpam-5490	127	4	∩	∩	X
ejpam-5490	127	5	(	(	PUNCT
ejpam-5490	127	6	x)d	x)d	NOUN
ejpam-5490	127	7	=	=	SYM
ejpam-5490	127	8	(	(	PUNCT
ejpam-5490	127	9	v	v	NUM
ejpam-5490	127	10	∧∗	∧∗	ADJ
ejpam-5490	127	11	x	x	X
ejpam-5490	127	12	)	)	PUNCT
ejpam-5490	127	13	d	d	NOUN
ejpam-5490	127	14	=	=	SYM
ejpam-5490	127	15	(	(	PUNCT
ejpam-5490	127	16	0)d	0)d	NUM
ejpam-5490	127	17	=	=	SYM
ejpam-5490	127	18	d	d	PROPN
ejpam-5490	127	19	and	and	CCONJ
ejpam-5490	127	20	(	(	PUNCT
ejpam-5490	127	21	v)d	v)d	X
ejpam-5490	127	22	⊔	⊔	INTJ
ejpam-5490	127	23	(	(	PUNCT
ejpam-5490	127	24	x)d	x)d	NOUN
ejpam-5490	127	25	=	=	SYM
ejpam-5490	127	26	(	(	PUNCT
ejpam-5490	127	27	v	v	NUM
ejpam-5490	127	28	∨∗	∨∗	NOUN
ejpam-5490	127	29	x	x	NOUN
ejpam-5490	127	30	)	)	PUNCT
ejpam-5490	127	31	d	d	X
ejpam-5490	127	32	=	=	PUNCT
ejpam-5490	127	33	a	a	PRON
ejpam-5490	127	34	(	(	PUNCT
ejpam-5490	127	35	since	since	SCONJ
ejpam-5490	127	36	v	v	INTJ
ejpam-5490	127	37	∨∗	∨∗	PROPN
ejpam-5490	127	38	x	x	PUNCT
ejpam-5490	127	39	is	be	AUX
ejpam-5490	127	40	dense	dense	ADJ
ejpam-5490	127	41	)	)	PUNCT
ejpam-5490	127	42	.	.	PUNCT
ejpam-5490	128	1	thus	thus	ADV
ejpam-5490	128	2	ad	ad	NOUN
ejpam-5490	128	3	is	be	AUX
ejpam-5490	128	4	a	a	DET
ejpam-5490	128	5	boolean	boolean	ADJ
ejpam-5490	128	6	algebra	algebra	NOUN
ejpam-5490	128	7	.	.	PUNCT
ejpam-5490	129	1	theorem	theorem	VERB
ejpam-5490	129	2	8	8	NUM
ejpam-5490	129	3	.	.	PUNCT
ejpam-5490	130	1	if	if	SCONJ
ejpam-5490	130	2	a	a	PRON
ejpam-5490	130	3	is	be	AUX
ejpam-5490	130	4	a	a	DET
ejpam-5490	130	5	finite	finite	ADJ
ejpam-5490	130	6	distributive	distributive	ADJ
ejpam-5490	130	7	lattice	lattice	NOUN
ejpam-5490	130	8	,	,	PUNCT
ejpam-5490	130	9	then	then	ADV
ejpam-5490	130	10	(	(	PUNCT
ejpam-5490	130	11	ad,∩,⊔	ad,∩,⊔	X
ejpam-5490	130	12	,	,	PUNCT
ejpam-5490	130	13	d	d	NOUN
ejpam-5490	130	14	,	,	PUNCT
ejpam-5490	130	15	a	a	PRON
ejpam-5490	130	16	)	)	PUNCT
ejpam-5490	130	17	is	be	AUX
ejpam-5490	130	18	a	a	DET
ejpam-5490	130	19	boolean	boolean	ADJ
ejpam-5490	130	20	algebra	algebra	NOUN
ejpam-5490	130	21	if	if	SCONJ
ejpam-5490	130	22	and	and	CCONJ
ejpam-5490	130	23	only	only	ADV
ejpam-5490	130	24	if	if	SCONJ
ejpam-5490	130	25	a	a	PRON
ejpam-5490	130	26	is	be	AUX
ejpam-5490	130	27	quasi	quasi	ADJ
ejpam-5490	130	28	-	-	VERB
ejpam-5490	130	29	complemented	complemented	ADJ
ejpam-5490	130	30	.	.	PUNCT
ejpam-5490	131	1	proof	proof	NOUN
ejpam-5490	131	2	.	.	PUNCT
ejpam-5490	132	1	if	if	SCONJ
ejpam-5490	132	2	ad	ad	NOUN
ejpam-5490	132	3	is	be	AUX
ejpam-5490	132	4	a	a	DET
ejpam-5490	132	5	boolean	boolean	ADJ
ejpam-5490	132	6	algebra	algebra	NOUN
ejpam-5490	132	7	,	,	PUNCT
ejpam-5490	132	8	then	then	ADV
ejpam-5490	132	9	a	a	PRON
ejpam-5490	132	10	is	be	AUX
ejpam-5490	132	11	quasi	quasi	ADJ
ejpam-5490	132	12	-	-	VERB
ejpam-5490	132	13	complemented	complemented	ADJ
ejpam-5490	132	14	,	,	PUNCT
ejpam-5490	132	15	as	as	SCONJ
ejpam-5490	132	16	required	require	VERB
ejpam-5490	132	17	by	by	ADP
ejpam-5490	132	18	theorem	theorem	NOUN
ejpam-5490	132	19	7	7	NUM
ejpam-5490	132	20	.	.	PUNCT
ejpam-5490	132	21	assume	assume	VERB
ejpam-5490	132	22	that	that	SCONJ
ejpam-5490	132	23	(	(	PUNCT
ejpam-5490	132	24	v)d	v)d	ADJ
ejpam-5490	132	25	,	,	PUNCT
ejpam-5490	132	26	(	(	PUNCT
ejpam-5490	132	27	w)d	w)d	X
ejpam-5490	132	28	∈	∈	PROPN
ejpam-5490	132	29	ad	ad	NOUN
ejpam-5490	132	30	.	.	PUNCT
ejpam-5490	133	1	since	since	SCONJ
ejpam-5490	133	2	ad	ad	NOUN
ejpam-5490	133	3	is	be	AUX
ejpam-5490	133	4	a	a	DET
ejpam-5490	133	5	boolean	boolean	ADJ
ejpam-5490	133	6	algebra	algebra	NOUN
ejpam-5490	133	7	,	,	PUNCT
ejpam-5490	133	8	(	(	PUNCT
ejpam-5490	133	9	x)d	x)d	X
ejpam-5490	133	10	,	,	PUNCT
ejpam-5490	133	11	(	(	PUNCT
ejpam-5490	133	12	t)d	t)d	ADJ
ejpam-5490	133	13	∈	∈	PROPN
ejpam-5490	133	14	ad	ad	NOUN
ejpam-5490	133	15	exist	exist	VERB
ejpam-5490	133	16	such	such	ADJ
ejpam-5490	133	17	that	that	SCONJ
ejpam-5490	133	18	d	d	NOUN
ejpam-5490	133	19	=	=	SYM
ejpam-5490	133	20	(	(	PUNCT
ejpam-5490	133	21	0)d	0)d	NUM
ejpam-5490	133	22	=	=	SYM
ejpam-5490	133	23	(	(	PUNCT
ejpam-5490	133	24	v	v	NUM
ejpam-5490	133	25	∧∗	∧∗	ADJ
ejpam-5490	133	26	x	x	X
ejpam-5490	133	27	)	)	PUNCT
ejpam-5490	133	28	d	d	X
ejpam-5490	133	29	=	=	SYM
ejpam-5490	133	30	(	(	PUNCT
ejpam-5490	133	31	v)d	v)d	X
ejpam-5490	133	32	∩	∩	NOUN
ejpam-5490	133	33	(	(	PUNCT
ejpam-5490	133	34	x)d	x)d	PUNCT
ejpam-5490	133	35	and	and	CCONJ
ejpam-5490	133	36	a	a	PRON
ejpam-5490	133	37	=	=	X
ejpam-5490	133	38	(	(	PUNCT
ejpam-5490	133	39	v	v	NUM
ejpam-5490	133	40	∨∗	∨∗	NOUN
ejpam-5490	133	41	x	x	X
ejpam-5490	133	42	)	)	PUNCT
ejpam-5490	133	43	d	d	NOUN
ejpam-5490	133	44	=	=	SYM
ejpam-5490	133	45	(	(	PUNCT
ejpam-5490	133	46	v)d	v)d	X
ejpam-5490	133	47	⊔	⊔	X
ejpam-5490	133	48	(	(	PUNCT
ejpam-5490	133	49	x)d	x)d	ADJ
ejpam-5490	133	50	.	.	PUNCT
ejpam-5490	134	1	as	as	SCONJ
ejpam-5490	134	2	we	we	PRON
ejpam-5490	134	3	have	have	VERB
ejpam-5490	134	4	0	0	NUM
ejpam-5490	134	5	∈	∈	PROPN
ejpam-5490	135	1	a	a	DET
ejpam-5490	135	2	=	=	PUNCT
ejpam-5490	135	3	(	(	PUNCT
ejpam-5490	135	4	v	v	NUM
ejpam-5490	135	5	∨∗	∨∗	NOUN
ejpam-5490	135	6	x	x	X
ejpam-5490	135	7	)	)	PUNCT
ejpam-5490	135	8	d	d	NOUN
ejpam-5490	135	9	,	,	PUNCT
ejpam-5490	135	10	v	v	X
ejpam-5490	135	11	∧∗	∧∗	ADJ
ejpam-5490	135	12	x	x	PUNCT
ejpam-5490	135	13	=	=	SYM
ejpam-5490	135	14	0	0	NUM
ejpam-5490	135	15	and	and	CCONJ
ejpam-5490	135	16	v	v	ADP
ejpam-5490	135	17	∨∗	∨∗	NOUN
ejpam-5490	135	18	x	x	PUNCT
ejpam-5490	135	19	is	be	AUX
ejpam-5490	135	20	dense	dense	ADJ
ejpam-5490	135	21	.	.	PUNCT
ejpam-5490	136	1	thus	thus	ADV
ejpam-5490	136	2	a	a	PRON
ejpam-5490	136	3	is	be	AUX
ejpam-5490	136	4	quasi	quasi	ADJ
ejpam-5490	136	5	-	-	VERB
ejpam-5490	136	6	complemented	complemented	ADJ
ejpam-5490	136	7	.	.	PUNCT
ejpam-5490	137	1	definition	definition	NOUN
ejpam-5490	137	2	4	4	NUM
ejpam-5490	137	3	.	.	PUNCT
ejpam-5490	138	1	if	if	SCONJ
ejpam-5490	138	2	there	there	PRON
ejpam-5490	138	3	is	be	VERB
ejpam-5490	138	4	a	a	DET
ejpam-5490	138	5	proper	proper	ADJ
ejpam-5490	138	6	filter	filter	NOUN
ejpam-5490	138	7	g	g	NOUN
ejpam-5490	138	8	such	such	ADJ
ejpam-5490	138	9	that	that	SCONJ
ejpam-5490	139	1	k	k	PROPN
ejpam-5490	139	2	∩g	∩g	PROPN
ejpam-5490	139	3	=	=	PUNCT
ejpam-5490	140	1	d	d	PROPN
ejpam-5490	140	2	and	and	CCONJ
ejpam-5490	140	3	k	k	PROPN
ejpam-5490	140	4	∨∗	∨∗	CCONJ
ejpam-5490	140	5	g	g	PROPN
ejpam-5490	140	6	=	=	SYM
ejpam-5490	140	7	a	a	PROPN
ejpam-5490	140	8	,	,	PUNCT
ejpam-5490	140	9	then	then	ADV
ejpam-5490	140	10	a	a	DET
ejpam-5490	140	11	filter	filter	NOUN
ejpam-5490	140	12	k	k	NOUN
ejpam-5490	140	13	of	of	ADP
ejpam-5490	140	14	a	a	PRON
ejpam-5490	140	15	is	be	AUX
ejpam-5490	140	16	called	call	VERB
ejpam-5490	140	17	a	a	DET
ejpam-5490	140	18	g	g	NOUN
ejpam-5490	140	19	-	-	PUNCT
ejpam-5490	140	20	factor	factor	NOUN
ejpam-5490	140	21	.	.	PUNCT
ejpam-5490	141	1	theorem	theorem	NOUN
ejpam-5490	141	2	9	9	NUM
ejpam-5490	141	3	.	.	X
ejpam-5490	142	1	for	for	ADP
ejpam-5490	142	2	any	any	DET
ejpam-5490	142	3	v	v	NOUN
ejpam-5490	142	4	∈	∈	PROPN
ejpam-5490	142	5	a	a	PRON
ejpam-5490	142	6	,	,	PUNCT
ejpam-5490	142	7	(	(	PUNCT
ejpam-5490	142	8	v)d	v)d	X
ejpam-5490	142	9	is	be	AUX
ejpam-5490	142	10	a	a	DET
ejpam-5490	142	11	g	g	NOUN
ejpam-5490	142	12	-	-	PUNCT
ejpam-5490	142	13	factor	factor	NOUN
ejpam-5490	142	14	if	if	SCONJ
ejpam-5490	142	15	and	and	CCONJ
ejpam-5490	142	16	only	only	ADV
ejpam-5490	142	17	if	if	SCONJ
ejpam-5490	142	18	(	(	PUNCT
ejpam-5490	142	19	v)d	v)d	X
ejpam-5490	142	20	∨∗	∨∗	X
ejpam-5490	142	21	(	(	PUNCT
ejpam-5490	142	22	v	v	NOUN
ejpam-5490	142	23	)	)	PUNCT
ejpam-5490	142	24	dd	dd	NOUN
ejpam-5490	142	25	=	=	PUNCT
ejpam-5490	142	26	a.	a.	NOUN
ejpam-5490	142	27	lemma	lemma	PROPN
ejpam-5490	142	28	6	6	NUM
ejpam-5490	142	29	.	.	PUNCT
ejpam-5490	143	1	if	if	SCONJ
ejpam-5490	143	2	v	v	NOUN
ejpam-5490	143	3	,	,	PUNCT
ejpam-5490	143	4	w,∈	w,∈	PROPN
ejpam-5490	143	5	a	a	NOUN
ejpam-5490	143	6	,	,	PUNCT
ejpam-5490	143	7	then	then	ADV
ejpam-5490	143	8	we	we	PRON
ejpam-5490	143	9	have	have	VERB
ejpam-5490	143	10	(	(	PUNCT
ejpam-5490	143	11	i	i	NOUN
ejpam-5490	143	12	)	)	PUNCT
ejpam-5490	143	13	(	(	PUNCT
ejpam-5490	143	14	v)d	v)d	X
ejpam-5490	143	15	=	=	SYM
ejpam-5490	143	16	(	(	PUNCT
ejpam-5490	143	17	w)d	w)d	ADJ
ejpam-5490	143	18	=	=	PRON
ejpam-5490	143	19	⇒	⇒	NOUN
ejpam-5490	143	20	(	(	PUNCT
ejpam-5490	143	21	v	v	NUM
ejpam-5490	143	22	∧∗	∧∗	ADJ
ejpam-5490	143	23	x	x	X
ejpam-5490	143	24	)	)	PUNCT
ejpam-5490	144	1	d	d	NOUN
ejpam-5490	144	2	=	=	SYM
ejpam-5490	144	3	(	(	PUNCT
ejpam-5490	144	4	w	w	PROPN
ejpam-5490	144	5	∧∗	∧∗	ADJ
ejpam-5490	144	6	x	x	X
ejpam-5490	144	7	)	)	PUNCT
ejpam-5490	144	8	d	d	NOUN
ejpam-5490	144	9	,	,	PUNCT
ejpam-5490	144	10	for	for	ADP
ejpam-5490	144	11	all	all	DET
ejpam-5490	144	12	x	x	SYM
ejpam-5490	144	13	∈	∈	PROPN
ejpam-5490	144	14	a.	a.	NOUN
ejpam-5490	144	15	(	(	PUNCT
ejpam-5490	144	16	ii	ii	NOUN
ejpam-5490	144	17	)	)	PUNCT
ejpam-5490	144	18	(	(	PUNCT
ejpam-5490	144	19	v)d	v)d	X
ejpam-5490	144	20	=	=	SYM
ejpam-5490	144	21	(	(	PUNCT
ejpam-5490	144	22	w)d	w)d	ADJ
ejpam-5490	144	23	=	=	PRON
ejpam-5490	144	24	⇒	⇒	NOUN
ejpam-5490	144	25	(	(	PUNCT
ejpam-5490	144	26	v	v	NUM
ejpam-5490	144	27	∨∗	∨∗	NOUN
ejpam-5490	144	28	x	x	X
ejpam-5490	144	29	)	)	PUNCT
ejpam-5490	144	30	d	d	NOUN
ejpam-5490	144	31	=	=	SYM
ejpam-5490	144	32	(	(	PUNCT
ejpam-5490	144	33	w	w	PROPN
ejpam-5490	144	34	∨∗	∨∗	NOUN
ejpam-5490	144	35	x	x	X
ejpam-5490	144	36	)	)	PUNCT
ejpam-5490	144	37	d	d	NOUN
ejpam-5490	144	38	,	,	PUNCT
ejpam-5490	144	39	for	for	ADP
ejpam-5490	144	40	all	all	DET
ejpam-5490	144	41	x	x	SYM
ejpam-5490	144	42	∈	∈	NOUN
ejpam-5490	144	43	a.	a.	NOUN
ejpam-5490	144	44	theorem	theorem	VERB
ejpam-5490	144	45	10	10	NUM
ejpam-5490	144	46	.	.	PUNCT
ejpam-5490	145	1	the	the	DET
ejpam-5490	145	2	following	follow	VERB
ejpam-5490	145	3	are	be	AUX
ejpam-5490	145	4	equivalent	equivalent	ADJ
ejpam-5490	145	5	for	for	ADP
ejpam-5490	145	6	any	any	DET
ejpam-5490	145	7	filter	filter	NOUN
ejpam-5490	145	8	k	k	NOUN
ejpam-5490	145	9	of	of	ADP
ejpam-5490	145	10	a	a	PRON
ejpam-5490	145	11	;	;	PUNCT
ejpam-5490	145	12	(	(	PUNCT
ejpam-5490	145	13	i	i	NOUN
ejpam-5490	145	14	)	)	PUNCT
ejpam-5490	146	1	k	k	PROPN
ejpam-5490	146	2	is	be	AUX
ejpam-5490	146	3	a	a	DET
ejpam-5490	146	4	g	g	NOUN
ejpam-5490	146	5	-	-	PUNCT
ejpam-5490	146	6	filter	filter	NOUN
ejpam-5490	146	7	j.	j.	PROPN
ejpam-5490	146	8	gunda	gunda	PROPN
ejpam-5490	146	9	et	et	PROPN
ejpam-5490	146	10	al	al	PROPN
ejpam-5490	146	11	.	.	PUNCT
ejpam-5490	146	12	/	/	SYM
ejpam-5490	146	13	eur	eur	PROPN
ejpam-5490	146	14	.	.	PUNCT
ejpam-5490	147	1	j.	j.	PROPN
ejpam-5490	147	2	pure	pure	PROPN
ejpam-5490	147	3	appl	appl	PROPN
ejpam-5490	147	4	.	.	PROPN
ejpam-5490	147	5	math	math	PROPN
ejpam-5490	147	6	,	,	PUNCT
ejpam-5490	147	7	18	18	NUM
ejpam-5490	147	8	(	(	PUNCT
ejpam-5490	147	9	1	1	NUM
ejpam-5490	147	10	)	)	PUNCT
ejpam-5490	147	11	(	(	PUNCT
ejpam-5490	147	12	2025	2025	NUM
ejpam-5490	147	13	)	)	PUNCT
ejpam-5490	147	14	,	,	PUNCT
ejpam-5490	147	15	5490	5490	NUM
ejpam-5490	147	16	6	6	NUM
ejpam-5490	147	17	of	of	ADP
ejpam-5490	147	18	11	11	NUM
ejpam-5490	147	19	(	(	PUNCT
ejpam-5490	147	20	ii	ii	NOUN
ejpam-5490	147	21	)	)	PUNCT
ejpam-5490	147	22	for	for	ADP
ejpam-5490	147	23	any	any	DET
ejpam-5490	147	24	v	v	NOUN
ejpam-5490	147	25	∈	∈	PROPN
ejpam-5490	147	26	a	a	PRON
ejpam-5490	147	27	,	,	PUNCT
ejpam-5490	147	28	v	v	PROPN
ejpam-5490	147	29	∈	∈	X
ejpam-5490	147	30	k	k	PROPN
ejpam-5490	147	31	implies	imply	VERB
ejpam-5490	147	32	(	(	PUNCT
ejpam-5490	147	33	v)dd	v)dd	PROPN
ejpam-5490	147	34	⊆	⊆	NUM
ejpam-5490	147	35	k	k	PROPN
ejpam-5490	147	36	(	(	PUNCT
ejpam-5490	147	37	iii	iii	NOUN
ejpam-5490	147	38	)	)	PUNCT
ejpam-5490	147	39	assuming	assume	VERB
ejpam-5490	147	40	v	v	ADP
ejpam-5490	147	41	∈	∈	PROPN
ejpam-5490	147	42	k	k	X
ejpam-5490	147	43	and	and	CCONJ
ejpam-5490	147	44	(	(	PUNCT
ejpam-5490	147	45	v)d	v)d	X
ejpam-5490	147	46	=	=	SYM
ejpam-5490	147	47	(	(	PUNCT
ejpam-5490	147	48	w)d	w)d	ADJ
ejpam-5490	147	49	,	,	PUNCT
ejpam-5490	147	50	for	for	ADP
ejpam-5490	147	51	every	every	DET
ejpam-5490	147	52	v	v	NOUN
ejpam-5490	147	53	,	,	PUNCT
ejpam-5490	147	54	w	w	PROPN
ejpam-5490	147	55	∈	∈	PROPN
ejpam-5490	147	56	a	a	DET
ejpam-5490	147	57	implies	imply	VERB
ejpam-5490	147	58	w	w	ADP
ejpam-5490	147	59	∈	∈	PROPN
ejpam-5490	147	60	k	k	X
ejpam-5490	147	61	(	(	PUNCT
ejpam-5490	147	62	iv	iv	X
ejpam-5490	147	63	)	)	PUNCT
ejpam-5490	147	64	k	k	NOUN
ejpam-5490	148	1	=	=	PUNCT
ejpam-5490	148	2	⋃	⋃	NOUN
ejpam-5490	148	3	v∈k	v∈k	NOUN
ejpam-5490	148	4	[	[	X
ejpam-5490	148	5	v)dd	v)dd	PROPN
ejpam-5490	148	6	.	.	PUNCT
ejpam-5490	148	7	definition	definition	NOUN
ejpam-5490	148	8	5	5	NUM
ejpam-5490	148	9	.	.	PUNCT
ejpam-5490	149	1	a	a	DET
ejpam-5490	149	2	filter	filter	NOUN
ejpam-5490	149	3	k	k	NOUN
ejpam-5490	149	4	of	of	ADP
ejpam-5490	149	5	a	a	PRON
ejpam-5490	149	6	is	be	AUX
ejpam-5490	149	7	said	say	VERB
ejpam-5490	149	8	to	to	PART
ejpam-5490	149	9	be	be	AUX
ejpam-5490	149	10	a	a	DET
ejpam-5490	149	11	normal	normal	ADJ
ejpam-5490	149	12	g	g	NOUN
ejpam-5490	149	13	-	-	PUNCT
ejpam-5490	149	14	filter	filter	NOUN
ejpam-5490	149	15	,	,	PUNCT
ejpam-5490	149	16	if	if	SCONJ
ejpam-5490	149	17	k	k	PROPN
ejpam-5490	149	18	=	=	PUNCT
ejpam-5490	149	19	(	(	PUNCT
ejpam-5490	149	20	v)d	v)d	ADJ
ejpam-5490	149	21	,	,	PUNCT
ejpam-5490	149	22	for	for	ADP
ejpam-5490	149	23	some	some	DET
ejpam-5490	149	24	v	v	NOUN
ejpam-5490	149	25	∈	∈	NOUN
ejpam-5490	149	26	a.	a.	NOUN
ejpam-5490	149	27	let	let	VERB
ejpam-5490	149	28	us	we	PRON
ejpam-5490	149	29	denote	denote	VERB
ejpam-5490	149	30	the	the	DET
ejpam-5490	149	31	class	class	NOUN
ejpam-5490	149	32	of	of	ADP
ejpam-5490	149	33	normal	normal	ADJ
ejpam-5490	149	34	g	g	NOUN
ejpam-5490	149	35	-	-	PUNCT
ejpam-5490	149	36	filters	filter	NOUN
ejpam-5490	149	37	of	of	ADP
ejpam-5490	149	38	a	a	DET
ejpam-5490	149	39	asngf	asngf	NOUN
ejpam-5490	149	40	(	(	PUNCT
ejpam-5490	149	41	a	a	NOUN
ejpam-5490	149	42	)	)	PUNCT
ejpam-5490	149	43	.	.	PUNCT
ejpam-5490	150	1	now	now	ADV
ejpam-5490	150	2	,	,	PUNCT
ejpam-5490	150	3	we	we	PRON
ejpam-5490	150	4	have	have	VERB
ejpam-5490	150	5	the	the	DET
ejpam-5490	150	6	following	following	NOUN
ejpam-5490	150	7	;	;	PUNCT
ejpam-5490	150	8	theorem	theorem	VERB
ejpam-5490	150	9	11	11	NUM
ejpam-5490	150	10	.	.	PUNCT
ejpam-5490	151	1	(	(	PUNCT
ejpam-5490	151	2	ngf	ngf	ADV
ejpam-5490	151	3	(	(	PUNCT
ejpam-5490	151	4	a),∩,⊔	a),∩,⊔	PROPN
ejpam-5490	151	5	)	)	PUNCT
ejpam-5490	151	6	is	be	AUX
ejpam-5490	151	7	a	a	DET
ejpam-5490	151	8	sublattice	sublattice	NOUN
ejpam-5490	151	9	of	of	ADP
ejpam-5490	151	10	gf	gf	X
ejpam-5490	151	11	(	(	PUNCT
ejpam-5490	151	12	a	a	NOUN
ejpam-5490	151	13	)	)	PUNCT
ejpam-5490	151	14	in	in	ADP
ejpam-5490	151	15	which	which	PRON
ejpam-5490	151	16	(	(	PUNCT
ejpam-5490	151	17	0)d	0)d	PROPN
ejpam-5490	151	18	is	be	AUX
ejpam-5490	151	19	the	the	DET
ejpam-5490	151	20	least	least	ADJ
ejpam-5490	151	21	and	and	CCONJ
ejpam-5490	151	22	(	(	PUNCT
ejpam-5490	151	23	v)d	v)d	X
ejpam-5490	151	24	is	be	AUX
ejpam-5490	151	25	the	the	DET
ejpam-5490	151	26	greatest	great	ADJ
ejpam-5490	151	27	elements	element	NOUN
ejpam-5490	151	28	in	in	ADP
ejpam-5490	151	29	ngf	ngf	PROPN
ejpam-5490	151	30	(	(	PUNCT
ejpam-5490	151	31	a	a	NOUN
ejpam-5490	151	32	)	)	PUNCT
ejpam-5490	151	33	,	,	PUNCT
ejpam-5490	151	34	for	for	ADP
ejpam-5490	151	35	some	some	DET
ejpam-5490	151	36	v	v	ADP
ejpam-5490	151	37	∈	∈	PROPN
ejpam-5490	151	38	d.	d.	NOUN
ejpam-5490	151	39	proof	proof	NOUN
ejpam-5490	151	40	.	.	PUNCT
ejpam-5490	152	1	assume	assume	VERB
ejpam-5490	152	2	that	that	SCONJ
ejpam-5490	152	3	k	k	X
ejpam-5490	152	4	,	,	PUNCT
ejpam-5490	152	5	g	g	PROPN
ejpam-5490	152	6	∈	∈	PROPN
ejpam-5490	152	7	ngf	ngf	ADV
ejpam-5490	152	8	(	(	PUNCT
ejpam-5490	152	9	a	a	NOUN
ejpam-5490	152	10	)	)	PUNCT
ejpam-5490	152	11	.	.	PUNCT
ejpam-5490	153	1	k	k	X
ejpam-5490	153	2	=	=	PRON
ejpam-5490	153	3	(	(	PUNCT
ejpam-5490	153	4	v)d	v)d	X
ejpam-5490	153	5	and	and	CCONJ
ejpam-5490	153	6	g	g	PROPN
ejpam-5490	153	7	=	=	SYM
ejpam-5490	153	8	(	(	PUNCT
ejpam-5490	153	9	y)d	y)d	ADV
ejpam-5490	153	10	then	then	ADV
ejpam-5490	153	11	exist	exist	VERB
ejpam-5490	153	12	a	a	DET
ejpam-5490	153	13	pair	pair	NOUN
ejpam-5490	153	14	of	of	ADP
ejpam-5490	153	15	v	v	NOUN
ejpam-5490	153	16	,	,	PUNCT
ejpam-5490	153	17	y	y	PROPN
ejpam-5490	153	18	∈	∈	PROPN
ejpam-5490	153	19	a.	a.	NOUN
ejpam-5490	153	20	it	it	PRON
ejpam-5490	153	21	is	be	AUX
ejpam-5490	153	22	observe	observe	VERB
ejpam-5490	153	23	that	that	SCONJ
ejpam-5490	153	24	(	(	PUNCT
ejpam-5490	153	25	x	x	X
ejpam-5490	153	26	∨∗	∨∗	X
ejpam-5490	153	27	y	y	X
ejpam-5490	153	28	)	)	PUNCT
ejpam-5490	153	29	d	d	NOUN
ejpam-5490	153	30	is	be	AUX
ejpam-5490	153	31	an	an	DET
ejpam-5490	153	32	upper	upper	ADJ
ejpam-5490	153	33	bound	bound	NOUN
ejpam-5490	153	34	of	of	ADP
ejpam-5490	153	35	k	k	PROPN
ejpam-5490	153	36	,	,	PUNCT
ejpam-5490	153	37	g.	g.	PROPN
ejpam-5490	153	38	let	let	VERB
ejpam-5490	153	39	h	h	NOUN
ejpam-5490	153	40	∈	∈	PROPN
ejpam-5490	153	41	ngf	ngf	ADV
ejpam-5490	153	42	(	(	PUNCT
ejpam-5490	153	43	a	a	X
ejpam-5490	153	44	)	)	PUNCT
ejpam-5490	153	45	be	be	AUX
ejpam-5490	153	46	an	an	DET
ejpam-5490	153	47	upper	upper	ADJ
ejpam-5490	153	48	bound	bound	NOUN
ejpam-5490	153	49	of	of	ADP
ejpam-5490	153	50	k	k	PROPN
ejpam-5490	153	51	,	,	PUNCT
ejpam-5490	154	1	g.	g.	PROPN
ejpam-5490	155	1	then	then	ADV
ejpam-5490	155	2	there	there	PRON
ejpam-5490	155	3	exists	exist	VERB
ejpam-5490	155	4	z	z	PROPN
ejpam-5490	155	5	∈	∈	PROPN
ejpam-5490	155	6	a	a	DET
ejpam-5490	155	7	such	such	ADJ
ejpam-5490	155	8	that	that	DET
ejpam-5490	155	9	h	h	NOUN
ejpam-5490	155	10	=	=	SYM
ejpam-5490	155	11	(	(	PUNCT
ejpam-5490	155	12	z)d	z)d	PUNCT
ejpam-5490	155	13	and	and	CCONJ
ejpam-5490	155	14	(	(	PUNCT
ejpam-5490	155	15	v)d	v)d	ADJ
ejpam-5490	155	16	,	,	PUNCT
ejpam-5490	155	17	(	(	PUNCT
ejpam-5490	155	18	y)d	y)d	NOUN
ejpam-5490	155	19	⊆	⊆	NUM
ejpam-5490	155	20	(	(	PUNCT
ejpam-5490	155	21	z)d	z)d	NOUN
ejpam-5490	155	22	.	.	PUNCT
ejpam-5490	156	1	so	so	ADV
ejpam-5490	156	2	that	that	SCONJ
ejpam-5490	156	3	(	(	PUNCT
ejpam-5490	156	4	z)dd	z)dd	PROPN
ejpam-5490	156	5	⊆	⊆	NUM
ejpam-5490	156	6	(	(	PUNCT
ejpam-5490	156	7	x)dd∩(y)dd	x)dd∩(y)dd	X
ejpam-5490	156	8	=	=	SYM
ejpam-5490	156	9	(	(	PUNCT
ejpam-5490	156	10	x∨∗	x∨∗	PROPN
ejpam-5490	156	11	y	y	NOUN
ejpam-5490	156	12	)	)	PUNCT
ejpam-5490	156	13	dd	dd	NOUN
ejpam-5490	156	14	.	.	PUNCT
ejpam-5490	157	1	therefore	therefore	ADV
ejpam-5490	157	2	(	(	PUNCT
ejpam-5490	157	3	x∨∗	x∨∗	PROPN
ejpam-5490	157	4	y	y	NOUN
ejpam-5490	157	5	)	)	PUNCT
ejpam-5490	157	6	d	d	X
ejpam-5490	157	7	⊆	⊆	NUM
ejpam-5490	157	8	(	(	PUNCT
ejpam-5490	157	9	z)d	z)d	NOUN
ejpam-5490	157	10	.	.	PUNCT
ejpam-5490	158	1	hence	hence	ADV
ejpam-5490	158	2	(	(	PUNCT
ejpam-5490	158	3	x∨∗	x∨∗	PROPN
ejpam-5490	158	4	y	y	X
ejpam-5490	158	5	)	)	PUNCT
ejpam-5490	158	6	d	d	NOUN
ejpam-5490	158	7	is	be	AUX
ejpam-5490	158	8	the	the	DET
ejpam-5490	158	9	least	least	ADJ
ejpam-5490	158	10	upper	upper	ADJ
ejpam-5490	158	11	bound	bind	VERB
ejpam-5490	158	12	of	of	ADP
ejpam-5490	158	13	k	k	PROPN
ejpam-5490	158	14	and	and	CCONJ
ejpam-5490	158	15	g	g	PROPN
ejpam-5490	158	16	and	and	CCONJ
ejpam-5490	158	17	it	it	PRON
ejpam-5490	158	18	is	be	AUX
ejpam-5490	158	19	indicated	indicate	VERB
ejpam-5490	158	20	by	by	ADP
ejpam-5490	158	21	k	k	PROPN
ejpam-5490	158	22	⊔g	⊔g	PROPN
ejpam-5490	158	23	.	.	PUNCT
ejpam-5490	159	1	thus	thus	ADV
ejpam-5490	159	2	ngf	ngf	ADV
ejpam-5490	159	3	(	(	PUNCT
ejpam-5490	159	4	a	a	X
ejpam-5490	159	5	)	)	PUNCT
ejpam-5490	159	6	is	be	AUX
ejpam-5490	159	7	a	a	DET
ejpam-5490	159	8	sub	sub	NOUN
ejpam-5490	159	9	-	-	NOUN
ejpam-5490	159	10	lattice	lattice	NOUN
ejpam-5490	159	11	of	of	ADP
ejpam-5490	159	12	gf	gf	PROPN
ejpam-5490	159	13	(	(	PUNCT
ejpam-5490	159	14	a	a	NOUN
ejpam-5490	159	15	)	)	PUNCT
ejpam-5490	159	16	.	.	PUNCT
ejpam-5490	160	1	for	for	ADP
ejpam-5490	160	2	any	any	DET
ejpam-5490	160	3	v	v	NOUN
ejpam-5490	160	4	∈	∈	PROPN
ejpam-5490	160	5	a	a	PRON
ejpam-5490	160	6	,	,	PUNCT
ejpam-5490	160	7	(	(	PUNCT
ejpam-5490	160	8	v)d∩(0)d	v)d∩(0)d	NOUN
ejpam-5490	160	9	=	=	SYM
ejpam-5490	160	10	(	(	PUNCT
ejpam-5490	160	11	x∧∗0	x∧∗0	NOUN
ejpam-5490	160	12	)	)	PUNCT
ejpam-5490	160	13	d	d	X
ejpam-5490	160	14	=	=	SYM
ejpam-5490	160	15	(	(	PUNCT
ejpam-5490	160	16	0)d	0)d	PROPN
ejpam-5490	160	17	.	.	PUNCT
ejpam-5490	160	18	therefore	therefore	ADV
ejpam-5490	160	19	(	(	PUNCT
ejpam-5490	160	20	0)d	0)d	PROPN
ejpam-5490	160	21	is	be	AUX
ejpam-5490	160	22	the	the	DET
ejpam-5490	160	23	least	least	ADJ
ejpam-5490	160	24	element	element	NOUN
ejpam-5490	160	25	in	in	ADP
ejpam-5490	160	26	ngf	ngf	PROPN
ejpam-5490	160	27	(	(	PUNCT
ejpam-5490	160	28	a	a	NOUN
ejpam-5490	160	29	)	)	PUNCT
ejpam-5490	160	30	.	.	PUNCT
ejpam-5490	161	1	let	let	VERB
ejpam-5490	161	2	w	w	PROPN
ejpam-5490	161	3	∈	∈	PROPN
ejpam-5490	161	4	d.	d.	PROPN
ejpam-5490	161	5	then	then	ADV
ejpam-5490	161	6	(	(	PUNCT
ejpam-5490	161	7	v)d	v)d	X
ejpam-5490	161	8	⊔	⊔	X
ejpam-5490	161	9	(	(	PUNCT
ejpam-5490	161	10	y)d	y)d	NOUN
ejpam-5490	161	11	=	=	PUNCT
ejpam-5490	162	1	(	(	PUNCT
ejpam-5490	162	2	x	x	X
ejpam-5490	162	3	∨∗	∨∗	PROPN
ejpam-5490	162	4	y	y	PROPN
ejpam-5490	162	5	)	)	PUNCT
ejpam-5490	162	6	d.	d.	NOUN
ejpam-5490	162	7	since	since	SCONJ
ejpam-5490	162	8	v	v	NUM
ejpam-5490	162	9	∨∗	∨∗	PROPN
ejpam-5490	162	10	y	y	PROPN
ejpam-5490	162	11	∈	∈	PROPN
ejpam-5490	162	12	d	d	PROPN
ejpam-5490	162	13	,	,	PUNCT
ejpam-5490	162	14	(	(	PUNCT
ejpam-5490	162	15	v)d	v)d	X
ejpam-5490	162	16	⊔	⊔	X
ejpam-5490	162	17	(	(	PUNCT
ejpam-5490	162	18	y)d	y)d	NOUN
ejpam-5490	162	19	=	=	PUNCT
ejpam-5490	162	20	a.	a.	NOUN
ejpam-5490	162	21	therefore	therefore	ADV
ejpam-5490	162	22	(	(	PUNCT
ejpam-5490	162	23	v)d	v)d	X
ejpam-5490	162	24	is	be	AUX
ejpam-5490	162	25	the	the	DET
ejpam-5490	162	26	greatest	great	ADJ
ejpam-5490	162	27	element	element	NOUN
ejpam-5490	162	28	in	in	ADP
ejpam-5490	162	29	ngf	ngf	PROPN
ejpam-5490	162	30	(	(	PUNCT
ejpam-5490	162	31	a	a	NOUN
ejpam-5490	162	32	)	)	PUNCT
ejpam-5490	162	33	.	.	PUNCT
ejpam-5490	163	1	thus	thus	ADV
ejpam-5490	163	2	ngf	ngf	ADV
ejpam-5490	163	3	(	(	PUNCT
ejpam-5490	163	4	a	a	X
ejpam-5490	163	5	)	)	PUNCT
ejpam-5490	163	6	is	be	AUX
ejpam-5490	163	7	bounded	bound	VERB
ejpam-5490	163	8	.	.	PUNCT
ejpam-5490	164	1	denote	denote	VERB
ejpam-5490	164	2	a	a	DET
ejpam-5490	164	3	relation	relation	NOUN
ejpam-5490	164	4	ψ	ψ	NOUN
ejpam-5490	164	5	:	:	PUNCT
ejpam-5490	164	6	=	=	SYM
ejpam-5490	164	7	{	{	PUNCT
ejpam-5490	164	8	(	(	PUNCT
ejpam-5490	164	9	v	v	NOUN
ejpam-5490	164	10	,	,	PUNCT
ejpam-5490	164	11	w	w	NOUN
ejpam-5490	164	12	)	)	PUNCT
ejpam-5490	164	13	∈	∈	PROPN
ejpam-5490	164	14	a	a	DET
ejpam-5490	164	15	×	×	NOUN
ejpam-5490	164	16	a	a	DET
ejpam-5490	164	17	|	|	NOUN
ejpam-5490	164	18	(	(	PUNCT
ejpam-5490	164	19	w)d	w)d	X
ejpam-5490	164	20	=	=	SYM
ejpam-5490	164	21	(	(	PUNCT
ejpam-5490	164	22	v)d	v)d	ADJ
ejpam-5490	164	23	}	}	PUNCT
ejpam-5490	164	24	.	.	PUNCT
ejpam-5490	165	1	then	then	ADV
ejpam-5490	165	2	it	it	PRON
ejpam-5490	165	3	is	be	AUX
ejpam-5490	165	4	easy	easy	ADJ
ejpam-5490	165	5	to	to	PART
ejpam-5490	165	6	prove	prove	VERB
ejpam-5490	165	7	that	that	SCONJ
ejpam-5490	165	8	ψ	ψ	NOUN
ejpam-5490	165	9	is	be	AUX
ejpam-5490	165	10	a	a	DET
ejpam-5490	165	11	congruence	congruence	NOUN
ejpam-5490	165	12	relation	relation	NOUN
ejpam-5490	165	13	on	on	ADP
ejpam-5490	165	14	a.	a.	PROPN
ejpam-5490	165	15	lemma	lemma	PROPN
ejpam-5490	165	16	7	7	X
ejpam-5490	165	17	.	.	X
ejpam-5490	165	18	for	for	ADP
ejpam-5490	165	19	any	any	DET
ejpam-5490	165	20	v	v	NOUN
ejpam-5490	165	21	∈	∈	PROPN
ejpam-5490	165	22	a	a	PRON
ejpam-5490	165	23	,	,	PUNCT
ejpam-5490	165	24	(	(	PUNCT
ejpam-5490	165	25	i	i	NOUN
ejpam-5490	165	26	)	)	PUNCT
ejpam-5490	165	27	v	v	NOUN
ejpam-5490	165	28	/	/	SYM
ejpam-5490	165	29	ψ	ψ	NOUN
ejpam-5490	165	30	=	=	PUNCT
ejpam-5490	165	31	{	{	PUNCT
ejpam-5490	165	32	0	0	NUM
ejpam-5490	165	33	}	}	PUNCT
ejpam-5490	165	34	if	if	SCONJ
ejpam-5490	166	1	and	and	CCONJ
ejpam-5490	166	2	only	only	ADV
ejpam-5490	166	3	if	if	SCONJ
ejpam-5490	166	4	v	v	NOUN
ejpam-5490	166	5	=	=	SYM
ejpam-5490	166	6	0	0	NUM
ejpam-5490	166	7	(	(	PUNCT
ejpam-5490	166	8	ii	ii	NOUN
ejpam-5490	166	9	)	)	PUNCT
ejpam-5490	166	10	v	v	NOUN
ejpam-5490	166	11	/	/	SYM
ejpam-5490	166	12	ψ	ψ	NOUN
ejpam-5490	167	1	=	=	SYM
ejpam-5490	167	2	d	d	NOUN
ejpam-5490	167	3	if	if	SCONJ
ejpam-5490	167	4	and	and	CCONJ
ejpam-5490	167	5	only	only	ADV
ejpam-5490	167	6	if	if	SCONJ
ejpam-5490	167	7	v	v	PROPN
ejpam-5490	167	8	∈	∈	PROPN
ejpam-5490	167	9	d.	d.	PROPN
ejpam-5490	167	10	theorem	theorem	VERB
ejpam-5490	167	11	12	12	NUM
ejpam-5490	167	12	.	.	PUNCT
ejpam-5490	168	1	the	the	DET
ejpam-5490	168	2	quotient	quotient	NOUN
ejpam-5490	168	3	lattice	lattice	VERB
ejpam-5490	168	4	a	a	PRON
ejpam-5490	168	5	/	/	SYM
ejpam-5490	168	6	ψ	ψ	NOUN
ejpam-5490	168	7	forms	form	VERB
ejpam-5490	168	8	a	a	DET
ejpam-5490	168	9	distributive	distributive	ADJ
ejpam-5490	168	10	lattice	lattice	NOUN
ejpam-5490	168	11	with	with	ADP
ejpam-5490	168	12	the	the	DET
ejpam-5490	168	13	operations	operation	NOUN
ejpam-5490	168	14	v	v	NOUN
ejpam-5490	168	15	/	/	SYM
ejpam-5490	168	16	ψ	ψ	X
ejpam-5490	168	17	∧∗	∧∗	ADJ
ejpam-5490	168	18	w	w	NOUN
ejpam-5490	168	19	/	/	SYM
ejpam-5490	168	20	ψ	ψ	NOUN
ejpam-5490	168	21	=	=	SYM
ejpam-5490	168	22	(	(	PUNCT
ejpam-5490	168	23	v	v	NUM
ejpam-5490	168	24	∧∗	∧∗	ADJ
ejpam-5490	168	25	w)/ψ	w)/ψ	NOUN
ejpam-5490	168	26	and	and	CCONJ
ejpam-5490	168	27	v	v	NOUN
ejpam-5490	168	28	/	/	SYM
ejpam-5490	168	29	ψ	ψ	NOUN
ejpam-5490	168	30	∨∗	∨∗	NOUN
ejpam-5490	168	31	w	w	NOUN
ejpam-5490	168	32	/	/	SYM
ejpam-5490	168	33	ψ	ψ	NOUN
ejpam-5490	168	34	=	=	SYM
ejpam-5490	168	35	(	(	PUNCT
ejpam-5490	168	36	v	v	ADP
ejpam-5490	168	37	∨∗	∨∗	NOUN
ejpam-5490	168	38	w)/ψ.furthermore	w)/ψ.furthermore	PROPN
ejpam-5490	168	39	,	,	PUNCT
ejpam-5490	168	40	the	the	DET
ejpam-5490	168	41	largest	large	ADJ
ejpam-5490	168	42	element	element	NOUN
ejpam-5490	168	43	in	in	ADP
ejpam-5490	168	44	a	a	DET
ejpam-5490	168	45	/	/	SYM
ejpam-5490	168	46	ψ	ψ	NOUN
ejpam-5490	168	47	exists	exist	VERB
ejpam-5490	168	48	only	only	ADV
ejpam-5490	168	49	when	when	SCONJ
ejpam-5490	168	50	a	a	PRON
ejpam-5490	168	51	is	be	AUX
ejpam-5490	168	52	dense	dense	ADJ
ejpam-5490	168	53	.	.	PUNCT
ejpam-5490	169	1	theorem	theorem	ADJ
ejpam-5490	169	2	13	13	NUM
ejpam-5490	169	3	.	.	PUNCT
ejpam-5490	170	1	the	the	DET
ejpam-5490	170	2	subsequent	subsequent	ADJ
ejpam-5490	170	3	algebras	algebra	NOUN
ejpam-5490	170	4	are	be	AUX
ejpam-5490	170	5	equivalent	equivalent	ADJ
ejpam-5490	170	6	;	;	PUNCT
ejpam-5490	170	7	(	(	PUNCT
ejpam-5490	170	8	1	1	X
ejpam-5490	170	9	)	)	PUNCT
ejpam-5490	170	10	a	a	PRON
ejpam-5490	170	11	is	be	AUX
ejpam-5490	170	12	quasi	quasi	NOUN
ejpam-5490	170	13	complemented	complement	VERB
ejpam-5490	170	14	(	(	PUNCT
ejpam-5490	170	15	2	2	NUM
ejpam-5490	170	16	)	)	PUNCT
ejpam-5490	170	17	(	(	PUNCT
ejpam-5490	170	18	ngf	ngf	ADV
ejpam-5490	170	19	(	(	PUNCT
ejpam-5490	170	20	a),∩,⊔	a),∩,⊔	PROPN
ejpam-5490	170	21	,	,	PUNCT
ejpam-5490	170	22	d	d	PROPN
ejpam-5490	170	23	,	,	PUNCT
ejpam-5490	170	24	a	a	PRON
ejpam-5490	170	25	)	)	PUNCT
ejpam-5490	170	26	is	be	AUX
ejpam-5490	170	27	a	a	DET
ejpam-5490	170	28	boolean	boolean	ADJ
ejpam-5490	170	29	algebra	algebra	NOUN
ejpam-5490	170	30	(	(	PUNCT
ejpam-5490	170	31	3	3	NUM
ejpam-5490	170	32	)	)	PUNCT
ejpam-5490	170	33	(	(	PUNCT
ejpam-5490	170	34	a	a	DET
ejpam-5490	170	35	/	/	SYM
ejpam-5490	170	36	ψ,∧∗,∨∗	ψ,∧∗,∨∗	NOUN
ejpam-5490	170	37	,	,	PUNCT
ejpam-5490	170	38	0	0	NUM
ejpam-5490	170	39	/	/	SYM
ejpam-5490	170	40	ψ	ψ	NOUN
ejpam-5490	170	41	,	,	PUNCT
ejpam-5490	170	42	d	d	NOUN
ejpam-5490	170	43	/	/	SYM
ejpam-5490	170	44	ψ	ψ	NOUN
ejpam-5490	170	45	)	)	PUNCT
ejpam-5490	170	46	is	be	AUX
ejpam-5490	170	47	a	a	DET
ejpam-5490	170	48	boolean	boolean	ADJ
ejpam-5490	170	49	algebra	algebra	NOUN
ejpam-5490	170	50	(	(	PUNCT
ejpam-5490	170	51	4	4	X
ejpam-5490	170	52	)	)	PUNCT
ejpam-5490	170	53	all	all	DET
ejpam-5490	170	54	principal	principal	ADJ
ejpam-5490	170	55	ideals	ideal	NOUN
ejpam-5490	170	56	are	be	AUX
ejpam-5490	170	57	quasi	quasi	ADJ
ejpam-5490	170	58	-	-	VERB
ejpam-5490	170	59	complemented	complemented	ADJ
ejpam-5490	170	60	.	.	PUNCT
ejpam-5490	171	1	proof	proof	NOUN
ejpam-5490	171	2	.	.	PUNCT
ejpam-5490	172	1	(	(	PUNCT
ejpam-5490	172	2	1	1	X
ejpam-5490	172	3	)	)	PUNCT
ejpam-5490	172	4	=	=	NOUN
ejpam-5490	172	5	⇒	⇒	NOUN
ejpam-5490	172	6	(	(	PUNCT
ejpam-5490	172	7	2	2	NUM
ejpam-5490	172	8	):	):	PUNCT
ejpam-5490	172	9	suppose	suppose	VERB
ejpam-5490	172	10	that	that	SCONJ
ejpam-5490	172	11	a	a	PRON
ejpam-5490	172	12	is	be	AUX
ejpam-5490	172	13	quasi	quasi	NOUN
ejpam-5490	172	14	complemented	complement	VERB
ejpam-5490	172	15	.	.	PUNCT
ejpam-5490	173	1	let	let	VERB
ejpam-5490	173	2	v	v	X
ejpam-5490	173	3	∈	∈	PROPN
ejpam-5490	173	4	a	a	DET
ejpam-5490	173	5	.then	.then	NOUN
ejpam-5490	173	6	,	,	PUNCT
ejpam-5490	173	7	v∧∗w	v∧∗w	NUM
ejpam-5490	173	8	=	=	SYM
ejpam-5490	173	9	0	0	NUM
ejpam-5490	173	10	and	and	CCONJ
ejpam-5490	173	11	v∨∗w	v∨∗w	NOUN
ejpam-5490	173	12	are	be	AUX
ejpam-5490	173	13	dense	dense	ADJ
ejpam-5490	173	14	for	for	ADP
ejpam-5490	173	15	some	some	DET
ejpam-5490	173	16	w	w	PROPN
ejpam-5490	173	17	∈	∈	PROPN
ejpam-5490	173	18	a.	a.	NOUN
ejpam-5490	174	1	so	so	SCONJ
ejpam-5490	174	2	that	that	SCONJ
ejpam-5490	174	3	d	d	NOUN
ejpam-5490	174	4	=	=	PRON
ejpam-5490	174	5	(	(	PUNCT
ejpam-5490	174	6	0)d	0)d	NUM
ejpam-5490	174	7	=	=	SYM
ejpam-5490	174	8	(	(	PUNCT
ejpam-5490	174	9	v∧∗w	v∧∗w	NUM
ejpam-5490	174	10	)	)	PUNCT
ejpam-5490	174	11	d	d	NOUN
ejpam-5490	174	12	=	=	SYM
ejpam-5490	174	13	(	(	PUNCT
ejpam-5490	174	14	v)d∩(w)d	v)d∩(w)d	ADJ
ejpam-5490	174	15	and	and	CCONJ
ejpam-5490	174	16	a	a	DET
ejpam-5490	174	17	=	=	X
ejpam-5490	174	18	(	(	PUNCT
ejpam-5490	174	19	v	v	NUM
ejpam-5490	174	20	∨∗	∨∗	NOUN
ejpam-5490	174	21	w	w	NOUN
ejpam-5490	174	22	)	)	PUNCT
ejpam-5490	174	23	d	d	NOUN
ejpam-5490	174	24	=	=	SYM
ejpam-5490	174	25	(	(	PUNCT
ejpam-5490	174	26	v)d	v)d	X
ejpam-5490	174	27	⊔	⊔	X
ejpam-5490	174	28	(	(	PUNCT
ejpam-5490	174	29	w)d	w)d	ADJ
ejpam-5490	174	30	.	.	PUNCT
ejpam-5490	175	1	therefore	therefore	ADV
ejpam-5490	175	2	ngf	ngf	ADV
ejpam-5490	175	3	(	(	PUNCT
ejpam-5490	175	4	a	a	X
ejpam-5490	175	5	)	)	PUNCT
ejpam-5490	175	6	is	be	AUX
ejpam-5490	175	7	a	a	DET
ejpam-5490	175	8	boolean	boolean	ADJ
ejpam-5490	175	9	algebra	algebra	NOUN
ejpam-5490	175	10	.	.	PUNCT
ejpam-5490	176	1	(	(	PUNCT
ejpam-5490	176	2	2	2	X
ejpam-5490	176	3	)	)	PUNCT
ejpam-5490	176	4	=	=	NOUN
ejpam-5490	176	5	⇒	⇒	NOUN
ejpam-5490	176	6	(	(	PUNCT
ejpam-5490	176	7	3	3	NUM
ejpam-5490	176	8	):	):	PUNCT
ejpam-5490	176	9	let	let	VERB
ejpam-5490	176	10	v	v	NUM
ejpam-5490	176	11	∈	∈	NOUN
ejpam-5490	176	12	a.	a.	NOUN
ejpam-5490	176	13	then	then	ADV
ejpam-5490	176	14	(	(	PUNCT
ejpam-5490	176	15	v)d	v)d	X
ejpam-5490	176	16	∈	∈	PROPN
ejpam-5490	176	17	ngf	ngf	ADV
ejpam-5490	176	18	(	(	PUNCT
ejpam-5490	176	19	a	a	NOUN
ejpam-5490	176	20	)	)	PUNCT
ejpam-5490	176	21	.	.	PUNCT
ejpam-5490	177	1	for	for	ADP
ejpam-5490	177	2	this	this	PRON
ejpam-5490	177	3	(	(	PUNCT
ejpam-5490	177	4	v)d	v)d	X
ejpam-5490	177	5	∈	∈	PROPN
ejpam-5490	177	6	ngf	ngf	ADV
ejpam-5490	177	7	(	(	PUNCT
ejpam-5490	177	8	a	a	X
ejpam-5490	177	9	)	)	PUNCT
ejpam-5490	177	10	,	,	PUNCT
ejpam-5490	177	11	there	there	PRON
ejpam-5490	177	12	exists	exist	VERB
ejpam-5490	177	13	j.	j.	PROPN
ejpam-5490	177	14	gunda	gunda	PROPN
ejpam-5490	177	15	et	et	PROPN
ejpam-5490	177	16	al	al	PROPN
ejpam-5490	177	17	.	.	PUNCT
ejpam-5490	177	18	/	/	SYM
ejpam-5490	177	19	eur	eur	PROPN
ejpam-5490	177	20	.	.	PUNCT
ejpam-5490	178	1	j.	j.	PROPN
ejpam-5490	178	2	pure	pure	PROPN
ejpam-5490	178	3	appl	appl	PROPN
ejpam-5490	178	4	.	.	PROPN
ejpam-5490	178	5	math	math	PROPN
ejpam-5490	178	6	,	,	PUNCT
ejpam-5490	178	7	18	18	NUM
ejpam-5490	178	8	(	(	PUNCT
ejpam-5490	178	9	1	1	NUM
ejpam-5490	178	10	)	)	PUNCT
ejpam-5490	178	11	(	(	PUNCT
ejpam-5490	178	12	2025	2025	NUM
ejpam-5490	178	13	)	)	PUNCT
ejpam-5490	178	14	,	,	PUNCT
ejpam-5490	178	15	5490	5490	NUM
ejpam-5490	178	16	7	7	NUM
ejpam-5490	178	17	of	of	ADP
ejpam-5490	178	18	11	11	NUM
ejpam-5490	178	19	w	w	NOUN
ejpam-5490	178	20	∈	∈	PROPN
ejpam-5490	178	21	a	a	DET
ejpam-5490	178	22	such	such	ADJ
ejpam-5490	178	23	that	that	DET
ejpam-5490	178	24	d	d	NOUN
ejpam-5490	178	25	=	=	SYM
ejpam-5490	178	26	(	(	PUNCT
ejpam-5490	178	27	0)d	0)d	NUM
ejpam-5490	178	28	=	=	SYM
ejpam-5490	178	29	(	(	PUNCT
ejpam-5490	178	30	v	v	NUM
ejpam-5490	178	31	∧∗	∧∗	ADJ
ejpam-5490	178	32	w	w	NOUN
ejpam-5490	178	33	)	)	PUNCT
ejpam-5490	178	34	d	d	NOUN
ejpam-5490	178	35	=	=	SYM
ejpam-5490	178	36	(	(	PUNCT
ejpam-5490	178	37	v)d	v)d	X
ejpam-5490	178	38	∩	∩	X
ejpam-5490	178	39	(	(	PUNCT
ejpam-5490	178	40	w)d	w)d	ADJ
ejpam-5490	178	41	and	and	CCONJ
ejpam-5490	178	42	a	a	DET
ejpam-5490	178	43	=	=	X
ejpam-5490	178	44	(	(	PUNCT
ejpam-5490	178	45	v	v	NUM
ejpam-5490	178	46	∨∗	∨∗	NOUN
ejpam-5490	178	47	w	w	NOUN
ejpam-5490	178	48	)	)	PUNCT
ejpam-5490	178	49	d	d	NOUN
ejpam-5490	178	50	=	=	SYM
ejpam-5490	178	51	(	(	PUNCT
ejpam-5490	178	52	v)d	v)d	X
ejpam-5490	178	53	⊔	⊔	X
ejpam-5490	178	54	(	(	PUNCT
ejpam-5490	178	55	w)d	w)d	ADJ
ejpam-5490	178	56	.	.	PUNCT
ejpam-5490	179	1	therefore	therefore	ADV
ejpam-5490	179	2	v	v	X
ejpam-5490	179	3	∨∗	∨∗	PROPN
ejpam-5490	179	4	w	w	NOUN
ejpam-5490	179	5	is	be	AUX
ejpam-5490	179	6	dense	dense	ADJ
ejpam-5490	179	7	and	and	CCONJ
ejpam-5490	179	8	v	v	ADP
ejpam-5490	179	9	∧∗	∧∗	ADJ
ejpam-5490	179	10	w	w	PROPN
ejpam-5490	180	1	=	=	NOUN
ejpam-5490	180	2	0	0	PROPN
ejpam-5490	180	3	.	.	PUNCT
ejpam-5490	181	1	hence	hence	ADV
ejpam-5490	181	2	{	{	PUNCT
ejpam-5490	181	3	0	0	NUM
ejpam-5490	181	4	}	}	PUNCT
ejpam-5490	181	5	=	=	SYM
ejpam-5490	181	6	0	0	NUM
ejpam-5490	181	7	/	/	SYM
ejpam-5490	181	8	ψ	ψ	NOUN
ejpam-5490	181	9	=	=	SYM
ejpam-5490	181	10	(	(	PUNCT
ejpam-5490	181	11	v	v	NUM
ejpam-5490	181	12	∧∗	∧∗	ADJ
ejpam-5490	181	13	w)/ψ	w)/ψ	NOUN
ejpam-5490	181	14	=	=	SYM
ejpam-5490	181	15	v	v	NOUN
ejpam-5490	181	16	/	/	SYM
ejpam-5490	181	17	ψ	ψ	NOUN
ejpam-5490	181	18	∧∗	∧∗	ADJ
ejpam-5490	181	19	w	w	NOUN
ejpam-5490	181	20	/	/	SYM
ejpam-5490	181	21	ψ	ψ	NOUN
ejpam-5490	181	22	and	and	CCONJ
ejpam-5490	181	23	d	d	NOUN
ejpam-5490	181	24	=	=	SYM
ejpam-5490	181	25	(	(	PUNCT
ejpam-5490	181	26	v∨∗w)/ψ	v∨∗w)/ψ	PROPN
ejpam-5490	181	27	=	=	SYM
ejpam-5490	181	28	v	v	NOUN
ejpam-5490	181	29	/	/	SYM
ejpam-5490	181	30	ψ∨∗w	ψ∨∗w	NOUN
ejpam-5490	181	31	/	/	SYM
ejpam-5490	181	32	ψ(since	ψ(since	NOUN
ejpam-5490	181	33	v∨∗w	v∨∗w	NOUN
ejpam-5490	181	34	is	be	AUX
ejpam-5490	181	35	dense	dense	ADJ
ejpam-5490	181	36	)	)	PUNCT
ejpam-5490	181	37	.	.	PUNCT
ejpam-5490	182	1	thus	thus	ADV
ejpam-5490	182	2	a	a	X
ejpam-5490	182	3	/	/	SYM
ejpam-5490	182	4	ψ	ψ	NOUN
ejpam-5490	182	5	is	be	AUX
ejpam-5490	182	6	a	a	DET
ejpam-5490	182	7	boolean	boolean	ADJ
ejpam-5490	182	8	algebra	algebra	NOUN
ejpam-5490	182	9	.	.	PUNCT
ejpam-5490	183	1	(	(	PUNCT
ejpam-5490	183	2	3	3	X
ejpam-5490	183	3	)	)	PUNCT
ejpam-5490	183	4	=	=	NOUN
ejpam-5490	183	5	⇒	⇒	NOUN
ejpam-5490	183	6	(	(	PUNCT
ejpam-5490	183	7	4	4	NUM
ejpam-5490	183	8	):	):	PUNCT
ejpam-5490	183	9	let	let	VERB
ejpam-5490	183	10	v	v	NUM
ejpam-5490	183	11	∈	∈	NOUN
ejpam-5490	183	12	a.	a.	NOUN
ejpam-5490	183	13	then	then	ADV
ejpam-5490	183	14	,	,	PUNCT
ejpam-5490	183	15	v	v	NOUN
ejpam-5490	183	16	/	/	SYM
ejpam-5490	183	17	ψ	ψ	NOUN
ejpam-5490	183	18	∧∗	∧∗	ADJ
ejpam-5490	183	19	w	w	NOUN
ejpam-5490	183	20	/	/	SYM
ejpam-5490	183	21	ψ	ψ	NOUN
ejpam-5490	183	22	=	=	PUNCT
ejpam-5490	183	23	{	{	PUNCT
ejpam-5490	183	24	0	0	NUM
ejpam-5490	183	25	}	}	PUNCT
ejpam-5490	183	26	and	and	CCONJ
ejpam-5490	183	27	v	v	NOUN
ejpam-5490	183	28	/	/	SYM
ejpam-5490	183	29	ψ	ψ	NOUN
ejpam-5490	183	30	∨∗	∨∗	NOUN
ejpam-5490	183	31	w	w	NOUN
ejpam-5490	183	32	/	/	SYM
ejpam-5490	183	33	ψ	ψ	NOUN
ejpam-5490	183	34	=	=	SYM
ejpam-5490	183	35	d	d	NOUN
ejpam-5490	183	36	exist	exist	VERB
ejpam-5490	183	37	for	for	ADP
ejpam-5490	183	38	some	some	DET
ejpam-5490	183	39	w	w	PROPN
ejpam-5490	183	40	∈	∈	PROPN
ejpam-5490	183	41	a.	a.	NOUN
ejpam-5490	183	42	so	so	SCONJ
ejpam-5490	183	43	that	that	SCONJ
ejpam-5490	183	44	v	v	X
ejpam-5490	183	45	∨∗	∨∗	PROPN
ejpam-5490	183	46	w	w	NOUN
ejpam-5490	183	47	is	be	AUX
ejpam-5490	183	48	dense	dense	ADJ
ejpam-5490	183	49	and	and	CCONJ
ejpam-5490	183	50	v	v	ADP
ejpam-5490	183	51	∧∗	∧∗	ADJ
ejpam-5490	183	52	w	w	PROPN
ejpam-5490	183	53	=	=	NOUN
ejpam-5490	183	54	0	0	PROPN
ejpam-5490	183	55	.	.	PUNCT
ejpam-5490	184	1	so	so	ADV
ejpam-5490	184	2	that	that	SCONJ
ejpam-5490	184	3	(	(	PUNCT
ejpam-5490	184	4	v	v	NOUN
ejpam-5490	184	5	]	]	X
ejpam-5490	184	6	∧∗	∧∗	ADJ
ejpam-5490	184	7	(	(	PUNCT
ejpam-5490	184	8	w	w	NOUN
ejpam-5490	184	9	]	]	X
ejpam-5490	184	10	=	=	SYM
ejpam-5490	184	11	(	(	PUNCT
ejpam-5490	184	12	v	v	NUM
ejpam-5490	184	13	∧∗	∧∗	ADJ
ejpam-5490	184	14	w	w	NOUN
ejpam-5490	184	15	]	]	X
ejpam-5490	184	16	=	=	SYM
ejpam-5490	184	17	(	(	PUNCT
ejpam-5490	184	18	0	0	NUM
ejpam-5490	184	19	]	]	X
ejpam-5490	184	20	=	=	X
ejpam-5490	184	21	{	{	PUNCT
ejpam-5490	184	22	0	0	NUM
ejpam-5490	184	23	}	}	PUNCT
ejpam-5490	184	24	and	and	CCONJ
ejpam-5490	184	25	(	(	PUNCT
ejpam-5490	184	26	v	v	NOUN
ejpam-5490	184	27	]	]	X
ejpam-5490	184	28	∨∗	∨∗	PROPN
ejpam-5490	184	29	(	(	PUNCT
ejpam-5490	184	30	w	w	NOUN
ejpam-5490	184	31	]	]	X
ejpam-5490	184	32	=	=	SYM
ejpam-5490	184	33	(	(	PUNCT
ejpam-5490	184	34	v	v	NUM
ejpam-5490	184	35	∨∗	∨∗	PROPN
ejpam-5490	184	36	w	w	NOUN
ejpam-5490	184	37	]	]	X
ejpam-5490	184	38	.	.	PUNCT
ejpam-5490	185	1	now	now	ADV
ejpam-5490	185	2	,	,	PUNCT
ejpam-5490	185	3	(	(	PUNCT
ejpam-5490	185	4	v	v	X
ejpam-5490	185	5	∧∗	∧∗	ADJ
ejpam-5490	185	6	w	w	NOUN
ejpam-5490	185	7	]	]	X
ejpam-5490	185	8	=	=	PUNCT
ejpam-5490	185	9	{	{	PUNCT
ejpam-5490	185	10	0	0	NUM
ejpam-5490	185	11	}	}	PUNCT
ejpam-5490	185	12	and	and	CCONJ
ejpam-5490	185	13	(	(	PUNCT
ejpam-5490	185	14	v	v	INTJ
ejpam-5490	185	15	∨∗	∨∗	NOUN
ejpam-5490	185	16	w	w	NOUN
ejpam-5490	185	17	]	]	X
ejpam-5490	185	18	is	be	AUX
ejpam-5490	185	19	a	a	DET
ejpam-5490	185	20	principal	principal	ADJ
ejpam-5490	185	21	ideal	ideal	NOUN
ejpam-5490	185	22	generated	generate	VERB
ejpam-5490	185	23	by	by	ADP
ejpam-5490	185	24	a	a	DET
ejpam-5490	185	25	dense	dense	ADJ
ejpam-5490	185	26	element	element	NOUN
ejpam-5490	185	27	v	v	ADP
ejpam-5490	185	28	∨∗	∨∗	PROPN
ejpam-5490	185	29	w.	w.	NOUN
ejpam-5490	185	30	hence	hence	ADV
ejpam-5490	185	31	every	every	DET
ejpam-5490	185	32	principal	principal	ADJ
ejpam-5490	185	33	ideal	ideal	NOUN
ejpam-5490	185	34	is	be	AUX
ejpam-5490	185	35	quasi	quasi	ADJ
ejpam-5490	185	36	-	-	VERB
ejpam-5490	185	37	complemented	complemented	ADJ
ejpam-5490	185	38	.	.	PUNCT
ejpam-5490	186	1	(	(	PUNCT
ejpam-5490	186	2	4	4	X
ejpam-5490	186	3	)	)	PUNCT
ejpam-5490	186	4	=	=	NOUN
ejpam-5490	186	5	⇒	⇒	NOUN
ejpam-5490	186	6	(	(	PUNCT
ejpam-5490	186	7	1	1	NUM
ejpam-5490	186	8	):	):	PUNCT
ejpam-5490	186	9	suppose	suppose	VERB
ejpam-5490	186	10	that	that	SCONJ
ejpam-5490	186	11	every	every	DET
ejpam-5490	186	12	principal	principal	ADJ
ejpam-5490	186	13	ideal	ideal	NOUN
ejpam-5490	186	14	is	be	AUX
ejpam-5490	186	15	quasi	quasi	ADJ
ejpam-5490	186	16	-	-	VERB
ejpam-5490	186	17	complemented	complemented	ADJ
ejpam-5490	186	18	.	.	PUNCT
ejpam-5490	187	1	assume	assume	VERB
ejpam-5490	187	2	v	v	ADP
ejpam-5490	187	3	∈	∈	NOUN
ejpam-5490	187	4	a.	a.	NOUN
ejpam-5490	187	5	then	then	ADV
ejpam-5490	187	6	,	,	PUNCT
ejpam-5490	187	7	(	(	PUNCT
ejpam-5490	187	8	v]∩	v]∩	NUM
ejpam-5490	187	9	(	(	PUNCT
ejpam-5490	187	10	w	w	NOUN
ejpam-5490	187	11	]	]	X
ejpam-5490	187	12	=	=	PUNCT
ejpam-5490	187	13	{	{	PUNCT
ejpam-5490	187	14	0	0	NUM
ejpam-5490	187	15	}	}	PUNCT
ejpam-5490	187	16	and	and	CCONJ
ejpam-5490	187	17	(	(	PUNCT
ejpam-5490	187	18	v]∨∗	v]∨∗	X
ejpam-5490	187	19	(	(	PUNCT
ejpam-5490	187	20	w	w	NOUN
ejpam-5490	187	21	]	]	X
ejpam-5490	187	22	exist	exist	VERB
ejpam-5490	187	23	for	for	ADP
ejpam-5490	187	24	some	some	DET
ejpam-5490	187	25	w	w	PROPN
ejpam-5490	187	26	∈	∈	PROPN
ejpam-5490	187	27	a	a	PRON
ejpam-5490	187	28	is	be	AUX
ejpam-5490	187	29	the	the	DET
ejpam-5490	187	30	principal	principal	ADJ
ejpam-5490	187	31	ideals	ideal	NOUN
ejpam-5490	187	32	produced	produce	VERB
ejpam-5490	187	33	by	by	ADP
ejpam-5490	187	34	v	v	NUM
ejpam-5490	187	35	∨∗	∨∗	NOUN
ejpam-5490	187	36	w	w	ADP
ejpam-5490	187	37	dense	dense	ADJ
ejpam-5490	187	38	elements	element	NOUN
ejpam-5490	187	39	.	.	PUNCT
ejpam-5490	188	1	as	as	ADP
ejpam-5490	188	2	a	a	DET
ejpam-5490	188	3	result	result	NOUN
ejpam-5490	188	4	,	,	PUNCT
ejpam-5490	188	5	both	both	PRON
ejpam-5490	188	6	v	v	ADP
ejpam-5490	188	7	∨∗	∨∗	NOUN
ejpam-5490	188	8	w	w	NOUN
ejpam-5490	188	9	is	be	AUX
ejpam-5490	188	10	dense	dense	ADJ
ejpam-5490	188	11	,	,	PUNCT
ejpam-5490	188	12	and	and	CCONJ
ejpam-5490	188	13	v	v	ADP
ejpam-5490	188	14	∧∗	∧∗	ADJ
ejpam-5490	188	15	w	w	PROPN
ejpam-5490	188	16	=	=	NOUN
ejpam-5490	188	17	0	0	NUM
ejpam-5490	188	18	.	.	PUNCT
ejpam-5490	189	1	thus	thus	ADV
ejpam-5490	189	2	a	a	PRON
ejpam-5490	189	3	is	be	AUX
ejpam-5490	189	4	quasi	quasi	ADJ
ejpam-5490	189	5	-	-	VERB
ejpam-5490	189	6	complemented	complemented	ADJ
ejpam-5490	189	7	.	.	PUNCT
ejpam-5490	190	1	4	4	X
ejpam-5490	190	2	.	.	NUM
ejpam-5490	190	3	generalized	generalize	VERB
ejpam-5490	190	4	complemented	complement	VERB
ejpam-5490	190	5	distributive	distributive	ADJ
ejpam-5490	190	6	lattice	lattice	NOUN
ejpam-5490	190	7	this	this	DET
ejpam-5490	190	8	section	section	NOUN
ejpam-5490	190	9	obtains	obtain	VERB
ejpam-5490	190	10	numerous	numerous	ADJ
ejpam-5490	190	11	algebraic	algebraic	ADJ
ejpam-5490	190	12	characteristics	characteristic	NOUN
ejpam-5490	190	13	and	and	CCONJ
ejpam-5490	190	14	introduces	introduce	VERB
ejpam-5490	190	15	a	a	DET
ejpam-5490	190	16	generalized	generalized	ADJ
ejpam-5490	190	17	complementation	complementation	NOUN
ejpam-5490	190	18	on	on	ADP
ejpam-5490	190	19	a	a	DET
ejpam-5490	190	20	distributive	distributive	ADJ
ejpam-5490	190	21	lattice	lattice	NOUN
ejpam-5490	190	22	.	.	PUNCT
ejpam-5490	191	1	for	for	ADP
ejpam-5490	191	2	a	a	DET
ejpam-5490	191	3	distributive	distributive	ADJ
ejpam-5490	191	4	lattice	lattice	NOUN
ejpam-5490	191	5	to	to	PART
ejpam-5490	191	6	become	become	VERB
ejpam-5490	191	7	a	a	DET
ejpam-5490	191	8	gcomplemented	gcomplemente	VERB
ejpam-5490	191	9	one	one	NUM
ejpam-5490	191	10	,	,	PUNCT
ejpam-5490	191	11	we	we	PRON
ejpam-5490	191	12	give	give	VERB
ejpam-5490	191	13	both	both	DET
ejpam-5490	191	14	required	require	VERB
ejpam-5490	191	15	and	and	CCONJ
ejpam-5490	191	16	sufficient	sufficient	ADJ
ejpam-5490	191	17	necessities	necessity	NOUN
ejpam-5490	191	18	.	.	PUNCT
ejpam-5490	192	1	furthermore	furthermore	ADV
ejpam-5490	192	2	,	,	PUNCT
ejpam-5490	192	3	we	we	PRON
ejpam-5490	192	4	derive	derive	VERB
ejpam-5490	192	5	sufficient	sufficient	ADJ
ejpam-5490	192	6	and	and	CCONJ
ejpam-5490	192	7	necessary	necessary	ADJ
ejpam-5490	192	8	conditions	condition	NOUN
ejpam-5490	192	9	under	under	ADP
ejpam-5490	192	10	which	which	PRON
ejpam-5490	192	11	a	a	DET
ejpam-5490	192	12	quasi	quasi	ADJ
ejpam-5490	192	13	-	-	ADJ
ejpam-5490	192	14	complemented	complemented	ADJ
ejpam-5490	192	15	distributive	distributive	ADJ
ejpam-5490	192	16	lattice	lattice	NOUN
ejpam-5490	192	17	can	can	AUX
ejpam-5490	192	18	be	be	AUX
ejpam-5490	192	19	formed	form	VERB
ejpam-5490	192	20	from	from	ADP
ejpam-5490	192	21	a	a	DET
ejpam-5490	192	22	generalized	generalize	VERB
ejpam-5490	192	23	complemented	complement	VERB
ejpam-5490	192	24	distributive	distributive	ADJ
ejpam-5490	192	25	lattice	lattice	NOUN
ejpam-5490	192	26	.	.	PUNCT
ejpam-5490	193	1	definition	definition	NOUN
ejpam-5490	193	2	6	6	NUM
ejpam-5490	193	3	.	.	PUNCT
ejpam-5490	194	1	if	if	SCONJ
ejpam-5490	194	2	a	a	DET
ejpam-5490	194	3	unary	unary	ADJ
ejpam-5490	194	4	operation	operation	NOUN
ejpam-5490	194	5	g	g	NOUN
ejpam-5490	194	6	on	on	ADP
ejpam-5490	194	7	a	a	DET
ejpam-5490	194	8	meets	meet	NOUN
ejpam-5490	194	9	these	these	DET
ejpam-5490	194	10	requirements	requirement	NOUN
ejpam-5490	194	11	,	,	PUNCT
ejpam-5490	194	12	it	it	PRON
ejpam-5490	194	13	is	be	AUX
ejpam-5490	194	14	called	call	VERB
ejpam-5490	194	15	a	a	DET
ejpam-5490	194	16	generalized	generalized	ADJ
ejpam-5490	194	17	complementation	complementation	NOUN
ejpam-5490	194	18	.	.	PUNCT
ejpam-5490	195	1	(	(	PUNCT
ejpam-5490	195	2	i	i	NOUN
ejpam-5490	195	3	)	)	PUNCT
ejpam-5490	195	4	for	for	ADP
ejpam-5490	195	5	any	any	DET
ejpam-5490	195	6	v	v	NOUN
ejpam-5490	195	7	∈	∈	PROPN
ejpam-5490	195	8	a	a	PRON
ejpam-5490	195	9	,	,	PUNCT
ejpam-5490	195	10	v	v	ADP
ejpam-5490	195	11	∨∗	∨∗	NOUN
ejpam-5490	195	12	v	v	NOUN
ejpam-5490	195	13	g	g	NOUN
ejpam-5490	195	14	∈	∈	PROPN
ejpam-5490	195	15	d	d	PROPN
ejpam-5490	195	16	(	(	PUNCT
ejpam-5490	195	17	ii	ii	NOUN
ejpam-5490	195	18	)	)	PUNCT
ejpam-5490	195	19	for	for	ADP
ejpam-5490	195	20	any	any	DET
ejpam-5490	195	21	w	w	PROPN
ejpam-5490	195	22	∈	∈	PROPN
ejpam-5490	195	23	a	a	DET
ejpam-5490	195	24	,	,	PUNCT
ejpam-5490	195	25	v	v	NOUN
ejpam-5490	195	26	∨∗	∨∗	NOUN
ejpam-5490	195	27	w	w	PROPN
ejpam-5490	195	28	∈	∈	PROPN
ejpam-5490	195	29	d	d	X
ejpam-5490	195	30	⇔	⇔	X
ejpam-5490	195	31	vg	vg	ADP
ejpam-5490	195	32	≤	≤	ADJ
ejpam-5490	195	33	w.	w.	NOUN
ejpam-5490	195	34	in	in	ADP
ejpam-5490	195	35	this	this	DET
ejpam-5490	195	36	case	case	NOUN
ejpam-5490	195	37	,	,	PUNCT
ejpam-5490	195	38	vg	vg	NOUN
ejpam-5490	195	39	is	be	AUX
ejpam-5490	195	40	called	call	VERB
ejpam-5490	195	41	a	a	DET
ejpam-5490	195	42	generalized	generalized	ADJ
ejpam-5490	195	43	complement	complement	NOUN
ejpam-5490	195	44	of	of	ADP
ejpam-5490	195	45	v	v	NOUN
ejpam-5490	195	46	and	and	CCONJ
ejpam-5490	195	47	a	a	PRON
ejpam-5490	195	48	is	be	AUX
ejpam-5490	195	49	called	call	VERB
ejpam-5490	195	50	a	a	DET
ejpam-5490	195	51	generalized	generalize	VERB
ejpam-5490	195	52	complemented	complement	VERB
ejpam-5490	195	53	distributive	distributive	ADJ
ejpam-5490	195	54	lattice	lattice	NOUN
ejpam-5490	195	55	.	.	PUNCT
ejpam-5490	195	56	example	example	NOUN
ejpam-5490	196	1	2	2	NUM
ejpam-5490	196	2	.	.	X
ejpam-5490	196	3	in	in	ADP
ejpam-5490	196	4	example	example	NOUN
ejpam-5490	196	5	1	1	NUM
ejpam-5490	196	6	,	,	PUNCT
ejpam-5490	196	7	let	let	VERB
ejpam-5490	196	8	us	we	PRON
ejpam-5490	196	9	define	define	VERB
ejpam-5490	196	10	0	0	NUM
ejpam-5490	196	11	g	g	NOUN
ejpam-5490	196	12	=	=	SYM
ejpam-5490	196	13	x	x	NOUN
ejpam-5490	196	14	,	,	PUNCT
ejpam-5490	196	15	vg	vg	NOUN
ejpam-5490	196	16	=	=	SYM
ejpam-5490	196	17	w	w	NOUN
ejpam-5490	196	18	,	,	PUNCT
ejpam-5490	196	19	wg	wg	PROPN
ejpam-5490	196	20	=	=	SYM
ejpam-5490	196	21	v	v	PROPN
ejpam-5490	196	22	,	,	PUNCT
ejpam-5490	196	23	xg	xg	PROPN
ejpam-5490	196	24	=	=	NOUN
ejpam-5490	196	25	1	1	NUM
ejpam-5490	196	26	g	g	NOUN
ejpam-5490	196	27	=	=	SYM
ejpam-5490	196	28	0	0	NUM
ejpam-5490	196	29	.	.	PUNCT
ejpam-5490	197	1	then	then	ADV
ejpam-5490	197	2	g	g	PROPN
ejpam-5490	197	3	is	be	AUX
ejpam-5490	197	4	a	a	DET
ejpam-5490	197	5	generalized	generalized	ADJ
ejpam-5490	197	6	complementation	complementation	NOUN
ejpam-5490	197	7	on	on	ADP
ejpam-5490	197	8	a.	a.	NOUN
ejpam-5490	197	9	example	example	NOUN
ejpam-5490	197	10	3	3	NUM
ejpam-5490	197	11	.	.	PUNCT
ejpam-5490	198	1	every	every	DET
ejpam-5490	198	2	complemented	complement	VERB
ejpam-5490	198	3	distributive	distributive	ADJ
ejpam-5490	198	4	lattice	lattice	NOUN
ejpam-5490	198	5	is	be	AUX
ejpam-5490	198	6	generalized	generalize	VERB
ejpam-5490	198	7	complemented	complement	VERB
ejpam-5490	198	8	.	.	PUNCT
ejpam-5490	199	1	remark	remark	NOUN
ejpam-5490	199	2	2	2	NUM
ejpam-5490	199	3	.	.	PUNCT
ejpam-5490	200	1	the	the	DET
ejpam-5490	200	2	converse	converse	NOUN
ejpam-5490	200	3	of	of	ADP
ejpam-5490	200	4	the	the	DET
ejpam-5490	200	5	above	above	ADJ
ejpam-5490	200	6	statement	statement	NOUN
ejpam-5490	200	7	need	need	AUX
ejpam-5490	200	8	not	not	PART
ejpam-5490	200	9	be	be	AUX
ejpam-5490	200	10	true	true	ADJ
ejpam-5490	200	11	.	.	PUNCT
ejpam-5490	201	1	for	for	ADP
ejpam-5490	201	2	,	,	PUNCT
ejpam-5490	201	3	in	in	ADP
ejpam-5490	201	4	example	example	NOUN
ejpam-5490	201	5	1	1	NUM
ejpam-5490	201	6	,	,	PUNCT
ejpam-5490	201	7	a	a	PRON
ejpam-5490	201	8	is	be	AUX
ejpam-5490	201	9	a	a	DET
ejpam-5490	201	10	generalized	generalize	VERB
ejpam-5490	201	11	complemented	complement	VERB
ejpam-5490	201	12	distributive	distributive	ADJ
ejpam-5490	201	13	lattice	lattice	NOUN
ejpam-5490	201	14	,	,	PUNCT
ejpam-5490	201	15	but	but	CCONJ
ejpam-5490	201	16	a	a	PRON
ejpam-5490	201	17	is	be	AUX
ejpam-5490	201	18	not	not	PART
ejpam-5490	201	19	complemented	complement	VERB
ejpam-5490	201	20	.	.	PUNCT
ejpam-5490	202	1	lemma	lemma	PROPN
ejpam-5490	202	2	8	8	NUM
ejpam-5490	202	3	.	.	PUNCT
ejpam-5490	203	1	if	if	SCONJ
ejpam-5490	203	2	g	g	PROPN
ejpam-5490	203	3	is	be	AUX
ejpam-5490	203	4	a	a	DET
ejpam-5490	203	5	generalized	generalized	ADJ
ejpam-5490	203	6	complementation	complementation	NOUN
ejpam-5490	203	7	on	on	ADP
ejpam-5490	203	8	a	a	PRON
ejpam-5490	203	9	and	and	CCONJ
ejpam-5490	203	10	v	v	NOUN
ejpam-5490	203	11	,	,	PUNCT
ejpam-5490	203	12	w	w	PROPN
ejpam-5490	203	13	∈	∈	PROPN
ejpam-5490	203	14	a	a	PRON
ejpam-5490	203	15	,	,	PUNCT
ejpam-5490	203	16	then	then	ADV
ejpam-5490	203	17	(	(	PUNCT
ejpam-5490	203	18	i	i	NOUN
ejpam-5490	203	19	)	)	PUNCT
ejpam-5490	203	20	0	0	PUNCT
ejpam-5490	203	21	g	g	NOUN
ejpam-5490	203	22	∈	∈	PROPN
ejpam-5490	203	23	d	d	X
ejpam-5490	203	24	(	(	PUNCT
ejpam-5490	203	25	ii	ii	NOUN
ejpam-5490	203	26	)	)	PUNCT
ejpam-5490	203	27	d	d	NOUN
ejpam-5490	203	28	∈	∈	PROPN
ejpam-5490	204	1	d	d	PUNCT
ejpam-5490	204	2	=	=	NOUN
ejpam-5490	204	3	⇒	⇒	NOUN
ejpam-5490	204	4	dg	dg	X
ejpam-5490	204	5	=	=	SYM
ejpam-5490	204	6	0	0	NUM
ejpam-5490	204	7	(	(	PUNCT
ejpam-5490	204	8	iii	iii	NOUN
ejpam-5490	204	9	)	)	PUNCT
ejpam-5490	204	10	v	v	NOUN
ejpam-5490	204	11	≤	≤	NUM
ejpam-5490	204	12	w	w	NOUN
ejpam-5490	204	13	=	=	NOUN
ejpam-5490	204	14	⇒	⇒	NOUN
ejpam-5490	204	15	wg	wg	VERB
ejpam-5490	204	16	≤	≤	ADJ
ejpam-5490	204	17	vg	vg	ADV
ejpam-5490	204	18	(	(	PUNCT
ejpam-5490	204	19	iv	iv	X
ejpam-5490	204	20	)	)	PUNCT
ejpam-5490	204	21	vgg	vgg	PROPN
ejpam-5490	204	22	≤	≤	NUM
ejpam-5490	204	23	v	v	ADP
ejpam-5490	204	24	j.	j.	PROPN
ejpam-5490	204	25	gunda	gunda	PROPN
ejpam-5490	204	26	et	et	PROPN
ejpam-5490	204	27	al	al	PROPN
ejpam-5490	204	28	.	.	PUNCT
ejpam-5490	204	29	/	/	SYM
ejpam-5490	204	30	eur	eur	PROPN
ejpam-5490	204	31	.	.	PUNCT
ejpam-5490	205	1	j.	j.	PROPN
ejpam-5490	205	2	pure	pure	PROPN
ejpam-5490	205	3	appl	appl	PROPN
ejpam-5490	205	4	.	.	PROPN
ejpam-5490	205	5	math	math	PROPN
ejpam-5490	205	6	,	,	PUNCT
ejpam-5490	205	7	18	18	NUM
ejpam-5490	205	8	(	(	PUNCT
ejpam-5490	205	9	1	1	NUM
ejpam-5490	205	10	)	)	PUNCT
ejpam-5490	205	11	(	(	PUNCT
ejpam-5490	205	12	2025	2025	NUM
ejpam-5490	205	13	)	)	PUNCT
ejpam-5490	205	14	,	,	PUNCT
ejpam-5490	205	15	5490	5490	NUM
ejpam-5490	205	16	8	8	NUM
ejpam-5490	205	17	of	of	ADP
ejpam-5490	205	18	11	11	NUM
ejpam-5490	205	19	(	(	PUNCT
ejpam-5490	205	20	v	v	NOUN
ejpam-5490	205	21	)	)	PUNCT
ejpam-5490	205	22	vggg	vggg	NOUN
ejpam-5490	205	23	=	=	SYM
ejpam-5490	205	24	vg	vg	NOUN
ejpam-5490	205	25	(	(	PUNCT
ejpam-5490	205	26	vi	vi	NOUN
ejpam-5490	205	27	)	)	PUNCT
ejpam-5490	205	28	0gg	0gg	NOUN
ejpam-5490	206	1	=	=	SYM
ejpam-5490	206	2	0	0	NUM
ejpam-5490	206	3	(	(	PUNCT
ejpam-5490	206	4	vii	vii	PROPN
ejpam-5490	206	5	)	)	PUNCT
ejpam-5490	206	6	v	v	ADP
ejpam-5490	206	7	∈	∈	PROPN
ejpam-5490	206	8	d	d	X
ejpam-5490	206	9	⇐	⇐	ADJ
ejpam-5490	206	10	⇒	⇒	NOUN
ejpam-5490	206	11	vg	vg	NOUN
ejpam-5490	206	12	=	=	SYM
ejpam-5490	206	13	0	0	NUM
ejpam-5490	206	14	⇐	⇐	ADJ
ejpam-5490	206	15	⇒	⇒	PROPN
ejpam-5490	206	16	vgg	vgg	PROPN
ejpam-5490	206	17	∈	∈	PROPN
ejpam-5490	206	18	d	d	PROPN
ejpam-5490	206	19	(	(	PUNCT
ejpam-5490	206	20	viii	viii	NOUN
ejpam-5490	206	21	)	)	PUNCT
ejpam-5490	206	22	vg	vg	ADP
ejpam-5490	206	23	≤	≤	NUM
ejpam-5490	206	24	0	0	NUM
ejpam-5490	206	25	g	g	NOUN
ejpam-5490	206	26	(	(	PUNCT
ejpam-5490	206	27	ix	ix	PROPN
ejpam-5490	206	28	)	)	PUNCT
ejpam-5490	206	29	vg	vg	ADP
ejpam-5490	206	30	≤	≤	NUM
ejpam-5490	206	31	wg	wg	VERB
ejpam-5490	206	32	⇐	⇐	ADJ
ejpam-5490	206	33	⇒	⇒	NOUN
ejpam-5490	206	34	wgg	wgg	VERB
ejpam-5490	206	35	≤	≤	PROPN
ejpam-5490	206	36	vgg	vgg	PROPN
ejpam-5490	206	37	(	(	PUNCT
ejpam-5490	206	38	x	x	NOUN
ejpam-5490	206	39	)	)	PUNCT
ejpam-5490	206	40	v	v	NOUN
ejpam-5490	206	41	=	=	SYM
ejpam-5490	206	42	0	0	PUNCT
ejpam-5490	207	1	=	=	NOUN
ejpam-5490	207	2	⇒	⇒	NOUN
ejpam-5490	207	3	vgg	vgg	NOUN
ejpam-5490	207	4	=	=	SYM
ejpam-5490	207	5	0	0	X
ejpam-5490	207	6	.	.	PUNCT
ejpam-5490	208	1	lemma	lemma	PROPN
ejpam-5490	208	2	9	9	NUM
ejpam-5490	208	3	.	.	PUNCT
ejpam-5490	209	1	if	if	SCONJ
ejpam-5490	209	2	g	g	PROPN
ejpam-5490	209	3	is	be	AUX
ejpam-5490	209	4	a	a	DET
ejpam-5490	209	5	generalized	generalized	ADJ
ejpam-5490	209	6	complementation	complementation	NOUN
ejpam-5490	209	7	on	on	ADP
ejpam-5490	209	8	a	a	PRON
ejpam-5490	209	9	,	,	PUNCT
ejpam-5490	209	10	then	then	ADV
ejpam-5490	209	11	the	the	DET
ejpam-5490	209	12	following	following	NOUN
ejpam-5490	209	13	are	be	AUX
ejpam-5490	209	14	equivalent	equivalent	ADJ
ejpam-5490	209	15	;	;	PUNCT
ejpam-5490	209	16	(	(	PUNCT
ejpam-5490	209	17	i	i	NOUN
ejpam-5490	209	18	)	)	PUNCT
ejpam-5490	209	19	v	v	ADP
ejpam-5490	209	20	∨∗	∨∗	NOUN
ejpam-5490	209	21	w	w	PROPN
ejpam-5490	209	22	∈	∈	PROPN
ejpam-5490	209	23	d	d	PROPN
ejpam-5490	209	24	,	,	PUNCT
ejpam-5490	209	25	for	for	ADP
ejpam-5490	209	26	all	all	DET
ejpam-5490	209	27	v	v	NOUN
ejpam-5490	209	28	,	,	PUNCT
ejpam-5490	209	29	w	w	PROPN
ejpam-5490	209	30	∈	∈	PROPN
ejpam-5490	209	31	a.	a.	NOUN
ejpam-5490	209	32	(	(	PUNCT
ejpam-5490	209	33	ii	ii	PROPN
ejpam-5490	209	34	)	)	PUNCT
ejpam-5490	209	35	vgg	vgg	NOUN
ejpam-5490	210	1	∨∗	∨∗	PROPN
ejpam-5490	210	2	w	w	PROPN
ejpam-5490	210	3	∈	∈	PROPN
ejpam-5490	210	4	d	d	PROPN
ejpam-5490	210	5	,	,	PUNCT
ejpam-5490	210	6	for	for	ADP
ejpam-5490	210	7	all	all	DET
ejpam-5490	210	8	v	v	NOUN
ejpam-5490	210	9	,	,	PUNCT
ejpam-5490	210	10	w	w	PROPN
ejpam-5490	210	11	∈	∈	PROPN
ejpam-5490	210	12	a.	a.	NOUN
ejpam-5490	210	13	(	(	PUNCT
ejpam-5490	210	14	iii	iii	NOUN
ejpam-5490	210	15	)	)	PUNCT
ejpam-5490	210	16	vgg	vgg	NOUN
ejpam-5490	210	17	∨∗	∨∗	PROPN
ejpam-5490	210	18	w	w	NOUN
ejpam-5490	210	19	gg	gg	PROPN
ejpam-5490	210	20	∈	∈	PROPN
ejpam-5490	210	21	d	d	PROPN
ejpam-5490	210	22	,	,	PUNCT
ejpam-5490	210	23	for	for	ADP
ejpam-5490	210	24	all	all	DET
ejpam-5490	210	25	v	v	NOUN
ejpam-5490	210	26	,	,	PUNCT
ejpam-5490	210	27	w	w	PROPN
ejpam-5490	210	28	∈	∈	PROPN
ejpam-5490	210	29	a.	a.	NOUN
ejpam-5490	210	30	(	(	PUNCT
ejpam-5490	210	31	iv	iv	X
ejpam-5490	210	32	)	)	PUNCT
ejpam-5490	210	33	v	v	ADP
ejpam-5490	210	34	∨∗	∨∗	PROPN
ejpam-5490	210	35	w	w	NOUN
ejpam-5490	210	36	gg	gg	NOUN
ejpam-5490	210	37	∈	∈	PROPN
ejpam-5490	210	38	d	d	PROPN
ejpam-5490	210	39	,	,	PUNCT
ejpam-5490	210	40	for	for	ADP
ejpam-5490	210	41	all	all	DET
ejpam-5490	210	42	v	v	NOUN
ejpam-5490	210	43	,	,	PUNCT
ejpam-5490	210	44	w	w	PROPN
ejpam-5490	210	45	∈	∈	PROPN
ejpam-5490	210	46	a.	a.	NOUN
ejpam-5490	210	47	proof	proof	NOUN
ejpam-5490	210	48	.	.	PUNCT
ejpam-5490	211	1	let	let	VERB
ejpam-5490	211	2	v	v	NOUN
ejpam-5490	211	3	,	,	PUNCT
ejpam-5490	211	4	w	w	PROPN
ejpam-5490	211	5	∈	∈	PROPN
ejpam-5490	211	6	a.	a.	NOUN
ejpam-5490	211	7	(	(	PUNCT
ejpam-5490	211	8	i	i	NOUN
ejpam-5490	211	9	)	)	PUNCT
ejpam-5490	212	1	=	=	NOUN
ejpam-5490	212	2	⇒	⇒	NOUN
ejpam-5490	212	3	(	(	PUNCT
ejpam-5490	212	4	ii	ii	PROPN
ejpam-5490	212	5	):	):	PUNCT
ejpam-5490	212	6	suppose	suppose	VERB
ejpam-5490	212	7	that	that	SCONJ
ejpam-5490	212	8	v	v	ADP
ejpam-5490	212	9	∨∗	∨∗	PROPN
ejpam-5490	212	10	w	w	PROPN
ejpam-5490	212	11	∈	∈	PROPN
ejpam-5490	212	12	d.	d.	PROPN
ejpam-5490	212	13	then	then	ADV
ejpam-5490	212	14	vg	vg	VERB
ejpam-5490	212	15	≤	≤	PROPN
ejpam-5490	212	16	w	w	NOUN
ejpam-5490	212	17	and	and	CCONJ
ejpam-5490	212	18	vg	vg	ADJ
ejpam-5490	212	19	∨∗w	∨∗w	PUNCT
ejpam-5490	212	20	=	=	SYM
ejpam-5490	212	21	w.	w.	PROPN
ejpam-5490	212	22	now	now	ADV
ejpam-5490	212	23	,	,	PUNCT
ejpam-5490	212	24	vgg	vgg	ADJ
ejpam-5490	212	25	∨∗w	∨∗w	PUNCT
ejpam-5490	212	26	=	=	PUNCT
ejpam-5490	212	27	vgg	vgg	ADJ
ejpam-5490	212	28	∨∗	∨∗	X
ejpam-5490	212	29	(	(	PUNCT
ejpam-5490	212	30	v	v	NOUN
ejpam-5490	212	31	g	g	NOUN
ejpam-5490	212	32	∨∗w	∨∗w	NOUN
ejpam-5490	212	33	)	)	PUNCT
ejpam-5490	212	34	=	=	SYM
ejpam-5490	212	35	(	(	PUNCT
ejpam-5490	212	36	vgg	vgg	PROPN
ejpam-5490	212	37	∨∗	∨∗	INTJ
ejpam-5490	212	38	v	v	X
ejpam-5490	212	39	g)∨∗w	g)∨∗w	NOUN
ejpam-5490	212	40	∈	∈	PROPN
ejpam-5490	212	41	d	d	NOUN
ejpam-5490	212	42	,	,	PUNCT
ejpam-5490	212	43	since	since	SCONJ
ejpam-5490	212	44	vgg	vgg	PROPN
ejpam-5490	212	45	∨∗	∨∗	PROPN
ejpam-5490	212	46	v	v	NOUN
ejpam-5490	212	47	g	g	PROPN
ejpam-5490	212	48	∈	∈	PROPN
ejpam-5490	212	49	d.	d.	PROPN
ejpam-5490	212	50	(	(	PUNCT
ejpam-5490	212	51	ii	ii	NOUN
ejpam-5490	212	52	)	)	PUNCT
ejpam-5490	212	53	=	=	NOUN
ejpam-5490	212	54	⇒	⇒	NOUN
ejpam-5490	212	55	(	(	PUNCT
ejpam-5490	212	56	iii	iii	NOUN
ejpam-5490	212	57	):	):	PUNCT
ejpam-5490	212	58	suppose	suppose	VERB
ejpam-5490	212	59	that	that	SCONJ
ejpam-5490	212	60	vgg	vgg	PROPN
ejpam-5490	212	61	∨∗	∨∗	PROPN
ejpam-5490	212	62	w	w	PROPN
ejpam-5490	212	63	∈	∈	PROPN
ejpam-5490	212	64	d.	d.	PROPN
ejpam-5490	212	65	then	then	ADV
ejpam-5490	212	66	w	w	PROPN
ejpam-5490	212	67	∨∗	∨∗	PROPN
ejpam-5490	212	68	v	v	ADP
ejpam-5490	212	69	gg	gg	PROPN
ejpam-5490	212	70	∈	∈	PROPN
ejpam-5490	212	71	d	d	NOUN
ejpam-5490	212	72	and	and	CCONJ
ejpam-5490	212	73	hence	hence	ADV
ejpam-5490	212	74	wgg	wgg	VERB
ejpam-5490	212	75	∨∗	∨∗	PRON
ejpam-5490	212	76	v	v	ADP
ejpam-5490	212	77	gg	gg	NOUN
ejpam-5490	213	1	=	=	NUM
ejpam-5490	213	2	vgg	vgg	NOUN
ejpam-5490	213	3	∨∗	∨∗	PROPN
ejpam-5490	213	4	w	w	PROPN
ejpam-5490	213	5	gg	gg	PROPN
ejpam-5490	213	6	∈	∈	PROPN
ejpam-5490	213	7	d.	d.	PROPN
ejpam-5490	213	8	(	(	PUNCT
ejpam-5490	213	9	iii	iii	NOUN
ejpam-5490	213	10	)	)	PUNCT
ejpam-5490	214	1	=	=	NOUN
ejpam-5490	214	2	⇒	⇒	NOUN
ejpam-5490	214	3	(	(	PUNCT
ejpam-5490	214	4	iv	iv	NUM
ejpam-5490	214	5	):	):	PUNCT
ejpam-5490	214	6	suppose	suppose	VERB
ejpam-5490	214	7	that	that	SCONJ
ejpam-5490	214	8	vgg	vgg	PROPN
ejpam-5490	214	9	∨∗	∨∗	PROPN
ejpam-5490	214	10	w	w	PROPN
ejpam-5490	214	11	gg	gg	PROPN
ejpam-5490	214	12	∈	∈	PROPN
ejpam-5490	214	13	d.	d.	PROPN
ejpam-5490	214	14	by	by	ADP
ejpam-5490	214	15	lemma	lemma	PROPN
ejpam-5490	214	16	8(iv	8(iv	NUM
ejpam-5490	214	17	)	)	PUNCT
ejpam-5490	214	18	,	,	PUNCT
ejpam-5490	214	19	vgg	vgg	NOUN
ejpam-5490	214	20	≤	≤	NUM
ejpam-5490	214	21	v.	v.	CCONJ
ejpam-5490	214	22	therefore	therefore	ADV
ejpam-5490	214	23	v	v	ADP
ejpam-5490	214	24	∨∗	∨∗	PROPN
ejpam-5490	214	25	w	w	PROPN
ejpam-5490	214	26	gg	gg	PROPN
ejpam-5490	214	27	∈	∈	PROPN
ejpam-5490	214	28	d.	d.	PROPN
ejpam-5490	214	29	(	(	PUNCT
ejpam-5490	214	30	iv	iv	X
ejpam-5490	214	31	)	)	PUNCT
ejpam-5490	215	1	=	=	NOUN
ejpam-5490	215	2	⇒	⇒	NOUN
ejpam-5490	215	3	(	(	PUNCT
ejpam-5490	215	4	i	i	NOUN
ejpam-5490	215	5	):	):	PUNCT
ejpam-5490	215	6	suppose	suppose	VERB
ejpam-5490	215	7	that	that	SCONJ
ejpam-5490	215	8	v∨∗w	v∨∗w	NOUN
ejpam-5490	215	9	gg	gg	PROPN
ejpam-5490	215	10	∈	∈	PROPN
ejpam-5490	215	11	d.	d.	PROPN
ejpam-5490	215	12	by	by	ADP
ejpam-5490	215	13	lemma	lemma	PROPN
ejpam-5490	215	14	8(iv	8(iv	NUM
ejpam-5490	215	15	)	)	PUNCT
ejpam-5490	215	16	,	,	PUNCT
ejpam-5490	215	17	vgg	vgg	ADJ
ejpam-5490	215	18	≤	≤	NUM
ejpam-5490	216	1	v.	v.	CCONJ
ejpam-5490	216	2	therefore	therefore	ADV
ejpam-5490	216	3	v∨∗w	v∨∗w	NOUN
ejpam-5490	216	4	∈	∈	PROPN
ejpam-5490	216	5	d.	d.	PROPN
ejpam-5490	216	6	lemma	lemma	PROPN
ejpam-5490	216	7	10	10	NUM
ejpam-5490	216	8	.	.	PUNCT
ejpam-5490	217	1	if	if	SCONJ
ejpam-5490	217	2	g	g	PROPN
ejpam-5490	217	3	is	be	AUX
ejpam-5490	217	4	a	a	DET
ejpam-5490	217	5	generalized	generalized	ADJ
ejpam-5490	217	6	complementation	complementation	NOUN
ejpam-5490	217	7	on	on	ADP
ejpam-5490	217	8	a	a	PRON
ejpam-5490	217	9	and	and	CCONJ
ejpam-5490	217	10	v	v	NOUN
ejpam-5490	217	11	,	,	PUNCT
ejpam-5490	217	12	w	w	PROPN
ejpam-5490	217	13	∈	∈	PROPN
ejpam-5490	217	14	a	a	DET
ejpam-5490	217	15	,	,	PUNCT
ejpam-5490	217	16	then	then	ADV
ejpam-5490	217	17	(	(	PUNCT
ejpam-5490	217	18	i	i	NOUN
ejpam-5490	217	19	)	)	PUNCT
ejpam-5490	217	20	(	(	PUNCT
ejpam-5490	217	21	v	v	NUM
ejpam-5490	217	22	∧∗	∧∗	ADJ
ejpam-5490	217	23	w	w	NOUN
ejpam-5490	217	24	)	)	PUNCT
ejpam-5490	217	25	g	g	NOUN
ejpam-5490	217	26	=	=	PUNCT
ejpam-5490	217	27	vg	vg	ADP
ejpam-5490	217	28	∨∗	∨∗	PROPN
ejpam-5490	217	29	w	w	PROPN
ejpam-5490	217	30	g	g	PROPN
ejpam-5490	217	31	(	(	PUNCT
ejpam-5490	217	32	ii	ii	NOUN
ejpam-5490	217	33	)	)	PUNCT
ejpam-5490	217	34	(	(	PUNCT
ejpam-5490	217	35	v	v	ADP
ejpam-5490	217	36	∨∗	∨∗	NOUN
ejpam-5490	217	37	w	w	NOUN
ejpam-5490	217	38	)	)	PUNCT
ejpam-5490	217	39	g	g	NOUN
ejpam-5490	217	40	≤	≤	NOUN
ejpam-5490	217	41	vg	vg	ADP
ejpam-5490	217	42	∧∗	∧∗	ADJ
ejpam-5490	217	43	w	w	PROPN
ejpam-5490	217	44	g	g	PROPN
ejpam-5490	217	45	(	(	PUNCT
ejpam-5490	217	46	iii	iii	NOUN
ejpam-5490	217	47	)	)	PUNCT
ejpam-5490	217	48	(	(	PUNCT
ejpam-5490	217	49	v	v	ADP
ejpam-5490	217	50	∨∗	∨∗	NOUN
ejpam-5490	217	51	w	w	NOUN
ejpam-5490	217	52	)	)	PUNCT
ejpam-5490	217	53	gg	gg	NOUN
ejpam-5490	217	54	=	=	NUM
ejpam-5490	217	55	vgg	vgg	NOUN
ejpam-5490	217	56	∨∗	∨∗	PROPN
ejpam-5490	217	57	w	w	NOUN
ejpam-5490	217	58	gg	gg	NOUN
ejpam-5490	217	59	=	=	SYM
ejpam-5490	217	60	(	(	PUNCT
ejpam-5490	217	61	vg	vg	ADP
ejpam-5490	217	62	∧∗	∧∗	PROPN
ejpam-5490	217	63	w	w	NOUN
ejpam-5490	217	64	g)g	g)g	NOUN
ejpam-5490	217	65	(	(	PUNCT
ejpam-5490	217	66	iv	iv	X
ejpam-5490	217	67	)	)	PUNCT
ejpam-5490	217	68	(	(	PUNCT
ejpam-5490	217	69	v	v	NUM
ejpam-5490	217	70	∧∗	∧∗	ADJ
ejpam-5490	217	71	w	w	NOUN
ejpam-5490	217	72	)	)	PUNCT
ejpam-5490	217	73	gg	gg	NOUN
ejpam-5490	217	74	=	=	PUNCT
ejpam-5490	217	75	(	(	PUNCT
ejpam-5490	217	76	vg	vg	ADP
ejpam-5490	217	77	∨∗	∨∗	PROPN
ejpam-5490	217	78	w	w	NOUN
ejpam-5490	217	79	g)g	g)g	NOUN
ejpam-5490	217	80	=	=	SYM
ejpam-5490	217	81	(	(	PUNCT
ejpam-5490	217	82	vgg	vgg	INTJ
ejpam-5490	217	83	∧∗	∧∗	PROPN
ejpam-5490	217	84	w	w	PROPN
ejpam-5490	217	85	gg)gg	gg)gg	PROPN
ejpam-5490	217	86	.	.	PUNCT
ejpam-5490	217	87	proof	proof	NOUN
ejpam-5490	217	88	.	.	PUNCT
ejpam-5490	218	1	(	(	PUNCT
ejpam-5490	218	2	i	i	NOUN
ejpam-5490	218	3	):	):	PUNCT
ejpam-5490	218	4	for	for	ADP
ejpam-5490	218	5	any	any	DET
ejpam-5490	218	6	v	v	NOUN
ejpam-5490	218	7	,	,	PUNCT
ejpam-5490	218	8	w	w	PROPN
ejpam-5490	218	9	∈	∈	PROPN
ejpam-5490	218	10	a	a	DET
ejpam-5490	218	11	,	,	PUNCT
ejpam-5490	218	12	v	v	NOUN
ejpam-5490	218	13	,	,	PUNCT
ejpam-5490	218	14	w	w	PROPN
ejpam-5490	218	15	≥	≥	NOUN
ejpam-5490	218	16	v	v	ADP
ejpam-5490	218	17	∧∗	∧∗	PROPN
ejpam-5490	218	18	w.	w.	PROPN
ejpam-5490	218	19	then	then	ADV
ejpam-5490	218	20	(	(	PUNCT
ejpam-5490	218	21	v	v	NUM
ejpam-5490	218	22	∧∗	∧∗	ADJ
ejpam-5490	218	23	w	w	NOUN
ejpam-5490	218	24	)	)	PUNCT
ejpam-5490	218	25	g	g	NOUN
ejpam-5490	218	26	≥	≥	NOUN
ejpam-5490	218	27	vg	vg	ADP
ejpam-5490	218	28	,	,	PUNCT
ejpam-5490	218	29	wg	wg	PROPN
ejpam-5490	218	30	.	.	PUNCT
ejpam-5490	219	1	therefore	therefore	ADV
ejpam-5490	219	2	vg	vg	ADP
ejpam-5490	219	3	∨∗	∨∗	PROPN
ejpam-5490	219	4	w	w	NOUN
ejpam-5490	219	5	g	g	NOUN
ejpam-5490	219	6	≤	≤	NUM
ejpam-5490	219	7	(	(	PUNCT
ejpam-5490	219	8	v	v	NUM
ejpam-5490	219	9	∧∗	∧∗	ADJ
ejpam-5490	219	10	w	w	PROPN
ejpam-5490	219	11	)	)	PUNCT
ejpam-5490	219	12	g.	g.	NOUN
ejpam-5490	219	13	now	now	ADV
ejpam-5490	219	14	,	,	PUNCT
ejpam-5490	219	15	(	(	PUNCT
ejpam-5490	219	16	v	v	X
ejpam-5490	219	17	∧∗	∧∗	ADJ
ejpam-5490	219	18	w	w	NOUN
ejpam-5490	219	19	)	)	PUNCT
ejpam-5490	219	20	∨∗	∨∗	NOUN
ejpam-5490	219	21	(	(	PUNCT
ejpam-5490	219	22	v	v	NOUN
ejpam-5490	219	23	g	g	NOUN
ejpam-5490	219	24	∨∗	∨∗	NOUN
ejpam-5490	219	25	w	w	NOUN
ejpam-5490	219	26	g	g	NOUN
ejpam-5490	219	27	)	)	PUNCT
ejpam-5490	219	28	=	=	PUNCT
ejpam-5490	220	1	[	[	X
ejpam-5490	220	2	v	v	NUM
ejpam-5490	220	3	∨∗	∨∗	NOUN
ejpam-5490	220	4	(	(	PUNCT
ejpam-5490	220	5	v	v	NOUN
ejpam-5490	220	6	g	g	NOUN
ejpam-5490	220	7	∨∗	∨∗	NOUN
ejpam-5490	220	8	w	w	PROPN
ejpam-5490	220	9	g	g	NOUN
ejpam-5490	220	10	)	)	PUNCT
ejpam-5490	220	11	]	]	PUNCT
ejpam-5490	221	1	∧∗	∧∗	PROPN
ejpam-5490	221	2	[	[	X
ejpam-5490	221	3	w	w	X
ejpam-5490	221	4	∨∗	∨∗	PROPN
ejpam-5490	221	5	(	(	PUNCT
ejpam-5490	221	6	v	v	NOUN
ejpam-5490	221	7	g	g	NOUN
ejpam-5490	221	8	∨∗	∨∗	NOUN
ejpam-5490	221	9	wg	wg	PROPN
ejpam-5490	221	10	)	)	PUNCT
ejpam-5490	221	11	]	]	PUNCT
ejpam-5490	222	1	=	=	PUNCT
ejpam-5490	223	1	[	[	X
ejpam-5490	223	2	(	(	PUNCT
ejpam-5490	223	3	v	v	NOUN
ejpam-5490	223	4	∨∗	∨∗	NOUN
ejpam-5490	223	5	v	v	ADP
ejpam-5490	223	6	g	g	NOUN
ejpam-5490	223	7	)	)	PUNCT
ejpam-5490	223	8	∨∗	∨∗	PRON
ejpam-5490	223	9	w	w	X
ejpam-5490	223	10	]	]	X
ejpam-5490	223	11	∧∗	∧∗	PROPN
ejpam-5490	224	1	[	[	X
ejpam-5490	224	2	v	v	NUM
ejpam-5490	224	3	g	g	NOUN
ejpam-5490	224	4	∨∗	∨∗	PROPN
ejpam-5490	224	5	(	(	PUNCT
ejpam-5490	224	6	w	w	NOUN
ejpam-5490	224	7	∨∗	∨∗	PROPN
ejpam-5490	224	8	w	w	PROPN
ejpam-5490	224	9	g	g	NOUN
ejpam-5490	224	10	)	)	PUNCT
ejpam-5490	224	11	]	]	PUNCT
ejpam-5490	225	1	∈	∈	PROPN
ejpam-5490	225	2	d	d	X
ejpam-5490	225	3	(	(	PUNCT
ejpam-5490	225	4	since	since	SCONJ
ejpam-5490	225	5	v	v	INTJ
ejpam-5490	225	6	∨∗	∨∗	NOUN
ejpam-5490	225	7	v	v	ADP
ejpam-5490	225	8	g	g	NOUN
ejpam-5490	225	9	,	,	PUNCT
ejpam-5490	225	10	w	w	PROPN
ejpam-5490	225	11	∨∗	∨∗	PROPN
ejpam-5490	225	12	w	w	NOUN
ejpam-5490	225	13	g	g	NOUN
ejpam-5490	225	14	∈	∈	PROPN
ejpam-5490	225	15	d	d	PROPN
ejpam-5490	225	16	)	)	PUNCT
ejpam-5490	225	17	.	.	PUNCT
ejpam-5490	226	1	so	so	ADV
ejpam-5490	226	2	that	that	SCONJ
ejpam-5490	226	3	(	(	PUNCT
ejpam-5490	226	4	v	v	NUM
ejpam-5490	226	5	∧∗	∧∗	ADJ
ejpam-5490	226	6	w	w	NOUN
ejpam-5490	226	7	)	)	PUNCT
ejpam-5490	226	8	g	g	NOUN
ejpam-5490	226	9	≤	≤	NOUN
ejpam-5490	226	10	vg	vg	ADP
ejpam-5490	226	11	∨∗	∨∗	PROPN
ejpam-5490	226	12	w	w	PROPN
ejpam-5490	226	13	g.	g.	PROPN
ejpam-5490	226	14	therefore	therefore	ADV
ejpam-5490	226	15	(	(	PUNCT
ejpam-5490	226	16	v	v	NUM
ejpam-5490	226	17	∧∗	∧∗	ADJ
ejpam-5490	226	18	w	w	NOUN
ejpam-5490	226	19	)	)	PUNCT
ejpam-5490	226	20	g	g	NOUN
ejpam-5490	226	21	=	=	PUNCT
ejpam-5490	226	22	vg	vg	ADP
ejpam-5490	226	23	∨∗	∨∗	PROPN
ejpam-5490	226	24	w	w	PROPN
ejpam-5490	226	25	g.	g.	PROPN
ejpam-5490	226	26	(	(	PUNCT
ejpam-5490	226	27	ii	ii	PROPN
ejpam-5490	226	28	):	):	PUNCT
ejpam-5490	226	29	we	we	PRON
ejpam-5490	226	30	have	have	VERB
ejpam-5490	226	31	v	v	NOUN
ejpam-5490	226	32	,	,	PUNCT
ejpam-5490	226	33	w	w	PROPN
ejpam-5490	226	34	≤	≤	NUM
ejpam-5490	226	35	v	v	ADP
ejpam-5490	226	36	∨∗	∨∗	PROPN
ejpam-5490	226	37	w.	w.	PROPN
ejpam-5490	226	38	then	then	ADV
ejpam-5490	226	39	(	(	PUNCT
ejpam-5490	226	40	v	v	ADP
ejpam-5490	226	41	∨∗	∨∗	NOUN
ejpam-5490	226	42	w	w	NOUN
ejpam-5490	226	43	)	)	PUNCT
ejpam-5490	226	44	g	g	NOUN
ejpam-5490	226	45	≤	≤	NOUN
ejpam-5490	226	46	vg	vg	ADP
ejpam-5490	226	47	,	,	PUNCT
ejpam-5490	226	48	wg	wg	PROPN
ejpam-5490	226	49	.	.	PUNCT
ejpam-5490	227	1	therefore	therefore	ADV
ejpam-5490	227	2	(	(	PUNCT
ejpam-5490	227	3	v	v	ADP
ejpam-5490	227	4	∨∗	∨∗	NOUN
ejpam-5490	227	5	w	w	NOUN
ejpam-5490	227	6	)	)	PUNCT
ejpam-5490	227	7	g	g	NOUN
ejpam-5490	227	8	≤	≤	NOUN
ejpam-5490	227	9	vg	vg	ADP
ejpam-5490	227	10	∧∗	∧∗	PROPN
ejpam-5490	227	11	w	w	PROPN
ejpam-5490	227	12	g.	g.	PROPN
ejpam-5490	227	13	j.	j.	PROPN
ejpam-5490	227	14	gunda	gunda	PROPN
ejpam-5490	227	15	et	et	PROPN
ejpam-5490	227	16	al	al	PROPN
ejpam-5490	227	17	.	.	PUNCT
ejpam-5490	227	18	/	/	SYM
ejpam-5490	227	19	eur	eur	PROPN
ejpam-5490	227	20	.	.	PUNCT
ejpam-5490	228	1	j.	j.	PROPN
ejpam-5490	228	2	pure	pure	PROPN
ejpam-5490	228	3	appl	appl	PROPN
ejpam-5490	228	4	.	.	PROPN
ejpam-5490	228	5	math	math	PROPN
ejpam-5490	228	6	,	,	PUNCT
ejpam-5490	228	7	18	18	NUM
ejpam-5490	228	8	(	(	PUNCT
ejpam-5490	228	9	1	1	NUM
ejpam-5490	228	10	)	)	PUNCT
ejpam-5490	228	11	(	(	PUNCT
ejpam-5490	228	12	2025	2025	NUM
ejpam-5490	228	13	)	)	PUNCT
ejpam-5490	228	14	,	,	PUNCT
ejpam-5490	228	15	5490	5490	NUM
ejpam-5490	228	16	9	9	NUM
ejpam-5490	228	17	of	of	ADP
ejpam-5490	228	18	11	11	NUM
ejpam-5490	228	19	(	(	PUNCT
ejpam-5490	228	20	iii	iii	NOUN
ejpam-5490	228	21	):	):	PUNCT
ejpam-5490	228	22	by	by	ADP
ejpam-5490	228	23	(	(	PUNCT
ejpam-5490	228	24	ii	ii	NOUN
ejpam-5490	228	25	)	)	PUNCT
ejpam-5490	228	26	,	,	PUNCT
ejpam-5490	228	27	(	(	PUNCT
ejpam-5490	228	28	vg	vg	ADP
ejpam-5490	228	29	∧∗	∧∗	ADJ
ejpam-5490	228	30	w	w	PROPN
ejpam-5490	228	31	g)g	g)g	NOUN
ejpam-5490	228	32	≤	≤	NUM
ejpam-5490	228	33	(	(	PUNCT
ejpam-5490	228	34	v	v	ADP
ejpam-5490	228	35	∨∗	∨∗	NOUN
ejpam-5490	228	36	w	w	NOUN
ejpam-5490	228	37	)	)	PUNCT
ejpam-5490	228	38	gg	gg	PROPN
ejpam-5490	228	39	.	.	PUNCT
ejpam-5490	229	1	then	then	ADV
ejpam-5490	229	2	vgg	vgg	VERB
ejpam-5490	229	3	∨∗	∨∗	PROPN
ejpam-5490	229	4	w	w	PROPN
ejpam-5490	229	5	gg	gg	PROPN
ejpam-5490	229	6	≤	≤	NUM
ejpam-5490	229	7	(	(	PUNCT
ejpam-5490	229	8	v	v	ADP
ejpam-5490	229	9	∨∗	∨∗	NOUN
ejpam-5490	229	10	w	w	NOUN
ejpam-5490	229	11	)	)	PUNCT
ejpam-5490	229	12	gg	gg	NOUN
ejpam-5490	229	13	.	.	PUNCT
ejpam-5490	230	1	on	on	ADP
ejpam-5490	230	2	the	the	DET
ejpam-5490	230	3	other	other	ADJ
ejpam-5490	230	4	hand	hand	NOUN
ejpam-5490	230	5	,	,	PUNCT
ejpam-5490	230	6	(	(	PUNCT
ejpam-5490	230	7	v	v	ADP
ejpam-5490	230	8	∨∗	∨∗	NOUN
ejpam-5490	230	9	w	w	NOUN
ejpam-5490	230	10	)	)	PUNCT
ejpam-5490	230	11	∨∗	∨∗	NOUN
ejpam-5490	230	12	(	(	PUNCT
ejpam-5490	230	13	v	v	ADP
ejpam-5490	230	14	∨∗	∨∗	NOUN
ejpam-5490	230	15	w	w	NOUN
ejpam-5490	230	16	)	)	PUNCT
ejpam-5490	230	17	g	g	PROPN
ejpam-5490	230	18	∈	∈	PROPN
ejpam-5490	230	19	d.	d.	PROPN
ejpam-5490	230	20	then	then	ADV
ejpam-5490	230	21	v	v	ADP
ejpam-5490	230	22	∨∗	∨∗	PROPN
ejpam-5490	231	1	[	[	X
ejpam-5490	231	2	w	w	X
ejpam-5490	231	3	∨∗	∨∗	PROPN
ejpam-5490	231	4	(	(	PUNCT
ejpam-5490	231	5	v	v	ADP
ejpam-5490	231	6	∨∗	∨∗	NOUN
ejpam-5490	231	7	w	w	NOUN
ejpam-5490	231	8	)	)	PUNCT
ejpam-5490	231	9	g	g	NOUN
ejpam-5490	231	10	]	]	X
ejpam-5490	231	11	∈	∈	PROPN
ejpam-5490	231	12	d.	d.	PROPN
ejpam-5490	231	13	by	by	ADP
ejpam-5490	231	14	lemma	lemma	PROPN
ejpam-5490	231	15	9	9	NUM
ejpam-5490	231	16	.	.	NUM
ejpam-5490	231	17	,	,	PUNCT
ejpam-5490	231	18	vgg	vgg	NOUN
ejpam-5490	232	1	∨∗	∨∗	X
ejpam-5490	233	1	[	[	X
ejpam-5490	233	2	w	w	X
ejpam-5490	233	3	∨∗	∨∗	PROPN
ejpam-5490	233	4	(	(	PUNCT
ejpam-5490	233	5	v	v	ADP
ejpam-5490	233	6	∨∗	∨∗	NOUN
ejpam-5490	233	7	w	w	NOUN
ejpam-5490	233	8	)	)	PUNCT
ejpam-5490	233	9	g	g	NOUN
ejpam-5490	233	10	]	]	X
ejpam-5490	233	11	∈	∈	PROPN
ejpam-5490	233	12	d	d	X
ejpam-5490	233	13	⇒	⇒	NOUN
ejpam-5490	234	1	[	[	X
ejpam-5490	234	2	vgg	vgg	NOUN
ejpam-5490	234	3	∨∗	∨∗	ADJ
ejpam-5490	234	4	w	w	X
ejpam-5490	234	5	]	]	X
ejpam-5490	234	6	∨∗	∨∗	PROPN
ejpam-5490	234	7	[	[	X
ejpam-5490	234	8	(	(	PUNCT
ejpam-5490	234	9	v	v	NUM
ejpam-5490	234	10	∨∗	∨∗	NOUN
ejpam-5490	234	11	w	w	NOUN
ejpam-5490	234	12	)	)	PUNCT
ejpam-5490	234	13	g	g	NOUN
ejpam-5490	234	14	]	]	X
ejpam-5490	234	15	∈	∈	PROPN
ejpam-5490	234	16	d	d	X
ejpam-5490	234	17	⇒	⇒	PROPN
ejpam-5490	234	18	w	w	ADP
ejpam-5490	234	19	∨∗	∨∗	ADJ
ejpam-5490	234	20	v	v	NOUN
ejpam-5490	234	21	gg	gg	NOUN
ejpam-5490	234	22	∨∗	∨∗	PROPN
ejpam-5490	234	23	(	(	PUNCT
ejpam-5490	234	24	v	v	ADP
ejpam-5490	234	25	∨∗	∨∗	NOUN
ejpam-5490	234	26	w	w	NOUN
ejpam-5490	234	27	)	)	PUNCT
ejpam-5490	234	28	g	g	NOUN
ejpam-5490	234	29	∈	∈	PROPN
ejpam-5490	234	30	d	d	PROPN
ejpam-5490	234	31	⇒	⇒	NOUN
ejpam-5490	234	32	wgg	wgg	VERB
ejpam-5490	234	33	∨∗	∨∗	INTJ
ejpam-5490	234	34	v	v	NUM
ejpam-5490	234	35	gg	gg	NOUN
ejpam-5490	234	36	∨∗	∨∗	PROPN
ejpam-5490	234	37	(	(	PUNCT
ejpam-5490	234	38	v	v	ADP
ejpam-5490	234	39	∨∗	∨∗	NOUN
ejpam-5490	234	40	w	w	NOUN
ejpam-5490	234	41	)	)	PUNCT
ejpam-5490	234	42	g	g	NOUN
ejpam-5490	234	43	∈	∈	PROPN
ejpam-5490	234	44	d	d	PROPN
ejpam-5490	234	45	⇒	⇒	NOUN
ejpam-5490	234	46	(	(	PUNCT
ejpam-5490	234	47	v	v	ADP
ejpam-5490	234	48	∨∗	∨∗	NOUN
ejpam-5490	234	49	w	w	NOUN
ejpam-5490	234	50	)	)	PUNCT
ejpam-5490	234	51	g	g	NOUN
ejpam-5490	234	52	∨∗	∨∗	PROPN
ejpam-5490	234	53	v	v	NUM
ejpam-5490	234	54	gg	gg	NOUN
ejpam-5490	234	55	∨∗	∨∗	PROPN
ejpam-5490	234	56	w	w	PROPN
ejpam-5490	234	57	gg	gg	PROPN
ejpam-5490	234	58	∈	∈	PROPN
ejpam-5490	234	59	d	d	PROPN
ejpam-5490	234	60	⇒	⇒	NOUN
ejpam-5490	234	61	(	(	PUNCT
ejpam-5490	234	62	v	v	ADP
ejpam-5490	234	63	∨∗	∨∗	NOUN
ejpam-5490	234	64	w	w	NOUN
ejpam-5490	234	65	)	)	PUNCT
ejpam-5490	234	66	gg	gg	PROPN
ejpam-5490	234	67	≤	≤	NUM
ejpam-5490	234	68	vgg	vgg	NOUN
ejpam-5490	234	69	∨∗	∨∗	PROPN
ejpam-5490	234	70	w	w	PROPN
ejpam-5490	234	71	gg	gg	PROPN
ejpam-5490	234	72	.	.	PUNCT
ejpam-5490	235	1	therefore	therefore	ADV
ejpam-5490	235	2	(	(	PUNCT
ejpam-5490	235	3	v	v	ADP
ejpam-5490	235	4	∨∗	∨∗	NOUN
ejpam-5490	235	5	w	w	NOUN
ejpam-5490	235	6	)	)	PUNCT
ejpam-5490	235	7	gg	gg	NOUN
ejpam-5490	235	8	=	=	NUM
ejpam-5490	235	9	vgg	vgg	NOUN
ejpam-5490	235	10	∨∗	∨∗	PROPN
ejpam-5490	235	11	w	w	PROPN
ejpam-5490	235	12	gg	gg	PROPN
ejpam-5490	235	13	.	.	PUNCT
ejpam-5490	236	1	(	(	PUNCT
ejpam-5490	236	2	iv	iv	X
ejpam-5490	236	3	):	):	PUNCT
ejpam-5490	236	4	(	(	PUNCT
ejpam-5490	236	5	v∧∗w	v∧∗w	NUM
ejpam-5490	236	6	)	)	PUNCT
ejpam-5490	236	7	gg	gg	NOUN
ejpam-5490	236	8	=	=	PUNCT
ejpam-5490	237	1	[	[	X
ejpam-5490	237	2	(	(	PUNCT
ejpam-5490	237	3	v∧∗w	v∧∗w	NUM
ejpam-5490	237	4	)	)	PUNCT
ejpam-5490	237	5	g]g	g]g	VERB
ejpam-5490	237	6	=	=	PUNCT
ejpam-5490	238	1	[	[	X
ejpam-5490	238	2	vg∨∗w	vg∨∗w	NOUN
ejpam-5490	238	3	g]g	g]g	VERB
ejpam-5490	238	4	=	=	PUNCT
ejpam-5490	239	1	[	[	X
ejpam-5490	239	2	vg∨∗w	vg∨∗w	NOUN
ejpam-5490	239	3	g]ggg	g]ggg	NOUN
ejpam-5490	239	4	=	=	PUNCT
ejpam-5490	240	1	[	[	X
ejpam-5490	240	2	vggg∨∗w	vggg∨∗w	NOUN
ejpam-5490	240	3	ggg]g	ggg]g	VERB
ejpam-5490	240	4	=	=	PUNCT
ejpam-5490	240	5	(	(	PUNCT
ejpam-5490	240	6	vg∨∗w	vg∨∗w	NOUN
ejpam-5490	240	7	g)g	g)g	NOUN
ejpam-5490	240	8	=	=	PUNCT
ejpam-5490	240	9	(	(	PUNCT
ejpam-5490	240	10	vgg	vgg	INTJ
ejpam-5490	240	11	∧∗	∧∗	PROPN
ejpam-5490	240	12	w	w	PROPN
ejpam-5490	240	13	gg)gg	gg)gg	PROPN
ejpam-5490	240	14	.	.	PUNCT
ejpam-5490	240	15	theorem	theorem	PROPN
ejpam-5490	240	16	14	14	NUM
ejpam-5490	240	17	.	.	PUNCT
ejpam-5490	241	1	every	every	DET
ejpam-5490	241	2	finite	finite	PROPN
ejpam-5490	241	3	distributive	distributive	ADJ
ejpam-5490	241	4	lattice	lattice	NOUN
ejpam-5490	241	5	is	be	AUX
ejpam-5490	241	6	generalized	generalize	VERB
ejpam-5490	241	7	complemented	complement	VERB
ejpam-5490	241	8	.	.	PUNCT
ejpam-5490	242	1	proof	proof	NOUN
ejpam-5490	242	2	.	.	PUNCT
ejpam-5490	243	1	let	let	VERB
ejpam-5490	243	2	a	a	PRON
ejpam-5490	243	3	be	be	AUX
ejpam-5490	243	4	a	a	DET
ejpam-5490	243	5	finite	finite	ADJ
ejpam-5490	243	6	distributive	distributive	ADJ
ejpam-5490	243	7	lattice	lattice	NOUN
ejpam-5490	243	8	and	and	CCONJ
ejpam-5490	243	9	d	d	ADP
ejpam-5490	243	10	̸=	̸=	PROPN
ejpam-5490	243	11	∅.	∅.	ADV
ejpam-5490	243	12	for	for	ADP
ejpam-5490	243	13	any	any	DET
ejpam-5490	243	14	v	v	NOUN
ejpam-5490	243	15	∈	∈	PROPN
ejpam-5490	243	16	a	a	PRON
ejpam-5490	243	17	,	,	PUNCT
ejpam-5490	243	18	define	define	VERB
ejpam-5490	243	19	vg	vg	NOUN
ejpam-5490	243	20	=	=	PUNCT
ejpam-5490	243	21	inf{w	inf{w	PROPN
ejpam-5490	243	22	∈	∈	PROPN
ejpam-5490	243	23	a	a	DET
ejpam-5490	243	24	|	|	NOUN
ejpam-5490	243	25	v	v	ADP
ejpam-5490	243	26	∨∗	∨∗	NOUN
ejpam-5490	243	27	w	w	PROPN
ejpam-5490	243	28	∈	∈	PROPN
ejpam-5490	243	29	d	d	NOUN
ejpam-5490	243	30	}	}	PUNCT
ejpam-5490	243	31	.	.	PUNCT
ejpam-5490	244	1	then	then	ADV
ejpam-5490	244	2	v	v	ADP
ejpam-5490	244	3	∨∗	∨∗	NOUN
ejpam-5490	244	4	v	v	NOUN
ejpam-5490	244	5	g	g	NOUN
ejpam-5490	244	6	=	=	SYM
ejpam-5490	244	7	v	v	ADP
ejpam-5490	244	8	∨∗	∨∗	NOUN
ejpam-5490	244	9	[	[	X
ejpam-5490	244	10	∧∗{w	∧∗{w	X
ejpam-5490	244	11	∈	∈	VERB
ejpam-5490	244	12	a	a	DET
ejpam-5490	244	13	|	|	NOUN
ejpam-5490	244	14	v	v	ADP
ejpam-5490	244	15	∨∗	∨∗	NOUN
ejpam-5490	244	16	w	w	PROPN
ejpam-5490	244	17	∈	∈	PROPN
ejpam-5490	244	18	d	d	NOUN
ejpam-5490	244	19	}	}	PUNCT
ejpam-5490	244	20	]	]	PUNCT
ejpam-5490	245	1	=	=	PUNCT
ejpam-5490	246	1	∧∗[{v	∧∗[{v	PROPN
ejpam-5490	247	1	∨∗	∨∗	INTJ
ejpam-5490	247	2	w	w	INTJ
ejpam-5490	247	3	|	|	NOUN
ejpam-5490	247	4	v	v	ADP
ejpam-5490	247	5	∨∗	∨∗	NOUN
ejpam-5490	247	6	w	w	PROPN
ejpam-5490	247	7	∈	∈	PROPN
ejpam-5490	247	8	d	d	NOUN
ejpam-5490	247	9	}	}	PUNCT
ejpam-5490	247	10	]	]	PUNCT
ejpam-5490	247	11	∈	∈	PROPN
ejpam-5490	247	12	d.	d.	PROPN
ejpam-5490	247	13	if	if	SCONJ
ejpam-5490	247	14	v	v	NUM
ejpam-5490	247	15	∨∗	∨∗	NOUN
ejpam-5490	247	16	x	x	X
ejpam-5490	247	17	∈	∈	PROPN
ejpam-5490	247	18	d	d	NOUN
ejpam-5490	247	19	,	,	PUNCT
ejpam-5490	247	20	then	then	ADV
ejpam-5490	247	21	x	x	SYM
ejpam-5490	247	22	∈	∈	PROPN
ejpam-5490	247	23	{	{	PUNCT
ejpam-5490	247	24	v	v	NOUN
ejpam-5490	247	25	∈	∈	PROPN
ejpam-5490	247	26	a	a	DET
ejpam-5490	247	27	|	|	NOUN
ejpam-5490	247	28	v	v	ADP
ejpam-5490	247	29	∨∗	∨∗	NOUN
ejpam-5490	247	30	v	v	ADP
ejpam-5490	247	31	∈	∈	NOUN
ejpam-5490	247	32	d	d	NOUN
ejpam-5490	247	33	}	}	PUNCT
ejpam-5490	247	34	.	.	PUNCT
ejpam-5490	248	1	therefore	therefore	ADV
ejpam-5490	248	2	∧∗{v	∧∗{v	PROPN
ejpam-5490	248	3	∈	∈	PROPN
ejpam-5490	248	4	a	a	DET
ejpam-5490	248	5	|	|	NOUN
ejpam-5490	248	6	v	v	ADP
ejpam-5490	248	7	∨∗	∨∗	NOUN
ejpam-5490	248	8	v	v	ADP
ejpam-5490	248	9	∈	∈	ADJ
ejpam-5490	248	10	d	d	NOUN
ejpam-5490	248	11	}	}	PUNCT
ejpam-5490	248	12	≤	≤	NUM
ejpam-5490	248	13	x	x	PUNCT
ejpam-5490	248	14	and	and	CCONJ
ejpam-5490	248	15	hence	hence	ADV
ejpam-5490	248	16	vg	vg	ADP
ejpam-5490	248	17	≤	≤	NUM
ejpam-5490	248	18	x.	x.	NOUN
ejpam-5490	248	19	on	on	ADP
ejpam-5490	248	20	other	other	ADJ
ejpam-5490	248	21	hand	hand	NOUN
ejpam-5490	248	22	,	,	PUNCT
ejpam-5490	248	23	suppose	suppose	VERB
ejpam-5490	248	24	vg	vg	ADP
ejpam-5490	248	25	≤	≤	NUM
ejpam-5490	248	26	x	x	NOUN
ejpam-5490	248	27	,	,	PUNCT
ejpam-5490	248	28	then	then	ADV
ejpam-5490	248	29	we	we	PRON
ejpam-5490	248	30	have	have	VERB
ejpam-5490	248	31	v	v	NUM
ejpam-5490	248	32	∨∗	∨∗	NOUN
ejpam-5490	248	33	v	v	NOUN
ejpam-5490	248	34	g	g	NOUN
ejpam-5490	248	35	∈	∈	PROPN
ejpam-5490	249	1	d	d	PROPN
ejpam-5490	249	2	,	,	PUNCT
ejpam-5490	249	3	v	v	ADP
ejpam-5490	249	4	∨∗	∨∗	NOUN
ejpam-5490	249	5	x	x	SYM
ejpam-5490	249	6	∈	∈	PROPN
ejpam-5490	249	7	d.	d.	NOUN
ejpam-5490	249	8	hence	hence	ADV
ejpam-5490	249	9	vg	vg	VERB
ejpam-5490	249	10	is	be	AUX
ejpam-5490	249	11	a	a	DET
ejpam-5490	249	12	generalized	generalized	ADJ
ejpam-5490	249	13	complementation	complementation	NOUN
ejpam-5490	249	14	of	of	ADP
ejpam-5490	249	15	v.	v.	ADP
ejpam-5490	249	16	thus	thus	ADV
ejpam-5490	249	17	a	a	PRON
ejpam-5490	249	18	is	be	AUX
ejpam-5490	249	19	generalized	generalize	VERB
ejpam-5490	249	20	complemented	complement	VERB
ejpam-5490	249	21	.	.	PUNCT
ejpam-5490	250	1	theorem	theorem	VERB
ejpam-5490	250	2	15	15	NUM
ejpam-5490	250	3	.	.	PUNCT
ejpam-5490	251	1	a	a	PRON
ejpam-5490	251	2	is	be	AUX
ejpam-5490	251	3	generalized	generalize	VERB
ejpam-5490	251	4	complemented	complement	VERB
ejpam-5490	251	5	if	if	SCONJ
ejpam-5490	251	6	and	and	CCONJ
ejpam-5490	251	7	only	only	ADV
ejpam-5490	251	8	if	if	SCONJ
ejpam-5490	251	9	[	[	X
ejpam-5490	251	10	0	0	NUM
ejpam-5490	251	11	,	,	PUNCT
ejpam-5490	251	12	d	d	X
ejpam-5490	251	13	]	]	X
ejpam-5490	251	14	is	be	AUX
ejpam-5490	251	15	generalized	generalize	VERB
ejpam-5490	251	16	complemented	complement	VERB
ejpam-5490	251	17	,	,	PUNCT
ejpam-5490	251	18	for	for	ADP
ejpam-5490	251	19	all	all	DET
ejpam-5490	251	20	dense	dense	ADJ
ejpam-5490	251	21	elements	element	NOUN
ejpam-5490	251	22	d	d	X
ejpam-5490	251	23	∈	∈	NOUN
ejpam-5490	251	24	a.	a.	NOUN
ejpam-5490	251	25	proof	proof	NOUN
ejpam-5490	251	26	.	.	PUNCT
ejpam-5490	252	1	suppose	suppose	VERB
ejpam-5490	252	2	that	that	SCONJ
ejpam-5490	252	3	a	a	PRON
ejpam-5490	252	4	is	be	AUX
ejpam-5490	252	5	a	a	DET
ejpam-5490	252	6	generalized	generalize	VERB
ejpam-5490	252	7	complemented	complement	VERB
ejpam-5490	252	8	and	and	CCONJ
ejpam-5490	252	9	g	g	NOUN
ejpam-5490	252	10	is	be	AUX
ejpam-5490	252	11	a	a	DET
ejpam-5490	252	12	generalized	generalized	ADJ
ejpam-5490	252	13	complementation	complementation	NOUN
ejpam-5490	252	14	on	on	ADP
ejpam-5490	252	15	a.	a.	NOUN
ejpam-5490	252	16	let	let	VERB
ejpam-5490	252	17	v	v	X
ejpam-5490	252	18	∈	∈	PROPN
ejpam-5490	253	1	[	[	X
ejpam-5490	253	2	0	0	NUM
ejpam-5490	253	3	,	,	PUNCT
ejpam-5490	253	4	d	d	NOUN
ejpam-5490	253	5	]	]	X
ejpam-5490	253	6	.	.	PUNCT
ejpam-5490	254	1	then	then	ADV
ejpam-5490	254	2	there	there	PRON
ejpam-5490	254	3	exists	exist	VERB
ejpam-5490	254	4	vg	vg	ADP
ejpam-5490	254	5	∈	∈	PROPN
ejpam-5490	254	6	a	a	DET
ejpam-5490	254	7	such	such	ADJ
ejpam-5490	254	8	that	that	DET
ejpam-5490	254	9	v	v	NOUN
ejpam-5490	254	10	∨∗	∨∗	NOUN
ejpam-5490	254	11	v	v	NOUN
ejpam-5490	254	12	g	g	NOUN
ejpam-5490	254	13	∈	∈	PROPN
ejpam-5490	254	14	d	d	NOUN
ejpam-5490	254	15	and	and	CCONJ
ejpam-5490	254	16	for	for	ADP
ejpam-5490	254	17	any	any	DET
ejpam-5490	254	18	w	w	PROPN
ejpam-5490	254	19	∈	∈	PROPN
ejpam-5490	254	20	a	a	PRON
ejpam-5490	254	21	,	,	PUNCT
ejpam-5490	254	22	v	v	NOUN
ejpam-5490	254	23	∨∗	∨∗	NOUN
ejpam-5490	254	24	w	w	PROPN
ejpam-5490	254	25	∈	∈	PROPN
ejpam-5490	255	1	d	d	NOUN
ejpam-5490	255	2	if	if	SCONJ
ejpam-5490	255	3	and	and	CCONJ
ejpam-5490	255	4	only	only	ADV
ejpam-5490	255	5	if	if	SCONJ
ejpam-5490	255	6	vg	vg	ADP
ejpam-5490	255	7	≤	≤	NOUN
ejpam-5490	255	8	w.	w.	NOUN
ejpam-5490	255	9	since	since	SCONJ
ejpam-5490	255	10	v	v	NUM
ejpam-5490	255	11	∨∗	∨∗	NOUN
ejpam-5490	255	12	d	d	X
ejpam-5490	255	13	∈	∈	PROPN
ejpam-5490	255	14	d	d	NOUN
ejpam-5490	255	15	,	,	PUNCT
ejpam-5490	255	16	vg	vg	ADP
ejpam-5490	255	17	≤	≤	PROPN
ejpam-5490	255	18	d.	d.	NOUN
ejpam-5490	255	19	therefore	therefore	ADV
ejpam-5490	255	20	vg	vg	ADP
ejpam-5490	255	21	∈	∈	PROPN
ejpam-5490	256	1	[	[	X
ejpam-5490	256	2	0	0	NUM
ejpam-5490	256	3	,	,	PUNCT
ejpam-5490	256	4	d	d	NOUN
ejpam-5490	256	5	]	]	X
ejpam-5490	256	6	.	.	PUNCT
ejpam-5490	257	1	hence	hence	ADV
ejpam-5490	257	2	[	[	X
ejpam-5490	257	3	0	0	NUM
ejpam-5490	257	4	,	,	PUNCT
ejpam-5490	257	5	d	d	X
ejpam-5490	257	6	]	]	X
ejpam-5490	257	7	is	be	AUX
ejpam-5490	257	8	generalized	generalize	VERB
ejpam-5490	257	9	complemented	complement	VERB
ejpam-5490	257	10	.	.	PUNCT
ejpam-5490	258	1	conversely	conversely	ADV
ejpam-5490	258	2	suppose	suppose	VERB
ejpam-5490	258	3	that	that	SCONJ
ejpam-5490	258	4	[	[	X
ejpam-5490	258	5	0	0	NUM
ejpam-5490	258	6	,	,	PUNCT
ejpam-5490	258	7	d	d	X
ejpam-5490	258	8	]	]	X
ejpam-5490	258	9	is	be	AUX
ejpam-5490	258	10	a	a	DET
ejpam-5490	258	11	generalized	generalize	VERB
ejpam-5490	258	12	complemented	complement	VERB
ejpam-5490	258	13	distributive	distributive	ADJ
ejpam-5490	258	14	lattice	lattice	NOUN
ejpam-5490	258	15	with	with	ADP
ejpam-5490	258	16	dense	dense	ADJ
ejpam-5490	258	17	element	element	NOUN
ejpam-5490	258	18	d.	d.	NOUN
ejpam-5490	258	19	let	let	VERB
ejpam-5490	258	20	v	v	NUM
ejpam-5490	258	21	∈	∈	PROPN
ejpam-5490	258	22	a.	a.	NOUN
ejpam-5490	258	23	then	then	ADV
ejpam-5490	258	24	v	v	ADP
ejpam-5490	258	25	∨∗	∨∗	PROPN
ejpam-5490	258	26	d	d	NOUN
ejpam-5490	258	27	is	be	AUX
ejpam-5490	258	28	dense	dense	ADJ
ejpam-5490	258	29	in	in	ADP
ejpam-5490	258	30	a.	a.	NOUN
ejpam-5490	258	31	therefore	therefore	ADV
ejpam-5490	258	32	v	v	ADP
ejpam-5490	258	33	∈	∈	PROPN
ejpam-5490	259	1	[	[	X
ejpam-5490	259	2	0	0	NUM
ejpam-5490	259	3	,	,	PUNCT
ejpam-5490	259	4	v	v	ADP
ejpam-5490	259	5	∨∗	∨∗	NOUN
ejpam-5490	259	6	d	d	X
ejpam-5490	259	7	]	]	X
ejpam-5490	259	8	.	.	PUNCT
ejpam-5490	260	1	hence	hence	ADV
ejpam-5490	260	2	there	there	PRON
ejpam-5490	260	3	exists	exist	VERB
ejpam-5490	260	4	vg	vg	ADV
ejpam-5490	260	5	in	in	ADP
ejpam-5490	260	6	[	[	X
ejpam-5490	260	7	0	0	NUM
ejpam-5490	260	8	,	,	PUNCT
ejpam-5490	260	9	v	v	ADP
ejpam-5490	260	10	∨∗	∨∗	NOUN
ejpam-5490	260	11	d	d	X
ejpam-5490	260	12	]	]	X
ejpam-5490	260	13	such	such	ADJ
ejpam-5490	260	14	that	that	PRON
ejpam-5490	260	15	v	v	NOUN
ejpam-5490	260	16	∨∗	∨∗	NOUN
ejpam-5490	260	17	v	v	NOUN
ejpam-5490	260	18	g	g	PROPN
ejpam-5490	260	19	is	be	AUX
ejpam-5490	260	20	dense	dense	ADJ
ejpam-5490	260	21	in	in	ADP
ejpam-5490	260	22	[	[	X
ejpam-5490	260	23	0	0	NUM
ejpam-5490	260	24	,	,	PUNCT
ejpam-5490	260	25	v	v	ADP
ejpam-5490	260	26	∨∗	∨∗	NOUN
ejpam-5490	260	27	d	d	X
ejpam-5490	260	28	]	]	X
ejpam-5490	260	29	.	.	PUNCT
ejpam-5490	261	1	let	let	VERB
ejpam-5490	261	2	w	w	NOUN
ejpam-5490	261	3	∈	∈	PROPN
ejpam-5490	261	4	a	a	PRON
ejpam-5490	261	5	,	,	PUNCT
ejpam-5490	261	6	such	such	ADJ
ejpam-5490	261	7	that	that	PRON
ejpam-5490	261	8	v	v	NOUN
ejpam-5490	261	9	∨∗	∨∗	PROPN
ejpam-5490	261	10	w	w	NOUN
ejpam-5490	261	11	is	be	AUX
ejpam-5490	261	12	dense	dense	ADJ
ejpam-5490	261	13	in	in	ADP
ejpam-5490	261	14	a.	a.	NOUN
ejpam-5490	261	15	then	then	ADV
ejpam-5490	261	16	(	(	PUNCT
ejpam-5490	261	17	v	v	X
ejpam-5490	261	18	∨∗	∨∗	NOUN
ejpam-5490	261	19	w)∧∗	w)∧∗	PROPN
ejpam-5490	261	20	d	d	NOUN
ejpam-5490	261	21	is	be	AUX
ejpam-5490	261	22	dense	dense	ADJ
ejpam-5490	261	23	in	in	ADP
ejpam-5490	261	24	[	[	X
ejpam-5490	261	25	0	0	NUM
ejpam-5490	261	26	,	,	PUNCT
ejpam-5490	261	27	v	v	ADP
ejpam-5490	261	28	∨∗	∨∗	NOUN
ejpam-5490	261	29	d	d	X
ejpam-5490	261	30	]	]	X
ejpam-5490	261	31	.	.	PUNCT
ejpam-5490	262	1	therefore	therefore	ADV
ejpam-5490	262	2	(	(	PUNCT
ejpam-5490	262	3	v	v	NUM
ejpam-5490	262	4	∧∗	∧∗	ADJ
ejpam-5490	262	5	d)∨∗	d)∨∗	NOUN
ejpam-5490	262	6	(	(	PUNCT
ejpam-5490	262	7	w	w	NOUN
ejpam-5490	262	8	∧∗	∧∗	ADJ
ejpam-5490	262	9	d	d	X
ejpam-5490	262	10	)	)	PUNCT
ejpam-5490	262	11	is	be	AUX
ejpam-5490	262	12	dense	dense	ADJ
ejpam-5490	262	13	in	in	ADP
ejpam-5490	262	14	[	[	X
ejpam-5490	262	15	0	0	NUM
ejpam-5490	262	16	,	,	PUNCT
ejpam-5490	262	17	v	v	ADP
ejpam-5490	262	18	∨∗	∨∗	NOUN
ejpam-5490	262	19	d	d	X
ejpam-5490	262	20	]	]	X
ejpam-5490	262	21	.	.	PUNCT
ejpam-5490	263	1	so	so	ADV
ejpam-5490	263	2	that	that	SCONJ
ejpam-5490	263	3	(	(	PUNCT
ejpam-5490	263	4	v	v	NUM
ejpam-5490	263	5	∧∗	∧∗	ADJ
ejpam-5490	263	6	d	d	NOUN
ejpam-5490	263	7	)	)	PUNCT
ejpam-5490	263	8	g	g	PROPN
ejpam-5490	263	9	≤	≤	NUM
ejpam-5490	263	10	w	w	ADP
ejpam-5490	263	11	∧∗	∧∗	PROPN
ejpam-5490	263	12	d	d	X
ejpam-5490	263	13	≤	≤	PROPN
ejpam-5490	263	14	w.	w.	NOUN
ejpam-5490	263	15	also	also	ADV
ejpam-5490	263	16	that	that	PRON
ejpam-5490	263	17	vg	vg	VERB
ejpam-5490	263	18	≤	≤	NOUN
ejpam-5490	263	19	vg	vg	ADP
ejpam-5490	263	20	∨∗	∨∗	PROPN
ejpam-5490	263	21	d	d	X
ejpam-5490	263	22	g	g	PROPN
ejpam-5490	263	23	≤	≤	PUNCT
ejpam-5490	263	24	w.	w.	NOUN
ejpam-5490	263	25	if	if	SCONJ
ejpam-5490	263	26	vg	vg	ADP
ejpam-5490	263	27	≤	≤	PROPN
ejpam-5490	263	28	w	w	NOUN
ejpam-5490	263	29	,	,	PUNCT
ejpam-5490	263	30	then	then	ADV
ejpam-5490	263	31	v	v	ADP
ejpam-5490	263	32	∨∗	∨∗	NOUN
ejpam-5490	263	33	v	v	NOUN
ejpam-5490	263	34	g	g	PROPN
ejpam-5490	263	35	∈	∈	PROPN
ejpam-5490	263	36	d.	d.	PROPN
ejpam-5490	263	37	therefore	therefore	ADV
ejpam-5490	263	38	v	v	ADP
ejpam-5490	263	39	∨∗	∨∗	PROPN
ejpam-5490	263	40	w	w	PROPN
ejpam-5490	263	41	∈	∈	PROPN
ejpam-5490	263	42	d.	d.	PROPN
ejpam-5490	263	43	hence	hence	ADV
ejpam-5490	263	44	a	a	DET
ejpam-5490	263	45	is	be	AUX
ejpam-5490	263	46	generalized	generalize	VERB
ejpam-5490	263	47	complemented	complement	VERB
ejpam-5490	263	48	distributive	distributive	ADJ
ejpam-5490	263	49	lattice	lattice	NOUN
ejpam-5490	263	50	with	with	ADP
ejpam-5490	263	51	the	the	DET
ejpam-5490	263	52	generalized	generalize	VERB
ejpam-5490	263	53	complementation	complementation	NOUN
ejpam-5490	263	54	g.	g.	NOUN
ejpam-5490	263	55	theorem	theorem	VERB
ejpam-5490	263	56	16	16	NUM
ejpam-5490	263	57	.	.	PUNCT
ejpam-5490	264	1	a	a	PRON
ejpam-5490	264	2	is	be	AUX
ejpam-5490	264	3	generalized	generalize	VERB
ejpam-5490	264	4	complemented	complement	VERB
ejpam-5490	264	5	if	if	SCONJ
ejpam-5490	264	6	and	and	CCONJ
ejpam-5490	264	7	only	only	ADV
ejpam-5490	264	8	if	if	SCONJ
ejpam-5490	264	9	pi(a	pi(a	NOUN
ejpam-5490	264	10	)	)	PUNCT
ejpam-5490	264	11	is	be	AUX
ejpam-5490	264	12	generalized	generalize	VERB
ejpam-5490	264	13	complemented	complement	VERB
ejpam-5490	264	14	.	.	PUNCT
ejpam-5490	265	1	proof	proof	NOUN
ejpam-5490	265	2	.	.	PUNCT
ejpam-5490	266	1	suppose	suppose	VERB
ejpam-5490	266	2	that	that	SCONJ
ejpam-5490	266	3	a	a	PRON
ejpam-5490	266	4	is	be	AUX
ejpam-5490	266	5	a	a	DET
ejpam-5490	266	6	generalized	generalize	VERB
ejpam-5490	266	7	complemented	complement	VERB
ejpam-5490	266	8	distributive	distributive	ADJ
ejpam-5490	266	9	lattice	lattice	NOUN
ejpam-5490	266	10	and	and	CCONJ
ejpam-5490	266	11	g	g	NOUN
ejpam-5490	266	12	is	be	AUX
ejpam-5490	266	13	the	the	DET
ejpam-5490	266	14	generalized	generalized	ADJ
ejpam-5490	266	15	complementation	complementation	NOUN
ejpam-5490	266	16	on	on	ADP
ejpam-5490	266	17	a.	a.	NOUN
ejpam-5490	266	18	let	let	NOUN
ejpam-5490	266	19	(	(	PUNCT
ejpam-5490	266	20	v	v	NOUN
ejpam-5490	266	21	]	]	X
ejpam-5490	266	22	∈	∈	PROPN
ejpam-5490	266	23	pi(a	pi(a	NOUN
ejpam-5490	266	24	)	)	PUNCT
ejpam-5490	266	25	,	,	PUNCT
ejpam-5490	266	26	for	for	ADP
ejpam-5490	266	27	some	some	DET
ejpam-5490	266	28	v	v	NOUN
ejpam-5490	266	29	∈	∈	NOUN
ejpam-5490	266	30	a.	a.	NOUN
ejpam-5490	266	31	then	then	ADV
ejpam-5490	266	32	there	there	PRON
ejpam-5490	266	33	exists	exist	VERB
ejpam-5490	266	34	vg	vg	ADP
ejpam-5490	266	35	∈	∈	PROPN
ejpam-5490	266	36	a	a	DET
ejpam-5490	266	37	such	such	ADJ
ejpam-5490	266	38	that	that	DET
ejpam-5490	266	39	v∨∗	v∨∗	NOUN
ejpam-5490	266	40	v	v	ADP
ejpam-5490	266	41	g	g	NOUN
ejpam-5490	266	42	∈	∈	PROPN
ejpam-5490	266	43	d	d	NOUN
ejpam-5490	266	44	and	and	CCONJ
ejpam-5490	266	45	,	,	PUNCT
ejpam-5490	266	46	v∨∗w	v∨∗w	NOUN
ejpam-5490	266	47	∈	∈	PROPN
ejpam-5490	267	1	d	d	NOUN
ejpam-5490	267	2	if	if	SCONJ
ejpam-5490	267	3	and	and	CCONJ
ejpam-5490	267	4	only	only	ADV
ejpam-5490	267	5	if	if	SCONJ
ejpam-5490	267	6	vg	vg	ADP
ejpam-5490	267	7	≤	≤	NOUN
ejpam-5490	267	8	w	w	NOUN
ejpam-5490	267	9	,	,	PUNCT
ejpam-5490	267	10	for	for	ADP
ejpam-5490	267	11	any	any	DET
ejpam-5490	267	12	w	w	PROPN
ejpam-5490	267	13	∈	∈	PROPN
ejpam-5490	267	14	a.	a.	NOUN
ejpam-5490	267	15	define	define	NOUN
ejpam-5490	267	16	j.	j.	PROPN
ejpam-5490	267	17	gunda	gunda	PROPN
ejpam-5490	267	18	et	et	PROPN
ejpam-5490	267	19	al	al	PROPN
ejpam-5490	267	20	.	.	PUNCT
ejpam-5490	267	21	/	/	SYM
ejpam-5490	267	22	eur	eur	PROPN
ejpam-5490	267	23	.	.	PUNCT
ejpam-5490	268	1	j.	j.	PROPN
ejpam-5490	268	2	pure	pure	PROPN
ejpam-5490	268	3	appl	appl	PROPN
ejpam-5490	268	4	.	.	PROPN
ejpam-5490	268	5	math	math	PROPN
ejpam-5490	268	6	,	,	PUNCT
ejpam-5490	268	7	18	18	NUM
ejpam-5490	268	8	(	(	PUNCT
ejpam-5490	268	9	1	1	NUM
ejpam-5490	268	10	)	)	PUNCT
ejpam-5490	268	11	(	(	PUNCT
ejpam-5490	268	12	2025	2025	NUM
ejpam-5490	268	13	)	)	PUNCT
ejpam-5490	268	14	,	,	PUNCT
ejpam-5490	268	15	5490	5490	NUM
ejpam-5490	268	16	10	10	NUM
ejpam-5490	268	17	of	of	ADP
ejpam-5490	268	18	11	11	NUM
ejpam-5490	268	19	(	(	PUNCT
ejpam-5490	268	20	v]g	v]g	NOUN
ejpam-5490	268	21	=	=	SYM
ejpam-5490	268	22	(	(	PUNCT
ejpam-5490	268	23	vg	vg	ADP
ejpam-5490	268	24	]	]	PUNCT
ejpam-5490	268	25	.	.	PUNCT
ejpam-5490	269	1	for	for	ADP
ejpam-5490	269	2	(	(	PUNCT
ejpam-5490	269	3	t	t	PROPN
ejpam-5490	269	4	]	]	PUNCT
ejpam-5490	269	5	∈	∈	PROPN
ejpam-5490	269	6	pi(a	pi(a	PROPN
ejpam-5490	269	7	)	)	PUNCT
ejpam-5490	269	8	,	,	PUNCT
ejpam-5490	269	9	(	(	PUNCT
ejpam-5490	269	10	t	t	X
ejpam-5490	269	11	]	]	X
ejpam-5490	269	12	∈	∈	PROPN
ejpam-5490	270	1	[	[	X
ejpam-5490	270	2	(	(	PUNCT
ejpam-5490	270	3	v	v	NOUN
ejpam-5490	270	4	]	]	X
ejpam-5490	270	5	∨∗	∨∗	PROPN
ejpam-5490	270	6	(	(	PUNCT
ejpam-5490	270	7	v	v	NOUN
ejpam-5490	270	8	]	]	X
ejpam-5490	270	9	g]∗	g]∗	PROPN
ejpam-5490	270	10	=	=	NOUN
ejpam-5490	270	11	⇒	⇒	NOUN
ejpam-5490	270	12	(	(	PUNCT
ejpam-5490	270	13	t	t	X
ejpam-5490	270	14	]	]	X
ejpam-5490	270	15	∈	∈	PROPN
ejpam-5490	270	16	[	[	X
ejpam-5490	270	17	(	(	PUNCT
ejpam-5490	270	18	v	v	NOUN
ejpam-5490	270	19	∨∗	∨∗	NOUN
ejpam-5490	270	20	v	v	ADP
ejpam-5490	270	21	g]]∗	g]]∗	NOUN
ejpam-5490	270	22	=	=	NOUN
ejpam-5490	270	23	⇒	⇒	NOUN
ejpam-5490	270	24	(	(	PUNCT
ejpam-5490	270	25	t	t	X
ejpam-5490	270	26	]	]	X
ejpam-5490	270	27	∧∗	∧∗	ADJ
ejpam-5490	270	28	(	(	PUNCT
ejpam-5490	270	29	v	v	NUM
ejpam-5490	270	30	∨∗	∨∗	NOUN
ejpam-5490	270	31	v	v	ADP
ejpam-5490	270	32	g	g	NOUN
ejpam-5490	270	33	]	]	X
ejpam-5490	270	34	=	=	PUNCT
ejpam-5490	270	35	(	(	PUNCT
ejpam-5490	270	36	0	0	NUM
ejpam-5490	270	37	]	]	X
ejpam-5490	270	38	=	=	NOUN
ejpam-5490	270	39	⇒	⇒	NOUN
ejpam-5490	270	40	(	(	PUNCT
ejpam-5490	270	41	t	t	NOUN
ejpam-5490	270	42	∧∗	∧∗	ADJ
ejpam-5490	270	43	(	(	PUNCT
ejpam-5490	270	44	v	v	NUM
ejpam-5490	270	45	∨∗	∨∗	NOUN
ejpam-5490	270	46	v	v	NOUN
ejpam-5490	270	47	g	g	NOUN
ejpam-5490	270	48	)	)	PUNCT
ejpam-5490	270	49	]	]	PUNCT
ejpam-5490	271	1	=	=	PUNCT
ejpam-5490	271	2	(	(	PUNCT
ejpam-5490	271	3	0	0	X
ejpam-5490	271	4	]	]	X
ejpam-5490	272	1	=	=	NOUN
ejpam-5490	272	2	⇒	⇒	PROPN
ejpam-5490	272	3	t	t	PROPN
ejpam-5490	272	4	∧∗	∧∗	ADJ
ejpam-5490	272	5	(	(	PUNCT
ejpam-5490	272	6	v	v	NUM
ejpam-5490	272	7	∨∗	∨∗	NOUN
ejpam-5490	272	8	v	v	NOUN
ejpam-5490	272	9	g	g	NOUN
ejpam-5490	272	10	)	)	PUNCT
ejpam-5490	272	11	=	=	SYM
ejpam-5490	272	12	0	0	PUNCT
ejpam-5490	273	1	=	=	NOUN
ejpam-5490	273	2	⇒	⇒	NOUN
ejpam-5490	273	3	t	t	NOUN
ejpam-5490	273	4	=	=	SYM
ejpam-5490	273	5	0	0	PUNCT
ejpam-5490	274	1	(	(	PUNCT
ejpam-5490	274	2	since	since	SCONJ
ejpam-5490	274	3	v	v	INTJ
ejpam-5490	274	4	∨∗	∨∗	NOUN
ejpam-5490	274	5	v	v	NOUN
ejpam-5490	274	6	g	g	NOUN
ejpam-5490	274	7	=	=	SYM
ejpam-5490	274	8	0	0	NUM
ejpam-5490	274	9	)	)	PUNCT
ejpam-5490	274	10	=	=	NOUN
ejpam-5490	274	11	⇒	⇒	NOUN
ejpam-5490	274	12	(	(	PUNCT
ejpam-5490	274	13	t	t	X
ejpam-5490	274	14	]	]	X
ejpam-5490	274	15	=	=	PUNCT
ejpam-5490	274	16	(	(	PUNCT
ejpam-5490	274	17	0	0	NUM
ejpam-5490	274	18	]	]	PUNCT
ejpam-5490	274	19	.	.	PUNCT
ejpam-5490	275	1	therefore	therefore	ADV
ejpam-5490	275	2	(	(	PUNCT
ejpam-5490	275	3	v	v	NOUN
ejpam-5490	275	4	]	]	X
ejpam-5490	275	5	∨∗	∨∗	PROPN
ejpam-5490	275	6	(	(	PUNCT
ejpam-5490	275	7	v	v	PART
ejpam-5490	275	8	]	]	X
ejpam-5490	276	1	g	g	NOUN
ejpam-5490	276	2	is	be	AUX
ejpam-5490	276	3	dense	dense	ADJ
ejpam-5490	276	4	in	in	ADP
ejpam-5490	276	5	pi(a	pi(a	NOUN
ejpam-5490	276	6	)	)	PUNCT
ejpam-5490	276	7	.	.	PUNCT
ejpam-5490	277	1	if	if	SCONJ
ejpam-5490	277	2	(	(	PUNCT
ejpam-5490	277	3	v	v	NOUN
ejpam-5490	277	4	]	]	X
ejpam-5490	277	5	∨∗	∨∗	PROPN
ejpam-5490	277	6	(	(	PUNCT
ejpam-5490	277	7	w	w	X
ejpam-5490	277	8	]	]	X
ejpam-5490	277	9	is	be	AUX
ejpam-5490	277	10	dense	dense	ADJ
ejpam-5490	277	11	in	in	ADP
ejpam-5490	277	12	pi(a	pi(a	NOUN
ejpam-5490	277	13	)	)	PUNCT
ejpam-5490	277	14	,	,	PUNCT
ejpam-5490	277	15	for	for	ADP
ejpam-5490	277	16	some	some	DET
ejpam-5490	277	17	w	w	PROPN
ejpam-5490	277	18	∈	∈	PROPN
ejpam-5490	277	19	a.	a.	NOUN
ejpam-5490	277	20	then	then	ADV
ejpam-5490	277	21	(	(	PUNCT
ejpam-5490	277	22	v	v	X
ejpam-5490	277	23	∨∗	∨∗	NOUN
ejpam-5490	277	24	w	w	NOUN
ejpam-5490	277	25	]	]	X
ejpam-5490	277	26	is	be	AUX
ejpam-5490	277	27	dense	dense	ADJ
ejpam-5490	277	28	in	in	ADP
ejpam-5490	277	29	pi(a	pi(a	NOUN
ejpam-5490	277	30	)	)	PUNCT
ejpam-5490	277	31	if	if	SCONJ
ejpam-5490	277	32	and	and	CCONJ
ejpam-5490	278	1	only	only	ADV
ejpam-5490	278	2	if	if	SCONJ
ejpam-5490	278	3	v	v	NUM
ejpam-5490	278	4	∨∗	∨∗	PROPN
ejpam-5490	278	5	w	w	NOUN
ejpam-5490	278	6	is	be	AUX
ejpam-5490	278	7	dense	dense	ADJ
ejpam-5490	278	8	in	in	ADP
ejpam-5490	278	9	a.	a.	NOUN
ejpam-5490	278	10	therefore	therefore	ADV
ejpam-5490	278	11	vg	vg	ADP
ejpam-5490	278	12	≤	≤	NUM
ejpam-5490	278	13	w.	w.	NOUN
ejpam-5490	278	14	so	so	SCONJ
ejpam-5490	278	15	that	that	SCONJ
ejpam-5490	278	16	(	(	PUNCT
ejpam-5490	278	17	vg	vg	X
ejpam-5490	278	18	]	]	X
ejpam-5490	278	19	⊆	⊆	NUM
ejpam-5490	278	20	(	(	PUNCT
ejpam-5490	278	21	w	w	NOUN
ejpam-5490	278	22	]	]	X
ejpam-5490	278	23	.	.	PUNCT
ejpam-5490	279	1	hence	hence	ADV
ejpam-5490	279	2	(	(	PUNCT
ejpam-5490	279	3	v]g	v]g	NOUN
ejpam-5490	279	4	⊆	⊆	NUM
ejpam-5490	279	5	(	(	PUNCT
ejpam-5490	279	6	w	w	NOUN
ejpam-5490	279	7	]	]	X
ejpam-5490	279	8	.	.	PUNCT
ejpam-5490	280	1	if	if	SCONJ
ejpam-5490	280	2	(	(	PUNCT
ejpam-5490	280	3	v]g	v]g	NOUN
ejpam-5490	280	4	⊆	⊆	NUM
ejpam-5490	280	5	(	(	PUNCT
ejpam-5490	280	6	w	w	NOUN
ejpam-5490	280	7	]	]	X
ejpam-5490	280	8	.	.	PUNCT
ejpam-5490	281	1	since	since	SCONJ
ejpam-5490	281	2	(	(	PUNCT
ejpam-5490	281	3	v	v	NOUN
ejpam-5490	281	4	]	]	X
ejpam-5490	281	5	∨∗	∨∗	PROPN
ejpam-5490	281	6	(	(	PUNCT
ejpam-5490	281	7	vg	vg	X
ejpam-5490	281	8	]	]	PUNCT
ejpam-5490	281	9	is	be	AUX
ejpam-5490	281	10	dense	dense	ADJ
ejpam-5490	281	11	in	in	ADP
ejpam-5490	281	12	pi(a	pi(a	NOUN
ejpam-5490	281	13	)	)	PUNCT
ejpam-5490	281	14	,	,	PUNCT
ejpam-5490	281	15	(	(	PUNCT
ejpam-5490	281	16	vg	vg	NOUN
ejpam-5490	281	17	]	]	X
ejpam-5490	281	18	∨∗	∨∗	NOUN
ejpam-5490	281	19	(	(	PUNCT
ejpam-5490	281	20	w	w	X
ejpam-5490	281	21	]	]	X
ejpam-5490	281	22	is	be	AUX
ejpam-5490	281	23	dense	dense	ADJ
ejpam-5490	281	24	in	in	ADP
ejpam-5490	281	25	pi(a	pi(a	NOUN
ejpam-5490	281	26	)	)	PUNCT
ejpam-5490	281	27	.	.	PUNCT
ejpam-5490	282	1	hence	hence	ADV
ejpam-5490	282	2	(	(	PUNCT
ejpam-5490	282	3	v	v	NOUN
ejpam-5490	282	4	]	]	X
ejpam-5490	282	5	∨∗	∨∗	PROPN
ejpam-5490	282	6	(	(	PUNCT
ejpam-5490	282	7	w	w	X
ejpam-5490	282	8	]	]	X
ejpam-5490	282	9	is	be	AUX
ejpam-5490	282	10	dense	dense	ADJ
ejpam-5490	282	11	in	in	ADP
ejpam-5490	282	12	pi(a	pi(a	NOUN
ejpam-5490	282	13	)	)	PUNCT
ejpam-5490	282	14	.	.	PUNCT
ejpam-5490	283	1	conversely	conversely	ADV
ejpam-5490	283	2	suppose	suppose	VERB
ejpam-5490	283	3	that	that	SCONJ
ejpam-5490	283	4	pi(a	pi(a	PUNCT
ejpam-5490	283	5	)	)	PUNCT
ejpam-5490	283	6	is	be	AUX
ejpam-5490	283	7	generalized	generalize	VERB
ejpam-5490	283	8	complemented	complement	VERB
ejpam-5490	283	9	.	.	PUNCT
ejpam-5490	284	1	let	let	VERB
ejpam-5490	284	2	v	v	NUM
ejpam-5490	284	3	∈	∈	NOUN
ejpam-5490	284	4	a.	a.	NOUN
ejpam-5490	284	5	then	then	ADV
ejpam-5490	284	6	(	(	PUNCT
ejpam-5490	284	7	v	v	NOUN
ejpam-5490	284	8	]	]	X
ejpam-5490	284	9	∈	∈	NOUN
ejpam-5490	284	10	pi(a	pi(a	PROPN
ejpam-5490	284	11	)	)	PUNCT
ejpam-5490	284	12	.	.	PUNCT
ejpam-5490	285	1	then	then	ADV
ejpam-5490	285	2	there	there	PRON
ejpam-5490	285	3	exists	exist	VERB
ejpam-5490	285	4	(	(	PUNCT
ejpam-5490	285	5	v]g	v]g	NOUN
ejpam-5490	285	6	in	in	ADP
ejpam-5490	285	7	pi(a	pi(a	NOUN
ejpam-5490	285	8	)	)	PUNCT
ejpam-5490	285	9	such	such	ADJ
ejpam-5490	285	10	that	that	SCONJ
ejpam-5490	285	11	(	(	PUNCT
ejpam-5490	285	12	v	v	NOUN
ejpam-5490	285	13	]	]	X
ejpam-5490	285	14	∨∗	∨∗	PROPN
ejpam-5490	285	15	(	(	PUNCT
ejpam-5490	285	16	v	v	PART
ejpam-5490	285	17	]	]	X
ejpam-5490	285	18	g	g	NOUN
ejpam-5490	285	19	is	be	AUX
ejpam-5490	285	20	dense	dense	ADJ
ejpam-5490	285	21	in	in	ADP
ejpam-5490	285	22	pi(a	pi(a	NOUN
ejpam-5490	285	23	)	)	PUNCT
ejpam-5490	285	24	and	and	CCONJ
ejpam-5490	285	25	(	(	PUNCT
ejpam-5490	285	26	v	v	NOUN
ejpam-5490	285	27	]	]	X
ejpam-5490	285	28	∨∗	∨∗	PROPN
ejpam-5490	285	29	(	(	PUNCT
ejpam-5490	285	30	w	w	X
ejpam-5490	285	31	]	]	X
ejpam-5490	285	32	is	be	AUX
ejpam-5490	285	33	dense	dense	ADJ
ejpam-5490	285	34	if	if	SCONJ
ejpam-5490	285	35	and	and	CCONJ
ejpam-5490	285	36	only	only	ADV
ejpam-5490	285	37	if	if	SCONJ
ejpam-5490	285	38	(	(	PUNCT
ejpam-5490	285	39	v]g	v]g	NOUN
ejpam-5490	285	40	⊆	⊆	NUM
ejpam-5490	285	41	(	(	PUNCT
ejpam-5490	285	42	w	w	NOUN
ejpam-5490	285	43	]	]	X
ejpam-5490	285	44	.	.	PUNCT
ejpam-5490	286	1	now	now	ADV
ejpam-5490	286	2	,	,	PUNCT
ejpam-5490	286	3	we	we	PRON
ejpam-5490	286	4	can	can	AUX
ejpam-5490	286	5	write	write	VERB
ejpam-5490	286	6	(	(	PUNCT
ejpam-5490	286	7	v]g	v]g	NOUN
ejpam-5490	286	8	=	=	SYM
ejpam-5490	286	9	(	(	PUNCT
ejpam-5490	286	10	v+	v+	ADP
ejpam-5490	286	11	]	]	PUNCT
ejpam-5490	286	12	for	for	ADP
ejpam-5490	286	13	some	some	PRON
ejpam-5490	286	14	v+	v+	NOUN
ejpam-5490	286	15	∈	∈	PROPN
ejpam-5490	286	16	a	a	PRON
ejpam-5490	286	17	.	.	PUNCT
ejpam-5490	287	1	then	then	ADV
ejpam-5490	287	2	(	(	PUNCT
ejpam-5490	287	3	v]∨∗	v]∨∗	X
ejpam-5490	287	4	(	(	PUNCT
ejpam-5490	287	5	v	v	NOUN
ejpam-5490	287	6	]	]	X
ejpam-5490	287	7	g	g	NOUN
ejpam-5490	287	8	=	=	SYM
ejpam-5490	287	9	(	(	PUNCT
ejpam-5490	287	10	v]∨∗	v]∨∗	X
ejpam-5490	287	11	(	(	PUNCT
ejpam-5490	287	12	v	v	ADP
ejpam-5490	287	13	+	+	NOUN
ejpam-5490	287	14	]	]	X
ejpam-5490	287	15	=	=	SYM
ejpam-5490	287	16	(	(	PUNCT
ejpam-5490	287	17	v	v	NUM
ejpam-5490	287	18	∨∗	∨∗	NOUN
ejpam-5490	287	19	v	v	ADP
ejpam-5490	287	20	+	+	NOUN
ejpam-5490	287	21	]	]	X
ejpam-5490	287	22	is	be	AUX
ejpam-5490	287	23	dense	dense	ADJ
ejpam-5490	287	24	in	in	ADP
ejpam-5490	287	25	pi(a	pi(a	NOUN
ejpam-5490	287	26	)	)	PUNCT
ejpam-5490	288	1	if	if	SCONJ
ejpam-5490	288	2	and	and	CCONJ
ejpam-5490	288	3	only	only	ADV
ejpam-5490	288	4	if	if	SCONJ
ejpam-5490	288	5	v	v	AUX
ejpam-5490	288	6	∨∗	∨∗	NOUN
ejpam-5490	288	7	v	v	NOUN
ejpam-5490	288	8	+	+	CCONJ
ejpam-5490	288	9	is	be	AUX
ejpam-5490	288	10	dense	dense	ADJ
ejpam-5490	288	11	in	in	ADP
ejpam-5490	288	12	a.	a.	NOUN
ejpam-5490	288	13	if	if	SCONJ
ejpam-5490	288	14	v	v	NUM
ejpam-5490	288	15	∨∗	∨∗	PROPN
ejpam-5490	288	16	w	w	PROPN
ejpam-5490	288	17	∈	∈	PROPN
ejpam-5490	288	18	d	d	NOUN
ejpam-5490	288	19	for	for	ADP
ejpam-5490	288	20	some	some	DET
ejpam-5490	288	21	w	w	PROPN
ejpam-5490	288	22	∈	∈	PROPN
ejpam-5490	288	23	a.	a.	NOUN
ejpam-5490	288	24	then	then	ADV
ejpam-5490	288	25	(	(	PUNCT
ejpam-5490	288	26	v	v	NOUN
ejpam-5490	288	27	]	]	X
ejpam-5490	288	28	∨∗	∨∗	PROPN
ejpam-5490	288	29	(	(	PUNCT
ejpam-5490	288	30	w	w	X
ejpam-5490	288	31	]	]	X
ejpam-5490	288	32	is	be	AUX
ejpam-5490	288	33	dense	dense	ADJ
ejpam-5490	288	34	in	in	ADP
ejpam-5490	288	35	pi(a	pi(a	NOUN
ejpam-5490	288	36	)	)	PUNCT
ejpam-5490	288	37	.	.	PUNCT
ejpam-5490	289	1	therefore	therefore	ADV
ejpam-5490	289	2	(	(	PUNCT
ejpam-5490	289	3	v]g	v]g	NOUN
ejpam-5490	289	4	⊆	⊆	NUM
ejpam-5490	289	5	(	(	PUNCT
ejpam-5490	289	6	w	w	NOUN
ejpam-5490	289	7	]	]	X
ejpam-5490	289	8	.	.	PUNCT
ejpam-5490	290	1	hence	hence	ADV
ejpam-5490	290	2	(	(	PUNCT
ejpam-5490	290	3	v+	v+	NOUN
ejpam-5490	290	4	]	]	X
ejpam-5490	290	5	⊆	⊆	NUM
ejpam-5490	290	6	(	(	PUNCT
ejpam-5490	290	7	w	w	NOUN
ejpam-5490	290	8	]	]	X
ejpam-5490	290	9	.	.	PUNCT
ejpam-5490	291	1	so	so	ADV
ejpam-5490	291	2	that	that	SCONJ
ejpam-5490	291	3	(	(	PUNCT
ejpam-5490	291	4	v+]∩(w	v+]∩(w	X
ejpam-5490	291	5	]	]	X
ejpam-5490	291	6	=	=	X
ejpam-5490	291	7	(	(	PUNCT
ejpam-5490	291	8	v+	v+	ADP
ejpam-5490	291	9	]	]	PUNCT
ejpam-5490	291	10	and	and	CCONJ
ejpam-5490	291	11	also	also	ADV
ejpam-5490	291	12	(	(	PUNCT
ejpam-5490	291	13	v+∧∗w	v+∧∗w	X
ejpam-5490	291	14	]	]	X
ejpam-5490	291	15	=	=	SYM
ejpam-5490	291	16	(	(	PUNCT
ejpam-5490	291	17	v+	v+	NOUN
ejpam-5490	291	18	]	]	PUNCT
ejpam-5490	291	19	.	.	PUNCT
ejpam-5490	292	1	now	now	ADV
ejpam-5490	292	2	v+∧∗w	v+∧∗w	VERB
ejpam-5490	292	3	=	=	SYM
ejpam-5490	292	4	v+	v+	NOUN
ejpam-5490	292	5	.	.	PUNCT
ejpam-5490	293	1	hence	hence	ADV
ejpam-5490	293	2	v+	v+	X
ejpam-5490	293	3	≤	≤	ADJ
ejpam-5490	293	4	w.	w.	PROPN
ejpam-5490	293	5	if	if	SCONJ
ejpam-5490	293	6	v+	v+	ADV
ejpam-5490	293	7	≤	≤	PROPN
ejpam-5490	293	8	w.	w.	PROPN
ejpam-5490	293	9	then	then	ADV
ejpam-5490	293	10	(	(	PUNCT
ejpam-5490	293	11	v+	v+	NOUN
ejpam-5490	293	12	]	]	X
ejpam-5490	293	13	⊆	⊆	NUM
ejpam-5490	293	14	(	(	PUNCT
ejpam-5490	293	15	w	w	NOUN
ejpam-5490	293	16	]	]	X
ejpam-5490	293	17	.	.	PUNCT
ejpam-5490	294	1	therefore	therefore	ADV
ejpam-5490	294	2	(	(	PUNCT
ejpam-5490	294	3	v+	v+	NOUN
ejpam-5490	294	4	]	]	X
ejpam-5490	294	5	⊆	⊆	NUM
ejpam-5490	294	6	(	(	PUNCT
ejpam-5490	294	7	w	w	NOUN
ejpam-5490	294	8	]	]	X
ejpam-5490	294	9	.	.	PUNCT
ejpam-5490	295	1	so	so	ADV
ejpam-5490	295	2	that	that	SCONJ
ejpam-5490	295	3	(	(	PUNCT
ejpam-5490	295	4	v]g	v]g	NOUN
ejpam-5490	295	5	⊆	⊆	NUM
ejpam-5490	295	6	(	(	PUNCT
ejpam-5490	295	7	w	w	NOUN
ejpam-5490	295	8	]	]	X
ejpam-5490	295	9	if	if	SCONJ
ejpam-5490	295	10	and	and	CCONJ
ejpam-5490	295	11	only	only	ADV
ejpam-5490	295	12	if	if	SCONJ
ejpam-5490	295	13	(	(	PUNCT
ejpam-5490	295	14	v	v	NOUN
ejpam-5490	295	15	]	]	X
ejpam-5490	295	16	∨∗	∨∗	PROPN
ejpam-5490	295	17	(	(	PUNCT
ejpam-5490	295	18	w	w	NOUN
ejpam-5490	295	19	]	]	X
ejpam-5490	295	20	=	=	SYM
ejpam-5490	295	21	(	(	PUNCT
ejpam-5490	295	22	v	v	NUM
ejpam-5490	295	23	∨∗	∨∗	NOUN
ejpam-5490	295	24	w	w	NOUN
ejpam-5490	295	25	]	]	X
ejpam-5490	295	26	is	be	AUX
ejpam-5490	295	27	dense	dense	ADJ
ejpam-5490	295	28	in	in	ADP
ejpam-5490	295	29	pi(a	pi(a	NOUN
ejpam-5490	295	30	)	)	PUNCT
ejpam-5490	295	31	.	.	PUNCT
ejpam-5490	296	1	hence	hence	ADV
ejpam-5490	296	2	v	v	ADP
ejpam-5490	296	3	∨∗	∨∗	PROPN
ejpam-5490	296	4	w	w	NOUN
ejpam-5490	296	5	is	be	AUX
ejpam-5490	296	6	dense	dense	ADJ
ejpam-5490	296	7	in	in	ADP
ejpam-5490	296	8	a.	a.	NOUN
ejpam-5490	296	9	thus	thus	ADV
ejpam-5490	296	10	+	+	CCONJ
ejpam-5490	296	11	is	be	AUX
ejpam-5490	296	12	a	a	DET
ejpam-5490	296	13	generalized	generalized	ADJ
ejpam-5490	296	14	complementation	complementation	NOUN
ejpam-5490	296	15	on	on	ADP
ejpam-5490	296	16	a	a	PRON
ejpam-5490	296	17	and	and	CCONJ
ejpam-5490	296	18	a	a	PRON
ejpam-5490	296	19	is	be	AUX
ejpam-5490	296	20	generalized	generalize	VERB
ejpam-5490	296	21	complemented	complement	VERB
ejpam-5490	296	22	.	.	PUNCT
ejpam-5490	297	1	definition	definition	NOUN
ejpam-5490	297	2	7	7	NUM
ejpam-5490	297	3	.	.	PUNCT
ejpam-5490	298	1	a	a	DET
ejpam-5490	298	2	distributive	distributive	ADJ
ejpam-5490	298	3	lattice	lattice	NOUN
ejpam-5490	298	4	a	a	PRON
ejpam-5490	298	5	with	with	ADP
ejpam-5490	298	6	a	a	DET
ejpam-5490	298	7	generalized	generalized	ADJ
ejpam-5490	298	8	complementation	complementation	NOUN
ejpam-5490	298	9	g	g	NOUN
ejpam-5490	298	10	is	be	AUX
ejpam-5490	298	11	said	say	VERB
ejpam-5490	298	12	to	to	PART
ejpam-5490	298	13	be	be	AUX
ejpam-5490	298	14	p	p	NOUN
ejpam-5490	298	15	-	-	PUNCT
ejpam-5490	298	16	complemented	complement	VERB
ejpam-5490	298	17	if	if	SCONJ
ejpam-5490	298	18	for	for	ADP
ejpam-5490	298	19	any	any	DET
ejpam-5490	298	20	v	v	NOUN
ejpam-5490	298	21	∈	∈	PRON
ejpam-5490	298	22	a	a	PRON
ejpam-5490	298	23	,	,	PUNCT
ejpam-5490	298	24	there	there	PRON
ejpam-5490	298	25	exists	exist	VERB
ejpam-5490	298	26	vg	vg	ADP
ejpam-5490	298	27	∈	∈	PROPN
ejpam-5490	298	28	a	a	DET
ejpam-5490	298	29	such	such	ADJ
ejpam-5490	298	30	that	that	DET
ejpam-5490	298	31	v	v	NOUN
ejpam-5490	298	32	∧∗	∧∗	ADJ
ejpam-5490	298	33	v	v	ADP
ejpam-5490	298	34	g	g	NOUN
ejpam-5490	298	35	=	=	SYM
ejpam-5490	298	36	0	0	PROPN
ejpam-5490	298	37	.	.	PUNCT
ejpam-5490	298	38	theorem	theorem	VERB
ejpam-5490	298	39	17	17	NUM
ejpam-5490	298	40	.	.	PUNCT
ejpam-5490	299	1	every	every	DET
ejpam-5490	299	2	g	g	NOUN
ejpam-5490	299	3	-	-	PUNCT
ejpam-5490	299	4	complemented	complement	VERB
ejpam-5490	299	5	distributive	distributive	ADJ
ejpam-5490	299	6	lattice	lattice	NOUN
ejpam-5490	299	7	is	be	AUX
ejpam-5490	299	8	quasi	quasi	NOUN
ejpam-5490	299	9	complemented	complement	VERB
ejpam-5490	299	10	if	if	SCONJ
ejpam-5490	299	11	and	and	CCONJ
ejpam-5490	299	12	only	only	ADV
ejpam-5490	299	13	if	if	SCONJ
ejpam-5490	299	14	it	it	PRON
ejpam-5490	299	15	is	be	AUX
ejpam-5490	299	16	p	p	NOUN
ejpam-5490	299	17	-	-	PUNCT
ejpam-5490	299	18	complemented	complement	VERB
ejpam-5490	299	19	.	.	PUNCT
ejpam-5490	300	1	proof	proof	NOUN
ejpam-5490	300	2	.	.	PUNCT
ejpam-5490	301	1	let	let	VERB
ejpam-5490	301	2	g	g	PRON
ejpam-5490	301	3	be	be	AUX
ejpam-5490	301	4	a	a	DET
ejpam-5490	301	5	generalized	generalized	ADJ
ejpam-5490	301	6	complementation	complementation	NOUN
ejpam-5490	301	7	on	on	ADP
ejpam-5490	301	8	a.	a.	NOUN
ejpam-5490	301	9	suppose	suppose	VERB
ejpam-5490	301	10	a	a	PRON
ejpam-5490	301	11	is	be	AUX
ejpam-5490	301	12	quasi	quasi	NOUN
ejpam-5490	301	13	complemented	complement	VERB
ejpam-5490	301	14	.	.	PUNCT
ejpam-5490	302	1	let	let	VERB
ejpam-5490	302	2	v	v	NUM
ejpam-5490	302	3	∈	∈	NOUN
ejpam-5490	302	4	a.	a.	NOUN
ejpam-5490	302	5	then	then	ADV
ejpam-5490	302	6	there	there	PRON
ejpam-5490	302	7	exists	exist	VERB
ejpam-5490	302	8	w	w	PROPN
ejpam-5490	302	9	∈	∈	PROPN
ejpam-5490	302	10	a	a	DET
ejpam-5490	302	11	such	such	ADJ
ejpam-5490	302	12	that	that	DET
ejpam-5490	302	13	v	v	NOUN
ejpam-5490	302	14	∧∗	∧∗	ADJ
ejpam-5490	302	15	w	w	PROPN
ejpam-5490	302	16	=	=	NOUN
ejpam-5490	302	17	0	0	NUM
ejpam-5490	303	1	and	and	CCONJ
ejpam-5490	303	2	v	v	ADP
ejpam-5490	303	3	∨∗	∨∗	NOUN
ejpam-5490	303	4	w	w	NOUN
ejpam-5490	303	5	is	be	AUX
ejpam-5490	303	6	dense	dense	ADJ
ejpam-5490	303	7	.	.	PUNCT
ejpam-5490	304	1	since	since	SCONJ
ejpam-5490	304	2	g	g	PROPN
ejpam-5490	304	3	is	be	AUX
ejpam-5490	304	4	a	a	DET
ejpam-5490	304	5	generalized	generalized	ADJ
ejpam-5490	304	6	complementation	complementation	NOUN
ejpam-5490	304	7	,	,	PUNCT
ejpam-5490	304	8	vg	vg	ADP
ejpam-5490	304	9	≤	≤	NOUN
ejpam-5490	304	10	w.	w.	NOUN
ejpam-5490	304	11	now	now	ADV
ejpam-5490	304	12	0	0	X
ejpam-5490	305	1	=	=	SYM
ejpam-5490	305	2	v	v	NUM
ejpam-5490	305	3	∧∗	∧∗	ADJ
ejpam-5490	305	4	w	w	NOUN
ejpam-5490	305	5	=	=	SYM
ejpam-5490	305	6	v	v	X
ejpam-5490	305	7	∧∗	∧∗	ADJ
ejpam-5490	305	8	(	(	PUNCT
ejpam-5490	305	9	v	v	NOUN
ejpam-5490	305	10	g	g	NOUN
ejpam-5490	305	11	∨∗	∨∗	NOUN
ejpam-5490	305	12	w	w	NOUN
ejpam-5490	305	13	)	)	PUNCT
ejpam-5490	305	14	=	=	SYM
ejpam-5490	305	15	(	(	PUNCT
ejpam-5490	305	16	v	v	NUM
ejpam-5490	305	17	∧∗	∧∗	ADJ
ejpam-5490	305	18	v	v	ADP
ejpam-5490	305	19	g)∨∗	g)∨∗	NOUN
ejpam-5490	305	20	(	(	PUNCT
ejpam-5490	305	21	v	v	NUM
ejpam-5490	305	22	∧∗	∧∗	PROPN
ejpam-5490	305	23	w	w	NOUN
ejpam-5490	305	24	)	)	PUNCT
ejpam-5490	305	25	.	.	PUNCT
ejpam-5490	306	1	therefore	therefore	ADV
ejpam-5490	306	2	v	v	NUM
ejpam-5490	306	3	∧∗	∧∗	ADJ
ejpam-5490	306	4	v	v	ADP
ejpam-5490	306	5	g	g	NOUN
ejpam-5490	306	6	=	=	SYM
ejpam-5490	306	7	0	0	PROPN
ejpam-5490	306	8	.	.	PUNCT
ejpam-5490	307	1	hence	hence	ADV
ejpam-5490	307	2	a	a	PRON
ejpam-5490	307	3	is	be	AUX
ejpam-5490	307	4	p	p	NOUN
ejpam-5490	307	5	-	-	PUNCT
ejpam-5490	307	6	complemented	complement	VERB
ejpam-5490	307	7	.	.	PUNCT
ejpam-5490	308	1	conversely	conversely	ADV
ejpam-5490	308	2	suppose	suppose	VERB
ejpam-5490	308	3	that	that	SCONJ
ejpam-5490	308	4	a	a	PRON
ejpam-5490	308	5	is	be	AUX
ejpam-5490	308	6	p	p	NOUN
ejpam-5490	308	7	-	-	PUNCT
ejpam-5490	308	8	complemented	complement	VERB
ejpam-5490	308	9	.	.	PUNCT
ejpam-5490	309	1	let	let	VERB
ejpam-5490	309	2	v	v	NUM
ejpam-5490	309	3	∈	∈	NOUN
ejpam-5490	309	4	a.	a.	NOUN
ejpam-5490	309	5	then	then	ADV
ejpam-5490	309	6	there	there	PRON
ejpam-5490	309	7	exists	exist	VERB
ejpam-5490	309	8	vg	vg	ADP
ejpam-5490	309	9	∈	∈	PROPN
ejpam-5490	309	10	a	a	DET
ejpam-5490	309	11	such	such	ADJ
ejpam-5490	309	12	that	that	PRON
ejpam-5490	309	13	v∧∗v	v∧∗v	NUM
ejpam-5490	309	14	g	g	NOUN
ejpam-5490	309	15	=	=	SYM
ejpam-5490	309	16	0	0	NUM
ejpam-5490	309	17	.	.	PUNCT
ejpam-5490	310	1	by	by	ADP
ejpam-5490	310	2	definition	definition	NOUN
ejpam-5490	310	3	of	of	ADP
ejpam-5490	310	4	g	g	NOUN
ejpam-5490	310	5	-	-	PUNCT
ejpam-5490	310	6	complementation	complementation	NOUN
ejpam-5490	310	7	,	,	PUNCT
ejpam-5490	310	8	v	v	ADP
ejpam-5490	310	9	∨∗	∨∗	NOUN
ejpam-5490	310	10	v	v	NOUN
ejpam-5490	310	11	g	g	NOUN
ejpam-5490	310	12	is	be	AUX
ejpam-5490	310	13	dense	dense	ADJ
ejpam-5490	310	14	.	.	PUNCT
ejpam-5490	311	1	thus	thus	ADV
ejpam-5490	311	2	a	a	PRON
ejpam-5490	311	3	is	be	AUX
ejpam-5490	311	4	quasi	quasi	NOUN
ejpam-5490	311	5	complemented	complement	VERB
ejpam-5490	311	6	.	.	PUNCT
ejpam-5490	312	1	5	5	X
ejpam-5490	312	2	.	.	X
ejpam-5490	312	3	conclusions	conclusion	NOUN
ejpam-5490	312	4	this	this	DET
ejpam-5490	312	5	paper	paper	NOUN
ejpam-5490	312	6	extensively	extensively	ADV
ejpam-5490	312	7	studied	study	VERB
ejpam-5490	312	8	on	on	ADP
ejpam-5490	312	9	g	g	NOUN
ejpam-5490	312	10	-	-	PUNCT
ejpam-5490	312	11	filters	filter	NOUN
ejpam-5490	312	12	,	,	PUNCT
ejpam-5490	312	13	normal	normal	ADJ
ejpam-5490	312	14	g	g	NOUN
ejpam-5490	312	15	-	-	PUNCT
ejpam-5490	312	16	filters	filter	NOUN
ejpam-5490	312	17	,	,	PUNCT
ejpam-5490	312	18	co	co	ADJ
ejpam-5490	312	19	-	-	ADJ
ejpam-5490	312	20	dense	dense	ADJ
ejpam-5490	312	21	filters	filter	NOUN
ejpam-5490	312	22	and	and	CCONJ
ejpam-5490	312	23	generalized	generalized	ADJ
ejpam-5490	312	24	complementations	complementation	NOUN
ejpam-5490	312	25	in	in	ADP
ejpam-5490	312	26	a	a	DET
ejpam-5490	312	27	distributive	distributive	ADJ
ejpam-5490	312	28	lattice	lattice	NOUN
ejpam-5490	312	29	with	with	ADP
ejpam-5490	312	30	dense	dense	ADJ
ejpam-5490	312	31	elements	element	NOUN
ejpam-5490	312	32	.	.	PUNCT
ejpam-5490	313	1	the	the	DET
ejpam-5490	313	2	class	class	NOUN
ejpam-5490	313	3	of	of	ADP
ejpam-5490	313	4	quasi	quasi	NOUN
ejpam-5490	313	5	complemented	complement	VERB
ejpam-5490	313	6	distributive	distributive	ADJ
ejpam-5490	313	7	lattices	lattice	NOUN
ejpam-5490	313	8	and	and	CCONJ
ejpam-5490	313	9	the	the	DET
ejpam-5490	313	10	class	class	NOUN
ejpam-5490	313	11	of	of	ADP
ejpam-5490	313	12	generalized	generalized	ADJ
ejpam-5490	313	13	complemented	complement	VERB
ejpam-5490	313	14	distributive	distributive	ADJ
ejpam-5490	313	15	lattices	lattice	NOUN
ejpam-5490	313	16	are	be	AUX
ejpam-5490	313	17	characterized	characterize	VERB
ejpam-5490	313	18	.	.	PUNCT
ejpam-5490	314	1	further	far	ADV
ejpam-5490	314	2	we	we	PRON
ejpam-5490	314	3	can	can	AUX
ejpam-5490	314	4	co	co	AUX
ejpam-5490	314	5	relate	relate	VERB
ejpam-5490	314	6	the	the	DET
ejpam-5490	314	7	class	class	NOUN
ejpam-5490	314	8	of	of	ADP
ejpam-5490	314	9	relatively	relatively	ADV
ejpam-5490	314	10	complemented	complemented	ADJ
ejpam-5490	314	11	distributive	distributive	ADJ
ejpam-5490	314	12	lattices	lattice	NOUN
ejpam-5490	314	13	and	and	CCONJ
ejpam-5490	314	14	the	the	DET
ejpam-5490	314	15	class	class	NOUN
ejpam-5490	314	16	of	of	ADP
ejpam-5490	314	17	ortho	ortho	PROPN
ejpam-5490	314	18	-	-	PUNCT
ejpam-5490	314	19	complemented	complement	VERB
ejpam-5490	314	20	distributive	distributive	ADJ
ejpam-5490	314	21	lattices	lattice	NOUN
ejpam-5490	314	22	,	,	PUNCT
ejpam-5490	314	23	using	use	VERB
ejpam-5490	314	24	the	the	DET
ejpam-5490	314	25	class	class	NOUN
ejpam-5490	314	26	of	of	ADP
ejpam-5490	314	27	g	g	NOUN
ejpam-5490	314	28	-	-	PUNCT
ejpam-5490	314	29	filters	filter	NOUN
ejpam-5490	314	30	and	and	CCONJ
ejpam-5490	314	31	the	the	DET
ejpam-5490	314	32	class	class	NOUN
ejpam-5490	314	33	of	of	ADP
ejpam-5490	314	34	generalized	generalized	ADJ
ejpam-5490	314	35	complemented	complemented	ADJ
ejpam-5490	314	36	distributive	distributive	ADJ
ejpam-5490	314	37	lattices	lattice	NOUN
ejpam-5490	314	38	.	.	PUNCT
ejpam-5490	315	1	j.	j.	PROPN
ejpam-5490	315	2	gunda	gunda	PROPN
ejpam-5490	315	3	et	et	PROPN
ejpam-5490	315	4	al	al	PROPN
ejpam-5490	315	5	.	.	PUNCT
ejpam-5490	315	6	/	/	SYM
ejpam-5490	315	7	eur	eur	PROPN
ejpam-5490	315	8	.	.	PUNCT
ejpam-5490	316	1	j.	j.	PROPN
ejpam-5490	316	2	pure	pure	PROPN
ejpam-5490	316	3	appl	appl	PROPN
ejpam-5490	316	4	.	.	PROPN
ejpam-5490	316	5	math	math	PROPN
ejpam-5490	316	6	,	,	PUNCT
ejpam-5490	316	7	18	18	NUM
ejpam-5490	316	8	(	(	PUNCT
ejpam-5490	316	9	1	1	NUM
ejpam-5490	316	10	)	)	PUNCT
ejpam-5490	316	11	(	(	PUNCT
ejpam-5490	316	12	2025	2025	NUM
ejpam-5490	316	13	)	)	PUNCT
ejpam-5490	316	14	,	,	PUNCT
ejpam-5490	316	15	5490	5490	NUM
ejpam-5490	316	16	11	11	NUM
ejpam-5490	316	17	of	of	ADP
ejpam-5490	316	18	11	11	NUM
ejpam-5490	316	19	acknowledgements	acknowledgement	NOUN
ejpam-5490	316	20	the	the	DET
ejpam-5490	316	21	authors	author	NOUN
ejpam-5490	316	22	wish	wish	VERB
ejpam-5490	316	23	to	to	PART
ejpam-5490	316	24	thank	thank	VERB
ejpam-5490	316	25	the	the	DET
ejpam-5490	316	26	anonymous	anonymous	ADJ
ejpam-5490	316	27	reviewers	reviewer	NOUN
ejpam-5490	316	28	for	for	ADP
ejpam-5490	316	29	their	their	PRON
ejpam-5490	316	30	valuable	valuable	ADJ
ejpam-5490	316	31	suggestions	suggestion	NOUN
ejpam-5490	316	32	.	.	PUNCT
ejpam-5490	317	1	this	this	DET
ejpam-5490	317	2	work	work	NOUN
ejpam-5490	317	3	was	be	AUX
ejpam-5490	317	4	supported	support	VERB
ejpam-5490	317	5	by	by	ADP
ejpam-5490	317	6	directorate	directorate	NOUN
ejpam-5490	317	7	of	of	ADP
ejpam-5490	317	8	research	research	NOUN
ejpam-5490	317	9	and	and	CCONJ
ejpam-5490	317	10	innovation	innovation	NOUN
ejpam-5490	317	11	,	,	PUNCT
ejpam-5490	317	12	walter	walter	PROPN
ejpam-5490	317	13	sisulu	sisulu	PROPN
ejpam-5490	317	14	university	university	PROPN
ejpam-5490	317	15	,	,	PUNCT
ejpam-5490	317	16	south	south	PROPN
ejpam-5490	317	17	africa	africa	PROPN
ejpam-5490	317	18	.	.	PUNCT
ejpam-5490	318	1	conflicts	conflict	NOUN
ejpam-5490	318	2	of	of	ADP
ejpam-5490	318	3	interest	interest	NOUN
ejpam-5490	318	4	or	or	CCONJ
ejpam-5490	318	5	competing	compete	VERB
ejpam-5490	318	6	interests	interest	NOUN
ejpam-5490	318	7	the	the	DET
ejpam-5490	318	8	authors	author	NOUN
ejpam-5490	318	9	declare	declare	VERB
ejpam-5490	318	10	that	that	SCONJ
ejpam-5490	318	11	they	they	PRON
ejpam-5490	318	12	have	have	VERB
ejpam-5490	318	13	no	no	DET
ejpam-5490	318	14	conflicts	conflict	NOUN
ejpam-5490	318	15	of	of	ADP
ejpam-5490	318	16	interest	interest	NOUN
ejpam-5490	318	17	.	.	PUNCT
ejpam-5490	319	1	informed	inform	VERB
ejpam-5490	319	2	consent	consent	VERB
ejpam-5490	319	3	the	the	DET
ejpam-5490	319	4	authors	author	NOUN
ejpam-5490	319	5	are	be	AUX
ejpam-5490	319	6	fully	fully	ADV
ejpam-5490	319	7	aware	aware	ADJ
ejpam-5490	319	8	and	and	CCONJ
ejpam-5490	319	9	satisfied	satisfied	ADJ
ejpam-5490	319	10	with	with	ADP
ejpam-5490	319	11	the	the	DET
ejpam-5490	319	12	contents	content	NOUN
ejpam-5490	319	13	of	of	ADP
ejpam-5490	319	14	the	the	DET
ejpam-5490	319	15	article	article	NOUN
ejpam-5490	319	16	.	.	PUNCT
ejpam-5490	320	1	references	reference	NOUN
ejpam-5490	320	2	[	[	X
ejpam-5490	320	3	1	1	NUM
ejpam-5490	320	4	]	]	PUNCT
ejpam-5490	320	5	g	g	NOUN
ejpam-5490	320	6	birkhoff	birkhoff	NOUN
ejpam-5490	320	7	.	.	PUNCT
ejpam-5490	321	1	lattice	lattice	PROPN
ejpam-5490	321	2	theory	theory	PROPN
ejpam-5490	321	3	.	.	PUNCT
ejpam-5490	322	1	amer	amer	PROPN
ejpam-5490	322	2	.	.	PUNCT
ejpam-5490	322	3	math	math	PROPN
ejpam-5490	322	4	.	.	PUNCT
ejpam-5490	323	1	soc	soc	PROPN
ejpam-5490	323	2	.	.	PUNCT
ejpam-5490	324	1	collequium	collequium	NOUN
ejpam-5490	324	2	pub	pub	NOUN
ejpam-5490	324	3	,	,	PUNCT
ejpam-5490	324	4	1967	1967	NUM
ejpam-5490	324	5	.	.	PUNCT
ejpam-5490	325	1	[	[	X
ejpam-5490	325	2	2	2	NUM
ejpam-5490	325	3	]	]	PUNCT
ejpam-5490	325	4	w	w	PROPN
ejpam-5490	325	5	h	h	PROPN
ejpam-5490	325	6	cornish	cornish	PROPN
ejpam-5490	325	7	.	.	PUNCT
ejpam-5490	325	8	normal	normal	ADJ
ejpam-5490	325	9	lattice	lattice	PROPN
ejpam-5490	325	10	.	.	PUNCT
ejpam-5490	326	1	journal	journal	NOUN
ejpam-5490	326	2	of	of	ADP
ejpam-5490	326	3	the	the	DET
ejpam-5490	326	4	australian	australian	ADJ
ejpam-5490	326	5	mathematical	mathematical	ADJ
ejpam-5490	326	6	society	society	NOUN
ejpam-5490	326	7	,	,	PUNCT
ejpam-5490	326	8	14:200	14:200	NUM
ejpam-5490	326	9	–	–	PUNCT
ejpam-5490	326	10	215	215	NUM
ejpam-5490	326	11	,	,	PUNCT
ejpam-5490	326	12	1972	1972	NUM
ejpam-5490	326	13	.	.	PUNCT
ejpam-5490	327	1	[	[	X
ejpam-5490	327	2	3	3	X
ejpam-5490	327	3	]	]	X
ejpam-5490	327	4	w	w	PROPN
ejpam-5490	327	5	h	h	PROPN
ejpam-5490	327	6	cornish	cornish	PROPN
ejpam-5490	327	7	.	.	PUNCT
ejpam-5490	328	1	quasi	quasi	ADJ
ejpam-5490	328	2	-	-	ADJ
ejpam-5490	328	3	complemented	complemented	ADJ
ejpam-5490	328	4	lattices	lattice	NOUN
ejpam-5490	328	5	.	.	PUNCT
ejpam-5490	329	1	commentationes	commentatione	NOUN
ejpam-5490	329	2	mathematicae	mathematicae	VERB
ejpam-5490	329	3	universitatis	universitatis	PROPN
ejpam-5490	329	4	,	,	PUNCT
ejpam-5490	329	5	carolinae	carolinae	PROPN
ejpam-5490	329	6	,	,	PUNCT
ejpam-5490	329	7	15:501–511	15:501–511	NUM
ejpam-5490	329	8	,	,	PUNCT
ejpam-5490	329	9	1974	1974	NUM
ejpam-5490	329	10	.	.	PUNCT
ejpam-5490	330	1	[	[	X
ejpam-5490	330	2	4	4	X
ejpam-5490	330	3	]	]	X
ejpam-5490	330	4	a	a	DET
ejpam-5490	330	5	p	p	X
ejpam-5490	330	6	p	p	X
ejpam-5490	330	7	kumar	kumar	PROPN
ejpam-5490	330	8	and	and	CCONJ
ejpam-5490	330	9	m	m	PROPN
ejpam-5490	330	10	s	s	PROPN
ejpam-5490	330	11	rao	rao	PROPN
ejpam-5490	330	12	.	.	PUNCT
ejpam-5490	331	1	divisibility	divisibility	NOUN
ejpam-5490	331	2	and	and	CCONJ
ejpam-5490	331	3	filters	filter	NOUN
ejpam-5490	331	4	in	in	ADP
ejpam-5490	331	5	distributive	distributive	ADJ
ejpam-5490	331	6	lattices	lattice	NOUN
ejpam-5490	331	7	.	.	PUNCT
ejpam-5490	332	1	palestine	palestine	PROPN
ejpam-5490	332	2	journal	journal	PROPN
ejpam-5490	332	3	of	of	ADP
ejpam-5490	332	4	mathematics	mathematic	NOUN
ejpam-5490	332	5	,	,	PUNCT
ejpam-5490	332	6	11:143–151	11:143–151	PROPN
ejpam-5490	332	7	,	,	PUNCT
ejpam-5490	332	8	2022	2022	NUM
ejpam-5490	332	9	.	.	PUNCT
ejpam-5490	333	1	[	[	X
ejpam-5490	333	2	5	5	NUM
ejpam-5490	333	3	]	]	PUNCT
ejpam-5490	333	4	a	a	DET
ejpam-5490	333	5	p	p	X
ejpam-5490	333	6	p	p	PROPN
ejpam-5490	333	7	kumar	kumar	PROPN
ejpam-5490	333	8	,	,	PUNCT
ejpam-5490	333	9	m	m	PROPN
ejpam-5490	333	10	s	s	PROPN
ejpam-5490	333	11	rao	rao	NOUN
ejpam-5490	333	12	,	,	PUNCT
ejpam-5490	333	13	and	and	CCONJ
ejpam-5490	333	14	k	k	PROPN
ejpam-5490	333	15	s	s	X
ejpam-5490	333	16	babu	babu	PROPN
ejpam-5490	333	17	.	.	PUNCT
ejpam-5490	334	1	generalized	generalize	VERB
ejpam-5490	334	2	prime	prime	ADJ
ejpam-5490	334	3	d	d	NOUN
ejpam-5490	334	4	-	-	PUNCT
ejpam-5490	334	5	filters	filter	NOUN
ejpam-5490	334	6	of	of	ADP
ejpam-5490	334	7	distributive	distributive	ADJ
ejpam-5490	334	8	lattices	lattice	NOUN
ejpam-5490	334	9	.	.	PUNCT
ejpam-5490	335	1	archivum	archivum	PROPN
ejpam-5490	335	2	mathematicum	mathematicum	PROPN
ejpam-5490	335	3	,	,	PUNCT
ejpam-5490	335	4	57:157–174	57:157–174	NUM
ejpam-5490	335	5	,	,	PUNCT
ejpam-5490	335	6	2021	2021	NUM
ejpam-5490	335	7	.	.	PUNCT
ejpam-5490	336	1	[	[	X
ejpam-5490	336	2	6	6	NUM
ejpam-5490	336	3	]	]	PUNCT
ejpam-5490	336	4	m	m	PROPN
ejpam-5490	336	5	s	s	NOUN
ejpam-5490	336	6	rao	rao	NOUN
ejpam-5490	336	7	and	and	CCONJ
ejpam-5490	336	8	a	a	DET
ejpam-5490	336	9	e	e	NOUN
ejpam-5490	336	10	badawy	badawy	NOUN
ejpam-5490	336	11	.	.	PUNCT
ejpam-5490	337	1	µ-filters	µ-filter	NOUN
ejpam-5490	337	2	of	of	ADP
ejpam-5490	337	3	distributive	distributive	ADJ
ejpam-5490	337	4	lattices	lattice	NOUN
ejpam-5490	337	5	.	.	PUNCT
ejpam-5490	338	1	southeast	southeast	ADJ
ejpam-5490	338	2	asian	asian	ADJ
ejpam-5490	338	3	bulletin	bulletin	NOUN
ejpam-5490	338	4	of	of	ADP
ejpam-5490	338	5	mathematics	mathematic	NOUN
ejpam-5490	338	6	,	,	PUNCT
ejpam-5490	338	7	40:251–264	40:251–264	PROPN
ejpam-5490	338	8	,	,	PUNCT
ejpam-5490	338	9	2016	2016	NUM
ejpam-5490	338	10	.	.	PUNCT
ejpam-5490	339	1	[	[	X
ejpam-5490	339	2	7	7	X
ejpam-5490	339	3	]	]	X
ejpam-5490	339	4	m	m	PROPN
ejpam-5490	339	5	s	s	NOUN
ejpam-5490	339	6	rao	rao	NOUN
ejpam-5490	339	7	and	and	CCONJ
ejpam-5490	339	8	ch	ch	PROPN
ejpam-5490	339	9	v	v	PROPN
ejpam-5490	339	10	rao	rao	PROPN
ejpam-5490	339	11	.	.	PUNCT
ejpam-5490	340	1	ω	ω	NOUN
ejpam-5490	340	2	-	-	NOUN
ejpam-5490	340	3	filters	filter	NOUN
ejpam-5490	340	4	of	of	ADP
ejpam-5490	340	5	distributive	distributive	ADJ
ejpam-5490	340	6	lattices	lattice	NOUN
ejpam-5490	340	7	.	.	PUNCT
ejpam-5490	341	1	algebraic	algebraic	ADJ
ejpam-5490	341	2	structures	structure	NOUN
ejpam-5490	341	3	and	and	CCONJ
ejpam-5490	341	4	their	their	PRON
ejpam-5490	341	5	applications	application	NOUN
ejpam-5490	341	6	,	,	PUNCT
ejpam-5490	341	7	9:145–159	9:145–159	NUM
ejpam-5490	341	8	,	,	PUNCT
ejpam-5490	341	9	2022	2022	NUM
ejpam-5490	341	10	.	.	PUNCT
ejpam-5490	342	1	[	[	X
ejpam-5490	342	2	8	8	X
ejpam-5490	342	3	]	]	X
ejpam-5490	342	4	p	p	X
ejpam-5490	342	5	v	v	X
ejpam-5490	342	6	venkatanarasimhan	venkatanarasimhan	PROPN
ejpam-5490	342	7	.	.	PUNCT
ejpam-5490	343	1	psuedo	psuedo	ADJ
ejpam-5490	343	2	-	-	PUNCT
ejpam-5490	343	3	complements	complement	NOUN
ejpam-5490	343	4	in	in	ADP
ejpam-5490	343	5	posets	poset	NOUN
ejpam-5490	343	6	.	.	PUNCT
ejpam-5490	344	1	american	american	PROPN
ejpam-5490	344	2	mathematical	mathematical	PROPN
ejpam-5490	344	3	society	society	NOUN
ejpam-5490	344	4	,	,	PUNCT
ejpam-5490	344	5	28:9–17	28:9–17	NUM
ejpam-5490	344	6	,	,	PUNCT
ejpam-5490	344	7	1971	1971	NUM
ejpam-5490	344	8	.	.	PUNCT
ejpam-5490	345	1	introduction	introduction	NOUN
ejpam-5490	345	2	g	g	NOUN
ejpam-5490	345	3	-	-	PUNCT
ejpam-5490	345	4	filters	filter	NOUN
ejpam-5490	345	5	normal	normal	ADJ
ejpam-5490	345	6	g	g	NOUN
ejpam-5490	345	7	-	-	PUNCT
ejpam-5490	345	8	filters	filter	NOUN
ejpam-5490	345	9	generalized	generalize	VERB
ejpam-5490	345	10	complemented	complemented	ADJ
ejpam-5490	345	11	distributive	distributive	ADJ
ejpam-5490	345	12	lattice	lattice	NOUN
ejpam-5490	345	13	conclusions	conclusion	NOUN