id	sid	tid	token	lemma	pos
ejpam-4329	1	1	european	european	PROPN
ejpam-4329	1	2	journal	journal	PROPN
ejpam-4329	1	3	of	of	ADP
ejpam-4329	1	4	pure	pure	ADJ
ejpam-4329	1	5	and	and	CCONJ
ejpam-4329	1	6	applied	apply	VERB
ejpam-4329	1	7	mathematics	mathematic	NOUN
ejpam-4329	1	8	vol	vol	NOUN
ejpam-4329	1	9	.	.	PROPN
ejpam-4329	2	1	15	15	NUM
ejpam-4329	2	2	,	,	PUNCT
ejpam-4329	2	3	no	no	INTJ
ejpam-4329	2	4	.	.	NOUN
ejpam-4329	2	5	2	2	NUM
ejpam-4329	2	6	,	,	PUNCT
ejpam-4329	2	7	2022	2022	NUM
ejpam-4329	2	8	,	,	PUNCT
ejpam-4329	2	9	486	486	NUM
ejpam-4329	2	10	-	-	SYM
ejpam-4329	2	11	495	495	NUM
ejpam-4329	2	12	issn	issn	PROPN
ejpam-4329	2	13	1307	1307	NUM
ejpam-4329	2	14	-	-	SYM
ejpam-4329	2	15	5543	5543	NUM
ejpam-4329	2	16	–	–	PUNCT
ejpam-4329	2	17	ejpam.com	ejpam.com	X
ejpam-4329	2	18	published	publish	VERB
ejpam-4329	2	19	by	by	ADP
ejpam-4329	2	20	new	new	PROPN
ejpam-4329	2	21	york	york	PROPN
ejpam-4329	2	22	business	business	PROPN
ejpam-4329	2	23	global	global	ADJ
ejpam-4329	2	24	closed	close	VERB
ejpam-4329	2	25	ideals	ideal	NOUN
ejpam-4329	2	26	and	and	CCONJ
ejpam-4329	2	27	annihilators	annihilator	NOUN
ejpam-4329	2	28	of	of	ADP
ejpam-4329	2	29	distributive	distributive	ADJ
ejpam-4329	2	30	dual	dual	ADJ
ejpam-4329	2	31	weakly	weakly	ADJ
ejpam-4329	2	32	complemented	complemented	ADJ
ejpam-4329	2	33	lattice	lattice	PROPN
ejpam-4329	2	34	eman	eman	NOUN
ejpam-4329	2	35	ghareeb	ghareeb	NOUN
ejpam-4329	2	36	rezk1,2	rezk1,2	PROPN
ejpam-4329	2	37	1	1	NUM
ejpam-4329	2	38	department	department	NOUN
ejpam-4329	2	39	of	of	ADP
ejpam-4329	2	40	mathematics	mathematic	NOUN
ejpam-4329	2	41	,	,	PUNCT
ejpam-4329	2	42	faculty	faculty	NOUN
ejpam-4329	2	43	of	of	ADP
ejpam-4329	2	44	science	science	NOUN
ejpam-4329	2	45	,	,	PUNCT
ejpam-4329	2	46	tanta	tanta	PROPN
ejpam-4329	2	47	university	university	PROPN
ejpam-4329	2	48	,	,	PUNCT
ejpam-4329	2	49	egypt	egypt	PROPN
ejpam-4329	2	50	2	2	NUM
ejpam-4329	2	51	princess	princess	PROPN
ejpam-4329	2	52	nourah	nourah	PROPN
ejpam-4329	2	53	bint	bint	PROPN
ejpam-4329	2	54	abdulrahman	abdulrahman	PROPN
ejpam-4329	2	55	university	university	PROPN
ejpam-4329	2	56	,	,	PUNCT
ejpam-4329	2	57	p.o.box	p.o.box	PROPN
ejpam-4329	2	58	84428	84428	NUM
ejpam-4329	2	59	,	,	PUNCT
ejpam-4329	2	60	riyadh	riyadh	PROPN
ejpam-4329	2	61	11671	11671	NUM
ejpam-4329	2	62	,	,	PUNCT
ejpam-4329	2	63	saudi	saudi	PROPN
ejpam-4329	2	64	arabia	arabia	PROPN
ejpam-4329	2	65	abstract	abstract	NOUN
ejpam-4329	2	66	.	.	PUNCT
ejpam-4329	3	1	the	the	DET
ejpam-4329	3	2	goal	goal	NOUN
ejpam-4329	3	3	of	of	ADP
ejpam-4329	3	4	this	this	DET
ejpam-4329	3	5	paper	paper	NOUN
ejpam-4329	3	6	is	be	AUX
ejpam-4329	3	7	to	to	PART
ejpam-4329	3	8	study	study	VERB
ejpam-4329	3	9	closed	closed	ADJ
ejpam-4329	3	10	ideals	ideal	NOUN
ejpam-4329	3	11	and	and	CCONJ
ejpam-4329	3	12	annihilators	annihilator	NOUN
ejpam-4329	3	13	over	over	ADP
ejpam-4329	3	14	the	the	DET
ejpam-4329	3	15	class	class	NOUN
ejpam-4329	3	16	of	of	ADP
ejpam-4329	3	17	distributive	distributive	ADJ
ejpam-4329	3	18	dual	dual	ADJ
ejpam-4329	3	19	weakly	weakly	ADJ
ejpam-4329	3	20	complemented	complemented	ADJ
ejpam-4329	3	21	lattices	lattice	NOUN
ejpam-4329	3	22	(	(	PUNCT
ejpam-4329	3	23	ddwcls	ddwcls	NOUN
ejpam-4329	3	24	)	)	PUNCT
ejpam-4329	3	25	.	.	PUNCT
ejpam-4329	4	1	the	the	DET
ejpam-4329	4	2	algebraic	algebraic	ADJ
ejpam-4329	4	3	structure	structure	NOUN
ejpam-4329	4	4	of	of	ADP
ejpam-4329	4	5	ideals	ideal	NOUN
ejpam-4329	4	6	,	,	PUNCT
ejpam-4329	4	7	closed	closed	ADJ
ejpam-4329	4	8	ideals	ideal	NOUN
ejpam-4329	4	9	,	,	PUNCT
ejpam-4329	4	10	and	and	CCONJ
ejpam-4329	4	11	dense	dense	ADJ
ejpam-4329	4	12	ideals	ideal	NOUN
ejpam-4329	4	13	are	be	AUX
ejpam-4329	4	14	shown	show	VERB
ejpam-4329	4	15	.	.	PUNCT
ejpam-4329	5	1	the	the	DET
ejpam-4329	5	2	connection	connection	NOUN
ejpam-4329	5	3	between	between	ADP
ejpam-4329	5	4	closed	close	VERB
ejpam-4329	5	5	ideals	ideal	NOUN
ejpam-4329	5	6	and	and	CCONJ
ejpam-4329	5	7	annihilators	annihilator	NOUN
ejpam-4329	5	8	in	in	ADP
ejpam-4329	5	9	this	this	DET
ejpam-4329	5	10	class	class	NOUN
ejpam-4329	5	11	is	be	AUX
ejpam-4329	5	12	obtained	obtain	VERB
ejpam-4329	5	13	.	.	PUNCT
ejpam-4329	6	1	2020	2020	NUM
ejpam-4329	6	2	mathematics	mathematic	NOUN
ejpam-4329	6	3	subject	subject	NOUN
ejpam-4329	6	4	classifications	classification	NOUN
ejpam-4329	6	5	:	:	PUNCT
ejpam-4329	6	6	06c15	06c15	NOUN
ejpam-4329	6	7	,	,	PUNCT
ejpam-4329	6	8	06b10	06b10	NUM
ejpam-4329	6	9	,	,	PUNCT
ejpam-4329	6	10	06d15	06d15	NUM
ejpam-4329	6	11	,	,	PUNCT
ejpam-4329	6	12	06e75	06e75	NUM
ejpam-4329	6	13	key	key	ADJ
ejpam-4329	6	14	words	word	NOUN
ejpam-4329	6	15	and	and	CCONJ
ejpam-4329	6	16	phrases	phrase	NOUN
ejpam-4329	6	17	:	:	PUNCT
ejpam-4329	6	18	dual	dual	ADJ
ejpam-4329	6	19	weakly	weakly	ADJ
ejpam-4329	6	20	complemented	complemented	ADJ
ejpam-4329	6	21	lattices	lattice	NOUN
ejpam-4329	6	22	,	,	PUNCT
ejpam-4329	6	23	distributive	distributive	ADJ
ejpam-4329	6	24	lattices	lattice	NOUN
ejpam-4329	6	25	,	,	PUNCT
ejpam-4329	6	26	ideals	ideal	NOUN
ejpam-4329	6	27	,	,	PUNCT
ejpam-4329	6	28	annihilators	annihilators	PROPN
ejpam-4329	6	29	1	1	NUM
ejpam-4329	6	30	.	.	PUNCT
ejpam-4329	7	1	introduction	introduction	NOUN
ejpam-4329	7	2	a	a	DET
ejpam-4329	7	3	dual	dual	ADJ
ejpam-4329	7	4	weakly	weakly	ADJ
ejpam-4329	7	5	complemented	complemented	ADJ
ejpam-4329	7	6	lattice	lattice	NOUN
ejpam-4329	7	7	was	be	AUX
ejpam-4329	7	8	introduced	introduce	VERB
ejpam-4329	7	9	by	by	ADP
ejpam-4329	7	10	wille	wille	NOUN
ejpam-4329	7	11	and	and	CCONJ
ejpam-4329	7	12	kwuida	kwuida	PROPN
ejpam-4329	7	13	in[9	in[9	PROPN
ejpam-4329	7	14	]	]	PUNCT
ejpam-4329	7	15	and	and	CCONJ
ejpam-4329	7	16	[	[	X
ejpam-4329	7	17	18	18	NUM
ejpam-4329	7	18	]	]	PUNCT
ejpam-4329	7	19	.	.	PUNCT
ejpam-4329	8	1	it	it	PRON
ejpam-4329	8	2	is	be	AUX
ejpam-4329	8	3	a	a	DET
ejpam-4329	8	4	bounded	bounded	ADJ
ejpam-4329	8	5	lattice	lattice	NOUN
ejpam-4329	8	6	equipped	equip	VERB
ejpam-4329	8	7	with	with	ADP
ejpam-4329	8	8	a	a	DET
ejpam-4329	8	9	unary	unary	ADJ
ejpam-4329	8	10	operation	operation	NOUN
ejpam-4329	8	11	called	call	VERB
ejpam-4329	8	12	a	a	DET
ejpam-4329	8	13	dual	dual	ADJ
ejpam-4329	8	14	weak	weak	ADJ
ejpam-4329	8	15	complementation	complementation	NOUN
ejpam-4329	8	16	.	.	PUNCT
ejpam-4329	9	1	m.mandelker	m.mandelker	ADV
ejpam-4329	9	2	introduced	introduce	VERB
ejpam-4329	9	3	the	the	DET
ejpam-4329	9	4	concept	concept	NOUN
ejpam-4329	9	5	of	of	ADP
ejpam-4329	9	6	annihilator	annihilator	NOUN
ejpam-4329	9	7	in	in	ADP
ejpam-4329	9	8	lattices	lattice	NOUN
ejpam-4329	9	9	in[11	in[11	VERB
ejpam-4329	9	10	]	]	PUNCT
ejpam-4329	9	11	.	.	PUNCT
ejpam-4329	10	1	cornish	cornish	PROPN
ejpam-4329	10	2	defined	define	VERB
ejpam-4329	10	3	an	an	DET
ejpam-4329	10	4	annihilator	annihilator	NOUN
ejpam-4329	10	5	on	on	ADP
ejpam-4329	10	6	a	a	DET
ejpam-4329	10	7	distributive	distributive	ADJ
ejpam-4329	10	8	lattice	lattice	NOUN
ejpam-4329	10	9	in	in	ADP
ejpam-4329	10	10	[	[	X
ejpam-4329	10	11	3	3	NUM
ejpam-4329	10	12	]	]	PUNCT
ejpam-4329	10	13	and	and	CCONJ
ejpam-4329	10	14	[	[	X
ejpam-4329	10	15	4	4	X
ejpam-4329	10	16	]	]	PUNCT
ejpam-4329	10	17	and	and	CCONJ
ejpam-4329	10	18	discussed	discuss	VERB
ejpam-4329	10	19	its	its	PRON
ejpam-4329	10	20	properties	property	NOUN
ejpam-4329	10	21	.	.	PUNCT
ejpam-4329	11	1	later	later	ADV
ejpam-4329	11	2	many	many	ADJ
ejpam-4329	11	3	authors	author	NOUN
ejpam-4329	11	4	discussed	discuss	VERB
ejpam-4329	11	5	the	the	DET
ejpam-4329	11	6	concept	concept	NOUN
ejpam-4329	11	7	of	of	ADP
ejpam-4329	11	8	annihilator	annihilator	NOUN
ejpam-4329	11	9	in	in	ADP
ejpam-4329	11	10	different	different	ADJ
ejpam-4329	11	11	algebraic	algebraic	ADJ
ejpam-4329	11	12	structures	structure	NOUN
ejpam-4329	11	13	and	and	CCONJ
ejpam-4329	11	14	classes	class	NOUN
ejpam-4329	11	15	e.g.[1],[2],[5],[7	e.g.[1],[2],[5],[7	NOUN
ejpam-4329	11	16	]	]	PUNCT
ejpam-4329	11	17	,	,	PUNCT
ejpam-4329	11	18	[	[	X
ejpam-4329	11	19	8	8	NUM
ejpam-4329	11	20	]	]	PUNCT
ejpam-4329	11	21	,	,	PUNCT
ejpam-4329	11	22	[	[	X
ejpam-4329	11	23	10	10	NUM
ejpam-4329	11	24	]	]	PUNCT
ejpam-4329	11	25	,	,	PUNCT
ejpam-4329	11	26	[	[	X
ejpam-4329	11	27	12],[13],[14],[15	12],[13],[14],[15	NUM
ejpam-4329	11	28	]	]	PUNCT
ejpam-4329	11	29	,	,	PUNCT
ejpam-4329	11	30	[	[	X
ejpam-4329	11	31	16	16	NUM
ejpam-4329	11	32	]	]	PUNCT
ejpam-4329	11	33	and	and	CCONJ
ejpam-4329	11	34	[	[	X
ejpam-4329	11	35	17	17	NUM
ejpam-4329	11	36	]	]	PUNCT
ejpam-4329	11	37	.	.	PUNCT
ejpam-4329	12	1	this	this	DET
ejpam-4329	12	2	contribution	contribution	NOUN
ejpam-4329	12	3	connected	connect	VERB
ejpam-4329	12	4	the	the	DET
ejpam-4329	12	5	notion	notion	NOUN
ejpam-4329	12	6	of	of	ADP
ejpam-4329	12	7	annihilators	annihilator	NOUN
ejpam-4329	12	8	of	of	ADP
ejpam-4329	12	9	ddwcl	ddwcl	NOUN
ejpam-4329	12	10	with	with	ADP
ejpam-4329	12	11	a	a	DET
ejpam-4329	12	12	certain	certain	ADJ
ejpam-4329	12	13	type	type	NOUN
ejpam-4329	12	14	of	of	ADP
ejpam-4329	12	15	ideals	ideal	NOUN
ejpam-4329	12	16	is	be	AUX
ejpam-4329	12	17	called	call	VERB
ejpam-4329	12	18	closed	closed	ADJ
ejpam-4329	12	19	ideals	ideal	NOUN
ejpam-4329	12	20	.	.	PUNCT
ejpam-4329	13	1	the	the	DET
ejpam-4329	13	2	given	give	VERB
ejpam-4329	13	3	definition	definition	NOUN
ejpam-4329	13	4	of	of	ADP
ejpam-4329	13	5	closed	closed	ADJ
ejpam-4329	13	6	ideal	ideal	NOUN
ejpam-4329	13	7	depends	depend	VERB
ejpam-4329	13	8	on	on	ADP
ejpam-4329	13	9	the	the	DET
ejpam-4329	13	10	dual	dual	ADJ
ejpam-4329	13	11	weak	weak	ADJ
ejpam-4329	13	12	complementation	complementation	NOUN
ejpam-4329	13	13	operation	operation	NOUN
ejpam-4329	13	14	on	on	ADP
ejpam-4329	13	15	the	the	DET
ejpam-4329	13	16	lattice	lattice	NOUN
ejpam-4329	13	17	of	of	ADP
ejpam-4329	13	18	all	all	DET
ejpam-4329	13	19	ideals	ideal	NOUN
ejpam-4329	13	20	i(l	i(l	PROPN
ejpam-4329	13	21	)	)	PUNCT
ejpam-4329	13	22	of	of	ADP
ejpam-4329	13	23	l.	l.	PROPN
ejpam-4329	13	24	some	some	DET
ejpam-4329	13	25	important	important	ADJ
ejpam-4329	13	26	properties	property	NOUN
ejpam-4329	13	27	of	of	ADP
ejpam-4329	13	28	closed	closed	ADJ
ejpam-4329	13	29	and	and	CCONJ
ejpam-4329	13	30	dense	dense	ADJ
ejpam-4329	13	31	ideals	ideal	NOUN
ejpam-4329	13	32	are	be	AUX
ejpam-4329	13	33	proved	prove	VERB
ejpam-4329	13	34	.	.	PUNCT
ejpam-4329	14	1	a	a	DET
ejpam-4329	14	2	new	new	ADJ
ejpam-4329	14	3	entry	entry	NOUN
ejpam-4329	14	4	to	to	ADP
ejpam-4329	14	5	the	the	DET
ejpam-4329	14	6	concept	concept	NOUN
ejpam-4329	14	7	of	of	ADP
ejpam-4329	14	8	annihilator	annihilator	NOUN
ejpam-4329	14	9	in	in	ADP
ejpam-4329	14	10	the	the	DET
ejpam-4329	14	11	class	class	NOUN
ejpam-4329	14	12	of	of	ADP
ejpam-4329	14	13	ddwcls	ddwcls	NOUN
ejpam-4329	14	14	is	be	AUX
ejpam-4329	14	15	displayed	display	VERB
ejpam-4329	14	16	.	.	PUNCT
ejpam-4329	15	1	after	after	ADP
ejpam-4329	15	2	preliminaries	preliminary	NOUN
ejpam-4329	15	3	in	in	ADP
ejpam-4329	15	4	section	section	NOUN
ejpam-4329	15	5	2	2	NUM
ejpam-4329	15	6	,	,	PUNCT
ejpam-4329	15	7	the	the	DET
ejpam-4329	15	8	definition	definition	NOUN
ejpam-4329	15	9	of	of	ADP
ejpam-4329	15	10	closed	closed	ADJ
ejpam-4329	15	11	and	and	CCONJ
ejpam-4329	15	12	dense	dense	ADJ
ejpam-4329	15	13	ideals	ideal	NOUN
ejpam-4329	15	14	are	be	AUX
ejpam-4329	15	15	given	give	VERB
ejpam-4329	15	16	and	and	CCONJ
ejpam-4329	15	17	some	some	DET
ejpam-4329	15	18	properties	property	NOUN
ejpam-4329	15	19	are	be	AUX
ejpam-4329	15	20	discussed	discuss	VERB
ejpam-4329	15	21	in	in	ADP
ejpam-4329	15	22	section	section	NOUN
ejpam-4329	15	23	3	3	NUM
ejpam-4329	15	24	.	.	PUNCT
ejpam-4329	16	1	in	in	ADP
ejpam-4329	16	2	addition	addition	NOUN
ejpam-4329	16	3	,	,	PUNCT
ejpam-4329	16	4	algebraic	algebraic	ADJ
ejpam-4329	16	5	structures	structure	NOUN
ejpam-4329	16	6	of	of	ADP
ejpam-4329	16	7	them	they	PRON
ejpam-4329	16	8	are	be	AUX
ejpam-4329	16	9	obtained	obtain	VERB
ejpam-4329	16	10	.	.	PUNCT
ejpam-4329	17	1	in	in	ADP
ejpam-4329	17	2	section	section	NOUN
ejpam-4329	17	3	4	4	NUM
ejpam-4329	17	4	,	,	PUNCT
ejpam-4329	17	5	the	the	DET
ejpam-4329	17	6	definition	definition	NOUN
ejpam-4329	17	7	of	of	ADP
ejpam-4329	17	8	a	a	DET
ejpam-4329	17	9	closed	closed	ADJ
ejpam-4329	17	10	annihilator	annihilator	NOUN
ejpam-4329	17	11	is	be	AUX
ejpam-4329	17	12	given	give	VERB
ejpam-4329	17	13	,	,	PUNCT
ejpam-4329	17	14	and	and	CCONJ
ejpam-4329	17	15	we	we	PRON
ejpam-4329	17	16	prove	prove	VERB
ejpam-4329	17	17	that	that	SCONJ
ejpam-4329	17	18	doi	doi	NOUN
ejpam-4329	17	19	:	:	PUNCT
ejpam-4329	17	20	https://doi.org/10.29020/nybg.ejpam.v15i2.4329	https://doi.org/10.29020/nybg.ejpam.v15i2.4329	PROPN
ejpam-4329	17	21	email	email	NOUN
ejpam-4329	17	22	address	address	NOUN
ejpam-4329	17	23	:	:	PUNCT
ejpam-4329	17	24	eman.rezk@science.tanta.edu.eg	eman.rezk@science.tanta.edu.eg	X
ejpam-4329	17	25	(	(	PUNCT
ejpam-4329	17	26	e.	e.	PROPN
ejpam-4329	17	27	g.	g.	PROPN
ejpam-4329	17	28	rezk	rezk	PROPN
ejpam-4329	17	29	)	)	PUNCT
ejpam-4329	17	30	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4329	18	1	486	486	NUM
ejpam-4329	18	2	©	©	PROPN
ejpam-4329	18	3	2022	2022	NUM
ejpam-4329	18	4	ejpam	ejpam	VERB
ejpam-4329	18	5	all	all	DET
ejpam-4329	18	6	rights	right	NOUN
ejpam-4329	18	7	reserved	reserve	VERB
ejpam-4329	18	8	.	.	PUNCT
ejpam-4329	19	1	e.	e.	PROPN
ejpam-4329	19	2	g.	g.	PROPN
ejpam-4329	19	3	rezk	rezk	PROPN
ejpam-4329	19	4	/	/	SYM
ejpam-4329	19	5	eur	eur	PROPN
ejpam-4329	19	6	.	.	PUNCT
ejpam-4329	20	1	j.	j.	PROPN
ejpam-4329	20	2	pure	pure	PROPN
ejpam-4329	20	3	appl	appl	PROPN
ejpam-4329	20	4	.	.	PROPN
ejpam-4329	20	5	math	math	PROPN
ejpam-4329	20	6	,	,	PUNCT
ejpam-4329	20	7	15	15	NUM
ejpam-4329	20	8	(	(	PUNCT
ejpam-4329	20	9	2	2	NUM
ejpam-4329	20	10	)	)	PUNCT
ejpam-4329	20	11	(	(	PUNCT
ejpam-4329	20	12	2022	2022	NUM
ejpam-4329	20	13	)	)	PUNCT
ejpam-4329	20	14	,	,	PUNCT
ejpam-4329	20	15	486	486	NUM
ejpam-4329	20	16	-	-	SYM
ejpam-4329	20	17	495	495	NUM
ejpam-4329	20	18	487	487	NUM
ejpam-4329	20	19	the	the	DET
ejpam-4329	20	20	set	set	NOUN
ejpam-4329	20	21	of	of	ADP
ejpam-4329	20	22	all	all	DET
ejpam-4329	20	23	closed	closed	ADJ
ejpam-4329	20	24	annihilators	annihilators	PROPN
ejpam-4329	20	25	forms	form	VERB
ejpam-4329	20	26	a	a	DET
ejpam-4329	20	27	maximal	maximal	ADJ
ejpam-4329	20	28	boolean	boolean	ADJ
ejpam-4329	20	29	algebra	algebra	NOUN
ejpam-4329	20	30	which	which	PRON
ejpam-4329	20	31	is	be	AUX
ejpam-4329	20	32	contained	contain	VERB
ejpam-4329	20	33	in	in	ADP
ejpam-4329	20	34	the	the	DET
ejpam-4329	20	35	ortho	ortho	PROPN
ejpam-4329	20	36	lattice	lattice	PROPN
ejpam-4329	20	37	s(i(l	s(i(l	PROPN
ejpam-4329	20	38	)	)	PUNCT
ejpam-4329	20	39	)	)	PUNCT
ejpam-4329	20	40	of	of	ADP
ejpam-4329	20	41	closed	closed	ADJ
ejpam-4329	20	42	ideals	ideal	NOUN
ejpam-4329	20	43	of	of	ADP
ejpam-4329	20	44	a	a	DET
ejpam-4329	20	45	ddwcl	ddwcl	NOUN
ejpam-4329	20	46	l.	l.	NOUN
ejpam-4329	20	47	in	in	ADP
ejpam-4329	20	48	the	the	DET
ejpam-4329	20	49	special	special	ADJ
ejpam-4329	20	50	case	case	NOUN
ejpam-4329	20	51	,	,	PUNCT
ejpam-4329	20	52	if	if	SCONJ
ejpam-4329	20	53	the	the	DET
ejpam-4329	20	54	unary	unary	ADJ
ejpam-4329	20	55	operation	operation	NOUN
ejpam-4329	20	56	is	be	AUX
ejpam-4329	20	57	a	a	DET
ejpam-4329	20	58	pseudocomplementation	pseudocomplementation	NOUN
ejpam-4329	20	59	,	,	PUNCT
ejpam-4329	20	60	there	there	PRON
ejpam-4329	20	61	is	be	VERB
ejpam-4329	20	62	a	a	DET
ejpam-4329	20	63	one	one	NUM
ejpam-4329	20	64	-	-	PUNCT
ejpam-4329	20	65	to	to	ADP
ejpam-4329	20	66	-	-	PUNCT
ejpam-4329	20	67	one	one	NUM
ejpam-4329	20	68	corresponding	corresponding	NOUN
ejpam-4329	20	69	between	between	ADP
ejpam-4329	20	70	the	the	DET
ejpam-4329	20	71	annihilators	annihilator	NOUN
ejpam-4329	20	72	and	and	CCONJ
ejpam-4329	20	73	the	the	DET
ejpam-4329	20	74	closed	closed	ADJ
ejpam-4329	20	75	ideals	ideal	NOUN
ejpam-4329	20	76	of	of	ADP
ejpam-4329	20	77	l.	l.	PROPN
ejpam-4329	20	78	2	2	NUM
ejpam-4329	20	79	.	.	PUNCT
ejpam-4329	20	80	preliminaries	preliminary	NOUN
ejpam-4329	20	81	in	in	ADP
ejpam-4329	20	82	this	this	DET
ejpam-4329	20	83	section	section	NOUN
ejpam-4329	20	84	,	,	PUNCT
ejpam-4329	20	85	we	we	PRON
ejpam-4329	20	86	recall	recall	VERB
ejpam-4329	20	87	some	some	DET
ejpam-4329	20	88	basic	basic	ADJ
ejpam-4329	20	89	definitions	definition	NOUN
ejpam-4329	20	90	and	and	CCONJ
ejpam-4329	20	91	results	result	NOUN
ejpam-4329	20	92	that	that	PRON
ejpam-4329	20	93	are	be	AUX
ejpam-4329	20	94	needed	need	VERB
ejpam-4329	20	95	in	in	ADP
ejpam-4329	20	96	the	the	DET
ejpam-4329	20	97	remaining	remain	VERB
ejpam-4329	20	98	parts	part	NOUN
ejpam-4329	20	99	.	.	PUNCT
ejpam-4329	21	1	definition	definition	NOUN
ejpam-4329	21	2	1	1	NUM
ejpam-4329	21	3	.	.	PUNCT
ejpam-4329	22	1	[	[	X
ejpam-4329	22	2	9	9	NUM
ejpam-4329	22	3	]	]	X
ejpam-4329	22	4	a	a	DET
ejpam-4329	22	5	dual	dual	ADJ
ejpam-4329	22	6	weakly	weakly	ADJ
ejpam-4329	22	7	complemented	complemented	ADJ
ejpam-4329	22	8	lattice	lattice	NOUN
ejpam-4329	22	9	is	be	AUX
ejpam-4329	22	10	a	a	DET
ejpam-4329	22	11	bounded	bounded	ADJ
ejpam-4329	22	12	lattice	lattice	PROPN
ejpam-4329	22	13	l	l	PROPN
ejpam-4329	22	14	equipped	equip	VERB
ejpam-4329	22	15	with	with	ADP
ejpam-4329	22	16	one	one	NUM
ejpam-4329	22	17	unary	unary	ADJ
ejpam-4329	22	18	operation	operation	NOUN
ejpam-4329	22	19	h	h	NOUN
ejpam-4329	22	20	called	call	VERB
ejpam-4329	22	21	dual	dual	ADJ
ejpam-4329	22	22	weak	weak	ADJ
ejpam-4329	22	23	complementation	complementation	NOUN
ejpam-4329	22	24	,	,	PUNCT
ejpam-4329	22	25	and	and	CCONJ
ejpam-4329	22	26	satisfied	satisfy	VERB
ejpam-4329	22	27	the	the	DET
ejpam-4329	22	28	following	follow	VERB
ejpam-4329	22	29	conditions	condition	NOUN
ejpam-4329	22	30	for	for	ADP
ejpam-4329	22	31	all	all	DET
ejpam-4329	22	32	a	a	PRON
ejpam-4329	22	33	,	,	PUNCT
ejpam-4329	22	34	b	b	X
ejpam-4329	22	35	∈	∈	PROPN
ejpam-4329	22	36	l	l	NOUN
ejpam-4329	22	37	(	(	PUNCT
ejpam-4329	22	38	1	1	X
ejpam-4329	22	39	)	)	PUNCT
ejpam-4329	22	40	a	a	DET
ejpam-4329	22	41	≤	≤	NUM
ejpam-4329	22	42	ahh	ahh	NOUN
ejpam-4329	22	43	,	,	PUNCT
ejpam-4329	22	44	(	(	PUNCT
ejpam-4329	22	45	2	2	X
ejpam-4329	22	46	)	)	PUNCT
ejpam-4329	22	47	if	if	SCONJ
ejpam-4329	22	48	a	a	DET
ejpam-4329	22	49	≤	≤	NUM
ejpam-4329	22	50	b	b	NOUN
ejpam-4329	22	51	implies	imply	VERB
ejpam-4329	22	52	ah	ah	INTJ
ejpam-4329	22	53	≥	≥	NUM
ejpam-4329	22	54	bh	bh	NOUN
ejpam-4329	22	55	,	,	PUNCT
ejpam-4329	22	56	(	(	PUNCT
ejpam-4329	22	57	3	3	X
ejpam-4329	22	58	)	)	PUNCT
ejpam-4329	22	59	(	(	PUNCT
ejpam-4329	22	60	a	a	DET
ejpam-4329	22	61	∨	∨	NUM
ejpam-4329	22	62	b	b	NOUN
ejpam-4329	22	63	)	)	PUNCT
ejpam-4329	22	64	∧	∧	NOUN
ejpam-4329	22	65	(	(	PUNCT
ejpam-4329	22	66	a	a	DET
ejpam-4329	22	67	∨	∨	NUM
ejpam-4329	22	68	bh	bh	NOUN
ejpam-4329	22	69	)	)	PUNCT
ejpam-4329	22	70	=	=	SYM
ejpam-4329	22	71	a.	a.	NOUN
ejpam-4329	22	72	in	in	ADP
ejpam-4329	22	73	a	a	DET
ejpam-4329	22	74	distributive	distributive	ADJ
ejpam-4329	22	75	lattice	lattice	NOUN
ejpam-4329	22	76	,	,	PUNCT
ejpam-4329	22	77	the	the	DET
ejpam-4329	22	78	condition	condition	NOUN
ejpam-4329	22	79	(	(	PUNCT
ejpam-4329	22	80	3	3	X
ejpam-4329	22	81	)	)	PUNCT
ejpam-4329	22	82	becomes	become	VERB
ejpam-4329	22	83	a	a	DET
ejpam-4329	22	84	∧	∧	PROPN
ejpam-4329	22	85	ah	ah	INTJ
ejpam-4329	22	86	=	=	NOUN
ejpam-4329	22	87	0	0	PROPN
ejpam-4329	22	88	.	.	PUNCT
ejpam-4329	23	1	the	the	DET
ejpam-4329	23	2	trivial	trivial	ADJ
ejpam-4329	23	3	dual	dual	ADJ
ejpam-4329	23	4	weakly	weakly	ADJ
ejpam-4329	23	5	complemented	complemented	ADJ
ejpam-4329	23	6	lattice	lattice	NOUN
ejpam-4329	23	7	is	be	AUX
ejpam-4329	23	8	the	the	DET
ejpam-4329	23	9	lattice	lattice	NOUN
ejpam-4329	23	10	in	in	ADP
ejpam-4329	23	11	which	which	PRON
ejpam-4329	23	12	every	every	DET
ejpam-4329	23	13	dual	dual	ADJ
ejpam-4329	23	14	weak	weak	ADJ
ejpam-4329	23	15	complementation	complementation	NOUN
ejpam-4329	23	16	of	of	ADP
ejpam-4329	23	17	any	any	DET
ejpam-4329	23	18	non	non	ADJ
ejpam-4329	23	19	-	-	ADJ
ejpam-4329	23	20	zero	zero	NUM
ejpam-4329	23	21	element	element	NOUN
ejpam-4329	23	22	is	be	AUX
ejpam-4329	23	23	zero	zero	NUM
ejpam-4329	23	24	.	.	PUNCT
ejpam-4329	24	1	a	a	DET
ejpam-4329	24	2	distributive	distributive	ADJ
ejpam-4329	24	3	pseudocomplemented	pseudocomplemented	ADJ
ejpam-4329	24	4	lattice	lattice	NOUN
ejpam-4329	24	5	(	(	PUNCT
ejpam-4329	24	6	p	p	NOUN
ejpam-4329	24	7	-	-	PUNCT
ejpam-4329	24	8	algebra	algebra	NOUN
ejpam-4329	24	9	)	)	PUNCT
ejpam-4329	24	10	is	be	AUX
ejpam-4329	24	11	an	an	DET
ejpam-4329	24	12	algebra	algebra	NOUN
ejpam-4329	24	13	<	<	X
ejpam-4329	24	14	l;∧,∨,∗	l;∧,∨,∗	NOUN
ejpam-4329	24	15	,	,	PUNCT
ejpam-4329	24	16	0	0	NUM
ejpam-4329	24	17	,	,	PUNCT
ejpam-4329	24	18	1	1	NUM
ejpam-4329	24	19	>	>	PUNCT
ejpam-4329	24	20	,	,	PUNCT
ejpam-4329	24	21	where	where	SCONJ
ejpam-4329	24	22	<	<	X
ejpam-4329	24	23	l;∧,∨	l;∧,∨	NOUN
ejpam-4329	24	24	,	,	PUNCT
ejpam-4329	24	25	0	0	NUM
ejpam-4329	24	26	,	,	PUNCT
ejpam-4329	24	27	1	1	NUM
ejpam-4329	24	28	>	>	X
ejpam-4329	24	29	is	be	AUX
ejpam-4329	24	30	a	a	DET
ejpam-4329	24	31	bounded	bounded	ADJ
ejpam-4329	24	32	distributive	distributive	ADJ
ejpam-4329	24	33	lattice	lattice	NOUN
ejpam-4329	24	34	and	and	CCONJ
ejpam-4329	24	35	the	the	DET
ejpam-4329	24	36	unary	unary	ADJ
ejpam-4329	24	37	operation	operation	NOUN
ejpam-4329	24	38	∗	∗	NOUN
ejpam-4329	24	39	is	be	AUX
ejpam-4329	24	40	defined	define	VERB
ejpam-4329	24	41	by	by	ADP
ejpam-4329	24	42	:	:	PUNCT
ejpam-4329	24	43	x	x	SYM
ejpam-4329	24	44	≤	≤	ADJ
ejpam-4329	24	45	a∗	a∗	PROPN
ejpam-4329	24	46	iff	iff	PROPN
ejpam-4329	24	47	x	x	PROPN
ejpam-4329	24	48	∧	∧	PROPN
ejpam-4329	24	49	a	a	PRON
ejpam-4329	24	50	=	=	SYM
ejpam-4329	24	51	0	0	NUM
ejpam-4329	24	52	,	,	PUNCT
ejpam-4329	24	53	a	a	DET
ejpam-4329	24	54	∈	∈	PROPN
ejpam-4329	24	55	l.	l.	NOUN
ejpam-4329	24	56	the	the	DET
ejpam-4329	24	57	operation	operation	NOUN
ejpam-4329	24	58	∗	∗	NOUN
ejpam-4329	24	59	is	be	AUX
ejpam-4329	24	60	called	call	VERB
ejpam-4329	24	61	pseudocomplementation	pseudocomplementation	NOUN
ejpam-4329	24	62	on	on	ADP
ejpam-4329	24	63	l.	l.	NOUN
ejpam-4329	24	64	the	the	DET
ejpam-4329	24	65	distributive	distributive	ADJ
ejpam-4329	24	66	pseudocomplemented	pseudocomplemente	VERB
ejpam-4329	24	67	lattice	lattice	NOUN
ejpam-4329	24	68	is	be	AUX
ejpam-4329	24	69	a	a	DET
ejpam-4329	24	70	perfect	perfect	ADJ
ejpam-4329	24	71	example	example	NOUN
ejpam-4329	24	72	of	of	ADP
ejpam-4329	24	73	the	the	DET
ejpam-4329	24	74	distributive	distributive	ADJ
ejpam-4329	24	75	dual	dual	ADJ
ejpam-4329	24	76	weakly	weakly	ADJ
ejpam-4329	24	77	complemented	complemented	ADJ
ejpam-4329	24	78	lattice	lattice	NOUN
ejpam-4329	24	79	.	.	PUNCT
ejpam-4329	25	1	some	some	DET
ejpam-4329	25	2	properties	property	NOUN
ejpam-4329	25	3	of	of	ADP
ejpam-4329	25	4	the	the	DET
ejpam-4329	25	5	operation	operation	NOUN
ejpam-4329	25	6	h	h	NOUN
ejpam-4329	25	7	are	be	AUX
ejpam-4329	25	8	listed	list	VERB
ejpam-4329	25	9	in	in	ADP
ejpam-4329	25	10	the	the	DET
ejpam-4329	25	11	following	follow	VERB
ejpam-4329	25	12	theorem	theorem	PROPN
ejpam-4329	25	13	.	.	PUNCT
ejpam-4329	25	14	theorem	theorem	NOUN
ejpam-4329	25	15	1	1	NUM
ejpam-4329	25	16	.	.	PUNCT
ejpam-4329	26	1	[	[	X
ejpam-4329	26	2	9	9	NUM
ejpam-4329	26	3	]	]	PUNCT
ejpam-4329	26	4	for	for	ADP
ejpam-4329	26	5	any	any	DET
ejpam-4329	26	6	a	a	DET
ejpam-4329	26	7	,	,	PUNCT
ejpam-4329	26	8	b	b	PROPN
ejpam-4329	26	9	of	of	ADP
ejpam-4329	26	10	dual	dual	ADJ
ejpam-4329	26	11	weakly	weakly	ADJ
ejpam-4329	26	12	complemented	complemented	ADJ
ejpam-4329	26	13	lattices	lattice	NOUN
ejpam-4329	26	14	l	l	NOUN
ejpam-4329	26	15	,	,	PUNCT
ejpam-4329	26	16	we	we	PRON
ejpam-4329	26	17	have	have	VERB
ejpam-4329	26	18	the	the	DET
ejpam-4329	26	19	following	following	NOUN
ejpam-4329	26	20	:	:	PUNCT
ejpam-4329	26	21	(	(	PUNCT
ejpam-4329	26	22	1	1	X
ejpam-4329	26	23	)	)	PUNCT
ejpam-4329	26	24	0h	0h	NOUN
ejpam-4329	26	25	=	=	SYM
ejpam-4329	26	26	1	1	NUM
ejpam-4329	26	27	,	,	PUNCT
ejpam-4329	26	28	1h	1h	NUM
ejpam-4329	26	29	=	=	SYM
ejpam-4329	26	30	0	0	NUM
ejpam-4329	26	31	,	,	PUNCT
ejpam-4329	26	32	(	(	PUNCT
ejpam-4329	26	33	2	2	X
ejpam-4329	26	34	)	)	PUNCT
ejpam-4329	26	35	ahhh	ahhh	INTJ
ejpam-4329	27	1	=	=	SYM
ejpam-4329	27	2	ah	ah	INTJ
ejpam-4329	27	3	,	,	PUNCT
ejpam-4329	27	4	(	(	PUNCT
ejpam-4329	27	5	3	3	X
ejpam-4329	27	6	)	)	PUNCT
ejpam-4329	27	7	(	(	PUNCT
ejpam-4329	27	8	a	a	DET
ejpam-4329	27	9	∨	∨	NOUN
ejpam-4329	27	10	ah)h	ah)h	X
ejpam-4329	27	11	=	=	SYM
ejpam-4329	27	12	0	0	NUM
ejpam-4329	27	13	,	,	PUNCT
ejpam-4329	27	14	(	(	PUNCT
ejpam-4329	27	15	4	4	X
ejpam-4329	27	16	)	)	PUNCT
ejpam-4329	27	17	ah	ah	INTJ
ejpam-4329	27	18	≥	≥	NUM
ejpam-4329	27	19	b	b	X
ejpam-4329	27	20	iff	iff	PROPN
ejpam-4329	27	21	bh	bh	PROPN
ejpam-4329	27	22	≥	≥	PROPN
ejpam-4329	27	23	a	a	PROPN
ejpam-4329	27	24	,	,	PUNCT
ejpam-4329	27	25	(	(	PUNCT
ejpam-4329	27	26	5	5	NUM
ejpam-4329	27	27	)	)	PUNCT
ejpam-4329	27	28	(	(	PUNCT
ejpam-4329	27	29	a	a	DET
ejpam-4329	27	30	∨	∨	NOUN
ejpam-4329	27	31	b)h	b)h	X
ejpam-4329	27	32	=	=	PUNCT
ejpam-4329	27	33	ah	ah	INTJ
ejpam-4329	27	34	∧	∧	PROPN
ejpam-4329	27	35	bh	bh	NOUN
ejpam-4329	27	36	,	,	PUNCT
ejpam-4329	27	37	(	(	PUNCT
ejpam-4329	27	38	6	6	NUM
ejpam-4329	27	39	)	)	PUNCT
ejpam-4329	27	40	(	(	PUNCT
ejpam-4329	27	41	a	a	DET
ejpam-4329	27	42	∨	∨	NUM
ejpam-4329	27	43	b)hh	b)hh	PROPN
ejpam-4329	27	44	≥	≥	NUM
ejpam-4329	27	45	ahh	ahh	NOUN
ejpam-4329	27	46	∨	∨	NUM
ejpam-4329	27	47	bhh	bhh	PROPN
ejpam-4329	27	48	,	,	PUNCT
ejpam-4329	27	49	(	(	PUNCT
ejpam-4329	27	50	7	7	X
ejpam-4329	27	51	)	)	PUNCT
ejpam-4329	27	52	a	a	DET
ejpam-4329	27	53	∨	∨	NUM
ejpam-4329	27	54	bh	bh	PROPN
ejpam-4329	27	55	≥	≥	PROPN
ejpam-4329	27	56	b	b	PROPN
ejpam-4329	27	57	iff	iff	PROPN
ejpam-4329	27	58	a	a	DET
ejpam-4329	27	59	≥	≥	NOUN
ejpam-4329	27	60	b	b	NOUN
ejpam-4329	27	61	,	,	PUNCT
ejpam-4329	27	62	(	(	PUNCT
ejpam-4329	27	63	8)	8)	NUM
ejpam-4329	27	64	if	if	SCONJ
ejpam-4329	27	65	ah	ah	INTJ
ejpam-4329	27	66	≥	≥	X
ejpam-4329	27	67	b	b	NOUN
ejpam-4329	27	68	then	then	ADV
ejpam-4329	27	69	a	a	DET
ejpam-4329	27	70	∧	∧	PROPN
ejpam-4329	27	71	b	b	PROPN
ejpam-4329	27	72	=	=	SYM
ejpam-4329	27	73	0	0	PROPN
ejpam-4329	27	74	,	,	PUNCT
ejpam-4329	27	75	(	(	PUNCT
ejpam-4329	27	76	9	9	X
ejpam-4329	27	77	)	)	PUNCT
ejpam-4329	27	78	tf	tf	NOUN
ejpam-4329	27	79	a	a	DET
ejpam-4329	27	80	∨	∨	NUM
ejpam-4329	27	81	b	b	NOUN
ejpam-4329	27	82	=	=	SYM
ejpam-4329	27	83	1	1	NUM
ejpam-4329	27	84	then	then	ADV
ejpam-4329	27	85	bh	bh	PROPN
ejpam-4329	27	86	≤	≤	PROPN
ejpam-4329	27	87	a	a	PRON
ejpam-4329	27	88	,	,	PUNCT
ejpam-4329	27	89	(	(	PUNCT
ejpam-4329	27	90	10	10	NUM
ejpam-4329	27	91	)	)	PUNCT
ejpam-4329	27	92	if	if	SCONJ
ejpam-4329	27	93	a	a	DET
ejpam-4329	27	94	∨	∨	NOUN
ejpam-4329	27	95	ah	ah	INTJ
ejpam-4329	27	96	=	=	NOUN
ejpam-4329	27	97	1	1	NUM
ejpam-4329	27	98	then	then	ADV
ejpam-4329	27	99	a	a	DET
ejpam-4329	27	100	=	=	SYM
ejpam-4329	27	101	ahh	ahh	PROPN
ejpam-4329	27	102	,	,	PUNCT
ejpam-4329	27	103	(	(	PUNCT
ejpam-4329	27	104	11	11	NUM
ejpam-4329	27	105	)	)	PUNCT
ejpam-4329	27	106	a	a	DET
ejpam-4329	27	107	∧	∧	PROPN
ejpam-4329	27	108	(	(	PUNCT
ejpam-4329	27	109	a	a	DET
ejpam-4329	27	110	∧	∧	PROPN
ejpam-4329	27	111	b)h	b)h	X
ejpam-4329	27	112	≥	≥	NOUN
ejpam-4329	27	113	a	a	DET
ejpam-4329	27	114	∧	∧	PROPN
ejpam-4329	27	115	bh	bh	PROPN
ejpam-4329	27	116	.	.	PROPN
ejpam-4329	27	117	e.	e.	PROPN
ejpam-4329	27	118	g.	g.	PROPN
ejpam-4329	27	119	rezk	rezk	PROPN
ejpam-4329	27	120	/	/	SYM
ejpam-4329	27	121	eur	eur	PROPN
ejpam-4329	27	122	.	.	PUNCT
ejpam-4329	28	1	j.	j.	PROPN
ejpam-4329	28	2	pure	pure	PROPN
ejpam-4329	28	3	appl	appl	PROPN
ejpam-4329	28	4	.	.	PROPN
ejpam-4329	28	5	math	math	PROPN
ejpam-4329	28	6	,	,	PUNCT
ejpam-4329	28	7	15	15	NUM
ejpam-4329	28	8	(	(	PUNCT
ejpam-4329	28	9	2	2	NUM
ejpam-4329	28	10	)	)	PUNCT
ejpam-4329	28	11	(	(	PUNCT
ejpam-4329	28	12	2022	2022	NUM
ejpam-4329	28	13	)	)	PUNCT
ejpam-4329	28	14	,	,	PUNCT
ejpam-4329	28	15	486	486	NUM
ejpam-4329	28	16	-	-	SYM
ejpam-4329	28	17	495	495	NUM
ejpam-4329	28	18	488	488	NUM
ejpam-4329	28	19	definition	definition	NOUN
ejpam-4329	28	20	2	2	NUM
ejpam-4329	28	21	.	.	PUNCT
ejpam-4329	29	1	[	[	X
ejpam-4329	29	2	6	6	NUM
ejpam-4329	29	3	]	]	PUNCT
ejpam-4329	29	4	an	an	DET
ejpam-4329	29	5	orthocomplemented	orthocomplemented	ADJ
ejpam-4329	29	6	lattice	lattice	NOUN
ejpam-4329	29	7	(	(	PUNCT
ejpam-4329	29	8	ortho	ortho	PROPN
ejpam-4329	29	9	lattice	lattice	PROPN
ejpam-4329	29	10	)	)	PUNCT
ejpam-4329	29	11	is	be	AUX
ejpam-4329	29	12	a	a	DET
ejpam-4329	29	13	bounded	bounded	ADJ
ejpam-4329	29	14	lattice	lattice	NOUN
ejpam-4329	29	15	<	<	X
ejpam-4329	29	16	l;∧,∨	l;∧,∨	PROPN
ejpam-4329	29	17	>	>	X
ejpam-4329	29	18	equipped	equip	VERB
ejpam-4329	29	19	with	with	ADP
ejpam-4329	29	20	one	one	NUM
ejpam-4329	29	21	unary	unary	ADJ
ejpam-4329	29	22	operation	operation	NOUN
ejpam-4329	29	23	⊥	⊥	NOUN
ejpam-4329	29	24	called	call	VERB
ejpam-4329	29	25	orthocomplementation	orthocomplementation	NOUN
ejpam-4329	29	26	on	on	ADP
ejpam-4329	29	27	l	l	PROPN
ejpam-4329	29	28	and	and	CCONJ
ejpam-4329	29	29	satisfied	satisfy	VERB
ejpam-4329	29	30	the	the	DET
ejpam-4329	29	31	following	follow	VERB
ejpam-4329	29	32	conditions	condition	NOUN
ejpam-4329	29	33	,	,	PUNCT
ejpam-4329	29	34	for	for	SCONJ
ejpam-4329	29	35	all	all	DET
ejpam-4329	29	36	a	a	DET
ejpam-4329	29	37	,	,	PUNCT
ejpam-4329	29	38	b	b	X
ejpam-4329	29	39	∈	∈	PROPN
ejpam-4329	29	40	l	l	NOUN
ejpam-4329	29	41	(	(	PUNCT
ejpam-4329	29	42	i	i	NOUN
ejpam-4329	29	43	)	)	PUNCT
ejpam-4329	29	44	a	a	DET
ejpam-4329	29	45	≤	≤	PROPN
ejpam-4329	29	46	b	b	NOUN
ejpam-4329	29	47	implies	imply	VERB
ejpam-4329	29	48	a⊥	a⊥	NOUN
ejpam-4329	29	49	≥	≥	PRON
ejpam-4329	29	50	b⊥	b⊥	PROPN
ejpam-4329	29	51	,	,	PUNCT
ejpam-4329	29	52	(	(	PUNCT
ejpam-4329	29	53	ii	ii	NOUN
ejpam-4329	29	54	)	)	PUNCT
ejpam-4329	29	55	a⊥⊥	a⊥⊥	PROPN
ejpam-4329	29	56	=	=	PUNCT
ejpam-4329	29	57	a	a	PROPN
ejpam-4329	29	58	,	,	PUNCT
ejpam-4329	29	59	(	(	PUNCT
ejpam-4329	29	60	iii	iii	NOUN
ejpam-4329	29	61	)	)	PUNCT
ejpam-4329	29	62	a	a	DET
ejpam-4329	29	63	∧	∧	NOUN
ejpam-4329	29	64	a⊥	a⊥	NOUN
ejpam-4329	29	65	=	=	SYM
ejpam-4329	29	66	0	0	NUM
ejpam-4329	29	67	and	and	CCONJ
ejpam-4329	29	68	a	a	DET
ejpam-4329	29	69	∨	∨	NOUN
ejpam-4329	29	70	a⊥	a⊥	NOUN
ejpam-4329	29	71	=	=	PUNCT
ejpam-4329	29	72	1	1	X
ejpam-4329	29	73	.	.	X
ejpam-4329	29	74	a	a	DET
ejpam-4329	29	75	distributive	distributive	ADJ
ejpam-4329	29	76	ortho	ortho	PROPN
ejpam-4329	29	77	lattice	lattice	PROPN
ejpam-4329	29	78	is	be	AUX
ejpam-4329	29	79	a	a	DET
ejpam-4329	29	80	boolean	boolean	ADJ
ejpam-4329	29	81	algebra	algebra	NOUN
ejpam-4329	29	82	.	.	PUNCT
ejpam-4329	30	1	the	the	DET
ejpam-4329	30	2	skeleton	skeleton	NOUN
ejpam-4329	30	3	of	of	ADP
ejpam-4329	30	4	dual	dual	ADJ
ejpam-4329	30	5	weakly	weakly	ADJ
ejpam-4329	30	6	complemented	complemented	ADJ
ejpam-4329	30	7	lattice	lattice	NOUN
ejpam-4329	30	8	l	l	NOUN
ejpam-4329	30	9	is	be	AUX
ejpam-4329	30	10	defined	define	VERB
ejpam-4329	30	11	by	by	ADP
ejpam-4329	30	12	s(l	s(l	NUM
ejpam-4329	30	13	)	)	PUNCT
ejpam-4329	30	14	=	=	PRON
ejpam-4329	30	15	{	{	PUNCT
ejpam-4329	30	16	a	a	DET
ejpam-4329	30	17	∈	∈	ADJ
ejpam-4329	30	18	l	l	NOUN
ejpam-4329	30	19	:	:	PUNCT
ejpam-4329	30	20	a	a	PRON
ejpam-4329	30	21	=	=	X
ejpam-4329	30	22	ahh	ahh	NOUN
ejpam-4329	30	23	}	}	PUNCT
ejpam-4329	30	24	.	.	PUNCT
ejpam-4329	31	1	it	it	PRON
ejpam-4329	31	2	forms	form	VERB
ejpam-4329	31	3	an	an	DET
ejpam-4329	31	4	ortho	ortho	PROPN
ejpam-4329	31	5	lattice	lattice	PROPN
ejpam-4329	31	6	with	with	ADP
ejpam-4329	31	7	the	the	DET
ejpam-4329	31	8	same	same	ADJ
ejpam-4329	31	9	meet	meet	NOUN
ejpam-4329	31	10	operation	operation	NOUN
ejpam-4329	31	11	of	of	ADP
ejpam-4329	31	12	l	l	NOUN
ejpam-4329	31	13	and	and	CCONJ
ejpam-4329	31	14	join	join	VERB
ejpam-4329	31	15	”	"	PUNCT
ejpam-4329	31	16	y	y	PROPN
ejpam-4329	31	17	”	"	PUNCT
ejpam-4329	31	18	operation	operation	NOUN
ejpam-4329	31	19	defined	define	VERB
ejpam-4329	31	20	as	as	ADP
ejpam-4329	31	21	:	:	PUNCT
ejpam-4329	31	22	a	a	DET
ejpam-4329	31	23	y	y	PROPN
ejpam-4329	31	24	b	b	PROPN
ejpam-4329	31	25	=	=	PRON
ejpam-4329	31	26	(	(	PUNCT
ejpam-4329	31	27	ah	ah	INTJ
ejpam-4329	31	28	∧	∧	PROPN
ejpam-4329	31	29	bh)h	bh)h	PROPN
ejpam-4329	31	30	,	,	PUNCT
ejpam-4329	31	31	for	for	ADP
ejpam-4329	31	32	any	any	DET
ejpam-4329	31	33	a	a	DET
ejpam-4329	31	34	,	,	PUNCT
ejpam-4329	31	35	b	b	PROPN
ejpam-4329	31	36	∈	∈	PROPN
ejpam-4329	31	37	s(l	s(l	NUM
ejpam-4329	31	38	)	)	PUNCT
ejpam-4329	31	39	.	.	PUNCT
ejpam-4329	32	1	the	the	DET
ejpam-4329	32	2	dual	dual	ADJ
ejpam-4329	32	3	weak	weak	ADJ
ejpam-4329	32	4	complemented	complemented	NOUN
ejpam-4329	32	5	of	of	ADP
ejpam-4329	32	6	an	an	DET
ejpam-4329	32	7	element	element	NOUN
ejpam-4329	32	8	a	a	DET
ejpam-4329	32	9	∈	∈	PROPN
ejpam-4329	32	10	s(l	s(l	NUM
ejpam-4329	32	11	)	)	PUNCT
ejpam-4329	32	12	is	be	AUX
ejpam-4329	32	13	its	its	PRON
ejpam-4329	32	14	orthocomplemented	orthocomplemente	VERB
ejpam-4329	32	15	in	in	ADP
ejpam-4329	32	16	s(l	s(l	NUM
ejpam-4329	32	17	)	)	PUNCT
ejpam-4329	32	18	.	.	PUNCT
ejpam-4329	33	1	the	the	DET
ejpam-4329	33	2	set	set	NOUN
ejpam-4329	33	3	d(l	d(l	NOUN
ejpam-4329	33	4	)	)	PUNCT
ejpam-4329	33	5	of	of	ADP
ejpam-4329	33	6	dense	dense	ADJ
ejpam-4329	33	7	element	element	NOUN
ejpam-4329	33	8	of	of	ADP
ejpam-4329	33	9	l	l	NOUN
ejpam-4329	33	10	defined	define	VERB
ejpam-4329	33	11	as	as	ADP
ejpam-4329	33	12	d(l	d(l	ADJ
ejpam-4329	33	13	)	)	PUNCT
ejpam-4329	33	14	=	=	SYM
ejpam-4329	33	15	{	{	PUNCT
ejpam-4329	33	16	x	x	PUNCT
ejpam-4329	33	17	∈	∈	PROPN
ejpam-4329	33	18	l	l	NOUN
ejpam-4329	33	19	:	:	PUNCT
ejpam-4329	33	20	xh	xh	PROPN
ejpam-4329	33	21	=	=	PROPN
ejpam-4329	33	22	0	0	NUM
ejpam-4329	33	23	}	}	PUNCT
ejpam-4329	33	24	.	.	PUNCT
ejpam-4329	34	1	refer	refer	VERB
ejpam-4329	34	2	to	to	ADP
ejpam-4329	34	3	[	[	X
ejpam-4329	34	4	9	9	NUM
ejpam-4329	34	5	]	]	PUNCT
ejpam-4329	34	6	.	.	PUNCT
ejpam-4329	35	1	definition	definition	NOUN
ejpam-4329	35	2	3	3	NUM
ejpam-4329	35	3	.	.	PUNCT
ejpam-4329	36	1	[	[	X
ejpam-4329	36	2	6	6	NUM
ejpam-4329	36	3	]	]	PUNCT
ejpam-4329	36	4	a	a	DET
ejpam-4329	36	5	non	non	ADJ
ejpam-4329	36	6	-	-	ADJ
ejpam-4329	36	7	empty	empty	ADJ
ejpam-4329	36	8	subset	subset	NOUN
ejpam-4329	36	9	i	i	PRON
ejpam-4329	36	10	of	of	ADP
ejpam-4329	36	11	a	a	DET
ejpam-4329	36	12	lattice	lattice	NOUN
ejpam-4329	36	13	l	l	NOUN
ejpam-4329	36	14	is	be	AUX
ejpam-4329	36	15	called	call	VERB
ejpam-4329	36	16	an	an	DET
ejpam-4329	36	17	ideal	ideal	NOUN
ejpam-4329	36	18	of	of	ADP
ejpam-4329	36	19	l	l	NOUN
ejpam-4329	36	20	if	if	SCONJ
ejpam-4329	36	21	(	(	PUNCT
ejpam-4329	36	22	i	i	NOUN
ejpam-4329	36	23	)	)	PUNCT
ejpam-4329	36	24	a	a	PRON
ejpam-4329	36	25	,	,	PUNCT
ejpam-4329	36	26	b	b	X
ejpam-4329	36	27	∈	∈	PROPN
ejpam-4329	36	28	i	i	PRON
ejpam-4329	36	29	implies	imply	VERB
ejpam-4329	36	30	a	a	DET
ejpam-4329	36	31	∨	∨	NUM
ejpam-4329	36	32	b	b	X
ejpam-4329	36	33	∈	∈	PROPN
ejpam-4329	36	34	i	i	PRON
ejpam-4329	36	35	,	,	PUNCT
ejpam-4329	36	36	(	(	PUNCT
ejpam-4329	36	37	ii	ii	NOUN
ejpam-4329	36	38	)	)	PUNCT
ejpam-4329	36	39	a	a	DET
ejpam-4329	36	40	∈	∈	PROPN
ejpam-4329	36	41	l	l	NOUN
ejpam-4329	36	42	,	,	PUNCT
ejpam-4329	36	43	b	b	X
ejpam-4329	36	44	∈	∈	PROPN
ejpam-4329	36	45	i	i	PRON
ejpam-4329	36	46	and	and	CCONJ
ejpam-4329	36	47	a	a	DET
ejpam-4329	36	48	≤	≤	NUM
ejpam-4329	36	49	b	b	NOUN
ejpam-4329	36	50	implies	imply	VERB
ejpam-4329	36	51	a	a	DET
ejpam-4329	36	52	∈	∈	PROPN
ejpam-4329	36	53	i.	i.	NOUN
ejpam-4329	36	54	the	the	DET
ejpam-4329	36	55	ideal	ideal	NOUN
ejpam-4329	36	56	(	(	PUNCT
ejpam-4329	36	57	a	a	X
ejpam-4329	36	58	]	]	X
ejpam-4329	36	59	=	=	SYM
ejpam-4329	36	60	{	{	PUNCT
ejpam-4329	36	61	x	x	PUNCT
ejpam-4329	36	62	∈	∈	NOUN
ejpam-4329	36	63	l	l	NOUN
ejpam-4329	36	64	:	:	PUNCT
ejpam-4329	36	65	x	x	SYM
ejpam-4329	36	66	≤	≤	ADV
ejpam-4329	36	67	a	a	PRON
ejpam-4329	36	68	}	}	PUNCT
ejpam-4329	36	69	is	be	AUX
ejpam-4329	36	70	called	call	VERB
ejpam-4329	36	71	the	the	DET
ejpam-4329	36	72	principal	principal	ADJ
ejpam-4329	36	73	ideal	ideal	NOUN
ejpam-4329	36	74	generated	generate	VERB
ejpam-4329	36	75	by	by	ADP
ejpam-4329	36	76	a	a	DET
ejpam-4329	36	77	∈	∈	PROPN
ejpam-4329	36	78	l.	l.	NOUN
ejpam-4329	36	79	let	let	VERB
ejpam-4329	36	80	i(l	i(l	PROPN
ejpam-4329	36	81	)	)	PUNCT
ejpam-4329	36	82	be	be	AUX
ejpam-4329	36	83	the	the	DET
ejpam-4329	36	84	set	set	NOUN
ejpam-4329	36	85	of	of	ADP
ejpam-4329	36	86	all	all	DET
ejpam-4329	36	87	ideals	ideal	NOUN
ejpam-4329	36	88	of	of	ADP
ejpam-4329	36	89	l	l	NOUN
ejpam-4329	36	90	under	under	ADP
ejpam-4329	36	91	set	set	VERB
ejpam-4329	36	92	inclusion	inclusion	NOUN
ejpam-4329	36	93	forms	form	NOUN
ejpam-4329	36	94	a	a	DET
ejpam-4329	36	95	complete	complete	ADJ
ejpam-4329	36	96	lattice	lattice	NOUN
ejpam-4329	36	97	with	with	ADP
ejpam-4329	36	98	the	the	DET
ejpam-4329	36	99	smallest	small	ADJ
ejpam-4329	36	100	element	element	NOUN
ejpam-4329	36	101	(	(	PUNCT
ejpam-4329	36	102	0	0	NUM
ejpam-4329	36	103	]	]	X
ejpam-4329	36	104	=	=	X
ejpam-4329	36	105	{	{	PUNCT
ejpam-4329	36	106	0	0	NUM
ejpam-4329	36	107	}	}	PUNCT
ejpam-4329	36	108	and	and	CCONJ
ejpam-4329	36	109	the	the	DET
ejpam-4329	36	110	largest	large	ADJ
ejpam-4329	36	111	element	element	NOUN
ejpam-4329	36	112	(	(	PUNCT
ejpam-4329	36	113	1	1	NUM
ejpam-4329	36	114	]	]	PUNCT
ejpam-4329	36	115	=	=	PUNCT
ejpam-4329	36	116	l.	l.	NOUN
ejpam-4329	36	117	for	for	ADP
ejpam-4329	36	118	any	any	DET
ejpam-4329	36	119	i	i	PROPN
ejpam-4329	36	120	,	,	PUNCT
ejpam-4329	36	121	k	k	PROPN
ejpam-4329	36	122	∈	∈	PROPN
ejpam-4329	36	123	i(l	i(l	PROPN
ejpam-4329	36	124	)	)	PUNCT
ejpam-4329	36	125	,	,	PUNCT
ejpam-4329	36	126	the	the	DET
ejpam-4329	36	127	infimum	infimum	ADJ
ejpam-4329	36	128	i	i	NOUN
ejpam-4329	36	129	∧k	∧k	NUM
ejpam-4329	36	130	=	=	SYM
ejpam-4329	36	131	i	i	PRON
ejpam-4329	36	132	∩k	∩k	VERB
ejpam-4329	36	133	,	,	PUNCT
ejpam-4329	36	134	and	and	CCONJ
ejpam-4329	36	135	the	the	DET
ejpam-4329	36	136	supremum	supremum	ADJ
ejpam-4329	36	137	i	i	PRON
ejpam-4329	36	138	∨k	∨k	VERB
ejpam-4329	36	139	=	=	SYM
ejpam-4329	36	140	{	{	PUNCT
ejpam-4329	36	141	x	x	SYM
ejpam-4329	36	142	∈	∈	NOUN
ejpam-4329	36	143	l	l	NOUN
ejpam-4329	36	144	:	:	PUNCT
ejpam-4329	36	145	x	x	SYM
ejpam-4329	36	146	≤	≤	NUM
ejpam-4329	36	147	i∨	i∨	NOUN
ejpam-4329	36	148	k	k	PROPN
ejpam-4329	36	149	for	for	ADP
ejpam-4329	36	150	some	some	PRON
ejpam-4329	36	151	i	i	PRON
ejpam-4329	36	152	∈	∈	PROPN
ejpam-4329	37	1	i	i	PRON
ejpam-4329	37	2	and	and	CCONJ
ejpam-4329	37	3	some	some	DET
ejpam-4329	37	4	k	k	PROPN
ejpam-4329	37	5	∈	∈	PROPN
ejpam-4329	37	6	k	k	NOUN
ejpam-4329	37	7	}	}	PUNCT
ejpam-4329	37	8	.	.	PUNCT
ejpam-4329	38	1	the	the	DET
ejpam-4329	38	2	lattice	lattice	NOUN
ejpam-4329	38	3	of	of	ADP
ejpam-4329	38	4	all	all	DET
ejpam-4329	38	5	ideals	ideal	NOUN
ejpam-4329	38	6	i(l	i(l	PROPN
ejpam-4329	38	7	)	)	PUNCT
ejpam-4329	38	8	of	of	ADP
ejpam-4329	38	9	a	a	DET
ejpam-4329	38	10	distributive	distributive	ADJ
ejpam-4329	38	11	lattice	lattice	NOUN
ejpam-4329	38	12	l	l	NOUN
ejpam-4329	38	13	is	be	AUX
ejpam-4329	38	14	distributive	distributive	ADJ
ejpam-4329	38	15	.	.	PUNCT
ejpam-4329	39	1	for	for	ADP
ejpam-4329	39	2	a	a	DET
ejpam-4329	39	3	,	,	PUNCT
ejpam-4329	39	4	b	b	PROPN
ejpam-4329	39	5	∈	∈	PROPN
ejpam-4329	39	6	l	l	NOUN
ejpam-4329	39	7	,	,	PUNCT
ejpam-4329	39	8	meet	meet	VERB
ejpam-4329	39	9	and	and	CCONJ
ejpam-4329	39	10	join	join	VERB
ejpam-4329	39	11	operations	operation	NOUN
ejpam-4329	39	12	of	of	ADP
ejpam-4329	39	13	two	two	NUM
ejpam-4329	39	14	principal	principal	ADJ
ejpam-4329	39	15	ideals	ideal	NOUN
ejpam-4329	39	16	are	be	AUX
ejpam-4329	39	17	given	give	VERB
ejpam-4329	39	18	as	as	ADP
ejpam-4329	39	19	:	:	PUNCT
ejpam-4329	39	20	(	(	PUNCT
ejpam-4329	39	21	a	a	X
ejpam-4329	39	22	]	]	X
ejpam-4329	39	23	∧	∧	NOUN
ejpam-4329	39	24	(	(	PUNCT
ejpam-4329	39	25	b	b	NOUN
ejpam-4329	39	26	]	]	X
ejpam-4329	39	27	=	=	X
ejpam-4329	39	28	(	(	PUNCT
ejpam-4329	39	29	a	a	DET
ejpam-4329	39	30	∧	∧	PROPN
ejpam-4329	39	31	b	b	PROPN
ejpam-4329	39	32	]	]	PUNCT
ejpam-4329	39	33	and	and	CCONJ
ejpam-4329	39	34	(	(	PUNCT
ejpam-4329	39	35	a	a	PRON
ejpam-4329	39	36	]	]	X
ejpam-4329	39	37	∨	∨	X
ejpam-4329	39	38	(	(	PUNCT
ejpam-4329	39	39	b	b	NOUN
ejpam-4329	39	40	]	]	X
ejpam-4329	39	41	=	=	X
ejpam-4329	39	42	(	(	PUNCT
ejpam-4329	39	43	a	a	DET
ejpam-4329	39	44	∨	∨	NUM
ejpam-4329	39	45	b	b	NOUN
ejpam-4329	39	46	]	]	X
ejpam-4329	39	47	,	,	PUNCT
ejpam-4329	39	48	see[6	see[6	X
ejpam-4329	39	49	]	]	PUNCT
ejpam-4329	39	50	.	.	PUNCT
ejpam-4329	40	1	definition	definition	NOUN
ejpam-4329	40	2	4	4	NUM
ejpam-4329	40	3	.	.	PUNCT
ejpam-4329	41	1	[	[	X
ejpam-4329	41	2	4	4	X
ejpam-4329	41	3	]	]	PUNCT
ejpam-4329	41	4	for	for	ADP
ejpam-4329	41	5	a	a	DET
ejpam-4329	41	6	non	non	ADJ
ejpam-4329	41	7	-	-	ADJ
ejpam-4329	41	8	empty	empty	ADJ
ejpam-4329	41	9	subset	subset	NOUN
ejpam-4329	41	10	a	a	PRON
ejpam-4329	41	11	of	of	ADP
ejpam-4329	41	12	a	a	DET
ejpam-4329	41	13	lattice	lattice	PROPN
ejpam-4329	41	14	l.	l.	NOUN
ejpam-4329	41	15	define	define	VERB
ejpam-4329	41	16	the	the	DET
ejpam-4329	41	17	set	set	ADJ
ejpam-4329	41	18	a∗	a∗	NOUN
ejpam-4329	41	19	=	=	SYM
ejpam-4329	41	20	{	{	PUNCT
ejpam-4329	41	21	x	x	PUNCT
ejpam-4329	41	22	∈	∈	NOUN
ejpam-4329	41	23	l	l	NOUN
ejpam-4329	41	24	:	:	PUNCT
ejpam-4329	42	1	x	x	PUNCT
ejpam-4329	42	2	∧	∧	NOUN
ejpam-4329	42	3	a	a	PRON
ejpam-4329	42	4	=	=	NOUN
ejpam-4329	42	5	0	0	NUM
ejpam-4329	42	6	,	,	PUNCT
ejpam-4329	42	7	for	for	ADP
ejpam-4329	42	8	all	all	DET
ejpam-4329	42	9	a	a	DET
ejpam-4329	42	10	∈	∈	PROPN
ejpam-4329	42	11	a	a	PRON
ejpam-4329	42	12	}	}	PUNCT
ejpam-4329	42	13	is	be	AUX
ejpam-4329	42	14	called	call	VERB
ejpam-4329	42	15	the	the	DET
ejpam-4329	42	16	annihilator	annihilator	PROPN
ejpam-4329	42	17	ideal	ideal	NOUN
ejpam-4329	42	18	of	of	ADP
ejpam-4329	42	19	a	a	PRON
ejpam-4329	42	20	in	in	ADP
ejpam-4329	42	21	l.	l.	PROPN
ejpam-4329	42	22	the	the	DET
ejpam-4329	42	23	set	set	NOUN
ejpam-4329	42	24	of	of	ADP
ejpam-4329	42	25	annihilator	annihilator	PROPN
ejpam-4329	42	26	ideals	ideal	NOUN
ejpam-4329	42	27	a(l	a(l	NOUN
ejpam-4329	42	28	)	)	PUNCT
ejpam-4329	42	29	of	of	ADP
ejpam-4329	42	30	a	a	DET
ejpam-4329	42	31	distributive	distributive	ADJ
ejpam-4329	42	32	lattice	lattice	NOUN
ejpam-4329	42	33	l	l	NOUN
ejpam-4329	42	34	is	be	AUX
ejpam-4329	42	35	a	a	DET
ejpam-4329	42	36	complete	complete	ADJ
ejpam-4329	42	37	boolean	boolean	ADJ
ejpam-4329	42	38	algebra	algebra	NOUN
ejpam-4329	42	39	with	with	ADP
ejpam-4329	42	40	the	the	DET
ejpam-4329	42	41	smallest	small	ADJ
ejpam-4329	42	42	element	element	NOUN
ejpam-4329	42	43	(	(	PUNCT
ejpam-4329	42	44	0	0	NUM
ejpam-4329	42	45	]	]	PUNCT
ejpam-4329	42	46	,	,	PUNCT
ejpam-4329	42	47	the	the	DET
ejpam-4329	42	48	largest	large	ADJ
ejpam-4329	42	49	element	element	NOUN
ejpam-4329	42	50	l	l	NOUN
ejpam-4329	42	51	,	,	PUNCT
ejpam-4329	42	52	set	set	VERB
ejpam-4329	42	53	-	-	PUNCT
ejpam-4329	42	54	theoretic	theoretic	NOUN
ejpam-4329	42	55	intersection	intersection	NOUN
ejpam-4329	42	56	as	as	ADP
ejpam-4329	42	57	the	the	DET
ejpam-4329	42	58	infimum	infimum	NOUN
ejpam-4329	42	59	,	,	PUNCT
ejpam-4329	42	60	and	and	CCONJ
ejpam-4329	42	61	the	the	DET
ejpam-4329	42	62	map	map	NOUN
ejpam-4329	42	63	i	i	PRON
ejpam-4329	42	64	→	→	SYM
ejpam-4329	42	65	i∗	i∗	NOUN
ejpam-4329	42	66	as	as	ADP
ejpam-4329	42	67	complementation	complementation	NOUN
ejpam-4329	42	68	.	.	PUNCT
ejpam-4329	43	1	the	the	DET
ejpam-4329	43	2	supremum	supremum	NOUN
ejpam-4329	43	3	of	of	ADP
ejpam-4329	43	4	i	i	PRON
ejpam-4329	43	5	and	and	CCONJ
ejpam-4329	43	6	j	j	PROPN
ejpam-4329	43	7	in	in	ADP
ejpam-4329	43	8	a(l	a(l	NOUN
ejpam-4329	43	9	)	)	PUNCT
ejpam-4329	43	10	is	be	AUX
ejpam-4329	43	11	given	give	VERB
ejpam-4329	43	12	by	by	ADP
ejpam-4329	43	13	i	i	PROPN
ejpam-4329	43	14	y	y	PROPN
ejpam-4329	43	15	j	j	PROPN
ejpam-4329	44	1	=	=	PRON
ejpam-4329	44	2	(	(	PUNCT
ejpam-4329	44	3	i∗	i∗	NOUN
ejpam-4329	44	4	∩	∩	NOUN
ejpam-4329	44	5	j∗)∗.	j∗)∗.	NOUN
ejpam-4329	44	6	if	if	SCONJ
ejpam-4329	44	7	i∗	i∗	NOUN
ejpam-4329	44	8	=	=	SYM
ejpam-4329	44	9	(	(	PUNCT
ejpam-4329	44	10	0	0	NUM
ejpam-4329	44	11	]	]	PUNCT
ejpam-4329	44	12	then	then	ADV
ejpam-4329	44	13	i	i	PRON
ejpam-4329	44	14	is	be	AUX
ejpam-4329	44	15	called	call	VERB
ejpam-4329	44	16	dense	dense	ADJ
ejpam-4329	44	17	ideal	ideal	NOUN
ejpam-4329	44	18	.	.	PUNCT
ejpam-4329	45	1	the	the	DET
ejpam-4329	45	2	set	set	NOUN
ejpam-4329	45	3	of	of	ADP
ejpam-4329	45	4	all	all	DET
ejpam-4329	45	5	dense	dense	ADJ
ejpam-4329	45	6	ideals	ideal	NOUN
ejpam-4329	45	7	of	of	ADP
ejpam-4329	45	8	a	a	DET
ejpam-4329	45	9	distributive	distributive	ADJ
ejpam-4329	45	10	lattice	lattice	NOUN
ejpam-4329	45	11	l	l	NOUN
ejpam-4329	45	12	is	be	AUX
ejpam-4329	45	13	denoted	denote	VERB
ejpam-4329	45	14	by	by	ADP
ejpam-4329	45	15	d∗(l	d∗(l	PROPN
ejpam-4329	45	16	)	)	PUNCT
ejpam-4329	45	17	and	and	CCONJ
ejpam-4329	45	18	it	it	PRON
ejpam-4329	45	19	forms	form	VERB
ejpam-4329	45	20	a	a	DET
ejpam-4329	45	21	distributive	distributive	ADJ
ejpam-4329	45	22	lattice	lattice	NOUN
ejpam-4329	45	23	too	too	ADV
ejpam-4329	45	24	.	.	PUNCT
ejpam-4329	46	1	an	an	DET
ejpam-4329	46	2	ideal	ideal	NOUN
ejpam-4329	46	3	of	of	ADP
ejpam-4329	46	4	form	form	NOUN
ejpam-4329	46	5	(	(	PUNCT
ejpam-4329	46	6	a]∗	a]∗	PROPN
ejpam-4329	46	7	is	be	AUX
ejpam-4329	46	8	called	call	VERB
ejpam-4329	46	9	an	an	DET
ejpam-4329	46	10	annulet	annulet	NOUN
ejpam-4329	46	11	of	of	ADP
ejpam-4329	46	12	a	a	DET
ejpam-4329	46	13	∈	∈	PROPN
ejpam-4329	46	14	l.	l.	NOUN
ejpam-4329	46	15	each	each	DET
ejpam-4329	46	16	annulet	annulet	NOUN
ejpam-4329	46	17	is	be	AUX
ejpam-4329	46	18	an	an	DET
ejpam-4329	46	19	annihilator	annihilator	PROPN
ejpam-4329	46	20	ideal	ideal	NOUN
ejpam-4329	46	21	,	,	PUNCT
ejpam-4329	46	22	where	where	SCONJ
ejpam-4329	46	23	(	(	PUNCT
ejpam-4329	46	24	a]∗	a]∗	PROPN
ejpam-4329	46	25	=	=	SYM
ejpam-4329	46	26	(	(	PUNCT
ejpam-4329	46	27	a∗	a∗	PROPN
ejpam-4329	46	28	]	]	PUNCT
ejpam-4329	46	29	,	,	PUNCT
ejpam-4329	46	30	a∗	a∗	PROPN
ejpam-4329	46	31	is	be	AUX
ejpam-4329	46	32	the	the	DET
ejpam-4329	46	33	pseudocomplemented	pseudocomplemented	NOUN
ejpam-4329	46	34	of	of	ADP
ejpam-4329	46	35	a	a	PRON
ejpam-4329	46	36	in	in	ADP
ejpam-4329	46	37	l	l	NOUN
ejpam-4329	46	38	,	,	PUNCT
ejpam-4329	46	39	see[4	see[4	NOUN
ejpam-4329	46	40	]	]	PUNCT
ejpam-4329	46	41	.	.	PUNCT
ejpam-4329	47	1	from	from	ADP
ejpam-4329	47	2	now	now	ADV
ejpam-4329	47	3	on	on	ADV
ejpam-4329	47	4	,	,	PUNCT
ejpam-4329	47	5	l	l	NOUN
ejpam-4329	47	6	stands	stand	VERB
ejpam-4329	47	7	for	for	ADP
ejpam-4329	47	8	non	non	ADJ
ejpam-4329	47	9	-	-	ADJ
ejpam-4329	47	10	trivial	trivial	ADJ
ejpam-4329	47	11	distributive	distributive	ADJ
ejpam-4329	47	12	dual	dual	ADJ
ejpam-4329	47	13	weakly	weakly	ADJ
ejpam-4329	47	14	complemented	complemented	ADJ
ejpam-4329	47	15	lattice	lattice	NOUN
ejpam-4329	47	16	.	.	PUNCT
ejpam-4329	48	1	e.	e.	PROPN
ejpam-4329	48	2	g.	g.	PROPN
ejpam-4329	48	3	rezk	rezk	PROPN
ejpam-4329	48	4	/	/	SYM
ejpam-4329	48	5	eur	eur	PROPN
ejpam-4329	48	6	.	.	PUNCT
ejpam-4329	49	1	j.	j.	PROPN
ejpam-4329	49	2	pure	pure	PROPN
ejpam-4329	49	3	appl	appl	PROPN
ejpam-4329	49	4	.	.	PROPN
ejpam-4329	49	5	math	math	PROPN
ejpam-4329	49	6	,	,	PUNCT
ejpam-4329	49	7	15	15	NUM
ejpam-4329	49	8	(	(	PUNCT
ejpam-4329	49	9	2	2	NUM
ejpam-4329	49	10	)	)	PUNCT
ejpam-4329	49	11	(	(	PUNCT
ejpam-4329	49	12	2022	2022	NUM
ejpam-4329	49	13	)	)	PUNCT
ejpam-4329	49	14	,	,	PUNCT
ejpam-4329	49	15	486	486	NUM
ejpam-4329	49	16	-	-	SYM
ejpam-4329	49	17	495	495	NUM
ejpam-4329	49	18	489	489	NUM
ejpam-4329	49	19	3	3	NUM
ejpam-4329	49	20	.	.	PUNCT
ejpam-4329	49	21	closed	closed	ADJ
ejpam-4329	49	22	and	and	CCONJ
ejpam-4329	49	23	dense	dense	ADJ
ejpam-4329	49	24	ideals	ideal	NOUN
ejpam-4329	49	25	of	of	ADP
ejpam-4329	49	26	ddwcls	ddwcls	NOUN
ejpam-4329	49	27	in	in	ADP
ejpam-4329	49	28	the	the	DET
ejpam-4329	49	29	present	present	ADJ
ejpam-4329	49	30	section	section	NOUN
ejpam-4329	49	31	,	,	PUNCT
ejpam-4329	49	32	the	the	DET
ejpam-4329	49	33	dual	dual	ADJ
ejpam-4329	49	34	weak	weak	ADJ
ejpam-4329	49	35	complementation	complementation	NOUN
ejpam-4329	49	36	operation	operation	NOUN
ejpam-4329	49	37	is	be	AUX
ejpam-4329	49	38	defined	define	VERB
ejpam-4329	49	39	on	on	ADP
ejpam-4329	49	40	the	the	DET
ejpam-4329	49	41	lattice	lattice	NOUN
ejpam-4329	49	42	of	of	ADP
ejpam-4329	49	43	all	all	DET
ejpam-4329	49	44	ideals	ideal	NOUN
ejpam-4329	49	45	i(l	i(l	PROPN
ejpam-4329	49	46	)	)	PUNCT
ejpam-4329	49	47	of	of	ADP
ejpam-4329	49	48	l.	l.	PROPN
ejpam-4329	49	49	concepts	concept	NOUN
ejpam-4329	49	50	of	of	ADP
ejpam-4329	49	51	closed	closed	ADJ
ejpam-4329	49	52	and	and	CCONJ
ejpam-4329	49	53	dense	dense	ADJ
ejpam-4329	49	54	ideals	ideal	NOUN
ejpam-4329	49	55	are	be	AUX
ejpam-4329	49	56	introduced	introduce	VERB
ejpam-4329	49	57	and	and	CCONJ
ejpam-4329	49	58	it	it	PRON
ejpam-4329	49	59	’s	’	VERB
ejpam-4329	49	60	basic	basic	ADJ
ejpam-4329	49	61	properties	property	NOUN
ejpam-4329	49	62	are	be	AUX
ejpam-4329	49	63	proved	prove	VERB
ejpam-4329	49	64	.	.	PUNCT
ejpam-4329	50	1	definition	definition	NOUN
ejpam-4329	50	2	5	5	NUM
ejpam-4329	50	3	.	.	PUNCT
ejpam-4329	51	1	let	let	VERB
ejpam-4329	51	2	i	i	PRON
ejpam-4329	51	3	be	be	AUX
ejpam-4329	51	4	an	an	DET
ejpam-4329	51	5	ideal	ideal	NOUN
ejpam-4329	51	6	.	.	PUNCT
ejpam-4329	52	1	define	define	VERB
ejpam-4329	52	2	the	the	DET
ejpam-4329	52	3	set	set	NOUN
ejpam-4329	52	4	io	io	X
ejpam-4329	52	5	=	=	PUNCT
ejpam-4329	52	6	{	{	PUNCT
ejpam-4329	52	7	x	x	PUNCT
ejpam-4329	52	8	∈	∈	NOUN
ejpam-4329	52	9	l	l	NOUN
ejpam-4329	52	10	:	:	PUNCT
ejpam-4329	52	11	x	x	SYM
ejpam-4329	52	12	≤	≤	ADV
ejpam-4329	52	13	ah	ah	INTJ
ejpam-4329	52	14	,	,	PUNCT
ejpam-4329	52	15	for	for	ADP
ejpam-4329	52	16	all	all	DET
ejpam-4329	52	17	a	a	DET
ejpam-4329	52	18	∈	∈	NOUN
ejpam-4329	52	19	i	i	NOUN
ejpam-4329	52	20	}	}	PUNCT
ejpam-4329	52	21	.	.	PUNCT
ejpam-4329	53	1	note	note	VERB
ejpam-4329	53	2	that	that	SCONJ
ejpam-4329	54	1	,	,	PUNCT
ejpam-4329	54	2	if	if	SCONJ
ejpam-4329	54	3	i	i	PRON
ejpam-4329	54	4	is	be	AUX
ejpam-4329	54	5	an	an	DET
ejpam-4329	54	6	ideal	ideal	NOUN
ejpam-4329	54	7	and	and	CCONJ
ejpam-4329	54	8	x	x	SYM
ejpam-4329	54	9	∈	∈	NOUN
ejpam-4329	54	10	io	io	X
ejpam-4329	54	11	then	then	ADV
ejpam-4329	54	12	x	x	PROPN
ejpam-4329	54	13	∧	∧	PROPN
ejpam-4329	54	14	a	a	PRON
ejpam-4329	54	15	=	=	SYM
ejpam-4329	54	16	0	0	NUM
ejpam-4329	54	17	,	,	PUNCT
ejpam-4329	54	18	for	for	ADP
ejpam-4329	54	19	all	all	DET
ejpam-4329	54	20	a	a	DET
ejpam-4329	54	21	∈	∈	PROPN
ejpam-4329	54	22	i.	i.	NOUN
ejpam-4329	54	23	consequently	consequently	ADV
ejpam-4329	54	24	x	x	SYM
ejpam-4329	54	25	∈	∈	PROPN
ejpam-4329	54	26	i∗	i∗	NOUN
ejpam-4329	54	27	and	and	CCONJ
ejpam-4329	54	28	so	so	ADV
ejpam-4329	54	29	io	io	PROPN
ejpam-4329	54	30	⊆	⊆	NUM
ejpam-4329	54	31	i∗.	i∗.	PROPN
ejpam-4329	54	32	proposition	proposition	NOUN
ejpam-4329	54	33	1	1	NUM
ejpam-4329	54	34	.	.	PUNCT
ejpam-4329	55	1	a	a	DET
ejpam-4329	55	2	set	set	NOUN
ejpam-4329	55	3	io	io	PROPN
ejpam-4329	55	4	is	be	AUX
ejpam-4329	55	5	an	an	DET
ejpam-4329	55	6	ideal	ideal	NOUN
ejpam-4329	55	7	,	,	PUNCT
ejpam-4329	55	8	moreover	moreover	ADV
ejpam-4329	55	9	is	be	AUX
ejpam-4329	55	10	the	the	DET
ejpam-4329	55	11	dual	dual	ADJ
ejpam-4329	55	12	weak	weak	ADJ
ejpam-4329	55	13	complemented	complement	VERB
ejpam-4329	55	14	of	of	ADP
ejpam-4329	55	15	the	the	DET
ejpam-4329	55	16	ideal	ideal	NOUN
ejpam-4329	55	17	i	i	PRON
ejpam-4329	55	18	in	in	ADP
ejpam-4329	55	19	i(l	i(l	PROPN
ejpam-4329	55	20	)	)	PUNCT
ejpam-4329	55	21	.	.	PUNCT
ejpam-4329	56	1	proof	proof	NOUN
ejpam-4329	56	2	.	.	PUNCT
ejpam-4329	57	1	assume	assume	VERB
ejpam-4329	57	2	that	that	SCONJ
ejpam-4329	57	3	x	x	X
ejpam-4329	57	4	,	,	PUNCT
ejpam-4329	57	5	y	y	PROPN
ejpam-4329	57	6	∈	∈	PROPN
ejpam-4329	57	7	io	io	PROPN
ejpam-4329	57	8	,	,	PUNCT
ejpam-4329	57	9	then	then	ADV
ejpam-4329	57	10	x	x	X
ejpam-4329	57	11	,	,	PUNCT
ejpam-4329	57	12	y	y	PROPN
ejpam-4329	57	13	≤	≤	X
ejpam-4329	57	14	ah	ah	INTJ
ejpam-4329	57	15	for	for	ADP
ejpam-4329	57	16	all	all	DET
ejpam-4329	57	17	a	a	DET
ejpam-4329	57	18	∈	∈	PROPN
ejpam-4329	57	19	i.	i.	NOUN
ejpam-4329	57	20	thus	thus	ADV
ejpam-4329	57	21	x	x	PROPN
ejpam-4329	57	22	∨	∨	NUM
ejpam-4329	57	23	y	y	PROPN
ejpam-4329	57	24	≤	≤	X
ejpam-4329	57	25	ah	ah	INTJ
ejpam-4329	57	26	.	.	PUNCT
ejpam-4329	58	1	consequently	consequently	ADV
ejpam-4329	58	2	,	,	PUNCT
ejpam-4329	58	3	x	x	PROPN
ejpam-4329	58	4	∨	∨	NUM
ejpam-4329	58	5	y	y	PROPN
ejpam-4329	58	6	∈	∈	PROPN
ejpam-4329	58	7	io	io	PROPN
ejpam-4329	58	8	.	.	PROPN
ejpam-4329	58	9	let	let	VERB
ejpam-4329	58	10	z	z	NOUN
ejpam-4329	58	11	∈	∈	PROPN
ejpam-4329	58	12	l	l	NOUN
ejpam-4329	58	13	and	and	CCONJ
ejpam-4329	58	14	z	z	NOUN
ejpam-4329	58	15	≤	≤	NUM
ejpam-4329	58	16	x	x	PUNCT
ejpam-4329	58	17	for	for	ADP
ejpam-4329	58	18	some	some	DET
ejpam-4329	58	19	x	x	SYM
ejpam-4329	58	20	∈	∈	PROPN
ejpam-4329	58	21	io	io	PROPN
ejpam-4329	58	22	.	.	PROPN
ejpam-4329	59	1	then	then	ADV
ejpam-4329	59	2	z	z	NOUN
ejpam-4329	59	3	≤	≤	X
ejpam-4329	59	4	ah	ah	INTJ
ejpam-4329	59	5	for	for	ADP
ejpam-4329	59	6	all	all	DET
ejpam-4329	59	7	a	a	DET
ejpam-4329	59	8	∈	∈	PROPN
ejpam-4329	59	9	i.	i.	NOUN
ejpam-4329	59	10	therefore	therefore	ADV
ejpam-4329	59	11	io	io	PROPN
ejpam-4329	59	12	is	be	AUX
ejpam-4329	59	13	an	an	DET
ejpam-4329	59	14	ideal	ideal	NOUN
ejpam-4329	59	15	of	of	ADP
ejpam-4329	59	16	l.	l.	PROPN
ejpam-4329	59	17	now	now	ADV
ejpam-4329	59	18	we	we	PRON
ejpam-4329	59	19	show	show	VERB
ejpam-4329	59	20	that	that	SCONJ
ejpam-4329	59	21	io	io	PROPN
ejpam-4329	59	22	satisfies	satisfy	VERB
ejpam-4329	59	23	the	the	DET
ejpam-4329	59	24	conditions	condition	NOUN
ejpam-4329	59	25	of	of	ADP
ejpam-4329	59	26	dual	dual	ADJ
ejpam-4329	59	27	weak	weak	ADJ
ejpam-4329	59	28	complementation	complementation	NOUN
ejpam-4329	59	29	:	:	PUNCT
ejpam-4329	59	30	(	(	PUNCT
ejpam-4329	59	31	1	1	X
ejpam-4329	59	32	)	)	PUNCT
ejpam-4329	59	33	if	if	SCONJ
ejpam-4329	59	34	a	a	DET
ejpam-4329	59	35	∈	∈	X
ejpam-4329	59	36	i	i	PRON
ejpam-4329	59	37	and	and	CCONJ
ejpam-4329	59	38	b	b	X
ejpam-4329	59	39	∈	∈	NOUN
ejpam-4329	59	40	io	io	X
ejpam-4329	59	41	then	then	ADV
ejpam-4329	59	42	b	b	PROPN
ejpam-4329	59	43	≤	≤	X
ejpam-4329	59	44	ah	ah	INTJ
ejpam-4329	59	45	.	.	PUNCT
ejpam-4329	60	1	from	from	ADP
ejpam-4329	60	2	(	(	PUNCT
ejpam-4329	60	3	4	4	NUM
ejpam-4329	60	4	)	)	PUNCT
ejpam-4329	60	5	in	in	ADP
ejpam-4329	60	6	theorem	theorem	NOUN
ejpam-4329	60	7	1	1	NUM
ejpam-4329	60	8	,	,	PUNCT
ejpam-4329	60	9	this	this	PRON
ejpam-4329	60	10	is	be	AUX
ejpam-4329	60	11	equivalent	equivalent	ADJ
ejpam-4329	60	12	that	that	SCONJ
ejpam-4329	60	13	a	a	DET
ejpam-4329	60	14	≤	≤	NUM
ejpam-4329	60	15	bh	bh	NOUN
ejpam-4329	60	16	.	.	PUNCT
ejpam-4329	61	1	thus	thus	ADV
ejpam-4329	61	2	a	a	DET
ejpam-4329	61	3	∈	∈	PROPN
ejpam-4329	61	4	ioo	ioo	NOUN
ejpam-4329	61	5	.	.	PUNCT
ejpam-4329	62	1	(	(	PUNCT
ejpam-4329	62	2	2	2	X
ejpam-4329	62	3	)	)	PUNCT
ejpam-4329	62	4	let	let	VERB
ejpam-4329	62	5	i	i	PRON
ejpam-4329	62	6	≤	≤	ADJ
ejpam-4329	63	1	k	k	PROPN
ejpam-4329	63	2	and	and	CCONJ
ejpam-4329	63	3	x	x	PROPN
ejpam-4329	63	4	∈	∈	PROPN
ejpam-4329	63	5	ko	ko	PROPN
ejpam-4329	63	6	.	.	PUNCT
ejpam-4329	64	1	then	then	ADV
ejpam-4329	64	2	x	x	SYM
ejpam-4329	64	3	≤	≤	NUM
ejpam-4329	64	4	bh	bh	NOUN
ejpam-4329	64	5	for	for	ADP
ejpam-4329	64	6	all	all	DET
ejpam-4329	64	7	b	b	PROPN
ejpam-4329	64	8	∈	∈	PROPN
ejpam-4329	64	9	k.	k.	NOUN
ejpam-4329	65	1	so	so	ADV
ejpam-4329	65	2	x	x	SYM
ejpam-4329	65	3	≤	≤	NUM
ejpam-4329	65	4	bh	bh	NOUN
ejpam-4329	65	5	for	for	ADP
ejpam-4329	65	6	all	all	DET
ejpam-4329	65	7	b	b	PROPN
ejpam-4329	65	8	∈	∈	PROPN
ejpam-4329	65	9	i.	i.	NOUN
ejpam-4329	65	10	it	it	PRON
ejpam-4329	65	11	implies	imply	VERB
ejpam-4329	65	12	x	x	X
ejpam-4329	65	13	∈	∈	PROPN
ejpam-4329	65	14	io	io	PROPN
ejpam-4329	65	15	.	.	PUNCT
ejpam-4329	66	1	so	so	ADV
ejpam-4329	66	2	ko	ko	PROPN
ejpam-4329	66	3	≤	≤	PROPN
ejpam-4329	66	4	io	io	PROPN
ejpam-4329	66	5	,	,	PUNCT
ejpam-4329	66	6	(	(	PUNCT
ejpam-4329	66	7	3	3	X
ejpam-4329	66	8	)	)	PUNCT
ejpam-4329	66	9	clearly	clearly	ADV
ejpam-4329	66	10	i	i	PRON
ejpam-4329	66	11	∧	∧	NOUN
ejpam-4329	66	12	i∗	i∗	NOUN
ejpam-4329	66	13	=	=	SYM
ejpam-4329	66	14	(	(	PUNCT
ejpam-4329	66	15	0	0	NUM
ejpam-4329	66	16	]	]	PUNCT
ejpam-4329	66	17	,	,	PUNCT
ejpam-4329	66	18	then	then	ADV
ejpam-4329	66	19	i	i	PRON
ejpam-4329	66	20	∧	∧	PROPN
ejpam-4329	66	21	io	io	X
ejpam-4329	66	22	=	=	PUNCT
ejpam-4329	66	23	(	(	PUNCT
ejpam-4329	66	24	0	0	NUM
ejpam-4329	66	25	]	]	PUNCT
ejpam-4329	66	26	.	.	PUNCT
ejpam-4329	67	1	if	if	SCONJ
ejpam-4329	67	2	l	l	NOUN
ejpam-4329	67	3	is	be	AUX
ejpam-4329	67	4	a	a	DET
ejpam-4329	67	5	distributive	distributive	ADJ
ejpam-4329	67	6	pseuodocomplemented	pseuodocomplemente	VERB
ejpam-4329	67	7	lattice	lattice	NOUN
ejpam-4329	67	8	,	,	PUNCT
ejpam-4329	67	9	then	then	ADV
ejpam-4329	67	10	io	io	X
ejpam-4329	67	11	=	=	PROPN
ejpam-4329	67	12	i∗	i∗	PROPN
ejpam-4329	67	13	,	,	PUNCT
ejpam-4329	67	14	and	and	CCONJ
ejpam-4329	67	15	the	the	DET
ejpam-4329	67	16	lattice	lattice	PROPN
ejpam-4329	67	17	i(l	i(l	PROPN
ejpam-4329	67	18	)	)	PUNCT
ejpam-4329	67	19	of	of	ADP
ejpam-4329	67	20	its	its	PRON
ejpam-4329	67	21	ideals	ideal	NOUN
ejpam-4329	67	22	become	become	VERB
ejpam-4329	67	23	a	a	DET
ejpam-4329	67	24	distributive	distributive	ADJ
ejpam-4329	67	25	pseuodocomplemented	pseuodocomplemente	VERB
ejpam-4329	67	26	lattice	lattice	NOUN
ejpam-4329	67	27	.	.	PUNCT
ejpam-4329	68	1	lemma	lemma	PROPN
ejpam-4329	68	2	1	1	X
ejpam-4329	68	3	.	.	PUNCT
ejpam-4329	69	1	let	let	VERB
ejpam-4329	69	2	i	i	PRON
ejpam-4329	69	3	,	,	PUNCT
ejpam-4329	69	4	k	k	PROPN
ejpam-4329	69	5	be	be	VERB
ejpam-4329	69	6	two	two	NUM
ejpam-4329	69	7	ideals	ideal	NOUN
ejpam-4329	69	8	and	and	CCONJ
ejpam-4329	69	9	a	a	DET
ejpam-4329	69	10	∈	∈	PROPN
ejpam-4329	69	11	l.	l.	NOUN
ejpam-4329	69	12	then	then	ADV
ejpam-4329	69	13	,	,	PUNCT
ejpam-4329	69	14	:	:	PUNCT
ejpam-4329	69	15	(	(	PUNCT
ejpam-4329	69	16	1	1	X
ejpam-4329	69	17	)	)	PUNCT
ejpam-4329	69	18	(	(	PUNCT
ejpam-4329	69	19	a]o	a]o	NOUN
ejpam-4329	69	20	=	=	X
ejpam-4329	69	21	(	(	PUNCT
ejpam-4329	69	22	ah	ah	INTJ
ejpam-4329	69	23	]	]	X
ejpam-4329	69	24	,	,	PUNCT
ejpam-4329	69	25	(	(	PUNCT
ejpam-4329	69	26	2	2	X
ejpam-4329	69	27	)	)	PUNCT
ejpam-4329	69	28	io	io	NOUN
ejpam-4329	70	1	=	=	PUNCT
ejpam-4329	70	2	∩a∈i(a	∩a∈i(a	PROPN
ejpam-4329	70	3	]	]	X
ejpam-4329	70	4	o	o	X
ejpam-4329	70	5	,	,	PUNCT
ejpam-4329	70	6	(	(	PUNCT
ejpam-4329	70	7	3	3	NUM
ejpam-4329	70	8	)	)	PUNCT
ejpam-4329	70	9	(	(	PUNCT
ejpam-4329	70	10	0]o	0]o	NUM
ejpam-4329	70	11	=	=	SYM
ejpam-4329	70	12	(	(	PUNCT
ejpam-4329	70	13	1	1	X
ejpam-4329	70	14	]	]	PUNCT
ejpam-4329	70	15	and	and	CCONJ
ejpam-4329	70	16	(	(	PUNCT
ejpam-4329	70	17	1]o	1]o	NUM
ejpam-4329	70	18	=	=	SYM
ejpam-4329	70	19	(	(	PUNCT
ejpam-4329	70	20	0	0	NUM
ejpam-4329	70	21	]	]	PUNCT
ejpam-4329	70	22	,	,	PUNCT
ejpam-4329	70	23	(	(	PUNCT
ejpam-4329	70	24	4	4	X
ejpam-4329	70	25	)	)	PUNCT
ejpam-4329	70	26	io	io	NOUN
ejpam-4329	70	27	=	=	SYM
ejpam-4329	70	28	iooo	iooo	PROPN
ejpam-4329	70	29	,	,	PUNCT
ejpam-4329	70	30	(	(	PUNCT
ejpam-4329	70	31	5	5	X
ejpam-4329	70	32	)	)	PUNCT
ejpam-4329	70	33	io	io	X
ejpam-4329	70	34	≥	≥	PROPN
ejpam-4329	70	35	k	k	PROPN
ejpam-4329	70	36	iff	iff	PROPN
ejpam-4329	70	37	ko	ko	PROPN
ejpam-4329	70	38	≥	≥	PROPN
ejpam-4329	70	39	i	i	PRON
ejpam-4329	70	40	,	,	PUNCT
ejpam-4329	70	41	(	(	PUNCT
ejpam-4329	70	42	6	6	NUM
ejpam-4329	70	43	)	)	PUNCT
ejpam-4329	70	44	io	io	PROPN
ejpam-4329	70	45	⊆	⊆	NUM
ejpam-4329	70	46	ko	ko	PROPN
ejpam-4329	70	47	iff	iff	PROPN
ejpam-4329	70	48	koo	koo	PROPN
ejpam-4329	70	49	⊆	⊆	NUM
ejpam-4329	70	50	ioo	ioo	NOUN
ejpam-4329	70	51	,	,	PUNCT
ejpam-4329	70	52	(	(	PUNCT
ejpam-4329	70	53	7	7	X
ejpam-4329	70	54	)	)	PUNCT
ejpam-4329	70	55	i	i	PRON
ejpam-4329	71	1	⊆	⊆	NUM
ejpam-4329	71	2	ko	ko	PROPN
ejpam-4329	71	3	implies	imply	VERB
ejpam-4329	71	4	i	i	PRON
ejpam-4329	71	5	∩k	∩k	ADV
ejpam-4329	72	1	=	=	PUNCT
ejpam-4329	73	1	(	(	PUNCT
ejpam-4329	73	2	0	0	NUM
ejpam-4329	73	3	]	]	PUNCT
ejpam-4329	73	4	.	.	PUNCT
ejpam-4329	74	1	proof	proof	NOUN
ejpam-4329	74	2	.	.	PUNCT
ejpam-4329	75	1	(	(	PUNCT
ejpam-4329	75	2	1	1	X
ejpam-4329	75	3	)	)	PUNCT
ejpam-4329	75	4	suppose	suppose	VERB
ejpam-4329	75	5	x	x	X
ejpam-4329	75	6	∈	∈	PROPN
ejpam-4329	75	7	(	(	PUNCT
ejpam-4329	75	8	ah	ah	INTJ
ejpam-4329	75	9	]	]	X
ejpam-4329	75	10	,	,	PUNCT
ejpam-4329	75	11	then	then	ADV
ejpam-4329	75	12	x	x	SYM
ejpam-4329	75	13	≤	≤	NUM
ejpam-4329	75	14	yh	yh	NOUN
ejpam-4329	75	15	for	for	ADP
ejpam-4329	75	16	all	all	DET
ejpam-4329	75	17	y	y	PROPN
ejpam-4329	75	18	∈	∈	PROPN
ejpam-4329	75	19	(	(	PUNCT
ejpam-4329	75	20	a].so	a].so	ADJ
ejpam-4329	75	21	x	x	SYM
ejpam-4329	75	22	∈	∈	PROPN
ejpam-4329	75	23	(	(	PUNCT
ejpam-4329	75	24	a]o	a]o	PROPN
ejpam-4329	75	25	.	.	PUNCT
ejpam-4329	76	1	conversely	conversely	ADV
ejpam-4329	76	2	,	,	PUNCT
ejpam-4329	76	3	let	let	VERB
ejpam-4329	76	4	y	y	PROPN
ejpam-4329	76	5	∈	∈	PROPN
ejpam-4329	76	6	(	(	PUNCT
ejpam-4329	76	7	a]o	a]o	NOUN
ejpam-4329	76	8	and	and	CCONJ
ejpam-4329	76	9	ah	ah	INTJ
ejpam-4329	76	10	≤	≤	NUM
ejpam-4329	76	11	y.	y.	NOUN
ejpam-4329	76	12	thus	thus	ADV
ejpam-4329	76	13	yhh	yhh	X
ejpam-4329	76	14	≥	≥	PRON
ejpam-4329	76	15	ah	ah	INTJ
ejpam-4329	76	16	and	and	CCONJ
ejpam-4329	76	17	by	by	ADP
ejpam-4329	76	18	using	use	VERB
ejpam-4329	76	19	(	(	PUNCT
ejpam-4329	76	20	7	7	NUM
ejpam-4329	76	21	)	)	PUNCT
ejpam-4329	76	22	in	in	ADP
ejpam-4329	76	23	theorem	theorem	NOUN
ejpam-4329	76	24	1	1	NUM
ejpam-4329	76	25	we	we	PRON
ejpam-4329	76	26	get	get	VERB
ejpam-4329	76	27	yhh∨ahh	yhh∨ahh	PROPN
ejpam-4329	76	28	≥	≥	PUNCT
ejpam-4329	76	29	ah	ah	INTJ
ejpam-4329	76	30	.	.	PUNCT
ejpam-4329	77	1	hence	hence	ADV
ejpam-4329	77	2	,	,	PUNCT
ejpam-4329	77	3	ah	ah	INTJ
ejpam-4329	77	4	∧	∧	PROPN
ejpam-4329	77	5	(	(	PUNCT
ejpam-4329	77	6	yhh	yhh	PROPN
ejpam-4329	77	7	∨	∨	NUM
ejpam-4329	77	8	ahh	ahh	NOUN
ejpam-4329	77	9	)	)	PUNCT
ejpam-4329	77	10	=	=	SYM
ejpam-4329	78	1	(	(	PUNCT
ejpam-4329	78	2	ah	ah	INTJ
ejpam-4329	78	3	∧	∧	PROPN
ejpam-4329	78	4	yhh	yhh	NOUN
ejpam-4329	78	5	)	)	PUNCT
ejpam-4329	78	6	∨	∨	NOUN
ejpam-4329	78	7	(	(	PUNCT
ejpam-4329	78	8	ah	ah	INTJ
ejpam-4329	78	9	∧	∧	PROPN
ejpam-4329	78	10	ahh	ahh	PROPN
ejpam-4329	78	11	)	)	PUNCT
ejpam-4329	78	12	≥	≥	NOUN
ejpam-4329	78	13	ah	ah	INTJ
ejpam-4329	78	14	,	,	PUNCT
ejpam-4329	78	15	which	which	PRON
ejpam-4329	78	16	is	be	AUX
ejpam-4329	78	17	a	a	DET
ejpam-4329	78	18	contradiction	contradiction	NOUN
ejpam-4329	78	19	.	.	PUNCT
ejpam-4329	79	1	so	so	ADV
ejpam-4329	79	2	,	,	PUNCT
ejpam-4329	79	3	y	y	PROPN
ejpam-4329	79	4	≤	≤	PROPN
ejpam-4329	79	5	ah.therefore	ah.therefore	ADV
ejpam-4329	79	6	,	,	PUNCT
ejpam-4329	79	7	(	(	PUNCT
ejpam-4329	79	8	a]o	a]o	NOUN
ejpam-4329	79	9	=	=	X
ejpam-4329	79	10	(	(	PUNCT
ejpam-4329	79	11	ah	ah	INTJ
ejpam-4329	79	12	]	]	PUNCT
ejpam-4329	79	13	.	.	PUNCT
ejpam-4329	80	1	e.	e.	PROPN
ejpam-4329	80	2	g.	g.	PROPN
ejpam-4329	80	3	rezk	rezk	PROPN
ejpam-4329	80	4	/	/	SYM
ejpam-4329	80	5	eur	eur	PROPN
ejpam-4329	80	6	.	.	PUNCT
ejpam-4329	81	1	j.	j.	PROPN
ejpam-4329	81	2	pure	pure	PROPN
ejpam-4329	81	3	appl	appl	PROPN
ejpam-4329	81	4	.	.	PROPN
ejpam-4329	81	5	math	math	PROPN
ejpam-4329	81	6	,	,	PUNCT
ejpam-4329	81	7	15	15	NUM
ejpam-4329	81	8	(	(	PUNCT
ejpam-4329	81	9	2	2	NUM
ejpam-4329	81	10	)	)	PUNCT
ejpam-4329	81	11	(	(	PUNCT
ejpam-4329	81	12	2022	2022	NUM
ejpam-4329	81	13	)	)	PUNCT
ejpam-4329	81	14	,	,	PUNCT
ejpam-4329	81	15	486	486	NUM
ejpam-4329	81	16	-	-	SYM
ejpam-4329	81	17	495	495	NUM
ejpam-4329	81	18	490	490	NUM
ejpam-4329	81	19	(	(	PUNCT
ejpam-4329	81	20	2	2	NUM
ejpam-4329	81	21	)	)	PUNCT
ejpam-4329	81	22	let	let	VERB
ejpam-4329	81	23	x	x	PUNCT
ejpam-4329	81	24	∈	∈	PROPN
ejpam-4329	82	1	∩a∈i(a	∩a∈i(a	ADP
ejpam-4329	82	2	]	]	X
ejpam-4329	82	3	o	o	X
ejpam-4329	82	4	i.e.	i.e.	X
ejpam-4329	82	5	,	,	PUNCT
ejpam-4329	82	6	x	x	SYM
ejpam-4329	82	7	∈	∈	PROPN
ejpam-4329	82	8	(	(	PUNCT
ejpam-4329	82	9	a]o	a]o	PROPN
ejpam-4329	82	10	,	,	PUNCT
ejpam-4329	82	11	for	for	ADP
ejpam-4329	82	12	all	all	DET
ejpam-4329	82	13	a	a	DET
ejpam-4329	82	14	∈	∈	PROPN
ejpam-4329	82	15	i.	i.	NOUN
ejpam-4329	82	16	then	then	ADV
ejpam-4329	82	17	x	x	SYM
ejpam-4329	82	18	≤	≤	ADV
ejpam-4329	82	19	ah	ah	INTJ
ejpam-4329	82	20	and	and	CCONJ
ejpam-4329	82	21	x	x	SYM
ejpam-4329	82	22	∈	∈	PROPN
ejpam-4329	82	23	io	io	X
ejpam-4329	82	24	.	.	PUNCT
ejpam-4329	82	25	conversely	conversely	ADV
ejpam-4329	82	26	,	,	PUNCT
ejpam-4329	82	27	if	if	SCONJ
ejpam-4329	82	28	x	x	SYM
ejpam-4329	82	29	∈	∈	NOUN
ejpam-4329	82	30	io	io	X
ejpam-4329	82	31	then	then	ADV
ejpam-4329	82	32	x	x	X
ejpam-4329	82	33	≤	≤	ADV
ejpam-4329	82	34	ah	ah	INTJ
ejpam-4329	82	35	for	for	ADP
ejpam-4329	82	36	all	all	DET
ejpam-4329	82	37	a	a	DET
ejpam-4329	82	38	∈	∈	PROPN
ejpam-4329	82	39	i.	i.	NOUN
ejpam-4329	82	40	it	it	PRON
ejpam-4329	82	41	means	mean	VERB
ejpam-4329	82	42	x	x	SYM
ejpam-4329	82	43	∈	∈	PROPN
ejpam-4329	82	44	∩a∈i(a	∩a∈i(a	ADP
ejpam-4329	82	45	]	]	X
ejpam-4329	82	46	o.	o.	PROPN
ejpam-4329	82	47	therefore	therefore	ADV
ejpam-4329	82	48	io	io	X
ejpam-4329	83	1	=	=	SYM
ejpam-4329	83	2	∩a∈i(a	∩a∈i(a	PROPN
ejpam-4329	83	3	]	]	X
ejpam-4329	83	4	o.	o.	NOUN
ejpam-4329	83	5	(	(	PUNCT
ejpam-4329	83	6	3	3	X
ejpam-4329	83	7	)	)	PUNCT
ejpam-4329	83	8	we	we	PRON
ejpam-4329	83	9	get	get	VERB
ejpam-4329	83	10	(	(	PUNCT
ejpam-4329	83	11	0]o	0]o	NUM
ejpam-4329	83	12	=	=	SYM
ejpam-4329	83	13	{	{	PUNCT
ejpam-4329	83	14	x	x	PUNCT
ejpam-4329	83	15	∈	∈	NOUN
ejpam-4329	83	16	l	l	NOUN
ejpam-4329	83	17	:	:	PUNCT
ejpam-4329	83	18	x	x	SYM
ejpam-4329	83	19	≤	≤	X
ejpam-4329	83	20	0h	0h	X
ejpam-4329	83	21	=	=	SYM
ejpam-4329	83	22	1	1	NUM
ejpam-4329	83	23	}	}	PUNCT
ejpam-4329	83	24	=	=	SYM
ejpam-4329	83	25	(	(	PUNCT
ejpam-4329	83	26	1	1	NUM
ejpam-4329	83	27	]	]	PUNCT
ejpam-4329	83	28	,	,	PUNCT
ejpam-4329	83	29	(	(	PUNCT
ejpam-4329	83	30	1]o	1]o	NUM
ejpam-4329	83	31	=	=	SYM
ejpam-4329	83	32	{	{	PUNCT
ejpam-4329	83	33	x	x	PUNCT
ejpam-4329	83	34	∈	∈	NOUN
ejpam-4329	83	35	l	l	NOUN
ejpam-4329	83	36	:	:	PUNCT
ejpam-4329	84	1	x	x	SYM
ejpam-4329	84	2	≤	≤	ADV
ejpam-4329	84	3	1h	1h	NUM
ejpam-4329	84	4	=	=	SYM
ejpam-4329	84	5	0	0	NUM
ejpam-4329	84	6	}	}	PUNCT
ejpam-4329	84	7	=	=	SYM
ejpam-4329	84	8	(	(	PUNCT
ejpam-4329	84	9	0	0	NUM
ejpam-4329	84	10	]	]	PUNCT
ejpam-4329	84	11	.	.	PUNCT
ejpam-4329	85	1	(	(	PUNCT
ejpam-4329	85	2	4	4	NUM
ejpam-4329	85	3	)	)	PUNCT
ejpam-4329	85	4	by	by	ADP
ejpam-4329	85	5	using	use	VERB
ejpam-4329	85	6	proposition1	proposition1	NOUN
ejpam-4329	85	7	,	,	PUNCT
ejpam-4329	85	8	we	we	PRON
ejpam-4329	85	9	get	get	VERB
ejpam-4329	85	10	iooo	iooo	ADJ
ejpam-4329	85	11	≤	≤	NUM
ejpam-4329	85	12	io	io	NOUN
ejpam-4329	85	13	.	.	PUNCT
ejpam-4329	86	1	conversely	conversely	ADV
ejpam-4329	86	2	,	,	PUNCT
ejpam-4329	86	3	if	if	SCONJ
ejpam-4329	86	4	b	b	PROPN
ejpam-4329	86	5	∈	∈	PROPN
ejpam-4329	86	6	iooo	iooo	NOUN
ejpam-4329	86	7	,	,	PUNCT
ejpam-4329	86	8	then	then	ADV
ejpam-4329	86	9	b	b	X
ejpam-4329	86	10	≤	≤	X
ejpam-4329	86	11	ah	ah	INTJ
ejpam-4329	86	12	for	for	ADP
ejpam-4329	86	13	all	all	DET
ejpam-4329	86	14	a	a	DET
ejpam-4329	86	15	∈	∈	PROPN
ejpam-4329	86	16	ioo	ioo	NOUN
ejpam-4329	86	17	.	.	PUNCT
ejpam-4329	87	1	but	but	CCONJ
ejpam-4329	87	2	i	i	PRON
ejpam-4329	87	3	⊆	⊆	NUM
ejpam-4329	87	4	ioo	ioo	VERB
ejpam-4329	87	5	so	so	ADV
ejpam-4329	87	6	x	x	SYM
ejpam-4329	87	7	≤	≤	ADJ
ejpam-4329	87	8	ch	ch	NOUN
ejpam-4329	87	9	for	for	ADP
ejpam-4329	87	10	all	all	DET
ejpam-4329	87	11	c	c	NOUN
ejpam-4329	87	12	∈	∈	PRON
ejpam-4329	87	13	i.thus	i.thus	NOUN
ejpam-4329	87	14	x	x	SYM
ejpam-4329	87	15	∈	∈	PROPN
ejpam-4329	87	16	io	io	PROPN
ejpam-4329	87	17	.	.	PROPN
ejpam-4329	88	1	(	(	PUNCT
ejpam-4329	88	2	5	5	X
ejpam-4329	88	3	)	)	PUNCT
ejpam-4329	88	4	suppose	suppose	VERB
ejpam-4329	88	5	io	io	PROPN
ejpam-4329	88	6	≥	≥	PROPN
ejpam-4329	88	7	k	k	X
ejpam-4329	88	8	then	then	ADV
ejpam-4329	88	9	i	i	PRON
ejpam-4329	88	10	≤	≤	PUNCT
ejpam-4329	88	11	ioo	ioo	VERB
ejpam-4329	88	12	≤	≤	NUM
ejpam-4329	88	13	ko	ko	PROPN
ejpam-4329	88	14	and	and	CCONJ
ejpam-4329	88	15	vice	vice	ADV
ejpam-4329	88	16	versa	versa	ADV
ejpam-4329	88	17	.	.	PUNCT
ejpam-4329	89	1	(	(	PUNCT
ejpam-4329	89	2	6	6	X
ejpam-4329	89	3	)	)	PUNCT
ejpam-4329	89	4	let	let	VERB
ejpam-4329	89	5	io	io	PRON
ejpam-4329	89	6	≤	≤	PROPN
ejpam-4329	89	7	ko	ko	PROPN
ejpam-4329	89	8	.	.	PUNCT
ejpam-4329	90	1	then	then	ADV
ejpam-4329	90	2	,	,	PUNCT
ejpam-4329	90	3	from	from	ADP
ejpam-4329	90	4	proposition1	proposition1	NOUN
ejpam-4329	90	5	,	,	PUNCT
ejpam-4329	90	6	ioo	ioo	ADJ
ejpam-4329	90	7	≥	≥	NUM
ejpam-4329	90	8	koo	koo	PROPN
ejpam-4329	90	9	.	.	PUNCT
ejpam-4329	91	1	the	the	DET
ejpam-4329	91	2	opposite	opposite	ADJ
ejpam-4329	91	3	direction	direction	NOUN
ejpam-4329	91	4	can	can	AUX
ejpam-4329	91	5	be	be	AUX
ejpam-4329	91	6	get	get	VERB
ejpam-4329	91	7	by	by	ADP
ejpam-4329	91	8	using	use	VERB
ejpam-4329	91	9	(	(	PUNCT
ejpam-4329	91	10	4	4	NUM
ejpam-4329	91	11	)	)	PUNCT
ejpam-4329	91	12	.	.	PUNCT
ejpam-4329	92	1	(	(	PUNCT
ejpam-4329	92	2	7	7	X
ejpam-4329	92	3	)	)	PUNCT
ejpam-4329	92	4	assume	assume	VERB
ejpam-4329	92	5	i	i	PRON
ejpam-4329	92	6	⊆	⊆	NUM
ejpam-4329	92	7	ko	ko	PROPN
ejpam-4329	93	1	then	then	ADV
ejpam-4329	93	2	we	we	PRON
ejpam-4329	93	3	get	get	VERB
ejpam-4329	93	4	i	i	PRON
ejpam-4329	93	5	∧ko	∧ko	NOUN
ejpam-4329	93	6	=	=	SYM
ejpam-4329	93	7	(	(	PUNCT
ejpam-4329	93	8	0	0	NUM
ejpam-4329	93	9	]	]	PUNCT
ejpam-4329	93	10	,	,	PUNCT
ejpam-4329	93	11	since	since	SCONJ
ejpam-4329	93	12	k	k	PROPN
ejpam-4329	93	13	∧ko	∧ko	PROPN
ejpam-4329	93	14	=	=	SYM
ejpam-4329	93	15	(	(	PUNCT
ejpam-4329	93	16	0	0	NUM
ejpam-4329	93	17	]	]	PUNCT
ejpam-4329	93	18	.	.	PUNCT
ejpam-4329	94	1	proposition	proposition	NOUN
ejpam-4329	94	2	2	2	NUM
ejpam-4329	94	3	.	.	PUNCT
ejpam-4329	95	1	let	let	VERB
ejpam-4329	95	2	i	i	PRON
ejpam-4329	95	3	,	,	PUNCT
ejpam-4329	95	4	k	k	PROPN
ejpam-4329	95	5	∈	∈	PROPN
ejpam-4329	95	6	i(l	i(l	PROPN
ejpam-4329	95	7	)	)	PUNCT
ejpam-4329	95	8	.	.	PUNCT
ejpam-4329	96	1	then	then	ADV
ejpam-4329	96	2	:	:	PUNCT
ejpam-4329	96	3	(	(	PUNCT
ejpam-4329	96	4	1	1	X
ejpam-4329	96	5	)	)	PUNCT
ejpam-4329	96	6	i	i	PRON
ejpam-4329	96	7	∨ko	∨ko	VERB
ejpam-4329	96	8	≥	≥	PROPN
ejpam-4329	96	9	k	k	PROPN
ejpam-4329	96	10	iff	iff	PROPN
ejpam-4329	96	11	i	i	PRON
ejpam-4329	96	12	≥	≥	VERB
ejpam-4329	96	13	k	k	NOUN
ejpam-4329	96	14	,	,	PUNCT
ejpam-4329	96	15	(	(	PUNCT
ejpam-4329	96	16	2	2	X
ejpam-4329	96	17	)	)	PUNCT
ejpam-4329	96	18	i	i	PRON
ejpam-4329	96	19	∨k	∨k	ADJ
ejpam-4329	96	20	=	=	SYM
ejpam-4329	96	21	(	(	PUNCT
ejpam-4329	96	22	1	1	NUM
ejpam-4329	96	23	]	]	PUNCT
ejpam-4329	96	24	implies	imply	VERB
ejpam-4329	96	25	ko	ko	PROPN
ejpam-4329	96	26	≤	≤	PROPN
ejpam-4329	97	1	i	i	PRON
ejpam-4329	97	2	,	,	PUNCT
ejpam-4329	97	3	(	(	PUNCT
ejpam-4329	97	4	3	3	X
ejpam-4329	97	5	)	)	PUNCT
ejpam-4329	97	6	(	(	PUNCT
ejpam-4329	97	7	i	i	PRON
ejpam-4329	97	8	∨k)o	∨k)o	ADJ
ejpam-4329	97	9	=	=	SYM
ejpam-4329	97	10	io	io	X
ejpam-4329	97	11	∩ko	∩ko	PROPN
ejpam-4329	97	12	,	,	PUNCT
ejpam-4329	97	13	(	(	PUNCT
ejpam-4329	97	14	4	4	NUM
ejpam-4329	97	15	)	)	PUNCT
ejpam-4329	97	16	(	(	PUNCT
ejpam-4329	97	17	i	i	PRON
ejpam-4329	97	18	∩k)oo	∩k)oo	NOUN
ejpam-4329	97	19	≤	≤	NUM
ejpam-4329	97	20	ioo	ioo	ADJ
ejpam-4329	97	21	∩koo	∩koo	NOUN
ejpam-4329	97	22	,	,	PUNCT
ejpam-4329	97	23	(	(	PUNCT
ejpam-4329	97	24	5	5	NUM
ejpam-4329	97	25	)	)	PUNCT
ejpam-4329	97	26	(	(	PUNCT
ejpam-4329	97	27	i	i	PRON
ejpam-4329	97	28	∨	∨	VERB
ejpam-4329	97	29	io)o	io)o	PROPN
ejpam-4329	97	30	=	=	PUNCT
ejpam-4329	97	31	(	(	PUNCT
ejpam-4329	97	32	0	0	NUM
ejpam-4329	97	33	]	]	PUNCT
ejpam-4329	97	34	,	,	PUNCT
ejpam-4329	97	35	(	(	PUNCT
ejpam-4329	97	36	6	6	NUM
ejpam-4329	97	37	)	)	PUNCT
ejpam-4329	97	38	(	(	PUNCT
ejpam-4329	97	39	i	i	PROPN
ejpam-4329	97	40	∨k)oo	∨k)oo	VERB
ejpam-4329	97	41	≥	≥	NOUN
ejpam-4329	97	42	ioo	ioo	ADJ
ejpam-4329	97	43	∨koo	∨koo	NOUN
ejpam-4329	97	44	,	,	PUNCT
ejpam-4329	97	45	(	(	PUNCT
ejpam-4329	97	46	7	7	X
ejpam-4329	97	47	)	)	PUNCT
ejpam-4329	97	48	i	i	PRON
ejpam-4329	97	49	∩	∩	NOUN
ejpam-4329	97	50	(	(	PUNCT
ejpam-4329	97	51	i	i	PRON
ejpam-4329	97	52	∩k)o	∩k)o	PROPN
ejpam-4329	97	53	≥	≥	VERB
ejpam-4329	97	54	i	i	PRON
ejpam-4329	97	55	∩ko	∩ko	VERB
ejpam-4329	97	56	.	.	PUNCT
ejpam-4329	98	1	proof	proof	NOUN
ejpam-4329	98	2	.	.	PUNCT
ejpam-4329	99	1	(	(	PUNCT
ejpam-4329	99	2	1	1	X
ejpam-4329	99	3	)	)	PUNCT
ejpam-4329	99	4	suppose	suppose	VERB
ejpam-4329	99	5	that	that	SCONJ
ejpam-4329	99	6	i	i	PRON
ejpam-4329	99	7	∨	∨	PROPN
ejpam-4329	99	8	ko	ko	PROPN
ejpam-4329	99	9	≥	≥	PROPN
ejpam-4329	99	10	k	k	NOUN
ejpam-4329	99	11	,	,	PUNCT
ejpam-4329	99	12	we	we	PRON
ejpam-4329	99	13	get	get	VERB
ejpam-4329	99	14	k	k	NOUN
ejpam-4329	99	15	=	=	PUNCT
ejpam-4329	99	16	k	k	PROPN
ejpam-4329	99	17	∧	∧	PROPN
ejpam-4329	99	18	(	(	PUNCT
ejpam-4329	99	19	i	i	PROPN
ejpam-4329	99	20	∨	∨	PROPN
ejpam-4329	99	21	ko	ko	PROPN
ejpam-4329	99	22	)	)	PUNCT
ejpam-4329	99	23	=	=	PRON
ejpam-4329	100	1	(	(	PUNCT
ejpam-4329	100	2	k	k	PROPN
ejpam-4329	100	3	∧	∧	PROPN
ejpam-4329	100	4	i	i	PROPN
ejpam-4329	100	5	)	)	PUNCT
ejpam-4329	100	6	∨	∨	PROPN
ejpam-4329	100	7	(	(	PUNCT
ejpam-4329	100	8	k	k	PROPN
ejpam-4329	100	9	∧	∧	PROPN
ejpam-4329	100	10	ko	ko	PROPN
ejpam-4329	100	11	)	)	PUNCT
ejpam-4329	100	12	=	=	SYM
ejpam-4329	101	1	k	k	PROPN
ejpam-4329	101	2	∧	∧	PROPN
ejpam-4329	101	3	i	i	PROPN
ejpam-4329	101	4	,	,	PUNCT
ejpam-4329	101	5	which	which	PRON
ejpam-4329	101	6	means	mean	VERB
ejpam-4329	101	7	i	i	PRON
ejpam-4329	101	8	≥	≥	AUX
ejpam-4329	101	9	k.	k.	X
ejpam-4329	102	1	conversely	conversely	ADV
ejpam-4329	102	2	,	,	PUNCT
ejpam-4329	102	3	if	if	SCONJ
ejpam-4329	102	4	i	i	PRON
ejpam-4329	102	5	≥	≥	AUX
ejpam-4329	102	6	k	k	NOUN
ejpam-4329	102	7	then	then	ADV
ejpam-4329	102	8	io	io	X
ejpam-4329	102	9	≤	≤	PROPN
ejpam-4329	102	10	ko	ko	PROPN
ejpam-4329	102	11	.	.	PUNCT
ejpam-4329	103	1	so	so	ADV
ejpam-4329	103	2	i	i	PRON
ejpam-4329	103	3	∨ko	∨ko	VERB
ejpam-4329	103	4	≥	≥	NUM
ejpam-4329	103	5	i	i	PROPN
ejpam-4329	103	6	∨	∨	PROPN
ejpam-4329	103	7	io	io	PROPN
ejpam-4329	103	8	≥	≥	PROPN
ejpam-4329	103	9	i	i	PRON
ejpam-4329	103	10	≥	≥	PROPN
ejpam-4329	103	11	k.	k.	PROPN
ejpam-4329	103	12	(	(	PUNCT
ejpam-4329	103	13	2	2	X
ejpam-4329	103	14	)	)	PUNCT
ejpam-4329	103	15	assume	assume	VERB
ejpam-4329	103	16	i	i	PRON
ejpam-4329	103	17	∨k	∨k	ADJ
ejpam-4329	103	18	=	=	SYM
ejpam-4329	103	19	(	(	PUNCT
ejpam-4329	103	20	1	1	NUM
ejpam-4329	103	21	]	]	PUNCT
ejpam-4329	103	22	.	.	PUNCT
ejpam-4329	104	1	meet	meet	VERB
ejpam-4329	104	2	each	each	DET
ejpam-4329	104	3	side	side	NOUN
ejpam-4329	104	4	by	by	ADP
ejpam-4329	104	5	ko	ko	PROPN
ejpam-4329	104	6	to	to	PART
ejpam-4329	104	7	get	get	VERB
ejpam-4329	104	8	ko	ko	PROPN
ejpam-4329	104	9	∧	∧	PROPN
ejpam-4329	104	10	i	i	PRON
ejpam-4329	104	11	=	=	SYM
ejpam-4329	104	12	ko	ko	PROPN
ejpam-4329	104	13	.	.	PUNCT
ejpam-4329	105	1	thus	thus	ADV
ejpam-4329	105	2	ko	ko	PROPN
ejpam-4329	105	3	≤	≤	PROPN
ejpam-4329	105	4	i.	i.	NOUN
ejpam-4329	105	5	(	(	PUNCT
ejpam-4329	105	6	3	3	X
ejpam-4329	105	7	)	)	PUNCT
ejpam-4329	105	8	let	let	VERB
ejpam-4329	105	9	x	x	X
ejpam-4329	105	10	∈	∈	PROPN
ejpam-4329	105	11	io	io	X
ejpam-4329	105	12	∩	∩	PROPN
ejpam-4329	105	13	ko	ko	PROPN
ejpam-4329	105	14	and	and	CCONJ
ejpam-4329	105	15	z	z	NOUN
ejpam-4329	105	16	=	=	PUNCT
ejpam-4329	105	17	a	a	DET
ejpam-4329	105	18	∨	∨	NUM
ejpam-4329	105	19	b	b	X
ejpam-4329	105	20	∈	∈	PROPN
ejpam-4329	106	1	i	i	PRON
ejpam-4329	106	2	∨	∨	PROPN
ejpam-4329	106	3	k	k	PROPN
ejpam-4329	106	4	,	,	PUNCT
ejpam-4329	106	5	where	where	SCONJ
ejpam-4329	106	6	a	a	DET
ejpam-4329	106	7	∈	∈	NOUN
ejpam-4329	106	8	i	i	PRON
ejpam-4329	106	9	and	and	CCONJ
ejpam-4329	106	10	b	b	PROPN
ejpam-4329	106	11	∈	∈	PROPN
ejpam-4329	106	12	k.	k.	NOUN
ejpam-4329	107	1	then	then	ADV
ejpam-4329	107	2	x	x	X
ejpam-4329	107	3	≤	≤	ADV
ejpam-4329	107	4	ah	ah	INTJ
ejpam-4329	107	5	and	and	CCONJ
ejpam-4329	107	6	x	x	SYM
ejpam-4329	107	7	≤	≤	NUM
ejpam-4329	107	8	bh	bh	NOUN
ejpam-4329	107	9	.	.	PUNCT
ejpam-4329	108	1	it	it	PRON
ejpam-4329	108	2	implies	imply	VERB
ejpam-4329	108	3	x	x	PUNCT
ejpam-4329	108	4	≤	≤	ADV
ejpam-4329	108	5	ah	ah	INTJ
ejpam-4329	108	6	∧	∧	NOUN
ejpam-4329	108	7	bh	bh	NOUN
ejpam-4329	108	8	=	=	X
ejpam-4329	108	9	(	(	PUNCT
ejpam-4329	108	10	a	a	DET
ejpam-4329	108	11	∨	∨	NOUN
ejpam-4329	108	12	b)h	b)h	X
ejpam-4329	108	13	=	=	SYM
ejpam-4329	108	14	zh	zh	PROPN
ejpam-4329	108	15	.	.	PUNCT
ejpam-4329	109	1	hence	hence	ADV
ejpam-4329	109	2	,	,	PUNCT
ejpam-4329	109	3	x	x	X
ejpam-4329	109	4	∈	∈	PROPN
ejpam-4329	109	5	(	(	PUNCT
ejpam-4329	109	6	i	i	NOUN
ejpam-4329	109	7	∨	∨	X
ejpam-4329	109	8	k)o	k)o	ADJ
ejpam-4329	109	9	and	and	CCONJ
ejpam-4329	109	10	so	so	ADV
ejpam-4329	109	11	io	io	PROPN
ejpam-4329	109	12	∩ko	∩ko	PROPN
ejpam-4329	109	13	⊆	⊆	NUM
ejpam-4329	109	14	(	(	PUNCT
ejpam-4329	109	15	i	i	PRON
ejpam-4329	109	16	∨k)o	∨k)o	PROPN
ejpam-4329	109	17	.	.	PUNCT
ejpam-4329	110	1	the	the	DET
ejpam-4329	110	2	converse	converse	NOUN
ejpam-4329	110	3	is	be	AUX
ejpam-4329	110	4	trivial	trivial	ADJ
ejpam-4329	110	5	.	.	PUNCT
ejpam-4329	111	1	(	(	PUNCT
ejpam-4329	111	2	4	4	NUM
ejpam-4329	111	3	)	)	PUNCT
ejpam-4329	111	4	from	from	ADP
ejpam-4329	111	5	(	(	PUNCT
ejpam-4329	111	6	3	3	X
ejpam-4329	111	7	)	)	PUNCT
ejpam-4329	111	8	we	we	PRON
ejpam-4329	111	9	get	get	VERB
ejpam-4329	111	10	(	(	PUNCT
ejpam-4329	111	11	i	i	NOUN
ejpam-4329	111	12	∩k)oo	∩k)oo	NOUN
ejpam-4329	111	13	≤	≤	NUM
ejpam-4329	111	14	ioo	ioo	ADJ
ejpam-4329	111	15	∩koo	∩koo	NOUN
ejpam-4329	111	16	.	.	PUNCT
ejpam-4329	112	1	(	(	PUNCT
ejpam-4329	112	2	5	5	X
ejpam-4329	112	3	)	)	PUNCT
ejpam-4329	112	4	using	use	VERB
ejpam-4329	112	5	(	(	PUNCT
ejpam-4329	112	6	3	3	X
ejpam-4329	112	7	)	)	PUNCT
ejpam-4329	112	8	we	we	PRON
ejpam-4329	112	9	get	get	VERB
ejpam-4329	112	10	(	(	PUNCT
ejpam-4329	112	11	i	i	NOUN
ejpam-4329	112	12	∨	∨	VERB
ejpam-4329	112	13	io)o	io)o	PROPN
ejpam-4329	112	14	=	=	SYM
ejpam-4329	112	15	io	io	X
ejpam-4329	112	16	∩	∩	X
ejpam-4329	112	17	ioo	ioo	VERB
ejpam-4329	112	18	=	=	SYM
ejpam-4329	112	19	(	(	PUNCT
ejpam-4329	112	20	0	0	NUM
ejpam-4329	112	21	]	]	PUNCT
ejpam-4329	112	22	.	.	PUNCT
ejpam-4329	113	1	(	(	PUNCT
ejpam-4329	113	2	6	6	NUM
ejpam-4329	113	3	)	)	PUNCT
ejpam-4329	113	4	since	since	SCONJ
ejpam-4329	113	5	k	k	PROPN
ejpam-4329	113	6	,	,	PUNCT
ejpam-4329	114	1	i	i	PRON
ejpam-4329	114	2	≤	≤	ADV
ejpam-4329	114	3	i	i	PRON
ejpam-4329	114	4	∨k	∨k	VERB
ejpam-4329	114	5	,	,	PUNCT
ejpam-4329	114	6	then	then	ADV
ejpam-4329	114	7	ioo	ioo	VERB
ejpam-4329	114	8	,	,	PUNCT
ejpam-4329	114	9	koo	koo	NOUN
ejpam-4329	114	10	≤	≤	NUM
ejpam-4329	114	11	(	(	PUNCT
ejpam-4329	114	12	i	i	PRON
ejpam-4329	114	13	∨k)oo	∨k)oo	NOUN
ejpam-4329	114	14	.	.	PUNCT
ejpam-4329	115	1	hence	hence	ADV
ejpam-4329	115	2	ioo	ioo	VERB
ejpam-4329	115	3	∨koo	∨koo	NOUN
ejpam-4329	115	4	≤	≤	NOUN
ejpam-4329	115	5	(	(	PUNCT
ejpam-4329	115	6	i	i	NOUN
ejpam-4329	115	7	∨k)oo	∨k)oo	PROPN
ejpam-4329	115	8	.	.	PUNCT
ejpam-4329	116	1	(	(	PUNCT
ejpam-4329	116	2	7	7	NUM
ejpam-4329	116	3	)	)	PUNCT
ejpam-4329	116	4	since	since	SCONJ
ejpam-4329	116	5	(	(	PUNCT
ejpam-4329	116	6	i	i	PRON
ejpam-4329	116	7	∩k)o	∩k)o	PROPN
ejpam-4329	116	8	≥	≥	NOUN
ejpam-4329	116	9	ko	ko	NOUN
ejpam-4329	116	10	.	.	PUNCT
ejpam-4329	117	1	meeting	meet	VERB
ejpam-4329	117	2	both	both	DET
ejpam-4329	117	3	sides	side	NOUN
ejpam-4329	117	4	by	by	ADP
ejpam-4329	117	5	i	i	PRON
ejpam-4329	117	6	we	we	PRON
ejpam-4329	117	7	get	get	VERB
ejpam-4329	117	8	i	i	PRON
ejpam-4329	117	9	∩	∩	NOUN
ejpam-4329	117	10	(	(	PUNCT
ejpam-4329	117	11	i	i	PRON
ejpam-4329	117	12	∩k)o	∩k)o	PROPN
ejpam-4329	117	13	≥	≥	VERB
ejpam-4329	117	14	i	i	PRON
ejpam-4329	117	15	∩ko	∩ko	VERB
ejpam-4329	117	16	.	.	PUNCT
ejpam-4329	118	1	the	the	DET
ejpam-4329	118	2	skeleton	skeleton	PROPN
ejpam-4329	118	3	s(i(l	s(i(l	PROPN
ejpam-4329	118	4	)	)	PUNCT
ejpam-4329	118	5	)	)	PUNCT
ejpam-4329	119	1	and	and	CCONJ
ejpam-4329	119	2	the	the	DET
ejpam-4329	119	3	set	set	NOUN
ejpam-4329	119	4	of	of	ADP
ejpam-4329	119	5	dense	dense	ADJ
ejpam-4329	119	6	elements	element	NOUN
ejpam-4329	119	7	of	of	ADP
ejpam-4329	119	8	i(l	i(l	PROPN
ejpam-4329	119	9	)	)	PUNCT
ejpam-4329	119	10	are	be	AUX
ejpam-4329	119	11	defined	define	VERB
ejpam-4329	119	12	as	as	ADP
ejpam-4329	119	13	:	:	PUNCT
ejpam-4329	119	14	s(i(l	s(i(l	NOUN
ejpam-4329	119	15	)	)	PUNCT
ejpam-4329	119	16	)	)	PUNCT
ejpam-4329	120	1	=	=	PRON
ejpam-4329	120	2	{	{	PUNCT
ejpam-4329	121	1	i	i	NOUN
ejpam-4329	121	2	∈	∈	PROPN
ejpam-4329	121	3	i(l	i(l	PROPN
ejpam-4329	121	4	)	)	PUNCT
ejpam-4329	121	5	:	:	PUNCT
ejpam-4329	122	1	i	i	PRON
ejpam-4329	122	2	=	=	SYM
ejpam-4329	122	3	ioo	ioo	PROPN
ejpam-4329	122	4	}	}	PUNCT
ejpam-4329	122	5	,	,	PUNCT
ejpam-4329	122	6	and	and	CCONJ
ejpam-4329	122	7	d(i(l	d(i(l	PROPN
ejpam-4329	122	8	)	)	PUNCT
ejpam-4329	122	9	)	)	PUNCT
ejpam-4329	123	1	=	=	PRON
ejpam-4329	123	2	{	{	PUNCT
ejpam-4329	124	1	i	i	NOUN
ejpam-4329	124	2	∈	∈	PROPN
ejpam-4329	124	3	i(l	i(l	PROPN
ejpam-4329	124	4	)	)	PUNCT
ejpam-4329	124	5	:	:	PUNCT
ejpam-4329	125	1	io	io	X
ejpam-4329	125	2	=	=	PUNCT
ejpam-4329	125	3	(	(	PUNCT
ejpam-4329	125	4	0	0	NUM
ejpam-4329	125	5	]	]	PUNCT
ejpam-4329	125	6	}	}	PUNCT
ejpam-4329	125	7	.	.	PUNCT
ejpam-4329	126	1	the	the	DET
ejpam-4329	126	2	elements	element	NOUN
ejpam-4329	126	3	of	of	ADP
ejpam-4329	126	4	s(i(l	s(i(l	NOUN
ejpam-4329	126	5	)	)	PUNCT
ejpam-4329	126	6	)	)	PUNCT
ejpam-4329	126	7	and	and	CCONJ
ejpam-4329	126	8	d(i(l	d(i(l	PROPN
ejpam-4329	126	9	)	)	PUNCT
ejpam-4329	126	10	)	)	PUNCT
ejpam-4329	126	11	are	be	AUX
ejpam-4329	126	12	called	call	VERB
ejpam-4329	126	13	closed	closed	ADJ
ejpam-4329	126	14	and	and	CCONJ
ejpam-4329	126	15	dense	dense	ADJ
ejpam-4329	126	16	ideals	ideal	NOUN
ejpam-4329	126	17	,	,	PUNCT
ejpam-4329	126	18	respectively	respectively	ADV
ejpam-4329	126	19	.	.	PUNCT
ejpam-4329	127	1	e.	e.	PROPN
ejpam-4329	127	2	g.	g.	PROPN
ejpam-4329	127	3	rezk	rezk	PROPN
ejpam-4329	127	4	/	/	SYM
ejpam-4329	127	5	eur	eur	PROPN
ejpam-4329	127	6	.	.	PUNCT
ejpam-4329	128	1	j.	j.	PROPN
ejpam-4329	128	2	pure	pure	PROPN
ejpam-4329	128	3	appl	appl	PROPN
ejpam-4329	128	4	.	.	PROPN
ejpam-4329	128	5	math	math	PROPN
ejpam-4329	128	6	,	,	PUNCT
ejpam-4329	128	7	15	15	NUM
ejpam-4329	128	8	(	(	PUNCT
ejpam-4329	128	9	2	2	NUM
ejpam-4329	128	10	)	)	PUNCT
ejpam-4329	128	11	(	(	PUNCT
ejpam-4329	128	12	2022	2022	NUM
ejpam-4329	128	13	)	)	PUNCT
ejpam-4329	128	14	,	,	PUNCT
ejpam-4329	128	15	486	486	NUM
ejpam-4329	128	16	-	-	SYM
ejpam-4329	128	17	495	495	NUM
ejpam-4329	128	18	491	491	NUM
ejpam-4329	128	19	lemma	lemma	PROPN
ejpam-4329	128	20	2	2	NUM
ejpam-4329	128	21	.	.	PUNCT
ejpam-4329	129	1	let	let	VERB
ejpam-4329	129	2	i	i	PRON
ejpam-4329	129	3	and	and	CCONJ
ejpam-4329	129	4	k	k	PROPN
ejpam-4329	129	5	be	be	VERB
ejpam-4329	129	6	two	two	NUM
ejpam-4329	129	7	ideals	ideal	NOUN
ejpam-4329	129	8	.	.	PUNCT
ejpam-4329	130	1	then	then	ADV
ejpam-4329	130	2	:	:	PUNCT
ejpam-4329	130	3	(	(	PUNCT
ejpam-4329	130	4	1	1	X
ejpam-4329	130	5	)	)	PUNCT
ejpam-4329	130	6	(	(	PUNCT
ejpam-4329	130	7	a]oo	a]oo	NOUN
ejpam-4329	130	8	=	=	SYM
ejpam-4329	130	9	(	(	PUNCT
ejpam-4329	130	10	a	a	PRON
ejpam-4329	130	11	]	]	X
ejpam-4329	130	12	iff	iff	PROPN
ejpam-4329	130	13	a	a	DET
ejpam-4329	130	14	∈	∈	PROPN
ejpam-4329	130	15	s(l	s(l	NUM
ejpam-4329	130	16	)	)	PUNCT
ejpam-4329	130	17	,	,	PUNCT
ejpam-4329	130	18	(	(	PUNCT
ejpam-4329	130	19	2	2	X
ejpam-4329	130	20	)	)	PUNCT
ejpam-4329	130	21	i	i	PRON
ejpam-4329	130	22	∩k	∩k	ADV
ejpam-4329	130	23	=	=	SYM
ejpam-4329	130	24	(	(	PUNCT
ejpam-4329	130	25	io	io	X
ejpam-4329	130	26	∨ko)o	∨ko)o	PROPN
ejpam-4329	130	27	,	,	PUNCT
ejpam-4329	130	28	for	for	ADP
ejpam-4329	130	29	all	all	DET
ejpam-4329	130	30	i	i	PRON
ejpam-4329	130	31	,	,	PUNCT
ejpam-4329	130	32	k	k	PROPN
ejpam-4329	130	33	∈	∈	PROPN
ejpam-4329	130	34	s(i(l	s(i(l	PROPN
ejpam-4329	130	35	)	)	PUNCT
ejpam-4329	130	36	)	)	PUNCT
ejpam-4329	130	37	,	,	PUNCT
ejpam-4329	130	38	(	(	PUNCT
ejpam-4329	130	39	3	3	X
ejpam-4329	130	40	)	)	PUNCT
ejpam-4329	130	41	if	if	SCONJ
ejpam-4329	130	42	i	i	PRON
ejpam-4329	130	43	∨	∨	VERB
ejpam-4329	130	44	io	io	X
ejpam-4329	130	45	=	=	PUNCT
ejpam-4329	130	46	(	(	PUNCT
ejpam-4329	130	47	1	1	X
ejpam-4329	130	48	]	]	PUNCT
ejpam-4329	130	49	then	then	ADV
ejpam-4329	130	50	i	i	PROPN
ejpam-4329	130	51	∈	∈	PROPN
ejpam-4329	130	52	s(i(l	s(i(l	PROPN
ejpam-4329	130	53	)	)	PUNCT
ejpam-4329	130	54	)	)	PUNCT
ejpam-4329	130	55	,	,	PUNCT
ejpam-4329	130	56	(	(	PUNCT
ejpam-4329	130	57	4	4	X
ejpam-4329	130	58	)	)	PUNCT
ejpam-4329	130	59	if	if	SCONJ
ejpam-4329	130	60	i	i	PRON
ejpam-4329	130	61	is	be	AUX
ejpam-4329	130	62	an	an	DET
ejpam-4329	130	63	annihilator	annihilator	NOUN
ejpam-4329	130	64	then	then	ADV
ejpam-4329	130	65	i	i	PROPN
ejpam-4329	130	66	∈	∈	PROPN
ejpam-4329	130	67	s(i(l	s(i(l	PROPN
ejpam-4329	130	68	)	)	PUNCT
ejpam-4329	130	69	)	)	PUNCT
ejpam-4329	130	70	.	.	PUNCT
ejpam-4329	131	1	proof	proof	NOUN
ejpam-4329	131	2	.	.	PUNCT
ejpam-4329	132	1	(	(	PUNCT
ejpam-4329	132	2	1	1	X
ejpam-4329	132	3	)	)	PUNCT
ejpam-4329	132	4	immediately	immediately	ADV
ejpam-4329	132	5	from	from	ADP
ejpam-4329	132	6	(	(	PUNCT
ejpam-4329	132	7	1	1	NUM
ejpam-4329	132	8	)	)	PUNCT
ejpam-4329	132	9	in	in	ADP
ejpam-4329	132	10	lemma	lemma	PROPN
ejpam-4329	132	11	1	1	NUM
ejpam-4329	132	12	.	.	PUNCT
ejpam-4329	132	13	(	(	PUNCT
ejpam-4329	132	14	2	2	NUM
ejpam-4329	132	15	)	)	PUNCT
ejpam-4329	132	16	by	by	ADP
ejpam-4329	132	17	using	use	VERB
ejpam-4329	132	18	(	(	PUNCT
ejpam-4329	132	19	3	3	NUM
ejpam-4329	132	20	)	)	PUNCT
ejpam-4329	132	21	in	in	ADP
ejpam-4329	132	22	proposition	proposition	NOUN
ejpam-4329	132	23	2	2	NUM
ejpam-4329	132	24	,	,	PUNCT
ejpam-4329	132	25	i	i	PRON
ejpam-4329	132	26	∩k	∩k	VERB
ejpam-4329	132	27	=	=	SYM
ejpam-4329	132	28	ioo	ioo	ADJ
ejpam-4329	132	29	∩koo	∩koo	NOUN
ejpam-4329	132	30	=	=	SYM
ejpam-4329	132	31	(	(	PUNCT
ejpam-4329	132	32	io	io	X
ejpam-4329	132	33	∨ko)o	∨ko)o	PROPN
ejpam-4329	132	34	.	.	PUNCT
ejpam-4329	133	1	(	(	PUNCT
ejpam-4329	133	2	3	3	X
ejpam-4329	133	3	)	)	PUNCT
ejpam-4329	133	4	assume	assume	VERB
ejpam-4329	133	5	i	i	PRON
ejpam-4329	133	6	∨	∨	X
ejpam-4329	133	7	io	io	X
ejpam-4329	133	8	=	=	PUNCT
ejpam-4329	133	9	(	(	PUNCT
ejpam-4329	133	10	1	1	NUM
ejpam-4329	133	11	]	]	PUNCT
ejpam-4329	133	12	,	,	PUNCT
ejpam-4329	133	13	meet	meet	VERB
ejpam-4329	133	14	both	both	DET
ejpam-4329	133	15	sides	side	NOUN
ejpam-4329	133	16	by	by	ADP
ejpam-4329	133	17	ioo	ioo	ADJ
ejpam-4329	133	18	to	to	PART
ejpam-4329	133	19	get	get	VERB
ejpam-4329	133	20	ioo	ioo	VERB
ejpam-4329	133	21	=	=	SYM
ejpam-4329	133	22	ioo	ioo	VERB
ejpam-4329	133	23	∧	∧	PROPN
ejpam-4329	133	24	(	(	PUNCT
ejpam-4329	133	25	i	i	PROPN
ejpam-4329	133	26	∨	∨	PROPN
ejpam-4329	133	27	io	io	PROPN
ejpam-4329	133	28	)	)	PUNCT
ejpam-4329	133	29	=	=	SYM
ejpam-4329	133	30	(	(	PUNCT
ejpam-4329	133	31	ioo	ioo	ADJ
ejpam-4329	133	32	∧	∧	PROPN
ejpam-4329	133	33	i	i	PROPN
ejpam-4329	133	34	)	)	PUNCT
ejpam-4329	133	35	∨	∨	PROPN
ejpam-4329	133	36	(	(	PUNCT
ejpam-4329	133	37	ioo	ioo	VERB
ejpam-4329	133	38	∧	∧	PROPN
ejpam-4329	133	39	io	io	NOUN
ejpam-4329	133	40	)	)	PUNCT
ejpam-4329	133	41	=	=	SYM
ejpam-4329	134	1	ioo	ioo	VERB
ejpam-4329	134	2	∧	∧	PROPN
ejpam-4329	134	3	i	i	NOUN
ejpam-4329	134	4	=	=	NOUN
ejpam-4329	134	5	i.	i.	NOUN
ejpam-4329	134	6	therefore	therefore	ADV
ejpam-4329	134	7	i	i	PRON
ejpam-4329	134	8	=	=	SYM
ejpam-4329	134	9	ioo	ioo	PROPN
ejpam-4329	134	10	.	.	PUNCT
ejpam-4329	135	1	(	(	PUNCT
ejpam-4329	135	2	4	4	X
ejpam-4329	135	3	)	)	PUNCT
ejpam-4329	135	4	let	let	VERB
ejpam-4329	135	5	i	i	PRON
ejpam-4329	135	6	be	be	AUX
ejpam-4329	135	7	an	an	DET
ejpam-4329	135	8	annihilator	annihilator	NOUN
ejpam-4329	135	9	and	and	CCONJ
ejpam-4329	135	10	i∗o	i∗o	PROPN
ejpam-4329	135	11	be	be	AUX
ejpam-4329	135	12	a	a	DET
ejpam-4329	135	13	proper	proper	ADJ
ejpam-4329	135	14	subset	subset	NOUN
ejpam-4329	135	15	of	of	ADP
ejpam-4329	135	16	i	i	PROPN
ejpam-4329	135	17	=	=	PROPN
ejpam-4329	135	18	i∗∗.	i∗∗.	VERB
ejpam-4329	135	19	so	so	SCONJ
ejpam-4329	135	20	there	there	PRON
ejpam-4329	135	21	exists	exist	VERB
ejpam-4329	135	22	x	x	X
ejpam-4329	135	23	∈	∈	PROPN
ejpam-4329	135	24	i∗∗	i∗∗	PRON
ejpam-4329	135	25	such	such	ADJ
ejpam-4329	135	26	that	that	SCONJ
ejpam-4329	135	27	x	x	SYM
ejpam-4329	135	28	�	�	PROPN
ejpam-4329	135	29	ah	ah	INTJ
ejpam-4329	135	30	for	for	ADP
ejpam-4329	135	31	all	all	DET
ejpam-4329	135	32	a	a	DET
ejpam-4329	135	33	∈	∈	NOUN
ejpam-4329	135	34	i∗.	i∗.	NOUN
ejpam-4329	135	35	thus	thus	ADV
ejpam-4329	135	36	x	x	X
ejpam-4329	135	37	≤	≤	ADJ
ejpam-4329	135	38	a∗	a∗	NOUN
ejpam-4329	135	39	and	and	CCONJ
ejpam-4329	135	40	x	x	PART
ejpam-4329	135	41	�	�	PROPN
ejpam-4329	135	42	a∗	a∗	PROPN
ejpam-4329	135	43	,	,	PUNCT
ejpam-4329	135	44	at	at	ADP
ejpam-4329	135	45	the	the	DET
ejpam-4329	135	46	same	same	ADJ
ejpam-4329	135	47	time	time	NOUN
ejpam-4329	135	48	,	,	PUNCT
ejpam-4329	135	49	which	which	PRON
ejpam-4329	135	50	is	be	AUX
ejpam-4329	135	51	a	a	DET
ejpam-4329	135	52	contradiction	contradiction	NOUN
ejpam-4329	135	53	.	.	PUNCT
ejpam-4329	136	1	therefore	therefore	ADV
ejpam-4329	136	2	i	i	PRON
ejpam-4329	136	3	=	=	PUNCT
ejpam-4329	136	4	i∗o	i∗o	PROPN
ejpam-4329	136	5	∈	∈	PROPN
ejpam-4329	136	6	s(i(l	s(i(l	PROPN
ejpam-4329	136	7	)	)	PUNCT
ejpam-4329	136	8	)	)	PUNCT
ejpam-4329	136	9	.	.	PUNCT
ejpam-4329	137	1	theorem	theorem	NOUN
ejpam-4329	137	2	2	2	NUM
ejpam-4329	137	3	.	.	PUNCT
ejpam-4329	138	1	the	the	DET
ejpam-4329	138	2	skeleton	skeleton	NOUN
ejpam-4329	138	3	s(i(l	s(i(l	PROPN
ejpam-4329	138	4	)	)	PUNCT
ejpam-4329	138	5	)	)	PUNCT
ejpam-4329	138	6	of	of	ADP
ejpam-4329	138	7	the	the	DET
ejpam-4329	138	8	lattice	lattice	PROPN
ejpam-4329	138	9	i(l	i(l	PROPN
ejpam-4329	138	10	)	)	PUNCT
ejpam-4329	138	11	forms	form	VERB
ejpam-4329	138	12	an	an	DET
ejpam-4329	138	13	ortho	ortho	PROPN
ejpam-4329	138	14	lattice	lattice	PROPN
ejpam-4329	138	15	.	.	PUNCT
ejpam-4329	139	1	proof	proof	NOUN
ejpam-4329	139	2	.	.	PUNCT
ejpam-4329	140	1	two	two	NUM
ejpam-4329	140	2	binary	binary	ADJ
ejpam-4329	140	3	operations	operation	NOUN
ejpam-4329	140	4	∩	∩	NOUN
ejpam-4329	140	5	and	and	CCONJ
ejpam-4329	140	6	t	t	NOUN
ejpam-4329	140	7	will	will	AUX
ejpam-4329	140	8	be	be	AUX
ejpam-4329	140	9	defined	define	VERB
ejpam-4329	140	10	for	for	ADP
ejpam-4329	140	11	i	i	PRON
ejpam-4329	140	12	,	,	PUNCT
ejpam-4329	140	13	k	k	PROPN
ejpam-4329	140	14	∈	∈	PROPN
ejpam-4329	140	15	s(i(l	s(i(l	PROPN
ejpam-4329	140	16	)	)	PUNCT
ejpam-4329	140	17	)	)	PUNCT
ejpam-4329	141	1	by	by	ADP
ejpam-4329	141	2	:	:	PUNCT
ejpam-4329	141	3	i	i	PRON
ejpam-4329	141	4	∩k	∩k	NOUN
ejpam-4329	141	5	=	=	SYM
ejpam-4329	141	6	(	(	PUNCT
ejpam-4329	141	7	io	io	X
ejpam-4329	141	8	∨ko)o	∨ko)o	PROPN
ejpam-4329	141	9	and	and	CCONJ
ejpam-4329	141	10	i	i	PRON
ejpam-4329	141	11	tk	tk	PROPN
ejpam-4329	141	12	=	=	SYM
ejpam-4329	141	13	(	(	PUNCT
ejpam-4329	141	14	io	io	X
ejpam-4329	141	15	∩ko)o	∩ko)o	PROPN
ejpam-4329	141	16	.	.	PUNCT
ejpam-4329	142	1	it	it	PRON
ejpam-4329	142	2	is	be	AUX
ejpam-4329	142	3	clear	clear	ADJ
ejpam-4329	142	4	that	that	SCONJ
ejpam-4329	142	5	the	the	DET
ejpam-4329	142	6	meet	meet	ADJ
ejpam-4329	142	7	operation	operation	NOUN
ejpam-4329	142	8	∩	∩	NOUN
ejpam-4329	142	9	is	be	AUX
ejpam-4329	142	10	the	the	DET
ejpam-4329	142	11	usual	usual	ADJ
ejpam-4329	142	12	intersection	intersection	NOUN
ejpam-4329	142	13	of	of	ADP
ejpam-4329	142	14	i(l	i(l	PROPN
ejpam-4329	142	15	)	)	PUNCT
ejpam-4329	142	16	.	.	PUNCT
ejpam-4329	143	1	now	now	ADV
ejpam-4329	143	2	we	we	PRON
ejpam-4329	143	3	prove	prove	VERB
ejpam-4329	143	4	that	that	SCONJ
ejpam-4329	143	5	the	the	DET
ejpam-4329	143	6	supremum	supremum	ADJ
ejpam-4329	143	7	i	i	PRON
ejpam-4329	143	8	tk	tk	VERB
ejpam-4329	143	9	of	of	ADP
ejpam-4329	143	10	any	any	DET
ejpam-4329	143	11	two	two	NUM
ejpam-4329	143	12	ideals	ideal	NOUN
ejpam-4329	143	13	i	i	PRON
ejpam-4329	143	14	and	and	CCONJ
ejpam-4329	143	15	k	k	PROPN
ejpam-4329	143	16	of	of	ADP
ejpam-4329	143	17	s(i(l	s(i(l	PROPN
ejpam-4329	143	18	)	)	PUNCT
ejpam-4329	143	19	)	)	PUNCT
ejpam-4329	143	20	equals	equal	VERB
ejpam-4329	143	21	(	(	PUNCT
ejpam-4329	143	22	io	io	X
ejpam-4329	143	23	∩ko)o	∩ko)o	PROPN
ejpam-4329	143	24	:	:	PUNCT
ejpam-4329	143	25	since	since	SCONJ
ejpam-4329	143	26	io	io	PROPN
ejpam-4329	143	27	∩ko	∩ko	PROPN
ejpam-4329	143	28	≤	≤	PROPN
ejpam-4329	143	29	io	io	PROPN
ejpam-4329	143	30	,	,	PUNCT
ejpam-4329	143	31	ko	ko	PROPN
ejpam-4329	143	32	,	,	PUNCT
ejpam-4329	143	33	we	we	PRON
ejpam-4329	143	34	get	get	VERB
ejpam-4329	143	35	(	(	PUNCT
ejpam-4329	143	36	io	io	X
ejpam-4329	143	37	∩ko)o	∩ko)o	PROPN
ejpam-4329	143	38	≥	≥	NOUN
ejpam-4329	143	39	ioo	ioo	VERB
ejpam-4329	144	1	=	=	PUNCT
ejpam-4329	144	2	i	i	PROPN
ejpam-4329	144	3	,	,	PUNCT
ejpam-4329	144	4	koo	koo	PROPN
ejpam-4329	144	5	=	=	PUNCT
ejpam-4329	144	6	k.	k.	PROPN
ejpam-4329	145	1	if	if	SCONJ
ejpam-4329	145	2	j	j	PROPN
ejpam-4329	145	3	∈	∈	PROPN
ejpam-4329	145	4	s(i(l	s(i(l	PROPN
ejpam-4329	145	5	)	)	PUNCT
ejpam-4329	145	6	)	)	PUNCT
ejpam-4329	146	1	and	and	CCONJ
ejpam-4329	146	2	j	j	PROPN
ejpam-4329	146	3	≥	≥	NUM
ejpam-4329	146	4	i	i	PRON
ejpam-4329	146	5	,	,	PUNCT
ejpam-4329	146	6	k	k	PROPN
ejpam-4329	146	7	,	,	PUNCT
ejpam-4329	146	8	then	then	ADV
ejpam-4329	146	9	jo	jo	PROPN
ejpam-4329	146	10	≤	≤	PROPN
ejpam-4329	146	11	io	io	PROPN
ejpam-4329	146	12	,	,	PUNCT
ejpam-4329	146	13	ko	ko	PROPN
ejpam-4329	146	14	.	.	PUNCT
ejpam-4329	147	1	it	it	PRON
ejpam-4329	147	2	implies	imply	VERB
ejpam-4329	147	3	jo	jo	PROPN
ejpam-4329	147	4	≤	≤	PROPN
ejpam-4329	147	5	io	io	X
ejpam-4329	147	6	∩ko	∩ko	PROPN
ejpam-4329	147	7	i.e.	i.e.	X
ejpam-4329	147	8	,	,	PUNCT
ejpam-4329	147	9	joo	joo	PROPN
ejpam-4329	147	10	=	=	SYM
ejpam-4329	147	11	j	j	PROPN
ejpam-4329	147	12	≥	≥	X
ejpam-4329	147	13	(	(	PUNCT
ejpam-4329	147	14	io	io	X
ejpam-4329	147	15	∩ko)o	∩ko)o	PROPN
ejpam-4329	147	16	.	.	PUNCT
ejpam-4329	148	1	if	if	SCONJ
ejpam-4329	148	2	i	i	PRON
ejpam-4329	148	3	∈	∈	VERB
ejpam-4329	148	4	s(i(l)),then	s(i(l)),then	ADV
ejpam-4329	148	5	io	io	PROPN
ejpam-4329	148	6	is	be	AUX
ejpam-4329	148	7	the	the	DET
ejpam-4329	148	8	orthcomplemented	orthcomplemente	VERB
ejpam-4329	148	9	of	of	ADP
ejpam-4329	148	10	i.	i.	NOUN
ejpam-4329	148	11	especially	especially	ADV
ejpam-4329	148	12	,	,	PUNCT
ejpam-4329	148	13	(	(	PUNCT
ejpam-4329	148	14	0]o	0]o	PUNCT
ejpam-4329	148	15	=	=	SYM
ejpam-4329	148	16	(	(	PUNCT
ejpam-4329	148	17	1	1	X
ejpam-4329	148	18	]	]	PUNCT
ejpam-4329	148	19	and	and	CCONJ
ejpam-4329	148	20	(	(	PUNCT
ejpam-4329	148	21	1]o	1]o	NUM
ejpam-4329	148	22	=	=	SYM
ejpam-4329	148	23	(	(	PUNCT
ejpam-4329	148	24	0	0	NUM
ejpam-4329	148	25	]	]	PUNCT
ejpam-4329	148	26	.	.	PUNCT
ejpam-4329	149	1	therefore	therefore	ADV
ejpam-4329	149	2	<	<	X
ejpam-4329	149	3	s(i(l));∩,t	s(i(l));∩,t	NOUN
ejpam-4329	149	4	,	,	PUNCT
ejpam-4329	149	5	o	o	INTJ
ejpam-4329	149	6	,	,	PUNCT
ejpam-4329	149	7	(	(	PUNCT
ejpam-4329	149	8	0	0	NUM
ejpam-4329	149	9	]	]	PUNCT
ejpam-4329	149	10	,	,	PUNCT
ejpam-4329	149	11	(	(	PUNCT
ejpam-4329	149	12	1	1	X
ejpam-4329	149	13	]	]	PUNCT
ejpam-4329	149	14	>	>	X
ejpam-4329	149	15	forms	form	VERB
ejpam-4329	149	16	an	an	DET
ejpam-4329	149	17	ortho	ortho	PROPN
ejpam-4329	149	18	lattice	lattice	PROPN
ejpam-4329	149	19	.	.	PUNCT
ejpam-4329	150	1	theorem	theorem	VERB
ejpam-4329	150	2	3	3	NUM
ejpam-4329	150	3	.	.	PUNCT
ejpam-4329	151	1	the	the	DET
ejpam-4329	151	2	skeleton	skeleton	PROPN
ejpam-4329	151	3	s(l	s(l	NOUN
ejpam-4329	151	4	)	)	PUNCT
ejpam-4329	151	5	of	of	ADP
ejpam-4329	151	6	the	the	DET
ejpam-4329	151	7	lattice	lattice	PROPN
ejpam-4329	151	8	l	l	PROPN
ejpam-4329	151	9	is	be	AUX
ejpam-4329	151	10	embedded	embed	VERB
ejpam-4329	151	11	in	in	ADP
ejpam-4329	151	12	the	the	DET
ejpam-4329	151	13	skeleton	skeleton	NOUN
ejpam-4329	151	14	s(i(l	s(i(l	PROPN
ejpam-4329	151	15	)	)	PUNCT
ejpam-4329	151	16	)	)	PUNCT
ejpam-4329	151	17	of	of	ADP
ejpam-4329	151	18	its	its	PRON
ejpam-4329	151	19	lattice	lattice	NOUN
ejpam-4329	151	20	of	of	ADP
ejpam-4329	151	21	ideals	ideal	NOUN
ejpam-4329	151	22	i(l	i(l	PROPN
ejpam-4329	151	23	)	)	PUNCT
ejpam-4329	151	24	.	.	PUNCT
ejpam-4329	152	1	proof	proof	NOUN
ejpam-4329	152	2	.	.	PUNCT
ejpam-4329	153	1	consider	consider	VERB
ejpam-4329	153	2	the	the	DET
ejpam-4329	153	3	map	map	NOUN
ejpam-4329	153	4	ψ	ψ	X
ejpam-4329	153	5	from	from	ADP
ejpam-4329	153	6	s(l	s(l	NUM
ejpam-4329	153	7	)	)	PUNCT
ejpam-4329	153	8	into	into	ADP
ejpam-4329	153	9	s(i(l	s(i(l	PROPN
ejpam-4329	153	10	)	)	PUNCT
ejpam-4329	153	11	)	)	PUNCT
ejpam-4329	153	12	which	which	PRON
ejpam-4329	153	13	mapping	map	VERB
ejpam-4329	153	14	the	the	DET
ejpam-4329	153	15	element	element	NOUN
ejpam-4329	153	16	a	a	DET
ejpam-4329	153	17	∈	∈	PROPN
ejpam-4329	153	18	s(l	s(l	NOUN
ejpam-4329	153	19	)	)	PUNCT
ejpam-4329	153	20	to	to	ADP
ejpam-4329	153	21	(	(	PUNCT
ejpam-4329	153	22	a]oo	a]oo	PROPN
ejpam-4329	153	23	∈	∈	PROPN
ejpam-4329	153	24	s(i(l	s(i(l	PROPN
ejpam-4329	153	25	)	)	PUNCT
ejpam-4329	153	26	)	)	PUNCT
ejpam-4329	153	27	is	be	AUX
ejpam-4329	153	28	a	a	DET
ejpam-4329	153	29	well	well	ADV
ejpam-4329	153	30	defined	define	VERB
ejpam-4329	153	31	and	and	CCONJ
ejpam-4329	153	32	satisfies	satisfy	VERB
ejpam-4329	153	33	the	the	DET
ejpam-4329	153	34	following	following	NOUN
ejpam-4329	153	35	:	:	PUNCT
ejpam-4329	153	36	ψ(a	ψ(a	PROPN
ejpam-4329	153	37	∧	∧	PROPN
ejpam-4329	153	38	b	b	NOUN
ejpam-4329	153	39	)	)	PUNCT
ejpam-4329	154	1	=	=	SYM
ejpam-4329	154	2	(	(	PUNCT
ejpam-4329	154	3	a	a	DET
ejpam-4329	154	4	∧	∧	PROPN
ejpam-4329	154	5	b]oo	b]oo	PROPN
ejpam-4329	154	6	=	=	PUNCT
ejpam-4329	154	7	(	(	PUNCT
ejpam-4329	154	8	a	a	DET
ejpam-4329	154	9	∧	∧	PROPN
ejpam-4329	154	10	b	b	PROPN
ejpam-4329	154	11	]	]	X
ejpam-4329	154	12	=	=	X
ejpam-4329	154	13	(	(	PUNCT
ejpam-4329	154	14	a	a	X
ejpam-4329	154	15	]	]	X
ejpam-4329	154	16	∩	∩	NOUN
ejpam-4329	154	17	(	(	PUNCT
ejpam-4329	154	18	b	b	X
ejpam-4329	154	19	]	]	X
ejpam-4329	154	20	=	=	SYM
ejpam-4329	154	21	(	(	PUNCT
ejpam-4329	154	22	a]oo	a]oo	VERB
ejpam-4329	154	23	∧	∧	NOUN
ejpam-4329	154	24	(	(	PUNCT
ejpam-4329	154	25	b]oo	b]oo	PROPN
ejpam-4329	154	26	=	=	SYM
ejpam-4329	154	27	ψ(a	ψ(a	PROPN
ejpam-4329	154	28	)	)	PUNCT
ejpam-4329	154	29	∩	∩	PROPN
ejpam-4329	154	30	ψ(b	ψ(b	PROPN
ejpam-4329	154	31	)	)	PUNCT
ejpam-4329	154	32	,	,	PUNCT
ejpam-4329	154	33	ψ(a	ψ(a	PROPN
ejpam-4329	154	34	∨	∨	NUM
ejpam-4329	154	35	b	b	NOUN
ejpam-4329	154	36	)	)	PUNCT
ejpam-4329	154	37	=	=	SYM
ejpam-4329	155	1	ψ((ah	ψ((ah	X
ejpam-4329	155	2	∧	∧	PROPN
ejpam-4329	155	3	bh)h	bh)h	PROPN
ejpam-4329	155	4	)	)	PUNCT
ejpam-4329	155	5	=	=	SYM
ejpam-4329	155	6	(	(	PUNCT
ejpam-4329	155	7	(	(	PUNCT
ejpam-4329	155	8	ah	ah	INTJ
ejpam-4329	155	9	∧	∧	PROPN
ejpam-4329	155	10	bh)h]oo	bh)h]oo	PROPN
ejpam-4329	155	11	=	=	PUNCT
ejpam-4329	155	12	(	(	PUNCT
ejpam-4329	155	13	(	(	PUNCT
ejpam-4329	155	14	ah	ah	INTJ
ejpam-4329	155	15	∧	∧	PROPN
ejpam-4329	155	16	bh)h	bh)h	PROPN
ejpam-4329	155	17	]	]	X
ejpam-4329	155	18	=	=	SYM
ejpam-4329	155	19	(	(	PUNCT
ejpam-4329	155	20	ah	ah	INTJ
ejpam-4329	155	21	∧	∧	PROPN
ejpam-4329	155	22	bh]o	bh]o	NOUN
ejpam-4329	155	23	=	=	SYM
ejpam-4329	155	24	(	(	PUNCT
ejpam-4329	155	25	(	(	PUNCT
ejpam-4329	155	26	ah	ah	INTJ
ejpam-4329	155	27	]	]	X
ejpam-4329	155	28	∧	∧	PROPN
ejpam-4329	155	29	(	(	PUNCT
ejpam-4329	155	30	bh])o	bh])o	NOUN
ejpam-4329	155	31	=	=	SYM
ejpam-4329	155	32	(	(	PUNCT
ejpam-4329	155	33	(	(	PUNCT
ejpam-4329	155	34	a]o	a]o	PROPN
ejpam-4329	155	35	∧	∧	PROPN
ejpam-4329	155	36	(	(	PUNCT
ejpam-4329	155	37	b]o)o	b]o)o	X
ejpam-4329	155	38	=	=	SYM
ejpam-4329	155	39	(	(	PUNCT
ejpam-4329	155	40	a	a	X
ejpam-4329	155	41	]	]	X
ejpam-4329	155	42	t	t	PROPN
ejpam-4329	155	43	(	(	PUNCT
ejpam-4329	155	44	b	b	X
ejpam-4329	155	45	]	]	X
ejpam-4329	155	46	=	=	SYM
ejpam-4329	155	47	(	(	PUNCT
ejpam-4329	155	48	a]oo	a]oo	PROPN
ejpam-4329	155	49	t	t	NOUN
ejpam-4329	155	50	(	(	PUNCT
ejpam-4329	155	51	b]oo	b]oo	PROPN
ejpam-4329	155	52	=	=	SYM
ejpam-4329	155	53	ψ(a	ψ(a	PROPN
ejpam-4329	155	54	)	)	PUNCT
ejpam-4329	155	55	t	t	PROPN
ejpam-4329	155	56	ψ(b	ψ(b	PROPN
ejpam-4329	155	57	)	)	PUNCT
ejpam-4329	155	58	,	,	PUNCT
ejpam-4329	155	59	ψ(ah	ψ(ah	PROPN
ejpam-4329	155	60	)	)	PUNCT
ejpam-4329	155	61	=	=	SYM
ejpam-4329	155	62	(	(	PUNCT
ejpam-4329	155	63	ah]oo	ah]oo	NOUN
ejpam-4329	155	64	=	=	SYM
ejpam-4329	155	65	(	(	PUNCT
ejpam-4329	155	66	a]ooo	a]ooo	X
ejpam-4329	155	67	=	=	SYM
ejpam-4329	155	68	(	(	PUNCT
ejpam-4329	155	69	ψ(a))o	ψ(a))o	PROPN
ejpam-4329	155	70	,	,	PUNCT
ejpam-4329	155	71	ψ(0	ψ(0	NOUN
ejpam-4329	155	72	)	)	PUNCT
ejpam-4329	155	73	=	=	SYM
ejpam-4329	155	74	(	(	PUNCT
ejpam-4329	155	75	0]oo	0]oo	NUM
ejpam-4329	155	76	=	=	SYM
ejpam-4329	155	77	(	(	PUNCT
ejpam-4329	155	78	0	0	NUM
ejpam-4329	155	79	]	]	PUNCT
ejpam-4329	155	80	,	,	PUNCT
ejpam-4329	155	81	and	and	CCONJ
ejpam-4329	155	82	ψ(1	ψ(1	PRON
ejpam-4329	155	83	)	)	PUNCT
ejpam-4329	155	84	=	=	SYM
ejpam-4329	155	85	(	(	PUNCT
ejpam-4329	155	86	1]oo	1]oo	NUM
ejpam-4329	155	87	=	=	SYM
ejpam-4329	155	88	l.	l.	NOUN
ejpam-4329	155	89	it	it	PRON
ejpam-4329	155	90	is	be	AUX
ejpam-4329	155	91	easy	easy	ADJ
ejpam-4329	155	92	to	to	PART
ejpam-4329	155	93	show	show	VERB
ejpam-4329	155	94	that	that	SCONJ
ejpam-4329	155	95	ψ	ψ	NOUN
ejpam-4329	155	96	is	be	AUX
ejpam-4329	155	97	an	an	DET
ejpam-4329	155	98	injective	injective	ADJ
ejpam-4329	155	99	map	map	NOUN
ejpam-4329	155	100	and	and	CCONJ
ejpam-4329	155	101	this	this	PRON
ejpam-4329	155	102	completed	complete	VERB
ejpam-4329	155	103	the	the	DET
ejpam-4329	155	104	proof	proof	NOUN
ejpam-4329	155	105	.	.	PUNCT
ejpam-4329	156	1	theorem	theorem	ADJ
ejpam-4329	156	2	4	4	NUM
ejpam-4329	156	3	.	.	PUNCT
ejpam-4329	157	1	the	the	DET
ejpam-4329	157	2	following	follow	VERB
ejpam-4329	157	3	statements	statement	NOUN
ejpam-4329	157	4	are	be	AUX
ejpam-4329	157	5	equivalent	equivalent	ADJ
ejpam-4329	157	6	:	:	PUNCT
ejpam-4329	157	7	(	(	PUNCT
ejpam-4329	157	8	1	1	X
ejpam-4329	157	9	)	)	PUNCT
ejpam-4329	157	10	i	i	PRON
ejpam-4329	157	11	is	be	AUX
ejpam-4329	157	12	closed	close	VERB
ejpam-4329	157	13	ideal	ideal	ADJ
ejpam-4329	157	14	,	,	PUNCT
ejpam-4329	157	15	(	(	PUNCT
ejpam-4329	157	16	2	2	X
ejpam-4329	157	17	)	)	PUNCT
ejpam-4329	157	18	if	if	SCONJ
ejpam-4329	157	19	a	a	DET
ejpam-4329	157	20	∈	∈	PROPN
ejpam-4329	157	21	l	l	NOUN
ejpam-4329	157	22	and	and	CCONJ
ejpam-4329	157	23	a	a	DET
ejpam-4329	157	24	≤	≤	NUM
ejpam-4329	157	25	bh	bh	NOUN
ejpam-4329	157	26	,	,	PUNCT
ejpam-4329	157	27	for	for	ADP
ejpam-4329	157	28	all	all	DET
ejpam-4329	157	29	b	b	NOUN
ejpam-4329	157	30	∈	∈	NOUN
ejpam-4329	157	31	io	io	NOUN
ejpam-4329	157	32	then	then	ADV
ejpam-4329	157	33	a	a	DET
ejpam-4329	157	34	∈	∈	PROPN
ejpam-4329	158	1	i	i	PRON
ejpam-4329	158	2	,	,	PUNCT
ejpam-4329	158	3	(	(	PUNCT
ejpam-4329	158	4	3	3	X
ejpam-4329	158	5	)	)	PUNCT
ejpam-4329	158	6	i	i	PRON
ejpam-4329	158	7	=	=	SYM
ejpam-4329	158	8	ko	ko	PROPN
ejpam-4329	158	9	for	for	ADP
ejpam-4329	158	10	some	some	DET
ejpam-4329	158	11	ideal	ideal	NOUN
ejpam-4329	158	12	k	k	PROPN
ejpam-4329	158	13	∈	∈	PROPN
ejpam-4329	158	14	i(l	i(l	PROPN
ejpam-4329	158	15	)	)	PUNCT
ejpam-4329	158	16	.	.	PUNCT
ejpam-4329	159	1	e.	e.	PROPN
ejpam-4329	159	2	g.	g.	PROPN
ejpam-4329	159	3	rezk	rezk	PROPN
ejpam-4329	159	4	/	/	SYM
ejpam-4329	159	5	eur	eur	PROPN
ejpam-4329	159	6	.	.	PUNCT
ejpam-4329	160	1	j.	j.	PROPN
ejpam-4329	160	2	pure	pure	PROPN
ejpam-4329	160	3	appl	appl	PROPN
ejpam-4329	160	4	.	.	PROPN
ejpam-4329	160	5	math	math	PROPN
ejpam-4329	160	6	,	,	PUNCT
ejpam-4329	160	7	15	15	NUM
ejpam-4329	160	8	(	(	PUNCT
ejpam-4329	160	9	2	2	NUM
ejpam-4329	160	10	)	)	PUNCT
ejpam-4329	160	11	(	(	PUNCT
ejpam-4329	160	12	2022	2022	NUM
ejpam-4329	160	13	)	)	PUNCT
ejpam-4329	160	14	,	,	PUNCT
ejpam-4329	160	15	486	486	NUM
ejpam-4329	160	16	-	-	SYM
ejpam-4329	160	17	495	495	NUM
ejpam-4329	160	18	492	492	NUM
ejpam-4329	160	19	proof	proof	NOUN
ejpam-4329	160	20	.	.	PUNCT
ejpam-4329	161	1	let	let	VERB
ejpam-4329	161	2	i	i	PRON
ejpam-4329	161	3	be	be	AUX
ejpam-4329	161	4	a	a	DET
ejpam-4329	161	5	closed	closed	ADJ
ejpam-4329	161	6	ideal	ideal	NOUN
ejpam-4329	161	7	and	and	CCONJ
ejpam-4329	161	8	a	a	DET
ejpam-4329	161	9	∈	∈	NOUN
ejpam-4329	161	10	l	l	NOUN
ejpam-4329	161	11	such	such	ADJ
ejpam-4329	161	12	that	that	SCONJ
ejpam-4329	161	13	a	a	DET
ejpam-4329	161	14	≤	≤	ADJ
ejpam-4329	161	15	bh	bh	NOUN
ejpam-4329	161	16	for	for	ADP
ejpam-4329	161	17	all	all	DET
ejpam-4329	161	18	b	b	PROPN
ejpam-4329	161	19	∈	∈	PROPN
ejpam-4329	161	20	io	io	NOUN
ejpam-4329	161	21	,	,	PUNCT
ejpam-4329	161	22	then	then	ADV
ejpam-4329	161	23	a	a	DET
ejpam-4329	161	24	∈	∈	PROPN
ejpam-4329	161	25	ioo	ioo	VERB
ejpam-4329	161	26	=	=	NOUN
ejpam-4329	161	27	i.	i.	NOUN
ejpam-4329	161	28	let	let	VERB
ejpam-4329	161	29	(	(	PUNCT
ejpam-4329	161	30	2	2	X
ejpam-4329	161	31	)	)	PUNCT
ejpam-4329	161	32	be	be	AUX
ejpam-4329	161	33	satisfied	satisfied	ADJ
ejpam-4329	161	34	and	and	CCONJ
ejpam-4329	161	35	let	let	VERB
ejpam-4329	161	36	x	x	X
ejpam-4329	161	37	∈	∈	PROPN
ejpam-4329	161	38	ioo	ioo	PROPN
ejpam-4329	161	39	.	.	PUNCT
ejpam-4329	162	1	then	then	ADV
ejpam-4329	162	2	x	x	SYM
ejpam-4329	162	3	≤	≤	NUM
ejpam-4329	162	4	bh	bh	NOUN
ejpam-4329	162	5	for	for	ADP
ejpam-4329	162	6	all	all	DET
ejpam-4329	162	7	b	b	PROPN
ejpam-4329	162	8	∈	∈	PROPN
ejpam-4329	162	9	io	io	X
ejpam-4329	162	10	.	.	PUNCT
ejpam-4329	162	11	therefore	therefore	ADV
ejpam-4329	162	12	x	x	X
ejpam-4329	162	13	∈	∈	PROPN
ejpam-4329	162	14	i.	i.	NOUN
ejpam-4329	162	15	assume	assume	VERB
ejpam-4329	162	16	i	i	PRON
ejpam-4329	162	17	=	=	SYM
ejpam-4329	162	18	ioo	ioo	PROPN
ejpam-4329	162	19	,	,	PUNCT
ejpam-4329	162	20	set	set	VERB
ejpam-4329	162	21	k	k	PROPN
ejpam-4329	162	22	=	=	SYM
ejpam-4329	162	23	io	io	PROPN
ejpam-4329	162	24	then	then	ADV
ejpam-4329	162	25	ko	ko	PROPN
ejpam-4329	163	1	=	=	PROPN
ejpam-4329	163	2	i	i	PROPN
ejpam-4329	163	3	∈	∈	PROPN
ejpam-4329	163	4	s(i(l	s(i(l	PROPN
ejpam-4329	163	5	)	)	PUNCT
ejpam-4329	163	6	)	)	PUNCT
ejpam-4329	163	7	.	.	PUNCT
ejpam-4329	164	1	let	let	VERB
ejpam-4329	164	2	i	i	PRON
ejpam-4329	164	3	=	=	PUNCT
ejpam-4329	164	4	ko	ko	PROPN
ejpam-4329	164	5	for	for	ADP
ejpam-4329	164	6	some	some	DET
ejpam-4329	164	7	k	k	PROPN
ejpam-4329	164	8	∈	∈	PROPN
ejpam-4329	164	9	i(l	i(l	PROPN
ejpam-4329	164	10	)	)	PUNCT
ejpam-4329	164	11	.	.	PUNCT
ejpam-4329	165	1	thus	thus	ADV
ejpam-4329	165	2	ioo	ioo	ADJ
ejpam-4329	165	3	=	=	SYM
ejpam-4329	165	4	kooo	kooo	NOUN
ejpam-4329	165	5	=	=	SYM
ejpam-4329	165	6	ko	ko	PROPN
ejpam-4329	165	7	=	=	PROPN
ejpam-4329	165	8	i.	i.	PROPN
ejpam-4329	165	9	lemma	lemma	PROPN
ejpam-4329	165	10	3	3	X
ejpam-4329	165	11	.	.	PUNCT
ejpam-4329	165	12	let	let	VERB
ejpam-4329	165	13	d(i(l	d(i(l	PROPN
ejpam-4329	165	14	)	)	PUNCT
ejpam-4329	165	15	)	)	PUNCT
ejpam-4329	165	16	be	be	AUX
ejpam-4329	165	17	the	the	DET
ejpam-4329	165	18	set	set	NOUN
ejpam-4329	165	19	of	of	ADP
ejpam-4329	165	20	all	all	DET
ejpam-4329	165	21	dense	dense	ADJ
ejpam-4329	165	22	ideals	ideal	NOUN
ejpam-4329	165	23	of	of	ADP
ejpam-4329	165	24	l.	l.	PROPN
ejpam-4329	165	25	then	then	ADV
ejpam-4329	165	26	:	:	PUNCT
ejpam-4329	165	27	(	(	PUNCT
ejpam-4329	165	28	1	1	X
ejpam-4329	165	29	)	)	PUNCT
ejpam-4329	165	30	(	(	PUNCT
ejpam-4329	165	31	1	1	X
ejpam-4329	165	32	]	]	X
ejpam-4329	165	33	∈	∈	PROPN
ejpam-4329	165	34	d(i(l	d(i(l	PROPN
ejpam-4329	165	35	)	)	PUNCT
ejpam-4329	165	36	)	)	PUNCT
ejpam-4329	165	37	,	,	PUNCT
ejpam-4329	165	38	(	(	PUNCT
ejpam-4329	165	39	2	2	X
ejpam-4329	165	40	)	)	PUNCT
ejpam-4329	165	41	if	if	SCONJ
ejpam-4329	165	42	i	i	PRON
ejpam-4329	165	43	,	,	PUNCT
ejpam-4329	165	44	k	k	PROPN
ejpam-4329	165	45	∈	∈	PROPN
ejpam-4329	165	46	i(l	i(l	PROPN
ejpam-4329	165	47	)	)	PUNCT
ejpam-4329	165	48	such	such	ADJ
ejpam-4329	165	49	that	that	SCONJ
ejpam-4329	165	50	i	i	PRON
ejpam-4329	165	51	⊆	⊆	NUM
ejpam-4329	165	52	k	k	NOUN
ejpam-4329	165	53	and	and	CCONJ
ejpam-4329	165	54	i	i	PROPN
ejpam-4329	165	55	∈	∈	PROPN
ejpam-4329	165	56	d(i(l	d(i(l	PROPN
ejpam-4329	165	57	)	)	PUNCT
ejpam-4329	165	58	)	)	PUNCT
ejpam-4329	165	59	then	then	ADV
ejpam-4329	165	60	k	k	PROPN
ejpam-4329	165	61	∈	∈	PROPN
ejpam-4329	165	62	d(i(l	d(i(l	PROPN
ejpam-4329	165	63	)	)	PUNCT
ejpam-4329	165	64	)	)	PUNCT
ejpam-4329	165	65	,	,	PUNCT
ejpam-4329	165	66	(	(	PUNCT
ejpam-4329	165	67	3)if	3)if	X
ejpam-4329	165	68	i	i	INTJ
ejpam-4329	165	69	,	,	PUNCT
ejpam-4329	165	70	k	k	PROPN
ejpam-4329	165	71	∈	∈	PROPN
ejpam-4329	165	72	d(i(l	d(i(l	PROPN
ejpam-4329	165	73	)	)	PUNCT
ejpam-4329	165	74	)	)	PUNCT
ejpam-4329	165	75	,	,	PUNCT
ejpam-4329	165	76	then	then	ADV
ejpam-4329	165	77	i	i	PRON
ejpam-4329	165	78	∨k	∨k	VERB
ejpam-4329	165	79	∈	∈	PROPN
ejpam-4329	165	80	d(i(l	d(i(l	PROPN
ejpam-4329	165	81	)	)	PUNCT
ejpam-4329	165	82	)	)	PUNCT
ejpam-4329	165	83	,	,	PUNCT
ejpam-4329	165	84	(	(	PUNCT
ejpam-4329	166	1	4)if	4)if	NOUN
ejpam-4329	166	2	i	i	PRON
ejpam-4329	166	3	∈	∈	PROPN
ejpam-4329	166	4	d(i(l	d(i(l	PROPN
ejpam-4329	166	5	)	)	PUNCT
ejpam-4329	166	6	)	)	PUNCT
ejpam-4329	166	7	,	,	PUNCT
ejpam-4329	166	8	then	then	ADV
ejpam-4329	166	9	i	i	PRON
ejpam-4329	166	10	∨	∨	VERB
ejpam-4329	166	11	io	io	PROPN
ejpam-4329	166	12	∈	∈	PROPN
ejpam-4329	166	13	d(i(l	d(i(l	PROPN
ejpam-4329	166	14	)	)	PUNCT
ejpam-4329	166	15	)	)	PUNCT
ejpam-4329	166	16	,	,	PUNCT
ejpam-4329	166	17	(	(	PUNCT
ejpam-4329	166	18	5)if	5)if	NOUN
ejpam-4329	166	19	i	i	PRON
ejpam-4329	166	20	∩d(l	∩d(l	PROPN
ejpam-4329	166	21	)	)	PUNCT
ejpam-4329	166	22	6=	6=	ADP
ejpam-4329	167	1	φ	φ	PROPN
ejpam-4329	167	2	then	then	ADV
ejpam-4329	167	3	i	i	PRON
ejpam-4329	167	4	∈	∈	PROPN
ejpam-4329	167	5	d(i(l	d(i(l	PROPN
ejpam-4329	167	6	)	)	PUNCT
ejpam-4329	167	7	)	)	PUNCT
ejpam-4329	167	8	.	.	PUNCT
ejpam-4329	168	1	(	(	PUNCT
ejpam-4329	168	2	6	6	X
ejpam-4329	168	3	)	)	PUNCT
ejpam-4329	168	4	d∗(l	d∗(l	PROPN
ejpam-4329	168	5	)	)	PUNCT
ejpam-4329	168	6	⊆	⊆	NUM
ejpam-4329	168	7	d(i(l	d(i(l	NOUN
ejpam-4329	168	8	)	)	PUNCT
ejpam-4329	168	9	)	)	PUNCT
ejpam-4329	168	10	.	.	PUNCT
ejpam-4329	169	1	proof	proof	NOUN
ejpam-4329	169	2	.	.	PUNCT
ejpam-4329	170	1	(	(	PUNCT
ejpam-4329	170	2	1	1	X
ejpam-4329	170	3	)	)	PUNCT
ejpam-4329	170	4	since	since	SCONJ
ejpam-4329	170	5	(	(	PUNCT
ejpam-4329	170	6	1]o	1]o	NUM
ejpam-4329	170	7	=	=	SYM
ejpam-4329	170	8	(	(	PUNCT
ejpam-4329	170	9	0	0	NUM
ejpam-4329	170	10	]	]	PUNCT
ejpam-4329	170	11	,	,	PUNCT
ejpam-4329	170	12	then	then	ADV
ejpam-4329	170	13	(	(	PUNCT
ejpam-4329	170	14	1	1	X
ejpam-4329	170	15	]	]	X
ejpam-4329	170	16	∈	∈	PROPN
ejpam-4329	170	17	d(i(l	d(i(l	PROPN
ejpam-4329	170	18	)	)	PUNCT
ejpam-4329	170	19	)	)	PUNCT
ejpam-4329	170	20	.	.	PUNCT
ejpam-4329	171	1	(	(	PUNCT
ejpam-4329	171	2	2	2	X
ejpam-4329	171	3	)	)	PUNCT
ejpam-4329	171	4	let	let	VERB
ejpam-4329	171	5	i	i	PRON
ejpam-4329	171	6	,	,	PUNCT
ejpam-4329	171	7	k	k	PROPN
ejpam-4329	171	8	∈	∈	PROPN
ejpam-4329	171	9	i(l	i(l	PROPN
ejpam-4329	171	10	)	)	PUNCT
ejpam-4329	171	11	,	,	PUNCT
ejpam-4329	171	12	i	i	PRON
ejpam-4329	171	13	⊆	⊆	NUM
ejpam-4329	171	14	k	k	PROPN
ejpam-4329	171	15	and	and	CCONJ
ejpam-4329	171	16	io	io	X
ejpam-4329	171	17	=	=	PUNCT
ejpam-4329	171	18	(	(	PUNCT
ejpam-4329	171	19	0	0	NUM
ejpam-4329	171	20	]	]	PUNCT
ejpam-4329	171	21	.	.	PUNCT
ejpam-4329	172	1	this	this	PRON
ejpam-4329	172	2	implies	imply	VERB
ejpam-4329	172	3	(	(	PUNCT
ejpam-4329	172	4	0	0	NUM
ejpam-4329	172	5	]	]	X
ejpam-4329	172	6	=	=	SYM
ejpam-4329	172	7	io	io	PROPN
ejpam-4329	172	8	⊇	⊇	PROPN
ejpam-4329	172	9	ko	ko	PROPN
ejpam-4329	172	10	i.e.	i.e.	X
ejpam-4329	172	11	,	,	PUNCT
ejpam-4329	172	12	ko	ko	PROPN
ejpam-4329	172	13	=	=	PUNCT
ejpam-4329	172	14	(	(	PUNCT
ejpam-4329	172	15	0	0	NUM
ejpam-4329	172	16	]	]	PUNCT
ejpam-4329	172	17	and	and	CCONJ
ejpam-4329	172	18	k	k	PROPN
ejpam-4329	172	19	∈	∈	PROPN
ejpam-4329	172	20	d(i(l	d(i(l	PROPN
ejpam-4329	172	21	)	)	PUNCT
ejpam-4329	172	22	)	)	PUNCT
ejpam-4329	172	23	.	.	PUNCT
ejpam-4329	173	1	(	(	PUNCT
ejpam-4329	173	2	3	3	X
ejpam-4329	173	3	)	)	PUNCT
ejpam-4329	173	4	assume	assume	VERB
ejpam-4329	173	5	i	i	PRON
ejpam-4329	173	6	,	,	PUNCT
ejpam-4329	173	7	k	k	PROPN
ejpam-4329	173	8	∈	∈	PROPN
ejpam-4329	173	9	d(i(l	d(i(l	PROPN
ejpam-4329	173	10	)	)	PUNCT
ejpam-4329	173	11	)	)	PUNCT
ejpam-4329	173	12	,	,	PUNCT
ejpam-4329	173	13	from	from	ADP
ejpam-4329	173	14	(	(	PUNCT
ejpam-4329	173	15	3	3	X
ejpam-4329	173	16	)	)	PUNCT
ejpam-4329	173	17	in	in	ADP
ejpam-4329	173	18	proposition	proposition	NOUN
ejpam-4329	173	19	2	2	NUM
ejpam-4329	173	20	,	,	PUNCT
ejpam-4329	173	21	we	we	PRON
ejpam-4329	173	22	get	get	VERB
ejpam-4329	173	23	(	(	PUNCT
ejpam-4329	173	24	i	i	PRON
ejpam-4329	173	25	∨k)o	∨k)o	ADJ
ejpam-4329	173	26	=	=	SYM
ejpam-4329	173	27	io	io	PROPN
ejpam-4329	173	28	∩ko	∩ko	PROPN
ejpam-4329	173	29	=	=	PUNCT
ejpam-4329	173	30	(	(	PUNCT
ejpam-4329	173	31	0	0	NUM
ejpam-4329	173	32	]	]	PUNCT
ejpam-4329	173	33	.	.	PUNCT
ejpam-4329	174	1	thus	thus	ADV
ejpam-4329	174	2	i	i	PRON
ejpam-4329	174	3	∨k	∨k	ADJ
ejpam-4329	174	4	∈	∈	PROPN
ejpam-4329	174	5	d(i(l	d(i(l	PROPN
ejpam-4329	174	6	)	)	PUNCT
ejpam-4329	174	7	)	)	PUNCT
ejpam-4329	174	8	.	.	PUNCT
ejpam-4329	175	1	(	(	PUNCT
ejpam-4329	175	2	4	4	X
ejpam-4329	175	3	)	)	PUNCT
ejpam-4329	175	4	if	if	SCONJ
ejpam-4329	175	5	i	i	PRON
ejpam-4329	175	6	∈	∈	VERB
ejpam-4329	175	7	d(i(l	d(i(l	PROPN
ejpam-4329	175	8	)	)	PUNCT
ejpam-4329	175	9	)	)	PUNCT
ejpam-4329	176	1	then	then	ADV
ejpam-4329	176	2	i	i	PRON
ejpam-4329	176	3	⊆	⊆	NUM
ejpam-4329	176	4	i	i	PROPN
ejpam-4329	176	5	∨	∨	PROPN
ejpam-4329	176	6	io	io	PROPN
ejpam-4329	176	7	.	.	PUNCT
ejpam-4329	177	1	it	it	PRON
ejpam-4329	177	2	implies	imply	VERB
ejpam-4329	177	3	(	(	PUNCT
ejpam-4329	177	4	0	0	NUM
ejpam-4329	177	5	]	]	PUNCT
ejpam-4329	177	6	=	=	PUNCT
ejpam-4329	177	7	io	io	X
ejpam-4329	177	8	⊇	⊇	PROPN
ejpam-4329	177	9	(	(	PUNCT
ejpam-4329	177	10	i	i	PROPN
ejpam-4329	177	11	∨	∨	PROPN
ejpam-4329	177	12	io)o	io)o	PROPN
ejpam-4329	177	13	.	.	PUNCT
ejpam-4329	178	1	therefore	therefore	ADV
ejpam-4329	178	2	i	i	PRON
ejpam-4329	178	3	∨	∨	VERB
ejpam-4329	178	4	io	io	PROPN
ejpam-4329	178	5	∈	∈	PROPN
ejpam-4329	178	6	d(i(l	d(i(l	PROPN
ejpam-4329	178	7	)	)	PUNCT
ejpam-4329	178	8	)	)	PUNCT
ejpam-4329	178	9	.	.	PUNCT
ejpam-4329	179	1	(	(	PUNCT
ejpam-4329	179	2	5	5	X
ejpam-4329	179	3	)	)	PUNCT
ejpam-4329	179	4	assume	assume	VERB
ejpam-4329	179	5	i	i	PRON
ejpam-4329	179	6	∩d(l	∩d(l	PROPN
ejpam-4329	179	7	)	)	PUNCT
ejpam-4329	179	8	6=	6=	ADP
ejpam-4329	180	1	φ	φ	PROPN
ejpam-4329	180	2	,	,	PUNCT
ejpam-4329	180	3	then	then	ADV
ejpam-4329	180	4	there	there	PRON
ejpam-4329	180	5	exists	exist	VERB
ejpam-4329	180	6	a	a	DET
ejpam-4329	180	7	non	non	ADJ
ejpam-4329	180	8	-	-	ADJ
ejpam-4329	180	9	zero	zero	NUM
ejpam-4329	180	10	element	element	NOUN
ejpam-4329	180	11	a	a	DET
ejpam-4329	180	12	∈	∈	NOUN
ejpam-4329	180	13	i	i	PRON
ejpam-4329	180	14	such	such	ADJ
ejpam-4329	180	15	that	that	SCONJ
ejpam-4329	180	16	ah	ah	INTJ
ejpam-4329	180	17	=	=	NOUN
ejpam-4329	180	18	0	0	PROPN
ejpam-4329	180	19	.	.	PUNCT
ejpam-4329	181	1	hence	hence	ADV
ejpam-4329	181	2	io	io	X
ejpam-4329	181	3	=	=	PUNCT
ejpam-4329	181	4	(	(	PUNCT
ejpam-4329	181	5	0	0	NUM
ejpam-4329	181	6	]	]	PUNCT
ejpam-4329	181	7	and	and	CCONJ
ejpam-4329	181	8	i	i	PRON
ejpam-4329	181	9	∈	∈	PROPN
ejpam-4329	181	10	d(i(l	d(i(l	PROPN
ejpam-4329	181	11	)	)	PUNCT
ejpam-4329	181	12	)	)	PUNCT
ejpam-4329	181	13	.	.	PUNCT
ejpam-4329	182	1	(	(	PUNCT
ejpam-4329	182	2	6	6	X
ejpam-4329	182	3	)	)	PUNCT
ejpam-4329	182	4	assume	assume	VERB
ejpam-4329	182	5	i	i	PRON
ejpam-4329	182	6	∈	∈	PROPN
ejpam-4329	182	7	d∗(l	d∗(l	PROPN
ejpam-4329	182	8	)	)	PUNCT
ejpam-4329	182	9	.	.	PUNCT
ejpam-4329	183	1	since	since	SCONJ
ejpam-4329	183	2	io	io	PROPN
ejpam-4329	183	3	⊆	⊆	NUM
ejpam-4329	183	4	i∗	i∗	NOUN
ejpam-4329	183	5	=	=	SYM
ejpam-4329	183	6	(	(	PUNCT
ejpam-4329	183	7	0	0	NUM
ejpam-4329	183	8	]	]	PUNCT
ejpam-4329	183	9	,	,	PUNCT
ejpam-4329	183	10	then	then	ADV
ejpam-4329	183	11	i	i	PRON
ejpam-4329	183	12	∈	∈	PROPN
ejpam-4329	183	13	d(i(l	d(i(l	PROPN
ejpam-4329	183	14	)	)	PUNCT
ejpam-4329	183	15	)	)	PUNCT
ejpam-4329	183	16	.	.	PUNCT
ejpam-4329	183	17	theorem	theorem	ADJ
ejpam-4329	183	18	5	5	NUM
ejpam-4329	183	19	.	.	PUNCT
ejpam-4329	183	20	d(i(l	d(i(l	NOUN
ejpam-4329	183	21	)	)	PUNCT
ejpam-4329	183	22	)	)	PUNCT
ejpam-4329	183	23	forms	form	VERB
ejpam-4329	183	24	a	a	DET
ejpam-4329	183	25	join	join	NOUN
ejpam-4329	183	26	semilattice	semilattice	NOUN
ejpam-4329	183	27	with	with	ADP
ejpam-4329	183	28	one	one	NUM
ejpam-4329	183	29	.	.	PUNCT
ejpam-4329	184	1	4	4	X
ejpam-4329	184	2	.	.	NUM
ejpam-4329	184	3	closed	close	VERB
ejpam-4329	184	4	annihilators	annihilator	NOUN
ejpam-4329	184	5	of	of	ADP
ejpam-4329	184	6	ddwcls	ddwcls	NOUN
ejpam-4329	184	7	this	this	DET
ejpam-4329	184	8	section	section	NOUN
ejpam-4329	184	9	introduces	introduce	VERB
ejpam-4329	184	10	the	the	DET
ejpam-4329	184	11	concept	concept	NOUN
ejpam-4329	184	12	of	of	ADP
ejpam-4329	184	13	a	a	DET
ejpam-4329	184	14	closed	closed	ADJ
ejpam-4329	184	15	annihilator	annihilator	NOUN
ejpam-4329	184	16	.	.	PUNCT
ejpam-4329	185	1	the	the	DET
ejpam-4329	185	2	structure	structure	NOUN
ejpam-4329	185	3	of	of	ADP
ejpam-4329	185	4	the	the	DET
ejpam-4329	185	5	set	set	NOUN
ejpam-4329	185	6	of	of	ADP
ejpam-4329	185	7	all	all	DET
ejpam-4329	185	8	closed	closed	ADJ
ejpam-4329	185	9	annihilators	annihilator	NOUN
ejpam-4329	185	10	of	of	ADP
ejpam-4329	185	11	ddwcl	ddwcl	PROPN
ejpam-4329	185	12	l	l	PROPN
ejpam-4329	185	13	and	and	CCONJ
ejpam-4329	185	14	the	the	DET
ejpam-4329	185	15	connection	connection	NOUN
ejpam-4329	185	16	with	with	ADP
ejpam-4329	185	17	the	the	DET
ejpam-4329	185	18	set	set	NOUN
ejpam-4329	185	19	of	of	ADP
ejpam-4329	185	20	all	all	DET
ejpam-4329	185	21	closed	closed	ADJ
ejpam-4329	185	22	ideals	ideal	NOUN
ejpam-4329	185	23	s(i(l))are	s(i(l))are	AUX
ejpam-4329	185	24	investegated	investegate	VERB
ejpam-4329	185	25	.	.	PUNCT
ejpam-4329	186	1	definition	definition	NOUN
ejpam-4329	186	2	6	6	NUM
ejpam-4329	186	3	.	.	PUNCT
ejpam-4329	187	1	an	an	DET
ejpam-4329	187	2	ideal	ideal	NOUN
ejpam-4329	187	3	i	i	PRON
ejpam-4329	187	4	is	be	AUX
ejpam-4329	187	5	called	call	VERB
ejpam-4329	187	6	a	a	DET
ejpam-4329	187	7	closed	closed	ADJ
ejpam-4329	187	8	annihilator	annihilator	NOUN
ejpam-4329	187	9	iff	iff	NOUN
ejpam-4329	188	1	i	i	PRON
ejpam-4329	188	2	=	=	PROPN
ejpam-4329	188	3	io∗.	io∗.	PROPN
ejpam-4329	188	4	the	the	DET
ejpam-4329	188	5	set	set	NOUN
ejpam-4329	188	6	of	of	ADP
ejpam-4329	188	7	all	all	DET
ejpam-4329	188	8	annihilators	annihilator	NOUN
ejpam-4329	188	9	is	be	AUX
ejpam-4329	188	10	denoted	denote	VERB
ejpam-4329	188	11	by	by	ADP
ejpam-4329	188	12	io∗(l	io∗(l	PROPN
ejpam-4329	188	13	)	)	PUNCT
ejpam-4329	188	14	.	.	PUNCT
ejpam-4329	189	1	the	the	DET
ejpam-4329	189	2	only	only	ADJ
ejpam-4329	189	3	dense	dense	ADJ
ejpam-4329	189	4	ideal	ideal	NOUN
ejpam-4329	189	5	belongs	belong	VERB
ejpam-4329	189	6	to	to	ADP
ejpam-4329	189	7	io∗(l	io∗(l	PROPN
ejpam-4329	189	8	)	)	PUNCT
ejpam-4329	189	9	is	be	AUX
ejpam-4329	189	10	(	(	PUNCT
ejpam-4329	189	11	1	1	NUM
ejpam-4329	189	12	]	]	PUNCT
ejpam-4329	189	13	.	.	PUNCT
ejpam-4329	190	1	lemma	lemma	PROPN
ejpam-4329	190	2	4	4	NUM
ejpam-4329	190	3	.	.	PUNCT
ejpam-4329	191	1	(	(	PUNCT
ejpam-4329	191	2	1	1	X
ejpam-4329	191	3	)	)	PUNCT
ejpam-4329	191	4	if	if	SCONJ
ejpam-4329	191	5	i	i	PRON
ejpam-4329	191	6	is	be	AUX
ejpam-4329	191	7	an	an	DET
ejpam-4329	191	8	ideal	ideal	NOUN
ejpam-4329	191	9	then	then	ADV
ejpam-4329	191	10	i∗o	i∗o	VERB
ejpam-4329	191	11	⊆	⊆	NUM
ejpam-4329	191	12	ioo	ioo	ADJ
ejpam-4329	191	13	⊆	⊆	NUM
ejpam-4329	191	14	io∗	io∗	ADV
ejpam-4329	191	15	,	,	PUNCT
ejpam-4329	191	16	e.	e.	PROPN
ejpam-4329	191	17	g.	g.	PROPN
ejpam-4329	191	18	rezk	rezk	PROPN
ejpam-4329	191	19	/	/	SYM
ejpam-4329	191	20	eur	eur	PROPN
ejpam-4329	191	21	.	.	PUNCT
ejpam-4329	192	1	j.	j.	PROPN
ejpam-4329	192	2	pure	pure	PROPN
ejpam-4329	192	3	appl	appl	PROPN
ejpam-4329	192	4	.	.	PROPN
ejpam-4329	192	5	math	math	PROPN
ejpam-4329	192	6	,	,	PUNCT
ejpam-4329	192	7	15	15	NUM
ejpam-4329	192	8	(	(	PUNCT
ejpam-4329	192	9	2	2	NUM
ejpam-4329	192	10	)	)	PUNCT
ejpam-4329	192	11	(	(	PUNCT
ejpam-4329	192	12	2022	2022	NUM
ejpam-4329	192	13	)	)	PUNCT
ejpam-4329	192	14	,	,	PUNCT
ejpam-4329	192	15	486	486	NUM
ejpam-4329	192	16	-	-	SYM
ejpam-4329	192	17	495	495	NUM
ejpam-4329	192	18	493	493	NUM
ejpam-4329	192	19	(	(	PUNCT
ejpam-4329	192	20	2	2	NUM
ejpam-4329	192	21	)	)	PUNCT
ejpam-4329	192	22	if	if	SCONJ
ejpam-4329	192	23	i	i	PRON
ejpam-4329	192	24	is	be	AUX
ejpam-4329	192	25	a	a	DET
ejpam-4329	192	26	closed	closed	ADJ
ejpam-4329	192	27	annihilator	annihilator	NOUN
ejpam-4329	192	28	then	then	ADV
ejpam-4329	192	29	i∗	i∗	PROPN
ejpam-4329	192	30	=	=	SYM
ejpam-4329	192	31	io	io	PROPN
ejpam-4329	192	32	,	,	PUNCT
ejpam-4329	192	33	(	(	PUNCT
ejpam-4329	192	34	3	3	X
ejpam-4329	192	35	)	)	PUNCT
ejpam-4329	193	1	if	if	SCONJ
ejpam-4329	193	2	i	i	PRON
ejpam-4329	193	3	and	and	CCONJ
ejpam-4329	193	4	k	k	PROPN
ejpam-4329	193	5	are	be	AUX
ejpam-4329	193	6	closed	close	VERB
ejpam-4329	193	7	annihilators	annihilator	NOUN
ejpam-4329	193	8	then	then	ADV
ejpam-4329	193	9	i	i	PRON
ejpam-4329	193	10	∩k	∩k	VERB
ejpam-4329	194	1	and	and	CCONJ
ejpam-4329	194	2	i	i	PRON
ejpam-4329	194	3	tk	tk	PROPN
ejpam-4329	194	4	are	be	AUX
ejpam-4329	194	5	too	too	ADV
ejpam-4329	194	6	,	,	PUNCT
ejpam-4329	194	7	(	(	PUNCT
ejpam-4329	194	8	4	4	X
ejpam-4329	194	9	)	)	PUNCT
ejpam-4329	194	10	i	i	PRON
ejpam-4329	194	11	∈	∈	NOUN
ejpam-4329	194	12	a(l	a(l	PROPN
ejpam-4329	194	13	)	)	PUNCT
ejpam-4329	195	1	iff	iff	NOUN
ejpam-4329	195	2	i	i	PROPN
ejpam-4329	195	3	∈	∈	PROPN
ejpam-4329	195	4	io∗(l	io∗(l	PROPN
ejpam-4329	195	5	)	)	PUNCT
ejpam-4329	195	6	.	.	PUNCT
ejpam-4329	196	1	proof	proof	NOUN
ejpam-4329	196	2	.	.	PUNCT
ejpam-4329	197	1	(	(	PUNCT
ejpam-4329	197	2	1	1	X
ejpam-4329	197	3	)	)	PUNCT
ejpam-4329	197	4	we	we	PRON
ejpam-4329	197	5	have	have	VERB
ejpam-4329	197	6	that	that	PRON
ejpam-4329	197	7	io	io	PROPN
ejpam-4329	197	8	⊆	⊆	NUM
ejpam-4329	197	9	i∗.	i∗.	PROPN
ejpam-4329	197	10	then	then	ADV
ejpam-4329	197	11	ioo	ioo	PROPN
ejpam-4329	197	12	⊇	⊇	PROPN
ejpam-4329	197	13	i∗o	i∗o	PROPN
ejpam-4329	197	14	.	.	PUNCT
ejpam-4329	197	15	suppose	suppose	VERB
ejpam-4329	197	16	x	x	X
ejpam-4329	197	17	∈	∈	PROPN
ejpam-4329	197	18	ioo	ioo	VERB
ejpam-4329	197	19	i.e.	i.e.	X
ejpam-4329	197	20	,	,	PUNCT
ejpam-4329	197	21	x	x	SYM
ejpam-4329	197	22	≤	≤	ADV
ejpam-4329	197	23	ah	ah	INTJ
ejpam-4329	197	24	for	for	ADP
ejpam-4329	197	25	all	all	DET
ejpam-4329	197	26	a	a	DET
ejpam-4329	197	27	∈	∈	PROPN
ejpam-4329	197	28	io.it	io.it	NOUN
ejpam-4329	197	29	implies	imply	VERB
ejpam-4329	197	30	x	x	PUNCT
ejpam-4329	197	31	∧	∧	NOUN
ejpam-4329	197	32	a	a	PRON
ejpam-4329	197	33	=	=	NOUN
ejpam-4329	197	34	0	0	NUM
ejpam-4329	197	35	.	.	PUNCT
ejpam-4329	198	1	therefore	therefore	ADV
ejpam-4329	198	2	i∗o	i∗o	PROPN
ejpam-4329	198	3	⊆	⊆	NUM
ejpam-4329	198	4	ioo	ioo	ADJ
ejpam-4329	198	5	⊆	⊆	NUM
ejpam-4329	198	6	io∗.	io∗.	PROPN
ejpam-4329	198	7	(	(	PUNCT
ejpam-4329	198	8	2	2	NUM
ejpam-4329	198	9	)	)	PUNCT
ejpam-4329	198	10	if	if	SCONJ
ejpam-4329	198	11	i	i	PRON
ejpam-4329	198	12	is	be	AUX
ejpam-4329	198	13	a	a	DET
ejpam-4329	198	14	closed	closed	ADJ
ejpam-4329	198	15	annihilator	annihilator	NOUN
ejpam-4329	198	16	then	then	ADV
ejpam-4329	198	17	i	i	PRON
ejpam-4329	198	18	=	=	PUNCT
ejpam-4329	198	19	io∗	io∗	ADV
ejpam-4329	198	20	=	=	SYM
ejpam-4329	198	21	i∗o	i∗o	PROPN
ejpam-4329	198	22	.	.	PUNCT
ejpam-4329	199	1	the	the	DET
ejpam-4329	199	2	dual	dual	ADJ
ejpam-4329	199	3	weak	weak	ADJ
ejpam-4329	199	4	complementation	complementation	NOUN
ejpam-4329	199	5	of	of	ADP
ejpam-4329	199	6	i	i	PRON
ejpam-4329	199	7	is	be	AUX
ejpam-4329	199	8	given	give	VERB
ejpam-4329	199	9	by	by	ADP
ejpam-4329	199	10	io	io	X
ejpam-4329	199	11	=	=	SYM
ejpam-4329	199	12	io∗o	io∗o	PROPN
ejpam-4329	199	13	=	=	NOUN
ejpam-4329	199	14	i∗oo	i∗oo	PROPN
ejpam-4329	199	15	⊇	⊇	PROPN
ejpam-4329	199	16	i∗.	i∗.	PROPN
ejpam-4329	199	17	therefore	therefore	ADV
ejpam-4329	199	18	i∗	i∗	PROPN
ejpam-4329	199	19	=	=	SYM
ejpam-4329	199	20	io	io	PROPN
ejpam-4329	199	21	.	.	PROPN
ejpam-4329	199	22	(	(	PUNCT
ejpam-4329	199	23	3	3	X
ejpam-4329	199	24	)	)	PUNCT
ejpam-4329	199	25	for	for	ADP
ejpam-4329	199	26	meet	meet	ADJ
ejpam-4329	199	27	operation	operation	NOUN
ejpam-4329	199	28	we	we	PRON
ejpam-4329	199	29	have	have	VERB
ejpam-4329	199	30	i	i	PRON
ejpam-4329	199	31	∩k	∩k	VERB
ejpam-4329	199	32	≤	≤	X
ejpam-4329	200	1	i	i	PROPN
ejpam-4329	200	2	,	,	PUNCT
ejpam-4329	200	3	k.	k.	PROPN
ejpam-4329	201	1	thus	thus	ADV
ejpam-4329	201	2	(	(	PUNCT
ejpam-4329	201	3	i	i	PRON
ejpam-4329	201	4	∩k)o∗	∩k)o∗	VERB
ejpam-4329	201	5	≤	≤	PUNCT
ejpam-4329	201	6	io∗,ko∗.	io∗,ko∗.	ADV
ejpam-4329	201	7	accordingly	accordingly	ADV
ejpam-4329	201	8	,	,	PUNCT
ejpam-4329	201	9	(	(	PUNCT
ejpam-4329	201	10	i∩k)o∗	i∩k)o∗	PROPN
ejpam-4329	201	11	≤	≤	ADJ
ejpam-4329	201	12	io∗∩ko∗	io∗∩ko∗	ADJ
ejpam-4329	201	13	=	=	SYM
ejpam-4329	201	14	i∩k	i∩k	NOUN
ejpam-4329	201	15	,	,	PUNCT
ejpam-4329	201	16	and	and	CCONJ
ejpam-4329	201	17	i∩k	i∩k	NOUN
ejpam-4329	201	18	⊆	⊆	NUM
ejpam-4329	201	19	(	(	PUNCT
ejpam-4329	201	20	i∩k)oo	i∩k)oo	NOUN
ejpam-4329	201	21	⊆	⊆	NUM
ejpam-4329	201	22	(	(	PUNCT
ejpam-4329	201	23	i∩k)o∗.	i∩k)o∗.	NOUN
ejpam-4329	201	24	then	then	ADV
ejpam-4329	201	25	i∩k	i∩k	NOUN
ejpam-4329	201	26	∈	∈	PROPN
ejpam-4329	201	27	io∗(l).for	io∗(l).for	ADP
ejpam-4329	201	28	join	join	VERB
ejpam-4329	201	29	operation	operation	NOUN
ejpam-4329	201	30	we	we	PRON
ejpam-4329	201	31	have	have	VERB
ejpam-4329	201	32	[	[	X
ejpam-4329	201	33	i	i	NOUN
ejpam-4329	201	34	tk]o∗	tk]o∗	NOUN
ejpam-4329	201	35	=	=	SYM
ejpam-4329	201	36	(	(	PUNCT
ejpam-4329	202	1	io	io	X
ejpam-4329	202	2	∩ko)oo∗	∩ko)oo∗	PROPN
ejpam-4329	202	3	=	=	PUNCT
ejpam-4329	202	4	(	(	PUNCT
ejpam-4329	202	5	io	io	X
ejpam-4329	202	6	∩ko)o	∩ko)o	PROPN
ejpam-4329	202	7	=	=	PUNCT
ejpam-4329	203	1	i	i	PRON
ejpam-4329	203	2	tk	tk	VERB
ejpam-4329	203	3	.	.	PROPN
ejpam-4329	204	1	(	(	PUNCT
ejpam-4329	204	2	4	4	NUM
ejpam-4329	204	3	)	)	PUNCT
ejpam-4329	204	4	if	if	SCONJ
ejpam-4329	204	5	i	i	PRON
ejpam-4329	204	6	∈	∈	PROPN
ejpam-4329	204	7	a(l	a(l	VERB
ejpam-4329	204	8	)	)	PUNCT
ejpam-4329	204	9	then	then	ADV
ejpam-4329	204	10	i	i	PRON
ejpam-4329	204	11	=	=	PUNCT
ejpam-4329	204	12	i∗o	i∗o	PROPN
ejpam-4329	204	13	=	=	PUNCT
ejpam-4329	204	14	i∗∗	i∗∗	PROPN
ejpam-4329	204	15	and	and	CCONJ
ejpam-4329	204	16	i∗	i∗	NOUN
ejpam-4329	204	17	∈	∈	NOUN
ejpam-4329	204	18	a(l	a(l	PROPN
ejpam-4329	204	19	)	)	PUNCT
ejpam-4329	204	20	.	.	PUNCT
ejpam-4329	205	1	hence	hence	ADV
ejpam-4329	205	2	io∗	io∗	ADV
ejpam-4329	205	3	=	=	PUNCT
ejpam-4329	205	4	i∗oo∗	i∗oo∗	ADJ
ejpam-4329	205	5	=	=	PUNCT
ejpam-4329	205	6	i∗∗	i∗∗	PROPN
ejpam-4329	205	7	=	=	PUNCT
ejpam-4329	205	8	i.	i.	NOUN
ejpam-4329	205	9	conversely	conversely	ADV
ejpam-4329	205	10	,	,	PUNCT
ejpam-4329	205	11	if	if	SCONJ
ejpam-4329	205	12	i	i	PRON
ejpam-4329	205	13	∈	∈	PROPN
ejpam-4329	205	14	io∗(l	io∗(l	PROPN
ejpam-4329	205	15	)	)	PUNCT
ejpam-4329	205	16	then	then	ADV
ejpam-4329	205	17	i	i	PRON
ejpam-4329	205	18	=	=	PUNCT
ejpam-4329	205	19	io∗	io∗	ADV
ejpam-4329	205	20	=	=	PUNCT
ejpam-4329	205	21	i∗∗	i∗∗	PROPN
ejpam-4329	205	22	and	and	CCONJ
ejpam-4329	205	23	i∗	i∗	NOUN
ejpam-4329	205	24	=	=	SYM
ejpam-4329	205	25	io	io	PROPN
ejpam-4329	205	26	∈	∈	PROPN
ejpam-4329	206	1	io∗.	io∗.	PROPN
ejpam-4329	206	2	so	so	SCONJ
ejpam-4329	206	3	i∗o	i∗o	PROPN
ejpam-4329	206	4	=	=	SYM
ejpam-4329	206	5	io∗∗o	io∗∗o	PROPN
ejpam-4329	206	6	=	=	SYM
ejpam-4329	206	7	ioo	ioo	VERB
ejpam-4329	206	8	=	=	PUNCT
ejpam-4329	206	9	i.	i.	NOUN
ejpam-4329	206	10	the	the	DET
ejpam-4329	206	11	subset	subset	NOUN
ejpam-4329	206	12	of	of	ADP
ejpam-4329	206	13	ortho	ortho	PROPN
ejpam-4329	206	14	lattice	lattice	PROPN
ejpam-4329	206	15	l	l	PROPN
ejpam-4329	206	16	which	which	PRON
ejpam-4329	206	17	forms	form	VERB
ejpam-4329	206	18	a	a	DET
ejpam-4329	206	19	boolean	boolean	ADJ
ejpam-4329	206	20	algebra	algebra	NOUN
ejpam-4329	206	21	under	under	ADP
ejpam-4329	206	22	the	the	DET
ejpam-4329	206	23	same	same	ADJ
ejpam-4329	206	24	operations	operation	NOUN
ejpam-4329	206	25	of	of	ADP
ejpam-4329	206	26	l	l	NOUN
ejpam-4329	206	27	is	be	AUX
ejpam-4329	206	28	called	call	VERB
ejpam-4329	206	29	a	a	DET
ejpam-4329	206	30	boolean	boolean	ADJ
ejpam-4329	206	31	algebra	algebra	NOUN
ejpam-4329	206	32	induced	induce	VERB
ejpam-4329	206	33	from	from	ADP
ejpam-4329	206	34	l.	l.	PROPN
ejpam-4329	206	35	theorem	theorem	PROPN
ejpam-4329	206	36	6	6	NUM
ejpam-4329	206	37	.	.	PUNCT
ejpam-4329	207	1	the	the	DET
ejpam-4329	207	2	set	set	PROPN
ejpam-4329	207	3	io∗(l	io∗(l	PROPN
ejpam-4329	207	4	)	)	PUNCT
ejpam-4329	207	5	,	,	PUNCT
ejpam-4329	207	6	of	of	ADP
ejpam-4329	207	7	all	all	DET
ejpam-4329	207	8	closed	closed	ADJ
ejpam-4329	207	9	annihilators	annihilators	PROPN
ejpam-4329	207	10	forms	form	VERB
ejpam-4329	207	11	a	a	DET
ejpam-4329	207	12	maximal	maximal	ADJ
ejpam-4329	207	13	boolean	boolean	ADJ
ejpam-4329	207	14	algebra	algebra	NOUN
ejpam-4329	207	15	indued	indue	VERB
ejpam-4329	207	16	from	from	ADP
ejpam-4329	207	17	s(i(l	s(i(l	PROPN
ejpam-4329	207	18	)	)	PUNCT
ejpam-4329	207	19	)	)	PUNCT
ejpam-4329	207	20	.	.	PUNCT
ejpam-4329	208	1	proof	proof	NOUN
ejpam-4329	208	2	.	.	PUNCT
ejpam-4329	209	1	to	to	PART
ejpam-4329	209	2	prove	prove	VERB
ejpam-4329	209	3	io∗(l	io∗(l	NOUN
ejpam-4329	209	4	)	)	PUNCT
ejpam-4329	209	5	forms	form	VERB
ejpam-4329	209	6	a	a	DET
ejpam-4329	209	7	boolean	boolean	ADJ
ejpam-4329	209	8	algebra	algebra	NOUN
ejpam-4329	209	9	it	it	PRON
ejpam-4329	209	10	is	be	AUX
ejpam-4329	209	11	enough	enough	ADJ
ejpam-4329	209	12	to	to	PART
ejpam-4329	209	13	prove	prove	VERB
ejpam-4329	209	14	the	the	DET
ejpam-4329	209	15	distributivity	distributivity	NOUN
ejpam-4329	209	16	of	of	ADP
ejpam-4329	209	17	it	it	PRON
ejpam-4329	209	18	.	.	PUNCT
ejpam-4329	210	1	initially	initially	ADV
ejpam-4329	210	2	,	,	PUNCT
ejpam-4329	210	3	we	we	PRON
ejpam-4329	210	4	prove	prove	VERB
ejpam-4329	210	5	the	the	DET
ejpam-4329	210	6	inequality	inequality	NOUN
ejpam-4329	210	7	(	(	PUNCT
ejpam-4329	210	8	1	1	NUM
ejpam-4329	210	9	):	):	PUNCT
ejpam-4329	210	10	for	for	ADP
ejpam-4329	210	11	i	i	PROPN
ejpam-4329	210	12	,	,	PUNCT
ejpam-4329	210	13	j	j	PROPN
ejpam-4329	210	14	,	,	PUNCT
ejpam-4329	210	15	k	k	PROPN
ejpam-4329	210	16	,	,	PUNCT
ejpam-4329	210	17	h	h	PROPN
ejpam-4329	210	18	∈	∈	PROPN
ejpam-4329	210	19	io∗(l	io∗(l	PROPN
ejpam-4329	210	20	)	)	PUNCT
ejpam-4329	211	1	(	(	PUNCT
ejpam-4329	211	2	i	i	PRON
ejpam-4329	211	3	t	t	PROPN
ejpam-4329	211	4	j	j	PROPN
ejpam-4329	211	5	)	)	PUNCT
ejpam-4329	211	6	∩h	∩h	PROPN
ejpam-4329	211	7	≤	≤	PROPN
ejpam-4329	212	1	i	i	PRON
ejpam-4329	212	2	t	t	PROPN
ejpam-4329	212	3	(	(	PUNCT
ejpam-4329	212	4	j	j	PROPN
ejpam-4329	212	5	∩h	∩h	PROPN
ejpam-4329	212	6	)	)	PUNCT
ejpam-4329	212	7	...	...	PUNCT
ejpam-4329	213	1	(	(	PUNCT
ejpam-4329	213	2	1	1	X
ejpam-4329	213	3	)	)	PUNCT
ejpam-4329	213	4	since	since	ADV
ejpam-4329	213	5	,	,	PUNCT
ejpam-4329	213	6	h	h	PROPN
ejpam-4329	213	7	∩	∩	NOUN
ejpam-4329	213	8	io	io	X
ejpam-4329	213	9	∩	∩	X
ejpam-4329	213	10	(	(	PUNCT
ejpam-4329	213	11	j	j	PROPN
ejpam-4329	213	12	∩h)o	∩h)o	PROPN
ejpam-4329	213	13	≤	≤	NUM
ejpam-4329	213	14	io	io	X
ejpam-4329	213	15	...	...	PUNCT
ejpam-4329	213	16	(2	(2	NUM
ejpam-4329	213	17	)	)	PUNCT
ejpam-4329	213	18	and	and	CCONJ
ejpam-4329	213	19	,	,	PUNCT
ejpam-4329	213	20	j	j	PROPN
ejpam-4329	213	21	∩	∩	ADJ
ejpam-4329	213	22	h	h	NOUN
ejpam-4329	213	23	∩	∩	NOUN
ejpam-4329	213	24	(	(	PUNCT
ejpam-4329	213	25	io	io	X
ejpam-4329	213	26	∩	∩	X
ejpam-4329	213	27	(	(	PUNCT
ejpam-4329	213	28	j	j	PROPN
ejpam-4329	213	29	∩	∩	NOUN
ejpam-4329	213	30	h)o	h)o	ADJ
ejpam-4329	213	31	)	)	PUNCT
ejpam-4329	213	32	=	=	SYM
ejpam-4329	213	33	io	io	X
ejpam-4329	213	34	∩	∩	X
ejpam-4329	213	35	(	(	PUNCT
ejpam-4329	213	36	j	j	PROPN
ejpam-4329	213	37	∩	∩	ADJ
ejpam-4329	213	38	h	h	NOUN
ejpam-4329	213	39	)	)	PUNCT
ejpam-4329	213	40	∩	∩	NOUN
ejpam-4329	213	41	(	(	PUNCT
ejpam-4329	213	42	j	j	PROPN
ejpam-4329	213	43	∩	∩	ADJ
ejpam-4329	213	44	h)o	h)o	X
ejpam-4329	213	45	=	=	SYM
ejpam-4329	213	46	(	(	PUNCT
ejpam-4329	213	47	0	0	NUM
ejpam-4329	213	48	]	]	PUNCT
ejpam-4329	213	49	.	.	PUNCT
ejpam-4329	214	1	it	it	PRON
ejpam-4329	214	2	implies	imply	VERB
ejpam-4329	214	3	that	that	SCONJ
ejpam-4329	214	4	,	,	PUNCT
ejpam-4329	214	5	h	h	PROPN
ejpam-4329	214	6	∩	∩	NOUN
ejpam-4329	214	7	io	io	X
ejpam-4329	214	8	∩	∩	X
ejpam-4329	214	9	(	(	PUNCT
ejpam-4329	214	10	j	j	PROPN
ejpam-4329	214	11	∩h)o	∩h)o	PROPN
ejpam-4329	214	12	≤	≤	NUM
ejpam-4329	214	13	jo	jo	PROPN
ejpam-4329	214	14	thus	thus	ADV
ejpam-4329	214	15	,	,	PUNCT
ejpam-4329	214	16	h	h	PROPN
ejpam-4329	214	17	∩	∩	NOUN
ejpam-4329	214	18	io	io	X
ejpam-4329	214	19	∩	∩	X
ejpam-4329	214	20	(	(	PUNCT
ejpam-4329	214	21	j	j	PROPN
ejpam-4329	214	22	∩h)o	∩h)o	PROPN
ejpam-4329	214	23	≤	≤	NUM
ejpam-4329	214	24	jo	jo	PROPN
ejpam-4329	214	25	...	...	PUNCT
ejpam-4329	214	26	(3	(3	PROPN
ejpam-4329	214	27	)	)	PUNCT
ejpam-4329	214	28	from	from	ADP
ejpam-4329	214	29	(	(	PUNCT
ejpam-4329	214	30	2	2	NUM
ejpam-4329	214	31	)	)	PUNCT
ejpam-4329	214	32	and	and	CCONJ
ejpam-4329	214	33	(	(	PUNCT
ejpam-4329	214	34	3	3	NUM
ejpam-4329	214	35	)	)	PUNCT
ejpam-4329	214	36	,	,	PUNCT
ejpam-4329	214	37	h	h	PROPN
ejpam-4329	214	38	∩	∩	NOUN
ejpam-4329	214	39	io	io	X
ejpam-4329	214	40	∩	∩	X
ejpam-4329	214	41	(	(	PUNCT
ejpam-4329	214	42	j	j	PROPN
ejpam-4329	214	43	∩h)o	∩h)o	PROPN
ejpam-4329	214	44	≤	≤	NUM
ejpam-4329	214	45	io	io	ADP
ejpam-4329	214	46	∩jo	∩jo	PROPN
ejpam-4329	214	47	and	and	CCONJ
ejpam-4329	214	48	from	from	ADP
ejpam-4329	214	49	the	the	DET
ejpam-4329	214	50	properties	property	NOUN
ejpam-4329	214	51	of	of	ADP
ejpam-4329	214	52	”	"	PUNCT
ejpam-4329	214	53	o	o	NOUN
ejpam-4329	214	54	”	"	PUNCT
ejpam-4329	214	55	,	,	PUNCT
ejpam-4329	214	56	we	we	PRON
ejpam-4329	214	57	get	get	VERB
ejpam-4329	214	58	(	(	PUNCT
ejpam-4329	214	59	h∩io∩(j∩h)o)∩(io∩jo)o	h∩io∩(j∩h)o)∩(io∩jo)o	X
ejpam-4329	214	60	=	=	SYM
ejpam-4329	214	61	(	(	PUNCT
ejpam-4329	214	62	0	0	NUM
ejpam-4329	214	63	]	]	PUNCT
ejpam-4329	214	64	,	,	PUNCT
ejpam-4329	214	65	implies	imply	VERB
ejpam-4329	214	66	that	that	SCONJ
ejpam-4329	214	67	,	,	PUNCT
ejpam-4329	214	68	(	(	PUNCT
ejpam-4329	214	69	(	(	PUNCT
ejpam-4329	214	70	io∩jo)o∩h)∩(io∩(j∩h)o	io∩jo)o∩h)∩(io∩(j∩h)o	NOUN
ejpam-4329	214	71	)	)	PUNCT
ejpam-4329	214	72	=	=	SYM
ejpam-4329	214	73	(	(	PUNCT
ejpam-4329	214	74	0	0	NUM
ejpam-4329	214	75	]	]	PUNCT
ejpam-4329	214	76	.	.	PUNCT
ejpam-4329	215	1	so	so	ADV
ejpam-4329	215	2	,	,	PUNCT
ejpam-4329	215	3	h	h	NOUN
ejpam-4329	215	4	∩	∩	NOUN
ejpam-4329	215	5	(	(	PUNCT
ejpam-4329	215	6	io	io	X
ejpam-4329	215	7	∩	∩	X
ejpam-4329	215	8	jo)o	jo)o	PROPN
ejpam-4329	215	9	≤	≤	NUM
ejpam-4329	215	10	(	(	PUNCT
ejpam-4329	215	11	io	io	X
ejpam-4329	215	12	∩	∩	X
ejpam-4329	215	13	(	(	PUNCT
ejpam-4329	215	14	j	j	PROPN
ejpam-4329	215	15	∩h)o)o	∩h)o)o	PROPN
ejpam-4329	215	16	.	.	PUNCT
ejpam-4329	216	1	therefore	therefore	ADV
ejpam-4329	216	2	,	,	PUNCT
ejpam-4329	216	3	(	(	PUNCT
ejpam-4329	216	4	io	io	X
ejpam-4329	216	5	∩	∩	X
ejpam-4329	216	6	jo)o	jo)o	PROPN
ejpam-4329	216	7	∩h	∩h	NOUN
ejpam-4329	216	8	≤	≤	PROPN
ejpam-4329	216	9	(	(	PUNCT
ejpam-4329	216	10	io	io	X
ejpam-4329	216	11	∩	∩	X
ejpam-4329	216	12	(	(	PUNCT
ejpam-4329	216	13	j	j	PROPN
ejpam-4329	216	14	∩h)o)o	∩h)o)o	PROPN
ejpam-4329	216	15	.	.	PUNCT
ejpam-4329	217	1	by	by	ADP
ejpam-4329	217	2	putting	put	VERB
ejpam-4329	217	3	h	h	NOUN
ejpam-4329	218	1	=	=	NOUN
ejpam-4329	218	2	i	i	PRON
ejpam-4329	218	3	t	t	X
ejpam-4329	218	4	k	k	PROPN
ejpam-4329	218	5	in	in	ADP
ejpam-4329	218	6	inq.(1	inq.(1	PROPN
ejpam-4329	218	7	)	)	PUNCT
ejpam-4329	218	8	,	,	PUNCT
ejpam-4329	218	9	we	we	PRON
ejpam-4329	218	10	get	get	VERB
ejpam-4329	218	11	(	(	PUNCT
ejpam-4329	218	12	i	i	NOUN
ejpam-4329	218	13	t	t	PROPN
ejpam-4329	218	14	j	j	PROPN
ejpam-4329	218	15	)	)	PUNCT
ejpam-4329	218	16	∩	∩	NOUN
ejpam-4329	218	17	(	(	PUNCT
ejpam-4329	218	18	i	i	PROPN
ejpam-4329	218	19	t	t	PROPN
ejpam-4329	218	20	k	k	NOUN
ejpam-4329	218	21	)	)	PUNCT
ejpam-4329	218	22	≤	≤	PUNCT
ejpam-4329	219	1	i	i	PRON
ejpam-4329	219	2	t	t	X
ejpam-4329	220	1	[	[	X
ejpam-4329	220	2	(	(	PUNCT
ejpam-4329	220	3	j	j	PROPN
ejpam-4329	220	4	∩	∩	NOUN
ejpam-4329	220	5	i	i	PRON
ejpam-4329	220	6	t	t	PROPN
ejpam-4329	220	7	k	k	PROPN
ejpam-4329	220	8	)	)	PUNCT
ejpam-4329	220	9	]	]	PUNCT
ejpam-4329	221	1	≤	≤	ADV
ejpam-4329	222	1	i	i	PRON
ejpam-4329	222	2	t	t	X
ejpam-4329	223	1	[	[	X
ejpam-4329	223	2	i	i	X
ejpam-4329	223	3	t	t	X
ejpam-4329	223	4	(	(	PUNCT
ejpam-4329	223	5	j	j	PROPN
ejpam-4329	223	6	∩k	∩k	PROPN
ejpam-4329	223	7	)	)	PUNCT
ejpam-4329	223	8	]	]	PUNCT
ejpam-4329	224	1	=	=	PUNCT
ejpam-4329	224	2	i	i	PRON
ejpam-4329	224	3	t	t	PROPN
ejpam-4329	224	4	(	(	PUNCT
ejpam-4329	224	5	j	j	PROPN
ejpam-4329	224	6	∩k	∩k	PROPN
ejpam-4329	224	7	)	)	PUNCT
ejpam-4329	224	8	.	.	PUNCT
ejpam-4329	225	1	also	also	ADV
ejpam-4329	225	2	,	,	PUNCT
ejpam-4329	225	3	j	j	PROPN
ejpam-4329	225	4	∩k	∩k	PROPN
ejpam-4329	225	5	≤	≤	NOUN
ejpam-4329	226	1	(	(	PUNCT
ejpam-4329	226	2	i	i	PRON
ejpam-4329	226	3	t	t	VERB
ejpam-4329	226	4	j)∩	j)∩	PROPN
ejpam-4329	227	1	(	(	PUNCT
ejpam-4329	227	2	i	i	PRON
ejpam-4329	227	3	tk	tk	PROPN
ejpam-4329	227	4	)	)	PUNCT
ejpam-4329	228	1	and	and	CCONJ
ejpam-4329	228	2	i	i	PRON
ejpam-4329	228	3	≤	≤	X
ejpam-4329	228	4	(	(	PUNCT
ejpam-4329	228	5	i	i	PRON
ejpam-4329	228	6	t	t	VERB
ejpam-4329	228	7	j)∩	j)∩	PROPN
ejpam-4329	229	1	(	(	PUNCT
ejpam-4329	229	2	i	i	PRON
ejpam-4329	229	3	tk	tk	PROPN
ejpam-4329	229	4	)	)	PUNCT
ejpam-4329	229	5	.	.	PUNCT
ejpam-4329	230	1	then	then	ADV
ejpam-4329	230	2	,	,	PUNCT
ejpam-4329	230	3	i	i	PRON
ejpam-4329	230	4	t	t	X
ejpam-4329	230	5	(	(	PUNCT
ejpam-4329	230	6	j	j	PROPN
ejpam-4329	230	7	∩k	∩k	PROPN
ejpam-4329	230	8	)	)	PUNCT
ejpam-4329	230	9	≤	≤	NOUN
ejpam-4329	231	1	(	(	PUNCT
ejpam-4329	231	2	i	i	PRON
ejpam-4329	231	3	t	t	PROPN
ejpam-4329	231	4	j	j	PROPN
ejpam-4329	231	5	)	)	PUNCT
ejpam-4329	231	6	∩	∩	NOUN
ejpam-4329	231	7	(	(	PUNCT
ejpam-4329	231	8	i	i	PRON
ejpam-4329	231	9	tk	tk	PROPN
ejpam-4329	231	10	)	)	PUNCT
ejpam-4329	231	11	.	.	PUNCT
ejpam-4329	232	1	consequently	consequently	ADV
ejpam-4329	232	2	,	,	PUNCT
ejpam-4329	232	3	i	i	PRON
ejpam-4329	232	4	t	t	X
ejpam-4329	232	5	(	(	PUNCT
ejpam-4329	232	6	j	j	PROPN
ejpam-4329	232	7	∩k	∩k	PROPN
ejpam-4329	232	8	)	)	PUNCT
ejpam-4329	232	9	=	=	PUNCT
ejpam-4329	233	1	(	(	PUNCT
ejpam-4329	233	2	i	i	PRON
ejpam-4329	233	3	t	t	PROPN
ejpam-4329	233	4	j	j	PROPN
ejpam-4329	233	5	)	)	PUNCT
ejpam-4329	233	6	∩	∩	NOUN
ejpam-4329	233	7	(	(	PUNCT
ejpam-4329	233	8	i	i	PRON
ejpam-4329	233	9	tk	tk	PROPN
ejpam-4329	233	10	)	)	PUNCT
ejpam-4329	233	11	.	.	PUNCT
ejpam-4329	234	1	therefore	therefore	ADV
ejpam-4329	234	2	,	,	PUNCT
ejpam-4329	234	3	<	<	X
ejpam-4329	234	4	io∗(l);t,∩,o	io∗(l);t,∩,o	PROPN
ejpam-4329	234	5	,	,	PUNCT
ejpam-4329	234	6	(	(	PUNCT
ejpam-4329	234	7	0	0	NUM
ejpam-4329	234	8	]	]	PUNCT
ejpam-4329	234	9	,	,	PUNCT
ejpam-4329	234	10	(	(	PUNCT
ejpam-4329	234	11	1	1	X
ejpam-4329	234	12	]	]	PUNCT
ejpam-4329	234	13	>	>	X
ejpam-4329	234	14	forms	form	VERB
ejpam-4329	234	15	a	a	DET
ejpam-4329	234	16	boolean	boolean	ADJ
ejpam-4329	234	17	algebra	algebra	NOUN
ejpam-4329	234	18	.	.	PUNCT
ejpam-4329	235	1	next	next	ADV
ejpam-4329	235	2	,	,	PUNCT
ejpam-4329	235	3	we	we	PRON
ejpam-4329	235	4	prove	prove	VERB
ejpam-4329	235	5	the	the	DET
ejpam-4329	235	6	maximality	maximality	NOUN
ejpam-4329	235	7	of	of	ADP
ejpam-4329	235	8	io∗(l	io∗(l	PROPN
ejpam-4329	235	9	)	)	PUNCT
ejpam-4329	235	10	.	.	PUNCT
ejpam-4329	236	1	let	let	VERB
ejpam-4329	236	2	b	b	X
ejpam-4329	236	3	be	be	AUX
ejpam-4329	236	4	a	a	DET
ejpam-4329	236	5	boolean	boolean	ADJ
ejpam-4329	236	6	algebra	algebra	NOUN
ejpam-4329	236	7	induced	induce	VERB
ejpam-4329	236	8	from	from	ADP
ejpam-4329	236	9	s(i(l	s(i(l	PROPN
ejpam-4329	236	10	)	)	PUNCT
ejpam-4329	236	11	)	)	PUNCT
ejpam-4329	236	12	such	such	ADJ
ejpam-4329	236	13	that	that	DET
ejpam-4329	236	14	io∗(l	io∗(l	NOUN
ejpam-4329	236	15	)	)	PUNCT
ejpam-4329	236	16	⊂	⊂	PROPN
ejpam-4329	236	17	b.	b.	PROPN
ejpam-4329	237	1	then	then	ADV
ejpam-4329	237	2	there	there	PRON
ejpam-4329	237	3	exist	exist	VERB
ejpam-4329	237	4	ideal	ideal	ADJ
ejpam-4329	237	5	h	h	NOUN
ejpam-4329	237	6	∈	∈	PROPN
ejpam-4329	237	7	b	b	PROPN
ejpam-4329	237	8	and	and	CCONJ
ejpam-4329	237	9	h	h	PROPN
ejpam-4329	237	10	6∈	6∈	PROPN
ejpam-4329	237	11	io∗(l	io∗(l	PROPN
ejpam-4329	237	12	)	)	PUNCT
ejpam-4329	237	13	,	,	PUNCT
ejpam-4329	237	14	then	then	ADV
ejpam-4329	237	15	h	h	PROPN
ejpam-4329	237	16	⊂	⊂	PROPN
ejpam-4329	237	17	ho∗.	ho∗.	PROPN
ejpam-4329	237	18	since	since	SCONJ
ejpam-4329	237	19	ho	ho	PROPN
ejpam-4329	237	20	∩ho∗	∩ho∗	PROPN
ejpam-4329	237	21	=	=	PRON
ejpam-4329	237	22	(	(	PUNCT
ejpam-4329	237	23	0	0	NUM
ejpam-4329	237	24	]	]	PUNCT
ejpam-4329	237	25	then	then	ADV
ejpam-4329	237	26	.	.	PUNCT
ejpam-4329	238	1	ho∗	ho∗	PROPN
ejpam-4329	238	2	⊆	⊆	NUM
ejpam-4329	238	3	hoo	hoo	NOUN
ejpam-4329	238	4	=	=	SYM
ejpam-4329	238	5	h.	h.	PROPN
ejpam-4329	239	1	so	so	SCONJ
ejpam-4329	239	2	that	that	SCONJ
ejpam-4329	239	3	h	h	NOUN
ejpam-4329	239	4	=	=	PUNCT
ejpam-4329	239	5	ho∗	ho∗	PROPN
ejpam-4329	239	6	,	,	PUNCT
ejpam-4329	239	7	which	which	PRON
ejpam-4329	239	8	is	be	AUX
ejpam-4329	239	9	a	a	DET
ejpam-4329	239	10	contradiction	contradiction	NOUN
ejpam-4329	239	11	.	.	PUNCT
ejpam-4329	240	1	references	reference	NOUN
ejpam-4329	240	2	494	494	NUM
ejpam-4329	240	3	theorem	theorem	NOUN
ejpam-4329	240	4	7	7	NUM
ejpam-4329	240	5	.	.	PUNCT
ejpam-4329	240	6	(	(	PUNCT
ejpam-4329	240	7	1	1	NUM
ejpam-4329	240	8	)	)	PUNCT
ejpam-4329	240	9	a(l	a(l	PROPN
ejpam-4329	240	10	)	)	PUNCT
ejpam-4329	240	11	isomorphic	isomorphic	ADJ
ejpam-4329	240	12	to	to	ADP
ejpam-4329	240	13	io∗(l	io∗(l	NOUN
ejpam-4329	240	14	)	)	PUNCT
ejpam-4329	240	15	,	,	PUNCT
ejpam-4329	240	16	(	(	PUNCT
ejpam-4329	240	17	2	2	X
ejpam-4329	240	18	)	)	PUNCT
ejpam-4329	241	1	if	if	SCONJ
ejpam-4329	241	2	io	io	PROPN
ejpam-4329	241	3	=	=	SYM
ejpam-4329	241	4	ko	ko	PROPN
ejpam-4329	241	5	,	,	PUNCT
ejpam-4329	241	6	for	for	ADP
ejpam-4329	241	7	any	any	DET
ejpam-4329	241	8	closed	closed	ADJ
ejpam-4329	241	9	annihilator	annihilator	NOUN
ejpam-4329	241	10	i	i	PROPN
ejpam-4329	241	11	and	and	CCONJ
ejpam-4329	241	12	any	any	DET
ejpam-4329	241	13	ideal	ideal	NOUN
ejpam-4329	241	14	k	k	ADP
ejpam-4329	241	15	such	such	ADJ
ejpam-4329	241	16	that	that	SCONJ
ejpam-4329	241	17	i	i	PRON
ejpam-4329	241	18	⊂	⊂	PROPN
ejpam-4329	241	19	k	k	NOUN
ejpam-4329	241	20	,	,	PUNCT
ejpam-4329	241	21	then	then	ADV
ejpam-4329	241	22	s(i(l	s(i(l	PROPN
ejpam-4329	241	23	)	)	PUNCT
ejpam-4329	241	24	)	)	PUNCT
ejpam-4329	241	25	is	be	AUX
ejpam-4329	241	26	a	a	DET
ejpam-4329	241	27	boolean	boolean	ADJ
ejpam-4329	241	28	algebra	algebra	NOUN
ejpam-4329	241	29	,	,	PUNCT
ejpam-4329	241	30	(	(	PUNCT
ejpam-4329	241	31	3	3	X
ejpam-4329	241	32	)	)	PUNCT
ejpam-4329	241	33	if	if	SCONJ
ejpam-4329	241	34	there	there	PRON
ejpam-4329	241	35	exists	exist	VERB
ejpam-4329	241	36	closed	closed	ADJ
ejpam-4329	241	37	annihilator	annihilator	PROPN
ejpam-4329	241	38	i	i	PROPN
ejpam-4329	241	39	and	and	CCONJ
ejpam-4329	241	40	ideal	ideal	ADJ
ejpam-4329	242	1	k	k	PRON
ejpam-4329	242	2	such	such	ADJ
ejpam-4329	242	3	that	that	SCONJ
ejpam-4329	242	4	i	i	PRON
ejpam-4329	242	5	⊂	⊂	PROPN
ejpam-4329	242	6	k	k	PROPN
ejpam-4329	242	7	and	and	CCONJ
ejpam-4329	242	8	ko	ko	PROPN
ejpam-4329	242	9	⊂	⊂	PROPN
ejpam-4329	242	10	io	io	PROPN
ejpam-4329	242	11	then	then	ADV
ejpam-4329	242	12	s(i(l	s(i(l	PROPN
ejpam-4329	242	13	)	)	PUNCT
ejpam-4329	242	14	)	)	PUNCT
ejpam-4329	242	15	is	be	AUX
ejpam-4329	242	16	not	not	PART
ejpam-4329	242	17	boolean	boolean	ADJ
ejpam-4329	242	18	algebra	algebra	NOUN
ejpam-4329	242	19	.	.	PUNCT
ejpam-4329	243	1	proof	proof	NOUN
ejpam-4329	243	2	.	.	PUNCT
ejpam-4329	244	1	(	(	PUNCT
ejpam-4329	244	2	1	1	X
ejpam-4329	244	3	)	)	PUNCT
ejpam-4329	244	4	we	we	PRON
ejpam-4329	244	5	defined	define	VERB
ejpam-4329	244	6	a	a	DET
ejpam-4329	244	7	map	map	NOUN
ejpam-4329	244	8	α	α	NOUN
ejpam-4329	244	9	:	:	PUNCT
ejpam-4329	244	10	a(l	a(l	PROPN
ejpam-4329	244	11	)	)	PUNCT
ejpam-4329	244	12	→	→	SYM
ejpam-4329	244	13	io∗(l	io∗(l	NOUN
ejpam-4329	244	14	)	)	PUNCT
ejpam-4329	244	15	as	as	ADP
ejpam-4329	244	16	:	:	PUNCT
ejpam-4329	244	17	α(i	α(i	NOUN
ejpam-4329	244	18	)	)	PUNCT
ejpam-4329	245	1	=	=	SYM
ejpam-4329	245	2	io∗.	io∗.	PROPN
ejpam-4329	245	3	assume	assume	VERB
ejpam-4329	245	4	i	i	PRON
ejpam-4329	245	5	,	,	PUNCT
ejpam-4329	245	6	j	j	PROPN
ejpam-4329	245	7	∈	∈	PROPN
ejpam-4329	245	8	a(l	a(l	PROPN
ejpam-4329	245	9	)	)	PUNCT
ejpam-4329	245	10	then	then	ADV
ejpam-4329	245	11	:	:	PUNCT
ejpam-4329	245	12	α(i	α(i	PROPN
ejpam-4329	245	13	∩	∩	PROPN
ejpam-4329	245	14	j	j	PROPN
ejpam-4329	245	15	)	)	PUNCT
ejpam-4329	245	16	=	=	PUNCT
ejpam-4329	246	1	(	(	PUNCT
ejpam-4329	246	2	i	i	NOUN
ejpam-4329	246	3	∩	∩	X
ejpam-4329	246	4	j)o∗	j)o∗	PROPN
ejpam-4329	247	1	=	=	PUNCT
ejpam-4329	248	1	i	i	PROPN
ejpam-4329	248	2	∩	∩	NOUN
ejpam-4329	248	3	j	j	PROPN
ejpam-4329	248	4	=	=	PUNCT
ejpam-4329	248	5	io∗	io∗	ADV
ejpam-4329	248	6	∩	∩	ADJ
ejpam-4329	248	7	jo∗	jo∗	NOUN
ejpam-4329	248	8	,	,	PUNCT
ejpam-4329	248	9	α(i	α(i	PROPN
ejpam-4329	248	10	y	y	PROPN
ejpam-4329	248	11	j	j	PROPN
ejpam-4329	248	12	)	)	PUNCT
ejpam-4329	248	13	=	=	PUNCT
ejpam-4329	249	1	(	(	PUNCT
ejpam-4329	249	2	i	i	PRON
ejpam-4329	249	3	y	y	PROPN
ejpam-4329	249	4	j)o∗	j)o∗	PROPN
ejpam-4329	249	5	=	=	X
ejpam-4329	249	6	(	(	PUNCT
ejpam-4329	249	7	i∗	i∗	NOUN
ejpam-4329	249	8	∩	∩	NOUN
ejpam-4329	249	9	j∗)∗o∗	j∗)∗o∗	NOUN
ejpam-4329	249	10	=	=	SYM
ejpam-4329	249	11	(	(	PUNCT
ejpam-4329	249	12	io	io	X
ejpam-4329	249	13	∩	∩	X
ejpam-4329	249	14	jo)o	jo)o	X
ejpam-4329	250	1	=	=	PUNCT
ejpam-4329	250	2	i	i	PRON
ejpam-4329	250	3	t	t	PROPN
ejpam-4329	250	4	j	j	PROPN
ejpam-4329	250	5	,	,	PUNCT
ejpam-4329	250	6	α(i∗	α(i∗	NUM
ejpam-4329	250	7	)	)	PUNCT
ejpam-4329	250	8	=	=	SYM
ejpam-4329	250	9	i∗o∗	i∗o∗	X
ejpam-4329	251	1	=	=	PUNCT
ejpam-4329	251	2	i∗	i∗	NOUN
ejpam-4329	251	3	=	=	SYM
ejpam-4329	251	4	io	io	NOUN
ejpam-4329	251	5	,	,	PUNCT
ejpam-4329	251	6	clearly	clearly	ADV
ejpam-4329	251	7	that	that	SCONJ
ejpam-4329	251	8	α	α	PROPN
ejpam-4329	251	9	is	be	AUX
ejpam-4329	251	10	bijective	bijective	ADJ
ejpam-4329	251	11	map	map	NOUN
ejpam-4329	251	12	.	.	PUNCT
ejpam-4329	252	1	when	when	SCONJ
ejpam-4329	252	2	for	for	ADP
ejpam-4329	252	3	any	any	DET
ejpam-4329	252	4	closed	closed	ADJ
ejpam-4329	252	5	annihilator	annihilator	NOUN
ejpam-4329	252	6	i	i	PROPN
ejpam-4329	252	7	and	and	CCONJ
ejpam-4329	252	8	any	any	DET
ejpam-4329	252	9	ideal	ideal	NOUN
ejpam-4329	253	1	k	k	ADP
ejpam-4329	253	2	such	such	ADJ
ejpam-4329	253	3	that	that	SCONJ
ejpam-4329	254	1	i	i	PRON
ejpam-4329	254	2	⊂	⊂	PROPN
ejpam-4329	255	1	k	k	X
ejpam-4329	255	2	we	we	PRON
ejpam-4329	255	3	get	get	VERB
ejpam-4329	255	4	ko	ko	PROPN
ejpam-4329	255	5	=	=	SYM
ejpam-4329	255	6	io	io	PROPN
ejpam-4329	256	1	=	=	PUNCT
ejpam-4329	256	2	i∗.	i∗.	PROPN
ejpam-4329	256	3	then	then	ADV
ejpam-4329	256	4	the	the	DET
ejpam-4329	256	5	set	set	NOUN
ejpam-4329	256	6	of	of	ADP
ejpam-4329	256	7	all	all	DET
ejpam-4329	256	8	closed	closed	ADJ
ejpam-4329	256	9	ideals	ideal	NOUN
ejpam-4329	256	10	s(i(l	s(i(l	VERB
ejpam-4329	256	11	)	)	PUNCT
ejpam-4329	256	12	)	)	PUNCT
ejpam-4329	256	13	coincides	coincide	VERB
ejpam-4329	256	14	with	with	ADP
ejpam-4329	256	15	the	the	DET
ejpam-4329	256	16	set	set	PROPN
ejpam-4329	256	17	io∗(l	io∗(l	PROPN
ejpam-4329	256	18	)	)	PUNCT
ejpam-4329	256	19	of	of	ADP
ejpam-4329	256	20	all	all	DET
ejpam-4329	256	21	closed	closed	ADJ
ejpam-4329	256	22	annihilators	annihilator	NOUN
ejpam-4329	256	23	.	.	PUNCT
ejpam-4329	257	1	consequently	consequently	ADV
ejpam-4329	257	2	,	,	PUNCT
ejpam-4329	257	3	s(i(l	s(i(l	PROPN
ejpam-4329	257	4	)	)	PUNCT
ejpam-4329	257	5	)	)	PUNCT
ejpam-4329	257	6	becomes	become	VERB
ejpam-4329	257	7	a	a	DET
ejpam-4329	257	8	boolean	boolean	ADJ
ejpam-4329	257	9	algebra	algebra	NOUN
ejpam-4329	257	10	.	.	PUNCT
ejpam-4329	258	1	while	while	SCONJ
ejpam-4329	258	2	if	if	SCONJ
ejpam-4329	258	3	there	there	PRON
ejpam-4329	258	4	exists	exist	VERB
ejpam-4329	258	5	closed	closed	ADJ
ejpam-4329	258	6	annihilator	annihilator	PROPN
ejpam-4329	258	7	i	i	PROPN
ejpam-4329	258	8	and	and	CCONJ
ejpam-4329	258	9	ideal	ideal	ADJ
ejpam-4329	259	1	k	k	PRON
ejpam-4329	259	2	such	such	ADJ
ejpam-4329	259	3	that	that	SCONJ
ejpam-4329	260	1	i	i	PRON
ejpam-4329	260	2	⊂	⊂	PROPN
ejpam-4329	260	3	k	k	PROPN
ejpam-4329	260	4	and	and	CCONJ
ejpam-4329	260	5	ko	ko	PROPN
ejpam-4329	260	6	⊂	⊂	PROPN
ejpam-4329	260	7	io	io	PROPN
ejpam-4329	261	1	then	then	ADV
ejpam-4329	261	2	ko	ko	PROPN
ejpam-4329	261	3	and	and	CCONJ
ejpam-4329	261	4	its	its	PRON
ejpam-4329	261	5	dual	dual	ADJ
ejpam-4329	261	6	weak	weak	ADJ
ejpam-4329	261	7	complementation	complementation	NOUN
ejpam-4329	261	8	are	be	AUX
ejpam-4329	261	9	added	add	VERB
ejpam-4329	261	10	to	to	PART
ejpam-4329	261	11	s(i(l	s(i(l	VERB
ejpam-4329	261	12	)	)	PUNCT
ejpam-4329	261	13	)	)	PUNCT
ejpam-4329	261	14	.	.	PUNCT
ejpam-4329	262	1	so	so	ADV
ejpam-4329	262	2	it	it	PRON
ejpam-4329	262	3	does	do	AUX
ejpam-4329	262	4	not	not	PART
ejpam-4329	262	5	boolean	boolean	ADJ
ejpam-4329	262	6	algebra	algebra	NOUN
ejpam-4329	262	7	.	.	PUNCT
ejpam-4329	263	1	the	the	DET
ejpam-4329	263	2	following	follow	VERB
ejpam-4329	263	3	corollary	corollary	NOUN
ejpam-4329	263	4	is	be	AUX
ejpam-4329	263	5	immediately	immediately	ADV
ejpam-4329	263	6	proved	prove	VERB
ejpam-4329	263	7	from	from	ADP
ejpam-4329	263	8	theorem	theorem	ADJ
ejpam-4329	263	9	7	7	NUM
ejpam-4329	263	10	corollary	corollary	ADJ
ejpam-4329	263	11	1	1	NUM
ejpam-4329	263	12	.	.	PUNCT
ejpam-4329	264	1	let	let	VERB
ejpam-4329	264	2	l	l	NOUN
ejpam-4329	264	3	be	be	AUX
ejpam-4329	264	4	a	a	DET
ejpam-4329	264	5	distributive	distributive	ADJ
ejpam-4329	264	6	pseudocomplemented	pseudocomplemented	ADJ
ejpam-4329	264	7	lattice	lattice	NOUN
ejpam-4329	264	8	.	.	PUNCT
ejpam-4329	265	1	then	then	ADV
ejpam-4329	265	2	io∗(l	io∗(l	PROPN
ejpam-4329	265	3	)	)	PUNCT
ejpam-4329	265	4	,	,	PUNCT
ejpam-4329	265	5	a(l	a(l	PROPN
ejpam-4329	265	6	)	)	PUNCT
ejpam-4329	265	7	and	and	CCONJ
ejpam-4329	265	8	s(i(l	s(i(l	PROPN
ejpam-4329	265	9	)	)	PUNCT
ejpam-4329	265	10	)	)	PUNCT
ejpam-4329	265	11	are	be	AUX
ejpam-4329	265	12	isomorphic	isomorphic	ADJ
ejpam-4329	265	13	.	.	PUNCT
ejpam-4329	266	1	conclusion	conclusion	NOUN
ejpam-4329	266	2	this	this	DET
ejpam-4329	266	3	work	work	NOUN
ejpam-4329	266	4	introduces	introduce	VERB
ejpam-4329	266	5	the	the	DET
ejpam-4329	266	6	annihilator	annihilator	PROPN
ejpam-4329	266	7	concept	concept	NOUN
ejpam-4329	266	8	for	for	ADP
ejpam-4329	266	9	the	the	DET
ejpam-4329	266	10	class	class	NOUN
ejpam-4329	266	11	of	of	ADP
ejpam-4329	266	12	ddwcls	ddwcls	NOUN
ejpam-4329	266	13	,	,	PUNCT
ejpam-4329	266	14	the	the	DET
ejpam-4329	266	15	characterization	characterization	NOUN
ejpam-4329	266	16	and	and	CCONJ
ejpam-4329	266	17	important	important	ADJ
ejpam-4329	266	18	properties	property	NOUN
ejpam-4329	266	19	of	of	ADP
ejpam-4329	266	20	closed	closed	ADJ
ejpam-4329	266	21	and	and	CCONJ
ejpam-4329	266	22	dense	dense	ADJ
ejpam-4329	266	23	ideals	ideal	NOUN
ejpam-4329	266	24	are	be	AUX
ejpam-4329	266	25	proved	prove	VERB
ejpam-4329	266	26	.	.	PUNCT
ejpam-4329	267	1	the	the	DET
ejpam-4329	267	2	one	one	NUM
ejpam-4329	267	3	-	-	PUNCT
ejpam-4329	267	4	to	to	ADP
ejpam-4329	267	5	-	-	PUNCT
ejpam-4329	267	6	one	one	NUM
ejpam-4329	267	7	correspondence	correspondence	NOUN
ejpam-4329	267	8	between	between	ADP
ejpam-4329	267	9	closed	close	VERB
ejpam-4329	267	10	annihilators	annihilator	NOUN
ejpam-4329	267	11	and	and	CCONJ
ejpam-4329	267	12	usual	usual	ADJ
ejpam-4329	267	13	annihilators	annihilator	NOUN
ejpam-4329	267	14	of	of	ADP
ejpam-4329	267	15	a	a	DET
ejpam-4329	267	16	distributive	distributive	ADJ
ejpam-4329	267	17	lattice	lattice	NOUN
ejpam-4329	267	18	is	be	AUX
ejpam-4329	267	19	shown	show	VERB
ejpam-4329	267	20	.	.	PUNCT
ejpam-4329	268	1	especially	especially	ADV
ejpam-4329	268	2	,	,	PUNCT
ejpam-4329	268	3	over	over	ADP
ejpam-4329	268	4	the	the	DET
ejpam-4329	268	5	distributive	distributive	ADJ
ejpam-4329	268	6	pseudocomplemented	pseudocomplemented	ADJ
ejpam-4329	268	7	lattice	lattice	NOUN
ejpam-4329	268	8	there	there	PRON
ejpam-4329	268	9	is	be	VERB
ejpam-4329	268	10	correspondence	correspondence	NOUN
ejpam-4329	268	11	between	between	ADP
ejpam-4329	268	12	closed	close	VERB
ejpam-4329	268	13	annihilators	annihilator	NOUN
ejpam-4329	268	14	,	,	PUNCT
ejpam-4329	268	15	closed	closed	ADJ
ejpam-4329	268	16	ideals	ideal	NOUN
ejpam-4329	268	17	,	,	PUNCT
ejpam-4329	268	18	and	and	CCONJ
ejpam-4329	268	19	usual	usual	ADJ
ejpam-4329	268	20	annihilators	annihilator	NOUN
ejpam-4329	268	21	.	.	PUNCT
ejpam-4329	269	1	this	this	DET
ejpam-4329	269	2	new	new	ADJ
ejpam-4329	269	3	generalization	generalization	NOUN
ejpam-4329	269	4	of	of	ADP
ejpam-4329	269	5	the	the	DET
ejpam-4329	269	6	annihilator	annihilator	PROPN
ejpam-4329	269	7	concept	concept	NOUN
ejpam-4329	269	8	for	for	ADP
ejpam-4329	269	9	the	the	DET
ejpam-4329	269	10	class	class	NOUN
ejpam-4329	269	11	of	of	ADP
ejpam-4329	269	12	ddwcls	ddwcls	NOUN
ejpam-4329	269	13	can	can	AUX
ejpam-4329	269	14	be	be	AUX
ejpam-4329	269	15	extended	extend	VERB
ejpam-4329	269	16	to	to	ADP
ejpam-4329	269	17	the	the	DET
ejpam-4329	269	18	classes	class	NOUN
ejpam-4329	269	19	of	of	ADP
ejpam-4329	269	20	distributive	distributive	ADJ
ejpam-4329	269	21	weakly	weakly	ADV
ejpam-4329	269	22	complemented	complemented	ADJ
ejpam-4329	269	23	and	and	CCONJ
ejpam-4329	269	24	dicomplemented	dicomplemente	VERB
ejpam-4329	269	25	lattices	lattice	NOUN
ejpam-4329	269	26	,	,	PUNCT
ejpam-4329	269	27	refer	refer	VERB
ejpam-4329	269	28	to	to	ADP
ejpam-4329	269	29	[	[	X
ejpam-4329	269	30	9	9	NUM
ejpam-4329	269	31	]	]	PUNCT
ejpam-4329	269	32	.	.	PUNCT
ejpam-4329	270	1	references	reference	NOUN
ejpam-4329	270	2	[	[	X
ejpam-4329	270	3	1	1	X
ejpam-4329	270	4	]	]	X
ejpam-4329	270	5	gezahagne	gezahagne	PROPN
ejpam-4329	270	6	mulat	mulat	PROPN
ejpam-4329	270	7	addis	addis	PROPN
ejpam-4329	270	8	.	.	PUNCT
ejpam-4329	271	1	annihilators	annihilator	NOUN
ejpam-4329	271	2	in	in	ADP
ejpam-4329	271	3	universal	universal	ADJ
ejpam-4329	271	4	algebras	algebra	NOUN
ejpam-4329	271	5	:	:	PUNCT
ejpam-4329	271	6	a	a	DET
ejpam-4329	271	7	new	new	ADJ
ejpam-4329	271	8	approach	approach	NOUN
ejpam-4329	271	9	.	.	PUNCT
ejpam-4329	272	1	journal	journal	NOUN
ejpam-4329	272	2	of	of	ADP
ejpam-4329	272	3	mathematics	mathematic	NOUN
ejpam-4329	272	4	,	,	PUNCT
ejpam-4329	272	5	2020	2020	NUM
ejpam-4329	272	6	,	,	PUNCT
ejpam-4329	272	7	2020	2020	NUM
ejpam-4329	272	8	.	.	PUNCT
ejpam-4329	273	1	[	[	X
ejpam-4329	273	2	2	2	NUM
ejpam-4329	273	3	]	]	PUNCT
ejpam-4329	273	4	i.	i.	NOUN
ejpam-4329	273	5	chajad	chajad	PROPN
ejpam-4329	273	6	and	and	CCONJ
ejpam-4329	273	7	r.	r.	PROPN
ejpam-4329	273	8	halas	halas	PROPN
ejpam-4329	273	9	.	.	PUNCT
ejpam-4329	274	1	annihilators	annihilator	NOUN
ejpam-4329	274	2	in	in	ADP
ejpam-4329	274	3	universal	universal	ADJ
ejpam-4329	274	4	algebras	algebra	NOUN
ejpam-4329	274	5	.	.	PUNCT
ejpam-4329	275	1	contributions	contribution	NOUN
ejpam-4329	275	2	to	to	ADP
ejpam-4329	275	3	general	general	ADJ
ejpam-4329	275	4	algebra	algebra	NOUN
ejpam-4329	275	5	,	,	PUNCT
ejpam-4329	275	6	14:29–43	14:29–43	NUM
ejpam-4329	275	7	,	,	PUNCT
ejpam-4329	275	8	2004	2004	NUM
ejpam-4329	275	9	.	.	PUNCT
ejpam-4329	276	1	[	[	X
ejpam-4329	276	2	3	3	X
ejpam-4329	276	3	]	]	X
ejpam-4329	276	4	w.h	w.h	PROPN
ejpam-4329	276	5	.	.	PROPN
ejpam-4329	276	6	cornish	cornish	PROPN
ejpam-4329	276	7	.	.	PUNCT
ejpam-4329	276	8	normal	normal	ADJ
ejpam-4329	276	9	lattices	lattice	NOUN
ejpam-4329	276	10	.	.	PUNCT
ejpam-4329	277	1	j.	j.	PROPN
ejpam-4329	277	2	austral	austral	PROPN
ejpam-4329	277	3	.	.	PUNCT
ejpam-4329	278	1	math	math	NOUN
ejpam-4329	278	2	.	.	PUNCT
ejpam-4329	279	1	soc	soc	PROPN
ejpam-4329	279	2	.	.	PUNCT
ejpam-4329	279	3	,	,	PUNCT
ejpam-4329	279	4	14:200–215	14:200–215	NUM
ejpam-4329	279	5	,	,	PUNCT
ejpam-4329	279	6	1972	1972	NUM
ejpam-4329	279	7	.	.	PUNCT
ejpam-4329	280	1	[	[	X
ejpam-4329	280	2	4	4	NUM
ejpam-4329	280	3	]	]	X
ejpam-4329	280	4	w.h	w.h	PROPN
ejpam-4329	280	5	.	.	PROPN
ejpam-4329	280	6	cornish	cornish	PROPN
ejpam-4329	280	7	.	.	PUNCT
ejpam-4329	280	8	annulets	annulet	NOUN
ejpam-4329	280	9	and	and	CCONJ
ejpam-4329	280	10	α	α	NOUN
ejpam-4329	280	11	-	-	NOUN
ejpam-4329	280	12	ideals	ideal	NOUN
ejpam-4329	280	13	in	in	ADP
ejpam-4329	280	14	distributive	distributive	ADJ
ejpam-4329	280	15	lattices	lattice	NOUN
ejpam-4329	280	16	.	.	PUNCT
ejpam-4329	281	1	j.	j.	PROPN
ejpam-4329	281	2	austral	austral	PROPN
ejpam-4329	281	3	.	.	PUNCT
ejpam-4329	282	1	math	math	NOUN
ejpam-4329	282	2	.	.	PUNCT
ejpam-4329	283	1	soc	soc	PROPN
ejpam-4329	283	2	.	.	PUNCT
ejpam-4329	283	3	,	,	PUNCT
ejpam-4329	283	4	15:70–77	15:70–77	NUM
ejpam-4329	283	5	,	,	PUNCT
ejpam-4329	283	6	1973	1973	NUM
ejpam-4329	283	7	.	.	PUNCT
ejpam-4329	284	1	references	reference	NOUN
ejpam-4329	284	2	495	495	NUM
ejpam-4329	284	3	[	[	SYM
ejpam-4329	284	4	5	5	NUM
ejpam-4329	284	5	]	]	PUNCT
ejpam-4329	284	6	e.mehdi	e.mehdi	NOUN
ejpam-4329	284	7	-	-	PUNCT
ejpam-4329	284	8	nezhad	nezhad	VERB
ejpam-4329	284	9	and	and	CCONJ
ejpam-4329	284	10	a.	a.	NOUN
ejpam-4329	284	11	m.	m.	NOUN
ejpam-4329	284	12	rahimi	rahimi	NOUN
ejpam-4329	284	13	.	.	PUNCT
ejpam-4329	285	1	the	the	DET
ejpam-4329	285	2	annihilator	annihilator	PROPN
ejpam-4329	285	3	graphs	graph	NOUN
ejpam-4329	285	4	of	of	ADP
ejpam-4329	285	5	commutator	commutator	NOUN
ejpam-4329	285	6	posets	poset	NOUN
ejpam-4329	285	7	and	and	CCONJ
ejpam-4329	285	8	lattices	lattice	NOUN
ejpam-4329	285	9	with	with	ADP
ejpam-4329	285	10	respect	respect	NOUN
ejpam-4329	285	11	to	to	ADP
ejpam-4329	285	12	an	an	DET
ejpam-4329	285	13	elements	element	NOUN
ejpam-4329	285	14	.	.	PUNCT
ejpam-4329	286	1	journal	journal	NOUN
ejpam-4329	286	2	of	of	ADP
ejpam-4329	286	3	algebra	algebra	PROPN
ejpam-4329	286	4	and	and	CCONJ
ejpam-4329	286	5	its	its	PRON
ejpam-4329	286	6	applications	application	NOUN
ejpam-4329	286	7	,	,	PUNCT
ejpam-4329	286	8	16	16	NUM
ejpam-4329	286	9	,	,	PUNCT
ejpam-4329	286	10	2017	2017	NUM
ejpam-4329	286	11	.	.	PUNCT
ejpam-4329	287	1	[	[	X
ejpam-4329	287	2	6	6	NUM
ejpam-4329	287	3	]	]	PUNCT
ejpam-4329	287	4	g.	g.	PROPN
ejpam-4329	287	5	gretzer	gretzer	PROPN
ejpam-4329	287	6	.	.	PUNCT
ejpam-4329	288	1	lattice	lattice	PROPN
ejpam-4329	288	2	theory	theory	PROPN
ejpam-4329	288	3	:	:	PUNCT
ejpam-4329	288	4	foundation	foundation	NOUN
ejpam-4329	288	5	.	.	PUNCT
ejpam-4329	289	1	springer	springer	PROPN
ejpam-4329	289	2	basel	basel	PROPN
ejpam-4329	289	3	,	,	PUNCT
ejpam-4329	289	4	2011	2011	NUM
ejpam-4329	289	5	.	.	PUNCT
ejpam-4329	290	1	[	[	X
ejpam-4329	290	2	7	7	X
ejpam-4329	290	3	]	]	X
ejpam-4329	290	4	g.	g.	PROPN
ejpam-4329	290	5	muhiuddin	muhiuddin	PROPN
ejpam-4329	290	6	h.	h.	PROPN
ejpam-4329	290	7	bordbar	bordbar	PROPN
ejpam-4329	290	8	and	and	CCONJ
ejpam-4329	290	9	abdulaziz	abdulaziz	PROPN
ejpam-4329	290	10	m.	m.	PROPN
ejpam-4329	290	11	alanazi	alanazi	PROPN
ejpam-4329	290	12	.	.	PUNCT
ejpam-4329	291	1	primeness	primeness	NOUN
ejpam-4329	291	2	of	of	ADP
ejpam-4329	291	3	relative	relative	ADJ
ejpam-4329	291	4	annihilators	annihilator	NOUN
ejpam-4329	291	5	in	in	ADP
ejpam-4329	291	6	bck	bck	NOUN
ejpam-4329	291	7	-	-	PUNCT
ejpam-4329	291	8	algebra	algebra	NOUN
ejpam-4329	291	9	.	.	PUNCT
ejpam-4329	292	1	symmetry	symmetry	NOUN
ejpam-4329	292	2	,	,	PUNCT
ejpam-4329	292	3	12(286	12(286	NOUN
ejpam-4329	292	4	)	)	PUNCT
ejpam-4329	292	5	,	,	PUNCT
ejpam-4329	292	6	2020	2020	NUM
ejpam-4329	292	7	.	.	PUNCT
ejpam-4329	293	1	[	[	X
ejpam-4329	293	2	8	8	NUM
ejpam-4329	293	3	]	]	X
ejpam-4329	293	4	m.	m.	NOUN
ejpam-4329	293	5	jastrzebska	jastrzebska	PROPN
ejpam-4329	293	6	.	.	PUNCT
ejpam-4329	293	7	rings	ring	NOUN
ejpam-4329	293	8	with	with	ADP
ejpam-4329	293	9	boolean	boolean	ADJ
ejpam-4329	293	10	lattices	lattice	NOUN
ejpam-4329	293	11	of	of	ADP
ejpam-4329	293	12	one	one	NUM
ejpam-4329	293	13	-	-	PUNCT
ejpam-4329	293	14	sided	sided	ADJ
ejpam-4329	293	15	annihilators	annihilators	PROPN
ejpam-4329	293	16	.	.	PUNCT
ejpam-4329	294	1	symmetry	symmetry	PROPN
ejpam-4329	294	2	,	,	PUNCT
ejpam-4329	294	3	13	13	NUM
ejpam-4329	294	4	,	,	PUNCT
ejpam-4329	294	5	2021	2021	NUM
ejpam-4329	294	6	.	.	PUNCT
ejpam-4329	295	1	[	[	X
ejpam-4329	295	2	9	9	NUM
ejpam-4329	295	3	]	]	PUNCT
ejpam-4329	295	4	l.	l.	PROPN
ejpam-4329	295	5	kwuida	kwuida	PROPN
ejpam-4329	295	6	.	.	PUNCT
ejpam-4329	295	7	dicomplemented	dicomplemente	VERB
ejpam-4329	295	8	lattices	lattice	NOUN
ejpam-4329	295	9	.	.	PUNCT
ejpam-4329	296	1	a	a	DET
ejpam-4329	296	2	contextual	contextual	ADJ
ejpam-4329	296	3	generalization	generalization	NOUN
ejpam-4329	296	4	of	of	ADP
ejpam-4329	296	5	boolean	boolean	ADJ
ejpam-4329	296	6	algebras	algebra	NOUN
ejpam-4329	296	7	.	.	PUNCT
ejpam-4329	297	1	phd	phd	NOUN
ejpam-4329	297	2	thesis	thesis	PROPN
ejpam-4329	297	3	,	,	PUNCT
ejpam-4329	297	4	tu	tu	PROPN
ejpam-4329	297	5	dresden	dresden	PROPN
ejpam-4329	297	6	,	,	PUNCT
ejpam-4329	297	7	2004	2004	NUM
ejpam-4329	297	8	.	.	PUNCT
ejpam-4329	298	1	[	[	X
ejpam-4329	298	2	10	10	NUM
ejpam-4329	298	3	]	]	PUNCT
ejpam-4329	298	4	s.s.khopade	s.s.khopade	NOUN
ejpam-4329	298	5	m.a.gandhi	m.a.gandhi	NOUN
ejpam-4329	298	6	and	and	CCONJ
ejpam-4329	298	7	y.s.pawar	y.s.pawar	NOUN
ejpam-4329	298	8	.	.	PUNCT
ejpam-4329	299	1	epimorphisms	epimorphism	NOUN
ejpam-4329	299	2	and	and	CCONJ
ejpam-4329	299	3	ideals	ideal	NOUN
ejpam-4329	299	4	of	of	ADP
ejpam-4329	299	5	distributive	distributive	ADJ
ejpam-4329	299	6	nearlattices	nearlattice	NOUN
ejpam-4329	299	7	.	.	PUNCT
ejpam-4329	300	1	annals	annal	NOUN
ejpam-4329	300	2	of	of	ADP
ejpam-4329	300	3	pure	pure	ADJ
ejpam-4329	300	4	and	and	CCONJ
ejpam-4329	300	5	applied	applied	ADJ
ejpam-4329	300	6	mathematics	mathematic	NOUN
ejpam-4329	300	7	,	,	PUNCT
ejpam-4329	300	8	18(2):175–179	18(2):175–179	NOUN
ejpam-4329	300	9	,	,	PUNCT
ejpam-4329	300	10	2018	2018	NUM
ejpam-4329	300	11	.	.	PUNCT
ejpam-4329	301	1	[	[	X
ejpam-4329	301	2	11	11	NUM
ejpam-4329	301	3	]	]	PUNCT
ejpam-4329	301	4	m.	m.	NOUN
ejpam-4329	301	5	mandelker	mandelker	NOUN
ejpam-4329	301	6	.	.	PUNCT
ejpam-4329	302	1	relative	relative	ADJ
ejpam-4329	302	2	annihilators	annihilators	PROPN
ejpam-4329	302	3	in	in	ADP
ejpam-4329	302	4	lattices	lattice	NOUN
ejpam-4329	302	5	.	.	PUNCT
ejpam-4329	303	1	duke	duke	PROPN
ejpam-4329	303	2	math	math	PROPN
ejpam-4329	303	3	.	.	PUNCT
ejpam-4329	304	1	j.	j.	PROPN
ejpam-4329	304	2	,	,	PUNCT
ejpam-4329	304	3	37:377–386	37:377–386	NUM
ejpam-4329	304	4	,	,	PUNCT
ejpam-4329	304	5	1970	1970	NUM
ejpam-4329	304	6	.	.	PUNCT
ejpam-4329	305	1	[	[	X
ejpam-4329	305	2	12	12	NUM
ejpam-4329	305	3	]	]	X
ejpam-4329	305	4	g.	g.	PROPN
ejpam-4329	305	5	c.	c.	PROPN
ejpam-4329	305	6	rao	rao	PROPN
ejpam-4329	305	7	and	and	CCONJ
ejpam-4329	305	8	m.	m.	PROPN
ejpam-4329	305	9	sambasiva	sambasiva	PROPN
ejpam-4329	305	10	rao	rao	PROPN
ejpam-4329	305	11	.	.	PUNCT
ejpam-4329	306	1	annihilator	annihilator	PROPN
ejpam-4329	306	2	ideals	ideal	NOUN
ejpam-4329	306	3	in	in	ADP
ejpam-4329	306	4	almost	almost	ADV
ejpam-4329	306	5	distributive	distributive	ADJ
ejpam-4329	306	6	lattices	lattice	NOUN
ejpam-4329	306	7	.	.	PUNCT
ejpam-4329	307	1	international	international	ADJ
ejpam-4329	307	2	mathematical	mathematical	PROPN
ejpam-4329	307	3	forum	forum	PROPN
ejpam-4329	307	4	,	,	PUNCT
ejpam-4329	307	5	15(4):733–746	15(4):733–746	PROPN
ejpam-4329	307	6	,	,	PUNCT
ejpam-4329	307	7	2009	2009	NUM
ejpam-4329	307	8	.	.	PUNCT
ejpam-4329	308	1	[	[	X
ejpam-4329	308	2	13	13	NUM
ejpam-4329	308	3	]	]	X
ejpam-4329	308	4	g.	g.	PROPN
ejpam-4329	308	5	nanaji	nanaji	PROPN
ejpam-4329	308	6	rao	rao	PROPN
ejpam-4329	308	7	and	and	CCONJ
ejpam-4329	308	8	t.	t.	PROPN
ejpam-4329	308	9	g.	g.	PROPN
ejpam-4329	308	10	beyene	beyene	PROPN
ejpam-4329	308	11	.	.	PUNCT
ejpam-4329	309	1	relative	relative	ADJ
ejpam-4329	309	2	annihilators	annihilator	NOUN
ejpam-4329	309	3	and	and	CCONJ
ejpam-4329	309	4	filters	filter	NOUN
ejpam-4329	309	5	in	in	ADP
ejpam-4329	309	6	almost	almost	ADV
ejpam-4329	309	7	semilattice	semilattice	NOUN
ejpam-4329	309	8	.	.	PUNCT
ejpam-4329	310	1	southeast	southeast	ADJ
ejpam-4329	310	2	asian	asian	ADJ
ejpam-4329	310	3	bulletin	bulletin	NOUN
ejpam-4329	310	4	of	of	ADP
ejpam-4329	310	5	mathematics	mathematic	NOUN
ejpam-4329	310	6	,	,	PUNCT
ejpam-4329	310	7	43:553–576	43:553–576	PROPN
ejpam-4329	310	8	,	,	PUNCT
ejpam-4329	310	9	2019	2019	NUM
ejpam-4329	310	10	.	.	PUNCT
ejpam-4329	311	1	[	[	X
ejpam-4329	311	2	14	14	NUM
ejpam-4329	311	3	]	]	X
ejpam-4329	311	4	g.	g.	PROPN
ejpam-4329	311	5	nanaji	nanaji	PROPN
ejpam-4329	311	6	rao	rao	PROPN
ejpam-4329	311	7	and	and	CCONJ
ejpam-4329	311	8	r.	r.	PROPN
ejpam-4329	311	9	venkata	venkata	PROPN
ejpam-4329	311	10	aravinda	aravinda	PROPN
ejpam-4329	311	11	raju	raju	PROPN
ejpam-4329	311	12	.	.	PUNCT
ejpam-4329	312	1	annihilator	annihilator	PROPN
ejpam-4329	312	2	ideals	ideal	NOUN
ejpam-4329	312	3	in	in	ADP
ejpam-4329	312	4	0	0	NOUN
ejpam-4329	312	5	-	-	PUNCT
ejpam-4329	312	6	distributive	distributive	ADJ
ejpam-4329	312	7	almost	almost	ADV
ejpam-4329	312	8	lattices	lattice	NOUN
ejpam-4329	312	9	.	.	PUNCT
ejpam-4329	313	1	bull	bull	NOUN
ejpam-4329	313	2	.	.	PUNCT
ejpam-4329	314	1	int	int	NOUN
ejpam-4329	314	2	.	.	PUNCT
ejpam-4329	315	1	math	math	NOUN
ejpam-4329	315	2	.	.	PUNCT
ejpam-4329	316	1	virtual	virtual	ADJ
ejpam-4329	316	2	inst	inst	PROPN
ejpam-4329	316	3	.	.	PROPN
ejpam-4329	316	4	,	,	PUNCT
ejpam-4329	316	5	11(1):1–13	11(1):1–13	NUM
ejpam-4329	316	6	,	,	PUNCT
ejpam-4329	316	7	2021	2021	NUM
ejpam-4329	316	8	.	.	PUNCT
ejpam-4329	317	1	[	[	X
ejpam-4329	317	2	15	15	NUM
ejpam-4329	317	3	]	]	X
ejpam-4329	317	4	m.	m.	NOUN
ejpam-4329	317	5	sambasiva	sambasiva	PROPN
ejpam-4329	317	6	rao	rao	PROPN
ejpam-4329	317	7	.	.	PUNCT
ejpam-4329	318	1	on	on	ADP
ejpam-4329	318	2	annihilator	annihilator	PROPN
ejpam-4329	318	3	ideals	ideal	NOUN
ejpam-4329	318	4	of	of	ADP
ejpam-4329	318	5	c	c	NOUN
ejpam-4329	318	6	-	-	PUNCT
ejpam-4329	318	7	algebras	algebra	NOUN
ejpam-4329	318	8	.	.	PUNCT
ejpam-4329	319	1	asian	asian	ADJ
ejpam-4329	319	2	-	-	PUNCT
ejpam-4329	319	3	eur	eur	NOUN
ejpam-4329	319	4	.	.	PUNCT
ejpam-4329	320	1	j.	j.	PROPN
ejpam-4329	320	2	math	math	PROPN
ejpam-4329	320	3	.	.	PUNCT
ejpam-4329	320	4	,	,	PUNCT
ejpam-4329	320	5	6(1	6(1	NUM
ejpam-4329	320	6	)	)	PUNCT
ejpam-4329	320	7	,	,	PUNCT
ejpam-4329	320	8	2013	2013	NUM
ejpam-4329	320	9	.	.	PUNCT
ejpam-4329	321	1	[	[	X
ejpam-4329	321	2	16	16	NUM
ejpam-4329	321	3	]	]	PUNCT
ejpam-4329	321	4	a.	a.	NOUN
ejpam-4329	321	5	taherifar	taherifar	PROPN
ejpam-4329	321	6	and	and	CCONJ
ejpam-4329	321	7	t.	t.	PROPN
ejpam-4329	321	8	dube	dube	PROPN
ejpam-4329	321	9	.	.	PUNCT
ejpam-4329	322	1	on	on	ADP
ejpam-4329	322	2	the	the	DET
ejpam-4329	322	3	lattice	lattice	NOUN
ejpam-4329	322	4	of	of	ADP
ejpam-4329	322	5	annihilator	annihilator	PROPN
ejpam-4329	322	6	ideals	ideal	NOUN
ejpam-4329	322	7	and	and	CCONJ
ejpam-4329	322	8	its	its	PRON
ejpam-4329	322	9	applications	application	NOUN
ejpam-4329	322	10	.	.	PUNCT
ejpam-4329	323	1	communications	communication	NOUN
ejpam-4329	323	2	in	in	ADP
ejpam-4329	323	3	algebra	algebra	NOUN
ejpam-4329	323	4	,	,	PUNCT
ejpam-4329	323	5	49	49	NUM
ejpam-4329	323	6	,	,	PUNCT
ejpam-4329	323	7	2021	2021	NUM
ejpam-4329	323	8	.	.	PUNCT
ejpam-4329	324	1	[	[	X
ejpam-4329	324	2	17	17	NUM
ejpam-4329	324	3	]	]	X
ejpam-4329	324	4	lia	lia	PROPN
ejpam-4329	324	5	vas	vas	PROPN
ejpam-4329	324	6	.	.	PUNCT
ejpam-4329	325	1	annihilator	annihilator	PROPN
ejpam-4329	325	2	ideals	ideal	NOUN
ejpam-4329	325	3	of	of	ADP
ejpam-4329	325	4	graph	graph	NOUN
ejpam-4329	325	5	algebras	algebra	NOUN
ejpam-4329	325	6	.	.	PUNCT
ejpam-4329	326	1	arxivlabs	arxivlabs	PROPN
ejpam-4329	326	2	,	,	PUNCT
ejpam-4329	326	3	2021	2021	NUM
ejpam-4329	326	4	.	.	PUNCT
ejpam-4329	327	1	[	[	X
ejpam-4329	327	2	18	18	NUM
ejpam-4329	327	3	]	]	X
ejpam-4329	327	4	r.	r.	NOUN
ejpam-4329	327	5	wille	wille	NOUN
ejpam-4329	327	6	.	.	PUNCT
ejpam-4329	328	1	boolean	boolean	ADJ
ejpam-4329	328	2	concept	concept	NOUN
ejpam-4329	328	3	logic	logic	NOUN
ejpam-4329	328	4	.	.	PUNCT
ejpam-4329	329	1	in	in	ADP
ejpam-4329	329	2	b.	b.	PROPN
ejpam-4329	329	3	ganter	ganter	NOUN
ejpam-4329	329	4	and	and	CCONJ
ejpam-4329	329	5	g.	g.	PROPN
ejpam-4329	329	6	w.	w.	PROPN
ejpam-4329	329	7	mineau	mineau	PROPN
ejpam-4329	329	8	,	,	PUNCT
ejpam-4329	329	9	editors	editor	NOUN
ejpam-4329	329	10	,	,	PUNCT
ejpam-4329	329	11	iccs	iccs	VERB
ejpam-4329	329	12	2000	2000	NUM
ejpam-4329	329	13	conceptual	conceptual	ADJ
ejpam-4329	329	14	structures	structure	NOUN
ejpam-4329	329	15	:	:	PUNCT
ejpam-4329	329	16	logical	logical	ADJ
ejpam-4329	329	17	,	,	PUNCT
ejpam-4329	329	18	linguistic	linguistic	ADJ
ejpam-4329	329	19	and	and	CCONJ
ejpam-4329	329	20	computational	computational	ADJ
ejpam-4329	329	21	issues	issue	NOUN
ejpam-4329	329	22	.	.	PUNCT
ejpam-4329	330	1	,	,	PUNCT
ejpam-4329	330	2	pages	page	NOUN
ejpam-4329	330	3	14–18	14–18	NUM
ejpam-4329	330	4	,	,	PUNCT
ejpam-4329	330	5	germany	germany	PROPN
ejpam-4329	330	6	,	,	PUNCT
ejpam-4329	330	7	2000	2000	NUM
ejpam-4329	330	8	.	.	PUNCT
ejpam-4329	331	1	darmstadt	darmstadt	PROPN
ejpam-4329	331	2	.	.	PUNCT