id	sid	tid	token	lemma	pos
ejpam-6418	1	1	european	european	PROPN
ejpam-6418	1	2	journal	journal	PROPN
ejpam-6418	1	3	of	of	ADP
ejpam-6418	1	4	pure	pure	ADJ
ejpam-6418	1	5	and	and	CCONJ
ejpam-6418	1	6	applied	applied	ADJ
ejpam-6418	1	7	mathematics	mathematic	NOUN
ejpam-6418	1	8	2025	2025	NUM
ejpam-6418	1	9	,	,	PUNCT
ejpam-6418	1	10	vol	vol	NOUN
ejpam-6418	1	11	.	.	PROPN
ejpam-6418	1	12	18	18	NUM
ejpam-6418	1	13	,	,	PUNCT
ejpam-6418	1	14	issue	issue	NOUN
ejpam-6418	1	15	4	4	NUM
ejpam-6418	1	16	,	,	PUNCT
ejpam-6418	1	17	article	article	NOUN
ejpam-6418	1	18	number	number	NOUN
ejpam-6418	1	19	6418	6418	NUM
ejpam-6418	1	20	issn	issn	VERB
ejpam-6418	1	21	1307	1307	NUM
ejpam-6418	1	22	-	-	SYM
ejpam-6418	1	23	5543	5543	NUM
ejpam-6418	1	24	–	–	PUNCT
ejpam-6418	1	25	ejpam.com	ejpam.com	X
ejpam-6418	1	26	published	publish	VERB
ejpam-6418	1	27	by	by	ADP
ejpam-6418	1	28	new	new	PROPN
ejpam-6418	1	29	york	york	PROPN
ejpam-6418	1	30	business	business	PROPN
ejpam-6418	1	31	global	global	ADJ
ejpam-6418	1	32	amicable	amicable	ADJ
ejpam-6418	1	33	sets	set	NOUN
ejpam-6418	1	34	in	in	ADP
ejpam-6418	1	35	paradistributive	paradistributive	ADJ
ejpam-6418	1	36	latticoids	latticoids	PROPN
ejpam-6418	1	37	ramesh	ramesh	PROPN
ejpam-6418	1	38	sirisetti1	sirisetti1	PROPN
ejpam-6418	1	39	,	,	PUNCT
ejpam-6418	1	40	jogarao	jogarao	PROPN
ejpam-6418	1	41	gunda2	gunda2	PROPN
ejpam-6418	1	42	,	,	PUNCT
ejpam-6418	1	43	ravikumar	ravikumar	PROPN
ejpam-6418	1	44	bandaru3	bandaru3	PROPN
ejpam-6418	1	45	,	,	PUNCT
ejpam-6418	1	46	thiti	thiti	PROPN
ejpam-6418	1	47	gaketem4,∗	gaketem4,∗	PROPN
ejpam-6418	1	48	1	1	NUM
ejpam-6418	1	49	department	department	NOUN
ejpam-6418	1	50	of	of	ADP
ejpam-6418	1	51	mathematics	mathematics	PROPN
ejpam-6418	1	52	,	,	PUNCT
ejpam-6418	1	53	aditya	aditya	PROPN
ejpam-6418	1	54	university	university	PROPN
ejpam-6418	1	55	,	,	PUNCT
ejpam-6418	1	56	surampalem	surampalem	PROPN
ejpam-6418	1	57	,	,	PUNCT
ejpam-6418	1	58	kakinada	kakinada	PROPN
ejpam-6418	1	59	,	,	PUNCT
ejpam-6418	1	60	andhra	andhra	PROPN
ejpam-6418	1	61	pradesh	pradesh	PROPN
ejpam-6418	1	62	533437	533437	NUM
ejpam-6418	1	63	,	,	PUNCT
ejpam-6418	1	64	india	india	PROPN
ejpam-6418	1	65	2	2	NUM
ejpam-6418	1	66	department	department	NOUN
ejpam-6418	1	67	of	of	ADP
ejpam-6418	1	68	bs	bs	PROPN
ejpam-6418	1	69	&	&	CCONJ
ejpam-6418	1	70	h	h	PROPN
ejpam-6418	1	71	,	,	PUNCT
ejpam-6418	1	72	aditya	aditya	PROPN
ejpam-6418	1	73	institute	institute	PROPN
ejpam-6418	1	74	of	of	ADP
ejpam-6418	1	75	technology	technology	NOUN
ejpam-6418	1	76	and	and	CCONJ
ejpam-6418	1	77	management	management	NOUN
ejpam-6418	1	78	,	,	PUNCT
ejpam-6418	1	79	tekkali	tekkali	PROPN
ejpam-6418	1	80	,	,	PUNCT
ejpam-6418	1	81	srikakulam	srikakulam	PROPN
ejpam-6418	1	82	,	,	PUNCT
ejpam-6418	1	83	andhra	andhra	PROPN
ejpam-6418	1	84	pradesh	pradesh	PROPN
ejpam-6418	1	85	530021	530021	NUM
ejpam-6418	1	86	,	,	PUNCT
ejpam-6418	1	87	india	india	PROPN
ejpam-6418	1	88	3	3	PROPN
ejpam-6418	1	89	department	department	NOUN
ejpam-6418	1	90	of	of	ADP
ejpam-6418	1	91	mathematics	mathematic	NOUN
ejpam-6418	1	92	,	,	PUNCT
ejpam-6418	1	93	school	school	NOUN
ejpam-6418	1	94	of	of	ADP
ejpam-6418	1	95	advanced	advanced	ADJ
ejpam-6418	1	96	sciences	science	NOUN
ejpam-6418	1	97	,	,	PUNCT
ejpam-6418	1	98	vit	vit	PROPN
ejpam-6418	1	99	-	-	PUNCT
ejpam-6418	1	100	ap	ap	PROPN
ejpam-6418	1	101	university	university	PROPN
ejpam-6418	1	102	,	,	PUNCT
ejpam-6418	1	103	andhra	andhra	PROPN
ejpam-6418	1	104	pradesh	pradesh	PROPN
ejpam-6418	1	105	522237	522237	NUM
ejpam-6418	1	106	,	,	PUNCT
ejpam-6418	1	107	india	india	PROPN
ejpam-6418	1	108	4	4	NUM
ejpam-6418	1	109	department	department	NOUN
ejpam-6418	1	110	of	of	ADP
ejpam-6418	1	111	mathematics	mathematic	NOUN
ejpam-6418	1	112	,	,	PUNCT
ejpam-6418	1	113	school	school	NOUN
ejpam-6418	1	114	of	of	ADP
ejpam-6418	1	115	science	science	NOUN
ejpam-6418	1	116	,	,	PUNCT
ejpam-6418	1	117	university	university	NOUN
ejpam-6418	1	118	of	of	ADP
ejpam-6418	1	119	phayao	phayao	NOUN
ejpam-6418	1	120	,	,	PUNCT
ejpam-6418	1	121	phayao	phayao	NOUN
ejpam-6418	1	122	56000	56000	NUM
ejpam-6418	1	123	,	,	PUNCT
ejpam-6418	1	124	thailand	thailand	PROPN
ejpam-6418	1	125	abstract	abstract	NOUN
ejpam-6418	1	126	.	.	PUNCT
ejpam-6418	2	1	in	in	ADP
ejpam-6418	2	2	this	this	DET
ejpam-6418	2	3	work	work	NOUN
ejpam-6418	2	4	,	,	PUNCT
ejpam-6418	2	5	we	we	PRON
ejpam-6418	2	6	introduce	introduce	VERB
ejpam-6418	2	7	maximal	maximal	ADJ
ejpam-6418	2	8	sets	set	NOUN
ejpam-6418	2	9	and	and	CCONJ
ejpam-6418	2	10	amicable	amicable	ADJ
ejpam-6418	2	11	sets	set	NOUN
ejpam-6418	2	12	in	in	ADP
ejpam-6418	2	13	a	a	DET
ejpam-6418	2	14	paradistributive	paradistributive	ADJ
ejpam-6418	2	15	latticoid	latticoid	NOUN
ejpam-6418	2	16	.	.	PUNCT
ejpam-6418	3	1	we	we	PRON
ejpam-6418	3	2	present	present	VERB
ejpam-6418	3	3	a	a	DET
ejpam-6418	3	4	few	few	ADJ
ejpam-6418	3	5	number	number	NOUN
ejpam-6418	3	6	of	of	ADP
ejpam-6418	3	7	examples	example	NOUN
ejpam-6418	3	8	and	and	CCONJ
ejpam-6418	3	9	counter	counter	NOUN
ejpam-6418	3	10	-	-	NOUN
ejpam-6418	3	11	examples	example	NOUN
ejpam-6418	3	12	for	for	ADP
ejpam-6418	3	13	them	they	PRON
ejpam-6418	3	14	,	,	PUNCT
ejpam-6418	3	15	prove	prove	VERB
ejpam-6418	3	16	some	some	DET
ejpam-6418	3	17	algebraic	algebraic	ADJ
ejpam-6418	3	18	properties	property	NOUN
ejpam-6418	3	19	on	on	ADP
ejpam-6418	3	20	them	they	PRON
ejpam-6418	3	21	.	.	PUNCT
ejpam-6418	4	1	also	also	ADV
ejpam-6418	4	2	,	,	PUNCT
ejpam-6418	4	3	we	we	PRON
ejpam-6418	4	4	define	define	VERB
ejpam-6418	4	5	center	center	NOUN
ejpam-6418	4	6	of	of	ADP
ejpam-6418	4	7	a	a	DET
ejpam-6418	4	8	paradistributive	paradistributive	ADJ
ejpam-6418	4	9	latticoid	latticoid	NOUN
ejpam-6418	4	10	and	and	CCONJ
ejpam-6418	4	11	prove	prove	VERB
ejpam-6418	4	12	that	that	SCONJ
ejpam-6418	4	13	it	it	PRON
ejpam-6418	4	14	is	be	AUX
ejpam-6418	4	15	equal	equal	ADJ
ejpam-6418	4	16	to	to	ADP
ejpam-6418	4	17	the	the	DET
ejpam-6418	4	18	intersection	intersection	NOUN
ejpam-6418	4	19	of	of	ADP
ejpam-6418	4	20	all	all	DET
ejpam-6418	4	21	maximal	maximal	ADJ
ejpam-6418	4	22	sets	set	NOUN
ejpam-6418	4	23	.	.	PUNCT
ejpam-6418	5	1	finally	finally	ADV
ejpam-6418	5	2	,	,	PUNCT
ejpam-6418	5	3	we	we	PRON
ejpam-6418	5	4	obtain	obtain	VERB
ejpam-6418	5	5	some	some	DET
ejpam-6418	5	6	necessary	necessary	ADJ
ejpam-6418	5	7	and	and	CCONJ
ejpam-6418	5	8	sufficient	sufficient	ADJ
ejpam-6418	5	9	conditions	condition	NOUN
ejpam-6418	5	10	for	for	ADP
ejpam-6418	5	11	a	a	DET
ejpam-6418	5	12	paradistributive	paradistributive	ADJ
ejpam-6418	5	13	latticoid	latticoid	NOUN
ejpam-6418	5	14	to	to	PART
ejpam-6418	5	15	become	become	VERB
ejpam-6418	5	16	relatively	relatively	ADV
ejpam-6418	5	17	complemented	complemented	ADJ
ejpam-6418	5	18	.	.	PUNCT
ejpam-6418	6	1	2020	2020	NUM
ejpam-6418	6	2	mathematics	mathematic	NOUN
ejpam-6418	6	3	subject	subject	NOUN
ejpam-6418	6	4	classifications	classification	NOUN
ejpam-6418	6	5	:	:	PUNCT
ejpam-6418	6	6	06d99	06d99	NUM
ejpam-6418	6	7	,	,	PUNCT
ejpam-6418	6	8	06d20	06d20	VERB
ejpam-6418	6	9	key	key	ADJ
ejpam-6418	6	10	words	word	NOUN
ejpam-6418	6	11	and	and	CCONJ
ejpam-6418	6	12	phrases	phrase	NOUN
ejpam-6418	6	13	:	:	PUNCT
ejpam-6418	6	14	paradistributive	paradistributive	ADJ
ejpam-6418	6	15	latticoids	latticoids	PROPN
ejpam-6418	6	16	,	,	PUNCT
ejpam-6418	6	17	copatible	copatible	ADJ
ejpam-6418	6	18	sets	set	NOUN
ejpam-6418	6	19	,	,	PUNCT
ejpam-6418	6	20	maximal	maximal	ADJ
ejpam-6418	6	21	sets	set	NOUN
ejpam-6418	6	22	,	,	PUNCT
ejpam-6418	6	23	amicable	amicable	ADJ
ejpam-6418	6	24	sets	set	NOUN
ejpam-6418	6	25	,	,	PUNCT
ejpam-6418	6	26	relatively	relatively	ADV
ejpam-6418	6	27	complemented	complemented	ADJ
ejpam-6418	6	28	paradistributive	paradistributive	ADJ
ejpam-6418	6	29	latticoids	latticoid	NOUN
ejpam-6418	6	30	1	1	NUM
ejpam-6418	6	31	.	.	PUNCT
ejpam-6418	6	32	introduction	introduction	NOUN
ejpam-6418	6	33	the	the	DET
ejpam-6418	6	34	exploration	exploration	NOUN
ejpam-6418	6	35	of	of	ADP
ejpam-6418	6	36	algebraic	algebraic	ADJ
ejpam-6418	6	37	structures	structure	NOUN
ejpam-6418	6	38	such	such	ADJ
ejpam-6418	6	39	as	as	ADP
ejpam-6418	6	40	lattices	lattice	NOUN
ejpam-6418	6	41	and	and	CCONJ
ejpam-6418	6	42	their	their	PRON
ejpam-6418	6	43	generalizations	generalization	NOUN
ejpam-6418	6	44	constitutes	constitute	VERB
ejpam-6418	6	45	a	a	DET
ejpam-6418	6	46	fundamental	fundamental	ADJ
ejpam-6418	6	47	area	area	NOUN
ejpam-6418	6	48	of	of	ADP
ejpam-6418	6	49	study	study	NOUN
ejpam-6418	6	50	in	in	ADP
ejpam-6418	6	51	universal	universal	ADJ
ejpam-6418	6	52	algebra	algebra	NOUN
ejpam-6418	6	53	and	and	CCONJ
ejpam-6418	6	54	mathematical	mathematical	ADJ
ejpam-6418	6	55	logic	logic	NOUN
ejpam-6418	6	56	.	.	PUNCT
ejpam-6418	7	1	a	a	DET
ejpam-6418	7	2	recent	recent	ADJ
ejpam-6418	7	3	advancement	advancement	NOUN
ejpam-6418	7	4	in	in	ADP
ejpam-6418	7	5	this	this	DET
ejpam-6418	7	6	direction	direction	NOUN
ejpam-6418	7	7	is	be	AUX
ejpam-6418	7	8	the	the	DET
ejpam-6418	7	9	development	development	NOUN
ejpam-6418	7	10	of	of	ADP
ejpam-6418	7	11	the	the	DET
ejpam-6418	7	12	theory	theory	NOUN
ejpam-6418	7	13	of	of	ADP
ejpam-6418	7	14	paradistributive	paradistributive	ADJ
ejpam-6418	7	15	latticoids	latticoid	NOUN
ejpam-6418	7	16	(	(	PUNCT
ejpam-6418	7	17	pdls	pdl	NOUN
ejpam-6418	7	18	)	)	PUNCT
ejpam-6418	8	1	[	[	X
ejpam-6418	8	2	1	1	NUM
ejpam-6418	8	3	]	]	PUNCT
ejpam-6418	8	4	,	,	PUNCT
ejpam-6418	8	5	which	which	PRON
ejpam-6418	8	6	extend	extend	VERB
ejpam-6418	8	7	classical	classical	ADJ
ejpam-6418	8	8	distributive	distributive	ADJ
ejpam-6418	8	9	lattices	lattice	NOUN
ejpam-6418	8	10	by	by	ADP
ejpam-6418	8	11	relaxing	relax	VERB
ejpam-6418	8	12	conventional	conventional	ADJ
ejpam-6418	8	13	distributive	distributive	ADJ
ejpam-6418	8	14	constraints	constraint	NOUN
ejpam-6418	8	15	while	while	SCONJ
ejpam-6418	8	16	maintaining	maintain	VERB
ejpam-6418	8	17	essential	essential	ADJ
ejpam-6418	8	18	structural	structural	ADJ
ejpam-6418	8	19	properties	property	NOUN
ejpam-6418	8	20	.	.	PUNCT
ejpam-6418	8	21	introduced	introduce	VERB
ejpam-6418	8	22	by	by	ADP
ejpam-6418	8	23	bandaru	bandaru	NOUN
ejpam-6418	8	24	and	and	CCONJ
ejpam-6418	8	25	ajjarapu	ajjarapu	PROPN
ejpam-6418	8	26	,	,	PUNCT
ejpam-6418	8	27	pdls	pdl	NOUN
ejpam-6418	8	28	are	be	AUX
ejpam-6418	8	29	algebras	algebra	NOUN
ejpam-6418	8	30	of	of	ADP
ejpam-6418	8	31	type	type	NOUN
ejpam-6418	8	32	(	(	PUNCT
ejpam-6418	8	33	2	2	NUM
ejpam-6418	8	34	,	,	PUNCT
ejpam-6418	8	35	2	2	NUM
ejpam-6418	8	36	,	,	PUNCT
ejpam-6418	8	37	1	1	NUM
ejpam-6418	8	38	)	)	PUNCT
ejpam-6418	8	39	,	,	PUNCT
ejpam-6418	8	40	equipped	equip	VERB
ejpam-6418	8	41	with	with	ADP
ejpam-6418	8	42	binary	binary	ADJ
ejpam-6418	8	43	operations	operation	NOUN
ejpam-6418	8	44	∨	∨	NOUN
ejpam-6418	8	45	and	and	CCONJ
ejpam-6418	8	46	∧	∧	PROPN
ejpam-6418	8	47	and	and	CCONJ
ejpam-6418	8	48	a	a	DET
ejpam-6418	8	49	designated	designate	VERB
ejpam-6418	8	50	greatest	great	ADJ
ejpam-6418	8	51	element	element	NOUN
ejpam-6418	8	52	1	1	NUM
ejpam-6418	8	53	,	,	PUNCT
ejpam-6418	8	54	and	and	CCONJ
ejpam-6418	8	55	they	they	PRON
ejpam-6418	8	56	satisfy	satisfy	VERB
ejpam-6418	8	57	a	a	DET
ejpam-6418	8	58	set	set	NOUN
ejpam-6418	8	59	of	of	ADP
ejpam-6418	8	60	axioms	axiom	NOUN
ejpam-6418	8	61	that	that	PRON
ejpam-6418	8	62	emulate	emulate	VERB
ejpam-6418	8	63	distributive	distributive	ADJ
ejpam-6418	8	64	behavior	behavior	NOUN
ejpam-6418	8	65	within	within	ADP
ejpam-6418	8	66	a	a	DET
ejpam-6418	8	67	more	more	ADV
ejpam-6418	8	68	generalized	generalized	ADJ
ejpam-6418	8	69	algebraic	algebraic	ADJ
ejpam-6418	8	70	setting	setting	NOUN
ejpam-6418	8	71	.	.	PUNCT
ejpam-6418	9	1	this	this	DET
ejpam-6418	9	2	work	work	NOUN
ejpam-6418	9	3	builds	build	VERB
ejpam-6418	9	4	upon	upon	SCONJ
ejpam-6418	9	5	the	the	DET
ejpam-6418	9	6	foundational	foundational	ADJ
ejpam-6418	9	7	framework	framework	NOUN
ejpam-6418	9	8	of	of	ADP
ejpam-6418	9	9	pdls	pdl	NOUN
ejpam-6418	9	10	to	to	PART
ejpam-6418	9	11	introduce	introduce	VERB
ejpam-6418	9	12	and	and	CCONJ
ejpam-6418	9	13	systematically	systematically	ADV
ejpam-6418	9	14	investigate	investigate	VERB
ejpam-6418	9	15	the	the	DET
ejpam-6418	9	16	concepts	concept	NOUN
ejpam-6418	9	17	of	of	ADP
ejpam-6418	9	18	compatible	compatible	ADJ
ejpam-6418	9	19	sets	set	NOUN
ejpam-6418	9	20	,	,	PUNCT
ejpam-6418	9	21	maximal	maximal	ADJ
ejpam-6418	9	22	sets	set	NOUN
ejpam-6418	9	23	,	,	PUNCT
ejpam-6418	9	24	and	and	CCONJ
ejpam-6418	9	25	amicable	amicable	ADJ
ejpam-6418	9	26	sets	set	NOUN
ejpam-6418	9	27	.	.	PUNCT
ejpam-6418	10	1	a	a	DET
ejpam-6418	10	2	∗corresponding	∗corresponde	VERB
ejpam-6418	10	3	author	author	NOUN
ejpam-6418	10	4	.	.	PUNCT
ejpam-6418	11	1	doi	doi	NOUN
ejpam-6418	11	2	:	:	PUNCT
ejpam-6418	11	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6418	https://doi.org/10.29020/nybg.ejpam.v18i4.6418	PROPN
ejpam-6418	11	4	email	email	NOUN
ejpam-6418	11	5	addresses	address	NOUN
ejpam-6418	11	6	:	:	PUNCT
ejpam-6418	11	7	ramesh.sirisetti@gmail.com	ramesh.sirisetti@gmail.com	X
ejpam-6418	11	8	(	(	PUNCT
ejpam-6418	11	9	r.	r.	PROPN
ejpam-6418	11	10	sirisetti	sirisetti	PROPN
ejpam-6418	11	11	)	)	PUNCT
ejpam-6418	11	12	,	,	PUNCT
ejpam-6418	11	13	jogarao.gunda@gmail.com	jogarao.gunda@gmail.com	PROPN
ejpam-6418	11	14	(	(	PUNCT
ejpam-6418	11	15	j.	j.	PROPN
ejpam-6418	11	16	gunda	gunda	PROPN
ejpam-6418	11	17	)	)	PUNCT
ejpam-6418	11	18	,	,	PUNCT
ejpam-6418	11	19	ravimaths83@gmail.com	ravimaths83@gmail.com	PROPN
ejpam-6418	11	20	(	(	PUNCT
ejpam-6418	11	21	r.	r.	PROPN
ejpam-6418	11	22	bandaru	bandaru	PROPN
ejpam-6418	11	23	)	)	PUNCT
ejpam-6418	11	24	,	,	PUNCT
ejpam-6418	11	25	thiti.ga@up.ac.th	thiti.ga@up.ac.th	PROPN
ejpam-6418	11	26	(	(	PUNCT
ejpam-6418	11	27	t.	t.	NOUN
ejpam-6418	11	28	gaketem	gaketem	PROPN
ejpam-6418	11	29	)	)	PUNCT
ejpam-6418	11	30	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6418	11	31	1	1	NUM
ejpam-6418	11	32	copyright	copyright	NOUN
ejpam-6418	11	33	:	:	PUNCT
ejpam-6418	12	1	©	©	PROPN
ejpam-6418	12	2	2025	2025	NUM
ejpam-6418	12	3	the	the	DET
ejpam-6418	12	4	author(s	author(s	NOUN
ejpam-6418	12	5	)	)	PUNCT
ejpam-6418	12	6	.	.	PUNCT
ejpam-6418	13	1	(	(	PUNCT
ejpam-6418	13	2	cc	cc	NOUN
ejpam-6418	13	3	by	by	ADP
ejpam-6418	13	4	-	-	PUNCT
ejpam-6418	13	5	nc	nc	PROPN
ejpam-6418	13	6	4.0	4.0	NUM
ejpam-6418	13	7	)	)	PUNCT
ejpam-6418	13	8	r.	r.	PROPN
ejpam-6418	13	9	sirisetti	sirisetti	PROPN
ejpam-6418	13	10	et	et	PROPN
ejpam-6418	13	11	al	al	PROPN
ejpam-6418	13	12	.	.	PUNCT
ejpam-6418	13	13	/	/	SYM
ejpam-6418	13	14	eur	eur	PROPN
ejpam-6418	13	15	.	.	PUNCT
ejpam-6418	14	1	j.	j.	PROPN
ejpam-6418	14	2	pure	pure	PROPN
ejpam-6418	14	3	appl	appl	PROPN
ejpam-6418	14	4	.	.	PROPN
ejpam-6418	14	5	math	math	PROPN
ejpam-6418	14	6	,	,	PUNCT
ejpam-6418	14	7	18	18	NUM
ejpam-6418	14	8	(	(	PUNCT
ejpam-6418	14	9	4	4	NUM
ejpam-6418	14	10	)	)	PUNCT
ejpam-6418	14	11	(	(	PUNCT
ejpam-6418	14	12	2025	2025	NUM
ejpam-6418	14	13	)	)	PUNCT
ejpam-6418	14	14	,	,	PUNCT
ejpam-6418	14	15	6418	6418	NUM
ejpam-6418	14	16	2	2	NUM
ejpam-6418	14	17	of	of	ADP
ejpam-6418	14	18	13	13	NUM
ejpam-6418	14	19	compatible	compatible	ADJ
ejpam-6418	14	20	set	set	NOUN
ejpam-6418	14	21	is	be	AUX
ejpam-6418	14	22	defined	define	VERB
ejpam-6418	14	23	as	as	ADP
ejpam-6418	14	24	a	a	DET
ejpam-6418	14	25	subset	subset	NOUN
ejpam-6418	14	26	whose	whose	DET
ejpam-6418	14	27	elements	element	NOUN
ejpam-6418	14	28	are	be	AUX
ejpam-6418	14	29	mutually	mutually	ADV
ejpam-6418	14	30	commutative	commutative	ADJ
ejpam-6418	14	31	under	under	ADP
ejpam-6418	14	32	the	the	DET
ejpam-6418	14	33	operations	operation	NOUN
ejpam-6418	14	34	∨	∨	NOUN
ejpam-6418	14	35	and	and	CCONJ
ejpam-6418	14	36	∧	∧	PROPN
ejpam-6418	14	37	,	,	PUNCT
ejpam-6418	14	38	and	and	CCONJ
ejpam-6418	14	39	a	a	DET
ejpam-6418	14	40	maximal	maximal	ADJ
ejpam-6418	14	41	set	set	NOUN
ejpam-6418	14	42	is	be	AUX
ejpam-6418	14	43	characterized	characterize	VERB
ejpam-6418	14	44	as	as	ADP
ejpam-6418	14	45	a	a	DET
ejpam-6418	14	46	compatible	compatible	ADJ
ejpam-6418	14	47	set	set	NOUN
ejpam-6418	14	48	that	that	PRON
ejpam-6418	14	49	is	be	AUX
ejpam-6418	14	50	maximal	maximal	ADJ
ejpam-6418	14	51	with	with	ADP
ejpam-6418	14	52	respect	respect	NOUN
ejpam-6418	14	53	to	to	ADP
ejpam-6418	14	54	inclusion	inclusion	NOUN
ejpam-6418	14	55	.	.	PUNCT
ejpam-6418	15	1	the	the	DET
ejpam-6418	15	2	novel	novel	ADJ
ejpam-6418	15	3	notion	notion	NOUN
ejpam-6418	15	4	of	of	ADP
ejpam-6418	15	5	amicability	amicability	NOUN
ejpam-6418	15	6	is	be	AUX
ejpam-6418	15	7	introduced	introduce	VERB
ejpam-6418	15	8	to	to	PART
ejpam-6418	15	9	describe	describe	VERB
ejpam-6418	15	10	maximal	maximal	ADJ
ejpam-6418	15	11	sets	set	NOUN
ejpam-6418	15	12	that	that	PRON
ejpam-6418	15	13	exhibit	exhibit	VERB
ejpam-6418	15	14	a	a	DET
ejpam-6418	15	15	unifying	unifying	ADJ
ejpam-6418	15	16	interaction	interaction	NOUN
ejpam-6418	15	17	with	with	ADP
ejpam-6418	15	18	the	the	DET
ejpam-6418	15	19	entire	entire	ADJ
ejpam-6418	15	20	lattice	lattice	NOUN
ejpam-6418	15	21	,	,	PUNCT
ejpam-6418	15	22	thereby	thereby	ADV
ejpam-6418	15	23	revealing	reveal	VERB
ejpam-6418	15	24	new	new	ADJ
ejpam-6418	15	25	algebraic	algebraic	ADJ
ejpam-6418	15	26	insights	insight	NOUN
ejpam-6418	15	27	.	.	PUNCT
ejpam-6418	16	1	through	through	ADP
ejpam-6418	16	2	a	a	DET
ejpam-6418	16	3	rigorous	rigorous	ADJ
ejpam-6418	16	4	methodology	methodology	NOUN
ejpam-6418	16	5	comprising	comprise	VERB
ejpam-6418	16	6	formal	formal	ADJ
ejpam-6418	16	7	definitions	definition	NOUN
ejpam-6418	16	8	,	,	PUNCT
ejpam-6418	16	9	illustrative	illustrative	ADJ
ejpam-6418	16	10	examples	example	NOUN
ejpam-6418	16	11	,	,	PUNCT
ejpam-6418	16	12	counterexamples	counterexample	NOUN
ejpam-6418	16	13	,	,	PUNCT
ejpam-6418	16	14	and	and	CCONJ
ejpam-6418	16	15	theorems	theorem	NOUN
ejpam-6418	16	16	,	,	PUNCT
ejpam-6418	16	17	this	this	DET
ejpam-6418	16	18	paper	paper	NOUN
ejpam-6418	16	19	develops	develop	VERB
ejpam-6418	16	20	a	a	DET
ejpam-6418	16	21	comprehensive	comprehensive	ADJ
ejpam-6418	16	22	theory	theory	NOUN
ejpam-6418	16	23	surrounding	surround	VERB
ejpam-6418	16	24	these	these	DET
ejpam-6418	16	25	structures	structure	NOUN
ejpam-6418	16	26	.	.	PUNCT
ejpam-6418	17	1	in	in	ADP
ejpam-6418	17	2	particular	particular	ADJ
ejpam-6418	17	3	,	,	PUNCT
ejpam-6418	17	4	it	it	PRON
ejpam-6418	17	5	establishes	establish	VERB
ejpam-6418	17	6	that	that	SCONJ
ejpam-6418	17	7	the	the	DET
ejpam-6418	17	8	center	center	NOUN
ejpam-6418	17	9	of	of	ADP
ejpam-6418	17	10	a	a	DET
ejpam-6418	17	11	pdl	pdl	NOUN
ejpam-6418	17	12	defined	define	VERB
ejpam-6418	17	13	as	as	ADP
ejpam-6418	17	14	the	the	DET
ejpam-6418	17	15	set	set	NOUN
ejpam-6418	17	16	of	of	ADP
ejpam-6418	17	17	elements	element	NOUN
ejpam-6418	17	18	compatible	compatible	ADJ
ejpam-6418	17	19	with	with	ADP
ejpam-6418	17	20	all	all	DET
ejpam-6418	17	21	elements	element	NOUN
ejpam-6418	17	22	of	of	ADP
ejpam-6418	17	23	the	the	DET
ejpam-6418	17	24	lattice	lattice	NOUN
ejpam-6418	17	25	is	be	AUX
ejpam-6418	17	26	precisely	precisely	ADV
ejpam-6418	17	27	the	the	DET
ejpam-6418	17	28	intersection	intersection	NOUN
ejpam-6418	17	29	of	of	ADP
ejpam-6418	17	30	all	all	DET
ejpam-6418	17	31	maximal	maximal	ADJ
ejpam-6418	17	32	sets	set	NOUN
ejpam-6418	17	33	,	,	PUNCT
ejpam-6418	17	34	and	and	CCONJ
ejpam-6418	17	35	furthermore	furthermore	ADV
ejpam-6418	17	36	,	,	PUNCT
ejpam-6418	17	37	that	that	SCONJ
ejpam-6418	17	38	this	this	DET
ejpam-6418	17	39	center	center	NOUN
ejpam-6418	17	40	forms	form	VERB
ejpam-6418	17	41	a	a	DET
ejpam-6418	17	42	filter	filter	NOUN
ejpam-6418	17	43	.	.	PUNCT
ejpam-6418	18	1	the	the	DET
ejpam-6418	18	2	study	study	NOUN
ejpam-6418	18	3	of	of	ADP
ejpam-6418	18	4	amicable	amicable	ADJ
ejpam-6418	18	5	sets	set	NOUN
ejpam-6418	18	6	serves	serve	VERB
ejpam-6418	18	7	as	as	ADP
ejpam-6418	18	8	a	a	DET
ejpam-6418	18	9	key	key	ADJ
ejpam-6418	18	10	tool	tool	NOUN
ejpam-6418	18	11	in	in	ADP
ejpam-6418	18	12	the	the	DET
ejpam-6418	18	13	structural	structural	ADJ
ejpam-6418	18	14	analysis	analysis	NOUN
ejpam-6418	18	15	of	of	ADP
ejpam-6418	18	16	pdls	pdl	NOUN
ejpam-6418	18	17	,	,	PUNCT
ejpam-6418	18	18	leading	lead	VERB
ejpam-6418	18	19	to	to	ADP
ejpam-6418	18	20	a	a	DET
ejpam-6418	18	21	new	new	ADJ
ejpam-6418	18	22	characterization	characterization	NOUN
ejpam-6418	18	23	of	of	ADP
ejpam-6418	18	24	relatively	relatively	ADV
ejpam-6418	18	25	complemented	complemented	ADJ
ejpam-6418	18	26	pdls	pdl	NOUN
ejpam-6418	18	27	a	a	DET
ejpam-6418	18	28	property	property	NOUN
ejpam-6418	18	29	of	of	ADP
ejpam-6418	18	30	considerable	considerable	ADJ
ejpam-6418	18	31	interest	interest	NOUN
ejpam-6418	18	32	due	due	ADP
ejpam-6418	18	33	to	to	ADP
ejpam-6418	18	34	its	its	PRON
ejpam-6418	18	35	connections	connection	NOUN
ejpam-6418	18	36	with	with	ADP
ejpam-6418	18	37	completeness	completeness	NOUN
ejpam-6418	18	38	and	and	CCONJ
ejpam-6418	18	39	decomposability	decomposability	NOUN
ejpam-6418	18	40	in	in	ADP
ejpam-6418	18	41	lattice	lattice	NOUN
ejpam-6418	18	42	theory	theory	NOUN
ejpam-6418	18	43	[	[	X
ejpam-6418	18	44	2	2	NUM
ejpam-6418	18	45	,	,	PUNCT
ejpam-6418	18	46	3	3	NUM
ejpam-6418	18	47	]	]	PUNCT
ejpam-6418	18	48	.	.	PUNCT
ejpam-6418	19	1	the	the	DET
ejpam-6418	19	2	contributions	contribution	NOUN
ejpam-6418	19	3	of	of	ADP
ejpam-6418	19	4	this	this	DET
ejpam-6418	19	5	work	work	NOUN
ejpam-6418	19	6	enhance	enhance	VERB
ejpam-6418	19	7	the	the	DET
ejpam-6418	19	8	algebraic	algebraic	ADJ
ejpam-6418	19	9	understanding	understanding	NOUN
ejpam-6418	19	10	of	of	ADP
ejpam-6418	19	11	paradistributive	paradistributive	ADJ
ejpam-6418	19	12	latticoids	latticoid	NOUN
ejpam-6418	19	13	by	by	ADP
ejpam-6418	19	14	introducing	introduce	VERB
ejpam-6418	19	15	and	and	CCONJ
ejpam-6418	19	16	analyzing	analyze	VERB
ejpam-6418	19	17	new	new	ADJ
ejpam-6418	19	18	invariants	invariant	NOUN
ejpam-6418	19	19	and	and	CCONJ
ejpam-6418	19	20	internal	internal	ADJ
ejpam-6418	19	21	structures	structure	NOUN
ejpam-6418	19	22	.	.	PUNCT
ejpam-6418	20	1	these	these	DET
ejpam-6418	20	2	results	result	NOUN
ejpam-6418	20	3	extend	extend	VERB
ejpam-6418	20	4	earlier	early	ADJ
ejpam-6418	20	5	research	research	NOUN
ejpam-6418	20	6	on	on	ADP
ejpam-6418	20	7	normal	normal	ADJ
ejpam-6418	20	8	pdls	pdl	NOUN
ejpam-6418	20	9	[	[	X
ejpam-6418	20	10	4	4	NUM
ejpam-6418	20	11	]	]	PUNCT
ejpam-6418	20	12	and	and	CCONJ
ejpam-6418	20	13	parapseudo	parapseudo	NOUN
ejpam-6418	20	14	-	-	NOUN
ejpam-6418	20	15	complementation	complementation	NOUN
ejpam-6418	20	16	[	[	X
ejpam-6418	20	17	5	5	NUM
ejpam-6418	20	18	]	]	PUNCT
ejpam-6418	20	19	,	,	PUNCT
ejpam-6418	20	20	and	and	CCONJ
ejpam-6418	20	21	are	be	AUX
ejpam-6418	20	22	grounded	ground	VERB
ejpam-6418	20	23	in	in	ADP
ejpam-6418	20	24	the	the	DET
ejpam-6418	20	25	classical	classical	ADJ
ejpam-6418	20	26	algebraic	algebraic	ADJ
ejpam-6418	20	27	foundations	foundation	NOUN
ejpam-6418	20	28	laid	lay	VERB
ejpam-6418	20	29	by	by	ADP
ejpam-6418	20	30	birkhoff	birkhoff	NOUN
ejpam-6418	21	1	[	[	X
ejpam-6418	21	2	2	2	NUM
ejpam-6418	21	3	]	]	PUNCT
ejpam-6418	21	4	and	and	CCONJ
ejpam-6418	21	5	boole	boole	PROPN
ejpam-6418	22	1	[	[	X
ejpam-6418	22	2	6	6	NUM
ejpam-6418	22	3	]	]	PUNCT
ejpam-6418	22	4	.	.	PUNCT
ejpam-6418	23	1	as	as	ADP
ejpam-6418	23	2	such	such	ADJ
ejpam-6418	23	3	,	,	PUNCT
ejpam-6418	23	4	this	this	DET
ejpam-6418	23	5	paper	paper	NOUN
ejpam-6418	23	6	provides	provide	VERB
ejpam-6418	23	7	a	a	DET
ejpam-6418	23	8	substantive	substantive	ADJ
ejpam-6418	23	9	addition	addition	NOUN
ejpam-6418	23	10	to	to	ADP
ejpam-6418	23	11	the	the	DET
ejpam-6418	23	12	theoretical	theoretical	ADJ
ejpam-6418	23	13	landscape	landscape	NOUN
ejpam-6418	23	14	of	of	ADP
ejpam-6418	23	15	generalized	generalized	ADJ
ejpam-6418	23	16	lattice	lattice	NOUN
ejpam-6418	23	17	systems	system	NOUN
ejpam-6418	23	18	.	.	PUNCT
ejpam-6418	24	1	2	2	X
ejpam-6418	24	2	.	.	X
ejpam-6418	24	3	preliminaries	preliminary	NOUN
ejpam-6418	24	4	in	in	ADP
ejpam-6418	24	5	this	this	DET
ejpam-6418	24	6	section	section	NOUN
ejpam-6418	24	7	,	,	PUNCT
ejpam-6418	24	8	we	we	PRON
ejpam-6418	24	9	present	present	VERB
ejpam-6418	24	10	necessary	necessary	ADJ
ejpam-6418	24	11	definitions	definition	NOUN
ejpam-6418	24	12	and	and	CCONJ
ejpam-6418	24	13	properties	property	NOUN
ejpam-6418	24	14	of	of	ADP
ejpam-6418	24	15	paradistributive	paradistributive	ADJ
ejpam-6418	24	16	latticoids	latticoid	NOUN
ejpam-6418	24	17	which	which	PRON
ejpam-6418	24	18	are	be	AUX
ejpam-6418	24	19	taken	take	VERB
ejpam-6418	24	20	from	from	ADP
ejpam-6418	24	21	[	[	X
ejpam-6418	24	22	1	1	NUM
ejpam-6418	24	23	]	]	PUNCT
ejpam-6418	24	24	for	for	ADP
ejpam-6418	24	25	quick	quick	ADJ
ejpam-6418	24	26	reference	reference	NOUN
ejpam-6418	24	27	and	and	CCONJ
ejpam-6418	24	28	to	to	PART
ejpam-6418	24	29	develop	develop	VERB
ejpam-6418	24	30	the	the	DET
ejpam-6418	24	31	theory	theory	NOUN
ejpam-6418	24	32	.	.	PUNCT
ejpam-6418	25	1	definition	definition	NOUN
ejpam-6418	25	2	2.1	2.1	NUM
ejpam-6418	25	3	.	.	PUNCT
ejpam-6418	26	1	[	[	X
ejpam-6418	26	2	1	1	X
ejpam-6418	26	3	]	]	PUNCT
ejpam-6418	26	4	an	an	DET
ejpam-6418	26	5	algebra	algebra	NOUN
ejpam-6418	26	6	(	(	PUNCT
ejpam-6418	26	7	v,∨,∧	v,∨,∧	NOUN
ejpam-6418	26	8	,	,	PUNCT
ejpam-6418	26	9	1	1	NUM
ejpam-6418	26	10	)	)	PUNCT
ejpam-6418	26	11	of	of	ADP
ejpam-6418	26	12	type	type	NOUN
ejpam-6418	26	13	(	(	PUNCT
ejpam-6418	26	14	2	2	NUM
ejpam-6418	26	15	,	,	PUNCT
ejpam-6418	26	16	2	2	NUM
ejpam-6418	26	17	,	,	PUNCT
ejpam-6418	26	18	1	1	NUM
ejpam-6418	26	19	)	)	PUNCT
ejpam-6418	26	20	is	be	AUX
ejpam-6418	26	21	called	call	VERB
ejpam-6418	26	22	a	a	DET
ejpam-6418	26	23	paradistributive	paradistributive	ADJ
ejpam-6418	26	24	latticoid	latticoid	NOUN
ejpam-6418	26	25	(	(	PUNCT
ejpam-6418	26	26	abbreviated	abbreviate	VERB
ejpam-6418	26	27	as	as	ADP
ejpam-6418	26	28	pdl	pdl	NOUN
ejpam-6418	26	29	)	)	PUNCT
ejpam-6418	26	30	,	,	PUNCT
ejpam-6418	26	31	if	if	SCONJ
ejpam-6418	26	32	it	it	PRON
ejpam-6418	26	33	assures	assure	VERB
ejpam-6418	26	34	the	the	DET
ejpam-6418	26	35	following	follow	VERB
ejpam-6418	26	36	axioms	axiom	NOUN
ejpam-6418	26	37	:	:	PUNCT
ejpam-6418	26	38	(	(	PUNCT
ejpam-6418	26	39	i	i	NOUN
ejpam-6418	26	40	)	)	PUNCT
ejpam-6418	26	41	a	a	DET
ejpam-6418	26	42	∨	∨	NOUN
ejpam-6418	26	43	(	(	PUNCT
ejpam-6418	26	44	b	b	PROPN
ejpam-6418	26	45	∧	∧	PROPN
ejpam-6418	26	46	c	c	NOUN
ejpam-6418	26	47	)	)	PUNCT
ejpam-6418	26	48	=	=	NOUN
ejpam-6418	26	49	(	(	PUNCT
ejpam-6418	26	50	a	a	DET
ejpam-6418	26	51	∨	∨	NUM
ejpam-6418	26	52	b	b	NOUN
ejpam-6418	26	53	)	)	PUNCT
ejpam-6418	26	54	∧	∧	NOUN
ejpam-6418	26	55	(	(	PUNCT
ejpam-6418	26	56	a	a	DET
ejpam-6418	26	57	∨	∨	NUM
ejpam-6418	26	58	c	c	NOUN
ejpam-6418	26	59	)	)	PUNCT
ejpam-6418	26	60	(	(	PUNCT
ejpam-6418	26	61	ii	ii	NOUN
ejpam-6418	26	62	)	)	PUNCT
ejpam-6418	26	63	(	(	PUNCT
ejpam-6418	26	64	a	a	DET
ejpam-6418	26	65	∧	∧	PROPN
ejpam-6418	26	66	b	b	PROPN
ejpam-6418	26	67	)	)	PUNCT
ejpam-6418	26	68	∨	∨	NUM
ejpam-6418	26	69	c	c	NOUN
ejpam-6418	26	70	=	=	SYM
ejpam-6418	26	71	(	(	PUNCT
ejpam-6418	26	72	a	a	DET
ejpam-6418	26	73	∨	∨	NUM
ejpam-6418	26	74	c	c	NOUN
ejpam-6418	26	75	)	)	PUNCT
ejpam-6418	26	76	∧	∧	NOUN
ejpam-6418	26	77	(	(	PUNCT
ejpam-6418	26	78	b	b	PROPN
ejpam-6418	26	79	∨	∨	NUM
ejpam-6418	26	80	c	c	NOUN
ejpam-6418	26	81	)	)	PUNCT
ejpam-6418	26	82	(	(	PUNCT
ejpam-6418	26	83	iii	iii	NOUN
ejpam-6418	26	84	)	)	PUNCT
ejpam-6418	26	85	(	(	PUNCT
ejpam-6418	26	86	a	a	DET
ejpam-6418	26	87	∨	∨	NUM
ejpam-6418	26	88	b	b	NOUN
ejpam-6418	26	89	)	)	PUNCT
ejpam-6418	26	90	∧	∧	PROPN
ejpam-6418	26	91	b	b	NOUN
ejpam-6418	26	92	=	=	SYM
ejpam-6418	26	93	b	b	PROPN
ejpam-6418	26	94	(	(	PUNCT
ejpam-6418	26	95	iv	iv	NUM
ejpam-6418	26	96	)	)	PUNCT
ejpam-6418	26	97	(	(	PUNCT
ejpam-6418	26	98	a	a	DET
ejpam-6418	26	99	∨	∨	NUM
ejpam-6418	26	100	b	b	NOUN
ejpam-6418	26	101	)	)	PUNCT
ejpam-6418	26	102	∧	∧	NOUN
ejpam-6418	26	103	a	a	PRON
ejpam-6418	26	104	=	=	X
ejpam-6418	26	105	a	a	DET
ejpam-6418	26	106	(	(	PUNCT
ejpam-6418	26	107	v	v	NOUN
ejpam-6418	26	108	)	)	PUNCT
ejpam-6418	26	109	a	a	DET
ejpam-6418	26	110	∨	∨	NOUN
ejpam-6418	26	111	(	(	PUNCT
ejpam-6418	26	112	a	a	DET
ejpam-6418	26	113	∧	∧	PROPN
ejpam-6418	26	114	b	b	NOUN
ejpam-6418	26	115	)	)	PUNCT
ejpam-6418	26	116	=	=	SYM
ejpam-6418	26	117	a	a	DET
ejpam-6418	26	118	(	(	PUNCT
ejpam-6418	26	119	vi	vi	NOUN
ejpam-6418	26	120	)	)	PUNCT
ejpam-6418	26	121	a	a	DET
ejpam-6418	26	122	∨	∨	NUM
ejpam-6418	26	123	1	1	NUM
ejpam-6418	26	124	=	=	SYM
ejpam-6418	26	125	1	1	NUM
ejpam-6418	26	126	,	,	PUNCT
ejpam-6418	26	127	for	for	ADP
ejpam-6418	26	128	all	all	DET
ejpam-6418	26	129	a	a	DET
ejpam-6418	26	130	,	,	PUNCT
ejpam-6418	26	131	b	b	NOUN
ejpam-6418	26	132	,	,	PUNCT
ejpam-6418	26	133	c	c	PROPN
ejpam-6418	26	134	∈	∈	PROPN
ejpam-6418	26	135	v.	v.	ADP
ejpam-6418	26	136	given	give	VERB
ejpam-6418	26	137	a	a	DET
ejpam-6418	26	138	,	,	PUNCT
ejpam-6418	26	139	b	b	NOUN
ejpam-6418	26	140	in	in	ADP
ejpam-6418	26	141	a	a	DET
ejpam-6418	26	142	paradistributive	paradistributive	ADJ
ejpam-6418	26	143	latticoid	latticoid	NOUN
ejpam-6418	26	144	v	v	NOUN
ejpam-6418	26	145	,	,	PUNCT
ejpam-6418	26	146	we	we	PRON
ejpam-6418	26	147	say	say	VERB
ejpam-6418	26	148	that	that	SCONJ
ejpam-6418	26	149	a	a	PRON
ejpam-6418	26	150	is	be	AUX
ejpam-6418	26	151	less	less	ADJ
ejpam-6418	26	152	than	than	ADP
ejpam-6418	26	153	or	or	CCONJ
ejpam-6418	26	154	equal	equal	ADJ
ejpam-6418	26	155	to	to	ADP
ejpam-6418	26	156	b	b	NOUN
ejpam-6418	26	157	and	and	CCONJ
ejpam-6418	26	158	write	write	VERB
ejpam-6418	26	159	a	a	DET
ejpam-6418	26	160	≤	≤	NUM
ejpam-6418	26	161	b	b	NOUN
ejpam-6418	26	162	,	,	PUNCT
ejpam-6418	26	163	if	if	SCONJ
ejpam-6418	26	164	a	a	DET
ejpam-6418	26	165	∧	∧	PROPN
ejpam-6418	26	166	b	b	NOUN
ejpam-6418	26	167	=	=	PROPN
ejpam-6418	26	168	a	a	PRON
ejpam-6418	26	169	or	or	CCONJ
ejpam-6418	26	170	equivalently	equivalently	ADV
ejpam-6418	26	171	a	a	DET
ejpam-6418	26	172	∨	∨	NUM
ejpam-6418	26	173	b	b	X
ejpam-6418	26	174	=	=	PUNCT
ejpam-6418	26	175	b.	b.	PROPN
ejpam-6418	27	1	it	it	PRON
ejpam-6418	27	2	is	be	AUX
ejpam-6418	27	3	observed	observe	VERB
ejpam-6418	27	4	that	that	SCONJ
ejpam-6418	27	5	≤	≤	NUM
ejpam-6418	27	6	is	be	AUX
ejpam-6418	27	7	a	a	DET
ejpam-6418	27	8	partial	partial	ADJ
ejpam-6418	27	9	order	order	NOUN
ejpam-6418	27	10	on	on	ADP
ejpam-6418	27	11	v	v	NOUN
ejpam-6418	27	12	and	and	CCONJ
ejpam-6418	27	13	the	the	DET
ejpam-6418	27	14	element	element	NOUN
ejpam-6418	27	15	1	1	NUM
ejpam-6418	27	16	is	be	AUX
ejpam-6418	27	17	the	the	DET
ejpam-6418	27	18	greatest	great	ADJ
ejpam-6418	27	19	element	element	NOUN
ejpam-6418	27	20	.	.	PUNCT
ejpam-6418	28	1	throughout	throughout	ADP
ejpam-6418	28	2	this	this	DET
ejpam-6418	28	3	paper	paper	NOUN
ejpam-6418	28	4	,	,	PUNCT
ejpam-6418	28	5	we	we	PRON
ejpam-6418	28	6	refer	refer	VERB
ejpam-6418	28	7	v	v	NOUN
ejpam-6418	28	8	as	as	ADP
ejpam-6418	28	9	a	a	DET
ejpam-6418	28	10	paradistributive	paradistributive	ADJ
ejpam-6418	28	11	latticoid	latticoid	NOUN
ejpam-6418	28	12	with	with	ADP
ejpam-6418	28	13	the	the	DET
ejpam-6418	28	14	greatest	great	ADJ
ejpam-6418	28	15	element	element	NOUN
ejpam-6418	28	16	1	1	NUM
ejpam-6418	28	17	.	.	PUNCT
ejpam-6418	29	1	r.	r.	PROPN
ejpam-6418	29	2	sirisetti	sirisetti	PROPN
ejpam-6418	29	3	et	et	PROPN
ejpam-6418	29	4	al	al	PROPN
ejpam-6418	29	5	.	.	PUNCT
ejpam-6418	29	6	/	/	SYM
ejpam-6418	29	7	eur	eur	PROPN
ejpam-6418	29	8	.	.	PUNCT
ejpam-6418	30	1	j.	j.	PROPN
ejpam-6418	30	2	pure	pure	PROPN
ejpam-6418	30	3	appl	appl	PROPN
ejpam-6418	30	4	.	.	PROPN
ejpam-6418	30	5	math	math	PROPN
ejpam-6418	30	6	,	,	PUNCT
ejpam-6418	30	7	18	18	NUM
ejpam-6418	30	8	(	(	PUNCT
ejpam-6418	30	9	4	4	NUM
ejpam-6418	30	10	)	)	PUNCT
ejpam-6418	30	11	(	(	PUNCT
ejpam-6418	30	12	2025	2025	NUM
ejpam-6418	30	13	)	)	PUNCT
ejpam-6418	30	14	,	,	PUNCT
ejpam-6418	30	15	6418	6418	NUM
ejpam-6418	30	16	3	3	NUM
ejpam-6418	30	17	of	of	ADP
ejpam-6418	30	18	13	13	NUM
ejpam-6418	30	19	example	example	NOUN
ejpam-6418	30	20	2.2	2.2	NUM
ejpam-6418	30	21	.	.	PUNCT
ejpam-6418	31	1	[	[	X
ejpam-6418	31	2	1	1	X
ejpam-6418	31	3	]	]	PUNCT
ejpam-6418	31	4	let	let	VERB
ejpam-6418	31	5	v	v	PART
ejpam-6418	31	6	be	be	AUX
ejpam-6418	31	7	a	a	DET
ejpam-6418	31	8	non	non	ADJ
ejpam-6418	31	9	-	-	ADJ
ejpam-6418	31	10	empty	empty	ADJ
ejpam-6418	31	11	set	set	NOUN
ejpam-6418	31	12	.	.	PUNCT
ejpam-6418	32	1	fix	fix	VERB
ejpam-6418	32	2	some	some	DET
ejpam-6418	32	3	element	element	NOUN
ejpam-6418	32	4	b0	b0	NOUN
ejpam-6418	32	5	∈	∈	PROPN
ejpam-6418	32	6	v.	v.	CCONJ
ejpam-6418	32	7	for	for	ADP
ejpam-6418	32	8	any	any	DET
ejpam-6418	32	9	a	a	PRON
ejpam-6418	32	10	,	,	PUNCT
ejpam-6418	32	11	b	b	PROPN
ejpam-6418	32	12	∈	∈	PROPN
ejpam-6418	32	13	v	v	NOUN
ejpam-6418	32	14	,	,	PUNCT
ejpam-6418	32	15	define	define	VERB
ejpam-6418	32	16	∨	∨	NOUN
ejpam-6418	32	17	and	and	CCONJ
ejpam-6418	32	18	∧	∧	NOUN
ejpam-6418	32	19	on	on	ADP
ejpam-6418	32	20	v	v	NUM
ejpam-6418	32	21	by	by	ADP
ejpam-6418	32	22	a	a	DET
ejpam-6418	32	23	∨	∨	NOUN
ejpam-6418	32	24	b	b	NOUN
ejpam-6418	32	25	=	=	PUNCT
ejpam-6418	32	26	{	{	PUNCT
ejpam-6418	32	27	a	a	X
ejpam-6418	32	28	,	,	PUNCT
ejpam-6418	32	29	if	if	SCONJ
ejpam-6418	32	30	b	b	PROPN
ejpam-6418	32	31	̸=	̸=	PROPN
ejpam-6418	32	32	b0	b0	NOUN
ejpam-6418	32	33	b0	b0	NOUN
ejpam-6418	32	34	,	,	PUNCT
ejpam-6418	32	35	if	if	SCONJ
ejpam-6418	32	36	b	b	PROPN
ejpam-6418	32	37	=	=	PUNCT
ejpam-6418	32	38	b0	b0	NOUN
ejpam-6418	32	39	and	and	CCONJ
ejpam-6418	32	40	a	a	DET
ejpam-6418	32	41	∧	∧	PROPN
ejpam-6418	32	42	b	b	NOUN
ejpam-6418	32	43	=	=	PUNCT
ejpam-6418	32	44	{	{	PUNCT
ejpam-6418	32	45	b	b	NOUN
ejpam-6418	32	46	,	,	PUNCT
ejpam-6418	32	47	if	if	SCONJ
ejpam-6418	32	48	b	b	PROPN
ejpam-6418	32	49	̸=	̸=	PROPN
ejpam-6418	32	50	b0	b0	ADP
ejpam-6418	32	51	a	a	PRON
ejpam-6418	32	52	,	,	PUNCT
ejpam-6418	32	53	if	if	SCONJ
ejpam-6418	32	54	b	b	PROPN
ejpam-6418	32	55	=	=	SYM
ejpam-6418	32	56	b0	b0	NOUN
ejpam-6418	32	57	.	.	PUNCT
ejpam-6418	33	1	then	then	ADV
ejpam-6418	33	2	(	(	PUNCT
ejpam-6418	33	3	v,∨,∧	v,∨,∧	NOUN
ejpam-6418	33	4	,	,	PUNCT
ejpam-6418	33	5	b0	b0	NOUN
ejpam-6418	33	6	)	)	PUNCT
ejpam-6418	33	7	is	be	AUX
ejpam-6418	33	8	called	call	VERB
ejpam-6418	33	9	a	a	DET
ejpam-6418	33	10	disconnected	disconnected	ADJ
ejpam-6418	33	11	pdl	pdl	NOUN
ejpam-6418	33	12	,	,	PUNCT
ejpam-6418	33	13	and	and	CCONJ
ejpam-6418	33	14	b0	b0	NOUN
ejpam-6418	33	15	is	be	AUX
ejpam-6418	33	16	the	the	DET
ejpam-6418	33	17	greatest	great	ADJ
ejpam-6418	33	18	element	element	NOUN
ejpam-6418	33	19	.	.	PUNCT
ejpam-6418	34	1	lemma	lemma	PROPN
ejpam-6418	34	2	2.3	2.3	NUM
ejpam-6418	34	3	.	.	PUNCT
ejpam-6418	35	1	[	[	X
ejpam-6418	35	2	1	1	X
ejpam-6418	35	3	]	]	PUNCT
ejpam-6418	35	4	for	for	ADP
ejpam-6418	35	5	any	any	DET
ejpam-6418	35	6	a	a	PRON
ejpam-6418	35	7	,	,	PUNCT
ejpam-6418	35	8	b	b	PROPN
ejpam-6418	35	9	∈	∈	PROPN
ejpam-6418	35	10	v	v	NOUN
ejpam-6418	35	11	,	,	PUNCT
ejpam-6418	35	12	(	(	PUNCT
ejpam-6418	35	13	i	i	NOUN
ejpam-6418	35	14	)	)	PUNCT
ejpam-6418	35	15	a	a	DET
ejpam-6418	35	16	∧	∧	PROPN
ejpam-6418	35	17	a	a	DET
ejpam-6418	35	18	=	=	X
ejpam-6418	35	19	a	a	DET
ejpam-6418	35	20	(	(	PUNCT
ejpam-6418	35	21	ii	ii	NOUN
ejpam-6418	35	22	)	)	PUNCT
ejpam-6418	35	23	a	a	DET
ejpam-6418	35	24	∨	∨	NOUN
ejpam-6418	35	25	a	a	DET
ejpam-6418	35	26	=	=	NOUN
ejpam-6418	35	27	a	a	DET
ejpam-6418	35	28	(	(	PUNCT
ejpam-6418	35	29	iii	iii	NOUN
ejpam-6418	35	30	)	)	PUNCT
ejpam-6418	35	31	(	(	PUNCT
ejpam-6418	35	32	a	a	DET
ejpam-6418	35	33	∧	∧	PROPN
ejpam-6418	35	34	b	b	PROPN
ejpam-6418	35	35	)	)	PUNCT
ejpam-6418	35	36	∨	∨	NUM
ejpam-6418	35	37	b	b	X
ejpam-6418	35	38	=	=	SYM
ejpam-6418	35	39	b	b	PROPN
ejpam-6418	35	40	(	(	PUNCT
ejpam-6418	35	41	iv	iv	X
ejpam-6418	35	42	)	)	PUNCT
ejpam-6418	35	43	a	a	DET
ejpam-6418	35	44	∨	∨	NOUN
ejpam-6418	35	45	(	(	PUNCT
ejpam-6418	35	46	b	b	PROPN
ejpam-6418	35	47	∧	∧	PROPN
ejpam-6418	35	48	a	a	NOUN
ejpam-6418	35	49	)	)	PUNCT
ejpam-6418	35	50	=	=	SYM
ejpam-6418	35	51	a	a	DET
ejpam-6418	35	52	(	(	PUNCT
ejpam-6418	35	53	v	v	NOUN
ejpam-6418	35	54	)	)	PUNCT
ejpam-6418	35	55	a	a	DET
ejpam-6418	35	56	∧	∧	PROPN
ejpam-6418	35	57	(	(	PUNCT
ejpam-6418	35	58	a	a	DET
ejpam-6418	35	59	∨	∨	NUM
ejpam-6418	35	60	b	b	NOUN
ejpam-6418	35	61	)	)	PUNCT
ejpam-6418	35	62	=	=	PUNCT
ejpam-6418	35	63	a.	a.	NOUN
ejpam-6418	35	64	lemma	lemma	PROPN
ejpam-6418	35	65	2.4	2.4	NUM
ejpam-6418	35	66	.	.	PUNCT
ejpam-6418	36	1	[	[	X
ejpam-6418	36	2	1	1	X
ejpam-6418	36	3	]	]	PUNCT
ejpam-6418	36	4	for	for	ADP
ejpam-6418	36	5	any	any	DET
ejpam-6418	36	6	a	a	DET
ejpam-6418	36	7	,	,	PUNCT
ejpam-6418	36	8	b	b	NOUN
ejpam-6418	36	9	,	,	PUNCT
ejpam-6418	36	10	c	c	NOUN
ejpam-6418	36	11	,	,	PUNCT
ejpam-6418	36	12	d	d	PROPN
ejpam-6418	36	13	∈	∈	PROPN
ejpam-6418	36	14	v	v	NOUN
ejpam-6418	36	15	,	,	PUNCT
ejpam-6418	36	16	(	(	PUNCT
ejpam-6418	36	17	i	i	NOUN
ejpam-6418	36	18	)	)	PUNCT
ejpam-6418	36	19	a	a	DET
ejpam-6418	36	20	∧	∧	PROPN
ejpam-6418	36	21	1	1	NUM
ejpam-6418	36	22	=	=	SYM
ejpam-6418	36	23	a	a	DET
ejpam-6418	36	24	(	(	PUNCT
ejpam-6418	36	25	ii	ii	NOUN
ejpam-6418	36	26	)	)	PUNCT
ejpam-6418	36	27	1	1	NUM
ejpam-6418	36	28	∧	∧	PROPN
ejpam-6418	36	29	a	a	DET
ejpam-6418	36	30	=	=	PUNCT
ejpam-6418	36	31	a	a	DET
ejpam-6418	36	32	(	(	PUNCT
ejpam-6418	36	33	iii	iii	NOUN
ejpam-6418	36	34	)	)	PUNCT
ejpam-6418	36	35	1	1	NUM
ejpam-6418	36	36	∨	∨	NOUN
ejpam-6418	36	37	a	a	DET
ejpam-6418	36	38	=	=	SYM
ejpam-6418	36	39	1	1	NUM
ejpam-6418	36	40	(	(	PUNCT
ejpam-6418	36	41	iv	iv	NUM
ejpam-6418	36	42	)	)	PUNCT
ejpam-6418	36	43	(	(	PUNCT
ejpam-6418	36	44	a	a	DET
ejpam-6418	36	45	∨	∨	NUM
ejpam-6418	36	46	b	b	NOUN
ejpam-6418	36	47	)	)	PUNCT
ejpam-6418	36	48	∧	∧	NOUN
ejpam-6418	36	49	c	c	NOUN
ejpam-6418	36	50	=	=	PUNCT
ejpam-6418	36	51	(	(	PUNCT
ejpam-6418	36	52	a	a	DET
ejpam-6418	36	53	∧	∧	PROPN
ejpam-6418	36	54	c	c	NOUN
ejpam-6418	36	55	)	)	PUNCT
ejpam-6418	36	56	∨	∨	PROPN
ejpam-6418	36	57	(	(	PUNCT
ejpam-6418	36	58	b	b	PROPN
ejpam-6418	36	59	∧	∧	PROPN
ejpam-6418	36	60	c	c	NOUN
ejpam-6418	36	61	)	)	PUNCT
ejpam-6418	36	62	(	(	PUNCT
ejpam-6418	36	63	v	v	NOUN
ejpam-6418	36	64	)	)	PUNCT
ejpam-6418	36	65	a	a	DET
ejpam-6418	36	66	∨	∨	NOUN
ejpam-6418	36	67	(	(	PUNCT
ejpam-6418	36	68	b	b	PROPN
ejpam-6418	36	69	∧	∧	PROPN
ejpam-6418	36	70	c	c	NOUN
ejpam-6418	36	71	)	)	PUNCT
ejpam-6418	36	72	=	=	SYM
ejpam-6418	36	73	a	a	DET
ejpam-6418	36	74	∨	∨	NOUN
ejpam-6418	36	75	(	(	PUNCT
ejpam-6418	36	76	c	c	PROPN
ejpam-6418	36	77	∧	∧	PROPN
ejpam-6418	36	78	b	b	PROPN
ejpam-6418	36	79	)	)	PUNCT
ejpam-6418	36	80	(	(	PUNCT
ejpam-6418	36	81	vi	vi	NOUN
ejpam-6418	36	82	)	)	PUNCT
ejpam-6418	36	83	∨	∨	NUM
ejpam-6418	36	84	is	be	AUX
ejpam-6418	36	85	associative	associative	ADJ
ejpam-6418	36	86	in	in	ADP
ejpam-6418	36	87	v	v	PROPN
ejpam-6418	36	88	(	(	PUNCT
ejpam-6418	36	89	vii	vii	PROPN
ejpam-6418	36	90	)	)	PUNCT
ejpam-6418	36	91	d	d	NOUN
ejpam-6418	36	92	∨	∨	NUM
ejpam-6418	37	1	[	[	PUNCT
ejpam-6418	37	2	a	a	DET
ejpam-6418	37	3	∧	∧	PROPN
ejpam-6418	37	4	(	(	PUNCT
ejpam-6418	37	5	b	b	PROPN
ejpam-6418	37	6	∧	∧	PROPN
ejpam-6418	37	7	c	c	NOUN
ejpam-6418	37	8	)	)	PUNCT
ejpam-6418	37	9	]	]	PUNCT
ejpam-6418	38	1	=	=	PUNCT
ejpam-6418	38	2	d	d	X
ejpam-6418	38	3	∨	∨	X
ejpam-6418	38	4	[	[	X
ejpam-6418	38	5	(	(	PUNCT
ejpam-6418	38	6	a	a	DET
ejpam-6418	38	7	∧	∧	PROPN
ejpam-6418	38	8	b	b	NOUN
ejpam-6418	38	9	)	)	PUNCT
ejpam-6418	38	10	∧	∧	PROPN
ejpam-6418	38	11	c	c	NOUN
ejpam-6418	38	12	]	]	X
ejpam-6418	38	13	(	(	PUNCT
ejpam-6418	38	14	viii	viii	NOUN
ejpam-6418	38	15	)	)	PUNCT
ejpam-6418	38	16	a	a	DET
ejpam-6418	38	17	∨	∨	NOUN
ejpam-6418	38	18	(	(	PUNCT
ejpam-6418	38	19	b	b	PROPN
ejpam-6418	38	20	∨	∨	NUM
ejpam-6418	38	21	c	c	NOUN
ejpam-6418	38	22	)	)	PUNCT
ejpam-6418	38	23	=	=	SYM
ejpam-6418	38	24	a	a	DET
ejpam-6418	38	25	∨	∨	NOUN
ejpam-6418	38	26	(	(	PUNCT
ejpam-6418	38	27	c	c	PROPN
ejpam-6418	38	28	∨	∨	NUM
ejpam-6418	38	29	b	b	NOUN
ejpam-6418	38	30	)	)	PUNCT
ejpam-6418	38	31	(	(	PUNCT
ejpam-6418	38	32	ix	ix	PROPN
ejpam-6418	38	33	)	)	PUNCT
ejpam-6418	38	34	a	a	DET
ejpam-6418	38	35	∨	∨	NUM
ejpam-6418	38	36	b	b	NOUN
ejpam-6418	38	37	=	=	SYM
ejpam-6418	38	38	1	1	NUM
ejpam-6418	38	39	⇐	⇐	ADJ
ejpam-6418	38	40	⇒	⇒	PROPN
ejpam-6418	38	41	b	b	PROPN
ejpam-6418	38	42	∨	∨	NUM
ejpam-6418	38	43	a	a	DET
ejpam-6418	38	44	=	=	SYM
ejpam-6418	38	45	1	1	NUM
ejpam-6418	38	46	(	(	PUNCT
ejpam-6418	38	47	x	x	NOUN
ejpam-6418	38	48	)	)	PUNCT
ejpam-6418	38	49	a	a	DET
ejpam-6418	38	50	∨	∨	NUM
ejpam-6418	38	51	b	b	NOUN
ejpam-6418	38	52	=	=	SYM
ejpam-6418	38	53	1	1	NUM
ejpam-6418	38	54	=	=	NOUN
ejpam-6418	38	55	⇒	⇒	X
ejpam-6418	38	56	b	b	X
ejpam-6418	38	57	∧	∧	NOUN
ejpam-6418	38	58	a	a	PRON
ejpam-6418	38	59	=	=	X
ejpam-6418	38	60	a	a	DET
ejpam-6418	38	61	∧	∧	PROPN
ejpam-6418	38	62	b.	b.	PROPN
ejpam-6418	38	63	definition	definition	NOUN
ejpam-6418	38	64	2.5	2.5	NUM
ejpam-6418	38	65	.	.	PUNCT
ejpam-6418	39	1	[	[	X
ejpam-6418	39	2	1	1	X
ejpam-6418	39	3	]	]	X
ejpam-6418	39	4	an	an	DET
ejpam-6418	39	5	element	element	NOUN
ejpam-6418	39	6	m	m	PROPN
ejpam-6418	39	7	∈	∈	NOUN
ejpam-6418	39	8	v	v	NOUN
ejpam-6418	39	9	is	be	AUX
ejpam-6418	39	10	said	say	VERB
ejpam-6418	39	11	to	to	PART
ejpam-6418	39	12	be	be	AUX
ejpam-6418	39	13	minimal	minimal	ADJ
ejpam-6418	39	14	,	,	PUNCT
ejpam-6418	39	15	if	if	SCONJ
ejpam-6418	39	16	for	for	ADP
ejpam-6418	39	17	any	any	DET
ejpam-6418	39	18	a	a	DET
ejpam-6418	39	19	∈	∈	PROPN
ejpam-6418	39	20	v	v	NOUN
ejpam-6418	39	21	,	,	PUNCT
ejpam-6418	39	22	m	m	VERB
ejpam-6418	39	23	≤	≤	NOUN
ejpam-6418	39	24	a	a	DET
ejpam-6418	39	25	implies	implie	NOUN
ejpam-6418	39	26	m	m	VERB
ejpam-6418	39	27	=	=	SYM
ejpam-6418	39	28	a.	a.	NOUN
ejpam-6418	39	29	lemma	lemma	PROPN
ejpam-6418	39	30	2.6	2.6	NUM
ejpam-6418	39	31	.	.	PUNCT
ejpam-6418	40	1	[	[	X
ejpam-6418	40	2	1	1	X
ejpam-6418	40	3	]	]	PUNCT
ejpam-6418	40	4	for	for	ADP
ejpam-6418	40	5	any	any	DET
ejpam-6418	40	6	m	m	PROPN
ejpam-6418	40	7	∈	∈	PROPN
ejpam-6418	40	8	v	v	NOUN
ejpam-6418	40	9	,	,	PUNCT
ejpam-6418	40	10	the	the	DET
ejpam-6418	40	11	following	follow	VERB
ejpam-6418	40	12	are	be	AUX
ejpam-6418	40	13	equivalent	equivalent	ADJ
ejpam-6418	40	14	;	;	PUNCT
ejpam-6418	40	15	(	(	PUNCT
ejpam-6418	40	16	i	i	NOUN
ejpam-6418	40	17	)	)	PUNCT
ejpam-6418	40	18	m	m	AUX
ejpam-6418	40	19	is	be	AUX
ejpam-6418	40	20	minimal	minimal	ADJ
ejpam-6418	40	21	,	,	PUNCT
ejpam-6418	40	22	(	(	PUNCT
ejpam-6418	40	23	ii	ii	NOUN
ejpam-6418	40	24	)	)	PUNCT
ejpam-6418	40	25	a	a	DET
ejpam-6418	40	26	∧m	∧m	PROPN
ejpam-6418	40	27	=	=	PUNCT
ejpam-6418	40	28	m	m	PROPN
ejpam-6418	40	29	,	,	PUNCT
ejpam-6418	40	30	for	for	ADP
ejpam-6418	40	31	all	all	DET
ejpam-6418	40	32	a	a	DET
ejpam-6418	40	33	∈	∈	PROPN
ejpam-6418	40	34	v	v	ADP
ejpam-6418	40	35	(	(	PUNCT
ejpam-6418	40	36	iii	iii	NOUN
ejpam-6418	40	37	)	)	PUNCT
ejpam-6418	40	38	a	a	DET
ejpam-6418	40	39	∨m	∨m	NOUN
ejpam-6418	40	40	=	=	SYM
ejpam-6418	40	41	a	a	NOUN
ejpam-6418	40	42	,	,	PUNCT
ejpam-6418	40	43	for	for	ADP
ejpam-6418	40	44	all	all	DET
ejpam-6418	40	45	a	a	DET
ejpam-6418	40	46	∈	∈	PROPN
ejpam-6418	40	47	v.	v.	ADP
ejpam-6418	40	48	r.	r.	PROPN
ejpam-6418	40	49	sirisetti	sirisetti	PROPN
ejpam-6418	40	50	et	et	PROPN
ejpam-6418	40	51	al	al	PROPN
ejpam-6418	40	52	.	.	PUNCT
ejpam-6418	40	53	/	/	SYM
ejpam-6418	40	54	eur	eur	PROPN
ejpam-6418	40	55	.	.	PUNCT
ejpam-6418	41	1	j.	j.	PROPN
ejpam-6418	41	2	pure	pure	PROPN
ejpam-6418	41	3	appl	appl	PROPN
ejpam-6418	41	4	.	.	PROPN
ejpam-6418	41	5	math	math	PROPN
ejpam-6418	41	6	,	,	PUNCT
ejpam-6418	41	7	18	18	NUM
ejpam-6418	41	8	(	(	PUNCT
ejpam-6418	41	9	4	4	NUM
ejpam-6418	41	10	)	)	PUNCT
ejpam-6418	41	11	(	(	PUNCT
ejpam-6418	41	12	2025	2025	NUM
ejpam-6418	41	13	)	)	PUNCT
ejpam-6418	41	14	,	,	PUNCT
ejpam-6418	41	15	6418	6418	NUM
ejpam-6418	41	16	4	4	NUM
ejpam-6418	41	17	of	of	ADP
ejpam-6418	41	18	13	13	NUM
ejpam-6418	41	19	a	a	DET
ejpam-6418	41	20	non	non	ADJ
ejpam-6418	41	21	-	-	ADJ
ejpam-6418	41	22	empty	empty	ADJ
ejpam-6418	41	23	subset	subset	NOUN
ejpam-6418	41	24	f	f	PROPN
ejpam-6418	41	25	of	of	ADP
ejpam-6418	41	26	v	v	PROPN
ejpam-6418	41	27	is	be	AUX
ejpam-6418	41	28	said	say	VERB
ejpam-6418	41	29	to	to	PART
ejpam-6418	41	30	be	be	AUX
ejpam-6418	41	31	a	a	DET
ejpam-6418	41	32	filter	filter	NOUN
ejpam-6418	41	33	,	,	PUNCT
ejpam-6418	41	34	if	if	SCONJ
ejpam-6418	41	35	for	for	ADP
ejpam-6418	41	36	any	any	DET
ejpam-6418	41	37	a	a	NOUN
ejpam-6418	41	38	,	,	PUNCT
ejpam-6418	41	39	b	b	PROPN
ejpam-6418	41	40	∈	∈	PROPN
ejpam-6418	41	41	f	f	X
ejpam-6418	41	42	,	,	PUNCT
ejpam-6418	41	43	x	x	PROPN
ejpam-6418	41	44	∈	∈	PROPN
ejpam-6418	41	45	v	v	NOUN
ejpam-6418	41	46	,	,	PUNCT
ejpam-6418	41	47	a	a	DET
ejpam-6418	41	48	∧	∧	PROPN
ejpam-6418	41	49	b	b	PROPN
ejpam-6418	41	50	∈	∈	PROPN
ejpam-6418	41	51	f	f	PROPN
ejpam-6418	41	52	and	and	CCONJ
ejpam-6418	41	53	x	x	PROPN
ejpam-6418	41	54	∨	∨	NOUN
ejpam-6418	41	55	a	a	DET
ejpam-6418	41	56	∈	∈	PROPN
ejpam-6418	41	57	f	f	X
ejpam-6418	41	58	.	.	PUNCT
ejpam-6418	42	1	let	let	VERB
ejpam-6418	42	2	s	s	PRON
ejpam-6418	42	3	be	be	AUX
ejpam-6418	42	4	a	a	DET
ejpam-6418	42	5	non	non	ADJ
ejpam-6418	42	6	-	-	ADJ
ejpam-6418	42	7	empty	empty	ADJ
ejpam-6418	42	8	subset	subset	NOUN
ejpam-6418	42	9	of	of	ADP
ejpam-6418	42	10	v.	v.	ADV
ejpam-6418	42	11	then	then	ADV
ejpam-6418	42	12	[	[	X
ejpam-6418	42	13	s	s	X
ejpam-6418	42	14	)	)	PUNCT
ejpam-6418	42	15	=	=	SYM
ejpam-6418	42	16	{	{	PUNCT
ejpam-6418	42	17	a	a	DET
ejpam-6418	42	18	∨	∨	NOUN
ejpam-6418	42	19	(	(	PUNCT
ejpam-6418	42	20	∧n	∧n	NUM
ejpam-6418	42	21	i=1si	i=1si	NUM
ejpam-6418	42	22	)	)	PUNCT
ejpam-6418	43	1	|	|	ADV
ejpam-6418	43	2	si	si	PROPN
ejpam-6418	43	3	∈	∈	PROPN
ejpam-6418	43	4	s	s	PROPN
ejpam-6418	43	5	,	,	PUNCT
ejpam-6418	43	6	a	a	DET
ejpam-6418	43	7	∈	∈	PROPN
ejpam-6418	43	8	v	v	NOUN
ejpam-6418	43	9	,	,	PUNCT
ejpam-6418	43	10	1	1	NUM
ejpam-6418	43	11	≤	≤	NUM
ejpam-6418	43	12	i	i	PRON
ejpam-6418	43	13	≤	≤	ADJ
ejpam-6418	43	14	n	n	CCONJ
ejpam-6418	43	15	and	and	CCONJ
ejpam-6418	43	16	n	n	PROPN
ejpam-6418	43	17	is	be	AUX
ejpam-6418	43	18	a	a	DET
ejpam-6418	43	19	positive	positive	ADJ
ejpam-6418	43	20	integer	integer	NOUN
ejpam-6418	43	21	}	}	PUNCT
ejpam-6418	43	22	is	be	AUX
ejpam-6418	43	23	the	the	DET
ejpam-6418	43	24	smallest	small	ADJ
ejpam-6418	43	25	filter	filter	NOUN
ejpam-6418	43	26	of	of	ADP
ejpam-6418	43	27	v	v	NOUN
ejpam-6418	43	28	containing	contain	VERB
ejpam-6418	43	29	s.	s.	PROPN
ejpam-6418	43	30	if	if	SCONJ
ejpam-6418	43	31	s	s	VERB
ejpam-6418	43	32	=	=	X
ejpam-6418	43	33	{	{	PUNCT
ejpam-6418	43	34	a	a	NOUN
ejpam-6418	43	35	}	}	PUNCT
ejpam-6418	43	36	,	,	PUNCT
ejpam-6418	43	37	then	then	ADV
ejpam-6418	43	38	we	we	PRON
ejpam-6418	43	39	write	write	VERB
ejpam-6418	43	40	[	[	X
ejpam-6418	43	41	s	s	X
ejpam-6418	43	42	)	)	PUNCT
ejpam-6418	43	43	=	=	PUNCT
ejpam-6418	44	1	[	[	X
ejpam-6418	44	2	a	a	X
ejpam-6418	44	3	)	)	PUNCT
ejpam-6418	44	4	,	,	PUNCT
ejpam-6418	44	5	the	the	DET
ejpam-6418	44	6	principal	principal	ADJ
ejpam-6418	44	7	filter	filter	NOUN
ejpam-6418	44	8	generated	generate	VERB
ejpam-6418	44	9	by	by	ADP
ejpam-6418	44	10	a.	a.	NOUN
ejpam-6418	44	11	the	the	DET
ejpam-6418	44	12	collection	collection	NOUN
ejpam-6418	44	13	f	f	X
ejpam-6418	44	14	(	(	PUNCT
ejpam-6418	44	15	v	v	NOUN
ejpam-6418	44	16	)	)	PUNCT
ejpam-6418	44	17	of	of	ADP
ejpam-6418	44	18	all	all	DET
ejpam-6418	44	19	filters	filter	NOUN
ejpam-6418	44	20	of	of	ADP
ejpam-6418	44	21	v	v	NOUN
ejpam-6418	44	22	forms	form	VERB
ejpam-6418	44	23	a	a	DET
ejpam-6418	44	24	distributive	distributive	ADJ
ejpam-6418	44	25	lattice	lattice	NOUN
ejpam-6418	44	26	under	under	ADP
ejpam-6418	44	27	set	set	ADJ
ejpam-6418	44	28	inclusion	inclusion	NOUN
ejpam-6418	44	29	,	,	PUNCT
ejpam-6418	44	30	in	in	ADP
ejpam-6418	44	31	which	which	PRON
ejpam-6418	44	32	,	,	PUNCT
ejpam-6418	44	33	the	the	DET
ejpam-6418	44	34	glb	glb	NOUN
ejpam-6418	44	35	and	and	CCONJ
ejpam-6418	44	36	lub	lub	NOUN
ejpam-6418	44	37	of	of	ADP
ejpam-6418	44	38	any	any	DET
ejpam-6418	44	39	two	two	NUM
ejpam-6418	44	40	filters	filter	NOUN
ejpam-6418	44	41	f	f	PROPN
ejpam-6418	44	42	and	and	CCONJ
ejpam-6418	44	43	g	g	PROPN
ejpam-6418	44	44	are	be	AUX
ejpam-6418	44	45	given	give	VERB
ejpam-6418	44	46	by	by	ADP
ejpam-6418	44	47	f	f	PROPN
ejpam-6418	44	48	∧g	∧g	PROPN
ejpam-6418	44	49	=	=	SYM
ejpam-6418	44	50	f	f	PROPN
ejpam-6418	44	51	∩g	∩g	NOUN
ejpam-6418	44	52	and	and	CCONJ
ejpam-6418	44	53	f	f	PROPN
ejpam-6418	44	54	∨g	∨g	PROPN
ejpam-6418	44	55	=	=	SYM
ejpam-6418	44	56	{	{	PUNCT
ejpam-6418	44	57	f	f	PROPN
ejpam-6418	44	58	∧	∧	PROPN
ejpam-6418	44	59	g	g	PROPN
ejpam-6418	45	1	|	|	ADV
ejpam-6418	45	2	f	f	PROPN
ejpam-6418	45	3	∈	∈	PROPN
ejpam-6418	45	4	f	f	PROPN
ejpam-6418	45	5	and	and	CCONJ
ejpam-6418	45	6	g	g	PROPN
ejpam-6418	45	7	∈	∈	PROPN
ejpam-6418	45	8	g	g	PROPN
ejpam-6418	45	9	}	}	PUNCT
ejpam-6418	45	10	respectively	respectively	ADV
ejpam-6418	45	11	.	.	PUNCT
ejpam-6418	46	1	lemma	lemma	PROPN
ejpam-6418	46	2	2.7	2.7	NUM
ejpam-6418	46	3	.	.	PUNCT
ejpam-6418	47	1	[	[	X
ejpam-6418	47	2	1	1	X
ejpam-6418	47	3	]	]	PUNCT
ejpam-6418	47	4	given	give	VERB
ejpam-6418	47	5	a	a	DET
ejpam-6418	47	6	filter	filter	NOUN
ejpam-6418	47	7	f	f	NOUN
ejpam-6418	47	8	of	of	ADP
ejpam-6418	47	9	v	v	NOUN
ejpam-6418	47	10	and	and	CCONJ
ejpam-6418	47	11	a	a	DET
ejpam-6418	47	12	,	,	PUNCT
ejpam-6418	47	13	b	b	PROPN
ejpam-6418	47	14	∈	∈	PROPN
ejpam-6418	47	15	v	v	NOUN
ejpam-6418	47	16	,	,	PUNCT
ejpam-6418	47	17	(	(	PUNCT
ejpam-6418	47	18	i	i	NOUN
ejpam-6418	47	19	)	)	PUNCT
ejpam-6418	48	1	[	[	X
ejpam-6418	48	2	a	a	X
ejpam-6418	48	3	)	)	PUNCT
ejpam-6418	48	4	=	=	SYM
ejpam-6418	48	5	{	{	PUNCT
ejpam-6418	48	6	x	x	PROPN
ejpam-6418	48	7	∨	∨	NUM
ejpam-6418	48	8	a	a	DET
ejpam-6418	48	9	|	|	NOUN
ejpam-6418	48	10	x	x	SYM
ejpam-6418	48	11	∈	∈	PROPN
ejpam-6418	48	12	v	v	ADP
ejpam-6418	48	13	}	}	PUNCT
ejpam-6418	48	14	(	(	PUNCT
ejpam-6418	48	15	ii	ii	NOUN
ejpam-6418	48	16	)	)	PUNCT
ejpam-6418	48	17	a	a	DET
ejpam-6418	48	18	∈	∈	PROPN
ejpam-6418	49	1	[	[	X
ejpam-6418	49	2	b	b	NOUN
ejpam-6418	49	3	)	)	PUNCT
ejpam-6418	49	4	⇐	⇐	ADJ
ejpam-6418	49	5	⇒	⇒	NOUN
ejpam-6418	49	6	a	a	DET
ejpam-6418	49	7	=	=	NOUN
ejpam-6418	49	8	a	a	DET
ejpam-6418	49	9	∨	∨	NUM
ejpam-6418	49	10	b	b	PROPN
ejpam-6418	49	11	(	(	PUNCT
ejpam-6418	49	12	iii	iii	NOUN
ejpam-6418	49	13	)	)	PUNCT
ejpam-6418	49	14	a	a	DET
ejpam-6418	49	15	∨	∨	NUM
ejpam-6418	49	16	b	b	X
ejpam-6418	49	17	∈	∈	PROPN
ejpam-6418	49	18	f	f	X
ejpam-6418	49	19	⇐	⇐	PROPN
ejpam-6418	49	20	⇒	⇒	PROPN
ejpam-6418	49	21	b	b	PROPN
ejpam-6418	49	22	∨	∨	NUM
ejpam-6418	49	23	a	a	DET
ejpam-6418	49	24	∈	∈	PROPN
ejpam-6418	49	25	f	f	X
ejpam-6418	49	26	(	(	PUNCT
ejpam-6418	49	27	iv	iv	X
ejpam-6418	49	28	)	)	PUNCT
ejpam-6418	50	1	[	[	X
ejpam-6418	50	2	a	a	DET
ejpam-6418	50	3	∨	∨	NUM
ejpam-6418	50	4	b	b	NOUN
ejpam-6418	50	5	)	)	PUNCT
ejpam-6418	50	6	=	=	PUNCT
ejpam-6418	51	1	[	[	X
ejpam-6418	51	2	b	b	X
ejpam-6418	51	3	∨	∨	NUM
ejpam-6418	51	4	a	a	PRON
ejpam-6418	51	5	)	)	PUNCT
ejpam-6418	51	6	=	=	PUNCT
ejpam-6418	52	1	[	[	X
ejpam-6418	52	2	a	a	X
ejpam-6418	52	3	)	)	PUNCT
ejpam-6418	52	4	∧	∧	NOUN
ejpam-6418	52	5	[	[	X
ejpam-6418	52	6	b	b	NOUN
ejpam-6418	52	7	)	)	PUNCT
ejpam-6418	52	8	(	(	PUNCT
ejpam-6418	52	9	v	v	NOUN
ejpam-6418	52	10	)	)	PUNCT
ejpam-6418	53	1	[	[	X
ejpam-6418	53	2	a	a	DET
ejpam-6418	53	3	∧	∧	PROPN
ejpam-6418	53	4	b	b	NOUN
ejpam-6418	53	5	)	)	PUNCT
ejpam-6418	53	6	=	=	PUNCT
ejpam-6418	54	1	[	[	X
ejpam-6418	54	2	b	b	X
ejpam-6418	54	3	∧	∧	PROPN
ejpam-6418	54	4	a	a	NOUN
ejpam-6418	54	5	)	)	PUNCT
ejpam-6418	54	6	=	=	PUNCT
ejpam-6418	55	1	[	[	X
ejpam-6418	55	2	a	a	X
ejpam-6418	55	3	)	)	PUNCT
ejpam-6418	55	4	∨	∨	NOUN
ejpam-6418	56	1	[	[	X
ejpam-6418	56	2	b	b	NOUN
ejpam-6418	56	3	)	)	PUNCT
ejpam-6418	56	4	.	.	PUNCT
ejpam-6418	57	1	lemma	lemma	PROPN
ejpam-6418	57	2	2.8	2.8	NUM
ejpam-6418	57	3	.	.	PUNCT
ejpam-6418	58	1	[	[	X
ejpam-6418	58	2	1	1	X
ejpam-6418	58	3	]	]	PUNCT
ejpam-6418	58	4	for	for	ADP
ejpam-6418	58	5	any	any	DET
ejpam-6418	58	6	a	a	PRON
ejpam-6418	58	7	,	,	PUNCT
ejpam-6418	58	8	b	b	PROPN
ejpam-6418	58	9	∈	∈	PROPN
ejpam-6418	58	10	v	v	NOUN
ejpam-6418	58	11	,	,	PUNCT
ejpam-6418	58	12	(	(	PUNCT
ejpam-6418	58	13	i	i	NOUN
ejpam-6418	58	14	)	)	PUNCT
ejpam-6418	58	15	(	(	PUNCT
ejpam-6418	58	16	a	a	DET
ejpam-6418	58	17	∨	∨	NUM
ejpam-6418	58	18	b	b	NOUN
ejpam-6418	58	19	)	)	PUNCT
ejpam-6418	58	20	∨	∨	NUM
ejpam-6418	58	21	b	b	X
ejpam-6418	58	22	=	=	PUNCT
ejpam-6418	58	23	a	a	DET
ejpam-6418	58	24	∨	∨	NUM
ejpam-6418	58	25	b	b	PROPN
ejpam-6418	58	26	(	(	PUNCT
ejpam-6418	58	27	ii	ii	NOUN
ejpam-6418	58	28	)	)	PUNCT
ejpam-6418	58	29	(	(	PUNCT
ejpam-6418	58	30	a	a	DET
ejpam-6418	58	31	∨	∨	NUM
ejpam-6418	58	32	b	b	NOUN
ejpam-6418	58	33	)	)	PUNCT
ejpam-6418	58	34	∨	∨	NOUN
ejpam-6418	58	35	a	a	PRON
ejpam-6418	58	36	=	=	PUNCT
ejpam-6418	58	37	a	a	DET
ejpam-6418	58	38	∨	∨	NUM
ejpam-6418	58	39	b	b	PROPN
ejpam-6418	58	40	(	(	PUNCT
ejpam-6418	58	41	iii	iii	NOUN
ejpam-6418	58	42	)	)	PUNCT
ejpam-6418	58	43	a	a	DET
ejpam-6418	58	44	∨	∨	NOUN
ejpam-6418	58	45	(	(	PUNCT
ejpam-6418	58	46	a	a	DET
ejpam-6418	58	47	∨	∨	NUM
ejpam-6418	58	48	b	b	NOUN
ejpam-6418	58	49	)	)	PUNCT
ejpam-6418	58	50	=	=	PUNCT
ejpam-6418	58	51	a	a	DET
ejpam-6418	58	52	∨	∨	NUM
ejpam-6418	58	53	b	b	PROPN
ejpam-6418	58	54	(	(	PUNCT
ejpam-6418	58	55	iv	iv	X
ejpam-6418	58	56	)	)	PUNCT
ejpam-6418	58	57	a	a	DET
ejpam-6418	58	58	∧	∧	PROPN
ejpam-6418	58	59	(	(	PUNCT
ejpam-6418	58	60	a	a	DET
ejpam-6418	58	61	∧	∧	PROPN
ejpam-6418	58	62	b	b	NOUN
ejpam-6418	58	63	)	)	PUNCT
ejpam-6418	58	64	=	=	PUNCT
ejpam-6418	58	65	a	a	DET
ejpam-6418	58	66	∧	∧	PROPN
ejpam-6418	58	67	b	b	PROPN
ejpam-6418	58	68	(	(	PUNCT
ejpam-6418	58	69	v	v	NOUN
ejpam-6418	58	70	)	)	PUNCT
ejpam-6418	58	71	(	(	PUNCT
ejpam-6418	58	72	a	a	DET
ejpam-6418	58	73	∧	∧	PROPN
ejpam-6418	58	74	b	b	NOUN
ejpam-6418	58	75	)	)	PUNCT
ejpam-6418	58	76	∧	∧	PROPN
ejpam-6418	58	77	b	b	NOUN
ejpam-6418	58	78	=	=	PUNCT
ejpam-6418	58	79	a	a	DET
ejpam-6418	58	80	∧	∧	PROPN
ejpam-6418	58	81	b	b	PROPN
ejpam-6418	58	82	(	(	PUNCT
ejpam-6418	58	83	vi	vi	NOUN
ejpam-6418	58	84	)	)	PUNCT
ejpam-6418	58	85	b	b	NOUN
ejpam-6418	58	86	∧	∧	PROPN
ejpam-6418	58	87	(	(	PUNCT
ejpam-6418	58	88	a	a	DET
ejpam-6418	58	89	∧	∧	PROPN
ejpam-6418	58	90	b	b	NOUN
ejpam-6418	58	91	)	)	PUNCT
ejpam-6418	58	92	=	=	PUNCT
ejpam-6418	58	93	a	a	DET
ejpam-6418	58	94	∧	∧	PROPN
ejpam-6418	58	95	b.	b.	PROPN
ejpam-6418	58	96	theorem	theorem	VERB
ejpam-6418	58	97	2.9	2.9	NUM
ejpam-6418	58	98	.	.	PUNCT
ejpam-6418	59	1	[	[	X
ejpam-6418	59	2	1	1	X
ejpam-6418	59	3	]	]	X
ejpam-6418	59	4	the	the	DET
ejpam-6418	59	5	following	follow	VERB
ejpam-6418	59	6	are	be	AUX
ejpam-6418	59	7	equivalent	equivalent	ADJ
ejpam-6418	59	8	in	in	ADP
ejpam-6418	59	9	v	v	NOUN
ejpam-6418	59	10	;	;	PUNCT
ejpam-6418	59	11	(	(	PUNCT
ejpam-6418	59	12	i	i	NOUN
ejpam-6418	59	13	)	)	PUNCT
ejpam-6418	59	14	(	(	PUNCT
ejpam-6418	59	15	v,∨,∧	v,∨,∧	NOUN
ejpam-6418	59	16	,	,	PUNCT
ejpam-6418	59	17	1	1	NUM
ejpam-6418	59	18	)	)	PUNCT
ejpam-6418	59	19	is	be	AUX
ejpam-6418	59	20	a	a	DET
ejpam-6418	59	21	distributive	distributive	ADJ
ejpam-6418	59	22	lattice	lattice	NOUN
ejpam-6418	59	23	(	(	PUNCT
ejpam-6418	59	24	ii	ii	NOUN
ejpam-6418	59	25	)	)	PUNCT
ejpam-6418	59	26	the	the	DET
ejpam-6418	59	27	poset	poset	NOUN
ejpam-6418	59	28	(	(	PUNCT
ejpam-6418	59	29	v,≤	v,≤	X
ejpam-6418	59	30	)	)	PUNCT
ejpam-6418	59	31	is	be	AUX
ejpam-6418	59	32	directed	direct	VERB
ejpam-6418	59	33	below	below	ADP
ejpam-6418	59	34	(	(	PUNCT
ejpam-6418	59	35	iii	iii	NOUN
ejpam-6418	59	36	)	)	PUNCT
ejpam-6418	59	37	(	(	PUNCT
ejpam-6418	59	38	a	a	DET
ejpam-6418	59	39	∧	∧	PROPN
ejpam-6418	59	40	b	b	PROPN
ejpam-6418	59	41	)	)	PUNCT
ejpam-6418	59	42	∨	∨	NOUN
ejpam-6418	59	43	a	a	DET
ejpam-6418	59	44	=	=	X
ejpam-6418	59	45	a	a	NOUN
ejpam-6418	59	46	,	,	PUNCT
ejpam-6418	59	47	for	for	SCONJ
ejpam-6418	59	48	all	all	DET
ejpam-6418	59	49	a	a	DET
ejpam-6418	59	50	∈	∈	PROPN
ejpam-6418	59	51	v	v	NOUN
ejpam-6418	59	52	(	(	PUNCT
ejpam-6418	59	53	iv	iv	X
ejpam-6418	59	54	)	)	PUNCT
ejpam-6418	59	55	∧	∧	NOUN
ejpam-6418	59	56	is	be	AUX
ejpam-6418	59	57	commutative	commutative	ADJ
ejpam-6418	59	58	(	(	PUNCT
ejpam-6418	59	59	v	v	NOUN
ejpam-6418	59	60	)	)	PUNCT
ejpam-6418	59	61	∨	∨	NUM
ejpam-6418	59	62	is	be	AUX
ejpam-6418	59	63	commutative	commutative	ADJ
ejpam-6418	59	64	(	(	PUNCT
ejpam-6418	59	65	vi	vi	NOUN
ejpam-6418	59	66	)	)	PUNCT
ejpam-6418	59	67	the	the	DET
ejpam-6418	59	68	relation	relation	NOUN
ejpam-6418	60	1	r	r	NOUN
ejpam-6418	60	2	=	=	SYM
ejpam-6418	60	3	{	{	PUNCT
ejpam-6418	60	4	(	(	PUNCT
ejpam-6418	60	5	a	a	PRON
ejpam-6418	60	6	,	,	PUNCT
ejpam-6418	60	7	b	b	NOUN
ejpam-6418	60	8	)	)	PUNCT
ejpam-6418	60	9	∈	∈	NOUN
ejpam-6418	60	10	v×	v×	NOUN
ejpam-6418	60	11	v	v	ADP
ejpam-6418	60	12	|	|	ADV
ejpam-6418	60	13	b	b	PROPN
ejpam-6418	60	14	∨	∨	NOUN
ejpam-6418	60	15	a	a	DET
ejpam-6418	60	16	=	=	SYM
ejpam-6418	60	17	b	b	NOUN
ejpam-6418	60	18	}	}	PUNCT
ejpam-6418	60	19	is	be	AUX
ejpam-6418	60	20	anti	anti	ADJ
ejpam-6418	60	21	-	-	ADJ
ejpam-6418	60	22	symmetric	symmetric	ADJ
ejpam-6418	60	23	.	.	PUNCT
ejpam-6418	61	1	r.	r.	PROPN
ejpam-6418	61	2	sirisetti	sirisetti	PROPN
ejpam-6418	61	3	et	et	PROPN
ejpam-6418	61	4	al	al	PROPN
ejpam-6418	61	5	.	.	PUNCT
ejpam-6418	61	6	/	/	SYM
ejpam-6418	61	7	eur	eur	PROPN
ejpam-6418	61	8	.	.	PUNCT
ejpam-6418	62	1	j.	j.	PROPN
ejpam-6418	62	2	pure	pure	PROPN
ejpam-6418	62	3	appl	appl	PROPN
ejpam-6418	62	4	.	.	PROPN
ejpam-6418	62	5	math	math	PROPN
ejpam-6418	62	6	,	,	PUNCT
ejpam-6418	62	7	18	18	NUM
ejpam-6418	62	8	(	(	PUNCT
ejpam-6418	62	9	4	4	NUM
ejpam-6418	62	10	)	)	PUNCT
ejpam-6418	62	11	(	(	PUNCT
ejpam-6418	62	12	2025	2025	NUM
ejpam-6418	62	13	)	)	PUNCT
ejpam-6418	62	14	,	,	PUNCT
ejpam-6418	62	15	6418	6418	NUM
ejpam-6418	62	16	5	5	NUM
ejpam-6418	62	17	of	of	ADP
ejpam-6418	62	18	13	13	NUM
ejpam-6418	62	19	3	3	NUM
ejpam-6418	62	20	.	.	PUNCT
ejpam-6418	62	21	amicable	amicable	ADJ
ejpam-6418	62	22	sets	set	NOUN
ejpam-6418	62	23	in	in	ADP
ejpam-6418	62	24	paradistributive	paradistributive	ADJ
ejpam-6418	62	25	latticoid	latticoid	NOUN
ejpam-6418	62	26	in	in	ADP
ejpam-6418	62	27	this	this	DET
ejpam-6418	62	28	section	section	NOUN
ejpam-6418	62	29	we	we	PRON
ejpam-6418	62	30	define	define	VERB
ejpam-6418	62	31	compatible	compatible	ADJ
ejpam-6418	62	32	sets	set	NOUN
ejpam-6418	62	33	and	and	CCONJ
ejpam-6418	62	34	then	then	ADV
ejpam-6418	62	35	maximal	maximal	ADJ
ejpam-6418	62	36	sets	set	NOUN
ejpam-6418	62	37	in	in	ADP
ejpam-6418	62	38	a	a	DET
ejpam-6418	62	39	paradistributive	paradistributive	ADJ
ejpam-6418	62	40	latticoid	latticoid	NOUN
ejpam-6418	62	41	and	and	CCONJ
ejpam-6418	62	42	extensively	extensively	ADV
ejpam-6418	62	43	study	study	VERB
ejpam-6418	62	44	their	their	PRON
ejpam-6418	62	45	algebraic	algebraic	ADJ
ejpam-6418	62	46	properties	property	NOUN
ejpam-6418	62	47	,	,	PUNCT
ejpam-6418	62	48	and	and	CCONJ
ejpam-6418	62	49	provided	provide	VERB
ejpam-6418	62	50	a	a	DET
ejpam-6418	62	51	good	good	ADJ
ejpam-6418	62	52	number	number	NOUN
ejpam-6418	62	53	of	of	ADP
ejpam-6418	62	54	counter	counter	NOUN
ejpam-6418	62	55	-	-	NOUN
ejpam-6418	62	56	examples	example	NOUN
ejpam-6418	62	57	in	in	ADP
ejpam-6418	62	58	each	each	DET
ejpam-6418	62	59	case	case	NOUN
ejpam-6418	62	60	.	.	PUNCT
ejpam-6418	63	1	we	we	PRON
ejpam-6418	63	2	define	define	VERB
ejpam-6418	63	3	the	the	DET
ejpam-6418	63	4	center	center	NOUN
ejpam-6418	63	5	of	of	ADP
ejpam-6418	63	6	a	a	DET
ejpam-6418	63	7	paradistributive	paradistributive	ADJ
ejpam-6418	63	8	latticoid	latticoid	NOUN
ejpam-6418	63	9	using	use	VERB
ejpam-6418	63	10	compatibility	compatibility	NOUN
ejpam-6418	63	11	,	,	PUNCT
ejpam-6418	63	12	and	and	CCONJ
ejpam-6418	63	13	then	then	ADV
ejpam-6418	63	14	we	we	PRON
ejpam-6418	63	15	prove	prove	VERB
ejpam-6418	63	16	that	that	SCONJ
ejpam-6418	63	17	the	the	DET
ejpam-6418	63	18	center	center	NOUN
ejpam-6418	63	19	is	be	AUX
ejpam-6418	63	20	a	a	DET
ejpam-6418	63	21	filter	filter	NOUN
ejpam-6418	63	22	and	and	CCONJ
ejpam-6418	63	23	it	it	PRON
ejpam-6418	63	24	is	be	AUX
ejpam-6418	63	25	the	the	DET
ejpam-6418	63	26	intersection	intersection	NOUN
ejpam-6418	63	27	of	of	ADP
ejpam-6418	63	28	all	all	DET
ejpam-6418	63	29	maximal	maximal	ADJ
ejpam-6418	63	30	sets	set	NOUN
ejpam-6418	63	31	in	in	ADP
ejpam-6418	63	32	a	a	DET
ejpam-6418	63	33	paradistributive	paradistributive	ADJ
ejpam-6418	63	34	latticoid	latticoid	NOUN
ejpam-6418	63	35	.	.	PUNCT
ejpam-6418	64	1	finally	finally	ADV
ejpam-6418	64	2	,	,	PUNCT
ejpam-6418	64	3	we	we	PRON
ejpam-6418	64	4	define	define	VERB
ejpam-6418	64	5	amicable	amicable	ADJ
ejpam-6418	64	6	sets	set	NOUN
ejpam-6418	64	7	in	in	ADP
ejpam-6418	64	8	a	a	DET
ejpam-6418	64	9	paradistributive	paradistributive	ADJ
ejpam-6418	64	10	latticoid	latticoid	NOUN
ejpam-6418	64	11	and	and	CCONJ
ejpam-6418	64	12	then	then	ADV
ejpam-6418	64	13	we	we	PRON
ejpam-6418	64	14	characterize	characterize	VERB
ejpam-6418	64	15	paradistributive	paradistributive	ADJ
ejpam-6418	64	16	latticoids	latticoid	NOUN
ejpam-6418	64	17	using	use	VERB
ejpam-6418	64	18	amicable	amicable	ADJ
ejpam-6418	64	19	sets	set	NOUN
ejpam-6418	64	20	.	.	PUNCT
ejpam-6418	65	1	we	we	PRON
ejpam-6418	65	2	obtain	obtain	VERB
ejpam-6418	65	3	some	some	DET
ejpam-6418	65	4	necessary	necessary	ADJ
ejpam-6418	65	5	and	and	CCONJ
ejpam-6418	65	6	sufficient	sufficient	ADJ
ejpam-6418	65	7	conditions	condition	NOUN
ejpam-6418	65	8	for	for	ADP
ejpam-6418	65	9	a	a	DET
ejpam-6418	65	10	paradistributive	paradistributive	ADJ
ejpam-6418	65	11	latticoid	latticoid	NOUN
ejpam-6418	65	12	to	to	PART
ejpam-6418	65	13	become	become	VERB
ejpam-6418	65	14	relatively	relatively	ADV
ejpam-6418	65	15	complemented	complemented	ADJ
ejpam-6418	65	16	.	.	PUNCT
ejpam-6418	66	1	definition	definition	NOUN
ejpam-6418	66	2	3.1	3.1	NUM
ejpam-6418	66	3	.	.	PUNCT
ejpam-6418	67	1	an	an	DET
ejpam-6418	67	2	element	element	NOUN
ejpam-6418	67	3	a	a	DET
ejpam-6418	67	4	∈	∈	PROPN
ejpam-6418	67	5	v	v	NOUN
ejpam-6418	67	6	is	be	AUX
ejpam-6418	67	7	said	say	VERB
ejpam-6418	67	8	to	to	PART
ejpam-6418	67	9	be	be	AUX
ejpam-6418	67	10	compatible	compatible	ADJ
ejpam-6418	67	11	with	with	ADP
ejpam-6418	67	12	an	an	DET
ejpam-6418	67	13	element	element	NOUN
ejpam-6418	67	14	b	b	PROPN
ejpam-6418	67	15	∈	∈	PROPN
ejpam-6418	67	16	v	v	NOUN
ejpam-6418	67	17	,	,	PUNCT
ejpam-6418	67	18	if	if	SCONJ
ejpam-6418	67	19	a	a	DET
ejpam-6418	67	20	∨	∨	NUM
ejpam-6418	67	21	b	b	X
ejpam-6418	67	22	=	=	SYM
ejpam-6418	67	23	b	b	PROPN
ejpam-6418	67	24	∨	∨	NUM
ejpam-6418	67	25	a	a	PRON
ejpam-6418	67	26	or	or	CCONJ
ejpam-6418	67	27	equivalently	equivalently	ADV
ejpam-6418	67	28	a	a	DET
ejpam-6418	67	29	∧	∧	PROPN
ejpam-6418	67	30	b	b	NOUN
ejpam-6418	67	31	=	=	SYM
ejpam-6418	67	32	b	b	PROPN
ejpam-6418	67	33	∧	∧	PROPN
ejpam-6418	67	34	a	a	PRON
ejpam-6418	67	35	,	,	PUNCT
ejpam-6418	67	36	and	and	CCONJ
ejpam-6418	67	37	it	it	PRON
ejpam-6418	67	38	is	be	AUX
ejpam-6418	67	39	denoted	denote	VERB
ejpam-6418	67	40	by	by	ADP
ejpam-6418	67	41	a	a	DET
ejpam-6418	67	42	∼	∼	NOUN
ejpam-6418	67	43	b.	b.	NOUN
ejpam-6418	67	44	a	a	DET
ejpam-6418	67	45	subset	subset	NOUN
ejpam-6418	67	46	s	s	NOUN
ejpam-6418	67	47	of	of	ADP
ejpam-6418	67	48	v	v	NOUN
ejpam-6418	67	49	is	be	AUX
ejpam-6418	67	50	said	say	VERB
ejpam-6418	67	51	to	to	PART
ejpam-6418	67	52	be	be	AUX
ejpam-6418	67	53	compatible	compatible	ADJ
ejpam-6418	67	54	,	,	PUNCT
ejpam-6418	67	55	if	if	SCONJ
ejpam-6418	67	56	a	a	DET
ejpam-6418	67	57	∼	∼	NOUN
ejpam-6418	67	58	b	b	NOUN
ejpam-6418	67	59	,	,	PUNCT
ejpam-6418	67	60	for	for	ADP
ejpam-6418	67	61	all	all	DET
ejpam-6418	67	62	a	a	PRON
ejpam-6418	67	63	,	,	PUNCT
ejpam-6418	67	64	b	b	X
ejpam-6418	67	65	∈	∈	PROPN
ejpam-6418	67	66	s.	s.	PROPN
ejpam-6418	67	67	lemma	lemma	PROPN
ejpam-6418	67	68	3.2	3.2	NUM
ejpam-6418	67	69	.	.	PUNCT
ejpam-6418	68	1	for	for	ADP
ejpam-6418	68	2	any	any	DET
ejpam-6418	68	3	a	a	DET
ejpam-6418	68	4	,	,	PUNCT
ejpam-6418	68	5	b	b	NOUN
ejpam-6418	68	6	,	,	PUNCT
ejpam-6418	68	7	c	c	PROPN
ejpam-6418	68	8	∈	∈	PROPN
ejpam-6418	68	9	v	v	NOUN
ejpam-6418	68	10	,	,	PUNCT
ejpam-6418	68	11	we	we	PRON
ejpam-6418	68	12	have	have	VERB
ejpam-6418	68	13	the	the	DET
ejpam-6418	68	14	following	following	NOUN
ejpam-6418	68	15	;	;	PUNCT
ejpam-6418	68	16	(	(	PUNCT
ejpam-6418	68	17	i	i	NOUN
ejpam-6418	68	18	)	)	PUNCT
ejpam-6418	68	19	1	1	NUM
ejpam-6418	68	20	∼	∼	NOUN
ejpam-6418	68	21	a	a	DET
ejpam-6418	68	22	(	(	PUNCT
ejpam-6418	68	23	ii	ii	NOUN
ejpam-6418	68	24	)	)	PUNCT
ejpam-6418	68	25	∼	∼	NOUN
ejpam-6418	68	26	is	be	AUX
ejpam-6418	68	27	reflexive	reflexive	ADJ
ejpam-6418	68	28	(	(	PUNCT
ejpam-6418	68	29	iii	iii	NOUN
ejpam-6418	68	30	)	)	PUNCT
ejpam-6418	68	31	∼	∼	NOUN
ejpam-6418	68	32	is	be	AUX
ejpam-6418	68	33	symmetric	symmetric	ADJ
ejpam-6418	68	34	(	(	PUNCT
ejpam-6418	68	35	iv	iv	X
ejpam-6418	68	36	)	)	PUNCT
ejpam-6418	68	37	a	a	DET
ejpam-6418	68	38	≤	≤	PROPN
ejpam-6418	68	39	b	b	NOUN
ejpam-6418	69	1	=	=	NOUN
ejpam-6418	69	2	⇒	⇒	VERB
ejpam-6418	69	3	a	a	DET
ejpam-6418	69	4	∼	∼	NOUN
ejpam-6418	69	5	b	b	NOUN
ejpam-6418	69	6	(	(	PUNCT
ejpam-6418	69	7	v	v	NOUN
ejpam-6418	69	8	)	)	PUNCT
ejpam-6418	69	9	a	a	DET
ejpam-6418	69	10	∼	∼	NOUN
ejpam-6418	69	11	b	b	NOUN
ejpam-6418	69	12	=	=	NOUN
ejpam-6418	69	13	⇒	⇒	X
ejpam-6418	69	14	c	c	NOUN
ejpam-6418	69	15	∨	∨	NOUN
ejpam-6418	69	16	a	a	DET
ejpam-6418	69	17	∼	∼	NOUN
ejpam-6418	69	18	c	c	NOUN
ejpam-6418	69	19	∨	∨	NUM
ejpam-6418	69	20	b	b	PROPN
ejpam-6418	69	21	,	,	PUNCT
ejpam-6418	69	22	a	a	DET
ejpam-6418	69	23	∧	∧	PROPN
ejpam-6418	69	24	c	c	NOUN
ejpam-6418	69	25	∼	∼	NOUN
ejpam-6418	69	26	b	b	NOUN
ejpam-6418	69	27	∧	∧	PROPN
ejpam-6418	69	28	c	c	PROPN
ejpam-6418	69	29	,	,	PUNCT
ejpam-6418	69	30	a	a	DET
ejpam-6418	69	31	∨	∨	NOUN
ejpam-6418	69	32	c	c	NOUN
ejpam-6418	69	33	∼	∼	NOUN
ejpam-6418	69	34	b	b	PROPN
ejpam-6418	69	35	∨	∨	NOUN
ejpam-6418	69	36	c.	c.	PROPN
ejpam-6418	69	37	proof	proof	NOUN
ejpam-6418	69	38	.	.	PUNCT
ejpam-6418	70	1	let	let	VERB
ejpam-6418	70	2	a	a	DET
ejpam-6418	70	3	,	,	PUNCT
ejpam-6418	70	4	b	b	NOUN
ejpam-6418	70	5	,	,	PUNCT
ejpam-6418	70	6	c,∈	c,∈	NOUN
ejpam-6418	71	1	v.	v.	CCONJ
ejpam-6418	71	2	then	then	ADV
ejpam-6418	71	3	(	(	PUNCT
ejpam-6418	71	4	i	i	NOUN
ejpam-6418	71	5	)	)	PUNCT
ejpam-6418	71	6	a	a	DET
ejpam-6418	71	7	∧	∧	PROPN
ejpam-6418	71	8	1	1	NUM
ejpam-6418	71	9	=	=	SYM
ejpam-6418	71	10	a	a	PRON
ejpam-6418	71	11	=	=	SYM
ejpam-6418	71	12	1	1	NUM
ejpam-6418	71	13	∧	∧	PROPN
ejpam-6418	71	14	a	a	DET
ejpam-6418	71	15	⇒	⇒	NOUN
ejpam-6418	71	16	a	a	DET
ejpam-6418	71	17	∼	∼	NOUN
ejpam-6418	71	18	1	1	NUM
ejpam-6418	71	19	(	(	PUNCT
ejpam-6418	71	20	by	by	ADP
ejpam-6418	71	21	lemma	lemma	PROPN
ejpam-6418	71	22	2.4((i	2.4((i	NUM
ejpam-6418	71	23	)	)	PUNCT
ejpam-6418	71	24	&	&	CCONJ
ejpam-6418	71	25	(	(	PUNCT
ejpam-6418	71	26	ii	ii	NOUN
ejpam-6418	71	27	)	)	PUNCT
ejpam-6418	71	28	)	)	PUNCT
ejpam-6418	71	29	.	.	PUNCT
ejpam-6418	72	1	(	(	PUNCT
ejpam-6418	72	2	ii	ii	X
ejpam-6418	72	3	)	)	PUNCT
ejpam-6418	72	4	a	a	DET
ejpam-6418	72	5	∧	∧	PROPN
ejpam-6418	72	6	a	a	PRON
ejpam-6418	72	7	=	=	PUNCT
ejpam-6418	72	8	a	a	NOUN
ejpam-6418	72	9	=	=	X
ejpam-6418	72	10	a	a	DET
ejpam-6418	72	11	∧	∧	PROPN
ejpam-6418	72	12	a	a	DET
ejpam-6418	72	13	⇒	⇒	NOUN
ejpam-6418	72	14	a	a	DET
ejpam-6418	72	15	∼	∼	NOUN
ejpam-6418	72	16	a	a	PRON
ejpam-6418	72	17	(	(	PUNCT
ejpam-6418	72	18	by	by	ADP
ejpam-6418	72	19	lemma	lemma	PROPN
ejpam-6418	72	20	2.3(i	2.3(i	NUM
ejpam-6418	72	21	)	)	PUNCT
ejpam-6418	72	22	)	)	PUNCT
ejpam-6418	72	23	.	.	PUNCT
ejpam-6418	73	1	(	(	PUNCT
ejpam-6418	73	2	iii	iii	X
ejpam-6418	73	3	)	)	PUNCT
ejpam-6418	73	4	if	if	SCONJ
ejpam-6418	73	5	a	a	DET
ejpam-6418	73	6	∼	∼	NOUN
ejpam-6418	73	7	b	b	NOUN
ejpam-6418	73	8	,	,	PUNCT
ejpam-6418	73	9	then	then	ADV
ejpam-6418	73	10	a	a	DET
ejpam-6418	73	11	∧	∧	PROPN
ejpam-6418	73	12	b	b	PROPN
ejpam-6418	73	13	=	=	SYM
ejpam-6418	73	14	b	b	SYM
ejpam-6418	73	15	∧	∧	PROPN
ejpam-6418	73	16	a.	a.	NOUN
ejpam-6418	73	17	therefore	therefore	ADV
ejpam-6418	73	18	b	b	X
ejpam-6418	73	19	∼	∼	NOUN
ejpam-6418	73	20	a.	a.	NOUN
ejpam-6418	73	21	(	(	PUNCT
ejpam-6418	73	22	iv	iv	X
ejpam-6418	73	23	)	)	PUNCT
ejpam-6418	74	1	if	if	SCONJ
ejpam-6418	74	2	a	a	DET
ejpam-6418	74	3	≤	≤	NUM
ejpam-6418	74	4	b	b	NOUN
ejpam-6418	74	5	,	,	PUNCT
ejpam-6418	74	6	then	then	ADV
ejpam-6418	74	7	a∧b	a∧b	VERB
ejpam-6418	74	8	=	=	PUNCT
ejpam-6418	75	1	a.	a.	NOUN
ejpam-6418	75	2	now	now	ADV
ejpam-6418	75	3	,	,	PUNCT
ejpam-6418	75	4	b∧a	b∧a	ADV
ejpam-6418	75	5	=	=	SYM
ejpam-6418	75	6	b∧(a∧b	b∧(a∧b	PROPN
ejpam-6418	75	7	)	)	PUNCT
ejpam-6418	75	8	=	=	SYM
ejpam-6418	75	9	a∧b	a∧b	NOUN
ejpam-6418	75	10	(	(	PUNCT
ejpam-6418	75	11	by	by	ADP
ejpam-6418	75	12	lemma	lemma	PROPN
ejpam-6418	75	13	2.8(vi	2.8(vi	NUM
ejpam-6418	75	14	)	)	PUNCT
ejpam-6418	75	15	)	)	PUNCT
ejpam-6418	75	16	.	.	PUNCT
ejpam-6418	76	1	therefore	therefore	ADV
ejpam-6418	76	2	a	a	PRON
ejpam-6418	76	3	∼	∼	NOUN
ejpam-6418	76	4	b.	b.	NOUN
ejpam-6418	76	5	(	(	PUNCT
ejpam-6418	76	6	v	v	NOUN
ejpam-6418	76	7	)	)	PUNCT
ejpam-6418	76	8	suppose	suppose	VERB
ejpam-6418	76	9	a	a	DET
ejpam-6418	76	10	∼	∼	NOUN
ejpam-6418	76	11	b.	b.	NOUN
ejpam-6418	76	12	then	then	ADV
ejpam-6418	76	13	,	,	PUNCT
ejpam-6418	76	14	(	(	PUNCT
ejpam-6418	76	15	c	c	PROPN
ejpam-6418	76	16	∨	∨	NUM
ejpam-6418	76	17	a	a	PRON
ejpam-6418	76	18	)	)	PUNCT
ejpam-6418	76	19	∧	∧	NOUN
ejpam-6418	76	20	(	(	PUNCT
ejpam-6418	76	21	c	c	PROPN
ejpam-6418	76	22	∨	∨	NUM
ejpam-6418	76	23	b	b	NOUN
ejpam-6418	76	24	)	)	PUNCT
ejpam-6418	77	1	=	=	SYM
ejpam-6418	77	2	c	c	NOUN
ejpam-6418	77	3	∨	∨	NOUN
ejpam-6418	77	4	(	(	PUNCT
ejpam-6418	77	5	a	a	DET
ejpam-6418	77	6	∧	∧	PROPN
ejpam-6418	77	7	b	b	NOUN
ejpam-6418	77	8	)	)	PUNCT
ejpam-6418	77	9	(	(	PUNCT
ejpam-6418	77	10	by	by	ADP
ejpam-6418	77	11	definition	definition	NOUN
ejpam-6418	77	12	2.1(i	2.1(i	NUM
ejpam-6418	77	13	)	)	PUNCT
ejpam-6418	77	14	)	)	PUNCT
ejpam-6418	78	1	=	=	SYM
ejpam-6418	78	2	c	c	X
ejpam-6418	78	3	∨	∨	X
ejpam-6418	78	4	(	(	PUNCT
ejpam-6418	78	5	b	b	PROPN
ejpam-6418	78	6	∧	∧	PROPN
ejpam-6418	78	7	a	a	NOUN
ejpam-6418	78	8	)	)	PUNCT
ejpam-6418	78	9	(	(	PUNCT
ejpam-6418	78	10	by	by	ADP
ejpam-6418	78	11	lemma	lemma	PROPN
ejpam-6418	78	12	2.4(v	2.4(v	NUM
ejpam-6418	78	13	)	)	PUNCT
ejpam-6418	78	14	)	)	PUNCT
ejpam-6418	78	15	=(	=(	PROPN
ejpam-6418	78	16	c	c	PROPN
ejpam-6418	78	17	∨	∨	NUM
ejpam-6418	78	18	b	b	NOUN
ejpam-6418	78	19	)	)	PUNCT
ejpam-6418	78	20	∧	∧	NOUN
ejpam-6418	78	21	(	(	PUNCT
ejpam-6418	78	22	c	c	PROPN
ejpam-6418	78	23	∨	∨	PROPN
ejpam-6418	78	24	a	a	PRON
ejpam-6418	78	25	)	)	PUNCT
ejpam-6418	78	26	.	.	PUNCT
ejpam-6418	79	1	(	(	PUNCT
ejpam-6418	79	2	by	by	ADP
ejpam-6418	79	3	definition	definition	NOUN
ejpam-6418	79	4	2.1(i	2.1(i	NUM
ejpam-6418	79	5	)	)	PUNCT
ejpam-6418	79	6	)	)	PUNCT
ejpam-6418	79	7	therefore	therefore	ADV
ejpam-6418	79	8	c	c	PROPN
ejpam-6418	79	9	∨	∨	NUM
ejpam-6418	79	10	a	a	DET
ejpam-6418	79	11	∼	∼	NOUN
ejpam-6418	79	12	c	c	NOUN
ejpam-6418	79	13	∨	∨	PROPN
ejpam-6418	79	14	b.	b.	PROPN
ejpam-6418	79	15	now	now	ADV
ejpam-6418	79	16	,	,	PUNCT
ejpam-6418	79	17	(	(	PUNCT
ejpam-6418	79	18	a	a	DET
ejpam-6418	79	19	∧	∧	PROPN
ejpam-6418	79	20	c	c	NOUN
ejpam-6418	79	21	)	)	PUNCT
ejpam-6418	79	22	∨	∨	PROPN
ejpam-6418	79	23	(	(	PUNCT
ejpam-6418	79	24	b	b	PROPN
ejpam-6418	79	25	∧	∧	PROPN
ejpam-6418	79	26	c	c	NOUN
ejpam-6418	79	27	)	)	PUNCT
ejpam-6418	79	28	=	=	NOUN
ejpam-6418	80	1	(	(	PUNCT
ejpam-6418	80	2	a	a	DET
ejpam-6418	80	3	∨	∨	NUM
ejpam-6418	80	4	b	b	NOUN
ejpam-6418	80	5	)	)	PUNCT
ejpam-6418	80	6	∧	∧	PROPN
ejpam-6418	80	7	c	c	NOUN
ejpam-6418	80	8	(	(	PUNCT
ejpam-6418	80	9	by	by	ADP
ejpam-6418	80	10	lemma	lemma	PROPN
ejpam-6418	80	11	2.4(iv	2.4(iv	NUM
ejpam-6418	80	12	)	)	PUNCT
ejpam-6418	80	13	)	)	PUNCT
ejpam-6418	81	1	=	=	PRON
ejpam-6418	81	2	(	(	PUNCT
ejpam-6418	81	3	b	b	PROPN
ejpam-6418	81	4	∨	∨	NUM
ejpam-6418	81	5	a	a	PRON
ejpam-6418	81	6	)	)	PUNCT
ejpam-6418	81	7	∧	∧	PROPN
ejpam-6418	81	8	c	c	NOUN
ejpam-6418	81	9	(	(	PUNCT
ejpam-6418	81	10	since	since	SCONJ
ejpam-6418	81	11	a	a	DET
ejpam-6418	81	12	∼	∼	NOUN
ejpam-6418	81	13	b	b	NOUN
ejpam-6418	81	14	)	)	PUNCT
ejpam-6418	81	15	=	=	SYM
ejpam-6418	82	1	(	(	PUNCT
ejpam-6418	82	2	b	b	X
ejpam-6418	82	3	∧	∧	PROPN
ejpam-6418	82	4	c	c	NOUN
ejpam-6418	82	5	)	)	PUNCT
ejpam-6418	82	6	∨	∨	NOUN
ejpam-6418	82	7	(	(	PUNCT
ejpam-6418	82	8	a	a	DET
ejpam-6418	82	9	∧	∧	PROPN
ejpam-6418	82	10	c	c	NOUN
ejpam-6418	82	11	)	)	PUNCT
ejpam-6418	82	12	.	.	PUNCT
ejpam-6418	83	1	(	(	PUNCT
ejpam-6418	83	2	by	by	ADP
ejpam-6418	83	3	lemma	lemma	PROPN
ejpam-6418	83	4	2.4(iv	2.4(iv	NUM
ejpam-6418	83	5	)	)	PUNCT
ejpam-6418	83	6	)	)	PUNCT
ejpam-6418	83	7	therefore	therefore	ADV
ejpam-6418	83	8	a	a	DET
ejpam-6418	83	9	∧	∧	PROPN
ejpam-6418	83	10	c	c	NOUN
ejpam-6418	83	11	∼	∼	NOUN
ejpam-6418	83	12	b	b	NOUN
ejpam-6418	83	13	∧	∧	PROPN
ejpam-6418	83	14	c.	c.	NOUN
ejpam-6418	83	15	similarly	similarly	ADV
ejpam-6418	83	16	,	,	PUNCT
ejpam-6418	83	17	(	(	PUNCT
ejpam-6418	83	18	a	a	DET
ejpam-6418	83	19	∨	∨	NUM
ejpam-6418	83	20	c	c	NOUN
ejpam-6418	83	21	)	)	PUNCT
ejpam-6418	83	22	∧	∧	NOUN
ejpam-6418	83	23	(	(	PUNCT
ejpam-6418	83	24	b	b	PROPN
ejpam-6418	83	25	∨	∨	NUM
ejpam-6418	83	26	c	c	NOUN
ejpam-6418	83	27	)	)	PUNCT
ejpam-6418	83	28	=	=	NOUN
ejpam-6418	83	29	(	(	PUNCT
ejpam-6418	83	30	a	a	DET
ejpam-6418	83	31	∧	∧	PROPN
ejpam-6418	83	32	b	b	PROPN
ejpam-6418	83	33	)	)	PUNCT
ejpam-6418	83	34	∨	∨	PROPN
ejpam-6418	83	35	c	c	X
ejpam-6418	83	36	(	(	PUNCT
ejpam-6418	83	37	by	by	ADP
ejpam-6418	83	38	definition	definition	NOUN
ejpam-6418	83	39	2.1(ii	2.1(ii	NUM
ejpam-6418	83	40	)	)	PUNCT
ejpam-6418	83	41	)	)	PUNCT
ejpam-6418	84	1	=	=	PRON
ejpam-6418	84	2	(	(	PUNCT
ejpam-6418	84	3	b	b	X
ejpam-6418	84	4	∧	∧	PROPN
ejpam-6418	84	5	a	a	PRON
ejpam-6418	84	6	)	)	PUNCT
ejpam-6418	84	7	∨	∨	NUM
ejpam-6418	84	8	c	c	X
ejpam-6418	84	9	(	(	PUNCT
ejpam-6418	84	10	since	since	SCONJ
ejpam-6418	84	11	a	a	DET
ejpam-6418	84	12	∼	∼	NOUN
ejpam-6418	84	13	b	b	NOUN
ejpam-6418	84	14	)	)	PUNCT
ejpam-6418	84	15	=	=	SYM
ejpam-6418	85	1	(	(	PUNCT
ejpam-6418	85	2	b	b	PROPN
ejpam-6418	85	3	∨	∨	NUM
ejpam-6418	85	4	c	c	NOUN
ejpam-6418	85	5	)	)	PUNCT
ejpam-6418	85	6	∧	∧	NOUN
ejpam-6418	85	7	(	(	PUNCT
ejpam-6418	85	8	a	a	DET
ejpam-6418	85	9	∨	∨	NUM
ejpam-6418	85	10	c	c	NOUN
ejpam-6418	85	11	)	)	PUNCT
ejpam-6418	85	12	.	.	PUNCT
ejpam-6418	86	1	by	by	ADP
ejpam-6418	86	2	definition	definition	NOUN
ejpam-6418	86	3	2.1(ii	2.1(ii	NUM
ejpam-6418	86	4	)	)	PUNCT
ejpam-6418	86	5	)	)	PUNCT
ejpam-6418	87	1	r.	r.	PROPN
ejpam-6418	87	2	sirisetti	sirisetti	PROPN
ejpam-6418	87	3	et	et	PROPN
ejpam-6418	87	4	al	al	PROPN
ejpam-6418	87	5	.	.	PUNCT
ejpam-6418	87	6	/	/	SYM
ejpam-6418	87	7	eur	eur	PROPN
ejpam-6418	87	8	.	.	PUNCT
ejpam-6418	88	1	j.	j.	PROPN
ejpam-6418	88	2	pure	pure	PROPN
ejpam-6418	88	3	appl	appl	PROPN
ejpam-6418	88	4	.	.	PROPN
ejpam-6418	88	5	math	math	PROPN
ejpam-6418	88	6	,	,	PUNCT
ejpam-6418	88	7	18	18	NUM
ejpam-6418	88	8	(	(	PUNCT
ejpam-6418	88	9	4	4	NUM
ejpam-6418	88	10	)	)	PUNCT
ejpam-6418	88	11	(	(	PUNCT
ejpam-6418	88	12	2025	2025	NUM
ejpam-6418	88	13	)	)	PUNCT
ejpam-6418	88	14	,	,	PUNCT
ejpam-6418	88	15	6418	6418	NUM
ejpam-6418	88	16	6	6	NUM
ejpam-6418	88	17	of	of	ADP
ejpam-6418	88	18	13	13	NUM
ejpam-6418	88	19	therefore	therefore	ADV
ejpam-6418	88	20	a	a	DET
ejpam-6418	88	21	∨	∨	NOUN
ejpam-6418	88	22	c	c	NOUN
ejpam-6418	88	23	∼	∼	NOUN
ejpam-6418	88	24	b	b	PROPN
ejpam-6418	88	25	∨	∨	PROPN
ejpam-6418	88	26	c.	c.	PROPN
ejpam-6418	88	27	remark	remark	NOUN
ejpam-6418	88	28	3.3	3.3	NUM
ejpam-6418	88	29	.	.	PUNCT
ejpam-6418	89	1	given	give	VERB
ejpam-6418	89	2	a	a	DET
ejpam-6418	89	3	,	,	PUNCT
ejpam-6418	89	4	b	b	NOUN
ejpam-6418	89	5	,	,	PUNCT
ejpam-6418	89	6	c	c	PROPN
ejpam-6418	89	7	∈	∈	PROPN
ejpam-6418	89	8	v	v	NOUN
ejpam-6418	89	9	,	,	PUNCT
ejpam-6418	89	10	a	a	DET
ejpam-6418	89	11	∼	∼	NOUN
ejpam-6418	89	12	b	b	NOUN
ejpam-6418	89	13	does	do	AUX
ejpam-6418	89	14	not	not	PART
ejpam-6418	89	15	imply	imply	VERB
ejpam-6418	89	16	(	(	PUNCT
ejpam-6418	89	17	c	c	NOUN
ejpam-6418	89	18	∧	∧	PROPN
ejpam-6418	89	19	a	a	PRON
ejpam-6418	89	20	)	)	PUNCT
ejpam-6418	89	21	∼	∼	NOUN
ejpam-6418	89	22	(	(	PUNCT
ejpam-6418	89	23	c	c	NOUN
ejpam-6418	89	24	∧	∧	PROPN
ejpam-6418	89	25	b	b	PROPN
ejpam-6418	89	26	)	)	PUNCT
ejpam-6418	89	27	.	.	PUNCT
ejpam-6418	90	1	for	for	ADP
ejpam-6418	90	2	,	,	PUNCT
ejpam-6418	90	3	see	see	VERB
ejpam-6418	90	4	the	the	DET
ejpam-6418	90	5	following	follow	VERB
ejpam-6418	90	6	example	example	NOUN
ejpam-6418	90	7	;	;	PUNCT
ejpam-6418	90	8	example	example	NOUN
ejpam-6418	90	9	3.4	3.4	NUM
ejpam-6418	90	10	.	.	PUNCT
ejpam-6418	91	1	let	let	VERB
ejpam-6418	91	2	v	v	VERB
ejpam-6418	91	3	=	=	PUNCT
ejpam-6418	91	4	{	{	PUNCT
ejpam-6418	91	5	a	a	PRON
ejpam-6418	91	6	,	,	PUNCT
ejpam-6418	91	7	b	b	NOUN
ejpam-6418	91	8	,	,	PUNCT
ejpam-6418	91	9	c	c	NOUN
ejpam-6418	91	10	,	,	PUNCT
ejpam-6418	91	11	d	d	NOUN
ejpam-6418	91	12	,	,	PUNCT
ejpam-6418	91	13	1	1	NUM
ejpam-6418	91	14	}	}	PUNCT
ejpam-6418	91	15	be	be	AUX
ejpam-6418	91	16	a	a	DET
ejpam-6418	91	17	set	set	NOUN
ejpam-6418	91	18	with	with	ADP
ejpam-6418	91	19	binary	binary	ADJ
ejpam-6418	91	20	operations	operation	NOUN
ejpam-6418	91	21	∨	∨	NOUN
ejpam-6418	91	22	and	and	CCONJ
ejpam-6418	91	23	∧	∧	NOUN
ejpam-6418	91	24	given	give	VERB
ejpam-6418	91	25	in	in	ADP
ejpam-6418	91	26	the	the	DET
ejpam-6418	91	27	following	following	NOUN
ejpam-6418	91	28	;	;	PUNCT
ejpam-6418	91	29	∨	∨	NUM
ejpam-6418	91	30	a	a	DET
ejpam-6418	91	31	1	1	NUM
ejpam-6418	91	32	b	b	NOUN
ejpam-6418	91	33	c	c	NOUN
ejpam-6418	91	34	d	d	NOUN
ejpam-6418	91	35	a	a	DET
ejpam-6418	91	36	a	a	DET
ejpam-6418	91	37	1	1	NUM
ejpam-6418	91	38	a	a	PRON
ejpam-6418	91	39	c	c	NOUN
ejpam-6418	91	40	c	c	NOUN
ejpam-6418	91	41	1	1	NUM
ejpam-6418	91	42	1	1	NUM
ejpam-6418	91	43	1	1	NUM
ejpam-6418	91	44	1	1	NUM
ejpam-6418	91	45	1	1	NUM
ejpam-6418	91	46	1	1	NUM
ejpam-6418	91	47	b	b	SYM
ejpam-6418	91	48	b	b	PROPN
ejpam-6418	91	49	1	1	NUM
ejpam-6418	91	50	b	b	PROPN
ejpam-6418	91	51	d	d	PROPN
ejpam-6418	91	52	d	d	X
ejpam-6418	91	53	c	c	NOUN
ejpam-6418	91	54	c	c	NOUN
ejpam-6418	91	55	1	1	NUM
ejpam-6418	91	56	c	c	NOUN
ejpam-6418	91	57	c	c	NOUN
ejpam-6418	91	58	c	c	NOUN
ejpam-6418	92	1	d	d	X
ejpam-6418	92	2	d	d	PROPN
ejpam-6418	92	3	1	1	NUM
ejpam-6418	92	4	d	d	NOUN
ejpam-6418	92	5	d	d	PROPN
ejpam-6418	92	6	d	d	X
ejpam-6418	92	7	∧	∧	PROPN
ejpam-6418	92	8	a	a	PRON
ejpam-6418	92	9	1	1	NUM
ejpam-6418	92	10	b	b	NOUN
ejpam-6418	92	11	c	c	NOUN
ejpam-6418	92	12	d	d	NOUN
ejpam-6418	92	13	a	a	PRON
ejpam-6418	92	14	a	a	PRON
ejpam-6418	92	15	a	a	DET
ejpam-6418	92	16	b	b	NOUN
ejpam-6418	92	17	a	a	DET
ejpam-6418	92	18	b	b	NOUN
ejpam-6418	92	19	1	1	NUM
ejpam-6418	92	20	a	a	DET
ejpam-6418	92	21	1	1	NUM
ejpam-6418	92	22	b	b	NOUN
ejpam-6418	92	23	c	c	NOUN
ejpam-6418	92	24	d	d	PROPN
ejpam-6418	92	25	b	b	PROPN
ejpam-6418	92	26	a	a	DET
ejpam-6418	92	27	b	b	PROPN
ejpam-6418	92	28	b	b	PROPN
ejpam-6418	92	29	a	a	DET
ejpam-6418	92	30	b	b	NOUN
ejpam-6418	92	31	c	c	NOUN
ejpam-6418	92	32	a	a	DET
ejpam-6418	92	33	c	c	NOUN
ejpam-6418	92	34	b	b	PROPN
ejpam-6418	92	35	c	c	NOUN
ejpam-6418	92	36	d	d	PROPN
ejpam-6418	92	37	d	d	PROPN
ejpam-6418	92	38	a	a	PROPN
ejpam-6418	92	39	d	d	X
ejpam-6418	92	40	b	b	PROPN
ejpam-6418	92	41	c	c	NOUN
ejpam-6418	93	1	d	d	X
ejpam-6418	93	2	then	then	ADV
ejpam-6418	93	3	(	(	PUNCT
ejpam-6418	93	4	v,∨,∧	v,∨,∧	NOUN
ejpam-6418	93	5	,	,	PUNCT
ejpam-6418	93	6	1	1	NUM
ejpam-6418	93	7	)	)	PUNCT
ejpam-6418	93	8	is	be	AUX
ejpam-6418	93	9	a	a	DET
ejpam-6418	93	10	paradistributive	paradistributive	ADJ
ejpam-6418	93	11	latticoid	latticoid	NOUN
ejpam-6418	93	12	,	,	PUNCT
ejpam-6418	93	13	and	and	CCONJ
ejpam-6418	93	14	1	1	NUM
ejpam-6418	93	15	∼	∼	NOUN
ejpam-6418	93	16	b	b	NOUN
ejpam-6418	93	17	but	but	CCONJ
ejpam-6418	93	18	(	(	PUNCT
ejpam-6418	93	19	c∧	c∧	PROPN
ejpam-6418	93	20	1)∨	1)∨	PROPN
ejpam-6418	93	21	(	(	PUNCT
ejpam-6418	93	22	c∧	c∧	PROPN
ejpam-6418	93	23	b	b	NOUN
ejpam-6418	93	24	)	)	PUNCT
ejpam-6418	93	25	̸=	̸=	PROPN
ejpam-6418	93	26	(	(	PUNCT
ejpam-6418	93	27	c∧	c∧	ADJ
ejpam-6418	93	28	b)∨	b)∨	PROPN
ejpam-6418	93	29	(	(	PUNCT
ejpam-6418	93	30	c	c	NOUN
ejpam-6418	93	31	∧	∧	PROPN
ejpam-6418	93	32	1	1	NUM
ejpam-6418	93	33	)	)	PUNCT
ejpam-6418	93	34	)	)	PUNCT
ejpam-6418	93	35	.	.	PUNCT
ejpam-6418	94	1	theorem	theorem	VERB
ejpam-6418	94	2	3.5	3.5	NUM
ejpam-6418	94	3	.	.	PUNCT
ejpam-6418	95	1	v	v	NOUN
ejpam-6418	95	2	is	be	AUX
ejpam-6418	95	3	distributive	distributive	ADJ
ejpam-6418	95	4	if	if	SCONJ
ejpam-6418	96	1	and	and	CCONJ
ejpam-6418	96	2	only	only	ADV
ejpam-6418	96	3	if	if	SCONJ
ejpam-6418	96	4	a	a	DET
ejpam-6418	96	5	∼	∼	NOUN
ejpam-6418	96	6	b	b	NOUN
ejpam-6418	96	7	implies	imply	VERB
ejpam-6418	96	8	c∧a	c∧a	VERB
ejpam-6418	96	9	∼	∼	NOUN
ejpam-6418	96	10	c∧b	c∧b	NOUN
ejpam-6418	96	11	,	,	PUNCT
ejpam-6418	96	12	for	for	ADP
ejpam-6418	96	13	all	all	DET
ejpam-6418	96	14	a	a	DET
ejpam-6418	96	15	,	,	PUNCT
ejpam-6418	96	16	b	b	NOUN
ejpam-6418	96	17	,	,	PUNCT
ejpam-6418	96	18	c	c	PROPN
ejpam-6418	96	19	∈	∈	PROPN
ejpam-6418	96	20	v.	v.	ADP
ejpam-6418	96	21	proof	proof	NOUN
ejpam-6418	96	22	.	.	PUNCT
ejpam-6418	97	1	if	if	SCONJ
ejpam-6418	97	2	v	v	NOUN
ejpam-6418	97	3	is	be	AUX
ejpam-6418	97	4	distributive	distributive	ADJ
ejpam-6418	97	5	,	,	PUNCT
ejpam-6418	97	6	then	then	ADV
ejpam-6418	97	7	it	it	PRON
ejpam-6418	97	8	is	be	AUX
ejpam-6418	97	9	easy	easy	ADJ
ejpam-6418	97	10	to	to	PART
ejpam-6418	97	11	verify	verify	VERB
ejpam-6418	97	12	the	the	DET
ejpam-6418	97	13	result	result	NOUN
ejpam-6418	97	14	.	.	PUNCT
ejpam-6418	98	1	on	on	ADP
ejpam-6418	98	2	the	the	DET
ejpam-6418	98	3	other	other	ADJ
ejpam-6418	98	4	hand	hand	NOUN
ejpam-6418	98	5	,	,	PUNCT
ejpam-6418	98	6	let	let	VERB
ejpam-6418	98	7	a	a	DET
ejpam-6418	98	8	,	,	PUNCT
ejpam-6418	98	9	b	b	PROPN
ejpam-6418	98	10	∈	∈	PROPN
ejpam-6418	98	11	l.	l.	NOUN
ejpam-6418	98	12	by	by	ADP
ejpam-6418	98	13	our	our	PRON
ejpam-6418	98	14	assumption	assumption	NOUN
ejpam-6418	98	15	,	,	PUNCT
ejpam-6418	98	16	b	b	PROPN
ejpam-6418	98	17	∧	∧	NOUN
ejpam-6418	98	18	1	1	NUM
ejpam-6418	98	19	∼	∼	NOUN
ejpam-6418	98	20	b	b	NOUN
ejpam-6418	98	21	∧	∧	PROPN
ejpam-6418	98	22	a	a	PRON
ejpam-6418	98	23	(	(	PUNCT
ejpam-6418	98	24	that	that	ADV
ejpam-6418	98	25	is	is	ADV
ejpam-6418	98	26	(	(	PUNCT
ejpam-6418	98	27	b	b	PROPN
ejpam-6418	98	28	∧	∧	PROPN
ejpam-6418	98	29	1	1	NUM
ejpam-6418	98	30	)	)	PUNCT
ejpam-6418	98	31	∨	∨	NOUN
ejpam-6418	98	32	(	(	PUNCT
ejpam-6418	98	33	b	b	PROPN
ejpam-6418	98	34	∧	∧	PROPN
ejpam-6418	98	35	a	a	NOUN
ejpam-6418	98	36	)	)	PUNCT
ejpam-6418	98	37	=	=	PUNCT
ejpam-6418	98	38	(	(	PUNCT
ejpam-6418	98	39	b	b	X
ejpam-6418	98	40	∧	∧	PROPN
ejpam-6418	98	41	a	a	PRON
ejpam-6418	98	42	)	)	PUNCT
ejpam-6418	98	43	∨	∨	NOUN
ejpam-6418	98	44	(	(	PUNCT
ejpam-6418	98	45	b	b	PROPN
ejpam-6418	98	46	∧	∧	PROPN
ejpam-6418	98	47	1	1	NUM
ejpam-6418	98	48	)	)	PUNCT
ejpam-6418	98	49	)	)	PUNCT
ejpam-6418	98	50	.	.	PUNCT
ejpam-6418	99	1	so	so	ADV
ejpam-6418	99	2	that	that	PRON
ejpam-6418	99	3	b	b	X
ejpam-6418	99	4	∨	∨	X
ejpam-6418	99	5	(	(	PUNCT
ejpam-6418	99	6	b	b	PROPN
ejpam-6418	99	7	∧	∧	PROPN
ejpam-6418	99	8	a	a	NOUN
ejpam-6418	99	9	)	)	PUNCT
ejpam-6418	99	10	=	=	PUNCT
ejpam-6418	99	11	(	(	PUNCT
ejpam-6418	99	12	b	b	X
ejpam-6418	99	13	∧	∧	PROPN
ejpam-6418	99	14	a	a	PRON
ejpam-6418	99	15	)	)	PUNCT
ejpam-6418	99	16	∨	∨	PROPN
ejpam-6418	99	17	b.	b.	PROPN
ejpam-6418	99	18	by	by	ADP
ejpam-6418	99	19	definition	definition	NOUN
ejpam-6418	99	20	2.1(v	2.1(v	NUM
ejpam-6418	99	21	)	)	PUNCT
ejpam-6418	99	22	.	.	PUNCT
ejpam-6418	99	23	,	,	PUNCT
ejpam-6418	99	24	b	b	X
ejpam-6418	99	25	=	=	SYM
ejpam-6418	99	26	(	(	PUNCT
ejpam-6418	99	27	b	b	PROPN
ejpam-6418	99	28	∧	∧	PROPN
ejpam-6418	99	29	a	a	PRON
ejpam-6418	99	30	)	)	PUNCT
ejpam-6418	99	31	∨	∨	PROPN
ejpam-6418	99	32	b.	b.	PROPN
ejpam-6418	99	33	therefore	therefore	ADV
ejpam-6418	99	34	v	v	NOUN
ejpam-6418	99	35	is	be	AUX
ejpam-6418	99	36	a	a	DET
ejpam-6418	99	37	distributive	distributive	ADJ
ejpam-6418	99	38	lattice	lattice	NOUN
ejpam-6418	99	39	(	(	PUNCT
ejpam-6418	99	40	by	by	ADP
ejpam-6418	99	41	theorem	theorem	NOUN
ejpam-6418	99	42	2.9	2.9	NUM
ejpam-6418	99	43	.	.	PUNCT
ejpam-6418	99	44	)	)	PUNCT
ejpam-6418	99	45	.	.	PUNCT
ejpam-6418	100	1	example	example	NOUN
ejpam-6418	100	2	3.6	3.6	NUM
ejpam-6418	100	3	.	.	PUNCT
ejpam-6418	101	1	let	let	VERB
ejpam-6418	101	2	i	i	PRON
ejpam-6418	101	3	be	be	AUX
ejpam-6418	101	4	a	a	DET
ejpam-6418	101	5	non	non	ADJ
ejpam-6418	101	6	-	-	ADJ
ejpam-6418	101	7	empty	empty	ADJ
ejpam-6418	101	8	set	set	NOUN
ejpam-6418	101	9	and	and	CCONJ
ejpam-6418	101	10	v	v	NOUN
ejpam-6418	101	11	is	be	AUX
ejpam-6418	101	12	a	a	DET
ejpam-6418	101	13	disconnected	disconnected	ADJ
ejpam-6418	101	14	pdl	pdl	NOUN
ejpam-6418	101	15	.	.	PUNCT
ejpam-6418	102	1	then	then	ADV
ejpam-6418	102	2	(	(	PUNCT
ejpam-6418	102	3	vi	vi	PROPN
ejpam-6418	102	4	,	,	PUNCT
ejpam-6418	102	5	∨,∧	∨,∧	PROPN
ejpam-6418	102	6	,	,	PUNCT
ejpam-6418	102	7	1	1	NUM
ejpam-6418	102	8	)	)	PUNCT
ejpam-6418	102	9	is	be	AUX
ejpam-6418	102	10	a	a	DET
ejpam-6418	102	11	pdl	pdl	NOUN
ejpam-6418	102	12	with	with	ADP
ejpam-6418	102	13	respect	respect	NOUN
ejpam-6418	102	14	to	to	ADP
ejpam-6418	102	15	the	the	DET
ejpam-6418	102	16	point	point	NOUN
ejpam-6418	102	17	wise	wise	ADJ
ejpam-6418	102	18	operations	operation	NOUN
ejpam-6418	102	19	,	,	PUNCT
ejpam-6418	102	20	where	where	SCONJ
ejpam-6418	102	21	1̄	1̄	NUM
ejpam-6418	102	22	:	:	PUNCT
ejpam-6418	102	23	i	i	PRON
ejpam-6418	102	24	→	→	SYM
ejpam-6418	102	25	v	v	NOUN
ejpam-6418	102	26	defined	define	VERB
ejpam-6418	102	27	by	by	ADP
ejpam-6418	102	28	1̄(i	1̄(i	NUM
ejpam-6418	102	29	)	)	PUNCT
ejpam-6418	102	30	=	=	SYM
ejpam-6418	102	31	1	1	NUM
ejpam-6418	102	32	for	for	ADP
ejpam-6418	102	33	all	all	PRON
ejpam-6418	102	34	i	i	PRON
ejpam-6418	102	35	∈	∈	PROPN
ejpam-6418	103	1	i	i	PRON
ejpam-6418	103	2	,	,	PUNCT
ejpam-6418	103	3	is	be	AUX
ejpam-6418	103	4	the	the	DET
ejpam-6418	103	5	greatest	great	ADJ
ejpam-6418	103	6	element	element	NOUN
ejpam-6418	103	7	in	in	ADP
ejpam-6418	103	8	v.	v.	ADP
ejpam-6418	103	9	in	in	ADP
ejpam-6418	103	10	this	this	DET
ejpam-6418	103	11	v	v	NOUN
ejpam-6418	103	12	,	,	PUNCT
ejpam-6418	103	13	for	for	ADP
ejpam-6418	103	14	any	any	DET
ejpam-6418	103	15	x	x	NOUN
ejpam-6418	103	16	,	,	PUNCT
ejpam-6418	103	17	y	y	PROPN
ejpam-6418	103	18	∈	∈	PROPN
ejpam-6418	103	19	v	v	NOUN
ejpam-6418	103	20	,	,	PUNCT
ejpam-6418	103	21	we	we	PRON
ejpam-6418	103	22	have	have	AUX
ejpam-6418	103	23	(	(	PUNCT
ejpam-6418	103	24	i	i	NOUN
ejpam-6418	103	25	)	)	PUNCT
ejpam-6418	103	26	x	x	PUNCT
ejpam-6418	103	27	∼	∼	NOUN
ejpam-6418	103	28	y	y	PROPN
ejpam-6418	103	29	if	if	SCONJ
ejpam-6418	103	30	and	and	CCONJ
ejpam-6418	103	31	only	only	ADV
ejpam-6418	103	32	if	if	SCONJ
ejpam-6418	103	33	x||x|∩|y|	x||x|∩|y|	PROPN
ejpam-6418	103	34	=	=	SYM
ejpam-6418	103	35	y||x|∩|y|	y||x|∩|y|	PROPN
ejpam-6418	103	36	and	and	CCONJ
ejpam-6418	103	37	(	(	PUNCT
ejpam-6418	103	38	ii	ii	NOUN
ejpam-6418	103	39	)	)	PUNCT
ejpam-6418	103	40	x	x	SYM
ejpam-6418	103	41	≤	≤	ADJ
ejpam-6418	103	42	y	y	NOUN
ejpam-6418	104	1	if	if	SCONJ
ejpam-6418	104	2	and	and	CCONJ
ejpam-6418	104	3	only	only	ADV
ejpam-6418	104	4	if	if	SCONJ
ejpam-6418	104	5	x|x|	x|x|	PROPN
ejpam-6418	104	6	=	=	SYM
ejpam-6418	104	7	y|y|	y|y|	PROPN
ejpam-6418	104	8	,	,	PUNCT
ejpam-6418	104	9	where	where	SCONJ
ejpam-6418	104	10	|x|	|x|	PROPN
ejpam-6418	104	11	=	=	PRON
ejpam-6418	104	12	{	{	PUNCT
ejpam-6418	104	13	i	i	NOUN
ejpam-6418	104	14	∈	∈	PROPN
ejpam-6418	104	15	i|x(i	i|x(i	ADJ
ejpam-6418	104	16	)	)	PUNCT
ejpam-6418	104	17	̸=	̸=	PROPN
ejpam-6418	104	18	1	1	NUM
ejpam-6418	104	19	}	}	PUNCT
ejpam-6418	104	20	.	.	PUNCT
ejpam-6418	105	1	example	example	NOUN
ejpam-6418	105	2	3.7	3.7	NUM
ejpam-6418	105	3	.	.	PUNCT
ejpam-6418	106	1	let	let	VERB
ejpam-6418	106	2	r	r	PRON
ejpam-6418	106	3	be	be	AUX
ejpam-6418	106	4	a	a	DET
ejpam-6418	106	5	commutative	commutative	ADJ
ejpam-6418	106	6	regular	regular	ADJ
ejpam-6418	106	7	ring	ring	NOUN
ejpam-6418	106	8	with	with	ADP
ejpam-6418	106	9	unity	unity	NOUN
ejpam-6418	106	10	[	[	X
ejpam-6418	106	11	1	1	NUM
ejpam-6418	106	12	]	]	PUNCT
ejpam-6418	106	13	.	.	PUNCT
ejpam-6418	107	1	for	for	ADP
ejpam-6418	107	2	any	any	DET
ejpam-6418	107	3	a	a	PRON
ejpam-6418	107	4	,	,	PUNCT
ejpam-6418	107	5	b	b	X
ejpam-6418	107	6	∈	∈	PROPN
ejpam-6418	107	7	r	r	NOUN
ejpam-6418	107	8	,	,	PUNCT
ejpam-6418	107	9	a	a	DET
ejpam-6418	107	10	∼	∼	NOUN
ejpam-6418	107	11	b	b	NOUN
ejpam-6418	107	12	if	if	SCONJ
ejpam-6418	107	13	and	and	CCONJ
ejpam-6418	107	14	only	only	ADV
ejpam-6418	107	15	if	if	SCONJ
ejpam-6418	107	16	ab2	ab2	ADJ
ejpam-6418	107	17	=	=	SYM
ejpam-6418	107	18	a2b	a2b	NOUN
ejpam-6418	107	19	.	.	PUNCT
ejpam-6418	108	1	for	for	ADP
ejpam-6418	108	2	any	any	DET
ejpam-6418	108	3	a	a	PRON
ejpam-6418	108	4	,	,	PUNCT
ejpam-6418	108	5	b	b	PROPN
ejpam-6418	108	6	∈	∈	PROPN
ejpam-6418	108	7	v	v	NOUN
ejpam-6418	108	8	,	,	PUNCT
ejpam-6418	108	9	a	a	DET
ejpam-6418	108	10	∼	∼	NOUN
ejpam-6418	108	11	b	b	NOUN
ejpam-6418	108	12	⇒	⇒	NOUN
ejpam-6418	108	13	a	a	DET
ejpam-6418	108	14	∨	∨	NOUN
ejpam-6418	108	15	b	b	X
ejpam-6418	108	16	=	=	SYM
ejpam-6418	108	17	b	b	PROPN
ejpam-6418	108	18	∨	∨	NUM
ejpam-6418	108	19	a	a	DET
ejpam-6418	108	20	⇒	⇒	NOUN
ejpam-6418	108	21	b0a	b0a	PROPN
ejpam-6418	108	22	=	=	SYM
ejpam-6418	108	23	a0b	a0b	PROPN
ejpam-6418	108	24	(	(	PUNCT
ejpam-6418	108	25	a	a	DET
ejpam-6418	108	26	∨	∨	NUM
ejpam-6418	108	27	b	b	NOUN
ejpam-6418	108	28	=	=	PUNCT
ejpam-6418	108	29	b0a	b0a	PROPN
ejpam-6418	108	30	)	)	PUNCT
ejpam-6418	108	31	⇒	⇒	NOUN
ejpam-6418	108	32	bb0a	bb0a	VERB
ejpam-6418	108	33	=	=	SYM
ejpam-6418	108	34	ba0b	ba0b	PROPN
ejpam-6418	108	35	⇒	⇒	VERB
ejpam-6418	108	36	ba	ba	PROPN
ejpam-6418	109	1	=	=	PUNCT
ejpam-6418	109	2	b2a0	b2a0	PROPN
ejpam-6418	109	3	(	(	PUNCT
ejpam-6418	109	4	bb0	bb0	PROPN
ejpam-6418	109	5	=	=	SYM
ejpam-6418	109	6	b	b	PROPN
ejpam-6418	109	7	)	)	PUNCT
ejpam-6418	109	8	⇒	⇒	PROPN
ejpam-6418	109	9	baa	baa	PROPN
ejpam-6418	109	10	=	=	SYM
ejpam-6418	109	11	b2a0a	b2a0a	PUNCT
ejpam-6418	109	12	⇒	⇒	PROPN
ejpam-6418	109	13	ba2	ba2	PROPN
ejpam-6418	109	14	=	=	SYM
ejpam-6418	109	15	b2a	b2a	PROPN
ejpam-6418	109	16	(	(	PUNCT
ejpam-6418	109	17	a0a	a0a	PROPN
ejpam-6418	109	18	=	=	SYM
ejpam-6418	109	19	a	a	PRON
ejpam-6418	109	20	)	)	PUNCT
ejpam-6418	109	21	⇒	⇒	VERB
ejpam-6418	109	22	a2b	a2b	NOUN
ejpam-6418	109	23	=	=	PUNCT
ejpam-6418	109	24	ab2	ab2	PROPN
ejpam-6418	109	25	.	.	PUNCT
ejpam-6418	110	1	(	(	PUNCT
ejpam-6418	110	2	commutative	commutative	ADJ
ejpam-6418	110	3	)	)	PUNCT
ejpam-6418	110	4	now	now	ADV
ejpam-6418	110	5	,	,	PUNCT
ejpam-6418	110	6	a2b	a2b	PROPN
ejpam-6418	110	7	=	=	PUNCT
ejpam-6418	110	8	ab2	ab2	ADJ
ejpam-6418	110	9	⇒	⇒	NOUN
ejpam-6418	110	10	ab(a−	ab(a−	PUNCT
ejpam-6418	110	11	b	b	X
ejpam-6418	110	12	)	)	PUNCT
ejpam-6418	110	13	=	=	SYM
ejpam-6418	110	14	0	0	NUM
ejpam-6418	110	15	⇒	⇒	PROPN
ejpam-6418	110	16	a0b0(a−	a0b0(a−	NOUN
ejpam-6418	110	17	b	b	X
ejpam-6418	110	18	)	)	PUNCT
ejpam-6418	110	19	=	=	SYM
ejpam-6418	110	20	0	0	NUM
ejpam-6418	110	21	(	(	PUNCT
ejpam-6418	110	22	ar	ar	NOUN
ejpam-6418	110	23	=	=	PUNCT
ejpam-6418	110	24	a0r	a0r	NOUN
ejpam-6418	110	25	)	)	PUNCT
ejpam-6418	110	26	⇒	⇒	NOUN
ejpam-6418	110	27	a0b0a−	a0b0a−	PUNCT
ejpam-6418	110	28	a0b0b	a0b0b	NUM
ejpam-6418	110	29	=	=	SYM
ejpam-6418	110	30	0	0	NUM
ejpam-6418	110	31	⇒	⇒	NOUN
ejpam-6418	110	32	b0a0a	b0a0a	NUM
ejpam-6418	111	1	=	=	SYM
ejpam-6418	111	2	a0b	a0b	PROPN
ejpam-6418	111	3	(	(	PUNCT
ejpam-6418	111	4	bb0	bb0	PROPN
ejpam-6418	111	5	=	=	SYM
ejpam-6418	111	6	b	b	PROPN
ejpam-6418	111	7	)	)	PUNCT
ejpam-6418	111	8	⇒	⇒	NOUN
ejpam-6418	111	9	b0a	b0a	PROPN
ejpam-6418	111	10	=	=	SYM
ejpam-6418	111	11	a0b	a0b	PROPN
ejpam-6418	111	12	(	(	PUNCT
ejpam-6418	111	13	aa0	aa0	NOUN
ejpam-6418	111	14	=	=	SYM
ejpam-6418	111	15	a	a	X
ejpam-6418	111	16	)	)	PUNCT
ejpam-6418	111	17	⇒	⇒	VERB
ejpam-6418	111	18	a	a	DET
ejpam-6418	111	19	∧	∧	PROPN
ejpam-6418	111	20	b	b	PROPN
ejpam-6418	111	21	=	=	SYM
ejpam-6418	111	22	b	b	PROPN
ejpam-6418	111	23	∧	∧	PROPN
ejpam-6418	111	24	a.	a.	PROPN
ejpam-6418	111	25	r.	r.	PROPN
ejpam-6418	111	26	sirisetti	sirisetti	PROPN
ejpam-6418	111	27	et	et	PROPN
ejpam-6418	111	28	al	al	PROPN
ejpam-6418	111	29	.	.	PUNCT
ejpam-6418	111	30	/	/	SYM
ejpam-6418	111	31	eur	eur	PROPN
ejpam-6418	111	32	.	.	PUNCT
ejpam-6418	112	1	j.	j.	PROPN
ejpam-6418	112	2	pure	pure	PROPN
ejpam-6418	112	3	appl	appl	PROPN
ejpam-6418	112	4	.	.	PROPN
ejpam-6418	112	5	math	math	PROPN
ejpam-6418	112	6	,	,	PUNCT
ejpam-6418	112	7	18	18	NUM
ejpam-6418	112	8	(	(	PUNCT
ejpam-6418	112	9	4	4	NUM
ejpam-6418	112	10	)	)	PUNCT
ejpam-6418	112	11	(	(	PUNCT
ejpam-6418	112	12	2025	2025	NUM
ejpam-6418	112	13	)	)	PUNCT
ejpam-6418	112	14	,	,	PUNCT
ejpam-6418	112	15	6418	6418	NUM
ejpam-6418	112	16	7	7	NUM
ejpam-6418	112	17	of	of	ADP
ejpam-6418	112	18	13	13	NUM
ejpam-6418	112	19	therefore	therefore	ADV
ejpam-6418	112	20	a	a	DET
ejpam-6418	112	21	∼	∼	NOUN
ejpam-6418	112	22	b.	b.	NOUN
ejpam-6418	112	23	definition	definition	NOUN
ejpam-6418	112	24	3.8	3.8	NUM
ejpam-6418	112	25	.	.	PUNCT
ejpam-6418	113	1	a	a	DET
ejpam-6418	113	2	maximal	maximal	ADJ
ejpam-6418	113	3	compatible	compatible	ADJ
ejpam-6418	113	4	set	set	NOUN
ejpam-6418	113	5	in	in	ADP
ejpam-6418	113	6	v	v	NOUN
ejpam-6418	113	7	is	be	AUX
ejpam-6418	113	8	called	call	VERB
ejpam-6418	113	9	a	a	DET
ejpam-6418	113	10	maximal	maximal	ADJ
ejpam-6418	113	11	set	set	NOUN
ejpam-6418	113	12	.	.	PUNCT
ejpam-6418	114	1	example	example	NOUN
ejpam-6418	114	2	3.9	3.9	NUM
ejpam-6418	114	3	.	.	PUNCT
ejpam-6418	115	1	in	in	ADP
ejpam-6418	115	2	the	the	DET
ejpam-6418	115	3	example	example	NOUN
ejpam-6418	115	4	2.2	2.2	NUM
ejpam-6418	115	5	.	.	NUM
ejpam-6418	115	6	,	,	PUNCT
ejpam-6418	115	7	{	{	PUNCT
ejpam-6418	115	8	x	x	NOUN
ejpam-6418	115	9	,	,	PUNCT
ejpam-6418	115	10	1	1	NUM
ejpam-6418	115	11	}	}	PUNCT
ejpam-6418	115	12	is	be	AUX
ejpam-6418	115	13	a	a	DET
ejpam-6418	115	14	maximal	maximal	ADJ
ejpam-6418	115	15	set	set	NOUN
ejpam-6418	115	16	,	,	PUNCT
ejpam-6418	115	17	for	for	ADP
ejpam-6418	115	18	any	any	DET
ejpam-6418	115	19	x	x	SYM
ejpam-6418	115	20	∈	∈	PROPN
ejpam-6418	115	21	v	v	NOUN
ejpam-6418	115	22	and	and	CCONJ
ejpam-6418	115	23	x	x	SYM
ejpam-6418	115	24	̸=	̸=	PROPN
ejpam-6418	115	25	1	1	NUM
ejpam-6418	115	26	.	.	PUNCT
ejpam-6418	115	27	example	example	NOUN
ejpam-6418	116	1	3.10	3.10	NUM
ejpam-6418	116	2	.	.	PUNCT
ejpam-6418	117	1	let	let	VERB
ejpam-6418	117	2	v	v	PART
ejpam-6418	117	3	be	be	AUX
ejpam-6418	117	4	a	a	DET
ejpam-6418	117	5	disconnected	disconnected	ADJ
ejpam-6418	117	6	pdl	pdl	NOUN
ejpam-6418	117	7	,	,	PUNCT
ejpam-6418	117	8	i	i	PRON
ejpam-6418	117	9	an	an	DET
ejpam-6418	117	10	infinite	infinite	ADJ
ejpam-6418	117	11	set	set	NOUN
ejpam-6418	117	12	and	and	CCONJ
ejpam-6418	117	13	l	l	NOUN
ejpam-6418	118	1	=	=	SYM
ejpam-6418	118	2	{	{	PUNCT
ejpam-6418	118	3	x	x	SYM
ejpam-6418	118	4	∈	∈	PROPN
ejpam-6418	118	5	vi	vi	NOUN
ejpam-6418	119	1	|	|	ADV
ejpam-6418	119	2	|x|	|x|	PROPN
ejpam-6418	119	3	is	be	AUX
ejpam-6418	119	4	finite	finite	ADJ
ejpam-6418	119	5	}	}	PUNCT
ejpam-6418	119	6	,	,	PUNCT
ejpam-6418	119	7	where	where	SCONJ
ejpam-6418	119	8	|x|	|x|	PROPN
ejpam-6418	119	9	=	=	PRON
ejpam-6418	119	10	{	{	PUNCT
ejpam-6418	119	11	i	i	NOUN
ejpam-6418	119	12	∈	∈	PROPN
ejpam-6418	120	1	i	i	PRON
ejpam-6418	120	2	|	|	ADV
ejpam-6418	120	3	x(i	x(i	PROPN
ejpam-6418	120	4	)	)	PUNCT
ejpam-6418	120	5	̸=	̸=	PROPN
ejpam-6418	120	6	1	1	NUM
ejpam-6418	120	7	}	}	PUNCT
ejpam-6418	120	8	.	.	PUNCT
ejpam-6418	121	1	then	then	ADV
ejpam-6418	121	2	(	(	PUNCT
ejpam-6418	121	3	l,∨,∧	l,∨,∧	NOUN
ejpam-6418	121	4	,	,	PUNCT
ejpam-6418	121	5	1	1	NUM
ejpam-6418	121	6	)	)	PUNCT
ejpam-6418	121	7	is	be	AUX
ejpam-6418	121	8	a	a	DET
ejpam-6418	121	9	pdl	pdl	NOUN
ejpam-6418	121	10	with	with	ADP
ejpam-6418	121	11	respect	respect	NOUN
ejpam-6418	121	12	to	to	ADP
ejpam-6418	121	13	the	the	DET
ejpam-6418	121	14	point	point	NOUN
ejpam-6418	121	15	wise	wise	ADJ
ejpam-6418	121	16	operations	operation	NOUN
ejpam-6418	121	17	,	,	PUNCT
ejpam-6418	121	18	where	where	SCONJ
ejpam-6418	121	19	1̄	1̄	NUM
ejpam-6418	121	20	:	:	PUNCT
ejpam-6418	121	21	i	i	PRON
ejpam-6418	121	22	→	→	SYM
ejpam-6418	121	23	v	v	NOUN
ejpam-6418	121	24	,	,	PUNCT
ejpam-6418	121	25	defined	define	VERB
ejpam-6418	121	26	by	by	ADP
ejpam-6418	121	27	1̄(i	1̄(i	NUM
ejpam-6418	121	28	)	)	PUNCT
ejpam-6418	121	29	=	=	SYM
ejpam-6418	121	30	1	1	NUM
ejpam-6418	121	31	,	,	PUNCT
ejpam-6418	121	32	for	for	ADP
ejpam-6418	121	33	all	all	PRON
ejpam-6418	121	34	i	i	PRON
ejpam-6418	121	35	∈	∈	PROPN
ejpam-6418	121	36	i.	i.	NOUN
ejpam-6418	121	37	in	in	ADP
ejpam-6418	121	38	this	this	DET
ejpam-6418	121	39	l	l	NOUN
ejpam-6418	121	40	,	,	PUNCT
ejpam-6418	121	41	we	we	PRON
ejpam-6418	121	42	observe	observe	VERB
ejpam-6418	121	43	the	the	DET
ejpam-6418	121	44	following	following	NOUN
ejpam-6418	121	45	;	;	PUNCT
ejpam-6418	121	46	(	(	PUNCT
ejpam-6418	121	47	i	i	NOUN
ejpam-6418	121	48	)	)	PUNCT
ejpam-6418	121	49	l	l	NOUN
ejpam-6418	121	50	has	have	AUX
ejpam-6418	121	51	no	no	DET
ejpam-6418	121	52	minimal	minimal	ADJ
ejpam-6418	121	53	elements	element	NOUN
ejpam-6418	121	54	let	let	VERB
ejpam-6418	121	55	x	x	X
ejpam-6418	121	56	∈	∈	PROPN
ejpam-6418	121	57	l.	l.	NOUN
ejpam-6418	121	58	then	then	ADV
ejpam-6418	121	59	|x|	|x|	PROPN
ejpam-6418	121	60	is	be	AUX
ejpam-6418	121	61	finite	finite	PROPN
ejpam-6418	121	62	.	.	PUNCT
ejpam-6418	122	1	choose	choose	VERB
ejpam-6418	122	2	i0	i0	PROPN
ejpam-6418	122	3	∈	∈	PROPN
ejpam-6418	123	1	i	i	PRON
ejpam-6418	123	2	such	such	ADJ
ejpam-6418	123	3	that	that	SCONJ
ejpam-6418	123	4	i0	i0	PROPN
ejpam-6418	123	5	/∈	/∈	PUNCT
ejpam-6418	124	1	|x|	|x|	PROPN
ejpam-6418	124	2	and	and	CCONJ
ejpam-6418	124	3	fix	fix	VERB
ejpam-6418	124	4	1	1	NUM
ejpam-6418	124	5	̸=	̸=	PROPN
ejpam-6418	124	6	d	d	SYM
ejpam-6418	124	7	∈	∈	PROPN
ejpam-6418	124	8	v.	v.	CCONJ
ejpam-6418	124	9	now	now	ADV
ejpam-6418	124	10	,	,	PUNCT
ejpam-6418	124	11	for	for	ADP
ejpam-6418	124	12	i	i	PRON
ejpam-6418	124	13	∈	∈	PROPN
ejpam-6418	124	14	i	i	PRON
ejpam-6418	124	15	,	,	PUNCT
ejpam-6418	124	16	define	define	VERB
ejpam-6418	124	17	,	,	PUNCT
ejpam-6418	124	18	y(i	y(i	PROPN
ejpam-6418	124	19	)	)	PUNCT
ejpam-6418	125	1	=	=	SYM
ejpam-6418	125	2			PROPN
ejpam-6418	125	3	x(i	x(i	PROPN
ejpam-6418	125	4	)	)	PUNCT
ejpam-6418	125	5	,	,	PUNCT
ejpam-6418	125	6	if	if	SCONJ
ejpam-6418	125	7	i	i	PRON
ejpam-6418	125	8	∈	∈	VERB
ejpam-6418	126	1	|x|	|x|	PROPN
ejpam-6418	126	2	d	d	NOUN
ejpam-6418	126	3	,	,	PUNCT
ejpam-6418	126	4	if	if	SCONJ
ejpam-6418	126	5	i	i	PRON
ejpam-6418	126	6	=	=	SYM
ejpam-6418	126	7	i0	i0	PROPN
ejpam-6418	126	8	1	1	NUM
ejpam-6418	126	9	,	,	PUNCT
ejpam-6418	126	10	otherwise	otherwise	ADV
ejpam-6418	126	11	.	.	PUNCT
ejpam-6418	127	1	then	then	ADV
ejpam-6418	127	2	y	y	PROPN
ejpam-6418	127	3	∈	∈	PROPN
ejpam-6418	127	4	l	l	NOUN
ejpam-6418	127	5	and	and	CCONJ
ejpam-6418	127	6	y	y	PROPN
ejpam-6418	127	7	≤	≤	PROPN
ejpam-6418	127	8	x.	x.	PUNCT
ejpam-6418	128	1	therefore	therefore	ADV
ejpam-6418	128	2	l	l	PROPN
ejpam-6418	128	3	has	have	VERB
ejpam-6418	128	4	no	no	DET
ejpam-6418	128	5	minimal	minimal	ADJ
ejpam-6418	128	6	element	element	NOUN
ejpam-6418	128	7	.	.	PUNCT
ejpam-6418	129	1	(	(	PUNCT
ejpam-6418	129	2	ii	ii	NOUN
ejpam-6418	129	3	)	)	PUNCT
ejpam-6418	129	4	if	if	SCONJ
ejpam-6418	129	5	p	p	X
ejpam-6418	129	6	∈	∈	PROPN
ejpam-6418	129	7	(	(	PUNCT
ejpam-6418	129	8	v−	v−	NOUN
ejpam-6418	129	9	{	{	PUNCT
ejpam-6418	129	10	0})i	0})i	NUM
ejpam-6418	129	11	,	,	PUNCT
ejpam-6418	129	12	then	then	ADV
ejpam-6418	129	13	the	the	DET
ejpam-6418	129	14	set	set	NOUN
ejpam-6418	129	15	mp	mp	NOUN
ejpam-6418	129	16	=	=	PUNCT
ejpam-6418	129	17	{	{	PUNCT
ejpam-6418	129	18	ps	ps	INTJ
ejpam-6418	129	19	|	|	ADV
ejpam-6418	129	20	s	s	VERB
ejpam-6418	129	21	is	be	AUX
ejpam-6418	129	22	a	a	DET
ejpam-6418	129	23	finite	finite	NOUN
ejpam-6418	129	24	subset	subset	NOUN
ejpam-6418	129	25	of	of	ADP
ejpam-6418	129	26	i	i	PROPN
ejpam-6418	129	27	}	}	PUNCT
ejpam-6418	129	28	is	be	AUX
ejpam-6418	129	29	a	a	DET
ejpam-6418	129	30	maximal	maximal	ADJ
ejpam-6418	129	31	set	set	NOUN
ejpam-6418	129	32	in	in	ADP
ejpam-6418	129	33	l	l	NOUN
ejpam-6418	129	34	,	,	PUNCT
ejpam-6418	129	35	where	where	SCONJ
ejpam-6418	129	36	ps	ps	NOUN
ejpam-6418	129	37	:	:	PUNCT
ejpam-6418	129	38	i	i	PRON
ejpam-6418	129	39	→	→	SYM
ejpam-6418	129	40	v	v	PROPN
ejpam-6418	129	41	is	be	AUX
ejpam-6418	129	42	defined	define	VERB
ejpam-6418	129	43	by	by	ADP
ejpam-6418	129	44	ps(i	ps(i	NUM
ejpam-6418	129	45	)	)	PUNCT
ejpam-6418	130	1	=	=	PRON
ejpam-6418	130	2	{	{	PUNCT
ejpam-6418	130	3	p(i	p(i	PROPN
ejpam-6418	130	4	)	)	PUNCT
ejpam-6418	130	5	,	,	PUNCT
ejpam-6418	130	6	if	if	SCONJ
ejpam-6418	130	7	i	i	PRON
ejpam-6418	130	8	∈	∈	PROPN
ejpam-6418	130	9	s	s	PART
ejpam-6418	130	10	1	1	NUM
ejpam-6418	130	11	,	,	PUNCT
ejpam-6418	130	12	if	if	SCONJ
ejpam-6418	130	13	i	i	PRON
ejpam-6418	130	14	/∈	/∈	PUNCT
ejpam-6418	131	1	s	s	X
ejpam-6418	131	2	,	,	PUNCT
ejpam-6418	131	3	for	for	ADP
ejpam-6418	131	4	all	all	DET
ejpam-6418	131	5	i	i	PRON
ejpam-6418	131	6	∈	∈	PROPN
ejpam-6418	131	7	i.	i.	NOUN
ejpam-6418	131	8	let	let	VERB
ejpam-6418	131	9	s1	s1	NOUN
ejpam-6418	131	10	,	,	PUNCT
ejpam-6418	131	11	s2	s2	X
ejpam-6418	131	12	be	be	AUX
ejpam-6418	131	13	two	two	NUM
ejpam-6418	131	14	finite	finite	ADJ
ejpam-6418	131	15	subsets	subset	NOUN
ejpam-6418	131	16	of	of	ADP
ejpam-6418	131	17	i	i	PRON
ejpam-6418	132	1	and	and	CCONJ
ejpam-6418	132	2	i	i	PROPN
ejpam-6418	132	3	∈	∈	PROPN
ejpam-6418	132	4	s1	s1	PROPN
ejpam-6418	132	5	∩	∩	ADJ
ejpam-6418	132	6	s2	s2	PROPN
ejpam-6418	132	7	.	.	PUNCT
ejpam-6418	133	1	now	now	ADV
ejpam-6418	133	2	,	,	PUNCT
ejpam-6418	133	3	(	(	PUNCT
ejpam-6418	133	4	ps1	ps1	NOUN
ejpam-6418	133	5	∧	∧	PROPN
ejpam-6418	133	6	ps2)(i	ps2)(i	PROPN
ejpam-6418	133	7	)	)	PUNCT
ejpam-6418	133	8	⇒	⇒	NOUN
ejpam-6418	133	9	ps1(i	ps1(i	NUM
ejpam-6418	133	10	)	)	PUNCT
ejpam-6418	133	11	∧	∧	PROPN
ejpam-6418	133	12	ps2(i	ps2(i	PROPN
ejpam-6418	133	13	)	)	PUNCT
ejpam-6418	133	14	⇒	⇒	NOUN
ejpam-6418	133	15	p(i	p(i	PROPN
ejpam-6418	133	16	)	)	PUNCT
ejpam-6418	133	17	∧	∧	PROPN
ejpam-6418	133	18	p(i	p(i	PROPN
ejpam-6418	133	19	)	)	PUNCT
ejpam-6418	133	20	⇒	⇒	PROPN
ejpam-6418	133	21	ps2(i	ps2(i	PROPN
ejpam-6418	133	22	)	)	PUNCT
ejpam-6418	133	23	∧	∧	PROPN
ejpam-6418	133	24	ps1(i	ps1(i	PROPN
ejpam-6418	133	25	)	)	PUNCT
ejpam-6418	133	26	⇒	⇒	NOUN
ejpam-6418	133	27	(	(	PUNCT
ejpam-6418	133	28	ps2	ps2	PROPN
ejpam-6418	133	29	∧	∧	PROPN
ejpam-6418	133	30	ps1)(i	ps1)(i	PROPN
ejpam-6418	133	31	)	)	PUNCT
ejpam-6418	133	32	.	.	PUNCT
ejpam-6418	134	1	if	if	SCONJ
ejpam-6418	134	2	i	i	PRON
ejpam-6418	134	3	/∈	/∈	PUNCT
ejpam-6418	134	4	s1	s1	PROPN
ejpam-6418	134	5	∩	∩	ADJ
ejpam-6418	134	6	s2	s2	PROPN
ejpam-6418	134	7	,	,	PUNCT
ejpam-6418	134	8	then	then	ADV
ejpam-6418	134	9	(	(	PUNCT
ejpam-6418	134	10	ps1	ps1	PROPN
ejpam-6418	134	11	∧	∧	PROPN
ejpam-6418	134	12	ps2)(i	ps2)(i	PROPN
ejpam-6418	134	13	)	)	PUNCT
ejpam-6418	134	14	=	=	SYM
ejpam-6418	134	15	ps1(i	ps1(i	NUM
ejpam-6418	134	16	)	)	PUNCT
ejpam-6418	134	17	∧	∧	PROPN
ejpam-6418	134	18	ps2(i	ps2(i	PROPN
ejpam-6418	134	19	)	)	PUNCT
ejpam-6418	134	20	=	=	SYM
ejpam-6418	134	21	1	1	X
ejpam-6418	134	22	.	.	X
ejpam-6418	134	23	therefore	therefore	ADV
ejpam-6418	134	24	ps1	ps1	PROPN
ejpam-6418	134	25	∧	∧	PROPN
ejpam-6418	134	26	ps2	ps2	PROPN
ejpam-6418	134	27	=	=	SYM
ejpam-6418	134	28	ps2	ps2	PROPN
ejpam-6418	134	29	∧	∧	PROPN
ejpam-6418	134	30	ps1	ps1	PROPN
ejpam-6418	134	31	,	,	PUNCT
ejpam-6418	134	32	and	and	CCONJ
ejpam-6418	134	33	hence	hence	ADV
ejpam-6418	134	34	mp	mp	PROPN
ejpam-6418	134	35	is	be	AUX
ejpam-6418	134	36	a	a	DET
ejpam-6418	134	37	compatible	compatible	ADJ
ejpam-6418	134	38	set	set	NOUN
ejpam-6418	134	39	.	.	PUNCT
ejpam-6418	135	1	let	let	VERB
ejpam-6418	135	2	x	x	PUNCT
ejpam-6418	135	3	∈	∈	VERB
ejpam-6418	135	4	l	l	NOUN
ejpam-6418	135	5	such	such	ADJ
ejpam-6418	135	6	that	that	SCONJ
ejpam-6418	135	7	x	x	PUNCT
ejpam-6418	135	8	∼	∼	NOUN
ejpam-6418	135	9	ps	ps	NOUN
ejpam-6418	135	10	for	for	ADP
ejpam-6418	135	11	all	all	DET
ejpam-6418	135	12	finite	finite	PROPN
ejpam-6418	135	13	subset	subset	NOUN
ejpam-6418	135	14	s	s	PROPN
ejpam-6418	135	15	of	of	ADP
ejpam-6418	135	16	i.	i.	NOUN
ejpam-6418	135	17	since	since	SCONJ
ejpam-6418	135	18	|x|	|x|	PROPN
ejpam-6418	135	19	is	be	AUX
ejpam-6418	135	20	a	a	DET
ejpam-6418	135	21	finite	finite	NOUN
ejpam-6418	135	22	subset	subset	NOUN
ejpam-6418	135	23	of	of	ADP
ejpam-6418	135	24	i	i	PRON
ejpam-6418	135	25	,	,	PUNCT
ejpam-6418	135	26	we	we	PRON
ejpam-6418	135	27	have	have	VERB
ejpam-6418	135	28	x	x	NUM
ejpam-6418	135	29	∼	∼	NOUN
ejpam-6418	135	30	p|x|	p|x|	NOUN
ejpam-6418	135	31	.	.	PUNCT
ejpam-6418	136	1	therefore	therefore	ADV
ejpam-6418	136	2	x|x|	x|x|	PUNCT
ejpam-6418	136	3	=	=	SYM
ejpam-6418	136	4	p|x|	p|x|	NOUN
ejpam-6418	136	5	and	and	CCONJ
ejpam-6418	136	6	hence	hence	ADV
ejpam-6418	136	7	x	x	X
ejpam-6418	136	8	=	=	PUNCT
ejpam-6418	136	9	p|x|	p|x|	PROPN
ejpam-6418	136	10	∈	∈	PROPN
ejpam-6418	136	11	mp	mp	PROPN
ejpam-6418	136	12	.	.	PUNCT
ejpam-6418	137	1	thus	thus	ADV
ejpam-6418	137	2	mp	mp	PROPN
ejpam-6418	137	3	is	be	AUX
ejpam-6418	137	4	a	a	DET
ejpam-6418	137	5	maximal	maximal	ADJ
ejpam-6418	137	6	set	set	NOUN
ejpam-6418	137	7	.	.	PUNCT
ejpam-6418	138	1	example	example	NOUN
ejpam-6418	138	2	3.11	3.11	NUM
ejpam-6418	138	3	.	.	PUNCT
ejpam-6418	139	1	the	the	DET
ejpam-6418	139	2	set	set	NOUN
ejpam-6418	139	3	mm	mm	NOUN
ejpam-6418	139	4	=	=	PUNCT
ejpam-6418	139	5	{	{	PUNCT
ejpam-6418	139	6	a	a	DET
ejpam-6418	139	7	∈	∈	NOUN
ejpam-6418	139	8	v	v	ADP
ejpam-6418	139	9	|	|	ADV
ejpam-6418	139	10	m	m	VERB
ejpam-6418	139	11	≤	≤	NOUN
ejpam-6418	139	12	a	a	PRON
ejpam-6418	139	13	}	}	PUNCT
ejpam-6418	139	14	,	,	PUNCT
ejpam-6418	139	15	where	where	SCONJ
ejpam-6418	139	16	m	m	NOUN
ejpam-6418	139	17	is	be	AUX
ejpam-6418	139	18	a	a	DET
ejpam-6418	139	19	minimal	minimal	ADJ
ejpam-6418	139	20	element	element	NOUN
ejpam-6418	139	21	in	in	ADP
ejpam-6418	139	22	v	v	NOUN
ejpam-6418	139	23	,	,	PUNCT
ejpam-6418	139	24	is	be	AUX
ejpam-6418	139	25	a	a	DET
ejpam-6418	139	26	maximal	maximal	ADJ
ejpam-6418	139	27	set	set	NOUN
ejpam-6418	139	28	in	in	ADP
ejpam-6418	139	29	v.	v.	ADV
ejpam-6418	139	30	let	let	VERB
ejpam-6418	139	31	m	m	PRON
ejpam-6418	139	32	be	be	AUX
ejpam-6418	139	33	a	a	DET
ejpam-6418	139	34	minimal	minimal	ADJ
ejpam-6418	139	35	element	element	NOUN
ejpam-6418	139	36	in	in	ADP
ejpam-6418	139	37	v.	v.	ADP
ejpam-6418	139	38	then	then	ADV
ejpam-6418	139	39	m	m	VERB
ejpam-6418	139	40	∈	∈	PROPN
ejpam-6418	139	41	mm	mm	INTJ
ejpam-6418	139	42	.	.	PUNCT
ejpam-6418	140	1	therefore	therefore	ADV
ejpam-6418	140	2	mm	mm	PROPN
ejpam-6418	140	3	is	be	AUX
ejpam-6418	140	4	non	non	ADJ
ejpam-6418	140	5	-	-	ADJ
ejpam-6418	140	6	empty	empty	ADJ
ejpam-6418	140	7	.	.	PUNCT
ejpam-6418	141	1	let	let	VERB
ejpam-6418	141	2	a	a	PRON
ejpam-6418	141	3	,	,	PUNCT
ejpam-6418	141	4	b	b	X
ejpam-6418	141	5	∈	∈	PROPN
ejpam-6418	141	6	mm	mm	INTJ
ejpam-6418	141	7	.	.	PUNCT
ejpam-6418	142	1	then	then	ADV
ejpam-6418	142	2	m	m	VERB
ejpam-6418	142	3	≤	≤	PROPN
ejpam-6418	142	4	a	a	DET
ejpam-6418	142	5	,	,	PUNCT
ejpam-6418	142	6	b.	b.	PROPN
ejpam-6418	142	7	therefore	therefore	ADV
ejpam-6418	142	8	m∧a	m∧a	VERB
ejpam-6418	142	9	=	=	SYM
ejpam-6418	142	10	m∧b	m∧b	NOUN
ejpam-6418	142	11	=	=	SYM
ejpam-6418	142	12	m.	m.	NOUN
ejpam-6418	142	13	now	now	ADV
ejpam-6418	142	14	,	,	PUNCT
ejpam-6418	142	15	a∧b	a∧b	NOUN
ejpam-6418	142	16	=	=	SYM
ejpam-6418	142	17	(	(	PUNCT
ejpam-6418	142	18	m∨a)∧	m∨a)∧	PROPN
ejpam-6418	142	19	(	(	PUNCT
ejpam-6418	142	20	m∨b	m∨b	PROPN
ejpam-6418	142	21	)	)	PUNCT
ejpam-6418	143	1	=	=	SYM
ejpam-6418	143	2	m∨	m∨	NOUN
ejpam-6418	143	3	(	(	PUNCT
ejpam-6418	143	4	a∧	a∧	NOUN
ejpam-6418	143	5	b	b	NOUN
ejpam-6418	143	6	)	)	PUNCT
ejpam-6418	143	7	=	=	SYM
ejpam-6418	143	8	m∨	m∨	NOUN
ejpam-6418	143	9	(	(	PUNCT
ejpam-6418	143	10	b∧a	b∧a	ADV
ejpam-6418	143	11	)	)	PUNCT
ejpam-6418	143	12	=	=	SYM
ejpam-6418	143	13	(	(	PUNCT
ejpam-6418	143	14	m∨	m∨	PROPN
ejpam-6418	143	15	b)∧	b)∧	PROPN
ejpam-6418	143	16	(	(	PUNCT
ejpam-6418	143	17	m∨a	m∨a	PROPN
ejpam-6418	143	18	)	)	PUNCT
ejpam-6418	143	19	=	=	PUNCT
ejpam-6418	143	20	b∧a	b∧a	ADV
ejpam-6418	143	21	.	.	PUNCT
ejpam-6418	144	1	therefore	therefore	ADV
ejpam-6418	144	2	a∧	a∧	PROPN
ejpam-6418	144	3	b	b	PROPN
ejpam-6418	144	4	=	=	PUNCT
ejpam-6418	144	5	b∧a	b∧a	ADV
ejpam-6418	144	6	.	.	PUNCT
ejpam-6418	145	1	so	so	ADV
ejpam-6418	145	2	that	that	SCONJ
ejpam-6418	145	3	a	a	DET
ejpam-6418	145	4	∼	∼	NOUN
ejpam-6418	145	5	b.	b.	NOUN
ejpam-6418	145	6	hence	hence	ADV
ejpam-6418	145	7	mm	mm	PROPN
ejpam-6418	145	8	is	be	AUX
ejpam-6418	145	9	a	a	DET
ejpam-6418	145	10	compatible	compatible	ADJ
ejpam-6418	145	11	set	set	NOUN
ejpam-6418	145	12	.	.	PUNCT
ejpam-6418	146	1	assume	assume	VERB
ejpam-6418	146	2	that	that	SCONJ
ejpam-6418	146	3	s	s	VERB
ejpam-6418	146	4	is	be	AUX
ejpam-6418	146	5	a	a	DET
ejpam-6418	146	6	compatible	compatible	ADJ
ejpam-6418	146	7	set	set	NOUN
ejpam-6418	146	8	such	such	ADJ
ejpam-6418	146	9	that	that	SCONJ
ejpam-6418	146	10	mm	mm	PROPN
ejpam-6418	146	11	⊆	⊆	NUM
ejpam-6418	146	12	s.	s.	PROPN
ejpam-6418	146	13	let	let	VERB
ejpam-6418	146	14	c	c	PROPN
ejpam-6418	146	15	∈	∈	PROPN
ejpam-6418	146	16	s.	s.	PROPN
ejpam-6418	146	17	then	then	ADV
ejpam-6418	146	18	c	c	VERB
ejpam-6418	146	19	∼	∼	NOUN
ejpam-6418	146	20	s	s	NOUN
ejpam-6418	146	21	,	,	PUNCT
ejpam-6418	146	22	for	for	ADP
ejpam-6418	146	23	all	all	DET
ejpam-6418	146	24	s	s	PART
ejpam-6418	146	25	∈	∈	PROPN
ejpam-6418	146	26	s.	s.	PROPN
ejpam-6418	146	27	since	since	SCONJ
ejpam-6418	146	28	mm	mm	PROPN
ejpam-6418	146	29	⊆	⊆	NUM
ejpam-6418	146	30	s	s	NOUN
ejpam-6418	146	31	,	,	PUNCT
ejpam-6418	146	32	a	a	DET
ejpam-6418	146	33	∼	∼	NOUN
ejpam-6418	146	34	m.	m.	NOUN
ejpam-6418	146	35	now	now	ADV
ejpam-6418	146	36	,	,	PUNCT
ejpam-6418	146	37	m	m	VERB
ejpam-6418	146	38	=	=	SYM
ejpam-6418	146	39	a∧m	a∧m	PROPN
ejpam-6418	146	40	=	=	SYM
ejpam-6418	146	41	m∧	m∧	PROPN
ejpam-6418	146	42	a.	a.	NOUN
ejpam-6418	146	43	then	then	ADV
ejpam-6418	146	44	m	m	VERB
ejpam-6418	146	45	≤	≤	ADJ
ejpam-6418	146	46	a.	a.	NOUN
ejpam-6418	146	47	therefore	therefore	ADV
ejpam-6418	146	48	a	a	PRON
ejpam-6418	146	49	∈	∈	ADJ
ejpam-6418	146	50	mm	mm	INTJ
ejpam-6418	146	51	.	.	PUNCT
ejpam-6418	147	1	so	so	ADV
ejpam-6418	147	2	that	that	PRON
ejpam-6418	147	3	s	s	VERB
ejpam-6418	147	4	⊆	⊆	NUM
ejpam-6418	147	5	mm	mm	NOUN
ejpam-6418	147	6	.	.	PUNCT
ejpam-6418	148	1	hence	hence	ADV
ejpam-6418	148	2	mm	mm	PROPN
ejpam-6418	148	3	=	=	PUNCT
ejpam-6418	148	4	s.	s.	PROPN
ejpam-6418	148	5	thus	thus	ADV
ejpam-6418	148	6	mm	mm	PROPN
ejpam-6418	148	7	is	be	AUX
ejpam-6418	148	8	a	a	DET
ejpam-6418	148	9	maximal	maximal	ADJ
ejpam-6418	148	10	set	set	NOUN
ejpam-6418	148	11	in	in	ADP
ejpam-6418	148	12	v.	v.	PROPN
ejpam-6418	148	13	r.	r.	PROPN
ejpam-6418	148	14	sirisetti	sirisetti	PROPN
ejpam-6418	148	15	et	et	PROPN
ejpam-6418	148	16	al	al	PROPN
ejpam-6418	148	17	.	.	PUNCT
ejpam-6418	148	18	/	/	SYM
ejpam-6418	148	19	eur	eur	PROPN
ejpam-6418	148	20	.	.	PUNCT
ejpam-6418	149	1	j.	j.	PROPN
ejpam-6418	149	2	pure	pure	PROPN
ejpam-6418	149	3	appl	appl	PROPN
ejpam-6418	149	4	.	.	PROPN
ejpam-6418	149	5	math	math	PROPN
ejpam-6418	149	6	,	,	PUNCT
ejpam-6418	149	7	18	18	NUM
ejpam-6418	149	8	(	(	PUNCT
ejpam-6418	149	9	4	4	NUM
ejpam-6418	149	10	)	)	PUNCT
ejpam-6418	149	11	(	(	PUNCT
ejpam-6418	149	12	2025	2025	NUM
ejpam-6418	149	13	)	)	PUNCT
ejpam-6418	149	14	,	,	PUNCT
ejpam-6418	149	15	6418	6418	NUM
ejpam-6418	149	16	8	8	NUM
ejpam-6418	149	17	of	of	ADP
ejpam-6418	149	18	13	13	NUM
ejpam-6418	149	19	let	let	VERB
ejpam-6418	149	20	{	{	PUNCT
ejpam-6418	149	21	vi}i∈∆	vi}i∈∆	NOUN
ejpam-6418	149	22	be	be	AUX
ejpam-6418	149	23	a	a	DET
ejpam-6418	149	24	family	family	NOUN
ejpam-6418	149	25	of	of	ADP
ejpam-6418	149	26	pdls	pdl	NOUN
ejpam-6418	149	27	.	.	PUNCT
ejpam-6418	150	1	then	then	ADV
ejpam-6418	150	2	it	it	PRON
ejpam-6418	150	3	is	be	AUX
ejpam-6418	150	4	easy	easy	ADJ
ejpam-6418	150	5	to	to	PART
ejpam-6418	150	6	observe	observe	VERB
ejpam-6418	150	7	that	that	SCONJ
ejpam-6418	150	8	the	the	DET
ejpam-6418	150	9	product	product	NOUN
ejpam-6418	150	10	∏	∏	NUM
ejpam-6418	150	11	i∈∆vi	i∈∆vi	ADJ
ejpam-6418	150	12	with	with	ADP
ejpam-6418	150	13	point	point	NOUN
ejpam-6418	150	14	wise	wise	ADJ
ejpam-6418	150	15	operations	operation	NOUN
ejpam-6418	150	16	is	be	AUX
ejpam-6418	150	17	a	a	DET
ejpam-6418	150	18	pdl	pdl	NOUN
ejpam-6418	150	19	.	.	PUNCT
ejpam-6418	151	1	now	now	ADV
ejpam-6418	151	2	,	,	PUNCT
ejpam-6418	151	3	we	we	PRON
ejpam-6418	151	4	have	have	VERB
ejpam-6418	151	5	the	the	DET
ejpam-6418	151	6	following	following	NOUN
ejpam-6418	151	7	;	;	PUNCT
ejpam-6418	151	8	theorem	theorem	VERB
ejpam-6418	151	9	3.12	3.12	NUM
ejpam-6418	151	10	.	.	PUNCT
ejpam-6418	152	1	for	for	ADP
ejpam-6418	152	2	any	any	DET
ejpam-6418	152	3	non	non	ADJ
ejpam-6418	152	4	-	-	ADJ
ejpam-6418	152	5	empty	empty	ADJ
ejpam-6418	152	6	subset	subset	NOUN
ejpam-6418	152	7	m	m	NOUN
ejpam-6418	152	8	of	of	ADP
ejpam-6418	152	9	∏	∏	PROPN
ejpam-6418	152	10	i∈∆vi	i∈∆vi	PROPN
ejpam-6418	152	11	,	,	PUNCT
ejpam-6418	152	12	m	m	VERB
ejpam-6418	152	13	is	be	AUX
ejpam-6418	152	14	maximal	maximal	ADJ
ejpam-6418	152	15	set	set	VERB
ejpam-6418	152	16	in	in	ADP
ejpam-6418	152	17	∏	∏	NUM
ejpam-6418	152	18	i∈∆vi	i∈∆vi	ADJ
ejpam-6418	152	19	if	if	SCONJ
ejpam-6418	153	1	and	and	CCONJ
ejpam-6418	153	2	only	only	ADV
ejpam-6418	153	3	if	if	SCONJ
ejpam-6418	153	4	m	m	PROPN
ejpam-6418	153	5	=	=	SYM
ejpam-6418	153	6	∏	∏	PROPN
ejpam-6418	153	7	i∈∆mi	i∈∆mi	PROPN
ejpam-6418	153	8	,	,	PUNCT
ejpam-6418	153	9	where	where	SCONJ
ejpam-6418	153	10	mi	mi	PROPN
ejpam-6418	153	11	is	be	AUX
ejpam-6418	153	12	a	a	DET
ejpam-6418	153	13	maximal	maximal	ADJ
ejpam-6418	153	14	set	set	NOUN
ejpam-6418	153	15	in	in	ADP
ejpam-6418	153	16	vi	vi	PROPN
ejpam-6418	153	17	.	.	PUNCT
ejpam-6418	153	18	proof	proof	NOUN
ejpam-6418	153	19	.	.	PUNCT
ejpam-6418	154	1	let	let	VERB
ejpam-6418	154	2	{	{	PUNCT
ejpam-6418	154	3	vi}i∈∆	vi}i∈∆	NOUN
ejpam-6418	154	4	be	be	AUX
ejpam-6418	154	5	the	the	DET
ejpam-6418	154	6	family	family	NOUN
ejpam-6418	154	7	of	of	ADP
ejpam-6418	154	8	pdls	pdl	NOUN
ejpam-6418	154	9	.	.	PUNCT
ejpam-6418	155	1	if	if	SCONJ
ejpam-6418	155	2	mi	mi	PROPN
ejpam-6418	155	3	is	be	AUX
ejpam-6418	155	4	a	a	DET
ejpam-6418	155	5	maximal	maximal	ADJ
ejpam-6418	155	6	set	set	NOUN
ejpam-6418	155	7	in	in	ADP
ejpam-6418	155	8	vi	vi	PROPN
ejpam-6418	155	9	.	.	PUNCT
ejpam-6418	156	1	then	then	ADV
ejpam-6418	156	2	clearly∏	clearly∏	PROPN
ejpam-6418	157	1	i∈∆mi	i∈∆mi	PROPN
ejpam-6418	157	2	is	be	AUX
ejpam-6418	157	3	a	a	DET
ejpam-6418	157	4	maximal	maximal	ADJ
ejpam-6418	157	5	set	set	NOUN
ejpam-6418	157	6	.	.	PUNCT
ejpam-6418	158	1	on	on	ADP
ejpam-6418	158	2	the	the	DET
ejpam-6418	158	3	other	other	ADJ
ejpam-6418	158	4	hand	hand	NOUN
ejpam-6418	158	5	,	,	PUNCT
ejpam-6418	158	6	let	let	VERB
ejpam-6418	158	7	m	m	PRON
ejpam-6418	158	8	be	be	AUX
ejpam-6418	158	9	the	the	DET
ejpam-6418	158	10	set	set	NOUN
ejpam-6418	158	11	such	such	ADJ
ejpam-6418	158	12	that	that	DET
ejpam-6418	158	13	mi	mi	PROPN
ejpam-6418	158	14	=	=	PRON
ejpam-6418	158	15	{	{	PUNCT
ejpam-6418	158	16	a(i	a(i	NOUN
ejpam-6418	158	17	)	)	PUNCT
ejpam-6418	159	1	|	|	ADV
ejpam-6418	159	2	a	a	DET
ejpam-6418	159	3	∈	∈	PROPN
ejpam-6418	159	4	m	m	NOUN
ejpam-6418	159	5	}	}	PUNCT
ejpam-6418	159	6	,	,	PUNCT
ejpam-6418	159	7	then	then	ADV
ejpam-6418	159	8	mi	mi	PROPN
ejpam-6418	159	9	is	be	AUX
ejpam-6418	159	10	non	non	ADJ
ejpam-6418	159	11	-	-	ADJ
ejpam-6418	159	12	empty	empty	ADJ
ejpam-6418	159	13	and	and	CCONJ
ejpam-6418	159	14	compatible	compatible	ADJ
ejpam-6418	159	15	set	set	VERB
ejpam-6418	159	16	in	in	ADP
ejpam-6418	159	17	vi	vi	PROPN
ejpam-6418	159	18	.	.	PUNCT
ejpam-6418	160	1	let	let	VERB
ejpam-6418	160	2	b	b	X
ejpam-6418	160	3	∈	∈	PROPN
ejpam-6418	160	4	vi	vi	PROPN
ejpam-6418	160	5	is	be	AUX
ejpam-6418	160	6	such	such	ADJ
ejpam-6418	160	7	that	that	SCONJ
ejpam-6418	160	8	b	b	NOUN
ejpam-6418	160	9	∼	∼	NOUN
ejpam-6418	160	10	a(i	a(i	NOUN
ejpam-6418	160	11	)	)	PUNCT
ejpam-6418	160	12	,	,	PUNCT
ejpam-6418	160	13	for	for	ADP
ejpam-6418	160	14	all	all	DET
ejpam-6418	160	15	a	a	DET
ejpam-6418	160	16	∈	∈	NOUN
ejpam-6418	160	17	m	m	NOUN
ejpam-6418	160	18	.	.	PUNCT
ejpam-6418	161	1	now	now	ADV
ejpam-6418	161	2	,	,	PUNCT
ejpam-6418	161	3	define	define	VERB
ejpam-6418	161	4	c	c	PROPN
ejpam-6418	161	5	∈	∈	PROPN
ejpam-6418	161	6	∏	∏	PROPN
ejpam-6418	161	7	j∈∆vj	j∈∆vj	PROPN
ejpam-6418	161	8	by	by	ADP
ejpam-6418	161	9	c(j	c(j	PROPN
ejpam-6418	161	10	)	)	PUNCT
ejpam-6418	161	11	=	=	SYM
ejpam-6418	162	1	b	b	X
ejpam-6418	162	2	,	,	PUNCT
ejpam-6418	162	3	if	if	SCONJ
ejpam-6418	162	4	i	i	PRON
ejpam-6418	162	5	=	=	SYM
ejpam-6418	162	6	j	j	PROPN
ejpam-6418	162	7	and	and	CCONJ
ejpam-6418	162	8	1j	1j	NUM
ejpam-6418	162	9	if	if	SCONJ
ejpam-6418	162	10	i	i	PRON
ejpam-6418	162	11	̸=	̸=	PROPN
ejpam-6418	162	12	j.	j.	PROPN
ejpam-6418	162	13	now	now	ADV
ejpam-6418	162	14	,	,	PUNCT
ejpam-6418	162	15	d	d	PROPN
ejpam-6418	162	16	∈	∈	PROPN
ejpam-6418	162	17	m	m	NOUN
ejpam-6418	162	18	and	and	CCONJ
ejpam-6418	162	19	j	j	PROPN
ejpam-6418	162	20	∈	∈	PROPN
ejpam-6418	162	21	∆	∆	PROPN
ejpam-6418	162	22	,	,	PUNCT
ejpam-6418	162	23	(	(	PUNCT
ejpam-6418	162	24	d	d	X
ejpam-6418	162	25	∧	∧	PROPN
ejpam-6418	162	26	c)(j	c)(j	X
ejpam-6418	162	27	)	)	PUNCT
ejpam-6418	162	28	=	=	SYM
ejpam-6418	162	29	d(j	d(j	ADJ
ejpam-6418	162	30	)	)	PUNCT
ejpam-6418	162	31	∧	∧	PROPN
ejpam-6418	162	32	c(j	c(j	PROPN
ejpam-6418	162	33	)	)	PUNCT
ejpam-6418	162	34	=	=	SYM
ejpam-6418	162	35	c(j	c(j	PROPN
ejpam-6418	162	36	)	)	PUNCT
ejpam-6418	162	37	∧	∧	PROPN
ejpam-6418	162	38	d(j	d(j	NOUN
ejpam-6418	162	39	)	)	PUNCT
ejpam-6418	162	40	=	=	SYM
ejpam-6418	163	1	(	(	PUNCT
ejpam-6418	163	2	c	c	NOUN
ejpam-6418	163	3	∧	∧	NOUN
ejpam-6418	163	4	d)(j	d)(j	NOUN
ejpam-6418	163	5	)	)	PUNCT
ejpam-6418	163	6	.	.	PUNCT
ejpam-6418	164	1	therefore	therefore	ADV
ejpam-6418	164	2	c	c	VERB
ejpam-6418	164	3	∼	∼	NOUN
ejpam-6418	164	4	d	d	NOUN
ejpam-6418	164	5	,	,	PUNCT
ejpam-6418	164	6	for	for	ADP
ejpam-6418	164	7	all	all	DET
ejpam-6418	164	8	d	d	PROPN
ejpam-6418	164	9	∈	∈	PROPN
ejpam-6418	164	10	m	m	NOUN
ejpam-6418	164	11	.	.	PUNCT
ejpam-6418	165	1	so	so	ADV
ejpam-6418	165	2	that	that	SCONJ
ejpam-6418	165	3	c	c	PROPN
ejpam-6418	165	4	∈	∈	PROPN
ejpam-6418	165	5	m	m	NOUN
ejpam-6418	165	6	and	and	CCONJ
ejpam-6418	165	7	c(j	c(j	NOUN
ejpam-6418	165	8	)	)	PUNCT
ejpam-6418	165	9	=	=	SYM
ejpam-6418	165	10	b	b	PROPN
ejpam-6418	165	11	∈	∈	PROPN
ejpam-6418	165	12	mi	mi	PROPN
ejpam-6418	165	13	.	.	PROPN
ejpam-6418	165	14	hence	hence	PROPN
ejpam-6418	165	15	mi	mi	PROPN
ejpam-6418	165	16	is	be	AUX
ejpam-6418	165	17	a	a	DET
ejpam-6418	165	18	maximal	maximal	ADJ
ejpam-6418	165	19	set	set	NOUN
ejpam-6418	165	20	in	in	ADP
ejpam-6418	165	21	vi	vi	NOUN
ejpam-6418	165	22	for	for	ADP
ejpam-6418	165	23	all	all	PRON
ejpam-6418	165	24	i	i	PRON
ejpam-6418	165	25	∈	∈	PROPN
ejpam-6418	166	1	∆.	∆.	X
ejpam-6418	166	2	since∏	since∏	PROPN
ejpam-6418	166	3	i∈∆mi	i∈∆mi	PROPN
ejpam-6418	166	4	is	be	AUX
ejpam-6418	166	5	a	a	DET
ejpam-6418	166	6	compatible	compatible	ADJ
ejpam-6418	166	7	set	set	NOUN
ejpam-6418	166	8	containing	contain	VERB
ejpam-6418	166	9	m	m	PRON
ejpam-6418	166	10	.	.	PUNCT
ejpam-6418	167	1	therefore	therefore	ADV
ejpam-6418	167	2	m	m	VERB
ejpam-6418	167	3	=	=	SYM
ejpam-6418	167	4	∏	∏	PROPN
ejpam-6418	167	5	i∈∆mi	i∈∆mi	PROPN
ejpam-6418	167	6	.	.	PUNCT
ejpam-6418	168	1	lemma	lemma	PROPN
ejpam-6418	168	2	3.13	3.13	NUM
ejpam-6418	168	3	.	.	PUNCT
ejpam-6418	169	1	let	let	VERB
ejpam-6418	169	2	m	m	PRON
ejpam-6418	169	3	be	be	AUX
ejpam-6418	169	4	a	a	DET
ejpam-6418	169	5	maximal	maximal	ADJ
ejpam-6418	169	6	set	set	NOUN
ejpam-6418	169	7	in	in	ADP
ejpam-6418	169	8	v	v	NOUN
ejpam-6418	169	9	and	and	CCONJ
ejpam-6418	169	10	c	c	NOUN
ejpam-6418	169	11	∈	∈	PROPN
ejpam-6418	169	12	v	v	ADP
ejpam-6418	169	13	such	such	ADJ
ejpam-6418	169	14	that	that	SCONJ
ejpam-6418	169	15	c	c	NOUN
ejpam-6418	169	16	∼	∼	NOUN
ejpam-6418	169	17	a	a	PRON
ejpam-6418	169	18	,	,	PUNCT
ejpam-6418	169	19	for	for	ADP
ejpam-6418	169	20	all	all	DET
ejpam-6418	169	21	a	a	DET
ejpam-6418	169	22	∈	∈	NOUN
ejpam-6418	169	23	m	m	NOUN
ejpam-6418	169	24	.	.	PUNCT
ejpam-6418	170	1	then	then	ADV
ejpam-6418	170	2	c	c	PROPN
ejpam-6418	170	3	∈	∈	PROPN
ejpam-6418	170	4	m	m	VERB
ejpam-6418	170	5	.	.	PUNCT
ejpam-6418	171	1	proof	proof	NOUN
ejpam-6418	171	2	.	.	PUNCT
ejpam-6418	172	1	let	let	VERB
ejpam-6418	172	2	m	m	PRON
ejpam-6418	172	3	′	′	VERB
ejpam-6418	172	4	=	=	PUNCT
ejpam-6418	172	5	m∪{c	m∪{c	ADJ
ejpam-6418	172	6	}	}	PUNCT
ejpam-6418	172	7	.	.	PUNCT
ejpam-6418	173	1	then	then	ADV
ejpam-6418	173	2	m	m	VERB
ejpam-6418	173	3	′	′	NOUN
ejpam-6418	173	4	is	be	AUX
ejpam-6418	173	5	compatible	compatible	ADJ
ejpam-6418	173	6	set	set	NOUN
ejpam-6418	173	7	and	and	CCONJ
ejpam-6418	173	8	m	m	PROPN
ejpam-6418	173	9	⊆	⊆	NUM
ejpam-6418	173	10	m	m	NOUN
ejpam-6418	173	11	′.	′.	NOUN
ejpam-6418	173	12	by	by	ADP
ejpam-6418	173	13	the	the	DET
ejpam-6418	173	14	maximality	maximality	NOUN
ejpam-6418	173	15	of	of	ADP
ejpam-6418	173	16	m	m	PRON
ejpam-6418	173	17	,	,	PUNCT
ejpam-6418	173	18	m	m	VERB
ejpam-6418	173	19	=	=	ADJ
ejpam-6418	173	20	m	m	VERB
ejpam-6418	173	21	′	′	NOUN
ejpam-6418	174	1	and	and	CCONJ
ejpam-6418	174	2	hence	hence	ADV
ejpam-6418	174	3	c	c	PROPN
ejpam-6418	174	4	∈	∈	PROPN
ejpam-6418	174	5	m	m	VERB
ejpam-6418	174	6	.	.	PUNCT
ejpam-6418	175	1	theorem	theorem	VERB
ejpam-6418	175	2	3.14	3.14	NUM
ejpam-6418	175	3	.	.	PUNCT
ejpam-6418	176	1	let	let	VERB
ejpam-6418	176	2	m	m	PRON
ejpam-6418	176	3	be	be	AUX
ejpam-6418	176	4	a	a	DET
ejpam-6418	176	5	maximal	maximal	ADJ
ejpam-6418	176	6	set	set	NOUN
ejpam-6418	176	7	in	in	ADP
ejpam-6418	177	1	v.	v.	CCONJ
ejpam-6418	177	2	then	then	ADV
ejpam-6418	177	3	we	we	PRON
ejpam-6418	177	4	have	have	VERB
ejpam-6418	177	5	(	(	PUNCT
ejpam-6418	177	6	i	i	NOUN
ejpam-6418	177	7	)	)	PUNCT
ejpam-6418	177	8	m	m	VERB
ejpam-6418	177	9	contains	contain	VERB
ejpam-6418	177	10	1	1	NUM
ejpam-6418	177	11	(	(	PUNCT
ejpam-6418	177	12	ii	ii	NOUN
ejpam-6418	177	13	)	)	PUNCT
ejpam-6418	178	1	m	m	VERB
ejpam-6418	178	2	is	be	AUX
ejpam-6418	178	3	distributive	distributive	ADJ
ejpam-6418	178	4	lattice	lattice	NOUN
ejpam-6418	178	5	with	with	ADP
ejpam-6418	178	6	greatest	great	ADJ
ejpam-6418	178	7	element	element	NOUN
ejpam-6418	178	8	1	1	NUM
ejpam-6418	178	9	(	(	PUNCT
ejpam-6418	178	10	iii	iii	X
ejpam-6418	178	11	)	)	PUNCT
ejpam-6418	178	12	m	m	VERB
ejpam-6418	178	13	is	be	AUX
ejpam-6418	178	14	an	an	DET
ejpam-6418	178	15	initial	initial	ADJ
ejpam-6418	178	16	segment	segment	NOUN
ejpam-6418	178	17	.	.	PUNCT
ejpam-6418	179	1	proof	proof	NOUN
ejpam-6418	179	2	.	.	PUNCT
ejpam-6418	180	1	(	(	PUNCT
ejpam-6418	180	2	i	i	NOUN
ejpam-6418	180	3	)	)	PUNCT
ejpam-6418	180	4	let	let	VERB
ejpam-6418	180	5	a	a	DET
ejpam-6418	180	6	∈	∈	NOUN
ejpam-6418	180	7	m	m	NOUN
ejpam-6418	180	8	.	.	PUNCT
ejpam-6418	181	1	then	then	ADV
ejpam-6418	181	2	a	a	DET
ejpam-6418	181	3	∧	∧	PROPN
ejpam-6418	181	4	1	1	NUM
ejpam-6418	181	5	=	=	SYM
ejpam-6418	181	6	a	a	DET
ejpam-6418	181	7	=	=	SYM
ejpam-6418	181	8	1	1	NUM
ejpam-6418	181	9	∧	∧	PROPN
ejpam-6418	181	10	a.	a.	NOUN
ejpam-6418	181	11	therefore	therefore	ADV
ejpam-6418	181	12	1	1	NUM
ejpam-6418	181	13	∼	∼	NOUN
ejpam-6418	181	14	a	a	PRON
ejpam-6418	181	15	,	,	PUNCT
ejpam-6418	181	16	for	for	ADP
ejpam-6418	181	17	all	all	DET
ejpam-6418	181	18	a	a	DET
ejpam-6418	181	19	∈	∈	NOUN
ejpam-6418	181	20	m	m	NOUN
ejpam-6418	181	21	.	.	PUNCT
ejpam-6418	182	1	by	by	ADP
ejpam-6418	182	2	lemma	lemma	PROPN
ejpam-6418	182	3	3.13	3.13	NUM
ejpam-6418	182	4	.	.	PUNCT
ejpam-6418	182	5	,	,	PUNCT
ejpam-6418	182	6	1	1	NUM
ejpam-6418	182	7	∈	∈	NOUN
ejpam-6418	182	8	m	m	NOUN
ejpam-6418	182	9	.	.	PUNCT
ejpam-6418	183	1	(	(	PUNCT
ejpam-6418	183	2	ii	ii	NOUN
ejpam-6418	183	3	)	)	PUNCT
ejpam-6418	183	4	let	let	VERB
ejpam-6418	183	5	a	a	DET
ejpam-6418	183	6	,	,	PUNCT
ejpam-6418	183	7	b	b	X
ejpam-6418	183	8	∈	∈	ADV
ejpam-6418	183	9	m	m	VERB
ejpam-6418	183	10	.	.	PUNCT
ejpam-6418	184	1	then	then	ADV
ejpam-6418	184	2	a	a	DET
ejpam-6418	184	3	∼	∼	NOUN
ejpam-6418	184	4	b.	b.	NOUN
ejpam-6418	184	5	now	now	ADV
ejpam-6418	184	6	,	,	PUNCT
ejpam-6418	184	7	a	a	DET
ejpam-6418	184	8	∧	∧	PROPN
ejpam-6418	184	9	(	(	PUNCT
ejpam-6418	184	10	a	a	DET
ejpam-6418	184	11	∧	∧	PROPN
ejpam-6418	184	12	b	b	NOUN
ejpam-6418	184	13	)	)	PUNCT
ejpam-6418	184	14	=	=	PUNCT
ejpam-6418	184	15	a	a	DET
ejpam-6418	184	16	∧	∧	PROPN
ejpam-6418	184	17	b	b	PROPN
ejpam-6418	184	18	and	and	CCONJ
ejpam-6418	184	19	(	(	PUNCT
ejpam-6418	184	20	a∧	a∧	NOUN
ejpam-6418	184	21	b)∧	b)∧	VERB
ejpam-6418	184	22	a	a	DET
ejpam-6418	184	23	=	=	PUNCT
ejpam-6418	184	24	(	(	PUNCT
ejpam-6418	184	25	b∧	b∧	X
ejpam-6418	184	26	a)∧	a)∧	NOUN
ejpam-6418	184	27	a	a	X
ejpam-6418	184	28	=	=	PRON
ejpam-6418	184	29	b∧	b∧	NOUN
ejpam-6418	184	30	a	a	DET
ejpam-6418	184	31	=	=	X
ejpam-6418	184	32	a∧	a∧	PROPN
ejpam-6418	184	33	b.	b.	PROPN
ejpam-6418	184	34	therefore	therefore	ADV
ejpam-6418	184	35	a	a	DET
ejpam-6418	184	36	∼	∼	NOUN
ejpam-6418	184	37	a∧	a∧	NOUN
ejpam-6418	184	38	b.	b.	PROPN
ejpam-6418	184	39	by	by	ADP
ejpam-6418	184	40	lemma	lemma	PROPN
ejpam-6418	184	41	3.13	3.13	NUM
ejpam-6418	184	42	.	.	PUNCT
ejpam-6418	184	43	,	,	PUNCT
ejpam-6418	184	44	a∧	a∧	PROPN
ejpam-6418	184	45	b	b	PROPN
ejpam-6418	184	46	∈	∈	PROPN
ejpam-6418	184	47	m.	m.	NOUN
ejpam-6418	184	48	now	now	ADV
ejpam-6418	184	49	,	,	PUNCT
ejpam-6418	184	50	a	a	DET
ejpam-6418	184	51	∧	∧	PROPN
ejpam-6418	184	52	(	(	PUNCT
ejpam-6418	184	53	a	a	DET
ejpam-6418	184	54	∨	∨	NUM
ejpam-6418	184	55	b	b	NOUN
ejpam-6418	184	56	)	)	PUNCT
ejpam-6418	184	57	=	=	PUNCT
ejpam-6418	184	58	a	a	PROPN
ejpam-6418	184	59	and	and	CCONJ
ejpam-6418	184	60	(	(	PUNCT
ejpam-6418	184	61	a	a	DET
ejpam-6418	184	62	∨	∨	NUM
ejpam-6418	184	63	b	b	NOUN
ejpam-6418	184	64	)	)	PUNCT
ejpam-6418	184	65	∧	∧	NOUN
ejpam-6418	185	1	a	a	NOUN
ejpam-6418	185	2	=	=	X
ejpam-6418	185	3	(	(	PUNCT
ejpam-6418	185	4	b	b	PROPN
ejpam-6418	185	5	∨	∨	NUM
ejpam-6418	185	6	a	a	PRON
ejpam-6418	185	7	)	)	PUNCT
ejpam-6418	185	8	∧	∧	NOUN
ejpam-6418	185	9	a	a	PRON
ejpam-6418	185	10	=	=	NOUN
ejpam-6418	185	11	a.	a.	NOUN
ejpam-6418	185	12	so	so	SCONJ
ejpam-6418	185	13	that	that	SCONJ
ejpam-6418	185	14	m	m	NOUN
ejpam-6418	185	15	is	be	AUX
ejpam-6418	185	16	closed	close	VERB
ejpam-6418	185	17	under	under	ADP
ejpam-6418	185	18	∨	∨	NUM
ejpam-6418	185	19	and	and	CCONJ
ejpam-6418	185	20	∧.	∧.	PROPN
ejpam-6418	185	21	by	by	ADP
ejpam-6418	185	22	theorem	theorem	NOUN
ejpam-6418	185	23	2.9	2.9	NUM
ejpam-6418	185	24	.	.	PUNCT
ejpam-6418	185	25	,	,	PUNCT
ejpam-6418	185	26	m	m	PROPN
ejpam-6418	185	27	is	be	AUX
ejpam-6418	185	28	a	a	DET
ejpam-6418	185	29	distributive	distributive	ADJ
ejpam-6418	185	30	lattice	lattice	NOUN
ejpam-6418	185	31	with	with	ADP
ejpam-6418	185	32	greatest	great	ADJ
ejpam-6418	185	33	element	element	NOUN
ejpam-6418	185	34	1	1	NUM
ejpam-6418	185	35	.	.	PUNCT
ejpam-6418	186	1	(	(	PUNCT
ejpam-6418	186	2	iii	iii	X
ejpam-6418	186	3	)	)	PUNCT
ejpam-6418	186	4	let	let	VERB
ejpam-6418	186	5	a	a	DET
ejpam-6418	186	6	∈	∈	NOUN
ejpam-6418	186	7	m	m	NOUN
ejpam-6418	186	8	and	and	CCONJ
ejpam-6418	186	9	b	b	X
ejpam-6418	186	10	∈	∈	PROPN
ejpam-6418	187	1	v.	v.	ADP
ejpam-6418	187	2	if	if	SCONJ
ejpam-6418	187	3	b	b	PROPN
ejpam-6418	187	4	≤	≤	ADV
ejpam-6418	187	5	a	a	PRON
ejpam-6418	187	6	,	,	PUNCT
ejpam-6418	187	7	then	then	ADV
ejpam-6418	187	8	b	b	X
ejpam-6418	187	9	∧	∧	PROPN
ejpam-6418	187	10	a	a	DET
ejpam-6418	187	11	=	=	X
ejpam-6418	187	12	b.	b.	PROPN
ejpam-6418	187	13	now	now	ADV
ejpam-6418	187	14	,	,	PUNCT
ejpam-6418	187	15	a	a	DET
ejpam-6418	187	16	∧	∧	PROPN
ejpam-6418	187	17	b	b	NOUN
ejpam-6418	187	18	=	=	PUNCT
ejpam-6418	187	19	a	a	DET
ejpam-6418	187	20	∧	∧	PROPN
ejpam-6418	187	21	(	(	PUNCT
ejpam-6418	187	22	b	b	PROPN
ejpam-6418	187	23	∧	∧	PROPN
ejpam-6418	187	24	a	a	NOUN
ejpam-6418	187	25	)	)	PUNCT
ejpam-6418	187	26	=	=	SYM
ejpam-6418	188	1	b	b	X
ejpam-6418	188	2	∧	∧	PROPN
ejpam-6418	188	3	a	a	PRON
ejpam-6418	188	4	(	(	PUNCT
ejpam-6418	188	5	by	by	ADP
ejpam-6418	188	6	lemma	lemma	PROPN
ejpam-6418	188	7	2.8(vi	2.8(vi	NUM
ejpam-6418	188	8	)	)	PUNCT
ejpam-6418	188	9	)	)	PUNCT
ejpam-6418	188	10	.	.	PUNCT
ejpam-6418	189	1	therefore	therefore	ADV
ejpam-6418	189	2	a	a	DET
ejpam-6418	189	3	∼	∼	NOUN
ejpam-6418	189	4	b	b	NOUN
ejpam-6418	189	5	,	,	PUNCT
ejpam-6418	189	6	for	for	ADP
ejpam-6418	189	7	all	all	DET
ejpam-6418	189	8	a	a	DET
ejpam-6418	189	9	∈	∈	NOUN
ejpam-6418	189	10	m	m	NOUN
ejpam-6418	189	11	.	.	PUNCT
ejpam-6418	190	1	by	by	ADP
ejpam-6418	190	2	lemma	lemma	PROPN
ejpam-6418	190	3	3.13	3.13	NUM
ejpam-6418	190	4	.	.	PUNCT
ejpam-6418	190	5	,	,	PUNCT
ejpam-6418	190	6	b	b	X
ejpam-6418	190	7	∈	∈	ADV
ejpam-6418	190	8	m	m	VERB
ejpam-6418	190	9	.	.	PUNCT
ejpam-6418	191	1	hence	hence	ADV
ejpam-6418	191	2	m	m	PROPN
ejpam-6418	191	3	is	be	AUX
ejpam-6418	191	4	an	an	DET
ejpam-6418	191	5	initial	initial	ADJ
ejpam-6418	191	6	segment	segment	NOUN
ejpam-6418	191	7	.	.	PUNCT
ejpam-6418	192	1	definition	definition	NOUN
ejpam-6418	192	2	3.15	3.15	NUM
ejpam-6418	192	3	.	.	PUNCT
ejpam-6418	193	1	in	in	ADP
ejpam-6418	193	2	a	a	DET
ejpam-6418	193	3	pdl	pdl	NOUN
ejpam-6418	193	4	v	v	NOUN
ejpam-6418	193	5	,	,	PUNCT
ejpam-6418	193	6	we	we	PRON
ejpam-6418	193	7	define	define	VERB
ejpam-6418	193	8	the	the	DET
ejpam-6418	193	9	center	center	NOUN
ejpam-6418	193	10	of	of	ADP
ejpam-6418	193	11	v	v	NOUN
ejpam-6418	193	12	as	as	ADP
ejpam-6418	193	13	the	the	DET
ejpam-6418	193	14	set	set	NOUN
ejpam-6418	193	15	c(v	c(v	PROPN
ejpam-6418	193	16	)	)	PUNCT
ejpam-6418	193	17	=	=	PRON
ejpam-6418	193	18	{	{	PUNCT
ejpam-6418	193	19	a	a	DET
ejpam-6418	193	20	∈	∈	NOUN
ejpam-6418	193	21	v	v	ADP
ejpam-6418	193	22	|	|	ADV
ejpam-6418	193	23	a	a	DET
ejpam-6418	193	24	∼	∼	NOUN
ejpam-6418	193	25	c	c	NOUN
ejpam-6418	193	26	,	,	PUNCT
ejpam-6418	193	27	for	for	ADP
ejpam-6418	193	28	all	all	PRON
ejpam-6418	193	29	c	c	NOUN
ejpam-6418	193	30	∈	∈	ADV
ejpam-6418	193	31	v	v	ADP
ejpam-6418	193	32	}	}	PUNCT
ejpam-6418	193	33	.	.	PUNCT
ejpam-6418	194	1	theorem	theorem	VERB
ejpam-6418	194	2	3.16	3.16	NUM
ejpam-6418	194	3	.	.	PUNCT
ejpam-6418	195	1	c(v	c(v	PROPN
ejpam-6418	195	2	)	)	PUNCT
ejpam-6418	195	3	is	be	AUX
ejpam-6418	195	4	the	the	DET
ejpam-6418	195	5	intersection	intersection	NOUN
ejpam-6418	195	6	of	of	ADP
ejpam-6418	195	7	all	all	DET
ejpam-6418	195	8	maximal	maximal	ADJ
ejpam-6418	195	9	sets	set	NOUN
ejpam-6418	195	10	in	in	ADP
ejpam-6418	195	11	v.	v.	ADP
ejpam-6418	195	12	proof	proof	NOUN
ejpam-6418	195	13	.	.	PUNCT
ejpam-6418	196	1	if	if	SCONJ
ejpam-6418	196	2	a	a	DET
ejpam-6418	196	3	∈	∈	PROPN
ejpam-6418	196	4	c(v	c(v	PROPN
ejpam-6418	196	5	)	)	PUNCT
ejpam-6418	196	6	and	and	CCONJ
ejpam-6418	196	7	m	m	PROPN
ejpam-6418	196	8	is	be	AUX
ejpam-6418	196	9	a	a	DET
ejpam-6418	196	10	maximal	maximal	ADJ
ejpam-6418	196	11	set	set	NOUN
ejpam-6418	196	12	in	in	ADP
ejpam-6418	196	13	v.	v.	ADP
ejpam-6418	196	14	then	then	ADV
ejpam-6418	196	15	m	m	VERB
ejpam-6418	196	16	∪	∪	ADJ
ejpam-6418	196	17	{	{	PUNCT
ejpam-6418	196	18	a	a	PRON
ejpam-6418	196	19	}	}	PUNCT
ejpam-6418	196	20	is	be	AUX
ejpam-6418	196	21	compatible	compatible	ADJ
ejpam-6418	196	22	and	and	CCONJ
ejpam-6418	196	23	by	by	ADP
ejpam-6418	196	24	the	the	DET
ejpam-6418	196	25	maximality	maximality	NOUN
ejpam-6418	196	26	of	of	ADP
ejpam-6418	196	27	m	m	PROPN
ejpam-6418	196	28	,	,	PUNCT
ejpam-6418	196	29	a	a	DET
ejpam-6418	196	30	∈	∈	NOUN
ejpam-6418	196	31	m	m	VERB
ejpam-6418	196	32	(	(	PUNCT
ejpam-6418	196	33	by	by	ADP
ejpam-6418	196	34	lemma	lemma	PROPN
ejpam-6418	196	35	3.13	3.13	NUM
ejpam-6418	196	36	.	.	PUNCT
ejpam-6418	196	37	)	)	PUNCT
ejpam-6418	196	38	.	.	PUNCT
ejpam-6418	197	1	therefore	therefore	ADV
ejpam-6418	197	2	c(v	c(v	PROPN
ejpam-6418	197	3	)	)	PUNCT
ejpam-6418	197	4	⊆	⊆	NUM
ejpam-6418	197	5	m	m	NOUN
ejpam-6418	197	6	,	,	PUNCT
ejpam-6418	197	7	for	for	ADP
ejpam-6418	197	8	all	all	DET
ejpam-6418	197	9	maximal	maximal	ADJ
ejpam-6418	197	10	sets	set	NOUN
ejpam-6418	197	11	in	in	ADP
ejpam-6418	197	12	v.	v.	ADP
ejpam-6418	197	13	on	on	ADP
ejpam-6418	197	14	the	the	DET
ejpam-6418	197	15	other	other	ADJ
ejpam-6418	197	16	hand	hand	NOUN
ejpam-6418	197	17	,	,	PUNCT
ejpam-6418	197	18	let	let	VERB
ejpam-6418	197	19	a	a	DET
ejpam-6418	197	20	∈	∈	NOUN
ejpam-6418	197	21	v	v	ADP
ejpam-6418	197	22	such	such	DET
ejpam-6418	197	23	that	that	SCONJ
ejpam-6418	197	24	a	a	DET
ejpam-6418	197	25	/∈	/∈	NOUN
ejpam-6418	197	26	c(v	c(v	PROPN
ejpam-6418	197	27	)	)	PUNCT
ejpam-6418	197	28	.	.	PUNCT
ejpam-6418	198	1	then	then	ADV
ejpam-6418	198	2	there	there	PRON
ejpam-6418	198	3	exists	exist	VERB
ejpam-6418	198	4	c	c	NOUN
ejpam-6418	198	5	in	in	ADP
ejpam-6418	198	6	v	v	NUM
ejpam-6418	198	7	such	such	DET
ejpam-6418	198	8	that	that	SCONJ
ejpam-6418	198	9	a	a	PRON
ejpam-6418	198	10	is	be	AUX
ejpam-6418	198	11	not	not	PART
ejpam-6418	198	12	compatible	compatible	ADJ
ejpam-6418	198	13	with	with	ADP
ejpam-6418	198	14	c.	c.	PROPN
ejpam-6418	198	15	put	put	VERB
ejpam-6418	198	16	p	p	NOUN
ejpam-6418	198	17	=	=	PUNCT
ejpam-6418	198	18	{	{	PUNCT
ejpam-6418	198	19	c	c	NOUN
ejpam-6418	198	20	⊆	⊆	PROPN
ejpam-6418	198	21	v	v	ADP
ejpam-6418	198	22	|	|	ADV
ejpam-6418	198	23	c	c	NOUN
ejpam-6418	198	24	is	be	AUX
ejpam-6418	198	25	compatible	compatible	ADJ
ejpam-6418	198	26	,	,	PUNCT
ejpam-6418	198	27	c	c	PROPN
ejpam-6418	198	28	∈	∈	PROPN
ejpam-6418	198	29	c	c	PROPN
ejpam-6418	198	30	and	and	CCONJ
ejpam-6418	198	31	a	a	DET
ejpam-6418	198	32	/∈	/∈	NOUN
ejpam-6418	198	33	c	c	NOUN
ejpam-6418	198	34	}	}	PUNCT
ejpam-6418	198	35	.	.	PUNCT
ejpam-6418	199	1	then	then	ADV
ejpam-6418	199	2	{	{	PUNCT
ejpam-6418	199	3	c	c	X
ejpam-6418	199	4	}	}	PUNCT
ejpam-6418	199	5	∈	∈	PROPN
ejpam-6418	199	6	p.	p.	NOUN
ejpam-6418	199	7	therefore	therefore	ADV
ejpam-6418	199	8	p	p	PROPN
ejpam-6418	199	9	is	be	AUX
ejpam-6418	199	10	non	non	ADJ
ejpam-6418	199	11	-	-	ADJ
ejpam-6418	199	12	empty	empty	ADJ
ejpam-6418	199	13	and	and	CCONJ
ejpam-6418	199	14	(	(	PUNCT
ejpam-6418	199	15	p,⊆	p,⊆	ADJ
ejpam-6418	199	16	)	)	PUNCT
ejpam-6418	199	17	is	be	AUX
ejpam-6418	199	18	a	a	DET
ejpam-6418	199	19	partial	partial	ADJ
ejpam-6418	199	20	order	order	NOUN
ejpam-6418	199	21	set	set	NOUN
ejpam-6418	199	22	.	.	PUNCT
ejpam-6418	200	1	let	let	VERB
ejpam-6418	200	2	r.	r.	PROPN
ejpam-6418	200	3	sirisetti	sirisetti	VERB
ejpam-6418	200	4	et	et	PROPN
ejpam-6418	200	5	al	al	PROPN
ejpam-6418	200	6	.	.	PUNCT
ejpam-6418	200	7	/	/	SYM
ejpam-6418	200	8	eur	eur	PROPN
ejpam-6418	200	9	.	.	PUNCT
ejpam-6418	201	1	j.	j.	PROPN
ejpam-6418	201	2	pure	pure	PROPN
ejpam-6418	201	3	appl	appl	PROPN
ejpam-6418	201	4	.	.	PROPN
ejpam-6418	201	5	math	math	PROPN
ejpam-6418	201	6	,	,	PUNCT
ejpam-6418	201	7	18	18	NUM
ejpam-6418	201	8	(	(	PUNCT
ejpam-6418	201	9	4	4	NUM
ejpam-6418	201	10	)	)	PUNCT
ejpam-6418	201	11	(	(	PUNCT
ejpam-6418	201	12	2025	2025	NUM
ejpam-6418	201	13	)	)	PUNCT
ejpam-6418	201	14	,	,	PUNCT
ejpam-6418	201	15	6418	6418	NUM
ejpam-6418	201	16	9	9	NUM
ejpam-6418	201	17	of	of	ADP
ejpam-6418	201	18	13	13	NUM
ejpam-6418	201	19	c1	c1	NOUN
ejpam-6418	201	20	⊆	⊆	NUM
ejpam-6418	201	21	c2	c2	PROPN
ejpam-6418	201	22	⊆	⊆	NUM
ejpam-6418	201	23	c3	c3	PROPN
ejpam-6418	201	24	⊆	⊆	NUM
ejpam-6418	201	25	...	...	PUNCT
ejpam-6418	202	1	⊆	⊆	NUM
ejpam-6418	202	2	cn	cn	NUM
ejpam-6418	202	3	⊆	⊆	NUM
ejpam-6418	202	4	....	....	PUNCT
ejpam-6418	202	5	be	be	AUX
ejpam-6418	202	6	a	a	DET
ejpam-6418	202	7	chain	chain	NOUN
ejpam-6418	202	8	in	in	ADP
ejpam-6418	202	9	p.	p.	NOUN
ejpam-6418	202	10	if	if	SCONJ
ejpam-6418	202	11	a	a	DET
ejpam-6418	202	12	∈	∈	PROPN
ejpam-6418	202	13	∪i∈ici	∪i∈ici	NOUN
ejpam-6418	202	14	.	.	PUNCT
ejpam-6418	203	1	then	then	ADV
ejpam-6418	203	2	a	a	DET
ejpam-6418	203	3	∈	∈	PROPN
ejpam-6418	203	4	ci	ci	NOUN
ejpam-6418	203	5	,	,	PUNCT
ejpam-6418	203	6	for	for	ADP
ejpam-6418	203	7	some	some	DET
ejpam-6418	203	8	i	i	PRON
ejpam-6418	203	9	which	which	PRON
ejpam-6418	203	10	is	be	AUX
ejpam-6418	203	11	a	a	DET
ejpam-6418	203	12	contradiction	contradiction	NOUN
ejpam-6418	203	13	to	to	ADP
ejpam-6418	203	14	a	a	DET
ejpam-6418	203	15	/∈	/∈	NOUN
ejpam-6418	203	16	ci	ci	NOUN
ejpam-6418	203	17	,	,	PUNCT
ejpam-6418	203	18	for	for	ADP
ejpam-6418	203	19	every	every	DET
ejpam-6418	203	20	i.	i.	NOUN
ejpam-6418	203	21	if	if	SCONJ
ejpam-6418	203	22	∪i∈ici	∪i∈ici	NOUN
ejpam-6418	203	23	is	be	AUX
ejpam-6418	203	24	not	not	PART
ejpam-6418	203	25	comparable	comparable	ADJ
ejpam-6418	203	26	,	,	PUNCT
ejpam-6418	203	27	then	then	ADV
ejpam-6418	203	28	there	there	PRON
ejpam-6418	203	29	exist	exist	VERB
ejpam-6418	203	30	b	b	NOUN
ejpam-6418	203	31	,	,	PUNCT
ejpam-6418	203	32	c	c	PROPN
ejpam-6418	203	33	∈	∈	PROPN
ejpam-6418	203	34	∪i∈ici	∪i∈ici	NOUN
ejpam-6418	203	35	such	such	ADJ
ejpam-6418	203	36	that	that	SCONJ
ejpam-6418	203	37	b	b	NOUN
ejpam-6418	203	38	is	be	AUX
ejpam-6418	203	39	incomparable	incomparable	ADJ
ejpam-6418	203	40	with	with	ADP
ejpam-6418	203	41	c	c	PROPN
ejpam-6418	203	42	where	where	SCONJ
ejpam-6418	203	43	b	b	PROPN
ejpam-6418	203	44	∈	∈	PROPN
ejpam-6418	203	45	ci	ci	PROPN
ejpam-6418	203	46	,	,	PUNCT
ejpam-6418	203	47	c	c	PROPN
ejpam-6418	203	48	∈	∈	PROPN
ejpam-6418	203	49	cj	cj	NOUN
ejpam-6418	203	50	,	,	PUNCT
ejpam-6418	203	51	for	for	ADP
ejpam-6418	203	52	some	some	DET
ejpam-6418	203	53	i	i	PROPN
ejpam-6418	203	54	,	,	PUNCT
ejpam-6418	203	55	j	j	PROPN
ejpam-6418	203	56	∈	∈	PROPN
ejpam-6418	203	57	i.	i.	NOUN
ejpam-6418	203	58	but	but	CCONJ
ejpam-6418	203	59	ci	ci	PROPN
ejpam-6418	203	60	⊆	⊆	NUM
ejpam-6418	203	61	cj	cj	NOUN
ejpam-6418	203	62	or	or	CCONJ
ejpam-6418	203	63	cj	cj	NUM
ejpam-6418	203	64	⊆	⊆	NUM
ejpam-6418	203	65	ci	ci	PROPN
ejpam-6418	203	66	,	,	PUNCT
ejpam-6418	203	67	b	b	NOUN
ejpam-6418	203	68	,	,	PUNCT
ejpam-6418	203	69	c	c	PROPN
ejpam-6418	203	70	∈	∈	PROPN
ejpam-6418	203	71	ci	ci	PROPN
ejpam-6418	203	72	or	or	CCONJ
ejpam-6418	203	73	b	b	NOUN
ejpam-6418	203	74	,	,	PUNCT
ejpam-6418	203	75	c	c	PROPN
ejpam-6418	203	76	∈	∈	PROPN
ejpam-6418	203	77	cj	cj	X
ejpam-6418	203	78	.	.	PUNCT
ejpam-6418	204	1	then	then	ADV
ejpam-6418	204	2	b	b	X
ejpam-6418	204	3	∼	∼	NOUN
ejpam-6418	204	4	c	c	NOUN
ejpam-6418	204	5	which	which	PRON
ejpam-6418	204	6	is	be	AUX
ejpam-6418	204	7	contradiction	contradiction	NOUN
ejpam-6418	204	8	.	.	PUNCT
ejpam-6418	205	1	so	so	ADV
ejpam-6418	205	2	that	that	DET
ejpam-6418	205	3	∪i∈ici	∪i∈ici	NOUN
ejpam-6418	205	4	is	be	AUX
ejpam-6418	205	5	compatible	compatible	ADJ
ejpam-6418	205	6	.	.	PUNCT
ejpam-6418	206	1	therefore	therefore	ADV
ejpam-6418	206	2	∪i∈ici	∪i∈ici	NOUN
ejpam-6418	206	3	is	be	AUX
ejpam-6418	206	4	an	an	DET
ejpam-6418	206	5	upper	upper	ADJ
ejpam-6418	206	6	bound	bind	VERB
ejpam-6418	206	7	in	in	ADP
ejpam-6418	206	8	p.	p.	NOUN
ejpam-6418	206	9	by	by	ADP
ejpam-6418	206	10	zorn	zorn	PROPN
ejpam-6418	206	11	’s	’s	PART
ejpam-6418	206	12	lemma	lemma	PROPN
ejpam-6418	206	13	,	,	PUNCT
ejpam-6418	206	14	p	p	PROPN
ejpam-6418	206	15	has	have	VERB
ejpam-6418	206	16	a	a	DET
ejpam-6418	206	17	maximal	maximal	ADJ
ejpam-6418	206	18	member	member	NOUN
ejpam-6418	206	19	,	,	PUNCT
ejpam-6418	206	20	say	say	VERB
ejpam-6418	206	21	q.	q.	PROPN
ejpam-6418	206	22	suppose	suppose	VERB
ejpam-6418	206	23	n	n	PRON
ejpam-6418	206	24	is	be	AUX
ejpam-6418	206	25	compatible	compatible	ADJ
ejpam-6418	206	26	in	in	ADP
ejpam-6418	206	27	v	v	ADP
ejpam-6418	206	28	such	such	DET
ejpam-6418	207	1	that	that	PRON
ejpam-6418	207	2	q	q	PROPN
ejpam-6418	208	1	⊂	⊂	PROPN
ejpam-6418	208	2	n.	n.	PROPN
ejpam-6418	208	3	then	then	ADV
ejpam-6418	208	4	c	c	PROPN
ejpam-6418	208	5	∈	∈	PROPN
ejpam-6418	208	6	n.	n.	NOUN
ejpam-6418	208	7	since	since	SCONJ
ejpam-6418	208	8	c	c	PROPN
ejpam-6418	208	9	is	be	AUX
ejpam-6418	208	10	incomparable	incomparable	ADJ
ejpam-6418	208	11	a	a	DET
ejpam-6418	208	12	,	,	PUNCT
ejpam-6418	208	13	a	a	DET
ejpam-6418	208	14	/∈	/∈	X
ejpam-6418	208	15	n.	n.	NOUN
ejpam-6418	208	16	therefore	therefore	ADV
ejpam-6418	208	17	n	n	PROPN
ejpam-6418	208	18	∈	∈	PROPN
ejpam-6418	208	19	p.	p.	NOUN
ejpam-6418	208	20	by	by	ADP
ejpam-6418	208	21	maximality	maximality	NOUN
ejpam-6418	208	22	of	of	ADP
ejpam-6418	208	23	q	q	NOUN
ejpam-6418	208	24	in	in	ADP
ejpam-6418	208	25	p	p	X
ejpam-6418	208	26	,	,	PUNCT
ejpam-6418	208	27	we	we	PRON
ejpam-6418	208	28	get	get	VERB
ejpam-6418	208	29	q	q	NOUN
ejpam-6418	208	30	=	=	PUNCT
ejpam-6418	208	31	n.	n.	NOUN
ejpam-6418	208	32	thus	thus	ADV
ejpam-6418	208	33	q	q	X
ejpam-6418	208	34	is	be	AUX
ejpam-6418	208	35	maximal	maximal	ADJ
ejpam-6418	208	36	set	set	VERB
ejpam-6418	208	37	in	in	ADP
ejpam-6418	208	38	v	v	NOUN
ejpam-6418	208	39	and	and	CCONJ
ejpam-6418	208	40	a	a	DET
ejpam-6418	208	41	/∈	/∈	NOUN
ejpam-6418	208	42	q.	q.	NOUN
ejpam-6418	208	43	this	this	PRON
ejpam-6418	208	44	proves	prove	VERB
ejpam-6418	208	45	that	that	SCONJ
ejpam-6418	208	46	c(v	c(v	PROPN
ejpam-6418	208	47	)	)	PUNCT
ejpam-6418	208	48	is	be	AUX
ejpam-6418	208	49	equal	equal	ADJ
ejpam-6418	208	50	to	to	ADP
ejpam-6418	208	51	the	the	DET
ejpam-6418	208	52	intersection	intersection	NOUN
ejpam-6418	208	53	of	of	ADP
ejpam-6418	208	54	all	all	DET
ejpam-6418	208	55	maximal	maximal	ADJ
ejpam-6418	208	56	sets	set	NOUN
ejpam-6418	208	57	in	in	ADP
ejpam-6418	208	58	v.	v.	CCONJ
ejpam-6418	208	59	theorem	theorem	ADJ
ejpam-6418	208	60	3.17	3.17	NUM
ejpam-6418	208	61	.	.	PUNCT
ejpam-6418	209	1	c(v	c(v	PROPN
ejpam-6418	209	2	)	)	PUNCT
ejpam-6418	209	3	is	be	AUX
ejpam-6418	209	4	a	a	DET
ejpam-6418	209	5	filter	filter	NOUN
ejpam-6418	209	6	of	of	ADP
ejpam-6418	209	7	v.	v.	ADP
ejpam-6418	209	8	proof	proof	NOUN
ejpam-6418	209	9	.	.	PUNCT
ejpam-6418	210	1	it	it	PRON
ejpam-6418	210	2	is	be	AUX
ejpam-6418	210	3	easy	easy	ADJ
ejpam-6418	210	4	to	to	PART
ejpam-6418	210	5	observe	observe	VERB
ejpam-6418	210	6	that	that	SCONJ
ejpam-6418	210	7	c(v	c(v	PROPN
ejpam-6418	210	8	)	)	PUNCT
ejpam-6418	210	9	is	be	AUX
ejpam-6418	210	10	the	the	DET
ejpam-6418	210	11	intersection	intersection	NOUN
ejpam-6418	210	12	of	of	ADP
ejpam-6418	210	13	all	all	DET
ejpam-6418	210	14	maximal	maximal	ADJ
ejpam-6418	210	15	sets	set	NOUN
ejpam-6418	210	16	in	in	ADP
ejpam-6418	210	17	v.	v.	ADP
ejpam-6418	210	18	since	since	SCONJ
ejpam-6418	210	19	each	each	DET
ejpam-6418	210	20	maximal	maximal	ADJ
ejpam-6418	210	21	set	set	NOUN
ejpam-6418	210	22	is	be	AUX
ejpam-6418	210	23	closed	close	VERB
ejpam-6418	210	24	under	under	ADP
ejpam-6418	210	25	∧	∧	PROPN
ejpam-6418	210	26	and	and	CCONJ
ejpam-6418	210	27	∨	∨	NUM
ejpam-6418	210	28	,	,	PUNCT
ejpam-6418	210	29	we	we	PRON
ejpam-6418	210	30	have	have	AUX
ejpam-6418	210	31	c(v	c(v	PROPN
ejpam-6418	210	32	)	)	PUNCT
ejpam-6418	210	33	is	be	AUX
ejpam-6418	210	34	closed	close	VERB
ejpam-6418	210	35	under	under	ADP
ejpam-6418	210	36	∧	∧	NOUN
ejpam-6418	210	37	and	and	CCONJ
ejpam-6418	210	38	∨.	∨.	NOUN
ejpam-6418	210	39	let	let	VERB
ejpam-6418	210	40	a	a	DET
ejpam-6418	210	41	∈	∈	PROPN
ejpam-6418	210	42	c(v	c(v	PROPN
ejpam-6418	210	43	)	)	PUNCT
ejpam-6418	210	44	,	,	PUNCT
ejpam-6418	210	45	b	b	X
ejpam-6418	210	46	,	,	PUNCT
ejpam-6418	210	47	c	c	PROPN
ejpam-6418	210	48	∈	∈	PROPN
ejpam-6418	211	1	v.	v.	CCONJ
ejpam-6418	211	2	then	then	ADV
ejpam-6418	211	3	,	,	PUNCT
ejpam-6418	211	4	c	c	PROPN
ejpam-6418	211	5	∨	∨	X
ejpam-6418	211	6	(	(	PUNCT
ejpam-6418	211	7	b	b	PROPN
ejpam-6418	211	8	∨	∨	NUM
ejpam-6418	211	9	a	a	PRON
ejpam-6418	211	10	)	)	PUNCT
ejpam-6418	211	11	=	=	SYM
ejpam-6418	211	12	(	(	PUNCT
ejpam-6418	211	13	c	c	PROPN
ejpam-6418	211	14	∨	∨	NUM
ejpam-6418	211	15	b	b	NOUN
ejpam-6418	211	16	)	)	PUNCT
ejpam-6418	211	17	∨	∨	NUM
ejpam-6418	211	18	a	a	PRON
ejpam-6418	211	19	(	(	PUNCT
ejpam-6418	211	20	∨	∨	NOUN
ejpam-6418	211	21	is	be	AUX
ejpam-6418	211	22	associative	associative	ADJ
ejpam-6418	211	23	)	)	PUNCT
ejpam-6418	211	24	=	=	PUNCT
ejpam-6418	211	25	a	a	DET
ejpam-6418	211	26	∨	∨	NOUN
ejpam-6418	211	27	(	(	PUNCT
ejpam-6418	211	28	c	c	PROPN
ejpam-6418	211	29	∨	∨	NUM
ejpam-6418	211	30	b	b	NOUN
ejpam-6418	211	31	)	)	PUNCT
ejpam-6418	211	32	(	(	PUNCT
ejpam-6418	211	33	since	since	SCONJ
ejpam-6418	211	34	a	a	DET
ejpam-6418	211	35	∈	∈	PROPN
ejpam-6418	211	36	c(v	c(v	PROPN
ejpam-6418	211	37	)	)	PUNCT
ejpam-6418	211	38	)	)	PUNCT
ejpam-6418	212	1	=	=	PUNCT
ejpam-6418	212	2	a	a	DET
ejpam-6418	212	3	∨	∨	NOUN
ejpam-6418	212	4	(	(	PUNCT
ejpam-6418	212	5	b	b	PROPN
ejpam-6418	212	6	∨	∨	NUM
ejpam-6418	212	7	c	c	NOUN
ejpam-6418	212	8	)	)	PUNCT
ejpam-6418	212	9	(	(	PUNCT
ejpam-6418	212	10	by	by	ADP
ejpam-6418	212	11	lemma	lemma	PROPN
ejpam-6418	212	12	2.4(viii	2.4(viii	NUM
ejpam-6418	212	13	)	)	PUNCT
ejpam-6418	212	14	)	)	PUNCT
ejpam-6418	213	1	=	=	PRON
ejpam-6418	213	2	(	(	PUNCT
ejpam-6418	213	3	a	a	DET
ejpam-6418	213	4	∨	∨	NUM
ejpam-6418	213	5	b	b	NOUN
ejpam-6418	213	6	)	)	PUNCT
ejpam-6418	213	7	∨	∨	PROPN
ejpam-6418	213	8	c	c	PROPN
ejpam-6418	213	9	(	(	PUNCT
ejpam-6418	213	10	∨	∨	NOUN
ejpam-6418	213	11	is	be	AUX
ejpam-6418	213	12	associative	associative	ADJ
ejpam-6418	213	13	)	)	PUNCT
ejpam-6418	213	14	=	=	PUNCT
ejpam-6418	214	1	(	(	PUNCT
ejpam-6418	214	2	b	b	PROPN
ejpam-6418	214	3	∨	∨	NUM
ejpam-6418	214	4	a	a	PRON
ejpam-6418	214	5	)	)	PUNCT
ejpam-6418	214	6	∨	∨	NUM
ejpam-6418	214	7	c	c	X
ejpam-6418	214	8	(	(	PUNCT
ejpam-6418	214	9	since	since	SCONJ
ejpam-6418	214	10	a	a	DET
ejpam-6418	214	11	∈	∈	PROPN
ejpam-6418	214	12	c(v	c(v	PROPN
ejpam-6418	214	13	)	)	PUNCT
ejpam-6418	214	14	)	)	PUNCT
ejpam-6418	215	1	(	(	PUNCT
ejpam-6418	215	2	b	b	X
ejpam-6418	215	3	∨	∨	NUM
ejpam-6418	215	4	a	a	PRON
ejpam-6418	215	5	)	)	PUNCT
ejpam-6418	215	6	∨	∨	NUM
ejpam-6418	215	7	c	c	NOUN
ejpam-6418	215	8	=	=	SYM
ejpam-6418	215	9	c	c	PROPN
ejpam-6418	215	10	∨	∨	X
ejpam-6418	215	11	(	(	PUNCT
ejpam-6418	215	12	b	b	PROPN
ejpam-6418	215	13	∨	∨	NUM
ejpam-6418	215	14	a	a	PRON
ejpam-6418	215	15	)	)	PUNCT
ejpam-6418	215	16	.	.	PUNCT
ejpam-6418	216	1	therefore	therefore	ADV
ejpam-6418	216	2	b	b	X
ejpam-6418	216	3	∨	∨	NUM
ejpam-6418	216	4	a	a	DET
ejpam-6418	216	5	∈	∈	PROPN
ejpam-6418	216	6	c(v	c(v	PROPN
ejpam-6418	216	7	)	)	PUNCT
ejpam-6418	216	8	,	,	PUNCT
ejpam-6418	216	9	for	for	ADP
ejpam-6418	216	10	all	all	DET
ejpam-6418	216	11	b	b	NOUN
ejpam-6418	216	12	∈	∈	NOUN
ejpam-6418	216	13	v.	v.	ADP
ejpam-6418	216	14	thus	thus	ADV
ejpam-6418	216	15	c(v	c(v	PROPN
ejpam-6418	216	16	)	)	PUNCT
ejpam-6418	216	17	is	be	AUX
ejpam-6418	216	18	a	a	DET
ejpam-6418	216	19	filter	filter	NOUN
ejpam-6418	216	20	of	of	ADP
ejpam-6418	216	21	v.	v.	CCONJ
ejpam-6418	216	22	theorem	theorem	ADJ
ejpam-6418	216	23	3.18	3.18	NUM
ejpam-6418	216	24	.	.	PUNCT
ejpam-6418	217	1	if	if	SCONJ
ejpam-6418	217	2	{	{	PUNCT
ejpam-6418	217	3	vα}α∈∆	vα}α∈∆	NOUN
ejpam-6418	217	4	is	be	AUX
ejpam-6418	217	5	a	a	DET
ejpam-6418	217	6	family	family	NOUN
ejpam-6418	217	7	of	of	ADP
ejpam-6418	217	8	pdls	pdl	NOUN
ejpam-6418	217	9	,	,	PUNCT
ejpam-6418	217	10	then	then	ADV
ejpam-6418	217	11	c	c	X
ejpam-6418	217	12	(	(	PUNCT
ejpam-6418	217	13	∏	∏	PROPN
ejpam-6418	217	14	α∈∆vα	α∈∆vα	NUM
ejpam-6418	217	15	)	)	PUNCT
ejpam-6418	217	16	=	=	SYM
ejpam-6418	217	17	∏	∏	PROPN
ejpam-6418	217	18	α∈∆c(vα	α∈∆c(vα	NUM
ejpam-6418	217	19	)	)	PUNCT
ejpam-6418	217	20	.	.	PUNCT
ejpam-6418	218	1	proof	proof	NOUN
ejpam-6418	218	2	.	.	PUNCT
ejpam-6418	219	1	let	let	VERB
ejpam-6418	219	2	a	a	DET
ejpam-6418	219	3	∈	∈	ADJ
ejpam-6418	219	4	c	c	X
ejpam-6418	219	5	(	(	PUNCT
ejpam-6418	219	6	∏	∏	PROPN
ejpam-6418	219	7	β∈∆vβ	β∈∆vβ	NOUN
ejpam-6418	219	8	)	)	PUNCT
ejpam-6418	219	9	.	.	PUNCT
ejpam-6418	220	1	then	then	ADV
ejpam-6418	220	2	a	a	DET
ejpam-6418	220	3	∼	∼	NOUN
ejpam-6418	220	4	x	x	NOUN
ejpam-6418	220	5	,	,	PUNCT
ejpam-6418	220	6	for	for	ADP
ejpam-6418	220	7	all	all	DET
ejpam-6418	220	8	x	x	SYM
ejpam-6418	220	9	∈	∈	PROPN
ejpam-6418	220	10	∏	∏	NUM
ejpam-6418	220	11	β∈∆vβ	β∈∆vβ	NOUN
ejpam-6418	220	12	.	.	PUNCT
ejpam-6418	221	1	let	let	VERB
ejpam-6418	221	2	α	α	PRON
ejpam-6418	221	3	∈	∈	NOUN
ejpam-6418	221	4	∆	∆	PROPN
ejpam-6418	221	5	and	and	CCONJ
ejpam-6418	221	6	s	s	PROPN
ejpam-6418	221	7	∈	∈	NOUN
ejpam-6418	221	8	vα	vα	INTJ
ejpam-6418	221	9	.	.	PUNCT
ejpam-6418	222	1	if	if	SCONJ
ejpam-6418	222	2	x	x	PROPN
ejpam-6418	222	3	∈	∈	NOUN
ejpam-6418	222	4	∏	∏	X
ejpam-6418	222	5	β∈∆vβ	β∈∆vβ	NOUN
ejpam-6418	222	6	)	)	PUNCT
ejpam-6418	222	7	such	such	ADJ
ejpam-6418	222	8	that	that	SCONJ
ejpam-6418	222	9	x(α	x(α	PROPN
ejpam-6418	222	10	)	)	PUNCT
ejpam-6418	223	1	=	=	PUNCT
ejpam-6418	223	2	s.	s.	PROPN
ejpam-6418	223	3	since	since	SCONJ
ejpam-6418	223	4	a	a	DET
ejpam-6418	223	5	∈	∈	PROPN
ejpam-6418	223	6	c	c	X
ejpam-6418	223	7	(	(	PUNCT
ejpam-6418	223	8	∏	∏	PROPN
ejpam-6418	223	9	β∈∆vβ	β∈∆vβ	NOUN
ejpam-6418	223	10	)	)	PUNCT
ejpam-6418	223	11	,	,	PUNCT
ejpam-6418	223	12	a	a	DET
ejpam-6418	223	13	∼	∼	NOUN
ejpam-6418	223	14	x	x	PUNCT
ejpam-6418	223	15	and	and	CCONJ
ejpam-6418	223	16	hence	hence	ADV
ejpam-6418	223	17	a	a	DET
ejpam-6418	223	18	∧	∧	NOUN
ejpam-6418	223	19	x	x	X
ejpam-6418	223	20	=	=	PUNCT
ejpam-6418	223	21	x	x	SYM
ejpam-6418	223	22	∧	∧	NOUN
ejpam-6418	223	23	a.	a.	NOUN
ejpam-6418	223	24	therefore	therefore	ADV
ejpam-6418	223	25	(	(	PUNCT
ejpam-6418	223	26	a	a	DET
ejpam-6418	223	27	∧	∧	PROPN
ejpam-6418	223	28	x(α	x(α	PROPN
ejpam-6418	223	29	)	)	PUNCT
ejpam-6418	223	30	)	)	PUNCT
ejpam-6418	224	1	=	=	PUNCT
ejpam-6418	224	2	a(α	a(α	VERB
ejpam-6418	224	3	∧	∧	PROPN
ejpam-6418	224	4	x(α	x(α	PROPN
ejpam-6418	224	5	)	)	PUNCT
ejpam-6418	224	6	=	=	SYM
ejpam-6418	224	7	x(α	x(α	PROPN
ejpam-6418	224	8	)	)	PUNCT
ejpam-6418	224	9	∧	∧	NOUN
ejpam-6418	224	10	a(α	a(α	ADV
ejpam-6418	224	11	)	)	PUNCT
ejpam-6418	224	12	=	=	SYM
ejpam-6418	224	13	s	s	PART
ejpam-6418	224	14	∧	∧	PROPN
ejpam-6418	224	15	a(α	a(α	NOUN
ejpam-6418	224	16	)	)	PUNCT
ejpam-6418	224	17	.	.	PUNCT
ejpam-6418	225	1	this	this	PRON
ejpam-6418	225	2	is	be	AUX
ejpam-6418	225	3	true	true	ADJ
ejpam-6418	225	4	for	for	ADP
ejpam-6418	225	5	all	all	DET
ejpam-6418	225	6	s	s	PART
ejpam-6418	225	7	∈	∈	NOUN
ejpam-6418	225	8	vα	vα	NOUN
ejpam-6418	225	9	.	.	PUNCT
ejpam-6418	226	1	so	so	SCONJ
ejpam-6418	226	2	that	that	SCONJ
ejpam-6418	226	3	a(α	a(α	NOUN
ejpam-6418	226	4	)	)	PUNCT
ejpam-6418	226	5	∈	∈	PROPN
ejpam-6418	226	6	c(vα	c(vα	PROPN
ejpam-6418	226	7	)	)	PUNCT
ejpam-6418	226	8	,	,	PUNCT
ejpam-6418	226	9	for	for	ADP
ejpam-6418	226	10	all	all	DET
ejpam-6418	226	11	α	α	NOUN
ejpam-6418	226	12	∈	∈	NOUN
ejpam-6418	227	1	∆.	∆.	X
ejpam-6418	227	2	thus	thus	ADV
ejpam-6418	227	3	a	a	DET
ejpam-6418	227	4	∈	∈	PROPN
ejpam-6418	227	5	∏	∏	PROPN
ejpam-6418	227	6	α∈∆c(vα	α∈∆c(vα	NUM
ejpam-6418	227	7	)	)	PUNCT
ejpam-6418	227	8	.	.	PUNCT
ejpam-6418	228	1	on	on	ADP
ejpam-6418	228	2	the	the	DET
ejpam-6418	228	3	other	other	ADJ
ejpam-6418	228	4	hand	hand	NOUN
ejpam-6418	228	5	,	,	PUNCT
ejpam-6418	228	6	let	let	VERB
ejpam-6418	228	7	a	a	DET
ejpam-6418	228	8	∈	∈	PROPN
ejpam-6418	228	9	∏	∏	PROPN
ejpam-6418	228	10	α∈∆c(vα	α∈∆c(vα	NUM
ejpam-6418	228	11	)	)	PUNCT
ejpam-6418	228	12	.	.	PUNCT
ejpam-6418	229	1	then	then	ADV
ejpam-6418	229	2	a(α	a(α	VERB
ejpam-6418	229	3	)	)	PUNCT
ejpam-6418	229	4	∈	∈	PROPN
ejpam-6418	229	5	c(vα	c(vα	PROPN
ejpam-6418	229	6	)	)	PUNCT
ejpam-6418	229	7	,	,	PUNCT
ejpam-6418	229	8	for	for	ADP
ejpam-6418	229	9	all	all	DET
ejpam-6418	229	10	α	α	NOUN
ejpam-6418	229	11	∈	∈	NOUN
ejpam-6418	230	1	∆.	∆.	X
ejpam-6418	230	2	let	let	VERB
ejpam-6418	230	3	x	x	X
ejpam-6418	230	4	∈	∈	PROPN
ejpam-6418	230	5	∏	∏	PROPN
ejpam-6418	230	6	α∈∆vα	α∈∆vα	NUM
ejpam-6418	230	7	.	.	PUNCT
ejpam-6418	231	1	then	then	ADV
ejpam-6418	231	2	x(α	x(α	PROPN
ejpam-6418	231	3	)	)	PUNCT
ejpam-6418	231	4	∈	∈	PROPN
ejpam-6418	231	5	vα	vα	PROPN
ejpam-6418	231	6	,	,	PUNCT
ejpam-6418	231	7	for	for	ADP
ejpam-6418	231	8	all	all	DET
ejpam-6418	231	9	α	α	NOUN
ejpam-6418	231	10	∈	∈	PROPN
ejpam-6418	232	1	∆.	∆.	NOUN
ejpam-6418	232	2	since	since	SCONJ
ejpam-6418	232	3	a(α	a(α	NOUN
ejpam-6418	232	4	)	)	PUNCT
ejpam-6418	232	5	∈	∈	PROPN
ejpam-6418	232	6	c(vα	c(vα	PROPN
ejpam-6418	232	7	)	)	PUNCT
ejpam-6418	232	8	,	,	PUNCT
ejpam-6418	232	9	for	for	ADP
ejpam-6418	232	10	all	all	DET
ejpam-6418	232	11	α	α	DET
ejpam-6418	232	12	∈	∈	PROPN
ejpam-6418	232	13	∆	∆	PROPN
ejpam-6418	232	14	,	,	PUNCT
ejpam-6418	232	15	a(α	a(α	ADV
ejpam-6418	232	16	)	)	PUNCT
ejpam-6418	232	17	∼	∼	NOUN
ejpam-6418	232	18	x(α	x(α	PROPN
ejpam-6418	232	19	)	)	PUNCT
ejpam-6418	232	20	,	,	PUNCT
ejpam-6418	232	21	for	for	ADP
ejpam-6418	232	22	all	all	DET
ejpam-6418	232	23	α	α	NOUN
ejpam-6418	232	24	∈	∈	NOUN
ejpam-6418	233	1	∆.	∆.	X
ejpam-6418	233	2	therefore	therefore	ADV
ejpam-6418	233	3	a	a	DET
ejpam-6418	233	4	∼	∼	NOUN
ejpam-6418	233	5	x	x	PUNCT
ejpam-6418	233	6	and	and	CCONJ
ejpam-6418	233	7	hence	hence	ADV
ejpam-6418	233	8	a	a	DET
ejpam-6418	233	9	∈	∈	ADJ
ejpam-6418	233	10	c	c	X
ejpam-6418	233	11	(	(	PUNCT
ejpam-6418	233	12	∏	∏	PROPN
ejpam-6418	233	13	α∈∆vα	α∈∆vα	NUM
ejpam-6418	233	14	)	)	PUNCT
ejpam-6418	233	15	.	.	PUNCT
ejpam-6418	234	1	thus	thus	ADV
ejpam-6418	234	2	c	c	X
ejpam-6418	234	3	(	(	PUNCT
ejpam-6418	234	4	∏	∏	PROPN
ejpam-6418	234	5	α∈∆vα	α∈∆vα	NUM
ejpam-6418	234	6	)	)	PUNCT
ejpam-6418	234	7	=	=	SYM
ejpam-6418	234	8	∏	∏	PROPN
ejpam-6418	234	9	α∈∆c(vα	α∈∆c(vα	NUM
ejpam-6418	234	10	)	)	PUNCT
ejpam-6418	234	11	.	.	PUNCT
ejpam-6418	235	1	definition	definition	NOUN
ejpam-6418	235	2	3.19	3.19	NUM
ejpam-6418	235	3	.	.	PUNCT
ejpam-6418	236	1	a	a	DET
ejpam-6418	236	2	maximal	maximal	ADJ
ejpam-6418	236	3	set	set	NOUN
ejpam-6418	236	4	m	m	NOUN
ejpam-6418	236	5	in	in	ADP
ejpam-6418	236	6	v	v	NOUN
ejpam-6418	236	7	is	be	AUX
ejpam-6418	236	8	said	say	VERB
ejpam-6418	236	9	to	to	PART
ejpam-6418	236	10	be	be	AUX
ejpam-6418	236	11	amicable	amicable	ADJ
ejpam-6418	236	12	with	with	ADP
ejpam-6418	236	13	an	an	DET
ejpam-6418	236	14	element	element	NOUN
ejpam-6418	236	15	a	a	PRON
ejpam-6418	236	16	of	of	ADP
ejpam-6418	236	17	v	v	NOUN
ejpam-6418	236	18	,	,	PUNCT
ejpam-6418	236	19	if	if	SCONJ
ejpam-6418	236	20	there	there	PRON
ejpam-6418	236	21	exists	exist	VERB
ejpam-6418	236	22	b	b	PROPN
ejpam-6418	236	23	∈	∈	PROPN
ejpam-6418	236	24	m	m	VERB
ejpam-6418	236	25	such	such	ADJ
ejpam-6418	236	26	that	that	SCONJ
ejpam-6418	236	27	a	a	DET
ejpam-6418	236	28	∨	∨	PROPN
ejpam-6418	236	29	b	b	NOUN
ejpam-6418	236	30	=	=	NOUN
ejpam-6418	236	31	a.	a.	NOUN
ejpam-6418	236	32	the	the	DET
ejpam-6418	236	33	set	set	NOUN
ejpam-6418	236	34	m	m	VERB
ejpam-6418	236	35	is	be	AUX
ejpam-6418	236	36	said	say	VERB
ejpam-6418	236	37	to	to	PART
ejpam-6418	236	38	be	be	AUX
ejpam-6418	236	39	amicable	amicable	ADJ
ejpam-6418	236	40	if	if	SCONJ
ejpam-6418	236	41	it	it	PRON
ejpam-6418	236	42	is	be	AUX
ejpam-6418	236	43	amicable	amicable	ADJ
ejpam-6418	236	44	with	with	ADP
ejpam-6418	236	45	every	every	DET
ejpam-6418	236	46	element	element	NOUN
ejpam-6418	236	47	of	of	ADP
ejpam-6418	236	48	v.	v.	ADP
ejpam-6418	236	49	example	example	NOUN
ejpam-6418	236	50	3.20	3.20	NUM
ejpam-6418	236	51	.	.	PUNCT
ejpam-6418	237	1	in	in	ADP
ejpam-6418	237	2	example	example	NOUN
ejpam-6418	237	3	2.2	2.2	NUM
ejpam-6418	237	4	.	.	NUM
ejpam-6418	237	5	,	,	PUNCT
ejpam-6418	237	6	for	for	ADP
ejpam-6418	237	7	any	any	PRON
ejpam-6418	237	8	x	x	SYM
ejpam-6418	237	9	̸=	̸=	PROPN
ejpam-6418	237	10	1	1	NUM
ejpam-6418	237	11	,	,	PUNCT
ejpam-6418	237	12	{	{	PUNCT
ejpam-6418	237	13	x	x	NOUN
ejpam-6418	237	14	,	,	PUNCT
ejpam-6418	237	15	1	1	NUM
ejpam-6418	237	16	}	}	PUNCT
ejpam-6418	237	17	is	be	AUX
ejpam-6418	237	18	an	an	DET
ejpam-6418	237	19	amicable	amicable	ADJ
ejpam-6418	237	20	set	set	NOUN
ejpam-6418	237	21	.	.	PUNCT
ejpam-6418	238	1	example	example	NOUN
ejpam-6418	239	1	3.21	3.21	NUM
ejpam-6418	239	2	.	.	PUNCT
ejpam-6418	240	1	let	let	VERB
ejpam-6418	240	2	v	v	PART
ejpam-6418	240	3	be	be	AUX
ejpam-6418	240	4	a	a	DET
ejpam-6418	240	5	pdl	pdl	NOUN
ejpam-6418	240	6	with	with	ADP
ejpam-6418	240	7	minimal	minimal	ADJ
ejpam-6418	240	8	elements	element	NOUN
ejpam-6418	240	9	.	.	PUNCT
ejpam-6418	241	1	then	then	ADV
ejpam-6418	241	2	every	every	DET
ejpam-6418	241	3	amicable	amicable	ADJ
ejpam-6418	241	4	set	set	NOUN
ejpam-6418	241	5	is	be	AUX
ejpam-6418	241	6	of	of	ADP
ejpam-6418	241	7	the	the	DET
ejpam-6418	241	8	form	form	NOUN
ejpam-6418	241	9	mm	mm	NOUN
ejpam-6418	241	10	=	=	PUNCT
ejpam-6418	241	11	{	{	PUNCT
ejpam-6418	241	12	x	x	SYM
ejpam-6418	241	13	∈	∈	PROPN
ejpam-6418	241	14	v	v	ADP
ejpam-6418	241	15	|	|	NOUN
ejpam-6418	241	16	x	x	SYM
ejpam-6418	241	17	≤	≤	NOUN
ejpam-6418	241	18	m	m	ADP
ejpam-6418	241	19	}	}	PUNCT
ejpam-6418	241	20	,	,	PUNCT
ejpam-6418	241	21	where	where	SCONJ
ejpam-6418	241	22	m	m	NOUN
ejpam-6418	241	23	is	be	AUX
ejpam-6418	241	24	a	a	DET
ejpam-6418	241	25	minimal	minimal	ADJ
ejpam-6418	241	26	element	element	NOUN
ejpam-6418	241	27	in	in	ADP
ejpam-6418	241	28	v.	v.	CCONJ
ejpam-6418	241	29	theorem	theorem	VERB
ejpam-6418	241	30	3.22	3.22	NUM
ejpam-6418	241	31	.	.	PUNCT
ejpam-6418	242	1	let	let	VERB
ejpam-6418	242	2	m	m	PRON
ejpam-6418	242	3	be	be	AUX
ejpam-6418	242	4	a	a	DET
ejpam-6418	242	5	amicable	amicable	ADJ
ejpam-6418	242	6	set	set	NOUN
ejpam-6418	242	7	in	in	ADP
ejpam-6418	242	8	v.	v.	CCONJ
ejpam-6418	242	9	then	then	ADV
ejpam-6418	242	10	for	for	ADP
ejpam-6418	242	11	each	each	PRON
ejpam-6418	242	12	a	a	DET
ejpam-6418	242	13	∈	∈	PROPN
ejpam-6418	242	14	v	v	NOUN
ejpam-6418	242	15	,	,	PUNCT
ejpam-6418	242	16	there	there	PRON
ejpam-6418	242	17	exists	exist	VERB
ejpam-6418	242	18	a	a	DET
ejpam-6418	242	19	unique	unique	ADJ
ejpam-6418	242	20	a0	a0	NOUN
ejpam-6418	242	21	∈	∈	NOUN
ejpam-6418	242	22	m	m	VERB
ejpam-6418	242	23	such	such	ADJ
ejpam-6418	242	24	that	that	SCONJ
ejpam-6418	242	25	[	[	X
ejpam-6418	242	26	a0	a0	NOUN
ejpam-6418	242	27	)	)	PUNCT
ejpam-6418	242	28	=	=	PUNCT
ejpam-6418	243	1	[	[	X
ejpam-6418	243	2	a	a	X
ejpam-6418	243	3	)	)	PUNCT
ejpam-6418	243	4	i.e.	i.e.	X
ejpam-6418	243	5	,	,	PUNCT
ejpam-6418	243	6	a0	a0	PROPN
ejpam-6418	243	7	∨	∨	NUM
ejpam-6418	243	8	a	a	DET
ejpam-6418	243	9	=	=	X
ejpam-6418	243	10	a0	a0	PROPN
ejpam-6418	243	11	and	and	CCONJ
ejpam-6418	243	12	a	a	DET
ejpam-6418	243	13	∨	∨	NUM
ejpam-6418	243	14	a0	a0	NOUN
ejpam-6418	243	15	=	=	PROPN
ejpam-6418	243	16	a.	a.	PROPN
ejpam-6418	243	17	r.	r.	PROPN
ejpam-6418	243	18	sirisetti	sirisetti	PROPN
ejpam-6418	243	19	et	et	PROPN
ejpam-6418	243	20	al	al	PROPN
ejpam-6418	243	21	.	.	PUNCT
ejpam-6418	243	22	/	/	SYM
ejpam-6418	243	23	eur	eur	PROPN
ejpam-6418	243	24	.	.	PUNCT
ejpam-6418	244	1	j.	j.	PROPN
ejpam-6418	244	2	pure	pure	PROPN
ejpam-6418	244	3	appl	appl	PROPN
ejpam-6418	244	4	.	.	PROPN
ejpam-6418	244	5	math	math	PROPN
ejpam-6418	244	6	,	,	PUNCT
ejpam-6418	244	7	18	18	NUM
ejpam-6418	244	8	(	(	PUNCT
ejpam-6418	244	9	4	4	NUM
ejpam-6418	244	10	)	)	PUNCT
ejpam-6418	244	11	(	(	PUNCT
ejpam-6418	244	12	2025	2025	NUM
ejpam-6418	244	13	)	)	PUNCT
ejpam-6418	244	14	,	,	PUNCT
ejpam-6418	244	15	6418	6418	NUM
ejpam-6418	244	16	10	10	NUM
ejpam-6418	244	17	of	of	ADP
ejpam-6418	244	18	13	13	NUM
ejpam-6418	244	19	proof	proof	NOUN
ejpam-6418	244	20	.	.	PUNCT
ejpam-6418	245	1	let	let	VERB
ejpam-6418	245	2	a	a	DET
ejpam-6418	245	3	∈	∈	NOUN
ejpam-6418	245	4	∨.	∨.	NOUN
ejpam-6418	245	5	then	then	ADV
ejpam-6418	245	6	there	there	PRON
ejpam-6418	245	7	exists	exist	VERB
ejpam-6418	245	8	b	b	PROPN
ejpam-6418	245	9	∈	∈	PROPN
ejpam-6418	245	10	m	m	VERB
ejpam-6418	246	1	such	such	ADJ
ejpam-6418	246	2	that	that	SCONJ
ejpam-6418	246	3	a∨	a∨	PROPN
ejpam-6418	246	4	b	b	PROPN
ejpam-6418	247	1	=	=	NOUN
ejpam-6418	247	2	a.	a.	NOUN
ejpam-6418	247	3	take	take	NOUN
ejpam-6418	247	4	a0	a0	PROPN
ejpam-6418	247	5	=	=	PROPN
ejpam-6418	247	6	b∨	b∨	PROPN
ejpam-6418	247	7	a.	a.	NOUN
ejpam-6418	247	8	now	now	ADV
ejpam-6418	247	9	,	,	PUNCT
ejpam-6418	247	10	a0∨b	a0∨b	PROPN
ejpam-6418	247	11	=	=	PUNCT
ejpam-6418	247	12	(	(	PUNCT
ejpam-6418	247	13	b∨a)∨b	b∨a)∨b	X
ejpam-6418	247	14	=	=	SYM
ejpam-6418	247	15	b∨(a∨b	b∨(a∨b	NOUN
ejpam-6418	247	16	=	=	SYM
ejpam-6418	247	17	b∨a	b∨a	PROPN
ejpam-6418	247	18	=	=	PROPN
ejpam-6418	247	19	a0	a0	PROPN
ejpam-6418	247	20	(	(	PUNCT
ejpam-6418	247	21	by	by	ADP
ejpam-6418	247	22	lemma	lemma	PROPN
ejpam-6418	247	23	2.4(viii	2.4(viii	NUM
ejpam-6418	247	24	)	)	PUNCT
ejpam-6418	247	25	and	and	CCONJ
ejpam-6418	247	26	b∨a0	b∨a0	PUNCT
ejpam-6418	247	27	=	=	SYM
ejpam-6418	247	28	b∨b∨a	b∨b∨a	PROPN
ejpam-6418	247	29	=	=	SYM
ejpam-6418	247	30	b∨a	b∨a	PROPN
ejpam-6418	247	31	=	=	PROPN
ejpam-6418	247	32	a0	a0	PROPN
ejpam-6418	247	33	.	.	PUNCT
ejpam-6418	248	1	therefore	therefore	ADV
ejpam-6418	248	2	a0	a0	PROPN
ejpam-6418	248	3	∼	∼	PROPN
ejpam-6418	248	4	b.	b.	PROPN
ejpam-6418	248	5	since	since	SCONJ
ejpam-6418	248	6	b	b	PROPN
ejpam-6418	248	7	∈	∈	PROPN
ejpam-6418	248	8	m	m	PROPN
ejpam-6418	248	9	,	,	PUNCT
ejpam-6418	248	10	a0	a0	PROPN
ejpam-6418	248	11	∈	∈	PROPN
ejpam-6418	248	12	m	m	VERB
ejpam-6418	248	13	.	.	PUNCT
ejpam-6418	249	1	now	now	ADV
ejpam-6418	249	2	,	,	PUNCT
ejpam-6418	249	3	a0	a0	PROPN
ejpam-6418	249	4	∨	∨	NUM
ejpam-6418	249	5	a	a	DET
ejpam-6418	249	6	=	=	SYM
ejpam-6418	249	7	b	b	PROPN
ejpam-6418	249	8	∨	∨	NUM
ejpam-6418	249	9	a	a	DET
ejpam-6418	249	10	∨	∨	NOUN
ejpam-6418	249	11	a	a	DET
ejpam-6418	249	12	=	=	SYM
ejpam-6418	249	13	b	b	PROPN
ejpam-6418	249	14	∨	∨	NUM
ejpam-6418	249	15	a	a	DET
ejpam-6418	249	16	=	=	SYM
ejpam-6418	249	17	a0	a0	PROPN
ejpam-6418	249	18	.	.	PUNCT
ejpam-6418	250	1	then	then	ADV
ejpam-6418	250	2	[	[	X
ejpam-6418	250	3	a0	a0	NOUN
ejpam-6418	250	4	)	)	PUNCT
ejpam-6418	251	1	⊆	⊆	NUM
ejpam-6418	252	1	[	[	X
ejpam-6418	252	2	a	a	X
ejpam-6418	252	3	)	)	PUNCT
ejpam-6418	252	4	.	.	PUNCT
ejpam-6418	253	1	therefore	therefore	ADV
ejpam-6418	253	2	a	a	DET
ejpam-6418	253	3	∈	∈	PROPN
ejpam-6418	253	4	[	[	X
ejpam-6418	253	5	a0	a0	NOUN
ejpam-6418	253	6	)	)	PUNCT
ejpam-6418	253	7	.	.	PUNCT
ejpam-6418	254	1	now	now	ADV
ejpam-6418	254	2	,	,	PUNCT
ejpam-6418	254	3	a	a	DET
ejpam-6418	254	4	∨	∨	NOUN
ejpam-6418	254	5	a	a	PRON
ejpam-6418	254	6	=	=	NOUN
ejpam-6418	254	7	a	a	DET
ejpam-6418	254	8	∨	∨	NUM
ejpam-6418	254	9	b	b	NOUN
ejpam-6418	254	10	∨	∨	NOUN
ejpam-6418	254	11	a	a	PRON
ejpam-6418	254	12	=	=	NOUN
ejpam-6418	254	13	a	a	DET
ejpam-6418	254	14	∨	∨	NOUN
ejpam-6418	254	15	a	a	DET
ejpam-6418	254	16	∨	∨	NUM
ejpam-6418	254	17	b	b	NOUN
ejpam-6418	254	18	=	=	PUNCT
ejpam-6418	254	19	a	a	DET
ejpam-6418	254	20	∨	∨	NUM
ejpam-6418	254	21	b	b	X
ejpam-6418	254	22	=	=	SYM
ejpam-6418	254	23	a	a	X
ejpam-6418	254	24	(	(	PUNCT
ejpam-6418	254	25	by	by	ADP
ejpam-6418	254	26	lemma	lemma	PROPN
ejpam-6418	254	27	2.8(iii	2.8(iii	NUM
ejpam-6418	254	28	)	)	PUNCT
ejpam-6418	254	29	)	)	PUNCT
ejpam-6418	254	30	.	.	PUNCT
ejpam-6418	255	1	then	then	ADV
ejpam-6418	256	1	[	[	X
ejpam-6418	256	2	a	a	X
ejpam-6418	256	3	)	)	PUNCT
ejpam-6418	256	4	⊆	⊆	NUM
ejpam-6418	256	5	[	[	X
ejpam-6418	256	6	a0	a0	NOUN
ejpam-6418	256	7	)	)	PUNCT
ejpam-6418	256	8	.	.	PUNCT
ejpam-6418	257	1	therefore	therefore	ADV
ejpam-6418	257	2	a	a	DET
ejpam-6418	257	3	∈	∈	PROPN
ejpam-6418	257	4	[	[	X
ejpam-6418	257	5	a0	a0	NOUN
ejpam-6418	257	6	)	)	PUNCT
ejpam-6418	257	7	.	.	PUNCT
ejpam-6418	258	1	hence	hence	ADV
ejpam-6418	258	2	[	[	X
ejpam-6418	258	3	a0	a0	NOUN
ejpam-6418	258	4	)	)	PUNCT
ejpam-6418	258	5	=	=	PUNCT
ejpam-6418	259	1	[	[	X
ejpam-6418	259	2	a	a	X
ejpam-6418	259	3	)	)	PUNCT
ejpam-6418	259	4	.	.	PUNCT
ejpam-6418	260	1	suppose	suppose	VERB
ejpam-6418	260	2	there	there	PRON
ejpam-6418	260	3	exists	exist	VERB
ejpam-6418	260	4	c	c	NOUN
ejpam-6418	260	5	∈	∈	PROPN
ejpam-6418	260	6	m	m	VERB
ejpam-6418	260	7	such	such	ADJ
ejpam-6418	260	8	that	that	SCONJ
ejpam-6418	261	1	[	[	X
ejpam-6418	261	2	c	c	X
ejpam-6418	261	3	)	)	PUNCT
ejpam-6418	261	4	=	=	PUNCT
ejpam-6418	262	1	[	[	X
ejpam-6418	262	2	a	a	X
ejpam-6418	262	3	)	)	PUNCT
ejpam-6418	262	4	=	=	PUNCT
ejpam-6418	263	1	[	[	X
ejpam-6418	263	2	a0	a0	NOUN
ejpam-6418	263	3	)	)	PUNCT
ejpam-6418	263	4	.	.	PUNCT
ejpam-6418	264	1	since	since	SCONJ
ejpam-6418	264	2	a0	a0	PROPN
ejpam-6418	264	3	,	,	PUNCT
ejpam-6418	264	4	c	c	PROPN
ejpam-6418	264	5	∈	∈	PROPN
ejpam-6418	264	6	m	m	PROPN
ejpam-6418	264	7	,	,	PUNCT
ejpam-6418	264	8	a0	a0	NOUN
ejpam-6418	264	9	∼	∼	NOUN
ejpam-6418	264	10	c	c	PROPN
ejpam-6418	264	11	and	and	CCONJ
ejpam-6418	264	12	hence	hence	ADV
ejpam-6418	264	13	c	c	X
ejpam-6418	264	14	=	=	SYM
ejpam-6418	264	15	c	c	PROPN
ejpam-6418	264	16	∨	∨	NOUN
ejpam-6418	264	17	a0	a0	PROPN
ejpam-6418	264	18	=	=	PROPN
ejpam-6418	264	19	a0	a0	PROPN
ejpam-6418	264	20	∨	∨	PROPN
ejpam-6418	264	21	c.	c.	PROPN
ejpam-6418	264	22	therefore	therefore	ADV
ejpam-6418	264	23	a0	a0	PROPN
ejpam-6418	264	24	≤	≤	PROPN
ejpam-6418	264	25	c.	c.	PROPN
ejpam-6418	264	26	since	since	SCONJ
ejpam-6418	264	27	a0	a0	PROPN
ejpam-6418	264	28	∈	∈	PROPN
ejpam-6418	265	1	[	[	X
ejpam-6418	265	2	c	c	NOUN
ejpam-6418	265	3	)	)	PUNCT
ejpam-6418	265	4	,	,	PUNCT
ejpam-6418	265	5	a0	a0	PROPN
ejpam-6418	265	6	=	=	PROPN
ejpam-6418	265	7	a0	a0	PROPN
ejpam-6418	265	8	∨	∨	NUM
ejpam-6418	265	9	c	c	PROPN
ejpam-6418	265	10	=	=	SYM
ejpam-6418	265	11	c	c	PROPN
ejpam-6418	265	12	∨	∨	NOUN
ejpam-6418	265	13	a0	a0	PROPN
ejpam-6418	265	14	and	and	CCONJ
ejpam-6418	265	15	hence	hence	ADV
ejpam-6418	265	16	c	c	PROPN
ejpam-6418	265	17	≤	≤	PROPN
ejpam-6418	265	18	a0	a0	NOUN
ejpam-6418	265	19	.	.	PUNCT
ejpam-6418	266	1	thus	thus	ADV
ejpam-6418	266	2	a0	a0	PROPN
ejpam-6418	266	3	=	=	SYM
ejpam-6418	266	4	c.	c.	PROPN
ejpam-6418	266	5	let	let	VERB
ejpam-6418	266	6	us	we	PRON
ejpam-6418	266	7	denote	denote	VERB
ejpam-6418	266	8	η	η	NOUN
ejpam-6418	266	9	=	=	PRON
ejpam-6418	266	10	{	{	PUNCT
ejpam-6418	266	11	(	(	PUNCT
ejpam-6418	266	12	a	a	PRON
ejpam-6418	266	13	,	,	PUNCT
ejpam-6418	266	14	b	b	NOUN
ejpam-6418	266	15	)	)	PUNCT
ejpam-6418	266	16	∈	∈	NOUN
ejpam-6418	266	17	v×	v×	NOUN
ejpam-6418	266	18	v	v	ADP
ejpam-6418	266	19	|	|	NOUN
ejpam-6418	267	1	[	[	X
ejpam-6418	267	2	a	a	X
ejpam-6418	267	3	)	)	PUNCT
ejpam-6418	267	4	=	=	PUNCT
ejpam-6418	268	1	[	[	X
ejpam-6418	268	2	b	b	NOUN
ejpam-6418	268	3	)	)	PUNCT
ejpam-6418	268	4	}	}	PUNCT
ejpam-6418	268	5	.	.	PUNCT
ejpam-6418	269	1	then	then	ADV
ejpam-6418	269	2	we	we	PRON
ejpam-6418	269	3	have	have	VERB
ejpam-6418	269	4	the	the	DET
ejpam-6418	269	5	following	follow	VERB
ejpam-6418	269	6	theorem	theorem	NOUN
ejpam-6418	269	7	3.23	3.23	NUM
ejpam-6418	269	8	.	.	PUNCT
ejpam-6418	270	1	η	η	PROPN
ejpam-6418	270	2	is	be	AUX
ejpam-6418	270	3	a	a	DET
ejpam-6418	270	4	congruence	congruence	NOUN
ejpam-6418	270	5	relation	relation	NOUN
ejpam-6418	270	6	on	on	ADP
ejpam-6418	270	7	v.	v.	ADP
ejpam-6418	270	8	proof	proof	NOUN
ejpam-6418	270	9	.	.	PUNCT
ejpam-6418	271	1	let	let	VERB
ejpam-6418	271	2	a	a	DET
ejpam-6418	271	3	,	,	PUNCT
ejpam-6418	271	4	b	b	NOUN
ejpam-6418	271	5	,	,	PUNCT
ejpam-6418	271	6	c	c	PROPN
ejpam-6418	271	7	∈	∈	PROPN
ejpam-6418	271	8	v.	v.	ADP
ejpam-6418	271	9	(	(	PUNCT
ejpam-6418	271	10	i	i	NOUN
ejpam-6418	271	11	)	)	PUNCT
ejpam-6418	271	12	reflexive	reflexive	VERB
ejpam-6418	271	13	:	:	PUNCT
ejpam-6418	271	14	for	for	ADP
ejpam-6418	271	15	any	any	DET
ejpam-6418	271	16	a	a	DET
ejpam-6418	271	17	∈	∈	PROPN
ejpam-6418	271	18	v	v	NOUN
ejpam-6418	271	19	,	,	PUNCT
ejpam-6418	271	20	[	[	X
ejpam-6418	271	21	a	a	X
ejpam-6418	271	22	)	)	PUNCT
ejpam-6418	271	23	=	=	PUNCT
ejpam-6418	272	1	[	[	X
ejpam-6418	272	2	a	a	X
ejpam-6418	272	3	)	)	PUNCT
ejpam-6418	272	4	⇔	⇔	NOUN
ejpam-6418	272	5	(	(	PUNCT
ejpam-6418	272	6	a	a	PRON
ejpam-6418	272	7	,	,	PUNCT
ejpam-6418	272	8	a	a	PRON
ejpam-6418	272	9	)	)	PUNCT
ejpam-6418	272	10	∈	∈	PROPN
ejpam-6418	272	11	η	η	PROPN
ejpam-6418	272	12	.	.	PROPN
ejpam-6418	272	13	(	(	PUNCT
ejpam-6418	272	14	ii	ii	NOUN
ejpam-6418	272	15	)	)	PUNCT
ejpam-6418	272	16	transitive	transitive	ADJ
ejpam-6418	272	17	:	:	PUNCT
ejpam-6418	272	18	for	for	ADP
ejpam-6418	272	19	any	any	DET
ejpam-6418	272	20	(	(	PUNCT
ejpam-6418	272	21	a	a	PRON
ejpam-6418	272	22	,	,	PUNCT
ejpam-6418	272	23	b	b	NOUN
ejpam-6418	272	24	)	)	PUNCT
ejpam-6418	272	25	∈	∈	PROPN
ejpam-6418	272	26	η	η	PROPN
ejpam-6418	272	27	and	and	CCONJ
ejpam-6418	272	28	(	(	PUNCT
ejpam-6418	272	29	b	b	NOUN
ejpam-6418	272	30	,	,	PUNCT
ejpam-6418	272	31	c	c	NOUN
ejpam-6418	272	32	)	)	PUNCT
ejpam-6418	272	33	∈	∈	PROPN
ejpam-6418	272	34	η	η	PROPN
ejpam-6418	272	35	,	,	PUNCT
ejpam-6418	272	36	[	[	X
ejpam-6418	272	37	a	a	X
ejpam-6418	272	38	)	)	PUNCT
ejpam-6418	272	39	=	=	PUNCT
ejpam-6418	273	1	[	[	X
ejpam-6418	273	2	b	b	X
ejpam-6418	273	3	)	)	PUNCT
ejpam-6418	273	4	=	=	PUNCT
ejpam-6418	274	1	[	[	X
ejpam-6418	274	2	c	c	NOUN
ejpam-6418	274	3	)	)	PUNCT
ejpam-6418	274	4	.	.	PUNCT
ejpam-6418	275	1	therefore	therefore	ADV
ejpam-6418	275	2	[	[	X
ejpam-6418	275	3	a	a	X
ejpam-6418	275	4	)	)	PUNCT
ejpam-6418	275	5	=	=	PUNCT
ejpam-6418	276	1	[	[	X
ejpam-6418	276	2	c	c	NOUN
ejpam-6418	276	3	)	)	PUNCT
ejpam-6418	276	4	.	.	PUNCT
ejpam-6418	277	1	hence	hence	ADV
ejpam-6418	277	2	(	(	PUNCT
ejpam-6418	277	3	a	a	PRON
ejpam-6418	277	4	,	,	PUNCT
ejpam-6418	277	5	c	c	NOUN
ejpam-6418	277	6	)	)	PUNCT
ejpam-6418	277	7	∈	∈	PROPN
ejpam-6418	277	8	η	η	PROPN
ejpam-6418	277	9	.	.	PROPN
ejpam-6418	277	10	(	(	PUNCT
ejpam-6418	277	11	iii	iii	NOUN
ejpam-6418	277	12	)	)	PUNCT
ejpam-6418	277	13	symmetric	symmetric	NOUN
ejpam-6418	277	14	:	:	PUNCT
ejpam-6418	277	15	(	(	PUNCT
ejpam-6418	277	16	a	a	PRON
ejpam-6418	277	17	,	,	PUNCT
ejpam-6418	277	18	b	b	NOUN
ejpam-6418	277	19	)	)	PUNCT
ejpam-6418	277	20	∈	∈	PROPN
ejpam-6418	277	21	η	η	PROPN
ejpam-6418	277	22	⇔	⇔	X
ejpam-6418	278	1	[	[	X
ejpam-6418	278	2	a	a	X
ejpam-6418	278	3	)	)	PUNCT
ejpam-6418	278	4	=	=	PUNCT
ejpam-6418	279	1	[	[	X
ejpam-6418	279	2	b	b	X
ejpam-6418	279	3	)	)	PUNCT
ejpam-6418	279	4	⇔	⇔	X
ejpam-6418	279	5	(	(	PUNCT
ejpam-6418	279	6	b	b	PROPN
ejpam-6418	279	7	,	,	PUNCT
ejpam-6418	279	8	a	a	PRON
ejpam-6418	279	9	)	)	PUNCT
ejpam-6418	279	10	∈	∈	PROPN
ejpam-6418	279	11	η	η	PROPN
ejpam-6418	279	12	.	.	PROPN
ejpam-6418	279	13	therefore	therefore	PROPN
ejpam-6418	279	14	η	η	PROPN
ejpam-6418	279	15	is	be	AUX
ejpam-6418	279	16	an	an	DET
ejpam-6418	279	17	equivalence	equivalence	NOUN
ejpam-6418	279	18	relation	relation	NOUN
ejpam-6418	279	19	on	on	ADP
ejpam-6418	279	20	v.	v.	CCONJ
ejpam-6418	279	21	let	let	VERB
ejpam-6418	279	22	(	(	PUNCT
ejpam-6418	279	23	a	a	DET
ejpam-6418	279	24	,	,	PUNCT
ejpam-6418	279	25	b	b	NOUN
ejpam-6418	279	26	)	)	PUNCT
ejpam-6418	279	27	,	,	PUNCT
ejpam-6418	279	28	(	(	PUNCT
ejpam-6418	279	29	c	c	X
ejpam-6418	279	30	,	,	PUNCT
ejpam-6418	279	31	d	d	NOUN
ejpam-6418	279	32	)	)	PUNCT
ejpam-6418	279	33	∈	∈	PROPN
ejpam-6418	279	34	η	η	PROPN
ejpam-6418	279	35	.	.	PROPN
ejpam-6418	280	1	then	then	ADV
ejpam-6418	280	2	[	[	X
ejpam-6418	280	3	a∨	a∨	PROPN
ejpam-6418	280	4	c	c	X
ejpam-6418	280	5	)	)	PUNCT
ejpam-6418	280	6	=	=	NOUN
ejpam-6418	281	1	[	[	X
ejpam-6418	281	2	a)∧	a)∧	NOUN
ejpam-6418	281	3	[	[	X
ejpam-6418	281	4	c	c	NOUN
ejpam-6418	281	5	)	)	PUNCT
ejpam-6418	281	6	=	=	PUNCT
ejpam-6418	282	1	[	[	X
ejpam-6418	282	2	b)∧	b)∧	X
ejpam-6418	282	3	[	[	X
ejpam-6418	282	4	d	d	NOUN
ejpam-6418	282	5	)	)	PUNCT
ejpam-6418	282	6	=	=	NOUN
ejpam-6418	283	1	[	[	X
ejpam-6418	283	2	b∨d	b∨d	NOUN
ejpam-6418	283	3	)	)	PUNCT
ejpam-6418	283	4	and	and	CCONJ
ejpam-6418	283	5	[	[	X
ejpam-6418	283	6	a	a	DET
ejpam-6418	283	7	∧	∧	PROPN
ejpam-6418	283	8	c	c	NOUN
ejpam-6418	283	9	)	)	PUNCT
ejpam-6418	283	10	=	=	PUNCT
ejpam-6418	284	1	[	[	X
ejpam-6418	284	2	a	a	X
ejpam-6418	284	3	)	)	PUNCT
ejpam-6418	284	4	∨	∨	NOUN
ejpam-6418	285	1	[	[	X
ejpam-6418	285	2	c	c	X
ejpam-6418	285	3	)	)	PUNCT
ejpam-6418	285	4	=	=	PUNCT
ejpam-6418	286	1	[	[	X
ejpam-6418	286	2	b	b	X
ejpam-6418	286	3	)	)	PUNCT
ejpam-6418	286	4	∨	∨	NOUN
ejpam-6418	287	1	[	[	X
ejpam-6418	287	2	d	d	X
ejpam-6418	287	3	)	)	PUNCT
ejpam-6418	287	4	=	=	PUNCT
ejpam-6418	288	1	[	[	X
ejpam-6418	288	2	b	b	X
ejpam-6418	288	3	∧	∧	PROPN
ejpam-6418	288	4	d	d	PROPN
ejpam-6418	288	5	)	)	PUNCT
ejpam-6418	288	6	.	.	PUNCT
ejpam-6418	289	1	therefore	therefore	ADV
ejpam-6418	289	2	(	(	PUNCT
ejpam-6418	289	3	a	a	DET
ejpam-6418	289	4	∨	∨	PROPN
ejpam-6418	289	5	c	c	NOUN
ejpam-6418	289	6	,	,	PUNCT
ejpam-6418	289	7	b	b	PROPN
ejpam-6418	289	8	∨	∨	NUM
ejpam-6418	289	9	d	d	PROPN
ejpam-6418	289	10	)	)	PUNCT
ejpam-6418	289	11	,	,	PUNCT
ejpam-6418	289	12	(	(	PUNCT
ejpam-6418	289	13	a	a	DET
ejpam-6418	289	14	∧	∧	PROPN
ejpam-6418	289	15	c	c	PROPN
ejpam-6418	289	16	,	,	PUNCT
ejpam-6418	289	17	b	b	PROPN
ejpam-6418	289	18	∧	∧	PROPN
ejpam-6418	289	19	d	d	PROPN
ejpam-6418	289	20	)	)	PUNCT
ejpam-6418	289	21	∈	∈	PROPN
ejpam-6418	289	22	η	η	PROPN
ejpam-6418	289	23	.	.	PROPN
ejpam-6418	289	24	hence	hence	PROPN
ejpam-6418	289	25	η	η	PROPN
ejpam-6418	289	26	is	be	AUX
ejpam-6418	289	27	a	a	DET
ejpam-6418	289	28	congruence	congruence	NOUN
ejpam-6418	289	29	relation	relation	NOUN
ejpam-6418	289	30	on	on	ADP
ejpam-6418	289	31	v.	v.	ADP
ejpam-6418	289	32	lemma	lemma	PROPN
ejpam-6418	289	33	3.24	3.24	NUM
ejpam-6418	289	34	.	.	PUNCT
ejpam-6418	290	1	for	for	ADP
ejpam-6418	290	2	any	any	DET
ejpam-6418	290	3	element	element	NOUN
ejpam-6418	290	4	a	a	DET
ejpam-6418	290	5	∈	∈	PROPN
ejpam-6418	290	6	v	v	NOUN
ejpam-6418	290	7	,	,	PUNCT
ejpam-6418	290	8	a	a	DET
ejpam-6418	290	9	/	/	SYM
ejpam-6418	290	10	η	η	NOUN
ejpam-6418	290	11	=	=	X
ejpam-6418	290	12	{	{	PUNCT
ejpam-6418	290	13	1	1	NUM
ejpam-6418	290	14	}	}	PUNCT
ejpam-6418	290	15	if	if	SCONJ
ejpam-6418	291	1	and	and	CCONJ
ejpam-6418	291	2	only	only	ADV
ejpam-6418	291	3	if	if	SCONJ
ejpam-6418	291	4	a	a	DET
ejpam-6418	291	5	=	=	NOUN
ejpam-6418	291	6	1	1	X
ejpam-6418	291	7	.	.	PUNCT
ejpam-6418	292	1	proof	proof	NOUN
ejpam-6418	292	2	.	.	PUNCT
ejpam-6418	293	1	let	let	VERB
ejpam-6418	293	2	a	a	DET
ejpam-6418	293	3	∈	∈	NOUN
ejpam-6418	293	4	v.	v.	CCONJ
ejpam-6418	293	5	then	then	ADV
ejpam-6418	293	6	a	a	DET
ejpam-6418	293	7	∈	∈	PROPN
ejpam-6418	293	8	a	a	DET
ejpam-6418	293	9	/	/	SYM
ejpam-6418	293	10	η	η	PROPN
ejpam-6418	293	11	.	.	PROPN
ejpam-6418	293	12	suppose	suppose	VERB
ejpam-6418	293	13	that	that	SCONJ
ejpam-6418	293	14	a	a	DET
ejpam-6418	293	15	/	/	SYM
ejpam-6418	293	16	η	η	NOUN
ejpam-6418	293	17	=	=	X
ejpam-6418	293	18	{	{	PUNCT
ejpam-6418	293	19	1	1	NUM
ejpam-6418	293	20	}	}	PUNCT
ejpam-6418	293	21	.	.	PUNCT
ejpam-6418	294	1	then	then	ADV
ejpam-6418	294	2	[	[	X
ejpam-6418	294	3	a	a	X
ejpam-6418	294	4	)	)	PUNCT
ejpam-6418	294	5	=	=	PUNCT
ejpam-6418	295	1	[	[	X
ejpam-6418	295	2	1	1	NUM
ejpam-6418	295	3	)	)	PUNCT
ejpam-6418	295	4	.	.	PUNCT
ejpam-6418	296	1	therefore	therefore	ADV
ejpam-6418	296	2	a	a	DET
ejpam-6418	296	3	=	=	PUNCT
ejpam-6418	296	4	a	a	DET
ejpam-6418	296	5	∨	∨	NUM
ejpam-6418	296	6	1	1	NUM
ejpam-6418	296	7	=	=	SYM
ejpam-6418	296	8	1	1	NUM
ejpam-6418	296	9	.	.	PUNCT
ejpam-6418	297	1	hence	hence	ADV
ejpam-6418	297	2	a	a	DET
ejpam-6418	297	3	=	=	ADJ
ejpam-6418	297	4	1	1	X
ejpam-6418	297	5	.	.	PUNCT
ejpam-6418	298	1	on	on	ADP
ejpam-6418	298	2	the	the	DET
ejpam-6418	298	3	other	other	ADJ
ejpam-6418	298	4	hand	hand	NOUN
ejpam-6418	298	5	,	,	PUNCT
ejpam-6418	298	6	let	let	VERB
ejpam-6418	298	7	a	a	DET
ejpam-6418	298	8	=	=	SYM
ejpam-6418	298	9	1	1	NUM
ejpam-6418	298	10	,	,	PUNCT
ejpam-6418	298	11	1	1	NUM
ejpam-6418	298	12	/	/	SYM
ejpam-6418	298	13	η	η	NOUN
ejpam-6418	298	14	=	=	X
ejpam-6418	298	15	{	{	PUNCT
ejpam-6418	298	16	a	a	DET
ejpam-6418	298	17	∈	∈	NOUN
ejpam-6418	298	18	v	v	ADP
ejpam-6418	298	19	|	|	NOUN
ejpam-6418	298	20	(	(	PUNCT
ejpam-6418	298	21	a	a	PRON
ejpam-6418	298	22	,	,	PUNCT
ejpam-6418	298	23	1	1	NUM
ejpam-6418	298	24	)	)	PUNCT
ejpam-6418	298	25	∈	∈	PROPN
ejpam-6418	298	26	η	η	PROPN
ejpam-6418	298	27	}	}	PUNCT
ejpam-6418	298	28	=	=	PUNCT
ejpam-6418	298	29	{	{	PUNCT
ejpam-6418	298	30	a	a	DET
ejpam-6418	298	31	∈	∈	NOUN
ejpam-6418	298	32	v	v	ADP
ejpam-6418	298	33	|	|	NOUN
ejpam-6418	299	1	[	[	X
ejpam-6418	299	2	a	a	X
ejpam-6418	299	3	)	)	PUNCT
ejpam-6418	299	4	=	=	PUNCT
ejpam-6418	300	1	[	[	X
ejpam-6418	300	2	1	1	NUM
ejpam-6418	300	3	)	)	PUNCT
ejpam-6418	300	4	}	}	PUNCT
ejpam-6418	300	5	=	=	SYM
ejpam-6418	300	6	{	{	PUNCT
ejpam-6418	300	7	a	a	DET
ejpam-6418	300	8	∈	∈	NOUN
ejpam-6418	300	9	v	v	ADP
ejpam-6418	300	10	|	|	ADV
ejpam-6418	300	11	a	a	PRON
ejpam-6418	300	12	=	=	NOUN
ejpam-6418	300	13	a	a	DET
ejpam-6418	300	14	∨	∨	NUM
ejpam-6418	300	15	1	1	NUM
ejpam-6418	300	16	=	=	SYM
ejpam-6418	300	17	1	1	NUM
ejpam-6418	300	18	}	}	PUNCT
ejpam-6418	300	19	=	=	PUNCT
ejpam-6418	300	20	{	{	PUNCT
ejpam-6418	300	21	1	1	NUM
ejpam-6418	300	22	}	}	PUNCT
ejpam-6418	300	23	.	.	PUNCT
ejpam-6418	301	1	hence	hence	ADV
ejpam-6418	301	2	a	a	DET
ejpam-6418	301	3	/	/	SYM
ejpam-6418	301	4	η	η	NOUN
ejpam-6418	301	5	=	=	X
ejpam-6418	301	6	{	{	PUNCT
ejpam-6418	301	7	1	1	NUM
ejpam-6418	301	8	}	}	PUNCT
ejpam-6418	301	9	.	.	PUNCT
ejpam-6418	302	1	theorem	theorem	VERB
ejpam-6418	302	2	3.25	3.25	NUM
ejpam-6418	302	3	.	.	PUNCT
ejpam-6418	303	1	the	the	DET
ejpam-6418	303	2	quotient	quotient	NOUN
ejpam-6418	303	3	lattice	lattice	PROPN
ejpam-6418	303	4	v	v	PROPN
ejpam-6418	303	5	/	/	SYM
ejpam-6418	303	6	η	η	PROPN
ejpam-6418	303	7	forms	form	VERB
ejpam-6418	303	8	a	a	DET
ejpam-6418	303	9	distributive	distributive	ADJ
ejpam-6418	303	10	lattice	lattice	NOUN
ejpam-6418	303	11	with	with	ADP
ejpam-6418	303	12	the	the	DET
ejpam-6418	303	13	least	least	ADJ
ejpam-6418	303	14	element	element	ADJ
ejpam-6418	303	15	1	1	NUM
ejpam-6418	303	16	/	/	SYM
ejpam-6418	303	17	η	η	NOUN
ejpam-6418	303	18	=	=	X
ejpam-6418	303	19	{	{	PUNCT
ejpam-6418	303	20	1	1	NUM
ejpam-6418	303	21	}	}	PUNCT
ejpam-6418	303	22	and	and	CCONJ
ejpam-6418	303	23	the	the	DET
ejpam-6418	303	24	operations	operation	NOUN
ejpam-6418	303	25	a	a	DET
ejpam-6418	303	26	/	/	SYM
ejpam-6418	303	27	η	η	PROPN
ejpam-6418	303	28	∧	∧	PROPN
ejpam-6418	303	29	b	b	PROPN
ejpam-6418	303	30	/	/	SYM
ejpam-6418	303	31	η	η	PROPN
ejpam-6418	303	32	=	=	X
ejpam-6418	303	33	(	(	PUNCT
ejpam-6418	303	34	a	a	DET
ejpam-6418	303	35	∧	∧	PROPN
ejpam-6418	303	36	b)/η	b)/η	PROPN
ejpam-6418	303	37	and	and	CCONJ
ejpam-6418	303	38	a	a	PRON
ejpam-6418	303	39	/	/	SYM
ejpam-6418	303	40	η	η	PROPN
ejpam-6418	303	41	∨	∨	PROPN
ejpam-6418	303	42	b	b	PROPN
ejpam-6418	303	43	/	/	SYM
ejpam-6418	303	44	η	η	NOUN
ejpam-6418	303	45	=	=	X
ejpam-6418	303	46	(	(	PUNCT
ejpam-6418	303	47	a	a	DET
ejpam-6418	303	48	∨	∨	NUM
ejpam-6418	303	49	b)/η	b)/η	PROPN
ejpam-6418	303	50	.	.	PUNCT
ejpam-6418	304	1	it	it	PRON
ejpam-6418	304	2	is	be	AUX
ejpam-6418	304	3	easy	easy	ADJ
ejpam-6418	304	4	to	to	PART
ejpam-6418	304	5	observe	observe	VERB
ejpam-6418	304	6	that	that	SCONJ
ejpam-6418	304	7	η	η	PROPN
ejpam-6418	304	8	is	be	AUX
ejpam-6418	304	9	the	the	DET
ejpam-6418	304	10	smallest	small	ADJ
ejpam-6418	304	11	congruence	congruence	NOUN
ejpam-6418	304	12	on	on	ADP
ejpam-6418	304	13	v	v	ADP
ejpam-6418	304	14	such	such	ADJ
ejpam-6418	304	15	that	that	PRON
ejpam-6418	304	16	v	v	NOUN
ejpam-6418	304	17	/	/	SYM
ejpam-6418	304	18	η	η	PROPN
ejpam-6418	304	19	is	be	AUX
ejpam-6418	304	20	a	a	DET
ejpam-6418	304	21	distributive	distributive	ADJ
ejpam-6418	304	22	lattice	lattice	NOUN
ejpam-6418	304	23	.	.	PUNCT
ejpam-6418	305	1	theorem	theorem	VERB
ejpam-6418	305	2	3.26	3.26	NUM
ejpam-6418	305	3	.	.	PUNCT
ejpam-6418	306	1	a	a	DET
ejpam-6418	306	2	compatible	compatible	ADJ
ejpam-6418	306	3	set	set	NOUN
ejpam-6418	306	4	m	m	PROPN
ejpam-6418	306	5	in	in	ADP
ejpam-6418	306	6	v	v	NOUN
ejpam-6418	306	7	is	be	AUX
ejpam-6418	306	8	amicable	amicable	ADJ
ejpam-6418	306	9	if	if	SCONJ
ejpam-6418	306	10	and	and	CCONJ
ejpam-6418	306	11	only	only	ADV
ejpam-6418	306	12	if	if	SCONJ
ejpam-6418	306	13	m	m	PROPN
ejpam-6418	306	14	∩(a	∩(a	NOUN
ejpam-6418	306	15	/	/	SYM
ejpam-6418	306	16	η	η	NOUN
ejpam-6418	306	17	)	)	PUNCT
ejpam-6418	306	18	is	be	AUX
ejpam-6418	306	19	singleton	singleton	PROPN
ejpam-6418	306	20	set	set	NOUN
ejpam-6418	306	21	,	,	PUNCT
ejpam-6418	306	22	for	for	ADP
ejpam-6418	306	23	all	all	DET
ejpam-6418	306	24	a	a	DET
ejpam-6418	306	25	∈	∈	NOUN
ejpam-6418	306	26	v.	v.	ADP
ejpam-6418	306	27	proof	proof	NOUN
ejpam-6418	306	28	.	.	PUNCT
ejpam-6418	307	1	suppose	suppose	VERB
ejpam-6418	307	2	that	that	SCONJ
ejpam-6418	307	3	m	m	PROPN
ejpam-6418	307	4	is	be	AUX
ejpam-6418	307	5	amicable	amicable	ADJ
ejpam-6418	307	6	.	.	PUNCT
ejpam-6418	308	1	let	let	VERB
ejpam-6418	308	2	a	a	DET
ejpam-6418	308	3	∈	∈	NOUN
ejpam-6418	308	4	v.	v.	ADP
ejpam-6418	308	5	by	by	ADP
ejpam-6418	308	6	theorem	theorem	NOUN
ejpam-6418	308	7	3.22	3.22	NUM
ejpam-6418	308	8	.	.	PUNCT
ejpam-6418	308	9	,	,	PUNCT
ejpam-6418	308	10	there	there	PRON
ejpam-6418	308	11	exists	exist	VERB
ejpam-6418	308	12	a0	a0	PROPN
ejpam-6418	308	13	∈	∈	PROPN
ejpam-6418	308	14	m	m	VERB
ejpam-6418	308	15	such	such	ADJ
ejpam-6418	308	16	that	that	SCONJ
ejpam-6418	308	17	[	[	X
ejpam-6418	308	18	a0	a0	NOUN
ejpam-6418	308	19	)	)	PUNCT
ejpam-6418	308	20	=	=	PUNCT
ejpam-6418	309	1	[	[	X
ejpam-6418	309	2	a	a	X
ejpam-6418	309	3	)	)	PUNCT
ejpam-6418	309	4	.	.	PUNCT
ejpam-6418	310	1	then	then	ADV
ejpam-6418	310	2	a0	a0	PROPN
ejpam-6418	310	3	∈	∈	PROPN
ejpam-6418	310	4	m	m	PROPN
ejpam-6418	310	5	∩	∩	NOUN
ejpam-6418	310	6	(	(	PUNCT
ejpam-6418	310	7	a	a	PRON
ejpam-6418	310	8	/	/	SYM
ejpam-6418	310	9	η	η	NOUN
ejpam-6418	310	10	)	)	PUNCT
ejpam-6418	310	11	.	.	PUNCT
ejpam-6418	311	1	now	now	ADV
ejpam-6418	311	2	,	,	PUNCT
ejpam-6418	311	3	b	b	PROPN
ejpam-6418	311	4	∈	∈	PROPN
ejpam-6418	311	5	m	m	NOUN
ejpam-6418	311	6	∩	∩	NOUN
ejpam-6418	311	7	(	(	PUNCT
ejpam-6418	311	8	a	a	PRON
ejpam-6418	311	9	/	/	SYM
ejpam-6418	311	10	η	η	NOUN
ejpam-6418	311	11	)	)	PUNCT
ejpam-6418	311	12	⇒	⇒	NOUN
ejpam-6418	311	13	(	(	PUNCT
ejpam-6418	311	14	a	a	DET
ejpam-6418	311	15	,	,	PUNCT
ejpam-6418	311	16	b	b	NOUN
ejpam-6418	311	17	)	)	PUNCT
ejpam-6418	311	18	∈	∈	PROPN
ejpam-6418	311	19	η	η	PROPN
ejpam-6418	311	20	and	and	CCONJ
ejpam-6418	311	21	b	b	PROPN
ejpam-6418	311	22	∈	∈	PROPN
ejpam-6418	311	23	m	m	AUX
ejpam-6418	311	24	⇒	⇒	NOUN
ejpam-6418	311	25	[	[	X
ejpam-6418	311	26	a	a	X
ejpam-6418	311	27	)	)	PUNCT
ejpam-6418	311	28	=	=	PUNCT
ejpam-6418	312	1	[	[	X
ejpam-6418	312	2	b	b	NOUN
ejpam-6418	312	3	)	)	PUNCT
ejpam-6418	312	4	and	and	CCONJ
ejpam-6418	312	5	b	b	X
ejpam-6418	312	6	∈	∈	NOUN
ejpam-6418	312	7	m	m	AUX
ejpam-6418	312	8	⇒	⇒	NOUN
ejpam-6418	312	9	[	[	X
ejpam-6418	312	10	a0	a0	NOUN
ejpam-6418	312	11	)	)	PUNCT
ejpam-6418	312	12	=	=	PUNCT
ejpam-6418	313	1	[	[	X
ejpam-6418	313	2	b	b	NOUN
ejpam-6418	313	3	)	)	PUNCT
ejpam-6418	313	4	and	and	CCONJ
ejpam-6418	313	5	b	b	X
ejpam-6418	313	6	∈	∈	ADV
ejpam-6418	313	7	m	m	X
ejpam-6418	313	8	(	(	PUNCT
ejpam-6418	313	9	since	since	SCONJ
ejpam-6418	313	10	[	[	X
ejpam-6418	313	11	a0	a0	NOUN
ejpam-6418	313	12	)	)	PUNCT
ejpam-6418	313	13	=	=	PUNCT
ejpam-6418	314	1	[	[	X
ejpam-6418	314	2	a	a	X
ejpam-6418	314	3	)	)	PUNCT
ejpam-6418	314	4	)	)	PUNCT
ejpam-6418	314	5	⇒	⇒	PROPN
ejpam-6418	314	6	b	b	PROPN
ejpam-6418	314	7	=	=	SYM
ejpam-6418	314	8	a0	a0	PROPN
ejpam-6418	314	9	.	.	PUNCT
ejpam-6418	315	1	(	(	PUNCT
ejpam-6418	315	2	since	since	SCONJ
ejpam-6418	315	3	m	m	PROPN
ejpam-6418	315	4	is	be	AUX
ejpam-6418	315	5	distributive	distributive	ADJ
ejpam-6418	315	6	lattice	lattice	NOUN
ejpam-6418	315	7	)	)	PUNCT
ejpam-6418	315	8	therefore	therefore	ADV
ejpam-6418	315	9	m	m	VERB
ejpam-6418	315	10	∩	∩	NOUN
ejpam-6418	315	11	(	(	PUNCT
ejpam-6418	315	12	a	a	DET
ejpam-6418	315	13	/	/	SYM
ejpam-6418	315	14	η	η	NOUN
ejpam-6418	315	15	)	)	PUNCT
ejpam-6418	315	16	=	=	PROPN
ejpam-6418	315	17	{	{	PUNCT
ejpam-6418	315	18	a0	a0	NOUN
ejpam-6418	315	19	}	}	PUNCT
ejpam-6418	315	20	.	.	PUNCT
ejpam-6418	316	1	conversely	conversely	ADV
ejpam-6418	316	2	suppose	suppose	VERB
ejpam-6418	316	3	that	that	SCONJ
ejpam-6418	316	4	m	m	NOUN
ejpam-6418	316	5	∩	∩	NOUN
ejpam-6418	316	6	(	(	PUNCT
ejpam-6418	316	7	a	a	PRON
ejpam-6418	316	8	/	/	SYM
ejpam-6418	316	9	η	η	NOUN
ejpam-6418	316	10	)	)	PUNCT
ejpam-6418	316	11	is	be	AUX
ejpam-6418	316	12	a	a	DET
ejpam-6418	316	13	singleton	singleton	NOUN
ejpam-6418	316	14	,	,	PUNCT
ejpam-6418	316	15	for	for	ADP
ejpam-6418	316	16	all	all	DET
ejpam-6418	316	17	a	a	DET
ejpam-6418	316	18	∈	∈	NOUN
ejpam-6418	316	19	v.	v.	CCONJ
ejpam-6418	316	20	let	let	VERB
ejpam-6418	316	21	b	b	NOUN
ejpam-6418	316	22	∈	∈	NOUN
ejpam-6418	316	23	v	v	ADP
ejpam-6418	316	24	such	such	DET
ejpam-6418	316	25	that	that	DET
ejpam-6418	316	26	b	b	NOUN
ejpam-6418	316	27	∼	∼	NOUN
ejpam-6418	316	28	a	a	ADP
ejpam-6418	316	29	,	,	PUNCT
ejpam-6418	316	30	for	for	ADP
ejpam-6418	316	31	all	all	DET
ejpam-6418	316	32	a	a	DET
ejpam-6418	316	33	∈	∈	NOUN
ejpam-6418	316	34	m	m	NOUN
ejpam-6418	316	35	.	.	PUNCT
ejpam-6418	317	1	then	then	ADV
ejpam-6418	317	2	m	m	VERB
ejpam-6418	317	3	∩	∩	NOUN
ejpam-6418	317	4	(	(	PUNCT
ejpam-6418	317	5	b	b	X
ejpam-6418	317	6	/	/	SYM
ejpam-6418	317	7	η	η	NOUN
ejpam-6418	317	8	)	)	PUNCT
ejpam-6418	317	9	=	=	PUNCT
ejpam-6418	317	10	{	{	PUNCT
ejpam-6418	317	11	c	c	NOUN
ejpam-6418	317	12	}	}	PUNCT
ejpam-6418	317	13	,	,	PUNCT
ejpam-6418	317	14	for	for	ADP
ejpam-6418	317	15	some	some	DET
ejpam-6418	317	16	c	c	NOUN
ejpam-6418	317	17	∈	∈	PROPN
ejpam-6418	317	18	m(by	m(by	PROPN
ejpam-6418	317	19	our	our	PRON
ejpam-6418	317	20	assumption	assumption	NOUN
ejpam-6418	317	21	)	)	PUNCT
ejpam-6418	317	22	.	.	PUNCT
ejpam-6418	318	1	then	then	ADV
ejpam-6418	318	2	[	[	X
ejpam-6418	318	3	b	b	X
ejpam-6418	318	4	)	)	PUNCT
ejpam-6418	318	5	=	=	PUNCT
ejpam-6418	319	1	[	[	X
ejpam-6418	319	2	c	c	NOUN
ejpam-6418	319	3	)	)	PUNCT
ejpam-6418	319	4	.	.	PUNCT
ejpam-6418	320	1	since	since	SCONJ
ejpam-6418	320	2	b	b	NUM
ejpam-6418	320	3	∼	∼	NOUN
ejpam-6418	320	4	c	c	NOUN
ejpam-6418	320	5	,	,	PUNCT
ejpam-6418	320	6	b	b	X
ejpam-6418	320	7	=	=	SYM
ejpam-6418	320	8	c	c	PROPN
ejpam-6418	320	9	∈	∈	PROPN
ejpam-6418	320	10	m	m	VERB
ejpam-6418	320	11	.	.	PUNCT
ejpam-6418	321	1	hence	hence	ADV
ejpam-6418	321	2	m	m	VERB
ejpam-6418	321	3	is	be	AUX
ejpam-6418	321	4	maximal	maximal	ADJ
ejpam-6418	321	5	set	set	NOUN
ejpam-6418	321	6	.	.	PUNCT
ejpam-6418	322	1	now	now	ADV
ejpam-6418	322	2	,	,	PUNCT
ejpam-6418	322	3	we	we	PRON
ejpam-6418	322	4	show	show	VERB
ejpam-6418	322	5	that	that	SCONJ
ejpam-6418	322	6	m	m	NOUN
ejpam-6418	322	7	is	be	AUX
ejpam-6418	322	8	amicable	amicable	ADJ
ejpam-6418	322	9	.	.	PUNCT
ejpam-6418	323	1	let	let	VERB
ejpam-6418	323	2	a	a	DET
ejpam-6418	323	3	∈	∈	NOUN
ejpam-6418	323	4	v.	v.	ADP
ejpam-6418	323	5	by	by	ADP
ejpam-6418	323	6	our	our	PRON
ejpam-6418	323	7	assumption	assumption	NOUN
ejpam-6418	323	8	m	m	NOUN
ejpam-6418	323	9	∩	∩	NOUN
ejpam-6418	323	10	(	(	PUNCT
ejpam-6418	323	11	a	a	DET
ejpam-6418	323	12	/	/	SYM
ejpam-6418	323	13	η	η	NOUN
ejpam-6418	323	14	)	)	PUNCT
ejpam-6418	323	15	=	=	SYM
ejpam-6418	324	1	{	{	PUNCT
ejpam-6418	324	2	d	d	NOUN
ejpam-6418	324	3	}	}	PUNCT
ejpam-6418	324	4	,	,	PUNCT
ejpam-6418	324	5	for	for	ADP
ejpam-6418	324	6	some	some	DET
ejpam-6418	324	7	d	d	PROPN
ejpam-6418	324	8	∈	∈	PROPN
ejpam-6418	324	9	m	m	NOUN
ejpam-6418	324	10	.	.	PUNCT
ejpam-6418	325	1	then	then	ADV
ejpam-6418	325	2	[	[	X
ejpam-6418	325	3	a	a	X
ejpam-6418	325	4	)	)	PUNCT
ejpam-6418	325	5	=	=	PUNCT
ejpam-6418	326	1	[	[	X
ejpam-6418	326	2	d	d	NOUN
ejpam-6418	326	3	)	)	PUNCT
ejpam-6418	326	4	.	.	PUNCT
ejpam-6418	327	1	therefore	therefore	ADV
ejpam-6418	327	2	a	a	DET
ejpam-6418	327	3	=	=	PUNCT
ejpam-6418	327	4	a	a	DET
ejpam-6418	327	5	∨	∨	NUM
ejpam-6418	327	6	d	d	NOUN
ejpam-6418	327	7	and	and	CCONJ
ejpam-6418	327	8	d	d	PROPN
ejpam-6418	327	9	∈	∈	PROPN
ejpam-6418	327	10	m	m	VERB
ejpam-6418	327	11	.	.	PUNCT
ejpam-6418	328	1	hence	hence	ADV
ejpam-6418	328	2	m	m	PROPN
ejpam-6418	328	3	is	be	AUX
ejpam-6418	328	4	amicable	amicable	ADJ
ejpam-6418	328	5	.	.	PUNCT
ejpam-6418	329	1	r.	r.	PROPN
ejpam-6418	329	2	sirisetti	sirisetti	PROPN
ejpam-6418	329	3	et	et	PROPN
ejpam-6418	329	4	al	al	PROPN
ejpam-6418	329	5	.	.	PUNCT
ejpam-6418	329	6	/	/	SYM
ejpam-6418	329	7	eur	eur	PROPN
ejpam-6418	329	8	.	.	PUNCT
ejpam-6418	330	1	j.	j.	PROPN
ejpam-6418	330	2	pure	pure	PROPN
ejpam-6418	330	3	appl	appl	PROPN
ejpam-6418	330	4	.	.	PROPN
ejpam-6418	330	5	math	math	PROPN
ejpam-6418	330	6	,	,	PUNCT
ejpam-6418	330	7	18	18	NUM
ejpam-6418	330	8	(	(	PUNCT
ejpam-6418	330	9	4	4	NUM
ejpam-6418	330	10	)	)	PUNCT
ejpam-6418	330	11	(	(	PUNCT
ejpam-6418	330	12	2025	2025	NUM
ejpam-6418	330	13	)	)	PUNCT
ejpam-6418	330	14	,	,	PUNCT
ejpam-6418	330	15	6418	6418	NUM
ejpam-6418	330	16	11	11	NUM
ejpam-6418	330	17	of	of	ADP
ejpam-6418	330	18	13	13	NUM
ejpam-6418	330	19	theorem	theorem	VERB
ejpam-6418	330	20	3.27	3.27	NUM
ejpam-6418	330	21	.	.	PUNCT
ejpam-6418	331	1	let	let	VERB
ejpam-6418	331	2	m	m	PRON
ejpam-6418	331	3	be	be	AUX
ejpam-6418	331	4	an	an	DET
ejpam-6418	331	5	amicable	amicable	ADJ
ejpam-6418	331	6	set	set	NOUN
ejpam-6418	331	7	in	in	ADP
ejpam-6418	331	8	v	v	NOUN
ejpam-6418	331	9	and	and	CCONJ
ejpam-6418	331	10	x	x	PUNCT
ejpam-6418	331	11	∈	∈	PROPN
ejpam-6418	332	1	v.	v.	CCONJ
ejpam-6418	332	2	then	then	ADV
ejpam-6418	332	3	mx	mx	PROPN
ejpam-6418	332	4	=	=	SYM
ejpam-6418	332	5	{	{	PUNCT
ejpam-6418	332	6	(	(	PUNCT
ejpam-6418	332	7	a∧x)∨a	a∧x)∨a	NOUN
ejpam-6418	332	8	|	|	ADV
ejpam-6418	332	9	a	a	DET
ejpam-6418	332	10	∈	∈	PROPN
ejpam-6418	332	11	m	m	PRON
ejpam-6418	332	12	}	}	PUNCT
ejpam-6418	332	13	is	be	AUX
ejpam-6418	332	14	a	a	DET
ejpam-6418	332	15	compatible	compatible	ADJ
ejpam-6418	332	16	set	set	NOUN
ejpam-6418	332	17	.	.	PUNCT
ejpam-6418	333	1	proof	proof	NOUN
ejpam-6418	333	2	.	.	PUNCT
ejpam-6418	334	1	let	let	VERB
ejpam-6418	334	2	a	a	DET
ejpam-6418	334	3	,	,	PUNCT
ejpam-6418	334	4	b	b	X
ejpam-6418	334	5	∈	∈	ADV
ejpam-6418	334	6	m	m	VERB
ejpam-6418	334	7	.	.	PUNCT
ejpam-6418	335	1	then	then	ADV
ejpam-6418	335	2	[	[	X
ejpam-6418	335	3	(	(	PUNCT
ejpam-6418	335	4	b	b	PROPN
ejpam-6418	335	5	∧	∧	PROPN
ejpam-6418	335	6	x	x	PROPN
ejpam-6418	335	7	)	)	PUNCT
ejpam-6418	335	8	∨	∨	NUM
ejpam-6418	335	9	b	b	NOUN
ejpam-6418	335	10	]	]	PUNCT
ejpam-6418	335	11	∨	∨	NUM
ejpam-6418	335	12	[	[	X
ejpam-6418	335	13	(	(	PUNCT
ejpam-6418	335	14	a	a	DET
ejpam-6418	335	15	∧	∧	PROPN
ejpam-6418	335	16	x	x	NOUN
ejpam-6418	335	17	)	)	PUNCT
ejpam-6418	335	18	∨	∨	X
ejpam-6418	335	19	a	a	DET
ejpam-6418	335	20	]	]	X
ejpam-6418	335	21	⇒	⇒	NOUN
ejpam-6418	336	1	[	[	X
ejpam-6418	336	2	(	(	PUNCT
ejpam-6418	336	3	b	b	PROPN
ejpam-6418	336	4	∧	∧	PROPN
ejpam-6418	336	5	x	x	PROPN
ejpam-6418	336	6	)	)	PUNCT
ejpam-6418	336	7	∨	∨	NUM
ejpam-6418	336	8	b	b	NOUN
ejpam-6418	336	9	]	]	PUNCT
ejpam-6418	336	10	∨	∨	PUNCT
ejpam-6418	336	11	[	[	X
ejpam-6418	336	12	a	a	DET
ejpam-6418	336	13	∨	∨	NOUN
ejpam-6418	336	14	(	(	PUNCT
ejpam-6418	336	15	a	a	DET
ejpam-6418	336	16	∧	∧	PROPN
ejpam-6418	336	17	x	x	NOUN
ejpam-6418	336	18	)	)	PUNCT
ejpam-6418	336	19	]	]	PUNCT
ejpam-6418	336	20	(	(	PUNCT
ejpam-6418	336	21	by	by	ADP
ejpam-6418	336	22	lemma	lemma	PROPN
ejpam-6418	336	23	2.4(viii	2.4(viii	NUM
ejpam-6418	336	24	)	)	PUNCT
ejpam-6418	336	25	)	)	PUNCT
ejpam-6418	336	26	⇒	⇒	NOUN
ejpam-6418	337	1	[	[	X
ejpam-6418	337	2	(	(	PUNCT
ejpam-6418	337	3	b	b	PROPN
ejpam-6418	337	4	∧	∧	PROPN
ejpam-6418	337	5	x	x	PROPN
ejpam-6418	337	6	)	)	PUNCT
ejpam-6418	337	7	∨	∨	NUM
ejpam-6418	337	8	b	b	X
ejpam-6418	337	9	]	]	X
ejpam-6418	337	10	∨	∨	NUM
ejpam-6418	337	11	a	a	PRON
ejpam-6418	337	12	(	(	PUNCT
ejpam-6418	337	13	by	by	ADP
ejpam-6418	337	14	definition	definition	NOUN
ejpam-6418	337	15	2.1(v	2.1(v	NUM
ejpam-6418	337	16	)	)	PUNCT
ejpam-6418	337	17	)	)	PUNCT
ejpam-6418	337	18	⇒	⇒	NOUN
ejpam-6418	337	19	(	(	PUNCT
ejpam-6418	337	20	b	b	PROPN
ejpam-6418	337	21	∧	∧	PROPN
ejpam-6418	337	22	x	x	NOUN
ejpam-6418	337	23	)	)	PUNCT
ejpam-6418	337	24	∨	∨	PROPN
ejpam-6418	337	25	(	(	PUNCT
ejpam-6418	337	26	b	b	PROPN
ejpam-6418	337	27	∨	∨	NUM
ejpam-6418	337	28	a	a	NOUN
ejpam-6418	337	29	)	)	PUNCT
ejpam-6418	337	30	(	(	PUNCT
ejpam-6418	337	31	∨	∨	NOUN
ejpam-6418	337	32	is	be	AUX
ejpam-6418	337	33	associative	associative	ADJ
ejpam-6418	337	34	)	)	PUNCT
ejpam-6418	337	35	⇒	⇒	NOUN
ejpam-6418	337	36	(	(	PUNCT
ejpam-6418	337	37	b	b	PROPN
ejpam-6418	337	38	∨	∨	X
ejpam-6418	337	39	(	(	PUNCT
ejpam-6418	337	40	b	b	PROPN
ejpam-6418	337	41	∨	∨	NUM
ejpam-6418	337	42	a	a	NOUN
ejpam-6418	337	43	)	)	PUNCT
ejpam-6418	337	44	]	]	X
ejpam-6418	338	1	∧	∧	NOUN
ejpam-6418	338	2	(	(	PUNCT
ejpam-6418	338	3	x	x	SYM
ejpam-6418	338	4	∨	∨	X
ejpam-6418	338	5	(	(	PUNCT
ejpam-6418	338	6	b	b	PROPN
ejpam-6418	338	7	∨	∨	NUM
ejpam-6418	338	8	a	a	PRON
ejpam-6418	338	9	)	)	PUNCT
ejpam-6418	338	10	]	]	PUNCT
ejpam-6418	338	11	(	(	PUNCT
ejpam-6418	338	12	by	by	ADP
ejpam-6418	338	13	definition2.1(ii	definition2.1(ii	PROPN
ejpam-6418	338	14	)	)	PUNCT
ejpam-6418	338	15	)	)	PUNCT
ejpam-6418	338	16	⇒	⇒	NOUN
ejpam-6418	338	17	(	(	PUNCT
ejpam-6418	338	18	a	a	DET
ejpam-6418	338	19	∨	∨	NUM
ejpam-6418	338	20	b	b	NOUN
ejpam-6418	338	21	)	)	PUNCT
ejpam-6418	338	22	∧	∧	NOUN
ejpam-6418	338	23	(	(	PUNCT
ejpam-6418	338	24	x	x	SYM
ejpam-6418	338	25	∨	∨	X
ejpam-6418	338	26	(	(	PUNCT
ejpam-6418	338	27	a	a	DET
ejpam-6418	338	28	∨	∨	NUM
ejpam-6418	338	29	b	b	NOUN
ejpam-6418	338	30	)	)	PUNCT
ejpam-6418	338	31	]	]	PUNCT
ejpam-6418	338	32	(	(	PUNCT
ejpam-6418	338	33	since	since	SCONJ
ejpam-6418	338	34	a	a	DET
ejpam-6418	338	35	∼	∼	NOUN
ejpam-6418	338	36	b	b	NOUN
ejpam-6418	338	37	,	,	PUNCT
ejpam-6418	338	38	a	a	PRON
ejpam-6418	338	39	,	,	PUNCT
ejpam-6418	338	40	b	b	PROPN
ejpam-6418	338	41	∈	∈	PROPN
ejpam-6418	338	42	m	m	NOUN
ejpam-6418	338	43	)	)	PUNCT
ejpam-6418	338	44	⇒	⇒	NOUN
ejpam-6418	338	45	[	[	X
ejpam-6418	338	46	a	a	DET
ejpam-6418	338	47	∨	∨	NOUN
ejpam-6418	338	48	(	(	PUNCT
ejpam-6418	338	49	a	a	DET
ejpam-6418	338	50	∨	∨	NUM
ejpam-6418	338	51	b	b	NOUN
ejpam-6418	338	52	)	)	PUNCT
ejpam-6418	338	53	]	]	PUNCT
ejpam-6418	339	1	∧	∧	PROPN
ejpam-6418	339	2	[	[	X
ejpam-6418	339	3	x	x	X
ejpam-6418	339	4	∨	∨	X
ejpam-6418	339	5	(	(	PUNCT
ejpam-6418	339	6	a	a	DET
ejpam-6418	339	7	∨	∨	NUM
ejpam-6418	339	8	b	b	NOUN
ejpam-6418	339	9	)	)	PUNCT
ejpam-6418	339	10	]	]	PUNCT
ejpam-6418	339	11	(	(	PUNCT
ejpam-6418	339	12	by	by	ADP
ejpam-6418	339	13	lemma2.8(iii	lemma2.8(iii	NOUN
ejpam-6418	339	14	)	)	PUNCT
ejpam-6418	339	15	)	)	PUNCT
ejpam-6418	339	16	⇒	⇒	NOUN
ejpam-6418	339	17	(	(	PUNCT
ejpam-6418	339	18	a	a	DET
ejpam-6418	339	19	∧	∧	PROPN
ejpam-6418	339	20	x	x	NOUN
ejpam-6418	339	21	)	)	PUNCT
ejpam-6418	339	22	∨	∨	NOUN
ejpam-6418	339	23	(	(	PUNCT
ejpam-6418	339	24	a	a	DET
ejpam-6418	339	25	∨	∨	NUM
ejpam-6418	339	26	b	b	NOUN
ejpam-6418	339	27	)	)	PUNCT
ejpam-6418	339	28	⇒	⇒	NOUN
ejpam-6418	339	29	[	[	X
ejpam-6418	339	30	(	(	PUNCT
ejpam-6418	339	31	a	a	DET
ejpam-6418	339	32	∧	∧	PROPN
ejpam-6418	339	33	x	x	NOUN
ejpam-6418	339	34	)	)	PUNCT
ejpam-6418	339	35	∨	∨	X
ejpam-6418	339	36	a	a	DET
ejpam-6418	339	37	]	]	X
ejpam-6418	339	38	∨	∨	NUM
ejpam-6418	339	39	b	b	PROPN
ejpam-6418	339	40	(	(	PUNCT
ejpam-6418	339	41	∨	∨	NOUN
ejpam-6418	339	42	is	be	AUX
ejpam-6418	339	43	associative	associative	ADJ
ejpam-6418	339	44	)	)	PUNCT
ejpam-6418	339	45	⇒	⇒	NOUN
ejpam-6418	340	1	[	[	X
ejpam-6418	340	2	(	(	PUNCT
ejpam-6418	340	3	a	a	DET
ejpam-6418	340	4	∧	∧	PROPN
ejpam-6418	340	5	x	x	NOUN
ejpam-6418	340	6	)	)	PUNCT
ejpam-6418	340	7	∨	∨	X
ejpam-6418	340	8	a	a	X
ejpam-6418	340	9	]	]	X
ejpam-6418	340	10	∨	∨	NUM
ejpam-6418	340	11	[	[	X
ejpam-6418	340	12	b	b	X
ejpam-6418	340	13	∨	∨	X
ejpam-6418	340	14	(	(	PUNCT
ejpam-6418	340	15	b	b	PROPN
ejpam-6418	340	16	∧	∧	PROPN
ejpam-6418	340	17	x	x	X
ejpam-6418	340	18	)	)	PUNCT
ejpam-6418	340	19	]	]	PUNCT
ejpam-6418	340	20	(	(	PUNCT
ejpam-6418	340	21	by	by	ADP
ejpam-6418	340	22	definition	definition	NOUN
ejpam-6418	340	23	2.1(v	2.1(v	NUM
ejpam-6418	340	24	)	)	PUNCT
ejpam-6418	340	25	)	)	PUNCT
ejpam-6418	340	26	⇒	⇒	NOUN
ejpam-6418	340	27	[	[	X
ejpam-6418	340	28	(	(	PUNCT
ejpam-6418	340	29	a	a	DET
ejpam-6418	340	30	∧	∧	PROPN
ejpam-6418	340	31	x	x	NOUN
ejpam-6418	340	32	)	)	PUNCT
ejpam-6418	340	33	∨	∨	X
ejpam-6418	340	34	a	a	X
ejpam-6418	340	35	]	]	X
ejpam-6418	340	36	∨	∨	NUM
ejpam-6418	340	37	[	[	X
ejpam-6418	340	38	(	(	PUNCT
ejpam-6418	340	39	b	b	PROPN
ejpam-6418	340	40	∧	∧	PROPN
ejpam-6418	340	41	x	x	PROPN
ejpam-6418	340	42	)	)	PUNCT
ejpam-6418	340	43	∨	∨	NUM
ejpam-6418	340	44	b	b	NOUN
ejpam-6418	340	45	]	]	X
ejpam-6418	340	46	(	(	PUNCT
ejpam-6418	340	47	by	by	ADP
ejpam-6418	340	48	lemma	lemma	PROPN
ejpam-6418	340	49	2.4(viii	2.4(viii	NUM
ejpam-6418	340	50	)	)	PUNCT
ejpam-6418	340	51	therefore	therefore	ADV
ejpam-6418	340	52	mx	mx	PROPN
ejpam-6418	340	53	is	be	AUX
ejpam-6418	340	54	compatible	compatible	ADJ
ejpam-6418	340	55	set	set	NOUN
ejpam-6418	340	56	.	.	PUNCT
ejpam-6418	341	1	theorem	theorem	VERB
ejpam-6418	341	2	3.28	3.28	NUM
ejpam-6418	341	3	.	.	PUNCT
ejpam-6418	342	1	let	let	VERB
ejpam-6418	342	2	m	m	PRON
ejpam-6418	342	3	be	be	AUX
ejpam-6418	342	4	an	an	DET
ejpam-6418	342	5	amicable	amicable	ADJ
ejpam-6418	342	6	set	set	NOUN
ejpam-6418	342	7	in	in	ADP
ejpam-6418	343	1	v.	v.	ADP
ejpam-6418	343	2	then	then	ADV
ejpam-6418	343	3	m	m	VERB
ejpam-6418	343	4	is	be	AUX
ejpam-6418	343	5	isomorphic	isomorphic	ADJ
ejpam-6418	343	6	to	to	ADP
ejpam-6418	343	7	v	v	NOUN
ejpam-6418	343	8	/	/	SYM
ejpam-6418	343	9	η	η	NOUN
ejpam-6418	343	10	.	.	PROPN
ejpam-6418	343	11	proof	proof	NOUN
ejpam-6418	343	12	.	.	PUNCT
ejpam-6418	344	1	define	define	VERB
ejpam-6418	344	2	a	a	DET
ejpam-6418	344	3	map	map	NOUN
ejpam-6418	345	1	f	f	NOUN
ejpam-6418	345	2	:	:	PUNCT
ejpam-6418	345	3	m	m	PROPN
ejpam-6418	345	4	→	→	SYM
ejpam-6418	345	5	v	v	PROPN
ejpam-6418	345	6	/	/	SYM
ejpam-6418	345	7	η	η	PROPN
ejpam-6418	345	8	by	by	ADP
ejpam-6418	345	9	a	a	DET
ejpam-6418	345	10	/	/	SYM
ejpam-6418	345	11	η	η	NOUN
ejpam-6418	345	12	,	,	PUNCT
ejpam-6418	345	13	for	for	ADP
ejpam-6418	345	14	all	all	DET
ejpam-6418	345	15	a	a	DET
ejpam-6418	345	16	∈	∈	NOUN
ejpam-6418	345	17	m	m	NOUN
ejpam-6418	345	18	.	.	PUNCT
ejpam-6418	346	1	now	now	ADV
ejpam-6418	346	2	,	,	PUNCT
ejpam-6418	346	3	f(a∧	f(a∧	PROPN
ejpam-6418	346	4	b	b	X
ejpam-6418	346	5	)	)	PUNCT
ejpam-6418	346	6	=	=	SYM
ejpam-6418	346	7	(	(	PUNCT
ejpam-6418	346	8	a∧	a∧	NOUN
ejpam-6418	346	9	b)/η	b)/η	NOUN
ejpam-6418	346	10	=	=	SYM
ejpam-6418	346	11	a	a	PRON
ejpam-6418	346	12	/	/	SYM
ejpam-6418	346	13	η	η	PROPN
ejpam-6418	346	14	∧	∧	PROPN
ejpam-6418	346	15	b	b	PROPN
ejpam-6418	346	16	/	/	SYM
ejpam-6418	346	17	η	η	PROPN
ejpam-6418	346	18	=	=	SYM
ejpam-6418	346	19	f(a	f(a	PROPN
ejpam-6418	346	20	)	)	PUNCT
ejpam-6418	346	21	∧	∧	NOUN
ejpam-6418	346	22	f(b	f(b	PROPN
ejpam-6418	346	23	)	)	PUNCT
ejpam-6418	346	24	and	and	CCONJ
ejpam-6418	346	25	f(a	f(a	PROPN
ejpam-6418	346	26	∨	∨	NUM
ejpam-6418	346	27	b	b	NOUN
ejpam-6418	346	28	)	)	PUNCT
ejpam-6418	346	29	=	=	SYM
ejpam-6418	346	30	(	(	PUNCT
ejpam-6418	346	31	a	a	DET
ejpam-6418	346	32	∨	∨	NOUN
ejpam-6418	346	33	b)/η	b)/η	NOUN
ejpam-6418	346	34	=	=	SYM
ejpam-6418	346	35	a	a	PRON
ejpam-6418	346	36	/	/	SYM
ejpam-6418	346	37	η	η	PROPN
ejpam-6418	346	38	∨	∨	PROPN
ejpam-6418	346	39	b	b	PROPN
ejpam-6418	346	40	/	/	SYM
ejpam-6418	346	41	η	η	PROPN
ejpam-6418	346	42	=	=	SYM
ejpam-6418	346	43	f(a	f(a	PROPN
ejpam-6418	346	44	)	)	PUNCT
ejpam-6418	346	45	∨	∨	NUM
ejpam-6418	346	46	f(b	f(b	PROPN
ejpam-6418	346	47	)	)	PUNCT
ejpam-6418	346	48	,	,	PUNCT
ejpam-6418	346	49	for	for	ADP
ejpam-6418	346	50	all	all	DET
ejpam-6418	346	51	a	a	PRON
ejpam-6418	346	52	,	,	PUNCT
ejpam-6418	346	53	b	b	X
ejpam-6418	346	54	∈	∈	ADV
ejpam-6418	346	55	m	m	VERB
ejpam-6418	346	56	.	.	PUNCT
ejpam-6418	347	1	then	then	ADV
ejpam-6418	347	2	f	f	PROPN
ejpam-6418	347	3	is	be	AUX
ejpam-6418	347	4	a	a	DET
ejpam-6418	347	5	homomorphism	homomorphism	NOUN
ejpam-6418	347	6	.	.	PUNCT
ejpam-6418	348	1	now	now	ADV
ejpam-6418	348	2	,	,	PUNCT
ejpam-6418	348	3	f(a	f(a	NOUN
ejpam-6418	348	4	)	)	PUNCT
ejpam-6418	348	5	=	=	SYM
ejpam-6418	348	6	f(b	f(b	PROPN
ejpam-6418	348	7	)	)	PUNCT
ejpam-6418	348	8	⇒	⇒	VERB
ejpam-6418	348	9	a	a	DET
ejpam-6418	348	10	/	/	SYM
ejpam-6418	348	11	η	η	PROPN
ejpam-6418	348	12	=	=	SYM
ejpam-6418	348	13	b	b	PROPN
ejpam-6418	348	14	/	/	SYM
ejpam-6418	348	15	η	η	PROPN
ejpam-6418	348	16	.	.	PROPN
ejpam-6418	349	1	let	let	VERB
ejpam-6418	349	2	x	x	SYM
ejpam-6418	349	3	∈	∈	PROPN
ejpam-6418	349	4	a	a	DET
ejpam-6418	349	5	/	/	SYM
ejpam-6418	349	6	η	η	PROPN
ejpam-6418	349	7	.	.	PROPN
ejpam-6418	350	1	then	then	ADV
ejpam-6418	350	2	(	(	PUNCT
ejpam-6418	350	3	a	a	PRON
ejpam-6418	350	4	,	,	PUNCT
ejpam-6418	350	5	x	x	NOUN
ejpam-6418	350	6	)	)	PUNCT
ejpam-6418	350	7	,	,	PUNCT
ejpam-6418	350	8	(	(	PUNCT
ejpam-6418	350	9	b	b	X
ejpam-6418	350	10	,	,	PUNCT
ejpam-6418	350	11	x	x	NOUN
ejpam-6418	350	12	)	)	PUNCT
ejpam-6418	350	13	∈	∈	PROPN
ejpam-6418	350	14	η	η	PROPN
ejpam-6418	350	15	.	.	PROPN
ejpam-6418	351	1	therefore	therefore	ADV
ejpam-6418	351	2	[	[	X
ejpam-6418	351	3	a	a	X
ejpam-6418	351	4	)	)	PUNCT
ejpam-6418	351	5	=	=	PUNCT
ejpam-6418	352	1	[	[	X
ejpam-6418	352	2	x	x	X
ejpam-6418	352	3	)	)	PUNCT
ejpam-6418	352	4	=	=	PUNCT
ejpam-6418	353	1	[	[	X
ejpam-6418	353	2	b	b	NOUN
ejpam-6418	353	3	)	)	PUNCT
ejpam-6418	353	4	.	.	PUNCT
ejpam-6418	354	1	therefore	therefore	ADV
ejpam-6418	354	2	a	a	DET
ejpam-6418	354	3	=	=	X
ejpam-6418	354	4	b.	b.	PROPN
ejpam-6418	355	1	so	so	SCONJ
ejpam-6418	355	2	that	that	SCONJ
ejpam-6418	355	3	f	f	PROPN
ejpam-6418	355	4	is	be	AUX
ejpam-6418	355	5	oneone	oneone	NOUN
ejpam-6418	355	6	.	.	PUNCT
ejpam-6418	356	1	by	by	ADP
ejpam-6418	356	2	theorem	theorem	NOUN
ejpam-6418	356	3	3.22	3.22	NUM
ejpam-6418	356	4	.	.	PUNCT
ejpam-6418	356	5	,	,	PUNCT
ejpam-6418	356	6	for	for	ADP
ejpam-6418	356	7	x	x	PROPN
ejpam-6418	356	8	∈	∈	PROPN
ejpam-6418	356	9	v	v	NOUN
ejpam-6418	356	10	,	,	PUNCT
ejpam-6418	356	11	there	there	PRON
ejpam-6418	356	12	exists	exist	VERB
ejpam-6418	356	13	x0	x0	PROPN
ejpam-6418	356	14	∈	∈	PROPN
ejpam-6418	356	15	m	m	VERB
ejpam-6418	356	16	such	such	ADJ
ejpam-6418	356	17	that	that	SCONJ
ejpam-6418	356	18	[	[	X
ejpam-6418	356	19	x0	x0	X
ejpam-6418	356	20	)	)	PUNCT
ejpam-6418	357	1	=	=	PUNCT
ejpam-6418	358	1	[	[	X
ejpam-6418	358	2	x	x	X
ejpam-6418	358	3	)	)	PUNCT
ejpam-6418	358	4	.	.	PUNCT
ejpam-6418	359	1	therefore	therefore	ADV
ejpam-6418	359	2	x0	x0	PROPN
ejpam-6418	359	3	/	/	SYM
ejpam-6418	359	4	η	η	PROPN
ejpam-6418	359	5	=	=	SYM
ejpam-6418	359	6	x	x	PROPN
ejpam-6418	359	7	/	/	SYM
ejpam-6418	359	8	η	η	PROPN
ejpam-6418	359	9	=	=	PROPN
ejpam-6418	359	10	f(x0	f(x0	PROPN
ejpam-6418	359	11	)	)	PUNCT
ejpam-6418	359	12	.	.	PUNCT
ejpam-6418	360	1	so	so	ADV
ejpam-6418	360	2	that	that	SCONJ
ejpam-6418	360	3	f	f	PROPN
ejpam-6418	360	4	is	be	AUX
ejpam-6418	360	5	onto	onto	ADP
ejpam-6418	360	6	and	and	CCONJ
ejpam-6418	360	7	hence	hence	ADV
ejpam-6418	360	8	f	f	PROPN
ejpam-6418	360	9	is	be	AUX
ejpam-6418	360	10	bijective	bijective	ADJ
ejpam-6418	360	11	.	.	PUNCT
ejpam-6418	361	1	theorem	theorem	VERB
ejpam-6418	361	2	3.29	3.29	NUM
ejpam-6418	361	3	.	.	PUNCT
ejpam-6418	362	1	let	let	VERB
ejpam-6418	362	2	m	m	PRON
ejpam-6418	362	3	be	be	AUX
ejpam-6418	362	4	an	an	DET
ejpam-6418	362	5	amicable	amicable	ADJ
ejpam-6418	362	6	set	set	NOUN
ejpam-6418	362	7	in	in	ADP
ejpam-6418	362	8	v.	v.	ADP
ejpam-6418	362	9	then	then	ADV
ejpam-6418	362	10	the	the	DET
ejpam-6418	362	11	lattice	lattice	NOUN
ejpam-6418	362	12	of	of	ADP
ejpam-6418	362	13	filters	filter	NOUN
ejpam-6418	362	14	of	of	ADP
ejpam-6418	362	15	v	v	NOUN
ejpam-6418	362	16	is	be	AUX
ejpam-6418	362	17	isomorphic	isomorphic	ADJ
ejpam-6418	362	18	with	with	ADP
ejpam-6418	362	19	the	the	DET
ejpam-6418	362	20	lattice	lattice	NOUN
ejpam-6418	362	21	of	of	ADP
ejpam-6418	362	22	filters	filter	NOUN
ejpam-6418	362	23	of	of	ADP
ejpam-6418	362	24	m	m	PRON
ejpam-6418	362	25	.	.	PUNCT
ejpam-6418	363	1	proof	proof	NOUN
ejpam-6418	363	2	.	.	PUNCT
ejpam-6418	364	1	let	let	VERB
ejpam-6418	364	2	f	f	PROPN
ejpam-6418	364	3	(	(	PUNCT
ejpam-6418	364	4	v	v	NOUN
ejpam-6418	364	5	)	)	PUNCT
ejpam-6418	364	6	and	and	CCONJ
ejpam-6418	364	7	f	f	PROPN
ejpam-6418	364	8	(	(	PUNCT
ejpam-6418	364	9	m	m	PROPN
ejpam-6418	364	10	)	)	PUNCT
ejpam-6418	364	11	are	be	AUX
ejpam-6418	364	12	the	the	DET
ejpam-6418	364	13	lattices	lattice	NOUN
ejpam-6418	364	14	of	of	ADP
ejpam-6418	364	15	filters	filter	NOUN
ejpam-6418	364	16	of	of	ADP
ejpam-6418	364	17	v	v	NOUN
ejpam-6418	364	18	and	and	CCONJ
ejpam-6418	364	19	filters	filter	NOUN
ejpam-6418	364	20	of	of	ADP
ejpam-6418	364	21	m	m	PRON
ejpam-6418	364	22	respectively	respectively	ADV
ejpam-6418	364	23	.	.	PUNCT
ejpam-6418	365	1	define	define	VERB
ejpam-6418	365	2	a	a	DET
ejpam-6418	365	3	map	map	NOUN
ejpam-6418	365	4	g	g	NOUN
ejpam-6418	365	5	:	:	PUNCT
ejpam-6418	365	6	f	f	PROPN
ejpam-6418	365	7	(	(	PUNCT
ejpam-6418	365	8	v	v	NOUN
ejpam-6418	365	9	)	)	PUNCT
ejpam-6418	365	10	→	→	SYM
ejpam-6418	365	11	f	f	X
ejpam-6418	365	12	(	(	PUNCT
ejpam-6418	365	13	m	m	PROPN
ejpam-6418	365	14	)	)	PUNCT
ejpam-6418	365	15	by	by	ADP
ejpam-6418	365	16	g(f	g(f	PROPN
ejpam-6418	365	17	)	)	PUNCT
ejpam-6418	366	1	=	=	PUNCT
ejpam-6418	367	1	f	f	X
ejpam-6418	368	1	∩m	∩m	NOUN
ejpam-6418	368	2	,	,	PUNCT
ejpam-6418	368	3	for	for	ADP
ejpam-6418	368	4	all	all	DET
ejpam-6418	368	5	f	f	PROPN
ejpam-6418	368	6	∈	∈	PROPN
ejpam-6418	368	7	f	f	X
ejpam-6418	368	8	(	(	PUNCT
ejpam-6418	368	9	v	v	NOUN
ejpam-6418	368	10	)	)	PUNCT
ejpam-6418	368	11	.	.	PUNCT
ejpam-6418	369	1	then	then	ADV
ejpam-6418	369	2	clearly	clearly	ADV
ejpam-6418	369	3	g	g	PROPN
ejpam-6418	369	4	is	be	AUX
ejpam-6418	369	5	an	an	DET
ejpam-6418	369	6	order	order	NOUN
ejpam-6418	369	7	preserving	preserve	VERB
ejpam-6418	369	8	map	map	NOUN
ejpam-6418	369	9	.	.	PUNCT
ejpam-6418	370	1	suppose	suppose	VERB
ejpam-6418	370	2	f	f	X
ejpam-6418	370	3	,	,	PUNCT
ejpam-6418	370	4	g	g	PROPN
ejpam-6418	370	5	∈	∈	PROPN
ejpam-6418	370	6	f	f	X
ejpam-6418	370	7	(	(	PUNCT
ejpam-6418	370	8	v	v	NOUN
ejpam-6418	370	9	)	)	PUNCT
ejpam-6418	370	10	and	and	CCONJ
ejpam-6418	370	11	f	f	X
ejpam-6418	370	12	∩m	∩m	PROPN
ejpam-6418	371	1	⊆	⊆	NUM
ejpam-6418	371	2	g	g	ADP
ejpam-6418	371	3	∩m	∩m	PROPN
ejpam-6418	371	4	.	.	PUNCT
ejpam-6418	372	1	for	for	SCONJ
ejpam-6418	372	2	x	x	PROPN
ejpam-6418	372	3	∈	∈	PROPN
ejpam-6418	372	4	f	f	PROPN
ejpam-6418	372	5	,	,	PUNCT
ejpam-6418	372	6	there	there	PRON
ejpam-6418	372	7	exists	exist	VERB
ejpam-6418	372	8	x0	x0	PROPN
ejpam-6418	372	9	∈	∈	PROPN
ejpam-6418	372	10	m	m	VERB
ejpam-6418	372	11	such	such	ADJ
ejpam-6418	372	12	that	that	SCONJ
ejpam-6418	372	13	[	[	X
ejpam-6418	372	14	x0	x0	X
ejpam-6418	372	15	)	)	PUNCT
ejpam-6418	373	1	=	=	PUNCT
ejpam-6418	374	1	[	[	X
ejpam-6418	374	2	x	x	X
ejpam-6418	374	3	)	)	PUNCT
ejpam-6418	374	4	.	.	PUNCT
ejpam-6418	375	1	therefore	therefore	ADV
ejpam-6418	375	2	x0	x0	PROPN
ejpam-6418	375	3	∈	∈	PROPN
ejpam-6418	375	4	f	f	PROPN
ejpam-6418	375	5	and	and	CCONJ
ejpam-6418	375	6	hence	hence	ADV
ejpam-6418	375	7	x0	x0	PROPN
ejpam-6418	375	8	∈	∈	PROPN
ejpam-6418	376	1	f	f	X
ejpam-6418	376	2	∩m	∩m	PROPN
ejpam-6418	377	1	⊆	⊆	NUM
ejpam-6418	377	2	g	g	ADP
ejpam-6418	377	3	∩m	∩m	PROPN
ejpam-6418	377	4	.	.	PUNCT
ejpam-6418	378	1	for	for	ADP
ejpam-6418	378	2	this	this	DET
ejpam-6418	378	3	x0	x0	PROPN
ejpam-6418	378	4	∈	∈	PROPN
ejpam-6418	378	5	g	g	PROPN
ejpam-6418	378	6	∩	∩	PROPN
ejpam-6418	378	7	m	m	NOUN
ejpam-6418	378	8	,	,	PUNCT
ejpam-6418	378	9	x	x	SYM
ejpam-6418	378	10	∈	∈	PROPN
ejpam-6418	379	1	[	[	X
ejpam-6418	379	2	x	x	X
ejpam-6418	379	3	)	)	PUNCT
ejpam-6418	379	4	=	=	PUNCT
ejpam-6418	380	1	[	[	X
ejpam-6418	380	2	x0	x0	NUM
ejpam-6418	380	3	)	)	PUNCT
ejpam-6418	380	4	⊆	⊆	NUM
ejpam-6418	380	5	g	g	PROPN
ejpam-6418	380	6	∩	∩	X
ejpam-6418	380	7	m	m	VERB
ejpam-6418	380	8	.	.	PUNCT
ejpam-6418	381	1	therefore	therefore	ADV
ejpam-6418	381	2	x	x	SYM
ejpam-6418	381	3	∈	∈	PROPN
ejpam-6418	381	4	g.	g.	NOUN
ejpam-6418	382	1	so	so	SCONJ
ejpam-6418	382	2	that	that	SCONJ
ejpam-6418	382	3	f	f	PROPN
ejpam-6418	382	4	⊆	⊆	NUM
ejpam-6418	382	5	g.	g.	NOUN
ejpam-6418	382	6	hence	hence	ADV
ejpam-6418	382	7	g	g	PROPN
ejpam-6418	382	8	is	be	AUX
ejpam-6418	382	9	one	one	NUM
ejpam-6418	382	10	-	-	PUNCT
ejpam-6418	382	11	one	one	NUM
ejpam-6418	382	12	.	.	PUNCT
ejpam-6418	383	1	let	let	VERB
ejpam-6418	383	2	k	k	PROPN
ejpam-6418	383	3	∈	∈	PROPN
ejpam-6418	383	4	f	f	X
ejpam-6418	383	5	(	(	PUNCT
ejpam-6418	383	6	m	m	PROPN
ejpam-6418	383	7	)	)	PUNCT
ejpam-6418	383	8	.	.	PUNCT
ejpam-6418	384	1	put	put	VERB
ejpam-6418	384	2	q	q	NOUN
ejpam-6418	384	3	=	=	PUNCT
ejpam-6418	384	4	{	{	PUNCT
ejpam-6418	384	5	x	x	SYM
ejpam-6418	384	6	∈	∈	NOUN
ejpam-6418	384	7	v	v	ADP
ejpam-6418	385	1	|	|	ADV
ejpam-6418	385	2	x0	x0	PROPN
ejpam-6418	385	3	∈	∈	PROPN
ejpam-6418	386	1	k	k	X
ejpam-6418	386	2	such	such	ADJ
ejpam-6418	386	3	that	that	SCONJ
ejpam-6418	386	4	[	[	X
ejpam-6418	386	5	x	x	X
ejpam-6418	386	6	)	)	PUNCT
ejpam-6418	386	7	=	=	PUNCT
ejpam-6418	387	1	[	[	X
ejpam-6418	387	2	x0	x0	PROPN
ejpam-6418	387	3	)	)	PUNCT
ejpam-6418	387	4	}	}	PUNCT
ejpam-6418	387	5	.	.	PUNCT
ejpam-6418	388	1	let	let	VERB
ejpam-6418	388	2	x	x	PRON
ejpam-6418	388	3	,	,	PUNCT
ejpam-6418	388	4	y	y	PROPN
ejpam-6418	388	5	∈	∈	PROPN
ejpam-6418	388	6	q.	q.	NOUN
ejpam-6418	388	7	then	then	ADV
ejpam-6418	388	8	there	there	PRON
ejpam-6418	388	9	exist	exist	VERB
ejpam-6418	388	10	x0	x0	PROPN
ejpam-6418	388	11	,	,	PUNCT
ejpam-6418	388	12	y0	y0	PROPN
ejpam-6418	388	13	∈	∈	PROPN
ejpam-6418	388	14	k	k	NOUN
ejpam-6418	388	15	such	such	ADJ
ejpam-6418	389	1	that	that	SCONJ
ejpam-6418	389	2	[	[	X
ejpam-6418	389	3	x	x	X
ejpam-6418	389	4	)	)	PUNCT
ejpam-6418	389	5	=	=	PUNCT
ejpam-6418	390	1	[	[	X
ejpam-6418	390	2	x0	x0	X
ejpam-6418	390	3	)	)	PUNCT
ejpam-6418	390	4	and	and	CCONJ
ejpam-6418	390	5	[	[	X
ejpam-6418	390	6	y	y	NOUN
ejpam-6418	390	7	)	)	PUNCT
ejpam-6418	390	8	=	=	PUNCT
ejpam-6418	391	1	[	[	X
ejpam-6418	391	2	y0	y0	NOUN
ejpam-6418	391	3	)	)	PUNCT
ejpam-6418	391	4	.	.	PUNCT
ejpam-6418	392	1	now	now	ADV
ejpam-6418	392	2	,	,	PUNCT
ejpam-6418	392	3	[	[	X
ejpam-6418	392	4	x∧y	x∧y	X
ejpam-6418	392	5	)	)	PUNCT
ejpam-6418	392	6	=	=	PUNCT
ejpam-6418	393	1	[	[	X
ejpam-6418	393	2	x)∨[y	x)∨[y	X
ejpam-6418	393	3	)	)	PUNCT
ejpam-6418	394	1	=	=	PUNCT
ejpam-6418	395	1	[	[	X
ejpam-6418	395	2	x0)∨[y0	x0)∨[y0	PROPN
ejpam-6418	395	3	)	)	PUNCT
ejpam-6418	395	4	)	)	PUNCT
ejpam-6418	396	1	=	=	PUNCT
ejpam-6418	397	1	[	[	X
ejpam-6418	397	2	x0∧y0	x0∧y0	NOUN
ejpam-6418	397	3	)	)	PUNCT
ejpam-6418	397	4	and	and	CCONJ
ejpam-6418	397	5	[	[	X
ejpam-6418	397	6	x∨y	x∨y	PROPN
ejpam-6418	397	7	)	)	PUNCT
ejpam-6418	397	8	=	=	PUNCT
ejpam-6418	398	1	[	[	X
ejpam-6418	398	2	x)∧[y	x)∧[y	X
ejpam-6418	398	3	)	)	PUNCT
ejpam-6418	398	4	=	=	PUNCT
ejpam-6418	399	1	[	[	X
ejpam-6418	399	2	x0)∧[y0	x0)∧[y0	NOUN
ejpam-6418	399	3	)	)	PUNCT
ejpam-6418	399	4	)	)	PUNCT
ejpam-6418	400	1	=	=	PUNCT
ejpam-6418	401	1	[	[	X
ejpam-6418	401	2	x0∨y0)(since	x0∨y0)(since	NOUN
ejpam-6418	401	3	k	k	PROPN
ejpam-6418	401	4	is	be	AUX
ejpam-6418	401	5	a	a	DET
ejpam-6418	401	6	filter	filter	NOUN
ejpam-6418	401	7	)	)	PUNCT
ejpam-6418	401	8	.	.	PUNCT
ejpam-6418	402	1	let	let	VERB
ejpam-6418	402	2	a	a	DET
ejpam-6418	402	3	∈	∈	NOUN
ejpam-6418	403	1	v.	v.	CCONJ
ejpam-6418	403	2	then	then	ADV
ejpam-6418	403	3	there	there	PRON
ejpam-6418	403	4	exists	exist	VERB
ejpam-6418	403	5	a0	a0	PROPN
ejpam-6418	403	6	∈	∈	PROPN
ejpam-6418	403	7	m	m	VERB
ejpam-6418	403	8	such	such	ADJ
ejpam-6418	403	9	that	that	SCONJ
ejpam-6418	404	1	[	[	X
ejpam-6418	404	2	a	a	X
ejpam-6418	404	3	)	)	PUNCT
ejpam-6418	404	4	=	=	PUNCT
ejpam-6418	405	1	[	[	X
ejpam-6418	405	2	a0	a0	NOUN
ejpam-6418	405	3	)	)	PUNCT
ejpam-6418	405	4	.	.	PUNCT
ejpam-6418	406	1	now	now	ADV
ejpam-6418	406	2	,	,	PUNCT
ejpam-6418	406	3	[	[	X
ejpam-6418	406	4	x∨	x∨	PROPN
ejpam-6418	406	5	a	a	X
ejpam-6418	406	6	)	)	PUNCT
ejpam-6418	406	7	=	=	NOUN
ejpam-6418	407	1	[	[	X
ejpam-6418	407	2	x)∧	x)∧	X
ejpam-6418	407	3	[	[	X
ejpam-6418	407	4	a	a	X
ejpam-6418	407	5	)	)	PUNCT
ejpam-6418	407	6	=	=	PUNCT
ejpam-6418	408	1	[	[	X
ejpam-6418	408	2	x0)∧	x0)∧	X
ejpam-6418	408	3	[	[	X
ejpam-6418	408	4	a0	a0	NOUN
ejpam-6418	408	5	)	)	PUNCT
ejpam-6418	408	6	=	=	PUNCT
ejpam-6418	409	1	[	[	X
ejpam-6418	409	2	x0	x0	PROPN
ejpam-6418	409	3	∨	∨	NUM
ejpam-6418	409	4	a0	a0	PROPN
ejpam-6418	409	5	)	)	PUNCT
ejpam-6418	409	6	.	.	PUNCT
ejpam-6418	410	1	since	since	SCONJ
ejpam-6418	410	2	x0	x0	PROPN
ejpam-6418	410	3	∨	∨	NUM
ejpam-6418	410	4	a0	a0	PROPN
ejpam-6418	410	5	∈	∈	PROPN
ejpam-6418	410	6	m	m	PROPN
ejpam-6418	410	7	,	,	PUNCT
ejpam-6418	410	8	x∨	x∨	PROPN
ejpam-6418	410	9	a	a	DET
ejpam-6418	410	10	∈	∈	PROPN
ejpam-6418	410	11	f	f	NOUN
ejpam-6418	410	12	and	and	CCONJ
ejpam-6418	410	13	hence	hence	ADV
ejpam-6418	410	14	q	q	X
ejpam-6418	410	15	is	be	AUX
ejpam-6418	410	16	a	a	DET
ejpam-6418	410	17	filter	filter	NOUN
ejpam-6418	410	18	of	of	ADP
ejpam-6418	410	19	v	v	NOUN
ejpam-6418	410	20	and	and	CCONJ
ejpam-6418	410	21	g(q	g(q	NOUN
ejpam-6418	410	22	)	)	PUNCT
ejpam-6418	410	23	=	=	SYM
ejpam-6418	411	1	q	q	X
ejpam-6418	412	1	∩m	∩m	NOUN
ejpam-6418	412	2	=	=	PUNCT
ejpam-6418	412	3	k.	k.	PROPN
ejpam-6418	412	4	hence	hence	ADV
ejpam-6418	412	5	g	g	PROPN
ejpam-6418	412	6	is	be	AUX
ejpam-6418	412	7	bijective	bijective	ADJ
ejpam-6418	412	8	and	and	CCONJ
ejpam-6418	412	9	g−1	g−1	PROPN
ejpam-6418	412	10	is	be	AUX
ejpam-6418	412	11	also	also	ADV
ejpam-6418	412	12	order	order	NOUN
ejpam-6418	412	13	preserving	preserve	VERB
ejpam-6418	412	14	.	.	PUNCT
ejpam-6418	413	1	thus	thus	ADV
ejpam-6418	413	2	g	g	PROPN
ejpam-6418	413	3	is	be	AUX
ejpam-6418	413	4	isomorphic	isomorphic	ADJ
ejpam-6418	413	5	.	.	PUNCT
ejpam-6418	414	1	definition	definition	NOUN
ejpam-6418	414	2	3.30	3.30	NUM
ejpam-6418	414	3	.	.	PUNCT
ejpam-6418	415	1	a	a	DET
ejpam-6418	415	2	pdl	pdl	PROPN
ejpam-6418	415	3	(	(	PUNCT
ejpam-6418	415	4	v,∨,∧	v,∨,∧	NOUN
ejpam-6418	415	5	,	,	PUNCT
ejpam-6418	415	6	1	1	NUM
ejpam-6418	415	7	)	)	PUNCT
ejpam-6418	415	8	is	be	AUX
ejpam-6418	415	9	said	say	VERB
ejpam-6418	415	10	to	to	PART
ejpam-6418	415	11	be	be	AUX
ejpam-6418	415	12	relatively	relatively	ADV
ejpam-6418	415	13	complemented	complement	VERB
ejpam-6418	415	14	,	,	PUNCT
ejpam-6418	415	15	if	if	SCONJ
ejpam-6418	415	16	every	every	DET
ejpam-6418	415	17	interval	interval	NOUN
ejpam-6418	415	18	[	[	X
ejpam-6418	415	19	a	a	X
ejpam-6418	415	20	,	,	PUNCT
ejpam-6418	415	21	b	b	NOUN
ejpam-6418	415	22	]	]	X
ejpam-6418	415	23	,	,	PUNCT
ejpam-6418	415	24	in	in	ADP
ejpam-6418	415	25	v	v	NUM
ejpam-6418	415	26	is	be	AUX
ejpam-6418	415	27	a	a	DET
ejpam-6418	415	28	complemented	complemented	ADJ
ejpam-6418	415	29	lattice	lattice	NOUN
ejpam-6418	415	30	,	,	PUNCT
ejpam-6418	415	31	for	for	ADP
ejpam-6418	415	32	all	all	DET
ejpam-6418	415	33	a	a	PRON
ejpam-6418	415	34	,	,	PUNCT
ejpam-6418	415	35	b	b	X
ejpam-6418	415	36	∈	∈	PROPN
ejpam-6418	415	37	v.	v.	ADP
ejpam-6418	415	38	r.	r.	PROPN
ejpam-6418	415	39	sirisetti	sirisetti	PROPN
ejpam-6418	415	40	et	et	PROPN
ejpam-6418	415	41	al	al	PROPN
ejpam-6418	415	42	.	.	PUNCT
ejpam-6418	415	43	/	/	SYM
ejpam-6418	415	44	eur	eur	PROPN
ejpam-6418	415	45	.	.	PUNCT
ejpam-6418	416	1	j.	j.	PROPN
ejpam-6418	416	2	pure	pure	PROPN
ejpam-6418	416	3	appl	appl	PROPN
ejpam-6418	416	4	.	.	PROPN
ejpam-6418	416	5	math	math	PROPN
ejpam-6418	416	6	,	,	PUNCT
ejpam-6418	416	7	18	18	NUM
ejpam-6418	416	8	(	(	PUNCT
ejpam-6418	416	9	4	4	NUM
ejpam-6418	416	10	)	)	PUNCT
ejpam-6418	416	11	(	(	PUNCT
ejpam-6418	416	12	2025	2025	NUM
ejpam-6418	416	13	)	)	PUNCT
ejpam-6418	416	14	,	,	PUNCT
ejpam-6418	416	15	6418	6418	NUM
ejpam-6418	416	16	12	12	NUM
ejpam-6418	416	17	of	of	ADP
ejpam-6418	416	18	13	13	NUM
ejpam-6418	416	19	theorem	theorem	NOUN
ejpam-6418	416	20	3.31	3.31	NUM
ejpam-6418	416	21	.	.	PUNCT
ejpam-6418	417	1	v	v	NOUN
ejpam-6418	417	2	is	be	AUX
ejpam-6418	417	3	relatively	relatively	ADV
ejpam-6418	417	4	complemented	complemented	ADJ
ejpam-6418	417	5	if	if	SCONJ
ejpam-6418	417	6	and	and	CCONJ
ejpam-6418	417	7	only	only	ADV
ejpam-6418	417	8	if	if	SCONJ
ejpam-6418	417	9	every	every	DET
ejpam-6418	417	10	maximal	maximal	ADJ
ejpam-6418	417	11	set	set	NOUN
ejpam-6418	417	12	is	be	AUX
ejpam-6418	417	13	relatively	relatively	ADV
ejpam-6418	417	14	complemented	complemented	ADJ
ejpam-6418	417	15	.	.	PUNCT
ejpam-6418	418	1	proof	proof	NOUN
ejpam-6418	418	2	.	.	PUNCT
ejpam-6418	419	1	suppose	suppose	VERB
ejpam-6418	419	2	v	v	NOUN
ejpam-6418	419	3	is	be	AUX
ejpam-6418	419	4	relatively	relatively	ADV
ejpam-6418	419	5	complemented	complemented	ADJ
ejpam-6418	419	6	and	and	CCONJ
ejpam-6418	419	7	m	m	VERB
ejpam-6418	419	8	is	be	AUX
ejpam-6418	419	9	a	a	DET
ejpam-6418	419	10	maximal	maximal	ADJ
ejpam-6418	419	11	set	set	NOUN
ejpam-6418	419	12	in	in	ADP
ejpam-6418	419	13	v.	v.	ADP
ejpam-6418	419	14	for	for	ADP
ejpam-6418	419	15	any	any	DET
ejpam-6418	419	16	a	a	DET
ejpam-6418	419	17	,	,	PUNCT
ejpam-6418	419	18	b	b	PROPN
ejpam-6418	419	19	∈	∈	PROPN
ejpam-6418	419	20	m	m	VERB
ejpam-6418	419	21	with	with	ADP
ejpam-6418	419	22	a	a	DET
ejpam-6418	419	23	≤	≤	NUM
ejpam-6418	419	24	b	b	NOUN
ejpam-6418	419	25	,	,	PUNCT
ejpam-6418	419	26	the	the	DET
ejpam-6418	419	27	interval	interval	NOUN
ejpam-6418	419	28	[	[	X
ejpam-6418	419	29	a	a	X
ejpam-6418	419	30	,	,	PUNCT
ejpam-6418	419	31	b	b	NOUN
ejpam-6418	419	32	]	]	X
ejpam-6418	419	33	in	in	ADP
ejpam-6418	419	34	v	v	NUM
ejpam-6418	419	35	is	be	AUX
ejpam-6418	419	36	a	a	DET
ejpam-6418	419	37	subset	subset	NOUN
ejpam-6418	419	38	of	of	ADP
ejpam-6418	419	39	m	m	PROPN
ejpam-6418	419	40	.	.	PUNCT
ejpam-6418	420	1	let	let	VERB
ejpam-6418	420	2	x	x	PUNCT
ejpam-6418	420	3	∈	∈	PROPN
ejpam-6418	420	4	[	[	X
ejpam-6418	420	5	a	a	X
ejpam-6418	420	6	,	,	PUNCT
ejpam-6418	420	7	b	b	NOUN
ejpam-6418	420	8	]	]	X
ejpam-6418	420	9	.	.	PUNCT
ejpam-6418	421	1	then	then	ADV
ejpam-6418	421	2	a	a	DET
ejpam-6418	421	3	≤	≤	NUM
ejpam-6418	421	4	x.	x.	PUNCT
ejpam-6418	421	5	therefore	therefore	ADV
ejpam-6418	421	6	a	a	DET
ejpam-6418	421	7	∧	∧	NOUN
ejpam-6418	421	8	x	x	X
ejpam-6418	421	9	=	=	PUNCT
ejpam-6418	421	10	x	x	SYM
ejpam-6418	421	11	∧	∧	PROPN
ejpam-6418	421	12	a	a	PRON
ejpam-6418	421	13	and	and	CCONJ
ejpam-6418	421	14	a	a	DET
ejpam-6418	421	15	∈	∈	NOUN
ejpam-6418	421	16	m	m	NOUN
ejpam-6418	421	17	.	.	PUNCT
ejpam-6418	422	1	so	so	ADV
ejpam-6418	422	2	that	that	SCONJ
ejpam-6418	422	3	x	x	PUNCT
ejpam-6418	422	4	∈	∈	NOUN
ejpam-6418	422	5	m	m	VERB
ejpam-6418	422	6	.	.	PUNCT
ejpam-6418	423	1	hence	hence	ADV
ejpam-6418	423	2	[	[	X
ejpam-6418	423	3	a	a	DET
ejpam-6418	423	4	,	,	PUNCT
ejpam-6418	423	5	b	b	NOUN
ejpam-6418	423	6	]	]	X
ejpam-6418	423	7	⊆	⊆	NUM
ejpam-6418	423	8	m	m	NOUN
ejpam-6418	423	9	.	.	PUNCT
ejpam-6418	424	1	since	since	SCONJ
ejpam-6418	424	2	v	v	NOUN
ejpam-6418	424	3	is	be	AUX
ejpam-6418	424	4	relatively	relatively	ADV
ejpam-6418	424	5	complemented	complement	VERB
ejpam-6418	424	6	,	,	PUNCT
ejpam-6418	424	7	[	[	X
ejpam-6418	424	8	a	a	X
ejpam-6418	424	9	,	,	PUNCT
ejpam-6418	424	10	b	b	NOUN
ejpam-6418	424	11	]	]	X
ejpam-6418	424	12	is	be	AUX
ejpam-6418	424	13	relatively	relatively	ADV
ejpam-6418	424	14	complemented	complemented	ADJ
ejpam-6418	424	15	.	.	PUNCT
ejpam-6418	425	1	hence	hence	ADV
ejpam-6418	425	2	m	m	VERB
ejpam-6418	425	3	is	be	AUX
ejpam-6418	425	4	relatively	relatively	ADV
ejpam-6418	425	5	complemented	complement	VERB
ejpam-6418	425	6	.	.	PUNCT
ejpam-6418	426	1	conversely	conversely	ADV
ejpam-6418	426	2	suppose	suppose	VERB
ejpam-6418	426	3	that	that	SCONJ
ejpam-6418	426	4	every	every	DET
ejpam-6418	426	5	maximal	maximal	ADJ
ejpam-6418	426	6	set	set	NOUN
ejpam-6418	426	7	is	be	AUX
ejpam-6418	426	8	relatively	relatively	ADV
ejpam-6418	426	9	complemented	complemented	ADJ
ejpam-6418	426	10	.	.	PUNCT
ejpam-6418	427	1	let	let	VERB
ejpam-6418	427	2	a	a	DET
ejpam-6418	427	3	,	,	PUNCT
ejpam-6418	427	4	b	b	X
ejpam-6418	427	5	∈	∈	PROPN
ejpam-6418	428	1	v.	v.	CCONJ
ejpam-6418	428	2	then	then	ADV
ejpam-6418	428	3	[	[	X
ejpam-6418	428	4	a	a	X
ejpam-6418	428	5	,	,	PUNCT
ejpam-6418	428	6	b	b	NOUN
ejpam-6418	428	7	]	]	PUNCT
ejpam-6418	428	8	is	be	AUX
ejpam-6418	428	9	compatible	compatible	ADJ
ejpam-6418	428	10	and	and	CCONJ
ejpam-6418	428	11	it	it	PRON
ejpam-6418	428	12	contained	contain	VERB
ejpam-6418	428	13	in	in	ADP
ejpam-6418	428	14	a	a	DET
ejpam-6418	428	15	maximal	maximal	ADJ
ejpam-6418	428	16	set(since	set(since	NOUN
ejpam-6418	428	17	every	every	DET
ejpam-6418	428	18	maximal	maximal	ADJ
ejpam-6418	428	19	set	set	NOUN
ejpam-6418	428	20	is	be	AUX
ejpam-6418	428	21	compatible	compatible	ADJ
ejpam-6418	428	22	)	)	PUNCT
ejpam-6418	428	23	.	.	PUNCT
ejpam-6418	429	1	therefore	therefore	ADV
ejpam-6418	429	2	[	[	X
ejpam-6418	429	3	a	a	X
ejpam-6418	429	4	,	,	PUNCT
ejpam-6418	429	5	b	b	NOUN
ejpam-6418	429	6	]	]	X
ejpam-6418	429	7	is	be	AUX
ejpam-6418	429	8	relatively	relatively	ADV
ejpam-6418	429	9	complemented	complemented	ADJ
ejpam-6418	429	10	.	.	PUNCT
ejpam-6418	430	1	by	by	ADP
ejpam-6418	430	2	definition	definition	NOUN
ejpam-6418	430	3	3.30	3.30	NUM
ejpam-6418	430	4	.	.	PUNCT
ejpam-6418	431	1	,	,	PUNCT
ejpam-6418	431	2	v	v	NOUN
ejpam-6418	431	3	is	be	AUX
ejpam-6418	431	4	relatively	relatively	ADV
ejpam-6418	431	5	complemented	complemented	ADJ
ejpam-6418	431	6	.	.	PUNCT
ejpam-6418	432	1	theorem	theorem	VERB
ejpam-6418	432	2	3.32	3.32	NUM
ejpam-6418	432	3	.	.	PUNCT
ejpam-6418	433	1	v	v	NOUN
ejpam-6418	433	2	is	be	AUX
ejpam-6418	433	3	relatively	relatively	ADV
ejpam-6418	433	4	complemented	complemented	ADJ
ejpam-6418	433	5	if	if	SCONJ
ejpam-6418	433	6	and	and	CCONJ
ejpam-6418	433	7	only	only	ADV
ejpam-6418	433	8	if	if	SCONJ
ejpam-6418	433	9	every	every	DET
ejpam-6418	433	10	amicable	amicable	ADJ
ejpam-6418	433	11	is	be	AUX
ejpam-6418	433	12	relatively	relatively	ADV
ejpam-6418	433	13	complemented	complemented	ADJ
ejpam-6418	433	14	.	.	PUNCT
ejpam-6418	434	1	proof	proof	NOUN
ejpam-6418	434	2	.	.	PUNCT
ejpam-6418	435	1	let	let	VERB
ejpam-6418	435	2	m	m	PRON
ejpam-6418	435	3	be	be	AUX
ejpam-6418	435	4	an	an	DET
ejpam-6418	435	5	amicable	amicable	ADJ
ejpam-6418	435	6	set	set	NOUN
ejpam-6418	435	7	in	in	ADP
ejpam-6418	435	8	v	v	ADP
ejpam-6418	435	9	such	such	ADJ
ejpam-6418	435	10	that	that	SCONJ
ejpam-6418	435	11	m	m	PROPN
ejpam-6418	435	12	is	be	AUX
ejpam-6418	435	13	relatively	relatively	ADV
ejpam-6418	435	14	complemented	complemented	ADJ
ejpam-6418	435	15	.	.	PUNCT
ejpam-6418	436	1	let	let	VERB
ejpam-6418	436	2	a	a	DET
ejpam-6418	436	3	,	,	PUNCT
ejpam-6418	436	4	b	b	PROPN
ejpam-6418	436	5	∈	∈	PROPN
ejpam-6418	436	6	v	v	NOUN
ejpam-6418	436	7	and	and	CCONJ
ejpam-6418	436	8	a	a	DET
ejpam-6418	436	9	≤	≤	PROPN
ejpam-6418	436	10	b.	b.	NOUN
ejpam-6418	436	11	then	then	ADV
ejpam-6418	436	12	there	there	PRON
ejpam-6418	436	13	exists	exist	VERB
ejpam-6418	436	14	a0	a0	PROPN
ejpam-6418	436	15	,	,	PUNCT
ejpam-6418	436	16	b0	b0	PROPN
ejpam-6418	436	17	∈	∈	PROPN
ejpam-6418	436	18	m	m	VERB
ejpam-6418	436	19	such	such	ADJ
ejpam-6418	436	20	that	that	SCONJ
ejpam-6418	436	21	[	[	X
ejpam-6418	436	22	a0	a0	NOUN
ejpam-6418	436	23	)	)	PUNCT
ejpam-6418	436	24	=	=	PUNCT
ejpam-6418	437	1	[	[	X
ejpam-6418	437	2	a	a	X
ejpam-6418	437	3	)	)	PUNCT
ejpam-6418	437	4	and	and	CCONJ
ejpam-6418	437	5	[	[	X
ejpam-6418	437	6	b0	b0	NOUN
ejpam-6418	437	7	)	)	PUNCT
ejpam-6418	437	8	=	=	PUNCT
ejpam-6418	438	1	[	[	X
ejpam-6418	438	2	b	b	X
ejpam-6418	438	3	)	)	PUNCT
ejpam-6418	438	4	(	(	PUNCT
ejpam-6418	438	5	by	by	ADP
ejpam-6418	438	6	theorem	theorem	NOUN
ejpam-6418	438	7	3.22	3.22	NUM
ejpam-6418	438	8	.	.	PUNCT
ejpam-6418	438	9	)	)	PUNCT
ejpam-6418	439	1	now	now	ADV
ejpam-6418	439	2	,	,	PUNCT
ejpam-6418	439	3	a0	a0	PROPN
ejpam-6418	439	4	∨	∨	NUM
ejpam-6418	439	5	b0	b0	PROPN
ejpam-6418	439	6	=	=	PUNCT
ejpam-6418	439	7	b0	b0	PROPN
ejpam-6418	439	8	∨	∨	NOUN
ejpam-6418	439	9	a0	a0	NOUN
ejpam-6418	439	10	(	(	PUNCT
ejpam-6418	439	11	since	since	SCONJ
ejpam-6418	439	12	a0	a0	PROPN
ejpam-6418	439	13	,	,	PUNCT
ejpam-6418	439	14	b0	b0	NOUN
ejpam-6418	439	15	∈	∈	PROPN
ejpam-6418	439	16	m	m	NOUN
ejpam-6418	439	17	)	)	PUNCT
ejpam-6418	439	18	=	=	SYM
ejpam-6418	439	19	b0	b0	PROPN
ejpam-6418	439	20	∨	∨	NUM
ejpam-6418	439	21	a0	a0	PROPN
ejpam-6418	439	22	∨	∨	NUM
ejpam-6418	439	23	a	a	PRON
ejpam-6418	439	24	(	(	PUNCT
ejpam-6418	439	25	since	since	SCONJ
ejpam-6418	439	26	a0	a0	PROPN
ejpam-6418	439	27	∈	∈	PROPN
ejpam-6418	439	28	[	[	X
ejpam-6418	439	29	a	a	X
ejpam-6418	439	30	)	)	PUNCT
ejpam-6418	439	31	)	)	PUNCT
ejpam-6418	440	1	=	=	SYM
ejpam-6418	440	2	b0	b0	VERB
ejpam-6418	440	3	∨	∨	NUM
ejpam-6418	440	4	a	a	DET
ejpam-6418	440	5	∨	∨	NUM
ejpam-6418	440	6	a0	a0	NOUN
ejpam-6418	440	7	(	(	PUNCT
ejpam-6418	440	8	by	by	ADP
ejpam-6418	440	9	lemma	lemma	PROPN
ejpam-6418	440	10	2.4(viii	2.4(viii	NUM
ejpam-6418	440	11	)	)	PUNCT
ejpam-6418	440	12	)	)	PUNCT
ejpam-6418	441	1	=	=	PUNCT
ejpam-6418	441	2	b0	b0	VERB
ejpam-6418	441	3	∨	∨	NUM
ejpam-6418	441	4	a	a	PRON
ejpam-6418	441	5	(	(	PUNCT
ejpam-6418	441	6	since	since	SCONJ
ejpam-6418	441	7	a	a	DET
ejpam-6418	441	8	∈	∈	PROPN
ejpam-6418	441	9	[	[	X
ejpam-6418	441	10	a0	a0	NOUN
ejpam-6418	441	11	)	)	PUNCT
ejpam-6418	441	12	)	)	PUNCT
ejpam-6418	442	1	=	=	PUNCT
ejpam-6418	442	2	b0	b0	VERB
ejpam-6418	442	3	∨	∨	NUM
ejpam-6418	442	4	b	b	PROPN
ejpam-6418	442	5	∨	∨	NUM
ejpam-6418	442	6	a	a	PRON
ejpam-6418	442	7	(	(	PUNCT
ejpam-6418	442	8	since	since	SCONJ
ejpam-6418	442	9	b0	b0	VERB
ejpam-6418	442	10	∈	∈	PROPN
ejpam-6418	442	11	[	[	X
ejpam-6418	442	12	b	b	NOUN
ejpam-6418	442	13	)	)	PUNCT
ejpam-6418	442	14	)	)	PUNCT
ejpam-6418	443	1	=	=	SYM
ejpam-6418	443	2	b0	b0	VERB
ejpam-6418	443	3	∨	∨	NUM
ejpam-6418	443	4	b	b	PROPN
ejpam-6418	443	5	(	(	PUNCT
ejpam-6418	443	6	since	since	SCONJ
ejpam-6418	443	7	a	a	DET
ejpam-6418	443	8	≤	≤	NUM
ejpam-6418	443	9	b	b	NOUN
ejpam-6418	443	10	)	)	PUNCT
ejpam-6418	443	11	=	=	SYM
ejpam-6418	443	12	b0	b0	NOUN
ejpam-6418	443	13	.	.	PUNCT
ejpam-6418	444	1	(	(	PUNCT
ejpam-6418	444	2	since	since	SCONJ
ejpam-6418	444	3	b0	b0	VERB
ejpam-6418	444	4	∈	∈	PROPN
ejpam-6418	444	5	[	[	X
ejpam-6418	444	6	b	b	NOUN
ejpam-6418	444	7	)	)	PUNCT
ejpam-6418	444	8	)	)	PUNCT
ejpam-6418	444	9	therefore	therefore	ADV
ejpam-6418	444	10	a0	a0	PROPN
ejpam-6418	444	11	∧	∧	PROPN
ejpam-6418	444	12	b0	b0	PROPN
ejpam-6418	444	13	=	=	PUNCT
ejpam-6418	444	14	a0	a0	PROPN
ejpam-6418	444	15	and	and	CCONJ
ejpam-6418	444	16	hence	hence	ADV
ejpam-6418	444	17	a0	a0	PROPN
ejpam-6418	444	18	≤	≤	PROPN
ejpam-6418	444	19	b0	b0	NOUN
ejpam-6418	444	20	.	.	PUNCT
ejpam-6418	445	1	since	since	SCONJ
ejpam-6418	445	2	m	m	PROPN
ejpam-6418	445	3	is	be	AUX
ejpam-6418	445	4	relatively	relatively	ADV
ejpam-6418	445	5	complemented	complemented	ADJ
ejpam-6418	445	6	,	,	PUNCT
ejpam-6418	445	7	there	there	PRON
ejpam-6418	445	8	exists	exist	VERB
ejpam-6418	445	9	x	x	X
ejpam-6418	445	10	∈	∈	NOUN
ejpam-6418	445	11	m	m	VERB
ejpam-6418	445	12	such	such	ADJ
ejpam-6418	445	13	that	that	SCONJ
ejpam-6418	445	14	a0	a0	PROPN
ejpam-6418	445	15	∨	∨	NOUN
ejpam-6418	445	16	x	x	SYM
ejpam-6418	445	17	=	=	SYM
ejpam-6418	445	18	1	1	NUM
ejpam-6418	445	19	and	and	CCONJ
ejpam-6418	445	20	a0	a0	PROPN
ejpam-6418	445	21	∧	∧	PROPN
ejpam-6418	445	22	x	x	PUNCT
ejpam-6418	445	23	is	be	AUX
ejpam-6418	445	24	minimal	minimal	ADJ
ejpam-6418	445	25	.	.	PUNCT
ejpam-6418	446	1	for	for	ADP
ejpam-6418	446	2	x	x	PROPN
ejpam-6418	446	3	∨	∨	NUM
ejpam-6418	446	4	b	b	PROPN
ejpam-6418	446	5	∈	∈	PROPN
ejpam-6418	446	6	v	v	NOUN
ejpam-6418	446	7	,	,	PUNCT
ejpam-6418	446	8	a	a	DET
ejpam-6418	446	9	∨	∨	NOUN
ejpam-6418	446	10	(	(	PUNCT
ejpam-6418	446	11	x	x	PROPN
ejpam-6418	446	12	∨	∨	NUM
ejpam-6418	446	13	b	b	NOUN
ejpam-6418	446	14	)	)	PUNCT
ejpam-6418	446	15	=	=	SYM
ejpam-6418	446	16	a	a	DET
ejpam-6418	446	17	∨	∨	NUM
ejpam-6418	446	18	a0	a0	NOUN
ejpam-6418	446	19	∨	∨	NUM
ejpam-6418	446	20	x	x	SYM
ejpam-6418	446	21	∨	∨	NUM
ejpam-6418	446	22	b	b	PROPN
ejpam-6418	446	23	(	(	PUNCT
ejpam-6418	446	24	since	since	SCONJ
ejpam-6418	446	25	a	a	DET
ejpam-6418	446	26	∈	∈	PROPN
ejpam-6418	446	27	[	[	X
ejpam-6418	446	28	a0	a0	NOUN
ejpam-6418	446	29	)	)	PUNCT
ejpam-6418	446	30	=	=	PUNCT
ejpam-6418	446	31	a	a	DET
ejpam-6418	446	32	∨	∨	NUM
ejpam-6418	446	33	1	1	NUM
ejpam-6418	446	34	∨	∨	NUM
ejpam-6418	446	35	b	b	PROPN
ejpam-6418	446	36	(	(	PUNCT
ejpam-6418	446	37	since	since	SCONJ
ejpam-6418	446	38	a0	a0	PROPN
ejpam-6418	446	39	∨	∨	NUM
ejpam-6418	446	40	x	x	SYM
ejpam-6418	446	41	=	=	SYM
ejpam-6418	446	42	1	1	NUM
ejpam-6418	446	43	)	)	PUNCT
ejpam-6418	446	44	=	=	SYM
ejpam-6418	446	45	1	1	NUM
ejpam-6418	446	46	a	a	DET
ejpam-6418	446	47	∧	∧	PROPN
ejpam-6418	446	48	(	(	PUNCT
ejpam-6418	446	49	x	x	PROPN
ejpam-6418	446	50	∨	∨	NUM
ejpam-6418	446	51	b	b	NOUN
ejpam-6418	446	52	)	)	PUNCT
ejpam-6418	446	53	=	=	SYM
ejpam-6418	446	54	(	(	PUNCT
ejpam-6418	446	55	a	a	DET
ejpam-6418	446	56	∨	∨	NUM
ejpam-6418	446	57	a0	a0	NOUN
ejpam-6418	446	58	)	)	PUNCT
ejpam-6418	446	59	∧	∧	PROPN
ejpam-6418	446	60	(	(	PUNCT
ejpam-6418	446	61	x	x	PROPN
ejpam-6418	446	62	∨	∨	NUM
ejpam-6418	446	63	b	b	NUM
ejpam-6418	446	64	)	)	PUNCT
ejpam-6418	446	65	(	(	PUNCT
ejpam-6418	446	66	since	since	SCONJ
ejpam-6418	446	67	a	a	DET
ejpam-6418	446	68	∈	∈	PROPN
ejpam-6418	446	69	[	[	X
ejpam-6418	446	70	a0	a0	NOUN
ejpam-6418	446	71	)	)	PUNCT
ejpam-6418	446	72	=	=	PRON
ejpam-6418	446	73	{	{	PUNCT
ejpam-6418	446	74	a	a	DET
ejpam-6418	446	75	∧	∧	PROPN
ejpam-6418	446	76	(	(	PUNCT
ejpam-6418	446	77	x	x	PROPN
ejpam-6418	446	78	∨	∨	NUM
ejpam-6418	446	79	b	b	NOUN
ejpam-6418	446	80	)	)	PUNCT
ejpam-6418	446	81	}	}	PUNCT
ejpam-6418	446	82	∨	∨	X
ejpam-6418	446	83	{	{	PUNCT
ejpam-6418	446	84	a0	a0	NOUN
ejpam-6418	446	85	∧	∧	PROPN
ejpam-6418	446	86	(	(	PUNCT
ejpam-6418	446	87	x	x	PROPN
ejpam-6418	446	88	∨	∨	NUM
ejpam-6418	446	89	b	b	NOUN
ejpam-6418	446	90	)	)	PUNCT
ejpam-6418	446	91	}	}	PUNCT
ejpam-6418	446	92	(	(	PUNCT
ejpam-6418	446	93	by	by	ADP
ejpam-6418	446	94	lemma	lemma	PROPN
ejpam-6418	446	95	2.4(iv	2.4(iv	NUM
ejpam-6418	446	96	)	)	PUNCT
ejpam-6418	446	97	)	)	PUNCT
ejpam-6418	447	1	=	=	PRON
ejpam-6418	447	2	{	{	PUNCT
ejpam-6418	447	3	a	a	DET
ejpam-6418	447	4	∧	∧	PROPN
ejpam-6418	447	5	(	(	PUNCT
ejpam-6418	447	6	x	x	PROPN
ejpam-6418	447	7	∨	∨	NUM
ejpam-6418	447	8	b	b	NOUN
ejpam-6418	447	9	)	)	PUNCT
ejpam-6418	447	10	}	}	PUNCT
ejpam-6418	447	11	∨	∨	X
ejpam-6418	447	12	{	{	PUNCT
ejpam-6418	447	13	(	(	PUNCT
ejpam-6418	447	14	x	x	PROPN
ejpam-6418	447	15	∨	∨	NUM
ejpam-6418	447	16	b	b	NOUN
ejpam-6418	447	17	)	)	PUNCT
ejpam-6418	447	18	∧	∧	PROPN
ejpam-6418	447	19	a0	a0	PROPN
ejpam-6418	447	20	}	}	PUNCT
ejpam-6418	447	21	(	(	PUNCT
ejpam-6418	447	22	by	by	ADP
ejpam-6418	447	23	lemma	lemma	PROPN
ejpam-6418	447	24	2.4(v	2.4(v	NUM
ejpam-6418	447	25	)	)	PUNCT
ejpam-6418	447	26	)	)	PUNCT
ejpam-6418	447	27	=	=	SYM
ejpam-6418	448	1	(	(	PUNCT
ejpam-6418	448	2	x	x	PROPN
ejpam-6418	448	3	∨	∨	NUM
ejpam-6418	448	4	b	b	NOUN
ejpam-6418	448	5	)	)	PUNCT
ejpam-6418	448	6	∧	∧	NOUN
ejpam-6418	448	7	{	{	PUNCT
ejpam-6418	448	8	[	[	X
ejpam-6418	448	9	a	a	DET
ejpam-6418	448	10	∧	∧	NOUN
ejpam-6418	448	11	(	(	PUNCT
ejpam-6418	448	12	x	x	PROPN
ejpam-6418	448	13	∨	∨	NUM
ejpam-6418	448	14	b	b	NOUN
ejpam-6418	448	15	)	)	PUNCT
ejpam-6418	448	16	]	]	PUNCT
ejpam-6418	448	17	∨	∨	NUM
ejpam-6418	448	18	a0	a0	PROPN
ejpam-6418	448	19	}	}	PUNCT
ejpam-6418	448	20	(	(	PUNCT
ejpam-6418	448	21	by	by	ADP
ejpam-6418	448	22	lemma	lemma	PROPN
ejpam-6418	448	23	2.3(iii	2.3(iii	NUM
ejpam-6418	448	24	)	)	PUNCT
ejpam-6418	448	25	)	)	PUNCT
ejpam-6418	449	1	=	=	SYM
ejpam-6418	449	2	(	(	PUNCT
ejpam-6418	449	3	x	x	PROPN
ejpam-6418	449	4	∨	∨	NUM
ejpam-6418	449	5	b	b	NOUN
ejpam-6418	449	6	)	)	PUNCT
ejpam-6418	449	7	∧	∧	NOUN
ejpam-6418	449	8	{	{	PUNCT
ejpam-6418	449	9	(	(	PUNCT
ejpam-6418	449	10	a	a	DET
ejpam-6418	449	11	∨	∨	NUM
ejpam-6418	449	12	a0	a0	NOUN
ejpam-6418	449	13	)	)	PUNCT
ejpam-6418	449	14	∧	∧	PROPN
ejpam-6418	450	1	[	[	X
ejpam-6418	450	2	(	(	PUNCT
ejpam-6418	450	3	x	x	PROPN
ejpam-6418	450	4	∨	∨	NUM
ejpam-6418	450	5	b	b	NOUN
ejpam-6418	450	6	)	)	PUNCT
ejpam-6418	450	7	∨	∨	NUM
ejpam-6418	450	8	a0	a0	NOUN
ejpam-6418	450	9	]	]	PUNCT
ejpam-6418	450	10	}	}	PUNCT
ejpam-6418	450	11	(	(	PUNCT
ejpam-6418	450	12	by	by	ADP
ejpam-6418	450	13	definition	definition	NOUN
ejpam-6418	450	14	2.1(ii	2.1(ii	NUM
ejpam-6418	450	15	)	)	PUNCT
ejpam-6418	450	16	)	)	PUNCT
ejpam-6418	451	1	=	=	PRON
ejpam-6418	451	2	(	(	PUNCT
ejpam-6418	451	3	x	x	PROPN
ejpam-6418	451	4	∨	∨	NUM
ejpam-6418	451	5	b	b	NOUN
ejpam-6418	451	6	)	)	PUNCT
ejpam-6418	451	7	∧	∧	NOUN
ejpam-6418	451	8	{	{	PUNCT
ejpam-6418	451	9	(	(	PUNCT
ejpam-6418	451	10	a	a	DET
ejpam-6418	451	11	∨	∨	NUM
ejpam-6418	451	12	a0	a0	NOUN
ejpam-6418	451	13	)	)	PUNCT
ejpam-6418	451	14	∧	∧	PROPN
ejpam-6418	452	1	[	[	X
ejpam-6418	452	2	(	(	PUNCT
ejpam-6418	452	3	x	x	SYM
ejpam-6418	452	4	∨	∨	NUM
ejpam-6418	452	5	a0	a0	PROPN
ejpam-6418	452	6	∨	∨	NUM
ejpam-6418	452	7	b	b	NOUN
ejpam-6418	452	8	]	]	X
ejpam-6418	452	9	}	}	PUNCT
ejpam-6418	452	10	(	(	PUNCT
ejpam-6418	452	11	by	by	ADP
ejpam-6418	452	12	lemma	lemma	PROPN
ejpam-6418	452	13	2.4(vi)(viii	2.4(vi)(viii	PROPN
ejpam-6418	452	14	)	)	PUNCT
ejpam-6418	452	15	)	)	PUNCT
ejpam-6418	453	1	=	=	SYM
ejpam-6418	453	2	(	(	PUNCT
ejpam-6418	453	3	x	x	PROPN
ejpam-6418	453	4	∨	∨	NUM
ejpam-6418	453	5	b	b	NOUN
ejpam-6418	453	6	)	)	PUNCT
ejpam-6418	453	7	∧	∧	NOUN
ejpam-6418	453	8	(	(	PUNCT
ejpam-6418	453	9	a	a	DET
ejpam-6418	453	10	∨	∨	NUM
ejpam-6418	453	11	a0	a0	NOUN
ejpam-6418	453	12	)	)	PUNCT
ejpam-6418	453	13	(	(	PUNCT
ejpam-6418	453	14	since	since	SCONJ
ejpam-6418	453	15	a0	a0	PROPN
ejpam-6418	453	16	∨	∨	NUM
ejpam-6418	453	17	x	x	SYM
ejpam-6418	453	18	=	=	SYM
ejpam-6418	453	19	1	1	NUM
ejpam-6418	453	20	)	)	PUNCT
ejpam-6418	453	21	=	=	SYM
ejpam-6418	453	22	(	(	PUNCT
ejpam-6418	453	23	x	x	PROPN
ejpam-6418	453	24	∨	∨	NUM
ejpam-6418	453	25	b	b	NOUN
ejpam-6418	453	26	)	)	PUNCT
ejpam-6418	453	27	∧	∧	PROPN
ejpam-6418	453	28	a	a	PRON
ejpam-6418	453	29	(	(	PUNCT
ejpam-6418	453	30	since	since	SCONJ
ejpam-6418	453	31	a	a	DET
ejpam-6418	453	32	∈	∈	PROPN
ejpam-6418	453	33	[	[	X
ejpam-6418	453	34	a0	a0	NOUN
ejpam-6418	453	35	)	)	PUNCT
ejpam-6418	453	36	and	and	CCONJ
ejpam-6418	453	37	a0	a0	PROPN
ejpam-6418	453	38	∈	∈	PROPN
ejpam-6418	454	1	[	[	X
ejpam-6418	454	2	a	a	X
ejpam-6418	454	3	)	)	PUNCT
ejpam-6418	454	4	=	=	SYM
ejpam-6418	454	5	(	(	PUNCT
ejpam-6418	454	6	x	x	PUNCT
ejpam-6418	454	7	∧	∧	NOUN
ejpam-6418	454	8	a	a	PRON
ejpam-6418	454	9	)	)	PUNCT
ejpam-6418	454	10	∨	∨	NOUN
ejpam-6418	454	11	(	(	PUNCT
ejpam-6418	454	12	b	b	PROPN
ejpam-6418	454	13	∧	∧	PROPN
ejpam-6418	454	14	a	a	NOUN
ejpam-6418	454	15	)	)	PUNCT
ejpam-6418	454	16	(	(	PUNCT
ejpam-6418	454	17	by	by	ADP
ejpam-6418	454	18	lemma	lemma	PROPN
ejpam-6418	454	19	2.4(iv	2.4(iv	NUM
ejpam-6418	454	20	)	)	PUNCT
ejpam-6418	454	21	)	)	PUNCT
ejpam-6418	455	1	=	=	SYM
ejpam-6418	455	2	(	(	PUNCT
ejpam-6418	455	3	x	x	PUNCT
ejpam-6418	455	4	∧	∧	NOUN
ejpam-6418	455	5	a	a	PRON
ejpam-6418	455	6	)	)	PUNCT
ejpam-6418	455	7	∨	∨	NUM
ejpam-6418	455	8	a	a	PRON
ejpam-6418	455	9	(	(	PUNCT
ejpam-6418	455	10	since	since	SCONJ
ejpam-6418	455	11	a	a	DET
ejpam-6418	455	12	≤	≤	NUM
ejpam-6418	455	13	b	b	NOUN
ejpam-6418	455	14	)	)	PUNCT
ejpam-6418	455	15	)	)	PUNCT
ejpam-6418	456	1	=	=	PUNCT
ejpam-6418	457	1	a.	a.	NOUN
ejpam-6418	457	2	therefore	therefore	ADV
ejpam-6418	457	3	a	a	DET
ejpam-6418	457	4	≤	≤	ADJ
ejpam-6418	457	5	x∨	x∨	PROPN
ejpam-6418	457	6	b	b	PROPN
ejpam-6418	457	7	≤	≤	ADJ
ejpam-6418	457	8	1	1	NUM
ejpam-6418	457	9	.	.	PUNCT
ejpam-6418	458	1	so	so	SCONJ
ejpam-6418	458	2	that	that	SCONJ
ejpam-6418	458	3	a∨	a∨	PROPN
ejpam-6418	458	4	(	(	PUNCT
ejpam-6418	458	5	x∨	x∨	PROPN
ejpam-6418	458	6	b	b	PROPN
ejpam-6418	458	7	)	)	PUNCT
ejpam-6418	458	8	=	=	SYM
ejpam-6418	458	9	1	1	NUM
ejpam-6418	458	10	and	and	CCONJ
ejpam-6418	458	11	a∧	a∧	NOUN
ejpam-6418	458	12	(	(	PUNCT
ejpam-6418	458	13	x∨	x∨	PROPN
ejpam-6418	458	14	b	b	PROPN
ejpam-6418	458	15	)	)	PUNCT
ejpam-6418	458	16	=	=	NOUN
ejpam-6418	458	17	a.	a.	NOUN
ejpam-6418	458	18	hence	hence	ADV
ejpam-6418	458	19	v	v	NOUN
ejpam-6418	458	20	is	be	AUX
ejpam-6418	458	21	relatively	relatively	ADV
ejpam-6418	458	22	complemented	complemented	ADJ
ejpam-6418	458	23	.	.	PUNCT
ejpam-6418	459	1	r.	r.	PROPN
ejpam-6418	459	2	sirisetti	sirisetti	PROPN
ejpam-6418	459	3	et	et	PROPN
ejpam-6418	459	4	al	al	PROPN
ejpam-6418	459	5	.	.	PUNCT
ejpam-6418	459	6	/	/	SYM
ejpam-6418	459	7	eur	eur	PROPN
ejpam-6418	459	8	.	.	PUNCT
ejpam-6418	460	1	j.	j.	PROPN
ejpam-6418	460	2	pure	pure	PROPN
ejpam-6418	460	3	appl	appl	PROPN
ejpam-6418	460	4	.	.	PROPN
ejpam-6418	460	5	math	math	PROPN
ejpam-6418	460	6	,	,	PUNCT
ejpam-6418	460	7	18	18	NUM
ejpam-6418	460	8	(	(	PUNCT
ejpam-6418	460	9	4	4	NUM
ejpam-6418	460	10	)	)	PUNCT
ejpam-6418	460	11	(	(	PUNCT
ejpam-6418	460	12	2025	2025	NUM
ejpam-6418	460	13	)	)	PUNCT
ejpam-6418	460	14	,	,	PUNCT
ejpam-6418	460	15	6418	6418	NUM
ejpam-6418	460	16	13	13	NUM
ejpam-6418	460	17	of	of	ADP
ejpam-6418	460	18	13	13	NUM
ejpam-6418	460	19	4	4	NUM
ejpam-6418	460	20	.	.	PUNCT
ejpam-6418	460	21	conclusion	conclusion	NOUN
ejpam-6418	460	22	and	and	CCONJ
ejpam-6418	460	23	future	future	ADJ
ejpam-6418	460	24	work	work	NOUN
ejpam-6418	460	25	in	in	ADP
ejpam-6418	460	26	this	this	DET
ejpam-6418	460	27	paper	paper	NOUN
ejpam-6418	460	28	,	,	PUNCT
ejpam-6418	460	29	we	we	PRON
ejpam-6418	460	30	introduced	introduce	VERB
ejpam-6418	460	31	and	and	CCONJ
ejpam-6418	460	32	analyzed	analyze	VERB
ejpam-6418	460	33	maximal	maximal	ADJ
ejpam-6418	460	34	and	and	CCONJ
ejpam-6418	460	35	amicable	amicable	ADJ
ejpam-6418	460	36	sets	set	NOUN
ejpam-6418	460	37	in	in	ADP
ejpam-6418	460	38	paradistributive	paradistributive	ADJ
ejpam-6418	460	39	latticoids	latticoid	NOUN
ejpam-6418	460	40	(	(	PUNCT
ejpam-6418	460	41	pdls	pdl	NOUN
ejpam-6418	460	42	)	)	PUNCT
ejpam-6418	460	43	.	.	PUNCT
ejpam-6418	461	1	we	we	PRON
ejpam-6418	461	2	established	establish	VERB
ejpam-6418	461	3	key	key	ADJ
ejpam-6418	461	4	structural	structural	ADJ
ejpam-6418	461	5	properties	property	NOUN
ejpam-6418	461	6	,	,	PUNCT
ejpam-6418	461	7	including	include	VERB
ejpam-6418	461	8	that	that	SCONJ
ejpam-6418	461	9	the	the	DET
ejpam-6418	461	10	center	center	NOUN
ejpam-6418	461	11	of	of	ADP
ejpam-6418	461	12	a	a	DET
ejpam-6418	461	13	pdl	pdl	NOUN
ejpam-6418	461	14	is	be	AUX
ejpam-6418	461	15	the	the	DET
ejpam-6418	461	16	intersection	intersection	NOUN
ejpam-6418	461	17	of	of	ADP
ejpam-6418	461	18	all	all	DET
ejpam-6418	461	19	maximal	maximal	ADJ
ejpam-6418	461	20	sets	set	NOUN
ejpam-6418	461	21	and	and	CCONJ
ejpam-6418	461	22	forms	form	VERB
ejpam-6418	461	23	a	a	DET
ejpam-6418	461	24	filter	filter	NOUN
ejpam-6418	461	25	.	.	PUNCT
ejpam-6418	462	1	additionally	additionally	ADV
ejpam-6418	462	2	,	,	PUNCT
ejpam-6418	462	3	we	we	PRON
ejpam-6418	462	4	characterized	characterize	VERB
ejpam-6418	462	5	relatively	relatively	ADV
ejpam-6418	462	6	complemented	complement	VERB
ejpam-6418	462	7	pdls	pdl	NOUN
ejpam-6418	462	8	using	use	VERB
ejpam-6418	462	9	amicable	amicable	ADJ
ejpam-6418	462	10	sets	set	NOUN
ejpam-6418	462	11	.	.	PUNCT
ejpam-6418	463	1	these	these	DET
ejpam-6418	463	2	results	result	NOUN
ejpam-6418	463	3	contribute	contribute	VERB
ejpam-6418	463	4	to	to	ADP
ejpam-6418	463	5	the	the	DET
ejpam-6418	463	6	deeper	deep	ADJ
ejpam-6418	463	7	understanding	understanding	NOUN
ejpam-6418	463	8	of	of	ADP
ejpam-6418	463	9	compatibility	compatibility	NOUN
ejpam-6418	463	10	in	in	ADP
ejpam-6418	463	11	generalized	generalized	ADJ
ejpam-6418	463	12	lattices	lattice	NOUN
ejpam-6418	463	13	.	.	PUNCT
ejpam-6418	464	1	future	future	ADJ
ejpam-6418	464	2	work	work	NOUN
ejpam-6418	464	3	may	may	AUX
ejpam-6418	464	4	focus	focus	VERB
ejpam-6418	464	5	on	on	ADP
ejpam-6418	464	6	extending	extend	VERB
ejpam-6418	464	7	these	these	DET
ejpam-6418	464	8	concepts	concept	NOUN
ejpam-6418	464	9	to	to	PART
ejpam-6418	464	10	related	relate	VERB
ejpam-6418	464	11	algebraic	algebraic	ADJ
ejpam-6418	464	12	structures	structure	NOUN
ejpam-6418	464	13	,	,	PUNCT
ejpam-6418	464	14	exploring	explore	VERB
ejpam-6418	464	15	categorical	categorical	ADJ
ejpam-6418	464	16	properties	property	NOUN
ejpam-6418	464	17	,	,	PUNCT
ejpam-6418	464	18	and	and	CCONJ
ejpam-6418	464	19	developing	develop	VERB
ejpam-6418	464	20	computational	computational	ADJ
ejpam-6418	464	21	approaches	approach	NOUN
ejpam-6418	464	22	for	for	ADP
ejpam-6418	464	23	identifying	identify	VERB
ejpam-6418	464	24	maximal	maximal	ADJ
ejpam-6418	464	25	and	and	CCONJ
ejpam-6418	464	26	amicable	amicable	ADJ
ejpam-6418	464	27	sets	set	NOUN
ejpam-6418	464	28	in	in	ADP
ejpam-6418	464	29	practical	practical	ADJ
ejpam-6418	464	30	and	and	CCONJ
ejpam-6418	464	31	theoretical	theoretical	ADJ
ejpam-6418	464	32	applications	application	NOUN
ejpam-6418	464	33	.	.	PUNCT
ejpam-6418	465	1	5	5	X
ejpam-6418	465	2	.	.	X
ejpam-6418	465	3	conflict	conflict	NOUN
ejpam-6418	465	4	of	of	ADP
ejpam-6418	465	5	interest	interest	NOUN
ejpam-6418	465	6	the	the	DET
ejpam-6418	465	7	authors	author	NOUN
ejpam-6418	465	8	declare	declare	VERB
ejpam-6418	465	9	that	that	SCONJ
ejpam-6418	465	10	there	there	PRON
ejpam-6418	465	11	are	be	VERB
ejpam-6418	465	12	no	no	DET
ejpam-6418	465	13	conflicts	conflict	NOUN
ejpam-6418	465	14	of	of	ADP
ejpam-6418	465	15	interest	interest	NOUN
ejpam-6418	465	16	regarding	regard	VERB
ejpam-6418	465	17	the	the	DET
ejpam-6418	465	18	publication	publication	NOUN
ejpam-6418	465	19	of	of	ADP
ejpam-6418	465	20	this	this	DET
ejpam-6418	465	21	paper	paper	NOUN
ejpam-6418	465	22	.	.	PUNCT
ejpam-6418	466	1	acknowledgements	acknowledgement	NOUN
ejpam-6418	466	2	this	this	DET
ejpam-6418	466	3	research	research	NOUN
ejpam-6418	466	4	was	be	AUX
ejpam-6418	466	5	supported	support	VERB
ejpam-6418	466	6	by	by	ADP
ejpam-6418	466	7	university	university	NOUN
ejpam-6418	466	8	of	of	ADP
ejpam-6418	466	9	phayao	phayao	NOUN
ejpam-6418	466	10	and	and	CCONJ
ejpam-6418	466	11	thailand	thailand	PROPN
ejpam-6418	466	12	science	science	PROPN
ejpam-6418	466	13	research	research	PROPN
ejpam-6418	466	14	and	and	CCONJ
ejpam-6418	466	15	innovation	innovation	NOUN
ejpam-6418	466	16	fund	fund	NOUN
ejpam-6418	466	17	(	(	PUNCT
ejpam-6418	466	18	fundamental	fundamental	ADJ
ejpam-6418	466	19	fund	fund	NOUN
ejpam-6418	466	20	2026	2026	NUM
ejpam-6418	466	21	,	,	PUNCT
ejpam-6418	466	22	grant	grant	VERB
ejpam-6418	466	23	no	no	NOUN
ejpam-6418	466	24	.	.	NOUN
ejpam-6418	466	25	2287/2568	2287/2568	NUM
ejpam-6418	466	26	)	)	PUNCT
ejpam-6418	467	1	references	reference	NOUN
ejpam-6418	467	2	[	[	X
ejpam-6418	467	3	1	1	NUM
ejpam-6418	467	4	]	]	PUNCT
ejpam-6418	467	5	ravikumar	ravikumar	NOUN
ejpam-6418	467	6	bandaru	bandaru	PROPN
ejpam-6418	467	7	and	and	CCONJ
ejpam-6418	467	8	suryavardhani	suryavardhani	PROPN
ejpam-6418	467	9	ajjarapu	ajjarapu	PROPN
ejpam-6418	467	10	.	.	PUNCT
ejpam-6418	468	1	paradistributive	paradistributive	PROPN
ejpam-6418	468	2	latticoids	latticoids	PROPN
ejpam-6418	468	3	.	.	PUNCT
ejpam-6418	469	1	european	european	PROPN
ejpam-6418	469	2	journal	journal	PROPN
ejpam-6418	469	3	of	of	ADP
ejpam-6418	469	4	pure	pure	ADJ
ejpam-6418	469	5	and	and	CCONJ
ejpam-6418	469	6	applied	applied	ADJ
ejpam-6418	469	7	mathematics	mathematic	NOUN
ejpam-6418	469	8	,	,	PUNCT
ejpam-6418	469	9	17:819–834	17:819–834	PROPN
ejpam-6418	469	10	,	,	PUNCT
ejpam-6418	469	11	2024	2024	NUM
ejpam-6418	469	12	.	.	PUNCT
ejpam-6418	470	1	[	[	X
ejpam-6418	470	2	2	2	X
ejpam-6418	470	3	]	]	X
ejpam-6418	470	4	g.	g.	NOUN
ejpam-6418	470	5	birkhoff	birkhoff	PROPN
ejpam-6418	470	6	.	.	PUNCT
ejpam-6418	471	1	lattice	lattice	PROPN
ejpam-6418	471	2	theory	theory	PROPN
ejpam-6418	471	3	.	.	PUNCT
ejpam-6418	472	1	amer	amer	PROPN
ejpam-6418	472	2	.	.	PUNCT
ejpam-6418	472	3	math	math	PROPN
ejpam-6418	472	4	.	.	PUNCT
ejpam-6418	473	1	soc	soc	PROPN
ejpam-6418	473	2	.	.	PUNCT
ejpam-6418	474	1	collequium	collequium	NOUN
ejpam-6418	474	2	pub	pub	NOUN
ejpam-6418	474	3	,	,	PUNCT
ejpam-6418	474	4	1967	1967	NUM
ejpam-6418	474	5	.	.	PUNCT
ejpam-6418	475	1	[	[	X
ejpam-6418	475	2	3	3	X
ejpam-6418	475	3	]	]	X
ejpam-6418	475	4	y.	y.	PROPN
ejpam-6418	475	5	l.	l.	PROPN
ejpam-6418	475	6	ershov	ershov	PROPN
ejpam-6418	475	7	.	.	PUNCT
ejpam-6418	476	1	relatively	relatively	ADV
ejpam-6418	476	2	complemented	complement	VERB
ejpam-6418	476	3	distributive	distributive	ADJ
ejpam-6418	476	4	lattices	lattice	NOUN
ejpam-6418	476	5	.	.	PUNCT
ejpam-6418	477	1	algebra	algebra	NOUN
ejpam-6418	477	2	and	and	CCONJ
ejpam-6418	477	3	logic	logic	NOUN
ejpam-6418	477	4	,	,	PUNCT
ejpam-6418	477	5	18:431	18:431	NUM
ejpam-6418	477	6	–	–	PUNCT
ejpam-6418	477	7	459	459	NUM
ejpam-6418	477	8	,	,	PUNCT
ejpam-6418	477	9	1978	1978	NUM
ejpam-6418	477	10	.	.	PUNCT
ejpam-6418	478	1	[	[	X
ejpam-6418	478	2	4	4	NUM
ejpam-6418	478	3	]	]	PUNCT
ejpam-6418	478	4	ravikumar	ravikumar	NOUN
ejpam-6418	478	5	bandaru	bandaru	PROPN
ejpam-6418	478	6	,	,	PUNCT
ejpam-6418	478	7	prashant	prashant	PROPN
ejpam-6418	478	8	patel	patel	PROPN
ejpam-6418	478	9	,	,	PUNCT
ejpam-6418	478	10	noorbhasha	noorbhasha	PROPN
ejpam-6418	478	11	rafi	rafi	PROPN
ejpam-6418	478	12	,	,	PUNCT
ejpam-6418	478	13	rahul	rahul	NOUN
ejpam-6418	478	14	shukla	shukla	NOUN
ejpam-6418	478	15	,	,	PUNCT
ejpam-6418	478	16	and	and	CCONJ
ejpam-6418	478	17	suryavardhani	suryavardhani	PROPN
ejpam-6418	478	18	ajjarapu	ajjarapu	PROPN
ejpam-6418	478	19	.	.	PUNCT
ejpam-6418	479	1	normal	normal	ADJ
ejpam-6418	479	2	paradistributive	paradistributive	ADJ
ejpam-6418	479	3	latticoids	latticoid	NOUN
ejpam-6418	479	4	.	.	PUNCT
ejpam-6418	480	1	european	european	PROPN
ejpam-6418	480	2	journal	journal	PROPN
ejpam-6418	480	3	of	of	ADP
ejpam-6418	480	4	pure	pure	ADJ
ejpam-6418	480	5	and	and	CCONJ
ejpam-6418	480	6	applied	applied	ADJ
ejpam-6418	480	7	mathematics	mathematic	NOUN
ejpam-6418	480	8	,	,	PUNCT
ejpam-6418	480	9	17:1306–1320	17:1306–1320	NUM
ejpam-6418	480	10	,	,	PUNCT
ejpam-6418	480	11	2024	2024	NUM
ejpam-6418	480	12	.	.	PUNCT
ejpam-6418	481	1	[	[	X
ejpam-6418	481	2	5	5	NUM
ejpam-6418	481	3	]	]	SYM
ejpam-6418	481	4	suryavardhani	suryavardhani	NOUN
ejpam-6418	481	5	ajjarapu	ajjarapu	PROPN
ejpam-6418	481	6	,	,	PUNCT
ejpam-6418	481	7	ravikumar	ravikumar	PROPN
ejpam-6418	481	8	bandaru	bandaru	PROPN
ejpam-6418	481	9	,	,	PUNCT
ejpam-6418	481	10	rahul	rahul	NOUN
ejpam-6418	481	11	shukla	shukla	NOUN
ejpam-6418	481	12	,	,	PUNCT
ejpam-6418	481	13	and	and	CCONJ
ejpam-6418	481	14	young	young	ADJ
ejpam-6418	481	15	bae	bae	PROPN
ejpam-6418	481	16	jun	jun	PROPN
ejpam-6418	481	17	.	.	PUNCT
ejpam-6418	481	18	parapseudo	parapseudo	NOUN
ejpam-6418	481	19	-	-	NOUN
ejpam-6418	481	20	complementation	complementation	NOUN
ejpam-6418	481	21	on	on	ADP
ejpam-6418	481	22	paradistributive	paradistributive	ADJ
ejpam-6418	481	23	latticoids	latticoid	NOUN
ejpam-6418	481	24	.	.	PUNCT
ejpam-6418	482	1	european	european	PROPN
ejpam-6418	482	2	journal	journal	PROPN
ejpam-6418	482	3	of	of	ADP
ejpam-6418	482	4	pure	pure	ADJ
ejpam-6418	482	5	and	and	CCONJ
ejpam-6418	482	6	applied	applied	ADJ
ejpam-6418	482	7	mathematics	mathematic	NOUN
ejpam-6418	482	8	,	,	PUNCT
ejpam-6418	482	9	17:1129–1145	17:1129–1145	NUM
ejpam-6418	482	10	,	,	PUNCT
ejpam-6418	482	11	2024	2024	NUM
ejpam-6418	482	12	.	.	PUNCT
ejpam-6418	483	1	[	[	X
ejpam-6418	483	2	6	6	NUM
ejpam-6418	483	3	]	]	X
ejpam-6418	483	4	g.	g.	PROPN
ejpam-6418	483	5	boole	boole	PROPN
ejpam-6418	483	6	.	.	PUNCT
ejpam-6418	484	1	an	an	DET
ejpam-6418	484	2	investigation	investigation	NOUN
ejpam-6418	484	3	of	of	ADP
ejpam-6418	484	4	the	the	DET
ejpam-6418	484	5	laws	law	NOUN
ejpam-6418	484	6	of	of	ADP
ejpam-6418	484	7	thought	thought	NOUN
ejpam-6418	484	8	.	.	PUNCT
ejpam-6418	485	1	reprinted	reprint	VERB
ejpam-6418	485	2	by	by	ADP
ejpam-6418	485	3	open	open	ADJ
ejpam-6418	485	4	court	court	PROPN
ejpam-6418	485	5	publishing	publishing	PROPN
ejpam-6418	485	6	co.	co.	PROPN
ejpam-6418	485	7	,	,	PUNCT
ejpam-6418	485	8	chelsea	chelsea	PROPN
ejpam-6418	485	9	,	,	PUNCT
ejpam-6418	485	10	london	london	PROPN
ejpam-6418	485	11	,	,	PUNCT
ejpam-6418	485	12	1940	1940	NUM
ejpam-6418	485	13	.	.	PUNCT
ejpam-6418	486	1	originally	originally	ADV
ejpam-6418	486	2	published	publish	VERB
ejpam-6418	486	3	in	in	ADP
ejpam-6418	486	4	1854	1854	NUM
ejpam-6418	486	5	.	.	PUNCT
ejpam-6418	487	1	introduction	introduction	NOUN
ejpam-6418	487	2	preliminaries	preliminary	NOUN
ejpam-6418	487	3	amicable	amicable	ADJ
ejpam-6418	487	4	sets	set	NOUN
ejpam-6418	487	5	in	in	ADP
ejpam-6418	487	6	paradistributive	paradistributive	ADJ
ejpam-6418	487	7	latticoid	latticoid	NOUN
ejpam-6418	487	8	conclusion	conclusion	NOUN
ejpam-6418	487	9	and	and	CCONJ
ejpam-6418	487	10	future	future	ADJ
ejpam-6418	487	11	work	work	NOUN
ejpam-6418	487	12	conflict	conflict	NOUN
ejpam-6418	487	13	of	of	ADP
ejpam-6418	487	14	interest	interest	NOUN