id	sid	tid	token	lemma	pos
ejpam-5742	1	1	european	european	PROPN
ejpam-5742	1	2	journal	journal	PROPN
ejpam-5742	1	3	of	of	ADP
ejpam-5742	1	4	pure	pure	ADJ
ejpam-5742	1	5	and	and	CCONJ
ejpam-5742	1	6	applied	applied	ADJ
ejpam-5742	1	7	mathematics	mathematic	NOUN
ejpam-5742	1	8	2025	2025	NUM
ejpam-5742	1	9	,	,	PUNCT
ejpam-5742	1	10	vol	vol	NOUN
ejpam-5742	1	11	.	.	PROPN
ejpam-5742	1	12	18	18	NUM
ejpam-5742	1	13	,	,	PUNCT
ejpam-5742	1	14	issue	issue	NOUN
ejpam-5742	1	15	2	2	NUM
ejpam-5742	1	16	,	,	PUNCT
ejpam-5742	1	17	article	article	NOUN
ejpam-5742	1	18	number	number	NOUN
ejpam-5742	1	19	5742	5742	NUM
ejpam-5742	1	20	issn	issn	VERB
ejpam-5742	1	21	1307	1307	NUM
ejpam-5742	1	22	-	-	SYM
ejpam-5742	1	23	5543	5543	NUM
ejpam-5742	1	24	–	–	PUNCT
ejpam-5742	1	25	ejpam.com	ejpam.com	X
ejpam-5742	1	26	published	publish	VERB
ejpam-5742	1	27	by	by	ADP
ejpam-5742	1	28	new	new	PROPN
ejpam-5742	1	29	york	york	PROPN
ejpam-5742	1	30	business	business	PROPN
ejpam-5742	1	31	global	global	ADJ
ejpam-5742	1	32	m−homomorphisms	m−homomorphism	NOUN
ejpam-5742	1	33	of	of	ADP
ejpam-5742	1	34	almost	almost	ADV
ejpam-5742	1	35	distributive	distributive	ADJ
ejpam-5742	1	36	lattices	lattice	NOUN
ejpam-5742	1	37	n.	n.	PROPN
ejpam-5742	1	38	rafi1	rafi1	PROPN
ejpam-5742	1	39	,	,	PUNCT
ejpam-5742	1	40	thiti	thiti	PROPN
ejpam-5742	1	41	gaketem2,∗	gaketem2,∗	PROPN
ejpam-5742	1	42	,	,	PUNCT
ejpam-5742	1	43	ravi	ravi	NOUN
ejpam-5742	1	44	kumar	kumar	PROPN
ejpam-5742	1	45	bandaru3	bandaru3	PROPN
ejpam-5742	1	46	1	1	NUM
ejpam-5742	1	47	department	department	NOUN
ejpam-5742	1	48	of	of	ADP
ejpam-5742	1	49	mathematics	mathematic	NOUN
ejpam-5742	1	50	,	,	PUNCT
ejpam-5742	1	51	bapatla	bapatla	VERB
ejpam-5742	1	52	engineering	engineering	NOUN
ejpam-5742	1	53	college	college	NOUN
ejpam-5742	1	54	,	,	PUNCT
ejpam-5742	1	55	bapatla	bapatla	NOUN
ejpam-5742	1	56	,	,	PUNCT
ejpam-5742	1	57	andhra	andhra	PROPN
ejpam-5742	1	58	pradesh	pradesh	PROPN
ejpam-5742	1	59	,	,	PUNCT
ejpam-5742	1	60	india	india	PROPN
ejpam-5742	1	61	2	2	NUM
ejpam-5742	1	62	department	department	NOUN
ejpam-5742	1	63	of	of	ADP
ejpam-5742	1	64	mathematics	mathematic	NOUN
ejpam-5742	1	65	,	,	PUNCT
ejpam-5742	1	66	school	school	NOUN
ejpam-5742	1	67	of	of	ADP
ejpam-5742	1	68	science	science	NOUN
ejpam-5742	1	69	,	,	PUNCT
ejpam-5742	1	70	university	university	NOUN
ejpam-5742	1	71	of	of	ADP
ejpam-5742	1	72	phayao	phayao	NOUN
ejpam-5742	1	73	,	,	PUNCT
ejpam-5742	1	74	phayao	phayao	NOUN
ejpam-5742	1	75	56000	56000	NUM
ejpam-5742	1	76	,	,	PUNCT
ejpam-5742	1	77	thailand	thailand	PROPN
ejpam-5742	1	78	3	3	NUM
ejpam-5742	1	79	department	department	NOUN
ejpam-5742	1	80	of	of	ADP
ejpam-5742	1	81	mathematics	mathematic	NOUN
ejpam-5742	1	82	,	,	PUNCT
ejpam-5742	1	83	school	school	NOUN
ejpam-5742	1	84	of	of	ADP
ejpam-5742	1	85	advanced	advanced	ADJ
ejpam-5742	1	86	sciences	science	NOUN
ejpam-5742	1	87	,	,	PUNCT
ejpam-5742	1	88	vit	vit	PROPN
ejpam-5742	1	89	-	-	PUNCT
ejpam-5742	1	90	ap	ap	PROPN
ejpam-5742	1	91	university	university	PROPN
ejpam-5742	1	92	,	,	PUNCT
ejpam-5742	1	93	andhra	andhra	PROPN
ejpam-5742	1	94	pradesh	pradesh	PROPN
ejpam-5742	1	95	,	,	PUNCT
ejpam-5742	1	96	india	india	PROPN
ejpam-5742	1	97	abstract	abstract	PROPN
ejpam-5742	1	98	.	.	PUNCT
ejpam-5742	2	1	an	an	DET
ejpam-5742	2	2	m−homomorphism	m−homomorphism	NOUN
ejpam-5742	2	3	in	in	ADP
ejpam-5742	2	4	an	an	DET
ejpam-5742	2	5	almost	almost	ADV
ejpam-5742	2	6	distributive	distributive	ADJ
ejpam-5742	2	7	lattice(adl	lattice(adl	NOUN
ejpam-5742	2	8	)	)	PUNCT
ejpam-5742	2	9	is	be	AUX
ejpam-5742	2	10	introduced	introduce	VERB
ejpam-5742	2	11	,	,	PUNCT
ejpam-5742	2	12	with	with	ADP
ejpam-5742	2	13	a	a	DET
ejpam-5742	2	14	sufficient	sufficient	ADJ
ejpam-5742	2	15	condition	condition	NOUN
ejpam-5742	2	16	for	for	SCONJ
ejpam-5742	2	17	it	it	PRON
ejpam-5742	2	18	to	to	PART
ejpam-5742	2	19	be	be	AUX
ejpam-5742	2	20	an	an	DET
ejpam-5742	2	21	m−homomorphism	m−homomorphism	NOUN
ejpam-5742	2	22	.	.	PUNCT
ejpam-5742	3	1	the	the	DET
ejpam-5742	3	2	image	image	NOUN
ejpam-5742	3	3	and	and	CCONJ
ejpam-5742	3	4	inverse	inverse	NOUN
ejpam-5742	3	5	image	image	NOUN
ejpam-5742	3	6	of	of	ADP
ejpam-5742	3	7	anm−filter	anm−filt	ADJ
ejpam-5742	3	8	under	under	ADP
ejpam-5742	3	9	such	such	DET
ejpam-5742	3	10	a	a	DET
ejpam-5742	3	11	homomorphism	homomorphism	NOUN
ejpam-5742	3	12	are	be	AUX
ejpam-5742	3	13	shown	show	VERB
ejpam-5742	3	14	to	to	PART
ejpam-5742	3	15	be	be	AUX
ejpam-5742	3	16	m−filters	m−filter	NOUN
ejpam-5742	3	17	.	.	PUNCT
ejpam-5742	4	1	sufficient	sufficient	ADJ
ejpam-5742	4	2	conditions	condition	NOUN
ejpam-5742	4	3	for	for	ADP
ejpam-5742	4	4	a	a	DET
ejpam-5742	4	5	prime	prime	ADJ
ejpam-5742	4	6	filter	filter	NOUN
ejpam-5742	4	7	to	to	PART
ejpam-5742	4	8	be	be	AUX
ejpam-5742	4	9	an	an	DET
ejpam-5742	4	10	m−filter	m−filter	NOUN
ejpam-5742	4	11	are	be	AUX
ejpam-5742	4	12	established	establish	VERB
ejpam-5742	4	13	,	,	PUNCT
ejpam-5742	4	14	along	along	ADP
ejpam-5742	4	15	with	with	ADP
ejpam-5742	4	16	an	an	DET
ejpam-5742	4	17	equivalence	equivalence	NOUN
ejpam-5742	4	18	between	between	ADP
ejpam-5742	4	19	prime	prime	ADJ
ejpam-5742	4	20	m−filters	m−filter	NOUN
ejpam-5742	4	21	and	and	CCONJ
ejpam-5742	4	22	minimal	minimal	ADJ
ejpam-5742	4	23	prime	prime	ADJ
ejpam-5742	4	24	filters	filter	NOUN
ejpam-5742	4	25	.	.	PUNCT
ejpam-5742	5	1	finally	finally	ADV
ejpam-5742	5	2	,	,	PUNCT
ejpam-5742	5	3	any	any	DET
ejpam-5742	5	4	two	two	NUM
ejpam-5742	5	5	distinct	distinct	ADJ
ejpam-5742	5	6	prime	prime	ADJ
ejpam-5742	5	7	m−filters	m−filter	NOUN
ejpam-5742	5	8	in	in	ADP
ejpam-5742	5	9	an	an	DET
ejpam-5742	5	10	adl	adl	NOUN
ejpam-5742	5	11	are	be	AUX
ejpam-5742	5	12	shown	show	VERB
ejpam-5742	5	13	to	to	PART
ejpam-5742	5	14	be	be	AUX
ejpam-5742	5	15	comaximal	comaximal	ADJ
ejpam-5742	5	16	.	.	PUNCT
ejpam-5742	6	1	2020	2020	NUM
ejpam-5742	6	2	mathematics	mathematics	PROPN
ejpam-5742	6	3	subject	subject	NOUN
ejpam-5742	6	4	classifications	classification	NOUN
ejpam-5742	6	5	:	:	PUNCT
ejpam-5742	6	6	06d99	06d99	NUM
ejpam-5742	6	7	,	,	PUNCT
ejpam-5742	6	8	06d15	06d15	DET
ejpam-5742	6	9	key	key	ADJ
ejpam-5742	6	10	words	word	NOUN
ejpam-5742	6	11	and	and	CCONJ
ejpam-5742	6	12	phrases	phrase	NOUN
ejpam-5742	6	13	:	:	PUNCT
ejpam-5742	6	14	almost	almost	ADV
ejpam-5742	6	15	distributive	distributive	ADJ
ejpam-5742	6	16	lattice(adl	lattice(adl	NOUN
ejpam-5742	6	17	)	)	PUNCT
ejpam-5742	6	18	,	,	PUNCT
ejpam-5742	6	19	m−homomorphism	m−homomorphism	NOUN
ejpam-5742	6	20	,	,	PUNCT
ejpam-5742	6	21	m−filter	m−filter	NOUN
ejpam-5742	6	22	,	,	PUNCT
ejpam-5742	6	23	co	co	ADJ
ejpam-5742	6	24	-	-	ADJ
ejpam-5742	6	25	dense	dense	ADJ
ejpam-5742	6	26	,	,	PUNCT
ejpam-5742	6	27	co	co	NOUN
ejpam-5742	6	28	-	-	NOUN
ejpam-5742	6	29	kernel	kernel	ADJ
ejpam-5742	6	30	,	,	PUNCT
ejpam-5742	6	31	e−complemented	e−complemente	VERB
ejpam-5742	6	32	adl	adl	NOUN
ejpam-5742	6	33	,	,	PUNCT
ejpam-5742	6	34	dual	dual	ADV
ejpam-5742	6	35	dense	dense	ADJ
ejpam-5742	6	36	,	,	PUNCT
ejpam-5742	6	37	⊔−comaximal	⊔−comaximal	ADJ
ejpam-5742	6	38	1	1	NUM
ejpam-5742	6	39	.	.	PUNCT
ejpam-5742	7	1	introduction	introduction	NOUN
ejpam-5742	7	2	swamy	swamy	NOUN
ejpam-5742	7	3	and	and	CCONJ
ejpam-5742	7	4	rao	rao	NOUN
ejpam-5742	7	5	introduced	introduce	VERB
ejpam-5742	7	6	the	the	DET
ejpam-5742	7	7	concept	concept	NOUN
ejpam-5742	7	8	of	of	ADP
ejpam-5742	7	9	an	an	DET
ejpam-5742	7	10	almost	almost	ADV
ejpam-5742	7	11	distributive	distributive	ADJ
ejpam-5742	7	12	lattice(adl	lattice(adl	NOUN
ejpam-5742	7	13	)	)	PUNCT
ejpam-5742	8	1	[	[	X
ejpam-5742	8	2	1	1	NUM
ejpam-5742	8	3	]	]	PUNCT
ejpam-5742	8	4	,	,	PUNCT
ejpam-5742	8	5	which	which	PRON
ejpam-5742	8	6	serves	serve	VERB
ejpam-5742	8	7	as	as	ADP
ejpam-5742	8	8	a	a	DET
ejpam-5742	8	9	common	common	ADJ
ejpam-5742	8	10	abstraction	abstraction	NOUN
ejpam-5742	8	11	for	for	ADP
ejpam-5742	8	12	numerous	numerous	ADJ
ejpam-5742	8	13	ring	ring	NOUN
ejpam-5742	8	14	-	-	PUNCT
ejpam-5742	8	15	theoretic	theoretic	NOUN
ejpam-5742	8	16	generalizations	generalization	NOUN
ejpam-5742	8	17	of	of	ADP
ejpam-5742	8	18	boolean	boolean	ADJ
ejpam-5742	8	19	algebra	algebra	NOUN
ejpam-5742	8	20	and	and	CCONJ
ejpam-5742	8	21	the	the	DET
ejpam-5742	8	22	class	class	NOUN
ejpam-5742	8	23	of	of	ADP
ejpam-5742	8	24	distributive	distributive	ADJ
ejpam-5742	8	25	lattices	lattice	NOUN
ejpam-5742	8	26	.	.	PUNCT
ejpam-5742	9	1	in	in	ADP
ejpam-5742	9	2	their	their	PRON
ejpam-5742	9	3	paper	paper	NOUN
ejpam-5742	9	4	,	,	PUNCT
ejpam-5742	9	5	they	they	PRON
ejpam-5742	9	6	defined	define	VERB
ejpam-5742	9	7	the	the	DET
ejpam-5742	9	8	notion	notion	NOUN
ejpam-5742	9	9	of	of	ADP
ejpam-5742	9	10	an	an	DET
ejpam-5742	9	11	ideal	ideal	NOUN
ejpam-5742	9	12	in	in	ADP
ejpam-5742	9	13	an	an	DET
ejpam-5742	9	14	adl	adl	NOUN
ejpam-5742	9	15	,	,	PUNCT
ejpam-5742	9	16	drawing	draw	VERB
ejpam-5742	9	17	an	an	DET
ejpam-5742	9	18	analogy	analogy	NOUN
ejpam-5742	9	19	with	with	ADP
ejpam-5742	9	20	ideals	ideal	NOUN
ejpam-5742	9	21	in	in	ADP
ejpam-5742	9	22	distributive	distributive	ADJ
ejpam-5742	9	23	lattices	lattice	NOUN
ejpam-5742	9	24	.	.	PUNCT
ejpam-5742	10	1	they	they	PRON
ejpam-5742	10	2	observed	observe	VERB
ejpam-5742	10	3	that	that	SCONJ
ejpam-5742	10	4	the	the	DET
ejpam-5742	10	5	set	set	NOUN
ejpam-5742	10	6	pi(r	pi(r	NOUN
ejpam-5742	10	7	)	)	PUNCT
ejpam-5742	10	8	of	of	ADP
ejpam-5742	10	9	all	all	DET
ejpam-5742	10	10	principal	principal	ADJ
ejpam-5742	10	11	ideals	ideal	NOUN
ejpam-5742	10	12	in	in	ADP
ejpam-5742	10	13	an	an	DET
ejpam-5742	10	14	adl	adl	NOUN
ejpam-5742	10	15	forms	form	NOUN
ejpam-5742	10	16	a	a	DET
ejpam-5742	10	17	distributive	distributive	ADJ
ejpam-5742	10	18	lattice	lattice	NOUN
ejpam-5742	10	19	.	.	PUNCT
ejpam-5742	11	1	this	this	DET
ejpam-5742	11	2	observation	observation	NOUN
ejpam-5742	11	3	opened	open	VERB
ejpam-5742	11	4	up	up	ADP
ejpam-5742	11	5	avenues	avenue	NOUN
ejpam-5742	11	6	for	for	ADP
ejpam-5742	11	7	extending	extend	VERB
ejpam-5742	11	8	many	many	ADJ
ejpam-5742	11	9	existing	exist	VERB
ejpam-5742	11	10	lattice	lattice	NOUN
ejpam-5742	11	11	theory	theory	NOUN
ejpam-5742	11	12	concepts	concept	NOUN
ejpam-5742	11	13	to	to	ADP
ejpam-5742	11	14	the	the	DET
ejpam-5742	11	15	class	class	NOUN
ejpam-5742	11	16	of	of	ADP
ejpam-5742	11	17	adls	adls	PROPN
ejpam-5742	11	18	.	.	PUNCT
ejpam-5742	12	1	in	in	ADP
ejpam-5742	12	2	[	[	X
ejpam-5742	12	3	2	2	NUM
ejpam-5742	12	4	]	]	PUNCT
ejpam-5742	12	5	,	,	PUNCT
ejpam-5742	12	6	introduced	introduce	VERB
ejpam-5742	12	7	and	and	CCONJ
ejpam-5742	12	8	study	study	VERB
ejpam-5742	12	9	the	the	DET
ejpam-5742	12	10	properties	property	NOUN
ejpam-5742	12	11	of	of	ADP
ejpam-5742	12	12	µ−filters	µ−filter	NOUN
ejpam-5742	12	13	in	in	ADP
ejpam-5742	12	14	an	an	DET
ejpam-5742	12	15	adl	adl	PROPN
ejpam-5742	12	16	.	.	PUNCT
ejpam-5742	12	17	sambasiva	sambasiva	PROPN
ejpam-5742	12	18	rao	rao	PROPN
ejpam-5742	12	19	and	and	CCONJ
ejpam-5742	12	20	g.c	g.c	PROPN
ejpam-5742	12	21	.	.	PROPN
ejpam-5742	12	22	rao	rao	PROPN
ejpam-5742	12	23	introduced	introduce	VERB
ejpam-5742	12	24	the	the	DET
ejpam-5742	12	25	notion	notion	NOUN
ejpam-5742	12	26	of	of	ADP
ejpam-5742	12	27	o−homomorphisms	o−homomorphism	NOUN
ejpam-5742	12	28	within	within	ADP
ejpam-5742	12	29	the	the	DET
ejpam-5742	12	30	context	context	NOUN
ejpam-5742	12	31	of	of	ADP
ejpam-5742	12	32	almost	almost	ADV
ejpam-5742	12	33	distributive	distributive	ADJ
ejpam-5742	12	34	lattices(adls	lattices(adls	PROPN
ejpam-5742	12	35	)	)	PUNCT
ejpam-5742	12	36	in	in	ADP
ejpam-5742	12	37	[	[	X
ejpam-5742	12	38	3	3	NUM
ejpam-5742	12	39	]	]	PUNCT
ejpam-5742	12	40	,	,	PUNCT
ejpam-5742	12	41	exploring	explore	VERB
ejpam-5742	12	42	their	their	PRON
ejpam-5742	12	43	key	key	ADJ
ejpam-5742	12	44	properties	property	NOUN
ejpam-5742	12	45	.	.	PUNCT
ejpam-5742	13	1	in	in	ADP
ejpam-5742	13	2	[	[	X
ejpam-5742	13	3	4	4	NUM
ejpam-5742	13	4	]	]	PUNCT
ejpam-5742	13	5	,	,	PUNCT
ejpam-5742	13	6	author	author	NOUN
ejpam-5742	13	7	studied	study	VERB
ejpam-5742	13	8	the	the	DET
ejpam-5742	13	9	properties	property	NOUN
ejpam-5742	13	10	of	of	ADP
ejpam-5742	13	11	o−filters	o−filter	NOUN
ejpam-5742	13	12	in	in	ADP
ejpam-5742	13	13	lattices	lattice	NOUN
ejpam-5742	13	14	.	.	PUNCT
ejpam-5742	14	1	later	later	ADV
ejpam-5742	14	2	,	,	PUNCT
ejpam-5742	14	3	in	in	ADP
ejpam-5742	14	4	[	[	PUNCT
ejpam-5742	14	5	5	5	NUM
ejpam-5742	14	6	]	]	PUNCT
ejpam-5742	14	7	,	,	PUNCT
ejpam-5742	14	8	rafi	rafi	PROPN
ejpam-5742	14	9	established	establish	VERB
ejpam-5742	14	10	a	a	DET
ejpam-5742	14	11	correspondence	correspondence	NOUN
ejpam-5742	14	12	between	between	ADP
ejpam-5742	14	13	the	the	DET
ejpam-5742	14	14	set	set	NOUN
ejpam-5742	14	15	of	of	ADP
ejpam-5742	14	16	all	all	DET
ejpam-5742	14	17	prime	prime	ADJ
ejpam-5742	14	18	o−ideals	o−ideal	NOUN
ejpam-5742	14	19	and	and	CCONJ
ejpam-5742	14	20	the	the	DET
ejpam-5742	14	21	set	set	NOUN
ejpam-5742	14	22	of	of	ADP
ejpam-5742	14	23	minimal	minimal	ADJ
ejpam-5742	14	24	prime	prime	ADJ
ejpam-5742	14	25	ideals	ideal	NOUN
ejpam-5742	14	26	in	in	ADP
ejpam-5742	14	27	an	an	DET
ejpam-5742	14	28	adl	adl	NOUN
ejpam-5742	14	29	.	.	PUNCT
ejpam-5742	15	1	in	in	ADP
ejpam-5742	15	2	that	that	DET
ejpam-5742	15	3	work	work	NOUN
ejpam-5742	15	4	,	,	PUNCT
ejpam-5742	15	5	they	they	PRON
ejpam-5742	15	6	identified	identify	VERB
ejpam-5742	15	7	a	a	DET
ejpam-5742	15	8	necessary	necessary	ADJ
ejpam-5742	15	9	and	and	CCONJ
ejpam-5742	15	10	sufficient	sufficient	ADJ
ejpam-5742	15	11	condition	condition	NOUN
ejpam-5742	15	12	∗corresponding	∗corresponde	VERB
ejpam-5742	15	13	author	author	NOUN
ejpam-5742	15	14	.	.	PUNCT
ejpam-5742	16	1	doi	doi	NOUN
ejpam-5742	16	2	:	:	PUNCT
ejpam-5742	16	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5742	https://doi.org/10.29020/nybg.ejpam.v18i2.5742	PROPN
ejpam-5742	16	4	email	email	NOUN
ejpam-5742	16	5	addresses	address	NOUN
ejpam-5742	16	6	:	:	PUNCT
ejpam-5742	16	7	rafimaths@gmail.com	rafimaths@gmail.com	X
ejpam-5742	16	8	(	(	PUNCT
ejpam-5742	16	9	n.	n.	PROPN
ejpam-5742	16	10	rafi	rafi	PROPN
ejpam-5742	16	11	)	)	PUNCT
ejpam-5742	16	12	,	,	PUNCT
ejpam-5742	16	13	thiti.ga@up.ac.th	thiti.ga@up.ac.th	PROPN
ejpam-5742	16	14	(	(	PUNCT
ejpam-5742	16	15	t.	t.	NOUN
ejpam-5742	16	16	gaketem	gaketem	PROPN
ejpam-5742	16	17	)	)	PUNCT
ejpam-5742	16	18	,	,	PUNCT
ejpam-5742	16	19	ravimaths83@gmail.com	ravimaths83@gmail.com	PROPN
ejpam-5742	16	20	(	(	PUNCT
ejpam-5742	16	21	r.	r.	PROPN
ejpam-5742	16	22	bandaru	bandaru	PROPN
ejpam-5742	16	23	)	)	PUNCT
ejpam-5742	16	24	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5742	17	1	1	1	NUM
ejpam-5742	17	2	copyright	copyright	NOUN
ejpam-5742	17	3	:	:	PUNCT
ejpam-5742	17	4	©	©	PROPN
ejpam-5742	17	5	2025	2025	NUM
ejpam-5742	17	6	the	the	DET
ejpam-5742	17	7	author(s	author(s	NOUN
ejpam-5742	17	8	)	)	PUNCT
ejpam-5742	17	9	.	.	PUNCT
ejpam-5742	18	1	(	(	PUNCT
ejpam-5742	18	2	cc	cc	NOUN
ejpam-5742	18	3	by	by	ADP
ejpam-5742	18	4	-	-	PUNCT
ejpam-5742	18	5	nc	nc	PROPN
ejpam-5742	18	6	4.0	4.0	NUM
ejpam-5742	18	7	)	)	PUNCT
ejpam-5742	18	8	n.	n.	PROPN
ejpam-5742	18	9	rafi	rafi	PROPN
ejpam-5742	18	10	,	,	PUNCT
ejpam-5742	18	11	t.	t.	PROPN
ejpam-5742	18	12	gaketem	gaketem	PROPN
ejpam-5742	18	13	,	,	PUNCT
ejpam-5742	18	14	r.	r.	PROPN
ejpam-5742	18	15	k.	k.	PROPN
ejpam-5742	18	16	bandaru	bandaru	PROPN
ejpam-5742	18	17	/	/	SYM
ejpam-5742	18	18	eur	eur	PROPN
ejpam-5742	18	19	.	.	PUNCT
ejpam-5742	19	1	j.	j.	PROPN
ejpam-5742	19	2	pure	pure	PROPN
ejpam-5742	19	3	appl	appl	PROPN
ejpam-5742	19	4	.	.	PROPN
ejpam-5742	19	5	math	math	PROPN
ejpam-5742	19	6	,	,	PUNCT
ejpam-5742	19	7	18	18	NUM
ejpam-5742	19	8	(	(	PUNCT
ejpam-5742	19	9	2	2	NUM
ejpam-5742	19	10	)	)	PUNCT
ejpam-5742	19	11	(	(	PUNCT
ejpam-5742	19	12	2025	2025	NUM
ejpam-5742	19	13	)	)	PUNCT
ejpam-5742	19	14	,	,	PUNCT
ejpam-5742	19	15	5742	5742	NUM
ejpam-5742	19	16	2	2	NUM
ejpam-5742	19	17	of	of	ADP
ejpam-5742	19	18	14	14	NUM
ejpam-5742	19	19	for	for	ADP
ejpam-5742	19	20	an	an	DET
ejpam-5742	19	21	o−ideal	o−ideal	NOUN
ejpam-5742	19	22	to	to	PART
ejpam-5742	19	23	be	be	AUX
ejpam-5742	19	24	prime	prime	ADJ
ejpam-5742	19	25	and	and	CCONJ
ejpam-5742	19	26	demonstrated	demonstrate	VERB
ejpam-5742	19	27	that	that	SCONJ
ejpam-5742	19	28	distinct	distinct	ADJ
ejpam-5742	19	29	prime	prime	NOUN
ejpam-5742	19	30	o−ideals	o−ideal	NOUN
ejpam-5742	19	31	in	in	ADP
ejpam-5742	19	32	an	an	DET
ejpam-5742	19	33	adl	adl	NOUN
ejpam-5742	19	34	are	be	AUX
ejpam-5742	19	35	always	always	ADV
ejpam-5742	19	36	comaximal	comaximal	ADJ
ejpam-5742	19	37	.	.	PUNCT
ejpam-5742	20	1	in	in	ADP
ejpam-5742	20	2	this	this	DET
ejpam-5742	20	3	paper	paper	NOUN
ejpam-5742	20	4	,	,	PUNCT
ejpam-5742	20	5	we	we	PRON
ejpam-5742	20	6	introduce	introduce	VERB
ejpam-5742	20	7	the	the	DET
ejpam-5742	20	8	concept	concept	NOUN
ejpam-5742	20	9	of	of	ADP
ejpam-5742	20	10	an	an	DET
ejpam-5742	20	11	m−homomorphism	m−homomorphism	NOUN
ejpam-5742	20	12	within	within	ADP
ejpam-5742	20	13	the	the	DET
ejpam-5742	20	14	framework	framework	NOUN
ejpam-5742	20	15	of	of	ADP
ejpam-5742	20	16	almost	almost	ADV
ejpam-5742	20	17	distributive	distributive	ADJ
ejpam-5742	20	18	lattices	lattice	NOUN
ejpam-5742	20	19	and	and	CCONJ
ejpam-5742	20	20	examine	examine	VERB
ejpam-5742	20	21	its	its	PRON
ejpam-5742	20	22	properties	property	NOUN
ejpam-5742	20	23	.	.	PUNCT
ejpam-5742	21	1	we	we	PRON
ejpam-5742	21	2	establish	establish	VERB
ejpam-5742	21	3	a	a	DET
ejpam-5742	21	4	sufficient	sufficient	ADJ
ejpam-5742	21	5	condition	condition	NOUN
ejpam-5742	21	6	for	for	ADP
ejpam-5742	21	7	a	a	DET
ejpam-5742	21	8	general	general	ADJ
ejpam-5742	21	9	homomorphism	homomorphism	NOUN
ejpam-5742	21	10	of	of	ADP
ejpam-5742	21	11	an	an	DET
ejpam-5742	21	12	adl	adl	NOUN
ejpam-5742	21	13	to	to	PART
ejpam-5742	21	14	qualify	qualify	VERB
ejpam-5742	21	15	as	as	ADP
ejpam-5742	21	16	an	an	DET
ejpam-5742	21	17	m−homomorphism	m−homomorphism	NOUN
ejpam-5742	21	18	.	.	PUNCT
ejpam-5742	22	1	additionally	additionally	ADV
ejpam-5742	22	2	,	,	PUNCT
ejpam-5742	22	3	we	we	PRON
ejpam-5742	22	4	demonstrate	demonstrate	VERB
ejpam-5742	22	5	that	that	SCONJ
ejpam-5742	22	6	both	both	CCONJ
ejpam-5742	22	7	the	the	DET
ejpam-5742	22	8	image	image	NOUN
ejpam-5742	22	9	and	and	CCONJ
ejpam-5742	22	10	the	the	DET
ejpam-5742	22	11	preimage	preimage	NOUN
ejpam-5742	22	12	of	of	ADP
ejpam-5742	22	13	an	an	DET
ejpam-5742	22	14	m−filter	m−filter	NOUN
ejpam-5742	22	15	under	under	ADP
ejpam-5742	22	16	an	an	DET
ejpam-5742	22	17	m−homomorphism	m−homomorphism	NOUN
ejpam-5742	22	18	remain	remain	VERB
ejpam-5742	22	19	m−filters	m−filter	NOUN
ejpam-5742	22	20	.	.	PUNCT
ejpam-5742	23	1	we	we	PRON
ejpam-5742	23	2	also	also	ADV
ejpam-5742	23	3	show	show	VERB
ejpam-5742	23	4	that	that	SCONJ
ejpam-5742	23	5	the	the	DET
ejpam-5742	23	6	kernel	kernel	NOUN
ejpam-5742	23	7	of	of	ADP
ejpam-5742	23	8	a	a	DET
ejpam-5742	23	9	homomorphism	homomorphism	NOUN
ejpam-5742	23	10	is	be	AUX
ejpam-5742	23	11	an	an	DET
ejpam-5742	23	12	m−filter	m−filter	NOUN
ejpam-5742	23	13	.	.	PUNCT
ejpam-5742	24	1	furthermore	furthermore	ADV
ejpam-5742	24	2	,	,	PUNCT
ejpam-5742	24	3	we	we	PRON
ejpam-5742	24	4	derive	derive	VERB
ejpam-5742	24	5	an	an	DET
ejpam-5742	24	6	equivalence	equivalence	NOUN
ejpam-5742	24	7	between	between	ADP
ejpam-5742	24	8	the	the	DET
ejpam-5742	24	9	class	class	NOUN
ejpam-5742	24	10	of	of	ADP
ejpam-5742	24	11	all	all	DET
ejpam-5742	24	12	prime	prime	ADJ
ejpam-5742	24	13	m−filters	m−filter	NOUN
ejpam-5742	24	14	and	and	CCONJ
ejpam-5742	24	15	the	the	DET
ejpam-5742	24	16	class	class	NOUN
ejpam-5742	24	17	of	of	ADP
ejpam-5742	24	18	all	all	DET
ejpam-5742	24	19	minimal	minimal	ADJ
ejpam-5742	24	20	prime	prime	ADJ
ejpam-5742	24	21	filters	filter	NOUN
ejpam-5742	24	22	.	.	PUNCT
ejpam-5742	25	1	a	a	DET
ejpam-5742	25	2	necessary	necessary	ADJ
ejpam-5742	25	3	and	and	CCONJ
ejpam-5742	25	4	sufficient	sufficient	ADJ
ejpam-5742	25	5	condition	condition	NOUN
ejpam-5742	25	6	for	for	ADP
ejpam-5742	25	7	an	an	DET
ejpam-5742	25	8	m−filter	m−filter	NOUN
ejpam-5742	25	9	in	in	ADP
ejpam-5742	25	10	an	an	DET
ejpam-5742	25	11	adl	adl	NOUN
ejpam-5742	25	12	to	to	PART
ejpam-5742	25	13	be	be	AUX
ejpam-5742	25	14	a	a	DET
ejpam-5742	25	15	prime	prime	ADJ
ejpam-5742	25	16	filter	filter	NOUN
ejpam-5742	25	17	is	be	AUX
ejpam-5742	25	18	also	also	ADV
ejpam-5742	25	19	presented	present	VERB
ejpam-5742	25	20	.	.	PUNCT
ejpam-5742	26	1	we	we	PRON
ejpam-5742	26	2	introduce	introduce	VERB
ejpam-5742	26	3	the	the	DET
ejpam-5742	26	4	notion	notion	NOUN
ejpam-5742	26	5	of	of	ADP
ejpam-5742	26	6	an	an	DET
ejpam-5742	26	7	e−complemented	e−complemented	ADJ
ejpam-5742	26	8	adl	adl	NOUN
ejpam-5742	26	9	and	and	CCONJ
ejpam-5742	26	10	investigate	investigate	VERB
ejpam-5742	26	11	its	its	PRON
ejpam-5742	26	12	properties	property	NOUN
ejpam-5742	26	13	.	.	PUNCT
ejpam-5742	27	1	within	within	ADP
ejpam-5742	27	2	an	an	DET
ejpam-5742	27	3	e−complemented	e−complemented	ADJ
ejpam-5742	27	4	adl	adl	NOUN
ejpam-5742	27	5	,	,	PUNCT
ejpam-5742	27	6	we	we	PRON
ejpam-5742	27	7	establish	establish	VERB
ejpam-5742	27	8	several	several	ADJ
ejpam-5742	27	9	equivalent	equivalent	ADJ
ejpam-5742	27	10	conditions	condition	NOUN
ejpam-5742	27	11	for	for	ADP
ejpam-5742	27	12	an	an	DET
ejpam-5742	27	13	m−filter	m−filter	NOUN
ejpam-5742	27	14	to	to	PART
ejpam-5742	27	15	qualify	qualify	VERB
ejpam-5742	27	16	as	as	ADP
ejpam-5742	27	17	an	an	DET
ejpam-5742	27	18	annihilator	annihilator	NOUN
ejpam-5742	27	19	filter	filter	NOUN
ejpam-5742	27	20	.	.	PUNCT
ejpam-5742	28	1	finally	finally	ADV
ejpam-5742	28	2	,	,	PUNCT
ejpam-5742	28	3	we	we	PRON
ejpam-5742	28	4	prove	prove	VERB
ejpam-5742	28	5	that	that	SCONJ
ejpam-5742	28	6	any	any	DET
ejpam-5742	28	7	two	two	NUM
ejpam-5742	28	8	distinct	distinct	ADJ
ejpam-5742	28	9	prime	prime	ADJ
ejpam-5742	28	10	m−filters	m−filter	NOUN
ejpam-5742	28	11	in	in	ADP
ejpam-5742	28	12	an	an	DET
ejpam-5742	28	13	adl	adl	NOUN
ejpam-5742	28	14	are	be	AUX
ejpam-5742	28	15	comaximal	comaximal	ADJ
ejpam-5742	28	16	.	.	PUNCT
ejpam-5742	29	1	2	2	X
ejpam-5742	29	2	.	.	X
ejpam-5742	29	3	preliminaries	preliminary	NOUN
ejpam-5742	29	4	the	the	DET
ejpam-5742	29	5	definitions	definition	NOUN
ejpam-5742	29	6	and	and	CCONJ
ejpam-5742	29	7	significant	significant	ADJ
ejpam-5742	29	8	results	result	NOUN
ejpam-5742	29	9	from	from	ADP
ejpam-5742	29	10	[	[	X
ejpam-5742	29	11	1	1	NUM
ejpam-5742	29	12	,	,	PUNCT
ejpam-5742	29	13	6	6	NUM
ejpam-5742	29	14	]	]	PUNCT
ejpam-5742	29	15	are	be	AUX
ejpam-5742	29	16	gathered	gather	VERB
ejpam-5742	29	17	and	and	CCONJ
ejpam-5742	29	18	given	give	VERB
ejpam-5742	29	19	in	in	ADP
ejpam-5742	29	20	this	this	DET
ejpam-5742	29	21	part	part	NOUN
ejpam-5742	29	22	;	;	PUNCT
ejpam-5742	29	23	these	these	PRON
ejpam-5742	29	24	will	will	AUX
ejpam-5742	29	25	be	be	AUX
ejpam-5742	29	26	needed	need	VERB
ejpam-5742	29	27	during	during	ADP
ejpam-5742	29	28	the	the	DET
ejpam-5742	29	29	entire	entire	ADJ
ejpam-5742	29	30	document	document	NOUN
ejpam-5742	29	31	.	.	PUNCT
ejpam-5742	30	1	definition	definition	NOUN
ejpam-5742	30	2	1	1	NUM
ejpam-5742	30	3	.	.	PUNCT
ejpam-5742	31	1	[	[	X
ejpam-5742	31	2	1	1	X
ejpam-5742	31	3	]	]	PUNCT
ejpam-5742	31	4	an	an	DET
ejpam-5742	31	5	algebra	algebra	NOUN
ejpam-5742	31	6	(	(	PUNCT
ejpam-5742	31	7	r,∨,∧	r,∨,∧	NUM
ejpam-5742	31	8	,	,	PUNCT
ejpam-5742	31	9	0	0	NUM
ejpam-5742	31	10	)	)	PUNCT
ejpam-5742	31	11	of	of	ADP
ejpam-5742	31	12	type	type	NOUN
ejpam-5742	31	13	(	(	PUNCT
ejpam-5742	31	14	2,2,0	2,2,0	NUM
ejpam-5742	31	15	)	)	PUNCT
ejpam-5742	31	16	satisfying	satisfy	VERB
ejpam-5742	31	17	the	the	DET
ejpam-5742	31	18	following	follow	VERB
ejpam-5742	31	19	specifications	specification	NOUN
ejpam-5742	31	20	is	be	AUX
ejpam-5742	31	21	an	an	DET
ejpam-5742	31	22	almost	almost	ADV
ejpam-5742	31	23	distributive	distributive	ADJ
ejpam-5742	31	24	lattice(adl	lattice(adl	NOUN
ejpam-5742	31	25	)	)	PUNCT
ejpam-5742	31	26	with	with	ADP
ejpam-5742	31	27	zero	zero	NUM
ejpam-5742	31	28	:	:	PUNCT
ejpam-5742	31	29	(	(	PUNCT
ejpam-5742	31	30	1	1	X
ejpam-5742	31	31	)	)	PUNCT
ejpam-5742	31	32	(	(	PUNCT
ejpam-5742	31	33	θ	θ	PROPN
ejpam-5742	31	34	∨	∨	NUM
ejpam-5742	31	35	ϑ	ϑ	X
ejpam-5742	31	36	)	)	PUNCT
ejpam-5742	31	37	∧	∧	PROPN
ejpam-5742	31	38	σ	σ	NOUN
ejpam-5742	31	39	=	=	SYM
ejpam-5742	31	40	(	(	PUNCT
ejpam-5742	31	41	θ	θ	PROPN
ejpam-5742	31	42	∧	∧	PROPN
ejpam-5742	31	43	σ	σ	PROPN
ejpam-5742	31	44	)	)	PUNCT
ejpam-5742	31	45	∨	∨	NOUN
ejpam-5742	31	46	(	(	PUNCT
ejpam-5742	31	47	ϑ	ϑ	X
ejpam-5742	31	48	∧	∧	PROPN
ejpam-5742	31	49	σ	σ	PROPN
ejpam-5742	31	50	)	)	PUNCT
ejpam-5742	31	51	;	;	PUNCT
ejpam-5742	31	52	(	(	PUNCT
ejpam-5742	31	53	2	2	X
ejpam-5742	31	54	)	)	PUNCT
ejpam-5742	31	55	θ	θ	PROPN
ejpam-5742	31	56	∧	∧	PROPN
ejpam-5742	31	57	(	(	PUNCT
ejpam-5742	31	58	ϑ	ϑ	PROPN
ejpam-5742	31	59	∨	∨	PROPN
ejpam-5742	31	60	σ	σ	PROPN
ejpam-5742	31	61	)	)	PUNCT
ejpam-5742	31	62	=	=	PUNCT
ejpam-5742	31	63	(	(	PUNCT
ejpam-5742	31	64	θ	θ	PROPN
ejpam-5742	31	65	∧	∧	PROPN
ejpam-5742	31	66	ϑ	ϑ	X
ejpam-5742	31	67	)	)	PUNCT
ejpam-5742	31	68	∨	∨	PROPN
ejpam-5742	31	69	(	(	PUNCT
ejpam-5742	31	70	θ	θ	PROPN
ejpam-5742	31	71	∧	∧	PROPN
ejpam-5742	31	72	σ	σ	PROPN
ejpam-5742	31	73	)	)	PUNCT
ejpam-5742	31	74	;	;	PUNCT
ejpam-5742	31	75	(	(	PUNCT
ejpam-5742	31	76	3	3	X
ejpam-5742	31	77	)	)	PUNCT
ejpam-5742	31	78	(	(	PUNCT
ejpam-5742	31	79	θ	θ	PROPN
ejpam-5742	31	80	∨	∨	NUM
ejpam-5742	31	81	ϑ	ϑ	X
ejpam-5742	31	82	)	)	PUNCT
ejpam-5742	31	83	∧	∧	PROPN
ejpam-5742	31	84	ϑ	ϑ	X
ejpam-5742	31	85	=	=	X
ejpam-5742	31	86	ϑ	ϑ	X
ejpam-5742	31	87	;	;	PUNCT
ejpam-5742	31	88	(	(	PUNCT
ejpam-5742	31	89	4	4	NUM
ejpam-5742	31	90	)	)	PUNCT
ejpam-5742	31	91	(	(	PUNCT
ejpam-5742	31	92	θ	θ	PROPN
ejpam-5742	31	93	∨	∨	NUM
ejpam-5742	31	94	ϑ	ϑ	X
ejpam-5742	31	95	)	)	PUNCT
ejpam-5742	31	96	∧	∧	PROPN
ejpam-5742	31	97	θ	θ	NOUN
ejpam-5742	31	98	=	=	SYM
ejpam-5742	31	99	θ	θ	PROPN
ejpam-5742	31	100	;	;	PUNCT
ejpam-5742	31	101	(	(	PUNCT
ejpam-5742	31	102	5	5	X
ejpam-5742	31	103	)	)	PUNCT
ejpam-5742	31	104	θ	θ	NOUN
ejpam-5742	31	105	∨	∨	PROPN
ejpam-5742	31	106	(	(	PUNCT
ejpam-5742	31	107	θ	θ	PROPN
ejpam-5742	31	108	∧	∧	PROPN
ejpam-5742	31	109	ϑ	ϑ	X
ejpam-5742	31	110	)	)	PUNCT
ejpam-5742	31	111	=	=	SYM
ejpam-5742	31	112	θ	θ	PROPN
ejpam-5742	31	113	;	;	PUNCT
ejpam-5742	31	114	(	(	PUNCT
ejpam-5742	31	115	6	6	NUM
ejpam-5742	31	116	)	)	PUNCT
ejpam-5742	31	117	0	0	NUM
ejpam-5742	32	1	∧	∧	NOUN
ejpam-5742	32	2	θ	θ	NOUN
ejpam-5742	32	3	=	=	SYM
ejpam-5742	32	4	0	0	NUM
ejpam-5742	32	5	,	,	PUNCT
ejpam-5742	32	6	for	for	ADP
ejpam-5742	32	7	any	any	DET
ejpam-5742	32	8	θ	θ	PROPN
ejpam-5742	32	9	,	,	PUNCT
ejpam-5742	32	10	ϑ	ϑ	X
ejpam-5742	32	11	,	,	PUNCT
ejpam-5742	32	12	σ	σ	PROPN
ejpam-5742	32	13	∈	∈	PROPN
ejpam-5742	32	14	r.	r.	NOUN
ejpam-5742	32	15	when	when	SCONJ
ejpam-5742	32	16	θ	θ	PROPN
ejpam-5742	32	17	=	=	SYM
ejpam-5742	32	18	θ∧ϑ	θ∧ϑ	PROPN
ejpam-5742	32	19	,	,	PUNCT
ejpam-5742	32	20	or	or	CCONJ
ejpam-5742	32	21	equivalently	equivalently	ADV
ejpam-5742	32	22	,	,	PUNCT
ejpam-5742	32	23	θ∨ϑ	θ∨ϑ	PROPN
ejpam-5742	32	24	=	=	SYM
ejpam-5742	32	25	ϑ	ϑ	X
ejpam-5742	32	26	,	,	PUNCT
ejpam-5742	32	27	occurs	occur	VERB
ejpam-5742	32	28	for	for	ADP
ejpam-5742	32	29	every	every	DET
ejpam-5742	32	30	θ	θ	PROPN
ejpam-5742	32	31	,	,	PUNCT
ejpam-5742	32	32	ϑ	ϑ	X
ejpam-5742	32	33	∈	∈	PROPN
ejpam-5742	32	34	r	r	NOUN
ejpam-5742	32	35	,	,	PUNCT
ejpam-5742	32	36	then	then	ADV
ejpam-5742	32	37	θ	θ	PROPN
ejpam-5742	32	38	≤	≤	NOUN
ejpam-5742	32	39	ϑ.	ϑ.	NOUN
ejpam-5742	32	40	this	this	PRON
ejpam-5742	32	41	defines	define	VERB
ejpam-5742	32	42	a	a	DET
ejpam-5742	32	43	partial	partial	ADJ
ejpam-5742	32	44	≤	≤	NOUN
ejpam-5742	32	45	on	on	ADP
ejpam-5742	32	46	r	r	NOUN
ejpam-5742	32	47	in	in	ADP
ejpam-5742	32	48	an	an	DET
ejpam-5742	32	49	adl	adl	PROPN
ejpam-5742	32	50	(	(	PUNCT
ejpam-5742	32	51	r,∨,∧	r,∨,∧	NUM
ejpam-5742	32	52	,	,	PUNCT
ejpam-5742	32	53	0	0	NUM
ejpam-5742	32	54	)	)	PUNCT
ejpam-5742	32	55	.	.	PUNCT
ejpam-5742	33	1	as	as	ADP
ejpam-5742	33	2	a	a	DET
ejpam-5742	33	3	partial	partial	ADJ
ejpam-5742	33	4	ordering	ordering	NOUN
ejpam-5742	33	5	on	on	ADP
ejpam-5742	33	6	r	r	NOUN
ejpam-5742	33	7	,	,	PUNCT
ejpam-5742	33	8	this	this	DET
ejpam-5742	33	9	definition	definition	NOUN
ejpam-5742	33	10	establishes	establish	VERB
ejpam-5742	33	11	≤.	≤.	NOUN
ejpam-5742	33	12	when	when	SCONJ
ejpam-5742	33	13	m	m	VERB
ejpam-5742	33	14	in	in	ADP
ejpam-5742	33	15	r	r	NOUN
ejpam-5742	33	16	holds	hold	VERB
ejpam-5742	33	17	maximum	maximum	ADJ
ejpam-5742	33	18	with	with	ADP
ejpam-5742	33	19	respect	respect	NOUN
ejpam-5742	33	20	to	to	ADP
ejpam-5742	33	21	the	the	DET
ejpam-5742	33	22	partial	partial	ADJ
ejpam-5742	33	23	ordering	order	VERB
ejpam-5742	33	24	≤	≤	NOUN
ejpam-5742	33	25	on	on	ADP
ejpam-5742	33	26	r	r	NOUN
ejpam-5742	33	27	,	,	PUNCT
ejpam-5742	33	28	it	it	PRON
ejpam-5742	33	29	is	be	AUX
ejpam-5742	33	30	referred	refer	VERB
ejpam-5742	33	31	to	to	ADP
ejpam-5742	33	32	as	as	ADV
ejpam-5742	33	33	maximal	maximal	ADJ
ejpam-5742	33	34	i.e.	i.e.	X
ejpam-5742	33	35	,	,	PUNCT
ejpam-5742	33	36	for	for	ADP
ejpam-5742	33	37	any	any	DET
ejpam-5742	33	38	m	m	NOUN
ejpam-5742	33	39	∈	∈	ADJ
ejpam-5742	33	40	r	r	NOUN
ejpam-5742	33	41	,	,	PUNCT
ejpam-5742	33	42	m	m	VERB
ejpam-5742	33	43	≤	≤	NUM
ejpam-5742	33	44	θ	θ	PROPN
ejpam-5742	33	45	⇒	⇒	NOUN
ejpam-5742	33	46	m	m	VERB
ejpam-5742	33	47	=	=	SYM
ejpam-5742	33	48	θ	θ	PROPN
ejpam-5742	33	49	;	;	PUNCT
ejpam-5742	33	50	mmax.elt(r	mmax.elt(r	NUM
ejpam-5742	33	51	)	)	PUNCT
ejpam-5742	33	52	is	be	AUX
ejpam-5742	33	53	the	the	DET
ejpam-5742	33	54	collection	collection	NOUN
ejpam-5742	33	55	of	of	ADP
ejpam-5742	33	56	all	all	DET
ejpam-5742	33	57	such	such	ADJ
ejpam-5742	33	58	maximal	maximal	ADJ
ejpam-5742	33	59	elements	element	NOUN
ejpam-5742	33	60	within	within	ADP
ejpam-5742	33	61	r.	r.	PROPN
ejpam-5742	33	62	in	in	ADP
ejpam-5742	33	63	swamy	swamy	PROPN
ejpam-5742	33	64	’s	’s	PART
ejpam-5742	33	65	work[1	work[1	PROPN
ejpam-5742	33	66	]	]	X
ejpam-5742	33	67	,	,	PUNCT
ejpam-5742	33	68	it	it	PRON
ejpam-5742	33	69	is	be	AUX
ejpam-5742	33	70	noted	note	VERB
ejpam-5742	33	71	that	that	SCONJ
ejpam-5742	33	72	an	an	DET
ejpam-5742	33	73	adl	adl	NOUN
ejpam-5742	33	74	denoted	denote	VERB
ejpam-5742	33	75	as	as	SCONJ
ejpam-5742	33	76	r	r	NOUN
ejpam-5742	33	77	exhibits	exhibit	VERB
ejpam-5742	33	78	nearly	nearly	ADV
ejpam-5742	33	79	all	all	PRON
ejpam-5742	33	80	features	feature	NOUN
ejpam-5742	33	81	of	of	ADP
ejpam-5742	33	82	a	a	DET
ejpam-5742	33	83	distributive	distributive	ADJ
ejpam-5742	33	84	lattice[7	lattice[7	NOUN
ejpam-5742	33	85	,	,	PUNCT
ejpam-5742	33	86	8	8	NUM
ejpam-5742	33	87	]	]	PUNCT
ejpam-5742	33	88	,	,	PUNCT
ejpam-5742	33	89	apart	apart	ADV
ejpam-5742	33	90	from	from	ADP
ejpam-5742	33	91	the	the	DET
ejpam-5742	33	92	non	non	NOUN
ejpam-5742	33	93	-	-	NOUN
ejpam-5742	33	94	commutativity	commutativity	NOUN
ejpam-5742	33	95	between	between	ADP
ejpam-5742	33	96	∨	∨	NOUN
ejpam-5742	33	97	and	and	CCONJ
ejpam-5742	33	98	∧	∧	PROPN
ejpam-5742	33	99	and	and	CCONJ
ejpam-5742	33	100	the	the	DET
ejpam-5742	33	101	right	right	ADJ
ejpam-5742	33	102	distributivity	distributivity	NOUN
ejpam-5742	33	103	of	of	ADP
ejpam-5742	33	104	∨	∨	NUM
ejpam-5742	33	105	over	over	ADP
ejpam-5742	33	106	∧.	∧.	PROPN
ejpam-5742	33	107	either	either	ADV
ejpam-5742	33	108	of	of	ADP
ejpam-5742	33	109	these	these	DET
ejpam-5742	33	110	properties	property	NOUN
ejpam-5742	33	111	,	,	PUNCT
ejpam-5742	33	112	if	if	SCONJ
ejpam-5742	33	113	present	present	ADJ
ejpam-5742	33	114	,	,	PUNCT
ejpam-5742	33	115	would	would	AUX
ejpam-5742	33	116	classify	classify	VERB
ejpam-5742	33	117	r	r	NOUN
ejpam-5742	33	118	as	as	ADP
ejpam-5742	33	119	a	a	DET
ejpam-5742	33	120	distributive	distributive	ADJ
ejpam-5742	33	121	lattice	lattice	NOUN
ejpam-5742	33	122	.	.	PUNCT
ejpam-5742	34	1	if	if	SCONJ
ejpam-5742	34	2	,	,	PUNCT
ejpam-5742	34	3	for	for	ADP
ejpam-5742	34	4	every	every	DET
ejpam-5742	34	5	θ	θ	PROPN
ejpam-5742	34	6	,	,	PUNCT
ejpam-5742	34	7	ϑ	ϑ	X
ejpam-5742	34	8	∈	∈	X
ejpam-5742	34	9	i	i	PRON
ejpam-5742	34	10	and	and	CCONJ
ejpam-5742	34	11	every	every	DET
ejpam-5742	34	12	µ	µ	PROPN
ejpam-5742	34	13	∈	∈	NOUN
ejpam-5742	34	14	r	r	NOUN
ejpam-5742	34	15	,	,	PUNCT
ejpam-5742	34	16	there	there	PRON
ejpam-5742	34	17	is	be	VERB
ejpam-5742	34	18	a	a	DET
ejpam-5742	34	19	nonempty	nonempty	NOUN
ejpam-5742	34	20	subset	subset	VERB
ejpam-5742	34	21	i	i	PRON
ejpam-5742	34	22	of	of	ADP
ejpam-5742	34	23	r	r	NOUN
ejpam-5742	34	24	,	,	PUNCT
ejpam-5742	34	25	then	then	ADV
ejpam-5742	34	26	θ	θ	PROPN
ejpam-5742	34	27	∨	∨	NUM
ejpam-5742	34	28	ϑ	ϑ	PROPN
ejpam-5742	34	29	,	,	PUNCT
ejpam-5742	34	30	θ	θ	PROPN
ejpam-5742	34	31	∧	∧	PROPN
ejpam-5742	34	32	µ	µ	X
ejpam-5742	34	33	∈	∈	X
ejpam-5742	34	34	i	i	PRON
ejpam-5742	34	35	(	(	PUNCT
ejpam-5742	34	36	respectively	respectively	ADV
ejpam-5742	34	37	,	,	PUNCT
ejpam-5742	34	38	θ	θ	PROPN
ejpam-5742	34	39	∧	∧	PROPN
ejpam-5742	34	40	ϑ	ϑ	X
ejpam-5742	34	41	,	,	PUNCT
ejpam-5742	34	42	µ	µ	X
ejpam-5742	34	43	∨	∨	NUM
ejpam-5742	34	44	θ	θ	X
ejpam-5742	34	45	∈	∈	PROPN
ejpam-5742	34	46	f	f	X
ejpam-5742	34	47	)	)	PUNCT
ejpam-5742	34	48	for	for	ADP
ejpam-5742	34	49	every	every	DET
ejpam-5742	34	50	θ	θ	PROPN
ejpam-5742	34	51	,	,	PUNCT
ejpam-5742	34	52	ϑ	ϑ	X
ejpam-5742	34	53	∈	∈	PROPN
ejpam-5742	34	54	i.	i.	NOUN
ejpam-5742	34	55	a	a	DET
ejpam-5742	34	56	maximum	maximum	ADJ
ejpam-5742	34	57	ideal	ideal	NOUN
ejpam-5742	34	58	(	(	PUNCT
ejpam-5742	34	59	filter	filter	NOUN
ejpam-5742	34	60	)	)	PUNCT
ejpam-5742	34	61	contains	contain	VERB
ejpam-5742	34	62	every	every	DET
ejpam-5742	34	63	appropriate	appropriate	ADJ
ejpam-5742	34	64	ideal	ideal	NOUN
ejpam-5742	34	65	(	(	PUNCT
ejpam-5742	34	66	filter	filter	NOUN
ejpam-5742	34	67	)	)	PUNCT
ejpam-5742	34	68	of	of	ADP
ejpam-5742	34	69	r.	r.	PROPN
ejpam-5742	34	70	the	the	DET
ejpam-5742	34	71	smallest	small	ADJ
ejpam-5742	34	72	ideal	ideal	NOUN
ejpam-5742	34	73	that	that	PRON
ejpam-5742	34	74	contains	contain	VERB
ejpam-5742	34	75	a	a	PRON
ejpam-5742	34	76	for	for	ADP
ejpam-5742	34	77	each	each	DET
ejpam-5742	34	78	subset	subset	VERB
ejpam-5742	34	79	a	a	PRON
ejpam-5742	34	80	of	of	ADP
ejpam-5742	34	81	r	r	NOUN
ejpam-5742	34	82	is	be	AUX
ejpam-5742	34	83	(	(	PUNCT
ejpam-5742	34	84	a	a	X
ejpam-5742	34	85	]	]	X
ejpam-5742	34	86	:	:	PUNCT
ejpam-5742	34	87	=	=	SYM
ejpam-5742	34	88	{	{	PUNCT
ejpam-5742	34	89	(	(	PUNCT
ejpam-5742	34	90	n∨	n∨	PROPN
ejpam-5742	34	91	i=1	i=1	PROPN
ejpam-5742	34	92	θi)∧	θi)∧	PROPN
ejpam-5742	34	93	µ	µ	PROPN
ejpam-5742	34	94	|	|	NOUN
ejpam-5742	34	95	θi	θi	ADP
ejpam-5742	34	96	∈	∈	PROPN
ejpam-5742	34	97	a	a	PRON
ejpam-5742	34	98	,	,	PUNCT
ejpam-5742	34	99	µ	µ	X
ejpam-5742	34	100	∈	∈	NOUN
ejpam-5742	34	101	r	r	NOUN
ejpam-5742	34	102	and	and	CCONJ
ejpam-5742	34	103	n	n	CCONJ
ejpam-5742	34	104	∈	∈	PROPN
ejpam-5742	34	105	n	n	CCONJ
ejpam-5742	34	106	}	}	PUNCT
ejpam-5742	34	107	.	.	PUNCT
ejpam-5742	35	1	an	an	DET
ejpam-5742	35	2	ideal	ideal	NOUN
ejpam-5742	35	3	like	like	ADP
ejpam-5742	35	4	a	a	DET
ejpam-5742	35	5	=	=	SYM
ejpam-5742	35	6	{	{	PUNCT
ejpam-5742	35	7	θ	θ	NOUN
ejpam-5742	35	8	}	}	PUNCT
ejpam-5742	35	9	is	be	AUX
ejpam-5742	35	10	written	write	VERB
ejpam-5742	35	11	as	as	ADP
ejpam-5742	35	12	(	(	PUNCT
ejpam-5742	35	13	θ	θ	X
ejpam-5742	35	14	]	]	X
ejpam-5742	35	15	rather	rather	ADV
ejpam-5742	35	16	than	than	ADP
ejpam-5742	35	17	(	(	PUNCT
ejpam-5742	35	18	a	a	X
ejpam-5742	35	19	]	]	X
ejpam-5742	35	20	;	;	PUNCT
ejpam-5742	35	21	this	this	PRON
ejpam-5742	35	22	is	be	AUX
ejpam-5742	35	23	known	know	VERB
ejpam-5742	35	24	as	as	ADP
ejpam-5742	35	25	the	the	DET
ejpam-5742	35	26	principal	principal	ADJ
ejpam-5742	35	27	ideal	ideal	PROPN
ejpam-5742	35	28	n.	n.	PROPN
ejpam-5742	35	29	rafi	rafi	PROPN
ejpam-5742	35	30	,	,	PUNCT
ejpam-5742	35	31	t.	t.	PROPN
ejpam-5742	35	32	gaketem	gaketem	PROPN
ejpam-5742	35	33	,	,	PUNCT
ejpam-5742	35	34	r.	r.	PROPN
ejpam-5742	35	35	k.	k.	PROPN
ejpam-5742	35	36	bandaru	bandaru	PROPN
ejpam-5742	35	37	/	/	SYM
ejpam-5742	35	38	eur	eur	PROPN
ejpam-5742	35	39	.	.	PUNCT
ejpam-5742	36	1	j.	j.	PROPN
ejpam-5742	36	2	pure	pure	PROPN
ejpam-5742	36	3	appl	appl	PROPN
ejpam-5742	36	4	.	.	PROPN
ejpam-5742	36	5	math	math	PROPN
ejpam-5742	36	6	,	,	PUNCT
ejpam-5742	36	7	18	18	NUM
ejpam-5742	36	8	(	(	PUNCT
ejpam-5742	36	9	2	2	NUM
ejpam-5742	36	10	)	)	PUNCT
ejpam-5742	36	11	(	(	PUNCT
ejpam-5742	36	12	2025	2025	NUM
ejpam-5742	36	13	)	)	PUNCT
ejpam-5742	36	14	,	,	PUNCT
ejpam-5742	36	15	5742	5742	NUM
ejpam-5742	36	16	3	3	NUM
ejpam-5742	36	17	of	of	ADP
ejpam-5742	36	18	14	14	NUM
ejpam-5742	36	19	of	of	ADP
ejpam-5742	36	20	r.	r.	PROPN
ejpam-5742	36	21	the	the	DET
ejpam-5742	36	22	same	same	ADJ
ejpam-5742	36	23	way	way	NOUN
ejpam-5742	36	24	,	,	PUNCT
ejpam-5742	36	25	for	for	ADP
ejpam-5742	36	26	each	each	DET
ejpam-5742	36	27	a	a	DET
ejpam-5742	36	28	⊆	⊆	NUM
ejpam-5742	36	29	r	r	NOUN
ejpam-5742	36	30	,	,	PUNCT
ejpam-5742	36	31	[	[	X
ejpam-5742	36	32	a	a	X
ejpam-5742	36	33	)	)	PUNCT
ejpam-5742	36	34	:	:	PUNCT
ejpam-5742	36	35	=	=	SYM
ejpam-5742	36	36	{	{	PUNCT
ejpam-5742	36	37	µ	µ	X
ejpam-5742	36	38	∨	∨	NUM
ejpam-5742	36	39	(	(	PUNCT
ejpam-5742	36	40	n∧	n∧	NUM
ejpam-5742	36	41	i=1	i=1	PROPN
ejpam-5742	36	42	θi	θi	X
ejpam-5742	36	43	)	)	PUNCT
ejpam-5742	37	1	|	|	ADV
ejpam-5742	37	2	θi	θi	ADP
ejpam-5742	37	3	∈	∈	PROPN
ejpam-5742	37	4	a	a	PRON
ejpam-5742	37	5	,	,	PUNCT
ejpam-5742	37	6	µ	µ	X
ejpam-5742	37	7	∈	∈	NOUN
ejpam-5742	37	8	r	r	NOUN
ejpam-5742	37	9	and	and	CCONJ
ejpam-5742	37	10	n	n	CCONJ
ejpam-5742	37	11	∈	∈	PROPN
ejpam-5742	37	12	n	n	CCONJ
ejpam-5742	37	13	}	}	PUNCT
ejpam-5742	37	14	.	.	PUNCT
ejpam-5742	38	1	a	a	DET
ejpam-5742	38	2	filter	filter	NOUN
ejpam-5742	38	3	like	like	ADP
ejpam-5742	38	4	a	a	DET
ejpam-5742	38	5	=	=	SYM
ejpam-5742	38	6	{	{	PUNCT
ejpam-5742	38	7	θ	θ	NOUN
ejpam-5742	38	8	}	}	PUNCT
ejpam-5742	38	9	is	be	AUX
ejpam-5742	38	10	written	write	VERB
ejpam-5742	38	11	as	as	ADP
ejpam-5742	38	12	[	[	X
ejpam-5742	38	13	θ	θ	X
ejpam-5742	38	14	)	)	PUNCT
ejpam-5742	38	15	rather	rather	ADV
ejpam-5742	38	16	than	than	ADP
ejpam-5742	38	17	[	[	X
ejpam-5742	38	18	a	a	X
ejpam-5742	38	19	)	)	PUNCT
ejpam-5742	38	20	;	;	PUNCT
ejpam-5742	38	21	this	this	PRON
ejpam-5742	38	22	is	be	AUX
ejpam-5742	38	23	known	know	VERB
ejpam-5742	38	24	as	as	ADP
ejpam-5742	38	25	the	the	DET
ejpam-5742	38	26	principal	principal	ADJ
ejpam-5742	38	27	filter	filter	NOUN
ejpam-5742	38	28	of	of	ADP
ejpam-5742	38	29	r.	r.	PROPN
ejpam-5742	38	30	it	it	PRON
ejpam-5742	38	31	can	can	AUX
ejpam-5742	38	32	be	be	AUX
ejpam-5742	38	33	confirmed	confirm	VERB
ejpam-5742	38	34	that	that	SCONJ
ejpam-5742	38	35	(	(	PUNCT
ejpam-5742	38	36	θ	θ	X
ejpam-5742	38	37	]	]	X
ejpam-5742	38	38	∨	∨	X
ejpam-5742	38	39	(	(	PUNCT
ejpam-5742	38	40	ϑ	ϑ	X
ejpam-5742	38	41	]	]	X
ejpam-5742	38	42	=	=	SYM
ejpam-5742	38	43	(	(	PUNCT
ejpam-5742	38	44	θ	θ	PROPN
ejpam-5742	38	45	∨	∨	NUM
ejpam-5742	38	46	ϑ	ϑ	X
ejpam-5742	38	47	]	]	PUNCT
ejpam-5742	38	48	and	and	CCONJ
ejpam-5742	38	49	(	(	PUNCT
ejpam-5742	38	50	θ	θ	NOUN
ejpam-5742	38	51	]	]	X
ejpam-5742	38	52	∩	∩	NOUN
ejpam-5742	38	53	(	(	PUNCT
ejpam-5742	38	54	ϑ	ϑ	X
ejpam-5742	38	55	]	]	X
ejpam-5742	38	56	=	=	SYM
ejpam-5742	38	57	(	(	PUNCT
ejpam-5742	38	58	θ	θ	PROPN
ejpam-5742	38	59	∧	∧	PROPN
ejpam-5742	38	60	ϑ	ϑ	AUX
ejpam-5742	38	61	]	]	X
ejpam-5742	38	62	hold	hold	VERB
ejpam-5742	38	63	for	for	ADP
ejpam-5742	38	64	any	any	DET
ejpam-5742	38	65	θ	θ	PROPN
ejpam-5742	38	66	,	,	PUNCT
ejpam-5742	38	67	ϑ	ϑ	PROPN
ejpam-5742	38	68	∈	∈	PROPN
ejpam-5742	38	69	r.	r.	PROPN
ejpam-5742	38	70	a	a	DET
ejpam-5742	38	71	sublattice	sublattice	NOUN
ejpam-5742	38	72	of	of	ADP
ejpam-5742	38	73	the	the	DET
ejpam-5742	38	74	distributive	distributive	ADJ
ejpam-5742	38	75	lattice	lattice	NOUN
ejpam-5742	38	76	(	(	PUNCT
ejpam-5742	38	77	i(r),∨,∩	i(r),∨,∩	NOUN
ejpam-5742	38	78	)	)	PUNCT
ejpam-5742	38	79	of	of	ADP
ejpam-5742	38	80	all	all	DET
ejpam-5742	38	81	ideals	ideal	NOUN
ejpam-5742	38	82	of	of	ADP
ejpam-5742	38	83	r	r	NOUN
ejpam-5742	38	84	is	be	AUX
ejpam-5742	38	85	thus	thus	ADV
ejpam-5742	38	86	the	the	DET
ejpam-5742	38	87	set	set	NOUN
ejpam-5742	38	88	(	(	PUNCT
ejpam-5742	38	89	pi(r),∨,∩	pi(r),∨,∩	NOUN
ejpam-5742	38	90	)	)	PUNCT
ejpam-5742	38	91	of	of	ADP
ejpam-5742	38	92	all	all	DET
ejpam-5742	38	93	principal	principal	ADJ
ejpam-5742	38	94	ideals	ideal	NOUN
ejpam-5742	38	95	of	of	ADP
ejpam-5742	38	96	r.	r.	PROPN
ejpam-5742	38	97	for	for	ADP
ejpam-5742	38	98	any	any	DET
ejpam-5742	38	99	nonempty	nonempty	NOUN
ejpam-5742	38	100	subset	subset	VERB
ejpam-5742	38	101	a	a	PRON
ejpam-5742	38	102	of	of	ADP
ejpam-5742	38	103	an	an	DET
ejpam-5742	38	104	adl	adl	PROPN
ejpam-5742	38	105	r	r	NOUN
ejpam-5742	38	106	,	,	PUNCT
ejpam-5742	38	107	define	define	VERB
ejpam-5742	38	108	a+	a+	PUNCT
ejpam-5742	38	109	=	=	VERB
ejpam-5742	38	110	{	{	PUNCT
ejpam-5742	38	111	µ	µ	X
ejpam-5742	38	112	∈	∈	NOUN
ejpam-5742	38	113	r	r	NOUN
ejpam-5742	38	114	|	|	NOUN
ejpam-5742	38	115	θ	θ	PROPN
ejpam-5742	38	116	∨	∨	X
ejpam-5742	38	117	µ	µ	X
ejpam-5742	38	118	is	be	AUX
ejpam-5742	38	119	maximal	maximal	ADJ
ejpam-5742	38	120	,	,	PUNCT
ejpam-5742	38	121	for	for	ADP
ejpam-5742	38	122	all	all	PRON
ejpam-5742	38	123	θ	θ	PROPN
ejpam-5742	38	124	∈	∈	PROPN
ejpam-5742	38	125	a	a	PRON
ejpam-5742	38	126	}	}	PUNCT
ejpam-5742	38	127	.	.	PUNCT
ejpam-5742	39	1	here	here	ADV
ejpam-5742	39	2	a+	a+	PUNCT
ejpam-5742	39	3	is	be	AUX
ejpam-5742	39	4	called	call	VERB
ejpam-5742	39	5	the	the	DET
ejpam-5742	39	6	dual	dual	ADJ
ejpam-5742	39	7	annihilator	annihilator	NOUN
ejpam-5742	39	8	of	of	ADP
ejpam-5742	39	9	a	a	PRON
ejpam-5742	39	10	in	in	ADP
ejpam-5742	39	11	r.	r.	NOUN
ejpam-5742	39	12	for	for	ADP
ejpam-5742	39	13	any	any	DET
ejpam-5742	39	14	θ	θ	PROPN
ejpam-5742	39	15	∈	∈	PROPN
ejpam-5742	39	16	r	r	NOUN
ejpam-5742	39	17	,	,	PUNCT
ejpam-5742	39	18	we	we	PRON
ejpam-5742	39	19	have	have	VERB
ejpam-5742	39	20	{	{	PUNCT
ejpam-5742	39	21	θ}+	θ}+	NUM
ejpam-5742	39	22	=	=	PUNCT
ejpam-5742	40	1	[	[	X
ejpam-5742	40	2	θ)+	θ)+	X
ejpam-5742	40	3	,	,	PUNCT
ejpam-5742	40	4	where	where	SCONJ
ejpam-5742	40	5	[	[	X
ejpam-5742	40	6	θ	θ	NOUN
ejpam-5742	40	7	)	)	PUNCT
ejpam-5742	40	8	is	be	AUX
ejpam-5742	40	9	the	the	DET
ejpam-5742	40	10	principal	principal	ADJ
ejpam-5742	40	11	filter	filter	NOUN
ejpam-5742	40	12	generated	generate	VERB
ejpam-5742	40	13	by	by	ADP
ejpam-5742	40	14	θ	θ	PROPN
ejpam-5742	40	15	.	.	PUNCT
ejpam-5742	41	1	an	an	DET
ejpam-5742	41	2	element	element	ADJ
ejpam-5742	41	3	θ	θ	PROPN
ejpam-5742	41	4	of	of	ADP
ejpam-5742	41	5	an	an	DET
ejpam-5742	41	6	adl	adl	PROPN
ejpam-5742	41	7	r	r	NOUN
ejpam-5742	41	8	is	be	AUX
ejpam-5742	41	9	called	call	VERB
ejpam-5742	41	10	dual	dual	ADJ
ejpam-5742	41	11	dense	dense	ADJ
ejpam-5742	41	12	element	element	NOUN
ejpam-5742	41	13	if	if	SCONJ
ejpam-5742	41	14	[	[	X
ejpam-5742	41	15	θ)+	θ)+	X
ejpam-5742	41	16	=	=	SYM
ejpam-5742	41	17	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	41	18	)	)	PUNCT
ejpam-5742	41	19	and	and	CCONJ
ejpam-5742	41	20	the	the	DET
ejpam-5742	41	21	set	set	ADJ
ejpam-5742	41	22	e	e	NOUN
ejpam-5742	41	23	of	of	ADP
ejpam-5742	41	24	all	all	DET
ejpam-5742	41	25	dual	dual	ADJ
ejpam-5742	41	26	dense	dense	ADJ
ejpam-5742	41	27	elements	element	NOUN
ejpam-5742	41	28	in	in	ADP
ejpam-5742	41	29	an	an	DET
ejpam-5742	41	30	adl	adl	NOUN
ejpam-5742	41	31	r	r	NOUN
ejpam-5742	41	32	is	be	AUX
ejpam-5742	41	33	an	an	DET
ejpam-5742	41	34	ideal	ideal	NOUN
ejpam-5742	41	35	if	if	SCONJ
ejpam-5742	41	36	e	e	NOUN
ejpam-5742	41	37	is	be	AUX
ejpam-5742	41	38	non	non	ADJ
ejpam-5742	41	39	-	-	ADJ
ejpam-5742	41	40	empty	empty	ADJ
ejpam-5742	41	41	.	.	PUNCT
ejpam-5742	42	1	in	in	ADP
ejpam-5742	42	2	this	this	DET
ejpam-5742	42	3	paper	paper	NOUN
ejpam-5742	42	4	,	,	PUNCT
ejpam-5742	42	5	r	r	NOUN
ejpam-5742	42	6	and	and	CCONJ
ejpam-5742	42	7	r′	r′	NOUN
ejpam-5742	42	8	are	be	AUX
ejpam-5742	42	9	used	use	VERB
ejpam-5742	42	10	to	to	PART
ejpam-5742	42	11	represent	represent	VERB
ejpam-5742	42	12	two	two	NUM
ejpam-5742	42	13	adls	adl	NOUN
ejpam-5742	42	14	with	with	ADP
ejpam-5742	42	15	zero	zero	NUM
ejpam-5742	42	16	elements	element	NOUN
ejpam-5742	42	17	0	0	NUM
ejpam-5742	42	18	and	and	CCONJ
ejpam-5742	42	19	0′	0′	NUM
ejpam-5742	42	20	,	,	PUNCT
ejpam-5742	42	21	respectively	respectively	ADV
ejpam-5742	42	22	,	,	PUNCT
ejpam-5742	42	23	while	while	SCONJ
ejpam-5742	42	24	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	42	25	)	)	PUNCT
ejpam-5742	42	26	and	and	CCONJ
ejpam-5742	42	27	mmax.elt(r′	mmax.elt(r′	NOUN
ejpam-5742	42	28	)	)	PUNCT
ejpam-5742	42	29	denote	denote	VERB
ejpam-5742	42	30	the	the	DET
ejpam-5742	42	31	sets	set	NOUN
ejpam-5742	42	32	of	of	ADP
ejpam-5742	42	33	all	all	DET
ejpam-5742	42	34	maximal	maximal	ADJ
ejpam-5742	42	35	elements	element	NOUN
ejpam-5742	42	36	in	in	ADP
ejpam-5742	42	37	r	r	NOUN
ejpam-5742	42	38	and	and	CCONJ
ejpam-5742	42	39	r′	r′	PROPN
ejpam-5742	42	40	,	,	PUNCT
ejpam-5742	42	41	respectively	respectively	ADV
ejpam-5742	42	42	.	.	PUNCT
ejpam-5742	43	1	3	3	X
ejpam-5742	43	2	.	.	X
ejpam-5742	43	3	m−homomorphisms	m−homomorphism	NOUN
ejpam-5742	43	4	of	of	ADP
ejpam-5742	43	5	adls	adls	PROPN
ejpam-5742	43	6	in	in	ADP
ejpam-5742	43	7	this	this	DET
ejpam-5742	43	8	section	section	NOUN
ejpam-5742	43	9	,	,	PUNCT
ejpam-5742	43	10	we	we	PRON
ejpam-5742	43	11	introduce	introduce	VERB
ejpam-5742	43	12	and	and	CCONJ
ejpam-5742	43	13	analyze	analyze	VERB
ejpam-5742	43	14	m−homomorphisms	m−homomorphism	NOUN
ejpam-5742	43	15	in	in	ADP
ejpam-5742	43	16	almost	almost	ADV
ejpam-5742	43	17	distributive	distributive	ADJ
ejpam-5742	43	18	lattices	lattice	NOUN
ejpam-5742	43	19	,	,	PUNCT
ejpam-5742	43	20	establishing	establish	VERB
ejpam-5742	43	21	conditions	condition	NOUN
ejpam-5742	43	22	for	for	ADP
ejpam-5742	43	23	a	a	DET
ejpam-5742	43	24	general	general	ADJ
ejpam-5742	43	25	homomorphism	homomorphism	NOUN
ejpam-5742	43	26	to	to	PART
ejpam-5742	43	27	be	be	AUX
ejpam-5742	43	28	an	an	DET
ejpam-5742	43	29	m−homomorphism	m−homomorphism	NOUN
ejpam-5742	43	30	and	and	CCONJ
ejpam-5742	43	31	showing	show	VERB
ejpam-5742	43	32	that	that	SCONJ
ejpam-5742	43	33	both	both	DET
ejpam-5742	43	34	images	image	NOUN
ejpam-5742	43	35	and	and	CCONJ
ejpam-5742	43	36	pre	pre	VERB
ejpam-5742	43	37	images	image	NOUN
ejpam-5742	43	38	of	of	ADP
ejpam-5742	43	39	m−filters	m−filter	NOUN
ejpam-5742	43	40	under	under	ADP
ejpam-5742	43	41	these	these	DET
ejpam-5742	43	42	homomorphisms	homomorphism	NOUN
ejpam-5742	43	43	remain	remain	VERB
ejpam-5742	43	44	m−filters	m−filter	NOUN
ejpam-5742	43	45	.	.	PUNCT
ejpam-5742	44	1	we	we	PRON
ejpam-5742	44	2	also	also	ADV
ejpam-5742	44	3	derive	derive	VERB
ejpam-5742	44	4	equivalences	equivalence	NOUN
ejpam-5742	44	5	between	between	ADP
ejpam-5742	44	6	minimal	minimal	ADJ
ejpam-5742	44	7	prime	prime	ADJ
ejpam-5742	44	8	filters	filter	NOUN
ejpam-5742	44	9	and	and	CCONJ
ejpam-5742	44	10	prime	prime	ADJ
ejpam-5742	44	11	m−filters	m−filter	NOUN
ejpam-5742	44	12	,	,	PUNCT
ejpam-5742	44	13	present	present	ADJ
ejpam-5742	44	14	conditions	condition	NOUN
ejpam-5742	44	15	for	for	SCONJ
ejpam-5742	44	16	m−filters	m−filter	NOUN
ejpam-5742	44	17	to	to	PART
ejpam-5742	44	18	be	be	AUX
ejpam-5742	44	19	prime	prime	ADJ
ejpam-5742	44	20	,	,	PUNCT
ejpam-5742	44	21	and	and	CCONJ
ejpam-5742	44	22	explore	explore	VERB
ejpam-5742	44	23	the	the	DET
ejpam-5742	44	24	properties	property	NOUN
ejpam-5742	44	25	of	of	ADP
ejpam-5742	44	26	e−complemnted	e−complemnte	VERB
ejpam-5742	44	27	adls	adls	PROPN
ejpam-5742	44	28	.	.	PUNCT
ejpam-5742	45	1	we	we	PRON
ejpam-5742	45	2	will	will	AUX
ejpam-5742	45	3	start	start	VERB
ejpam-5742	45	4	this	this	DET
ejpam-5742	45	5	section	section	NOUN
ejpam-5742	45	6	by	by	ADP
ejpam-5742	45	7	presenting	present	VERB
ejpam-5742	45	8	the	the	DET
ejpam-5742	45	9	following	follow	VERB
ejpam-5742	45	10	definition	definition	NOUN
ejpam-5742	45	11	.	.	PUNCT
ejpam-5742	46	1	definition	definition	NOUN
ejpam-5742	46	2	2	2	NUM
ejpam-5742	46	3	.	.	PUNCT
ejpam-5742	47	1	let	let	VERB
ejpam-5742	47	2	m	m	PRON
ejpam-5742	47	3	and	and	CCONJ
ejpam-5742	47	4	m′	m′	NOUN
ejpam-5742	47	5	be	be	AUX
ejpam-5742	47	6	maximal	maximal	ADJ
ejpam-5742	47	7	elements	element	NOUN
ejpam-5742	47	8	of	of	ADP
ejpam-5742	47	9	r	r	NOUN
ejpam-5742	47	10	and	and	CCONJ
ejpam-5742	47	11	r′	r′	NOUN
ejpam-5742	47	12	respectively	respectively	ADV
ejpam-5742	47	13	.	.	PUNCT
ejpam-5742	48	1	then	then	ADV
ejpam-5742	48	2	the	the	DET
ejpam-5742	48	3	mapping	mapping	NOUN
ejpam-5742	48	4	ξ	ξ	NOUN
ejpam-5742	48	5	:	:	PUNCT
ejpam-5742	48	6	r	r	NOUN
ejpam-5742	48	7	−→	−→	NOUN
ejpam-5742	48	8	r′	r′	NOUN
ejpam-5742	48	9	is	be	AUX
ejpam-5742	48	10	known	know	VERB
ejpam-5742	48	11	as	as	ADP
ejpam-5742	48	12	homomorphism	homomorphism	NOUN
ejpam-5742	48	13	if	if	SCONJ
ejpam-5742	48	14	,	,	PUNCT
ejpam-5742	48	15	for	for	ADP
ejpam-5742	48	16	all	all	DET
ejpam-5742	48	17	θ	θ	PROPN
ejpam-5742	48	18	,	,	PUNCT
ejpam-5742	48	19	ϑ	ϑ	X
ejpam-5742	48	20	∈	∈	PROPN
ejpam-5742	48	21	r	r	NOUN
ejpam-5742	48	22	,	,	PUNCT
ejpam-5742	48	23	it	it	PRON
ejpam-5742	48	24	satisfies	satisfy	VERB
ejpam-5742	48	25	the	the	DET
ejpam-5742	48	26	following	following	NOUN
ejpam-5742	48	27	:	:	PUNCT
ejpam-5742	48	28	(	(	PUNCT
ejpam-5742	48	29	i	i	NOUN
ejpam-5742	48	30	)	)	PUNCT
ejpam-5742	48	31	ξ(θ	ξ(θ	PROPN
ejpam-5742	48	32	∨	∨	NUM
ejpam-5742	48	33	ϑ	ϑ	X
ejpam-5742	48	34	)	)	PUNCT
ejpam-5742	48	35	=	=	SYM
ejpam-5742	48	36	ξ(θ	ξ(θ	ADJ
ejpam-5742	48	37	)	)	PUNCT
ejpam-5742	48	38	∨	∨	NUM
ejpam-5742	48	39	ξ(ϑ	ξ(ϑ	PROPN
ejpam-5742	48	40	)	)	PUNCT
ejpam-5742	48	41	(	(	PUNCT
ejpam-5742	48	42	ii	ii	NOUN
ejpam-5742	48	43	)	)	PUNCT
ejpam-5742	48	44	ξ(θ	ξ(θ	PROPN
ejpam-5742	48	45	∧	∧	PROPN
ejpam-5742	48	46	ϑ	ϑ	NOUN
ejpam-5742	48	47	)	)	PUNCT
ejpam-5742	48	48	=	=	SYM
ejpam-5742	48	49	ξ(θ	ξ(θ	X
ejpam-5742	48	50	)	)	PUNCT
ejpam-5742	48	51	∧	∧	PROPN
ejpam-5742	48	52	ξ(ϑ	ξ(ϑ	PROPN
ejpam-5742	48	53	)	)	PUNCT
ejpam-5742	48	54	(	(	PUNCT
ejpam-5742	48	55	iii	iii	NOUN
ejpam-5742	48	56	)	)	PUNCT
ejpam-5742	48	57	ξ(0	ξ(0	NOUN
ejpam-5742	48	58	)	)	PUNCT
ejpam-5742	48	59	=	=	SYM
ejpam-5742	49	1	0′	0′	PROPN
ejpam-5742	50	1	(	(	PUNCT
ejpam-5742	50	2	iv	iv	X
ejpam-5742	50	3	)	)	PUNCT
ejpam-5742	50	4	ξ(m	ξ(m	NOUN
ejpam-5742	50	5	)	)	PUNCT
ejpam-5742	50	6	=	=	SYM
ejpam-5742	50	7	m′.	m′.	PROPN
ejpam-5742	50	8	the	the	DET
ejpam-5742	50	9	co	co	NOUN
ejpam-5742	50	10	-	-	NOUN
ejpam-5742	50	11	kernel	kernel	NOUN
ejpam-5742	50	12	of	of	ADP
ejpam-5742	50	13	the	the	DET
ejpam-5742	50	14	homomorphism	homomorphism	NOUN
ejpam-5742	50	15	ξ	ξ	X
ejpam-5742	50	16	is	be	AUX
ejpam-5742	50	17	defined	define	VERB
ejpam-5742	50	18	by	by	ADP
ejpam-5742	50	19	co	co	NOUN
ejpam-5742	50	20	−	−	PROPN
ejpam-5742	50	21	ker	ker	NOUN
ejpam-5742	51	1	ξ	ξ	X
ejpam-5742	51	2	=	=	SYM
ejpam-5742	51	3	{	{	PUNCT
ejpam-5742	51	4	θ	θ	PROPN
ejpam-5742	51	5	∈	∈	PROPN
ejpam-5742	51	6	r	r	NOUN
ejpam-5742	51	7	|	|	ADV
ejpam-5742	51	8	ξ(θ	ξ(θ	ADJ
ejpam-5742	51	9	)	)	PUNCT
ejpam-5742	51	10	∈	∈	PROPN
ejpam-5742	51	11	mmax.elt(r′	mmax.elt(r′	NOUN
ejpam-5742	51	12	)	)	PUNCT
ejpam-5742	51	13	}	}	PUNCT
ejpam-5742	51	14	.	.	PUNCT
ejpam-5742	52	1	clearly	clearly	ADV
ejpam-5742	52	2	co−ker	co−ker	X
ejpam-5742	52	3	ξ	ξ	PRON
ejpam-5742	52	4	is	be	AUX
ejpam-5742	52	5	filter	filter	NOUN
ejpam-5742	52	6	in	in	ADP
ejpam-5742	52	7	r.	r.	PROPN
ejpam-5742	52	8	the	the	DET
ejpam-5742	52	9	set	set	NOUN
ejpam-5742	52	10	of	of	ADP
ejpam-5742	52	11	all	all	DET
ejpam-5742	52	12	homomorphism	homomorphism	NOUN
ejpam-5742	52	13	functions	function	NOUN
ejpam-5742	52	14	from	from	ADP
ejpam-5742	52	15	r	r	NOUN
ejpam-5742	52	16	to	to	PART
ejpam-5742	52	17	r′	r′	PROPN
ejpam-5742	52	18	represented	represent	VERB
ejpam-5742	52	19	as	as	ADP
ejpam-5742	52	20	homr(r′	homr(r′	PROPN
ejpam-5742	52	21	)	)	PUNCT
ejpam-5742	52	22	.	.	PUNCT
ejpam-5742	53	1	lemma	lemma	PROPN
ejpam-5742	53	2	1	1	NUM
ejpam-5742	53	3	.	.	PUNCT
ejpam-5742	54	1	for	for	ADP
ejpam-5742	54	2	any	any	DET
ejpam-5742	54	3	ξ	ξ	PROPN
ejpam-5742	54	4	∈	∈	PROPN
ejpam-5742	54	5	homr(r′	homr(r′	PROPN
ejpam-5742	54	6	)	)	PUNCT
ejpam-5742	54	7	,	,	PUNCT
ejpam-5742	54	8	we	we	PRON
ejpam-5742	54	9	have	have	VERB
ejpam-5742	54	10	:	:	PUNCT
ejpam-5742	54	11	(	(	PUNCT
ejpam-5742	54	12	i	i	NOUN
ejpam-5742	54	13	)	)	PUNCT
ejpam-5742	54	14	.	.	PUNCT
ejpam-5742	55	1	for	for	ADP
ejpam-5742	55	2	each	each	DET
ejpam-5742	55	3	ideal	ideal	ADJ
ejpam-5742	55	4	f	f	PROPN
ejpam-5742	55	5	of	of	ADP
ejpam-5742	55	6	r′	r′	PROPN
ejpam-5742	55	7	with	with	ADP
ejpam-5742	55	8	ξ−1(f	ξ−1(f	PROPN
ejpam-5742	55	9	)	)	PUNCT
ejpam-5742	55	10	̸=	̸=	PROPN
ejpam-5742	55	11	∅	∅	NOUN
ejpam-5742	55	12	,	,	PUNCT
ejpam-5742	55	13	ξ−1(f	ξ−1(f	PROPN
ejpam-5742	55	14	)	)	PUNCT
ejpam-5742	55	15	is	be	AUX
ejpam-5742	55	16	an	an	DET
ejpam-5742	55	17	ideal	ideal	NOUN
ejpam-5742	55	18	of	of	ADP
ejpam-5742	55	19	r.	r.	PROPN
ejpam-5742	55	20	(	(	PUNCT
ejpam-5742	55	21	ii	ii	PROPN
ejpam-5742	55	22	)	)	PUNCT
ejpam-5742	55	23	.	.	PUNCT
ejpam-5742	56	1	if	if	SCONJ
ejpam-5742	56	2	ξ	ξ	PROPN
ejpam-5742	56	3	is	be	AUX
ejpam-5742	56	4	onto	onto	ADP
ejpam-5742	56	5	then	then	ADV
ejpam-5742	56	6	,	,	PUNCT
ejpam-5742	56	7	for	for	ADP
ejpam-5742	56	8	each	each	DET
ejpam-5742	56	9	ideal	ideal	ADJ
ejpam-5742	56	10	g	g	NOUN
ejpam-5742	56	11	of	of	ADP
ejpam-5742	56	12	r	r	NOUN
ejpam-5742	56	13	,	,	PUNCT
ejpam-5742	56	14	ξ(g	ξ(g	PROPN
ejpam-5742	56	15	)	)	PUNCT
ejpam-5742	56	16	is	be	AUX
ejpam-5742	56	17	an	an	DET
ejpam-5742	56	18	ideal	ideal	NOUN
ejpam-5742	56	19	of	of	ADP
ejpam-5742	56	20	r′.	r′.	PROPN
ejpam-5742	56	21	n.	n.	PROPN
ejpam-5742	56	22	rafi	rafi	PROPN
ejpam-5742	56	23	,	,	PUNCT
ejpam-5742	56	24	t.	t.	PROPN
ejpam-5742	56	25	gaketem	gaketem	PROPN
ejpam-5742	56	26	,	,	PUNCT
ejpam-5742	56	27	r.	r.	PROPN
ejpam-5742	56	28	k.	k.	PROPN
ejpam-5742	56	29	bandaru	bandaru	PROPN
ejpam-5742	56	30	/	/	SYM
ejpam-5742	56	31	eur	eur	PROPN
ejpam-5742	56	32	.	.	PUNCT
ejpam-5742	57	1	j.	j.	PROPN
ejpam-5742	57	2	pure	pure	PROPN
ejpam-5742	57	3	appl	appl	PROPN
ejpam-5742	57	4	.	.	PROPN
ejpam-5742	57	5	math	math	PROPN
ejpam-5742	57	6	,	,	PUNCT
ejpam-5742	57	7	18	18	NUM
ejpam-5742	57	8	(	(	PUNCT
ejpam-5742	57	9	2	2	NUM
ejpam-5742	57	10	)	)	PUNCT
ejpam-5742	57	11	(	(	PUNCT
ejpam-5742	57	12	2025	2025	NUM
ejpam-5742	57	13	)	)	PUNCT
ejpam-5742	57	14	,	,	PUNCT
ejpam-5742	57	15	5742	5742	NUM
ejpam-5742	57	16	4	4	NUM
ejpam-5742	57	17	of	of	ADP
ejpam-5742	57	18	14	14	NUM
ejpam-5742	57	19	proof	proof	NOUN
ejpam-5742	57	20	.	.	PUNCT
ejpam-5742	58	1	(	(	PUNCT
ejpam-5742	58	2	i	i	NOUN
ejpam-5742	58	3	)	)	PUNCT
ejpam-5742	58	4	.	.	PUNCT
ejpam-5742	59	1	consider	consider	VERB
ejpam-5742	59	2	f	f	PROPN
ejpam-5742	59	3	is	be	AUX
ejpam-5742	59	4	an	an	DET
ejpam-5742	59	5	ideal	ideal	NOUN
ejpam-5742	59	6	of	of	ADP
ejpam-5742	59	7	r′	r′	PROPN
ejpam-5742	59	8	with	with	ADP
ejpam-5742	59	9	ξ−1(f	ξ−1(f	PROPN
ejpam-5742	59	10	)	)	PUNCT
ejpam-5742	60	1	̸=	̸=	PROPN
ejpam-5742	60	2	∅.	∅.	ADV
ejpam-5742	60	3	let	let	VERB
ejpam-5742	60	4	ρ	ρ	NOUN
ejpam-5742	60	5	,	,	PUNCT
ejpam-5742	60	6	σ	σ	PROPN
ejpam-5742	60	7	∈	∈	PROPN
ejpam-5742	60	8	ξ−1(f	ξ−1(f	PROPN
ejpam-5742	60	9	)	)	PUNCT
ejpam-5742	60	10	.	.	PUNCT
ejpam-5742	61	1	then	then	ADV
ejpam-5742	61	2	ξ(ρ	ξ(ρ	NOUN
ejpam-5742	61	3	)	)	PUNCT
ejpam-5742	61	4	,	,	PUNCT
ejpam-5742	61	5	ξ(σ	ξ(σ	PROPN
ejpam-5742	61	6	)	)	PUNCT
ejpam-5742	61	7	∈	∈	PROPN
ejpam-5742	61	8	f	f	PROPN
ejpam-5742	61	9	.	.	PUNCT
ejpam-5742	62	1	since	since	SCONJ
ejpam-5742	62	2	f	f	PROPN
ejpam-5742	62	3	is	be	AUX
ejpam-5742	62	4	an	an	DET
ejpam-5742	62	5	ideal	ideal	ADJ
ejpam-5742	62	6	ofr′	ofr′	NOUN
ejpam-5742	62	7	,	,	PUNCT
ejpam-5742	62	8	we	we	PRON
ejpam-5742	62	9	get	get	VERB
ejpam-5742	62	10	that	that	DET
ejpam-5742	62	11	ξ(ρ)∨ξ(σ	ξ(ρ)∨ξ(σ	PROPN
ejpam-5742	62	12	)	)	PUNCT
ejpam-5742	62	13	∈	∈	PROPN
ejpam-5742	62	14	f	f	PROPN
ejpam-5742	62	15	and	and	CCONJ
ejpam-5742	63	1	hence	hence	ADV
ejpam-5742	63	2	ξ(ρ∨σ	ξ(ρ∨σ	NUM
ejpam-5742	63	3	)	)	PUNCT
ejpam-5742	63	4	∈	∈	PROPN
ejpam-5742	63	5	f	f	PROPN
ejpam-5742	63	6	.	.	PUNCT
ejpam-5742	64	1	therefore	therefore	ADV
ejpam-5742	64	2	ρ	ρ	PROPN
ejpam-5742	64	3	∨	∨	PROPN
ejpam-5742	64	4	σ	σ	PROPN
ejpam-5742	64	5	∈	∈	PROPN
ejpam-5742	64	6	ξ−1(f	ξ−1(f	PROPN
ejpam-5742	64	7	)	)	PUNCT
ejpam-5742	64	8	.	.	PUNCT
ejpam-5742	65	1	let	let	VERB
ejpam-5742	65	2	ρ	ρ	PROPN
ejpam-5742	65	3	∈	∈	PROPN
ejpam-5742	65	4	ξ−1(f	ξ−1(f	PROPN
ejpam-5742	65	5	)	)	PUNCT
ejpam-5742	65	6	and	and	CCONJ
ejpam-5742	65	7	ω	ω	NUM
ejpam-5742	65	8	∈	∈	PROPN
ejpam-5742	65	9	r.	r.	PROPN
ejpam-5742	65	10	then	then	ADV
ejpam-5742	65	11	ξ(ρ	ξ(ρ	PROPN
ejpam-5742	65	12	)	)	PUNCT
ejpam-5742	65	13	∈	∈	PROPN
ejpam-5742	65	14	f	f	PROPN
ejpam-5742	65	15	.	.	PUNCT
ejpam-5742	66	1	now	now	ADV
ejpam-5742	66	2	,	,	PUNCT
ejpam-5742	66	3	ξ(ρ	ξ(ρ	PROPN
ejpam-5742	66	4	∧	∧	PROPN
ejpam-5742	66	5	ω	ω	PROPN
ejpam-5742	66	6	)	)	PUNCT
ejpam-5742	66	7	=	=	SYM
ejpam-5742	66	8	ξ(ρ	ξ(ρ	PROPN
ejpam-5742	66	9	)	)	PUNCT
ejpam-5742	66	10	∧	∧	PROPN
ejpam-5742	66	11	ξ(ω	ξ(ω	NOUN
ejpam-5742	66	12	)	)	PUNCT
ejpam-5742	66	13	∈	∈	PROPN
ejpam-5742	66	14	f	f	X
ejpam-5742	66	15	,	,	PUNCT
ejpam-5742	66	16	since	since	SCONJ
ejpam-5742	66	17	ξ(ω	ξ(ω	NOUN
ejpam-5742	66	18	)	)	PUNCT
ejpam-5742	67	1	∈	∈	PROPN
ejpam-5742	67	2	r′.	r′.	NOUN
ejpam-5742	67	3	therefore	therefore	ADV
ejpam-5742	67	4	ρ	ρ	PROPN
ejpam-5742	67	5	∧	∧	PROPN
ejpam-5742	67	6	ω	ω	PROPN
ejpam-5742	67	7	∈	∈	PROPN
ejpam-5742	67	8	ξ−1(f	ξ−1(f	PROPN
ejpam-5742	67	9	)	)	PUNCT
ejpam-5742	67	10	.	.	PUNCT
ejpam-5742	68	1	(	(	PUNCT
ejpam-5742	68	2	ii	ii	NOUN
ejpam-5742	68	3	)	)	PUNCT
ejpam-5742	68	4	.	.	PUNCT
ejpam-5742	69	1	let	let	VERB
ejpam-5742	69	2	ξ	ξ	X
ejpam-5742	69	3	be	be	AUX
ejpam-5742	69	4	an	an	PRON
ejpam-5742	69	5	onto	onto	ADP
ejpam-5742	69	6	function	function	NOUN
ejpam-5742	69	7	and	and	CCONJ
ejpam-5742	69	8	g	g	NOUN
ejpam-5742	69	9	be	be	AUX
ejpam-5742	69	10	any	any	DET
ejpam-5742	69	11	ideal	ideal	NOUN
ejpam-5742	69	12	of	of	ADP
ejpam-5742	69	13	r.	r.	PROPN
ejpam-5742	69	14	then	then	ADV
ejpam-5742	69	15	ξ(g	ξ(g	PROPN
ejpam-5742	69	16	)	)	PUNCT
ejpam-5742	69	17	is	be	AUX
ejpam-5742	69	18	a	a	DET
ejpam-5742	69	19	non	non	ADJ
ejpam-5742	69	20	-	-	ADJ
ejpam-5742	69	21	empty	empty	ADJ
ejpam-5742	69	22	set	set	NOUN
ejpam-5742	69	23	.	.	PUNCT
ejpam-5742	70	1	let	let	VERB
ejpam-5742	70	2	δ	δ	PROPN
ejpam-5742	70	3	,	,	PUNCT
ejpam-5742	70	4	τ	τ	PROPN
ejpam-5742	70	5	∈	∈	PROPN
ejpam-5742	70	6	ξ(g	ξ(g	PROPN
ejpam-5742	70	7	)	)	PUNCT
ejpam-5742	70	8	.	.	PUNCT
ejpam-5742	71	1	then	then	ADV
ejpam-5742	71	2	δ	δ	PROPN
ejpam-5742	71	3	=	=	SYM
ejpam-5742	71	4	ξ(ρ	ξ(ρ	PROPN
ejpam-5742	71	5	)	)	PUNCT
ejpam-5742	71	6	and	and	CCONJ
ejpam-5742	71	7	τ	τ	PROPN
ejpam-5742	71	8	=	=	PROPN
ejpam-5742	71	9	ξ(σ	ξ(σ	PROPN
ejpam-5742	71	10	)	)	PUNCT
ejpam-5742	71	11	,	,	PUNCT
ejpam-5742	71	12	for	for	ADP
ejpam-5742	71	13	some	some	DET
ejpam-5742	71	14	ρ	ρ	PROPN
ejpam-5742	71	15	,	,	PUNCT
ejpam-5742	71	16	σ	σ	PROPN
ejpam-5742	71	17	∈	∈	PROPN
ejpam-5742	71	18	g.	g.	NOUN
ejpam-5742	71	19	now	now	ADV
ejpam-5742	71	20	δ	δ	PROPN
ejpam-5742	71	21	∨	∨	PROPN
ejpam-5742	71	22	τ	τ	X
ejpam-5742	71	23	=	=	SYM
ejpam-5742	71	24	ξ(ρ)∨	ξ(ρ)∨	PROPN
ejpam-5742	71	25	ξ(σ	ξ(σ	PROPN
ejpam-5742	71	26	)	)	PUNCT
ejpam-5742	71	27	=	=	SYM
ejpam-5742	71	28	ξ(ρ	ξ(ρ	PROPN
ejpam-5742	71	29	∨	∨	NOUN
ejpam-5742	71	30	σ	σ	PROPN
ejpam-5742	71	31	)	)	PUNCT
ejpam-5742	71	32	∈	∈	PROPN
ejpam-5742	71	33	ξ(g	ξ(g	PROPN
ejpam-5742	71	34	)	)	PUNCT
ejpam-5742	71	35	,	,	PUNCT
ejpam-5742	71	36	since	since	SCONJ
ejpam-5742	71	37	ρ	ρ	PROPN
ejpam-5742	71	38	∨	∨	PROPN
ejpam-5742	71	39	σ	σ	PROPN
ejpam-5742	71	40	∈	∈	PROPN
ejpam-5742	71	41	g.	g.	NOUN
ejpam-5742	71	42	therefore	therefore	ADV
ejpam-5742	71	43	δ	δ	PROPN
ejpam-5742	71	44	∨	∨	PROPN
ejpam-5742	71	45	τ	τ	PROPN
ejpam-5742	71	46	∈	∈	PROPN
ejpam-5742	71	47	ξ(g	ξ(g	PROPN
ejpam-5742	71	48	)	)	PUNCT
ejpam-5742	71	49	.	.	PUNCT
ejpam-5742	72	1	let	let	VERB
ejpam-5742	72	2	δ	δ	PROPN
ejpam-5742	72	3	∈	∈	PROPN
ejpam-5742	72	4	ξ(g	ξ(g	PROPN
ejpam-5742	72	5	)	)	PUNCT
ejpam-5742	72	6	and	and	CCONJ
ejpam-5742	72	7	κ	κ	PROPN
ejpam-5742	72	8	∈	∈	PROPN
ejpam-5742	72	9	r′.	r′.	NOUN
ejpam-5742	72	10	then	then	ADV
ejpam-5742	72	11	δ	δ	PROPN
ejpam-5742	72	12	=	=	SYM
ejpam-5742	72	13	ξ(ρ	ξ(ρ	PROPN
ejpam-5742	72	14	)	)	PUNCT
ejpam-5742	72	15	,	,	PUNCT
ejpam-5742	72	16	for	for	ADP
ejpam-5742	72	17	some	some	DET
ejpam-5742	72	18	ρ	ρ	PROPN
ejpam-5742	72	19	∈	∈	PROPN
ejpam-5742	72	20	g.	g.	NOUN
ejpam-5742	72	21	since	since	SCONJ
ejpam-5742	72	22	ξ	ξ	PROPN
ejpam-5742	72	23	is	be	AUX
ejpam-5742	72	24	onto	onto	ADP
ejpam-5742	72	25	and	and	CCONJ
ejpam-5742	72	26	κ	κ	PROPN
ejpam-5742	72	27	∈	∈	PROPN
ejpam-5742	72	28	r′	r′	PROPN
ejpam-5742	72	29	,	,	PUNCT
ejpam-5742	72	30	there	there	PRON
ejpam-5742	72	31	is	be	VERB
ejpam-5742	72	32	η	η	PROPN
ejpam-5742	72	33	∈	∈	PROPN
ejpam-5742	72	34	r	r	NOUN
ejpam-5742	72	35	satisfies	satisfie	NOUN
ejpam-5742	72	36	ξ(η	ξ(η	NUM
ejpam-5742	72	37	)	)	PUNCT
ejpam-5742	73	1	=	=	SYM
ejpam-5742	73	2	κ	κ	X
ejpam-5742	73	3	.	.	PUNCT
ejpam-5742	73	4	now	now	ADV
ejpam-5742	73	5	δ	δ	PROPN
ejpam-5742	73	6	∧	∧	PROPN
ejpam-5742	73	7	κ	κ	PROPN
ejpam-5742	73	8	=	=	SYM
ejpam-5742	73	9	ξ(ρ	ξ(ρ	PROPN
ejpam-5742	73	10	)	)	PUNCT
ejpam-5742	73	11	∧	∧	NOUN
ejpam-5742	73	12	ξ(η	ξ(η	NOUN
ejpam-5742	73	13	)	)	PUNCT
ejpam-5742	73	14	=	=	SYM
ejpam-5742	73	15	ξ(ρ	ξ(ρ	PROPN
ejpam-5742	73	16	∧	∧	PROPN
ejpam-5742	73	17	η	η	PROPN
ejpam-5742	73	18	)	)	PUNCT
ejpam-5742	73	19	∈	∈	PROPN
ejpam-5742	73	20	ξ(g	ξ(g	PROPN
ejpam-5742	73	21	)	)	PUNCT
ejpam-5742	73	22	,	,	PUNCT
ejpam-5742	73	23	since	since	SCONJ
ejpam-5742	73	24	ρ	ρ	PROPN
ejpam-5742	73	25	∧	∧	PROPN
ejpam-5742	73	26	η	η	PROPN
ejpam-5742	73	27	∈	∈	PROPN
ejpam-5742	73	28	g.	g.	NOUN
ejpam-5742	73	29	therefore	therefore	ADV
ejpam-5742	73	30	δ	δ	PROPN
ejpam-5742	73	31	∧	∧	PROPN
ejpam-5742	73	32	κ	κ	PROPN
ejpam-5742	73	33	∈	∈	PROPN
ejpam-5742	73	34	ξ(g	ξ(g	PROPN
ejpam-5742	73	35	)	)	PUNCT
ejpam-5742	73	36	.	.	PUNCT
ejpam-5742	74	1	hence	hence	ADV
ejpam-5742	74	2	ξ(g	ξ(g	PROPN
ejpam-5742	74	3	)	)	PUNCT
ejpam-5742	74	4	is	be	AUX
ejpam-5742	74	5	an	an	DET
ejpam-5742	74	6	ideal	ideal	NOUN
ejpam-5742	74	7	of	of	ADP
ejpam-5742	74	8	r′.	r′.	NOUN
ejpam-5742	74	9	definition	definition	NOUN
ejpam-5742	74	10	3	3	NUM
ejpam-5742	74	11	(	(	PUNCT
ejpam-5742	74	12	[	[	X
ejpam-5742	74	13	9	9	NUM
ejpam-5742	74	14	,	,	PUNCT
ejpam-5742	74	15	10	10	NUM
ejpam-5742	74	16	]	]	NUM
ejpam-5742	74	17	)	)	PUNCT
ejpam-5742	74	18	.	.	PUNCT
ejpam-5742	75	1	for	for	ADP
ejpam-5742	75	2	every	every	DET
ejpam-5742	75	3	ideal	ideal	ADJ
ejpam-5742	75	4	f	f	PROPN
ejpam-5742	75	5	of	of	ADP
ejpam-5742	75	6	r	r	PROPN
ejpam-5742	75	7	,	,	PUNCT
ejpam-5742	75	8	consider	consider	VERB
ejpam-5742	75	9	the	the	DET
ejpam-5742	75	10	set	set	NOUN
ejpam-5742	75	11	m(f	m(f	PROPN
ejpam-5742	75	12	)	)	PUNCT
ejpam-5742	76	1	=	=	PRON
ejpam-5742	76	2	{	{	PUNCT
ejpam-5742	76	3	κ	κ	NOUN
ejpam-5742	76	4	∈	∈	PROPN
ejpam-5742	76	5	r|κ	r|κ	X
ejpam-5742	77	1	∨	∨	NUM
ejpam-5742	77	2	ρ	ρ	PROPN
ejpam-5742	77	3	∈	∈	PROPN
ejpam-5742	77	4	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	77	5	)	)	PUNCT
ejpam-5742	77	6	,	,	PUNCT
ejpam-5742	77	7	for	for	ADP
ejpam-5742	77	8	some	some	DET
ejpam-5742	77	9	ρ	ρ	NOUN
ejpam-5742	77	10	∈	∈	PROPN
ejpam-5742	77	11	f	f	X
ejpam-5742	77	12	}	}	PUNCT
ejpam-5742	77	13	.	.	PUNCT
ejpam-5742	78	1	lemma	lemma	PROPN
ejpam-5742	78	2	2	2	NUM
ejpam-5742	78	3	.	.	X
ejpam-5742	79	1	for	for	ADP
ejpam-5742	79	2	any	any	DET
ejpam-5742	79	3	ξ	ξ	PROPN
ejpam-5742	79	4	∈	∈	PROPN
ejpam-5742	79	5	homr(r′	homr(r′	PROPN
ejpam-5742	79	6	)	)	PUNCT
ejpam-5742	79	7	and	and	CCONJ
ejpam-5742	79	8	any	any	DET
ejpam-5742	79	9	ideal	ideal	ADJ
ejpam-5742	79	10	f	f	NOUN
ejpam-5742	79	11	of	of	ADP
ejpam-5742	79	12	r	r	PROPN
ejpam-5742	79	13	,	,	PUNCT
ejpam-5742	79	14	we	we	PRON
ejpam-5742	79	15	have	have	VERB
ejpam-5742	79	16	ξ[m(f	ξ[m(f	NOUN
ejpam-5742	79	17	)	)	PUNCT
ejpam-5742	79	18	]	]	PUNCT
ejpam-5742	80	1	⊆	⊆	NUM
ejpam-5742	80	2	m[ξ(f	m[ξ(f	NOUN
ejpam-5742	80	3	)	)	PUNCT
ejpam-5742	80	4	]	]	PUNCT
ejpam-5742	80	5	.	.	PUNCT
ejpam-5742	81	1	proof	proof	NOUN
ejpam-5742	81	2	.	.	PUNCT
ejpam-5742	82	1	let	let	VERB
ejpam-5742	82	2	ξ	ξ	X
ejpam-5742	82	3	∈	∈	PROPN
ejpam-5742	82	4	homr(r′	homr(r′	PROPN
ejpam-5742	82	5	)	)	PUNCT
ejpam-5742	82	6	and	and	CCONJ
ejpam-5742	82	7	f	f	PROPN
ejpam-5742	82	8	be	be	AUX
ejpam-5742	82	9	any	any	DET
ejpam-5742	82	10	ideal	ideal	NOUN
ejpam-5742	82	11	of	of	ADP
ejpam-5742	82	12	r.	r.	PROPN
ejpam-5742	82	13	let	let	VERB
ejpam-5742	82	14	κ	κ	PROPN
ejpam-5742	82	15	∈	∈	PROPN
ejpam-5742	82	16	ξ[m(f	ξ[m(f	PROPN
ejpam-5742	82	17	)	)	PUNCT
ejpam-5742	82	18	]	]	PUNCT
ejpam-5742	82	19	.	.	PUNCT
ejpam-5742	83	1	then	then	ADV
ejpam-5742	83	2	there	there	PRON
ejpam-5742	83	3	is	be	VERB
ejpam-5742	83	4	ρ	ρ	PROPN
ejpam-5742	83	5	∈	∈	PROPN
ejpam-5742	83	6	m(f	m(f	PROPN
ejpam-5742	83	7	)	)	PUNCT
ejpam-5742	83	8	satisfying	satisfy	VERB
ejpam-5742	83	9	κ	κ	X
ejpam-5742	83	10	=	=	SYM
ejpam-5742	83	11	ξ(ρ	ξ(ρ	PROPN
ejpam-5742	83	12	)	)	PUNCT
ejpam-5742	83	13	.	.	PUNCT
ejpam-5742	84	1	as	as	ADP
ejpam-5742	84	2	ρ	ρ	PROPN
ejpam-5742	84	3	∈	∈	PROPN
ejpam-5742	84	4	m(f	m(f	PROPN
ejpam-5742	84	5	)	)	PUNCT
ejpam-5742	84	6	,	,	PUNCT
ejpam-5742	84	7	it	it	PRON
ejpam-5742	84	8	is	be	AUX
ejpam-5742	84	9	clear	clear	ADJ
ejpam-5742	84	10	that	that	SCONJ
ejpam-5742	84	11	ρ	ρ	PROPN
ejpam-5742	84	12	∨	∨	PROPN
ejpam-5742	84	13	σ	σ	PROPN
ejpam-5742	84	14	∈	∈	PROPN
ejpam-5742	84	15	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	84	16	)	)	PUNCT
ejpam-5742	84	17	,	,	PUNCT
ejpam-5742	84	18	for	for	ADP
ejpam-5742	84	19	some	some	DET
ejpam-5742	84	20	σ	σ	NOUN
ejpam-5742	84	21	∈	∈	PROPN
ejpam-5742	84	22	f	f	X
ejpam-5742	84	23	.	.	PUNCT
ejpam-5742	85	1	that	that	PRON
ejpam-5742	85	2	implies	imply	VERB
ejpam-5742	85	3	ξ(ρ	ξ(ρ	PROPN
ejpam-5742	85	4	∨	∨	PROPN
ejpam-5742	85	5	σ	σ	PROPN
ejpam-5742	85	6	)	)	PUNCT
ejpam-5742	85	7	∈	∈	PROPN
ejpam-5742	85	8	mmax.elt(r′	mmax.elt(r′	NOUN
ejpam-5742	85	9	)	)	PUNCT
ejpam-5742	85	10	.	.	PUNCT
ejpam-5742	86	1	let	let	VERB
ejpam-5742	86	2	η	η	PROPN
ejpam-5742	86	3	∈	∈	PROPN
ejpam-5742	87	1	r′.	r′.	NOUN
ejpam-5742	87	2	now	now	ADV
ejpam-5742	87	3	[	[	X
ejpam-5742	87	4	κ	κ	PROPN
ejpam-5742	87	5	∨	∨	PROPN
ejpam-5742	87	6	ξ(σ	ξ(σ	PROPN
ejpam-5742	87	7	)	)	PUNCT
ejpam-5742	87	8	]	]	PUNCT
ejpam-5742	88	1	∧	∧	PROPN
ejpam-5742	88	2	η	η	X
ejpam-5742	88	3	=	=	PROPN
ejpam-5742	88	4	[	[	X
ejpam-5742	88	5	ξ(ρ	ξ(ρ	NOUN
ejpam-5742	88	6	)	)	PUNCT
ejpam-5742	88	7	∨	∨	NUM
ejpam-5742	88	8	ξ(σ	ξ(σ	PROPN
ejpam-5742	88	9	)	)	PUNCT
ejpam-5742	88	10	]	]	PUNCT
ejpam-5742	89	1	∧	∧	PROPN
ejpam-5742	89	2	η	η	PROPN
ejpam-5742	89	3	=	=	SYM
ejpam-5742	89	4	ξ(ρ	ξ(ρ	PROPN
ejpam-5742	89	5	∨	∨	PROPN
ejpam-5742	89	6	σ	σ	PROPN
ejpam-5742	89	7	)	)	PUNCT
ejpam-5742	89	8	∧	∧	PROPN
ejpam-5742	89	9	η	η	PROPN
ejpam-5742	89	10	=	=	PROPN
ejpam-5742	89	11	η	η	PROPN
ejpam-5742	89	12	.	.	PROPN
ejpam-5742	89	13	therefore	therefore	ADV
ejpam-5742	89	14	κ	κ	PROPN
ejpam-5742	89	15	∨	∨	PROPN
ejpam-5742	89	16	ξ(σ	ξ(σ	PROPN
ejpam-5742	89	17	)	)	PUNCT
ejpam-5742	89	18	∈	∈	PROPN
ejpam-5742	89	19	mmax.elt(r′	mmax.elt(r′	NOUN
ejpam-5742	89	20	)	)	PUNCT
ejpam-5742	89	21	and	and	CCONJ
ejpam-5742	89	22	hence	hence	ADV
ejpam-5742	89	23	κ	κ	X
ejpam-5742	89	24	∈	∈	PROPN
ejpam-5742	89	25	m[ξ(f	m[ξ(f	PROPN
ejpam-5742	89	26	)	)	PUNCT
ejpam-5742	89	27	]	]	PUNCT
ejpam-5742	89	28	.	.	PUNCT
ejpam-5742	90	1	thus	thus	ADV
ejpam-5742	90	2	ξ[m(f	ξ[m(f	NOUN
ejpam-5742	90	3	)	)	PUNCT
ejpam-5742	90	4	]	]	PUNCT
ejpam-5742	90	5	⊆	⊆	NUM
ejpam-5742	90	6	m[ξ(f	m[ξ(f	NOUN
ejpam-5742	90	7	)	)	PUNCT
ejpam-5742	90	8	]	]	PUNCT
ejpam-5742	90	9	.	.	PUNCT
ejpam-5742	91	1	in	in	ADP
ejpam-5742	91	2	general	general	ADJ
ejpam-5742	91	3	,	,	PUNCT
ejpam-5742	91	4	m[ξ(f	m[ξ(f	PROPN
ejpam-5742	91	5	)	)	PUNCT
ejpam-5742	91	6	]	]	PUNCT
ejpam-5742	91	7	⊈	⊈	PROPN
ejpam-5742	91	8	ξ[m(f	ξ[m(f	NOUN
ejpam-5742	91	9	)	)	PUNCT
ejpam-5742	91	10	]	]	PUNCT
ejpam-5742	91	11	is	be	AUX
ejpam-5742	91	12	not	not	PART
ejpam-5742	91	13	true	true	ADJ
ejpam-5742	91	14	for	for	SCONJ
ejpam-5742	91	15	any	any	DET
ejpam-5742	91	16	ideal	ideal	ADJ
ejpam-5742	91	17	f	f	PROPN
ejpam-5742	91	18	of	of	ADP
ejpam-5742	91	19	r.	r.	PROPN
ejpam-5742	91	20	consider	consider	VERB
ejpam-5742	91	21	the	the	DET
ejpam-5742	91	22	subsequent	subsequent	ADJ
ejpam-5742	91	23	example	example	NOUN
ejpam-5742	91	24	.	.	PUNCT
ejpam-5742	92	1	example	example	NOUN
ejpam-5742	93	1	1	1	NUM
ejpam-5742	93	2	.	.	X
ejpam-5742	93	3	consider	consider	VERB
ejpam-5742	93	4	r	r	NOUN
ejpam-5742	93	5	=	=	SYM
ejpam-5742	93	6	{	{	PUNCT
ejpam-5742	93	7	0	0	NUM
ejpam-5742	93	8	,	,	PUNCT
ejpam-5742	93	9	θ	θ	PROPN
ejpam-5742	93	10	,	,	PUNCT
ejpam-5742	93	11	ϑ	ϑ	X
ejpam-5742	93	12	,	,	PUNCT
ejpam-5742	93	13	σ	σ	PROPN
ejpam-5742	93	14	}	}	PUNCT
ejpam-5742	93	15	.	.	PUNCT
ejpam-5742	94	1	two	two	NUM
ejpam-5742	94	2	binary	binary	ADJ
ejpam-5742	94	3	operations	operation	NOUN
ejpam-5742	94	4	∨	∨	NUM
ejpam-5742	94	5	,	,	PUNCT
ejpam-5742	94	6	∧	∧	PROPN
ejpam-5742	94	7	are	be	AUX
ejpam-5742	94	8	defined	define	VERB
ejpam-5742	94	9	on	on	ADP
ejpam-5742	94	10	r	r	NOUN
ejpam-5742	94	11	as	as	SCONJ
ejpam-5742	94	12	follows	follow	VERB
ejpam-5742	94	13	:	:	PUNCT
ejpam-5742	94	14	∨	∨	NUM
ejpam-5742	94	15	0	0	NUM
ejpam-5742	94	16	θ	θ	PROPN
ejpam-5742	94	17	ϑ	ϑ	PROPN
ejpam-5742	94	18	σ	σ	NOUN
ejpam-5742	94	19	0	0	NUM
ejpam-5742	94	20	0	0	NUM
ejpam-5742	94	21	θ	θ	NOUN
ejpam-5742	94	22	ϑ	ϑ	PROPN
ejpam-5742	94	23	σ	σ	X
ejpam-5742	94	24	θ	θ	NOUN
ejpam-5742	94	25	θ	θ	NOUN
ejpam-5742	94	26	θ	θ	X
ejpam-5742	94	27	θ	θ	X
ejpam-5742	94	28	θ	θ	X
ejpam-5742	94	29	ϑ	ϑ	X
ejpam-5742	94	30	ϑ	ϑ	X
ejpam-5742	94	31	ϑ	ϑ	X
ejpam-5742	94	32	ϑ	ϑ	X
ejpam-5742	94	33	ϑ	ϑ	X
ejpam-5742	94	34	σ	σ	PROPN
ejpam-5742	94	35	σ	σ	PROPN
ejpam-5742	94	36	θ	θ	PROPN
ejpam-5742	94	37	ϑ	ϑ	PROPN
ejpam-5742	94	38	σ	σ	X
ejpam-5742	94	39	∧	∧	PROPN
ejpam-5742	94	40	0	0	NUM
ejpam-5742	94	41	θ	θ	PROPN
ejpam-5742	94	42	ϑ	ϑ	PROPN
ejpam-5742	94	43	σ	σ	NOUN
ejpam-5742	94	44	0	0	NUM
ejpam-5742	94	45	0	0	NUM
ejpam-5742	94	46	0	0	NUM
ejpam-5742	94	47	0	0	NUM
ejpam-5742	94	48	0	0	NUM
ejpam-5742	94	49	θ	θ	NOUN
ejpam-5742	94	50	0	0	PUNCT
ejpam-5742	94	51	θ	θ	X
ejpam-5742	94	52	ϑ	ϑ	PROPN
ejpam-5742	94	53	σ	σ	X
ejpam-5742	94	54	ϑ	ϑ	X
ejpam-5742	94	55	0	0	NUM
ejpam-5742	94	56	θ	θ	PROPN
ejpam-5742	94	57	ϑ	ϑ	PROPN
ejpam-5742	94	58	σ	σ	X
ejpam-5742	94	59	σ	σ	PROPN
ejpam-5742	94	60	0	0	PUNCT
ejpam-5742	94	61	σ	σ	PROPN
ejpam-5742	94	62	σ	σ	PROPN
ejpam-5742	94	63	σ	σ	PROPN
ejpam-5742	94	64	it	it	PRON
ejpam-5742	94	65	is	be	AUX
ejpam-5742	94	66	observed	observe	VERB
ejpam-5742	94	67	easily	easily	ADV
ejpam-5742	94	68	that	that	SCONJ
ejpam-5742	94	69	(	(	PUNCT
ejpam-5742	94	70	r,∨,∧	r,∨,∧	NUM
ejpam-5742	94	71	,	,	PUNCT
ejpam-5742	94	72	0	0	NUM
ejpam-5742	94	73	)	)	PUNCT
ejpam-5742	94	74	is	be	AUX
ejpam-5742	94	75	an	an	DET
ejpam-5742	94	76	adl	adl	NOUN
ejpam-5742	94	77	with	with	ADP
ejpam-5742	94	78	0	0	NUM
ejpam-5742	94	79	.	.	PUNCT
ejpam-5742	95	1	define	define	VERB
ejpam-5742	95	2	ξ	ξ	NOUN
ejpam-5742	95	3	:	:	PUNCT
ejpam-5742	96	1	r	r	NOUN
ejpam-5742	96	2	−→	−→	NOUN
ejpam-5742	96	3	r	r	NOUN
ejpam-5742	96	4	by	by	ADP
ejpam-5742	96	5	ξ(κ	ξ(κ	NUM
ejpam-5742	96	6	)	)	PUNCT
ejpam-5742	97	1	=	=	PUNCT
ejpam-5742	98	1			NOUN
ejpam-5742	98	2	0	0	PUNCT
ejpam-5742	99	1	if	if	SCONJ
ejpam-5742	99	2	κ	κ	X
ejpam-5742	99	3	=	=	SYM
ejpam-5742	99	4	0	0	PUNCT
ejpam-5742	99	5	σ	σ	NOUN
ejpam-5742	99	6	if	if	SCONJ
ejpam-5742	99	7	κ	κ	X
ejpam-5742	99	8	=	=	SYM
ejpam-5742	99	9	σ	σ	NOUN
ejpam-5742	99	10	θ	θ	PROPN
ejpam-5742	99	11	otherwise	otherwise	ADV
ejpam-5742	99	12	.	.	PUNCT
ejpam-5742	100	1	take	take	VERB
ejpam-5742	100	2	an	an	DET
ejpam-5742	100	3	ideal	ideal	NOUN
ejpam-5742	100	4	f	f	NOUN
ejpam-5742	100	5	=	=	PUNCT
ejpam-5742	100	6	{	{	PUNCT
ejpam-5742	100	7	0	0	NUM
ejpam-5742	100	8	,	,	PUNCT
ejpam-5742	100	9	σ	σ	NOUN
ejpam-5742	100	10	}	}	PUNCT
ejpam-5742	100	11	of	of	ADP
ejpam-5742	100	12	an	an	DET
ejpam-5742	100	13	adl	adl	PROPN
ejpam-5742	100	14	r.	r.	PROPN
ejpam-5742	100	15	then	then	ADV
ejpam-5742	100	16	m(f	m(f	PROPN
ejpam-5742	100	17	)	)	PUNCT
ejpam-5742	100	18	=	=	SYM
ejpam-5742	100	19	{	{	PUNCT
ejpam-5742	100	20	θ	θ	PROPN
ejpam-5742	100	21	,	,	PUNCT
ejpam-5742	100	22	ϑ	ϑ	NOUN
ejpam-5742	100	23	}	}	PUNCT
ejpam-5742	100	24	.	.	PUNCT
ejpam-5742	101	1	that	that	PRON
ejpam-5742	101	2	implies	imply	VERB
ejpam-5742	101	3	ξ[m(f	ξ[m(f	NOUN
ejpam-5742	101	4	)	)	PUNCT
ejpam-5742	101	5	]	]	PUNCT
ejpam-5742	102	1	=	=	PUNCT
ejpam-5742	102	2	{	{	PUNCT
ejpam-5742	102	3	θ	θ	NOUN
ejpam-5742	102	4	}	}	PUNCT
ejpam-5742	102	5	.	.	PUNCT
ejpam-5742	103	1	clearly	clearly	ADV
ejpam-5742	103	2	we	we	PRON
ejpam-5742	103	3	have	have	VERB
ejpam-5742	103	4	that	that	PRON
ejpam-5742	103	5	ξ(f	ξ(f	PROPN
ejpam-5742	103	6	)	)	PUNCT
ejpam-5742	103	7	=	=	PUNCT
ejpam-5742	104	1	{	{	PUNCT
ejpam-5742	104	2	0	0	NUM
ejpam-5742	104	3	,	,	PUNCT
ejpam-5742	104	4	σ	σ	PROPN
ejpam-5742	104	5	}	}	PUNCT
ejpam-5742	104	6	.	.	PUNCT
ejpam-5742	105	1	that	that	PRON
ejpam-5742	105	2	implies	imply	VERB
ejpam-5742	105	3	m[ξ(f	m[ξ(f	NOUN
ejpam-5742	105	4	)	)	PUNCT
ejpam-5742	105	5	]	]	PUNCT
ejpam-5742	106	1	=	=	PUNCT
ejpam-5742	106	2	{	{	PUNCT
ejpam-5742	106	3	θ	θ	PROPN
ejpam-5742	106	4	,	,	PUNCT
ejpam-5742	106	5	ϑ	ϑ	NOUN
ejpam-5742	106	6	}	}	PUNCT
ejpam-5742	106	7	.	.	PUNCT
ejpam-5742	107	1	therefore	therefore	ADV
ejpam-5742	107	2	ξ[m(f	ξ[m(f	NOUN
ejpam-5742	107	3	)	)	PUNCT
ejpam-5742	107	4	]	]	PUNCT
ejpam-5742	108	1	̸=	̸=	PROPN
ejpam-5742	108	2	m[ξ(f	m[ξ(f	X
ejpam-5742	108	3	)	)	PUNCT
ejpam-5742	108	4	]	]	PUNCT
ejpam-5742	108	5	.	.	PUNCT
ejpam-5742	109	1	thus	thus	ADV
ejpam-5742	109	2	ξ	ξ	X
ejpam-5742	109	3	is	be	AUX
ejpam-5742	109	4	not	not	PART
ejpam-5742	109	5	an	an	DET
ejpam-5742	109	6	m−homomorphism	m−homomorphism	NOUN
ejpam-5742	109	7	.	.	PUNCT
ejpam-5742	110	1	now	now	ADV
ejpam-5742	110	2	we	we	PRON
ejpam-5742	110	3	present	present	VERB
ejpam-5742	110	4	the	the	DET
ejpam-5742	110	5	idea	idea	NOUN
ejpam-5742	110	6	of	of	ADP
ejpam-5742	110	7	an	an	DET
ejpam-5742	110	8	m−homomorphism	m−homomorphism	NOUN
ejpam-5742	110	9	.	.	PUNCT
ejpam-5742	111	1	n.	n.	PROPN
ejpam-5742	111	2	rafi	rafi	PROPN
ejpam-5742	111	3	,	,	PUNCT
ejpam-5742	111	4	t.	t.	PROPN
ejpam-5742	111	5	gaketem	gaketem	PROPN
ejpam-5742	111	6	,	,	PUNCT
ejpam-5742	111	7	r.	r.	PROPN
ejpam-5742	111	8	k.	k.	PROPN
ejpam-5742	111	9	bandaru	bandaru	PROPN
ejpam-5742	111	10	/	/	SYM
ejpam-5742	111	11	eur	eur	PROPN
ejpam-5742	111	12	.	.	PUNCT
ejpam-5742	112	1	j.	j.	PROPN
ejpam-5742	112	2	pure	pure	PROPN
ejpam-5742	112	3	appl	appl	PROPN
ejpam-5742	112	4	.	.	PROPN
ejpam-5742	112	5	math	math	PROPN
ejpam-5742	112	6	,	,	PUNCT
ejpam-5742	112	7	18	18	NUM
ejpam-5742	112	8	(	(	PUNCT
ejpam-5742	112	9	2	2	NUM
ejpam-5742	112	10	)	)	PUNCT
ejpam-5742	112	11	(	(	PUNCT
ejpam-5742	112	12	2025	2025	NUM
ejpam-5742	112	13	)	)	PUNCT
ejpam-5742	112	14	,	,	PUNCT
ejpam-5742	112	15	5742	5742	NUM
ejpam-5742	112	16	5	5	NUM
ejpam-5742	112	17	of	of	ADP
ejpam-5742	112	18	14	14	NUM
ejpam-5742	112	19	definition	definition	NOUN
ejpam-5742	112	20	4	4	NUM
ejpam-5742	112	21	.	.	PUNCT
ejpam-5742	113	1	a	a	DET
ejpam-5742	113	2	homomorphism	homomorphism	NOUN
ejpam-5742	113	3	ξ	ξ	PROPN
ejpam-5742	113	4	of	of	ADP
ejpam-5742	113	5	homr(r′	homr(r′	PROPN
ejpam-5742	113	6	)	)	PUNCT
ejpam-5742	113	7	is	be	AUX
ejpam-5742	113	8	said	say	VERB
ejpam-5742	113	9	to	to	PART
ejpam-5742	113	10	be	be	AUX
ejpam-5742	113	11	an	an	DET
ejpam-5742	113	12	m−homomorphism	m−homomorphism	NOUN
ejpam-5742	113	13	if	if	SCONJ
ejpam-5742	113	14	ξ[m(f	ξ[m(f	NOUN
ejpam-5742	113	15	)	)	PUNCT
ejpam-5742	113	16	]	]	PUNCT
ejpam-5742	114	1	=	=	SYM
ejpam-5742	114	2	m[ξ(f	m[ξ(f	X
ejpam-5742	114	3	)	)	PUNCT
ejpam-5742	114	4	]	]	PUNCT
ejpam-5742	114	5	.	.	PUNCT
ejpam-5742	115	1	example	example	NOUN
ejpam-5742	115	2	2	2	NUM
ejpam-5742	115	3	.	.	X
ejpam-5742	116	1	consider	consider	VERB
ejpam-5742	116	2	r	r	NOUN
ejpam-5742	116	3	=	=	SYM
ejpam-5742	116	4	{	{	PUNCT
ejpam-5742	116	5	0	0	NUM
ejpam-5742	116	6	,	,	PUNCT
ejpam-5742	116	7	θ	θ	PROPN
ejpam-5742	116	8	,	,	PUNCT
ejpam-5742	116	9	ϑ	ϑ	X
ejpam-5742	116	10	,	,	PUNCT
ejpam-5742	116	11	σ	σ	PROPN
ejpam-5742	116	12	}	}	PUNCT
ejpam-5742	116	13	.	.	PUNCT
ejpam-5742	117	1	two	two	NUM
ejpam-5742	117	2	binary	binary	ADJ
ejpam-5742	117	3	operations	operation	NOUN
ejpam-5742	117	4	∨	∨	NUM
ejpam-5742	117	5	,	,	PUNCT
ejpam-5742	117	6	∧	∧	PROPN
ejpam-5742	117	7	are	be	AUX
ejpam-5742	117	8	defined	define	VERB
ejpam-5742	117	9	on	on	ADP
ejpam-5742	117	10	r	r	NOUN
ejpam-5742	117	11	as	as	SCONJ
ejpam-5742	117	12	follows	follow	VERB
ejpam-5742	117	13	:	:	PUNCT
ejpam-5742	117	14	∨	∨	NUM
ejpam-5742	117	15	0	0	NUM
ejpam-5742	117	16	θ	θ	PROPN
ejpam-5742	117	17	ϑ	ϑ	PROPN
ejpam-5742	117	18	σ	σ	NOUN
ejpam-5742	117	19	0	0	NUM
ejpam-5742	117	20	0	0	NUM
ejpam-5742	117	21	θ	θ	NOUN
ejpam-5742	117	22	ϑ	ϑ	PROPN
ejpam-5742	117	23	σ	σ	X
ejpam-5742	117	24	θ	θ	NOUN
ejpam-5742	117	25	θ	θ	X
ejpam-5742	117	26	θ	θ	X
ejpam-5742	117	27	ϑ	ϑ	X
ejpam-5742	117	28	ϑ	ϑ	X
ejpam-5742	117	29	ϑ	ϑ	X
ejpam-5742	117	30	ϑ	ϑ	X
ejpam-5742	117	31	ϑ	ϑ	X
ejpam-5742	117	32	ϑ	ϑ	X
ejpam-5742	117	33	ϑ	ϑ	X
ejpam-5742	117	34	σ	σ	PROPN
ejpam-5742	117	35	σ	σ	PROPN
ejpam-5742	117	36	ϑ	ϑ	X
ejpam-5742	117	37	ϑ	ϑ	PROPN
ejpam-5742	117	38	σ	σ	X
ejpam-5742	117	39	∧	∧	PROPN
ejpam-5742	117	40	0	0	NUM
ejpam-5742	117	41	θ	θ	PROPN
ejpam-5742	117	42	ϑ	ϑ	PROPN
ejpam-5742	117	43	σ	σ	NOUN
ejpam-5742	117	44	0	0	NUM
ejpam-5742	117	45	0	0	NUM
ejpam-5742	117	46	0	0	NUM
ejpam-5742	117	47	0	0	NUM
ejpam-5742	117	48	0	0	NUM
ejpam-5742	117	49	θ	θ	NOUN
ejpam-5742	117	50	0	0	NUM
ejpam-5742	117	51	θ	θ	SYM
ejpam-5742	117	52	θ	θ	NOUN
ejpam-5742	117	53	0	0	PUNCT
ejpam-5742	118	1	ϑ	ϑ	NOUN
ejpam-5742	118	2	0	0	NUM
ejpam-5742	118	3	θ	θ	PROPN
ejpam-5742	118	4	ϑ	ϑ	PROPN
ejpam-5742	118	5	σ	σ	X
ejpam-5742	118	6	σ	σ	PROPN
ejpam-5742	118	7	0	0	NUM
ejpam-5742	118	8	0	0	NUM
ejpam-5742	119	1	σ	σ	NOUN
ejpam-5742	119	2	σ	σ	NOUN
ejpam-5742	119	3	it	it	PRON
ejpam-5742	119	4	is	be	AUX
ejpam-5742	119	5	observed	observe	VERB
ejpam-5742	119	6	easily	easily	ADV
ejpam-5742	119	7	that	that	SCONJ
ejpam-5742	119	8	(	(	PUNCT
ejpam-5742	119	9	r,∨,∧	r,∨,∧	NUM
ejpam-5742	119	10	,	,	PUNCT
ejpam-5742	119	11	0	0	NUM
ejpam-5742	119	12	)	)	PUNCT
ejpam-5742	119	13	is	be	AUX
ejpam-5742	119	14	an	an	DET
ejpam-5742	119	15	adl	adl	NOUN
ejpam-5742	119	16	with	with	ADP
ejpam-5742	119	17	0	0	NUM
ejpam-5742	119	18	.	.	PUNCT
ejpam-5742	120	1	let	let	VERB
ejpam-5742	120	2	ξ	ξ	X
ejpam-5742	120	3	be	be	AUX
ejpam-5742	120	4	an	an	DET
ejpam-5742	120	5	identity	identity	NOUN
ejpam-5742	120	6	mapping	mapping	NOUN
ejpam-5742	120	7	on	on	ADP
ejpam-5742	120	8	r.	r.	PROPN
ejpam-5742	120	9	then	then	ADV
ejpam-5742	120	10	,	,	PUNCT
ejpam-5742	120	11	ξ	ξ	PROPN
ejpam-5742	120	12	is	be	AUX
ejpam-5742	120	13	homomorphism	homomorphism	NOUN
ejpam-5742	120	14	on	on	ADP
ejpam-5742	120	15	r.	r.	PROPN
ejpam-5742	120	16	take	take	VERB
ejpam-5742	120	17	an	an	DET
ejpam-5742	120	18	ideal	ideal	NOUN
ejpam-5742	120	19	f	f	NOUN
ejpam-5742	120	20	=	=	PUNCT
ejpam-5742	120	21	{	{	PUNCT
ejpam-5742	120	22	0	0	NUM
ejpam-5742	120	23	,	,	PUNCT
ejpam-5742	120	24	θ	θ	NOUN
ejpam-5742	120	25	}	}	PUNCT
ejpam-5742	120	26	of	of	ADP
ejpam-5742	120	27	r.	r.	PROPN
ejpam-5742	120	28	now	now	ADV
ejpam-5742	120	29	m(f	m(f	PROPN
ejpam-5742	120	30	)	)	PUNCT
ejpam-5742	121	1	=	=	NOUN
ejpam-5742	121	2	⋃	⋃	NOUN
ejpam-5742	121	3	µ∈f	µ∈f	NOUN
ejpam-5742	121	4	(	(	PUNCT
ejpam-5742	121	5	µ)+	µ)+	X
ejpam-5742	121	6	=	=	SYM
ejpam-5742	121	7	{	{	PUNCT
ejpam-5742	121	8	ϑ	ϑ	X
ejpam-5742	121	9	,	,	PUNCT
ejpam-5742	121	10	σ	σ	PROPN
ejpam-5742	121	11	}	}	PUNCT
ejpam-5742	121	12	.	.	PUNCT
ejpam-5742	122	1	therefore	therefore	ADV
ejpam-5742	122	2	ξ[m(f	ξ[m(f	NOUN
ejpam-5742	122	3	)	)	PUNCT
ejpam-5742	122	4	]	]	PUNCT
ejpam-5742	123	1	=	=	PUNCT
ejpam-5742	123	2	{	{	PUNCT
ejpam-5742	123	3	ϑ	ϑ	X
ejpam-5742	123	4	,	,	PUNCT
ejpam-5742	123	5	σ	σ	NOUN
ejpam-5742	123	6	}	}	PUNCT
ejpam-5742	123	7	.	.	PUNCT
ejpam-5742	124	1	obviously	obviously	ADV
ejpam-5742	124	2	,	,	PUNCT
ejpam-5742	124	3	we	we	PRON
ejpam-5742	124	4	get	get	VERB
ejpam-5742	124	5	ξ(f	ξ(f	PROPN
ejpam-5742	124	6	)	)	PUNCT
ejpam-5742	124	7	=	=	PUNCT
ejpam-5742	125	1	{	{	PUNCT
ejpam-5742	125	2	0	0	NUM
ejpam-5742	125	3	,	,	PUNCT
ejpam-5742	125	4	θ	θ	NOUN
ejpam-5742	125	5	}	}	PUNCT
ejpam-5742	125	6	and	and	CCONJ
ejpam-5742	125	7	hence	hence	ADV
ejpam-5742	125	8	m[ξ(f	m[ξ(f	NOUN
ejpam-5742	125	9	)	)	PUNCT
ejpam-5742	125	10	]	]	PUNCT
ejpam-5742	126	1	=	=	PUNCT
ejpam-5742	126	2	{	{	PUNCT
ejpam-5742	126	3	ϑ	ϑ	X
ejpam-5742	126	4	,	,	PUNCT
ejpam-5742	126	5	σ	σ	PROPN
ejpam-5742	126	6	}	}	PUNCT
ejpam-5742	126	7	.	.	PUNCT
ejpam-5742	127	1	therefore	therefore	ADV
ejpam-5742	127	2	ξ[m(f	ξ[m(f	NOUN
ejpam-5742	127	3	)	)	PUNCT
ejpam-5742	127	4	]	]	PUNCT
ejpam-5742	128	1	=	=	SYM
ejpam-5742	128	2	m[ξ(f	m[ξ(f	X
ejpam-5742	128	3	)	)	PUNCT
ejpam-5742	128	4	]	]	PUNCT
ejpam-5742	128	5	.	.	PUNCT
ejpam-5742	129	1	thus	thus	ADV
ejpam-5742	129	2	ξ	ξ	X
ejpam-5742	129	3	is	be	AUX
ejpam-5742	129	4	an	an	DET
ejpam-5742	129	5	m−homomorphism	m−homomorphism	NOUN
ejpam-5742	129	6	.	.	PUNCT
ejpam-5742	130	1	theorem	theorem	NOUN
ejpam-5742	130	2	1	1	NUM
ejpam-5742	130	3	.	.	PUNCT
ejpam-5742	131	1	let	let	VERB
ejpam-5742	131	2	ξ	ξ	PROPN
ejpam-5742	131	3	∈	∈	PROPN
ejpam-5742	131	4	homr(r′	homr(r′	PROPN
ejpam-5742	131	5	)	)	PUNCT
ejpam-5742	131	6	with	with	ADP
ejpam-5742	131	7	onto	onto	ADP
ejpam-5742	131	8	property	property	NOUN
ejpam-5742	131	9	and	and	CCONJ
ejpam-5742	131	10	co	co	NOUN
ejpam-5742	131	11	−	−	PROPN
ejpam-5742	131	12	ker	ker	NOUN
ejpam-5742	132	1	ξ	ξ	X
ejpam-5742	132	2	=	=	SYM
ejpam-5742	132	3	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	132	4	)	)	PUNCT
ejpam-5742	132	5	.	.	PUNCT
ejpam-5742	133	1	then	then	ADV
ejpam-5742	133	2	ξ	ξ	PROPN
ejpam-5742	133	3	is	be	AUX
ejpam-5742	133	4	an	an	DET
ejpam-5742	133	5	m−homomorphism	m−homomorphism	NOUN
ejpam-5742	133	6	.	.	PUNCT
ejpam-5742	134	1	proof	proof	NOUN
ejpam-5742	134	2	.	.	PUNCT
ejpam-5742	135	1	clearly	clearly	ADV
ejpam-5742	135	2	,	,	PUNCT
ejpam-5742	135	3	we	we	PRON
ejpam-5742	135	4	have	have	VERB
ejpam-5742	135	5	that	that	PRON
ejpam-5742	135	6	ξ[m(f	ξ[m(f	NOUN
ejpam-5742	135	7	)	)	PUNCT
ejpam-5742	135	8	]	]	PUNCT
ejpam-5742	135	9	⊆	⊆	NUM
ejpam-5742	135	10	m[ξ(f	m[ξ(f	NOUN
ejpam-5742	135	11	)	)	PUNCT
ejpam-5742	135	12	]	]	PUNCT
ejpam-5742	135	13	.	.	PUNCT
ejpam-5742	136	1	let	let	VERB
ejpam-5742	136	2	κ	κ	PROPN
ejpam-5742	136	3	∈	∈	PROPN
ejpam-5742	136	4	m[ξ(f	m[ξ(f	PROPN
ejpam-5742	136	5	)	)	PUNCT
ejpam-5742	136	6	]	]	PUNCT
ejpam-5742	136	7	.	.	PUNCT
ejpam-5742	137	1	then	then	ADV
ejpam-5742	137	2	κ	κ	X
ejpam-5742	137	3	∨	∨	NUM
ejpam-5742	137	4	ρ	ρ	PROPN
ejpam-5742	137	5	∈	∈	PROPN
ejpam-5742	137	6	mmax.elt(r′	mmax.elt(r′	NOUN
ejpam-5742	137	7	)	)	PUNCT
ejpam-5742	137	8	,	,	PUNCT
ejpam-5742	137	9	for	for	ADP
ejpam-5742	137	10	some	some	DET
ejpam-5742	137	11	ρ	ρ	NUM
ejpam-5742	137	12	∈	∈	PROPN
ejpam-5742	137	13	ξ(f	ξ(f	PROPN
ejpam-5742	137	14	)	)	PUNCT
ejpam-5742	137	15	.	.	PUNCT
ejpam-5742	138	1	since	since	SCONJ
ejpam-5742	138	2	ρ	ρ	PROPN
ejpam-5742	138	3	∈	∈	PROPN
ejpam-5742	138	4	f(f	f(f	PROPN
ejpam-5742	138	5	)	)	PUNCT
ejpam-5742	138	6	,	,	PUNCT
ejpam-5742	138	7	there	there	PRON
ejpam-5742	138	8	exists	exist	VERB
ejpam-5742	138	9	an	an	DET
ejpam-5742	138	10	element	element	NOUN
ejpam-5742	138	11	σ	σ	PROPN
ejpam-5742	138	12	∈	∈	PROPN
ejpam-5742	138	13	f	f	PROPN
ejpam-5742	138	14	such	such	ADJ
ejpam-5742	138	15	that	that	PRON
ejpam-5742	138	16	ξ(σ	ξ(σ	PROPN
ejpam-5742	138	17	)	)	PUNCT
ejpam-5742	139	1	=	=	SYM
ejpam-5742	139	2	ρ	ρ	PROPN
ejpam-5742	139	3	.	.	PUNCT
ejpam-5742	140	1	since	since	SCONJ
ejpam-5742	140	2	κ	κ	PROPN
ejpam-5742	140	3	∈	∈	PROPN
ejpam-5742	140	4	r′	r′	PROPN
ejpam-5742	140	5	and	and	CCONJ
ejpam-5742	140	6	ξ	ξ	PROPN
ejpam-5742	140	7	is	be	AUX
ejpam-5742	140	8	onto	onto	ADP
ejpam-5742	140	9	,	,	PUNCT
ejpam-5742	140	10	there	there	PRON
ejpam-5742	140	11	exists	exist	VERB
ejpam-5742	140	12	an	an	DET
ejpam-5742	140	13	element	element	NOUN
ejpam-5742	140	14	η	η	PROPN
ejpam-5742	140	15	∈	∈	PROPN
ejpam-5742	140	16	r	r	NOUN
ejpam-5742	140	17	such	such	ADJ
ejpam-5742	140	18	that	that	SCONJ
ejpam-5742	140	19	ξ(η	ξ(η	NOUN
ejpam-5742	140	20	)	)	PUNCT
ejpam-5742	141	1	=	=	SYM
ejpam-5742	141	2	κ	κ	X
ejpam-5742	141	3	.	.	PUNCT
ejpam-5742	141	4	since	since	SCONJ
ejpam-5742	141	5	κ	κ	PROPN
ejpam-5742	141	6	∨	∨	NUM
ejpam-5742	141	7	ρ	ρ	PROPN
ejpam-5742	141	8	∈	∈	PROPN
ejpam-5742	141	9	mmax.elt(r′	mmax.elt(r′	NOUN
ejpam-5742	141	10	)	)	PUNCT
ejpam-5742	141	11	,	,	PUNCT
ejpam-5742	141	12	we	we	PRON
ejpam-5742	141	13	have	have	VERB
ejpam-5742	141	14	that	that	PRON
ejpam-5742	141	15	ξ(η	ξ(η	PROPN
ejpam-5742	141	16	)	)	PUNCT
ejpam-5742	141	17	∨	∨	PROPN
ejpam-5742	141	18	ξ(σ	ξ(σ	PROPN
ejpam-5742	141	19	)	)	PUNCT
ejpam-5742	141	20	∈	∈	PROPN
ejpam-5742	141	21	mmax.elt(r′	mmax.elt(r′	NOUN
ejpam-5742	141	22	)	)	PUNCT
ejpam-5742	141	23	.	.	PUNCT
ejpam-5742	142	1	that	that	PRON
ejpam-5742	142	2	implies	imply	VERB
ejpam-5742	142	3	ξ(η∨σ	ξ(η∨σ	NOUN
ejpam-5742	142	4	)	)	PUNCT
ejpam-5742	142	5	∈	∈	PROPN
ejpam-5742	142	6	mmax.elt(r′	mmax.elt(r′	NOUN
ejpam-5742	142	7	)	)	PUNCT
ejpam-5742	142	8	and	and	CCONJ
ejpam-5742	142	9	hence	hence	ADV
ejpam-5742	142	10	η∨σ	η∨σ	PROPN
ejpam-5742	142	11	∈	∈	PROPN
ejpam-5742	142	12	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	142	13	)	)	PUNCT
ejpam-5742	142	14	.	.	PUNCT
ejpam-5742	143	1	that	that	PRON
ejpam-5742	143	2	implies	imply	VERB
ejpam-5742	143	3	that	that	SCONJ
ejpam-5742	143	4	η	η	PROPN
ejpam-5742	143	5	∈	∈	PROPN
ejpam-5742	143	6	m(f	m(f	PROPN
ejpam-5742	143	7	)	)	PUNCT
ejpam-5742	143	8	and	and	CCONJ
ejpam-5742	143	9	hence	hence	ADV
ejpam-5742	143	10	κ	κ	X
ejpam-5742	143	11	=	=	SYM
ejpam-5742	143	12	ξ(η	ξ(η	PROPN
ejpam-5742	143	13	)	)	PUNCT
ejpam-5742	143	14	∈	∈	PROPN
ejpam-5742	143	15	ξ[m(f	ξ[m(f	PROPN
ejpam-5742	143	16	)	)	PUNCT
ejpam-5742	143	17	]	]	PUNCT
ejpam-5742	143	18	.	.	PUNCT
ejpam-5742	144	1	therefore	therefore	ADV
ejpam-5742	144	2	m[ξ(f	m[ξ(f	X
ejpam-5742	144	3	)	)	PUNCT
ejpam-5742	144	4	]	]	PUNCT
ejpam-5742	145	1	⊆	⊆	NUM
ejpam-5742	145	2	ξ[m(f	ξ[m(f	NOUN
ejpam-5742	145	3	)	)	PUNCT
ejpam-5742	145	4	]	]	PUNCT
ejpam-5742	145	5	.	.	PUNCT
ejpam-5742	146	1	thus	thus	ADV
ejpam-5742	146	2	ξ[m(f	ξ[m(f	NOUN
ejpam-5742	146	3	)	)	PUNCT
ejpam-5742	146	4	]	]	PUNCT
ejpam-5742	147	1	=	=	SYM
ejpam-5742	147	2	m[ξ(f	m[ξ(f	X
ejpam-5742	147	3	)	)	PUNCT
ejpam-5742	147	4	]	]	PUNCT
ejpam-5742	147	5	.	.	PUNCT
ejpam-5742	148	1	theorem	theorem	NOUN
ejpam-5742	148	2	2	2	NUM
ejpam-5742	148	3	.	.	PUNCT
ejpam-5742	149	1	let	let	VERB
ejpam-5742	149	2	ξ	ξ	PROPN
ejpam-5742	149	3	∈	∈	PROPN
ejpam-5742	149	4	homr(r′	homr(r′	PROPN
ejpam-5742	149	5	)	)	PUNCT
ejpam-5742	149	6	with	with	ADP
ejpam-5742	149	7	onto	onto	ADP
ejpam-5742	149	8	property	property	NOUN
ejpam-5742	149	9	and	and	CCONJ
ejpam-5742	149	10	co	co	NOUN
ejpam-5742	149	11	−	−	PROPN
ejpam-5742	149	12	ker	ker	NOUN
ejpam-5742	150	1	ξ	ξ	X
ejpam-5742	150	2	=	=	SYM
ejpam-5742	150	3	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	150	4	)	)	PUNCT
ejpam-5742	150	5	.	.	PUNCT
ejpam-5742	151	1	then	then	ADV
ejpam-5742	151	2	m(f	m(f	PROPN
ejpam-5742	151	3	)	)	PUNCT
ejpam-5742	151	4	=	=	SYM
ejpam-5742	151	5	m(g	m(g	PROPN
ejpam-5742	151	6	)	)	PUNCT
ejpam-5742	151	7	⇔	⇔	X
ejpam-5742	151	8	m[ξ(f	m[ξ(f	PROPN
ejpam-5742	151	9	)	)	PUNCT
ejpam-5742	151	10	]	]	PUNCT
ejpam-5742	152	1	=	=	PUNCT
ejpam-5742	152	2	m[ξ(g	m[ξ(g	NOUN
ejpam-5742	152	3	)	)	PUNCT
ejpam-5742	152	4	]	]	PUNCT
ejpam-5742	152	5	,	,	PUNCT
ejpam-5742	152	6	for	for	ADP
ejpam-5742	152	7	each	each	DET
ejpam-5742	152	8	two	two	NUM
ejpam-5742	152	9	ideals	ideal	NOUN
ejpam-5742	152	10	f	f	X
ejpam-5742	152	11	,	,	PUNCT
ejpam-5742	152	12	g	g	PROPN
ejpam-5742	152	13	of	of	ADP
ejpam-5742	152	14	r.	r.	PROPN
ejpam-5742	152	15	proof	proof	NOUN
ejpam-5742	152	16	.	.	PUNCT
ejpam-5742	153	1	by	by	ADP
ejpam-5742	153	2	theorem	theorem	NOUN
ejpam-5742	153	3	1	1	NUM
ejpam-5742	153	4	,	,	PUNCT
ejpam-5742	153	5	we	we	PRON
ejpam-5742	153	6	have	have	VERB
ejpam-5742	153	7	that	that	SCONJ
ejpam-5742	153	8	ξ	ξ	PROPN
ejpam-5742	153	9	is	be	AUX
ejpam-5742	153	10	an	an	DET
ejpam-5742	153	11	m−homomorphism	m−homomorphism	NOUN
ejpam-5742	153	12	.	.	PUNCT
ejpam-5742	154	1	assume	assume	VERB
ejpam-5742	154	2	that	that	SCONJ
ejpam-5742	154	3	m(f	m(f	PROPN
ejpam-5742	154	4	)	)	PUNCT
ejpam-5742	154	5	=	=	SYM
ejpam-5742	155	1	m(g	m(g	PROPN
ejpam-5742	155	2	)	)	PUNCT
ejpam-5742	155	3	.	.	PUNCT
ejpam-5742	156	1	now	now	ADV
ejpam-5742	156	2	m[ξ(f	m[ξ(f	X
ejpam-5742	156	3	)	)	PUNCT
ejpam-5742	156	4	]	]	PUNCT
ejpam-5742	157	1	=	=	PUNCT
ejpam-5742	157	2	ξ[m(f	ξ[m(f	NOUN
ejpam-5742	157	3	)	)	PUNCT
ejpam-5742	157	4	]	]	PUNCT
ejpam-5742	157	5	=	=	PUNCT
ejpam-5742	157	6	ξ[m(g	ξ[m(g	NOUN
ejpam-5742	157	7	)	)	PUNCT
ejpam-5742	157	8	]	]	PUNCT
ejpam-5742	158	1	=	=	PUNCT
ejpam-5742	158	2	m[ξ(g	m[ξ(g	NOUN
ejpam-5742	158	3	)	)	PUNCT
ejpam-5742	158	4	]	]	PUNCT
ejpam-5742	158	5	.	.	PUNCT
ejpam-5742	159	1	therefore	therefore	ADV
ejpam-5742	159	2	m[ξ(f	m[ξ(f	X
ejpam-5742	159	3	)	)	PUNCT
ejpam-5742	159	4	]	]	PUNCT
ejpam-5742	160	1	=	=	PUNCT
ejpam-5742	160	2	m[ξ(g	m[ξ(g	NOUN
ejpam-5742	160	3	)	)	PUNCT
ejpam-5742	160	4	]	]	PUNCT
ejpam-5742	160	5	.	.	PUNCT
ejpam-5742	161	1	conversely	conversely	ADV
ejpam-5742	161	2	assume	assume	VERB
ejpam-5742	161	3	that	that	SCONJ
ejpam-5742	161	4	m[ξ(f	m[ξ(f	NOUN
ejpam-5742	161	5	)	)	PUNCT
ejpam-5742	161	6	]	]	PUNCT
ejpam-5742	162	1	=	=	PUNCT
ejpam-5742	162	2	m[ξ(g	m[ξ(g	NOUN
ejpam-5742	162	3	)	)	PUNCT
ejpam-5742	162	4	]	]	PUNCT
ejpam-5742	162	5	.	.	PUNCT
ejpam-5742	163	1	let	let	VERB
ejpam-5742	163	2	κ	κ	PROPN
ejpam-5742	163	3	∈	∈	PROPN
ejpam-5742	163	4	m(f	m(f	PROPN
ejpam-5742	163	5	)	)	PUNCT
ejpam-5742	163	6	.	.	PUNCT
ejpam-5742	164	1	then	then	ADV
ejpam-5742	164	2	ξ(κ	ξ(κ	NUM
ejpam-5742	164	3	)	)	PUNCT
ejpam-5742	164	4	∈	∈	PROPN
ejpam-5742	164	5	ξ[m(f	ξ[m(f	PROPN
ejpam-5742	164	6	)	)	PUNCT
ejpam-5742	164	7	]	]	PUNCT
ejpam-5742	164	8	.	.	PUNCT
ejpam-5742	165	1	that	that	PRON
ejpam-5742	165	2	implies	imply	VERB
ejpam-5742	165	3	ξ(κ	ξ(κ	NOUN
ejpam-5742	165	4	)	)	PUNCT
ejpam-5742	165	5	∈	∈	PROPN
ejpam-5742	165	6	m[ξ(f	m[ξ(f	PROPN
ejpam-5742	165	7	)	)	PUNCT
ejpam-5742	165	8	]	]	PUNCT
ejpam-5742	166	1	=	=	PUNCT
ejpam-5742	166	2	m[ξ(g	m[ξ(g	NOUN
ejpam-5742	166	3	)	)	PUNCT
ejpam-5742	166	4	]	]	PUNCT
ejpam-5742	166	5	.	.	PUNCT
ejpam-5742	167	1	that	that	PRON
ejpam-5742	167	2	implies	imply	VERB
ejpam-5742	167	3	ξ(κ	ξ(κ	PROPN
ejpam-5742	167	4	)	)	PUNCT
ejpam-5742	167	5	∨	∨	NUM
ejpam-5742	167	6	ξ(η	ξ(η	PROPN
ejpam-5742	167	7	)	)	PUNCT
ejpam-5742	167	8	∈	∈	PROPN
ejpam-5742	167	9	mmax.elt(r′	mmax.elt(r′	NOUN
ejpam-5742	167	10	)	)	PUNCT
ejpam-5742	167	11	,	,	PUNCT
ejpam-5742	167	12	for	for	ADP
ejpam-5742	167	13	some	some	DET
ejpam-5742	167	14	η	η	PROPN
ejpam-5742	167	15	∈	∈	PROPN
ejpam-5742	167	16	g.	g.	NOUN
ejpam-5742	167	17	hence	hence	ADV
ejpam-5742	167	18	κ	κ	PROPN
ejpam-5742	167	19	∨	∨	PROPN
ejpam-5742	167	20	η	η	PROPN
ejpam-5742	167	21	∈	∈	PROPN
ejpam-5742	167	22	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	167	23	)	)	PUNCT
ejpam-5742	167	24	.	.	PUNCT
ejpam-5742	168	1	that	that	PRON
ejpam-5742	168	2	gives	give	VERB
ejpam-5742	168	3	κ	κ	PROPN
ejpam-5742	168	4	∈	∈	PROPN
ejpam-5742	168	5	m(g	m(g	PROPN
ejpam-5742	168	6	)	)	PUNCT
ejpam-5742	168	7	.	.	PUNCT
ejpam-5742	169	1	therefore	therefore	ADV
ejpam-5742	169	2	m(f	m(f	PROPN
ejpam-5742	169	3	)	)	PUNCT
ejpam-5742	169	4	⊆	⊆	NUM
ejpam-5742	169	5	m(g	m(g	PROPN
ejpam-5742	169	6	)	)	PUNCT
ejpam-5742	169	7	.	.	PUNCT
ejpam-5742	170	1	similarly	similarly	ADV
ejpam-5742	170	2	,	,	PUNCT
ejpam-5742	170	3	we	we	PRON
ejpam-5742	170	4	get	get	VERB
ejpam-5742	170	5	that	that	DET
ejpam-5742	170	6	m(g	m(g	NOUN
ejpam-5742	170	7	)	)	PUNCT
ejpam-5742	170	8	⊆	⊆	NUM
ejpam-5742	170	9	m(f	m(f	PROPN
ejpam-5742	170	10	)	)	PUNCT
ejpam-5742	170	11	.	.	PUNCT
ejpam-5742	171	1	hence	hence	ADV
ejpam-5742	171	2	m(f	m(f	PROPN
ejpam-5742	171	3	)	)	PUNCT
ejpam-5742	171	4	=	=	SYM
ejpam-5742	171	5	m(g	m(g	PROPN
ejpam-5742	171	6	)	)	PUNCT
ejpam-5742	171	7	.	.	PUNCT
ejpam-5742	172	1	definition	definition	NOUN
ejpam-5742	172	2	5	5	NUM
ejpam-5742	172	3	.	.	PUNCT
ejpam-5742	173	1	[	[	X
ejpam-5742	173	2	9	9	NUM
ejpam-5742	173	3	]	]	PUNCT
ejpam-5742	173	4	a	a	DET
ejpam-5742	173	5	filter	filter	NOUN
ejpam-5742	173	6	s	s	NOUN
ejpam-5742	173	7	of	of	ADP
ejpam-5742	173	8	r	r	NOUN
ejpam-5742	173	9	is	be	AUX
ejpam-5742	173	10	referred	refer	VERB
ejpam-5742	173	11	to	to	ADP
ejpam-5742	173	12	as	as	ADP
ejpam-5742	173	13	an	an	DET
ejpam-5742	173	14	m−filter	m−filter	NOUN
ejpam-5742	173	15	if	if	SCONJ
ejpam-5742	173	16	there	there	PRON
ejpam-5742	173	17	exists	exist	VERB
ejpam-5742	173	18	an	an	DET
ejpam-5742	173	19	ideal	ideal	ADJ
ejpam-5742	173	20	f	f	NOUN
ejpam-5742	173	21	of	of	ADP
ejpam-5742	173	22	r	r	NOUN
ejpam-5742	173	23	such	such	ADJ
ejpam-5742	173	24	that	that	DET
ejpam-5742	173	25	s	s	NOUN
ejpam-5742	173	26	=	=	SYM
ejpam-5742	173	27	m(f	m(f	PROPN
ejpam-5742	173	28	)	)	PUNCT
ejpam-5742	173	29	.	.	PUNCT
ejpam-5742	174	1	it	it	PRON
ejpam-5742	174	2	is	be	AUX
ejpam-5742	174	3	evident	evident	ADJ
ejpam-5742	174	4	that	that	SCONJ
ejpam-5742	174	5	for	for	ADP
ejpam-5742	174	6	any	any	DET
ejpam-5742	174	7	κ	κ	PROPN
ejpam-5742	174	8	∈	∈	PROPN
ejpam-5742	174	9	r	r	NOUN
ejpam-5742	174	10	,	,	PUNCT
ejpam-5742	174	11	the	the	DET
ejpam-5742	174	12	filter	filter	NOUN
ejpam-5742	174	13	(	(	PUNCT
ejpam-5742	174	14	κ)+	κ)+	PRON
ejpam-5742	174	15	is	be	AUX
ejpam-5742	174	16	an	an	DET
ejpam-5742	174	17	m−filter	m−filter	NOUN
ejpam-5742	174	18	of	of	ADP
ejpam-5742	174	19	r.	r.	PROPN
ejpam-5742	174	20	theorem	theorem	NOUN
ejpam-5742	174	21	3	3	NUM
ejpam-5742	174	22	.	.	X
ejpam-5742	174	23	for	for	ADP
ejpam-5742	174	24	any	any	DET
ejpam-5742	174	25	ξ	ξ	PROPN
ejpam-5742	174	26	∈	∈	PROPN
ejpam-5742	174	27	homr(r′	homr(r′	PROPN
ejpam-5742	174	28	)	)	PUNCT
ejpam-5742	174	29	and	and	CCONJ
ejpam-5742	174	30	m−filter	m−filter	X
ejpam-5742	174	31	v	v	ADP
ejpam-5742	174	32	of	of	ADP
ejpam-5742	174	33	r	r	NOUN
ejpam-5742	174	34	,	,	PUNCT
ejpam-5742	174	35	ξ(v	ξ(v	PROPN
ejpam-5742	174	36	)	)	PUNCT
ejpam-5742	174	37	is	be	AUX
ejpam-5742	174	38	an	an	DET
ejpam-5742	174	39	m−filter	m−filter	NOUN
ejpam-5742	174	40	of	of	ADP
ejpam-5742	174	41	r′.	r′.	PROPN
ejpam-5742	174	42	n.	n.	PROPN
ejpam-5742	174	43	rafi	rafi	PROPN
ejpam-5742	174	44	,	,	PUNCT
ejpam-5742	174	45	t.	t.	PROPN
ejpam-5742	174	46	gaketem	gaketem	PROPN
ejpam-5742	174	47	,	,	PUNCT
ejpam-5742	174	48	r.	r.	PROPN
ejpam-5742	174	49	k.	k.	PROPN
ejpam-5742	174	50	bandaru	bandaru	PROPN
ejpam-5742	174	51	/	/	SYM
ejpam-5742	174	52	eur	eur	PROPN
ejpam-5742	174	53	.	.	PUNCT
ejpam-5742	175	1	j.	j.	PROPN
ejpam-5742	175	2	pure	pure	PROPN
ejpam-5742	175	3	appl	appl	PROPN
ejpam-5742	175	4	.	.	PROPN
ejpam-5742	175	5	math	math	PROPN
ejpam-5742	175	6	,	,	PUNCT
ejpam-5742	175	7	18	18	NUM
ejpam-5742	175	8	(	(	PUNCT
ejpam-5742	175	9	2	2	NUM
ejpam-5742	175	10	)	)	PUNCT
ejpam-5742	175	11	(	(	PUNCT
ejpam-5742	175	12	2025	2025	NUM
ejpam-5742	175	13	)	)	PUNCT
ejpam-5742	175	14	,	,	PUNCT
ejpam-5742	175	15	5742	5742	NUM
ejpam-5742	175	16	6	6	NUM
ejpam-5742	175	17	of	of	ADP
ejpam-5742	175	18	14	14	NUM
ejpam-5742	175	19	proof	proof	NOUN
ejpam-5742	175	20	.	.	PUNCT
ejpam-5742	176	1	let	let	VERB
ejpam-5742	176	2	v	v	PART
ejpam-5742	176	3	be	be	AUX
ejpam-5742	176	4	an	an	DET
ejpam-5742	176	5	m−filter	m−filter	NOUN
ejpam-5742	176	6	of	of	ADP
ejpam-5742	176	7	r.	r.	PROPN
ejpam-5742	176	8	then	then	ADV
ejpam-5742	176	9	,	,	PUNCT
ejpam-5742	176	10	there	there	PRON
ejpam-5742	176	11	exists	exist	VERB
ejpam-5742	176	12	an	an	DET
ejpam-5742	176	13	ideal	ideal	ADJ
ejpam-5742	176	14	f	f	NOUN
ejpam-5742	176	15	of	of	ADP
ejpam-5742	176	16	r	r	NOUN
ejpam-5742	176	17	such	such	ADJ
ejpam-5742	176	18	that	that	DET
ejpam-5742	176	19	v	v	NOUN
ejpam-5742	176	20	=	=	SYM
ejpam-5742	176	21	m(f	m(f	PROPN
ejpam-5742	176	22	)	)	PUNCT
ejpam-5742	176	23	.	.	PUNCT
ejpam-5742	177	1	from	from	ADP
ejpam-5742	177	2	lemma	lemma	PROPN
ejpam-5742	177	3	1	1	NUM
ejpam-5742	177	4	,	,	PUNCT
ejpam-5742	177	5	it	it	PRON
ejpam-5742	177	6	follows	follow	VERB
ejpam-5742	177	7	that	that	SCONJ
ejpam-5742	177	8	ξ(f	ξ(f	PROPN
ejpam-5742	177	9	)	)	PUNCT
ejpam-5742	177	10	forms	form	VERB
ejpam-5742	177	11	an	an	DET
ejpam-5742	177	12	ideal	ideal	NOUN
ejpam-5742	177	13	of	of	ADP
ejpam-5742	177	14	r′.	r′.	PROPN
ejpam-5742	177	15	now	now	ADV
ejpam-5742	177	16	ξ(v	ξ(v	PROPN
ejpam-5742	177	17	)	)	PUNCT
ejpam-5742	177	18	=	=	PUNCT
ejpam-5742	177	19	ξ[m(f	ξ[m(f	NOUN
ejpam-5742	177	20	)	)	PUNCT
ejpam-5742	177	21	]	]	PUNCT
ejpam-5742	178	1	=	=	SYM
ejpam-5742	178	2	m[ξ(f	m[ξ(f	X
ejpam-5742	178	3	)	)	PUNCT
ejpam-5742	178	4	]	]	X
ejpam-5742	178	5	,	,	PUNCT
ejpam-5742	178	6	since	since	SCONJ
ejpam-5742	178	7	ξ	ξ	PROPN
ejpam-5742	178	8	is	be	AUX
ejpam-5742	178	9	an	an	DET
ejpam-5742	178	10	m−homomorphism	m−homomorphism	NOUN
ejpam-5742	178	11	.	.	PUNCT
ejpam-5742	179	1	therefore	therefore	ADV
ejpam-5742	179	2	ξ(v	ξ(v	NOUN
ejpam-5742	179	3	)	)	PUNCT
ejpam-5742	179	4	is	be	AUX
ejpam-5742	179	5	an	an	DET
ejpam-5742	179	6	m−filter	m−filter	NOUN
ejpam-5742	179	7	of	of	ADP
ejpam-5742	179	8	r′.	r′.	NOUN
ejpam-5742	179	9	definition	definition	NOUN
ejpam-5742	179	10	6	6	NUM
ejpam-5742	179	11	.	.	PUNCT
ejpam-5742	180	1	let	let	VERB
ejpam-5742	180	2	ξ	ξ	PROPN
ejpam-5742	180	3	∈	∈	PROPN
ejpam-5742	180	4	homr(r′	homr(r′	PROPN
ejpam-5742	180	5	)	)	PUNCT
ejpam-5742	180	6	and	and	CCONJ
ejpam-5742	180	7	s	s	AUX
ejpam-5742	180	8	be	be	AUX
ejpam-5742	180	9	a	a	DET
ejpam-5742	180	10	filter	filter	NOUN
ejpam-5742	180	11	of	of	ADP
ejpam-5742	180	12	r′.	r′.	PROPN
ejpam-5742	180	13	a	a	DET
ejpam-5742	180	14	filter	filter	NOUN
ejpam-5742	180	15	ξ−1(s	ξ−1(s	PROPN
ejpam-5742	180	16	)	)	PUNCT
ejpam-5742	180	17	of	of	ADP
ejpam-5742	180	18	r	r	NOUN
ejpam-5742	180	19	is	be	AUX
ejpam-5742	180	20	refereed	refereed	ADJ
ejpam-5742	180	21	as	as	ADP
ejpam-5742	180	22	the	the	DET
ejpam-5742	180	23	contraction	contraction	NOUN
ejpam-5742	180	24	of	of	ADP
ejpam-5742	180	25	s	s	PRON
ejpam-5742	180	26	with	with	ADP
ejpam-5742	180	27	respect	respect	NOUN
ejpam-5742	180	28	to	to	ADP
ejpam-5742	180	29	ξ	ξ	PROPN
ejpam-5742	180	30	.	.	PUNCT
ejpam-5742	180	31	example	example	NOUN
ejpam-5742	181	1	3	3	X
ejpam-5742	181	2	.	.	PUNCT
ejpam-5742	182	1	let	let	VERB
ejpam-5742	182	2	r	r	NOUN
ejpam-5742	182	3	=	=	SYM
ejpam-5742	182	4	{	{	PUNCT
ejpam-5742	182	5	0	0	NUM
ejpam-5742	182	6	,	,	PUNCT
ejpam-5742	182	7	1	1	NUM
ejpam-5742	182	8	,	,	PUNCT
ejpam-5742	182	9	2	2	NUM
ejpam-5742	182	10	,	,	PUNCT
ejpam-5742	182	11	3	3	NUM
ejpam-5742	182	12	}	}	PUNCT
ejpam-5742	182	13	and	and	CCONJ
ejpam-5742	182	14	define	define	VERB
ejpam-5742	182	15	∨	∨	NUM
ejpam-5742	182	16	,	,	PUNCT
ejpam-5742	182	17	∧	∧	NOUN
ejpam-5742	182	18	on	on	ADP
ejpam-5742	182	19	r	r	NOUN
ejpam-5742	182	20	as	as	SCONJ
ejpam-5742	182	21	follows	follow	VERB
ejpam-5742	182	22	:	:	PUNCT
ejpam-5742	182	23	∧	∧	NOUN
ejpam-5742	182	24	0	0	NUM
ejpam-5742	182	25	1	1	NUM
ejpam-5742	182	26	2	2	NUM
ejpam-5742	182	27	3	3	NUM
ejpam-5742	182	28	0	0	NUM
ejpam-5742	182	29	0	0	NUM
ejpam-5742	182	30	0	0	NUM
ejpam-5742	182	31	0	0	NUM
ejpam-5742	182	32	0	0	NUM
ejpam-5742	182	33	1	1	NUM
ejpam-5742	182	34	0	0	NUM
ejpam-5742	182	35	1	1	NUM
ejpam-5742	182	36	2	2	NUM
ejpam-5742	182	37	3	3	NUM
ejpam-5742	182	38	2	2	NUM
ejpam-5742	182	39	0	0	NUM
ejpam-5742	182	40	1	1	NUM
ejpam-5742	182	41	2	2	NUM
ejpam-5742	182	42	3	3	NUM
ejpam-5742	182	43	3	3	NUM
ejpam-5742	182	44	0	0	NUM
ejpam-5742	182	45	3	3	NUM
ejpam-5742	182	46	3	3	NUM
ejpam-5742	182	47	3	3	NUM
ejpam-5742	182	48	∨	∨	NUM
ejpam-5742	182	49	0	0	NUM
ejpam-5742	182	50	1	1	NUM
ejpam-5742	182	51	2	2	NUM
ejpam-5742	182	52	3	3	NUM
ejpam-5742	182	53	0	0	NUM
ejpam-5742	182	54	0	0	NUM
ejpam-5742	182	55	1	1	NUM
ejpam-5742	182	56	2	2	NUM
ejpam-5742	182	57	3	3	NUM
ejpam-5742	182	58	1	1	NUM
ejpam-5742	182	59	1	1	NUM
ejpam-5742	182	60	1	1	NUM
ejpam-5742	182	61	1	1	NUM
ejpam-5742	182	62	1	1	NUM
ejpam-5742	182	63	2	2	NUM
ejpam-5742	182	64	2	2	NUM
ejpam-5742	182	65	2	2	NUM
ejpam-5742	182	66	2	2	NUM
ejpam-5742	182	67	2	2	NUM
ejpam-5742	182	68	3	3	NUM
ejpam-5742	182	69	3	3	NUM
ejpam-5742	182	70	1	1	NUM
ejpam-5742	182	71	2	2	NUM
ejpam-5742	182	72	3	3	NUM
ejpam-5742	182	73	clearly	clearly	ADV
ejpam-5742	182	74	,	,	PUNCT
ejpam-5742	182	75	(	(	PUNCT
ejpam-5742	182	76	r,∨,∧	r,∨,∧	NUM
ejpam-5742	182	77	,	,	PUNCT
ejpam-5742	182	78	0	0	NUM
ejpam-5742	182	79	)	)	PUNCT
ejpam-5742	182	80	is	be	AUX
ejpam-5742	182	81	an	an	DET
ejpam-5742	182	82	adl	adl	PROPN
ejpam-5742	182	83	.	.	PUNCT
ejpam-5742	183	1	let	let	VERB
ejpam-5742	183	2	a	a	PRON
ejpam-5742	183	3	=	=	PUNCT
ejpam-5742	183	4	{	{	PUNCT
ejpam-5742	183	5	0̆	0̆	PROPN
ejpam-5742	183	6	,	,	PUNCT
ejpam-5742	183	7	1̆	1̆	NUM
ejpam-5742	183	8	}	}	PUNCT
ejpam-5742	183	9	and	and	CCONJ
ejpam-5742	183	10	b	b	X
ejpam-5742	183	11	=	=	PUNCT
ejpam-5742	183	12	{	{	PUNCT
ejpam-5742	183	13	0̄	0̄	PROPN
ejpam-5742	183	14	,	,	PUNCT
ejpam-5742	183	15	1̄	1̄	NUM
ejpam-5742	183	16	,	,	PUNCT
ejpam-5742	183	17	2̄	2̄	NOUN
ejpam-5742	183	18	}	}	PUNCT
ejpam-5742	183	19	be	be	AUX
ejpam-5742	183	20	two	two	NUM
ejpam-5742	183	21	discrete	discrete	ADJ
ejpam-5742	183	22	adls	adls	NOUN
ejpam-5742	183	23	.	.	PUNCT
ejpam-5742	184	1	then	then	ADV
ejpam-5742	184	2	(	(	PUNCT
ejpam-5742	184	3	r′,∨,∧	r′,∨,∧	PROPN
ejpam-5742	184	4	,	,	PUNCT
ejpam-5742	184	5	0̃	0̃	PROPN
ejpam-5742	184	6	)	)	PUNCT
ejpam-5742	184	7	is	be	AUX
ejpam-5742	184	8	an	an	DET
ejpam-5742	184	9	adl	adl	NOUN
ejpam-5742	184	10	with	with	ADP
ejpam-5742	184	11	respect	respect	NOUN
ejpam-5742	184	12	to	to	ADP
ejpam-5742	184	13	the	the	DET
ejpam-5742	184	14	point	point	NOUN
ejpam-5742	184	15	wise	wise	ADJ
ejpam-5742	184	16	operations	operation	NOUN
ejpam-5742	184	17	and	and	CCONJ
ejpam-5742	184	18	0̃	0̃	NOUN
ejpam-5742	184	19	=	=	SYM
ejpam-5742	184	20	(	(	PUNCT
ejpam-5742	184	21	0̆	0̆	PROPN
ejpam-5742	184	22	,	,	PUNCT
ejpam-5742	184	23	0̄	0̄	NUM
ejpam-5742	184	24	)	)	PUNCT
ejpam-5742	184	25	.	.	PUNCT
ejpam-5742	185	1	define	define	VERB
ejpam-5742	185	2	a	a	DET
ejpam-5742	185	3	mapping	mapping	NOUN
ejpam-5742	185	4	f	f	NOUN
ejpam-5742	185	5	:	:	PUNCT
ejpam-5742	185	6	r	r	NOUN
ejpam-5742	185	7	−→	−→	NOUN
ejpam-5742	185	8	r′	r′	NUM
ejpam-5742	185	9	as	as	SCONJ
ejpam-5742	185	10	follows	follow	VERB
ejpam-5742	185	11	:	:	PUNCT
ejpam-5742	185	12	f(0	f(0	NOUN
ejpam-5742	185	13	)	)	PUNCT
ejpam-5742	185	14	=	=	SYM
ejpam-5742	185	15	0̃	0̃	NOUN
ejpam-5742	185	16	,	,	PUNCT
ejpam-5742	185	17	f(1	f(1	PROPN
ejpam-5742	185	18	)	)	PUNCT
ejpam-5742	185	19	=	=	PUNCT
ejpam-5742	185	20	(	(	PUNCT
ejpam-5742	185	21	1̆	1̆	NUM
ejpam-5742	185	22	,	,	PUNCT
ejpam-5742	185	23	1̄	1̄	NUM
ejpam-5742	185	24	)	)	PUNCT
ejpam-5742	185	25	,	,	PUNCT
ejpam-5742	185	26	f(2	f(2	PROPN
ejpam-5742	185	27	)	)	PUNCT
ejpam-5742	186	1	=	=	PUNCT
ejpam-5742	186	2	(	(	PUNCT
ejpam-5742	186	3	1̆	1̆	NUM
ejpam-5742	186	4	,	,	PUNCT
ejpam-5742	186	5	2̄	2̄	NOUN
ejpam-5742	186	6	)	)	PUNCT
ejpam-5742	186	7	,	,	PUNCT
ejpam-5742	186	8	f(3	f(3	PROPN
ejpam-5742	186	9	)	)	PUNCT
ejpam-5742	186	10	=	=	PUNCT
ejpam-5742	186	11	(	(	PUNCT
ejpam-5742	186	12	1̆	1̆	NUM
ejpam-5742	186	13	,	,	PUNCT
ejpam-5742	186	14	0̄	0̄	NUM
ejpam-5742	186	15	)	)	PUNCT
ejpam-5742	186	16	.	.	PUNCT
ejpam-5742	187	1	clearly	clearly	ADV
ejpam-5742	187	2	f	f	PROPN
ejpam-5742	187	3	is	be	AUX
ejpam-5742	187	4	a	a	DET
ejpam-5742	187	5	homomorphism	homomorphism	NOUN
ejpam-5742	187	6	from	from	ADP
ejpam-5742	187	7	r	r	NOUN
ejpam-5742	187	8	into	into	ADP
ejpam-5742	187	9	r′.	r′.	NOUN
ejpam-5742	187	10	now	now	ADV
ejpam-5742	187	11	consider	consider	VERB
ejpam-5742	187	12	the	the	DET
ejpam-5742	187	13	filter	filter	NOUN
ejpam-5742	187	14	s	s	PART
ejpam-5742	187	15	=	=	X
ejpam-5742	187	16	{	{	PUNCT
ejpam-5742	187	17	(	(	PUNCT
ejpam-5742	187	18	1̆	1̆	NUM
ejpam-5742	187	19	,	,	PUNCT
ejpam-5742	187	20	0̄	0̄	NUM
ejpam-5742	187	21	)	)	PUNCT
ejpam-5742	187	22	,	,	PUNCT
ejpam-5742	187	23	(	(	PUNCT
ejpam-5742	187	24	1̆	1̆	NUM
ejpam-5742	187	25	,	,	PUNCT
ejpam-5742	187	26	1̄	1̄	NUM
ejpam-5742	187	27	)	)	PUNCT
ejpam-5742	187	28	,	,	PUNCT
ejpam-5742	187	29	(	(	PUNCT
ejpam-5742	187	30	1̆	1̆	NUM
ejpam-5742	187	31	,	,	PUNCT
ejpam-5742	187	32	2̄	2̄	NOUN
ejpam-5742	187	33	)	)	PUNCT
ejpam-5742	187	34	}	}	PUNCT
ejpam-5742	187	35	and	and	CCONJ
ejpam-5742	187	36	the	the	DET
ejpam-5742	187	37	ideal	ideal	NOUN
ejpam-5742	187	38	t	t	PROPN
ejpam-5742	187	39	=	=	SYM
ejpam-5742	187	40	{	{	PUNCT
ejpam-5742	187	41	(	(	PUNCT
ejpam-5742	187	42	0̆	0̆	NUM
ejpam-5742	187	43	,	,	PUNCT
ejpam-5742	187	44	0̄	0̄	NUM
ejpam-5742	187	45	)	)	PUNCT
ejpam-5742	187	46	,	,	PUNCT
ejpam-5742	187	47	(	(	PUNCT
ejpam-5742	187	48	0̆	0̆	NUM
ejpam-5742	187	49	,	,	PUNCT
ejpam-5742	187	50	1̄	1̄	NUM
ejpam-5742	187	51	)	)	PUNCT
ejpam-5742	187	52	,	,	PUNCT
ejpam-5742	187	53	(	(	PUNCT
ejpam-5742	187	54	0̆	0̆	NUM
ejpam-5742	187	55	,	,	PUNCT
ejpam-5742	187	56	2̄	2̄	NOUN
ejpam-5742	187	57	)	)	PUNCT
ejpam-5742	187	58	}	}	PUNCT
ejpam-5742	187	59	in	in	ADP
ejpam-5742	187	60	r′.	r′.	PROPN
ejpam-5742	187	61	clearly	clearly	ADV
ejpam-5742	187	62	,	,	PUNCT
ejpam-5742	187	63	m(t	m(t	NOUN
ejpam-5742	187	64	)	)	PUNCT
ejpam-5742	188	1	=	=	PUNCT
ejpam-5742	188	2	s.	s.	PROPN
ejpam-5742	188	3	hence	hence	ADV
ejpam-5742	188	4	s	s	VERB
ejpam-5742	188	5	is	be	AUX
ejpam-5742	188	6	an	an	DET
ejpam-5742	188	7	m−filter	m−filter	NOUN
ejpam-5742	188	8	of	of	ADP
ejpam-5742	188	9	r′.	r′.	PROPN
ejpam-5742	188	10	but	but	CCONJ
ejpam-5742	188	11	f−1(s	f−1(s	PROPN
ejpam-5742	188	12	)	)	PUNCT
ejpam-5742	188	13	=	=	PRON
ejpam-5742	188	14	{	{	PUNCT
ejpam-5742	188	15	1	1	NUM
ejpam-5742	188	16	,	,	PUNCT
ejpam-5742	188	17	2	2	NUM
ejpam-5742	188	18	,	,	PUNCT
ejpam-5742	188	19	3	3	NUM
ejpam-5742	188	20	}	}	PUNCT
ejpam-5742	188	21	is	be	AUX
ejpam-5742	188	22	a	a	DET
ejpam-5742	188	23	filter	filter	NOUN
ejpam-5742	188	24	of	of	ADP
ejpam-5742	188	25	r	r	NOUN
ejpam-5742	188	26	but	but	CCONJ
ejpam-5742	188	27	not	not	PART
ejpam-5742	188	28	an	an	DET
ejpam-5742	188	29	m−filter	m−filter	NOUN
ejpam-5742	188	30	,	,	PUNCT
ejpam-5742	188	31	because	because	SCONJ
ejpam-5742	188	32	3	3	NUM
ejpam-5742	188	33	∈	∈	PROPN
ejpam-5742	188	34	f−1(s	f−1(s	PROPN
ejpam-5742	188	35	)	)	PUNCT
ejpam-5742	188	36	and	and	CCONJ
ejpam-5742	188	37	(	(	PUNCT
ejpam-5742	188	38	3)+	3)+	NUM
ejpam-5742	188	39	=	=	SYM
ejpam-5742	188	40	{	{	PUNCT
ejpam-5742	188	41	1	1	NUM
ejpam-5742	188	42	,	,	PUNCT
ejpam-5742	188	43	2	2	NUM
ejpam-5742	188	44	}	}	PUNCT
ejpam-5742	188	45	.	.	PUNCT
ejpam-5742	189	1	next	next	ADV
ejpam-5742	189	2	,	,	PUNCT
ejpam-5742	189	3	we	we	PRON
ejpam-5742	189	4	establish	establish	VERB
ejpam-5742	189	5	a	a	DET
ejpam-5742	189	6	sufficient	sufficient	ADJ
ejpam-5742	189	7	condition	condition	NOUN
ejpam-5742	189	8	under	under	ADP
ejpam-5742	189	9	which	which	PRON
ejpam-5742	189	10	the	the	DET
ejpam-5742	189	11	contraction	contraction	NOUN
ejpam-5742	189	12	of	of	ADP
ejpam-5742	189	13	an	an	DET
ejpam-5742	189	14	m−filter	m−filter	NOUN
ejpam-5742	189	15	remains	remain	VERB
ejpam-5742	189	16	an	an	DET
ejpam-5742	189	17	m−filter	m−filter	NOUN
ejpam-5742	189	18	.	.	PUNCT
ejpam-5742	190	1	theorem	theorem	NOUN
ejpam-5742	190	2	4	4	NUM
ejpam-5742	190	3	.	.	PUNCT
ejpam-5742	191	1	let	let	VERB
ejpam-5742	191	2	ξ	ξ	PROPN
ejpam-5742	191	3	∈	∈	PROPN
ejpam-5742	191	4	homr(r′	homr(r′	PROPN
ejpam-5742	191	5	)	)	PUNCT
ejpam-5742	191	6	with	with	ADP
ejpam-5742	191	7	onto	onto	ADP
ejpam-5742	191	8	property	property	NOUN
ejpam-5742	191	9	and	and	CCONJ
ejpam-5742	191	10	co	co	NOUN
ejpam-5742	191	11	−ker	−ker	NOUN
ejpam-5742	191	12	ξ	ξ	X
ejpam-5742	191	13	=	=	SYM
ejpam-5742	191	14	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	191	15	)	)	PUNCT
ejpam-5742	191	16	.	.	PUNCT
ejpam-5742	192	1	if	if	SCONJ
ejpam-5742	192	2	every	every	DET
ejpam-5742	192	3	ideal	ideal	NOUN
ejpam-5742	192	4	of	of	ADP
ejpam-5742	192	5	r′	r′	PROPN
ejpam-5742	192	6	contracts	contract	NOUN
ejpam-5742	192	7	to	to	ADP
ejpam-5742	192	8	an	an	DET
ejpam-5742	192	9	ideal	ideal	NOUN
ejpam-5742	192	10	of	of	ADP
ejpam-5742	192	11	r	r	NOUN
ejpam-5742	192	12	,	,	PUNCT
ejpam-5742	192	13	then	then	ADV
ejpam-5742	192	14	every	every	DET
ejpam-5742	192	15	m−filter	m−filter	NOUN
ejpam-5742	192	16	of	of	ADP
ejpam-5742	192	17	r′	r′	PROPN
ejpam-5742	192	18	contracts	contract	NOUN
ejpam-5742	192	19	to	to	ADP
ejpam-5742	192	20	an	an	DET
ejpam-5742	192	21	m−filter	m−filter	NOUN
ejpam-5742	192	22	of	of	ADP
ejpam-5742	192	23	r.	r.	NOUN
ejpam-5742	192	24	proof	proof	NOUN
ejpam-5742	192	25	.	.	PUNCT
ejpam-5742	193	1	let	let	VERB
ejpam-5742	193	2	s	s	PRON
ejpam-5742	193	3	be	be	AUX
ejpam-5742	193	4	an	an	DET
ejpam-5742	193	5	m−filter	m−filter	NOUN
ejpam-5742	193	6	of	of	ADP
ejpam-5742	193	7	r′.	r′.	PROPN
ejpam-5742	193	8	then	then	ADV
ejpam-5742	193	9	s	s	PART
ejpam-5742	193	10	=	=	SYM
ejpam-5742	193	11	m(f	m(f	PROPN
ejpam-5742	193	12	)	)	PUNCT
ejpam-5742	193	13	,	,	PUNCT
ejpam-5742	193	14	for	for	ADP
ejpam-5742	193	15	some	some	DET
ejpam-5742	193	16	ideal	ideal	ADJ
ejpam-5742	193	17	f	f	PROPN
ejpam-5742	193	18	of	of	ADP
ejpam-5742	193	19	r′.	r′.	PROPN
ejpam-5742	193	20	as	as	ADP
ejpam-5742	193	21	per	per	ADP
ejpam-5742	193	22	our	our	PRON
ejpam-5742	193	23	hypothesis	hypothesis	NOUN
ejpam-5742	193	24	,	,	PUNCT
ejpam-5742	193	25	we	we	PRON
ejpam-5742	193	26	have	have	VERB
ejpam-5742	193	27	that	that	DET
ejpam-5742	193	28	ξ−1(f	ξ−1(f	PROPN
ejpam-5742	193	29	)	)	PUNCT
ejpam-5742	193	30	is	be	AUX
ejpam-5742	193	31	an	an	DET
ejpam-5742	193	32	ideal	ideal	NOUN
ejpam-5742	193	33	of	of	ADP
ejpam-5742	193	34	r.	r.	PROPN
ejpam-5742	193	35	we	we	PRON
ejpam-5742	193	36	derive	derive	VERB
ejpam-5742	193	37	that	that	SCONJ
ejpam-5742	193	38	ξ−1[m(f	ξ−1[m(f	NOUN
ejpam-5742	193	39	)	)	PUNCT
ejpam-5742	193	40	]	]	PUNCT
ejpam-5742	194	1	=	=	PUNCT
ejpam-5742	194	2	m[ξ−1(f	m[ξ−1(f	NOUN
ejpam-5742	194	3	)	)	PUNCT
ejpam-5742	194	4	]	]	PUNCT
ejpam-5742	194	5	.	.	PUNCT
ejpam-5742	195	1	let	let	VERB
ejpam-5742	195	2	κ	κ	PROPN
ejpam-5742	195	3	∈	∈	PROPN
ejpam-5742	195	4	m[ξ−1(f	m[ξ−1(f	PROPN
ejpam-5742	195	5	)	)	PUNCT
ejpam-5742	195	6	]	]	PUNCT
ejpam-5742	195	7	.	.	PUNCT
ejpam-5742	196	1	then	then	ADV
ejpam-5742	196	2	κ	κ	X
ejpam-5742	196	3	∨	∨	PROPN
ejpam-5742	196	4	τ	τ	PROPN
ejpam-5742	196	5	∈	∈	PROPN
ejpam-5742	196	6	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	196	7	)	)	PUNCT
ejpam-5742	196	8	,	,	PUNCT
ejpam-5742	196	9	for	for	ADP
ejpam-5742	196	10	some	some	DET
ejpam-5742	196	11	τ	τ	PROPN
ejpam-5742	196	12	∈	∈	PROPN
ejpam-5742	196	13	ξ−1(f	ξ−1(f	PROPN
ejpam-5742	196	14	)	)	PUNCT
ejpam-5742	196	15	.	.	PUNCT
ejpam-5742	197	1	that	that	PRON
ejpam-5742	197	2	implies	imply	VERB
ejpam-5742	197	3	ξ(κ∨τ	ξ(κ∨τ	NOUN
ejpam-5742	197	4	)	)	PUNCT
ejpam-5742	197	5	∈	∈	PROPN
ejpam-5742	197	6	mmax.elt(r′	mmax.elt(r′	NOUN
ejpam-5742	197	7	)	)	PUNCT
ejpam-5742	197	8	and	and	CCONJ
ejpam-5742	197	9	hence	hence	ADV
ejpam-5742	197	10	ξ(κ)∨ξ(τ	ξ(κ)∨ξ(τ	NOUN
ejpam-5742	197	11	)	)	PUNCT
ejpam-5742	197	12	∈	∈	PROPN
ejpam-5742	197	13	mmax.elt(r′	mmax.elt(r′	NOUN
ejpam-5742	197	14	)	)	PUNCT
ejpam-5742	197	15	.	.	PUNCT
ejpam-5742	198	1	that	that	PRON
ejpam-5742	198	2	implies	imply	VERB
ejpam-5742	198	3	ξ(κ	ξ(κ	NOUN
ejpam-5742	198	4	)	)	PUNCT
ejpam-5742	198	5	∈	∈	PROPN
ejpam-5742	198	6	m(f	m(f	PROPN
ejpam-5742	198	7	)	)	PUNCT
ejpam-5742	198	8	,	,	PUNCT
ejpam-5742	199	1	since	since	SCONJ
ejpam-5742	199	2	ξ(τ	ξ(τ	PROPN
ejpam-5742	199	3	)	)	PUNCT
ejpam-5742	199	4	∈	∈	PROPN
ejpam-5742	199	5	f	f	PROPN
ejpam-5742	199	6	.	.	PUNCT
ejpam-5742	200	1	that	that	PRON
ejpam-5742	200	2	implies	imply	VERB
ejpam-5742	200	3	κ	κ	PROPN
ejpam-5742	200	4	∈	∈	PROPN
ejpam-5742	200	5	ξ−1[m(f	ξ−1[m(f	PROPN
ejpam-5742	200	6	)	)	PUNCT
ejpam-5742	200	7	]	]	PUNCT
ejpam-5742	200	8	.	.	PUNCT
ejpam-5742	201	1	therefore	therefore	ADV
ejpam-5742	201	2	m[ξ−1(f	m[ξ−1(f	NOUN
ejpam-5742	201	3	)	)	PUNCT
ejpam-5742	201	4	]	]	PUNCT
ejpam-5742	202	1	⊆	⊆	NUM
ejpam-5742	202	2	ξ−1[m(f	ξ−1[m(f	NOUN
ejpam-5742	202	3	)	)	PUNCT
ejpam-5742	202	4	]	]	PUNCT
ejpam-5742	202	5	.	.	PUNCT
ejpam-5742	203	1	let	let	VERB
ejpam-5742	203	2	κ	κ	PROPN
ejpam-5742	203	3	∈	∈	PROPN
ejpam-5742	203	4	ξ−1[m(f	ξ−1[m(f	PROPN
ejpam-5742	203	5	)	)	PUNCT
ejpam-5742	203	6	]	]	PUNCT
ejpam-5742	203	7	.	.	PUNCT
ejpam-5742	204	1	then	then	ADV
ejpam-5742	204	2	ξ(κ	ξ(κ	NUM
ejpam-5742	204	3	)	)	PUNCT
ejpam-5742	204	4	∈	∈	PROPN
ejpam-5742	204	5	m(f	m(f	PROPN
ejpam-5742	204	6	)	)	PUNCT
ejpam-5742	204	7	.	.	PUNCT
ejpam-5742	205	1	that	that	PRON
ejpam-5742	205	2	implies	imply	VERB
ejpam-5742	205	3	ξ(κ	ξ(κ	PROPN
ejpam-5742	205	4	)	)	PUNCT
ejpam-5742	205	5	∨	∨	NUM
ejpam-5742	205	6	ω	ω	PROPN
ejpam-5742	205	7	∈	∈	PROPN
ejpam-5742	205	8	mmax.elt(r′	mmax.elt(r′	NOUN
ejpam-5742	205	9	)	)	PUNCT
ejpam-5742	205	10	,	,	PUNCT
ejpam-5742	205	11	for	for	ADP
ejpam-5742	205	12	some	some	DET
ejpam-5742	205	13	ω	ω	NUM
ejpam-5742	205	14	∈	∈	PROPN
ejpam-5742	205	15	f	f	X
ejpam-5742	205	16	.	.	PUNCT
ejpam-5742	206	1	since	since	SCONJ
ejpam-5742	206	2	ω	ω	PROPN
ejpam-5742	206	3	is	be	AUX
ejpam-5742	206	4	an	an	DET
ejpam-5742	206	5	element	element	NOUN
ejpam-5742	206	6	of	of	ADP
ejpam-5742	206	7	an	an	DET
ejpam-5742	206	8	ideal	ideal	ADJ
ejpam-5742	206	9	f	f	PROPN
ejpam-5742	206	10	of	of	ADP
ejpam-5742	206	11	r′	r′	PROPN
ejpam-5742	206	12	and	and	CCONJ
ejpam-5742	206	13	ξ	ξ	PROPN
ejpam-5742	206	14	is	be	AUX
ejpam-5742	206	15	an	an	DET
ejpam-5742	206	16	epimorphism	epimorphism	NOUN
ejpam-5742	206	17	,	,	PUNCT
ejpam-5742	206	18	there	there	PRON
ejpam-5742	206	19	exists	exist	VERB
ejpam-5742	206	20	an	an	DET
ejpam-5742	206	21	element	element	NOUN
ejpam-5742	206	22	ν	ν	NOUN
ejpam-5742	206	23	∈	∈	NOUN
ejpam-5742	206	24	r	r	NOUN
ejpam-5742	206	25	such	such	ADJ
ejpam-5742	206	26	that	that	DET
ejpam-5742	206	27	ξ(ν	ξ(ν	NUM
ejpam-5742	206	28	)	)	PUNCT
ejpam-5742	207	1	=	=	SYM
ejpam-5742	207	2	ω	ω	X
ejpam-5742	207	3	.	.	PUNCT
ejpam-5742	208	1	that	that	PRON
ejpam-5742	208	2	implies	imply	VERB
ejpam-5742	208	3	ξ(κ	ξ(κ	NOUN
ejpam-5742	208	4	)	)	PUNCT
ejpam-5742	208	5	∨	∨	NUM
ejpam-5742	208	6	ξ(ν	ξ(ν	NUM
ejpam-5742	208	7	)	)	PUNCT
ejpam-5742	208	8	∈	∈	PROPN
ejpam-5742	208	9	mmax.elt(r′	mmax.elt(r′	NOUN
ejpam-5742	208	10	)	)	PUNCT
ejpam-5742	208	11	and	and	CCONJ
ejpam-5742	208	12	hence	hence	ADV
ejpam-5742	208	13	ξ(κ	ξ(κ	NUM
ejpam-5742	208	14	∨	∨	NUM
ejpam-5742	208	15	ν	ν	NOUN
ejpam-5742	208	16	)	)	PUNCT
ejpam-5742	208	17	∈	∈	PROPN
ejpam-5742	208	18	mmax.elt(r′	mmax.elt(r′	NOUN
ejpam-5742	208	19	)	)	PUNCT
ejpam-5742	208	20	.	.	PUNCT
ejpam-5742	209	1	therefore	therefore	ADV
ejpam-5742	209	2	κ	κ	X
ejpam-5742	209	3	∨	∨	NUM
ejpam-5742	209	4	ν	ν	X
ejpam-5742	209	5	∈	∈	PROPN
ejpam-5742	209	6	co	co	NOUN
ejpam-5742	209	7	−	−	PROPN
ejpam-5742	209	8	ker	ker	PROPN
ejpam-5742	210	1	ξ	ξ	X
ejpam-5742	210	2	=	=	SYM
ejpam-5742	210	3	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	210	4	)	)	PUNCT
ejpam-5742	210	5	.	.	PUNCT
ejpam-5742	211	1	so	so	ADV
ejpam-5742	211	2	that	that	SCONJ
ejpam-5742	211	3	κ	κ	PROPN
ejpam-5742	211	4	∈	∈	PROPN
ejpam-5742	211	5	m[ξ−1(f	m[ξ−1(f	PROPN
ejpam-5742	211	6	)	)	PUNCT
ejpam-5742	211	7	]	]	PUNCT
ejpam-5742	211	8	.	.	PUNCT
ejpam-5742	212	1	hence	hence	ADV
ejpam-5742	212	2	ξ−1[m(f	ξ−1[m(f	PROPN
ejpam-5742	212	3	)	)	PUNCT
ejpam-5742	212	4	]	]	PUNCT
ejpam-5742	213	1	⊆	⊆	NUM
ejpam-5742	213	2	m[ξ−1(f	m[ξ−1(f	NOUN
ejpam-5742	213	3	)	)	PUNCT
ejpam-5742	213	4	]	]	PUNCT
ejpam-5742	213	5	.	.	PUNCT
ejpam-5742	214	1	thus	thus	ADV
ejpam-5742	214	2	ξ−1[m(f	ξ−1[m(f	PROPN
ejpam-5742	214	3	)	)	PUNCT
ejpam-5742	214	4	]	]	PUNCT
ejpam-5742	215	1	=	=	PUNCT
ejpam-5742	215	2	m[ξ−1(f	m[ξ−1(f	NOUN
ejpam-5742	215	3	)	)	PUNCT
ejpam-5742	215	4	]	]	PUNCT
ejpam-5742	215	5	.	.	PUNCT
ejpam-5742	216	1	theorem	theorem	NOUN
ejpam-5742	216	2	5	5	NUM
ejpam-5742	216	3	.	.	PUNCT
ejpam-5742	217	1	let	let	VERB
ejpam-5742	217	2	ξ	ξ	PROPN
ejpam-5742	217	3	∈	∈	PROPN
ejpam-5742	217	4	homr(r′	homr(r′	PROPN
ejpam-5742	217	5	)	)	PUNCT
ejpam-5742	217	6	and	and	CCONJ
ejpam-5742	217	7	every	every	DET
ejpam-5742	217	8	m−filter	m−filter	NOUN
ejpam-5742	217	9	of	of	ADP
ejpam-5742	217	10	r′	r′	PROPN
ejpam-5742	217	11	contracts	contract	NOUN
ejpam-5742	217	12	to	to	ADP
ejpam-5742	217	13	an	an	DET
ejpam-5742	217	14	m−filter	m−filter	NOUN
ejpam-5742	217	15	of	of	ADP
ejpam-5742	217	16	r.	r.	PROPN
ejpam-5742	217	17	if	if	SCONJ
ejpam-5742	217	18	r′	r′	PROPN
ejpam-5742	217	19	has	have	VERB
ejpam-5742	217	20	dual	dual	ADJ
ejpam-5742	217	21	dense	dense	ADJ
ejpam-5742	217	22	elements	element	NOUN
ejpam-5742	217	23	,	,	PUNCT
ejpam-5742	217	24	then	then	ADV
ejpam-5742	217	25	co	co	NOUN
ejpam-5742	217	26	-	-	NOUN
ejpam-5742	217	27	ker	ker	X
ejpam-5742	217	28	ξ	ξ	X
ejpam-5742	217	29	is	be	AUX
ejpam-5742	217	30	an	an	DET
ejpam-5742	217	31	m−filter	m−filter	NOUN
ejpam-5742	217	32	of	of	ADP
ejpam-5742	217	33	r.	r.	PROPN
ejpam-5742	217	34	n.	n.	PROPN
ejpam-5742	217	35	rafi	rafi	PROPN
ejpam-5742	217	36	,	,	PUNCT
ejpam-5742	217	37	t.	t.	PROPN
ejpam-5742	217	38	gaketem	gaketem	PROPN
ejpam-5742	217	39	,	,	PUNCT
ejpam-5742	217	40	r.	r.	PROPN
ejpam-5742	217	41	k.	k.	PROPN
ejpam-5742	217	42	bandaru	bandaru	PROPN
ejpam-5742	217	43	/	/	SYM
ejpam-5742	217	44	eur	eur	PROPN
ejpam-5742	217	45	.	.	PUNCT
ejpam-5742	218	1	j.	j.	PROPN
ejpam-5742	218	2	pure	pure	PROPN
ejpam-5742	218	3	appl	appl	PROPN
ejpam-5742	218	4	.	.	PROPN
ejpam-5742	218	5	math	math	PROPN
ejpam-5742	218	6	,	,	PUNCT
ejpam-5742	218	7	18	18	NUM
ejpam-5742	218	8	(	(	PUNCT
ejpam-5742	218	9	2	2	NUM
ejpam-5742	218	10	)	)	PUNCT
ejpam-5742	218	11	(	(	PUNCT
ejpam-5742	218	12	2025	2025	NUM
ejpam-5742	218	13	)	)	PUNCT
ejpam-5742	218	14	,	,	PUNCT
ejpam-5742	218	15	5742	5742	NUM
ejpam-5742	218	16	7	7	NUM
ejpam-5742	218	17	of	of	ADP
ejpam-5742	218	18	14	14	NUM
ejpam-5742	218	19	proof	proof	NOUN
ejpam-5742	218	20	.	.	PUNCT
ejpam-5742	219	1	let	let	VERB
ejpam-5742	219	2	e′	e′	PART
ejpam-5742	219	3	be	be	AUX
ejpam-5742	219	4	the	the	DET
ejpam-5742	219	5	set	set	NOUN
ejpam-5742	219	6	of	of	ADP
ejpam-5742	219	7	all	all	DET
ejpam-5742	219	8	dual	dual	ADJ
ejpam-5742	219	9	dense	dense	ADJ
ejpam-5742	219	10	elements	element	NOUN
ejpam-5742	219	11	of	of	ADP
ejpam-5742	219	12	r′.	r′.	PROPN
ejpam-5742	219	13	clearly	clearly	ADV
ejpam-5742	219	14	e′	e′	PROPN
ejpam-5742	219	15	is	be	AUX
ejpam-5742	219	16	an	an	DET
ejpam-5742	219	17	ideal	ideal	NOUN
ejpam-5742	219	18	of	of	ADP
ejpam-5742	219	19	r′.	r′.	PROPN
ejpam-5742	219	20	then	then	ADV
ejpam-5742	219	21	m(e′	m(e′	PROPN
ejpam-5742	219	22	)	)	PUNCT
ejpam-5742	219	23	=	=	SYM
ejpam-5742	219	24	mmax.elt(r′	mmax.elt(r′	PROPN
ejpam-5742	219	25	)	)	PUNCT
ejpam-5742	219	26	.	.	PUNCT
ejpam-5742	220	1	clearly	clearly	ADV
ejpam-5742	220	2	we	we	PRON
ejpam-5742	220	3	have	have	VERB
ejpam-5742	220	4	that	that	DET
ejpam-5742	220	5	mmax.elt(r′	mmax.elt(r′	NOUN
ejpam-5742	220	6	)	)	PUNCT
ejpam-5742	220	7	is	be	AUX
ejpam-5742	220	8	a	a	DET
ejpam-5742	220	9	filter	filter	NOUN
ejpam-5742	220	10	of	of	ADP
ejpam-5742	220	11	r′	r′	PROPN
ejpam-5742	220	12	and	and	CCONJ
ejpam-5742	220	13	hence	hence	ADV
ejpam-5742	220	14	it	it	PRON
ejpam-5742	220	15	is	be	AUX
ejpam-5742	220	16	an	an	DET
ejpam-5742	220	17	m−filter	m−filter	NOUN
ejpam-5742	220	18	of	of	ADP
ejpam-5742	220	19	r′.	r′.	PROPN
ejpam-5742	220	20	clearly	clearly	ADV
ejpam-5742	220	21	,	,	PUNCT
ejpam-5742	220	22	we	we	PRON
ejpam-5742	220	23	have	have	VERB
ejpam-5742	220	24	that	that	PRON
ejpam-5742	220	25	co−	co−	NUM
ejpam-5742	220	26	ker	ker	X
ejpam-5742	221	1	ξ	ξ	X
ejpam-5742	221	2	=	=	SYM
ejpam-5742	221	3	ξ−1(mmax.elt(r′)).therefore	ξ−1(mmax.elt(r′)).therefore	ADP
ejpam-5742	221	4	co−	co−	NOUN
ejpam-5742	221	5	ker	ker	X
ejpam-5742	221	6	ξ	ξ	X
ejpam-5742	221	7	is	be	AUX
ejpam-5742	221	8	an	an	DET
ejpam-5742	221	9	m−filter	m−filter	NOUN
ejpam-5742	221	10	of	of	ADP
ejpam-5742	221	11	r.	r.	PROPN
ejpam-5742	221	12	definition	definition	NOUN
ejpam-5742	221	13	7	7	NUM
ejpam-5742	221	14	.	.	PUNCT
ejpam-5742	222	1	for	for	ADP
ejpam-5742	222	2	any	any	DET
ejpam-5742	222	3	filter	filter	NOUN
ejpam-5742	222	4	s	s	VERB
ejpam-5742	222	5	of	of	ADP
ejpam-5742	222	6	r	r	NOUN
ejpam-5742	222	7	,	,	PUNCT
ejpam-5742	222	8	define	define	VERB
ejpam-5742	222	9	h(s	h(	NOUN
ejpam-5742	222	10	)	)	PUNCT
ejpam-5742	223	1	=	=	PRON
ejpam-5742	223	2	{	{	PUNCT
ejpam-5742	223	3	κ	κ	NOUN
ejpam-5742	223	4	∈	∈	PROPN
ejpam-5742	223	5	r	r	NOUN
ejpam-5742	223	6	|	|	ADV
ejpam-5742	223	7	η∨κ	η∨κ	PROPN
ejpam-5742	223	8	∈	∈	PROPN
ejpam-5742	223	9	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	223	10	)	)	PUNCT
ejpam-5742	223	11	,	,	PUNCT
ejpam-5742	223	12	for	for	ADP
ejpam-5742	223	13	some	some	DET
ejpam-5742	223	14	η	η	PROPN
ejpam-5742	223	15	∈	∈	PROPN
ejpam-5742	223	16	r	r	NOUN
ejpam-5742	223	17	\	\	NOUN
ejpam-5742	223	18	s	s	PART
ejpam-5742	223	19	}	}	PUNCT
ejpam-5742	223	20	the	the	DET
ejpam-5742	223	21	following	follow	VERB
ejpam-5742	223	22	lemma	lemma	PROPN
ejpam-5742	223	23	is	be	AUX
ejpam-5742	223	24	straightforward	straightforward	ADJ
ejpam-5742	223	25	to	to	PART
ejpam-5742	223	26	prove	prove	VERB
ejpam-5742	223	27	,	,	PUNCT
ejpam-5742	223	28	so	so	ADV
ejpam-5742	223	29	we	we	PRON
ejpam-5742	223	30	omit	omit	VERB
ejpam-5742	223	31	the	the	DET
ejpam-5742	223	32	proof	proof	NOUN
ejpam-5742	223	33	.	.	PUNCT
ejpam-5742	224	1	lemma	lemma	PROPN
ejpam-5742	224	2	3	3	X
ejpam-5742	224	3	.	.	X
ejpam-5742	225	1	for	for	ADP
ejpam-5742	225	2	any	any	DET
ejpam-5742	225	3	prime	prime	ADJ
ejpam-5742	225	4	filter	filter	NOUN
ejpam-5742	225	5	s	s	NOUN
ejpam-5742	225	6	of	of	ADP
ejpam-5742	225	7	r	r	NOUN
ejpam-5742	225	8	,	,	PUNCT
ejpam-5742	225	9	h(s	h(s	PROPN
ejpam-5742	225	10	)	)	PUNCT
ejpam-5742	225	11	is	be	AUX
ejpam-5742	225	12	a	a	DET
ejpam-5742	225	13	filter	filter	NOUN
ejpam-5742	225	14	of	of	ADP
ejpam-5742	225	15	r	r	NOUN
ejpam-5742	225	16	contained	contain	VERB
ejpam-5742	225	17	in	in	ADP
ejpam-5742	225	18	s.	s.	PROPN
ejpam-5742	225	19	lemma	lemma	PROPN
ejpam-5742	225	20	4	4	X
ejpam-5742	225	21	.	.	X
ejpam-5742	226	1	for	for	ADP
ejpam-5742	226	2	any	any	DET
ejpam-5742	226	3	prime	prime	ADJ
ejpam-5742	226	4	filter	filter	NOUN
ejpam-5742	226	5	s	s	NOUN
ejpam-5742	226	6	of	of	ADP
ejpam-5742	226	7	r	r	NOUN
ejpam-5742	226	8	,	,	PUNCT
ejpam-5742	226	9	h(x	h(x	PROPN
ejpam-5742	226	10	)	)	PUNCT
ejpam-5742	226	11	=	=	PUNCT
ejpam-5742	226	12	m(r	m(r	VERB
ejpam-5742	226	13	\	\	PUNCT
ejpam-5742	226	14	x	x	PUNCT
ejpam-5742	226	15	)	)	PUNCT
ejpam-5742	226	16	.	.	PUNCT
ejpam-5742	227	1	proof	proof	NOUN
ejpam-5742	227	2	.	.	PUNCT
ejpam-5742	228	1	let	let	VERB
ejpam-5742	228	2	κ	κ	PROPN
ejpam-5742	228	3	∈	∈	PROPN
ejpam-5742	228	4	h(x	h(x	PROPN
ejpam-5742	228	5	)	)	PUNCT
ejpam-5742	228	6	.	.	PUNCT
ejpam-5742	229	1	then	then	ADV
ejpam-5742	229	2	κ	κ	PROPN
ejpam-5742	229	3	∨	∨	PROPN
ejpam-5742	229	4	η	η	PROPN
ejpam-5742	229	5	∈	∈	PROPN
ejpam-5742	229	6	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	229	7	)	)	PUNCT
ejpam-5742	229	8	,	,	PUNCT
ejpam-5742	229	9	for	for	ADP
ejpam-5742	229	10	some	some	DET
ejpam-5742	229	11	η	η	PROPN
ejpam-5742	229	12	∈	∈	PROPN
ejpam-5742	229	13	r	r	NOUN
ejpam-5742	229	14	\	\	PUNCT
ejpam-5742	229	15	x	x	X
ejpam-5742	229	16	.	.	PUNCT
ejpam-5742	230	1	since	since	SCONJ
ejpam-5742	230	2	r	r	NOUN
ejpam-5742	230	3	\	\	PUNCT
ejpam-5742	230	4	x	x	PUNCT
ejpam-5742	230	5	is	be	AUX
ejpam-5742	230	6	an	an	DET
ejpam-5742	230	7	ideal	ideal	NOUN
ejpam-5742	230	8	of	of	ADP
ejpam-5742	230	9	r	r	NOUN
ejpam-5742	230	10	,	,	PUNCT
ejpam-5742	230	11	we	we	PRON
ejpam-5742	230	12	get	get	VERB
ejpam-5742	230	13	that	that	DET
ejpam-5742	230	14	κ	κ	PROPN
ejpam-5742	230	15	∈	∈	PROPN
ejpam-5742	230	16	m(r\x	m(r\x	PROPN
ejpam-5742	230	17	)	)	PUNCT
ejpam-5742	230	18	and	and	CCONJ
ejpam-5742	230	19	hence	hence	ADV
ejpam-5742	230	20	h(x	h(x	PROPN
ejpam-5742	230	21	)	)	PUNCT
ejpam-5742	230	22	⊆	⊆	NUM
ejpam-5742	230	23	m(r\x	m(r\x	PROPN
ejpam-5742	230	24	)	)	PUNCT
ejpam-5742	230	25	.	.	PUNCT
ejpam-5742	231	1	similarly	similarly	ADV
ejpam-5742	231	2	,	,	PUNCT
ejpam-5742	231	3	we	we	PRON
ejpam-5742	231	4	get	get	VERB
ejpam-5742	231	5	that	that	DET
ejpam-5742	231	6	m(r	m(r	VERB
ejpam-5742	231	7	\	\	PUNCT
ejpam-5742	231	8	x	x	SYM
ejpam-5742	231	9	)	)	PUNCT
ejpam-5742	231	10	⊆	⊆	NUM
ejpam-5742	231	11	h(x	h(x	PROPN
ejpam-5742	231	12	)	)	PUNCT
ejpam-5742	231	13	.	.	PUNCT
ejpam-5742	232	1	therefore	therefore	ADV
ejpam-5742	232	2	h(x	h(x	PROPN
ejpam-5742	232	3	)	)	PUNCT
ejpam-5742	233	1	=	=	PUNCT
ejpam-5742	233	2	m(r	m(r	VERB
ejpam-5742	233	3	\	\	PUNCT
ejpam-5742	233	4	x	x	SYM
ejpam-5742	233	5	)	)	PUNCT
ejpam-5742	233	6	.	.	PUNCT
ejpam-5742	234	1	theorem	theorem	ADJ
ejpam-5742	234	2	6	6	NUM
ejpam-5742	234	3	.	.	PUNCT
ejpam-5742	235	1	let	let	AUX
ejpam-5742	235	2	{	{	PUNCT
ejpam-5742	235	3	tα}α∈	tα}α∈	VERB
ejpam-5742	235	4	△	△	X
ejpam-5742	235	5	be	be	VERB
ejpam-5742	235	6	a	a	DET
ejpam-5742	235	7	class	class	NOUN
ejpam-5742	235	8	of	of	ADP
ejpam-5742	235	9	m−filters	m−filter	NOUN
ejpam-5742	235	10	of	of	ADP
ejpam-5742	235	11	an	an	DET
ejpam-5742	235	12	adl	adl	PROPN
ejpam-5742	235	13	r.	r.	PROPN
ejpam-5742	235	14	then	then	ADV
ejpam-5742	235	15	⋂	⋂	PROPN
ejpam-5742	235	16	α∈	α∈	PROPN
ejpam-5742	235	17	△	△	PROPN
ejpam-5742	235	18	tα	tα	PROPN
ejpam-5742	235	19	is	be	AUX
ejpam-5742	235	20	an	an	DET
ejpam-5742	235	21	m−filter	m−filter	NOUN
ejpam-5742	235	22	of	of	ADP
ejpam-5742	235	23	r.	r.	NOUN
ejpam-5742	235	24	proof	proof	NOUN
ejpam-5742	235	25	.	.	PUNCT
ejpam-5742	236	1	for	for	SCONJ
ejpam-5742	236	2	each	each	DET
ejpam-5742	236	3	α	α	PROPN
ejpam-5742	236	4	∈	∈	PROPN
ejpam-5742	236	5	△	△	PROPN
ejpam-5742	236	6	,	,	PUNCT
ejpam-5742	236	7	let	let	VERB
ejpam-5742	236	8	tα	tα	PROPN
ejpam-5742	236	9	=	=	SYM
ejpam-5742	236	10	m(fα	m(fα	PROPN
ejpam-5742	236	11	)	)	PUNCT
ejpam-5742	236	12	where	where	SCONJ
ejpam-5742	236	13	fα	fα	NOUN
ejpam-5742	236	14	is	be	AUX
ejpam-5742	236	15	an	an	DET
ejpam-5742	236	16	ideal	ideal	NOUN
ejpam-5742	236	17	of	of	ADP
ejpam-5742	236	18	r.	r.	PROPN
ejpam-5742	236	19	then	then	ADV
ejpam-5742	236	20	{	{	PUNCT
ejpam-5742	236	21	fα}α∈	fα}α∈	X
ejpam-5742	236	22	△	△	X
ejpam-5742	236	23	will	will	AUX
ejpam-5742	236	24	be	be	AUX
ejpam-5742	236	25	an	an	DET
ejpam-5742	236	26	arbitrary	arbitrary	ADJ
ejpam-5742	236	27	family	family	NOUN
ejpam-5742	236	28	of	of	ADP
ejpam-5742	236	29	ideals	ideal	NOUN
ejpam-5742	236	30	in	in	ADP
ejpam-5742	236	31	r.	r.	PROPN
ejpam-5742	236	32	for	for	ADP
ejpam-5742	236	33	each	each	DET
ejpam-5742	236	34	α	α	PROPN
ejpam-5742	236	35	∈	∈	PROPN
ejpam-5742	236	36	△	△	PROPN
ejpam-5742	236	37	.	.	PUNCT
ejpam-5742	237	1	hence	hence	ADV
ejpam-5742	237	2	⋂	⋂	PROPN
ejpam-5742	237	3	α∈	α∈	NOUN
ejpam-5742	237	4	△	△	X
ejpam-5742	237	5	fα	fα	NOUN
ejpam-5742	237	6	is	be	AUX
ejpam-5742	237	7	an	an	DET
ejpam-5742	237	8	ideal	ideal	NOUN
ejpam-5742	237	9	of	of	ADP
ejpam-5742	237	10	r.	r.	PROPN
ejpam-5742	237	11	thus	thus	ADV
ejpam-5742	237	12	we	we	PRON
ejpam-5742	237	13	get	get	VERB
ejpam-5742	237	14	⋂	⋂	PROPN
ejpam-5742	237	15	α∈	α∈	NOUN
ejpam-5742	237	16	△	△	X
ejpam-5742	237	17	m(fα	m(fα	PROPN
ejpam-5742	237	18	)	)	PUNCT
ejpam-5742	237	19	=	=	SYM
ejpam-5742	238	1	m	m	PROPN
ejpam-5742	238	2	(	(	PUNCT
ejpam-5742	238	3	⋂	⋂	PROPN
ejpam-5742	238	4	α∈	α∈	NOUN
ejpam-5742	238	5	△	△	X
ejpam-5742	238	6	fα	fα	ADP
ejpam-5742	238	7	)	)	PUNCT
ejpam-5742	238	8	.	.	PUNCT
ejpam-5742	239	1	therefore	therefore	ADV
ejpam-5742	239	2	⋂	⋂	PROPN
ejpam-5742	239	3	α∈	α∈	PROPN
ejpam-5742	239	4	△	△	PROPN
ejpam-5742	239	5	tα	tα	PROPN
ejpam-5742	239	6	is	be	AUX
ejpam-5742	239	7	an	an	DET
ejpam-5742	239	8	m−filter	m−filter	NOUN
ejpam-5742	239	9	of	of	ADP
ejpam-5742	239	10	r.	r.	PROPN
ejpam-5742	239	11	theorem	theorem	NOUN
ejpam-5742	239	12	7	7	NUM
ejpam-5742	239	13	.	.	PUNCT
ejpam-5742	240	1	let	let	VERB
ejpam-5742	240	2	f	f	PROPN
ejpam-5742	240	3	,	,	PUNCT
ejpam-5742	240	4	g	g	PROPN
ejpam-5742	240	5	be	be	AUX
ejpam-5742	240	6	two	two	NUM
ejpam-5742	240	7	ideals	ideal	NOUN
ejpam-5742	240	8	of	of	ADP
ejpam-5742	240	9	an	an	DET
ejpam-5742	240	10	adl	adl	PROPN
ejpam-5742	240	11	r.	r.	PROPN
ejpam-5742	240	12	then	then	ADV
ejpam-5742	240	13	m(f∨g	m(f∨g	PROPN
ejpam-5742	240	14	)	)	PUNCT
ejpam-5742	240	15	is	be	AUX
ejpam-5742	240	16	the	the	DET
ejpam-5742	240	17	smallest	small	ADJ
ejpam-5742	240	18	m−filter	m−filter	NOUN
ejpam-5742	240	19	containing	contain	VERB
ejpam-5742	240	20	both	both	DET
ejpam-5742	240	21	m(f	m(f	PROPN
ejpam-5742	240	22	)	)	PUNCT
ejpam-5742	240	23	and	and	CCONJ
ejpam-5742	240	24	m(g	m(g	NOUN
ejpam-5742	240	25	)	)	PUNCT
ejpam-5742	240	26	.	.	PUNCT
ejpam-5742	241	1	proof	proof	NOUN
ejpam-5742	241	2	.	.	PUNCT
ejpam-5742	242	1	clearly	clearly	ADV
ejpam-5742	242	2	,	,	PUNCT
ejpam-5742	242	3	we	we	PRON
ejpam-5742	242	4	get	get	VERB
ejpam-5742	242	5	m(f	m(f	PROPN
ejpam-5742	242	6	)	)	PUNCT
ejpam-5742	243	1	⊆	⊆	NUM
ejpam-5742	243	2	m(f	m(f	PROPN
ejpam-5742	243	3	∨	∨	NUM
ejpam-5742	243	4	g	g	NOUN
ejpam-5742	243	5	)	)	PUNCT
ejpam-5742	243	6	and	and	CCONJ
ejpam-5742	243	7	m(g	m(g	NOUN
ejpam-5742	243	8	)	)	PUNCT
ejpam-5742	243	9	⊆	⊆	NUM
ejpam-5742	243	10	m(f	m(f	PROPN
ejpam-5742	243	11	∨	∨	NUM
ejpam-5742	243	12	g	g	NOUN
ejpam-5742	243	13	)	)	PUNCT
ejpam-5742	243	14	.	.	PUNCT
ejpam-5742	243	15	suppose	suppose	VERB
ejpam-5742	243	16	m(f	m(f	NOUN
ejpam-5742	243	17	)	)	PUNCT
ejpam-5742	243	18	⊆	⊆	NUM
ejpam-5742	243	19	m(v	m(v	NOUN
ejpam-5742	243	20	)	)	PUNCT
ejpam-5742	243	21	and	and	CCONJ
ejpam-5742	243	22	m(g	m(g	NOUN
ejpam-5742	243	23	)	)	PUNCT
ejpam-5742	243	24	⊆	⊆	NUM
ejpam-5742	243	25	m(v	m(v	NOUN
ejpam-5742	243	26	)	)	PUNCT
ejpam-5742	243	27	,	,	PUNCT
ejpam-5742	243	28	for	for	ADP
ejpam-5742	243	29	some	some	DET
ejpam-5742	243	30	ideal	ideal	ADJ
ejpam-5742	243	31	v	v	NOUN
ejpam-5742	243	32	of	of	ADP
ejpam-5742	243	33	r.	r.	PROPN
ejpam-5742	243	34	let	let	VERB
ejpam-5742	243	35	θ	θ	PROPN
ejpam-5742	243	36	∈	∈	PROPN
ejpam-5742	243	37	m(f	m(f	PROPN
ejpam-5742	243	38	∨	∨	NUM
ejpam-5742	243	39	g	g	NOUN
ejpam-5742	243	40	)	)	PUNCT
ejpam-5742	243	41	.	.	PUNCT
ejpam-5742	244	1	then	then	ADV
ejpam-5742	244	2	there	there	PRON
ejpam-5742	244	3	exist	exist	VERB
ejpam-5742	244	4	χ	χ	DET
ejpam-5742	244	5	∈	∈	PROPN
ejpam-5742	244	6	f	f	PROPN
ejpam-5742	244	7	and	and	CCONJ
ejpam-5742	244	8	υ	υ	PROPN
ejpam-5742	244	9	∈	∈	PROPN
ejpam-5742	244	10	g	g	NOUN
ejpam-5742	244	11	such	such	ADJ
ejpam-5742	244	12	that	that	SCONJ
ejpam-5742	244	13	θ	θ	PROPN
ejpam-5742	244	14	∨	∨	NOUN
ejpam-5742	244	15	(	(	PUNCT
ejpam-5742	244	16	χ	χ	PROPN
ejpam-5742	244	17	∨	∨	NUM
ejpam-5742	244	18	υ	υ	NOUN
ejpam-5742	244	19	)	)	PUNCT
ejpam-5742	244	20	∈	∈	PROPN
ejpam-5742	244	21	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	244	22	)	)	PUNCT
ejpam-5742	244	23	.	.	PUNCT
ejpam-5742	245	1	therefore	therefore	ADV
ejpam-5742	245	2	θ	θ	X
ejpam-5742	245	3	∨	∨	NUM
ejpam-5742	245	4	χ	χ	PROPN
ejpam-5742	245	5	∈	∈	PROPN
ejpam-5742	245	6	m(g	m(g	PROPN
ejpam-5742	245	7	)	)	PUNCT
ejpam-5742	245	8	⊆	⊆	NUM
ejpam-5742	245	9	m(v	m(v	NOUN
ejpam-5742	245	10	)	)	PUNCT
ejpam-5742	245	11	.	.	PUNCT
ejpam-5742	246	1	there	there	PRON
ejpam-5742	246	2	exists	exist	VERB
ejpam-5742	246	3	µ	µ	PRON
ejpam-5742	246	4	∈	∈	NOUN
ejpam-5742	246	5	v	v	ADP
ejpam-5742	246	6	such	such	ADJ
ejpam-5742	246	7	that	that	SCONJ
ejpam-5742	246	8	θ	θ	PROPN
ejpam-5742	246	9	∨	∨	PROPN
ejpam-5742	246	10	χ∨	χ∨	PROPN
ejpam-5742	246	11	µ	µ	PROPN
ejpam-5742	246	12	∈	∈	PROPN
ejpam-5742	246	13	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	246	14	)	)	PUNCT
ejpam-5742	246	15	.	.	PUNCT
ejpam-5742	247	1	since	since	SCONJ
ejpam-5742	247	2	µ∨	µ∨	NOUN
ejpam-5742	247	3	π	π	PROPN
ejpam-5742	247	4	∈	∈	PROPN
ejpam-5742	247	5	v	v	NOUN
ejpam-5742	247	6	,	,	PUNCT
ejpam-5742	247	7	we	we	PRON
ejpam-5742	247	8	get	get	VERB
ejpam-5742	247	9	θ	θ	PROPN
ejpam-5742	247	10	∈	∈	PROPN
ejpam-5742	247	11	m(v	m(v	NOUN
ejpam-5742	247	12	)	)	PUNCT
ejpam-5742	247	13	.	.	PUNCT
ejpam-5742	248	1	therefore	therefore	ADV
ejpam-5742	248	2	m(f	m(f	PROPN
ejpam-5742	248	3	∨	∨	NUM
ejpam-5742	248	4	g	g	NOUN
ejpam-5742	248	5	)	)	PUNCT
ejpam-5742	248	6	is	be	AUX
ejpam-5742	248	7	the	the	DET
ejpam-5742	248	8	supremum	supremum	NOUN
ejpam-5742	248	9	of	of	ADP
ejpam-5742	248	10	m(f	m(f	PROPN
ejpam-5742	248	11	)	)	PUNCT
ejpam-5742	248	12	and	and	CCONJ
ejpam-5742	248	13	m(g	m(g	PROPN
ejpam-5742	248	14	)	)	PUNCT
ejpam-5742	248	15	.	.	PUNCT
ejpam-5742	249	1	corollary	corollary	ADJ
ejpam-5742	249	2	1	1	NUM
ejpam-5742	249	3	.	.	PUNCT
ejpam-5742	250	1	let	let	AUX
ejpam-5742	250	2	{	{	PUNCT
ejpam-5742	250	3	m(fα)}α∈	m(fα)}α∈	NOUN
ejpam-5742	250	4	△	△	NOUN
ejpam-5742	250	5	be	be	VERB
ejpam-5742	250	6	a	a	DET
ejpam-5742	250	7	class	class	NOUN
ejpam-5742	250	8	of	of	ADP
ejpam-5742	250	9	m−filters	m−filter	NOUN
ejpam-5742	250	10	of	of	ADP
ejpam-5742	250	11	an	an	DET
ejpam-5742	250	12	adl	adl	NOUN
ejpam-5742	250	13	r	r	NOUN
ejpam-5742	250	14	,	,	PUNCT
ejpam-5742	250	15	for	for	ADP
ejpam-5742	250	16	each	each	DET
ejpam-5742	250	17	α	α	PROPN
ejpam-5742	250	18	∈	∈	PROPN
ejpam-5742	250	19	△	△	PROPN
ejpam-5742	250	20	.	.	PUNCT
ejpam-5742	251	1	then	then	ADV
ejpam-5742	251	2	⊔	⊔	PROPN
ejpam-5742	251	3	α∈	α∈	PROPN
ejpam-5742	251	4	△	△	PROPN
ejpam-5742	251	5	m(fα	m(fα	PROPN
ejpam-5742	251	6	)	)	PUNCT
ejpam-5742	251	7	is	be	AUX
ejpam-5742	251	8	the	the	DET
ejpam-5742	251	9	smallest	small	ADJ
ejpam-5742	251	10	m−filter	m−filter	NOUN
ejpam-5742	251	11	containing	contain	VERB
ejpam-5742	251	12	each	each	DET
ejpam-5742	251	13	m(fα	m(fα	PROPN
ejpam-5742	251	14	)	)	PUNCT
ejpam-5742	251	15	.	.	PUNCT
ejpam-5742	252	1	the	the	DET
ejpam-5742	252	2	set	set	NOUN
ejpam-5742	252	3	of	of	ADP
ejpam-5742	252	4	all	all	DET
ejpam-5742	252	5	m−filters	m−filter	NOUN
ejpam-5742	252	6	of	of	ADP
ejpam-5742	252	7	r	r	NOUN
ejpam-5742	252	8	is	be	AUX
ejpam-5742	252	9	denoted	denote	VERB
ejpam-5742	252	10	by	by	ADP
ejpam-5742	252	11	fm(r	fm(r	NUM
ejpam-5742	252	12	)	)	PUNCT
ejpam-5742	252	13	theorem	theorem	NOUN
ejpam-5742	252	14	8	8	NUM
ejpam-5742	252	15	.	.	PUNCT
ejpam-5742	253	1	let	let	AUX
ejpam-5742	253	2	fm(r	fm(r	PUNCT
ejpam-5742	253	3	)	)	PUNCT
ejpam-5742	253	4	be	be	AUX
ejpam-5742	253	5	a	a	DET
ejpam-5742	253	6	sublattice	sublattice	NOUN
ejpam-5742	253	7	of	of	ADP
ejpam-5742	253	8	f(r	f(r	NOUN
ejpam-5742	253	9	)	)	PUNCT
ejpam-5742	253	10	.	.	PUNCT
ejpam-5742	254	1	if	if	SCONJ
ejpam-5742	254	2	{	{	PUNCT
ejpam-5742	254	3	tα}α∈	tα}α∈	NOUN
ejpam-5742	254	4	△	△	X
ejpam-5742	254	5	be	be	VERB
ejpam-5742	254	6	any	any	DET
ejpam-5742	254	7	class	class	NOUN
ejpam-5742	254	8	of	of	ADP
ejpam-5742	254	9	m−filters	m−filter	NOUN
ejpam-5742	254	10	of	of	ADP
ejpam-5742	254	11	r	r	NOUN
ejpam-5742	254	12	,	,	PUNCT
ejpam-5742	254	13	then	then	ADV
ejpam-5742	254	14	∨	∨	NUM
ejpam-5742	254	15	α∈	α∈	NOUN
ejpam-5742	254	16	△	△	PROPN
ejpam-5742	254	17	tα	tα	PROPN
ejpam-5742	254	18	is	be	AUX
ejpam-5742	254	19	again	again	ADV
ejpam-5742	254	20	an	an	DET
ejpam-5742	254	21	m−filter	m−filter	NOUN
ejpam-5742	254	22	of	of	ADP
ejpam-5742	254	23	r.	r.	PROPN
ejpam-5742	254	24	n.	n.	PROPN
ejpam-5742	254	25	rafi	rafi	PROPN
ejpam-5742	254	26	,	,	PUNCT
ejpam-5742	254	27	t.	t.	PROPN
ejpam-5742	254	28	gaketem	gaketem	PROPN
ejpam-5742	254	29	,	,	PUNCT
ejpam-5742	254	30	r.	r.	PROPN
ejpam-5742	254	31	k.	k.	PROPN
ejpam-5742	254	32	bandaru	bandaru	PROPN
ejpam-5742	254	33	/	/	SYM
ejpam-5742	254	34	eur	eur	PROPN
ejpam-5742	254	35	.	.	PUNCT
ejpam-5742	255	1	j.	j.	PROPN
ejpam-5742	255	2	pure	pure	PROPN
ejpam-5742	255	3	appl	appl	PROPN
ejpam-5742	255	4	.	.	PROPN
ejpam-5742	255	5	math	math	PROPN
ejpam-5742	255	6	,	,	PUNCT
ejpam-5742	255	7	18	18	NUM
ejpam-5742	255	8	(	(	PUNCT
ejpam-5742	255	9	2	2	NUM
ejpam-5742	255	10	)	)	PUNCT
ejpam-5742	255	11	(	(	PUNCT
ejpam-5742	255	12	2025	2025	NUM
ejpam-5742	255	13	)	)	PUNCT
ejpam-5742	255	14	,	,	PUNCT
ejpam-5742	255	15	5742	5742	NUM
ejpam-5742	255	16	8	8	NUM
ejpam-5742	255	17	of	of	ADP
ejpam-5742	255	18	14	14	NUM
ejpam-5742	255	19	proof	proof	NOUN
ejpam-5742	255	20	.	.	PUNCT
ejpam-5742	256	1	for	for	SCONJ
ejpam-5742	256	2	each	each	DET
ejpam-5742	256	3	α	α	PROPN
ejpam-5742	256	4	∈	∈	PROPN
ejpam-5742	256	5	△	△	PROPN
ejpam-5742	256	6	,	,	PUNCT
ejpam-5742	256	7	let	let	VERB
ejpam-5742	256	8	tα	tα	PROPN
ejpam-5742	256	9	=	=	SYM
ejpam-5742	256	10	m(fα	m(fα	PROPN
ejpam-5742	256	11	)	)	PUNCT
ejpam-5742	256	12	where	where	SCONJ
ejpam-5742	256	13	fα	fα	NOUN
ejpam-5742	256	14	is	be	AUX
ejpam-5742	256	15	an	an	DET
ejpam-5742	256	16	ideal	ideal	NOUN
ejpam-5742	256	17	of	of	ADP
ejpam-5742	256	18	r.	r.	PROPN
ejpam-5742	256	19	then	then	ADV
ejpam-5742	256	20	{	{	PUNCT
ejpam-5742	256	21	fα}α∈	fα}α∈	X
ejpam-5742	256	22	△	△	X
ejpam-5742	256	23	will	will	AUX
ejpam-5742	256	24	be	be	AUX
ejpam-5742	256	25	any	any	DET
ejpam-5742	256	26	class	class	NOUN
ejpam-5742	256	27	family	family	NOUN
ejpam-5742	256	28	of	of	ADP
ejpam-5742	256	29	ideals	ideal	NOUN
ejpam-5742	256	30	of	of	ADP
ejpam-5742	256	31	r.	r.	PROPN
ejpam-5742	256	32	since	since	SCONJ
ejpam-5742	256	33	tα	tα	PROPN
ejpam-5742	256	34	=	=	SYM
ejpam-5742	256	35	m(fα	m(fα	PROPN
ejpam-5742	256	36	)	)	PUNCT
ejpam-5742	256	37	⊆	⊆	NUM
ejpam-5742	256	38	m(∨fα	m(∨fα	NOUN
ejpam-5742	256	39	)	)	PUNCT
ejpam-5742	256	40	for	for	ADP
ejpam-5742	256	41	each	each	DET
ejpam-5742	256	42	α	α	NOUN
ejpam-5742	256	43	∈	∈	PROPN
ejpam-5742	256	44	△	△	PROPN
ejpam-5742	256	45	,	,	PUNCT
ejpam-5742	256	46	we	we	PRON
ejpam-5742	256	47	get	get	VERB
ejpam-5742	256	48	∨	∨	NUM
ejpam-5742	256	49	tα	tα	PROPN
ejpam-5742	256	50	⊆	⊆	NUM
ejpam-5742	256	51	m	m	PROPN
ejpam-5742	256	52	(	(	PUNCT
ejpam-5742	256	53	∨	∨	NUM
ejpam-5742	256	54	fα	fα	NOUN
ejpam-5742	256	55	)	)	PUNCT
ejpam-5742	256	56	.	.	PUNCT
ejpam-5742	257	1	let	let	VERB
ejpam-5742	257	2	θ	θ	PROPN
ejpam-5742	257	3	∈	∈	PROPN
ejpam-5742	257	4	m	m	PROPN
ejpam-5742	257	5	(	(	PUNCT
ejpam-5742	257	6	∨	∨	NUM
ejpam-5742	257	7	fα	fα	NOUN
ejpam-5742	257	8	)	)	PUNCT
ejpam-5742	257	9	.	.	PUNCT
ejpam-5742	258	1	then	then	ADV
ejpam-5742	258	2	there	there	PRON
ejpam-5742	258	3	exists	exist	VERB
ejpam-5742	258	4	χ	χ	PRON
ejpam-5742	258	5	∈	∈	PROPN
ejpam-5742	258	6	∨	∨	NUM
ejpam-5742	258	7	fα	fα	ADP
ejpam-5742	258	8	such	such	ADJ
ejpam-5742	258	9	that	that	SCONJ
ejpam-5742	258	10	θ∨χ	θ∨χ	PROPN
ejpam-5742	258	11	∈	∈	PROPN
ejpam-5742	258	12	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	258	13	)	)	PUNCT
ejpam-5742	258	14	.	.	PUNCT
ejpam-5742	259	1	then	then	ADV
ejpam-5742	259	2	there	there	PRON
ejpam-5742	259	3	exists	exist	VERB
ejpam-5742	259	4	a	a	DET
ejpam-5742	259	5	positive	positive	ADJ
ejpam-5742	259	6	integer	integer	NOUN
ejpam-5742	259	7	n	n	CCONJ
ejpam-5742	259	8	such	such	ADJ
ejpam-5742	259	9	that	that	SCONJ
ejpam-5742	259	10	χ	χ	NOUN
ejpam-5742	259	11	=	=	PUNCT
ejpam-5742	259	12	χ1∨χ2∨	χ1∨χ2∨	PROPN
ejpam-5742	259	13	·	·	PUNCT
ejpam-5742	259	14	·	·	PUNCT
ejpam-5742	259	15	·	·	PUNCT
ejpam-5742	259	16	∨χn	∨χn	NOUN
ejpam-5742	259	17	where	where	SCONJ
ejpam-5742	259	18	χi	χi	NOUN
ejpam-5742	259	19	∈	∈	PROPN
ejpam-5742	259	20	fαi	fαi	NOUN
ejpam-5742	259	21	.	.	PUNCT
ejpam-5742	260	1	thus	thus	ADV
ejpam-5742	260	2	we	we	PRON
ejpam-5742	260	3	get	get	VERB
ejpam-5742	260	4	θ∨χ	θ∨χ	NOUN
ejpam-5742	260	5	∈	∈	PROPN
ejpam-5742	260	6	mmax.elt(r	mmax.elt(r	NOUN
ejpam-5742	260	7	)	)	PUNCT
ejpam-5742	260	8	⇒	⇒	PROPN
ejpam-5742	260	9	θ∨(χ1∨χ2∨	θ∨(χ1∨χ2∨	PROPN
ejpam-5742	260	10	·	·	PUNCT
ejpam-5742	260	11	·	·	PUNCT
ejpam-5742	260	12	·	·	PUNCT
ejpam-5742	260	13	∨χn	∨χn	NOUN
ejpam-5742	260	14	)	)	PUNCT
ejpam-5742	260	15	∈	∈	PROPN
ejpam-5742	260	16	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	260	17	)	)	PUNCT
ejpam-5742	260	18	⇒	⇒	NOUN
ejpam-5742	260	19	(	(	PUNCT
ejpam-5742	260	20	θ∨χ1)∨	θ∨χ1)∨	NOUN
ejpam-5742	260	21	(	(	PUNCT
ejpam-5742	260	22	θ∨χ2)∨	θ∨χ2)∨	PROPN
ejpam-5742	260	23	·	·	PUNCT
ejpam-5742	260	24	·	·	PUNCT
ejpam-5742	260	25	·	·	PUNCT
ejpam-5742	260	26	∨	∨	X
ejpam-5742	260	27	(	(	PUNCT
ejpam-5742	260	28	θ∨χn	θ∨χn	NOUN
ejpam-5742	260	29	)	)	PUNCT
ejpam-5742	260	30	∈	∈	PROPN
ejpam-5742	260	31	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	260	32	)	)	PUNCT
ejpam-5742	260	33	⇒	⇒	NOUN
ejpam-5742	260	34	(	(	PUNCT
ejpam-5742	260	35	θ∨χ1]∨	θ∨χ1]∨	X
ejpam-5742	260	36	(	(	PUNCT
ejpam-5742	260	37	θ∨χ2]∨	θ∨χ2]∨	PROPN
ejpam-5742	260	38	·	·	PUNCT
ejpam-5742	260	39	·	·	PUNCT
ejpam-5742	260	40	·	·	PUNCT
ejpam-5742	260	41	∨	∨	X
ejpam-5742	260	42	(	(	PUNCT
ejpam-5742	260	43	θ∨χn	θ∨χn	NOUN
ejpam-5742	260	44	]	]	PUNCT
ejpam-5742	260	45	=	=	SYM
ejpam-5742	260	46	r	r	NOUN
ejpam-5742	260	47	⇒	⇒	NOUN
ejpam-5742	260	48	m((θ∨χ1])∨m((θ∨χ2])∨	m((θ∨χ1])∨m((θ∨χ2])∨	NOUN
ejpam-5742	260	49	·	·	PUNCT
ejpam-5742	260	50	·	·	PUNCT
ejpam-5742	260	51	·	·	PUNCT
ejpam-5742	260	52	∨m((θ∨χn	∨m((θ∨χn	NOUN
ejpam-5742	260	53	]	]	X
ejpam-5742	260	54	)	)	PUNCT
ejpam-5742	261	1	=	=	SYM
ejpam-5742	261	2	r	r	NOUN
ejpam-5742	261	3	⇒	⇒	NOUN
ejpam-5742	261	4	(	(	PUNCT
ejpam-5742	261	5	θ∨χ1	θ∨χ1	PROPN
ejpam-5742	261	6	)	)	PUNCT
ejpam-5742	261	7	+	+	NOUN
ejpam-5742	261	8	∨(θ∨χ2	∨(θ∨χ2	X
ejpam-5742	261	9	)	)	PUNCT
ejpam-5742	261	10	+	+	NOUN
ejpam-5742	261	11	∨	∨	NOUN
ejpam-5742	261	12	·	·	SYM
ejpam-5742	261	13	·	·	PUNCT
ejpam-5742	261	14	·	·	PUNCT
ejpam-5742	261	15	∨(θ∨χn	∨(θ∨χn	NOUN
ejpam-5742	261	16	)	)	PUNCT
ejpam-5742	261	17	+	+	PUNCT
ejpam-5742	261	18	=	=	SYM
ejpam-5742	261	19	r.	r.	NOUN
ejpam-5742	261	20	since	since	SCONJ
ejpam-5742	261	21	θ	θ	PROPN
ejpam-5742	261	22	∈	∈	PROPN
ejpam-5742	261	23	r	r	NOUN
ejpam-5742	261	24	we	we	PRON
ejpam-5742	261	25	get	get	VERB
ejpam-5742	261	26	θ	θ	PROPN
ejpam-5742	261	27	∈	∈	PROPN
ejpam-5742	261	28	(	(	PUNCT
ejpam-5742	261	29	θ∨χ1	θ∨χ1	PROPN
ejpam-5742	261	30	)	)	PUNCT
ejpam-5742	261	31	+	+	NOUN
ejpam-5742	261	32	∨(θ∨χ2	∨(θ∨χ2	X
ejpam-5742	261	33	)	)	PUNCT
ejpam-5742	261	34	+	+	NOUN
ejpam-5742	261	35	∨	∨	NOUN
ejpam-5742	261	36	·	·	SYM
ejpam-5742	261	37	·	·	PUNCT
ejpam-5742	261	38	·	·	PUNCT
ejpam-5742	261	39	∨(θ∨χn	∨(θ∨χn	NOUN
ejpam-5742	261	40	)	)	PUNCT
ejpam-5742	262	1	+	+	X
ejpam-5742	262	2	.	.	PUNCT
ejpam-5742	263	1	then	then	ADV
ejpam-5742	263	2	there	there	PRON
ejpam-5742	263	3	exists	exist	VERB
ejpam-5742	263	4	υi	υi	PRON
ejpam-5742	263	5	∈	∈	PROPN
ejpam-5742	263	6	(	(	PUNCT
ejpam-5742	263	7	θ∨χi	θ∨χi	X
ejpam-5742	263	8	)	)	PUNCT
ejpam-5742	263	9	+	+	CCONJ
ejpam-5742	263	10	for	for	ADP
ejpam-5742	263	11	i	i	PRON
ejpam-5742	263	12	=	=	NOUN
ejpam-5742	263	13	1	1	NUM
ejpam-5742	263	14	,	,	PUNCT
ejpam-5742	263	15	2	2	NUM
ejpam-5742	263	16	,	,	PUNCT
ejpam-5742	263	17	·	·	PUNCT
ejpam-5742	263	18	·	·	PUNCT
ejpam-5742	263	19	·	·	PUNCT
ejpam-5742	263	20	,	,	PUNCT
ejpam-5742	263	21	n	n	PRON
ejpam-5742	264	1	such	such	ADJ
ejpam-5742	264	2	that	that	SCONJ
ejpam-5742	264	3	θ	θ	PROPN
ejpam-5742	264	4	=	=	SYM
ejpam-5742	264	5	υ1∧υ2∧	υ1∧υ2∧	PROPN
ejpam-5742	264	6	·	·	PUNCT
ejpam-5742	264	7	·	·	PUNCT
ejpam-5742	264	8	·	·	PUNCT
ejpam-5742	264	9	∧υn	∧υn	NOUN
ejpam-5742	264	10	.	.	PUNCT
ejpam-5742	265	1	now	now	ADV
ejpam-5742	265	2	,	,	PUNCT
ejpam-5742	265	3	θ	θ	X
ejpam-5742	265	4	=	=	SYM
ejpam-5742	265	5	θ∨θ	θ∨θ	NOUN
ejpam-5742	265	6	=	=	PUNCT
ejpam-5742	265	7	θ∨(υ1∧υ2∧	θ∨(υ1∧υ2∧	PROPN
ejpam-5742	265	8	·	·	PUNCT
ejpam-5742	265	9	·	·	PUNCT
ejpam-5742	265	10	·	·	PUNCT
ejpam-5742	265	11	∧υn	∧υn	NOUN
ejpam-5742	265	12	)	)	PUNCT
ejpam-5742	265	13	=	=	PUNCT
ejpam-5742	265	14	(	(	PUNCT
ejpam-5742	265	15	θ∨υ1)∧(θ∨υ2)∧	θ∨υ1)∧(θ∨υ2)∧	X
ejpam-5742	265	16	·	·	PUNCT
ejpam-5742	265	17	·	·	PUNCT
ejpam-5742	265	18	·	·	PUNCT
ejpam-5742	265	19	∧(θ∨υn	∧(θ∨υn	NOUN
ejpam-5742	265	20	)	)	PUNCT
ejpam-5742	265	21	∈	∈	PROPN
ejpam-5742	265	22	(	(	PUNCT
ejpam-5742	265	23	χ1	χ1	NOUN
ejpam-5742	265	24	)	)	PUNCT
ejpam-5742	265	25	+	+	NOUN
ejpam-5742	265	26	∨(χ2	∨(χ2	NOUN
ejpam-5742	265	27	)	)	PUNCT
ejpam-5742	265	28	+	+	NOUN
ejpam-5742	265	29	∨	∨	NOUN
ejpam-5742	265	30	·	·	PUNCT
ejpam-5742	265	31	·	·	PUNCT
ejpam-5742	265	32	·	·	PUNCT
ejpam-5742	265	33	∨(χn	∨(χn	NOUN
ejpam-5742	265	34	)	)	PUNCT
ejpam-5742	265	35	+	+	CCONJ
ejpam-5742	265	36	⊆	⊆	NUM
ejpam-5742	265	37	m(f1)∨m(f2)∨	m(f1)∨m(f2)∨	X
ejpam-5742	265	38	·	·	PUNCT
ejpam-5742	265	39	·	·	PUNCT
ejpam-5742	265	40	·	·	PUNCT
ejpam-5742	265	41	∨m(fn	∨m(fn	PROPN
ejpam-5742	265	42	)	)	PUNCT
ejpam-5742	265	43	=	=	PUNCT
ejpam-5742	265	44	t1	t1	PROPN
ejpam-5742	265	45	∨	∨	NUM
ejpam-5742	265	46	t2	t2	PROPN
ejpam-5742	265	47	∨	∨	NUM
ejpam-5742	265	48	·	·	PUNCT
ejpam-5742	265	49	·	·	PUNCT
ejpam-5742	265	50	·	·	PUNCT
ejpam-5742	266	1	∨	∨	NUM
ejpam-5742	266	2	tn	tn	PROPN
ejpam-5742	266	3	⊆	⊆	NUM
ejpam-5742	266	4	∨tα	∨tα	NOUN
ejpam-5742	266	5	.	.	PUNCT
ejpam-5742	267	1	that	that	PRON
ejpam-5742	267	2	implies	imply	VERB
ejpam-5742	267	3	m	m	PROPN
ejpam-5742	267	4	(	(	PUNCT
ejpam-5742	267	5	∨	∨	NUM
ejpam-5742	267	6	fα	fα	NOUN
ejpam-5742	267	7	)	)	PUNCT
ejpam-5742	267	8	⊆	⊆	NUM
ejpam-5742	267	9	∨tα	∨tα	NOUN
ejpam-5742	267	10	.	.	PUNCT
ejpam-5742	268	1	thus	thus	ADV
ejpam-5742	268	2	∨	∨	NUM
ejpam-5742	268	3	tα	tα	PROPN
ejpam-5742	268	4	is	be	AUX
ejpam-5742	268	5	an	an	DET
ejpam-5742	268	6	m−filter	m−filter	NOUN
ejpam-5742	268	7	of	of	ADP
ejpam-5742	268	8	r.	r.	PROPN
ejpam-5742	268	9	theorem	theorem	NOUN
ejpam-5742	268	10	9	9	NUM
ejpam-5742	268	11	.	.	PUNCT
ejpam-5742	269	1	consider	consider	VERB
ejpam-5742	269	2	the	the	DET
ejpam-5742	269	3	set	set	NOUN
ejpam-5742	269	4	fm(r	fm(r	NOUN
ejpam-5742	269	5	)	)	PUNCT
ejpam-5742	269	6	of	of	ADP
ejpam-5742	269	7	all	all	DET
ejpam-5742	269	8	m−filters	m−filter	NOUN
ejpam-5742	269	9	of	of	ADP
ejpam-5742	269	10	r	r	NOUN
ejpam-5742	269	11	is	be	AUX
ejpam-5742	269	12	a	a	DET
ejpam-5742	269	13	sublattice	sublattice	NOUN
ejpam-5742	269	14	of	of	ADP
ejpam-5742	269	15	f(r	f(r	NOUN
ejpam-5742	269	16	)	)	PUNCT
ejpam-5742	269	17	.	.	PUNCT
ejpam-5742	270	1	for	for	ADP
ejpam-5742	270	2	any	any	DET
ejpam-5742	270	3	filter	filter	NOUN
ejpam-5742	270	4	t	t	NOUN
ejpam-5742	270	5	,	,	PUNCT
ejpam-5742	270	6	there	there	PRON
ejpam-5742	270	7	exists	exist	VERB
ejpam-5742	270	8	a	a	DET
ejpam-5742	270	9	unique	unique	ADJ
ejpam-5742	270	10	m−filter	m−filter	NOUN
ejpam-5742	270	11	contained	contain	VERB
ejpam-5742	270	12	in	in	ADP
ejpam-5742	270	13	t	t	PROPN
ejpam-5742	270	14	.	.	PUNCT
ejpam-5742	271	1	proof	proof	NOUN
ejpam-5742	271	2	.	.	PUNCT
ejpam-5742	272	1	let	let	VERB
ejpam-5742	272	2	t	t	NOUN
ejpam-5742	272	3	be	be	AUX
ejpam-5742	272	4	any	any	DET
ejpam-5742	272	5	filter	filter	NOUN
ejpam-5742	272	6	of	of	ADP
ejpam-5742	272	7	r.	r.	PROPN
ejpam-5742	272	8	consider	consider	VERB
ejpam-5742	272	9	m	m	VERB
ejpam-5742	272	10	=	=	PUNCT
ejpam-5742	272	11	{	{	PUNCT
ejpam-5742	272	12	u	u	NOUN
ejpam-5742	272	13	∈	∈	PROPN
ejpam-5742	272	14	fm(r	fm(r	PRON
ejpam-5742	272	15	)	)	PUNCT
ejpam-5742	273	1	|	|	ADV
ejpam-5742	273	2	u	u	NOUN
ejpam-5742	273	3	⊆	⊆	NUM
ejpam-5742	273	4	t	t	NOUN
ejpam-5742	273	5	}	}	PUNCT
ejpam-5742	273	6	.	.	PUNCT
ejpam-5742	274	1	since	since	SCONJ
ejpam-5742	274	2	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	274	3	)	)	PUNCT
ejpam-5742	274	4	is	be	AUX
ejpam-5742	274	5	the	the	DET
ejpam-5742	274	6	m−filter	m−filter	NOUN
ejpam-5742	274	7	and	and	CCONJ
ejpam-5742	274	8	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	274	9	)	)	PUNCT
ejpam-5742	274	10	⊆	⊆	NUM
ejpam-5742	274	11	t	t	NOUN
ejpam-5742	274	12	,	,	PUNCT
ejpam-5742	274	13	we	we	PRON
ejpam-5742	274	14	get	get	VERB
ejpam-5742	274	15	mmax.elt(r	mmax.elt(r	NOUN
ejpam-5742	274	16	)	)	PUNCT
ejpam-5742	274	17	∈	∈	PROPN
ejpam-5742	274	18	m.	m.	NOUN
ejpam-5742	274	19	clearly	clearly	ADV
ejpam-5742	274	20	,	,	PUNCT
ejpam-5742	274	21	m	m	VERB
ejpam-5742	274	22	satisfies	satisfy	VERB
ejpam-5742	274	23	the	the	DET
ejpam-5742	274	24	hypothesis	hypothesis	NOUN
ejpam-5742	274	25	of	of	ADP
ejpam-5742	274	26	zorn	zorn	PROPN
ejpam-5742	274	27	’s	’s	PART
ejpam-5742	274	28	lemma	lemma	PROPN
ejpam-5742	274	29	.	.	PUNCT
ejpam-5742	275	1	then	then	ADV
ejpam-5742	275	2	m	m	PROPN
ejpam-5742	275	3	has	have	VERB
ejpam-5742	275	4	a	a	DET
ejpam-5742	275	5	maximal	maximal	ADJ
ejpam-5742	275	6	element	element	NOUN
ejpam-5742	275	7	let	let	VERB
ejpam-5742	275	8	it	it	PRON
ejpam-5742	275	9	be	be	AUX
ejpam-5742	275	10	n	n	PRON
ejpam-5742	275	11	.	.	PUNCT
ejpam-5742	276	1	it	it	PRON
ejpam-5742	276	2	is	be	AUX
ejpam-5742	276	3	enough	enough	ADJ
ejpam-5742	276	4	to	to	PART
ejpam-5742	276	5	show	show	VERB
ejpam-5742	276	6	that	that	SCONJ
ejpam-5742	276	7	n	n	PRON
ejpam-5742	276	8	is	be	AUX
ejpam-5742	276	9	unique	unique	ADJ
ejpam-5742	276	10	.	.	PUNCT
ejpam-5742	277	1	let	let	VERB
ejpam-5742	277	2	y	y	PRON
ejpam-5742	277	3	be	be	AUX
ejpam-5742	277	4	any	any	DET
ejpam-5742	277	5	maximal	maximal	ADJ
ejpam-5742	277	6	element	element	NOUN
ejpam-5742	277	7	of	of	ADP
ejpam-5742	277	8	m	m	PRON
ejpam-5742	277	9	such	such	ADJ
ejpam-5742	277	10	that	that	SCONJ
ejpam-5742	277	11	n	n	PROPN
ejpam-5742	277	12	⊆	⊆	NUM
ejpam-5742	277	13	y.	y.	PROPN
ejpam-5742	277	14	clearly	clearly	ADV
ejpam-5742	277	15	,	,	PUNCT
ejpam-5742	277	16	n	n	PRON
ejpam-5742	277	17	∨y	∨y	VERB
ejpam-5742	277	18	⊆	⊆	NUM
ejpam-5742	277	19	t	t	NOUN
ejpam-5742	277	20	.	.	PUNCT
ejpam-5742	278	1	hence	hence	ADV
ejpam-5742	278	2	n	n	DET
ejpam-5742	278	3	∨y	∨y	PROPN
ejpam-5742	278	4	∈	∈	PROPN
ejpam-5742	278	5	m.	m.	NOUN
ejpam-5742	278	6	therefore	therefore	ADV
ejpam-5742	278	7	n	n	CCONJ
ejpam-5742	278	8	=	=	SYM
ejpam-5742	278	9	n	n	PRON
ejpam-5742	278	10	∨y	∨y	NOUN
ejpam-5742	278	11	=	=	SYM
ejpam-5742	278	12	y.	y.	NOUN
ejpam-5742	278	13	thus	thus	ADV
ejpam-5742	278	14	m	m	AUX
ejpam-5742	278	15	has	have	VERB
ejpam-5742	278	16	a	a	DET
ejpam-5742	278	17	unique	unique	ADJ
ejpam-5742	278	18	maximal	maximal	ADJ
ejpam-5742	278	19	element	element	NOUN
ejpam-5742	278	20	,	,	PUNCT
ejpam-5742	278	21	which	which	PRON
ejpam-5742	278	22	is	be	AUX
ejpam-5742	278	23	the	the	DET
ejpam-5742	278	24	required	require	VERB
ejpam-5742	278	25	m−filter	m−filter	NOUN
ejpam-5742	278	26	contained	contain	VERB
ejpam-5742	278	27	in	in	ADP
ejpam-5742	278	28	t	t	PROPN
ejpam-5742	278	29	.	.	PUNCT
ejpam-5742	279	1	definition	definition	NOUN
ejpam-5742	279	2	8	8	NUM
ejpam-5742	279	3	.	.	PUNCT
ejpam-5742	280	1	a	a	DET
ejpam-5742	280	2	filter	filter	NOUN
ejpam-5742	280	3	s	s	NOUN
ejpam-5742	280	4	of	of	ADP
ejpam-5742	280	5	r	r	NOUN
ejpam-5742	280	6	is	be	AUX
ejpam-5742	280	7	referred	refer	VERB
ejpam-5742	280	8	as	as	ADP
ejpam-5742	280	9	co	co	NOUN
ejpam-5742	280	10	-	-	ADJ
ejpam-5742	280	11	dense	dense	ADJ
ejpam-5742	280	12	if	if	SCONJ
ejpam-5742	280	13	s+	s+	ADV
ejpam-5742	280	14	=	=	SYM
ejpam-5742	280	15	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	280	16	)	)	PUNCT
ejpam-5742	280	17	.	.	PUNCT
ejpam-5742	281	1	example	example	NOUN
ejpam-5742	282	1	4	4	X
ejpam-5742	282	2	.	.	PUNCT
ejpam-5742	283	1	let	let	VERB
ejpam-5742	283	2	r	r	NOUN
ejpam-5742	283	3	=	=	SYM
ejpam-5742	283	4	{	{	PUNCT
ejpam-5742	283	5	0	0	NUM
ejpam-5742	283	6	,	,	PUNCT
ejpam-5742	283	7	1	1	NUM
ejpam-5742	283	8	,	,	PUNCT
ejpam-5742	283	9	2	2	NUM
ejpam-5742	283	10	,	,	PUNCT
ejpam-5742	283	11	3	3	NUM
ejpam-5742	283	12	,	,	PUNCT
ejpam-5742	283	13	4	4	NUM
ejpam-5742	283	14	,	,	PUNCT
ejpam-5742	283	15	5	5	NUM
ejpam-5742	283	16	,	,	PUNCT
ejpam-5742	283	17	6	6	NUM
ejpam-5742	283	18	,	,	PUNCT
ejpam-5742	283	19	7	7	NUM
ejpam-5742	283	20	}	}	PUNCT
ejpam-5742	283	21	and	and	CCONJ
ejpam-5742	283	22	define	define	VERB
ejpam-5742	283	23	∨	∨	NUM
ejpam-5742	283	24	,	,	PUNCT
ejpam-5742	283	25	∧	∧	NOUN
ejpam-5742	283	26	on	on	ADP
ejpam-5742	283	27	r	r	NOUN
ejpam-5742	283	28	as	as	SCONJ
ejpam-5742	283	29	follows	follow	VERB
ejpam-5742	283	30	:	:	PUNCT
ejpam-5742	283	31	∧	∧	NOUN
ejpam-5742	283	32	0	0	NUM
ejpam-5742	283	33	1	1	NUM
ejpam-5742	283	34	2	2	NUM
ejpam-5742	283	35	3	3	NUM
ejpam-5742	283	36	4	4	NUM
ejpam-5742	283	37	5	5	NUM
ejpam-5742	283	38	6	6	NUM
ejpam-5742	283	39	7	7	NUM
ejpam-5742	283	40	0	0	NUM
ejpam-5742	283	41	0	0	NUM
ejpam-5742	283	42	0	0	NUM
ejpam-5742	283	43	0	0	NUM
ejpam-5742	283	44	0	0	NUM
ejpam-5742	283	45	0	0	NUM
ejpam-5742	283	46	0	0	NUM
ejpam-5742	283	47	0	0	NUM
ejpam-5742	283	48	0	0	NUM
ejpam-5742	283	49	1	1	NUM
ejpam-5742	283	50	0	0	NUM
ejpam-5742	283	51	1	1	NUM
ejpam-5742	283	52	2	2	NUM
ejpam-5742	283	53	3	3	NUM
ejpam-5742	283	54	4	4	NUM
ejpam-5742	283	55	5	5	NUM
ejpam-5742	283	56	6	6	NUM
ejpam-5742	283	57	7	7	NUM
ejpam-5742	283	58	2	2	NUM
ejpam-5742	283	59	0	0	NUM
ejpam-5742	283	60	1	1	NUM
ejpam-5742	283	61	2	2	NUM
ejpam-5742	283	62	3	3	NUM
ejpam-5742	283	63	4	4	NUM
ejpam-5742	283	64	5	5	NUM
ejpam-5742	283	65	6	6	NUM
ejpam-5742	283	66	7	7	NUM
ejpam-5742	283	67	3	3	NUM
ejpam-5742	283	68	0	0	NUM
ejpam-5742	283	69	3	3	NUM
ejpam-5742	283	70	3	3	NUM
ejpam-5742	283	71	3	3	NUM
ejpam-5742	283	72	0	0	NUM
ejpam-5742	283	73	0	0	NUM
ejpam-5742	283	74	3	3	NUM
ejpam-5742	283	75	0	0	NUM
ejpam-5742	283	76	4	4	NUM
ejpam-5742	283	77	0	0	NUM
ejpam-5742	283	78	4	4	NUM
ejpam-5742	283	79	5	5	NUM
ejpam-5742	283	80	0	0	NUM
ejpam-5742	283	81	4	4	NUM
ejpam-5742	283	82	5	5	NUM
ejpam-5742	283	83	7	7	NUM
ejpam-5742	283	84	7	7	NUM
ejpam-5742	283	85	5	5	NUM
ejpam-5742	283	86	0	0	NUM
ejpam-5742	283	87	4	4	NUM
ejpam-5742	283	88	5	5	NUM
ejpam-5742	283	89	0	0	NUM
ejpam-5742	283	90	4	4	NUM
ejpam-5742	283	91	5	5	NUM
ejpam-5742	283	92	7	7	NUM
ejpam-5742	283	93	7	7	NUM
ejpam-5742	283	94	6	6	NUM
ejpam-5742	283	95	0	0	NUM
ejpam-5742	283	96	6	6	NUM
ejpam-5742	283	97	6	6	NUM
ejpam-5742	283	98	3	3	NUM
ejpam-5742	283	99	7	7	NUM
ejpam-5742	283	100	7	7	NUM
ejpam-5742	283	101	6	6	NUM
ejpam-5742	283	102	7	7	NUM
ejpam-5742	283	103	7	7	NUM
ejpam-5742	283	104	0	0	NUM
ejpam-5742	283	105	7	7	NUM
ejpam-5742	283	106	7	7	NUM
ejpam-5742	283	107	0	0	NUM
ejpam-5742	283	108	7	7	NUM
ejpam-5742	283	109	7	7	NUM
ejpam-5742	283	110	7	7	NUM
ejpam-5742	283	111	7	7	NUM
ejpam-5742	283	112	∨	∨	NUM
ejpam-5742	283	113	0	0	NUM
ejpam-5742	283	114	1	1	NUM
ejpam-5742	283	115	2	2	NUM
ejpam-5742	283	116	3	3	NUM
ejpam-5742	283	117	4	4	NUM
ejpam-5742	283	118	5	5	NUM
ejpam-5742	283	119	6	6	NUM
ejpam-5742	283	120	7	7	NUM
ejpam-5742	283	121	0	0	NUM
ejpam-5742	283	122	0	0	NUM
ejpam-5742	283	123	1	1	NUM
ejpam-5742	283	124	2	2	NUM
ejpam-5742	283	125	3	3	NUM
ejpam-5742	283	126	4	4	NUM
ejpam-5742	283	127	5	5	NUM
ejpam-5742	283	128	6	6	NUM
ejpam-5742	283	129	7	7	NUM
ejpam-5742	283	130	1	1	NUM
ejpam-5742	283	131	1	1	NUM
ejpam-5742	283	132	1	1	NUM
ejpam-5742	283	133	1	1	NUM
ejpam-5742	283	134	1	1	NUM
ejpam-5742	283	135	1	1	NUM
ejpam-5742	283	136	1	1	NUM
ejpam-5742	283	137	1	1	NUM
ejpam-5742	283	138	1	1	NUM
ejpam-5742	283	139	2	2	NUM
ejpam-5742	283	140	2	2	NUM
ejpam-5742	283	141	2	2	NUM
ejpam-5742	283	142	2	2	NUM
ejpam-5742	283	143	2	2	NUM
ejpam-5742	283	144	2	2	NUM
ejpam-5742	283	145	2	2	NUM
ejpam-5742	283	146	2	2	NUM
ejpam-5742	283	147	2	2	NUM
ejpam-5742	283	148	3	3	NUM
ejpam-5742	283	149	3	3	NUM
ejpam-5742	283	150	1	1	NUM
ejpam-5742	283	151	2	2	NUM
ejpam-5742	283	152	3	3	NUM
ejpam-5742	283	153	1	1	NUM
ejpam-5742	283	154	2	2	NUM
ejpam-5742	283	155	6	6	NUM
ejpam-5742	283	156	6	6	NUM
ejpam-5742	283	157	4	4	NUM
ejpam-5742	283	158	4	4	NUM
ejpam-5742	283	159	1	1	NUM
ejpam-5742	283	160	1	1	NUM
ejpam-5742	283	161	1	1	NUM
ejpam-5742	283	162	4	4	NUM
ejpam-5742	283	163	4	4	NUM
ejpam-5742	283	164	1	1	NUM
ejpam-5742	283	165	4	4	NUM
ejpam-5742	283	166	5	5	NUM
ejpam-5742	283	167	5	5	NUM
ejpam-5742	283	168	2	2	NUM
ejpam-5742	283	169	2	2	NUM
ejpam-5742	283	170	2	2	NUM
ejpam-5742	283	171	5	5	NUM
ejpam-5742	283	172	5	5	NUM
ejpam-5742	283	173	2	2	NUM
ejpam-5742	283	174	5	5	NUM
ejpam-5742	283	175	6	6	NUM
ejpam-5742	283	176	6	6	NUM
ejpam-5742	283	177	1	1	NUM
ejpam-5742	283	178	2	2	NUM
ejpam-5742	283	179	6	6	NUM
ejpam-5742	283	180	1	1	NUM
ejpam-5742	283	181	2	2	NUM
ejpam-5742	283	182	6	6	NUM
ejpam-5742	283	183	6	6	NUM
ejpam-5742	283	184	7	7	NUM
ejpam-5742	283	185	7	7	NUM
ejpam-5742	283	186	1	1	NUM
ejpam-5742	283	187	2	2	NUM
ejpam-5742	283	188	6	6	NUM
ejpam-5742	283	189	4	4	NUM
ejpam-5742	283	190	5	5	NUM
ejpam-5742	283	191	6	6	NUM
ejpam-5742	283	192	7	7	NUM
ejpam-5742	283	193	then	then	ADV
ejpam-5742	283	194	(	(	PUNCT
ejpam-5742	283	195	r,∨	r,∨	PROPN
ejpam-5742	283	196	,	,	PUNCT
ejpam-5742	283	197	∧	∧	PROPN
ejpam-5742	283	198	)	)	PUNCT
ejpam-5742	283	199	is	be	AUX
ejpam-5742	283	200	an	an	DET
ejpam-5742	283	201	adl	adl	PROPN
ejpam-5742	283	202	.	.	PUNCT
ejpam-5742	284	1	clearly	clearly	ADV
ejpam-5742	284	2	a	a	DET
ejpam-5742	284	3	filter	filter	NOUN
ejpam-5742	284	4	s	s	PART
ejpam-5742	284	5	=	=	X
ejpam-5742	284	6	{	{	PUNCT
ejpam-5742	284	7	1	1	NUM
ejpam-5742	284	8	,	,	PUNCT
ejpam-5742	284	9	2	2	NUM
ejpam-5742	284	10	,	,	PUNCT
ejpam-5742	284	11	4	4	NUM
ejpam-5742	284	12	,	,	PUNCT
ejpam-5742	284	13	5	5	NUM
ejpam-5742	284	14	,	,	PUNCT
ejpam-5742	284	15	6	6	NUM
ejpam-5742	284	16	,	,	PUNCT
ejpam-5742	284	17	7	7	NUM
ejpam-5742	284	18	}	}	PUNCT
ejpam-5742	284	19	is	be	AUX
ejpam-5742	284	20	a	a	DET
ejpam-5742	284	21	co	co	ADJ
ejpam-5742	284	22	-	-	ADJ
ejpam-5742	284	23	dense	dense	ADJ
ejpam-5742	284	24	filter	filter	NOUN
ejpam-5742	284	25	of	of	ADP
ejpam-5742	284	26	r.	r.	PROPN
ejpam-5742	284	27	lemma	lemma	PROPN
ejpam-5742	284	28	5	5	NUM
ejpam-5742	284	29	.	.	PUNCT
ejpam-5742	285	1	any	any	DET
ejpam-5742	285	2	non	non	ADJ
ejpam-5742	285	3	co	co	ADJ
ejpam-5742	285	4	-	-	ADJ
ejpam-5742	285	5	dense	dense	ADJ
ejpam-5742	285	6	prime	prime	ADJ
ejpam-5742	285	7	filter	filter	NOUN
ejpam-5742	285	8	of	of	ADP
ejpam-5742	285	9	an	an	DET
ejpam-5742	285	10	adl	adl	NOUN
ejpam-5742	285	11	is	be	AUX
ejpam-5742	285	12	an	an	DET
ejpam-5742	285	13	m−filter	m−filter	NOUN
ejpam-5742	285	14	.	.	PUNCT
ejpam-5742	286	1	proof	proof	NOUN
ejpam-5742	286	2	.	.	PUNCT
ejpam-5742	287	1	let	let	VERB
ejpam-5742	287	2	s	s	PRON
ejpam-5742	287	3	be	be	AUX
ejpam-5742	287	4	any	any	DET
ejpam-5742	287	5	non	non	ADJ
ejpam-5742	287	6	co	co	ADJ
ejpam-5742	287	7	-	-	ADJ
ejpam-5742	287	8	dense	dense	ADJ
ejpam-5742	287	9	prime	prime	ADJ
ejpam-5742	287	10	filter	filter	NOUN
ejpam-5742	287	11	of	of	ADP
ejpam-5742	287	12	r.	r.	PROPN
ejpam-5742	287	13	then	then	ADV
ejpam-5742	287	14	there	there	PRON
ejpam-5742	287	15	exists	exist	VERB
ejpam-5742	287	16	an	an	DET
ejpam-5742	287	17	element	element	NOUN
ejpam-5742	287	18	κ	κ	PROPN
ejpam-5742	287	19	/∈	/∈	PROPN
ejpam-5742	287	20	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	287	21	)	)	PUNCT
ejpam-5742	287	22	such	such	ADJ
ejpam-5742	287	23	that	that	SCONJ
ejpam-5742	287	24	κ	κ	PROPN
ejpam-5742	287	25	∈	∈	PROPN
ejpam-5742	287	26	s+	s+	ADV
ejpam-5742	287	27	.	.	PUNCT
ejpam-5742	288	1	that	that	PRON
ejpam-5742	288	2	implies	imply	VERB
ejpam-5742	288	3	[	[	X
ejpam-5742	288	4	κ	κ	X
ejpam-5742	288	5	)	)	PUNCT
ejpam-5742	288	6	⊆	⊆	NUM
ejpam-5742	288	7	s+	s+	ADV
ejpam-5742	288	8	and	and	CCONJ
ejpam-5742	288	9	hence	hence	ADV
ejpam-5742	288	10	s++	s++	NOUN
ejpam-5742	288	11	⊆	⊆	NUM
ejpam-5742	288	12	[	[	X
ejpam-5742	288	13	κ)+	κ)+	X
ejpam-5742	288	14	.	.	PUNCT
ejpam-5742	289	1	that	that	PRON
ejpam-5742	289	2	implies	imply	VERB
ejpam-5742	289	3	s	s	PRON
ejpam-5742	289	4	⊆	⊆	NUM
ejpam-5742	289	5	[	[	X
ejpam-5742	289	6	κ)+	κ)+	X
ejpam-5742	289	7	,	,	PUNCT
ejpam-5742	289	8	since	since	SCONJ
ejpam-5742	289	9	s	s	PRON
ejpam-5742	289	10	⊆	⊆	NUM
ejpam-5742	289	11	s++	s++	NOUN
ejpam-5742	289	12	.	.	PUNCT
ejpam-5742	290	1	let	let	VERB
ejpam-5742	290	2	τ	τ	PROPN
ejpam-5742	290	3	∈	∈	PROPN
ejpam-5742	290	4	[	[	X
ejpam-5742	290	5	κ)+	κ)+	X
ejpam-5742	290	6	.	.	PUNCT
ejpam-5742	291	1	then	then	ADV
ejpam-5742	291	2	τ	τ	PROPN
ejpam-5742	291	3	∨	∨	NUM
ejpam-5742	291	4	κ	κ	PROPN
ejpam-5742	291	5	∈	∈	PROPN
ejpam-5742	291	6	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	291	7	)	)	PUNCT
ejpam-5742	291	8	and	and	CCONJ
ejpam-5742	291	9	hence	hence	ADV
ejpam-5742	291	10	τ	τ	PROPN
ejpam-5742	291	11	∨	∨	NUM
ejpam-5742	291	12	κ	κ	PROPN
ejpam-5742	291	13	∈	∈	PROPN
ejpam-5742	291	14	s.	s.	PROPN
ejpam-5742	291	15	since	since	SCONJ
ejpam-5742	291	16	s	s	PROPN
ejpam-5742	291	17	is	be	AUX
ejpam-5742	291	18	prime	prime	ADJ
ejpam-5742	291	19	,	,	PUNCT
ejpam-5742	291	20	we	we	PRON
ejpam-5742	291	21	get	get	VERB
ejpam-5742	291	22	that	that	SCONJ
ejpam-5742	291	23	either	either	CCONJ
ejpam-5742	291	24	κ	κ	PROPN
ejpam-5742	291	25	∈	∈	PROPN
ejpam-5742	291	26	s	s	PART
ejpam-5742	291	27	or	or	CCONJ
ejpam-5742	291	28	τ	τ	PROPN
ejpam-5742	291	29	∈	∈	PROPN
ejpam-5742	291	30	s.	s.	PROPN
ejpam-5742	291	31	suppose	suppose	VERB
ejpam-5742	291	32	κ	κ	PROPN
ejpam-5742	291	33	∈	∈	PROPN
ejpam-5742	291	34	s.	s.	PROPN
ejpam-5742	291	35	since	since	SCONJ
ejpam-5742	291	36	n.	n.	PROPN
ejpam-5742	291	37	rafi	rafi	PROPN
ejpam-5742	291	38	,	,	PUNCT
ejpam-5742	291	39	t.	t.	PROPN
ejpam-5742	291	40	gaketem	gaketem	PROPN
ejpam-5742	291	41	,	,	PUNCT
ejpam-5742	291	42	r.	r.	PROPN
ejpam-5742	291	43	k.	k.	PROPN
ejpam-5742	291	44	bandaru	bandaru	PROPN
ejpam-5742	291	45	/	/	SYM
ejpam-5742	291	46	eur	eur	PROPN
ejpam-5742	291	47	.	.	PUNCT
ejpam-5742	292	1	j.	j.	PROPN
ejpam-5742	292	2	pure	pure	PROPN
ejpam-5742	292	3	appl	appl	PROPN
ejpam-5742	292	4	.	.	PROPN
ejpam-5742	292	5	math	math	PROPN
ejpam-5742	292	6	,	,	PUNCT
ejpam-5742	292	7	18	18	NUM
ejpam-5742	292	8	(	(	PUNCT
ejpam-5742	292	9	2	2	NUM
ejpam-5742	292	10	)	)	PUNCT
ejpam-5742	292	11	(	(	PUNCT
ejpam-5742	292	12	2025	2025	NUM
ejpam-5742	292	13	)	)	PUNCT
ejpam-5742	292	14	,	,	PUNCT
ejpam-5742	292	15	5742	5742	NUM
ejpam-5742	292	16	9	9	NUM
ejpam-5742	292	17	of	of	ADP
ejpam-5742	292	18	14	14	NUM
ejpam-5742	292	19	[	[	X
ejpam-5742	292	20	κ	κ	X
ejpam-5742	292	21	)	)	PUNCT
ejpam-5742	292	22	⊆	⊆	NUM
ejpam-5742	292	23	s+	s+	ADV
ejpam-5742	292	24	,	,	PUNCT
ejpam-5742	292	25	we	we	PRON
ejpam-5742	292	26	get	get	VERB
ejpam-5742	292	27	easily	easily	ADV
ejpam-5742	292	28	that	that	SCONJ
ejpam-5742	292	29	[	[	X
ejpam-5742	292	30	κ)∩s	κ)∩s	ADJ
ejpam-5742	292	31	=	=	SYM
ejpam-5742	292	32	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	292	33	)	)	PUNCT
ejpam-5742	292	34	.	.	PUNCT
ejpam-5742	293	1	that	that	PRON
ejpam-5742	293	2	implies	imply	VERB
ejpam-5742	293	3	κ	κ	PROPN
ejpam-5742	293	4	∈	∈	PROPN
ejpam-5742	293	5	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	293	6	)	)	PUNCT
ejpam-5742	293	7	,	,	PUNCT
ejpam-5742	293	8	which	which	PRON
ejpam-5742	293	9	is	be	AUX
ejpam-5742	293	10	a	a	DET
ejpam-5742	293	11	contradiction	contradiction	NOUN
ejpam-5742	293	12	to	to	ADP
ejpam-5742	293	13	κ	κ	PROPN
ejpam-5742	293	14	/∈	/∈	PROPN
ejpam-5742	293	15	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	293	16	)	)	PUNCT
ejpam-5742	293	17	.	.	PUNCT
ejpam-5742	294	1	which	which	PRON
ejpam-5742	294	2	gives	give	VERB
ejpam-5742	294	3	τ	τ	PROPN
ejpam-5742	294	4	∈	∈	NOUN
ejpam-5742	294	5	s	s	NOUN
ejpam-5742	294	6	and	and	CCONJ
ejpam-5742	294	7	hence	hence	ADV
ejpam-5742	295	1	[	[	X
ejpam-5742	295	2	κ)+	κ)+	PROPN
ejpam-5742	295	3	⊆	⊆	NUM
ejpam-5742	295	4	s.	s.	PROPN
ejpam-5742	295	5	thus	thus	ADV
ejpam-5742	295	6	s	s	VERB
ejpam-5742	295	7	=	=	PUNCT
ejpam-5742	296	1	[	[	X
ejpam-5742	296	2	κ)+	κ)+	X
ejpam-5742	296	3	=	=	SYM
ejpam-5742	296	4	m((κ	m((κ	PROPN
ejpam-5742	296	5	]	]	X
ejpam-5742	296	6	)	)	PUNCT
ejpam-5742	296	7	.	.	PUNCT
ejpam-5742	297	1	therefore	therefore	ADV
ejpam-5742	297	2	s	s	VERB
ejpam-5742	297	3	is	be	AUX
ejpam-5742	297	4	an	an	DET
ejpam-5742	297	5	m−filter	m−filter	NOUN
ejpam-5742	297	6	of	of	ADP
ejpam-5742	297	7	r.	r.	NOUN
ejpam-5742	297	8	we	we	PRON
ejpam-5742	297	9	will	will	AUX
ejpam-5742	297	10	now	now	ADV
ejpam-5742	297	11	present	present	VERB
ejpam-5742	297	12	the	the	DET
ejpam-5742	297	13	definition	definition	NOUN
ejpam-5742	297	14	of	of	ADP
ejpam-5742	297	15	an	an	DET
ejpam-5742	297	16	e−complemented	e−complemented	ADJ
ejpam-5742	297	17	adl	adl	PROPN
ejpam-5742	297	18	.	.	PUNCT
ejpam-5742	297	19	definition	definition	NOUN
ejpam-5742	297	20	9	9	NUM
ejpam-5742	297	21	.	.	PUNCT
ejpam-5742	298	1	an	an	DET
ejpam-5742	298	2	adl	adl	PROPN
ejpam-5742	298	3	r	r	NOUN
ejpam-5742	298	4	is	be	AUX
ejpam-5742	298	5	classified	classify	VERB
ejpam-5742	298	6	as	as	ADP
ejpam-5742	298	7	an	an	DET
ejpam-5742	298	8	e−complemented	e−complemented	ADJ
ejpam-5742	298	9	adl	adl	NOUN
ejpam-5742	298	10	if	if	SCONJ
ejpam-5742	298	11	,	,	PUNCT
ejpam-5742	298	12	for	for	ADP
ejpam-5742	298	13	every	every	DET
ejpam-5742	298	14	κ	κ	PROPN
ejpam-5742	298	15	∈	∈	PROPN
ejpam-5742	298	16	r	r	NOUN
ejpam-5742	298	17	,	,	PUNCT
ejpam-5742	298	18	there	there	PRON
ejpam-5742	298	19	exists	exist	VERB
ejpam-5742	298	20	η	η	PROPN
ejpam-5742	298	21	∈	∈	PROPN
ejpam-5742	298	22	r	r	NOUN
ejpam-5742	298	23	such	such	ADJ
ejpam-5742	298	24	that	that	SCONJ
ejpam-5742	298	25	both	both	PRON
ejpam-5742	298	26	κ	κ	PROPN
ejpam-5742	298	27	∧	∧	PROPN
ejpam-5742	298	28	η	η	PROPN
ejpam-5742	298	29	∈	∈	PROPN
ejpam-5742	298	30	e	e	PROPN
ejpam-5742	298	31	and	and	CCONJ
ejpam-5742	298	32	κ	κ	PROPN
ejpam-5742	298	33	∨	∨	PROPN
ejpam-5742	298	34	η	η	PROPN
ejpam-5742	298	35	∈	∈	PROPN
ejpam-5742	298	36	mmax.elt(r	mmax.elt(r	NOUN
ejpam-5742	298	37	)	)	PUNCT
ejpam-5742	298	38	hold	hold	VERB
ejpam-5742	298	39	true	true	ADJ
ejpam-5742	298	40	.	.	PUNCT
ejpam-5742	299	1	example	example	NOUN
ejpam-5742	299	2	5	5	NUM
ejpam-5742	299	3	.	.	X
ejpam-5742	300	1	consider	consider	VERB
ejpam-5742	300	2	two	two	NUM
ejpam-5742	300	3	discrete	discrete	ADJ
ejpam-5742	300	4	adls	adls	PROPN
ejpam-5742	300	5	a	a	PROPN
ejpam-5742	300	6	=	=	X
ejpam-5742	300	7	{	{	PUNCT
ejpam-5742	300	8	0	0	NUM
ejpam-5742	300	9	,	,	PUNCT
ejpam-5742	300	10	τ	τ	X
ejpam-5742	300	11	}	}	PUNCT
ejpam-5742	300	12	and	and	CCONJ
ejpam-5742	300	13	b	b	X
ejpam-5742	300	14	=	=	SYM
ejpam-5742	300	15	{	{	PUNCT
ejpam-5742	300	16	0	0	NUM
ejpam-5742	300	17	,	,	PUNCT
ejpam-5742	300	18	ν1	ν1	NOUN
ejpam-5742	300	19	,	,	PUNCT
ejpam-5742	300	20	ν2	ν2	NOUN
ejpam-5742	300	21	}	}	PUNCT
ejpam-5742	300	22	.	.	PUNCT
ejpam-5742	301	1	we	we	PRON
ejpam-5742	301	2	have	have	VERB
ejpam-5742	301	3	a×	a×	PROPN
ejpam-5742	301	4	b	b	NOUN
ejpam-5742	301	5	=	=	PRON
ejpam-5742	301	6	{	{	PUNCT
ejpam-5742	301	7	(	(	PUNCT
ejpam-5742	301	8	0	0	NUM
ejpam-5742	301	9	,	,	PUNCT
ejpam-5742	301	10	0	0	NUM
ejpam-5742	301	11	)	)	PUNCT
ejpam-5742	301	12	,	,	PUNCT
ejpam-5742	301	13	(	(	PUNCT
ejpam-5742	301	14	0	0	NUM
ejpam-5742	301	15	,	,	PUNCT
ejpam-5742	301	16	ν1	ν1	NOUN
ejpam-5742	301	17	)	)	PUNCT
ejpam-5742	301	18	,	,	PUNCT
ejpam-5742	301	19	(	(	PUNCT
ejpam-5742	301	20	0	0	NUM
ejpam-5742	301	21	,	,	PUNCT
ejpam-5742	301	22	ν2	ν2	NOUN
ejpam-5742	301	23	)	)	PUNCT
ejpam-5742	301	24	,	,	PUNCT
ejpam-5742	301	25	(	(	PUNCT
ejpam-5742	301	26	τ	τ	X
ejpam-5742	301	27	,	,	PUNCT
ejpam-5742	301	28	0	0	NUM
ejpam-5742	301	29	)	)	PUNCT
ejpam-5742	301	30	,	,	PUNCT
ejpam-5742	301	31	(	(	PUNCT
ejpam-5742	301	32	τ	τ	PROPN
ejpam-5742	301	33	,	,	PUNCT
ejpam-5742	301	34	ν1	ν1	PROPN
ejpam-5742	301	35	)	)	PUNCT
ejpam-5742	301	36	,	,	PUNCT
ejpam-5742	301	37	(	(	PUNCT
ejpam-5742	301	38	τ	τ	NOUN
ejpam-5742	301	39	,	,	PUNCT
ejpam-5742	301	40	ν2	ν2	NOUN
ejpam-5742	301	41	)	)	PUNCT
ejpam-5742	301	42	}	}	PUNCT
ejpam-5742	301	43	let	let	VERB
ejpam-5742	301	44	it	it	PRON
ejpam-5742	301	45	be	be	AUX
ejpam-5742	301	46	r.	r.	NOUN
ejpam-5742	301	47	define	define	VERB
ejpam-5742	301	48	∨	∨	NOUN
ejpam-5742	301	49	and	and	CCONJ
ejpam-5742	301	50	∧	∧	NOUN
ejpam-5742	301	51	on	on	ADP
ejpam-5742	301	52	r	r	NOUN
ejpam-5742	301	53	under	under	ADP
ejpam-5742	301	54	point	point	NOUN
ejpam-5742	301	55	-	-	PUNCT
ejpam-5742	301	56	wise	wise	ADJ
ejpam-5742	301	57	:	:	PUNCT
ejpam-5742	301	58	∨	∨	NUM
ejpam-5742	301	59	(	(	PUNCT
ejpam-5742	301	60	0	0	NUM
ejpam-5742	301	61	,	,	PUNCT
ejpam-5742	301	62	0	0	NUM
ejpam-5742	301	63	)	)	PUNCT
ejpam-5742	301	64	(	(	PUNCT
ejpam-5742	301	65	0	0	NUM
ejpam-5742	301	66	,	,	PUNCT
ejpam-5742	301	67	ν1	ν1	NOUN
ejpam-5742	301	68	)	)	PUNCT
ejpam-5742	301	69	(	(	PUNCT
ejpam-5742	301	70	0	0	NUM
ejpam-5742	301	71	,	,	PUNCT
ejpam-5742	301	72	ν2	ν2	NOUN
ejpam-5742	301	73	)	)	PUNCT
ejpam-5742	301	74	(	(	PUNCT
ejpam-5742	301	75	τ	τ	PROPN
ejpam-5742	301	76	,	,	PUNCT
ejpam-5742	301	77	0	0	NUM
ejpam-5742	301	78	)	)	PUNCT
ejpam-5742	301	79	(	(	PUNCT
ejpam-5742	301	80	τ	τ	PROPN
ejpam-5742	301	81	,	,	PUNCT
ejpam-5742	301	82	ν1	ν1	PROPN
ejpam-5742	301	83	)	)	PUNCT
ejpam-5742	301	84	(	(	PUNCT
ejpam-5742	301	85	τ	τ	PROPN
ejpam-5742	301	86	,	,	PUNCT
ejpam-5742	301	87	ν2	ν2	NOUN
ejpam-5742	301	88	)	)	PUNCT
ejpam-5742	301	89	(	(	PUNCT
ejpam-5742	301	90	0	0	NUM
ejpam-5742	301	91	,	,	PUNCT
ejpam-5742	301	92	0	0	NUM
ejpam-5742	301	93	)	)	PUNCT
ejpam-5742	301	94	(	(	PUNCT
ejpam-5742	301	95	0	0	NUM
ejpam-5742	301	96	,	,	PUNCT
ejpam-5742	301	97	0	0	NUM
ejpam-5742	301	98	)	)	PUNCT
ejpam-5742	301	99	(	(	PUNCT
ejpam-5742	301	100	0	0	NUM
ejpam-5742	301	101	,	,	PUNCT
ejpam-5742	301	102	ν1	ν1	NOUN
ejpam-5742	301	103	)	)	PUNCT
ejpam-5742	301	104	(	(	PUNCT
ejpam-5742	301	105	0	0	NUM
ejpam-5742	301	106	,	,	PUNCT
ejpam-5742	301	107	ν2	ν2	NOUN
ejpam-5742	301	108	)	)	PUNCT
ejpam-5742	301	109	(	(	PUNCT
ejpam-5742	301	110	τ	τ	PROPN
ejpam-5742	301	111	,	,	PUNCT
ejpam-5742	301	112	0	0	NUM
ejpam-5742	301	113	)	)	PUNCT
ejpam-5742	301	114	(	(	PUNCT
ejpam-5742	301	115	τ	τ	PROPN
ejpam-5742	301	116	,	,	PUNCT
ejpam-5742	301	117	ν1	ν1	PROPN
ejpam-5742	301	118	)	)	PUNCT
ejpam-5742	301	119	(	(	PUNCT
ejpam-5742	301	120	τ	τ	PROPN
ejpam-5742	301	121	,	,	PUNCT
ejpam-5742	301	122	ν2	ν2	NOUN
ejpam-5742	301	123	)	)	PUNCT
ejpam-5742	301	124	(	(	PUNCT
ejpam-5742	301	125	0	0	NUM
ejpam-5742	301	126	,	,	PUNCT
ejpam-5742	301	127	ν1	ν1	NOUN
ejpam-5742	301	128	)	)	PUNCT
ejpam-5742	301	129	(	(	PUNCT
ejpam-5742	301	130	0	0	NUM
ejpam-5742	301	131	,	,	PUNCT
ejpam-5742	301	132	ν1	ν1	NOUN
ejpam-5742	301	133	)	)	PUNCT
ejpam-5742	301	134	(	(	PUNCT
ejpam-5742	301	135	0	0	NUM
ejpam-5742	301	136	,	,	PUNCT
ejpam-5742	301	137	ν1	ν1	NOUN
ejpam-5742	301	138	)	)	PUNCT
ejpam-5742	301	139	(	(	PUNCT
ejpam-5742	301	140	0	0	NUM
ejpam-5742	301	141	,	,	PUNCT
ejpam-5742	301	142	ν1	ν1	NOUN
ejpam-5742	301	143	)	)	PUNCT
ejpam-5742	301	144	(	(	PUNCT
ejpam-5742	301	145	τ	τ	PROPN
ejpam-5742	301	146	,	,	PUNCT
ejpam-5742	301	147	ν1	ν1	PROPN
ejpam-5742	301	148	)	)	PUNCT
ejpam-5742	301	149	(	(	PUNCT
ejpam-5742	301	150	τ	τ	PROPN
ejpam-5742	301	151	,	,	PUNCT
ejpam-5742	301	152	ν1	ν1	PROPN
ejpam-5742	301	153	)	)	PUNCT
ejpam-5742	301	154	(	(	PUNCT
ejpam-5742	301	155	τ	τ	PROPN
ejpam-5742	301	156	,	,	PUNCT
ejpam-5742	301	157	ν1	ν1	PROPN
ejpam-5742	301	158	)	)	PUNCT
ejpam-5742	301	159	(	(	PUNCT
ejpam-5742	301	160	0	0	NUM
ejpam-5742	301	161	,	,	PUNCT
ejpam-5742	301	162	ν2	ν2	NOUN
ejpam-5742	301	163	)	)	PUNCT
ejpam-5742	301	164	(	(	PUNCT
ejpam-5742	301	165	0	0	NUM
ejpam-5742	301	166	,	,	PUNCT
ejpam-5742	301	167	ν2	ν2	NOUN
ejpam-5742	301	168	)	)	PUNCT
ejpam-5742	301	169	(	(	PUNCT
ejpam-5742	301	170	0	0	NUM
ejpam-5742	301	171	,	,	PUNCT
ejpam-5742	301	172	ν2	ν2	NOUN
ejpam-5742	301	173	)	)	PUNCT
ejpam-5742	301	174	(	(	PUNCT
ejpam-5742	301	175	0	0	NUM
ejpam-5742	301	176	,	,	PUNCT
ejpam-5742	301	177	ν2	ν2	NOUN
ejpam-5742	301	178	)	)	PUNCT
ejpam-5742	301	179	(	(	PUNCT
ejpam-5742	301	180	τ	τ	PROPN
ejpam-5742	301	181	,	,	PUNCT
ejpam-5742	301	182	ν2	ν2	PROPN
ejpam-5742	301	183	)	)	PUNCT
ejpam-5742	301	184	(	(	PUNCT
ejpam-5742	301	185	τ	τ	PROPN
ejpam-5742	301	186	,	,	PUNCT
ejpam-5742	301	187	ν2	ν2	PROPN
ejpam-5742	301	188	)	)	PUNCT
ejpam-5742	301	189	(	(	PUNCT
ejpam-5742	301	190	τ	τ	PROPN
ejpam-5742	301	191	,	,	PUNCT
ejpam-5742	301	192	ν2	ν2	PROPN
ejpam-5742	301	193	)	)	PUNCT
ejpam-5742	301	194	(	(	PUNCT
ejpam-5742	301	195	τ	τ	PROPN
ejpam-5742	301	196	,	,	PUNCT
ejpam-5742	301	197	0	0	NUM
ejpam-5742	301	198	)	)	PUNCT
ejpam-5742	301	199	(	(	PUNCT
ejpam-5742	301	200	τ	τ	PROPN
ejpam-5742	301	201	,	,	PUNCT
ejpam-5742	301	202	0	0	NUM
ejpam-5742	301	203	)	)	PUNCT
ejpam-5742	301	204	(	(	PUNCT
ejpam-5742	301	205	τ	τ	PROPN
ejpam-5742	301	206	,	,	PUNCT
ejpam-5742	301	207	ν1	ν1	PROPN
ejpam-5742	301	208	)	)	PUNCT
ejpam-5742	301	209	(	(	PUNCT
ejpam-5742	301	210	τ	τ	PROPN
ejpam-5742	301	211	,	,	PUNCT
ejpam-5742	301	212	ν2	ν2	PROPN
ejpam-5742	301	213	)	)	PUNCT
ejpam-5742	301	214	(	(	PUNCT
ejpam-5742	301	215	τ	τ	PROPN
ejpam-5742	301	216	,	,	PUNCT
ejpam-5742	301	217	0	0	NUM
ejpam-5742	301	218	)	)	PUNCT
ejpam-5742	301	219	(	(	PUNCT
ejpam-5742	301	220	τ	τ	PROPN
ejpam-5742	301	221	,	,	PUNCT
ejpam-5742	301	222	ν1	ν1	PROPN
ejpam-5742	301	223	)	)	PUNCT
ejpam-5742	301	224	(	(	PUNCT
ejpam-5742	301	225	τ	τ	PROPN
ejpam-5742	301	226	,	,	PUNCT
ejpam-5742	301	227	ν2	ν2	PROPN
ejpam-5742	301	228	)	)	PUNCT
ejpam-5742	301	229	(	(	PUNCT
ejpam-5742	301	230	τ	τ	PROPN
ejpam-5742	301	231	,	,	PUNCT
ejpam-5742	301	232	ν1	ν1	PROPN
ejpam-5742	301	233	)	)	PUNCT
ejpam-5742	301	234	(	(	PUNCT
ejpam-5742	301	235	τ	τ	PROPN
ejpam-5742	301	236	,	,	PUNCT
ejpam-5742	301	237	ν1	ν1	PROPN
ejpam-5742	301	238	)	)	PUNCT
ejpam-5742	301	239	(	(	PUNCT
ejpam-5742	301	240	τ	τ	PROPN
ejpam-5742	301	241	,	,	PUNCT
ejpam-5742	301	242	ν1	ν1	PROPN
ejpam-5742	301	243	)	)	PUNCT
ejpam-5742	301	244	(	(	PUNCT
ejpam-5742	301	245	τ	τ	PROPN
ejpam-5742	301	246	,	,	PUNCT
ejpam-5742	301	247	ν1	ν1	PROPN
ejpam-5742	301	248	)	)	PUNCT
ejpam-5742	301	249	(	(	PUNCT
ejpam-5742	301	250	τ	τ	PROPN
ejpam-5742	301	251	,	,	PUNCT
ejpam-5742	301	252	ν1	ν1	PROPN
ejpam-5742	301	253	)	)	PUNCT
ejpam-5742	301	254	(	(	PUNCT
ejpam-5742	301	255	τ	τ	PROPN
ejpam-5742	301	256	,	,	PUNCT
ejpam-5742	301	257	ν1	ν1	PROPN
ejpam-5742	301	258	)	)	PUNCT
ejpam-5742	301	259	(	(	PUNCT
ejpam-5742	301	260	τ	τ	PROPN
ejpam-5742	301	261	,	,	PUNCT
ejpam-5742	301	262	ν1	ν1	PROPN
ejpam-5742	301	263	)	)	PUNCT
ejpam-5742	301	264	(	(	PUNCT
ejpam-5742	301	265	τ	τ	PROPN
ejpam-5742	301	266	,	,	PUNCT
ejpam-5742	301	267	ν2	ν2	PROPN
ejpam-5742	301	268	)	)	PUNCT
ejpam-5742	301	269	(	(	PUNCT
ejpam-5742	301	270	τ	τ	PROPN
ejpam-5742	301	271	,	,	PUNCT
ejpam-5742	301	272	ν2	ν2	PROPN
ejpam-5742	301	273	)	)	PUNCT
ejpam-5742	301	274	(	(	PUNCT
ejpam-5742	301	275	τ	τ	PROPN
ejpam-5742	301	276	,	,	PUNCT
ejpam-5742	301	277	ν2	ν2	PROPN
ejpam-5742	301	278	)	)	PUNCT
ejpam-5742	301	279	(	(	PUNCT
ejpam-5742	301	280	τ	τ	PROPN
ejpam-5742	301	281	,	,	PUNCT
ejpam-5742	301	282	ν2	ν2	PROPN
ejpam-5742	301	283	)	)	PUNCT
ejpam-5742	301	284	(	(	PUNCT
ejpam-5742	301	285	τ	τ	PROPN
ejpam-5742	301	286	,	,	PUNCT
ejpam-5742	301	287	ν2	ν2	PROPN
ejpam-5742	301	288	)	)	PUNCT
ejpam-5742	301	289	(	(	PUNCT
ejpam-5742	301	290	τ	τ	PROPN
ejpam-5742	301	291	,	,	PUNCT
ejpam-5742	301	292	ν2	ν2	PROPN
ejpam-5742	301	293	)	)	PUNCT
ejpam-5742	301	294	(	(	PUNCT
ejpam-5742	301	295	τ	τ	PROPN
ejpam-5742	301	296	,	,	PUNCT
ejpam-5742	301	297	ν2	ν2	NOUN
ejpam-5742	301	298	)	)	PUNCT
ejpam-5742	301	299	∧	∧	PROPN
ejpam-5742	301	300	(	(	PUNCT
ejpam-5742	301	301	0	0	NUM
ejpam-5742	301	302	,	,	PUNCT
ejpam-5742	301	303	0	0	NUM
ejpam-5742	301	304	)	)	PUNCT
ejpam-5742	301	305	(	(	PUNCT
ejpam-5742	301	306	0	0	NUM
ejpam-5742	301	307	,	,	PUNCT
ejpam-5742	301	308	ν1	ν1	NOUN
ejpam-5742	301	309	)	)	PUNCT
ejpam-5742	301	310	(	(	PUNCT
ejpam-5742	301	311	0	0	NUM
ejpam-5742	301	312	,	,	PUNCT
ejpam-5742	301	313	ν2	ν2	NOUN
ejpam-5742	301	314	)	)	PUNCT
ejpam-5742	301	315	(	(	PUNCT
ejpam-5742	301	316	τ	τ	PROPN
ejpam-5742	301	317	,	,	PUNCT
ejpam-5742	301	318	0	0	NUM
ejpam-5742	301	319	)	)	PUNCT
ejpam-5742	301	320	(	(	PUNCT
ejpam-5742	301	321	τ	τ	PROPN
ejpam-5742	301	322	,	,	PUNCT
ejpam-5742	301	323	ν1	ν1	PROPN
ejpam-5742	301	324	)	)	PUNCT
ejpam-5742	301	325	(	(	PUNCT
ejpam-5742	301	326	τ	τ	PROPN
ejpam-5742	301	327	,	,	PUNCT
ejpam-5742	301	328	ν2	ν2	NOUN
ejpam-5742	301	329	)	)	PUNCT
ejpam-5742	301	330	(	(	PUNCT
ejpam-5742	301	331	0	0	NUM
ejpam-5742	301	332	,	,	PUNCT
ejpam-5742	301	333	0	0	NUM
ejpam-5742	301	334	)	)	PUNCT
ejpam-5742	301	335	(	(	PUNCT
ejpam-5742	301	336	0	0	NUM
ejpam-5742	301	337	,	,	PUNCT
ejpam-5742	301	338	0	0	NUM
ejpam-5742	301	339	)	)	PUNCT
ejpam-5742	301	340	(	(	PUNCT
ejpam-5742	301	341	0	0	NUM
ejpam-5742	301	342	,	,	PUNCT
ejpam-5742	301	343	0	0	NUM
ejpam-5742	301	344	)	)	PUNCT
ejpam-5742	301	345	(	(	PUNCT
ejpam-5742	301	346	0	0	NUM
ejpam-5742	301	347	,	,	PUNCT
ejpam-5742	301	348	0	0	NUM
ejpam-5742	301	349	)	)	PUNCT
ejpam-5742	301	350	(	(	PUNCT
ejpam-5742	301	351	0	0	NUM
ejpam-5742	301	352	,	,	PUNCT
ejpam-5742	301	353	0	0	NUM
ejpam-5742	301	354	)	)	PUNCT
ejpam-5742	301	355	(	(	PUNCT
ejpam-5742	301	356	0	0	NUM
ejpam-5742	301	357	,	,	PUNCT
ejpam-5742	301	358	0	0	NUM
ejpam-5742	301	359	)	)	PUNCT
ejpam-5742	301	360	(	(	PUNCT
ejpam-5742	301	361	0	0	NUM
ejpam-5742	301	362	,	,	PUNCT
ejpam-5742	301	363	0	0	NUM
ejpam-5742	301	364	)	)	PUNCT
ejpam-5742	301	365	(	(	PUNCT
ejpam-5742	301	366	0	0	NUM
ejpam-5742	301	367	,	,	PUNCT
ejpam-5742	301	368	ν1	ν1	NOUN
ejpam-5742	301	369	)	)	PUNCT
ejpam-5742	301	370	(	(	PUNCT
ejpam-5742	301	371	0	0	NUM
ejpam-5742	301	372	,	,	PUNCT
ejpam-5742	301	373	0	0	NUM
ejpam-5742	301	374	)	)	PUNCT
ejpam-5742	301	375	(	(	PUNCT
ejpam-5742	301	376	0	0	NUM
ejpam-5742	301	377	,	,	PUNCT
ejpam-5742	301	378	ν1	ν1	NOUN
ejpam-5742	301	379	)	)	PUNCT
ejpam-5742	301	380	(	(	PUNCT
ejpam-5742	301	381	0	0	NUM
ejpam-5742	301	382	,	,	PUNCT
ejpam-5742	301	383	ν2	ν2	NOUN
ejpam-5742	301	384	)	)	PUNCT
ejpam-5742	301	385	(	(	PUNCT
ejpam-5742	301	386	0	0	NUM
ejpam-5742	301	387	,	,	PUNCT
ejpam-5742	301	388	0	0	NUM
ejpam-5742	301	389	)	)	PUNCT
ejpam-5742	301	390	(	(	PUNCT
ejpam-5742	301	391	0	0	NUM
ejpam-5742	301	392	,	,	PUNCT
ejpam-5742	301	393	ν1	ν1	NOUN
ejpam-5742	301	394	)	)	PUNCT
ejpam-5742	301	395	(	(	PUNCT
ejpam-5742	301	396	0	0	NUM
ejpam-5742	301	397	,	,	PUNCT
ejpam-5742	301	398	ν2	ν2	NOUN
ejpam-5742	301	399	)	)	PUNCT
ejpam-5742	301	400	(	(	PUNCT
ejpam-5742	301	401	0	0	NUM
ejpam-5742	301	402	,	,	PUNCT
ejpam-5742	301	403	ν2	ν2	NOUN
ejpam-5742	301	404	)	)	PUNCT
ejpam-5742	301	405	(	(	PUNCT
ejpam-5742	301	406	0	0	NUM
ejpam-5742	301	407	,	,	PUNCT
ejpam-5742	301	408	0	0	NUM
ejpam-5742	301	409	)	)	PUNCT
ejpam-5742	301	410	(	(	PUNCT
ejpam-5742	301	411	0	0	NUM
ejpam-5742	301	412	,	,	PUNCT
ejpam-5742	301	413	ν1	ν1	NOUN
ejpam-5742	301	414	)	)	PUNCT
ejpam-5742	301	415	(	(	PUNCT
ejpam-5742	301	416	0	0	NUM
ejpam-5742	301	417	,	,	PUNCT
ejpam-5742	301	418	ν2	ν2	NOUN
ejpam-5742	301	419	)	)	PUNCT
ejpam-5742	301	420	(	(	PUNCT
ejpam-5742	301	421	0	0	NUM
ejpam-5742	301	422	,	,	PUNCT
ejpam-5742	301	423	0	0	NUM
ejpam-5742	301	424	)	)	PUNCT
ejpam-5742	301	425	(	(	PUNCT
ejpam-5742	301	426	0	0	NUM
ejpam-5742	301	427	,	,	PUNCT
ejpam-5742	301	428	ν1	ν1	NOUN
ejpam-5742	301	429	)	)	PUNCT
ejpam-5742	301	430	(	(	PUNCT
ejpam-5742	301	431	0	0	NUM
ejpam-5742	301	432	,	,	PUNCT
ejpam-5742	301	433	ν2	ν2	NOUN
ejpam-5742	301	434	)	)	PUNCT
ejpam-5742	301	435	(	(	PUNCT
ejpam-5742	301	436	τ	τ	PROPN
ejpam-5742	301	437	,	,	PUNCT
ejpam-5742	301	438	0	0	NUM
ejpam-5742	301	439	)	)	PUNCT
ejpam-5742	301	440	(	(	PUNCT
ejpam-5742	301	441	0	0	NUM
ejpam-5742	301	442	,	,	PUNCT
ejpam-5742	301	443	0	0	NUM
ejpam-5742	301	444	)	)	PUNCT
ejpam-5742	301	445	(	(	PUNCT
ejpam-5742	301	446	0	0	NUM
ejpam-5742	301	447	,	,	PUNCT
ejpam-5742	301	448	0	0	NUM
ejpam-5742	301	449	)	)	PUNCT
ejpam-5742	301	450	(	(	PUNCT
ejpam-5742	301	451	0	0	NUM
ejpam-5742	301	452	,	,	PUNCT
ejpam-5742	301	453	0	0	NUM
ejpam-5742	301	454	)	)	PUNCT
ejpam-5742	301	455	(	(	PUNCT
ejpam-5742	301	456	τ	τ	PROPN
ejpam-5742	301	457	,	,	PUNCT
ejpam-5742	301	458	0	0	NUM
ejpam-5742	301	459	)	)	PUNCT
ejpam-5742	301	460	(	(	PUNCT
ejpam-5742	301	461	τ	τ	PROPN
ejpam-5742	301	462	,	,	PUNCT
ejpam-5742	301	463	0	0	NUM
ejpam-5742	301	464	)	)	PUNCT
ejpam-5742	301	465	(	(	PUNCT
ejpam-5742	301	466	τ	τ	PROPN
ejpam-5742	301	467	,	,	PUNCT
ejpam-5742	301	468	0	0	NUM
ejpam-5742	301	469	)	)	PUNCT
ejpam-5742	301	470	(	(	PUNCT
ejpam-5742	301	471	τ	τ	PROPN
ejpam-5742	301	472	,	,	PUNCT
ejpam-5742	301	473	ν1	ν1	PROPN
ejpam-5742	301	474	)	)	PUNCT
ejpam-5742	301	475	(	(	PUNCT
ejpam-5742	301	476	0	0	NUM
ejpam-5742	301	477	,	,	PUNCT
ejpam-5742	301	478	0	0	NUM
ejpam-5742	301	479	)	)	PUNCT
ejpam-5742	301	480	(	(	PUNCT
ejpam-5742	301	481	0	0	NUM
ejpam-5742	301	482	,	,	PUNCT
ejpam-5742	301	483	ν1	ν1	NOUN
ejpam-5742	301	484	)	)	PUNCT
ejpam-5742	301	485	(	(	PUNCT
ejpam-5742	301	486	0	0	NUM
ejpam-5742	301	487	,	,	PUNCT
ejpam-5742	301	488	ν2	ν2	NOUN
ejpam-5742	301	489	)	)	PUNCT
ejpam-5742	301	490	(	(	PUNCT
ejpam-5742	301	491	τ	τ	PROPN
ejpam-5742	301	492	,	,	PUNCT
ejpam-5742	301	493	0	0	NUM
ejpam-5742	301	494	)	)	PUNCT
ejpam-5742	301	495	(	(	PUNCT
ejpam-5742	301	496	τ	τ	PROPN
ejpam-5742	301	497	,	,	PUNCT
ejpam-5742	301	498	ν1	ν1	PROPN
ejpam-5742	301	499	)	)	PUNCT
ejpam-5742	301	500	(	(	PUNCT
ejpam-5742	301	501	τ	τ	PROPN
ejpam-5742	301	502	,	,	PUNCT
ejpam-5742	301	503	ν2	ν2	PROPN
ejpam-5742	301	504	)	)	PUNCT
ejpam-5742	301	505	(	(	PUNCT
ejpam-5742	301	506	τ	τ	PROPN
ejpam-5742	301	507	,	,	PUNCT
ejpam-5742	301	508	ν2	ν2	NOUN
ejpam-5742	301	509	)	)	PUNCT
ejpam-5742	301	510	(	(	PUNCT
ejpam-5742	301	511	0	0	NUM
ejpam-5742	301	512	,	,	PUNCT
ejpam-5742	301	513	0	0	NUM
ejpam-5742	301	514	)	)	PUNCT
ejpam-5742	301	515	(	(	PUNCT
ejpam-5742	301	516	0	0	NUM
ejpam-5742	301	517	,	,	PUNCT
ejpam-5742	301	518	ν1	ν1	NOUN
ejpam-5742	301	519	)	)	PUNCT
ejpam-5742	301	520	(	(	PUNCT
ejpam-5742	301	521	0	0	NUM
ejpam-5742	301	522	,	,	PUNCT
ejpam-5742	301	523	ν2	ν2	NOUN
ejpam-5742	301	524	)	)	PUNCT
ejpam-5742	301	525	(	(	PUNCT
ejpam-5742	301	526	τ	τ	PROPN
ejpam-5742	301	527	,	,	PUNCT
ejpam-5742	301	528	0	0	NUM
ejpam-5742	301	529	)	)	PUNCT
ejpam-5742	301	530	(	(	PUNCT
ejpam-5742	301	531	τ	τ	PROPN
ejpam-5742	301	532	,	,	PUNCT
ejpam-5742	301	533	ν1	ν1	PROPN
ejpam-5742	301	534	)	)	PUNCT
ejpam-5742	301	535	(	(	PUNCT
ejpam-5742	301	536	τ	τ	PROPN
ejpam-5742	301	537	,	,	PUNCT
ejpam-5742	301	538	ν2	ν2	PROPN
ejpam-5742	301	539	)	)	PUNCT
ejpam-5742	301	540	clearly	clearly	ADV
ejpam-5742	301	541	,	,	PUNCT
ejpam-5742	301	542	(	(	PUNCT
ejpam-5742	301	543	r,∨,∧	r,∨,∧	NUM
ejpam-5742	301	544	,	,	PUNCT
ejpam-5742	301	545	0′	0′	NUM
ejpam-5742	301	546	)	)	PUNCT
ejpam-5742	301	547	is	be	AUX
ejpam-5742	301	548	an	an	DET
ejpam-5742	301	549	adl	adl	NOUN
ejpam-5742	301	550	,	,	PUNCT
ejpam-5742	301	551	where	where	SCONJ
ejpam-5742	301	552	0′	0′	X
ejpam-5742	302	1	=	=	SYM
ejpam-5742	303	1	(	(	PUNCT
ejpam-5742	303	2	0	0	NUM
ejpam-5742	303	3	,	,	PUNCT
ejpam-5742	303	4	0	0	NUM
ejpam-5742	303	5	)	)	PUNCT
ejpam-5742	303	6	.	.	PUNCT
ejpam-5742	304	1	we	we	PRON
ejpam-5742	304	2	have	have	VERB
ejpam-5742	304	3	that	that	PRON
ejpam-5742	304	4	(	(	PUNCT
ejpam-5742	304	5	i	i	NOUN
ejpam-5742	304	6	)	)	PUNCT
ejpam-5742	304	7	(	(	PUNCT
ejpam-5742	304	8	0	0	NUM
ejpam-5742	304	9	,	,	PUNCT
ejpam-5742	304	10	0)++	0)++	NOUN
ejpam-5742	304	11	=	=	SYM
ejpam-5742	304	12	{	{	PUNCT
ejpam-5742	304	13	(	(	PUNCT
ejpam-5742	304	14	τ	τ	PROPN
ejpam-5742	304	15	,	,	PUNCT
ejpam-5742	304	16	ν1	ν1	PROPN
ejpam-5742	304	17	)	)	PUNCT
ejpam-5742	304	18	,	,	PUNCT
ejpam-5742	304	19	(	(	PUNCT
ejpam-5742	304	20	τ	τ	PROPN
ejpam-5742	304	21	,	,	PUNCT
ejpam-5742	304	22	ν2)}+	ν2)}+	PROPN
ejpam-5742	304	23	=	=	SYM
ejpam-5742	304	24	r	r	NOUN
ejpam-5742	304	25	=	=	SYM
ejpam-5742	304	26	(	(	PUNCT
ejpam-5742	304	27	τ	τ	PROPN
ejpam-5742	304	28	,	,	PUNCT
ejpam-5742	304	29	ν1	ν1	NOUN
ejpam-5742	304	30	)	)	PUNCT
ejpam-5742	304	31	+	+	CCONJ
ejpam-5742	304	32	(	(	PUNCT
ejpam-5742	304	33	ii	ii	NOUN
ejpam-5742	304	34	)	)	PUNCT
ejpam-5742	304	35	(	(	PUNCT
ejpam-5742	304	36	0	0	NUM
ejpam-5742	304	37	,	,	PUNCT
ejpam-5742	304	38	ν1	ν1	NOUN
ejpam-5742	304	39	)	)	PUNCT
ejpam-5742	305	1	+	+	PROPN
ejpam-5742	305	2	+	+	NOUN
ejpam-5742	305	3	=	=	SYM
ejpam-5742	305	4	{	{	PUNCT
ejpam-5742	305	5	(	(	PUNCT
ejpam-5742	305	6	τ	τ	PROPN
ejpam-5742	305	7	,	,	PUNCT
ejpam-5742	305	8	0	0	NUM
ejpam-5742	305	9	)	)	PUNCT
ejpam-5742	305	10	,	,	PUNCT
ejpam-5742	305	11	(	(	PUNCT
ejpam-5742	305	12	τ	τ	PROPN
ejpam-5742	305	13	,	,	PUNCT
ejpam-5742	305	14	ν1	ν1	PROPN
ejpam-5742	305	15	)	)	PUNCT
ejpam-5742	305	16	,	,	PUNCT
ejpam-5742	305	17	(	(	PUNCT
ejpam-5742	305	18	τ	τ	PROPN
ejpam-5742	305	19	,	,	PUNCT
ejpam-5742	305	20	ν2)}+	ν2)}+	PROPN
ejpam-5742	305	21	=	=	SYM
ejpam-5742	305	22	{	{	PUNCT
ejpam-5742	305	23	(	(	PUNCT
ejpam-5742	305	24	0	0	NUM
ejpam-5742	305	25	,	,	PUNCT
ejpam-5742	305	26	ν1	ν1	NOUN
ejpam-5742	305	27	)	)	PUNCT
ejpam-5742	305	28	,	,	PUNCT
ejpam-5742	305	29	(	(	PUNCT
ejpam-5742	305	30	0	0	NUM
ejpam-5742	305	31	,	,	PUNCT
ejpam-5742	305	32	ν2	ν2	NOUN
ejpam-5742	305	33	)	)	PUNCT
ejpam-5742	305	34	,	,	PUNCT
ejpam-5742	305	35	(	(	PUNCT
ejpam-5742	305	36	τ	τ	PROPN
ejpam-5742	305	37	,	,	PUNCT
ejpam-5742	305	38	ν1	ν1	PROPN
ejpam-5742	305	39	)	)	PUNCT
ejpam-5742	305	40	,	,	PUNCT
ejpam-5742	305	41	(	(	PUNCT
ejpam-5742	305	42	τ	τ	NOUN
ejpam-5742	305	43	,	,	PUNCT
ejpam-5742	305	44	ν2	ν2	NOUN
ejpam-5742	305	45	)	)	PUNCT
ejpam-5742	305	46	}	}	PUNCT
ejpam-5742	305	47	=	=	SYM
ejpam-5742	305	48	(	(	PUNCT
ejpam-5742	305	49	τ	τ	PROPN
ejpam-5742	305	50	,	,	PUNCT
ejpam-5742	305	51	0)+	0)+	NUM
ejpam-5742	305	52	(	(	PUNCT
ejpam-5742	305	53	iii	iii	NOUN
ejpam-5742	305	54	)	)	PUNCT
ejpam-5742	305	55	(	(	PUNCT
ejpam-5742	305	56	0	0	NUM
ejpam-5742	305	57	,	,	PUNCT
ejpam-5742	305	58	ν2	ν2	NOUN
ejpam-5742	305	59	)	)	PUNCT
ejpam-5742	305	60	+	+	PROPN
ejpam-5742	305	61	+	+	NOUN
ejpam-5742	305	62	=	=	SYM
ejpam-5742	305	63	{	{	PUNCT
ejpam-5742	305	64	(	(	PUNCT
ejpam-5742	305	65	τ	τ	PROPN
ejpam-5742	305	66	,	,	PUNCT
ejpam-5742	305	67	0	0	NUM
ejpam-5742	305	68	)	)	PUNCT
ejpam-5742	305	69	,	,	PUNCT
ejpam-5742	305	70	(	(	PUNCT
ejpam-5742	305	71	τ	τ	PROPN
ejpam-5742	305	72	,	,	PUNCT
ejpam-5742	305	73	ν1	ν1	PROPN
ejpam-5742	305	74	)	)	PUNCT
ejpam-5742	305	75	,	,	PUNCT
ejpam-5742	305	76	(	(	PUNCT
ejpam-5742	305	77	τ	τ	PROPN
ejpam-5742	305	78	,	,	PUNCT
ejpam-5742	305	79	ν2)}+	ν2)}+	PROPN
ejpam-5742	305	80	=	=	SYM
ejpam-5742	305	81	{	{	PUNCT
ejpam-5742	305	82	(	(	PUNCT
ejpam-5742	305	83	0	0	NUM
ejpam-5742	305	84	,	,	PUNCT
ejpam-5742	305	85	ν1	ν1	NOUN
ejpam-5742	305	86	)	)	PUNCT
ejpam-5742	305	87	,	,	PUNCT
ejpam-5742	305	88	(	(	PUNCT
ejpam-5742	305	89	0	0	NUM
ejpam-5742	305	90	,	,	PUNCT
ejpam-5742	305	91	ν2	ν2	NOUN
ejpam-5742	305	92	)	)	PUNCT
ejpam-5742	305	93	,	,	PUNCT
ejpam-5742	305	94	(	(	PUNCT
ejpam-5742	305	95	τ	τ	PROPN
ejpam-5742	305	96	,	,	PUNCT
ejpam-5742	305	97	ν1	ν1	PROPN
ejpam-5742	305	98	)	)	PUNCT
ejpam-5742	305	99	,	,	PUNCT
ejpam-5742	305	100	(	(	PUNCT
ejpam-5742	305	101	τ	τ	NOUN
ejpam-5742	305	102	,	,	PUNCT
ejpam-5742	305	103	ν2	ν2	NOUN
ejpam-5742	305	104	)	)	PUNCT
ejpam-5742	305	105	}	}	PUNCT
ejpam-5742	305	106	=	=	SYM
ejpam-5742	305	107	(	(	PUNCT
ejpam-5742	305	108	τ	τ	PROPN
ejpam-5742	305	109	,	,	PUNCT
ejpam-5742	305	110	0)+	0)+	NUM
ejpam-5742	305	111	(	(	PUNCT
ejpam-5742	305	112	iv	iv	NUM
ejpam-5742	305	113	)	)	PUNCT
ejpam-5742	305	114	(	(	PUNCT
ejpam-5742	305	115	τ	τ	PROPN
ejpam-5742	305	116	,	,	PUNCT
ejpam-5742	305	117	0)++	0)++	NOUN
ejpam-5742	305	118	=	=	SYM
ejpam-5742	305	119	{	{	PUNCT
ejpam-5742	305	120	(	(	PUNCT
ejpam-5742	305	121	0	0	NUM
ejpam-5742	305	122	,	,	PUNCT
ejpam-5742	305	123	ν1	ν1	NOUN
ejpam-5742	305	124	)	)	PUNCT
ejpam-5742	305	125	,	,	PUNCT
ejpam-5742	305	126	(	(	PUNCT
ejpam-5742	305	127	0	0	NUM
ejpam-5742	305	128	,	,	PUNCT
ejpam-5742	305	129	ν2	ν2	NOUN
ejpam-5742	305	130	)	)	PUNCT
ejpam-5742	305	131	,	,	PUNCT
ejpam-5742	305	132	(	(	PUNCT
ejpam-5742	305	133	τ	τ	PROPN
ejpam-5742	305	134	,	,	PUNCT
ejpam-5742	305	135	ν1	ν1	PROPN
ejpam-5742	305	136	)	)	PUNCT
ejpam-5742	305	137	,	,	PUNCT
ejpam-5742	305	138	(	(	PUNCT
ejpam-5742	305	139	τ	τ	PROPN
ejpam-5742	305	140	,	,	PUNCT
ejpam-5742	305	141	ν2)}+	ν2)}+	PROPN
ejpam-5742	305	142	=	=	SYM
ejpam-5742	305	143	{	{	PUNCT
ejpam-5742	305	144	(	(	PUNCT
ejpam-5742	305	145	τ	τ	PROPN
ejpam-5742	305	146	,	,	PUNCT
ejpam-5742	305	147	0	0	NUM
ejpam-5742	305	148	)	)	PUNCT
ejpam-5742	305	149	,	,	PUNCT
ejpam-5742	305	150	(	(	PUNCT
ejpam-5742	305	151	τ	τ	PROPN
ejpam-5742	305	152	,	,	PUNCT
ejpam-5742	305	153	ν1	ν1	PROPN
ejpam-5742	305	154	)	)	PUNCT
ejpam-5742	305	155	,	,	PUNCT
ejpam-5742	305	156	(	(	PUNCT
ejpam-5742	305	157	τ	τ	NOUN
ejpam-5742	305	158	,	,	PUNCT
ejpam-5742	305	159	ν2	ν2	NOUN
ejpam-5742	305	160	)	)	PUNCT
ejpam-5742	305	161	}	}	PUNCT
ejpam-5742	305	162	=	=	SYM
ejpam-5742	305	163	(	(	PUNCT
ejpam-5742	305	164	0	0	NUM
ejpam-5742	305	165	,	,	PUNCT
ejpam-5742	305	166	ν1	ν1	NOUN
ejpam-5742	305	167	)	)	PUNCT
ejpam-5742	305	168	+	+	CCONJ
ejpam-5742	305	169	(	(	PUNCT
ejpam-5742	305	170	v	v	NOUN
ejpam-5742	305	171	)	)	PUNCT
ejpam-5742	305	172	(	(	PUNCT
ejpam-5742	305	173	τ	τ	PROPN
ejpam-5742	305	174	,	,	PUNCT
ejpam-5742	305	175	ν1	ν1	NOUN
ejpam-5742	305	176	)	)	PUNCT
ejpam-5742	306	1	+	+	PROPN
ejpam-5742	306	2	+	+	CCONJ
ejpam-5742	306	3	=	=	SYM
ejpam-5742	306	4	r+	r+	NOUN
ejpam-5742	306	5	=	=	PUNCT
ejpam-5742	306	6	{	{	PUNCT
ejpam-5742	306	7	(	(	PUNCT
ejpam-5742	306	8	τ	τ	PROPN
ejpam-5742	306	9	,	,	PUNCT
ejpam-5742	306	10	ν1	ν1	PROPN
ejpam-5742	306	11	)	)	PUNCT
ejpam-5742	306	12	,	,	PUNCT
ejpam-5742	306	13	(	(	PUNCT
ejpam-5742	306	14	τ	τ	NOUN
ejpam-5742	306	15	,	,	PUNCT
ejpam-5742	306	16	ν2	ν2	NOUN
ejpam-5742	306	17	)	)	PUNCT
ejpam-5742	306	18	}	}	PUNCT
ejpam-5742	306	19	=	=	SYM
ejpam-5742	306	20	(	(	PUNCT
ejpam-5742	306	21	0	0	NUM
ejpam-5742	306	22	,	,	PUNCT
ejpam-5742	306	23	0)+	0)+	NUM
ejpam-5742	306	24	(	(	PUNCT
ejpam-5742	306	25	vi	vi	NOUN
ejpam-5742	306	26	)	)	PUNCT
ejpam-5742	306	27	(	(	PUNCT
ejpam-5742	306	28	τ	τ	PROPN
ejpam-5742	306	29	,	,	PUNCT
ejpam-5742	306	30	ν2	ν2	NOUN
ejpam-5742	306	31	)	)	PUNCT
ejpam-5742	307	1	+	+	PROPN
ejpam-5742	307	2	+	+	CCONJ
ejpam-5742	307	3	=	=	SYM
ejpam-5742	307	4	r+	r+	NOUN
ejpam-5742	307	5	=	=	PUNCT
ejpam-5742	307	6	{	{	PUNCT
ejpam-5742	307	7	(	(	PUNCT
ejpam-5742	307	8	τ	τ	PROPN
ejpam-5742	307	9	,	,	PUNCT
ejpam-5742	307	10	ν1	ν1	PROPN
ejpam-5742	307	11	)	)	PUNCT
ejpam-5742	307	12	,	,	PUNCT
ejpam-5742	307	13	(	(	PUNCT
ejpam-5742	307	14	τ	τ	NOUN
ejpam-5742	307	15	,	,	PUNCT
ejpam-5742	307	16	ν2	ν2	NOUN
ejpam-5742	307	17	)	)	PUNCT
ejpam-5742	307	18	}	}	PUNCT
ejpam-5742	307	19	=	=	SYM
ejpam-5742	307	20	(	(	PUNCT
ejpam-5742	307	21	0	0	NUM
ejpam-5742	307	22	,	,	PUNCT
ejpam-5742	307	23	0)+	0)+	NOUN
ejpam-5742	307	24	thus	thus	ADV
ejpam-5742	307	25	(	(	PUNCT
ejpam-5742	307	26	r,∨,∧	r,∨,∧	NUM
ejpam-5742	307	27	,	,	PUNCT
ejpam-5742	307	28	0′	0′	NUM
ejpam-5742	307	29	)	)	PUNCT
ejpam-5742	307	30	is	be	AUX
ejpam-5742	307	31	an	an	DET
ejpam-5742	307	32	e−complemented	e−complemented	ADJ
ejpam-5742	307	33	adl	adl	PROPN
ejpam-5742	307	34	.	.	PUNCT
ejpam-5742	307	35	n.	n.	PROPN
ejpam-5742	307	36	rafi	rafi	PROPN
ejpam-5742	307	37	,	,	PUNCT
ejpam-5742	307	38	t.	t.	PROPN
ejpam-5742	307	39	gaketem	gaketem	PROPN
ejpam-5742	307	40	,	,	PUNCT
ejpam-5742	307	41	r.	r.	PROPN
ejpam-5742	307	42	k.	k.	PROPN
ejpam-5742	307	43	bandaru	bandaru	PROPN
ejpam-5742	307	44	/	/	SYM
ejpam-5742	307	45	eur	eur	PROPN
ejpam-5742	307	46	.	.	PUNCT
ejpam-5742	308	1	j.	j.	PROPN
ejpam-5742	308	2	pure	pure	PROPN
ejpam-5742	308	3	appl	appl	PROPN
ejpam-5742	308	4	.	.	PROPN
ejpam-5742	308	5	math	math	PROPN
ejpam-5742	308	6	,	,	PUNCT
ejpam-5742	308	7	18	18	NUM
ejpam-5742	308	8	(	(	PUNCT
ejpam-5742	308	9	2	2	NUM
ejpam-5742	308	10	)	)	PUNCT
ejpam-5742	308	11	(	(	PUNCT
ejpam-5742	308	12	2025	2025	NUM
ejpam-5742	308	13	)	)	PUNCT
ejpam-5742	308	14	,	,	PUNCT
ejpam-5742	308	15	5742	5742	NUM
ejpam-5742	308	16	10	10	NUM
ejpam-5742	308	17	of	of	ADP
ejpam-5742	308	18	14	14	NUM
ejpam-5742	308	19	lemma	lemma	PROPN
ejpam-5742	308	20	6	6	NUM
ejpam-5742	308	21	.	.	PUNCT
ejpam-5742	309	1	in	in	ADP
ejpam-5742	309	2	an	an	DET
ejpam-5742	309	3	e−complemented	e−complemented	ADJ
ejpam-5742	309	4	adl	adl	NOUN
ejpam-5742	309	5	r	r	NOUN
ejpam-5742	309	6	,	,	PUNCT
ejpam-5742	309	7	every	every	DET
ejpam-5742	309	8	prime	prime	ADJ
ejpam-5742	309	9	filter	filter	NOUN
ejpam-5742	309	10	x	x	PUNCT
ejpam-5742	309	11	with	with	ADP
ejpam-5742	309	12	x	x	X
ejpam-5742	309	13	∩	∩	ADJ
ejpam-5742	309	14	e	e	NOUN
ejpam-5742	309	15	=	=	NOUN
ejpam-5742	309	16	∅	∅	NOUN
ejpam-5742	309	17	is	be	AUX
ejpam-5742	309	18	an	an	DET
ejpam-5742	309	19	m−filter	m−filter	NOUN
ejpam-5742	309	20	.	.	PUNCT
ejpam-5742	310	1	proof	proof	NOUN
ejpam-5742	310	2	.	.	PUNCT
ejpam-5742	311	1	let	let	VERB
ejpam-5742	311	2	x	x	PRON
ejpam-5742	311	3	be	be	AUX
ejpam-5742	311	4	any	any	DET
ejpam-5742	311	5	prime	prime	ADJ
ejpam-5742	311	6	filter	filter	NOUN
ejpam-5742	311	7	of	of	ADP
ejpam-5742	311	8	r	r	NOUN
ejpam-5742	311	9	with	with	ADP
ejpam-5742	311	10	x	x	X
ejpam-5742	311	11	∩	∩	ADJ
ejpam-5742	311	12	e	e	NOUN
ejpam-5742	311	13	=	=	PUNCT
ejpam-5742	311	14	∅.	∅.	PRON
ejpam-5742	311	15	we	we	PRON
ejpam-5742	311	16	have	have	VERB
ejpam-5742	311	17	that	that	DET
ejpam-5742	311	18	m(r	m(r	VERB
ejpam-5742	311	19	\	\	PUNCT
ejpam-5742	311	20	x	x	X
ejpam-5742	311	21	)	)	PUNCT
ejpam-5742	312	1	=	=	SYM
ejpam-5742	312	2	h(x	h(x	PROPN
ejpam-5742	312	3	)	)	PUNCT
ejpam-5742	313	1	⊆	⊆	NUM
ejpam-5742	313	2	x	x	X
ejpam-5742	313	3	.	.	PUNCT
ejpam-5742	314	1	let	let	VERB
ejpam-5742	314	2	κ	κ	PRON
ejpam-5742	314	3	∈	∈	PROPN
ejpam-5742	314	4	x	x	X
ejpam-5742	314	5	.	.	PUNCT
ejpam-5742	315	1	as	as	ADP
ejpam-5742	315	2	per	per	ADP
ejpam-5742	315	3	our	our	PRON
ejpam-5742	315	4	hypothesis	hypothesis	NOUN
ejpam-5742	315	5	,	,	PUNCT
ejpam-5742	315	6	there	there	PRON
ejpam-5742	315	7	is	be	VERB
ejpam-5742	315	8	η	η	PROPN
ejpam-5742	315	9	∈	∈	PROPN
ejpam-5742	315	10	r	r	NOUN
ejpam-5742	315	11	such	such	ADJ
ejpam-5742	315	12	that	that	SCONJ
ejpam-5742	315	13	κ	κ	PROPN
ejpam-5742	315	14	∧	∧	PROPN
ejpam-5742	315	15	η	η	PROPN
ejpam-5742	315	16	∈	∈	PROPN
ejpam-5742	315	17	e	e	PROPN
ejpam-5742	315	18	and	and	CCONJ
ejpam-5742	315	19	κ∨	κ∨	PROPN
ejpam-5742	315	20	η	η	PROPN
ejpam-5742	315	21	∈	∈	PROPN
ejpam-5742	315	22	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	315	23	)	)	PUNCT
ejpam-5742	315	24	.	.	PUNCT
ejpam-5742	316	1	that	that	PRON
ejpam-5742	316	2	implies	imply	VERB
ejpam-5742	316	3	κ∧	κ∧	PROPN
ejpam-5742	316	4	η	η	PROPN
ejpam-5742	316	5	/∈	/∈	PROPN
ejpam-5742	316	6	x	x	X
ejpam-5742	316	7	and	and	CCONJ
ejpam-5742	316	8	hence	hence	ADV
ejpam-5742	316	9	η	η	PROPN
ejpam-5742	316	10	/∈	/∈	PROPN
ejpam-5742	316	11	x	x	X
ejpam-5742	316	12	.	.	PUNCT
ejpam-5742	317	1	since	since	SCONJ
ejpam-5742	317	2	κ∨	κ∨	PROPN
ejpam-5742	317	3	η	η	PROPN
ejpam-5742	317	4	∈	∈	PROPN
ejpam-5742	317	5	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	317	6	)	)	PUNCT
ejpam-5742	317	7	and	and	CCONJ
ejpam-5742	317	8	η	η	PROPN
ejpam-5742	317	9	/∈	/∈	PROPN
ejpam-5742	317	10	x	x	X
ejpam-5742	317	11	,	,	PUNCT
ejpam-5742	317	12	we	we	PRON
ejpam-5742	317	13	get	get	VERB
ejpam-5742	317	14	that	that	PRON
ejpam-5742	317	15	κ	κ	PROPN
ejpam-5742	317	16	∈	∈	PROPN
ejpam-5742	317	17	h(x	h(x	PROPN
ejpam-5742	317	18	)	)	PUNCT
ejpam-5742	318	1	=	=	PUNCT
ejpam-5742	318	2	m(r	m(r	VERB
ejpam-5742	318	3	\	\	PUNCT
ejpam-5742	318	4	x	x	PUNCT
ejpam-5742	318	5	)	)	PUNCT
ejpam-5742	318	6	.	.	PUNCT
ejpam-5742	319	1	which	which	PRON
ejpam-5742	319	2	gives	give	VERB
ejpam-5742	319	3	x	x	NUM
ejpam-5742	319	4	⊆	⊆	NUM
ejpam-5742	319	5	m(r	m(r	NOUN
ejpam-5742	319	6	\	\	PUNCT
ejpam-5742	319	7	x	x	PUNCT
ejpam-5742	319	8	)	)	PUNCT
ejpam-5742	319	9	.	.	PUNCT
ejpam-5742	320	1	therefore	therefore	ADV
ejpam-5742	320	2	x	x	X
ejpam-5742	320	3	=	=	SYM
ejpam-5742	320	4	m(r	m(r	PROPN
ejpam-5742	320	5	\	\	PUNCT
ejpam-5742	320	6	x	x	PUNCT
ejpam-5742	320	7	)	)	PUNCT
ejpam-5742	320	8	.	.	PUNCT
ejpam-5742	321	1	thus	thus	ADV
ejpam-5742	321	2	x	x	X
ejpam-5742	321	3	is	be	AUX
ejpam-5742	321	4	an	an	DET
ejpam-5742	321	5	m−filter	m−filter	NOUN
ejpam-5742	321	6	of	of	ADP
ejpam-5742	321	7	r.	r.	PROPN
ejpam-5742	321	8	theorem	theorem	PROPN
ejpam-5742	321	9	10	10	NUM
ejpam-5742	321	10	.	.	PUNCT
ejpam-5742	322	1	for	for	ADP
ejpam-5742	322	2	any	any	DET
ejpam-5742	322	3	proper	proper	ADJ
ejpam-5742	322	4	m−filter	m−filter	NOUN
ejpam-5742	322	5	s	s	NOUN
ejpam-5742	322	6	of	of	ADP
ejpam-5742	322	7	r	r	NOUN
ejpam-5742	322	8	,	,	PUNCT
ejpam-5742	322	9	s	s	PART
ejpam-5742	322	10	is	be	AUX
ejpam-5742	322	11	prime	prime	ADJ
ejpam-5742	322	12	if	if	SCONJ
ejpam-5742	322	13	and	and	CCONJ
ejpam-5742	322	14	only	only	ADV
ejpam-5742	322	15	if	if	SCONJ
ejpam-5742	322	16	s	s	NOUN
ejpam-5742	322	17	contains	contain	VERB
ejpam-5742	322	18	a	a	DET
ejpam-5742	322	19	prime	prime	ADJ
ejpam-5742	322	20	filter	filter	NOUN
ejpam-5742	322	21	.	.	PUNCT
ejpam-5742	323	1	proof	proof	NOUN
ejpam-5742	323	2	.	.	PUNCT
ejpam-5742	324	1	assume	assume	VERB
ejpam-5742	324	2	that	that	SCONJ
ejpam-5742	324	3	s	s	VERB
ejpam-5742	324	4	contains	contain	VERB
ejpam-5742	324	5	a	a	DET
ejpam-5742	324	6	prime	prime	ADJ
ejpam-5742	324	7	filter	filter	NOUN
ejpam-5742	324	8	,	,	PUNCT
ejpam-5742	324	9	say	say	VERB
ejpam-5742	324	10	x	x	X
ejpam-5742	324	11	.	.	PUNCT
ejpam-5742	325	1	since	since	SCONJ
ejpam-5742	325	2	s	s	PROPN
ejpam-5742	325	3	is	be	AUX
ejpam-5742	325	4	an	an	DET
ejpam-5742	325	5	m−filter	m−filter	NOUN
ejpam-5742	325	6	of	of	ADP
ejpam-5742	325	7	r	r	NOUN
ejpam-5742	325	8	,	,	PUNCT
ejpam-5742	325	9	we	we	PRON
ejpam-5742	325	10	have	have	VERB
ejpam-5742	325	11	that	that	DET
ejpam-5742	325	12	s	s	PART
ejpam-5742	325	13	=	=	SYM
ejpam-5742	325	14	m(f	m(f	PROPN
ejpam-5742	325	15	)	)	PUNCT
ejpam-5742	325	16	,	,	PUNCT
ejpam-5742	325	17	for	for	ADP
ejpam-5742	325	18	some	some	DET
ejpam-5742	325	19	ideal	ideal	ADJ
ejpam-5742	325	20	f	f	PROPN
ejpam-5742	325	21	of	of	ADP
ejpam-5742	325	22	r.	r.	PROPN
ejpam-5742	325	23	we	we	PRON
ejpam-5742	325	24	prove	prove	VERB
ejpam-5742	325	25	that	that	SCONJ
ejpam-5742	325	26	s	s	VERB
ejpam-5742	325	27	is	be	AUX
ejpam-5742	325	28	prime	prime	ADJ
ejpam-5742	325	29	filter	filter	NOUN
ejpam-5742	325	30	of	of	ADP
ejpam-5742	325	31	r.	r.	PROPN
ejpam-5742	325	32	let	let	VERB
ejpam-5742	325	33	κ	κ	NOUN
ejpam-5742	325	34	,	,	PUNCT
ejpam-5742	325	35	η	η	PROPN
ejpam-5742	325	36	∈	∈	PROPN
ejpam-5742	325	37	r	r	NOUN
ejpam-5742	325	38	with	with	ADP
ejpam-5742	325	39	κ∨η	κ∨η	PROPN
ejpam-5742	325	40	∈	∈	PROPN
ejpam-5742	325	41	s.	s.	PROPN
ejpam-5742	325	42	suppose	suppose	VERB
ejpam-5742	325	43	that	that	SCONJ
ejpam-5742	325	44	κ	κ	PROPN
ejpam-5742	325	45	/∈	/∈	PROPN
ejpam-5742	325	46	s	s	PROPN
ejpam-5742	325	47	and	and	CCONJ
ejpam-5742	325	48	η	η	PROPN
ejpam-5742	325	49	/∈	/∈	PROPN
ejpam-5742	325	50	s.	s.	PROPN
ejpam-5742	325	51	then	then	ADV
ejpam-5742	325	52	κ	κ	X
ejpam-5742	325	53	/∈	/∈	PROPN
ejpam-5742	325	54	x	x	PUNCT
ejpam-5742	325	55	and	and	CCONJ
ejpam-5742	325	56	η	η	PROPN
ejpam-5742	325	57	/∈	/∈	PROPN
ejpam-5742	325	58	x	x	X
ejpam-5742	325	59	.	.	PUNCT
ejpam-5742	326	1	since	since	SCONJ
ejpam-5742	326	2	x	x	PRON
ejpam-5742	326	3	is	be	AUX
ejpam-5742	326	4	prime	prime	ADJ
ejpam-5742	326	5	,	,	PUNCT
ejpam-5742	326	6	we	we	PRON
ejpam-5742	326	7	get	get	VERB
ejpam-5742	326	8	κ∨η	κ∨η	PROPN
ejpam-5742	326	9	/∈	/∈	PUNCT
ejpam-5742	327	1	x	x	X
ejpam-5742	327	2	.	.	PUNCT
ejpam-5742	328	1	that	that	PRON
ejpam-5742	328	2	implies	imply	VERB
ejpam-5742	328	3	(	(	PUNCT
ejpam-5742	328	4	κ∨η)+	κ∨η)+	NOUN
ejpam-5742	328	5	⊆	⊆	NUM
ejpam-5742	328	6	x	x	SYM
ejpam-5742	328	7	⊆	⊆	NUM
ejpam-5742	328	8	s	s	NOUN
ejpam-5742	328	9	=	=	SYM
ejpam-5742	328	10	m(f	m(f	PROPN
ejpam-5742	328	11	)	)	PUNCT
ejpam-5742	328	12	.	.	PUNCT
ejpam-5742	329	1	suppose	suppose	VERB
ejpam-5742	329	2	κ∨η	κ∨η	PROPN
ejpam-5742	329	3	∈	∈	PROPN
ejpam-5742	329	4	m(f	m(f	PROPN
ejpam-5742	329	5	)	)	PUNCT
ejpam-5742	329	6	.	.	PUNCT
ejpam-5742	330	1	then	then	ADV
ejpam-5742	330	2	(	(	PUNCT
ejpam-5742	330	3	κ∨	κ∨	PROPN
ejpam-5742	330	4	η)∨ω	η)∨ω	VERB
ejpam-5742	330	5	∈	∈	PROPN
ejpam-5742	330	6	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	330	7	)	)	PUNCT
ejpam-5742	330	8	,	,	PUNCT
ejpam-5742	330	9	for	for	ADP
ejpam-5742	330	10	some	some	DET
ejpam-5742	330	11	ω	ω	NUM
ejpam-5742	330	12	∈	∈	PROPN
ejpam-5742	330	13	f	f	X
ejpam-5742	330	14	.	.	PUNCT
ejpam-5742	331	1	it	it	PRON
ejpam-5742	331	2	gives	give	VERB
ejpam-5742	331	3	ω	ω	NUM
ejpam-5742	331	4	∈	∈	PROPN
ejpam-5742	331	5	(	(	PUNCT
ejpam-5742	331	6	κ∨	κ∨	PROPN
ejpam-5742	331	7	η)+	η)+	VERB
ejpam-5742	331	8	⊆	⊆	NUM
ejpam-5742	331	9	x	x	SYM
ejpam-5742	331	10	⊆	⊆	NUM
ejpam-5742	331	11	s	s	NOUN
ejpam-5742	331	12	=	=	SYM
ejpam-5742	331	13	m(f	m(f	PROPN
ejpam-5742	331	14	)	)	PUNCT
ejpam-5742	331	15	.	.	PUNCT
ejpam-5742	332	1	therefore	therefore	ADV
ejpam-5742	332	2	ω	ω	PROPN
ejpam-5742	332	3	∈	∈	PROPN
ejpam-5742	332	4	f	f	PROPN
ejpam-5742	332	5	∩	∩	PROPN
ejpam-5742	332	6	m(f	m(f	PROPN
ejpam-5742	332	7	)	)	PUNCT
ejpam-5742	332	8	and	and	CCONJ
ejpam-5742	332	9	hence	hence	ADV
ejpam-5742	332	10	f	f	PROPN
ejpam-5742	332	11	∩	∩	ADJ
ejpam-5742	332	12	m(f	m(f	PROPN
ejpam-5742	332	13	)	)	PUNCT
ejpam-5742	332	14	̸=	̸=	PROPN
ejpam-5742	332	15	∅.	∅.	AUX
ejpam-5742	332	16	thus	thus	ADV
ejpam-5742	332	17	s	s	PART
ejpam-5742	332	18	=	=	SYM
ejpam-5742	332	19	f	f	PROPN
ejpam-5742	332	20	=	=	SYM
ejpam-5742	332	21	m(f	m(f	PROPN
ejpam-5742	332	22	)	)	PUNCT
ejpam-5742	332	23	=	=	SYM
ejpam-5742	333	1	r	r	NOUN
ejpam-5742	333	2	,	,	PUNCT
ejpam-5742	333	3	which	which	PRON
ejpam-5742	333	4	leads	lead	VERB
ejpam-5742	333	5	a	a	DET
ejpam-5742	333	6	contradiction	contradiction	NOUN
ejpam-5742	333	7	.	.	PUNCT
ejpam-5742	334	1	therefore	therefore	ADV
ejpam-5742	334	2	κ∨η	κ∨η	PROPN
ejpam-5742	334	3	/∈	/∈	PUNCT
ejpam-5742	335	1	m(f	m(f	PROPN
ejpam-5742	335	2	)	)	PUNCT
ejpam-5742	335	3	and	and	CCONJ
ejpam-5742	335	4	hence	hence	ADV
ejpam-5742	335	5	κ∨η	κ∨η	PROPN
ejpam-5742	335	6	/∈	/∈	PUNCT
ejpam-5742	336	1	s	s	X
ejpam-5742	336	2	,	,	PUNCT
ejpam-5742	336	3	we	we	PRON
ejpam-5742	336	4	get	get	VERB
ejpam-5742	336	5	a	a	DET
ejpam-5742	336	6	contradiction	contradiction	NOUN
ejpam-5742	336	7	.	.	PUNCT
ejpam-5742	337	1	which	which	PRON
ejpam-5742	337	2	leads	lead	VERB
ejpam-5742	337	3	either	either	CCONJ
ejpam-5742	337	4	κ	κ	PROPN
ejpam-5742	337	5	∈	∈	PROPN
ejpam-5742	337	6	s	s	PART
ejpam-5742	337	7	or	or	CCONJ
ejpam-5742	337	8	η	η	PROPN
ejpam-5742	337	9	∈	∈	PROPN
ejpam-5742	337	10	s.	s.	PROPN
ejpam-5742	337	11	thus	thus	ADV
ejpam-5742	337	12	s	s	AUX
ejpam-5742	337	13	is	be	AUX
ejpam-5742	337	14	prime	prime	ADJ
ejpam-5742	337	15	.	.	PUNCT
ejpam-5742	338	1	theorem	theorem	ADJ
ejpam-5742	338	2	11	11	NUM
ejpam-5742	338	3	.	.	PUNCT
ejpam-5742	339	1	in	in	ADP
ejpam-5742	339	2	adl	adl	PROPN
ejpam-5742	339	3	r	r	PROPN
ejpam-5742	339	4	,	,	PUNCT
ejpam-5742	339	5	every	every	DET
ejpam-5742	339	6	prime	prime	NOUN
ejpam-5742	339	7	m−filter	m−filter	NOUN
ejpam-5742	339	8	is	be	AUX
ejpam-5742	339	9	minimal	minimal	ADJ
ejpam-5742	339	10	.	.	PUNCT
ejpam-5742	340	1	proof	proof	NOUN
ejpam-5742	340	2	.	.	PUNCT
ejpam-5742	341	1	let	let	VERB
ejpam-5742	341	2	x	x	PRON
ejpam-5742	341	3	be	be	AUX
ejpam-5742	341	4	a	a	DET
ejpam-5742	341	5	prime	prime	NOUN
ejpam-5742	341	6	m−filter	m−filter	NOUN
ejpam-5742	341	7	of	of	ADP
ejpam-5742	341	8	r.	r.	PROPN
ejpam-5742	341	9	then	then	ADV
ejpam-5742	341	10	,	,	PUNCT
ejpam-5742	341	11	there	there	PRON
ejpam-5742	341	12	exists	exist	VERB
ejpam-5742	341	13	an	an	DET
ejpam-5742	341	14	ideal	ideal	ADJ
ejpam-5742	341	15	f	f	NOUN
ejpam-5742	341	16	of	of	ADP
ejpam-5742	341	17	r	r	NOUN
ejpam-5742	341	18	such	such	ADJ
ejpam-5742	341	19	that	that	SCONJ
ejpam-5742	341	20	x	x	X
ejpam-5742	341	21	=	=	SYM
ejpam-5742	341	22	m(f	m(f	PROPN
ejpam-5742	341	23	)	)	PUNCT
ejpam-5742	341	24	.	.	PUNCT
ejpam-5742	342	1	for	for	ADP
ejpam-5742	342	2	an	an	DET
ejpam-5742	342	3	element	element	NOUN
ejpam-5742	342	4	κ	κ	ADP
ejpam-5742	342	5	∈	∈	PROPN
ejpam-5742	342	6	x	x	INTJ
ejpam-5742	342	7	,	,	PUNCT
ejpam-5742	342	8	there	there	PRON
ejpam-5742	342	9	is	be	VERB
ejpam-5742	342	10	an	an	DET
ejpam-5742	342	11	element	element	NOUN
ejpam-5742	342	12	η	η	PROPN
ejpam-5742	342	13	∈	∈	PROPN
ejpam-5742	342	14	f	f	PROPN
ejpam-5742	342	15	satisfying	satisfy	VERB
ejpam-5742	342	16	κ	κ	PROPN
ejpam-5742	342	17	∨	∨	PROPN
ejpam-5742	342	18	η	η	PROPN
ejpam-5742	342	19	∈	∈	PROPN
ejpam-5742	342	20	mmax	mmax	NOUN
ejpam-5742	342	21	.	.	PUNCT
ejpam-5742	343	1	elt(r	elt(r	X
ejpam-5742	343	2	)	)	PUNCT
ejpam-5742	343	3	.	.	PUNCT
ejpam-5742	344	1	assuming	assume	VERB
ejpam-5742	344	2	that	that	SCONJ
ejpam-5742	344	3	η	η	PROPN
ejpam-5742	344	4	∈	∈	PROPN
ejpam-5742	344	5	x	x	X
ejpam-5742	344	6	,	,	PUNCT
ejpam-5742	344	7	it	it	PRON
ejpam-5742	344	8	follows	follow	VERB
ejpam-5742	344	9	that	that	SCONJ
ejpam-5742	344	10	η	η	PROPN
ejpam-5742	344	11	∈	∈	PROPN
ejpam-5742	344	12	m(f	m(f	PROPN
ejpam-5742	344	13	)	)	PUNCT
ejpam-5742	344	14	.	.	PUNCT
ejpam-5742	345	1	this	this	PRON
ejpam-5742	345	2	leads	lead	VERB
ejpam-5742	345	3	to	to	ADP
ejpam-5742	345	4	the	the	DET
ejpam-5742	345	5	conclusion	conclusion	NOUN
ejpam-5742	345	6	that	that	SCONJ
ejpam-5742	345	7	f	f	PROPN
ejpam-5742	345	8	∩m(f	∩m(f	PROPN
ejpam-5742	345	9	)	)	PUNCT
ejpam-5742	345	10	̸=	̸=	PROPN
ejpam-5742	345	11	∅	∅	NOUN
ejpam-5742	345	12	,	,	PUNCT
ejpam-5742	345	13	resulting	result	VERB
ejpam-5742	345	14	in	in	ADP
ejpam-5742	345	15	the	the	DET
ejpam-5742	345	16	equality	equality	NOUN
ejpam-5742	345	17	x	x	X
ejpam-5742	345	18	=	=	SYM
ejpam-5742	345	19	m(f	m(f	PROPN
ejpam-5742	345	20	)	)	PUNCT
ejpam-5742	345	21	=	=	SYM
ejpam-5742	346	1	f	f	X
ejpam-5742	346	2	=	=	SYM
ejpam-5742	346	3	r	r	NOUN
ejpam-5742	346	4	,	,	PUNCT
ejpam-5742	346	5	which	which	PRON
ejpam-5742	346	6	gives	give	VERB
ejpam-5742	346	7	a	a	DET
ejpam-5742	346	8	contradiction	contradiction	NOUN
ejpam-5742	346	9	.	.	PUNCT
ejpam-5742	347	1	thus	thus	ADV
ejpam-5742	347	2	,	,	PUNCT
ejpam-5742	347	3	we	we	PRON
ejpam-5742	347	4	conclude	conclude	VERB
ejpam-5742	347	5	that	that	SCONJ
ejpam-5742	347	6	η	η	PROPN
ejpam-5742	347	7	/∈	/∈	PROPN
ejpam-5742	347	8	x	x	X
ejpam-5742	347	9	.	.	PUNCT
ejpam-5742	348	1	therefore	therefore	ADV
ejpam-5742	348	2	,	,	PUNCT
ejpam-5742	348	3	x	x	PUNCT
ejpam-5742	348	4	is	be	AUX
ejpam-5742	348	5	minimal	minimal	ADJ
ejpam-5742	348	6	.	.	PUNCT
ejpam-5742	349	1	definition	definition	NOUN
ejpam-5742	349	2	10	10	NUM
ejpam-5742	349	3	.	.	PUNCT
ejpam-5742	350	1	a	a	DET
ejpam-5742	350	2	filter	filter	NOUN
ejpam-5742	350	3	s	s	NOUN
ejpam-5742	350	4	is	be	AUX
ejpam-5742	350	5	referred	refer	VERB
ejpam-5742	350	6	to	to	ADP
ejpam-5742	350	7	as	as	ADP
ejpam-5742	350	8	annihilator	annihilator	NOUN
ejpam-5742	350	9	of	of	ADP
ejpam-5742	350	10	r	r	NOUN
ejpam-5742	350	11	if	if	SCONJ
ejpam-5742	350	12	it	it	PRON
ejpam-5742	350	13	satisfies	satisfy	VERB
ejpam-5742	350	14	the	the	DET
ejpam-5742	350	15	condition	condition	NOUN
ejpam-5742	350	16	s	s	PART
ejpam-5742	350	17	=	=	NOUN
ejpam-5742	350	18	s++	s++	PROPN
ejpam-5742	350	19	.	.	PUNCT
ejpam-5742	351	1	example	example	NOUN
ejpam-5742	352	1	6	6	NUM
ejpam-5742	352	2	.	.	PUNCT
ejpam-5742	353	1	from	from	ADP
ejpam-5742	353	2	the	the	DET
ejpam-5742	353	3	example	example	NOUN
ejpam-5742	353	4	4	4	NUM
ejpam-5742	353	5	,	,	PUNCT
ejpam-5742	353	6	consider	consider	VERB
ejpam-5742	353	7	a	a	DET
ejpam-5742	353	8	filter	filter	NOUN
ejpam-5742	353	9	t	t	NOUN
ejpam-5742	353	10	=	=	SYM
ejpam-5742	353	11	{	{	PUNCT
ejpam-5742	353	12	1	1	NUM
ejpam-5742	353	13	,	,	PUNCT
ejpam-5742	353	14	2	2	NUM
ejpam-5742	353	15	,	,	PUNCT
ejpam-5742	353	16	3	3	NUM
ejpam-5742	353	17	,	,	PUNCT
ejpam-5742	353	18	6	6	NUM
ejpam-5742	353	19	}	}	PUNCT
ejpam-5742	353	20	.	.	PUNCT
ejpam-5742	354	1	it	it	PRON
ejpam-5742	354	2	is	be	AUX
ejpam-5742	354	3	clear	clear	ADJ
ejpam-5742	354	4	that	that	SCONJ
ejpam-5742	354	5	t	t	PROPN
ejpam-5742	354	6	is	be	AUX
ejpam-5742	354	7	an	an	DET
ejpam-5742	354	8	annihilator	annihilator	NOUN
ejpam-5742	354	9	filter	filter	NOUN
ejpam-5742	354	10	of	of	ADP
ejpam-5742	354	11	r	r	NOUN
ejpam-5742	354	12	,	,	PUNCT
ejpam-5742	354	13	because	because	SCONJ
ejpam-5742	354	14	t	t	PROPN
ejpam-5742	354	15	=	=	SYM
ejpam-5742	354	16	t	t	PROPN
ejpam-5742	355	1	+	+	PROPN
ejpam-5742	355	2	+	+	PROPN
ejpam-5742	355	3	.	.	PUNCT
ejpam-5742	355	4	theorem	theorem	NOUN
ejpam-5742	355	5	12	12	NUM
ejpam-5742	355	6	.	.	PUNCT
ejpam-5742	356	1	in	in	ADP
ejpam-5742	356	2	an	an	DET
ejpam-5742	356	3	e−complemented	e−complemented	ADJ
ejpam-5742	356	4	adl	adl	NOUN
ejpam-5742	356	5	r	r	NOUN
ejpam-5742	356	6	,	,	PUNCT
ejpam-5742	356	7	the	the	DET
ejpam-5742	356	8	statements	statement	NOUN
ejpam-5742	356	9	listed	list	VERB
ejpam-5742	356	10	below	below	ADV
ejpam-5742	356	11	are	be	AUX
ejpam-5742	356	12	equivalent	equivalent	ADJ
ejpam-5742	356	13	:	:	PUNCT
ejpam-5742	356	14	(	(	PUNCT
ejpam-5742	356	15	i	i	NOUN
ejpam-5742	356	16	)	)	PUNCT
ejpam-5742	356	17	every	every	DET
ejpam-5742	356	18	m−filter	m−filter	NOUN
ejpam-5742	356	19	is	be	AUX
ejpam-5742	356	20	an	an	DET
ejpam-5742	356	21	annihilator	annihilator	NOUN
ejpam-5742	356	22	filter	filter	NOUN
ejpam-5742	356	23	(	(	PUNCT
ejpam-5742	356	24	ii	ii	NOUN
ejpam-5742	356	25	)	)	PUNCT
ejpam-5742	356	26	every	every	DET
ejpam-5742	356	27	minimal	minimal	ADJ
ejpam-5742	356	28	prime	prime	ADJ
ejpam-5742	356	29	filter	filter	NOUN
ejpam-5742	356	30	is	be	AUX
ejpam-5742	356	31	an	an	DET
ejpam-5742	356	32	annihilator	annihilator	NOUN
ejpam-5742	356	33	filter	filter	NOUN
ejpam-5742	356	34	(	(	PUNCT
ejpam-5742	356	35	iii	iii	NOUN
ejpam-5742	356	36	)	)	PUNCT
ejpam-5742	356	37	every	every	DET
ejpam-5742	356	38	prime	prime	NOUN
ejpam-5742	356	39	m−filter	m−filter	NOUN
ejpam-5742	356	40	is	be	AUX
ejpam-5742	356	41	of	of	ADP
ejpam-5742	356	42	the	the	DET
ejpam-5742	356	43	form	form	NOUN
ejpam-5742	356	44	(	(	PUNCT
ejpam-5742	356	45	κ)++	κ)++	PROPN
ejpam-5742	356	46	,	,	PUNCT
ejpam-5742	356	47	for	for	ADP
ejpam-5742	356	48	some	some	PRON
ejpam-5742	356	49	κ	κ	NOUN
ejpam-5742	356	50	∈	∈	PROPN
ejpam-5742	356	51	r	r	NOUN
ejpam-5742	356	52	(	(	PUNCT
ejpam-5742	356	53	iv	iv	X
ejpam-5742	356	54	)	)	PUNCT
ejpam-5742	356	55	every	every	DET
ejpam-5742	356	56	m−filter	m−filter	NOUN
ejpam-5742	356	57	is	be	AUX
ejpam-5742	356	58	of	of	ADP
ejpam-5742	356	59	the	the	DET
ejpam-5742	356	60	form	form	NOUN
ejpam-5742	356	61	(	(	PUNCT
ejpam-5742	356	62	κ)++	κ)++	PROPN
ejpam-5742	356	63	,	,	PUNCT
ejpam-5742	356	64	for	for	ADP
ejpam-5742	356	65	some	some	DET
ejpam-5742	356	66	κ	κ	NOUN
ejpam-5742	356	67	∈	∈	PROPN
ejpam-5742	356	68	r	r	NOUN
ejpam-5742	356	69	(	(	PUNCT
ejpam-5742	356	70	v	v	NOUN
ejpam-5742	356	71	)	)	PUNCT
ejpam-5742	356	72	every	every	DET
ejpam-5742	356	73	minimal	minimal	ADJ
ejpam-5742	356	74	prime	prime	ADJ
ejpam-5742	356	75	filter	filter	NOUN
ejpam-5742	356	76	is	be	AUX
ejpam-5742	356	77	non	non	ADJ
ejpam-5742	356	78	co	co	ADJ
ejpam-5742	356	79	-	-	ADJ
ejpam-5742	356	80	dense	dense	ADJ
ejpam-5742	356	81	.	.	PUNCT
ejpam-5742	357	1	n.	n.	PROPN
ejpam-5742	357	2	rafi	rafi	PROPN
ejpam-5742	357	3	,	,	PUNCT
ejpam-5742	357	4	t.	t.	PROPN
ejpam-5742	357	5	gaketem	gaketem	PROPN
ejpam-5742	357	6	,	,	PUNCT
ejpam-5742	357	7	r.	r.	PROPN
ejpam-5742	357	8	k.	k.	PROPN
ejpam-5742	357	9	bandaru	bandaru	PROPN
ejpam-5742	357	10	/	/	SYM
ejpam-5742	357	11	eur	eur	PROPN
ejpam-5742	357	12	.	.	PUNCT
ejpam-5742	358	1	j.	j.	PROPN
ejpam-5742	358	2	pure	pure	PROPN
ejpam-5742	358	3	appl	appl	PROPN
ejpam-5742	358	4	.	.	PROPN
ejpam-5742	358	5	math	math	PROPN
ejpam-5742	358	6	,	,	PUNCT
ejpam-5742	358	7	18	18	NUM
ejpam-5742	358	8	(	(	PUNCT
ejpam-5742	358	9	2	2	NUM
ejpam-5742	358	10	)	)	PUNCT
ejpam-5742	358	11	(	(	PUNCT
ejpam-5742	358	12	2025	2025	NUM
ejpam-5742	358	13	)	)	PUNCT
ejpam-5742	358	14	,	,	PUNCT
ejpam-5742	358	15	5742	5742	NUM
ejpam-5742	358	16	11	11	NUM
ejpam-5742	358	17	of	of	ADP
ejpam-5742	358	18	14	14	NUM
ejpam-5742	358	19	proof	proof	NOUN
ejpam-5742	358	20	.	.	PUNCT
ejpam-5742	359	1	1	1	NUM
ejpam-5742	359	2	⇒	⇒	NOUN
ejpam-5742	359	3	2	2	NUM
ejpam-5742	359	4	:	:	PUNCT
ejpam-5742	359	5	obvious	obvious	ADJ
ejpam-5742	359	6	2	2	NUM
ejpam-5742	359	7	⇒	⇒	NOUN
ejpam-5742	359	8	3	3	NUM
ejpam-5742	359	9	:	:	PUNCT
ejpam-5742	359	10	assume	assume	VERB
ejpam-5742	359	11	condition	condition	NOUN
ejpam-5742	359	12	2	2	X
ejpam-5742	359	13	.	.	PUNCT
ejpam-5742	359	14	consider	consider	VERB
ejpam-5742	359	15	any	any	DET
ejpam-5742	359	16	prime	prime	ADJ
ejpam-5742	359	17	m−filter	m−filter	NOUN
ejpam-5742	359	18	x	x	PUNCT
ejpam-5742	359	19	of	of	ADP
ejpam-5742	359	20	r.	r.	PROPN
ejpam-5742	359	21	it	it	PRON
ejpam-5742	359	22	follows	follow	VERB
ejpam-5742	359	23	that	that	SCONJ
ejpam-5742	359	24	x	x	PRON
ejpam-5742	359	25	qualifies	qualify	VERB
ejpam-5742	359	26	as	as	ADP
ejpam-5742	359	27	a	a	DET
ejpam-5742	359	28	minimal	minimal	ADJ
ejpam-5742	359	29	prime	prime	ADJ
ejpam-5742	359	30	filter	filter	NOUN
ejpam-5742	359	31	of	of	ADP
ejpam-5742	359	32	r.	r.	PROPN
ejpam-5742	359	33	by	by	ADP
ejpam-5742	359	34	2	2	NUM
ejpam-5742	359	35	,	,	PUNCT
ejpam-5742	359	36	we	we	PRON
ejpam-5742	359	37	get	get	VERB
ejpam-5742	359	38	x	x	X
ejpam-5742	359	39	=	=	SYM
ejpam-5742	359	40	(	(	PUNCT
ejpam-5742	359	41	κ)+	κ)+	PROPN
ejpam-5742	359	42	,	,	PUNCT
ejpam-5742	359	43	for	for	ADP
ejpam-5742	359	44	some	some	DET
ejpam-5742	359	45	non	non	ADJ
ejpam-5742	359	46	maximal	maximal	ADJ
ejpam-5742	359	47	element	element	NOUN
ejpam-5742	359	48	κ	κ	NOUN
ejpam-5742	359	49	of	of	ADP
ejpam-5742	359	50	x+	x+	PROPN
ejpam-5742	359	51	.	.	PUNCT
ejpam-5742	360	1	since	since	SCONJ
ejpam-5742	360	2	r	r	NOUN
ejpam-5742	360	3	is	be	AUX
ejpam-5742	360	4	an	an	DET
ejpam-5742	360	5	e−complemented	e−complemented	ADJ
ejpam-5742	360	6	adl	adl	NOUN
ejpam-5742	360	7	,	,	PUNCT
ejpam-5742	360	8	there	there	PRON
ejpam-5742	360	9	is	be	VERB
ejpam-5742	360	10	η	η	PROPN
ejpam-5742	360	11	of	of	ADP
ejpam-5742	360	12	r	r	NOUN
ejpam-5742	360	13	satisfying	satisfy	VERB
ejpam-5742	360	14	κ∧η	κ∧η	NOUN
ejpam-5742	360	15	∈	∈	PROPN
ejpam-5742	360	16	e	e	NOUN
ejpam-5742	360	17	and	and	CCONJ
ejpam-5742	360	18	κ∨η	κ∨η	PROPN
ejpam-5742	360	19	∈	∈	PROPN
ejpam-5742	360	20	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	360	21	)	)	PUNCT
ejpam-5742	360	22	.	.	PUNCT
ejpam-5742	361	1	it	it	PRON
ejpam-5742	361	2	gives	give	VERB
ejpam-5742	361	3	η	η	PROPN
ejpam-5742	361	4	∈	∈	PROPN
ejpam-5742	361	5	(	(	PUNCT
ejpam-5742	361	6	κ)+	κ)+	X
ejpam-5742	362	1	=	=	SYM
ejpam-5742	362	2	x	x	PROPN
ejpam-5742	362	3	.	.	PUNCT
ejpam-5742	363	1	therefore	therefore	ADV
ejpam-5742	363	2	(	(	PUNCT
ejpam-5742	363	3	η)++	η)++	PROPN
ejpam-5742	363	4	⊆	⊆	NUM
ejpam-5742	363	5	p++	p++	NOUN
ejpam-5742	363	6	=	=	SYM
ejpam-5742	363	7	x	x	SYM
ejpam-5742	363	8	=	=	SYM
ejpam-5742	363	9	(	(	PUNCT
ejpam-5742	363	10	κ)+	κ)+	NUM
ejpam-5742	363	11	and	and	CCONJ
ejpam-5742	363	12	it	it	PRON
ejpam-5742	363	13	gives	give	VERB
ejpam-5742	363	14	(	(	PUNCT
ejpam-5742	363	15	η)++	η)++	PROPN
ejpam-5742	363	16	⊆	⊆	NUM
ejpam-5742	363	17	(	(	PUNCT
ejpam-5742	363	18	κ)+	κ)+	X
ejpam-5742	363	19	.	.	PUNCT
ejpam-5742	364	1	let	let	VERB
ejpam-5742	364	2	τ	τ	PROPN
ejpam-5742	364	3	∈	∈	PROPN
ejpam-5742	364	4	(	(	PUNCT
ejpam-5742	364	5	κ)+	κ)+	PROPN
ejpam-5742	364	6	.	.	PUNCT
ejpam-5742	365	1	then	then	ADV
ejpam-5742	365	2	τ	τ	PROPN
ejpam-5742	365	3	∨	∨	NUM
ejpam-5742	365	4	κ	κ	PROPN
ejpam-5742	365	5	∈	∈	PROPN
ejpam-5742	365	6	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	365	7	)	)	PUNCT
ejpam-5742	365	8	.	.	PUNCT
ejpam-5742	366	1	which	which	PRON
ejpam-5742	366	2	leads	lead	VERB
ejpam-5742	366	3	τ	τ	PROPN
ejpam-5742	366	4	∈	∈	PROPN
ejpam-5742	366	5	(	(	PUNCT
ejpam-5742	366	6	η)++	η)++	PROPN
ejpam-5742	366	7	,	,	PUNCT
ejpam-5742	366	8	because	because	SCONJ
ejpam-5742	366	9	κ	κ	PROPN
ejpam-5742	366	10	∈	∈	PROPN
ejpam-5742	366	11	(	(	PUNCT
ejpam-5742	366	12	η)+	η)+	X
ejpam-5742	366	13	.	.	PUNCT
ejpam-5742	367	1	therefore	therefore	ADV
ejpam-5742	367	2	(	(	PUNCT
ejpam-5742	367	3	κ)+	κ)+	NOUN
ejpam-5742	367	4	⊆	⊆	NUM
ejpam-5742	367	5	(	(	PUNCT
ejpam-5742	367	6	η)++	η)++	NOUN
ejpam-5742	367	7	.	.	PUNCT
ejpam-5742	368	1	hence	hence	ADV
ejpam-5742	368	2	(	(	PUNCT
ejpam-5742	368	3	κ)+	κ)+	X
ejpam-5742	368	4	=	=	SYM
ejpam-5742	368	5	(	(	PUNCT
ejpam-5742	368	6	η)++	η)++	NOUN
ejpam-5742	368	7	=	=	PUNCT
ejpam-5742	368	8	x	x	PROPN
ejpam-5742	368	9	.	.	PUNCT
ejpam-5742	368	10	3	3	NUM
ejpam-5742	368	11	⇒	⇒	NOUN
ejpam-5742	368	12	4	4	NUM
ejpam-5742	368	13	:	:	PUNCT
ejpam-5742	368	14	assume	assume	VERB
ejpam-5742	368	15	condition	condition	NOUN
ejpam-5742	368	16	3	3	X
ejpam-5742	368	17	.	.	PUNCT
ejpam-5742	369	1	let	let	VERB
ejpam-5742	369	2	s	s	PRON
ejpam-5742	369	3	be	be	AUX
ejpam-5742	369	4	any	any	DET
ejpam-5742	369	5	m−filter	m−filter	NOUN
ejpam-5742	369	6	of	of	ADP
ejpam-5742	369	7	r.	r.	PROPN
ejpam-5742	369	8	suppose	suppose	VERB
ejpam-5742	369	9	that	that	SCONJ
ejpam-5742	369	10	s	s	AUX
ejpam-5742	369	11	̸=	̸=	PROPN
ejpam-5742	369	12	(	(	PUNCT
ejpam-5742	369	13	κ)++	κ)++	PROPN
ejpam-5742	369	14	,	,	PUNCT
ejpam-5742	369	15	for	for	ADP
ejpam-5742	369	16	all	all	DET
ejpam-5742	369	17	κ	κ	PROPN
ejpam-5742	369	18	∈	∈	PROPN
ejpam-5742	369	19	r.	r.	NOUN
ejpam-5742	369	20	consider	consider	VERB
ejpam-5742	369	21	f	f	PROPN
ejpam-5742	369	22	=	=	PRON
ejpam-5742	369	23	{	{	PUNCT
ejpam-5742	369	24	t	t	PROPN
ejpam-5742	369	25	|	|	ADV
ejpam-5742	369	26	t	t	PROPN
ejpam-5742	369	27	is	be	AUX
ejpam-5742	369	28	an	an	DET
ejpam-5742	369	29	m−	m−	PROPN
ejpam-5742	369	30	filter	filter	NOUN
ejpam-5742	369	31	and	and	CCONJ
ejpam-5742	369	32	t	t	PROPN
ejpam-5742	369	33	̸=	̸=	PROPN
ejpam-5742	369	34	(	(	PUNCT
ejpam-5742	369	35	κ)++	κ)++	PROPN
ejpam-5742	369	36	,	,	PUNCT
ejpam-5742	369	37	for	for	ADP
ejpam-5742	369	38	all	all	PRON
ejpam-5742	369	39	κ	κ	PART
ejpam-5742	369	40	∈	∈	PROPN
ejpam-5742	369	41	r	r	NOUN
ejpam-5742	369	42	}	}	PUNCT
ejpam-5742	369	43	.	.	PUNCT
ejpam-5742	370	1	clearly	clearly	ADV
ejpam-5742	370	2	,	,	PUNCT
ejpam-5742	370	3	s	s	VERB
ejpam-5742	370	4	∈	∈	PROPN
ejpam-5742	370	5	f	f	NOUN
ejpam-5742	371	1	and	and	CCONJ
ejpam-5742	371	2	hence	hence	ADV
ejpam-5742	371	3	f	f	PROPN
ejpam-5742	371	4	̸=	̸=	PROPN
ejpam-5742	371	5	∅.	∅.	ADV
ejpam-5742	371	6	by	by	ADP
ejpam-5742	371	7	the	the	DET
ejpam-5742	371	8	zorn	zorn	PROPN
ejpam-5742	371	9	’s	’s	PART
ejpam-5742	371	10	lemma	lemma	PROPN
ejpam-5742	371	11	,	,	PUNCT
ejpam-5742	371	12	f	f	PROPN
ejpam-5742	371	13	has	have	VERB
ejpam-5742	371	14	a	a	DET
ejpam-5742	371	15	maximal	maximal	ADJ
ejpam-5742	371	16	element	element	NOUN
ejpam-5742	371	17	say	say	VERB
ejpam-5742	371	18	p.	p.	NOUN
ejpam-5742	371	19	clearly	clearly	ADV
ejpam-5742	371	20	,	,	PUNCT
ejpam-5742	371	21	p	p	PRON
ejpam-5742	371	22	is	be	AUX
ejpam-5742	371	23	a	a	DET
ejpam-5742	371	24	prime	prime	ADJ
ejpam-5742	371	25	filter	filter	NOUN
ejpam-5742	371	26	and	and	CCONJ
ejpam-5742	371	27	m	m	PROPN
ejpam-5742	371	28	̸=	̸=	PROPN
ejpam-5742	371	29	(	(	PUNCT
ejpam-5742	371	30	κ)++	κ)++	PROPN
ejpam-5742	371	31	,	,	PUNCT
ejpam-5742	371	32	for	for	ADP
ejpam-5742	371	33	all	all	PRON
ejpam-5742	371	34	κ	κ	PART
ejpam-5742	371	35	∈	∈	PROPN
ejpam-5742	371	36	r	r	NOUN
ejpam-5742	371	37	,	,	PUNCT
ejpam-5742	371	38	this	this	PRON
ejpam-5742	371	39	leads	lead	VERB
ejpam-5742	371	40	a	a	DET
ejpam-5742	371	41	contradiction	contradiction	NOUN
ejpam-5742	371	42	.	.	PUNCT
ejpam-5742	372	1	hence	hence	ADV
ejpam-5742	372	2	s	s	PART
ejpam-5742	372	3	=	=	SYM
ejpam-5742	372	4	(	(	PUNCT
ejpam-5742	372	5	κ)++	κ)++	PROPN
ejpam-5742	372	6	,	,	PUNCT
ejpam-5742	372	7	for	for	ADP
ejpam-5742	372	8	some	some	DET
ejpam-5742	372	9	κ	κ	PROPN
ejpam-5742	372	10	∈	∈	PROPN
ejpam-5742	372	11	r.	r.	PROPN
ejpam-5742	372	12	4	4	NUM
ejpam-5742	372	13	⇒	⇒	PROPN
ejpam-5742	372	14	5	5	NUM
ejpam-5742	372	15	:	:	PUNCT
ejpam-5742	372	16	assume	assume	VERB
ejpam-5742	372	17	condition	condition	NOUN
ejpam-5742	372	18	4	4	X
ejpam-5742	372	19	.	.	PUNCT
ejpam-5742	373	1	let	let	VERB
ejpam-5742	373	2	x	x	PRON
ejpam-5742	373	3	be	be	AUX
ejpam-5742	373	4	a	a	DET
ejpam-5742	373	5	minimal	minimal	ADJ
ejpam-5742	373	6	prime	prime	ADJ
ejpam-5742	373	7	filter	filter	NOUN
ejpam-5742	373	8	of	of	ADP
ejpam-5742	373	9	r.	r.	PROPN
ejpam-5742	373	10	then	then	ADV
ejpam-5742	373	11	x	x	PUNCT
ejpam-5742	373	12	is	be	AUX
ejpam-5742	373	13	an	an	DET
ejpam-5742	373	14	m−filter	m−filter	NOUN
ejpam-5742	373	15	of	of	ADP
ejpam-5742	373	16	r.	r.	PROPN
ejpam-5742	373	17	by	by	ADP
ejpam-5742	373	18	4	4	NUM
ejpam-5742	373	19	,	,	PUNCT
ejpam-5742	373	20	we	we	PRON
ejpam-5742	373	21	get	get	VERB
ejpam-5742	373	22	that	that	PRON
ejpam-5742	373	23	x	x	PUNCT
ejpam-5742	373	24	=	=	PRON
ejpam-5742	373	25	(	(	PUNCT
ejpam-5742	373	26	κ)++	κ)++	PROPN
ejpam-5742	373	27	,	,	PUNCT
ejpam-5742	373	28	for	for	ADP
ejpam-5742	373	29	some	some	DET
ejpam-5742	373	30	κ	κ	PROPN
ejpam-5742	373	31	∈	∈	PROPN
ejpam-5742	373	32	r.	r.	PROPN
ejpam-5742	373	33	clearly	clearly	ADV
ejpam-5742	373	34	κ	κ	VERB
ejpam-5742	373	35	∈	∈	PROPN
ejpam-5742	373	36	x	x	X
ejpam-5742	373	37	.	.	PUNCT
ejpam-5742	374	1	as	as	SCONJ
ejpam-5742	374	2	p	p	PRON
ejpam-5742	374	3	is	be	AUX
ejpam-5742	374	4	minimal	minimal	ADJ
ejpam-5742	374	5	and	and	CCONJ
ejpam-5742	374	6	κ	κ	ADP
ejpam-5742	374	7	∈	∈	PROPN
ejpam-5742	374	8	x	x	INTJ
ejpam-5742	374	9	,	,	PUNCT
ejpam-5742	374	10	there	there	PRON
ejpam-5742	374	11	is	be	VERB
ejpam-5742	374	12	η	η	PROPN
ejpam-5742	374	13	/∈	/∈	PROPN
ejpam-5742	374	14	x	x	PUNCT
ejpam-5742	374	15	satisfying	satisfy	VERB
ejpam-5742	374	16	the	the	DET
ejpam-5742	374	17	property	property	NOUN
ejpam-5742	374	18	that	that	PRON
ejpam-5742	374	19	κ	κ	PROPN
ejpam-5742	374	20	∨	∨	PROPN
ejpam-5742	374	21	η	η	PROPN
ejpam-5742	374	22	∈	∈	PROPN
ejpam-5742	374	23	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	374	24	)	)	PUNCT
ejpam-5742	374	25	.	.	PUNCT
ejpam-5742	375	1	it	it	PRON
ejpam-5742	375	2	gives	give	VERB
ejpam-5742	375	3	η	η	PROPN
ejpam-5742	375	4	∈	∈	PROPN
ejpam-5742	375	5	(	(	PUNCT
ejpam-5742	375	6	κ)+	κ)+	X
ejpam-5742	375	7	=	=	PUNCT
ejpam-5742	375	8	x+	x+	PROPN
ejpam-5742	375	9	and	and	CCONJ
ejpam-5742	375	10	hence	hence	ADV
ejpam-5742	375	11	η	η	PROPN
ejpam-5742	375	12	∈	∈	PROPN
ejpam-5742	375	13	x+	x+	PROPN
ejpam-5742	375	14	.	.	PUNCT
ejpam-5742	376	1	we	we	PRON
ejpam-5742	376	2	derive	derive	VERB
ejpam-5742	376	3	that	that	SCONJ
ejpam-5742	376	4	x+	x+	PROPN
ejpam-5742	376	5	̸=	̸=	PROPN
ejpam-5742	376	6	mmax.elt(r	mmax.elt(r	NUM
ejpam-5742	376	7	)	)	PUNCT
ejpam-5742	376	8	.	.	PUNCT
ejpam-5742	377	1	if	if	SCONJ
ejpam-5742	377	2	x+	x+	PROPN
ejpam-5742	377	3	=	=	SYM
ejpam-5742	377	4	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	377	5	)	)	PUNCT
ejpam-5742	378	1	then	then	ADV
ejpam-5742	378	2	η	η	PROPN
ejpam-5742	378	3	∈	∈	PROPN
ejpam-5742	378	4	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	378	5	)	)	PUNCT
ejpam-5742	378	6	,	,	PUNCT
ejpam-5742	378	7	get	get	VERB
ejpam-5742	378	8	a	a	DET
ejpam-5742	378	9	contradiction	contradiction	NOUN
ejpam-5742	378	10	to	to	ADP
ejpam-5742	378	11	η	η	PROPN
ejpam-5742	378	12	/∈	/∈	PROPN
ejpam-5742	378	13	x	x	X
ejpam-5742	378	14	.	.	PUNCT
ejpam-5742	379	1	hence	hence	ADV
ejpam-5742	379	2	x+	x+	PUNCT
ejpam-5742	379	3	̸=	̸=	PROPN
ejpam-5742	379	4	mmax.elt(r	mmax.elt(r	NUM
ejpam-5742	379	5	)	)	PUNCT
ejpam-5742	379	6	.	.	PUNCT
ejpam-5742	380	1	thus	thus	ADV
ejpam-5742	380	2	x	x	PRON
ejpam-5742	380	3	is	be	AUX
ejpam-5742	380	4	non	non	ADJ
ejpam-5742	380	5	co	co	ADJ
ejpam-5742	380	6	-	-	ADJ
ejpam-5742	380	7	dense	dense	ADJ
ejpam-5742	380	8	.	.	PUNCT
ejpam-5742	381	1	5	5	NUM
ejpam-5742	381	2	⇒	⇒	NOUN
ejpam-5742	381	3	1	1	NUM
ejpam-5742	381	4	:	:	PUNCT
ejpam-5742	381	5	assume	assume	VERB
ejpam-5742	381	6	condition	condition	NOUN
ejpam-5742	381	7	5	5	NUM
ejpam-5742	381	8	.	.	PUNCT
ejpam-5742	382	1	let	let	VERB
ejpam-5742	382	2	s	s	PRON
ejpam-5742	382	3	be	be	AUX
ejpam-5742	382	4	an	an	DET
ejpam-5742	382	5	m−filter	m−filter	NOUN
ejpam-5742	382	6	of	of	ADP
ejpam-5742	382	7	r.	r.	PROPN
ejpam-5742	382	8	then	then	ADV
ejpam-5742	382	9	s	s	VERB
ejpam-5742	382	10	=	=	SYM
ejpam-5742	382	11	m(f	m(f	PROPN
ejpam-5742	382	12	)	)	PUNCT
ejpam-5742	382	13	,	,	PUNCT
ejpam-5742	382	14	for	for	ADP
ejpam-5742	382	15	some	some	DET
ejpam-5742	382	16	ideal	ideal	ADJ
ejpam-5742	382	17	f	f	PROPN
ejpam-5742	382	18	of	of	ADP
ejpam-5742	382	19	r.	r.	PROPN
ejpam-5742	382	20	now	now	ADV
ejpam-5742	382	21	we	we	PRON
ejpam-5742	382	22	prove	prove	VERB
ejpam-5742	382	23	that	that	PRON
ejpam-5742	382	24	s	s	VERB
ejpam-5742	382	25	=	=	NOUN
ejpam-5742	382	26	s++	s++	NOUN
ejpam-5742	382	27	.	.	PUNCT
ejpam-5742	383	1	clearly	clearly	ADV
ejpam-5742	383	2	,	,	PUNCT
ejpam-5742	383	3	we	we	PRON
ejpam-5742	383	4	have	have	VERB
ejpam-5742	383	5	that	that	PRON
ejpam-5742	383	6	s	s	VERB
ejpam-5742	383	7	⊆	⊆	NUM
ejpam-5742	383	8	s++	s++	NOUN
ejpam-5742	383	9	.	.	PUNCT
ejpam-5742	384	1	let	let	VERB
ejpam-5742	384	2	ν	ν	PRON
ejpam-5742	384	3	∈	∈	PROPN
ejpam-5742	384	4	s++	s++	NOUN
ejpam-5742	384	5	.	.	PUNCT
ejpam-5742	385	1	we	we	PRON
ejpam-5742	385	2	show	show	VERB
ejpam-5742	385	3	that	that	SCONJ
ejpam-5742	385	4	(	(	PUNCT
ejpam-5742	385	5	s	s	NOUN
ejpam-5742	385	6	∨	∨	NUM
ejpam-5742	385	7	s+	s+	NUM
ejpam-5742	385	8	)	)	PUNCT
ejpam-5742	385	9	∩	∩	NOUN
ejpam-5742	385	10	e	e	AUX
ejpam-5742	385	11	̸=	̸=	PROPN
ejpam-5742	385	12	∅.	∅.	ADV
ejpam-5742	385	13	suppose	suppose	VERB
ejpam-5742	385	14	(	(	PUNCT
ejpam-5742	385	15	s	s	NOUN
ejpam-5742	385	16	∨	∨	NUM
ejpam-5742	385	17	s+	s+	NUM
ejpam-5742	385	18	)	)	PUNCT
ejpam-5742	385	19	∩	∩	NOUN
ejpam-5742	385	20	e	e	NOUN
ejpam-5742	385	21	=	=	PRON
ejpam-5742	385	22	∅.	∅.	NOUN
ejpam-5742	385	23	as	as	SCONJ
ejpam-5742	385	24	e	e	PROPN
ejpam-5742	385	25	is	be	AUX
ejpam-5742	385	26	an	an	DET
ejpam-5742	385	27	ideal	ideal	NOUN
ejpam-5742	385	28	of	of	ADP
ejpam-5742	385	29	r	r	NOUN
ejpam-5742	385	30	,	,	PUNCT
ejpam-5742	385	31	there	there	PRON
ejpam-5742	385	32	is	be	VERB
ejpam-5742	385	33	a	a	DET
ejpam-5742	385	34	prime	prime	ADJ
ejpam-5742	385	35	filter	filter	NOUN
ejpam-5742	385	36	x	x	NOUN
ejpam-5742	385	37	of	of	ADP
ejpam-5742	385	38	r	r	NOUN
ejpam-5742	385	39	satisfies	satisfie	NOUN
ejpam-5742	385	40	s	s	PART
ejpam-5742	385	41	∨	∨	NOUN
ejpam-5742	385	42	s+	s+	PUNCT
ejpam-5742	385	43	⊆	⊆	NUM
ejpam-5742	385	44	x	x	SYM
ejpam-5742	385	45	and	and	CCONJ
ejpam-5742	385	46	x	x	X
ejpam-5742	385	47	∩	∩	ADJ
ejpam-5742	385	48	e	e	NOUN
ejpam-5742	385	49	=	=	PRON
ejpam-5742	385	50	∅.	∅.	ADV
ejpam-5742	385	51	let	let	VERB
ejpam-5742	385	52	κ	κ	PRON
ejpam-5742	385	53	∈	∈	PROPN
ejpam-5742	385	54	x	x	X
ejpam-5742	385	55	.	.	PUNCT
ejpam-5742	386	1	since	since	SCONJ
ejpam-5742	386	2	r	r	NOUN
ejpam-5742	386	3	is	be	AUX
ejpam-5742	386	4	an	an	DET
ejpam-5742	386	5	e−complemented	e−complemented	ADJ
ejpam-5742	386	6	adl	adl	NOUN
ejpam-5742	386	7	,	,	PUNCT
ejpam-5742	386	8	there	there	PRON
ejpam-5742	386	9	is	be	VERB
ejpam-5742	386	10	η	η	PROPN
ejpam-5742	386	11	∈	∈	PROPN
ejpam-5742	386	12	r	r	NOUN
ejpam-5742	386	13	such	such	ADJ
ejpam-5742	386	14	that	that	SCONJ
ejpam-5742	386	15	κ	κ	PROPN
ejpam-5742	386	16	∧	∧	PROPN
ejpam-5742	386	17	η	η	PROPN
ejpam-5742	386	18	∈	∈	PROPN
ejpam-5742	386	19	e	e	PROPN
ejpam-5742	386	20	and	and	CCONJ
ejpam-5742	386	21	κ	κ	PROPN
ejpam-5742	386	22	∨	∨	PROPN
ejpam-5742	386	23	η	η	PROPN
ejpam-5742	386	24	∈	∈	PROPN
ejpam-5742	386	25	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	386	26	)	)	PUNCT
ejpam-5742	386	27	.	.	PUNCT
ejpam-5742	387	1	which	which	PRON
ejpam-5742	387	2	gives	give	VERB
ejpam-5742	387	3	κ	κ	ADP
ejpam-5742	387	4	∧	∧	PROPN
ejpam-5742	387	5	η	η	PROPN
ejpam-5742	387	6	/∈	/∈	PROPN
ejpam-5742	387	7	x	x	X
ejpam-5742	387	8	and	and	CCONJ
ejpam-5742	387	9	hence	hence	ADV
ejpam-5742	387	10	η	η	PROPN
ejpam-5742	387	11	/∈	/∈	PROPN
ejpam-5742	388	1	x	x	X
ejpam-5742	388	2	.	.	PUNCT
ejpam-5742	389	1	therefore	therefore	ADV
ejpam-5742	389	2	x	x	X
ejpam-5742	389	3	is	be	AUX
ejpam-5742	389	4	a	a	DET
ejpam-5742	389	5	minimal	minimal	ADJ
ejpam-5742	389	6	prime	prime	ADJ
ejpam-5742	389	7	filter	filter	NOUN
ejpam-5742	389	8	of	of	ADP
ejpam-5742	389	9	r.	r.	PROPN
ejpam-5742	389	10	by	by	ADP
ejpam-5742	389	11	our	our	PRON
ejpam-5742	389	12	assumption	assumption	NOUN
ejpam-5742	389	13	we	we	PRON
ejpam-5742	389	14	have	have	VERB
ejpam-5742	389	15	x	x	PROPN
ejpam-5742	389	16	is	be	AUX
ejpam-5742	389	17	non	non	ADJ
ejpam-5742	389	18	co	co	ADJ
ejpam-5742	389	19	-	-	ADJ
ejpam-5742	389	20	dense	dense	ADJ
ejpam-5742	389	21	.	.	PUNCT
ejpam-5742	390	1	since	since	SCONJ
ejpam-5742	390	2	(	(	PUNCT
ejpam-5742	390	3	s	s	NOUN
ejpam-5742	390	4	∨	∨	NUM
ejpam-5742	390	5	s+	s+	PUNCT
ejpam-5742	390	6	)	)	PUNCT
ejpam-5742	390	7	⊆	⊆	NUM
ejpam-5742	390	8	x	x	X
ejpam-5742	390	9	,	,	PUNCT
ejpam-5742	390	10	we	we	PRON
ejpam-5742	390	11	have	have	VERB
ejpam-5742	390	12	that	that	PRON
ejpam-5742	390	13	x+	x+	PROPN
ejpam-5742	390	14	⊆	⊆	NUM
ejpam-5742	390	15	(	(	PUNCT
ejpam-5742	390	16	s	s	NOUN
ejpam-5742	390	17	∨	∨	NOUN
ejpam-5742	390	18	s+)+	s+)+	ADJ
ejpam-5742	390	19	=	=	SYM
ejpam-5742	390	20	s+	s+	NOUN
ejpam-5742	390	21	∩	∩	PROPN
ejpam-5742	390	22	s++	s++	NOUN
ejpam-5742	390	23	=	=	SYM
ejpam-5742	390	24	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	390	25	)	)	PUNCT
ejpam-5742	390	26	.	.	PUNCT
ejpam-5742	391	1	that	that	PRON
ejpam-5742	391	2	implies	imply	VERB
ejpam-5742	391	3	x+	x+	NUM
ejpam-5742	391	4	⊆	⊆	NUM
ejpam-5742	391	5	mmax.elt(r	mmax.elt(r	NUM
ejpam-5742	391	6	)	)	PUNCT
ejpam-5742	391	7	and	and	CCONJ
ejpam-5742	391	8	hence	hence	ADV
ejpam-5742	391	9	x+	x+	ADJ
ejpam-5742	391	10	=	=	SYM
ejpam-5742	391	11	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	391	12	)	)	PUNCT
ejpam-5742	391	13	,	,	PUNCT
ejpam-5742	391	14	it	it	PRON
ejpam-5742	391	15	gives	give	VERB
ejpam-5742	391	16	a	a	DET
ejpam-5742	391	17	contradiction	contradiction	NOUN
ejpam-5742	391	18	to	to	ADP
ejpam-5742	391	19	x	x	VERB
ejpam-5742	391	20	is	be	AUX
ejpam-5742	391	21	a	a	DET
ejpam-5742	391	22	non	non	X
ejpam-5742	391	23	co	co	NOUN
ejpam-5742	391	24	-	-	ADJ
ejpam-5742	391	25	dense	dense	ADJ
ejpam-5742	391	26	.	.	PUNCT
ejpam-5742	392	1	therefore	therefore	ADV
ejpam-5742	392	2	(	(	PUNCT
ejpam-5742	392	3	s	s	NOUN
ejpam-5742	392	4	∨	∨	NUM
ejpam-5742	392	5	s+	s+	NUM
ejpam-5742	392	6	)	)	PUNCT
ejpam-5742	392	7	∩	∩	NOUN
ejpam-5742	392	8	e	e	X
ejpam-5742	392	9	̸=	̸=	PROPN
ejpam-5742	392	10	∅.	∅.	ADV
ejpam-5742	392	11	now	now	ADV
ejpam-5742	392	12	choose	choose	VERB
ejpam-5742	392	13	µ	µ	PRON
ejpam-5742	392	14	∈	∈	NOUN
ejpam-5742	392	15	(	(	PUNCT
ejpam-5742	392	16	s	s	NOUN
ejpam-5742	392	17	∨	∨	NUM
ejpam-5742	392	18	s+	s+	NUM
ejpam-5742	392	19	)	)	PUNCT
ejpam-5742	392	20	∩	∩	PROPN
ejpam-5742	392	21	e.	e.	PROPN
ejpam-5742	392	22	then	then	ADV
ejpam-5742	392	23	µ	µ	PROPN
ejpam-5742	392	24	∈	∈	PROPN
ejpam-5742	392	25	s	s	PART
ejpam-5742	392	26	∨	∨	NOUN
ejpam-5742	392	27	s+	s+	NUM
ejpam-5742	392	28	and	and	CCONJ
ejpam-5742	392	29	µ	µ	PROPN
ejpam-5742	392	30	∈	∈	PROPN
ejpam-5742	392	31	e.	e.	PROPN
ejpam-5742	392	32	that	that	PRON
ejpam-5742	392	33	implies	imply	VERB
ejpam-5742	392	34	µ	µ	PROPN
ejpam-5742	392	35	=	=	SYM
ejpam-5742	392	36	δ	δ	PROPN
ejpam-5742	392	37	∧	∧	PROPN
ejpam-5742	392	38	σ	σ	PROPN
ejpam-5742	392	39	,	,	PUNCT
ejpam-5742	392	40	for	for	ADP
ejpam-5742	392	41	some	some	DET
ejpam-5742	392	42	δ	δ	PROPN
ejpam-5742	392	43	∈	∈	PROPN
ejpam-5742	392	44	s	s	PROPN
ejpam-5742	392	45	,	,	PUNCT
ejpam-5742	392	46	σ	σ	PROPN
ejpam-5742	392	47	∈	∈	PROPN
ejpam-5742	392	48	s+	s+	PUNCT
ejpam-5742	392	49	and	and	CCONJ
ejpam-5742	392	50	(	(	PUNCT
ejpam-5742	392	51	µ)+	µ)+	PROPN
ejpam-5742	392	52	=	=	SYM
ejpam-5742	392	53	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	392	54	)	)	PUNCT
ejpam-5742	392	55	.	.	PUNCT
ejpam-5742	393	1	now	now	ADV
ejpam-5742	393	2	(	(	PUNCT
ejpam-5742	393	3	δ)+	δ)+	NUM
ejpam-5742	393	4	∩	∩	NOUN
ejpam-5742	393	5	(	(	PUNCT
ejpam-5742	393	6	σ)+	σ)+	X
ejpam-5742	393	7	=	=	SYM
ejpam-5742	393	8	(	(	PUNCT
ejpam-5742	393	9	δ	δ	PROPN
ejpam-5742	393	10	∧	∧	PROPN
ejpam-5742	393	11	σ)+	σ)+	PROPN
ejpam-5742	394	1	=	=	SYM
ejpam-5742	395	1	(	(	PUNCT
ejpam-5742	395	2	µ)+	µ)+	PROPN
ejpam-5742	395	3	=	=	SYM
ejpam-5742	395	4	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	395	5	)	)	PUNCT
ejpam-5742	395	6	.	.	PUNCT
ejpam-5742	396	1	since	since	SCONJ
ejpam-5742	396	2	δ	δ	PROPN
ejpam-5742	396	3	∈	∈	PROPN
ejpam-5742	396	4	s	s	PART
ejpam-5742	396	5	=	=	SYM
ejpam-5742	396	6	m(f	m(f	PROPN
ejpam-5742	396	7	)	)	PUNCT
ejpam-5742	396	8	,	,	PUNCT
ejpam-5742	396	9	there	there	PRON
ejpam-5742	396	10	is	be	VERB
ejpam-5742	396	11	τ	τ	PROPN
ejpam-5742	396	12	∈	∈	PROPN
ejpam-5742	396	13	f	f	NOUN
ejpam-5742	396	14	and	and	CCONJ
ejpam-5742	396	15	it	it	PRON
ejpam-5742	396	16	satisfying	satisfy	VERB
ejpam-5742	396	17	δ∨	δ∨	PROPN
ejpam-5742	396	18	τ	τ	X
ejpam-5742	396	19	∈	∈	PROPN
ejpam-5742	396	20	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	396	21	)	)	PUNCT
ejpam-5742	396	22	.	.	PUNCT
ejpam-5742	397	1	since	since	SCONJ
ejpam-5742	397	2	ν	ν	PROPN
ejpam-5742	397	3	∈	∈	PROPN
ejpam-5742	397	4	s++	s++	NOUN
ejpam-5742	397	5	and	and	CCONJ
ejpam-5742	397	6	σ	σ	PROPN
ejpam-5742	397	7	∈	∈	PROPN
ejpam-5742	397	8	s+	s+	ADV
ejpam-5742	397	9	,	,	PUNCT
ejpam-5742	397	10	we	we	PRON
ejpam-5742	397	11	get	get	VERB
ejpam-5742	397	12	that	that	PRON
ejpam-5742	397	13	ν	ν	PROPN
ejpam-5742	397	14	∨σ	∨σ	PROPN
ejpam-5742	397	15	∈	∈	PROPN
ejpam-5742	397	16	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	397	17	)	)	PUNCT
ejpam-5742	397	18	.	.	PUNCT
ejpam-5742	398	1	which	which	PRON
ejpam-5742	398	2	gives	give	VERB
ejpam-5742	398	3	ν	ν	PRON
ejpam-5742	398	4	∈	∈	PROPN
ejpam-5742	398	5	(	(	PUNCT
ejpam-5742	398	6	σ)+	σ)+	PROPN
ejpam-5742	398	7	.	.	PUNCT
ejpam-5742	399	1	since	since	SCONJ
ejpam-5742	399	2	(	(	PUNCT
ejpam-5742	399	3	δ)+	δ)+	NUM
ejpam-5742	399	4	∩	∩	NOUN
ejpam-5742	399	5	(	(	PUNCT
ejpam-5742	399	6	σ)+	σ)+	PROPN
ejpam-5742	399	7	=	=	SYM
ejpam-5742	399	8	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	399	9	)	)	PUNCT
ejpam-5742	399	10	,	,	PUNCT
ejpam-5742	399	11	we	we	PRON
ejpam-5742	399	12	get	get	VERB
ejpam-5742	399	13	that	that	PRON
ejpam-5742	399	14	(	(	PUNCT
ejpam-5742	399	15	σ)+	σ)+	PROPN
ejpam-5742	399	16	⊆	⊆	NUM
ejpam-5742	399	17	(	(	PUNCT
ejpam-5742	399	18	δ)++	δ)++	NOUN
ejpam-5742	399	19	⊆	⊆	NUM
ejpam-5742	399	20	(	(	PUNCT
ejpam-5742	399	21	τ)+	τ)+	NOUN
ejpam-5742	399	22	⊆	⊆	NUM
ejpam-5742	399	23	m(f	m(f	PROPN
ejpam-5742	399	24	)	)	PUNCT
ejpam-5742	399	25	=	=	VERB
ejpam-5742	400	1	s.	s.	PROPN
ejpam-5742	400	2	therefore	therefore	ADV
ejpam-5742	400	3	ν	ν	PROPN
ejpam-5742	400	4	∈	∈	PROPN
ejpam-5742	400	5	s	s	X
ejpam-5742	400	6	and	and	CCONJ
ejpam-5742	400	7	hence	hence	ADV
ejpam-5742	400	8	s++	s++	NOUN
ejpam-5742	400	9	⊆	⊆	NUM
ejpam-5742	400	10	s.	s.	PROPN
ejpam-5742	400	11	thus	thus	ADV
ejpam-5742	400	12	s	s	PART
ejpam-5742	400	13	=	=	PUNCT
ejpam-5742	400	14	s++	s++	PROPN
ejpam-5742	400	15	.	.	PUNCT
ejpam-5742	401	1	therefore	therefore	ADV
ejpam-5742	401	2	s	s	VERB
ejpam-5742	401	3	is	be	AUX
ejpam-5742	401	4	an	an	DET
ejpam-5742	401	5	annihilator	annihilator	NOUN
ejpam-5742	401	6	filter	filter	NOUN
ejpam-5742	401	7	of	of	ADP
ejpam-5742	401	8	r.	r.	PROPN
ejpam-5742	401	9	it	it	PRON
ejpam-5742	401	10	is	be	AUX
ejpam-5742	401	11	straightforward	straightforward	ADJ
ejpam-5742	401	12	to	to	PART
ejpam-5742	401	13	demonstrate	demonstrate	VERB
ejpam-5742	401	14	that	that	SCONJ
ejpam-5742	401	15	the	the	DET
ejpam-5742	401	16	set	set	NOUN
ejpam-5742	401	17	(	(	PUNCT
ejpam-5742	401	18	mf	mf	X
ejpam-5742	401	19	(	(	PUNCT
ejpam-5742	401	20	r),⊔,∩	r),⊔,∩	NOUN
ejpam-5742	401	21	)	)	PUNCT
ejpam-5742	401	22	of	of	ADP
ejpam-5742	401	23	all	all	DET
ejpam-5742	401	24	m−filters	m−filter	NOUN
ejpam-5742	401	25	of	of	ADP
ejpam-5742	401	26	r	r	NOUN
ejpam-5742	401	27	forms	form	VERB
ejpam-5742	401	28	a	a	DET
ejpam-5742	401	29	distributive	distributive	ADJ
ejpam-5742	401	30	lattice	lattice	NOUN
ejpam-5742	401	31	,	,	PUNCT
ejpam-5742	401	32	where	where	SCONJ
ejpam-5742	401	33	m(f	m(f	NOUN
ejpam-5742	401	34	)	)	PUNCT
ejpam-5742	401	35	∩	∩	NOUN
ejpam-5742	401	36	m(g	m(g	NOUN
ejpam-5742	401	37	)	)	PUNCT
ejpam-5742	401	38	=	=	PUNCT
ejpam-5742	402	1	m(f	m(f	PROPN
ejpam-5742	402	2	∩	∩	PROPN
ejpam-5742	402	3	g	g	NOUN
ejpam-5742	402	4	)	)	PUNCT
ejpam-5742	402	5	and	and	CCONJ
ejpam-5742	402	6	m(f	m(f	PROPN
ejpam-5742	402	7	)	)	PUNCT
ejpam-5742	402	8	⊔	⊔	PROPN
ejpam-5742	402	9	m(g	m(g	PROPN
ejpam-5742	402	10	)	)	PUNCT
ejpam-5742	402	11	=	=	PUNCT
ejpam-5742	402	12	m(f	m(f	NOUN
ejpam-5742	402	13	∨g	∨g	PROPN
ejpam-5742	402	14	)	)	PUNCT
ejpam-5742	402	15	,	,	PUNCT
ejpam-5742	402	16	for	for	ADP
ejpam-5742	402	17	some	some	DET
ejpam-5742	402	18	ideals	ideal	NOUN
ejpam-5742	402	19	f	f	X
ejpam-5742	402	20	,	,	PUNCT
ejpam-5742	402	21	g	g	PROPN
ejpam-5742	402	22	of	of	ADP
ejpam-5742	402	23	r.	r.	PROPN
ejpam-5742	402	24	let	let	VERB
ejpam-5742	402	25	us	we	PRON
ejpam-5742	402	26	recall	recall	VERB
ejpam-5742	402	27	that	that	SCONJ
ejpam-5742	402	28	two	two	NUM
ejpam-5742	402	29	filters	filter	NOUN
ejpam-5742	402	30	s	s	PROPN
ejpam-5742	402	31	,	,	PUNCT
ejpam-5742	402	32	t	t	PROPN
ejpam-5742	402	33	of	of	ADP
ejpam-5742	402	34	an	an	DET
ejpam-5742	402	35	adl	adl	PROPN
ejpam-5742	402	36	r	r	NOUN
ejpam-5742	402	37	are	be	AUX
ejpam-5742	402	38	comaximal	comaximal	ADJ
ejpam-5742	402	39	if	if	SCONJ
ejpam-5742	402	40	s	s	VERB
ejpam-5742	402	41	∨	∨	NOUN
ejpam-5742	402	42	t	t	NOUN
ejpam-5742	402	43	=	=	SYM
ejpam-5742	402	44	r.	r.	NOUN
ejpam-5742	402	45	we	we	PRON
ejpam-5742	402	46	now	now	ADV
ejpam-5742	402	47	introduce	introduce	VERB
ejpam-5742	402	48	⊔−comaximality	⊔−comaximality	NOUN
ejpam-5742	402	49	of	of	ADP
ejpam-5742	402	50	m−filters	m−filter	NOUN
ejpam-5742	402	51	of	of	ADP
ejpam-5742	402	52	an	an	DET
ejpam-5742	402	53	adl	adl	PROPN
ejpam-5742	402	54	.	.	PUNCT
ejpam-5742	402	55	definition	definition	NOUN
ejpam-5742	402	56	11	11	NUM
ejpam-5742	402	57	.	.	PUNCT
ejpam-5742	403	1	two	two	NUM
ejpam-5742	403	2	m−filters	m−filter	NOUN
ejpam-5742	403	3	s	s	PROPN
ejpam-5742	403	4	,	,	PUNCT
ejpam-5742	403	5	t	t	PROPN
ejpam-5742	403	6	of	of	ADP
ejpam-5742	403	7	an	an	DET
ejpam-5742	403	8	adl	adl	NOUN
ejpam-5742	403	9	r	r	NOUN
ejpam-5742	403	10	are	be	AUX
ejpam-5742	403	11	referred	refer	VERB
ejpam-5742	403	12	as	as	ADP
ejpam-5742	403	13	⊔−comaximal	⊔−comaximal	ADJ
ejpam-5742	403	14	if	if	SCONJ
ejpam-5742	403	15	s⊔t	s⊔t	PROPN
ejpam-5742	403	16	=	=	PUNCT
ejpam-5742	403	17	r.	r.	NOUN
ejpam-5742	403	18	if	if	SCONJ
ejpam-5742	403	19	two	two	NUM
ejpam-5742	403	20	m−filters	m−filter	NOUN
ejpam-5742	403	21	are	be	AUX
ejpam-5742	403	22	comaximal	comaximal	ADJ
ejpam-5742	403	23	,	,	PUNCT
ejpam-5742	403	24	then	then	ADV
ejpam-5742	403	25	they	they	PRON
ejpam-5742	403	26	are	be	AUX
ejpam-5742	403	27	necessarily	necessarily	ADV
ejpam-5742	403	28	⊔−comaximal	⊔−comaximal	ADJ
ejpam-5742	403	29	.	.	PUNCT
ejpam-5742	404	1	however	however	ADV
ejpam-5742	404	2	,	,	PUNCT
ejpam-5742	404	3	the	the	DET
ejpam-5742	404	4	opposite	opposite	NOUN
ejpam-5742	404	5	is	be	AUX
ejpam-5742	404	6	not	not	PART
ejpam-5742	404	7	true	true	ADJ
ejpam-5742	404	8	.	.	PUNCT
ejpam-5742	405	1	any	any	DET
ejpam-5742	405	2	two	two	NUM
ejpam-5742	405	3	comaximal	comaximal	ADJ
ejpam-5742	405	4	m−filters	m−filter	NOUN
ejpam-5742	405	5	are	be	AUX
ejpam-5742	405	6	⊔−comaximal	⊔−comaximal	ADJ
ejpam-5742	405	7	.	.	PUNCT
ejpam-5742	406	1	but	but	CCONJ
ejpam-5742	406	2	the	the	DET
ejpam-5742	406	3	converse	converse	PROPN
ejpam-5742	406	4	n.	n.	PROPN
ejpam-5742	406	5	rafi	rafi	PROPN
ejpam-5742	406	6	,	,	PUNCT
ejpam-5742	406	7	t.	t.	PROPN
ejpam-5742	406	8	gaketem	gaketem	PROPN
ejpam-5742	406	9	,	,	PUNCT
ejpam-5742	406	10	r.	r.	PROPN
ejpam-5742	406	11	k.	k.	PROPN
ejpam-5742	406	12	bandaru	bandaru	PROPN
ejpam-5742	406	13	/	/	SYM
ejpam-5742	406	14	eur	eur	PROPN
ejpam-5742	406	15	.	.	PUNCT
ejpam-5742	407	1	j.	j.	PROPN
ejpam-5742	407	2	pure	pure	PROPN
ejpam-5742	407	3	appl	appl	PROPN
ejpam-5742	407	4	.	.	PROPN
ejpam-5742	407	5	math	math	PROPN
ejpam-5742	407	6	,	,	PUNCT
ejpam-5742	407	7	18	18	NUM
ejpam-5742	407	8	(	(	PUNCT
ejpam-5742	407	9	2	2	NUM
ejpam-5742	407	10	)	)	PUNCT
ejpam-5742	407	11	(	(	PUNCT
ejpam-5742	407	12	2025	2025	NUM
ejpam-5742	407	13	)	)	PUNCT
ejpam-5742	407	14	,	,	PUNCT
ejpam-5742	407	15	5742	5742	NUM
ejpam-5742	407	16	12	12	NUM
ejpam-5742	407	17	of	of	ADP
ejpam-5742	407	18	14	14	NUM
ejpam-5742	407	19	is	be	AUX
ejpam-5742	407	20	not	not	PART
ejpam-5742	407	21	true	true	ADJ
ejpam-5742	407	22	.	.	PUNCT
ejpam-5742	408	1	this	this	PRON
ejpam-5742	408	2	can	can	AUX
ejpam-5742	408	3	be	be	AUX
ejpam-5742	408	4	demonstrated	demonstrate	VERB
ejpam-5742	408	5	with	with	ADP
ejpam-5742	408	6	the	the	DET
ejpam-5742	408	7	following	follow	VERB
ejpam-5742	408	8	example	example	NOUN
ejpam-5742	408	9	.	.	PUNCT
ejpam-5742	409	1	example	example	NOUN
ejpam-5742	410	1	7	7	NUM
ejpam-5742	410	2	.	.	PUNCT
ejpam-5742	411	1	let	let	AUX
ejpam-5742	411	2	r	r	NOUN
ejpam-5742	411	3	=	=	SYM
ejpam-5742	411	4	{	{	PUNCT
ejpam-5742	411	5	0	0	NUM
ejpam-5742	411	6	,	,	PUNCT
ejpam-5742	411	7	θ	θ	PROPN
ejpam-5742	411	8	,	,	PUNCT
ejpam-5742	411	9	ϑ	ϑ	X
ejpam-5742	411	10	,	,	PUNCT
ejpam-5742	411	11	σ	σ	PROPN
ejpam-5742	411	12	,	,	PUNCT
ejpam-5742	411	13	1	1	NUM
ejpam-5742	411	14	}	}	PUNCT
ejpam-5742	411	15	represent	represent	VERB
ejpam-5742	411	16	a	a	DET
ejpam-5742	411	17	distributive	distributive	ADJ
ejpam-5742	411	18	lattice	lattice	NOUN
ejpam-5742	411	19	,	,	PUNCT
ejpam-5742	411	20	with	with	ADP
ejpam-5742	411	21	its	its	PRON
ejpam-5742	411	22	hasse	hasse	ADJ
ejpam-5742	411	23	diagram	diagram	NOUN
ejpam-5742	411	24	shown	show	VERB
ejpam-5742	411	25	below	below	ADP
ejpam-5742	411	26	�	�	PROPN
ejpam-5742	411	27	�	�	PROPN
ejpam-5742	411	28	�	�	PROPN
ejpam-5742	411	29	@	@	ADP
ejpam-5742	411	30	@	@	ADP
ejpam-5742	411	31	@	@	ADP
ejpam-5742	411	32	@	@	ADP
ejpam-5742	411	33	@	@	ADP
ejpam-5742	411	34	@	@	ADP
ejpam-5742	412	1	�	�	PROPN
ejpam-5742	412	2	�	�	PROPN
ejpam-5742	412	3	�	�	PROPN
ejpam-5742	413	1	d	d	PROPN
ejpam-5742	414	1	d	d	PROPN
ejpam-5742	415	1	d	d	PROPN
ejpam-5742	416	1	d	d	PROPN
ejpam-5742	417	1	d	d	X
ejpam-5742	417	2	θ	θ	PROPN
ejpam-5742	417	3	1	1	NUM
ejpam-5742	417	4	0	0	NUM
ejpam-5742	417	5	ϑ	ϑ	PROPN
ejpam-5742	417	6	σ	σ	NOUN
ejpam-5742	417	7	consider	consider	VERB
ejpam-5742	417	8	the	the	DET
ejpam-5742	417	9	filters	filter	NOUN
ejpam-5742	417	10	s	s	PART
ejpam-5742	417	11	=	=	PUNCT
ejpam-5742	417	12	{	{	PUNCT
ejpam-5742	417	13	ϑ	ϑ	X
ejpam-5742	417	14	,	,	PUNCT
ejpam-5742	417	15	1	1	NUM
ejpam-5742	417	16	}	}	PUNCT
ejpam-5742	417	17	and	and	CCONJ
ejpam-5742	417	18	t	t	NOUN
ejpam-5742	417	19	=	=	SYM
ejpam-5742	417	20	{	{	PUNCT
ejpam-5742	417	21	σ	σ	PROPN
ejpam-5742	417	22	,	,	PUNCT
ejpam-5742	417	23	1	1	NUM
ejpam-5742	417	24	}	}	PUNCT
ejpam-5742	417	25	.	.	PUNCT
ejpam-5742	418	1	clearly	clearly	ADV
ejpam-5742	418	2	f	f	X
ejpam-5742	418	3	=	=	PUNCT
ejpam-5742	418	4	{	{	PUNCT
ejpam-5742	418	5	0	0	NUM
ejpam-5742	418	6	,	,	PUNCT
ejpam-5742	418	7	θ	θ	PROPN
ejpam-5742	418	8	,	,	PUNCT
ejpam-5742	418	9	ϑ	ϑ	NOUN
ejpam-5742	418	10	}	}	PUNCT
ejpam-5742	418	11	and	and	CCONJ
ejpam-5742	418	12	g	g	NOUN
ejpam-5742	418	13	=	=	SYM
ejpam-5742	418	14	{	{	PUNCT
ejpam-5742	418	15	0	0	NUM
ejpam-5742	418	16	,	,	PUNCT
ejpam-5742	418	17	θ	θ	PROPN
ejpam-5742	418	18	,	,	PUNCT
ejpam-5742	418	19	σ	σ	NOUN
ejpam-5742	418	20	}	}	PUNCT
ejpam-5742	418	21	are	be	AUX
ejpam-5742	418	22	ideals	ideal	NOUN
ejpam-5742	418	23	in	in	ADP
ejpam-5742	418	24	r.	r.	PROPN
ejpam-5742	418	25	it	it	PRON
ejpam-5742	418	26	is	be	AUX
ejpam-5742	418	27	straightforward	straightforward	ADJ
ejpam-5742	418	28	to	to	PART
ejpam-5742	418	29	derive	derive	VERB
ejpam-5742	418	30	that	that	SCONJ
ejpam-5742	418	31	m(f	m(f	NOUN
ejpam-5742	418	32	)	)	PUNCT
ejpam-5742	418	33	=	=	SYM
ejpam-5742	418	34	t	t	PROPN
ejpam-5742	418	35	and	and	CCONJ
ejpam-5742	418	36	m(g	m(g	PROPN
ejpam-5742	418	37	)	)	PUNCT
ejpam-5742	418	38	=	=	PUNCT
ejpam-5742	419	1	s.	s.	PROPN
ejpam-5742	419	2	consequently	consequently	ADV
ejpam-5742	419	3	,	,	PUNCT
ejpam-5742	419	4	s	s	PRON
ejpam-5742	419	5	and	and	CCONJ
ejpam-5742	419	6	t	t	PROPN
ejpam-5742	419	7	are	be	AUX
ejpam-5742	419	8	two	two	NUM
ejpam-5742	419	9	distinct	distinct	ADJ
ejpam-5742	419	10	m−filters	m−filter	NOUN
ejpam-5742	419	11	of	of	ADP
ejpam-5742	419	12	r.	r.	PROPN
ejpam-5742	419	13	now	now	ADV
ejpam-5742	419	14	s⊔t	s⊔t	PROPN
ejpam-5742	419	15	=	=	SYM
ejpam-5742	419	16	m(g)⊔m(f	m(g)⊔m(f	PROPN
ejpam-5742	419	17	)	)	PUNCT
ejpam-5742	419	18	=	=	SYM
ejpam-5742	420	1	m(f∨g	m(f∨g	NOUN
ejpam-5742	420	2	)	)	PUNCT
ejpam-5742	420	3	=	=	SYM
ejpam-5742	420	4	m(r	m(r	PROPN
ejpam-5742	420	5	)	)	PUNCT
ejpam-5742	420	6	=	=	PUNCT
ejpam-5742	421	1	r.	r.	NOUN
ejpam-5742	421	2	this	this	PRON
ejpam-5742	421	3	implies	imply	VERB
ejpam-5742	421	4	that	that	PRON
ejpam-5742	421	5	s	s	VERB
ejpam-5742	421	6	and	and	CCONJ
ejpam-5742	421	7	t	t	PROPN
ejpam-5742	421	8	are	be	AUX
ejpam-5742	421	9	⊔−comaximal	⊔−comaximal	ADJ
ejpam-5742	421	10	.	.	PUNCT
ejpam-5742	422	1	however	however	ADV
ejpam-5742	422	2	,	,	PUNCT
ejpam-5742	422	3	since	since	SCONJ
ejpam-5742	422	4	s	s	PRON
ejpam-5742	422	5	∨t	∨t	NOUN
ejpam-5742	422	6	=	=	SYM
ejpam-5742	422	7	{	{	PUNCT
ejpam-5742	422	8	θ	θ	PROPN
ejpam-5742	422	9	,	,	PUNCT
ejpam-5742	422	10	ϑ	ϑ	X
ejpam-5742	422	11	,	,	PUNCT
ejpam-5742	422	12	σ	σ	PROPN
ejpam-5742	422	13	,	,	PUNCT
ejpam-5742	422	14	1	1	NUM
ejpam-5742	422	15	}	}	PUNCT
ejpam-5742	422	16	=	=	NOUN
ejpam-5742	422	17	̸	̸	NOUN
ejpam-5742	422	18	r	r	NOUN
ejpam-5742	422	19	,	,	PUNCT
ejpam-5742	422	20	it	it	PRON
ejpam-5742	422	21	follows	follow	VERB
ejpam-5742	422	22	that	that	PRON
ejpam-5742	422	23	s	s	VERB
ejpam-5742	422	24	and	and	CCONJ
ejpam-5742	422	25	t	t	PROPN
ejpam-5742	422	26	are	be	AUX
ejpam-5742	422	27	not	not	PART
ejpam-5742	422	28	comaximal	comaximal	ADJ
ejpam-5742	422	29	in	in	ADP
ejpam-5742	422	30	r.	r.	PROPN
ejpam-5742	422	31	lemma	lemma	PROPN
ejpam-5742	422	32	7	7	X
ejpam-5742	422	33	.	.	X
ejpam-5742	422	34	for	for	ADP
ejpam-5742	422	35	every	every	DET
ejpam-5742	422	36	µ	µ	NOUN
ejpam-5742	422	37	,	,	PUNCT
ejpam-5742	422	38	π	π	PROPN
ejpam-5742	422	39	∈	∈	NOUN
ejpam-5742	422	40	r	r	NOUN
ejpam-5742	422	41	with	with	ADP
ejpam-5742	422	42	κ∨η	κ∨η	PROPN
ejpam-5742	422	43	∈	∈	PROPN
ejpam-5742	422	44	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	422	45	)	)	PUNCT
ejpam-5742	422	46	,	,	PUNCT
ejpam-5742	422	47	(	(	PUNCT
ejpam-5742	422	48	κ)+	κ)+	PRON
ejpam-5742	422	49	and	and	CCONJ
ejpam-5742	422	50	(	(	PUNCT
ejpam-5742	422	51	η)+	η)+	NOUN
ejpam-5742	422	52	are	be	AUX
ejpam-5742	422	53	⊔−comaximal	⊔−comaximal	ADJ
ejpam-5742	422	54	.	.	PUNCT
ejpam-5742	423	1	proof	proof	NOUN
ejpam-5742	423	2	.	.	PUNCT
ejpam-5742	424	1	let	let	VERB
ejpam-5742	424	2	κ	κ	NOUN
ejpam-5742	424	3	,	,	PUNCT
ejpam-5742	424	4	η	η	PROPN
ejpam-5742	424	5	∈	∈	PROPN
ejpam-5742	424	6	r	r	NOUN
ejpam-5742	424	7	with	with	ADP
ejpam-5742	424	8	κ	κ	PROPN
ejpam-5742	424	9	∨	∨	NUM
ejpam-5742	424	10	η	η	X
ejpam-5742	424	11	∈	∈	PROPN
ejpam-5742	424	12	mmaκ.elt(r	mmaκ.elt(r	NOUN
ejpam-5742	424	13	)	)	PUNCT
ejpam-5742	424	14	.	.	PUNCT
ejpam-5742	425	1	clearly	clearly	ADV
ejpam-5742	425	2	,	,	PUNCT
ejpam-5742	425	3	we	we	PRON
ejpam-5742	425	4	have	have	VERB
ejpam-5742	425	5	that	that	PRON
ejpam-5742	425	6	(	(	PUNCT
ejpam-5742	425	7	κ)+	κ)+	X
ejpam-5742	425	8	=	=	SYM
ejpam-5742	425	9	m((κ	m((κ	PROPN
ejpam-5742	425	10	]	]	PUNCT
ejpam-5742	425	11	)	)	PUNCT
ejpam-5742	425	12	and	and	CCONJ
ejpam-5742	425	13	(	(	PUNCT
ejpam-5742	425	14	η)+	η)+	NOUN
ejpam-5742	425	15	=	=	PUNCT
ejpam-5742	425	16	m((η	m((η	NOUN
ejpam-5742	425	17	]	]	X
ejpam-5742	425	18	)	)	PUNCT
ejpam-5742	425	19	.	.	PUNCT
ejpam-5742	426	1	now	now	ADV
ejpam-5742	426	2	(	(	PUNCT
ejpam-5742	426	3	κ)+	κ)+	PROPN
ejpam-5742	426	4	⊔	⊔	INTJ
ejpam-5742	426	5	(	(	PUNCT
ejpam-5742	426	6	η)+	η)+	X
ejpam-5742	426	7	=	=	PUNCT
ejpam-5742	426	8	m((κ	m((κ	PROPN
ejpam-5742	426	9	]	]	X
ejpam-5742	426	10	)	)	PUNCT
ejpam-5742	426	11	⊔m((η	⊔m((η	PROPN
ejpam-5742	426	12	]	]	PUNCT
ejpam-5742	426	13	)	)	PUNCT
ejpam-5742	427	1	=	=	SYM
ejpam-5742	427	2	m((κ	m((κ	PROPN
ejpam-5742	427	3	]	]	X
ejpam-5742	427	4	∨	∨	X
ejpam-5742	427	5	(	(	PUNCT
ejpam-5742	427	6	η	η	NOUN
ejpam-5742	427	7	]	]	X
ejpam-5742	427	8	)	)	PUNCT
ejpam-5742	427	9	=	=	SYM
ejpam-5742	427	10	m((κ	m((κ	PROPN
ejpam-5742	427	11	∨	∨	PROPN
ejpam-5742	427	12	η	η	PROPN
ejpam-5742	427	13	]	]	X
ejpam-5742	427	14	)	)	PUNCT
ejpam-5742	427	15	=	=	SYM
ejpam-5742	427	16	m(r	m(r	PROPN
ejpam-5742	427	17	)	)	PUNCT
ejpam-5742	427	18	=	=	PUNCT
ejpam-5742	428	1	r.	r.	PROPN
ejpam-5742	428	2	therefore	therefore	ADV
ejpam-5742	428	3	(	(	PUNCT
ejpam-5742	428	4	κ)+	κ)+	PRON
ejpam-5742	428	5	and	and	CCONJ
ejpam-5742	428	6	(	(	PUNCT
ejpam-5742	428	7	η)+	η)+	NOUN
ejpam-5742	428	8	are	be	AUX
ejpam-5742	428	9	⊔−comaximal	⊔−comaximal	ADJ
ejpam-5742	428	10	.	.	PUNCT
ejpam-5742	429	1	theorem	theorem	VERB
ejpam-5742	429	2	13	13	NUM
ejpam-5742	429	3	.	.	PUNCT
ejpam-5742	430	1	any	any	DET
ejpam-5742	430	2	two	two	NUM
ejpam-5742	430	3	distinct	distinct	ADJ
ejpam-5742	430	4	prime	prime	ADJ
ejpam-5742	430	5	m−filters	m−filter	NOUN
ejpam-5742	430	6	of	of	ADP
ejpam-5742	430	7	r	r	NOUN
ejpam-5742	430	8	are	be	AUX
ejpam-5742	430	9	necessarily	necessarily	ADV
ejpam-5742	430	10	⊔−comaximal	⊔−comaximal	ADJ
ejpam-5742	430	11	.	.	PUNCT
ejpam-5742	431	1	proof	proof	NOUN
ejpam-5742	431	2	.	.	PUNCT
ejpam-5742	432	1	let	let	VERB
ejpam-5742	432	2	x	x	PRON
ejpam-5742	432	3	and	and	CCONJ
ejpam-5742	432	4	y	y	PROPN
ejpam-5742	432	5	be	be	AUX
ejpam-5742	432	6	two	two	NUM
ejpam-5742	432	7	distinct	distinct	ADJ
ejpam-5742	432	8	prime	prime	ADJ
ejpam-5742	432	9	m−filters	m−filter	NOUN
ejpam-5742	432	10	of	of	ADP
ejpam-5742	432	11	r.	r.	PROPN
ejpam-5742	432	12	consequently	consequently	ADV
ejpam-5742	432	13	,	,	PUNCT
ejpam-5742	432	14	x	x	PUNCT
ejpam-5742	432	15	and	and	CCONJ
ejpam-5742	432	16	y	y	PROPN
ejpam-5742	432	17	are	be	AUX
ejpam-5742	432	18	minimal	minimal	ADJ
ejpam-5742	432	19	.	.	PUNCT
ejpam-5742	433	1	choose	choose	VERB
ejpam-5742	433	2	σ	σ	PROPN
ejpam-5742	433	3	∈	∈	PROPN
ejpam-5742	433	4	y	y	PROPN
ejpam-5742	433	5	\	\	PROPN
ejpam-5742	433	6	x	x	PUNCT
ejpam-5742	433	7	and	and	CCONJ
ejpam-5742	433	8	τ	τ	PROPN
ejpam-5742	433	9	∈	∈	PROPN
ejpam-5742	433	10	x	x	PUNCT
ejpam-5742	433	11	\	\	NOUN
ejpam-5742	433	12	y.	y.	PROPN
ejpam-5742	433	13	therefore	therefore	ADV
ejpam-5742	433	14	τ	τ	PROPN
ejpam-5742	433	15	∨	∨	NUM
ejpam-5742	433	16	κ	κ	PROPN
ejpam-5742	433	17	,	,	PUNCT
ejpam-5742	433	18	σ	σ	PROPN
ejpam-5742	433	19	∨	∨	PROPN
ejpam-5742	433	20	η	η	PROPN
ejpam-5742	433	21	∈	∈	PROPN
ejpam-5742	433	22	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	433	23	)	)	PUNCT
ejpam-5742	433	24	,	,	PUNCT
ejpam-5742	433	25	for	for	ADP
ejpam-5742	433	26	some	some	DET
ejpam-5742	433	27	κ	κ	NOUN
ejpam-5742	433	28	/∈	/∈	PUNCT
ejpam-5742	433	29	x	x	PUNCT
ejpam-5742	433	30	and	and	CCONJ
ejpam-5742	433	31	η	η	PROPN
ejpam-5742	433	32	/∈	/∈	PROPN
ejpam-5742	433	33	y.	y.	PROPN
ejpam-5742	433	34	which	which	PRON
ejpam-5742	433	35	gives	give	VERB
ejpam-5742	433	36	σ	σ	PROPN
ejpam-5742	433	37	∨	∨	NUM
ejpam-5742	433	38	κ	κ	X
ejpam-5742	433	39	/∈	/∈	PUNCT
ejpam-5742	433	40	x	x	SYM
ejpam-5742	433	41	and	and	CCONJ
ejpam-5742	433	42	η	η	PROPN
ejpam-5742	433	43	∨	∨	X
ejpam-5742	433	44	τ	τ	PROPN
ejpam-5742	433	45	/∈	/∈	PUNCT
ejpam-5742	434	1	y.	y.	NOUN
ejpam-5742	434	2	hence	hence	ADV
ejpam-5742	434	3	(	(	PUNCT
ejpam-5742	434	4	σ	σ	PROPN
ejpam-5742	434	5	∨	∨	PROPN
ejpam-5742	434	6	κ)+	κ)+	PROPN
ejpam-5742	435	1	⊆	⊆	NUM
ejpam-5742	435	2	x	x	PUNCT
ejpam-5742	435	3	and	and	CCONJ
ejpam-5742	435	4	(	(	PUNCT
ejpam-5742	435	5	η	η	PROPN
ejpam-5742	435	6	∨	∨	X
ejpam-5742	435	7	τ)+	τ)+	NUM
ejpam-5742	435	8	⊆	⊆	NUM
ejpam-5742	435	9	y.	y.	NOUN
ejpam-5742	435	10	clearly	clearly	ADV
ejpam-5742	435	11	we	we	PRON
ejpam-5742	435	12	have	have	VERB
ejpam-5742	435	13	that	that	PRON
ejpam-5742	435	14	(	(	PUNCT
ejpam-5742	435	15	σ	σ	PROPN
ejpam-5742	435	16	∨	∨	NUM
ejpam-5742	435	17	κ	κ	NOUN
ejpam-5742	435	18	)	)	PUNCT
ejpam-5742	435	19	∨	∨	PROPN
ejpam-5742	435	20	(	(	PUNCT
ejpam-5742	435	21	τ	τ	PROPN
ejpam-5742	435	22	∨	∨	PROPN
ejpam-5742	435	23	η	η	PROPN
ejpam-5742	435	24	)	)	PUNCT
ejpam-5742	435	25	∈	∈	PROPN
ejpam-5742	435	26	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	435	27	)	)	PUNCT
ejpam-5742	435	28	.	.	PUNCT
ejpam-5742	436	1	by	by	ADP
ejpam-5742	436	2	above	above	ADP
ejpam-5742	436	3	result	result	NOUN
ejpam-5742	436	4	,	,	PUNCT
ejpam-5742	436	5	we	we	PRON
ejpam-5742	436	6	get	get	VERB
ejpam-5742	436	7	that	that	DET
ejpam-5742	436	8	(	(	PUNCT
ejpam-5742	436	9	σ∨κ)+	σ∨κ)+	X
ejpam-5742	436	10	⊔	⊔	PROPN
ejpam-5742	436	11	(	(	PUNCT
ejpam-5742	436	12	τ	τ	PROPN
ejpam-5742	436	13	∨	∨	NOUN
ejpam-5742	436	14	η)+	η)+	NOUN
ejpam-5742	436	15	=	=	SYM
ejpam-5742	436	16	r	r	NOUN
ejpam-5742	436	17	and	and	CCONJ
ejpam-5742	436	18	hence	hence	ADV
ejpam-5742	436	19	x	x	X
ejpam-5742	436	20	⊔y	⊔y	PUNCT
ejpam-5742	436	21	=	=	SYM
ejpam-5742	436	22	r.	r.	PROPN
ejpam-5742	436	23	thus	thus	ADV
ejpam-5742	436	24	x	x	X
ejpam-5742	436	25	and	and	CCONJ
ejpam-5742	436	26	y	y	PROPN
ejpam-5742	436	27	are	be	AUX
ejpam-5742	436	28	⊔−comaximal	⊔−comaximal	ADJ
ejpam-5742	436	29	.	.	PUNCT
ejpam-5742	437	1	definition	definition	NOUN
ejpam-5742	437	2	12	12	NUM
ejpam-5742	437	3	.	.	PUNCT
ejpam-5742	438	1	for	for	ADP
ejpam-5742	438	2	any	any	DET
ejpam-5742	438	3	filter	filter	NOUN
ejpam-5742	438	4	s	s	NOUN
ejpam-5742	438	5	of	of	ADP
ejpam-5742	438	6	r	r	NOUN
ejpam-5742	438	7	and	and	CCONJ
ejpam-5742	438	8	κ	κ	NOUN
ejpam-5742	438	9	∈	∈	PROPN
ejpam-5742	438	10	r	r	NOUN
ejpam-5742	438	11	,	,	PUNCT
ejpam-5742	438	12	define	define	VERB
ejpam-5742	438	13	[	[	X
ejpam-5742	438	14	κ]s	κ]s	ADV
ejpam-5742	438	15	=	=	SYM
ejpam-5742	438	16	{	{	PUNCT
ejpam-5742	438	17	τ	τ	PROPN
ejpam-5742	438	18	∈	∈	PROPN
ejpam-5742	438	19	s	s	X
ejpam-5742	438	20	|	|	ADV
ejpam-5742	438	21	τ	τ	PROPN
ejpam-5742	438	22	∨	∨	NOUN
ejpam-5742	438	23	κ	κ	PROPN
ejpam-5742	438	24	∈	∈	PROPN
ejpam-5742	438	25	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	438	26	)	)	PUNCT
ejpam-5742	438	27	}	}	PUNCT
ejpam-5742	438	28	lemma	lemma	PROPN
ejpam-5742	438	29	8	8	NUM
ejpam-5742	438	30	.	.	PUNCT
ejpam-5742	439	1	for	for	ADP
ejpam-5742	439	2	any	any	DET
ejpam-5742	439	3	filter	filter	NOUN
ejpam-5742	439	4	s	s	NOUN
ejpam-5742	439	5	of	of	ADP
ejpam-5742	439	6	r	r	NOUN
ejpam-5742	439	7	and	and	CCONJ
ejpam-5742	439	8	κ	κ	NOUN
ejpam-5742	439	9	∈	∈	PROPN
ejpam-5742	439	10	r	r	NOUN
ejpam-5742	439	11	,	,	PUNCT
ejpam-5742	439	12	we	we	PRON
ejpam-5742	439	13	have	have	VERB
ejpam-5742	439	14	the	the	DET
ejpam-5742	439	15	the	the	DET
ejpam-5742	439	16	subsequent	subsequent	ADJ
ejpam-5742	439	17	conditions	condition	NOUN
ejpam-5742	439	18	(	(	PUNCT
ejpam-5742	439	19	i	i	NOUN
ejpam-5742	439	20	)	)	PUNCT
ejpam-5742	440	1	[	[	X
ejpam-5742	440	2	κ]s	κ]s	ADV
ejpam-5742	440	3	=	=	SYM
ejpam-5742	440	4	s	s	NOUN
ejpam-5742	440	5	∩	∩	NOUN
ejpam-5742	440	6	(	(	PUNCT
ejpam-5742	440	7	κ)+	κ)+	PRON
ejpam-5742	440	8	is	be	AUX
ejpam-5742	440	9	a	a	DET
ejpam-5742	440	10	filter	filter	NOUN
ejpam-5742	440	11	in	in	ADP
ejpam-5742	440	12	s	s	PROPN
ejpam-5742	440	13	(	(	PUNCT
ejpam-5742	440	14	ii	ii	NOUN
ejpam-5742	440	15	)	)	PUNCT
ejpam-5742	440	16	if	if	SCONJ
ejpam-5742	440	17	s	s	NOUN
ejpam-5742	440	18	is	be	AUX
ejpam-5742	440	19	an	an	DET
ejpam-5742	440	20	m−filter	m−filter	NOUN
ejpam-5742	440	21	then	then	ADV
ejpam-5742	440	22	[	[	X
ejpam-5742	440	23	κ]s	κ]s	ADV
ejpam-5742	440	24	is	be	AUX
ejpam-5742	440	25	an	an	DET
ejpam-5742	440	26	m−filter	m−filter	NOUN
ejpam-5742	440	27	.	.	PUNCT
ejpam-5742	441	1	n.	n.	PROPN
ejpam-5742	441	2	rafi	rafi	PROPN
ejpam-5742	441	3	,	,	PUNCT
ejpam-5742	441	4	t.	t.	PROPN
ejpam-5742	441	5	gaketem	gaketem	PROPN
ejpam-5742	441	6	,	,	PUNCT
ejpam-5742	441	7	r.	r.	PROPN
ejpam-5742	441	8	k.	k.	PROPN
ejpam-5742	441	9	bandaru	bandaru	PROPN
ejpam-5742	441	10	/	/	SYM
ejpam-5742	441	11	eur	eur	PROPN
ejpam-5742	441	12	.	.	PUNCT
ejpam-5742	442	1	j.	j.	PROPN
ejpam-5742	442	2	pure	pure	PROPN
ejpam-5742	442	3	appl	appl	PROPN
ejpam-5742	442	4	.	.	PROPN
ejpam-5742	442	5	math	math	PROPN
ejpam-5742	442	6	,	,	PUNCT
ejpam-5742	442	7	18	18	NUM
ejpam-5742	442	8	(	(	PUNCT
ejpam-5742	442	9	2	2	NUM
ejpam-5742	442	10	)	)	PUNCT
ejpam-5742	442	11	(	(	PUNCT
ejpam-5742	442	12	2025	2025	NUM
ejpam-5742	442	13	)	)	PUNCT
ejpam-5742	442	14	,	,	PUNCT
ejpam-5742	442	15	5742	5742	NUM
ejpam-5742	442	16	13	13	NUM
ejpam-5742	442	17	of	of	ADP
ejpam-5742	442	18	14	14	NUM
ejpam-5742	442	19	proof	proof	NOUN
ejpam-5742	442	20	.	.	PUNCT
ejpam-5742	443	1	1	1	X
ejpam-5742	443	2	.	.	X
ejpam-5742	443	3	clearly	clearly	ADV
ejpam-5742	443	4	,	,	PUNCT
ejpam-5742	443	5	[	[	X
ejpam-5742	443	6	κ]s	κ]s	ADV
ejpam-5742	443	7	̸=	̸=	PROPN
ejpam-5742	443	8	∅.	∅.	ADV
ejpam-5742	443	9	let	let	VERB
ejpam-5742	443	10	θ	θ	NOUN
ejpam-5742	443	11	,	,	PUNCT
ejpam-5742	443	12	ϑ	ϑ	X
ejpam-5742	443	13	∈	∈	X
ejpam-5742	443	14	[	[	X
ejpam-5742	443	15	κ]s	κ]s	X
ejpam-5742	443	16	.	.	PUNCT
ejpam-5742	444	1	then	then	ADV
ejpam-5742	444	2	θ∨κ	θ∨κ	ADJ
ejpam-5742	444	3	,	,	PUNCT
ejpam-5742	444	4	ϑ∨κ	ϑ∨κ	PROPN
ejpam-5742	444	5	∈	∈	PROPN
ejpam-5742	444	6	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	444	7	)	)	PUNCT
ejpam-5742	444	8	and	and	CCONJ
ejpam-5742	444	9	hence	hence	ADV
ejpam-5742	444	10	(	(	PUNCT
ejpam-5742	444	11	θ∧ϑ)∨κ	θ∧ϑ)∨κ	X
ejpam-5742	444	12	∈	∈	PROPN
ejpam-5742	444	13	mmax.elt(r	mmax.elt(r	NOUN
ejpam-5742	444	14	)	)	PUNCT
ejpam-5742	444	15	therefore	therefore	ADV
ejpam-5742	444	16	θ∧ϑ	θ∧ϑ	PROPN
ejpam-5742	444	17	∈	∈	PROPN
ejpam-5742	445	1	[	[	X
ejpam-5742	445	2	κ]s	κ]s	ADV
ejpam-5742	445	3	.	.	PUNCT
ejpam-5742	446	1	let	let	VERB
ejpam-5742	446	2	θ	θ	PROPN
ejpam-5742	446	3	∈	∈	PROPN
ejpam-5742	447	1	[	[	X
ejpam-5742	447	2	κ]s	κ]s	X
ejpam-5742	447	3	.	.	PUNCT
ejpam-5742	448	1	then	then	ADV
ejpam-5742	448	2	θ∨κ	θ∨κ	ADJ
ejpam-5742	448	3	∈	∈	PROPN
ejpam-5742	448	4	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	448	5	)	)	PUNCT
ejpam-5742	448	6	.	.	PUNCT
ejpam-5742	449	1	for	for	ADP
ejpam-5742	449	2	any	any	DET
ejpam-5742	449	3	σ	σ	PROPN
ejpam-5742	449	4	∈	∈	PROPN
ejpam-5742	449	5	s	s	PART
ejpam-5742	449	6	,	,	PUNCT
ejpam-5742	449	7	we	we	PRON
ejpam-5742	449	8	have	have	VERB
ejpam-5742	449	9	σ	σ	NOUN
ejpam-5742	449	10	∨	∨	NUM
ejpam-5742	449	11	θ	θ	PROPN
ejpam-5742	449	12	∨	∨	NUM
ejpam-5742	449	13	κ	κ	PROPN
ejpam-5742	449	14	∈	∈	PROPN
ejpam-5742	449	15	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	449	16	)	)	PUNCT
ejpam-5742	449	17	.	.	PUNCT
ejpam-5742	450	1	therefore	therefore	ADV
ejpam-5742	450	2	σ	σ	X
ejpam-5742	450	3	∨	∨	NUM
ejpam-5742	450	4	θ	θ	X
ejpam-5742	450	5	∈	∈	PROPN
ejpam-5742	450	6	[	[	X
ejpam-5742	450	7	κ]s	κ]s	X
ejpam-5742	450	8	.	.	PUNCT
ejpam-5742	451	1	thus	thus	ADV
ejpam-5742	451	2	[	[	X
ejpam-5742	451	3	κ]s	κ]s	ADV
ejpam-5742	451	4	is	be	AUX
ejpam-5742	451	5	a	a	DET
ejpam-5742	451	6	filter	filter	NOUN
ejpam-5742	451	7	2	2	NUM
ejpam-5742	451	8	.	.	PUNCT
ejpam-5742	452	1	let	let	VERB
ejpam-5742	452	2	s	s	PRON
ejpam-5742	452	3	is	be	AUX
ejpam-5742	452	4	an	an	DET
ejpam-5742	452	5	m−filter	m−filter	NOUN
ejpam-5742	452	6	of	of	ADP
ejpam-5742	452	7	r.	r.	PROPN
ejpam-5742	452	8	there	there	PRON
ejpam-5742	452	9	there	there	PRON
ejpam-5742	452	10	exists	exist	VERB
ejpam-5742	452	11	an	an	DET
ejpam-5742	452	12	ideal	ideal	ADJ
ejpam-5742	452	13	f	f	NOUN
ejpam-5742	452	14	of	of	ADP
ejpam-5742	452	15	r	r	NOUN
ejpam-5742	452	16	such	such	ADJ
ejpam-5742	452	17	that	that	DET
ejpam-5742	452	18	s	s	NOUN
ejpam-5742	452	19	=	=	SYM
ejpam-5742	452	20	m(f	m(f	PROPN
ejpam-5742	452	21	)	)	PUNCT
ejpam-5742	452	22	.	.	PUNCT
ejpam-5742	453	1	clearly	clearly	ADV
ejpam-5742	453	2	we	we	PRON
ejpam-5742	453	3	have	have	VERB
ejpam-5742	453	4	(	(	PUNCT
ejpam-5742	453	5	κ)+	κ)+	X
ejpam-5742	453	6	=	=	SYM
ejpam-5742	453	7	m((κ	m((κ	PROPN
ejpam-5742	453	8	]	]	X
ejpam-5742	453	9	)	)	PUNCT
ejpam-5742	453	10	.	.	PUNCT
ejpam-5742	454	1	therefore	therefore	ADV
ejpam-5742	454	2	(	(	PUNCT
ejpam-5742	454	3	κ)+	κ)+	PROPN
ejpam-5742	454	4	∩	∩	PROPN
ejpam-5742	454	5	s	s	PART
ejpam-5742	454	6	=	=	SYM
ejpam-5742	454	7	m(f	m(f	PROPN
ejpam-5742	454	8	)	)	PUNCT
ejpam-5742	454	9	∩	∩	NOUN
ejpam-5742	454	10	m((κ	m((κ	PROPN
ejpam-5742	454	11	]	]	X
ejpam-5742	454	12	)	)	PUNCT
ejpam-5742	455	1	=	=	SYM
ejpam-5742	455	2	m(f	m(f	NOUN
ejpam-5742	455	3	∩	∩	NOUN
ejpam-5742	455	4	(	(	PUNCT
ejpam-5742	455	5	κ	κ	NOUN
ejpam-5742	455	6	]	]	X
ejpam-5742	455	7	)	)	PUNCT
ejpam-5742	455	8	.	.	PUNCT
ejpam-5742	456	1	hence	hence	ADV
ejpam-5742	456	2	[	[	X
ejpam-5742	456	3	κ]s	κ]s	ADV
ejpam-5742	456	4	is	be	AUX
ejpam-5742	456	5	an	an	DET
ejpam-5742	456	6	m−filter	m−filter	NOUN
ejpam-5742	456	7	.	.	PUNCT
ejpam-5742	457	1	theorem	theorem	NOUN
ejpam-5742	457	2	14	14	NUM
ejpam-5742	457	3	.	.	PUNCT
ejpam-5742	458	1	let	let	VERB
ejpam-5742	458	2	s	s	PRON
ejpam-5742	458	3	be	be	AUX
ejpam-5742	458	4	an	an	DET
ejpam-5742	458	5	m−filter	m−filter	NOUN
ejpam-5742	458	6	of	of	ADP
ejpam-5742	458	7	an	an	DET
ejpam-5742	458	8	adl	adl	NOUN
ejpam-5742	458	9	r	r	NOUN
ejpam-5742	458	10	with	with	ADP
ejpam-5742	458	11	maximal	maximal	ADJ
ejpam-5742	458	12	elements	element	NOUN
ejpam-5742	458	13	.	.	PUNCT
ejpam-5742	459	1	if	if	SCONJ
ejpam-5742	459	2	for	for	ADP
ejpam-5742	459	3	any	any	DET
ejpam-5742	459	4	κ	κ	NOUN
ejpam-5742	459	5	,	,	PUNCT
ejpam-5742	459	6	η	η	PROPN
ejpam-5742	459	7	∈	∈	PROPN
ejpam-5742	459	8	r	r	NOUN
ejpam-5742	459	9	with	with	ADP
ejpam-5742	459	10	κ	κ	PROPN
ejpam-5742	459	11	∨	∨	NUM
ejpam-5742	459	12	η	η	PROPN
ejpam-5742	459	13	∈	∈	PROPN
ejpam-5742	459	14	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	459	15	)	)	PUNCT
ejpam-5742	459	16	,	,	PUNCT
ejpam-5742	459	17	then	then	ADV
ejpam-5742	460	1	[	[	X
ejpam-5742	460	2	κ]s	κ]s	NOUN
ejpam-5742	460	3	and	and	CCONJ
ejpam-5742	460	4	[	[	X
ejpam-5742	460	5	η]s	η]s	NOUN
ejpam-5742	460	6	are	be	AUX
ejpam-5742	460	7	⊔−comaximal	⊔−comaximal	ADJ
ejpam-5742	460	8	in	in	ADP
ejpam-5742	460	9	s.	s.	PROPN
ejpam-5742	460	10	proof	proof	PROPN
ejpam-5742	460	11	.	.	PUNCT
ejpam-5742	461	1	let	let	VERB
ejpam-5742	461	2	κ	κ	NOUN
ejpam-5742	461	3	,	,	PUNCT
ejpam-5742	461	4	η	η	PROPN
ejpam-5742	461	5	∈	∈	PROPN
ejpam-5742	461	6	r	r	NOUN
ejpam-5742	461	7	with	with	ADP
ejpam-5742	461	8	κ∨η	κ∨η	PROPN
ejpam-5742	461	9	∈	∈	PROPN
ejpam-5742	461	10	mmax.elt(r	mmax.elt(r	PROPN
ejpam-5742	461	11	)	)	PUNCT
ejpam-5742	461	12	.	.	PUNCT
ejpam-5742	462	1	by	by	ADP
ejpam-5742	462	2	lemma-7	lemma-7	PROPN
ejpam-5742	462	3	,	,	PUNCT
ejpam-5742	462	4	we	we	PRON
ejpam-5742	462	5	have	have	VERB
ejpam-5742	462	6	that	that	PRON
ejpam-5742	462	7	(	(	PUNCT
ejpam-5742	462	8	κ)+⊔(η)+	κ)+⊔(η)+	PROPN
ejpam-5742	462	9	=	=	PUNCT
ejpam-5742	462	10	r.	r.	PROPN
ejpam-5742	462	11	now	now	ADV
ejpam-5742	462	12	,	,	PUNCT
ejpam-5742	462	13	s	s	VERB
ejpam-5742	462	14	=	=	SYM
ejpam-5742	462	15	s	s	PART
ejpam-5742	462	16	∩r	∩r	NOUN
ejpam-5742	462	17	=	=	SYM
ejpam-5742	462	18	s	s	PART
ejpam-5742	462	19	∩	∩	NOUN
ejpam-5742	462	20	(	(	PUNCT
ejpam-5742	462	21	(	(	PUNCT
ejpam-5742	462	22	κ)+	κ)+	PRON
ejpam-5742	462	23	⊔	⊔	INTJ
ejpam-5742	462	24	(	(	PUNCT
ejpam-5742	462	25	η)+	η)+	X
ejpam-5742	462	26	)	)	PUNCT
ejpam-5742	462	27	=	=	SYM
ejpam-5742	462	28	(	(	PUNCT
ejpam-5742	462	29	s	s	X
ejpam-5742	462	30	∩	∩	NOUN
ejpam-5742	462	31	(	(	PUNCT
ejpam-5742	462	32	κ)+)⊔	κ)+)⊔	X
ejpam-5742	462	33	(	(	PUNCT
ejpam-5742	462	34	s	s	NOUN
ejpam-5742	462	35	∩	∩	NOUN
ejpam-5742	462	36	(	(	PUNCT
ejpam-5742	462	37	η)+	η)+	X
ejpam-5742	462	38	)	)	PUNCT
ejpam-5742	462	39	=	=	PUNCT
ejpam-5742	463	1	[	[	X
ejpam-5742	463	2	κ]s	κ]s	X
ejpam-5742	463	3	⊔	⊔	NOUN
ejpam-5742	464	1	[	[	X
ejpam-5742	464	2	η]s	η]s	NOUN
ejpam-5742	464	3	.	.	PUNCT
ejpam-5742	465	1	therefore	therefore	ADV
ejpam-5742	465	2	[	[	X
ejpam-5742	465	3	κ]s	κ]s	ADV
ejpam-5742	465	4	⊔	⊔	NOUN
ejpam-5742	466	1	[	[	X
ejpam-5742	466	2	η]s	η]s	NOUN
ejpam-5742	466	3	=	=	PUNCT
ejpam-5742	466	4	s	s	X
ejpam-5742	466	5	and	and	CCONJ
ejpam-5742	466	6	hence	hence	ADV
ejpam-5742	466	7	[	[	X
ejpam-5742	466	8	κ]s	κ]s	ADV
ejpam-5742	467	1	and	and	CCONJ
ejpam-5742	467	2	[	[	X
ejpam-5742	467	3	η]s	η]s	NOUN
ejpam-5742	467	4	are	be	AUX
ejpam-5742	467	5	⊔−comaximal	⊔−comaximal	ADJ
ejpam-5742	467	6	in	in	ADP
ejpam-5742	467	7	s.	s.	PROPN
ejpam-5742	467	8	conclusions	conclusion	NOUN
ejpam-5742	467	9	in	in	ADP
ejpam-5742	467	10	this	this	DET
ejpam-5742	467	11	paper	paper	NOUN
ejpam-5742	467	12	,	,	PUNCT
ejpam-5742	467	13	we	we	PRON
ejpam-5742	467	14	introduced	introduce	VERB
ejpam-5742	467	15	the	the	DET
ejpam-5742	467	16	notion	notion	NOUN
ejpam-5742	467	17	of	of	ADP
ejpam-5742	467	18	m−homomorphism	m−homomorphism	NOUN
ejpam-5742	467	19	in	in	ADP
ejpam-5742	467	20	the	the	DET
ejpam-5742	467	21	context	context	NOUN
ejpam-5742	467	22	of	of	ADP
ejpam-5742	467	23	an	an	DET
ejpam-5742	467	24	almost	almost	ADV
ejpam-5742	467	25	distributive	distributive	ADJ
ejpam-5742	467	26	lattice(adl	lattice(adl	NOUN
ejpam-5742	467	27	)	)	PUNCT
ejpam-5742	467	28	.	.	PUNCT
ejpam-5742	468	1	we	we	PRON
ejpam-5742	468	2	have	have	AUX
ejpam-5742	468	3	derived	derive	VERB
ejpam-5742	468	4	a	a	DET
ejpam-5742	468	5	sufficient	sufficient	ADJ
ejpam-5742	468	6	condition	condition	NOUN
ejpam-5742	468	7	for	for	ADP
ejpam-5742	468	8	a	a	DET
ejpam-5742	468	9	homomorphism	homomorphism	NOUN
ejpam-5742	468	10	to	to	PART
ejpam-5742	468	11	become	become	VERB
ejpam-5742	468	12	an	an	DET
ejpam-5742	468	13	m−homomorphism	m−homomorphism	NOUN
ejpam-5742	468	14	.	.	PUNCT
ejpam-5742	469	1	we	we	PRON
ejpam-5742	469	2	have	have	AUX
ejpam-5742	469	3	proved	prove	VERB
ejpam-5742	469	4	that	that	SCONJ
ejpam-5742	469	5	the	the	DET
ejpam-5742	469	6	image	image	NOUN
ejpam-5742	469	7	and	and	CCONJ
ejpam-5742	469	8	the	the	DET
ejpam-5742	469	9	inverse	inverse	ADJ
ejpam-5742	469	10	image	image	NOUN
ejpam-5742	469	11	of	of	ADP
ejpam-5742	469	12	an	an	DET
ejpam-5742	469	13	m−filter	m−filter	NOUN
ejpam-5742	469	14	of	of	ADP
ejpam-5742	469	15	an	an	DET
ejpam-5742	469	16	adl	adl	NOUN
ejpam-5742	469	17	under	under	ADP
ejpam-5742	469	18	an	an	DET
ejpam-5742	469	19	m−homomorphism	m−homomorphism	NOUN
ejpam-5742	469	20	again	again	ADV
ejpam-5742	469	21	m−filters	m−filter	NOUN
ejpam-5742	469	22	.	.	PUNCT
ejpam-5742	470	1	we	we	PRON
ejpam-5742	470	2	have	have	AUX
ejpam-5742	470	3	derived	derive	VERB
ejpam-5742	470	4	some	some	DET
ejpam-5742	470	5	sufficient	sufficient	ADJ
ejpam-5742	470	6	conditions	condition	NOUN
ejpam-5742	470	7	for	for	ADP
ejpam-5742	470	8	a	a	DET
ejpam-5742	470	9	prime	prime	ADJ
ejpam-5742	470	10	filter	filter	NOUN
ejpam-5742	470	11	of	of	ADP
ejpam-5742	470	12	an	an	DET
ejpam-5742	470	13	almost	almost	ADV
ejpam-5742	470	14	distributive	distributive	ADJ
ejpam-5742	470	15	lattice	lattice	NOUN
ejpam-5742	470	16	to	to	PART
ejpam-5742	470	17	be	be	AUX
ejpam-5742	470	18	an	an	DET
ejpam-5742	470	19	m−filter	m−filter	NOUN
ejpam-5742	470	20	.	.	PUNCT
ejpam-5742	471	1	we	we	PRON
ejpam-5742	471	2	have	have	AUX
ejpam-5742	471	3	established	establish	VERB
ejpam-5742	471	4	a	a	DET
ejpam-5742	471	5	set	set	NOUN
ejpam-5742	471	6	of	of	ADP
ejpam-5742	471	7	equivalent	equivalent	ADJ
ejpam-5742	471	8	conditions	condition	NOUN
ejpam-5742	471	9	for	for	ADP
ejpam-5742	471	10	every	every	DET
ejpam-5742	471	11	m−filter	m−filter	NOUN
ejpam-5742	471	12	to	to	PART
ejpam-5742	471	13	be	be	AUX
ejpam-5742	471	14	an	an	DET
ejpam-5742	471	15	annihilator	annihilator	NOUN
ejpam-5742	471	16	filter	filter	NOUN
ejpam-5742	471	17	.	.	PUNCT
ejpam-5742	472	1	we	we	PRON
ejpam-5742	472	2	have	have	AUX
ejpam-5742	472	3	obtained	obtain	VERB
ejpam-5742	472	4	an	an	DET
ejpam-5742	472	5	equivalency	equivalency	NOUN
ejpam-5742	472	6	between	between	ADP
ejpam-5742	472	7	prime	prime	ADJ
ejpam-5742	472	8	m−filters	m−filter	NOUN
ejpam-5742	472	9	and	and	CCONJ
ejpam-5742	472	10	minimal	minimal	ADJ
ejpam-5742	472	11	prime	prime	ADJ
ejpam-5742	472	12	filters	filter	NOUN
ejpam-5742	472	13	of	of	ADP
ejpam-5742	472	14	an	an	DET
ejpam-5742	472	15	adl	adl	NOUN
ejpam-5742	472	16	.	.	PUNCT
ejpam-5742	473	1	we	we	PRON
ejpam-5742	473	2	have	have	AUX
ejpam-5742	473	3	proved	prove	VERB
ejpam-5742	473	4	that	that	SCONJ
ejpam-5742	473	5	any	any	DET
ejpam-5742	473	6	two	two	NUM
ejpam-5742	473	7	distinct	distinct	ADJ
ejpam-5742	473	8	prime	prime	ADJ
ejpam-5742	473	9	m−filters	m−filter	NOUN
ejpam-5742	473	10	of	of	ADP
ejpam-5742	473	11	an	an	DET
ejpam-5742	473	12	adl	adl	NOUN
ejpam-5742	473	13	are	be	AUX
ejpam-5742	473	14	comaximal	comaximal	ADJ
ejpam-5742	473	15	.	.	PUNCT
ejpam-5742	474	1	acknowledgements	acknowledgement	NOUN
ejpam-5742	474	2	the	the	DET
ejpam-5742	474	3	authors	author	NOUN
ejpam-5742	474	4	wish	wish	VERB
ejpam-5742	474	5	to	to	PART
ejpam-5742	474	6	thank	thank	VERB
ejpam-5742	474	7	the	the	DET
ejpam-5742	474	8	anonymous	anonymous	ADJ
ejpam-5742	474	9	reviewers	reviewer	NOUN
ejpam-5742	474	10	for	for	ADP
ejpam-5742	474	11	their	their	PRON
ejpam-5742	474	12	valuable	valuable	ADJ
ejpam-5742	474	13	suggestions	suggestion	NOUN
ejpam-5742	474	14	.	.	PUNCT
ejpam-5742	475	1	conflicts	conflict	NOUN
ejpam-5742	475	2	of	of	ADP
ejpam-5742	475	3	interest	interest	NOUN
ejpam-5742	475	4	or	or	CCONJ
ejpam-5742	475	5	competing	compete	VERB
ejpam-5742	475	6	interests	interest	NOUN
ejpam-5742	475	7	the	the	DET
ejpam-5742	475	8	authors	author	NOUN
ejpam-5742	475	9	declare	declare	VERB
ejpam-5742	475	10	that	that	SCONJ
ejpam-5742	475	11	they	they	PRON
ejpam-5742	475	12	have	have	VERB
ejpam-5742	475	13	no	no	DET
ejpam-5742	475	14	conflicts	conflict	NOUN
ejpam-5742	475	15	of	of	ADP
ejpam-5742	475	16	interest	interest	NOUN
ejpam-5742	475	17	.	.	PUNCT
ejpam-5742	476	1	informed	inform	VERB
ejpam-5742	476	2	consent	consent	VERB
ejpam-5742	476	3	the	the	DET
ejpam-5742	476	4	authors	author	NOUN
ejpam-5742	476	5	are	be	AUX
ejpam-5742	476	6	fully	fully	ADV
ejpam-5742	476	7	aware	aware	ADJ
ejpam-5742	476	8	and	and	CCONJ
ejpam-5742	476	9	satisfied	satisfied	ADJ
ejpam-5742	476	10	with	with	ADP
ejpam-5742	476	11	the	the	DET
ejpam-5742	476	12	contents	content	NOUN
ejpam-5742	476	13	of	of	ADP
ejpam-5742	476	14	the	the	DET
ejpam-5742	476	15	article	article	NOUN
ejpam-5742	476	16	.	.	PUNCT
ejpam-5742	477	1	references	reference	NOUN
ejpam-5742	477	2	[	[	X
ejpam-5742	477	3	1	1	X
ejpam-5742	477	4	]	]	X
ejpam-5742	477	5	u.m	u.m	PROPN
ejpam-5742	477	6	.	.	PROPN
ejpam-5742	477	7	swamy	swamy	PROPN
ejpam-5742	477	8	and	and	CCONJ
ejpam-5742	477	9	g.c	g.c	PROPN
ejpam-5742	477	10	.	.	PROPN
ejpam-5742	477	11	rao	rao	PROPN
ejpam-5742	477	12	.	.	PUNCT
ejpam-5742	478	1	almost	almost	ADV
ejpam-5742	478	2	distributive	distributive	ADJ
ejpam-5742	478	3	lattices	lattice	NOUN
ejpam-5742	478	4	.	.	PUNCT
ejpam-5742	479	1	j.	j.	PROPN
ejpam-5742	479	2	aust	aust	PROPN
ejpam-5742	479	3	.	.	PUNCT
ejpam-5742	480	1	math	math	PROPN
ejpam-5742	480	2	.	.	PUNCT
ejpam-5742	481	1	soc	soc	PROPN
ejpam-5742	481	2	.	.	PUNCT
ejpam-5742	482	1	(	(	PUNCT
ejpam-5742	482	2	series	series	NOUN
ejpam-5742	482	3	a	a	PRON
ejpam-5742	482	4	,	,	PUNCT
ejpam-5742	482	5	31:77–91	31:77–91	NUM
ejpam-5742	482	6	,	,	PUNCT
ejpam-5742	482	7	1981	1981	NUM
ejpam-5742	482	8	.	.	PUNCT
ejpam-5742	483	1	n.	n.	PROPN
ejpam-5742	483	2	rafi	rafi	PROPN
ejpam-5742	483	3	,	,	PUNCT
ejpam-5742	483	4	t.	t.	PROPN
ejpam-5742	483	5	gaketem	gaketem	PROPN
ejpam-5742	483	6	,	,	PUNCT
ejpam-5742	483	7	r.	r.	PROPN
ejpam-5742	483	8	k.	k.	PROPN
ejpam-5742	483	9	bandaru	bandaru	PROPN
ejpam-5742	483	10	/	/	SYM
ejpam-5742	483	11	eur	eur	PROPN
ejpam-5742	483	12	.	.	PUNCT
ejpam-5742	484	1	j.	j.	PROPN
ejpam-5742	484	2	pure	pure	PROPN
ejpam-5742	484	3	appl	appl	PROPN
ejpam-5742	484	4	.	.	PROPN
ejpam-5742	484	5	math	math	PROPN
ejpam-5742	484	6	,	,	PUNCT
ejpam-5742	484	7	18	18	NUM
ejpam-5742	484	8	(	(	PUNCT
ejpam-5742	484	9	2	2	NUM
ejpam-5742	484	10	)	)	PUNCT
ejpam-5742	484	11	(	(	PUNCT
ejpam-5742	484	12	2025	2025	NUM
ejpam-5742	484	13	)	)	PUNCT
ejpam-5742	484	14	,	,	PUNCT
ejpam-5742	484	15	5742	5742	NUM
ejpam-5742	484	16	14	14	NUM
ejpam-5742	484	17	of	of	ADP
ejpam-5742	484	18	14	14	NUM
ejpam-5742	484	19	[	[	X
ejpam-5742	484	20	2	2	NUM
ejpam-5742	484	21	]	]	X
ejpam-5742	484	22	n.	n.	NOUN
ejpam-5742	484	23	rafi	rafi	PROPN
ejpam-5742	484	24	and	and	CCONJ
ejpam-5742	484	25	ravi	ravi	PROPN
ejpam-5742	484	26	kumar	kumar	PROPN
ejpam-5742	484	27	bandaru	bandaru	PROPN
ejpam-5742	484	28	.	.	PUNCT
ejpam-5742	485	1	µ-filters	µ-filter	NOUN
ejpam-5742	485	2	of	of	ADP
ejpam-5742	485	3	almost	almost	ADV
ejpam-5742	485	4	distributive	distributive	ADJ
ejpam-5742	485	5	lattices	lattice	NOUN
ejpam-5742	485	6	.	.	PUNCT
ejpam-5742	486	1	chamchuri	chamchuri	PROPN
ejpam-5742	486	2	j.	j.	PROPN
ejpam-5742	486	3	math	math	PROPN
ejpam-5742	486	4	.	.	PUNCT
ejpam-5742	486	5	,	,	PUNCT
ejpam-5742	486	6	10:53–65	10:53–65	NUM
ejpam-5742	486	7	,	,	PUNCT
ejpam-5742	486	8	2018	2018	NUM
ejpam-5742	486	9	.	.	PUNCT
ejpam-5742	487	1	[	[	X
ejpam-5742	487	2	3	3	X
ejpam-5742	487	3	]	]	PUNCT
ejpam-5742	487	4	m.	m.	NOUN
ejpam-5742	487	5	sambasiva	sambasiva	PROPN
ejpam-5742	487	6	rao	rao	PROPN
ejpam-5742	487	7	and	and	CCONJ
ejpam-5742	487	8	g.c	g.c	PROPN
ejpam-5742	487	9	.	.	PROPN
ejpam-5742	487	10	rao	rao	PROPN
ejpam-5742	487	11	.	.	PUNCT
ejpam-5742	488	1	o	o	X
ejpam-5742	488	2	-	-	PUNCT
ejpam-5742	488	3	homomorphisms	homomorphism	NOUN
ejpam-5742	488	4	of	of	ADP
ejpam-5742	488	5	almost	almost	ADV
ejpam-5742	488	6	distributive	distributive	ADJ
ejpam-5742	488	7	lattices	lattice	NOUN
ejpam-5742	488	8	.	.	PUNCT
ejpam-5742	489	1	chamchuri	chamchuri	PROPN
ejpam-5742	489	2	journal	journal	PROPN
ejpam-5742	489	3	of	of	ADP
ejpam-5742	489	4	mathematics	mathematic	NOUN
ejpam-5742	489	5	,	,	PUNCT
ejpam-5742	489	6	4:13	4:13	NUM
ejpam-5742	489	7	–	–	PUNCT
ejpam-5742	489	8	21	21	NUM
ejpam-5742	489	9	,	,	PUNCT
ejpam-5742	489	10	2012	2012	NUM
ejpam-5742	489	11	.	.	PUNCT
ejpam-5742	490	1	[	[	X
ejpam-5742	490	2	4	4	X
ejpam-5742	490	3	]	]	PUNCT
ejpam-5742	490	4	m.	m.	NOUN
ejpam-5742	490	5	sambasiva	sambasiva	PROPN
ejpam-5742	490	6	rao	rao	PROPN
ejpam-5742	490	7	.	.	PUNCT
ejpam-5742	491	1	o	o	X
ejpam-5742	491	2	-	-	NOUN
ejpam-5742	491	3	filters	filter	NOUN
ejpam-5742	491	4	and	and	CCONJ
ejpam-5742	491	5	minimal	minimal	ADJ
ejpam-5742	491	6	prime	prime	ADJ
ejpam-5742	491	7	filters	filter	NOUN
ejpam-5742	491	8	of	of	ADP
ejpam-5742	491	9	lattices	lattice	NOUN
ejpam-5742	491	10	.	.	PUNCT
ejpam-5742	492	1	southeast	southeast	ADJ
ejpam-5742	492	2	asian	asian	ADJ
ejpam-5742	492	3	bulletin	bulletin	NOUN
ejpam-5742	492	4	of	of	ADP
ejpam-5742	492	5	mathematics	mathematic	NOUN
ejpam-5742	492	6	,	,	PUNCT
ejpam-5742	492	7	39:113	39:113	NUM
ejpam-5742	492	8	–	–	PUNCT
ejpam-5742	492	9	121	121	NUM
ejpam-5742	492	10	,	,	PUNCT
ejpam-5742	492	11	2015	2015	NUM
ejpam-5742	492	12	.	.	PUNCT
ejpam-5742	493	1	[	[	X
ejpam-5742	493	2	5	5	X
ejpam-5742	493	3	]	]	PUNCT
ejpam-5742	493	4	ravi	ravi	NOUN
ejpam-5742	493	5	kumar	kumar	PROPN
ejpam-5742	493	6	bandaru	bandaru	PROPN
ejpam-5742	493	7	n.	n.	PROPN
ejpam-5742	493	8	rafi	rafi	PROPN
ejpam-5742	493	9	and	and	CCONJ
ejpam-5742	493	10	g.c	g.c	PROPN
ejpam-5742	493	11	.	.	PROPN
ejpam-5742	493	12	rao	rao	PROPN
ejpam-5742	493	13	.	.	PUNCT
ejpam-5742	494	1	prime	prime	ADJ
ejpam-5742	494	2	o	o	NOUN
ejpam-5742	494	3	-	-	NOUN
ejpam-5742	494	4	ideals	ideal	NOUN
ejpam-5742	494	5	in	in	ADP
ejpam-5742	494	6	almost	almost	ADV
ejpam-5742	494	7	distributive	distributive	ADJ
ejpam-5742	494	8	lattices	lattice	NOUN
ejpam-5742	494	9	.	.	PUNCT
ejpam-5742	495	1	southeast	southeast	ADJ
ejpam-5742	495	2	asian	asian	ADJ
ejpam-5742	495	3	bulletin	bulletin	NOUN
ejpam-5742	495	4	of	of	ADP
ejpam-5742	495	5	mathematics	mathematic	NOUN
ejpam-5742	495	6	,	,	PUNCT
ejpam-5742	495	7	39:841–850	39:841–850	NUM
ejpam-5742	495	8	,	,	PUNCT
ejpam-5742	495	9	2015	2015	NUM
ejpam-5742	495	10	.	.	PUNCT
ejpam-5742	496	1	[	[	X
ejpam-5742	496	2	6	6	NUM
ejpam-5742	496	3	]	]	X
ejpam-5742	496	4	g.c	g.c	PROPN
ejpam-5742	496	5	.	.	PROPN
ejpam-5742	496	6	rao	rao	PROPN
ejpam-5742	496	7	.	.	PUNCT
ejpam-5742	497	1	almost	almost	ADV
ejpam-5742	497	2	distributive	distributive	ADJ
ejpam-5742	497	3	lattices	lattice	NOUN
ejpam-5742	497	4	.	.	PUNCT
ejpam-5742	498	1	doctoral	doctoral	ADJ
ejpam-5742	498	2	thesis	thesis	NOUN
ejpam-5742	498	3	,	,	PUNCT
ejpam-5742	498	4	dept	dept	NOUN
ejpam-5742	498	5	.	.	PROPN
ejpam-5742	498	6	of	of	ADP
ejpam-5742	498	7	mathematics	mathematics	PROPN
ejpam-5742	498	8	,	,	PUNCT
ejpam-5742	498	9	andhra	andhra	PROPN
ejpam-5742	498	10	university	university	PROPN
ejpam-5742	498	11	,	,	PUNCT
ejpam-5742	498	12	visakhapatnam	visakhapatnam	PROPN
ejpam-5742	498	13	.	.	PUNCT
ejpam-5742	498	14	1980	1980	NUM
ejpam-5742	498	15	.	.	PUNCT
ejpam-5742	499	1	[	[	X
ejpam-5742	499	2	7	7	X
ejpam-5742	499	3	]	]	SYM
ejpam-5742	499	4	g	g	NOUN
ejpam-5742	499	5	birkhoff	birkhoff	NOUN
ejpam-5742	499	6	.	.	PUNCT
ejpam-5742	500	1	lattice	lattice	PROPN
ejpam-5742	500	2	theory	theory	PROPN
ejpam-5742	500	3	.	.	PUNCT
ejpam-5742	501	1	amer	amer	PROPN
ejpam-5742	501	2	.	.	PUNCT
ejpam-5742	501	3	math	math	PROPN
ejpam-5742	501	4	.	.	PUNCT
ejpam-5742	502	1	soc	soc	PROPN
ejpam-5742	502	2	.	.	PUNCT
ejpam-5742	503	1	collequium	collequium	NOUN
ejpam-5742	503	2	pub	pub	NOUN
ejpam-5742	503	3	,	,	PUNCT
ejpam-5742	503	4	1967	1967	NUM
ejpam-5742	503	5	.	.	PUNCT
ejpam-5742	504	1	[	[	X
ejpam-5742	504	2	8	8	NUM
ejpam-5742	504	3	]	]	X
ejpam-5742	504	4	g.	g.	PROPN
ejpam-5742	504	5	gratzer	gratzer	PROPN
ejpam-5742	504	6	.	.	PUNCT
ejpam-5742	505	1	general	general	PROPN
ejpam-5742	505	2	lattice	lattice	PROPN
ejpam-5742	505	3	theory	theory	NOUN
ejpam-5742	505	4	.	.	PUNCT
ejpam-5742	506	1	academic	academic	ADJ
ejpam-5742	506	2	press	press	NOUN
ejpam-5742	506	3	,	,	PUNCT
ejpam-5742	506	4	new	new	PROPN
ejpam-5742	506	5	york	york	PROPN
ejpam-5742	506	6	,	,	PUNCT
ejpam-5742	506	7	sanfransisco	sanfransisco	PROPN
ejpam-5742	506	8	,	,	PUNCT
ejpam-5742	506	9	1978	1978	NUM
ejpam-5742	506	10	.	.	PUNCT
ejpam-5742	507	1	[	[	X
ejpam-5742	507	2	9	9	NUM
ejpam-5742	507	3	]	]	X
ejpam-5742	507	4	n.	n.	PROPN
ejpam-5742	507	5	rafi	rafi	PROPN
ejpam-5742	507	6	.	.	PUNCT
ejpam-5742	508	1	a	a	DET
ejpam-5742	508	2	special	special	ADJ
ejpam-5742	508	3	case	case	NOUN
ejpam-5742	508	4	of	of	ADP
ejpam-5742	508	5	complemented	complemented	ADJ
ejpam-5742	508	6	almost	almost	ADV
ejpam-5742	508	7	distributive	distributive	ADJ
ejpam-5742	508	8	lattices	lattice	NOUN
ejpam-5742	508	9	.	.	PUNCT
ejpam-5742	509	1	international	international	ADJ
ejpam-5742	509	2	journal	journal	PROPN
ejpam-5742	509	3	of	of	ADP
ejpam-5742	509	4	scientific	scientific	ADJ
ejpam-5742	509	5	and	and	CCONJ
ejpam-5742	509	6	innovative	innovative	ADJ
ejpam-5742	509	7	mathematical	mathematical	ADJ
ejpam-5742	509	8	research	research	NOUN
ejpam-5742	509	9	,	,	PUNCT
ejpam-5742	509	10	3(12):17–23	3(12):17–23	NUM
ejpam-5742	509	11	,	,	PUNCT
ejpam-5742	509	12	2015	2015	NUM
ejpam-5742	509	13	.	.	PUNCT
ejpam-5742	510	1	[	[	X
ejpam-5742	510	2	10	10	NUM
ejpam-5742	510	3	]	]	X
ejpam-5742	510	4	n.	n.	PROPN
ejpam-5742	510	5	rafi	rafi	PROPN
ejpam-5742	510	6	.	.	PUNCT
ejpam-5742	511	1	on	on	ADP
ejpam-5742	511	2	m	m	NOUN
ejpam-5742	511	3	-	-	NOUN
ejpam-5742	511	4	filters	filter	NOUN
ejpam-5742	511	5	of	of	ADP
ejpam-5742	511	6	almost	almost	ADV
ejpam-5742	511	7	distributive	distributive	ADJ
ejpam-5742	511	8	lattices	lattice	NOUN
ejpam-5742	511	9	.	.	PUNCT
ejpam-5742	512	1	international	international	ADJ
ejpam-5742	512	2	conference	conference	NOUN
ejpam-5742	512	3	on	on	ADP
ejpam-5742	512	4	electrical	electrical	ADJ
ejpam-5742	512	5	,	,	PUNCT
ejpam-5742	512	6	electronics	electronic	NOUN
ejpam-5742	512	7	,	,	PUNCT
ejpam-5742	512	8	and	and	CCONJ
ejpam-5742	512	9	optimization	optimization	NOUN
ejpam-5742	512	10	techniques	technique	NOUN
ejpam-5742	512	11	(	(	PUNCT
ejpam-5742	512	12	iceeot	iceeot	ADJ
ejpam-5742	512	13	)	)	PUNCT
ejpam-5742	512	14	2016	2016	NUM
ejpam-5742	512	15	,	,	PUNCT
ejpam-5742	512	16	pages	page	NOUN
ejpam-5742	512	17	4518	4518	NUM
ejpam-5742	512	18	–	–	PUNCT
ejpam-5742	512	19	4521	4521	NUM
ejpam-5742	512	20	,	,	PUNCT
ejpam-5742	512	21	2016	2016	NUM
ejpam-5742	512	22	.	.	PUNCT