id	sid	tid	token	lemma	pos
ejpam-2660	1	1	european	european	PROPN
ejpam-2660	1	2	journal	journal	PROPN
ejpam-2660	1	3	of	of	ADP
ejpam-2660	1	4	pure	pure	ADJ
ejpam-2660	1	5	and	and	CCONJ
ejpam-2660	1	6	applied	apply	VERB
ejpam-2660	1	7	mathematics	mathematic	NOUN
ejpam-2660	1	8	vol	vol	NOUN
ejpam-2660	1	9	.	.	PUNCT
ejpam-2660	2	1	11	11	NUM
ejpam-2660	2	2	,	,	PUNCT
ejpam-2660	2	3	no	no	INTJ
ejpam-2660	2	4	.	.	NOUN
ejpam-2660	2	5	1	1	NUM
ejpam-2660	2	6	,	,	PUNCT
ejpam-2660	2	7	2018	2018	NUM
ejpam-2660	2	8	,	,	PUNCT
ejpam-2660	2	9	169	169	NUM
ejpam-2660	2	10	-	-	SYM
ejpam-2660	2	11	188	188	NUM
ejpam-2660	2	12	issn	issn	PROPN
ejpam-2660	2	13	1307	1307	NUM
ejpam-2660	2	14	-	-	SYM
ejpam-2660	2	15	5543	5543	NUM
ejpam-2660	2	16	–	–	PUNCT
ejpam-2660	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-2660	2	18	published	publish	VERB
ejpam-2660	2	19	by	by	ADP
ejpam-2660	2	20	new	new	PROPN
ejpam-2660	2	21	york	york	PROPN
ejpam-2660	2	22	business	business	PROPN
ejpam-2660	2	23	global	global	PROPN
ejpam-2660	2	24	on	on	ADP
ejpam-2660	2	25	prime	prime	ADJ
ejpam-2660	2	26	hyperfilters	hyperfilter	NOUN
ejpam-2660	2	27	(	(	PUNCT
ejpam-2660	2	28	hyperideals	hyperideal	NOUN
ejpam-2660	2	29	)	)	PUNCT
ejpam-2660	2	30	in	in	ADP
ejpam-2660	2	31	∧	∧	PROPN
ejpam-2660	2	32	-hyperlattices	-hyperlattice	NOUN
ejpam-2660	2	33	m.	m.	NOUN
ejpam-2660	2	34	amiri	amiri	PROPN
ejpam-2660	2	35	bideshki1	bideshki1	PROPN
ejpam-2660	2	36	,	,	PUNCT
ejpam-2660	2	37	r.	r.	PROPN
ejpam-2660	2	38	ameri	ameri	PROPN
ejpam-2660	2	39	2	2	NUM
ejpam-2660	2	40	,	,	PUNCT
ejpam-2660	2	41	∗	∗	NOUN
ejpam-2660	2	42	,	,	PUNCT
ejpam-2660	2	43	a.	a.	NOUN
ejpam-2660	2	44	borumand	borumand	NOUN
ejpam-2660	2	45	saeid3	saeid3	PROPN
ejpam-2660	2	46	1	1	NUM
ejpam-2660	2	47	department	department	NOUN
ejpam-2660	2	48	of	of	ADP
ejpam-2660	2	49	mathematics	mathematic	NOUN
ejpam-2660	2	50	,	,	PUNCT
ejpam-2660	2	51	farhangian	farhangian	ADJ
ejpam-2660	2	52	university	university	NOUN
ejpam-2660	2	53	,	,	PUNCT
ejpam-2660	2	54	kerman	kerman	PROPN
ejpam-2660	2	55	,	,	PUNCT
ejpam-2660	2	56	iran	iran	PROPN
ejpam-2660	2	57	2	2	NUM
ejpam-2660	2	58	school	school	NOUN
ejpam-2660	2	59	of	of	ADP
ejpam-2660	2	60	mathematics	mathematic	NOUN
ejpam-2660	2	61	,	,	PUNCT
ejpam-2660	2	62	statistic	statistic	NOUN
ejpam-2660	2	63	and	and	CCONJ
ejpam-2660	2	64	computer	computer	NOUN
ejpam-2660	2	65	sciences	science	NOUN
ejpam-2660	2	66	,	,	PUNCT
ejpam-2660	2	67	university	university	NOUN
ejpam-2660	2	68	of	of	ADP
ejpam-2660	2	69	tehran	tehran	PROPN
ejpam-2660	2	70	,	,	PUNCT
ejpam-2660	2	71	tehran	tehran	PROPN
ejpam-2660	2	72	,	,	PUNCT
ejpam-2660	2	73	iran	iran	PROPN
ejpam-2660	2	74	3	3	NUM
ejpam-2660	2	75	department	department	NOUN
ejpam-2660	2	76	of	of	ADP
ejpam-2660	2	77	mathematics	mathematic	NOUN
ejpam-2660	2	78	,	,	PUNCT
ejpam-2660	2	79	shahid	shahid	PROPN
ejpam-2660	2	80	bahonar	bahonar	PROPN
ejpam-2660	2	81	university	university	PROPN
ejpam-2660	2	82	,	,	PUNCT
ejpam-2660	2	83	kerman	kerman	PROPN
ejpam-2660	2	84	,	,	PUNCT
ejpam-2660	2	85	iran	iran	PROPN
ejpam-2660	2	86	abstract	abstract	NOUN
ejpam-2660	2	87	.	.	PUNCT
ejpam-2660	3	1	in	in	ADP
ejpam-2660	3	2	this	this	DET
ejpam-2660	3	3	paper	paper	NOUN
ejpam-2660	3	4	,	,	PUNCT
ejpam-2660	3	5	we	we	PRON
ejpam-2660	3	6	introduce	introduce	VERB
ejpam-2660	3	7	the	the	DET
ejpam-2660	3	8	notions	notion	NOUN
ejpam-2660	3	9	of	of	ADP
ejpam-2660	3	10	strong	strong	ADJ
ejpam-2660	3	11	”	"	PUNCT
ejpam-2660	3	12	∧	∧	NOUN
ejpam-2660	3	13	”	"	PUNCT
ejpam-2660	3	14	-hyperlattices	-hyperlattice	NOUN
ejpam-2660	3	15	,	,	PUNCT
ejpam-2660	3	16	hyperideals	hyperideal	NOUN
ejpam-2660	3	17	and	and	CCONJ
ejpam-2660	3	18	hyperfilters	hyperfilter	NOUN
ejpam-2660	3	19	in	in	ADP
ejpam-2660	3	20	strong	strong	ADJ
ejpam-2660	3	21	”	"	PUNCT
ejpam-2660	3	22	∧”-hyperlattices	∧”-hyperlattice	NOUN
ejpam-2660	3	23	.	.	PUNCT
ejpam-2660	4	1	also	also	ADV
ejpam-2660	4	2	,	,	PUNCT
ejpam-2660	4	3	we	we	PRON
ejpam-2660	4	4	give	give	VERB
ejpam-2660	4	5	equivalence	equivalence	NOUN
ejpam-2660	4	6	conditions	condition	NOUN
ejpam-2660	4	7	for	for	ADP
ejpam-2660	4	8	prime	prime	ADJ
ejpam-2660	4	9	hyperfilters	hyperfilter	NOUN
ejpam-2660	4	10	(	(	PUNCT
ejpam-2660	4	11	hyperideal	hyperideal	NOUN
ejpam-2660	4	12	)	)	PUNCT
ejpam-2660	4	13	in	in	ADP
ejpam-2660	4	14	strong	strong	ADJ
ejpam-2660	4	15	∧-hyperlattices	∧-hyperlattice	NOUN
ejpam-2660	4	16	.	.	PUNCT
ejpam-2660	5	1	distributivity	distributivity	NOUN
ejpam-2660	5	2	(	(	PUNCT
ejpam-2660	5	3	dual	dual	ADJ
ejpam-2660	5	4	distributivity	distributivity	NOUN
ejpam-2660	5	5	)	)	PUNCT
ejpam-2660	5	6	in	in	ADP
ejpam-2660	5	7	”	"	PUNCT
ejpam-2660	5	8	∧”-hyperlattices	∧”-hyperlattice	NOUN
ejpam-2660	5	9	,	,	PUNCT
ejpam-2660	5	10	iahyperideals	iahyperideal	NOUN
ejpam-2660	5	11	and	and	CCONJ
ejpam-2660	5	12	prime	prime	ADJ
ejpam-2660	5	13	hyperfilters	hyperfilter	NOUN
ejpam-2660	5	14	in	in	ADP
ejpam-2660	5	15	strong	strong	ADJ
ejpam-2660	5	16	”	"	PUNCT
ejpam-2660	5	17	∧	∧	NOUN
ejpam-2660	5	18	”	"	PUNCT
ejpam-2660	5	19	-hyperlattices	-hyperlattice	NOUN
ejpam-2660	5	20	are	be	AUX
ejpam-2660	5	21	investigated	investigate	VERB
ejpam-2660	5	22	.	.	PUNCT
ejpam-2660	6	1	2010	2010	NUM
ejpam-2660	6	2	mathematics	mathematic	NOUN
ejpam-2660	6	3	subject	subject	NOUN
ejpam-2660	6	4	classifications	classification	NOUN
ejpam-2660	6	5	:	:	PUNCT
ejpam-2660	6	6	20n20	20n20	NUM
ejpam-2660	6	7	key	key	ADJ
ejpam-2660	6	8	words	word	NOUN
ejpam-2660	6	9	and	and	CCONJ
ejpam-2660	6	10	phrases	phrase	NOUN
ejpam-2660	6	11	:	:	PUNCT
ejpam-2660	6	12	hyperideal	hyperideal	ADJ
ejpam-2660	6	13	,	,	PUNCT
ejpam-2660	6	14	hyperfilter	hyperfilter	ADJ
ejpam-2660	6	15	,	,	PUNCT
ejpam-2660	6	16	hyperlattice	hyperlattice	NOUN
ejpam-2660	6	17	,	,	PUNCT
ejpam-2660	6	18	strong	strong	ADJ
ejpam-2660	6	19	∧	∧	PROPN
ejpam-2660	6	20	hyperlattice	hyperlattice	NOUN
ejpam-2660	6	21	,	,	PUNCT
ejpam-2660	6	22	iahyperideal	iahyperideal	NOUN
ejpam-2660	6	23	1	1	NUM
ejpam-2660	6	24	.	.	PUNCT
ejpam-2660	7	1	introduction	introduction	NOUN
ejpam-2660	7	2	theory	theory	NOUN
ejpam-2660	7	3	of	of	ADP
ejpam-2660	7	4	hyperalgebra	hyperalgebra	NOUN
ejpam-2660	7	5	has	have	AUX
ejpam-2660	7	6	been	be	AUX
ejpam-2660	7	7	introduced	introduce	VERB
ejpam-2660	7	8	by	by	ADP
ejpam-2660	7	9	f.	f.	PROPN
ejpam-2660	7	10	marty	marty	PROPN
ejpam-2660	7	11	in	in	ADP
ejpam-2660	7	12	the	the	DET
ejpam-2660	7	13	eighth	eighth	ADJ
ejpam-2660	7	14	congress	congress	PROPN
ejpam-2660	7	15	of	of	ADP
ejpam-2660	7	16	scandinavians	scandinavians	PROPN
ejpam-2660	7	17	in	in	ADP
ejpam-2660	7	18	1934	1934	NUM
ejpam-2660	7	19	[	[	X
ejpam-2660	7	20	11	11	NUM
ejpam-2660	7	21	]	]	PUNCT
ejpam-2660	7	22	.	.	PUNCT
ejpam-2660	8	1	several	several	ADJ
ejpam-2660	8	2	aspects	aspect	NOUN
ejpam-2660	8	3	of	of	ADP
ejpam-2660	8	4	subalgebra	subalgebra	NOUN
ejpam-2660	8	5	and	and	CCONJ
ejpam-2660	8	6	subdirect	subdirect	NOUN
ejpam-2660	8	7	decompositions	decomposition	NOUN
ejpam-2660	8	8	of	of	ADP
ejpam-2660	8	9	hyperalgebra	hyperalgebra	NOUN
ejpam-2660	8	10	were	be	AUX
ejpam-2660	8	11	studied	study	VERB
ejpam-2660	8	12	by	by	ADP
ejpam-2660	8	13	pickett	pickett	PROPN
ejpam-2660	8	14	and	and	CCONJ
ejpam-2660	8	15	by	by	ADP
ejpam-2660	8	16	hansoul	hansoul	ADJ
ejpam-2660	8	17	,	,	PUNCT
ejpam-2660	8	18	for	for	SCONJ
ejpam-2660	8	19	more	more	ADJ
ejpam-2660	8	20	details	detail	NOUN
ejpam-2660	8	21	see	see	VERB
ejpam-2660	8	22	[	[	X
ejpam-2660	8	23	5	5	NUM
ejpam-2660	8	24	]	]	PUNCT
ejpam-2660	8	25	,	,	PUNCT
ejpam-2660	9	1	[	[	X
ejpam-2660	9	2	17	17	NUM
ejpam-2660	9	3	]	]	PUNCT
ejpam-2660	9	4	,	,	PUNCT
ejpam-2660	9	5	and	and	CCONJ
ejpam-2660	9	6	[	[	X
ejpam-2660	9	7	18	18	NUM
ejpam-2660	9	8	]	]	PUNCT
ejpam-2660	9	9	.	.	PUNCT
ejpam-2660	10	1	in	in	ADP
ejpam-2660	10	2	[	[	X
ejpam-2660	10	3	22	22	NUM
ejpam-2660	10	4	]	]	X
ejpam-2660	10	5	congruence	congruence	NOUN
ejpam-2660	10	6	of	of	ADP
ejpam-2660	10	7	multialgebra	multialgebra	NOUN
ejpam-2660	10	8	has	have	AUX
ejpam-2660	10	9	been	be	AUX
ejpam-2660	10	10	studied	study	VERB
ejpam-2660	10	11	by	by	ADP
ejpam-2660	10	12	d.	d.	PROPN
ejpam-2660	10	13	schweigrt	schweigrt	PROPN
ejpam-2660	10	14	.	.	PUNCT
ejpam-2660	11	1	in[3	in[3	PROPN
ejpam-2660	11	2	]	]	PUNCT
ejpam-2660	11	3	ameri	ameri	PROPN
ejpam-2660	11	4	and	and	CCONJ
ejpam-2660	11	5	m.	m.	PROPN
ejpam-2660	11	6	m.	m.	PROPN
ejpam-2660	11	7	zahedi	zahedi	PROPN
ejpam-2660	11	8	introduced	introduce	VERB
ejpam-2660	11	9	and	and	CCONJ
ejpam-2660	11	10	studied	study	VERB
ejpam-2660	11	11	notion	notion	NOUN
ejpam-2660	11	12	of	of	ADP
ejpam-2660	11	13	hyperalgebraic	hyperalgebraic	PROPN
ejpam-2660	11	14	systems	system	NOUN
ejpam-2660	11	15	.	.	PUNCT
ejpam-2660	12	1	in[1	in[1	PROPN
ejpam-2660	12	2	]	]	PUNCT
ejpam-2660	13	1	ameri	ameri	PROPN
ejpam-2660	13	2	and	and	CCONJ
ejpam-2660	13	3	nozari	nozari	ADJ
ejpam-2660	13	4	studied	study	VERB
ejpam-2660	13	5	relationship	relationship	NOUN
ejpam-2660	13	6	between	between	ADP
ejpam-2660	13	7	the	the	DET
ejpam-2660	13	8	categories	category	NOUN
ejpam-2660	13	9	of	of	ADP
ejpam-2660	13	10	multialgebra	multialgebra	NOUN
ejpam-2660	13	11	and	and	CCONJ
ejpam-2660	13	12	algebra	algebra	NOUN
ejpam-2660	13	13	;	;	PUNCT
ejpam-2660	13	14	in	in	ADP
ejpam-2660	13	15	[	[	PUNCT
ejpam-2660	13	16	2	2	X
ejpam-2660	13	17	]	]	X
ejpam-2660	13	18	ameri	ameri	PROPN
ejpam-2660	13	19	and	and	CCONJ
ejpam-2660	13	20	rosenberg	rosenberg	PROPN
ejpam-2660	13	21	studied	study	VERB
ejpam-2660	13	22	congruences	congruence	NOUN
ejpam-2660	13	23	and	and	CCONJ
ejpam-2660	13	24	strongly	strongly	ADV
ejpam-2660	13	25	congruences	congruence	NOUN
ejpam-2660	13	26	of	of	ADP
ejpam-2660	13	27	multialgebras	multialgebra	NOUN
ejpam-2660	13	28	.	.	PUNCT
ejpam-2660	14	1	some	some	DET
ejpam-2660	14	2	more	more	ADJ
ejpam-2660	14	3	basic	basic	ADJ
ejpam-2660	14	4	properties	property	NOUN
ejpam-2660	14	5	of	of	ADP
ejpam-2660	14	6	hyperalgebra	hyperalgebra	NOUN
ejpam-2660	14	7	such	such	ADJ
ejpam-2660	14	8	as	as	ADP
ejpam-2660	14	9	,	,	PUNCT
ejpam-2660	14	10	identities	identity	NOUN
ejpam-2660	14	11	,	,	PUNCT
ejpam-2660	14	12	term	term	NOUN
ejpam-2660	14	13	function	function	NOUN
ejpam-2660	14	14	and	and	CCONJ
ejpam-2660	14	15	fundamental	fundamental	ADJ
ejpam-2660	14	16	relation	relation	NOUN
ejpam-2660	14	17	,	,	PUNCT
ejpam-2660	14	18	direct	direct	ADJ
ejpam-2660	14	19	limit	limit	NOUN
ejpam-2660	14	20	of	of	ADP
ejpam-2660	14	21	hyperalgebra	hyperalgebra	NOUN
ejpam-2660	14	22	,	,	PUNCT
ejpam-2660	14	23	and	and	CCONJ
ejpam-2660	14	24	the	the	DET
ejpam-2660	14	25	exponentiation	exponentiation	NOUN
ejpam-2660	14	26	of	of	ADP
ejpam-2660	14	27	universal	universal	ADJ
ejpam-2660	14	28	hyperalgebra	hyperalgebra	NOUN
ejpam-2660	14	29	have	have	AUX
ejpam-2660	14	30	been	be	AUX
ejpam-2660	14	31	studied	study	VERB
ejpam-2660	14	32	by	by	ADP
ejpam-2660	14	33	c.	c.	PROPN
ejpam-2660	14	34	pelea	pelea	PROPN
ejpam-2660	14	35	and	and	CCONJ
ejpam-2660	14	36	others	other	NOUN
ejpam-2660	14	37	,	,	PUNCT
ejpam-2660	14	38	for	for	SCONJ
ejpam-2660	14	39	more	more	ADJ
ejpam-2660	14	40	details	detail	NOUN
ejpam-2660	14	41	see	see	VERB
ejpam-2660	14	42	[	[	X
ejpam-2660	14	43	13	13	NUM
ejpam-2660	14	44	]	]	PUNCT
ejpam-2660	14	45	,	,	PUNCT
ejpam-2660	15	1	[	[	X
ejpam-2660	15	2	14	14	NUM
ejpam-2660	15	3	]	]	PUNCT
ejpam-2660	15	4	,	,	PUNCT
ejpam-2660	15	5	and	and	CCONJ
ejpam-2660	15	6	[	[	X
ejpam-2660	15	7	15	15	NUM
ejpam-2660	15	8	]	]	PUNCT
ejpam-2660	15	9	.	.	PUNCT
ejpam-2660	16	1	in[16	in[16	PUNCT
ejpam-2660	16	2	]	]	PUNCT
ejpam-2660	16	3	c.	c.	PROPN
ejpam-2660	16	4	pelea	pelea	PROPN
ejpam-2660	16	5	and	and	CCONJ
ejpam-2660	16	6	i.	i.	PROPN
ejpam-2660	16	7	purdea	purdea	PROPN
ejpam-2660	16	8	have	have	AUX
ejpam-2660	16	9	been	be	AUX
ejpam-2660	16	10	proved	prove	VERB
ejpam-2660	16	11	that	that	SCONJ
ejpam-2660	16	12	complete	complete	ADJ
ejpam-2660	16	13	hyperalgebra	hyperalgebra	NOUN
ejpam-2660	16	14	can	can	AUX
ejpam-2660	16	15	be	be	AUX
ejpam-2660	16	16	obtained	obtain	VERB
ejpam-2660	16	17	from	from	ADP
ejpam-2660	16	18	a	a	DET
ejpam-2660	16	19	universal	universal	ADJ
ejpam-2660	16	20	algebra	algebra	NOUN
ejpam-2660	16	21	and	and	CCONJ
ejpam-2660	16	22	a	a	DET
ejpam-2660	16	23	appropriate	appropriate	ADJ
ejpam-2660	16	24	congruence	congruence	NOUN
ejpam-2660	16	25	on	on	ADP
ejpam-2660	16	26	it	it	PRON
ejpam-2660	16	27	.	.	PUNCT
ejpam-2660	17	1	theory	theory	NOUN
ejpam-2660	17	2	of	of	ADP
ejpam-2660	17	3	hyperlattices	hyperlattice	NOUN
ejpam-2660	17	4	introduced	introduce	VERB
ejpam-2660	17	5	by	by	ADP
ejpam-2660	17	6	konstantinidou	konstantinidou	NOUN
ejpam-2660	17	7	and	and	CCONJ
ejpam-2660	17	8	j.	j.	PROPN
ejpam-2660	17	9	mittas	mittas	PROPN
ejpam-2660	17	10	in	in	ADP
ejpam-2660	17	11	1977	1977	NUM
ejpam-2660	17	12	[	[	X
ejpam-2660	17	13	10	10	NUM
ejpam-2660	17	14	]	]	PUNCT
ejpam-2660	17	15	.	.	PUNCT
ejpam-2660	18	1	m.	m.	PROPN
ejpam-2660	18	2	konstantinidou	konstantinidou	PROPN
ejpam-2660	18	3	,	,	PUNCT
ejpam-2660	18	4	also	also	ADV
ejpam-2660	18	5	studied	study	VERB
ejpam-2660	18	6	distributive	distributive	ADJ
ejpam-2660	18	7	,	,	PUNCT
ejpam-2660	18	8	modular	modular	ADJ
ejpam-2660	18	9	,	,	PUNCT
ejpam-2660	18	10	and	and	CCONJ
ejpam-2660	18	11	complemented	complemented	ADJ
ejpam-2660	18	12	hyperlattices	hyperlattice	NOUN
ejpam-2660	18	13	,	,	PUNCT
ejpam-2660	18	14	for	for	SCONJ
ejpam-2660	18	15	more	more	ADJ
ejpam-2660	18	16	details	detail	NOUN
ejpam-2660	18	17	see	see	VERB
ejpam-2660	18	18	[	[	X
ejpam-2660	18	19	8	8	NUM
ejpam-2660	18	20	]	]	PUNCT
ejpam-2660	18	21	and	and	CCONJ
ejpam-2660	19	1	[	[	X
ejpam-2660	19	2	9	9	NUM
ejpam-2660	19	3	]	]	PUNCT
ejpam-2660	19	4	.	.	PUNCT
ejpam-2660	20	1	in	in	ADP
ejpam-2660	20	2	[	[	X
ejpam-2660	20	3	19	19	NUM
ejpam-2660	20	4	]	]	PUNCT
ejpam-2660	20	5	rahnemaei	rahnemaei	NOUN
ejpam-2660	20	6	barghi	barghi	PROPN
ejpam-2660	20	7	considered	consider	VERB
ejpam-2660	20	8	the	the	DET
ejpam-2660	20	9	prime	prime	ADJ
ejpam-2660	20	10	ideal	ideal	NOUN
ejpam-2660	20	11	theorem	theorem	NOUN
ejpam-2660	20	12	for	for	ADP
ejpam-2660	20	13	∗corresponding	∗corresponde	VERB
ejpam-2660	20	14	author	author	NOUN
ejpam-2660	20	15	.	.	PUNCT
ejpam-2660	21	1	email	email	NOUN
ejpam-2660	21	2	addresses	address	NOUN
ejpam-2660	21	3	:	:	PUNCT
ejpam-2660	21	4	amirimohsen61@gmail.com	amirimohsen61@gmail.com	X
ejpam-2660	21	5	(	(	PUNCT
ejpam-2660	21	6	m.	m.	NOUN
ejpam-2660	21	7	amiri	amiri	PROPN
ejpam-2660	21	8	bideshki	bideshki	PROPN
ejpam-2660	21	9	)	)	PUNCT
ejpam-2660	21	10	,	,	PUNCT
ejpam-2660	21	11	r.	r.	PROPN
ejpam-2660	21	12	ameri@ut.ac.ir	ameri@ut.ac.ir	PROPN
ejpam-2660	21	13	(	(	PUNCT
ejpam-2660	21	14	r.	r.	PROPN
ejpam-2660	21	15	ameri	ameri	PROPN
ejpam-2660	21	16	)	)	PUNCT
ejpam-2660	21	17	,	,	PUNCT
ejpam-2660	21	18	arsham@uk.ac.ir	arsham@uk.ac.ir	PROPN
ejpam-2660	21	19	(	(	PUNCT
ejpam-2660	21	20	a.	a.	PROPN
ejpam-2660	21	21	borumand	borumand	PROPN
ejpam-2660	21	22	saeid	saeid	PROPN
ejpam-2660	21	23	)	)	PUNCT
ejpam-2660	21	24	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2660	22	1	169	169	NUM
ejpam-2660	22	2	c	c	NOUN
ejpam-2660	22	3	©	©	PROPN
ejpam-2660	22	4	2018	2018	NUM
ejpam-2660	22	5	ejpam	ejpam	VERB
ejpam-2660	22	6	all	all	DET
ejpam-2660	22	7	rights	right	NOUN
ejpam-2660	22	8	reserved	reserve	VERB
ejpam-2660	22	9	.	.	PUNCT
ejpam-2660	23	1	m.	m.	NOUN
ejpam-2660	23	2	amiri	amiri	PROPN
ejpam-2660	23	3	bideshki	bideshki	PROPN
ejpam-2660	23	4	,	,	PUNCT
ejpam-2660	23	5	r.	r.	PROPN
ejpam-2660	23	6	ameri	ameri	PROPN
ejpam-2660	23	7	,	,	PUNCT
ejpam-2660	23	8	a.	a.	PROPN
ejpam-2660	23	9	borumand	borumand	PROPN
ejpam-2660	23	10	saeid	saeid	PROPN
ejpam-2660	23	11	/	/	SYM
ejpam-2660	23	12	eur	eur	PROPN
ejpam-2660	23	13	.	.	PUNCT
ejpam-2660	24	1	j.	j.	PROPN
ejpam-2660	24	2	pure	pure	PROPN
ejpam-2660	24	3	appl	appl	PROPN
ejpam-2660	24	4	.	.	PROPN
ejpam-2660	24	5	math	math	PROPN
ejpam-2660	24	6	,	,	PUNCT
ejpam-2660	24	7	11	11	NUM
ejpam-2660	24	8	(	(	PUNCT
ejpam-2660	24	9	1	1	NUM
ejpam-2660	24	10	)	)	PUNCT
ejpam-2660	24	11	(	(	PUNCT
ejpam-2660	24	12	2018	2018	NUM
ejpam-2660	24	13	)	)	PUNCT
ejpam-2660	24	14	,	,	PUNCT
ejpam-2660	24	15	169	169	NUM
ejpam-2660	24	16	-	-	SYM
ejpam-2660	24	17	188	188	NUM
ejpam-2660	24	18	170	170	NUM
ejpam-2660	24	19	distributive	distributive	ADJ
ejpam-2660	24	20	hyperlattices	hyperlattice	NOUN
ejpam-2660	24	21	.	.	PUNCT
ejpam-2660	25	1	in	in	ADP
ejpam-2660	25	2	[	[	X
ejpam-2660	25	3	12	12	NUM
ejpam-2660	25	4	]	]	PUNCT
ejpam-2660	25	5	,	,	PUNCT
ejpam-2660	25	6	g.	g.	PROPN
ejpam-2660	25	7	a.	a.	PROPN
ejpam-2660	25	8	moghani	moghani	PROPN
ejpam-2660	25	9	and	and	CCONJ
ejpam-2660	25	10	a.	a.	PROPN
ejpam-2660	25	11	r.	r.	PROPN
ejpam-2660	25	12	ashrafi	ashrafi	PROPN
ejpam-2660	25	13	proved	prove	VERB
ejpam-2660	25	14	that	that	SCONJ
ejpam-2660	25	15	in	in	ADP
ejpam-2660	25	16	some	some	DET
ejpam-2660	25	17	cases	case	NOUN
ejpam-2660	25	18	the	the	DET
ejpam-2660	25	19	set	set	NOUN
ejpam-2660	25	20	of	of	ADP
ejpam-2660	25	21	all	all	DET
ejpam-2660	25	22	subhypergroups	subhypergroup	NOUN
ejpam-2660	25	23	g	g	PROPN
ejpam-2660	25	24	has	have	VERB
ejpam-2660	25	25	a	a	DET
ejpam-2660	25	26	hyperlattice	hyperlattice	NOUN
ejpam-2660	25	27	structure	structure	NOUN
ejpam-2660	25	28	.	.	PUNCT
ejpam-2660	26	1	in	in	ADP
ejpam-2660	26	2	[	[	X
ejpam-2660	26	3	23	23	NUM
ejpam-2660	26	4	]	]	PUNCT
ejpam-2660	26	5	,	,	PUNCT
ejpam-2660	26	6	x.	x.	PROPN
ejpam-2660	26	7	l.	l.	PROPN
ejpam-2660	26	8	xin	xin	PROPN
ejpam-2660	26	9	and	and	CCONJ
ejpam-2660	26	10	x.	x.	PROPN
ejpam-2660	26	11	g.	g.	PROPN
ejpam-2660	26	12	li	li	PROPN
ejpam-2660	26	13	studied	study	VERB
ejpam-2660	26	14	hyperlattices	hyperlattice	NOUN
ejpam-2660	26	15	and	and	CCONJ
ejpam-2660	26	16	quotient	quotient	NOUN
ejpam-2660	26	17	hyperlattices	hyperlattice	NOUN
ejpam-2660	26	18	.	.	PUNCT
ejpam-2660	27	1	in	in	ADP
ejpam-2660	27	2	[	[	X
ejpam-2660	27	3	4	4	NUM
ejpam-2660	27	4	]	]	PUNCT
ejpam-2660	27	5	,	,	PUNCT
ejpam-2660	27	6	a.	a.	PROPN
ejpam-2660	27	7	asokkumar	asokkumar	PROPN
ejpam-2660	27	8	proved	prove	VERB
ejpam-2660	27	9	that	that	SCONJ
ejpam-2660	27	10	under	under	ADP
ejpam-2660	27	11	certain	certain	ADJ
ejpam-2660	27	12	conditions	condition	NOUN
ejpam-2660	27	13	,	,	PUNCT
ejpam-2660	27	14	the	the	DET
ejpam-2660	27	15	idempotent	idempotent	ADJ
ejpam-2660	27	16	elements	element	NOUN
ejpam-2660	27	17	of	of	ADP
ejpam-2660	27	18	a	a	DET
ejpam-2660	27	19	hyperring	hyperring	NOUN
ejpam-2660	27	20	form	form	NOUN
ejpam-2660	27	21	a	a	DET
ejpam-2660	27	22	hyperlattice	hyperlattice	NOUN
ejpam-2660	27	23	and	and	CCONJ
ejpam-2660	27	24	the	the	DET
ejpam-2660	27	25	orthogonal	orthogonal	ADJ
ejpam-2660	27	26	idempotent	idempotent	ADJ
ejpam-2660	27	27	elements	element	NOUN
ejpam-2660	27	28	form	form	VERB
ejpam-2660	27	29	a	a	DET
ejpam-2660	27	30	quassi	quassi	ADV
ejpam-2660	27	31	-	-	PUNCT
ejpam-2660	27	32	distributive	distributive	ADJ
ejpam-2660	27	33	hyperboolean	hyperboolean	ADJ
ejpam-2660	27	34	algebra	algebra	NOUN
ejpam-2660	27	35	.	.	PUNCT
ejpam-2660	28	1	in	in	ADP
ejpam-2660	28	2	[	[	X
ejpam-2660	28	3	7	7	NUM
ejpam-2660	28	4	]	]	PUNCT
ejpam-2660	28	5	,	,	PUNCT
ejpam-2660	28	6	b.	b.	PROPN
ejpam-2660	28	7	b.	b.	PROPN
ejpam-2660	28	8	n.	n.	PROPN
ejpam-2660	28	9	koguep	koguep	PROPN
ejpam-2660	28	10	,	,	PUNCT
ejpam-2660	28	11	c.	c.	PROPN
ejpam-2660	28	12	nkuimi	nkuimi	PROPN
ejpam-2660	28	13	,	,	PUNCT
ejpam-2660	28	14	and	and	CCONJ
ejpam-2660	28	15	c.	c.	PROPN
ejpam-2660	28	16	lele	lele	PROPN
ejpam-2660	28	17	studied	study	VERB
ejpam-2660	28	18	ideals	ideal	NOUN
ejpam-2660	28	19	and	and	CCONJ
ejpam-2660	28	20	filters	filter	NOUN
ejpam-2660	28	21	in	in	ADP
ejpam-2660	28	22	hyperlattices	hyperlattice	NOUN
ejpam-2660	28	23	.	.	PUNCT
ejpam-2660	29	1	rasouli	rasouli	PROPN
ejpam-2660	29	2	and	and	CCONJ
ejpam-2660	29	3	davvaz	davvaz	NOUN
ejpam-2660	29	4	defined	define	VERB
ejpam-2660	29	5	fundemental	fundemental	ADJ
ejpam-2660	29	6	relation	relation	NOUN
ejpam-2660	29	7	on	on	ADP
ejpam-2660	29	8	a	a	DET
ejpam-2660	29	9	hyperlattice	hyperlattice	NOUN
ejpam-2660	29	10	and	and	CCONJ
ejpam-2660	29	11	obtained	obtain	VERB
ejpam-2660	29	12	a	a	DET
ejpam-2660	29	13	lattice	lattice	NOUN
ejpam-2660	29	14	from	from	ADP
ejpam-2660	29	15	a	a	DET
ejpam-2660	29	16	hyperlattice	hyperlattice	NOUN
ejpam-2660	29	17	;	;	PUNCT
ejpam-2660	29	18	also	also	ADV
ejpam-2660	29	19	they	they	PRON
ejpam-2660	29	20	defined	define	VERB
ejpam-2660	29	21	a	a	DET
ejpam-2660	29	22	topology	topology	NOUN
ejpam-2660	29	23	on	on	ADP
ejpam-2660	29	24	the	the	DET
ejpam-2660	29	25	set	set	NOUN
ejpam-2660	29	26	of	of	ADP
ejpam-2660	29	27	prime	prime	ADJ
ejpam-2660	29	28	ideals	ideal	NOUN
ejpam-2660	29	29	of	of	ADP
ejpam-2660	29	30	a	a	DET
ejpam-2660	29	31	distributive	distributive	ADJ
ejpam-2660	29	32	hyperlattice	hyperlattice	NOUN
ejpam-2660	29	33	,	,	PUNCT
ejpam-2660	29	34	see	see	VERB
ejpam-2660	29	35	[	[	X
ejpam-2660	29	36	20	20	NUM
ejpam-2660	29	37	]	]	PUNCT
ejpam-2660	29	38	and	and	CCONJ
ejpam-2660	29	39	[	[	X
ejpam-2660	29	40	21	21	NUM
ejpam-2660	29	41	]	]	PUNCT
ejpam-2660	29	42	.	.	PUNCT
ejpam-2660	30	1	p.	p.	NOUN
ejpam-2660	30	2	he	he	PRON
ejpam-2660	30	3	,	,	PUNCT
ejpam-2660	30	4	x.	x.	PROPN
ejpam-2660	30	5	xin	xin	PROPN
ejpam-2660	31	1	and	and	CCONJ
ejpam-2660	31	2	jianming	jianme	VERB
ejpam-2660	31	3	zhan	zhan	PROPN
ejpam-2660	31	4	studied	study	VERB
ejpam-2660	31	5	and	and	CCONJ
ejpam-2660	31	6	introduced	introduce	VERB
ejpam-2660	31	7	rough	rough	ADJ
ejpam-2660	31	8	hyperideal	hyperideal	NOUN
ejpam-2660	31	9	in	in	ADP
ejpam-2660	31	10	a	a	DET
ejpam-2660	31	11	hyperlattice	hyperlattice	NOUN
ejpam-2660	31	12	,	,	PUNCT
ejpam-2660	31	13	also	also	ADV
ejpam-2660	31	14	they	they	PRON
ejpam-2660	31	15	investigated	investigate	VERB
ejpam-2660	31	16	some	some	DET
ejpam-2660	31	17	properties	property	NOUN
ejpam-2660	31	18	about	about	ADP
ejpam-2660	31	19	homomorphic	homomorphic	ADJ
ejpam-2660	31	20	images	image	NOUN
ejpam-2660	31	21	of	of	ADP
ejpam-2660	31	22	rough	rough	ADJ
ejpam-2660	31	23	hyperideals	hyperideal	NOUN
ejpam-2660	31	24	in	in	ADP
ejpam-2660	31	25	hyperlattices	hyperlattice	NOUN
ejpam-2660	31	26	[	[	X
ejpam-2660	31	27	6	6	NUM
ejpam-2660	31	28	]	]	PUNCT
ejpam-2660	31	29	.	.	PUNCT
ejpam-2660	32	1	in	in	ADP
ejpam-2660	32	2	section	section	NOUN
ejpam-2660	32	3	2	2	NUM
ejpam-2660	32	4	,	,	PUNCT
ejpam-2660	32	5	we	we	PRON
ejpam-2660	32	6	study	study	VERB
ejpam-2660	32	7	”	"	PUNCT
ejpam-2660	32	8	∧	∧	PROPN
ejpam-2660	32	9	”	"	PUNCT
ejpam-2660	32	10	-hyperlattice	-hyperlattice	NOUN
ejpam-2660	32	11	and	and	CCONJ
ejpam-2660	32	12	some	some	DET
ejpam-2660	32	13	properties	property	NOUN
ejpam-2660	32	14	of	of	ADP
ejpam-2660	32	15	it	it	PRON
ejpam-2660	32	16	.	.	PUNCT
ejpam-2660	33	1	also	also	ADV
ejpam-2660	33	2	in	in	ADP
ejpam-2660	33	3	this	this	DET
ejpam-2660	33	4	section	section	NOUN
ejpam-2660	33	5	distributivity	distributivity	NOUN
ejpam-2660	33	6	and	and	CCONJ
ejpam-2660	33	7	dual	dual	ADJ
ejpam-2660	33	8	distributivity	distributivity	NOUN
ejpam-2660	33	9	in	in	ADP
ejpam-2660	33	10	∧−hyperlattices	∧−hyperlattice	NOUN
ejpam-2660	33	11	are	be	AUX
ejpam-2660	33	12	studied	study	VERB
ejpam-2660	33	13	.	.	PUNCT
ejpam-2660	34	1	in	in	ADP
ejpam-2660	34	2	section	section	NOUN
ejpam-2660	34	3	3	3	NUM
ejpam-2660	34	4	,	,	PUNCT
ejpam-2660	34	5	we	we	PRON
ejpam-2660	34	6	investigate	investigate	VERB
ejpam-2660	34	7	hyperideals	hyperideal	NOUN
ejpam-2660	34	8	and	and	CCONJ
ejpam-2660	34	9	hyperfilters	hyperfilter	NOUN
ejpam-2660	34	10	in	in	ADP
ejpam-2660	34	11	∧-hyperlattice	∧-hyperlattice	NOUN
ejpam-2660	34	12	l	l	NOUN
ejpam-2660	34	13	and	and	CCONJ
ejpam-2660	34	14	we	we	PRON
ejpam-2660	34	15	prove	prove	VERB
ejpam-2660	34	16	that	that	SCONJ
ejpam-2660	34	17	(	(	PUNCT
ejpam-2660	34	18	p	p	X
ejpam-2660	34	19	∧f	∧f	X
ejpam-2660	34	20	(	(	PUNCT
ejpam-2660	34	21	a))∨	a))∨	NOUN
ejpam-2660	34	22	(	(	PUNCT
ejpam-2660	34	23	p	p	X
ejpam-2660	34	24	∧f	∧f	X
ejpam-2660	34	25	(	(	PUNCT
ejpam-2660	34	26	b	b	NOUN
ejpam-2660	34	27	)	)	PUNCT
ejpam-2660	34	28	)	)	PUNCT
ejpam-2660	35	1	=	=	PUNCT
ejpam-2660	36	1	p	p	X
ejpam-2660	36	2	∧f	∧f	X
ejpam-2660	36	3	(	(	PUNCT
ejpam-2660	36	4	a∨	a∨	PROPN
ejpam-2660	36	5	b	b	PROPN
ejpam-2660	36	6	)	)	PUNCT
ejpam-2660	36	7	,	,	PUNCT
ejpam-2660	36	8	where	where	SCONJ
ejpam-2660	36	9	p	p	NOUN
ejpam-2660	36	10	is	be	AUX
ejpam-2660	36	11	a	a	DET
ejpam-2660	36	12	hyperfilter	hyperfilter	NOUN
ejpam-2660	36	13	and	and	CCONJ
ejpam-2660	36	14	f	f	PROPN
ejpam-2660	36	15	(	(	PUNCT
ejpam-2660	36	16	a	a	NOUN
ejpam-2660	36	17	)	)	PUNCT
ejpam-2660	36	18	is	be	AUX
ejpam-2660	36	19	the	the	DET
ejpam-2660	36	20	generating	generate	VERB
ejpam-2660	36	21	filter	filter	NOUN
ejpam-2660	36	22	by	by	ADP
ejpam-2660	36	23	a	a	DET
ejpam-2660	36	24	∈	∈	PROPN
ejpam-2660	36	25	l.	l.	NOUN
ejpam-2660	36	26	in	in	ADP
ejpam-2660	36	27	section	section	NOUN
ejpam-2660	36	28	4	4	NUM
ejpam-2660	36	29	,	,	PUNCT
ejpam-2660	36	30	we	we	PRON
ejpam-2660	36	31	introduce	introduce	VERB
ejpam-2660	36	32	ia	ia	NOUN
ejpam-2660	36	33	-	-	NOUN
ejpam-2660	36	34	hyperideal	hyperideal	ADJ
ejpam-2660	36	35	,	,	PUNCT
ejpam-2660	36	36	for	for	ADP
ejpam-2660	36	37	some	some	DET
ejpam-2660	36	38	non	non	ADJ
ejpam-2660	36	39	-	-	ADJ
ejpam-2660	36	40	empty	empty	ADJ
ejpam-2660	36	41	subset	subset	VERB
ejpam-2660	36	42	a	a	PRON
ejpam-2660	36	43	of	of	ADP
ejpam-2660	36	44	a	a	DET
ejpam-2660	36	45	dual	dual	ADJ
ejpam-2660	36	46	distributive	distributive	ADJ
ejpam-2660	36	47	”	"	PUNCT
ejpam-2660	36	48	∧	∧	NOUN
ejpam-2660	36	49	”	"	PUNCT
ejpam-2660	36	50	-hyperlattice	-hyperlattice	NOUN
ejpam-2660	36	51	l	l	NOUN
ejpam-2660	36	52	;	;	PUNCT
ejpam-2660	36	53	also	also	ADV
ejpam-2660	36	54	in	in	ADP
ejpam-2660	36	55	this	this	DET
ejpam-2660	36	56	section	section	NOUN
ejpam-2660	36	57	,	,	PUNCT
ejpam-2660	36	58	”	"	PUNCT
ejpam-2660	36	59	∧	∧	NOUN
ejpam-2660	36	60	”	"	PUNCT
ejpam-2660	36	61	-subhyperlattices	-subhyperlattice	NOUN
ejpam-2660	36	62	are	be	AUX
ejpam-2660	36	63	studied	study	VERB
ejpam-2660	36	64	.	.	PUNCT
ejpam-2660	37	1	2	2	X
ejpam-2660	37	2	.	.	X
ejpam-2660	37	3	preliminaries	preliminary	NOUN
ejpam-2660	37	4	before	before	SCONJ
ejpam-2660	37	5	we	we	PRON
ejpam-2660	37	6	study	study	VERB
ejpam-2660	37	7	∧-hyperlattice	∧-hyperlattice	NOUN
ejpam-2660	37	8	and	and	CCONJ
ejpam-2660	37	9	some	some	DET
ejpam-2660	37	10	result	result	NOUN
ejpam-2660	37	11	of	of	ADP
ejpam-2660	37	12	it	it	PRON
ejpam-2660	37	13	,	,	PUNCT
ejpam-2660	37	14	let	let	VERB
ejpam-2660	37	15	us	we	PRON
ejpam-2660	37	16	state	state	VERB
ejpam-2660	37	17	some	some	DET
ejpam-2660	37	18	terminologies	terminology	NOUN
ejpam-2660	37	19	.	.	PUNCT
ejpam-2660	38	1	definition	definition	NOUN
ejpam-2660	38	2	1	1	NUM
ejpam-2660	38	3	.	.	PUNCT
ejpam-2660	39	1	[	[	X
ejpam-2660	39	2	11	11	NUM
ejpam-2660	39	3	]	]	PUNCT
ejpam-2660	39	4	let	let	VERB
ejpam-2660	39	5	h	h	PRON
ejpam-2660	39	6	be	be	AUX
ejpam-2660	39	7	a	a	DET
ejpam-2660	39	8	non	non	ADJ
ejpam-2660	39	9	-	-	ADJ
ejpam-2660	39	10	empty	empty	ADJ
ejpam-2660	39	11	set	set	NOUN
ejpam-2660	39	12	and	and	CCONJ
ejpam-2660	39	13	p>(h	p>(h	NOUN
ejpam-2660	39	14	)	)	PUNCT
ejpam-2660	39	15	denotes	denote	VERB
ejpam-2660	39	16	the	the	DET
ejpam-2660	39	17	set	set	NOUN
ejpam-2660	39	18	of	of	ADP
ejpam-2660	39	19	all	all	DET
ejpam-2660	39	20	nonempty	nonempty	ADJ
ejpam-2660	39	21	subsets	subset	NOUN
ejpam-2660	39	22	of	of	ADP
ejpam-2660	39	23	h.	h.	PROPN
ejpam-2660	39	24	maps	map	NOUN
ejpam-2660	39	25	of	of	ADP
ejpam-2660	39	26	the	the	DET
ejpam-2660	39	27	following	follow	VERB
ejpam-2660	39	28	type	type	NOUN
ejpam-2660	39	29	:	:	PUNCT
ejpam-2660	39	30	f	f	NOUN
ejpam-2660	39	31	:	:	PUNCT
ejpam-2660	39	32	h	h	NOUN
ejpam-2660	39	33	×h	×h	PROPN
ejpam-2660	39	34	−→	−→	NOUN
ejpam-2660	39	35	p>(h	p>(h	NOUN
ejpam-2660	39	36	)	)	PUNCT
ejpam-2660	39	37	,	,	PUNCT
ejpam-2660	39	38	are	be	AUX
ejpam-2660	39	39	called	call	VERB
ejpam-2660	39	40	hyper	hyper	ADJ
ejpam-2660	39	41	operation	operation	NOUN
ejpam-2660	39	42	and	and	CCONJ
ejpam-2660	39	43	(	(	PUNCT
ejpam-2660	39	44	h	h	NOUN
ejpam-2660	39	45	,	,	PUNCT
ejpam-2660	39	46	f	f	NOUN
ejpam-2660	39	47	)	)	PUNCT
ejpam-2660	39	48	that	that	PRON
ejpam-2660	39	49	satisfies	satisfy	VERB
ejpam-2660	39	50	some	some	DET
ejpam-2660	39	51	axioms	axiom	NOUN
ejpam-2660	39	52	is	be	AUX
ejpam-2660	39	53	called	call	VERB
ejpam-2660	39	54	a	a	DET
ejpam-2660	39	55	hyperalgebra	hyperalgebra	NOUN
ejpam-2660	39	56	.	.	PUNCT
ejpam-2660	40	1	definition	definition	NOUN
ejpam-2660	40	2	2	2	NUM
ejpam-2660	40	3	.	.	PUNCT
ejpam-2660	41	1	[	[	X
ejpam-2660	41	2	10	10	NUM
ejpam-2660	41	3	]	]	PUNCT
ejpam-2660	41	4	let	let	AUX
ejpam-2660	41	5	l	l	NOUN
ejpam-2660	41	6	be	be	AUX
ejpam-2660	41	7	a	a	DET
ejpam-2660	41	8	nonempty	nonempty	ADJ
ejpam-2660	41	9	set	set	VERB
ejpam-2660	41	10	,	,	PUNCT
ejpam-2660	41	11	∧−	∧−	PRON
ejpam-2660	41	12	be	be	VERB
ejpam-2660	41	13	a	a	DET
ejpam-2660	41	14	binary	binary	ADJ
ejpam-2660	41	15	operation	operation	NOUN
ejpam-2660	41	16	,	,	PUNCT
ejpam-2660	41	17	and	and	CCONJ
ejpam-2660	41	18	∨−	∨−	PROPN
ejpam-2660	41	19	be	be	VERB
ejpam-2660	41	20	a	a	DET
ejpam-2660	41	21	hyper	hyper	ADJ
ejpam-2660	41	22	operation	operation	NOUN
ejpam-2660	41	23	on	on	ADP
ejpam-2660	41	24	l.	l.	PROPN
ejpam-2660	41	25	then	then	ADV
ejpam-2660	41	26	l	l	PROPN
ejpam-2660	41	27	is	be	AUX
ejpam-2660	41	28	called	call	VERB
ejpam-2660	41	29	a	a	DET
ejpam-2660	41	30	hyperlattice	hyperlattice	NOUN
ejpam-2660	41	31	,	,	PUNCT
ejpam-2660	41	32	if	if	SCONJ
ejpam-2660	41	33	for	for	ADP
ejpam-2660	41	34	all	all	DET
ejpam-2660	41	35	a	a	DET
ejpam-2660	41	36	,	,	PUNCT
ejpam-2660	41	37	b	b	NOUN
ejpam-2660	41	38	,	,	PUNCT
ejpam-2660	41	39	c	c	PROPN
ejpam-2660	41	40	∈	∈	PROPN
ejpam-2660	41	41	l	l	NOUN
ejpam-2660	41	42	,	,	PUNCT
ejpam-2660	41	43	the	the	DET
ejpam-2660	41	44	following	follow	VERB
ejpam-2660	41	45	conditions	condition	NOUN
ejpam-2660	41	46	hold	hold	VERB
ejpam-2660	41	47	:	:	PUNCT
ejpam-2660	41	48	(	(	PUNCT
ejpam-2660	41	49	i	i	NOUN
ejpam-2660	41	50	)	)	PUNCT
ejpam-2660	41	51	a	a	DET
ejpam-2660	41	52	∈	∈	PROPN
ejpam-2660	41	53	a	a	DET
ejpam-2660	41	54	∨	∨	NOUN
ejpam-2660	41	55	a	a	NOUN
ejpam-2660	41	56	,	,	PUNCT
ejpam-2660	41	57	and	and	CCONJ
ejpam-2660	41	58	a	a	DET
ejpam-2660	41	59	∧	∧	NOUN
ejpam-2660	41	60	a	a	DET
ejpam-2660	41	61	=	=	SYM
ejpam-2660	41	62	a	a	NOUN
ejpam-2660	41	63	;	;	PUNCT
ejpam-2660	41	64	(	(	PUNCT
ejpam-2660	41	65	ii	ii	NOUN
ejpam-2660	41	66	)	)	PUNCT
ejpam-2660	41	67	a	a	DET
ejpam-2660	41	68	∨	∨	NUM
ejpam-2660	41	69	b	b	X
ejpam-2660	41	70	=	=	SYM
ejpam-2660	41	71	b	b	PROPN
ejpam-2660	41	72	∨	∨	NUM
ejpam-2660	41	73	a	a	NOUN
ejpam-2660	41	74	,	,	PUNCT
ejpam-2660	41	75	and	and	CCONJ
ejpam-2660	41	76	a	a	DET
ejpam-2660	41	77	∧	∧	PROPN
ejpam-2660	41	78	b	b	PROPN
ejpam-2660	41	79	=	=	SYM
ejpam-2660	41	80	b	b	PROPN
ejpam-2660	41	81	∧	∧	PROPN
ejpam-2660	41	82	a	a	PRON
ejpam-2660	41	83	;	;	PUNCT
ejpam-2660	41	84	(	(	PUNCT
ejpam-2660	41	85	iii	iii	X
ejpam-2660	41	86	)	)	PUNCT
ejpam-2660	41	87	a	a	DET
ejpam-2660	41	88	∈	∈	NOUN
ejpam-2660	41	89	[	[	X
ejpam-2660	41	90	a	a	DET
ejpam-2660	41	91	∧	∧	PROPN
ejpam-2660	41	92	(	(	PUNCT
ejpam-2660	41	93	a	a	DET
ejpam-2660	41	94	∨	∨	NUM
ejpam-2660	41	95	b	b	NOUN
ejpam-2660	41	96	)	)	PUNCT
ejpam-2660	41	97	]	]	PUNCT
ejpam-2660	41	98	∩	∩	NOUN
ejpam-2660	41	99	[	[	X
ejpam-2660	41	100	a	a	DET
ejpam-2660	41	101	∨	∨	NOUN
ejpam-2660	41	102	(	(	PUNCT
ejpam-2660	41	103	a	a	DET
ejpam-2660	41	104	∧	∧	PROPN
ejpam-2660	41	105	b	b	NOUN
ejpam-2660	41	106	)	)	PUNCT
ejpam-2660	41	107	]	]	X
ejpam-2660	41	108	;	;	PUNCT
ejpam-2660	41	109	(	(	PUNCT
ejpam-2660	41	110	iv	iv	X
ejpam-2660	41	111	)	)	PUNCT
ejpam-2660	41	112	a	a	DET
ejpam-2660	41	113	∨	∨	NOUN
ejpam-2660	41	114	(	(	PUNCT
ejpam-2660	41	115	b	b	PROPN
ejpam-2660	41	116	∨	∨	NUM
ejpam-2660	41	117	c	c	NOUN
ejpam-2660	41	118	)	)	PUNCT
ejpam-2660	41	119	=	=	NOUN
ejpam-2660	41	120	(	(	PUNCT
ejpam-2660	41	121	a	a	DET
ejpam-2660	41	122	∨	∨	NUM
ejpam-2660	41	123	b	b	NOUN
ejpam-2660	41	124	)	)	PUNCT
ejpam-2660	41	125	∨	∨	NUM
ejpam-2660	41	126	c	c	PROPN
ejpam-2660	41	127	,	,	PUNCT
ejpam-2660	41	128	and	and	CCONJ
ejpam-2660	41	129	a	a	DET
ejpam-2660	41	130	∧	∧	PROPN
ejpam-2660	41	131	(	(	PUNCT
ejpam-2660	41	132	b	b	PROPN
ejpam-2660	41	133	∧	∧	NOUN
ejpam-2660	41	134	c	c	NOUN
ejpam-2660	41	135	)	)	PUNCT
ejpam-2660	41	136	=	=	NOUN
ejpam-2660	41	137	(	(	PUNCT
ejpam-2660	41	138	a	a	DET
ejpam-2660	41	139	∧	∧	PROPN
ejpam-2660	41	140	b	b	NOUN
ejpam-2660	41	141	)	)	PUNCT
ejpam-2660	41	142	∧	∧	PROPN
ejpam-2660	41	143	c	c	NOUN
ejpam-2660	41	144	;	;	PUNCT
ejpam-2660	41	145	(	(	PUNCT
ejpam-2660	41	146	v	v	NOUN
ejpam-2660	41	147	)	)	PUNCT
ejpam-2660	41	148	a	a	DET
ejpam-2660	41	149	∈	∈	PROPN
ejpam-2660	41	150	a	a	DET
ejpam-2660	41	151	∨	∨	NOUN
ejpam-2660	41	152	b	b	X
ejpam-2660	41	153	=	=	NOUN
ejpam-2660	41	154	⇒	⇒	VERB
ejpam-2660	41	155	a	a	DET
ejpam-2660	41	156	∧	∧	PROPN
ejpam-2660	41	157	b	b	PROPN
ejpam-2660	41	158	=	=	PROPN
ejpam-2660	41	159	b.	b.	PROPN
ejpam-2660	41	160	definition	definition	NOUN
ejpam-2660	41	161	3	3	NUM
ejpam-2660	41	162	.	.	PUNCT
ejpam-2660	42	1	[	[	X
ejpam-2660	42	2	9	9	NUM
ejpam-2660	42	3	]	]	PUNCT
ejpam-2660	42	4	a	a	DET
ejpam-2660	42	5	hyperlattice	hyperlattice	NOUN
ejpam-2660	42	6	l	l	NOUN
ejpam-2660	42	7	is	be	AUX
ejpam-2660	42	8	called	call	VERB
ejpam-2660	42	9	bounded	bounded	ADJ
ejpam-2660	42	10	if	if	SCONJ
ejpam-2660	42	11	there	there	PRON
ejpam-2660	42	12	exist	exist	VERB
ejpam-2660	42	13	0	0	NUM
ejpam-2660	42	14	,	,	PUNCT
ejpam-2660	42	15	1	1	NUM
ejpam-2660	42	16	∈	∈	NOUN
ejpam-2660	42	17	l	l	NOUN
ejpam-2660	42	18	such	such	ADJ
ejpam-2660	42	19	that	that	PRON
ejpam-2660	42	20	for	for	ADP
ejpam-2660	42	21	all	all	DET
ejpam-2660	42	22	x	x	SYM
ejpam-2660	42	23	∈	∈	PROPN
ejpam-2660	42	24	l	l	NOUN
ejpam-2660	42	25	,	,	PUNCT
ejpam-2660	42	26	0	0	NUM
ejpam-2660	42	27	≤	≤	NUM
ejpam-2660	42	28	x	x	SYM
ejpam-2660	42	29	≤	≤	NUM
ejpam-2660	42	30	1	1	NUM
ejpam-2660	42	31	.	.	PUNCT
ejpam-2660	42	32	m.	m.	NOUN
ejpam-2660	42	33	amiri	amiri	PROPN
ejpam-2660	42	34	bideshki	bideshki	PROPN
ejpam-2660	42	35	,	,	PUNCT
ejpam-2660	42	36	r.	r.	PROPN
ejpam-2660	42	37	ameri	ameri	PROPN
ejpam-2660	42	38	,	,	PUNCT
ejpam-2660	42	39	a.	a.	PROPN
ejpam-2660	42	40	borumand	borumand	PROPN
ejpam-2660	42	41	saeid	saeid	PROPN
ejpam-2660	42	42	/	/	SYM
ejpam-2660	42	43	eur	eur	PROPN
ejpam-2660	42	44	.	.	PUNCT
ejpam-2660	43	1	j.	j.	PROPN
ejpam-2660	43	2	pure	pure	PROPN
ejpam-2660	43	3	appl	appl	PROPN
ejpam-2660	43	4	.	.	PROPN
ejpam-2660	43	5	math	math	PROPN
ejpam-2660	43	6	,	,	PUNCT
ejpam-2660	43	7	11	11	NUM
ejpam-2660	43	8	(	(	PUNCT
ejpam-2660	43	9	1	1	NUM
ejpam-2660	43	10	)	)	PUNCT
ejpam-2660	43	11	(	(	PUNCT
ejpam-2660	43	12	2018	2018	NUM
ejpam-2660	43	13	)	)	PUNCT
ejpam-2660	43	14	,	,	PUNCT
ejpam-2660	43	15	169	169	NUM
ejpam-2660	43	16	-	-	SYM
ejpam-2660	43	17	188	188	NUM
ejpam-2660	43	18	171	171	NUM
ejpam-2660	43	19	let	let	NOUN
ejpam-2660	43	20	(	(	PUNCT
ejpam-2660	43	21	l,⊕,⊗	l,⊕,⊗	NOUN
ejpam-2660	43	22	)	)	PUNCT
ejpam-2660	43	23	be	be	VERB
ejpam-2660	43	24	a	a	DET
ejpam-2660	43	25	hyperalgebra	hyperalgebra	NOUN
ejpam-2660	43	26	and	and	CCONJ
ejpam-2660	43	27	a	a	DET
ejpam-2660	43	28	⊆	⊆	NUM
ejpam-2660	43	29	l.	l.	NOUN
ejpam-2660	43	30	we	we	PRON
ejpam-2660	43	31	say	say	VERB
ejpam-2660	43	32	that	that	SCONJ
ejpam-2660	43	33	a	a	PRON
ejpam-2660	43	34	is	be	AUX
ejpam-2660	43	35	⊕-closed	⊕-close	VERB
ejpam-2660	43	36	,	,	PUNCT
ejpam-2660	43	37	if	if	SCONJ
ejpam-2660	43	38	a⊕	a⊕	PROPN
ejpam-2660	43	39	b	b	PROPN
ejpam-2660	43	40	⊆	⊆	NUM
ejpam-2660	43	41	a	a	PRON
ejpam-2660	43	42	,	,	PUNCT
ejpam-2660	43	43	for	for	ADP
ejpam-2660	43	44	all	all	DET
ejpam-2660	43	45	a	a	PRON
ejpam-2660	43	46	,	,	PUNCT
ejpam-2660	43	47	b	b	X
ejpam-2660	43	48	∈	∈	PROPN
ejpam-2660	43	49	a.	a.	NOUN
ejpam-2660	43	50	definition	definition	NOUN
ejpam-2660	43	51	4	4	NUM
ejpam-2660	43	52	.	.	PUNCT
ejpam-2660	44	1	let	let	VERB
ejpam-2660	44	2	l	l	NOUN
ejpam-2660	44	3	be	be	AUX
ejpam-2660	44	4	a	a	DET
ejpam-2660	44	5	nonempty	nonempty	ADJ
ejpam-2660	44	6	set	set	VERB
ejpam-2660	44	7	,	,	PUNCT
ejpam-2660	44	8	”	"	PUNCT
ejpam-2660	44	9	∧	∧	NOUN
ejpam-2660	44	10	”	"	PUNCT
ejpam-2660	44	11	and	and	CCONJ
ejpam-2660	44	12	”	"	PUNCT
ejpam-2660	44	13	∨	∨	PROPN
ejpam-2660	44	14	”	"	PUNCT
ejpam-2660	44	15	are	be	AUX
ejpam-2660	44	16	hyperoperation	hyperoperation	NOUN
ejpam-2660	44	17	and	and	CCONJ
ejpam-2660	44	18	binary	binary	ADJ
ejpam-2660	44	19	operation	operation	NOUN
ejpam-2660	44	20	,	,	PUNCT
ejpam-2660	44	21	respectively	respectively	ADV
ejpam-2660	44	22	.	.	PUNCT
ejpam-2660	45	1	tnen	tnen	NOUN
ejpam-2660	45	2	l	l	PROPN
ejpam-2660	45	3	is	be	AUX
ejpam-2660	45	4	called	call	VERB
ejpam-2660	45	5	a	a	DET
ejpam-2660	45	6	”	"	PUNCT
ejpam-2660	45	7	∧	∧	NOUN
ejpam-2660	45	8	”	"	PUNCT
ejpam-2660	45	9	−	−	PROPN
ejpam-2660	45	10	hyperlattice	hyperlattice	NOUN
ejpam-2660	45	11	if	if	SCONJ
ejpam-2660	45	12	(	(	PUNCT
ejpam-2660	45	13	i	i	NOUN
ejpam-2660	45	14	)	)	PUNCT
ejpam-2660	45	15	a	a	DET
ejpam-2660	45	16	∈	∈	PROPN
ejpam-2660	45	17	a	a	DET
ejpam-2660	45	18	∧	∧	PROPN
ejpam-2660	45	19	a	a	PROPN
ejpam-2660	45	20	,	,	PUNCT
ejpam-2660	45	21	a	a	DET
ejpam-2660	45	22	∨	∨	NOUN
ejpam-2660	45	23	a	a	DET
ejpam-2660	45	24	=	=	SYM
ejpam-2660	45	25	a	a	NOUN
ejpam-2660	45	26	,	,	PUNCT
ejpam-2660	45	27	(	(	PUNCT
ejpam-2660	45	28	ii	ii	NOUN
ejpam-2660	45	29	)	)	PUNCT
ejpam-2660	45	30	a	a	DET
ejpam-2660	45	31	∧	∧	PROPN
ejpam-2660	45	32	b	b	NOUN
ejpam-2660	45	33	=	=	SYM
ejpam-2660	45	34	b	b	PROPN
ejpam-2660	45	35	∧	∧	PROPN
ejpam-2660	45	36	a	a	PROPN
ejpam-2660	45	37	,	,	PUNCT
ejpam-2660	45	38	a	a	DET
ejpam-2660	45	39	∨	∨	NUM
ejpam-2660	46	1	b	b	X
ejpam-2660	46	2	=	=	SYM
ejpam-2660	46	3	b	b	PROPN
ejpam-2660	46	4	∨	∨	NUM
ejpam-2660	46	5	a	a	PRON
ejpam-2660	46	6	,	,	PUNCT
ejpam-2660	46	7	(	(	PUNCT
ejpam-2660	46	8	iii	iii	NOUN
ejpam-2660	46	9	)	)	PUNCT
ejpam-2660	46	10	a	a	DET
ejpam-2660	46	11	∧	∧	PROPN
ejpam-2660	46	12	(	(	PUNCT
ejpam-2660	46	13	b	b	PROPN
ejpam-2660	46	14	∧	∧	NOUN
ejpam-2660	46	15	c	c	NOUN
ejpam-2660	46	16	)	)	PUNCT
ejpam-2660	46	17	=	=	NOUN
ejpam-2660	46	18	(	(	PUNCT
ejpam-2660	46	19	a	a	DET
ejpam-2660	46	20	∧	∧	PROPN
ejpam-2660	46	21	b	b	NOUN
ejpam-2660	46	22	)	)	PUNCT
ejpam-2660	46	23	∧	∧	PROPN
ejpam-2660	46	24	c	c	NOUN
ejpam-2660	46	25	,	,	PUNCT
ejpam-2660	46	26	a	a	DET
ejpam-2660	46	27	∨	∨	NOUN
ejpam-2660	46	28	(	(	PUNCT
ejpam-2660	46	29	b	b	PROPN
ejpam-2660	46	30	∨	∨	NUM
ejpam-2660	46	31	c	c	NOUN
ejpam-2660	46	32	)	)	PUNCT
ejpam-2660	46	33	=	=	NOUN
ejpam-2660	46	34	(	(	PUNCT
ejpam-2660	46	35	a	a	DET
ejpam-2660	46	36	∨	∨	NUM
ejpam-2660	46	37	b	b	NOUN
ejpam-2660	46	38	)	)	PUNCT
ejpam-2660	46	39	∨	∨	PROPN
ejpam-2660	46	40	c	c	X
ejpam-2660	46	41	,	,	PUNCT
ejpam-2660	46	42	(	(	PUNCT
ejpam-2660	46	43	iv	iv	X
ejpam-2660	46	44	)	)	PUNCT
ejpam-2660	46	45	a	a	DET
ejpam-2660	46	46	∈	∈	NOUN
ejpam-2660	46	47	(	(	PUNCT
ejpam-2660	46	48	a	a	DET
ejpam-2660	46	49	∧	∧	PROPN
ejpam-2660	46	50	(	(	PUNCT
ejpam-2660	46	51	a	a	DET
ejpam-2660	46	52	∨	∨	NUM
ejpam-2660	46	53	b	b	NOUN
ejpam-2660	46	54	)	)	PUNCT
ejpam-2660	46	55	)	)	PUNCT
ejpam-2660	46	56	∩	∩	NOUN
ejpam-2660	46	57	(	(	PUNCT
ejpam-2660	46	58	a	a	DET
ejpam-2660	46	59	∨	∨	NOUN
ejpam-2660	46	60	(	(	PUNCT
ejpam-2660	46	61	a	a	DET
ejpam-2660	46	62	∧	∧	PROPN
ejpam-2660	46	63	b	b	NOUN
ejpam-2660	46	64	)	)	PUNCT
ejpam-2660	46	65	)	)	PUNCT
ejpam-2660	46	66	,	,	PUNCT
ejpam-2660	46	67	and	and	CCONJ
ejpam-2660	46	68	l	l	NOUN
ejpam-2660	46	69	is	be	AUX
ejpam-2660	46	70	called	call	VERB
ejpam-2660	46	71	strong	strong	ADJ
ejpam-2660	46	72	hyperlattice	hyperlattice	NOUN
ejpam-2660	46	73	,	,	PUNCT
ejpam-2660	46	74	if	if	SCONJ
ejpam-2660	46	75	(	(	PUNCT
ejpam-2660	46	76	v	v	NOUN
ejpam-2660	46	77	)	)	PUNCT
ejpam-2660	46	78	a	a	DET
ejpam-2660	46	79	∈	∈	PROPN
ejpam-2660	46	80	a	a	DET
ejpam-2660	46	81	∧	∧	PROPN
ejpam-2660	46	82	b	b	NOUN
ejpam-2660	46	83	=	=	NOUN
ejpam-2660	46	84	⇒	⇒	VERB
ejpam-2660	46	85	a	a	DET
ejpam-2660	46	86	∨	∨	NOUN
ejpam-2660	46	87	b	b	PROPN
ejpam-2660	46	88	=	=	SYM
ejpam-2660	46	89	b	b	PROPN
ejpam-2660	46	90	,	,	PUNCT
ejpam-2660	46	91	for	for	ADP
ejpam-2660	46	92	all	all	DET
ejpam-2660	46	93	a	a	DET
ejpam-2660	46	94	,	,	PUNCT
ejpam-2660	46	95	b	b	NOUN
ejpam-2660	46	96	,	,	PUNCT
ejpam-2660	46	97	c	c	PROPN
ejpam-2660	46	98	∈	∈	PROPN
ejpam-2660	46	99	l.	l.	NOUN
ejpam-2660	46	100	in	in	ADP
ejpam-2660	46	101	a	a	DET
ejpam-2660	46	102	natural	natural	ADJ
ejpam-2660	46	103	way	way	NOUN
ejpam-2660	46	104	,	,	PUNCT
ejpam-2660	46	105	we	we	PRON
ejpam-2660	46	106	can	can	AUX
ejpam-2660	46	107	extend	extend	VERB
ejpam-2660	46	108	”	"	PUNCT
ejpam-2660	46	109	∧	∧	PROPN
ejpam-2660	46	110	”	"	PUNCT
ejpam-2660	46	111	and	and	CCONJ
ejpam-2660	46	112	”	"	PUNCT
ejpam-2660	46	113	∨	∨	NUM
ejpam-2660	46	114	”	"	PUNCT
ejpam-2660	46	115	to	to	ADP
ejpam-2660	46	116	subsets	subset	NOUN
ejpam-2660	46	117	of	of	ADP
ejpam-2660	46	118	h	h	NOUN
ejpam-2660	46	119	,	,	PUNCT
ejpam-2660	46	120	as	as	SCONJ
ejpam-2660	46	121	follows	follow	VERB
ejpam-2660	46	122	a	a	DET
ejpam-2660	46	123	∧b	∧b	NOUN
ejpam-2660	46	124	=	=	SYM
ejpam-2660	46	125	∪{a	∪{a	NOUN
ejpam-2660	46	126	∧	∧	PROPN
ejpam-2660	46	127	b|a	b|a	PROPN
ejpam-2660	46	128	∈	∈	PROPN
ejpam-2660	46	129	a	a	DET
ejpam-2660	46	130	,	,	PUNCT
ejpam-2660	46	131	b	b	PROPN
ejpam-2660	46	132	∈	∈	PROPN
ejpam-2660	46	133	b	b	NOUN
ejpam-2660	46	134	}	}	PUNCT
ejpam-2660	46	135	,	,	PUNCT
ejpam-2660	46	136	a	a	DET
ejpam-2660	46	137	∨b	∨b	NOUN
ejpam-2660	46	138	=	=	PUNCT
ejpam-2660	46	139	{	{	PUNCT
ejpam-2660	46	140	a	a	DET
ejpam-2660	46	141	∨	∨	NOUN
ejpam-2660	46	142	b|a	b|a	X
ejpam-2660	47	1	∈	∈	PROPN
ejpam-2660	47	2	a	a	PRON
ejpam-2660	47	3	,	,	PUNCT
ejpam-2660	47	4	b	b	PROPN
ejpam-2660	47	5	∈	∈	PROPN
ejpam-2660	47	6	b	b	NOUN
ejpam-2660	47	7	}	}	PUNCT
ejpam-2660	47	8	,	,	PUNCT
ejpam-2660	47	9	where	where	SCONJ
ejpam-2660	47	10	,	,	PUNCT
ejpam-2660	47	11	a	a	DET
ejpam-2660	47	12	,	,	PUNCT
ejpam-2660	47	13	b	b	PROPN
ejpam-2660	47	14	∈	∈	PROPN
ejpam-2660	47	15	p	p	PROPN
ejpam-2660	47	16	∗(h	∗(h	PROPN
ejpam-2660	47	17	)	)	PUNCT
ejpam-2660	47	18	.	.	PUNCT
ejpam-2660	48	1	example	example	NOUN
ejpam-2660	49	1	5	5	NUM
ejpam-2660	49	2	.	.	PUNCT
ejpam-2660	50	1	let	let	AUX
ejpam-2660	50	2	(	(	PUNCT
ejpam-2660	50	3	l,∨,∧	l,∨,∧	NOUN
ejpam-2660	50	4	)	)	PUNCT
ejpam-2660	50	5	be	be	VERB
ejpam-2660	50	6	a	a	DET
ejpam-2660	50	7	lattice	lattice	NOUN
ejpam-2660	50	8	and	and	CCONJ
ejpam-2660	50	9	define	define	VERB
ejpam-2660	50	10	a⊕	a⊕	PROPN
ejpam-2660	50	11	b	b	NOUN
ejpam-2660	50	12	=	=	PRON
ejpam-2660	50	13	{	{	PUNCT
ejpam-2660	50	14	x	x	X
ejpam-2660	50	15	|	|	NOUN
ejpam-2660	50	16	x	x	SYM
ejpam-2660	50	17	≤	≤	NOUN
ejpam-2660	50	18	a	a	DET
ejpam-2660	50	19	∧	∧	PROPN
ejpam-2660	50	20	b	b	PROPN
ejpam-2660	50	21	}	}	PUNCT
ejpam-2660	50	22	.	.	PUNCT
ejpam-2660	51	1	then	then	ADV
ejpam-2660	51	2	(	(	PUNCT
ejpam-2660	51	3	l,∨,⊕	l,∨,⊕	NOUN
ejpam-2660	51	4	)	)	PUNCT
ejpam-2660	51	5	is	be	AUX
ejpam-2660	51	6	a	a	DET
ejpam-2660	51	7	”	"	PUNCT
ejpam-2660	51	8	∧	∧	NOUN
ejpam-2660	51	9	”	"	PUNCT
ejpam-2660	51	10	−	−	PROPN
ejpam-2660	51	11	hyperlattice	hyperlattice	NOUN
ejpam-2660	51	12	.	.	PUNCT
ejpam-2660	52	1	remark	remark	PROPN
ejpam-2660	52	2	6	6	NUM
ejpam-2660	52	3	.	.	PUNCT
ejpam-2660	53	1	the	the	DET
ejpam-2660	53	2	converse	converse	NOUN
ejpam-2660	53	3	of	of	ADP
ejpam-2660	53	4	(	(	PUNCT
ejpam-2660	53	5	v	v	NOUN
ejpam-2660	53	6	)	)	PUNCT
ejpam-2660	53	7	in	in	ADP
ejpam-2660	53	8	definition	definition	NOUN
ejpam-2660	53	9	4	4	NUM
ejpam-2660	53	10	is	be	AUX
ejpam-2660	53	11	true	true	ADJ
ejpam-2660	53	12	.	.	PUNCT
ejpam-2660	54	1	if	if	SCONJ
ejpam-2660	54	2	a∨	a∨	PROPN
ejpam-2660	54	3	b	b	PROPN
ejpam-2660	54	4	=	=	SYM
ejpam-2660	54	5	b	b	PROPN
ejpam-2660	54	6	,	,	PUNCT
ejpam-2660	54	7	by	by	ADP
ejpam-2660	54	8	definition	definition	NOUN
ejpam-2660	54	9	4	4	NUM
ejpam-2660	54	10	(	(	PUNCT
ejpam-2660	54	11	iv	iv	NUM
ejpam-2660	54	12	)	)	PUNCT
ejpam-2660	54	13	,	,	PUNCT
ejpam-2660	54	14	we	we	PRON
ejpam-2660	54	15	have	have	VERB
ejpam-2660	54	16	a	a	DET
ejpam-2660	54	17	∈	∈	PROPN
ejpam-2660	54	18	a∧(a∨b	a∧(a∨b	NOUN
ejpam-2660	54	19	)	)	PUNCT
ejpam-2660	54	20	.	.	PUNCT
ejpam-2660	55	1	since	since	SCONJ
ejpam-2660	55	2	a∨b	a∨b	PROPN
ejpam-2660	55	3	=	=	SYM
ejpam-2660	55	4	b	b	PROPN
ejpam-2660	55	5	,	,	PUNCT
ejpam-2660	55	6	a	a	DET
ejpam-2660	55	7	∈	∈	PROPN
ejpam-2660	55	8	a∧b	a∧b	PROPN
ejpam-2660	55	9	.	.	PUNCT
ejpam-2660	56	1	then	then	ADV
ejpam-2660	56	2	we	we	PRON
ejpam-2660	56	3	define	define	VERB
ejpam-2660	56	4	the	the	DET
ejpam-2660	56	5	relation	relation	NOUN
ejpam-2660	56	6	≤	≤	NOUN
ejpam-2660	56	7	on	on	ADP
ejpam-2660	56	8	a	a	DET
ejpam-2660	56	9	strong	strong	ADJ
ejpam-2660	56	10	∧−	∧−	NUM
ejpam-2660	56	11	hyperlattice	hyperlattice	NOUN
ejpam-2660	56	12	l	l	NOUN
ejpam-2660	56	13	;	;	PUNCT
ejpam-2660	56	14	it	it	PRON
ejpam-2660	56	15	is	be	AUX
ejpam-2660	56	16	clear	clear	ADJ
ejpam-2660	56	17	that	that	SCONJ
ejpam-2660	56	18	(	(	PUNCT
ejpam-2660	56	19	l,≤	l,≤	PROPN
ejpam-2660	56	20	)	)	PUNCT
ejpam-2660	56	21	is	be	AUX
ejpam-2660	56	22	a	a	DET
ejpam-2660	56	23	poset	poset	NOUN
ejpam-2660	56	24	.	.	PUNCT
ejpam-2660	57	1	a	a	DET
ejpam-2660	57	2	≤	≤	NUM
ejpam-2660	57	3	b	b	NUM
ejpam-2660	57	4	⇐	⇐	ADJ
ejpam-2660	57	5	⇒	⇒	NOUN
ejpam-2660	57	6	a	a	DET
ejpam-2660	57	7	∈	∈	PROPN
ejpam-2660	57	8	a	a	DET
ejpam-2660	57	9	∧	∧	PROPN
ejpam-2660	57	10	b	b	PROPN
ejpam-2660	57	11	⇐	⇐	PROPN
ejpam-2660	57	12	⇒	⇒	NOUN
ejpam-2660	57	13	a	a	DET
ejpam-2660	57	14	∨	∨	PROPN
ejpam-2660	57	15	b	b	PROPN
ejpam-2660	57	16	=	=	PROPN
ejpam-2660	57	17	b.	b.	PROPN
ejpam-2660	57	18	definition	definition	NOUN
ejpam-2660	57	19	7	7	NUM
ejpam-2660	57	20	.	.	PUNCT
ejpam-2660	58	1	let	let	VERB
ejpam-2660	58	2	l	l	NOUN
ejpam-2660	58	3	be	be	AUX
ejpam-2660	58	4	a	a	DET
ejpam-2660	58	5	∧-hyperlattice	∧-hyperlattice	NOUN
ejpam-2660	58	6	.	.	PUNCT
ejpam-2660	59	1	we	we	PRON
ejpam-2660	59	2	say	say	VERB
ejpam-2660	59	3	that	that	SCONJ
ejpam-2660	59	4	l	l	NOUN
ejpam-2660	59	5	is	be	AUX
ejpam-2660	59	6	bounded	bound	VERB
ejpam-2660	59	7	if	if	SCONJ
ejpam-2660	59	8	there	there	PRON
ejpam-2660	59	9	exist	exist	VERB
ejpam-2660	59	10	0	0	NUM
ejpam-2660	59	11	,	,	PUNCT
ejpam-2660	59	12	1	1	NUM
ejpam-2660	59	13	∈	∈	PROPN
ejpam-2660	59	14	l	l	NOUN
ejpam-2660	59	15	,	,	PUNCT
ejpam-2660	59	16	such	such	ADJ
ejpam-2660	59	17	that	that	SCONJ
ejpam-2660	59	18	0	0	NUM
ejpam-2660	59	19	≤	≤	NUM
ejpam-2660	59	20	x	x	SYM
ejpam-2660	59	21	≤	≤	NUM
ejpam-2660	59	22	1	1	NUM
ejpam-2660	59	23	,	,	PUNCT
ejpam-2660	59	24	for	for	ADP
ejpam-2660	59	25	all	all	DET
ejpam-2660	59	26	x	x	SYM
ejpam-2660	59	27	∈	∈	PROPN
ejpam-2660	59	28	l.	l.	NOUN
ejpam-2660	59	29	we	we	PRON
ejpam-2660	59	30	say	say	VERB
ejpam-2660	59	31	that	that	SCONJ
ejpam-2660	59	32	0	0	NUM
ejpam-2660	59	33	is	be	AUX
ejpam-2660	59	34	the	the	DET
ejpam-2660	59	35	least	least	ADJ
ejpam-2660	59	36	element	element	NOUN
ejpam-2660	59	37	of	of	ADP
ejpam-2660	59	38	l	l	NOUN
ejpam-2660	59	39	and	and	CCONJ
ejpam-2660	59	40	1	1	NUM
ejpam-2660	59	41	is	be	AUX
ejpam-2660	59	42	the	the	DET
ejpam-2660	59	43	greatest	great	ADJ
ejpam-2660	59	44	element	element	NOUN
ejpam-2660	59	45	of	of	ADP
ejpam-2660	59	46	l.	l.	PROPN
ejpam-2660	59	47	example	example	PROPN
ejpam-2660	59	48	8	8	NUM
ejpam-2660	59	49	.	.	PUNCT
ejpam-2660	60	1	let	let	VERB
ejpam-2660	60	2	l	l	NOUN
ejpam-2660	60	3	=	=	PUNCT
ejpam-2660	60	4	{	{	PUNCT
ejpam-2660	60	5	0	0	NUM
ejpam-2660	60	6	,	,	PUNCT
ejpam-2660	60	7	a	a	DET
ejpam-2660	60	8	,	,	PUNCT
ejpam-2660	60	9	1	1	NUM
ejpam-2660	60	10	}	}	PUNCT
ejpam-2660	60	11	,	,	PUNCT
ejpam-2660	60	12	and	and	CCONJ
ejpam-2660	60	13	define	define	VERB
ejpam-2660	60	14	∧-hyperoperation	∧-hyperoperation	NOUN
ejpam-2660	60	15	and	and	CCONJ
ejpam-2660	60	16	∨-operation	∨-operation	NOUN
ejpam-2660	60	17	on	on	ADP
ejpam-2660	60	18	l	l	NOUN
ejpam-2660	60	19	with	with	ADP
ejpam-2660	60	20	tables	table	NOUN
ejpam-2660	60	21	1	1	NUM
ejpam-2660	60	22	.	.	PUNCT
ejpam-2660	61	1	then	then	ADV
ejpam-2660	61	2	(	(	PUNCT
ejpam-2660	61	3	l,∧,∨	l,∧,∨	X
ejpam-2660	61	4	)	)	PUNCT
ejpam-2660	61	5	is	be	AUX
ejpam-2660	61	6	a	a	DET
ejpam-2660	61	7	bounded	bounded	ADJ
ejpam-2660	61	8	”	"	PUNCT
ejpam-2660	61	9	∧	∧	PROPN
ejpam-2660	61	10	”	"	PUNCT
ejpam-2660	61	11	-hyperlattice	-hyperlattice	NOUN
ejpam-2660	61	12	.	.	PUNCT
ejpam-2660	62	1	∧	∧	NOUN
ejpam-2660	62	2	0	0	PUNCT
ejpam-2660	62	3	a	a	DET
ejpam-2660	62	4	1	1	NUM
ejpam-2660	62	5	0	0	NUM
ejpam-2660	62	6	{	{	PUNCT
ejpam-2660	62	7	0	0	NUM
ejpam-2660	62	8	}	}	PUNCT
ejpam-2660	62	9	{	{	PUNCT
ejpam-2660	62	10	0	0	NUM
ejpam-2660	62	11	}	}	PUNCT
ejpam-2660	62	12	{	{	PUNCT
ejpam-2660	62	13	0	0	NUM
ejpam-2660	62	14	}	}	PUNCT
ejpam-2660	62	15	a	a	DET
ejpam-2660	62	16	{	{	PUNCT
ejpam-2660	62	17	0	0	NUM
ejpam-2660	62	18	}	}	PUNCT
ejpam-2660	62	19	{	{	PUNCT
ejpam-2660	62	20	a	a	PRON
ejpam-2660	62	21	,	,	PUNCT
ejpam-2660	62	22	0	0	NUM
ejpam-2660	62	23	}	}	PUNCT
ejpam-2660	62	24	{	{	PUNCT
ejpam-2660	62	25	a	a	PRON
ejpam-2660	62	26	,	,	PUNCT
ejpam-2660	62	27	0	0	NUM
ejpam-2660	62	28	}	}	SYM
ejpam-2660	62	29	1	1	NUM
ejpam-2660	62	30	{	{	PUNCT
ejpam-2660	62	31	0	0	NUM
ejpam-2660	62	32	}	}	PUNCT
ejpam-2660	62	33	{	{	PUNCT
ejpam-2660	62	34	a	a	PRON
ejpam-2660	62	35	,	,	PUNCT
ejpam-2660	62	36	0	0	NUM
ejpam-2660	62	37	}	}	PUNCT
ejpam-2660	62	38	l	l	NOUN
ejpam-2660	62	39	(	(	PUNCT
ejpam-2660	62	40	a	a	NOUN
ejpam-2660	62	41	)	)	PUNCT
ejpam-2660	62	42	∨	∨	NOUN
ejpam-2660	62	43	0	0	NUM
ejpam-2660	63	1	a	a	DET
ejpam-2660	63	2	1	1	NUM
ejpam-2660	63	3	0	0	NUM
ejpam-2660	63	4	0	0	NUM
ejpam-2660	63	5	a	a	DET
ejpam-2660	63	6	1	1	NUM
ejpam-2660	63	7	a	a	DET
ejpam-2660	63	8	a	a	DET
ejpam-2660	63	9	a	a	DET
ejpam-2660	63	10	1	1	NUM
ejpam-2660	63	11	1	1	NUM
ejpam-2660	63	12	1	1	NUM
ejpam-2660	63	13	1	1	NUM
ejpam-2660	63	14	1	1	NUM
ejpam-2660	63	15	(	(	PUNCT
ejpam-2660	63	16	b	b	NOUN
ejpam-2660	63	17	)	)	PUNCT
ejpam-2660	63	18	table	table	NOUN
ejpam-2660	63	19	1	1	NUM
ejpam-2660	63	20	m.	m.	NOUN
ejpam-2660	63	21	amiri	amiri	PROPN
ejpam-2660	63	22	bideshki	bideshki	PROPN
ejpam-2660	63	23	,	,	PUNCT
ejpam-2660	63	24	r.	r.	PROPN
ejpam-2660	63	25	ameri	ameri	PROPN
ejpam-2660	63	26	,	,	PUNCT
ejpam-2660	64	1	a.	a.	PROPN
ejpam-2660	64	2	borumand	borumand	PROPN
ejpam-2660	65	1	saeid	saeid	PROPN
ejpam-2660	65	2	/	/	SYM
ejpam-2660	65	3	eur	eur	PROPN
ejpam-2660	65	4	.	.	PUNCT
ejpam-2660	66	1	j.	j.	PROPN
ejpam-2660	66	2	pure	pure	PROPN
ejpam-2660	66	3	appl	appl	PROPN
ejpam-2660	66	4	.	.	PROPN
ejpam-2660	66	5	math	math	PROPN
ejpam-2660	66	6	,	,	PUNCT
ejpam-2660	66	7	11	11	NUM
ejpam-2660	66	8	(	(	PUNCT
ejpam-2660	66	9	1	1	NUM
ejpam-2660	66	10	)	)	PUNCT
ejpam-2660	66	11	(	(	PUNCT
ejpam-2660	66	12	2018	2018	NUM
ejpam-2660	66	13	)	)	PUNCT
ejpam-2660	66	14	,	,	PUNCT
ejpam-2660	66	15	169	169	NUM
ejpam-2660	66	16	-	-	SYM
ejpam-2660	66	17	188	188	NUM
ejpam-2660	66	18	172	172	NUM
ejpam-2660	66	19	proposition	proposition	NOUN
ejpam-2660	66	20	9	9	NUM
ejpam-2660	66	21	.	.	PUNCT
ejpam-2660	67	1	let	let	VERB
ejpam-2660	67	2	l	l	NOUN
ejpam-2660	67	3	be	be	AUX
ejpam-2660	67	4	a	a	DET
ejpam-2660	67	5	bounded	bounded	ADJ
ejpam-2660	67	6	strong	strong	ADJ
ejpam-2660	67	7	∧-hyperlattice	∧-hyperlattice	NOUN
ejpam-2660	67	8	.	.	PUNCT
ejpam-2660	68	1	then	then	ADV
ejpam-2660	68	2	the	the	DET
ejpam-2660	68	3	following	follow	VERB
ejpam-2660	68	4	statements	statement	NOUN
ejpam-2660	68	5	hold	hold	VERB
ejpam-2660	68	6	.	.	PUNCT
ejpam-2660	69	1	(	(	PUNCT
ejpam-2660	69	2	i	i	NOUN
ejpam-2660	69	3	)	)	PUNCT
ejpam-2660	69	4	if	if	SCONJ
ejpam-2660	69	5	a	a	DET
ejpam-2660	69	6	,	,	PUNCT
ejpam-2660	69	7	b	b	PROPN
ejpam-2660	69	8	6=	6=	NUM
ejpam-2660	69	9	1	1	NUM
ejpam-2660	69	10	,	,	PUNCT
ejpam-2660	69	11	and	and	CCONJ
ejpam-2660	69	12	a	a	DET
ejpam-2660	69	13	∨	∨	NUM
ejpam-2660	69	14	b	b	NOUN
ejpam-2660	69	15	=	=	SYM
ejpam-2660	69	16	1	1	NUM
ejpam-2660	69	17	,	,	PUNCT
ejpam-2660	69	18	then	then	ADV
ejpam-2660	69	19	a	a	PRON
ejpam-2660	69	20	,	,	PUNCT
ejpam-2660	69	21	b	b	NOUN
ejpam-2660	69	22	/∈	/∈	PUNCT
ejpam-2660	69	23	a	a	DET
ejpam-2660	69	24	∧	∧	PROPN
ejpam-2660	69	25	b	b	PROPN
ejpam-2660	69	26	;	;	PUNCT
ejpam-2660	69	27	(	(	PUNCT
ejpam-2660	69	28	ii	ii	NOUN
ejpam-2660	69	29	)	)	PUNCT
ejpam-2660	69	30	if	if	SCONJ
ejpam-2660	69	31	a	a	DET
ejpam-2660	69	32	∧	∧	PROPN
ejpam-2660	69	33	b	b	NOUN
ejpam-2660	69	34	=	=	SYM
ejpam-2660	69	35	l	l	NOUN
ejpam-2660	69	36	or	or	CCONJ
ejpam-2660	69	37	a	a	PRON
ejpam-2660	69	38	,	,	PUNCT
ejpam-2660	69	39	b	b	X
ejpam-2660	69	40	∈	∈	PROPN
ejpam-2660	69	41	a	a	DET
ejpam-2660	69	42	∧	∧	PROPN
ejpam-2660	69	43	b	b	PROPN
ejpam-2660	69	44	,	,	PUNCT
ejpam-2660	69	45	then	then	ADV
ejpam-2660	69	46	a	a	DET
ejpam-2660	69	47	=	=	SYM
ejpam-2660	69	48	b	b	NOUN
ejpam-2660	69	49	;	;	PUNCT
ejpam-2660	69	50	(	(	PUNCT
ejpam-2660	69	51	iii	iii	X
ejpam-2660	69	52	)	)	PUNCT
ejpam-2660	69	53	∀a	∀a	NOUN
ejpam-2660	69	54	∈	∈	PROPN
ejpam-2660	69	55	l	l	NOUN
ejpam-2660	69	56	,	,	PUNCT
ejpam-2660	69	57	a	a	DET
ejpam-2660	69	58	∈	∈	PROPN
ejpam-2660	69	59	a	a	DET
ejpam-2660	69	60	∧	∧	PROPN
ejpam-2660	69	61	1	1	NUM
ejpam-2660	69	62	and	and	CCONJ
ejpam-2660	69	63	0	0	NUM
ejpam-2660	69	64	∈	∈	NOUN
ejpam-2660	69	65	x	x	X
ejpam-2660	69	66	∧	∧	NOUN
ejpam-2660	69	67	0	0	NUM
ejpam-2660	69	68	.	.	PUNCT
ejpam-2660	70	1	proof	proof	NOUN
ejpam-2660	70	2	.	.	PUNCT
ejpam-2660	71	1	(	(	PUNCT
ejpam-2660	71	2	i	i	NOUN
ejpam-2660	71	3	)	)	PUNCT
ejpam-2660	71	4	let	let	VERB
ejpam-2660	71	5	a	a	DET
ejpam-2660	71	6	or	or	CCONJ
ejpam-2660	71	7	b	b	NOUN
ejpam-2660	71	8	∈	∈	PROPN
ejpam-2660	71	9	a∧b	a∧b	PROPN
ejpam-2660	71	10	.	.	PUNCT
ejpam-2660	72	1	if	if	SCONJ
ejpam-2660	72	2	a	a	DET
ejpam-2660	72	3	∈	∈	PROPN
ejpam-2660	72	4	a∧b	a∧b	NOUN
ejpam-2660	72	5	,	,	PUNCT
ejpam-2660	72	6	by	by	ADP
ejpam-2660	72	7	remark	remark	NOUN
ejpam-2660	72	8	6	6	NUM
ejpam-2660	72	9	,	,	PUNCT
ejpam-2660	72	10	a∨b	a∨b	NOUN
ejpam-2660	72	11	=	=	SYM
ejpam-2660	72	12	b	b	PROPN
ejpam-2660	72	13	,	,	PUNCT
ejpam-2660	72	14	also	also	ADV
ejpam-2660	72	15	we	we	PRON
ejpam-2660	72	16	have	have	VERB
ejpam-2660	72	17	a∨b	a∨b	NOUN
ejpam-2660	72	18	=	=	NOUN
ejpam-2660	72	19	1	1	X
ejpam-2660	72	20	.	.	PUNCT
ejpam-2660	73	1	so	so	ADV
ejpam-2660	73	2	b	b	X
ejpam-2660	73	3	=	=	SYM
ejpam-2660	73	4	1	1	NUM
ejpam-2660	73	5	,	,	PUNCT
ejpam-2660	73	6	which	which	PRON
ejpam-2660	73	7	is	be	AUX
ejpam-2660	73	8	a	a	DET
ejpam-2660	73	9	contradiction	contradiction	NOUN
ejpam-2660	73	10	.	.	PUNCT
ejpam-2660	74	1	if	if	SCONJ
ejpam-2660	74	2	b	b	X
ejpam-2660	74	3	∈	∈	PROPN
ejpam-2660	74	4	a	a	DET
ejpam-2660	74	5	∧	∧	PROPN
ejpam-2660	74	6	b	b	PROPN
ejpam-2660	74	7	,	,	PUNCT
ejpam-2660	74	8	similarly	similarly	ADV
ejpam-2660	74	9	is	be	AUX
ejpam-2660	74	10	proved	prove	VERB
ejpam-2660	74	11	that	that	SCONJ
ejpam-2660	74	12	a	a	DET
ejpam-2660	74	13	=	=	SYM
ejpam-2660	74	14	1	1	NUM
ejpam-2660	75	1	and	and	CCONJ
ejpam-2660	75	2	it	it	PRON
ejpam-2660	75	3	is	be	AUX
ejpam-2660	75	4	a	a	DET
ejpam-2660	75	5	contradiction	contradiction	NOUN
ejpam-2660	75	6	.	.	PUNCT
ejpam-2660	76	1	(	(	PUNCT
ejpam-2660	76	2	ii	ii	NOUN
ejpam-2660	76	3	):	):	PUNCT
ejpam-2660	76	4	let	let	VERB
ejpam-2660	76	5	a	a	DET
ejpam-2660	76	6	∧	∧	PROPN
ejpam-2660	76	7	b	b	NOUN
ejpam-2660	76	8	=	=	SYM
ejpam-2660	76	9	l.	l.	PROPN
ejpam-2660	76	10	then	then	ADV
ejpam-2660	76	11	a	a	PRON
ejpam-2660	76	12	,	,	PUNCT
ejpam-2660	76	13	b	b	X
ejpam-2660	76	14	∈	∈	PROPN
ejpam-2660	76	15	a	a	DET
ejpam-2660	76	16	∧	∧	PROPN
ejpam-2660	76	17	b.	b.	NOUN
ejpam-2660	76	18	so	so	ADV
ejpam-2660	76	19	by	by	ADP
ejpam-2660	76	20	remark	remark	NOUN
ejpam-2660	76	21	6	6	NUM
ejpam-2660	76	22	and	and	CCONJ
ejpam-2660	76	23	a	a	DET
ejpam-2660	76	24	∈	∈	PROPN
ejpam-2660	76	25	a	a	DET
ejpam-2660	76	26	∧	∧	PROPN
ejpam-2660	76	27	b	b	PROPN
ejpam-2660	76	28	,	,	PUNCT
ejpam-2660	76	29	we	we	PRON
ejpam-2660	76	30	have	have	VERB
ejpam-2660	76	31	a	a	DET
ejpam-2660	76	32	∨	∨	NUM
ejpam-2660	76	33	b	b	X
ejpam-2660	76	34	=	=	PROPN
ejpam-2660	76	35	b.	b.	PROPN
ejpam-2660	76	36	also	also	ADV
ejpam-2660	76	37	by	by	ADP
ejpam-2660	76	38	b	b	PROPN
ejpam-2660	76	39	∈	∈	PROPN
ejpam-2660	76	40	a	a	DET
ejpam-2660	76	41	∧	∧	PROPN
ejpam-2660	76	42	b	b	PROPN
ejpam-2660	76	43	,	,	PUNCT
ejpam-2660	76	44	we	we	PRON
ejpam-2660	76	45	conclude	conclude	VERB
ejpam-2660	76	46	a	a	DET
ejpam-2660	76	47	∨	∨	PROPN
ejpam-2660	76	48	b	b	NOUN
ejpam-2660	76	49	=	=	NOUN
ejpam-2660	76	50	a.	a.	NOUN
ejpam-2660	77	1	so	so	ADV
ejpam-2660	77	2	a	a	DET
ejpam-2660	77	3	=	=	X
ejpam-2660	77	4	b.	b.	PROPN
ejpam-2660	77	5	(	(	PUNCT
ejpam-2660	77	6	iii	iii	NOUN
ejpam-2660	77	7	):	):	PUNCT
ejpam-2660	77	8	∀a	∀a	NOUN
ejpam-2660	77	9	∈	∈	PROPN
ejpam-2660	77	10	l	l	NOUN
ejpam-2660	77	11	,	,	PUNCT
ejpam-2660	77	12	we	we	PRON
ejpam-2660	77	13	have	have	VERB
ejpam-2660	77	14	0	0	NUM
ejpam-2660	77	15	≤	≤	NOUN
ejpam-2660	77	16	a	a	DET
ejpam-2660	77	17	≤	≤	NUM
ejpam-2660	77	18	1	1	NUM
ejpam-2660	77	19	.	.	PUNCT
ejpam-2660	78	1	so	so	ADV
ejpam-2660	78	2	by	by	ADP
ejpam-2660	78	3	remark	remark	NOUN
ejpam-2660	78	4	6	6	NUM
ejpam-2660	78	5	,	,	PUNCT
ejpam-2660	78	6	proof	proof	NOUN
ejpam-2660	78	7	is	be	AUX
ejpam-2660	78	8	obvious	obvious	ADJ
ejpam-2660	78	9	.	.	PUNCT
ejpam-2660	79	1	definition	definition	NOUN
ejpam-2660	79	2	10	10	NUM
ejpam-2660	79	3	.	.	PUNCT
ejpam-2660	80	1	let	let	VERB
ejpam-2660	80	2	l	l	NOUN
ejpam-2660	80	3	be	be	AUX
ejpam-2660	80	4	a	a	DET
ejpam-2660	80	5	∧−	∧−	NUM
ejpam-2660	80	6	hyperlattice	hyperlattice	NOUN
ejpam-2660	80	7	.	.	PUNCT
ejpam-2660	81	1	then	then	ADV
ejpam-2660	81	2	:	:	PUNCT
ejpam-2660	81	3	(	(	PUNCT
ejpam-2660	81	4	i	i	NOUN
ejpam-2660	81	5	)	)	PUNCT
ejpam-2660	81	6	l	l	NOUN
ejpam-2660	81	7	is	be	AUX
ejpam-2660	81	8	called	call	VERB
ejpam-2660	81	9	distributive	distributive	ADJ
ejpam-2660	81	10	if	if	SCONJ
ejpam-2660	81	11	a	a	DET
ejpam-2660	81	12	∨	∨	NOUN
ejpam-2660	81	13	(	(	PUNCT
ejpam-2660	81	14	b	b	PROPN
ejpam-2660	81	15	∧	∧	PROPN
ejpam-2660	81	16	c	c	NOUN
ejpam-2660	81	17	)	)	PUNCT
ejpam-2660	81	18	=	=	NOUN
ejpam-2660	81	19	(	(	PUNCT
ejpam-2660	81	20	a	a	DET
ejpam-2660	81	21	∨	∨	NUM
ejpam-2660	81	22	b	b	NOUN
ejpam-2660	81	23	)	)	PUNCT
ejpam-2660	81	24	∧	∧	NOUN
ejpam-2660	81	25	(	(	PUNCT
ejpam-2660	81	26	a	a	DET
ejpam-2660	81	27	∨	∨	NUM
ejpam-2660	81	28	c	c	NOUN
ejpam-2660	81	29	)	)	PUNCT
ejpam-2660	81	30	,	,	PUNCT
ejpam-2660	81	31	for	for	ADP
ejpam-2660	81	32	all	all	DET
ejpam-2660	81	33	a	a	DET
ejpam-2660	81	34	,	,	PUNCT
ejpam-2660	81	35	b	b	NOUN
ejpam-2660	81	36	,	,	PUNCT
ejpam-2660	81	37	c	c	PROPN
ejpam-2660	81	38	∈	∈	PROPN
ejpam-2660	81	39	l.	l.	PROPN
ejpam-2660	81	40	(	(	PUNCT
ejpam-2660	81	41	ii	ii	PROPN
ejpam-2660	81	42	)	)	PUNCT
ejpam-2660	81	43	l	l	NOUN
ejpam-2660	81	44	is	be	AUX
ejpam-2660	81	45	called	call	VERB
ejpam-2660	81	46	dual	dual	ADV
ejpam-2660	81	47	distributive	distributive	ADJ
ejpam-2660	81	48	if	if	SCONJ
ejpam-2660	81	49	a	a	DET
ejpam-2660	81	50	∧	∧	PROPN
ejpam-2660	81	51	(	(	PUNCT
ejpam-2660	81	52	b	b	PROPN
ejpam-2660	81	53	∨	∨	NUM
ejpam-2660	81	54	c	c	NOUN
ejpam-2660	81	55	)	)	PUNCT
ejpam-2660	82	1	=	=	NOUN
ejpam-2660	82	2	(	(	PUNCT
ejpam-2660	82	3	a	a	DET
ejpam-2660	82	4	∧	∧	PROPN
ejpam-2660	82	5	b	b	PROPN
ejpam-2660	82	6	)	)	PUNCT
ejpam-2660	82	7	∨	∨	NOUN
ejpam-2660	82	8	(	(	PUNCT
ejpam-2660	82	9	a	a	DET
ejpam-2660	82	10	∧	∧	PROPN
ejpam-2660	82	11	c	c	NOUN
ejpam-2660	82	12	)	)	PUNCT
ejpam-2660	82	13	,	,	PUNCT
ejpam-2660	82	14	for	for	ADP
ejpam-2660	82	15	all	all	DET
ejpam-2660	82	16	a	a	DET
ejpam-2660	82	17	,	,	PUNCT
ejpam-2660	82	18	b	b	NOUN
ejpam-2660	82	19	,	,	PUNCT
ejpam-2660	82	20	c	c	PROPN
ejpam-2660	82	21	∈	∈	PROPN
ejpam-2660	82	22	l.	l.	PROPN
ejpam-2660	82	23	(	(	PUNCT
ejpam-2660	82	24	iii	iii	NOUN
ejpam-2660	82	25	)	)	PUNCT
ejpam-2660	82	26	l	l	NOUN
ejpam-2660	82	27	is	be	AUX
ejpam-2660	82	28	called	call	VERB
ejpam-2660	82	29	strongly	strongly	ADV
ejpam-2660	82	30	distributive	distributive	ADJ
ejpam-2660	82	31	if	if	SCONJ
ejpam-2660	82	32	l	l	NOUN
ejpam-2660	82	33	is	be	AUX
ejpam-2660	82	34	both	both	PRON
ejpam-2660	82	35	distributive	distributive	ADJ
ejpam-2660	82	36	and	and	CCONJ
ejpam-2660	82	37	dual	dual	ADJ
ejpam-2660	82	38	distributive	distributive	ADJ
ejpam-2660	82	39	.	.	PUNCT
ejpam-2660	82	40	example	example	NOUN
ejpam-2660	83	1	11	11	NUM
ejpam-2660	83	2	.	.	PUNCT
ejpam-2660	84	1	let	let	VERB
ejpam-2660	84	2	l	l	NOUN
ejpam-2660	84	3	=	=	PUNCT
ejpam-2660	84	4	{	{	PUNCT
ejpam-2660	84	5	a	a	PRON
ejpam-2660	84	6	,	,	PUNCT
ejpam-2660	84	7	b	b	NOUN
ejpam-2660	84	8	}	}	PUNCT
ejpam-2660	84	9	.	.	PUNCT
ejpam-2660	84	10	”	"	PUNCT
ejpam-2660	85	1	∧	∧	NOUN
ejpam-2660	85	2	”	"	PUNCT
ejpam-2660	85	3	hyperoperation	hyperoperation	NOUN
ejpam-2660	85	4	and	and	CCONJ
ejpam-2660	85	5	”	"	PUNCT
ejpam-2660	85	6	∨	∨	NUM
ejpam-2660	85	7	”	"	PUNCT
ejpam-2660	85	8	operation	operation	NOUN
ejpam-2660	85	9	are	be	AUX
ejpam-2660	85	10	given	give	VERB
ejpam-2660	85	11	with	with	ADP
ejpam-2660	85	12	tables	table	NOUN
ejpam-2660	85	13	2	2	NUM
ejpam-2660	85	14	.	.	PUNCT
ejpam-2660	86	1	then	then	ADV
ejpam-2660	86	2	(	(	PUNCT
ejpam-2660	86	3	l,∧,∨	l,∧,∨	X
ejpam-2660	86	4	)	)	PUNCT
ejpam-2660	86	5	is	be	AUX
ejpam-2660	86	6	a	a	DET
ejpam-2660	86	7	distributive	distributive	ADJ
ejpam-2660	86	8	”	"	PUNCT
ejpam-2660	86	9	∧	∧	NOUN
ejpam-2660	86	10	”	"	PUNCT
ejpam-2660	86	11	-hyperlattice	-hyperlattice	NOUN
ejpam-2660	86	12	,	,	PUNCT
ejpam-2660	86	13	but	but	CCONJ
ejpam-2660	86	14	since	since	SCONJ
ejpam-2660	86	15	b∧	b∧	NOUN
ejpam-2660	86	16	(	(	PUNCT
ejpam-2660	86	17	a∨a	a∨a	PROPN
ejpam-2660	86	18	)	)	PUNCT
ejpam-2660	86	19	=	=	PRON
ejpam-2660	87	1	{	{	PUNCT
ejpam-2660	87	2	a	a	NOUN
ejpam-2660	87	3	}	}	PUNCT
ejpam-2660	87	4	,	,	PUNCT
ejpam-2660	87	5	and	and	CCONJ
ejpam-2660	87	6	(	(	PUNCT
ejpam-2660	87	7	b	b	X
ejpam-2660	87	8	∧	∧	PROPN
ejpam-2660	87	9	a	a	PRON
ejpam-2660	87	10	)	)	PUNCT
ejpam-2660	87	11	∨	∨	NOUN
ejpam-2660	87	12	(	(	PUNCT
ejpam-2660	87	13	b	b	PROPN
ejpam-2660	87	14	∧	∧	PROPN
ejpam-2660	87	15	a	a	NOUN
ejpam-2660	87	16	)	)	PUNCT
ejpam-2660	87	17	=	=	PRON
ejpam-2660	87	18	{	{	PUNCT
ejpam-2660	87	19	a	a	DET
ejpam-2660	87	20	,	,	PUNCT
ejpam-2660	87	21	b	b	NOUN
ejpam-2660	87	22	}	}	PUNCT
ejpam-2660	87	23	,	,	PUNCT
ejpam-2660	87	24	l	l	NOUN
ejpam-2660	87	25	is	be	AUX
ejpam-2660	87	26	not	not	PART
ejpam-2660	87	27	dual	dual	ADV
ejpam-2660	87	28	distributive	distributive	ADJ
ejpam-2660	87	29	.	.	PUNCT
ejpam-2660	88	1	∧	∧	NOUN
ejpam-2660	88	2	a	a	DET
ejpam-2660	88	3	b	b	NOUN
ejpam-2660	88	4	a	a	PRON
ejpam-2660	88	5	{	{	PUNCT
ejpam-2660	88	6	a	a	PROPN
ejpam-2660	88	7	,	,	PUNCT
ejpam-2660	88	8	b	b	NOUN
ejpam-2660	88	9	}	}	PUNCT
ejpam-2660	88	10	{	{	PUNCT
ejpam-2660	88	11	a	a	PRON
ejpam-2660	88	12	}	}	PUNCT
ejpam-2660	88	13	b	b	PROPN
ejpam-2660	88	14	{	{	PUNCT
ejpam-2660	88	15	a	a	NOUN
ejpam-2660	88	16	}	}	PUNCT
ejpam-2660	88	17	{	{	PUNCT
ejpam-2660	88	18	b	b	NOUN
ejpam-2660	88	19	}	}	PUNCT
ejpam-2660	88	20	(	(	PUNCT
ejpam-2660	88	21	a	a	X
ejpam-2660	88	22	)	)	PUNCT
ejpam-2660	88	23	∨	∨	NOUN
ejpam-2660	88	24	a	a	DET
ejpam-2660	88	25	b	b	NOUN
ejpam-2660	88	26	a	a	DET
ejpam-2660	88	27	a	a	DET
ejpam-2660	88	28	b	b	PROPN
ejpam-2660	88	29	b	b	PROPN
ejpam-2660	88	30	b	b	PROPN
ejpam-2660	88	31	b	b	PROPN
ejpam-2660	88	32	(	(	PUNCT
ejpam-2660	88	33	b	b	NOUN
ejpam-2660	88	34	)	)	PUNCT
ejpam-2660	88	35	table	table	NOUN
ejpam-2660	88	36	2	2	NUM
ejpam-2660	88	37	:	:	PUNCT
ejpam-2660	88	38	example	example	NOUN
ejpam-2660	88	39	12	12	NUM
ejpam-2660	88	40	.	.	PUNCT
ejpam-2660	89	1	let	let	VERB
ejpam-2660	89	2	l	l	NOUN
ejpam-2660	89	3	=	=	PUNCT
ejpam-2660	89	4	{	{	PUNCT
ejpam-2660	89	5	a	a	PRON
ejpam-2660	89	6	,	,	PUNCT
ejpam-2660	89	7	b	b	NOUN
ejpam-2660	89	8	}	}	PUNCT
ejpam-2660	89	9	.	.	PUNCT
ejpam-2660	89	10	”	"	PUNCT
ejpam-2660	90	1	∧	∧	NOUN
ejpam-2660	90	2	”	"	PUNCT
ejpam-2660	90	3	hyperoperation	hyperoperation	NOUN
ejpam-2660	90	4	and	and	CCONJ
ejpam-2660	90	5	”	"	PUNCT
ejpam-2660	90	6	∨	∨	NUM
ejpam-2660	90	7	”	"	PUNCT
ejpam-2660	90	8	operation	operation	NOUN
ejpam-2660	90	9	are	be	AUX
ejpam-2660	90	10	given	give	VERB
ejpam-2660	90	11	with	with	ADP
ejpam-2660	90	12	tables	table	NOUN
ejpam-2660	90	13	3	3	NUM
ejpam-2660	90	14	.	.	PUNCT
ejpam-2660	91	1	then	then	ADV
ejpam-2660	91	2	(	(	PUNCT
ejpam-2660	91	3	l,∧,∨	l,∧,∨	X
ejpam-2660	91	4	)	)	PUNCT
ejpam-2660	91	5	is	be	AUX
ejpam-2660	91	6	a	a	DET
ejpam-2660	91	7	dual	dual	ADJ
ejpam-2660	91	8	distributive	distributive	ADJ
ejpam-2660	91	9	∧-hyperlattice	∧-hyperlattice	NOUN
ejpam-2660	91	10	,	,	PUNCT
ejpam-2660	91	11	but	but	CCONJ
ejpam-2660	91	12	since	since	SCONJ
ejpam-2660	91	13	b	b	PROPN
ejpam-2660	91	14	∨	∨	X
ejpam-2660	91	15	(	(	PUNCT
ejpam-2660	91	16	a	a	DET
ejpam-2660	91	17	∧	∧	PROPN
ejpam-2660	91	18	a	a	NOUN
ejpam-2660	91	19	)	)	PUNCT
ejpam-2660	91	20	6=	6=	ADP
ejpam-2660	91	21	(	(	PUNCT
ejpam-2660	91	22	b	b	PROPN
ejpam-2660	91	23	∨	∨	NUM
ejpam-2660	91	24	a	a	PRON
ejpam-2660	91	25	)	)	PUNCT
ejpam-2660	91	26	∧	∧	PROPN
ejpam-2660	91	27	(	(	PUNCT
ejpam-2660	91	28	b	b	PROPN
ejpam-2660	91	29	∨	∨	NUM
ejpam-2660	91	30	a	a	PRON
ejpam-2660	91	31	)	)	PUNCT
ejpam-2660	91	32	,	,	PUNCT
ejpam-2660	91	33	l	l	NOUN
ejpam-2660	91	34	is	be	AUX
ejpam-2660	91	35	not	not	PART
ejpam-2660	91	36	distributive	distributive	ADJ
ejpam-2660	91	37	.	.	PUNCT
ejpam-2660	92	1	∧	∧	NOUN
ejpam-2660	92	2	a	a	DET
ejpam-2660	92	3	b	b	NOUN
ejpam-2660	92	4	a	a	PRON
ejpam-2660	92	5	{	{	PUNCT
ejpam-2660	92	6	a	a	NOUN
ejpam-2660	92	7	}	}	PUNCT
ejpam-2660	92	8	{	{	PUNCT
ejpam-2660	92	9	a	a	PRON
ejpam-2660	92	10	}	}	PUNCT
ejpam-2660	92	11	b	b	PROPN
ejpam-2660	92	12	{	{	PUNCT
ejpam-2660	92	13	a	a	NOUN
ejpam-2660	92	14	}	}	PUNCT
ejpam-2660	92	15	{	{	PUNCT
ejpam-2660	92	16	a	a	PRON
ejpam-2660	92	17	,	,	PUNCT
ejpam-2660	92	18	b	b	NOUN
ejpam-2660	92	19	}	}	PUNCT
ejpam-2660	92	20	(	(	PUNCT
ejpam-2660	92	21	a	a	X
ejpam-2660	92	22	)	)	PUNCT
ejpam-2660	92	23	∨	∨	NOUN
ejpam-2660	92	24	a	a	DET
ejpam-2660	92	25	b	b	NOUN
ejpam-2660	92	26	a	a	DET
ejpam-2660	92	27	a	a	DET
ejpam-2660	92	28	b	b	PROPN
ejpam-2660	92	29	b	b	PROPN
ejpam-2660	92	30	b	b	PROPN
ejpam-2660	92	31	b	b	PROPN
ejpam-2660	92	32	(	(	PUNCT
ejpam-2660	92	33	b	b	NOUN
ejpam-2660	92	34	)	)	PUNCT
ejpam-2660	92	35	table	table	NOUN
ejpam-2660	92	36	3	3	NUM
ejpam-2660	92	37	m.	m.	NOUN
ejpam-2660	92	38	amiri	amiri	PROPN
ejpam-2660	92	39	bideshki	bideshki	PROPN
ejpam-2660	92	40	,	,	PUNCT
ejpam-2660	92	41	r.	r.	PROPN
ejpam-2660	92	42	ameri	ameri	PROPN
ejpam-2660	92	43	,	,	PUNCT
ejpam-2660	92	44	a.	a.	PROPN
ejpam-2660	92	45	borumand	borumand	PROPN
ejpam-2660	92	46	saeid	saeid	PROPN
ejpam-2660	92	47	/	/	SYM
ejpam-2660	92	48	eur	eur	PROPN
ejpam-2660	92	49	.	.	PUNCT
ejpam-2660	93	1	j.	j.	PROPN
ejpam-2660	93	2	pure	pure	PROPN
ejpam-2660	93	3	appl	appl	PROPN
ejpam-2660	93	4	.	.	PROPN
ejpam-2660	93	5	math	math	PROPN
ejpam-2660	93	6	,	,	PUNCT
ejpam-2660	93	7	11	11	NUM
ejpam-2660	93	8	(	(	PUNCT
ejpam-2660	93	9	1	1	NUM
ejpam-2660	93	10	)	)	PUNCT
ejpam-2660	93	11	(	(	PUNCT
ejpam-2660	93	12	2018	2018	NUM
ejpam-2660	93	13	)	)	PUNCT
ejpam-2660	93	14	,	,	PUNCT
ejpam-2660	93	15	169	169	NUM
ejpam-2660	93	16	-	-	SYM
ejpam-2660	93	17	188	188	NUM
ejpam-2660	93	18	173	173	NUM
ejpam-2660	93	19	∧	∧	PROPN
ejpam-2660	93	20	a	a	DET
ejpam-2660	93	21	b	b	NOUN
ejpam-2660	93	22	a	a	DET
ejpam-2660	93	23	{	{	PUNCT
ejpam-2660	93	24	a	a	PROPN
ejpam-2660	93	25	,	,	PUNCT
ejpam-2660	93	26	b	b	NOUN
ejpam-2660	93	27	}	}	PUNCT
ejpam-2660	93	28	{	{	PUNCT
ejpam-2660	93	29	a	a	PRON
ejpam-2660	93	30	,	,	PUNCT
ejpam-2660	93	31	b	b	NOUN
ejpam-2660	93	32	}	}	PUNCT
ejpam-2660	93	33	b	b	PROPN
ejpam-2660	93	34	{	{	PUNCT
ejpam-2660	93	35	a	a	PROPN
ejpam-2660	93	36	,	,	PUNCT
ejpam-2660	93	37	b	b	NOUN
ejpam-2660	93	38	}	}	PUNCT
ejpam-2660	93	39	{	{	PUNCT
ejpam-2660	93	40	b	b	NOUN
ejpam-2660	93	41	}	}	PUNCT
ejpam-2660	93	42	(	(	PUNCT
ejpam-2660	93	43	a	a	X
ejpam-2660	93	44	)	)	PUNCT
ejpam-2660	93	45	∨	∨	NOUN
ejpam-2660	93	46	a	a	DET
ejpam-2660	93	47	b	b	NOUN
ejpam-2660	93	48	a	a	DET
ejpam-2660	93	49	a	a	DET
ejpam-2660	93	50	b	b	PROPN
ejpam-2660	93	51	b	b	PROPN
ejpam-2660	93	52	b	b	PROPN
ejpam-2660	93	53	b	b	PROPN
ejpam-2660	93	54	(	(	PUNCT
ejpam-2660	93	55	b	b	NOUN
ejpam-2660	93	56	)	)	PUNCT
ejpam-2660	93	57	table	table	NOUN
ejpam-2660	93	58	4	4	NUM
ejpam-2660	93	59	example	example	NOUN
ejpam-2660	93	60	13	13	NUM
ejpam-2660	93	61	.	.	PUNCT
ejpam-2660	94	1	let	let	VERB
ejpam-2660	94	2	l	l	NOUN
ejpam-2660	94	3	=	=	PUNCT
ejpam-2660	94	4	{	{	PUNCT
ejpam-2660	94	5	a	a	PRON
ejpam-2660	94	6	,	,	PUNCT
ejpam-2660	94	7	b	b	NOUN
ejpam-2660	94	8	}	}	PUNCT
ejpam-2660	94	9	.	.	PUNCT
ejpam-2660	94	10	”	"	PUNCT
ejpam-2660	95	1	∧	∧	NOUN
ejpam-2660	95	2	”	"	PUNCT
ejpam-2660	95	3	hyperoperation	hyperoperation	NOUN
ejpam-2660	95	4	and	and	CCONJ
ejpam-2660	95	5	”	"	PUNCT
ejpam-2660	95	6	∨	∨	NUM
ejpam-2660	95	7	”	"	PUNCT
ejpam-2660	95	8	operation	operation	NOUN
ejpam-2660	95	9	are	be	AUX
ejpam-2660	95	10	given	give	VERB
ejpam-2660	95	11	with	with	ADP
ejpam-2660	95	12	tables	table	NOUN
ejpam-2660	95	13	4	4	NUM
ejpam-2660	95	14	,	,	PUNCT
ejpam-2660	95	15	then	then	ADV
ejpam-2660	95	16	(	(	PUNCT
ejpam-2660	95	17	l,∧,∨	l,∧,∨	X
ejpam-2660	95	18	)	)	PUNCT
ejpam-2660	95	19	is	be	AUX
ejpam-2660	95	20	a	a	DET
ejpam-2660	95	21	strongly	strongly	ADV
ejpam-2660	95	22	distributive	distributive	ADJ
ejpam-2660	95	23	”	"	PUNCT
ejpam-2660	95	24	∧	∧	NOUN
ejpam-2660	95	25	”	"	PUNCT
ejpam-2660	95	26	-hyperlattice	-hyperlattice	NOUN
ejpam-2660	95	27	.	.	PUNCT
ejpam-2660	96	1	proposition	proposition	NOUN
ejpam-2660	96	2	14	14	NUM
ejpam-2660	96	3	.	.	PUNCT
ejpam-2660	97	1	if	if	SCONJ
ejpam-2660	97	2	l	l	NOUN
ejpam-2660	97	3	is	be	AUX
ejpam-2660	97	4	distributive	distributive	ADJ
ejpam-2660	97	5	,	,	PUNCT
ejpam-2660	97	6	then	then	ADV
ejpam-2660	97	7	there	there	PRON
ejpam-2660	97	8	is	be	VERB
ejpam-2660	97	9	not	not	PART
ejpam-2660	97	10	x	x	SYM
ejpam-2660	97	11	∈	∈	PROPN
ejpam-2660	97	12	a	a	DET
ejpam-2660	97	13	∧	∧	PROPN
ejpam-2660	97	14	a	a	NOUN
ejpam-2660	97	15	,	,	PUNCT
ejpam-2660	97	16	such	such	ADJ
ejpam-2660	97	17	that	that	SCONJ
ejpam-2660	97	18	x	x	PART
ejpam-2660	97	19	�	�	PROPN
ejpam-2660	97	20	a	a	X
ejpam-2660	97	21	,	,	PUNCT
ejpam-2660	97	22	for	for	ADP
ejpam-2660	97	23	all	all	DET
ejpam-2660	97	24	a	a	DET
ejpam-2660	97	25	∈	∈	NOUN
ejpam-2660	97	26	l.	l.	NOUN
ejpam-2660	97	27	proof	proof	NOUN
ejpam-2660	97	28	.	.	PUNCT
ejpam-2660	98	1	suppose	suppose	VERB
ejpam-2660	98	2	that	that	SCONJ
ejpam-2660	98	3	there	there	PRON
ejpam-2660	98	4	exists	exist	VERB
ejpam-2660	98	5	x	x	X
ejpam-2660	98	6	∈	∈	PROPN
ejpam-2660	98	7	a∧	a∧	NOUN
ejpam-2660	98	8	a	a	DET
ejpam-2660	98	9	such	such	ADJ
ejpam-2660	98	10	that	that	SCONJ
ejpam-2660	98	11	x	x	SYM
ejpam-2660	98	12	�	�	PROPN
ejpam-2660	98	13	a.	a.	NOUN
ejpam-2660	99	1	so	so	ADV
ejpam-2660	99	2	we	we	PRON
ejpam-2660	99	3	have	have	VERB
ejpam-2660	99	4	a∨	a∨	PROPN
ejpam-2660	99	5	x	x	X
ejpam-2660	99	6	=	=	PUNCT
ejpam-2660	99	7	a	a	NOUN
ejpam-2660	99	8	,	,	PUNCT
ejpam-2660	99	9	and	and	CCONJ
ejpam-2660	99	10	since	since	SCONJ
ejpam-2660	99	11	l	l	NOUN
ejpam-2660	99	12	is	be	AUX
ejpam-2660	99	13	distributive	distributive	ADJ
ejpam-2660	99	14	,	,	PUNCT
ejpam-2660	99	15	we	we	PRON
ejpam-2660	99	16	have	have	VERB
ejpam-2660	99	17	a	a	DET
ejpam-2660	99	18	∨	∨	NOUN
ejpam-2660	99	19	(	(	PUNCT
ejpam-2660	99	20	a	a	DET
ejpam-2660	99	21	∧	∧	PROPN
ejpam-2660	99	22	x	x	NOUN
ejpam-2660	99	23	)	)	PUNCT
ejpam-2660	100	1	=	=	SYM
ejpam-2660	100	2	(	(	PUNCT
ejpam-2660	100	3	a	a	DET
ejpam-2660	100	4	∨	∨	NOUN
ejpam-2660	100	5	a	a	DET
ejpam-2660	100	6	)	)	PUNCT
ejpam-2660	100	7	∧	∧	PROPN
ejpam-2660	100	8	(	(	PUNCT
ejpam-2660	100	9	a	a	DET
ejpam-2660	100	10	∨	∨	NUM
ejpam-2660	100	11	x	x	X
ejpam-2660	100	12	)	)	PUNCT
ejpam-2660	100	13	=	=	PUNCT
ejpam-2660	100	14	a	a	DET
ejpam-2660	100	15	∧	∧	PROPN
ejpam-2660	100	16	a.	a.	NOUN
ejpam-2660	100	17	since	since	SCONJ
ejpam-2660	100	18	x	x	PROPN
ejpam-2660	100	19	∈	∈	PROPN
ejpam-2660	100	20	a	a	DET
ejpam-2660	100	21	∧	∧	PROPN
ejpam-2660	100	22	a	a	PROPN
ejpam-2660	100	23	,	,	PUNCT
ejpam-2660	100	24	there	there	PRON
ejpam-2660	100	25	exists	exist	VERB
ejpam-2660	100	26	t	t	PROPN
ejpam-2660	100	27	∈	∈	PROPN
ejpam-2660	100	28	a	a	DET
ejpam-2660	100	29	∧	∧	PROPN
ejpam-2660	100	30	x	x	NOUN
ejpam-2660	100	31	,	,	PUNCT
ejpam-2660	100	32	such	such	ADJ
ejpam-2660	100	33	that	that	SCONJ
ejpam-2660	100	34	a	a	DET
ejpam-2660	100	35	∨	∨	NOUN
ejpam-2660	100	36	t	t	NOUN
ejpam-2660	100	37	=	=	PUNCT
ejpam-2660	101	1	x.	x.	NOUN
ejpam-2660	101	2	we	we	PRON
ejpam-2660	101	3	know	know	VERB
ejpam-2660	101	4	that	that	SCONJ
ejpam-2660	101	5	a	a	DET
ejpam-2660	101	6	≤	≤	NOUN
ejpam-2660	101	7	a	a	DET
ejpam-2660	101	8	∨	∨	NOUN
ejpam-2660	101	9	t	t	NOUN
ejpam-2660	101	10	and	and	CCONJ
ejpam-2660	101	11	it	it	PRON
ejpam-2660	101	12	implies	imply	VERB
ejpam-2660	101	13	that	that	SCONJ
ejpam-2660	101	14	a	a	DET
ejpam-2660	101	15	≤	≤	NUM
ejpam-2660	101	16	x	x	NOUN
ejpam-2660	101	17	,	,	PUNCT
ejpam-2660	101	18	which	which	PRON
ejpam-2660	101	19	is	be	AUX
ejpam-2660	101	20	a	a	DET
ejpam-2660	101	21	contradiction	contradiction	NOUN
ejpam-2660	101	22	.	.	PUNCT
ejpam-2660	102	1	lemma	lemma	PROPN
ejpam-2660	102	2	15	15	NUM
ejpam-2660	102	3	.	.	PUNCT
ejpam-2660	103	1	for	for	ADP
ejpam-2660	103	2	all	all	DET
ejpam-2660	103	3	a	a	DET
ejpam-2660	103	4	,	,	PUNCT
ejpam-2660	103	5	b	b	PROPN
ejpam-2660	103	6	∈	∈	PROPN
ejpam-2660	103	7	l	l	NOUN
ejpam-2660	103	8	,	,	PUNCT
ejpam-2660	103	9	there	there	PRON
ejpam-2660	103	10	exist	exist	VERB
ejpam-2660	103	11	c	c	NOUN
ejpam-2660	103	12	,	,	PUNCT
ejpam-2660	103	13	d	d	PROPN
ejpam-2660	103	14	∈	∈	PROPN
ejpam-2660	103	15	a	a	DET
ejpam-2660	103	16	∧	∧	PROPN
ejpam-2660	103	17	b	b	PROPN
ejpam-2660	103	18	,	,	PUNCT
ejpam-2660	103	19	such	such	ADJ
ejpam-2660	103	20	that	that	SCONJ
ejpam-2660	103	21	c	c	PROPN
ejpam-2660	103	22	≤	≤	NOUN
ejpam-2660	104	1	a	a	PRON
ejpam-2660	105	1	and	and	CCONJ
ejpam-2660	106	1	d	d	NOUN
ejpam-2660	106	2	≤	≤	PROPN
ejpam-2660	106	3	b.	b.	PROPN
ejpam-2660	106	4	proof	proof	NOUN
ejpam-2660	106	5	.	.	PUNCT
ejpam-2660	107	1	since	since	SCONJ
ejpam-2660	107	2	a	a	DET
ejpam-2660	107	3	∈	∈	PROPN
ejpam-2660	107	4	a	a	DET
ejpam-2660	107	5	∨	∨	NOUN
ejpam-2660	107	6	(	(	PUNCT
ejpam-2660	107	7	a	a	DET
ejpam-2660	107	8	∧	∧	PROPN
ejpam-2660	107	9	b	b	PROPN
ejpam-2660	107	10	)	)	PUNCT
ejpam-2660	107	11	,	,	PUNCT
ejpam-2660	107	12	then	then	ADV
ejpam-2660	107	13	there	there	PRON
ejpam-2660	107	14	exists	exist	VERB
ejpam-2660	107	15	c	c	NOUN
ejpam-2660	107	16	∈	∈	PROPN
ejpam-2660	107	17	a	a	DET
ejpam-2660	107	18	∧	∧	PROPN
ejpam-2660	107	19	b	b	PROPN
ejpam-2660	107	20	,	,	PUNCT
ejpam-2660	107	21	such	such	ADJ
ejpam-2660	107	22	that	that	SCONJ
ejpam-2660	107	23	a	a	DET
ejpam-2660	107	24	=	=	X
ejpam-2660	107	25	a	a	DET
ejpam-2660	107	26	∨	∨	NUM
ejpam-2660	107	27	c	c	NOUN
ejpam-2660	107	28	,	,	PUNCT
ejpam-2660	107	29	and	and	CCONJ
ejpam-2660	107	30	it	it	PRON
ejpam-2660	107	31	implies	imply	VERB
ejpam-2660	107	32	that	that	SCONJ
ejpam-2660	107	33	c	c	PROPN
ejpam-2660	107	34	≤	≤	NUM
ejpam-2660	107	35	a.	a.	NOUN
ejpam-2660	107	36	also	also	ADV
ejpam-2660	107	37	since	since	SCONJ
ejpam-2660	107	38	b	b	PROPN
ejpam-2660	107	39	∈	∈	PROPN
ejpam-2660	107	40	b	b	PROPN
ejpam-2660	107	41	∨	∨	X
ejpam-2660	107	42	(	(	PUNCT
ejpam-2660	107	43	a	a	DET
ejpam-2660	107	44	∧	∧	PROPN
ejpam-2660	107	45	b	b	NOUN
ejpam-2660	107	46	)	)	PUNCT
ejpam-2660	107	47	,	,	PUNCT
ejpam-2660	107	48	there	there	PRON
ejpam-2660	107	49	exists	exist	VERB
ejpam-2660	107	50	d	d	PROPN
ejpam-2660	107	51	∈	∈	PROPN
ejpam-2660	107	52	a	a	DET
ejpam-2660	107	53	∧	∧	PROPN
ejpam-2660	107	54	b	b	PROPN
ejpam-2660	107	55	,	,	PUNCT
ejpam-2660	107	56	such	such	ADJ
ejpam-2660	107	57	that	that	DET
ejpam-2660	107	58	b	b	X
ejpam-2660	107	59	=	=	SYM
ejpam-2660	107	60	b	b	PROPN
ejpam-2660	107	61	∨	∨	NUM
ejpam-2660	107	62	d	d	PROPN
ejpam-2660	107	63	,	,	PUNCT
ejpam-2660	107	64	and	and	CCONJ
ejpam-2660	107	65	implies	imply	VERB
ejpam-2660	107	66	d	d	PROPN
ejpam-2660	107	67	≤	≤	PROPN
ejpam-2660	107	68	b.	b.	PROPN
ejpam-2660	107	69	theorem	theorem	VERB
ejpam-2660	107	70	16	16	NUM
ejpam-2660	107	71	.	.	PUNCT
ejpam-2660	108	1	let	let	VERB
ejpam-2660	108	2	a	a	DET
ejpam-2660	108	3	,	,	PUNCT
ejpam-2660	108	4	b	b	NOUN
ejpam-2660	108	5	,	,	PUNCT
ejpam-2660	108	6	1	1	NUM
ejpam-2660	108	7	∈	∈	PROPN
ejpam-2660	108	8	l.	l.	NOUN
ejpam-2660	108	9	then	then	ADV
ejpam-2660	108	10	the	the	DET
ejpam-2660	108	11	following	follow	VERB
ejpam-2660	108	12	conditions	condition	NOUN
ejpam-2660	108	13	hold	hold	VERB
ejpam-2660	108	14	.	.	PUNCT
ejpam-2660	109	1	(	(	PUNCT
ejpam-2660	109	2	i	i	NOUN
ejpam-2660	109	3	)	)	PUNCT
ejpam-2660	109	4	if	if	SCONJ
ejpam-2660	109	5	a	a	DET
ejpam-2660	109	6	∧	∧	PROPN
ejpam-2660	109	7	b	b	NOUN
ejpam-2660	109	8	=	=	PUNCT
ejpam-2660	109	9	{	{	PUNCT
ejpam-2660	109	10	1	1	NUM
ejpam-2660	109	11	}	}	PUNCT
ejpam-2660	109	12	,	,	PUNCT
ejpam-2660	109	13	then	then	ADV
ejpam-2660	109	14	a	a	DET
ejpam-2660	109	15	=	=	X
ejpam-2660	109	16	b.	b.	PROPN
ejpam-2660	109	17	(	(	PUNCT
ejpam-2660	109	18	ii	ii	PROPN
ejpam-2660	109	19	)	)	PUNCT
ejpam-2660	109	20	if	if	SCONJ
ejpam-2660	109	21	l	l	NOUN
ejpam-2660	109	22	is	be	AUX
ejpam-2660	109	23	distributive	distributive	ADJ
ejpam-2660	109	24	,	,	PUNCT
ejpam-2660	109	25	then	then	ADV
ejpam-2660	109	26	1	1	NUM
ejpam-2660	109	27	∧	∧	PROPN
ejpam-2660	109	28	1	1	NUM
ejpam-2660	109	29	=	=	SYM
ejpam-2660	109	30	{	{	PUNCT
ejpam-2660	109	31	1	1	NUM
ejpam-2660	109	32	}	}	PUNCT
ejpam-2660	109	33	.	.	PUNCT
ejpam-2660	110	1	proof	proof	NOUN
ejpam-2660	110	2	.	.	PUNCT
ejpam-2660	111	1	(	(	PUNCT
ejpam-2660	111	2	i	i	NOUN
ejpam-2660	111	3	)	)	PUNCT
ejpam-2660	111	4	by	by	ADP
ejpam-2660	111	5	proposition	proposition	NOUN
ejpam-2660	111	6	15	15	NUM
ejpam-2660	111	7	,	,	PUNCT
ejpam-2660	111	8	1	1	NUM
ejpam-2660	111	9	≤	≤	NOUN
ejpam-2660	111	10	a	a	PRON
ejpam-2660	111	11	and	and	CCONJ
ejpam-2660	111	12	1	1	NUM
ejpam-2660	111	13	≤	≤	NUM
ejpam-2660	111	14	b	b	NOUN
ejpam-2660	111	15	,	,	PUNCT
ejpam-2660	111	16	so	so	SCONJ
ejpam-2660	111	17	they	they	PRON
ejpam-2660	111	18	imply	imply	VERB
ejpam-2660	111	19	that	that	SCONJ
ejpam-2660	111	20	a	a	DET
ejpam-2660	111	21	=	=	SYM
ejpam-2660	111	22	b	b	NOUN
ejpam-2660	111	23	=	=	SYM
ejpam-2660	111	24	1	1	PROPN
ejpam-2660	111	25	.	.	PUNCT
ejpam-2660	111	26	(	(	PUNCT
ejpam-2660	111	27	ii	ii	NOUN
ejpam-2660	111	28	)	)	PUNCT
ejpam-2660	111	29	since	since	SCONJ
ejpam-2660	111	30	l	l	NOUN
ejpam-2660	111	31	is	be	AUX
ejpam-2660	111	32	distributive	distributive	ADJ
ejpam-2660	111	33	,	,	PUNCT
ejpam-2660	111	34	1	1	NUM
ejpam-2660	111	35	∨	∨	NUM
ejpam-2660	111	36	(	(	PUNCT
ejpam-2660	111	37	a	a	DET
ejpam-2660	111	38	∧	∧	PROPN
ejpam-2660	111	39	b	b	NOUN
ejpam-2660	111	40	)	)	PUNCT
ejpam-2660	111	41	=	=	PUNCT
ejpam-2660	111	42	(	(	PUNCT
ejpam-2660	111	43	1	1	NUM
ejpam-2660	111	44	∨	∨	NUM
ejpam-2660	111	45	a	a	PRON
ejpam-2660	111	46	)	)	PUNCT
ejpam-2660	111	47	∧	∧	NOUN
ejpam-2660	111	48	(	(	PUNCT
ejpam-2660	111	49	1	1	NUM
ejpam-2660	111	50	∨	∨	NUM
ejpam-2660	111	51	b	b	NUM
ejpam-2660	111	52	)	)	PUNCT
ejpam-2660	111	53	.	.	PUNCT
ejpam-2660	112	1	also	also	ADV
ejpam-2660	112	2	we	we	PRON
ejpam-2660	112	3	have	have	VERB
ejpam-2660	112	4	1	1	NUM
ejpam-2660	112	5	∨	∨	NUM
ejpam-2660	112	6	(	(	PUNCT
ejpam-2660	112	7	a	a	DET
ejpam-2660	112	8	∧	∧	PROPN
ejpam-2660	112	9	b	b	NOUN
ejpam-2660	112	10	)	)	PUNCT
ejpam-2660	112	11	=	=	PUNCT
ejpam-2660	112	12	{	{	PUNCT
ejpam-2660	112	13	1	1	NUM
ejpam-2660	112	14	}	}	PUNCT
ejpam-2660	112	15	and	and	CCONJ
ejpam-2660	112	16	(	(	PUNCT
ejpam-2660	112	17	1	1	NUM
ejpam-2660	112	18	∨	∨	NUM
ejpam-2660	112	19	a	a	PRON
ejpam-2660	112	20	)	)	PUNCT
ejpam-2660	112	21	∧	∧	NOUN
ejpam-2660	112	22	(	(	PUNCT
ejpam-2660	112	23	1	1	NUM
ejpam-2660	112	24	∨	∨	NUM
ejpam-2660	112	25	b	b	NOUN
ejpam-2660	112	26	)	)	PUNCT
ejpam-2660	112	27	=	=	SYM
ejpam-2660	112	28	1	1	NUM
ejpam-2660	112	29	∧	∧	PROPN
ejpam-2660	112	30	1	1	NUM
ejpam-2660	112	31	.	.	PUNCT
ejpam-2660	113	1	so	so	ADV
ejpam-2660	113	2	1	1	NUM
ejpam-2660	113	3	∧	∧	PROPN
ejpam-2660	113	4	1	1	NUM
ejpam-2660	113	5	=	=	SYM
ejpam-2660	113	6	{	{	PUNCT
ejpam-2660	113	7	1	1	NUM
ejpam-2660	113	8	}	}	PUNCT
ejpam-2660	113	9	.	.	PUNCT
ejpam-2660	114	1	3	3	X
ejpam-2660	114	2	.	.	X
ejpam-2660	114	3	hyperideals	hyperideal	NOUN
ejpam-2660	114	4	and	and	CCONJ
ejpam-2660	114	5	hyperfilters	hyperfilter	NOUN
ejpam-2660	114	6	in	in	ADP
ejpam-2660	114	7	strong	strong	ADJ
ejpam-2660	114	8	”	"	PUNCT
ejpam-2660	114	9	∧	∧	NOUN
ejpam-2660	114	10	”	"	PUNCT
ejpam-2660	114	11	-hyperlattices	-hyperlattice	NOUN
ejpam-2660	114	12	in	in	ADP
ejpam-2660	114	13	this	this	DET
ejpam-2660	114	14	section	section	NOUN
ejpam-2660	114	15	,	,	PUNCT
ejpam-2660	114	16	notaions	notaion	NOUN
ejpam-2660	114	17	of	of	ADP
ejpam-2660	114	18	hyperideals	hyperideal	NOUN
ejpam-2660	114	19	(	(	PUNCT
ejpam-2660	114	20	hyperfilters	hyperfilter	NOUN
ejpam-2660	114	21	)	)	PUNCT
ejpam-2660	114	22	in	in	ADP
ejpam-2660	114	23	strong	strong	ADJ
ejpam-2660	114	24	”	"	PUNCT
ejpam-2660	114	25	∧	∧	NOUN
ejpam-2660	114	26	”	"	PUNCT
ejpam-2660	114	27	-hyperlattices	-hyperlattice	NOUN
ejpam-2660	114	28	are	be	AUX
ejpam-2660	114	29	given	give	VERB
ejpam-2660	114	30	.	.	PUNCT
ejpam-2660	115	1	in	in	ADP
ejpam-2660	115	2	the	the	DET
ejpam-2660	115	3	sequel	sequel	NOUN
ejpam-2660	115	4	,	,	PUNCT
ejpam-2660	115	5	l	l	NOUN
ejpam-2660	115	6	denotes	denote	VERB
ejpam-2660	115	7	a	a	DET
ejpam-2660	115	8	strong	strong	ADJ
ejpam-2660	115	9	”	"	PUNCT
ejpam-2660	115	10	∧	∧	NOUN
ejpam-2660	115	11	”	"	PUNCT
ejpam-2660	115	12	-hyperlattice	-hyperlattice	NOUN
ejpam-2660	115	13	.	.	PUNCT
ejpam-2660	116	1	definition	definition	NOUN
ejpam-2660	116	2	17	17	NUM
ejpam-2660	116	3	.	.	PUNCT
ejpam-2660	117	1	let	let	VERB
ejpam-2660	117	2	i	i	PRON
ejpam-2660	117	3	and	and	CCONJ
ejpam-2660	117	4	f	f	PROPN
ejpam-2660	117	5	are	be	AUX
ejpam-2660	117	6	nonempty	nonempty	ADJ
ejpam-2660	117	7	subsets	subset	NOUN
ejpam-2660	117	8	of	of	ADP
ejpam-2660	117	9	l.	l.	PROPN
ejpam-2660	117	10	then	then	ADV
ejpam-2660	117	11	:	:	PUNCT
ejpam-2660	117	12	(	(	PUNCT
ejpam-2660	117	13	i	i	NOUN
ejpam-2660	117	14	)	)	PUNCT
ejpam-2660	118	1	i	i	PRON
ejpam-2660	118	2	is	be	AUX
ejpam-2660	118	3	called	call	VERB
ejpam-2660	118	4	a	a	DET
ejpam-2660	118	5	hyperideal	hyperideal	NOUN
ejpam-2660	118	6	if	if	SCONJ
ejpam-2660	118	7	the	the	DET
ejpam-2660	118	8	following	follow	VERB
ejpam-2660	118	9	conditions	condition	NOUN
ejpam-2660	118	10	hold	hold	VERB
ejpam-2660	118	11	.	.	PUNCT
ejpam-2660	119	1	(	(	PUNCT
ejpam-2660	119	2	a	a	X
ejpam-2660	119	3	)	)	PUNCT
ejpam-2660	119	4	if	if	SCONJ
ejpam-2660	119	5	x	x	X
ejpam-2660	119	6	,	,	PUNCT
ejpam-2660	119	7	y	y	PROPN
ejpam-2660	119	8	∈	∈	PROPN
ejpam-2660	120	1	i	i	PRON
ejpam-2660	120	2	,	,	PUNCT
ejpam-2660	120	3	then	then	ADV
ejpam-2660	120	4	x	x	PROPN
ejpam-2660	120	5	∨	∨	NUM
ejpam-2660	120	6	y	y	PROPN
ejpam-2660	120	7	∈	∈	PROPN
ejpam-2660	121	1	i	i	PRON
ejpam-2660	121	2	,	,	PUNCT
ejpam-2660	121	3	(	(	PUNCT
ejpam-2660	121	4	b	b	X
ejpam-2660	121	5	)	)	PUNCT
ejpam-2660	121	6	if	if	SCONJ
ejpam-2660	121	7	x	x	SYM
ejpam-2660	121	8	∈	∈	PROPN
ejpam-2660	121	9	i	i	PRON
ejpam-2660	121	10	and	and	CCONJ
ejpam-2660	121	11	y	y	PROPN
ejpam-2660	121	12	∈	∈	PROPN
ejpam-2660	121	13	l	l	NOUN
ejpam-2660	121	14	,	,	PUNCT
ejpam-2660	121	15	such	such	ADJ
ejpam-2660	121	16	that	that	SCONJ
ejpam-2660	121	17	y	y	PROPN
ejpam-2660	121	18	≤	≤	PROPN
ejpam-2660	121	19	x	x	PUNCT
ejpam-2660	121	20	,	,	PUNCT
ejpam-2660	121	21	then	then	ADV
ejpam-2660	121	22	y	y	PROPN
ejpam-2660	121	23	∈	∈	PROPN
ejpam-2660	121	24	i.	i.	PROPN
ejpam-2660	121	25	(	(	PUNCT
ejpam-2660	121	26	ii	ii	PROPN
ejpam-2660	121	27	)	)	PUNCT
ejpam-2660	121	28	f	f	PROPN
ejpam-2660	121	29	is	be	AUX
ejpam-2660	121	30	called	call	VERB
ejpam-2660	121	31	a	a	DET
ejpam-2660	121	32	hyperfilter	hyperfilter	NOUN
ejpam-2660	121	33	if	if	SCONJ
ejpam-2660	121	34	the	the	DET
ejpam-2660	121	35	following	follow	VERB
ejpam-2660	121	36	conditions	condition	NOUN
ejpam-2660	121	37	hold	hold	VERB
ejpam-2660	121	38	.	.	PUNCT
ejpam-2660	122	1	m.	m.	NOUN
ejpam-2660	122	2	amiri	amiri	PROPN
ejpam-2660	122	3	bideshki	bideshki	PROPN
ejpam-2660	122	4	,	,	PUNCT
ejpam-2660	122	5	r.	r.	PROPN
ejpam-2660	122	6	ameri	ameri	PROPN
ejpam-2660	122	7	,	,	PUNCT
ejpam-2660	122	8	a.	a.	PROPN
ejpam-2660	122	9	borumand	borumand	PROPN
ejpam-2660	122	10	saeid	saeid	PROPN
ejpam-2660	122	11	/	/	SYM
ejpam-2660	122	12	eur	eur	PROPN
ejpam-2660	122	13	.	.	PUNCT
ejpam-2660	123	1	j.	j.	PROPN
ejpam-2660	123	2	pure	pure	PROPN
ejpam-2660	123	3	appl	appl	PROPN
ejpam-2660	123	4	.	.	PROPN
ejpam-2660	123	5	math	math	PROPN
ejpam-2660	123	6	,	,	PUNCT
ejpam-2660	123	7	11	11	NUM
ejpam-2660	123	8	(	(	PUNCT
ejpam-2660	123	9	1	1	NUM
ejpam-2660	123	10	)	)	PUNCT
ejpam-2660	123	11	(	(	PUNCT
ejpam-2660	123	12	2018	2018	NUM
ejpam-2660	123	13	)	)	PUNCT
ejpam-2660	123	14	,	,	PUNCT
ejpam-2660	123	15	169	169	NUM
ejpam-2660	123	16	-	-	SYM
ejpam-2660	123	17	188	188	NUM
ejpam-2660	123	18	174	174	NUM
ejpam-2660	123	19	(	(	PUNCT
ejpam-2660	123	20	a	a	NOUN
ejpam-2660	123	21	)	)	PUNCT
ejpam-2660	123	22	if	if	SCONJ
ejpam-2660	123	23	x	x	X
ejpam-2660	123	24	,	,	PUNCT
ejpam-2660	123	25	y	y	PROPN
ejpam-2660	123	26	∈	∈	PROPN
ejpam-2660	123	27	f	f	PROPN
ejpam-2660	123	28	,	,	PUNCT
ejpam-2660	123	29	then	then	ADV
ejpam-2660	123	30	x	x	PART
ejpam-2660	123	31	∧	∧	NOUN
ejpam-2660	123	32	y	y	PROPN
ejpam-2660	123	33	⊆	⊆	NUM
ejpam-2660	123	34	f	f	PROPN
ejpam-2660	123	35	,	,	PUNCT
ejpam-2660	123	36	(	(	PUNCT
ejpam-2660	123	37	b	b	X
ejpam-2660	123	38	)	)	PUNCT
ejpam-2660	124	1	if	if	SCONJ
ejpam-2660	124	2	x	x	SYM
ejpam-2660	124	3	∈	∈	PROPN
ejpam-2660	124	4	f	f	PROPN
ejpam-2660	124	5	and	and	CCONJ
ejpam-2660	124	6	y	y	PROPN
ejpam-2660	124	7	∈	∈	PROPN
ejpam-2660	124	8	l	l	NOUN
ejpam-2660	124	9	,	,	PUNCT
ejpam-2660	124	10	such	such	ADJ
ejpam-2660	124	11	that	that	SCONJ
ejpam-2660	124	12	x	x	X
ejpam-2660	124	13	≤	≤	NUM
ejpam-2660	124	14	y	y	NOUN
ejpam-2660	124	15	,	,	PUNCT
ejpam-2660	124	16	then	then	ADV
ejpam-2660	124	17	y	y	PROPN
ejpam-2660	124	18	∈	∈	PROPN
ejpam-2660	124	19	f	f	X
ejpam-2660	124	20	.	.	PUNCT
ejpam-2660	125	1	(	(	PUNCT
ejpam-2660	125	2	iii	iii	X
ejpam-2660	125	3	)	)	PUNCT
ejpam-2660	125	4	a	a	DET
ejpam-2660	125	5	hyperideal	hyperideal	NOUN
ejpam-2660	125	6	i	i	PRON
ejpam-2660	125	7	is	be	AUX
ejpam-2660	125	8	called	call	VERB
ejpam-2660	125	9	prime	prime	ADJ
ejpam-2660	125	10	if	if	SCONJ
ejpam-2660	125	11	(	(	PUNCT
ejpam-2660	125	12	x∧	x∧	PROPN
ejpam-2660	125	13	y)∩	y)∩	PROPN
ejpam-2660	125	14	i	i	PROPN
ejpam-2660	125	15	6=	6=	PROPN
ejpam-2660	125	16	∅	∅	NOUN
ejpam-2660	125	17	,	,	PUNCT
ejpam-2660	125	18	then	then	ADV
ejpam-2660	125	19	x	x	SYM
ejpam-2660	125	20	∈	∈	PROPN
ejpam-2660	125	21	i	i	PRON
ejpam-2660	125	22	or	or	CCONJ
ejpam-2660	125	23	y	y	PROPN
ejpam-2660	125	24	∈	∈	PROPN
ejpam-2660	126	1	i	i	PRON
ejpam-2660	126	2	,	,	PUNCT
ejpam-2660	126	3	for	for	ADP
ejpam-2660	126	4	all	all	DET
ejpam-2660	126	5	x	x	NOUN
ejpam-2660	126	6	,	,	PUNCT
ejpam-2660	126	7	y	y	PROPN
ejpam-2660	126	8	∈	∈	PROPN
ejpam-2660	126	9	l.	l.	PROPN
ejpam-2660	126	10	(	(	PUNCT
ejpam-2660	126	11	iv	iv	X
ejpam-2660	126	12	)	)	PUNCT
ejpam-2660	126	13	a	a	DET
ejpam-2660	126	14	hyperfilter	hyperfilter	ADJ
ejpam-2660	126	15	f	f	PROPN
ejpam-2660	126	16	is	be	AUX
ejpam-2660	126	17	called	call	VERB
ejpam-2660	126	18	prime	prime	ADJ
ejpam-2660	126	19	if	if	SCONJ
ejpam-2660	126	20	x	x	PROPN
ejpam-2660	126	21	∨	∨	NUM
ejpam-2660	126	22	y	y	PROPN
ejpam-2660	126	23	∈	∈	PROPN
ejpam-2660	126	24	f	f	PROPN
ejpam-2660	126	25	,	,	PUNCT
ejpam-2660	126	26	then	then	ADV
ejpam-2660	126	27	x	x	SYM
ejpam-2660	126	28	∈	∈	PROPN
ejpam-2660	126	29	f	f	PROPN
ejpam-2660	126	30	or	or	CCONJ
ejpam-2660	126	31	y	y	PROPN
ejpam-2660	126	32	∈	∈	PROPN
ejpam-2660	126	33	f	f	PROPN
ejpam-2660	126	34	,	,	PUNCT
ejpam-2660	126	35	for	for	ADP
ejpam-2660	126	36	all	all	DET
ejpam-2660	126	37	x	x	NOUN
ejpam-2660	126	38	,	,	PUNCT
ejpam-2660	126	39	y	y	PROPN
ejpam-2660	126	40	∈	∈	PROPN
ejpam-2660	126	41	l.	l.	PROPN
ejpam-2660	126	42	example	example	NOUN
ejpam-2660	126	43	18	18	NUM
ejpam-2660	126	44	.	.	PUNCT
ejpam-2660	127	1	(	(	PUNCT
ejpam-2660	127	2	i	i	NOUN
ejpam-2660	127	3	)	)	PUNCT
ejpam-2660	127	4	let	let	VERB
ejpam-2660	127	5	l	l	NOUN
ejpam-2660	127	6	=	=	PUNCT
ejpam-2660	127	7	{	{	PUNCT
ejpam-2660	127	8	0	0	NUM
ejpam-2660	127	9	,	,	PUNCT
ejpam-2660	127	10	a	a	DET
ejpam-2660	127	11	,	,	PUNCT
ejpam-2660	127	12	b	b	NOUN
ejpam-2660	127	13	,	,	PUNCT
ejpam-2660	127	14	1	1	NUM
ejpam-2660	127	15	}	}	PUNCT
ejpam-2660	127	16	.	.	PUNCT
ejpam-2660	128	1	∧-hyperoperation	∧-hyperoperation	NOUN
ejpam-2660	128	2	and	and	CCONJ
ejpam-2660	128	3	∨	∨	NUM
ejpam-2660	128	4	operation	operation	NOUN
ejpam-2660	128	5	are	be	AUX
ejpam-2660	128	6	given	give	VERB
ejpam-2660	128	7	with	with	ADP
ejpam-2660	128	8	tables	table	NOUN
ejpam-2660	128	9	5	5	NUM
ejpam-2660	128	10	.	.	PUNCT
ejpam-2660	129	1	then	then	ADV
ejpam-2660	129	2	(	(	PUNCT
ejpam-2660	129	3	l,∧,∨	l,∧,∨	X
ejpam-2660	129	4	)	)	PUNCT
ejpam-2660	129	5	is	be	AUX
ejpam-2660	129	6	a	a	DET
ejpam-2660	129	7	∧-hyperlattice	∧-hyperlattice	NOUN
ejpam-2660	129	8	.	.	PUNCT
ejpam-2660	130	1	{	{	PUNCT
ejpam-2660	130	2	0	0	NUM
ejpam-2660	130	3	,	,	PUNCT
ejpam-2660	130	4	a	a	PRON
ejpam-2660	130	5	}	}	PUNCT
ejpam-2660	130	6	is	be	AUX
ejpam-2660	130	7	an	an	DET
ejpam-2660	130	8	hyperideal	hyperideal	NOUN
ejpam-2660	130	9	,	,	PUNCT
ejpam-2660	130	10	but	but	CCONJ
ejpam-2660	130	11	since	since	SCONJ
ejpam-2660	130	12	b∧1	b∧1	NOUN
ejpam-2660	130	13	=	=	SYM
ejpam-2660	130	14	{	{	PUNCT
ejpam-2660	130	15	0	0	NUM
ejpam-2660	130	16	,	,	PUNCT
ejpam-2660	130	17	b	b	NOUN
ejpam-2660	130	18	}	}	PUNCT
ejpam-2660	130	19	,	,	PUNCT
ejpam-2660	130	20	(	(	PUNCT
ejpam-2660	130	21	b	b	X
ejpam-2660	130	22	∧	∧	PROPN
ejpam-2660	130	23	1	1	NUM
ejpam-2660	130	24	)	)	PUNCT
ejpam-2660	130	25	∩	∩	NOUN
ejpam-2660	130	26	{	{	PUNCT
ejpam-2660	130	27	0	0	NUM
ejpam-2660	130	28	,	,	PUNCT
ejpam-2660	130	29	a	a	DET
ejpam-2660	130	30	}	}	PUNCT
ejpam-2660	130	31	6=	6=	NOUN
ejpam-2660	130	32	∅	∅	NOUN
ejpam-2660	130	33	,	,	PUNCT
ejpam-2660	130	34	it	it	PRON
ejpam-2660	130	35	is	be	AUX
ejpam-2660	130	36	not	not	PART
ejpam-2660	130	37	a	a	DET
ejpam-2660	130	38	prime	prime	ADJ
ejpam-2660	130	39	ideal	ideal	NOUN
ejpam-2660	130	40	.	.	PUNCT
ejpam-2660	131	1	also	also	ADV
ejpam-2660	131	2	{	{	PUNCT
ejpam-2660	131	3	0	0	NUM
ejpam-2660	131	4	}	}	PUNCT
ejpam-2660	131	5	is	be	AUX
ejpam-2660	131	6	an	an	DET
ejpam-2660	131	7	hyperideal	hyperideal	NOUN
ejpam-2660	131	8	that	that	PRON
ejpam-2660	131	9	is	be	AUX
ejpam-2660	131	10	not	not	PART
ejpam-2660	131	11	prime	prime	ADJ
ejpam-2660	131	12	.	.	PUNCT
ejpam-2660	132	1	{	{	PUNCT
ejpam-2660	132	2	b	b	X
ejpam-2660	132	3	,	,	PUNCT
ejpam-2660	132	4	1	1	NUM
ejpam-2660	132	5	}	}	PUNCT
ejpam-2660	132	6	is	be	AUX
ejpam-2660	132	7	neither	neither	CCONJ
ejpam-2660	132	8	a	a	DET
ejpam-2660	132	9	hyperideal	hyperideal	NOUN
ejpam-2660	132	10	nor	nor	CCONJ
ejpam-2660	132	11	a	a	DET
ejpam-2660	132	12	hyperfilter	hyperfilter	NOUN
ejpam-2660	132	13	of	of	ADP
ejpam-2660	132	14	l.	l.	PROPN
ejpam-2660	132	15	both	both	PRON
ejpam-2660	132	16	{	{	PUNCT
ejpam-2660	132	17	1	1	NUM
ejpam-2660	132	18	}	}	PUNCT
ejpam-2660	132	19	and	and	CCONJ
ejpam-2660	132	20	l	l	NOUN
ejpam-2660	132	21	are	be	AUX
ejpam-2660	132	22	hyperfilters	hyperfilter	NOUN
ejpam-2660	132	23	of	of	ADP
ejpam-2660	132	24	l	l	NOUN
ejpam-2660	132	25	that	that	SCONJ
ejpam-2660	132	26	{	{	PUNCT
ejpam-2660	132	27	1	1	X
ejpam-2660	132	28	}	}	PUNCT
ejpam-2660	132	29	is	be	AUX
ejpam-2660	132	30	not	not	PART
ejpam-2660	132	31	prime	prime	ADJ
ejpam-2660	132	32	.	.	PUNCT
ejpam-2660	133	1	∧	∧	NOUN
ejpam-2660	133	2	0	0	NUM
ejpam-2660	133	3	a	a	DET
ejpam-2660	133	4	b	b	NOUN
ejpam-2660	133	5	1	1	NUM
ejpam-2660	133	6	0	0	NUM
ejpam-2660	133	7	{	{	PUNCT
ejpam-2660	133	8	0	0	NUM
ejpam-2660	133	9	}	}	PUNCT
ejpam-2660	133	10	{	{	PUNCT
ejpam-2660	133	11	0	0	NUM
ejpam-2660	133	12	}	}	PUNCT
ejpam-2660	133	13	{	{	PUNCT
ejpam-2660	133	14	0	0	NUM
ejpam-2660	133	15	}	}	PUNCT
ejpam-2660	133	16	{	{	PUNCT
ejpam-2660	133	17	0	0	NUM
ejpam-2660	133	18	}	}	PUNCT
ejpam-2660	133	19	a	a	DET
ejpam-2660	133	20	{	{	PUNCT
ejpam-2660	133	21	0	0	NUM
ejpam-2660	133	22	}	}	PUNCT
ejpam-2660	133	23	{	{	PUNCT
ejpam-2660	133	24	0	0	NUM
ejpam-2660	133	25	,	,	PUNCT
ejpam-2660	133	26	a	a	PRON
ejpam-2660	133	27	}	}	PUNCT
ejpam-2660	133	28	{	{	PUNCT
ejpam-2660	133	29	0	0	NUM
ejpam-2660	133	30	}	}	PUNCT
ejpam-2660	133	31	{	{	PUNCT
ejpam-2660	133	32	0	0	NUM
ejpam-2660	133	33	,	,	PUNCT
ejpam-2660	133	34	a	a	DET
ejpam-2660	133	35	}	}	PUNCT
ejpam-2660	133	36	b	b	NOUN
ejpam-2660	133	37	{	{	PUNCT
ejpam-2660	133	38	0	0	NUM
ejpam-2660	133	39	}	}	PUNCT
ejpam-2660	133	40	{	{	PUNCT
ejpam-2660	133	41	0	0	NUM
ejpam-2660	133	42	}	}	PUNCT
ejpam-2660	133	43	{	{	PUNCT
ejpam-2660	133	44	0	0	NUM
ejpam-2660	133	45	,	,	PUNCT
ejpam-2660	133	46	b	b	NOUN
ejpam-2660	133	47	}	}	PUNCT
ejpam-2660	133	48	{	{	PUNCT
ejpam-2660	133	49	0	0	NUM
ejpam-2660	133	50	,	,	PUNCT
ejpam-2660	133	51	b	b	NOUN
ejpam-2660	133	52	}	}	PUNCT
ejpam-2660	133	53	1	1	NUM
ejpam-2660	133	54	{	{	PUNCT
ejpam-2660	133	55	0	0	NUM
ejpam-2660	133	56	}	}	PUNCT
ejpam-2660	133	57	{	{	PUNCT
ejpam-2660	133	58	a	a	NOUN
ejpam-2660	133	59	}	}	PUNCT
ejpam-2660	133	60	{	{	PUNCT
ejpam-2660	133	61	b	b	NOUN
ejpam-2660	133	62	}	}	PUNCT
ejpam-2660	133	63	{	{	PUNCT
ejpam-2660	133	64	1	1	NUM
ejpam-2660	133	65	}	}	PUNCT
ejpam-2660	133	66	(	(	PUNCT
ejpam-2660	133	67	a	a	X
ejpam-2660	133	68	)	)	PUNCT
ejpam-2660	133	69	∨	∨	NOUN
ejpam-2660	133	70	0	0	NUM
ejpam-2660	134	1	a	a	DET
ejpam-2660	134	2	b	b	NOUN
ejpam-2660	134	3	1	1	NUM
ejpam-2660	134	4	0	0	NUM
ejpam-2660	134	5	0	0	NUM
ejpam-2660	134	6	a	a	DET
ejpam-2660	134	7	b	b	PROPN
ejpam-2660	134	8	1	1	NUM
ejpam-2660	134	9	a	a	PRON
ejpam-2660	134	10	a	a	DET
ejpam-2660	134	11	a	a	DET
ejpam-2660	134	12	1	1	NUM
ejpam-2660	134	13	1	1	NUM
ejpam-2660	134	14	b	b	SYM
ejpam-2660	134	15	b	b	SYM
ejpam-2660	134	16	1	1	NUM
ejpam-2660	134	17	b	b	SYM
ejpam-2660	134	18	1	1	NUM
ejpam-2660	134	19	1	1	NUM
ejpam-2660	134	20	1	1	NUM
ejpam-2660	134	21	1	1	NUM
ejpam-2660	134	22	1	1	NUM
ejpam-2660	134	23	1	1	NUM
ejpam-2660	134	24	(	(	PUNCT
ejpam-2660	134	25	b	b	NOUN
ejpam-2660	134	26	)	)	PUNCT
ejpam-2660	134	27	table	table	NOUN
ejpam-2660	134	28	5	5	NUM
ejpam-2660	134	29	:	:	PUNCT
ejpam-2660	134	30	(	(	PUNCT
ejpam-2660	134	31	ii	ii	NOUN
ejpam-2660	134	32	)	)	PUNCT
ejpam-2660	134	33	consider	consider	VERB
ejpam-2660	134	34	”	"	PUNCT
ejpam-2660	134	35	∧	∧	NOUN
ejpam-2660	134	36	”	"	PUNCT
ejpam-2660	134	37	-hyperlattice	-hyperlattice	NOUN
ejpam-2660	134	38	l	l	NOUN
ejpam-2660	134	39	in	in	ADP
ejpam-2660	134	40	example	example	NOUN
ejpam-2660	134	41	8	8	NUM
ejpam-2660	134	42	.	.	PUNCT
ejpam-2660	135	1	then	then	ADV
ejpam-2660	135	2	{	{	PUNCT
ejpam-2660	135	3	0	0	NUM
ejpam-2660	135	4	,	,	PUNCT
ejpam-2660	135	5	a	a	PRON
ejpam-2660	135	6	}	}	PUNCT
ejpam-2660	135	7	is	be	AUX
ejpam-2660	135	8	a	a	DET
ejpam-2660	135	9	prime	prime	ADJ
ejpam-2660	135	10	hyperideal	hyperideal	NOUN
ejpam-2660	135	11	.	.	PUNCT
ejpam-2660	136	1	proposition	proposition	NOUN
ejpam-2660	136	2	19	19	NUM
ejpam-2660	136	3	.	.	PUNCT
ejpam-2660	137	1	let	let	VERB
ejpam-2660	137	2	f	f	PRON
ejpam-2660	137	3	be	be	AUX
ejpam-2660	137	4	a	a	DET
ejpam-2660	137	5	nonempty	nonempty	ADJ
ejpam-2660	137	6	subset	subset	NOUN
ejpam-2660	137	7	of	of	ADP
ejpam-2660	137	8	l.	l.	PROPN
ejpam-2660	137	9	then	then	ADV
ejpam-2660	137	10	f	f	PROPN
ejpam-2660	137	11	is	be	AUX
ejpam-2660	137	12	a	a	DET
ejpam-2660	137	13	hyperfilter	hyperfilter	ADJ
ejpam-2660	137	14	if	if	SCONJ
ejpam-2660	137	15	and	and	CCONJ
ejpam-2660	137	16	only	only	ADV
ejpam-2660	137	17	if	if	SCONJ
ejpam-2660	137	18	f	f	PROPN
ejpam-2660	137	19	is	be	AUX
ejpam-2660	137	20	”	"	PUNCT
ejpam-2660	137	21	∧	∧	PROPN
ejpam-2660	137	22	”	"	PUNCT
ejpam-2660	137	23	-closed	-close	VERB
ejpam-2660	137	24	and	and	CCONJ
ejpam-2660	137	25	for	for	ADP
ejpam-2660	137	26	all	all	DET
ejpam-2660	137	27	x	x	SYM
ejpam-2660	137	28	∈	∈	PROPN
ejpam-2660	137	29	l	l	NOUN
ejpam-2660	137	30	and	and	CCONJ
ejpam-2660	137	31	a	a	DET
ejpam-2660	137	32	∈	∈	PROPN
ejpam-2660	137	33	f	f	X
ejpam-2660	137	34	,	,	PUNCT
ejpam-2660	137	35	x	x	PROPN
ejpam-2660	137	36	∨	∨	NUM
ejpam-2660	137	37	a	a	DET
ejpam-2660	137	38	∈	∈	PROPN
ejpam-2660	137	39	f.	f.	NOUN
ejpam-2660	137	40	let	let	VERB
ejpam-2660	137	41	l	l	NOUN
ejpam-2660	137	42	be	be	AUX
ejpam-2660	137	43	a	a	DET
ejpam-2660	137	44	bounded	bounded	ADJ
ejpam-2660	137	45	”	"	PUNCT
ejpam-2660	137	46	∧	∧	PROPN
ejpam-2660	137	47	”	"	PUNCT
ejpam-2660	137	48	-hyperlattice	-hyperlattice	NOUN
ejpam-2660	137	49	.	.	PUNCT
ejpam-2660	138	1	it	it	PRON
ejpam-2660	138	2	is	be	AUX
ejpam-2660	138	3	clear	clear	ADJ
ejpam-2660	138	4	that	that	SCONJ
ejpam-2660	138	5	if	if	SCONJ
ejpam-2660	138	6	i	i	PRON
ejpam-2660	138	7	is	be	AUX
ejpam-2660	138	8	a	a	DET
ejpam-2660	138	9	hyperideal	hyperideal	NOUN
ejpam-2660	138	10	of	of	ADP
ejpam-2660	138	11	l	l	NOUN
ejpam-2660	138	12	and	and	CCONJ
ejpam-2660	138	13	1	1	NUM
ejpam-2660	138	14	∈	∈	PROPN
ejpam-2660	138	15	i	i	PRON
ejpam-2660	138	16	,	,	PUNCT
ejpam-2660	138	17	then	then	ADV
ejpam-2660	138	18	i	i	PRON
ejpam-2660	138	19	=	=	PUNCT
ejpam-2660	138	20	l.	l.	PROPN
ejpam-2660	138	21	also	also	ADV
ejpam-2660	138	22	if	if	SCONJ
ejpam-2660	138	23	f	f	PROPN
ejpam-2660	138	24	is	be	AUX
ejpam-2660	138	25	a	a	DET
ejpam-2660	138	26	hyperfilter	hyperfilter	NOUN
ejpam-2660	138	27	of	of	ADP
ejpam-2660	138	28	l	l	NOUN
ejpam-2660	138	29	and	and	CCONJ
ejpam-2660	138	30	0	0	NUM
ejpam-2660	138	31	∈	∈	PROPN
ejpam-2660	138	32	f	f	NOUN
ejpam-2660	138	33	,	,	PUNCT
ejpam-2660	138	34	then	then	ADV
ejpam-2660	138	35	f	f	PROPN
ejpam-2660	138	36	=	=	PUNCT
ejpam-2660	138	37	l.	l.	PROPN
ejpam-2660	138	38	if	if	SCONJ
ejpam-2660	138	39	1	1	NUM
ejpam-2660	138	40	∧	∧	PROPN
ejpam-2660	138	41	1	1	NUM
ejpam-2660	138	42	=	=	SYM
ejpam-2660	138	43	l	l	NOUN
ejpam-2660	138	44	,	,	PUNCT
ejpam-2660	138	45	then	then	ADV
ejpam-2660	138	46	hyperlattice	hyperlattice	PROPN
ejpam-2660	138	47	l	l	NOUN
ejpam-2660	138	48	does	do	AUX
ejpam-2660	138	49	not	not	PART
ejpam-2660	138	50	have	have	VERB
ejpam-2660	138	51	trivial	trivial	ADJ
ejpam-2660	138	52	hyperfilter	hyperfilter	NOUN
ejpam-2660	138	53	.	.	PUNCT
ejpam-2660	139	1	we	we	PRON
ejpam-2660	139	2	have	have	VERB
ejpam-2660	139	3	0	0	NUM
ejpam-2660	139	4	∈	∈	PROPN
ejpam-2660	139	5	i	i	PRON
ejpam-2660	139	6	,	,	PUNCT
ejpam-2660	139	7	and	and	CCONJ
ejpam-2660	139	8	1	1	NUM
ejpam-2660	139	9	∈	∈	PROPN
ejpam-2660	139	10	f	f	NOUN
ejpam-2660	139	11	,	,	PUNCT
ejpam-2660	139	12	where	where	SCONJ
ejpam-2660	139	13	i	i	PRON
ejpam-2660	139	14	is	be	AUX
ejpam-2660	139	15	a	a	DET
ejpam-2660	139	16	hyperideal	hyperideal	NOUN
ejpam-2660	139	17	and	and	CCONJ
ejpam-2660	139	18	f	f	PROPN
ejpam-2660	139	19	is	be	AUX
ejpam-2660	139	20	a	a	DET
ejpam-2660	139	21	hyperfilter	hyperfilter	NOUN
ejpam-2660	139	22	of	of	ADP
ejpam-2660	139	23	l.	l.	PROPN
ejpam-2660	139	24	now	now	ADV
ejpam-2660	139	25	,	,	PUNCT
ejpam-2660	139	26	we	we	PRON
ejpam-2660	139	27	are	be	AUX
ejpam-2660	139	28	going	go	VERB
ejpam-2660	139	29	to	to	PART
ejpam-2660	139	30	define	define	VERB
ejpam-2660	139	31	two	two	NUM
ejpam-2660	139	32	types	type	NOUN
ejpam-2660	139	33	of	of	ADP
ejpam-2660	139	34	hyperideals	hyperideal	NOUN
ejpam-2660	139	35	in	in	ADP
ejpam-2660	139	36	a	a	DET
ejpam-2660	139	37	”	"	PUNCT
ejpam-2660	139	38	∧	∧	NOUN
ejpam-2660	139	39	”	"	PUNCT
ejpam-2660	139	40	-hyperlattice	-hyperlattice	NOUN
ejpam-2660	139	41	l.	l.	NOUN
ejpam-2660	139	42	proposition	proposition	NOUN
ejpam-2660	139	43	20	20	NUM
ejpam-2660	139	44	.	.	PUNCT
ejpam-2660	140	1	let	let	VERB
ejpam-2660	140	2	l	l	NOUN
ejpam-2660	140	3	be	be	AUX
ejpam-2660	140	4	dual	dual	ADV
ejpam-2660	140	5	distributive	distributive	ADJ
ejpam-2660	140	6	.	.	PUNCT
ejpam-2660	141	1	if	if	SCONJ
ejpam-2660	141	2	∀i	∀i	NOUN
ejpam-2660	141	3	∈	∈	PROPN
ejpam-2660	141	4	i	i	PRON
ejpam-2660	141	5	,	,	PUNCT
ejpam-2660	141	6	li	li	PROPN
ejpam-2660	141	7	is	be	AUX
ejpam-2660	141	8	a	a	DET
ejpam-2660	141	9	hyperideal	hyperideal	NOUN
ejpam-2660	141	10	of	of	ADP
ejpam-2660	141	11	l	l	NOUN
ejpam-2660	141	12	,	,	PUNCT
ejpam-2660	141	13	then	then	ADV
ejpam-2660	141	14	∩i∈ili	∩i∈ili	PRON
ejpam-2660	141	15	is	be	AUX
ejpam-2660	141	16	a	a	DET
ejpam-2660	141	17	hyperideal	hyperideal	NOUN
ejpam-2660	141	18	of	of	ADP
ejpam-2660	141	19	l	l	NOUN
ejpam-2660	141	20	proposition	proposition	NOUN
ejpam-2660	141	21	21	21	NUM
ejpam-2660	141	22	.	.	PUNCT
ejpam-2660	142	1	let	let	VERB
ejpam-2660	142	2	i	i	PRON
ejpam-2660	142	3	,	,	PUNCT
ejpam-2660	142	4	j	j	PROPN
ejpam-2660	142	5	are	be	AUX
ejpam-2660	142	6	hyperideals	hyperideal	NOUN
ejpam-2660	142	7	of	of	ADP
ejpam-2660	142	8	l.	l.	PROPN
ejpam-2660	143	1	then	then	ADV
ejpam-2660	143	2	i	i	PRON
ejpam-2660	143	3	∪	∪	VERB
ejpam-2660	143	4	j	j	PROPN
ejpam-2660	143	5	is	be	AUX
ejpam-2660	143	6	hyperideal	hyperideal	ADJ
ejpam-2660	143	7	if	if	SCONJ
ejpam-2660	144	1	and	and	CCONJ
ejpam-2660	144	2	only	only	ADV
ejpam-2660	144	3	if	if	SCONJ
ejpam-2660	144	4	i	i	PRON
ejpam-2660	144	5	⊆	⊆	NUM
ejpam-2660	144	6	j	j	PROPN
ejpam-2660	144	7	or	or	CCONJ
ejpam-2660	144	8	j	j	PROPN
ejpam-2660	144	9	⊆	⊆	NUM
ejpam-2660	144	10	i.	i.	NOUN
ejpam-2660	144	11	theorem	theorem	VERB
ejpam-2660	144	12	22	22	NUM
ejpam-2660	144	13	.	.	PUNCT
ejpam-2660	145	1	let	let	VERB
ejpam-2660	145	2	i	i	PRON
ejpam-2660	145	3	,	,	PUNCT
ejpam-2660	145	4	j	j	PROPN
ejpam-2660	145	5	be	be	VERB
ejpam-2660	145	6	hyperideals	hyperideal	NOUN
ejpam-2660	145	7	of	of	ADP
ejpam-2660	145	8	l.	l.	PROPN
ejpam-2660	145	9	define	define	VERB
ejpam-2660	145	10	i	i	PROPN
ejpam-2660	145	11	∨	∨	PROPN
ejpam-2660	146	1	j	j	PROPN
ejpam-2660	146	2	=	=	PRON
ejpam-2660	146	3	{	{	PUNCT
ejpam-2660	146	4	x	x	PUNCT
ejpam-2660	146	5	∈	∈	NOUN
ejpam-2660	146	6	l	l	NOUN
ejpam-2660	147	1	|	|	NOUN
ejpam-2660	147	2	x	x	SYM
ejpam-2660	147	3	≤	≤	ADV
ejpam-2660	147	4	a	a	DET
ejpam-2660	147	5	∨	∨	NUM
ejpam-2660	147	6	b,∃a	b,∃a	NOUN
ejpam-2660	147	7	∈	∈	PROPN
ejpam-2660	148	1	i	i	PROPN
ejpam-2660	148	2	,	,	PUNCT
ejpam-2660	148	3	b	b	PROPN
ejpam-2660	148	4	∈	∈	PROPN
ejpam-2660	148	5	j	j	PROPN
ejpam-2660	148	6	}	}	PUNCT
ejpam-2660	148	7	.	.	PUNCT
ejpam-2660	149	1	then	then	ADV
ejpam-2660	149	2	i	i	PRON
ejpam-2660	149	3	∨	∨	PROPN
ejpam-2660	149	4	j	j	PROPN
ejpam-2660	149	5	is	be	AUX
ejpam-2660	149	6	a	a	DET
ejpam-2660	149	7	hyperideal	hyperideal	NOUN
ejpam-2660	149	8	of	of	ADP
ejpam-2660	149	9	l	l	NOUN
ejpam-2660	149	10	and	and	CCONJ
ejpam-2660	149	11	we	we	PRON
ejpam-2660	149	12	have	have	VERB
ejpam-2660	149	13	:	:	PUNCT
ejpam-2660	149	14	i	i	PROPN
ejpam-2660	149	15	∨	∨	PROPN
ejpam-2660	149	16	j	j	PROPN
ejpam-2660	150	1	=	=	PRON
ejpam-2660	150	2	{	{	PUNCT
ejpam-2660	150	3	x	x	PUNCT
ejpam-2660	150	4	∈	∈	PROPN
ejpam-2660	150	5	l	l	NOUN
ejpam-2660	151	1	|	|	NOUN
ejpam-2660	151	2	∃a	∃a	NOUN
ejpam-2660	151	3	∈	∈	PROPN
ejpam-2660	152	1	i	i	PRON
ejpam-2660	152	2	,	,	PUNCT
ejpam-2660	152	3	∃b	∃b	PROPN
ejpam-2660	152	4	∈	∈	PROPN
ejpam-2660	152	5	j	j	PROPN
ejpam-2660	152	6	,	,	PUNCT
ejpam-2660	152	7	x	x	SYM
ejpam-2660	152	8	∈	∈	PROPN
ejpam-2660	152	9	x	x	SYM
ejpam-2660	152	10	∧	∧	NOUN
ejpam-2660	152	11	(	(	PUNCT
ejpam-2660	152	12	a	a	DET
ejpam-2660	152	13	∨	∨	NUM
ejpam-2660	152	14	b	b	NOUN
ejpam-2660	152	15	)	)	PUNCT
ejpam-2660	152	16	}	}	PUNCT
ejpam-2660	152	17	.	.	PUNCT
ejpam-2660	153	1	theorem	theorem	VERB
ejpam-2660	153	2	23	23	NUM
ejpam-2660	153	3	.	.	PUNCT
ejpam-2660	154	1	let	let	VERB
ejpam-2660	154	2	l	l	NOUN
ejpam-2660	154	3	be	be	AUX
ejpam-2660	154	4	dual	dual	ADV
ejpam-2660	154	5	distributive	distributive	ADJ
ejpam-2660	154	6	that	that	PRON
ejpam-2660	154	7	contains	contain	VERB
ejpam-2660	154	8	the	the	DET
ejpam-2660	154	9	least	least	ADJ
ejpam-2660	154	10	element	element	NOUN
ejpam-2660	154	11	0	0	PUNCT
ejpam-2660	154	12	and	and	CCONJ
ejpam-2660	154	13	a	a	DET
ejpam-2660	154	14	∈	∈	PROPN
ejpam-2660	154	15	l.	l.	NOUN
ejpam-2660	154	16	then	then	ADV
ejpam-2660	154	17	:	:	PUNCT
ejpam-2660	154	18	m.	m.	NOUN
ejpam-2660	154	19	amiri	amiri	PROPN
ejpam-2660	154	20	bideshki	bideshki	PROPN
ejpam-2660	154	21	,	,	PUNCT
ejpam-2660	154	22	r.	r.	PROPN
ejpam-2660	154	23	ameri	ameri	PROPN
ejpam-2660	154	24	,	,	PUNCT
ejpam-2660	155	1	a.	a.	PROPN
ejpam-2660	155	2	borumand	borumand	PROPN
ejpam-2660	156	1	saeid	saeid	PROPN
ejpam-2660	156	2	/	/	SYM
ejpam-2660	156	3	eur	eur	PROPN
ejpam-2660	156	4	.	.	PUNCT
ejpam-2660	157	1	j.	j.	PROPN
ejpam-2660	157	2	pure	pure	PROPN
ejpam-2660	157	3	appl	appl	PROPN
ejpam-2660	157	4	.	.	PROPN
ejpam-2660	157	5	math	math	PROPN
ejpam-2660	157	6	,	,	PUNCT
ejpam-2660	157	7	11	11	NUM
ejpam-2660	157	8	(	(	PUNCT
ejpam-2660	157	9	1	1	NUM
ejpam-2660	157	10	)	)	PUNCT
ejpam-2660	157	11	(	(	PUNCT
ejpam-2660	157	12	2018	2018	NUM
ejpam-2660	157	13	)	)	PUNCT
ejpam-2660	157	14	,	,	PUNCT
ejpam-2660	157	15	169	169	NUM
ejpam-2660	157	16	-	-	SYM
ejpam-2660	157	17	188	188	NUM
ejpam-2660	157	18	175	175	NUM
ejpam-2660	157	19	(	(	PUNCT
ejpam-2660	157	20	i	i	NOUN
ejpam-2660	157	21	)	)	PUNCT
ejpam-2660	157	22	ia	ia	PROPN
ejpam-2660	157	23	=	=	SYM
ejpam-2660	157	24	{	{	PUNCT
ejpam-2660	157	25	x	x	PUNCT
ejpam-2660	157	26	∈	∈	NOUN
ejpam-2660	157	27	l	l	NOUN
ejpam-2660	158	1	|	|	NOUN
ejpam-2660	158	2	0	0	NUM
ejpam-2660	158	3	∈	∈	PROPN
ejpam-2660	158	4	x	x	PUNCT
ejpam-2660	158	5	∧	∧	NOUN
ejpam-2660	158	6	a	a	PRON
ejpam-2660	158	7	}	}	PUNCT
ejpam-2660	158	8	is	be	AUX
ejpam-2660	158	9	a	a	DET
ejpam-2660	158	10	hyperideal	hyperideal	NOUN
ejpam-2660	158	11	of	of	ADP
ejpam-2660	158	12	l.	l.	PROPN
ejpam-2660	158	13	(	(	PUNCT
ejpam-2660	158	14	ii	ii	PROPN
ejpam-2660	158	15	)	)	PUNCT
ejpam-2660	158	16	i(a	i(a	PROPN
ejpam-2660	158	17	)	)	PUNCT
ejpam-2660	159	1	=	=	PRON
ejpam-2660	159	2	{	{	PUNCT
ejpam-2660	159	3	x	x	PUNCT
ejpam-2660	159	4	∈	∈	NOUN
ejpam-2660	159	5	l	l	NOUN
ejpam-2660	160	1	|	|	NOUN
ejpam-2660	160	2	x	x	SYM
ejpam-2660	160	3	∈	∈	NOUN
ejpam-2660	160	4	x	x	PUNCT
ejpam-2660	160	5	∧	∧	NOUN
ejpam-2660	160	6	a	a	PRON
ejpam-2660	160	7	}	}	PUNCT
ejpam-2660	160	8	is	be	AUX
ejpam-2660	160	9	the	the	DET
ejpam-2660	160	10	least	least	ADJ
ejpam-2660	160	11	hyperideal	hyperideal	NOUN
ejpam-2660	160	12	of	of	ADP
ejpam-2660	160	13	l	l	NOUN
ejpam-2660	160	14	that	that	PRON
ejpam-2660	160	15	contains	contain	VERB
ejpam-2660	160	16	a.	a.	NOUN
ejpam-2660	160	17	proof	proof	NOUN
ejpam-2660	160	18	.	.	PUNCT
ejpam-2660	161	1	(	(	PUNCT
ejpam-2660	161	2	i	i	NOUN
ejpam-2660	161	3	):	):	PUNCT
ejpam-2660	161	4	let	let	VERB
ejpam-2660	161	5	x	x	PRON
ejpam-2660	161	6	,	,	PUNCT
ejpam-2660	161	7	y	y	PROPN
ejpam-2660	161	8	∈	∈	PROPN
ejpam-2660	161	9	ia	ia	PROPN
ejpam-2660	161	10	.	.	PUNCT
ejpam-2660	162	1	so	so	ADV
ejpam-2660	162	2	0	0	NUM
ejpam-2660	162	3	∈	∈	PROPN
ejpam-2660	162	4	x	x	X
ejpam-2660	162	5	∧	∧	NOUN
ejpam-2660	162	6	a	a	PRON
ejpam-2660	162	7	and	and	CCONJ
ejpam-2660	162	8	0	0	NUM
ejpam-2660	162	9	∈	∈	PROPN
ejpam-2660	162	10	y	y	PROPN
ejpam-2660	162	11	∧	∧	PROPN
ejpam-2660	162	12	a.	a.	NOUN
ejpam-2660	162	13	we	we	PRON
ejpam-2660	162	14	have	have	VERB
ejpam-2660	162	15	0	0	NUM
ejpam-2660	162	16	∨	∨	NUM
ejpam-2660	162	17	0	0	NUM
ejpam-2660	163	1	=	=	SYM
ejpam-2660	163	2	0	0	NUM
ejpam-2660	163	3	,	,	PUNCT
ejpam-2660	163	4	therefore	therefore	ADV
ejpam-2660	163	5	0	0	X
ejpam-2660	163	6	∈	∈	NOUN
ejpam-2660	163	7	(	(	PUNCT
ejpam-2660	163	8	x	x	PART
ejpam-2660	163	9	∧	∧	NOUN
ejpam-2660	163	10	a	a	PRON
ejpam-2660	163	11	)	)	PUNCT
ejpam-2660	163	12	∨	∨	NOUN
ejpam-2660	163	13	(	(	PUNCT
ejpam-2660	163	14	y	y	PROPN
ejpam-2660	163	15	∧	∧	PROPN
ejpam-2660	163	16	a	a	PRON
ejpam-2660	163	17	)	)	PUNCT
ejpam-2660	163	18	,	,	PUNCT
ejpam-2660	163	19	and	and	CCONJ
ejpam-2660	163	20	since	since	SCONJ
ejpam-2660	163	21	l	l	NOUN
ejpam-2660	163	22	is	be	AUX
ejpam-2660	163	23	dual	dual	ADV
ejpam-2660	163	24	distributive	distributive	ADJ
ejpam-2660	163	25	,	,	PUNCT
ejpam-2660	163	26	0	0	NUM
ejpam-2660	163	27	∈	∈	PROPN
ejpam-2660	163	28	a	a	DET
ejpam-2660	163	29	∧	∧	PROPN
ejpam-2660	163	30	(	(	PUNCT
ejpam-2660	163	31	x	x	PROPN
ejpam-2660	163	32	∨	∨	NUM
ejpam-2660	163	33	y	y	PROPN
ejpam-2660	163	34	)	)	PUNCT
ejpam-2660	164	1	,	,	PUNCT
ejpam-2660	164	2	it	it	PRON
ejpam-2660	164	3	implies	imply	VERB
ejpam-2660	164	4	that	that	SCONJ
ejpam-2660	164	5	x	x	PROPN
ejpam-2660	164	6	∨	∨	NUM
ejpam-2660	164	7	y	y	PROPN
ejpam-2660	164	8	∈	∈	PROPN
ejpam-2660	164	9	ia	ia	PROPN
ejpam-2660	164	10	.	.	PUNCT
ejpam-2660	165	1	now	now	ADV
ejpam-2660	165	2	,	,	PUNCT
ejpam-2660	165	3	let	let	VERB
ejpam-2660	165	4	x	x	X
ejpam-2660	165	5	∈	∈	PROPN
ejpam-2660	165	6	ia	ia	PROPN
ejpam-2660	165	7	,	,	PUNCT
ejpam-2660	165	8	and	and	CCONJ
ejpam-2660	165	9	y	y	PROPN
ejpam-2660	165	10	≤	≤	PROPN
ejpam-2660	165	11	x.	x.	PUNCT
ejpam-2660	166	1	so	so	CCONJ
ejpam-2660	166	2	0	0	NUM
ejpam-2660	166	3	∈	∈	PROPN
ejpam-2660	166	4	x	x	PUNCT
ejpam-2660	166	5	∧	∧	NOUN
ejpam-2660	166	6	a	a	PRON
ejpam-2660	166	7	and	and	CCONJ
ejpam-2660	166	8	x	x	SYM
ejpam-2660	166	9	∨	∨	NOUN
ejpam-2660	166	10	y	y	NOUN
ejpam-2660	166	11	=	=	PUNCT
ejpam-2660	166	12	x.	x.	NOUN
ejpam-2660	166	13	thus	thus	ADV
ejpam-2660	166	14	we	we	PRON
ejpam-2660	166	15	have	have	VERB
ejpam-2660	166	16	0	0	NUM
ejpam-2660	166	17	∈	∈	NOUN
ejpam-2660	166	18	(	(	PUNCT
ejpam-2660	166	19	x	x	PROPN
ejpam-2660	166	20	∨	∨	NUM
ejpam-2660	166	21	y	y	NOUN
ejpam-2660	166	22	)	)	PUNCT
ejpam-2660	166	23	∧	∧	PROPN
ejpam-2660	166	24	a	a	NOUN
ejpam-2660	166	25	,	,	PUNCT
ejpam-2660	166	26	and	and	CCONJ
ejpam-2660	166	27	since	since	SCONJ
ejpam-2660	166	28	l	l	NOUN
ejpam-2660	166	29	is	be	AUX
ejpam-2660	166	30	dual	dual	ADV
ejpam-2660	166	31	distributive	distributive	ADJ
ejpam-2660	166	32	,	,	PUNCT
ejpam-2660	166	33	0	0	NUM
ejpam-2660	166	34	∈	∈	NOUN
ejpam-2660	166	35	(	(	PUNCT
ejpam-2660	166	36	x	x	PART
ejpam-2660	166	37	∧	∧	NOUN
ejpam-2660	166	38	a	a	PRON
ejpam-2660	166	39	)	)	PUNCT
ejpam-2660	166	40	∨	∨	NOUN
ejpam-2660	166	41	(	(	PUNCT
ejpam-2660	166	42	y	y	PROPN
ejpam-2660	166	43	∧	∧	PROPN
ejpam-2660	166	44	a	a	PRON
ejpam-2660	166	45	)	)	PUNCT
ejpam-2660	166	46	.	.	PUNCT
ejpam-2660	167	1	since	since	SCONJ
ejpam-2660	167	2	0	0	NUM
ejpam-2660	167	3	∈	∈	PROPN
ejpam-2660	167	4	(	(	PUNCT
ejpam-2660	167	5	x	x	PART
ejpam-2660	167	6	∧	∧	NOUN
ejpam-2660	167	7	a	a	NOUN
ejpam-2660	167	8	)	)	PUNCT
ejpam-2660	167	9	and	and	CCONJ
ejpam-2660	167	10	0	0	NUM
ejpam-2660	167	11	∨	∨	NUM
ejpam-2660	167	12	0	0	NUM
ejpam-2660	168	1	=	=	SYM
ejpam-2660	168	2	0	0	NUM
ejpam-2660	168	3	,	,	PUNCT
ejpam-2660	168	4	we	we	PRON
ejpam-2660	168	5	conclude	conclude	VERB
ejpam-2660	168	6	0	0	NUM
ejpam-2660	168	7	∈	∈	PROPN
ejpam-2660	168	8	y	y	PROPN
ejpam-2660	168	9	∧	∧	PROPN
ejpam-2660	168	10	a.	a.	NOUN
ejpam-2660	168	11	(	(	PUNCT
ejpam-2660	168	12	ii	ii	PROPN
ejpam-2660	168	13	):	):	PUNCT
ejpam-2660	168	14	let	let	VERB
ejpam-2660	168	15	x	x	PRON
ejpam-2660	168	16	,	,	PUNCT
ejpam-2660	168	17	y	y	PROPN
ejpam-2660	168	18	∈	∈	PROPN
ejpam-2660	168	19	i(a	i(a	PROPN
ejpam-2660	168	20	)	)	PUNCT
ejpam-2660	168	21	.	.	PUNCT
ejpam-2660	169	1	then	then	ADV
ejpam-2660	169	2	a	a	DET
ejpam-2660	169	3	∈	∈	NOUN
ejpam-2660	169	4	x	x	PUNCT
ejpam-2660	169	5	∧	∧	PROPN
ejpam-2660	169	6	a	a	PRON
ejpam-2660	169	7	and	and	CCONJ
ejpam-2660	169	8	a	a	DET
ejpam-2660	169	9	∈	∈	NOUN
ejpam-2660	169	10	y	y	PROPN
ejpam-2660	169	11	∧	∧	PROPN
ejpam-2660	169	12	a.	a.	NOUN
ejpam-2660	169	13	since	since	SCONJ
ejpam-2660	169	14	l	l	PROPN
ejpam-2660	169	15	is	be	AUX
ejpam-2660	169	16	dual	dual	ADV
ejpam-2660	169	17	distributive	distributive	ADJ
ejpam-2660	169	18	and	and	CCONJ
ejpam-2660	169	19	a	a	DET
ejpam-2660	169	20	∨	∨	NOUN
ejpam-2660	169	21	a	a	DET
ejpam-2660	169	22	=	=	NOUN
ejpam-2660	169	23	a	a	NOUN
ejpam-2660	169	24	,	,	PUNCT
ejpam-2660	169	25	we	we	PRON
ejpam-2660	169	26	have	have	VERB
ejpam-2660	169	27	a	a	DET
ejpam-2660	169	28	∈	∈	NOUN
ejpam-2660	169	29	(	(	PUNCT
ejpam-2660	169	30	x	x	PART
ejpam-2660	169	31	∧	∧	NOUN
ejpam-2660	169	32	a	a	PRON
ejpam-2660	169	33	)	)	PUNCT
ejpam-2660	169	34	∨	∨	NOUN
ejpam-2660	169	35	(	(	PUNCT
ejpam-2660	169	36	y	y	PROPN
ejpam-2660	169	37	∧	∧	PROPN
ejpam-2660	169	38	a	a	X
ejpam-2660	169	39	)	)	PUNCT
ejpam-2660	169	40	=	=	PUNCT
ejpam-2660	169	41	a	a	DET
ejpam-2660	169	42	∧	∧	PROPN
ejpam-2660	169	43	(	(	PUNCT
ejpam-2660	169	44	x	x	PROPN
ejpam-2660	169	45	∨	∨	NUM
ejpam-2660	169	46	y	y	PROPN
ejpam-2660	169	47	)	)	PUNCT
ejpam-2660	169	48	and	and	CCONJ
ejpam-2660	169	49	it	it	PRON
ejpam-2660	169	50	implies	imply	VERB
ejpam-2660	169	51	that	that	SCONJ
ejpam-2660	169	52	x	x	PROPN
ejpam-2660	169	53	∨	∨	NUM
ejpam-2660	169	54	y	y	PROPN
ejpam-2660	169	55	∈	∈	PROPN
ejpam-2660	169	56	i(a	i(a	PROPN
ejpam-2660	169	57	)	)	PUNCT
ejpam-2660	169	58	.	.	PUNCT
ejpam-2660	170	1	now	now	ADV
ejpam-2660	170	2	,	,	PUNCT
ejpam-2660	170	3	let	let	VERB
ejpam-2660	170	4	x	x	X
ejpam-2660	170	5	∈	∈	PROPN
ejpam-2660	170	6	i(a	i(a	PROPN
ejpam-2660	170	7	)	)	PUNCT
ejpam-2660	170	8	,	,	PUNCT
ejpam-2660	170	9	and	and	CCONJ
ejpam-2660	170	10	y	y	PROPN
ejpam-2660	170	11	≤	≤	PROPN
ejpam-2660	170	12	x.	x.	PUNCT
ejpam-2660	171	1	so	so	ADV
ejpam-2660	171	2	x	x	SYM
ejpam-2660	171	3	∈	∈	PROPN
ejpam-2660	171	4	x	x	X
ejpam-2660	171	5	∧	∧	NOUN
ejpam-2660	171	6	a	a	PRON
ejpam-2660	171	7	,	,	PUNCT
ejpam-2660	171	8	and	and	CCONJ
ejpam-2660	171	9	y	y	PROPN
ejpam-2660	171	10	∈	∈	PROPN
ejpam-2660	171	11	x	x	PUNCT
ejpam-2660	171	12	∧	∧	NOUN
ejpam-2660	171	13	y.	y.	NOUN
ejpam-2660	171	14	thus	thus	ADV
ejpam-2660	171	15	we	we	PRON
ejpam-2660	171	16	have	have	VERB
ejpam-2660	171	17	a	a	DET
ejpam-2660	171	18	∨	∨	NOUN
ejpam-2660	171	19	x	x	SYM
ejpam-2660	171	20	=	=	PUNCT
ejpam-2660	171	21	a	a	PROPN
ejpam-2660	171	22	and	and	CCONJ
ejpam-2660	171	23	x	x	SYM
ejpam-2660	171	24	∨	∨	NUM
ejpam-2660	171	25	y	y	NOUN
ejpam-2660	171	26	=	=	SYM
ejpam-2660	171	27	x	x	PROPN
ejpam-2660	171	28	,	,	PUNCT
ejpam-2660	171	29	so	so	ADV
ejpam-2660	171	30	a	a	DET
ejpam-2660	171	31	∨	∨	NUM
ejpam-2660	171	32	y	y	NOUN
ejpam-2660	171	33	=	=	PUNCT
ejpam-2660	171	34	(	(	PUNCT
ejpam-2660	171	35	a	a	DET
ejpam-2660	171	36	∨	∨	NUM
ejpam-2660	171	37	x	x	SYM
ejpam-2660	171	38	)	)	PUNCT
ejpam-2660	171	39	∨	∨	NUM
ejpam-2660	171	40	y	y	PROPN
ejpam-2660	171	41	=	=	PUNCT
ejpam-2660	171	42	a	a	DET
ejpam-2660	171	43	∨	∨	NOUN
ejpam-2660	171	44	(	(	PUNCT
ejpam-2660	171	45	x	x	PROPN
ejpam-2660	171	46	∨	∨	NUM
ejpam-2660	171	47	y	y	PROPN
ejpam-2660	171	48	)	)	PUNCT
ejpam-2660	171	49	=	=	PUNCT
ejpam-2660	171	50	a	a	DET
ejpam-2660	171	51	∨	∨	NOUN
ejpam-2660	171	52	x	x	X
ejpam-2660	171	53	=	=	PUNCT
ejpam-2660	171	54	a.	a.	NOUN
ejpam-2660	171	55	then	then	ADV
ejpam-2660	171	56	a	a	DET
ejpam-2660	171	57	∨	∨	NOUN
ejpam-2660	171	58	y	y	NOUN
ejpam-2660	171	59	=	=	PUNCT
ejpam-2660	171	60	a	a	PROPN
ejpam-2660	172	1	and	and	CCONJ
ejpam-2660	172	2	it	it	PRON
ejpam-2660	172	3	implies	imply	VERB
ejpam-2660	172	4	that	that	SCONJ
ejpam-2660	172	5	y	y	PROPN
ejpam-2660	172	6	∈	∈	PROPN
ejpam-2660	172	7	a	a	DET
ejpam-2660	172	8	∧	∧	PROPN
ejpam-2660	172	9	y	y	PROPN
ejpam-2660	172	10	;	;	PUNCT
ejpam-2660	172	11	therefore	therefore	ADV
ejpam-2660	172	12	y	y	PROPN
ejpam-2660	172	13	∈	∈	PROPN
ejpam-2660	172	14	i(a	i(a	PROPN
ejpam-2660	172	15	)	)	PUNCT
ejpam-2660	172	16	.	.	PUNCT
ejpam-2660	173	1	corollary	corollary	ADJ
ejpam-2660	173	2	24	24	NUM
ejpam-2660	173	3	.	.	PUNCT
ejpam-2660	174	1	let	let	VERB
ejpam-2660	174	2	l	l	NOUN
ejpam-2660	174	3	be	be	AUX
ejpam-2660	174	4	bounded	bound	VERB
ejpam-2660	174	5	dual	dual	ADJ
ejpam-2660	174	6	distributive	distributive	ADJ
ejpam-2660	174	7	.	.	PUNCT
ejpam-2660	175	1	then	then	ADV
ejpam-2660	175	2	we	we	PRON
ejpam-2660	175	3	have	have	VERB
ejpam-2660	175	4	:	:	PUNCT
ejpam-2660	175	5	(	(	PUNCT
ejpam-2660	175	6	i	i	NOUN
ejpam-2660	175	7	)	)	PUNCT
ejpam-2660	175	8	i(0	i(0	PROPN
ejpam-2660	175	9	)	)	PUNCT
ejpam-2660	175	10	=	=	PRON
ejpam-2660	175	11	{	{	PUNCT
ejpam-2660	175	12	0	0	NUM
ejpam-2660	175	13	}	}	PUNCT
ejpam-2660	175	14	;	;	PUNCT
ejpam-2660	175	15	(	(	PUNCT
ejpam-2660	175	16	ii	ii	NOUN
ejpam-2660	175	17	)	)	PUNCT
ejpam-2660	175	18	i(1	i(1	PROPN
ejpam-2660	175	19	)	)	PUNCT
ejpam-2660	175	20	=	=	SYM
ejpam-2660	176	1	l	l	NOUN
ejpam-2660	176	2	;	;	PUNCT
ejpam-2660	176	3	(	(	PUNCT
ejpam-2660	176	4	iii	iii	X
ejpam-2660	176	5	)	)	PUNCT
ejpam-2660	176	6	if	if	SCONJ
ejpam-2660	176	7	a	a	PRON
ejpam-2660	176	8	,	,	PUNCT
ejpam-2660	176	9	b	b	PROPN
ejpam-2660	176	10	∈	∈	PROPN
ejpam-2660	176	11	l	l	NOUN
ejpam-2660	176	12	,	,	PUNCT
ejpam-2660	176	13	and	and	CCONJ
ejpam-2660	176	14	a	a	DET
ejpam-2660	176	15	≤	≤	NUM
ejpam-2660	176	16	b	b	NOUN
ejpam-2660	176	17	,	,	PUNCT
ejpam-2660	176	18	then	then	ADV
ejpam-2660	176	19	i(a	i(a	PROPN
ejpam-2660	176	20	)	)	PUNCT
ejpam-2660	176	21	⊆	⊆	NUM
ejpam-2660	176	22	i(b	i(b	NOUN
ejpam-2660	176	23	)	)	PUNCT
ejpam-2660	176	24	,	,	PUNCT
ejpam-2660	176	25	and	and	CCONJ
ejpam-2660	176	26	ib	ib	VERB
ejpam-2660	176	27	⊆	⊆	NUM
ejpam-2660	176	28	ia	ia	PROPN
ejpam-2660	176	29	;	;	PUNCT
ejpam-2660	176	30	(	(	PUNCT
ejpam-2660	176	31	iv	iv	X
ejpam-2660	176	32	)	)	PUNCT
ejpam-2660	176	33	i0	i0	PROPN
ejpam-2660	176	34	=	=	SYM
ejpam-2660	176	35	l	l	PROPN
ejpam-2660	176	36	;	;	PUNCT
ejpam-2660	176	37	(	(	PUNCT
ejpam-2660	176	38	v	v	NOUN
ejpam-2660	176	39	)	)	PUNCT
ejpam-2660	176	40	i(a	i(a	PROPN
ejpam-2660	176	41	)	)	PUNCT
ejpam-2660	176	42	,	,	PUNCT
ejpam-2660	176	43	i(b	i(b	PROPN
ejpam-2660	176	44	)	)	PUNCT
ejpam-2660	176	45	⊆	⊆	NUM
ejpam-2660	176	46	i(a	i(a	PROPN
ejpam-2660	176	47	∨	∨	NUM
ejpam-2660	176	48	b	b	NOUN
ejpam-2660	176	49	)	)	PUNCT
ejpam-2660	176	50	.	.	PUNCT
ejpam-2660	177	1	lemma	lemma	PROPN
ejpam-2660	177	2	25	25	NUM
ejpam-2660	177	3	.	.	PUNCT
ejpam-2660	178	1	let	let	VERB
ejpam-2660	178	2	l	l	NOUN
ejpam-2660	178	3	be	be	AUX
ejpam-2660	178	4	dual	dual	ADV
ejpam-2660	178	5	distributive	distributive	ADJ
ejpam-2660	178	6	.	.	PUNCT
ejpam-2660	179	1	if	if	SCONJ
ejpam-2660	179	2	i	i	PRON
ejpam-2660	179	3	is	be	AUX
ejpam-2660	179	4	a	a	DET
ejpam-2660	179	5	hyperideal	hyperideal	NOUN
ejpam-2660	179	6	of	of	ADP
ejpam-2660	179	7	l	l	NOUN
ejpam-2660	179	8	and	and	CCONJ
ejpam-2660	179	9	a	a	DET
ejpam-2660	179	10	∈	∈	PROPN
ejpam-2660	179	11	l	l	NOUN
ejpam-2660	179	12	,	,	PUNCT
ejpam-2660	179	13	then	then	ADV
ejpam-2660	179	14	i	i	PRON
ejpam-2660	179	15	∨	∨	PROPN
ejpam-2660	179	16	i(a	i(a	PROPN
ejpam-2660	179	17	)	)	PUNCT
ejpam-2660	179	18	is	be	AUX
ejpam-2660	179	19	a	a	DET
ejpam-2660	179	20	”	"	PUNCT
ejpam-2660	179	21	∨	∨	NUM
ejpam-2660	179	22	”	"	PUNCT
ejpam-2660	179	23	-closed	-close	VERB
ejpam-2660	179	24	subset	subset	NOUN
ejpam-2660	179	25	of	of	ADP
ejpam-2660	179	26	l.	l.	PROPN
ejpam-2660	179	27	proof	proof	PROPN
ejpam-2660	179	28	.	.	PUNCT
ejpam-2660	180	1	let	let	VERB
ejpam-2660	180	2	x	x	PRON
ejpam-2660	180	3	,	,	PUNCT
ejpam-2660	180	4	y	y	PROPN
ejpam-2660	180	5	∈	∈	PROPN
ejpam-2660	180	6	i	i	PROPN
ejpam-2660	180	7	∨	∨	NUM
ejpam-2660	180	8	i(a	i(a	PROPN
ejpam-2660	180	9	)	)	PUNCT
ejpam-2660	180	10	.	.	PUNCT
ejpam-2660	181	1	so	so	ADV
ejpam-2660	181	2	there	there	PRON
ejpam-2660	181	3	exist	exist	VERB
ejpam-2660	181	4	p1	p1	NOUN
ejpam-2660	181	5	,	,	PUNCT
ejpam-2660	181	6	p2	p2	PROPN
ejpam-2660	181	7	∈	∈	PROPN
ejpam-2660	182	1	i	i	PROPN
ejpam-2660	182	2	and	and	CCONJ
ejpam-2660	182	3	a1	a1	PROPN
ejpam-2660	182	4	,	,	PUNCT
ejpam-2660	182	5	a2	a2	PROPN
ejpam-2660	182	6	∈	∈	PROPN
ejpam-2660	182	7	i(a	i(a	PROPN
ejpam-2660	182	8	)	)	PUNCT
ejpam-2660	182	9	,	,	PUNCT
ejpam-2660	182	10	such	such	ADJ
ejpam-2660	182	11	that	that	SCONJ
ejpam-2660	182	12	x	x	SYM
ejpam-2660	182	13	=	=	SYM
ejpam-2660	182	14	p1	p1	PROPN
ejpam-2660	182	15	∨	∨	NUM
ejpam-2660	182	16	a1	a1	PROPN
ejpam-2660	182	17	,	,	PUNCT
ejpam-2660	182	18	y	y	NOUN
ejpam-2660	182	19	=	=	PUNCT
ejpam-2660	182	20	p2	p2	PROPN
ejpam-2660	182	21	∨	∨	NUM
ejpam-2660	182	22	a2	a2	PROPN
ejpam-2660	182	23	.	.	PUNCT
ejpam-2660	183	1	we	we	PRON
ejpam-2660	183	2	have	have	VERB
ejpam-2660	183	3	:	:	PUNCT
ejpam-2660	183	4	x	x	PROPN
ejpam-2660	183	5	∨	∨	NUM
ejpam-2660	183	6	y	y	PROPN
ejpam-2660	183	7	=	=	PROPN
ejpam-2660	183	8	p1	p1	PROPN
ejpam-2660	183	9	∨	∨	NUM
ejpam-2660	183	10	a1	a1	PROPN
ejpam-2660	183	11	∨	∨	NOUN
ejpam-2660	183	12	p2	p2	PROPN
ejpam-2660	183	13	∨	∨	NUM
ejpam-2660	183	14	a2	a2	PROPN
ejpam-2660	183	15	=	=	PUNCT
ejpam-2660	183	16	(	(	PUNCT
ejpam-2660	183	17	p1	p1	PROPN
ejpam-2660	183	18	∨	∨	NUM
ejpam-2660	183	19	p2	p2	PROPN
ejpam-2660	183	20	)	)	PUNCT
ejpam-2660	183	21	∨	∨	NOUN
ejpam-2660	183	22	(	(	PUNCT
ejpam-2660	183	23	a1	a1	PROPN
ejpam-2660	183	24	∨	∨	NUM
ejpam-2660	183	25	a2	a2	PROPN
ejpam-2660	183	26	)	)	PUNCT
ejpam-2660	183	27	.	.	PUNCT
ejpam-2660	184	1	we	we	PRON
ejpam-2660	184	2	know	know	VERB
ejpam-2660	184	3	p1	p1	PROPN
ejpam-2660	184	4	∨	∨	NUM
ejpam-2660	184	5	p2	p2	PROPN
ejpam-2660	184	6	∈	∈	PROPN
ejpam-2660	185	1	i	i	PRON
ejpam-2660	185	2	and	and	CCONJ
ejpam-2660	185	3	a1	a1	NOUN
ejpam-2660	185	4	∨	∨	NUM
ejpam-2660	185	5	a2	a2	PROPN
ejpam-2660	185	6	∈	∈	PROPN
ejpam-2660	185	7	i(a	i(a	PROPN
ejpam-2660	185	8	)	)	PUNCT
ejpam-2660	185	9	.	.	PUNCT
ejpam-2660	186	1	therefore	therefore	ADV
ejpam-2660	186	2	x	x	PROPN
ejpam-2660	186	3	∨	∨	NUM
ejpam-2660	186	4	y	y	PROPN
ejpam-2660	186	5	∈	∈	PROPN
ejpam-2660	186	6	i	i	PRON
ejpam-2660	186	7	∨	∨	NUM
ejpam-2660	186	8	i(a	i(a	PROPN
ejpam-2660	186	9	)	)	PUNCT
ejpam-2660	186	10	.	.	PUNCT
ejpam-2660	187	1	definition	definition	NOUN
ejpam-2660	187	2	26	26	NUM
ejpam-2660	187	3	.	.	PUNCT
ejpam-2660	188	1	let	let	VERB
ejpam-2660	188	2	l	l	NOUN
ejpam-2660	188	3	be	be	AUX
ejpam-2660	188	4	distributive	distributive	ADJ
ejpam-2660	188	5	and	and	CCONJ
ejpam-2660	188	6	a	a	DET
ejpam-2660	188	7	⊆	⊆	NUM
ejpam-2660	188	8	l.	l.	NOUN
ejpam-2660	188	9	then	then	ADV
ejpam-2660	188	10	the	the	DET
ejpam-2660	188	11	least	least	ADJ
ejpam-2660	188	12	hyperfilter	hyperfilter	NOUN
ejpam-2660	188	13	of	of	ADP
ejpam-2660	188	14	l	l	NOUN
ejpam-2660	188	15	that	that	PRON
ejpam-2660	188	16	contains	contain	VERB
ejpam-2660	188	17	a	a	PRON
ejpam-2660	188	18	,	,	PUNCT
ejpam-2660	188	19	is	be	AUX
ejpam-2660	188	20	called	call	VERB
ejpam-2660	188	21	the	the	DET
ejpam-2660	188	22	generating	generate	VERB
ejpam-2660	188	23	hyperfilter	hyperfilter	NOUN
ejpam-2660	188	24	by	by	ADP
ejpam-2660	188	25	subset	subset	NOUN
ejpam-2660	188	26	a	a	X
ejpam-2660	188	27	,	,	PUNCT
ejpam-2660	188	28	and	and	CCONJ
ejpam-2660	188	29	it	it	PRON
ejpam-2660	188	30	is	be	AUX
ejpam-2660	188	31	denoted	denote	VERB
ejpam-2660	188	32	by	by	ADP
ejpam-2660	188	33	f	f	PROPN
ejpam-2660	188	34	(	(	PUNCT
ejpam-2660	188	35	a	a	NOUN
ejpam-2660	188	36	)	)	PUNCT
ejpam-2660	188	37	.	.	PUNCT
ejpam-2660	189	1	proposition	proposition	NOUN
ejpam-2660	189	2	27	27	NUM
ejpam-2660	189	3	.	.	PUNCT
ejpam-2660	190	1	let	let	VERB
ejpam-2660	190	2	l	l	NOUN
ejpam-2660	190	3	be	be	AUX
ejpam-2660	190	4	distributive	distributive	ADJ
ejpam-2660	190	5	and	and	CCONJ
ejpam-2660	190	6	a	a	DET
ejpam-2660	190	7	∈	∈	PROPN
ejpam-2660	190	8	l.	l.	NOUN
ejpam-2660	191	1	then	then	ADV
ejpam-2660	191	2	f	f	PROPN
ejpam-2660	191	3	(	(	PUNCT
ejpam-2660	191	4	a	a	X
ejpam-2660	191	5	)	)	PUNCT
ejpam-2660	191	6	=	=	SYM
ejpam-2660	191	7	{	{	PUNCT
ejpam-2660	191	8	x	x	PUNCT
ejpam-2660	191	9	∈	∈	NOUN
ejpam-2660	191	10	l	l	NOUN
ejpam-2660	192	1	|	|	ADV
ejpam-2660	192	2	a	a	DET
ejpam-2660	192	3	∈	∈	PROPN
ejpam-2660	192	4	a	a	DET
ejpam-2660	192	5	∧	∧	PROPN
ejpam-2660	192	6	x	x	X
ejpam-2660	192	7	}	}	PUNCT
ejpam-2660	192	8	=	=	SYM
ejpam-2660	192	9	{	{	PUNCT
ejpam-2660	192	10	x	x	PUNCT
ejpam-2660	192	11	∈	∈	NOUN
ejpam-2660	192	12	l	l	NOUN
ejpam-2660	193	1	|	|	ADV
ejpam-2660	193	2	a	a	DET
ejpam-2660	193	3	≤	≤	NOUN
ejpam-2660	193	4	x	x	X
ejpam-2660	193	5	}	}	PUNCT
ejpam-2660	193	6	.	.	PUNCT
ejpam-2660	194	1	corollary	corollary	ADJ
ejpam-2660	194	2	28	28	NUM
ejpam-2660	194	3	.	.	PUNCT
ejpam-2660	195	1	let	let	VERB
ejpam-2660	195	2	l	l	NOUN
ejpam-2660	195	3	be	be	AUX
ejpam-2660	195	4	a	a	DET
ejpam-2660	195	5	bounded	bounded	ADJ
ejpam-2660	195	6	distributive	distributive	ADJ
ejpam-2660	195	7	”	"	PUNCT
ejpam-2660	195	8	∧	∧	NOUN
ejpam-2660	195	9	”	"	PUNCT
ejpam-2660	195	10	-hyperlattice	-hyperlattice	NOUN
ejpam-2660	195	11	and	and	CCONJ
ejpam-2660	195	12	a	a	DET
ejpam-2660	195	13	,	,	PUNCT
ejpam-2660	195	14	b	b	X
ejpam-2660	195	15	∈	∈	PROPN
ejpam-2660	195	16	l.	l.	NOUN
ejpam-2660	195	17	then	then	ADV
ejpam-2660	195	18	the	the	DET
ejpam-2660	195	19	following	follow	VERB
ejpam-2660	195	20	conditions	condition	NOUN
ejpam-2660	195	21	hold	hold	VERB
ejpam-2660	195	22	.	.	PUNCT
ejpam-2660	196	1	(	(	PUNCT
ejpam-2660	196	2	i	i	NOUN
ejpam-2660	196	3	)	)	PUNCT
ejpam-2660	196	4	f	f	PROPN
ejpam-2660	196	5	(	(	PUNCT
ejpam-2660	196	6	1	1	NUM
ejpam-2660	196	7	)	)	PUNCT
ejpam-2660	196	8	=	=	NOUN
ejpam-2660	196	9	{	{	PUNCT
ejpam-2660	196	10	1	1	NUM
ejpam-2660	196	11	}	}	PUNCT
ejpam-2660	196	12	.	.	PUNCT
ejpam-2660	197	1	m.	m.	NOUN
ejpam-2660	197	2	amiri	amiri	PROPN
ejpam-2660	197	3	bideshki	bideshki	PROPN
ejpam-2660	197	4	,	,	PUNCT
ejpam-2660	197	5	r.	r.	PROPN
ejpam-2660	197	6	ameri	ameri	PROPN
ejpam-2660	197	7	,	,	PUNCT
ejpam-2660	197	8	a.	a.	PROPN
ejpam-2660	197	9	borumand	borumand	PROPN
ejpam-2660	197	10	saeid	saeid	PROPN
ejpam-2660	197	11	/	/	SYM
ejpam-2660	197	12	eur	eur	PROPN
ejpam-2660	197	13	.	.	PUNCT
ejpam-2660	198	1	j.	j.	PROPN
ejpam-2660	198	2	pure	pure	PROPN
ejpam-2660	198	3	appl	appl	PROPN
ejpam-2660	198	4	.	.	PROPN
ejpam-2660	198	5	math	math	PROPN
ejpam-2660	198	6	,	,	PUNCT
ejpam-2660	198	7	11	11	NUM
ejpam-2660	198	8	(	(	PUNCT
ejpam-2660	198	9	1	1	NUM
ejpam-2660	198	10	)	)	PUNCT
ejpam-2660	198	11	(	(	PUNCT
ejpam-2660	198	12	2018	2018	NUM
ejpam-2660	198	13	)	)	PUNCT
ejpam-2660	198	14	,	,	PUNCT
ejpam-2660	198	15	169	169	NUM
ejpam-2660	198	16	-	-	SYM
ejpam-2660	198	17	188	188	NUM
ejpam-2660	198	18	176	176	NUM
ejpam-2660	198	19	(	(	PUNCT
ejpam-2660	198	20	ii	ii	NOUN
ejpam-2660	198	21	)	)	PUNCT
ejpam-2660	198	22	f	f	PROPN
ejpam-2660	198	23	(	(	PUNCT
ejpam-2660	198	24	0	0	NUM
ejpam-2660	198	25	)	)	PUNCT
ejpam-2660	198	26	=	=	SYM
ejpam-2660	199	1	l.	l.	PROPN
ejpam-2660	199	2	(	(	PUNCT
ejpam-2660	199	3	iii	iii	PROPN
ejpam-2660	199	4	)	)	PUNCT
ejpam-2660	199	5	f	f	NOUN
ejpam-2660	199	6	(	(	PUNCT
ejpam-2660	199	7	a	a	NOUN
ejpam-2660	199	8	)	)	PUNCT
ejpam-2660	199	9	∨	∨	PROPN
ejpam-2660	199	10	f	f	X
ejpam-2660	199	11	(	(	PUNCT
ejpam-2660	199	12	b	b	NOUN
ejpam-2660	199	13	)	)	PUNCT
ejpam-2660	199	14	=	=	SYM
ejpam-2660	199	15	f	f	PROPN
ejpam-2660	199	16	(	(	PUNCT
ejpam-2660	199	17	a	a	DET
ejpam-2660	199	18	∨	∨	NUM
ejpam-2660	199	19	b	b	NOUN
ejpam-2660	199	20	)	)	PUNCT
ejpam-2660	199	21	.	.	PUNCT
ejpam-2660	200	1	(	(	PUNCT
ejpam-2660	200	2	iv	iv	X
ejpam-2660	200	3	)	)	PUNCT
ejpam-2660	200	4	if	if	SCONJ
ejpam-2660	200	5	a	a	DET
ejpam-2660	200	6	≤	≤	NUM
ejpam-2660	200	7	b	b	NOUN
ejpam-2660	200	8	,	,	PUNCT
ejpam-2660	200	9	then	then	ADV
ejpam-2660	200	10	f	f	PROPN
ejpam-2660	200	11	(	(	PUNCT
ejpam-2660	200	12	b	b	NOUN
ejpam-2660	200	13	)	)	PUNCT
ejpam-2660	200	14	⊆	⊆	NUM
ejpam-2660	200	15	f	f	NOUN
ejpam-2660	200	16	(	(	PUNCT
ejpam-2660	200	17	a	a	NOUN
ejpam-2660	200	18	)	)	PUNCT
ejpam-2660	200	19	.	.	PUNCT
ejpam-2660	201	1	lemma	lemma	PROPN
ejpam-2660	201	2	29	29	NUM
ejpam-2660	201	3	.	.	PUNCT
ejpam-2660	202	1	let	let	VERB
ejpam-2660	202	2	l	l	NOUN
ejpam-2660	202	3	be	be	AUX
ejpam-2660	202	4	a	a	DET
ejpam-2660	202	5	distributive	distributive	ADJ
ejpam-2660	202	6	”	"	PUNCT
ejpam-2660	202	7	∧	∧	NOUN
ejpam-2660	202	8	”	"	PUNCT
ejpam-2660	202	9	-hyperlattice	-hyperlattice	NOUN
ejpam-2660	202	10	and	and	CCONJ
ejpam-2660	202	11	a	a	DET
ejpam-2660	202	12	,	,	PUNCT
ejpam-2660	202	13	1	1	NUM
ejpam-2660	202	14	∈	∈	PROPN
ejpam-2660	202	15	l	l	NOUN
ejpam-2660	202	16	,	,	PUNCT
ejpam-2660	202	17	such	such	ADJ
ejpam-2660	202	18	that	that	SCONJ
ejpam-2660	202	19	a	a	PRON
ejpam-2660	202	20	/∈	/∈	NOUN
ejpam-2660	202	21	f	f	X
ejpam-2660	202	22	.	.	PUNCT
ejpam-2660	203	1	if	if	SCONJ
ejpam-2660	203	2	f	f	PROPN
ejpam-2660	203	3	is	be	AUX
ejpam-2660	203	4	a	a	DET
ejpam-2660	203	5	hyperfilter	hyperfilter	NOUN
ejpam-2660	203	6	of	of	ADP
ejpam-2660	203	7	l	l	NOUN
ejpam-2660	203	8	,	,	PUNCT
ejpam-2660	203	9	then	then	ADV
ejpam-2660	203	10	f	f	PROPN
ejpam-2660	203	11	∧	∧	PROPN
ejpam-2660	203	12	f	f	PROPN
ejpam-2660	203	13	(	(	PUNCT
ejpam-2660	203	14	a	a	NOUN
ejpam-2660	203	15	)	)	PUNCT
ejpam-2660	203	16	is	be	AUX
ejpam-2660	203	17	so	so	ADV
ejpam-2660	203	18	.	.	PUNCT
ejpam-2660	204	1	also	also	ADV
ejpam-2660	204	2	f	f	X
ejpam-2660	204	3	,	,	PUNCT
ejpam-2660	204	4	f	f	PROPN
ejpam-2660	204	5	(	(	PUNCT
ejpam-2660	204	6	a	a	X
ejpam-2660	204	7	)	)	PUNCT
ejpam-2660	204	8	$	$	SYM
ejpam-2660	204	9	(	(	PUNCT
ejpam-2660	204	10	f	f	PROPN
ejpam-2660	204	11	∧	∧	PROPN
ejpam-2660	204	12	f	f	PROPN
ejpam-2660	204	13	(	(	PUNCT
ejpam-2660	204	14	a	a	NOUN
ejpam-2660	204	15	)	)	PUNCT
ejpam-2660	204	16	)	)	PUNCT
ejpam-2660	204	17	.	.	PUNCT
ejpam-2660	205	1	proof	proof	NOUN
ejpam-2660	205	2	.	.	PUNCT
ejpam-2660	206	1	we	we	PRON
ejpam-2660	206	2	prove	prove	VERB
ejpam-2660	206	3	f	f	PROPN
ejpam-2660	206	4	,	,	PUNCT
ejpam-2660	206	5	f	f	PROPN
ejpam-2660	206	6	(	(	PUNCT
ejpam-2660	206	7	a	a	X
ejpam-2660	206	8	)	)	PUNCT
ejpam-2660	206	9	$	$	SYM
ejpam-2660	206	10	f	f	PROPN
ejpam-2660	206	11	∧	∧	PROPN
ejpam-2660	206	12	f	f	PROPN
ejpam-2660	206	13	(	(	PUNCT
ejpam-2660	206	14	a	a	NOUN
ejpam-2660	206	15	)	)	PUNCT
ejpam-2660	206	16	,	,	PUNCT
ejpam-2660	206	17	only	only	ADV
ejpam-2660	206	18	.	.	PUNCT
ejpam-2660	207	1	let	let	VERB
ejpam-2660	207	2	x	x	SYM
ejpam-2660	207	3	∈	∈	PROPN
ejpam-2660	207	4	f	f	X
ejpam-2660	207	5	.	.	PUNCT
ejpam-2660	208	1	we	we	PRON
ejpam-2660	208	2	have	have	VERB
ejpam-2660	208	3	x	x	NOUN
ejpam-2660	208	4	≤	≤	NUM
ejpam-2660	208	5	1	1	NUM
ejpam-2660	208	6	so	so	ADV
ejpam-2660	208	7	,	,	PUNCT
ejpam-2660	208	8	by	by	ADP
ejpam-2660	208	9	remark	remark	NOUN
ejpam-2660	208	10	6	6	NUM
ejpam-2660	208	11	,	,	PUNCT
ejpam-2660	208	12	x	x	SYM
ejpam-2660	208	13	∈	∈	NOUN
ejpam-2660	208	14	x	x	PUNCT
ejpam-2660	208	15	∧	∧	NOUN
ejpam-2660	208	16	1	1	NUM
ejpam-2660	208	17	,	,	PUNCT
ejpam-2660	208	18	and	and	CCONJ
ejpam-2660	208	19	since	since	SCONJ
ejpam-2660	208	20	1	1	NUM
ejpam-2660	208	21	∈	∈	PROPN
ejpam-2660	208	22	f	f	X
ejpam-2660	208	23	(	(	PUNCT
ejpam-2660	208	24	a	a	NOUN
ejpam-2660	208	25	)	)	PUNCT
ejpam-2660	208	26	,	,	PUNCT
ejpam-2660	208	27	then	then	ADV
ejpam-2660	208	28	x	x	SYM
ejpam-2660	208	29	∈	∈	PROPN
ejpam-2660	208	30	f	f	PROPN
ejpam-2660	208	31	∧	∧	PROPN
ejpam-2660	208	32	f	f	PROPN
ejpam-2660	208	33	(	(	PUNCT
ejpam-2660	208	34	a	a	NOUN
ejpam-2660	208	35	)	)	PUNCT
ejpam-2660	208	36	.	.	PUNCT
ejpam-2660	209	1	now	now	ADV
ejpam-2660	209	2	,	,	PUNCT
ejpam-2660	209	3	suppose	suppose	VERB
ejpam-2660	209	4	that	that	SCONJ
ejpam-2660	209	5	x	x	SYM
ejpam-2660	209	6	∈	∈	PROPN
ejpam-2660	209	7	f	f	X
ejpam-2660	209	8	(	(	PUNCT
ejpam-2660	209	9	a	a	NOUN
ejpam-2660	209	10	)	)	PUNCT
ejpam-2660	209	11	.	.	PUNCT
ejpam-2660	210	1	so	so	ADV
ejpam-2660	210	2	x	x	SYM
ejpam-2660	210	3	∈	∈	PROPN
ejpam-2660	210	4	1	1	NUM
ejpam-2660	210	5	∧	∧	PROPN
ejpam-2660	210	6	x	x	NOUN
ejpam-2660	210	7	,	,	PUNCT
ejpam-2660	210	8	and	and	CCONJ
ejpam-2660	210	9	it	it	PRON
ejpam-2660	210	10	implies	imply	VERB
ejpam-2660	210	11	that	that	SCONJ
ejpam-2660	210	12	x	x	SYM
ejpam-2660	210	13	∈	∈	NOUN
ejpam-2660	210	14	f	f	PROPN
ejpam-2660	210	15	∧	∧	PROPN
ejpam-2660	210	16	f	f	PROPN
ejpam-2660	210	17	(	(	PUNCT
ejpam-2660	210	18	a	a	NOUN
ejpam-2660	210	19	)	)	PUNCT
ejpam-2660	210	20	.	.	PUNCT
ejpam-2660	211	1	theorem	theorem	NOUN
ejpam-2660	211	2	30	30	NUM
ejpam-2660	211	3	.	.	PUNCT
ejpam-2660	212	1	let	let	VERB
ejpam-2660	212	2	l	l	NOUN
ejpam-2660	212	3	be	be	AUX
ejpam-2660	212	4	a	a	DET
ejpam-2660	212	5	distributive	distributive	ADJ
ejpam-2660	212	6	strong	strong	ADJ
ejpam-2660	212	7	∧−	∧−	NUM
ejpam-2660	212	8	hyperlattice	hyperlattice	NOUN
ejpam-2660	212	9	and	and	CCONJ
ejpam-2660	212	10	a	a	DET
ejpam-2660	212	11	,	,	PUNCT
ejpam-2660	212	12	b	b	PROPN
ejpam-2660	212	13	∈	∈	PROPN
ejpam-2660	212	14	l.	l.	NOUN
ejpam-2660	213	1	if	if	SCONJ
ejpam-2660	213	2	p	p	NOUN
ejpam-2660	213	3	is	be	AUX
ejpam-2660	213	4	a	a	DET
ejpam-2660	213	5	hyperfilter	hyperfilter	NOUN
ejpam-2660	213	6	of	of	ADP
ejpam-2660	213	7	l	l	NOUN
ejpam-2660	213	8	,	,	PUNCT
ejpam-2660	213	9	then	then	ADV
ejpam-2660	213	10	(	(	PUNCT
ejpam-2660	213	11	p	p	PROPN
ejpam-2660	213	12	∧	∧	PROPN
ejpam-2660	213	13	f	f	X
ejpam-2660	213	14	(	(	PUNCT
ejpam-2660	213	15	a	a	NOUN
ejpam-2660	213	16	)	)	PUNCT
ejpam-2660	213	17	)	)	PUNCT
ejpam-2660	213	18	∨	∨	PROPN
ejpam-2660	213	19	(	(	PUNCT
ejpam-2660	213	20	p	p	PROPN
ejpam-2660	213	21	∧	∧	PROPN
ejpam-2660	213	22	f	f	X
ejpam-2660	213	23	(	(	PUNCT
ejpam-2660	213	24	b	b	NOUN
ejpam-2660	213	25	)	)	PUNCT
ejpam-2660	213	26	)	)	PUNCT
ejpam-2660	214	1	=	=	PUNCT
ejpam-2660	215	1	p	p	X
ejpam-2660	215	2	∧	∧	PROPN
ejpam-2660	215	3	f	f	PROPN
ejpam-2660	215	4	(	(	PUNCT
ejpam-2660	215	5	a	a	DET
ejpam-2660	215	6	∨	∨	NUM
ejpam-2660	215	7	b	b	NOUN
ejpam-2660	215	8	)	)	PUNCT
ejpam-2660	215	9	.	.	PUNCT
ejpam-2660	216	1	proof	proof	NOUN
ejpam-2660	216	2	.	.	PUNCT
ejpam-2660	217	1	let	let	VERB
ejpam-2660	217	2	x	x	PUNCT
ejpam-2660	217	3	∈	∈	PROPN
ejpam-2660	217	4	p	p	PROPN
ejpam-2660	217	5	∧	∧	PROPN
ejpam-2660	217	6	(	(	PUNCT
ejpam-2660	217	7	f	f	PROPN
ejpam-2660	217	8	(	(	PUNCT
ejpam-2660	217	9	a	a	DET
ejpam-2660	217	10	∨	∨	NUM
ejpam-2660	217	11	b	b	NOUN
ejpam-2660	217	12	)	)	PUNCT
ejpam-2660	217	13	.	.	PUNCT
ejpam-2660	218	1	so	so	ADV
ejpam-2660	218	2	there	there	PRON
ejpam-2660	218	3	exist	exist	VERB
ejpam-2660	218	4	p	p	PROPN
ejpam-2660	218	5	∈	∈	PROPN
ejpam-2660	218	6	p	p	NOUN
ejpam-2660	218	7	,	,	PUNCT
ejpam-2660	218	8	and	and	CCONJ
ejpam-2660	218	9	c	c	X
ejpam-2660	218	10	∈	∈	PROPN
ejpam-2660	218	11	f	f	X
ejpam-2660	218	12	(	(	PUNCT
ejpam-2660	218	13	a	a	DET
ejpam-2660	218	14	∨	∨	NUM
ejpam-2660	218	15	b	b	NOUN
ejpam-2660	218	16	)	)	PUNCT
ejpam-2660	218	17	,	,	PUNCT
ejpam-2660	218	18	such	such	ADJ
ejpam-2660	218	19	that	that	SCONJ
ejpam-2660	218	20	x	x	SYM
ejpam-2660	218	21	∈	∈	PROPN
ejpam-2660	218	22	p	p	PROPN
ejpam-2660	218	23	∧	∧	PROPN
ejpam-2660	218	24	c	c	PROPN
ejpam-2660	218	25	,	,	PUNCT
ejpam-2660	218	26	and	and	CCONJ
ejpam-2660	218	27	a	a	DET
ejpam-2660	218	28	∨	∨	NUM
ejpam-2660	218	29	b	b	PROPN
ejpam-2660	218	30	≤	≤	PROPN
ejpam-2660	218	31	c.	c.	NOUN
ejpam-2660	218	32	we	we	PRON
ejpam-2660	218	33	have	have	VERB
ejpam-2660	218	34	a	a	DET
ejpam-2660	218	35	≤	≤	NUM
ejpam-2660	218	36	a	a	DET
ejpam-2660	218	37	∨	∨	NUM
ejpam-2660	218	38	b	b	NOUN
ejpam-2660	218	39	,	,	PUNCT
ejpam-2660	218	40	a	a	DET
ejpam-2660	218	41	∨	∨	NUM
ejpam-2660	218	42	b	b	NOUN
ejpam-2660	218	43	≤	≤	NOUN
ejpam-2660	218	44	c	c	NOUN
ejpam-2660	218	45	,	,	PUNCT
ejpam-2660	218	46	and	and	CCONJ
ejpam-2660	218	47	≤	≤	NOUN
ejpam-2660	218	48	is	be	AUX
ejpam-2660	218	49	transitive	transitive	ADJ
ejpam-2660	218	50	,	,	PUNCT
ejpam-2660	218	51	so	so	CCONJ
ejpam-2660	218	52	a	a	DET
ejpam-2660	218	53	≤	≤	ADJ
ejpam-2660	218	54	c	c	NOUN
ejpam-2660	219	1	and	and	CCONJ
ejpam-2660	219	2	it	it	PRON
ejpam-2660	219	3	implies	imply	VERB
ejpam-2660	219	4	that	that	SCONJ
ejpam-2660	219	5	c	c	PROPN
ejpam-2660	219	6	∈	∈	PROPN
ejpam-2660	219	7	f	f	X
ejpam-2660	219	8	(	(	PUNCT
ejpam-2660	219	9	a	a	NOUN
ejpam-2660	219	10	)	)	PUNCT
ejpam-2660	219	11	.	.	PUNCT
ejpam-2660	220	1	therefore	therefore	ADV
ejpam-2660	220	2	x	x	X
ejpam-2660	220	3	∈	∈	PROPN
ejpam-2660	220	4	p	p	PROPN
ejpam-2660	220	5	∧	∧	PROPN
ejpam-2660	220	6	f	f	X
ejpam-2660	220	7	(	(	PUNCT
ejpam-2660	220	8	a	a	NOUN
ejpam-2660	220	9	)	)	PUNCT
ejpam-2660	220	10	.	.	PUNCT
ejpam-2660	221	1	similarly	similarly	ADV
ejpam-2660	221	2	,	,	PUNCT
ejpam-2660	221	3	it	it	PRON
ejpam-2660	221	4	is	be	AUX
ejpam-2660	221	5	proved	prove	VERB
ejpam-2660	221	6	that	that	SCONJ
ejpam-2660	221	7	x	x	SYM
ejpam-2660	221	8	∈	∈	PROPN
ejpam-2660	221	9	p	p	PROPN
ejpam-2660	221	10	∧	∧	PROPN
ejpam-2660	221	11	f	f	PROPN
ejpam-2660	221	12	(	(	PUNCT
ejpam-2660	221	13	b	b	NOUN
ejpam-2660	221	14	)	)	PUNCT
ejpam-2660	221	15	.	.	PUNCT
ejpam-2660	222	1	since	since	SCONJ
ejpam-2660	222	2	x	x	PROPN
ejpam-2660	222	3	∨	∨	NUM
ejpam-2660	222	4	x	x	SYM
ejpam-2660	222	5	=	=	SYM
ejpam-2660	222	6	x	x	NOUN
ejpam-2660	222	7	,	,	PUNCT
ejpam-2660	222	8	x	x	SYM
ejpam-2660	222	9	∈	∈	PROPN
ejpam-2660	222	10	(	(	PUNCT
ejpam-2660	222	11	p	p	NOUN
ejpam-2660	222	12	∧	∧	PROPN
ejpam-2660	222	13	f	f	X
ejpam-2660	222	14	(	(	PUNCT
ejpam-2660	222	15	a	a	NOUN
ejpam-2660	222	16	)	)	PUNCT
ejpam-2660	222	17	)	)	PUNCT
ejpam-2660	222	18	∨	∨	PROPN
ejpam-2660	222	19	(	(	PUNCT
ejpam-2660	222	20	p	p	PROPN
ejpam-2660	222	21	∧	∧	PROPN
ejpam-2660	222	22	f	f	X
ejpam-2660	222	23	(	(	PUNCT
ejpam-2660	222	24	b	b	NOUN
ejpam-2660	222	25	)	)	PUNCT
ejpam-2660	222	26	)	)	PUNCT
ejpam-2660	222	27	,	,	PUNCT
ejpam-2660	222	28	it	it	PRON
ejpam-2660	222	29	implies	imply	VERB
ejpam-2660	222	30	that	that	SCONJ
ejpam-2660	222	31	:	:	PUNCT
ejpam-2660	222	32	p	p	X
ejpam-2660	222	33	∧	∧	PROPN
ejpam-2660	222	34	f	f	PROPN
ejpam-2660	222	35	(	(	PUNCT
ejpam-2660	222	36	a	a	DET
ejpam-2660	222	37	∨	∨	NUM
ejpam-2660	222	38	b	b	NOUN
ejpam-2660	222	39	)	)	PUNCT
ejpam-2660	222	40	⊆	⊆	NUM
ejpam-2660	222	41	(	(	PUNCT
ejpam-2660	222	42	p	p	NOUN
ejpam-2660	222	43	∧	∧	PROPN
ejpam-2660	222	44	f	f	X
ejpam-2660	222	45	(	(	PUNCT
ejpam-2660	222	46	a	a	NOUN
ejpam-2660	222	47	)	)	PUNCT
ejpam-2660	222	48	)	)	PUNCT
ejpam-2660	222	49	∨	∨	PROPN
ejpam-2660	222	50	(	(	PUNCT
ejpam-2660	222	51	p	p	PROPN
ejpam-2660	222	52	∧	∧	PROPN
ejpam-2660	222	53	f	f	X
ejpam-2660	222	54	(	(	PUNCT
ejpam-2660	222	55	b	b	NOUN
ejpam-2660	222	56	)	)	PUNCT
ejpam-2660	222	57	)	)	PUNCT
ejpam-2660	222	58	.	.	PUNCT
ejpam-2660	223	1	let	let	VERB
ejpam-2660	223	2	x	x	X
ejpam-2660	223	3	∈	∈	PROPN
ejpam-2660	223	4	(	(	PUNCT
ejpam-2660	223	5	p	p	NOUN
ejpam-2660	223	6	∧	∧	PROPN
ejpam-2660	223	7	f	f	X
ejpam-2660	223	8	(	(	PUNCT
ejpam-2660	223	9	a	a	NOUN
ejpam-2660	223	10	)	)	PUNCT
ejpam-2660	223	11	)	)	PUNCT
ejpam-2660	223	12	∨	∨	PROPN
ejpam-2660	223	13	(	(	PUNCT
ejpam-2660	223	14	p	p	PROPN
ejpam-2660	223	15	∧	∧	PROPN
ejpam-2660	223	16	f	f	X
ejpam-2660	223	17	(	(	PUNCT
ejpam-2660	223	18	b	b	NOUN
ejpam-2660	223	19	)	)	PUNCT
ejpam-2660	223	20	)	)	PUNCT
ejpam-2660	223	21	.	.	PUNCT
ejpam-2660	224	1	so	so	ADV
ejpam-2660	224	2	there	there	PRON
ejpam-2660	224	3	exist	exist	VERB
ejpam-2660	224	4	p1	p1	NOUN
ejpam-2660	224	5	,	,	PUNCT
ejpam-2660	224	6	p2	p2	PROPN
ejpam-2660	224	7	∈	∈	PROPN
ejpam-2660	224	8	p	p	NOUN
ejpam-2660	224	9	,	,	PUNCT
ejpam-2660	224	10	a1	a1	PROPN
ejpam-2660	224	11	∈	∈	PROPN
ejpam-2660	224	12	f	f	X
ejpam-2660	224	13	(	(	PUNCT
ejpam-2660	224	14	a	a	NOUN
ejpam-2660	224	15	)	)	PUNCT
ejpam-2660	224	16	,	,	PUNCT
ejpam-2660	224	17	b1	b1	PROPN
ejpam-2660	224	18	∈	∈	PROPN
ejpam-2660	224	19	f	f	X
ejpam-2660	224	20	(	(	PUNCT
ejpam-2660	224	21	b	b	NOUN
ejpam-2660	224	22	)	)	PUNCT
ejpam-2660	224	23	,	,	PUNCT
ejpam-2660	224	24	such	such	ADJ
ejpam-2660	224	25	that	that	SCONJ
ejpam-2660	224	26	x	x	SYM
ejpam-2660	224	27	∈	∈	PROPN
ejpam-2660	224	28	(	(	PUNCT
ejpam-2660	224	29	p1	p1	NOUN
ejpam-2660	224	30	∧	∧	PROPN
ejpam-2660	224	31	a1	a1	PROPN
ejpam-2660	224	32	)	)	PUNCT
ejpam-2660	224	33	∨	∨	NUM
ejpam-2660	224	34	(	(	PUNCT
ejpam-2660	224	35	p2	p2	PROPN
ejpam-2660	224	36	∧	∧	PROPN
ejpam-2660	224	37	b1	b1	NOUN
ejpam-2660	224	38	)	)	PUNCT
ejpam-2660	224	39	,	,	PUNCT
ejpam-2660	224	40	and	and	CCONJ
ejpam-2660	224	41	a	a	DET
ejpam-2660	224	42	≤	≤	NUM
ejpam-2660	224	43	a1	a1	NOUN
ejpam-2660	224	44	,	,	PUNCT
ejpam-2660	224	45	b	b	PROPN
ejpam-2660	224	46	≤	≤	NUM
ejpam-2660	224	47	b1	b1	NOUN
ejpam-2660	224	48	.	.	PUNCT
ejpam-2660	225	1	since	since	SCONJ
ejpam-2660	225	2	l	l	NOUN
ejpam-2660	225	3	is	be	AUX
ejpam-2660	225	4	distributive	distributive	ADJ
ejpam-2660	225	5	,	,	PUNCT
ejpam-2660	225	6	we	we	PRON
ejpam-2660	225	7	have	have	VERB
ejpam-2660	225	8	:	:	PUNCT
ejpam-2660	225	9	x	x	SYM
ejpam-2660	225	10	∈	∈	PROPN
ejpam-2660	225	11	(	(	PUNCT
ejpam-2660	225	12	p1	p1	NOUN
ejpam-2660	225	13	∧	∧	PROPN
ejpam-2660	225	14	a1	a1	PROPN
ejpam-2660	225	15	)	)	PUNCT
ejpam-2660	225	16	∨	∨	NUM
ejpam-2660	225	17	(	(	PUNCT
ejpam-2660	225	18	p2	p2	PROPN
ejpam-2660	225	19	∧	∧	PROPN
ejpam-2660	225	20	b1	b1	NOUN
ejpam-2660	225	21	)	)	PUNCT
ejpam-2660	225	22	=	=	PUNCT
ejpam-2660	226	1	[	[	X
ejpam-2660	226	2	(	(	PUNCT
ejpam-2660	226	3	p1	p1	PROPN
ejpam-2660	226	4	∧	∧	PROPN
ejpam-2660	226	5	a1	a1	PROPN
ejpam-2660	226	6	)	)	PUNCT
ejpam-2660	226	7	∨	∨	NUM
ejpam-2660	226	8	p2	p2	X
ejpam-2660	226	9	]	]	X
ejpam-2660	226	10	∧	∧	PROPN
ejpam-2660	226	11	[	[	X
ejpam-2660	226	12	(	(	PUNCT
ejpam-2660	226	13	p1	p1	PROPN
ejpam-2660	226	14	∧	∧	PROPN
ejpam-2660	226	15	a1	a1	PROPN
ejpam-2660	226	16	)	)	PUNCT
ejpam-2660	226	17	∨	∨	NUM
ejpam-2660	226	18	b1	b1	NOUN
ejpam-2660	226	19	]	]	X
ejpam-2660	226	20	=	=	SYM
ejpam-2660	226	21	(	(	PUNCT
ejpam-2660	226	22	p2	p2	PROPN
ejpam-2660	226	23	∨	∨	NUM
ejpam-2660	226	24	p1	p1	NOUN
ejpam-2660	226	25	)	)	PUNCT
ejpam-2660	226	26	∧	∧	PROPN
ejpam-2660	226	27	(	(	PUNCT
ejpam-2660	226	28	p2	p2	PROPN
ejpam-2660	226	29	∨	∨	NUM
ejpam-2660	226	30	a1	a1	NOUN
ejpam-2660	226	31	)	)	PUNCT
ejpam-2660	226	32	∧	∧	PROPN
ejpam-2660	226	33	(	(	PUNCT
ejpam-2660	226	34	b1	b1	PROPN
ejpam-2660	226	35	∨	∨	NUM
ejpam-2660	226	36	p1	p1	PROPN
ejpam-2660	226	37	)	)	PUNCT
ejpam-2660	226	38	∧	∧	PROPN
ejpam-2660	226	39	(	(	PUNCT
ejpam-2660	226	40	b1	b1	PROPN
ejpam-2660	226	41	∨	∨	NUM
ejpam-2660	226	42	a1	a1	NOUN
ejpam-2660	226	43	)	)	PUNCT
ejpam-2660	226	44	.	.	PUNCT
ejpam-2660	227	1	since	since	SCONJ
ejpam-2660	227	2	p	p	NOUN
ejpam-2660	227	3	is	be	AUX
ejpam-2660	227	4	a	a	DET
ejpam-2660	227	5	hyperfilter	hyperfilter	NOUN
ejpam-2660	227	6	,	,	PUNCT
ejpam-2660	227	7	p2	p2	PROPN
ejpam-2660	227	8	≤	≤	NUM
ejpam-2660	227	9	p2	p2	PROPN
ejpam-2660	227	10	∨	∨	NUM
ejpam-2660	227	11	p1	p1	NOUN
ejpam-2660	227	12	,	,	PUNCT
ejpam-2660	227	13	p2	p2	PROPN
ejpam-2660	227	14	≤	≤	NUM
ejpam-2660	227	15	p2	p2	PROPN
ejpam-2660	227	16	∨	∨	NUM
ejpam-2660	227	17	a1	a1	NOUN
ejpam-2660	227	18	,	,	PUNCT
ejpam-2660	227	19	and	and	CCONJ
ejpam-2660	227	20	p1	p1	PROPN
ejpam-2660	227	21	≤	≤	PROPN
ejpam-2660	227	22	b1	b1	PROPN
ejpam-2660	227	23	∨	∨	NUM
ejpam-2660	227	24	p1	p1	PROPN
ejpam-2660	227	25	,	,	PUNCT
ejpam-2660	227	26	then	then	ADV
ejpam-2660	227	27	p2	p2	PROPN
ejpam-2660	227	28	∨	∨	NUM
ejpam-2660	227	29	p1	p1	NOUN
ejpam-2660	227	30	,	,	PUNCT
ejpam-2660	227	31	p2	p2	PROPN
ejpam-2660	227	32	∨	∨	NUM
ejpam-2660	227	33	a1	a1	NOUN
ejpam-2660	227	34	,	,	PUNCT
ejpam-2660	227	35	b1	b1	NOUN
ejpam-2660	227	36	∨	∨	NUM
ejpam-2660	227	37	p1	p1	PROPN
ejpam-2660	227	38	∈	∈	PROPN
ejpam-2660	227	39	p	p	NOUN
ejpam-2660	227	40	.	.	PUNCT
ejpam-2660	228	1	so	so	ADV
ejpam-2660	228	2	,	,	PUNCT
ejpam-2660	228	3	we	we	PRON
ejpam-2660	228	4	conclude	conclude	VERB
ejpam-2660	228	5	that	that	PRON
ejpam-2660	228	6	(	(	PUNCT
ejpam-2660	228	7	p2	p2	PROPN
ejpam-2660	228	8	∨	∨	NUM
ejpam-2660	228	9	p1	p1	NOUN
ejpam-2660	228	10	)	)	PUNCT
ejpam-2660	228	11	∧	∧	PROPN
ejpam-2660	228	12	(	(	PUNCT
ejpam-2660	228	13	p2	p2	PROPN
ejpam-2660	228	14	∨	∨	NUM
ejpam-2660	228	15	a1	a1	NOUN
ejpam-2660	228	16	)	)	PUNCT
ejpam-2660	228	17	∧	∧	PROPN
ejpam-2660	228	18	(	(	PUNCT
ejpam-2660	228	19	b1	b1	PROPN
ejpam-2660	228	20	∨	∨	NUM
ejpam-2660	228	21	p1	p1	PROPN
ejpam-2660	228	22	)	)	PUNCT
ejpam-2660	228	23	⊆	⊆	NUM
ejpam-2660	228	24	p.	p.	NOUN
ejpam-2660	228	25	since	since	SCONJ
ejpam-2660	228	26	a	a	DET
ejpam-2660	228	27	≤	≤	NUM
ejpam-2660	228	28	a1	a1	NOUN
ejpam-2660	228	29	,	,	PUNCT
ejpam-2660	228	30	b	b	PROPN
ejpam-2660	228	31	≤	≤	NUM
ejpam-2660	228	32	b1	b1	NOUN
ejpam-2660	228	33	,	,	PUNCT
ejpam-2660	228	34	a∨b	a∨b	NOUN
ejpam-2660	228	35	≤	≤	NOUN
ejpam-2660	228	36	a1∨b1	a1∨b1	NOUN
ejpam-2660	228	37	,	,	PUNCT
ejpam-2660	228	38	and	and	CCONJ
ejpam-2660	228	39	it	it	PRON
ejpam-2660	228	40	implies	imply	VERB
ejpam-2660	228	41	that	that	SCONJ
ejpam-2660	228	42	a1∨b1	a1∨b1	NOUN
ejpam-2660	228	43	∈	∈	PROPN
ejpam-2660	228	44	f	f	X
ejpam-2660	228	45	(	(	PUNCT
ejpam-2660	228	46	a∨b	a∨b	PROPN
ejpam-2660	228	47	)	)	PUNCT
ejpam-2660	228	48	.	.	PUNCT
ejpam-2660	229	1	so	so	ADV
ejpam-2660	229	2	x	x	SYM
ejpam-2660	229	3	∈	∈	PROPN
ejpam-2660	229	4	p∧f	p∧f	NOUN
ejpam-2660	229	5	(	(	PUNCT
ejpam-2660	229	6	a∨b	a∨b	NOUN
ejpam-2660	229	7	)	)	PUNCT
ejpam-2660	229	8	.	.	PUNCT
ejpam-2660	230	1	thus	thus	ADV
ejpam-2660	230	2	:	:	PUNCT
ejpam-2660	230	3	(	(	PUNCT
ejpam-2660	230	4	p	p	X
ejpam-2660	230	5	∧	∧	PROPN
ejpam-2660	230	6	f	f	X
ejpam-2660	230	7	(	(	PUNCT
ejpam-2660	230	8	a	a	NOUN
ejpam-2660	230	9	)	)	PUNCT
ejpam-2660	230	10	)	)	PUNCT
ejpam-2660	230	11	∨	∨	PROPN
ejpam-2660	230	12	(	(	PUNCT
ejpam-2660	230	13	p	p	PROPN
ejpam-2660	230	14	∧	∧	PROPN
ejpam-2660	230	15	f	f	X
ejpam-2660	230	16	(	(	PUNCT
ejpam-2660	230	17	b	b	NOUN
ejpam-2660	230	18	)	)	PUNCT
ejpam-2660	230	19	)	)	PUNCT
ejpam-2660	231	1	⊆	⊆	NUM
ejpam-2660	231	2	p	p	X
ejpam-2660	231	3	∧	∧	PROPN
ejpam-2660	231	4	f	f	X
ejpam-2660	231	5	(	(	PUNCT
ejpam-2660	231	6	a	a	DET
ejpam-2660	231	7	∨	∨	NUM
ejpam-2660	231	8	b	b	NOUN
ejpam-2660	231	9	)	)	PUNCT
ejpam-2660	231	10	.	.	PUNCT
ejpam-2660	232	1	theorem	theorem	NOUN
ejpam-2660	232	2	31	31	NUM
ejpam-2660	232	3	.	.	PUNCT
ejpam-2660	233	1	let	let	VERB
ejpam-2660	233	2	x	x	PRON
ejpam-2660	233	3	,	,	PUNCT
ejpam-2660	233	4	y	y	PROPN
ejpam-2660	233	5	∈	∈	PROPN
ejpam-2660	233	6	l.	l.	NOUN
ejpam-2660	233	7	if	if	SCONJ
ejpam-2660	233	8	x	x	SYM
ejpam-2660	233	9	∧	∧	NOUN
ejpam-2660	233	10	y	y	PROPN
ejpam-2660	233	11	is	be	AUX
ejpam-2660	233	12	a	a	DET
ejpam-2660	233	13	hyperfilter	hyperfilter	NOUN
ejpam-2660	233	14	of	of	ADP
ejpam-2660	233	15	l	l	NOUN
ejpam-2660	233	16	,	,	PUNCT
ejpam-2660	233	17	then	then	ADV
ejpam-2660	233	18	x	x	X
ejpam-2660	233	19	=	=	PUNCT
ejpam-2660	233	20	y.	y.	NOUN
ejpam-2660	233	21	proof	proof	NOUN
ejpam-2660	233	22	.	.	PUNCT
ejpam-2660	234	1	let	let	VERB
ejpam-2660	234	2	x	x	PRON
ejpam-2660	234	3	∧	∧	NOUN
ejpam-2660	234	4	y	y	PROPN
ejpam-2660	234	5	be	be	AUX
ejpam-2660	234	6	a	a	DET
ejpam-2660	234	7	hyperfilter	hyperfilter	NOUN
ejpam-2660	234	8	.	.	PUNCT
ejpam-2660	235	1	by	by	ADP
ejpam-2660	235	2	lemma	lemma	PROPN
ejpam-2660	235	3	15	15	NUM
ejpam-2660	235	4	,	,	PUNCT
ejpam-2660	235	5	there	there	PRON
ejpam-2660	235	6	exist	exist	VERB
ejpam-2660	235	7	a	a	DET
ejpam-2660	235	8	,	,	PUNCT
ejpam-2660	235	9	b	b	X
ejpam-2660	235	10	∈	∈	PROPN
ejpam-2660	235	11	x	x	PUNCT
ejpam-2660	235	12	∧	∧	PROPN
ejpam-2660	235	13	y	y	PROPN
ejpam-2660	235	14	,	,	PUNCT
ejpam-2660	235	15	such	such	ADJ
ejpam-2660	235	16	that	that	SCONJ
ejpam-2660	235	17	a	a	DET
ejpam-2660	235	18	≤	≤	NOUN
ejpam-2660	235	19	x	x	PUNCT
ejpam-2660	235	20	and	and	CCONJ
ejpam-2660	235	21	b	b	PROPN
ejpam-2660	235	22	≤	≤	NOUN
ejpam-2660	235	23	y.	y.	NOUN
ejpam-2660	235	24	then	then	ADV
ejpam-2660	235	25	x	x	PRON
ejpam-2660	235	26	,	,	PUNCT
ejpam-2660	235	27	y	y	PROPN
ejpam-2660	235	28	∈	∈	PROPN
ejpam-2660	236	1	x	x	PUNCT
ejpam-2660	236	2	∧	∧	NOUN
ejpam-2660	236	3	y	y	PROPN
ejpam-2660	236	4	and	and	CCONJ
ejpam-2660	236	5	by	by	ADP
ejpam-2660	236	6	proposition	proposition	NOUN
ejpam-2660	236	7	9	9	NUM
ejpam-2660	236	8	,	,	PUNCT
ejpam-2660	236	9	(	(	PUNCT
ejpam-2660	236	10	ii	ii	NOUN
ejpam-2660	236	11	)	)	PUNCT
ejpam-2660	236	12	,	,	PUNCT
ejpam-2660	236	13	x	x	X
ejpam-2660	236	14	=	=	PUNCT
ejpam-2660	236	15	y.	y.	PROPN
ejpam-2660	236	16	m.	m.	PROPN
ejpam-2660	236	17	amiri	amiri	PROPN
ejpam-2660	236	18	bideshki	bideshki	PROPN
ejpam-2660	236	19	,	,	PUNCT
ejpam-2660	236	20	r.	r.	PROPN
ejpam-2660	236	21	ameri	ameri	PROPN
ejpam-2660	236	22	,	,	PUNCT
ejpam-2660	237	1	a.	a.	PROPN
ejpam-2660	237	2	borumand	borumand	PROPN
ejpam-2660	238	1	saeid	saeid	PROPN
ejpam-2660	238	2	/	/	SYM
ejpam-2660	238	3	eur	eur	PROPN
ejpam-2660	238	4	.	.	PUNCT
ejpam-2660	239	1	j.	j.	PROPN
ejpam-2660	239	2	pure	pure	PROPN
ejpam-2660	239	3	appl	appl	PROPN
ejpam-2660	239	4	.	.	PROPN
ejpam-2660	239	5	math	math	PROPN
ejpam-2660	239	6	,	,	PUNCT
ejpam-2660	239	7	11	11	NUM
ejpam-2660	239	8	(	(	PUNCT
ejpam-2660	239	9	1	1	NUM
ejpam-2660	239	10	)	)	PUNCT
ejpam-2660	239	11	(	(	PUNCT
ejpam-2660	239	12	2018	2018	NUM
ejpam-2660	239	13	)	)	PUNCT
ejpam-2660	239	14	,	,	PUNCT
ejpam-2660	239	15	169	169	NUM
ejpam-2660	239	16	-	-	SYM
ejpam-2660	239	17	188	188	NUM
ejpam-2660	239	18	177	177	NUM
ejpam-2660	239	19	4	4	NUM
ejpam-2660	239	20	.	.	PUNCT
ejpam-2660	239	21	iahyperideals	iahyperideal	NOUN
ejpam-2660	239	22	in	in	ADP
ejpam-2660	239	23	strong	strong	ADJ
ejpam-2660	239	24	”	"	PUNCT
ejpam-2660	239	25	∧	∧	NOUN
ejpam-2660	239	26	”	"	PUNCT
ejpam-2660	239	27	-hyperlattices	-hyperlattice	NOUN
ejpam-2660	239	28	in	in	ADP
ejpam-2660	239	29	this	this	DET
ejpam-2660	239	30	section	section	NOUN
ejpam-2660	239	31	,	,	PUNCT
ejpam-2660	239	32	we	we	PRON
ejpam-2660	239	33	are	be	AUX
ejpam-2660	239	34	going	go	VERB
ejpam-2660	239	35	to	to	PART
ejpam-2660	239	36	define	define	VERB
ejpam-2660	239	37	some	some	DET
ejpam-2660	239	38	types	type	NOUN
ejpam-2660	239	39	of	of	ADP
ejpam-2660	239	40	hyperideals	hyperideal	NOUN
ejpam-2660	239	41	in	in	ADP
ejpam-2660	239	42	a	a	DET
ejpam-2660	239	43	dual	dual	ADJ
ejpam-2660	239	44	distributive	distributive	ADJ
ejpam-2660	239	45	”	"	PUNCT
ejpam-2660	239	46	∧	∧	NOUN
ejpam-2660	239	47	”	"	PUNCT
ejpam-2660	239	48	-hyperlattices	-hyperlattice	NOUN
ejpam-2660	239	49	.	.	PUNCT
ejpam-2660	240	1	we	we	PRON
ejpam-2660	240	2	assume	assume	VERB
ejpam-2660	240	3	that	that	SCONJ
ejpam-2660	240	4	l	l	NOUN
ejpam-2660	240	5	is	be	AUX
ejpam-2660	240	6	a	a	DET
ejpam-2660	240	7	dual	dual	ADJ
ejpam-2660	240	8	distributive	distributive	ADJ
ejpam-2660	240	9	and	and	CCONJ
ejpam-2660	240	10	bounded	bound	VERB
ejpam-2660	240	11	strong	strong	ADJ
ejpam-2660	240	12	”	"	PUNCT
ejpam-2660	240	13	∧	∧	PROPN
ejpam-2660	240	14	”	"	PUNCT
ejpam-2660	240	15	hyperlattice	hyperlattice	NOUN
ejpam-2660	240	16	.	.	PUNCT
ejpam-2660	241	1	theorem	theorem	VERB
ejpam-2660	241	2	32	32	NUM
ejpam-2660	241	3	.	.	PUNCT
ejpam-2660	242	1	let	let	VERB
ejpam-2660	242	2	∅	∅	NOUN
ejpam-2660	242	3	6=	6=	ADP
ejpam-2660	242	4	a	a	DET
ejpam-2660	242	5	⊆	⊆	NUM
ejpam-2660	242	6	l.	l.	NOUN
ejpam-2660	242	7	if	if	SCONJ
ejpam-2660	242	8	ia	ia	PROPN
ejpam-2660	242	9	=	=	SYM
ejpam-2660	242	10	{	{	PUNCT
ejpam-2660	242	11	x	x	PUNCT
ejpam-2660	242	12	∈	∈	NOUN
ejpam-2660	242	13	l	l	NOUN
ejpam-2660	243	1	|	|	NOUN
ejpam-2660	243	2	0	0	NUM
ejpam-2660	243	3	∈	∈	NOUN
ejpam-2660	243	4	x	x	PUNCT
ejpam-2660	243	5	∧	∧	PROPN
ejpam-2660	243	6	a,∀a	a,∀a	X
ejpam-2660	243	7	∈	∈	PROPN
ejpam-2660	243	8	a	a	PRON
ejpam-2660	243	9	}	}	PUNCT
ejpam-2660	243	10	,	,	PUNCT
ejpam-2660	243	11	then	then	ADV
ejpam-2660	243	12	ia	ia	PROPN
ejpam-2660	243	13	is	be	AUX
ejpam-2660	243	14	a	a	DET
ejpam-2660	243	15	hyperideal	hyperideal	NOUN
ejpam-2660	243	16	of	of	ADP
ejpam-2660	243	17	l.	l.	PROPN
ejpam-2660	243	18	proof	proof	PROPN
ejpam-2660	243	19	.	.	PUNCT
ejpam-2660	244	1	since	since	SCONJ
ejpam-2660	244	2	0	0	NUM
ejpam-2660	244	3	≤	≤	NUM
ejpam-2660	245	1	a,∀a	a,∀a	PUNCT
ejpam-2660	245	2	∈	∈	PROPN
ejpam-2660	245	3	a	a	PRON
ejpam-2660	245	4	,	,	PUNCT
ejpam-2660	245	5	by	by	ADP
ejpam-2660	245	6	remark	remark	NOUN
ejpam-2660	245	7	6	6	NUM
ejpam-2660	245	8	,	,	PUNCT
ejpam-2660	245	9	0	0	NUM
ejpam-2660	245	10	∈	∈	NOUN
ejpam-2660	245	11	0	0	NUM
ejpam-2660	246	1	∧	∧	PROPN
ejpam-2660	246	2	a	a	PROPN
ejpam-2660	246	3	,	,	PUNCT
ejpam-2660	246	4	and	and	CCONJ
ejpam-2660	246	5	it	it	PRON
ejpam-2660	246	6	implies	imply	VERB
ejpam-2660	246	7	that	that	SCONJ
ejpam-2660	246	8	0	0	NUM
ejpam-2660	246	9	∈	∈	PROPN
ejpam-2660	246	10	ia	ia	PROPN
ejpam-2660	246	11	,	,	PUNCT
ejpam-2660	246	12	and	and	CCONJ
ejpam-2660	246	13	ia	ia	PROPN
ejpam-2660	246	14	6=	6=	PUNCT
ejpam-2660	246	15	∅.	∅.	ADV
ejpam-2660	246	16	let	let	VERB
ejpam-2660	246	17	x	x	PRON
ejpam-2660	246	18	,	,	PUNCT
ejpam-2660	246	19	y	y	PROPN
ejpam-2660	246	20	∈	∈	PROPN
ejpam-2660	246	21	ia	ia	PROPN
ejpam-2660	246	22	.	.	PROPN
ejpam-2660	247	1	then	then	ADV
ejpam-2660	247	2	0	0	NUM
ejpam-2660	247	3	∈	∈	PROPN
ejpam-2660	247	4	x∧a	x∧a	PROPN
ejpam-2660	247	5	,	,	PUNCT
ejpam-2660	247	6	and	and	CCONJ
ejpam-2660	247	7	0	0	NUM
ejpam-2660	247	8	∈	∈	PROPN
ejpam-2660	247	9	y∧a	y∧a	PROPN
ejpam-2660	247	10	,	,	PUNCT
ejpam-2660	247	11	for	for	ADP
ejpam-2660	247	12	all	all	DET
ejpam-2660	247	13	a	a	DET
ejpam-2660	247	14	∈	∈	NOUN
ejpam-2660	247	15	a.	a.	NOUN
ejpam-2660	247	16	so	so	ADV
ejpam-2660	247	17	0	0	NUM
ejpam-2660	247	18	∈	∈	PROPN
ejpam-2660	247	19	(	(	PUNCT
ejpam-2660	247	20	x∧a)∨	x∧a)∨	X
ejpam-2660	247	21	(	(	PUNCT
ejpam-2660	247	22	y∧a	y∧a	PROPN
ejpam-2660	247	23	)	)	PUNCT
ejpam-2660	247	24	,	,	PUNCT
ejpam-2660	247	25	for	for	ADP
ejpam-2660	247	26	all	all	DET
ejpam-2660	247	27	a	a	DET
ejpam-2660	247	28	∈	∈	NOUN
ejpam-2660	247	29	a	a	PRON
ejpam-2660	247	30	;	;	PUNCT
ejpam-2660	247	31	since	since	SCONJ
ejpam-2660	247	32	l	l	NOUN
ejpam-2660	247	33	is	be	AUX
ejpam-2660	247	34	dual	dual	ADV
ejpam-2660	247	35	distributive	distributive	ADJ
ejpam-2660	247	36	,	,	PUNCT
ejpam-2660	247	37	0	0	NUM
ejpam-2660	247	38	∈	∈	NOUN
ejpam-2660	247	39	(	(	PUNCT
ejpam-2660	247	40	x	x	PROPN
ejpam-2660	247	41	∨	∨	NUM
ejpam-2660	247	42	y	y	NOUN
ejpam-2660	247	43	)	)	PUNCT
ejpam-2660	247	44	∧	∧	PROPN
ejpam-2660	247	45	a	a	ADP
ejpam-2660	247	46	,	,	PUNCT
ejpam-2660	247	47	for	for	ADP
ejpam-2660	247	48	all	all	DET
ejpam-2660	247	49	a	a	DET
ejpam-2660	247	50	∈	∈	NOUN
ejpam-2660	247	51	a.	a.	NOUN
ejpam-2660	248	1	so	so	ADV
ejpam-2660	248	2	x	x	PROPN
ejpam-2660	248	3	∨	∨	NUM
ejpam-2660	248	4	y	y	PROPN
ejpam-2660	248	5	∈	∈	PROPN
ejpam-2660	248	6	ia	ia	PROPN
ejpam-2660	248	7	.	.	PUNCT
ejpam-2660	249	1	now	now	ADV
ejpam-2660	249	2	,	,	PUNCT
ejpam-2660	249	3	let	let	VERB
ejpam-2660	249	4	x	x	X
ejpam-2660	249	5	∈	∈	PROPN
ejpam-2660	249	6	ia	ia	PROPN
ejpam-2660	249	7	and	and	CCONJ
ejpam-2660	249	8	y	y	PROPN
ejpam-2660	249	9	≤	≤	PROPN
ejpam-2660	249	10	x.	x.	NOUN
ejpam-2660	250	1	then	then	ADV
ejpam-2660	250	2	0	0	NUM
ejpam-2660	250	3	∈	∈	PROPN
ejpam-2660	250	4	x	x	X
ejpam-2660	250	5	∧	∧	NOUN
ejpam-2660	250	6	a	a	X
ejpam-2660	250	7	,	,	PUNCT
ejpam-2660	250	8	for	for	ADP
ejpam-2660	250	9	all	all	DET
ejpam-2660	250	10	a	a	DET
ejpam-2660	250	11	∈	∈	PROPN
ejpam-2660	250	12	a	a	PRON
ejpam-2660	250	13	,	,	PUNCT
ejpam-2660	250	14	and	and	CCONJ
ejpam-2660	250	15	x	x	SYM
ejpam-2660	250	16	∨	∨	NUM
ejpam-2660	250	17	y	y	NOUN
ejpam-2660	250	18	=	=	PUNCT
ejpam-2660	250	19	x.	x.	NOUN
ejpam-2660	251	1	we	we	PRON
ejpam-2660	251	2	have	have	VERB
ejpam-2660	251	3	0	0	NUM
ejpam-2660	251	4	∈	∈	PROPN
ejpam-2660	251	5	x∧	x∧	PROPN
ejpam-2660	251	6	a	a	DET
ejpam-2660	251	7	=	=	X
ejpam-2660	251	8	(	(	PUNCT
ejpam-2660	251	9	x∨	x∨	PROPN
ejpam-2660	251	10	y)∧	y)∧	PROPN
ejpam-2660	251	11	a	a	X
ejpam-2660	251	12	,	,	PUNCT
ejpam-2660	251	13	for	for	ADP
ejpam-2660	251	14	all	all	DET
ejpam-2660	251	15	a	a	DET
ejpam-2660	251	16	∈	∈	PROPN
ejpam-2660	251	17	a	a	PRON
ejpam-2660	251	18	,	,	PUNCT
ejpam-2660	251	19	and	and	CCONJ
ejpam-2660	251	20	since	since	SCONJ
ejpam-2660	251	21	l	l	NOUN
ejpam-2660	251	22	is	be	AUX
ejpam-2660	251	23	dual	dual	ADV
ejpam-2660	251	24	distributive	distributive	ADJ
ejpam-2660	251	25	,	,	PUNCT
ejpam-2660	251	26	0	0	NUM
ejpam-2660	251	27	∈	∈	PROPN
ejpam-2660	251	28	(	(	PUNCT
ejpam-2660	251	29	x∧	x∧	PROPN
ejpam-2660	251	30	a)∨	a)∨	PROPN
ejpam-2660	251	31	(	(	PUNCT
ejpam-2660	251	32	y	y	PROPN
ejpam-2660	251	33	∧	∧	PROPN
ejpam-2660	251	34	a	a	PRON
ejpam-2660	251	35	)	)	PUNCT
ejpam-2660	251	36	,	,	PUNCT
ejpam-2660	251	37	for	for	ADP
ejpam-2660	251	38	all	all	DET
ejpam-2660	251	39	a	a	DET
ejpam-2660	251	40	∈	∈	NOUN
ejpam-2660	251	41	a.	a.	NOUN
ejpam-2660	251	42	since	since	SCONJ
ejpam-2660	251	43	0	0	NUM
ejpam-2660	251	44	∨	∨	NUM
ejpam-2660	251	45	0	0	NUM
ejpam-2660	252	1	=	=	SYM
ejpam-2660	252	2	0	0	NUM
ejpam-2660	252	3	and	and	CCONJ
ejpam-2660	252	4	0	0	NUM
ejpam-2660	252	5	∈	∈	NOUN
ejpam-2660	252	6	x	x	X
ejpam-2660	252	7	∧	∧	NOUN
ejpam-2660	252	8	a	a	X
ejpam-2660	252	9	,	,	PUNCT
ejpam-2660	252	10	for	for	ADP
ejpam-2660	252	11	all	all	DET
ejpam-2660	252	12	a	a	DET
ejpam-2660	252	13	∈	∈	PROPN
ejpam-2660	252	14	a	a	PRON
ejpam-2660	252	15	,	,	PUNCT
ejpam-2660	252	16	we	we	PRON
ejpam-2660	252	17	conclude	conclude	VERB
ejpam-2660	252	18	that	that	SCONJ
ejpam-2660	252	19	0	0	NUM
ejpam-2660	252	20	∈	∈	PROPN
ejpam-2660	252	21	y	y	PROPN
ejpam-2660	252	22	∧	∧	PROPN
ejpam-2660	252	23	a	a	PROPN
ejpam-2660	252	24	,	,	PUNCT
ejpam-2660	252	25	for	for	ADP
ejpam-2660	252	26	all	all	DET
ejpam-2660	252	27	a	a	DET
ejpam-2660	252	28	∈	∈	PROPN
ejpam-2660	252	29	a	a	PRON
ejpam-2660	252	30	,	,	PUNCT
ejpam-2660	252	31	and	and	CCONJ
ejpam-2660	252	32	it	it	PRON
ejpam-2660	252	33	implies	imply	VERB
ejpam-2660	252	34	that	that	SCONJ
ejpam-2660	252	35	y	y	PROPN
ejpam-2660	252	36	∈	∈	PROPN
ejpam-2660	252	37	ia	ia	PROPN
ejpam-2660	252	38	.	.	PUNCT
ejpam-2660	253	1	so	so	ADV
ejpam-2660	253	2	ia	ia	PROPN
ejpam-2660	253	3	is	be	AUX
ejpam-2660	253	4	a	a	DET
ejpam-2660	253	5	hyperideal	hyperideal	NOUN
ejpam-2660	253	6	of	of	ADP
ejpam-2660	253	7	l.	l.	PROPN
ejpam-2660	253	8	corollary	corollary	PROPN
ejpam-2660	253	9	33	33	NUM
ejpam-2660	253	10	.	.	PUNCT
ejpam-2660	254	1	let	let	VERB
ejpam-2660	254	2	l	l	NOUN
ejpam-2660	254	3	be	be	AUX
ejpam-2660	254	4	a	a	DET
ejpam-2660	254	5	∧-hyperlattice	∧-hyperlattice	NOUN
ejpam-2660	254	6	and	and	CCONJ
ejpam-2660	254	7	a	a	PRON
ejpam-2660	254	8	,	,	PUNCT
ejpam-2660	254	9	b	b	PROPN
ejpam-2660	254	10	⊆	⊆	NUM
ejpam-2660	254	11	l.	l.	NOUN
ejpam-2660	254	12	then	then	ADV
ejpam-2660	254	13	we	we	PRON
ejpam-2660	254	14	have	have	VERB
ejpam-2660	254	15	:	:	PUNCT
ejpam-2660	254	16	(	(	PUNCT
ejpam-2660	254	17	i	i	NOUN
ejpam-2660	254	18	)	)	PUNCT
ejpam-2660	254	19	ia	ia	PROPN
ejpam-2660	254	20	⊆	⊆	NUM
ejpam-2660	254	21	ia	ia	PROPN
ejpam-2660	254	22	,	,	PUNCT
ejpam-2660	255	1	∀a	∀a	NOUN
ejpam-2660	255	2	∈	∈	NOUN
ejpam-2660	255	3	a	a	DET
ejpam-2660	255	4	;	;	PUNCT
ejpam-2660	255	5	(	(	PUNCT
ejpam-2660	255	6	ii	ii	NOUN
ejpam-2660	255	7	)	)	PUNCT
ejpam-2660	255	8	if	if	SCONJ
ejpam-2660	255	9	a	a	DET
ejpam-2660	255	10	⊆	⊆	NUM
ejpam-2660	255	11	b	b	NOUN
ejpam-2660	255	12	,	,	PUNCT
ejpam-2660	255	13	then	then	ADV
ejpam-2660	255	14	ib	ib	PROPN
ejpam-2660	255	15	⊆	⊆	NUM
ejpam-2660	255	16	ia	ia	PROPN
ejpam-2660	255	17	;	;	PUNCT
ejpam-2660	255	18	(	(	PUNCT
ejpam-2660	255	19	iii	iii	X
ejpam-2660	255	20	)	)	PUNCT
ejpam-2660	255	21	ia	ia	NOUN
ejpam-2660	255	22	=	=	SYM
ejpam-2660	255	23	∩{ia	∩{ia	PROPN
ejpam-2660	255	24	:	:	PUNCT
ejpam-2660	255	25	a	a	DET
ejpam-2660	255	26	∈	∈	PROPN
ejpam-2660	255	27	a	a	PRON
ejpam-2660	255	28	}	}	PUNCT
ejpam-2660	255	29	.	.	PUNCT
ejpam-2660	256	1	(	(	PUNCT
ejpam-2660	256	2	iv	iv	X
ejpam-2660	256	3	)	)	PUNCT
ejpam-2660	256	4	ia	ia	PROPN
ejpam-2660	256	5	∩	∩	ADJ
ejpam-2660	256	6	ib	ib	NOUN
ejpam-2660	256	7	=	=	SYM
ejpam-2660	256	8	ia∪b	ia∪b	ADJ
ejpam-2660	256	9	.	.	PUNCT
ejpam-2660	257	1	now	now	ADV
ejpam-2660	257	2	,	,	PUNCT
ejpam-2660	257	3	we	we	PRON
ejpam-2660	257	4	define	define	VERB
ejpam-2660	257	5	the	the	DET
ejpam-2660	257	6	least	least	ADJ
ejpam-2660	257	7	hyperideal	hyperideal	NOUN
ejpam-2660	257	8	generating	generating	NOUN
ejpam-2660	257	9	by	by	ADP
ejpam-2660	257	10	a	a	DET
ejpam-2660	257	11	⊆	⊆	NUM
ejpam-2660	257	12	l	l	NOUN
ejpam-2660	257	13	,	,	PUNCT
ejpam-2660	257	14	and	and	CCONJ
ejpam-2660	257	15	we	we	PRON
ejpam-2660	257	16	denote	denote	VERB
ejpam-2660	257	17	it	it	PRON
ejpam-2660	257	18	by	by	ADP
ejpam-2660	257	19	i(a	i(a	PROPN
ejpam-2660	257	20	)	)	PUNCT
ejpam-2660	257	21	.	.	PUNCT
ejpam-2660	258	1	definition	definition	NOUN
ejpam-2660	258	2	34	34	NUM
ejpam-2660	258	3	.	.	PUNCT
ejpam-2660	259	1	let	let	VERB
ejpam-2660	259	2	a	a	DET
ejpam-2660	259	3	⊆	⊆	NUM
ejpam-2660	259	4	l.	l.	NOUN
ejpam-2660	259	5	we	we	PRON
ejpam-2660	259	6	define	define	VERB
ejpam-2660	259	7	i(a	i(a	PROPN
ejpam-2660	259	8	)	)	PUNCT
ejpam-2660	260	1	=	=	SYM
ejpam-2660	260	2	⋂	⋂	PROPN
ejpam-2660	260	3	a⊆i{i	a⊆i{i	NOUN
ejpam-2660	261	1	|	|	ADV
ejpam-2660	261	2	i	i	PRON
ejpam-2660	261	3	is	be	AUX
ejpam-2660	261	4	a	a	DET
ejpam-2660	261	5	hyperideal	hyperideal	NOUN
ejpam-2660	261	6	of	of	ADP
ejpam-2660	261	7	l	l	NOUN
ejpam-2660	261	8	}	}	PUNCT
ejpam-2660	261	9	,	,	PUNCT
ejpam-2660	261	10	and	and	CCONJ
ejpam-2660	261	11	i(a	i(a	NOUN
ejpam-2660	261	12	)	)	PUNCT
ejpam-2660	261	13	is	be	AUX
ejpam-2660	261	14	said	say	VERB
ejpam-2660	261	15	to	to	PART
ejpam-2660	261	16	be	be	AUX
ejpam-2660	261	17	the	the	DET
ejpam-2660	261	18	least	least	ADJ
ejpam-2660	261	19	hyperideal	hyperideal	ADJ
ejpam-2660	261	20	generating	generating	NOUN
ejpam-2660	261	21	by	by	ADP
ejpam-2660	261	22	a.	a.	NOUN
ejpam-2660	261	23	example	example	NOUN
ejpam-2660	261	24	35	35	NUM
ejpam-2660	261	25	.	.	PUNCT
ejpam-2660	262	1	(	(	PUNCT
ejpam-2660	262	2	i	i	NOUN
ejpam-2660	262	3	)	)	PUNCT
ejpam-2660	262	4	consider	consider	VERB
ejpam-2660	262	5	∧−	∧−	PRON
ejpam-2660	262	6	hyperlattice	hyperlattice	PROPN
ejpam-2660	262	7	l	l	NOUN
ejpam-2660	262	8	in	in	ADP
ejpam-2660	262	9	example	example	NOUN
ejpam-2660	262	10	18	18	NUM
ejpam-2660	262	11	.	.	PUNCT
ejpam-2660	263	1	let	let	VERB
ejpam-2660	263	2	i(l	i(l	PRON
ejpam-2660	263	3	)	)	PUNCT
ejpam-2660	263	4	be	be	AUX
ejpam-2660	263	5	the	the	DET
ejpam-2660	263	6	set	set	NOUN
ejpam-2660	263	7	of	of	ADP
ejpam-2660	263	8	all	all	DET
ejpam-2660	263	9	hyperideals	hyperideal	NOUN
ejpam-2660	263	10	of	of	ADP
ejpam-2660	263	11	l.	l.	PROPN
ejpam-2660	263	12	then	then	ADV
ejpam-2660	263	13	we	we	PRON
ejpam-2660	263	14	have	have	VERB
ejpam-2660	263	15	i(l	i(l	PROPN
ejpam-2660	263	16	)	)	PUNCT
ejpam-2660	264	1	=	=	PRON
ejpam-2660	264	2	{	{	PUNCT
ejpam-2660	264	3	{	{	PUNCT
ejpam-2660	264	4	0	0	NUM
ejpam-2660	264	5	}	}	PUNCT
ejpam-2660	264	6	,	,	PUNCT
ejpam-2660	264	7	{	{	PUNCT
ejpam-2660	264	8	0	0	NUM
ejpam-2660	264	9	,	,	PUNCT
ejpam-2660	264	10	a	a	DET
ejpam-2660	264	11	}	}	PUNCT
ejpam-2660	264	12	,	,	PUNCT
ejpam-2660	264	13	{	{	PUNCT
ejpam-2660	264	14	0	0	NUM
ejpam-2660	264	15	,	,	PUNCT
ejpam-2660	264	16	b	b	NOUN
ejpam-2660	264	17	}	}	PUNCT
ejpam-2660	264	18	,	,	PUNCT
ejpam-2660	264	19	l	l	NOUN
ejpam-2660	264	20	}	}	PUNCT
ejpam-2660	264	21	.	.	PUNCT
ejpam-2660	265	1	if	if	SCONJ
ejpam-2660	265	2	a	a	PRON
ejpam-2660	265	3	=	=	X
ejpam-2660	265	4	{	{	PUNCT
ejpam-2660	265	5	a	a	PROPN
ejpam-2660	265	6	,	,	PUNCT
ejpam-2660	265	7	b	b	NOUN
ejpam-2660	265	8	}	}	PUNCT
ejpam-2660	265	9	,	,	PUNCT
ejpam-2660	265	10	then	then	ADV
ejpam-2660	265	11	i(a	i(a	PROPN
ejpam-2660	265	12	)	)	PUNCT
ejpam-2660	266	1	=	=	PUNCT
ejpam-2660	266	2	l.	l.	PROPN
ejpam-2660	267	1	also	also	ADV
ejpam-2660	267	2	,	,	PUNCT
ejpam-2660	267	3	if	if	SCONJ
ejpam-2660	267	4	a	a	PRON
ejpam-2660	267	5	=	=	X
ejpam-2660	267	6	{	{	PUNCT
ejpam-2660	267	7	a	a	NOUN
ejpam-2660	267	8	}	}	PUNCT
ejpam-2660	267	9	,	,	PUNCT
ejpam-2660	267	10	then	then	ADV
ejpam-2660	267	11	i(a	i(a	NUM
ejpam-2660	267	12	)	)	PUNCT
ejpam-2660	267	13	=	=	PRON
ejpam-2660	267	14	{	{	PUNCT
ejpam-2660	267	15	0	0	NUM
ejpam-2660	267	16	,	,	PUNCT
ejpam-2660	267	17	a	a	PRON
ejpam-2660	267	18	}	}	PUNCT
ejpam-2660	267	19	.	.	PUNCT
ejpam-2660	268	1	(	(	PUNCT
ejpam-2660	268	2	ii	ii	NOUN
ejpam-2660	268	3	)	)	PUNCT
ejpam-2660	268	4	consider	consider	VERB
ejpam-2660	268	5	∧−	∧−	PRON
ejpam-2660	268	6	hyperlattice	hyperlattice	PROPN
ejpam-2660	268	7	l	l	NOUN
ejpam-2660	268	8	in	in	ADP
ejpam-2660	268	9	example	example	NOUN
ejpam-2660	268	10	13	13	NUM
ejpam-2660	268	11	.	.	PUNCT
ejpam-2660	269	1	let	let	VERB
ejpam-2660	269	2	a	a	PRON
ejpam-2660	269	3	=	=	X
ejpam-2660	269	4	{	{	PUNCT
ejpam-2660	269	5	a	a	NOUN
ejpam-2660	269	6	}	}	PUNCT
ejpam-2660	269	7	and	and	CCONJ
ejpam-2660	269	8	b	b	X
ejpam-2660	269	9	=	=	SYM
ejpam-2660	269	10	{	{	PUNCT
ejpam-2660	269	11	b	b	NOUN
ejpam-2660	269	12	}	}	PUNCT
ejpam-2660	269	13	.	.	PUNCT
ejpam-2660	270	1	then	then	ADV
ejpam-2660	270	2	ia	ia	PROPN
ejpam-2660	270	3	=	=	PROPN
ejpam-2660	270	4	l	l	PROPN
ejpam-2660	270	5	and	and	CCONJ
ejpam-2660	270	6	ib	ib	NOUN
ejpam-2660	271	1	=	=	PUNCT
ejpam-2660	271	2	{	{	PUNCT
ejpam-2660	271	3	a	a	X
ejpam-2660	271	4	}	}	PUNCT
ejpam-2660	271	5	.	.	PUNCT
ejpam-2660	272	1	also	also	ADV
ejpam-2660	272	2	,	,	PUNCT
ejpam-2660	272	3	we	we	PRON
ejpam-2660	272	4	have	have	VERB
ejpam-2660	272	5	b	b	NOUN
ejpam-2660	272	6	∩	∩	ADJ
ejpam-2660	272	7	ib	ib	NOUN
ejpam-2660	272	8	=	=	PUNCT
ejpam-2660	272	9	∅.	∅.	NOUN
ejpam-2660	272	10	proposition	proposition	NOUN
ejpam-2660	272	11	36	36	NUM
ejpam-2660	272	12	.	.	PUNCT
ejpam-2660	273	1	the	the	DET
ejpam-2660	273	2	following	follow	VERB
ejpam-2660	273	3	statements	statement	NOUN
ejpam-2660	273	4	hold	hold	VERB
ejpam-2660	273	5	.	.	PUNCT
ejpam-2660	274	1	(	(	PUNCT
ejpam-2660	274	2	i	i	NOUN
ejpam-2660	274	3	)	)	PUNCT
ejpam-2660	274	4	i(∅	i(∅	NOUN
ejpam-2660	274	5	)	)	PUNCT
ejpam-2660	274	6	=	=	PUNCT
ejpam-2660	274	7	{	{	PUNCT
ejpam-2660	274	8	0	0	NUM
ejpam-2660	274	9	}	}	PUNCT
ejpam-2660	274	10	;	;	PUNCT
ejpam-2660	274	11	(	(	PUNCT
ejpam-2660	274	12	ii	ii	NOUN
ejpam-2660	274	13	)	)	PUNCT
ejpam-2660	274	14	i({0	i({0	NOUN
ejpam-2660	274	15	}	}	PUNCT
ejpam-2660	274	16	)	)	PUNCT
ejpam-2660	275	1	=	=	PUNCT
ejpam-2660	275	2	{	{	PUNCT
ejpam-2660	275	3	0	0	NUM
ejpam-2660	275	4	}	}	PUNCT
ejpam-2660	275	5	;	;	PUNCT
ejpam-2660	275	6	m.	m.	NOUN
ejpam-2660	275	7	amiri	amiri	PROPN
ejpam-2660	275	8	bideshki	bideshki	PROPN
ejpam-2660	275	9	,	,	PUNCT
ejpam-2660	275	10	r.	r.	PROPN
ejpam-2660	275	11	ameri	ameri	PROPN
ejpam-2660	275	12	,	,	PUNCT
ejpam-2660	275	13	a.	a.	PROPN
ejpam-2660	275	14	borumand	borumand	PROPN
ejpam-2660	275	15	saeid	saeid	PROPN
ejpam-2660	275	16	/	/	SYM
ejpam-2660	275	17	eur	eur	PROPN
ejpam-2660	275	18	.	.	PUNCT
ejpam-2660	276	1	j.	j.	PROPN
ejpam-2660	276	2	pure	pure	PROPN
ejpam-2660	276	3	appl	appl	PROPN
ejpam-2660	276	4	.	.	PROPN
ejpam-2660	276	5	math	math	PROPN
ejpam-2660	276	6	,	,	PUNCT
ejpam-2660	276	7	11	11	NUM
ejpam-2660	276	8	(	(	PUNCT
ejpam-2660	276	9	1	1	NUM
ejpam-2660	276	10	)	)	PUNCT
ejpam-2660	276	11	(	(	PUNCT
ejpam-2660	276	12	2018	2018	NUM
ejpam-2660	276	13	)	)	PUNCT
ejpam-2660	276	14	,	,	PUNCT
ejpam-2660	276	15	169	169	NUM
ejpam-2660	276	16	-	-	SYM
ejpam-2660	276	17	188	188	NUM
ejpam-2660	276	18	178	178	NUM
ejpam-2660	276	19	(	(	PUNCT
ejpam-2660	276	20	iii	iii	NOUN
ejpam-2660	276	21	)	)	PUNCT
ejpam-2660	276	22	if	if	SCONJ
ejpam-2660	276	23	a	a	DET
ejpam-2660	276	24	⊆	⊆	NUM
ejpam-2660	276	25	b	b	NOUN
ejpam-2660	276	26	,	,	PUNCT
ejpam-2660	276	27	then	then	ADV
ejpam-2660	276	28	i(a	i(a	PROPN
ejpam-2660	276	29	)	)	PUNCT
ejpam-2660	276	30	⊆	⊆	NUM
ejpam-2660	276	31	i(b	i(b	NOUN
ejpam-2660	276	32	)	)	PUNCT
ejpam-2660	276	33	.	.	PUNCT
ejpam-2660	277	1	proposition	proposition	NOUN
ejpam-2660	277	2	37	37	NUM
ejpam-2660	277	3	.	.	PUNCT
ejpam-2660	278	1	if	if	SCONJ
ejpam-2660	278	2	a	a	PRON
ejpam-2660	278	3	,	,	PUNCT
ejpam-2660	278	4	b	b	PROPN
ejpam-2660	278	5	∈	∈	PROPN
ejpam-2660	278	6	l	l	NOUN
ejpam-2660	278	7	,	,	PUNCT
ejpam-2660	278	8	such	such	ADJ
ejpam-2660	278	9	that	that	SCONJ
ejpam-2660	278	10	a	a	DET
ejpam-2660	278	11	≤	≤	PROPN
ejpam-2660	278	12	b	b	NOUN
ejpam-2660	278	13	,	,	PUNCT
ejpam-2660	278	14	then	then	ADV
ejpam-2660	278	15	i(a	i(a	PROPN
ejpam-2660	278	16	)	)	PUNCT
ejpam-2660	278	17	⊆	⊆	NUM
ejpam-2660	278	18	i(a	i(a	PROPN
ejpam-2660	278	19	∧	∧	PROPN
ejpam-2660	278	20	b	b	PROPN
ejpam-2660	278	21	)	)	PUNCT
ejpam-2660	278	22	.	.	PUNCT
ejpam-2660	279	1	proof	proof	NOUN
ejpam-2660	279	2	.	.	PUNCT
ejpam-2660	280	1	let	let	VERB
ejpam-2660	280	2	a	a	DET
ejpam-2660	280	3	,	,	PUNCT
ejpam-2660	280	4	b	b	PROPN
ejpam-2660	280	5	∈	∈	PROPN
ejpam-2660	280	6	l	l	NOUN
ejpam-2660	280	7	,	,	PUNCT
ejpam-2660	280	8	such	such	ADJ
ejpam-2660	280	9	that	that	SCONJ
ejpam-2660	280	10	a	a	DET
ejpam-2660	280	11	≤	≤	PROPN
ejpam-2660	280	12	b.	b.	NOUN
ejpam-2660	280	13	by	by	ADP
ejpam-2660	280	14	remark	remark	NOUN
ejpam-2660	280	15	6	6	NUM
ejpam-2660	280	16	,	,	PUNCT
ejpam-2660	280	17	a	a	DET
ejpam-2660	280	18	∈	∈	PROPN
ejpam-2660	280	19	a	a	DET
ejpam-2660	280	20	∧	∧	PROPN
ejpam-2660	280	21	b	b	PROPN
ejpam-2660	280	22	,	,	PUNCT
ejpam-2660	280	23	and	and	CCONJ
ejpam-2660	280	24	it	it	PRON
ejpam-2660	280	25	implies	imply	VERB
ejpam-2660	280	26	that	that	SCONJ
ejpam-2660	280	27	{	{	PUNCT
ejpam-2660	280	28	a	a	PRON
ejpam-2660	280	29	}	}	PUNCT
ejpam-2660	280	30	⊆	⊆	NUM
ejpam-2660	280	31	(	(	PUNCT
ejpam-2660	280	32	a	a	DET
ejpam-2660	280	33	∧	∧	PROPN
ejpam-2660	280	34	b	b	NOUN
ejpam-2660	280	35	)	)	PUNCT
ejpam-2660	280	36	.	.	PUNCT
ejpam-2660	281	1	so	so	ADV
ejpam-2660	281	2	by	by	ADP
ejpam-2660	281	3	proposition	proposition	NOUN
ejpam-2660	281	4	48	48	NUM
ejpam-2660	281	5	,	,	PUNCT
ejpam-2660	281	6	(	(	PUNCT
ejpam-2660	281	7	iii	iii	NOUN
ejpam-2660	281	8	)	)	PUNCT
ejpam-2660	281	9	,	,	PUNCT
ejpam-2660	281	10	i(a	i(a	PROPN
ejpam-2660	281	11	)	)	PUNCT
ejpam-2660	281	12	⊆	⊆	NUM
ejpam-2660	281	13	i(a	i(a	PROPN
ejpam-2660	281	14	∧	∧	PROPN
ejpam-2660	281	15	b	b	PROPN
ejpam-2660	281	16	)	)	PUNCT
ejpam-2660	281	17	.	.	PUNCT
ejpam-2660	282	1	theorem	theorem	VERB
ejpam-2660	282	2	38	38	NUM
ejpam-2660	282	3	.	.	PUNCT
ejpam-2660	283	1	i(a	i(a	PROPN
ejpam-2660	283	2	)	)	PUNCT
ejpam-2660	284	1	=	=	PRON
ejpam-2660	284	2	{	{	PUNCT
ejpam-2660	284	3	x	x	PUNCT
ejpam-2660	284	4	∈	∈	NOUN
ejpam-2660	284	5	l	l	NOUN
ejpam-2660	285	1	|	|	NOUN
ejpam-2660	285	2	x	x	SYM
ejpam-2660	285	3	∈	∈	NOUN
ejpam-2660	285	4	x	x	SYM
ejpam-2660	285	5	∧	∧	NOUN
ejpam-2660	285	6	(	(	PUNCT
ejpam-2660	285	7	a1	a1	PROPN
ejpam-2660	285	8	∨	∨	PROPN
ejpam-2660	285	9	a2	a2	PROPN
ejpam-2660	285	10	∨	∨	PROPN
ejpam-2660	285	11	...	...	PUNCT
ejpam-2660	285	12	∨	∨	NUM
ejpam-2660	285	13	an),∃a1	an),∃a1	NOUN
ejpam-2660	285	14	,	,	PUNCT
ejpam-2660	285	15	...	...	PUNCT
ejpam-2660	285	16	,	,	PUNCT
ejpam-2660	285	17	an	an	DET
ejpam-2660	285	18	∈	∈	PROPN
ejpam-2660	285	19	a	a	PRON
ejpam-2660	285	20	}	}	PUNCT
ejpam-2660	285	21	.	.	PUNCT
ejpam-2660	286	1	proof	proof	NOUN
ejpam-2660	286	2	.	.	PUNCT
ejpam-2660	287	1	let	let	VERB
ejpam-2660	287	2	b	b	NOUN
ejpam-2660	287	3	=	=	PRON
ejpam-2660	287	4	{	{	PUNCT
ejpam-2660	287	5	x	x	PUNCT
ejpam-2660	287	6	∈	∈	NOUN
ejpam-2660	287	7	l	l	NOUN
ejpam-2660	288	1	|	|	NOUN
ejpam-2660	288	2	x	x	SYM
ejpam-2660	288	3	∈	∈	NOUN
ejpam-2660	288	4	x	x	SYM
ejpam-2660	288	5	∧	∧	NOUN
ejpam-2660	288	6	(	(	PUNCT
ejpam-2660	288	7	a1	a1	PROPN
ejpam-2660	288	8	∨	∨	PROPN
ejpam-2660	288	9	a2	a2	PROPN
ejpam-2660	288	10	∨	∨	PROPN
ejpam-2660	288	11	...	...	PUNCT
ejpam-2660	288	12	∨	∨	NUM
ejpam-2660	288	13	an	an	PRON
ejpam-2660	288	14	)	)	PUNCT
ejpam-2660	288	15	,	,	PUNCT
ejpam-2660	288	16	∃a1	∃a1	NOUN
ejpam-2660	288	17	,	,	PUNCT
ejpam-2660	288	18	...	...	PUNCT
ejpam-2660	288	19	,	,	PUNCT
ejpam-2660	288	20	an	an	DET
ejpam-2660	288	21	∈	∈	PROPN
ejpam-2660	288	22	a	a	PRON
ejpam-2660	288	23	}	}	PUNCT
ejpam-2660	288	24	.	.	PUNCT
ejpam-2660	289	1	we	we	PRON
ejpam-2660	289	2	show	show	VERB
ejpam-2660	289	3	that	that	SCONJ
ejpam-2660	289	4	b	b	NOUN
ejpam-2660	289	5	is	be	AUX
ejpam-2660	289	6	a	a	DET
ejpam-2660	289	7	hyperideal	hyperideal	NOUN
ejpam-2660	289	8	and	and	CCONJ
ejpam-2660	289	9	we	we	PRON
ejpam-2660	289	10	show	show	VERB
ejpam-2660	289	11	that	that	SCONJ
ejpam-2660	289	12	if	if	SCONJ
ejpam-2660	289	13	i	i	PRON
ejpam-2660	289	14	is	be	AUX
ejpam-2660	289	15	a	a	DET
ejpam-2660	289	16	hyperideal	hyperideal	NOUN
ejpam-2660	289	17	,	,	PUNCT
ejpam-2660	289	18	such	such	ADJ
ejpam-2660	289	19	that	that	SCONJ
ejpam-2660	289	20	a	a	DET
ejpam-2660	289	21	⊆	⊆	NUM
ejpam-2660	289	22	i	i	PRON
ejpam-2660	289	23	,	,	PUNCT
ejpam-2660	289	24	then	then	ADV
ejpam-2660	289	25	b	b	PROPN
ejpam-2660	289	26	⊆	⊆	NUM
ejpam-2660	289	27	i.	i.	NOUN
ejpam-2660	289	28	assume	assume	VERB
ejpam-2660	289	29	x	x	X
ejpam-2660	289	30	,	,	PUNCT
ejpam-2660	289	31	y	y	PROPN
ejpam-2660	289	32	∈	∈	PROPN
ejpam-2660	289	33	b.	b.	PROPN
ejpam-2660	290	1	so	so	ADV
ejpam-2660	290	2	there	there	PRON
ejpam-2660	290	3	exist	exist	VERB
ejpam-2660	290	4	a1	a1	NOUN
ejpam-2660	290	5	,	,	PUNCT
ejpam-2660	290	6	a2	a2	PROPN
ejpam-2660	290	7	,	,	PUNCT
ejpam-2660	290	8	...	...	PUNCT
ejpam-2660	290	9	,	,	PUNCT
ejpam-2660	290	10	an	an	PRON
ejpam-2660	290	11	,	,	PUNCT
ejpam-2660	290	12	b1	b1	NOUN
ejpam-2660	290	13	,	,	PUNCT
ejpam-2660	290	14	b1	b1	NOUN
ejpam-2660	290	15	,	,	PUNCT
ejpam-2660	290	16	b2	b2	NOUN
ejpam-2660	290	17	,	,	PUNCT
ejpam-2660	290	18	...	...	PUNCT
ejpam-2660	290	19	,	,	PUNCT
ejpam-2660	290	20	bm	bm	PROPN
ejpam-2660	290	21	∈	∈	PROPN
ejpam-2660	290	22	a	a	PRON
ejpam-2660	290	23	,	,	PUNCT
ejpam-2660	290	24	such	such	ADJ
ejpam-2660	290	25	that	that	SCONJ
ejpam-2660	290	26	:	:	PUNCT
ejpam-2660	290	27	x	x	SYM
ejpam-2660	290	28	∈	∈	NOUN
ejpam-2660	290	29	x	x	X
ejpam-2660	290	30	∧	∧	NOUN
ejpam-2660	290	31	(	(	PUNCT
ejpam-2660	290	32	a1	a1	PROPN
ejpam-2660	290	33	∨	∨	PROPN
ejpam-2660	290	34	a2	a2	PROPN
ejpam-2660	290	35	∨	∨	PROPN
ejpam-2660	290	36	...	...	PUNCT
ejpam-2660	290	37	∨	∨	NUM
ejpam-2660	290	38	an	an	PRON
ejpam-2660	290	39	)	)	PUNCT
ejpam-2660	290	40	,	,	PUNCT
ejpam-2660	290	41	y	y	PROPN
ejpam-2660	290	42	∈	∈	PROPN
ejpam-2660	290	43	y	y	PROPN
ejpam-2660	290	44	∧	∧	PROPN
ejpam-2660	290	45	(	(	PUNCT
ejpam-2660	290	46	b1	b1	PROPN
ejpam-2660	290	47	∨	∨	NUM
ejpam-2660	290	48	b2	b2	PROPN
ejpam-2660	290	49	∨	∨	NUM
ejpam-2660	290	50	...	...	PUNCT
ejpam-2660	290	51	∨	∨	NUM
ejpam-2660	290	52	bm	bm	PROPN
ejpam-2660	290	53	)	)	PUNCT
ejpam-2660	290	54	.	.	PUNCT
ejpam-2660	291	1	so	so	ADV
ejpam-2660	291	2	,	,	PUNCT
ejpam-2660	291	3	we	we	PRON
ejpam-2660	291	4	have	have	VERB
ejpam-2660	291	5	:	:	PUNCT
ejpam-2660	291	6	x∨(a1∨a2∨	x∨(a1∨a2∨	PROPN
ejpam-2660	291	7	...	...	PUNCT
ejpam-2660	291	8	∨an	∨an	NOUN
ejpam-2660	291	9	)	)	PUNCT
ejpam-2660	291	10	=	=	SYM
ejpam-2660	291	11	(	(	PUNCT
ejpam-2660	291	12	a1∨a2∨	a1∨a2∨	PROPN
ejpam-2660	291	13	...	...	PUNCT
ejpam-2660	291	14	∨an	∨an	NOUN
ejpam-2660	291	15	)	)	PUNCT
ejpam-2660	291	16	,	,	PUNCT
ejpam-2660	291	17	y∨(b1∨b2∨	y∨(b1∨b2∨	PROPN
ejpam-2660	291	18	...	...	PUNCT
ejpam-2660	291	19	∨bm	∨bm	X
ejpam-2660	291	20	)	)	PUNCT
ejpam-2660	291	21	=	=	SYM
ejpam-2660	291	22	(	(	PUNCT
ejpam-2660	291	23	b1∨b2∨	b1∨b2∨	PROPN
ejpam-2660	291	24	...	...	PUNCT
ejpam-2660	291	25	∨bm	∨bm	X
ejpam-2660	291	26	)	)	PUNCT
ejpam-2660	291	27	.	.	PUNCT
ejpam-2660	292	1	also	also	ADV
ejpam-2660	292	2	,	,	PUNCT
ejpam-2660	292	3	we	we	PRON
ejpam-2660	292	4	have	have	VERB
ejpam-2660	292	5	:	:	PUNCT
ejpam-2660	292	6	x	x	X
ejpam-2660	292	7	∨	∨	NUM
ejpam-2660	292	8	y	y	PROPN
ejpam-2660	292	9	∨	∨	NOUN
ejpam-2660	292	10	(	(	PUNCT
ejpam-2660	292	11	a1	a1	PROPN
ejpam-2660	292	12	∨	∨	PROPN
ejpam-2660	292	13	a2	a2	PROPN
ejpam-2660	292	14	∨	∨	PROPN
ejpam-2660	292	15	...	...	PUNCT
ejpam-2660	292	16	∨	∨	NUM
ejpam-2660	292	17	an	an	DET
ejpam-2660	292	18	∨	∨	NUM
ejpam-2660	292	19	b1	b1	PROPN
ejpam-2660	292	20	∨	∨	NOUN
ejpam-2660	292	21	b2	b2	PROPN
ejpam-2660	292	22	∨	∨	NUM
ejpam-2660	292	23	...	...	PUNCT
ejpam-2660	292	24	∨	∨	NUM
ejpam-2660	292	25	bm	bm	PROPN
ejpam-2660	292	26	)	)	PUNCT
ejpam-2660	292	27	=	=	PUNCT
ejpam-2660	293	1	=	=	PUNCT
ejpam-2660	294	1	[	[	X
ejpam-2660	294	2	x	x	X
ejpam-2660	294	3	∨	∨	NOUN
ejpam-2660	294	4	(	(	PUNCT
ejpam-2660	294	5	a1	a1	PROPN
ejpam-2660	294	6	∨	∨	PROPN
ejpam-2660	294	7	a2	a2	PROPN
ejpam-2660	294	8	∨	∨	PROPN
ejpam-2660	294	9	...	...	PUNCT
ejpam-2660	294	10	∨	∨	NUM
ejpam-2660	294	11	an	an	PRON
ejpam-2660	294	12	)	)	PUNCT
ejpam-2660	294	13	]	]	PUNCT
ejpam-2660	295	1	∨	∨	NUM
ejpam-2660	295	2	[	[	X
ejpam-2660	295	3	y	y	PROPN
ejpam-2660	295	4	∨	∨	PROPN
ejpam-2660	295	5	(	(	PUNCT
ejpam-2660	295	6	b1	b1	PROPN
ejpam-2660	295	7	∨	∨	NOUN
ejpam-2660	295	8	b2	b2	PROPN
ejpam-2660	295	9	∨	∨	NUM
ejpam-2660	295	10	...	...	PUNCT
ejpam-2660	295	11	∨	∨	NUM
ejpam-2660	295	12	bm	bm	PROPN
ejpam-2660	295	13	)	)	PUNCT
ejpam-2660	295	14	]	]	PUNCT
ejpam-2660	296	1	=	=	PUNCT
ejpam-2660	296	2	(	(	PUNCT
ejpam-2660	296	3	a1	a1	PROPN
ejpam-2660	296	4	∨	∨	PROPN
ejpam-2660	296	5	a2	a2	PROPN
ejpam-2660	296	6	∨	∨	PROPN
ejpam-2660	296	7	...	...	PUNCT
ejpam-2660	296	8	∨	∨	NUM
ejpam-2660	296	9	an	an	DET
ejpam-2660	296	10	)	)	PUNCT
ejpam-2660	296	11	∨	∨	NOUN
ejpam-2660	296	12	(	(	PUNCT
ejpam-2660	296	13	b1	b1	PROPN
ejpam-2660	296	14	∨	∨	NOUN
ejpam-2660	296	15	b2	b2	PROPN
ejpam-2660	296	16	∨	∨	NUM
ejpam-2660	296	17	...	...	PUNCT
ejpam-2660	296	18	∨	∨	NUM
ejpam-2660	296	19	bm	bm	PROPN
ejpam-2660	296	20	)	)	PUNCT
ejpam-2660	296	21	.	.	PUNCT
ejpam-2660	297	1	so	so	ADV
ejpam-2660	297	2	x	x	SYM
ejpam-2660	297	3	∨	∨	NUM
ejpam-2660	297	4	y	y	PROPN
ejpam-2660	297	5	∈	∈	PROPN
ejpam-2660	297	6	(	(	PUNCT
ejpam-2660	297	7	x	x	PROPN
ejpam-2660	297	8	∨	∨	NUM
ejpam-2660	297	9	y	y	NOUN
ejpam-2660	297	10	)	)	PUNCT
ejpam-2660	297	11	∧	∧	PROPN
ejpam-2660	297	12	(	(	PUNCT
ejpam-2660	297	13	a1	a1	PROPN
ejpam-2660	297	14	∨	∨	PROPN
ejpam-2660	297	15	a2	a2	PROPN
ejpam-2660	297	16	∨	∨	PROPN
ejpam-2660	297	17	...	...	PUNCT
ejpam-2660	297	18	∨	∨	NUM
ejpam-2660	297	19	an	an	DET
ejpam-2660	297	20	∨	∨	NUM
ejpam-2660	297	21	b1	b1	PROPN
ejpam-2660	297	22	∨	∨	NOUN
ejpam-2660	297	23	b2	b2	PROPN
ejpam-2660	297	24	∨	∨	NUM
ejpam-2660	297	25	...	...	PUNCT
ejpam-2660	297	26	∨	∨	NUM
ejpam-2660	297	27	bm	bm	PROPN
ejpam-2660	297	28	)	)	PUNCT
ejpam-2660	297	29	.	.	PUNCT
ejpam-2660	298	1	let	let	VERB
ejpam-2660	298	2	x	x	PUNCT
ejpam-2660	298	3	∈	∈	PROPN
ejpam-2660	298	4	b	b	PROPN
ejpam-2660	298	5	,	,	PUNCT
ejpam-2660	298	6	and	and	CCONJ
ejpam-2660	298	7	y	y	PROPN
ejpam-2660	298	8	≤	≤	PROPN
ejpam-2660	298	9	x.	x.	PUNCT
ejpam-2660	299	1	therefore	therefore	ADV
ejpam-2660	299	2	there	there	PRON
ejpam-2660	299	3	exist	exist	VERB
ejpam-2660	299	4	a1	a1	NOUN
ejpam-2660	299	5	,	,	PUNCT
ejpam-2660	299	6	a2	a2	PROPN
ejpam-2660	299	7	,	,	PUNCT
ejpam-2660	299	8	...	...	PUNCT
ejpam-2660	299	9	,	,	PUNCT
ejpam-2660	299	10	an	an	DET
ejpam-2660	299	11	∈	∈	PROPN
ejpam-2660	299	12	a	a	PRON
ejpam-2660	299	13	,	,	PUNCT
ejpam-2660	299	14	such	such	ADJ
ejpam-2660	299	15	that	that	SCONJ
ejpam-2660	299	16	x	x	SYM
ejpam-2660	299	17	∈	∈	PRON
ejpam-2660	299	18	x∧	x∧	PROPN
ejpam-2660	299	19	(	(	PUNCT
ejpam-2660	299	20	a1	a1	PROPN
ejpam-2660	299	21	∨	∨	PROPN
ejpam-2660	299	22	a2	a2	PROPN
ejpam-2660	299	23	∨	∨	PROPN
ejpam-2660	299	24	...	...	PUNCT
ejpam-2660	299	25	∨	∨	NUM
ejpam-2660	299	26	an	an	PRON
ejpam-2660	299	27	)	)	PUNCT
ejpam-2660	299	28	,	,	PUNCT
ejpam-2660	299	29	by	by	ADP
ejpam-2660	299	30	remark	remark	NOUN
ejpam-2660	299	31	6	6	NUM
ejpam-2660	299	32	,	,	PUNCT
ejpam-2660	299	33	we	we	PRON
ejpam-2660	299	34	have	have	VERB
ejpam-2660	299	35	x	x	NOUN
ejpam-2660	299	36	≤	≤	NUM
ejpam-2660	299	37	a1	a1	NOUN
ejpam-2660	299	38	∨	∨	PROPN
ejpam-2660	299	39	a2	a2	PROPN
ejpam-2660	299	40	∨	∨	PROPN
ejpam-2660	299	41	...	...	PUNCT
ejpam-2660	300	1	∨	∨	NUM
ejpam-2660	300	2	an	an	DET
ejpam-2660	300	3	,	,	PUNCT
ejpam-2660	300	4	since	since	SCONJ
ejpam-2660	300	5	y	y	PROPN
ejpam-2660	300	6	≤	≤	NUM
ejpam-2660	300	7	x	x	PUNCT
ejpam-2660	300	8	,	,	PUNCT
ejpam-2660	300	9	and	and	CCONJ
ejpam-2660	300	10	≤	≤	NOUN
ejpam-2660	300	11	is	be	AUX
ejpam-2660	300	12	a	a	DET
ejpam-2660	300	13	transitive	transitive	ADJ
ejpam-2660	300	14	relation	relation	NOUN
ejpam-2660	300	15	,	,	PUNCT
ejpam-2660	300	16	y	y	PROPN
ejpam-2660	300	17	≤	≤	PROPN
ejpam-2660	300	18	(	(	PUNCT
ejpam-2660	300	19	a1	a1	PROPN
ejpam-2660	300	20	∨	∨	PROPN
ejpam-2660	300	21	a2	a2	PROPN
ejpam-2660	300	22	∨	∨	PROPN
ejpam-2660	300	23	...	...	PUNCT
ejpam-2660	300	24	∨	∨	NUM
ejpam-2660	300	25	an	an	PRON
ejpam-2660	300	26	)	)	PUNCT
ejpam-2660	300	27	,	,	PUNCT
ejpam-2660	300	28	it	it	PRON
ejpam-2660	300	29	implies	imply	VERB
ejpam-2660	300	30	that	that	SCONJ
ejpam-2660	300	31	y	y	PROPN
ejpam-2660	300	32	∈	∈	PROPN
ejpam-2660	300	33	y	y	PROPN
ejpam-2660	300	34	∧	∧	PROPN
ejpam-2660	300	35	(	(	PUNCT
ejpam-2660	300	36	a1	a1	PROPN
ejpam-2660	300	37	∨	∨	PROPN
ejpam-2660	300	38	a2	a2	PROPN
ejpam-2660	300	39	∨	∨	PROPN
ejpam-2660	300	40	...	...	PUNCT
ejpam-2660	300	41	∨	∨	NUM
ejpam-2660	300	42	an	an	PRON
ejpam-2660	300	43	)	)	PUNCT
ejpam-2660	300	44	.	.	PUNCT
ejpam-2660	301	1	so	so	ADV
ejpam-2660	301	2	y	y	PROPN
ejpam-2660	301	3	∈	∈	PROPN
ejpam-2660	301	4	b.	b.	PROPN
ejpam-2660	301	5	we	we	PRON
ejpam-2660	301	6	showed	show	VERB
ejpam-2660	301	7	that	that	SCONJ
ejpam-2660	301	8	b	b	NOUN
ejpam-2660	301	9	is	be	AUX
ejpam-2660	301	10	a	a	DET
ejpam-2660	301	11	hyperideal	hyperideal	NOUN
ejpam-2660	301	12	.	.	PUNCT
ejpam-2660	302	1	now	now	ADV
ejpam-2660	302	2	,	,	PUNCT
ejpam-2660	302	3	we	we	PRON
ejpam-2660	302	4	show	show	VERB
ejpam-2660	302	5	that	that	SCONJ
ejpam-2660	302	6	if	if	SCONJ
ejpam-2660	302	7	i	i	PRON
ejpam-2660	302	8	is	be	AUX
ejpam-2660	302	9	a	a	DET
ejpam-2660	302	10	hyperideal	hyperideal	NOUN
ejpam-2660	302	11	of	of	ADP
ejpam-2660	302	12	l	l	NOUN
ejpam-2660	302	13	,	,	PUNCT
ejpam-2660	302	14	such	such	ADJ
ejpam-2660	302	15	that	that	SCONJ
ejpam-2660	302	16	a	a	DET
ejpam-2660	302	17	⊆	⊆	NUM
ejpam-2660	302	18	i	i	PRON
ejpam-2660	302	19	,	,	PUNCT
ejpam-2660	302	20	then	then	ADV
ejpam-2660	302	21	b	b	PROPN
ejpam-2660	302	22	⊆	⊆	NUM
ejpam-2660	302	23	i.	i.	NOUN
ejpam-2660	302	24	let	let	VERB
ejpam-2660	302	25	x	x	SYM
ejpam-2660	302	26	∈	∈	PROPN
ejpam-2660	302	27	b.	b.	PROPN
ejpam-2660	302	28	therefore	therefore	ADV
ejpam-2660	302	29	there	there	PRON
ejpam-2660	302	30	exist	exist	VERB
ejpam-2660	302	31	a1	a1	NOUN
ejpam-2660	302	32	,	,	PUNCT
ejpam-2660	302	33	a2	a2	PROPN
ejpam-2660	302	34	,	,	PUNCT
ejpam-2660	302	35	...	...	PUNCT
ejpam-2660	302	36	,	,	PUNCT
ejpam-2660	302	37	an	an	DET
ejpam-2660	302	38	∈	∈	PROPN
ejpam-2660	302	39	a	a	PRON
ejpam-2660	302	40	,	,	PUNCT
ejpam-2660	302	41	such	such	ADJ
ejpam-2660	302	42	that	that	SCONJ
ejpam-2660	302	43	x	x	SYM
ejpam-2660	302	44	∈	∈	PRON
ejpam-2660	302	45	x∧	x∧	PROPN
ejpam-2660	302	46	(	(	PUNCT
ejpam-2660	302	47	a1	a1	PROPN
ejpam-2660	302	48	∨a2∨	∨a2∨	PROPN
ejpam-2660	302	49	...	...	PUNCT
ejpam-2660	302	50	∨an	∨an	NOUN
ejpam-2660	302	51	)	)	PUNCT
ejpam-2660	302	52	,	,	PUNCT
ejpam-2660	302	53	and	and	CCONJ
ejpam-2660	302	54	it	it	PRON
ejpam-2660	302	55	implies	imply	VERB
ejpam-2660	302	56	that	that	SCONJ
ejpam-2660	303	1	x	x	SYM
ejpam-2660	303	2	≤	≤	ADJ
ejpam-2660	303	3	a1	a1	NOUN
ejpam-2660	303	4	∨a2∨	∨a2∨	PROPN
ejpam-2660	303	5	...	...	PUNCT
ejpam-2660	303	6	∨an	∨an	PROPN
ejpam-2660	303	7	.	.	NOUN
ejpam-2660	303	8	since	since	SCONJ
ejpam-2660	303	9	a	a	DET
ejpam-2660	303	10	⊆	⊆	NUM
ejpam-2660	303	11	i	i	PRON
ejpam-2660	303	12	,	,	PUNCT
ejpam-2660	303	13	and	and	CCONJ
ejpam-2660	303	14	i	i	PRON
ejpam-2660	303	15	is	be	AUX
ejpam-2660	303	16	a	a	DET
ejpam-2660	303	17	hyperideal	hyperideal	NOUN
ejpam-2660	303	18	,	,	PUNCT
ejpam-2660	303	19	a1	a1	NOUN
ejpam-2660	303	20	∨	∨	PROPN
ejpam-2660	303	21	a2	a2	PROPN
ejpam-2660	303	22	∨	∨	PROPN
ejpam-2660	303	23	...	...	PUNCT
ejpam-2660	303	24	∨	∨	NUM
ejpam-2660	303	25	an	an	DET
ejpam-2660	303	26	∈	∈	PROPN
ejpam-2660	303	27	i.	i.	NOUN
ejpam-2660	303	28	we	we	PRON
ejpam-2660	303	29	have	have	VERB
ejpam-2660	303	30	x	x	NOUN
ejpam-2660	303	31	≤	≤	NUM
ejpam-2660	303	32	a1	a1	NOUN
ejpam-2660	303	33	∨	∨	PROPN
ejpam-2660	303	34	a2	a2	PROPN
ejpam-2660	303	35	∨	∨	PROPN
ejpam-2660	303	36	...	...	PUNCT
ejpam-2660	303	37	∨	∨	NUM
ejpam-2660	303	38	an	an	DET
ejpam-2660	303	39	∈	∈	PROPN
ejpam-2660	304	1	i	i	PRON
ejpam-2660	304	2	,	,	PUNCT
ejpam-2660	304	3	then	then	ADV
ejpam-2660	304	4	x	x	PART
ejpam-2660	304	5	∈	∈	PROPN
ejpam-2660	304	6	i.	i.	NOUN
ejpam-2660	305	1	so	so	SCONJ
ejpam-2660	305	2	b	b	PROPN
ejpam-2660	305	3	⊆	⊆	NUM
ejpam-2660	305	4	i.	i.	NOUN
ejpam-2660	305	5	definition	definition	NOUN
ejpam-2660	305	6	39	39	NUM
ejpam-2660	305	7	.	.	PUNCT
ejpam-2660	306	1	let	let	VERB
ejpam-2660	306	2	∅	∅	NOUN
ejpam-2660	306	3	6=	6=	ADP
ejpam-2660	306	4	s	s	PROPN
ejpam-2660	306	5	⊆	⊆	NUM
ejpam-2660	306	6	l.	l.	NOUN
ejpam-2660	307	1	then	then	ADV
ejpam-2660	307	2	s	s	VERB
ejpam-2660	307	3	is	be	AUX
ejpam-2660	307	4	called	call	VERB
ejpam-2660	307	5	a	a	DET
ejpam-2660	307	6	subhyperlattice	subhyperlattice	NOUN
ejpam-2660	307	7	if	if	SCONJ
ejpam-2660	307	8	x	x	PROPN
ejpam-2660	307	9	∨	∨	NUM
ejpam-2660	307	10	y	y	PROPN
ejpam-2660	307	11	∈	∈	PROPN
ejpam-2660	307	12	s	s	PROPN
ejpam-2660	307	13	,	,	PUNCT
ejpam-2660	307	14	and	and	CCONJ
ejpam-2660	307	15	x	x	PART
ejpam-2660	307	16	∧	∧	PROPN
ejpam-2660	307	17	y	y	PROPN
ejpam-2660	307	18	⊆	⊆	NUM
ejpam-2660	307	19	s	s	NOUN
ejpam-2660	307	20	,	,	PUNCT
ejpam-2660	307	21	for	for	ADP
ejpam-2660	307	22	all	all	DET
ejpam-2660	307	23	x	x	NOUN
ejpam-2660	307	24	,	,	PUNCT
ejpam-2660	307	25	y	y	PROPN
ejpam-2660	307	26	∈	∈	PROPN
ejpam-2660	307	27	s.	s.	PROPN
ejpam-2660	307	28	example	example	NOUN
ejpam-2660	307	29	40	40	NUM
ejpam-2660	307	30	.	.	PUNCT
ejpam-2660	308	1	consider	consider	VERB
ejpam-2660	308	2	∧-hyperlattice	∧-hyperlattice	NOUN
ejpam-2660	308	3	l	l	NOUN
ejpam-2660	308	4	in	in	ADP
ejpam-2660	308	5	example	example	NOUN
ejpam-2660	308	6	18	18	NUM
ejpam-2660	308	7	.	.	PUNCT
ejpam-2660	309	1	it	it	PRON
ejpam-2660	309	2	is	be	AUX
ejpam-2660	309	3	clear	clear	ADJ
ejpam-2660	309	4	that	that	SCONJ
ejpam-2660	309	5	{	{	PUNCT
ejpam-2660	309	6	0	0	NUM
ejpam-2660	309	7	,	,	PUNCT
ejpam-2660	309	8	a	a	PRON
ejpam-2660	309	9	,	,	PUNCT
ejpam-2660	309	10	1	1	NUM
ejpam-2660	309	11	}	}	PUNCT
ejpam-2660	309	12	is	be	AUX
ejpam-2660	309	13	a	a	DET
ejpam-2660	309	14	∧-subhyperlattice	∧-subhyperlattice	NOUN
ejpam-2660	309	15	of	of	ADP
ejpam-2660	309	16	l	l	NOUN
ejpam-2660	309	17	,	,	PUNCT
ejpam-2660	309	18	but	but	CCONJ
ejpam-2660	309	19	{	{	PUNCT
ejpam-2660	309	20	b	b	NOUN
ejpam-2660	309	21	,	,	PUNCT
ejpam-2660	309	22	1	1	NUM
ejpam-2660	309	23	}	}	PUNCT
ejpam-2660	309	24	is	be	AUX
ejpam-2660	309	25	not	not	PART
ejpam-2660	309	26	a	a	DET
ejpam-2660	309	27	∧-subhyperlattice	∧-subhyperlattice	NOUN
ejpam-2660	309	28	,	,	PUNCT
ejpam-2660	309	29	since	since	SCONJ
ejpam-2660	309	30	b	b	PROPN
ejpam-2660	309	31	∧	∧	PROPN
ejpam-2660	309	32	b	b	PROPN
ejpam-2660	309	33	=	=	SYM
ejpam-2660	309	34	{	{	PUNCT
ejpam-2660	309	35	0	0	NUM
ejpam-2660	309	36	,	,	PUNCT
ejpam-2660	309	37	b	b	NOUN
ejpam-2660	309	38	}	}	PUNCT
ejpam-2660	309	39	and	and	CCONJ
ejpam-2660	309	40	{	{	PUNCT
ejpam-2660	309	41	0	0	NUM
ejpam-2660	309	42	,	,	PUNCT
ejpam-2660	309	43	b	b	NOUN
ejpam-2660	309	44	}	}	PUNCT
ejpam-2660	309	45	*	*	PUNCT
ejpam-2660	309	46	{	{	PUNCT
ejpam-2660	309	47	b	b	NUM
ejpam-2660	309	48	,	,	PUNCT
ejpam-2660	309	49	1	1	NUM
ejpam-2660	309	50	}	}	PUNCT
ejpam-2660	309	51	.	.	PUNCT
ejpam-2660	310	1	also	also	ADV
ejpam-2660	310	2	,	,	PUNCT
ejpam-2660	310	3	both	both	CCONJ
ejpam-2660	310	4	{	{	PUNCT
ejpam-2660	310	5	0	0	NUM
ejpam-2660	310	6	}	}	PUNCT
ejpam-2660	310	7	and	and	CCONJ
ejpam-2660	310	8	{	{	PUNCT
ejpam-2660	310	9	1	1	X
ejpam-2660	310	10	}	}	PUNCT
ejpam-2660	310	11	are	be	AUX
ejpam-2660	310	12	”	"	PUNCT
ejpam-2660	310	13	∧	∧	NOUN
ejpam-2660	310	14	”	"	PUNCT
ejpam-2660	310	15	-subhyperlattices	-subhyperlattice	NOUN
ejpam-2660	310	16	of	of	ADP
ejpam-2660	310	17	l.	l.	PROPN
ejpam-2660	310	18	theorem	theorem	VERB
ejpam-2660	310	19	41	41	NUM
ejpam-2660	310	20	.	.	PUNCT
ejpam-2660	311	1	let	let	VERB
ejpam-2660	311	2	i	i	PRON
ejpam-2660	311	3	⊆	⊆	NUM
ejpam-2660	311	4	l.	l.	NOUN
ejpam-2660	311	5	if	if	SCONJ
ejpam-2660	311	6	the	the	DET
ejpam-2660	311	7	following	follow	VERB
ejpam-2660	311	8	conditions	condition	NOUN
ejpam-2660	311	9	hold	hold	VERB
ejpam-2660	311	10	,	,	PUNCT
ejpam-2660	311	11	then	then	ADV
ejpam-2660	311	12	i	i	PRON
ejpam-2660	311	13	is	be	AUX
ejpam-2660	311	14	a	a	DET
ejpam-2660	311	15	hyperideal	hyperideal	NOUN
ejpam-2660	311	16	of	of	ADP
ejpam-2660	311	17	l.	l.	PROPN
ejpam-2660	311	18	(	(	PUNCT
ejpam-2660	311	19	i	i	NOUN
ejpam-2660	311	20	)	)	PUNCT
ejpam-2660	312	1	i	i	PRON
ejpam-2660	312	2	is	be	AUX
ejpam-2660	312	3	”	"	PUNCT
ejpam-2660	312	4	∨	∨	NUM
ejpam-2660	312	5	”	"	PUNCT
ejpam-2660	312	6	-closed	-close	VERB
ejpam-2660	312	7	,	,	PUNCT
ejpam-2660	312	8	(	(	PUNCT
ejpam-2660	312	9	ii	ii	NOUN
ejpam-2660	312	10	)	)	PUNCT
ejpam-2660	312	11	if	if	SCONJ
ejpam-2660	312	12	a	a	DET
ejpam-2660	312	13	∈	∈	PROPN
ejpam-2660	312	14	i	i	X
ejpam-2660	312	15	,	,	PUNCT
ejpam-2660	312	16	and	and	CCONJ
ejpam-2660	312	17	x	x	PUNCT
ejpam-2660	312	18	∈	∈	PROPN
ejpam-2660	312	19	l	l	NOUN
ejpam-2660	312	20	,	,	PUNCT
ejpam-2660	312	21	then	then	ADV
ejpam-2660	312	22	a	a	DET
ejpam-2660	312	23	∧	∧	PROPN
ejpam-2660	312	24	x	x	PUNCT
ejpam-2660	312	25	⊆	⊆	NUM
ejpam-2660	312	26	i	i	PROPN
ejpam-2660	312	27	,	,	PUNCT
ejpam-2660	312	28	m.	m.	PROPN
ejpam-2660	312	29	amiri	amiri	PROPN
ejpam-2660	312	30	bideshki	bideshki	PROPN
ejpam-2660	312	31	,	,	PUNCT
ejpam-2660	312	32	r.	r.	PROPN
ejpam-2660	312	33	ameri	ameri	PROPN
ejpam-2660	312	34	,	,	PUNCT
ejpam-2660	312	35	a.	a.	PROPN
ejpam-2660	312	36	borumand	borumand	PROPN
ejpam-2660	312	37	saeid	saeid	PROPN
ejpam-2660	312	38	/	/	SYM
ejpam-2660	312	39	eur	eur	PROPN
ejpam-2660	312	40	.	.	PUNCT
ejpam-2660	313	1	j.	j.	PROPN
ejpam-2660	313	2	pure	pure	PROPN
ejpam-2660	313	3	appl	appl	PROPN
ejpam-2660	313	4	.	.	PROPN
ejpam-2660	313	5	math	math	PROPN
ejpam-2660	313	6	,	,	PUNCT
ejpam-2660	313	7	11	11	NUM
ejpam-2660	313	8	(	(	PUNCT
ejpam-2660	313	9	1	1	NUM
ejpam-2660	313	10	)	)	PUNCT
ejpam-2660	313	11	(	(	PUNCT
ejpam-2660	313	12	2018	2018	NUM
ejpam-2660	313	13	)	)	PUNCT
ejpam-2660	313	14	,	,	PUNCT
ejpam-2660	313	15	169	169	NUM
ejpam-2660	313	16	-	-	SYM
ejpam-2660	313	17	188	188	NUM
ejpam-2660	313	18	179	179	NUM
ejpam-2660	313	19	proof	proof	NOUN
ejpam-2660	313	20	.	.	PUNCT
ejpam-2660	314	1	it	it	PRON
ejpam-2660	314	2	is	be	AUX
ejpam-2660	314	3	enough	enough	ADJ
ejpam-2660	314	4	prove	prove	VERB
ejpam-2660	314	5	that	that	SCONJ
ejpam-2660	314	6	if	if	SCONJ
ejpam-2660	314	7	a	a	DET
ejpam-2660	314	8	∈	∈	NOUN
ejpam-2660	314	9	i	i	PRON
ejpam-2660	314	10	,	,	PUNCT
ejpam-2660	314	11	and	and	CCONJ
ejpam-2660	314	12	x	x	SYM
ejpam-2660	314	13	≤	≤	NOUN
ejpam-2660	314	14	a	a	PRON
ejpam-2660	314	15	,	,	PUNCT
ejpam-2660	314	16	then	then	ADV
ejpam-2660	314	17	x	x	PART
ejpam-2660	314	18	∈	∈	PROPN
ejpam-2660	314	19	i.	i.	NOUN
ejpam-2660	314	20	by	by	ADP
ejpam-2660	314	21	(	(	PUNCT
ejpam-2660	314	22	ii	ii	PROPN
ejpam-2660	314	23	)	)	PUNCT
ejpam-2660	314	24	,	,	PUNCT
ejpam-2660	314	25	a	a	DET
ejpam-2660	314	26	∧	∧	PROPN
ejpam-2660	314	27	x	x	X
ejpam-2660	314	28	⊆	⊆	NUM
ejpam-2660	314	29	i.	i.	NOUN
ejpam-2660	314	30	it	it	PRON
ejpam-2660	314	31	is	be	AUX
ejpam-2660	314	32	clear	clear	ADJ
ejpam-2660	314	33	that	that	SCONJ
ejpam-2660	314	34	x	x	PUNCT
ejpam-2660	314	35	∈	∈	NOUN
ejpam-2660	314	36	x	x	X
ejpam-2660	314	37	∧	∧	NOUN
ejpam-2660	314	38	a	a	NOUN
ejpam-2660	314	39	,	,	PUNCT
ejpam-2660	314	40	and	and	CCONJ
ejpam-2660	314	41	since	since	SCONJ
ejpam-2660	314	42	a	a	DET
ejpam-2660	314	43	∧	∧	PROPN
ejpam-2660	314	44	x	x	PUNCT
ejpam-2660	314	45	⊆	⊆	NUM
ejpam-2660	314	46	i	i	PRON
ejpam-2660	314	47	,	,	PUNCT
ejpam-2660	314	48	x	x	PROPN
ejpam-2660	314	49	∈	∈	PROPN
ejpam-2660	314	50	i.	i.	NOUN
ejpam-2660	314	51	remark	remark	NOUN
ejpam-2660	314	52	42	42	NUM
ejpam-2660	314	53	.	.	PUNCT
ejpam-2660	315	1	the	the	DET
ejpam-2660	315	2	converse	converse	NOUN
ejpam-2660	315	3	of	of	ADP
ejpam-2660	315	4	theorem	theorem	NOUN
ejpam-2660	315	5	53	53	NUM
ejpam-2660	315	6	does	do	AUX
ejpam-2660	315	7	not	not	PART
ejpam-2660	315	8	hold	hold	VERB
ejpam-2660	315	9	.	.	PUNCT
ejpam-2660	316	1	consider	consider	VERB
ejpam-2660	316	2	the	the	DET
ejpam-2660	316	3	”	"	PUNCT
ejpam-2660	316	4	∧	∧	PROPN
ejpam-2660	316	5	”	"	PUNCT
ejpam-2660	316	6	hyperlattice	hyperlattice	NOUN
ejpam-2660	316	7	l	l	NOUN
ejpam-2660	316	8	in	in	ADP
ejpam-2660	316	9	example	example	NOUN
ejpam-2660	316	10	11	11	NUM
ejpam-2660	316	11	.	.	PUNCT
ejpam-2660	317	1	it	it	PRON
ejpam-2660	317	2	is	be	AUX
ejpam-2660	317	3	clear	clear	ADJ
ejpam-2660	317	4	that	that	SCONJ
ejpam-2660	317	5	{	{	PUNCT
ejpam-2660	317	6	a	a	PRON
ejpam-2660	317	7	}	}	PUNCT
ejpam-2660	317	8	is	be	AUX
ejpam-2660	317	9	a	a	DET
ejpam-2660	317	10	hyperideal	hyperideal	NOUN
ejpam-2660	317	11	of	of	ADP
ejpam-2660	317	12	l	l	NOUN
ejpam-2660	317	13	;	;	PUNCT
ejpam-2660	317	14	since	since	SCONJ
ejpam-2660	317	15	a	a	DET
ejpam-2660	317	16	∧	∧	PROPN
ejpam-2660	317	17	a	a	X
ejpam-2660	317	18	=	=	X
ejpam-2660	317	19	{	{	PUNCT
ejpam-2660	317	20	a	a	PROPN
ejpam-2660	317	21	,	,	PUNCT
ejpam-2660	317	22	b	b	NOUN
ejpam-2660	317	23	}	}	PUNCT
ejpam-2660	317	24	,	,	PUNCT
ejpam-2660	317	25	condition	condition	NOUN
ejpam-2660	317	26	(	(	PUNCT
ejpam-2660	317	27	ii	ii	NOUN
ejpam-2660	317	28	)	)	PUNCT
ejpam-2660	317	29	in	in	ADP
ejpam-2660	317	30	theorem	theorem	NOUN
ejpam-2660	317	31	53	53	NUM
ejpam-2660	317	32	does	do	AUX
ejpam-2660	317	33	not	not	PART
ejpam-2660	317	34	hold	hold	VERB
ejpam-2660	317	35	.	.	PUNCT
ejpam-2660	318	1	so	so	ADV
ejpam-2660	318	2	,	,	PUNCT
ejpam-2660	318	3	we	we	PRON
ejpam-2660	318	4	conclude	conclude	VERB
ejpam-2660	318	5	that	that	DET
ejpam-2660	318	6	concept	concept	NOUN
ejpam-2660	318	7	of	of	ADP
ejpam-2660	318	8	hyperideal	hyperideal	NOUN
ejpam-2660	318	9	in	in	ADP
ejpam-2660	318	10	hyperlattice	hyperlattice	NOUN
ejpam-2660	318	11	and	and	CCONJ
ejpam-2660	318	12	concept	concept	NOUN
ejpam-2660	318	13	of	of	ADP
ejpam-2660	318	14	ideal	ideal	NOUN
ejpam-2660	318	15	in	in	ADP
ejpam-2660	318	16	lattice	lattice	NOUN
ejpam-2660	318	17	are	be	AUX
ejpam-2660	318	18	different	different	ADJ
ejpam-2660	318	19	.	.	PUNCT
ejpam-2660	319	1	if	if	SCONJ
ejpam-2660	319	2	i	i	PRON
ejpam-2660	319	3	⊆	⊆	NUM
ejpam-2660	319	4	l	l	NOUN
ejpam-2660	319	5	is	be	AUX
ejpam-2660	319	6	both	both	PRON
ejpam-2660	319	7	a	a	DET
ejpam-2660	319	8	subhyperlattice	subhyperlattice	NOUN
ejpam-2660	319	9	and	and	CCONJ
ejpam-2660	319	10	a	a	DET
ejpam-2660	319	11	hyperideal	hyperideal	NOUN
ejpam-2660	319	12	,	,	PUNCT
ejpam-2660	319	13	then	then	ADV
ejpam-2660	319	14	condition	condition	NOUN
ejpam-2660	319	15	(	(	PUNCT
ejpam-2660	319	16	ii	ii	NOUN
ejpam-2660	319	17	)	)	PUNCT
ejpam-2660	319	18	in	in	ADP
ejpam-2660	319	19	theorem	theorem	NOUN
ejpam-2660	319	20	53	53	NUM
ejpam-2660	319	21	,	,	PUNCT
ejpam-2660	319	22	is	be	AUX
ejpam-2660	319	23	satisfied	satisfied	ADJ
ejpam-2660	319	24	.	.	PUNCT
ejpam-2660	320	1	so	so	ADV
ejpam-2660	320	2	we	we	PRON
ejpam-2660	320	3	state	state	VERB
ejpam-2660	320	4	the	the	DET
ejpam-2660	320	5	following	follow	VERB
ejpam-2660	320	6	theorem	theorem	PROPN
ejpam-2660	320	7	.	.	PUNCT
ejpam-2660	320	8	theorem	theorem	PROPN
ejpam-2660	320	9	43	43	NUM
ejpam-2660	320	10	.	.	PUNCT
ejpam-2660	321	1	a	a	DET
ejpam-2660	321	2	subhyperlattice	subhyperlattice	NOUN
ejpam-2660	321	3	i	i	PRON
ejpam-2660	321	4	is	be	AUX
ejpam-2660	321	5	a	a	DET
ejpam-2660	321	6	hyperideal	hyperideal	NOUN
ejpam-2660	321	7	if	if	SCONJ
ejpam-2660	321	8	and	and	CCONJ
ejpam-2660	321	9	only	only	ADV
ejpam-2660	321	10	if	if	SCONJ
ejpam-2660	321	11	a	a	DET
ejpam-2660	321	12	∧	∧	NOUN
ejpam-2660	321	13	x	x	PUNCT
ejpam-2660	321	14	⊆	⊆	NUM
ejpam-2660	321	15	i	i	PRON
ejpam-2660	321	16	,	,	PUNCT
ejpam-2660	321	17	where	where	SCONJ
ejpam-2660	321	18	a	a	DET
ejpam-2660	321	19	∈	∈	PROPN
ejpam-2660	321	20	i	i	X
ejpam-2660	321	21	,	,	PUNCT
ejpam-2660	321	22	and	and	CCONJ
ejpam-2660	321	23	x	x	X
ejpam-2660	321	24	∈	∈	PROPN
ejpam-2660	321	25	l.	l.	NOUN
ejpam-2660	321	26	5	5	NUM
ejpam-2660	321	27	.	.	PUNCT
ejpam-2660	321	28	iahyperideals	iahyperideal	NOUN
ejpam-2660	321	29	in	in	ADP
ejpam-2660	321	30	strong	strong	ADJ
ejpam-2660	321	31	”	"	PUNCT
ejpam-2660	321	32	∧	∧	NOUN
ejpam-2660	321	33	”	"	PUNCT
ejpam-2660	321	34	-hyperlattices	-hyperlattice	NOUN
ejpam-2660	321	35	in	in	ADP
ejpam-2660	321	36	this	this	DET
ejpam-2660	321	37	section	section	NOUN
ejpam-2660	321	38	,	,	PUNCT
ejpam-2660	321	39	we	we	PRON
ejpam-2660	321	40	are	be	AUX
ejpam-2660	321	41	going	go	VERB
ejpam-2660	321	42	to	to	PART
ejpam-2660	321	43	define	define	VERB
ejpam-2660	321	44	some	some	DET
ejpam-2660	321	45	types	type	NOUN
ejpam-2660	321	46	of	of	ADP
ejpam-2660	321	47	hyperideals	hyperideal	NOUN
ejpam-2660	321	48	in	in	ADP
ejpam-2660	321	49	a	a	DET
ejpam-2660	321	50	dual	dual	ADJ
ejpam-2660	321	51	distributive	distributive	ADJ
ejpam-2660	321	52	”	"	PUNCT
ejpam-2660	321	53	∧	∧	NOUN
ejpam-2660	321	54	”	"	PUNCT
ejpam-2660	321	55	-hyperlattices	-hyperlattice	NOUN
ejpam-2660	321	56	.	.	PUNCT
ejpam-2660	322	1	we	we	PRON
ejpam-2660	322	2	assume	assume	VERB
ejpam-2660	322	3	that	that	SCONJ
ejpam-2660	322	4	l	l	NOUN
ejpam-2660	322	5	is	be	AUX
ejpam-2660	322	6	a	a	DET
ejpam-2660	322	7	dual	dual	ADJ
ejpam-2660	322	8	distributive	distributive	ADJ
ejpam-2660	322	9	and	and	CCONJ
ejpam-2660	322	10	bounded	bound	VERB
ejpam-2660	322	11	strong	strong	ADJ
ejpam-2660	322	12	”	"	PUNCT
ejpam-2660	322	13	∧	∧	PROPN
ejpam-2660	322	14	”	"	PUNCT
ejpam-2660	322	15	hyperlattice	hyperlattice	NOUN
ejpam-2660	322	16	.	.	PUNCT
ejpam-2660	323	1	theorem	theorem	VERB
ejpam-2660	323	2	44	44	NUM
ejpam-2660	323	3	.	.	PUNCT
ejpam-2660	324	1	let	let	VERB
ejpam-2660	324	2	∅	∅	NOUN
ejpam-2660	324	3	6=	6=	ADP
ejpam-2660	324	4	a	a	DET
ejpam-2660	324	5	⊆	⊆	NUM
ejpam-2660	324	6	l.	l.	NOUN
ejpam-2660	324	7	if	if	SCONJ
ejpam-2660	324	8	ia	ia	PROPN
ejpam-2660	324	9	=	=	SYM
ejpam-2660	324	10	{	{	PUNCT
ejpam-2660	324	11	x	x	PUNCT
ejpam-2660	324	12	∈	∈	NOUN
ejpam-2660	324	13	l	l	NOUN
ejpam-2660	325	1	|	|	NOUN
ejpam-2660	325	2	0	0	NUM
ejpam-2660	325	3	∈	∈	NOUN
ejpam-2660	325	4	x	x	PUNCT
ejpam-2660	325	5	∧	∧	PROPN
ejpam-2660	325	6	a,∀a	a,∀a	X
ejpam-2660	325	7	∈	∈	PROPN
ejpam-2660	325	8	a	a	PRON
ejpam-2660	325	9	}	}	PUNCT
ejpam-2660	325	10	,	,	PUNCT
ejpam-2660	325	11	then	then	ADV
ejpam-2660	325	12	ia	ia	PROPN
ejpam-2660	325	13	is	be	AUX
ejpam-2660	325	14	a	a	DET
ejpam-2660	325	15	hyperideal	hyperideal	NOUN
ejpam-2660	325	16	of	of	ADP
ejpam-2660	325	17	l.	l.	PROPN
ejpam-2660	325	18	proof	proof	PROPN
ejpam-2660	325	19	.	.	PUNCT
ejpam-2660	326	1	since	since	SCONJ
ejpam-2660	326	2	0	0	NUM
ejpam-2660	326	3	≤	≤	NUM
ejpam-2660	327	1	a,∀a	a,∀a	PUNCT
ejpam-2660	327	2	∈	∈	PROPN
ejpam-2660	327	3	a	a	PRON
ejpam-2660	327	4	,	,	PUNCT
ejpam-2660	327	5	by	by	ADP
ejpam-2660	327	6	remark	remark	NOUN
ejpam-2660	327	7	6	6	NUM
ejpam-2660	327	8	,	,	PUNCT
ejpam-2660	327	9	0	0	NUM
ejpam-2660	327	10	∈	∈	NOUN
ejpam-2660	327	11	0	0	NUM
ejpam-2660	328	1	∧	∧	PROPN
ejpam-2660	328	2	a	a	PROPN
ejpam-2660	328	3	,	,	PUNCT
ejpam-2660	328	4	and	and	CCONJ
ejpam-2660	328	5	it	it	PRON
ejpam-2660	328	6	implies	imply	VERB
ejpam-2660	328	7	that	that	SCONJ
ejpam-2660	328	8	0	0	NUM
ejpam-2660	328	9	∈	∈	PROPN
ejpam-2660	328	10	ia	ia	PROPN
ejpam-2660	328	11	,	,	PUNCT
ejpam-2660	328	12	and	and	CCONJ
ejpam-2660	328	13	ia	ia	PROPN
ejpam-2660	328	14	6=	6=	PUNCT
ejpam-2660	328	15	∅.	∅.	ADV
ejpam-2660	328	16	let	let	VERB
ejpam-2660	328	17	x	x	PRON
ejpam-2660	328	18	,	,	PUNCT
ejpam-2660	328	19	y	y	PROPN
ejpam-2660	328	20	∈	∈	PROPN
ejpam-2660	328	21	ia	ia	PROPN
ejpam-2660	328	22	.	.	PROPN
ejpam-2660	329	1	then	then	ADV
ejpam-2660	329	2	0	0	NUM
ejpam-2660	329	3	∈	∈	PROPN
ejpam-2660	329	4	x∧a	x∧a	PROPN
ejpam-2660	329	5	,	,	PUNCT
ejpam-2660	329	6	and	and	CCONJ
ejpam-2660	329	7	0	0	NUM
ejpam-2660	329	8	∈	∈	PROPN
ejpam-2660	329	9	y∧a	y∧a	PROPN
ejpam-2660	329	10	,	,	PUNCT
ejpam-2660	329	11	for	for	ADP
ejpam-2660	329	12	all	all	DET
ejpam-2660	329	13	a	a	DET
ejpam-2660	329	14	∈	∈	NOUN
ejpam-2660	329	15	a.	a.	NOUN
ejpam-2660	329	16	so	so	ADV
ejpam-2660	329	17	0	0	NUM
ejpam-2660	329	18	∈	∈	PROPN
ejpam-2660	329	19	(	(	PUNCT
ejpam-2660	329	20	x∧a)∨	x∧a)∨	X
ejpam-2660	329	21	(	(	PUNCT
ejpam-2660	329	22	y∧a	y∧a	PROPN
ejpam-2660	329	23	)	)	PUNCT
ejpam-2660	329	24	,	,	PUNCT
ejpam-2660	329	25	for	for	ADP
ejpam-2660	329	26	all	all	DET
ejpam-2660	329	27	a	a	DET
ejpam-2660	329	28	∈	∈	NOUN
ejpam-2660	329	29	a	a	PRON
ejpam-2660	329	30	;	;	PUNCT
ejpam-2660	329	31	since	since	SCONJ
ejpam-2660	329	32	l	l	NOUN
ejpam-2660	329	33	is	be	AUX
ejpam-2660	329	34	dual	dual	ADV
ejpam-2660	329	35	distributive	distributive	ADJ
ejpam-2660	329	36	,	,	PUNCT
ejpam-2660	329	37	0	0	NUM
ejpam-2660	329	38	∈	∈	NOUN
ejpam-2660	329	39	(	(	PUNCT
ejpam-2660	329	40	x	x	PROPN
ejpam-2660	329	41	∨	∨	NUM
ejpam-2660	329	42	y	y	NOUN
ejpam-2660	329	43	)	)	PUNCT
ejpam-2660	329	44	∧	∧	PROPN
ejpam-2660	329	45	a	a	ADP
ejpam-2660	329	46	,	,	PUNCT
ejpam-2660	329	47	for	for	ADP
ejpam-2660	329	48	all	all	DET
ejpam-2660	329	49	a	a	DET
ejpam-2660	329	50	∈	∈	NOUN
ejpam-2660	329	51	a.	a.	NOUN
ejpam-2660	330	1	so	so	ADV
ejpam-2660	330	2	x	x	PROPN
ejpam-2660	330	3	∨	∨	NUM
ejpam-2660	330	4	y	y	PROPN
ejpam-2660	330	5	∈	∈	PROPN
ejpam-2660	330	6	ia	ia	PROPN
ejpam-2660	330	7	.	.	PUNCT
ejpam-2660	331	1	now	now	ADV
ejpam-2660	331	2	,	,	PUNCT
ejpam-2660	331	3	let	let	VERB
ejpam-2660	331	4	x	x	X
ejpam-2660	331	5	∈	∈	PROPN
ejpam-2660	331	6	ia	ia	PROPN
ejpam-2660	331	7	and	and	CCONJ
ejpam-2660	331	8	y	y	PROPN
ejpam-2660	331	9	≤	≤	PROPN
ejpam-2660	331	10	x.	x.	NOUN
ejpam-2660	332	1	then	then	ADV
ejpam-2660	332	2	0	0	NUM
ejpam-2660	332	3	∈	∈	PROPN
ejpam-2660	332	4	x	x	X
ejpam-2660	332	5	∧	∧	NOUN
ejpam-2660	332	6	a	a	X
ejpam-2660	332	7	,	,	PUNCT
ejpam-2660	332	8	for	for	ADP
ejpam-2660	332	9	all	all	DET
ejpam-2660	332	10	a	a	DET
ejpam-2660	332	11	∈	∈	PROPN
ejpam-2660	332	12	a	a	PRON
ejpam-2660	332	13	,	,	PUNCT
ejpam-2660	332	14	and	and	CCONJ
ejpam-2660	332	15	x	x	SYM
ejpam-2660	332	16	∨	∨	NUM
ejpam-2660	332	17	y	y	NOUN
ejpam-2660	332	18	=	=	PUNCT
ejpam-2660	332	19	x.	x.	NOUN
ejpam-2660	333	1	we	we	PRON
ejpam-2660	333	2	have	have	VERB
ejpam-2660	333	3	0	0	NUM
ejpam-2660	333	4	∈	∈	PROPN
ejpam-2660	333	5	x∧	x∧	PROPN
ejpam-2660	333	6	a	a	DET
ejpam-2660	333	7	=	=	X
ejpam-2660	333	8	(	(	PUNCT
ejpam-2660	333	9	x∨	x∨	PROPN
ejpam-2660	333	10	y)∧	y)∧	PROPN
ejpam-2660	333	11	a	a	X
ejpam-2660	333	12	,	,	PUNCT
ejpam-2660	333	13	for	for	ADP
ejpam-2660	333	14	all	all	DET
ejpam-2660	333	15	a	a	DET
ejpam-2660	333	16	∈	∈	PROPN
ejpam-2660	333	17	a	a	PRON
ejpam-2660	333	18	,	,	PUNCT
ejpam-2660	333	19	and	and	CCONJ
ejpam-2660	333	20	since	since	SCONJ
ejpam-2660	333	21	l	l	NOUN
ejpam-2660	333	22	is	be	AUX
ejpam-2660	333	23	dual	dual	ADV
ejpam-2660	333	24	distributive	distributive	ADJ
ejpam-2660	333	25	,	,	PUNCT
ejpam-2660	333	26	0	0	NUM
ejpam-2660	333	27	∈	∈	PROPN
ejpam-2660	333	28	(	(	PUNCT
ejpam-2660	333	29	x∧	x∧	PROPN
ejpam-2660	333	30	a)∨	a)∨	PROPN
ejpam-2660	333	31	(	(	PUNCT
ejpam-2660	333	32	y	y	PROPN
ejpam-2660	333	33	∧	∧	PROPN
ejpam-2660	333	34	a	a	PRON
ejpam-2660	333	35	)	)	PUNCT
ejpam-2660	333	36	,	,	PUNCT
ejpam-2660	333	37	for	for	ADP
ejpam-2660	333	38	all	all	DET
ejpam-2660	333	39	a	a	DET
ejpam-2660	333	40	∈	∈	NOUN
ejpam-2660	333	41	a.	a.	NOUN
ejpam-2660	333	42	since	since	SCONJ
ejpam-2660	333	43	0	0	NUM
ejpam-2660	333	44	∨	∨	NUM
ejpam-2660	333	45	0	0	NUM
ejpam-2660	334	1	=	=	SYM
ejpam-2660	334	2	0	0	NUM
ejpam-2660	334	3	and	and	CCONJ
ejpam-2660	334	4	0	0	NUM
ejpam-2660	334	5	∈	∈	NOUN
ejpam-2660	334	6	x	x	X
ejpam-2660	334	7	∧	∧	NOUN
ejpam-2660	334	8	a	a	X
ejpam-2660	334	9	,	,	PUNCT
ejpam-2660	334	10	for	for	ADP
ejpam-2660	334	11	all	all	DET
ejpam-2660	334	12	a	a	DET
ejpam-2660	334	13	∈	∈	PROPN
ejpam-2660	334	14	a	a	PRON
ejpam-2660	334	15	,	,	PUNCT
ejpam-2660	334	16	we	we	PRON
ejpam-2660	334	17	conclude	conclude	VERB
ejpam-2660	334	18	that	that	SCONJ
ejpam-2660	334	19	0	0	NUM
ejpam-2660	334	20	∈	∈	PROPN
ejpam-2660	334	21	y	y	PROPN
ejpam-2660	334	22	∧	∧	PROPN
ejpam-2660	334	23	a	a	PROPN
ejpam-2660	334	24	,	,	PUNCT
ejpam-2660	334	25	for	for	ADP
ejpam-2660	334	26	all	all	DET
ejpam-2660	334	27	a	a	DET
ejpam-2660	334	28	∈	∈	PROPN
ejpam-2660	334	29	a	a	PRON
ejpam-2660	334	30	,	,	PUNCT
ejpam-2660	334	31	and	and	CCONJ
ejpam-2660	334	32	it	it	PRON
ejpam-2660	334	33	implies	imply	VERB
ejpam-2660	334	34	that	that	SCONJ
ejpam-2660	334	35	y	y	PROPN
ejpam-2660	334	36	∈	∈	PROPN
ejpam-2660	334	37	ia	ia	PROPN
ejpam-2660	334	38	.	.	PUNCT
ejpam-2660	335	1	so	so	ADV
ejpam-2660	335	2	ia	ia	PROPN
ejpam-2660	335	3	is	be	AUX
ejpam-2660	335	4	a	a	DET
ejpam-2660	335	5	hyperideal	hyperideal	NOUN
ejpam-2660	335	6	of	of	ADP
ejpam-2660	335	7	l.	l.	PROPN
ejpam-2660	335	8	corollary	corollary	PROPN
ejpam-2660	335	9	45	45	PROPN
ejpam-2660	335	10	.	.	PUNCT
ejpam-2660	336	1	let	let	VERB
ejpam-2660	336	2	l	l	NOUN
ejpam-2660	336	3	be	be	AUX
ejpam-2660	336	4	a	a	DET
ejpam-2660	336	5	∧-hyperlattice	∧-hyperlattice	NOUN
ejpam-2660	336	6	and	and	CCONJ
ejpam-2660	336	7	a	a	PRON
ejpam-2660	336	8	,	,	PUNCT
ejpam-2660	336	9	b	b	PROPN
ejpam-2660	336	10	⊆	⊆	NUM
ejpam-2660	336	11	l.	l.	NOUN
ejpam-2660	336	12	then	then	ADV
ejpam-2660	336	13	we	we	PRON
ejpam-2660	336	14	have	have	VERB
ejpam-2660	336	15	:	:	PUNCT
ejpam-2660	336	16	(	(	PUNCT
ejpam-2660	336	17	i	i	NOUN
ejpam-2660	336	18	)	)	PUNCT
ejpam-2660	336	19	ia	ia	PROPN
ejpam-2660	336	20	⊆	⊆	NUM
ejpam-2660	336	21	ia	ia	PROPN
ejpam-2660	336	22	,	,	PUNCT
ejpam-2660	337	1	∀a	∀a	NOUN
ejpam-2660	337	2	∈	∈	NOUN
ejpam-2660	337	3	a	a	DET
ejpam-2660	337	4	;	;	PUNCT
ejpam-2660	337	5	(	(	PUNCT
ejpam-2660	337	6	ii	ii	NOUN
ejpam-2660	337	7	)	)	PUNCT
ejpam-2660	337	8	if	if	SCONJ
ejpam-2660	337	9	a	a	DET
ejpam-2660	337	10	⊆	⊆	NUM
ejpam-2660	337	11	b	b	NOUN
ejpam-2660	337	12	,	,	PUNCT
ejpam-2660	337	13	then	then	ADV
ejpam-2660	337	14	ib	ib	PROPN
ejpam-2660	337	15	⊆	⊆	NUM
ejpam-2660	337	16	ia	ia	PROPN
ejpam-2660	337	17	;	;	PUNCT
ejpam-2660	337	18	(	(	PUNCT
ejpam-2660	337	19	iii	iii	X
ejpam-2660	337	20	)	)	PUNCT
ejpam-2660	337	21	ia	ia	NOUN
ejpam-2660	337	22	=	=	SYM
ejpam-2660	337	23	∩{ia	∩{ia	PROPN
ejpam-2660	337	24	:	:	PUNCT
ejpam-2660	337	25	a	a	DET
ejpam-2660	337	26	∈	∈	PROPN
ejpam-2660	337	27	a	a	PRON
ejpam-2660	337	28	}	}	PUNCT
ejpam-2660	337	29	.	.	PUNCT
ejpam-2660	338	1	(	(	PUNCT
ejpam-2660	338	2	iv	iv	X
ejpam-2660	338	3	)	)	PUNCT
ejpam-2660	338	4	ia	ia	PROPN
ejpam-2660	338	5	∩	∩	ADJ
ejpam-2660	338	6	ib	ib	NOUN
ejpam-2660	338	7	=	=	SYM
ejpam-2660	338	8	ia∪b	ia∪b	ADJ
ejpam-2660	338	9	.	.	PUNCT
ejpam-2660	339	1	now	now	ADV
ejpam-2660	339	2	,	,	PUNCT
ejpam-2660	339	3	we	we	PRON
ejpam-2660	339	4	define	define	VERB
ejpam-2660	339	5	the	the	DET
ejpam-2660	339	6	least	least	ADJ
ejpam-2660	339	7	hyperideal	hyperideal	NOUN
ejpam-2660	339	8	generating	generating	NOUN
ejpam-2660	339	9	by	by	ADP
ejpam-2660	339	10	a	a	DET
ejpam-2660	339	11	⊆	⊆	NUM
ejpam-2660	339	12	l	l	NOUN
ejpam-2660	339	13	,	,	PUNCT
ejpam-2660	339	14	and	and	CCONJ
ejpam-2660	339	15	we	we	PRON
ejpam-2660	339	16	denote	denote	VERB
ejpam-2660	339	17	it	it	PRON
ejpam-2660	339	18	by	by	ADP
ejpam-2660	339	19	i(a	i(a	PROPN
ejpam-2660	339	20	)	)	PUNCT
ejpam-2660	339	21	.	.	PUNCT
ejpam-2660	340	1	m.	m.	PROPN
ejpam-2660	340	2	amiri	amiri	PROPN
ejpam-2660	340	3	bideshki	bideshki	PROPN
ejpam-2660	340	4	,	,	PUNCT
ejpam-2660	340	5	r.	r.	PROPN
ejpam-2660	340	6	ameri	ameri	PROPN
ejpam-2660	340	7	,	,	PUNCT
ejpam-2660	340	8	a.	a.	PROPN
ejpam-2660	340	9	borumand	borumand	PROPN
ejpam-2660	340	10	saeid	saeid	PROPN
ejpam-2660	340	11	/	/	SYM
ejpam-2660	340	12	eur	eur	PROPN
ejpam-2660	340	13	.	.	PUNCT
ejpam-2660	341	1	j.	j.	PROPN
ejpam-2660	341	2	pure	pure	PROPN
ejpam-2660	341	3	appl	appl	PROPN
ejpam-2660	341	4	.	.	PROPN
ejpam-2660	341	5	math	math	PROPN
ejpam-2660	341	6	,	,	PUNCT
ejpam-2660	341	7	11	11	NUM
ejpam-2660	341	8	(	(	PUNCT
ejpam-2660	341	9	1	1	NUM
ejpam-2660	341	10	)	)	PUNCT
ejpam-2660	341	11	(	(	PUNCT
ejpam-2660	341	12	2018	2018	NUM
ejpam-2660	341	13	)	)	PUNCT
ejpam-2660	341	14	,	,	PUNCT
ejpam-2660	341	15	169	169	NUM
ejpam-2660	341	16	-	-	SYM
ejpam-2660	341	17	188	188	NUM
ejpam-2660	341	18	180	180	NUM
ejpam-2660	341	19	definition	definition	NOUN
ejpam-2660	341	20	46	46	NUM
ejpam-2660	341	21	.	.	PUNCT
ejpam-2660	342	1	let	let	VERB
ejpam-2660	342	2	a	a	DET
ejpam-2660	342	3	⊆	⊆	NUM
ejpam-2660	342	4	l.	l.	NOUN
ejpam-2660	342	5	we	we	PRON
ejpam-2660	342	6	define	define	VERB
ejpam-2660	342	7	i(a	i(a	PROPN
ejpam-2660	342	8	)	)	PUNCT
ejpam-2660	343	1	=	=	SYM
ejpam-2660	343	2	⋂	⋂	PROPN
ejpam-2660	343	3	a⊆i{i	a⊆i{i	NOUN
ejpam-2660	344	1	|	|	ADV
ejpam-2660	344	2	i	i	PRON
ejpam-2660	344	3	is	be	AUX
ejpam-2660	344	4	a	a	DET
ejpam-2660	344	5	hyperideal	hyperideal	NOUN
ejpam-2660	344	6	of	of	ADP
ejpam-2660	344	7	l	l	NOUN
ejpam-2660	344	8	}	}	PUNCT
ejpam-2660	344	9	,	,	PUNCT
ejpam-2660	344	10	and	and	CCONJ
ejpam-2660	344	11	i(a	i(a	NOUN
ejpam-2660	344	12	)	)	PUNCT
ejpam-2660	344	13	is	be	AUX
ejpam-2660	344	14	said	say	VERB
ejpam-2660	344	15	to	to	PART
ejpam-2660	344	16	be	be	AUX
ejpam-2660	344	17	the	the	DET
ejpam-2660	344	18	least	least	ADJ
ejpam-2660	344	19	hyperideal	hyperideal	ADJ
ejpam-2660	344	20	generating	generating	NOUN
ejpam-2660	344	21	by	by	ADP
ejpam-2660	344	22	a.	a.	NOUN
ejpam-2660	344	23	example	example	NOUN
ejpam-2660	345	1	47	47	NUM
ejpam-2660	345	2	.	.	PUNCT
ejpam-2660	346	1	(	(	PUNCT
ejpam-2660	346	2	i	i	NOUN
ejpam-2660	346	3	)	)	PUNCT
ejpam-2660	346	4	consider	consider	VERB
ejpam-2660	346	5	∧−	∧−	PRON
ejpam-2660	346	6	hyperlattice	hyperlattice	PROPN
ejpam-2660	346	7	l	l	NOUN
ejpam-2660	346	8	in	in	ADP
ejpam-2660	346	9	example	example	NOUN
ejpam-2660	346	10	18	18	NUM
ejpam-2660	346	11	.	.	PUNCT
ejpam-2660	347	1	let	let	VERB
ejpam-2660	347	2	i(l	i(l	PRON
ejpam-2660	347	3	)	)	PUNCT
ejpam-2660	347	4	be	be	AUX
ejpam-2660	347	5	the	the	DET
ejpam-2660	347	6	set	set	NOUN
ejpam-2660	347	7	of	of	ADP
ejpam-2660	347	8	all	all	DET
ejpam-2660	347	9	hyperideals	hyperideal	NOUN
ejpam-2660	347	10	of	of	ADP
ejpam-2660	347	11	l.	l.	PROPN
ejpam-2660	347	12	then	then	ADV
ejpam-2660	347	13	we	we	PRON
ejpam-2660	347	14	have	have	VERB
ejpam-2660	347	15	i(l	i(l	PROPN
ejpam-2660	347	16	)	)	PUNCT
ejpam-2660	348	1	=	=	PRON
ejpam-2660	348	2	{	{	PUNCT
ejpam-2660	348	3	{	{	PUNCT
ejpam-2660	348	4	0	0	NUM
ejpam-2660	348	5	}	}	PUNCT
ejpam-2660	348	6	,	,	PUNCT
ejpam-2660	348	7	{	{	PUNCT
ejpam-2660	348	8	0	0	NUM
ejpam-2660	348	9	,	,	PUNCT
ejpam-2660	348	10	a	a	DET
ejpam-2660	348	11	}	}	PUNCT
ejpam-2660	348	12	,	,	PUNCT
ejpam-2660	348	13	{	{	PUNCT
ejpam-2660	348	14	0	0	NUM
ejpam-2660	348	15	,	,	PUNCT
ejpam-2660	348	16	b	b	NOUN
ejpam-2660	348	17	}	}	PUNCT
ejpam-2660	348	18	,	,	PUNCT
ejpam-2660	348	19	l	l	NOUN
ejpam-2660	348	20	}	}	PUNCT
ejpam-2660	348	21	.	.	PUNCT
ejpam-2660	349	1	if	if	SCONJ
ejpam-2660	349	2	a	a	PRON
ejpam-2660	349	3	=	=	X
ejpam-2660	349	4	{	{	PUNCT
ejpam-2660	349	5	a	a	PROPN
ejpam-2660	349	6	,	,	PUNCT
ejpam-2660	349	7	b	b	NOUN
ejpam-2660	349	8	}	}	PUNCT
ejpam-2660	349	9	,	,	PUNCT
ejpam-2660	349	10	then	then	ADV
ejpam-2660	349	11	i(a	i(a	PROPN
ejpam-2660	349	12	)	)	PUNCT
ejpam-2660	350	1	=	=	PUNCT
ejpam-2660	350	2	l.	l.	PROPN
ejpam-2660	351	1	also	also	ADV
ejpam-2660	351	2	,	,	PUNCT
ejpam-2660	351	3	if	if	SCONJ
ejpam-2660	351	4	a	a	PRON
ejpam-2660	351	5	=	=	X
ejpam-2660	351	6	{	{	PUNCT
ejpam-2660	351	7	a	a	NOUN
ejpam-2660	351	8	}	}	PUNCT
ejpam-2660	351	9	,	,	PUNCT
ejpam-2660	351	10	then	then	ADV
ejpam-2660	351	11	i(a	i(a	NUM
ejpam-2660	351	12	)	)	PUNCT
ejpam-2660	351	13	=	=	PRON
ejpam-2660	351	14	{	{	PUNCT
ejpam-2660	351	15	0	0	NUM
ejpam-2660	351	16	,	,	PUNCT
ejpam-2660	351	17	a	a	PRON
ejpam-2660	351	18	}	}	PUNCT
ejpam-2660	351	19	.	.	PUNCT
ejpam-2660	352	1	(	(	PUNCT
ejpam-2660	352	2	ii	ii	NOUN
ejpam-2660	352	3	)	)	PUNCT
ejpam-2660	352	4	consider	consider	VERB
ejpam-2660	352	5	∧−	∧−	PRON
ejpam-2660	352	6	hyperlattice	hyperlattice	PROPN
ejpam-2660	352	7	l	l	NOUN
ejpam-2660	352	8	in	in	ADP
ejpam-2660	352	9	example	example	NOUN
ejpam-2660	352	10	13	13	NUM
ejpam-2660	352	11	.	.	PUNCT
ejpam-2660	353	1	let	let	VERB
ejpam-2660	353	2	a	a	PRON
ejpam-2660	353	3	=	=	X
ejpam-2660	353	4	{	{	PUNCT
ejpam-2660	353	5	a	a	NOUN
ejpam-2660	353	6	}	}	PUNCT
ejpam-2660	353	7	and	and	CCONJ
ejpam-2660	353	8	b	b	X
ejpam-2660	353	9	=	=	SYM
ejpam-2660	353	10	{	{	PUNCT
ejpam-2660	353	11	b	b	NOUN
ejpam-2660	353	12	}	}	PUNCT
ejpam-2660	353	13	.	.	PUNCT
ejpam-2660	354	1	then	then	ADV
ejpam-2660	354	2	ia	ia	PROPN
ejpam-2660	354	3	=	=	PROPN
ejpam-2660	354	4	l	l	PROPN
ejpam-2660	354	5	and	and	CCONJ
ejpam-2660	354	6	ib	ib	NOUN
ejpam-2660	355	1	=	=	PUNCT
ejpam-2660	355	2	{	{	PUNCT
ejpam-2660	355	3	a	a	X
ejpam-2660	355	4	}	}	PUNCT
ejpam-2660	355	5	.	.	PUNCT
ejpam-2660	356	1	also	also	ADV
ejpam-2660	356	2	,	,	PUNCT
ejpam-2660	356	3	we	we	PRON
ejpam-2660	356	4	have	have	VERB
ejpam-2660	356	5	b	b	NOUN
ejpam-2660	356	6	∩	∩	ADJ
ejpam-2660	356	7	ib	ib	NOUN
ejpam-2660	356	8	=	=	PUNCT
ejpam-2660	356	9	∅.	∅.	NOUN
ejpam-2660	356	10	proposition	proposition	NOUN
ejpam-2660	356	11	48	48	NUM
ejpam-2660	356	12	.	.	PUNCT
ejpam-2660	357	1	the	the	DET
ejpam-2660	357	2	following	follow	VERB
ejpam-2660	357	3	statements	statement	NOUN
ejpam-2660	357	4	hold	hold	VERB
ejpam-2660	357	5	.	.	PUNCT
ejpam-2660	358	1	(	(	PUNCT
ejpam-2660	358	2	i	i	NOUN
ejpam-2660	358	3	)	)	PUNCT
ejpam-2660	358	4	i(∅	i(∅	NOUN
ejpam-2660	358	5	)	)	PUNCT
ejpam-2660	358	6	=	=	PUNCT
ejpam-2660	358	7	{	{	PUNCT
ejpam-2660	358	8	0	0	NUM
ejpam-2660	358	9	}	}	PUNCT
ejpam-2660	358	10	;	;	PUNCT
ejpam-2660	358	11	(	(	PUNCT
ejpam-2660	358	12	ii	ii	NOUN
ejpam-2660	358	13	)	)	PUNCT
ejpam-2660	358	14	i({0	i({0	NOUN
ejpam-2660	358	15	}	}	PUNCT
ejpam-2660	358	16	)	)	PUNCT
ejpam-2660	359	1	=	=	PUNCT
ejpam-2660	359	2	{	{	PUNCT
ejpam-2660	359	3	0	0	NUM
ejpam-2660	359	4	}	}	PUNCT
ejpam-2660	359	5	;	;	PUNCT
ejpam-2660	359	6	(	(	PUNCT
ejpam-2660	359	7	iii	iii	X
ejpam-2660	359	8	)	)	PUNCT
ejpam-2660	359	9	if	if	SCONJ
ejpam-2660	359	10	a	a	DET
ejpam-2660	359	11	⊆	⊆	NUM
ejpam-2660	359	12	b	b	NOUN
ejpam-2660	359	13	,	,	PUNCT
ejpam-2660	359	14	then	then	ADV
ejpam-2660	359	15	i(a	i(a	PROPN
ejpam-2660	359	16	)	)	PUNCT
ejpam-2660	359	17	⊆	⊆	NUM
ejpam-2660	359	18	i(b	i(b	NOUN
ejpam-2660	359	19	)	)	PUNCT
ejpam-2660	359	20	.	.	PUNCT
ejpam-2660	360	1	proposition	proposition	NOUN
ejpam-2660	360	2	49	49	NUM
ejpam-2660	360	3	.	.	PUNCT
ejpam-2660	361	1	if	if	SCONJ
ejpam-2660	361	2	a	a	PRON
ejpam-2660	361	3	,	,	PUNCT
ejpam-2660	361	4	b	b	PROPN
ejpam-2660	361	5	∈	∈	PROPN
ejpam-2660	361	6	l	l	NOUN
ejpam-2660	361	7	,	,	PUNCT
ejpam-2660	361	8	such	such	ADJ
ejpam-2660	361	9	that	that	SCONJ
ejpam-2660	361	10	a	a	DET
ejpam-2660	361	11	≤	≤	PROPN
ejpam-2660	361	12	b	b	NOUN
ejpam-2660	361	13	,	,	PUNCT
ejpam-2660	361	14	then	then	ADV
ejpam-2660	361	15	i(a	i(a	PROPN
ejpam-2660	361	16	)	)	PUNCT
ejpam-2660	361	17	⊆	⊆	NUM
ejpam-2660	361	18	i(a	i(a	PROPN
ejpam-2660	361	19	∧	∧	PROPN
ejpam-2660	361	20	b	b	PROPN
ejpam-2660	361	21	)	)	PUNCT
ejpam-2660	361	22	.	.	PUNCT
ejpam-2660	362	1	proof	proof	NOUN
ejpam-2660	362	2	.	.	PUNCT
ejpam-2660	363	1	let	let	VERB
ejpam-2660	363	2	a	a	DET
ejpam-2660	363	3	,	,	PUNCT
ejpam-2660	363	4	b	b	PROPN
ejpam-2660	363	5	∈	∈	PROPN
ejpam-2660	363	6	l	l	NOUN
ejpam-2660	363	7	,	,	PUNCT
ejpam-2660	363	8	such	such	ADJ
ejpam-2660	363	9	that	that	SCONJ
ejpam-2660	363	10	a	a	DET
ejpam-2660	363	11	≤	≤	PROPN
ejpam-2660	363	12	b.	b.	NOUN
ejpam-2660	363	13	by	by	ADP
ejpam-2660	363	14	remark	remark	NOUN
ejpam-2660	363	15	6	6	NUM
ejpam-2660	363	16	,	,	PUNCT
ejpam-2660	363	17	a	a	DET
ejpam-2660	363	18	∈	∈	PROPN
ejpam-2660	363	19	a	a	DET
ejpam-2660	363	20	∧	∧	PROPN
ejpam-2660	363	21	b	b	PROPN
ejpam-2660	363	22	,	,	PUNCT
ejpam-2660	363	23	and	and	CCONJ
ejpam-2660	363	24	it	it	PRON
ejpam-2660	363	25	implies	imply	VERB
ejpam-2660	363	26	that	that	SCONJ
ejpam-2660	363	27	{	{	PUNCT
ejpam-2660	363	28	a	a	PRON
ejpam-2660	363	29	}	}	PUNCT
ejpam-2660	363	30	⊆	⊆	NUM
ejpam-2660	363	31	(	(	PUNCT
ejpam-2660	363	32	a	a	DET
ejpam-2660	363	33	∧	∧	PROPN
ejpam-2660	363	34	b	b	NOUN
ejpam-2660	363	35	)	)	PUNCT
ejpam-2660	363	36	.	.	PUNCT
ejpam-2660	364	1	so	so	ADV
ejpam-2660	364	2	by	by	ADP
ejpam-2660	364	3	proposition	proposition	NOUN
ejpam-2660	364	4	48	48	NUM
ejpam-2660	364	5	,	,	PUNCT
ejpam-2660	364	6	(	(	PUNCT
ejpam-2660	364	7	iii	iii	NOUN
ejpam-2660	364	8	)	)	PUNCT
ejpam-2660	364	9	,	,	PUNCT
ejpam-2660	364	10	i(a	i(a	PROPN
ejpam-2660	364	11	)	)	PUNCT
ejpam-2660	364	12	⊆	⊆	NUM
ejpam-2660	364	13	i(a	i(a	PROPN
ejpam-2660	364	14	∧	∧	PROPN
ejpam-2660	364	15	b	b	PROPN
ejpam-2660	364	16	)	)	PUNCT
ejpam-2660	364	17	.	.	PUNCT
ejpam-2660	365	1	theorem	theorem	VERB
ejpam-2660	365	2	50	50	NUM
ejpam-2660	365	3	.	.	PUNCT
ejpam-2660	366	1	i(a	i(a	NUM
ejpam-2660	366	2	)	)	PUNCT
ejpam-2660	367	1	=	=	PRON
ejpam-2660	367	2	{	{	PUNCT
ejpam-2660	367	3	x	x	PUNCT
ejpam-2660	367	4	∈	∈	NOUN
ejpam-2660	367	5	l	l	NOUN
ejpam-2660	368	1	|	|	NOUN
ejpam-2660	368	2	x	x	SYM
ejpam-2660	368	3	∈	∈	NOUN
ejpam-2660	368	4	x	x	SYM
ejpam-2660	368	5	∧	∧	NOUN
ejpam-2660	368	6	(	(	PUNCT
ejpam-2660	368	7	a1	a1	PROPN
ejpam-2660	368	8	∨	∨	PROPN
ejpam-2660	368	9	a2	a2	PROPN
ejpam-2660	368	10	∨	∨	PROPN
ejpam-2660	368	11	...	...	PUNCT
ejpam-2660	368	12	∨	∨	NUM
ejpam-2660	368	13	an),∃a1	an),∃a1	NOUN
ejpam-2660	368	14	,	,	PUNCT
ejpam-2660	368	15	...	...	PUNCT
ejpam-2660	368	16	,	,	PUNCT
ejpam-2660	368	17	an	an	DET
ejpam-2660	368	18	∈	∈	PROPN
ejpam-2660	368	19	a	a	PRON
ejpam-2660	368	20	}	}	PUNCT
ejpam-2660	368	21	.	.	PUNCT
ejpam-2660	369	1	proof	proof	NOUN
ejpam-2660	369	2	.	.	PUNCT
ejpam-2660	370	1	let	let	VERB
ejpam-2660	370	2	b	b	NOUN
ejpam-2660	370	3	=	=	PRON
ejpam-2660	370	4	{	{	PUNCT
ejpam-2660	370	5	x	x	PUNCT
ejpam-2660	370	6	∈	∈	NOUN
ejpam-2660	370	7	l	l	NOUN
ejpam-2660	371	1	|	|	NOUN
ejpam-2660	371	2	x	x	SYM
ejpam-2660	371	3	∈	∈	NOUN
ejpam-2660	371	4	x	x	SYM
ejpam-2660	371	5	∧	∧	NOUN
ejpam-2660	371	6	(	(	PUNCT
ejpam-2660	371	7	a1	a1	PROPN
ejpam-2660	371	8	∨	∨	PROPN
ejpam-2660	371	9	a2	a2	PROPN
ejpam-2660	371	10	∨	∨	PROPN
ejpam-2660	371	11	...	...	PUNCT
ejpam-2660	371	12	∨	∨	NUM
ejpam-2660	371	13	an	an	PRON
ejpam-2660	371	14	)	)	PUNCT
ejpam-2660	371	15	,	,	PUNCT
ejpam-2660	371	16	∃a1	∃a1	NOUN
ejpam-2660	371	17	,	,	PUNCT
ejpam-2660	371	18	...	...	PUNCT
ejpam-2660	371	19	,	,	PUNCT
ejpam-2660	371	20	an	an	DET
ejpam-2660	371	21	∈	∈	PROPN
ejpam-2660	371	22	a	a	PRON
ejpam-2660	371	23	}	}	PUNCT
ejpam-2660	371	24	.	.	PUNCT
ejpam-2660	372	1	we	we	PRON
ejpam-2660	372	2	show	show	VERB
ejpam-2660	372	3	that	that	SCONJ
ejpam-2660	372	4	b	b	NOUN
ejpam-2660	372	5	is	be	AUX
ejpam-2660	372	6	a	a	DET
ejpam-2660	372	7	hyperideal	hyperideal	NOUN
ejpam-2660	372	8	and	and	CCONJ
ejpam-2660	372	9	we	we	PRON
ejpam-2660	372	10	show	show	VERB
ejpam-2660	372	11	that	that	SCONJ
ejpam-2660	372	12	if	if	SCONJ
ejpam-2660	372	13	i	i	PRON
ejpam-2660	372	14	is	be	AUX
ejpam-2660	372	15	a	a	DET
ejpam-2660	372	16	hyperideal	hyperideal	NOUN
ejpam-2660	372	17	,	,	PUNCT
ejpam-2660	372	18	such	such	ADJ
ejpam-2660	372	19	that	that	SCONJ
ejpam-2660	372	20	a	a	DET
ejpam-2660	372	21	⊆	⊆	NUM
ejpam-2660	372	22	i	i	PRON
ejpam-2660	372	23	,	,	PUNCT
ejpam-2660	372	24	then	then	ADV
ejpam-2660	372	25	b	b	PROPN
ejpam-2660	372	26	⊆	⊆	NUM
ejpam-2660	372	27	i.	i.	NOUN
ejpam-2660	372	28	assume	assume	VERB
ejpam-2660	372	29	x	x	X
ejpam-2660	372	30	,	,	PUNCT
ejpam-2660	372	31	y	y	PROPN
ejpam-2660	372	32	∈	∈	PROPN
ejpam-2660	372	33	b.	b.	PROPN
ejpam-2660	373	1	so	so	ADV
ejpam-2660	373	2	there	there	PRON
ejpam-2660	373	3	exist	exist	VERB
ejpam-2660	373	4	a1	a1	NOUN
ejpam-2660	373	5	,	,	PUNCT
ejpam-2660	373	6	a2	a2	PROPN
ejpam-2660	373	7	,	,	PUNCT
ejpam-2660	373	8	...	...	PUNCT
ejpam-2660	373	9	,	,	PUNCT
ejpam-2660	373	10	an	an	PRON
ejpam-2660	373	11	,	,	PUNCT
ejpam-2660	373	12	b1	b1	NOUN
ejpam-2660	373	13	,	,	PUNCT
ejpam-2660	373	14	b1	b1	NOUN
ejpam-2660	373	15	,	,	PUNCT
ejpam-2660	373	16	b2	b2	NOUN
ejpam-2660	373	17	,	,	PUNCT
ejpam-2660	373	18	...	...	PUNCT
ejpam-2660	373	19	,	,	PUNCT
ejpam-2660	373	20	bm	bm	PROPN
ejpam-2660	373	21	∈	∈	PROPN
ejpam-2660	373	22	a	a	PRON
ejpam-2660	373	23	,	,	PUNCT
ejpam-2660	373	24	such	such	ADJ
ejpam-2660	373	25	that	that	SCONJ
ejpam-2660	373	26	:	:	PUNCT
ejpam-2660	373	27	x	x	SYM
ejpam-2660	373	28	∈	∈	NOUN
ejpam-2660	373	29	x	x	X
ejpam-2660	373	30	∧	∧	NOUN
ejpam-2660	373	31	(	(	PUNCT
ejpam-2660	373	32	a1	a1	PROPN
ejpam-2660	373	33	∨	∨	PROPN
ejpam-2660	373	34	a2	a2	PROPN
ejpam-2660	373	35	∨	∨	PROPN
ejpam-2660	373	36	...	...	PUNCT
ejpam-2660	373	37	∨	∨	NUM
ejpam-2660	373	38	an	an	PRON
ejpam-2660	373	39	)	)	PUNCT
ejpam-2660	373	40	,	,	PUNCT
ejpam-2660	373	41	y	y	PROPN
ejpam-2660	373	42	∈	∈	PROPN
ejpam-2660	373	43	y	y	PROPN
ejpam-2660	373	44	∧	∧	PROPN
ejpam-2660	373	45	(	(	PUNCT
ejpam-2660	373	46	b1	b1	PROPN
ejpam-2660	373	47	∨	∨	NUM
ejpam-2660	373	48	b2	b2	PROPN
ejpam-2660	373	49	∨	∨	NUM
ejpam-2660	373	50	...	...	PUNCT
ejpam-2660	373	51	∨	∨	NUM
ejpam-2660	373	52	bm	bm	PROPN
ejpam-2660	373	53	)	)	PUNCT
ejpam-2660	373	54	.	.	PUNCT
ejpam-2660	374	1	so	so	ADV
ejpam-2660	374	2	,	,	PUNCT
ejpam-2660	374	3	we	we	PRON
ejpam-2660	374	4	have	have	VERB
ejpam-2660	374	5	:	:	PUNCT
ejpam-2660	374	6	x	x	SYM
ejpam-2660	374	7	∨	∨	NOUN
ejpam-2660	374	8	(	(	PUNCT
ejpam-2660	374	9	a1	a1	PROPN
ejpam-2660	374	10	∨	∨	PROPN
ejpam-2660	374	11	a2	a2	PROPN
ejpam-2660	374	12	∨	∨	PROPN
ejpam-2660	374	13	...	...	PUNCT
ejpam-2660	374	14	∨	∨	NUM
ejpam-2660	374	15	an	an	PRON
ejpam-2660	374	16	)	)	PUNCT
ejpam-2660	374	17	=	=	PUNCT
ejpam-2660	374	18	(	(	PUNCT
ejpam-2660	374	19	a1	a1	PROPN
ejpam-2660	374	20	∨	∨	PROPN
ejpam-2660	374	21	a2	a2	PROPN
ejpam-2660	374	22	∨	∨	PROPN
ejpam-2660	374	23	...	...	PUNCT
ejpam-2660	374	24	∨	∨	NUM
ejpam-2660	374	25	an	an	PRON
ejpam-2660	374	26	)	)	PUNCT
ejpam-2660	374	27	,	,	PUNCT
ejpam-2660	374	28	y	y	PROPN
ejpam-2660	374	29	∨	∨	PROPN
ejpam-2660	374	30	(	(	PUNCT
ejpam-2660	374	31	b1	b1	PROPN
ejpam-2660	374	32	∨	∨	NOUN
ejpam-2660	374	33	b2	b2	PROPN
ejpam-2660	374	34	∨	∨	NUM
ejpam-2660	374	35	...	...	PUNCT
ejpam-2660	374	36	∨	∨	NUM
ejpam-2660	374	37	bm	bm	PROPN
ejpam-2660	374	38	)	)	PUNCT
ejpam-2660	374	39	=	=	PUNCT
ejpam-2660	374	40	(	(	PUNCT
ejpam-2660	374	41	b1	b1	PROPN
ejpam-2660	374	42	∨	∨	NUM
ejpam-2660	374	43	b2	b2	PROPN
ejpam-2660	374	44	∨	∨	NUM
ejpam-2660	374	45	...	...	PUNCT
ejpam-2660	374	46	∨	∨	NUM
ejpam-2660	374	47	bm	bm	PROPN
ejpam-2660	374	48	)	)	PUNCT
ejpam-2660	374	49	.	.	PUNCT
ejpam-2660	375	1	also	also	ADV
ejpam-2660	375	2	,	,	PUNCT
ejpam-2660	375	3	we	we	PRON
ejpam-2660	375	4	have	have	VERB
ejpam-2660	375	5	:	:	PUNCT
ejpam-2660	375	6	x	x	X
ejpam-2660	375	7	∨	∨	NUM
ejpam-2660	375	8	y	y	PROPN
ejpam-2660	375	9	∨	∨	NOUN
ejpam-2660	375	10	(	(	PUNCT
ejpam-2660	375	11	a1	a1	PROPN
ejpam-2660	375	12	∨	∨	PROPN
ejpam-2660	375	13	a2	a2	PROPN
ejpam-2660	375	14	∨	∨	PROPN
ejpam-2660	375	15	...	...	PUNCT
ejpam-2660	375	16	∨	∨	NUM
ejpam-2660	375	17	an	an	DET
ejpam-2660	375	18	∨	∨	NUM
ejpam-2660	375	19	b1	b1	PROPN
ejpam-2660	375	20	∨	∨	NOUN
ejpam-2660	375	21	b2	b2	PROPN
ejpam-2660	375	22	∨	∨	NUM
ejpam-2660	375	23	...	...	PUNCT
ejpam-2660	375	24	∨	∨	NUM
ejpam-2660	375	25	bm	bm	PROPN
ejpam-2660	375	26	)	)	PUNCT
ejpam-2660	375	27	=	=	PUNCT
ejpam-2660	376	1	=	=	PUNCT
ejpam-2660	377	1	[	[	X
ejpam-2660	377	2	x	x	X
ejpam-2660	377	3	∨	∨	NOUN
ejpam-2660	377	4	(	(	PUNCT
ejpam-2660	377	5	a1	a1	PROPN
ejpam-2660	377	6	∨	∨	PROPN
ejpam-2660	377	7	a2	a2	PROPN
ejpam-2660	377	8	∨	∨	PROPN
ejpam-2660	377	9	...	...	PUNCT
ejpam-2660	377	10	∨	∨	NUM
ejpam-2660	377	11	an	an	PRON
ejpam-2660	377	12	)	)	PUNCT
ejpam-2660	377	13	]	]	PUNCT
ejpam-2660	378	1	∨	∨	NUM
ejpam-2660	378	2	[	[	X
ejpam-2660	378	3	y	y	PROPN
ejpam-2660	378	4	∨	∨	PROPN
ejpam-2660	378	5	(	(	PUNCT
ejpam-2660	378	6	b1	b1	PROPN
ejpam-2660	378	7	∨	∨	NOUN
ejpam-2660	378	8	b2	b2	PROPN
ejpam-2660	378	9	∨	∨	NUM
ejpam-2660	378	10	...	...	PUNCT
ejpam-2660	378	11	∨	∨	NUM
ejpam-2660	378	12	bm	bm	PROPN
ejpam-2660	378	13	)	)	PUNCT
ejpam-2660	378	14	]	]	PUNCT
ejpam-2660	379	1	=	=	PUNCT
ejpam-2660	379	2	(	(	PUNCT
ejpam-2660	379	3	a1	a1	PROPN
ejpam-2660	379	4	∨	∨	PROPN
ejpam-2660	379	5	a2	a2	PROPN
ejpam-2660	379	6	∨	∨	PROPN
ejpam-2660	379	7	...	...	PUNCT
ejpam-2660	379	8	∨	∨	NUM
ejpam-2660	379	9	an	an	DET
ejpam-2660	379	10	)	)	PUNCT
ejpam-2660	379	11	∨	∨	NOUN
ejpam-2660	379	12	(	(	PUNCT
ejpam-2660	379	13	b1	b1	PROPN
ejpam-2660	379	14	∨	∨	NOUN
ejpam-2660	379	15	b2	b2	PROPN
ejpam-2660	379	16	∨	∨	NUM
ejpam-2660	379	17	...	...	PUNCT
ejpam-2660	379	18	∨	∨	NUM
ejpam-2660	379	19	bm	bm	PROPN
ejpam-2660	379	20	)	)	PUNCT
ejpam-2660	379	21	.	.	PUNCT
ejpam-2660	380	1	so	so	ADV
ejpam-2660	380	2	x	x	SYM
ejpam-2660	380	3	∨	∨	NUM
ejpam-2660	380	4	y	y	PROPN
ejpam-2660	380	5	∈	∈	PROPN
ejpam-2660	380	6	(	(	PUNCT
ejpam-2660	380	7	x	x	PROPN
ejpam-2660	380	8	∨	∨	NUM
ejpam-2660	380	9	y	y	NOUN
ejpam-2660	380	10	)	)	PUNCT
ejpam-2660	380	11	∧	∧	PROPN
ejpam-2660	380	12	(	(	PUNCT
ejpam-2660	380	13	a1	a1	PROPN
ejpam-2660	380	14	∨	∨	PROPN
ejpam-2660	380	15	a2	a2	PROPN
ejpam-2660	380	16	∨	∨	PROPN
ejpam-2660	380	17	...	...	PUNCT
ejpam-2660	380	18	∨	∨	NUM
ejpam-2660	380	19	an	an	DET
ejpam-2660	380	20	∨	∨	NUM
ejpam-2660	380	21	b1	b1	PROPN
ejpam-2660	380	22	∨	∨	NOUN
ejpam-2660	380	23	b2	b2	PROPN
ejpam-2660	380	24	∨	∨	NUM
ejpam-2660	380	25	...	...	PUNCT
ejpam-2660	380	26	∨	∨	NUM
ejpam-2660	380	27	bm	bm	PROPN
ejpam-2660	380	28	)	)	PUNCT
ejpam-2660	380	29	.	.	PUNCT
ejpam-2660	381	1	let	let	VERB
ejpam-2660	381	2	x	x	PUNCT
ejpam-2660	381	3	∈	∈	PROPN
ejpam-2660	381	4	b	b	PROPN
ejpam-2660	381	5	,	,	PUNCT
ejpam-2660	381	6	and	and	CCONJ
ejpam-2660	381	7	y	y	PROPN
ejpam-2660	381	8	≤	≤	PROPN
ejpam-2660	381	9	x.	x.	PUNCT
ejpam-2660	382	1	therefore	therefore	ADV
ejpam-2660	382	2	there	there	PRON
ejpam-2660	382	3	exist	exist	VERB
ejpam-2660	382	4	a1	a1	NOUN
ejpam-2660	382	5	,	,	PUNCT
ejpam-2660	382	6	a2	a2	PROPN
ejpam-2660	382	7	,	,	PUNCT
ejpam-2660	382	8	...	...	PUNCT
ejpam-2660	382	9	,	,	PUNCT
ejpam-2660	382	10	an	an	DET
ejpam-2660	382	11	∈	∈	PROPN
ejpam-2660	382	12	a	a	PRON
ejpam-2660	382	13	,	,	PUNCT
ejpam-2660	382	14	such	such	ADJ
ejpam-2660	382	15	that	that	SCONJ
ejpam-2660	382	16	x	x	SYM
ejpam-2660	382	17	∈	∈	PRON
ejpam-2660	382	18	x∧	x∧	PROPN
ejpam-2660	382	19	(	(	PUNCT
ejpam-2660	382	20	a1	a1	PROPN
ejpam-2660	382	21	∨	∨	PROPN
ejpam-2660	382	22	a2	a2	PROPN
ejpam-2660	382	23	∨	∨	PROPN
ejpam-2660	382	24	m.	m.	PROPN
ejpam-2660	382	25	amiri	amiri	PROPN
ejpam-2660	382	26	bideshki	bideshki	PROPN
ejpam-2660	382	27	,	,	PUNCT
ejpam-2660	382	28	r.	r.	PROPN
ejpam-2660	382	29	ameri	ameri	PROPN
ejpam-2660	382	30	,	,	PUNCT
ejpam-2660	382	31	a.	a.	PROPN
ejpam-2660	382	32	borumand	borumand	PROPN
ejpam-2660	382	33	saeid	saeid	PROPN
ejpam-2660	382	34	/	/	SYM
ejpam-2660	382	35	eur	eur	PROPN
ejpam-2660	382	36	.	.	PUNCT
ejpam-2660	383	1	j.	j.	PROPN
ejpam-2660	383	2	pure	pure	PROPN
ejpam-2660	383	3	appl	appl	PROPN
ejpam-2660	383	4	.	.	PROPN
ejpam-2660	383	5	math	math	PROPN
ejpam-2660	383	6	,	,	PUNCT
ejpam-2660	383	7	11	11	NUM
ejpam-2660	383	8	(	(	PUNCT
ejpam-2660	383	9	1	1	NUM
ejpam-2660	383	10	)	)	PUNCT
ejpam-2660	383	11	(	(	PUNCT
ejpam-2660	383	12	2018	2018	NUM
ejpam-2660	383	13	)	)	PUNCT
ejpam-2660	383	14	,	,	PUNCT
ejpam-2660	383	15	169	169	NUM
ejpam-2660	383	16	-	-	SYM
ejpam-2660	383	17	188	188	NUM
ejpam-2660	383	18	181	181	NUM
ejpam-2660	383	19	...	...	PUNCT
ejpam-2660	383	20	∨	∨	NUM
ejpam-2660	383	21	an	an	PRON
ejpam-2660	383	22	)	)	PUNCT
ejpam-2660	383	23	,	,	PUNCT
ejpam-2660	383	24	by	by	ADP
ejpam-2660	383	25	remark	remark	NOUN
ejpam-2660	383	26	6	6	NUM
ejpam-2660	383	27	,	,	PUNCT
ejpam-2660	383	28	we	we	PRON
ejpam-2660	383	29	have	have	VERB
ejpam-2660	383	30	x	x	NOUN
ejpam-2660	383	31	≤	≤	NUM
ejpam-2660	383	32	a1	a1	NOUN
ejpam-2660	383	33	∨	∨	PROPN
ejpam-2660	383	34	a2	a2	PROPN
ejpam-2660	383	35	∨	∨	PROPN
ejpam-2660	383	36	...	...	PUNCT
ejpam-2660	383	37	∨	∨	NUM
ejpam-2660	383	38	an	an	DET
ejpam-2660	383	39	,	,	PUNCT
ejpam-2660	383	40	since	since	SCONJ
ejpam-2660	383	41	y	y	PROPN
ejpam-2660	383	42	≤	≤	NUM
ejpam-2660	383	43	x	x	PUNCT
ejpam-2660	383	44	,	,	PUNCT
ejpam-2660	383	45	and	and	CCONJ
ejpam-2660	383	46	≤	≤	NOUN
ejpam-2660	383	47	is	be	AUX
ejpam-2660	383	48	a	a	DET
ejpam-2660	383	49	transitive	transitive	ADJ
ejpam-2660	383	50	relation	relation	NOUN
ejpam-2660	383	51	,	,	PUNCT
ejpam-2660	383	52	y	y	PROPN
ejpam-2660	383	53	≤	≤	PROPN
ejpam-2660	383	54	(	(	PUNCT
ejpam-2660	383	55	a1	a1	PROPN
ejpam-2660	383	56	∨	∨	PROPN
ejpam-2660	383	57	a2	a2	PROPN
ejpam-2660	383	58	∨	∨	PROPN
ejpam-2660	383	59	...	...	PUNCT
ejpam-2660	384	1	∨	∨	NUM
ejpam-2660	384	2	an	an	PRON
ejpam-2660	384	3	)	)	PUNCT
ejpam-2660	384	4	,	,	PUNCT
ejpam-2660	384	5	it	it	PRON
ejpam-2660	384	6	implies	imply	VERB
ejpam-2660	384	7	that	that	SCONJ
ejpam-2660	384	8	y	y	PROPN
ejpam-2660	384	9	∈	∈	PROPN
ejpam-2660	384	10	y	y	PROPN
ejpam-2660	384	11	∧	∧	PROPN
ejpam-2660	384	12	(	(	PUNCT
ejpam-2660	384	13	a1	a1	PROPN
ejpam-2660	384	14	∨	∨	PROPN
ejpam-2660	384	15	a2	a2	PROPN
ejpam-2660	384	16	∨	∨	PROPN
ejpam-2660	384	17	...	...	PUNCT
ejpam-2660	384	18	∨	∨	NUM
ejpam-2660	384	19	an	an	PRON
ejpam-2660	384	20	)	)	PUNCT
ejpam-2660	384	21	.	.	PUNCT
ejpam-2660	385	1	so	so	ADV
ejpam-2660	385	2	y	y	PROPN
ejpam-2660	385	3	∈	∈	PROPN
ejpam-2660	385	4	b.	b.	PROPN
ejpam-2660	385	5	we	we	PRON
ejpam-2660	385	6	showed	show	VERB
ejpam-2660	385	7	that	that	SCONJ
ejpam-2660	385	8	b	b	NOUN
ejpam-2660	385	9	is	be	AUX
ejpam-2660	385	10	a	a	DET
ejpam-2660	385	11	hyperideal	hyperideal	NOUN
ejpam-2660	385	12	.	.	PUNCT
ejpam-2660	386	1	now	now	ADV
ejpam-2660	386	2	,	,	PUNCT
ejpam-2660	386	3	we	we	PRON
ejpam-2660	386	4	show	show	VERB
ejpam-2660	386	5	that	that	SCONJ
ejpam-2660	386	6	if	if	SCONJ
ejpam-2660	386	7	i	i	PRON
ejpam-2660	386	8	is	be	AUX
ejpam-2660	386	9	a	a	DET
ejpam-2660	386	10	hyperideal	hyperideal	NOUN
ejpam-2660	386	11	of	of	ADP
ejpam-2660	386	12	l	l	NOUN
ejpam-2660	386	13	,	,	PUNCT
ejpam-2660	386	14	such	such	ADJ
ejpam-2660	386	15	that	that	SCONJ
ejpam-2660	386	16	a	a	DET
ejpam-2660	386	17	⊆	⊆	NUM
ejpam-2660	386	18	i	i	PRON
ejpam-2660	386	19	,	,	PUNCT
ejpam-2660	386	20	then	then	ADV
ejpam-2660	386	21	b	b	PROPN
ejpam-2660	386	22	⊆	⊆	NUM
ejpam-2660	386	23	i.	i.	NOUN
ejpam-2660	386	24	let	let	VERB
ejpam-2660	386	25	x	x	SYM
ejpam-2660	386	26	∈	∈	PROPN
ejpam-2660	386	27	b.	b.	PROPN
ejpam-2660	386	28	therefore	therefore	ADV
ejpam-2660	386	29	there	there	PRON
ejpam-2660	386	30	exist	exist	VERB
ejpam-2660	386	31	a1	a1	NOUN
ejpam-2660	386	32	,	,	PUNCT
ejpam-2660	386	33	a2	a2	PROPN
ejpam-2660	386	34	,	,	PUNCT
ejpam-2660	386	35	...	...	PUNCT
ejpam-2660	386	36	,	,	PUNCT
ejpam-2660	386	37	an	an	DET
ejpam-2660	386	38	∈	∈	PROPN
ejpam-2660	386	39	a	a	PRON
ejpam-2660	386	40	,	,	PUNCT
ejpam-2660	386	41	such	such	ADJ
ejpam-2660	386	42	that	that	SCONJ
ejpam-2660	386	43	x	x	SYM
ejpam-2660	386	44	∈	∈	PRON
ejpam-2660	386	45	x∧	x∧	PROPN
ejpam-2660	386	46	(	(	PUNCT
ejpam-2660	386	47	a1	a1	PROPN
ejpam-2660	386	48	∨a2	∨a2	NOUN
ejpam-2660	386	49	∨	∨	NOUN
ejpam-2660	386	50	...	...	PUNCT
ejpam-2660	386	51	∨an	∨an	NOUN
ejpam-2660	386	52	)	)	PUNCT
ejpam-2660	386	53	,	,	PUNCT
ejpam-2660	386	54	and	and	CCONJ
ejpam-2660	386	55	it	it	PRON
ejpam-2660	386	56	implies	imply	VERB
ejpam-2660	386	57	that	that	SCONJ
ejpam-2660	387	1	x	x	SYM
ejpam-2660	387	2	≤	≤	ADJ
ejpam-2660	387	3	a1	a1	NOUN
ejpam-2660	387	4	∨a2∨	∨a2∨	PROPN
ejpam-2660	387	5	...	...	PUNCT
ejpam-2660	387	6	∨an	∨an	PROPN
ejpam-2660	387	7	.	.	NOUN
ejpam-2660	387	8	since	since	SCONJ
ejpam-2660	387	9	a	a	DET
ejpam-2660	387	10	⊆	⊆	NUM
ejpam-2660	387	11	i	i	PRON
ejpam-2660	387	12	,	,	PUNCT
ejpam-2660	387	13	and	and	CCONJ
ejpam-2660	387	14	i	i	PRON
ejpam-2660	387	15	is	be	AUX
ejpam-2660	387	16	a	a	DET
ejpam-2660	387	17	hyperideal	hyperideal	NOUN
ejpam-2660	387	18	,	,	PUNCT
ejpam-2660	387	19	a1	a1	NOUN
ejpam-2660	387	20	∨	∨	PROPN
ejpam-2660	387	21	a2	a2	PROPN
ejpam-2660	387	22	∨	∨	PROPN
ejpam-2660	387	23	...	...	PUNCT
ejpam-2660	387	24	∨	∨	NUM
ejpam-2660	387	25	an	an	DET
ejpam-2660	387	26	∈	∈	PROPN
ejpam-2660	387	27	i.	i.	NOUN
ejpam-2660	387	28	we	we	PRON
ejpam-2660	387	29	have	have	VERB
ejpam-2660	387	30	x	x	NOUN
ejpam-2660	387	31	≤	≤	NUM
ejpam-2660	387	32	a1	a1	NOUN
ejpam-2660	387	33	∨	∨	PROPN
ejpam-2660	387	34	a2	a2	PROPN
ejpam-2660	387	35	∨	∨	PROPN
ejpam-2660	387	36	...	...	PUNCT
ejpam-2660	387	37	∨	∨	NUM
ejpam-2660	387	38	an	an	DET
ejpam-2660	387	39	∈	∈	PROPN
ejpam-2660	388	1	i	i	PRON
ejpam-2660	388	2	,	,	PUNCT
ejpam-2660	388	3	then	then	ADV
ejpam-2660	388	4	x	x	PART
ejpam-2660	388	5	∈	∈	PROPN
ejpam-2660	388	6	i.	i.	NOUN
ejpam-2660	389	1	so	so	SCONJ
ejpam-2660	389	2	b	b	PROPN
ejpam-2660	389	3	⊆	⊆	NUM
ejpam-2660	389	4	i.	i.	NOUN
ejpam-2660	389	5	definition	definition	NOUN
ejpam-2660	389	6	51	51	NUM
ejpam-2660	389	7	.	.	PUNCT
ejpam-2660	390	1	let	let	VERB
ejpam-2660	390	2	∅	∅	NOUN
ejpam-2660	390	3	6=	6=	ADP
ejpam-2660	390	4	s	s	PROPN
ejpam-2660	390	5	⊆	⊆	NUM
ejpam-2660	390	6	l.	l.	NOUN
ejpam-2660	391	1	then	then	ADV
ejpam-2660	391	2	s	s	VERB
ejpam-2660	391	3	is	be	AUX
ejpam-2660	391	4	called	call	VERB
ejpam-2660	391	5	a	a	DET
ejpam-2660	391	6	subhyperlattice	subhyperlattice	NOUN
ejpam-2660	391	7	if	if	SCONJ
ejpam-2660	391	8	x	x	PROPN
ejpam-2660	391	9	∨	∨	NUM
ejpam-2660	391	10	y	y	PROPN
ejpam-2660	391	11	∈	∈	PROPN
ejpam-2660	391	12	s	s	PROPN
ejpam-2660	391	13	,	,	PUNCT
ejpam-2660	391	14	and	and	CCONJ
ejpam-2660	391	15	x	x	PART
ejpam-2660	391	16	∧	∧	PROPN
ejpam-2660	391	17	y	y	PROPN
ejpam-2660	391	18	⊆	⊆	NUM
ejpam-2660	391	19	s	s	NOUN
ejpam-2660	391	20	,	,	PUNCT
ejpam-2660	391	21	for	for	ADP
ejpam-2660	391	22	all	all	DET
ejpam-2660	391	23	x	x	NOUN
ejpam-2660	391	24	,	,	PUNCT
ejpam-2660	391	25	y	y	PROPN
ejpam-2660	391	26	∈	∈	PROPN
ejpam-2660	391	27	s.	s.	PROPN
ejpam-2660	391	28	example	example	NOUN
ejpam-2660	391	29	52	52	NUM
ejpam-2660	391	30	.	.	PUNCT
ejpam-2660	392	1	consider	consider	VERB
ejpam-2660	392	2	∧-hyperlattice	∧-hyperlattice	NOUN
ejpam-2660	392	3	l	l	NOUN
ejpam-2660	392	4	in	in	ADP
ejpam-2660	392	5	example	example	NOUN
ejpam-2660	392	6	18	18	NUM
ejpam-2660	392	7	.	.	PUNCT
ejpam-2660	393	1	it	it	PRON
ejpam-2660	393	2	is	be	AUX
ejpam-2660	393	3	clear	clear	ADJ
ejpam-2660	393	4	that	that	SCONJ
ejpam-2660	393	5	{	{	PUNCT
ejpam-2660	393	6	0	0	NUM
ejpam-2660	393	7	,	,	PUNCT
ejpam-2660	393	8	a	a	PRON
ejpam-2660	393	9	,	,	PUNCT
ejpam-2660	393	10	1	1	NUM
ejpam-2660	393	11	}	}	PUNCT
ejpam-2660	393	12	is	be	AUX
ejpam-2660	393	13	a	a	DET
ejpam-2660	393	14	∧-subhyperlattice	∧-subhyperlattice	NOUN
ejpam-2660	393	15	of	of	ADP
ejpam-2660	393	16	l	l	NOUN
ejpam-2660	393	17	,	,	PUNCT
ejpam-2660	393	18	but	but	CCONJ
ejpam-2660	393	19	{	{	PUNCT
ejpam-2660	393	20	b	b	NOUN
ejpam-2660	393	21	,	,	PUNCT
ejpam-2660	393	22	1	1	NUM
ejpam-2660	393	23	}	}	PUNCT
ejpam-2660	393	24	is	be	AUX
ejpam-2660	393	25	not	not	PART
ejpam-2660	393	26	a	a	DET
ejpam-2660	393	27	∧-subhyperlattice	∧-subhyperlattice	NOUN
ejpam-2660	393	28	,	,	PUNCT
ejpam-2660	393	29	since	since	SCONJ
ejpam-2660	393	30	b	b	PROPN
ejpam-2660	393	31	∧	∧	PROPN
ejpam-2660	393	32	b	b	PROPN
ejpam-2660	393	33	=	=	SYM
ejpam-2660	393	34	{	{	PUNCT
ejpam-2660	393	35	0	0	NUM
ejpam-2660	393	36	,	,	PUNCT
ejpam-2660	393	37	b	b	NOUN
ejpam-2660	393	38	}	}	PUNCT
ejpam-2660	393	39	and	and	CCONJ
ejpam-2660	393	40	{	{	PUNCT
ejpam-2660	393	41	0	0	NUM
ejpam-2660	393	42	,	,	PUNCT
ejpam-2660	393	43	b	b	NOUN
ejpam-2660	393	44	}	}	PUNCT
ejpam-2660	393	45	*	*	PUNCT
ejpam-2660	393	46	{	{	PUNCT
ejpam-2660	393	47	b	b	NUM
ejpam-2660	393	48	,	,	PUNCT
ejpam-2660	393	49	1	1	NUM
ejpam-2660	393	50	}	}	PUNCT
ejpam-2660	393	51	.	.	PUNCT
ejpam-2660	394	1	also	also	ADV
ejpam-2660	394	2	,	,	PUNCT
ejpam-2660	394	3	both	both	CCONJ
ejpam-2660	394	4	{	{	PUNCT
ejpam-2660	394	5	0	0	NUM
ejpam-2660	394	6	}	}	PUNCT
ejpam-2660	394	7	and	and	CCONJ
ejpam-2660	394	8	{	{	PUNCT
ejpam-2660	394	9	1	1	X
ejpam-2660	394	10	}	}	PUNCT
ejpam-2660	394	11	are	be	AUX
ejpam-2660	394	12	”	"	PUNCT
ejpam-2660	394	13	∧	∧	NOUN
ejpam-2660	394	14	”	"	PUNCT
ejpam-2660	394	15	-subhyperlattices	-subhyperlattice	NOUN
ejpam-2660	394	16	of	of	ADP
ejpam-2660	394	17	l.	l.	PROPN
ejpam-2660	394	18	theorem	theorem	PROPN
ejpam-2660	394	19	53	53	NUM
ejpam-2660	394	20	.	.	PUNCT
ejpam-2660	395	1	let	let	VERB
ejpam-2660	395	2	i	i	PRON
ejpam-2660	395	3	⊆	⊆	NUM
ejpam-2660	395	4	l.	l.	NOUN
ejpam-2660	395	5	if	if	SCONJ
ejpam-2660	395	6	the	the	DET
ejpam-2660	395	7	following	follow	VERB
ejpam-2660	395	8	conditions	condition	NOUN
ejpam-2660	395	9	hold	hold	VERB
ejpam-2660	395	10	,	,	PUNCT
ejpam-2660	395	11	then	then	ADV
ejpam-2660	395	12	i	i	PRON
ejpam-2660	395	13	is	be	AUX
ejpam-2660	395	14	a	a	DET
ejpam-2660	395	15	hyperideal	hyperideal	NOUN
ejpam-2660	395	16	of	of	ADP
ejpam-2660	395	17	l.	l.	PROPN
ejpam-2660	395	18	(	(	PUNCT
ejpam-2660	395	19	i	i	NOUN
ejpam-2660	395	20	)	)	PUNCT
ejpam-2660	396	1	i	i	PRON
ejpam-2660	396	2	is	be	AUX
ejpam-2660	396	3	”	"	PUNCT
ejpam-2660	396	4	∨	∨	NUM
ejpam-2660	396	5	”	"	PUNCT
ejpam-2660	396	6	-closed	-close	VERB
ejpam-2660	396	7	,	,	PUNCT
ejpam-2660	396	8	(	(	PUNCT
ejpam-2660	396	9	ii	ii	NOUN
ejpam-2660	396	10	)	)	PUNCT
ejpam-2660	396	11	if	if	SCONJ
ejpam-2660	396	12	a	a	DET
ejpam-2660	396	13	∈	∈	PROPN
ejpam-2660	396	14	i	i	X
ejpam-2660	396	15	,	,	PUNCT
ejpam-2660	396	16	and	and	CCONJ
ejpam-2660	396	17	x	x	PUNCT
ejpam-2660	396	18	∈	∈	PROPN
ejpam-2660	396	19	l	l	NOUN
ejpam-2660	396	20	,	,	PUNCT
ejpam-2660	396	21	then	then	ADV
ejpam-2660	396	22	a	a	DET
ejpam-2660	396	23	∧	∧	PROPN
ejpam-2660	396	24	x	x	PUNCT
ejpam-2660	396	25	⊆	⊆	NUM
ejpam-2660	396	26	i	i	NOUN
ejpam-2660	396	27	,	,	PUNCT
ejpam-2660	396	28	proof	proof	NOUN
ejpam-2660	396	29	.	.	PUNCT
ejpam-2660	397	1	it	it	PRON
ejpam-2660	397	2	is	be	AUX
ejpam-2660	397	3	enough	enough	ADJ
ejpam-2660	397	4	prove	prove	VERB
ejpam-2660	397	5	that	that	SCONJ
ejpam-2660	397	6	if	if	SCONJ
ejpam-2660	397	7	a	a	DET
ejpam-2660	397	8	∈	∈	NOUN
ejpam-2660	397	9	i	i	PRON
ejpam-2660	397	10	,	,	PUNCT
ejpam-2660	397	11	and	and	CCONJ
ejpam-2660	397	12	x	x	SYM
ejpam-2660	397	13	≤	≤	NOUN
ejpam-2660	397	14	a	a	PRON
ejpam-2660	397	15	,	,	PUNCT
ejpam-2660	397	16	then	then	ADV
ejpam-2660	397	17	x	x	PART
ejpam-2660	397	18	∈	∈	PROPN
ejpam-2660	397	19	i.	i.	NOUN
ejpam-2660	397	20	by	by	ADP
ejpam-2660	397	21	(	(	PUNCT
ejpam-2660	397	22	ii	ii	PROPN
ejpam-2660	397	23	)	)	PUNCT
ejpam-2660	397	24	,	,	PUNCT
ejpam-2660	397	25	a	a	DET
ejpam-2660	397	26	∧	∧	PROPN
ejpam-2660	397	27	x	x	X
ejpam-2660	397	28	⊆	⊆	NUM
ejpam-2660	397	29	i.	i.	NOUN
ejpam-2660	397	30	it	it	PRON
ejpam-2660	397	31	is	be	AUX
ejpam-2660	397	32	clear	clear	ADJ
ejpam-2660	397	33	that	that	SCONJ
ejpam-2660	397	34	x	x	PUNCT
ejpam-2660	397	35	∈	∈	NOUN
ejpam-2660	397	36	x	x	X
ejpam-2660	397	37	∧	∧	NOUN
ejpam-2660	397	38	a	a	NOUN
ejpam-2660	397	39	,	,	PUNCT
ejpam-2660	397	40	and	and	CCONJ
ejpam-2660	397	41	since	since	SCONJ
ejpam-2660	397	42	a	a	DET
ejpam-2660	397	43	∧	∧	PROPN
ejpam-2660	397	44	x	x	PUNCT
ejpam-2660	397	45	⊆	⊆	NUM
ejpam-2660	397	46	i	i	PRON
ejpam-2660	397	47	,	,	PUNCT
ejpam-2660	397	48	x	x	PROPN
ejpam-2660	397	49	∈	∈	PROPN
ejpam-2660	397	50	i.	i.	NOUN
ejpam-2660	397	51	remark	remark	NOUN
ejpam-2660	397	52	54	54	NUM
ejpam-2660	397	53	.	.	PUNCT
ejpam-2660	398	1	the	the	DET
ejpam-2660	398	2	converse	converse	NOUN
ejpam-2660	398	3	of	of	ADP
ejpam-2660	398	4	theorem	theorem	NOUN
ejpam-2660	398	5	53	53	NUM
ejpam-2660	398	6	does	do	AUX
ejpam-2660	398	7	not	not	PART
ejpam-2660	398	8	hold	hold	VERB
ejpam-2660	398	9	.	.	PUNCT
ejpam-2660	399	1	consider	consider	VERB
ejpam-2660	399	2	the	the	DET
ejpam-2660	399	3	”	"	PUNCT
ejpam-2660	399	4	∧	∧	PROPN
ejpam-2660	399	5	”	"	PUNCT
ejpam-2660	399	6	hyperlattice	hyperlattice	NOUN
ejpam-2660	399	7	l	l	NOUN
ejpam-2660	399	8	in	in	ADP
ejpam-2660	399	9	example	example	NOUN
ejpam-2660	399	10	11	11	NUM
ejpam-2660	399	11	.	.	PUNCT
ejpam-2660	400	1	it	it	PRON
ejpam-2660	400	2	is	be	AUX
ejpam-2660	400	3	clear	clear	ADJ
ejpam-2660	400	4	that	that	SCONJ
ejpam-2660	400	5	{	{	PUNCT
ejpam-2660	400	6	a	a	PRON
ejpam-2660	400	7	}	}	PUNCT
ejpam-2660	400	8	is	be	AUX
ejpam-2660	400	9	a	a	DET
ejpam-2660	400	10	hyperideal	hyperideal	NOUN
ejpam-2660	400	11	of	of	ADP
ejpam-2660	400	12	l	l	NOUN
ejpam-2660	400	13	;	;	PUNCT
ejpam-2660	400	14	since	since	SCONJ
ejpam-2660	400	15	a	a	DET
ejpam-2660	400	16	∧	∧	PROPN
ejpam-2660	400	17	a	a	X
ejpam-2660	400	18	=	=	X
ejpam-2660	400	19	{	{	PUNCT
ejpam-2660	400	20	a	a	PROPN
ejpam-2660	400	21	,	,	PUNCT
ejpam-2660	400	22	b	b	NOUN
ejpam-2660	400	23	}	}	PUNCT
ejpam-2660	400	24	,	,	PUNCT
ejpam-2660	400	25	condition	condition	NOUN
ejpam-2660	400	26	(	(	PUNCT
ejpam-2660	400	27	ii	ii	NOUN
ejpam-2660	400	28	)	)	PUNCT
ejpam-2660	400	29	in	in	ADP
ejpam-2660	400	30	theorem	theorem	NOUN
ejpam-2660	400	31	53	53	NUM
ejpam-2660	400	32	does	do	AUX
ejpam-2660	400	33	not	not	PART
ejpam-2660	400	34	hold	hold	VERB
ejpam-2660	400	35	.	.	PUNCT
ejpam-2660	401	1	so	so	ADV
ejpam-2660	401	2	,	,	PUNCT
ejpam-2660	401	3	we	we	PRON
ejpam-2660	401	4	conclude	conclude	VERB
ejpam-2660	401	5	that	that	DET
ejpam-2660	401	6	concept	concept	NOUN
ejpam-2660	401	7	of	of	ADP
ejpam-2660	401	8	hyperideal	hyperideal	NOUN
ejpam-2660	401	9	in	in	ADP
ejpam-2660	401	10	hyperlattice	hyperlattice	NOUN
ejpam-2660	401	11	and	and	CCONJ
ejpam-2660	401	12	concept	concept	NOUN
ejpam-2660	401	13	of	of	ADP
ejpam-2660	401	14	ideal	ideal	NOUN
ejpam-2660	401	15	in	in	ADP
ejpam-2660	401	16	lattice	lattice	NOUN
ejpam-2660	401	17	are	be	AUX
ejpam-2660	401	18	different	different	ADJ
ejpam-2660	401	19	.	.	PUNCT
ejpam-2660	402	1	if	if	SCONJ
ejpam-2660	402	2	i	i	PRON
ejpam-2660	402	3	⊆	⊆	NUM
ejpam-2660	402	4	l	l	NOUN
ejpam-2660	402	5	is	be	AUX
ejpam-2660	402	6	both	both	PRON
ejpam-2660	402	7	a	a	DET
ejpam-2660	402	8	subhyperlattice	subhyperlattice	NOUN
ejpam-2660	402	9	and	and	CCONJ
ejpam-2660	402	10	a	a	DET
ejpam-2660	402	11	hyperideal	hyperideal	NOUN
ejpam-2660	402	12	,	,	PUNCT
ejpam-2660	402	13	then	then	ADV
ejpam-2660	402	14	condition	condition	NOUN
ejpam-2660	402	15	(	(	PUNCT
ejpam-2660	402	16	ii	ii	NOUN
ejpam-2660	402	17	)	)	PUNCT
ejpam-2660	402	18	in	in	ADP
ejpam-2660	402	19	theorem	theorem	NOUN
ejpam-2660	402	20	53	53	NUM
ejpam-2660	402	21	,	,	PUNCT
ejpam-2660	402	22	is	be	AUX
ejpam-2660	402	23	satisfied	satisfied	ADJ
ejpam-2660	402	24	.	.	PUNCT
ejpam-2660	403	1	so	so	ADV
ejpam-2660	403	2	we	we	PRON
ejpam-2660	403	3	state	state	VERB
ejpam-2660	403	4	the	the	DET
ejpam-2660	403	5	following	follow	VERB
ejpam-2660	403	6	theorem	theorem	PROPN
ejpam-2660	403	7	.	.	PUNCT
ejpam-2660	403	8	theorem	theorem	VERB
ejpam-2660	403	9	55	55	NUM
ejpam-2660	403	10	.	.	PUNCT
ejpam-2660	404	1	a	a	DET
ejpam-2660	404	2	subhyperlattice	subhyperlattice	NOUN
ejpam-2660	404	3	i	i	PRON
ejpam-2660	404	4	is	be	AUX
ejpam-2660	404	5	a	a	DET
ejpam-2660	404	6	hyperideal	hyperideal	NOUN
ejpam-2660	404	7	if	if	SCONJ
ejpam-2660	404	8	and	and	CCONJ
ejpam-2660	404	9	only	only	ADV
ejpam-2660	404	10	if	if	SCONJ
ejpam-2660	404	11	a	a	DET
ejpam-2660	404	12	∧	∧	NOUN
ejpam-2660	404	13	x	x	PUNCT
ejpam-2660	404	14	⊆	⊆	NUM
ejpam-2660	404	15	i	i	PRON
ejpam-2660	404	16	,	,	PUNCT
ejpam-2660	404	17	where	where	SCONJ
ejpam-2660	404	18	a	a	DET
ejpam-2660	404	19	∈	∈	PROPN
ejpam-2660	404	20	i	i	X
ejpam-2660	404	21	,	,	PUNCT
ejpam-2660	404	22	and	and	CCONJ
ejpam-2660	404	23	x	x	X
ejpam-2660	404	24	∈	∈	PROPN
ejpam-2660	404	25	l.	l.	NOUN
ejpam-2660	404	26	6	6	NUM
ejpam-2660	404	27	.	.	PUNCT
ejpam-2660	405	1	some	some	DET
ejpam-2660	405	2	results	result	NOUN
ejpam-2660	405	3	in	in	ADP
ejpam-2660	405	4	prime	prime	ADJ
ejpam-2660	405	5	hyperideals	hyperideal	NOUN
ejpam-2660	405	6	of	of	ADP
ejpam-2660	405	7	strong	strong	ADJ
ejpam-2660	405	8	”	"	PUNCT
ejpam-2660	405	9	∧	∧	NOUN
ejpam-2660	405	10	”	"	PUNCT
ejpam-2660	405	11	-hyperlattices	-hyperlattice	NOUN
ejpam-2660	405	12	proposition	proposition	NOUN
ejpam-2660	405	13	56	56	NUM
ejpam-2660	405	14	.	.	PUNCT
ejpam-2660	406	1	let	let	VERB
ejpam-2660	406	2	p	p	PRON
ejpam-2660	406	3	⊆	⊆	NUM
ejpam-2660	406	4	l	l	NOUN
ejpam-2660	406	5	,	,	PUNCT
ejpam-2660	406	6	and	and	CCONJ
ejpam-2660	406	7	p	p	NOUN
ejpam-2660	406	8	is	be	AUX
ejpam-2660	406	9	∨-closed	∨-close	VERB
ejpam-2660	406	10	.	.	PUNCT
ejpam-2660	407	1	then	then	ADV
ejpam-2660	407	2	p	p	PROPN
ejpam-2660	407	3	is	be	AUX
ejpam-2660	407	4	a	a	DET
ejpam-2660	407	5	prime	prime	ADJ
ejpam-2660	407	6	hyperideal	hyperideal	NOUN
ejpam-2660	407	7	if	if	SCONJ
ejpam-2660	407	8	and	and	CCONJ
ejpam-2660	407	9	only	only	ADV
ejpam-2660	407	10	if	if	SCONJ
ejpam-2660	407	11	the	the	DET
ejpam-2660	407	12	following	follow	VERB
ejpam-2660	407	13	statements	statement	NOUN
ejpam-2660	407	14	hold	hold	VERB
ejpam-2660	407	15	.	.	PUNCT
ejpam-2660	408	1	(	(	PUNCT
ejpam-2660	408	2	i	i	NOUN
ejpam-2660	408	3	)	)	PUNCT
ejpam-2660	408	4	if	if	SCONJ
ejpam-2660	408	5	a	a	PRON
ejpam-2660	408	6	,	,	PUNCT
ejpam-2660	408	7	b	b	NOUN
ejpam-2660	408	8	/∈	/∈	PUNCT
ejpam-2660	409	1	p	p	NOUN
ejpam-2660	409	2	,	,	PUNCT
ejpam-2660	410	1	then	then	ADV
ejpam-2660	410	2	a	a	DET
ejpam-2660	410	3	∧	∧	PROPN
ejpam-2660	410	4	b	b	PROPN
ejpam-2660	410	5	⊆	⊆	NUM
ejpam-2660	410	6	l	l	NOUN
ejpam-2660	410	7	\	\	PROPN
ejpam-2660	410	8	p	p	X
ejpam-2660	410	9	,	,	PUNCT
ejpam-2660	410	10	(	(	PUNCT
ejpam-2660	410	11	ii	ii	NOUN
ejpam-2660	410	12	)	)	PUNCT
ejpam-2660	410	13	if	if	SCONJ
ejpam-2660	410	14	a	a	DET
ejpam-2660	410	15	∈	∈	PROPN
ejpam-2660	410	16	p	p	NOUN
ejpam-2660	410	17	,	,	PUNCT
ejpam-2660	410	18	and	and	CCONJ
ejpam-2660	410	19	a	a	DET
ejpam-2660	410	20	∈	∈	PROPN
ejpam-2660	410	21	a	a	DET
ejpam-2660	410	22	∧	∧	PROPN
ejpam-2660	410	23	x	x	NOUN
ejpam-2660	410	24	,	,	PUNCT
ejpam-2660	410	25	then	then	ADV
ejpam-2660	410	26	x	x	SYM
ejpam-2660	410	27	∈	∈	PROPN
ejpam-2660	410	28	p	p	X
ejpam-2660	410	29	.	.	PUNCT
ejpam-2660	410	30	theorem	theorem	VERB
ejpam-2660	410	31	57	57	NUM
ejpam-2660	410	32	.	.	PUNCT
ejpam-2660	411	1	if	if	SCONJ
ejpam-2660	411	2	p	p	NOUN
ejpam-2660	411	3	is	be	AUX
ejpam-2660	411	4	a	a	DET
ejpam-2660	411	5	prime	prime	ADJ
ejpam-2660	411	6	hyperideal	hyperideal	NOUN
ejpam-2660	411	7	of	of	ADP
ejpam-2660	411	8	l	l	NOUN
ejpam-2660	411	9	,	,	PUNCT
ejpam-2660	411	10	then	then	ADV
ejpam-2660	411	11	l	l	NOUN
ejpam-2660	411	12	\	\	PROPN
ejpam-2660	412	1	p	p	NOUN
ejpam-2660	412	2	is	be	AUX
ejpam-2660	412	3	a	a	DET
ejpam-2660	412	4	hyperfilter	hyperfilter	NOUN
ejpam-2660	412	5	of	of	ADP
ejpam-2660	412	6	l.	l.	PROPN
ejpam-2660	412	7	proof	proof	PROPN
ejpam-2660	412	8	.	.	PUNCT
ejpam-2660	413	1	let	let	VERB
ejpam-2660	413	2	x	x	PRON
ejpam-2660	413	3	,	,	PUNCT
ejpam-2660	413	4	y	y	PROPN
ejpam-2660	413	5	∈	∈	PROPN
ejpam-2660	413	6	l	l	NOUN
ejpam-2660	413	7	\p	\p	ADV
ejpam-2660	413	8	.	.	PUNCT
ejpam-2660	414	1	then	then	ADV
ejpam-2660	414	2	x	x	PRON
ejpam-2660	414	3	,	,	PUNCT
ejpam-2660	414	4	y	y	PROPN
ejpam-2660	414	5	/∈	/∈	PUNCT
ejpam-2660	415	1	p	p	X
ejpam-2660	415	2	.	.	PUNCT
ejpam-2660	416	1	since	since	SCONJ
ejpam-2660	416	2	p	p	NOUN
ejpam-2660	416	3	is	be	AUX
ejpam-2660	416	4	a	a	DET
ejpam-2660	416	5	prime	prime	ADJ
ejpam-2660	416	6	hyperideal	hyperideal	NOUN
ejpam-2660	416	7	,	,	PUNCT
ejpam-2660	416	8	(	(	PUNCT
ejpam-2660	416	9	x∧	x∧	PROPN
ejpam-2660	416	10	y)∩p	y)∩p	NOUN
ejpam-2660	416	11	=	=	SYM
ejpam-2660	416	12	∅	∅	NOUN
ejpam-2660	416	13	,	,	PUNCT
ejpam-2660	416	14	so	so	CCONJ
ejpam-2660	416	15	(	(	PUNCT
ejpam-2660	416	16	x	x	PUNCT
ejpam-2660	416	17	∧	∧	PROPN
ejpam-2660	416	18	y	y	PROPN
ejpam-2660	416	19	)	)	PUNCT
ejpam-2660	416	20	⊆	⊆	NUM
ejpam-2660	416	21	l	l	NOUN
ejpam-2660	416	22	\	\	PUNCT
ejpam-2660	417	1	p	p	NOUN
ejpam-2660	417	2	.	.	PUNCT
ejpam-2660	418	1	let	let	VERB
ejpam-2660	418	2	a	a	DET
ejpam-2660	418	3	∈	∈	NOUN
ejpam-2660	418	4	l	l	NOUN
ejpam-2660	418	5	\	\	PROPN
ejpam-2660	418	6	p	p	NOUN
ejpam-2660	418	7	,	,	PUNCT
ejpam-2660	418	8	and	and	CCONJ
ejpam-2660	418	9	x	x	PUNCT
ejpam-2660	418	10	∈	∈	PROPN
ejpam-2660	418	11	l	l	NOUN
ejpam-2660	418	12	,	,	PUNCT
ejpam-2660	418	13	such	such	ADJ
ejpam-2660	418	14	that	that	SCONJ
ejpam-2660	418	15	a	a	DET
ejpam-2660	418	16	≤	≤	NOUN
ejpam-2660	418	17	x.	x.	NOUN
ejpam-2660	419	1	so	so	ADV
ejpam-2660	419	2	we	we	PRON
ejpam-2660	419	3	have	have	VERB
ejpam-2660	419	4	a	a	DET
ejpam-2660	419	5	/∈	/∈	NOUN
ejpam-2660	419	6	p	p	NOUN
ejpam-2660	419	7	,	,	PUNCT
ejpam-2660	419	8	and	and	CCONJ
ejpam-2660	419	9	since	since	SCONJ
ejpam-2660	419	10	p	p	NOUN
ejpam-2660	419	11	is	be	AUX
ejpam-2660	419	12	a	a	DET
ejpam-2660	419	13	hyperideal	hyperideal	NOUN
ejpam-2660	419	14	,	,	PUNCT
ejpam-2660	419	15	x	x	PUNCT
ejpam-2660	419	16	/∈	/∈	PUNCT
ejpam-2660	420	1	p	p	NOUN
ejpam-2660	420	2	,	,	PUNCT
ejpam-2660	420	3	it	it	PRON
ejpam-2660	420	4	implies	imply	VERB
ejpam-2660	420	5	that	that	SCONJ
ejpam-2660	420	6	x	x	PUNCT
ejpam-2660	420	7	∈	∈	PROPN
ejpam-2660	421	1	l	l	NOUN
ejpam-2660	421	2	\	\	PROPN
ejpam-2660	421	3	p	p	NOUN
ejpam-2660	421	4	.	.	PUNCT
ejpam-2660	422	1	in	in	ADP
ejpam-2660	422	2	theorem	theorem	NOUN
ejpam-2660	422	3	57	57	NUM
ejpam-2660	422	4	,	,	PUNCT
ejpam-2660	422	5	p	p	PRON
ejpam-2660	422	6	must	must	AUX
ejpam-2660	422	7	be	be	AUX
ejpam-2660	422	8	prime	prime	ADJ
ejpam-2660	422	9	and	and	CCONJ
ejpam-2660	422	10	the	the	DET
ejpam-2660	422	11	converse	converse	NOUN
ejpam-2660	422	12	of	of	ADP
ejpam-2660	422	13	it	it	PRON
ejpam-2660	422	14	is	be	AUX
ejpam-2660	422	15	not	not	PART
ejpam-2660	422	16	true	true	ADJ
ejpam-2660	422	17	.	.	PUNCT
ejpam-2660	423	1	m.	m.	NOUN
ejpam-2660	423	2	amiri	amiri	PROPN
ejpam-2660	423	3	bideshki	bideshki	PROPN
ejpam-2660	423	4	,	,	PUNCT
ejpam-2660	423	5	r.	r.	PROPN
ejpam-2660	423	6	ameri	ameri	PROPN
ejpam-2660	423	7	,	,	PUNCT
ejpam-2660	423	8	a.	a.	PROPN
ejpam-2660	423	9	borumand	borumand	PROPN
ejpam-2660	423	10	saeid	saeid	PROPN
ejpam-2660	423	11	/	/	SYM
ejpam-2660	423	12	eur	eur	PROPN
ejpam-2660	423	13	.	.	PUNCT
ejpam-2660	424	1	j.	j.	PROPN
ejpam-2660	424	2	pure	pure	PROPN
ejpam-2660	424	3	appl	appl	PROPN
ejpam-2660	424	4	.	.	PROPN
ejpam-2660	424	5	math	math	PROPN
ejpam-2660	424	6	,	,	PUNCT
ejpam-2660	424	7	11	11	NUM
ejpam-2660	424	8	(	(	PUNCT
ejpam-2660	424	9	1	1	NUM
ejpam-2660	424	10	)	)	PUNCT
ejpam-2660	424	11	(	(	PUNCT
ejpam-2660	424	12	2018	2018	NUM
ejpam-2660	424	13	)	)	PUNCT
ejpam-2660	424	14	,	,	PUNCT
ejpam-2660	424	15	169	169	NUM
ejpam-2660	424	16	-	-	SYM
ejpam-2660	424	17	188	188	NUM
ejpam-2660	424	18	182	182	NUM
ejpam-2660	424	19	example	example	NOUN
ejpam-2660	424	20	58	58	NUM
ejpam-2660	424	21	.	.	PUNCT
ejpam-2660	425	1	consider	consider	VERB
ejpam-2660	425	2	”	"	PUNCT
ejpam-2660	425	3	∧	∧	NOUN
ejpam-2660	425	4	”	"	PUNCT
ejpam-2660	425	5	-hyperlattice	-hyperlattice	NOUN
ejpam-2660	425	6	l	l	NOUN
ejpam-2660	425	7	in	in	ADP
ejpam-2660	425	8	example	example	NOUN
ejpam-2660	425	9	18	18	NUM
ejpam-2660	425	10	.	.	PUNCT
ejpam-2660	426	1	then	then	ADV
ejpam-2660	426	2	{	{	PUNCT
ejpam-2660	426	3	0	0	X
ejpam-2660	426	4	}	}	PUNCT
ejpam-2660	426	5	is	be	AUX
ejpam-2660	426	6	a	a	DET
ejpam-2660	426	7	hyperideal	hyperideal	NOUN
ejpam-2660	426	8	of	of	ADP
ejpam-2660	426	9	l.	l.	PROPN
ejpam-2660	426	10	l	l	PROPN
ejpam-2660	426	11	\	\	PROPN
ejpam-2660	426	12	{	{	PUNCT
ejpam-2660	426	13	0	0	NUM
ejpam-2660	426	14	}	}	PUNCT
ejpam-2660	426	15	=	=	PRON
ejpam-2660	426	16	{	{	PUNCT
ejpam-2660	426	17	a	a	DET
ejpam-2660	426	18	,	,	PUNCT
ejpam-2660	426	19	b	b	NOUN
ejpam-2660	426	20	,	,	PUNCT
ejpam-2660	426	21	1	1	NUM
ejpam-2660	426	22	}	}	PUNCT
ejpam-2660	426	23	.	.	PUNCT
ejpam-2660	427	1	since	since	SCONJ
ejpam-2660	427	2	a	a	DET
ejpam-2660	427	3	∧	∧	PROPN
ejpam-2660	427	4	b	b	NOUN
ejpam-2660	427	5	=	=	SYM
ejpam-2660	427	6	{	{	PUNCT
ejpam-2660	427	7	0	0	NUM
ejpam-2660	427	8	}	}	PUNCT
ejpam-2660	427	9	and	and	CCONJ
ejpam-2660	427	10	0	0	NUM
ejpam-2660	427	11	/∈	/∈	INTJ
ejpam-2660	427	12	{	{	PUNCT
ejpam-2660	427	13	a	a	DET
ejpam-2660	427	14	,	,	PUNCT
ejpam-2660	427	15	b	b	NOUN
ejpam-2660	427	16	,	,	PUNCT
ejpam-2660	427	17	1	1	NUM
ejpam-2660	427	18	}	}	PUNCT
ejpam-2660	427	19	,	,	PUNCT
ejpam-2660	427	20	{	{	PUNCT
ejpam-2660	427	21	a	a	DET
ejpam-2660	427	22	,	,	PUNCT
ejpam-2660	427	23	b	b	NOUN
ejpam-2660	427	24	,	,	PUNCT
ejpam-2660	427	25	1	1	NUM
ejpam-2660	427	26	}	}	PUNCT
ejpam-2660	427	27	is	be	AUX
ejpam-2660	427	28	not	not	PART
ejpam-2660	427	29	a	a	DET
ejpam-2660	427	30	hyperfilter	hyperfilter	NOUN
ejpam-2660	427	31	.	.	PUNCT
ejpam-2660	428	1	{	{	PUNCT
ejpam-2660	428	2	b	b	X
ejpam-2660	428	3	,	,	PUNCT
ejpam-2660	428	4	1	1	NUM
ejpam-2660	428	5	}	}	PUNCT
ejpam-2660	428	6	is	be	AUX
ejpam-2660	428	7	a	a	DET
ejpam-2660	428	8	hyperfilter	hyperfilter	NOUN
ejpam-2660	428	9	,	,	PUNCT
ejpam-2660	428	10	but	but	CCONJ
ejpam-2660	428	11	l\{0	l\{0	PROPN
ejpam-2660	428	12	,	,	PUNCT
ejpam-2660	428	13	a	a	PRON
ejpam-2660	428	14	}	}	PUNCT
ejpam-2660	428	15	is	be	AUX
ejpam-2660	428	16	not	not	PART
ejpam-2660	428	17	a	a	DET
ejpam-2660	428	18	prime	prime	ADJ
ejpam-2660	428	19	hyperideal	hyperideal	NOUN
ejpam-2660	428	20	.	.	PUNCT
ejpam-2660	429	1	we	we	PRON
ejpam-2660	429	2	have	have	VERB
ejpam-2660	429	3	(	(	PUNCT
ejpam-2660	429	4	b∧b)∩{0	b∧b)∩{0	PROPN
ejpam-2660	429	5	,	,	PUNCT
ejpam-2660	429	6	a	a	DET
ejpam-2660	429	7	}	}	PUNCT
ejpam-2660	429	8	6=	6=	NOUN
ejpam-2660	429	9	∅	∅	NOUN
ejpam-2660	429	10	,	,	PUNCT
ejpam-2660	429	11	but	but	CCONJ
ejpam-2660	429	12	b	b	X
ejpam-2660	429	13	/∈	/∈	PUNCT
ejpam-2660	429	14	{	{	PUNCT
ejpam-2660	429	15	0	0	NUM
ejpam-2660	429	16	,	,	PUNCT
ejpam-2660	429	17	a	a	PRON
ejpam-2660	429	18	}	}	PUNCT
ejpam-2660	429	19	.	.	PUNCT
ejpam-2660	430	1	theorem	theorem	VERB
ejpam-2660	430	2	59	59	NUM
ejpam-2660	430	3	.	.	PUNCT
ejpam-2660	431	1	p	p	NOUN
ejpam-2660	431	2	is	be	AUX
ejpam-2660	431	3	a	a	DET
ejpam-2660	431	4	prime	prime	ADJ
ejpam-2660	431	5	hyperideal	hyperideal	NOUN
ejpam-2660	431	6	of	of	ADP
ejpam-2660	431	7	l	l	NOUN
ejpam-2660	431	8	if	if	SCONJ
ejpam-2660	432	1	and	and	CCONJ
ejpam-2660	432	2	only	only	ADV
ejpam-2660	432	3	if	if	SCONJ
ejpam-2660	432	4	l	l	NOUN
ejpam-2660	432	5	\	\	PROPN
ejpam-2660	433	1	p	p	NOUN
ejpam-2660	433	2	is	be	AUX
ejpam-2660	433	3	a	a	DET
ejpam-2660	433	4	prime	prime	ADJ
ejpam-2660	433	5	hyperfilter	hyperfilter	NOUN
ejpam-2660	433	6	of	of	ADP
ejpam-2660	433	7	l.	l.	PROPN
ejpam-2660	433	8	proof	proof	PROPN
ejpam-2660	433	9	.	.	PUNCT
ejpam-2660	434	1	let	let	VERB
ejpam-2660	434	2	p	p	PRON
ejpam-2660	434	3	be	be	AUX
ejpam-2660	434	4	a	a	DET
ejpam-2660	434	5	prime	prime	ADJ
ejpam-2660	434	6	hyperideal	hyperideal	NOUN
ejpam-2660	434	7	of	of	ADP
ejpam-2660	434	8	l.	l.	NOUN
ejpam-2660	434	9	by	by	ADP
ejpam-2660	434	10	theorem	theorem	NOUN
ejpam-2660	434	11	57	57	NUM
ejpam-2660	434	12	,	,	PUNCT
ejpam-2660	434	13	l	l	NOUN
ejpam-2660	434	14	\	\	PROPN
ejpam-2660	435	1	p	p	NOUN
ejpam-2660	435	2	is	be	AUX
ejpam-2660	435	3	a	a	DET
ejpam-2660	435	4	hyperfilter	hyperfilter	NOUN
ejpam-2660	435	5	of	of	ADP
ejpam-2660	435	6	l.	l.	PROPN
ejpam-2660	435	7	now	now	ADV
ejpam-2660	435	8	,	,	PUNCT
ejpam-2660	435	9	assume	assume	VERB
ejpam-2660	435	10	x	x	X
ejpam-2660	435	11	,	,	PUNCT
ejpam-2660	435	12	y	y	PROPN
ejpam-2660	435	13	∈	∈	PROPN
ejpam-2660	435	14	l	l	NOUN
ejpam-2660	435	15	,	,	PUNCT
ejpam-2660	435	16	x	x	PROPN
ejpam-2660	435	17	∨	∨	NUM
ejpam-2660	435	18	y	y	PROPN
ejpam-2660	435	19	∈	∈	PROPN
ejpam-2660	435	20	l	l	NOUN
ejpam-2660	435	21	\	\	PROPN
ejpam-2660	435	22	p	p	NOUN
ejpam-2660	435	23	,	,	PUNCT
ejpam-2660	435	24	but	but	CCONJ
ejpam-2660	435	25	x	x	X
ejpam-2660	435	26	,	,	PUNCT
ejpam-2660	435	27	y	y	PROPN
ejpam-2660	435	28	/∈	/∈	PUNCT
ejpam-2660	436	1	l	l	NOUN
ejpam-2660	436	2	\	\	PROPN
ejpam-2660	437	1	p	p	NOUN
ejpam-2660	437	2	.	.	PUNCT
ejpam-2660	438	1	so	so	ADV
ejpam-2660	438	2	,	,	PUNCT
ejpam-2660	438	3	we	we	PRON
ejpam-2660	438	4	have	have	VERB
ejpam-2660	438	5	x	x	NOUN
ejpam-2660	438	6	∨	∨	NUM
ejpam-2660	438	7	y	y	PROPN
ejpam-2660	438	8	/∈	/∈	PROPN
ejpam-2660	439	1	p	p	NOUN
ejpam-2660	439	2	,	,	PUNCT
ejpam-2660	439	3	but	but	CCONJ
ejpam-2660	439	4	x	x	X
ejpam-2660	439	5	,	,	PUNCT
ejpam-2660	439	6	y	y	PROPN
ejpam-2660	439	7	∈	∈	PROPN
ejpam-2660	439	8	p	p	X
ejpam-2660	439	9	;	;	PUNCT
ejpam-2660	439	10	since	since	SCONJ
ejpam-2660	439	11	p	p	NOUN
ejpam-2660	439	12	is	be	AUX
ejpam-2660	439	13	a	a	DET
ejpam-2660	439	14	hyperideal	hyperideal	NOUN
ejpam-2660	439	15	,	,	PUNCT
ejpam-2660	439	16	x	x	PROPN
ejpam-2660	439	17	∨	∨	NUM
ejpam-2660	439	18	y	y	PROPN
ejpam-2660	439	19	∈	∈	PROPN
ejpam-2660	439	20	p	p	PROPN
ejpam-2660	439	21	,	,	PUNCT
ejpam-2660	439	22	which	which	PRON
ejpam-2660	439	23	is	be	AUX
ejpam-2660	439	24	a	a	DET
ejpam-2660	439	25	contradiction	contradiction	NOUN
ejpam-2660	439	26	.	.	PUNCT
ejpam-2660	440	1	conversely	conversely	ADV
ejpam-2660	440	2	,	,	PUNCT
ejpam-2660	440	3	let	let	VERB
ejpam-2660	440	4	l	l	NOUN
ejpam-2660	440	5	\	\	PUNCT
ejpam-2660	441	1	p	p	NOUN
ejpam-2660	441	2	is	be	AUX
ejpam-2660	441	3	a	a	DET
ejpam-2660	441	4	prime	prime	ADJ
ejpam-2660	441	5	hyperfilter	hyperfilter	NOUN
ejpam-2660	441	6	of	of	ADP
ejpam-2660	441	7	l.	l.	PROPN
ejpam-2660	441	8	we	we	PRON
ejpam-2660	441	9	assume	assume	VERB
ejpam-2660	441	10	x	x	PRON
ejpam-2660	441	11	,	,	PUNCT
ejpam-2660	441	12	y	y	PROPN
ejpam-2660	441	13	∈	∈	PROPN
ejpam-2660	441	14	p	p	PROPN
ejpam-2660	441	15	.	.	PUNCT
ejpam-2660	442	1	so	so	ADV
ejpam-2660	442	2	x	x	X
ejpam-2660	442	3	,	,	PUNCT
ejpam-2660	442	4	y	y	PROPN
ejpam-2660	442	5	/∈	/∈	PUNCT
ejpam-2660	443	1	l	l	NOUN
ejpam-2660	443	2	\	\	PROPN
ejpam-2660	444	1	p	p	X
ejpam-2660	444	2	,	,	PUNCT
ejpam-2660	444	3	since	since	SCONJ
ejpam-2660	444	4	l	l	NOUN
ejpam-2660	444	5	\	\	PROPN
ejpam-2660	444	6	p	p	NOUN
ejpam-2660	444	7	is	be	AUX
ejpam-2660	444	8	a	a	DET
ejpam-2660	444	9	prime	prime	ADJ
ejpam-2660	444	10	hyperfilter	hyperfilter	NOUN
ejpam-2660	444	11	of	of	ADP
ejpam-2660	444	12	l	l	NOUN
ejpam-2660	444	13	,	,	PUNCT
ejpam-2660	444	14	x	x	PROPN
ejpam-2660	444	15	∨	∨	NUM
ejpam-2660	444	16	y	y	PROPN
ejpam-2660	444	17	/∈	/∈	PUNCT
ejpam-2660	445	1	l	l	NOUN
ejpam-2660	445	2	\	\	PROPN
ejpam-2660	446	1	p	p	X
ejpam-2660	446	2	,	,	PUNCT
ejpam-2660	446	3	and	and	CCONJ
ejpam-2660	446	4	it	it	PRON
ejpam-2660	446	5	implies	imply	VERB
ejpam-2660	446	6	that	that	SCONJ
ejpam-2660	446	7	x	x	PROPN
ejpam-2660	446	8	∨	∨	NUM
ejpam-2660	446	9	y	y	PROPN
ejpam-2660	446	10	∈	∈	PROPN
ejpam-2660	446	11	p	p	PROPN
ejpam-2660	446	12	.	.	PUNCT
ejpam-2660	447	1	assume	assume	VERB
ejpam-2660	447	2	a	a	DET
ejpam-2660	447	3	∈	∈	PROPN
ejpam-2660	447	4	p	p	NOUN
ejpam-2660	447	5	,	,	PUNCT
ejpam-2660	447	6	x	x	PUNCT
ejpam-2660	447	7	∈	∈	PROPN
ejpam-2660	447	8	l	l	NOUN
ejpam-2660	447	9	,	,	PUNCT
ejpam-2660	447	10	and	and	CCONJ
ejpam-2660	447	11	x	x	SYM
ejpam-2660	447	12	≤	≤	NUM
ejpam-2660	447	13	a.	a.	NOUN
ejpam-2660	448	1	if	if	SCONJ
ejpam-2660	448	2	x	x	PROPN
ejpam-2660	448	3	/∈	/∈	PROPN
ejpam-2660	449	1	p	p	NOUN
ejpam-2660	449	2	,	,	PUNCT
ejpam-2660	449	3	then	then	ADV
ejpam-2660	449	4	x	x	SYM
ejpam-2660	449	5	∈	∈	PROPN
ejpam-2660	449	6	l\p	l\p	NOUN
ejpam-2660	449	7	,	,	PUNCT
ejpam-2660	449	8	and	and	CCONJ
ejpam-2660	449	9	since	since	SCONJ
ejpam-2660	449	10	l\p	l\p	NUM
ejpam-2660	449	11	is	be	AUX
ejpam-2660	449	12	a	a	DET
ejpam-2660	449	13	hyperfilter	hyperfilter	NOUN
ejpam-2660	449	14	,	,	PUNCT
ejpam-2660	449	15	a	a	DET
ejpam-2660	449	16	∈	∈	PROPN
ejpam-2660	449	17	l	l	NOUN
ejpam-2660	449	18	\p	\p	ADV
ejpam-2660	449	19	,	,	PUNCT
ejpam-2660	449	20	which	which	PRON
ejpam-2660	449	21	is	be	AUX
ejpam-2660	449	22	a	a	DET
ejpam-2660	449	23	contradiction	contradiction	NOUN
ejpam-2660	449	24	.	.	PUNCT
ejpam-2660	450	1	therefore	therefore	ADV
ejpam-2660	450	2	p	p	PROPN
ejpam-2660	450	3	is	be	AUX
ejpam-2660	450	4	a	a	DET
ejpam-2660	450	5	hyperideal	hyperideal	NOUN
ejpam-2660	450	6	of	of	ADP
ejpam-2660	450	7	l.	l.	PROPN
ejpam-2660	450	8	let	let	VERB
ejpam-2660	450	9	(	(	PUNCT
ejpam-2660	450	10	x∧	x∧	PROPN
ejpam-2660	450	11	y)∩p	y)∩p	PROPN
ejpam-2660	450	12	6=	6=	NOUN
ejpam-2660	450	13	∅	∅	NOUN
ejpam-2660	450	14	,	,	PUNCT
ejpam-2660	450	15	but	but	CCONJ
ejpam-2660	450	16	x	x	X
ejpam-2660	450	17	,	,	PUNCT
ejpam-2660	450	18	y	y	PROPN
ejpam-2660	450	19	/∈	/∈	PUNCT
ejpam-2660	451	1	p	p	X
ejpam-2660	451	2	.	.	PUNCT
ejpam-2660	452	1	so	so	ADV
ejpam-2660	452	2	x	x	X
ejpam-2660	452	3	,	,	PUNCT
ejpam-2660	452	4	y	y	PROPN
ejpam-2660	452	5	∈	∈	PROPN
ejpam-2660	452	6	l	l	NOUN
ejpam-2660	452	7	\	\	PROPN
ejpam-2660	452	8	p	p	X
ejpam-2660	452	9	;	;	PUNCT
ejpam-2660	452	10	since	since	SCONJ
ejpam-2660	452	11	l	l	NOUN
ejpam-2660	452	12	\	\	PROPN
ejpam-2660	452	13	p	p	NOUN
ejpam-2660	452	14	is	be	AUX
ejpam-2660	452	15	a	a	DET
ejpam-2660	452	16	hyperfilter	hyperfilter	NOUN
ejpam-2660	452	17	,	,	PUNCT
ejpam-2660	452	18	x	x	PUNCT
ejpam-2660	452	19	∧	∧	NOUN
ejpam-2660	452	20	y	y	PROPN
ejpam-2660	452	21	⊆	⊆	NUM
ejpam-2660	452	22	l	l	NOUN
ejpam-2660	452	23	\	\	PROPN
ejpam-2660	452	24	p	p	NOUN
ejpam-2660	452	25	,	,	PUNCT
ejpam-2660	452	26	and	and	CCONJ
ejpam-2660	452	27	it	it	PRON
ejpam-2660	452	28	implies	imply	VERB
ejpam-2660	452	29	that	that	SCONJ
ejpam-2660	452	30	(	(	PUNCT
ejpam-2660	452	31	x	x	PUNCT
ejpam-2660	452	32	∧	∧	PROPN
ejpam-2660	452	33	y	y	PROPN
ejpam-2660	452	34	)	)	PUNCT
ejpam-2660	452	35	∩	∩	NOUN
ejpam-2660	452	36	p	p	NOUN
ejpam-2660	452	37	=	=	NOUN
ejpam-2660	452	38	∅	∅	NOUN
ejpam-2660	452	39	,	,	PUNCT
ejpam-2660	452	40	which	which	PRON
ejpam-2660	452	41	is	be	AUX
ejpam-2660	452	42	a	a	DET
ejpam-2660	452	43	contradiction	contradiction	NOUN
ejpam-2660	452	44	.	.	PUNCT
ejpam-2660	453	1	thus	thus	ADV
ejpam-2660	453	2	p	p	X
ejpam-2660	453	3	is	be	AUX
ejpam-2660	453	4	a	a	DET
ejpam-2660	453	5	prime	prime	ADJ
ejpam-2660	453	6	hyperfilter	hyperfilter	NOUN
ejpam-2660	453	7	.	.	PUNCT
ejpam-2660	454	1	theorem	theorem	ADJ
ejpam-2660	454	2	60	60	NUM
ejpam-2660	454	3	.	.	PUNCT
ejpam-2660	455	1	let	let	VERB
ejpam-2660	455	2	l	l	NOUN
ejpam-2660	455	3	be	be	AUX
ejpam-2660	455	4	dual	dual	ADV
ejpam-2660	455	5	distributive	distributive	ADJ
ejpam-2660	455	6	,	,	PUNCT
ejpam-2660	455	7	a	a	DET
ejpam-2660	455	8	,	,	PUNCT
ejpam-2660	455	9	b	b	NOUN
ejpam-2660	455	10	⊆	⊆	NUM
ejpam-2660	455	11	l	l	NOUN
ejpam-2660	455	12	,	,	PUNCT
ejpam-2660	455	13	and	and	CCONJ
ejpam-2660	455	14	p	p	NOUN
ejpam-2660	455	15	is	be	AUX
ejpam-2660	455	16	a	a	DET
ejpam-2660	455	17	prime	prime	ADJ
ejpam-2660	455	18	hyperideal	hyperideal	NOUN
ejpam-2660	455	19	of	of	ADP
ejpam-2660	455	20	l.	l.	PROPN
ejpam-2660	455	21	then	then	ADV
ejpam-2660	455	22	the	the	DET
ejpam-2660	455	23	following	follow	VERB
ejpam-2660	455	24	conditions	condition	NOUN
ejpam-2660	455	25	hold	hold	VERB
ejpam-2660	455	26	.	.	PUNCT
ejpam-2660	456	1	(	(	PUNCT
ejpam-2660	456	2	i	i	NOUN
ejpam-2660	456	3	)	)	PUNCT
ejpam-2660	456	4	if	if	SCONJ
ejpam-2660	456	5	a	a	DET
ejpam-2660	456	6	∧b	∧b	NOUN
ejpam-2660	456	7	⊆	⊆	NUM
ejpam-2660	456	8	p	p	NOUN
ejpam-2660	456	9	,	,	PUNCT
ejpam-2660	456	10	then	then	ADV
ejpam-2660	456	11	a	a	DET
ejpam-2660	456	12	⊆	⊆	NUM
ejpam-2660	456	13	p	p	NOUN
ejpam-2660	456	14	or	or	CCONJ
ejpam-2660	456	15	b	b	NOUN
ejpam-2660	456	16	⊆	⊆	NUM
ejpam-2660	456	17	p	p	NOUN
ejpam-2660	456	18	.	.	PUNCT
ejpam-2660	457	1	(	(	PUNCT
ejpam-2660	457	2	ii	ii	NOUN
ejpam-2660	457	3	)	)	PUNCT
ejpam-2660	457	4	if	if	SCONJ
ejpam-2660	457	5	i(a	i(a	NUM
ejpam-2660	457	6	)	)	PUNCT
ejpam-2660	457	7	∧	∧	PROPN
ejpam-2660	457	8	i(b	i(b	NOUN
ejpam-2660	457	9	)	)	PUNCT
ejpam-2660	458	1	⊆	⊆	NUM
ejpam-2660	458	2	p	p	NOUN
ejpam-2660	458	3	,	,	PUNCT
ejpam-2660	458	4	then	then	ADV
ejpam-2660	458	5	a	a	DET
ejpam-2660	458	6	∈	∈	PROPN
ejpam-2660	458	7	p	p	NOUN
ejpam-2660	458	8	or	or	CCONJ
ejpam-2660	458	9	b	b	NOUN
ejpam-2660	458	10	∈	∈	PROPN
ejpam-2660	458	11	p.	p.	NOUN
ejpam-2660	458	12	proof	proof	NOUN
ejpam-2660	458	13	.	.	PUNCT
ejpam-2660	459	1	(	(	PUNCT
ejpam-2660	459	2	i	i	NOUN
ejpam-2660	459	3	):	):	PUNCT
ejpam-2660	459	4	let	let	VERB
ejpam-2660	459	5	a	a	DET
ejpam-2660	459	6	*	*	PUNCT
ejpam-2660	459	7	p	p	NOUN
ejpam-2660	459	8	and	and	CCONJ
ejpam-2660	459	9	b	b	NOUN
ejpam-2660	459	10	*	*	PUNCT
ejpam-2660	459	11	p	p	NOUN
ejpam-2660	459	12	.	.	PUNCT
ejpam-2660	460	1	so	so	ADV
ejpam-2660	460	2	there	there	PRON
ejpam-2660	460	3	exist	exist	VERB
ejpam-2660	460	4	a	a	DET
ejpam-2660	460	5	∈	∈	NOUN
ejpam-2660	460	6	a	a	DET
ejpam-2660	460	7	\	\	NOUN
ejpam-2660	460	8	p	p	NOUN
ejpam-2660	460	9	and	and	CCONJ
ejpam-2660	460	10	b	b	PROPN
ejpam-2660	460	11	∈	∈	PROPN
ejpam-2660	460	12	b	b	X
ejpam-2660	460	13	\	\	PROPN
ejpam-2660	460	14	p	p	NOUN
ejpam-2660	460	15	;	;	PUNCT
ejpam-2660	460	16	we	we	PRON
ejpam-2660	460	17	have	have	VERB
ejpam-2660	460	18	a∧	a∧	PROPN
ejpam-2660	460	19	b	b	PROPN
ejpam-2660	460	20	⊆	⊆	NUM
ejpam-2660	460	21	a∧b	a∧b	NOUN
ejpam-2660	460	22	⊆	⊆	NUM
ejpam-2660	460	23	p	p	NOUN
ejpam-2660	460	24	,	,	PUNCT
ejpam-2660	460	25	so	so	ADV
ejpam-2660	460	26	a∧	a∧	NOUN
ejpam-2660	460	27	b	b	PROPN
ejpam-2660	460	28	⊆	⊆	NUM
ejpam-2660	460	29	p	p	NOUN
ejpam-2660	460	30	,	,	PUNCT
ejpam-2660	460	31	and	and	CCONJ
ejpam-2660	460	32	since	since	SCONJ
ejpam-2660	460	33	p	p	NOUN
ejpam-2660	460	34	is	be	AUX
ejpam-2660	460	35	a	a	DET
ejpam-2660	460	36	prime	prime	ADJ
ejpam-2660	460	37	hyperideal	hyperideal	NOUN
ejpam-2660	460	38	,	,	PUNCT
ejpam-2660	460	39	a	a	DET
ejpam-2660	460	40	∈	∈	PROPN
ejpam-2660	460	41	p	p	NOUN
ejpam-2660	460	42	or	or	CCONJ
ejpam-2660	460	43	b	b	NOUN
ejpam-2660	460	44	∈	∈	PROPN
ejpam-2660	460	45	p	p	NOUN
ejpam-2660	460	46	,	,	PUNCT
ejpam-2660	460	47	which	which	PRON
ejpam-2660	460	48	is	be	AUX
ejpam-2660	460	49	a	a	DET
ejpam-2660	460	50	contradiction	contradiction	NOUN
ejpam-2660	460	51	.	.	PUNCT
ejpam-2660	461	1	(	(	PUNCT
ejpam-2660	461	2	ii	ii	NOUN
ejpam-2660	461	3	):	):	PUNCT
ejpam-2660	461	4	let	let	VERB
ejpam-2660	461	5	i(a	i(a	NUM
ejpam-2660	461	6	)	)	PUNCT
ejpam-2660	461	7	∧	∧	PROPN
ejpam-2660	461	8	i(b	i(b	NOUN
ejpam-2660	461	9	)	)	PUNCT
ejpam-2660	461	10	⊆	⊆	NUM
ejpam-2660	461	11	p	p	NOUN
ejpam-2660	461	12	.	.	PUNCT
ejpam-2660	462	1	by	by	ADP
ejpam-2660	462	2	(	(	PUNCT
ejpam-2660	462	3	i	i	NOUN
ejpam-2660	462	4	)	)	PUNCT
ejpam-2660	462	5	,	,	PUNCT
ejpam-2660	462	6	i(a	i(a	PROPN
ejpam-2660	462	7	)	)	PUNCT
ejpam-2660	462	8	⊆	⊆	NUM
ejpam-2660	462	9	p	p	NOUN
ejpam-2660	462	10	or	or	CCONJ
ejpam-2660	462	11	i(b	i(b	NOUN
ejpam-2660	462	12	)	)	PUNCT
ejpam-2660	462	13	⊆	⊆	NUM
ejpam-2660	462	14	p	p	NOUN
ejpam-2660	462	15	.	.	PUNCT
ejpam-2660	463	1	since	since	SCONJ
ejpam-2660	463	2	a	a	DET
ejpam-2660	463	3	∈	∈	PROPN
ejpam-2660	463	4	i(a	i(a	PROPN
ejpam-2660	463	5	)	)	PUNCT
ejpam-2660	463	6	and	and	CCONJ
ejpam-2660	463	7	b	b	X
ejpam-2660	463	8	∈	∈	PROPN
ejpam-2660	463	9	i(b	i(b	PROPN
ejpam-2660	463	10	)	)	PUNCT
ejpam-2660	463	11	,	,	PUNCT
ejpam-2660	463	12	we	we	PRON
ejpam-2660	463	13	conclude	conclude	VERB
ejpam-2660	463	14	that	that	SCONJ
ejpam-2660	463	15	a	a	DET
ejpam-2660	463	16	∈	∈	PROPN
ejpam-2660	463	17	p	p	NOUN
ejpam-2660	463	18	or	or	CCONJ
ejpam-2660	463	19	b	b	NOUN
ejpam-2660	463	20	∈	∈	PROPN
ejpam-2660	463	21	p	p	NOUN
ejpam-2660	463	22	.	.	PUNCT
ejpam-2660	464	1	theorem	theorem	PROPN
ejpam-2660	464	2	61	61	NUM
ejpam-2660	464	3	.	.	PUNCT
ejpam-2660	465	1	let	let	VERB
ejpam-2660	465	2	l	l	NOUN
ejpam-2660	465	3	be	be	AUX
ejpam-2660	465	4	distributive	distributive	ADJ
ejpam-2660	465	5	,	,	PUNCT
ejpam-2660	465	6	a	a	PRON
ejpam-2660	465	7	,	,	PUNCT
ejpam-2660	465	8	b	b	NOUN
ejpam-2660	465	9	⊆	⊆	NUM
ejpam-2660	465	10	l	l	NOUN
ejpam-2660	465	11	,	,	PUNCT
ejpam-2660	465	12	and	and	CCONJ
ejpam-2660	465	13	d	d	NOUN
ejpam-2660	465	14	is	be	AUX
ejpam-2660	465	15	a	a	DET
ejpam-2660	465	16	hyperfilter	hyperfilter	NOUN
ejpam-2660	465	17	of	of	ADP
ejpam-2660	465	18	l.	l.	PROPN
ejpam-2660	465	19	then	then	ADV
ejpam-2660	465	20	the	the	DET
ejpam-2660	465	21	following	follow	VERB
ejpam-2660	465	22	conditions	condition	NOUN
ejpam-2660	465	23	are	be	AUX
ejpam-2660	465	24	equivalent	equivalent	ADJ
ejpam-2660	465	25	.	.	PUNCT
ejpam-2660	466	1	(	(	PUNCT
ejpam-2660	466	2	i	i	NOUN
ejpam-2660	466	3	)	)	PUNCT
ejpam-2660	466	4	d	d	NOUN
ejpam-2660	466	5	is	be	AUX
ejpam-2660	466	6	a	a	DET
ejpam-2660	466	7	prime	prime	ADJ
ejpam-2660	466	8	hyperfilter	hyperfilter	NOUN
ejpam-2660	466	9	.	.	PUNCT
ejpam-2660	467	1	(	(	PUNCT
ejpam-2660	467	2	ii	ii	NOUN
ejpam-2660	467	3	)	)	PUNCT
ejpam-2660	467	4	l	l	PROPN
ejpam-2660	467	5	\d	\d	NOUN
ejpam-2660	467	6	is	be	AUX
ejpam-2660	467	7	a	a	DET
ejpam-2660	467	8	prime	prime	ADJ
ejpam-2660	467	9	hyperideal	hyperideal	NOUN
ejpam-2660	467	10	.	.	PUNCT
ejpam-2660	468	1	(	(	PUNCT
ejpam-2660	468	2	iii	iii	X
ejpam-2660	468	3	)	)	PUNCT
ejpam-2660	468	4	if	if	SCONJ
ejpam-2660	468	5	a	a	DET
ejpam-2660	468	6	∨b	∨b	NOUN
ejpam-2660	468	7	⊆	⊆	NUM
ejpam-2660	468	8	d	d	PROPN
ejpam-2660	468	9	,	,	PUNCT
ejpam-2660	468	10	then	then	ADV
ejpam-2660	468	11	a	a	DET
ejpam-2660	468	12	⊆	⊆	NUM
ejpam-2660	468	13	d	d	NOUN
ejpam-2660	468	14	or	or	CCONJ
ejpam-2660	468	15	b	b	PROPN
ejpam-2660	468	16	⊆	⊆	NUM
ejpam-2660	468	17	d.	d.	NOUN
ejpam-2660	468	18	(	(	PUNCT
ejpam-2660	468	19	iv	iv	X
ejpam-2660	468	20	)	)	PUNCT
ejpam-2660	468	21	if	if	SCONJ
ejpam-2660	468	22	f	f	PROPN
ejpam-2660	468	23	(	(	PUNCT
ejpam-2660	468	24	a	a	NOUN
ejpam-2660	468	25	)	)	PUNCT
ejpam-2660	468	26	∨	∨	PROPN
ejpam-2660	468	27	f	f	X
ejpam-2660	468	28	(	(	PUNCT
ejpam-2660	468	29	b	b	NOUN
ejpam-2660	468	30	)	)	PUNCT
ejpam-2660	468	31	⊆	⊆	NUM
ejpam-2660	468	32	d	d	NOUN
ejpam-2660	468	33	,	,	PUNCT
ejpam-2660	468	34	then	then	ADV
ejpam-2660	468	35	a	a	DET
ejpam-2660	468	36	∈	∈	PROPN
ejpam-2660	468	37	d	d	NOUN
ejpam-2660	468	38	or	or	CCONJ
ejpam-2660	468	39	b	b	NOUN
ejpam-2660	468	40	∈	∈	PROPN
ejpam-2660	468	41	d	d	NOUN
ejpam-2660	468	42	,	,	PUNCT
ejpam-2660	468	43	for	for	ADP
ejpam-2660	468	44	all	all	DET
ejpam-2660	468	45	a	a	DET
ejpam-2660	468	46	,	,	PUNCT
ejpam-2660	468	47	b	b	PROPN
ejpam-2660	468	48	∈	∈	PROPN
ejpam-2660	468	49	l.	l.	NOUN
ejpam-2660	468	50	proof	proof	NOUN
ejpam-2660	468	51	.	.	PUNCT
ejpam-2660	469	1	by	by	ADP
ejpam-2660	469	2	theorem	theorem	NOUN
ejpam-2660	469	3	59	59	NUM
ejpam-2660	469	4	,	,	PUNCT
ejpam-2660	469	5	(	(	PUNCT
ejpam-2660	469	6	i	i	NOUN
ejpam-2660	469	7	)	)	PUNCT
ejpam-2660	469	8	,	,	PUNCT
ejpam-2660	469	9	(	(	PUNCT
ejpam-2660	469	10	ii	ii	NOUN
ejpam-2660	469	11	)	)	PUNCT
ejpam-2660	469	12	are	be	AUX
ejpam-2660	469	13	equivalent	equivalent	ADJ
ejpam-2660	469	14	.	.	PUNCT
ejpam-2660	470	1	(	(	PUNCT
ejpam-2660	470	2	i	i	NOUN
ejpam-2660	470	3	)	)	PUNCT
ejpam-2660	471	1	=	=	NOUN
ejpam-2660	471	2	⇒	⇒	NOUN
ejpam-2660	471	3	(	(	PUNCT
ejpam-2660	471	4	iii	iii	NOUN
ejpam-2660	471	5	):	):	PUNCT
ejpam-2660	471	6	let	let	VERB
ejpam-2660	471	7	a∨b	a∨b	NOUN
ejpam-2660	471	8	⊆	⊆	NUM
ejpam-2660	471	9	d	d	PROPN
ejpam-2660	471	10	,	,	PUNCT
ejpam-2660	471	11	and	and	CCONJ
ejpam-2660	471	12	a	a	DET
ejpam-2660	471	13	*	*	PUNCT
ejpam-2660	471	14	d	d	NOUN
ejpam-2660	471	15	,	,	PUNCT
ejpam-2660	471	16	b	b	PROPN
ejpam-2660	471	17	*	*	PUNCT
ejpam-2660	471	18	d.	d.	PROPN
ejpam-2660	471	19	so	so	ADV
ejpam-2660	471	20	there	there	PRON
ejpam-2660	471	21	exist	exist	VERB
ejpam-2660	471	22	a	a	DET
ejpam-2660	471	23	∈	∈	PROPN
ejpam-2660	471	24	a\d	a\d	NOUN
ejpam-2660	471	25	,	,	PUNCT
ejpam-2660	471	26	and	and	CCONJ
ejpam-2660	471	27	b	b	X
ejpam-2660	471	28	∈	∈	PROPN
ejpam-2660	471	29	b	b	PROPN
ejpam-2660	471	30	\d	\d	NOUN
ejpam-2660	471	31	,	,	PUNCT
ejpam-2660	471	32	since	since	SCONJ
ejpam-2660	471	33	a∨	a∨	PROPN
ejpam-2660	471	34	b	b	PROPN
ejpam-2660	471	35	∈	∈	PROPN
ejpam-2660	471	36	a∨b	a∨b	PROPN
ejpam-2660	471	37	,	,	PUNCT
ejpam-2660	471	38	and	and	CCONJ
ejpam-2660	471	39	a∨b	a∨b	PROPN
ejpam-2660	471	40	⊆	⊆	NUM
ejpam-2660	471	41	d	d	PROPN
ejpam-2660	471	42	,	,	PUNCT
ejpam-2660	471	43	a∨	a∨	PROPN
ejpam-2660	471	44	b	b	X
ejpam-2660	471	45	∈	∈	PROPN
ejpam-2660	471	46	d	d	X
ejpam-2660	471	47	;	;	PUNCT
ejpam-2660	471	48	since	since	SCONJ
ejpam-2660	471	49	d	d	NOUN
ejpam-2660	471	50	is	be	AUX
ejpam-2660	471	51	a	a	DET
ejpam-2660	471	52	prime	prime	ADJ
ejpam-2660	471	53	hyperfilter	hyperfilter	NOUN
ejpam-2660	471	54	,	,	PUNCT
ejpam-2660	471	55	a	a	DET
ejpam-2660	471	56	∈	∈	PROPN
ejpam-2660	471	57	d	d	NOUN
ejpam-2660	471	58	and	and	CCONJ
ejpam-2660	471	59	b	b	PROPN
ejpam-2660	471	60	∈	∈	PROPN
ejpam-2660	471	61	d	d	NOUN
ejpam-2660	471	62	,	,	PUNCT
ejpam-2660	471	63	which	which	PRON
ejpam-2660	471	64	is	be	AUX
ejpam-2660	471	65	a	a	DET
ejpam-2660	471	66	contradiction	contradiction	NOUN
ejpam-2660	471	67	.	.	PUNCT
ejpam-2660	472	1	m.	m.	NOUN
ejpam-2660	472	2	amiri	amiri	PROPN
ejpam-2660	472	3	bideshki	bideshki	PROPN
ejpam-2660	472	4	,	,	PUNCT
ejpam-2660	472	5	r.	r.	PROPN
ejpam-2660	472	6	ameri	ameri	PROPN
ejpam-2660	472	7	,	,	PUNCT
ejpam-2660	472	8	a.	a.	PROPN
ejpam-2660	472	9	borumand	borumand	PROPN
ejpam-2660	472	10	saeid	saeid	PROPN
ejpam-2660	472	11	/	/	SYM
ejpam-2660	472	12	eur	eur	PROPN
ejpam-2660	472	13	.	.	PUNCT
ejpam-2660	473	1	j.	j.	PROPN
ejpam-2660	473	2	pure	pure	PROPN
ejpam-2660	473	3	appl	appl	PROPN
ejpam-2660	473	4	.	.	PROPN
ejpam-2660	473	5	math	math	PROPN
ejpam-2660	473	6	,	,	PUNCT
ejpam-2660	473	7	11	11	NUM
ejpam-2660	473	8	(	(	PUNCT
ejpam-2660	473	9	1	1	NUM
ejpam-2660	473	10	)	)	PUNCT
ejpam-2660	473	11	(	(	PUNCT
ejpam-2660	473	12	2018	2018	NUM
ejpam-2660	473	13	)	)	PUNCT
ejpam-2660	473	14	,	,	PUNCT
ejpam-2660	473	15	169	169	NUM
ejpam-2660	473	16	-	-	SYM
ejpam-2660	473	17	188	188	NUM
ejpam-2660	473	18	183	183	NUM
ejpam-2660	473	19	(	(	PUNCT
ejpam-2660	473	20	iii	iii	NOUN
ejpam-2660	473	21	)	)	PUNCT
ejpam-2660	473	22	=	=	NOUN
ejpam-2660	473	23	⇒	⇒	NOUN
ejpam-2660	473	24	(	(	PUNCT
ejpam-2660	473	25	iv	iv	NUM
ejpam-2660	473	26	):	):	PUNCT
ejpam-2660	473	27	it	it	PRON
ejpam-2660	473	28	is	be	AUX
ejpam-2660	473	29	obvious	obvious	ADJ
ejpam-2660	473	30	.	.	PUNCT
ejpam-2660	474	1	(	(	PUNCT
ejpam-2660	474	2	iv	iv	X
ejpam-2660	474	3	)	)	PUNCT
ejpam-2660	474	4	=	=	NOUN
ejpam-2660	474	5	⇒	⇒	NOUN
ejpam-2660	474	6	(	(	PUNCT
ejpam-2660	474	7	1	1	NUM
ejpam-2660	474	8	):	):	PUNCT
ejpam-2660	474	9	let	let	VERB
ejpam-2660	474	10	x	x	PRON
ejpam-2660	474	11	,	,	PUNCT
ejpam-2660	474	12	y	y	PROPN
ejpam-2660	474	13	∈	∈	PROPN
ejpam-2660	474	14	l	l	NOUN
ejpam-2660	474	15	,	,	PUNCT
ejpam-2660	474	16	and	and	CCONJ
ejpam-2660	474	17	(	(	PUNCT
ejpam-2660	474	18	x	x	PROPN
ejpam-2660	474	19	∨	∨	NUM
ejpam-2660	474	20	y	y	NOUN
ejpam-2660	474	21	)	)	PUNCT
ejpam-2660	474	22	∈	∈	PROPN
ejpam-2660	474	23	d.	d.	PROPN
ejpam-2660	474	24	assume	assume	VERB
ejpam-2660	474	25	that	that	SCONJ
ejpam-2660	474	26	x	x	X
ejpam-2660	474	27	/∈	/∈	PUNCT
ejpam-2660	475	1	d	d	NOUN
ejpam-2660	475	2	,	,	PUNCT
ejpam-2660	475	3	and	and	CCONJ
ejpam-2660	475	4	y	y	PROPN
ejpam-2660	475	5	/∈	/∈	PUNCT
ejpam-2660	475	6	d.	d.	PROPN
ejpam-2660	476	1	by	by	ADP
ejpam-2660	476	2	(	(	PUNCT
ejpam-2660	476	3	iv	iv	X
ejpam-2660	476	4	)	)	PUNCT
ejpam-2660	476	5	,	,	PUNCT
ejpam-2660	476	6	f	f	PROPN
ejpam-2660	476	7	(	(	PUNCT
ejpam-2660	476	8	x	x	X
ejpam-2660	476	9	)	)	PUNCT
ejpam-2660	476	10	∨	∨	NUM
ejpam-2660	476	11	f	f	PROPN
ejpam-2660	476	12	(	(	PUNCT
ejpam-2660	476	13	y	y	PROPN
ejpam-2660	476	14	)	)	PUNCT
ejpam-2660	476	15	*	*	PUNCT
ejpam-2660	477	1	d.	d.	PROPN
ejpam-2660	477	2	therefore	therefore	ADV
ejpam-2660	477	3	there	there	PRON
ejpam-2660	477	4	exists	exist	VERB
ejpam-2660	477	5	c	c	PROPN
ejpam-2660	477	6	∈	∈	PROPN
ejpam-2660	477	7	(	(	PUNCT
ejpam-2660	477	8	f	f	X
ejpam-2660	477	9	(	(	PUNCT
ejpam-2660	477	10	x	x	NOUN
ejpam-2660	477	11	)	)	PUNCT
ejpam-2660	477	12	∨	∨	NUM
ejpam-2660	477	13	f	f	PROPN
ejpam-2660	477	14	(	(	PUNCT
ejpam-2660	477	15	y	y	NOUN
ejpam-2660	477	16	)	)	PUNCT
ejpam-2660	477	17	)	)	PUNCT
ejpam-2660	477	18	\	\	PROPN
ejpam-2660	478	1	d.	d.	PROPN
ejpam-2660	478	2	so	so	ADV
ejpam-2660	478	3	there	there	PRON
ejpam-2660	478	4	exist	exist	VERB
ejpam-2660	478	5	a	a	DET
ejpam-2660	478	6	∈	∈	ADJ
ejpam-2660	478	7	f	f	X
ejpam-2660	478	8	(	(	PUNCT
ejpam-2660	478	9	x	x	NOUN
ejpam-2660	478	10	)	)	PUNCT
ejpam-2660	478	11	,	,	PUNCT
ejpam-2660	478	12	b	b	X
ejpam-2660	478	13	∈	∈	PROPN
ejpam-2660	478	14	f	f	X
ejpam-2660	478	15	(	(	PUNCT
ejpam-2660	478	16	y	y	PROPN
ejpam-2660	478	17	)	)	PUNCT
ejpam-2660	478	18	,	,	PUNCT
ejpam-2660	478	19	such	such	ADJ
ejpam-2660	478	20	that	that	SCONJ
ejpam-2660	478	21	c	c	NOUN
ejpam-2660	478	22	=	=	PUNCT
ejpam-2660	478	23	a	a	DET
ejpam-2660	478	24	∨	∨	NUM
ejpam-2660	478	25	b	b	PROPN
ejpam-2660	478	26	and	and	CCONJ
ejpam-2660	478	27	x	x	SYM
ejpam-2660	478	28	≤	≤	PROPN
ejpam-2660	478	29	a	a	X
ejpam-2660	478	30	,	,	PUNCT
ejpam-2660	478	31	y	y	PROPN
ejpam-2660	478	32	≤	≤	PROPN
ejpam-2660	478	33	b.	b.	PROPN
ejpam-2660	479	1	so	so	ADV
ejpam-2660	479	2	,	,	PUNCT
ejpam-2660	479	3	we	we	PRON
ejpam-2660	479	4	have	have	VERB
ejpam-2660	479	5	a	a	DET
ejpam-2660	479	6	∨	∨	NUM
ejpam-2660	479	7	b	b	NOUN
ejpam-2660	479	8	/∈	/∈	PUNCT
ejpam-2660	480	1	d	d	NOUN
ejpam-2660	480	2	,	,	PUNCT
ejpam-2660	480	3	and	and	CCONJ
ejpam-2660	480	4	x	x	X
ejpam-2660	480	5	∨	∨	NUM
ejpam-2660	480	6	y	y	PROPN
ejpam-2660	480	7	≤	≤	NUM
ejpam-2660	480	8	a	a	DET
ejpam-2660	480	9	∨	∨	PROPN
ejpam-2660	480	10	b.	b.	NOUN
ejpam-2660	480	11	since	since	SCONJ
ejpam-2660	480	12	d	d	PROPN
ejpam-2660	480	13	is	be	AUX
ejpam-2660	480	14	a	a	DET
ejpam-2660	480	15	hyperfilter	hyperfilter	NOUN
ejpam-2660	480	16	,	,	PUNCT
ejpam-2660	481	1	x	x	PROPN
ejpam-2660	481	2	∨	∨	NUM
ejpam-2660	481	3	y	y	PROPN
ejpam-2660	481	4	/∈	/∈	PUNCT
ejpam-2660	482	1	d	d	NOUN
ejpam-2660	482	2	,	,	PUNCT
ejpam-2660	482	3	which	which	PRON
ejpam-2660	482	4	is	be	AUX
ejpam-2660	482	5	a	a	DET
ejpam-2660	482	6	contradiction	contradiction	NOUN
ejpam-2660	482	7	.	.	PUNCT
ejpam-2660	482	8	.	.	PUNCT
ejpam-2660	483	1	theorem	theorem	VERB
ejpam-2660	483	2	62	62	NUM
ejpam-2660	483	3	(	(	PUNCT
ejpam-2660	483	4	prime	prime	ADJ
ejpam-2660	483	5	hyperfilter	hyperfilter	NOUN
ejpam-2660	483	6	theorem	theorem	PROPN
ejpam-2660	483	7	)	)	PUNCT
ejpam-2660	483	8	.	.	PUNCT
ejpam-2660	484	1	let	let	VERB
ejpam-2660	484	2	l	l	NOUN
ejpam-2660	484	3	be	be	AUX
ejpam-2660	484	4	distributive	distributive	ADJ
ejpam-2660	484	5	.	.	PUNCT
ejpam-2660	485	1	if	if	SCONJ
ejpam-2660	485	2	i	i	PRON
ejpam-2660	485	3	is	be	AUX
ejpam-2660	485	4	a	a	DET
ejpam-2660	485	5	hyperideal	hyperideal	NOUN
ejpam-2660	485	6	and	and	CCONJ
ejpam-2660	485	7	f	f	PROPN
ejpam-2660	485	8	is	be	AUX
ejpam-2660	485	9	a	a	DET
ejpam-2660	485	10	hyperfilter	hyperfilter	NOUN
ejpam-2660	485	11	of	of	ADP
ejpam-2660	485	12	l	l	NOUN
ejpam-2660	485	13	,	,	PUNCT
ejpam-2660	485	14	such	such	ADJ
ejpam-2660	485	15	that	that	SCONJ
ejpam-2660	485	16	i	i	PRON
ejpam-2660	485	17	∩	∩	NOUN
ejpam-2660	485	18	f	f	X
ejpam-2660	485	19	=	=	SYM
ejpam-2660	485	20	∅	∅	NOUN
ejpam-2660	485	21	,	,	PUNCT
ejpam-2660	485	22	then	then	ADV
ejpam-2660	485	23	there	there	PRON
ejpam-2660	485	24	exists	exist	VERB
ejpam-2660	485	25	prime	prime	ADJ
ejpam-2660	485	26	hyperfilter	hyperfilter	PROPN
ejpam-2660	485	27	d	d	PROPN
ejpam-2660	485	28	of	of	ADP
ejpam-2660	485	29	l	l	NOUN
ejpam-2660	485	30	,	,	PUNCT
ejpam-2660	485	31	such	such	ADJ
ejpam-2660	485	32	that	that	SCONJ
ejpam-2660	485	33	f	f	PROPN
ejpam-2660	485	34	⊆	⊆	NUM
ejpam-2660	485	35	d	d	PROPN
ejpam-2660	485	36	and	and	CCONJ
ejpam-2660	485	37	i	i	PRON
ejpam-2660	485	38	∩d	∩d	VERB
ejpam-2660	485	39	=	=	PUNCT
ejpam-2660	485	40	∅.	∅.	VERB
ejpam-2660	485	41	proof	proof	NOUN
ejpam-2660	485	42	.	.	PUNCT
ejpam-2660	486	1	let	let	VERB
ejpam-2660	486	2	σ	σ	NOUN
ejpam-2660	486	3	=	=	PRON
ejpam-2660	486	4	{	{	PUNCT
ejpam-2660	486	5	j	j	PROPN
ejpam-2660	486	6	⊆	⊆	NUM
ejpam-2660	486	7	l	l	NOUN
ejpam-2660	486	8	|	|	ADV
ejpam-2660	486	9	j	j	PROPN
ejpam-2660	486	10	is	be	AUX
ejpam-2660	486	11	a	a	DET
ejpam-2660	486	12	hyperfilter	hyperfilter	ADJ
ejpam-2660	486	13	andj	andj	NOUN
ejpam-2660	486	14	∩	∩	NOUN
ejpam-2660	486	15	i	i	NOUN
ejpam-2660	486	16	=	=	SYM
ejpam-2660	486	17	∅	∅	NOUN
ejpam-2660	486	18	}	}	PUNCT
ejpam-2660	486	19	.	.	PUNCT
ejpam-2660	487	1	since	since	SCONJ
ejpam-2660	487	2	f	f	PROPN
ejpam-2660	487	3	∈	∈	PROPN
ejpam-2660	487	4	σ	σ	PROPN
ejpam-2660	487	5	,	,	PUNCT
ejpam-2660	487	6	σ	σ	PROPN
ejpam-2660	487	7	6=	6=	AUX
ejpam-2660	487	8	∅.	∅.	ADV
ejpam-2660	487	9	suppose	suppose	VERB
ejpam-2660	487	10	{	{	PUNCT
ejpam-2660	487	11	li}i∈i	li}i∈i	INTJ
ejpam-2660	487	12	is	be	AUX
ejpam-2660	487	13	a	a	DET
ejpam-2660	487	14	chain	chain	NOUN
ejpam-2660	487	15	in	in	ADP
ejpam-2660	487	16	σ	σ	PROPN
ejpam-2660	487	17	.	.	PUNCT
ejpam-2660	488	1	we	we	PRON
ejpam-2660	488	2	show	show	VERB
ejpam-2660	488	3	that	that	SCONJ
ejpam-2660	488	4	⋃	⋃	ADP
ejpam-2660	488	5	i∈i	i∈i	ADJ
ejpam-2660	488	6	li	li	PROPN
ejpam-2660	488	7	∈	∈	PROPN
ejpam-2660	488	8	σ	σ	PROPN
ejpam-2660	488	9	.	.	PUNCT
ejpam-2660	488	10	let	let	VERB
ejpam-2660	488	11	a	a	DET
ejpam-2660	488	12	,	,	PUNCT
ejpam-2660	488	13	b	b	PROPN
ejpam-2660	488	14	∈	∈	PROPN
ejpam-2660	488	15	⋃	⋃	PROPN
ejpam-2660	488	16	i∈i	i∈i	ADJ
ejpam-2660	488	17	li	li	PROPN
ejpam-2660	488	18	.	.	PUNCT
ejpam-2660	489	1	so	so	ADV
ejpam-2660	489	2	there	there	PRON
ejpam-2660	489	3	exist	exist	VERB
ejpam-2660	489	4	i	i	PRON
ejpam-2660	489	5	,	,	PUNCT
ejpam-2660	490	1	j	j	PROPN
ejpam-2660	490	2	∈	∈	PROPN
ejpam-2660	490	3	i	i	PRON
ejpam-2660	490	4	,	,	PUNCT
ejpam-2660	490	5	such	such	ADJ
ejpam-2660	490	6	that	that	SCONJ
ejpam-2660	490	7	a	a	DET
ejpam-2660	490	8	∈	∈	PROPN
ejpam-2660	490	9	li	li	NOUN
ejpam-2660	490	10	,	,	PUNCT
ejpam-2660	490	11	and	and	CCONJ
ejpam-2660	490	12	b	b	X
ejpam-2660	490	13	∈	∈	PROPN
ejpam-2660	490	14	lj	lj	INTJ
ejpam-2660	490	15	;	;	PUNCT
ejpam-2660	490	16	since	since	SCONJ
ejpam-2660	490	17	{	{	PUNCT
ejpam-2660	490	18	li}i∈i	li}i∈i	INTJ
ejpam-2660	490	19	is	be	AUX
ejpam-2660	490	20	a	a	DET
ejpam-2660	490	21	chain	chain	NOUN
ejpam-2660	490	22	,	,	PUNCT
ejpam-2660	490	23	li	li	PROPN
ejpam-2660	490	24	⊆	⊆	NUM
ejpam-2660	490	25	lj	lj	PROPN
ejpam-2660	490	26	or	or	CCONJ
ejpam-2660	490	27	lj	lj	PROPN
ejpam-2660	490	28	⊆	⊆	NUM
ejpam-2660	490	29	li	li	NOUN
ejpam-2660	490	30	.	.	PUNCT
ejpam-2660	491	1	we	we	PRON
ejpam-2660	491	2	assume	assume	VERB
ejpam-2660	491	3	li	li	PROPN
ejpam-2660	491	4	⊆	⊆	NUM
ejpam-2660	491	5	lj	lj	PROPN
ejpam-2660	491	6	.	.	PUNCT
ejpam-2660	492	1	so	so	ADV
ejpam-2660	492	2	a	a	DET
ejpam-2660	492	3	,	,	PUNCT
ejpam-2660	492	4	b	b	X
ejpam-2660	492	5	∈	∈	ADJ
ejpam-2660	492	6	lj	lj	ADV
ejpam-2660	492	7	and	and	CCONJ
ejpam-2660	492	8	since	since	SCONJ
ejpam-2660	492	9	lj	lj	PROPN
ejpam-2660	492	10	is	be	AUX
ejpam-2660	492	11	a	a	DET
ejpam-2660	492	12	hyperfilter	hyperfilter	NOUN
ejpam-2660	492	13	,	,	PUNCT
ejpam-2660	492	14	a∧b	a∧b	NOUN
ejpam-2660	492	15	∈	∈	PROPN
ejpam-2660	492	16	lj	lj	INTJ
ejpam-2660	492	17	.	.	PUNCT
ejpam-2660	493	1	thus	thus	ADV
ejpam-2660	493	2	a∧b	a∧b	VERB
ejpam-2660	493	3	∈	∈	PROPN
ejpam-2660	493	4	⋃	⋃	PROPN
ejpam-2660	493	5	i∈i	i∈i	ADJ
ejpam-2660	493	6	li	li	PROPN
ejpam-2660	493	7	.	.	PUNCT
ejpam-2660	494	1	let	let	VERB
ejpam-2660	494	2	a	a	DET
ejpam-2660	494	3	∈	∈	NOUN
ejpam-2660	494	4	⋃	⋃	NOUN
ejpam-2660	494	5	i∈i	i∈i	ADJ
ejpam-2660	494	6	li	li	PROPN
ejpam-2660	494	7	and	and	CCONJ
ejpam-2660	494	8	x	x	PRON
ejpam-2660	494	9	≥	≥	NUM
ejpam-2660	494	10	a.	a.	NOUN
ejpam-2660	495	1	so	so	ADV
ejpam-2660	495	2	there	there	PRON
ejpam-2660	495	3	exists	exist	VERB
ejpam-2660	495	4	i	i	PRON
ejpam-2660	495	5	∈	∈	PROPN
ejpam-2660	496	1	i	i	PRON
ejpam-2660	496	2	,	,	PUNCT
ejpam-2660	496	3	such	such	ADJ
ejpam-2660	496	4	that	that	SCONJ
ejpam-2660	496	5	a	a	DET
ejpam-2660	496	6	∈	∈	PROPN
ejpam-2660	496	7	li	li	PROPN
ejpam-2660	496	8	.	.	PROPN
ejpam-2660	497	1	since	since	SCONJ
ejpam-2660	497	2	li	li	PROPN
ejpam-2660	497	3	is	be	AUX
ejpam-2660	497	4	a	a	DET
ejpam-2660	497	5	hyperfilter	hyperfilter	NOUN
ejpam-2660	497	6	and	and	CCONJ
ejpam-2660	497	7	x	x	X
ejpam-2660	497	8	≥	≥	NOUN
ejpam-2660	497	9	a	a	PRON
ejpam-2660	497	10	,	,	PUNCT
ejpam-2660	497	11	x	x	PROPN
ejpam-2660	497	12	∈	∈	PROPN
ejpam-2660	497	13	li	li	PROPN
ejpam-2660	497	14	,	,	PUNCT
ejpam-2660	497	15	it	it	PRON
ejpam-2660	497	16	implies	imply	VERB
ejpam-2660	497	17	that	that	SCONJ
ejpam-2660	497	18	x	x	PUNCT
ejpam-2660	497	19	∈	∈	PROPN
ejpam-2660	497	20	⋃	⋃	PROPN
ejpam-2660	497	21	i∈i	i∈i	ADJ
ejpam-2660	497	22	li	li	PROPN
ejpam-2660	497	23	.	.	PUNCT
ejpam-2660	498	1	so	so	ADV
ejpam-2660	498	2	⋃	⋃	PROPN
ejpam-2660	498	3	i∈i	i∈i	ADJ
ejpam-2660	498	4	li	li	PROPN
ejpam-2660	498	5	is	be	AUX
ejpam-2660	498	6	a	a	DET
ejpam-2660	498	7	hyperfilter	hyperfilter	NOUN
ejpam-2660	498	8	of	of	ADP
ejpam-2660	498	9	l.	l.	PROPN
ejpam-2660	498	10	we	we	PRON
ejpam-2660	498	11	claim	claim	VERB
ejpam-2660	498	12	that	that	SCONJ
ejpam-2660	498	13	(	(	PUNCT
ejpam-2660	498	14	⋃	⋃	PROPN
ejpam-2660	498	15	i∈i	i∈i	ADJ
ejpam-2660	498	16	li	li	NOUN
ejpam-2660	498	17	)	)	PUNCT
ejpam-2660	498	18	∩	∩	NOUN
ejpam-2660	498	19	i	i	PRON
ejpam-2660	498	20	=	=	PUNCT
ejpam-2660	498	21	∅.	∅.	VERB
ejpam-2660	498	22	if	if	SCONJ
ejpam-2660	498	23	(	(	PUNCT
ejpam-2660	498	24	⋃	⋃	PROPN
ejpam-2660	498	25	i∈i	i∈i	ADJ
ejpam-2660	498	26	li	li	NOUN
ejpam-2660	498	27	)	)	PUNCT
ejpam-2660	498	28	∩	∩	PROPN
ejpam-2660	498	29	i	i	PROPN
ejpam-2660	498	30	6=	6=	PROPN
ejpam-2660	498	31	∅	∅	NOUN
ejpam-2660	498	32	,	,	PUNCT
ejpam-2660	498	33	then	then	ADV
ejpam-2660	498	34	there	there	PRON
ejpam-2660	498	35	exists	exist	VERB
ejpam-2660	498	36	a	a	DET
ejpam-2660	498	37	∈	∈	PROPN
ejpam-2660	498	38	⋃	⋃	PUNCT
ejpam-2660	498	39	i∈i	i∈i	ADJ
ejpam-2660	498	40	li	li	PROPN
ejpam-2660	498	41	,	,	PUNCT
ejpam-2660	498	42	and	and	CCONJ
ejpam-2660	498	43	a	a	DET
ejpam-2660	498	44	∈	∈	PROPN
ejpam-2660	498	45	i.	i.	NOUN
ejpam-2660	498	46	so	so	SCONJ
ejpam-2660	498	47	there	there	PRON
ejpam-2660	498	48	exists	exist	VERB
ejpam-2660	498	49	i	i	PRON
ejpam-2660	498	50	∈	∈	PROPN
ejpam-2660	499	1	i	i	PRON
ejpam-2660	499	2	,	,	PUNCT
ejpam-2660	500	1	such	such	ADJ
ejpam-2660	500	2	that	that	SCONJ
ejpam-2660	500	3	a	a	DET
ejpam-2660	500	4	∈	∈	PROPN
ejpam-2660	500	5	li	li	NOUN
ejpam-2660	500	6	and	and	CCONJ
ejpam-2660	500	7	a	a	DET
ejpam-2660	500	8	∈	∈	PROPN
ejpam-2660	500	9	i	i	PRON
ejpam-2660	500	10	,	,	PUNCT
ejpam-2660	500	11	it	it	PRON
ejpam-2660	500	12	implies	imply	VERB
ejpam-2660	500	13	that	that	SCONJ
ejpam-2660	500	14	li	li	PROPN
ejpam-2660	500	15	∩	∩	PROPN
ejpam-2660	500	16	i	i	PROPN
ejpam-2660	500	17	6=	6=	PROPN
ejpam-2660	500	18	∅	∅	NOUN
ejpam-2660	500	19	,	,	PUNCT
ejpam-2660	500	20	which	which	PRON
ejpam-2660	500	21	is	be	AUX
ejpam-2660	500	22	a	a	DET
ejpam-2660	500	23	contradiction	contradiction	NOUN
ejpam-2660	500	24	.	.	PUNCT
ejpam-2660	501	1	thus	thus	ADV
ejpam-2660	501	2	⋃	⋃	PUNCT
ejpam-2660	501	3	i∈i	i∈i	ADJ
ejpam-2660	501	4	li	li	PROPN
ejpam-2660	501	5	∈	∈	PROPN
ejpam-2660	501	6	σ	σ	PROPN
ejpam-2660	501	7	.	.	PUNCT
ejpam-2660	501	8	by	by	ADP
ejpam-2660	501	9	zorn	zorn	PROPN
ejpam-2660	501	10	lemma	lemma	PROPN
ejpam-2660	501	11	,	,	PUNCT
ejpam-2660	501	12	σ	σ	PROPN
ejpam-2660	501	13	has	have	VERB
ejpam-2660	501	14	a	a	DET
ejpam-2660	501	15	maximal	maximal	ADJ
ejpam-2660	501	16	element	element	NOUN
ejpam-2660	501	17	d.	d.	NOUN
ejpam-2660	501	18	we	we	PRON
ejpam-2660	501	19	claim	claim	VERB
ejpam-2660	501	20	that	that	SCONJ
ejpam-2660	501	21	d	d	NOUN
ejpam-2660	501	22	is	be	AUX
ejpam-2660	501	23	a	a	DET
ejpam-2660	501	24	prime	prime	ADJ
ejpam-2660	501	25	hyperfilter	hyperfilter	NOUN
ejpam-2660	501	26	.	.	PUNCT
ejpam-2660	502	1	let	let	VERB
ejpam-2660	502	2	a	a	DET
ejpam-2660	502	3	,	,	PUNCT
ejpam-2660	502	4	b	b	PROPN
ejpam-2660	502	5	∈	∈	PROPN
ejpam-2660	502	6	l	l	NOUN
ejpam-2660	502	7	,	,	PUNCT
ejpam-2660	502	8	and	and	CCONJ
ejpam-2660	502	9	(	(	PUNCT
ejpam-2660	502	10	a	a	DET
ejpam-2660	502	11	∨	∨	NUM
ejpam-2660	502	12	b	b	NOUN
ejpam-2660	502	13	)	)	PUNCT
ejpam-2660	502	14	∈	∈	PROPN
ejpam-2660	502	15	d.	d.	NOUN
ejpam-2660	502	16	we	we	PRON
ejpam-2660	502	17	suppose	suppose	VERB
ejpam-2660	502	18	that	that	SCONJ
ejpam-2660	502	19	a	a	DET
ejpam-2660	502	20	/∈	/∈	NOUN
ejpam-2660	502	21	d	d	NOUN
ejpam-2660	502	22	and	and	CCONJ
ejpam-2660	502	23	b	b	PROPN
ejpam-2660	502	24	/∈	/∈	PROPN
ejpam-2660	502	25	d.	d.	PROPN
ejpam-2660	502	26	set	set	VERB
ejpam-2660	502	27	f1	f1	PROPN
ejpam-2660	503	1	=	=	SYM
ejpam-2660	503	2	d	d	PROPN
ejpam-2660	503	3	∧	∧	PROPN
ejpam-2660	503	4	f	f	X
ejpam-2660	503	5	(	(	PUNCT
ejpam-2660	503	6	a	a	NOUN
ejpam-2660	503	7	)	)	PUNCT
ejpam-2660	503	8	and	and	CCONJ
ejpam-2660	503	9	f2	f2	X
ejpam-2660	503	10	=	=	SYM
ejpam-2660	503	11	d	d	X
ejpam-2660	503	12	∧	∧	PROPN
ejpam-2660	503	13	f	f	PROPN
ejpam-2660	503	14	(	(	PUNCT
ejpam-2660	503	15	b	b	NOUN
ejpam-2660	503	16	)	)	PUNCT
ejpam-2660	503	17	.	.	PUNCT
ejpam-2660	504	1	since	since	SCONJ
ejpam-2660	504	2	a	a	DET
ejpam-2660	504	3	∈	∈	PROPN
ejpam-2660	504	4	f1	f1	NOUN
ejpam-2660	504	5	,	,	PUNCT
ejpam-2660	504	6	d	d	NOUN
ejpam-2660	504	7	$	$	SYM
ejpam-2660	504	8	f1	f1	NOUN
ejpam-2660	504	9	;	;	PUNCT
ejpam-2660	504	10	also	also	ADV
ejpam-2660	504	11	we	we	PRON
ejpam-2660	504	12	have	have	VERB
ejpam-2660	504	13	d	d	PROPN
ejpam-2660	504	14	$	$	SYM
ejpam-2660	504	15	f2	f2	PROPN
ejpam-2660	504	16	.	.	PUNCT
ejpam-2660	505	1	d	d	X
ejpam-2660	505	2	is	be	AUX
ejpam-2660	505	3	a	a	DET
ejpam-2660	505	4	maximal	maximal	ADJ
ejpam-2660	505	5	element	element	NOUN
ejpam-2660	505	6	of	of	ADP
ejpam-2660	505	7	σ	σ	PROPN
ejpam-2660	505	8	,	,	PUNCT
ejpam-2660	505	9	so	so	ADV
ejpam-2660	505	10	f1	f1	NOUN
ejpam-2660	505	11	∩	∩	NOUN
ejpam-2660	505	12	i	i	ADP
ejpam-2660	505	13	6=	6=	NOUN
ejpam-2660	505	14	∅	∅	NOUN
ejpam-2660	505	15	and	and	CCONJ
ejpam-2660	505	16	f2	f2	PROPN
ejpam-2660	505	17	∩	∩	PROPN
ejpam-2660	505	18	i	i	PRON
ejpam-2660	505	19	6=	6=	NOUN
ejpam-2660	505	20	∅.	∅.	VERB
ejpam-2660	505	21	therefore	therefore	ADV
ejpam-2660	505	22	∃a1	∃a1	NOUN
ejpam-2660	505	23	∈	∈	PROPN
ejpam-2660	505	24	f1	f1	NOUN
ejpam-2660	505	25	∩	∩	ADJ
ejpam-2660	505	26	i	i	PRON
ejpam-2660	505	27	and	and	CCONJ
ejpam-2660	505	28	∃b1	∃b1	PROPN
ejpam-2660	505	29	∈	∈	PROPN
ejpam-2660	505	30	f2	f2	PROPN
ejpam-2660	505	31	∩	∩	NOUN
ejpam-2660	505	32	i	i	PRON
ejpam-2660	505	33	,	,	PUNCT
ejpam-2660	505	34	so	so	ADV
ejpam-2660	505	35	there	there	PRON
ejpam-2660	505	36	exist	exist	VERB
ejpam-2660	505	37	d1	d1	NOUN
ejpam-2660	505	38	,	,	PUNCT
ejpam-2660	506	1	d2	d2	PROPN
ejpam-2660	506	2	∈	∈	PROPN
ejpam-2660	506	3	d	d	PROPN
ejpam-2660	506	4	,	,	PUNCT
ejpam-2660	506	5	such	such	ADJ
ejpam-2660	506	6	that	that	DET
ejpam-2660	506	7	a1	a1	NOUN
ejpam-2660	506	8	∈	∈	NOUN
ejpam-2660	506	9	d1	d1	PROPN
ejpam-2660	506	10	∧	∧	PROPN
ejpam-2660	506	11	a′	a′	PROPN
ejpam-2660	506	12	,	,	PUNCT
ejpam-2660	506	13	a′	a′	PROPN
ejpam-2660	506	14	≥	≥	PROPN
ejpam-2660	506	15	a	a	DET
ejpam-2660	506	16	and	and	CCONJ
ejpam-2660	506	17	b1	b1	PROPN
ejpam-2660	506	18	∈	∈	PROPN
ejpam-2660	506	19	d2	d2	PROPN
ejpam-2660	506	20	∧	∧	PROPN
ejpam-2660	506	21	b′	b′	NUM
ejpam-2660	506	22	,	,	PUNCT
ejpam-2660	506	23	b′	b′	NUM
ejpam-2660	506	24	≥	≥	NOUN
ejpam-2660	506	25	b.	b.	NOUN
ejpam-2660	507	1	we	we	PRON
ejpam-2660	507	2	claim	claim	VERB
ejpam-2660	507	3	that	that	SCONJ
ejpam-2660	507	4	a1	a1	NOUN
ejpam-2660	507	5	∨	∨	NUM
ejpam-2660	507	6	b1	b1	NOUN
ejpam-2660	507	7	∈	∈	PROPN
ejpam-2660	507	8	d	d	PROPN
ejpam-2660	507	9	∩	∩	X
ejpam-2660	507	10	i	i	PRON
ejpam-2660	507	11	,	,	PUNCT
ejpam-2660	507	12	which	which	PRON
ejpam-2660	507	13	is	be	AUX
ejpam-2660	507	14	a	a	DET
ejpam-2660	507	15	contradiction	contradiction	NOUN
ejpam-2660	507	16	.	.	PUNCT
ejpam-2660	508	1	by	by	ADP
ejpam-2660	508	2	a′	a′	PROPN
ejpam-2660	508	3	≥	≥	PROPN
ejpam-2660	508	4	a	a	DET
ejpam-2660	508	5	and	and	CCONJ
ejpam-2660	508	6	b′	b′	NUM
ejpam-2660	508	7	≥	≥	NOUN
ejpam-2660	508	8	b	b	X
ejpam-2660	508	9	,	,	PUNCT
ejpam-2660	508	10	we	we	PRON
ejpam-2660	508	11	have	have	VERB
ejpam-2660	508	12	a	a	DET
ejpam-2660	508	13	∨	∨	NUM
ejpam-2660	508	14	b	b	NOUN
ejpam-2660	508	15	≤	≤	NOUN
ejpam-2660	508	16	a′	a′	NOUN
ejpam-2660	508	17	∨	∨	NUM
ejpam-2660	508	18	b′	b′	NUM
ejpam-2660	508	19	and	and	CCONJ
ejpam-2660	508	20	since	since	SCONJ
ejpam-2660	508	21	a	a	DET
ejpam-2660	508	22	∨	∨	NUM
ejpam-2660	508	23	b	b	NOUN
ejpam-2660	508	24	∈	∈	PROPN
ejpam-2660	508	25	d	d	NOUN
ejpam-2660	508	26	and	and	CCONJ
ejpam-2660	508	27	d	d	PROPN
ejpam-2660	508	28	is	be	AUX
ejpam-2660	508	29	a	a	DET
ejpam-2660	508	30	hyperfilter	hyperfilter	NOUN
ejpam-2660	508	31	,	,	PUNCT
ejpam-2660	508	32	a′	a′	PROPN
ejpam-2660	508	33	∨	∨	NUM
ejpam-2660	508	34	b′	b′	ADJ
ejpam-2660	508	35	∈	∈	PROPN
ejpam-2660	508	36	d.	d.	NOUN
ejpam-2660	508	37	since	since	SCONJ
ejpam-2660	508	38	a1	a1	PROPN
ejpam-2660	508	39	,	,	PUNCT
ejpam-2660	508	40	b1	b1	NOUN
ejpam-2660	508	41	∈	∈	PROPN
ejpam-2660	509	1	i	i	PRON
ejpam-2660	509	2	and	and	CCONJ
ejpam-2660	509	3	i	i	PRON
ejpam-2660	509	4	is	be	AUX
ejpam-2660	509	5	a	a	DET
ejpam-2660	509	6	hyperideal	hyperideal	NOUN
ejpam-2660	509	7	,	,	PUNCT
ejpam-2660	509	8	a1∨b1	a1∨b1	NOUN
ejpam-2660	509	9	∈	∈	PROPN
ejpam-2660	509	10	i.	i.	NOUN
ejpam-2660	509	11	also	also	ADV
ejpam-2660	509	12	we	we	PRON
ejpam-2660	509	13	have	have	VERB
ejpam-2660	509	14	a1∨b1	a1∨b1	NOUN
ejpam-2660	509	15	∈	∈	PROPN
ejpam-2660	509	16	(	(	PUNCT
ejpam-2660	509	17	d1∧a′)∨(d2∧b′	d1∧a′)∨(d2∧b′	PROPN
ejpam-2660	509	18	)	)	PUNCT
ejpam-2660	509	19	.	.	PUNCT
ejpam-2660	510	1	l	l	NOUN
ejpam-2660	510	2	is	be	AUX
ejpam-2660	510	3	distributive	distributive	ADJ
ejpam-2660	510	4	,	,	PUNCT
ejpam-2660	510	5	so	so	SCONJ
ejpam-2660	510	6	we	we	PRON
ejpam-2660	510	7	have	have	VERB
ejpam-2660	510	8	:	:	PUNCT
ejpam-2660	510	9	(	(	PUNCT
ejpam-2660	510	10	d1	d1	PROPN
ejpam-2660	510	11	∧	∧	PROPN
ejpam-2660	510	12	a′	a′	NOUN
ejpam-2660	510	13	)	)	PUNCT
ejpam-2660	510	14	∨	∨	PROPN
ejpam-2660	510	15	(	(	PUNCT
ejpam-2660	510	16	d2	d2	PROPN
ejpam-2660	510	17	∧	∧	PROPN
ejpam-2660	510	18	b′	b′	NUM
ejpam-2660	510	19	)	)	PUNCT
ejpam-2660	510	20	=	=	PRON
ejpam-2660	510	21	(	(	PUNCT
ejpam-2660	510	22	d2	d2	PROPN
ejpam-2660	510	23	∨	∨	NUM
ejpam-2660	510	24	d1	d1	NOUN
ejpam-2660	510	25	)	)	PUNCT
ejpam-2660	511	1	∧	∧	PROPN
ejpam-2660	511	2	(	(	PUNCT
ejpam-2660	511	3	d2	d2	PROPN
ejpam-2660	511	4	∨	∨	PROPN
ejpam-2660	511	5	a′	a′	PROPN
ejpam-2660	511	6	)	)	PUNCT
ejpam-2660	511	7	∧	∧	PROPN
ejpam-2660	511	8	(	(	PUNCT
ejpam-2660	511	9	b′	b′	ADJ
ejpam-2660	511	10	∨	∨	NUM
ejpam-2660	511	11	d1	d1	NOUN
ejpam-2660	511	12	)	)	PUNCT
ejpam-2660	511	13	∧	∧	NOUN
ejpam-2660	511	14	(	(	PUNCT
ejpam-2660	511	15	b′	b′	NOUN
ejpam-2660	511	16	∨	∨	NUM
ejpam-2660	511	17	a′	a′	NOUN
ejpam-2660	511	18	)	)	PUNCT
ejpam-2660	512	1	∈	∈	PROPN
ejpam-2660	512	2	d.	d.	NOUN
ejpam-2660	512	3	so	so	ADV
ejpam-2660	512	4	a1	a1	PROPN
ejpam-2660	512	5	∨	∨	NUM
ejpam-2660	512	6	b1	b1	PROPN
ejpam-2660	512	7	∈	∈	PROPN
ejpam-2660	512	8	d.	d.	NOUN
ejpam-2660	512	9	thus	thus	ADV
ejpam-2660	512	10	a1	a1	VERB
ejpam-2660	512	11	∨	∨	NUM
ejpam-2660	512	12	b1	b1	NOUN
ejpam-2660	512	13	∈	∈	PROPN
ejpam-2660	512	14	d	d	PROPN
ejpam-2660	512	15	∩	∩	PROPN
ejpam-2660	512	16	i.	i.	PROPN
ejpam-2660	512	17	corollary	corollary	PROPN
ejpam-2660	512	18	63	63	NUM
ejpam-2660	512	19	.	.	PUNCT
ejpam-2660	513	1	(	(	PUNCT
ejpam-2660	513	2	i	i	NOUN
ejpam-2660	513	3	)	)	PUNCT
ejpam-2660	513	4	let	let	VERB
ejpam-2660	513	5	l	l	NOUN
ejpam-2660	513	6	be	be	AUX
ejpam-2660	513	7	distributive	distributive	ADJ
ejpam-2660	513	8	,	,	PUNCT
ejpam-2660	513	9	and	and	CCONJ
ejpam-2660	513	10	a	a	DET
ejpam-2660	513	11	∈	∈	PROPN
ejpam-2660	513	12	l.	l.	NOUN
ejpam-2660	513	13	if	if	SCONJ
ejpam-2660	513	14	f	f	PROPN
ejpam-2660	513	15	is	be	AUX
ejpam-2660	513	16	a	a	DET
ejpam-2660	513	17	hyperfilter	hyperfilter	NOUN
ejpam-2660	513	18	of	of	ADP
ejpam-2660	513	19	l	l	NOUN
ejpam-2660	513	20	,	,	PUNCT
ejpam-2660	513	21	such	such	ADJ
ejpam-2660	513	22	that	that	SCONJ
ejpam-2660	513	23	a	a	DET
ejpam-2660	513	24	/∈	/∈	NOUN
ejpam-2660	513	25	f	f	NOUN
ejpam-2660	513	26	,	,	PUNCT
ejpam-2660	513	27	then	then	ADV
ejpam-2660	513	28	there	there	PRON
ejpam-2660	513	29	exists	exist	VERB
ejpam-2660	513	30	prime	prime	ADJ
ejpam-2660	513	31	hyperfilter	hyperfilter	PROPN
ejpam-2660	513	32	d	d	PROPN
ejpam-2660	513	33	,	,	PUNCT
ejpam-2660	513	34	such	such	ADJ
ejpam-2660	513	35	that	that	SCONJ
ejpam-2660	513	36	f	f	PROPN
ejpam-2660	513	37	⊆	⊆	NUM
ejpam-2660	513	38	d	d	PROPN
ejpam-2660	513	39	,	,	PUNCT
ejpam-2660	513	40	and	and	CCONJ
ejpam-2660	513	41	a	a	DET
ejpam-2660	513	42	/∈	/∈	INTJ
ejpam-2660	513	43	d.	d.	PROPN
ejpam-2660	513	44	(	(	PUNCT
ejpam-2660	513	45	ii	ii	PROPN
ejpam-2660	513	46	)	)	PUNCT
ejpam-2660	513	47	let	let	VERB
ejpam-2660	513	48	l	l	NOUN
ejpam-2660	513	49	be	be	AUX
ejpam-2660	513	50	a	a	DET
ejpam-2660	513	51	distributive	distributive	ADJ
ejpam-2660	513	52	”	"	PUNCT
ejpam-2660	513	53	∧	∧	NOUN
ejpam-2660	513	54	”	"	PUNCT
ejpam-2660	513	55	-hyperlattice	-hyperlattice	NOUN
ejpam-2660	513	56	,	,	PUNCT
ejpam-2660	513	57	and	and	CCONJ
ejpam-2660	513	58	a	a	DET
ejpam-2660	513	59	,	,	PUNCT
ejpam-2660	513	60	b	b	PROPN
ejpam-2660	513	61	∈	∈	PROPN
ejpam-2660	513	62	l.	l.	NOUN
ejpam-2660	513	63	if	if	SCONJ
ejpam-2660	513	64	a	a	DET
ejpam-2660	513	65	6=	6=	PROPN
ejpam-2660	513	66	b	b	NOUN
ejpam-2660	513	67	,	,	PUNCT
ejpam-2660	513	68	then	then	ADV
ejpam-2660	513	69	there	there	PRON
ejpam-2660	513	70	exists	exist	VERB
ejpam-2660	513	71	prime	prime	ADJ
ejpam-2660	513	72	hyperfilter	hyperfilter	PROPN
ejpam-2660	513	73	d	d	PROPN
ejpam-2660	513	74	of	of	ADP
ejpam-2660	513	75	l	l	NOUN
ejpam-2660	513	76	,	,	PUNCT
ejpam-2660	513	77	such	such	ADJ
ejpam-2660	513	78	that	that	SCONJ
ejpam-2660	513	79	a	a	DET
ejpam-2660	513	80	∈	∈	ADJ
ejpam-2660	513	81	d	d	NOUN
ejpam-2660	513	82	,	,	PUNCT
ejpam-2660	513	83	and	and	CCONJ
ejpam-2660	513	84	b	b	X
ejpam-2660	513	85	/∈	/∈	PROPN
ejpam-2660	513	86	d.	d.	PROPN
ejpam-2660	513	87	theorem	theorem	VERB
ejpam-2660	513	88	64	64	NUM
ejpam-2660	513	89	(	(	PUNCT
ejpam-2660	513	90	prime	prime	ADJ
ejpam-2660	513	91	hyperideal	hyperideal	NOUN
ejpam-2660	513	92	theorem	theorem	NOUN
ejpam-2660	513	93	)	)	PUNCT
ejpam-2660	513	94	.	.	PUNCT
ejpam-2660	514	1	let	let	VERB
ejpam-2660	514	2	l	l	NOUN
ejpam-2660	514	3	be	be	AUX
ejpam-2660	514	4	dual	dual	ADV
ejpam-2660	514	5	distributive	distributive	ADJ
ejpam-2660	514	6	.	.	PUNCT
ejpam-2660	515	1	if	if	SCONJ
ejpam-2660	515	2	i	i	PRON
ejpam-2660	515	3	is	be	AUX
ejpam-2660	515	4	a	a	DET
ejpam-2660	515	5	hyperideal	hyperideal	NOUN
ejpam-2660	515	6	and	and	CCONJ
ejpam-2660	515	7	f	f	PROPN
ejpam-2660	515	8	is	be	AUX
ejpam-2660	515	9	a	a	DET
ejpam-2660	515	10	hyperfilter	hyperfilter	NOUN
ejpam-2660	515	11	of	of	ADP
ejpam-2660	515	12	l	l	NOUN
ejpam-2660	515	13	,	,	PUNCT
ejpam-2660	515	14	such	such	ADJ
ejpam-2660	515	15	that	that	SCONJ
ejpam-2660	515	16	i	i	PRON
ejpam-2660	515	17	∩	∩	NOUN
ejpam-2660	515	18	f	f	X
ejpam-2660	515	19	=	=	SYM
ejpam-2660	515	20	∅	∅	NOUN
ejpam-2660	515	21	,	,	PUNCT
ejpam-2660	515	22	then	then	ADV
ejpam-2660	515	23	there	there	PRON
ejpam-2660	515	24	exists	exist	VERB
ejpam-2660	515	25	prime	prime	ADJ
ejpam-2660	515	26	hyperideal	hyperideal	NOUN
ejpam-2660	515	27	p	p	NOUN
ejpam-2660	515	28	of	of	ADP
ejpam-2660	515	29	l	l	NOUN
ejpam-2660	515	30	,	,	PUNCT
ejpam-2660	515	31	such	such	ADJ
ejpam-2660	515	32	that	that	SCONJ
ejpam-2660	515	33	i	i	PRON
ejpam-2660	515	34	⊆	⊆	NUM
ejpam-2660	515	35	p	p	NOUN
ejpam-2660	515	36	and	and	CCONJ
ejpam-2660	515	37	p	p	NOUN
ejpam-2660	515	38	∩	∩	ADJ
ejpam-2660	515	39	f	f	X
ejpam-2660	515	40	=	=	PUNCT
ejpam-2660	515	41	∅.	∅.	PROPN
ejpam-2660	515	42	definition	definition	NOUN
ejpam-2660	515	43	65	65	NUM
ejpam-2660	515	44	.	.	PUNCT
ejpam-2660	516	1	let	let	VERB
ejpam-2660	516	2	l	l	NOUN
ejpam-2660	516	3	be	be	AUX
ejpam-2660	516	4	a	a	DET
ejpam-2660	516	5	bounded	bounded	ADJ
ejpam-2660	516	6	∧−hyperlattice	∧−hyperlattice	NOUN
ejpam-2660	516	7	.	.	PUNCT
ejpam-2660	517	1	then	then	ADV
ejpam-2660	517	2	:	:	PUNCT
ejpam-2660	517	3	m.	m.	NOUN
ejpam-2660	517	4	amiri	amiri	PROPN
ejpam-2660	517	5	bideshki	bideshki	PROPN
ejpam-2660	517	6	,	,	PUNCT
ejpam-2660	517	7	r.	r.	PROPN
ejpam-2660	517	8	ameri	ameri	PROPN
ejpam-2660	517	9	,	,	PUNCT
ejpam-2660	517	10	a.	a.	PROPN
ejpam-2660	517	11	borumand	borumand	PROPN
ejpam-2660	517	12	saeid	saeid	PROPN
ejpam-2660	517	13	/	/	SYM
ejpam-2660	517	14	eur	eur	PROPN
ejpam-2660	517	15	.	.	PUNCT
ejpam-2660	518	1	j.	j.	PROPN
ejpam-2660	518	2	pure	pure	PROPN
ejpam-2660	518	3	appl	appl	PROPN
ejpam-2660	518	4	.	.	PROPN
ejpam-2660	518	5	math	math	PROPN
ejpam-2660	518	6	,	,	PUNCT
ejpam-2660	518	7	11	11	NUM
ejpam-2660	518	8	(	(	PUNCT
ejpam-2660	518	9	1	1	NUM
ejpam-2660	518	10	)	)	PUNCT
ejpam-2660	518	11	(	(	PUNCT
ejpam-2660	518	12	2018	2018	NUM
ejpam-2660	518	13	)	)	PUNCT
ejpam-2660	518	14	,	,	PUNCT
ejpam-2660	518	15	169	169	NUM
ejpam-2660	518	16	-	-	SYM
ejpam-2660	518	17	188	188	NUM
ejpam-2660	518	18	184	184	NUM
ejpam-2660	518	19	(	(	PUNCT
ejpam-2660	518	20	i	i	NOUN
ejpam-2660	518	21	)	)	PUNCT
ejpam-2660	518	22	x′	x′	PROPN
ejpam-2660	519	1	∈	∈	PROPN
ejpam-2660	519	2	l	l	NOUN
ejpam-2660	519	3	is	be	AUX
ejpam-2660	519	4	called	call	VERB
ejpam-2660	519	5	a	a	DET
ejpam-2660	519	6	complement	complement	NOUN
ejpam-2660	519	7	of	of	ADP
ejpam-2660	519	8	x	x	X
ejpam-2660	519	9	∈	∈	PROPN
ejpam-2660	519	10	l	l	NOUN
ejpam-2660	519	11	,	,	PUNCT
ejpam-2660	519	12	if	if	SCONJ
ejpam-2660	519	13	0	0	NUM
ejpam-2660	519	14	∈	∈	NOUN
ejpam-2660	519	15	x	x	X
ejpam-2660	519	16	∧	∧	PROPN
ejpam-2660	519	17	x′	x′	PROPN
ejpam-2660	519	18	and	and	CCONJ
ejpam-2660	519	19	x	x	PROPN
ejpam-2660	519	20	∨	∨	NUM
ejpam-2660	519	21	x′	x′	PROPN
ejpam-2660	520	1	=	=	SYM
ejpam-2660	520	2	1	1	X
ejpam-2660	520	3	.	.	PUNCT
ejpam-2660	521	1	also	also	ADV
ejpam-2660	521	2	,	,	PUNCT
ejpam-2660	521	3	we	we	PRON
ejpam-2660	521	4	say	say	VERB
ejpam-2660	521	5	that	that	SCONJ
ejpam-2660	521	6	x	x	PUNCT
ejpam-2660	521	7	∈	∈	NOUN
ejpam-2660	521	8	l	l	NOUN
ejpam-2660	521	9	has	have	VERB
ejpam-2660	521	10	a	a	DET
ejpam-2660	521	11	complement	complement	NOUN
ejpam-2660	521	12	if	if	SCONJ
ejpam-2660	521	13	there	there	PRON
ejpam-2660	521	14	exists	exist	VERB
ejpam-2660	521	15	x′	x′	PROPN
ejpam-2660	521	16	∈	∈	PROPN
ejpam-2660	521	17	l	l	NOUN
ejpam-2660	522	1	such	such	ADJ
ejpam-2660	522	2	that	that	DET
ejpam-2660	522	3	0	0	NUM
ejpam-2660	522	4	∈	∈	NOUN
ejpam-2660	522	5	x	x	X
ejpam-2660	522	6	∧	∧	PROPN
ejpam-2660	522	7	x′	x′	PROPN
ejpam-2660	522	8	and	and	CCONJ
ejpam-2660	522	9	x	x	PROPN
ejpam-2660	522	10	∨	∨	NUM
ejpam-2660	522	11	x′	x′	PROPN
ejpam-2660	522	12	=	=	SYM
ejpam-2660	522	13	1	1	X
ejpam-2660	522	14	.	.	PUNCT
ejpam-2660	523	1	also	also	ADV
ejpam-2660	523	2	we	we	PRON
ejpam-2660	523	3	say	say	VERB
ejpam-2660	523	4	that	that	SCONJ
ejpam-2660	523	5	the	the	DET
ejpam-2660	523	6	∧-hyperlattice	∧-hyperlattice	NOUN
ejpam-2660	523	7	l	l	NOUN
ejpam-2660	523	8	is	be	AUX
ejpam-2660	523	9	complemented	complement	VERB
ejpam-2660	523	10	if	if	SCONJ
ejpam-2660	523	11	every	every	DET
ejpam-2660	523	12	element	element	NOUN
ejpam-2660	523	13	x	x	SYM
ejpam-2660	523	14	∈	∈	NOUN
ejpam-2660	523	15	l	l	NOUN
ejpam-2660	523	16	has	have	VERB
ejpam-2660	523	17	a	a	DET
ejpam-2660	523	18	complement	complement	NOUN
ejpam-2660	523	19	.	.	PUNCT
ejpam-2660	524	1	(	(	PUNCT
ejpam-2660	524	2	ii	ii	NOUN
ejpam-2660	524	3	)	)	PUNCT
ejpam-2660	524	4	l	l	NOUN
ejpam-2660	524	5	is	be	AUX
ejpam-2660	524	6	called	call	VERB
ejpam-2660	524	7	a	a	DET
ejpam-2660	524	8	good	good	ADJ
ejpam-2660	524	9	complemented	complemented	ADJ
ejpam-2660	524	10	∧-hyperlattice	∧-hyperlattice	NOUN
ejpam-2660	524	11	,	,	PUNCT
ejpam-2660	524	12	if	if	SCONJ
ejpam-2660	524	13	for	for	ADP
ejpam-2660	524	14	all	all	DET
ejpam-2660	524	15	x	x	SYM
ejpam-2660	524	16	∈	∈	NOUN
ejpam-2660	524	17	l	l	NOUN
ejpam-2660	524	18	,	,	PUNCT
ejpam-2660	524	19	there	there	PRON
ejpam-2660	524	20	exists	exist	VERB
ejpam-2660	524	21	x′	x′	PROPN
ejpam-2660	524	22	∈	∈	PROPN
ejpam-2660	524	23	l	l	NOUN
ejpam-2660	524	24	such	such	ADJ
ejpam-2660	524	25	that	that	SCONJ
ejpam-2660	524	26	x	x	X
ejpam-2660	524	27	∧	∧	NOUN
ejpam-2660	524	28	x′	x′	X
ejpam-2660	524	29	=	=	PUNCT
ejpam-2660	524	30	{	{	PUNCT
ejpam-2660	524	31	0	0	NUM
ejpam-2660	524	32	}	}	PUNCT
ejpam-2660	524	33	and	and	CCONJ
ejpam-2660	524	34	x	x	X
ejpam-2660	524	35	∨	∨	NUM
ejpam-2660	524	36	x′	x′	X
ejpam-2660	524	37	=	=	SYM
ejpam-2660	524	38	1	1	NUM
ejpam-2660	524	39	example	example	NOUN
ejpam-2660	524	40	66	66	NUM
ejpam-2660	524	41	.	.	PUNCT
ejpam-2660	525	1	let	let	VERB
ejpam-2660	525	2	l	l	NOUN
ejpam-2660	525	3	=	=	PUNCT
ejpam-2660	525	4	{	{	PUNCT
ejpam-2660	525	5	0	0	NUM
ejpam-2660	525	6	,	,	PUNCT
ejpam-2660	525	7	x	x	NOUN
ejpam-2660	525	8	,	,	PUNCT
ejpam-2660	525	9	y	y	PROPN
ejpam-2660	525	10	,	,	PUNCT
ejpam-2660	525	11	z	z	PROPN
ejpam-2660	525	12	,	,	PUNCT
ejpam-2660	525	13	1	1	NUM
ejpam-2660	525	14	}	}	PUNCT
ejpam-2660	525	15	.	.	PUNCT
ejpam-2660	526	1	define	define	VERB
ejpam-2660	526	2	∧	∧	PROPN
ejpam-2660	526	3	and	and	CCONJ
ejpam-2660	526	4	∨	∨	NOUN
ejpam-2660	526	5	with	with	ADP
ejpam-2660	526	6	tables	table	NOUN
ejpam-2660	526	7	6	6	NUM
ejpam-2660	526	8	then	then	ADV
ejpam-2660	526	9	(	(	PUNCT
ejpam-2660	526	10	l,∧,∨	l,∧,∨	X
ejpam-2660	526	11	)	)	PUNCT
ejpam-2660	526	12	is	be	AUX
ejpam-2660	526	13	a	a	DET
ejpam-2660	526	14	∧	∧	PROPN
ejpam-2660	526	15	0	0	PUNCT
ejpam-2660	526	16	x	x	SYM
ejpam-2660	526	17	y	y	PROPN
ejpam-2660	526	18	z	z	PROPN
ejpam-2660	526	19	1	1	NUM
ejpam-2660	526	20	0	0	NUM
ejpam-2660	526	21	{	{	PUNCT
ejpam-2660	526	22	0	0	NUM
ejpam-2660	526	23	}	}	PUNCT
ejpam-2660	526	24	{	{	PUNCT
ejpam-2660	526	25	0	0	NUM
ejpam-2660	526	26	}	}	PUNCT
ejpam-2660	526	27	{	{	PUNCT
ejpam-2660	526	28	0	0	NUM
ejpam-2660	526	29	}	}	PUNCT
ejpam-2660	526	30	{	{	PUNCT
ejpam-2660	526	31	0	0	NUM
ejpam-2660	526	32	}	}	PUNCT
ejpam-2660	526	33	{	{	PUNCT
ejpam-2660	526	34	0	0	NUM
ejpam-2660	526	35	}	}	PUNCT
ejpam-2660	526	36	x	x	X
ejpam-2660	526	37	{	{	PUNCT
ejpam-2660	526	38	0	0	NUM
ejpam-2660	526	39	}	}	PUNCT
ejpam-2660	526	40	{	{	PUNCT
ejpam-2660	526	41	0	0	NUM
ejpam-2660	526	42	,	,	PUNCT
ejpam-2660	526	43	x	x	NOUN
ejpam-2660	526	44	}	}	PUNCT
ejpam-2660	526	45	{	{	PUNCT
ejpam-2660	526	46	0	0	NUM
ejpam-2660	526	47	,	,	PUNCT
ejpam-2660	526	48	x	x	NOUN
ejpam-2660	526	49	}	}	PUNCT
ejpam-2660	526	50	{	{	PUNCT
ejpam-2660	526	51	0	0	NUM
ejpam-2660	526	52	}	}	PUNCT
ejpam-2660	526	53	{	{	PUNCT
ejpam-2660	526	54	0	0	NUM
ejpam-2660	526	55	,	,	PUNCT
ejpam-2660	526	56	x	x	ADJ
ejpam-2660	526	57	}	}	PUNCT
ejpam-2660	526	58	y	y	PROPN
ejpam-2660	526	59	{	{	PUNCT
ejpam-2660	526	60	0	0	NUM
ejpam-2660	526	61	}	}	PUNCT
ejpam-2660	526	62	{	{	PUNCT
ejpam-2660	526	63	0	0	NUM
ejpam-2660	526	64	,	,	PUNCT
ejpam-2660	526	65	x	x	NOUN
ejpam-2660	526	66	}	}	PUNCT
ejpam-2660	526	67	{	{	PUNCT
ejpam-2660	526	68	y	y	NOUN
ejpam-2660	526	69	}	}	PUNCT
ejpam-2660	526	70	{	{	PUNCT
ejpam-2660	526	71	0	0	NUM
ejpam-2660	526	72	}	}	PUNCT
ejpam-2660	526	73	{	{	PUNCT
ejpam-2660	526	74	y	y	NOUN
ejpam-2660	526	75	}	}	PUNCT
ejpam-2660	526	76	z	z	NOUN
ejpam-2660	526	77	{	{	PUNCT
ejpam-2660	526	78	0	0	NUM
ejpam-2660	526	79	}	}	PUNCT
ejpam-2660	526	80	{	{	PUNCT
ejpam-2660	526	81	0	0	NUM
ejpam-2660	526	82	}	}	PUNCT
ejpam-2660	526	83	{	{	PUNCT
ejpam-2660	526	84	0	0	NUM
ejpam-2660	526	85	}	}	PUNCT
ejpam-2660	526	86	{	{	PUNCT
ejpam-2660	526	87	z	z	NOUN
ejpam-2660	526	88	}	}	PUNCT
ejpam-2660	526	89	{	{	PUNCT
ejpam-2660	526	90	z	z	NOUN
ejpam-2660	526	91	}	}	PUNCT
ejpam-2660	526	92	1	1	NUM
ejpam-2660	526	93	{	{	PUNCT
ejpam-2660	526	94	0	0	NUM
ejpam-2660	526	95	}	}	PUNCT
ejpam-2660	526	96	{	{	PUNCT
ejpam-2660	526	97	0	0	NUM
ejpam-2660	526	98	,	,	PUNCT
ejpam-2660	526	99	x	x	NOUN
ejpam-2660	526	100	}	}	PUNCT
ejpam-2660	526	101	{	{	PUNCT
ejpam-2660	526	102	y	y	NOUN
ejpam-2660	526	103	}	}	PUNCT
ejpam-2660	526	104	{	{	PUNCT
ejpam-2660	526	105	z	z	NOUN
ejpam-2660	526	106	}	}	PUNCT
ejpam-2660	526	107	{	{	PUNCT
ejpam-2660	526	108	1	1	NUM
ejpam-2660	526	109	}	}	PUNCT
ejpam-2660	526	110	(	(	PUNCT
ejpam-2660	526	111	a	a	X
ejpam-2660	526	112	)	)	PUNCT
ejpam-2660	526	113	∨	∨	NOUN
ejpam-2660	526	114	0	0	NUM
ejpam-2660	527	1	x	x	SYM
ejpam-2660	527	2	y	y	PROPN
ejpam-2660	527	3	z	z	PROPN
ejpam-2660	527	4	1	1	NUM
ejpam-2660	527	5	0	0	NUM
ejpam-2660	527	6	0	0	NUM
ejpam-2660	527	7	x	x	SYM
ejpam-2660	527	8	y	y	PROPN
ejpam-2660	527	9	z	z	PROPN
ejpam-2660	527	10	1	1	NUM
ejpam-2660	527	11	x	x	SYM
ejpam-2660	527	12	x	x	SYM
ejpam-2660	527	13	x	x	SYM
ejpam-2660	527	14	y	y	NOUN
ejpam-2660	527	15	1	1	NUM
ejpam-2660	527	16	1	1	NUM
ejpam-2660	527	17	y	y	PROPN
ejpam-2660	527	18	y	y	PROPN
ejpam-2660	527	19	y	y	PROPN
ejpam-2660	527	20	y	y	PROPN
ejpam-2660	527	21	1	1	NUM
ejpam-2660	527	22	1	1	NUM
ejpam-2660	527	23	1	1	NUM
ejpam-2660	527	24	1	1	NUM
ejpam-2660	527	25	1	1	NUM
ejpam-2660	527	26	1	1	NUM
ejpam-2660	527	27	1	1	NUM
ejpam-2660	527	28	1	1	NUM
ejpam-2660	527	29	(	(	PUNCT
ejpam-2660	527	30	b	b	NOUN
ejpam-2660	527	31	)	)	PUNCT
ejpam-2660	527	32	table	table	NOUN
ejpam-2660	527	33	6	6	NUM
ejpam-2660	527	34	∧−hyperlattice	∧−hyperlattice	NOUN
ejpam-2660	527	35	;	;	PUNCT
ejpam-2660	527	36	we	we	PRON
ejpam-2660	527	37	have	have	VERB
ejpam-2660	527	38	0	0	NUM
ejpam-2660	527	39	∈	∈	PROPN
ejpam-2660	527	40	y	y	PROPN
ejpam-2660	527	41	∧	∧	PROPN
ejpam-2660	527	42	z	z	PROPN
ejpam-2660	527	43	and	and	CCONJ
ejpam-2660	527	44	y	y	PROPN
ejpam-2660	527	45	∨	∨	PROPN
ejpam-2660	527	46	z	z	PROPN
ejpam-2660	527	47	=	=	SYM
ejpam-2660	527	48	1	1	NUM
ejpam-2660	527	49	also	also	ADV
ejpam-2660	527	50	,	,	PUNCT
ejpam-2660	527	51	0	0	NUM
ejpam-2660	527	52	∈	∈	PROPN
ejpam-2660	527	53	x∧	x∧	PROPN
ejpam-2660	527	54	z	z	PROPN
ejpam-2660	527	55	and	and	CCONJ
ejpam-2660	527	56	x∨	x∨	PROPN
ejpam-2660	527	57	z	z	NOUN
ejpam-2660	527	58	=	=	SYM
ejpam-2660	527	59	1	1	NUM
ejpam-2660	527	60	,	,	PUNCT
ejpam-2660	527	61	so	so	ADV
ejpam-2660	527	62	y	y	PROPN
ejpam-2660	527	63	,	,	PUNCT
ejpam-2660	527	64	x	x	PRON
ejpam-2660	527	65	are	be	AUX
ejpam-2660	527	66	complement	complement	NOUN
ejpam-2660	527	67	of	of	ADP
ejpam-2660	527	68	z.	z.	PROPN
ejpam-2660	527	69	also	also	ADV
ejpam-2660	527	70	l	l	PROPN
ejpam-2660	527	71	is	be	AUX
ejpam-2660	527	72	a	a	DET
ejpam-2660	527	73	good	good	ADJ
ejpam-2660	527	74	complemented	complemented	ADJ
ejpam-2660	527	75	∧-hyperlattice	∧-hyperlattice	NOUN
ejpam-2660	527	76	.	.	PUNCT
ejpam-2660	528	1	proposition	proposition	NOUN
ejpam-2660	528	2	67	67	NUM
ejpam-2660	528	3	.	.	PUNCT
ejpam-2660	529	1	let	let	VERB
ejpam-2660	529	2	l	l	NOUN
ejpam-2660	529	3	be	be	AUX
ejpam-2660	529	4	a	a	DET
ejpam-2660	529	5	bounded	bound	VERB
ejpam-2660	529	6	strongly	strongly	ADV
ejpam-2660	529	7	distributive	distributive	ADJ
ejpam-2660	529	8	∧-hyperlattice	∧-hyperlattice	NOUN
ejpam-2660	529	9	.	.	PUNCT
ejpam-2660	530	1	then	then	ADV
ejpam-2660	530	2	the	the	DET
ejpam-2660	530	3	following	follow	VERB
ejpam-2660	530	4	conditions	condition	NOUN
ejpam-2660	530	5	hold	hold	VERB
ejpam-2660	530	6	.	.	PUNCT
ejpam-2660	531	1	(	(	PUNCT
ejpam-2660	531	2	i	i	NOUN
ejpam-2660	531	3	)	)	PUNCT
ejpam-2660	531	4	if	if	SCONJ
ejpam-2660	531	5	a	a	PRON
ejpam-2660	531	6	,	,	PUNCT
ejpam-2660	531	7	b	b	NOUN
ejpam-2660	531	8	are	be	AUX
ejpam-2660	531	9	complement	complement	NOUN
ejpam-2660	531	10	of	of	ADP
ejpam-2660	531	11	x	x	NOUN
ejpam-2660	531	12	,	,	PUNCT
ejpam-2660	531	13	then	then	ADV
ejpam-2660	531	14	a	a	DET
ejpam-2660	531	15	∨	∨	PROPN
ejpam-2660	531	16	b	b	NOUN
ejpam-2660	531	17	is	be	AUX
ejpam-2660	531	18	so	so	ADV
ejpam-2660	531	19	.	.	PUNCT
ejpam-2660	532	1	(	(	PUNCT
ejpam-2660	532	2	ii	ii	NOUN
ejpam-2660	532	3	)	)	PUNCT
ejpam-2660	532	4	if	if	SCONJ
ejpam-2660	532	5	a	a	PRON
ejpam-2660	532	6	,	,	PUNCT
ejpam-2660	532	7	b	b	NOUN
ejpam-2660	532	8	are	be	AUX
ejpam-2660	532	9	complements	complement	NOUN
ejpam-2660	532	10	of	of	ADP
ejpam-2660	532	11	x	x	PUNCT
ejpam-2660	532	12	and	and	CCONJ
ejpam-2660	532	13	x	x	PART
ejpam-2660	532	14	∧	∧	NOUN
ejpam-2660	532	15	x	x	X
ejpam-2660	532	16	=	=	SYM
ejpam-2660	532	17	x	x	NOUN
ejpam-2660	532	18	,	,	PUNCT
ejpam-2660	532	19	then	then	ADV
ejpam-2660	532	20	there	there	PRON
ejpam-2660	532	21	exists	exist	VERB
ejpam-2660	532	22	c	c	NOUN
ejpam-2660	532	23	,	,	PUNCT
ejpam-2660	532	24	d	d	PROPN
ejpam-2660	532	25	∈	∈	PROPN
ejpam-2660	532	26	a	a	DET
ejpam-2660	532	27	∧	∧	PROPN
ejpam-2660	532	28	b	b	PROPN
ejpam-2660	532	29	such	such	ADJ
ejpam-2660	532	30	that	that	DET
ejpam-2660	532	31	1	1	NUM
ejpam-2660	532	32	=	=	SYM
ejpam-2660	532	33	x	x	SYM
ejpam-2660	532	34	∨	∨	NUM
ejpam-2660	532	35	c	c	NOUN
ejpam-2660	532	36	and	and	CCONJ
ejpam-2660	532	37	0	0	NUM
ejpam-2660	532	38	∈	∈	NOUN
ejpam-2660	532	39	x	x	PUNCT
ejpam-2660	532	40	∧	∧	NOUN
ejpam-2660	532	41	d.	d.	PROPN
ejpam-2660	532	42	proof	proof	NOUN
ejpam-2660	532	43	.	.	PUNCT
ejpam-2660	533	1	(	(	PUNCT
ejpam-2660	533	2	i	i	NOUN
ejpam-2660	533	3	):	):	PUNCT
ejpam-2660	533	4	we	we	PRON
ejpam-2660	533	5	have	have	VERB
ejpam-2660	533	6	0	0	NUM
ejpam-2660	533	7	∈	∈	NOUN
ejpam-2660	533	8	x	x	PUNCT
ejpam-2660	533	9	∧	∧	NOUN
ejpam-2660	533	10	a	a	PRON
ejpam-2660	533	11	and	and	CCONJ
ejpam-2660	533	12	x	x	SYM
ejpam-2660	533	13	∨	∨	NOUN
ejpam-2660	533	14	a	a	DET
ejpam-2660	533	15	=	=	SYM
ejpam-2660	533	16	1	1	NUM
ejpam-2660	533	17	,	,	PUNCT
ejpam-2660	533	18	also	also	ADV
ejpam-2660	533	19	0	0	NUM
ejpam-2660	533	20	∈	∈	ADJ
ejpam-2660	533	21	x	x	X
ejpam-2660	533	22	∧	∧	PROPN
ejpam-2660	533	23	b	b	PROPN
ejpam-2660	533	24	and	and	CCONJ
ejpam-2660	533	25	x	x	PROPN
ejpam-2660	533	26	∨	∨	NUM
ejpam-2660	533	27	b	b	NOUN
ejpam-2660	533	28	=	=	SYM
ejpam-2660	533	29	1	1	X
ejpam-2660	533	30	.	.	PUNCT
ejpam-2660	534	1	since	since	SCONJ
ejpam-2660	534	2	0	0	NUM
ejpam-2660	534	3	∧	∧	NOUN
ejpam-2660	534	4	0	0	NUM
ejpam-2660	535	1	=	=	SYM
ejpam-2660	535	2	0	0	NUM
ejpam-2660	535	3	and	and	CCONJ
ejpam-2660	535	4	l	l	NOUN
ejpam-2660	535	5	is	be	AUX
ejpam-2660	535	6	dual	dual	ADV
ejpam-2660	535	7	distributive	distributive	ADJ
ejpam-2660	535	8	,	,	PUNCT
ejpam-2660	535	9	we	we	PRON
ejpam-2660	535	10	have	have	VERB
ejpam-2660	535	11	:	:	PUNCT
ejpam-2660	535	12	0	0	NUM
ejpam-2660	535	13	∈	∈	NOUN
ejpam-2660	535	14	(	(	PUNCT
ejpam-2660	535	15	x	x	PART
ejpam-2660	535	16	∧	∧	NOUN
ejpam-2660	535	17	a	a	PRON
ejpam-2660	535	18	)	)	PUNCT
ejpam-2660	535	19	∨	∨	NOUN
ejpam-2660	535	20	(	(	PUNCT
ejpam-2660	535	21	x	x	PROPN
ejpam-2660	535	22	∧	∧	PROPN
ejpam-2660	535	23	b	b	NOUN
ejpam-2660	535	24	)	)	PUNCT
ejpam-2660	535	25	=	=	SYM
ejpam-2660	535	26	x	x	SYM
ejpam-2660	535	27	∧	∧	PROPN
ejpam-2660	535	28	(	(	PUNCT
ejpam-2660	535	29	a	a	DET
ejpam-2660	535	30	∨	∨	NUM
ejpam-2660	535	31	b	b	NOUN
ejpam-2660	535	32	)	)	PUNCT
ejpam-2660	535	33	,	,	PUNCT
ejpam-2660	535	34	thus	thus	ADV
ejpam-2660	535	35	0	0	NUM
ejpam-2660	535	36	∈	∈	NOUN
ejpam-2660	535	37	x	x	PUNCT
ejpam-2660	535	38	∧	∧	NOUN
ejpam-2660	535	39	(	(	PUNCT
ejpam-2660	535	40	a	a	DET
ejpam-2660	535	41	∨	∨	NUM
ejpam-2660	535	42	b	b	NOUN
ejpam-2660	535	43	)	)	PUNCT
ejpam-2660	535	44	.	.	PUNCT
ejpam-2660	536	1	also	also	ADV
ejpam-2660	536	2	1	1	NUM
ejpam-2660	536	3	=	=	SYM
ejpam-2660	536	4	1	1	NUM
ejpam-2660	536	5	∨	∨	NUM
ejpam-2660	536	6	1	1	NUM
ejpam-2660	537	1	and	and	CCONJ
ejpam-2660	537	2	we	we	PRON
ejpam-2660	537	3	have	have	VERB
ejpam-2660	537	4	:	:	PUNCT
ejpam-2660	537	5	1	1	NUM
ejpam-2660	537	6	=	=	SYM
ejpam-2660	537	7	1	1	NUM
ejpam-2660	537	8	∨	∨	NUM
ejpam-2660	537	9	1	1	NUM
ejpam-2660	537	10	=	=	SYM
ejpam-2660	537	11	(	(	PUNCT
ejpam-2660	537	12	x	x	PROPN
ejpam-2660	537	13	∨	∨	NUM
ejpam-2660	537	14	a	a	PRON
ejpam-2660	537	15	)	)	PUNCT
ejpam-2660	537	16	∨	∨	NOUN
ejpam-2660	537	17	(	(	PUNCT
ejpam-2660	537	18	x	x	PROPN
ejpam-2660	537	19	∨	∨	NUM
ejpam-2660	537	20	b	b	NOUN
ejpam-2660	537	21	)	)	PUNCT
ejpam-2660	537	22	=	=	SYM
ejpam-2660	538	1	x	x	SYM
ejpam-2660	538	2	∨	∨	X
ejpam-2660	538	3	(	(	PUNCT
ejpam-2660	538	4	a	a	DET
ejpam-2660	538	5	∨	∨	PROPN
ejpam-2660	538	6	b	b	NOUN
ejpam-2660	538	7	)	)	PUNCT
ejpam-2660	538	8	,	,	PUNCT
ejpam-2660	538	9	thus	thus	ADV
ejpam-2660	538	10	x	x	X
ejpam-2660	538	11	∨	∨	NOUN
ejpam-2660	538	12	(	(	PUNCT
ejpam-2660	538	13	a	a	DET
ejpam-2660	538	14	∨	∨	NUM
ejpam-2660	538	15	b	b	NOUN
ejpam-2660	538	16	)	)	PUNCT
ejpam-2660	538	17	=	=	SYM
ejpam-2660	538	18	1	1	X
ejpam-2660	538	19	.	.	PUNCT
ejpam-2660	539	1	so	so	ADV
ejpam-2660	539	2	a	a	DET
ejpam-2660	539	3	∨	∨	PROPN
ejpam-2660	539	4	b	b	PROPN
ejpam-2660	539	5	is	be	AUX
ejpam-2660	539	6	a	a	DET
ejpam-2660	539	7	complement	complement	NOUN
ejpam-2660	539	8	of	of	ADP
ejpam-2660	539	9	x.	x.	PROPN
ejpam-2660	539	10	(	(	PUNCT
ejpam-2660	539	11	ii):since	ii):since	NOUN
ejpam-2660	539	12	1	1	NUM
ejpam-2660	539	13	∈	∈	NOUN
ejpam-2660	539	14	1	1	NUM
ejpam-2660	539	15	∧	∧	PROPN
ejpam-2660	539	16	1	1	NUM
ejpam-2660	539	17	,	,	PUNCT
ejpam-2660	539	18	0	0	NUM
ejpam-2660	539	19	∨	∨	NUM
ejpam-2660	539	20	0	0	NUM
ejpam-2660	540	1	=	=	SYM
ejpam-2660	540	2	0,and	0,and	NUM
ejpam-2660	540	3	l	l	NOUN
ejpam-2660	540	4	is	be	AUX
ejpam-2660	540	5	strongly	strongly	ADV
ejpam-2660	540	6	distributive	distributive	ADJ
ejpam-2660	540	7	,	,	PUNCT
ejpam-2660	540	8	we	we	PRON
ejpam-2660	540	9	have	have	VERB
ejpam-2660	540	10	:	:	PUNCT
ejpam-2660	540	11	1	1	NUM
ejpam-2660	540	12	∈	∈	NOUN
ejpam-2660	540	13	1	1	NUM
ejpam-2660	540	14	∧	∧	PROPN
ejpam-2660	540	15	1	1	NUM
ejpam-2660	540	16	=	=	SYM
ejpam-2660	540	17	(	(	PUNCT
ejpam-2660	540	18	x	x	PROPN
ejpam-2660	540	19	∨	∨	NUM
ejpam-2660	540	20	a	a	PRON
ejpam-2660	540	21	)	)	PUNCT
ejpam-2660	540	22	∧	∧	NOUN
ejpam-2660	540	23	(	(	PUNCT
ejpam-2660	540	24	x	x	PROPN
ejpam-2660	540	25	∨	∨	NUM
ejpam-2660	540	26	b	b	NOUN
ejpam-2660	540	27	)	)	PUNCT
ejpam-2660	540	28	=	=	SYM
ejpam-2660	540	29	x	x	SYM
ejpam-2660	540	30	∨	∨	X
ejpam-2660	540	31	(	(	PUNCT
ejpam-2660	540	32	a	a	DET
ejpam-2660	540	33	∧	∧	PROPN
ejpam-2660	540	34	b	b	NOUN
ejpam-2660	540	35	)	)	PUNCT
ejpam-2660	540	36	,	,	PUNCT
ejpam-2660	540	37	so	so	CCONJ
ejpam-2660	540	38	there	there	PRON
ejpam-2660	540	39	exists	exist	VERB
ejpam-2660	540	40	c	c	PROPN
ejpam-2660	540	41	∈	∈	PROPN
ejpam-2660	540	42	a	a	DET
ejpam-2660	540	43	∧	∧	PROPN
ejpam-2660	540	44	b	b	PROPN
ejpam-2660	540	45	,	,	PUNCT
ejpam-2660	540	46	such	such	ADJ
ejpam-2660	540	47	that	that	SCONJ
ejpam-2660	540	48	1	1	NUM
ejpam-2660	540	49	=	=	SYM
ejpam-2660	540	50	x	x	SYM
ejpam-2660	540	51	∨	∨	PROPN
ejpam-2660	540	52	c.	c.	NOUN
ejpam-2660	540	53	0	0	NUM
ejpam-2660	540	54	∈	∈	NOUN
ejpam-2660	540	55	0∧	0∧	NOUN
ejpam-2660	540	56	0	0	SYM
ejpam-2660	540	57	⊆	⊆	NUM
ejpam-2660	540	58	(	(	PUNCT
ejpam-2660	540	59	x∧	x∧	PROPN
ejpam-2660	540	60	a)∧	a)∧	PROPN
ejpam-2660	540	61	(	(	PUNCT
ejpam-2660	540	62	x∧	x∧	PROPN
ejpam-2660	540	63	b	b	X
ejpam-2660	540	64	)	)	PUNCT
ejpam-2660	540	65	=	=	SYM
ejpam-2660	540	66	(	(	PUNCT
ejpam-2660	540	67	x∧	x∧	PROPN
ejpam-2660	540	68	x)∧	x)∧	PROPN
ejpam-2660	540	69	(	(	PUNCT
ejpam-2660	540	70	a∧	a∧	NOUN
ejpam-2660	540	71	b	b	NOUN
ejpam-2660	540	72	)	)	PUNCT
ejpam-2660	541	1	=	=	SYM
ejpam-2660	541	2	x∧	x∧	PROPN
ejpam-2660	541	3	(	(	PUNCT
ejpam-2660	541	4	a∧	a∧	NOUN
ejpam-2660	541	5	b	b	PROPN
ejpam-2660	541	6	)	)	PUNCT
ejpam-2660	541	7	;	;	PUNCT
ejpam-2660	541	8	so	so	CCONJ
ejpam-2660	541	9	,	,	PUNCT
ejpam-2660	541	10	there	there	PRON
ejpam-2660	541	11	exists	exist	VERB
ejpam-2660	541	12	d	d	PROPN
ejpam-2660	541	13	∈	∈	PROPN
ejpam-2660	541	14	a∧	a∧	NOUN
ejpam-2660	541	15	b	b	PROPN
ejpam-2660	541	16	such	such	ADJ
ejpam-2660	541	17	that	that	DET
ejpam-2660	541	18	0	0	NUM
ejpam-2660	541	19	∈	∈	NOUN
ejpam-2660	541	20	x	x	PUNCT
ejpam-2660	541	21	∧	∧	PROPN
ejpam-2660	541	22	d.	d.	PROPN
ejpam-2660	541	23	lemma	lemma	PROPN
ejpam-2660	541	24	68	68	NUM
ejpam-2660	541	25	.	.	PUNCT
ejpam-2660	542	1	(	(	PUNCT
ejpam-2660	542	2	demorgan	demorgan	ADJ
ejpam-2660	542	3	laws	law	NOUN
ejpam-2660	542	4	)	)	PUNCT
ejpam-2660	542	5	let	let	VERB
ejpam-2660	542	6	l	l	NOUN
ejpam-2660	542	7	be	be	AUX
ejpam-2660	542	8	a	a	DET
ejpam-2660	542	9	good	good	ADJ
ejpam-2660	542	10	complemented	complemented	ADJ
ejpam-2660	542	11	and	and	CCONJ
ejpam-2660	542	12	strongly	strongly	ADV
ejpam-2660	542	13	distributive	distributive	ADJ
ejpam-2660	542	14	”	"	PUNCT
ejpam-2660	542	15	∧	∧	NOUN
ejpam-2660	542	16	”	"	PUNCT
ejpam-2660	542	17	-hyperlattice	-hyperlattice	NOUN
ejpam-2660	542	18	.	.	PUNCT
ejpam-2660	543	1	then	then	ADV
ejpam-2660	543	2	the	the	DET
ejpam-2660	543	3	following	following	ADJ
ejpam-2660	543	4	statements	statement	NOUN
ejpam-2660	543	5	for	for	ADP
ejpam-2660	543	6	all	all	DET
ejpam-2660	543	7	x	x	NOUN
ejpam-2660	543	8	,	,	PUNCT
ejpam-2660	543	9	y	y	PROPN
ejpam-2660	543	10	∈	∈	PROPN
ejpam-2660	543	11	l	l	NOUN
ejpam-2660	543	12	,	,	PUNCT
ejpam-2660	543	13	hold	hold	VERB
ejpam-2660	543	14	.	.	PUNCT
ejpam-2660	544	1	(	(	PUNCT
ejpam-2660	544	2	i	i	NOUN
ejpam-2660	544	3	)	)	PUNCT
ejpam-2660	544	4	(	(	PUNCT
ejpam-2660	544	5	x	x	PROPN
ejpam-2660	544	6	∨	∨	NUM
ejpam-2660	544	7	y)′	y)′	PROPN
ejpam-2660	544	8	∈	∈	PROPN
ejpam-2660	544	9	x′	x′	PROPN
ejpam-2660	545	1	∧	∧	NOUN
ejpam-2660	545	2	y′.	y′.	PROPN
ejpam-2660	545	3	m.	m.	NOUN
ejpam-2660	545	4	amiri	amiri	PROPN
ejpam-2660	545	5	bideshki	bideshki	PROPN
ejpam-2660	545	6	,	,	PUNCT
ejpam-2660	545	7	r.	r.	PROPN
ejpam-2660	545	8	ameri	ameri	PROPN
ejpam-2660	545	9	,	,	PUNCT
ejpam-2660	545	10	a.	a.	PROPN
ejpam-2660	545	11	borumand	borumand	PROPN
ejpam-2660	546	1	saeid	saeid	PROPN
ejpam-2660	546	2	/	/	SYM
ejpam-2660	546	3	eur	eur	PROPN
ejpam-2660	546	4	.	.	PUNCT
ejpam-2660	547	1	j.	j.	PROPN
ejpam-2660	547	2	pure	pure	PROPN
ejpam-2660	547	3	appl	appl	PROPN
ejpam-2660	547	4	.	.	PROPN
ejpam-2660	547	5	math	math	PROPN
ejpam-2660	547	6	,	,	PUNCT
ejpam-2660	547	7	11	11	NUM
ejpam-2660	547	8	(	(	PUNCT
ejpam-2660	547	9	1	1	NUM
ejpam-2660	547	10	)	)	PUNCT
ejpam-2660	547	11	(	(	PUNCT
ejpam-2660	547	12	2018	2018	NUM
ejpam-2660	547	13	)	)	PUNCT
ejpam-2660	547	14	,	,	PUNCT
ejpam-2660	547	15	169	169	NUM
ejpam-2660	547	16	-	-	SYM
ejpam-2660	547	17	188	188	NUM
ejpam-2660	547	18	185	185	NUM
ejpam-2660	547	19	(	(	PUNCT
ejpam-2660	547	20	ii	ii	NOUN
ejpam-2660	547	21	)	)	PUNCT
ejpam-2660	547	22	x′	x′	PROPN
ejpam-2660	548	1	∨	∨	NUM
ejpam-2660	548	2	y′	y′	NOUN
ejpam-2660	548	3	∈	∈	PROPN
ejpam-2660	548	4	(	(	PUNCT
ejpam-2660	548	5	x	x	PART
ejpam-2660	548	6	∧	∧	PROPN
ejpam-2660	548	7	y)′.	y)′.	PROPN
ejpam-2660	548	8	example	example	NOUN
ejpam-2660	548	9	69	69	NUM
ejpam-2660	548	10	.	.	PUNCT
ejpam-2660	549	1	let	let	VERB
ejpam-2660	549	2	l	l	NOUN
ejpam-2660	549	3	=	=	PUNCT
ejpam-2660	549	4	{	{	PUNCT
ejpam-2660	549	5	0	0	NUM
ejpam-2660	549	6	,	,	PUNCT
ejpam-2660	549	7	x	x	NOUN
ejpam-2660	549	8	,	,	PUNCT
ejpam-2660	549	9	y	y	PROPN
ejpam-2660	549	10	,	,	PUNCT
ejpam-2660	549	11	z	z	PROPN
ejpam-2660	549	12	,	,	PUNCT
ejpam-2660	549	13	1	1	NUM
ejpam-2660	549	14	}	}	PUNCT
ejpam-2660	549	15	.	.	PUNCT
ejpam-2660	550	1	∧−hyperoperation	∧−hyperoperation	NOUN
ejpam-2660	550	2	and	and	CCONJ
ejpam-2660	550	3	∨-operation	∨-operation	NOUN
ejpam-2660	550	4	are	be	AUX
ejpam-2660	550	5	given	give	VERB
ejpam-2660	550	6	by	by	ADP
ejpam-2660	550	7	tables7	tables7	PROPN
ejpam-2660	550	8	.	.	PUNCT
ejpam-2660	551	1	we	we	PRON
ejpam-2660	551	2	have	have	VERB
ejpam-2660	551	3	(	(	PUNCT
ejpam-2660	551	4	y	y	PROPN
ejpam-2660	551	5	∨	∨	NUM
ejpam-2660	551	6	0)′	0)′	NOUN
ejpam-2660	551	7	6=	6=	ADP
ejpam-2660	551	8	y′	y′	X
ejpam-2660	551	9	∧	∧	PROPN
ejpam-2660	551	10	0′	0′	PROPN
ejpam-2660	551	11	,	,	PUNCT
ejpam-2660	551	12	because	because	SCONJ
ejpam-2660	551	13	(	(	PUNCT
ejpam-2660	551	14	y	y	PROPN
ejpam-2660	551	15	∨	∨	NUM
ejpam-2660	551	16	0)′	0)′	X
ejpam-2660	551	17	=	=	PUNCT
ejpam-2660	551	18	y′	y′	NOUN
ejpam-2660	551	19	=	=	SYM
ejpam-2660	551	20	z	z	NOUN
ejpam-2660	551	21	and	and	CCONJ
ejpam-2660	551	22	y′	y′	NUM
ejpam-2660	551	23	∧	∧	NOUN
ejpam-2660	551	24	0′	0′	X
ejpam-2660	552	1	=	=	PUNCT
ejpam-2660	552	2	{	{	PUNCT
ejpam-2660	552	3	0	0	NUM
ejpam-2660	552	4	,	,	PUNCT
ejpam-2660	552	5	z	z	NOUN
ejpam-2660	552	6	}	}	PUNCT
ejpam-2660	552	7	.	.	PUNCT
ejpam-2660	553	1	thus	thus	ADV
ejpam-2660	553	2	(	(	PUNCT
ejpam-2660	553	3	y	y	PROPN
ejpam-2660	553	4	∨	∨	NUM
ejpam-2660	553	5	0)′	0)′	NOUN
ejpam-2660	553	6	$	$	SYM
ejpam-2660	553	7	y′	y′	NOUN
ejpam-2660	553	8	∧	∧	NOUN
ejpam-2660	553	9	0′.	0′.	NOUN
ejpam-2660	553	10	also	also	ADV
ejpam-2660	553	11	in	in	ADP
ejpam-2660	553	12	this	this	DET
ejpam-2660	553	13	example	example	NOUN
ejpam-2660	553	14	,	,	PUNCT
ejpam-2660	553	15	every	every	PRON
ejpam-2660	553	16	of	of	ADP
ejpam-2660	553	17	x	x	PROPN
ejpam-2660	553	18	,	,	PUNCT
ejpam-2660	553	19	y	y	PROPN
ejpam-2660	553	20	,	,	PUNCT
ejpam-2660	553	21	z	z	PROPN
ejpam-2660	553	22	has	have	VERB
ejpam-2660	553	23	two	two	NUM
ejpam-2660	553	24	complements	complement	NOUN
ejpam-2660	553	25	.	.	PUNCT
ejpam-2660	554	1	we	we	PRON
ejpam-2660	554	2	have	have	VERB
ejpam-2660	554	3	∧	∧	PROPN
ejpam-2660	554	4	0	0	NUM
ejpam-2660	554	5	x	x	SYM
ejpam-2660	554	6	y	y	PROPN
ejpam-2660	554	7	z	z	PROPN
ejpam-2660	554	8	1	1	NUM
ejpam-2660	554	9	0	0	NUM
ejpam-2660	554	10	0	0	NUM
ejpam-2660	554	11	0	0	NUM
ejpam-2660	554	12	0	0	NUM
ejpam-2660	554	13	0	0	NUM
ejpam-2660	554	14	0	0	NUM
ejpam-2660	554	15	x	x	SYM
ejpam-2660	554	16	0	0	NUM
ejpam-2660	554	17	{	{	PUNCT
ejpam-2660	554	18	0	0	NUM
ejpam-2660	554	19	,	,	PUNCT
ejpam-2660	554	20	x	x	NOUN
ejpam-2660	554	21	}	}	PUNCT
ejpam-2660	554	22	0	0	NUM
ejpam-2660	554	23	0	0	NUM
ejpam-2660	554	24	{	{	PUNCT
ejpam-2660	554	25	0	0	NUM
ejpam-2660	554	26	,	,	PUNCT
ejpam-2660	554	27	x	x	NOUN
ejpam-2660	554	28	}	}	PUNCT
ejpam-2660	554	29	y	y	PROPN
ejpam-2660	554	30	0	0	NUM
ejpam-2660	554	31	0	0	NUM
ejpam-2660	554	32	{	{	PUNCT
ejpam-2660	554	33	0	0	NUM
ejpam-2660	554	34	,	,	PUNCT
ejpam-2660	554	35	y	y	NOUN
ejpam-2660	554	36	}	}	PUNCT
ejpam-2660	554	37	0	0	NUM
ejpam-2660	554	38	{	{	PUNCT
ejpam-2660	554	39	0	0	NUM
ejpam-2660	554	40	,	,	PUNCT
ejpam-2660	554	41	y	y	NOUN
ejpam-2660	554	42	}	}	PUNCT
ejpam-2660	554	43	z	z	NOUN
ejpam-2660	554	44	0	0	NUM
ejpam-2660	554	45	0	0	NUM
ejpam-2660	554	46	0	0	NUM
ejpam-2660	554	47	{	{	PUNCT
ejpam-2660	554	48	0	0	NUM
ejpam-2660	554	49	,	,	PUNCT
ejpam-2660	554	50	z	z	NOUN
ejpam-2660	554	51	}	}	PUNCT
ejpam-2660	554	52	{	{	PUNCT
ejpam-2660	554	53	0	0	NUM
ejpam-2660	554	54	,	,	PUNCT
ejpam-2660	554	55	z	z	NOUN
ejpam-2660	554	56	}	}	PUNCT
ejpam-2660	554	57	1	1	NUM
ejpam-2660	554	58	0	0	NUM
ejpam-2660	554	59	{	{	PUNCT
ejpam-2660	554	60	0	0	NUM
ejpam-2660	554	61	,	,	PUNCT
ejpam-2660	554	62	x	x	NOUN
ejpam-2660	554	63	}	}	PUNCT
ejpam-2660	554	64	{	{	PUNCT
ejpam-2660	554	65	0	0	NUM
ejpam-2660	554	66	,	,	PUNCT
ejpam-2660	554	67	y	y	NOUN
ejpam-2660	554	68	}	}	PUNCT
ejpam-2660	554	69	{	{	PUNCT
ejpam-2660	554	70	0	0	NUM
ejpam-2660	554	71	,	,	PUNCT
ejpam-2660	554	72	z	z	NOUN
ejpam-2660	554	73	}	}	PUNCT
ejpam-2660	554	74	l	l	NOUN
ejpam-2660	554	75	(	(	PUNCT
ejpam-2660	554	76	a	a	NOUN
ejpam-2660	554	77	)	)	PUNCT
ejpam-2660	554	78	∨	∨	NOUN
ejpam-2660	554	79	0	0	NUM
ejpam-2660	555	1	x	x	SYM
ejpam-2660	555	2	y	y	PROPN
ejpam-2660	555	3	z	z	PROPN
ejpam-2660	555	4	1	1	NUM
ejpam-2660	555	5	0	0	NUM
ejpam-2660	555	6	0	0	NUM
ejpam-2660	555	7	x	x	SYM
ejpam-2660	555	8	y	y	PROPN
ejpam-2660	555	9	z	z	PROPN
ejpam-2660	555	10	1	1	NUM
ejpam-2660	555	11	x	x	SYM
ejpam-2660	555	12	x	x	SYM
ejpam-2660	555	13	x	x	SYM
ejpam-2660	555	14	1	1	NUM
ejpam-2660	555	15	1	1	NUM
ejpam-2660	555	16	1	1	NUM
ejpam-2660	555	17	y	y	PROPN
ejpam-2660	555	18	y	y	PROPN
ejpam-2660	555	19	1	1	NUM
ejpam-2660	555	20	y	y	PROPN
ejpam-2660	555	21	1	1	NUM
ejpam-2660	555	22	1	1	NUM
ejpam-2660	555	23	z	z	NOUN
ejpam-2660	555	24	z	z	NOUN
ejpam-2660	555	25	1	1	NUM
ejpam-2660	555	26	1	1	NUM
ejpam-2660	555	27	z	z	NOUN
ejpam-2660	555	28	1	1	NUM
ejpam-2660	555	29	1	1	NUM
ejpam-2660	555	30	1	1	NUM
ejpam-2660	555	31	1	1	NUM
ejpam-2660	555	32	1	1	NUM
ejpam-2660	555	33	1	1	NUM
ejpam-2660	555	34	1	1	NUM
ejpam-2660	555	35	(	(	PUNCT
ejpam-2660	555	36	b	b	NOUN
ejpam-2660	555	37	)	)	PUNCT
ejpam-2660	555	38	table	table	NOUN
ejpam-2660	555	39	7	7	NUM
ejpam-2660	555	40	x′	x′	PROPN
ejpam-2660	555	41	=	=	PRON
ejpam-2660	555	42	{	{	PUNCT
ejpam-2660	555	43	y	y	PROPN
ejpam-2660	555	44	,	,	PUNCT
ejpam-2660	555	45	z	z	NOUN
ejpam-2660	555	46	}	}	PUNCT
ejpam-2660	555	47	,	,	PUNCT
ejpam-2660	555	48	y′	y′	NOUN
ejpam-2660	555	49	=	=	SYM
ejpam-2660	555	50	{	{	PUNCT
ejpam-2660	555	51	x	x	NOUN
ejpam-2660	555	52	,	,	PUNCT
ejpam-2660	555	53	z	z	NOUN
ejpam-2660	555	54	}	}	PUNCT
ejpam-2660	555	55	,	,	PUNCT
ejpam-2660	555	56	z′	z′	NUM
ejpam-2660	555	57	=	=	SYM
ejpam-2660	555	58	{	{	PUNCT
ejpam-2660	555	59	x	x	NOUN
ejpam-2660	555	60	,	,	PUNCT
ejpam-2660	555	61	y	y	PROPN
ejpam-2660	555	62	}	}	PUNCT
ejpam-2660	555	63	.	.	PUNCT
ejpam-2660	556	1	it	it	PRON
ejpam-2660	556	2	is	be	AUX
ejpam-2660	556	3	obvious	obvious	ADJ
ejpam-2660	556	4	that	that	SCONJ
ejpam-2660	556	5	if	if	SCONJ
ejpam-2660	556	6	complement	complement	NOUN
ejpam-2660	556	7	of	of	ADP
ejpam-2660	556	8	x	x	PUNCT
ejpam-2660	556	9	is	be	AUX
ejpam-2660	556	10	unique	unique	ADJ
ejpam-2660	556	11	,	,	PUNCT
ejpam-2660	556	12	then	then	ADV
ejpam-2660	556	13	x	x	X
ejpam-2660	556	14	=	=	PUNCT
ejpam-2660	557	1	x′′.	x′′.	PUNCT
ejpam-2660	557	2	x	x	X
ejpam-2660	557	3	and	and	CCONJ
ejpam-2660	557	4	its	its	PRON
ejpam-2660	557	5	complemet	complemet	NOUN
ejpam-2660	557	6	are	be	AUX
ejpam-2660	557	7	not	not	PART
ejpam-2660	557	8	comparable	comparable	ADJ
ejpam-2660	557	9	where	where	SCONJ
ejpam-2660	557	10	x	x	PUNCT
ejpam-2660	557	11	6=	6=	ADP
ejpam-2660	557	12	0	0	NUM
ejpam-2660	557	13	,	,	PUNCT
ejpam-2660	557	14	1	1	NUM
ejpam-2660	557	15	.	.	PUNCT
ejpam-2660	557	16	corollary	corollary	ADJ
ejpam-2660	557	17	70	70	NUM
ejpam-2660	557	18	.	.	PUNCT
ejpam-2660	558	1	let	let	VERB
ejpam-2660	558	2	l	l	NOUN
ejpam-2660	558	3	be	be	AUX
ejpam-2660	558	4	a	a	DET
ejpam-2660	558	5	good	good	ADJ
ejpam-2660	558	6	complemented	complemented	ADJ
ejpam-2660	558	7	and	and	CCONJ
ejpam-2660	558	8	strongly	strongly	ADV
ejpam-2660	558	9	distributive	distributive	ADJ
ejpam-2660	558	10	”	"	PUNCT
ejpam-2660	558	11	∧	∧	NOUN
ejpam-2660	558	12	”	"	PUNCT
ejpam-2660	558	13	-hyperlattice	-hyperlattice	NOUN
ejpam-2660	558	14	.	.	PUNCT
ejpam-2660	559	1	if	if	SCONJ
ejpam-2660	559	2	x	x	PRON
ejpam-2660	559	3	is	be	AUX
ejpam-2660	559	4	a	a	DET
ejpam-2660	559	5	complement	complement	NOUN
ejpam-2660	559	6	of	of	ADP
ejpam-2660	559	7	y	y	PRON
ejpam-2660	559	8	then	then	ADV
ejpam-2660	559	9	we	we	PRON
ejpam-2660	559	10	have	have	VERB
ejpam-2660	559	11	:	:	PUNCT
ejpam-2660	559	12	(	(	PUNCT
ejpam-2660	559	13	i	i	NOUN
ejpam-2660	559	14	)	)	PUNCT
ejpam-2660	559	15	(	(	PUNCT
ejpam-2660	560	1	x	x	PROPN
ejpam-2660	560	2	∨	∨	NUM
ejpam-2660	560	3	y)′	y)′	PROPN
ejpam-2660	560	4	=	=	SYM
ejpam-2660	560	5	x′	x′	PROPN
ejpam-2660	560	6	∧	∧	PROPN
ejpam-2660	560	7	y′	y′	NUM
ejpam-2660	560	8	;	;	PUNCT
ejpam-2660	560	9	(	(	PUNCT
ejpam-2660	560	10	ii	ii	NOUN
ejpam-2660	560	11	)	)	PUNCT
ejpam-2660	560	12	(	(	PUNCT
ejpam-2660	560	13	x	x	PUNCT
ejpam-2660	560	14	∧	∧	NOUN
ejpam-2660	560	15	y)′	y)′	PROPN
ejpam-2660	560	16	=	=	SYM
ejpam-2660	560	17	x′	x′	PROPN
ejpam-2660	561	1	∨	∨	NUM
ejpam-2660	561	2	y′.	y′.	PROPN
ejpam-2660	561	3	theorem	theorem	VERB
ejpam-2660	561	4	71	71	NUM
ejpam-2660	561	5	.	.	PUNCT
ejpam-2660	562	1	let	let	VERB
ejpam-2660	562	2	l	l	NOUN
ejpam-2660	562	3	be	be	AUX
ejpam-2660	562	4	a	a	DET
ejpam-2660	562	5	distributive	distributive	ADJ
ejpam-2660	562	6	and	and	CCONJ
ejpam-2660	562	7	good	good	ADJ
ejpam-2660	562	8	complemented	complemented	ADJ
ejpam-2660	562	9	∧-hyperlattice	∧-hyperlattice	NOUN
ejpam-2660	562	10	.	.	PUNCT
ejpam-2660	563	1	then	then	ADV
ejpam-2660	563	2	we	we	PRON
ejpam-2660	563	3	have	have	VERB
ejpam-2660	563	4	:	:	PUNCT
ejpam-2660	563	5	(	(	PUNCT
ejpam-2660	563	6	i	i	NOUN
ejpam-2660	563	7	)	)	PUNCT
ejpam-2660	563	8	complement	complement	NOUN
ejpam-2660	563	9	of	of	ADP
ejpam-2660	563	10	any	any	DET
ejpam-2660	563	11	element	element	NOUN
ejpam-2660	563	12	of	of	ADP
ejpam-2660	563	13	l	l	NOUN
ejpam-2660	563	14	is	be	AUX
ejpam-2660	563	15	unique	unique	ADJ
ejpam-2660	563	16	.	.	PUNCT
ejpam-2660	564	1	(	(	PUNCT
ejpam-2660	564	2	ii	ii	NOUN
ejpam-2660	564	3	)	)	PUNCT
ejpam-2660	564	4	if	if	SCONJ
ejpam-2660	564	5	x	x	X
ejpam-2660	564	6	,	,	PUNCT
ejpam-2660	564	7	y	y	PROPN
ejpam-2660	564	8	∈	∈	PROPN
ejpam-2660	564	9	l	l	NOUN
ejpam-2660	564	10	such	such	ADJ
ejpam-2660	564	11	that	that	SCONJ
ejpam-2660	564	12	x	x	X
ejpam-2660	564	13	≤	≤	NUM
ejpam-2660	564	14	y	y	NOUN
ejpam-2660	564	15	,	,	PUNCT
ejpam-2660	564	16	then	then	ADV
ejpam-2660	564	17	y′	y′	ADV
ejpam-2660	564	18	≤	≤	ADJ
ejpam-2660	564	19	x′.	x′.	PROPN
ejpam-2660	564	20	proof	proof	NOUN
ejpam-2660	564	21	.	.	PUNCT
ejpam-2660	565	1	(	(	PUNCT
ejpam-2660	565	2	i	i	NOUN
ejpam-2660	565	3	):	):	PUNCT
ejpam-2660	565	4	let	let	VERB
ejpam-2660	565	5	a	a	DET
ejpam-2660	565	6	,	,	PUNCT
ejpam-2660	565	7	b	b	NOUN
ejpam-2660	565	8	be	be	AUX
ejpam-2660	565	9	complements	complement	NOUN
ejpam-2660	565	10	of	of	ADP
ejpam-2660	565	11	x.	x.	NOUN
ejpam-2660	565	12	then	then	ADV
ejpam-2660	565	13	b	b	X
ejpam-2660	565	14	∧	∧	NOUN
ejpam-2660	565	15	x	x	X
ejpam-2660	565	16	=	=	PUNCT
ejpam-2660	565	17	{	{	PUNCT
ejpam-2660	565	18	0	0	NUM
ejpam-2660	565	19	}	}	PUNCT
ejpam-2660	565	20	and	and	CCONJ
ejpam-2660	565	21	we	we	PRON
ejpam-2660	565	22	have	have	VERB
ejpam-2660	565	23	:	:	PUNCT
ejpam-2660	565	24	a	a	DET
ejpam-2660	565	25	=	=	PUNCT
ejpam-2660	565	26	a	a	DET
ejpam-2660	565	27	∨	∨	NOUN
ejpam-2660	565	28	0	0	NUM
ejpam-2660	565	29	=	=	SYM
ejpam-2660	565	30	a	a	DET
ejpam-2660	565	31	∨	∨	X
ejpam-2660	565	32	(	(	PUNCT
ejpam-2660	565	33	b	b	PROPN
ejpam-2660	565	34	∧	∧	PROPN
ejpam-2660	565	35	x	x	NOUN
ejpam-2660	565	36	)	)	PUNCT
ejpam-2660	566	1	=	=	SYM
ejpam-2660	567	1	(	(	PUNCT
ejpam-2660	567	2	a	a	DET
ejpam-2660	567	3	∨	∨	NUM
ejpam-2660	567	4	b	b	NOUN
ejpam-2660	567	5	)	)	PUNCT
ejpam-2660	567	6	∧	∧	NOUN
ejpam-2660	567	7	(	(	PUNCT
ejpam-2660	567	8	a	a	DET
ejpam-2660	567	9	∨	∨	NUM
ejpam-2660	567	10	x	x	NOUN
ejpam-2660	567	11	)	)	PUNCT
ejpam-2660	567	12	=	=	SYM
ejpam-2660	567	13	(	(	PUNCT
ejpam-2660	567	14	a	a	DET
ejpam-2660	567	15	∨	∨	NUM
ejpam-2660	567	16	b	b	NOUN
ejpam-2660	567	17	)	)	PUNCT
ejpam-2660	567	18	∧	∧	NOUN
ejpam-2660	567	19	1	1	NUM
ejpam-2660	567	20	.	.	PUNCT
ejpam-2660	568	1	since	since	SCONJ
ejpam-2660	568	2	a	a	DET
ejpam-2660	568	3	∨	∨	NUM
ejpam-2660	568	4	b	b	NOUN
ejpam-2660	568	5	≤	≤	NUM
ejpam-2660	568	6	1	1	NUM
ejpam-2660	568	7	,	,	PUNCT
ejpam-2660	568	8	a	a	DET
ejpam-2660	568	9	∨	∨	NUM
ejpam-2660	568	10	b	b	X
ejpam-2660	568	11	∈	∈	PROPN
ejpam-2660	568	12	(	(	PUNCT
ejpam-2660	568	13	a	a	DET
ejpam-2660	568	14	∨	∨	NUM
ejpam-2660	568	15	b	b	NOUN
ejpam-2660	568	16	)	)	PUNCT
ejpam-2660	568	17	∧	∧	NOUN
ejpam-2660	568	18	1	1	NUM
ejpam-2660	568	19	.	.	PUNCT
ejpam-2660	569	1	so	so	ADV
ejpam-2660	569	2	a	a	DET
ejpam-2660	569	3	∨	∨	NUM
ejpam-2660	569	4	b	b	NOUN
ejpam-2660	569	5	=	=	NOUN
ejpam-2660	569	6	a	a	PROPN
ejpam-2660	570	1	and	and	CCONJ
ejpam-2660	570	2	it	it	PRON
ejpam-2660	570	3	implies	imply	VERB
ejpam-2660	570	4	that	that	SCONJ
ejpam-2660	570	5	b	b	X
ejpam-2660	570	6	≤	≤	ADV
ejpam-2660	570	7	a	a	PRON
ejpam-2660	570	8	,	,	PUNCT
ejpam-2660	570	9	similarly	similarly	ADV
ejpam-2660	570	10	,	,	PUNCT
ejpam-2660	570	11	it	it	PRON
ejpam-2660	570	12	is	be	AUX
ejpam-2660	570	13	proved	prove	VERB
ejpam-2660	570	14	that	that	SCONJ
ejpam-2660	570	15	a	a	DET
ejpam-2660	570	16	≤	≤	PROPN
ejpam-2660	570	17	b	b	NOUN
ejpam-2660	570	18	;	;	PUNCT
ejpam-2660	570	19	so	so	ADV
ejpam-2660	570	20	a	a	DET
ejpam-2660	570	21	=	=	X
ejpam-2660	570	22	b.	b.	PROPN
ejpam-2660	570	23	(	(	PUNCT
ejpam-2660	570	24	ii	ii	PROPN
ejpam-2660	570	25	):	):	PUNCT
ejpam-2660	570	26	since	since	SCONJ
ejpam-2660	570	27	x	x	PROPN
ejpam-2660	570	28	≤	≤	PROPN
ejpam-2660	570	29	y	y	PROPN
ejpam-2660	570	30	,	,	PUNCT
ejpam-2660	570	31	x∨y	x∨y	PROPN
ejpam-2660	571	1	=	=	PUNCT
ejpam-2660	571	2	y.	y.	NOUN
ejpam-2660	571	3	so	so	ADV
ejpam-2660	571	4	y′	y′	ADV
ejpam-2660	571	5	=	=	SYM
ejpam-2660	571	6	(	(	PUNCT
ejpam-2660	571	7	x∨y)′.	x∨y)′.	NUM
ejpam-2660	571	8	by	by	ADP
ejpam-2660	571	9	demorgan	demorgan	ADJ
ejpam-2660	571	10	law	law	NOUN
ejpam-2660	571	11	,	,	PUNCT
ejpam-2660	571	12	we	we	PRON
ejpam-2660	571	13	have	have	VERB
ejpam-2660	571	14	(	(	PUNCT
ejpam-2660	571	15	x∨y)′	x∨y)′	PROPN
ejpam-2660	571	16	∈	∈	PROPN
ejpam-2660	571	17	x′∧y′	x′∧y′	PROPN
ejpam-2660	571	18	,	,	PUNCT
ejpam-2660	571	19	then	then	ADV
ejpam-2660	571	20	y′	y′	NOUN
ejpam-2660	571	21	∈	∈	PROPN
ejpam-2660	571	22	x′	x′	PROPN
ejpam-2660	572	1	∧	∧	PROPN
ejpam-2660	572	2	y′	y′	PROPN
ejpam-2660	572	3	,	,	PUNCT
ejpam-2660	572	4	and	and	CCONJ
ejpam-2660	572	5	it	it	PRON
ejpam-2660	572	6	implies	imply	VERB
ejpam-2660	572	7	that	that	SCONJ
ejpam-2660	572	8	y′	y′	ADV
ejpam-2660	572	9	≤	≤	PROPN
ejpam-2660	572	10	x′.	x′.	PROPN
ejpam-2660	572	11	remark	remark	VERB
ejpam-2660	572	12	72	72	NUM
ejpam-2660	572	13	.	.	PUNCT
ejpam-2660	573	1	in	in	ADP
ejpam-2660	573	2	theorem	theorem	NOUN
ejpam-2660	573	3	71	71	NUM
ejpam-2660	573	4	,	,	PUNCT
ejpam-2660	573	5	if	if	SCONJ
ejpam-2660	573	6	l	l	NOUN
ejpam-2660	573	7	is	be	AUX
ejpam-2660	573	8	a	a	DET
ejpam-2660	573	9	dual	dual	ADJ
ejpam-2660	573	10	distributive	distributive	ADJ
ejpam-2660	573	11	good	good	ADJ
ejpam-2660	573	12	complemented	complemented	ADJ
ejpam-2660	573	13	”	"	PUNCT
ejpam-2660	573	14	∧”-hyperlattice	∧”-hyperlattice	PROPN
ejpam-2660	573	15	,	,	PUNCT
ejpam-2660	573	16	then	then	ADV
ejpam-2660	573	17	(	(	PUNCT
ejpam-2660	573	18	i	i	NOUN
ejpam-2660	573	19	)	)	PUNCT
ejpam-2660	573	20	holds	hold	VERB
ejpam-2660	573	21	.	.	PUNCT
ejpam-2660	574	1	since	since	SCONJ
ejpam-2660	574	2	a	a	DET
ejpam-2660	574	3	≤	≤	NUM
ejpam-2660	574	4	1	1	NUM
ejpam-2660	574	5	,	,	PUNCT
ejpam-2660	574	6	we	we	PRON
ejpam-2660	574	7	have	have	VERB
ejpam-2660	574	8	:	:	PUNCT
ejpam-2660	574	9	a	a	DET
ejpam-2660	574	10	∈	∈	NOUN
ejpam-2660	574	11	a∧1	a∧1	NOUN
ejpam-2660	574	12	=	=	SYM
ejpam-2660	574	13	a∧(b∨x	a∧(b∨x	NOUN
ejpam-2660	574	14	)	)	PUNCT
ejpam-2660	575	1	=	=	PRON
ejpam-2660	575	2	(	(	PUNCT
ejpam-2660	575	3	a∧b)∨(a∧x	a∧b)∨(a∧x	NOUN
ejpam-2660	575	4	)	)	PUNCT
ejpam-2660	575	5	=	=	SYM
ejpam-2660	576	1	(	(	PUNCT
ejpam-2660	576	2	a∧b)∨0	a∧b)∨0	SYM
ejpam-2660	576	3	=	=	PUNCT
ejpam-2660	576	4	a	a	DET
ejpam-2660	576	5	∧	∧	PROPN
ejpam-2660	576	6	b	b	PROPN
ejpam-2660	576	7	,	,	PUNCT
ejpam-2660	576	8	so	so	SCONJ
ejpam-2660	576	9	a	a	DET
ejpam-2660	576	10	∈	∈	PROPN
ejpam-2660	576	11	a	a	DET
ejpam-2660	576	12	∧	∧	PROPN
ejpam-2660	576	13	b	b	PROPN
ejpam-2660	577	1	and	and	CCONJ
ejpam-2660	577	2	it	it	PRON
ejpam-2660	577	3	implies	imply	VERB
ejpam-2660	577	4	that	that	SCONJ
ejpam-2660	577	5	a	a	DET
ejpam-2660	577	6	≤	≤	PROPN
ejpam-2660	577	7	b.	b.	NOUN
ejpam-2660	577	8	similarly	similarly	ADV
ejpam-2660	577	9	,	,	PUNCT
ejpam-2660	577	10	it	it	PRON
ejpam-2660	577	11	is	be	AUX
ejpam-2660	577	12	proved	prove	VERB
ejpam-2660	577	13	that	that	SCONJ
ejpam-2660	577	14	b	b	X
ejpam-2660	577	15	≤	≤	NUM
ejpam-2660	577	16	a.	a.	NOUN
ejpam-2660	578	1	so	so	ADV
ejpam-2660	578	2	a	a	DET
ejpam-2660	578	3	=	=	X
ejpam-2660	578	4	b.	b.	PROPN
ejpam-2660	578	5	m.	m.	NOUN
ejpam-2660	578	6	amiri	amiri	PROPN
ejpam-2660	578	7	bideshki	bideshki	PROPN
ejpam-2660	578	8	,	,	PUNCT
ejpam-2660	578	9	r.	r.	PROPN
ejpam-2660	578	10	ameri	ameri	PROPN
ejpam-2660	578	11	,	,	PUNCT
ejpam-2660	578	12	a.	a.	PROPN
ejpam-2660	578	13	borumand	borumand	PROPN
ejpam-2660	578	14	saeid	saeid	PROPN
ejpam-2660	578	15	/	/	SYM
ejpam-2660	578	16	eur	eur	PROPN
ejpam-2660	578	17	.	.	PUNCT
ejpam-2660	579	1	j.	j.	PROPN
ejpam-2660	579	2	pure	pure	PROPN
ejpam-2660	579	3	appl	appl	PROPN
ejpam-2660	579	4	.	.	PROPN
ejpam-2660	579	5	math	math	PROPN
ejpam-2660	579	6	,	,	PUNCT
ejpam-2660	579	7	11	11	NUM
ejpam-2660	579	8	(	(	PUNCT
ejpam-2660	579	9	1	1	NUM
ejpam-2660	579	10	)	)	PUNCT
ejpam-2660	579	11	(	(	PUNCT
ejpam-2660	579	12	2018	2018	NUM
ejpam-2660	579	13	)	)	PUNCT
ejpam-2660	579	14	,	,	PUNCT
ejpam-2660	579	15	169	169	NUM
ejpam-2660	579	16	-	-	SYM
ejpam-2660	579	17	188	188	NUM
ejpam-2660	579	18	186	186	NUM
ejpam-2660	579	19	theorem	theorem	NOUN
ejpam-2660	579	20	73	73	NUM
ejpam-2660	579	21	.	.	PUNCT
ejpam-2660	580	1	let	let	VERB
ejpam-2660	580	2	p	p	PRON
ejpam-2660	580	3	be	be	AUX
ejpam-2660	580	4	a	a	DET
ejpam-2660	580	5	proper	proper	ADJ
ejpam-2660	580	6	hyperfilter	hyperfilter	NOUN
ejpam-2660	580	7	of	of	ADP
ejpam-2660	580	8	a	a	DET
ejpam-2660	580	9	complemented	complemented	ADJ
ejpam-2660	580	10	”	"	PUNCT
ejpam-2660	580	11	∧	∧	NOUN
ejpam-2660	580	12	”	"	PUNCT
ejpam-2660	580	13	-hyperlattice	-hyperlattice	NOUN
ejpam-2660	580	14	l.	l.	NOUN
ejpam-2660	580	15	then	then	ADV
ejpam-2660	580	16	p	p	PROPN
ejpam-2660	580	17	is	be	AUX
ejpam-2660	580	18	a	a	DET
ejpam-2660	580	19	prime	prime	ADJ
ejpam-2660	580	20	hyperfilter	hyperfilter	NOUN
ejpam-2660	580	21	,	,	PUNCT
ejpam-2660	581	1	if	if	SCONJ
ejpam-2660	581	2	and	and	CCONJ
ejpam-2660	581	3	only	only	ADV
ejpam-2660	581	4	if	if	SCONJ
ejpam-2660	581	5	x	x	PROPN
ejpam-2660	581	6	∨	∨	NUM
ejpam-2660	581	7	y′	y′	NOUN
ejpam-2660	581	8	∈	∈	PROPN
ejpam-2660	581	9	p	p	NOUN
ejpam-2660	581	10	and	and	CCONJ
ejpam-2660	581	11	y	y	PROPN
ejpam-2660	581	12	∨	∨	NUM
ejpam-2660	581	13	x′	x′	PROPN
ejpam-2660	581	14	∈	∈	PROPN
ejpam-2660	581	15	p	p	NOUN
ejpam-2660	581	16	,	,	PUNCT
ejpam-2660	581	17	where	where	SCONJ
ejpam-2660	581	18	x	x	X
ejpam-2660	581	19	,	,	PUNCT
ejpam-2660	581	20	y	y	PROPN
ejpam-2660	581	21	∈	∈	PROPN
ejpam-2660	581	22	l	l	NOUN
ejpam-2660	581	23	\	\	PROPN
ejpam-2660	582	1	p	p	X
ejpam-2660	582	2	,	,	PUNCT
ejpam-2660	582	3	example	example	NOUN
ejpam-2660	582	4	74	74	NUM
ejpam-2660	582	5	.	.	PUNCT
ejpam-2660	583	1	consider	consider	VERB
ejpam-2660	583	2	”	"	PUNCT
ejpam-2660	583	3	∧	∧	NOUN
ejpam-2660	583	4	”	"	PUNCT
ejpam-2660	583	5	-hyperlattice	-hyperlattice	NOUN
ejpam-2660	583	6	l	l	NOUN
ejpam-2660	583	7	in	in	ADP
ejpam-2660	583	8	example	example	NOUN
ejpam-2660	583	9	66	66	NUM
ejpam-2660	583	10	.	.	PUNCT
ejpam-2660	584	1	then	then	ADV
ejpam-2660	584	2	{	{	PUNCT
ejpam-2660	584	3	z	z	NOUN
ejpam-2660	584	4	,	,	PUNCT
ejpam-2660	584	5	1	1	NUM
ejpam-2660	584	6	}	}	PUNCT
ejpam-2660	584	7	and	and	CCONJ
ejpam-2660	584	8	{	{	PUNCT
ejpam-2660	584	9	0	0	NUM
ejpam-2660	584	10	,	,	PUNCT
ejpam-2660	584	11	x	x	NOUN
ejpam-2660	584	12	,	,	PUNCT
ejpam-2660	584	13	y	y	PROPN
ejpam-2660	584	14	,	,	PUNCT
ejpam-2660	584	15	1	1	NUM
ejpam-2660	584	16	}	}	PUNCT
ejpam-2660	584	17	are	be	AUX
ejpam-2660	584	18	two	two	NUM
ejpam-2660	584	19	prime	prime	ADJ
ejpam-2660	584	20	hyperfilters	hyperfilter	NOUN
ejpam-2660	584	21	of	of	ADP
ejpam-2660	584	22	l.	l.	PROPN
ejpam-2660	584	23	f	f	PROPN
ejpam-2660	585	1	=	=	PRON
ejpam-2660	585	2	{	{	PUNCT
ejpam-2660	585	3	y	y	PROPN
ejpam-2660	585	4	,	,	PUNCT
ejpam-2660	585	5	1	1	NUM
ejpam-2660	585	6	}	}	PUNCT
ejpam-2660	585	7	is	be	AUX
ejpam-2660	585	8	a	a	DET
ejpam-2660	585	9	hyperfilter	hyperfilter	NOUN
ejpam-2660	585	10	of	of	ADP
ejpam-2660	585	11	l	l	NOUN
ejpam-2660	585	12	,	,	PUNCT
ejpam-2660	585	13	but	but	CCONJ
ejpam-2660	585	14	it	it	PRON
ejpam-2660	585	15	is	be	AUX
ejpam-2660	585	16	not	not	PART
ejpam-2660	585	17	an	an	DET
ejpam-2660	585	18	prime	prime	ADJ
ejpam-2660	585	19	hyperfilter	hyperfilter	NOUN
ejpam-2660	585	20	,	,	PUNCT
ejpam-2660	585	21	because	because	SCONJ
ejpam-2660	585	22	of	of	ADP
ejpam-2660	585	23	x	x	X
ejpam-2660	585	24	,	,	PUNCT
ejpam-2660	585	25	z	z	NOUN
ejpam-2660	585	26	/∈	/∈	PUNCT
ejpam-2660	585	27	f	f	PROPN
ejpam-2660	585	28	,	,	PUNCT
ejpam-2660	585	29	but	but	CCONJ
ejpam-2660	586	1	x′	x′	PROPN
ejpam-2660	586	2	∨	∨	NOUN
ejpam-2660	586	3	z	z	PROPN
ejpam-2660	587	1	=	=	SYM
ejpam-2660	588	1	z	z	PROPN
ejpam-2660	589	1	∨	∨	NOUN
ejpam-2660	589	2	z	z	PROPN
ejpam-2660	589	3	=	=	SYM
ejpam-2660	589	4	z	z	NOUN
ejpam-2660	589	5	/∈	/∈	PUNCT
ejpam-2660	590	1	f	f	PROPN
ejpam-2660	590	2	.	.	PUNCT
ejpam-2660	591	1	theorem	theorem	VERB
ejpam-2660	591	2	75	75	NUM
ejpam-2660	591	3	.	.	PUNCT
ejpam-2660	592	1	let	let	VERB
ejpam-2660	592	2	p	p	PRON
ejpam-2660	592	3	be	be	AUX
ejpam-2660	592	4	a	a	DET
ejpam-2660	592	5	proper	proper	ADJ
ejpam-2660	592	6	hyperfilter	hyperfilter	NOUN
ejpam-2660	592	7	of	of	ADP
ejpam-2660	592	8	a	a	DET
ejpam-2660	592	9	good	good	ADJ
ejpam-2660	592	10	complemented	complemented	ADJ
ejpam-2660	592	11	”	"	PUNCT
ejpam-2660	592	12	∧	∧	NOUN
ejpam-2660	592	13	”	"	PUNCT
ejpam-2660	592	14	-hyperlattice	-hyperlattice	NOUN
ejpam-2660	592	15	l.	l.	NOUN
ejpam-2660	592	16	then	then	ADV
ejpam-2660	592	17	p	p	PROPN
ejpam-2660	592	18	is	be	AUX
ejpam-2660	592	19	a	a	DET
ejpam-2660	592	20	prime	prime	ADJ
ejpam-2660	592	21	hyperfilter	hyperfilter	NOUN
ejpam-2660	592	22	of	of	ADP
ejpam-2660	592	23	l	l	NOUN
ejpam-2660	592	24	if	if	SCONJ
ejpam-2660	593	1	and	and	CCONJ
ejpam-2660	593	2	only	only	ADV
ejpam-2660	593	3	if	if	SCONJ
ejpam-2660	593	4	x	x	PROPN
ejpam-2660	593	5	∈	∈	PROPN
ejpam-2660	593	6	p	p	NOUN
ejpam-2660	593	7	or	or	CCONJ
ejpam-2660	593	8	x′	x′	PROPN
ejpam-2660	593	9	∈	∈	PROPN
ejpam-2660	593	10	p	p	NOUN
ejpam-2660	593	11	,	,	PUNCT
ejpam-2660	593	12	∀x	∀x	X
ejpam-2660	593	13	∈	∈	PROPN
ejpam-2660	593	14	l	l	NOUN
ejpam-2660	593	15	(	(	PUNCT
ejpam-2660	593	16	x	x	SYM
ejpam-2660	593	17	∈	∈	PROPN
ejpam-2660	593	18	p	p	NOUN
ejpam-2660	593	19	iff	iff	PROPN
ejpam-2660	593	20	x′	x′	PROPN
ejpam-2660	593	21	/∈	/∈	PUNCT
ejpam-2660	593	22	p	p	NOUN
ejpam-2660	593	23	)	)	PUNCT
ejpam-2660	593	24	.	.	PUNCT
ejpam-2660	594	1	proof	proof	NOUN
ejpam-2660	594	2	.	.	PUNCT
ejpam-2660	595	1	let	let	VERB
ejpam-2660	595	2	p	p	PRON
ejpam-2660	595	3	be	be	AUX
ejpam-2660	595	4	a	a	DET
ejpam-2660	595	5	prime	prime	ADJ
ejpam-2660	595	6	hyperfilter	hyperfilter	NOUN
ejpam-2660	595	7	and	and	CCONJ
ejpam-2660	595	8	there	there	PRON
ejpam-2660	595	9	exists	exist	VERB
ejpam-2660	595	10	x	x	X
ejpam-2660	595	11	∈	∈	NOUN
ejpam-2660	595	12	l	l	NOUN
ejpam-2660	595	13	such	such	ADJ
ejpam-2660	595	14	that	that	PRON
ejpam-2660	595	15	x	x	PROPN
ejpam-2660	595	16	/∈	/∈	PUNCT
ejpam-2660	596	1	p	p	NOUN
ejpam-2660	596	2	and	and	CCONJ
ejpam-2660	596	3	x′	x′	PROPN
ejpam-2660	596	4	/∈	/∈	PUNCT
ejpam-2660	597	1	p	p	X
ejpam-2660	597	2	.	.	PUNCT
ejpam-2660	598	1	by	by	ADP
ejpam-2660	598	2	theorem	theorem	NOUN
ejpam-2660	598	3	73	73	NUM
ejpam-2660	598	4	,	,	PUNCT
ejpam-2660	598	5	x	x	PROPN
ejpam-2660	598	6	∨	∨	NUM
ejpam-2660	598	7	x′′	x′′	PROPN
ejpam-2660	598	8	∈	∈	PROPN
ejpam-2660	598	9	p	p	PROPN
ejpam-2660	598	10	and	and	CCONJ
ejpam-2660	598	11	x′	x′	PROPN
ejpam-2660	599	1	∨	∨	NOUN
ejpam-2660	599	2	x′	x′	PROPN
ejpam-2660	600	1	∈	∈	PROPN
ejpam-2660	600	2	p	p	PROPN
ejpam-2660	600	3	.	.	PUNCT
ejpam-2660	601	1	therefore	therefore	ADV
ejpam-2660	601	2	x	x	SYM
ejpam-2660	601	3	∈	∈	PROPN
ejpam-2660	601	4	p	p	NOUN
ejpam-2660	601	5	and	and	CCONJ
ejpam-2660	601	6	x′	x′	PROPN
ejpam-2660	601	7	∈	∈	PROPN
ejpam-2660	601	8	p	p	PROPN
ejpam-2660	601	9	,	,	PUNCT
ejpam-2660	601	10	which	which	PRON
ejpam-2660	601	11	is	be	AUX
ejpam-2660	601	12	a	a	DET
ejpam-2660	601	13	contradiction	contradiction	NOUN
ejpam-2660	601	14	.	.	PUNCT
ejpam-2660	602	1	conversely	conversely	ADV
ejpam-2660	602	2	,	,	PUNCT
ejpam-2660	602	3	let	let	VERB
ejpam-2660	602	4	x	x	PUNCT
ejpam-2660	602	5	∈	∈	PROPN
ejpam-2660	602	6	p	p	NOUN
ejpam-2660	602	7	or	or	CCONJ
ejpam-2660	602	8	x′	x′	PROPN
ejpam-2660	602	9	∈	∈	PROPN
ejpam-2660	602	10	p	p	PROPN
ejpam-2660	602	11	,	,	PUNCT
ejpam-2660	602	12	for	for	ADP
ejpam-2660	602	13	all	all	DET
ejpam-2660	602	14	x	x	SYM
ejpam-2660	602	15	∈	∈	PROPN
ejpam-2660	602	16	l.	l.	NOUN
ejpam-2660	602	17	suppose	suppose	VERB
ejpam-2660	602	18	that	that	SCONJ
ejpam-2660	602	19	x	x	PROPN
ejpam-2660	602	20	,	,	PUNCT
ejpam-2660	602	21	y	y	PROPN
ejpam-2660	602	22	/∈	/∈	PUNCT
ejpam-2660	603	1	p	p	X
ejpam-2660	603	2	.	.	PUNCT
ejpam-2660	604	1	if	if	SCONJ
ejpam-2660	604	2	x	x	PROPN
ejpam-2660	604	3	∨	∨	NUM
ejpam-2660	604	4	y′	y′	X
ejpam-2660	604	5	/∈	/∈	PUNCT
ejpam-2660	605	1	p	p	NOUN
ejpam-2660	605	2	or	or	CCONJ
ejpam-2660	605	3	y	y	PROPN
ejpam-2660	605	4	∨	∨	NUM
ejpam-2660	605	5	x′	x′	PROPN
ejpam-2660	605	6	/∈	/∈	PUNCT
ejpam-2660	606	1	p	p	NOUN
ejpam-2660	606	2	,	,	PUNCT
ejpam-2660	606	3	then	then	ADV
ejpam-2660	606	4	(	(	PUNCT
ejpam-2660	606	5	x	x	PROPN
ejpam-2660	606	6	∨	∨	NUM
ejpam-2660	606	7	y′)′	y′)′	PROPN
ejpam-2660	606	8	∈	∈	PROPN
ejpam-2660	606	9	p	p	NOUN
ejpam-2660	606	10	or	or	CCONJ
ejpam-2660	606	11	(	(	PUNCT
ejpam-2660	606	12	y	y	PROPN
ejpam-2660	606	13	∨	∨	PROPN
ejpam-2660	606	14	x′)′	x′)′	PROPN
ejpam-2660	607	1	∈	∈	PROPN
ejpam-2660	607	2	p	p	NOUN
ejpam-2660	607	3	.	.	PUNCT
ejpam-2660	608	1	we	we	PRON
ejpam-2660	608	2	have	have	VERB
ejpam-2660	608	3	y′	y′	NOUN
ejpam-2660	608	4	≤	≤	NUM
ejpam-2660	608	5	x	x	PUNCT
ejpam-2660	608	6	∨	∨	NUM
ejpam-2660	608	7	y′	y′	NUM
ejpam-2660	608	8	,	,	PUNCT
ejpam-2660	608	9	by	by	ADP
ejpam-2660	608	10	theorem	theorem	NOUN
ejpam-2660	608	11	71	71	NUM
ejpam-2660	608	12	,	,	PUNCT
ejpam-2660	608	13	(	(	PUNCT
ejpam-2660	608	14	x	x	SYM
ejpam-2660	608	15	∨	∨	NUM
ejpam-2660	608	16	y′)′	y′)′	PROPN
ejpam-2660	608	17	≤	≤	NUM
ejpam-2660	608	18	y.	y.	NOUN
ejpam-2660	608	19	since	since	SCONJ
ejpam-2660	608	20	p	p	NOUN
ejpam-2660	608	21	is	be	AUX
ejpam-2660	608	22	a	a	DET
ejpam-2660	608	23	hyperfilter	hyperfilter	NOUN
ejpam-2660	608	24	and	and	CCONJ
ejpam-2660	608	25	(	(	PUNCT
ejpam-2660	608	26	x	x	PROPN
ejpam-2660	608	27	∨	∨	NUM
ejpam-2660	608	28	y′)′	y′)′	PROPN
ejpam-2660	608	29	∈	∈	PROPN
ejpam-2660	608	30	p	p	NOUN
ejpam-2660	608	31	,	,	PUNCT
ejpam-2660	608	32	y	y	PROPN
ejpam-2660	608	33	∈	∈	PROPN
ejpam-2660	608	34	p	p	PROPN
ejpam-2660	608	35	,	,	PUNCT
ejpam-2660	608	36	which	which	PRON
ejpam-2660	608	37	is	be	AUX
ejpam-2660	608	38	a	a	DET
ejpam-2660	608	39	contradiction	contradiction	NOUN
ejpam-2660	608	40	.	.	PUNCT
ejpam-2660	609	1	if	if	SCONJ
ejpam-2660	609	2	(	(	PUNCT
ejpam-2660	609	3	y	y	PROPN
ejpam-2660	609	4	∨	∨	PROPN
ejpam-2660	609	5	x′)′	x′)′	PROPN
ejpam-2660	610	1	∈	∈	PROPN
ejpam-2660	610	2	p	p	NOUN
ejpam-2660	610	3	,	,	PUNCT
ejpam-2660	610	4	similarly	similarly	ADV
ejpam-2660	610	5	,	,	PUNCT
ejpam-2660	610	6	it	it	PRON
ejpam-2660	610	7	is	be	AUX
ejpam-2660	610	8	proved	prove	VERB
ejpam-2660	610	9	that	that	SCONJ
ejpam-2660	610	10	x	x	PUNCT
ejpam-2660	610	11	∈	∈	PROPN
ejpam-2660	610	12	p	p	NOUN
ejpam-2660	610	13	,	,	PUNCT
ejpam-2660	610	14	which	which	PRON
ejpam-2660	610	15	is	be	AUX
ejpam-2660	610	16	a	a	DET
ejpam-2660	610	17	contradiction	contradiction	NOUN
ejpam-2660	610	18	.	.	PUNCT
ejpam-2660	611	1	theorem	theorem	NOUN
ejpam-2660	611	2	76	76	NUM
ejpam-2660	611	3	.	.	PUNCT
ejpam-2660	612	1	let	let	VERB
ejpam-2660	612	2	l	l	NOUN
ejpam-2660	612	3	be	be	AUX
ejpam-2660	612	4	a	a	DET
ejpam-2660	612	5	complemented	complemented	ADJ
ejpam-2660	612	6	∧-hyperlattice	∧-hyperlattice	NOUN
ejpam-2660	612	7	.	.	PUNCT
ejpam-2660	613	1	then	then	ADV
ejpam-2660	613	2	every	every	DET
ejpam-2660	613	3	prime	prime	ADJ
ejpam-2660	613	4	hyperfilter	hyperfilter	NOUN
ejpam-2660	613	5	of	of	ADP
ejpam-2660	613	6	l	l	NOUN
ejpam-2660	613	7	is	be	AUX
ejpam-2660	613	8	a	a	DET
ejpam-2660	613	9	maximal	maximal	ADJ
ejpam-2660	613	10	hyperfilter	hyperfilter	NOUN
ejpam-2660	613	11	.	.	PUNCT
ejpam-2660	614	1	proof	proof	NOUN
ejpam-2660	614	2	.	.	PUNCT
ejpam-2660	615	1	let	let	VERB
ejpam-2660	615	2	p	p	PRON
ejpam-2660	615	3	be	be	AUX
ejpam-2660	615	4	a	a	DET
ejpam-2660	615	5	prime	prime	ADJ
ejpam-2660	615	6	hyperfilter	hyperfilter	NOUN
ejpam-2660	615	7	and	and	CCONJ
ejpam-2660	615	8	f	f	PROPN
ejpam-2660	615	9	be	be	AUX
ejpam-2660	615	10	a	a	DET
ejpam-2660	615	11	hyperfilter	hyperfilter	NOUN
ejpam-2660	615	12	of	of	ADP
ejpam-2660	615	13	l	l	NOUN
ejpam-2660	615	14	such	such	ADJ
ejpam-2660	615	15	that	that	SCONJ
ejpam-2660	615	16	p	p	PROPN
ejpam-2660	615	17	$	$	SYM
ejpam-2660	615	18	f	f	NOUN
ejpam-2660	615	19	.	.	PUNCT
ejpam-2660	616	1	so	so	ADV
ejpam-2660	616	2	there	there	PRON
ejpam-2660	616	3	exists	exist	VERB
ejpam-2660	617	1	a	a	DET
ejpam-2660	617	2	∈	∈	PROPN
ejpam-2660	617	3	f	f	X
ejpam-2660	617	4	\	\	PROPN
ejpam-2660	617	5	p	p	X
ejpam-2660	617	6	,	,	PUNCT
ejpam-2660	617	7	since	since	SCONJ
ejpam-2660	617	8	p	p	NOUN
ejpam-2660	617	9	is	be	AUX
ejpam-2660	617	10	a	a	DET
ejpam-2660	617	11	prime	prime	ADJ
ejpam-2660	617	12	hyperfilter	hyperfilter	NOUN
ejpam-2660	617	13	and	and	CCONJ
ejpam-2660	617	14	a	a	DET
ejpam-2660	617	15	/∈	/∈	NOUN
ejpam-2660	617	16	p	p	NOUN
ejpam-2660	617	17	,	,	PUNCT
ejpam-2660	617	18	a′	a′	PROPN
ejpam-2660	617	19	∈	∈	PROPN
ejpam-2660	617	20	p	p	VERB
ejpam-2660	617	21	⊆	⊆	NUM
ejpam-2660	617	22	f	f	NOUN
ejpam-2660	617	23	.	.	PUNCT
ejpam-2660	618	1	we	we	PRON
ejpam-2660	618	2	have	have	VERB
ejpam-2660	618	3	a	a	PRON
ejpam-2660	618	4	,	,	PUNCT
ejpam-2660	618	5	a′	a′	PROPN
ejpam-2660	618	6	∈	∈	PROPN
ejpam-2660	618	7	f	f	PROPN
ejpam-2660	618	8	;	;	PUNCT
ejpam-2660	618	9	since	since	SCONJ
ejpam-2660	618	10	f	f	PROPN
ejpam-2660	618	11	is	be	AUX
ejpam-2660	618	12	a	a	DET
ejpam-2660	618	13	hyperfilter	hyperfilter	NOUN
ejpam-2660	618	14	,	,	PUNCT
ejpam-2660	618	15	x	x	X
ejpam-2660	618	16	∧	∧	NOUN
ejpam-2660	618	17	x′	x′	PROPN
ejpam-2660	618	18	⊆	⊆	NUM
ejpam-2660	618	19	f	f	NOUN
ejpam-2660	618	20	.	.	PUNCT
ejpam-2660	619	1	so	so	ADV
ejpam-2660	619	2	0	0	NUM
ejpam-2660	619	3	∈	∈	ADJ
ejpam-2660	619	4	f	f	NOUN
ejpam-2660	619	5	,	,	PUNCT
ejpam-2660	619	6	since	since	SCONJ
ejpam-2660	619	7	0	0	NUM
ejpam-2660	619	8	≤	≤	NUM
ejpam-2660	619	9	x	x	PUNCT
ejpam-2660	619	10	for	for	ADP
ejpam-2660	619	11	all	all	DET
ejpam-2660	619	12	x	x	SYM
ejpam-2660	619	13	∈	∈	PROPN
ejpam-2660	619	14	l	l	NOUN
ejpam-2660	619	15	,	,	PUNCT
ejpam-2660	619	16	x	x	PROPN
ejpam-2660	619	17	∈	∈	PROPN
ejpam-2660	619	18	f	f	X
ejpam-2660	619	19	.	.	PUNCT
ejpam-2660	620	1	then	then	ADV
ejpam-2660	620	2	f	f	PROPN
ejpam-2660	620	3	=	=	SYM
ejpam-2660	620	4	l	l	PROPN
ejpam-2660	620	5	,	,	PUNCT
ejpam-2660	620	6	and	and	CCONJ
ejpam-2660	620	7	we	we	PRON
ejpam-2660	620	8	conclude	conclude	VERB
ejpam-2660	620	9	that	that	SCONJ
ejpam-2660	620	10	p	p	NOUN
ejpam-2660	620	11	is	be	AUX
ejpam-2660	620	12	a	a	DET
ejpam-2660	620	13	maximal	maximal	ADJ
ejpam-2660	620	14	hyperfilter	hyperfilter	NOUN
ejpam-2660	620	15	.	.	PUNCT
ejpam-2660	621	1	problem	problem	NOUN
ejpam-2660	621	2	:	:	PUNCT
ejpam-2660	621	3	under	under	ADP
ejpam-2660	621	4	what	what	PRON
ejpam-2660	621	5	suitable	suitable	ADJ
ejpam-2660	621	6	condition	condition	NOUN
ejpam-2660	621	7	the	the	DET
ejpam-2660	621	8	converse	converse	NOUN
ejpam-2660	621	9	of	of	ADP
ejpam-2660	621	10	theorem76	theorem76	NOUN
ejpam-2660	621	11	is	be	AUX
ejpam-2660	621	12	correct	correct	ADJ
ejpam-2660	621	13	?	?	PUNCT
ejpam-2660	622	1	theorem	theorem	VERB
ejpam-2660	622	2	77	77	NUM
ejpam-2660	622	3	.	.	PUNCT
ejpam-2660	623	1	let	let	VERB
ejpam-2660	623	2	l	l	NOUN
ejpam-2660	623	3	be	be	AUX
ejpam-2660	623	4	a	a	DET
ejpam-2660	623	5	distributive	distributive	ADJ
ejpam-2660	623	6	good	good	ADJ
ejpam-2660	623	7	complemented	complemented	ADJ
ejpam-2660	623	8	∧-hyperlattice	∧-hyperlattice	NOUN
ejpam-2660	623	9	.	.	PUNCT
ejpam-2660	624	1	then	then	ADV
ejpam-2660	624	2	the	the	DET
ejpam-2660	624	3	following	follow	VERB
ejpam-2660	624	4	conditions	condition	NOUN
ejpam-2660	624	5	are	be	AUX
ejpam-2660	624	6	equivalent	equivalent	ADJ
ejpam-2660	624	7	.	.	PUNCT
ejpam-2660	625	1	(	(	PUNCT
ejpam-2660	625	2	i	i	NOUN
ejpam-2660	625	3	)	)	PUNCT
ejpam-2660	625	4	{	{	PUNCT
ejpam-2660	625	5	1	1	NUM
ejpam-2660	625	6	}	}	PUNCT
ejpam-2660	625	7	is	be	AUX
ejpam-2660	625	8	a	a	DET
ejpam-2660	625	9	prime	prime	ADJ
ejpam-2660	625	10	hyperfilter	hyperfilter	NOUN
ejpam-2660	625	11	of	of	ADP
ejpam-2660	625	12	l.	l.	PROPN
ejpam-2660	625	13	(	(	PUNCT
ejpam-2660	625	14	ii	ii	PROPN
ejpam-2660	625	15	)	)	PUNCT
ejpam-2660	625	16	all	all	DET
ejpam-2660	625	17	the	the	DET
ejpam-2660	625	18	hyperfilters	hyperfilter	NOUN
ejpam-2660	625	19	of	of	ADP
ejpam-2660	625	20	l	l	NOUN
ejpam-2660	625	21	are	be	AUX
ejpam-2660	625	22	prime	prime	ADJ
ejpam-2660	625	23	.	.	PUNCT
ejpam-2660	626	1	(	(	PUNCT
ejpam-2660	626	2	iii	iii	NOUN
ejpam-2660	626	3	)	)	PUNCT
ejpam-2660	626	4	(	(	PUNCT
ejpam-2660	626	5	l,≤	l,≤	PROPN
ejpam-2660	626	6	)	)	PUNCT
ejpam-2660	626	7	is	be	AUX
ejpam-2660	626	8	a	a	DET
ejpam-2660	626	9	chain	chain	NOUN
ejpam-2660	626	10	and	and	CCONJ
ejpam-2660	626	11	l	l	NOUN
ejpam-2660	626	12	=	=	PUNCT
ejpam-2660	627	1	{	{	PUNCT
ejpam-2660	627	2	0	0	NUM
ejpam-2660	627	3	,	,	PUNCT
ejpam-2660	627	4	1	1	NUM
ejpam-2660	627	5	}	}	PUNCT
ejpam-2660	627	6	.	.	PUNCT
ejpam-2660	628	1	proof	proof	NOUN
ejpam-2660	628	2	.	.	PUNCT
ejpam-2660	629	1	(	(	PUNCT
ejpam-2660	629	2	i	i	NOUN
ejpam-2660	629	3	)	)	PUNCT
ejpam-2660	630	1	=	=	NOUN
ejpam-2660	630	2	⇒	⇒	NOUN
ejpam-2660	630	3	(	(	PUNCT
ejpam-2660	630	4	ii	ii	NOUN
ejpam-2660	630	5	)	)	PUNCT
ejpam-2660	630	6	let	let	VERB
ejpam-2660	630	7	f	f	PRON
ejpam-2660	630	8	be	be	AUX
ejpam-2660	630	9	a	a	DET
ejpam-2660	630	10	filter	filter	NOUN
ejpam-2660	630	11	of	of	ADP
ejpam-2660	630	12	l.	l.	PROPN
ejpam-2660	630	13	assume	assume	VERB
ejpam-2660	630	14	that	that	SCONJ
ejpam-2660	630	15	x	x	PUNCT
ejpam-2660	630	16	∈	∈	PROPN
ejpam-2660	630	17	l	l	NOUN
ejpam-2660	630	18	and	and	CCONJ
ejpam-2660	630	19	x	x	SYM
ejpam-2660	630	20	/∈	/∈	PROPN
ejpam-2660	631	1	f	f	PROPN
ejpam-2660	631	2	.	.	PUNCT
ejpam-2660	632	1	we	we	PRON
ejpam-2660	632	2	must	must	AUX
ejpam-2660	632	3	show	show	VERB
ejpam-2660	632	4	that	that	SCONJ
ejpam-2660	632	5	x′	x′	PROPN
ejpam-2660	632	6	∈	∈	PROPN
ejpam-2660	632	7	f	f	PROPN
ejpam-2660	632	8	.	.	PUNCT
ejpam-2660	633	1	since	since	SCONJ
ejpam-2660	633	2	x∨	x∨	PROPN
ejpam-2660	633	3	x′	x′	PROPN
ejpam-2660	633	4	=	=	SYM
ejpam-2660	633	5	1	1	NUM
ejpam-2660	633	6	and	and	CCONJ
ejpam-2660	633	7	{	{	PUNCT
ejpam-2660	633	8	1	1	NUM
ejpam-2660	633	9	}	}	PUNCT
ejpam-2660	633	10	is	be	AUX
ejpam-2660	633	11	a	a	DET
ejpam-2660	633	12	prime	prime	ADJ
ejpam-2660	633	13	filter	filter	NOUN
ejpam-2660	633	14	,	,	PUNCT
ejpam-2660	633	15	so	so	ADV
ejpam-2660	633	16	x	x	SYM
ejpam-2660	634	1	=	=	SYM
ejpam-2660	634	2	1	1	NUM
ejpam-2660	634	3	or	or	CCONJ
ejpam-2660	634	4	x′	x′	NUM
ejpam-2660	634	5	=	=	SYM
ejpam-2660	634	6	1	1	X
ejpam-2660	634	7	.	.	X
ejpam-2660	635	1	we	we	PRON
ejpam-2660	635	2	know	know	VERB
ejpam-2660	635	3	that	that	SCONJ
ejpam-2660	635	4	x	x	PROPN
ejpam-2660	635	5	6=	6=	ADP
ejpam-2660	635	6	1	1	NUM
ejpam-2660	635	7	,	,	PUNCT
ejpam-2660	635	8	thus	thus	ADV
ejpam-2660	635	9	x′	x′	X
ejpam-2660	636	1	=	=	SYM
ejpam-2660	636	2	1	1	NUM
ejpam-2660	636	3	∈	∈	PROPN
ejpam-2660	636	4	f	f	NOUN
ejpam-2660	636	5	.	.	PUNCT
ejpam-2660	637	1	(	(	PUNCT
ejpam-2660	637	2	ii	ii	NOUN
ejpam-2660	637	3	)	)	PUNCT
ejpam-2660	637	4	=	=	NOUN
ejpam-2660	637	5	⇒	⇒	NOUN
ejpam-2660	637	6	(	(	PUNCT
ejpam-2660	637	7	i	i	NOUN
ejpam-2660	637	8	)	)	PUNCT
ejpam-2660	637	9	is	be	AUX
ejpam-2660	637	10	obvious	obvious	ADJ
ejpam-2660	637	11	.	.	PUNCT
ejpam-2660	638	1	(	(	PUNCT
ejpam-2660	638	2	i	i	NOUN
ejpam-2660	638	3	)	)	PUNCT
ejpam-2660	639	1	=	=	NOUN
ejpam-2660	639	2	⇒	⇒	NOUN
ejpam-2660	639	3	(	(	PUNCT
ejpam-2660	639	4	iii	iii	NOUN
ejpam-2660	639	5	)	)	PUNCT
ejpam-2660	639	6	since	since	SCONJ
ejpam-2660	639	7	{	{	PUNCT
ejpam-2660	639	8	1	1	NUM
ejpam-2660	639	9	}	}	PUNCT
ejpam-2660	639	10	is	be	AUX
ejpam-2660	639	11	a	a	DET
ejpam-2660	639	12	prime	prime	ADJ
ejpam-2660	639	13	hyperfilter	hyperfilter	NOUN
ejpam-2660	639	14	of	of	ADP
ejpam-2660	639	15	l	l	NOUN
ejpam-2660	639	16	,	,	PUNCT
ejpam-2660	639	17	∀x	∀x	VERB
ejpam-2660	639	18	∈	∈	PROPN
ejpam-2660	639	19	l	l	NOUN
ejpam-2660	639	20	,	,	PUNCT
ejpam-2660	639	21	x	x	SYM
ejpam-2660	639	22	=	=	SYM
ejpam-2660	639	23	1	1	NUM
ejpam-2660	639	24	or	or	CCONJ
ejpam-2660	639	25	x′	x′	NUM
ejpam-2660	639	26	=	=	SYM
ejpam-2660	639	27	1	1	X
ejpam-2660	639	28	.	.	X
ejpam-2660	640	1	we	we	PRON
ejpam-2660	640	2	have	have	VERB
ejpam-2660	640	3	x	x	X
ejpam-2660	640	4	6=	6=	ADP
ejpam-2660	640	5	1	1	NUM
ejpam-2660	640	6	,	,	PUNCT
ejpam-2660	640	7	also	also	ADV
ejpam-2660	640	8	since	since	SCONJ
ejpam-2660	640	9	l	l	NOUN
ejpam-2660	640	10	is	be	AUX
ejpam-2660	640	11	distributive	distributive	ADJ
ejpam-2660	640	12	good	good	ADJ
ejpam-2660	640	13	complemented	complemented	ADJ
ejpam-2660	640	14	and	and	CCONJ
ejpam-2660	640	15	x′	x′	NUM
ejpam-2660	640	16	=	=	SYM
ejpam-2660	640	17	1	1	NUM
ejpam-2660	640	18	,	,	PUNCT
ejpam-2660	640	19	by	by	ADP
ejpam-2660	640	20	theorem	theorem	NOUN
ejpam-2660	640	21	71	71	NUM
ejpam-2660	640	22	,	,	PUNCT
ejpam-2660	640	23	we	we	PRON
ejpam-2660	640	24	conclude	conclude	VERB
ejpam-2660	640	25	that	that	SCONJ
ejpam-2660	640	26	x	x	X
ejpam-2660	641	1	=	=	SYM
ejpam-2660	641	2	0	0	X
ejpam-2660	641	3	.	.	PUNCT
ejpam-2660	642	1	therefore	therefore	ADV
ejpam-2660	642	2	l	l	NOUN
ejpam-2660	642	3	=	=	PUNCT
ejpam-2660	642	4	{	{	PUNCT
ejpam-2660	642	5	0	0	NUM
ejpam-2660	642	6	,	,	PUNCT
ejpam-2660	642	7	1	1	NUM
ejpam-2660	642	8	}	}	PUNCT
ejpam-2660	642	9	and	and	CCONJ
ejpam-2660	642	10	l	l	NOUN
ejpam-2660	642	11	is	be	AUX
ejpam-2660	642	12	a	a	DET
ejpam-2660	642	13	chain	chain	NOUN
ejpam-2660	642	14	.	.	PUNCT
ejpam-2660	643	1	(	(	PUNCT
ejpam-2660	643	2	iii	iii	X
ejpam-2660	643	3	)	)	PUNCT
ejpam-2660	643	4	=	=	NOUN
ejpam-2660	643	5	⇒	⇒	NOUN
ejpam-2660	643	6	(	(	PUNCT
ejpam-2660	643	7	i	i	NOUN
ejpam-2660	643	8	)	)	PUNCT
ejpam-2660	643	9	is	be	AUX
ejpam-2660	643	10	obvious	obvious	ADJ
ejpam-2660	643	11	.	.	PUNCT
ejpam-2660	644	1	references	reference	NOUN
ejpam-2660	644	2	187	187	NUM
ejpam-2660	644	3	references	reference	NOUN
ejpam-2660	644	4	[	[	X
ejpam-2660	644	5	1	1	NUM
ejpam-2660	644	6	]	]	X
ejpam-2660	644	7	r.	r.	PROPN
ejpam-2660	644	8	ameri	ameri	PROPN
ejpam-2660	644	9	and	and	CCONJ
ejpam-2660	644	10	t.	t.	PROPN
ejpam-2660	644	11	nozari	nozari	PROPN
ejpam-2660	644	12	,	,	PUNCT
ejpam-2660	644	13	”	"	PUNCT
ejpam-2660	644	14	a	a	DET
ejpam-2660	644	15	connection	connection	NOUN
ejpam-2660	644	16	between	between	ADP
ejpam-2660	644	17	categories	category	NOUN
ejpam-2660	644	18	of	of	ADP
ejpam-2660	644	19	multialgebras	multialgebra	NOUN
ejpam-2660	644	20	and	and	CCONJ
ejpam-2660	644	21	algebra	algebra	PROPN
ejpam-2660	644	22	”	"	PUNCT
ejpam-2660	644	23	,	,	PUNCT
ejpam-2660	644	24	italian	italian	ADJ
ejpam-2660	644	25	journal	journal	NOUN
ejpam-2660	644	26	of	of	ADP
ejpam-2660	644	27	pure	pure	ADJ
ejpam-2660	644	28	and	and	CCONJ
ejpam-2660	644	29	applied	applied	ADJ
ejpam-2660	644	30	mathematics	mathematic	NOUN
ejpam-2660	644	31	,	,	PUNCT
ejpam-2660	644	32	vol	vol	NOUN
ejpam-2660	644	33	.	.	PROPN
ejpam-2660	644	34	27	27	NUM
ejpam-2660	644	35	,	,	PUNCT
ejpam-2660	644	36	201	201	NUM
ejpam-2660	644	37	-	-	SYM
ejpam-2660	644	38	208	208	NUM
ejpam-2660	644	39	,	,	PUNCT
ejpam-2660	644	40	2010	2010	NUM
ejpam-2660	644	41	.	.	PUNCT
ejpam-2660	645	1	[	[	X
ejpam-2660	645	2	2	2	NUM
ejpam-2660	645	3	]	]	X
ejpam-2660	645	4	r.	r.	PROPN
ejpam-2660	645	5	ameri	ameri	PROPN
ejpam-2660	645	6	and	and	CCONJ
ejpam-2660	645	7	i.	i.	PROPN
ejpam-2660	645	8	g.	g.	PROPN
ejpam-2660	645	9	rosenberg	rosenberg	PROPN
ejpam-2660	645	10	,	,	PUNCT
ejpam-2660	645	11	”	"	PUNCT
ejpam-2660	645	12	congruences	congruence	NOUN
ejpam-2660	645	13	of	of	ADP
ejpam-2660	645	14	multialgebras	multialgebra	NOUN
ejpam-2660	645	15	”	"	PUNCT
ejpam-2660	645	16	,	,	PUNCT
ejpam-2660	645	17	j.	j.	PROPN
ejpam-2660	645	18	of	of	ADP
ejpam-2660	645	19	multi	multi	ADJ
ejpam-2660	645	20	-	-	ADJ
ejpam-2660	645	21	valued	value	VERB
ejpam-2660	645	22	logic	logic	NOUN
ejpam-2660	645	23	&	&	CCONJ
ejpam-2660	645	24	soft	soft	ADJ
ejpam-2660	645	25	computing	computing	NOUN
ejpam-2660	645	26	,	,	PUNCT
ejpam-2660	645	27	vol	vol	NOUN
ejpam-2660	645	28	.	.	PROPN
ejpam-2660	645	29	00	00	NUM
ejpam-2660	645	30	,	,	PUNCT
ejpam-2660	645	31	1	1	NUM
ejpam-2660	645	32	-	-	SYM
ejpam-2660	645	33	12	12	NUM
ejpam-2660	645	34	,	,	PUNCT
ejpam-2660	645	35	2009	2009	NUM
ejpam-2660	645	36	.	.	PUNCT
ejpam-2660	646	1	[	[	X
ejpam-2660	646	2	3	3	NUM
ejpam-2660	646	3	]	]	X
ejpam-2660	646	4	r.	r.	PROPN
ejpam-2660	646	5	ameri	ameri	PROPN
ejpam-2660	646	6	and	and	CCONJ
ejpam-2660	646	7	m.	m.	PROPN
ejpam-2660	646	8	m.	m.	PROPN
ejpam-2660	646	9	zahedi	zahedi	PROPN
ejpam-2660	646	10	,	,	PUNCT
ejpam-2660	646	11	”	"	PUNCT
ejpam-2660	646	12	hyperalgebraic	hyperalgebraic	ADJ
ejpam-2660	646	13	system	system	NOUN
ejpam-2660	646	14	”	"	PUNCT
ejpam-2660	646	15	,	,	PUNCT
ejpam-2660	646	16	italian	italian	ADJ
ejpam-2660	646	17	journal	journal	NOUN
ejpam-2660	646	18	of	of	ADP
ejpam-2660	646	19	pure	pure	ADJ
ejpam-2660	646	20	and	and	CCONJ
ejpam-2660	646	21	applied	applied	ADJ
ejpam-2660	646	22	mathematics	mathematic	NOUN
ejpam-2660	646	23	,	,	PUNCT
ejpam-2660	646	24	vol	vol	NOUN
ejpam-2660	646	25	.	.	PROPN
ejpam-2660	646	26	6	6	NUM
ejpam-2660	646	27	,	,	PUNCT
ejpam-2660	646	28	21	21	NUM
ejpam-2660	646	29	-	-	SYM
ejpam-2660	646	30	39	39	NUM
ejpam-2660	646	31	,	,	PUNCT
ejpam-2660	646	32	1999	1999	NUM
ejpam-2660	646	33	.	.	PUNCT
ejpam-2660	647	1	[	[	X
ejpam-2660	647	2	4	4	NUM
ejpam-2660	647	3	]	]	PUNCT
ejpam-2660	647	4	a.	a.	NOUN
ejpam-2660	647	5	asokkumar	asokkumar	PROPN
ejpam-2660	647	6	,	,	PUNCT
ejpam-2660	647	7	”	"	PUNCT
ejpam-2660	647	8	hyperlattice	hyperlattice	NOUN
ejpam-2660	647	9	formed	form	VERB
ejpam-2660	647	10	by	by	ADP
ejpam-2660	647	11	the	the	DET
ejpam-2660	647	12	idempotents	idempotent	NOUN
ejpam-2660	647	13	of	of	ADP
ejpam-2660	647	14	a	a	DET
ejpam-2660	647	15	hyperring	hyperring	NOUN
ejpam-2660	647	16	”	"	PUNCT
ejpam-2660	647	17	,	,	PUNCT
ejpam-2660	647	18	international	international	ADJ
ejpam-2660	647	19	journal	journal	NOUN
ejpam-2660	647	20	of	of	ADP
ejpam-2660	647	21	mathematics	mathematics	PROPN
ejpam-2660	647	22	,	,	PUNCT
ejpam-2660	647	23	vol	vol	NOUN
ejpam-2660	647	24	.	.	PROPN
ejpam-2660	648	1	38	38	NUM
ejpam-2660	648	2	,	,	PUNCT
ejpam-2660	648	3	209	209	NUM
ejpam-2660	648	4	-	-	SYM
ejpam-2660	648	5	215	215	NUM
ejpam-2660	648	6	,	,	PUNCT
ejpam-2660	648	7	2007	2007	NUM
ejpam-2660	648	8	.	.	PUNCT
ejpam-2660	649	1	[	[	X
ejpam-2660	649	2	5	5	X
ejpam-2660	649	3	]	]	PUNCT
ejpam-2660	649	4	g.	g.	PROPN
ejpam-2660	649	5	e.	e.	PROPN
ejpam-2660	649	6	hansoul	hansoul	PROPN
ejpam-2660	649	7	,	,	PUNCT
ejpam-2660	649	8	”	"	PUNCT
ejpam-2660	649	9	a	a	DET
ejpam-2660	649	10	simultianeous	simultianeous	ADJ
ejpam-2660	649	11	characterization	characterization	NOUN
ejpam-2660	649	12	of	of	ADP
ejpam-2660	649	13	subalgebras	subalgebras	PROPN
ejpam-2660	649	14	and	and	CCONJ
ejpam-2660	649	15	conditional	conditional	ADJ
ejpam-2660	649	16	sunalgebras	sunalgebra	NOUN
ejpam-2660	649	17	of	of	ADP
ejpam-2660	649	18	a	a	DET
ejpam-2660	649	19	multialgebra	multialgebra	NOUN
ejpam-2660	649	20	”	"	PUNCT
ejpam-2660	649	21	,	,	PUNCT
ejpam-2660	649	22	bull	bull	NOUN
ejpam-2660	649	23	.	.	PUNCT
ejpam-2660	650	1	soc	soc	PROPN
ejpam-2660	650	2	.	.	PUNCT
ejpam-2660	651	1	roy	roy	PROPN
ejpam-2660	651	2	.	.	PROPN
ejpam-2660	651	3	science	science	PROPN
ejpam-2660	651	4	liego	liego	PROPN
ejpam-2660	651	5	,	,	PUNCT
ejpam-2660	651	6	vol	vol	NOUN
ejpam-2660	651	7	.	.	PROPN
ejpam-2660	652	1	50	50	NUM
ejpam-2660	652	2	,	,	PUNCT
ejpam-2660	652	3	16	16	NUM
ejpam-2660	652	4	-	-	SYM
ejpam-2660	652	5	19	19	NUM
ejpam-2660	652	6	,	,	PUNCT
ejpam-2660	652	7	1981	1981	NUM
ejpam-2660	652	8	.	.	PUNCT
ejpam-2660	653	1	[	[	X
ejpam-2660	653	2	6	6	NUM
ejpam-2660	653	3	]	]	PUNCT
ejpam-2660	653	4	p.	p.	NOUN
ejpam-2660	653	5	he	he	PRON
ejpam-2660	653	6	,	,	PUNCT
ejpam-2660	653	7	x.	x.	PROPN
ejpam-2660	653	8	xin	xin	PROPN
ejpam-2660	653	9	,	,	PUNCT
ejpam-2660	653	10	and	and	CCONJ
ejpam-2660	653	11	jianming	jianme	VERB
ejpam-2660	653	12	zhan	zhan	PROPN
ejpam-2660	653	13	,	,	PUNCT
ejpam-2660	653	14	”	"	PUNCT
ejpam-2660	653	15	on	on	ADP
ejpam-2660	653	16	rough	rough	ADJ
ejpam-2660	653	17	hyperideals	hyperideal	NOUN
ejpam-2660	653	18	in	in	ADP
ejpam-2660	653	19	hyperlattices	hyperlattice	NOUN
ejpam-2660	653	20	”	"	PUNCT
ejpam-2660	653	21	,	,	PUNCT
ejpam-2660	653	22	journal	journal	NOUN
ejpam-2660	653	23	of	of	ADP
ejpam-2660	653	24	applied	apply	VERB
ejpam-2660	653	25	and	and	CCONJ
ejpam-2660	653	26	mathematics	mathematic	NOUN
ejpam-2660	653	27	,	,	PUNCT
ejpam-2660	653	28	vol	vol	NOUN
ejpam-2660	653	29	.	.	PROPN
ejpam-2660	653	30	2013	2013	NUM
ejpam-2660	653	31	,	,	PUNCT
ejpam-2660	653	32	10	10	NUM
ejpam-2660	653	33	page	page	NOUN
ejpam-2660	653	34	.	.	PUNCT
ejpam-2660	654	1	[	[	X
ejpam-2660	654	2	7	7	X
ejpam-2660	654	3	]	]	X
ejpam-2660	654	4	b.	b.	PROPN
ejpam-2660	654	5	b.	b.	PROPN
ejpam-2660	654	6	n.	n.	PROPN
ejpam-2660	654	7	koguep	koguep	PROPN
ejpam-2660	654	8	,	,	PUNCT
ejpam-2660	654	9	c.	c.	PROPN
ejpam-2660	654	10	nkuimi	nkuimi	PROPN
ejpam-2660	654	11	,	,	PUNCT
ejpam-2660	654	12	c.	c.	PROPN
ejpam-2660	654	13	lele	lele	PROPN
ejpam-2660	654	14	,	,	PUNCT
ejpam-2660	654	15	”	"	PUNCT
ejpam-2660	654	16	on	on	ADP
ejpam-2660	654	17	fuzzy	fuzzy	ADJ
ejpam-2660	654	18	ideals	ideal	NOUN
ejpam-2660	654	19	of	of	ADP
ejpam-2660	654	20	hyperlattice	hyperlattice	NOUN
ejpam-2660	654	21	,	,	PUNCT
ejpam-2660	654	22	”	"	PUNCT
ejpam-2660	654	23	international	international	ADJ
ejpam-2660	654	24	journal	journal	NOUN
ejpam-2660	654	25	of	of	ADP
ejpam-2660	654	26	algebra	algebra	PROPN
ejpam-2660	654	27	,	,	PUNCT
ejpam-2660	654	28	vol	vol	NOUN
ejpam-2660	654	29	.	.	PROPN
ejpam-2660	654	30	2	2	NUM
ejpam-2660	654	31	,	,	PUNCT
ejpam-2660	654	32	739	739	NUM
ejpam-2660	654	33	-	-	SYM
ejpam-2660	654	34	750	750	NUM
ejpam-2660	654	35	.	.	PUNCT
ejpam-2660	654	36	2008	2008	NUM
ejpam-2660	654	37	.	.	PUNCT
ejpam-2660	655	1	[	[	X
ejpam-2660	655	2	8	8	NUM
ejpam-2660	655	3	]	]	PUNCT
ejpam-2660	655	4	m.	m.	NOUN
ejpam-2660	655	5	konstantinidou	konstantinidou	NOUN
ejpam-2660	655	6	-	-	PUNCT
ejpam-2660	655	7	serafimidou	serafimidou	NOUN
ejpam-2660	655	8	,	,	PUNCT
ejpam-2660	655	9	”	"	PUNCT
ejpam-2660	655	10	modular	modular	ADJ
ejpam-2660	655	11	hyperlattices	hyperlattice	NOUN
ejpam-2660	655	12	”	"	PUNCT
ejpam-2660	655	13	,	,	PUNCT
ejpam-2660	655	14	γ	γ	PROPN
ejpam-2660	655	15	ranktika	ranktika	PROPN
ejpam-2660	655	16	tes	tes	PROPN
ejpam-2660	655	17	akademias	akademias	PROPN
ejpam-2660	655	18	athenon	athenon	PROPN
ejpam-2660	655	19	,	,	PUNCT
ejpam-2660	655	20	vol	vol	NOUN
ejpam-2660	655	21	.	.	PROPN
ejpam-2660	655	22	53	53	NUM
ejpam-2660	655	23	,	,	PUNCT
ejpam-2660	655	24	202	202	NUM
ejpam-2660	655	25	-	-	SYM
ejpam-2660	655	26	218	218	NUM
ejpam-2660	655	27	,	,	PUNCT
ejpam-2660	655	28	1978	1978	NUM
ejpam-2660	655	29	.	.	PUNCT
ejpam-2660	656	1	[	[	X
ejpam-2660	656	2	9	9	NUM
ejpam-2660	656	3	]	]	PUNCT
ejpam-2660	656	4	m.	m.	NOUN
ejpam-2660	656	5	konstantinidou	konstantinidou	NOUN
ejpam-2660	656	6	-	-	PUNCT
ejpam-2660	656	7	serafimidou	serafimidou	NOUN
ejpam-2660	656	8	,	,	PUNCT
ejpam-2660	656	9	”	"	PUNCT
ejpam-2660	656	10	distributive	distributive	ADJ
ejpam-2660	656	11	and	and	CCONJ
ejpam-2660	656	12	complemented	complemented	ADJ
ejpam-2660	656	13	hyperlattices	hyperlattice	NOUN
ejpam-2660	656	14	”	"	PUNCT
ejpam-2660	656	15	,	,	PUNCT
ejpam-2660	656	16	praktika	praktika	NOUN
ejpam-2660	656	17	tes	tes	PROPN
ejpam-2660	656	18	akademias	akademias	PROPN
ejpam-2660	656	19	athenon	athenon	PROPN
ejpam-2660	656	20	,	,	PUNCT
ejpam-2660	656	21	vol	vol	NOUN
ejpam-2660	656	22	.	.	PROPN
ejpam-2660	656	23	56	56	NUM
ejpam-2660	656	24	,	,	PUNCT
ejpam-2660	656	25	339	339	NUM
ejpam-2660	656	26	-	-	SYM
ejpam-2660	656	27	360	360	NUM
ejpam-2660	656	28	,	,	PUNCT
ejpam-2660	656	29	1981	1981	NUM
ejpam-2660	656	30	.	.	PUNCT
ejpam-2660	657	1	[	[	X
ejpam-2660	657	2	10	10	NUM
ejpam-2660	657	3	]	]	PUNCT
ejpam-2660	657	4	m.	m.	NOUN
ejpam-2660	657	5	konstantinidou	konstantinidou	PROPN
ejpam-2660	657	6	,	,	PUNCT
ejpam-2660	657	7	j.	j.	PROPN
ejpam-2660	657	8	mittas	mittas	PROPN
ejpam-2660	657	9	,	,	PUNCT
ejpam-2660	657	10	”	"	PUNCT
ejpam-2660	657	11	an	an	DET
ejpam-2660	657	12	introduction	introduction	NOUN
ejpam-2660	657	13	to	to	ADP
ejpam-2660	657	14	the	the	DET
ejpam-2660	657	15	theory	theory	NOUN
ejpam-2660	657	16	of	of	ADP
ejpam-2660	657	17	hyperlattice	hyperlattice	NOUN
ejpam-2660	657	18	,	,	PUNCT
ejpam-2660	657	19	”	"	PUNCT
ejpam-2660	657	20	math	math	NOUN
ejpam-2660	657	21	.	.	PUNCT
ejpam-2660	658	1	balcanica	balcanica	ADV
ejpam-2660	658	2	,	,	PUNCT
ejpam-2660	658	3	vol	vol	NOUN
ejpam-2660	658	4	.	.	PROPN
ejpam-2660	658	5	7	7	NUM
ejpam-2660	658	6	,	,	PUNCT
ejpam-2660	658	7	187193	187193	NUM
ejpam-2660	658	8	,	,	PUNCT
ejpam-2660	658	9	1977	1977	NUM
ejpam-2660	658	10	.	.	PUNCT
ejpam-2660	659	1	[	[	X
ejpam-2660	659	2	11	11	NUM
ejpam-2660	659	3	]	]	X
ejpam-2660	659	4	f.	f.	PROPN
ejpam-2660	659	5	marty	marty	PROPN
ejpam-2660	659	6	,	,	PUNCT
ejpam-2660	659	7	”	"	PUNCT
ejpam-2660	659	8	surene	surene	NOUN
ejpam-2660	659	9	generalization	generalization	NOUN
ejpam-2660	659	10	de	de	X
ejpam-2660	659	11	la	la	PROPN
ejpam-2660	659	12	notion	notion	NOUN
ejpam-2660	659	13	de	de	PROPN
ejpam-2660	659	14	group	group	NOUN
ejpam-2660	659	15	,	,	PUNCT
ejpam-2660	659	16	in	in	ADP
ejpam-2660	659	17	eighth	eighth	ADJ
ejpam-2660	659	18	congress	congress	PROPN
ejpam-2660	659	19	scandinaves	scandinave	NOUN
ejpam-2660	659	20	,	,	PUNCT
ejpam-2660	659	21	”	"	PUNCT
ejpam-2660	659	22	stockholm	stockholm	PROPN
ejpam-2660	659	23	,	,	PUNCT
ejpam-2660	659	24	45	45	NUM
ejpam-2660	659	25	-	-	SYM
ejpam-2660	659	26	49	49	NUM
ejpam-2660	659	27	,	,	PUNCT
ejpam-2660	659	28	1934	1934	NUM
ejpam-2660	659	29	.	.	PUNCT
ejpam-2660	660	1	[	[	X
ejpam-2660	660	2	12	12	NUM
ejpam-2660	660	3	]	]	X
ejpam-2660	660	4	g.	g.	PROPN
ejpam-2660	660	5	a.	a.	PROPN
ejpam-2660	660	6	moghani	moghani	PROPN
ejpam-2660	660	7	,	,	PUNCT
ejpam-2660	660	8	a.	a.	NOUN
ejpam-2660	660	9	r	r	NOUN
ejpam-2660	660	10	,	,	PUNCT
ejpam-2660	660	11	ashrafi	ashrafi	ADV
ejpam-2660	660	12	,	,	PUNCT
ejpam-2660	660	13	”	"	PUNCT
ejpam-2660	660	14	on	on	ADP
ejpam-2660	660	15	some	some	DET
ejpam-2660	660	16	hypergroups	hypergroup	NOUN
ejpam-2660	660	17	and	and	CCONJ
ejpam-2660	660	18	their	their	PRON
ejpam-2660	660	19	hyperlattice	hyperlattice	NOUN
ejpam-2660	660	20	structures	structure	NOUN
ejpam-2660	660	21	”	"	PUNCT
ejpam-2660	660	22	,	,	PUNCT
ejpam-2660	660	23	buletinul	buletinul	NOUN
ejpam-2660	660	24	academiei	academiei	PROPN
ejpam-2660	660	25	de	de	X
ejpam-2660	660	26	stiinte	stiinte	NOUN
ejpam-2660	660	27	,	,	PUNCT
ejpam-2660	660	28	vol	vol	NOUN
ejpam-2660	660	29	.	.	PROPN
ejpam-2660	660	30	3	3	NUM
ejpam-2660	660	31	,	,	PUNCT
ejpam-2660	660	32	15	15	NUM
ejpam-2660	660	33	-	-	SYM
ejpam-2660	660	34	24	24	NUM
ejpam-2660	660	35	,	,	PUNCT
ejpam-2660	660	36	2003	2003	NUM
ejpam-2660	660	37	.	.	PUNCT
ejpam-2660	661	1	[	[	X
ejpam-2660	661	2	13	13	NUM
ejpam-2660	661	3	]	]	PUNCT
ejpam-2660	661	4	c.	c.	NOUN
ejpam-2660	661	5	pelea	pelea	PROPN
ejpam-2660	661	6	,	,	PUNCT
ejpam-2660	661	7	”	"	PUNCT
ejpam-2660	661	8	multialgebras	multialgebra	NOUN
ejpam-2660	661	9	,	,	PUNCT
ejpam-2660	661	10	universal	universal	ADJ
ejpam-2660	661	11	algebra	algebra	NOUN
ejpam-2660	661	12	,	,	PUNCT
ejpam-2660	661	13	and	and	CCONJ
ejpam-2660	661	14	identities	identity	NOUN
ejpam-2660	661	15	”	"	PUNCT
ejpam-2660	661	16	,	,	PUNCT
ejpam-2660	661	17	j.	j.	PROPN
ejpam-2660	661	18	aust	aust	PROPN
ejpam-2660	661	19	.	.	PUNCT
ejpam-2660	661	20	math	math	PROPN
ejpam-2660	661	21	,	,	PUNCT
ejpam-2660	661	22	vol	vol	NOUN
ejpam-2660	661	23	.	.	PROPN
ejpam-2660	661	24	81	81	NUM
ejpam-2660	661	25	,	,	PUNCT
ejpam-2660	661	26	121	121	NUM
ejpam-2660	661	27	-	-	SYM
ejpam-2660	661	28	139	139	NUM
ejpam-2660	661	29	,	,	PUNCT
ejpam-2660	661	30	2006	2006	NUM
ejpam-2660	661	31	.	.	PUNCT
ejpam-2660	662	1	[	[	X
ejpam-2660	662	2	14	14	NUM
ejpam-2660	662	3	]	]	X
ejpam-2660	662	4	c.	c.	NOUN
ejpam-2660	662	5	pelea	pelea	PROPN
ejpam-2660	662	6	,	,	PUNCT
ejpam-2660	662	7	”	"	PUNCT
ejpam-2660	662	8	on	on	ADP
ejpam-2660	662	9	the	the	DET
ejpam-2660	662	10	direct	direct	ADJ
ejpam-2660	662	11	limit	limit	NOUN
ejpam-2660	662	12	of	of	ADP
ejpam-2660	662	13	a	a	DET
ejpam-2660	662	14	direct	direct	ADJ
ejpam-2660	662	15	system	system	NOUN
ejpam-2660	662	16	of	of	ADP
ejpam-2660	662	17	multialgebras”,direct	multialgebras”,direct	PROPN
ejpam-2660	662	18	mathematics	mathematic	NOUN
ejpam-2660	662	19	,	,	PUNCT
ejpam-2660	662	20	vol	vol	NOUN
ejpam-2660	662	21	.	.	PROPN
ejpam-2660	662	22	306	306	NUM
ejpam-2660	662	23	,	,	PUNCT
ejpam-2660	662	24	2916	2916	NUM
ejpam-2660	662	25	-	-	SYM
ejpam-2660	662	26	2930	2930	NUM
ejpam-2660	662	27	,	,	PUNCT
ejpam-2660	662	28	2006	2006	NUM
ejpam-2660	662	29	.	.	PUNCT
ejpam-2660	663	1	[	[	X
ejpam-2660	663	2	15	15	NUM
ejpam-2660	663	3	]	]	X
ejpam-2660	663	4	c.	c.	NOUN
ejpam-2660	663	5	pelea	pelea	PROPN
ejpam-2660	663	6	,	,	PUNCT
ejpam-2660	663	7	”	"	PUNCT
ejpam-2660	663	8	hyperring	hyperring	NOUN
ejpam-2660	663	9	and	and	CCONJ
ejpam-2660	663	10	α∗relations	α∗relation	NOUN
ejpam-2660	663	11	.	.	PUNCT
ejpam-2660	664	1	a	a	DET
ejpam-2660	664	2	general	general	ADJ
ejpam-2660	664	3	approach	approach	NOUN
ejpam-2660	664	4	”	"	PUNCT
ejpam-2660	664	5	,	,	PUNCT
ejpam-2660	664	6	journal	journal	NOUN
ejpam-2660	664	7	of	of	ADP
ejpam-2660	664	8	algebra	algebra	PROPN
ejpam-2660	664	9	,	,	PUNCT
ejpam-2660	664	10	vol	vol	NOUN
ejpam-2660	664	11	.	.	NOUN
ejpam-2660	664	12	383	383	NUM
ejpam-2660	664	13	,	,	PUNCT
ejpam-2660	664	14	104	104	NUM
ejpam-2660	664	15	-	-	SYM
ejpam-2660	664	16	128	128	NUM
ejpam-2660	664	17	,	,	PUNCT
ejpam-2660	664	18	2013	2013	NUM
ejpam-2660	664	19	.	.	PUNCT
ejpam-2660	665	1	[	[	X
ejpam-2660	665	2	16	16	NUM
ejpam-2660	665	3	]	]	X
ejpam-2660	665	4	c.	c.	PROPN
ejpam-2660	665	5	pelea	pelea	PROPN
ejpam-2660	665	6	and	and	CCONJ
ejpam-2660	665	7	i.	i.	PROPN
ejpam-2660	665	8	purdea	purdea	PROPN
ejpam-2660	665	9	,	,	PUNCT
ejpam-2660	665	10	”	"	PUNCT
ejpam-2660	665	11	a	a	DET
ejpam-2660	665	12	characterization	characterization	NOUN
ejpam-2660	665	13	theorem	theorem	VERB
ejpam-2660	665	14	for	for	ADP
ejpam-2660	665	15	complete	complete	ADJ
ejpam-2660	665	16	multialgebras	multialgebra	NOUN
ejpam-2660	665	17	”	"	PUNCT
ejpam-2660	665	18	,	,	PUNCT
ejpam-2660	665	19	mathematica	mathematica	PROPN
ejpam-2660	665	20	,	,	PUNCT
ejpam-2660	665	21	205	205	NUM
ejpam-2660	665	22	-	-	SYM
ejpam-2660	665	23	211	211	NUM
ejpam-2660	665	24	,	,	PUNCT
ejpam-2660	665	25	2004	2004	NUM
ejpam-2660	665	26	.	.	PUNCT
ejpam-2660	666	1	references	reference	NOUN
ejpam-2660	666	2	188	188	NUM
ejpam-2660	666	3	[	[	SYM
ejpam-2660	666	4	17	17	NUM
ejpam-2660	666	5	]	]	PUNCT
ejpam-2660	666	6	h.	h.	PROPN
ejpam-2660	666	7	e.	e.	PROPN
ejpam-2660	666	8	pickett	pickett	PROPN
ejpam-2660	666	9	,	,	PUNCT
ejpam-2660	666	10	”	"	PUNCT
ejpam-2660	666	11	subdirect	subdirect	VERB
ejpam-2660	666	12	representations	representation	NOUN
ejpam-2660	666	13	of	of	ADP
ejpam-2660	666	14	related	related	ADJ
ejpam-2660	666	15	system	system	NOUN
ejpam-2660	666	16	”	"	PUNCT
ejpam-2660	666	17	,	,	PUNCT
ejpam-2660	666	18	fund	fund	NOUN
ejpam-2660	666	19	.	.	PUNCT
ejpam-2660	667	1	math	math	PROPN
ejpam-2660	667	2	,	,	PUNCT
ejpam-2660	667	3	vol	vol	NOUN
ejpam-2660	667	4	.	.	PROPN
ejpam-2660	667	5	56	56	NUM
ejpam-2660	667	6	,	,	PUNCT
ejpam-2660	667	7	223	223	NUM
ejpam-2660	667	8	-	-	SYM
ejpam-2660	667	9	240	240	NUM
ejpam-2660	667	10	,	,	PUNCT
ejpam-2660	667	11	1964	1964	NUM
ejpam-2660	667	12	.	.	PUNCT
ejpam-2660	668	1	[	[	X
ejpam-2660	668	2	18	18	NUM
ejpam-2660	668	3	]	]	X
ejpam-2660	668	4	h.	h.	PROPN
ejpam-2660	668	5	e.	e.	PROPN
ejpam-2660	668	6	pickett	pickett	PROPN
ejpam-2660	668	7	,	,	PUNCT
ejpam-2660	668	8	”	"	PUNCT
ejpam-2660	668	9	homomorphisms	homomorphism	NOUN
ejpam-2660	668	10	and	and	CCONJ
ejpam-2660	668	11	subalgebras	subalgebra	NOUN
ejpam-2660	668	12	of	of	ADP
ejpam-2660	668	13	multialgebras	multialgebra	NOUN
ejpam-2660	668	14	”	"	PUNCT
ejpam-2660	668	15	,	,	PUNCT
ejpam-2660	668	16	pacific	pacific	PROPN
ejpam-2660	668	17	j.	j.	PROPN
ejpam-2660	668	18	of	of	ADP
ejpam-2660	668	19	math	math	NOUN
ejpam-2660	668	20	,	,	PUNCT
ejpam-2660	668	21	vol	vol	NOUN
ejpam-2660	668	22	.	.	PROPN
ejpam-2660	668	23	21	21	NUM
ejpam-2660	668	24	,	,	PUNCT
ejpam-2660	668	25	327	327	NUM
ejpam-2660	668	26	-	-	SYM
ejpam-2660	668	27	343	343	NUM
ejpam-2660	668	28	,	,	PUNCT
ejpam-2660	668	29	1967	1967	NUM
ejpam-2660	668	30	.	.	PUNCT
ejpam-2660	669	1	[	[	X
ejpam-2660	669	2	19	19	NUM
ejpam-2660	669	3	]	]	PUNCT
ejpam-2660	669	4	a.	a.	NOUN
ejpam-2660	669	5	rahnemai	rahnemai	PROPN
ejpam-2660	669	6	-	-	PUNCT
ejpam-2660	669	7	barghi	barghi	PROPN
ejpam-2660	669	8	,	,	PUNCT
ejpam-2660	669	9	”	"	PUNCT
ejpam-2660	669	10	the	the	DET
ejpam-2660	669	11	prime	prime	ADJ
ejpam-2660	669	12	ideal	ideal	NOUN
ejpam-2660	669	13	theorem	theorem	NOUN
ejpam-2660	669	14	for	for	ADP
ejpam-2660	669	15	distributive	distributive	ADJ
ejpam-2660	669	16	hyperlattices	hyperlattice	NOUN
ejpam-2660	669	17	,	,	PUNCT
ejpam-2660	669	18	”	"	PUNCT
ejpam-2660	669	19	ital	ital	NOUN
ejpam-2660	669	20	.	.	PUNCT
ejpam-2660	670	1	j.	j.	PROPN
ejpam-2660	670	2	pure	pure	PROPN
ejpam-2660	670	3	appl	appl	PROPN
ejpam-2660	670	4	.	.	PUNCT
ejpam-2660	670	5	math	math	PROPN
ejpam-2660	670	6	.	.	PUNCT
ejpam-2660	671	1	,	,	PUNCT
ejpam-2660	671	2	vol	vol	NOUN
ejpam-2660	671	3	.	.	PROPN
ejpam-2660	671	4	10	10	NUM
ejpam-2660	671	5	,	,	PUNCT
ejpam-2660	671	6	75	75	NUM
ejpam-2660	671	7	-	-	SYM
ejpam-2660	671	8	78	78	NUM
ejpam-2660	671	9	,	,	PUNCT
ejpam-2660	671	10	2001	2001	NUM
ejpam-2660	671	11	.	.	PUNCT
ejpam-2660	672	1	[	[	X
ejpam-2660	672	2	20	20	NUM
ejpam-2660	672	3	]	]	X
ejpam-2660	672	4	s.	s.	PROPN
ejpam-2660	672	5	rasouli	rasouli	PROPN
ejpam-2660	672	6	,	,	PUNCT
ejpam-2660	672	7	b.	b.	PROPN
ejpam-2660	672	8	davvaz	davvaz	PROPN
ejpam-2660	672	9	,	,	PUNCT
ejpam-2660	672	10	”	"	PUNCT
ejpam-2660	672	11	lattice	lattice	NOUN
ejpam-2660	672	12	derived	derive	VERB
ejpam-2660	672	13	from	from	ADP
ejpam-2660	672	14	hyperlattices	hyperlattice	NOUN
ejpam-2660	672	15	”	"	PUNCT
ejpam-2660	672	16	,	,	PUNCT
ejpam-2660	672	17	communications	communication	NOUN
ejpam-2660	672	18	in	in	ADP
ejpam-2660	672	19	algebra	algebra	NOUN
ejpam-2660	672	20	,	,	PUNCT
ejpam-2660	672	21	vol	vol	NOUN
ejpam-2660	672	22	.	.	PROPN
ejpam-2660	672	23	38	38	NUM
ejpam-2660	672	24	,	,	PUNCT
ejpam-2660	672	25	27202737	27202737	NUM
ejpam-2660	672	26	,	,	PUNCT
ejpam-2660	672	27	2010	2010	NUM
ejpam-2660	672	28	.	.	PUNCT
ejpam-2660	673	1	[	[	X
ejpam-2660	673	2	21	21	NUM
ejpam-2660	673	3	]	]	X
ejpam-2660	673	4	s.	s.	PROPN
ejpam-2660	673	5	rasouli	rasouli	PROPN
ejpam-2660	673	6	,	,	PUNCT
ejpam-2660	673	7	b.	b.	PROPN
ejpam-2660	673	8	davvaz	davvaz	PROPN
ejpam-2660	673	9	,	,	PUNCT
ejpam-2660	673	10	”	"	PUNCT
ejpam-2660	673	11	construction	construction	NOUN
ejpam-2660	673	12	and	and	CCONJ
ejpam-2660	673	13	spectral	spectral	ADJ
ejpam-2660	673	14	topology	topology	NOUN
ejpam-2660	673	15	on	on	ADP
ejpam-2660	673	16	hyperlattice	hyperlattice	NOUN
ejpam-2660	673	17	”	"	PUNCT
ejpam-2660	673	18	,	,	PUNCT
ejpam-2660	673	19	mediterr	mediterr	NOUN
ejpam-2660	673	20	.	.	PUNCT
ejpam-2660	674	1	j.	j.	PROPN
ejpam-2660	674	2	math	math	PROPN
ejpam-2660	674	3	.	.	PUNCT
ejpam-2660	675	1	,	,	PUNCT
ejpam-2660	675	2	vol	vol	NOUN
ejpam-2660	675	3	.	.	PROPN
ejpam-2660	675	4	7	7	NUM
ejpam-2660	675	5	,	,	PUNCT
ejpam-2660	675	6	249262	249262	NUM
ejpam-2660	675	7	,	,	PUNCT
ejpam-2660	675	8	2010	2010	NUM
ejpam-2660	675	9	.	.	PUNCT
ejpam-2660	676	1	[	[	X
ejpam-2660	676	2	22	22	NUM
ejpam-2660	676	3	]	]	X
ejpam-2660	676	4	d.	d.	PROPN
ejpam-2660	676	5	schweigrt	schweigrt	PROPN
ejpam-2660	676	6	,	,	PUNCT
ejpam-2660	676	7	”	"	PUNCT
ejpam-2660	676	8	congruence	congruence	NOUN
ejpam-2660	676	9	relation	relation	NOUN
ejpam-2660	676	10	of	of	ADP
ejpam-2660	676	11	multialgebra	multialgebra	NOUN
ejpam-2660	676	12	”	"	PUNCT
ejpam-2660	676	13	,	,	PUNCT
ejpam-2660	676	14	discrete	discrete	ADJ
ejpam-2660	676	15	mathematics	mathematic	NOUN
ejpam-2660	676	16	”	"	PUNCT
ejpam-2660	676	17	,	,	PUNCT
ejpam-2660	676	18	vol	vol	NOUN
ejpam-2660	676	19	.	.	PROPN
ejpam-2660	676	20	53	53	NUM
ejpam-2660	676	21	,	,	PUNCT
ejpam-2660	676	22	249	249	NUM
ejpam-2660	676	23	-	-	SYM
ejpam-2660	676	24	253	253	NUM
ejpam-2660	676	25	,	,	PUNCT
ejpam-2660	676	26	1985	1985	NUM
ejpam-2660	676	27	.	.	PUNCT
ejpam-2660	677	1	[	[	X
ejpam-2660	677	2	23	23	NUM
ejpam-2660	677	3	]	]	PUNCT
ejpam-2660	677	4	x.	x.	PROPN
ejpam-2660	677	5	l.	l.	PROPN
ejpam-2660	677	6	xin	xin	PROPN
ejpam-2660	677	7	and	and	CCONJ
ejpam-2660	677	8	x.	x.	PROPN
ejpam-2660	677	9	g.	g.	PROPN
ejpam-2660	677	10	li	li	PROPN
ejpam-2660	677	11	,	,	PUNCT
ejpam-2660	677	12	”	"	PUNCT
ejpam-2660	677	13	on	on	ADP
ejpam-2660	677	14	hyperlattice	hyperlattice	NOUN
ejpam-2660	677	15	and	and	CCONJ
ejpam-2660	677	16	quotient	quotient	PROPN
ejpam-2660	677	17	hyperlattice	hyperlattice	PROPN
ejpam-2660	677	18	”	"	PUNCT
ejpam-2660	677	19	,	,	PUNCT