id	sid	tid	token	lemma	pos
ejpam-5226	1	1	european	european	PROPN
ejpam-5226	1	2	journal	journal	PROPN
ejpam-5226	1	3	of	of	ADP
ejpam-5226	1	4	pure	pure	ADJ
ejpam-5226	1	5	and	and	CCONJ
ejpam-5226	1	6	applied	apply	VERB
ejpam-5226	1	7	mathematics	mathematic	NOUN
ejpam-5226	1	8	vol	vol	NOUN
ejpam-5226	1	9	.	.	PROPN
ejpam-5226	2	1	17	17	NUM
ejpam-5226	2	2	,	,	PUNCT
ejpam-5226	2	3	no	no	INTJ
ejpam-5226	2	4	.	.	NOUN
ejpam-5226	2	5	3	3	NUM
ejpam-5226	2	6	,	,	PUNCT
ejpam-5226	2	7	2024	2024	NUM
ejpam-5226	2	8	,	,	PUNCT
ejpam-5226	2	9	1691	1691	NUM
ejpam-5226	2	10	-	-	SYM
ejpam-5226	2	11	1704	1704	NUM
ejpam-5226	2	12	issn	issn	PROPN
ejpam-5226	2	13	1307	1307	NUM
ejpam-5226	2	14	-	-	SYM
ejpam-5226	2	15	5543	5543	NUM
ejpam-5226	2	16	–	–	PUNCT
ejpam-5226	3	1	ejpam.com	ejpam.com	X
ejpam-5226	3	2	published	publish	VERB
ejpam-5226	3	3	by	by	ADP
ejpam-5226	3	4	new	new	PROPN
ejpam-5226	3	5	york	york	PROPN
ejpam-5226	3	6	business	business	PROPN
ejpam-5226	3	7	global	global	ADJ
ejpam-5226	3	8	hierarchy	hierarchy	NOUN
ejpam-5226	3	9	elements	element	NOUN
ejpam-5226	3	10	in	in	ADP
ejpam-5226	3	11	an	an	DET
ejpam-5226	3	12	almost	almost	ADV
ejpam-5226	3	13	distributive	distributive	ADJ
ejpam-5226	3	14	lattice	lattice	NOUN
ejpam-5226	3	15	s.	s.	PROPN
ejpam-5226	3	16	ramesh1	ramesh1	PROPN
ejpam-5226	3	17	,	,	PUNCT
ejpam-5226	3	18	g.	g.	PROPN
ejpam-5226	3	19	chinnayya1	chinnayya1	PROPN
ejpam-5226	3	20	,	,	PUNCT
ejpam-5226	3	21	g.	g.	PROPN
ejpam-5226	3	22	jogarao1	jogarao1	PROPN
ejpam-5226	3	23	,	,	PUNCT
ejpam-5226	3	24	ravikumar	ravikumar	PROPN
ejpam-5226	3	25	bandaru2	bandaru2	PROPN
ejpam-5226	3	26	,	,	PUNCT
ejpam-5226	3	27	aiyared	aiyare	VERB
ejpam-5226	3	28	iampan3,∗	iampan3,∗	ADJ
ejpam-5226	3	29	1	1	NUM
ejpam-5226	3	30	department	department	NOUN
ejpam-5226	3	31	of	of	ADP
ejpam-5226	3	32	mathematics	mathematic	NOUN
ejpam-5226	3	33	,	,	PUNCT
ejpam-5226	3	34	gitam	gitam	NOUN
ejpam-5226	3	35	school	school	NOUN
ejpam-5226	3	36	of	of	ADP
ejpam-5226	3	37	science	science	NOUN
ejpam-5226	3	38	,	,	PUNCT
ejpam-5226	3	39	gitam	gitam	NOUN
ejpam-5226	3	40	(	(	PUNCT
ejpam-5226	3	41	deemed	deem	VERB
ejpam-5226	3	42	to	to	PART
ejpam-5226	3	43	be	be	AUX
ejpam-5226	3	44	university	university	NOUN
ejpam-5226	3	45	)	)	PUNCT
ejpam-5226	3	46	,	,	PUNCT
ejpam-5226	3	47	visakhapatnam-530045	visakhapatnam-530045	ADV
ejpam-5226	3	48	,	,	PUNCT
ejpam-5226	3	49	india	india	PROPN
ejpam-5226	3	50	2	2	NUM
ejpam-5226	3	51	department	department	NOUN
ejpam-5226	3	52	of	of	ADP
ejpam-5226	3	53	mathematics	mathematic	NOUN
ejpam-5226	3	54	,	,	PUNCT
ejpam-5226	3	55	school	school	NOUN
ejpam-5226	3	56	of	of	ADP
ejpam-5226	3	57	advanced	advanced	ADJ
ejpam-5226	3	58	sciences	science	NOUN
ejpam-5226	3	59	,	,	PUNCT
ejpam-5226	3	60	vit	vit	PROPN
ejpam-5226	3	61	-	-	PUNCT
ejpam-5226	3	62	ap	ap	PROPN
ejpam-5226	3	63	university	university	PROPN
ejpam-5226	3	64	,	,	PUNCT
ejpam-5226	3	65	andhra	andhra	PROPN
ejpam-5226	3	66	pradesh-522237	pradesh-522237	NOUN
ejpam-5226	3	67	,	,	PUNCT
ejpam-5226	3	68	india	india	PROPN
ejpam-5226	3	69	3	3	NUM
ejpam-5226	3	70	department	department	NOUN
ejpam-5226	3	71	of	of	ADP
ejpam-5226	3	72	mathematics	mathematic	NOUN
ejpam-5226	3	73	,	,	PUNCT
ejpam-5226	3	74	school	school	NOUN
ejpam-5226	3	75	of	of	ADP
ejpam-5226	3	76	science	science	NOUN
ejpam-5226	3	77	,	,	PUNCT
ejpam-5226	3	78	university	university	NOUN
ejpam-5226	3	79	of	of	ADP
ejpam-5226	3	80	phayao	phayao	NOUN
ejpam-5226	3	81	,	,	PUNCT
ejpam-5226	3	82	mae	mae	PROPN
ejpam-5226	3	83	ka	ka	PROPN
ejpam-5226	3	84	,	,	PUNCT
ejpam-5226	3	85	mueang	mueang	PROPN
ejpam-5226	3	86	,	,	PUNCT
ejpam-5226	3	87	phayao	phayao	NOUN
ejpam-5226	3	88	56000	56000	NUM
ejpam-5226	3	89	,	,	PUNCT
ejpam-5226	3	90	thailand	thailand	PROPN
ejpam-5226	3	91	abstract	abstract	NOUN
ejpam-5226	3	92	.	.	PUNCT
ejpam-5226	4	1	in	in	ADP
ejpam-5226	4	2	this	this	DET
ejpam-5226	4	3	paper	paper	NOUN
ejpam-5226	4	4	,	,	PUNCT
ejpam-5226	4	5	we	we	PRON
ejpam-5226	4	6	introduce	introduce	VERB
ejpam-5226	4	7	hierarchy	hierarchy	NOUN
ejpam-5226	4	8	elements	element	NOUN
ejpam-5226	4	9	in	in	ADP
ejpam-5226	4	10	an	an	DET
ejpam-5226	4	11	almost	almost	ADV
ejpam-5226	4	12	distributive	distributive	ADJ
ejpam-5226	4	13	lattice	lattice	NOUN
ejpam-5226	4	14	with	with	ADP
ejpam-5226	4	15	respect	respect	NOUN
ejpam-5226	4	16	to	to	ADP
ejpam-5226	4	17	a	a	DET
ejpam-5226	4	18	non	non	ADJ
ejpam-5226	4	19	-	-	ADJ
ejpam-5226	4	20	empty	empty	ADJ
ejpam-5226	4	21	set	set	NOUN
ejpam-5226	4	22	and	and	CCONJ
ejpam-5226	4	23	obtain	obtain	VERB
ejpam-5226	4	24	some	some	PRON
ejpam-5226	4	25	of	of	ADP
ejpam-5226	4	26	their	their	PRON
ejpam-5226	4	27	algebraic	algebraic	ADJ
ejpam-5226	4	28	properties	property	NOUN
ejpam-5226	4	29	.	.	PUNCT
ejpam-5226	5	1	we	we	PRON
ejpam-5226	5	2	characterize	characterize	VERB
ejpam-5226	5	3	initial	initial	ADJ
ejpam-5226	5	4	segments	segment	NOUN
ejpam-5226	5	5	,	,	PUNCT
ejpam-5226	5	6	ideals	ideal	NOUN
ejpam-5226	5	7	,	,	PUNCT
ejpam-5226	5	8	and	and	CCONJ
ejpam-5226	5	9	maximal	maximal	ADJ
ejpam-5226	5	10	sets	set	NOUN
ejpam-5226	5	11	in	in	ADP
ejpam-5226	5	12	almost	almost	ADV
ejpam-5226	5	13	distributive	distributive	ADJ
ejpam-5226	5	14	lattices	lattice	NOUN
ejpam-5226	5	15	in	in	ADP
ejpam-5226	5	16	terms	term	NOUN
ejpam-5226	5	17	of	of	ADP
ejpam-5226	5	18	hierarchy	hierarchy	NOUN
ejpam-5226	5	19	sets	set	NOUN
ejpam-5226	5	20	and	and	CCONJ
ejpam-5226	5	21	prove	prove	VERB
ejpam-5226	5	22	that	that	SCONJ
ejpam-5226	5	23	the	the	DET
ejpam-5226	5	24	class	class	NOUN
ejpam-5226	5	25	of	of	ADP
ejpam-5226	5	26	hierarchy	hierarchy	NOUN
ejpam-5226	5	27	sets	set	VERB
ejpam-5226	5	28	forms	form	NOUN
ejpam-5226	5	29	a	a	DET
ejpam-5226	5	30	distributive	distributive	ADJ
ejpam-5226	5	31	lattice	lattice	NOUN
ejpam-5226	5	32	,	,	PUNCT
ejpam-5226	5	33	which	which	PRON
ejpam-5226	5	34	is	be	AUX
ejpam-5226	5	35	not	not	PART
ejpam-5226	5	36	an	an	DET
ejpam-5226	5	37	induced	induced	ADJ
ejpam-5226	5	38	sublattice	sublattice	NOUN
ejpam-5226	5	39	.	.	PUNCT
ejpam-5226	6	1	also	also	ADV
ejpam-5226	6	2	,	,	PUNCT
ejpam-5226	6	3	we	we	PRON
ejpam-5226	6	4	characterize	characterize	VERB
ejpam-5226	6	5	hierarchy	hierarchy	NOUN
ejpam-5226	6	6	sets	set	NOUN
ejpam-5226	6	7	using	use	VERB
ejpam-5226	6	8	compatible	compatible	ADJ
ejpam-5226	6	9	sets	set	NOUN
ejpam-5226	6	10	in	in	ADP
ejpam-5226	6	11	an	an	DET
ejpam-5226	6	12	almost	almost	ADV
ejpam-5226	6	13	distributive	distributive	ADJ
ejpam-5226	6	14	lattice	lattice	NOUN
ejpam-5226	6	15	.	.	PUNCT
ejpam-5226	7	1	2020	2020	NUM
ejpam-5226	7	2	mathematics	mathematic	NOUN
ejpam-5226	7	3	subject	subject	NOUN
ejpam-5226	7	4	classifications	classification	NOUN
ejpam-5226	7	5	:	:	PUNCT
ejpam-5226	7	6	06d99	06d99	NUM
ejpam-5226	7	7	,	,	PUNCT
ejpam-5226	7	8	06d75	06d75	NUM
ejpam-5226	7	9	key	key	ADJ
ejpam-5226	7	10	words	word	NOUN
ejpam-5226	7	11	and	and	CCONJ
ejpam-5226	7	12	phrases	phrase	NOUN
ejpam-5226	7	13	:	:	PUNCT
ejpam-5226	7	14	hierarchy	hierarchy	NOUN
ejpam-5226	7	15	elements	element	NOUN
ejpam-5226	7	16	,	,	PUNCT
ejpam-5226	7	17	ideals	ideal	NOUN
ejpam-5226	7	18	,	,	PUNCT
ejpam-5226	7	19	principal	principal	ADJ
ejpam-5226	7	20	ideals	ideal	NOUN
ejpam-5226	7	21	,	,	PUNCT
ejpam-5226	7	22	almost	almost	ADV
ejpam-5226	7	23	distributive	distributive	ADJ
ejpam-5226	7	24	lattices	lattice	NOUN
ejpam-5226	7	25	1	1	NUM
ejpam-5226	7	26	.	.	PUNCT
ejpam-5226	7	27	introduction	introduction	NOUN
ejpam-5226	7	28	one	one	NUM
ejpam-5226	7	29	of	of	ADP
ejpam-5226	7	30	both	both	CCONJ
ejpam-5226	7	31	the	the	DET
ejpam-5226	7	32	lattice	lattice	PROPN
ejpam-5226	7	33	theoretic	theoretic	NOUN
ejpam-5226	7	34	and	and	CCONJ
ejpam-5226	7	35	ring	ring	NOUN
ejpam-5226	7	36	theoretic	theoretic	ADJ
ejpam-5226	7	37	generalizations	generalization	NOUN
ejpam-5226	7	38	of	of	ADP
ejpam-5226	7	39	a	a	DET
ejpam-5226	7	40	distributive	distributive	ADJ
ejpam-5226	7	41	lattice	lattice	NOUN
ejpam-5226	7	42	(	(	PUNCT
ejpam-5226	7	43	boolean	boolean	ADJ
ejpam-5226	7	44	algebra	algebra	NOUN
ejpam-5226	7	45	)	)	PUNCT
ejpam-5226	8	1	[	[	X
ejpam-5226	8	2	7	7	NUM
ejpam-5226	8	3	]	]	PUNCT
ejpam-5226	8	4	,	,	PUNCT
ejpam-5226	8	5	led	lead	VERB
ejpam-5226	8	6	by	by	ADP
ejpam-5226	8	7	swamy	swamy	NOUN
ejpam-5226	8	8	and	and	CCONJ
ejpam-5226	8	9	rao	rao	NOUN
ejpam-5226	8	10	in	in	ADP
ejpam-5226	8	11	1981	1981	NUM
ejpam-5226	8	12	and	and	CCONJ
ejpam-5226	8	13	called	call	VERB
ejpam-5226	8	14	an	an	DET
ejpam-5226	8	15	almost	almost	ADV
ejpam-5226	8	16	distributive	distributive	ADJ
ejpam-5226	8	17	lattice	lattice	NOUN
ejpam-5226	8	18	[	[	X
ejpam-5226	8	19	8	8	NUM
ejpam-5226	8	20	]	]	PUNCT
ejpam-5226	8	21	.	.	PUNCT
ejpam-5226	9	1	almost	almost	ADV
ejpam-5226	9	2	distributive	distributive	ADJ
ejpam-5226	9	3	lattices	lattice	NOUN
ejpam-5226	9	4	is	be	AUX
ejpam-5226	9	5	an	an	DET
ejpam-5226	9	6	algebraic	algebraic	ADJ
ejpam-5226	9	7	structure	structure	NOUN
ejpam-5226	9	8	(	(	PUNCT
ejpam-5226	9	9	l,∨,∧	l,∨,∧	NOUN
ejpam-5226	9	10	,	,	PUNCT
ejpam-5226	9	11	0	0	NUM
ejpam-5226	9	12	)	)	PUNCT
ejpam-5226	9	13	that	that	PRON
ejpam-5226	9	14	satisfies	satisfy	VERB
ejpam-5226	9	15	almost	almost	ADV
ejpam-5226	9	16	every	every	PRON
ejpam-5226	9	17	axiom	axiom	NOUN
ejpam-5226	9	18	of	of	ADP
ejpam-5226	9	19	a	a	DET
ejpam-5226	9	20	distributive	distributive	ADJ
ejpam-5226	9	21	lattice	lattice	NOUN
ejpam-5226	9	22	with	with	ADP
ejpam-5226	9	23	zero	zero	NUM
ejpam-5226	9	24	,	,	PUNCT
ejpam-5226	9	25	not	not	PART
ejpam-5226	9	26	including	include	VERB
ejpam-5226	9	27	the	the	DET
ejpam-5226	9	28	three	three	NUM
ejpam-5226	9	29	identities	identity	NOUN
ejpam-5226	9	30	(	(	PUNCT
ejpam-5226	9	31	the	the	DET
ejpam-5226	9	32	commutativity	commutativity	NOUN
ejpam-5226	9	33	of	of	ADP
ejpam-5226	9	34	∧,∨	∧,∨	ADJ
ejpam-5226	9	35	and	and	CCONJ
ejpam-5226	9	36	the	the	DET
ejpam-5226	9	37	right	right	ADJ
ejpam-5226	9	38	distributivity	distributivity	NOUN
ejpam-5226	9	39	of	of	ADP
ejpam-5226	9	40	∨	∨	NUM
ejpam-5226	9	41	over	over	ADP
ejpam-5226	9	42	∧	∧	PROPN
ejpam-5226	9	43	)	)	PUNCT
ejpam-5226	9	44	.	.	PUNCT
ejpam-5226	10	1	each	each	PRON
ejpam-5226	10	2	of	of	ADP
ejpam-5226	10	3	these	these	DET
ejpam-5226	10	4	three	three	NUM
ejpam-5226	10	5	identities	identity	NOUN
ejpam-5226	10	6	is	be	AUX
ejpam-5226	10	7	equivalent	equivalent	ADJ
ejpam-5226	10	8	to	to	ADP
ejpam-5226	10	9	each	each	DET
ejpam-5226	10	10	other	other	ADJ
ejpam-5226	10	11	in	in	ADP
ejpam-5226	10	12	an	an	DET
ejpam-5226	10	13	almost	almost	ADV
ejpam-5226	10	14	distributive	distributive	ADJ
ejpam-5226	10	15	lattice	lattice	NOUN
ejpam-5226	10	16	,	,	PUNCT
ejpam-5226	10	17	and	and	CCONJ
ejpam-5226	10	18	an	an	DET
ejpam-5226	10	19	almost	almost	ADV
ejpam-5226	10	20	distributive	distributive	ADJ
ejpam-5226	10	21	lattice	lattice	NOUN
ejpam-5226	10	22	with	with	ADP
ejpam-5226	10	23	any	any	PRON
ejpam-5226	10	24	of	of	ADP
ejpam-5226	10	25	the	the	DET
ejpam-5226	10	26	above	above	ADJ
ejpam-5226	10	27	identities	identity	NOUN
ejpam-5226	10	28	gives	give	VERB
ejpam-5226	10	29	a	a	DET
ejpam-5226	10	30	distributive	distributive	ADJ
ejpam-5226	10	31	lattice	lattice	NOUN
ejpam-5226	10	32	.	.	PUNCT
ejpam-5226	11	1	the	the	DET
ejpam-5226	11	2	structure	structure	NOUN
ejpam-5226	11	3	of	of	ADP
ejpam-5226	11	4	an	an	DET
ejpam-5226	11	5	almost	almost	ADV
ejpam-5226	11	6	distributive	distributive	ADJ
ejpam-5226	11	7	lattice	lattice	NOUN
ejpam-5226	11	8	is	be	AUX
ejpam-5226	11	9	not	not	PART
ejpam-5226	11	10	even	even	ADV
ejpam-5226	11	11	distributive	distributive	ADJ
ejpam-5226	11	12	;	;	PUNCT
ejpam-5226	11	13	the	the	DET
ejpam-5226	11	14	lattice	lattice	NOUN
ejpam-5226	11	15	and	and	CCONJ
ejpam-5226	11	16	the	the	DET
ejpam-5226	11	17	associativity	associativity	NOUN
ejpam-5226	11	18	of	of	ADP
ejpam-5226	11	19	∨	∨	NUM
ejpam-5226	11	20	are	be	AUX
ejpam-5226	11	21	not	not	PART
ejpam-5226	11	22	yet	yet	ADV
ejpam-5226	11	23	to	to	PART
ejpam-5226	11	24	be	be	AUX
ejpam-5226	11	25	known	know	VERB
ejpam-5226	11	26	.	.	PUNCT
ejpam-5226	12	1	hence	hence	ADV
ejpam-5226	12	2	,	,	PUNCT
ejpam-5226	12	3	it	it	PRON
ejpam-5226	12	4	is	be	AUX
ejpam-5226	12	5	difficult	difficult	ADJ
ejpam-5226	12	6	to	to	PART
ejpam-5226	12	7	deal	deal	VERB
ejpam-5226	12	8	with	with	ADP
ejpam-5226	12	9	it	it	PRON
ejpam-5226	12	10	.	.	PUNCT
ejpam-5226	13	1	for	for	ADP
ejpam-5226	13	2	example	example	NOUN
ejpam-5226	13	3	,	,	PUNCT
ejpam-5226	13	4	fix	fix	VERB
ejpam-5226	13	5	an	an	DET
ejpam-5226	13	6	element	element	NOUN
ejpam-5226	13	7	x0	x0	PROPN
ejpam-5226	13	8	in	in	ADP
ejpam-5226	13	9	a	a	DET
ejpam-5226	13	10	non	non	ADJ
ejpam-5226	13	11	-	-	ADJ
ejpam-5226	13	12	empty	empty	ADJ
ejpam-5226	13	13	set	set	VERB
ejpam-5226	13	14	l.	l.	NOUN
ejpam-5226	13	15	given	give	VERB
ejpam-5226	13	16	x	x	PROPN
ejpam-5226	13	17	,	,	PUNCT
ejpam-5226	13	18	y	y	PROPN
ejpam-5226	13	19	∈	∈	PROPN
ejpam-5226	13	20	l	l	NOUN
ejpam-5226	13	21	,	,	PUNCT
ejpam-5226	13	22	define	define	VERB
ejpam-5226	13	23	x	x	PUNCT
ejpam-5226	13	24	∧	∧	PROPN
ejpam-5226	13	25	y	y	PROPN
ejpam-5226	13	26	=	=	SYM
ejpam-5226	13	27	y	y	PROPN
ejpam-5226	13	28	,	,	PUNCT
ejpam-5226	13	29	x0	x0	PROPN
ejpam-5226	13	30	∧	∧	PROPN
ejpam-5226	13	31	y	y	PROPN
ejpam-5226	13	32	=	=	SYM
ejpam-5226	13	33	x0	x0	PROPN
ejpam-5226	13	34	,	,	PUNCT
ejpam-5226	13	35	x	x	PROPN
ejpam-5226	13	36	∨	∨	NUM
ejpam-5226	13	37	y	y	NOUN
ejpam-5226	13	38	=	=	PUNCT
ejpam-5226	13	39	x	x	PROPN
ejpam-5226	13	40	and	and	CCONJ
ejpam-5226	13	41	x0	x0	PROPN
ejpam-5226	13	42	∨	∨	NUM
ejpam-5226	13	43	y	y	PROPN
ejpam-5226	13	44	=	=	PUNCT
ejpam-5226	13	45	y.	y.	PROPN
ejpam-5226	13	46	then	then	ADV
ejpam-5226	13	47	(	(	PUNCT
ejpam-5226	13	48	l,∧,∨	l,∧,∨	ADV
ejpam-5226	13	49	,	,	PUNCT
ejpam-5226	13	50	x0	x0	PROPN
ejpam-5226	13	51	)	)	PUNCT
ejpam-5226	13	52	is	be	AUX
ejpam-5226	13	53	an	an	DET
ejpam-5226	13	54	almost	almost	ADV
ejpam-5226	13	55	distributive	distributive	ADJ
ejpam-5226	13	56	lattice	lattice	NOUN
ejpam-5226	13	57	.	.	PUNCT
ejpam-5226	14	1	this	this	DET
ejpam-5226	14	2	l	l	NOUN
ejpam-5226	14	3	is	be	AUX
ejpam-5226	14	4	neither	neither	CCONJ
ejpam-5226	14	5	lattice	lattice	NOUN
ejpam-5226	14	6	nor	nor	CCONJ
ejpam-5226	14	7	distributive	distributive	ADJ
ejpam-5226	14	8	.	.	PUNCT
ejpam-5226	15	1	it	it	PRON
ejpam-5226	15	2	is	be	AUX
ejpam-5226	15	3	called	call	VERB
ejpam-5226	15	4	a	a	DET
ejpam-5226	15	5	discrete	discrete	NOUN
ejpam-5226	15	6	[	[	X
ejpam-5226	15	7	8	8	NUM
ejpam-5226	15	8	]	]	PUNCT
ejpam-5226	15	9	almost	almost	ADV
ejpam-5226	15	10	distributive	distributive	ADJ
ejpam-5226	15	11	lattice	lattice	NOUN
ejpam-5226	15	12	.	.	PUNCT
ejpam-5226	16	1	given	give	VERB
ejpam-5226	16	2	a	a	DET
ejpam-5226	16	3	,	,	PUNCT
ejpam-5226	16	4	b	b	NOUN
ejpam-5226	16	5	in	in	ADP
ejpam-5226	16	6	∗corresponding	∗corresponde	VERB
ejpam-5226	16	7	author	author	NOUN
ejpam-5226	16	8	.	.	PUNCT
ejpam-5226	17	1	doi	doi	NOUN
ejpam-5226	17	2	:	:	PUNCT
ejpam-5226	17	3	https://doi.org/10.29020/nybg.ejpam.v17i3.5226	https://doi.org/10.29020/nybg.ejpam.v17i3.5226	PRON
ejpam-5226	17	4	email	email	NOUN
ejpam-5226	17	5	addresses	address	NOUN
ejpam-5226	17	6	:	:	PUNCT
ejpam-5226	17	7	ramesh.sirisetti@gmail.com	ramesh.sirisetti@gmail.com	X
ejpam-5226	17	8	(	(	PUNCT
ejpam-5226	17	9	s.	s.	PROPN
ejpam-5226	17	10	ramesh	ramesh	PROPN
ejpam-5226	17	11	)	)	PUNCT
ejpam-5226	17	12	,	,	PUNCT
ejpam-5226	17	13	cgondu@gitam.in	cgondu@gitam.in	PROPN
ejpam-5226	17	14	(	(	PUNCT
ejpam-5226	17	15	g.	g.	PROPN
ejpam-5226	17	16	chinnayya	chinnayya	PROPN
ejpam-5226	17	17	)	)	PUNCT
ejpam-5226	17	18	,	,	PUNCT
ejpam-5226	17	19	jogarao.gunda@gmail.com	jogarao.gunda@gmail.com	PROPN
ejpam-5226	17	20	(	(	PUNCT
ejpam-5226	17	21	g.	g.	PROPN
ejpam-5226	17	22	jogarao	jogarao	PROPN
ejpam-5226	17	23	)	)	PUNCT
ejpam-5226	17	24	,	,	PUNCT
ejpam-5226	17	25	ravimaths83@gmail.com	ravimaths83@gmail.com	PROPN
ejpam-5226	17	26	(	(	PUNCT
ejpam-5226	17	27	r.	r.	PROPN
ejpam-5226	17	28	bandaru	bandaru	PROPN
ejpam-5226	17	29	)	)	PUNCT
ejpam-5226	17	30	,	,	PUNCT
ejpam-5226	17	31	aiyared.ia@up.ac.th	aiyared.ia@up.ac.th	NOUN
ejpam-5226	17	32	(	(	PUNCT
ejpam-5226	17	33	a.	a.	NOUN
ejpam-5226	17	34	iampan	iampan	PROPN
ejpam-5226	17	35	)	)	PUNCT
ejpam-5226	17	36	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5226	17	37	1691	1691	NUM
ejpam-5226	17	38	©	©	ADP
ejpam-5226	17	39	2024	2024	NUM
ejpam-5226	17	40	ejpam	ejpam	NOUN
ejpam-5226	17	41	all	all	DET
ejpam-5226	17	42	rights	right	NOUN
ejpam-5226	17	43	reserved	reserve	VERB
ejpam-5226	17	44	.	.	PUNCT
ejpam-5226	18	1	a.	a.	PROPN
ejpam-5226	18	2	iampan	iampan	PROPN
ejpam-5226	18	3	et	et	PROPN
ejpam-5226	18	4	al	al	PROPN
ejpam-5226	18	5	.	.	PUNCT
ejpam-5226	18	6	/	/	SYM
ejpam-5226	18	7	eur	eur	PROPN
ejpam-5226	18	8	.	.	PUNCT
ejpam-5226	19	1	j.	j.	PROPN
ejpam-5226	19	2	pure	pure	PROPN
ejpam-5226	19	3	appl	appl	PROPN
ejpam-5226	19	4	.	.	PROPN
ejpam-5226	19	5	math	math	PROPN
ejpam-5226	19	6	,	,	PUNCT
ejpam-5226	19	7	17	17	NUM
ejpam-5226	19	8	(	(	PUNCT
ejpam-5226	19	9	3	3	NUM
ejpam-5226	19	10	)	)	PUNCT
ejpam-5226	19	11	(	(	PUNCT
ejpam-5226	19	12	2024	2024	NUM
ejpam-5226	19	13	)	)	PUNCT
ejpam-5226	19	14	,	,	PUNCT
ejpam-5226	19	15	1691	1691	NUM
ejpam-5226	19	16	-	-	SYM
ejpam-5226	19	17	1704	1704	NUM
ejpam-5226	19	18	1692	1692	NUM
ejpam-5226	19	19	an	an	DET
ejpam-5226	19	20	almost	almost	ADV
ejpam-5226	19	21	distributive	distributive	ADJ
ejpam-5226	19	22	lattice	lattice	NOUN
ejpam-5226	19	23	l	l	NOUN
ejpam-5226	19	24	,	,	PUNCT
ejpam-5226	19	25	we	we	PRON
ejpam-5226	19	26	say	say	VERB
ejpam-5226	19	27	that	that	SCONJ
ejpam-5226	19	28	a	a	DET
ejpam-5226	19	29	≤	≤	PROPN
ejpam-5226	19	30	b	b	NOUN
ejpam-5226	19	31	if	if	SCONJ
ejpam-5226	19	32	a∧	a∧	PROPN
ejpam-5226	19	33	b	b	X
ejpam-5226	19	34	=	=	SYM
ejpam-5226	19	35	a	a	X
ejpam-5226	19	36	(	(	PUNCT
ejpam-5226	19	37	or	or	CCONJ
ejpam-5226	19	38	equivalently	equivalently	ADV
ejpam-5226	19	39	,	,	PUNCT
ejpam-5226	19	40	a∨	a∨	PROPN
ejpam-5226	19	41	b	b	PROPN
ejpam-5226	19	42	=	=	SYM
ejpam-5226	19	43	b	b	PROPN
ejpam-5226	19	44	)	)	PUNCT
ejpam-5226	19	45	.	.	PUNCT
ejpam-5226	20	1	then	then	ADV
ejpam-5226	20	2	,	,	PUNCT
ejpam-5226	20	3	≤	≤	PROPN
ejpam-5226	20	4	is	be	AUX
ejpam-5226	20	5	a	a	DET
ejpam-5226	20	6	partial	partial	ADJ
ejpam-5226	20	7	ordering	ordering	NOUN
ejpam-5226	20	8	on	on	ADP
ejpam-5226	20	9	l.	l.	PROPN
ejpam-5226	20	10	an	an	DET
ejpam-5226	20	11	element	element	NOUN
ejpam-5226	20	12	m	m	PROPN
ejpam-5226	20	13	∈	∈	NOUN
ejpam-5226	20	14	l	l	NOUN
ejpam-5226	20	15	is	be	AUX
ejpam-5226	20	16	called	call	VERB
ejpam-5226	20	17	a	a	DET
ejpam-5226	20	18	maximal	maximal	ADJ
ejpam-5226	20	19	element	element	NOUN
ejpam-5226	20	20	[	[	X
ejpam-5226	20	21	8	8	NUM
ejpam-5226	20	22	]	]	X
ejpam-5226	20	23	if	if	SCONJ
ejpam-5226	20	24	m	m	VERB
ejpam-5226	20	25	∧	∧	NOUN
ejpam-5226	20	26	x	x	X
ejpam-5226	21	1	=	=	PUNCT
ejpam-5226	21	2	x	x	PROPN
ejpam-5226	21	3	for	for	ADP
ejpam-5226	21	4	all	all	DET
ejpam-5226	21	5	x	x	SYM
ejpam-5226	21	6	∈	∈	PROPN
ejpam-5226	21	7	l.	l.	NOUN
ejpam-5226	21	8	the	the	DET
ejpam-5226	21	9	authors	author	NOUN
ejpam-5226	21	10	[	[	X
ejpam-5226	21	11	3–5	3–5	NUM
ejpam-5226	21	12	,	,	PUNCT
ejpam-5226	21	13	8	8	NUM
ejpam-5226	21	14	,	,	PUNCT
ejpam-5226	21	15	9	9	NUM
ejpam-5226	21	16	]	]	PUNCT
ejpam-5226	21	17	developed	develop	VERB
ejpam-5226	21	18	the	the	DET
ejpam-5226	21	19	theory	theory	NOUN
ejpam-5226	21	20	of	of	ADP
ejpam-5226	21	21	initial	initial	ADJ
ejpam-5226	21	22	segments	segment	NOUN
ejpam-5226	21	23	,	,	PUNCT
ejpam-5226	21	24	ideals	ideal	NOUN
ejpam-5226	21	25	,	,	PUNCT
ejpam-5226	21	26	and	and	CCONJ
ejpam-5226	21	27	filters	filter	VERB
ejpam-5226	21	28	in	in	ADP
ejpam-5226	21	29	almost	almost	ADV
ejpam-5226	21	30	distributive	distributive	ADJ
ejpam-5226	21	31	lattices	lattice	NOUN
ejpam-5226	21	32	analogous	analogous	ADJ
ejpam-5226	21	33	to	to	ADP
ejpam-5226	21	34	the	the	DET
ejpam-5226	21	35	concepts	concept	NOUN
ejpam-5226	21	36	in	in	ADP
ejpam-5226	21	37	distributive	distributive	ADJ
ejpam-5226	21	38	lattices	lattice	NOUN
ejpam-5226	21	39	.	.	PUNCT
ejpam-5226	22	1	it	it	PRON
ejpam-5226	22	2	is	be	AUX
ejpam-5226	22	3	wellknown	wellknown	ADJ
ejpam-5226	22	4	that	that	SCONJ
ejpam-5226	22	5	“	"	PUNCT
ejpam-5226	22	6	every	every	DET
ejpam-5226	22	7	distributive	distributive	ADJ
ejpam-5226	22	8	lattice	lattice	NOUN
ejpam-5226	22	9	is	be	AUX
ejpam-5226	22	10	a	a	DET
ejpam-5226	22	11	one	one	NUM
ejpam-5226	22	12	-	-	PUNCT
ejpam-5226	22	13	to	to	ADP
ejpam-5226	22	14	-	-	PUNCT
ejpam-5226	22	15	one	one	NUM
ejpam-5226	22	16	correspondence	correspondence	NOUN
ejpam-5226	22	17	with	with	ADP
ejpam-5226	22	18	the	the	DET
ejpam-5226	22	19	class	class	NOUN
ejpam-5226	22	20	of	of	ADP
ejpam-5226	22	21	principal	principal	ADJ
ejpam-5226	22	22	ideals	ideal	NOUN
ejpam-5226	22	23	”	"	PUNCT
ejpam-5226	22	24	in	in	ADP
ejpam-5226	22	25	it	it	PRON
ejpam-5226	23	1	[	[	X
ejpam-5226	23	2	1	1	NUM
ejpam-5226	23	3	]	]	PUNCT
ejpam-5226	23	4	.	.	PUNCT
ejpam-5226	24	1	the	the	DET
ejpam-5226	24	2	above	above	ADV
ejpam-5226	24	3	-	-	PUNCT
ejpam-5226	24	4	mentioned	mention	VERB
ejpam-5226	24	5	property	property	NOUN
ejpam-5226	24	6	does	do	AUX
ejpam-5226	24	7	not	not	PART
ejpam-5226	24	8	hold	hold	VERB
ejpam-5226	24	9	in	in	ADP
ejpam-5226	24	10	an	an	DET
ejpam-5226	24	11	almost	almost	ADV
ejpam-5226	24	12	distributive	distributive	ADJ
ejpam-5226	24	13	lattice	lattice	NOUN
ejpam-5226	24	14	l	l	NOUN
ejpam-5226	24	15	because	because	SCONJ
ejpam-5226	24	16	“	"	PUNCT
ejpam-5226	24	17	given	give	VERB
ejpam-5226	24	18	a	a	DET
ejpam-5226	24	19	,	,	PUNCT
ejpam-5226	24	20	b	b	PROPN
ejpam-5226	24	21	∈	∈	PROPN
ejpam-5226	24	22	l	l	NOUN
ejpam-5226	24	23	,	,	PUNCT
ejpam-5226	24	24	(	(	PUNCT
ejpam-5226	24	25	a	a	X
ejpam-5226	24	26	]	]	X
ejpam-5226	24	27	=	=	SYM
ejpam-5226	24	28	(	(	PUNCT
ejpam-5226	24	29	b	b	X
ejpam-5226	24	30	]	]	X
ejpam-5226	24	31	does	do	AUX
ejpam-5226	24	32	not	not	PART
ejpam-5226	24	33	imply	imply	VERB
ejpam-5226	24	34	a	a	DET
ejpam-5226	24	35	=	=	ADJ
ejpam-5226	24	36	b	b	NOUN
ejpam-5226	24	37	”	"	PUNCT
ejpam-5226	24	38	[	[	X
ejpam-5226	24	39	8	8	NUM
ejpam-5226	24	40	]	]	PUNCT
ejpam-5226	24	41	,	,	PUNCT
ejpam-5226	24	42	where	where	SCONJ
ejpam-5226	25	1	(	(	PUNCT
ejpam-5226	25	2	a	a	X
ejpam-5226	25	3	]	]	X
ejpam-5226	25	4	=	=	X
ejpam-5226	25	5	{	{	PUNCT
ejpam-5226	25	6	a	a	DET
ejpam-5226	25	7	∧	∧	PROPN
ejpam-5226	25	8	x	x	SYM
ejpam-5226	25	9	|	|	ADV
ejpam-5226	25	10	x	x	SYM
ejpam-5226	25	11	∈	∈	PROPN
ejpam-5226	25	12	l	l	NOUN
ejpam-5226	25	13	}	}	PUNCT
ejpam-5226	25	14	is	be	AUX
ejpam-5226	25	15	the	the	DET
ejpam-5226	25	16	smallest	small	ADJ
ejpam-5226	25	17	ideal	ideal	NOUN
ejpam-5226	25	18	containing	contain	VERB
ejpam-5226	25	19	a.	a.	NOUN
ejpam-5226	25	20	given	give	VERB
ejpam-5226	25	21	an	an	DET
ejpam-5226	25	22	initial	initial	ADJ
ejpam-5226	25	23	segment	segment	NOUN
ejpam-5226	25	24	[	[	X
ejpam-5226	25	25	0	0	NUM
ejpam-5226	25	26	,	,	PUNCT
ejpam-5226	25	27	a	a	PRON
ejpam-5226	25	28	]	]	X
ejpam-5226	25	29	=	=	SYM
ejpam-5226	25	30	{	{	PUNCT
ejpam-5226	25	31	x	x	PUNCT
ejpam-5226	25	32	∈	∈	NOUN
ejpam-5226	25	33	l	l	NOUN
ejpam-5226	26	1	|	|	NOUN
ejpam-5226	26	2	0	0	NUM
ejpam-5226	26	3	≤	≤	NUM
ejpam-5226	26	4	x	x	SYM
ejpam-5226	26	5	≤	≤	NUM
ejpam-5226	26	6	a	a	PRON
ejpam-5226	26	7	}	}	PUNCT
ejpam-5226	26	8	in	in	ADP
ejpam-5226	26	9	an	an	DET
ejpam-5226	26	10	almost	almost	ADV
ejpam-5226	26	11	distributive	distributive	ADJ
ejpam-5226	26	12	lattice	lattice	NOUN
ejpam-5226	26	13	l	l	NOUN
ejpam-5226	26	14	,	,	PUNCT
ejpam-5226	26	15	the	the	DET
ejpam-5226	26	16	authors	author	NOUN
ejpam-5226	26	17	[	[	X
ejpam-5226	26	18	8	8	NUM
ejpam-5226	26	19	]	]	PUNCT
ejpam-5226	26	20	observed	observe	VERB
ejpam-5226	26	21	that	that	SCONJ
ejpam-5226	26	22	given	give	VERB
ejpam-5226	26	23	b	b	PROPN
ejpam-5226	26	24	∈	∈	PROPN
ejpam-5226	26	25	l	l	NOUN
ejpam-5226	26	26	,	,	PUNCT
ejpam-5226	26	27	b	b	X
ejpam-5226	26	28	∈	∈	PROPN
ejpam-5226	27	1	[	[	X
ejpam-5226	27	2	0	0	NUM
ejpam-5226	27	3	,	,	PUNCT
ejpam-5226	27	4	a	a	PRON
ejpam-5226	27	5	]	]	X
ejpam-5226	27	6	if	if	SCONJ
ejpam-5226	27	7	and	and	CCONJ
ejpam-5226	27	8	only	only	ADV
ejpam-5226	27	9	if	if	SCONJ
ejpam-5226	27	10	a	a	DET
ejpam-5226	27	11	∧	∧	PROPN
ejpam-5226	27	12	b	b	NOUN
ejpam-5226	27	13	=	=	SYM
ejpam-5226	27	14	b	b	PROPN
ejpam-5226	27	15	∧	∧	PROPN
ejpam-5226	27	16	a.	a.	NOUN
ejpam-5226	27	17	further	far	ADV
ejpam-5226	27	18	,	,	PUNCT
ejpam-5226	27	19	the	the	DET
ejpam-5226	27	20	authors	author	NOUN
ejpam-5226	27	21	extended	extend	VERB
ejpam-5226	27	22	the	the	DET
ejpam-5226	27	23	above	above	ADJ
ejpam-5226	27	24	properties	property	NOUN
ejpam-5226	27	25	to	to	ADP
ejpam-5226	27	26	the	the	DET
ejpam-5226	27	27	concept	concept	NOUN
ejpam-5226	27	28	of	of	ADP
ejpam-5226	27	29	principal	principal	ADJ
ejpam-5226	27	30	ideals	ideal	NOUN
ejpam-5226	27	31	and	and	CCONJ
ejpam-5226	27	32	stated	state	VERB
ejpam-5226	27	33	that	that	SCONJ
ejpam-5226	27	34	“	"	PUNCT
ejpam-5226	27	35	given	give	VERB
ejpam-5226	27	36	b	b	PROPN
ejpam-5226	27	37	∈	∈	PROPN
ejpam-5226	27	38	l	l	NOUN
ejpam-5226	27	39	,	,	PUNCT
ejpam-5226	27	40	b	b	X
ejpam-5226	27	41	∈	∈	PROPN
ejpam-5226	27	42	(	(	PUNCT
ejpam-5226	27	43	a	a	X
ejpam-5226	27	44	]	]	X
ejpam-5226	27	45	if	if	SCONJ
ejpam-5226	27	46	and	and	CCONJ
ejpam-5226	27	47	only	only	ADV
ejpam-5226	27	48	if	if	SCONJ
ejpam-5226	27	49	a	a	DET
ejpam-5226	27	50	∧	∧	PROPN
ejpam-5226	27	51	b	b	PROPN
ejpam-5226	27	52	=	=	SYM
ejpam-5226	27	53	b	b	NOUN
ejpam-5226	27	54	”	"	PUNCT
ejpam-5226	27	55	[	[	X
ejpam-5226	27	56	8	8	NUM
ejpam-5226	27	57	]	]	PUNCT
ejpam-5226	27	58	.	.	PUNCT
ejpam-5226	28	1	in	in	ADP
ejpam-5226	28	2	2024	2024	NUM
ejpam-5226	28	3	,	,	PUNCT
ejpam-5226	28	4	noorbhasha	noorbhasha	VERB
ejpam-5226	28	5	et	et	PROPN
ejpam-5226	28	6	al	al	PROPN
ejpam-5226	28	7	.	.	PUNCT
ejpam-5226	29	1	[	[	X
ejpam-5226	29	2	2	2	NUM
ejpam-5226	29	3	]	]	PUNCT
ejpam-5226	29	4	proved	prove	VERB
ejpam-5226	29	5	some	some	DET
ejpam-5226	29	6	properties	property	NOUN
ejpam-5226	29	7	of	of	ADP
ejpam-5226	29	8	prime	prime	ADJ
ejpam-5226	29	9	σ	σ	NOUN
ejpam-5226	29	10	-	-	PUNCT
ejpam-5226	29	11	ideals	ideal	NOUN
ejpam-5226	29	12	of	of	ADP
ejpam-5226	29	13	a	a	DET
ejpam-5226	29	14	normal	normal	ADJ
ejpam-5226	29	15	almost	almost	ADV
ejpam-5226	29	16	distributive	distributive	ADJ
ejpam-5226	29	17	lattice	lattice	NOUN
ejpam-5226	29	18	topologically	topologically	ADV
ejpam-5226	29	19	.	.	PUNCT
ejpam-5226	30	1	srikanth	srikanth	PROPN
ejpam-5226	30	2	et	et	PROPN
ejpam-5226	30	3	al	al	PROPN
ejpam-5226	30	4	.	.	PUNCT
ejpam-5226	31	1	[	[	X
ejpam-5226	31	2	6	6	NUM
ejpam-5226	31	3	]	]	PUNCT
ejpam-5226	31	4	looked	look	VERB
ejpam-5226	31	5	into	into	ADP
ejpam-5226	31	6	why	why	SCONJ
ejpam-5226	31	7	the	the	DET
ejpam-5226	31	8	binary	binary	PROPN
ejpam-5226	31	9	operation	operation	PROPN
ejpam-5226	31	10	ρ	ρ	PROPN
ejpam-5226	31	11	does	do	AUX
ejpam-5226	31	12	not	not	PART
ejpam-5226	31	13	work	work	VERB
ejpam-5226	31	14	in	in	ADP
ejpam-5226	31	15	semi	semi	ADJ
ejpam-5226	31	16	-	-	ADJ
ejpam-5226	31	17	brouwerian	brouwerian	ADJ
ejpam-5226	31	18	almost	almost	ADV
ejpam-5226	31	19	distributive	distributive	ADJ
ejpam-5226	31	20	lattices	lattice	NOUN
ejpam-5226	31	21	.	.	PUNCT
ejpam-5226	32	1	they	they	PRON
ejpam-5226	32	2	found	find	VERB
ejpam-5226	32	3	that	that	SCONJ
ejpam-5226	32	4	it	it	PRON
ejpam-5226	32	5	does	do	AUX
ejpam-5226	32	6	not	not	PART
ejpam-5226	32	7	work	work	VERB
ejpam-5226	32	8	associatively	associatively	ADV
ejpam-5226	32	9	or	or	CCONJ
ejpam-5226	32	10	commutatively	commutatively	ADV
ejpam-5226	32	11	.	.	PUNCT
ejpam-5226	33	1	with	with	ADP
ejpam-5226	33	2	this	this	DET
ejpam-5226	33	3	motivation	motivation	NOUN
ejpam-5226	33	4	,	,	PUNCT
ejpam-5226	33	5	we	we	PRON
ejpam-5226	33	6	find	find	VERB
ejpam-5226	33	7	an	an	DET
ejpam-5226	33	8	arbitrary	arbitrary	ADJ
ejpam-5226	33	9	non	non	ADJ
ejpam-5226	33	10	-	-	ADJ
ejpam-5226	33	11	empty	empty	ADJ
ejpam-5226	33	12	set	set	NOUN
ejpam-5226	33	13	s	s	PRON
ejpam-5226	33	14	in	in	ADP
ejpam-5226	33	15	an	an	DET
ejpam-5226	33	16	almost	almost	ADV
ejpam-5226	33	17	distributive	distributive	ADJ
ejpam-5226	33	18	lattice	lattice	NOUN
ejpam-5226	33	19	l	l	NOUN
ejpam-5226	33	20	with	with	ADP
ejpam-5226	33	21	the	the	DET
ejpam-5226	33	22	property	property	NOUN
ejpam-5226	33	23	that	that	PRON
ejpam-5226	33	24	for	for	ADP
ejpam-5226	33	25	any	any	DET
ejpam-5226	33	26	h	h	NOUN
ejpam-5226	33	27	∈	∈	PROPN
ejpam-5226	33	28	l	l	NOUN
ejpam-5226	33	29	,	,	PUNCT
ejpam-5226	33	30	s	s	VERB
ejpam-5226	33	31	∧	∧	NOUN
ejpam-5226	33	32	h	h	NOUN
ejpam-5226	33	33	=	=	NOUN
ejpam-5226	33	34	h	h	NOUN
ejpam-5226	33	35	,	,	PUNCT
ejpam-5226	33	36	for	for	ADP
ejpam-5226	33	37	some	some	DET
ejpam-5226	33	38	s	s	NOUN
ejpam-5226	33	39	∈	∈	NOUN
ejpam-5226	33	40	s.	s.	PROPN
ejpam-5226	33	41	we	we	PRON
ejpam-5226	33	42	derive	derive	VERB
ejpam-5226	33	43	algebraic	algebraic	ADJ
ejpam-5226	33	44	properties	property	NOUN
ejpam-5226	33	45	from	from	ADP
ejpam-5226	33	46	the	the	DET
ejpam-5226	33	47	class	class	NOUN
ejpam-5226	33	48	of	of	ADP
ejpam-5226	33	49	hierarchy	hierarchy	NOUN
ejpam-5226	33	50	elements	element	NOUN
ejpam-5226	33	51	with	with	ADP
ejpam-5226	33	52	respect	respect	NOUN
ejpam-5226	33	53	to	to	ADP
ejpam-5226	33	54	a	a	DET
ejpam-5226	33	55	set	set	NOUN
ejpam-5226	33	56	s.	s.	PROPN
ejpam-5226	33	57	also	also	ADV
ejpam-5226	33	58	,	,	PUNCT
ejpam-5226	33	59	we	we	PRON
ejpam-5226	33	60	characterize	characterize	VERB
ejpam-5226	33	61	the	the	DET
ejpam-5226	33	62	class	class	NOUN
ejpam-5226	33	63	of	of	ADP
ejpam-5226	33	64	hierarchy	hierarchy	NOUN
ejpam-5226	33	65	sets	set	NOUN
ejpam-5226	33	66	in	in	ADP
ejpam-5226	33	67	an	an	DET
ejpam-5226	33	68	almost	almost	ADV
ejpam-5226	33	69	distributive	distributive	ADJ
ejpam-5226	33	70	lattice	lattice	NOUN
ejpam-5226	33	71	and	and	CCONJ
ejpam-5226	33	72	provide	provide	VERB
ejpam-5226	33	73	sufficient	sufficient	ADJ
ejpam-5226	33	74	counterexamples	counterexample	NOUN
ejpam-5226	33	75	.	.	PUNCT
ejpam-5226	34	1	mainly	mainly	ADV
ejpam-5226	34	2	,	,	PUNCT
ejpam-5226	34	3	we	we	PRON
ejpam-5226	34	4	observe	observe	VERB
ejpam-5226	34	5	that	that	SCONJ
ejpam-5226	34	6	the	the	DET
ejpam-5226	34	7	class	class	NOUN
ejpam-5226	34	8	of	of	ADP
ejpam-5226	34	9	hierarchy	hierarchy	NOUN
ejpam-5226	34	10	sets	set	NOUN
ejpam-5226	34	11	is	be	AUX
ejpam-5226	34	12	a	a	DET
ejpam-5226	34	13	distributive	distributive	ADJ
ejpam-5226	34	14	lattice	lattice	NOUN
ejpam-5226	34	15	with	with	ADP
ejpam-5226	34	16	respect	respect	NOUN
ejpam-5226	34	17	to	to	ADP
ejpam-5226	34	18	the	the	DET
ejpam-5226	34	19	operations	operation	NOUN
ejpam-5226	34	20	∪	∪	ADJ
ejpam-5226	34	21	and	and	CCONJ
ejpam-5226	34	22	∧	∧	PROPN
ejpam-5226	34	23	where	where	SCONJ
ejpam-5226	34	24	s1	s1	PROPN
ejpam-5226	34	25	∧	∧	PROPN
ejpam-5226	34	26	s2	s2	NOUN
ejpam-5226	34	27	=	=	SYM
ejpam-5226	34	28	{	{	PUNCT
ejpam-5226	34	29	s1	s1	NOUN
ejpam-5226	34	30	∧	∧	PROPN
ejpam-5226	34	31	s2	s2	NOUN
ejpam-5226	35	1	|	|	ADV
ejpam-5226	35	2	s1	s1	PROPN
ejpam-5226	35	3	∈	∈	PROPN
ejpam-5226	35	4	s1	s1	PROPN
ejpam-5226	35	5	and	and	CCONJ
ejpam-5226	35	6	s2	s2	PROPN
ejpam-5226	35	7	∈	∈	PROPN
ejpam-5226	35	8	s2	s2	PROPN
ejpam-5226	35	9	}	}	PUNCT
ejpam-5226	35	10	,	,	PUNCT
ejpam-5226	35	11	for	for	ADP
ejpam-5226	35	12	all	all	DET
ejpam-5226	35	13	non	non	ADJ
ejpam-5226	35	14	-	-	ADJ
ejpam-5226	35	15	empty	empty	ADJ
ejpam-5226	35	16	subsets	subset	NOUN
ejpam-5226	35	17	s1	s1	NOUN
ejpam-5226	35	18	,	,	PUNCT
ejpam-5226	35	19	s2	s2	NOUN
ejpam-5226	35	20	of	of	ADP
ejpam-5226	35	21	l.	l.	PROPN
ejpam-5226	35	22	2	2	NUM
ejpam-5226	35	23	.	.	PUNCT
ejpam-5226	35	24	hierarchy	hierarchy	NOUN
ejpam-5226	35	25	sets	set	NOUN
ejpam-5226	35	26	in	in	ADP
ejpam-5226	35	27	almost	almost	ADV
ejpam-5226	35	28	distributive	distributive	ADJ
ejpam-5226	35	29	lattices	lattice	NOUN
ejpam-5226	35	30	in	in	ADP
ejpam-5226	35	31	this	this	DET
ejpam-5226	35	32	section	section	NOUN
ejpam-5226	35	33	,	,	PUNCT
ejpam-5226	35	34	we	we	PRON
ejpam-5226	35	35	define	define	VERB
ejpam-5226	35	36	hierarchy	hierarchy	NOUN
ejpam-5226	35	37	elements	element	NOUN
ejpam-5226	35	38	with	with	ADP
ejpam-5226	35	39	respect	respect	NOUN
ejpam-5226	35	40	to	to	ADP
ejpam-5226	35	41	a	a	DET
ejpam-5226	35	42	non	non	ADJ
ejpam-5226	35	43	-	-	ADJ
ejpam-5226	35	44	empty	empty	ADJ
ejpam-5226	35	45	set	set	NOUN
ejpam-5226	35	46	in	in	ADP
ejpam-5226	35	47	an	an	DET
ejpam-5226	35	48	almost	almost	ADV
ejpam-5226	35	49	distributive	distributive	ADJ
ejpam-5226	35	50	lattice	lattice	NOUN
ejpam-5226	35	51	.	.	PUNCT
ejpam-5226	36	1	we	we	PRON
ejpam-5226	36	2	prove	prove	VERB
ejpam-5226	36	3	several	several	ADJ
ejpam-5226	36	4	algebraic	algebraic	ADJ
ejpam-5226	36	5	properties	property	NOUN
ejpam-5226	36	6	in	in	ADP
ejpam-5226	36	7	the	the	DET
ejpam-5226	36	8	class	class	NOUN
ejpam-5226	36	9	of	of	ADP
ejpam-5226	36	10	hierarchy	hierarchy	NOUN
ejpam-5226	36	11	elements	element	NOUN
ejpam-5226	36	12	and	and	CCONJ
ejpam-5226	36	13	hierarchy	hierarchy	NOUN
ejpam-5226	36	14	sets	set	NOUN
ejpam-5226	36	15	.	.	PUNCT
ejpam-5226	37	1	finally	finally	ADV
ejpam-5226	37	2	,	,	PUNCT
ejpam-5226	37	3	we	we	PRON
ejpam-5226	37	4	obtain	obtain	VERB
ejpam-5226	37	5	that	that	SCONJ
ejpam-5226	37	6	the	the	DET
ejpam-5226	37	7	class	class	NOUN
ejpam-5226	37	8	of	of	ADP
ejpam-5226	37	9	hierarchy	hierarchy	NOUN
ejpam-5226	37	10	sets	set	VERB
ejpam-5226	37	11	forms	form	NOUN
ejpam-5226	37	12	a	a	DET
ejpam-5226	37	13	distributive	distributive	ADJ
ejpam-5226	37	14	lattice	lattice	NOUN
ejpam-5226	37	15	,	,	PUNCT
ejpam-5226	37	16	which	which	PRON
ejpam-5226	37	17	is	be	AUX
ejpam-5226	37	18	not	not	PART
ejpam-5226	37	19	an	an	DET
ejpam-5226	37	20	induced	induced	ADJ
ejpam-5226	37	21	sub	sub	ADJ
ejpam-5226	37	22	-	-	ADJ
ejpam-5226	37	23	distributive	distributive	ADJ
ejpam-5226	37	24	lattice	lattice	NOUN
ejpam-5226	37	25	of	of	ADP
ejpam-5226	37	26	the	the	DET
ejpam-5226	37	27	class	class	NOUN
ejpam-5226	37	28	of	of	ADP
ejpam-5226	37	29	ideals	ideal	NOUN
ejpam-5226	37	30	of	of	ADP
ejpam-5226	37	31	almost	almost	ADV
ejpam-5226	37	32	distributive	distributive	ADJ
ejpam-5226	37	33	lattices	lattice	NOUN
ejpam-5226	37	34	.	.	PUNCT
ejpam-5226	38	1	finally	finally	ADV
ejpam-5226	38	2	,	,	PUNCT
ejpam-5226	38	3	we	we	PRON
ejpam-5226	38	4	derive	derive	VERB
ejpam-5226	38	5	some	some	DET
ejpam-5226	38	6	equivalent	equivalent	ADJ
ejpam-5226	38	7	conditions	condition	NOUN
ejpam-5226	38	8	for	for	ADP
ejpam-5226	38	9	a	a	DET
ejpam-5226	38	10	hierarchy	hierarchy	NOUN
ejpam-5226	38	11	set	set	VERB
ejpam-5226	38	12	in	in	ADP
ejpam-5226	38	13	an	an	DET
ejpam-5226	38	14	almost	almost	ADV
ejpam-5226	38	15	distributive	distributive	ADJ
ejpam-5226	38	16	lattice	lattice	NOUN
ejpam-5226	38	17	to	to	PART
ejpam-5226	38	18	become	become	VERB
ejpam-5226	38	19	an	an	DET
ejpam-5226	38	20	ideal	ideal	NOUN
ejpam-5226	38	21	.	.	PUNCT
ejpam-5226	39	1	definition	definition	NOUN
ejpam-5226	39	2	1	1	NUM
ejpam-5226	39	3	.	.	PUNCT
ejpam-5226	40	1	an	an	DET
ejpam-5226	40	2	element	element	NOUN
ejpam-5226	40	3	h	h	NOUN
ejpam-5226	40	4	∈	∈	PROPN
ejpam-5226	40	5	l	l	NOUN
ejpam-5226	40	6	is	be	AUX
ejpam-5226	40	7	said	say	VERB
ejpam-5226	40	8	to	to	PART
ejpam-5226	40	9	be	be	AUX
ejpam-5226	40	10	a	a	DET
ejpam-5226	40	11	hierarchy	hierarchy	NOUN
ejpam-5226	40	12	with	with	ADP
ejpam-5226	40	13	respect	respect	NOUN
ejpam-5226	40	14	to	to	ADP
ejpam-5226	40	15	a	a	DET
ejpam-5226	40	16	non	non	ADJ
ejpam-5226	40	17	-	-	ADJ
ejpam-5226	40	18	empty	empty	ADJ
ejpam-5226	40	19	subset	subset	NOUN
ejpam-5226	40	20	s	s	PROPN
ejpam-5226	40	21	of	of	ADP
ejpam-5226	40	22	l	l	NOUN
ejpam-5226	40	23	if	if	SCONJ
ejpam-5226	40	24	s	s	VERB
ejpam-5226	40	25	∧	∧	NOUN
ejpam-5226	40	26	h	h	NOUN
ejpam-5226	40	27	=	=	NOUN
ejpam-5226	40	28	h	h	NOUN
ejpam-5226	40	29	,	,	PUNCT
ejpam-5226	40	30	for	for	ADP
ejpam-5226	40	31	some	some	DET
ejpam-5226	40	32	s	s	NOUN
ejpam-5226	40	33	∈	∈	PROPN
ejpam-5226	40	34	s.	s.	PROPN
ejpam-5226	40	35	the	the	DET
ejpam-5226	40	36	set	set	NOUN
ejpam-5226	40	37	of	of	ADP
ejpam-5226	40	38	hierarchy	hierarchy	NOUN
ejpam-5226	40	39	elements	element	NOUN
ejpam-5226	40	40	with	with	ADP
ejpam-5226	40	41	respect	respect	NOUN
ejpam-5226	40	42	to	to	ADP
ejpam-5226	40	43	s	s	PRON
ejpam-5226	40	44	is	be	AUX
ejpam-5226	40	45	denoted	denote	VERB
ejpam-5226	40	46	by	by	ADP
ejpam-5226	40	47	hs	hs	X
ejpam-5226	40	48	.	.	PUNCT
ejpam-5226	41	1	it	it	PRON
ejpam-5226	41	2	is	be	AUX
ejpam-5226	41	3	easy	easy	ADJ
ejpam-5226	41	4	to	to	PART
ejpam-5226	41	5	observe	observe	VERB
ejpam-5226	41	6	that	that	SCONJ
ejpam-5226	41	7	hs	hs	PROPN
ejpam-5226	41	8	̸=	̸=	PROPN
ejpam-5226	41	9	∅	∅	NOUN
ejpam-5226	41	10	(	(	PUNCT
ejpam-5226	41	11	since	since	SCONJ
ejpam-5226	41	12	0	0	NUM
ejpam-5226	41	13	∈	∈	PROPN
ejpam-5226	41	14	hs	hs	PROPN
ejpam-5226	41	15	)	)	PUNCT
ejpam-5226	41	16	.	.	PUNCT
ejpam-5226	42	1	proposition	proposition	NOUN
ejpam-5226	42	2	1	1	NUM
ejpam-5226	42	3	.	.	PUNCT
ejpam-5226	43	1	for	for	ADP
ejpam-5226	43	2	any	any	DET
ejpam-5226	43	3	∅	∅	NOUN
ejpam-5226	43	4	=	=	NOUN
ejpam-5226	43	5	̸	̸	NUM
ejpam-5226	43	6	s	s	PART
ejpam-5226	43	7	⊆	⊆	NUM
ejpam-5226	43	8	l	l	NOUN
ejpam-5226	43	9	,	,	PUNCT
ejpam-5226	43	10	we	we	PRON
ejpam-5226	43	11	have	have	VERB
ejpam-5226	43	12	(	(	PUNCT
ejpam-5226	43	13	i	i	NOUN
ejpam-5226	43	14	)	)	PUNCT
ejpam-5226	43	15	s	s	PROPN
ejpam-5226	43	16	⊆	⊆	NUM
ejpam-5226	43	17	hs	hs	X
ejpam-5226	43	18	.	.	PROPN
ejpam-5226	44	1	(	(	PUNCT
ejpam-5226	44	2	ii	ii	PROPN
ejpam-5226	44	3	)	)	PUNCT
ejpam-5226	44	4	hs	hs	PROPN
ejpam-5226	44	5	is	be	AUX
ejpam-5226	44	6	closed	close	VERB
ejpam-5226	44	7	under	under	ADP
ejpam-5226	44	8	∧.	∧.	PROPN
ejpam-5226	44	9	(	(	PUNCT
ejpam-5226	44	10	iii	iii	NOUN
ejpam-5226	44	11	)	)	PUNCT
ejpam-5226	44	12	hl	hl	NOUN
ejpam-5226	44	13	=	=	SYM
ejpam-5226	44	14	l	l	NOUN
ejpam-5226	44	15	and	and	CCONJ
ejpam-5226	44	16	h{0	h{0	ADJ
ejpam-5226	44	17	}	}	PUNCT
ejpam-5226	44	18	=	=	SYM
ejpam-5226	44	19	{	{	PUNCT
ejpam-5226	44	20	0	0	NUM
ejpam-5226	44	21	}	}	PUNCT
ejpam-5226	44	22	,	,	PUNCT
ejpam-5226	44	23	where	where	SCONJ
ejpam-5226	44	24	1	1	NUM
ejpam-5226	44	25	is	be	AUX
ejpam-5226	44	26	the	the	DET
ejpam-5226	44	27	greatest	great	ADJ
ejpam-5226	44	28	element	element	NOUN
ejpam-5226	44	29	in	in	ADP
ejpam-5226	44	30	l.	l.	PROPN
ejpam-5226	44	31	a.	a.	PROPN
ejpam-5226	44	32	iampan	iampan	PROPN
ejpam-5226	44	33	et	et	PROPN
ejpam-5226	44	34	al	al	PROPN
ejpam-5226	44	35	.	.	PUNCT
ejpam-5226	44	36	/	/	SYM
ejpam-5226	44	37	eur	eur	PROPN
ejpam-5226	44	38	.	.	PUNCT
ejpam-5226	45	1	j.	j.	PROPN
ejpam-5226	45	2	pure	pure	PROPN
ejpam-5226	45	3	appl	appl	PROPN
ejpam-5226	45	4	.	.	PROPN
ejpam-5226	45	5	math	math	PROPN
ejpam-5226	45	6	,	,	PUNCT
ejpam-5226	45	7	17	17	NUM
ejpam-5226	45	8	(	(	PUNCT
ejpam-5226	45	9	3	3	NUM
ejpam-5226	45	10	)	)	PUNCT
ejpam-5226	45	11	(	(	PUNCT
ejpam-5226	45	12	2024	2024	NUM
ejpam-5226	45	13	)	)	PUNCT
ejpam-5226	45	14	,	,	PUNCT
ejpam-5226	45	15	1691	1691	NUM
ejpam-5226	45	16	-	-	SYM
ejpam-5226	45	17	1704	1704	NUM
ejpam-5226	45	18	1693	1693	NUM
ejpam-5226	45	19	(	(	PUNCT
ejpam-5226	45	20	iv	iv	X
ejpam-5226	45	21	)	)	PUNCT
ejpam-5226	45	22	if	if	SCONJ
ejpam-5226	45	23	1	1	NUM
ejpam-5226	45	24	∈	∈	PROPN
ejpam-5226	45	25	hs	hs	PROPN
ejpam-5226	45	26	,	,	PUNCT
ejpam-5226	45	27	then	then	ADV
ejpam-5226	45	28	hs	hs	PROPN
ejpam-5226	45	29	=	=	PROPN
ejpam-5226	45	30	l.	l.	PROPN
ejpam-5226	45	31	(	(	PUNCT
ejpam-5226	45	32	v	v	NOUN
ejpam-5226	45	33	)	)	PUNCT
ejpam-5226	45	34	if	if	SCONJ
ejpam-5226	45	35	m	m	VERB
ejpam-5226	45	36	∈	∈	PROPN
ejpam-5226	45	37	hs	hs	PROPN
ejpam-5226	45	38	,	,	PUNCT
ejpam-5226	45	39	then	then	ADV
ejpam-5226	45	40	hs	hs	PROPN
ejpam-5226	45	41	=	=	PROPN
ejpam-5226	45	42	l	l	PROPN
ejpam-5226	45	43	,	,	PUNCT
ejpam-5226	45	44	where	where	SCONJ
ejpam-5226	45	45	m	m	NOUN
ejpam-5226	45	46	is	be	AUX
ejpam-5226	45	47	a	a	DET
ejpam-5226	45	48	maximal	maximal	ADJ
ejpam-5226	45	49	element	element	NOUN
ejpam-5226	45	50	in	in	ADP
ejpam-5226	45	51	l.	l.	PROPN
ejpam-5226	45	52	proof	proof	PROPN
ejpam-5226	45	53	.	.	PUNCT
ejpam-5226	46	1	(	(	PUNCT
ejpam-5226	46	2	i	i	NOUN
ejpam-5226	46	3	)	)	PUNCT
ejpam-5226	46	4	let	let	VERB
ejpam-5226	46	5	s	s	PRON
ejpam-5226	46	6	∈	∈	VERB
ejpam-5226	46	7	s.	s.	PROPN
ejpam-5226	46	8	now	now	ADV
ejpam-5226	46	9	,	,	PUNCT
ejpam-5226	46	10	s	s	VERB
ejpam-5226	46	11	∧	∧	PROPN
ejpam-5226	46	12	s	s	PART
ejpam-5226	46	13	=	=	PROPN
ejpam-5226	46	14	s.	s.	PROPN
ejpam-5226	46	15	therefore	therefore	ADV
ejpam-5226	46	16	,	,	PUNCT
ejpam-5226	46	17	s	s	PROPN
ejpam-5226	46	18	∈	∈	PROPN
ejpam-5226	46	19	hs	hs	INTJ
ejpam-5226	46	20	.	.	PUNCT
ejpam-5226	47	1	hence	hence	ADV
ejpam-5226	47	2	,	,	PUNCT
ejpam-5226	47	3	s	s	VERB
ejpam-5226	47	4	⊆	⊆	NUM
ejpam-5226	47	5	hs	hs	X
ejpam-5226	47	6	.	.	PUNCT
ejpam-5226	48	1	(	(	PUNCT
ejpam-5226	48	2	ii	ii	NOUN
ejpam-5226	48	3	)	)	PUNCT
ejpam-5226	48	4	let	let	VERB
ejpam-5226	48	5	h1	h1	PROPN
ejpam-5226	48	6	,	,	PUNCT
ejpam-5226	48	7	h2	h2	PROPN
ejpam-5226	48	8	∈	∈	PROPN
ejpam-5226	48	9	hs	hs	PROPN
ejpam-5226	48	10	.	.	PUNCT
ejpam-5226	49	1	then	then	ADV
ejpam-5226	49	2	we	we	PRON
ejpam-5226	49	3	can	can	AUX
ejpam-5226	49	4	find	find	VERB
ejpam-5226	49	5	s1	s1	NOUN
ejpam-5226	49	6	,	,	PUNCT
ejpam-5226	49	7	s2	s2	NOUN
ejpam-5226	49	8	∈	∈	PROPN
ejpam-5226	49	9	s	s	VERB
ejpam-5226	49	10	such	such	ADJ
ejpam-5226	49	11	that	that	SCONJ
ejpam-5226	49	12	s1∧h1	s1∧h1	PROPN
ejpam-5226	49	13	=	=	PUNCT
ejpam-5226	49	14	h1	h1	NOUN
ejpam-5226	49	15	and	and	CCONJ
ejpam-5226	49	16	s2∧h2	s2∧h2	PROPN
ejpam-5226	49	17	=	=	PUNCT
ejpam-5226	49	18	h2	h2	PROPN
ejpam-5226	49	19	.	.	PUNCT
ejpam-5226	50	1	now	now	ADV
ejpam-5226	50	2	,	,	PUNCT
ejpam-5226	50	3	s1	s1	PROPN
ejpam-5226	50	4	∧	∧	PROPN
ejpam-5226	50	5	(	(	PUNCT
ejpam-5226	50	6	h1	h1	PROPN
ejpam-5226	50	7	∧	∧	PROPN
ejpam-5226	50	8	h2	h2	NOUN
ejpam-5226	50	9	)	)	PUNCT
ejpam-5226	50	10	=	=	SYM
ejpam-5226	50	11	(	(	PUNCT
ejpam-5226	50	12	s1	s1	PROPN
ejpam-5226	50	13	∧	∧	PROPN
ejpam-5226	50	14	h1	h1	PROPN
ejpam-5226	50	15	)	)	PUNCT
ejpam-5226	50	16	∧	∧	PROPN
ejpam-5226	50	17	h2	h2	NOUN
ejpam-5226	50	18	=	=	SYM
ejpam-5226	50	19	h1	h1	PROPN
ejpam-5226	50	20	∧	∧	PROPN
ejpam-5226	50	21	h2	h2	NOUN
ejpam-5226	50	22	.	.	PUNCT
ejpam-5226	51	1	therefore	therefore	ADV
ejpam-5226	51	2	,	,	PUNCT
ejpam-5226	51	3	h1	h1	PROPN
ejpam-5226	51	4	∧	∧	PROPN
ejpam-5226	51	5	h2	h2	PROPN
ejpam-5226	51	6	∈	∈	PROPN
ejpam-5226	51	7	hs	hs	PROPN
ejpam-5226	51	8	.	.	PUNCT
ejpam-5226	52	1	hence	hence	ADV
ejpam-5226	52	2	,	,	PUNCT
ejpam-5226	52	3	hs	hs	PROPN
ejpam-5226	52	4	is	be	AUX
ejpam-5226	52	5	closed	close	VERB
ejpam-5226	52	6	under	under	ADP
ejpam-5226	52	7	∧.	∧.	PROPN
ejpam-5226	52	8	(	(	PUNCT
ejpam-5226	52	9	iii	iii	NOUN
ejpam-5226	52	10	)	)	PUNCT
ejpam-5226	52	11	from	from	ADP
ejpam-5226	52	12	(	(	PUNCT
ejpam-5226	52	13	i	i	NOUN
ejpam-5226	52	14	)	)	PUNCT
ejpam-5226	52	15	,	,	PUNCT
ejpam-5226	52	16	it	it	PRON
ejpam-5226	52	17	is	be	AUX
ejpam-5226	52	18	easy	easy	ADJ
ejpam-5226	52	19	to	to	PART
ejpam-5226	52	20	observe	observe	VERB
ejpam-5226	52	21	that	that	DET
ejpam-5226	52	22	hl	hl	NOUN
ejpam-5226	52	23	=	=	PUNCT
ejpam-5226	52	24	l.	l.	PROPN
ejpam-5226	52	25	let	let	VERB
ejpam-5226	52	26	x	x	X
ejpam-5226	52	27	∈	∈	PROPN
ejpam-5226	52	28	h{0	h{0	PROPN
ejpam-5226	52	29	}	}	PUNCT
ejpam-5226	52	30	.	.	PUNCT
ejpam-5226	53	1	then	then	ADV
ejpam-5226	53	2	0	0	NUM
ejpam-5226	53	3	∧	∧	NOUN
ejpam-5226	53	4	x	x	X
ejpam-5226	53	5	=	=	PUNCT
ejpam-5226	53	6	x.	x.	NOUN
ejpam-5226	53	7	therefore	therefore	ADV
ejpam-5226	53	8	,	,	PUNCT
ejpam-5226	53	9	x	x	PUNCT
ejpam-5226	53	10	=	=	SYM
ejpam-5226	53	11	0	0	NUM
ejpam-5226	53	12	.	.	PUNCT
ejpam-5226	54	1	hence	hence	ADV
ejpam-5226	54	2	,	,	PUNCT
ejpam-5226	54	3	h{0	h{0	X
ejpam-5226	54	4	}	}	PUNCT
ejpam-5226	54	5	=	=	SYM
ejpam-5226	54	6	{	{	PUNCT
ejpam-5226	54	7	0	0	NUM
ejpam-5226	54	8	}	}	PUNCT
ejpam-5226	54	9	.	.	PUNCT
ejpam-5226	55	1	(	(	PUNCT
ejpam-5226	55	2	iv	iv	X
ejpam-5226	55	3	)	)	PUNCT
ejpam-5226	55	4	if	if	SCONJ
ejpam-5226	55	5	1	1	NUM
ejpam-5226	55	6	∈	∈	PROPN
ejpam-5226	55	7	hs	hs	INTJ
ejpam-5226	55	8	,	,	PUNCT
ejpam-5226	55	9	then	then	ADV
ejpam-5226	55	10	there	there	PRON
ejpam-5226	55	11	is	be	VERB
ejpam-5226	55	12	an	an	DET
ejpam-5226	55	13	element	element	NOUN
ejpam-5226	55	14	s	s	PART
ejpam-5226	55	15	∈	∈	NOUN
ejpam-5226	55	16	s	s	VERB
ejpam-5226	55	17	such	such	ADJ
ejpam-5226	55	18	that	that	SCONJ
ejpam-5226	55	19	1	1	NUM
ejpam-5226	55	20	=	=	SYM
ejpam-5226	55	21	s	s	PART
ejpam-5226	55	22	∧	∧	NOUN
ejpam-5226	55	23	1	1	NUM
ejpam-5226	55	24	=	=	SYM
ejpam-5226	55	25	s	s	PART
ejpam-5226	55	26	∈	∈	PROPN
ejpam-5226	55	27	s.	s.	PROPN
ejpam-5226	55	28	for	for	ADP
ejpam-5226	55	29	this	this	DET
ejpam-5226	55	30	1	1	NUM
ejpam-5226	55	31	∈	∈	PROPN
ejpam-5226	55	32	s	s	NOUN
ejpam-5226	55	33	,	,	PUNCT
ejpam-5226	55	34	1	1	NUM
ejpam-5226	55	35	∧	∧	NOUN
ejpam-5226	55	36	x	x	X
ejpam-5226	56	1	=	=	PUNCT
ejpam-5226	56	2	x	x	PROPN
ejpam-5226	56	3	for	for	ADP
ejpam-5226	56	4	all	all	DET
ejpam-5226	56	5	x	x	SYM
ejpam-5226	56	6	∈	∈	PROPN
ejpam-5226	56	7	l.	l.	NOUN
ejpam-5226	56	8	therefore	therefore	ADV
ejpam-5226	56	9	,	,	PUNCT
ejpam-5226	56	10	l	l	PROPN
ejpam-5226	56	11	⊆	⊆	NUM
ejpam-5226	56	12	hs	hs	INTJ
ejpam-5226	56	13	.	.	PUNCT
ejpam-5226	57	1	hence	hence	ADV
ejpam-5226	57	2	,	,	PUNCT
ejpam-5226	57	3	hs	hs	PROPN
ejpam-5226	57	4	=	=	PROPN
ejpam-5226	57	5	l.	l.	PROPN
ejpam-5226	57	6	(	(	PUNCT
ejpam-5226	57	7	v	v	NOUN
ejpam-5226	57	8	)	)	PUNCT
ejpam-5226	57	9	for	for	ADP
ejpam-5226	57	10	m	m	PROPN
ejpam-5226	57	11	∈	∈	PROPN
ejpam-5226	57	12	hs	hs	X
ejpam-5226	57	13	,	,	PUNCT
ejpam-5226	57	14	there	there	PRON
ejpam-5226	57	15	is	be	VERB
ejpam-5226	57	16	an	an	DET
ejpam-5226	57	17	element	element	NOUN
ejpam-5226	57	18	s	s	PART
ejpam-5226	57	19	∈	∈	NOUN
ejpam-5226	57	20	s	s	VERB
ejpam-5226	57	21	such	such	ADJ
ejpam-5226	57	22	that	that	DET
ejpam-5226	57	23	s	s	VERB
ejpam-5226	57	24	∧	∧	PROPN
ejpam-5226	57	25	m	m	NOUN
ejpam-5226	57	26	=	=	NOUN
ejpam-5226	57	27	m.	m.	NOUN
ejpam-5226	57	28	let	let	VERB
ejpam-5226	57	29	x	x	X
ejpam-5226	57	30	∈	∈	PROPN
ejpam-5226	57	31	l.	l.	NOUN
ejpam-5226	57	32	now	now	ADV
ejpam-5226	57	33	,	,	PUNCT
ejpam-5226	57	34	s	s	VERB
ejpam-5226	57	35	∧	∧	NOUN
ejpam-5226	57	36	x	x	PUNCT
ejpam-5226	58	1	=	=	PUNCT
ejpam-5226	58	2	m	m	VERB
ejpam-5226	58	3	∧	∧	NOUN
ejpam-5226	58	4	(	(	PUNCT
ejpam-5226	58	5	s	s	PROPN
ejpam-5226	58	6	∧	∧	PROPN
ejpam-5226	58	7	x	x	NOUN
ejpam-5226	58	8	)	)	PUNCT
ejpam-5226	58	9	=	=	SYM
ejpam-5226	58	10	(	(	PUNCT
ejpam-5226	58	11	m	m	PROPN
ejpam-5226	58	12	∧	∧	PROPN
ejpam-5226	58	13	s	s	PART
ejpam-5226	58	14	)	)	PUNCT
ejpam-5226	58	15	∧	∧	NOUN
ejpam-5226	58	16	x	x	X
ejpam-5226	58	17	=	=	PUNCT
ejpam-5226	58	18	(	(	PUNCT
ejpam-5226	58	19	s	s	NOUN
ejpam-5226	58	20	∧m	∧m	ADJ
ejpam-5226	58	21	)	)	PUNCT
ejpam-5226	58	22	∧	∧	NOUN
ejpam-5226	58	23	x	x	X
ejpam-5226	59	1	=	=	PUNCT
ejpam-5226	59	2	m	m	VERB
ejpam-5226	59	3	∧	∧	NOUN
ejpam-5226	59	4	x	x	PUNCT
ejpam-5226	59	5	=	=	PUNCT
ejpam-5226	59	6	x.	x.	NOUN
ejpam-5226	59	7	therefore	therefore	ADV
ejpam-5226	59	8	,	,	PUNCT
ejpam-5226	59	9	x	x	PROPN
ejpam-5226	59	10	∈	∈	PROPN
ejpam-5226	59	11	hs	hs	INTJ
ejpam-5226	59	12	.	.	PUNCT
ejpam-5226	60	1	hence	hence	ADV
ejpam-5226	60	2	,	,	PUNCT
ejpam-5226	60	3	l	l	PROPN
ejpam-5226	60	4	⊆	⊆	NUM
ejpam-5226	60	5	hs	hs	X
ejpam-5226	60	6	.	.	PUNCT
ejpam-5226	61	1	thus	thus	ADV
ejpam-5226	61	2	,	,	PUNCT
ejpam-5226	61	3	hs	hs	PROPN
ejpam-5226	61	4	=	=	PROPN
ejpam-5226	61	5	l.	l.	PROPN
ejpam-5226	61	6	remark	remark	PROPN
ejpam-5226	61	7	1	1	NUM
ejpam-5226	61	8	.	.	PUNCT
ejpam-5226	62	1	for	for	ADP
ejpam-5226	62	2	any	any	DET
ejpam-5226	62	3	∅	∅	NOUN
ejpam-5226	62	4	̸=	̸=	PROPN
ejpam-5226	62	5	s	s	NOUN
ejpam-5226	62	6	⊆	⊆	NUM
ejpam-5226	62	7	l	l	NOUN
ejpam-5226	62	8	,	,	PUNCT
ejpam-5226	62	9	hs	hs	PRON
ejpam-5226	62	10	need	need	AUX
ejpam-5226	62	11	not	not	PART
ejpam-5226	62	12	be	be	AUX
ejpam-5226	62	13	closed	close	VERB
ejpam-5226	62	14	under	under	ADP
ejpam-5226	62	15	∨	∨	NUM
ejpam-5226	62	16	by	by	ADP
ejpam-5226	62	17	the	the	DET
ejpam-5226	62	18	following	follow	VERB
ejpam-5226	62	19	counterexample	counterexample	NOUN
ejpam-5226	62	20	:	:	PUNCT
ejpam-5226	62	21	example	example	NOUN
ejpam-5226	63	1	1	1	X
ejpam-5226	63	2	.	.	PUNCT
ejpam-5226	64	1	let	let	VERB
ejpam-5226	64	2	l	l	NOUN
ejpam-5226	64	3	=	=	PUNCT
ejpam-5226	64	4	{	{	PUNCT
ejpam-5226	64	5	0	0	NUM
ejpam-5226	64	6	,	,	PUNCT
ejpam-5226	64	7	a	a	DET
ejpam-5226	64	8	,	,	PUNCT
ejpam-5226	64	9	b	b	NOUN
ejpam-5226	64	10	,	,	PUNCT
ejpam-5226	64	11	c	c	NOUN
ejpam-5226	64	12	,	,	PUNCT
ejpam-5226	64	13	1	1	NUM
ejpam-5226	64	14	}	}	PUNCT
ejpam-5226	64	15	,	,	PUNCT
ejpam-5226	64	16	whose	whose	DET
ejpam-5226	64	17	hasse	hasse	NOUN
ejpam-5226	64	18	diagram	diagram	NOUN
ejpam-5226	64	19	is	be	AUX
ejpam-5226	64	20	given	give	VERB
ejpam-5226	64	21	below	below	ADV
ejpam-5226	64	22	:	:	PUNCT
ejpam-5226	64	23	c	c	NOUN
ejpam-5226	64	24	a	a	DET
ejpam-5226	64	25	0	0	NUM
ejpam-5226	64	26	b	b	SYM
ejpam-5226	64	27	1	1	NUM
ejpam-5226	64	28	for	for	ADP
ejpam-5226	64	29	s1	s1	NOUN
ejpam-5226	64	30	=	=	PUNCT
ejpam-5226	64	31	{	{	PUNCT
ejpam-5226	64	32	a	a	DET
ejpam-5226	64	33	,	,	PUNCT
ejpam-5226	64	34	b	b	NOUN
ejpam-5226	64	35	}	}	PUNCT
ejpam-5226	64	36	,	,	PUNCT
ejpam-5226	64	37	it	it	PRON
ejpam-5226	64	38	is	be	AUX
ejpam-5226	64	39	easy	easy	ADJ
ejpam-5226	64	40	to	to	PART
ejpam-5226	64	41	verify	verify	VERB
ejpam-5226	64	42	that	that	SCONJ
ejpam-5226	64	43	a∨	a∨	PROPN
ejpam-5226	64	44	b	b	PROPN
ejpam-5226	65	1	=	=	SYM
ejpam-5226	65	2	c	c	PROPN
ejpam-5226	65	3	/∈	/∈	PUNCT
ejpam-5226	66	1	hs1	hs1	X
ejpam-5226	66	2	=	=	PUNCT
ejpam-5226	66	3	{	{	PUNCT
ejpam-5226	66	4	0	0	NUM
ejpam-5226	66	5	,	,	PUNCT
ejpam-5226	66	6	a	a	DET
ejpam-5226	66	7	,	,	PUNCT
ejpam-5226	66	8	b	b	NOUN
ejpam-5226	66	9	}	}	PUNCT
ejpam-5226	66	10	.	.	PUNCT
ejpam-5226	67	1	therefore	therefore	ADV
ejpam-5226	67	2	,	,	PUNCT
ejpam-5226	67	3	hs1	hs1	PROPN
ejpam-5226	67	4	is	be	AUX
ejpam-5226	67	5	not	not	PART
ejpam-5226	67	6	closed	close	VERB
ejpam-5226	67	7	under	under	ADP
ejpam-5226	67	8	∨.	∨.	NOUN
ejpam-5226	67	9	proposition	proposition	NOUN
ejpam-5226	67	10	2	2	NUM
ejpam-5226	67	11	.	.	X
ejpam-5226	68	1	for	for	ADP
ejpam-5226	68	2	any	any	DET
ejpam-5226	68	3	∅	∅	NOUN
ejpam-5226	68	4	=	=	NOUN
ejpam-5226	68	5	̸	̸	NUM
ejpam-5226	68	6	s	s	PART
ejpam-5226	68	7	⊆	⊆	NUM
ejpam-5226	68	8	l	l	NOUN
ejpam-5226	68	9	,	,	PUNCT
ejpam-5226	68	10	and	and	CCONJ
ejpam-5226	68	11	a	a	DET
ejpam-5226	68	12	,	,	PUNCT
ejpam-5226	68	13	b	b	NOUN
ejpam-5226	68	14	,	,	PUNCT
ejpam-5226	68	15	h	h	NOUN
ejpam-5226	68	16	∈	∈	PROPN
ejpam-5226	68	17	l	l	NOUN
ejpam-5226	68	18	,	,	PUNCT
ejpam-5226	68	19	we	we	PRON
ejpam-5226	68	20	have	have	VERB
ejpam-5226	68	21	(	(	PUNCT
ejpam-5226	68	22	i	i	NOUN
ejpam-5226	68	23	)	)	PUNCT
ejpam-5226	68	24	a	a	DET
ejpam-5226	68	25	≤	≤	PROPN
ejpam-5226	68	26	b	b	NOUN
ejpam-5226	68	27	implies	imply	VERB
ejpam-5226	68	28	ha	ha	INTJ
ejpam-5226	68	29	⊆	⊆	NUM
ejpam-5226	68	30	hb	hb	NOUN
ejpam-5226	68	31	,	,	PUNCT
ejpam-5226	68	32	(	(	PUNCT
ejpam-5226	68	33	ii	ii	NOUN
ejpam-5226	68	34	)	)	PUNCT
ejpam-5226	68	35	a	a	DET
ejpam-5226	68	36	≤	≤	PROPN
ejpam-5226	68	37	b	b	NOUN
ejpam-5226	68	38	and	and	CCONJ
ejpam-5226	68	39	b	b	PROPN
ejpam-5226	68	40	∈	∈	PROPN
ejpam-5226	68	41	hs	hs	PROPN
ejpam-5226	68	42	implies	imply	VERB
ejpam-5226	68	43	a	a	DET
ejpam-5226	68	44	∈	∈	ADJ
ejpam-5226	68	45	hs	hs	PROPN
ejpam-5226	68	46	,	,	PUNCT
ejpam-5226	68	47	(	(	PUNCT
ejpam-5226	68	48	iii	iii	X
ejpam-5226	69	1	)	)	PUNCT
ejpam-5226	69	2	h	h	NOUN
ejpam-5226	69	3	∈	∈	PROPN
ejpam-5226	69	4	hs	hs	PROPN
ejpam-5226	69	5	implies	imply	VERB
ejpam-5226	69	6	(	(	PUNCT
ejpam-5226	69	7	h	h	X
ejpam-5226	69	8	]	]	X
ejpam-5226	69	9	⊆	⊆	NUM
ejpam-5226	69	10	hs	hs	X
ejpam-5226	69	11	,	,	PUNCT
ejpam-5226	69	12	(	(	PUNCT
ejpam-5226	69	13	iv	iv	X
ejpam-5226	69	14	)	)	PUNCT
ejpam-5226	70	1	ha	ha	X
ejpam-5226	70	2	is	be	AUX
ejpam-5226	70	3	an	an	DET
ejpam-5226	70	4	ideal	ideal	NOUN
ejpam-5226	70	5	of	of	ADP
ejpam-5226	70	6	l.	l.	PROPN
ejpam-5226	70	7	a.	a.	PROPN
ejpam-5226	70	8	iampan	iampan	PROPN
ejpam-5226	70	9	et	et	PROPN
ejpam-5226	70	10	al	al	PROPN
ejpam-5226	70	11	.	.	PUNCT
ejpam-5226	70	12	/	/	SYM
ejpam-5226	70	13	eur	eur	PROPN
ejpam-5226	70	14	.	.	PUNCT
ejpam-5226	71	1	j.	j.	PROPN
ejpam-5226	71	2	pure	pure	PROPN
ejpam-5226	71	3	appl	appl	PROPN
ejpam-5226	71	4	.	.	PROPN
ejpam-5226	71	5	math	math	PROPN
ejpam-5226	71	6	,	,	PUNCT
ejpam-5226	71	7	17	17	NUM
ejpam-5226	71	8	(	(	PUNCT
ejpam-5226	71	9	3	3	NUM
ejpam-5226	71	10	)	)	PUNCT
ejpam-5226	71	11	(	(	PUNCT
ejpam-5226	71	12	2024	2024	NUM
ejpam-5226	71	13	)	)	PUNCT
ejpam-5226	71	14	,	,	PUNCT
ejpam-5226	71	15	1691	1691	NUM
ejpam-5226	71	16	-	-	SYM
ejpam-5226	71	17	1704	1704	NUM
ejpam-5226	71	18	1694	1694	NUM
ejpam-5226	71	19	proof	proof	NOUN
ejpam-5226	71	20	.	.	PUNCT
ejpam-5226	72	1	(	(	PUNCT
ejpam-5226	72	2	i	i	NOUN
ejpam-5226	72	3	)	)	PUNCT
ejpam-5226	72	4	assume	assume	VERB
ejpam-5226	72	5	that	that	SCONJ
ejpam-5226	72	6	a	a	DET
ejpam-5226	72	7	≤	≤	PROPN
ejpam-5226	72	8	b.	b.	PROPN
ejpam-5226	72	9	let	let	VERB
ejpam-5226	72	10	x	x	PUNCT
ejpam-5226	72	11	∈	∈	PROPN
ejpam-5226	72	12	ha	ha	INTJ
ejpam-5226	72	13	.	.	PUNCT
ejpam-5226	73	1	then	then	ADV
ejpam-5226	73	2	a∧	a∧	NOUN
ejpam-5226	73	3	x	x	PUNCT
ejpam-5226	74	1	=	=	PUNCT
ejpam-5226	74	2	x.	x.	NOUN
ejpam-5226	74	3	now	now	ADV
ejpam-5226	74	4	,	,	PUNCT
ejpam-5226	74	5	b∧	b∧	PROPN
ejpam-5226	74	6	x	x	X
ejpam-5226	74	7	=	=	SYM
ejpam-5226	74	8	b∧	b∧	NOUN
ejpam-5226	74	9	(	(	PUNCT
ejpam-5226	74	10	a∧	a∧	NOUN
ejpam-5226	74	11	x	x	NOUN
ejpam-5226	74	12	)	)	PUNCT
ejpam-5226	74	13	=	=	SYM
ejpam-5226	75	1	(	(	PUNCT
ejpam-5226	75	2	b	b	X
ejpam-5226	75	3	∧	∧	PROPN
ejpam-5226	75	4	a	a	PRON
ejpam-5226	75	5	)	)	PUNCT
ejpam-5226	75	6	∧	∧	NOUN
ejpam-5226	75	7	x	x	X
ejpam-5226	75	8	=	=	PUNCT
ejpam-5226	75	9	a	a	DET
ejpam-5226	75	10	∧	∧	PROPN
ejpam-5226	75	11	x	x	X
ejpam-5226	75	12	=	=	PUNCT
ejpam-5226	75	13	x.	x.	NOUN
ejpam-5226	75	14	therefore	therefore	ADV
ejpam-5226	75	15	,	,	PUNCT
ejpam-5226	75	16	x	x	PROPN
ejpam-5226	75	17	∈	∈	PROPN
ejpam-5226	75	18	hb	hb	PROPN
ejpam-5226	75	19	.	.	PUNCT
ejpam-5226	76	1	hence	hence	ADV
ejpam-5226	76	2	,	,	PUNCT
ejpam-5226	76	3	ha	ha	INTJ
ejpam-5226	76	4	⊆	⊆	NUM
ejpam-5226	76	5	hb	hb	X
ejpam-5226	76	6	.	.	PUNCT
ejpam-5226	76	7	(	(	PUNCT
ejpam-5226	76	8	ii	ii	NOUN
ejpam-5226	76	9	)	)	PUNCT
ejpam-5226	76	10	assume	assume	VERB
ejpam-5226	76	11	that	that	SCONJ
ejpam-5226	76	12	a	a	DET
ejpam-5226	76	13	≤	≤	PROPN
ejpam-5226	76	14	b	b	NOUN
ejpam-5226	76	15	and	and	CCONJ
ejpam-5226	76	16	b	b	PROPN
ejpam-5226	76	17	∈	∈	PROPN
ejpam-5226	76	18	hs	hs	PROPN
ejpam-5226	76	19	.	.	PUNCT
ejpam-5226	77	1	for	for	ADP
ejpam-5226	77	2	this	this	DET
ejpam-5226	77	3	b	b	PROPN
ejpam-5226	77	4	∈	∈	PROPN
ejpam-5226	77	5	hs	hs	INTJ
ejpam-5226	77	6	,	,	PUNCT
ejpam-5226	77	7	there	there	PRON
ejpam-5226	77	8	is	be	VERB
ejpam-5226	77	9	an	an	DET
ejpam-5226	77	10	element	element	NOUN
ejpam-5226	77	11	s	s	PART
ejpam-5226	77	12	∈	∈	NOUN
ejpam-5226	77	13	s	s	VERB
ejpam-5226	77	14	such	such	ADJ
ejpam-5226	77	15	that	that	DET
ejpam-5226	77	16	s	s	PROPN
ejpam-5226	77	17	∧	∧	PROPN
ejpam-5226	77	18	b	b	PROPN
ejpam-5226	77	19	=	=	PROPN
ejpam-5226	77	20	b.	b.	PROPN
ejpam-5226	77	21	now	now	ADV
ejpam-5226	77	22	,	,	PUNCT
ejpam-5226	77	23	s	s	VERB
ejpam-5226	77	24	∧	∧	NOUN
ejpam-5226	77	25	a	a	DET
ejpam-5226	77	26	=	=	X
ejpam-5226	77	27	s	s	PROPN
ejpam-5226	77	28	∧	∧	PROPN
ejpam-5226	77	29	(	(	PUNCT
ejpam-5226	77	30	a	a	DET
ejpam-5226	77	31	∧	∧	PROPN
ejpam-5226	77	32	b	b	NOUN
ejpam-5226	77	33	)	)	PUNCT
ejpam-5226	77	34	=	=	PUNCT
ejpam-5226	77	35	(	(	PUNCT
ejpam-5226	77	36	s	s	VERB
ejpam-5226	77	37	∧	∧	NOUN
ejpam-5226	77	38	a	a	PRON
ejpam-5226	77	39	)	)	PUNCT
ejpam-5226	77	40	∧	∧	PROPN
ejpam-5226	77	41	b	b	NOUN
ejpam-5226	77	42	=	=	PUNCT
ejpam-5226	77	43	a	a	DET
ejpam-5226	77	44	∧	∧	PROPN
ejpam-5226	77	45	(	(	PUNCT
ejpam-5226	77	46	s	s	PROPN
ejpam-5226	77	47	∧	∧	PROPN
ejpam-5226	77	48	b	b	NOUN
ejpam-5226	77	49	)	)	PUNCT
ejpam-5226	77	50	=	=	PUNCT
ejpam-5226	77	51	a	a	DET
ejpam-5226	77	52	∧	∧	PROPN
ejpam-5226	77	53	b	b	NOUN
ejpam-5226	77	54	=	=	NOUN
ejpam-5226	77	55	a.	a.	NOUN
ejpam-5226	77	56	therefore	therefore	ADV
ejpam-5226	77	57	,	,	PUNCT
ejpam-5226	77	58	a	a	DET
ejpam-5226	77	59	∈	∈	PROPN
ejpam-5226	77	60	hs	hs	INTJ
ejpam-5226	77	61	.	.	PUNCT
ejpam-5226	78	1	(	(	PUNCT
ejpam-5226	78	2	iii	iii	X
ejpam-5226	78	3	)	)	PUNCT
ejpam-5226	78	4	let	let	VERB
ejpam-5226	78	5	h	h	PROPN
ejpam-5226	78	6	∈	∈	PROPN
ejpam-5226	79	1	hs	hs	PROPN
ejpam-5226	79	2	.	.	PUNCT
ejpam-5226	80	1	then	then	ADV
ejpam-5226	80	2	s	s	VERB
ejpam-5226	80	3	∧	∧	PROPN
ejpam-5226	80	4	h	h	NOUN
ejpam-5226	80	5	=	=	NOUN
ejpam-5226	80	6	h	h	PROPN
ejpam-5226	80	7	for	for	ADP
ejpam-5226	80	8	some	some	DET
ejpam-5226	80	9	s	s	NOUN
ejpam-5226	80	10	∈	∈	PROPN
ejpam-5226	80	11	s.	s.	PROPN
ejpam-5226	80	12	for	for	ADP
ejpam-5226	80	13	any	any	DET
ejpam-5226	80	14	x	x	SYM
ejpam-5226	80	15	∈	∈	PROPN
ejpam-5226	80	16	(	(	PUNCT
ejpam-5226	80	17	h	h	NOUN
ejpam-5226	80	18	]	]	X
ejpam-5226	80	19	,	,	PUNCT
ejpam-5226	80	20	x	x	SYM
ejpam-5226	80	21	=	=	SYM
ejpam-5226	80	22	h	h	NOUN
ejpam-5226	80	23	∧	∧	PROPN
ejpam-5226	80	24	x.	x.	NOUN
ejpam-5226	80	25	now	now	ADV
ejpam-5226	80	26	,	,	PUNCT
ejpam-5226	80	27	s	s	VERB
ejpam-5226	80	28	∧	∧	NOUN
ejpam-5226	80	29	x	x	PUNCT
ejpam-5226	80	30	=	=	SYM
ejpam-5226	80	31	s	s	PART
ejpam-5226	80	32	∧	∧	PROPN
ejpam-5226	80	33	(	(	PUNCT
ejpam-5226	80	34	h	h	NOUN
ejpam-5226	80	35	∧	∧	PROPN
ejpam-5226	80	36	x	x	X
ejpam-5226	80	37	)	)	PUNCT
ejpam-5226	80	38	=	=	SYM
ejpam-5226	81	1	(	(	PUNCT
ejpam-5226	81	2	s	s	NOUN
ejpam-5226	81	3	∧	∧	PROPN
ejpam-5226	81	4	h	h	NOUN
ejpam-5226	81	5	)	)	PUNCT
ejpam-5226	81	6	∧	∧	NOUN
ejpam-5226	81	7	x	x	X
ejpam-5226	82	1	=	=	PUNCT
ejpam-5226	82	2	h	h	NOUN
ejpam-5226	82	3	∧	∧	NOUN
ejpam-5226	82	4	x	x	PUNCT
ejpam-5226	82	5	=	=	PUNCT
ejpam-5226	82	6	x.	x.	NOUN
ejpam-5226	82	7	therefore	therefore	ADV
ejpam-5226	82	8	,	,	PUNCT
ejpam-5226	82	9	x	x	PROPN
ejpam-5226	82	10	∈	∈	PROPN
ejpam-5226	82	11	hs	hs	INTJ
ejpam-5226	82	12	.	.	PUNCT
ejpam-5226	83	1	hence	hence	ADV
ejpam-5226	83	2	,	,	PUNCT
ejpam-5226	83	3	(	(	PUNCT
ejpam-5226	83	4	h	h	X
ejpam-5226	83	5	]	]	X
ejpam-5226	83	6	⊆	⊆	NUM
ejpam-5226	83	7	hs	hs	X
ejpam-5226	83	8	.	.	PUNCT
ejpam-5226	84	1	(	(	PUNCT
ejpam-5226	84	2	iv	iv	X
ejpam-5226	84	3	)	)	PUNCT
ejpam-5226	84	4	let	let	VERB
ejpam-5226	84	5	x	x	PRON
ejpam-5226	84	6	,	,	PUNCT
ejpam-5226	84	7	y	y	PROPN
ejpam-5226	84	8	∈	∈	PROPN
ejpam-5226	84	9	ha	ha	INTJ
ejpam-5226	84	10	.	.	PUNCT
ejpam-5226	85	1	then	then	ADV
ejpam-5226	85	2	a∧x	a∧x	NOUN
ejpam-5226	86	1	=	=	SYM
ejpam-5226	86	2	x	x	PROPN
ejpam-5226	86	3	and	and	CCONJ
ejpam-5226	86	4	a∧y	a∧y	PROPN
ejpam-5226	86	5	=	=	SYM
ejpam-5226	86	6	y.	y.	PROPN
ejpam-5226	86	7	now	now	ADV
ejpam-5226	86	8	,	,	PUNCT
ejpam-5226	86	9	a∧(x∨y	a∧(x∨y	ADJ
ejpam-5226	86	10	)	)	PUNCT
ejpam-5226	86	11	=	=	PRON
ejpam-5226	86	12	(	(	PUNCT
ejpam-5226	86	13	a∧x)∨(a∧y	a∧x)∨(a∧y	NOUN
ejpam-5226	86	14	)	)	PUNCT
ejpam-5226	86	15	=	=	SYM
ejpam-5226	86	16	x∨y	x∨y	PROPN
ejpam-5226	86	17	.	.	PUNCT
ejpam-5226	87	1	therefore	therefore	ADV
ejpam-5226	87	2	,	,	PUNCT
ejpam-5226	87	3	x	x	PROPN
ejpam-5226	87	4	∨	∨	NUM
ejpam-5226	87	5	y	y	PROPN
ejpam-5226	87	6	∈	∈	PROPN
ejpam-5226	87	7	ha	ha	INTJ
ejpam-5226	87	8	.	.	PUNCT
ejpam-5226	87	9	let	let	VERB
ejpam-5226	87	10	l	l	PROPN
ejpam-5226	87	11	∈	∈	PROPN
ejpam-5226	87	12	l.	l.	NOUN
ejpam-5226	87	13	then	then	ADV
ejpam-5226	87	14	a	a	DET
ejpam-5226	87	15	∧	∧	PROPN
ejpam-5226	87	16	(	(	PUNCT
ejpam-5226	87	17	l	l	NOUN
ejpam-5226	87	18	∧	∧	PROPN
ejpam-5226	87	19	x	x	NOUN
ejpam-5226	87	20	)	)	PUNCT
ejpam-5226	88	1	=	=	SYM
ejpam-5226	88	2	(	(	PUNCT
ejpam-5226	88	3	a	a	DET
ejpam-5226	88	4	∧	∧	PROPN
ejpam-5226	88	5	l	l	NOUN
ejpam-5226	88	6	)	)	PUNCT
ejpam-5226	88	7	∧	∧	NOUN
ejpam-5226	88	8	x	x	X
ejpam-5226	88	9	=	=	PUNCT
ejpam-5226	88	10	l	l	NOUN
ejpam-5226	88	11	∧	∧	PROPN
ejpam-5226	88	12	(	(	PUNCT
ejpam-5226	88	13	a	a	DET
ejpam-5226	88	14	∧	∧	PROPN
ejpam-5226	88	15	x	x	NOUN
ejpam-5226	88	16	)	)	PUNCT
ejpam-5226	88	17	=	=	SYM
ejpam-5226	89	1	l	l	NOUN
ejpam-5226	89	2	∧	∧	PROPN
ejpam-5226	89	3	x.	x.	NOUN
ejpam-5226	89	4	therefore	therefore	ADV
ejpam-5226	89	5	,	,	PUNCT
ejpam-5226	89	6	l	l	PROPN
ejpam-5226	89	7	∧	∧	NOUN
ejpam-5226	89	8	x	x	SYM
ejpam-5226	89	9	∈	∈	PROPN
ejpam-5226	89	10	ha	ha	INTJ
ejpam-5226	89	11	and	and	CCONJ
ejpam-5226	89	12	x	x	SYM
ejpam-5226	89	13	∧	∧	PROPN
ejpam-5226	89	14	l	l	NOUN
ejpam-5226	89	15	∈	∈	PROPN
ejpam-5226	89	16	ha	ha	INTJ
ejpam-5226	89	17	.	.	PUNCT
ejpam-5226	90	1	thus	thus	ADV
ejpam-5226	90	2	,	,	PUNCT
ejpam-5226	90	3	ha	ha	INTJ
ejpam-5226	90	4	is	be	AUX
ejpam-5226	90	5	an	an	DET
ejpam-5226	90	6	ideal	ideal	NOUN
ejpam-5226	90	7	of	of	ADP
ejpam-5226	90	8	l.	l.	PROPN
ejpam-5226	90	9	remark	remark	PROPN
ejpam-5226	90	10	2	2	NUM
ejpam-5226	90	11	.	.	PUNCT
ejpam-5226	91	1	for	for	ADP
ejpam-5226	91	2	any	any	DET
ejpam-5226	91	3	non	non	ADJ
ejpam-5226	91	4	-	-	ADJ
ejpam-5226	91	5	empty	empty	ADJ
ejpam-5226	91	6	subsets	subset	NOUN
ejpam-5226	91	7	s	s	PRON
ejpam-5226	91	8	of	of	ADP
ejpam-5226	91	9	a	a	DET
ejpam-5226	91	10	discrete	discrete	ADJ
ejpam-5226	91	11	almost	almost	ADV
ejpam-5226	91	12	distributive	distributive	ADJ
ejpam-5226	91	13	lattice	lattice	NOUN
ejpam-5226	91	14	x	x	NOUN
ejpam-5226	91	15	,	,	PUNCT
ejpam-5226	91	16	either	either	CCONJ
ejpam-5226	91	17	hs	hs	PROPN
ejpam-5226	91	18	=	=	X
ejpam-5226	91	19	{	{	PUNCT
ejpam-5226	91	20	0	0	NUM
ejpam-5226	91	21	}	}	PUNCT
ejpam-5226	91	22	or	or	CCONJ
ejpam-5226	91	23	hs	hs	PROPN
ejpam-5226	91	24	=	=	PROPN
ejpam-5226	91	25	l.	l.	PROPN
ejpam-5226	91	26	suppose	suppose	VERB
ejpam-5226	91	27	hs	hs	PROPN
ejpam-5226	91	28	̸=	̸=	PROPN
ejpam-5226	91	29	{	{	PUNCT
ejpam-5226	91	30	0	0	NUM
ejpam-5226	91	31	}	}	PUNCT
ejpam-5226	91	32	.	.	PUNCT
ejpam-5226	92	1	then	then	ADV
ejpam-5226	92	2	there	there	PRON
ejpam-5226	92	3	exists	exist	VERB
ejpam-5226	92	4	a	a	DET
ejpam-5226	92	5	non	non	ADJ
ejpam-5226	92	6	-	-	ADJ
ejpam-5226	92	7	zero	zero	NUM
ejpam-5226	92	8	element	element	NOUN
ejpam-5226	92	9	h	h	NOUN
ejpam-5226	92	10	in	in	ADP
ejpam-5226	92	11	hs	hs	PRON
ejpam-5226	92	12	such	such	ADJ
ejpam-5226	92	13	that	that	PRON
ejpam-5226	92	14	s	s	VERB
ejpam-5226	92	15	∧	∧	NOUN
ejpam-5226	92	16	h	h	NOUN
ejpam-5226	92	17	=	=	NOUN
ejpam-5226	92	18	h	h	PROPN
ejpam-5226	92	19	for	for	ADP
ejpam-5226	92	20	some	some	DET
ejpam-5226	92	21	non	non	ADJ
ejpam-5226	92	22	-	-	ADJ
ejpam-5226	92	23	zero	zero	NUM
ejpam-5226	92	24	element	element	NOUN
ejpam-5226	92	25	s	s	PART
ejpam-5226	92	26	∈	∈	NOUN
ejpam-5226	92	27	s	s	X
ejpam-5226	92	28	(	(	PUNCT
ejpam-5226	92	29	if	if	SCONJ
ejpam-5226	92	30	s	s	VERB
ejpam-5226	92	31	=	=	NOUN
ejpam-5226	92	32	0	0	NUM
ejpam-5226	92	33	,	,	PUNCT
ejpam-5226	92	34	then	then	ADV
ejpam-5226	92	35	h	h	NOUN
ejpam-5226	92	36	=	=	NOUN
ejpam-5226	92	37	0	0	NUM
ejpam-5226	92	38	)	)	PUNCT
ejpam-5226	92	39	.	.	PUNCT
ejpam-5226	93	1	let	let	VERB
ejpam-5226	93	2	y	y	PROPN
ejpam-5226	93	3	∈	∈	PROPN
ejpam-5226	93	4	l.	l.	PROPN
ejpam-5226	93	5	now	now	ADV
ejpam-5226	93	6	,	,	PUNCT
ejpam-5226	93	7	s	s	VERB
ejpam-5226	94	1	∧	∧	PROPN
ejpam-5226	94	2	y	y	PROPN
ejpam-5226	94	3	=	=	PUNCT
ejpam-5226	94	4	(	(	PUNCT
ejpam-5226	94	5	s	s	PROPN
ejpam-5226	94	6	∨	∨	NUM
ejpam-5226	94	7	h	h	NOUN
ejpam-5226	94	8	)	)	PUNCT
ejpam-5226	94	9	∧	∧	NOUN
ejpam-5226	94	10	y	y	NOUN
ejpam-5226	95	1	=	=	PUNCT
ejpam-5226	96	1	(	(	PUNCT
ejpam-5226	96	2	s	s	PROPN
ejpam-5226	96	3	∧	∧	PROPN
ejpam-5226	96	4	y	y	PROPN
ejpam-5226	96	5	)	)	PUNCT
ejpam-5226	96	6	∨	∨	PROPN
ejpam-5226	96	7	(	(	PUNCT
ejpam-5226	96	8	h	h	NOUN
ejpam-5226	96	9	∧	∧	PROPN
ejpam-5226	96	10	y	y	PROPN
ejpam-5226	96	11	)	)	PUNCT
ejpam-5226	96	12	=	=	PUNCT
ejpam-5226	97	1	(	(	PUNCT
ejpam-5226	97	2	s	s	PROPN
ejpam-5226	97	3	∧	∧	PROPN
ejpam-5226	97	4	y	y	PROPN
ejpam-5226	97	5	)	)	PUNCT
ejpam-5226	97	6	∨	∨	PROPN
ejpam-5226	97	7	y	y	PROPN
ejpam-5226	97	8	=	=	SYM
ejpam-5226	97	9	y	y	PROPN
ejpam-5226	97	10	(	(	PUNCT
ejpam-5226	97	11	since	since	SCONJ
ejpam-5226	97	12	h	h	PROPN
ejpam-5226	97	13	̸=	̸=	PROPN
ejpam-5226	97	14	0	0	NUM
ejpam-5226	97	15	)	)	PUNCT
ejpam-5226	97	16	.	.	PUNCT
ejpam-5226	98	1	therefore	therefore	ADV
ejpam-5226	98	2	,	,	PUNCT
ejpam-5226	98	3	y	y	PROPN
ejpam-5226	98	4	∈	∈	PROPN
ejpam-5226	98	5	hs	hs	PROPN
ejpam-5226	98	6	.	.	PROPN
ejpam-5226	98	7	hence	hence	ADV
ejpam-5226	98	8	,	,	PUNCT
ejpam-5226	98	9	l	l	PROPN
ejpam-5226	98	10	⊆	⊆	NUM
ejpam-5226	98	11	hs	hs	X
ejpam-5226	98	12	.	.	PUNCT
ejpam-5226	98	13	thus	thus	ADV
ejpam-5226	98	14	,	,	PUNCT
ejpam-5226	98	15	hs	hs	PROPN
ejpam-5226	98	16	=	=	PROPN
ejpam-5226	98	17	l.	l.	PROPN
ejpam-5226	98	18	proposition	proposition	NOUN
ejpam-5226	98	19	3	3	NUM
ejpam-5226	98	20	.	.	X
ejpam-5226	99	1	for	for	ADP
ejpam-5226	99	2	any	any	DET
ejpam-5226	99	3	∅	∅	NOUN
ejpam-5226	99	4	=	=	NOUN
ejpam-5226	99	5	̸	̸	NUM
ejpam-5226	99	6	s1	s1	NOUN
ejpam-5226	99	7	,	,	PUNCT
ejpam-5226	99	8	s2	s2	NOUN
ejpam-5226	99	9	⊆	⊆	NUM
ejpam-5226	99	10	l	l	NOUN
ejpam-5226	99	11	,	,	PUNCT
ejpam-5226	99	12	we	we	PRON
ejpam-5226	99	13	have	have	VERB
ejpam-5226	99	14	(	(	PUNCT
ejpam-5226	99	15	i	i	NOUN
ejpam-5226	99	16	)	)	PUNCT
ejpam-5226	99	17	s1	s1	PROPN
ejpam-5226	99	18	⊆	⊆	NUM
ejpam-5226	99	19	s2	s2	PROPN
ejpam-5226	99	20	implies	imply	VERB
ejpam-5226	99	21	hs1	hs1	PROPN
ejpam-5226	99	22	⊆	⊆	NUM
ejpam-5226	99	23	hs2	hs2	PROPN
ejpam-5226	99	24	,	,	PUNCT
ejpam-5226	99	25	(	(	PUNCT
ejpam-5226	99	26	ii	ii	NOUN
ejpam-5226	99	27	)	)	PUNCT
ejpam-5226	99	28	hs1∪s2	hs1∪s2	PROPN
ejpam-5226	99	29	=	=	PUNCT
ejpam-5226	99	30	hs1	hs1	PROPN
ejpam-5226	99	31	∪hs2	∪hs2	PROPN
ejpam-5226	99	32	,	,	PUNCT
ejpam-5226	99	33	(	(	PUNCT
ejpam-5226	99	34	iii	iii	X
ejpam-5226	99	35	)	)	PUNCT
ejpam-5226	99	36	hs1∩s2	hs1∩s2	PROPN
ejpam-5226	99	37	⊆	⊆	NUM
ejpam-5226	99	38	hs1	hs1	PROPN
ejpam-5226	99	39	∩hs2	∩hs2	PROPN
ejpam-5226	99	40	.	.	PUNCT
ejpam-5226	100	1	proof	proof	NOUN
ejpam-5226	100	2	.	.	PUNCT
ejpam-5226	101	1	(	(	PUNCT
ejpam-5226	101	2	i	i	NOUN
ejpam-5226	101	3	)	)	PUNCT
ejpam-5226	101	4	let	let	VERB
ejpam-5226	101	5	x	x	SYM
ejpam-5226	101	6	∈	∈	PROPN
ejpam-5226	101	7	hs1	hs1	PROPN
ejpam-5226	101	8	.	.	PUNCT
ejpam-5226	102	1	then	then	ADV
ejpam-5226	102	2	s1	s1	PROPN
ejpam-5226	102	3	∧	∧	PROPN
ejpam-5226	102	4	x	x	X
ejpam-5226	103	1	=	=	PUNCT
ejpam-5226	103	2	x	x	PROPN
ejpam-5226	103	3	for	for	ADP
ejpam-5226	103	4	some	some	DET
ejpam-5226	103	5	s1	s1	PROPN
ejpam-5226	103	6	∈	∈	PROPN
ejpam-5226	103	7	s1	s1	NOUN
ejpam-5226	103	8	.	.	PUNCT
ejpam-5226	104	1	since	since	SCONJ
ejpam-5226	104	2	s1	s1	PROPN
ejpam-5226	104	3	⊆	⊆	NUM
ejpam-5226	104	4	s2	s2	PROPN
ejpam-5226	104	5	,	,	PUNCT
ejpam-5226	104	6	x	x	SYM
ejpam-5226	104	7	∈	∈	PROPN
ejpam-5226	104	8	hs2	hs2	NOUN
ejpam-5226	104	9	.	.	PUNCT
ejpam-5226	105	1	hence	hence	ADV
ejpam-5226	105	2	,	,	PUNCT
ejpam-5226	105	3	hs1	hs1	PROPN
ejpam-5226	105	4	⊆	⊆	NUM
ejpam-5226	105	5	hs2	hs2	NOUN
ejpam-5226	105	6	.	.	PUNCT
ejpam-5226	106	1	(	(	PUNCT
ejpam-5226	106	2	ii	ii	NOUN
ejpam-5226	106	3	)	)	PUNCT
ejpam-5226	106	4	since	since	SCONJ
ejpam-5226	106	5	s1	s1	NOUN
ejpam-5226	106	6	,	,	PUNCT
ejpam-5226	106	7	s2	s2	NOUN
ejpam-5226	106	8	⊆	⊆	NUM
ejpam-5226	106	9	s1∪s2	s1∪s2	NOUN
ejpam-5226	106	10	,	,	PUNCT
ejpam-5226	106	11	we	we	PRON
ejpam-5226	106	12	havehs1	havehs1	NOUN
ejpam-5226	106	13	,	,	PUNCT
ejpam-5226	106	14	hs2	hs2	PROPN
ejpam-5226	106	15	⊆	⊆	NUM
ejpam-5226	106	16	hs1∪s2	hs1∪s2	ADV
ejpam-5226	106	17	.	.	PUNCT
ejpam-5226	107	1	therefore	therefore	ADV
ejpam-5226	107	2	,	,	PUNCT
ejpam-5226	107	3	hs1∪hs2	hs1∪hs2	PROPN
ejpam-5226	107	4	⊆	⊆	NUM
ejpam-5226	107	5	hs1∪s2	hs1∪s2	ADV
ejpam-5226	107	6	.	.	PUNCT
ejpam-5226	108	1	let	let	VERB
ejpam-5226	108	2	h	h	NOUN
ejpam-5226	108	3	∈	∈	PROPN
ejpam-5226	108	4	hs1∪s2	hs1∪s2	ADV
ejpam-5226	108	5	.	.	PUNCT
ejpam-5226	109	1	then	then	ADV
ejpam-5226	109	2	there	there	PRON
ejpam-5226	109	3	is	be	VERB
ejpam-5226	109	4	an	an	DET
ejpam-5226	109	5	element	element	NOUN
ejpam-5226	109	6	s	s	PART
ejpam-5226	109	7	∈	∈	NOUN
ejpam-5226	109	8	s1	s1	NOUN
ejpam-5226	109	9	∪s2	∪s2	VERB
ejpam-5226	109	10	such	such	ADJ
ejpam-5226	109	11	that	that	DET
ejpam-5226	109	12	s∧	s∧	PROPN
ejpam-5226	109	13	h	h	NOUN
ejpam-5226	110	1	=	=	PUNCT
ejpam-5226	110	2	h.	h.	NOUN
ejpam-5226	111	1	if	if	SCONJ
ejpam-5226	111	2	s	s	PROPN
ejpam-5226	111	3	∈	∈	PROPN
ejpam-5226	111	4	s1	s1	NOUN
ejpam-5226	111	5	,	,	PUNCT
ejpam-5226	111	6	then	then	ADV
ejpam-5226	111	7	h	h	PROPN
ejpam-5226	111	8	∈	∈	PROPN
ejpam-5226	111	9	hs1	hs1	INTJ
ejpam-5226	111	10	;	;	PUNCT
ejpam-5226	111	11	if	if	SCONJ
ejpam-5226	111	12	s	s	PROPN
ejpam-5226	111	13	∈	∈	PROPN
ejpam-5226	111	14	s2	s2	NOUN
ejpam-5226	111	15	,	,	PUNCT
ejpam-5226	111	16	then	then	ADV
ejpam-5226	111	17	h	h	PROPN
ejpam-5226	111	18	∈	∈	PROPN
ejpam-5226	111	19	hs2	hs2	NOUN
ejpam-5226	111	20	;	;	PUNCT
ejpam-5226	111	21	and	and	CCONJ
ejpam-5226	111	22	if	if	SCONJ
ejpam-5226	111	23	s	s	X
ejpam-5226	111	24	∈	∈	PROPN
ejpam-5226	111	25	s1	s1	NOUN
ejpam-5226	111	26	∩	∩	ADJ
ejpam-5226	111	27	s2	s2	NOUN
ejpam-5226	111	28	,	,	PUNCT
ejpam-5226	111	29	then	then	ADV
ejpam-5226	111	30	h	h	PROPN
ejpam-5226	111	31	∈	∈	PROPN
ejpam-5226	111	32	hs1	hs1	PROPN
ejpam-5226	111	33	∩	∩	PROPN
ejpam-5226	111	34	hs2	hs2	PROPN
ejpam-5226	111	35	.	.	PUNCT
ejpam-5226	112	1	therefore	therefore	ADV
ejpam-5226	112	2	,	,	PUNCT
ejpam-5226	112	3	h	h	PROPN
ejpam-5226	112	4	∈	∈	PROPN
ejpam-5226	112	5	hs1	hs1	PROPN
ejpam-5226	112	6	∪hs2	∪hs2	PROPN
ejpam-5226	112	7	.	.	PUNCT
ejpam-5226	113	1	so	so	ADV
ejpam-5226	113	2	that	that	PRON
ejpam-5226	113	3	hs1∪s2	hs1∪s2	PROPN
ejpam-5226	113	4	⊆	⊆	NUM
ejpam-5226	113	5	hs1	hs1	PROPN
ejpam-5226	113	6	∪hs2	∪hs2	PROPN
ejpam-5226	113	7	.	.	PUNCT
ejpam-5226	114	1	hence	hence	ADV
ejpam-5226	114	2	,	,	PUNCT
ejpam-5226	114	3	hs1∪s2	hs1∪s2	PROPN
ejpam-5226	114	4	=	=	PUNCT
ejpam-5226	114	5	hs1	hs1	PROPN
ejpam-5226	114	6	∪hs2	∪hs2	PROPN
ejpam-5226	114	7	.	.	PUNCT
ejpam-5226	115	1	(	(	PUNCT
ejpam-5226	115	2	iii	iii	X
ejpam-5226	115	3	)	)	PUNCT
ejpam-5226	115	4	let	let	VERB
ejpam-5226	115	5	h	h	PRON
ejpam-5226	115	6	∈	∈	PROPN
ejpam-5226	115	7	hs1∩s2	hs1∩s2	PROPN
ejpam-5226	115	8	.	.	PUNCT
ejpam-5226	116	1	then	then	ADV
ejpam-5226	116	2	there	there	PRON
ejpam-5226	116	3	is	be	VERB
ejpam-5226	116	4	an	an	DET
ejpam-5226	116	5	element	element	NOUN
ejpam-5226	116	6	s	s	PART
ejpam-5226	116	7	∈	∈	NOUN
ejpam-5226	116	8	s1	s1	NOUN
ejpam-5226	116	9	∩	∩	NOUN
ejpam-5226	116	10	s2	s2	VERB
ejpam-5226	116	11	such	such	ADJ
ejpam-5226	116	12	that	that	DET
ejpam-5226	116	13	s	s	VERB
ejpam-5226	116	14	∧	∧	NOUN
ejpam-5226	116	15	h	h	NOUN
ejpam-5226	116	16	=	=	PROPN
ejpam-5226	116	17	h.	h.	PROPN
ejpam-5226	116	18	therefore	therefore	ADV
ejpam-5226	116	19	,	,	PUNCT
ejpam-5226	116	20	h	h	PROPN
ejpam-5226	116	21	∈	∈	PROPN
ejpam-5226	116	22	hs1	hs1	PROPN
ejpam-5226	116	23	∩hs2	∩hs2	PROPN
ejpam-5226	116	24	(	(	PUNCT
ejpam-5226	116	25	since	since	SCONJ
ejpam-5226	116	26	s	s	PROPN
ejpam-5226	116	27	∈	∈	PROPN
ejpam-5226	116	28	s1	s1	NOUN
ejpam-5226	116	29	∩	∩	ADJ
ejpam-5226	116	30	s2	s2	PROPN
ejpam-5226	116	31	)	)	PUNCT
ejpam-5226	116	32	.	.	PUNCT
ejpam-5226	117	1	hence	hence	ADV
ejpam-5226	117	2	,	,	PUNCT
ejpam-5226	117	3	hs1∩s2	hs1∩s2	PROPN
ejpam-5226	117	4	⊆	⊆	NUM
ejpam-5226	117	5	hs1	hs1	NOUN
ejpam-5226	117	6	∩hs2	∩hs2	PROPN
ejpam-5226	117	7	.	.	PUNCT
ejpam-5226	118	1	remark	remark	VERB
ejpam-5226	118	2	3	3	NUM
ejpam-5226	118	3	.	.	PUNCT
ejpam-5226	119	1	for	for	ADP
ejpam-5226	119	2	any	any	DET
ejpam-5226	119	3	non	non	ADJ
ejpam-5226	119	4	-	-	ADJ
ejpam-5226	119	5	empty	empty	ADJ
ejpam-5226	119	6	subsets	subset	NOUN
ejpam-5226	119	7	s1	s1	NOUN
ejpam-5226	119	8	,	,	PUNCT
ejpam-5226	119	9	s2	s2	NOUN
ejpam-5226	119	10	of	of	ADP
ejpam-5226	119	11	l	l	PROPN
ejpam-5226	119	12	,	,	PUNCT
ejpam-5226	119	13	hs1∩s2	hs1∩s2	PROPN
ejpam-5226	119	14	need	need	AUX
ejpam-5226	119	15	not	not	PART
ejpam-5226	119	16	be	be	AUX
ejpam-5226	119	17	equal	equal	ADJ
ejpam-5226	119	18	to	to	PART
ejpam-5226	119	19	hs1∩hs2	hs1∩hs2	VERB
ejpam-5226	119	20	by	by	ADP
ejpam-5226	119	21	the	the	DET
ejpam-5226	119	22	following	follow	VERB
ejpam-5226	119	23	counterexample	counterexample	NOUN
ejpam-5226	119	24	:	:	PUNCT
ejpam-5226	119	25	example	example	NOUN
ejpam-5226	120	1	2	2	X
ejpam-5226	120	2	.	.	PUNCT
ejpam-5226	120	3	let	let	VERB
ejpam-5226	120	4	l	l	NOUN
ejpam-5226	120	5	=	=	PUNCT
ejpam-5226	120	6	{	{	PUNCT
ejpam-5226	120	7	0	0	NUM
ejpam-5226	120	8	,	,	PUNCT
ejpam-5226	120	9	a	a	DET
ejpam-5226	120	10	,	,	PUNCT
ejpam-5226	120	11	b	b	NOUN
ejpam-5226	120	12	,	,	PUNCT
ejpam-5226	120	13	1	1	NUM
ejpam-5226	120	14	}	}	PUNCT
ejpam-5226	120	15	,	,	PUNCT
ejpam-5226	120	16	whose	whose	DET
ejpam-5226	120	17	hasse	hasse	NOUN
ejpam-5226	120	18	diagram	diagram	NOUN
ejpam-5226	120	19	is	be	AUX
ejpam-5226	120	20	given	give	VERB
ejpam-5226	120	21	below	below	ADP
ejpam-5226	120	22	:	:	PUNCT
ejpam-5226	120	23	1	1	NUM
ejpam-5226	120	24	a	a	DET
ejpam-5226	120	25	0	0	NUM
ejpam-5226	120	26	b	b	NOUN
ejpam-5226	120	27	a.	a.	NOUN
ejpam-5226	120	28	iampan	iampan	NOUN
ejpam-5226	120	29	et	et	PROPN
ejpam-5226	120	30	al	al	PROPN
ejpam-5226	120	31	.	.	PUNCT
ejpam-5226	120	32	/	/	SYM
ejpam-5226	120	33	eur	eur	PROPN
ejpam-5226	120	34	.	.	PUNCT
ejpam-5226	121	1	j.	j.	PROPN
ejpam-5226	121	2	pure	pure	PROPN
ejpam-5226	121	3	appl	appl	PROPN
ejpam-5226	121	4	.	.	PROPN
ejpam-5226	121	5	math	math	PROPN
ejpam-5226	121	6	,	,	PUNCT
ejpam-5226	121	7	17	17	NUM
ejpam-5226	121	8	(	(	PUNCT
ejpam-5226	121	9	3	3	NUM
ejpam-5226	121	10	)	)	PUNCT
ejpam-5226	121	11	(	(	PUNCT
ejpam-5226	121	12	2024	2024	NUM
ejpam-5226	121	13	)	)	PUNCT
ejpam-5226	121	14	,	,	PUNCT
ejpam-5226	121	15	1691	1691	NUM
ejpam-5226	121	16	-	-	SYM
ejpam-5226	121	17	1704	1704	NUM
ejpam-5226	121	18	1695	1695	NUM
ejpam-5226	121	19	for	for	ADP
ejpam-5226	121	20	s1	s1	NOUN
ejpam-5226	121	21	=	=	PUNCT
ejpam-5226	121	22	{	{	PUNCT
ejpam-5226	121	23	a	a	DET
ejpam-5226	121	24	,	,	PUNCT
ejpam-5226	121	25	b	b	NOUN
ejpam-5226	121	26	}	}	PUNCT
ejpam-5226	121	27	and	and	CCONJ
ejpam-5226	121	28	s2	s2	VERB
ejpam-5226	121	29	=	=	PUNCT
ejpam-5226	121	30	{	{	PUNCT
ejpam-5226	121	31	a	a	DET
ejpam-5226	121	32	,	,	PUNCT
ejpam-5226	121	33	1	1	NUM
ejpam-5226	121	34	}	}	PUNCT
ejpam-5226	121	35	,	,	PUNCT
ejpam-5226	121	36	it	it	PRON
ejpam-5226	121	37	is	be	AUX
ejpam-5226	121	38	clearly	clearly	ADV
ejpam-5226	121	39	to	to	PART
ejpam-5226	121	40	observe	observe	VERB
ejpam-5226	121	41	that	that	DET
ejpam-5226	121	42	s1∩s2	s1∩s2	NOUN
ejpam-5226	121	43	=	=	SYM
ejpam-5226	121	44	{	{	PUNCT
ejpam-5226	121	45	a	a	NOUN
ejpam-5226	121	46	}	}	PUNCT
ejpam-5226	121	47	,	,	PUNCT
ejpam-5226	121	48	hs1	hs1	X
ejpam-5226	121	49	=	=	PUNCT
ejpam-5226	121	50	{	{	PUNCT
ejpam-5226	121	51	0	0	NUM
ejpam-5226	121	52	,	,	PUNCT
ejpam-5226	121	53	a	a	DET
ejpam-5226	121	54	,	,	PUNCT
ejpam-5226	121	55	b	b	NOUN
ejpam-5226	121	56	}	}	PUNCT
ejpam-5226	121	57	,	,	PUNCT
ejpam-5226	121	58	hs2	hs2	NOUN
ejpam-5226	121	59	=	=	SYM
ejpam-5226	121	60	{	{	PUNCT
ejpam-5226	121	61	0	0	NUM
ejpam-5226	121	62	,	,	PUNCT
ejpam-5226	121	63	a	a	DET
ejpam-5226	121	64	,	,	PUNCT
ejpam-5226	121	65	b	b	NOUN
ejpam-5226	121	66	,	,	PUNCT
ejpam-5226	121	67	1	1	NUM
ejpam-5226	121	68	}	}	PUNCT
ejpam-5226	121	69	,	,	PUNCT
ejpam-5226	121	70	hs1∩s2	hs1∩s2	PROPN
ejpam-5226	121	71	=	=	PUNCT
ejpam-5226	121	72	{	{	PUNCT
ejpam-5226	121	73	0	0	NUM
ejpam-5226	121	74	,	,	PUNCT
ejpam-5226	121	75	a	a	PRON
ejpam-5226	121	76	}	}	PUNCT
ejpam-5226	121	77	and	and	CCONJ
ejpam-5226	121	78	hs1∩hs2	hs1∩hs2	VERB
ejpam-5226	121	79	=	=	SYM
ejpam-5226	121	80	{	{	PUNCT
ejpam-5226	121	81	0	0	NUM
ejpam-5226	121	82	,	,	PUNCT
ejpam-5226	121	83	a	a	DET
ejpam-5226	121	84	,	,	PUNCT
ejpam-5226	121	85	b	b	NOUN
ejpam-5226	121	86	}	}	PUNCT
ejpam-5226	121	87	.	.	PUNCT
ejpam-5226	122	1	hence	hence	ADV
ejpam-5226	122	2	,	,	PUNCT
ejpam-5226	122	3	hs1∩s2	hs1∩s2	PROPN
ejpam-5226	122	4	̸=	̸=	PROPN
ejpam-5226	122	5	hs1∩hs2	hs1∩hs2	NOUN
ejpam-5226	122	6	.	.	PUNCT
ejpam-5226	123	1	theorem	theorem	NOUN
ejpam-5226	123	2	1	1	NUM
ejpam-5226	123	3	.	.	PUNCT
ejpam-5226	124	1	if	if	SCONJ
ejpam-5226	124	2	∅	∅	NOUN
ejpam-5226	124	3	=	=	NOUN
ejpam-5226	124	4	̸	̸	NUM
ejpam-5226	124	5	s	s	PART
ejpam-5226	124	6	⊆	⊆	NUM
ejpam-5226	124	7	l	l	NOUN
ejpam-5226	124	8	,	,	PUNCT
ejpam-5226	124	9	is	be	AUX
ejpam-5226	124	10	closed	close	VERB
ejpam-5226	124	11	under	under	ADP
ejpam-5226	124	12	∨	∨	NOUN
ejpam-5226	124	13	,	,	PUNCT
ejpam-5226	124	14	then	then	ADV
ejpam-5226	124	15	(	(	PUNCT
ejpam-5226	124	16	i	i	NOUN
ejpam-5226	124	17	)	)	PUNCT
ejpam-5226	124	18	hs	hs	PROPN
ejpam-5226	124	19	is	be	AUX
ejpam-5226	124	20	closed	close	VERB
ejpam-5226	124	21	under	under	ADP
ejpam-5226	124	22	∨	∨	NUM
ejpam-5226	124	23	,	,	PUNCT
ejpam-5226	124	24	(	(	PUNCT
ejpam-5226	124	25	ii	ii	NOUN
ejpam-5226	124	26	)	)	PUNCT
ejpam-5226	124	27	hs	hs	PROPN
ejpam-5226	124	28	is	be	AUX
ejpam-5226	124	29	a	a	DET
ejpam-5226	124	30	sub	sub	ADJ
ejpam-5226	124	31	-	-	ADJ
ejpam-5226	124	32	almost	almost	ADV
ejpam-5226	124	33	distributive	distributive	ADJ
ejpam-5226	124	34	lattice	lattice	NOUN
ejpam-5226	124	35	of	of	ADP
ejpam-5226	124	36	l	l	NOUN
ejpam-5226	124	37	,	,	PUNCT
ejpam-5226	124	38	(	(	PUNCT
ejpam-5226	124	39	iii	iii	X
ejpam-5226	124	40	)	)	PUNCT
ejpam-5226	124	41	hs	hs	PROPN
ejpam-5226	124	42	is	be	AUX
ejpam-5226	124	43	an	an	DET
ejpam-5226	124	44	ideal	ideal	NOUN
ejpam-5226	124	45	of	of	ADP
ejpam-5226	124	46	l	l	NOUN
ejpam-5226	124	47	,	,	PUNCT
ejpam-5226	124	48	(	(	PUNCT
ejpam-5226	124	49	iv	iv	X
ejpam-5226	124	50	)	)	PUNCT
ejpam-5226	124	51	hs	hs	PROPN
ejpam-5226	124	52	is	be	AUX
ejpam-5226	124	53	the	the	DET
ejpam-5226	124	54	smallest	small	ADJ
ejpam-5226	124	55	ideal	ideal	NOUN
ejpam-5226	124	56	generated	generate	VERB
ejpam-5226	124	57	by	by	ADP
ejpam-5226	124	58	s(hs	s(hs	PROPN
ejpam-5226	124	59	=	=	SYM
ejpam-5226	124	60	(	(	PUNCT
ejpam-5226	124	61	s	s	PROPN
ejpam-5226	124	62	]	]	X
ejpam-5226	124	63	)	)	PUNCT
ejpam-5226	124	64	.	.	PUNCT
ejpam-5226	125	1	proof	proof	NOUN
ejpam-5226	125	2	.	.	PUNCT
ejpam-5226	126	1	suppose	suppose	VERB
ejpam-5226	126	2	that	that	SCONJ
ejpam-5226	126	3	s	s	VERB
ejpam-5226	126	4	is	be	AUX
ejpam-5226	126	5	closed	close	VERB
ejpam-5226	126	6	under	under	ADP
ejpam-5226	126	7	∨.	∨.	NOUN
ejpam-5226	126	8	(	(	PUNCT
ejpam-5226	126	9	i	i	NOUN
ejpam-5226	126	10	)	)	PUNCT
ejpam-5226	126	11	let	let	VERB
ejpam-5226	126	12	h1	h1	PROPN
ejpam-5226	126	13	,	,	PUNCT
ejpam-5226	126	14	h2	h2	PROPN
ejpam-5226	126	15	∈	∈	PROPN
ejpam-5226	127	1	hs	hs	PROPN
ejpam-5226	127	2	.	.	PUNCT
ejpam-5226	128	1	then	then	ADV
ejpam-5226	128	2	there	there	PRON
ejpam-5226	128	3	exist	exist	VERB
ejpam-5226	128	4	s1	s1	NOUN
ejpam-5226	128	5	,	,	PUNCT
ejpam-5226	128	6	s2	s2	NOUN
ejpam-5226	128	7	∈	∈	PROPN
ejpam-5226	128	8	s	s	VERB
ejpam-5226	128	9	such	such	ADJ
ejpam-5226	128	10	that	that	SCONJ
ejpam-5226	128	11	s1∧h1	s1∧h1	PROPN
ejpam-5226	128	12	=	=	PUNCT
ejpam-5226	128	13	h1	h1	NOUN
ejpam-5226	128	14	and	and	CCONJ
ejpam-5226	128	15	s2∧h2	s2∧h2	PROPN
ejpam-5226	128	16	=	=	PUNCT
ejpam-5226	128	17	h2	h2	PROPN
ejpam-5226	128	18	.	.	PUNCT
ejpam-5226	129	1	now	now	ADV
ejpam-5226	129	2	,	,	PUNCT
ejpam-5226	129	3	(	(	PUNCT
ejpam-5226	129	4	s1	s1	PROPN
ejpam-5226	129	5	∨	∨	NUM
ejpam-5226	129	6	s2	s2	PROPN
ejpam-5226	129	7	)	)	PUNCT
ejpam-5226	129	8	∧	∧	PROPN
ejpam-5226	129	9	(	(	PUNCT
ejpam-5226	129	10	h1	h1	PROPN
ejpam-5226	129	11	∨	∨	NUM
ejpam-5226	129	12	h2	h2	NOUN
ejpam-5226	129	13	)	)	PUNCT
ejpam-5226	129	14	=	=	PUNCT
ejpam-5226	129	15	(	(	PUNCT
ejpam-5226	129	16	s2	s2	PROPN
ejpam-5226	129	17	∨	∨	NUM
ejpam-5226	129	18	s1	s1	NOUN
ejpam-5226	129	19	)	)	PUNCT
ejpam-5226	129	20	∧	∧	PROPN
ejpam-5226	129	21	(	(	PUNCT
ejpam-5226	129	22	h1	h1	PROPN
ejpam-5226	129	23	∨	∨	NUM
ejpam-5226	129	24	h2	h2	NOUN
ejpam-5226	129	25	)	)	PUNCT
ejpam-5226	129	26	=	=	PUNCT
ejpam-5226	130	1	[	[	X
ejpam-5226	130	2	(	(	PUNCT
ejpam-5226	130	3	s2	s2	PROPN
ejpam-5226	130	4	∨	∨	NUM
ejpam-5226	130	5	s1	s1	NOUN
ejpam-5226	130	6	)	)	PUNCT
ejpam-5226	130	7	∧	∧	PROPN
ejpam-5226	130	8	h1	h1	PROPN
ejpam-5226	130	9	]	]	X
ejpam-5226	130	10	∨	∨	PROPN
ejpam-5226	130	11	[	[	X
ejpam-5226	130	12	(	(	PUNCT
ejpam-5226	130	13	s2	s2	PROPN
ejpam-5226	130	14	∨	∨	NUM
ejpam-5226	130	15	s1	s1	NOUN
ejpam-5226	130	16	)	)	PUNCT
ejpam-5226	130	17	∧	∧	PROPN
ejpam-5226	130	18	h2	h2	NOUN
ejpam-5226	130	19	)	)	PUNCT
ejpam-5226	130	20	]	]	PUNCT
ejpam-5226	131	1	=	=	PUNCT
ejpam-5226	132	1	[	[	X
ejpam-5226	132	2	(	(	PUNCT
ejpam-5226	132	3	s2	s2	PROPN
ejpam-5226	132	4	∨	∨	NUM
ejpam-5226	132	5	s1	s1	NOUN
ejpam-5226	132	6	)	)	PUNCT
ejpam-5226	132	7	∧	∧	PROPN
ejpam-5226	132	8	h1	h1	PROPN
ejpam-5226	132	9	]	]	X
ejpam-5226	132	10	∨	∨	PROPN
ejpam-5226	132	11	[	[	X
ejpam-5226	132	12	(	(	PUNCT
ejpam-5226	132	13	s1	s1	PROPN
ejpam-5226	132	14	∨	∨	NUM
ejpam-5226	132	15	s2	s2	PROPN
ejpam-5226	132	16	)	)	PUNCT
ejpam-5226	132	17	∧	∧	PROPN
ejpam-5226	132	18	h2	h2	NOUN
ejpam-5226	132	19	)	)	PUNCT
ejpam-5226	132	20	]	]	PUNCT
ejpam-5226	133	1	=	=	PUNCT
ejpam-5226	134	1	[	[	X
ejpam-5226	134	2	(	(	PUNCT
ejpam-5226	134	3	s2	s2	NOUN
ejpam-5226	134	4	∧	∧	PROPN
ejpam-5226	134	5	h1	h1	PROPN
ejpam-5226	134	6	)	)	PUNCT
ejpam-5226	134	7	∨	∨	PROPN
ejpam-5226	134	8	(	(	PUNCT
ejpam-5226	134	9	s1	s1	PROPN
ejpam-5226	134	10	∧	∧	PROPN
ejpam-5226	134	11	h1	h1	PROPN
ejpam-5226	134	12	]	]	X
ejpam-5226	134	13	∨	∨	PROPN
ejpam-5226	134	14	[	[	X
ejpam-5226	134	15	(	(	PUNCT
ejpam-5226	134	16	s1	s1	PROPN
ejpam-5226	134	17	∧	∧	PROPN
ejpam-5226	134	18	h2	h2	PROPN
ejpam-5226	134	19	)	)	PUNCT
ejpam-5226	134	20	∨	∨	NUM
ejpam-5226	134	21	(	(	PUNCT
ejpam-5226	134	22	s2	s2	NOUN
ejpam-5226	134	23	∧	∧	PROPN
ejpam-5226	134	24	h2	h2	NOUN
ejpam-5226	134	25	)	)	PUNCT
ejpam-5226	134	26	]	]	PUNCT
ejpam-5226	135	1	=	=	PUNCT
ejpam-5226	136	1	[	[	X
ejpam-5226	136	2	(	(	PUNCT
ejpam-5226	136	3	s2∧h1)∨h1]∨	s2∧h1)∨h1]∨	ADJ
ejpam-5226	136	4	[	[	X
ejpam-5226	136	5	(	(	PUNCT
ejpam-5226	136	6	s1∧h2)∨h2	s1∧h2)∨h2	X
ejpam-5226	136	7	]	]	X
ejpam-5226	136	8	=	=	PUNCT
ejpam-5226	136	9	h1∨h2	h1∨h2	NOUN
ejpam-5226	136	10	.	.	PUNCT
ejpam-5226	137	1	since	since	SCONJ
ejpam-5226	137	2	s	s	NOUN
ejpam-5226	137	3	is	be	AUX
ejpam-5226	137	4	closed	close	VERB
ejpam-5226	137	5	under	under	ADP
ejpam-5226	137	6	∨	∨	NUM
ejpam-5226	137	7	,	,	PUNCT
ejpam-5226	137	8	h1∨h2	h1∨h2	PROPN
ejpam-5226	137	9	∈	∈	PROPN
ejpam-5226	137	10	hs	hs	PROPN
ejpam-5226	137	11	.	.	PUNCT
ejpam-5226	138	1	hence	hence	ADV
ejpam-5226	138	2	,	,	PUNCT
ejpam-5226	138	3	hs	hs	PROPN
ejpam-5226	138	4	is	be	AUX
ejpam-5226	138	5	closed	close	VERB
ejpam-5226	138	6	under	under	ADP
ejpam-5226	138	7	∨.	∨.	NOUN
ejpam-5226	138	8	(	(	PUNCT
ejpam-5226	138	9	ii	ii	NOUN
ejpam-5226	138	10	)	)	PUNCT
ejpam-5226	138	11	by	by	ADP
ejpam-5226	138	12	proposition	proposition	NOUN
ejpam-5226	138	13	1(ii	1(ii	NUM
ejpam-5226	138	14	)	)	PUNCT
ejpam-5226	138	15	and	and	CCONJ
ejpam-5226	138	16	definition	definition	NOUN
ejpam-5226	138	17	1	1	NUM
ejpam-5226	138	18	,	,	PUNCT
ejpam-5226	138	19	we	we	PRON
ejpam-5226	138	20	can	can	AUX
ejpam-5226	138	21	clearly	clearly	ADV
ejpam-5226	138	22	observe	observe	VERB
ejpam-5226	138	23	that	that	SCONJ
ejpam-5226	138	24	the	the	DET
ejpam-5226	138	25	set	set	NOUN
ejpam-5226	138	26	hs	hs	PROPN
ejpam-5226	138	27	is	be	AUX
ejpam-5226	138	28	a	a	DET
ejpam-5226	138	29	sub	sub	ADJ
ejpam-5226	138	30	-	-	ADJ
ejpam-5226	138	31	almost	almost	ADV
ejpam-5226	138	32	distributive	distributive	ADJ
ejpam-5226	138	33	lattice	lattice	NOUN
ejpam-5226	138	34	of	of	ADP
ejpam-5226	138	35	l.	l.	PROPN
ejpam-5226	138	36	(	(	PUNCT
ejpam-5226	138	37	iii	iii	NOUN
ejpam-5226	138	38	)	)	PUNCT
ejpam-5226	138	39	let	let	VERB
ejpam-5226	138	40	l	l	NOUN
ejpam-5226	138	41	∈	∈	PROPN
ejpam-5226	138	42	l	l	NOUN
ejpam-5226	138	43	and	and	CCONJ
ejpam-5226	138	44	h	h	NOUN
ejpam-5226	138	45	∈	∈	PROPN
ejpam-5226	139	1	hs	hs	INTJ
ejpam-5226	139	2	.	.	PUNCT
ejpam-5226	140	1	then	then	ADV
ejpam-5226	140	2	s∧h	s∧h	PROPN
ejpam-5226	140	3	=	=	ADJ
ejpam-5226	140	4	h	h	PROPN
ejpam-5226	140	5	for	for	ADP
ejpam-5226	140	6	some	some	DET
ejpam-5226	140	7	s	s	NOUN
ejpam-5226	140	8	∈	∈	PROPN
ejpam-5226	140	9	s.	s.	PROPN
ejpam-5226	140	10	now	now	ADV
ejpam-5226	140	11	,	,	PUNCT
ejpam-5226	140	12	s∧(h∧l	s∧(h∧l	PROPN
ejpam-5226	140	13	)	)	PUNCT
ejpam-5226	140	14	=	=	SYM
ejpam-5226	140	15	(	(	PUNCT
ejpam-5226	140	16	s∧h)∧l	s∧h)∧l	NOUN
ejpam-5226	140	17	=	=	PUNCT
ejpam-5226	140	18	h∧	h∧	NOUN
ejpam-5226	140	19	l	l	NOUN
ejpam-5226	140	20	and	and	CCONJ
ejpam-5226	140	21	s∧	s∧	PROPN
ejpam-5226	140	22	(	(	PUNCT
ejpam-5226	140	23	l	l	NOUN
ejpam-5226	140	24	∧	∧	PROPN
ejpam-5226	140	25	h	h	NOUN
ejpam-5226	140	26	)	)	PUNCT
ejpam-5226	140	27	=	=	PUNCT
ejpam-5226	141	1	(	(	PUNCT
ejpam-5226	141	2	s∧	s∧	VERB
ejpam-5226	141	3	l)∧	l)∧	PROPN
ejpam-5226	141	4	h	h	NOUN
ejpam-5226	141	5	=	=	PUNCT
ejpam-5226	141	6	l	l	NOUN
ejpam-5226	141	7	∧	∧	PROPN
ejpam-5226	141	8	(	(	PUNCT
ejpam-5226	141	9	s∧	s∧	PROPN
ejpam-5226	141	10	h	h	NOUN
ejpam-5226	141	11	)	)	PUNCT
ejpam-5226	141	12	=	=	PUNCT
ejpam-5226	141	13	l	l	NOUN
ejpam-5226	141	14	∧	∧	PROPN
ejpam-5226	141	15	h.	h.	PROPN
ejpam-5226	141	16	therefore	therefore	ADV
ejpam-5226	141	17	,	,	PUNCT
ejpam-5226	141	18	h∧	h∧	PROPN
ejpam-5226	141	19	l	l	NOUN
ejpam-5226	141	20	,	,	PUNCT
ejpam-5226	141	21	l	l	NOUN
ejpam-5226	141	22	∧	∧	PROPN
ejpam-5226	141	23	h	h	NOUN
ejpam-5226	141	24	∈	∈	PROPN
ejpam-5226	141	25	hs	hs	PROPN
ejpam-5226	141	26	.	.	PUNCT
ejpam-5226	142	1	hence	hence	ADV
ejpam-5226	142	2	,	,	PUNCT
ejpam-5226	142	3	hs	hs	PROPN
ejpam-5226	142	4	is	be	AUX
ejpam-5226	142	5	an	an	DET
ejpam-5226	142	6	ideal	ideal	NOUN
ejpam-5226	142	7	of	of	ADP
ejpam-5226	142	8	l	l	NOUN
ejpam-5226	142	9	(	(	PUNCT
ejpam-5226	142	10	since	since	SCONJ
ejpam-5226	142	11	hs	hs	PROPN
ejpam-5226	142	12	is	be	AUX
ejpam-5226	142	13	a	a	DET
ejpam-5226	142	14	sub	sub	ADJ
ejpam-5226	142	15	-	-	ADJ
ejpam-5226	142	16	almost	almost	ADV
ejpam-5226	142	17	distributive	distributive	ADJ
ejpam-5226	142	18	lattice	lattice	NOUN
ejpam-5226	142	19	of	of	ADP
ejpam-5226	142	20	l	l	NOUN
ejpam-5226	142	21	)	)	PUNCT
ejpam-5226	142	22	.	.	PUNCT
ejpam-5226	143	1	(	(	PUNCT
ejpam-5226	143	2	iv	iv	X
ejpam-5226	143	3	)	)	PUNCT
ejpam-5226	143	4	since	since	SCONJ
ejpam-5226	143	5	s	s	NOUN
ejpam-5226	143	6	⊆	⊆	NUM
ejpam-5226	143	7	hs	hs	PROPN
ejpam-5226	143	8	and	and	CCONJ
ejpam-5226	143	9	hs	hs	PROPN
ejpam-5226	143	10	is	be	AUX
ejpam-5226	143	11	an	an	DET
ejpam-5226	143	12	ideal	ideal	NOUN
ejpam-5226	143	13	of	of	ADP
ejpam-5226	143	14	l	l	NOUN
ejpam-5226	143	15	,	,	PUNCT
ejpam-5226	143	16	(	(	PUNCT
ejpam-5226	143	17	s	s	X
ejpam-5226	143	18	]	]	X
ejpam-5226	143	19	⊆	⊆	NUM
ejpam-5226	143	20	hs	hs	INTJ
ejpam-5226	143	21	.	.	PUNCT
ejpam-5226	144	1	let	let	VERB
ejpam-5226	144	2	h	h	PRON
ejpam-5226	144	3	∈	∈	PROPN
ejpam-5226	145	1	hs	hs	PROPN
ejpam-5226	145	2	.	.	PUNCT
ejpam-5226	146	1	then	then	ADV
ejpam-5226	146	2	s∧	s∧	PROPN
ejpam-5226	146	3	h	h	NOUN
ejpam-5226	147	1	=	=	NOUN
ejpam-5226	147	2	h	h	PROPN
ejpam-5226	147	3	for	for	ADP
ejpam-5226	147	4	some	some	DET
ejpam-5226	147	5	s	s	NOUN
ejpam-5226	147	6	∈	∈	PROPN
ejpam-5226	147	7	s.	s.	PROPN
ejpam-5226	147	8	therefore	therefore	ADV
ejpam-5226	147	9	,	,	PUNCT
ejpam-5226	147	10	h	h	NOUN
ejpam-5226	148	1	=	=	SYM
ejpam-5226	148	2	s	s	PART
ejpam-5226	148	3	∧	∧	PROPN
ejpam-5226	148	4	h	h	NOUN
ejpam-5226	148	5	∈	∈	PROPN
ejpam-5226	148	6	(	(	PUNCT
ejpam-5226	148	7	s	s	NOUN
ejpam-5226	148	8	]	]	X
ejpam-5226	148	9	.	.	PUNCT
ejpam-5226	149	1	hence	hence	ADV
ejpam-5226	149	2	,	,	PUNCT
ejpam-5226	149	3	hs	hs	PROPN
ejpam-5226	149	4	⊆	⊆	NUM
ejpam-5226	149	5	(	(	PUNCT
ejpam-5226	149	6	s	s	X
ejpam-5226	149	7	]	]	X
ejpam-5226	149	8	.	.	PUNCT
ejpam-5226	150	1	thus	thus	ADV
ejpam-5226	150	2	,	,	PUNCT
ejpam-5226	150	3	hs	hs	PROPN
ejpam-5226	150	4	=	=	PUNCT
ejpam-5226	150	5	(	(	PUNCT
ejpam-5226	150	6	s	s	X
ejpam-5226	150	7	]	]	PUNCT
ejpam-5226	150	8	.	.	PUNCT
ejpam-5226	151	1	let	let	VERB
ejpam-5226	151	2	us	we	PRON
ejpam-5226	151	3	denote	denote	VERB
ejpam-5226	151	4	s1	s1	PROPN
ejpam-5226	151	5	∧	∧	PROPN
ejpam-5226	151	6	s2	s2	NOUN
ejpam-5226	151	7	=	=	SYM
ejpam-5226	151	8	{	{	PUNCT
ejpam-5226	152	1	s1	s1	NOUN
ejpam-5226	152	2	∧	∧	PROPN
ejpam-5226	152	3	s2	s2	NOUN
ejpam-5226	152	4	∈	∈	PROPN
ejpam-5226	152	5	l	l	NOUN
ejpam-5226	153	1	|	|	NOUN
ejpam-5226	153	2	s1	s1	PROPN
ejpam-5226	153	3	∈	∈	PROPN
ejpam-5226	153	4	s1	s1	PROPN
ejpam-5226	153	5	and	and	CCONJ
ejpam-5226	153	6	s2	s2	PROPN
ejpam-5226	153	7	∈	∈	PROPN
ejpam-5226	153	8	s2	s2	PROPN
ejpam-5226	153	9	}	}	PUNCT
ejpam-5226	153	10	,	,	PUNCT
ejpam-5226	153	11	where	where	SCONJ
ejpam-5226	153	12	s1	s1	NOUN
ejpam-5226	153	13	and	and	CCONJ
ejpam-5226	153	14	s2	s2	PROPN
ejpam-5226	153	15	are	be	AUX
ejpam-5226	153	16	two	two	NUM
ejpam-5226	153	17	non	non	ADJ
ejpam-5226	153	18	-	-	ADJ
ejpam-5226	153	19	empty	empty	ADJ
ejpam-5226	153	20	subsets	subset	NOUN
ejpam-5226	153	21	of	of	ADP
ejpam-5226	153	22	l.	l.	PROPN
ejpam-5226	153	23	proposition	proposition	PROPN
ejpam-5226	153	24	4	4	NUM
ejpam-5226	153	25	.	.	X
ejpam-5226	154	1	for	for	ADP
ejpam-5226	154	2	any	any	DET
ejpam-5226	154	3	∅	∅	NOUN
ejpam-5226	154	4	=	=	NOUN
ejpam-5226	154	5	̸	̸	NUM
ejpam-5226	154	6	s1	s1	NOUN
ejpam-5226	154	7	,	,	PUNCT
ejpam-5226	154	8	s2	s2	PROPN
ejpam-5226	154	9	,	,	PUNCT
ejpam-5226	154	10	s3	s3	PROPN
ejpam-5226	154	11	⊆	⊆	NUM
ejpam-5226	154	12	l	l	NOUN
ejpam-5226	154	13	,	,	PUNCT
ejpam-5226	154	14	we	we	PRON
ejpam-5226	154	15	have	have	VERB
ejpam-5226	154	16	(	(	PUNCT
ejpam-5226	154	17	i	i	NOUN
ejpam-5226	154	18	)	)	PUNCT
ejpam-5226	154	19	s1	s1	PROPN
ejpam-5226	154	20	∧	∧	PROPN
ejpam-5226	154	21	s2	s2	NOUN
ejpam-5226	154	22	̸=	̸=	PROPN
ejpam-5226	154	23	∅	∅	NOUN
ejpam-5226	154	24	,	,	PUNCT
ejpam-5226	154	25	(	(	PUNCT
ejpam-5226	154	26	ii	ii	NOUN
ejpam-5226	154	27	)	)	PUNCT
ejpam-5226	154	28	s1	s1	NOUN
ejpam-5226	154	29	⊆	⊆	NUM
ejpam-5226	154	30	s1	s1	NOUN
ejpam-5226	154	31	∧	∧	PROPN
ejpam-5226	154	32	s1	s1	PROPN
ejpam-5226	154	33	,	,	PUNCT
ejpam-5226	154	34	(	(	PUNCT
ejpam-5226	154	35	iii	iii	NOUN
ejpam-5226	154	36	)	)	PUNCT
ejpam-5226	154	37	(	(	PUNCT
ejpam-5226	154	38	s1	s1	PROPN
ejpam-5226	154	39	∧	∧	PROPN
ejpam-5226	154	40	s2	s2	PROPN
ejpam-5226	154	41	)	)	PUNCT
ejpam-5226	154	42	∧	∧	PROPN
ejpam-5226	154	43	s3	s3	NOUN
ejpam-5226	154	44	=	=	PROPN
ejpam-5226	154	45	s1	s1	PROPN
ejpam-5226	154	46	∧	∧	PROPN
ejpam-5226	154	47	(	(	PUNCT
ejpam-5226	154	48	s2	s2	NOUN
ejpam-5226	154	49	∧	∧	PROPN
ejpam-5226	154	50	s3	s3	PROPN
ejpam-5226	154	51	)	)	PUNCT
ejpam-5226	154	52	.	.	PUNCT
ejpam-5226	155	1	proof	proof	NOUN
ejpam-5226	155	2	.	.	PUNCT
ejpam-5226	156	1	(	(	PUNCT
ejpam-5226	156	2	i	i	NOUN
ejpam-5226	156	3	)	)	PUNCT
ejpam-5226	156	4	for	for	ADP
ejpam-5226	156	5	any	any	DET
ejpam-5226	156	6	s1	s1	PROPN
ejpam-5226	156	7	∈	∈	PROPN
ejpam-5226	156	8	s1	s1	NOUN
ejpam-5226	156	9	and	and	CCONJ
ejpam-5226	156	10	s2	s2	PROPN
ejpam-5226	156	11	∈	∈	PROPN
ejpam-5226	156	12	s2	s2	PROPN
ejpam-5226	156	13	,	,	PUNCT
ejpam-5226	156	14	we	we	PRON
ejpam-5226	156	15	have	have	VERB
ejpam-5226	156	16	s1∧s2	s1∧s2	PROPN
ejpam-5226	156	17	∈	∈	PROPN
ejpam-5226	156	18	l.	l.	NOUN
ejpam-5226	156	19	therefore	therefore	ADV
ejpam-5226	156	20	,	,	PUNCT
ejpam-5226	156	21	s1∧s2	s1∧s2	PROPN
ejpam-5226	156	22	∈	∈	PROPN
ejpam-5226	156	23	s1	s1	NOUN
ejpam-5226	156	24	∧	∧	PROPN
ejpam-5226	156	25	s2	s2	PROPN
ejpam-5226	156	26	.	.	PUNCT
ejpam-5226	157	1	hence	hence	ADV
ejpam-5226	157	2	,	,	PUNCT
ejpam-5226	157	3	s1	s1	PROPN
ejpam-5226	157	4	∧	∧	PROPN
ejpam-5226	157	5	s2	s2	NOUN
ejpam-5226	157	6	̸=	̸=	PROPN
ejpam-5226	157	7	∅.	∅.	ADP
ejpam-5226	157	8	(	(	PUNCT
ejpam-5226	157	9	ii	ii	NOUN
ejpam-5226	157	10	)	)	PUNCT
ejpam-5226	157	11	for	for	ADP
ejpam-5226	157	12	any	any	DET
ejpam-5226	157	13	s1	s1	PROPN
ejpam-5226	157	14	∈	∈	PROPN
ejpam-5226	157	15	s1	s1	NOUN
ejpam-5226	157	16	,	,	PUNCT
ejpam-5226	157	17	s1	s1	NOUN
ejpam-5226	157	18	=	=	SYM
ejpam-5226	157	19	s1	s1	PROPN
ejpam-5226	157	20	∧	∧	PROPN
ejpam-5226	157	21	s1	s1	PROPN
ejpam-5226	157	22	∈	∈	PROPN
ejpam-5226	157	23	s1	s1	NOUN
ejpam-5226	157	24	∧	∧	PROPN
ejpam-5226	157	25	s1	s1	PROPN
ejpam-5226	157	26	.	.	PUNCT
ejpam-5226	158	1	therefore	therefore	ADV
ejpam-5226	158	2	,	,	PUNCT
ejpam-5226	158	3	s1	s1	PROPN
ejpam-5226	158	4	⊆	⊆	NUM
ejpam-5226	158	5	s1	s1	NOUN
ejpam-5226	158	6	∧	∧	PROPN
ejpam-5226	158	7	s1	s1	PROPN
ejpam-5226	158	8	.	.	PUNCT
ejpam-5226	159	1	(	(	PUNCT
ejpam-5226	159	2	iii	iii	X
ejpam-5226	159	3	)	)	PUNCT
ejpam-5226	159	4	let	let	VERB
ejpam-5226	159	5	s	s	PRON
ejpam-5226	159	6	∈	∈	PROPN
ejpam-5226	159	7	(	(	PUNCT
ejpam-5226	159	8	s1	s1	PROPN
ejpam-5226	159	9	∧	∧	PROPN
ejpam-5226	159	10	s2	s2	PROPN
ejpam-5226	159	11	)	)	PUNCT
ejpam-5226	159	12	∧	∧	PROPN
ejpam-5226	159	13	s3	s3	PROPN
ejpam-5226	159	14	.	.	PUNCT
ejpam-5226	160	1	then	then	ADV
ejpam-5226	160	2	s	s	VERB
ejpam-5226	160	3	=	=	PUNCT
ejpam-5226	160	4	(	(	PUNCT
ejpam-5226	160	5	s1	s1	PROPN
ejpam-5226	160	6	∧	∧	PROPN
ejpam-5226	160	7	s2	s2	PROPN
ejpam-5226	160	8	)	)	PUNCT
ejpam-5226	160	9	∧	∧	PROPN
ejpam-5226	160	10	s3	s3	PROPN
ejpam-5226	160	11	for	for	ADP
ejpam-5226	160	12	some	some	DET
ejpam-5226	160	13	s1	s1	PROPN
ejpam-5226	160	14	∈	∈	PROPN
ejpam-5226	160	15	s1	s1	NOUN
ejpam-5226	160	16	,	,	PUNCT
ejpam-5226	160	17	s2	s2	PROPN
ejpam-5226	160	18	∈	∈	PROPN
ejpam-5226	160	19	s2	s2	PROPN
ejpam-5226	160	20	,	,	PUNCT
ejpam-5226	160	21	s3	s3	PROPN
ejpam-5226	160	22	∈	∈	PROPN
ejpam-5226	160	23	s3	s3	PROPN
ejpam-5226	160	24	.	.	PUNCT
ejpam-5226	161	1	since	since	SCONJ
ejpam-5226	161	2	l	l	NOUN
ejpam-5226	161	3	is	be	AUX
ejpam-5226	161	4	∧-associative	∧-associative	ADJ
ejpam-5226	161	5	,	,	PUNCT
ejpam-5226	161	6	s	s	PART
ejpam-5226	161	7	=	=	SYM
ejpam-5226	161	8	s1	s1	PROPN
ejpam-5226	161	9	∧	∧	PROPN
ejpam-5226	161	10	(	(	PUNCT
ejpam-5226	161	11	s2	s2	NOUN
ejpam-5226	161	12	∧	∧	PROPN
ejpam-5226	161	13	s3	s3	PROPN
ejpam-5226	161	14	)	)	PUNCT
ejpam-5226	161	15	.	.	PUNCT
ejpam-5226	162	1	therefore	therefore	ADV
ejpam-5226	162	2	,	,	PUNCT
ejpam-5226	162	3	s	s	NOUN
ejpam-5226	162	4	∈	∈	PROPN
ejpam-5226	162	5	s1	s1	NOUN
ejpam-5226	162	6	∧	∧	PROPN
ejpam-5226	162	7	(	(	PUNCT
ejpam-5226	162	8	s2	s2	NOUN
ejpam-5226	162	9	∧	∧	PROPN
ejpam-5226	162	10	s3	s3	PROPN
ejpam-5226	162	11	)	)	PUNCT
ejpam-5226	162	12	.	.	PUNCT
ejpam-5226	163	1	hence	hence	ADV
ejpam-5226	163	2	,	,	PUNCT
ejpam-5226	163	3	(	(	PUNCT
ejpam-5226	163	4	s1	s1	PROPN
ejpam-5226	163	5	∧	∧	PROPN
ejpam-5226	163	6	s2	s2	PROPN
ejpam-5226	163	7	)	)	PUNCT
ejpam-5226	163	8	∧	∧	PROPN
ejpam-5226	163	9	s3	s3	PROPN
ejpam-5226	163	10	⊆	⊆	NUM
ejpam-5226	163	11	s1	s1	PROPN
ejpam-5226	163	12	∧	∧	PROPN
ejpam-5226	163	13	(	(	PUNCT
ejpam-5226	163	14	s2	s2	NOUN
ejpam-5226	163	15	∧	∧	PROPN
ejpam-5226	163	16	s3	s3	PROPN
ejpam-5226	163	17	)	)	PUNCT
ejpam-5226	163	18	.	.	PUNCT
ejpam-5226	164	1	similarly	similarly	ADV
ejpam-5226	164	2	,	,	PUNCT
ejpam-5226	164	3	we	we	PRON
ejpam-5226	164	4	can	can	AUX
ejpam-5226	164	5	prove	prove	VERB
ejpam-5226	164	6	the	the	DET
ejpam-5226	164	7	converse	converse	NOUN
ejpam-5226	164	8	.	.	PUNCT
ejpam-5226	165	1	thus	thus	ADV
ejpam-5226	165	2	,	,	PUNCT
ejpam-5226	165	3	(	(	PUNCT
ejpam-5226	165	4	s1	s1	PROPN
ejpam-5226	165	5	∧	∧	PROPN
ejpam-5226	165	6	s2)∧	s2)∧	NOUN
ejpam-5226	165	7	s3	s3	NOUN
ejpam-5226	165	8	=	=	PROPN
ejpam-5226	165	9	s1	s1	PROPN
ejpam-5226	165	10	∧	∧	PROPN
ejpam-5226	165	11	(	(	PUNCT
ejpam-5226	165	12	s2	s2	NOUN
ejpam-5226	165	13	∧	∧	PROPN
ejpam-5226	165	14	s3	s3	PROPN
ejpam-5226	165	15	)	)	PUNCT
ejpam-5226	165	16	.	.	PUNCT
ejpam-5226	166	1	remark	remark	PROPN
ejpam-5226	166	2	4	4	NUM
ejpam-5226	166	3	.	.	PUNCT
ejpam-5226	167	1	for	for	ADP
ejpam-5226	167	2	any	any	DET
ejpam-5226	167	3	∅	∅	NOUN
ejpam-5226	167	4	=	=	NOUN
ejpam-5226	167	5	̸	̸	NUM
ejpam-5226	167	6	s	s	PART
ejpam-5226	167	7	⊆	⊆	NUM
ejpam-5226	167	8	l	l	NOUN
ejpam-5226	167	9	,	,	PUNCT
ejpam-5226	167	10	s	s	NOUN
ejpam-5226	167	11	need	need	AUX
ejpam-5226	167	12	not	not	PART
ejpam-5226	167	13	be	be	AUX
ejpam-5226	167	14	idempotent	idempotent	ADJ
ejpam-5226	167	15	under	under	ADP
ejpam-5226	167	16	the	the	DET
ejpam-5226	167	17	operation	operation	NOUN
ejpam-5226	167	18	∧	∧	PROPN
ejpam-5226	167	19	.	.	PUNCT
ejpam-5226	168	1	in	in	ADP
ejpam-5226	168	2	example	example	NOUN
ejpam-5226	168	3	1	1	NUM
ejpam-5226	168	4	,	,	PUNCT
ejpam-5226	168	5	s1	s1	PROPN
ejpam-5226	168	6	̸=	̸=	PROPN
ejpam-5226	168	7	s1	s1	PROPN
ejpam-5226	168	8	∧	∧	PROPN
ejpam-5226	168	9	s1	s1	PROPN
ejpam-5226	168	10	(	(	PUNCT
ejpam-5226	168	11	assume	assume	VERB
ejpam-5226	168	12	s1	s1	NOUN
ejpam-5226	168	13	=	=	PUNCT
ejpam-5226	168	14	{	{	PUNCT
ejpam-5226	168	15	a	a	DET
ejpam-5226	168	16	,	,	PUNCT
ejpam-5226	168	17	b	b	NOUN
ejpam-5226	168	18	}	}	PUNCT
ejpam-5226	168	19	)	)	PUNCT
ejpam-5226	168	20	.	.	PUNCT
ejpam-5226	169	1	a.	a.	PROPN
ejpam-5226	169	2	iampan	iampan	PROPN
ejpam-5226	169	3	et	et	PROPN
ejpam-5226	169	4	al	al	PROPN
ejpam-5226	169	5	.	.	PUNCT
ejpam-5226	169	6	/	/	SYM
ejpam-5226	169	7	eur	eur	PROPN
ejpam-5226	169	8	.	.	PUNCT
ejpam-5226	170	1	j.	j.	PROPN
ejpam-5226	170	2	pure	pure	PROPN
ejpam-5226	170	3	appl	appl	PROPN
ejpam-5226	170	4	.	.	PROPN
ejpam-5226	170	5	math	math	PROPN
ejpam-5226	170	6	,	,	PUNCT
ejpam-5226	170	7	17	17	NUM
ejpam-5226	170	8	(	(	PUNCT
ejpam-5226	170	9	3	3	NUM
ejpam-5226	170	10	)	)	PUNCT
ejpam-5226	170	11	(	(	PUNCT
ejpam-5226	170	12	2024	2024	NUM
ejpam-5226	170	13	)	)	PUNCT
ejpam-5226	170	14	,	,	PUNCT
ejpam-5226	170	15	1691	1691	NUM
ejpam-5226	170	16	-	-	SYM
ejpam-5226	170	17	1704	1704	NUM
ejpam-5226	170	18	1696	1696	NUM
ejpam-5226	170	19	remark	remark	NOUN
ejpam-5226	170	20	5	5	NUM
ejpam-5226	170	21	.	.	PUNCT
ejpam-5226	171	1	any	any	DET
ejpam-5226	171	2	∅	∅	NOUN
ejpam-5226	171	3	=	=	NOUN
ejpam-5226	171	4	̸	̸	NUM
ejpam-5226	171	5	s1	s1	NOUN
ejpam-5226	171	6	,	,	PUNCT
ejpam-5226	171	7	s2	s2	NOUN
ejpam-5226	171	8	⊆	⊆	NUM
ejpam-5226	171	9	l	l	NOUN
ejpam-5226	171	10	need	need	AUX
ejpam-5226	171	11	not	not	PART
ejpam-5226	171	12	be	be	AUX
ejpam-5226	171	13	commutative	commutative	ADJ
ejpam-5226	171	14	under	under	ADP
ejpam-5226	171	15	∧	∧	PROPN
ejpam-5226	171	16	.	.	PUNCT
ejpam-5226	172	1	in	in	ADP
ejpam-5226	172	2	a	a	DET
ejpam-5226	172	3	discrete	discrete	ADJ
ejpam-5226	172	4	almost	almost	ADV
ejpam-5226	172	5	distributive	distributive	ADJ
ejpam-5226	172	6	lattice	lattice	NOUN
ejpam-5226	172	7	x	x	NOUN
ejpam-5226	172	8	,	,	PUNCT
ejpam-5226	172	9	let	let	VERB
ejpam-5226	172	10	s1	s1	PROPN
ejpam-5226	172	11	=	=	PUNCT
ejpam-5226	172	12	{	{	PUNCT
ejpam-5226	172	13	x	x	NOUN
ejpam-5226	172	14	}	}	PUNCT
ejpam-5226	172	15	and	and	CCONJ
ejpam-5226	172	16	s2	s2	VERB
ejpam-5226	172	17	=	=	SYM
ejpam-5226	172	18	{	{	PUNCT
ejpam-5226	172	19	y	y	NOUN
ejpam-5226	172	20	}	}	PUNCT
ejpam-5226	172	21	,	,	PUNCT
ejpam-5226	172	22	then	then	ADV
ejpam-5226	172	23	it	it	PRON
ejpam-5226	172	24	can	can	AUX
ejpam-5226	172	25	be	be	AUX
ejpam-5226	172	26	easy	easy	ADJ
ejpam-5226	172	27	to	to	PART
ejpam-5226	172	28	verify	verify	VERB
ejpam-5226	172	29	that	that	SCONJ
ejpam-5226	172	30	s1	s1	PROPN
ejpam-5226	172	31	∧	∧	PROPN
ejpam-5226	172	32	s2	s2	NOUN
ejpam-5226	172	33	̸=	̸=	PROPN
ejpam-5226	172	34	s2	s2	NOUN
ejpam-5226	172	35	∧	∧	PROPN
ejpam-5226	172	36	s1	s1	PROPN
ejpam-5226	172	37	.	.	PUNCT
ejpam-5226	173	1	proposition	proposition	NOUN
ejpam-5226	173	2	5	5	NUM
ejpam-5226	173	3	.	.	PUNCT
ejpam-5226	174	1	for	for	ADP
ejpam-5226	174	2	any	any	DET
ejpam-5226	174	3	∅	∅	NOUN
ejpam-5226	174	4	=	=	NOUN
ejpam-5226	174	5	̸	̸	NUM
ejpam-5226	174	6	s1	s1	NOUN
ejpam-5226	174	7	,	,	PUNCT
ejpam-5226	174	8	s2	s2	PROPN
ejpam-5226	174	9	,	,	PUNCT
ejpam-5226	174	10	s3	s3	PROPN
ejpam-5226	174	11	⊆	⊆	NUM
ejpam-5226	174	12	l	l	NOUN
ejpam-5226	174	13	,	,	PUNCT
ejpam-5226	174	14	we	we	PRON
ejpam-5226	174	15	have	have	VERB
ejpam-5226	174	16	(	(	PUNCT
ejpam-5226	174	17	i	i	NOUN
ejpam-5226	174	18	)	)	PUNCT
ejpam-5226	174	19	hs1	hs1	PROPN
ejpam-5226	174	20	∧	∧	PROPN
ejpam-5226	174	21	hs2	hs2	PROPN
ejpam-5226	174	22	=	=	PUNCT
ejpam-5226	174	23	hs1	hs1	X
ejpam-5226	174	24	∧	∧	PROPN
ejpam-5226	174	25	s2	s2	PROPN
ejpam-5226	174	26	,	,	PUNCT
ejpam-5226	174	27	(	(	PUNCT
ejpam-5226	174	28	ii	ii	NOUN
ejpam-5226	174	29	)	)	PUNCT
ejpam-5226	174	30	hs1	hs1	PROPN
ejpam-5226	175	1	∧	∧	PROPN
ejpam-5226	175	2	hs1	hs1	PROPN
ejpam-5226	175	3	=	=	PUNCT
ejpam-5226	175	4	hs1	hs1	PROPN
ejpam-5226	175	5	(	(	PUNCT
ejpam-5226	175	6	idempotent	idempotent	ADJ
ejpam-5226	175	7	law	law	NOUN
ejpam-5226	175	8	)	)	PUNCT
ejpam-5226	175	9	,	,	PUNCT
ejpam-5226	175	10	(	(	PUNCT
ejpam-5226	175	11	iii	iii	X
ejpam-5226	175	12	)	)	PUNCT
ejpam-5226	175	13	hs1	hs1	NOUN
ejpam-5226	175	14	∧	∧	PROPN
ejpam-5226	175	15	hs2	hs2	NOUN
ejpam-5226	175	16	=	=	SYM
ejpam-5226	175	17	hs2	hs2	PROPN
ejpam-5226	175	18	∧	∧	NOUN
ejpam-5226	175	19	hs1	hs1	PROPN
ejpam-5226	175	20	(	(	PUNCT
ejpam-5226	175	21	commutative	commutative	ADJ
ejpam-5226	175	22	law	law	NOUN
ejpam-5226	175	23	)	)	PUNCT
ejpam-5226	175	24	,	,	PUNCT
ejpam-5226	175	25	(	(	PUNCT
ejpam-5226	175	26	iv	iv	X
ejpam-5226	175	27	)	)	PUNCT
ejpam-5226	175	28	hs1	hs1	PROPN
ejpam-5226	175	29	∧	∧	PROPN
ejpam-5226	175	30	(	(	PUNCT
ejpam-5226	175	31	hs2	hs2	NOUN
ejpam-5226	175	32	∧	∧	PROPN
ejpam-5226	175	33	hs3	hs3	NOUN
ejpam-5226	175	34	)	)	PUNCT
ejpam-5226	175	35	=	=	NOUN
ejpam-5226	175	36	(	(	PUNCT
ejpam-5226	175	37	hs1	hs1	PROPN
ejpam-5226	175	38	∧	∧	PROPN
ejpam-5226	175	39	hs2	hs2	PROPN
ejpam-5226	175	40	)	)	PUNCT
ejpam-5226	175	41	∧	∧	NOUN
ejpam-5226	175	42	hs3	hs3	X
ejpam-5226	175	43	(	(	PUNCT
ejpam-5226	175	44	distributive	distributive	ADJ
ejpam-5226	175	45	law	law	NOUN
ejpam-5226	175	46	)	)	PUNCT
ejpam-5226	175	47	.	.	PUNCT
ejpam-5226	176	1	proof	proof	NOUN
ejpam-5226	176	2	.	.	PUNCT
ejpam-5226	177	1	(	(	PUNCT
ejpam-5226	177	2	i	i	NOUN
ejpam-5226	177	3	)	)	PUNCT
ejpam-5226	177	4	let	let	VERB
ejpam-5226	177	5	h	h	NOUN
ejpam-5226	177	6	∈	∈	PROPN
ejpam-5226	177	7	hs1	hs1	PROPN
ejpam-5226	177	8	∧	∧	PROPN
ejpam-5226	177	9	hs2	hs2	PROPN
ejpam-5226	177	10	.	.	PUNCT
ejpam-5226	178	1	then	then	ADV
ejpam-5226	178	2	h	h	NOUN
ejpam-5226	178	3	=	=	NOUN
ejpam-5226	178	4	h1	h1	PROPN
ejpam-5226	178	5	∧	∧	PROPN
ejpam-5226	178	6	h2	h2	NOUN
ejpam-5226	178	7	for	for	ADP
ejpam-5226	178	8	some	some	DET
ejpam-5226	178	9	h1	h1	PROPN
ejpam-5226	178	10	∈	∈	PROPN
ejpam-5226	178	11	hs1	hs1	NOUN
ejpam-5226	178	12	and	and	CCONJ
ejpam-5226	178	13	h2	h2	PROPN
ejpam-5226	178	14	∈	∈	PROPN
ejpam-5226	178	15	hs2	hs2	NOUN
ejpam-5226	178	16	.	.	PUNCT
ejpam-5226	179	1	for	for	ADP
ejpam-5226	179	2	this	this	DET
ejpam-5226	179	3	h1	h1	PROPN
ejpam-5226	179	4	∈	∈	PROPN
ejpam-5226	179	5	hs1	hs1	NOUN
ejpam-5226	179	6	and	and	CCONJ
ejpam-5226	179	7	h2	h2	PROPN
ejpam-5226	179	8	∈	∈	PROPN
ejpam-5226	179	9	hs2	hs2	NOUN
ejpam-5226	179	10	,	,	PUNCT
ejpam-5226	179	11	there	there	PRON
ejpam-5226	179	12	exist	exist	VERB
ejpam-5226	179	13	s1	s1	PROPN
ejpam-5226	179	14	∈	∈	PROPN
ejpam-5226	179	15	s1	s1	NOUN
ejpam-5226	179	16	,	,	PUNCT
ejpam-5226	179	17	s2	s2	NOUN
ejpam-5226	179	18	∈	∈	PROPN
ejpam-5226	179	19	s2	s2	NOUN
ejpam-5226	179	20	such	such	ADJ
ejpam-5226	179	21	that	that	SCONJ
ejpam-5226	179	22	s1	s1	PROPN
ejpam-5226	179	23	∧	∧	PROPN
ejpam-5226	179	24	h1	h1	NOUN
ejpam-5226	179	25	=	=	PUNCT
ejpam-5226	179	26	h1	h1	PROPN
ejpam-5226	179	27	and	and	CCONJ
ejpam-5226	179	28	s2	s2	VERB
ejpam-5226	179	29	∧	∧	PROPN
ejpam-5226	179	30	h2	h2	NOUN
ejpam-5226	179	31	=	=	SYM
ejpam-5226	179	32	h2	h2	PROPN
ejpam-5226	179	33	.	.	PUNCT
ejpam-5226	180	1	now	now	ADV
ejpam-5226	180	2	,	,	PUNCT
ejpam-5226	180	3	s1	s1	PROPN
ejpam-5226	180	4	∧	∧	PROPN
ejpam-5226	180	5	s2	s2	NOUN
ejpam-5226	180	6	∧	∧	NOUN
ejpam-5226	180	7	h	h	NOUN
ejpam-5226	180	8	=	=	SYM
ejpam-5226	180	9	s1	s1	PROPN
ejpam-5226	180	10	∧	∧	PROPN
ejpam-5226	180	11	s2	s2	NOUN
ejpam-5226	180	12	∧	∧	NOUN
ejpam-5226	180	13	h1	h1	PROPN
ejpam-5226	180	14	∧	∧	PROPN
ejpam-5226	180	15	h2	h2	NOUN
ejpam-5226	180	16	=	=	SYM
ejpam-5226	180	17	s1	s1	PROPN
ejpam-5226	180	18	∧	∧	PROPN
ejpam-5226	180	19	h1	h1	PROPN
ejpam-5226	180	20	∧	∧	PROPN
ejpam-5226	180	21	s2	s2	NOUN
ejpam-5226	180	22	∧	∧	PROPN
ejpam-5226	180	23	h2	h2	NOUN
ejpam-5226	180	24	=	=	SYM
ejpam-5226	180	25	h1	h1	PROPN
ejpam-5226	180	26	∧	∧	PROPN
ejpam-5226	180	27	h2	h2	NOUN
ejpam-5226	180	28	=	=	NOUN
ejpam-5226	181	1	h	h	NOUN
ejpam-5226	181	2	where	where	SCONJ
ejpam-5226	181	3	s1	s1	PROPN
ejpam-5226	181	4	∧	∧	PROPN
ejpam-5226	181	5	s2	s2	NOUN
ejpam-5226	181	6	∈	∈	PROPN
ejpam-5226	181	7	s1	s1	PROPN
ejpam-5226	181	8	∧	∧	PROPN
ejpam-5226	181	9	s2	s2	PROPN
ejpam-5226	181	10	.	.	PUNCT
ejpam-5226	182	1	therefore	therefore	ADV
ejpam-5226	182	2	,	,	PUNCT
ejpam-5226	182	3	h	h	PROPN
ejpam-5226	182	4	∈	∈	PROPN
ejpam-5226	182	5	hs1	hs1	PROPN
ejpam-5226	182	6	∧	∧	PROPN
ejpam-5226	182	7	s2	s2	PROPN
ejpam-5226	182	8	.	.	PUNCT
ejpam-5226	183	1	hence	hence	ADV
ejpam-5226	183	2	,	,	PUNCT
ejpam-5226	183	3	hs1	hs1	PROPN
ejpam-5226	183	4	∧	∧	PROPN
ejpam-5226	183	5	hs2	hs2	PROPN
ejpam-5226	183	6	⊆	⊆	NUM
ejpam-5226	183	7	hs1	hs1	PROPN
ejpam-5226	183	8	∧	∧	PROPN
ejpam-5226	183	9	s2	s2	PROPN
ejpam-5226	183	10	.	.	PUNCT
ejpam-5226	184	1	let	let	VERB
ejpam-5226	184	2	h	h	PRON
ejpam-5226	184	3	∈	∈	PROPN
ejpam-5226	184	4	hs1	hs1	PROPN
ejpam-5226	184	5	∧	∧	PROPN
ejpam-5226	184	6	s2	s2	PROPN
ejpam-5226	184	7	.	.	PUNCT
ejpam-5226	185	1	then	then	ADV
ejpam-5226	185	2	there	there	PRON
ejpam-5226	185	3	exist	exist	VERB
ejpam-5226	185	4	s1	s1	PROPN
ejpam-5226	185	5	∈	∈	PROPN
ejpam-5226	185	6	s1	s1	NOUN
ejpam-5226	185	7	,	,	PUNCT
ejpam-5226	185	8	s2	s2	NOUN
ejpam-5226	185	9	∈	∈	PROPN
ejpam-5226	185	10	s2	s2	NOUN
ejpam-5226	185	11	such	such	ADJ
ejpam-5226	185	12	that	that	SCONJ
ejpam-5226	185	13	s1	s1	PROPN
ejpam-5226	185	14	∧	∧	PROPN
ejpam-5226	185	15	s2	s2	NOUN
ejpam-5226	185	16	∧	∧	NOUN
ejpam-5226	185	17	h	h	NOUN
ejpam-5226	185	18	=	=	PROPN
ejpam-5226	185	19	h.	h.	PROPN
ejpam-5226	186	1	now	now	ADV
ejpam-5226	186	2	,	,	PUNCT
ejpam-5226	186	3	s1	s1	PROPN
ejpam-5226	186	4	∧	∧	PROPN
ejpam-5226	186	5	h	h	NOUN
ejpam-5226	186	6	=	=	NOUN
ejpam-5226	186	7	s1∧s1∧s2∧h	s1∧s1∧s2∧h	PROPN
ejpam-5226	186	8	=	=	X
ejpam-5226	186	9	s1∧s2∧h	s1∧s2∧h	NOUN
ejpam-5226	186	10	=	=	SYM
ejpam-5226	186	11	h	h	NOUN
ejpam-5226	186	12	and	and	CCONJ
ejpam-5226	186	13	s2∧h	s2∧h	PROPN
ejpam-5226	186	14	=	=	SYM
ejpam-5226	186	15	s2∧	s2∧	NOUN
ejpam-5226	186	16	(	(	PUNCT
ejpam-5226	186	17	s1∧s2∧h	s1∧s2∧h	NOUN
ejpam-5226	186	18	)	)	PUNCT
ejpam-5226	186	19	=	=	SYM
ejpam-5226	186	20	s1∧s2∧h	s1∧s2∧h	NOUN
ejpam-5226	186	21	=	=	SYM
ejpam-5226	186	22	h.	h.	PROPN
ejpam-5226	186	23	therefore	therefore	ADV
ejpam-5226	186	24	,	,	PUNCT
ejpam-5226	186	25	h	h	PROPN
ejpam-5226	186	26	∈	∈	PROPN
ejpam-5226	186	27	hs1	hs1	PROPN
ejpam-5226	186	28	and	and	CCONJ
ejpam-5226	186	29	h	h	NOUN
ejpam-5226	186	30	∈	∈	PROPN
ejpam-5226	186	31	hs2	hs2	NOUN
ejpam-5226	186	32	.	.	PUNCT
ejpam-5226	187	1	hence	hence	ADV
ejpam-5226	187	2	,	,	PUNCT
ejpam-5226	187	3	h	h	NOUN
ejpam-5226	187	4	=	=	NOUN
ejpam-5226	187	5	h	h	NOUN
ejpam-5226	187	6	∧	∧	NOUN
ejpam-5226	187	7	h	h	NOUN
ejpam-5226	187	8	=	=	PUNCT
ejpam-5226	187	9	hs1	hs1	X
ejpam-5226	187	10	∧	∧	PROPN
ejpam-5226	187	11	hs2	hs2	PROPN
ejpam-5226	187	12	.	.	PUNCT
ejpam-5226	188	1	thus	thus	ADV
ejpam-5226	188	2	,	,	PUNCT
ejpam-5226	188	3	hs1	hs1	PROPN
ejpam-5226	188	4	∧	∧	PROPN
ejpam-5226	188	5	hs2	hs2	PROPN
ejpam-5226	188	6	=	=	PUNCT
ejpam-5226	188	7	hs1	hs1	X
ejpam-5226	188	8	∧	∧	PROPN
ejpam-5226	188	9	s2	s2	PROPN
ejpam-5226	188	10	.	.	PUNCT
ejpam-5226	189	1	(	(	PUNCT
ejpam-5226	189	2	ii	ii	NOUN
ejpam-5226	189	3	)	)	PUNCT
ejpam-5226	189	4	let	let	VERB
ejpam-5226	189	5	h	h	NOUN
ejpam-5226	189	6	∈	∈	PROPN
ejpam-5226	189	7	hs1	hs1	PROPN
ejpam-5226	189	8	∧	∧	NOUN
ejpam-5226	189	9	hs1	hs1	X
ejpam-5226	189	10	=	=	PUNCT
ejpam-5226	189	11	hs1	hs1	PROPN
ejpam-5226	189	12	∧	∧	PROPN
ejpam-5226	189	13	s1	s1	PROPN
ejpam-5226	189	14	(	(	PUNCT
ejpam-5226	189	15	from	from	ADP
ejpam-5226	189	16	(	(	PUNCT
ejpam-5226	189	17	i	i	NOUN
ejpam-5226	189	18	)	)	PUNCT
ejpam-5226	189	19	)	)	PUNCT
ejpam-5226	189	20	.	.	PUNCT
ejpam-5226	190	1	then	then	ADV
ejpam-5226	190	2	there	there	PRON
ejpam-5226	190	3	exist	exist	VERB
ejpam-5226	190	4	s1	s1	NOUN
ejpam-5226	190	5	,	,	PUNCT
ejpam-5226	190	6	s	s	PART
ejpam-5226	190	7	′	′	NUM
ejpam-5226	190	8	1	1	NUM
ejpam-5226	190	9	∈	∈	NOUN
ejpam-5226	190	10	s1	s1	NOUN
ejpam-5226	190	11	such	such	ADJ
ejpam-5226	190	12	that	that	SCONJ
ejpam-5226	190	13	s1	s1	PROPN
ejpam-5226	190	14	∧	∧	PROPN
ejpam-5226	190	15	s′1	s′1	VERB
ejpam-5226	190	16	∧	∧	PROPN
ejpam-5226	190	17	h	h	NOUN
ejpam-5226	190	18	=	=	PROPN
ejpam-5226	190	19	h.	h.	PROPN
ejpam-5226	191	1	now	now	ADV
ejpam-5226	191	2	,	,	PUNCT
ejpam-5226	191	3	s1	s1	PROPN
ejpam-5226	191	4	∧	∧	PROPN
ejpam-5226	191	5	h	h	NOUN
ejpam-5226	191	6	=	=	SYM
ejpam-5226	191	7	s1	s1	PROPN
ejpam-5226	191	8	∧	∧	PROPN
ejpam-5226	191	9	(	(	PUNCT
ejpam-5226	191	10	s1	s1	PROPN
ejpam-5226	191	11	∧	∧	PROPN
ejpam-5226	191	12	s′1	s′1	VERB
ejpam-5226	191	13	∧	∧	PROPN
ejpam-5226	191	14	h	h	NOUN
ejpam-5226	191	15	)	)	PUNCT
ejpam-5226	191	16	=	=	SYM
ejpam-5226	191	17	s1	s1	PROPN
ejpam-5226	191	18	∧	∧	PROPN
ejpam-5226	191	19	s′1	s′1	NOUN
ejpam-5226	191	20	∧	∧	PROPN
ejpam-5226	191	21	h	h	NOUN
ejpam-5226	191	22	=	=	PROPN
ejpam-5226	191	23	h.	h.	PROPN
ejpam-5226	191	24	therefore	therefore	ADV
ejpam-5226	191	25	,	,	PUNCT
ejpam-5226	191	26	h	h	PROPN
ejpam-5226	191	27	∈	∈	PROPN
ejpam-5226	191	28	hs1	hs1	PROPN
ejpam-5226	191	29	.	.	PUNCT
ejpam-5226	192	1	hence	hence	ADV
ejpam-5226	192	2	,	,	PUNCT
ejpam-5226	192	3	hs1	hs1	PROPN
ejpam-5226	192	4	∧	∧	PROPN
ejpam-5226	192	5	hs1	hs1	PROPN
ejpam-5226	192	6	⊆	⊆	NUM
ejpam-5226	192	7	hs1	hs1	PROPN
ejpam-5226	192	8	.	.	PUNCT
ejpam-5226	193	1	by	by	ADP
ejpam-5226	193	2	proposition	proposition	NOUN
ejpam-5226	193	3	4(ii	4(ii	NUM
ejpam-5226	193	4	)	)	PUNCT
ejpam-5226	193	5	,	,	PUNCT
ejpam-5226	193	6	s1	s1	PROPN
ejpam-5226	193	7	⊆	⊆	NUM
ejpam-5226	193	8	s1	s1	NOUN
ejpam-5226	193	9	∧	∧	PROPN
ejpam-5226	193	10	s1	s1	PROPN
ejpam-5226	193	11	.	.	PUNCT
ejpam-5226	194	1	therefore	therefore	ADV
ejpam-5226	194	2	,	,	PUNCT
ejpam-5226	194	3	hs1	hs1	PROPN
ejpam-5226	194	4	⊆	⊆	NUM
ejpam-5226	194	5	hs1	hs1	PROPN
ejpam-5226	194	6	∧	∧	PROPN
ejpam-5226	194	7	hs1	hs1	PROPN
ejpam-5226	194	8	.	.	PUNCT
ejpam-5226	195	1	thus	thus	ADV
ejpam-5226	195	2	,	,	PUNCT
ejpam-5226	195	3	hs1	hs1	PROPN
ejpam-5226	195	4	=	=	SYM
ejpam-5226	195	5	hs1	hs1	X
ejpam-5226	195	6	∧	∧	PROPN
ejpam-5226	195	7	hs1	hs1	PROPN
ejpam-5226	195	8	.	.	PUNCT
ejpam-5226	196	1	(	(	PUNCT
ejpam-5226	196	2	iii	iii	X
ejpam-5226	196	3	)	)	PUNCT
ejpam-5226	196	4	let	let	VERB
ejpam-5226	196	5	h	h	NOUN
ejpam-5226	196	6	∈	∈	PROPN
ejpam-5226	196	7	hs1	hs1	PROPN
ejpam-5226	196	8	∧	∧	PROPN
ejpam-5226	196	9	hs2	hs2	PROPN
ejpam-5226	196	10	=	=	PUNCT
ejpam-5226	196	11	hs1	hs1	PROPN
ejpam-5226	196	12	∧	∧	PROPN
ejpam-5226	196	13	s2	s2	PROPN
ejpam-5226	196	14	(	(	PUNCT
ejpam-5226	196	15	from	from	ADP
ejpam-5226	196	16	(	(	PUNCT
ejpam-5226	196	17	i	i	NOUN
ejpam-5226	196	18	)	)	PUNCT
ejpam-5226	196	19	)	)	PUNCT
ejpam-5226	196	20	.	.	PUNCT
ejpam-5226	197	1	then	then	ADV
ejpam-5226	197	2	s1	s1	PROPN
ejpam-5226	197	3	∧	∧	PROPN
ejpam-5226	197	4	s2	s2	NOUN
ejpam-5226	197	5	∧	∧	NOUN
ejpam-5226	197	6	h	h	NOUN
ejpam-5226	197	7	=	=	NOUN
ejpam-5226	197	8	h	h	NOUN
ejpam-5226	197	9	=	=	NOUN
ejpam-5226	197	10	s2	s2	NOUN
ejpam-5226	197	11	∧	∧	NOUN
ejpam-5226	197	12	s1	s1	NOUN
ejpam-5226	197	13	∧	∧	PROPN
ejpam-5226	197	14	h	h	NOUN
ejpam-5226	197	15	for	for	ADP
ejpam-5226	197	16	some	some	DET
ejpam-5226	197	17	s1	s1	PROPN
ejpam-5226	197	18	∈	∈	PROPN
ejpam-5226	197	19	s1	s1	NOUN
ejpam-5226	197	20	and	and	CCONJ
ejpam-5226	197	21	s2	s2	PROPN
ejpam-5226	197	22	∈	∈	PROPN
ejpam-5226	197	23	s2	s2	PROPN
ejpam-5226	197	24	.	.	PUNCT
ejpam-5226	198	1	therefore	therefore	ADV
ejpam-5226	198	2	,	,	PUNCT
ejpam-5226	198	3	h	h	PROPN
ejpam-5226	198	4	∈	∈	PROPN
ejpam-5226	198	5	hs2	hs2	PROPN
ejpam-5226	198	6	∧	∧	PROPN
ejpam-5226	198	7	hs1	hs1	PROPN
ejpam-5226	198	8	.	.	PUNCT
ejpam-5226	199	1	hence	hence	ADV
ejpam-5226	199	2	,	,	PUNCT
ejpam-5226	199	3	hs1	hs1	PROPN
ejpam-5226	199	4	∧	∧	PROPN
ejpam-5226	199	5	hs2	hs2	PROPN
ejpam-5226	199	6	⊆	⊆	NUM
ejpam-5226	199	7	hs2	hs2	NOUN
ejpam-5226	199	8	∧	∧	PROPN
ejpam-5226	199	9	hs1	hs1	PROPN
ejpam-5226	199	10	.	.	PUNCT
ejpam-5226	200	1	similarly	similarly	ADV
ejpam-5226	200	2	,	,	PUNCT
ejpam-5226	200	3	we	we	PRON
ejpam-5226	200	4	can	can	AUX
ejpam-5226	200	5	prove	prove	VERB
ejpam-5226	200	6	the	the	DET
ejpam-5226	200	7	converse	converse	NOUN
ejpam-5226	200	8	.	.	PUNCT
ejpam-5226	201	1	hence	hence	ADV
ejpam-5226	201	2	,	,	PUNCT
ejpam-5226	201	3	hs1	hs1	PROPN
ejpam-5226	201	4	∧	∧	PROPN
ejpam-5226	201	5	hs2	hs2	NOUN
ejpam-5226	201	6	=	=	SYM
ejpam-5226	201	7	hs2	hs2	PROPN
ejpam-5226	201	8	∧	∧	NOUN
ejpam-5226	201	9	hs1	hs1	PROPN
ejpam-5226	201	10	.	.	PUNCT
ejpam-5226	202	1	(	(	PUNCT
ejpam-5226	202	2	iv	iv	X
ejpam-5226	202	3	)	)	PUNCT
ejpam-5226	202	4	by	by	ADP
ejpam-5226	202	5	proposition	proposition	NOUN
ejpam-5226	202	6	4(iii	4(iii	NUM
ejpam-5226	202	7	)	)	PUNCT
ejpam-5226	202	8	,	,	PUNCT
ejpam-5226	202	9	we	we	PRON
ejpam-5226	202	10	havehs1	havehs1	PROPN
ejpam-5226	202	11	∧	∧	PROPN
ejpam-5226	202	12	(	(	PUNCT
ejpam-5226	202	13	hs2	hs2	NOUN
ejpam-5226	202	14	∧	∧	PROPN
ejpam-5226	202	15	hs3	hs3	NOUN
ejpam-5226	202	16	)	)	PUNCT
ejpam-5226	202	17	=	=	PUNCT
ejpam-5226	202	18	hs1	hs1	X
ejpam-5226	202	19	∧	∧	PROPN
ejpam-5226	202	20	hs2	hs2	PROPN
ejpam-5226	202	21	∧	∧	PROPN
ejpam-5226	202	22	s3	s3	PROPN
ejpam-5226	202	23	=	=	SYM
ejpam-5226	202	24	hs1	hs1	PROPN
ejpam-5226	202	25	∧	∧	PROPN
ejpam-5226	202	26	(	(	PUNCT
ejpam-5226	202	27	s2	s2	NOUN
ejpam-5226	202	28	∧	∧	PROPN
ejpam-5226	202	29	s3	s3	PROPN
ejpam-5226	202	30	)	)	PUNCT
ejpam-5226	202	31	=	=	SYM
ejpam-5226	202	32	h(s1	h(s1	PUNCT
ejpam-5226	202	33	∧	∧	PROPN
ejpam-5226	202	34	s2	s2	PROPN
ejpam-5226	202	35	)	)	PUNCT
ejpam-5226	202	36	∧	∧	PROPN
ejpam-5226	202	37	s3	s3	PROPN
ejpam-5226	202	38	=	=	SYM
ejpam-5226	202	39	h(s1	h(s1	X
ejpam-5226	202	40	∧	∧	PROPN
ejpam-5226	202	41	s2	s2	PROPN
ejpam-5226	202	42	)	)	PUNCT
ejpam-5226	202	43	∧	∧	NOUN
ejpam-5226	202	44	hs3	hs3	NOUN
ejpam-5226	202	45	=	=	SYM
ejpam-5226	202	46	(	(	PUNCT
ejpam-5226	202	47	hs1	hs1	PROPN
ejpam-5226	202	48	∧	∧	PROPN
ejpam-5226	202	49	hs2	hs2	PROPN
ejpam-5226	202	50	)	)	PUNCT
ejpam-5226	202	51	∧	∧	NOUN
ejpam-5226	202	52	hs3	hs3	NOUN
ejpam-5226	202	53	.	.	PUNCT
ejpam-5226	203	1	proposition	proposition	NOUN
ejpam-5226	203	2	6	6	NUM
ejpam-5226	203	3	.	.	PUNCT
ejpam-5226	204	1	for	for	ADP
ejpam-5226	204	2	any	any	DET
ejpam-5226	204	3	∅	∅	NOUN
ejpam-5226	204	4	=	=	NOUN
ejpam-5226	204	5	̸	̸	NUM
ejpam-5226	204	6	s1	s1	NOUN
ejpam-5226	204	7	,	,	PUNCT
ejpam-5226	204	8	s2	s2	NOUN
ejpam-5226	204	9	⊆	⊆	NUM
ejpam-5226	204	10	l	l	NOUN
ejpam-5226	204	11	,	,	PUNCT
ejpam-5226	204	12	we	we	PRON
ejpam-5226	204	13	have	have	VERB
ejpam-5226	204	14	(	(	PUNCT
ejpam-5226	204	15	i	i	NOUN
ejpam-5226	204	16	)	)	PUNCT
ejpam-5226	204	17	hs1	hs1	PROPN
ejpam-5226	205	1	∪hs2	∪hs2	PROPN
ejpam-5226	206	1	=	=	PUNCT
ejpam-5226	207	1	hs1∪s2	hs1∪s2	PROPN
ejpam-5226	207	2	,	,	PUNCT
ejpam-5226	207	3	(	(	PUNCT
ejpam-5226	207	4	ii	ii	NOUN
ejpam-5226	207	5	)	)	PUNCT
ejpam-5226	207	6	hs1	hs1	PROPN
ejpam-5226	207	7	∪hs1	∪hs1	PROPN
ejpam-5226	207	8	=	=	SYM
ejpam-5226	207	9	hs1	hs1	PROPN
ejpam-5226	207	10	(	(	PUNCT
ejpam-5226	207	11	idempotent	idempotent	NOUN
ejpam-5226	207	12	)	)	PUNCT
ejpam-5226	207	13	,	,	PUNCT
ejpam-5226	207	14	(	(	PUNCT
ejpam-5226	207	15	iii	iii	X
ejpam-5226	207	16	)	)	PUNCT
ejpam-5226	207	17	hs1	hs1	PROPN
ejpam-5226	207	18	∪hs2	∪hs2	PROPN
ejpam-5226	207	19	=	=	SYM
ejpam-5226	207	20	hs2	hs2	PROPN
ejpam-5226	207	21	∪hs1	∪hs1	PROPN
ejpam-5226	207	22	(	(	PUNCT
ejpam-5226	207	23	commutative	commutative	ADJ
ejpam-5226	207	24	)	)	PUNCT
ejpam-5226	207	25	,	,	PUNCT
ejpam-5226	207	26	(	(	PUNCT
ejpam-5226	207	27	iv	iv	X
ejpam-5226	207	28	)	)	PUNCT
ejpam-5226	207	29	hs1	hs1	PROPN
ejpam-5226	207	30	∪	∪	X
ejpam-5226	207	31	(	(	PUNCT
ejpam-5226	207	32	hs2	hs2	PROPN
ejpam-5226	207	33	∪hs3	∪hs3	PROPN
ejpam-5226	207	34	)	)	PUNCT
ejpam-5226	207	35	=	=	PUNCT
ejpam-5226	207	36	(	(	PUNCT
ejpam-5226	207	37	hs1	hs1	PROPN
ejpam-5226	207	38	∪hs2	∪hs2	PROPN
ejpam-5226	207	39	)	)	PUNCT
ejpam-5226	207	40	∪hs3	∪hs3	X
ejpam-5226	207	41	(	(	PUNCT
ejpam-5226	207	42	associative	associative	NOUN
ejpam-5226	207	43	)	)	PUNCT
ejpam-5226	207	44	.	.	PUNCT
ejpam-5226	208	1	proposition	proposition	NOUN
ejpam-5226	208	2	7	7	NUM
ejpam-5226	208	3	.	.	X
ejpam-5226	208	4	for	for	ADP
ejpam-5226	208	5	any	any	DET
ejpam-5226	208	6	∅	∅	NOUN
ejpam-5226	208	7	=	=	NOUN
ejpam-5226	208	8	̸	̸	NUM
ejpam-5226	208	9	s	s	PART
ejpam-5226	208	10	⊆	⊆	NUM
ejpam-5226	208	11	l	l	NOUN
ejpam-5226	208	12	and	and	CCONJ
ejpam-5226	208	13	a	a	PRON
ejpam-5226	208	14	is	be	AUX
ejpam-5226	208	15	an	an	DET
ejpam-5226	208	16	element	element	NOUN
ejpam-5226	208	17	in	in	ADP
ejpam-5226	208	18	l	l	NOUN
ejpam-5226	208	19	,	,	PUNCT
ejpam-5226	208	20	we	we	PRON
ejpam-5226	208	21	have	have	VERB
ejpam-5226	208	22	(	(	PUNCT
ejpam-5226	208	23	i	i	NOUN
ejpam-5226	208	24	)	)	PUNCT
ejpam-5226	208	25	ha	ha	INTJ
ejpam-5226	209	1	=	=	X
ejpam-5226	209	2	(	(	PUNCT
ejpam-5226	209	3	a	a	X
ejpam-5226	209	4	]	]	X
ejpam-5226	209	5	,	,	PUNCT
ejpam-5226	209	6	(	(	PUNCT
ejpam-5226	209	7	ii	ii	NOUN
ejpam-5226	209	8	)	)	PUNCT
ejpam-5226	209	9	hs	hs	PROPN
ejpam-5226	210	1	=	=	SYM
ejpam-5226	210	2	⋃	⋃	PROPN
ejpam-5226	210	3	s∈s	s∈s	NOUN
ejpam-5226	210	4	(	(	PUNCT
ejpam-5226	210	5	s	s	PROPN
ejpam-5226	210	6	]	]	PUNCT
ejpam-5226	210	7	.	.	PUNCT
ejpam-5226	211	1	a.	a.	PROPN
ejpam-5226	211	2	iampan	iampan	PROPN
ejpam-5226	211	3	et	et	PROPN
ejpam-5226	211	4	al	al	PROPN
ejpam-5226	211	5	.	.	PUNCT
ejpam-5226	211	6	/	/	SYM
ejpam-5226	211	7	eur	eur	PROPN
ejpam-5226	211	8	.	.	PUNCT
ejpam-5226	212	1	j.	j.	PROPN
ejpam-5226	212	2	pure	pure	PROPN
ejpam-5226	212	3	appl	appl	PROPN
ejpam-5226	212	4	.	.	PROPN
ejpam-5226	212	5	math	math	PROPN
ejpam-5226	212	6	,	,	PUNCT
ejpam-5226	212	7	17	17	NUM
ejpam-5226	212	8	(	(	PUNCT
ejpam-5226	212	9	3	3	NUM
ejpam-5226	212	10	)	)	PUNCT
ejpam-5226	212	11	(	(	PUNCT
ejpam-5226	212	12	2024	2024	NUM
ejpam-5226	212	13	)	)	PUNCT
ejpam-5226	212	14	,	,	PUNCT
ejpam-5226	212	15	1691	1691	NUM
ejpam-5226	212	16	-	-	SYM
ejpam-5226	212	17	1704	1704	NUM
ejpam-5226	212	18	1697	1697	NUM
ejpam-5226	212	19	proof	proof	NOUN
ejpam-5226	212	20	.	.	PUNCT
ejpam-5226	213	1	(	(	PUNCT
ejpam-5226	213	2	i	i	NOUN
ejpam-5226	213	3	)	)	PUNCT
ejpam-5226	213	4	by	by	ADP
ejpam-5226	213	5	proposition	proposition	NOUN
ejpam-5226	213	6	2(iv	2(iv	NUM
ejpam-5226	213	7	)	)	PUNCT
ejpam-5226	213	8	,	,	PUNCT
ejpam-5226	213	9	ha	ha	INTJ
ejpam-5226	213	10	is	be	AUX
ejpam-5226	213	11	an	an	DET
ejpam-5226	213	12	ideal	ideal	NOUN
ejpam-5226	213	13	of	of	ADP
ejpam-5226	213	14	l	l	NOUN
ejpam-5226	213	15	and	and	CCONJ
ejpam-5226	213	16	a	a	DET
ejpam-5226	213	17	∈	∈	ADJ
ejpam-5226	213	18	ha	ha	INTJ
ejpam-5226	213	19	.	.	PUNCT
ejpam-5226	214	1	then	then	ADV
ejpam-5226	214	2	(	(	PUNCT
ejpam-5226	214	3	a	a	X
ejpam-5226	214	4	]	]	X
ejpam-5226	214	5	⊆	⊆	NUM
ejpam-5226	214	6	ha	ha	INTJ
ejpam-5226	214	7	.	.	PUNCT
ejpam-5226	214	8	let	let	VERB
ejpam-5226	214	9	h	h	PRON
ejpam-5226	214	10	∈	∈	PROPN
ejpam-5226	215	1	ha	ha	INTJ
ejpam-5226	215	2	.	.	PUNCT
ejpam-5226	216	1	then	then	ADV
ejpam-5226	216	2	a	a	DET
ejpam-5226	216	3	∧	∧	PROPN
ejpam-5226	216	4	h	h	NOUN
ejpam-5226	216	5	=	=	PROPN
ejpam-5226	216	6	h.	h.	PROPN
ejpam-5226	216	7	therefore	therefore	ADV
ejpam-5226	216	8	,	,	PUNCT
ejpam-5226	216	9	h	h	NOUN
ejpam-5226	216	10	=	=	PUNCT
ejpam-5226	216	11	a	a	DET
ejpam-5226	216	12	∧	∧	PROPN
ejpam-5226	216	13	h	h	NOUN
ejpam-5226	216	14	∈	∈	PROPN
ejpam-5226	216	15	(	(	PUNCT
ejpam-5226	216	16	a	a	X
ejpam-5226	216	17	]	]	X
ejpam-5226	216	18	.	.	PUNCT
ejpam-5226	217	1	so	so	ADV
ejpam-5226	217	2	that	that	SCONJ
ejpam-5226	217	3	ha	ha	INTJ
ejpam-5226	217	4	⊆	⊆	NUM
ejpam-5226	217	5	(	(	PUNCT
ejpam-5226	217	6	a	a	PRON
ejpam-5226	217	7	]	]	X
ejpam-5226	217	8	.	.	PUNCT
ejpam-5226	218	1	hence	hence	ADV
ejpam-5226	218	2	,	,	PUNCT
ejpam-5226	218	3	ha	ha	INTJ
ejpam-5226	218	4	=	=	X
ejpam-5226	218	5	(	(	PUNCT
ejpam-5226	218	6	a	a	PRON
ejpam-5226	218	7	]	]	X
ejpam-5226	218	8	.	.	PUNCT
ejpam-5226	219	1	(	(	PUNCT
ejpam-5226	219	2	ii	ii	NOUN
ejpam-5226	219	3	)	)	PUNCT
ejpam-5226	219	4	let	let	VERB
ejpam-5226	219	5	h	h	PROPN
ejpam-5226	219	6	∈	∈	PROPN
ejpam-5226	220	1	hs	hs	PROPN
ejpam-5226	220	2	.	.	PUNCT
ejpam-5226	221	1	then	then	ADV
ejpam-5226	221	2	,	,	PUNCT
ejpam-5226	221	3	we	we	PRON
ejpam-5226	221	4	have	have	VERB
ejpam-5226	221	5	an	an	DET
ejpam-5226	221	6	element	element	NOUN
ejpam-5226	221	7	s	s	PART
ejpam-5226	221	8	∈	∈	NOUN
ejpam-5226	221	9	s	s	VERB
ejpam-5226	221	10	such	such	ADJ
ejpam-5226	221	11	that	that	DET
ejpam-5226	221	12	h	h	NOUN
ejpam-5226	222	1	=	=	PUNCT
ejpam-5226	222	2	s∧h	s∧h	PROPN
ejpam-5226	222	3	∈	∈	PROPN
ejpam-5226	222	4	(	(	PUNCT
ejpam-5226	222	5	s	s	NOUN
ejpam-5226	222	6	]	]	X
ejpam-5226	222	7	.	.	PUNCT
ejpam-5226	223	1	therefore	therefore	ADV
ejpam-5226	223	2	,	,	PUNCT
ejpam-5226	223	3	hs	hs	PROPN
ejpam-5226	223	4	⊆	⊆	NUM
ejpam-5226	223	5	⋃	⋃	PUNCT
ejpam-5226	223	6	s∈s	s∈s	NOUN
ejpam-5226	223	7	(	(	PUNCT
ejpam-5226	223	8	s	s	X
ejpam-5226	223	9	]	]	PUNCT
ejpam-5226	223	10	.	.	PUNCT
ejpam-5226	224	1	let	let	VERB
ejpam-5226	224	2	y	y	PROPN
ejpam-5226	224	3	∈	∈	PROPN
ejpam-5226	224	4	⋃	⋃	PROPN
ejpam-5226	224	5	s∈s	s∈s	NOUN
ejpam-5226	224	6	(	(	PUNCT
ejpam-5226	224	7	s	s	PROPN
ejpam-5226	224	8	]	]	X
ejpam-5226	224	9	.	.	PUNCT
ejpam-5226	225	1	then	then	ADV
ejpam-5226	225	2	y	y	PROPN
ejpam-5226	225	3	∈	∈	PROPN
ejpam-5226	225	4	(	(	PUNCT
ejpam-5226	225	5	s	s	X
ejpam-5226	225	6	]	]	X
ejpam-5226	225	7	for	for	ADP
ejpam-5226	225	8	some	some	DET
ejpam-5226	225	9	s	s	ADP
ejpam-5226	225	10	∈	∈	PROPN
ejpam-5226	225	11	s.	s.	PROPN
ejpam-5226	225	12	therefore	therefore	ADV
ejpam-5226	225	13	,	,	PUNCT
ejpam-5226	225	14	y	y	PROPN
ejpam-5226	225	15	=	=	SYM
ejpam-5226	225	16	s	s	PART
ejpam-5226	225	17	∧	∧	PROPN
ejpam-5226	225	18	y.	y.	NOUN
ejpam-5226	226	1	so	so	SCONJ
ejpam-5226	226	2	that	that	SCONJ
ejpam-5226	226	3	y	y	PROPN
ejpam-5226	226	4	∈	∈	PROPN
ejpam-5226	226	5	hs	hs	PROPN
ejpam-5226	226	6	.	.	PUNCT
ejpam-5226	227	1	hence	hence	ADV
ejpam-5226	227	2	,	,	PUNCT
ejpam-5226	227	3	⋃	⋃	PUNCT
ejpam-5226	227	4	s∈s	s∈s	NOUN
ejpam-5226	227	5	(	(	PUNCT
ejpam-5226	227	6	s	s	X
ejpam-5226	227	7	]	]	X
ejpam-5226	227	8	⊆	⊆	NUM
ejpam-5226	227	9	hs	hs	X
ejpam-5226	227	10	.	.	PUNCT
ejpam-5226	228	1	thus	thus	ADV
ejpam-5226	228	2	,	,	PUNCT
ejpam-5226	228	3	hs	hs	PROPN
ejpam-5226	228	4	=	=	SYM
ejpam-5226	228	5	⋃	⋃	PROPN
ejpam-5226	228	6	s∈s	s∈s	NOUN
ejpam-5226	228	7	(	(	PUNCT
ejpam-5226	228	8	s	s	PROPN
ejpam-5226	228	9	]	]	PUNCT
ejpam-5226	228	10	.	.	PUNCT
ejpam-5226	229	1	proposition	proposition	NOUN
ejpam-5226	229	2	8	8	NUM
ejpam-5226	229	3	.	.	PUNCT
ejpam-5226	230	1	for	for	ADP
ejpam-5226	230	2	any	any	DET
ejpam-5226	230	3	∅	∅	NOUN
ejpam-5226	230	4	=	=	NOUN
ejpam-5226	230	5	̸	̸	NUM
ejpam-5226	230	6	s	s	PART
ejpam-5226	230	7	⊆	⊆	NUM
ejpam-5226	230	8	l	l	NOUN
ejpam-5226	230	9	,	,	PUNCT
ejpam-5226	230	10	s	s	VERB
ejpam-5226	230	11	⊆	⊆	NUM
ejpam-5226	230	12	hs	hs	NUM
ejpam-5226	230	13	⊆	⊆	NUM
ejpam-5226	230	14	(	(	PUNCT
ejpam-5226	230	15	s	s	X
ejpam-5226	230	16	]	]	PUNCT
ejpam-5226	230	17	.	.	PUNCT
ejpam-5226	231	1	remark	remark	PROPN
ejpam-5226	231	2	6	6	NUM
ejpam-5226	231	3	.	.	PUNCT
ejpam-5226	232	1	for	for	ADP
ejpam-5226	232	2	any	any	DET
ejpam-5226	232	3	∅	∅	NOUN
ejpam-5226	232	4	=	=	NOUN
ejpam-5226	232	5	̸	̸	NUM
ejpam-5226	232	6	s	s	PART
ejpam-5226	232	7	⊆	⊆	NUM
ejpam-5226	232	8	l	l	NOUN
ejpam-5226	232	9	,	,	PUNCT
ejpam-5226	232	10	hs	hs	PRON
ejpam-5226	232	11	need	need	AUX
ejpam-5226	232	12	not	not	PART
ejpam-5226	232	13	be	be	AUX
ejpam-5226	232	14	equal	equal	ADJ
ejpam-5226	232	15	to	to	ADP
ejpam-5226	232	16	(	(	PUNCT
ejpam-5226	232	17	s	s	X
ejpam-5226	232	18	]	]	X
ejpam-5226	232	19	.	.	PUNCT
ejpam-5226	233	1	in	in	ADP
ejpam-5226	233	2	example	example	NOUN
ejpam-5226	233	3	2	2	NUM
ejpam-5226	233	4	,	,	PUNCT
ejpam-5226	233	5	let	let	VERB
ejpam-5226	233	6	s	s	PRON
ejpam-5226	233	7	=	=	X
ejpam-5226	233	8	{	{	PUNCT
ejpam-5226	233	9	a	a	DET
ejpam-5226	233	10	,	,	PUNCT
ejpam-5226	233	11	b	b	NOUN
ejpam-5226	233	12	}	}	PUNCT
ejpam-5226	233	13	,	,	PUNCT
ejpam-5226	233	14	then	then	ADV
ejpam-5226	233	15	hs	hs	INTJ
ejpam-5226	233	16	=	=	PUNCT
ejpam-5226	233	17	{	{	PUNCT
ejpam-5226	233	18	0	0	NUM
ejpam-5226	233	19	,	,	PUNCT
ejpam-5226	233	20	a	a	DET
ejpam-5226	233	21	,	,	PUNCT
ejpam-5226	233	22	b	b	NOUN
ejpam-5226	233	23	}	}	PUNCT
ejpam-5226	233	24	and	and	CCONJ
ejpam-5226	233	25	(	(	PUNCT
ejpam-5226	233	26	s	s	X
ejpam-5226	233	27	]	]	X
ejpam-5226	233	28	=	=	X
ejpam-5226	233	29	{	{	PUNCT
ejpam-5226	233	30	0	0	NUM
ejpam-5226	233	31	,	,	PUNCT
ejpam-5226	233	32	a	a	DET
ejpam-5226	233	33	,	,	PUNCT
ejpam-5226	233	34	b	b	NOUN
ejpam-5226	233	35	,	,	PUNCT
ejpam-5226	233	36	1	1	NUM
ejpam-5226	233	37	}	}	PUNCT
ejpam-5226	233	38	=	=	PUNCT
ejpam-5226	233	39	l.	l.	PROPN
ejpam-5226	233	40	therefore	therefore	ADV
ejpam-5226	233	41	,	,	PUNCT
ejpam-5226	233	42	hs	hs	PROPN
ejpam-5226	233	43	⊂	⊂	PROPN
ejpam-5226	233	44	(	(	PUNCT
ejpam-5226	233	45	s	s	X
ejpam-5226	233	46	]	]	PUNCT
ejpam-5226	233	47	but	but	CCONJ
ejpam-5226	233	48	hs	hs	PROPN
ejpam-5226	233	49	̸=	̸=	PROPN
ejpam-5226	233	50	(	(	PUNCT
ejpam-5226	233	51	s	s	PROPN
ejpam-5226	233	52	]	]	PUNCT
ejpam-5226	233	53	.	.	PUNCT
ejpam-5226	234	1	proposition	proposition	NOUN
ejpam-5226	234	2	9	9	NUM
ejpam-5226	234	3	.	.	PUNCT
ejpam-5226	235	1	for	for	ADP
ejpam-5226	235	2	any	any	DET
ejpam-5226	235	3	∅	∅	NOUN
ejpam-5226	235	4	=	=	NOUN
ejpam-5226	235	5	̸	̸	NUM
ejpam-5226	235	6	s1	s1	NOUN
ejpam-5226	235	7	,	,	PUNCT
ejpam-5226	235	8	s2	s2	PROPN
ejpam-5226	235	9	,	,	PUNCT
ejpam-5226	235	10	s3	s3	PROPN
ejpam-5226	235	11	⊆	⊆	NUM
ejpam-5226	235	12	l	l	NOUN
ejpam-5226	235	13	,	,	PUNCT
ejpam-5226	235	14	we	we	PRON
ejpam-5226	235	15	have	have	VERB
ejpam-5226	235	16	(	(	PUNCT
ejpam-5226	235	17	i	i	NOUN
ejpam-5226	235	18	)	)	PUNCT
ejpam-5226	235	19	s1	s1	PROPN
ejpam-5226	235	20	⊆	⊆	NUM
ejpam-5226	235	21	s1	s1	NOUN
ejpam-5226	235	22	∪	∪	NOUN
ejpam-5226	235	23	(	(	PUNCT
ejpam-5226	235	24	s2	s2	NOUN
ejpam-5226	235	25	∧	∧	PROPN
ejpam-5226	235	26	s1	s1	PROPN
ejpam-5226	235	27	)	)	PUNCT
ejpam-5226	235	28	,	,	PUNCT
ejpam-5226	235	29	(	(	PUNCT
ejpam-5226	235	30	ii	ii	NOUN
ejpam-5226	235	31	)	)	PUNCT
ejpam-5226	235	32	s1	s1	NOUN
ejpam-5226	235	33	⊆	⊆	NUM
ejpam-5226	235	34	s1	s1	PROPN
ejpam-5226	235	35	∧	∧	PROPN
ejpam-5226	235	36	(	(	PUNCT
ejpam-5226	235	37	s2	s2	NOUN
ejpam-5226	235	38	∪	∪	NOUN
ejpam-5226	235	39	s1	s1	NOUN
ejpam-5226	235	40	)	)	PUNCT
ejpam-5226	235	41	,	,	PUNCT
ejpam-5226	235	42	(	(	PUNCT
ejpam-5226	235	43	iii	iii	X
ejpam-5226	235	44	)	)	PUNCT
ejpam-5226	235	45	s1	s1	NOUN
ejpam-5226	235	46	∪	∪	NOUN
ejpam-5226	235	47	(	(	PUNCT
ejpam-5226	235	48	s2	s2	NOUN
ejpam-5226	235	49	∧	∧	PROPN
ejpam-5226	235	50	s3	s3	PROPN
ejpam-5226	235	51	)	)	PUNCT
ejpam-5226	235	52	⊆	⊆	NUM
ejpam-5226	235	53	(	(	PUNCT
ejpam-5226	235	54	s1	s1	PROPN
ejpam-5226	235	55	∪	∪	X
ejpam-5226	235	56	s2	s2	PROPN
ejpam-5226	235	57	)	)	PUNCT
ejpam-5226	235	58	∧	∧	PROPN
ejpam-5226	235	59	(	(	PUNCT
ejpam-5226	235	60	s1	s1	PROPN
ejpam-5226	235	61	∪	∪	PROPN
ejpam-5226	235	62	s3	s3	PROPN
ejpam-5226	235	63	)	)	PUNCT
ejpam-5226	235	64	,	,	PUNCT
ejpam-5226	235	65	(	(	PUNCT
ejpam-5226	235	66	iv	iv	X
ejpam-5226	235	67	)	)	PUNCT
ejpam-5226	235	68	(	(	PUNCT
ejpam-5226	235	69	s1	s1	PROPN
ejpam-5226	235	70	∧	∧	PROPN
ejpam-5226	235	71	s2	s2	PROPN
ejpam-5226	235	72	)	)	PUNCT
ejpam-5226	235	73	∪	∪	X
ejpam-5226	235	74	s3	s3	PROPN
ejpam-5226	235	75	⊆	⊆	NUM
ejpam-5226	235	76	(	(	PUNCT
ejpam-5226	235	77	s1	s1	PROPN
ejpam-5226	235	78	∪	∪	PROPN
ejpam-5226	235	79	s3	s3	PROPN
ejpam-5226	235	80	)	)	PUNCT
ejpam-5226	235	81	∧	∧	PROPN
ejpam-5226	235	82	(	(	PUNCT
ejpam-5226	235	83	s2	s2	PROPN
ejpam-5226	235	84	∪	∪	PROPN
ejpam-5226	235	85	s3	s3	PROPN
ejpam-5226	235	86	)	)	PUNCT
ejpam-5226	235	87	,	,	PUNCT
ejpam-5226	235	88	(	(	PUNCT
ejpam-5226	235	89	v	v	NOUN
ejpam-5226	235	90	)	)	PUNCT
ejpam-5226	235	91	s1	s1	NOUN
ejpam-5226	235	92	∧	∧	PROPN
ejpam-5226	235	93	(	(	PUNCT
ejpam-5226	235	94	s2	s2	PROPN
ejpam-5226	235	95	∪	∪	X
ejpam-5226	235	96	s3	s3	PROPN
ejpam-5226	235	97	)	)	PUNCT
ejpam-5226	235	98	=	=	PUNCT
ejpam-5226	236	1	(	(	PUNCT
ejpam-5226	236	2	s1	s1	PROPN
ejpam-5226	236	3	∧	∧	PROPN
ejpam-5226	236	4	s2	s2	PROPN
ejpam-5226	236	5	)	)	PUNCT
ejpam-5226	236	6	∪	∪	NOUN
ejpam-5226	236	7	(	(	PUNCT
ejpam-5226	236	8	s1	s1	PROPN
ejpam-5226	236	9	∧	∧	PROPN
ejpam-5226	236	10	s3	s3	PROPN
ejpam-5226	236	11	)	)	PUNCT
ejpam-5226	236	12	(	(	PUNCT
ejpam-5226	236	13	distributive	distributive	ADJ
ejpam-5226	236	14	law	law	NOUN
ejpam-5226	236	15	)	)	PUNCT
ejpam-5226	236	16	,	,	PUNCT
ejpam-5226	236	17	(	(	PUNCT
ejpam-5226	236	18	vi	vi	NOUN
ejpam-5226	236	19	)	)	PUNCT
ejpam-5226	236	20	(	(	PUNCT
ejpam-5226	236	21	s1	s1	PROPN
ejpam-5226	236	22	∪	∪	X
ejpam-5226	236	23	s2	s2	PROPN
ejpam-5226	236	24	)	)	PUNCT
ejpam-5226	236	25	∧	∧	PROPN
ejpam-5226	236	26	s3	s3	NOUN
ejpam-5226	236	27	=	=	SYM
ejpam-5226	236	28	(	(	PUNCT
ejpam-5226	236	29	s1	s1	PROPN
ejpam-5226	236	30	∧	∧	PROPN
ejpam-5226	236	31	s3	s3	PROPN
ejpam-5226	236	32	)	)	PUNCT
ejpam-5226	236	33	∪	∪	NOUN
ejpam-5226	236	34	(	(	PUNCT
ejpam-5226	236	35	s2	s2	NOUN
ejpam-5226	236	36	∧	∧	PROPN
ejpam-5226	236	37	s3	s3	PROPN
ejpam-5226	236	38	)	)	PUNCT
ejpam-5226	236	39	(	(	PUNCT
ejpam-5226	236	40	distributive	distributive	ADJ
ejpam-5226	236	41	law	law	NOUN
ejpam-5226	236	42	)	)	PUNCT
ejpam-5226	236	43	.	.	PUNCT
ejpam-5226	237	1	remark	remark	PROPN
ejpam-5226	237	2	7	7	NUM
ejpam-5226	237	3	.	.	PUNCT
ejpam-5226	238	1	for	for	ADP
ejpam-5226	238	2	any	any	DET
ejpam-5226	238	3	non	non	ADJ
ejpam-5226	238	4	-	-	ADJ
ejpam-5226	238	5	empty	empty	ADJ
ejpam-5226	238	6	subsets	subset	NOUN
ejpam-5226	238	7	s1	s1	NOUN
ejpam-5226	238	8	,	,	PUNCT
ejpam-5226	238	9	s2	s2	NOUN
ejpam-5226	238	10	of	of	ADP
ejpam-5226	238	11	l	l	PROPN
ejpam-5226	238	12	,	,	PUNCT
ejpam-5226	238	13	the	the	DET
ejpam-5226	238	14	following	follow	VERB
ejpam-5226	238	15	absorption	absorption	NOUN
ejpam-5226	238	16	laws	law	NOUN
ejpam-5226	238	17	need	need	AUX
ejpam-5226	238	18	not	not	PART
ejpam-5226	238	19	be	be	AUX
ejpam-5226	238	20	held	hold	VERB
ejpam-5226	238	21	:	:	PUNCT
ejpam-5226	238	22	(	(	PUNCT
ejpam-5226	238	23	i	i	NOUN
ejpam-5226	238	24	)	)	PUNCT
ejpam-5226	238	25	s1	s1	NOUN
ejpam-5226	238	26	∪	∪	NOUN
ejpam-5226	238	27	(	(	PUNCT
ejpam-5226	238	28	s2	s2	NOUN
ejpam-5226	238	29	∧	∧	PROPN
ejpam-5226	238	30	s1	s1	NOUN
ejpam-5226	238	31	)	)	PUNCT
ejpam-5226	238	32	=	=	SYM
ejpam-5226	238	33	s1	s1	NOUN
ejpam-5226	238	34	,	,	PUNCT
ejpam-5226	238	35	(	(	PUNCT
ejpam-5226	238	36	ii	ii	NOUN
ejpam-5226	238	37	)	)	PUNCT
ejpam-5226	238	38	s1	s1	PROPN
ejpam-5226	238	39	∧	∧	PROPN
ejpam-5226	238	40	(	(	PUNCT
ejpam-5226	238	41	s2	s2	NOUN
ejpam-5226	238	42	∪	∪	NOUN
ejpam-5226	238	43	s1	s1	NOUN
ejpam-5226	238	44	)	)	PUNCT
ejpam-5226	238	45	=	=	SYM
ejpam-5226	238	46	s1	s1	PROPN
ejpam-5226	238	47	.	.	PUNCT
ejpam-5226	239	1	in	in	ADP
ejpam-5226	239	2	example	example	NOUN
ejpam-5226	239	3	1	1	NUM
ejpam-5226	239	4	,	,	PUNCT
ejpam-5226	239	5	(	(	PUNCT
ejpam-5226	239	6	i	i	NOUN
ejpam-5226	239	7	)	)	PUNCT
ejpam-5226	239	8	take	take	VERB
ejpam-5226	239	9	s1	s1	NOUN
ejpam-5226	239	10	=	=	PUNCT
ejpam-5226	239	11	{	{	PUNCT
ejpam-5226	239	12	a	a	NOUN
ejpam-5226	239	13	}	}	PUNCT
ejpam-5226	239	14	and	and	CCONJ
ejpam-5226	239	15	s2	s2	VERB
ejpam-5226	239	16	=	=	SYM
ejpam-5226	239	17	{	{	PUNCT
ejpam-5226	239	18	b	b	NOUN
ejpam-5226	239	19	}	}	PUNCT
ejpam-5226	239	20	.	.	PUNCT
ejpam-5226	240	1	then	then	ADV
ejpam-5226	240	2	s2	s2	VERB
ejpam-5226	240	3	∧	∧	PROPN
ejpam-5226	240	4	s1	s1	NOUN
ejpam-5226	240	5	=	=	PUNCT
ejpam-5226	240	6	{	{	PUNCT
ejpam-5226	240	7	0	0	NUM
ejpam-5226	240	8	}	}	PUNCT
ejpam-5226	240	9	.	.	PUNCT
ejpam-5226	241	1	therefore	therefore	ADV
ejpam-5226	241	2	,	,	PUNCT
ejpam-5226	241	3	s1	s1	NOUN
ejpam-5226	241	4	∪	∪	NOUN
ejpam-5226	241	5	(	(	PUNCT
ejpam-5226	241	6	s2	s2	NOUN
ejpam-5226	241	7	∧	∧	PROPN
ejpam-5226	241	8	s1	s1	NOUN
ejpam-5226	241	9	)	)	PUNCT
ejpam-5226	241	10	=	=	PUNCT
ejpam-5226	241	11	{	{	PUNCT
ejpam-5226	241	12	0	0	NUM
ejpam-5226	241	13	,	,	PUNCT
ejpam-5226	241	14	a	a	DET
ejpam-5226	241	15	}	}	PUNCT
ejpam-5226	241	16	=	=	NOUN
ejpam-5226	241	17	̸	̸	NUM
ejpam-5226	241	18	s1	s1	NOUN
ejpam-5226	241	19	.	.	PUNCT
ejpam-5226	241	20	(	(	PUNCT
ejpam-5226	241	21	ii	ii	NOUN
ejpam-5226	241	22	)	)	PUNCT
ejpam-5226	241	23	take	take	VERB
ejpam-5226	241	24	s2∪s1	s2∪s1	NOUN
ejpam-5226	241	25	=	=	PUNCT
ejpam-5226	241	26	{	{	PUNCT
ejpam-5226	241	27	a	a	PRON
ejpam-5226	241	28	,	,	PUNCT
ejpam-5226	241	29	b	b	NOUN
ejpam-5226	241	30	}	}	PUNCT
ejpam-5226	241	31	.	.	PUNCT
ejpam-5226	242	1	then	then	ADV
ejpam-5226	242	2	s1	s1	PROPN
ejpam-5226	242	3	∧	∧	PROPN
ejpam-5226	242	4	(	(	PUNCT
ejpam-5226	242	5	s2∪s1	s2∪s1	NOUN
ejpam-5226	242	6	)	)	PUNCT
ejpam-5226	242	7	=	=	SYM
ejpam-5226	242	8	{	{	PUNCT
ejpam-5226	242	9	0	0	NUM
ejpam-5226	242	10	,	,	PUNCT
ejpam-5226	242	11	a	a	PRON
ejpam-5226	242	12	}	}	PUNCT
ejpam-5226	242	13	.	.	PUNCT
ejpam-5226	243	1	therefore	therefore	ADV
ejpam-5226	243	2	,	,	PUNCT
ejpam-5226	243	3	s1	s1	PROPN
ejpam-5226	243	4	∧	∧	PROPN
ejpam-5226	243	5	(	(	PUNCT
ejpam-5226	243	6	s2∪s1	s2∪s1	NOUN
ejpam-5226	243	7	)	)	PUNCT
ejpam-5226	243	8	̸=	̸=	PROPN
ejpam-5226	243	9	s1	s1	NOUN
ejpam-5226	243	10	.	.	PUNCT
ejpam-5226	243	11	remark	remark	PROPN
ejpam-5226	243	12	8	8	NUM
ejpam-5226	243	13	.	.	PUNCT
ejpam-5226	244	1	for	for	ADP
ejpam-5226	244	2	any	any	DET
ejpam-5226	244	3	∅	∅	NOUN
ejpam-5226	244	4	=	=	NOUN
ejpam-5226	244	5	̸	̸	NUM
ejpam-5226	244	6	s1	s1	NOUN
ejpam-5226	244	7	,	,	PUNCT
ejpam-5226	244	8	s2	s2	PROPN
ejpam-5226	244	9	,	,	PUNCT
ejpam-5226	244	10	s3	s3	PROPN
ejpam-5226	244	11	⊆	⊆	NUM
ejpam-5226	244	12	l	l	NOUN
ejpam-5226	244	13	,	,	PUNCT
ejpam-5226	244	14	the	the	DET
ejpam-5226	244	15	following	follow	VERB
ejpam-5226	244	16	distributive	distributive	ADJ
ejpam-5226	244	17	laws	law	NOUN
ejpam-5226	244	18	need	need	AUX
ejpam-5226	244	19	not	not	PART
ejpam-5226	244	20	be	be	AUX
ejpam-5226	244	21	held	hold	VERB
ejpam-5226	244	22	:	:	PUNCT
ejpam-5226	244	23	(	(	PUNCT
ejpam-5226	244	24	i	i	NOUN
ejpam-5226	244	25	)	)	PUNCT
ejpam-5226	244	26	s1	s1	NOUN
ejpam-5226	244	27	∪	∪	NOUN
ejpam-5226	244	28	(	(	PUNCT
ejpam-5226	244	29	s2	s2	NOUN
ejpam-5226	244	30	∧	∧	PROPN
ejpam-5226	244	31	s3	s3	PROPN
ejpam-5226	244	32	)	)	PUNCT
ejpam-5226	244	33	=	=	PUNCT
ejpam-5226	245	1	(	(	PUNCT
ejpam-5226	245	2	s1	s1	PROPN
ejpam-5226	245	3	∪	∪	X
ejpam-5226	245	4	s2	s2	PROPN
ejpam-5226	245	5	)	)	PUNCT
ejpam-5226	245	6	∧	∧	PROPN
ejpam-5226	245	7	(	(	PUNCT
ejpam-5226	245	8	s1	s1	PROPN
ejpam-5226	245	9	∪	∪	PROPN
ejpam-5226	245	10	s3	s3	PROPN
ejpam-5226	245	11	)	)	PUNCT
ejpam-5226	245	12	(	(	PUNCT
ejpam-5226	245	13	distributive	distributive	ADJ
ejpam-5226	245	14	law	law	NOUN
ejpam-5226	245	15	)	)	PUNCT
ejpam-5226	245	16	,	,	PUNCT
ejpam-5226	245	17	(	(	PUNCT
ejpam-5226	245	18	ii	ii	NOUN
ejpam-5226	245	19	)	)	PUNCT
ejpam-5226	245	20	(	(	PUNCT
ejpam-5226	245	21	s1	s1	PROPN
ejpam-5226	245	22	∧	∧	PROPN
ejpam-5226	245	23	s2	s2	PROPN
ejpam-5226	245	24	)	)	PUNCT
ejpam-5226	245	25	∪	∪	NOUN
ejpam-5226	245	26	s3	s3	PROPN
ejpam-5226	245	27	=	=	SYM
ejpam-5226	245	28	(	(	PUNCT
ejpam-5226	245	29	s1	s1	PROPN
ejpam-5226	245	30	∪	∪	PROPN
ejpam-5226	245	31	s3	s3	PROPN
ejpam-5226	245	32	)	)	PUNCT
ejpam-5226	245	33	∧	∧	PROPN
ejpam-5226	245	34	(	(	PUNCT
ejpam-5226	245	35	s2	s2	PROPN
ejpam-5226	245	36	∪	∪	PROPN
ejpam-5226	245	37	s3	s3	PROPN
ejpam-5226	245	38	)	)	PUNCT
ejpam-5226	245	39	(	(	PUNCT
ejpam-5226	245	40	distributive	distributive	ADJ
ejpam-5226	245	41	law	law	NOUN
ejpam-5226	245	42	)	)	PUNCT
ejpam-5226	245	43	.	.	PUNCT
ejpam-5226	246	1	in	in	ADP
ejpam-5226	246	2	example	example	NOUN
ejpam-5226	246	3	1	1	NUM
ejpam-5226	246	4	,	,	PUNCT
ejpam-5226	246	5	(	(	PUNCT
ejpam-5226	246	6	i	i	NOUN
ejpam-5226	246	7	)	)	PUNCT
ejpam-5226	246	8	take	take	VERB
ejpam-5226	246	9	s1	s1	NOUN
ejpam-5226	246	10	=	=	PUNCT
ejpam-5226	246	11	{	{	PUNCT
ejpam-5226	246	12	a	a	DET
ejpam-5226	246	13	,	,	PUNCT
ejpam-5226	246	14	b	b	NOUN
ejpam-5226	246	15	}	}	PUNCT
ejpam-5226	246	16	,	,	PUNCT
ejpam-5226	246	17	s2	s2	NOUN
ejpam-5226	246	18	=	=	PUNCT
ejpam-5226	246	19	{	{	PUNCT
ejpam-5226	246	20	1	1	NUM
ejpam-5226	246	21	}	}	PUNCT
ejpam-5226	246	22	and	and	CCONJ
ejpam-5226	246	23	s3	s3	PROPN
ejpam-5226	246	24	=	=	SYM
ejpam-5226	246	25	{	{	PUNCT
ejpam-5226	246	26	c	c	NOUN
ejpam-5226	246	27	}	}	PUNCT
ejpam-5226	246	28	.	.	PUNCT
ejpam-5226	247	1	then	then	ADV
ejpam-5226	247	2	s2	s2	VERB
ejpam-5226	247	3	∧	∧	PROPN
ejpam-5226	247	4	s3	s3	PROPN
ejpam-5226	247	5	=	=	SYM
ejpam-5226	247	6	{	{	PUNCT
ejpam-5226	247	7	c	c	NOUN
ejpam-5226	247	8	}	}	PUNCT
ejpam-5226	247	9	,	,	PUNCT
ejpam-5226	247	10	s1	s1	NOUN
ejpam-5226	247	11	∪	∪	NOUN
ejpam-5226	247	12	s2	s2	NOUN
ejpam-5226	247	13	=	=	PUNCT
ejpam-5226	247	14	{	{	PUNCT
ejpam-5226	247	15	a	a	PRON
ejpam-5226	247	16	,	,	PUNCT
ejpam-5226	247	17	b	b	NOUN
ejpam-5226	247	18	,	,	PUNCT
ejpam-5226	247	19	1	1	NUM
ejpam-5226	247	20	}	}	PUNCT
ejpam-5226	247	21	and	and	CCONJ
ejpam-5226	247	22	s1	s1	NOUN
ejpam-5226	247	23	∪s3	∪s3	NOUN
ejpam-5226	248	1	=	=	PUNCT
ejpam-5226	248	2	{	{	PUNCT
ejpam-5226	248	3	a	a	PRON
ejpam-5226	248	4	,	,	PUNCT
ejpam-5226	248	5	b	b	NOUN
ejpam-5226	248	6	,	,	PUNCT
ejpam-5226	248	7	c	c	NOUN
ejpam-5226	248	8	}	}	PUNCT
ejpam-5226	248	9	.	.	PUNCT
ejpam-5226	249	1	now	now	ADV
ejpam-5226	249	2	,	,	PUNCT
ejpam-5226	249	3	s1	s1	PROPN
ejpam-5226	249	4	∪	∪	NOUN
ejpam-5226	249	5	(	(	PUNCT
ejpam-5226	249	6	s2	s2	NOUN
ejpam-5226	249	7	∧	∧	PROPN
ejpam-5226	249	8	s3	s3	PROPN
ejpam-5226	249	9	)	)	PUNCT
ejpam-5226	249	10	=	=	PRON
ejpam-5226	249	11	{	{	PUNCT
ejpam-5226	249	12	a	a	PRON
ejpam-5226	249	13	,	,	PUNCT
ejpam-5226	249	14	b	b	NOUN
ejpam-5226	249	15	,	,	PUNCT
ejpam-5226	249	16	c	c	NOUN
ejpam-5226	249	17	}	}	PUNCT
ejpam-5226	249	18	and	and	CCONJ
ejpam-5226	249	19	(	(	PUNCT
ejpam-5226	249	20	s1∪s2	s1∪s2	NOUN
ejpam-5226	249	21	)	)	PUNCT
ejpam-5226	249	22	∧	∧	NOUN
ejpam-5226	249	23	(	(	PUNCT
ejpam-5226	249	24	s1∪	s1∪	NOUN
ejpam-5226	249	25	s3	s3	PROPN
ejpam-5226	249	26	)	)	PUNCT
ejpam-5226	249	27	=	=	PUNCT
ejpam-5226	249	28	{	{	PUNCT
ejpam-5226	249	29	0	0	NUM
ejpam-5226	249	30	,	,	PUNCT
ejpam-5226	249	31	a	a	DET
ejpam-5226	249	32	,	,	PUNCT
ejpam-5226	249	33	b	b	NOUN
ejpam-5226	249	34	,	,	PUNCT
ejpam-5226	249	35	c	c	NOUN
ejpam-5226	249	36	}	}	PUNCT
ejpam-5226	249	37	.	.	PUNCT
ejpam-5226	250	1	therefore	therefore	ADV
ejpam-5226	250	2	,	,	PUNCT
ejpam-5226	250	3	s1	s1	NOUN
ejpam-5226	250	4	∪	∪	NOUN
ejpam-5226	250	5	(	(	PUNCT
ejpam-5226	250	6	s2	s2	NOUN
ejpam-5226	250	7	∧	∧	PROPN
ejpam-5226	250	8	s3	s3	PROPN
ejpam-5226	250	9	)	)	PUNCT
ejpam-5226	250	10	̸=	̸=	PROPN
ejpam-5226	250	11	(	(	PUNCT
ejpam-5226	250	12	s1	s1	PROPN
ejpam-5226	250	13	∪	∪	X
ejpam-5226	250	14	s2	s2	PROPN
ejpam-5226	250	15	)	)	PUNCT
ejpam-5226	250	16	∧	∧	PROPN
ejpam-5226	250	17	(	(	PUNCT
ejpam-5226	250	18	s1	s1	PROPN
ejpam-5226	250	19	∪	∪	PROPN
ejpam-5226	250	20	s3	s3	PROPN
ejpam-5226	250	21	)	)	PUNCT
ejpam-5226	250	22	.	.	PUNCT
ejpam-5226	251	1	(	(	PUNCT
ejpam-5226	251	2	ii	ii	NOUN
ejpam-5226	251	3	)	)	PUNCT
ejpam-5226	251	4	take	take	VERB
ejpam-5226	251	5	s1	s1	NOUN
ejpam-5226	251	6	=	=	PUNCT
ejpam-5226	251	7	{	{	PUNCT
ejpam-5226	251	8	a	a	NOUN
ejpam-5226	251	9	}	}	PUNCT
ejpam-5226	251	10	,	,	PUNCT
ejpam-5226	251	11	s2	s2	NOUN
ejpam-5226	251	12	=	=	SYM
ejpam-5226	251	13	{	{	PUNCT
ejpam-5226	251	14	1	1	NUM
ejpam-5226	251	15	}	}	PUNCT
ejpam-5226	251	16	and	and	CCONJ
ejpam-5226	251	17	s3	s3	PROPN
ejpam-5226	251	18	=	=	SYM
ejpam-5226	251	19	{	{	PUNCT
ejpam-5226	251	20	b	b	PROPN
ejpam-5226	251	21	,	,	PUNCT
ejpam-5226	251	22	c	c	NOUN
ejpam-5226	251	23	}	}	PUNCT
ejpam-5226	251	24	.	.	PUNCT
ejpam-5226	252	1	then	then	ADV
ejpam-5226	252	2	s1	s1	PROPN
ejpam-5226	252	3	∧	∧	PROPN
ejpam-5226	252	4	s2	s2	NOUN
ejpam-5226	252	5	=	=	PRON
ejpam-5226	252	6	{	{	PUNCT
ejpam-5226	252	7	a	a	NOUN
ejpam-5226	252	8	}	}	PUNCT
ejpam-5226	252	9	,	,	PUNCT
ejpam-5226	252	10	s1	s1	PROPN
ejpam-5226	252	11	∪	∪	NOUN
ejpam-5226	252	12	s3	s3	PROPN
ejpam-5226	252	13	=	=	PUNCT
ejpam-5226	252	14	{	{	PUNCT
ejpam-5226	252	15	a	a	PRON
ejpam-5226	252	16	,	,	PUNCT
ejpam-5226	252	17	b	b	NOUN
ejpam-5226	252	18	,	,	PUNCT
ejpam-5226	252	19	c	c	NOUN
ejpam-5226	252	20	}	}	PUNCT
ejpam-5226	252	21	and	and	CCONJ
ejpam-5226	252	22	s2∪s3	s2∪s3	NOUN
ejpam-5226	252	23	=	=	SYM
ejpam-5226	252	24	{	{	PUNCT
ejpam-5226	252	25	b	b	PROPN
ejpam-5226	252	26	,	,	PUNCT
ejpam-5226	252	27	c	c	NOUN
ejpam-5226	252	28	,	,	PUNCT
ejpam-5226	252	29	1	1	NUM
ejpam-5226	252	30	}	}	PUNCT
ejpam-5226	252	31	.	.	PUNCT
ejpam-5226	253	1	now	now	ADV
ejpam-5226	253	2	,	,	PUNCT
ejpam-5226	253	3	(	(	PUNCT
ejpam-5226	253	4	s1	s1	PROPN
ejpam-5226	253	5	∧	∧	PROPN
ejpam-5226	253	6	s2)∪s3	s2)∪s3	PRON
ejpam-5226	253	7	=	=	SYM
ejpam-5226	253	8	{	{	PUNCT
ejpam-5226	253	9	a	a	PRON
ejpam-5226	253	10	,	,	PUNCT
ejpam-5226	253	11	b	b	NOUN
ejpam-5226	253	12	,	,	PUNCT
ejpam-5226	253	13	c	c	NOUN
ejpam-5226	253	14	}	}	PUNCT
ejpam-5226	253	15	and	and	CCONJ
ejpam-5226	253	16	(	(	PUNCT
ejpam-5226	253	17	s1∪s3	s1∪s3	NOUN
ejpam-5226	253	18	)	)	PUNCT
ejpam-5226	253	19	∧	∧	PROPN
ejpam-5226	253	20	(	(	PUNCT
ejpam-5226	253	21	s2∪s3	s2∪s3	NOUN
ejpam-5226	253	22	)	)	PUNCT
ejpam-5226	253	23	=	=	PUNCT
ejpam-5226	253	24	{	{	PUNCT
ejpam-5226	253	25	0	0	NUM
ejpam-5226	253	26	,	,	PUNCT
ejpam-5226	253	27	a	a	DET
ejpam-5226	253	28	,	,	PUNCT
ejpam-5226	253	29	b	b	NOUN
ejpam-5226	253	30	,	,	PUNCT
ejpam-5226	253	31	c	c	NOUN
ejpam-5226	253	32	}	}	PUNCT
ejpam-5226	253	33	.	.	PUNCT
ejpam-5226	254	1	therefore	therefore	ADV
ejpam-5226	254	2	,	,	PUNCT
ejpam-5226	254	3	(	(	PUNCT
ejpam-5226	254	4	s1	s1	PROPN
ejpam-5226	254	5	∧	∧	PROPN
ejpam-5226	254	6	s2	s2	PROPN
ejpam-5226	254	7	)	)	PUNCT
ejpam-5226	254	8	∪	∪	ADP
ejpam-5226	254	9	s3	s3	PROPN
ejpam-5226	254	10	̸=	̸=	PROPN
ejpam-5226	254	11	(	(	PUNCT
ejpam-5226	254	12	s1	s1	PROPN
ejpam-5226	254	13	∪	∪	PROPN
ejpam-5226	254	14	s3	s3	PROPN
ejpam-5226	254	15	)	)	PUNCT
ejpam-5226	254	16	∧	∧	PROPN
ejpam-5226	254	17	(	(	PUNCT
ejpam-5226	254	18	s2	s2	PROPN
ejpam-5226	254	19	∪	∪	X
ejpam-5226	254	20	s3	s3	PROPN
ejpam-5226	254	21	)	)	PUNCT
ejpam-5226	254	22	.	.	PUNCT
ejpam-5226	255	1	a.	a.	PROPN
ejpam-5226	255	2	iampan	iampan	PROPN
ejpam-5226	255	3	et	et	PROPN
ejpam-5226	255	4	al	al	PROPN
ejpam-5226	255	5	.	.	PUNCT
ejpam-5226	255	6	/	/	SYM
ejpam-5226	255	7	eur	eur	PROPN
ejpam-5226	255	8	.	.	PUNCT
ejpam-5226	256	1	j.	j.	PROPN
ejpam-5226	256	2	pure	pure	PROPN
ejpam-5226	256	3	appl	appl	PROPN
ejpam-5226	256	4	.	.	PROPN
ejpam-5226	256	5	math	math	PROPN
ejpam-5226	256	6	,	,	PUNCT
ejpam-5226	256	7	17	17	NUM
ejpam-5226	256	8	(	(	PUNCT
ejpam-5226	256	9	3	3	NUM
ejpam-5226	256	10	)	)	PUNCT
ejpam-5226	256	11	(	(	PUNCT
ejpam-5226	256	12	2024	2024	NUM
ejpam-5226	256	13	)	)	PUNCT
ejpam-5226	256	14	,	,	PUNCT
ejpam-5226	256	15	1691	1691	NUM
ejpam-5226	256	16	-	-	SYM
ejpam-5226	256	17	1704	1704	NUM
ejpam-5226	256	18	1698	1698	NUM
ejpam-5226	256	19	proposition	proposition	NOUN
ejpam-5226	256	20	10	10	NUM
ejpam-5226	256	21	.	.	PUNCT
ejpam-5226	257	1	for	for	ADP
ejpam-5226	257	2	any	any	DET
ejpam-5226	257	3	∅	∅	NOUN
ejpam-5226	257	4	=	=	NOUN
ejpam-5226	257	5	̸	̸	NUM
ejpam-5226	257	6	s1	s1	NOUN
ejpam-5226	257	7	,	,	PUNCT
ejpam-5226	257	8	s2	s2	PROPN
ejpam-5226	257	9	,	,	PUNCT
ejpam-5226	257	10	s3	s3	PROPN
ejpam-5226	257	11	⊆	⊆	NUM
ejpam-5226	257	12	l	l	NOUN
ejpam-5226	257	13	,	,	PUNCT
ejpam-5226	257	14	we	we	PRON
ejpam-5226	257	15	have	have	VERB
ejpam-5226	257	16	(	(	PUNCT
ejpam-5226	257	17	i	i	NOUN
ejpam-5226	257	18	)	)	PUNCT
ejpam-5226	257	19	hs1	hs1	PROPN
ejpam-5226	257	20	∪	∪	X
ejpam-5226	257	21	(	(	PUNCT
ejpam-5226	257	22	hs2	hs2	NOUN
ejpam-5226	257	23	∧	∧	PROPN
ejpam-5226	257	24	hs1	hs1	PROPN
ejpam-5226	257	25	)	)	PUNCT
ejpam-5226	258	1	=	=	SYM
ejpam-5226	258	2	hs1	hs1	PROPN
ejpam-5226	258	3	(	(	PUNCT
ejpam-5226	258	4	absorption	absorption	NOUN
ejpam-5226	258	5	law	law	NOUN
ejpam-5226	258	6	)	)	PUNCT
ejpam-5226	258	7	,	,	PUNCT
ejpam-5226	258	8	(	(	PUNCT
ejpam-5226	258	9	ii	ii	NOUN
ejpam-5226	258	10	)	)	PUNCT
ejpam-5226	258	11	hs1	hs1	PROPN
ejpam-5226	258	12	∧	∧	PROPN
ejpam-5226	258	13	(	(	PUNCT
ejpam-5226	258	14	hs2	hs2	PROPN
ejpam-5226	258	15	∪hs1	∪hs1	PROPN
ejpam-5226	258	16	)	)	PUNCT
ejpam-5226	258	17	=	=	SYM
ejpam-5226	258	18	hs1	hs1	PROPN
ejpam-5226	258	19	(	(	PUNCT
ejpam-5226	258	20	absorption	absorption	NOUN
ejpam-5226	258	21	law	law	NOUN
ejpam-5226	258	22	)	)	PUNCT
ejpam-5226	258	23	,	,	PUNCT
ejpam-5226	258	24	(	(	PUNCT
ejpam-5226	258	25	iii	iii	X
ejpam-5226	258	26	)	)	PUNCT
ejpam-5226	258	27	hs1	hs1	PROPN
ejpam-5226	258	28	∪	∪	X
ejpam-5226	258	29	(	(	PUNCT
ejpam-5226	258	30	hs2	hs2	PROPN
ejpam-5226	258	31	∧	∧	PROPN
ejpam-5226	258	32	hs3	hs3	NOUN
ejpam-5226	258	33	)	)	PUNCT
ejpam-5226	258	34	=	=	PUNCT
ejpam-5226	258	35	(	(	PUNCT
ejpam-5226	258	36	hs1	hs1	PROPN
ejpam-5226	258	37	∪hs2	∪hs2	PROPN
ejpam-5226	258	38	)	)	PUNCT
ejpam-5226	258	39	∧	∧	NOUN
ejpam-5226	258	40	(	(	PUNCT
ejpam-5226	258	41	hs1	hs1	PROPN
ejpam-5226	258	42	∪hs3	∪hs3	PROPN
ejpam-5226	258	43	)	)	PUNCT
ejpam-5226	258	44	(	(	PUNCT
ejpam-5226	258	45	distributive	distributive	ADJ
ejpam-5226	258	46	law	law	NOUN
ejpam-5226	258	47	)	)	PUNCT
ejpam-5226	258	48	,	,	PUNCT
ejpam-5226	258	49	(	(	PUNCT
ejpam-5226	258	50	iv	iv	X
ejpam-5226	258	51	)	)	PUNCT
ejpam-5226	258	52	hs1	hs1	PROPN
ejpam-5226	258	53	∧	∧	PROPN
ejpam-5226	258	54	(	(	PUNCT
ejpam-5226	258	55	hs2	hs2	PROPN
ejpam-5226	258	56	∪hs3	∪hs3	PROPN
ejpam-5226	258	57	)	)	PUNCT
ejpam-5226	258	58	=	=	PUNCT
ejpam-5226	258	59	(	(	PUNCT
ejpam-5226	258	60	hs1	hs1	PROPN
ejpam-5226	258	61	∧	∧	PROPN
ejpam-5226	258	62	hs2	hs2	PROPN
ejpam-5226	258	63	)	)	PUNCT
ejpam-5226	258	64	∪	∪	NOUN
ejpam-5226	258	65	(	(	PUNCT
ejpam-5226	258	66	hs1	hs1	PROPN
ejpam-5226	258	67	∧	∧	PROPN
ejpam-5226	258	68	hs3	hs3	NOUN
ejpam-5226	258	69	)	)	PUNCT
ejpam-5226	258	70	(	(	PUNCT
ejpam-5226	258	71	distributive	distributive	ADJ
ejpam-5226	258	72	law	law	NOUN
ejpam-5226	258	73	)	)	PUNCT
ejpam-5226	258	74	.	.	PUNCT
ejpam-5226	259	1	proof	proof	NOUN
ejpam-5226	259	2	.	.	PUNCT
ejpam-5226	260	1	(	(	PUNCT
ejpam-5226	260	2	i	i	NOUN
ejpam-5226	260	3	)	)	PUNCT
ejpam-5226	260	4	let	let	VERB
ejpam-5226	260	5	x	x	PUNCT
ejpam-5226	260	6	∈	∈	PROPN
ejpam-5226	260	7	hs1	hs1	NOUN
ejpam-5226	260	8	∪	∪	X
ejpam-5226	260	9	(	(	PUNCT
ejpam-5226	260	10	hs2	hs2	NOUN
ejpam-5226	260	11	∧	∧	PROPN
ejpam-5226	260	12	hs1	hs1	PROPN
ejpam-5226	260	13	)	)	PUNCT
ejpam-5226	260	14	=	=	PUNCT
ejpam-5226	260	15	hs1	hs1	PROPN
ejpam-5226	260	16	∪	∪	VERB
ejpam-5226	260	17	hs2	hs2	NOUN
ejpam-5226	260	18	∧	∧	PROPN
ejpam-5226	260	19	s1	s1	PROPN
ejpam-5226	260	20	.	.	PUNCT
ejpam-5226	261	1	if	if	SCONJ
ejpam-5226	261	2	x	x	SYM
ejpam-5226	261	3	∈	∈	PROPN
ejpam-5226	261	4	hs1	hs1	PROPN
ejpam-5226	261	5	,	,	PUNCT
ejpam-5226	261	6	then	then	ADV
ejpam-5226	261	7	hs1	hs1	PROPN
ejpam-5226	261	8	∪	∪	X
ejpam-5226	261	9	(	(	PUNCT
ejpam-5226	261	10	hs2	hs2	NOUN
ejpam-5226	261	11	∧	∧	PROPN
ejpam-5226	261	12	hs1	hs1	PROPN
ejpam-5226	261	13	)	)	PUNCT
ejpam-5226	261	14	⊆	⊆	NUM
ejpam-5226	261	15	hs1	hs1	NOUN
ejpam-5226	261	16	.	.	PUNCT
ejpam-5226	262	1	if	if	SCONJ
ejpam-5226	262	2	x	x	SYM
ejpam-5226	262	3	∈	∈	PROPN
ejpam-5226	262	4	hs2	hs2	NOUN
ejpam-5226	262	5	∧	∧	PROPN
ejpam-5226	262	6	s1	s1	PROPN
ejpam-5226	262	7	,	,	PUNCT
ejpam-5226	262	8	then	then	ADV
ejpam-5226	262	9	there	there	PRON
ejpam-5226	262	10	exists	exist	VERB
ejpam-5226	262	11	s	s	PART
ejpam-5226	262	12	=	=	NOUN
ejpam-5226	262	13	s2	s2	NOUN
ejpam-5226	262	14	∧	∧	PROPN
ejpam-5226	262	15	s1	s1	PROPN
ejpam-5226	262	16	∈	∈	PROPN
ejpam-5226	262	17	s2	s2	NOUN
ejpam-5226	262	18	∧	∧	PROPN
ejpam-5226	262	19	s1	s1	PROPN
ejpam-5226	262	20	such	such	ADJ
ejpam-5226	262	21	that	that	PRON
ejpam-5226	262	22	s	s	VERB
ejpam-5226	262	23	∧	∧	NOUN
ejpam-5226	262	24	x	x	PUNCT
ejpam-5226	262	25	=	=	SYM
ejpam-5226	262	26	s2	s2	NOUN
ejpam-5226	262	27	∧	∧	NOUN
ejpam-5226	262	28	s1	s1	NOUN
ejpam-5226	262	29	∧	∧	NOUN
ejpam-5226	262	30	x	x	X
ejpam-5226	262	31	=	=	PUNCT
ejpam-5226	262	32	x	x	PUNCT
ejpam-5226	262	33	for	for	ADP
ejpam-5226	262	34	some	some	DET
ejpam-5226	262	35	s2	s2	NOUN
ejpam-5226	262	36	∈	∈	PROPN
ejpam-5226	262	37	s2	s2	NOUN
ejpam-5226	262	38	and	and	CCONJ
ejpam-5226	262	39	s1	s1	PROPN
ejpam-5226	262	40	∈	∈	PROPN
ejpam-5226	262	41	s1	s1	NOUN
ejpam-5226	262	42	,	,	PUNCT
ejpam-5226	262	43	then	then	ADV
ejpam-5226	262	44	s1	s1	PROPN
ejpam-5226	262	45	∧	∧	PROPN
ejpam-5226	262	46	x	x	PUNCT
ejpam-5226	262	47	=	=	SYM
ejpam-5226	262	48	s1	s1	PROPN
ejpam-5226	262	49	∧	∧	PROPN
ejpam-5226	262	50	s2	s2	NOUN
ejpam-5226	262	51	∧	∧	NOUN
ejpam-5226	262	52	s1	s1	NOUN
ejpam-5226	262	53	∧	∧	PROPN
ejpam-5226	262	54	x	x	X
ejpam-5226	262	55	=	=	SYM
ejpam-5226	262	56	s2∧s1∧x	s2∧s1∧x	PROPN
ejpam-5226	262	57	=	=	PUNCT
ejpam-5226	262	58	x.	x.	NOUN
ejpam-5226	262	59	therefore	therefore	ADV
ejpam-5226	262	60	,	,	PUNCT
ejpam-5226	262	61	x	x	PROPN
ejpam-5226	262	62	∈	∈	PROPN
ejpam-5226	262	63	hs1	hs1	NOUN
ejpam-5226	262	64	.	.	PUNCT
ejpam-5226	263	1	hence	hence	ADV
ejpam-5226	263	2	,	,	PUNCT
ejpam-5226	263	3	hs1∪(hs2	hs1∪(hs2	PROPN
ejpam-5226	263	4	∧	∧	PROPN
ejpam-5226	263	5	hs1	hs1	PROPN
ejpam-5226	263	6	)	)	PUNCT
ejpam-5226	263	7	⊆	⊆	NUM
ejpam-5226	263	8	hs1	hs1	X
ejpam-5226	263	9	.	.	PUNCT
ejpam-5226	264	1	by	by	ADP
ejpam-5226	264	2	proposition	proposition	NOUN
ejpam-5226	264	3	9(i	9(i	NUM
ejpam-5226	264	4	)	)	PUNCT
ejpam-5226	264	5	,	,	PUNCT
ejpam-5226	264	6	s1	s1	PROPN
ejpam-5226	264	7	⊆	⊆	NUM
ejpam-5226	264	8	s1	s1	NOUN
ejpam-5226	264	9	∪	∪	NOUN
ejpam-5226	264	10	(	(	PUNCT
ejpam-5226	264	11	s2	s2	NOUN
ejpam-5226	264	12	∧	∧	PROPN
ejpam-5226	264	13	s1	s1	PROPN
ejpam-5226	264	14	)	)	PUNCT
ejpam-5226	264	15	.	.	PUNCT
ejpam-5226	265	1	therefore	therefore	ADV
ejpam-5226	265	2	,	,	PUNCT
ejpam-5226	265	3	hs1	hs1	PROPN
ejpam-5226	265	4	⊆	⊆	NUM
ejpam-5226	265	5	hs1∪(s2	hs1∪(s2	PROPN
ejpam-5226	265	6	∧	∧	PROPN
ejpam-5226	265	7	s1	s1	PROPN
ejpam-5226	265	8	)	)	PUNCT
ejpam-5226	265	9	.	.	PUNCT
ejpam-5226	266	1	hence	hence	ADV
ejpam-5226	266	2	,	,	PUNCT
ejpam-5226	266	3	hs1	hs1	PROPN
ejpam-5226	266	4	⊆	⊆	NUM
ejpam-5226	266	5	hs1	hs1	PROPN
ejpam-5226	266	6	∪	∪	X
ejpam-5226	266	7	(	(	PUNCT
ejpam-5226	266	8	hs2	hs2	PROPN
ejpam-5226	266	9	∧	∧	PROPN
ejpam-5226	266	10	hs1	hs1	PROPN
ejpam-5226	266	11	)	)	PUNCT
ejpam-5226	266	12	.	.	PUNCT
ejpam-5226	267	1	thus	thus	ADV
ejpam-5226	267	2	,	,	PUNCT
ejpam-5226	267	3	hs1	hs1	PROPN
ejpam-5226	267	4	∪	∪	X
ejpam-5226	267	5	(	(	PUNCT
ejpam-5226	267	6	hs2	hs2	NOUN
ejpam-5226	267	7	∧	∧	PROPN
ejpam-5226	267	8	hs1	hs1	PROPN
ejpam-5226	267	9	)	)	PUNCT
ejpam-5226	267	10	=	=	SYM
ejpam-5226	267	11	hs1	hs1	PROPN
ejpam-5226	267	12	.	.	PUNCT
ejpam-5226	268	1	(	(	PUNCT
ejpam-5226	268	2	ii	ii	NOUN
ejpam-5226	268	3	)	)	PUNCT
ejpam-5226	268	4	let	let	VERB
ejpam-5226	268	5	x	x	SYM
ejpam-5226	268	6	∈	∈	PROPN
ejpam-5226	268	7	hs1	hs1	PROPN
ejpam-5226	268	8	∧	∧	PROPN
ejpam-5226	268	9	(	(	PUNCT
ejpam-5226	268	10	hs2	hs2	PROPN
ejpam-5226	268	11	∪	∪	X
ejpam-5226	268	12	hs1	hs1	PROPN
ejpam-5226	268	13	)	)	PUNCT
ejpam-5226	269	1	=	=	PUNCT
ejpam-5226	269	2	hs1	hs1	X
ejpam-5226	269	3	∧	∧	PROPN
ejpam-5226	269	4	(	(	PUNCT
ejpam-5226	269	5	hs2∪s1	hs2∪s1	NOUN
ejpam-5226	269	6	)	)	PUNCT
ejpam-5226	269	7	=	=	PUNCT
ejpam-5226	270	1	hs1	hs1	X
ejpam-5226	270	2	∧	∧	PROPN
ejpam-5226	270	3	(	(	PUNCT
ejpam-5226	270	4	s2∪s1	s2∪s1	NOUN
ejpam-5226	270	5	)	)	PUNCT
ejpam-5226	270	6	.	.	PUNCT
ejpam-5226	271	1	then	then	ADV
ejpam-5226	271	2	there	there	PRON
ejpam-5226	271	3	exists	exist	VERB
ejpam-5226	271	4	s	s	PART
ejpam-5226	271	5	∈	∈	PROPN
ejpam-5226	271	6	s1	s1	NOUN
ejpam-5226	271	7	∧	∧	PROPN
ejpam-5226	271	8	(	(	PUNCT
ejpam-5226	271	9	s2∪s1	s2∪s1	NOUN
ejpam-5226	271	10	)	)	PUNCT
ejpam-5226	271	11	such	such	ADJ
ejpam-5226	271	12	that	that	DET
ejpam-5226	271	13	s∧x	s∧x	PROPN
ejpam-5226	271	14	=	=	PUNCT
ejpam-5226	271	15	x.	x.	NOUN
ejpam-5226	271	16	therefore	therefore	ADV
ejpam-5226	271	17	,	,	PUNCT
ejpam-5226	271	18	for	for	ADP
ejpam-5226	271	19	this	this	DET
ejpam-5226	271	20	s	s	PART
ejpam-5226	271	21	∈	∈	PROPN
ejpam-5226	271	22	s1	s1	NOUN
ejpam-5226	271	23	∧	∧	PROPN
ejpam-5226	271	24	(	(	PUNCT
ejpam-5226	271	25	s2∪s1	s2∪s1	NOUN
ejpam-5226	271	26	)	)	PUNCT
ejpam-5226	271	27	,	,	PUNCT
ejpam-5226	271	28	s	s	PART
ejpam-5226	271	29	=	=	PROPN
ejpam-5226	271	30	s1∧	s1∧	PROPN
ejpam-5226	271	31	s′	s′	NOUN
ejpam-5226	271	32	for	for	ADP
ejpam-5226	271	33	some	some	DET
ejpam-5226	271	34	s1	s1	PROPN
ejpam-5226	271	35	∈	∈	PROPN
ejpam-5226	271	36	s1	s1	NOUN
ejpam-5226	271	37	and	and	CCONJ
ejpam-5226	271	38	s′	s′	ADJ
ejpam-5226	271	39	∈	∈	PROPN
ejpam-5226	271	40	s2∪s1	s2∪s1	NOUN
ejpam-5226	271	41	.	.	PUNCT
ejpam-5226	272	1	now	now	ADV
ejpam-5226	272	2	,	,	PUNCT
ejpam-5226	272	3	s1∧x	s1∧x	PROPN
ejpam-5226	272	4	=	=	PROPN
ejpam-5226	272	5	s1∧	s1∧	PROPN
ejpam-5226	272	6	(	(	PUNCT
ejpam-5226	272	7	s∧x	s∧x	PROPN
ejpam-5226	272	8	)	)	PUNCT
ejpam-5226	272	9	=	=	SYM
ejpam-5226	272	10	s1∧	s1∧	NOUN
ejpam-5226	272	11	(	(	PUNCT
ejpam-5226	272	12	s1∧	s1∧	NOUN
ejpam-5226	272	13	s′)∧x	s′)∧x	NOUN
ejpam-5226	272	14	=	=	SYM
ejpam-5226	272	15	s1∧	s1∧	NOUN
ejpam-5226	272	16	s′∧x	s′∧x	NOUN
ejpam-5226	272	17	=	=	SYM
ejpam-5226	272	18	s	s	PART
ejpam-5226	272	19	∧	∧	NOUN
ejpam-5226	272	20	x	x	PUNCT
ejpam-5226	272	21	=	=	PUNCT
ejpam-5226	272	22	x.	x.	NOUN
ejpam-5226	272	23	therefore	therefore	ADV
ejpam-5226	272	24	,	,	PUNCT
ejpam-5226	272	25	x	x	PROPN
ejpam-5226	272	26	∈	∈	PROPN
ejpam-5226	272	27	hs1	hs1	NOUN
ejpam-5226	272	28	.	.	PUNCT
ejpam-5226	273	1	hence	hence	ADV
ejpam-5226	273	2	,	,	PUNCT
ejpam-5226	273	3	hs1	hs1	PROPN
ejpam-5226	273	4	∧	∧	PROPN
ejpam-5226	273	5	(	(	PUNCT
ejpam-5226	273	6	hs2	hs2	PROPN
ejpam-5226	273	7	∪hs1	∪hs1	PROPN
ejpam-5226	273	8	)	)	PUNCT
ejpam-5226	273	9	⊆	⊆	NUM
ejpam-5226	273	10	hs1	hs1	PROPN
ejpam-5226	273	11	.	.	PUNCT
ejpam-5226	274	1	by	by	ADP
ejpam-5226	274	2	proposition	proposition	NOUN
ejpam-5226	274	3	9(ii	9(ii	NUM
ejpam-5226	274	4	)	)	PUNCT
ejpam-5226	274	5	,	,	PUNCT
ejpam-5226	274	6	s1	s1	PROPN
ejpam-5226	274	7	⊆	⊆	NUM
ejpam-5226	274	8	s1	s1	PROPN
ejpam-5226	274	9	∧	∧	PROPN
ejpam-5226	274	10	(	(	PUNCT
ejpam-5226	274	11	s2∪s1	s2∪s1	NOUN
ejpam-5226	274	12	)	)	PUNCT
ejpam-5226	274	13	.	.	PUNCT
ejpam-5226	275	1	therefore	therefore	ADV
ejpam-5226	275	2	,	,	PUNCT
ejpam-5226	275	3	hs1	hs1	PROPN
ejpam-5226	275	4	⊆	⊆	NUM
ejpam-5226	275	5	hs1	hs1	PROPN
ejpam-5226	275	6	∧	∧	PROPN
ejpam-5226	275	7	(	(	PUNCT
ejpam-5226	275	8	s2∪s1	s2∪s1	NOUN
ejpam-5226	275	9	)	)	PUNCT
ejpam-5226	275	10	=	=	PUNCT
ejpam-5226	275	11	hs1	hs1	X
ejpam-5226	275	12	∧	∧	PROPN
ejpam-5226	275	13	h(s2∪s1	h(s2∪s1	PROPN
ejpam-5226	275	14	)	)	PUNCT
ejpam-5226	276	1	=	=	PUNCT
ejpam-5226	276	2	hs1	hs1	X
ejpam-5226	276	3	∧	∧	PROPN
ejpam-5226	276	4	(	(	PUNCT
ejpam-5226	276	5	hs2∪hs1	hs2∪hs1	NOUN
ejpam-5226	276	6	)	)	PUNCT
ejpam-5226	276	7	.	.	PUNCT
ejpam-5226	277	1	hence	hence	ADV
ejpam-5226	277	2	,	,	PUNCT
ejpam-5226	277	3	hs1	hs1	PROPN
ejpam-5226	277	4	∧	∧	PROPN
ejpam-5226	277	5	(	(	PUNCT
ejpam-5226	277	6	hs2	hs2	PROPN
ejpam-5226	277	7	∪hs1	∪hs1	PROPN
ejpam-5226	277	8	)	)	PUNCT
ejpam-5226	277	9	=	=	SYM
ejpam-5226	277	10	hs1	hs1	PROPN
ejpam-5226	277	11	.	.	PUNCT
ejpam-5226	278	1	(	(	PUNCT
ejpam-5226	278	2	iii	iii	X
ejpam-5226	278	3	)	)	PUNCT
ejpam-5226	278	4	let	let	VERB
ejpam-5226	278	5	x	x	SYM
ejpam-5226	278	6	∈	∈	PROPN
ejpam-5226	278	7	(	(	PUNCT
ejpam-5226	278	8	hs1	hs1	PROPN
ejpam-5226	278	9	∪	∪	PROPN
ejpam-5226	278	10	hs2	hs2	PROPN
ejpam-5226	278	11	)	)	PUNCT
ejpam-5226	278	12	∧	∧	PROPN
ejpam-5226	278	13	(	(	PUNCT
ejpam-5226	278	14	hs1	hs1	PROPN
ejpam-5226	278	15	∪	∪	ADP
ejpam-5226	278	16	hs3	hs3	NOUN
ejpam-5226	278	17	)	)	PUNCT
ejpam-5226	278	18	=	=	SYM
ejpam-5226	278	19	h(s1∪s2	h(s1∪s2	X
ejpam-5226	278	20	)	)	PUNCT
ejpam-5226	278	21	∧	∧	PROPN
ejpam-5226	278	22	h(s1∪s3	h(s1∪s3	NOUN
ejpam-5226	278	23	)	)	PUNCT
ejpam-5226	278	24	=	=	SYM
ejpam-5226	278	25	h(s1∪s2	h(s1∪s2	X
ejpam-5226	278	26	)	)	PUNCT
ejpam-5226	278	27	∧	∧	PROPN
ejpam-5226	278	28	(	(	PUNCT
ejpam-5226	278	29	s1∪s3	s1∪s3	NOUN
ejpam-5226	278	30	)	)	PUNCT
ejpam-5226	278	31	.	.	PUNCT
ejpam-5226	279	1	then	then	ADV
ejpam-5226	279	2	there	there	PRON
ejpam-5226	279	3	exists	exist	VERB
ejpam-5226	279	4	s	s	PROPN
ejpam-5226	279	5	∈	∈	PROPN
ejpam-5226	279	6	(	(	PUNCT
ejpam-5226	279	7	s1	s1	PROPN
ejpam-5226	279	8	∪	∪	X
ejpam-5226	279	9	s2	s2	PROPN
ejpam-5226	279	10	)	)	PUNCT
ejpam-5226	279	11	∧	∧	PROPN
ejpam-5226	279	12	(	(	PUNCT
ejpam-5226	279	13	s1	s1	PROPN
ejpam-5226	279	14	∪	∪	PROPN
ejpam-5226	279	15	s3	s3	PROPN
ejpam-5226	279	16	)	)	PUNCT
ejpam-5226	279	17	such	such	ADJ
ejpam-5226	279	18	that	that	PRON
ejpam-5226	279	19	s	s	VERB
ejpam-5226	279	20	∧	∧	NOUN
ejpam-5226	279	21	x	x	PUNCT
ejpam-5226	279	22	=	=	PUNCT
ejpam-5226	279	23	x.	x.	NOUN
ejpam-5226	279	24	for	for	ADP
ejpam-5226	279	25	this	this	DET
ejpam-5226	279	26	s	s	X
ejpam-5226	279	27	∈	∈	PROPN
ejpam-5226	279	28	(	(	PUNCT
ejpam-5226	279	29	s1	s1	PROPN
ejpam-5226	279	30	∪	∪	X
ejpam-5226	279	31	s2	s2	PROPN
ejpam-5226	279	32	)	)	PUNCT
ejpam-5226	279	33	∧	∧	PROPN
ejpam-5226	279	34	(	(	PUNCT
ejpam-5226	279	35	s1	s1	PROPN
ejpam-5226	279	36	∪	∪	PROPN
ejpam-5226	279	37	s3	s3	PROPN
ejpam-5226	279	38	)	)	PUNCT
ejpam-5226	279	39	,	,	PUNCT
ejpam-5226	279	40	s	s	VERB
ejpam-5226	279	41	=	=	PUNCT
ejpam-5226	279	42	a	a	DET
ejpam-5226	279	43	∧	∧	PROPN
ejpam-5226	279	44	b	b	PROPN
ejpam-5226	279	45	for	for	ADP
ejpam-5226	279	46	some	some	PRON
ejpam-5226	279	47	a	a	DET
ejpam-5226	279	48	∈	∈	NOUN
ejpam-5226	279	49	(	(	PUNCT
ejpam-5226	279	50	s1	s1	PROPN
ejpam-5226	279	51	∪	∪	X
ejpam-5226	279	52	s2	s2	PROPN
ejpam-5226	279	53	)	)	PUNCT
ejpam-5226	279	54	,	,	PUNCT
ejpam-5226	279	55	b	b	X
ejpam-5226	279	56	∈	∈	PROPN
ejpam-5226	279	57	(	(	PUNCT
ejpam-5226	279	58	s1	s1	PROPN
ejpam-5226	279	59	∪	∪	PROPN
ejpam-5226	279	60	s3	s3	PROPN
ejpam-5226	279	61	)	)	PUNCT
ejpam-5226	279	62	.	.	PUNCT
ejpam-5226	280	1	if	if	SCONJ
ejpam-5226	280	2	a	a	DET
ejpam-5226	280	3	∈	∈	PROPN
ejpam-5226	280	4	s1	s1	NOUN
ejpam-5226	280	5	and	and	CCONJ
ejpam-5226	280	6	b	b	PROPN
ejpam-5226	280	7	∈	∈	PROPN
ejpam-5226	280	8	s1	s1	NOUN
ejpam-5226	280	9	,	,	PUNCT
ejpam-5226	280	10	then	then	ADV
ejpam-5226	280	11	a	a	DET
ejpam-5226	280	12	∧	∧	PROPN
ejpam-5226	280	13	x	x	X
ejpam-5226	280	14	=	=	PUNCT
ejpam-5226	280	15	a	a	DET
ejpam-5226	280	16	∧	∧	PROPN
ejpam-5226	280	17	s	s	PART
ejpam-5226	280	18	∧	∧	PROPN
ejpam-5226	280	19	x	x	X
ejpam-5226	280	20	=	=	PUNCT
ejpam-5226	280	21	a	a	DET
ejpam-5226	280	22	∧	∧	PROPN
ejpam-5226	280	23	a	a	DET
ejpam-5226	280	24	∧	∧	PROPN
ejpam-5226	280	25	b	b	PROPN
ejpam-5226	280	26	∧	∧	PROPN
ejpam-5226	280	27	x	x	X
ejpam-5226	280	28	=	=	PUNCT
ejpam-5226	280	29	a	a	DET
ejpam-5226	280	30	∧	∧	PROPN
ejpam-5226	280	31	b	b	PROPN
ejpam-5226	280	32	∧	∧	PROPN
ejpam-5226	280	33	x	x	X
ejpam-5226	280	34	=	=	SYM
ejpam-5226	280	35	s	s	PART
ejpam-5226	280	36	∧	∧	NOUN
ejpam-5226	280	37	x	x	PUNCT
ejpam-5226	280	38	=	=	PUNCT
ejpam-5226	280	39	x.	x.	NOUN
ejpam-5226	280	40	therefore	therefore	ADV
ejpam-5226	280	41	,	,	PUNCT
ejpam-5226	280	42	x	x	PROPN
ejpam-5226	280	43	∈	∈	PROPN
ejpam-5226	280	44	hs1	hs1	NOUN
ejpam-5226	280	45	.	.	PUNCT
ejpam-5226	281	1	if	if	SCONJ
ejpam-5226	281	2	a	a	DET
ejpam-5226	281	3	∈	∈	PROPN
ejpam-5226	281	4	s2	s2	NOUN
ejpam-5226	281	5	and	and	CCONJ
ejpam-5226	281	6	b	b	NOUN
ejpam-5226	281	7	∈	∈	PROPN
ejpam-5226	281	8	s1	s1	NOUN
ejpam-5226	281	9	,	,	PUNCT
ejpam-5226	281	10	then	then	ADV
ejpam-5226	281	11	b∧	b∧	NUM
ejpam-5226	281	12	x	x	PUNCT
ejpam-5226	281	13	=	=	SYM
ejpam-5226	281	14	b∧	b∧	NOUN
ejpam-5226	281	15	s∧	s∧	NOUN
ejpam-5226	281	16	x	x	X
ejpam-5226	282	1	=	=	SYM
ejpam-5226	282	2	b∧	b∧	ADJ
ejpam-5226	282	3	a∧	a∧	NOUN
ejpam-5226	282	4	b∧	b∧	VERB
ejpam-5226	282	5	x	x	X
ejpam-5226	282	6	=	=	PUNCT
ejpam-5226	282	7	a∧	a∧	NOUN
ejpam-5226	282	8	b∧	b∧	NOUN
ejpam-5226	282	9	x	x	X
ejpam-5226	283	1	=	=	PUNCT
ejpam-5226	283	2	s∧	s∧	ADJ
ejpam-5226	283	3	x	x	X
ejpam-5226	283	4	=	=	PUNCT
ejpam-5226	283	5	x.	x.	NOUN
ejpam-5226	284	1	hence	hence	ADV
ejpam-5226	284	2	,	,	PUNCT
ejpam-5226	284	3	x	x	X
ejpam-5226	284	4	∈	∈	PROPN
ejpam-5226	284	5	hs1	hs1	NOUN
ejpam-5226	284	6	.	.	PUNCT
ejpam-5226	285	1	if	if	SCONJ
ejpam-5226	285	2	a	a	DET
ejpam-5226	285	3	∈	∈	PROPN
ejpam-5226	285	4	s2	s2	NOUN
ejpam-5226	285	5	and	and	CCONJ
ejpam-5226	285	6	b	b	PROPN
ejpam-5226	285	7	∈	∈	PROPN
ejpam-5226	285	8	s3	s3	PROPN
ejpam-5226	285	9	,	,	PUNCT
ejpam-5226	285	10	then	then	ADV
ejpam-5226	285	11	s	s	VERB
ejpam-5226	285	12	=	=	PUNCT
ejpam-5226	285	13	a	a	DET
ejpam-5226	285	14	∧	∧	PROPN
ejpam-5226	285	15	b	b	PROPN
ejpam-5226	285	16	∈	∈	PROPN
ejpam-5226	285	17	s2	s2	NOUN
ejpam-5226	285	18	∧	∧	PROPN
ejpam-5226	285	19	s3	s3	PROPN
ejpam-5226	285	20	and	and	CCONJ
ejpam-5226	285	21	s	s	X
ejpam-5226	285	22	∧	∧	NOUN
ejpam-5226	285	23	x	x	PUNCT
ejpam-5226	285	24	=	=	PUNCT
ejpam-5226	285	25	x.	x.	NOUN
ejpam-5226	285	26	therefore	therefore	ADV
ejpam-5226	285	27	,	,	PUNCT
ejpam-5226	285	28	x	x	PROPN
ejpam-5226	285	29	∈	∈	PROPN
ejpam-5226	285	30	hs2	hs2	NOUN
ejpam-5226	285	31	∧	∧	PROPN
ejpam-5226	285	32	s3	s3	PROPN
ejpam-5226	285	33	.	.	PUNCT
ejpam-5226	286	1	hence	hence	ADV
ejpam-5226	286	2	,	,	PUNCT
ejpam-5226	286	3	(	(	PUNCT
ejpam-5226	286	4	hs1	hs1	PROPN
ejpam-5226	286	5	∪	∪	PROPN
ejpam-5226	286	6	hs2	hs2	PROPN
ejpam-5226	286	7	)	)	PUNCT
ejpam-5226	286	8	∧	∧	PROPN
ejpam-5226	286	9	(	(	PUNCT
ejpam-5226	286	10	hs1	hs1	PROPN
ejpam-5226	286	11	∪	∪	ADP
ejpam-5226	286	12	hs3	hs3	NOUN
ejpam-5226	286	13	)	)	PUNCT
ejpam-5226	287	1	⊆	⊆	NUM
ejpam-5226	287	2	hs1	hs1	PROPN
ejpam-5226	287	3	∪	∪	X
ejpam-5226	287	4	(	(	PUNCT
ejpam-5226	287	5	hs2	hs2	PROPN
ejpam-5226	287	6	∧	∧	PROPN
ejpam-5226	287	7	hs3	hs3	NOUN
ejpam-5226	287	8	)	)	PUNCT
ejpam-5226	287	9	.	.	PUNCT
ejpam-5226	288	1	by	by	ADP
ejpam-5226	288	2	proposition	proposition	NOUN
ejpam-5226	288	3	9(iii	9(iii	NUM
ejpam-5226	288	4	)	)	PUNCT
ejpam-5226	288	5	,	,	PUNCT
ejpam-5226	288	6	s1	s1	NOUN
ejpam-5226	288	7	∪	∪	NOUN
ejpam-5226	288	8	(	(	PUNCT
ejpam-5226	288	9	s2	s2	NOUN
ejpam-5226	288	10	∧	∧	PROPN
ejpam-5226	288	11	s3	s3	PROPN
ejpam-5226	288	12	)	)	PUNCT
ejpam-5226	288	13	⊆	⊆	NUM
ejpam-5226	288	14	(	(	PUNCT
ejpam-5226	288	15	s1	s1	PROPN
ejpam-5226	288	16	∪	∪	X
ejpam-5226	288	17	s2	s2	PROPN
ejpam-5226	288	18	)	)	PUNCT
ejpam-5226	288	19	∧	∧	PROPN
ejpam-5226	288	20	(	(	PUNCT
ejpam-5226	288	21	s1	s1	PROPN
ejpam-5226	288	22	∪	∪	PROPN
ejpam-5226	288	23	s3	s3	PROPN
ejpam-5226	288	24	)	)	PUNCT
ejpam-5226	288	25	.	.	PUNCT
ejpam-5226	289	1	therefore	therefore	ADV
ejpam-5226	289	2	,	,	PUNCT
ejpam-5226	289	3	hs1∪(s2	hs1∪(s2	PROPN
ejpam-5226	289	4	∧	∧	PROPN
ejpam-5226	289	5	s3	s3	PROPN
ejpam-5226	289	6	)	)	PUNCT
ejpam-5226	289	7	⊆	⊆	NUM
ejpam-5226	289	8	h(s1∪s2	h(s1∪s2	ADJ
ejpam-5226	289	9	)	)	PUNCT
ejpam-5226	289	10	∧	∧	PROPN
ejpam-5226	289	11	(	(	PUNCT
ejpam-5226	289	12	s1∪s3	s1∪s3	NOUN
ejpam-5226	289	13	)	)	PUNCT
ejpam-5226	289	14	.	.	PUNCT
ejpam-5226	290	1	hence	hence	ADV
ejpam-5226	290	2	,	,	PUNCT
ejpam-5226	290	3	hs1	hs1	PROPN
ejpam-5226	290	4	∪	∪	X
ejpam-5226	290	5	(	(	PUNCT
ejpam-5226	290	6	hs2	hs2	PROPN
ejpam-5226	290	7	∧	∧	PROPN
ejpam-5226	290	8	hs3	hs3	NOUN
ejpam-5226	290	9	)	)	PUNCT
ejpam-5226	290	10	⊆	⊆	NUM
ejpam-5226	290	11	(	(	PUNCT
ejpam-5226	290	12	hs1	hs1	PROPN
ejpam-5226	290	13	∪	∪	PROPN
ejpam-5226	290	14	hs2	hs2	PROPN
ejpam-5226	290	15	)	)	PUNCT
ejpam-5226	290	16	∧	∧	PROPN
ejpam-5226	290	17	(	(	PUNCT
ejpam-5226	290	18	hs1	hs1	PROPN
ejpam-5226	290	19	∪	∪	ADP
ejpam-5226	290	20	hs3	hs3	NUM
ejpam-5226	290	21	)	)	PUNCT
ejpam-5226	290	22	.	.	PUNCT
ejpam-5226	291	1	thus	thus	ADV
ejpam-5226	291	2	,	,	PUNCT
ejpam-5226	291	3	hs1	hs1	PROPN
ejpam-5226	291	4	∪	∪	X
ejpam-5226	291	5	(	(	PUNCT
ejpam-5226	291	6	hs2	hs2	PROPN
ejpam-5226	291	7	∧	∧	PROPN
ejpam-5226	291	8	hs3	hs3	NOUN
ejpam-5226	291	9	)	)	PUNCT
ejpam-5226	291	10	=	=	NOUN
ejpam-5226	291	11	(	(	PUNCT
ejpam-5226	291	12	hs1	hs1	PROPN
ejpam-5226	291	13	∪	∪	PROPN
ejpam-5226	291	14	hs2	hs2	PROPN
ejpam-5226	291	15	)	)	PUNCT
ejpam-5226	291	16	∧	∧	PROPN
ejpam-5226	291	17	(	(	PUNCT
ejpam-5226	291	18	hs1	hs1	PROPN
ejpam-5226	291	19	∪hs3	∪hs3	PROPN
ejpam-5226	291	20	)	)	PUNCT
ejpam-5226	291	21	.	.	PUNCT
ejpam-5226	292	1	(	(	PUNCT
ejpam-5226	292	2	iv	iv	X
ejpam-5226	292	3	)	)	PUNCT
ejpam-5226	292	4	we	we	PRON
ejpam-5226	292	5	can	can	AUX
ejpam-5226	292	6	prove	prove	VERB
ejpam-5226	292	7	similarly	similarly	ADV
ejpam-5226	292	8	by	by	ADP
ejpam-5226	292	9	proposition	proposition	NOUN
ejpam-5226	292	10	9(v	9(v	NUM
ejpam-5226	292	11	)	)	PUNCT
ejpam-5226	292	12	.	.	PUNCT
ejpam-5226	293	1	let	let	VERB
ejpam-5226	293	2	us	we	PRON
ejpam-5226	293	3	denote	denote	VERB
ejpam-5226	293	4	the	the	DET
ejpam-5226	293	5	hierarchy	hierarchy	NOUN
ejpam-5226	293	6	sets	set	NOUN
ejpam-5226	293	7	of	of	ADP
ejpam-5226	293	8	l	l	NOUN
ejpam-5226	293	9	by	by	ADP
ejpam-5226	293	10	hs(=	hs(=	X
ejpam-5226	293	11	{	{	PUNCT
ejpam-5226	293	12	hs	hs	INTJ
ejpam-5226	293	13	|	|	ADV
ejpam-5226	293	14	s	s	VERB
ejpam-5226	293	15	⊆	⊆	NUM
ejpam-5226	293	16	l	l	NOUN
ejpam-5226	293	17	and	and	CCONJ
ejpam-5226	293	18	s	s	PROPN
ejpam-5226	293	19	̸=	̸=	PROPN
ejpam-5226	293	20	∅	∅	NOUN
ejpam-5226	293	21	}	}	PUNCT
ejpam-5226	293	22	)	)	PUNCT
ejpam-5226	293	23	.	.	PUNCT
ejpam-5226	294	1	we	we	PRON
ejpam-5226	294	2	have	have	VERB
ejpam-5226	294	3	the	the	DET
ejpam-5226	294	4	final	final	ADJ
ejpam-5226	294	5	conclusion	conclusion	NOUN
ejpam-5226	294	6	from	from	ADP
ejpam-5226	294	7	proposition	proposition	NOUN
ejpam-5226	294	8	10	10	NUM
ejpam-5226	294	9	,	,	PUNCT
ejpam-5226	294	10	below	below	ADV
ejpam-5226	294	11	.	.	PUNCT
ejpam-5226	295	1	theorem	theorem	NOUN
ejpam-5226	295	2	2	2	NUM
ejpam-5226	295	3	.	.	PUNCT
ejpam-5226	295	4	(	(	PUNCT
ejpam-5226	295	5	hs	hs	INTJ
ejpam-5226	295	6	,	,	PUNCT
ejpam-5226	295	7	∧	∧	PROPN
ejpam-5226	295	8	,	,	PUNCT
ejpam-5226	295	9	∪	∪	NOUN
ejpam-5226	295	10	,	,	PUNCT
ejpam-5226	295	11	{	{	PUNCT
ejpam-5226	295	12	0	0	NUM
ejpam-5226	295	13	}	}	PUNCT
ejpam-5226	295	14	,	,	PUNCT
ejpam-5226	295	15	l	l	NOUN
ejpam-5226	295	16	)	)	PUNCT
ejpam-5226	295	17	becomes	become	VERB
ejpam-5226	295	18	a	a	DET
ejpam-5226	295	19	bounded	bounded	ADJ
ejpam-5226	295	20	distributive	distributive	ADJ
ejpam-5226	295	21	lattice	lattice	NOUN
ejpam-5226	295	22	.	.	PUNCT
ejpam-5226	296	1	proof	proof	NOUN
ejpam-5226	296	2	.	.	PUNCT
ejpam-5226	297	1	by	by	ADP
ejpam-5226	297	2	the	the	DET
ejpam-5226	297	3	above	above	ADJ
ejpam-5226	297	4	propositions	proposition	NOUN
ejpam-5226	297	5	5	5	NUM
ejpam-5226	297	6	,	,	PUNCT
ejpam-5226	297	7	6	6	NUM
ejpam-5226	297	8	,	,	PUNCT
ejpam-5226	297	9	and	and	CCONJ
ejpam-5226	297	10	10	10	NUM
ejpam-5226	297	11	,	,	PUNCT
ejpam-5226	297	12	we	we	PRON
ejpam-5226	297	13	observe	observe	VERB
ejpam-5226	297	14	that	that	SCONJ
ejpam-5226	297	15	the	the	DET
ejpam-5226	297	16	set	set	NOUN
ejpam-5226	297	17	of	of	ADP
ejpam-5226	297	18	hierarchy	hierarchy	NOUN
ejpam-5226	297	19	sets	set	NOUN
ejpam-5226	297	20	hs	hs	PROPN
ejpam-5226	297	21	is	be	AUX
ejpam-5226	297	22	a	a	DET
ejpam-5226	297	23	distributive	distributive	ADJ
ejpam-5226	297	24	lattice	lattice	NOUN
ejpam-5226	297	25	with	with	ADP
ejpam-5226	297	26	the	the	DET
ejpam-5226	297	27	operations	operation	NOUN
ejpam-5226	297	28	∧	∧	NOUN
ejpam-5226	297	29	and	and	CCONJ
ejpam-5226	297	30	∪	∪	NOUN
ejpam-5226	297	31	and	and	CCONJ
ejpam-5226	297	32	hence	hence	ADV
ejpam-5226	297	33	,	,	PUNCT
ejpam-5226	297	34	h{0	h{0	X
ejpam-5226	297	35	}	}	PUNCT
ejpam-5226	297	36	=	=	SYM
ejpam-5226	297	37	{	{	PUNCT
ejpam-5226	297	38	0	0	NUM
ejpam-5226	297	39	}	}	PUNCT
ejpam-5226	297	40	is	be	AUX
ejpam-5226	297	41	the	the	DET
ejpam-5226	297	42	least	least	ADJ
ejpam-5226	297	43	element	element	NOUN
ejpam-5226	297	44	and	and	CCONJ
ejpam-5226	297	45	hl	hl	NOUN
ejpam-5226	298	1	=	=	NOUN
ejpam-5226	298	2	l	l	NOUN
ejpam-5226	298	3	is	be	AUX
ejpam-5226	298	4	the	the	DET
ejpam-5226	298	5	greatest	great	ADJ
ejpam-5226	298	6	element	element	NOUN
ejpam-5226	298	7	in	in	ADP
ejpam-5226	298	8	hs	hs	PROPN
ejpam-5226	298	9	.	.	PUNCT
ejpam-5226	299	1	a.	a.	PROPN
ejpam-5226	299	2	iampan	iampan	PROPN
ejpam-5226	299	3	et	et	PROPN
ejpam-5226	299	4	al	al	PROPN
ejpam-5226	299	5	.	.	PUNCT
ejpam-5226	299	6	/	/	SYM
ejpam-5226	299	7	eur	eur	PROPN
ejpam-5226	299	8	.	.	PUNCT
ejpam-5226	300	1	j.	j.	PROPN
ejpam-5226	300	2	pure	pure	PROPN
ejpam-5226	300	3	appl	appl	PROPN
ejpam-5226	300	4	.	.	PROPN
ejpam-5226	300	5	math	math	PROPN
ejpam-5226	300	6	,	,	PUNCT
ejpam-5226	300	7	17	17	NUM
ejpam-5226	300	8	(	(	PUNCT
ejpam-5226	300	9	3	3	NUM
ejpam-5226	300	10	)	)	PUNCT
ejpam-5226	300	11	(	(	PUNCT
ejpam-5226	300	12	2024	2024	NUM
ejpam-5226	300	13	)	)	PUNCT
ejpam-5226	300	14	,	,	PUNCT
ejpam-5226	300	15	1691	1691	NUM
ejpam-5226	300	16	-	-	SYM
ejpam-5226	300	17	1704	1704	NUM
ejpam-5226	300	18	1699	1699	NUM
ejpam-5226	300	19	theorem	theorem	NOUN
ejpam-5226	300	20	3	3	NUM
ejpam-5226	300	21	.	.	X
ejpam-5226	301	1	for	for	ADP
ejpam-5226	301	2	any	any	DET
ejpam-5226	301	3	non	non	ADJ
ejpam-5226	301	4	-	-	ADJ
ejpam-5226	301	5	empty	empty	ADJ
ejpam-5226	301	6	subsets	subset	NOUN
ejpam-5226	301	7	s0	s0	PROPN
ejpam-5226	301	8	,	,	PUNCT
ejpam-5226	301	9	s1	s1	PROPN
ejpam-5226	301	10	of	of	ADP
ejpam-5226	301	11	l	l	NOUN
ejpam-5226	301	12	,	,	PUNCT
ejpam-5226	301	13	hs0	hs0	NOUN
ejpam-5226	301	14	∧	∧	NOUN
ejpam-5226	301	15	hs1	hs1	NOUN
ejpam-5226	301	16	=	=	PUNCT
ejpam-5226	301	17	{	{	PUNCT
ejpam-5226	301	18	0	0	NUM
ejpam-5226	301	19	}	}	PUNCT
ejpam-5226	301	20	and	and	CCONJ
ejpam-5226	301	21	hs0∪hs1	hs0∪hs1	NOUN
ejpam-5226	302	1	=	=	NOUN
ejpam-5226	302	2	l	l	NOUN
ejpam-5226	302	3	if	if	SCONJ
ejpam-5226	302	4	and	and	CCONJ
ejpam-5226	302	5	only	only	ADV
ejpam-5226	302	6	if	if	SCONJ
ejpam-5226	302	7	s0	s0	PROPN
ejpam-5226	302	8	∧	∧	PROPN
ejpam-5226	302	9	s1	s1	PROPN
ejpam-5226	302	10	=	=	PUNCT
ejpam-5226	302	11	{	{	PUNCT
ejpam-5226	302	12	0	0	NUM
ejpam-5226	302	13	}	}	PUNCT
ejpam-5226	302	14	and	and	CCONJ
ejpam-5226	302	15	s0	s0	PROPN
ejpam-5226	302	16	∪	∪	NOUN
ejpam-5226	302	17	s1	s1	PROPN
ejpam-5226	302	18	contains	contain	VERB
ejpam-5226	302	19	a	a	DET
ejpam-5226	302	20	maximal	maximal	ADJ
ejpam-5226	302	21	element	element	NOUN
ejpam-5226	302	22	if	if	SCONJ
ejpam-5226	302	23	and	and	CCONJ
ejpam-5226	302	24	only	only	ADV
ejpam-5226	302	25	if	if	SCONJ
ejpam-5226	302	26	s0	s0	PROPN
ejpam-5226	302	27	=	=	PUNCT
ejpam-5226	302	28	{	{	PUNCT
ejpam-5226	302	29	0	0	NUM
ejpam-5226	302	30	}	}	PUNCT
ejpam-5226	302	31	⇒	⇒	NOUN
ejpam-5226	302	32	s1	s1	NOUN
ejpam-5226	302	33	contains	contain	VERB
ejpam-5226	302	34	a	a	DET
ejpam-5226	302	35	maximal	maximal	ADJ
ejpam-5226	302	36	element	element	NOUN
ejpam-5226	302	37	or	or	CCONJ
ejpam-5226	302	38	s1	s1	NOUN
ejpam-5226	302	39	=	=	PUNCT
ejpam-5226	302	40	{	{	PUNCT
ejpam-5226	302	41	0	0	NUM
ejpam-5226	302	42	}	}	PUNCT
ejpam-5226	302	43	⇒	⇒	NOUN
ejpam-5226	302	44	s0	s0	PROPN
ejpam-5226	302	45	contains	contain	VERB
ejpam-5226	302	46	a	a	DET
ejpam-5226	302	47	maximal	maximal	ADJ
ejpam-5226	302	48	element	element	NOUN
ejpam-5226	302	49	.	.	PUNCT
ejpam-5226	303	1	theorem	theorem	ADJ
ejpam-5226	303	2	4	4	NUM
ejpam-5226	303	3	.	.	X
ejpam-5226	304	1	for	for	ADP
ejpam-5226	304	2	any	any	DET
ejpam-5226	304	3	non	non	ADJ
ejpam-5226	304	4	-	-	ADJ
ejpam-5226	304	5	empty	empty	ADJ
ejpam-5226	304	6	subset	subset	NOUN
ejpam-5226	304	7	s	s	PROPN
ejpam-5226	304	8	of	of	ADP
ejpam-5226	304	9	l	l	NOUN
ejpam-5226	304	10	,	,	PUNCT
ejpam-5226	304	11	the	the	DET
ejpam-5226	304	12	following	follow	VERB
ejpam-5226	304	13	are	be	AUX
ejpam-5226	304	14	equivalent	equivalent	ADJ
ejpam-5226	304	15	:	:	PUNCT
ejpam-5226	304	16	(	(	PUNCT
ejpam-5226	304	17	i	i	NOUN
ejpam-5226	304	18	)	)	PUNCT
ejpam-5226	304	19	hs	hs	PROPN
ejpam-5226	304	20	is	be	AUX
ejpam-5226	304	21	closed	close	VERB
ejpam-5226	304	22	under	under	ADP
ejpam-5226	304	23	∨	∨	NUM
ejpam-5226	304	24	,	,	PUNCT
ejpam-5226	304	25	(	(	PUNCT
ejpam-5226	304	26	ii	ii	NOUN
ejpam-5226	304	27	)	)	PUNCT
ejpam-5226	304	28	hs	hs	PROPN
ejpam-5226	304	29	is	be	AUX
ejpam-5226	304	30	a	a	DET
ejpam-5226	304	31	subadl	subadl	NOUN
ejpam-5226	304	32	of	of	ADP
ejpam-5226	304	33	l	l	PROPN
ejpam-5226	304	34	,	,	PUNCT
ejpam-5226	304	35	(	(	PUNCT
ejpam-5226	304	36	iii	iii	X
ejpam-5226	304	37	)	)	PUNCT
ejpam-5226	304	38	hs	hs	PROPN
ejpam-5226	304	39	is	be	AUX
ejpam-5226	304	40	an	an	DET
ejpam-5226	304	41	ideal	ideal	NOUN
ejpam-5226	304	42	of	of	ADP
ejpam-5226	304	43	l	l	NOUN
ejpam-5226	304	44	,	,	PUNCT
ejpam-5226	304	45	(	(	PUNCT
ejpam-5226	304	46	iv	iv	X
ejpam-5226	304	47	)	)	PUNCT
ejpam-5226	304	48	hs	hs	PROPN
ejpam-5226	304	49	is	be	AUX
ejpam-5226	304	50	a	a	DET
ejpam-5226	304	51	smallest	small	ADJ
ejpam-5226	304	52	ideal	ideal	NOUN
ejpam-5226	304	53	containing	contain	VERB
ejpam-5226	304	54	s.	s.	PROPN
ejpam-5226	304	55	lemma	lemma	PROPN
ejpam-5226	305	1	1	1	X
ejpam-5226	305	2	.	.	PUNCT
ejpam-5226	306	1	let	let	VERB
ejpam-5226	306	2	s	s	PRON
ejpam-5226	306	3	be	be	AUX
ejpam-5226	306	4	a	a	DET
ejpam-5226	306	5	non	non	ADJ
ejpam-5226	306	6	-	-	ADJ
ejpam-5226	306	7	empty	empty	ADJ
ejpam-5226	306	8	subset	subset	NOUN
ejpam-5226	307	1	and	and	CCONJ
ejpam-5226	307	2	i	i	PRON
ejpam-5226	307	3	be	be	VERB
ejpam-5226	307	4	an	an	DET
ejpam-5226	307	5	ideal	ideal	NOUN
ejpam-5226	307	6	of	of	ADP
ejpam-5226	307	7	l.	l.	PROPN
ejpam-5226	307	8	if	if	SCONJ
ejpam-5226	307	9	hs	hs	PROPN
ejpam-5226	308	1	=	=	NOUN
ejpam-5226	308	2	hi	hi	INTJ
ejpam-5226	308	3	,	,	PUNCT
ejpam-5226	308	4	then	then	ADV
ejpam-5226	308	5	(	(	PUNCT
ejpam-5226	308	6	s	s	X
ejpam-5226	308	7	]	]	X
ejpam-5226	308	8	=	=	PUNCT
ejpam-5226	308	9	i.	i.	NOUN
ejpam-5226	308	10	remark	remark	NOUN
ejpam-5226	308	11	9	9	NUM
ejpam-5226	308	12	.	.	PUNCT
ejpam-5226	309	1	the	the	DET
ejpam-5226	309	2	converse	converse	NOUN
ejpam-5226	309	3	of	of	ADP
ejpam-5226	309	4	lemma	lemma	PROPN
ejpam-5226	309	5	1	1	NUM
ejpam-5226	309	6	need	need	AUX
ejpam-5226	309	7	not	not	PART
ejpam-5226	309	8	be	be	AUX
ejpam-5226	309	9	true	true	ADJ
ejpam-5226	309	10	.	.	PUNCT
ejpam-5226	310	1	we	we	PRON
ejpam-5226	310	2	can	can	AUX
ejpam-5226	310	3	see	see	VERB
ejpam-5226	310	4	the	the	DET
ejpam-5226	310	5	following	follow	VERB
ejpam-5226	310	6	counterexample	counterexample	NOUN
ejpam-5226	310	7	:	:	PUNCT
ejpam-5226	310	8	example	example	NOUN
ejpam-5226	311	1	3	3	X
ejpam-5226	311	2	.	.	PUNCT
ejpam-5226	311	3	let	let	VERB
ejpam-5226	311	4	l	l	NOUN
ejpam-5226	311	5	=	=	PUNCT
ejpam-5226	311	6	{	{	PUNCT
ejpam-5226	311	7	0	0	NUM
ejpam-5226	311	8	,	,	PUNCT
ejpam-5226	311	9	a	a	DET
ejpam-5226	311	10	,	,	PUNCT
ejpam-5226	311	11	b	b	NOUN
ejpam-5226	311	12	,	,	PUNCT
ejpam-5226	311	13	c	c	NOUN
ejpam-5226	311	14	,	,	PUNCT
ejpam-5226	311	15	d	d	NOUN
ejpam-5226	311	16	,	,	PUNCT
ejpam-5226	311	17	e	e	NOUN
ejpam-5226	311	18	,	,	PUNCT
ejpam-5226	311	19	f	f	PROPN
ejpam-5226	311	20	,	,	PUNCT
ejpam-5226	311	21	1	1	NUM
ejpam-5226	311	22	}	}	PUNCT
ejpam-5226	311	23	be	be	AUX
ejpam-5226	311	24	an	an	DET
ejpam-5226	311	25	adl	adl	NOUN
ejpam-5226	311	26	whose	whose	DET
ejpam-5226	311	27	hasse	hasse	NOUN
ejpam-5226	311	28	diagram	diagram	NOUN
ejpam-5226	311	29	is	be	AUX
ejpam-5226	311	30	given	give	VERB
ejpam-5226	311	31	below	below	ADP
ejpam-5226	311	32	:	:	PUNCT
ejpam-5226	311	33	1	1	NUM
ejpam-5226	311	34	d	d	SYM
ejpam-5226	311	35	b	b	X
ejpam-5226	311	36	f	f	X
ejpam-5226	311	37	e	e	PROPN
ejpam-5226	311	38	a	a	DET
ejpam-5226	311	39	0	0	NUM
ejpam-5226	311	40	c	c	NOUN
ejpam-5226	311	41	let	let	VERB
ejpam-5226	311	42	s1	s1	PROPN
ejpam-5226	311	43	=	=	PUNCT
ejpam-5226	311	44	{	{	PUNCT
ejpam-5226	311	45	a	a	DET
ejpam-5226	311	46	,	,	PUNCT
ejpam-5226	311	47	b	b	NOUN
ejpam-5226	311	48	}	}	PUNCT
ejpam-5226	311	49	.	.	PUNCT
ejpam-5226	312	1	then	then	ADV
ejpam-5226	312	2	(	(	PUNCT
ejpam-5226	312	3	s1	s1	NOUN
ejpam-5226	312	4	]	]	X
ejpam-5226	312	5	=	=	PUNCT
ejpam-5226	312	6	{	{	PUNCT
ejpam-5226	312	7	0	0	NUM
ejpam-5226	312	8	,	,	PUNCT
ejpam-5226	312	9	a	a	DET
ejpam-5226	312	10	,	,	PUNCT
ejpam-5226	312	11	b	b	NOUN
ejpam-5226	312	12	,	,	PUNCT
ejpam-5226	312	13	d	d	NOUN
ejpam-5226	312	14	}	}	PUNCT
ejpam-5226	312	15	:	:	PUNCT
ejpam-5226	312	16	=	=	X
ejpam-5226	312	17	i.	i.	PROPN
ejpam-5226	312	18	but	but	CCONJ
ejpam-5226	312	19	hs1	hs1	PROPN
ejpam-5226	312	20	=	=	PUNCT
ejpam-5226	312	21	{	{	PUNCT
ejpam-5226	312	22	0	0	NUM
ejpam-5226	312	23	,	,	PUNCT
ejpam-5226	312	24	a	a	PRON
ejpam-5226	312	25	,	,	PUNCT
ejpam-5226	312	26	b	b	NOUN
ejpam-5226	312	27	}	}	PUNCT
ejpam-5226	312	28	=	=	ADJ
ejpam-5226	312	29	̸	̸	NUM
ejpam-5226	312	30	{	{	PUNCT
ejpam-5226	312	31	0	0	NUM
ejpam-5226	312	32	,	,	PUNCT
ejpam-5226	312	33	a	a	DET
ejpam-5226	312	34	,	,	PUNCT
ejpam-5226	312	35	b	b	NOUN
ejpam-5226	312	36	,	,	PUNCT
ejpam-5226	312	37	d	d	NOUN
ejpam-5226	312	38	}	}	PUNCT
ejpam-5226	312	39	=	=	SYM
ejpam-5226	312	40	hi	hi	INTJ
ejpam-5226	312	41	.	.	PUNCT
ejpam-5226	313	1	lemma	lemma	PROPN
ejpam-5226	313	2	2	2	NUM
ejpam-5226	313	3	.	.	X
ejpam-5226	314	1	for	for	ADP
ejpam-5226	314	2	any	any	DET
ejpam-5226	314	3	non	non	ADJ
ejpam-5226	314	4	-	-	ADJ
ejpam-5226	314	5	empty	empty	ADJ
ejpam-5226	314	6	subset	subset	NOUN
ejpam-5226	314	7	s	s	PROPN
ejpam-5226	314	8	of	of	ADP
ejpam-5226	314	9	l	l	NOUN
ejpam-5226	314	10	,	,	PUNCT
ejpam-5226	314	11	we	we	PRON
ejpam-5226	314	12	have	have	VERB
ejpam-5226	314	13	(	(	PUNCT
ejpam-5226	314	14	i	i	NOUN
ejpam-5226	314	15	)	)	PUNCT
ejpam-5226	315	1	⋂	⋂	PROPN
ejpam-5226	316	1	s⊆l	s⊆l	PROPN
ejpam-5226	316	2	hs	hs	PROPN
ejpam-5226	316	3	=	=	PUNCT
ejpam-5226	316	4	{	{	PUNCT
ejpam-5226	316	5	0	0	NUM
ejpam-5226	316	6	}	}	PUNCT
ejpam-5226	316	7	,	,	PUNCT
ejpam-5226	316	8	(	(	PUNCT
ejpam-5226	316	9	ii	ii	NOUN
ejpam-5226	316	10	)	)	PUNCT
ejpam-5226	316	11	⋃	⋃	PROPN
ejpam-5226	316	12	s⊆l	s⊆l	PROPN
ejpam-5226	316	13	hs	hs	PROPN
ejpam-5226	316	14	=	=	PROPN
ejpam-5226	316	15	l	l	PROPN
ejpam-5226	316	16	,	,	PUNCT
ejpam-5226	316	17	(	(	PUNCT
ejpam-5226	316	18	iii	iii	NOUN
ejpam-5226	316	19	)	)	PUNCT
ejpam-5226	316	20	hhs	hhs	PROPN
ejpam-5226	316	21	=	=	SYM
ejpam-5226	316	22	hs	hs	PROPN
ejpam-5226	316	23	.	.	PROPN
ejpam-5226	316	24	let	let	VERB
ejpam-5226	316	25	us	we	PRON
ejpam-5226	316	26	denote	denote	VERB
ejpam-5226	316	27	the	the	DET
ejpam-5226	316	28	set	set	NOUN
ejpam-5226	316	29	sm	sm	X
ejpam-5226	316	30	=	=	PUNCT
ejpam-5226	316	31	set	set	NOUN
ejpam-5226	316	32	of	of	ADP
ejpam-5226	316	33	maximal	maximal	ADJ
ejpam-5226	316	34	elements	element	NOUN
ejpam-5226	316	35	of	of	ADP
ejpam-5226	316	36	s	s	PROPN
ejpam-5226	316	37	,	,	PUNCT
ejpam-5226	316	38	and	and	CCONJ
ejpam-5226	316	39	we	we	PRON
ejpam-5226	316	40	can	can	AUX
ejpam-5226	316	41	prove	prove	VERB
ejpam-5226	316	42	the	the	DET
ejpam-5226	316	43	following	follow	VERB
ejpam-5226	316	44	theorem	theorem	NOUN
ejpam-5226	316	45	on	on	ADP
ejpam-5226	316	46	an	an	DET
ejpam-5226	316	47	adl	adl	NOUN
ejpam-5226	316	48	with	with	ADP
ejpam-5226	316	49	maximal	maximal	ADJ
ejpam-5226	316	50	elements	element	NOUN
ejpam-5226	316	51	.	.	PUNCT
ejpam-5226	317	1	a.	a.	NOUN
ejpam-5226	317	2	iampan	iampan	PROPN
ejpam-5226	317	3	et	et	PROPN
ejpam-5226	317	4	al	al	PROPN
ejpam-5226	317	5	.	.	PUNCT
ejpam-5226	317	6	/	/	SYM
ejpam-5226	317	7	eur	eur	PROPN
ejpam-5226	317	8	.	.	PUNCT
ejpam-5226	318	1	j.	j.	PROPN
ejpam-5226	318	2	pure	pure	PROPN
ejpam-5226	318	3	appl	appl	PROPN
ejpam-5226	318	4	.	.	PROPN
ejpam-5226	318	5	math	math	PROPN
ejpam-5226	318	6	,	,	PUNCT
ejpam-5226	318	7	17	17	NUM
ejpam-5226	318	8	(	(	PUNCT
ejpam-5226	318	9	3	3	NUM
ejpam-5226	318	10	)	)	PUNCT
ejpam-5226	318	11	(	(	PUNCT
ejpam-5226	318	12	2024	2024	NUM
ejpam-5226	318	13	)	)	PUNCT
ejpam-5226	318	14	,	,	PUNCT
ejpam-5226	318	15	1691	1691	NUM
ejpam-5226	318	16	-	-	SYM
ejpam-5226	318	17	1704	1704	NUM
ejpam-5226	318	18	1700	1700	NUM
ejpam-5226	318	19	theorem	theorem	NOUN
ejpam-5226	318	20	5	5	NUM
ejpam-5226	318	21	.	.	X
ejpam-5226	318	22	for	for	ADP
ejpam-5226	318	23	any	any	DET
ejpam-5226	318	24	non	non	ADJ
ejpam-5226	318	25	-	-	ADJ
ejpam-5226	318	26	empty	empty	ADJ
ejpam-5226	318	27	subset	subset	NOUN
ejpam-5226	318	28	s	s	PROPN
ejpam-5226	318	29	of	of	ADP
ejpam-5226	318	30	l	l	NOUN
ejpam-5226	318	31	,	,	PUNCT
ejpam-5226	318	32	we	we	PRON
ejpam-5226	318	33	have	have	VERB
ejpam-5226	318	34	(	(	PUNCT
ejpam-5226	318	35	i	i	NOUN
ejpam-5226	318	36	)	)	PUNCT
ejpam-5226	318	37	(	(	PUNCT
ejpam-5226	318	38	s	s	X
ejpam-5226	318	39	]	]	X
ejpam-5226	318	40	=	=	SYM
ejpam-5226	318	41	(	(	PUNCT
ejpam-5226	318	42	sm	sm	X
ejpam-5226	318	43	]	]	X
ejpam-5226	318	44	,	,	PUNCT
ejpam-5226	318	45	(	(	PUNCT
ejpam-5226	318	46	ii	ii	NOUN
ejpam-5226	318	47	)	)	PUNCT
ejpam-5226	318	48	⋃	⋃	NOUN
ejpam-5226	318	49	sm∈sm	sm∈sm	NOUN
ejpam-5226	318	50	hsm	hsm	NOUN
ejpam-5226	318	51	=	=	SYM
ejpam-5226	318	52	hs	hs	PROPN
ejpam-5226	318	53	.	.	NOUN
ejpam-5226	318	54	proof	proof	NOUN
ejpam-5226	318	55	.	.	PUNCT
ejpam-5226	319	1	(	(	PUNCT
ejpam-5226	319	2	i	i	NOUN
ejpam-5226	319	3	)	)	PUNCT
ejpam-5226	319	4	let	let	VERB
ejpam-5226	319	5	h	h	PRON
ejpam-5226	319	6	∈	∈	PROPN
ejpam-5226	319	7	(	(	PUNCT
ejpam-5226	319	8	s	s	NOUN
ejpam-5226	319	9	]	]	X
ejpam-5226	319	10	.	.	PUNCT
ejpam-5226	320	1	then	then	ADV
ejpam-5226	320	2	h	h	NOUN
ejpam-5226	320	3	=	=	PUNCT
ejpam-5226	320	4	(	(	PUNCT
ejpam-5226	320	5	m∨	m∨	NOUN
ejpam-5226	320	6	i=1	i=1	PROPN
ejpam-5226	320	7	si	si	PROPN
ejpam-5226	320	8	)	)	PUNCT
ejpam-5226	320	9	∧	∧	PROPN
ejpam-5226	320	10	x	x	PUNCT
ejpam-5226	320	11	for	for	ADP
ejpam-5226	320	12	some	some	DET
ejpam-5226	320	13	x	x	SYM
ejpam-5226	320	14	∈	∈	PROPN
ejpam-5226	320	15	l	l	NOUN
ejpam-5226	320	16	and	and	CCONJ
ejpam-5226	320	17	si	si	PROPN
ejpam-5226	320	18	∈	∈	PROPN
ejpam-5226	320	19	s	s	PROPN
ejpam-5226	320	20	for	for	ADP
ejpam-5226	320	21	all	all	DET
ejpam-5226	320	22	1	1	NUM
ejpam-5226	320	23	≤	≤	NUM
ejpam-5226	320	24	i	i	PRON
ejpam-5226	320	25	≤	≤	NUM
ejpam-5226	320	26	m.	m.	NOUN
ejpam-5226	320	27	let	let	VERB
ejpam-5226	320	28	sm	sm	PROPN
ejpam-5226	320	29	∈	∈	PROPN
ejpam-5226	320	30	sm	sm	INTJ
ejpam-5226	320	31	.	.	PUNCT
ejpam-5226	321	1	then	then	ADV
ejpam-5226	321	2	sm	sm	PROPN
ejpam-5226	321	3	∧	∧	PROPN
ejpam-5226	321	4	si	si	PROPN
ejpam-5226	321	5	=	=	PUNCT
ejpam-5226	321	6	si	si	X
ejpam-5226	321	7	for	for	ADP
ejpam-5226	321	8	all	all	DET
ejpam-5226	321	9	1	1	NUM
ejpam-5226	321	10	≤	≤	NUM
ejpam-5226	321	11	i	i	PRON
ejpam-5226	321	12	≤	≤	NUM
ejpam-5226	321	13	m.	m.	NOUN
ejpam-5226	321	14	therefore	therefore	ADV
ejpam-5226	321	15	,	,	PUNCT
ejpam-5226	321	16	sm	sm	PROPN
ejpam-5226	321	17	∧	∧	PROPN
ejpam-5226	321	18	si	si	PROPN
ejpam-5226	321	19	∈	∈	PROPN
ejpam-5226	321	20	(	(	PUNCT
ejpam-5226	321	21	sm	sm	X
ejpam-5226	321	22	]	]	PUNCT
ejpam-5226	321	23	for	for	ADP
ejpam-5226	321	24	all	all	DET
ejpam-5226	321	25	1	1	NUM
ejpam-5226	321	26	≤	≤	NUM
ejpam-5226	321	27	i	i	PRON
ejpam-5226	321	28	≤	≤	NUM
ejpam-5226	321	29	m.	m.	NOUN
ejpam-5226	321	30	so	so	SCONJ
ejpam-5226	321	31	that	that	DET
ejpam-5226	321	32	m∨	m∨	NOUN
ejpam-5226	321	33	i=1	i=1	PROPN
ejpam-5226	321	34	si	si	PROPN
ejpam-5226	322	1	=	=	PROPN
ejpam-5226	322	2	m∨	m∨	PROPN
ejpam-5226	322	3	i=1	i=1	PROPN
ejpam-5226	322	4	(	(	PUNCT
ejpam-5226	322	5	sm	sm	PROPN
ejpam-5226	322	6	∧	∧	PROPN
ejpam-5226	322	7	si	si	PROPN
ejpam-5226	322	8	)	)	PUNCT
ejpam-5226	322	9	∈	∈	PROPN
ejpam-5226	322	10	(	(	PUNCT
ejpam-5226	322	11	sm	sm	X
ejpam-5226	322	12	]	]	X
ejpam-5226	322	13	.	.	PUNCT
ejpam-5226	323	1	hence	hence	ADV
ejpam-5226	323	2	,	,	PUNCT
ejpam-5226	323	3	h	h	NOUN
ejpam-5226	323	4	=	=	PRON
ejpam-5226	323	5	(	(	PUNCT
ejpam-5226	323	6	m∨	m∨	NOUN
ejpam-5226	323	7	i=1	i=1	PROPN
ejpam-5226	323	8	si	si	PROPN
ejpam-5226	323	9	)	)	PUNCT
ejpam-5226	323	10	∧	∧	PROPN
ejpam-5226	323	11	x	x	SYM
ejpam-5226	323	12	∈	∈	PROPN
ejpam-5226	323	13	(	(	PUNCT
ejpam-5226	323	14	sm	sm	X
ejpam-5226	323	15	]	]	X
ejpam-5226	323	16	.	.	PUNCT
ejpam-5226	324	1	since	since	SCONJ
ejpam-5226	324	2	sm	sm	PROPN
ejpam-5226	324	3	⊆	⊆	NUM
ejpam-5226	324	4	s	s	NOUN
ejpam-5226	324	5	,	,	PUNCT
ejpam-5226	324	6	(	(	PUNCT
ejpam-5226	324	7	sm	sm	X
ejpam-5226	324	8	]	]	PUNCT
ejpam-5226	324	9	⊆	⊆	NUM
ejpam-5226	324	10	(	(	PUNCT
ejpam-5226	324	11	s	s	X
ejpam-5226	324	12	]	]	X
ejpam-5226	324	13	.	.	PUNCT
ejpam-5226	325	1	therefore	therefore	ADV
ejpam-5226	325	2	,	,	PUNCT
ejpam-5226	325	3	(	(	PUNCT
ejpam-5226	325	4	s	s	X
ejpam-5226	325	5	]	]	X
ejpam-5226	325	6	=	=	SYM
ejpam-5226	325	7	(	(	PUNCT
ejpam-5226	325	8	sm	sm	X
ejpam-5226	325	9	]	]	X
ejpam-5226	325	10	.	.	PUNCT
ejpam-5226	326	1	(	(	PUNCT
ejpam-5226	326	2	ii	ii	NOUN
ejpam-5226	326	3	)	)	PUNCT
ejpam-5226	326	4	let	let	VERB
ejpam-5226	326	5	h	h	NOUN
ejpam-5226	326	6	∈	∈	PROPN
ejpam-5226	326	7	⋃	⋃	NOUN
ejpam-5226	326	8	sm∈sm	sm∈sm	NOUN
ejpam-5226	326	9	hsm	hsm	NOUN
ejpam-5226	326	10	.	.	PUNCT
ejpam-5226	327	1	then	then	ADV
ejpam-5226	327	2	h	h	PROPN
ejpam-5226	327	3	∈	∈	PROPN
ejpam-5226	327	4	hsm	hsm	NOUN
ejpam-5226	327	5	for	for	ADP
ejpam-5226	327	6	some	some	DET
ejpam-5226	327	7	sm	sm	PROPN
ejpam-5226	327	8	∈	∈	PROPN
ejpam-5226	327	9	sm	sm	INTJ
ejpam-5226	327	10	and	and	CCONJ
ejpam-5226	327	11	sm	sm	PROPN
ejpam-5226	327	12	∧	∧	PROPN
ejpam-5226	327	13	h	h	NOUN
ejpam-5226	327	14	=	=	PROPN
ejpam-5226	327	15	h.	h.	PROPN
ejpam-5226	327	16	since	since	SCONJ
ejpam-5226	327	17	sm	sm	PROPN
ejpam-5226	327	18	⊆	⊆	NUM
ejpam-5226	327	19	s	s	NOUN
ejpam-5226	327	20	,	,	PUNCT
ejpam-5226	327	21	h	h	PROPN
ejpam-5226	327	22	∈	∈	PROPN
ejpam-5226	327	23	hs	hs	PROPN
ejpam-5226	327	24	.	.	PUNCT
ejpam-5226	328	1	therefore	therefore	ADV
ejpam-5226	328	2	,	,	PUNCT
ejpam-5226	328	3	⋃	⋃	ADP
ejpam-5226	328	4	sm∈sm	sm∈sm	NOUN
ejpam-5226	328	5	hsm	hsm	NOUN
ejpam-5226	328	6	⊆	⊆	NUM
ejpam-5226	328	7	hs	hs	PROPN
ejpam-5226	328	8	.	.	PUNCT
ejpam-5226	329	1	let	let	VERB
ejpam-5226	329	2	h	h	PRON
ejpam-5226	329	3	∈	∈	PROPN
ejpam-5226	330	1	hs	hs	PROPN
ejpam-5226	330	2	.	.	PUNCT
ejpam-5226	331	1	then	then	ADV
ejpam-5226	331	2	there	there	PRON
ejpam-5226	331	3	exists	exist	VERB
ejpam-5226	331	4	s	s	X
ejpam-5226	331	5	∈	∈	PROPN
ejpam-5226	331	6	s	s	VERB
ejpam-5226	331	7	such	such	ADJ
ejpam-5226	331	8	that	that	DET
ejpam-5226	331	9	s	s	PART
ejpam-5226	331	10	∧	∧	NOUN
ejpam-5226	331	11	h	h	NOUN
ejpam-5226	331	12	=	=	NOUN
ejpam-5226	331	13	h.	h.	PROPN
ejpam-5226	331	14	let	let	VERB
ejpam-5226	331	15	sm	sm	PROPN
ejpam-5226	331	16	∈	∈	PROPN
ejpam-5226	331	17	sm	sm	INTJ
ejpam-5226	331	18	.	.	PUNCT
ejpam-5226	332	1	then	then	ADV
ejpam-5226	332	2	sm	sm	PROPN
ejpam-5226	332	3	∧	∧	PROPN
ejpam-5226	332	4	s	s	PART
ejpam-5226	332	5	=	=	PUNCT
ejpam-5226	332	6	s.	s.	PROPN
ejpam-5226	332	7	now	now	ADV
ejpam-5226	332	8	,	,	PUNCT
ejpam-5226	332	9	sm	sm	PROPN
ejpam-5226	332	10	∧	∧	PROPN
ejpam-5226	332	11	h	h	NOUN
ejpam-5226	332	12	=	=	NOUN
ejpam-5226	333	1	sm	sm	PROPN
ejpam-5226	333	2	∧	∧	PROPN
ejpam-5226	333	3	s	s	PART
ejpam-5226	333	4	∧	∧	PROPN
ejpam-5226	333	5	h	h	NOUN
ejpam-5226	333	6	=	=	SYM
ejpam-5226	333	7	s	s	PART
ejpam-5226	333	8	∧	∧	PROPN
ejpam-5226	333	9	h	h	NOUN
ejpam-5226	333	10	=	=	PROPN
ejpam-5226	333	11	h.	h.	PROPN
ejpam-5226	333	12	therefore	therefore	ADV
ejpam-5226	333	13	,	,	PUNCT
ejpam-5226	333	14	h	h	PROPN
ejpam-5226	333	15	∈	∈	PROPN
ejpam-5226	333	16	hsm	hsm	NOUN
ejpam-5226	333	17	for	for	ADP
ejpam-5226	333	18	some	some	DET
ejpam-5226	333	19	sm	sm	PROPN
ejpam-5226	333	20	∈	∈	PROPN
ejpam-5226	333	21	sm	sm	INTJ
ejpam-5226	333	22	.	.	PUNCT
ejpam-5226	334	1	so	so	ADV
ejpam-5226	334	2	that	that	SCONJ
ejpam-5226	334	3	h	h	NOUN
ejpam-5226	334	4	∈	∈	PROPN
ejpam-5226	334	5	⋃	⋃	NOUN
ejpam-5226	334	6	sm∈sm	sm∈sm	NOUN
ejpam-5226	334	7	hsm	hsm	NOUN
ejpam-5226	334	8	.	.	PUNCT
ejpam-5226	335	1	hence	hence	ADV
ejpam-5226	335	2	,	,	PUNCT
ejpam-5226	335	3	hs	hs	PROPN
ejpam-5226	335	4	⊆	⊆	NUM
ejpam-5226	335	5	⋃	⋃	NOUN
ejpam-5226	335	6	sm∈sm	sm∈sm	NOUN
ejpam-5226	335	7	hsm	hsm	NOUN
ejpam-5226	335	8	.	.	PUNCT
ejpam-5226	336	1	thus	thus	ADV
ejpam-5226	336	2	,	,	PUNCT
ejpam-5226	336	3	hs	hs	PROPN
ejpam-5226	336	4	=	=	SYM
ejpam-5226	336	5	⋃	⋃	NOUN
ejpam-5226	336	6	sm∈sm	sm∈sm	X
ejpam-5226	336	7	hsm	hsm	NOUN
ejpam-5226	336	8	.	.	PUNCT
ejpam-5226	337	1	3	3	X
ejpam-5226	337	2	.	.	X
ejpam-5226	337	3	characterization	characterization	NOUN
ejpam-5226	337	4	of	of	ADP
ejpam-5226	337	5	hierarchy	hierarchy	NOUN
ejpam-5226	337	6	sets	set	NOUN
ejpam-5226	337	7	with	with	ADP
ejpam-5226	337	8	respect	respect	NOUN
ejpam-5226	337	9	to	to	ADP
ejpam-5226	337	10	a	a	DET
ejpam-5226	337	11	compatible	compatible	ADJ
ejpam-5226	337	12	set	set	NOUN
ejpam-5226	337	13	in	in	ADP
ejpam-5226	337	14	this	this	DET
ejpam-5226	337	15	section	section	NOUN
ejpam-5226	337	16	,	,	PUNCT
ejpam-5226	337	17	we	we	PRON
ejpam-5226	337	18	characterize	characterize	VERB
ejpam-5226	337	19	the	the	DET
ejpam-5226	337	20	class	class	NOUN
ejpam-5226	337	21	of	of	ADP
ejpam-5226	337	22	hierarchy	hierarchy	NOUN
ejpam-5226	337	23	sets	set	NOUN
ejpam-5226	337	24	in	in	ADP
ejpam-5226	337	25	terms	term	NOUN
ejpam-5226	337	26	of	of	ADP
ejpam-5226	337	27	compatible	compatible	ADJ
ejpam-5226	337	28	sets	set	NOUN
ejpam-5226	337	29	,	,	PUNCT
ejpam-5226	337	30	introduce	introduce	VERB
ejpam-5226	337	31	a	a	DET
ejpam-5226	337	32	new	new	ADJ
ejpam-5226	337	33	class	class	NOUN
ejpam-5226	337	34	of	of	ADP
ejpam-5226	337	35	sets	set	NOUN
ejpam-5226	337	36	in	in	ADP
ejpam-5226	337	37	an	an	DET
ejpam-5226	337	38	almost	almost	ADV
ejpam-5226	337	39	distributive	distributive	ADJ
ejpam-5226	337	40	lattice	lattice	NOUN
ejpam-5226	337	41	,	,	PUNCT
ejpam-5226	337	42	and	and	CCONJ
ejpam-5226	337	43	study	study	VERB
ejpam-5226	337	44	rigorously	rigorously	ADV
ejpam-5226	337	45	.	.	PUNCT
ejpam-5226	338	1	a	a	DET
ejpam-5226	338	2	non	non	ADJ
ejpam-5226	338	3	-	-	ADJ
ejpam-5226	338	4	empty	empty	ADJ
ejpam-5226	338	5	subset	subset	NOUN
ejpam-5226	338	6	s	s	NOUN
ejpam-5226	338	7	of	of	ADP
ejpam-5226	338	8	l	l	NOUN
ejpam-5226	338	9	is	be	AUX
ejpam-5226	338	10	said	say	VERB
ejpam-5226	338	11	to	to	PART
ejpam-5226	338	12	be	be	AUX
ejpam-5226	338	13	compatible	compatible	ADJ
ejpam-5226	338	14	if	if	SCONJ
ejpam-5226	338	15	for	for	ADP
ejpam-5226	338	16	each	each	DET
ejpam-5226	338	17	s1	s1	NOUN
ejpam-5226	338	18	,	,	PUNCT
ejpam-5226	338	19	s2	s2	NOUN
ejpam-5226	338	20	∈	∈	PROPN
ejpam-5226	338	21	s	s	PROPN
ejpam-5226	338	22	,	,	PUNCT
ejpam-5226	338	23	s1∧s2	s1∧s2	PROPN
ejpam-5226	338	24	=	=	SYM
ejpam-5226	338	25	s2∧s1	s2∧s1	PROPN
ejpam-5226	338	26	or	or	CCONJ
ejpam-5226	338	27	equivalently	equivalently	ADV
ejpam-5226	338	28	,	,	PUNCT
ejpam-5226	338	29	s1	s1	PROPN
ejpam-5226	338	30	∨	∨	NUM
ejpam-5226	338	31	s2	s2	PROPN
ejpam-5226	338	32	=	=	SYM
ejpam-5226	338	33	s2	s2	PROPN
ejpam-5226	338	34	∨	∨	NUM
ejpam-5226	338	35	s1	s1	NOUN
ejpam-5226	338	36	.	.	PUNCT
ejpam-5226	339	1	lemma	lemma	PROPN
ejpam-5226	339	2	3	3	X
ejpam-5226	339	3	.	.	PUNCT
ejpam-5226	340	1	let	let	VERB
ejpam-5226	340	2	h	h	PRON
ejpam-5226	340	3	∈	∈	PROPN
ejpam-5226	340	4	l	l	NOUN
ejpam-5226	340	5	and	and	CCONJ
ejpam-5226	340	6	a	a	DET
ejpam-5226	340	7	non	non	ADJ
ejpam-5226	340	8	-	-	ADJ
ejpam-5226	340	9	empty	empty	ADJ
ejpam-5226	340	10	subset	subset	NOUN
ejpam-5226	340	11	s	s	PROPN
ejpam-5226	340	12	of	of	ADP
ejpam-5226	340	13	l.	l.	NOUN
ejpam-5226	340	14	if	if	SCONJ
ejpam-5226	340	15	there	there	PRON
ejpam-5226	340	16	exists	exist	VERB
ejpam-5226	340	17	s	s	X
ejpam-5226	340	18	∈	∈	NOUN
ejpam-5226	340	19	s	s	VERB
ejpam-5226	340	20	such	such	ADJ
ejpam-5226	340	21	that	that	DET
ejpam-5226	340	22	h	h	PROPN
ejpam-5226	340	23	≤	≤	NOUN
ejpam-5226	340	24	s	s	X
ejpam-5226	340	25	,	,	PUNCT
ejpam-5226	340	26	then	then	ADV
ejpam-5226	340	27	h	h	PROPN
ejpam-5226	340	28	∈	∈	PROPN
ejpam-5226	340	29	hs	hs	PROPN
ejpam-5226	340	30	.	.	PROPN
ejpam-5226	340	31	proof	proof	NOUN
ejpam-5226	340	32	.	.	PUNCT
ejpam-5226	341	1	if	if	SCONJ
ejpam-5226	341	2	h	h	PRON
ejpam-5226	341	3	≤	≤	X
ejpam-5226	341	4	s	s	VERB
ejpam-5226	341	5	for	for	ADP
ejpam-5226	341	6	some	some	DET
ejpam-5226	341	7	s	s	PART
ejpam-5226	341	8	∈	∈	PROPN
ejpam-5226	341	9	s	s	NOUN
ejpam-5226	341	10	,	,	PUNCT
ejpam-5226	341	11	then	then	ADV
ejpam-5226	341	12	s	s	VERB
ejpam-5226	341	13	∧	∧	PROPN
ejpam-5226	341	14	h	h	NOUN
ejpam-5226	342	1	=	=	NOUN
ejpam-5226	343	1	h	h	NOUN
ejpam-5226	344	1	=	=	NOUN
ejpam-5226	344	2	h	h	NOUN
ejpam-5226	344	3	∧	∧	PROPN
ejpam-5226	344	4	s.	s.	PROPN
ejpam-5226	344	5	therefore	therefore	ADV
ejpam-5226	344	6	,	,	PUNCT
ejpam-5226	344	7	h	h	PROPN
ejpam-5226	344	8	∈	∈	PROPN
ejpam-5226	344	9	hs	hs	PROPN
ejpam-5226	344	10	.	.	PUNCT
ejpam-5226	344	11	remark	remark	PROPN
ejpam-5226	344	12	10	10	NUM
ejpam-5226	344	13	.	.	PUNCT
ejpam-5226	345	1	the	the	DET
ejpam-5226	345	2	converse	converse	NOUN
ejpam-5226	345	3	of	of	ADP
ejpam-5226	345	4	lemma	lemma	PROPN
ejpam-5226	345	5	3	3	NUM
ejpam-5226	345	6	need	need	AUX
ejpam-5226	345	7	not	not	PART
ejpam-5226	345	8	be	be	AUX
ejpam-5226	345	9	true	true	ADJ
ejpam-5226	345	10	.	.	PUNCT
ejpam-5226	346	1	in	in	ADP
ejpam-5226	346	2	a	a	DET
ejpam-5226	346	3	discrete	discrete	ADJ
ejpam-5226	346	4	adl	adl	NOUN
ejpam-5226	346	5	x	x	NOUN
ejpam-5226	346	6	,	,	PUNCT
ejpam-5226	346	7	let	let	VERB
ejpam-5226	346	8	s	s	PRON
ejpam-5226	346	9	=	=	X
ejpam-5226	346	10	{	{	PUNCT
ejpam-5226	346	11	s	s	NOUN
ejpam-5226	346	12	}	}	PUNCT
ejpam-5226	346	13	for	for	ADP
ejpam-5226	346	14	some	some	DET
ejpam-5226	346	15	s	s	PART
ejpam-5226	346	16	∈	∈	NOUN
ejpam-5226	346	17	x	x	SYM
ejpam-5226	346	18	\	\	X
ejpam-5226	346	19	{	{	PUNCT
ejpam-5226	346	20	0	0	NUM
ejpam-5226	346	21	}	}	PUNCT
ejpam-5226	346	22	.	.	PUNCT
ejpam-5226	347	1	then	then	ADV
ejpam-5226	347	2	hs	hs	PROPN
ejpam-5226	347	3	=	=	NOUN
ejpam-5226	347	4	x.	x.	NOUN
ejpam-5226	347	5	let	let	VERB
ejpam-5226	347	6	h	h	PRON
ejpam-5226	347	7	∈	∈	PROPN
ejpam-5226	347	8	x.	x.	NOUN
ejpam-5226	348	1	then	then	ADV
ejpam-5226	348	2	h	h	PROPN
ejpam-5226	348	3	∈	∈	PROPN
ejpam-5226	348	4	hs	hs	PROPN
ejpam-5226	348	5	and	and	CCONJ
ejpam-5226	348	6	h	h	PROPN
ejpam-5226	348	7	∧	∧	PROPN
ejpam-5226	348	8	s	s	PART
ejpam-5226	348	9	=	=	X
ejpam-5226	348	10	s	s	X
ejpam-5226	348	11	and	and	CCONJ
ejpam-5226	348	12	s	s	VERB
ejpam-5226	348	13	∧	∧	PROPN
ejpam-5226	348	14	h	h	NOUN
ejpam-5226	348	15	=	=	NOUN
ejpam-5226	348	16	h	h	PROPN
ejpam-5226	348	17	for	for	ADP
ejpam-5226	348	18	all	all	PRON
ejpam-5226	348	19	s	s	PROPN
ejpam-5226	348	20	∈	∈	PROPN
ejpam-5226	348	21	s.	s.	PROPN
ejpam-5226	348	22	therefore	therefore	ADV
ejpam-5226	348	23	,	,	PUNCT
ejpam-5226	348	24	h	h	PROPN
ejpam-5226	348	25	⩽̸	⩽̸	PROPN
ejpam-5226	348	26	s.	s.	PROPN
ejpam-5226	348	27	remark	remark	VERB
ejpam-5226	348	28	11	11	NUM
ejpam-5226	348	29	.	.	PUNCT
ejpam-5226	349	1	if	if	SCONJ
ejpam-5226	349	2	hs	hs	PROPN
ejpam-5226	349	3	is	be	AUX
ejpam-5226	349	4	compatible	compatible	ADJ
ejpam-5226	349	5	,	,	PUNCT
ejpam-5226	349	6	then	then	ADV
ejpam-5226	349	7	the	the	DET
ejpam-5226	349	8	converse	converse	NOUN
ejpam-5226	349	9	of	of	ADP
ejpam-5226	349	10	lemma	lemma	PROPN
ejpam-5226	349	11	3	3	NUM
ejpam-5226	349	12	is	be	AUX
ejpam-5226	349	13	true	true	ADJ
ejpam-5226	349	14	.	.	PUNCT
ejpam-5226	350	1	proof	proof	NOUN
ejpam-5226	350	2	.	.	PUNCT
ejpam-5226	351	1	let	let	VERB
ejpam-5226	351	2	h	h	PRON
ejpam-5226	351	3	∈	∈	PROPN
ejpam-5226	351	4	hs	hs	PROPN
ejpam-5226	351	5	for	for	ADP
ejpam-5226	351	6	some	some	DET
ejpam-5226	351	7	h	h	NOUN
ejpam-5226	351	8	∈	∈	PROPN
ejpam-5226	351	9	l.	l.	NOUN
ejpam-5226	351	10	then	then	ADV
ejpam-5226	351	11	,	,	PUNCT
ejpam-5226	351	12	an	an	DET
ejpam-5226	351	13	element	element	NOUN
ejpam-5226	351	14	s	s	PART
ejpam-5226	351	15	∈	∈	NOUN
ejpam-5226	351	16	s	s	PART
ejpam-5226	351	17	exists	exist	VERB
ejpam-5226	351	18	such	such	ADJ
ejpam-5226	351	19	that	that	SCONJ
ejpam-5226	351	20	s∧h	s∧h	PROPN
ejpam-5226	351	21	=	=	X
ejpam-5226	351	22	h.	h.	PROPN
ejpam-5226	351	23	since	since	SCONJ
ejpam-5226	351	24	s	s	PROPN
ejpam-5226	351	25	⊆	⊆	NUM
ejpam-5226	351	26	hs	hs	PROPN
ejpam-5226	351	27	,	,	PUNCT
ejpam-5226	351	28	s	s	PART
ejpam-5226	352	1	∧	∧	PROPN
ejpam-5226	352	2	h	h	NOUN
ejpam-5226	353	1	=	=	NOUN
ejpam-5226	354	1	h	h	NOUN
ejpam-5226	355	1	∧	∧	PROPN
ejpam-5226	355	2	s	s	PART
ejpam-5226	355	3	=	=	PROPN
ejpam-5226	355	4	h.	h.	PROPN
ejpam-5226	355	5	hence	hence	ADV
ejpam-5226	355	6	,	,	PUNCT
ejpam-5226	355	7	h	h	PROPN
ejpam-5226	355	8	≤	≤	PROPN
ejpam-5226	355	9	s.	s.	PROPN
ejpam-5226	355	10	definition	definition	NOUN
ejpam-5226	355	11	2	2	NUM
ejpam-5226	355	12	.	.	X
ejpam-5226	356	1	for	for	ADP
ejpam-5226	356	2	any	any	DET
ejpam-5226	356	3	non	non	ADJ
ejpam-5226	356	4	-	-	ADJ
ejpam-5226	356	5	empty	empty	ADJ
ejpam-5226	356	6	subset	subset	NOUN
ejpam-5226	356	7	s	s	PROPN
ejpam-5226	356	8	of	of	ADP
ejpam-5226	356	9	l	l	NOUN
ejpam-5226	356	10	,	,	PUNCT
ejpam-5226	356	11	define	define	VERB
ejpam-5226	356	12	a	a	DET
ejpam-5226	356	13	set	set	NOUN
ejpam-5226	356	14	ŝ	ŝ	X
ejpam-5226	356	15	=	=	SYM
ejpam-5226	356	16	{	{	PUNCT
ejpam-5226	356	17	x	x	PUNCT
ejpam-5226	356	18	∈	∈	NOUN
ejpam-5226	356	19	l	l	NOUN
ejpam-5226	357	1	|	|	NOUN
ejpam-5226	357	2	x	x	SYM
ejpam-5226	357	3	≤	≤	NOUN
ejpam-5226	357	4	s	s	NOUN
ejpam-5226	357	5	,	,	PUNCT
ejpam-5226	357	6	for	for	ADP
ejpam-5226	357	7	some	some	PRON
ejpam-5226	357	8	s	s	PART
ejpam-5226	357	9	∈	∈	NOUN
ejpam-5226	357	10	s	s	PART
ejpam-5226	357	11	}	}	PUNCT
ejpam-5226	357	12	.	.	PUNCT
ejpam-5226	358	1	remark	remark	PROPN
ejpam-5226	358	2	12	12	NUM
ejpam-5226	358	3	.	.	PUNCT
ejpam-5226	359	1	for	for	ADP
ejpam-5226	359	2	any	any	DET
ejpam-5226	359	3	non	non	ADJ
ejpam-5226	359	4	-	-	ADJ
ejpam-5226	359	5	empty	empty	ADJ
ejpam-5226	359	6	subset	subset	NOUN
ejpam-5226	359	7	s	s	PROPN
ejpam-5226	359	8	of	of	ADP
ejpam-5226	359	9	l	l	NOUN
ejpam-5226	359	10	,	,	PUNCT
ejpam-5226	359	11	we	we	PRON
ejpam-5226	359	12	can	can	AUX
ejpam-5226	359	13	observe	observe	VERB
ejpam-5226	359	14	that	that	SCONJ
ejpam-5226	359	15	ŝ	ŝ	VERB
ejpam-5226	359	16	̸=	̸=	PROPN
ejpam-5226	359	17	∅	∅	NOUN
ejpam-5226	359	18	and	and	CCONJ
ejpam-5226	359	19	s	s	NOUN
ejpam-5226	359	20	⊆	⊆	NUM
ejpam-5226	359	21	ŝ.	ŝ.	NOUN
ejpam-5226	359	22	a.	a.	NOUN
ejpam-5226	359	23	iampan	iampan	NOUN
ejpam-5226	359	24	et	et	PROPN
ejpam-5226	359	25	al	al	PROPN
ejpam-5226	359	26	.	.	PUNCT
ejpam-5226	359	27	/	/	SYM
ejpam-5226	359	28	eur	eur	PROPN
ejpam-5226	359	29	.	.	PUNCT
ejpam-5226	360	1	j.	j.	PROPN
ejpam-5226	360	2	pure	pure	PROPN
ejpam-5226	360	3	appl	appl	PROPN
ejpam-5226	360	4	.	.	PROPN
ejpam-5226	360	5	math	math	PROPN
ejpam-5226	360	6	,	,	PUNCT
ejpam-5226	360	7	17	17	NUM
ejpam-5226	360	8	(	(	PUNCT
ejpam-5226	360	9	3	3	NUM
ejpam-5226	360	10	)	)	PUNCT
ejpam-5226	360	11	(	(	PUNCT
ejpam-5226	360	12	2024	2024	NUM
ejpam-5226	360	13	)	)	PUNCT
ejpam-5226	360	14	,	,	PUNCT
ejpam-5226	360	15	1691	1691	NUM
ejpam-5226	360	16	-	-	SYM
ejpam-5226	360	17	1704	1704	NUM
ejpam-5226	360	18	1701	1701	NUM
ejpam-5226	360	19	lemma	lemma	PROPN
ejpam-5226	360	20	4	4	NUM
ejpam-5226	360	21	.	.	X
ejpam-5226	361	1	for	for	ADP
ejpam-5226	361	2	any	any	DET
ejpam-5226	361	3	non	non	ADJ
ejpam-5226	361	4	-	-	ADJ
ejpam-5226	361	5	empty	empty	ADJ
ejpam-5226	361	6	subset	subset	NOUN
ejpam-5226	361	7	s	s	PROPN
ejpam-5226	361	8	of	of	ADP
ejpam-5226	361	9	l	l	NOUN
ejpam-5226	361	10	,	,	PUNCT
ejpam-5226	361	11	we	we	PRON
ejpam-5226	361	12	have	have	VERB
ejpam-5226	361	13	the	the	DET
ejpam-5226	361	14	following	following	NOUN
ejpam-5226	361	15	:	:	PUNCT
ejpam-5226	361	16	(	(	PUNCT
ejpam-5226	361	17	i	i	NOUN
ejpam-5226	361	18	)	)	PUNCT
ejpam-5226	361	19	ŝ	ŝ	NUM
ejpam-5226	361	20	is	be	AUX
ejpam-5226	361	21	closed	close	VERB
ejpam-5226	361	22	under	under	ADP
ejpam-5226	361	23	∧	∧	PROPN
ejpam-5226	361	24	,	,	PUNCT
ejpam-5226	361	25	(	(	PUNCT
ejpam-5226	361	26	ii	ii	NOUN
ejpam-5226	361	27	)	)	PUNCT
ejpam-5226	361	28	h	h	NOUN
ejpam-5226	362	1	∧	∧	PROPN
ejpam-5226	362	2	ŝ1	ŝ1	PROPN
ejpam-5226	362	3	∈	∈	PROPN
ejpam-5226	362	4	ŝ	ŝ	NOUN
ejpam-5226	362	5	,	,	PUNCT
ejpam-5226	362	6	for	for	ADP
ejpam-5226	362	7	any	any	DET
ejpam-5226	362	8	h	h	NOUN
ejpam-5226	362	9	∈	∈	PROPN
ejpam-5226	362	10	l	l	NOUN
ejpam-5226	362	11	,	,	PUNCT
ejpam-5226	362	12	(	(	PUNCT
ejpam-5226	362	13	iii	iii	NOUN
ejpam-5226	362	14	)	)	PUNCT
ejpam-5226	362	15	ŝ	ŝ	VERB
ejpam-5226	362	16	⊆	⊆	NUM
ejpam-5226	362	17	hs	hs	PROPN
ejpam-5226	362	18	,	,	PUNCT
ejpam-5226	362	19	(	(	PUNCT
ejpam-5226	362	20	iv	iv	X
ejpam-5226	362	21	)	)	PUNCT
ejpam-5226	362	22	hs	hs	PROPN
ejpam-5226	363	1	=	=	NOUN
ejpam-5226	363	2	h	h	PROPN
ejpam-5226	363	3	ŝ	ŝ	X
ejpam-5226	363	4	.	.	PUNCT
ejpam-5226	364	1	proof	proof	NOUN
ejpam-5226	364	2	.	.	PUNCT
ejpam-5226	365	1	(	(	PUNCT
ejpam-5226	365	2	i	i	NOUN
ejpam-5226	365	3	)	)	PUNCT
ejpam-5226	365	4	let	let	VERB
ejpam-5226	365	5	ŝ1	ŝ1	PROPN
ejpam-5226	365	6	,	,	PUNCT
ejpam-5226	365	7	ŝ2	ŝ2	PROPN
ejpam-5226	365	8	∈	∈	PROPN
ejpam-5226	365	9	ŝ.	ŝ.	NOUN
ejpam-5226	365	10	then	then	ADV
ejpam-5226	365	11	there	there	PRON
ejpam-5226	365	12	exist	exist	VERB
ejpam-5226	365	13	s1	s1	NOUN
ejpam-5226	365	14	,	,	PUNCT
ejpam-5226	365	15	s2	s2	NOUN
ejpam-5226	365	16	∈	∈	PROPN
ejpam-5226	365	17	s	s	VERB
ejpam-5226	365	18	such	such	ADJ
ejpam-5226	365	19	that	that	SCONJ
ejpam-5226	365	20	ŝ1	ŝ1	PROPN
ejpam-5226	365	21	≤	≤	ADJ
ejpam-5226	365	22	s1	s1	NOUN
ejpam-5226	365	23	and	and	CCONJ
ejpam-5226	365	24	ŝ2	ŝ2	ADJ
ejpam-5226	365	25	≤	≤	NUM
ejpam-5226	365	26	s2	s2	PROPN
ejpam-5226	365	27	.	.	PUNCT
ejpam-5226	366	1	now	now	ADV
ejpam-5226	366	2	,	,	PUNCT
ejpam-5226	366	3	(	(	PUNCT
ejpam-5226	366	4	ŝ1	ŝ1	PROPN
ejpam-5226	366	5	∧	∧	PROPN
ejpam-5226	366	6	ŝ2)∧	ŝ2)∧	SCONJ
ejpam-5226	366	7	s2	s2	NOUN
ejpam-5226	366	8	=	=	PUNCT
ejpam-5226	367	1	ŝ1	ŝ1	PROPN
ejpam-5226	367	2	∧	∧	PROPN
ejpam-5226	367	3	(	(	PUNCT
ejpam-5226	367	4	ŝ2	ŝ2	ADJ
ejpam-5226	367	5	∧	∧	PROPN
ejpam-5226	367	6	s2	s2	PROPN
ejpam-5226	367	7	)	)	PUNCT
ejpam-5226	367	8	=	=	SYM
ejpam-5226	368	1	ŝ1	ŝ1	PROPN
ejpam-5226	368	2	∧	∧	PROPN
ejpam-5226	368	3	ŝ2	ŝ2	PROPN
ejpam-5226	368	4	.	.	PUNCT
ejpam-5226	369	1	therefore	therefore	ADV
ejpam-5226	369	2	,	,	PUNCT
ejpam-5226	369	3	ŝ1	ŝ1	DET
ejpam-5226	369	4	∧	∧	PROPN
ejpam-5226	369	5	ŝ2	ŝ2	PROPN
ejpam-5226	369	6	≤	≤	NUM
ejpam-5226	369	7	s2	s2	PROPN
ejpam-5226	369	8	.	.	PUNCT
ejpam-5226	370	1	so	so	SCONJ
ejpam-5226	370	2	that	that	SCONJ
ejpam-5226	370	3	ŝ1	ŝ1	PROPN
ejpam-5226	370	4	∧	∧	PROPN
ejpam-5226	370	5	ŝ2	ŝ2	PROPN
ejpam-5226	370	6	∈	∈	PROPN
ejpam-5226	370	7	ŝ.	ŝ.	NOUN
ejpam-5226	370	8	hence	hence	ADV
ejpam-5226	370	9	,	,	PUNCT
ejpam-5226	370	10	ŝ	ŝ	X
ejpam-5226	370	11	is	be	AUX
ejpam-5226	370	12	closed	close	VERB
ejpam-5226	370	13	under	under	ADP
ejpam-5226	370	14	∧.	∧.	PROPN
ejpam-5226	370	15	(	(	PUNCT
ejpam-5226	370	16	ii	ii	NOUN
ejpam-5226	370	17	)	)	PUNCT
ejpam-5226	370	18	let	let	VERB
ejpam-5226	370	19	h	h	NOUN
ejpam-5226	370	20	∈	∈	PROPN
ejpam-5226	370	21	l	l	NOUN
ejpam-5226	370	22	and	and	CCONJ
ejpam-5226	371	1	ŝ1	ŝ1	PROPN
ejpam-5226	371	2	∈	∈	PROPN
ejpam-5226	371	3	ŝ.	ŝ.	NOUN
ejpam-5226	371	4	then	then	ADV
ejpam-5226	371	5	there	there	PRON
ejpam-5226	371	6	exists	exist	VERB
ejpam-5226	371	7	s1	s1	PROPN
ejpam-5226	371	8	∈	∈	PROPN
ejpam-5226	371	9	s	s	VERB
ejpam-5226	371	10	such	such	ADJ
ejpam-5226	371	11	that	that	SCONJ
ejpam-5226	371	12	ŝ1	ŝ1	PROPN
ejpam-5226	371	13	≤	≤	NUM
ejpam-5226	371	14	s1	s1	NOUN
ejpam-5226	371	15	.	.	PUNCT
ejpam-5226	372	1	now	now	ADV
ejpam-5226	372	2	,	,	PUNCT
ejpam-5226	372	3	(	(	PUNCT
ejpam-5226	372	4	h	h	NOUN
ejpam-5226	372	5	∧	∧	PROPN
ejpam-5226	372	6	ŝ1	ŝ1	PROPN
ejpam-5226	372	7	)	)	PUNCT
ejpam-5226	372	8	∧	∧	NOUN
ejpam-5226	372	9	s1	s1	NOUN
ejpam-5226	372	10	=	=	SYM
ejpam-5226	372	11	h	h	NOUN
ejpam-5226	372	12	∧	∧	PROPN
ejpam-5226	372	13	(	(	PUNCT
ejpam-5226	372	14	ŝ1	ŝ1	PROPN
ejpam-5226	372	15	∧	∧	PROPN
ejpam-5226	372	16	s1	s1	NOUN
ejpam-5226	372	17	)	)	PUNCT
ejpam-5226	372	18	=	=	SYM
ejpam-5226	372	19	h	h	NOUN
ejpam-5226	372	20	∧	∧	PROPN
ejpam-5226	372	21	ŝ1	ŝ1	PROPN
ejpam-5226	372	22	.	.	PUNCT
ejpam-5226	373	1	then	then	ADV
ejpam-5226	373	2	h	h	PROPN
ejpam-5226	373	3	∧	∧	PROPN
ejpam-5226	373	4	ŝ1	ŝ1	PROPN
ejpam-5226	373	5	≤	≤	NUM
ejpam-5226	373	6	s1	s1	NOUN
ejpam-5226	373	7	.	.	PUNCT
ejpam-5226	374	1	therefore	therefore	ADV
ejpam-5226	374	2	,	,	PUNCT
ejpam-5226	374	3	h	h	NOUN
ejpam-5226	374	4	∧	∧	PROPN
ejpam-5226	374	5	ŝ1	ŝ1	PROPN
ejpam-5226	374	6	∈	∈	PROPN
ejpam-5226	374	7	ŝ.	ŝ.	NOUN
ejpam-5226	374	8	(	(	PUNCT
ejpam-5226	374	9	iii	iii	NOUN
ejpam-5226	374	10	)	)	PUNCT
ejpam-5226	374	11	let	let	VERB
ejpam-5226	374	12	ŝ1	ŝ1	PROPN
ejpam-5226	374	13	∈	∈	PROPN
ejpam-5226	374	14	ŝ.	ŝ.	NOUN
ejpam-5226	374	15	then	then	ADV
ejpam-5226	374	16	ŝ1	ŝ1	PROPN
ejpam-5226	374	17	∧	∧	PROPN
ejpam-5226	374	18	s1	s1	NOUN
ejpam-5226	374	19	=	=	SYM
ejpam-5226	374	20	s1	s1	PROPN
ejpam-5226	374	21	∧	∧	PROPN
ejpam-5226	374	22	ŝ1	ŝ1	PROPN
ejpam-5226	375	1	=	=	SYM
ejpam-5226	375	2	ŝ1	ŝ1	PROPN
ejpam-5226	375	3	.	.	PUNCT
ejpam-5226	376	1	therefore	therefore	ADV
ejpam-5226	376	2	,	,	PUNCT
ejpam-5226	376	3	ŝ1	ŝ1	PROPN
ejpam-5226	376	4	∈	∈	PROPN
ejpam-5226	376	5	hs	hs	INTJ
ejpam-5226	376	6	(	(	PUNCT
ejpam-5226	376	7	since	since	SCONJ
ejpam-5226	376	8	s1	s1	PROPN
ejpam-5226	376	9	∈	∈	PROPN
ejpam-5226	376	10	s	s	PART
ejpam-5226	376	11	)	)	PUNCT
ejpam-5226	376	12	.	.	PUNCT
ejpam-5226	377	1	hence	hence	ADV
ejpam-5226	377	2	,	,	PUNCT
ejpam-5226	377	3	ŝ	ŝ	VERB
ejpam-5226	377	4	⊆	⊆	NUM
ejpam-5226	377	5	hs	hs	PROPN
ejpam-5226	377	6	.	.	PUNCT
ejpam-5226	378	1	(	(	PUNCT
ejpam-5226	378	2	iv	iv	X
ejpam-5226	378	3	)	)	PUNCT
ejpam-5226	378	4	by	by	ADP
ejpam-5226	378	5	definition	definition	NOUN
ejpam-5226	378	6	2	2	NUM
ejpam-5226	378	7	,	,	PUNCT
ejpam-5226	378	8	s	s	VERB
ejpam-5226	378	9	⊆	⊆	NUM
ejpam-5226	378	10	ŝ.	ŝ.	NOUN
ejpam-5226	378	11	then	then	ADV
ejpam-5226	378	12	hs	hs	PROPN
ejpam-5226	378	13	⊆	⊆	NUM
ejpam-5226	378	14	h	h	NOUN
ejpam-5226	378	15	ŝ	ŝ	X
ejpam-5226	378	16	.	.	PUNCT
ejpam-5226	379	1	let	let	VERB
ejpam-5226	379	2	h	h	PRON
ejpam-5226	379	3	∈	∈	PROPN
ejpam-5226	379	4	h	h	NOUN
ejpam-5226	379	5	ŝ	ŝ	X
ejpam-5226	379	6	.	.	PUNCT
ejpam-5226	380	1	then	then	ADV
ejpam-5226	380	2	ŝ1	ŝ1	PROPN
ejpam-5226	380	3	∧	∧	PROPN
ejpam-5226	380	4	h	h	NOUN
ejpam-5226	380	5	=	=	NOUN
ejpam-5226	380	6	h	h	PROPN
ejpam-5226	380	7	for	for	ADP
ejpam-5226	380	8	some	some	DET
ejpam-5226	380	9	ŝ1	ŝ1	PROPN
ejpam-5226	380	10	∈	∈	PROPN
ejpam-5226	380	11	ŝ.	ŝ.	NOUN
ejpam-5226	380	12	for	for	ADP
ejpam-5226	380	13	this	this	PRON
ejpam-5226	380	14	ŝ1	ŝ1	PROPN
ejpam-5226	380	15	∈	∈	PROPN
ejpam-5226	380	16	ŝ	ŝ	NOUN
ejpam-5226	380	17	,	,	PUNCT
ejpam-5226	380	18	there	there	PRON
ejpam-5226	380	19	exists	exist	VERB
ejpam-5226	380	20	s1	s1	PROPN
ejpam-5226	380	21	∈	∈	PROPN
ejpam-5226	380	22	s	s	VERB
ejpam-5226	380	23	such	such	ADJ
ejpam-5226	380	24	that	that	SCONJ
ejpam-5226	380	25	ŝ1	ŝ1	PROPN
ejpam-5226	380	26	≤	≤	NUM
ejpam-5226	380	27	s1	s1	NOUN
ejpam-5226	380	28	.	.	PUNCT
ejpam-5226	381	1	now	now	ADV
ejpam-5226	381	2	,	,	PUNCT
ejpam-5226	381	3	s1	s1	PROPN
ejpam-5226	381	4	∧	∧	PROPN
ejpam-5226	381	5	h	h	NOUN
ejpam-5226	381	6	=	=	SYM
ejpam-5226	381	7	s1	s1	PROPN
ejpam-5226	381	8	∧	∧	PROPN
ejpam-5226	381	9	(	(	PUNCT
ejpam-5226	381	10	ŝ1	ŝ1	ADV
ejpam-5226	381	11	∧	∧	PROPN
ejpam-5226	381	12	h	h	NOUN
ejpam-5226	381	13	)	)	PUNCT
ejpam-5226	381	14	=	=	SYM
ejpam-5226	381	15	(	(	PUNCT
ejpam-5226	381	16	s1	s1	PROPN
ejpam-5226	381	17	∧	∧	PROPN
ejpam-5226	381	18	ŝ1	ŝ1	PROPN
ejpam-5226	381	19	)	)	PUNCT
ejpam-5226	381	20	∧	∧	NOUN
ejpam-5226	381	21	h	h	NOUN
ejpam-5226	381	22	=	=	PUNCT
ejpam-5226	381	23	ŝ1	ŝ1	PROPN
ejpam-5226	381	24	∧	∧	PROPN
ejpam-5226	381	25	h	h	NOUN
ejpam-5226	381	26	=	=	PROPN
ejpam-5226	381	27	h.	h.	PROPN
ejpam-5226	381	28	then	then	ADV
ejpam-5226	381	29	h	h	PROPN
ejpam-5226	381	30	∈	∈	PROPN
ejpam-5226	381	31	hs	hs	INTJ
ejpam-5226	381	32	(	(	PUNCT
ejpam-5226	381	33	since	since	SCONJ
ejpam-5226	381	34	s1	s1	PROPN
ejpam-5226	381	35	∈	∈	PROPN
ejpam-5226	381	36	s	s	PART
ejpam-5226	381	37	)	)	PUNCT
ejpam-5226	381	38	.	.	PUNCT
ejpam-5226	382	1	hence	hence	ADV
ejpam-5226	382	2	,	,	PUNCT
ejpam-5226	382	3	h	h	NOUN
ejpam-5226	382	4	ŝ	ŝ	VERB
ejpam-5226	382	5	⊆	⊆	NUM
ejpam-5226	382	6	hs	hs	PROPN
ejpam-5226	382	7	.	.	PUNCT
ejpam-5226	383	1	thus	thus	ADV
ejpam-5226	383	2	,	,	PUNCT
ejpam-5226	383	3	hs	hs	PROPN
ejpam-5226	383	4	=	=	PROPN
ejpam-5226	383	5	h	h	PROPN
ejpam-5226	383	6	ŝ	ŝ	X
ejpam-5226	383	7	.	.	PUNCT
ejpam-5226	384	1	remark	remark	PROPN
ejpam-5226	384	2	13	13	NUM
ejpam-5226	384	3	.	.	PUNCT
ejpam-5226	384	4	ŝ	ŝ	PROPN
ejpam-5226	384	5	need	need	AUX
ejpam-5226	384	6	not	not	PART
ejpam-5226	384	7	be	be	AUX
ejpam-5226	384	8	closed	close	VERB
ejpam-5226	384	9	under	under	ADP
ejpam-5226	384	10	∨.	∨.	NOUN
ejpam-5226	384	11	in	in	ADP
ejpam-5226	384	12	example	example	NOUN
ejpam-5226	384	13	2	2	NUM
ejpam-5226	384	14	,	,	PUNCT
ejpam-5226	384	15	let	let	VERB
ejpam-5226	384	16	s	s	PRON
ejpam-5226	384	17	=	=	X
ejpam-5226	384	18	{	{	PUNCT
ejpam-5226	384	19	a	a	PRON
ejpam-5226	384	20	,	,	PUNCT
ejpam-5226	384	21	b	b	NOUN
ejpam-5226	384	22	}	}	PUNCT
ejpam-5226	384	23	.	.	PUNCT
ejpam-5226	385	1	then	then	ADV
ejpam-5226	385	2	ŝ	ŝ	VERB
ejpam-5226	385	3	=	=	PUNCT
ejpam-5226	385	4	{	{	PUNCT
ejpam-5226	385	5	0	0	NUM
ejpam-5226	385	6	,	,	PUNCT
ejpam-5226	385	7	a	a	DET
ejpam-5226	385	8	,	,	PUNCT
ejpam-5226	385	9	b	b	NOUN
ejpam-5226	385	10	}	}	PUNCT
ejpam-5226	385	11	.	.	PUNCT
ejpam-5226	386	1	now	now	ADV
ejpam-5226	386	2	,	,	PUNCT
ejpam-5226	386	3	a	a	DET
ejpam-5226	386	4	∨	∨	NOUN
ejpam-5226	386	5	b	b	X
ejpam-5226	386	6	=	=	SYM
ejpam-5226	386	7	c	c	PROPN
ejpam-5226	386	8	/∈	/∈	PUNCT
ejpam-5226	386	9	ŝ.	ŝ.	NOUN
ejpam-5226	386	10	hence	hence	ADV
ejpam-5226	386	11	,	,	PUNCT
ejpam-5226	386	12	ŝ	ŝ	NUM
ejpam-5226	386	13	is	be	AUX
ejpam-5226	386	14	not	not	PART
ejpam-5226	386	15	closed	close	VERB
ejpam-5226	386	16	under	under	ADP
ejpam-5226	386	17	∨.	∨.	NOUN
ejpam-5226	386	18	remark	remark	VERB
ejpam-5226	386	19	14	14	NUM
ejpam-5226	386	20	.	.	PUNCT
ejpam-5226	387	1	for	for	ADP
ejpam-5226	387	2	any	any	DET
ejpam-5226	387	3	h	h	NOUN
ejpam-5226	387	4	∈	∈	PROPN
ejpam-5226	387	5	l	l	NOUN
ejpam-5226	387	6	and	and	CCONJ
ejpam-5226	387	7	ŝ1	ŝ1	PROPN
ejpam-5226	387	8	∈	∈	PROPN
ejpam-5226	387	9	ŝ	ŝ	PROPN
ejpam-5226	387	10	,	,	PUNCT
ejpam-5226	387	11	ŝ1	ŝ1	PRON
ejpam-5226	387	12	∧	∧	NOUN
ejpam-5226	387	13	h	h	NOUN
ejpam-5226	387	14	need	need	AUX
ejpam-5226	387	15	not	not	PART
ejpam-5226	387	16	be	be	AUX
ejpam-5226	387	17	in	in	ADP
ejpam-5226	387	18	ŝ.	ŝ.	NOUN
ejpam-5226	387	19	in	in	ADP
ejpam-5226	387	20	a	a	DET
ejpam-5226	387	21	discrete	discrete	ADJ
ejpam-5226	387	22	adl	adl	NOUN
ejpam-5226	387	23	x	x	NOUN
ejpam-5226	387	24	,	,	PUNCT
ejpam-5226	387	25	let	let	VERB
ejpam-5226	387	26	s	s	PRON
ejpam-5226	387	27	=	=	X
ejpam-5226	387	28	{	{	PUNCT
ejpam-5226	387	29	a	a	NOUN
ejpam-5226	387	30	}	}	PUNCT
ejpam-5226	387	31	for	for	ADP
ejpam-5226	387	32	some	some	DET
ejpam-5226	387	33	non	non	ADJ
ejpam-5226	387	34	-	-	ADJ
ejpam-5226	387	35	zero	zero	NUM
ejpam-5226	387	36	element	element	NOUN
ejpam-5226	387	37	a	a	DET
ejpam-5226	387	38	∈	∈	NOUN
ejpam-5226	387	39	x.	x.	NOUN
ejpam-5226	387	40	then	then	ADV
ejpam-5226	387	41	ŝ	ŝ	VERB
ejpam-5226	387	42	=	=	PUNCT
ejpam-5226	387	43	{	{	PUNCT
ejpam-5226	387	44	0	0	NUM
ejpam-5226	387	45	,	,	PUNCT
ejpam-5226	387	46	a	a	PRON
ejpam-5226	387	47	}	}	PUNCT
ejpam-5226	387	48	.	.	PUNCT
ejpam-5226	388	1	let	let	VERB
ejpam-5226	388	2	x	x	SYM
ejpam-5226	388	3	∈	∈	PROPN
ejpam-5226	388	4	x.	x.	NOUN
ejpam-5226	388	5	then	then	ADV
ejpam-5226	388	6	a	a	DET
ejpam-5226	388	7	∧	∧	PROPN
ejpam-5226	388	8	x	x	X
ejpam-5226	388	9	=	=	PUNCT
ejpam-5226	388	10	x	x	X
ejpam-5226	388	11	/∈	/∈	PUNCT
ejpam-5226	388	12	ŝ.	ŝ.	ADJ
ejpam-5226	388	13	remark	remark	NOUN
ejpam-5226	388	14	15	15	NUM
ejpam-5226	388	15	.	.	PUNCT
ejpam-5226	389	1	for	for	ADP
ejpam-5226	389	2	any	any	DET
ejpam-5226	389	3	non	non	ADJ
ejpam-5226	389	4	-	-	ADJ
ejpam-5226	389	5	empty	empty	ADJ
ejpam-5226	389	6	subset	subset	NOUN
ejpam-5226	389	7	s	s	PROPN
ejpam-5226	389	8	of	of	ADP
ejpam-5226	389	9	l	l	NOUN
ejpam-5226	389	10	,	,	PUNCT
ejpam-5226	389	11	ŝ	ŝ	X
ejpam-5226	389	12	need	need	AUX
ejpam-5226	389	13	not	not	PART
ejpam-5226	389	14	be	be	AUX
ejpam-5226	389	15	equal	equal	ADJ
ejpam-5226	389	16	to	to	ADP
ejpam-5226	389	17	h	h	PROPN
ejpam-5226	389	18	ŝ	ŝ	NOUN
ejpam-5226	389	19	.	.	PUNCT
ejpam-5226	390	1	in	in	ADP
ejpam-5226	390	2	a	a	DET
ejpam-5226	390	3	discrete	discrete	ADJ
ejpam-5226	390	4	adl	adl	NOUN
ejpam-5226	390	5	x	x	NOUN
ejpam-5226	390	6	,	,	PUNCT
ejpam-5226	390	7	let	let	VERB
ejpam-5226	390	8	s	s	PRON
ejpam-5226	390	9	=	=	VERB
ejpam-5226	390	10	{	{	PUNCT
ejpam-5226	390	11	a	a	NOUN
ejpam-5226	390	12	}	}	PUNCT
ejpam-5226	390	13	,	,	PUNCT
ejpam-5226	390	14	for	for	ADP
ejpam-5226	390	15	some	some	DET
ejpam-5226	390	16	non	non	ADJ
ejpam-5226	390	17	-	-	ADJ
ejpam-5226	390	18	zero	zero	NUM
ejpam-5226	390	19	element	element	NOUN
ejpam-5226	390	20	a	a	DET
ejpam-5226	390	21	∈	∈	NOUN
ejpam-5226	390	22	x.	x.	NOUN
ejpam-5226	390	23	then	then	ADV
ejpam-5226	390	24	hs	hs	PROPN
ejpam-5226	390	25	=	=	NOUN
ejpam-5226	390	26	ha	ha	INTJ
ejpam-5226	390	27	=	=	PUNCT
ejpam-5226	390	28	x	x	PROPN
ejpam-5226	390	29	and	and	CCONJ
ejpam-5226	390	30	ŝ	ŝ	X
ejpam-5226	390	31	=	=	PUNCT
ejpam-5226	390	32	{	{	PUNCT
ejpam-5226	390	33	0	0	NUM
ejpam-5226	390	34	,	,	PUNCT
ejpam-5226	390	35	a	a	PRON
ejpam-5226	390	36	}	}	PUNCT
ejpam-5226	390	37	.	.	PUNCT
ejpam-5226	391	1	therefore	therefore	ADV
ejpam-5226	391	2	,	,	PUNCT
ejpam-5226	391	3	hs	hs	PROPN
ejpam-5226	391	4	̸=	̸=	PROPN
ejpam-5226	391	5	ŝ.	ŝ.	VERB
ejpam-5226	391	6	lemma	lemma	PROPN
ejpam-5226	391	7	5	5	NUM
ejpam-5226	391	8	.	.	PUNCT
ejpam-5226	392	1	if	if	SCONJ
ejpam-5226	392	2	hs	hs	PROPN
ejpam-5226	392	3	is	be	AUX
ejpam-5226	392	4	compatible	compatible	ADJ
ejpam-5226	392	5	,	,	PUNCT
ejpam-5226	392	6	then	then	ADV
ejpam-5226	392	7	hs	hs	PROPN
ejpam-5226	392	8	=	=	PUNCT
ejpam-5226	392	9	ŝ	ŝ	PROPN
ejpam-5226	392	10	,	,	PUNCT
ejpam-5226	392	11	where	where	SCONJ
ejpam-5226	392	12	s	s	VERB
ejpam-5226	392	13	⊆	⊆	NUM
ejpam-5226	392	14	l	l	NOUN
ejpam-5226	392	15	and	and	CCONJ
ejpam-5226	392	16	s	s	VERB
ejpam-5226	392	17	̸=	̸=	PROPN
ejpam-5226	392	18	∅.	∅.	PRON
ejpam-5226	392	19	proof	proof	NOUN
ejpam-5226	392	20	.	.	PUNCT
ejpam-5226	393	1	let	let	VERB
ejpam-5226	393	2	h	h	PRON
ejpam-5226	393	3	∈	∈	PROPN
ejpam-5226	394	1	hs	hs	PROPN
ejpam-5226	394	2	.	.	PUNCT
ejpam-5226	395	1	then	then	ADV
ejpam-5226	395	2	,	,	PUNCT
ejpam-5226	395	3	an	an	DET
ejpam-5226	395	4	element	element	NOUN
ejpam-5226	395	5	s	s	PART
ejpam-5226	395	6	∈	∈	NOUN
ejpam-5226	395	7	s	s	PART
ejpam-5226	395	8	exists	exist	VERB
ejpam-5226	395	9	such	such	ADJ
ejpam-5226	395	10	that	that	DET
ejpam-5226	395	11	s	s	VERB
ejpam-5226	395	12	∧	∧	PROPN
ejpam-5226	395	13	h	h	NOUN
ejpam-5226	395	14	=	=	PROPN
ejpam-5226	395	15	h.	h.	PROPN
ejpam-5226	395	16	since	since	SCONJ
ejpam-5226	395	17	s	s	PROPN
ejpam-5226	395	18	⊆	⊆	NUM
ejpam-5226	395	19	hs	hs	PROPN
ejpam-5226	395	20	,	,	PUNCT
ejpam-5226	395	21	s	s	PART
ejpam-5226	395	22	∧	∧	PROPN
ejpam-5226	395	23	h	h	NOUN
ejpam-5226	396	1	=	=	NOUN
ejpam-5226	396	2	h	h	NOUN
ejpam-5226	396	3	∧	∧	PROPN
ejpam-5226	396	4	s	s	PART
ejpam-5226	396	5	=	=	PROPN
ejpam-5226	396	6	h.	h.	PROPN
ejpam-5226	396	7	therefore	therefore	ADV
ejpam-5226	396	8	,	,	PUNCT
ejpam-5226	396	9	h	h	PROPN
ejpam-5226	396	10	≤	≤	PROPN
ejpam-5226	396	11	s	s	PART
ejpam-5226	396	12	and	and	CCONJ
ejpam-5226	396	13	s	s	PROPN
ejpam-5226	396	14	∈	∈	PROPN
ejpam-5226	396	15	s.	s.	PROPN
ejpam-5226	397	1	so	so	SCONJ
ejpam-5226	397	2	that	that	SCONJ
ejpam-5226	397	3	h	h	PROPN
ejpam-5226	397	4	∈	∈	PROPN
ejpam-5226	397	5	ŝ.	ŝ.	NOUN
ejpam-5226	397	6	hence	hence	ADV
ejpam-5226	397	7	,	,	PUNCT
ejpam-5226	397	8	hs	hs	PROPN
ejpam-5226	397	9	⊆	⊆	NUM
ejpam-5226	397	10	ŝ.	ŝ.	NOUN
ejpam-5226	397	11	by	by	ADP
ejpam-5226	397	12	lemma	lemma	PROPN
ejpam-5226	397	13	4(iii	4(iii	NUM
ejpam-5226	397	14	)	)	PUNCT
ejpam-5226	397	15	,	,	PUNCT
ejpam-5226	397	16	hs	hs	PROPN
ejpam-5226	397	17	=	=	NOUN
ejpam-5226	397	18	ŝ.	ŝ.	NOUN
ejpam-5226	397	19	theorem	theorem	VERB
ejpam-5226	397	20	6	6	NUM
ejpam-5226	397	21	.	.	PUNCT
ejpam-5226	397	22	for	for	ADP
ejpam-5226	397	23	any	any	DET
ejpam-5226	397	24	compatible	compatible	ADJ
ejpam-5226	397	25	subset	subset	NOUN
ejpam-5226	397	26	s	s	PROPN
ejpam-5226	397	27	of	of	ADP
ejpam-5226	397	28	l	l	NOUN
ejpam-5226	397	29	,	,	PUNCT
ejpam-5226	397	30	we	we	PRON
ejpam-5226	397	31	have	have	VERB
ejpam-5226	397	32	the	the	DET
ejpam-5226	397	33	following	following	NOUN
ejpam-5226	397	34	:	:	PUNCT
ejpam-5226	397	35	(	(	PUNCT
ejpam-5226	397	36	i	i	NOUN
ejpam-5226	397	37	)	)	PUNCT
ejpam-5226	397	38	ŝ	ŝ	X
ejpam-5226	397	39	is	be	AUX
ejpam-5226	397	40	compatible	compatible	ADJ
ejpam-5226	397	41	,	,	PUNCT
ejpam-5226	397	42	(	(	PUNCT
ejpam-5226	397	43	ii	ii	NOUN
ejpam-5226	397	44	)	)	PUNCT
ejpam-5226	397	45	for	for	ADP
ejpam-5226	397	46	each	each	DET
ejpam-5226	397	47	h	h	NOUN
ejpam-5226	397	48	∈	∈	PROPN
ejpam-5226	398	1	hs	hs	PROPN
ejpam-5226	398	2	,	,	PUNCT
ejpam-5226	398	3	there	there	PRON
ejpam-5226	398	4	exists	exist	VERB
ejpam-5226	398	5	unique	unique	ADJ
ejpam-5226	398	6	ŝ	ŝ	X
ejpam-5226	398	7	∈	∈	PROPN
ejpam-5226	398	8	ŝ	ŝ	VERB
ejpam-5226	398	9	such	such	ADJ
ejpam-5226	398	10	that	that	SCONJ
ejpam-5226	398	11	ŝ	ŝ	X
ejpam-5226	398	12	∧	∧	PROPN
ejpam-5226	398	13	h	h	NOUN
ejpam-5226	398	14	=	=	NOUN
ejpam-5226	398	15	h	h	NOUN
ejpam-5226	398	16	and	and	CCONJ
ejpam-5226	398	17	h	h	NOUN
ejpam-5226	398	18	∧	∧	NOUN
ejpam-5226	398	19	ŝ	ŝ	X
ejpam-5226	398	20	=	=	SYM
ejpam-5226	398	21	ŝ.	ŝ.	ADJ
ejpam-5226	398	22	a.	a.	NOUN
ejpam-5226	398	23	iampan	iampan	PROPN
ejpam-5226	398	24	et	et	PROPN
ejpam-5226	398	25	al	al	PROPN
ejpam-5226	398	26	.	.	PUNCT
ejpam-5226	398	27	/	/	SYM
ejpam-5226	398	28	eur	eur	PROPN
ejpam-5226	398	29	.	.	PUNCT
ejpam-5226	399	1	j.	j.	PROPN
ejpam-5226	399	2	pure	pure	PROPN
ejpam-5226	399	3	appl	appl	PROPN
ejpam-5226	399	4	.	.	PROPN
ejpam-5226	399	5	math	math	PROPN
ejpam-5226	399	6	,	,	PUNCT
ejpam-5226	399	7	17	17	NUM
ejpam-5226	399	8	(	(	PUNCT
ejpam-5226	399	9	3	3	NUM
ejpam-5226	399	10	)	)	PUNCT
ejpam-5226	399	11	(	(	PUNCT
ejpam-5226	399	12	2024	2024	NUM
ejpam-5226	399	13	)	)	PUNCT
ejpam-5226	399	14	,	,	PUNCT
ejpam-5226	399	15	1691	1691	NUM
ejpam-5226	399	16	-	-	SYM
ejpam-5226	399	17	1704	1704	NUM
ejpam-5226	399	18	1702	1702	NUM
ejpam-5226	399	19	proof	proof	NOUN
ejpam-5226	399	20	.	.	PUNCT
ejpam-5226	400	1	(	(	PUNCT
ejpam-5226	400	2	i	i	NOUN
ejpam-5226	400	3	)	)	PUNCT
ejpam-5226	400	4	let	let	VERB
ejpam-5226	400	5	ŝ1	ŝ1	PROPN
ejpam-5226	400	6	,	,	PUNCT
ejpam-5226	400	7	ŝ2	ŝ2	PROPN
ejpam-5226	400	8	∈	∈	PROPN
ejpam-5226	400	9	ŝ.	ŝ.	NOUN
ejpam-5226	400	10	then	then	ADV
ejpam-5226	400	11	there	there	PRON
ejpam-5226	400	12	exist	exist	VERB
ejpam-5226	400	13	s1	s1	NOUN
ejpam-5226	400	14	,	,	PUNCT
ejpam-5226	400	15	s2	s2	NOUN
ejpam-5226	400	16	∈	∈	PROPN
ejpam-5226	400	17	s	s	VERB
ejpam-5226	400	18	such	such	ADJ
ejpam-5226	400	19	that	that	SCONJ
ejpam-5226	400	20	ŝ1	ŝ1	PROPN
ejpam-5226	400	21	≤	≤	ADJ
ejpam-5226	400	22	s1	s1	NOUN
ejpam-5226	400	23	and	and	CCONJ
ejpam-5226	400	24	ŝ2	ŝ2	ADJ
ejpam-5226	400	25	≤	≤	NUM
ejpam-5226	400	26	s2	s2	PROPN
ejpam-5226	400	27	.	.	PUNCT
ejpam-5226	401	1	now	now	ADV
ejpam-5226	401	2	,	,	PUNCT
ejpam-5226	401	3	ŝ1∧ŝ2	ŝ1∧ŝ2	NOUN
ejpam-5226	401	4	=	=	SYM
ejpam-5226	401	5	(	(	PUNCT
ejpam-5226	401	6	ŝ1∧s1)∧(ŝ2∧s2	ŝ1∧s1)∧(ŝ2∧s2	ADJ
ejpam-5226	401	7	)	)	PUNCT
ejpam-5226	401	8	=	=	SYM
ejpam-5226	401	9	ŝ2∧ŝ1∧(s1∧s2	ŝ2∧ŝ1∧(s1∧s2	NOUN
ejpam-5226	401	10	)	)	PUNCT
ejpam-5226	401	11	=	=	SYM
ejpam-5226	401	12	ŝ2∧ŝ1∧(s2∧s1	ŝ2∧ŝ1∧(s2∧s1	X
ejpam-5226	401	13	)	)	PUNCT
ejpam-5226	401	14	=	=	SYM
ejpam-5226	401	15	(	(	PUNCT
ejpam-5226	401	16	ŝ2∧s2)∧(ŝ1∧s1	ŝ2∧s2)∧(ŝ1∧s1	NOUN
ejpam-5226	401	17	)	)	PUNCT
ejpam-5226	401	18	=	=	PUNCT
ejpam-5226	402	1	ŝ2	ŝ2	ADJ
ejpam-5226	402	2	∧	∧	PROPN
ejpam-5226	402	3	ŝ1	ŝ1	PROPN
ejpam-5226	402	4	(	(	PUNCT
ejpam-5226	402	5	since	since	SCONJ
ejpam-5226	402	6	s	s	PROPN
ejpam-5226	402	7	is	be	AUX
ejpam-5226	402	8	compatible	compatible	ADJ
ejpam-5226	402	9	)	)	PUNCT
ejpam-5226	402	10	.	.	PUNCT
ejpam-5226	403	1	therefore	therefore	ADV
ejpam-5226	403	2	,	,	PUNCT
ejpam-5226	403	3	ŝ	ŝ	X
ejpam-5226	403	4	is	be	AUX
ejpam-5226	403	5	compatible	compatible	ADJ
ejpam-5226	403	6	.	.	PUNCT
ejpam-5226	404	1	(	(	PUNCT
ejpam-5226	404	2	ii	ii	NOUN
ejpam-5226	404	3	)	)	PUNCT
ejpam-5226	404	4	let	let	VERB
ejpam-5226	404	5	h	h	PROPN
ejpam-5226	404	6	∈	∈	PROPN
ejpam-5226	404	7	hs	hs	PROPN
ejpam-5226	404	8	.	.	PUNCT
ejpam-5226	405	1	by	by	ADP
ejpam-5226	405	2	lemma	lemma	PROPN
ejpam-5226	405	3	4(iv	4(iv	NUM
ejpam-5226	405	4	)	)	PUNCT
ejpam-5226	405	5	,	,	PUNCT
ejpam-5226	405	6	h	h	NOUN
ejpam-5226	405	7	∈	∈	PROPN
ejpam-5226	405	8	h	h	NOUN
ejpam-5226	405	9	ŝ	ŝ	X
ejpam-5226	405	10	=	=	SYM
ejpam-5226	405	11	hs	hs	PROPN
ejpam-5226	405	12	.	.	PUNCT
ejpam-5226	406	1	for	for	ADP
ejpam-5226	406	2	this	this	DET
ejpam-5226	406	3	h	h	NOUN
ejpam-5226	406	4	∈	∈	PROPN
ejpam-5226	406	5	h	h	NOUN
ejpam-5226	406	6	ŝ	ŝ	NOUN
ejpam-5226	406	7	,	,	PUNCT
ejpam-5226	406	8	there	there	PRON
ejpam-5226	406	9	exists	exist	VERB
ejpam-5226	406	10	ŝ	ŝ	X
ejpam-5226	406	11	∈	∈	PROPN
ejpam-5226	406	12	ŝ	ŝ	VERB
ejpam-5226	406	13	such	such	ADJ
ejpam-5226	406	14	that	that	SCONJ
ejpam-5226	406	15	ŝ	ŝ	X
ejpam-5226	406	16	∧	∧	PROPN
ejpam-5226	406	17	h	h	NOUN
ejpam-5226	406	18	=	=	NOUN
ejpam-5226	406	19	h	h	NOUN
ejpam-5226	406	20	and	and	CCONJ
ejpam-5226	406	21	for	for	ADP
ejpam-5226	406	22	this	this	PRON
ejpam-5226	406	23	ŝ	ŝ	CCONJ
ejpam-5226	406	24	∈	∈	PROPN
ejpam-5226	406	25	ŝ	ŝ	NOUN
ejpam-5226	406	26	,	,	PUNCT
ejpam-5226	406	27	there	there	PRON
ejpam-5226	406	28	exists	exist	VERB
ejpam-5226	406	29	s	s	PROPN
ejpam-5226	406	30	∈	∈	PROPN
ejpam-5226	406	31	s	s	VERB
ejpam-5226	406	32	such	such	ADJ
ejpam-5226	406	33	that	that	SCONJ
ejpam-5226	406	34	ŝ	ŝ	PROPN
ejpam-5226	406	35	≤	≤	NUM
ejpam-5226	406	36	s.	s.	PROPN
ejpam-5226	406	37	let	let	VERB
ejpam-5226	406	38	s0	s0	PROPN
ejpam-5226	406	39	=	=	PUNCT
ejpam-5226	406	40	h∧s	h∧s	PROPN
ejpam-5226	406	41	.	.	PUNCT
ejpam-5226	407	1	than	than	ADP
ejpam-5226	407	2	s0∧s	s0∧s	NUM
ejpam-5226	407	3	=	=	SYM
ejpam-5226	407	4	(	(	PUNCT
ejpam-5226	407	5	h∧s)∧s	h∧s)∧s	PROPN
ejpam-5226	407	6	=	=	SYM
ejpam-5226	407	7	h∧s	h∧s	NOUN
ejpam-5226	407	8	=	=	SYM
ejpam-5226	407	9	s0	s0	PROPN
ejpam-5226	407	10	.	.	PUNCT
ejpam-5226	408	1	therefore	therefore	ADV
ejpam-5226	408	2	,	,	PUNCT
ejpam-5226	408	3	s0	s0	PROPN
ejpam-5226	408	4	≤	≤	PROPN
ejpam-5226	408	5	s.	s.	PROPN
ejpam-5226	408	6	so	so	SCONJ
ejpam-5226	408	7	that	that	SCONJ
ejpam-5226	408	8	s0	s0	PROPN
ejpam-5226	408	9	∈	∈	PROPN
ejpam-5226	408	10	ŝ.	ŝ.	NOUN
ejpam-5226	408	11	now	now	ADV
ejpam-5226	408	12	,	,	PUNCT
ejpam-5226	408	13	h∧s0	h∧s0	PROPN
ejpam-5226	408	14	=	=	SYM
ejpam-5226	408	15	h∧h∧s	h∧h∧s	PROPN
ejpam-5226	408	16	=	=	SYM
ejpam-5226	408	17	h∧s	h∧s	PROPN
ejpam-5226	408	18	=	=	SYM
ejpam-5226	408	19	s0	s0	PROPN
ejpam-5226	408	20	and	and	CCONJ
ejpam-5226	408	21	s0∧h	s0∧h	PROPN
ejpam-5226	408	22	=	=	SYM
ejpam-5226	408	23	h∧s∧h	h∧s∧h	PROPN
ejpam-5226	408	24	=	=	SYM
ejpam-5226	408	25	s∧h∧h	s∧h∧h	NOUN
ejpam-5226	408	26	=	=	SYM
ejpam-5226	408	27	s∧h	s∧h	PROPN
ejpam-5226	408	28	=	=	PUNCT
ejpam-5226	408	29	h.	h.	PROPN
ejpam-5226	408	30	let	let	VERB
ejpam-5226	408	31	â	â	X
ejpam-5226	408	32	∈	∈	PROPN
ejpam-5226	408	33	ŝ	ŝ	VERB
ejpam-5226	408	34	such	such	ADJ
ejpam-5226	408	35	that	that	DET
ejpam-5226	408	36	h∧	h∧	PROPN
ejpam-5226	408	37	â	â	PROPN
ejpam-5226	408	38	=	=	SYM
ejpam-5226	408	39	â	â	X
ejpam-5226	408	40	and	and	CCONJ
ejpam-5226	408	41	â∧	â∧	VERB
ejpam-5226	408	42	h	h	NOUN
ejpam-5226	409	1	=	=	SYM
ejpam-5226	409	2	h.	h.	PROPN
ejpam-5226	409	3	now	now	ADV
ejpam-5226	409	4	,	,	PUNCT
ejpam-5226	409	5	s0	s0	PROPN
ejpam-5226	409	6	∧	∧	PROPN
ejpam-5226	409	7	â	â	PRON
ejpam-5226	409	8	=	=	SYM
ejpam-5226	409	9	h∧	h∧	PROPN
ejpam-5226	409	10	s∧	s∧	ADJ
ejpam-5226	409	11	â	â	X
ejpam-5226	410	1	=	=	SYM
ejpam-5226	410	2	h∧	h∧	PROPN
ejpam-5226	410	3	â∧	â∧	NOUN
ejpam-5226	410	4	s	s	PART
ejpam-5226	410	5	=	=	NOUN
ejpam-5226	410	6	â∧	â∧	VERB
ejpam-5226	410	7	h∧	h∧	PROPN
ejpam-5226	410	8	s	s	PART
ejpam-5226	410	9	=	=	X
ejpam-5226	410	10	h∧	h∧	PROPN
ejpam-5226	410	11	s	s	PART
ejpam-5226	410	12	=	=	SYM
ejpam-5226	410	13	s0	s0	PROPN
ejpam-5226	410	14	(	(	PUNCT
ejpam-5226	410	15	since	since	SCONJ
ejpam-5226	410	16	ŝ	ŝ	NOUN
ejpam-5226	410	17	is	be	AUX
ejpam-5226	410	18	compatible	compatible	ADJ
ejpam-5226	410	19	)	)	PUNCT
ejpam-5226	410	20	.	.	PUNCT
ejpam-5226	411	1	therefore	therefore	ADV
ejpam-5226	411	2	,	,	PUNCT
ejpam-5226	411	3	s0	s0	PROPN
ejpam-5226	411	4	≤	≤	NOUN
ejpam-5226	411	5	â	â	PUNCT
ejpam-5226	411	6	and	and	CCONJ
ejpam-5226	411	7	â∧	â∧	VERB
ejpam-5226	411	8	s0	s0	NOUN
ejpam-5226	411	9	=	=	PUNCT
ejpam-5226	411	10	â∧	â∧	VERB
ejpam-5226	411	11	h∧	h∧	PROPN
ejpam-5226	411	12	s	s	PART
ejpam-5226	411	13	=	=	X
ejpam-5226	411	14	h∧	h∧	PROPN
ejpam-5226	411	15	â∧	â∧	NOUN
ejpam-5226	411	16	s	s	PART
ejpam-5226	411	17	=	=	X
ejpam-5226	411	18	h∧	h∧	PROPN
ejpam-5226	411	19	s∧	s∧	NOUN
ejpam-5226	411	20	â	â	PUNCT
ejpam-5226	411	21	=	=	SYM
ejpam-5226	411	22	s	s	PART
ejpam-5226	411	23	∧	∧	PROPN
ejpam-5226	411	24	h	h	NOUN
ejpam-5226	411	25	∧	∧	PROPN
ejpam-5226	411	26	â	â	X
ejpam-5226	412	1	=	=	SYM
ejpam-5226	412	2	h	h	NOUN
ejpam-5226	412	3	∧	∧	PROPN
ejpam-5226	412	4	â	â	X
ejpam-5226	412	5	=	=	SYM
ejpam-5226	412	6	â.	â.	PROPN
ejpam-5226	412	7	therefore	therefore	ADV
ejpam-5226	412	8	,	,	PUNCT
ejpam-5226	412	9	â	â	PUNCT
ejpam-5226	412	10	≤	≤	PROPN
ejpam-5226	412	11	s0	s0	NOUN
ejpam-5226	412	12	.	.	PUNCT
ejpam-5226	413	1	hence	hence	ADV
ejpam-5226	413	2	,	,	PUNCT
ejpam-5226	413	3	s0	s0	PROPN
ejpam-5226	413	4	is	be	AUX
ejpam-5226	413	5	unique	unique	ADJ
ejpam-5226	413	6	.	.	PUNCT
ejpam-5226	414	1	theorem	theorem	ADJ
ejpam-5226	414	2	7	7	NUM
ejpam-5226	414	3	.	.	PUNCT
ejpam-5226	415	1	let	let	VERB
ejpam-5226	415	2	s	s	PRON
ejpam-5226	415	3	be	be	AUX
ejpam-5226	415	4	a	a	DET
ejpam-5226	415	5	non	non	ADJ
ejpam-5226	415	6	-	-	ADJ
ejpam-5226	415	7	empty	empty	ADJ
ejpam-5226	415	8	compatible	compatible	ADJ
ejpam-5226	415	9	subset	subset	NOUN
ejpam-5226	415	10	of	of	ADP
ejpam-5226	415	11	l.	l.	NOUN
ejpam-5226	415	12	for	for	ADP
ejpam-5226	415	13	any	any	DET
ejpam-5226	415	14	h1	h1	NOUN
ejpam-5226	415	15	,	,	PUNCT
ejpam-5226	415	16	h2	h2	PROPN
ejpam-5226	415	17	∈	∈	PROPN
ejpam-5226	415	18	hs	hs	PROPN
ejpam-5226	415	19	,	,	PUNCT
ejpam-5226	415	20	we	we	PRON
ejpam-5226	415	21	have	have	VERB
ejpam-5226	415	22	(	(	PUNCT
ejpam-5226	415	23	i	i	NOUN
ejpam-5226	415	24	)	)	PUNCT
ejpam-5226	416	1	̂(h1	̂(h1	PROPN
ejpam-5226	416	2	∨	∨	NUM
ejpam-5226	416	3	h2	h2	NOUN
ejpam-5226	416	4	)	)	PUNCT
ejpam-5226	416	5	=	=	PRON
ejpam-5226	417	1	ĥ1	ĥ1	AUX
ejpam-5226	417	2	∨	∨	NUM
ejpam-5226	417	3	ĥ2	ĥ2	PROPN
ejpam-5226	417	4	,	,	PUNCT
ejpam-5226	417	5	(	(	PUNCT
ejpam-5226	417	6	ii	ii	NOUN
ejpam-5226	417	7	)	)	PUNCT
ejpam-5226	417	8	̂(h1	̂(h1	PUNCT
ejpam-5226	418	1	∧	∧	PROPN
ejpam-5226	418	2	h2	h2	NOUN
ejpam-5226	418	3	)	)	PUNCT
ejpam-5226	419	1	=	=	PRON
ejpam-5226	420	1	ĥ1	ĥ1	VERB
ejpam-5226	420	2	∧	∧	NOUN
ejpam-5226	420	3	ĥ2	ĥ2	PROPN
ejpam-5226	420	4	,	,	PUNCT
ejpam-5226	420	5	(	(	PUNCT
ejpam-5226	420	6	iii	iii	X
ejpam-5226	420	7	)	)	PUNCT
ejpam-5226	421	1	h	h	NOUN
ejpam-5226	422	1	∈	∈	PROPN
ejpam-5226	422	2	hs	hs	PROPN
ejpam-5226	422	3	⇔	⇔	PROPN
ejpam-5226	422	4	h	h	PROPN
ejpam-5226	422	5	=	=	PUNCT
ejpam-5226	422	6	ĥ	ĥ	PROPN
ejpam-5226	422	7	,	,	PUNCT
ejpam-5226	422	8	for	for	ADP
ejpam-5226	422	9	any	any	DET
ejpam-5226	422	10	∅	∅	NOUN
ejpam-5226	422	11	=	=	NOUN
ejpam-5226	422	12	̸	̸	NUM
ejpam-5226	422	13	s	s	PART
ejpam-5226	422	14	⊆	⊆	NUM
ejpam-5226	422	15	l	l	NOUN
ejpam-5226	422	16	,	,	PUNCT
ejpam-5226	422	17	(	(	PUNCT
ejpam-5226	422	18	iv	iv	X
ejpam-5226	422	19	)	)	PUNCT
ejpam-5226	422	20	0̂	0̂	PROPN
ejpam-5226	423	1	=	=	PUNCT
ejpam-5226	423	2	0	0	X
ejpam-5226	423	3	.	.	PUNCT
ejpam-5226	424	1	proof	proof	NOUN
ejpam-5226	424	2	.	.	PUNCT
ejpam-5226	425	1	let	let	VERB
ejpam-5226	425	2	h1	h1	PROPN
ejpam-5226	425	3	,	,	PUNCT
ejpam-5226	425	4	h2	h2	PROPN
ejpam-5226	425	5	∈	∈	PROPN
ejpam-5226	425	6	hs	hs	PROPN
ejpam-5226	425	7	.	.	PUNCT
ejpam-5226	426	1	by	by	ADP
ejpam-5226	426	2	theorem	theorem	PROPN
ejpam-5226	426	3	6(ii	6(ii	PROPN
ejpam-5226	426	4	)	)	PUNCT
ejpam-5226	426	5	,	,	PUNCT
ejpam-5226	426	6	there	there	PRON
ejpam-5226	426	7	exists	exist	VERB
ejpam-5226	426	8	ĥ1	ĥ1	PRON
ejpam-5226	426	9	,	,	PUNCT
ejpam-5226	426	10	ĥ2	ĥ2	SYM
ejpam-5226	426	11	∈	∈	PROPN
ejpam-5226	426	12	ŝ	ŝ	NOUN
ejpam-5226	426	13	such	such	ADJ
ejpam-5226	426	14	that	that	PRON
ejpam-5226	426	15	h1	h1	PROPN
ejpam-5226	426	16	∧	∧	PROPN
ejpam-5226	426	17	ĥ1	ĥ1	NOUN
ejpam-5226	426	18	=	=	PUNCT
ejpam-5226	427	1	ĥ1	ĥ1	PROPN
ejpam-5226	427	2	,	,	PUNCT
ejpam-5226	427	3	h2	h2	NOUN
ejpam-5226	427	4	∧	∧	PROPN
ejpam-5226	427	5	ĥ2	ĥ2	NOUN
ejpam-5226	427	6	=	=	PUNCT
ejpam-5226	427	7	ĥ2	ĥ2	NOUN
ejpam-5226	427	8	and	and	CCONJ
ejpam-5226	427	9	ĥ1	ĥ1	PROPN
ejpam-5226	427	10	∧	∧	NOUN
ejpam-5226	427	11	h1	h1	NOUN
ejpam-5226	427	12	=	=	PUNCT
ejpam-5226	427	13	h1	h1	PROPN
ejpam-5226	427	14	,	,	PUNCT
ejpam-5226	427	15	ĥ2	ĥ2	ADJ
ejpam-5226	427	16	∧	∧	PROPN
ejpam-5226	427	17	h2	h2	NOUN
ejpam-5226	427	18	=	=	SYM
ejpam-5226	427	19	h2	h2	PROPN
ejpam-5226	427	20	.	.	PUNCT
ejpam-5226	428	1	(	(	PUNCT
ejpam-5226	428	2	i	i	NOUN
ejpam-5226	428	3	)	)	PUNCT
ejpam-5226	428	4	now	now	ADV
ejpam-5226	428	5	,	,	PUNCT
ejpam-5226	428	6	(	(	PUNCT
ejpam-5226	428	7	ĥ1	ĥ1	PROPN
ejpam-5226	428	8	∨	∨	NUM
ejpam-5226	428	9	ĥ2	ĥ2	NOUN
ejpam-5226	428	10	)	)	PUNCT
ejpam-5226	428	11	∧	∧	PROPN
ejpam-5226	428	12	(	(	PUNCT
ejpam-5226	428	13	h1	h1	PROPN
ejpam-5226	428	14	∨	∨	NUM
ejpam-5226	428	15	h2	h2	NOUN
ejpam-5226	428	16	)	)	PUNCT
ejpam-5226	428	17	=	=	PUNCT
ejpam-5226	429	1	[	[	X
ejpam-5226	429	2	ĥ1	ĥ1	X
ejpam-5226	429	3	∨	∨	NUM
ejpam-5226	429	4	ĥ2	ĥ2	NOUN
ejpam-5226	429	5	)	)	PUNCT
ejpam-5226	429	6	∧	∧	PROPN
ejpam-5226	429	7	h1	h1	PROPN
ejpam-5226	429	8	]	]	PUNCT
ejpam-5226	429	9	∨	∨	NUM
ejpam-5226	429	10	[	[	X
ejpam-5226	429	11	ĥ1	ĥ1	PROPN
ejpam-5226	429	12	∨	∨	NUM
ejpam-5226	429	13	ĥ2	ĥ2	NOUN
ejpam-5226	429	14	)	)	PUNCT
ejpam-5226	429	15	∧	∧	PROPN
ejpam-5226	429	16	h2	h2	NOUN
ejpam-5226	429	17	]	]	PUNCT
ejpam-5226	429	18	=	=	PUNCT
ejpam-5226	430	1	[	[	X
ejpam-5226	430	2	(	(	PUNCT
ejpam-5226	430	3	ĥ1	ĥ1	PROPN
ejpam-5226	430	4	∧	∧	PROPN
ejpam-5226	430	5	h1	h1	PROPN
ejpam-5226	430	6	)	)	PUNCT
ejpam-5226	430	7	∨	∨	NOUN
ejpam-5226	430	8	(	(	PUNCT
ejpam-5226	430	9	ĥ2	ĥ2	NOUN
ejpam-5226	430	10	∧	∧	PROPN
ejpam-5226	430	11	h1	h1	PROPN
ejpam-5226	430	12	)	)	PUNCT
ejpam-5226	430	13	]	]	PUNCT
ejpam-5226	431	1	∨	∨	NUM
ejpam-5226	431	2	[	[	X
ejpam-5226	431	3	(	(	PUNCT
ejpam-5226	431	4	ĥ1	ĥ1	PROPN
ejpam-5226	431	5	∧	∧	PROPN
ejpam-5226	431	6	h2	h2	NOUN
ejpam-5226	431	7	)	)	PUNCT
ejpam-5226	431	8	∨	∨	NUM
ejpam-5226	431	9	(	(	PUNCT
ejpam-5226	431	10	ĥ2	ĥ2	NOUN
ejpam-5226	431	11	∧	∧	PROPN
ejpam-5226	431	12	h2	h2	NOUN
ejpam-5226	431	13	)	)	PUNCT
ejpam-5226	431	14	]	]	PUNCT
ejpam-5226	432	1	=	=	PUNCT
ejpam-5226	433	1	[	[	X
ejpam-5226	433	2	h1	h1	X
ejpam-5226	433	3	∨	∨	NUM
ejpam-5226	433	4	(	(	PUNCT
ejpam-5226	433	5	ĥ2	ĥ2	NOUN
ejpam-5226	433	6	∧	∧	PROPN
ejpam-5226	433	7	h1	h1	PROPN
ejpam-5226	433	8	)	)	PUNCT
ejpam-5226	433	9	]	]	PUNCT
ejpam-5226	434	1	∨	∨	NUM
ejpam-5226	434	2	[	[	X
ejpam-5226	434	3	(	(	PUNCT
ejpam-5226	434	4	ĥ1	ĥ1	PROPN
ejpam-5226	434	5	∧	∧	PROPN
ejpam-5226	434	6	h2	h2	NOUN
ejpam-5226	434	7	)	)	PUNCT
ejpam-5226	434	8	∨	∨	NUM
ejpam-5226	434	9	h2	h2	NOUN
ejpam-5226	434	10	]	]	X
ejpam-5226	434	11	=	=	PUNCT
ejpam-5226	435	1	[	[	X
ejpam-5226	435	2	(	(	PUNCT
ejpam-5226	435	3	h1	h1	PROPN
ejpam-5226	435	4	∨	∨	NUM
ejpam-5226	435	5	(	(	PUNCT
ejpam-5226	435	6	ĥ2	ĥ2	NOUN
ejpam-5226	435	7	∧	∧	PROPN
ejpam-5226	435	8	h1	h1	PROPN
ejpam-5226	435	9	)	)	PUNCT
ejpam-5226	435	10	]	]	PUNCT
ejpam-5226	435	11	∨	∨	NUM
ejpam-5226	435	12	h2	h2	NOUN
ejpam-5226	435	13	=	=	PUNCT
ejpam-5226	436	1	[	[	X
ejpam-5226	436	2	(	(	PUNCT
ejpam-5226	436	3	h1	h1	PROPN
ejpam-5226	436	4	∨	∨	NUM
ejpam-5226	436	5	ĥ2	ĥ2	NOUN
ejpam-5226	436	6	)	)	PUNCT
ejpam-5226	436	7	∧	∧	PROPN
ejpam-5226	436	8	h1	h1	PROPN
ejpam-5226	436	9	)	)	PUNCT
ejpam-5226	436	10	]	]	PUNCT
ejpam-5226	436	11	∨	∨	NUM
ejpam-5226	436	12	h2	h2	NOUN
ejpam-5226	436	13	=	=	PUNCT
ejpam-5226	437	1	[	[	X
ejpam-5226	437	2	(	(	PUNCT
ejpam-5226	437	3	ĥ2	ĥ2	NOUN
ejpam-5226	437	4	∨	∨	NUM
ejpam-5226	437	5	h1	h1	NOUN
ejpam-5226	437	6	)	)	PUNCT
ejpam-5226	437	7	∧	∧	PROPN
ejpam-5226	437	8	h1	h1	PROPN
ejpam-5226	437	9	]	]	PUNCT
ejpam-5226	437	10	∨	∨	NUM
ejpam-5226	437	11	h2	h2	NOUN
ejpam-5226	437	12	=	=	PROPN
ejpam-5226	437	13	h1	h1	PROPN
ejpam-5226	437	14	∨	∨	NUM
ejpam-5226	437	15	h2	h2	NOUN
ejpam-5226	437	16	,	,	PUNCT
ejpam-5226	437	17	(	(	PUNCT
ejpam-5226	437	18	h1	h1	PROPN
ejpam-5226	437	19	∨	∨	NUM
ejpam-5226	437	20	h2	h2	NOUN
ejpam-5226	437	21	)	)	PUNCT
ejpam-5226	438	1	∧	∧	NOUN
ejpam-5226	438	2	(	(	PUNCT
ejpam-5226	438	3	ĥ1	ĥ1	PROPN
ejpam-5226	438	4	∨	∨	NUM
ejpam-5226	438	5	ĥ2	ĥ2	NOUN
ejpam-5226	438	6	)	)	PUNCT
ejpam-5226	438	7	=	=	PUNCT
ejpam-5226	439	1	[	[	X
ejpam-5226	439	2	(	(	PUNCT
ejpam-5226	439	3	h1	h1	PROPN
ejpam-5226	439	4	∨	∨	NUM
ejpam-5226	439	5	h2	h2	NOUN
ejpam-5226	439	6	)	)	PUNCT
ejpam-5226	439	7	∧	∧	PROPN
ejpam-5226	439	8	ĥ1	ĥ1	PROPN
ejpam-5226	439	9	]	]	PUNCT
ejpam-5226	439	10	∨	∨	X
ejpam-5226	439	11	[	[	X
ejpam-5226	439	12	(	(	PUNCT
ejpam-5226	439	13	h1	h1	PROPN
ejpam-5226	439	14	∨	∨	NUM
ejpam-5226	439	15	h2	h2	NOUN
ejpam-5226	439	16	)	)	PUNCT
ejpam-5226	439	17	∧	∧	NOUN
ejpam-5226	439	18	ĥ2	ĥ2	NOUN
ejpam-5226	439	19	]	]	PUNCT
ejpam-5226	439	20	=	=	PUNCT
ejpam-5226	440	1	[	[	X
ejpam-5226	440	2	(	(	PUNCT
ejpam-5226	440	3	h1	h1	PROPN
ejpam-5226	440	4	∧	∧	PROPN
ejpam-5226	440	5	ĥ1	ĥ1	PROPN
ejpam-5226	440	6	)	)	PUNCT
ejpam-5226	440	7	∨	∨	PROPN
ejpam-5226	440	8	(	(	PUNCT
ejpam-5226	440	9	h2	h2	NOUN
ejpam-5226	440	10	∧	∧	PROPN
ejpam-5226	440	11	ĥ1	ĥ1	PROPN
ejpam-5226	440	12	)	)	PUNCT
ejpam-5226	440	13	]	]	PUNCT
ejpam-5226	441	1	∨	∨	NUM
ejpam-5226	441	2	[	[	X
ejpam-5226	441	3	(	(	PUNCT
ejpam-5226	441	4	h1	h1	PROPN
ejpam-5226	441	5	∧	∧	PROPN
ejpam-5226	441	6	ĥ2	ĥ2	NOUN
ejpam-5226	441	7	)	)	PUNCT
ejpam-5226	441	8	∨	∨	PROPN
ejpam-5226	441	9	(	(	PUNCT
ejpam-5226	441	10	h2	h2	NOUN
ejpam-5226	441	11	∧	∧	PROPN
ejpam-5226	441	12	ĥ2	ĥ2	NOUN
ejpam-5226	441	13	)	)	PUNCT
ejpam-5226	441	14	]	]	PUNCT
ejpam-5226	442	1	=	=	PUNCT
ejpam-5226	443	1	[	[	X
ejpam-5226	443	2	ĥ1	ĥ1	PROPN
ejpam-5226	443	3	∨	∨	ADV
ejpam-5226	443	4	(	(	PUNCT
ejpam-5226	443	5	h2	h2	NOUN
ejpam-5226	443	6	∧	∧	PROPN
ejpam-5226	443	7	ĥ1	ĥ1	PROPN
ejpam-5226	443	8	)	)	PUNCT
ejpam-5226	443	9	]	]	PUNCT
ejpam-5226	444	1	∨	∨	NUM
ejpam-5226	444	2	[	[	X
ejpam-5226	444	3	(	(	PUNCT
ejpam-5226	444	4	h1	h1	PROPN
ejpam-5226	444	5	∧	∧	PROPN
ejpam-5226	444	6	ĥ2	ĥ2	NOUN
ejpam-5226	444	7	)	)	PUNCT
ejpam-5226	444	8	∨	∨	NUM
ejpam-5226	444	9	ĥ2	ĥ2	NOUN
ejpam-5226	444	10	]	]	PUNCT
ejpam-5226	444	11	=	=	PUNCT
ejpam-5226	445	1	[	[	X
ejpam-5226	445	2	(	(	PUNCT
ejpam-5226	445	3	ĥ1	ĥ1	PROPN
ejpam-5226	445	4	∨	∨	NUM
ejpam-5226	445	5	h2	h2	NOUN
ejpam-5226	445	6	)	)	PUNCT
ejpam-5226	445	7	∧	∧	PROPN
ejpam-5226	445	8	ĥ1	ĥ1	PROPN
ejpam-5226	445	9	]	]	PUNCT
ejpam-5226	445	10	∨	∨	NUM
ejpam-5226	445	11	ĥ2	ĥ2	NOUN
ejpam-5226	445	12	=	=	PUNCT
ejpam-5226	446	1	[	[	X
ejpam-5226	446	2	(	(	PUNCT
ejpam-5226	446	3	h2	h2	PROPN
ejpam-5226	446	4	∨	∨	NUM
ejpam-5226	446	5	ĥ1	ĥ1	PROPN
ejpam-5226	446	6	)	)	PUNCT
ejpam-5226	446	7	∧	∧	PROPN
ejpam-5226	446	8	ĥ1	ĥ1	PROPN
ejpam-5226	446	9	]	]	PUNCT
ejpam-5226	446	10	∨	∨	NUM
ejpam-5226	446	11	ĥ2	ĥ2	NOUN
ejpam-5226	446	12	=	=	SYM
ejpam-5226	446	13	ĥ1	ĥ1	X
ejpam-5226	446	14	∨	∨	NUM
ejpam-5226	446	15	ĥ2	ĥ2	NOUN
ejpam-5226	446	16	.	.	PUNCT
ejpam-5226	447	1	therefore	therefore	ADV
ejpam-5226	447	2	,	,	PUNCT
ejpam-5226	447	3	̂(h1	̂(h1	PROPN
ejpam-5226	447	4	∨	∨	NUM
ejpam-5226	447	5	h2	h2	NOUN
ejpam-5226	447	6	)	)	PUNCT
ejpam-5226	447	7	=	=	PRON
ejpam-5226	448	1	ĥ1	ĥ1	PROPN
ejpam-5226	448	2	∨	∨	NUM
ejpam-5226	448	3	ĥ2	ĥ2	NOUN
ejpam-5226	448	4	.	.	PUNCT
ejpam-5226	449	1	(	(	PUNCT
ejpam-5226	449	2	ii	ii	NOUN
ejpam-5226	449	3	)	)	PUNCT
ejpam-5226	449	4	now	now	ADV
ejpam-5226	449	5	,	,	PUNCT
ejpam-5226	449	6	(	(	PUNCT
ejpam-5226	449	7	ĥ1	ĥ1	AUX
ejpam-5226	449	8	∧	∧	NOUN
ejpam-5226	449	9	ĥ2	ĥ2	NOUN
ejpam-5226	449	10	)	)	PUNCT
ejpam-5226	449	11	∧	∧	PROPN
ejpam-5226	449	12	h1	h1	PROPN
ejpam-5226	449	13	∧	∧	PROPN
ejpam-5226	449	14	h2	h2	NOUN
ejpam-5226	449	15	=	=	PRON
ejpam-5226	449	16	ĥ1	ĥ1	PROPN
ejpam-5226	449	17	∧	∧	NOUN
ejpam-5226	449	18	h1	h1	PROPN
ejpam-5226	449	19	∧	∧	PROPN
ejpam-5226	449	20	ĥ2	ĥ2	ADJ
ejpam-5226	449	21	∧	∧	PROPN
ejpam-5226	449	22	h2	h2	NOUN
ejpam-5226	449	23	=	=	SYM
ejpam-5226	449	24	h1	h1	PROPN
ejpam-5226	449	25	∧	∧	PROPN
ejpam-5226	449	26	h2	h2	NOUN
ejpam-5226	449	27	,	,	PUNCT
ejpam-5226	449	28	a.	a.	NOUN
ejpam-5226	449	29	iampan	iampan	NOUN
ejpam-5226	449	30	et	et	PROPN
ejpam-5226	449	31	al	al	PROPN
ejpam-5226	449	32	.	.	PUNCT
ejpam-5226	449	33	/	/	SYM
ejpam-5226	449	34	eur	eur	PROPN
ejpam-5226	449	35	.	.	PUNCT
ejpam-5226	450	1	j.	j.	PROPN
ejpam-5226	450	2	pure	pure	PROPN
ejpam-5226	450	3	appl	appl	PROPN
ejpam-5226	450	4	.	.	PROPN
ejpam-5226	450	5	math	math	PROPN
ejpam-5226	450	6	,	,	PUNCT
ejpam-5226	450	7	17	17	NUM
ejpam-5226	450	8	(	(	PUNCT
ejpam-5226	450	9	3	3	NUM
ejpam-5226	450	10	)	)	PUNCT
ejpam-5226	450	11	(	(	PUNCT
ejpam-5226	450	12	2024	2024	NUM
ejpam-5226	450	13	)	)	PUNCT
ejpam-5226	450	14	,	,	PUNCT
ejpam-5226	450	15	1691	1691	NUM
ejpam-5226	450	16	-	-	SYM
ejpam-5226	450	17	1704	1704	NUM
ejpam-5226	450	18	1703	1703	NUM
ejpam-5226	450	19	h1	h1	PROPN
ejpam-5226	450	20	∧	∧	PROPN
ejpam-5226	450	21	h2	h2	NOUN
ejpam-5226	450	22	∧	∧	PROPN
ejpam-5226	450	23	(	(	PUNCT
ejpam-5226	450	24	ĥ1	ĥ1	PROPN
ejpam-5226	450	25	∧	∧	NOUN
ejpam-5226	450	26	ĥ2	ĥ2	NOUN
ejpam-5226	450	27	)	)	PUNCT
ejpam-5226	450	28	=	=	PUNCT
ejpam-5226	451	1	h1	h1	VERB
ejpam-5226	451	2	∧	∧	PROPN
ejpam-5226	451	3	ĥ1	ĥ1	NOUN
ejpam-5226	451	4	∧	∧	PROPN
ejpam-5226	451	5	h2	h2	NOUN
ejpam-5226	451	6	∧	∧	PROPN
ejpam-5226	451	7	ĥ2	ĥ2	NOUN
ejpam-5226	452	1	=	=	PRON
ejpam-5226	452	2	ĥ1	ĥ1	VERB
ejpam-5226	452	3	∧	∧	NOUN
ejpam-5226	452	4	ĥ2	ĥ2	NOUN
ejpam-5226	452	5	.	.	PUNCT
ejpam-5226	453	1	therefore	therefore	ADV
ejpam-5226	453	2	,	,	PUNCT
ejpam-5226	453	3	̂(h1	̂(h1	PROPN
ejpam-5226	453	4	∧	∧	PROPN
ejpam-5226	453	5	h2	h2	NOUN
ejpam-5226	453	6	)	)	PUNCT
ejpam-5226	454	1	=	=	PRON
ejpam-5226	455	1	ĥ1	ĥ1	VERB
ejpam-5226	455	2	∧	∧	NOUN
ejpam-5226	455	3	ĥ2	ĥ2	NOUN
ejpam-5226	455	4	.	.	PUNCT
ejpam-5226	456	1	(	(	PUNCT
ejpam-5226	456	2	iii	iii	X
ejpam-5226	456	3	)	)	PUNCT
ejpam-5226	456	4	let	let	VERB
ejpam-5226	456	5	h	h	PROPN
ejpam-5226	456	6	∈	∈	PROPN
ejpam-5226	456	7	s.	s.	PROPN
ejpam-5226	457	1	then	then	ADV
ejpam-5226	457	2	h	h	PROPN
ejpam-5226	457	3	∈	∈	PROPN
ejpam-5226	457	4	hs	hs	INTJ
ejpam-5226	457	5	.	.	PUNCT
ejpam-5226	458	1	by	by	ADP
ejpam-5226	458	2	theorem	theorem	ADJ
ejpam-5226	458	3	6(iii	6(iii	NOUN
ejpam-5226	458	4	)	)	PUNCT
ejpam-5226	458	5	,	,	PUNCT
ejpam-5226	458	6	there	there	PRON
ejpam-5226	458	7	exists	exist	VERB
ejpam-5226	458	8	a	a	DET
ejpam-5226	458	9	unique	unique	ADJ
ejpam-5226	458	10	ĥ	ĥ	X
ejpam-5226	458	11	∈	∈	PROPN
ejpam-5226	458	12	ŝ	ŝ	VERB
ejpam-5226	458	13	such	such	ADJ
ejpam-5226	458	14	that	that	SCONJ
ejpam-5226	458	15	h∧	h∧	PROPN
ejpam-5226	458	16	ĥ	ĥ	X
ejpam-5226	458	17	=	=	PRON
ejpam-5226	458	18	ĥ	ĥ	X
ejpam-5226	458	19	and	and	CCONJ
ejpam-5226	459	1	ĥ∧	ĥ∧	NOUN
ejpam-5226	459	2	h	h	NOUN
ejpam-5226	460	1	=	=	PUNCT
ejpam-5226	460	2	h.	h.	PROPN
ejpam-5226	460	3	since	since	SCONJ
ejpam-5226	460	4	h	h	PROPN
ejpam-5226	460	5	,	,	PUNCT
ejpam-5226	460	6	ĥ	ĥ	X
ejpam-5226	460	7	∈	∈	PROPN
ejpam-5226	460	8	ŝ	ŝ	X
ejpam-5226	460	9	and	and	CCONJ
ejpam-5226	460	10	ŝ	ŝ	NOUN
ejpam-5226	460	11	is	be	AUX
ejpam-5226	460	12	compatible	compatible	ADJ
ejpam-5226	460	13	,	,	PUNCT
ejpam-5226	460	14	h	h	NOUN
ejpam-5226	460	15	=	=	NOUN
ejpam-5226	460	16	ĥ.	ĥ.	NOUN
ejpam-5226	460	17	the	the	DET
ejpam-5226	460	18	converse	converse	NOUN
ejpam-5226	460	19	is	be	AUX
ejpam-5226	460	20	trivial	trivial	ADJ
ejpam-5226	460	21	.	.	PUNCT
ejpam-5226	461	1	(	(	PUNCT
ejpam-5226	461	2	iv	iv	X
ejpam-5226	461	3	)	)	PUNCT
ejpam-5226	461	4	it	it	PRON
ejpam-5226	461	5	’s	’	VERB
ejpam-5226	461	6	clear	clear	ADJ
ejpam-5226	461	7	from	from	ADP
ejpam-5226	461	8	(	(	PUNCT
ejpam-5226	461	9	iii	iii	NOUN
ejpam-5226	461	10	)	)	PUNCT
ejpam-5226	461	11	.	.	PUNCT
ejpam-5226	462	1	theorem	theorem	ADJ
ejpam-5226	462	2	8	8	NUM
ejpam-5226	462	3	.	.	PUNCT
ejpam-5226	463	1	let	let	VERB
ejpam-5226	463	2	s	s	PRON
ejpam-5226	463	3	be	be	AUX
ejpam-5226	463	4	a	a	DET
ejpam-5226	463	5	compatible	compatible	ADJ
ejpam-5226	463	6	subset	subset	NOUN
ejpam-5226	463	7	of	of	ADP
ejpam-5226	463	8	l	l	PROPN
ejpam-5226	463	9	and	and	CCONJ
ejpam-5226	464	1	hs	hs	PROPN
ejpam-5226	464	2	=	=	PROPN
ejpam-5226	464	3	l.	l.	PROPN
ejpam-5226	465	1	then	then	ADV
ejpam-5226	465	2	the	the	DET
ejpam-5226	465	3	following	follow	VERB
ejpam-5226	465	4	are	be	AUX
ejpam-5226	465	5	equivalent	equivalent	ADJ
ejpam-5226	465	6	:	:	PUNCT
ejpam-5226	465	7	(	(	PUNCT
ejpam-5226	465	8	i	i	NOUN
ejpam-5226	465	9	)	)	PUNCT
ejpam-5226	465	10	hs	hs	PROPN
ejpam-5226	465	11	=	=	SYM
ejpam-5226	465	12	l	l	PROPN
ejpam-5226	465	13	⇒	⇒	NOUN
ejpam-5226	465	14	ŝ	ŝ	X
ejpam-5226	465	15	has	have	VERB
ejpam-5226	465	16	large	large	ADJ
ejpam-5226	465	17	element	element	NOUN
ejpam-5226	465	18	,	,	PUNCT
ejpam-5226	465	19	(	(	PUNCT
ejpam-5226	465	20	ii	ii	NOUN
ejpam-5226	465	21	)	)	PUNCT
ejpam-5226	465	22	l	l	NOUN
ejpam-5226	465	23	has	have	VERB
ejpam-5226	465	24	a	a	DET
ejpam-5226	465	25	maximal	maximal	ADJ
ejpam-5226	465	26	element	element	NOUN
ejpam-5226	465	27	.	.	PUNCT
ejpam-5226	466	1	proof	proof	NOUN
ejpam-5226	466	2	.	.	PUNCT
ejpam-5226	467	1	(	(	PUNCT
ejpam-5226	467	2	i	i	NOUN
ejpam-5226	467	3	)	)	PUNCT
ejpam-5226	467	4	⇒	⇒	PROPN
ejpam-5226	467	5	(	(	PUNCT
ejpam-5226	467	6	ii	ii	NOUN
ejpam-5226	467	7	)	)	PUNCT
ejpam-5226	467	8	suppose	suppose	VERB
ejpam-5226	467	9	that	that	SCONJ
ejpam-5226	467	10	hs	hs	PROPN
ejpam-5226	467	11	=	=	SYM
ejpam-5226	467	12	l	l	PROPN
ejpam-5226	467	13	implies	imply	VERB
ejpam-5226	467	14	ŝ	ŝ	X
ejpam-5226	467	15	has	have	VERB
ejpam-5226	467	16	the	the	DET
ejpam-5226	467	17	largest	large	ADJ
ejpam-5226	467	18	element	element	NOUN
ejpam-5226	467	19	.	.	PUNCT
ejpam-5226	468	1	let	let	VERB
ejpam-5226	468	2	l	l	NOUN
ejpam-5226	468	3	be	be	AUX
ejpam-5226	468	4	the	the	DET
ejpam-5226	468	5	largest	large	ADJ
ejpam-5226	468	6	element	element	NOUN
ejpam-5226	468	7	in	in	ADP
ejpam-5226	468	8	ŝ.	ŝ.	NOUN
ejpam-5226	468	9	let	let	VERB
ejpam-5226	468	10	x	x	X
ejpam-5226	468	11	∈	∈	NOUN
ejpam-5226	468	12	l	l	NOUN
ejpam-5226	468	13	=	=	SYM
ejpam-5226	468	14	hs	hs	PROPN
ejpam-5226	468	15	.	.	PUNCT
ejpam-5226	469	1	by	by	ADP
ejpam-5226	469	2	theorem	theorem	PROPN
ejpam-5226	469	3	6(ii	6(ii	PROPN
ejpam-5226	469	4	)	)	PUNCT
ejpam-5226	469	5	,	,	PUNCT
ejpam-5226	469	6	there	there	PRON
ejpam-5226	469	7	exists	exist	VERB
ejpam-5226	469	8	x̂	x̂	PUNCT
ejpam-5226	470	1	∈	∈	PROPN
ejpam-5226	470	2	ŝ	ŝ	VERB
ejpam-5226	470	3	such	such	ADJ
ejpam-5226	470	4	that	that	PRON
ejpam-5226	470	5	x̂	x̂	PUNCT
ejpam-5226	471	1	∧	∧	NOUN
ejpam-5226	471	2	x	x	X
ejpam-5226	471	3	=	=	PUNCT
ejpam-5226	471	4	x	x	X
ejpam-5226	471	5	and	and	CCONJ
ejpam-5226	471	6	x	x	ADJ
ejpam-5226	471	7	∧	∧	PROPN
ejpam-5226	471	8	x̂	x̂	PUNCT
ejpam-5226	471	9	=	=	PUNCT
ejpam-5226	472	1	x.	x.	NOUN
ejpam-5226	472	2	now	now	ADV
ejpam-5226	472	3	,	,	PUNCT
ejpam-5226	472	4	l	l	PROPN
ejpam-5226	472	5	∧	∧	NOUN
ejpam-5226	472	6	x	x	X
ejpam-5226	472	7	=	=	PUNCT
ejpam-5226	472	8	l	l	NOUN
ejpam-5226	472	9	∧	∧	PROPN
ejpam-5226	472	10	(	(	PUNCT
ejpam-5226	472	11	x̂	x̂	NUM
ejpam-5226	472	12	∧	∧	PROPN
ejpam-5226	472	13	x	x	NOUN
ejpam-5226	472	14	)	)	PUNCT
ejpam-5226	472	15	=	=	SYM
ejpam-5226	472	16	(	(	PUNCT
ejpam-5226	472	17	l	l	NOUN
ejpam-5226	472	18	∧	∧	NOUN
ejpam-5226	472	19	x̂	x̂	NUM
ejpam-5226	472	20	)	)	PUNCT
ejpam-5226	473	1	∧	∧	NOUN
ejpam-5226	473	2	x	x	X
ejpam-5226	473	3	=	=	SYM
ejpam-5226	473	4	x̂	x̂	NUM
ejpam-5226	473	5	∧	∧	NOUN
ejpam-5226	473	6	x	x	X
ejpam-5226	473	7	=	=	PUNCT
ejpam-5226	473	8	x.	x.	NOUN
ejpam-5226	473	9	therefore	therefore	ADV
ejpam-5226	473	10	,	,	PUNCT
ejpam-5226	473	11	l	l	NOUN
ejpam-5226	473	12	has	have	VERB
ejpam-5226	473	13	a	a	DET
ejpam-5226	473	14	maximal	maximal	ADJ
ejpam-5226	473	15	element	element	NOUN
ejpam-5226	473	16	of	of	ADP
ejpam-5226	473	17	l.	l.	PROPN
ejpam-5226	473	18	(	(	PUNCT
ejpam-5226	473	19	ii	ii	PROPN
ejpam-5226	473	20	)	)	PUNCT
ejpam-5226	473	21	⇒	⇒	NOUN
ejpam-5226	473	22	(	(	PUNCT
ejpam-5226	473	23	i	i	NOUN
ejpam-5226	473	24	)	)	PUNCT
ejpam-5226	473	25	suppose	suppose	VERB
ejpam-5226	473	26	that	that	SCONJ
ejpam-5226	473	27	l	l	NOUN
ejpam-5226	473	28	has	have	VERB
ejpam-5226	473	29	a	a	DET
ejpam-5226	473	30	maximal	maximal	ADJ
ejpam-5226	473	31	element	element	NOUN
ejpam-5226	473	32	,	,	PUNCT
ejpam-5226	473	33	say	say	VERB
ejpam-5226	473	34	m.	m.	NOUN
ejpam-5226	473	35	if	if	SCONJ
ejpam-5226	473	36	hs	hs	PROPN
ejpam-5226	473	37	=	=	SYM
ejpam-5226	473	38	l	l	PROPN
ejpam-5226	473	39	,	,	PUNCT
ejpam-5226	473	40	for	for	ADP
ejpam-5226	473	41	some	some	DET
ejpam-5226	473	42	s	s	ADP
ejpam-5226	473	43	⊆	⊆	NUM
ejpam-5226	473	44	l	l	NOUN
ejpam-5226	473	45	and	and	CCONJ
ejpam-5226	473	46	s	s	PROPN
ejpam-5226	473	47	̸=	̸=	PROPN
ejpam-5226	473	48	∅	∅	NOUN
ejpam-5226	473	49	,	,	PUNCT
ejpam-5226	473	50	then	then	ADV
ejpam-5226	473	51	m	m	PROPN
ejpam-5226	473	52	∈	∈	PROPN
ejpam-5226	473	53	hs	hs	INTJ
ejpam-5226	473	54	.	.	PUNCT
ejpam-5226	474	1	by	by	ADP
ejpam-5226	474	2	theorem	theorem	PROPN
ejpam-5226	474	3	6(ii	6(ii	PROPN
ejpam-5226	474	4	)	)	PUNCT
ejpam-5226	474	5	,	,	PUNCT
ejpam-5226	474	6	there	there	PRON
ejpam-5226	474	7	exists	exist	VERB
ejpam-5226	474	8	m̂	m̂	NOUN
ejpam-5226	474	9	∈	∈	PROPN
ejpam-5226	474	10	ŝ	ŝ	VERB
ejpam-5226	474	11	such	such	ADJ
ejpam-5226	474	12	that	that	DET
ejpam-5226	474	13	m̂	m̂	PROPN
ejpam-5226	475	1	∧	∧	PROPN
ejpam-5226	475	2	m	m	PROPN
ejpam-5226	475	3	=	=	VERB
ejpam-5226	475	4	m	m	PROPN
ejpam-5226	475	5	and	and	CCONJ
ejpam-5226	475	6	m	m	PROPN
ejpam-5226	475	7	∧	∧	PROPN
ejpam-5226	475	8	m̂	m̂	NOUN
ejpam-5226	475	9	=	=	PUNCT
ejpam-5226	475	10	m̂.	m̂.	VERB
ejpam-5226	475	11	now	now	ADV
ejpam-5226	475	12	,	,	PUNCT
ejpam-5226	475	13	for	for	ADP
ejpam-5226	475	14	any	any	DET
ejpam-5226	475	15	ŝ	ŝ	X
ejpam-5226	475	16	∈	∈	PROPN
ejpam-5226	475	17	ŝ	ŝ	NOUN
ejpam-5226	475	18	,	,	PUNCT
ejpam-5226	475	19	ŝ	ŝ	VERB
ejpam-5226	475	20	∧	∧	PROPN
ejpam-5226	475	21	m̂	m̂	PROPN
ejpam-5226	476	1	=	=	SYM
ejpam-5226	476	2	m̂	m̂	PROPN
ejpam-5226	476	3	∧	∧	PROPN
ejpam-5226	476	4	ŝ	ŝ	X
ejpam-5226	476	5	(	(	PUNCT
ejpam-5226	476	6	since	since	SCONJ
ejpam-5226	476	7	ŝ	ŝ	NOUN
ejpam-5226	476	8	is	be	AUX
ejpam-5226	476	9	compatible	compatible	ADJ
ejpam-5226	476	10	)	)	PUNCT
ejpam-5226	477	1	=	=	SYM
ejpam-5226	478	1	̂(m	̂(m	NOUN
ejpam-5226	478	2	∧	∧	PROPN
ejpam-5226	478	3	s	s	PART
ejpam-5226	478	4	)	)	PUNCT
ejpam-5226	478	5	=	=	VERB
ejpam-5226	478	6	ŝ.	ŝ.	NOUN
ejpam-5226	478	7	therefore	therefore	ADV
ejpam-5226	478	8	,	,	PUNCT
ejpam-5226	478	9	ŝ	ŝ	X
ejpam-5226	478	10	≤	≤	NUM
ejpam-5226	478	11	m̂.	m̂.	VERB
ejpam-5226	478	12	hence	hence	ADV
ejpam-5226	478	13	,	,	PUNCT
ejpam-5226	478	14	ŝ	ŝ	X
ejpam-5226	478	15	has	have	VERB
ejpam-5226	478	16	the	the	DET
ejpam-5226	478	17	largest	large	ADJ
ejpam-5226	478	18	element	element	NOUN
ejpam-5226	478	19	m̂.	m̂.	NOUN
ejpam-5226	478	20	4	4	NUM
ejpam-5226	478	21	.	.	PUNCT
ejpam-5226	479	1	conclusions	conclusion	NOUN
ejpam-5226	479	2	and	and	CCONJ
ejpam-5226	479	3	future	future	ADJ
ejpam-5226	479	4	work	work	NOUN
ejpam-5226	479	5	we	we	PRON
ejpam-5226	479	6	identify	identify	VERB
ejpam-5226	479	7	a	a	DET
ejpam-5226	479	8	distributive	distributive	ADJ
ejpam-5226	479	9	lattice	lattice	NOUN
ejpam-5226	479	10	structure	structure	NOUN
ejpam-5226	479	11	in	in	ADP
ejpam-5226	479	12	an	an	DET
ejpam-5226	479	13	almost	almost	ADV
ejpam-5226	479	14	distributive	distributive	ADJ
ejpam-5226	479	15	lattice	lattice	NOUN
ejpam-5226	479	16	that	that	PRON
ejpam-5226	479	17	is	be	AUX
ejpam-5226	479	18	not	not	PART
ejpam-5226	479	19	induced	induce	VERB
ejpam-5226	479	20	with	with	ADP
ejpam-5226	479	21	respect	respect	NOUN
ejpam-5226	479	22	to	to	ADP
ejpam-5226	479	23	the	the	DET
ejpam-5226	479	24	operations	operation	NOUN
ejpam-5226	479	25	in	in	ADP
ejpam-5226	479	26	the	the	DET
ejpam-5226	479	27	almost	almost	ADV
ejpam-5226	479	28	distributive	distributive	ADJ
ejpam-5226	479	29	lattice	lattice	NOUN
ejpam-5226	479	30	.	.	PUNCT
ejpam-5226	480	1	it	it	PRON
ejpam-5226	480	2	helps	help	VERB
ejpam-5226	480	3	us	we	PRON
ejpam-5226	480	4	to	to	PART
ejpam-5226	480	5	discuss	discuss	VERB
ejpam-5226	480	6	(	(	PUNCT
ejpam-5226	480	7	extend	extend	VERB
ejpam-5226	480	8	)	)	PUNCT
ejpam-5226	480	9	several	several	ADJ
ejpam-5226	480	10	properties	property	NOUN
ejpam-5226	480	11	of	of	ADP
ejpam-5226	480	12	a	a	DET
ejpam-5226	480	13	distributive	distributive	ADJ
ejpam-5226	480	14	lattice	lattice	NOUN
ejpam-5226	480	15	via	via	ADP
ejpam-5226	480	16	hierarchy	hierarchy	NOUN
ejpam-5226	480	17	elements	element	NOUN
ejpam-5226	480	18	in	in	ADP
ejpam-5226	480	19	an	an	DET
ejpam-5226	480	20	almost	almost	ADV
ejpam-5226	480	21	distributive	distributive	ADJ
ejpam-5226	480	22	lattice	lattice	NOUN
ejpam-5226	480	23	.	.	PUNCT
ejpam-5226	481	1	acknowledgements	acknowledgement	NOUN
ejpam-5226	481	2	this	this	DET
ejpam-5226	481	3	research	research	NOUN
ejpam-5226	481	4	was	be	AUX
ejpam-5226	481	5	supported	support	VERB
ejpam-5226	481	6	by	by	ADP
ejpam-5226	481	7	the	the	DET
ejpam-5226	481	8	university	university	NOUN
ejpam-5226	481	9	of	of	ADP
ejpam-5226	481	10	phayao	phayao	NOUN
ejpam-5226	481	11	and	and	CCONJ
ejpam-5226	481	12	the	the	DET
ejpam-5226	481	13	thailand	thailand	PROPN
ejpam-5226	481	14	science	science	PROPN
ejpam-5226	481	15	research	research	PROPN
ejpam-5226	481	16	and	and	CCONJ
ejpam-5226	481	17	innovation	innovation	NOUN
ejpam-5226	481	18	fund	fund	NOUN
ejpam-5226	481	19	(	(	PUNCT
ejpam-5226	481	20	fundamental	fundamental	ADJ
ejpam-5226	481	21	fund	fund	NOUN
ejpam-5226	481	22	2024	2024	NUM
ejpam-5226	481	23	)	)	PUNCT
ejpam-5226	481	24	.	.	PUNCT
ejpam-5226	482	1	references	reference	NOUN
ejpam-5226	482	2	1704	1704	NUM
ejpam-5226	482	3	references	reference	NOUN
ejpam-5226	482	4	[	[	X
ejpam-5226	482	5	1	1	NUM
ejpam-5226	482	6	]	]	PUNCT
ejpam-5226	482	7	g.	g.	NOUN
ejpam-5226	482	8	birkhoff	birkhoff	PROPN
ejpam-5226	482	9	.	.	PUNCT
ejpam-5226	483	1	lattice	lattice	PROPN
ejpam-5226	483	2	theory	theory	NOUN
ejpam-5226	483	3	.	.	PUNCT
ejpam-5226	484	1	american	american	PROPN
ejpam-5226	484	2	mathematical	mathematical	PROPN
ejpam-5226	484	3	society	society	NOUN
ejpam-5226	484	4	colloquium	colloquium	NOUN
ejpam-5226	484	5	publications	publication	NOUN
ejpam-5226	484	6	xxv	xxv	PROPN
ejpam-5226	484	7	,	,	PUNCT
ejpam-5226	484	8	providence	providence	NOUN
ejpam-5226	484	9	,	,	PUNCT
ejpam-5226	484	10	u.s.a	u.s.a	PROPN
ejpam-5226	484	11	.	.	PROPN
ejpam-5226	484	12	,	,	PUNCT
ejpam-5226	484	13	1967	1967	NUM
ejpam-5226	484	14	.	.	PUNCT
ejpam-5226	485	1	[	[	X
ejpam-5226	485	2	2	2	NUM
ejpam-5226	485	3	]	]	X
ejpam-5226	485	4	r.	r.	PROPN
ejpam-5226	485	5	noorbhasha	noorbhasha	PROPN
ejpam-5226	485	6	,	,	PUNCT
ejpam-5226	485	7	r.	r.	PROPN
ejpam-5226	485	8	bandaru	bandaru	PROPN
ejpam-5226	485	9	,	,	PUNCT
ejpam-5226	485	10	and	and	CCONJ
ejpam-5226	485	11	a.	a.	NOUN
ejpam-5226	485	12	iampan	iampan	PROPN
ejpam-5226	485	13	.	.	PUNCT
ejpam-5226	486	1	σ	σ	NOUN
ejpam-5226	486	2	-	-	PUNCT
ejpam-5226	486	3	prime	prime	ADJ
ejpam-5226	486	4	spectrum	spectrum	NOUN
ejpam-5226	486	5	of	of	ADP
ejpam-5226	486	6	almost	almost	ADV
ejpam-5226	486	7	distributive	distributive	ADJ
ejpam-5226	486	8	lattices	lattice	NOUN
ejpam-5226	486	9	.	.	PUNCT
ejpam-5226	487	1	eur	eur	PROPN
ejpam-5226	487	2	.	.	PUNCT
ejpam-5226	488	1	j.	j.	PROPN
ejpam-5226	488	2	pure	pure	PROPN
ejpam-5226	488	3	appl	appl	PROPN
ejpam-5226	488	4	.	.	PUNCT
ejpam-5226	488	5	math	math	PROPN
ejpam-5226	488	6	.	.	PUNCT
ejpam-5226	488	7	,	,	PUNCT
ejpam-5226	489	1	17(2):1094–1112	17(2):1094–1112	NUM
ejpam-5226	489	2	,	,	PUNCT
ejpam-5226	489	3	2024	2024	NUM
ejpam-5226	489	4	.	.	PUNCT
ejpam-5226	490	1	[	[	X
ejpam-5226	490	2	3	3	X
ejpam-5226	490	3	]	]	X
ejpam-5226	490	4	y.s	y.s	PROPN
ejpam-5226	490	5	.	.	PROPN
ejpam-5226	490	6	pawar	pawar	PROPN
ejpam-5226	490	7	and	and	CCONJ
ejpam-5226	490	8	i.a	i.a	PROPN
ejpam-5226	490	9	.	.	PROPN
ejpam-5226	490	10	shaikh	shaikh	PROPN
ejpam-5226	490	11	.	.	PUNCT
ejpam-5226	491	1	on	on	ADP
ejpam-5226	491	2	prime	prime	ADJ
ejpam-5226	491	3	,	,	PUNCT
ejpam-5226	491	4	minimal	minimal	ADJ
ejpam-5226	491	5	prime	prime	NOUN
ejpam-5226	491	6	and	and	CCONJ
ejpam-5226	491	7	annihilator	annihilator	NOUN
ejpam-5226	491	8	ideals	ideal	NOUN
ejpam-5226	491	9	in	in	ADP
ejpam-5226	491	10	an	an	DET
ejpam-5226	491	11	almost	almost	ADV
ejpam-5226	491	12	distributive	distributive	ADJ
ejpam-5226	491	13	lattice	lattice	NOUN
ejpam-5226	491	14	.	.	PUNCT
ejpam-5226	492	1	eur	eur	PROPN
ejpam-5226	492	2	.	.	PUNCT
ejpam-5226	493	1	j.	j.	PROPN
ejpam-5226	493	2	pure	pure	PROPN
ejpam-5226	493	3	appl	appl	PROPN
ejpam-5226	493	4	.	.	PUNCT
ejpam-5226	493	5	math	math	PROPN
ejpam-5226	493	6	.	.	PUNCT
ejpam-5226	493	7	,	,	PUNCT
ejpam-5226	493	8	6(1):107–118	6(1):107–118	NUM
ejpam-5226	493	9	,	,	PUNCT
ejpam-5226	493	10	2013	2013	NUM
ejpam-5226	493	11	.	.	PUNCT
ejpam-5226	494	1	[	[	X
ejpam-5226	494	2	4	4	X
ejpam-5226	494	3	]	]	X
ejpam-5226	494	4	g.c	g.c	PROPN
ejpam-5226	494	5	.	.	PROPN
ejpam-5226	494	6	rao	rao	PROPN
ejpam-5226	494	7	and	and	CCONJ
ejpam-5226	494	8	s.	s.	PROPN
ejpam-5226	494	9	ravi	ravi	PROPN
ejpam-5226	494	10	kumar	kumar	PROPN
ejpam-5226	494	11	.	.	PROPN
ejpam-5226	494	12	minimal	minimal	ADJ
ejpam-5226	494	13	prime	prime	ADJ
ejpam-5226	494	14	ideals	ideal	NOUN
ejpam-5226	494	15	in	in	ADP
ejpam-5226	494	16	almost	almost	ADV
ejpam-5226	494	17	distributive	distributive	ADJ
ejpam-5226	494	18	lattices	lattice	NOUN
ejpam-5226	494	19	.	.	PUNCT
ejpam-5226	495	1	int	int	NOUN
ejpam-5226	495	2	.	.	PUNCT
ejpam-5226	496	1	j.	j.	PROPN
ejpam-5226	496	2	contemp	contemp	PROPN
ejpam-5226	496	3	.	.	PUNCT
ejpam-5226	497	1	math	math	NOUN
ejpam-5226	497	2	.	.	PUNCT
ejpam-5226	498	1	sci	sci	PROPN
ejpam-5226	498	2	.	.	PROPN
ejpam-5226	498	3	,	,	PUNCT
ejpam-5226	498	4	4(9	4(9	PROPN
ejpam-5226	498	5	-	-	SYM
ejpam-5226	498	6	12):475–484	12):475–484	PROPN
ejpam-5226	498	7	,	,	PUNCT
ejpam-5226	498	8	2009	2009	NUM
ejpam-5226	498	9	.	.	PUNCT
ejpam-5226	499	1	[	[	X
ejpam-5226	499	2	5	5	X
ejpam-5226	499	3	]	]	X
ejpam-5226	499	4	g.c	g.c	PROPN
ejpam-5226	499	5	.	.	PROPN
ejpam-5226	499	6	rao	rao	PROPN
ejpam-5226	499	7	,	,	PUNCT
ejpam-5226	499	8	n.	n.	PROPN
ejpam-5226	499	9	rafi	rafi	PROPN
ejpam-5226	499	10	,	,	PUNCT
ejpam-5226	499	11	and	and	CCONJ
ejpam-5226	499	12	r.	r.	PROPN
ejpam-5226	499	13	bandaru	bandaru	PROPN
ejpam-5226	499	14	.	.	PUNCT
ejpam-5226	500	1	s	s	X
ejpam-5226	500	2	-	-	PUNCT
ejpam-5226	500	3	linear	linear	ADJ
ejpam-5226	500	4	almost	almost	ADV
ejpam-5226	500	5	distributive	distributive	ADJ
ejpam-5226	500	6	lattices	lattice	NOUN
ejpam-5226	500	7	.	.	PUNCT
ejpam-5226	501	1	eur	eur	PROPN
ejpam-5226	501	2	.	.	PUNCT
ejpam-5226	502	1	j.	j.	PROPN
ejpam-5226	502	2	pure	pure	PROPN
ejpam-5226	502	3	appl	appl	PROPN
ejpam-5226	502	4	.	.	PUNCT
ejpam-5226	502	5	math	math	PROPN
ejpam-5226	502	6	.	.	PUNCT
ejpam-5226	503	1	,	,	PUNCT
ejpam-5226	503	2	3(4):704–716	3(4):704–716	NUM
ejpam-5226	503	3	,	,	PUNCT
ejpam-5226	503	4	2010	2010	NUM
ejpam-5226	503	5	.	.	PUNCT
ejpam-5226	504	1	[	[	X
ejpam-5226	504	2	6	6	NUM
ejpam-5226	504	3	]	]	SYM
ejpam-5226	504	4	v.v.v.s.s.p.s	v.v.v.s.s.p.s	NOUN
ejpam-5226	504	5	.	.	PUNCT
ejpam-5226	505	1	srikanth	srikanth	PROPN
ejpam-5226	505	2	,	,	PUNCT
ejpam-5226	505	3	s.	s.	PROPN
ejpam-5226	505	4	ramesh	ramesh	PROPN
ejpam-5226	505	5	,	,	PUNCT
ejpam-5226	505	6	m.v	m.v	PROPN
ejpam-5226	505	7	.	.	PROPN
ejpam-5226	505	8	ratnamani	ratnamani	PROPN
ejpam-5226	505	9	,	,	PUNCT
ejpam-5226	505	10	r.	r.	PROPN
ejpam-5226	505	11	bandaru	bandaru	PROPN
ejpam-5226	505	12	,	,	PUNCT
ejpam-5226	505	13	and	and	CCONJ
ejpam-5226	505	14	a.	a.	NOUN
ejpam-5226	505	15	iampan	iampan	PROPN
ejpam-5226	505	16	.	.	PUNCT
ejpam-5226	506	1	associative	associative	ADJ
ejpam-5226	506	2	types	type	NOUN
ejpam-5226	506	3	in	in	ADP
ejpam-5226	506	4	a	a	DET
ejpam-5226	506	5	semi	semi	ADJ
ejpam-5226	506	6	-	-	ADJ
ejpam-5226	506	7	brouwerian	brouwerian	ADJ
ejpam-5226	506	8	almost	almost	ADV
ejpam-5226	506	9	distributive	distributive	ADJ
ejpam-5226	506	10	lattice	lattice	NOUN
ejpam-5226	506	11	with	with	ADP
ejpam-5226	506	12	respect	respect	NOUN
ejpam-5226	506	13	to	to	ADP
ejpam-5226	506	14	the	the	DET
ejpam-5226	506	15	binary	binary	PROPN
ejpam-5226	506	16	operation	operation	PROPN
ejpam-5226	506	17	ρ	ρ	PROPN
ejpam-5226	506	18	.	.	PUNCT
ejpam-5226	507	1	int	int	NOUN
ejpam-5226	507	2	.	.	PUNCT
ejpam-5226	508	1	j.	j.	PROPN
ejpam-5226	508	2	anal	anal	PROPN
ejpam-5226	508	3	.	.	PUNCT
ejpam-5226	509	1	appl	appl	PROPN
ejpam-5226	509	2	.	.	PROPN
ejpam-5226	509	3	,	,	PUNCT
ejpam-5226	509	4	22	22	NUM
ejpam-5226	509	5	:	:	PUNCT
ejpam-5226	509	6	article	article	NOUN
ejpam-5226	509	7	no	no	NOUN
ejpam-5226	509	8	.	.	PROPN
ejpam-5226	509	9	13	13	NUM
ejpam-5226	509	10	,	,	PUNCT
ejpam-5226	509	11	2024	2024	NUM
ejpam-5226	509	12	.	.	PUNCT
ejpam-5226	510	1	[	[	X
ejpam-5226	510	2	7	7	X
ejpam-5226	510	3	]	]	X
ejpam-5226	510	4	m.h	m.h	PROPN
ejpam-5226	510	5	.	.	PROPN
ejpam-5226	510	6	stone	stone	PROPN
ejpam-5226	510	7	.	.	PUNCT
ejpam-5226	511	1	the	the	DET
ejpam-5226	511	2	theory	theory	NOUN
ejpam-5226	511	3	of	of	ADP
ejpam-5226	511	4	representation	representation	NOUN
ejpam-5226	511	5	for	for	ADP
ejpam-5226	511	6	boolean	boolean	ADJ
ejpam-5226	511	7	algebras	algebra	NOUN
ejpam-5226	511	8	.	.	PUNCT
ejpam-5226	512	1	trans	trans	AUX
ejpam-5226	512	2	.	.	PROPN
ejpam-5226	512	3	am	be	AUX
ejpam-5226	512	4	.	.	PUNCT
ejpam-5226	513	1	math	math	NOUN
ejpam-5226	513	2	.	.	PUNCT
ejpam-5226	514	1	soc	soc	PROPN
ejpam-5226	514	2	.	.	PUNCT
ejpam-5226	514	3	,	,	PUNCT
ejpam-5226	514	4	40:37–111	40:37–111	NUM
ejpam-5226	514	5	,	,	PUNCT
ejpam-5226	514	6	1936	1936	NUM
ejpam-5226	514	7	.	.	PUNCT
ejpam-5226	515	1	[	[	X
ejpam-5226	515	2	8	8	NUM
ejpam-5226	515	3	]	]	X
ejpam-5226	515	4	u.m	u.m	PROPN
ejpam-5226	515	5	.	.	PROPN
ejpam-5226	515	6	swamy	swamy	PROPN
ejpam-5226	515	7	and	and	CCONJ
ejpam-5226	515	8	g.c	g.c	PROPN
ejpam-5226	515	9	.	.	PROPN
ejpam-5226	515	10	rao	rao	PROPN
ejpam-5226	515	11	.	.	PUNCT
ejpam-5226	516	1	almost	almost	ADV
ejpam-5226	516	2	distributive	distributive	ADJ
ejpam-5226	516	3	lattices	lattice	NOUN
ejpam-5226	516	4	.	.	PUNCT
ejpam-5226	517	1	j.	j.	PROPN
ejpam-5226	517	2	aust	aust	PROPN
ejpam-5226	517	3	.	.	PUNCT
ejpam-5226	518	1	math	math	PROPN
ejpam-5226	518	2	.	.	PUNCT
ejpam-5226	519	1	soc	soc	PROPN
ejpam-5226	519	2	.	.	PUNCT
ejpam-5226	519	3	,	,	PUNCT
ejpam-5226	519	4	ser	ser	PROPN
ejpam-5226	519	5	.	.	PUNCT
ejpam-5226	520	1	a	a	DET
ejpam-5226	520	2	,	,	PUNCT
ejpam-5226	520	3	31:77–91	31:77–91	NUM
ejpam-5226	520	4	,	,	PUNCT
ejpam-5226	520	5	1981	1981	NUM
ejpam-5226	520	6	.	.	PUNCT
ejpam-5226	521	1	[	[	X
ejpam-5226	521	2	9	9	NUM
ejpam-5226	521	3	]	]	PUNCT
ejpam-5226	521	4	r.	r.	PROPN
ejpam-5226	521	5	vasu	vasu	PROPN
ejpam-5226	521	6	babu	babu	PROPN
ejpam-5226	521	7	and	and	CCONJ
ejpam-5226	521	8	b.	b.	PROPN
ejpam-5226	521	9	venkateswarallu	venkateswarallu	PROPN
ejpam-5226	521	10	.	.	PUNCT
ejpam-5226	522	1	initial	initial	ADJ
ejpam-5226	522	2	and	and	CCONJ
ejpam-5226	522	3	final	final	ADJ
ejpam-5226	522	4	segments	segment	NOUN
ejpam-5226	522	5	in	in	ADP
ejpam-5226	522	6	almost	almost	ADV
ejpam-5226	522	7	distributive	distributive	ADJ
ejpam-5226	522	8	lattices	lattice	NOUN
ejpam-5226	522	9	.	.	PUNCT
ejpam-5226	523	1	southeast	southeast	ADJ
ejpam-5226	523	2	asian	asian	ADJ
ejpam-5226	523	3	bull	bull	PROPN
ejpam-5226	523	4	.	.	PUNCT
ejpam-5226	524	1	math	math	NOUN
ejpam-5226	524	2	.	.	PUNCT
ejpam-5226	524	3	,	,	PUNCT
ejpam-5226	525	1	41:127–131	41:127–131	NUM
ejpam-5226	525	2	,	,	PUNCT
ejpam-5226	525	3	2017	2017	NUM
ejpam-5226	525	4	.	.	PUNCT