id	sid	tid	token	lemma	pos
ejpam-3415	1	1	compile	compile	NOUN
ejpam-3415	1	2	/	/	SYM
ejpam-3415	1	3	output.dvi	output.dvi	NOUN
ejpam-3415	1	4	european	european	ADJ
ejpam-3415	1	5	journal	journal	NOUN
ejpam-3415	1	6	of	of	ADP
ejpam-3415	1	7	pure	pure	ADJ
ejpam-3415	1	8	and	and	CCONJ
ejpam-3415	1	9	applied	apply	VERB
ejpam-3415	1	10	mathematics	mathematic	NOUN
ejpam-3415	1	11	vol	vol	NOUN
ejpam-3415	1	12	.	.	PROPN
ejpam-3415	2	1	12	12	NUM
ejpam-3415	2	2	,	,	PUNCT
ejpam-3415	2	3	no	no	INTJ
ejpam-3415	2	4	.	.	NOUN
ejpam-3415	2	5	2	2	NUM
ejpam-3415	2	6	,	,	PUNCT
ejpam-3415	2	7	2019	2019	NUM
ejpam-3415	2	8	,	,	PUNCT
ejpam-3415	2	9	252	252	NUM
ejpam-3415	2	10	-	-	SYM
ejpam-3415	2	11	269	269	NUM
ejpam-3415	2	12	issn	issn	PROPN
ejpam-3415	2	13	1307	1307	NUM
ejpam-3415	2	14	-	-	SYM
ejpam-3415	2	15	5543	5543	NUM
ejpam-3415	2	16	–	–	PUNCT
ejpam-3415	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3415	2	18	published	publish	VERB
ejpam-3415	2	19	by	by	ADP
ejpam-3415	2	20	new	new	PROPN
ejpam-3415	2	21	york	york	PROPN
ejpam-3415	2	22	business	business	PROPN
ejpam-3415	2	23	global	global	ADJ
ejpam-3415	2	24	correction	correction	NOUN
ejpam-3415	2	25	to	to	ADP
ejpam-3415	2	26	the	the	DET
ejpam-3415	2	27	article	article	NOUN
ejpam-3415	2	28	:	:	PUNCT
ejpam-3415	2	29	“	"	PUNCT
ejpam-3415	2	30	an	an	DET
ejpam-3415	2	31	introduction	introduction	NOUN
ejpam-3415	2	32	to	to	ADP
ejpam-3415	2	33	the	the	DET
ejpam-3415	2	34	theory	theory	NOUN
ejpam-3415	2	35	of	of	ADP
ejpam-3415	2	36	hyperlattices	hyperlattice	NOUN
ejpam-3415	2	37	”	"	PUNCT
ejpam-3415	2	38	niovi	niovi	NOUN
ejpam-3415	2	39	kehayopulu	kehayopulu	VERB
ejpam-3415	2	40	abstract	abstract	NOUN
ejpam-3415	2	41	.	.	PUNCT
ejpam-3415	3	1	the	the	DET
ejpam-3415	3	2	definition	definition	NOUN
ejpam-3415	3	3	of	of	ADP
ejpam-3415	3	4	hyperlattices	hyperlattice	NOUN
ejpam-3415	3	5	introduced	introduce	VERB
ejpam-3415	3	6	in	in	ADP
ejpam-3415	3	7	mathematica	mathematica	PROPN
ejpam-3415	3	8	balkanica	balkanica	PROPN
ejpam-3415	3	9	,	,	PUNCT
ejpam-3415	3	10	1977	1977	NUM
ejpam-3415	3	11	by	by	ADP
ejpam-3415	3	12	konstantinidou	konstantinidou	NOUN
ejpam-3415	3	13	and	and	CCONJ
ejpam-3415	3	14	mittas	mitta	NOUN
ejpam-3415	3	15	in	in	ADP
ejpam-3415	3	16	their	their	PRON
ejpam-3415	3	17	paper	paper	NOUN
ejpam-3415	3	18	“	"	PUNCT
ejpam-3415	3	19	an	an	DET
ejpam-3415	3	20	introduction	introduction	NOUN
ejpam-3415	3	21	to	to	ADP
ejpam-3415	3	22	the	the	DET
ejpam-3415	3	23	theory	theory	NOUN
ejpam-3415	3	24	of	of	ADP
ejpam-3415	3	25	hyperlattices	hyperlattice	NOUN
ejpam-3415	3	26	”	"	PUNCT
ejpam-3415	3	27	should	should	AUX
ejpam-3415	3	28	be	be	AUX
ejpam-3415	3	29	corrected	correct	VERB
ejpam-3415	3	30	.	.	PUNCT
ejpam-3415	4	1	as	as	ADP
ejpam-3415	4	2	a	a	DET
ejpam-3415	4	3	result	result	NOUN
ejpam-3415	4	4	,	,	PUNCT
ejpam-3415	4	5	the	the	DET
ejpam-3415	4	6	definition	definition	NOUN
ejpam-3415	4	7	of	of	ADP
ejpam-3415	4	8	distributive	distributive	ADJ
ejpam-3415	4	9	and	and	CCONJ
ejpam-3415	4	10	modular	modular	ADJ
ejpam-3415	4	11	hyperlattices	hyperlattice	NOUN
ejpam-3415	4	12	introduced	introduce	VERB
ejpam-3415	4	13	by	by	ADP
ejpam-3415	4	14	konstantinidou	konstantinidou	NOUN
ejpam-3415	4	15	should	should	AUX
ejpam-3415	4	16	be	be	AUX
ejpam-3415	4	17	also	also	ADV
ejpam-3415	4	18	corrected	correct	VERB
ejpam-3415	4	19	.	.	PUNCT
ejpam-3415	5	1	in	in	ADP
ejpam-3415	5	2	the	the	DET
ejpam-3415	5	3	present	present	ADJ
ejpam-3415	5	4	paper	paper	NOUN
ejpam-3415	5	5	we	we	PRON
ejpam-3415	5	6	correct	correct	VERB
ejpam-3415	5	7	these	these	DET
ejpam-3415	5	8	definitions	definition	NOUN
ejpam-3415	5	9	and	and	CCONJ
ejpam-3415	5	10	give	give	VERB
ejpam-3415	5	11	some	some	DET
ejpam-3415	5	12	examples	example	NOUN
ejpam-3415	5	13	to	to	PART
ejpam-3415	5	14	show	show	VERB
ejpam-3415	5	15	that	that	SCONJ
ejpam-3415	5	16	these	these	DET
ejpam-3415	5	17	corrected	correct	VERB
ejpam-3415	5	18	forms	form	NOUN
ejpam-3415	5	19	work	work	VERB
ejpam-3415	5	20	.	.	PUNCT
ejpam-3415	6	1	2010	2010	NUM
ejpam-3415	6	2	mathematics	mathematic	NOUN
ejpam-3415	6	3	subject	subject	NOUN
ejpam-3415	6	4	classifications	classification	NOUN
ejpam-3415	6	5	:	:	PUNCT
ejpam-3415	6	6	06b75	06b75	NUM
ejpam-3415	6	7	key	key	ADJ
ejpam-3415	6	8	words	word	NOUN
ejpam-3415	6	9	and	and	CCONJ
ejpam-3415	6	10	phrases	phrase	NOUN
ejpam-3415	6	11	:	:	PUNCT
ejpam-3415	6	12	hyperlattice	hyperlattice	NOUN
ejpam-3415	6	13	,	,	PUNCT
ejpam-3415	6	14	distributive	distributive	ADJ
ejpam-3415	6	15	,	,	PUNCT
ejpam-3415	6	16	modular	modular	ADJ
ejpam-3415	6	17	1	1	NUM
ejpam-3415	6	18	.	.	PUNCT
ejpam-3415	6	19	introduction	introduction	NOUN
ejpam-3415	6	20	according	accord	VERB
ejpam-3415	6	21	to	to	ADP
ejpam-3415	6	22	the	the	DET
ejpam-3415	6	23	bibliography	bibliography	NOUN
ejpam-3415	6	24	,	,	PUNCT
ejpam-3415	6	25	the	the	DET
ejpam-3415	6	26	concept	concept	NOUN
ejpam-3415	6	27	of	of	ADP
ejpam-3415	6	28	hyperlattices	hyperlattice	NOUN
ejpam-3415	6	29	has	have	AUX
ejpam-3415	6	30	been	be	AUX
ejpam-3415	6	31	introduced	introduce	VERB
ejpam-3415	6	32	by	by	ADP
ejpam-3415	6	33	konstantinidou	konstantinidou	NOUN
ejpam-3415	6	34	and	and	CCONJ
ejpam-3415	6	35	mittas	mitta	NOUN
ejpam-3415	6	36	in	in	ADP
ejpam-3415	6	37	math	math	NOUN
ejpam-3415	6	38	.	.	PUNCT
ejpam-3415	7	1	balkanica	balkanica	PROPN
ejpam-3415	8	1	[	[	X
ejpam-3415	8	2	4	4	NUM
ejpam-3415	8	3	]	]	PUNCT
ejpam-3415	8	4	.	.	PUNCT
ejpam-3415	9	1	the	the	DET
ejpam-3415	9	2	aim	aim	NOUN
ejpam-3415	9	3	of	of	ADP
ejpam-3415	9	4	this	this	DET
ejpam-3415	9	5	note	note	NOUN
ejpam-3415	9	6	is	be	AUX
ejpam-3415	9	7	to	to	PART
ejpam-3415	9	8	correct	correct	VERB
ejpam-3415	9	9	the	the	DET
ejpam-3415	9	10	definition	definition	NOUN
ejpam-3415	9	11	of	of	ADP
ejpam-3415	9	12	hyperlattice	hyperlattice	NOUN
ejpam-3415	9	13	introduced	introduce	VERB
ejpam-3415	9	14	in	in	ADP
ejpam-3415	9	15	[	[	X
ejpam-3415	9	16	4	4	NUM
ejpam-3415	9	17	]	]	PUNCT
ejpam-3415	9	18	,	,	PUNCT
ejpam-3415	9	19	and	and	CCONJ
ejpam-3415	9	20	the	the	DET
ejpam-3415	9	21	definitions	definition	NOUN
ejpam-3415	9	22	of	of	ADP
ejpam-3415	9	23	distributive	distributive	ADJ
ejpam-3415	9	24	and	and	CCONJ
ejpam-3415	9	25	modular	modular	ADJ
ejpam-3415	9	26	hyperlattices	hyperlattice	NOUN
ejpam-3415	9	27	based	base	VERB
ejpam-3415	9	28	on	on	ADP
ejpam-3415	9	29	it	it	PRON
ejpam-3415	9	30	,	,	PUNCT
ejpam-3415	9	31	introduced	introduce	VERB
ejpam-3415	9	32	in	in	ADP
ejpam-3415	9	33	[	[	X
ejpam-3415	9	34	5	5	NUM
ejpam-3415	9	35	,	,	PUNCT
ejpam-3415	9	36	6	6	NUM
ejpam-3415	9	37	]	]	PUNCT
ejpam-3415	9	38	,	,	PUNCT
ejpam-3415	9	39	and	and	CCONJ
ejpam-3415	9	40	give	give	VERB
ejpam-3415	9	41	some	some	DET
ejpam-3415	9	42	examples	example	NOUN
ejpam-3415	9	43	to	to	PART
ejpam-3415	9	44	show	show	VERB
ejpam-3415	9	45	that	that	SCONJ
ejpam-3415	9	46	these	these	PRON
ejpam-3415	9	47	corrected	correct	VERB
ejpam-3415	9	48	forms	form	NOUN
ejpam-3415	9	49	work	work	VERB
ejpam-3415	9	50	.	.	PUNCT
ejpam-3415	10	1	for	for	ADP
ejpam-3415	10	2	the	the	DET
ejpam-3415	10	3	sake	sake	NOUN
ejpam-3415	10	4	of	of	ADP
ejpam-3415	10	5	completeness	completeness	NOUN
ejpam-3415	10	6	,	,	PUNCT
ejpam-3415	10	7	we	we	PRON
ejpam-3415	10	8	first	first	ADV
ejpam-3415	10	9	mention	mention	VERB
ejpam-3415	10	10	the	the	DET
ejpam-3415	10	11	definition	definition	NOUN
ejpam-3415	10	12	of	of	ADP
ejpam-3415	10	13	lattices	lattice	NOUN
ejpam-3415	10	14	just	just	ADV
ejpam-3415	10	15	to	to	PART
ejpam-3415	10	16	see	see	VERB
ejpam-3415	10	17	,	,	PUNCT
ejpam-3415	10	18	step	step	NOUN
ejpam-3415	10	19	by	by	ADP
ejpam-3415	10	20	step	step	NOUN
ejpam-3415	10	21	,	,	PUNCT
ejpam-3415	10	22	how	how	SCONJ
ejpam-3415	10	23	we	we	PRON
ejpam-3415	10	24	could	could	AUX
ejpam-3415	10	25	generalize	generalize	VERB
ejpam-3415	10	26	it	it	PRON
ejpam-3415	10	27	to	to	ADP
ejpam-3415	10	28	a	a	DET
ejpam-3415	10	29	hyperlattice	hyperlattice	NOUN
ejpam-3415	10	30	.	.	PUNCT
ejpam-3415	11	1	a	a	DET
ejpam-3415	11	2	lattice	lattice	NOUN
ejpam-3415	11	3	is	be	AUX
ejpam-3415	11	4	a	a	DET
ejpam-3415	11	5	nonempty	nonempty	ADJ
ejpam-3415	11	6	set	set	VERB
ejpam-3415	11	7	l	l	NOUN
ejpam-3415	11	8	with	with	ADP
ejpam-3415	11	9	two	two	NUM
ejpam-3415	11	10	binary	binary	ADJ
ejpam-3415	11	11	operations	operation	NOUN
ejpam-3415	11	12	“	"	PUNCT
ejpam-3415	11	13	∧	∧	PROPN
ejpam-3415	11	14	”	"	PUNCT
ejpam-3415	11	15	and	and	CCONJ
ejpam-3415	11	16	“	"	PUNCT
ejpam-3415	11	17	∨	∨	NOUN
ejpam-3415	11	18	”	"	PUNCT
ejpam-3415	11	19	on	on	ADP
ejpam-3415	11	20	l	l	NOUN
ejpam-3415	11	21	such	such	ADJ
ejpam-3415	11	22	that	that	SCONJ
ejpam-3415	11	23	(	(	PUNCT
ejpam-3415	11	24	1	1	X
ejpam-3415	11	25	)	)	PUNCT
ejpam-3415	11	26	a	a	DET
ejpam-3415	11	27	∧	∧	NOUN
ejpam-3415	11	28	a	a	DET
ejpam-3415	11	29	=	=	PUNCT
ejpam-3415	11	30	a	a	NOUN
ejpam-3415	11	31	and	and	CCONJ
ejpam-3415	11	32	a	a	DET
ejpam-3415	11	33	∨	∨	NOUN
ejpam-3415	11	34	a	a	DET
ejpam-3415	11	35	=	=	NOUN
ejpam-3415	11	36	a	a	DET
ejpam-3415	11	37	(	(	PUNCT
ejpam-3415	11	38	2	2	NUM
ejpam-3415	11	39	)	)	PUNCT
ejpam-3415	11	40	a	a	DET
ejpam-3415	11	41	∧	∧	PROPN
ejpam-3415	11	42	b	b	NOUN
ejpam-3415	11	43	=	=	SYM
ejpam-3415	11	44	b	b	PROPN
ejpam-3415	11	45	∧	∧	PROPN
ejpam-3415	11	46	a	a	PRON
ejpam-3415	11	47	and	and	CCONJ
ejpam-3415	11	48	a	a	DET
ejpam-3415	11	49	∨	∨	NUM
ejpam-3415	11	50	b	b	X
ejpam-3415	11	51	=	=	SYM
ejpam-3415	11	52	b	b	PROPN
ejpam-3415	11	53	∨	∨	NUM
ejpam-3415	11	54	a	a	DET
ejpam-3415	11	55	(	(	PUNCT
ejpam-3415	11	56	3	3	NUM
ejpam-3415	11	57	)	)	PUNCT
ejpam-3415	11	58	(	(	PUNCT
ejpam-3415	11	59	a	a	DET
ejpam-3415	11	60	∧	∧	PROPN
ejpam-3415	11	61	b	b	NOUN
ejpam-3415	11	62	)	)	PUNCT
ejpam-3415	11	63	∧	∧	PROPN
ejpam-3415	11	64	c	c	NOUN
ejpam-3415	11	65	=	=	PUNCT
ejpam-3415	11	66	a	a	DET
ejpam-3415	11	67	∧	∧	PROPN
ejpam-3415	11	68	(	(	PUNCT
ejpam-3415	11	69	b	b	PROPN
ejpam-3415	11	70	∧	∧	PROPN
ejpam-3415	11	71	c	c	NOUN
ejpam-3415	11	72	)	)	PUNCT
ejpam-3415	11	73	and	and	CCONJ
ejpam-3415	11	74	(	(	PUNCT
ejpam-3415	11	75	a	a	DET
ejpam-3415	11	76	∨	∨	NUM
ejpam-3415	11	77	b	b	NOUN
ejpam-3415	11	78	)	)	PUNCT
ejpam-3415	11	79	∨	∨	NUM
ejpam-3415	11	80	c	c	NOUN
ejpam-3415	11	81	=	=	PUNCT
ejpam-3415	11	82	a	a	DET
ejpam-3415	11	83	∨	∨	NOUN
ejpam-3415	11	84	(	(	PUNCT
ejpam-3415	11	85	b	b	PROPN
ejpam-3415	11	86	∨	∨	NUM
ejpam-3415	11	87	c	c	NOUN
ejpam-3415	11	88	)	)	PUNCT
ejpam-3415	11	89	(	(	PUNCT
ejpam-3415	11	90	4	4	X
ejpam-3415	11	91	)	)	PUNCT
ejpam-3415	11	92	a	a	DET
ejpam-3415	11	93	∧	∧	PROPN
ejpam-3415	11	94	(	(	PUNCT
ejpam-3415	11	95	a	a	DET
ejpam-3415	11	96	∨	∨	NUM
ejpam-3415	11	97	b	b	NOUN
ejpam-3415	11	98	)	)	PUNCT
ejpam-3415	11	99	=	=	PUNCT
ejpam-3415	11	100	a	a	PRON
ejpam-3415	11	101	and	and	CCONJ
ejpam-3415	11	102	a	a	DET
ejpam-3415	11	103	∨	∨	NOUN
ejpam-3415	11	104	(	(	PUNCT
ejpam-3415	11	105	a	a	DET
ejpam-3415	11	106	∧	∧	PROPN
ejpam-3415	11	107	b	b	NOUN
ejpam-3415	11	108	)	)	PUNCT
ejpam-3415	11	109	=	=	PUNCT
ejpam-3415	11	110	a.	a.	NOUN
ejpam-3415	11	111	according	accord	VERB
ejpam-3415	11	112	to	to	ADP
ejpam-3415	11	113	[	[	X
ejpam-3415	11	114	4–7	4–7	NOUN
ejpam-3415	11	115	]	]	X
ejpam-3415	11	116	,	,	PUNCT
ejpam-3415	11	117	the	the	DET
ejpam-3415	11	118	definition	definition	NOUN
ejpam-3415	11	119	of	of	ADP
ejpam-3415	11	120	a	a	DET
ejpam-3415	11	121	hyperlattice	hyperlattice	NOUN
ejpam-3415	11	122	is	be	AUX
ejpam-3415	11	123	given	give	VERB
ejpam-3415	11	124	as	as	SCONJ
ejpam-3415	11	125	follows	follow	VERB
ejpam-3415	11	126	:	:	PUNCT
ejpam-3415	11	127	definition	definition	NOUN
ejpam-3415	11	128	1.1	1.1	NUM
ejpam-3415	11	129	[	[	X
ejpam-3415	11	130	4	4	NUM
ejpam-3415	11	131	]	]	PUNCT
ejpam-3415	11	132	a	a	DET
ejpam-3415	11	133	hyperlattice	hyperlattice	NOUN
ejpam-3415	11	134	is	be	AUX
ejpam-3415	11	135	a	a	DET
ejpam-3415	11	136	nonempty	nonempty	ADJ
ejpam-3415	11	137	set	set	VERB
ejpam-3415	11	138	l	l	NOUN
ejpam-3415	11	139	with	with	ADP
ejpam-3415	11	140	an	an	DET
ejpam-3415	11	141	hyperoperation	hyperoperation	NOUN
ejpam-3415	11	142	“	"	PUNCT
ejpam-3415	11	143	∨	∨	NOUN
ejpam-3415	11	144	”	"	PUNCT
ejpam-3415	11	145	(	(	PUNCT
ejpam-3415	11	146	that	that	PRON
ejpam-3415	11	147	is	be	AUX
ejpam-3415	11	148	a	a	DET
ejpam-3415	11	149	mapping	mapping	NOUN
ejpam-3415	11	150	that	that	PRON
ejpam-3415	11	151	assigns	assign	VERB
ejpam-3415	11	152	to	to	ADP
ejpam-3415	11	153	each	each	DET
ejpam-3415	11	154	couple	couple	NOUN
ejpam-3415	11	155	a	a	DET
ejpam-3415	11	156	,	,	PUNCT
ejpam-3415	11	157	b	b	NOUN
ejpam-3415	11	158	of	of	ADP
ejpam-3415	11	159	elements	element	NOUN
ejpam-3415	11	160	of	of	ADP
ejpam-3415	11	161	l	l	NOUN
ejpam-3415	11	162	a	a	DET
ejpam-3415	11	163	nonempty	nonempty	ADJ
ejpam-3415	11	164	subset	subset	NOUN
ejpam-3415	11	165	of	of	ADP
ejpam-3415	11	166	l	l	NOUN
ejpam-3415	11	167	)	)	PUNCT
ejpam-3415	11	168	and	and	CCONJ
ejpam-3415	11	169	an	an	DET
ejpam-3415	11	170	operation	operation	NOUN
ejpam-3415	11	171	“	"	PUNCT
ejpam-3415	11	172	∧	∧	PROPN
ejpam-3415	11	173	”	"	PUNCT
ejpam-3415	11	174	on	on	ADP
ejpam-3415	11	175	l	l	NOUN
ejpam-3415	11	176	such	such	ADJ
ejpam-3415	11	177	that	that	SCONJ
ejpam-3415	11	178	(	(	PUNCT
ejpam-3415	11	179	1	1	X
ejpam-3415	11	180	)	)	PUNCT
ejpam-3415	11	181	a	a	DET
ejpam-3415	11	182	∈	∈	PROPN
ejpam-3415	11	183	a	a	DET
ejpam-3415	11	184	∨	∨	NOUN
ejpam-3415	11	185	a	a	DET
ejpam-3415	11	186	a	a	DET
ejpam-3415	11	187	∧	∧	NOUN
ejpam-3415	11	188	a	a	DET
ejpam-3415	11	189	=	=	X
ejpam-3415	11	190	a	a	DET
ejpam-3415	11	191	doi	doi	NOUN
ejpam-3415	11	192	:	:	PUNCT
ejpam-3415	11	193	https://doi.org/10.29020/nybg.ejpam.v12i2.3415	https://doi.org/10.29020/nybg.ejpam.v12i2.3415	ADJ
ejpam-3415	11	194	email	email	NOUN
ejpam-3415	11	195	address	address	NOUN
ejpam-3415	11	196	:	:	PUNCT
ejpam-3415	11	197	nkehayop@math.uoa.gr	nkehayop@math.uoa.gr	ADV
ejpam-3415	11	198	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3415	12	1	252	252	NUM
ejpam-3415	12	2	c	c	NOUN
ejpam-3415	12	3	©	©	PROPN
ejpam-3415	12	4	2019	2019	NUM
ejpam-3415	12	5	ejpam	ejpam	NOUN
ejpam-3415	12	6	all	all	DET
ejpam-3415	12	7	rights	right	NOUN
ejpam-3415	12	8	reserved	reserve	VERB
ejpam-3415	12	9	.	.	PUNCT
ejpam-3415	13	1	niovi	niovi	PROPN
ejpam-3415	13	2	kehayopulu	kehayopulu	PROPN
ejpam-3415	13	3	/	/	SYM
ejpam-3415	13	4	eur	eur	PROPN
ejpam-3415	13	5	.	.	PUNCT
ejpam-3415	14	1	j.	j.	PROPN
ejpam-3415	14	2	pure	pure	PROPN
ejpam-3415	14	3	appl	appl	PROPN
ejpam-3415	14	4	.	.	PROPN
ejpam-3415	14	5	math	math	PROPN
ejpam-3415	14	6	,	,	PUNCT
ejpam-3415	14	7	12	12	NUM
ejpam-3415	14	8	(	(	PUNCT
ejpam-3415	14	9	2	2	NUM
ejpam-3415	14	10	)	)	PUNCT
ejpam-3415	14	11	(	(	PUNCT
ejpam-3415	14	12	2019	2019	NUM
ejpam-3415	14	13	)	)	PUNCT
ejpam-3415	14	14	,	,	PUNCT
ejpam-3415	14	15	252	252	NUM
ejpam-3415	14	16	-	-	SYM
ejpam-3415	14	17	269	269	NUM
ejpam-3415	14	18	253	253	NUM
ejpam-3415	14	19	(	(	PUNCT
ejpam-3415	14	20	2	2	NUM
ejpam-3415	14	21	)	)	PUNCT
ejpam-3415	14	22	a	a	DET
ejpam-3415	14	23	∨	∨	NUM
ejpam-3415	14	24	b	b	X
ejpam-3415	14	25	=	=	SYM
ejpam-3415	14	26	b	b	PROPN
ejpam-3415	14	27	∨	∨	X
ejpam-3415	14	28	a	a	PRON
ejpam-3415	14	29	a	a	DET
ejpam-3415	14	30	∧	∧	PROPN
ejpam-3415	14	31	b	b	NOUN
ejpam-3415	15	1	=	=	SYM
ejpam-3415	15	2	b	b	PROPN
ejpam-3415	15	3	∧	∧	PROPN
ejpam-3415	15	4	a	a	PRON
ejpam-3415	15	5	(	(	PUNCT
ejpam-3415	15	6	3	3	NUM
ejpam-3415	15	7	)	)	PUNCT
ejpam-3415	15	8	(	(	PUNCT
ejpam-3415	15	9	a	a	DET
ejpam-3415	15	10	∨	∨	NUM
ejpam-3415	15	11	b	b	NOUN
ejpam-3415	15	12	)	)	PUNCT
ejpam-3415	15	13	∨	∨	NUM
ejpam-3415	15	14	c	c	NOUN
ejpam-3415	15	15	=	=	PUNCT
ejpam-3415	15	16	a	a	DET
ejpam-3415	15	17	∨	∨	NOUN
ejpam-3415	15	18	(	(	PUNCT
ejpam-3415	15	19	b	b	PROPN
ejpam-3415	15	20	∨	∨	NUM
ejpam-3415	15	21	c	c	NOUN
ejpam-3415	15	22	)	)	PUNCT
ejpam-3415	15	23	(	(	PUNCT
ejpam-3415	15	24	a	a	DET
ejpam-3415	15	25	∧	∧	PROPN
ejpam-3415	15	26	b	b	NOUN
ejpam-3415	15	27	)	)	PUNCT
ejpam-3415	15	28	∧	∧	PROPN
ejpam-3415	15	29	c	c	NOUN
ejpam-3415	15	30	=	=	PUNCT
ejpam-3415	15	31	a	a	DET
ejpam-3415	15	32	∧	∧	PROPN
ejpam-3415	15	33	(	(	PUNCT
ejpam-3415	15	34	b	b	PROPN
ejpam-3415	15	35	∧	∧	PROPN
ejpam-3415	15	36	c	c	NOUN
ejpam-3415	15	37	)	)	PUNCT
ejpam-3415	15	38	(	(	PUNCT
ejpam-3415	15	39	4	4	X
ejpam-3415	15	40	)	)	PUNCT
ejpam-3415	15	41	a	a	DET
ejpam-3415	15	42	∈	∈	NOUN
ejpam-3415	15	43	[	[	PUNCT
ejpam-3415	15	44	a	a	DET
ejpam-3415	15	45	∨	∨	NOUN
ejpam-3415	15	46	(	(	PUNCT
ejpam-3415	15	47	a	a	DET
ejpam-3415	15	48	∧	∧	PROPN
ejpam-3415	15	49	b	b	NOUN
ejpam-3415	15	50	)	)	PUNCT
ejpam-3415	15	51	]	]	PUNCT
ejpam-3415	16	1	∩	∩	NOUN
ejpam-3415	16	2	[	[	PUNCT
ejpam-3415	16	3	a	a	DET
ejpam-3415	16	4	∧	∧	PROPN
ejpam-3415	16	5	(	(	PUNCT
ejpam-3415	16	6	a	a	DET
ejpam-3415	16	7	∨	∨	NUM
ejpam-3415	16	8	b	b	NOUN
ejpam-3415	16	9	)	)	PUNCT
ejpam-3415	16	10	]	]	PUNCT
ejpam-3415	16	11	(	(	PUNCT
ejpam-3415	16	12	5	5	X
ejpam-3415	16	13	)	)	PUNCT
ejpam-3415	16	14	a	a	PRON
ejpam-3415	16	15	∈	∈	PROPN
ejpam-3415	16	16	a	a	DET
ejpam-3415	16	17	∨	∨	PROPN
ejpam-3415	16	18	b	b	PROPN
ejpam-3415	16	19	⇒	⇒	NOUN
ejpam-3415	16	20	a	a	DET
ejpam-3415	16	21	∧	∧	PROPN
ejpam-3415	16	22	b	b	PROPN
ejpam-3415	16	23	=	=	PROPN
ejpam-3415	16	24	b.	b.	PROPN
ejpam-3415	16	25	in	in	ADP
ejpam-3415	16	26	[	[	X
ejpam-3415	16	27	5	5	NUM
ejpam-3415	16	28	]	]	PUNCT
ejpam-3415	16	29	,	,	PUNCT
ejpam-3415	16	30	immediately	immediately	ADV
ejpam-3415	16	31	after	after	ADP
ejpam-3415	16	32	this	this	DET
ejpam-3415	16	33	definition	definition	NOUN
ejpam-3415	16	34	,	,	PUNCT
ejpam-3415	16	35	the	the	DET
ejpam-3415	16	36	following	follow	VERB
ejpam-3415	16	37	is	be	AUX
ejpam-3415	16	38	written	write	VERB
ejpam-3415	16	39	:	:	PUNCT
ejpam-3415	16	40	“	"	PUNCT
ejpam-3415	16	41	the	the	DET
ejpam-3415	16	42	set	set	NOUN
ejpam-3415	16	43	h	h	NOUN
ejpam-3415	16	44	=	=	SYM
ejpam-3415	16	45	{	{	PUNCT
ejpam-3415	16	46	0	0	NUM
ejpam-3415	16	47	,	,	PUNCT
ejpam-3415	16	48	1	1	NUM
ejpam-3415	16	49	}	}	PUNCT
ejpam-3415	16	50	with	with	ADP
ejpam-3415	16	51	a	a	DET
ejpam-3415	16	52	hyperoperation	hyperoperation	NOUN
ejpam-3415	16	53	0	0	NUM
ejpam-3415	16	54	∨	∨	NOUN
ejpam-3415	16	55	0	0	NUM
ejpam-3415	17	1	=	=	SYM
ejpam-3415	17	2	0	0	NUM
ejpam-3415	17	3	,	,	PUNCT
ejpam-3415	17	4	0	0	NUM
ejpam-3415	17	5	∨	∨	NUM
ejpam-3415	17	6	1	1	NUM
ejpam-3415	17	7	=	=	SYM
ejpam-3415	17	8	1	1	NUM
ejpam-3415	17	9	∨	∨	NUM
ejpam-3415	17	10	0	0	NUM
ejpam-3415	18	1	=	=	SYM
ejpam-3415	18	2	1	1	NUM
ejpam-3415	18	3	,	,	PUNCT
ejpam-3415	18	4	1	1	NUM
ejpam-3415	18	5	∨	∨	NUM
ejpam-3415	18	6	1	1	NUM
ejpam-3415	18	7	=	=	SYM
ejpam-3415	18	8	h	h	NOUN
ejpam-3415	18	9	and	and	CCONJ
ejpam-3415	18	10	an	an	DET
ejpam-3415	18	11	operation	operation	NOUN
ejpam-3415	18	12	0	0	NUM
ejpam-3415	19	1	∧	∧	NOUN
ejpam-3415	19	2	0	0	NUM
ejpam-3415	19	3	=	=	SYM
ejpam-3415	19	4	1	1	NUM
ejpam-3415	19	5	∧	∧	NOUN
ejpam-3415	19	6	0	0	NUM
ejpam-3415	20	1	=	=	SYM
ejpam-3415	20	2	0	0	NUM
ejpam-3415	20	3	∧	∧	NOUN
ejpam-3415	20	4	1	1	NUM
ejpam-3415	20	5	=	=	SYM
ejpam-3415	20	6	0	0	NUM
ejpam-3415	20	7	,	,	PUNCT
ejpam-3415	20	8	1	1	NUM
ejpam-3415	20	9	∧	∧	PROPN
ejpam-3415	20	10	1	1	NUM
ejpam-3415	20	11	=	=	SYM
ejpam-3415	20	12	1	1	NUM
ejpam-3415	20	13	is	be	AUX
ejpam-3415	20	14	a	a	DET
ejpam-3415	20	15	hyperlattice	hyperlattice	NOUN
ejpam-3415	20	16	.	.	PUNCT
ejpam-3415	21	1	respectively	respectively	ADV
ejpam-3415	21	2	,	,	PUNCT
ejpam-3415	21	3	for	for	ADP
ejpam-3415	21	4	0	0	NUM
ejpam-3415	21	5	∨	∨	NUM
ejpam-3415	21	6	0	0	NUM
ejpam-3415	22	1	=	=	SYM
ejpam-3415	22	2	h	h	NOUN
ejpam-3415	22	3	,	,	PUNCT
ejpam-3415	22	4	0	0	NUM
ejpam-3415	22	5	∨	∨	NUM
ejpam-3415	22	6	1	1	NUM
ejpam-3415	22	7	=	=	SYM
ejpam-3415	22	8	1	1	NUM
ejpam-3415	22	9	∨	∨	NUM
ejpam-3415	22	10	0	0	NUM
ejpam-3415	23	1	=	=	SYM
ejpam-3415	23	2	1	1	NUM
ejpam-3415	23	3	∨	∨	NUM
ejpam-3415	23	4	1	1	NUM
ejpam-3415	23	5	=	=	SYM
ejpam-3415	23	6	1	1	NUM
ejpam-3415	23	7	and	and	CCONJ
ejpam-3415	23	8	0	0	NUM
ejpam-3415	24	1	∧	∧	NOUN
ejpam-3415	24	2	0	0	NUM
ejpam-3415	24	3	=	=	SYM
ejpam-3415	24	4	1	1	NUM
ejpam-3415	24	5	∧	∧	NOUN
ejpam-3415	24	6	0	0	NUM
ejpam-3415	25	1	=	=	SYM
ejpam-3415	25	2	0	0	NUM
ejpam-3415	25	3	∧	∧	NOUN
ejpam-3415	25	4	1	1	NUM
ejpam-3415	25	5	=	=	SYM
ejpam-3415	25	6	0	0	NUM
ejpam-3415	25	7	,	,	PUNCT
ejpam-3415	25	8	1	1	NUM
ejpam-3415	25	9	∧	∧	PROPN
ejpam-3415	25	10	1	1	NUM
ejpam-3415	25	11	=	=	SYM
ejpam-3415	25	12	1	1	NUM
ejpam-3415	25	13	.	.	PUNCT
ejpam-3415	25	14	”	"	PUNCT
ejpam-3415	26	1	there	there	PRON
ejpam-3415	26	2	are	be	VERB
ejpam-3415	26	3	two	two	NUM
ejpam-3415	26	4	examples	example	NOUN
ejpam-3415	26	5	here	here	ADV
ejpam-3415	26	6	.	.	PUNCT
ejpam-3415	27	1	as	as	SCONJ
ejpam-3415	27	2	they	they	PRON
ejpam-3415	27	3	are	be	AUX
ejpam-3415	27	4	similar	similar	ADJ
ejpam-3415	27	5	,	,	PUNCT
ejpam-3415	27	6	we	we	PRON
ejpam-3415	27	7	deal	deal	VERB
ejpam-3415	27	8	with	with	ADP
ejpam-3415	27	9	the	the	DET
ejpam-3415	27	10	first	first	ADJ
ejpam-3415	27	11	one	one	NUM
ejpam-3415	27	12	.	.	PUNCT
ejpam-3415	28	1	we	we	PRON
ejpam-3415	28	2	write	write	VERB
ejpam-3415	28	3	a	a	DET
ejpam-3415	28	4	instead	instead	NOUN
ejpam-3415	28	5	of	of	ADP
ejpam-3415	28	6	0	0	NUM
ejpam-3415	28	7	and	and	CCONJ
ejpam-3415	28	8	b	b	NOUN
ejpam-3415	28	9	instead	instead	ADV
ejpam-3415	28	10	of	of	ADP
ejpam-3415	28	11	1	1	NUM
ejpam-3415	28	12	.	.	PUNCT
ejpam-3415	29	1	we	we	PRON
ejpam-3415	29	2	also	also	ADV
ejpam-3415	29	3	correct	correct	VERB
ejpam-3415	29	4	it	it	PRON
ejpam-3415	29	5	somehow	somehow	ADV
ejpam-3415	29	6	by	by	ADP
ejpam-3415	29	7	writing	write	VERB
ejpam-3415	29	8	a	a	DET
ejpam-3415	29	9	∨	∨	NOUN
ejpam-3415	29	10	a	a	DET
ejpam-3415	29	11	=	=	X
ejpam-3415	29	12	{	{	PUNCT
ejpam-3415	29	13	a	a	NOUN
ejpam-3415	29	14	}	}	PUNCT
ejpam-3415	29	15	,	,	PUNCT
ejpam-3415	29	16	a	a	DET
ejpam-3415	29	17	∨	∨	NUM
ejpam-3415	29	18	b	b	X
ejpam-3415	29	19	=	=	SYM
ejpam-3415	29	20	b	b	PROPN
ejpam-3415	29	21	∨	∨	NUM
ejpam-3415	29	22	a	a	PRON
ejpam-3415	29	23	=	=	X
ejpam-3415	29	24	{	{	PUNCT
ejpam-3415	29	25	b	b	NOUN
ejpam-3415	29	26	}	}	PUNCT
ejpam-3415	29	27	as	as	SCONJ
ejpam-3415	29	28	can	can	AUX
ejpam-3415	29	29	not	not	PART
ejpam-3415	29	30	be	be	AUX
ejpam-3415	29	31	a	a	DET
ejpam-3415	29	32	∨	∨	NOUN
ejpam-3415	29	33	a	a	DET
ejpam-3415	29	34	=	=	SYM
ejpam-3415	29	35	a	a	NOUN
ejpam-3415	29	36	,	,	PUNCT
ejpam-3415	29	37	a	a	DET
ejpam-3415	29	38	∨	∨	NUM
ejpam-3415	29	39	b	b	NOUN
ejpam-3415	29	40	=	=	SYM
ejpam-3415	29	41	b	b	PROPN
ejpam-3415	29	42	,	,	PUNCT
ejpam-3415	29	43	b	b	PROPN
ejpam-3415	29	44	∨	∨	NUM
ejpam-3415	29	45	a	a	DET
ejpam-3415	29	46	=	=	X
ejpam-3415	29	47	b.	b.	PROPN
ejpam-3415	29	48	there	there	PRON
ejpam-3415	29	49	is	be	VERB
ejpam-3415	29	50	no	no	DET
ejpam-3415	29	51	mention	mention	NOUN
ejpam-3415	29	52	in	in	ADP
ejpam-3415	29	53	the	the	DET
ejpam-3415	29	54	paper	paper	NOUN
ejpam-3415	29	55	of	of	ADP
ejpam-3415	29	56	identifying	identify	VERB
ejpam-3415	29	57	the	the	DET
ejpam-3415	29	58	{	{	PUNCT
ejpam-3415	29	59	a	a	NOUN
ejpam-3415	29	60	}	}	PUNCT
ejpam-3415	29	61	by	by	ADP
ejpam-3415	29	62	a.	a.	NOUN
ejpam-3415	29	63	thus	thus	ADV
ejpam-3415	29	64	this	this	DET
ejpam-3415	29	65	example	example	NOUN
ejpam-3415	29	66	in	in	ADP
ejpam-3415	29	67	[	[	X
ejpam-3415	29	68	5	5	NUM
ejpam-3415	29	69	]	]	PUNCT
ejpam-3415	29	70	is	be	AUX
ejpam-3415	29	71	the	the	DET
ejpam-3415	29	72	following	follow	VERB
ejpam-3415	29	73	example	example	NOUN
ejpam-3415	29	74	.	.	PUNCT
ejpam-3415	30	1	example	example	NOUN
ejpam-3415	30	2	1.2	1.2	NUM
ejpam-3415	30	3	the	the	DET
ejpam-3415	30	4	set	set	ADJ
ejpam-3415	30	5	h	h	NOUN
ejpam-3415	30	6	=	=	PUNCT
ejpam-3415	30	7	{	{	PUNCT
ejpam-3415	30	8	a	a	DET
ejpam-3415	30	9	,	,	PUNCT
ejpam-3415	30	10	b	b	NOUN
ejpam-3415	30	11	}	}	PUNCT
ejpam-3415	30	12	with	with	ADP
ejpam-3415	30	13	the	the	DET
ejpam-3415	30	14	operation	operation	NOUN
ejpam-3415	30	15	and	and	CCONJ
ejpam-3415	30	16	the	the	DET
ejpam-3415	30	17	hyperoperation	hyperoperation	NOUN
ejpam-3415	30	18	defined	define	VERB
ejpam-3415	30	19	by	by	ADP
ejpam-3415	30	20	table	table	NOUN
ejpam-3415	30	21	1	1	NUM
ejpam-3415	30	22	is	be	AUX
ejpam-3415	30	23	a	a	DET
ejpam-3415	30	24	hyperlattice	hyperlattice	NOUN
ejpam-3415	30	25	.	.	PUNCT
ejpam-3415	31	1	table	table	NOUN
ejpam-3415	31	2	1	1	NUM
ejpam-3415	31	3	:	:	PUNCT
ejpam-3415	31	4	the	the	DET
ejpam-3415	31	5	operation	operation	NOUN
ejpam-3415	31	6	and	and	CCONJ
ejpam-3415	31	7	the	the	DET
ejpam-3415	31	8	hyperoperation	hyperoperation	NOUN
ejpam-3415	31	9	of	of	ADP
ejpam-3415	31	10	the	the	DET
ejpam-3415	31	11	example	example	NOUN
ejpam-3415	31	12	1.2	1.2	NUM
ejpam-3415	31	13	.	.	PUNCT
ejpam-3415	32	1	∧	∧	NOUN
ejpam-3415	32	2	a	a	DET
ejpam-3415	32	3	b	b	NOUN
ejpam-3415	32	4	a	a	DET
ejpam-3415	32	5	a	a	DET
ejpam-3415	32	6	a	a	DET
ejpam-3415	32	7	b	b	NOUN
ejpam-3415	32	8	a	a	DET
ejpam-3415	32	9	b	b	PROPN
ejpam-3415	32	10	(	(	PUNCT
ejpam-3415	32	11	a	a	NOUN
ejpam-3415	32	12	)	)	PUNCT
ejpam-3415	32	13	∨	∨	NOUN
ejpam-3415	32	14	a	a	DET
ejpam-3415	32	15	b	b	NOUN
ejpam-3415	32	16	a	a	DET
ejpam-3415	32	17	{	{	PUNCT
ejpam-3415	32	18	a	a	NOUN
ejpam-3415	32	19	}	}	PUNCT
ejpam-3415	32	20	{	{	PUNCT
ejpam-3415	32	21	b	b	NOUN
ejpam-3415	32	22	}	}	PUNCT
ejpam-3415	32	23	b	b	PROPN
ejpam-3415	32	24	{	{	PUNCT
ejpam-3415	32	25	b	b	NOUN
ejpam-3415	32	26	}	}	PUNCT
ejpam-3415	32	27	{	{	PUNCT
ejpam-3415	32	28	a	a	DET
ejpam-3415	32	29	,	,	PUNCT
ejpam-3415	32	30	b	b	NOUN
ejpam-3415	32	31	}	}	PUNCT
ejpam-3415	32	32	(	(	PUNCT
ejpam-3415	32	33	b	b	NOUN
ejpam-3415	32	34	)	)	PUNCT
ejpam-3415	32	35	to	to	PART
ejpam-3415	32	36	show	show	VERB
ejpam-3415	32	37	that	that	SCONJ
ejpam-3415	32	38	this	this	PRON
ejpam-3415	32	39	is	be	AUX
ejpam-3415	32	40	a	a	DET
ejpam-3415	32	41	hyperlattice	hyperlattice	NOUN
ejpam-3415	32	42	,	,	PUNCT
ejpam-3415	32	43	we	we	PRON
ejpam-3415	32	44	must	must	AUX
ejpam-3415	32	45	show	show	VERB
ejpam-3415	32	46	that	that	SCONJ
ejpam-3415	32	47	a	a	DET
ejpam-3415	32	48	∈	∈	PROPN
ejpam-3415	32	49	a∧	a∧	NOUN
ejpam-3415	32	50	(	(	PUNCT
ejpam-3415	32	51	a∨	a∨	PROPN
ejpam-3415	32	52	b	b	PROPN
ejpam-3415	32	53	)	)	PUNCT
ejpam-3415	32	54	and	and	CCONJ
ejpam-3415	32	55	(	(	PUNCT
ejpam-3415	32	56	a∨	a∨	PROPN
ejpam-3415	32	57	b)∨	b)∨	PROPN
ejpam-3415	32	58	c	c	NOUN
ejpam-3415	32	59	=	=	PUNCT
ejpam-3415	32	60	a	a	DET
ejpam-3415	32	61	∨	∨	NOUN
ejpam-3415	32	62	(	(	PUNCT
ejpam-3415	32	63	b	b	PROPN
ejpam-3415	32	64	∨	∨	NUM
ejpam-3415	32	65	c	c	NOUN
ejpam-3415	32	66	)	)	PUNCT
ejpam-3415	32	67	for	for	ADP
ejpam-3415	32	68	all	all	DET
ejpam-3415	32	69	a	a	DET
ejpam-3415	32	70	,	,	PUNCT
ejpam-3415	32	71	b	b	NOUN
ejpam-3415	32	72	,	,	PUNCT
ejpam-3415	32	73	c	c	PROPN
ejpam-3415	32	74	∈	∈	PROPN
ejpam-3415	32	75	h.	h.	PROPN
ejpam-3415	32	76	according	accord	VERB
ejpam-3415	32	77	to	to	ADP
ejpam-3415	32	78	table	table	NOUN
ejpam-3415	32	79	1	1	NUM
ejpam-3415	32	80	,	,	PUNCT
ejpam-3415	32	81	we	we	PRON
ejpam-3415	32	82	have	have	VERB
ejpam-3415	32	83	a	a	DET
ejpam-3415	32	84	∧	∧	NOUN
ejpam-3415	32	85	(	(	PUNCT
ejpam-3415	32	86	a	a	DET
ejpam-3415	32	87	∨	∨	NUM
ejpam-3415	32	88	b	b	NOUN
ejpam-3415	32	89	)	)	PUNCT
ejpam-3415	32	90	=	=	PUNCT
ejpam-3415	32	91	a	a	DET
ejpam-3415	32	92	∧	∧	PROPN
ejpam-3415	32	93	{	{	PUNCT
ejpam-3415	32	94	b	b	NOUN
ejpam-3415	32	95	}	}	PUNCT
ejpam-3415	32	96	,	,	PUNCT
ejpam-3415	32	97	but	but	CCONJ
ejpam-3415	32	98	the	the	DET
ejpam-3415	32	99	a∧{b	a∧{b	NOUN
ejpam-3415	32	100	}	}	PUNCT
ejpam-3415	32	101	has	have	VERB
ejpam-3415	32	102	no	no	DET
ejpam-3415	32	103	sense	sense	NOUN
ejpam-3415	32	104	.	.	PUNCT
ejpam-3415	33	1	the	the	DET
ejpam-3415	33	2	associativity	associativity	NOUN
ejpam-3415	33	3	of	of	ADP
ejpam-3415	33	4	the	the	DET
ejpam-3415	33	5	hyperoperation	hyperoperation	NOUN
ejpam-3415	33	6	“	"	PUNCT
ejpam-3415	33	7	∨	∨	NOUN
ejpam-3415	33	8	”	"	PUNCT
ejpam-3415	33	9	has	have	VERB
ejpam-3415	33	10	no	no	DET
ejpam-3415	33	11	sense	sense	NOUN
ejpam-3415	33	12	as	as	ADV
ejpam-3415	33	13	well	well	ADV
ejpam-3415	33	14	.	.	PUNCT
ejpam-3415	34	1	so	so	ADV
ejpam-3415	34	2	the	the	DET
ejpam-3415	34	3	table	table	NOUN
ejpam-3415	34	4	1	1	NUM
ejpam-3415	34	5	can	can	AUX
ejpam-3415	34	6	not	not	PART
ejpam-3415	34	7	define	define	VERB
ejpam-3415	34	8	a	a	DET
ejpam-3415	34	9	hyperlattice	hyperlattice	NOUN
ejpam-3415	34	10	.	.	PUNCT
ejpam-3415	35	1	according	accord	VERB
ejpam-3415	35	2	[	[	X
ejpam-3415	35	3	4	4	NUM
ejpam-3415	35	4	;	;	PUNCT
ejpam-3415	35	5	remark	remark	NOUN
ejpam-3415	35	6	1(a	1(a	NUM
ejpam-3415	35	7	)	)	PUNCT
ejpam-3415	35	8	]	]	PUNCT
ejpam-3415	35	9	,	,	PUNCT
ejpam-3415	35	10	the	the	DET
ejpam-3415	35	11	definition	definition	NOUN
ejpam-3415	35	12	1.1	1.1	NUM
ejpam-3415	35	13	implies	imply	VERB
ejpam-3415	35	14	that	that	SCONJ
ejpam-3415	35	15	each	each	DET
ejpam-3415	35	16	lattice	lattice	NOUN
ejpam-3415	35	17	is	be	AUX
ejpam-3415	35	18	a	a	DET
ejpam-3415	35	19	hyperlattice	hyperlattice	NOUN
ejpam-3415	35	20	.	.	PUNCT
ejpam-3415	36	1	this	this	PRON
ejpam-3415	36	2	,	,	PUNCT
ejpam-3415	36	3	stated	state	VERB
ejpam-3415	36	4	without	without	ADP
ejpam-3415	36	5	proof	proof	NOUN
ejpam-3415	36	6	in	in	ADP
ejpam-3415	36	7	[	[	X
ejpam-3415	36	8	4	4	NUM
ejpam-3415	36	9	]	]	PUNCT
ejpam-3415	36	10	,	,	PUNCT
ejpam-3415	36	11	can	can	AUX
ejpam-3415	36	12	not	not	PART
ejpam-3415	36	13	be	be	AUX
ejpam-3415	36	14	proved	prove	VERB
ejpam-3415	36	15	by	by	ADP
ejpam-3415	36	16	the	the	DET
ejpam-3415	36	17	definition	definition	NOUN
ejpam-3415	36	18	1.1	1.1	NUM
ejpam-3415	36	19	as	as	SCONJ
ejpam-3415	36	20	this	this	DET
ejpam-3415	36	21	definition	definition	NOUN
ejpam-3415	36	22	has	have	VERB
ejpam-3415	36	23	no	no	DET
ejpam-3415	36	24	sense	sense	NOUN
ejpam-3415	36	25	.	.	PUNCT
ejpam-3415	37	1	as	as	SCONJ
ejpam-3415	37	2	we	we	PRON
ejpam-3415	37	3	see	see	VERB
ejpam-3415	37	4	in	in	ADP
ejpam-3415	37	5	proposition	proposition	NOUN
ejpam-3415	37	6	2.5	2.5	NUM
ejpam-3415	37	7	of	of	ADP
ejpam-3415	37	8	the	the	DET
ejpam-3415	37	9	present	present	ADJ
ejpam-3415	37	10	paper	paper	NOUN
ejpam-3415	37	11	,	,	PUNCT
ejpam-3415	37	12	this	this	PRON
ejpam-3415	37	13	is	be	AUX
ejpam-3415	37	14	true	true	ADJ
ejpam-3415	37	15	.	.	PUNCT
ejpam-3415	38	1	the	the	DET
ejpam-3415	38	2	modular	modular	ADJ
ejpam-3415	38	3	and	and	CCONJ
ejpam-3415	38	4	distributive	distributive	ADJ
ejpam-3415	38	5	hyperlattices	hyperlattice	NOUN
ejpam-3415	38	6	have	have	AUX
ejpam-3415	38	7	been	be	AUX
ejpam-3415	38	8	defined	define	VERB
ejpam-3415	38	9	in	in	ADP
ejpam-3415	38	10	[	[	X
ejpam-3415	38	11	5	5	NUM
ejpam-3415	38	12	]	]	PUNCT
ejpam-3415	38	13	and	and	CCONJ
ejpam-3415	38	14	[	[	X
ejpam-3415	38	15	6	6	NUM
ejpam-3415	38	16	]	]	PUNCT
ejpam-3415	38	17	,	,	PUNCT
ejpam-3415	38	18	respectively	respectively	ADV
ejpam-3415	38	19	,	,	PUNCT
ejpam-3415	38	20	as	as	SCONJ
ejpam-3415	38	21	follows	follow	VERB
ejpam-3415	38	22	:	:	PUNCT
ejpam-3415	38	23	“	"	PUNCT
ejpam-3415	38	24	a	a	DET
ejpam-3415	38	25	hyperlattice	hyperlattice	NOUN
ejpam-3415	38	26	l	l	NOUN
ejpam-3415	38	27	is	be	AUX
ejpam-3415	38	28	said	say	VERB
ejpam-3415	38	29	to	to	PART
ejpam-3415	38	30	be	be	AUX
ejpam-3415	38	31	modular	modular	ADJ
ejpam-3415	38	32	if	if	SCONJ
ejpam-3415	38	33	a	a	DET
ejpam-3415	38	34	≤	≤	NUM
ejpam-3415	38	35	b	b	NOUN
ejpam-3415	38	36	⇒	⇒	NOUN
ejpam-3415	38	37	a∨(c∧b	a∨(c∧b	NOUN
ejpam-3415	38	38	)	)	PUNCT
ejpam-3415	38	39	=	=	SYM
ejpam-3415	38	40	(	(	PUNCT
ejpam-3415	38	41	a∨c)∧b	a∨c)∧b	NOUN
ejpam-3415	38	42	for	for	ADP
ejpam-3415	38	43	any	any	DET
ejpam-3415	38	44	c	c	PROPN
ejpam-3415	38	45	∈	∈	PROPN
ejpam-3415	38	46	h	h	NOUN
ejpam-3415	38	47	(	(	PUNCT
ejpam-3415	38	48	as	as	ADP
ejpam-3415	38	49	in	in	ADP
ejpam-3415	38	50	the	the	DET
ejpam-3415	38	51	case	case	NOUN
ejpam-3415	38	52	of	of	ADP
ejpam-3415	38	53	lattices	lattice	NOUN
ejpam-3415	38	54	)	)	PUNCT
ejpam-3415	38	55	.	.	PUNCT
ejpam-3415	39	1	a	a	DET
ejpam-3415	39	2	hyperlattice	hyperlattice	NOUN
ejpam-3415	39	3	l	l	NOUN
ejpam-3415	39	4	is	be	AUX
ejpam-3415	39	5	said	say	VERB
ejpam-3415	39	6	to	to	PART
ejpam-3415	39	7	be	be	AUX
ejpam-3415	39	8	distributive	distributive	ADJ
ejpam-3415	39	9	if	if	SCONJ
ejpam-3415	39	10	a	a	DET
ejpam-3415	39	11	∧	∧	PROPN
ejpam-3415	39	12	(	(	PUNCT
ejpam-3415	39	13	b	b	PROPN
ejpam-3415	39	14	∨	∨	NUM
ejpam-3415	39	15	c	c	NOUN
ejpam-3415	39	16	)	)	PUNCT
ejpam-3415	39	17	=	=	NOUN
ejpam-3415	39	18	(	(	PUNCT
ejpam-3415	39	19	a	a	DET
ejpam-3415	39	20	∧	∧	PROPN
ejpam-3415	39	21	b	b	PROPN
ejpam-3415	39	22	)	)	PUNCT
ejpam-3415	39	23	∨	∨	NOUN
ejpam-3415	39	24	(	(	PUNCT
ejpam-3415	39	25	a	a	DET
ejpam-3415	39	26	∧	∧	PROPN
ejpam-3415	39	27	c	c	NOUN
ejpam-3415	39	28	)	)	PUNCT
ejpam-3415	39	29	for	for	ADP
ejpam-3415	39	30	every	every	DET
ejpam-3415	39	31	a	a	DET
ejpam-3415	39	32	,	,	PUNCT
ejpam-3415	39	33	b	b	NOUN
ejpam-3415	39	34	,	,	PUNCT
ejpam-3415	39	35	c	c	PROPN
ejpam-3415	39	36	∈	∈	PROPN
ejpam-3415	39	37	l.	l.	PROPN
ejpam-3415	39	38	”	"	PUNCT
ejpam-3415	39	39	this	this	PRON
ejpam-3415	39	40	is	be	AUX
ejpam-3415	39	41	the	the	DET
ejpam-3415	39	42	remark	remark	NOUN
ejpam-3415	39	43	1	1	NUM
ejpam-3415	39	44	in	in	ADP
ejpam-3415	39	45	[	[	X
ejpam-3415	39	46	5	5	NUM
ejpam-3415	39	47	]	]	PUNCT
ejpam-3415	39	48	:	:	PUNCT
ejpam-3415	39	49	“	"	PUNCT
ejpam-3415	39	50	obviously	obviously	ADV
ejpam-3415	39	51	,	,	PUNCT
ejpam-3415	39	52	in	in	ADP
ejpam-3415	39	53	every	every	DET
ejpam-3415	39	54	modular	modular	ADJ
ejpam-3415	39	55	hyperlattice	hyperlattice	NOUN
ejpam-3415	39	56	we	we	PRON
ejpam-3415	39	57	have	have	VERB
ejpam-3415	39	58	a	a	DET
ejpam-3415	39	59	∨	∨	NOUN
ejpam-3415	39	60	(	(	PUNCT
ejpam-3415	39	61	b	b	PROPN
ejpam-3415	39	62	∧	∧	PROPN
ejpam-3415	39	63	a	a	NOUN
ejpam-3415	39	64	)	)	PUNCT
ejpam-3415	39	65	=	=	SYM
ejpam-3415	39	66	(	(	PUNCT
ejpam-3415	39	67	a	a	DET
ejpam-3415	39	68	∨	∨	NUM
ejpam-3415	39	69	b	b	NOUN
ejpam-3415	39	70	)	)	PUNCT
ejpam-3415	39	71	∧	∧	PROPN
ejpam-3415	39	72	a.	a.	NOUN
ejpam-3415	39	73	”	"	PUNCT
ejpam-3415	39	74	this	this	PRON
ejpam-3415	39	75	being	be	AUX
ejpam-3415	39	76	obvious	obvious	ADJ
ejpam-3415	39	77	for	for	ADP
ejpam-3415	39	78	lattices	lattice	NOUN
ejpam-3415	39	79	,	,	PUNCT
ejpam-3415	39	80	can	can	AUX
ejpam-3415	39	81	not	not	PART
ejpam-3415	39	82	be	be	AUX
ejpam-3415	39	83	proved	prove	VERB
ejpam-3415	39	84	by	by	ADP
ejpam-3415	39	85	the	the	DET
ejpam-3415	39	86	definition	definition	NOUN
ejpam-3415	39	87	of	of	ADP
ejpam-3415	39	88	modular	modular	ADJ
ejpam-3415	39	89	hyperlattices	hyperlattice	NOUN
ejpam-3415	39	90	given	give	VERB
ejpam-3415	39	91	in	in	ADP
ejpam-3415	39	92	[	[	X
ejpam-3415	39	93	5	5	NUM
ejpam-3415	39	94	]	]	PUNCT
ejpam-3415	39	95	.	.	PUNCT
ejpam-3415	40	1	as	as	SCONJ
ejpam-3415	40	2	we	we	PRON
ejpam-3415	40	3	will	will	AUX
ejpam-3415	40	4	see	see	VERB
ejpam-3415	40	5	later	later	ADV
ejpam-3415	40	6	in	in	ADP
ejpam-3415	40	7	section	section	NOUN
ejpam-3415	40	8	4	4	NUM
ejpam-3415	40	9	,	,	PUNCT
ejpam-3415	40	10	in	in	ADP
ejpam-3415	40	11	a	a	DET
ejpam-3415	40	12	modular	modular	ADJ
ejpam-3415	40	13	niovi	niovi	NOUN
ejpam-3415	40	14	kehayopulu	kehayopulu	ADJ
ejpam-3415	40	15	/	/	SYM
ejpam-3415	40	16	eur	eur	PROPN
ejpam-3415	40	17	.	.	PUNCT
ejpam-3415	41	1	j.	j.	PROPN
ejpam-3415	41	2	pure	pure	PROPN
ejpam-3415	41	3	appl	appl	PROPN
ejpam-3415	41	4	.	.	PROPN
ejpam-3415	41	5	math	math	PROPN
ejpam-3415	41	6	,	,	PUNCT
ejpam-3415	41	7	12	12	NUM
ejpam-3415	41	8	(	(	PUNCT
ejpam-3415	41	9	2	2	NUM
ejpam-3415	41	10	)	)	PUNCT
ejpam-3415	41	11	(	(	PUNCT
ejpam-3415	41	12	2019	2019	NUM
ejpam-3415	41	13	)	)	PUNCT
ejpam-3415	41	14	,	,	PUNCT
ejpam-3415	41	15	252	252	NUM
ejpam-3415	41	16	-	-	SYM
ejpam-3415	41	17	269	269	NUM
ejpam-3415	41	18	254	254	NUM
ejpam-3415	41	19	hyperlattice	hyperlattice	NOUN
ejpam-3415	41	20	we	we	PRON
ejpam-3415	41	21	have	have	VERB
ejpam-3415	41	22	{	{	PUNCT
ejpam-3415	41	23	v∧a	v∧a	NOUN
ejpam-3415	41	24	|	|	ADV
ejpam-3415	41	25	v	v	NOUN
ejpam-3415	41	26	∈	∈	PROPN
ejpam-3415	41	27	a∨	a∨	PROPN
ejpam-3415	41	28	b	b	PROPN
ejpam-3415	41	29	}	}	PUNCT
ejpam-3415	41	30	=	=	SYM
ejpam-3415	41	31	a∨	a∨	PROPN
ejpam-3415	41	32	(	(	PUNCT
ejpam-3415	41	33	b∧a	b∧a	ADV
ejpam-3415	41	34	)	)	PUNCT
ejpam-3415	41	35	;	;	PUNCT
ejpam-3415	41	36	and	and	CCONJ
ejpam-3415	41	37	if	if	SCONJ
ejpam-3415	41	38	for	for	ADP
ejpam-3415	41	39	the	the	DET
ejpam-3415	41	40	set	set	NOUN
ejpam-3415	41	41	{	{	PUNCT
ejpam-3415	41	42	v∧a	v∧a	NOUN
ejpam-3415	41	43	|	|	ADV
ejpam-3415	41	44	v	v	NOUN
ejpam-3415	41	45	∈	∈	PROPN
ejpam-3415	41	46	a∨	a∨	PROPN
ejpam-3415	41	47	b	b	PROPN
ejpam-3415	41	48	}	}	PUNCT
ejpam-3415	41	49	we	we	PRON
ejpam-3415	41	50	use	use	VERB
ejpam-3415	41	51	the	the	DET
ejpam-3415	41	52	notation	notation	NOUN
ejpam-3415	41	53	(	(	PUNCT
ejpam-3415	41	54	a	a	DET
ejpam-3415	41	55	∨	∨	PROPN
ejpam-3415	41	56	b	b	NOUN
ejpam-3415	41	57	)	)	PUNCT
ejpam-3415	41	58	∧	∧	PROPN
ejpam-3415	41	59	a	a	PROPN
ejpam-3415	41	60	,	,	PUNCT
ejpam-3415	41	61	then	then	ADV
ejpam-3415	41	62	we	we	PRON
ejpam-3415	41	63	can	can	AUX
ejpam-3415	41	64	say	say	VERB
ejpam-3415	41	65	that	that	SCONJ
ejpam-3415	41	66	in	in	ADP
ejpam-3415	41	67	a	a	DET
ejpam-3415	41	68	modular	modular	ADJ
ejpam-3415	41	69	hyperlattice	hyperlattice	NOUN
ejpam-3415	41	70	the	the	DET
ejpam-3415	41	71	property	property	NOUN
ejpam-3415	41	72	a	a	DET
ejpam-3415	41	73	∨	∨	NOUN
ejpam-3415	41	74	(	(	PUNCT
ejpam-3415	41	75	b	b	PROPN
ejpam-3415	41	76	∧	∧	PROPN
ejpam-3415	41	77	a	a	NOUN
ejpam-3415	41	78	)	)	PUNCT
ejpam-3415	41	79	=	=	SYM
ejpam-3415	41	80	(	(	PUNCT
ejpam-3415	41	81	a	a	DET
ejpam-3415	41	82	∨	∨	NUM
ejpam-3415	41	83	b	b	NOUN
ejpam-3415	41	84	)	)	PUNCT
ejpam-3415	41	85	∧	∧	NOUN
ejpam-3415	41	86	a	a	DET
ejpam-3415	41	87	holds	hold	NOUN
ejpam-3415	41	88	.	.	PUNCT
ejpam-3415	42	1	after	after	ADP
ejpam-3415	42	2	this	this	DET
ejpam-3415	42	3	remark	remark	NOUN
ejpam-3415	42	4	,	,	PUNCT
ejpam-3415	42	5	there	there	PRON
ejpam-3415	42	6	is	be	VERB
ejpam-3415	42	7	the	the	DET
ejpam-3415	42	8	example	example	NOUN
ejpam-3415	42	9	2(a	2(a	NUM
ejpam-3415	42	10	)	)	PUNCT
ejpam-3415	42	11	in	in	ADP
ejpam-3415	42	12	[	[	X
ejpam-3415	42	13	5	5	NUM
ejpam-3415	42	14	]	]	PUNCT
ejpam-3415	42	15	.	.	PUNCT
ejpam-3415	43	1	it	it	PRON
ejpam-3415	43	2	is	be	AUX
ejpam-3415	43	3	no	no	ADV
ejpam-3415	43	4	clear	clear	ADJ
ejpam-3415	43	5	what	what	PRON
ejpam-3415	43	6	“	"	PUNCT
ejpam-3415	43	7	the	the	DET
ejpam-3415	43	8	obvious	obvious	ADJ
ejpam-3415	43	9	operation	operation	NOUN
ejpam-3415	43	10	”	"	PUNCT
ejpam-3415	43	11	in	in	ADP
ejpam-3415	43	12	this	this	DET
ejpam-3415	43	13	example	example	NOUN
ejpam-3415	43	14	means	mean	VERB
ejpam-3415	43	15	.	.	PUNCT
ejpam-3415	44	1	in	in	ADP
ejpam-3415	44	2	the	the	DET
ejpam-3415	44	3	example	example	NOUN
ejpam-3415	44	4	2(b	2(b	NUM
ejpam-3415	44	5	)	)	PUNCT
ejpam-3415	44	6	,	,	PUNCT
ejpam-3415	44	7	the	the	DET
ejpam-3415	44	8	b	b	PROPN
ejpam-3415	44	9	∧	∧	PROPN
ejpam-3415	44	10	b	b	PROPN
ejpam-3415	44	11	and	and	CCONJ
ejpam-3415	44	12	c	c	PROPN
ejpam-3415	44	13	∧	∧	PROPN
ejpam-3415	44	14	c	c	PROPN
ejpam-3415	44	15	are	be	AUX
ejpam-3415	44	16	missing	miss	VERB
ejpam-3415	44	17	.	.	PUNCT
ejpam-3415	45	1	later	later	ADV
ejpam-3415	45	2	konstantinidou	konstantinidou	PROPN
ejpam-3415	45	3	and	and	CCONJ
ejpam-3415	45	4	serafimidis	serafimidi	NOUN
ejpam-3415	45	5	changed	change	VERB
ejpam-3415	45	6	the	the	DET
ejpam-3415	45	7	property	property	NOUN
ejpam-3415	45	8	(	(	PUNCT
ejpam-3415	45	9	5	5	NUM
ejpam-3415	45	10	)	)	PUNCT
ejpam-3415	45	11	of	of	ADP
ejpam-3415	45	12	definition	definition	NOUN
ejpam-3415	45	13	1.1	1.1	NUM
ejpam-3415	45	14	and	and	CCONJ
ejpam-3415	45	15	wrote	write	VERB
ejpam-3415	45	16	“	"	PUNCT
ejpam-3415	45	17	a	a	DET
ejpam-3415	45	18	∈	∈	PROPN
ejpam-3415	45	19	a∨	a∨	PROPN
ejpam-3415	45	20	b	b	PROPN
ejpam-3415	45	21	⇔	⇔	PROPN
ejpam-3415	45	22	a∧	a∧	PROPN
ejpam-3415	45	23	b	b	PROPN
ejpam-3415	45	24	=	=	SYM
ejpam-3415	45	25	b	b	PROPN
ejpam-3415	45	26	”	"	PUNCT
ejpam-3415	45	27	instead	instead	ADV
ejpam-3415	45	28	of	of	ADP
ejpam-3415	45	29	“	"	PUNCT
ejpam-3415	45	30	a	a	DET
ejpam-3415	45	31	∈	∈	PROPN
ejpam-3415	45	32	a∨	a∨	PROPN
ejpam-3415	45	33	b	b	PROPN
ejpam-3415	45	34	⇒	⇒	PROPN
ejpam-3415	45	35	a∧	a∧	NOUN
ejpam-3415	45	36	b	b	PROPN
ejpam-3415	45	37	=	=	SYM
ejpam-3415	45	38	b	b	NOUN
ejpam-3415	45	39	”	"	PUNCT
ejpam-3415	45	40	[	[	X
ejpam-3415	45	41	7	7	NUM
ejpam-3415	45	42	]	]	PUNCT
ejpam-3415	45	43	(	(	PUNCT
ejpam-3415	45	44	the	the	DET
ejpam-3415	45	45	“	"	PUNCT
ejpam-3415	45	46	⇐	⇐	ADJ
ejpam-3415	45	47	-part	-part	NOUN
ejpam-3415	45	48	”	"	PUNCT
ejpam-3415	45	49	being	be	AUX
ejpam-3415	45	50	a	a	DET
ejpam-3415	45	51	consequence	consequence	NOUN
ejpam-3415	45	52	of	of	ADP
ejpam-3415	45	53	definition	definition	NOUN
ejpam-3415	45	54	1.1	1.1	NUM
ejpam-3415	45	55	,	,	PUNCT
ejpam-3415	45	56	should	should	AUX
ejpam-3415	45	57	be	be	AUX
ejpam-3415	45	58	omitted	omit	VERB
ejpam-3415	45	59	from	from	ADP
ejpam-3415	45	60	the	the	DET
ejpam-3415	45	61	definition	definition	NOUN
ejpam-3415	45	62	)	)	PUNCT
ejpam-3415	45	63	.	.	PUNCT
ejpam-3415	46	1	they	they	PRON
ejpam-3415	46	2	also	also	ADV
ejpam-3415	46	3	defined	define	VERB
ejpam-3415	46	4	the	the	DET
ejpam-3415	46	5	concepts	concept	NOUN
ejpam-3415	46	6	of	of	ADP
ejpam-3415	46	7	∧-distributive	∧-distributive	ADJ
ejpam-3415	46	8	and	and	CCONJ
ejpam-3415	46	9	∨-distributive	∨-distributive	ADJ
ejpam-3415	46	10	hyperlattices	hyperlattice	NOUN
ejpam-3415	46	11	as	as	ADP
ejpam-3415	46	12	the	the	DET
ejpam-3415	46	13	hyperlattices	hyperlattice	NOUN
ejpam-3415	46	14	in	in	ADP
ejpam-3415	46	15	which	which	PRON
ejpam-3415	46	16	the	the	DET
ejpam-3415	46	17	properties	property	NOUN
ejpam-3415	46	18	(	(	PUNCT
ejpam-3415	46	19	a∨b)∧c	a∨b)∧c	PROPN
ejpam-3415	46	20	⊆	⊆	NUM
ejpam-3415	46	21	(	(	PUNCT
ejpam-3415	46	22	a∧c)∨(b∧c	a∧c)∨(b∧c	PROPN
ejpam-3415	46	23	)	)	PUNCT
ejpam-3415	46	24	and	and	CCONJ
ejpam-3415	46	25	(	(	PUNCT
ejpam-3415	46	26	a∧b)∨c	a∧b)∨c	NOUN
ejpam-3415	46	27	⊆	⊆	NUM
ejpam-3415	46	28	(	(	PUNCT
ejpam-3415	46	29	a∨c)∧(b∨c	a∨c)∧(b∨c	NUM
ejpam-3415	46	30	)	)	PUNCT
ejpam-3415	46	31	,	,	PUNCT
ejpam-3415	46	32	respectively	respectively	ADV
ejpam-3415	46	33	hold	hold	VERB
ejpam-3415	46	34	.	.	PUNCT
ejpam-3415	47	1	some	some	DET
ejpam-3415	47	2	authors	author	NOUN
ejpam-3415	47	3	consider	consider	VERB
ejpam-3415	47	4	only	only	ADV
ejpam-3415	47	5	the	the	DET
ejpam-3415	47	6	properties	property	NOUN
ejpam-3415	47	7	(	(	PUNCT
ejpam-3415	47	8	1)–(4	1)–(4	NUM
ejpam-3415	47	9	)	)	PUNCT
ejpam-3415	47	10	as	as	ADP
ejpam-3415	47	11	the	the	DET
ejpam-3415	47	12	definition	definition	NOUN
ejpam-3415	47	13	of	of	ADP
ejpam-3415	47	14	the	the	DET
ejpam-3415	47	15	hyperlattice	hyperlattice	NOUN
ejpam-3415	47	16	and	and	CCONJ
ejpam-3415	47	17	study	study	NOUN
ejpam-3415	47	18	hyperlattices	hyperlattice	NOUN
ejpam-3415	47	19	having	have	VERB
ejpam-3415	47	20	the	the	DET
ejpam-3415	47	21	property	property	NOUN
ejpam-3415	47	22	(	(	PUNCT
ejpam-3415	47	23	5	5	NUM
ejpam-3415	47	24	)	)	PUNCT
ejpam-3415	47	25	as	as	ADP
ejpam-3415	47	26	an	an	DET
ejpam-3415	47	27	additional	additional	ADJ
ejpam-3415	47	28	property	property	NOUN
ejpam-3415	47	29	.	.	PUNCT
ejpam-3415	48	1	trying	try	VERB
ejpam-3415	48	2	to	to	PART
ejpam-3415	48	3	transfer	transfer	VERB
ejpam-3415	48	4	the	the	DET
ejpam-3415	48	5	definition	definition	NOUN
ejpam-3415	48	6	of	of	ADP
ejpam-3415	48	7	lattices	lattice	NOUN
ejpam-3415	48	8	to	to	PART
ejpam-3415	48	9	hyperlattices	hyperlattice	NOUN
ejpam-3415	48	10	it	it	PRON
ejpam-3415	48	11	is	be	AUX
ejpam-3415	48	12	much	much	ADV
ejpam-3415	48	13	better	well	ADJ
ejpam-3415	48	14	not	not	PART
ejpam-3415	48	15	to	to	PART
ejpam-3415	48	16	include	include	VERB
ejpam-3415	48	17	condition	condition	NOUN
ejpam-3415	48	18	(	(	PUNCT
ejpam-3415	48	19	5	5	NUM
ejpam-3415	48	20	)	)	PUNCT
ejpam-3415	48	21	in	in	ADP
ejpam-3415	48	22	the	the	DET
ejpam-3415	48	23	definition	definition	NOUN
ejpam-3415	48	24	of	of	ADP
ejpam-3415	48	25	hyperlattices	hyperlattice	NOUN
ejpam-3415	48	26	.	.	PUNCT
ejpam-3415	49	1	in	in	ADP
ejpam-3415	49	2	the	the	DET
ejpam-3415	49	3	present	present	ADJ
ejpam-3415	49	4	paper	paper	NOUN
ejpam-3415	49	5	we	we	PRON
ejpam-3415	49	6	will	will	AUX
ejpam-3415	49	7	do	do	VERB
ejpam-3415	49	8	so	so	ADV
ejpam-3415	49	9	.	.	PUNCT
ejpam-3415	50	1	in	in	ADP
ejpam-3415	50	2	the	the	DET
ejpam-3415	50	3	definition	definition	NOUN
ejpam-3415	50	4	of	of	ADP
ejpam-3415	50	5	hyperlattices	hyperlattice	NOUN
ejpam-3415	50	6	the	the	DET
ejpam-3415	50	7	part	part	NOUN
ejpam-3415	50	8	related	relate	VERB
ejpam-3415	50	9	to	to	ADP
ejpam-3415	50	10	“	"	PUNCT
ejpam-3415	50	11	∧	∧	PROPN
ejpam-3415	50	12	”	"	PUNCT
ejpam-3415	50	13	is	be	AUX
ejpam-3415	50	14	the	the	DET
ejpam-3415	50	15	same	same	ADJ
ejpam-3415	50	16	as	as	ADP
ejpam-3415	50	17	in	in	ADP
ejpam-3415	50	18	the	the	DET
ejpam-3415	50	19	theory	theory	NOUN
ejpam-3415	50	20	of	of	ADP
ejpam-3415	50	21	lattices	lattice	NOUN
ejpam-3415	50	22	,	,	PUNCT
ejpam-3415	50	23	so	so	SCONJ
ejpam-3415	50	24	it	it	PRON
ejpam-3415	50	25	has	have	VERB
ejpam-3415	50	26	the	the	DET
ejpam-3415	50	27	same	same	ADJ
ejpam-3415	50	28	properties	property	NOUN
ejpam-3415	50	29	as	as	ADP
ejpam-3415	50	30	in	in	ADP
ejpam-3415	50	31	lattices	lattice	NOUN
ejpam-3415	50	32	.	.	PUNCT
ejpam-3415	51	1	concerning	concern	VERB
ejpam-3415	51	2	the	the	DET
ejpam-3415	51	3	“	"	PUNCT
ejpam-3415	51	4	∨	∨	NOUN
ejpam-3415	51	5	”	"	PUNCT
ejpam-3415	51	6	:	:	PUNCT
ejpam-3415	51	7	we	we	PRON
ejpam-3415	51	8	can	can	AUX
ejpam-3415	51	9	not	not	PART
ejpam-3415	51	10	write	write	VERB
ejpam-3415	51	11	a	a	DET
ejpam-3415	51	12	∈	∈	PROPN
ejpam-3415	51	13	a∧	a∧	NOUN
ejpam-3415	51	14	(	(	PUNCT
ejpam-3415	51	15	a∨	a∨	PROPN
ejpam-3415	51	16	b	b	PROPN
ejpam-3415	51	17	)	)	PUNCT
ejpam-3415	51	18	as	as	SCONJ
ejpam-3415	51	19	a	a	PRON
ejpam-3415	51	20	is	be	AUX
ejpam-3415	51	21	an	an	DET
ejpam-3415	51	22	element	element	NOUN
ejpam-3415	51	23	,	,	PUNCT
ejpam-3415	51	24	a∨	a∨	PROPN
ejpam-3415	51	25	b	b	PROPN
ejpam-3415	51	26	is	be	AUX
ejpam-3415	51	27	a	a	DET
ejpam-3415	51	28	set	set	VERB
ejpam-3415	51	29	and	and	CCONJ
ejpam-3415	51	30	“	"	PUNCT
ejpam-3415	51	31	∧	∧	PROPN
ejpam-3415	51	32	”	"	PUNCT
ejpam-3415	51	33	is	be	AUX
ejpam-3415	51	34	an	an	DET
ejpam-3415	51	35	operation	operation	NOUN
ejpam-3415	51	36	between	between	ADP
ejpam-3415	51	37	elements	element	NOUN
ejpam-3415	51	38	.	.	PUNCT
ejpam-3415	52	1	also	also	ADV
ejpam-3415	52	2	we	we	PRON
ejpam-3415	52	3	can	can	AUX
ejpam-3415	52	4	not	not	PART
ejpam-3415	52	5	write	write	VERB
ejpam-3415	52	6	a∨(b∨c	a∨(b∨c	PROPN
ejpam-3415	52	7	)	)	PUNCT
ejpam-3415	53	1	=	=	PUNCT
ejpam-3415	53	2	(	(	PUNCT
ejpam-3415	53	3	a∨b)∨c	a∨b)∨c	PROPN
ejpam-3415	53	4	as	as	ADP
ejpam-3415	53	5	b∨c	b∨c	PROPN
ejpam-3415	53	6	,	,	PUNCT
ejpam-3415	53	7	a∨b	a∨b	PROPN
ejpam-3415	53	8	are	be	AUX
ejpam-3415	53	9	sets	set	NOUN
ejpam-3415	53	10	,	,	PUNCT
ejpam-3415	53	11	c	c	X
ejpam-3415	53	12	,	,	PUNCT
ejpam-3415	53	13	a	a	DET
ejpam-3415	53	14	elements	element	NOUN
ejpam-3415	53	15	and	and	CCONJ
ejpam-3415	53	16	“	"	PUNCT
ejpam-3415	53	17	∨	∨	NOUN
ejpam-3415	53	18	”	"	PUNCT
ejpam-3415	53	19	and	and	CCONJ
ejpam-3415	53	20	operation	operation	NOUN
ejpam-3415	53	21	between	between	ADP
ejpam-3415	53	22	elements	element	NOUN
ejpam-3415	53	23	(	(	PUNCT
ejpam-3415	53	24	the	the	DET
ejpam-3415	53	25	so	so	ADV
ejpam-3415	53	26	called	call	VERB
ejpam-3415	53	27	“	"	PUNCT
ejpam-3415	53	28	hyperoperation	hyperoperation	NOUN
ejpam-3415	53	29	”	"	PUNCT
ejpam-3415	53	30	)	)	PUNCT
ejpam-3415	53	31	.	.	PUNCT
ejpam-3415	54	1	that	that	PRON
ejpam-3415	54	2	is	be	AUX
ejpam-3415	54	3	expressions	expression	NOUN
ejpam-3415	54	4	of	of	ADP
ejpam-3415	54	5	the	the	DET
ejpam-3415	54	6	form	form	NOUN
ejpam-3415	54	7	a	a	DET
ejpam-3415	54	8	∈	∈	PROPN
ejpam-3415	54	9	a∧(a∨b	a∧(a∨b	NOUN
ejpam-3415	54	10	)	)	PUNCT
ejpam-3415	54	11	,	,	PUNCT
ejpam-3415	54	12	a∨(b∨c	a∨(b∨c	PROPN
ejpam-3415	54	13	)	)	PUNCT
ejpam-3415	54	14	and	and	CCONJ
ejpam-3415	54	15	(	(	PUNCT
ejpam-3415	54	16	a∨b)∨c	a∨b)∨c	NOUN
ejpam-3415	54	17	have	have	VERB
ejpam-3415	54	18	no	no	DET
ejpam-3415	54	19	sense	sense	NOUN
ejpam-3415	54	20	.	.	PUNCT
ejpam-3415	55	1	for	for	ADP
ejpam-3415	55	2	the	the	DET
ejpam-3415	55	3	same	same	ADJ
ejpam-3415	55	4	reason	reason	NOUN
ejpam-3415	55	5	the	the	DET
ejpam-3415	55	6	concepts	concept	NOUN
ejpam-3415	55	7	of	of	ADP
ejpam-3415	55	8	distributive	distributive	ADJ
ejpam-3415	55	9	and	and	CCONJ
ejpam-3415	55	10	modular	modular	ADJ
ejpam-3415	55	11	hyperlattices	hyperlattice	NOUN
ejpam-3415	55	12	[	[	X
ejpam-3415	55	13	5	5	NUM
ejpam-3415	55	14	,	,	PUNCT
ejpam-3415	55	15	6	6	NUM
ejpam-3415	55	16	]	]	PUNCT
ejpam-3415	55	17	and	and	CCONJ
ejpam-3415	55	18	the	the	DET
ejpam-3415	55	19	concepts	concept	NOUN
ejpam-3415	55	20	of	of	ADP
ejpam-3415	55	21	∧-distributive	∧-distributive	ADJ
ejpam-3415	55	22	and	and	CCONJ
ejpam-3415	55	23	∨distributive	∨distributive	NOUN
ejpam-3415	55	24	hyperlattices	hyperlattice	NOUN
ejpam-3415	55	25	considered	consider	VERB
ejpam-3415	55	26	in	in	ADP
ejpam-3415	55	27	[	[	X
ejpam-3415	55	28	7	7	X
ejpam-3415	55	29	]	]	PUNCT
ejpam-3415	55	30	have	have	VERB
ejpam-3415	55	31	no	no	DET
ejpam-3415	55	32	sense	sense	NOUN
ejpam-3415	55	33	as	as	ADV
ejpam-3415	55	34	well	well	ADV
ejpam-3415	55	35	.	.	PUNCT
ejpam-3415	56	1	what	what	PRON
ejpam-3415	56	2	we	we	PRON
ejpam-3415	56	3	have	have	AUX
ejpam-3415	56	4	already	already	ADV
ejpam-3415	56	5	said	say	VERB
ejpam-3415	56	6	is	be	AUX
ejpam-3415	56	7	about	about	ADP
ejpam-3415	56	8	the	the	DET
ejpam-3415	56	9	definition	definition	NOUN
ejpam-3415	56	10	of	of	ADP
ejpam-3415	56	11	hyperlattice	hyperlattice	NOUN
ejpam-3415	56	12	introduced	introduce	VERB
ejpam-3415	56	13	by	by	ADP
ejpam-3415	56	14	konstantinidou	konstantinidou	NOUN
ejpam-3415	56	15	and	and	CCONJ
ejpam-3415	56	16	mittas	mitta	NOUN
ejpam-3415	56	17	in	in	ADP
ejpam-3415	56	18	[	[	X
ejpam-3415	56	19	4	4	NUM
ejpam-3415	56	20	]	]	PUNCT
ejpam-3415	56	21	and	and	CCONJ
ejpam-3415	56	22	used	use	VERB
ejpam-3415	56	23	in	in	ADP
ejpam-3415	56	24	[	[	X
ejpam-3415	56	25	5–7	5–7	NOUN
ejpam-3415	56	26	]	]	PUNCT
ejpam-3415	56	27	as	as	ADV
ejpam-3415	56	28	well	well	ADV
ejpam-3415	56	29	.	.	PUNCT
ejpam-3415	57	1	later	later	ADV
ejpam-3415	57	2	some	some	DET
ejpam-3415	57	3	authors	author	NOUN
ejpam-3415	57	4	working	work	VERB
ejpam-3415	57	5	on	on	ADP
ejpam-3415	57	6	the	the	DET
ejpam-3415	57	7	subject	subject	NOUN
ejpam-3415	57	8	,	,	PUNCT
ejpam-3415	57	9	just	just	ADV
ejpam-3415	57	10	after	after	ADP
ejpam-3415	57	11	the	the	DET
ejpam-3415	57	12	definition	definition	NOUN
ejpam-3415	57	13	1.1	1.1	NUM
ejpam-3415	57	14	,	,	PUNCT
ejpam-3415	57	15	they	they	PRON
ejpam-3415	57	16	added	add	VERB
ejpam-3415	57	17	:	:	PUNCT
ejpam-3415	57	18	“	"	PUNCT
ejpam-3415	57	19	let	let	VERB
ejpam-3415	57	20	a	a	PRON
ejpam-3415	57	21	,	,	PUNCT
ejpam-3415	57	22	b	b	PROPN
ejpam-3415	57	23	⊆	⊆	NUM
ejpam-3415	57	24	l.	l.	NOUN
ejpam-3415	57	25	then	then	ADV
ejpam-3415	57	26	define	define	VERB
ejpam-3415	57	27	a	a	DET
ejpam-3415	57	28	∨b	∨b	NOUN
ejpam-3415	57	29	=	=	SYM
ejpam-3415	57	30	⋃	⋃	PROPN
ejpam-3415	57	31	{	{	PUNCT
ejpam-3415	57	32	a	a	DET
ejpam-3415	57	33	∨	∨	NUM
ejpam-3415	57	34	b	b	NOUN
ejpam-3415	57	35	|	|	NOUN
ejpam-3415	57	36	a	a	PRON
ejpam-3415	57	37	∈	∈	PROPN
ejpam-3415	57	38	a	a	PRON
ejpam-3415	57	39	,	,	PUNCT
ejpam-3415	57	40	b	b	PROPN
ejpam-3415	57	41	∈	∈	PROPN
ejpam-3415	57	42	b	b	NOUN
ejpam-3415	57	43	}	}	PUNCT
ejpam-3415	57	44	and	and	CCONJ
ejpam-3415	57	45	a∧b	a∧b	NOUN
ejpam-3415	57	46	=	=	PRON
ejpam-3415	57	47	{	{	PUNCT
ejpam-3415	57	48	a∧	a∧	NOUN
ejpam-3415	57	49	b	b	PROPN
ejpam-3415	57	50	|	|	ADV
ejpam-3415	57	51	a	a	PRON
ejpam-3415	57	52	∈	∈	PROPN
ejpam-3415	57	53	a	a	PRON
ejpam-3415	57	54	,	,	PUNCT
ejpam-3415	57	55	b	b	PROPN
ejpam-3415	57	56	∈	∈	PROPN
ejpam-3415	57	57	b	b	NOUN
ejpam-3415	57	58	}	}	PUNCT
ejpam-3415	57	59	”	"	PUNCT
ejpam-3415	57	60	(	(	PUNCT
ejpam-3415	57	61	see	see	VERB
ejpam-3415	57	62	,	,	PUNCT
ejpam-3415	57	63	for	for	ADP
ejpam-3415	57	64	example	example	NOUN
ejpam-3415	58	1	[	[	X
ejpam-3415	58	2	1	1	NUM
ejpam-3415	58	3	,	,	PUNCT
ejpam-3415	58	4	2	2	NUM
ejpam-3415	58	5	]	]	PUNCT
ejpam-3415	58	6	)	)	PUNCT
ejpam-3415	58	7	.	.	PUNCT
ejpam-3415	59	1	but	but	CCONJ
ejpam-3415	59	2	this	this	PRON
ejpam-3415	59	3	,	,	PUNCT
ejpam-3415	59	4	written	write	VERB
ejpam-3415	59	5	in	in	ADP
ejpam-3415	59	6	a	a	DET
ejpam-3415	59	7	wrong	wrong	ADJ
ejpam-3415	59	8	place	place	NOUN
ejpam-3415	59	9	(	(	PUNCT
ejpam-3415	59	10	and	and	CCONJ
ejpam-3415	59	11	not	not	PART
ejpam-3415	59	12	only	only	ADV
ejpam-3415	59	13	)	)	PUNCT
ejpam-3415	59	14	,	,	PUNCT
ejpam-3415	59	15	make	make	VERB
ejpam-3415	59	16	the	the	DET
ejpam-3415	59	17	definition	definition	NOUN
ejpam-3415	59	18	still	still	ADV
ejpam-3415	59	19	unreadable	unreadable	ADJ
ejpam-3415	59	20	.	.	PUNCT
ejpam-3415	60	1	2	2	X
ejpam-3415	60	2	.	.	NUM
ejpam-3415	60	3	hyperlattices	hyperlattice	NOUN
ejpam-3415	60	4	to	to	PART
ejpam-3415	60	5	pass	pass	VERB
ejpam-3415	60	6	from	from	ADP
ejpam-3415	60	7	lattices	lattice	NOUN
ejpam-3415	60	8	to	to	ADP
ejpam-3415	60	9	hyperlattices	hyperlattice	NOUN
ejpam-3415	60	10	,	,	PUNCT
ejpam-3415	60	11	we	we	PRON
ejpam-3415	60	12	only	only	ADV
ejpam-3415	60	13	have	have	VERB
ejpam-3415	60	14	to	to	PART
ejpam-3415	60	15	transfer	transfer	VERB
ejpam-3415	60	16	the	the	DET
ejpam-3415	60	17	properties	property	NOUN
ejpam-3415	60	18	(	(	PUNCT
ejpam-3415	61	1	a∨b)∨c	a∨b)∨c	NOUN
ejpam-3415	61	2	=	=	SYM
ejpam-3415	61	3	a∨	a∨	PROPN
ejpam-3415	61	4	(	(	PUNCT
ejpam-3415	61	5	b∨	b∨	PROPN
ejpam-3415	61	6	c	c	PROPN
ejpam-3415	61	7	)	)	PUNCT
ejpam-3415	61	8	,	,	PUNCT
ejpam-3415	61	9	a∧	a∧	NOUN
ejpam-3415	61	10	(	(	PUNCT
ejpam-3415	61	11	a∨	a∨	PROPN
ejpam-3415	61	12	b	b	PROPN
ejpam-3415	61	13	)	)	PUNCT
ejpam-3415	61	14	=	=	SYM
ejpam-3415	61	15	a	a	PRON
ejpam-3415	61	16	and	and	CCONJ
ejpam-3415	61	17	a∨	a∨	PROPN
ejpam-3415	61	18	(	(	PUNCT
ejpam-3415	61	19	a∧	a∧	NOUN
ejpam-3415	61	20	b	b	NOUN
ejpam-3415	61	21	)	)	PUNCT
ejpam-3415	61	22	=	=	VERB
ejpam-3415	61	23	a.	a.	NOUN
ejpam-3415	61	24	the	the	DET
ejpam-3415	61	25	property	property	NOUN
ejpam-3415	61	26	(	(	PUNCT
ejpam-3415	61	27	a∨	a∨	PROPN
ejpam-3415	61	28	b)∨	b)∨	PROPN
ejpam-3415	61	29	c	c	NOUN
ejpam-3415	61	30	=	=	SYM
ejpam-3415	61	31	a∨	a∨	PROPN
ejpam-3415	61	32	(	(	PUNCT
ejpam-3415	61	33	b∨	b∨	PROPN
ejpam-3415	61	34	c	c	PROPN
ejpam-3415	61	35	)	)	PUNCT
ejpam-3415	61	36	can	can	AUX
ejpam-3415	61	37	be	be	AUX
ejpam-3415	61	38	naturally	naturally	ADV
ejpam-3415	61	39	transferred	transfer	VERB
ejpam-3415	61	40	as	as	SCONJ
ejpam-3415	61	41	follows	follow	VERB
ejpam-3415	61	42	:	:	PUNCT
ejpam-3415	61	43	x	x	SYM
ejpam-3415	61	44	∈	∈	PROPN
ejpam-3415	61	45	u	u	NOUN
ejpam-3415	61	46	∨	∨	X
ejpam-3415	61	47	c	c	NOUN
ejpam-3415	61	48	for	for	ADP
ejpam-3415	61	49	some	some	DET
ejpam-3415	61	50	x	x	SYM
ejpam-3415	61	51	∈	∈	PROPN
ejpam-3415	61	52	a	a	DET
ejpam-3415	61	53	∨	∨	NUM
ejpam-3415	61	54	b	b	NOUN
ejpam-3415	62	1	if	if	SCONJ
ejpam-3415	63	1	and	and	CCONJ
ejpam-3415	63	2	only	only	ADV
ejpam-3415	63	3	if	if	SCONJ
ejpam-3415	63	4	x	x	SYM
ejpam-3415	63	5	∈	∈	PROPN
ejpam-3415	63	6	a	a	DET
ejpam-3415	63	7	∨	∨	NUM
ejpam-3415	63	8	v	v	NOUN
ejpam-3415	63	9	for	for	ADP
ejpam-3415	63	10	some	some	DET
ejpam-3415	63	11	v	v	ADP
ejpam-3415	63	12	∈	∈	PROPN
ejpam-3415	63	13	b	b	PROPN
ejpam-3415	63	14	∨	∨	PROPN
ejpam-3415	63	15	c.	c.	PROPN
ejpam-3415	63	16	the	the	DET
ejpam-3415	63	17	a	a	DET
ejpam-3415	63	18	∧	∧	PROPN
ejpam-3415	63	19	(	(	PUNCT
ejpam-3415	63	20	a	a	DET
ejpam-3415	63	21	∨	∨	NUM
ejpam-3415	63	22	b	b	NOUN
ejpam-3415	63	23	)	)	PUNCT
ejpam-3415	63	24	=	=	NOUN
ejpam-3415	64	1	a	a	PRON
ejpam-3415	64	2	can	can	AUX
ejpam-3415	64	3	be	be	AUX
ejpam-3415	64	4	transferred	transfer	VERB
ejpam-3415	64	5	as	as	SCONJ
ejpam-3415	64	6	follows	follow	VERB
ejpam-3415	64	7	:	:	PUNCT
ejpam-3415	64	8	there	there	PRON
ejpam-3415	64	9	exists	exist	VERB
ejpam-3415	64	10	u	u	PROPN
ejpam-3415	64	11	∈	∈	PROPN
ejpam-3415	64	12	a	a	DET
ejpam-3415	64	13	∨	∨	NUM
ejpam-3415	64	14	b	b	NOUN
ejpam-3415	64	15	such	such	ADJ
ejpam-3415	64	16	that	that	DET
ejpam-3415	64	17	a∧	a∧	NOUN
ejpam-3415	64	18	u	u	NOUN
ejpam-3415	64	19	=	=	X
ejpam-3415	64	20	a	a	NOUN
ejpam-3415	64	21	;	;	PUNCT
ejpam-3415	64	22	or	or	CCONJ
ejpam-3415	64	23	for	for	ADP
ejpam-3415	64	24	every	every	DET
ejpam-3415	64	25	u	u	PROPN
ejpam-3415	64	26	∈	∈	PROPN
ejpam-3415	64	27	a∨	a∨	PROPN
ejpam-3415	64	28	b	b	PROPN
ejpam-3415	64	29	,	,	PUNCT
ejpam-3415	64	30	a∧	a∧	NOUN
ejpam-3415	64	31	u	u	NOUN
ejpam-3415	64	32	=	=	NOUN
ejpam-3415	64	33	a.	a.	NOUN
ejpam-3415	64	34	finally	finally	ADV
ejpam-3415	64	35	,	,	PUNCT
ejpam-3415	64	36	the	the	DET
ejpam-3415	64	37	property	property	NOUN
ejpam-3415	64	38	a∨	a∨	PROPN
ejpam-3415	64	39	(	(	PUNCT
ejpam-3415	64	40	a∧	a∧	NOUN
ejpam-3415	64	41	b	b	NOUN
ejpam-3415	64	42	)	)	PUNCT
ejpam-3415	64	43	=	=	NOUN
ejpam-3415	65	1	a	a	PRON
ejpam-3415	65	2	could	could	AUX
ejpam-3415	65	3	be	be	AUX
ejpam-3415	65	4	transferred	transfer	VERB
ejpam-3415	65	5	as	as	ADP
ejpam-3415	65	6	a	a	DET
ejpam-3415	65	7	∈	∈	PROPN
ejpam-3415	65	8	a∨	a∨	PROPN
ejpam-3415	65	9	(	(	PUNCT
ejpam-3415	65	10	a∧	a∧	PROPN
ejpam-3415	65	11	b	b	PROPN
ejpam-3415	65	12	)	)	PUNCT
ejpam-3415	65	13	;	;	PUNCT
ejpam-3415	65	14	if	if	SCONJ
ejpam-3415	65	15	x	x	PROPN
ejpam-3415	65	16	∈	∈	PROPN
ejpam-3415	65	17	a∨	a∨	PROPN
ejpam-3415	65	18	(	(	PUNCT
ejpam-3415	65	19	a∧	a∧	PROPN
ejpam-3415	65	20	b	b	PROPN
ejpam-3415	65	21	)	)	PUNCT
ejpam-3415	65	22	,	,	PUNCT
ejpam-3415	65	23	then	then	ADV
ejpam-3415	65	24	x	x	X
ejpam-3415	65	25	=	=	PUNCT
ejpam-3415	65	26	a	a	PRON
ejpam-3415	65	27	or	or	CCONJ
ejpam-3415	65	28	both	both	PRON
ejpam-3415	65	29	.	.	PUNCT
ejpam-3415	66	1	as	as	SCONJ
ejpam-3415	66	2	we	we	PRON
ejpam-3415	66	3	see	see	VERB
ejpam-3415	66	4	,	,	PUNCT
ejpam-3415	66	5	the	the	DET
ejpam-3415	66	6	concept	concept	NOUN
ejpam-3415	66	7	of	of	ADP
ejpam-3415	66	8	a	a	DET
ejpam-3415	66	9	lattice	lattice	NOUN
ejpam-3415	66	10	can	can	AUX
ejpam-3415	66	11	be	be	AUX
ejpam-3415	66	12	extended	extend	VERB
ejpam-3415	66	13	not	not	PART
ejpam-3415	66	14	only	only	ADV
ejpam-3415	66	15	in	in	ADP
ejpam-3415	66	16	one	one	NUM
ejpam-3415	66	17	way	way	NOUN
ejpam-3415	66	18	.	.	PUNCT
ejpam-3415	67	1	to	to	PART
ejpam-3415	67	2	keep	keep	VERB
ejpam-3415	67	3	the	the	DET
ejpam-3415	67	4	existing	exist	VERB
ejpam-3415	67	5	definition	definition	NOUN
ejpam-3415	67	6	in	in	ADP
ejpam-3415	67	7	the	the	DET
ejpam-3415	67	8	bibliography	bibliography	NOUN
ejpam-3415	67	9	,	,	PUNCT
ejpam-3415	67	10	the	the	DET
ejpam-3415	67	11	concept	concept	NOUN
ejpam-3415	67	12	of	of	ADP
ejpam-3415	67	13	a	a	DET
ejpam-3415	67	14	lattice	lattice	NOUN
ejpam-3415	67	15	can	can	AUX
ejpam-3415	67	16	be	be	AUX
ejpam-3415	67	17	naturally	naturally	ADV
ejpam-3415	67	18	transferred	transfer	VERB
ejpam-3415	67	19	to	to	ADP
ejpam-3415	67	20	a	a	DET
ejpam-3415	67	21	hyperlattice	hyperlattice	NOUN
ejpam-3415	67	22	by	by	ADP
ejpam-3415	67	23	the	the	DET
ejpam-3415	67	24	definition	definition	NOUN
ejpam-3415	67	25	below	below	ADV
ejpam-3415	67	26	.	.	PUNCT
ejpam-3415	68	1	we	we	PRON
ejpam-3415	68	2	denote	denote	VERB
ejpam-3415	68	3	by	by	ADP
ejpam-3415	68	4	p∗(l	p∗(l	NOUN
ejpam-3415	68	5	)	)	PUNCT
ejpam-3415	68	6	the	the	DET
ejpam-3415	68	7	set	set	NOUN
ejpam-3415	68	8	of	of	ADP
ejpam-3415	68	9	(	(	PUNCT
ejpam-3415	68	10	all	all	ADV
ejpam-3415	68	11	)	)	PUNCT
ejpam-3415	68	12	nonempty	nonempty	VERB
ejpam-3415	68	13	subsets	subset	NOUN
ejpam-3415	68	14	of	of	ADP
ejpam-3415	68	15	l.	l.	PROPN
ejpam-3415	68	16	definition	definition	NOUN
ejpam-3415	68	17	2.1	2.1	NUM
ejpam-3415	68	18	let	let	VERB
ejpam-3415	68	19	l	l	NOUN
ejpam-3415	68	20	be	be	AUX
ejpam-3415	68	21	a	a	DET
ejpam-3415	68	22	nonempty	nonempty	ADJ
ejpam-3415	68	23	set	set	VERB
ejpam-3415	68	24	,	,	PUNCT
ejpam-3415	68	25	∧	∧	NOUN
ejpam-3415	68	26	:	:	PUNCT
ejpam-3415	68	27	l×	l×	PROPN
ejpam-3415	68	28	l	l	NOUN
ejpam-3415	68	29	→	→	PUNCT
ejpam-3415	68	30	l	l	NOUN
ejpam-3415	69	1	|	|	ADV
ejpam-3415	69	2	(	(	PUNCT
ejpam-3415	69	3	a	a	DET
ejpam-3415	69	4	,	,	PUNCT
ejpam-3415	69	5	b	b	NOUN
ejpam-3415	69	6	)	)	PUNCT
ejpam-3415	69	7	→	→	PUNCT
ejpam-3415	69	8	a	a	DET
ejpam-3415	69	9	∧	∧	PROPN
ejpam-3415	69	10	b	b	PROPN
ejpam-3415	69	11	an	an	DET
ejpam-3415	69	12	operation	operation	NOUN
ejpam-3415	69	13	on	on	ADP
ejpam-3415	69	14	l	l	PROPN
ejpam-3415	69	15	and	and	CCONJ
ejpam-3415	69	16	∨	∨	NUM
ejpam-3415	69	17	:	:	PUNCT
ejpam-3415	69	18	l×	l×	PROPN
ejpam-3415	69	19	l	l	NOUN
ejpam-3415	69	20	→	→	SYM
ejpam-3415	69	21	p∗(l	p∗(l	NOUN
ejpam-3415	69	22	)	)	PUNCT
ejpam-3415	69	23	|	|	NOUN
ejpam-3415	69	24	(	(	PUNCT
ejpam-3415	69	25	a	a	DET
ejpam-3415	69	26	,	,	PUNCT
ejpam-3415	69	27	b	b	NOUN
ejpam-3415	69	28	)	)	PUNCT
ejpam-3415	69	29	→	→	PUNCT
ejpam-3415	69	30	a	a	DET
ejpam-3415	69	31	∨	∨	NUM
ejpam-3415	69	32	b	b	PROPN
ejpam-3415	69	33	a	a	DET
ejpam-3415	69	34	hyperoperation	hyperoperation	NOUN
ejpam-3415	69	35	on	on	ADP
ejpam-3415	69	36	l.	l.	PROPN
ejpam-3415	69	37	niovi	niovi	PROPN
ejpam-3415	69	38	kehayopulu	kehayopulu	PROPN
ejpam-3415	69	39	/	/	SYM
ejpam-3415	69	40	eur	eur	PROPN
ejpam-3415	69	41	.	.	PUNCT
ejpam-3415	70	1	j.	j.	PROPN
ejpam-3415	70	2	pure	pure	PROPN
ejpam-3415	70	3	appl	appl	PROPN
ejpam-3415	70	4	.	.	PROPN
ejpam-3415	70	5	math	math	PROPN
ejpam-3415	70	6	,	,	PUNCT
ejpam-3415	70	7	12	12	NUM
ejpam-3415	70	8	(	(	PUNCT
ejpam-3415	70	9	2	2	NUM
ejpam-3415	70	10	)	)	PUNCT
ejpam-3415	70	11	(	(	PUNCT
ejpam-3415	70	12	2019	2019	NUM
ejpam-3415	70	13	)	)	PUNCT
ejpam-3415	70	14	,	,	PUNCT
ejpam-3415	70	15	252	252	NUM
ejpam-3415	70	16	-	-	SYM
ejpam-3415	70	17	269	269	NUM
ejpam-3415	70	18	255	255	NUM
ejpam-3415	70	19	we	we	PRON
ejpam-3415	70	20	say	say	VERB
ejpam-3415	70	21	that	that	SCONJ
ejpam-3415	70	22	(	(	PUNCT
ejpam-3415	70	23	l,∧,∨	l,∧,∨	X
ejpam-3415	70	24	)	)	PUNCT
ejpam-3415	70	25	is	be	AUX
ejpam-3415	70	26	a	a	DET
ejpam-3415	70	27	hyperlattice	hyperlattice	NOUN
ejpam-3415	70	28	if	if	SCONJ
ejpam-3415	70	29	,	,	PUNCT
ejpam-3415	70	30	for	for	ADP
ejpam-3415	70	31	every	every	DET
ejpam-3415	70	32	a	a	DET
ejpam-3415	70	33	,	,	PUNCT
ejpam-3415	70	34	b	b	NOUN
ejpam-3415	70	35	,	,	PUNCT
ejpam-3415	70	36	c	c	PROPN
ejpam-3415	70	37	∈	∈	PROPN
ejpam-3415	70	38	l	l	NOUN
ejpam-3415	70	39	,	,	PUNCT
ejpam-3415	70	40	the	the	DET
ejpam-3415	70	41	following	follow	VERB
ejpam-3415	70	42	assertions	assertion	NOUN
ejpam-3415	70	43	are	be	AUX
ejpam-3415	70	44	satisfied	satisfied	ADJ
ejpam-3415	70	45	:	:	PUNCT
ejpam-3415	70	46	(	(	PUNCT
ejpam-3415	70	47	1	1	X
ejpam-3415	70	48	)	)	PUNCT
ejpam-3415	70	49	a	a	DET
ejpam-3415	70	50	∧	∧	NOUN
ejpam-3415	70	51	a	a	DET
ejpam-3415	70	52	=	=	PUNCT
ejpam-3415	70	53	a	a	NOUN
ejpam-3415	70	54	and	and	CCONJ
ejpam-3415	70	55	a	a	DET
ejpam-3415	70	56	∈	∈	PROPN
ejpam-3415	70	57	a	a	DET
ejpam-3415	70	58	∨	∨	NOUN
ejpam-3415	70	59	a	a	DET
ejpam-3415	70	60	(	(	PUNCT
ejpam-3415	70	61	2	2	NUM
ejpam-3415	70	62	)	)	PUNCT
ejpam-3415	70	63	a	a	DET
ejpam-3415	70	64	∧	∧	PROPN
ejpam-3415	70	65	b	b	NOUN
ejpam-3415	70	66	=	=	SYM
ejpam-3415	70	67	b	b	PROPN
ejpam-3415	70	68	∧	∧	PROPN
ejpam-3415	70	69	a	a	PRON
ejpam-3415	70	70	and	and	CCONJ
ejpam-3415	70	71	a	a	DET
ejpam-3415	70	72	∨	∨	NUM
ejpam-3415	70	73	b	b	X
ejpam-3415	70	74	=	=	SYM
ejpam-3415	70	75	b	b	PROPN
ejpam-3415	70	76	∨	∨	NUM
ejpam-3415	70	77	a	a	DET
ejpam-3415	70	78	(	(	PUNCT
ejpam-3415	70	79	3	3	NUM
ejpam-3415	70	80	)	)	PUNCT
ejpam-3415	70	81	(	(	PUNCT
ejpam-3415	70	82	a	a	DET
ejpam-3415	70	83	∧	∧	PROPN
ejpam-3415	70	84	b	b	NOUN
ejpam-3415	70	85	)	)	PUNCT
ejpam-3415	70	86	∧	∧	NOUN
ejpam-3415	70	87	c	c	NOUN
ejpam-3415	70	88	=	=	PUNCT
ejpam-3415	70	89	(	(	PUNCT
ejpam-3415	70	90	a	a	DET
ejpam-3415	70	91	∧	∧	PROPN
ejpam-3415	70	92	b	b	NOUN
ejpam-3415	70	93	)	)	PUNCT
ejpam-3415	70	94	∧	∧	PROPN
ejpam-3415	70	95	c	c	NOUN
ejpam-3415	70	96	;	;	PUNCT
ejpam-3415	70	97	and	and	CCONJ
ejpam-3415	70	98	(	(	PUNCT
ejpam-3415	70	99	a	a	DET
ejpam-3415	70	100	∨	∨	NUM
ejpam-3415	70	101	b	b	NOUN
ejpam-3415	70	102	)	)	PUNCT
ejpam-3415	70	103	∨	∨	NUM
ejpam-3415	70	104	c	c	NOUN
ejpam-3415	70	105	=	=	PUNCT
ejpam-3415	70	106	a	a	DET
ejpam-3415	70	107	∨	∨	NOUN
ejpam-3415	70	108	(	(	PUNCT
ejpam-3415	70	109	b	b	PROPN
ejpam-3415	70	110	∨	∨	NUM
ejpam-3415	70	111	c	c	NOUN
ejpam-3415	70	112	)	)	PUNCT
ejpam-3415	70	113	in	in	ADP
ejpam-3415	70	114	the	the	DET
ejpam-3415	70	115	sense	sense	NOUN
ejpam-3415	70	116	that	that	SCONJ
ejpam-3415	70	117	x	x	SYM
ejpam-3415	70	118	∈	∈	PROPN
ejpam-3415	70	119	u	u	NOUN
ejpam-3415	70	120	∨	∨	X
ejpam-3415	70	121	c	c	NOUN
ejpam-3415	70	122	for	for	ADP
ejpam-3415	70	123	some	some	DET
ejpam-3415	70	124	u	u	NOUN
ejpam-3415	70	125	∈	∈	PROPN
ejpam-3415	70	126	a	a	DET
ejpam-3415	70	127	∨	∨	NUM
ejpam-3415	70	128	b	b	NOUN
ejpam-3415	71	1	if	if	SCONJ
ejpam-3415	72	1	and	and	CCONJ
ejpam-3415	72	2	only	only	ADV
ejpam-3415	72	3	if	if	SCONJ
ejpam-3415	72	4	x	x	SYM
ejpam-3415	72	5	∈	∈	PROPN
ejpam-3415	72	6	a	a	DET
ejpam-3415	72	7	∨	∨	NUM
ejpam-3415	72	8	v	v	NOUN
ejpam-3415	72	9	for	for	ADP
ejpam-3415	72	10	some	some	DET
ejpam-3415	72	11	v	v	ADP
ejpam-3415	72	12	∈	∈	PROPN
ejpam-3415	72	13	b	b	PROPN
ejpam-3415	72	14	∨	∨	PROPN
ejpam-3415	72	15	c.	c.	PROPN
ejpam-3415	72	16	(	(	PUNCT
ejpam-3415	72	17	4	4	NUM
ejpam-3415	72	18	)	)	PUNCT
ejpam-3415	72	19	a	a	DET
ejpam-3415	72	20	∧	∧	PROPN
ejpam-3415	72	21	(	(	PUNCT
ejpam-3415	72	22	a	a	DET
ejpam-3415	72	23	∨	∨	NUM
ejpam-3415	72	24	b	b	NOUN
ejpam-3415	72	25	)	)	PUNCT
ejpam-3415	72	26	=	=	PUNCT
ejpam-3415	73	1	a	a	PRON
ejpam-3415	73	2	in	in	ADP
ejpam-3415	73	3	the	the	DET
ejpam-3415	73	4	sense	sense	NOUN
ejpam-3415	73	5	that	that	SCONJ
ejpam-3415	73	6	there	there	PRON
ejpam-3415	73	7	exists	exist	VERB
ejpam-3415	73	8	u	u	PROPN
ejpam-3415	73	9	∈	∈	PROPN
ejpam-3415	73	10	a	a	DET
ejpam-3415	73	11	∨	∨	NUM
ejpam-3415	73	12	b	b	NOUN
ejpam-3415	73	13	such	such	ADJ
ejpam-3415	73	14	that	that	SCONJ
ejpam-3415	73	15	a	a	DET
ejpam-3415	73	16	∧	∧	PROPN
ejpam-3415	73	17	u	u	NOUN
ejpam-3415	73	18	=	=	X
ejpam-3415	73	19	a	a	NOUN
ejpam-3415	73	20	;	;	PUNCT
ejpam-3415	73	21	and	and	CCONJ
ejpam-3415	73	22	a	a	DET
ejpam-3415	73	23	∈	∈	PROPN
ejpam-3415	73	24	a	a	DET
ejpam-3415	73	25	∨	∨	NOUN
ejpam-3415	73	26	(	(	PUNCT
ejpam-3415	73	27	a	a	DET
ejpam-3415	73	28	∧	∧	PROPN
ejpam-3415	73	29	b	b	NOUN
ejpam-3415	73	30	)	)	PUNCT
ejpam-3415	73	31	.	.	PUNCT
ejpam-3415	74	1	remark	remark	VERB
ejpam-3415	74	2	2.2	2.2	NUM
ejpam-3415	74	3	(	(	PUNCT
ejpam-3415	74	4	a	a	X
ejpam-3415	74	5	)	)	PUNCT
ejpam-3415	74	6	the	the	DET
ejpam-3415	74	7	property	property	NOUN
ejpam-3415	74	8	(	(	PUNCT
ejpam-3415	74	9	a	a	DET
ejpam-3415	74	10	∨	∨	NUM
ejpam-3415	74	11	b	b	NOUN
ejpam-3415	74	12	)	)	PUNCT
ejpam-3415	74	13	∨	∨	NUM
ejpam-3415	74	14	c	c	NOUN
ejpam-3415	74	15	=	=	PUNCT
ejpam-3415	74	16	a	a	DET
ejpam-3415	74	17	∨	∨	NOUN
ejpam-3415	74	18	(	(	PUNCT
ejpam-3415	74	19	b	b	PROPN
ejpam-3415	74	20	∨	∨	NUM
ejpam-3415	74	21	c	c	NOUN
ejpam-3415	74	22	)	)	PUNCT
ejpam-3415	74	23	is	be	AUX
ejpam-3415	74	24	clearly	clearly	ADV
ejpam-3415	74	25	equivalent	equivalent	ADJ
ejpam-3415	74	26	to	to	ADP
ejpam-3415	74	27	⋃	⋃	PROPN
ejpam-3415	74	28	u∈a∨b	u∈a∨b	PROPN
ejpam-3415	74	29	u	u	NOUN
ejpam-3415	74	30	∨	∨	NOUN
ejpam-3415	74	31	c	c	NOUN
ejpam-3415	74	32	=	=	PUNCT
ejpam-3415	75	1	⋃	⋃	PROPN
ejpam-3415	75	2	v∈b∨c	v∈b∨c	PROPN
ejpam-3415	75	3	a	a	DET
ejpam-3415	75	4	∨	∨	NUM
ejpam-3415	75	5	v.	v.	ADP
ejpam-3415	75	6	(	(	PUNCT
ejpam-3415	75	7	b	b	X
ejpam-3415	75	8	)	)	PUNCT
ejpam-3415	75	9	there	there	PRON
ejpam-3415	75	10	exists	exist	VERB
ejpam-3415	75	11	u	u	PROPN
ejpam-3415	75	12	∈	∈	PROPN
ejpam-3415	75	13	a	a	DET
ejpam-3415	75	14	∨	∨	NUM
ejpam-3415	75	15	b	b	NOUN
ejpam-3415	75	16	such	such	ADJ
ejpam-3415	75	17	that	that	SCONJ
ejpam-3415	75	18	a	a	DET
ejpam-3415	75	19	∧	∧	PROPN
ejpam-3415	75	20	u	u	NOUN
ejpam-3415	75	21	=	=	NOUN
ejpam-3415	75	22	a	a	PRON
ejpam-3415	75	23	if	if	NOUN
ejpam-3415	76	1	and	and	CCONJ
ejpam-3415	76	2	only	only	ADV
ejpam-3415	76	3	if	if	SCONJ
ejpam-3415	76	4	a	a	DET
ejpam-3415	76	5	∈	∈	NOUN
ejpam-3415	76	6	{	{	PUNCT
ejpam-3415	76	7	a	a	DET
ejpam-3415	76	8	∧	∧	PROPN
ejpam-3415	76	9	u	u	NOUN
ejpam-3415	76	10	|	|	ADV
ejpam-3415	76	11	u	u	NOUN
ejpam-3415	76	12	∈	∈	PROPN
ejpam-3415	76	13	a	a	DET
ejpam-3415	76	14	∨	∨	NUM
ejpam-3415	76	15	b	b	NOUN
ejpam-3415	76	16	}	}	PUNCT
ejpam-3415	76	17	.	.	PUNCT
ejpam-3415	77	1	if	if	SCONJ
ejpam-3415	77	2	in	in	ADP
ejpam-3415	77	3	definition	definition	NOUN
ejpam-3415	77	4	2.1	2.1	NUM
ejpam-3415	77	5	we	we	PRON
ejpam-3415	77	6	add	add	VERB
ejpam-3415	77	7	the	the	DET
ejpam-3415	77	8	property	property	NOUN
ejpam-3415	77	9	a	a	DET
ejpam-3415	77	10	∈	∈	PROPN
ejpam-3415	77	11	a	a	DET
ejpam-3415	77	12	∨	∨	PROPN
ejpam-3415	77	13	b	b	PROPN
ejpam-3415	77	14	⇒	⇒	NOUN
ejpam-3415	77	15	a	a	DET
ejpam-3415	77	16	∧	∧	PROPN
ejpam-3415	77	17	b	b	PROPN
ejpam-3415	77	18	=	=	SYM
ejpam-3415	77	19	b	b	PROPN
ejpam-3415	77	20	,	,	PUNCT
ejpam-3415	77	21	then	then	ADV
ejpam-3415	77	22	this	this	DET
ejpam-3415	77	23	definition	definition	NOUN
ejpam-3415	77	24	is	be	AUX
ejpam-3415	77	25	equivalent	equivalent	ADJ
ejpam-3415	77	26	to	to	ADP
ejpam-3415	77	27	definition	definition	NOUN
ejpam-3415	77	28	1.1	1.1	NUM
ejpam-3415	77	29	but	but	CCONJ
ejpam-3415	77	30	only	only	ADV
ejpam-3415	77	31	if	if	SCONJ
ejpam-3415	77	32	,	,	PUNCT
ejpam-3415	77	33	for	for	ADP
ejpam-3415	77	34	any	any	DET
ejpam-3415	77	35	nonempty	nonempty	ADJ
ejpam-3415	77	36	subsets	subset	NOUN
ejpam-3415	77	37	a	a	PRON
ejpam-3415	77	38	and	and	CCONJ
ejpam-3415	77	39	b	b	PROPN
ejpam-3415	77	40	of	of	ADP
ejpam-3415	77	41	l	l	NOUN
ejpam-3415	77	42	,	,	PUNCT
ejpam-3415	77	43	we	we	PRON
ejpam-3415	77	44	define	define	VERB
ejpam-3415	77	45	the	the	DET
ejpam-3415	77	46	a∨b	a∨b	NOUN
ejpam-3415	77	47	and	and	CCONJ
ejpam-3415	77	48	a∧b	a∧b	PROPN
ejpam-3415	77	49	(	(	PUNCT
ejpam-3415	77	50	there	there	PRON
ejpam-3415	77	51	is	be	VERB
ejpam-3415	77	52	no	no	DET
ejpam-3415	77	53	such	such	DET
ejpam-3415	77	54	a	a	DET
ejpam-3415	77	55	definition	definition	NOUN
ejpam-3415	77	56	in	in	ADP
ejpam-3415	77	57	[	[	X
ejpam-3415	77	58	4–7	4–7	NOUN
ejpam-3415	77	59	]	]	X
ejpam-3415	77	60	)	)	PUNCT
ejpam-3415	77	61	,	,	PUNCT
ejpam-3415	77	62	preferable	preferable	ADJ
ejpam-3415	77	63	before	before	ADP
ejpam-3415	77	64	the	the	DET
ejpam-3415	77	65	definition	definition	NOUN
ejpam-3415	77	66	or	or	CCONJ
ejpam-3415	77	67	in	in	ADP
ejpam-3415	77	68	a	a	DET
ejpam-3415	77	69	correct	correct	ADJ
ejpam-3415	77	70	way	way	NOUN
ejpam-3415	77	71	if	if	SCONJ
ejpam-3415	77	72	it	it	PRON
ejpam-3415	77	73	is	be	AUX
ejpam-3415	77	74	after	after	ADP
ejpam-3415	77	75	that	that	PRON
ejpam-3415	77	76	(	(	PUNCT
ejpam-3415	77	77	i	i	PRON
ejpam-3415	77	78	mean	mean	VERB
ejpam-3415	77	79	,	,	PUNCT
ejpam-3415	77	80	not	not	PART
ejpam-3415	77	81	as	as	ADP
ejpam-3415	77	82	in	in	ADP
ejpam-3415	77	83	[	[	X
ejpam-3415	77	84	1–2	1–2	NUM
ejpam-3415	77	85	]	]	PUNCT
ejpam-3415	77	86	)	)	PUNCT
ejpam-3415	77	87	;	;	PUNCT
ejpam-3415	77	88	and	and	CCONJ
ejpam-3415	77	89	emphasize	emphasize	VERB
ejpam-3415	77	90	the	the	DET
ejpam-3415	77	91	fact	fact	NOUN
ejpam-3415	77	92	that	that	SCONJ
ejpam-3415	77	93	the	the	DET
ejpam-3415	77	94	element	element	NOUN
ejpam-3415	77	95	a	a	PRON
ejpam-3415	77	96	should	should	AUX
ejpam-3415	77	97	be	be	AUX
ejpam-3415	77	98	identified	identify	VERB
ejpam-3415	77	99	by	by	ADP
ejpam-3415	77	100	the	the	DET
ejpam-3415	77	101	singleton	singleton	PROPN
ejpam-3415	77	102	{	{	PUNCT
ejpam-3415	77	103	a	a	NOUN
ejpam-3415	77	104	}	}	PUNCT
ejpam-3415	77	105	if	if	SCONJ
ejpam-3415	77	106	and	and	CCONJ
ejpam-3415	77	107	when	when	SCONJ
ejpam-3415	77	108	is	be	AUX
ejpam-3415	77	109	convenient	convenient	ADJ
ejpam-3415	77	110	and	and	CCONJ
ejpam-3415	77	111	no	no	DET
ejpam-3415	77	112	confusion	confusion	NOUN
ejpam-3415	77	113	is	be	AUX
ejpam-3415	77	114	possible	possible	ADJ
ejpam-3415	77	115	.	.	PUNCT
ejpam-3415	78	1	remark	remark	VERB
ejpam-3415	78	2	2.3	2.3	NUM
ejpam-3415	78	3	(	(	PUNCT
ejpam-3415	78	4	see	see	VERB
ejpam-3415	78	5	,	,	PUNCT
ejpam-3415	78	6	for	for	ADP
ejpam-3415	78	7	example	example	NOUN
ejpam-3415	78	8	[	[	X
ejpam-3415	78	9	1	1	NUM
ejpam-3415	78	10	]	]	PUNCT
ejpam-3415	78	11	)	)	PUNCT
ejpam-3415	78	12	in	in	ADP
ejpam-3415	78	13	a	a	DET
ejpam-3415	78	14	hyperlattice	hyperlattice	NOUN
ejpam-3415	78	15	,	,	PUNCT
ejpam-3415	78	16	a∧	a∧	NOUN
ejpam-3415	78	17	b	b	PROPN
ejpam-3415	78	18	=	=	SYM
ejpam-3415	78	19	b	b	PROPN
ejpam-3415	78	20	implies	imply	VERB
ejpam-3415	78	21	a	a	DET
ejpam-3415	78	22	∈	∈	PROPN
ejpam-3415	78	23	a∨	a∨	PROPN
ejpam-3415	78	24	b.	b.	PROPN
ejpam-3415	79	1	[	[	X
ejpam-3415	79	2	indeed	indeed	ADV
ejpam-3415	79	3	,	,	PUNCT
ejpam-3415	79	4	by	by	ADP
ejpam-3415	79	5	definition	definition	NOUN
ejpam-3415	79	6	2.1(4	2.1(4	NUM
ejpam-3415	79	7	)	)	PUNCT
ejpam-3415	79	8	,	,	PUNCT
ejpam-3415	79	9	we	we	PRON
ejpam-3415	79	10	have	have	VERB
ejpam-3415	79	11	a	a	DET
ejpam-3415	79	12	∈	∈	PROPN
ejpam-3415	79	13	a∨	a∨	PROPN
ejpam-3415	79	14	(	(	PUNCT
ejpam-3415	79	15	a∧	a∧	NOUN
ejpam-3415	79	16	b	b	NOUN
ejpam-3415	79	17	)	)	PUNCT
ejpam-3415	79	18	=	=	SYM
ejpam-3415	80	1	a∨	a∨	PROPN
ejpam-3415	80	2	b	b	PROPN
ejpam-3415	80	3	]	]	X
ejpam-3415	80	4	.	.	PUNCT
ejpam-3415	81	1	as	as	SCONJ
ejpam-3415	81	2	we	we	PRON
ejpam-3415	81	3	see	see	VERB
ejpam-3415	81	4	later	later	ADV
ejpam-3415	81	5	,	,	PUNCT
ejpam-3415	81	6	the	the	DET
ejpam-3415	81	7	converse	converse	NOUN
ejpam-3415	81	8	of	of	ADP
ejpam-3415	81	9	this	this	DET
ejpam-3415	81	10	statement	statement	NOUN
ejpam-3415	81	11	does	do	AUX
ejpam-3415	81	12	not	not	PART
ejpam-3415	81	13	hold	hold	VERB
ejpam-3415	81	14	in	in	ADP
ejpam-3415	81	15	general	general	ADJ
ejpam-3415	81	16	.	.	PUNCT
ejpam-3415	82	1	example	example	NOUN
ejpam-3415	82	2	2.4	2.4	NUM
ejpam-3415	82	3	the	the	DET
ejpam-3415	82	4	set	set	ADJ
ejpam-3415	82	5	l	l	NOUN
ejpam-3415	82	6	=	=	PUNCT
ejpam-3415	82	7	{	{	PUNCT
ejpam-3415	82	8	a	a	PRON
ejpam-3415	82	9	,	,	PUNCT
ejpam-3415	82	10	b	b	NOUN
ejpam-3415	82	11	,	,	PUNCT
ejpam-3415	82	12	c	c	NOUN
ejpam-3415	82	13	}	}	PUNCT
ejpam-3415	82	14	with	with	ADP
ejpam-3415	82	15	the	the	DET
ejpam-3415	82	16	operation	operation	NOUN
ejpam-3415	82	17	“	"	PUNCT
ejpam-3415	82	18	∧	∧	PROPN
ejpam-3415	82	19	”	"	PUNCT
ejpam-3415	82	20	and	and	CCONJ
ejpam-3415	82	21	the	the	DET
ejpam-3415	82	22	hyperoperation	hyperoperation	NOUN
ejpam-3415	82	23	“	"	PUNCT
ejpam-3415	82	24	∨	∨	NOUN
ejpam-3415	82	25	”	"	PUNCT
ejpam-3415	82	26	given	give	VERB
ejpam-3415	82	27	by	by	ADP
ejpam-3415	82	28	table	table	NOUN
ejpam-3415	82	29	2	2	NUM
ejpam-3415	82	30	is	be	AUX
ejpam-3415	82	31	a	a	DET
ejpam-3415	82	32	hyperlattice	hyperlattice	NOUN
ejpam-3415	82	33	.	.	PUNCT
ejpam-3415	83	1	table	table	NOUN
ejpam-3415	83	2	2	2	NUM
ejpam-3415	83	3	:	:	PUNCT
ejpam-3415	83	4	the	the	DET
ejpam-3415	83	5	hyperlattice	hyperlattice	NOUN
ejpam-3415	83	6	of	of	ADP
ejpam-3415	83	7	the	the	DET
ejpam-3415	83	8	example	example	NOUN
ejpam-3415	83	9	2.4	2.4	NUM
ejpam-3415	83	10	.	.	PUNCT
ejpam-3415	84	1	∧	∧	NOUN
ejpam-3415	84	2	a	a	DET
ejpam-3415	84	3	b	b	X
ejpam-3415	84	4	c	c	NOUN
ejpam-3415	84	5	a	a	DET
ejpam-3415	84	6	a	a	PRON
ejpam-3415	84	7	a	a	PRON
ejpam-3415	84	8	a	a	DET
ejpam-3415	84	9	b	b	NOUN
ejpam-3415	84	10	a	a	DET
ejpam-3415	84	11	b	b	PROPN
ejpam-3415	84	12	b	b	PROPN
ejpam-3415	84	13	c	c	PROPN
ejpam-3415	84	14	a	a	DET
ejpam-3415	84	15	b	b	X
ejpam-3415	84	16	c	c	X
ejpam-3415	84	17	(	(	PUNCT
ejpam-3415	84	18	a	a	NOUN
ejpam-3415	84	19	)	)	PUNCT
ejpam-3415	84	20	∨	∨	NOUN
ejpam-3415	84	21	a	a	DET
ejpam-3415	84	22	b	b	NOUN
ejpam-3415	84	23	c	c	X
ejpam-3415	84	24	a	a	DET
ejpam-3415	84	25	{	{	PUNCT
ejpam-3415	84	26	a	a	PROPN
ejpam-3415	84	27	,	,	PUNCT
ejpam-3415	84	28	b	b	NOUN
ejpam-3415	84	29	,	,	PUNCT
ejpam-3415	84	30	c	c	NOUN
ejpam-3415	84	31	}	}	PUNCT
ejpam-3415	84	32	{	{	PUNCT
ejpam-3415	84	33	b	b	NOUN
ejpam-3415	84	34	,	,	PUNCT
ejpam-3415	84	35	c	c	NOUN
ejpam-3415	84	36	}	}	PUNCT
ejpam-3415	84	37	{	{	PUNCT
ejpam-3415	84	38	c	c	NOUN
ejpam-3415	84	39	}	}	PUNCT
ejpam-3415	84	40	b	b	PROPN
ejpam-3415	84	41	{	{	PUNCT
ejpam-3415	84	42	b	b	NOUN
ejpam-3415	84	43	,	,	PUNCT
ejpam-3415	84	44	c	c	NOUN
ejpam-3415	84	45	}	}	PUNCT
ejpam-3415	84	46	{	{	PUNCT
ejpam-3415	84	47	b	b	NOUN
ejpam-3415	84	48	}	}	PUNCT
ejpam-3415	84	49	{	{	PUNCT
ejpam-3415	84	50	c	c	NOUN
ejpam-3415	84	51	}	}	PUNCT
ejpam-3415	84	52	c	c	NOUN
ejpam-3415	84	53	{	{	PUNCT
ejpam-3415	84	54	c	c	NOUN
ejpam-3415	84	55	}	}	PUNCT
ejpam-3415	84	56	{	{	PUNCT
ejpam-3415	84	57	c	c	NOUN
ejpam-3415	84	58	}	}	PUNCT
ejpam-3415	84	59	{	{	PUNCT
ejpam-3415	84	60	c	c	NOUN
ejpam-3415	84	61	}	}	PUNCT
ejpam-3415	84	62	(	(	PUNCT
ejpam-3415	84	63	b	b	NOUN
ejpam-3415	84	64	)	)	PUNCT
ejpam-3415	84	65	niovi	niovi	NOUN
ejpam-3415	84	66	kehayopulu	kehayopulu	ADJ
ejpam-3415	84	67	/	/	SYM
ejpam-3415	84	68	eur	eur	PROPN
ejpam-3415	84	69	.	.	PUNCT
ejpam-3415	85	1	j.	j.	PROPN
ejpam-3415	85	2	pure	pure	PROPN
ejpam-3415	85	3	appl	appl	PROPN
ejpam-3415	85	4	.	.	PROPN
ejpam-3415	85	5	math	math	PROPN
ejpam-3415	85	6	,	,	PUNCT
ejpam-3415	85	7	12	12	NUM
ejpam-3415	85	8	(	(	PUNCT
ejpam-3415	85	9	2	2	NUM
ejpam-3415	85	10	)	)	PUNCT
ejpam-3415	85	11	(	(	PUNCT
ejpam-3415	85	12	2019	2019	NUM
ejpam-3415	85	13	)	)	PUNCT
ejpam-3415	85	14	,	,	PUNCT
ejpam-3415	85	15	252	252	NUM
ejpam-3415	85	16	-	-	SYM
ejpam-3415	85	17	269	269	NUM
ejpam-3415	85	18	256	256	NUM
ejpam-3415	85	19	proposition	proposition	NOUN
ejpam-3415	85	20	2.5	2.5	NUM
ejpam-3415	85	21	every	every	DET
ejpam-3415	85	22	lattice	lattice	NOUN
ejpam-3415	85	23	(	(	PUNCT
ejpam-3415	85	24	l,∧,∨	l,∧,∨	X
ejpam-3415	85	25	)	)	PUNCT
ejpam-3415	85	26	is	be	AUX
ejpam-3415	85	27	a	a	DET
ejpam-3415	85	28	hyperlattice	hyperlattice	NOUN
ejpam-3415	85	29	.	.	PUNCT
ejpam-3415	86	1	proof	proof	NOUN
ejpam-3415	86	2	we	we	PRON
ejpam-3415	86	3	consider	consider	VERB
ejpam-3415	86	4	the	the	DET
ejpam-3415	86	5	operation	operation	NOUN
ejpam-3415	86	6	∧	∧	NOUN
ejpam-3415	86	7	:	:	PUNCT
ejpam-3415	86	8	l×	l×	PROPN
ejpam-3415	86	9	l	l	NOUN
ejpam-3415	86	10	→	→	PUNCT
ejpam-3415	86	11	l	l	NOUN
ejpam-3415	87	1	|	|	ADV
ejpam-3415	87	2	(	(	PUNCT
ejpam-3415	87	3	a	a	DET
ejpam-3415	87	4	,	,	PUNCT
ejpam-3415	87	5	b	b	NOUN
ejpam-3415	87	6	)	)	PUNCT
ejpam-3415	87	7	→	→	PUNCT
ejpam-3415	87	8	a	a	DET
ejpam-3415	87	9	∧	∧	PROPN
ejpam-3415	87	10	b	b	PROPN
ejpam-3415	87	11	and	and	CCONJ
ejpam-3415	87	12	the	the	DET
ejpam-3415	87	13	hyperoperation	hyperoperation	NOUN
ejpam-3415	87	14	“	"	PUNCT
ejpam-3415	87	15	.	.	PUNCT
ejpam-3415	88	1	∨	∨	NOUN
ejpam-3415	88	2	”	"	PUNCT
ejpam-3415	88	3	on	on	ADP
ejpam-3415	88	4	l	l	NOUN
ejpam-3415	88	5	defined	define	VERB
ejpam-3415	88	6	by	by	ADP
ejpam-3415	88	7	.	.	PUNCT
ejpam-3415	89	1	∨	∨	NUM
ejpam-3415	89	2	:	:	PUNCT
ejpam-3415	89	3	l×	l×	PROPN
ejpam-3415	89	4	l	l	NOUN
ejpam-3415	89	5	→	→	SYM
ejpam-3415	89	6	p∗(l	p∗(l	NOUN
ejpam-3415	89	7	)	)	PUNCT
ejpam-3415	89	8	|	|	NOUN
ejpam-3415	89	9	(	(	PUNCT
ejpam-3415	89	10	a	a	DET
ejpam-3415	89	11	,	,	PUNCT
ejpam-3415	89	12	b	b	NOUN
ejpam-3415	89	13	)	)	PUNCT
ejpam-3415	89	14	→	→	SYM
ejpam-3415	89	15	a	a	PRON
ejpam-3415	89	16	.	.	PUNCT
ejpam-3415	90	1	∨	∨	NUM
ejpam-3415	90	2	b	b	X
ejpam-3415	90	3	:	:	PUNCT
ejpam-3415	90	4	=	=	X
ejpam-3415	90	5	{	{	PUNCT
ejpam-3415	90	6	a	a	DET
ejpam-3415	90	7	∨	∨	NUM
ejpam-3415	90	8	b	b	NOUN
ejpam-3415	90	9	}	}	PUNCT
ejpam-3415	90	10	.	.	PUNCT
ejpam-3415	91	1	then	then	ADV
ejpam-3415	91	2	(	(	PUNCT
ejpam-3415	91	3	l,∧	l,∧	NOUN
ejpam-3415	91	4	,	,	PUNCT
ejpam-3415	91	5	.	.	PUNCT
ejpam-3415	91	6	∨	∨	NUM
ejpam-3415	91	7	)	)	PUNCT
ejpam-3415	91	8	is	be	AUX
ejpam-3415	91	9	a	a	DET
ejpam-3415	91	10	hyperlattice	hyperlattice	NOUN
ejpam-3415	91	11	.	.	PUNCT
ejpam-3415	92	1	indeed	indeed	ADV
ejpam-3415	92	2	:	:	PUNCT
ejpam-3415	92	3	the	the	DET
ejpam-3415	92	4	operation	operation	NOUN
ejpam-3415	92	5	.	.	PUNCT
ejpam-3415	93	1	∨	∨	NOUN
ejpam-3415	93	2	is	be	AUX
ejpam-3415	93	3	well	well	ADV
ejpam-3415	93	4	defined	define	VERB
ejpam-3415	93	5	,	,	PUNCT
ejpam-3415	93	6	the	the	DET
ejpam-3415	93	7	properties	property	NOUN
ejpam-3415	93	8	(	(	PUNCT
ejpam-3415	93	9	1	1	NUM
ejpam-3415	93	10	)	)	PUNCT
ejpam-3415	93	11	and	and	CCONJ
ejpam-3415	93	12	(	(	PUNCT
ejpam-3415	93	13	2	2	X
ejpam-3415	93	14	)	)	PUNCT
ejpam-3415	93	15	of	of	ADP
ejpam-3415	93	16	definition	definition	NOUN
ejpam-3415	93	17	2.1	2.1	NUM
ejpam-3415	93	18	are	be	AUX
ejpam-3415	93	19	satisfied	satisfied	ADJ
ejpam-3415	93	20	,	,	PUNCT
ejpam-3415	93	21	the	the	DET
ejpam-3415	93	22	operation	operation	NOUN
ejpam-3415	93	23	“	"	PUNCT
ejpam-3415	93	24	.	.	PUNCT
ejpam-3415	94	1	∨	∨	NOUN
ejpam-3415	94	2	”	"	PUNCT
ejpam-3415	94	3	is	be	AUX
ejpam-3415	94	4	associative	associative	ADJ
ejpam-3415	94	5	,	,	PUNCT
ejpam-3415	94	6	indeed	indeed	ADV
ejpam-3415	94	7	⋃	⋃	VERB
ejpam-3415	94	8	u∈a	u∈a	NOUN
ejpam-3415	94	9	.	.	PUNCT
ejpam-3415	95	1	∨	∨	NUM
ejpam-3415	95	2	b	b	PROPN
ejpam-3415	95	3	u	u	PROPN
ejpam-3415	95	4	.	.	PUNCT
ejpam-3415	96	1	∨	∨	NUM
ejpam-3415	96	2	c	c	X
ejpam-3415	96	3	=	=	PUNCT
ejpam-3415	97	1	⋃	⋃	NOUN
ejpam-3415	97	2	u	u	NOUN
ejpam-3415	97	3	=	=	NOUN
ejpam-3415	97	4	a∨b	a∨b	NOUN
ejpam-3415	97	5	u	u	NOUN
ejpam-3415	97	6	.	.	PUNCT
ejpam-3415	98	1	∨	∨	NUM
ejpam-3415	98	2	c	c	X
ejpam-3415	98	3	=	=	SYM
ejpam-3415	98	4	(	(	PUNCT
ejpam-3415	98	5	a	a	DET
ejpam-3415	98	6	∨	∨	NUM
ejpam-3415	98	7	b	b	NOUN
ejpam-3415	98	8	)	)	PUNCT
ejpam-3415	98	9	.	.	PUNCT
ejpam-3415	99	1	∨	∨	NUM
ejpam-3415	99	2	c	c	X
ejpam-3415	99	3	=	=	PRON
ejpam-3415	99	4	{	{	PUNCT
ejpam-3415	99	5	(	(	PUNCT
ejpam-3415	99	6	a	a	DET
ejpam-3415	99	7	∨	∨	NUM
ejpam-3415	99	8	b	b	NOUN
ejpam-3415	99	9	)	)	PUNCT
ejpam-3415	99	10	∨	∨	NUM
ejpam-3415	99	11	c	c	NOUN
ejpam-3415	99	12	}	}	PUNCT
ejpam-3415	99	13	,	,	PUNCT
ejpam-3415	99	14	⋃	⋃	SCONJ
ejpam-3415	99	15	v∈b	v∈b	NOUN
ejpam-3415	99	16	.	.	PUNCT
ejpam-3415	100	1	∨	∨	PROPN
ejpam-3415	100	2	c	c	PROPN
ejpam-3415	100	3	a	a	PRON
ejpam-3415	100	4	.	.	PUNCT
ejpam-3415	101	1	∨	∨	NUM
ejpam-3415	101	2	v	v	NOUN
ejpam-3415	101	3	=	=	PUNCT
ejpam-3415	101	4	⋃	⋃	NOUN
ejpam-3415	101	5	v	v	NOUN
ejpam-3415	101	6	=	=	PROPN
ejpam-3415	101	7	b∨c	b∨c	PROPN
ejpam-3415	101	8	a	a	X
ejpam-3415	101	9	.	.	PUNCT
ejpam-3415	102	1	∨	∨	NUM
ejpam-3415	102	2	v	v	NOUN
ejpam-3415	102	3	=	=	SYM
ejpam-3415	102	4	a	a	DET
ejpam-3415	102	5	.	.	PUNCT
ejpam-3415	102	6	∨(b	∨(b	ADJ
ejpam-3415	102	7	∨	∨	NUM
ejpam-3415	102	8	c	c	NOUN
ejpam-3415	102	9	)	)	PUNCT
ejpam-3415	102	10	=	=	PRON
ejpam-3415	102	11	{	{	PUNCT
ejpam-3415	102	12	a	a	DET
ejpam-3415	102	13	∨	∨	X
ejpam-3415	102	14	(	(	PUNCT
ejpam-3415	102	15	b	b	PROPN
ejpam-3415	102	16	∨	∨	NUM
ejpam-3415	102	17	c	c	NOUN
ejpam-3415	102	18	)	)	PUNCT
ejpam-3415	102	19	}	}	PUNCT
ejpam-3415	102	20	and	and	CCONJ
ejpam-3415	102	21	since	since	SCONJ
ejpam-3415	102	22	(	(	PUNCT
ejpam-3415	102	23	a	a	DET
ejpam-3415	102	24	∨	∨	NUM
ejpam-3415	102	25	b	b	NOUN
ejpam-3415	102	26	)	)	PUNCT
ejpam-3415	102	27	∨	∨	NUM
ejpam-3415	102	28	c	c	NOUN
ejpam-3415	102	29	=	=	PUNCT
ejpam-3415	102	30	a	a	DET
ejpam-3415	102	31	∨	∨	NOUN
ejpam-3415	102	32	(	(	PUNCT
ejpam-3415	102	33	b	b	PROPN
ejpam-3415	102	34	∨	∨	NUM
ejpam-3415	102	35	c	c	PROPN
ejpam-3415	102	36	)	)	PUNCT
ejpam-3415	102	37	,	,	PUNCT
ejpam-3415	102	38	we	we	PRON
ejpam-3415	102	39	have	have	VERB
ejpam-3415	102	40	⋃	⋃	VERB
ejpam-3415	102	41	u∈a	u∈a	NOUN
ejpam-3415	102	42	.	.	PUNCT
ejpam-3415	103	1	∨	∨	NUM
ejpam-3415	103	2	b	b	PROPN
ejpam-3415	103	3	u	u	PROPN
ejpam-3415	103	4	.	.	PUNCT
ejpam-3415	104	1	∨	∨	NUM
ejpam-3415	104	2	c	c	X
ejpam-3415	104	3	=	=	PUNCT
ejpam-3415	104	4	⋃	⋃	NOUN
ejpam-3415	104	5	v∈b	v∈b	NOUN
ejpam-3415	104	6	.	.	PUNCT
ejpam-3415	105	1	∨	∨	PROPN
ejpam-3415	105	2	c	c	PROPN
ejpam-3415	105	3	a	a	PRON
ejpam-3415	105	4	.	.	PUNCT
ejpam-3415	106	1	∨	∨	NOUN
ejpam-3415	106	2	v.	v.	CCONJ
ejpam-3415	106	3	if	if	SCONJ
ejpam-3415	106	4	a	a	DET
ejpam-3415	106	5	,	,	PUNCT
ejpam-3415	106	6	b	b	X
ejpam-3415	106	7	∈	∈	NOUN
ejpam-3415	106	8	l	l	NOUN
ejpam-3415	106	9	then	then	ADV
ejpam-3415	106	10	,	,	PUNCT
ejpam-3415	106	11	for	for	ADP
ejpam-3415	106	12	the	the	DET
ejpam-3415	106	13	element	element	ADJ
ejpam-3415	106	14	u	u	NOUN
ejpam-3415	106	15	:	:	PUNCT
ejpam-3415	106	16	=	=	PUNCT
ejpam-3415	106	17	a	a	DET
ejpam-3415	106	18	∨	∨	NUM
ejpam-3415	106	19	b	b	X
ejpam-3415	106	20	∈	∈	PROPN
ejpam-3415	106	21	a	a	PRON
ejpam-3415	106	22	.	.	PUNCT
ejpam-3415	107	1	∨	∨	NUM
ejpam-3415	107	2	b	b	PROPN
ejpam-3415	107	3	,	,	PUNCT
ejpam-3415	107	4	we	we	PRON
ejpam-3415	107	5	have	have	VERB
ejpam-3415	107	6	a	a	DET
ejpam-3415	107	7	∧	∧	PROPN
ejpam-3415	107	8	u	u	NOUN
ejpam-3415	107	9	=	=	PROPN
ejpam-3415	107	10	a	a	DET
ejpam-3415	107	11	∧	∧	PROPN
ejpam-3415	107	12	(	(	PUNCT
ejpam-3415	107	13	a	a	DET
ejpam-3415	107	14	∨	∨	NUM
ejpam-3415	107	15	b	b	NOUN
ejpam-3415	107	16	)	)	PUNCT
ejpam-3415	107	17	=	=	SYM
ejpam-3415	107	18	a	a	NOUN
ejpam-3415	107	19	;	;	PUNCT
ejpam-3415	107	20	and	and	CCONJ
ejpam-3415	107	21	a	a	DET
ejpam-3415	107	22	∈	∈	NOUN
ejpam-3415	107	23	{	{	PUNCT
ejpam-3415	107	24	a	a	NOUN
ejpam-3415	107	25	}	}	PUNCT
ejpam-3415	107	26	=	=	SYM
ejpam-3415	107	27	{	{	PUNCT
ejpam-3415	107	28	a	a	DET
ejpam-3415	107	29	∨	∨	NOUN
ejpam-3415	107	30	(	(	PUNCT
ejpam-3415	107	31	a	a	DET
ejpam-3415	107	32	∧	∧	PROPN
ejpam-3415	107	33	b	b	NOUN
ejpam-3415	107	34	)	)	PUNCT
ejpam-3415	107	35	}	}	PUNCT
ejpam-3415	107	36	=	=	SYM
ejpam-3415	107	37	a	a	PRON
ejpam-3415	107	38	.	.	PUNCT
ejpam-3415	108	1	∨(a	∨(a	PROPN
ejpam-3415	108	2	∧	∧	PROPN
ejpam-3415	108	3	b	b	PROPN
ejpam-3415	108	4	)	)	PUNCT
ejpam-3415	108	5	.	.	PUNCT
ejpam-3415	109	1	second	second	ADJ
ejpam-3415	109	2	proof	proof	NOUN
ejpam-3415	109	3	we	we	PRON
ejpam-3415	109	4	consider	consider	VERB
ejpam-3415	109	5	the	the	DET
ejpam-3415	109	6	operation	operation	NOUN
ejpam-3415	109	7	∧	∧	NOUN
ejpam-3415	109	8	:	:	PUNCT
ejpam-3415	109	9	l×	l×	PROPN
ejpam-3415	109	10	l	l	NOUN
ejpam-3415	109	11	→	→	PUNCT
ejpam-3415	109	12	l	l	NOUN
ejpam-3415	110	1	|	|	ADV
ejpam-3415	110	2	(	(	PUNCT
ejpam-3415	110	3	a	a	DET
ejpam-3415	110	4	,	,	PUNCT
ejpam-3415	110	5	b	b	NOUN
ejpam-3415	110	6	)	)	PUNCT
ejpam-3415	110	7	→	→	PUNCT
ejpam-3415	110	8	a	a	DET
ejpam-3415	110	9	∧	∧	PROPN
ejpam-3415	110	10	b	b	PROPN
ejpam-3415	110	11	and	and	CCONJ
ejpam-3415	110	12	the	the	DET
ejpam-3415	110	13	hyperoperation	hyperoperation	NOUN
ejpam-3415	110	14	“	"	PUNCT
ejpam-3415	110	15	.	.	PUNCT
ejpam-3415	111	1	∨	∨	NOUN
ejpam-3415	111	2	”	"	PUNCT
ejpam-3415	111	3	on	on	ADP
ejpam-3415	111	4	l	l	NOUN
ejpam-3415	111	5	defined	define	VERB
ejpam-3415	111	6	by	by	ADP
ejpam-3415	111	7	.	.	PUNCT
ejpam-3415	112	1	∨	∨	NUM
ejpam-3415	112	2	:	:	PUNCT
ejpam-3415	112	3	l×	l×	PROPN
ejpam-3415	112	4	l	l	NOUN
ejpam-3415	112	5	→	→	SYM
ejpam-3415	112	6	p∗(l	p∗(l	NOUN
ejpam-3415	112	7	)	)	PUNCT
ejpam-3415	112	8	|	|	NOUN
ejpam-3415	112	9	(	(	PUNCT
ejpam-3415	112	10	a	a	DET
ejpam-3415	112	11	,	,	PUNCT
ejpam-3415	112	12	b	b	NOUN
ejpam-3415	112	13	)	)	PUNCT
ejpam-3415	112	14	→	→	SYM
ejpam-3415	112	15	a	a	PRON
ejpam-3415	112	16	.	.	PUNCT
ejpam-3415	113	1	∨	∨	NUM
ejpam-3415	113	2	b	b	X
ejpam-3415	113	3	:	:	PUNCT
ejpam-3415	113	4	=	=	X
ejpam-3415	113	5	{	{	PUNCT
ejpam-3415	113	6	a	a	DET
ejpam-3415	113	7	,	,	PUNCT
ejpam-3415	113	8	b	b	NOUN
ejpam-3415	113	9	,	,	PUNCT
ejpam-3415	113	10	a	a	DET
ejpam-3415	113	11	∨	∨	NOUN
ejpam-3415	113	12	b	b	NOUN
ejpam-3415	113	13	}	}	PUNCT
ejpam-3415	113	14	.	.	PUNCT
ejpam-3415	114	1	then	then	ADV
ejpam-3415	114	2	(	(	PUNCT
ejpam-3415	114	3	l,∧	l,∧	NOUN
ejpam-3415	114	4	,	,	PUNCT
ejpam-3415	114	5	.	.	PUNCT
ejpam-3415	114	6	∨	∨	NUM
ejpam-3415	114	7	)	)	PUNCT
ejpam-3415	114	8	is	be	AUX
ejpam-3415	114	9	a	a	DET
ejpam-3415	114	10	hyperlattice	hyperlattice	NOUN
ejpam-3415	114	11	.	.	PUNCT
ejpam-3415	115	1	indeed	indeed	ADV
ejpam-3415	115	2	:	:	PUNCT
ejpam-3415	115	3	the	the	DET
ejpam-3415	115	4	hyperoperation	hyperoperation	NOUN
ejpam-3415	115	5	“	"	PUNCT
ejpam-3415	115	6	.	.	PUNCT
ejpam-3415	116	1	∨	∨	NOUN
ejpam-3415	116	2	”	"	PUNCT
ejpam-3415	116	3	is	be	AUX
ejpam-3415	116	4	well	well	ADV
ejpam-3415	116	5	defined	define	VERB
ejpam-3415	116	6	and	and	CCONJ
ejpam-3415	116	7	the	the	DET
ejpam-3415	116	8	following	follow	VERB
ejpam-3415	116	9	assertions	assertion	NOUN
ejpam-3415	116	10	are	be	AUX
ejpam-3415	116	11	satisfied	satisfied	ADJ
ejpam-3415	116	12	:	:	PUNCT
ejpam-3415	116	13	(	(	PUNCT
ejpam-3415	116	14	1	1	X
ejpam-3415	116	15	)	)	PUNCT
ejpam-3415	116	16	a	a	DET
ejpam-3415	116	17	∈	∈	PROPN
ejpam-3415	116	18	a	a	PRON
ejpam-3415	116	19	.	.	PUNCT
ejpam-3415	117	1	∨	∨	NUM
ejpam-3415	117	2	a	a	DET
ejpam-3415	117	3	,	,	PUNCT
ejpam-3415	117	4	since	since	SCONJ
ejpam-3415	117	5	a	a	PRON
ejpam-3415	117	6	.	.	PUNCT
ejpam-3415	118	1	∨	∨	NOUN
ejpam-3415	118	2	a	a	PRON
ejpam-3415	118	3	:	:	PUNCT
ejpam-3415	118	4	=	=	X
ejpam-3415	118	5	{	{	PUNCT
ejpam-3415	118	6	a	a	X
ejpam-3415	118	7	,	,	PUNCT
ejpam-3415	118	8	a	a	PRON
ejpam-3415	118	9	,	,	PUNCT
ejpam-3415	118	10	a	a	DET
ejpam-3415	118	11	∨	∨	NOUN
ejpam-3415	118	12	a	a	DET
ejpam-3415	118	13	}	}	PUNCT
ejpam-3415	118	14	=	=	SYM
ejpam-3415	118	15	{	{	PUNCT
ejpam-3415	118	16	a	a	X
ejpam-3415	118	17	}	}	PUNCT
ejpam-3415	118	18	.	.	PUNCT
ejpam-3415	119	1	(	(	PUNCT
ejpam-3415	119	2	2	2	X
ejpam-3415	119	3	)	)	PUNCT
ejpam-3415	119	4	it	it	PRON
ejpam-3415	119	5	is	be	AUX
ejpam-3415	119	6	clear	clear	ADJ
ejpam-3415	119	7	.	.	PUNCT
ejpam-3415	120	1	(	(	PUNCT
ejpam-3415	120	2	3	3	X
ejpam-3415	120	3	)	)	PUNCT
ejpam-3415	120	4	we	we	PRON
ejpam-3415	120	5	have	have	AUX
ejpam-3415	120	6	⋃	⋃	VERB
ejpam-3415	120	7	u∈a	u∈a	NOUN
ejpam-3415	120	8	.	.	PUNCT
ejpam-3415	121	1	∨	∨	NUM
ejpam-3415	121	2	b	b	PROPN
ejpam-3415	121	3	u	u	PROPN
ejpam-3415	121	4	.	.	PUNCT
ejpam-3415	122	1	∨	∨	NUM
ejpam-3415	122	2	c	c	X
ejpam-3415	122	3	=	=	PUNCT
ejpam-3415	122	4	⋃	⋃	NOUN
ejpam-3415	122	5	u∈{a	u∈{a	NOUN
ejpam-3415	122	6	,	,	PUNCT
ejpam-3415	122	7	b	b	NOUN
ejpam-3415	122	8	,	,	PUNCT
ejpam-3415	122	9	a∨b	a∨b	PROPN
ejpam-3415	122	10	}	}	PUNCT
ejpam-3415	122	11	u	u	PROPN
ejpam-3415	122	12	.	.	PUNCT
ejpam-3415	123	1	∨	∨	NUM
ejpam-3415	123	2	c	c	X
ejpam-3415	123	3	=	=	SYM
ejpam-3415	123	4	(	(	PUNCT
ejpam-3415	123	5	a	a	NOUN
ejpam-3415	123	6	.	.	PUNCT
ejpam-3415	124	1	∨	∨	NUM
ejpam-3415	124	2	c	c	NOUN
ejpam-3415	124	3	)	)	PUNCT
ejpam-3415	124	4	∨	∨	NOUN
ejpam-3415	124	5	(	(	PUNCT
ejpam-3415	124	6	b	b	PROPN
ejpam-3415	124	7	.	.	PUNCT
ejpam-3415	125	1	∨	∨	NUM
ejpam-3415	125	2	c	c	NOUN
ejpam-3415	125	3	)	)	PUNCT
ejpam-3415	125	4	∨	∨	NOUN
ejpam-3415	125	5	(	(	PUNCT
ejpam-3415	125	6	(	(	PUNCT
ejpam-3415	125	7	a	a	DET
ejpam-3415	125	8	∨	∨	NUM
ejpam-3415	125	9	b	b	NOUN
ejpam-3415	125	10	)	)	PUNCT
ejpam-3415	125	11	.	.	PUNCT
ejpam-3415	126	1	∨	∨	NUM
ejpam-3415	126	2	c	c	NOUN
ejpam-3415	126	3	)	)	PUNCT
ejpam-3415	127	1	=	=	PRON
ejpam-3415	127	2	{	{	PUNCT
ejpam-3415	127	3	a	a	X
ejpam-3415	127	4	,	,	PUNCT
ejpam-3415	127	5	c	c	NOUN
ejpam-3415	127	6	,	,	PUNCT
ejpam-3415	127	7	a	a	DET
ejpam-3415	127	8	∨	∨	NOUN
ejpam-3415	127	9	c	c	X
ejpam-3415	127	10	,	,	PUNCT
ejpam-3415	127	11	b	b	PROPN
ejpam-3415	127	12	,	,	PUNCT
ejpam-3415	127	13	c	c	NOUN
ejpam-3415	127	14	,	,	PUNCT
ejpam-3415	127	15	b	b	PROPN
ejpam-3415	127	16	∨	∨	NUM
ejpam-3415	127	17	c	c	PROPN
ejpam-3415	127	18	,	,	PUNCT
ejpam-3415	127	19	a	a	DET
ejpam-3415	127	20	∨	∨	PROPN
ejpam-3415	127	21	b	b	PROPN
ejpam-3415	127	22	,	,	PUNCT
ejpam-3415	127	23	c	c	PROPN
ejpam-3415	127	24	,	,	PUNCT
ejpam-3415	127	25	(	(	PUNCT
ejpam-3415	127	26	a	a	DET
ejpam-3415	127	27	∨	∨	NUM
ejpam-3415	127	28	b	b	NOUN
ejpam-3415	127	29	)	)	PUNCT
ejpam-3415	127	30	∨	∨	NUM
ejpam-3415	127	31	c	c	NOUN
ejpam-3415	127	32	}	}	PUNCT
ejpam-3415	127	33	.	.	PUNCT
ejpam-3415	128	1	⋃	⋃	VERB
ejpam-3415	128	2	v∈b	v∈b	NOUN
ejpam-3415	128	3	.	.	PUNCT
ejpam-3415	129	1	∨	∨	PROPN
ejpam-3415	129	2	c	c	PROPN
ejpam-3415	129	3	a	a	PRON
ejpam-3415	129	4	.	.	PUNCT
ejpam-3415	130	1	∨	∨	NUM
ejpam-3415	130	2	v	v	NOUN
ejpam-3415	130	3	=	=	SYM
ejpam-3415	130	4	⋃	⋃	NOUN
ejpam-3415	130	5	v∈{b	v∈{b	ADJ
ejpam-3415	130	6	,	,	PUNCT
ejpam-3415	130	7	c	c	NOUN
ejpam-3415	130	8	,	,	PUNCT
ejpam-3415	130	9	b∨c	b∨c	PROPN
ejpam-3415	130	10	}	}	PUNCT
ejpam-3415	130	11	a	a	PRON
ejpam-3415	130	12	.	.	PUNCT
ejpam-3415	131	1	∨	∨	NUM
ejpam-3415	131	2	v	v	NOUN
ejpam-3415	131	3	=	=	SYM
ejpam-3415	131	4	(	(	PUNCT
ejpam-3415	131	5	a	a	NOUN
ejpam-3415	131	6	.	.	PUNCT
ejpam-3415	132	1	∨	∨	NUM
ejpam-3415	132	2	b	b	NOUN
ejpam-3415	132	3	)	)	PUNCT
ejpam-3415	132	4	∨	∨	NOUN
ejpam-3415	132	5	(	(	PUNCT
ejpam-3415	132	6	a	a	PRON
ejpam-3415	132	7	.	.	PUNCT
ejpam-3415	133	1	∨	∨	NUM
ejpam-3415	133	2	c	c	NOUN
ejpam-3415	133	3	)	)	PUNCT
ejpam-3415	133	4	∨	∨	NOUN
ejpam-3415	133	5	(	(	PUNCT
ejpam-3415	133	6	a	a	PRON
ejpam-3415	133	7	.	.	PUNCT
ejpam-3415	133	8	∨(b	∨(b	ADJ
ejpam-3415	133	9	∨	∨	NUM
ejpam-3415	133	10	c	c	NOUN
ejpam-3415	133	11	)	)	PUNCT
ejpam-3415	133	12	)	)	PUNCT
ejpam-3415	134	1	=	=	PRON
ejpam-3415	134	2	{	{	PUNCT
ejpam-3415	134	3	a	a	DET
ejpam-3415	134	4	,	,	PUNCT
ejpam-3415	134	5	b	b	NOUN
ejpam-3415	134	6	,	,	PUNCT
ejpam-3415	134	7	a	a	DET
ejpam-3415	134	8	∨	∨	PROPN
ejpam-3415	134	9	b	b	PROPN
ejpam-3415	134	10	,	,	PUNCT
ejpam-3415	134	11	a	a	DET
ejpam-3415	134	12	,	,	PUNCT
ejpam-3415	134	13	c	c	NOUN
ejpam-3415	134	14	,	,	PUNCT
ejpam-3415	134	15	a	a	DET
ejpam-3415	134	16	∨	∨	PROPN
ejpam-3415	134	17	c	c	NOUN
ejpam-3415	134	18	,	,	PUNCT
ejpam-3415	134	19	a	a	PRON
ejpam-3415	134	20	,	,	PUNCT
ejpam-3415	134	21	b	b	PROPN
ejpam-3415	134	22	∨	∨	NUM
ejpam-3415	134	23	c	c	PROPN
ejpam-3415	134	24	,	,	PUNCT
ejpam-3415	134	25	a	a	DET
ejpam-3415	134	26	∨	∨	NOUN
ejpam-3415	134	27	(	(	PUNCT
ejpam-3415	134	28	b	b	PROPN
ejpam-3415	134	29	∨	∨	NUM
ejpam-3415	134	30	c	c	NOUN
ejpam-3415	134	31	)	)	PUNCT
ejpam-3415	134	32	}	}	PUNCT
ejpam-3415	134	33	.	.	PUNCT
ejpam-3415	135	1	since	since	SCONJ
ejpam-3415	135	2	l	l	NOUN
ejpam-3415	135	3	is	be	AUX
ejpam-3415	135	4	a	a	DET
ejpam-3415	135	5	lattice	lattice	NOUN
ejpam-3415	135	6	,	,	PUNCT
ejpam-3415	135	7	we	we	PRON
ejpam-3415	135	8	have	have	VERB
ejpam-3415	135	9	(	(	PUNCT
ejpam-3415	135	10	a	a	DET
ejpam-3415	135	11	∨	∨	NUM
ejpam-3415	135	12	b	b	NOUN
ejpam-3415	135	13	)	)	PUNCT
ejpam-3415	135	14	∨	∨	NUM
ejpam-3415	135	15	c	c	NOUN
ejpam-3415	135	16	=	=	PUNCT
ejpam-3415	135	17	a	a	DET
ejpam-3415	135	18	∨	∨	NOUN
ejpam-3415	135	19	(	(	PUNCT
ejpam-3415	135	20	b	b	PROPN
ejpam-3415	135	21	∨	∨	NUM
ejpam-3415	135	22	c	c	NOUN
ejpam-3415	135	23	)	)	PUNCT
ejpam-3415	135	24	and	and	CCONJ
ejpam-3415	135	25	so	so	ADV
ejpam-3415	135	26	⋃	⋃	PUNCT
ejpam-3415	135	27	u∈a	u∈a	NOUN
ejpam-3415	135	28	.	.	PUNCT
ejpam-3415	136	1	∨	∨	NUM
ejpam-3415	136	2	b	b	PROPN
ejpam-3415	136	3	u	u	PROPN
ejpam-3415	136	4	.	.	PUNCT
ejpam-3415	137	1	∨	∨	NUM
ejpam-3415	137	2	c	c	X
ejpam-3415	137	3	=	=	PUNCT
ejpam-3415	137	4	⋃	⋃	NOUN
ejpam-3415	137	5	v∈b	v∈b	NOUN
ejpam-3415	137	6	.	.	PUNCT
ejpam-3415	138	1	∨	∨	PROPN
ejpam-3415	138	2	c	c	PROPN
ejpam-3415	138	3	a	a	PRON
ejpam-3415	138	4	.	.	PUNCT
ejpam-3415	139	1	∨	∨	NUM
ejpam-3415	139	2	v.	v.	CCONJ
ejpam-3415	139	3	(	(	PUNCT
ejpam-3415	139	4	4	4	X
ejpam-3415	139	5	)	)	PUNCT
ejpam-3415	139	6	there	there	PRON
ejpam-3415	139	7	exists	exist	VERB
ejpam-3415	139	8	u	u	PROPN
ejpam-3415	139	9	∈	∈	PROPN
ejpam-3415	139	10	a	a	PRON
ejpam-3415	139	11	.	.	PUNCT
ejpam-3415	140	1	∨	∨	NUM
ejpam-3415	140	2	b	b	X
ejpam-3415	140	3	such	such	ADJ
ejpam-3415	140	4	that	that	PRON
ejpam-3415	140	5	a∧u	a∧u	VERB
ejpam-3415	140	6	=	=	SYM
ejpam-3415	140	7	a.	a.	NOUN
ejpam-3415	140	8	indeed	indeed	ADV
ejpam-3415	140	9	,	,	PUNCT
ejpam-3415	140	10	for	for	ADP
ejpam-3415	140	11	the	the	DET
ejpam-3415	140	12	element	element	ADJ
ejpam-3415	140	13	u	u	NOUN
ejpam-3415	140	14	:	:	PUNCT
ejpam-3415	140	15	=	=	PROPN
ejpam-3415	140	16	a∨b	a∨b	PROPN
ejpam-3415	140	17	∈	∈	PROPN
ejpam-3415	141	1	a	a	PRON
ejpam-3415	141	2	.	.	PUNCT
ejpam-3415	142	1	∨	∨	NUM
ejpam-3415	142	2	b	b	PROPN
ejpam-3415	142	3	,	,	PUNCT
ejpam-3415	142	4	we	we	PRON
ejpam-3415	142	5	have	have	VERB
ejpam-3415	142	6	a∧u	a∧u	VERB
ejpam-3415	142	7	=	=	SYM
ejpam-3415	142	8	a∧	a∧	NOUN
ejpam-3415	142	9	(	(	PUNCT
ejpam-3415	142	10	a∨	a∨	PROPN
ejpam-3415	142	11	b	b	PROPN
ejpam-3415	142	12	)	)	PUNCT
ejpam-3415	142	13	=	=	SYM
ejpam-3415	142	14	a	a	NOUN
ejpam-3415	142	15	;	;	PUNCT
ejpam-3415	142	16	and	and	CCONJ
ejpam-3415	142	17	a	a	DET
ejpam-3415	142	18	∈	∈	PROPN
ejpam-3415	142	19	a	a	PRON
ejpam-3415	142	20	.	.	PUNCT
ejpam-3415	143	1	∨(a∧	∨(a∧	PROPN
ejpam-3415	143	2	b	b	PROPN
ejpam-3415	143	3	)	)	PUNCT
ejpam-3415	143	4	since	since	SCONJ
ejpam-3415	143	5	a	a	PRON
ejpam-3415	143	6	.	.	PUNCT
ejpam-3415	144	1	∨(a∧	∨(a∧	PROPN
ejpam-3415	144	2	b	b	PROPN
ejpam-3415	144	3	)	)	PUNCT
ejpam-3415	144	4	=	=	PRON
ejpam-3415	144	5	{	{	PUNCT
ejpam-3415	144	6	a	a	NOUN
ejpam-3415	144	7	,	,	PUNCT
ejpam-3415	144	8	a∧	a∧	NOUN
ejpam-3415	144	9	b	b	PROPN
ejpam-3415	144	10	,	,	PUNCT
ejpam-3415	144	11	a∨	a∨	PROPN
ejpam-3415	144	12	(	(	PUNCT
ejpam-3415	144	13	a∧	a∧	PROPN
ejpam-3415	144	14	b	b	NOUN
ejpam-3415	144	15	)	)	PUNCT
ejpam-3415	144	16	}	}	PUNCT
ejpam-3415	144	17	=	=	SYM
ejpam-3415	144	18	{	{	PUNCT
ejpam-3415	144	19	a	a	X
ejpam-3415	144	20	,	,	PUNCT
ejpam-3415	144	21	a	a	DET
ejpam-3415	144	22	∧	∧	PROPN
ejpam-3415	144	23	b	b	PROPN
ejpam-3415	144	24	}	}	PUNCT
ejpam-3415	144	25	.	.	PUNCT
ejpam-3415	145	1	�	�	PROPN
ejpam-3415	145	2	we	we	PRON
ejpam-3415	145	3	apply	apply	VERB
ejpam-3415	145	4	proposition	proposition	NOUN
ejpam-3415	145	5	2.5	2.5	NUM
ejpam-3415	145	6	to	to	ADP
ejpam-3415	145	7	the	the	DET
ejpam-3415	145	8	following	follow	VERB
ejpam-3415	145	9	example	example	NOUN
ejpam-3415	145	10	.	.	PUNCT
ejpam-3415	146	1	example	example	NOUN
ejpam-3415	146	2	2.6	2.6	NUM
ejpam-3415	146	3	we	we	PRON
ejpam-3415	146	4	consider	consider	VERB
ejpam-3415	146	5	the	the	DET
ejpam-3415	146	6	lattice	lattice	PROPN
ejpam-3415	146	7	l	l	NOUN
ejpam-3415	146	8	defined	define	VERB
ejpam-3415	146	9	by	by	ADP
ejpam-3415	146	10	figure	figure	NOUN
ejpam-3415	146	11	1	1	NUM
ejpam-3415	146	12	.	.	PUNCT
ejpam-3415	147	1	niovi	niovi	PROPN
ejpam-3415	147	2	kehayopulu	kehayopulu	PROPN
ejpam-3415	147	3	/	/	SYM
ejpam-3415	147	4	eur	eur	PROPN
ejpam-3415	147	5	.	.	PUNCT
ejpam-3415	148	1	j.	j.	PROPN
ejpam-3415	148	2	pure	pure	PROPN
ejpam-3415	148	3	appl	appl	PROPN
ejpam-3415	148	4	.	.	PROPN
ejpam-3415	148	5	math	math	PROPN
ejpam-3415	148	6	,	,	PUNCT
ejpam-3415	148	7	12	12	NUM
ejpam-3415	148	8	(	(	PUNCT
ejpam-3415	148	9	2	2	NUM
ejpam-3415	148	10	)	)	PUNCT
ejpam-3415	148	11	(	(	PUNCT
ejpam-3415	148	12	2019	2019	NUM
ejpam-3415	148	13	)	)	PUNCT
ejpam-3415	148	14	,	,	PUNCT
ejpam-3415	148	15	252	252	NUM
ejpam-3415	148	16	-	-	SYM
ejpam-3415	148	17	269	269	NUM
ejpam-3415	148	18	257	257	NUM
ejpam-3415	148	19	a	a	DET
ejpam-3415	148	20	c	c	NOUN
ejpam-3415	148	21	d	d	X
ejpam-3415	148	22	b	b	X
ejpam-3415	148	23	figure	figure	NOUN
ejpam-3415	148	24	1	1	NUM
ejpam-3415	148	25	:	:	PUNCT
ejpam-3415	148	26	the	the	DET
ejpam-3415	148	27	lattice	lattice	NOUN
ejpam-3415	148	28	of	of	ADP
ejpam-3415	148	29	the	the	DET
ejpam-3415	148	30	example	example	NOUN
ejpam-3415	148	31	2.6	2.6	NUM
ejpam-3415	148	32	.	.	PUNCT
ejpam-3415	149	1	according	accord	VERB
ejpam-3415	149	2	to	to	ADP
ejpam-3415	149	3	the	the	DET
ejpam-3415	149	4	first	first	ADJ
ejpam-3415	149	5	proof	proof	NOUN
ejpam-3415	149	6	of	of	ADP
ejpam-3415	149	7	proposition	proposition	NOUN
ejpam-3415	149	8	2.5	2.5	NUM
ejpam-3415	149	9	,	,	PUNCT
ejpam-3415	149	10	the	the	DET
ejpam-3415	149	11	set	set	ADJ
ejpam-3415	149	12	l	l	NOUN
ejpam-3415	149	13	with	with	ADP
ejpam-3415	149	14	the	the	DET
ejpam-3415	149	15	operation	operation	NOUN
ejpam-3415	149	16	and	and	CCONJ
ejpam-3415	149	17	the	the	DET
ejpam-3415	149	18	hyperoperation	hyperoperation	NOUN
ejpam-3415	149	19	of	of	ADP
ejpam-3415	149	20	table	table	NOUN
ejpam-3415	149	21	3	3	NUM
ejpam-3415	149	22	is	be	AUX
ejpam-3415	149	23	a	a	DET
ejpam-3415	149	24	hyperlattice	hyperlattice	NOUN
ejpam-3415	149	25	.	.	PUNCT
ejpam-3415	150	1	table	table	NOUN
ejpam-3415	150	2	3	3	NUM
ejpam-3415	150	3	:	:	PUNCT
ejpam-3415	150	4	the	the	DET
ejpam-3415	150	5	hyperlattice	hyperlattice	NOUN
ejpam-3415	150	6	of	of	ADP
ejpam-3415	150	7	the	the	DET
ejpam-3415	150	8	example	example	NOUN
ejpam-3415	150	9	2.6	2.6	NUM
ejpam-3415	150	10	that	that	PRON
ejpam-3415	150	11	corresponds	correspond	VERB
ejpam-3415	150	12	to	to	ADP
ejpam-3415	150	13	the	the	DET
ejpam-3415	150	14	first	first	ADJ
ejpam-3415	150	15	proof	proof	NOUN
ejpam-3415	150	16	of	of	ADP
ejpam-3415	150	17	proposition	proposition	NOUN
ejpam-3415	150	18	2.5	2.5	NUM
ejpam-3415	150	19	.	.	PUNCT
ejpam-3415	151	1	∧	∧	NOUN
ejpam-3415	151	2	a	a	DET
ejpam-3415	151	3	b	b	NOUN
ejpam-3415	151	4	c	c	NOUN
ejpam-3415	151	5	d	d	NOUN
ejpam-3415	151	6	a	a	PRON
ejpam-3415	151	7	a	a	PRON
ejpam-3415	151	8	a	a	DET
ejpam-3415	151	9	a	a	DET
ejpam-3415	151	10	a	a	DET
ejpam-3415	151	11	b	b	NOUN
ejpam-3415	151	12	a	a	DET
ejpam-3415	151	13	b	b	NOUN
ejpam-3415	151	14	a	a	DET
ejpam-3415	151	15	b	b	NOUN
ejpam-3415	151	16	c	c	NOUN
ejpam-3415	151	17	a	a	DET
ejpam-3415	151	18	a	a	NOUN
ejpam-3415	151	19	c	c	NOUN
ejpam-3415	151	20	c	c	NOUN
ejpam-3415	152	1	d	d	NOUN
ejpam-3415	152	2	a	a	DET
ejpam-3415	152	3	b	b	NOUN
ejpam-3415	152	4	c	c	X
ejpam-3415	152	5	d	d	X
ejpam-3415	152	6	(	(	PUNCT
ejpam-3415	152	7	a	a	NOUN
ejpam-3415	152	8	)	)	PUNCT
ejpam-3415	152	9	∨	∨	NOUN
ejpam-3415	152	10	a	a	DET
ejpam-3415	152	11	b	b	NOUN
ejpam-3415	152	12	c	c	NOUN
ejpam-3415	152	13	d	d	X
ejpam-3415	152	14	a	a	X
ejpam-3415	152	15	{	{	PUNCT
ejpam-3415	152	16	a	a	NOUN
ejpam-3415	152	17	}	}	PUNCT
ejpam-3415	152	18	{	{	PUNCT
ejpam-3415	152	19	a	a	NOUN
ejpam-3415	152	20	}	}	PUNCT
ejpam-3415	152	21	{	{	PUNCT
ejpam-3415	152	22	a	a	NOUN
ejpam-3415	152	23	}	}	PUNCT
ejpam-3415	152	24	{	{	PUNCT
ejpam-3415	152	25	a	a	DET
ejpam-3415	152	26	}	}	PUNCT
ejpam-3415	152	27	b	b	PROPN
ejpam-3415	152	28	{	{	PUNCT
ejpam-3415	152	29	b	b	NOUN
ejpam-3415	152	30	}	}	PUNCT
ejpam-3415	152	31	{	{	PUNCT
ejpam-3415	152	32	b	b	NOUN
ejpam-3415	152	33	}	}	PUNCT
ejpam-3415	152	34	{	{	PUNCT
ejpam-3415	152	35	d	d	NOUN
ejpam-3415	152	36	}	}	PUNCT
ejpam-3415	152	37	{	{	PUNCT
ejpam-3415	152	38	d	d	NOUN
ejpam-3415	152	39	}	}	PUNCT
ejpam-3415	152	40	c	c	NOUN
ejpam-3415	152	41	{	{	PUNCT
ejpam-3415	152	42	c	c	NOUN
ejpam-3415	152	43	}	}	PUNCT
ejpam-3415	152	44	{	{	PUNCT
ejpam-3415	152	45	d	d	NOUN
ejpam-3415	152	46	}	}	PUNCT
ejpam-3415	152	47	{	{	PUNCT
ejpam-3415	152	48	c	c	NOUN
ejpam-3415	152	49	}	}	PUNCT
ejpam-3415	152	50	{	{	PUNCT
ejpam-3415	152	51	d	d	NOUN
ejpam-3415	152	52	}	}	PUNCT
ejpam-3415	152	53	d	d	NOUN
ejpam-3415	152	54	{	{	PUNCT
ejpam-3415	152	55	d	d	NOUN
ejpam-3415	152	56	}	}	PUNCT
ejpam-3415	152	57	{	{	PUNCT
ejpam-3415	152	58	d	d	NOUN
ejpam-3415	152	59	}	}	PUNCT
ejpam-3415	152	60	{	{	PUNCT
ejpam-3415	152	61	d	d	NOUN
ejpam-3415	152	62	}	}	PUNCT
ejpam-3415	152	63	{	{	PUNCT
ejpam-3415	152	64	d	d	NOUN
ejpam-3415	152	65	}	}	PUNCT
ejpam-3415	152	66	(	(	PUNCT
ejpam-3415	152	67	b	b	NOUN
ejpam-3415	152	68	)	)	PUNCT
ejpam-3415	152	69	according	accord	VERB
ejpam-3415	152	70	to	to	ADP
ejpam-3415	152	71	the	the	DET
ejpam-3415	152	72	second	second	ADJ
ejpam-3415	152	73	proof	proof	NOUN
ejpam-3415	152	74	of	of	ADP
ejpam-3415	152	75	proposition	proposition	NOUN
ejpam-3415	152	76	2.5	2.5	NUM
ejpam-3415	152	77	,	,	PUNCT
ejpam-3415	152	78	the	the	DET
ejpam-3415	152	79	same	same	ADJ
ejpam-3415	152	80	lattice	lattice	NOUN
ejpam-3415	152	81	with	with	ADP
ejpam-3415	152	82	the	the	DET
ejpam-3415	152	83	operation	operation	NOUN
ejpam-3415	152	84	and	and	CCONJ
ejpam-3415	152	85	the	the	DET
ejpam-3415	152	86	hyperoperation	hyperoperation	NOUN
ejpam-3415	152	87	of	of	ADP
ejpam-3415	152	88	table	table	NOUN
ejpam-3415	152	89	4	4	NUM
ejpam-3415	152	90	is	be	AUX
ejpam-3415	152	91	a	a	DET
ejpam-3415	152	92	hyperlattice	hyperlattice	NOUN
ejpam-3415	152	93	.	.	PUNCT
ejpam-3415	153	1	in	in	ADP
ejpam-3415	153	2	addition	addition	NOUN
ejpam-3415	153	3	,	,	PUNCT
ejpam-3415	153	4	table	table	NOUN
ejpam-3415	153	5	4	4	NUM
ejpam-3415	153	6	provides	provide	VERB
ejpam-3415	153	7	us	we	PRON
ejpam-3415	153	8	with	with	ADP
ejpam-3415	153	9	an	an	DET
ejpam-3415	153	10	example	example	NOUN
ejpam-3415	153	11	of	of	ADP
ejpam-3415	153	12	a	a	DET
ejpam-3415	153	13	hyperlattice	hyperlattice	NOUN
ejpam-3415	153	14	for	for	ADP
ejpam-3415	153	15	which	which	PRON
ejpam-3415	153	16	the	the	DET
ejpam-3415	153	17	converse	converse	NOUN
ejpam-3415	153	18	statement	statement	NOUN
ejpam-3415	153	19	in	in	ADP
ejpam-3415	153	20	remark	remark	NOUN
ejpam-3415	153	21	2.3	2.3	NUM
ejpam-3415	153	22	does	do	AUX
ejpam-3415	153	23	not	not	PART
ejpam-3415	153	24	hold	hold	VERB
ejpam-3415	153	25	.	.	PUNCT
ejpam-3415	154	1	indeed	indeed	ADV
ejpam-3415	154	2	,	,	PUNCT
ejpam-3415	154	3	c	c	PROPN
ejpam-3415	154	4	∈	∈	PROPN
ejpam-3415	154	5	c	c	PROPN
ejpam-3415	154	6	∨	∨	NUM
ejpam-3415	154	7	b	b	PROPN
ejpam-3415	154	8	but	but	CCONJ
ejpam-3415	154	9	c	c	PROPN
ejpam-3415	154	10	∧	∧	PROPN
ejpam-3415	154	11	b	b	PROPN
ejpam-3415	154	12	6=	6=	PROPN
ejpam-3415	154	13	b.	b.	PROPN
ejpam-3415	154	14	table	table	NOUN
ejpam-3415	154	15	4	4	NUM
ejpam-3415	154	16	:	:	PUNCT
ejpam-3415	154	17	the	the	DET
ejpam-3415	154	18	hyperlattice	hyperlattice	NOUN
ejpam-3415	154	19	of	of	ADP
ejpam-3415	154	20	the	the	DET
ejpam-3415	154	21	example	example	NOUN
ejpam-3415	154	22	2.6	2.6	NUM
ejpam-3415	154	23	that	that	PRON
ejpam-3415	154	24	corresponds	correspond	VERB
ejpam-3415	154	25	to	to	ADP
ejpam-3415	154	26	the	the	DET
ejpam-3415	154	27	second	second	ADJ
ejpam-3415	154	28	proof	proof	NOUN
ejpam-3415	154	29	of	of	ADP
ejpam-3415	154	30	proposition	proposition	NOUN
ejpam-3415	154	31	2.5	2.5	NUM
ejpam-3415	154	32	.	.	PUNCT
ejpam-3415	155	1	∧	∧	NOUN
ejpam-3415	155	2	a	a	DET
ejpam-3415	155	3	b	b	NOUN
ejpam-3415	155	4	c	c	NOUN
ejpam-3415	155	5	d	d	NOUN
ejpam-3415	155	6	a	a	PRON
ejpam-3415	155	7	a	a	PRON
ejpam-3415	155	8	a	a	DET
ejpam-3415	155	9	a	a	DET
ejpam-3415	155	10	a	a	DET
ejpam-3415	155	11	b	b	NOUN
ejpam-3415	155	12	a	a	DET
ejpam-3415	155	13	b	b	NOUN
ejpam-3415	155	14	a	a	DET
ejpam-3415	155	15	b	b	NOUN
ejpam-3415	155	16	c	c	NOUN
ejpam-3415	155	17	a	a	DET
ejpam-3415	155	18	a	a	NOUN
ejpam-3415	155	19	c	c	NOUN
ejpam-3415	155	20	c	c	NOUN
ejpam-3415	156	1	d	d	NOUN
ejpam-3415	156	2	a	a	DET
ejpam-3415	156	3	b	b	NOUN
ejpam-3415	156	4	c	c	NOUN
ejpam-3415	156	5	d	d	NOUN
ejpam-3415	156	6	niovi	niovi	ADJ
ejpam-3415	156	7	kehayopulu	kehayopulu	ADJ
ejpam-3415	156	8	/	/	SYM
ejpam-3415	156	9	eur	eur	PROPN
ejpam-3415	156	10	.	.	PUNCT
ejpam-3415	157	1	j.	j.	PROPN
ejpam-3415	157	2	pure	pure	PROPN
ejpam-3415	157	3	appl	appl	PROPN
ejpam-3415	157	4	.	.	PROPN
ejpam-3415	157	5	math	math	PROPN
ejpam-3415	157	6	,	,	PUNCT
ejpam-3415	157	7	12	12	NUM
ejpam-3415	157	8	(	(	PUNCT
ejpam-3415	157	9	2	2	NUM
ejpam-3415	157	10	)	)	PUNCT
ejpam-3415	157	11	(	(	PUNCT
ejpam-3415	157	12	2019	2019	NUM
ejpam-3415	157	13	)	)	PUNCT
ejpam-3415	157	14	,	,	PUNCT
ejpam-3415	157	15	252	252	NUM
ejpam-3415	157	16	-	-	SYM
ejpam-3415	157	17	269	269	NUM
ejpam-3415	157	18	258	258	NUM
ejpam-3415	157	19	(	(	PUNCT
ejpam-3415	157	20	a	a	NOUN
ejpam-3415	157	21	)	)	PUNCT
ejpam-3415	157	22	∨	∨	NOUN
ejpam-3415	157	23	a	a	DET
ejpam-3415	157	24	b	b	NOUN
ejpam-3415	157	25	c	c	NOUN
ejpam-3415	157	26	d	d	X
ejpam-3415	157	27	a	a	X
ejpam-3415	157	28	{	{	PUNCT
ejpam-3415	157	29	a	a	NOUN
ejpam-3415	157	30	}	}	PUNCT
ejpam-3415	157	31	{	{	PUNCT
ejpam-3415	157	32	a	a	DET
ejpam-3415	157	33	,	,	PUNCT
ejpam-3415	157	34	b	b	NOUN
ejpam-3415	157	35	}	}	PUNCT
ejpam-3415	157	36	{	{	PUNCT
ejpam-3415	157	37	a	a	PROPN
ejpam-3415	157	38	,	,	PUNCT
ejpam-3415	157	39	c	c	NOUN
ejpam-3415	157	40	}	}	PUNCT
ejpam-3415	157	41	{	{	PUNCT
ejpam-3415	157	42	a	a	PRON
ejpam-3415	157	43	,	,	PUNCT
ejpam-3415	157	44	d	d	NOUN
ejpam-3415	157	45	}	}	PUNCT
ejpam-3415	157	46	b	b	PROPN
ejpam-3415	157	47	{	{	PUNCT
ejpam-3415	157	48	a	a	PROPN
ejpam-3415	157	49	,	,	PUNCT
ejpam-3415	157	50	b	b	NOUN
ejpam-3415	157	51	}	}	PUNCT
ejpam-3415	157	52	{	{	PUNCT
ejpam-3415	157	53	b	b	NOUN
ejpam-3415	157	54	}	}	PUNCT
ejpam-3415	157	55	{	{	PUNCT
ejpam-3415	157	56	b	b	PROPN
ejpam-3415	157	57	,	,	PUNCT
ejpam-3415	157	58	c	c	NOUN
ejpam-3415	157	59	,	,	PUNCT
ejpam-3415	157	60	d	d	NOUN
ejpam-3415	157	61	}	}	PUNCT
ejpam-3415	157	62	{	{	PUNCT
ejpam-3415	157	63	b	b	NOUN
ejpam-3415	157	64	,	,	PUNCT
ejpam-3415	157	65	d	d	NOUN
ejpam-3415	157	66	}	}	PUNCT
ejpam-3415	157	67	c	c	NOUN
ejpam-3415	157	68	{	{	PUNCT
ejpam-3415	157	69	a	a	NOUN
ejpam-3415	157	70	,	,	PUNCT
ejpam-3415	157	71	c	c	NOUN
ejpam-3415	157	72	}	}	PUNCT
ejpam-3415	157	73	{	{	PUNCT
ejpam-3415	157	74	b	b	PROPN
ejpam-3415	157	75	,	,	PUNCT
ejpam-3415	157	76	c	c	NOUN
ejpam-3415	157	77	,	,	PUNCT
ejpam-3415	157	78	d	d	NOUN
ejpam-3415	157	79	}	}	PUNCT
ejpam-3415	157	80	{	{	PUNCT
ejpam-3415	157	81	c	c	NOUN
ejpam-3415	157	82	}	}	PUNCT
ejpam-3415	157	83	{	{	PUNCT
ejpam-3415	157	84	c	c	NOUN
ejpam-3415	157	85	,	,	PUNCT
ejpam-3415	157	86	d	d	NOUN
ejpam-3415	157	87	}	}	PUNCT
ejpam-3415	157	88	d	d	NOUN
ejpam-3415	157	89	{	{	PUNCT
ejpam-3415	157	90	a	a	PRON
ejpam-3415	157	91	,	,	PUNCT
ejpam-3415	157	92	d	d	NOUN
ejpam-3415	157	93	}	}	PUNCT
ejpam-3415	157	94	{	{	PUNCT
ejpam-3415	157	95	b	b	NOUN
ejpam-3415	157	96	,	,	PUNCT
ejpam-3415	157	97	d	d	NOUN
ejpam-3415	157	98	}	}	PUNCT
ejpam-3415	157	99	{	{	PUNCT
ejpam-3415	157	100	c	c	NOUN
ejpam-3415	157	101	,	,	PUNCT
ejpam-3415	157	102	d	d	NOUN
ejpam-3415	157	103	}	}	PUNCT
ejpam-3415	157	104	{	{	PUNCT
ejpam-3415	157	105	d	d	NOUN
ejpam-3415	157	106	}	}	PUNCT
ejpam-3415	157	107	(	(	PUNCT
ejpam-3415	157	108	b	b	X
ejpam-3415	157	109	)	)	PUNCT
ejpam-3415	157	110	proposition	proposition	NOUN
ejpam-3415	157	111	2.7	2.7	NUM
ejpam-3415	157	112	in	in	ADP
ejpam-3415	157	113	a	a	DET
ejpam-3415	157	114	hyperlattice	hyperlattice	NOUN
ejpam-3415	157	115	the	the	DET
ejpam-3415	157	116	following	following	NOUN
ejpam-3415	157	117	are	be	AUX
ejpam-3415	157	118	equivalent	equivalent	ADJ
ejpam-3415	157	119	:	:	PUNCT
ejpam-3415	157	120	(	(	PUNCT
ejpam-3415	157	121	1	1	X
ejpam-3415	157	122	)	)	PUNCT
ejpam-3415	157	123	for	for	ADP
ejpam-3415	157	124	every	every	DET
ejpam-3415	157	125	u	u	PROPN
ejpam-3415	157	126	∈	∈	PROPN
ejpam-3415	157	127	a	a	DET
ejpam-3415	157	128	∨	∨	NUM
ejpam-3415	157	129	b	b	NOUN
ejpam-3415	158	1	we	we	PRON
ejpam-3415	158	2	have	have	VERB
ejpam-3415	158	3	a	a	DET
ejpam-3415	158	4	∧	∧	PROPN
ejpam-3415	158	5	u	u	NOUN
ejpam-3415	158	6	=	=	NOUN
ejpam-3415	158	7	a.	a.	NOUN
ejpam-3415	158	8	(	(	PUNCT
ejpam-3415	158	9	2	2	NUM
ejpam-3415	158	10	)	)	PUNCT
ejpam-3415	158	11	{	{	PUNCT
ejpam-3415	158	12	a	a	DET
ejpam-3415	158	13	∧	∧	PROPN
ejpam-3415	158	14	x	x	SYM
ejpam-3415	158	15	|	|	ADV
ejpam-3415	158	16	x	x	SYM
ejpam-3415	158	17	∈	∈	PROPN
ejpam-3415	158	18	a	a	DET
ejpam-3415	158	19	∨	∨	NUM
ejpam-3415	158	20	b	b	NOUN
ejpam-3415	158	21	}	}	PUNCT
ejpam-3415	158	22	=	=	SYM
ejpam-3415	158	23	{	{	PUNCT
ejpam-3415	158	24	a	a	NOUN
ejpam-3415	158	25	}	}	PUNCT
ejpam-3415	158	26	.	.	PUNCT
ejpam-3415	159	1	proof	proof	NOUN
ejpam-3415	159	2	(	(	PUNCT
ejpam-3415	159	3	1	1	X
ejpam-3415	159	4	)	)	PUNCT
ejpam-3415	159	5	=	=	NOUN
ejpam-3415	159	6	⇒	⇒	NOUN
ejpam-3415	159	7	(	(	PUNCT
ejpam-3415	159	8	2	2	NUM
ejpam-3415	159	9	)	)	PUNCT
ejpam-3415	159	10	.	.	PUNCT
ejpam-3415	160	1	if	if	SCONJ
ejpam-3415	160	2	t	t	PROPN
ejpam-3415	160	3	∈	∈	PROPN
ejpam-3415	160	4	{	{	PUNCT
ejpam-3415	160	5	a	a	DET
ejpam-3415	160	6	∧	∧	PROPN
ejpam-3415	160	7	x	x	SYM
ejpam-3415	160	8	|	|	ADV
ejpam-3415	160	9	x	x	SYM
ejpam-3415	160	10	∈	∈	PROPN
ejpam-3415	160	11	a	a	DET
ejpam-3415	160	12	∨	∨	NUM
ejpam-3415	160	13	b	b	NOUN
ejpam-3415	160	14	}	}	PUNCT
ejpam-3415	160	15	,	,	PUNCT
ejpam-3415	160	16	then	then	ADV
ejpam-3415	160	17	t	t	PROPN
ejpam-3415	160	18	=	=	PUNCT
ejpam-3415	160	19	a	a	DET
ejpam-3415	160	20	∧	∧	PROPN
ejpam-3415	160	21	x	x	PUNCT
ejpam-3415	160	22	for	for	ADP
ejpam-3415	160	23	some	some	DET
ejpam-3415	160	24	x	x	SYM
ejpam-3415	160	25	∈	∈	PROPN
ejpam-3415	160	26	a	a	DET
ejpam-3415	160	27	∨	∨	PROPN
ejpam-3415	160	28	b.	b.	NOUN
ejpam-3415	160	29	since	since	SCONJ
ejpam-3415	160	30	x	x	PROPN
ejpam-3415	160	31	∈	∈	PROPN
ejpam-3415	160	32	a∨	a∨	PROPN
ejpam-3415	160	33	b	b	PROPN
ejpam-3415	160	34	,	,	PUNCT
ejpam-3415	160	35	by	by	ADP
ejpam-3415	160	36	(	(	PUNCT
ejpam-3415	160	37	1	1	NUM
ejpam-3415	160	38	)	)	PUNCT
ejpam-3415	160	39	,	,	PUNCT
ejpam-3415	160	40	we	we	PRON
ejpam-3415	160	41	have	have	VERB
ejpam-3415	160	42	a∧x	a∧x	NOUN
ejpam-3415	160	43	=	=	SYM
ejpam-3415	160	44	a	a	X
ejpam-3415	160	45	,	,	PUNCT
ejpam-3415	160	46	thus	thus	ADV
ejpam-3415	160	47	we	we	PRON
ejpam-3415	160	48	get	get	VERB
ejpam-3415	160	49	t	t	NOUN
ejpam-3415	160	50	=	=	PUNCT
ejpam-3415	160	51	a.	a.	NOUN
ejpam-3415	160	52	on	on	ADP
ejpam-3415	160	53	the	the	DET
ejpam-3415	160	54	other	other	ADJ
ejpam-3415	160	55	hand	hand	NOUN
ejpam-3415	160	56	,	,	PUNCT
ejpam-3415	160	57	since	since	SCONJ
ejpam-3415	160	58	a	a	DET
ejpam-3415	160	59	∈	∈	PROPN
ejpam-3415	160	60	a∨	a∨	PROPN
ejpam-3415	160	61	a	a	PROPN
ejpam-3415	160	62	and	and	CCONJ
ejpam-3415	160	63	a	a	DET
ejpam-3415	160	64	=	=	NOUN
ejpam-3415	160	65	a	a	DET
ejpam-3415	160	66	∧	∧	PROPN
ejpam-3415	160	67	a	a	X
ejpam-3415	160	68	,	,	PUNCT
ejpam-3415	160	69	we	we	PRON
ejpam-3415	160	70	have	have	VERB
ejpam-3415	160	71	a	a	DET
ejpam-3415	160	72	∈	∈	NOUN
ejpam-3415	160	73	{	{	PUNCT
ejpam-3415	160	74	a	a	DET
ejpam-3415	160	75	∧	∧	PROPN
ejpam-3415	160	76	x	x	SYM
ejpam-3415	160	77	|	|	ADV
ejpam-3415	160	78	x	x	SYM
ejpam-3415	160	79	∈	∈	PROPN
ejpam-3415	160	80	a	a	DET
ejpam-3415	160	81	∨	∨	NUM
ejpam-3415	160	82	b	b	NOUN
ejpam-3415	160	83	}	}	PUNCT
ejpam-3415	160	84	.	.	PUNCT
ejpam-3415	161	1	(	(	PUNCT
ejpam-3415	161	2	2	2	X
ejpam-3415	161	3	)	)	PUNCT
ejpam-3415	161	4	=	=	NOUN
ejpam-3415	161	5	⇒	⇒	NOUN
ejpam-3415	161	6	(	(	PUNCT
ejpam-3415	161	7	1	1	NUM
ejpam-3415	161	8	)	)	PUNCT
ejpam-3415	161	9	.	.	PUNCT
ejpam-3415	162	1	if	if	SCONJ
ejpam-3415	162	2	u	u	PROPN
ejpam-3415	162	3	∈	∈	VERB
ejpam-3415	162	4	a	a	DET
ejpam-3415	162	5	∨	∨	NUM
ejpam-3415	162	6	b	b	PROPN
ejpam-3415	162	7	,	,	PUNCT
ejpam-3415	162	8	then	then	ADV
ejpam-3415	162	9	a	a	DET
ejpam-3415	162	10	∧	∧	PROPN
ejpam-3415	162	11	u	u	NOUN
ejpam-3415	162	12	∈	∈	PROPN
ejpam-3415	162	13	{	{	PUNCT
ejpam-3415	162	14	a	a	DET
ejpam-3415	162	15	∧	∧	PROPN
ejpam-3415	162	16	x	x	SYM
ejpam-3415	162	17	|	|	ADV
ejpam-3415	162	18	x	x	SYM
ejpam-3415	162	19	∈	∈	PROPN
ejpam-3415	162	20	a	a	DET
ejpam-3415	162	21	∨	∨	NUM
ejpam-3415	162	22	b	b	NOUN
ejpam-3415	162	23	}	}	PUNCT
ejpam-3415	162	24	=	=	SYM
ejpam-3415	162	25	{	{	PUNCT
ejpam-3415	162	26	a	a	NOUN
ejpam-3415	162	27	}	}	PUNCT
ejpam-3415	162	28	and	and	CCONJ
ejpam-3415	162	29	so	so	ADV
ejpam-3415	162	30	a	a	DET
ejpam-3415	162	31	∧	∧	PROPN
ejpam-3415	162	32	u	u	NOUN
ejpam-3415	162	33	=	=	NOUN
ejpam-3415	162	34	a.	a.	NOUN
ejpam-3415	162	35	�	�	PROPN
ejpam-3415	162	36	3	3	NUM
ejpam-3415	162	37	.	.	PUNCT
ejpam-3415	162	38	distributive	distributive	ADJ
ejpam-3415	162	39	hyperlattices	hyperlattice	NOUN
ejpam-3415	162	40	a	a	DET
ejpam-3415	162	41	lattice	lattice	NOUN
ejpam-3415	162	42	l	l	NOUN
ejpam-3415	162	43	is	be	AUX
ejpam-3415	162	44	called	call	VERB
ejpam-3415	162	45	distributive	distributive	ADJ
ejpam-3415	162	46	if	if	SCONJ
ejpam-3415	162	47	,	,	PUNCT
ejpam-3415	162	48	for	for	ADP
ejpam-3415	162	49	any	any	DET
ejpam-3415	162	50	a	a	DET
ejpam-3415	162	51	,	,	PUNCT
ejpam-3415	162	52	b	b	NOUN
ejpam-3415	162	53	,	,	PUNCT
ejpam-3415	162	54	c	c	PROPN
ejpam-3415	162	55	∈	∈	PROPN
ejpam-3415	162	56	l	l	NOUN
ejpam-3415	162	57	,	,	PUNCT
ejpam-3415	162	58	we	we	PRON
ejpam-3415	162	59	have	have	VERB
ejpam-3415	162	60	a∧(b∨c	a∧(b∨c	PROPN
ejpam-3415	162	61	)	)	PUNCT
ejpam-3415	163	1	=	=	SYM
ejpam-3415	163	2	(	(	PUNCT
ejpam-3415	163	3	a∧b)∨(a∧c	a∧b)∨(a∧c	NOUN
ejpam-3415	163	4	)	)	PUNCT
ejpam-3415	163	5	.	.	PUNCT
ejpam-3415	164	1	this	this	DET
ejpam-3415	164	2	concept	concept	NOUN
ejpam-3415	164	3	can	can	AUX
ejpam-3415	164	4	be	be	AUX
ejpam-3415	164	5	naturally	naturally	ADV
ejpam-3415	164	6	transferred	transfer	VERB
ejpam-3415	164	7	to	to	ADP
ejpam-3415	164	8	hyperlattices	hyperlattice	NOUN
ejpam-3415	164	9	as	as	SCONJ
ejpam-3415	164	10	follows	follow	VERB
ejpam-3415	164	11	:	:	PUNCT
ejpam-3415	164	12	definition	definition	NOUN
ejpam-3415	164	13	3.1(1	3.1(1	NUM
ejpam-3415	164	14	)	)	PUNCT
ejpam-3415	164	15	a	a	DET
ejpam-3415	164	16	hyperlattice	hyperlattice	NOUN
ejpam-3415	164	17	(	(	PUNCT
ejpam-3415	164	18	l,∧,∨	l,∧,∨	X
ejpam-3415	164	19	)	)	PUNCT
ejpam-3415	164	20	is	be	AUX
ejpam-3415	164	21	called	call	VERB
ejpam-3415	164	22	distributive	distributive	ADJ
ejpam-3415	164	23	if	if	SCONJ
ejpam-3415	164	24	the	the	DET
ejpam-3415	164	25	following	follow	VERB
ejpam-3415	164	26	assertions	assertion	NOUN
ejpam-3415	164	27	are	be	AUX
ejpam-3415	164	28	satisfied	satisfied	ADJ
ejpam-3415	164	29	:	:	PUNCT
ejpam-3415	164	30	(	(	PUNCT
ejpam-3415	164	31	1	1	X
ejpam-3415	164	32	)	)	PUNCT
ejpam-3415	164	33	if	if	SCONJ
ejpam-3415	164	34	u	u	PROPN
ejpam-3415	164	35	∈	∈	PROPN
ejpam-3415	164	36	b	b	PROPN
ejpam-3415	164	37	∨	∨	NUM
ejpam-3415	164	38	c	c	PROPN
ejpam-3415	164	39	,	,	PUNCT
ejpam-3415	164	40	then	then	ADV
ejpam-3415	164	41	a	a	DET
ejpam-3415	164	42	∧	∧	PROPN
ejpam-3415	164	43	u	u	X
ejpam-3415	164	44	∈	∈	PROPN
ejpam-3415	164	45	(	(	PUNCT
ejpam-3415	164	46	a	a	DET
ejpam-3415	164	47	∧	∧	PROPN
ejpam-3415	164	48	b	b	PROPN
ejpam-3415	164	49	)	)	PUNCT
ejpam-3415	164	50	∨	∨	NOUN
ejpam-3415	164	51	(	(	PUNCT
ejpam-3415	164	52	a	a	DET
ejpam-3415	164	53	∧	∧	PROPN
ejpam-3415	164	54	c	c	NOUN
ejpam-3415	164	55	)	)	PUNCT
ejpam-3415	164	56	and	and	CCONJ
ejpam-3415	164	57	(	(	PUNCT
ejpam-3415	164	58	2	2	X
ejpam-3415	164	59	)	)	PUNCT
ejpam-3415	164	60	if	if	SCONJ
ejpam-3415	164	61	u	u	NOUN
ejpam-3415	164	62	∈	∈	PROPN
ejpam-3415	164	63	(	(	PUNCT
ejpam-3415	164	64	a	a	DET
ejpam-3415	164	65	∧	∧	PROPN
ejpam-3415	164	66	b	b	PROPN
ejpam-3415	164	67	)	)	PUNCT
ejpam-3415	164	68	∨	∨	NOUN
ejpam-3415	164	69	(	(	PUNCT
ejpam-3415	164	70	a	a	DET
ejpam-3415	164	71	∧	∧	PROPN
ejpam-3415	164	72	c	c	NOUN
ejpam-3415	164	73	)	)	PUNCT
ejpam-3415	164	74	,	,	PUNCT
ejpam-3415	164	75	then	then	ADV
ejpam-3415	164	76	there	there	PRON
ejpam-3415	164	77	exists	exist	VERB
ejpam-3415	164	78	v	v	ADP
ejpam-3415	164	79	∈	∈	PROPN
ejpam-3415	164	80	b	b	PROPN
ejpam-3415	164	81	∨	∨	NUM
ejpam-3415	164	82	c	c	PROPN
ejpam-3415	164	83	such	such	ADJ
ejpam-3415	164	84	that	that	DET
ejpam-3415	164	85	u	u	NOUN
ejpam-3415	164	86	=	=	PUNCT
ejpam-3415	164	87	a	a	DET
ejpam-3415	164	88	∧	∧	PROPN
ejpam-3415	164	89	v.	v.	ADP
ejpam-3415	164	90	in	in	ADP
ejpam-3415	164	91	other	other	ADJ
ejpam-3415	164	92	words	word	NOUN
ejpam-3415	164	93	,	,	PUNCT
ejpam-3415	164	94	u	u	NOUN
ejpam-3415	164	95	∈	∈	PROPN
ejpam-3415	164	96	(	(	PUNCT
ejpam-3415	164	97	a	a	DET
ejpam-3415	164	98	∧	∧	PROPN
ejpam-3415	164	99	b	b	PROPN
ejpam-3415	164	100	)	)	PUNCT
ejpam-3415	164	101	∨	∨	NOUN
ejpam-3415	164	102	(	(	PUNCT
ejpam-3415	164	103	a	a	DET
ejpam-3415	164	104	∧	∧	PROPN
ejpam-3415	164	105	c	c	NOUN
ejpam-3415	164	106	)	)	PUNCT
ejpam-3415	165	1	if	if	SCONJ
ejpam-3415	165	2	and	and	CCONJ
ejpam-3415	165	3	only	only	ADV
ejpam-3415	165	4	if	if	SCONJ
ejpam-3415	165	5	there	there	PRON
ejpam-3415	165	6	exists	exist	VERB
ejpam-3415	165	7	v	v	ADP
ejpam-3415	165	8	∈	∈	PROPN
ejpam-3415	165	9	b	b	PROPN
ejpam-3415	165	10	∨	∨	NUM
ejpam-3415	165	11	c	c	PROPN
ejpam-3415	165	12	such	such	ADJ
ejpam-3415	165	13	that	that	DET
ejpam-3415	165	14	u	u	NOUN
ejpam-3415	165	15	=	=	PUNCT
ejpam-3415	165	16	a	a	DET
ejpam-3415	165	17	∧	∧	PROPN
ejpam-3415	165	18	v.	v.	ADP
ejpam-3415	165	19	that	that	PRON
ejpam-3415	165	20	is	be	AUX
ejpam-3415	165	21	,	,	PUNCT
ejpam-3415	165	22	if	if	SCONJ
ejpam-3415	165	23	{	{	PUNCT
ejpam-3415	165	24	a	a	DET
ejpam-3415	165	25	∧	∧	NOUN
ejpam-3415	165	26	v	v	ADP
ejpam-3415	165	27	|	|	ADV
ejpam-3415	165	28	v	v	ADP
ejpam-3415	165	29	∈	∈	PROPN
ejpam-3415	165	30	b	b	PROPN
ejpam-3415	165	31	∨	∨	NUM
ejpam-3415	165	32	c	c	NOUN
ejpam-3415	165	33	}	}	PUNCT
ejpam-3415	165	34	=	=	SYM
ejpam-3415	165	35	(	(	PUNCT
ejpam-3415	165	36	a	a	DET
ejpam-3415	165	37	∧	∧	PROPN
ejpam-3415	165	38	b	b	PROPN
ejpam-3415	165	39	)	)	PUNCT
ejpam-3415	165	40	∨	∨	NOUN
ejpam-3415	165	41	(	(	PUNCT
ejpam-3415	165	42	a	a	DET
ejpam-3415	165	43	∧	∧	PROPN
ejpam-3415	165	44	c	c	NOUN
ejpam-3415	165	45	)	)	PUNCT
ejpam-3415	165	46	for	for	ADP
ejpam-3415	165	47	every	every	DET
ejpam-3415	165	48	a	a	DET
ejpam-3415	165	49	,	,	PUNCT
ejpam-3415	165	50	b	b	NOUN
ejpam-3415	165	51	,	,	PUNCT
ejpam-3415	165	52	c	c	PROPN
ejpam-3415	165	53	∈	∈	PROPN
ejpam-3415	165	54	l.	l.	NOUN
ejpam-3415	165	55	the	the	DET
ejpam-3415	165	56	equivalent	equivalent	ADJ
ejpam-3415	165	57	definition	definition	NOUN
ejpam-3415	165	58	a	a	DET
ejpam-3415	165	59	∨	∨	NOUN
ejpam-3415	165	60	(	(	PUNCT
ejpam-3415	165	61	b	b	PROPN
ejpam-3415	165	62	∧	∧	PROPN
ejpam-3415	165	63	c	c	NOUN
ejpam-3415	165	64	)	)	PUNCT
ejpam-3415	165	65	=	=	NOUN
ejpam-3415	165	66	(	(	PUNCT
ejpam-3415	166	1	a	a	DET
ejpam-3415	166	2	∨	∨	NUM
ejpam-3415	166	3	b	b	NOUN
ejpam-3415	166	4	)	)	PUNCT
ejpam-3415	166	5	∧	∧	NOUN
ejpam-3415	166	6	(	(	PUNCT
ejpam-3415	166	7	a	a	DET
ejpam-3415	166	8	∨	∨	NUM
ejpam-3415	166	9	c	c	NOUN
ejpam-3415	166	10	)	)	PUNCT
ejpam-3415	166	11	of	of	ADP
ejpam-3415	166	12	distributive	distributive	ADJ
ejpam-3415	166	13	lattices	lattice	NOUN
ejpam-3415	166	14	can	can	AUX
ejpam-3415	166	15	be	be	AUX
ejpam-3415	166	16	transferred	transfer	VERB
ejpam-3415	166	17	to	to	ADP
ejpam-3415	166	18	hyperlattices	hyperlattice	NOUN
ejpam-3415	166	19	in	in	ADP
ejpam-3415	166	20	definition	definition	NOUN
ejpam-3415	166	21	3.1(2	3.1(2	NUM
ejpam-3415	166	22	)	)	PUNCT
ejpam-3415	166	23	.	.	PUNCT
ejpam-3415	167	1	according	accord	VERB
ejpam-3415	167	2	to	to	ADP
ejpam-3415	167	3	the	the	DET
ejpam-3415	167	4	problem	problem	NOUN
ejpam-3415	167	5	we	we	PRON
ejpam-3415	167	6	face	face	VERB
ejpam-3415	167	7	we	we	PRON
ejpam-3415	167	8	use	use	VERB
ejpam-3415	167	9	either	either	CCONJ
ejpam-3415	167	10	the	the	DET
ejpam-3415	167	11	first	first	ADJ
ejpam-3415	167	12	or	or	CCONJ
ejpam-3415	167	13	the	the	DET
ejpam-3415	167	14	second	second	ADJ
ejpam-3415	167	15	definition	definition	NOUN
ejpam-3415	167	16	.	.	PUNCT
ejpam-3415	168	1	definition	definition	NOUN
ejpam-3415	168	2	3.1(2	3.1(2	NUM
ejpam-3415	168	3	)	)	PUNCT
ejpam-3415	168	4	a	a	DET
ejpam-3415	168	5	hyperlattice	hyperlattice	NOUN
ejpam-3415	168	6	(	(	PUNCT
ejpam-3415	168	7	l,∧,∨	l,∧,∨	X
ejpam-3415	168	8	)	)	PUNCT
ejpam-3415	168	9	is	be	AUX
ejpam-3415	168	10	called	call	VERB
ejpam-3415	168	11	distributive	distributive	ADJ
ejpam-3415	168	12	if	if	SCONJ
ejpam-3415	168	13	the	the	DET
ejpam-3415	168	14	following	follow	VERB
ejpam-3415	168	15	assertions	assertion	NOUN
ejpam-3415	168	16	are	be	AUX
ejpam-3415	168	17	satisfied	satisfied	ADJ
ejpam-3415	168	18	:	:	PUNCT
ejpam-3415	168	19	(	(	PUNCT
ejpam-3415	168	20	1	1	X
ejpam-3415	168	21	)	)	PUNCT
ejpam-3415	168	22	if	if	SCONJ
ejpam-3415	168	23	u	u	PROPN
ejpam-3415	168	24	∈	∈	VERB
ejpam-3415	168	25	a	a	DET
ejpam-3415	168	26	∨	∨	NOUN
ejpam-3415	168	27	(	(	PUNCT
ejpam-3415	168	28	b	b	PROPN
ejpam-3415	168	29	∧	∧	PROPN
ejpam-3415	168	30	c	c	NOUN
ejpam-3415	168	31	)	)	PUNCT
ejpam-3415	168	32	,	,	PUNCT
ejpam-3415	168	33	then	then	ADV
ejpam-3415	168	34	there	there	PRON
ejpam-3415	168	35	exist	exist	VERB
ejpam-3415	168	36	v	v	ADP
ejpam-3415	168	37	∈	∈	PROPN
ejpam-3415	168	38	a	a	DET
ejpam-3415	168	39	∨	∨	NOUN
ejpam-3415	168	40	b	b	NOUN
ejpam-3415	168	41	and	and	CCONJ
ejpam-3415	168	42	w	w	PROPN
ejpam-3415	168	43	∈	∈	PROPN
ejpam-3415	168	44	a	a	DET
ejpam-3415	168	45	∨	∨	NOUN
ejpam-3415	168	46	c	c	NOUN
ejpam-3415	168	47	such	such	ADJ
ejpam-3415	168	48	that	that	DET
ejpam-3415	168	49	u	u	NOUN
ejpam-3415	168	50	=	=	X
ejpam-3415	168	51	v	v	ADP
ejpam-3415	168	52	∧	∧	PROPN
ejpam-3415	168	53	w	w	PROPN
ejpam-3415	168	54	and	and	CCONJ
ejpam-3415	168	55	(	(	PUNCT
ejpam-3415	168	56	2	2	X
ejpam-3415	168	57	)	)	PUNCT
ejpam-3415	168	58	if	if	SCONJ
ejpam-3415	168	59	u	u	PROPN
ejpam-3415	168	60	∈	∈	VERB
ejpam-3415	168	61	a	a	DET
ejpam-3415	168	62	∨	∨	NOUN
ejpam-3415	168	63	b	b	NOUN
ejpam-3415	168	64	and	and	CCONJ
ejpam-3415	168	65	v	v	ADP
ejpam-3415	168	66	∈	∈	PROPN
ejpam-3415	168	67	a	a	DET
ejpam-3415	168	68	∨	∨	NUM
ejpam-3415	168	69	c	c	NOUN
ejpam-3415	168	70	,	,	PUNCT
ejpam-3415	168	71	then	then	ADV
ejpam-3415	168	72	u	u	PROPN
ejpam-3415	168	73	∧	∧	PROPN
ejpam-3415	168	74	v	v	ADP
ejpam-3415	168	75	∈	∈	PROPN
ejpam-3415	168	76	a	a	DET
ejpam-3415	168	77	∨	∨	NOUN
ejpam-3415	168	78	(	(	PUNCT
ejpam-3415	168	79	b	b	PROPN
ejpam-3415	168	80	∧	∧	PROPN
ejpam-3415	168	81	c	c	NOUN
ejpam-3415	168	82	)	)	PUNCT
ejpam-3415	168	83	.	.	PUNCT
ejpam-3415	169	1	niovi	niovi	PROPN
ejpam-3415	169	2	kehayopulu	kehayopulu	PROPN
ejpam-3415	169	3	/	/	SYM
ejpam-3415	169	4	eur	eur	PROPN
ejpam-3415	169	5	.	.	PUNCT
ejpam-3415	170	1	j.	j.	PROPN
ejpam-3415	170	2	pure	pure	PROPN
ejpam-3415	170	3	appl	appl	PROPN
ejpam-3415	170	4	.	.	PROPN
ejpam-3415	170	5	math	math	PROPN
ejpam-3415	170	6	,	,	PUNCT
ejpam-3415	170	7	12	12	NUM
ejpam-3415	170	8	(	(	PUNCT
ejpam-3415	170	9	2	2	NUM
ejpam-3415	170	10	)	)	PUNCT
ejpam-3415	170	11	(	(	PUNCT
ejpam-3415	170	12	2019	2019	NUM
ejpam-3415	170	13	)	)	PUNCT
ejpam-3415	170	14	,	,	PUNCT
ejpam-3415	170	15	252	252	NUM
ejpam-3415	170	16	-	-	SYM
ejpam-3415	170	17	269	269	NUM
ejpam-3415	170	18	259	259	NUM
ejpam-3415	170	19	in	in	ADP
ejpam-3415	170	20	other	other	ADJ
ejpam-3415	170	21	words	word	NOUN
ejpam-3415	170	22	,	,	PUNCT
ejpam-3415	170	23	u	u	NOUN
ejpam-3415	170	24	∈	∈	PROPN
ejpam-3415	170	25	a	a	DET
ejpam-3415	170	26	∨	∨	NOUN
ejpam-3415	170	27	(	(	PUNCT
ejpam-3415	170	28	b	b	PROPN
ejpam-3415	170	29	∧	∧	PROPN
ejpam-3415	170	30	c	c	NOUN
ejpam-3415	170	31	)	)	PUNCT
ejpam-3415	170	32	if	if	SCONJ
ejpam-3415	170	33	and	and	CCONJ
ejpam-3415	170	34	only	only	ADV
ejpam-3415	170	35	if	if	SCONJ
ejpam-3415	170	36	there	there	PRON
ejpam-3415	170	37	exist	exist	VERB
ejpam-3415	170	38	v	v	ADP
ejpam-3415	170	39	∈	∈	PROPN
ejpam-3415	170	40	a	a	DET
ejpam-3415	170	41	∨	∨	NOUN
ejpam-3415	170	42	b	b	NOUN
ejpam-3415	170	43	and	and	CCONJ
ejpam-3415	170	44	w	w	PROPN
ejpam-3415	170	45	∈	∈	PROPN
ejpam-3415	170	46	a	a	DET
ejpam-3415	170	47	∨	∨	NOUN
ejpam-3415	170	48	c	c	NOUN
ejpam-3415	170	49	such	such	ADJ
ejpam-3415	170	50	that	that	DET
ejpam-3415	170	51	u	u	NOUN
ejpam-3415	170	52	=	=	PROPN
ejpam-3415	170	53	v	v	ADP
ejpam-3415	170	54	∧	∧	PROPN
ejpam-3415	170	55	w.	w.	PROPN
ejpam-3415	170	56	that	that	PRON
ejpam-3415	170	57	is	be	AUX
ejpam-3415	170	58	,	,	PUNCT
ejpam-3415	170	59	if	if	SCONJ
ejpam-3415	170	60	{	{	PUNCT
ejpam-3415	170	61	v	v	ADP
ejpam-3415	170	62	∧	∧	PROPN
ejpam-3415	170	63	w	w	NOUN
ejpam-3415	171	1	|	|	NOUN
ejpam-3415	172	1	v	v	ADP
ejpam-3415	172	2	∈	∈	PROPN
ejpam-3415	172	3	a	a	DET
ejpam-3415	172	4	∨	∨	NUM
ejpam-3415	172	5	b	b	PROPN
ejpam-3415	172	6	,	,	PUNCT
ejpam-3415	172	7	w	w	PROPN
ejpam-3415	172	8	∈	∈	PROPN
ejpam-3415	172	9	a	a	DET
ejpam-3415	172	10	∨	∨	NOUN
ejpam-3415	172	11	c	c	NOUN
ejpam-3415	172	12	}	}	PUNCT
ejpam-3415	172	13	=	=	PUNCT
ejpam-3415	172	14	a	a	DET
ejpam-3415	172	15	∨	∨	NOUN
ejpam-3415	172	16	(	(	PUNCT
ejpam-3415	172	17	b	b	PROPN
ejpam-3415	172	18	∧	∧	PROPN
ejpam-3415	172	19	c	c	NOUN
ejpam-3415	172	20	)	)	PUNCT
ejpam-3415	172	21	for	for	ADP
ejpam-3415	172	22	all	all	DET
ejpam-3415	172	23	a	a	DET
ejpam-3415	172	24	,	,	PUNCT
ejpam-3415	172	25	b	b	NOUN
ejpam-3415	172	26	,	,	PUNCT
ejpam-3415	172	27	c	c	PROPN
ejpam-3415	172	28	∈	∈	PROPN
ejpam-3415	172	29	l.	l.	PROPN
ejpam-3415	172	30	example	example	NOUN
ejpam-3415	172	31	3.2	3.2	NUM
ejpam-3415	172	32	(	(	PUNCT
ejpam-3415	172	33	see	see	VERB
ejpam-3415	172	34	also	also	ADV
ejpam-3415	172	35	[	[	X
ejpam-3415	172	36	1	1	NUM
ejpam-3415	172	37	;	;	PUNCT
ejpam-3415	172	38	lemma	lemma	PROPN
ejpam-3415	172	39	3.20	3.20	NUM
ejpam-3415	172	40	]	]	PUNCT
ejpam-3415	172	41	)	)	PUNCT
ejpam-3415	172	42	the	the	DET
ejpam-3415	172	43	hyperlattice	hyperlattice	NOUN
ejpam-3415	172	44	of	of	ADP
ejpam-3415	172	45	table	table	NOUN
ejpam-3415	172	46	5	5	NUM
ejpam-3415	172	47	is	be	AUX
ejpam-3415	172	48	not	not	PART
ejpam-3415	172	49	distributive	distributive	ADJ
ejpam-3415	172	50	in	in	ADP
ejpam-3415	172	51	the	the	DET
ejpam-3415	172	52	sense	sense	NOUN
ejpam-3415	172	53	of	of	ADP
ejpam-3415	172	54	definition	definition	NOUN
ejpam-3415	172	55	3.1(2	3.1(2	NUM
ejpam-3415	172	56	)	)	PUNCT
ejpam-3415	172	57	.	.	PUNCT
ejpam-3415	173	1	this	this	PRON
ejpam-3415	173	2	is	be	AUX
ejpam-3415	173	3	because	because	SCONJ
ejpam-3415	173	4	for	for	ADP
ejpam-3415	173	5	the	the	DET
ejpam-3415	173	6	element	element	NOUN
ejpam-3415	173	7	c	c	PROPN
ejpam-3415	173	8	∈	∈	PROPN
ejpam-3415	173	9	b	b	PROPN
ejpam-3415	173	10	∨	∨	X
ejpam-3415	173	11	(	(	PUNCT
ejpam-3415	173	12	a	a	DET
ejpam-3415	173	13	∧	∧	PROPN
ejpam-3415	173	14	b	b	NOUN
ejpam-3415	173	15	)	)	PUNCT
ejpam-3415	173	16	,	,	PUNCT
ejpam-3415	173	17	there	there	PRON
ejpam-3415	173	18	are	be	VERB
ejpam-3415	173	19	no	no	DET
ejpam-3415	173	20	v	v	NUM
ejpam-3415	173	21	∈	∈	PROPN
ejpam-3415	173	22	b	b	PROPN
ejpam-3415	173	23	∨	∨	NUM
ejpam-3415	173	24	a	a	PRON
ejpam-3415	173	25	and	and	CCONJ
ejpam-3415	173	26	w	w	PROPN
ejpam-3415	173	27	∈	∈	PROPN
ejpam-3415	173	28	b	b	PROPN
ejpam-3415	173	29	∨	∨	NUM
ejpam-3415	173	30	b	b	PROPN
ejpam-3415	173	31	such	such	ADJ
ejpam-3415	173	32	that	that	DET
ejpam-3415	173	33	c	c	NOUN
ejpam-3415	173	34	=	=	SYM
ejpam-3415	173	35	v	v	NUM
ejpam-3415	173	36	∧	∧	PROPN
ejpam-3415	173	37	w.	w.	PROPN
ejpam-3415	173	38	it	it	PRON
ejpam-3415	173	39	is	be	AUX
ejpam-3415	173	40	not	not	PART
ejpam-3415	173	41	distributive	distributive	ADJ
ejpam-3415	173	42	in	in	ADP
ejpam-3415	173	43	the	the	DET
ejpam-3415	173	44	sense	sense	NOUN
ejpam-3415	173	45	of	of	ADP
ejpam-3415	173	46	definition	definition	NOUN
ejpam-3415	173	47	3.1(1	3.1(1	NUM
ejpam-3415	173	48	)	)	PUNCT
ejpam-3415	173	49	as	as	ADV
ejpam-3415	173	50	well	well	ADV
ejpam-3415	173	51	,	,	PUNCT
ejpam-3415	173	52	since	since	SCONJ
ejpam-3415	173	53	c	c	PROPN
ejpam-3415	173	54	∈	∈	PROPN
ejpam-3415	173	55	(	(	PUNCT
ejpam-3415	173	56	b	b	NOUN
ejpam-3415	173	57	∧	∧	PROPN
ejpam-3415	173	58	a	a	PRON
ejpam-3415	173	59	)	)	PUNCT
ejpam-3415	173	60	∨	∨	NOUN
ejpam-3415	173	61	(	(	PUNCT
ejpam-3415	173	62	b	b	PROPN
ejpam-3415	173	63	∧	∧	PROPN
ejpam-3415	173	64	c	c	NOUN
ejpam-3415	173	65	)	)	PUNCT
ejpam-3415	173	66	but	but	CCONJ
ejpam-3415	173	67	there	there	PRON
ejpam-3415	173	68	is	be	VERB
ejpam-3415	173	69	no	no	DET
ejpam-3415	173	70	v	v	NOUN
ejpam-3415	173	71	∈	∈	PROPN
ejpam-3415	173	72	a	a	DET
ejpam-3415	173	73	∨	∨	NOUN
ejpam-3415	173	74	c	c	NOUN
ejpam-3415	173	75	such	such	ADJ
ejpam-3415	173	76	that	that	DET
ejpam-3415	173	77	c	c	NOUN
ejpam-3415	173	78	=	=	SYM
ejpam-3415	173	79	b	b	PROPN
ejpam-3415	173	80	∧	∧	PROPN
ejpam-3415	173	81	v.	v.	ADP
ejpam-3415	173	82	table	table	NOUN
ejpam-3415	173	83	5	5	NUM
ejpam-3415	173	84	:	:	PUNCT
ejpam-3415	173	85	the	the	DET
ejpam-3415	173	86	hyperlattice	hyperlattice	NOUN
ejpam-3415	173	87	of	of	ADP
ejpam-3415	173	88	the	the	DET
ejpam-3415	173	89	example	example	NOUN
ejpam-3415	173	90	3.2	3.2	NUM
ejpam-3415	173	91	.	.	PUNCT
ejpam-3415	174	1	∧	∧	NOUN
ejpam-3415	174	2	a	a	DET
ejpam-3415	174	3	b	b	X
ejpam-3415	174	4	c	c	NOUN
ejpam-3415	174	5	a	a	DET
ejpam-3415	174	6	a	a	PRON
ejpam-3415	174	7	a	a	PRON
ejpam-3415	174	8	a	a	DET
ejpam-3415	174	9	b	b	NOUN
ejpam-3415	174	10	a	a	DET
ejpam-3415	174	11	b	b	PROPN
ejpam-3415	174	12	b	b	PROPN
ejpam-3415	174	13	c	c	PROPN
ejpam-3415	174	14	a	a	DET
ejpam-3415	174	15	b	b	X
ejpam-3415	174	16	c	c	X
ejpam-3415	174	17	(	(	PUNCT
ejpam-3415	174	18	a	a	NOUN
ejpam-3415	174	19	)	)	PUNCT
ejpam-3415	174	20	∨	∨	NOUN
ejpam-3415	174	21	a	a	DET
ejpam-3415	174	22	b	b	NOUN
ejpam-3415	174	23	c	c	X
ejpam-3415	174	24	a	a	DET
ejpam-3415	174	25	{	{	PUNCT
ejpam-3415	174	26	a	a	NOUN
ejpam-3415	174	27	}	}	PUNCT
ejpam-3415	174	28	{	{	PUNCT
ejpam-3415	174	29	b	b	NOUN
ejpam-3415	174	30	,	,	PUNCT
ejpam-3415	174	31	c	c	NOUN
ejpam-3415	174	32	}	}	PUNCT
ejpam-3415	174	33	{	{	PUNCT
ejpam-3415	174	34	c	c	NOUN
ejpam-3415	174	35	}	}	PUNCT
ejpam-3415	174	36	b	b	PROPN
ejpam-3415	174	37	{	{	PUNCT
ejpam-3415	174	38	b	b	NOUN
ejpam-3415	174	39	,	,	PUNCT
ejpam-3415	174	40	c	c	NOUN
ejpam-3415	174	41	}	}	PUNCT
ejpam-3415	174	42	{	{	PUNCT
ejpam-3415	174	43	b	b	NOUN
ejpam-3415	174	44	}	}	PUNCT
ejpam-3415	174	45	{	{	PUNCT
ejpam-3415	174	46	c	c	NOUN
ejpam-3415	174	47	}	}	PUNCT
ejpam-3415	174	48	c	c	NOUN
ejpam-3415	174	49	{	{	PUNCT
ejpam-3415	174	50	c	c	NOUN
ejpam-3415	174	51	}	}	PUNCT
ejpam-3415	174	52	{	{	PUNCT
ejpam-3415	174	53	c	c	NOUN
ejpam-3415	174	54	}	}	PUNCT
ejpam-3415	174	55	{	{	PUNCT
ejpam-3415	174	56	c	c	NOUN
ejpam-3415	174	57	}	}	PUNCT
ejpam-3415	174	58	(	(	PUNCT
ejpam-3415	174	59	b	b	NOUN
ejpam-3415	174	60	)	)	PUNCT
ejpam-3415	174	61	example	example	NOUN
ejpam-3415	174	62	3.3	3.3	NUM
ejpam-3415	174	63	(	(	PUNCT
ejpam-3415	174	64	see	see	VERB
ejpam-3415	174	65	also	also	ADV
ejpam-3415	174	66	[	[	X
ejpam-3415	174	67	3	3	NUM
ejpam-3415	174	68	;	;	PUNCT
ejpam-3415	174	69	example	example	NOUN
ejpam-3415	174	70	1.8	1.8	NUM
ejpam-3415	174	71	]	]	PUNCT
ejpam-3415	174	72	)	)	PUNCT
ejpam-3415	174	73	the	the	DET
ejpam-3415	174	74	hyperlattice	hyperlattice	NOUN
ejpam-3415	174	75	defined	define	VERB
ejpam-3415	174	76	by	by	ADP
ejpam-3415	174	77	table	table	NOUN
ejpam-3415	174	78	6	6	NUM
ejpam-3415	174	79	is	be	AUX
ejpam-3415	174	80	a	a	DET
ejpam-3415	174	81	distributive	distributive	ADJ
ejpam-3415	174	82	hyperlattice	hyperlattice	NOUN
ejpam-3415	174	83	in	in	ADP
ejpam-3415	174	84	the	the	DET
ejpam-3415	174	85	sense	sense	NOUN
ejpam-3415	174	86	of	of	ADP
ejpam-3415	174	87	definition	definition	NOUN
ejpam-3415	174	88	3.1(1	3.1(1	NUM
ejpam-3415	174	89	)	)	PUNCT
ejpam-3415	174	90	since	since	SCONJ
ejpam-3415	174	91	for	for	ADP
ejpam-3415	174	92	all	all	DET
ejpam-3415	174	93	a	a	DET
ejpam-3415	174	94	,	,	PUNCT
ejpam-3415	174	95	b	b	NOUN
ejpam-3415	174	96	,	,	PUNCT
ejpam-3415	174	97	c	c	PROPN
ejpam-3415	174	98	∈	∈	PROPN
ejpam-3415	174	99	l	l	NOUN
ejpam-3415	174	100	,	,	PUNCT
ejpam-3415	174	101	we	we	PRON
ejpam-3415	174	102	have	have	VERB
ejpam-3415	174	103	{	{	PUNCT
ejpam-3415	174	104	a	a	DET
ejpam-3415	174	105	∧	∧	PROPN
ejpam-3415	174	106	v	v	ADP
ejpam-3415	174	107	|	|	ADV
ejpam-3415	174	108	v	v	ADP
ejpam-3415	174	109	∈	∈	PROPN
ejpam-3415	174	110	b	b	PROPN
ejpam-3415	174	111	∨	∨	NUM
ejpam-3415	174	112	c	c	NOUN
ejpam-3415	174	113	}	}	PUNCT
ejpam-3415	174	114	=	=	SYM
ejpam-3415	174	115	(	(	PUNCT
ejpam-3415	174	116	a	a	DET
ejpam-3415	174	117	∧	∧	PROPN
ejpam-3415	174	118	b	b	PROPN
ejpam-3415	174	119	)	)	PUNCT
ejpam-3415	174	120	∨	∨	NOUN
ejpam-3415	174	121	(	(	PUNCT
ejpam-3415	174	122	a	a	DET
ejpam-3415	174	123	∧	∧	PROPN
ejpam-3415	174	124	c	c	NOUN
ejpam-3415	174	125	)	)	PUNCT
ejpam-3415	174	126	;	;	PUNCT
ejpam-3415	174	127	but	but	CCONJ
ejpam-3415	174	128	it	it	PRON
ejpam-3415	174	129	is	be	AUX
ejpam-3415	174	130	not	not	PART
ejpam-3415	174	131	distributive	distributive	ADJ
ejpam-3415	174	132	in	in	ADP
ejpam-3415	174	133	the	the	DET
ejpam-3415	174	134	sense	sense	NOUN
ejpam-3415	174	135	of	of	ADP
ejpam-3415	174	136	definition	definition	NOUN
ejpam-3415	174	137	3.1(2	3.1(2	NUM
ejpam-3415	174	138	)	)	PUNCT
ejpam-3415	174	139	as	as	ADP
ejpam-3415	174	140	c	c	PROPN
ejpam-3415	174	141	∈	∈	PROPN
ejpam-3415	174	142	d	d	PROPN
ejpam-3415	174	143	∨	∨	NUM
ejpam-3415	174	144	b	b	PROPN
ejpam-3415	174	145	,	,	PUNCT
ejpam-3415	174	146	d	d	PROPN
ejpam-3415	174	147	∈	∈	PROPN
ejpam-3415	174	148	d	d	X
ejpam-3415	174	149	∨	∨	PROPN
ejpam-3415	174	150	c	c	PROPN
ejpam-3415	175	1	but	but	CCONJ
ejpam-3415	175	2	c	c	PROPN
ejpam-3415	175	3	∧	∧	PROPN
ejpam-3415	175	4	d	d	PROPN
ejpam-3415	175	5	/∈	/∈	PUNCT
ejpam-3415	176	1	d	d	X
ejpam-3415	176	2	∨	∨	NOUN
ejpam-3415	176	3	(	(	PUNCT
ejpam-3415	176	4	b	b	PROPN
ejpam-3415	176	5	∧	∧	PROPN
ejpam-3415	176	6	c	c	NOUN
ejpam-3415	176	7	)	)	PUNCT
ejpam-3415	176	8	.	.	PUNCT
ejpam-3415	177	1	table	table	NOUN
ejpam-3415	177	2	6	6	NUM
ejpam-3415	177	3	:	:	PUNCT
ejpam-3415	177	4	the	the	DET
ejpam-3415	177	5	hyperlattice	hyperlattice	NOUN
ejpam-3415	177	6	of	of	ADP
ejpam-3415	177	7	the	the	DET
ejpam-3415	177	8	example	example	NOUN
ejpam-3415	177	9	3.3	3.3	NUM
ejpam-3415	177	10	.	.	PUNCT
ejpam-3415	178	1	∧	∧	NOUN
ejpam-3415	178	2	a	a	DET
ejpam-3415	178	3	b	b	NOUN
ejpam-3415	178	4	c	c	NOUN
ejpam-3415	178	5	d	d	NOUN
ejpam-3415	178	6	a	a	PRON
ejpam-3415	178	7	a	a	PRON
ejpam-3415	178	8	a	a	DET
ejpam-3415	178	9	a	a	DET
ejpam-3415	178	10	a	a	DET
ejpam-3415	178	11	b	b	NOUN
ejpam-3415	178	12	a	a	DET
ejpam-3415	178	13	b	b	NOUN
ejpam-3415	178	14	a	a	DET
ejpam-3415	178	15	b	b	NOUN
ejpam-3415	178	16	c	c	NOUN
ejpam-3415	178	17	a	a	DET
ejpam-3415	178	18	a	a	NOUN
ejpam-3415	178	19	c	c	NOUN
ejpam-3415	178	20	c	c	NOUN
ejpam-3415	179	1	d	d	NOUN
ejpam-3415	179	2	a	a	DET
ejpam-3415	179	3	b	b	NOUN
ejpam-3415	179	4	c	c	X
ejpam-3415	179	5	d	d	X
ejpam-3415	179	6	(	(	PUNCT
ejpam-3415	179	7	a	a	NOUN
ejpam-3415	179	8	)	)	PUNCT
ejpam-3415	179	9	∨	∨	NOUN
ejpam-3415	179	10	a	a	DET
ejpam-3415	179	11	b	b	NOUN
ejpam-3415	179	12	c	c	NOUN
ejpam-3415	179	13	d	d	X
ejpam-3415	179	14	a	a	X
ejpam-3415	179	15	{	{	PUNCT
ejpam-3415	179	16	a	a	NOUN
ejpam-3415	179	17	}	}	PUNCT
ejpam-3415	179	18	{	{	PUNCT
ejpam-3415	179	19	b	b	NOUN
ejpam-3415	179	20	}	}	PUNCT
ejpam-3415	179	21	{	{	PUNCT
ejpam-3415	179	22	c	c	NOUN
ejpam-3415	179	23	}	}	PUNCT
ejpam-3415	179	24	{	{	PUNCT
ejpam-3415	179	25	d	d	NOUN
ejpam-3415	179	26	}	}	PUNCT
ejpam-3415	179	27	b	b	PROPN
ejpam-3415	179	28	{	{	PUNCT
ejpam-3415	179	29	b	b	NOUN
ejpam-3415	179	30	}	}	PUNCT
ejpam-3415	179	31	{	{	PUNCT
ejpam-3415	179	32	a	a	DET
ejpam-3415	179	33	,	,	PUNCT
ejpam-3415	179	34	b	b	NOUN
ejpam-3415	179	35	}	}	PUNCT
ejpam-3415	179	36	{	{	PUNCT
ejpam-3415	179	37	d	d	NOUN
ejpam-3415	179	38	}	}	PUNCT
ejpam-3415	179	39	{	{	PUNCT
ejpam-3415	179	40	c	c	NOUN
ejpam-3415	179	41	,	,	PUNCT
ejpam-3415	179	42	d	d	NOUN
ejpam-3415	179	43	}	}	PUNCT
ejpam-3415	179	44	c	c	NOUN
ejpam-3415	179	45	{	{	PUNCT
ejpam-3415	179	46	c	c	NOUN
ejpam-3415	179	47	}	}	PUNCT
ejpam-3415	179	48	{	{	PUNCT
ejpam-3415	179	49	d	d	NOUN
ejpam-3415	179	50	}	}	PUNCT
ejpam-3415	179	51	{	{	PUNCT
ejpam-3415	179	52	a	a	PROPN
ejpam-3415	179	53	,	,	PUNCT
ejpam-3415	179	54	c	c	NOUN
ejpam-3415	179	55	}	}	PUNCT
ejpam-3415	179	56	{	{	PUNCT
ejpam-3415	179	57	b	b	NOUN
ejpam-3415	179	58	,	,	PUNCT
ejpam-3415	179	59	d	d	NOUN
ejpam-3415	179	60	}	}	PUNCT
ejpam-3415	179	61	d	d	NOUN
ejpam-3415	179	62	{	{	PUNCT
ejpam-3415	179	63	d	d	NOUN
ejpam-3415	179	64	}	}	PUNCT
ejpam-3415	179	65	{	{	PUNCT
ejpam-3415	179	66	c	c	NOUN
ejpam-3415	179	67	,	,	PUNCT
ejpam-3415	179	68	d	d	NOUN
ejpam-3415	179	69	}	}	PUNCT
ejpam-3415	179	70	{	{	PUNCT
ejpam-3415	179	71	b	b	NOUN
ejpam-3415	179	72	,	,	PUNCT
ejpam-3415	179	73	d	d	NOUN
ejpam-3415	179	74	}	}	PUNCT
ejpam-3415	179	75	{	{	PUNCT
ejpam-3415	179	76	a	a	DET
ejpam-3415	179	77	,	,	PUNCT
ejpam-3415	179	78	b	b	NOUN
ejpam-3415	179	79	,	,	PUNCT
ejpam-3415	179	80	c	c	NOUN
ejpam-3415	179	81	,	,	PUNCT
ejpam-3415	179	82	d	d	NOUN
ejpam-3415	179	83	}	}	PUNCT
ejpam-3415	179	84	(	(	PUNCT
ejpam-3415	179	85	b	b	NOUN
ejpam-3415	179	86	)	)	PUNCT
ejpam-3415	179	87	niovi	niovi	NOUN
ejpam-3415	179	88	kehayopulu	kehayopulu	ADJ
ejpam-3415	179	89	/	/	SYM
ejpam-3415	179	90	eur	eur	PROPN
ejpam-3415	179	91	.	.	PUNCT
ejpam-3415	180	1	j.	j.	PROPN
ejpam-3415	180	2	pure	pure	PROPN
ejpam-3415	180	3	appl	appl	PROPN
ejpam-3415	180	4	.	.	PROPN
ejpam-3415	180	5	math	math	PROPN
ejpam-3415	180	6	,	,	PUNCT
ejpam-3415	180	7	12	12	NUM
ejpam-3415	180	8	(	(	PUNCT
ejpam-3415	180	9	2	2	NUM
ejpam-3415	180	10	)	)	PUNCT
ejpam-3415	180	11	(	(	PUNCT
ejpam-3415	180	12	2019	2019	NUM
ejpam-3415	180	13	)	)	PUNCT
ejpam-3415	180	14	,	,	PUNCT
ejpam-3415	180	15	252	252	NUM
ejpam-3415	180	16	-	-	SYM
ejpam-3415	180	17	269	269	NUM
ejpam-3415	180	18	260	260	NUM
ejpam-3415	180	19	proposition	proposition	NOUN
ejpam-3415	180	20	3.4	3.4	NUM
ejpam-3415	180	21	if	if	SCONJ
ejpam-3415	180	22	(	(	PUNCT
ejpam-3415	180	23	l,∧,∨	l,∧,∨	X
ejpam-3415	180	24	)	)	PUNCT
ejpam-3415	180	25	is	be	AUX
ejpam-3415	180	26	a	a	DET
ejpam-3415	180	27	distributive	distributive	ADJ
ejpam-3415	180	28	lattice	lattice	NOUN
ejpam-3415	180	29	,	,	PUNCT
ejpam-3415	180	30	then	then	ADV
ejpam-3415	180	31	the	the	DET
ejpam-3415	180	32	hyperlattice	hyperlattice	NOUN
ejpam-3415	180	33	(	(	PUNCT
ejpam-3415	180	34	l,∧	l,∧	NOUN
ejpam-3415	180	35	,	,	PUNCT
ejpam-3415	180	36	.	.	PUNCT
ejpam-3415	181	1	∨	∨	NUM
ejpam-3415	181	2	)	)	PUNCT
ejpam-3415	181	3	,	,	PUNCT
ejpam-3415	181	4	where	where	SCONJ
ejpam-3415	181	5	.	.	PUNCT
ejpam-3415	182	1	∨	∨	NOUN
ejpam-3415	182	2	:	:	PUNCT
ejpam-3415	182	3	(	(	PUNCT
ejpam-3415	182	4	a	a	DET
ejpam-3415	182	5	,	,	PUNCT
ejpam-3415	182	6	b	b	NOUN
ejpam-3415	182	7	)	)	PUNCT
ejpam-3415	182	8	→	→	SYM
ejpam-3415	182	9	a	a	PRON
ejpam-3415	182	10	.	.	PUNCT
ejpam-3415	183	1	∨	∨	NUM
ejpam-3415	183	2	b	b	X
ejpam-3415	183	3	∈	∈	PROPN
ejpam-3415	183	4	{	{	PUNCT
ejpam-3415	183	5	a	a	DET
ejpam-3415	183	6	∨	∨	PROPN
ejpam-3415	183	7	b	b	NOUN
ejpam-3415	183	8	}	}	PUNCT
ejpam-3415	183	9	considered	consider	VERB
ejpam-3415	183	10	in	in	ADP
ejpam-3415	183	11	the	the	DET
ejpam-3415	183	12	first	first	ADJ
ejpam-3415	183	13	part	part	NOUN
ejpam-3415	183	14	of	of	ADP
ejpam-3415	183	15	proposition	proposition	NOUN
ejpam-3415	183	16	2.5	2.5	NUM
ejpam-3415	183	17	is	be	AUX
ejpam-3415	183	18	a	a	DET
ejpam-3415	183	19	distributive	distributive	ADJ
ejpam-3415	183	20	hyperlattice	hyperlattice	NOUN
ejpam-3415	183	21	in	in	ADP
ejpam-3415	183	22	the	the	DET
ejpam-3415	183	23	sense	sense	NOUN
ejpam-3415	183	24	of	of	ADP
ejpam-3415	183	25	definition	definition	NOUN
ejpam-3415	183	26	3.1(1	3.1(1	NUM
ejpam-3415	183	27	)	)	PUNCT
ejpam-3415	183	28	and	and	CCONJ
ejpam-3415	183	29	in	in	ADP
ejpam-3415	183	30	the	the	DET
ejpam-3415	183	31	sense	sense	NOUN
ejpam-3415	183	32	of	of	ADP
ejpam-3415	183	33	definition	definition	NOUN
ejpam-3415	183	34	3.1(2	3.1(2	NUM
ejpam-3415	183	35	)	)	PUNCT
ejpam-3415	183	36	.	.	PUNCT
ejpam-3415	184	1	proof	proof	NOUN
ejpam-3415	184	2	the	the	DET
ejpam-3415	184	3	hyperlattice	hyperlattice	NOUN
ejpam-3415	184	4	(	(	PUNCT
ejpam-3415	184	5	l,∧	l,∧	NOUN
ejpam-3415	184	6	,	,	PUNCT
ejpam-3415	184	7	.	.	PUNCT
ejpam-3415	185	1	∨	∨	NUM
ejpam-3415	185	2	)	)	PUNCT
ejpam-3415	185	3	is	be	AUX
ejpam-3415	185	4	distributive	distributive	ADJ
ejpam-3415	185	5	in	in	ADP
ejpam-3415	185	6	the	the	DET
ejpam-3415	185	7	sense	sense	NOUN
ejpam-3415	185	8	of	of	ADP
ejpam-3415	185	9	definition	definition	NOUN
ejpam-3415	185	10	3.1(1	3.1(1	NUM
ejpam-3415	185	11	)	)	PUNCT
ejpam-3415	185	12	.	.	PUNCT
ejpam-3415	186	1	in	in	ADP
ejpam-3415	186	2	fact	fact	NOUN
ejpam-3415	186	3	:	:	PUNCT
ejpam-3415	186	4	if	if	SCONJ
ejpam-3415	186	5	u	u	PROPN
ejpam-3415	186	6	∈	∈	PROPN
ejpam-3415	186	7	b	b	PROPN
ejpam-3415	186	8	.	.	PUNCT
ejpam-3415	187	1	∨	∨	PROPN
ejpam-3415	187	2	c	c	PROPN
ejpam-3415	187	3	,	,	PUNCT
ejpam-3415	187	4	then	then	ADV
ejpam-3415	187	5	u	u	PROPN
ejpam-3415	187	6	=	=	PROPN
ejpam-3415	187	7	b	b	PROPN
ejpam-3415	187	8	∨	∨	NUM
ejpam-3415	187	9	c	c	PROPN
ejpam-3415	187	10	and	and	CCONJ
ejpam-3415	187	11	a	a	DET
ejpam-3415	187	12	∧	∧	PROPN
ejpam-3415	187	13	u	u	NOUN
ejpam-3415	187	14	=	=	PROPN
ejpam-3415	187	15	a	a	DET
ejpam-3415	187	16	∧	∧	PROPN
ejpam-3415	187	17	(	(	PUNCT
ejpam-3415	187	18	b	b	PROPN
ejpam-3415	187	19	∨	∨	NUM
ejpam-3415	187	20	c	c	NOUN
ejpam-3415	187	21	)	)	PUNCT
ejpam-3415	187	22	=	=	NOUN
ejpam-3415	187	23	(	(	PUNCT
ejpam-3415	187	24	a	a	DET
ejpam-3415	187	25	∧	∧	PROPN
ejpam-3415	187	26	b	b	PROPN
ejpam-3415	187	27	)	)	PUNCT
ejpam-3415	187	28	∨	∨	NOUN
ejpam-3415	187	29	(	(	PUNCT
ejpam-3415	187	30	a	a	DET
ejpam-3415	187	31	∧	∧	PROPN
ejpam-3415	187	32	c	c	NOUN
ejpam-3415	187	33	)	)	PUNCT
ejpam-3415	187	34	∈	∈	PROPN
ejpam-3415	187	35	(	(	PUNCT
ejpam-3415	187	36	a	a	DET
ejpam-3415	187	37	∧	∧	PROPN
ejpam-3415	187	38	b	b	NOUN
ejpam-3415	187	39	)	)	PUNCT
ejpam-3415	187	40	.	.	PUNCT
ejpam-3415	188	1	∨(a	∨(a	PROPN
ejpam-3415	188	2	∧	∧	PROPN
ejpam-3415	188	3	c	c	NOUN
ejpam-3415	188	4	)	)	PUNCT
ejpam-3415	188	5	.	.	PUNCT
ejpam-3415	189	1	if	if	SCONJ
ejpam-3415	189	2	u	u	PROPN
ejpam-3415	189	3	∈	∈	PROPN
ejpam-3415	189	4	(	(	PUNCT
ejpam-3415	189	5	a∧	a∧	NOUN
ejpam-3415	189	6	b	b	NOUN
ejpam-3415	189	7	)	)	PUNCT
ejpam-3415	189	8	.	.	PUNCT
ejpam-3415	190	1	∨(a∧	∨(a∧	PROPN
ejpam-3415	190	2	c	c	PROPN
ejpam-3415	190	3	)	)	PUNCT
ejpam-3415	190	4	,	,	PUNCT
ejpam-3415	190	5	then	then	ADV
ejpam-3415	190	6	u	u	X
ejpam-3415	190	7	=	=	PUNCT
ejpam-3415	190	8	(	(	PUNCT
ejpam-3415	190	9	a∧	a∧	NOUN
ejpam-3415	190	10	b)∨	b)∨	PROPN
ejpam-3415	190	11	(	(	PUNCT
ejpam-3415	190	12	a∧	a∧	NOUN
ejpam-3415	190	13	c	c	PROPN
ejpam-3415	190	14	)	)	PUNCT
ejpam-3415	190	15	and	and	CCONJ
ejpam-3415	190	16	,	,	PUNCT
ejpam-3415	190	17	for	for	ADP
ejpam-3415	190	18	the	the	DET
ejpam-3415	190	19	element	element	NOUN
ejpam-3415	190	20	v	v	NOUN
ejpam-3415	190	21	:	:	PUNCT
ejpam-3415	190	22	=	=	PROPN
ejpam-3415	190	23	b∨	b∨	PROPN
ejpam-3415	190	24	c	c	PROPN
ejpam-3415	190	25	∈	∈	PROPN
ejpam-3415	190	26	b	b	PROPN
ejpam-3415	190	27	.	.	PUNCT
ejpam-3415	191	1	∨	∨	PROPN
ejpam-3415	191	2	c	c	X
ejpam-3415	191	3	,	,	PUNCT
ejpam-3415	191	4	we	we	PRON
ejpam-3415	191	5	have	have	VERB
ejpam-3415	191	6	u	u	NOUN
ejpam-3415	191	7	=	=	NOUN
ejpam-3415	191	8	a	a	DET
ejpam-3415	191	9	∧	∧	PROPN
ejpam-3415	191	10	v.	v.	ADP
ejpam-3415	191	11	it	it	PRON
ejpam-3415	191	12	is	be	AUX
ejpam-3415	191	13	distributive	distributive	ADJ
ejpam-3415	191	14	in	in	ADP
ejpam-3415	191	15	the	the	DET
ejpam-3415	191	16	sense	sense	NOUN
ejpam-3415	191	17	of	of	ADP
ejpam-3415	191	18	definition	definition	NOUN
ejpam-3415	191	19	3.1(2	3.1(2	NUM
ejpam-3415	191	20	)	)	PUNCT
ejpam-3415	191	21	as	as	ADV
ejpam-3415	191	22	well	well	ADV
ejpam-3415	191	23	.	.	PUNCT
ejpam-3415	192	1	indeed	indeed	ADV
ejpam-3415	192	2	:	:	PUNCT
ejpam-3415	192	3	if	if	SCONJ
ejpam-3415	192	4	u	u	PROPN
ejpam-3415	192	5	∈	∈	PROPN
ejpam-3415	192	6	a	a	PRON
ejpam-3415	192	7	.	.	PUNCT
ejpam-3415	193	1	∨(b	∨(b	ADJ
ejpam-3415	193	2	∧	∧	PROPN
ejpam-3415	193	3	c	c	NOUN
ejpam-3415	193	4	)	)	PUNCT
ejpam-3415	193	5	,	,	PUNCT
ejpam-3415	193	6	then	then	ADV
ejpam-3415	193	7	u	u	X
ejpam-3415	193	8	=	=	PUNCT
ejpam-3415	193	9	a	a	DET
ejpam-3415	193	10	∨	∨	NOUN
ejpam-3415	193	11	(	(	PUNCT
ejpam-3415	193	12	b	b	PROPN
ejpam-3415	193	13	∧	∧	PROPN
ejpam-3415	193	14	c	c	NOUN
ejpam-3415	193	15	)	)	PUNCT
ejpam-3415	193	16	and	and	CCONJ
ejpam-3415	193	17	,	,	PUNCT
ejpam-3415	193	18	for	for	ADP
ejpam-3415	193	19	the	the	DET
ejpam-3415	193	20	elements	element	NOUN
ejpam-3415	193	21	v	v	X
ejpam-3415	193	22	:	:	PUNCT
ejpam-3415	193	23	=	=	PUNCT
ejpam-3415	193	24	a	a	DET
ejpam-3415	193	25	∨	∨	NUM
ejpam-3415	193	26	b	b	X
ejpam-3415	193	27	∈	∈	PROPN
ejpam-3415	193	28	a	a	PRON
ejpam-3415	193	29	.	.	PUNCT
ejpam-3415	194	1	∨	∨	NUM
ejpam-3415	194	2	b	b	PROPN
ejpam-3415	194	3	and	and	CCONJ
ejpam-3415	194	4	w	w	NOUN
ejpam-3415	194	5	:	:	PUNCT
ejpam-3415	194	6	=	=	PUNCT
ejpam-3415	194	7	a	a	DET
ejpam-3415	194	8	∨	∨	NUM
ejpam-3415	194	9	c	c	X
ejpam-3415	194	10	∈	∈	PROPN
ejpam-3415	194	11	a	a	PRON
ejpam-3415	194	12	.	.	PUNCT
ejpam-3415	195	1	∨	∨	NUM
ejpam-3415	195	2	c	c	X
ejpam-3415	195	3	,	,	PUNCT
ejpam-3415	195	4	we	we	PRON
ejpam-3415	195	5	have	have	VERB
ejpam-3415	195	6	u	u	NOUN
ejpam-3415	195	7	=	=	NOUN
ejpam-3415	195	8	a	a	DET
ejpam-3415	195	9	∨	∨	NOUN
ejpam-3415	195	10	(	(	PUNCT
ejpam-3415	195	11	b	b	PROPN
ejpam-3415	195	12	∧	∧	PROPN
ejpam-3415	195	13	c	c	NOUN
ejpam-3415	195	14	)	)	PUNCT
ejpam-3415	195	15	=	=	NOUN
ejpam-3415	195	16	(	(	PUNCT
ejpam-3415	195	17	a	a	DET
ejpam-3415	195	18	∨	∨	NUM
ejpam-3415	195	19	b	b	NOUN
ejpam-3415	195	20	)	)	PUNCT
ejpam-3415	195	21	∧	∧	NOUN
ejpam-3415	195	22	(	(	PUNCT
ejpam-3415	195	23	a	a	DET
ejpam-3415	195	24	∨	∨	NUM
ejpam-3415	195	25	c	c	NOUN
ejpam-3415	195	26	)	)	PUNCT
ejpam-3415	195	27	=	=	SYM
ejpam-3415	196	1	v	v	ADP
ejpam-3415	196	2	∧	∧	PROPN
ejpam-3415	196	3	w.	w.	NOUN
ejpam-3415	196	4	if	if	SCONJ
ejpam-3415	196	5	u	u	PROPN
ejpam-3415	196	6	∈	∈	PROPN
ejpam-3415	196	7	a	a	PRON
ejpam-3415	196	8	.	.	PUNCT
ejpam-3415	197	1	∨	∨	NUM
ejpam-3415	197	2	b	b	PROPN
ejpam-3415	197	3	and	and	CCONJ
ejpam-3415	197	4	v	v	ADP
ejpam-3415	197	5	∈	∈	PROPN
ejpam-3415	197	6	a	a	PRON
ejpam-3415	197	7	.	.	PUNCT
ejpam-3415	198	1	∨	∨	NUM
ejpam-3415	198	2	c	c	PROPN
ejpam-3415	198	3	,	,	PUNCT
ejpam-3415	198	4	then	then	ADV
ejpam-3415	198	5	u	u	X
ejpam-3415	198	6	=	=	PUNCT
ejpam-3415	198	7	a	a	DET
ejpam-3415	198	8	∨	∨	NUM
ejpam-3415	198	9	b	b	NOUN
ejpam-3415	198	10	,	,	PUNCT
ejpam-3415	198	11	v	v	NOUN
ejpam-3415	198	12	=	=	PUNCT
ejpam-3415	198	13	a	a	DET
ejpam-3415	198	14	∨	∨	NUM
ejpam-3415	198	15	c	c	NOUN
ejpam-3415	198	16	and	and	CCONJ
ejpam-3415	198	17	then	then	ADV
ejpam-3415	198	18	u	u	PROPN
ejpam-3415	198	19	∧	∧	PROPN
ejpam-3415	198	20	v	v	NOUN
ejpam-3415	198	21	=	=	PUNCT
ejpam-3415	198	22	(	(	PUNCT
ejpam-3415	198	23	a	a	DET
ejpam-3415	198	24	∨	∨	NUM
ejpam-3415	198	25	b	b	NOUN
ejpam-3415	198	26	)	)	PUNCT
ejpam-3415	198	27	∧	∧	NOUN
ejpam-3415	198	28	(	(	PUNCT
ejpam-3415	198	29	a	a	DET
ejpam-3415	198	30	∨	∨	NUM
ejpam-3415	198	31	c	c	NOUN
ejpam-3415	198	32	)	)	PUNCT
ejpam-3415	198	33	=	=	SYM
ejpam-3415	198	34	a	a	DET
ejpam-3415	198	35	∨	∨	X
ejpam-3415	198	36	(	(	PUNCT
ejpam-3415	198	37	b	b	PROPN
ejpam-3415	198	38	∧	∧	PROPN
ejpam-3415	198	39	c	c	NOUN
ejpam-3415	198	40	)	)	PUNCT
ejpam-3415	198	41	.	.	PUNCT
ejpam-3415	199	1	�	�	PROPN
ejpam-3415	199	2	proposition	proposition	NOUN
ejpam-3415	199	3	3.5	3.5	NUM
ejpam-3415	199	4	if	if	SCONJ
ejpam-3415	199	5	(	(	PUNCT
ejpam-3415	199	6	l,∧,∨	l,∧,∨	X
ejpam-3415	199	7	)	)	PUNCT
ejpam-3415	199	8	is	be	AUX
ejpam-3415	199	9	a	a	DET
ejpam-3415	199	10	distributive	distributive	ADJ
ejpam-3415	199	11	lattice	lattice	NOUN
ejpam-3415	199	12	,	,	PUNCT
ejpam-3415	199	13	then	then	ADV
ejpam-3415	199	14	the	the	DET
ejpam-3415	199	15	hyperlattice	hyperlattice	NOUN
ejpam-3415	199	16	(	(	PUNCT
ejpam-3415	199	17	l,∧	l,∧	NOUN
ejpam-3415	199	18	,	,	PUNCT
ejpam-3415	199	19	.	.	PUNCT
ejpam-3415	200	1	∨	∨	NUM
ejpam-3415	200	2	)	)	PUNCT
ejpam-3415	200	3	,	,	PUNCT
ejpam-3415	200	4	where	where	SCONJ
ejpam-3415	200	5	.	.	PUNCT
ejpam-3415	201	1	∨	∨	NOUN
ejpam-3415	201	2	:	:	PUNCT
ejpam-3415	201	3	(	(	PUNCT
ejpam-3415	201	4	a	a	DET
ejpam-3415	201	5	,	,	PUNCT
ejpam-3415	201	6	b	b	NOUN
ejpam-3415	201	7	)	)	PUNCT
ejpam-3415	201	8	→	→	SYM
ejpam-3415	201	9	a	a	PRON
ejpam-3415	201	10	.	.	PUNCT
ejpam-3415	202	1	∨	∨	NUM
ejpam-3415	202	2	b	b	X
ejpam-3415	202	3	∈	∈	PROPN
ejpam-3415	202	4	{	{	PUNCT
ejpam-3415	202	5	a	a	PROPN
ejpam-3415	202	6	,	,	PUNCT
ejpam-3415	202	7	b	b	NOUN
ejpam-3415	202	8	,	,	PUNCT
ejpam-3415	202	9	a	a	DET
ejpam-3415	202	10	∨	∨	PROPN
ejpam-3415	202	11	b	b	NOUN
ejpam-3415	202	12	}	}	PUNCT
ejpam-3415	202	13	considered	consider	VERB
ejpam-3415	202	14	in	in	ADP
ejpam-3415	202	15	the	the	DET
ejpam-3415	202	16	second	second	ADJ
ejpam-3415	202	17	part	part	NOUN
ejpam-3415	202	18	of	of	ADP
ejpam-3415	202	19	proposition	proposition	NOUN
ejpam-3415	202	20	2.5	2.5	NUM
ejpam-3415	202	21	is	be	AUX
ejpam-3415	202	22	a	a	DET
ejpam-3415	202	23	distributive	distributive	ADJ
ejpam-3415	202	24	hyperlattice	hyperlattice	NOUN
ejpam-3415	202	25	in	in	ADP
ejpam-3415	202	26	the	the	DET
ejpam-3415	202	27	sense	sense	NOUN
ejpam-3415	202	28	of	of	ADP
ejpam-3415	202	29	definition	definition	NOUN
ejpam-3415	202	30	3.1(1	3.1(1	NUM
ejpam-3415	202	31	)	)	PUNCT
ejpam-3415	202	32	.	.	PUNCT
ejpam-3415	203	1	it	it	PRON
ejpam-3415	203	2	is	be	AUX
ejpam-3415	203	3	not	not	PART
ejpam-3415	203	4	a	a	DET
ejpam-3415	203	5	distributive	distributive	ADJ
ejpam-3415	203	6	hyperlattice	hyperlattice	NOUN
ejpam-3415	203	7	in	in	ADP
ejpam-3415	203	8	the	the	DET
ejpam-3415	203	9	sense	sense	NOUN
ejpam-3415	203	10	of	of	ADP
ejpam-3415	203	11	definition	definition	NOUN
ejpam-3415	203	12	3.1(2	3.1(2	NUM
ejpam-3415	203	13	)	)	PUNCT
ejpam-3415	203	14	in	in	ADP
ejpam-3415	203	15	general	general	ADJ
ejpam-3415	203	16	,	,	PUNCT
ejpam-3415	203	17	but	but	CCONJ
ejpam-3415	203	18	it	it	PRON
ejpam-3415	203	19	satisfies	satisfy	VERB
ejpam-3415	203	20	the	the	DET
ejpam-3415	203	21	property	property	NOUN
ejpam-3415	203	22	(	(	PUNCT
ejpam-3415	203	23	1	1	NUM
ejpam-3415	203	24	)	)	PUNCT
ejpam-3415	203	25	of	of	ADP
ejpam-3415	203	26	definition	definition	NOUN
ejpam-3415	203	27	3.1(2	3.1(2	NUM
ejpam-3415	203	28	)	)	PUNCT
ejpam-3415	203	29	.	.	PUNCT
ejpam-3415	204	1	proof	proof	NOUN
ejpam-3415	204	2	let	let	VERB
ejpam-3415	204	3	u	u	PROPN
ejpam-3415	204	4	∈	∈	PROPN
ejpam-3415	204	5	b	b	PROPN
ejpam-3415	204	6	.	.	PUNCT
ejpam-3415	205	1	∨	∨	PROPN
ejpam-3415	205	2	c.	c.	PROPN
ejpam-3415	205	3	then	then	ADV
ejpam-3415	205	4	a	a	DET
ejpam-3415	205	5	∧	∧	PROPN
ejpam-3415	205	6	u	u	X
ejpam-3415	205	7	∈	∈	PROPN
ejpam-3415	205	8	(	(	PUNCT
ejpam-3415	205	9	a	a	DET
ejpam-3415	205	10	∧	∧	PROPN
ejpam-3415	205	11	b	b	NOUN
ejpam-3415	205	12	)	)	PUNCT
ejpam-3415	205	13	.	.	PUNCT
ejpam-3415	206	1	∨(a	∨(a	PROPN
ejpam-3415	206	2	∧	∧	PROPN
ejpam-3415	206	3	c	c	NOUN
ejpam-3415	206	4	)	)	PUNCT
ejpam-3415	206	5	.	.	PUNCT
ejpam-3415	207	1	indeed	indeed	ADV
ejpam-3415	207	2	:	:	PUNCT
ejpam-3415	207	3	if	if	SCONJ
ejpam-3415	207	4	u	u	PROPN
ejpam-3415	207	5	=	=	SYM
ejpam-3415	207	6	b	b	PROPN
ejpam-3415	207	7	,	,	PUNCT
ejpam-3415	207	8	then	then	ADV
ejpam-3415	207	9	a	a	DET
ejpam-3415	207	10	∧	∧	PROPN
ejpam-3415	207	11	u	u	NOUN
ejpam-3415	207	12	=	=	PROPN
ejpam-3415	207	13	a	a	DET
ejpam-3415	207	14	∧	∧	PROPN
ejpam-3415	207	15	b	b	PROPN
ejpam-3415	207	16	∈	∈	PROPN
ejpam-3415	207	17	(	(	PUNCT
ejpam-3415	207	18	a	a	DET
ejpam-3415	207	19	∧	∧	PROPN
ejpam-3415	207	20	b	b	NOUN
ejpam-3415	207	21	)	)	PUNCT
ejpam-3415	207	22	.	.	PUNCT
ejpam-3415	208	1	∨(a	∨(a	PROPN
ejpam-3415	208	2	∧	∧	PROPN
ejpam-3415	208	3	c	c	NOUN
ejpam-3415	208	4	)	)	PUNCT
ejpam-3415	208	5	;	;	PUNCT
ejpam-3415	208	6	if	if	SCONJ
ejpam-3415	208	7	u	u	NOUN
ejpam-3415	208	8	=	=	SYM
ejpam-3415	208	9	c	c	PROPN
ejpam-3415	208	10	,	,	PUNCT
ejpam-3415	208	11	then	then	ADV
ejpam-3415	208	12	a	a	DET
ejpam-3415	208	13	∧	∧	PROPN
ejpam-3415	208	14	u	u	NOUN
ejpam-3415	208	15	=	=	PROPN
ejpam-3415	208	16	a	a	DET
ejpam-3415	208	17	∧	∧	PROPN
ejpam-3415	208	18	c	c	PROPN
ejpam-3415	208	19	∈	∈	PROPN
ejpam-3415	208	20	(	(	PUNCT
ejpam-3415	208	21	a	a	DET
ejpam-3415	208	22	∧	∧	PROPN
ejpam-3415	208	23	b	b	NOUN
ejpam-3415	208	24	)	)	PUNCT
ejpam-3415	208	25	.	.	PUNCT
ejpam-3415	209	1	∨(a	∨(a	PROPN
ejpam-3415	209	2	∧	∧	PROPN
ejpam-3415	209	3	c	c	NOUN
ejpam-3415	209	4	)	)	PUNCT
ejpam-3415	209	5	;	;	PUNCT
ejpam-3415	209	6	if	if	SCONJ
ejpam-3415	209	7	u	u	PROPN
ejpam-3415	209	8	=	=	SYM
ejpam-3415	209	9	b	b	PROPN
ejpam-3415	209	10	∨	∨	NUM
ejpam-3415	209	11	c	c	PROPN
ejpam-3415	209	12	,	,	PUNCT
ejpam-3415	209	13	then	then	ADV
ejpam-3415	209	14	a	a	DET
ejpam-3415	209	15	∧	∧	PROPN
ejpam-3415	209	16	u	u	NOUN
ejpam-3415	209	17	=	=	PROPN
ejpam-3415	209	18	a	a	DET
ejpam-3415	209	19	∧	∧	PROPN
ejpam-3415	209	20	(	(	PUNCT
ejpam-3415	209	21	b	b	PROPN
ejpam-3415	209	22	∨	∨	NUM
ejpam-3415	209	23	c	c	NOUN
ejpam-3415	209	24	)	)	PUNCT
ejpam-3415	210	1	=	=	NOUN
ejpam-3415	210	2	(	(	PUNCT
ejpam-3415	210	3	a	a	DET
ejpam-3415	210	4	∧	∧	PROPN
ejpam-3415	210	5	b	b	PROPN
ejpam-3415	210	6	)	)	PUNCT
ejpam-3415	210	7	∨	∨	NOUN
ejpam-3415	210	8	(	(	PUNCT
ejpam-3415	210	9	a	a	DET
ejpam-3415	210	10	∧	∧	PROPN
ejpam-3415	210	11	c	c	NOUN
ejpam-3415	210	12	)	)	PUNCT
ejpam-3415	210	13	∈	∈	PROPN
ejpam-3415	210	14	(	(	PUNCT
ejpam-3415	210	15	a	a	DET
ejpam-3415	210	16	∧	∧	PROPN
ejpam-3415	210	17	b	b	NOUN
ejpam-3415	210	18	)	)	PUNCT
ejpam-3415	210	19	.	.	PUNCT
ejpam-3415	211	1	∨(a	∨(a	PROPN
ejpam-3415	211	2	∧	∧	PROPN
ejpam-3415	211	3	c	c	NOUN
ejpam-3415	211	4	)	)	PUNCT
ejpam-3415	211	5	.	.	PUNCT
ejpam-3415	212	1	if	if	SCONJ
ejpam-3415	212	2	u	u	PROPN
ejpam-3415	212	3	∈	∈	PROPN
ejpam-3415	212	4	(	(	PUNCT
ejpam-3415	212	5	a	a	DET
ejpam-3415	212	6	∧	∧	PROPN
ejpam-3415	212	7	b	b	NOUN
ejpam-3415	212	8	)	)	PUNCT
ejpam-3415	212	9	.	.	PUNCT
ejpam-3415	213	1	∨(a	∨(a	PROPN
ejpam-3415	213	2	∧	∧	PROPN
ejpam-3415	213	3	c	c	NOUN
ejpam-3415	213	4	)	)	PUNCT
ejpam-3415	213	5	,	,	PUNCT
ejpam-3415	213	6	then	then	ADV
ejpam-3415	213	7	there	there	PRON
ejpam-3415	213	8	exists	exist	VERB
ejpam-3415	213	9	v	v	ADP
ejpam-3415	213	10	∈	∈	PROPN
ejpam-3415	213	11	b	b	PROPN
ejpam-3415	213	12	.	.	PUNCT
ejpam-3415	214	1	∨	∨	PROPN
ejpam-3415	214	2	c	c	X
ejpam-3415	214	3	such	such	ADJ
ejpam-3415	214	4	that	that	DET
ejpam-3415	214	5	u	u	NOUN
ejpam-3415	214	6	=	=	PUNCT
ejpam-3415	214	7	a	a	DET
ejpam-3415	214	8	∧	∧	PROPN
ejpam-3415	214	9	v.	v.	ADP
ejpam-3415	214	10	indeed	indeed	ADV
ejpam-3415	214	11	:	:	PUNCT
ejpam-3415	214	12	if	if	SCONJ
ejpam-3415	214	13	u	u	PRON
ejpam-3415	214	14	=	=	PUNCT
ejpam-3415	214	15	a	a	DET
ejpam-3415	214	16	∧	∧	PROPN
ejpam-3415	214	17	b	b	PROPN
ejpam-3415	214	18	then	then	ADV
ejpam-3415	214	19	,	,	PUNCT
ejpam-3415	214	20	for	for	ADP
ejpam-3415	214	21	the	the	DET
ejpam-3415	214	22	element	element	NOUN
ejpam-3415	214	23	v	v	NOUN
ejpam-3415	214	24	:	:	PUNCT
ejpam-3415	214	25	=	=	SYM
ejpam-3415	214	26	b	b	X
ejpam-3415	214	27	∈	∈	PROPN
ejpam-3415	214	28	b	b	PROPN
ejpam-3415	214	29	.	.	PUNCT
ejpam-3415	215	1	∨	∨	PROPN
ejpam-3415	215	2	c	c	X
ejpam-3415	215	3	,	,	PUNCT
ejpam-3415	215	4	we	we	PRON
ejpam-3415	215	5	have	have	VERB
ejpam-3415	215	6	u	u	NOUN
ejpam-3415	215	7	=	=	NOUN
ejpam-3415	215	8	a	a	DET
ejpam-3415	215	9	∧	∧	PROPN
ejpam-3415	215	10	v	v	ADP
ejpam-3415	215	11	;	;	PUNCT
ejpam-3415	215	12	if	if	SCONJ
ejpam-3415	215	13	u	u	PRON
ejpam-3415	215	14	=	=	PUNCT
ejpam-3415	215	15	a	a	DET
ejpam-3415	215	16	∧	∧	PROPN
ejpam-3415	215	17	c	c	NOUN
ejpam-3415	215	18	then	then	ADV
ejpam-3415	215	19	,	,	PUNCT
ejpam-3415	215	20	for	for	ADP
ejpam-3415	215	21	the	the	DET
ejpam-3415	215	22	element	element	NOUN
ejpam-3415	215	23	v	v	NOUN
ejpam-3415	215	24	:	:	PUNCT
ejpam-3415	215	25	=	=	PUNCT
ejpam-3415	215	26	c	c	X
ejpam-3415	215	27	∈	∈	PROPN
ejpam-3415	215	28	b	b	PROPN
ejpam-3415	215	29	.	.	PUNCT
ejpam-3415	216	1	∨	∨	PROPN
ejpam-3415	216	2	c	c	X
ejpam-3415	216	3	,	,	PUNCT
ejpam-3415	216	4	we	we	PRON
ejpam-3415	216	5	have	have	VERB
ejpam-3415	216	6	u	u	NOUN
ejpam-3415	216	7	=	=	NOUN
ejpam-3415	216	8	a	a	DET
ejpam-3415	216	9	∧	∧	PROPN
ejpam-3415	216	10	v	v	ADP
ejpam-3415	216	11	;	;	PUNCT
ejpam-3415	216	12	if	if	SCONJ
ejpam-3415	216	13	u	u	PRON
ejpam-3415	216	14	=	=	X
ejpam-3415	216	15	(	(	PUNCT
ejpam-3415	216	16	a	a	DET
ejpam-3415	216	17	∧	∧	PROPN
ejpam-3415	216	18	b	b	PROPN
ejpam-3415	216	19	)	)	PUNCT
ejpam-3415	216	20	∨	∨	NOUN
ejpam-3415	216	21	(	(	PUNCT
ejpam-3415	216	22	a	a	DET
ejpam-3415	216	23	∧	∧	PROPN
ejpam-3415	216	24	c	c	NOUN
ejpam-3415	216	25	)	)	PUNCT
ejpam-3415	216	26	,	,	PUNCT
ejpam-3415	216	27	then	then	ADV
ejpam-3415	216	28	for	for	ADP
ejpam-3415	216	29	the	the	DET
ejpam-3415	216	30	element	element	NOUN
ejpam-3415	216	31	v	v	NOUN
ejpam-3415	216	32	:	:	PUNCT
ejpam-3415	216	33	=	=	SYM
ejpam-3415	216	34	b	b	PROPN
ejpam-3415	216	35	∨	∨	NUM
ejpam-3415	216	36	c	c	PROPN
ejpam-3415	216	37	∈	∈	PROPN
ejpam-3415	216	38	b	b	PROPN
ejpam-3415	216	39	.	.	PUNCT
ejpam-3415	217	1	∨	∨	PROPN
ejpam-3415	217	2	c	c	X
ejpam-3415	217	3	,	,	PUNCT
ejpam-3415	217	4	we	we	PRON
ejpam-3415	217	5	have	have	VERB
ejpam-3415	217	6	u	u	NOUN
ejpam-3415	217	7	=	=	X
ejpam-3415	217	8	(	(	PUNCT
ejpam-3415	217	9	a	a	DET
ejpam-3415	217	10	∧	∧	PROPN
ejpam-3415	217	11	b	b	PROPN
ejpam-3415	217	12	)	)	PUNCT
ejpam-3415	217	13	∨	∨	NOUN
ejpam-3415	217	14	(	(	PUNCT
ejpam-3415	217	15	a	a	DET
ejpam-3415	217	16	∧	∧	PROPN
ejpam-3415	217	17	c	c	NOUN
ejpam-3415	217	18	)	)	PUNCT
ejpam-3415	217	19	=	=	PUNCT
ejpam-3415	217	20	a	a	DET
ejpam-3415	217	21	∧	∧	PROPN
ejpam-3415	217	22	(	(	PUNCT
ejpam-3415	217	23	b	b	PROPN
ejpam-3415	217	24	∨	∨	NUM
ejpam-3415	217	25	c	c	NOUN
ejpam-3415	217	26	)	)	PUNCT
ejpam-3415	217	27	=	=	PUNCT
ejpam-3415	217	28	a	a	DET
ejpam-3415	217	29	∧	∧	PROPN
ejpam-3415	217	30	v.	v.	ADP
ejpam-3415	217	31	the	the	DET
ejpam-3415	217	32	hyperlattice	hyperlattice	NOUN
ejpam-3415	217	33	l	l	NOUN
ejpam-3415	217	34	satisfies	satisfy	VERB
ejpam-3415	217	35	the	the	DET
ejpam-3415	217	36	property	property	NOUN
ejpam-3415	217	37	(	(	PUNCT
ejpam-3415	217	38	1	1	NUM
ejpam-3415	217	39	)	)	PUNCT
ejpam-3415	217	40	of	of	ADP
ejpam-3415	217	41	definition	definition	NOUN
ejpam-3415	217	42	3.1(2	3.1(2	NUM
ejpam-3415	217	43	)	)	PUNCT
ejpam-3415	217	44	;	;	PUNCT
ejpam-3415	217	45	that	that	PRON
ejpam-3415	217	46	is	be	AUX
ejpam-3415	217	47	,	,	PUNCT
ejpam-3415	217	48	if	if	SCONJ
ejpam-3415	217	49	u	u	PROPN
ejpam-3415	217	50	∈	∈	PROPN
ejpam-3415	217	51	a	a	PRON
ejpam-3415	217	52	.	.	PUNCT
ejpam-3415	218	1	∨(b∧c	∨(b∧c	NOUN
ejpam-3415	218	2	)	)	PUNCT
ejpam-3415	219	1	,	,	PUNCT
ejpam-3415	219	2	then	then	ADV
ejpam-3415	219	3	there	there	PRON
ejpam-3415	219	4	exist	exist	VERB
ejpam-3415	219	5	v	v	ADP
ejpam-3415	219	6	∈	∈	PROPN
ejpam-3415	219	7	a	a	PRON
ejpam-3415	219	8	.	.	PUNCT
ejpam-3415	220	1	∨	∨	NUM
ejpam-3415	220	2	b	b	PROPN
ejpam-3415	220	3	and	and	CCONJ
ejpam-3415	220	4	w	w	PROPN
ejpam-3415	220	5	∈	∈	PROPN
ejpam-3415	220	6	a	a	PRON
ejpam-3415	220	7	.	.	PUNCT
ejpam-3415	221	1	∨	∨	NUM
ejpam-3415	221	2	c	c	X
ejpam-3415	221	3	such	such	ADJ
ejpam-3415	221	4	that	that	DET
ejpam-3415	221	5	u	u	NOUN
ejpam-3415	221	6	=	=	PROPN
ejpam-3415	221	7	v	v	ADP
ejpam-3415	221	8	∧	∧	PROPN
ejpam-3415	221	9	w.	w.	PROPN
ejpam-3415	221	10	indeed	indeed	ADV
ejpam-3415	221	11	:	:	PUNCT
ejpam-3415	221	12	if	if	SCONJ
ejpam-3415	221	13	u	u	PRON
ejpam-3415	221	14	=	=	NOUN
ejpam-3415	221	15	a	a	PRON
ejpam-3415	221	16	then	then	ADV
ejpam-3415	221	17	,	,	PUNCT
ejpam-3415	221	18	for	for	ADP
ejpam-3415	221	19	the	the	DET
ejpam-3415	221	20	elements	element	NOUN
ejpam-3415	221	21	v	v	X
ejpam-3415	221	22	:	:	PUNCT
ejpam-3415	221	23	=	=	PUNCT
ejpam-3415	221	24	a	a	DET
ejpam-3415	221	25	∈	∈	PROPN
ejpam-3415	221	26	a	a	PRON
ejpam-3415	221	27	.	.	PUNCT
ejpam-3415	222	1	∨	∨	NUM
ejpam-3415	222	2	b	b	PROPN
ejpam-3415	222	3	and	and	CCONJ
ejpam-3415	222	4	w	w	NOUN
ejpam-3415	222	5	:	:	PUNCT
ejpam-3415	222	6	=	=	PUNCT
ejpam-3415	222	7	a	a	DET
ejpam-3415	222	8	∈	∈	PROPN
ejpam-3415	222	9	a	a	PRON
ejpam-3415	222	10	.	.	PUNCT
ejpam-3415	223	1	∨	∨	NUM
ejpam-3415	223	2	c	c	X
ejpam-3415	223	3	,	,	PUNCT
ejpam-3415	223	4	we	we	PRON
ejpam-3415	223	5	have	have	VERB
ejpam-3415	223	6	u	u	NOUN
ejpam-3415	223	7	=	=	PROPN
ejpam-3415	223	8	v	v	ADP
ejpam-3415	223	9	∧	∧	PROPN
ejpam-3415	223	10	w	w	PROPN
ejpam-3415	223	11	;	;	PUNCT
ejpam-3415	223	12	if	if	SCONJ
ejpam-3415	223	13	u	u	PROPN
ejpam-3415	223	14	=	=	SYM
ejpam-3415	223	15	b	b	PROPN
ejpam-3415	223	16	∧	∧	PROPN
ejpam-3415	223	17	c	c	PROPN
ejpam-3415	223	18	then	then	ADV
ejpam-3415	223	19	,	,	PUNCT
ejpam-3415	223	20	for	for	SCONJ
ejpam-3415	223	21	the	the	DET
ejpam-3415	223	22	elements	element	NOUN
ejpam-3415	223	23	v	v	ADP
ejpam-3415	223	24	:	:	PUNCT
ejpam-3415	223	25	=	=	SYM
ejpam-3415	223	26	b	b	X
ejpam-3415	223	27	∈	∈	PROPN
ejpam-3415	223	28	a	a	PRON
ejpam-3415	223	29	.	.	PUNCT
ejpam-3415	224	1	∨	∨	NUM
ejpam-3415	224	2	b	b	PROPN
ejpam-3415	224	3	and	and	CCONJ
ejpam-3415	224	4	w	w	NOUN
ejpam-3415	224	5	:	:	PUNCT
ejpam-3415	224	6	=	=	NOUN
ejpam-3415	224	7	c	c	X
ejpam-3415	224	8	∈	∈	PROPN
ejpam-3415	225	1	a	a	PRON
ejpam-3415	225	2	.	.	PUNCT
ejpam-3415	226	1	∨	∨	NUM
ejpam-3415	226	2	c	c	X
ejpam-3415	226	3	,	,	PUNCT
ejpam-3415	226	4	we	we	PRON
ejpam-3415	226	5	have	have	VERB
ejpam-3415	226	6	u	u	NOUN
ejpam-3415	226	7	=	=	PROPN
ejpam-3415	226	8	v	v	ADP
ejpam-3415	226	9	∧	∧	PROPN
ejpam-3415	226	10	w	w	PROPN
ejpam-3415	226	11	;	;	PUNCT
ejpam-3415	226	12	if	if	SCONJ
ejpam-3415	226	13	u	u	PRON
ejpam-3415	226	14	=	=	PUNCT
ejpam-3415	226	15	a	a	DET
ejpam-3415	226	16	∨	∨	NOUN
ejpam-3415	226	17	(	(	PUNCT
ejpam-3415	226	18	b	b	PROPN
ejpam-3415	226	19	∧	∧	PROPN
ejpam-3415	226	20	c	c	PROPN
ejpam-3415	226	21	)	)	PUNCT
ejpam-3415	226	22	then	then	ADV
ejpam-3415	226	23	,	,	PUNCT
ejpam-3415	226	24	for	for	ADP
ejpam-3415	226	25	the	the	DET
ejpam-3415	226	26	elements	element	NOUN
ejpam-3415	226	27	v	v	X
ejpam-3415	226	28	:	:	PUNCT
ejpam-3415	226	29	=	=	PUNCT
ejpam-3415	226	30	a	a	DET
ejpam-3415	226	31	∨	∨	NUM
ejpam-3415	226	32	b	b	X
ejpam-3415	226	33	∈	∈	PROPN
ejpam-3415	226	34	a	a	PRON
ejpam-3415	226	35	.	.	PUNCT
ejpam-3415	227	1	∨	∨	NUM
ejpam-3415	227	2	b	b	PROPN
ejpam-3415	227	3	and	and	CCONJ
ejpam-3415	227	4	w	w	NOUN
ejpam-3415	227	5	:	:	PUNCT
ejpam-3415	227	6	=	=	PUNCT
ejpam-3415	227	7	a	a	DET
ejpam-3415	227	8	∨	∨	NUM
ejpam-3415	227	9	c	c	X
ejpam-3415	227	10	∈	∈	PROPN
ejpam-3415	227	11	a	a	PRON
ejpam-3415	227	12	.	.	PUNCT
ejpam-3415	228	1	∨	∨	NUM
ejpam-3415	228	2	c	c	X
ejpam-3415	228	3	,	,	PUNCT
ejpam-3415	228	4	we	we	PRON
ejpam-3415	228	5	have	have	VERB
ejpam-3415	228	6	u	u	NOUN
ejpam-3415	228	7	=	=	NOUN
ejpam-3415	228	8	a	a	DET
ejpam-3415	228	9	∨	∨	NOUN
ejpam-3415	228	10	(	(	PUNCT
ejpam-3415	228	11	b	b	PROPN
ejpam-3415	228	12	∧	∧	PROPN
ejpam-3415	228	13	c	c	NOUN
ejpam-3415	228	14	)	)	PUNCT
ejpam-3415	228	15	=	=	NOUN
ejpam-3415	228	16	(	(	PUNCT
ejpam-3415	228	17	a	a	DET
ejpam-3415	228	18	∨	∨	NUM
ejpam-3415	228	19	b	b	NOUN
ejpam-3415	228	20	)	)	PUNCT
ejpam-3415	228	21	∧	∧	NOUN
ejpam-3415	228	22	(	(	PUNCT
ejpam-3415	228	23	a	a	DET
ejpam-3415	228	24	∨	∨	NUM
ejpam-3415	228	25	c	c	NOUN
ejpam-3415	228	26	)	)	PUNCT
ejpam-3415	228	27	=	=	SYM
ejpam-3415	229	1	v	v	ADP
ejpam-3415	229	2	∧	∧	PROPN
ejpam-3415	229	3	w.	w.	NOUN
ejpam-3415	229	4	we	we	PRON
ejpam-3415	229	5	prove	prove	VERB
ejpam-3415	229	6	the	the	DET
ejpam-3415	229	7	rest	rest	NOUN
ejpam-3415	229	8	of	of	ADP
ejpam-3415	229	9	the	the	DET
ejpam-3415	229	10	proposition	proposition	NOUN
ejpam-3415	229	11	by	by	ADP
ejpam-3415	229	12	the	the	DET
ejpam-3415	229	13	following	follow	VERB
ejpam-3415	229	14	example	example	NOUN
ejpam-3415	229	15	.	.	PUNCT
ejpam-3415	230	1	let	let	VERB
ejpam-3415	230	2	us	we	PRON
ejpam-3415	230	3	consider	consider	VERB
ejpam-3415	230	4	the	the	DET
ejpam-3415	230	5	distributive	distributive	ADJ
ejpam-3415	230	6	lattice	lattice	NOUN
ejpam-3415	230	7	of	of	ADP
ejpam-3415	230	8	figure	figure	NOUN
ejpam-3415	230	9	2	2	NUM
ejpam-3415	230	10	.	.	PUNCT
ejpam-3415	231	1	the	the	DET
ejpam-3415	231	2	hyperlattice	hyperlattice	NOUN
ejpam-3415	231	3	l	l	NOUN
ejpam-3415	231	4	with	with	ADP
ejpam-3415	231	5	the	the	DET
ejpam-3415	231	6	operation	operation	NOUN
ejpam-3415	231	7	∧	∧	NOUN
ejpam-3415	231	8	and	and	CCONJ
ejpam-3415	231	9	the	the	DET
ejpam-3415	231	10	hyperoperation	hyperoperation	NOUN
ejpam-3415	231	11	.	.	PUNCT
ejpam-3415	232	1	∨	∨	NUM
ejpam-3415	232	2	defined	define	VERB
ejpam-3415	232	3	in	in	ADP
ejpam-3415	232	4	the	the	DET
ejpam-3415	232	5	second	second	ADJ
ejpam-3415	232	6	proof	proof	NOUN
ejpam-3415	232	7	of	of	ADP
ejpam-3415	232	8	proposition	proposition	NOUN
ejpam-3415	232	9	2.5	2.5	NUM
ejpam-3415	232	10	is	be	AUX
ejpam-3415	232	11	given	give	VERB
ejpam-3415	232	12	by	by	ADP
ejpam-3415	232	13	table	table	NOUN
ejpam-3415	232	14	7	7	NUM
ejpam-3415	232	15	and	and	CCONJ
ejpam-3415	232	16	,	,	PUNCT
ejpam-3415	232	17	according	accord	VERB
ejpam-3415	232	18	to	to	ADP
ejpam-3415	232	19	what	what	PRON
ejpam-3415	232	20	we	we	PRON
ejpam-3415	232	21	already	already	ADV
ejpam-3415	232	22	said	say	VERB
ejpam-3415	232	23	,	,	PUNCT
ejpam-3415	232	24	it	it	PRON
ejpam-3415	232	25	is	be	AUX
ejpam-3415	232	26	a	a	DET
ejpam-3415	232	27	distributive	distributive	ADJ
ejpam-3415	232	28	hyperlattice	hyperlattice	NOUN
ejpam-3415	232	29	in	in	ADP
ejpam-3415	232	30	the	the	DET
ejpam-3415	232	31	sense	sense	NOUN
ejpam-3415	232	32	of	of	ADP
ejpam-3415	232	33	definition	definition	NOUN
ejpam-3415	232	34	3.1(1	3.1(1	NUM
ejpam-3415	232	35	)	)	PUNCT
ejpam-3415	232	36	and	and	CCONJ
ejpam-3415	232	37	satisfies	satisfy	VERB
ejpam-3415	232	38	condition	condition	NOUN
ejpam-3415	232	39	(	(	PUNCT
ejpam-3415	232	40	1	1	NUM
ejpam-3415	232	41	)	)	PUNCT
ejpam-3415	232	42	of	of	ADP
ejpam-3415	232	43	definition	definition	NOUN
ejpam-3415	232	44	3.1(2	3.1(2	NUM
ejpam-3415	232	45	)	)	PUNCT
ejpam-3415	232	46	.	.	PUNCT
ejpam-3415	233	1	but	but	CCONJ
ejpam-3415	233	2	it	it	PRON
ejpam-3415	233	3	is	be	AUX
ejpam-3415	233	4	not	not	PART
ejpam-3415	233	5	distributive	distributive	ADJ
ejpam-3415	233	6	in	in	ADP
ejpam-3415	233	7	the	the	DET
ejpam-3415	233	8	sense	sense	NOUN
ejpam-3415	233	9	of	of	ADP
ejpam-3415	233	10	definition	definition	NOUN
ejpam-3415	233	11	3.1(2	3.1(2	NUM
ejpam-3415	233	12	)	)	PUNCT
ejpam-3415	233	13	as	as	ADP
ejpam-3415	233	14	c	c	PROPN
ejpam-3415	233	15	∈	∈	PROPN
ejpam-3415	233	16	c	c	PROPN
ejpam-3415	233	17	.	.	PUNCT
ejpam-3415	234	1	∨	∨	NOUN
ejpam-3415	234	2	a	a	DET
ejpam-3415	234	3	,	,	PUNCT
ejpam-3415	234	4	b	b	X
ejpam-3415	234	5	∈	∈	PROPN
ejpam-3415	234	6	c	c	X
ejpam-3415	234	7	.	.	PUNCT
ejpam-3415	235	1	∨	∨	NUM
ejpam-3415	235	2	b	b	PROPN
ejpam-3415	235	3	but	but	CCONJ
ejpam-3415	235	4	c	c	PROPN
ejpam-3415	235	5	∧	∧	PROPN
ejpam-3415	235	6	b	b	PROPN
ejpam-3415	235	7	/∈	/∈	PROPN
ejpam-3415	235	8	c	c	NOUN
ejpam-3415	235	9	.	.	PUNCT
ejpam-3415	236	1	∨(a	∨(a	PROPN
ejpam-3415	236	2	∧	∧	PROPN
ejpam-3415	236	3	b	b	PROPN
ejpam-3415	236	4	)	)	PUNCT
ejpam-3415	236	5	.	.	PUNCT
ejpam-3415	237	1	niovi	niovi	PROPN
ejpam-3415	237	2	kehayopulu	kehayopulu	PROPN
ejpam-3415	237	3	/	/	SYM
ejpam-3415	237	4	eur	eur	PROPN
ejpam-3415	237	5	.	.	PUNCT
ejpam-3415	238	1	j.	j.	PROPN
ejpam-3415	238	2	pure	pure	PROPN
ejpam-3415	238	3	appl	appl	PROPN
ejpam-3415	238	4	.	.	PROPN
ejpam-3415	238	5	math	math	PROPN
ejpam-3415	238	6	,	,	PUNCT
ejpam-3415	238	7	12	12	NUM
ejpam-3415	238	8	(	(	PUNCT
ejpam-3415	238	9	2	2	NUM
ejpam-3415	238	10	)	)	PUNCT
ejpam-3415	238	11	(	(	PUNCT
ejpam-3415	238	12	2019	2019	NUM
ejpam-3415	238	13	)	)	PUNCT
ejpam-3415	238	14	,	,	PUNCT
ejpam-3415	238	15	252	252	NUM
ejpam-3415	238	16	-	-	SYM
ejpam-3415	238	17	269	269	NUM
ejpam-3415	238	18	261	261	NUM
ejpam-3415	238	19	a	a	DET
ejpam-3415	238	20	b	b	NOUN
ejpam-3415	238	21	c	c	NOUN
ejpam-3415	238	22	d	d	X
ejpam-3415	238	23	e	e	X
ejpam-3415	238	24	figure	figure	NOUN
ejpam-3415	238	25	2	2	NUM
ejpam-3415	238	26	:	:	PUNCT
ejpam-3415	238	27	the	the	DET
ejpam-3415	238	28	distributive	distributive	ADJ
ejpam-3415	238	29	hyperlattice	hyperlattice	NOUN
ejpam-3415	238	30	of	of	ADP
ejpam-3415	238	31	proposition	proposition	NOUN
ejpam-3415	238	32	3.5	3.5	NUM
ejpam-3415	238	33	.	.	PUNCT
ejpam-3415	238	34	table	table	NOUN
ejpam-3415	238	35	7	7	NUM
ejpam-3415	238	36	:	:	PUNCT
ejpam-3415	238	37	the	the	DET
ejpam-3415	238	38	hyperlattice	hyperlattice	NOUN
ejpam-3415	238	39	in	in	ADP
ejpam-3415	238	40	proposition	proposition	NOUN
ejpam-3415	238	41	3.5	3.5	NUM
ejpam-3415	238	42	.	.	PUNCT
ejpam-3415	239	1	∧	∧	NOUN
ejpam-3415	239	2	a	a	DET
ejpam-3415	239	3	b	b	NOUN
ejpam-3415	239	4	c	c	NOUN
ejpam-3415	239	5	d	d	PROPN
ejpam-3415	239	6	e	e	X
ejpam-3415	239	7	a	a	PRON
ejpam-3415	239	8	a	a	PRON
ejpam-3415	239	9	a	a	DET
ejpam-3415	239	10	a	a	DET
ejpam-3415	239	11	a	a	DET
ejpam-3415	239	12	a	a	DET
ejpam-3415	239	13	b	b	NOUN
ejpam-3415	239	14	a	a	DET
ejpam-3415	239	15	b	b	PROPN
ejpam-3415	239	16	b	b	PROPN
ejpam-3415	239	17	b	b	PROPN
ejpam-3415	239	18	b	b	PROPN
ejpam-3415	239	19	c	c	PROPN
ejpam-3415	239	20	a	a	DET
ejpam-3415	239	21	b	b	NOUN
ejpam-3415	239	22	c	c	NOUN
ejpam-3415	239	23	b	b	PROPN
ejpam-3415	239	24	c	c	PROPN
ejpam-3415	240	1	d	d	PROPN
ejpam-3415	240	2	a	a	DET
ejpam-3415	240	3	b	b	PROPN
ejpam-3415	240	4	b	b	PROPN
ejpam-3415	240	5	d	d	PROPN
ejpam-3415	240	6	d	d	PROPN
ejpam-3415	240	7	e	e	PROPN
ejpam-3415	240	8	a	a	PRON
ejpam-3415	240	9	b	b	NOUN
ejpam-3415	240	10	c	c	NOUN
ejpam-3415	240	11	d	d	X
ejpam-3415	240	12	e	e	X
ejpam-3415	240	13	(	(	PUNCT
ejpam-3415	240	14	a	a	NOUN
ejpam-3415	240	15	)	)	PUNCT
ejpam-3415	240	16	.	.	PUNCT
ejpam-3415	241	1	∨	∨	NOUN
ejpam-3415	241	2	a	a	DET
ejpam-3415	241	3	b	b	NOUN
ejpam-3415	241	4	c	c	NOUN
ejpam-3415	241	5	d	d	X
ejpam-3415	241	6	e	e	X
ejpam-3415	241	7	a	a	X
ejpam-3415	241	8	{	{	PUNCT
ejpam-3415	241	9	a	a	NOUN
ejpam-3415	241	10	}	}	PUNCT
ejpam-3415	241	11	{	{	PUNCT
ejpam-3415	241	12	a	a	DET
ejpam-3415	241	13	,	,	PUNCT
ejpam-3415	241	14	b	b	NOUN
ejpam-3415	241	15	}	}	PUNCT
ejpam-3415	241	16	{	{	PUNCT
ejpam-3415	241	17	a	a	PROPN
ejpam-3415	241	18	,	,	PUNCT
ejpam-3415	241	19	c	c	NOUN
ejpam-3415	241	20	}	}	PUNCT
ejpam-3415	241	21	{	{	PUNCT
ejpam-3415	241	22	a	a	DET
ejpam-3415	241	23	,	,	PUNCT
ejpam-3415	241	24	d	d	NOUN
ejpam-3415	241	25	}	}	PUNCT
ejpam-3415	241	26	{	{	PUNCT
ejpam-3415	241	27	a	a	NOUN
ejpam-3415	241	28	,	,	PUNCT
ejpam-3415	241	29	e	e	NOUN
ejpam-3415	241	30	}	}	PUNCT
ejpam-3415	241	31	b	b	PROPN
ejpam-3415	241	32	{	{	PUNCT
ejpam-3415	241	33	a	a	PROPN
ejpam-3415	241	34	,	,	PUNCT
ejpam-3415	241	35	b	b	NOUN
ejpam-3415	241	36	}	}	PUNCT
ejpam-3415	241	37	{	{	PUNCT
ejpam-3415	241	38	b	b	NOUN
ejpam-3415	241	39	}	}	PUNCT
ejpam-3415	241	40	{	{	PUNCT
ejpam-3415	241	41	b	b	NOUN
ejpam-3415	241	42	,	,	PUNCT
ejpam-3415	241	43	c	c	NOUN
ejpam-3415	241	44	}	}	PUNCT
ejpam-3415	241	45	{	{	PUNCT
ejpam-3415	241	46	b	b	NOUN
ejpam-3415	241	47	,	,	PUNCT
ejpam-3415	241	48	d	d	NOUN
ejpam-3415	241	49	}	}	PUNCT
ejpam-3415	241	50	{	{	PUNCT
ejpam-3415	241	51	b	b	NOUN
ejpam-3415	241	52	,	,	PUNCT
ejpam-3415	241	53	e	e	NOUN
ejpam-3415	241	54	}	}	PUNCT
ejpam-3415	241	55	c	c	NOUN
ejpam-3415	241	56	{	{	PUNCT
ejpam-3415	241	57	a	a	NOUN
ejpam-3415	241	58	,	,	PUNCT
ejpam-3415	241	59	c	c	NOUN
ejpam-3415	241	60	}	}	PUNCT
ejpam-3415	241	61	{	{	PUNCT
ejpam-3415	241	62	b	b	NOUN
ejpam-3415	241	63	,	,	PUNCT
ejpam-3415	241	64	c	c	NOUN
ejpam-3415	241	65	}	}	PUNCT
ejpam-3415	241	66	{	{	PUNCT
ejpam-3415	241	67	c	c	NOUN
ejpam-3415	241	68	}	}	PUNCT
ejpam-3415	241	69	{	{	PUNCT
ejpam-3415	241	70	c	c	NOUN
ejpam-3415	241	71	,	,	PUNCT
ejpam-3415	241	72	d	d	NOUN
ejpam-3415	241	73	,	,	PUNCT
ejpam-3415	241	74	e	e	NOUN
ejpam-3415	241	75	}	}	PUNCT
ejpam-3415	241	76	{	{	PUNCT
ejpam-3415	241	77	c	c	NOUN
ejpam-3415	241	78	,	,	PUNCT
ejpam-3415	241	79	e	e	NOUN
ejpam-3415	241	80	}	}	PUNCT
ejpam-3415	241	81	d	d	X
ejpam-3415	241	82	{	{	PUNCT
ejpam-3415	241	83	a	a	PRON
ejpam-3415	241	84	,	,	PUNCT
ejpam-3415	241	85	d	d	NOUN
ejpam-3415	241	86	}	}	PUNCT
ejpam-3415	241	87	{	{	PUNCT
ejpam-3415	241	88	b	b	NOUN
ejpam-3415	241	89	,	,	PUNCT
ejpam-3415	241	90	d	d	NOUN
ejpam-3415	241	91	}	}	PUNCT
ejpam-3415	241	92	{	{	PUNCT
ejpam-3415	241	93	c	c	NOUN
ejpam-3415	241	94	,	,	PUNCT
ejpam-3415	241	95	d	d	NOUN
ejpam-3415	241	96	,	,	PUNCT
ejpam-3415	241	97	e	e	NOUN
ejpam-3415	241	98	}	}	PUNCT
ejpam-3415	241	99	{	{	PUNCT
ejpam-3415	241	100	d	d	NOUN
ejpam-3415	241	101	}	}	PUNCT
ejpam-3415	241	102	{	{	PUNCT
ejpam-3415	241	103	d	d	NOUN
ejpam-3415	241	104	,	,	PUNCT
ejpam-3415	241	105	e	e	NOUN
ejpam-3415	241	106	}	}	PUNCT
ejpam-3415	241	107	e	e	X
ejpam-3415	241	108	{	{	PUNCT
ejpam-3415	241	109	a	a	PRON
ejpam-3415	241	110	,	,	PUNCT
ejpam-3415	241	111	e	e	NOUN
ejpam-3415	241	112	}	}	PUNCT
ejpam-3415	241	113	{	{	PUNCT
ejpam-3415	241	114	b	b	NOUN
ejpam-3415	241	115	,	,	PUNCT
ejpam-3415	241	116	e	e	NOUN
ejpam-3415	241	117	}	}	PUNCT
ejpam-3415	241	118	{	{	PUNCT
ejpam-3415	241	119	c	c	NOUN
ejpam-3415	241	120	,	,	PUNCT
ejpam-3415	241	121	e	e	NOUN
ejpam-3415	241	122	}	}	PUNCT
ejpam-3415	241	123	{	{	PUNCT
ejpam-3415	241	124	d	d	NOUN
ejpam-3415	241	125	,	,	PUNCT
ejpam-3415	241	126	e	e	NOUN
ejpam-3415	241	127	}	}	PUNCT
ejpam-3415	241	128	{	{	PUNCT
ejpam-3415	241	129	e	e	NOUN
ejpam-3415	241	130	}	}	PUNCT
ejpam-3415	241	131	(	(	PUNCT
ejpam-3415	241	132	b	b	X
ejpam-3415	241	133	)	)	PUNCT
ejpam-3415	241	134	�	�	PROPN
ejpam-3415	241	135	example	example	NOUN
ejpam-3415	241	136	3.6	3.6	NUM
ejpam-3415	241	137	let	let	VERB
ejpam-3415	241	138	us	we	PRON
ejpam-3415	241	139	consider	consider	VERB
ejpam-3415	241	140	the	the	DET
ejpam-3415	241	141	no	no	DET
ejpam-3415	241	142	distributive	distributive	ADJ
ejpam-3415	241	143	lattice	lattice	NOUN
ejpam-3415	241	144	of	of	ADP
ejpam-3415	241	145	figure	figure	NOUN
ejpam-3415	241	146	3	3	NUM
ejpam-3415	241	147	.	.	PUNCT
ejpam-3415	242	1	the	the	DET
ejpam-3415	242	2	hyperlattice	hyperlattice	NOUN
ejpam-3415	242	3	(	(	PUNCT
ejpam-3415	242	4	l,∧	l,∧	NOUN
ejpam-3415	242	5	,	,	PUNCT
ejpam-3415	242	6	.	.	PUNCT
ejpam-3415	243	1	∨	∨	NUM
ejpam-3415	243	2	)	)	PUNCT
ejpam-3415	243	3	that	that	PRON
ejpam-3415	243	4	corresponds	correspond	VERB
ejpam-3415	243	5	to	to	PART
ejpam-3415	243	6	figure	figure	VERB
ejpam-3415	243	7	3	3	NUM
ejpam-3415	243	8	using	use	VERB
ejpam-3415	243	9	the	the	DET
ejpam-3415	243	10	second	second	ADJ
ejpam-3415	243	11	proof	proof	NOUN
ejpam-3415	243	12	of	of	ADP
ejpam-3415	243	13	proposition	proposition	NOUN
ejpam-3415	243	14	2.5	2.5	NUM
ejpam-3415	243	15	is	be	AUX
ejpam-3415	243	16	given	give	VERB
ejpam-3415	243	17	by	by	ADP
ejpam-3415	243	18	table	table	NOUN
ejpam-3415	243	19	8	8	NUM
ejpam-3415	243	20	.	.	PUNCT
ejpam-3415	244	1	this	this	PRON
ejpam-3415	244	2	is	be	AUX
ejpam-3415	244	3	not	not	PART
ejpam-3415	244	4	distributive	distributive	ADJ
ejpam-3415	244	5	hyperlattice	hyperlattice	NOUN
ejpam-3415	244	6	in	in	ADP
ejpam-3415	244	7	the	the	DET
ejpam-3415	244	8	sense	sense	NOUN
ejpam-3415	244	9	of	of	ADP
ejpam-3415	244	10	definition	definition	NOUN
ejpam-3415	244	11	3.1(1	3.1(1	NUM
ejpam-3415	244	12	)	)	PUNCT
ejpam-3415	244	13	as	as	ADP
ejpam-3415	244	14	e	e	PROPN
ejpam-3415	244	15	∈	∈	PROPN
ejpam-3415	244	16	b	b	PROPN
ejpam-3415	244	17	.	.	PUNCT
ejpam-3415	245	1	∨	∨	NUM
ejpam-3415	245	2	c	c	PROPN
ejpam-3415	245	3	and	and	CCONJ
ejpam-3415	245	4	d∧e	d∧e	PROPN
ejpam-3415	245	5	/∈	/∈	PUNCT
ejpam-3415	245	6	(	(	PUNCT
ejpam-3415	245	7	d∧b	d∧b	PROPN
ejpam-3415	245	8	)	)	PUNCT
ejpam-3415	245	9	.	.	PUNCT
ejpam-3415	246	1	∨(d∧c	∨(d∧c	NOUN
ejpam-3415	246	2	)	)	PUNCT
ejpam-3415	246	3	,	,	PUNCT
ejpam-3415	246	4	that	that	PRON
ejpam-3415	246	5	is	be	AUX
ejpam-3415	246	6	condition	condition	NOUN
ejpam-3415	246	7	(	(	PUNCT
ejpam-3415	246	8	1	1	NUM
ejpam-3415	246	9	)	)	PUNCT
ejpam-3415	246	10	of	of	ADP
ejpam-3415	246	11	definition	definition	NOUN
ejpam-3415	246	12	3.1(1	3.1(1	NUM
ejpam-3415	246	13	)	)	PUNCT
ejpam-3415	246	14	does	do	AUX
ejpam-3415	246	15	not	not	PART
ejpam-3415	246	16	hold	hold	VERB
ejpam-3415	246	17	;	;	PUNCT
ejpam-3415	246	18	and	and	CCONJ
ejpam-3415	246	19	not	not	PART
ejpam-3415	246	20	distributive	distributive	ADJ
ejpam-3415	246	21	hyperlattice	hyperlattice	NOUN
ejpam-3415	246	22	in	in	ADP
ejpam-3415	246	23	the	the	DET
ejpam-3415	246	24	sense	sense	NOUN
ejpam-3415	246	25	of	of	ADP
ejpam-3415	246	26	definition	definition	NOUN
ejpam-3415	246	27	3.1(2	3.1(2	NUM
ejpam-3415	246	28	)	)	PUNCT
ejpam-3415	246	29	as	as	ADP
ejpam-3415	246	30	e	e	PROPN
ejpam-3415	246	31	∈	∈	PROPN
ejpam-3415	246	32	d	d	X
ejpam-3415	246	33	.	.	PUNCT
ejpam-3415	247	1	∨	∨	NUM
ejpam-3415	247	2	b	b	PROPN
ejpam-3415	247	3	,	,	PUNCT
ejpam-3415	247	4	e	e	PROPN
ejpam-3415	247	5	∈	∈	PROPN
ejpam-3415	247	6	d	d	PROPN
ejpam-3415	247	7	.	.	PUNCT
ejpam-3415	248	1	∨	∨	NUM
ejpam-3415	248	2	c	c	PROPN
ejpam-3415	248	3	and	and	CCONJ
ejpam-3415	248	4	e∧	e∧	PROPN
ejpam-3415	248	5	e	e	NOUN
ejpam-3415	248	6	/∈	/∈	PUNCT
ejpam-3415	249	1	d	d	INTJ
ejpam-3415	249	2	.	.	PUNCT
ejpam-3415	250	1	∨(b∧	∨(b∧	NOUN
ejpam-3415	250	2	c	c	NOUN
ejpam-3415	250	3	)	)	PUNCT
ejpam-3415	251	1	=	=	PRON
ejpam-3415	251	2	{	{	PUNCT
ejpam-3415	251	3	d	d	NOUN
ejpam-3415	251	4	,	,	PUNCT
ejpam-3415	251	5	a	a	PRON
ejpam-3415	251	6	}	}	PUNCT
ejpam-3415	251	7	,	,	PUNCT
ejpam-3415	251	8	that	that	PRON
ejpam-3415	251	9	is	be	AUX
ejpam-3415	251	10	condition	condition	NOUN
ejpam-3415	251	11	(	(	PUNCT
ejpam-3415	251	12	2	2	NUM
ejpam-3415	251	13	)	)	PUNCT
ejpam-3415	251	14	of	of	ADP
ejpam-3415	251	15	definition	definition	NOUN
ejpam-3415	251	16	2.8(2	2.8(2	NUM
ejpam-3415	251	17	)	)	PUNCT
ejpam-3415	251	18	does	do	AUX
ejpam-3415	251	19	not	not	PART
ejpam-3415	251	20	hold	hold	VERB
ejpam-3415	251	21	.	.	PUNCT
ejpam-3415	252	1	niovi	niovi	PROPN
ejpam-3415	252	2	kehayopulu	kehayopulu	PROPN
ejpam-3415	252	3	/	/	SYM
ejpam-3415	252	4	eur	eur	PROPN
ejpam-3415	252	5	.	.	PUNCT
ejpam-3415	253	1	j.	j.	PROPN
ejpam-3415	253	2	pure	pure	PROPN
ejpam-3415	253	3	appl	appl	PROPN
ejpam-3415	253	4	.	.	PROPN
ejpam-3415	253	5	math	math	PROPN
ejpam-3415	253	6	,	,	PUNCT
ejpam-3415	253	7	12	12	NUM
ejpam-3415	253	8	(	(	PUNCT
ejpam-3415	253	9	2	2	NUM
ejpam-3415	253	10	)	)	PUNCT
ejpam-3415	253	11	(	(	PUNCT
ejpam-3415	253	12	2019	2019	NUM
ejpam-3415	253	13	)	)	PUNCT
ejpam-3415	253	14	,	,	PUNCT
ejpam-3415	253	15	252	252	NUM
ejpam-3415	253	16	-	-	SYM
ejpam-3415	253	17	269	269	NUM
ejpam-3415	253	18	262	262	NUM
ejpam-3415	253	19	a	a	DET
ejpam-3415	253	20	b	b	NOUN
ejpam-3415	253	21	c	c	NOUN
ejpam-3415	253	22	d	d	X
ejpam-3415	253	23	e	e	X
ejpam-3415	253	24	figure	figure	NOUN
ejpam-3415	253	25	3	3	NUM
ejpam-3415	253	26	:	:	PUNCT
ejpam-3415	253	27	the	the	DET
ejpam-3415	253	28	no	no	DET
ejpam-3415	253	29	distributive	distributive	ADJ
ejpam-3415	253	30	lattice	lattice	NOUN
ejpam-3415	253	31	of	of	ADP
ejpam-3415	253	32	the	the	DET
ejpam-3415	253	33	example	example	NOUN
ejpam-3415	253	34	3.6	3.6	NUM
ejpam-3415	253	35	.	.	PUNCT
ejpam-3415	253	36	table	table	NOUN
ejpam-3415	253	37	8	8	NUM
ejpam-3415	253	38	:	:	PUNCT
ejpam-3415	253	39	the	the	DET
ejpam-3415	253	40	hyperlattice	hyperlattice	NOUN
ejpam-3415	253	41	of	of	ADP
ejpam-3415	253	42	the	the	DET
ejpam-3415	253	43	example	example	NOUN
ejpam-3415	253	44	3.6	3.6	NUM
ejpam-3415	253	45	.	.	PUNCT
ejpam-3415	254	1	∧	∧	NOUN
ejpam-3415	254	2	a	a	DET
ejpam-3415	254	3	b	b	NOUN
ejpam-3415	254	4	c	c	NOUN
ejpam-3415	254	5	d	d	PROPN
ejpam-3415	254	6	e	e	X
ejpam-3415	254	7	a	a	DET
ejpam-3415	254	8	a	a	DET
ejpam-3415	254	9	a	a	DET
ejpam-3415	254	10	a	a	DET
ejpam-3415	254	11	a	a	DET
ejpam-3415	254	12	a	a	DET
ejpam-3415	254	13	b	b	NOUN
ejpam-3415	254	14	a	a	DET
ejpam-3415	254	15	b	b	NOUN
ejpam-3415	254	16	a	a	DET
ejpam-3415	254	17	a	a	DET
ejpam-3415	254	18	b	b	NOUN
ejpam-3415	254	19	c	c	NOUN
ejpam-3415	254	20	a	a	DET
ejpam-3415	254	21	a	a	PROPN
ejpam-3415	254	22	c	c	NOUN
ejpam-3415	254	23	a	a	DET
ejpam-3415	254	24	c	c	NOUN
ejpam-3415	254	25	d	d	NOUN
ejpam-3415	254	26	a	a	PRON
ejpam-3415	254	27	a	a	PRON
ejpam-3415	254	28	a	a	PROPN
ejpam-3415	254	29	d	d	X
ejpam-3415	254	30	d	d	X
ejpam-3415	254	31	e	e	PROPN
ejpam-3415	254	32	a	a	DET
ejpam-3415	254	33	b	b	NOUN
ejpam-3415	254	34	c	c	NOUN
ejpam-3415	254	35	d	d	X
ejpam-3415	254	36	e	e	X
ejpam-3415	254	37	(	(	PUNCT
ejpam-3415	254	38	a	a	NOUN
ejpam-3415	254	39	)	)	PUNCT
ejpam-3415	254	40	.	.	PUNCT
ejpam-3415	255	1	∨	∨	NOUN
ejpam-3415	255	2	a	a	DET
ejpam-3415	255	3	b	b	NOUN
ejpam-3415	255	4	c	c	NOUN
ejpam-3415	255	5	d	d	X
ejpam-3415	255	6	e	e	X
ejpam-3415	255	7	a	a	X
ejpam-3415	255	8	{	{	PUNCT
ejpam-3415	255	9	a	a	NOUN
ejpam-3415	255	10	}	}	PUNCT
ejpam-3415	255	11	{	{	PUNCT
ejpam-3415	255	12	a	a	DET
ejpam-3415	255	13	,	,	PUNCT
ejpam-3415	255	14	b	b	NOUN
ejpam-3415	255	15	}	}	PUNCT
ejpam-3415	255	16	{	{	PUNCT
ejpam-3415	255	17	a	a	PROPN
ejpam-3415	255	18	,	,	PUNCT
ejpam-3415	255	19	c	c	NOUN
ejpam-3415	255	20	}	}	PUNCT
ejpam-3415	255	21	{	{	PUNCT
ejpam-3415	255	22	a	a	DET
ejpam-3415	255	23	,	,	PUNCT
ejpam-3415	255	24	d	d	NOUN
ejpam-3415	255	25	}	}	PUNCT
ejpam-3415	255	26	{	{	PUNCT
ejpam-3415	255	27	a	a	NOUN
ejpam-3415	255	28	,	,	PUNCT
ejpam-3415	255	29	e	e	NOUN
ejpam-3415	255	30	}	}	PUNCT
ejpam-3415	255	31	b	b	PROPN
ejpam-3415	255	32	{	{	PUNCT
ejpam-3415	255	33	a	a	PROPN
ejpam-3415	255	34	,	,	PUNCT
ejpam-3415	255	35	b	b	NOUN
ejpam-3415	255	36	}	}	PUNCT
ejpam-3415	255	37	{	{	PUNCT
ejpam-3415	255	38	b	b	NOUN
ejpam-3415	255	39	}	}	PUNCT
ejpam-3415	255	40	{	{	PUNCT
ejpam-3415	255	41	b	b	PROPN
ejpam-3415	255	42	,	,	PUNCT
ejpam-3415	255	43	c	c	X
ejpam-3415	255	44	,	,	PUNCT
ejpam-3415	255	45	e	e	NOUN
ejpam-3415	255	46	}	}	PUNCT
ejpam-3415	255	47	{	{	PUNCT
ejpam-3415	255	48	b	b	NOUN
ejpam-3415	255	49	,	,	PUNCT
ejpam-3415	255	50	d	d	NOUN
ejpam-3415	255	51	,	,	PUNCT
ejpam-3415	255	52	e	e	NOUN
ejpam-3415	255	53	}	}	PUNCT
ejpam-3415	255	54	{	{	PUNCT
ejpam-3415	255	55	b	b	NOUN
ejpam-3415	255	56	,	,	PUNCT
ejpam-3415	255	57	e	e	NOUN
ejpam-3415	255	58	}	}	PUNCT
ejpam-3415	255	59	c	c	NOUN
ejpam-3415	255	60	{	{	PUNCT
ejpam-3415	255	61	a	a	NOUN
ejpam-3415	255	62	,	,	PUNCT
ejpam-3415	255	63	c	c	NOUN
ejpam-3415	255	64	}	}	PUNCT
ejpam-3415	255	65	{	{	PUNCT
ejpam-3415	255	66	b	b	PROPN
ejpam-3415	255	67	,	,	PUNCT
ejpam-3415	255	68	c	c	X
ejpam-3415	255	69	,	,	PUNCT
ejpam-3415	255	70	e	e	NOUN
ejpam-3415	255	71	}	}	PUNCT
ejpam-3415	255	72	{	{	PUNCT
ejpam-3415	255	73	c	c	NOUN
ejpam-3415	255	74	}	}	PUNCT
ejpam-3415	255	75	{	{	PUNCT
ejpam-3415	255	76	c	c	NOUN
ejpam-3415	255	77	,	,	PUNCT
ejpam-3415	255	78	d	d	NOUN
ejpam-3415	255	79	,	,	PUNCT
ejpam-3415	255	80	e	e	NOUN
ejpam-3415	255	81	}	}	PUNCT
ejpam-3415	255	82	{	{	PUNCT
ejpam-3415	255	83	c	c	NOUN
ejpam-3415	255	84	,	,	PUNCT
ejpam-3415	255	85	e	e	NOUN
ejpam-3415	255	86	}	}	PUNCT
ejpam-3415	255	87	d	d	X
ejpam-3415	255	88	{	{	PUNCT
ejpam-3415	255	89	a	a	PRON
ejpam-3415	255	90	,	,	PUNCT
ejpam-3415	255	91	d	d	NOUN
ejpam-3415	255	92	}	}	PUNCT
ejpam-3415	255	93	{	{	PUNCT
ejpam-3415	255	94	b	b	NOUN
ejpam-3415	255	95	,	,	PUNCT
ejpam-3415	255	96	d	d	NOUN
ejpam-3415	255	97	,	,	PUNCT
ejpam-3415	255	98	e	e	NOUN
ejpam-3415	255	99	}	}	PUNCT
ejpam-3415	255	100	{	{	PUNCT
ejpam-3415	255	101	c	c	NOUN
ejpam-3415	255	102	,	,	PUNCT
ejpam-3415	255	103	d	d	NOUN
ejpam-3415	255	104	,	,	PUNCT
ejpam-3415	255	105	e	e	NOUN
ejpam-3415	255	106	}	}	PUNCT
ejpam-3415	255	107	{	{	PUNCT
ejpam-3415	255	108	d	d	NOUN
ejpam-3415	255	109	}	}	PUNCT
ejpam-3415	255	110	{	{	PUNCT
ejpam-3415	255	111	d	d	NOUN
ejpam-3415	255	112	,	,	PUNCT
ejpam-3415	255	113	e	e	NOUN
ejpam-3415	255	114	}	}	PUNCT
ejpam-3415	255	115	e	e	X
ejpam-3415	255	116	{	{	PUNCT
ejpam-3415	255	117	a	a	PRON
ejpam-3415	255	118	,	,	PUNCT
ejpam-3415	255	119	e	e	NOUN
ejpam-3415	255	120	}	}	PUNCT
ejpam-3415	255	121	{	{	PUNCT
ejpam-3415	255	122	b	b	NOUN
ejpam-3415	255	123	,	,	PUNCT
ejpam-3415	255	124	e	e	NOUN
ejpam-3415	255	125	}	}	PUNCT
ejpam-3415	255	126	{	{	PUNCT
ejpam-3415	255	127	c	c	NOUN
ejpam-3415	255	128	,	,	PUNCT
ejpam-3415	255	129	e	e	NOUN
ejpam-3415	255	130	}	}	PUNCT
ejpam-3415	255	131	{	{	PUNCT
ejpam-3415	255	132	d	d	NOUN
ejpam-3415	255	133	,	,	PUNCT
ejpam-3415	255	134	e	e	NOUN
ejpam-3415	255	135	}	}	PUNCT
ejpam-3415	255	136	{	{	PUNCT
ejpam-3415	255	137	e	e	NOUN
ejpam-3415	255	138	}	}	PUNCT
ejpam-3415	255	139	(	(	PUNCT
ejpam-3415	255	140	b	b	X
ejpam-3415	255	141	)	)	PUNCT
ejpam-3415	255	142	now	now	ADV
ejpam-3415	255	143	we	we	PRON
ejpam-3415	255	144	will	will	AUX
ejpam-3415	255	145	give	give	VERB
ejpam-3415	255	146	another	another	DET
ejpam-3415	255	147	proof	proof	NOUN
ejpam-3415	255	148	of	of	ADP
ejpam-3415	255	149	proposition	proposition	NOUN
ejpam-3415	255	150	2.5	2.5	NUM
ejpam-3415	255	151	in	in	ADP
ejpam-3415	255	152	the	the	DET
ejpam-3415	255	153	next	next	ADJ
ejpam-3415	255	154	proposition	proposition	NOUN
ejpam-3415	255	155	.	.	PUNCT
ejpam-3415	256	1	proposition	proposition	NOUN
ejpam-3415	256	2	3.7	3.7	NUM
ejpam-3415	256	3	let	let	VERB
ejpam-3415	256	4	(	(	PUNCT
ejpam-3415	256	5	l,∧,∨	l,∧,∨	ADV
ejpam-3415	256	6	)	)	PUNCT
ejpam-3415	256	7	be	be	AUX
ejpam-3415	256	8	a	a	DET
ejpam-3415	256	9	lattice	lattice	NOUN
ejpam-3415	256	10	and	and	CCONJ
ejpam-3415	256	11	“	"	PUNCT
ejpam-3415	256	12	.	.	PUNCT
ejpam-3415	257	1	∨	∨	NOUN
ejpam-3415	257	2	”	"	PUNCT
ejpam-3415	257	3	the	the	DET
ejpam-3415	257	4	hyperoperation	hyperoperation	NOUN
ejpam-3415	257	5	on	on	ADP
ejpam-3415	257	6	l	l	NOUN
ejpam-3415	257	7	defined	define	VERB
ejpam-3415	257	8	by	by	ADP
ejpam-3415	257	9	:	:	PUNCT
ejpam-3415	257	10	.	.	PUNCT
ejpam-3415	258	1	∨	∨	NOUN
ejpam-3415	258	2	:	:	PUNCT
ejpam-3415	258	3	l×	l×	PROPN
ejpam-3415	258	4	l	l	NOUN
ejpam-3415	258	5	→	→	SYM
ejpam-3415	258	6	p∗(l	p∗(l	NOUN
ejpam-3415	258	7	)	)	PUNCT
ejpam-3415	258	8	|	|	NOUN
ejpam-3415	258	9	(	(	PUNCT
ejpam-3415	258	10	a	a	DET
ejpam-3415	258	11	,	,	PUNCT
ejpam-3415	258	12	b	b	NOUN
ejpam-3415	258	13	)	)	PUNCT
ejpam-3415	258	14	→	→	SYM
ejpam-3415	258	15	a	a	PRON
ejpam-3415	258	16	.	.	PUNCT
ejpam-3415	259	1	∨	∨	NUM
ejpam-3415	259	2	b	b	X
ejpam-3415	259	3	:	:	PUNCT
ejpam-3415	259	4	=	=	X
ejpam-3415	259	5	{	{	PUNCT
ejpam-3415	259	6	t	t	NOUN
ejpam-3415	259	7	∈	∈	PROPN
ejpam-3415	259	8	l	l	NOUN
ejpam-3415	260	1	|	|	NOUN
ejpam-3415	260	2	t	t	X
ejpam-3415	260	3	≤	≤	NOUN
ejpam-3415	260	4	a	a	DET
ejpam-3415	260	5	∨	∨	NUM
ejpam-3415	260	6	b	b	NOUN
ejpam-3415	260	7	}	}	PUNCT
ejpam-3415	260	8	.	.	PUNCT
ejpam-3415	261	1	then	then	ADV
ejpam-3415	261	2	(	(	PUNCT
ejpam-3415	261	3	l,∧	l,∧	NOUN
ejpam-3415	261	4	,	,	PUNCT
ejpam-3415	261	5	.	.	PUNCT
ejpam-3415	261	6	∨	∨	NUM
ejpam-3415	261	7	)	)	PUNCT
ejpam-3415	261	8	is	be	AUX
ejpam-3415	261	9	a	a	DET
ejpam-3415	261	10	hyperlattice	hyperlattice	NOUN
ejpam-3415	261	11	.	.	PUNCT
ejpam-3415	262	1	proof	proof	NOUN
ejpam-3415	262	2	let	let	VERB
ejpam-3415	262	3	x	x	SYM
ejpam-3415	262	4	∈	∈	PROPN
ejpam-3415	262	5	u	u	NOUN
ejpam-3415	262	6	.	.	PUNCT
ejpam-3415	263	1	∨	∨	NUM
ejpam-3415	263	2	c	c	X
ejpam-3415	263	3	for	for	ADP
ejpam-3415	263	4	some	some	DET
ejpam-3415	263	5	u	u	NOUN
ejpam-3415	263	6	∈	∈	PROPN
ejpam-3415	263	7	a	a	PRON
ejpam-3415	263	8	.	.	PUNCT
ejpam-3415	263	9	∨	∨	PROPN
ejpam-3415	263	10	b.	b.	PROPN
ejpam-3415	264	1	then	then	ADV
ejpam-3415	264	2	x	x	X
ejpam-3415	264	3	≤	≤	ADV
ejpam-3415	264	4	u∨	u∨	PROPN
ejpam-3415	264	5	c	c	NOUN
ejpam-3415	264	6	and	and	CCONJ
ejpam-3415	264	7	u	u	NOUN
ejpam-3415	264	8	≤	≤	PROPN
ejpam-3415	264	9	a∨	a∨	PROPN
ejpam-3415	264	10	b	b	PROPN
ejpam-3415	264	11	,	,	PUNCT
ejpam-3415	264	12	so	so	ADV
ejpam-3415	264	13	x	x	SYM
ejpam-3415	264	14	≤	≤	X
ejpam-3415	264	15	(	(	PUNCT
ejpam-3415	264	16	a∨	a∨	PROPN
ejpam-3415	264	17	b)∨	b)∨	PROPN
ejpam-3415	264	18	c	c	NOUN
ejpam-3415	264	19	=	=	PUNCT
ejpam-3415	264	20	a	a	DET
ejpam-3415	264	21	∨	∨	NOUN
ejpam-3415	264	22	(	(	PUNCT
ejpam-3415	264	23	b	b	PROPN
ejpam-3415	264	24	∨	∨	NUM
ejpam-3415	264	25	c	c	NOUN
ejpam-3415	264	26	)	)	PUNCT
ejpam-3415	264	27	.	.	PUNCT
ejpam-3415	265	1	for	for	ADP
ejpam-3415	265	2	the	the	DET
ejpam-3415	265	3	element	element	NOUN
ejpam-3415	265	4	v	v	NOUN
ejpam-3415	265	5	:	:	PUNCT
ejpam-3415	265	6	=	=	SYM
ejpam-3415	265	7	b	b	PROPN
ejpam-3415	265	8	∨	∨	NUM
ejpam-3415	265	9	c	c	PROPN
ejpam-3415	265	10	∈	∈	PROPN
ejpam-3415	265	11	b	b	PROPN
ejpam-3415	265	12	.	.	PUNCT
ejpam-3415	266	1	∨	∨	PROPN
ejpam-3415	266	2	c	c	X
ejpam-3415	266	3	,	,	PUNCT
ejpam-3415	266	4	we	we	PRON
ejpam-3415	266	5	have	have	VERB
ejpam-3415	266	6	x	x	PROPN
ejpam-3415	266	7	∈	∈	PROPN
ejpam-3415	266	8	a	a	PRON
ejpam-3415	266	9	.	.	PUNCT
ejpam-3415	267	1	∨	∨	NUM
ejpam-3415	267	2	v	v	NOUN
ejpam-3415	267	3	,	,	PUNCT
ejpam-3415	267	4	so	so	ADV
ejpam-3415	267	5	condition	condition	NOUN
ejpam-3415	267	6	(	(	PUNCT
ejpam-3415	267	7	3	3	NUM
ejpam-3415	267	8	)	)	PUNCT
ejpam-3415	267	9	of	of	ADP
ejpam-3415	267	10	definition	definition	NOUN
ejpam-3415	267	11	2.1	2.1	NUM
ejpam-3415	267	12	is	be	AUX
ejpam-3415	267	13	satisfied	satisfied	ADJ
ejpam-3415	267	14	.	.	PUNCT
ejpam-3415	268	1	let	let	VERB
ejpam-3415	268	2	now	now	ADV
ejpam-3415	268	3	a	a	PRON
ejpam-3415	268	4	,	,	PUNCT
ejpam-3415	268	5	b	b	PROPN
ejpam-3415	268	6	∈	∈	PROPN
ejpam-3415	268	7	l.	l.	NOUN
ejpam-3415	268	8	for	for	ADP
ejpam-3415	268	9	the	the	DET
ejpam-3415	268	10	element	element	NOUN
ejpam-3415	268	11	u	u	NOUN
ejpam-3415	268	12	:	:	PUNCT
ejpam-3415	268	13	=	=	PUNCT
ejpam-3415	268	14	a	a	DET
ejpam-3415	268	15	∨	∨	NUM
ejpam-3415	268	16	b	b	X
ejpam-3415	268	17	∈	∈	PROPN
ejpam-3415	268	18	a	a	PRON
ejpam-3415	268	19	.	.	PUNCT
ejpam-3415	269	1	∨	∨	NUM
ejpam-3415	269	2	b	b	PROPN
ejpam-3415	269	3	,	,	PUNCT
ejpam-3415	269	4	we	we	PRON
ejpam-3415	269	5	have	have	VERB
ejpam-3415	269	6	a∧	a∧	NOUN
ejpam-3415	269	7	u	u	NOUN
ejpam-3415	269	8	=	=	NOUN
ejpam-3415	269	9	a∧	a∧	NOUN
ejpam-3415	269	10	(	(	PUNCT
ejpam-3415	269	11	a∨	a∨	PROPN
ejpam-3415	269	12	b	b	PROPN
ejpam-3415	269	13	)	)	PUNCT
ejpam-3415	269	14	=	=	SYM
ejpam-3415	269	15	a	a	NOUN
ejpam-3415	269	16	;	;	PUNCT
ejpam-3415	269	17	and	and	CCONJ
ejpam-3415	269	18	since	since	SCONJ
ejpam-3415	269	19	a	a	DET
ejpam-3415	269	20	≤	≤	ADJ
ejpam-3415	269	21	a∨	a∨	PROPN
ejpam-3415	269	22	(	(	PUNCT
ejpam-3415	269	23	a∧	a∧	PROPN
ejpam-3415	269	24	b	b	PROPN
ejpam-3415	269	25	)	)	PUNCT
ejpam-3415	269	26	,	,	PUNCT
ejpam-3415	269	27	we	we	PRON
ejpam-3415	269	28	have	have	VERB
ejpam-3415	269	29	a	a	DET
ejpam-3415	269	30	∈	∈	NOUN
ejpam-3415	269	31	a	a	PRON
ejpam-3415	269	32	.	.	PUNCT
ejpam-3415	270	1	∨(a∧	∨(a∧	PROPN
ejpam-3415	270	2	b	b	PROPN
ejpam-3415	270	3	)	)	PUNCT
ejpam-3415	270	4	and	and	CCONJ
ejpam-3415	270	5	condition	condition	NOUN
ejpam-3415	270	6	(	(	PUNCT
ejpam-3415	270	7	4	4	NUM
ejpam-3415	270	8	)	)	PUNCT
ejpam-3415	270	9	of	of	ADP
ejpam-3415	270	10	definition	definition	NOUN
ejpam-3415	270	11	2.1	2.1	NUM
ejpam-3415	270	12	also	also	ADV
ejpam-3415	270	13	holds	hold	VERB
ejpam-3415	270	14	.	.	PUNCT
ejpam-3415	271	1	�	�	PROPN
ejpam-3415	271	2	proposition	proposition	VERB
ejpam-3415	271	3	3.8	3.8	NUM
ejpam-3415	271	4	if	if	SCONJ
ejpam-3415	271	5	(	(	PUNCT
ejpam-3415	271	6	l,∧,∨	l,∧,∨	X
ejpam-3415	271	7	)	)	PUNCT
ejpam-3415	271	8	is	be	AUX
ejpam-3415	271	9	a	a	DET
ejpam-3415	271	10	distributive	distributive	ADJ
ejpam-3415	271	11	lattice	lattice	NOUN
ejpam-3415	271	12	,	,	PUNCT
ejpam-3415	271	13	then	then	ADV
ejpam-3415	271	14	the	the	DET
ejpam-3415	271	15	hyperlattice	hyperlattice	NOUN
ejpam-3415	271	16	(	(	PUNCT
ejpam-3415	271	17	l,∧	l,∧	NOUN
ejpam-3415	271	18	,	,	PUNCT
ejpam-3415	271	19	.	.	PUNCT
ejpam-3415	272	1	∨	∨	NUM
ejpam-3415	272	2	)	)	PUNCT
ejpam-3415	272	3	,	,	PUNCT
ejpam-3415	272	4	where	where	SCONJ
ejpam-3415	272	5	a	a	PRON
ejpam-3415	272	6	.	.	PUNCT
ejpam-3415	273	1	∨	∨	NUM
ejpam-3415	273	2	b	b	X
ejpam-3415	273	3	:	:	PUNCT
ejpam-3415	273	4	=	=	X
ejpam-3415	273	5	{	{	PUNCT
ejpam-3415	273	6	t	t	NOUN
ejpam-3415	273	7	∈	∈	PROPN
ejpam-3415	273	8	l	l	NOUN
ejpam-3415	273	9	|	|	NOUN
ejpam-3415	273	10	t	t	X
ejpam-3415	273	11	≤	≤	PROPN
ejpam-3415	273	12	a∨b	a∨b	PROPN
ejpam-3415	273	13	}	}	PUNCT
ejpam-3415	273	14	considered	consider	VERB
ejpam-3415	273	15	in	in	ADP
ejpam-3415	273	16	proposition	proposition	NOUN
ejpam-3415	273	17	3.7	3.7	NUM
ejpam-3415	273	18	satisfies	satisfie	NOUN
ejpam-3415	273	19	condition	condition	NOUN
ejpam-3415	273	20	(	(	PUNCT
ejpam-3415	273	21	1	1	NUM
ejpam-3415	273	22	)	)	PUNCT
ejpam-3415	273	23	of	of	ADP
ejpam-3415	273	24	definition	definition	NOUN
ejpam-3415	273	25	3.1(1	3.1(1	NUM
ejpam-3415	273	26	)	)	PUNCT
ejpam-3415	273	27	and	and	CCONJ
ejpam-3415	273	28	condition	condition	NOUN
ejpam-3415	273	29	(	(	PUNCT
ejpam-3415	273	30	2	2	NUM
ejpam-3415	273	31	)	)	PUNCT
ejpam-3415	273	32	of	of	ADP
ejpam-3415	273	33	definition	definition	NOUN
ejpam-3415	273	34	3.1(2	3.1(2	NUM
ejpam-3415	273	35	)	)	PUNCT
ejpam-3415	273	36	.	.	PUNCT
ejpam-3415	274	1	niovi	niovi	PROPN
ejpam-3415	274	2	kehayopulu	kehayopulu	PROPN
ejpam-3415	274	3	/	/	SYM
ejpam-3415	274	4	eur	eur	PROPN
ejpam-3415	274	5	.	.	PUNCT
ejpam-3415	275	1	j.	j.	PROPN
ejpam-3415	275	2	pure	pure	PROPN
ejpam-3415	275	3	appl	appl	PROPN
ejpam-3415	275	4	.	.	PROPN
ejpam-3415	275	5	math	math	PROPN
ejpam-3415	275	6	,	,	PUNCT
ejpam-3415	275	7	12	12	NUM
ejpam-3415	275	8	(	(	PUNCT
ejpam-3415	275	9	2	2	NUM
ejpam-3415	275	10	)	)	PUNCT
ejpam-3415	275	11	(	(	PUNCT
ejpam-3415	275	12	2019	2019	NUM
ejpam-3415	275	13	)	)	PUNCT
ejpam-3415	275	14	,	,	PUNCT
ejpam-3415	275	15	252	252	NUM
ejpam-3415	275	16	-	-	SYM
ejpam-3415	275	17	269	269	NUM
ejpam-3415	275	18	263	263	NUM
ejpam-3415	275	19	proof	proof	NOUN
ejpam-3415	275	20	let	let	VERB
ejpam-3415	275	21	u	u	PROPN
ejpam-3415	275	22	∈	∈	PROPN
ejpam-3415	275	23	b	b	PROPN
ejpam-3415	275	24	.	.	PUNCT
ejpam-3415	276	1	∨	∨	PROPN
ejpam-3415	276	2	c.	c.	PROPN
ejpam-3415	276	3	then	then	ADV
ejpam-3415	276	4	a	a	DET
ejpam-3415	276	5	∧	∧	PROPN
ejpam-3415	276	6	u	u	X
ejpam-3415	276	7	∈	∈	PROPN
ejpam-3415	276	8	(	(	PUNCT
ejpam-3415	276	9	a	a	DET
ejpam-3415	276	10	∧	∧	PROPN
ejpam-3415	276	11	b	b	NOUN
ejpam-3415	276	12	)	)	PUNCT
ejpam-3415	276	13	.	.	PUNCT
ejpam-3415	277	1	∨(a	∨(a	PROPN
ejpam-3415	277	2	∧	∧	PROPN
ejpam-3415	277	3	c	c	NOUN
ejpam-3415	277	4	)	)	PUNCT
ejpam-3415	277	5	.	.	PUNCT
ejpam-3415	278	1	indeed	indeed	ADV
ejpam-3415	278	2	:	:	PUNCT
ejpam-3415	278	3	since	since	SCONJ
ejpam-3415	278	4	u	u	PROPN
ejpam-3415	278	5	≤	≤	X
ejpam-3415	278	6	b	b	PROPN
ejpam-3415	278	7	∨	∨	NUM
ejpam-3415	278	8	c	c	PROPN
ejpam-3415	278	9	,	,	PUNCT
ejpam-3415	278	10	we	we	PRON
ejpam-3415	278	11	have	have	VERB
ejpam-3415	278	12	a	a	DET
ejpam-3415	278	13	∧	∧	PROPN
ejpam-3415	278	14	u	u	NOUN
ejpam-3415	278	15	≤	≤	NOUN
ejpam-3415	278	16	a	a	DET
ejpam-3415	278	17	∧	∧	PROPN
ejpam-3415	278	18	(	(	PUNCT
ejpam-3415	278	19	b	b	PROPN
ejpam-3415	278	20	∨	∨	NUM
ejpam-3415	278	21	c	c	NOUN
ejpam-3415	278	22	)	)	PUNCT
ejpam-3415	278	23	=	=	NOUN
ejpam-3415	278	24	(	(	PUNCT
ejpam-3415	278	25	a	a	DET
ejpam-3415	278	26	∧	∧	PROPN
ejpam-3415	278	27	b	b	PROPN
ejpam-3415	278	28	)	)	PUNCT
ejpam-3415	278	29	∨	∨	NOUN
ejpam-3415	278	30	(	(	PUNCT
ejpam-3415	278	31	a	a	DET
ejpam-3415	278	32	∧	∧	PROPN
ejpam-3415	278	33	c	c	NOUN
ejpam-3415	278	34	)	)	PUNCT
ejpam-3415	278	35	,	,	PUNCT
ejpam-3415	278	36	so	so	CCONJ
ejpam-3415	278	37	a	a	DET
ejpam-3415	278	38	∧	∧	PROPN
ejpam-3415	278	39	u	u	NOUN
ejpam-3415	278	40	∈	∈	PROPN
ejpam-3415	278	41	(	(	PUNCT
ejpam-3415	278	42	a	a	DET
ejpam-3415	278	43	∧	∧	PROPN
ejpam-3415	278	44	b	b	NOUN
ejpam-3415	278	45	)	)	PUNCT
ejpam-3415	278	46	.	.	PUNCT
ejpam-3415	279	1	∨(a	∨(a	PROPN
ejpam-3415	279	2	∧	∧	PROPN
ejpam-3415	279	3	c	c	NOUN
ejpam-3415	279	4	)	)	PUNCT
ejpam-3415	279	5	and	and	CCONJ
ejpam-3415	279	6	condition	condition	NOUN
ejpam-3415	279	7	(	(	PUNCT
ejpam-3415	279	8	1	1	NUM
ejpam-3415	279	9	)	)	PUNCT
ejpam-3415	279	10	of	of	ADP
ejpam-3415	279	11	definition	definition	NOUN
ejpam-3415	279	12	3.1(1	3.1(1	NUM
ejpam-3415	279	13	)	)	PUNCT
ejpam-3415	279	14	is	be	AUX
ejpam-3415	279	15	satisfied	satisfied	ADJ
ejpam-3415	279	16	.	.	PUNCT
ejpam-3415	280	1	let	let	VERB
ejpam-3415	280	2	now	now	ADV
ejpam-3415	280	3	u	u	X
ejpam-3415	280	4	∈	∈	PROPN
ejpam-3415	280	5	a	a	PRON
ejpam-3415	280	6	.	.	PUNCT
ejpam-3415	281	1	∨	∨	NUM
ejpam-3415	281	2	b	b	PROPN
ejpam-3415	281	3	and	and	CCONJ
ejpam-3415	281	4	v	v	ADP
ejpam-3415	281	5	∈	∈	PROPN
ejpam-3415	281	6	a	a	PRON
ejpam-3415	281	7	.	.	PUNCT
ejpam-3415	282	1	∨	∨	PROPN
ejpam-3415	282	2	c.	c.	PROPN
ejpam-3415	283	1	then	then	ADV
ejpam-3415	283	2	u	u	PROPN
ejpam-3415	283	3	∧	∧	PROPN
ejpam-3415	283	4	v	v	ADP
ejpam-3415	283	5	∈	∈	PROPN
ejpam-3415	283	6	a	a	PRON
ejpam-3415	283	7	.	.	PUNCT
ejpam-3415	283	8	∨(b	∨(b	ADJ
ejpam-3415	283	9	∧	∧	PROPN
ejpam-3415	283	10	c	c	NOUN
ejpam-3415	283	11	)	)	PUNCT
ejpam-3415	283	12	.	.	PUNCT
ejpam-3415	284	1	indeed	indeed	ADV
ejpam-3415	284	2	,	,	PUNCT
ejpam-3415	284	3	since	since	SCONJ
ejpam-3415	284	4	u	u	NOUN
ejpam-3415	284	5	≤	≤	VERB
ejpam-3415	284	6	a	a	DET
ejpam-3415	284	7	∨	∨	NOUN
ejpam-3415	284	8	b	b	NOUN
ejpam-3415	284	9	and	and	CCONJ
ejpam-3415	284	10	v	v	ADP
ejpam-3415	284	11	≤	≤	NOUN
ejpam-3415	284	12	a	a	DET
ejpam-3415	284	13	∨	∨	NUM
ejpam-3415	284	14	c	c	NOUN
ejpam-3415	284	15	,	,	PUNCT
ejpam-3415	284	16	we	we	PRON
ejpam-3415	284	17	have	have	VERB
ejpam-3415	284	18	u	u	NOUN
ejpam-3415	284	19	∧	∧	PROPN
ejpam-3415	284	20	v	v	NOUN
ejpam-3415	284	21	≤	≤	NOUN
ejpam-3415	284	22	(	(	PUNCT
ejpam-3415	284	23	a	a	DET
ejpam-3415	284	24	∨	∨	NUM
ejpam-3415	284	25	b	b	NOUN
ejpam-3415	284	26	)	)	PUNCT
ejpam-3415	284	27	∧	∧	NOUN
ejpam-3415	284	28	(	(	PUNCT
ejpam-3415	284	29	a	a	DET
ejpam-3415	284	30	∨	∨	NUM
ejpam-3415	284	31	c	c	NOUN
ejpam-3415	284	32	)	)	PUNCT
ejpam-3415	284	33	=	=	SYM
ejpam-3415	284	34	a	a	DET
ejpam-3415	284	35	∨	∨	X
ejpam-3415	284	36	(	(	PUNCT
ejpam-3415	284	37	b	b	PROPN
ejpam-3415	284	38	∧	∧	PROPN
ejpam-3415	284	39	c	c	NOUN
ejpam-3415	284	40	)	)	PUNCT
ejpam-3415	284	41	,	,	PUNCT
ejpam-3415	284	42	then	then	ADV
ejpam-3415	284	43	u	u	PROPN
ejpam-3415	284	44	∧	∧	PROPN
ejpam-3415	284	45	v	v	ADP
ejpam-3415	284	46	∈	∈	PROPN
ejpam-3415	284	47	a	a	PRON
ejpam-3415	284	48	.	.	PUNCT
ejpam-3415	285	1	∨(b	∨(b	ADJ
ejpam-3415	285	2	∧	∧	PROPN
ejpam-3415	285	3	c	c	NOUN
ejpam-3415	285	4	)	)	PUNCT
ejpam-3415	285	5	and	and	CCONJ
ejpam-3415	285	6	condition	condition	NOUN
ejpam-3415	285	7	(	(	PUNCT
ejpam-3415	285	8	2	2	NUM
ejpam-3415	285	9	)	)	PUNCT
ejpam-3415	285	10	of	of	ADP
ejpam-3415	285	11	definition	definition	NOUN
ejpam-3415	285	12	3.1(2	3.1(2	NUM
ejpam-3415	285	13	)	)	PUNCT
ejpam-3415	285	14	also	also	ADV
ejpam-3415	285	15	holds	hold	VERB
ejpam-3415	285	16	.	.	PUNCT
ejpam-3415	286	1	�	�	PROPN
ejpam-3415	286	2	the	the	DET
ejpam-3415	286	3	question	question	NOUN
ejpam-3415	286	4	is	be	AUX
ejpam-3415	286	5	:	:	PUNCT
ejpam-3415	286	6	given	give	VERB
ejpam-3415	286	7	a	a	DET
ejpam-3415	286	8	distributive	distributive	ADJ
ejpam-3415	286	9	lattice	lattice	NOUN
ejpam-3415	286	10	(	(	PUNCT
ejpam-3415	286	11	l,∧,∨	l,∧,∨	ADV
ejpam-3415	286	12	)	)	PUNCT
ejpam-3415	286	13	and	and	CCONJ
ejpam-3415	286	14	the	the	DET
ejpam-3415	286	15	hyperlattice	hyperlattice	NOUN
ejpam-3415	286	16	(	(	PUNCT
ejpam-3415	286	17	l,∧	l,∧	NOUN
ejpam-3415	286	18	,	,	PUNCT
ejpam-3415	286	19	.	.	PUNCT
ejpam-3415	287	1	∨	∨	NUM
ejpam-3415	287	2	)	)	PUNCT
ejpam-3415	287	3	,	,	PUNCT
ejpam-3415	287	4	where	where	SCONJ
ejpam-3415	287	5	a	a	PRON
ejpam-3415	287	6	.	.	PUNCT
ejpam-3415	288	1	∨	∨	NUM
ejpam-3415	288	2	b	b	X
ejpam-3415	288	3	:	:	PUNCT
ejpam-3415	288	4	=	=	X
ejpam-3415	288	5	{	{	PUNCT
ejpam-3415	288	6	t	t	NOUN
ejpam-3415	288	7	∈	∈	PROPN
ejpam-3415	288	8	l	l	NOUN
ejpam-3415	289	1	|	|	NOUN
ejpam-3415	289	2	t	t	X
ejpam-3415	289	3	≤	≤	NOUN
ejpam-3415	289	4	a	a	DET
ejpam-3415	289	5	∨	∨	NUM
ejpam-3415	289	6	b	b	NOUN
ejpam-3415	289	7	}	}	PUNCT
ejpam-3415	289	8	,	,	PUNCT
ejpam-3415	289	9	under	under	ADP
ejpam-3415	289	10	what	what	DET
ejpam-3415	289	11	conditions	condition	NOUN
ejpam-3415	289	12	the	the	DET
ejpam-3415	289	13	hyperlattice	hyperlattice	NOUN
ejpam-3415	289	14	(	(	PUNCT
ejpam-3415	289	15	l,∧	l,∧	NOUN
ejpam-3415	289	16	,	,	PUNCT
ejpam-3415	289	17	.	.	PUNCT
ejpam-3415	290	1	∨	∨	NUM
ejpam-3415	290	2	)	)	PUNCT
ejpam-3415	290	3	is	be	AUX
ejpam-3415	290	4	a	a	DET
ejpam-3415	290	5	distributive	distributive	ADJ
ejpam-3415	290	6	hyperlattice	hyperlattice	NOUN
ejpam-3415	290	7	in	in	ADP
ejpam-3415	290	8	the	the	DET
ejpam-3415	290	9	sense	sense	NOUN
ejpam-3415	290	10	of	of	ADP
ejpam-3415	290	11	definitions	definition	NOUN
ejpam-3415	290	12	3.1(1	3.1(1	NUM
ejpam-3415	290	13	)	)	PUNCT
ejpam-3415	290	14	and	and	CCONJ
ejpam-3415	290	15	3.1(2	3.1(2	NUM
ejpam-3415	290	16	)	)	PUNCT
ejpam-3415	290	17	?	?	PUNCT
ejpam-3415	291	1	as	as	SCONJ
ejpam-3415	291	2	answer	answer	NOUN
ejpam-3415	291	3	is	be	AUX
ejpam-3415	291	4	given	give	VERB
ejpam-3415	291	5	in	in	ADP
ejpam-3415	291	6	the	the	DET
ejpam-3415	291	7	rest	rest	NOUN
ejpam-3415	291	8	of	of	ADP
ejpam-3415	291	9	this	this	DET
ejpam-3415	291	10	section	section	NOUN
ejpam-3415	291	11	.	.	PUNCT
ejpam-3415	292	1	proposition	proposition	NOUN
ejpam-3415	292	2	3.9	3.9	NUM
ejpam-3415	292	3	let	let	VERB
ejpam-3415	292	4	(	(	PUNCT
ejpam-3415	292	5	l,∧,∨	l,∧,∨	ADV
ejpam-3415	292	6	)	)	PUNCT
ejpam-3415	292	7	be	be	AUX
ejpam-3415	292	8	a	a	DET
ejpam-3415	292	9	distributive	distributive	ADJ
ejpam-3415	292	10	lattice	lattice	NOUN
ejpam-3415	292	11	and	and	CCONJ
ejpam-3415	292	12	(	(	PUNCT
ejpam-3415	292	13	l,∧	l,∧	NOUN
ejpam-3415	292	14	,	,	PUNCT
ejpam-3415	292	15	.	.	PUNCT
ejpam-3415	293	1	∨	∨	NUM
ejpam-3415	293	2	)	)	PUNCT
ejpam-3415	293	3	the	the	DET
ejpam-3415	293	4	hyperlattice	hyperlattice	NOUN
ejpam-3415	293	5	with	with	ADP
ejpam-3415	293	6	the	the	DET
ejpam-3415	293	7	hyperoperation	hyperoperation	NOUN
ejpam-3415	293	8	a	a	PRON
ejpam-3415	293	9	.	.	PUNCT
ejpam-3415	294	1	∨	∨	NUM
ejpam-3415	294	2	b	b	X
ejpam-3415	294	3	:	:	PUNCT
ejpam-3415	294	4	=	=	X
ejpam-3415	294	5	{	{	PUNCT
ejpam-3415	294	6	t	t	NOUN
ejpam-3415	294	7	∈	∈	PROPN
ejpam-3415	294	8	l	l	NOUN
ejpam-3415	295	1	|	|	NOUN
ejpam-3415	295	2	t	t	X
ejpam-3415	295	3	≤	≤	NOUN
ejpam-3415	295	4	a	a	DET
ejpam-3415	295	5	∨	∨	NUM
ejpam-3415	295	6	b	b	NOUN
ejpam-3415	295	7	}	}	PUNCT
ejpam-3415	295	8	satisfying	satisfy	VERB
ejpam-3415	295	9	the	the	DET
ejpam-3415	295	10	property	property	NOUN
ejpam-3415	295	11	u	u	NOUN
ejpam-3415	295	12	∈	∈	PROPN
ejpam-3415	295	13	(	(	PUNCT
ejpam-3415	295	14	a	a	DET
ejpam-3415	295	15	∧	∧	PROPN
ejpam-3415	295	16	b	b	NOUN
ejpam-3415	295	17	)	)	PUNCT
ejpam-3415	295	18	.	.	PUNCT
ejpam-3415	296	1	∨(a	∨(a	PROPN
ejpam-3415	296	2	∧	∧	PROPN
ejpam-3415	296	3	c	c	NOUN
ejpam-3415	296	4	)	)	PUNCT
ejpam-3415	296	5	and	and	CCONJ
ejpam-3415	296	6	v	v	ADP
ejpam-3415	296	7	∈	∈	PROPN
ejpam-3415	296	8	b	b	PROPN
ejpam-3415	296	9	.	.	PUNCT
ejpam-3415	297	1	∨	∨	PROPN
ejpam-3415	297	2	c	c	X
ejpam-3415	297	3	imply	imply	VERB
ejpam-3415	297	4	a	a	DET
ejpam-3415	297	5	∧	∧	PROPN
ejpam-3415	297	6	v	v	ADJ
ejpam-3415	297	7	≤	≤	NOUN
ejpam-3415	297	8	u	u	NOUN
ejpam-3415	297	9	(	(	PUNCT
ejpam-3415	297	10	3.1	3.1	NUM
ejpam-3415	297	11	)	)	PUNCT
ejpam-3415	297	12	then	then	ADV
ejpam-3415	297	13	(	(	PUNCT
ejpam-3415	297	14	l,∧	l,∧	NOUN
ejpam-3415	297	15	,	,	PUNCT
ejpam-3415	297	16	.	.	PUNCT
ejpam-3415	298	1	∨	∨	NUM
ejpam-3415	298	2	)	)	PUNCT
ejpam-3415	298	3	satisfies	satisfy	VERB
ejpam-3415	298	4	condition	condition	NOUN
ejpam-3415	298	5	(	(	PUNCT
ejpam-3415	298	6	2	2	NUM
ejpam-3415	298	7	)	)	PUNCT
ejpam-3415	298	8	of	of	ADP
ejpam-3415	298	9	definition	definition	NOUN
ejpam-3415	298	10	3.1(1	3.1(1	NUM
ejpam-3415	298	11	)	)	PUNCT
ejpam-3415	298	12	.	.	PUNCT
ejpam-3415	299	1	proof	proof	NOUN
ejpam-3415	299	2	let	let	VERB
ejpam-3415	299	3	u	u	PRON
ejpam-3415	299	4	∈	∈	PROPN
ejpam-3415	299	5	(	(	PUNCT
ejpam-3415	299	6	a∧	a∧	NOUN
ejpam-3415	299	7	b	b	NOUN
ejpam-3415	299	8	)	)	PUNCT
ejpam-3415	299	9	.	.	PUNCT
ejpam-3415	300	1	∨(a∧	∨(a∧	PROPN
ejpam-3415	300	2	c	c	PROPN
ejpam-3415	300	3	)	)	PUNCT
ejpam-3415	300	4	.	.	PUNCT
ejpam-3415	301	1	then	then	ADV
ejpam-3415	301	2	u	u	X
ejpam-3415	301	3	≤	≤	X
ejpam-3415	301	4	(	(	PUNCT
ejpam-3415	301	5	a∧	a∧	NOUN
ejpam-3415	301	6	b)∨	b)∨	PROPN
ejpam-3415	301	7	(	(	PUNCT
ejpam-3415	301	8	a∧	a∧	NOUN
ejpam-3415	301	9	c	c	NOUN
ejpam-3415	301	10	)	)	PUNCT
ejpam-3415	302	1	=	=	SYM
ejpam-3415	302	2	a∧	a∧	NOUN
ejpam-3415	302	3	(	(	PUNCT
ejpam-3415	302	4	b∨	b∨	PROPN
ejpam-3415	302	5	c	c	PROPN
ejpam-3415	302	6	)	)	PUNCT
ejpam-3415	302	7	.	.	PUNCT
ejpam-3415	303	1	we	we	PRON
ejpam-3415	303	2	put	put	VERB
ejpam-3415	303	3	v	v	NOUN
ejpam-3415	303	4	:	:	PUNCT
ejpam-3415	303	5	=	=	PROPN
ejpam-3415	303	6	b∨	b∨	PROPN
ejpam-3415	303	7	c	c	PROPN
ejpam-3415	303	8	and	and	CCONJ
ejpam-3415	303	9	we	we	PRON
ejpam-3415	303	10	have	have	VERB
ejpam-3415	303	11	u	u	NOUN
ejpam-3415	303	12	≤	≤	NOUN
ejpam-3415	303	13	a	a	DET
ejpam-3415	303	14	∧	∧	PROPN
ejpam-3415	303	15	v.	v.	ADP
ejpam-3415	303	16	on	on	ADP
ejpam-3415	303	17	the	the	DET
ejpam-3415	303	18	other	other	ADJ
ejpam-3415	303	19	hand	hand	NOUN
ejpam-3415	303	20	,	,	PUNCT
ejpam-3415	303	21	since	since	SCONJ
ejpam-3415	303	22	u	u	PROPN
ejpam-3415	303	23	∈	∈	PROPN
ejpam-3415	303	24	(	(	PUNCT
ejpam-3415	303	25	a	a	DET
ejpam-3415	303	26	∧	∧	PROPN
ejpam-3415	303	27	b	b	NOUN
ejpam-3415	303	28	)	)	PUNCT
ejpam-3415	303	29	.	.	PUNCT
ejpam-3415	304	1	∨(a	∨(a	PROPN
ejpam-3415	304	2	∧	∧	PROPN
ejpam-3415	304	3	c	c	NOUN
ejpam-3415	304	4	)	)	PUNCT
ejpam-3415	304	5	and	and	CCONJ
ejpam-3415	304	6	v	v	ADP
ejpam-3415	304	7	∈	∈	PROPN
ejpam-3415	304	8	b	b	PROPN
ejpam-3415	304	9	.	.	PUNCT
ejpam-3415	305	1	∨	∨	PROPN
ejpam-3415	305	2	c	c	PROPN
ejpam-3415	305	3	,	,	PUNCT
ejpam-3415	305	4	by	by	ADP
ejpam-3415	305	5	(	(	PUNCT
ejpam-3415	305	6	3.1	3.1	NUM
ejpam-3415	305	7	)	)	PUNCT
ejpam-3415	305	8	,	,	PUNCT
ejpam-3415	305	9	we	we	PRON
ejpam-3415	305	10	have	have	VERB
ejpam-3415	305	11	a	a	DET
ejpam-3415	305	12	∧	∧	PROPN
ejpam-3415	305	13	v	v	NOUN
ejpam-3415	305	14	≤	≤	NOUN
ejpam-3415	305	15	u.	u.	NOUN
ejpam-3415	306	1	hence	hence	ADV
ejpam-3415	306	2	we	we	PRON
ejpam-3415	306	3	get	get	VERB
ejpam-3415	306	4	u	u	NOUN
ejpam-3415	306	5	=	=	NOUN
ejpam-3415	306	6	a	a	DET
ejpam-3415	306	7	∧	∧	PROPN
ejpam-3415	306	8	v	v	NOUN
ejpam-3415	306	9	and	and	CCONJ
ejpam-3415	306	10	the	the	DET
ejpam-3415	306	11	hyperlattice	hyperlattice	NOUN
ejpam-3415	306	12	(	(	PUNCT
ejpam-3415	306	13	l,∧	l,∧	NOUN
ejpam-3415	306	14	,	,	PUNCT
ejpam-3415	306	15	.	.	PUNCT
ejpam-3415	307	1	∨	∨	NUM
ejpam-3415	307	2	)	)	PUNCT
ejpam-3415	307	3	satisfies	satisfy	VERB
ejpam-3415	307	4	condition	condition	NOUN
ejpam-3415	307	5	(	(	PUNCT
ejpam-3415	307	6	2	2	NUM
ejpam-3415	307	7	)	)	PUNCT
ejpam-3415	307	8	of	of	ADP
ejpam-3415	307	9	definition	definition	NOUN
ejpam-3415	307	10	3.1(1	3.1(1	NUM
ejpam-3415	307	11	)	)	PUNCT
ejpam-3415	307	12	.	.	PUNCT
ejpam-3415	308	1	�	�	PROPN
ejpam-3415	308	2	by	by	ADP
ejpam-3415	308	3	propositions	proposition	NOUN
ejpam-3415	308	4	3.8	3.8	NUM
ejpam-3415	308	5	and	and	CCONJ
ejpam-3415	308	6	3.9	3.9	NUM
ejpam-3415	308	7	we	we	PRON
ejpam-3415	308	8	have	have	VERB
ejpam-3415	308	9	the	the	DET
ejpam-3415	308	10	following	follow	VERB
ejpam-3415	308	11	corollary	corollary	NOUN
ejpam-3415	308	12	.	.	PUNCT
ejpam-3415	309	1	corollary	corollary	ADJ
ejpam-3415	309	2	3.10	3.10	NUM
ejpam-3415	309	3	let	let	NOUN
ejpam-3415	309	4	(	(	PUNCT
ejpam-3415	309	5	l,∧,∨	l,∧,∨	ADV
ejpam-3415	309	6	)	)	PUNCT
ejpam-3415	309	7	be	be	AUX
ejpam-3415	309	8	a	a	DET
ejpam-3415	309	9	distributive	distributive	ADJ
ejpam-3415	309	10	lattice	lattice	NOUN
ejpam-3415	309	11	and	and	CCONJ
ejpam-3415	309	12	(	(	PUNCT
ejpam-3415	309	13	l,∧	l,∧	NOUN
ejpam-3415	309	14	,	,	PUNCT
ejpam-3415	309	15	.	.	PUNCT
ejpam-3415	310	1	∨	∨	NUM
ejpam-3415	310	2	)	)	PUNCT
ejpam-3415	310	3	the	the	DET
ejpam-3415	310	4	hyperlattice	hyperlattice	NOUN
ejpam-3415	310	5	defined	define	VERB
ejpam-3415	310	6	by	by	ADP
ejpam-3415	310	7	a	a	PRON
ejpam-3415	310	8	.	.	PUNCT
ejpam-3415	311	1	∨	∨	NUM
ejpam-3415	311	2	b	b	X
ejpam-3415	311	3	:	:	PUNCT
ejpam-3415	311	4	=	=	X
ejpam-3415	311	5	{	{	PUNCT
ejpam-3415	311	6	t	t	NOUN
ejpam-3415	311	7	∈	∈	PROPN
ejpam-3415	311	8	l	l	NOUN
ejpam-3415	312	1	|	|	NOUN
ejpam-3415	312	2	t	t	X
ejpam-3415	312	3	≤	≤	PROPN
ejpam-3415	312	4	a∨b	a∨b	PROPN
ejpam-3415	312	5	}	}	PUNCT
ejpam-3415	312	6	and	and	CCONJ
ejpam-3415	312	7	having	have	VERB
ejpam-3415	312	8	the	the	DET
ejpam-3415	312	9	property	property	NOUN
ejpam-3415	312	10	(	(	PUNCT
ejpam-3415	312	11	3.1	3.1	NUM
ejpam-3415	312	12	)	)	PUNCT
ejpam-3415	312	13	.	.	PUNCT
ejpam-3415	313	1	then	then	ADV
ejpam-3415	313	2	(	(	PUNCT
ejpam-3415	313	3	l,∧	l,∧	NOUN
ejpam-3415	313	4	,	,	PUNCT
ejpam-3415	313	5	.	.	PUNCT
ejpam-3415	313	6	∨	∨	NUM
ejpam-3415	313	7	)	)	PUNCT
ejpam-3415	313	8	is	be	AUX
ejpam-3415	313	9	a	a	DET
ejpam-3415	313	10	distributive	distributive	ADJ
ejpam-3415	313	11	hyperlattice	hyperlattice	NOUN
ejpam-3415	313	12	in	in	ADP
ejpam-3415	313	13	the	the	DET
ejpam-3415	313	14	sense	sense	NOUN
ejpam-3415	313	15	of	of	ADP
ejpam-3415	313	16	definition	definition	NOUN
ejpam-3415	313	17	3.1(1	3.1(1	NUM
ejpam-3415	313	18	)	)	PUNCT
ejpam-3415	313	19	.	.	PUNCT
ejpam-3415	314	1	proposition	proposition	NOUN
ejpam-3415	314	2	3.11	3.11	NUM
ejpam-3415	314	3	let	let	VERB
ejpam-3415	314	4	(	(	PUNCT
ejpam-3415	314	5	l,∧,∨	l,∧,∨	ADV
ejpam-3415	314	6	)	)	PUNCT
ejpam-3415	314	7	be	be	AUX
ejpam-3415	314	8	a	a	DET
ejpam-3415	314	9	distributive	distributive	ADJ
ejpam-3415	314	10	lattice	lattice	NOUN
ejpam-3415	314	11	and	and	CCONJ
ejpam-3415	314	12	(	(	PUNCT
ejpam-3415	314	13	l,∧	l,∧	NOUN
ejpam-3415	314	14	,	,	PUNCT
ejpam-3415	314	15	.	.	PUNCT
ejpam-3415	315	1	∨	∨	NUM
ejpam-3415	315	2	)	)	PUNCT
ejpam-3415	315	3	the	the	DET
ejpam-3415	315	4	hyperlattice	hyperlattice	NOUN
ejpam-3415	315	5	with	with	ADP
ejpam-3415	315	6	the	the	DET
ejpam-3415	315	7	hyperoperation	hyperoperation	NOUN
ejpam-3415	315	8	a	a	PRON
ejpam-3415	315	9	.	.	PUNCT
ejpam-3415	316	1	∨	∨	NUM
ejpam-3415	316	2	b	b	X
ejpam-3415	316	3	:	:	PUNCT
ejpam-3415	316	4	=	=	X
ejpam-3415	316	5	{	{	PUNCT
ejpam-3415	316	6	t	t	NOUN
ejpam-3415	316	7	∈	∈	PROPN
ejpam-3415	316	8	l	l	NOUN
ejpam-3415	317	1	|	|	NOUN
ejpam-3415	317	2	t	t	X
ejpam-3415	317	3	≤	≤	NOUN
ejpam-3415	317	4	a	a	DET
ejpam-3415	317	5	∨	∨	NUM
ejpam-3415	317	6	b	b	NOUN
ejpam-3415	317	7	}	}	PUNCT
ejpam-3415	317	8	satisfying	satisfy	VERB
ejpam-3415	317	9	the	the	DET
ejpam-3415	317	10	property	property	NOUN
ejpam-3415	317	11	u	u	NOUN
ejpam-3415	317	12	∈	∈	PROPN
ejpam-3415	317	13	a	a	PRON
ejpam-3415	317	14	.	.	PUNCT
ejpam-3415	318	1	∨(b	∨(b	ADJ
ejpam-3415	318	2	∧	∧	PROPN
ejpam-3415	318	3	c	c	NOUN
ejpam-3415	318	4	)	)	PUNCT
ejpam-3415	318	5	,	,	PUNCT
ejpam-3415	318	6	v	v	X
ejpam-3415	318	7	∈	∈	PROPN
ejpam-3415	318	8	a	a	PRON
ejpam-3415	318	9	.	.	PUNCT
ejpam-3415	319	1	∨	∨	NUM
ejpam-3415	319	2	b	b	PROPN
ejpam-3415	319	3	and	and	CCONJ
ejpam-3415	319	4	w	w	PROPN
ejpam-3415	319	5	∈	∈	PROPN
ejpam-3415	319	6	a	a	PRON
ejpam-3415	319	7	.	.	PUNCT
ejpam-3415	320	1	∨	∨	NOUN
ejpam-3415	320	2	c	c	PRON
ejpam-3415	320	3	imply	imply	VERB
ejpam-3415	320	4	u	u	NOUN
ejpam-3415	320	5	≥	≥	NOUN
ejpam-3415	320	6	v	v	ADP
ejpam-3415	320	7	∧	∧	PROPN
ejpam-3415	320	8	w	w	PROPN
ejpam-3415	320	9	(	(	PUNCT
ejpam-3415	320	10	3.2	3.2	NUM
ejpam-3415	320	11	)	)	PUNCT
ejpam-3415	320	12	then	then	ADV
ejpam-3415	320	13	(	(	PUNCT
ejpam-3415	320	14	l,∧	l,∧	NOUN
ejpam-3415	320	15	,	,	PUNCT
ejpam-3415	320	16	.	.	PUNCT
ejpam-3415	321	1	∨	∨	NUM
ejpam-3415	321	2	)	)	PUNCT
ejpam-3415	321	3	satisfies	satisfy	VERB
ejpam-3415	321	4	condition	condition	NOUN
ejpam-3415	321	5	(	(	PUNCT
ejpam-3415	321	6	1	1	NUM
ejpam-3415	321	7	)	)	PUNCT
ejpam-3415	321	8	of	of	ADP
ejpam-3415	321	9	definition	definition	NOUN
ejpam-3415	321	10	3.1(2	3.1(2	NUM
ejpam-3415	321	11	)	)	PUNCT
ejpam-3415	321	12	.	.	PUNCT
ejpam-3415	322	1	proof	proof	NOUN
ejpam-3415	322	2	let	let	VERB
ejpam-3415	322	3	u	u	PRON
ejpam-3415	322	4	∈	∈	PROPN
ejpam-3415	322	5	a	a	PRON
ejpam-3415	322	6	.	.	PUNCT
ejpam-3415	323	1	∨(b∧	∨(b∧	NOUN
ejpam-3415	323	2	c	c	NOUN
ejpam-3415	323	3	)	)	PUNCT
ejpam-3415	323	4	then	then	ADV
ejpam-3415	323	5	u	u	X
ejpam-3415	323	6	≤	≤	PROPN
ejpam-3415	323	7	a∨	a∨	PROPN
ejpam-3415	323	8	(	(	PUNCT
ejpam-3415	323	9	b∧	b∧	PROPN
ejpam-3415	323	10	c	c	NOUN
ejpam-3415	323	11	)	)	PUNCT
ejpam-3415	324	1	=	=	SYM
ejpam-3415	324	2	(	(	PUNCT
ejpam-3415	324	3	a∨	a∨	PROPN
ejpam-3415	324	4	b)∧	b)∧	PROPN
ejpam-3415	324	5	(	(	PUNCT
ejpam-3415	324	6	a∨	a∨	PROPN
ejpam-3415	324	7	c	c	PROPN
ejpam-3415	324	8	)	)	PUNCT
ejpam-3415	324	9	.	.	PUNCT
ejpam-3415	325	1	we	we	PRON
ejpam-3415	325	2	put	put	VERB
ejpam-3415	325	3	v	v	NOUN
ejpam-3415	325	4	:	:	PUNCT
ejpam-3415	325	5	=	=	SYM
ejpam-3415	325	6	a∨	a∨	PROPN
ejpam-3415	325	7	b	b	X
ejpam-3415	326	1	∈	∈	PROPN
ejpam-3415	326	2	a	a	PRON
ejpam-3415	326	3	.	.	PUNCT
ejpam-3415	327	1	∨	∨	NUM
ejpam-3415	327	2	b	b	PROPN
ejpam-3415	327	3	and	and	CCONJ
ejpam-3415	327	4	w	w	NOUN
ejpam-3415	327	5	:	:	PUNCT
ejpam-3415	327	6	=	=	PUNCT
ejpam-3415	327	7	a	a	DET
ejpam-3415	327	8	∨	∨	NUM
ejpam-3415	327	9	c	c	X
ejpam-3415	327	10	∈	∈	PROPN
ejpam-3415	327	11	a	a	PRON
ejpam-3415	327	12	.	.	PUNCT
ejpam-3415	328	1	∨	∨	NUM
ejpam-3415	328	2	c	c	PROPN
ejpam-3415	329	1	and	and	CCONJ
ejpam-3415	329	2	we	we	PRON
ejpam-3415	329	3	have	have	VERB
ejpam-3415	329	4	u	u	NOUN
ejpam-3415	329	5	≤	≤	NOUN
ejpam-3415	329	6	v	v	ADP
ejpam-3415	329	7	∧	∧	PROPN
ejpam-3415	329	8	w.	w.	PROPN
ejpam-3415	329	9	on	on	ADP
ejpam-3415	329	10	the	the	DET
ejpam-3415	329	11	other	other	ADJ
ejpam-3415	329	12	hand	hand	NOUN
ejpam-3415	329	13	,	,	PUNCT
ejpam-3415	329	14	by	by	ADP
ejpam-3415	329	15	(	(	PUNCT
ejpam-3415	329	16	3.2	3.2	NUM
ejpam-3415	329	17	)	)	PUNCT
ejpam-3415	329	18	we	we	PRON
ejpam-3415	329	19	have	have	VERB
ejpam-3415	329	20	u	u	PROPN
ejpam-3415	329	21	≥	≥	NOUN
ejpam-3415	329	22	v	v	ADP
ejpam-3415	329	23	∧	∧	PROPN
ejpam-3415	329	24	w	w	PROPN
ejpam-3415	329	25	,	,	PUNCT
ejpam-3415	329	26	then	then	ADV
ejpam-3415	329	27	u	u	NOUN
ejpam-3415	329	28	=	=	PROPN
ejpam-3415	329	29	v	v	ADP
ejpam-3415	329	30	∧	∧	PROPN
ejpam-3415	329	31	w	w	PROPN
ejpam-3415	329	32	and	and	CCONJ
ejpam-3415	329	33	so	so	ADV
ejpam-3415	329	34	condition	condition	NOUN
ejpam-3415	329	35	(	(	PUNCT
ejpam-3415	329	36	1	1	NUM
ejpam-3415	329	37	)	)	PUNCT
ejpam-3415	329	38	of	of	ADP
ejpam-3415	329	39	definition	definition	NOUN
ejpam-3415	329	40	3.1(2	3.1(2	NUM
ejpam-3415	329	41	)	)	PUNCT
ejpam-3415	329	42	is	be	AUX
ejpam-3415	329	43	satisfied	satisfied	ADJ
ejpam-3415	329	44	.	.	PUNCT
ejpam-3415	330	1	�	�	NOUN
ejpam-3415	330	2	by	by	ADP
ejpam-3415	330	3	propositions	proposition	NOUN
ejpam-3415	330	4	3.8	3.8	NUM
ejpam-3415	330	5	and	and	CCONJ
ejpam-3415	330	6	3.11	3.11	NUM
ejpam-3415	330	7	we	we	PRON
ejpam-3415	330	8	have	have	VERB
ejpam-3415	330	9	the	the	DET
ejpam-3415	330	10	following	follow	VERB
ejpam-3415	330	11	corollary	corollary	NOUN
ejpam-3415	330	12	.	.	PUNCT
ejpam-3415	331	1	corollary	corollary	ADJ
ejpam-3415	331	2	3.12	3.12	NUM
ejpam-3415	331	3	let	let	NOUN
ejpam-3415	331	4	(	(	PUNCT
ejpam-3415	331	5	l,∧,∨	l,∧,∨	ADV
ejpam-3415	331	6	)	)	PUNCT
ejpam-3415	331	7	be	be	AUX
ejpam-3415	331	8	a	a	DET
ejpam-3415	331	9	distributive	distributive	ADJ
ejpam-3415	331	10	lattice	lattice	NOUN
ejpam-3415	331	11	and	and	CCONJ
ejpam-3415	331	12	(	(	PUNCT
ejpam-3415	331	13	l,∧	l,∧	NOUN
ejpam-3415	331	14	,	,	PUNCT
ejpam-3415	331	15	.	.	PUNCT
ejpam-3415	332	1	∨	∨	NUM
ejpam-3415	332	2	)	)	PUNCT
ejpam-3415	332	3	the	the	DET
ejpam-3415	332	4	hyperlattice	hyperlattice	NOUN
ejpam-3415	332	5	defined	define	VERB
ejpam-3415	332	6	by	by	ADP
ejpam-3415	332	7	a	a	PRON
ejpam-3415	332	8	.	.	PUNCT
ejpam-3415	333	1	∨	∨	NUM
ejpam-3415	333	2	b	b	X
ejpam-3415	333	3	:	:	PUNCT
ejpam-3415	333	4	=	=	X
ejpam-3415	333	5	{	{	PUNCT
ejpam-3415	333	6	t	t	NOUN
ejpam-3415	333	7	∈	∈	PROPN
ejpam-3415	333	8	l	l	NOUN
ejpam-3415	334	1	|	|	NOUN
ejpam-3415	334	2	t	t	X
ejpam-3415	334	3	≤	≤	PROPN
ejpam-3415	334	4	a∨b	a∨b	PROPN
ejpam-3415	334	5	}	}	PUNCT
ejpam-3415	334	6	and	and	CCONJ
ejpam-3415	334	7	having	have	VERB
ejpam-3415	334	8	the	the	DET
ejpam-3415	334	9	property	property	NOUN
ejpam-3415	334	10	(	(	PUNCT
ejpam-3415	334	11	3.2	3.2	NUM
ejpam-3415	334	12	)	)	PUNCT
ejpam-3415	334	13	.	.	PUNCT
ejpam-3415	335	1	then	then	ADV
ejpam-3415	335	2	(	(	PUNCT
ejpam-3415	335	3	l,∧	l,∧	NOUN
ejpam-3415	335	4	,	,	PUNCT
ejpam-3415	335	5	.	.	PUNCT
ejpam-3415	335	6	∨	∨	NUM
ejpam-3415	335	7	)	)	PUNCT
ejpam-3415	335	8	is	be	AUX
ejpam-3415	335	9	a	a	DET
ejpam-3415	335	10	distributive	distributive	ADJ
ejpam-3415	335	11	hyperlattice	hyperlattice	NOUN
ejpam-3415	335	12	in	in	ADP
ejpam-3415	335	13	the	the	DET
ejpam-3415	335	14	sense	sense	NOUN
ejpam-3415	335	15	of	of	ADP
ejpam-3415	335	16	definition	definition	NOUN
ejpam-3415	335	17	3.1(2	3.1(2	NUM
ejpam-3415	335	18	)	)	PUNCT
ejpam-3415	335	19	.	.	PUNCT
ejpam-3415	336	1	problem	problem	NOUN
ejpam-3415	336	2	3.13	3.13	NUM
ejpam-3415	336	3	write	write	VERB
ejpam-3415	336	4	a	a	DET
ejpam-3415	336	5	program	program	NOUN
ejpam-3415	336	6	to	to	PART
ejpam-3415	336	7	show	show	VERB
ejpam-3415	336	8	that	that	SCONJ
ejpam-3415	336	9	the	the	DET
ejpam-3415	336	10	hyperlattice	hyperlattice	NOUN
ejpam-3415	336	11	considered	consider	VERB
ejpam-3415	336	12	in	in	ADP
ejpam-3415	336	13	proposition	proposition	NOUN
ejpam-3415	336	14	3.8	3.8	NUM
ejpam-3415	336	15	does	do	AUX
ejpam-3415	336	16	not	not	PART
ejpam-3415	336	17	satisfy	satisfy	VERB
ejpam-3415	336	18	condition	condition	NOUN
ejpam-3415	336	19	(	(	PUNCT
ejpam-3415	336	20	2	2	NUM
ejpam-3415	336	21	)	)	PUNCT
ejpam-3415	336	22	of	of	ADP
ejpam-3415	336	23	definition	definition	NOUN
ejpam-3415	336	24	3.1(1	3.1(1	NUM
ejpam-3415	336	25	)	)	PUNCT
ejpam-3415	336	26	and	and	CCONJ
ejpam-3415	336	27	condition	condition	NOUN
ejpam-3415	336	28	(	(	PUNCT
ejpam-3415	336	29	1	1	NUM
ejpam-3415	336	30	)	)	PUNCT
ejpam-3415	336	31	of	of	ADP
ejpam-3415	336	32	definition	definition	NOUN
ejpam-3415	336	33	3.1(2	3.1(2	NUM
ejpam-3415	336	34	)	)	PUNCT
ejpam-3415	336	35	in	in	ADP
ejpam-3415	336	36	general	general	ADJ
ejpam-3415	336	37	.	.	PUNCT
ejpam-3415	337	1	niovi	niovi	PROPN
ejpam-3415	337	2	kehayopulu	kehayopulu	PROPN
ejpam-3415	337	3	/	/	SYM
ejpam-3415	337	4	eur	eur	PROPN
ejpam-3415	337	5	.	.	PUNCT
ejpam-3415	338	1	j.	j.	PROPN
ejpam-3415	338	2	pure	pure	PROPN
ejpam-3415	338	3	appl	appl	PROPN
ejpam-3415	338	4	.	.	PROPN
ejpam-3415	338	5	math	math	PROPN
ejpam-3415	338	6	,	,	PUNCT
ejpam-3415	338	7	12	12	NUM
ejpam-3415	338	8	(	(	PUNCT
ejpam-3415	338	9	2	2	NUM
ejpam-3415	338	10	)	)	PUNCT
ejpam-3415	338	11	(	(	PUNCT
ejpam-3415	338	12	2019	2019	NUM
ejpam-3415	338	13	)	)	PUNCT
ejpam-3415	338	14	,	,	PUNCT
ejpam-3415	338	15	252	252	NUM
ejpam-3415	338	16	-	-	SYM
ejpam-3415	338	17	269	269	NUM
ejpam-3415	338	18	264	264	NUM
ejpam-3415	338	19	4	4	NUM
ejpam-3415	338	20	.	.	PUNCT
ejpam-3415	339	1	modular	modular	ADJ
ejpam-3415	339	2	hyperlattices	hyperlattice	NOUN
ejpam-3415	339	3	a	a	DET
ejpam-3415	339	4	lattice	lattice	NOUN
ejpam-3415	339	5	l	l	NOUN
ejpam-3415	339	6	is	be	AUX
ejpam-3415	339	7	called	call	VERB
ejpam-3415	339	8	modular	modular	ADJ
ejpam-3415	339	9	if	if	SCONJ
ejpam-3415	339	10	,	,	PUNCT
ejpam-3415	339	11	for	for	ADP
ejpam-3415	339	12	any	any	DET
ejpam-3415	339	13	a	a	DET
ejpam-3415	339	14	,	,	PUNCT
ejpam-3415	339	15	b	b	NOUN
ejpam-3415	339	16	,	,	PUNCT
ejpam-3415	339	17	c	c	PROPN
ejpam-3415	339	18	∈	∈	PROPN
ejpam-3415	339	19	l	l	NOUN
ejpam-3415	339	20	,	,	PUNCT
ejpam-3415	339	21	a	a	DET
ejpam-3415	339	22	≤	≤	NUM
ejpam-3415	339	23	c	c	NOUN
ejpam-3415	339	24	implies	imply	VERB
ejpam-3415	339	25	a∨	a∨	PROPN
ejpam-3415	339	26	(	(	PUNCT
ejpam-3415	339	27	b∧c	b∧c	X
ejpam-3415	339	28	)	)	PUNCT
ejpam-3415	340	1	=	=	SYM
ejpam-3415	340	2	(	(	PUNCT
ejpam-3415	340	3	a∨b)∧c	a∨b)∧c	PROPN
ejpam-3415	340	4	.	.	PUNCT
ejpam-3415	341	1	this	this	DET
ejpam-3415	341	2	concept	concept	NOUN
ejpam-3415	341	3	can	can	AUX
ejpam-3415	341	4	be	be	AUX
ejpam-3415	341	5	naturally	naturally	ADV
ejpam-3415	341	6	transferred	transfer	VERB
ejpam-3415	341	7	to	to	ADP
ejpam-3415	341	8	a	a	DET
ejpam-3415	341	9	hyperlattice	hyperlattice	NOUN
ejpam-3415	341	10	by	by	ADP
ejpam-3415	341	11	the	the	DET
ejpam-3415	341	12	following	follow	VERB
ejpam-3415	341	13	definition	definition	NOUN
ejpam-3415	341	14	.	.	PUNCT
ejpam-3415	342	1	definition	definition	NOUN
ejpam-3415	342	2	4.1	4.1	NUM
ejpam-3415	342	3	a	a	DET
ejpam-3415	342	4	hyperlattice	hyperlattice	NOUN
ejpam-3415	342	5	l	l	NOUN
ejpam-3415	342	6	is	be	AUX
ejpam-3415	342	7	called	call	VERB
ejpam-3415	342	8	modular	modular	ADJ
ejpam-3415	342	9	if	if	SCONJ
ejpam-3415	342	10	the	the	DET
ejpam-3415	342	11	following	follow	VERB
ejpam-3415	342	12	assertions	assertion	NOUN
ejpam-3415	342	13	are	be	AUX
ejpam-3415	342	14	satisfied	satisfied	ADJ
ejpam-3415	342	15	:	:	PUNCT
ejpam-3415	342	16	(	(	PUNCT
ejpam-3415	342	17	1	1	X
ejpam-3415	342	18	)	)	PUNCT
ejpam-3415	342	19	if	if	SCONJ
ejpam-3415	342	20	a	a	DET
ejpam-3415	342	21	∧	∧	PROPN
ejpam-3415	342	22	c	c	NOUN
ejpam-3415	342	23	=	=	SYM
ejpam-3415	342	24	a	a	PROPN
ejpam-3415	342	25	and	and	CCONJ
ejpam-3415	342	26	u	u	NOUN
ejpam-3415	342	27	∈	∈	PROPN
ejpam-3415	342	28	a	a	DET
ejpam-3415	342	29	∨	∨	NOUN
ejpam-3415	342	30	(	(	PUNCT
ejpam-3415	342	31	b	b	PROPN
ejpam-3415	342	32	∧	∧	PROPN
ejpam-3415	342	33	c	c	NOUN
ejpam-3415	342	34	)	)	PUNCT
ejpam-3415	342	35	,	,	PUNCT
ejpam-3415	342	36	then	then	ADV
ejpam-3415	342	37	there	there	PRON
ejpam-3415	342	38	exists	exist	VERB
ejpam-3415	342	39	v	v	ADP
ejpam-3415	342	40	∈	∈	PROPN
ejpam-3415	342	41	a	a	DET
ejpam-3415	342	42	∨	∨	NUM
ejpam-3415	342	43	b	b	NOUN
ejpam-3415	342	44	such	such	ADJ
ejpam-3415	342	45	that	that	DET
ejpam-3415	342	46	u	u	NOUN
ejpam-3415	342	47	=	=	X
ejpam-3415	342	48	v	v	ADP
ejpam-3415	342	49	∧	∧	PROPN
ejpam-3415	342	50	c	c	PROPN
ejpam-3415	342	51	and	and	CCONJ
ejpam-3415	342	52	(	(	PUNCT
ejpam-3415	342	53	2	2	X
ejpam-3415	342	54	)	)	PUNCT
ejpam-3415	342	55	if	if	SCONJ
ejpam-3415	342	56	a	a	DET
ejpam-3415	342	57	∧	∧	PROPN
ejpam-3415	342	58	c	c	NOUN
ejpam-3415	342	59	=	=	SYM
ejpam-3415	342	60	a	a	PROPN
ejpam-3415	342	61	and	and	CCONJ
ejpam-3415	342	62	u	u	NOUN
ejpam-3415	342	63	∈	∈	PROPN
ejpam-3415	342	64	a	a	DET
ejpam-3415	342	65	∨	∨	NUM
ejpam-3415	342	66	b	b	PROPN
ejpam-3415	342	67	,	,	PUNCT
ejpam-3415	342	68	then	then	ADV
ejpam-3415	342	69	u	u	PROPN
ejpam-3415	342	70	∧	∧	PROPN
ejpam-3415	342	71	c	c	PROPN
ejpam-3415	342	72	∈	∈	PROPN
ejpam-3415	342	73	a	a	DET
ejpam-3415	342	74	∨	∨	NOUN
ejpam-3415	342	75	(	(	PUNCT
ejpam-3415	342	76	b	b	PROPN
ejpam-3415	342	77	∧	∧	PROPN
ejpam-3415	342	78	c	c	NOUN
ejpam-3415	342	79	)	)	PUNCT
ejpam-3415	342	80	.	.	PUNCT
ejpam-3415	343	1	in	in	ADP
ejpam-3415	343	2	other	other	ADJ
ejpam-3415	343	3	words	word	NOUN
ejpam-3415	343	4	,	,	PUNCT
ejpam-3415	343	5	if	if	SCONJ
ejpam-3415	343	6	a∧	a∧	NOUN
ejpam-3415	343	7	c	c	NOUN
ejpam-3415	343	8	=	=	SYM
ejpam-3415	343	9	a	a	PROPN
ejpam-3415	343	10	,	,	PUNCT
ejpam-3415	343	11	then	then	ADV
ejpam-3415	343	12	we	we	PRON
ejpam-3415	343	13	have	have	VERB
ejpam-3415	343	14	u	u	PROPN
ejpam-3415	343	15	∈	∈	PROPN
ejpam-3415	343	16	a∨	a∨	PROPN
ejpam-3415	343	17	(	(	PUNCT
ejpam-3415	343	18	b∧	b∧	PROPN
ejpam-3415	343	19	c	c	NOUN
ejpam-3415	343	20	)	)	PUNCT
ejpam-3415	343	21	if	if	SCONJ
ejpam-3415	344	1	and	and	CCONJ
ejpam-3415	344	2	only	only	ADV
ejpam-3415	344	3	if	if	SCONJ
ejpam-3415	344	4	there	there	PRON
ejpam-3415	344	5	exists	exist	VERB
ejpam-3415	344	6	v	v	ADP
ejpam-3415	344	7	∈	∈	PROPN
ejpam-3415	344	8	a∨	a∨	PROPN
ejpam-3415	344	9	b	b	PROPN
ejpam-3415	344	10	such	such	ADJ
ejpam-3415	344	11	that	that	PRON
ejpam-3415	344	12	u	u	NOUN
ejpam-3415	344	13	=	=	X
ejpam-3415	344	14	v	v	ADP
ejpam-3415	344	15	∧	∧	PROPN
ejpam-3415	344	16	c.	c.	PROPN
ejpam-3415	344	17	that	that	PRON
ejpam-3415	344	18	is	be	AUX
ejpam-3415	344	19	,	,	PUNCT
ejpam-3415	344	20	if	if	SCONJ
ejpam-3415	344	21	a	a	DET
ejpam-3415	344	22	∧	∧	PROPN
ejpam-3415	344	23	c	c	NOUN
ejpam-3415	344	24	=	=	PRON
ejpam-3415	344	25	a	a	PRON
ejpam-3415	344	26	implies	imply	VERB
ejpam-3415	344	27	{	{	PUNCT
ejpam-3415	344	28	v	v	NUM
ejpam-3415	344	29	∧	∧	PROPN
ejpam-3415	344	30	c	c	NOUN
ejpam-3415	344	31	|	|	NOUN
ejpam-3415	344	32	v	v	ADP
ejpam-3415	344	33	∈	∈	PROPN
ejpam-3415	344	34	a	a	DET
ejpam-3415	344	35	∨	∨	NOUN
ejpam-3415	344	36	b	b	NOUN
ejpam-3415	344	37	}	}	PUNCT
ejpam-3415	344	38	=	=	PUNCT
ejpam-3415	344	39	a	a	DET
ejpam-3415	344	40	∨	∨	NOUN
ejpam-3415	344	41	(	(	PUNCT
ejpam-3415	344	42	b	b	PROPN
ejpam-3415	344	43	∧	∧	PROPN
ejpam-3415	344	44	c	c	NOUN
ejpam-3415	344	45	)	)	PUNCT
ejpam-3415	344	46	.	.	PUNCT
ejpam-3415	345	1	since	since	SCONJ
ejpam-3415	345	2	a	a	DET
ejpam-3415	345	3	∧	∧	PROPN
ejpam-3415	345	4	a	a	DET
ejpam-3415	345	5	=	=	X
ejpam-3415	345	6	a	a	NOUN
ejpam-3415	345	7	,	,	PUNCT
ejpam-3415	345	8	in	in	ADP
ejpam-3415	345	9	a	a	DET
ejpam-3415	345	10	modular	modular	ADJ
ejpam-3415	345	11	hyperlattice	hyperlattice	NOUN
ejpam-3415	345	12	we	we	PRON
ejpam-3415	345	13	have	have	VERB
ejpam-3415	345	14	{	{	PUNCT
ejpam-3415	345	15	v	v	NUM
ejpam-3415	345	16	∧	∧	PROPN
ejpam-3415	345	17	a	a	DET
ejpam-3415	345	18	|	|	NOUN
ejpam-3415	345	19	v	v	ADP
ejpam-3415	345	20	∈	∈	PROPN
ejpam-3415	345	21	a	a	DET
ejpam-3415	345	22	∨	∨	NOUN
ejpam-3415	345	23	b	b	NOUN
ejpam-3415	345	24	}	}	PUNCT
ejpam-3415	345	25	=	=	PUNCT
ejpam-3415	345	26	a	a	DET
ejpam-3415	345	27	∨	∨	NOUN
ejpam-3415	345	28	(	(	PUNCT
ejpam-3415	345	29	b	b	PROPN
ejpam-3415	345	30	∧	∧	PROPN
ejpam-3415	345	31	a	a	NOUN
ejpam-3415	345	32	)	)	PUNCT
ejpam-3415	345	33	.	.	PUNCT
ejpam-3415	346	1	remark	remark	VERB
ejpam-3415	346	2	4.2	4.2	NUM
ejpam-3415	346	3	while	while	NOUN
ejpam-3415	346	4	to	to	ADP
ejpam-3415	346	5	a	a	DET
ejpam-3415	346	6	distributive	distributive	ADJ
ejpam-3415	346	7	lattice	lattice	NOUN
ejpam-3415	346	8	correspond	correspond	VERB
ejpam-3415	346	9	two	two	NUM
ejpam-3415	346	10	definitions	definition	NOUN
ejpam-3415	346	11	of	of	ADP
ejpam-3415	346	12	a	a	DET
ejpam-3415	346	13	distributive	distributive	ADJ
ejpam-3415	346	14	hyperlattice	hyperlattice	NOUN
ejpam-3415	346	15	,	,	PUNCT
ejpam-3415	346	16	to	to	ADP
ejpam-3415	346	17	a	a	DET
ejpam-3415	346	18	modular	modular	ADJ
ejpam-3415	346	19	lattice	lattice	NOUN
ejpam-3415	346	20	corresponds	correspond	VERB
ejpam-3415	346	21	only	only	ADV
ejpam-3415	346	22	one	one	NUM
ejpam-3415	346	23	.	.	PUNCT
ejpam-3415	347	1	indeed	indeed	ADV
ejpam-3415	347	2	,	,	PUNCT
ejpam-3415	347	3	if	if	SCONJ
ejpam-3415	347	4	we	we	PRON
ejpam-3415	347	5	get	get	VERB
ejpam-3415	347	6	the	the	DET
ejpam-3415	347	7	equivalent	equivalent	ADJ
ejpam-3415	347	8	definition	definition	NOUN
ejpam-3415	347	9	of	of	ADP
ejpam-3415	347	10	a	a	DET
ejpam-3415	347	11	modular	modular	ADJ
ejpam-3415	347	12	lattice	lattice	NOUN
ejpam-3415	347	13	(	(	PUNCT
ejpam-3415	347	14	the	the	DET
ejpam-3415	347	15	dual	dual	ADJ
ejpam-3415	347	16	definition	definition	NOUN
ejpam-3415	347	17	)	)	PUNCT
ejpam-3415	347	18	which	which	PRON
ejpam-3415	347	19	is	be	AUX
ejpam-3415	347	20	a	a	DET
ejpam-3415	347	21	≥	≥	NOUN
ejpam-3415	347	22	c	c	NOUN
ejpam-3415	347	23	implies	imply	VERB
ejpam-3415	347	24	a	a	DET
ejpam-3415	347	25	∧	∧	PROPN
ejpam-3415	347	26	(	(	PUNCT
ejpam-3415	347	27	b	b	PROPN
ejpam-3415	347	28	∨	∨	NUM
ejpam-3415	347	29	c	c	NOUN
ejpam-3415	347	30	)	)	PUNCT
ejpam-3415	347	31	=	=	NOUN
ejpam-3415	347	32	(	(	PUNCT
ejpam-3415	347	33	a	a	DET
ejpam-3415	347	34	∧	∧	PROPN
ejpam-3415	347	35	b	b	PROPN
ejpam-3415	347	36	)	)	PUNCT
ejpam-3415	347	37	∨	∨	PROPN
ejpam-3415	347	38	c	c	PROPN
ejpam-3415	347	39	,	,	PUNCT
ejpam-3415	347	40	this	this	PRON
ejpam-3415	347	41	can	can	AUX
ejpam-3415	347	42	be	be	AUX
ejpam-3415	347	43	transferred	transfer	VERB
ejpam-3415	347	44	to	to	ADP
ejpam-3415	347	45	hyperlattices	hyperlattice	NOUN
ejpam-3415	347	46	as	as	SCONJ
ejpam-3415	347	47	follows	follow	VERB
ejpam-3415	347	48	:	:	PUNCT
ejpam-3415	347	49	(	(	PUNCT
ejpam-3415	348	1	1	1	X
ejpam-3415	348	2	)	)	PUNCT
ejpam-3415	348	3	if	if	SCONJ
ejpam-3415	348	4	a	a	DET
ejpam-3415	348	5	∧	∧	NOUN
ejpam-3415	348	6	c	c	NOUN
ejpam-3415	348	7	=	=	SYM
ejpam-3415	348	8	c	c	PROPN
ejpam-3415	348	9	and	and	CCONJ
ejpam-3415	348	10	u	u	PROPN
ejpam-3415	348	11	∈	∈	PROPN
ejpam-3415	348	12	b	b	PROPN
ejpam-3415	348	13	∨	∨	NUM
ejpam-3415	348	14	c	c	PROPN
ejpam-3415	348	15	,	,	PUNCT
ejpam-3415	348	16	then	then	ADV
ejpam-3415	348	17	a	a	DET
ejpam-3415	348	18	∧	∧	PROPN
ejpam-3415	348	19	u	u	X
ejpam-3415	348	20	∈	∈	PROPN
ejpam-3415	348	21	(	(	PUNCT
ejpam-3415	348	22	a	a	DET
ejpam-3415	348	23	∧	∧	PROPN
ejpam-3415	348	24	b	b	PROPN
ejpam-3415	348	25	)	)	PUNCT
ejpam-3415	348	26	∨	∨	NUM
ejpam-3415	348	27	c	c	PROPN
ejpam-3415	348	28	and	and	CCONJ
ejpam-3415	348	29	(	(	PUNCT
ejpam-3415	348	30	2	2	X
ejpam-3415	348	31	)	)	PUNCT
ejpam-3415	348	32	if	if	SCONJ
ejpam-3415	348	33	a	a	DET
ejpam-3415	348	34	∧	∧	NOUN
ejpam-3415	348	35	c	c	NOUN
ejpam-3415	348	36	=	=	SYM
ejpam-3415	348	37	c	c	PROPN
ejpam-3415	348	38	and	and	CCONJ
ejpam-3415	348	39	u	u	PROPN
ejpam-3415	348	40	∈	∈	PROPN
ejpam-3415	348	41	(	(	PUNCT
ejpam-3415	348	42	a	a	DET
ejpam-3415	348	43	∧	∧	PROPN
ejpam-3415	348	44	b	b	PROPN
ejpam-3415	348	45	)	)	PUNCT
ejpam-3415	348	46	∨	∨	PROPN
ejpam-3415	348	47	c	c	PROPN
ejpam-3415	348	48	,	,	PUNCT
ejpam-3415	348	49	then	then	ADV
ejpam-3415	348	50	there	there	PRON
ejpam-3415	348	51	exists	exist	VERB
ejpam-3415	348	52	v	v	ADP
ejpam-3415	348	53	∈	∈	PROPN
ejpam-3415	348	54	b	b	PROPN
ejpam-3415	348	55	∨	∨	NUM
ejpam-3415	348	56	c	c	PROPN
ejpam-3415	348	57	such	such	ADJ
ejpam-3415	348	58	that	that	SCONJ
ejpam-3415	348	59	u	u	PROPN
ejpam-3415	348	60	∈	∈	PROPN
ejpam-3415	348	61	a	a	DET
ejpam-3415	348	62	∧	∧	PROPN
ejpam-3415	348	63	v.	v.	ADP
ejpam-3415	348	64	in	in	ADP
ejpam-3415	348	65	other	other	ADJ
ejpam-3415	348	66	words	word	NOUN
ejpam-3415	348	67	,	,	PUNCT
ejpam-3415	348	68	if	if	SCONJ
ejpam-3415	348	69	a	a	DET
ejpam-3415	348	70	∧	∧	PROPN
ejpam-3415	348	71	c	c	NOUN
ejpam-3415	348	72	=	=	SYM
ejpam-3415	348	73	c	c	PROPN
ejpam-3415	348	74	implies	imply	VERB
ejpam-3415	348	75	{	{	PUNCT
ejpam-3415	348	76	a	a	DET
ejpam-3415	348	77	∧	∧	PROPN
ejpam-3415	348	78	u	u	NOUN
ejpam-3415	348	79	|	|	ADV
ejpam-3415	348	80	u	u	NOUN
ejpam-3415	348	81	∈	∈	PROPN
ejpam-3415	348	82	b	b	PROPN
ejpam-3415	348	83	∨	∨	NUM
ejpam-3415	348	84	c	c	NOUN
ejpam-3415	348	85	}	}	PUNCT
ejpam-3415	348	86	=	=	SYM
ejpam-3415	348	87	(	(	PUNCT
ejpam-3415	348	88	a	a	DET
ejpam-3415	348	89	∧	∧	PROPN
ejpam-3415	348	90	b	b	PROPN
ejpam-3415	348	91	)	)	PUNCT
ejpam-3415	348	92	∨	∨	NOUN
ejpam-3415	348	93	c.	c.	NOUN
ejpam-3415	348	94	as	as	SCONJ
ejpam-3415	348	95	we	we	PRON
ejpam-3415	348	96	see	see	VERB
ejpam-3415	348	97	,	,	PUNCT
ejpam-3415	348	98	this	this	PRON
ejpam-3415	348	99	is	be	AUX
ejpam-3415	348	100	the	the	DET
ejpam-3415	348	101	same	same	ADJ
ejpam-3415	348	102	with	with	ADP
ejpam-3415	348	103	the	the	DET
ejpam-3415	348	104	definition	definition	NOUN
ejpam-3415	348	105	of	of	ADP
ejpam-3415	348	106	modular	modular	ADJ
ejpam-3415	348	107	hyperlattice	hyperlattice	NOUN
ejpam-3415	348	108	given	give	VERB
ejpam-3415	348	109	by	by	ADP
ejpam-3415	348	110	definition	definition	NOUN
ejpam-3415	348	111	4.1	4.1	NUM
ejpam-3415	348	112	(	(	PUNCT
ejpam-3415	348	113	by	by	ADP
ejpam-3415	348	114	interchanging	interchange	VERB
ejpam-3415	348	115	a	a	PRON
ejpam-3415	348	116	and	and	CCONJ
ejpam-3415	348	117	c	c	X
ejpam-3415	348	118	the	the	DET
ejpam-3415	348	119	two	two	NUM
ejpam-3415	348	120	definitions	definition	NOUN
ejpam-3415	348	121	coincide	coincide	NOUN
ejpam-3415	348	122	)	)	PUNCT
ejpam-3415	348	123	.	.	PUNCT
ejpam-3415	349	1	example	example	NOUN
ejpam-3415	349	2	4.3	4.3	NUM
ejpam-3415	349	3	we	we	PRON
ejpam-3415	349	4	consider	consider	VERB
ejpam-3415	349	5	the	the	DET
ejpam-3415	349	6	no	no	DET
ejpam-3415	349	7	modular	modular	ADJ
ejpam-3415	349	8	lattice	lattice	NOUN
ejpam-3415	349	9	of	of	ADP
ejpam-3415	349	10	figure	figure	NOUN
ejpam-3415	349	11	4	4	NUM
ejpam-3415	349	12	.	.	PUNCT
ejpam-3415	350	1	a	a	DET
ejpam-3415	350	2	b	b	NOUN
ejpam-3415	350	3	c	c	NOUN
ejpam-3415	350	4	d	d	X
ejpam-3415	350	5	e	e	X
ejpam-3415	350	6	figure	figure	NOUN
ejpam-3415	350	7	4	4	NUM
ejpam-3415	350	8	:	:	PUNCT
ejpam-3415	350	9	the	the	DET
ejpam-3415	350	10	no	no	DET
ejpam-3415	350	11	modular	modular	ADJ
ejpam-3415	350	12	lattice	lattice	NOUN
ejpam-3415	350	13	of	of	ADP
ejpam-3415	350	14	the	the	DET
ejpam-3415	350	15	example	example	NOUN
ejpam-3415	350	16	4.3	4.3	NUM
ejpam-3415	350	17	.	.	PUNCT
ejpam-3415	351	1	the	the	DET
ejpam-3415	351	2	hyperlattice	hyperlattice	NOUN
ejpam-3415	351	3	l	l	NOUN
ejpam-3415	351	4	with	with	ADP
ejpam-3415	351	5	the	the	DET
ejpam-3415	351	6	operation	operation	NOUN
ejpam-3415	351	7	∧	∧	NOUN
ejpam-3415	351	8	and	and	CCONJ
ejpam-3415	351	9	the	the	DET
ejpam-3415	351	10	hyperoperation	hyperoperation	NOUN
ejpam-3415	351	11	.	.	PUNCT
ejpam-3415	352	1	∨	∨	NUM
ejpam-3415	352	2	defined	define	VERB
ejpam-3415	352	3	in	in	ADP
ejpam-3415	352	4	the	the	DET
ejpam-3415	352	5	second	second	ADJ
ejpam-3415	352	6	proof	proof	NOUN
ejpam-3415	352	7	of	of	ADP
ejpam-3415	352	8	proposition	proposition	NOUN
ejpam-3415	352	9	2.5	2.5	NUM
ejpam-3415	352	10	is	be	AUX
ejpam-3415	352	11	given	give	VERB
ejpam-3415	352	12	by	by	ADP
ejpam-3415	352	13	table	table	NOUN
ejpam-3415	352	14	9	9	NUM
ejpam-3415	352	15	and	and	CCONJ
ejpam-3415	352	16	it	it	PRON
ejpam-3415	352	17	is	be	AUX
ejpam-3415	352	18	not	not	PART
ejpam-3415	352	19	modular	modular	ADJ
ejpam-3415	352	20	as	as	ADP
ejpam-3415	352	21	c∧	c∧	ADJ
ejpam-3415	352	22	d	d	NOUN
ejpam-3415	352	23	=	=	SYM
ejpam-3415	352	24	c	c	PROPN
ejpam-3415	352	25	and	and	CCONJ
ejpam-3415	352	26	e	e	PROPN
ejpam-3415	352	27	∈	∈	PROPN
ejpam-3415	352	28	c	c	PROPN
ejpam-3415	352	29	.	.	PUNCT
ejpam-3415	353	1	∨	∨	NUM
ejpam-3415	353	2	b	b	PROPN
ejpam-3415	353	3	but	but	CCONJ
ejpam-3415	353	4	e	e	PROPN
ejpam-3415	353	5	∧	∧	PROPN
ejpam-3415	353	6	d	d	PROPN
ejpam-3415	353	7	/∈	/∈	PUNCT
ejpam-3415	354	1	c	c	NOUN
ejpam-3415	354	2	.	.	PUNCT
ejpam-3415	355	1	∨(b	∨(b	ADJ
ejpam-3415	355	2	∧	∧	PROPN
ejpam-3415	355	3	d	d	PROPN
ejpam-3415	355	4	)	)	PUNCT
ejpam-3415	355	5	;	;	PUNCT
ejpam-3415	355	6	that	that	PRON
ejpam-3415	355	7	is	be	AUX
ejpam-3415	355	8	condition	condition	NOUN
ejpam-3415	355	9	(	(	PUNCT
ejpam-3415	355	10	2	2	NUM
ejpam-3415	355	11	)	)	PUNCT
ejpam-3415	355	12	of	of	ADP
ejpam-3415	355	13	definition	definition	NOUN
ejpam-3415	355	14	4.1	4.1	NUM
ejpam-3415	355	15	does	do	AUX
ejpam-3415	355	16	not	not	PART
ejpam-3415	355	17	hold	hold	VERB
ejpam-3415	355	18	.	.	PUNCT
ejpam-3415	356	1	niovi	niovi	PROPN
ejpam-3415	356	2	kehayopulu	kehayopulu	PROPN
ejpam-3415	356	3	/	/	SYM
ejpam-3415	356	4	eur	eur	PROPN
ejpam-3415	356	5	.	.	PUNCT
ejpam-3415	357	1	j.	j.	PROPN
ejpam-3415	357	2	pure	pure	PROPN
ejpam-3415	357	3	appl	appl	PROPN
ejpam-3415	357	4	.	.	PROPN
ejpam-3415	357	5	math	math	PROPN
ejpam-3415	357	6	,	,	PUNCT
ejpam-3415	357	7	12	12	NUM
ejpam-3415	357	8	(	(	PUNCT
ejpam-3415	357	9	2	2	NUM
ejpam-3415	357	10	)	)	PUNCT
ejpam-3415	357	11	(	(	PUNCT
ejpam-3415	357	12	2019	2019	NUM
ejpam-3415	357	13	)	)	PUNCT
ejpam-3415	357	14	,	,	PUNCT
ejpam-3415	357	15	252	252	NUM
ejpam-3415	357	16	-	-	SYM
ejpam-3415	357	17	269	269	NUM
ejpam-3415	357	18	265	265	NUM
ejpam-3415	357	19	table	table	NOUN
ejpam-3415	357	20	9	9	NUM
ejpam-3415	357	21	:	:	PUNCT
ejpam-3415	357	22	the	the	DET
ejpam-3415	357	23	no	no	DET
ejpam-3415	357	24	modular	modular	ADJ
ejpam-3415	357	25	hyperlattice	hyperlattice	NOUN
ejpam-3415	357	26	of	of	ADP
ejpam-3415	357	27	the	the	DET
ejpam-3415	357	28	example	example	NOUN
ejpam-3415	357	29	4.3	4.3	NUM
ejpam-3415	357	30	.	.	PUNCT
ejpam-3415	358	1	∧	∧	PROPN
ejpam-3415	358	2	a	a	DET
ejpam-3415	358	3	b	b	NOUN
ejpam-3415	358	4	c	c	NOUN
ejpam-3415	358	5	d	d	PROPN
ejpam-3415	358	6	e	e	X
ejpam-3415	358	7	a	a	DET
ejpam-3415	358	8	a	a	DET
ejpam-3415	358	9	a	a	DET
ejpam-3415	358	10	a	a	DET
ejpam-3415	358	11	a	a	DET
ejpam-3415	358	12	a	a	DET
ejpam-3415	358	13	b	b	NOUN
ejpam-3415	358	14	a	a	DET
ejpam-3415	358	15	b	b	NOUN
ejpam-3415	358	16	a	a	DET
ejpam-3415	358	17	a	a	DET
ejpam-3415	358	18	b	b	NOUN
ejpam-3415	358	19	c	c	NOUN
ejpam-3415	358	20	a	a	PRON
ejpam-3415	358	21	a	a	PRON
ejpam-3415	358	22	c	c	NOUN
ejpam-3415	358	23	c	c	NOUN
ejpam-3415	358	24	e	e	PROPN
ejpam-3415	358	25	d	d	X
ejpam-3415	358	26	a	a	PRON
ejpam-3415	358	27	a	a	DET
ejpam-3415	358	28	c	c	NOUN
ejpam-3415	359	1	d	d	NOUN
ejpam-3415	359	2	d	d	PROPN
ejpam-3415	359	3	e	e	PROPN
ejpam-3415	359	4	a	a	PRON
ejpam-3415	359	5	b	b	NOUN
ejpam-3415	359	6	c	c	NOUN
ejpam-3415	359	7	d	d	X
ejpam-3415	359	8	e	e	X
ejpam-3415	359	9	(	(	PUNCT
ejpam-3415	359	10	a	a	NOUN
ejpam-3415	359	11	)	)	PUNCT
ejpam-3415	359	12	.	.	PUNCT
ejpam-3415	360	1	∨	∨	NOUN
ejpam-3415	360	2	a	a	DET
ejpam-3415	360	3	b	b	NOUN
ejpam-3415	360	4	c	c	NOUN
ejpam-3415	360	5	d	d	X
ejpam-3415	360	6	e	e	X
ejpam-3415	360	7	a	a	X
ejpam-3415	360	8	{	{	PUNCT
ejpam-3415	360	9	a	a	NOUN
ejpam-3415	360	10	}	}	PUNCT
ejpam-3415	360	11	{	{	PUNCT
ejpam-3415	360	12	a	a	DET
ejpam-3415	360	13	,	,	PUNCT
ejpam-3415	360	14	b	b	NOUN
ejpam-3415	360	15	}	}	PUNCT
ejpam-3415	360	16	{	{	PUNCT
ejpam-3415	360	17	a	a	PROPN
ejpam-3415	360	18	,	,	PUNCT
ejpam-3415	360	19	c	c	NOUN
ejpam-3415	360	20	}	}	PUNCT
ejpam-3415	360	21	{	{	PUNCT
ejpam-3415	360	22	a	a	DET
ejpam-3415	360	23	,	,	PUNCT
ejpam-3415	360	24	d	d	NOUN
ejpam-3415	360	25	}	}	PUNCT
ejpam-3415	360	26	{	{	PUNCT
ejpam-3415	360	27	a	a	NOUN
ejpam-3415	360	28	,	,	PUNCT
ejpam-3415	360	29	e	e	NOUN
ejpam-3415	360	30	}	}	PUNCT
ejpam-3415	360	31	b	b	PROPN
ejpam-3415	360	32	{	{	PUNCT
ejpam-3415	360	33	a	a	PROPN
ejpam-3415	360	34	,	,	PUNCT
ejpam-3415	360	35	b	b	NOUN
ejpam-3415	360	36	}	}	PUNCT
ejpam-3415	360	37	{	{	PUNCT
ejpam-3415	360	38	b	b	NOUN
ejpam-3415	360	39	}	}	PUNCT
ejpam-3415	360	40	{	{	PUNCT
ejpam-3415	360	41	b	b	PROPN
ejpam-3415	360	42	,	,	PUNCT
ejpam-3415	360	43	c	c	X
ejpam-3415	360	44	,	,	PUNCT
ejpam-3415	360	45	e	e	NOUN
ejpam-3415	360	46	}	}	PUNCT
ejpam-3415	360	47	{	{	PUNCT
ejpam-3415	360	48	b	b	NOUN
ejpam-3415	360	49	,	,	PUNCT
ejpam-3415	360	50	d	d	NOUN
ejpam-3415	360	51	,	,	PUNCT
ejpam-3415	360	52	e	e	NOUN
ejpam-3415	360	53	}	}	PUNCT
ejpam-3415	360	54	{	{	PUNCT
ejpam-3415	360	55	b	b	NOUN
ejpam-3415	360	56	,	,	PUNCT
ejpam-3415	360	57	e	e	NOUN
ejpam-3415	360	58	}	}	PUNCT
ejpam-3415	360	59	c	c	NOUN
ejpam-3415	360	60	{	{	PUNCT
ejpam-3415	360	61	a	a	NOUN
ejpam-3415	360	62	,	,	PUNCT
ejpam-3415	360	63	c	c	NOUN
ejpam-3415	360	64	}	}	PUNCT
ejpam-3415	360	65	{	{	PUNCT
ejpam-3415	360	66	b	b	PROPN
ejpam-3415	360	67	,	,	PUNCT
ejpam-3415	360	68	c	c	X
ejpam-3415	360	69	,	,	PUNCT
ejpam-3415	360	70	e	e	NOUN
ejpam-3415	360	71	}	}	PUNCT
ejpam-3415	360	72	{	{	PUNCT
ejpam-3415	360	73	c	c	NOUN
ejpam-3415	360	74	}	}	PUNCT
ejpam-3415	360	75	{	{	PUNCT
ejpam-3415	360	76	c	c	NOUN
ejpam-3415	360	77	,	,	PUNCT
ejpam-3415	360	78	d	d	NOUN
ejpam-3415	360	79	}	}	PUNCT
ejpam-3415	360	80	{	{	PUNCT
ejpam-3415	360	81	c	c	NOUN
ejpam-3415	360	82	,	,	PUNCT
ejpam-3415	360	83	e	e	NOUN
ejpam-3415	360	84	}	}	PUNCT
ejpam-3415	360	85	d	d	X
ejpam-3415	360	86	{	{	PUNCT
ejpam-3415	360	87	a	a	PRON
ejpam-3415	360	88	,	,	PUNCT
ejpam-3415	360	89	d	d	NOUN
ejpam-3415	360	90	}	}	PUNCT
ejpam-3415	360	91	{	{	PUNCT
ejpam-3415	360	92	b	b	NOUN
ejpam-3415	360	93	,	,	PUNCT
ejpam-3415	360	94	d	d	NOUN
ejpam-3415	360	95	,	,	PUNCT
ejpam-3415	360	96	e	e	NOUN
ejpam-3415	360	97	}	}	PUNCT
ejpam-3415	360	98	{	{	PUNCT
ejpam-3415	360	99	c	c	X
ejpam-3415	360	100	,	,	PUNCT
ejpam-3415	360	101	d	d	NOUN
ejpam-3415	360	102	}	}	PUNCT
ejpam-3415	360	103	{	{	PUNCT
ejpam-3415	360	104	d	d	NOUN
ejpam-3415	360	105	}	}	PUNCT
ejpam-3415	360	106	{	{	PUNCT
ejpam-3415	360	107	d	d	NOUN
ejpam-3415	360	108	,	,	PUNCT
ejpam-3415	360	109	e	e	NOUN
ejpam-3415	360	110	}	}	PUNCT
ejpam-3415	360	111	e	e	X
ejpam-3415	360	112	{	{	PUNCT
ejpam-3415	360	113	a	a	PRON
ejpam-3415	360	114	,	,	PUNCT
ejpam-3415	360	115	e	e	NOUN
ejpam-3415	360	116	}	}	PUNCT
ejpam-3415	360	117	{	{	PUNCT
ejpam-3415	360	118	b	b	NOUN
ejpam-3415	360	119	,	,	PUNCT
ejpam-3415	360	120	e	e	NOUN
ejpam-3415	360	121	}	}	PUNCT
ejpam-3415	360	122	{	{	PUNCT
ejpam-3415	360	123	c	c	NOUN
ejpam-3415	360	124	,	,	PUNCT
ejpam-3415	360	125	e	e	NOUN
ejpam-3415	360	126	}	}	PUNCT
ejpam-3415	360	127	{	{	PUNCT
ejpam-3415	360	128	d	d	NOUN
ejpam-3415	360	129	,	,	PUNCT
ejpam-3415	360	130	e	e	NOUN
ejpam-3415	360	131	}	}	PUNCT
ejpam-3415	360	132	{	{	PUNCT
ejpam-3415	360	133	e	e	NOUN
ejpam-3415	360	134	}	}	PUNCT
ejpam-3415	360	135	(	(	PUNCT
ejpam-3415	360	136	b	b	X
ejpam-3415	360	137	)	)	PUNCT
ejpam-3415	360	138	proposition	proposition	NOUN
ejpam-3415	360	139	4.4	4.4	NUM
ejpam-3415	360	140	if	if	SCONJ
ejpam-3415	360	141	l	l	NOUN
ejpam-3415	360	142	is	be	AUX
ejpam-3415	360	143	a	a	DET
ejpam-3415	360	144	distributive	distributive	ADJ
ejpam-3415	360	145	hyperlattice	hyperlattice	NOUN
ejpam-3415	360	146	in	in	ADP
ejpam-3415	360	147	the	the	DET
ejpam-3415	360	148	sense	sense	NOUN
ejpam-3415	360	149	of	of	ADP
ejpam-3415	360	150	definition	definition	NOUN
ejpam-3415	360	151	3.1(1	3.1(1	NUM
ejpam-3415	360	152	)	)	PUNCT
ejpam-3415	361	1	,	,	PUNCT
ejpam-3415	361	2	then	then	ADV
ejpam-3415	361	3	it	it	PRON
ejpam-3415	361	4	is	be	AUX
ejpam-3415	361	5	modular	modular	ADJ
ejpam-3415	361	6	.	.	PUNCT
ejpam-3415	362	1	proof	proof	NOUN
ejpam-3415	362	2	let	let	VERB
ejpam-3415	362	3	a∧c	a∧c	NOUN
ejpam-3415	362	4	=	=	PUNCT
ejpam-3415	362	5	a	a	PRON
ejpam-3415	362	6	and	and	CCONJ
ejpam-3415	362	7	u	u	PROPN
ejpam-3415	362	8	∈	∈	PROPN
ejpam-3415	362	9	a∨	a∨	PROPN
ejpam-3415	362	10	(	(	PUNCT
ejpam-3415	362	11	b∧c	b∧c	PROPN
ejpam-3415	362	12	)	)	PUNCT
ejpam-3415	362	13	.	.	PUNCT
ejpam-3415	363	1	then	then	ADV
ejpam-3415	363	2	u	u	PROPN
ejpam-3415	363	3	∈	∈	PROPN
ejpam-3415	363	4	(	(	PUNCT
ejpam-3415	363	5	a∧c)∨	a∧c)∨	PROPN
ejpam-3415	363	6	(	(	PUNCT
ejpam-3415	363	7	b∧c	b∧c	NOUN
ejpam-3415	363	8	)	)	PUNCT
ejpam-3415	363	9	=	=	SYM
ejpam-3415	363	10	(	(	PUNCT
ejpam-3415	363	11	c∧a)∨	c∧a)∨	X
ejpam-3415	363	12	(	(	PUNCT
ejpam-3415	363	13	c∧b	c∧b	PROPN
ejpam-3415	363	14	)	)	PUNCT
ejpam-3415	363	15	and	and	CCONJ
ejpam-3415	363	16	,	,	PUNCT
ejpam-3415	363	17	by	by	ADP
ejpam-3415	363	18	the	the	DET
ejpam-3415	363	19	second	second	ADJ
ejpam-3415	363	20	property	property	NOUN
ejpam-3415	363	21	of	of	ADP
ejpam-3415	363	22	definition	definition	NOUN
ejpam-3415	363	23	3.1(1	3.1(1	NUM
ejpam-3415	363	24	)	)	PUNCT
ejpam-3415	363	25	,	,	PUNCT
ejpam-3415	363	26	there	there	PRON
ejpam-3415	363	27	exists	exist	VERB
ejpam-3415	363	28	v	v	ADP
ejpam-3415	363	29	∈	∈	PROPN
ejpam-3415	363	30	a∨b	a∨b	NOUN
ejpam-3415	363	31	such	such	ADJ
ejpam-3415	363	32	that	that	SCONJ
ejpam-3415	363	33	u	u	NOUN
ejpam-3415	364	1	=	=	NOUN
ejpam-3415	364	2	c∧v	c∧v	X
ejpam-3415	364	3	(=	(=	ADV
ejpam-3415	364	4	v∧c	v∧c	PROPN
ejpam-3415	364	5	)	)	PUNCT
ejpam-3415	364	6	.	.	PUNCT
ejpam-3415	365	1	let	let	VERB
ejpam-3415	365	2	now	now	ADV
ejpam-3415	365	3	a∧	a∧	VERB
ejpam-3415	365	4	c	c	NOUN
ejpam-3415	365	5	=	=	SYM
ejpam-3415	365	6	a	a	PROPN
ejpam-3415	365	7	and	and	CCONJ
ejpam-3415	365	8	u	u	PROPN
ejpam-3415	365	9	∈	∈	PROPN
ejpam-3415	365	10	a∨	a∨	PROPN
ejpam-3415	365	11	b.	b.	PROPN
ejpam-3415	365	12	since	since	SCONJ
ejpam-3415	365	13	u	u	PROPN
ejpam-3415	365	14	∈	∈	PROPN
ejpam-3415	365	15	a∨	a∨	PROPN
ejpam-3415	365	16	b	b	PROPN
ejpam-3415	365	17	,	,	PUNCT
ejpam-3415	365	18	by	by	ADP
ejpam-3415	365	19	the	the	DET
ejpam-3415	365	20	first	first	ADJ
ejpam-3415	365	21	property	property	NOUN
ejpam-3415	365	22	of	of	ADP
ejpam-3415	365	23	definition	definition	NOUN
ejpam-3415	365	24	3.1(1	3.1(1	NUM
ejpam-3415	365	25	)	)	PUNCT
ejpam-3415	365	26	,	,	PUNCT
ejpam-3415	365	27	we	we	PRON
ejpam-3415	365	28	have	have	AUX
ejpam-3415	365	29	c∧	c∧	VERB
ejpam-3415	365	30	u	u	PRON
ejpam-3415	365	31	∈	∈	PROPN
ejpam-3415	365	32	(	(	PUNCT
ejpam-3415	365	33	c∧	c∧	ADJ
ejpam-3415	365	34	a)∨	a)∨	PROPN
ejpam-3415	365	35	(	(	PUNCT
ejpam-3415	365	36	c∧	c∧	PROPN
ejpam-3415	365	37	b	b	PROPN
ejpam-3415	365	38	)	)	PUNCT
ejpam-3415	365	39	.	.	PUNCT
ejpam-3415	366	1	since	since	SCONJ
ejpam-3415	366	2	a∧	a∧	NOUN
ejpam-3415	366	3	c	c	PROPN
ejpam-3415	366	4	=	=	SYM
ejpam-3415	366	5	a	a	PROPN
ejpam-3415	366	6	,	,	PUNCT
ejpam-3415	366	7	we	we	PRON
ejpam-3415	366	8	have	have	VERB
ejpam-3415	366	9	u∧	u∧	PROPN
ejpam-3415	366	10	c	c	PROPN
ejpam-3415	366	11	∈	∈	PROPN
ejpam-3415	366	12	a∨	a∨	PROPN
ejpam-3415	366	13	(	(	PUNCT
ejpam-3415	366	14	b∧	b∧	PROPN
ejpam-3415	366	15	c	c	NOUN
ejpam-3415	366	16	)	)	PUNCT
ejpam-3415	366	17	and	and	CCONJ
ejpam-3415	366	18	the	the	DET
ejpam-3415	366	19	proof	proof	NOUN
ejpam-3415	366	20	is	be	AUX
ejpam-3415	366	21	complete	complete	ADJ
ejpam-3415	366	22	.	.	PUNCT
ejpam-3415	367	1	�	�	PROPN
ejpam-3415	367	2	according	accord	VERB
ejpam-3415	367	3	to	to	ADP
ejpam-3415	367	4	proposition	proposition	NOUN
ejpam-3415	367	5	4.4	4.4	NUM
ejpam-3415	367	6	,	,	PUNCT
ejpam-3415	367	7	the	the	DET
ejpam-3415	367	8	distributive	distributive	ADJ
ejpam-3415	367	9	hyperlattice	hyperlattice	NOUN
ejpam-3415	367	10	of	of	ADP
ejpam-3415	367	11	table	table	NOUN
ejpam-3415	367	12	6	6	NUM
ejpam-3415	367	13	(	(	PUNCT
ejpam-3415	367	14	example	example	NOUN
ejpam-3415	367	15	3.3	3.3	NUM
ejpam-3415	367	16	)	)	PUNCT
ejpam-3415	367	17	is	be	AUX
ejpam-3415	367	18	modular	modular	ADJ
ejpam-3415	367	19	.	.	PUNCT
ejpam-3415	368	1	proposition	proposition	NOUN
ejpam-3415	368	2	4.5	4.5	NUM
ejpam-3415	368	3	let	let	VERB
ejpam-3415	368	4	(	(	PUNCT
ejpam-3415	368	5	l,∧,∨	l,∧,∨	ADV
ejpam-3415	368	6	)	)	PUNCT
ejpam-3415	368	7	be	be	AUX
ejpam-3415	368	8	a	a	DET
ejpam-3415	368	9	modular	modular	ADJ
ejpam-3415	368	10	lattice	lattice	NOUN
ejpam-3415	368	11	.	.	PUNCT
ejpam-3415	369	1	then	then	ADV
ejpam-3415	369	2	(	(	PUNCT
ejpam-3415	369	3	1	1	X
ejpam-3415	369	4	)	)	PUNCT
ejpam-3415	369	5	the	the	DET
ejpam-3415	369	6	hyperlattice	hyperlattice	NOUN
ejpam-3415	369	7	(	(	PUNCT
ejpam-3415	369	8	l,∧	l,∧	NOUN
ejpam-3415	369	9	,	,	PUNCT
ejpam-3415	369	10	.	.	PUNCT
ejpam-3415	370	1	∨	∨	NUM
ejpam-3415	370	2	)	)	PUNCT
ejpam-3415	370	3	,	,	PUNCT
ejpam-3415	370	4	where	where	SCONJ
ejpam-3415	370	5	.	.	PUNCT
ejpam-3415	371	1	∨	∨	NOUN
ejpam-3415	371	2	:	:	PUNCT
ejpam-3415	371	3	(	(	PUNCT
ejpam-3415	371	4	a	a	DET
ejpam-3415	371	5	,	,	PUNCT
ejpam-3415	371	6	b	b	NOUN
ejpam-3415	371	7	)	)	PUNCT
ejpam-3415	371	8	→	→	SYM
ejpam-3415	371	9	a	a	PRON
ejpam-3415	371	10	.	.	PUNCT
ejpam-3415	372	1	∨	∨	NUM
ejpam-3415	372	2	b	b	X
ejpam-3415	372	3	:	:	PUNCT
ejpam-3415	372	4	=	=	X
ejpam-3415	372	5	{	{	PUNCT
ejpam-3415	372	6	a	a	DET
ejpam-3415	372	7	∨	∨	NUM
ejpam-3415	372	8	b	b	NOUN
ejpam-3415	372	9	}	}	PUNCT
ejpam-3415	372	10	considered	consider	VERB
ejpam-3415	372	11	in	in	ADP
ejpam-3415	372	12	the	the	DET
ejpam-3415	372	13	first	first	ADJ
ejpam-3415	372	14	part	part	NOUN
ejpam-3415	372	15	of	of	ADP
ejpam-3415	372	16	proposition	proposition	NOUN
ejpam-3415	372	17	2.5	2.5	NUM
ejpam-3415	372	18	is	be	AUX
ejpam-3415	372	19	modular	modular	ADJ
ejpam-3415	372	20	;	;	PUNCT
ejpam-3415	372	21	(	(	PUNCT
ejpam-3415	372	22	2	2	X
ejpam-3415	372	23	)	)	PUNCT
ejpam-3415	372	24	the	the	DET
ejpam-3415	372	25	hyperlattice	hyperlattice	NOUN
ejpam-3415	372	26	(	(	PUNCT
ejpam-3415	372	27	l,∧	l,∧	NOUN
ejpam-3415	372	28	,	,	PUNCT
ejpam-3415	372	29	.	.	PUNCT
ejpam-3415	373	1	∨	∨	NUM
ejpam-3415	373	2	)	)	PUNCT
ejpam-3415	373	3	,	,	PUNCT
ejpam-3415	373	4	where	where	SCONJ
ejpam-3415	373	5	.	.	PUNCT
ejpam-3415	374	1	∨	∨	NOUN
ejpam-3415	374	2	:	:	PUNCT
ejpam-3415	374	3	(	(	PUNCT
ejpam-3415	374	4	a	a	DET
ejpam-3415	374	5	,	,	PUNCT
ejpam-3415	374	6	b	b	NOUN
ejpam-3415	374	7	)	)	PUNCT
ejpam-3415	374	8	→	→	SYM
ejpam-3415	374	9	a	a	PRON
ejpam-3415	374	10	.	.	PUNCT
ejpam-3415	375	1	∨	∨	NUM
ejpam-3415	375	2	b	b	X
ejpam-3415	375	3	:	:	PUNCT
ejpam-3415	375	4	=	=	X
ejpam-3415	375	5	{	{	PUNCT
ejpam-3415	375	6	a	a	DET
ejpam-3415	375	7	,	,	PUNCT
ejpam-3415	375	8	b	b	NOUN
ejpam-3415	375	9	,	,	PUNCT
ejpam-3415	375	10	a	a	DET
ejpam-3415	375	11	∨	∨	PROPN
ejpam-3415	375	12	b	b	NOUN
ejpam-3415	375	13	}	}	PUNCT
ejpam-3415	375	14	considered	consider	VERB
ejpam-3415	375	15	in	in	ADP
ejpam-3415	375	16	the	the	DET
ejpam-3415	375	17	second	second	ADJ
ejpam-3415	375	18	part	part	NOUN
ejpam-3415	375	19	of	of	ADP
ejpam-3415	375	20	proposition	proposition	NOUN
ejpam-3415	375	21	2.5	2.5	NUM
ejpam-3415	375	22	is	be	AUX
ejpam-3415	375	23	also	also	ADV
ejpam-3415	375	24	modular	modular	ADJ
ejpam-3415	375	25	.	.	PUNCT
ejpam-3415	376	1	proof	proof	NOUN
ejpam-3415	376	2	(	(	PUNCT
ejpam-3415	376	3	1	1	X
ejpam-3415	376	4	)	)	PUNCT
ejpam-3415	376	5	let	let	VERB
ejpam-3415	376	6	a	a	DET
ejpam-3415	376	7	∧	∧	NOUN
ejpam-3415	376	8	c	c	NOUN
ejpam-3415	376	9	=	=	SYM
ejpam-3415	376	10	a	a	PROPN
ejpam-3415	376	11	and	and	CCONJ
ejpam-3415	376	12	u	u	NOUN
ejpam-3415	376	13	∈	∈	PROPN
ejpam-3415	376	14	a	a	PRON
ejpam-3415	376	15	.	.	PUNCT
ejpam-3415	377	1	∨(b	∨(b	ADJ
ejpam-3415	377	2	∧	∧	PROPN
ejpam-3415	377	3	c	c	NOUN
ejpam-3415	377	4	)	)	PUNCT
ejpam-3415	377	5	.	.	PUNCT
ejpam-3415	378	1	since	since	SCONJ
ejpam-3415	378	2	a	a	DET
ejpam-3415	378	3	≤	≤	NUM
ejpam-3415	378	4	c	c	NOUN
ejpam-3415	378	5	,	,	PUNCT
ejpam-3415	378	6	u	u	NOUN
ejpam-3415	378	7	=	=	PUNCT
ejpam-3415	378	8	a	a	DET
ejpam-3415	378	9	∨	∨	X
ejpam-3415	378	10	(	(	PUNCT
ejpam-3415	378	11	b	b	PROPN
ejpam-3415	378	12	∧	∧	PROPN
ejpam-3415	378	13	c	c	NOUN
ejpam-3415	378	14	)	)	PUNCT
ejpam-3415	378	15	and	and	CCONJ
ejpam-3415	378	16	(	(	PUNCT
ejpam-3415	378	17	l,∧,∨	l,∧,∨	X
ejpam-3415	378	18	)	)	PUNCT
ejpam-3415	378	19	is	be	AUX
ejpam-3415	378	20	modular	modular	ADJ
ejpam-3415	378	21	,	,	PUNCT
ejpam-3415	378	22	for	for	ADP
ejpam-3415	378	23	the	the	DET
ejpam-3415	378	24	element	element	NOUN
ejpam-3415	378	25	v	v	NOUN
ejpam-3415	378	26	:	:	PUNCT
ejpam-3415	378	27	=	=	PROPN
ejpam-3415	378	28	a∨b	a∨b	PROPN
ejpam-3415	378	29	∈	∈	PROPN
ejpam-3415	378	30	a	a	PRON
ejpam-3415	378	31	.	.	PUNCT
ejpam-3415	379	1	∨	∨	NUM
ejpam-3415	379	2	b	b	PROPN
ejpam-3415	379	3	of	of	ADP
ejpam-3415	379	4	l	l	NOUN
ejpam-3415	379	5	,	,	PUNCT
ejpam-3415	379	6	we	we	PRON
ejpam-3415	379	7	have	have	VERB
ejpam-3415	379	8	u	u	NOUN
ejpam-3415	379	9	=	=	NOUN
ejpam-3415	379	10	a∨(b∧c	a∨(b∧c	NOUN
ejpam-3415	379	11	)	)	PUNCT
ejpam-3415	380	1	=	=	SYM
ejpam-3415	381	1	(	(	PUNCT
ejpam-3415	381	2	a∨b)∧c	a∨b)∧c	PROPN
ejpam-3415	381	3	=	=	SYM
ejpam-3415	381	4	v∧c	v∧c	PROPN
ejpam-3415	381	5	,	,	PUNCT
ejpam-3415	381	6	so	so	SCONJ
ejpam-3415	381	7	condition	condition	NOUN
ejpam-3415	381	8	(	(	PUNCT
ejpam-3415	381	9	1	1	NUM
ejpam-3415	381	10	)	)	PUNCT
ejpam-3415	381	11	of	of	ADP
ejpam-3415	381	12	definition	definition	NOUN
ejpam-3415	381	13	4.1	4.1	NUM
ejpam-3415	381	14	is	be	AUX
ejpam-3415	381	15	satisfied	satisfied	ADJ
ejpam-3415	381	16	.	.	PUNCT
ejpam-3415	382	1	let	let	VERB
ejpam-3415	382	2	now	now	ADV
ejpam-3415	382	3	a∧	a∧	VERB
ejpam-3415	382	4	c	c	NOUN
ejpam-3415	382	5	=	=	SYM
ejpam-3415	382	6	a	a	PROPN
ejpam-3415	382	7	and	and	CCONJ
ejpam-3415	382	8	u	u	NOUN
ejpam-3415	382	9	∈	∈	PROPN
ejpam-3415	382	10	a	a	PRON
ejpam-3415	382	11	.	.	PUNCT
ejpam-3415	383	1	∨	∨	PROPN
ejpam-3415	383	2	b.	b.	PROPN
ejpam-3415	383	3	since	since	SCONJ
ejpam-3415	383	4	a	a	DET
ejpam-3415	383	5	≤	≤	NUM
ejpam-3415	383	6	c	c	NOUN
ejpam-3415	383	7	,	,	PUNCT
ejpam-3415	383	8	u	u	NOUN
ejpam-3415	383	9	=	=	PUNCT
ejpam-3415	383	10	a	a	DET
ejpam-3415	383	11	∨	∨	NUM
ejpam-3415	383	12	b	b	PROPN
ejpam-3415	383	13	and	and	CCONJ
ejpam-3415	383	14	(	(	PUNCT
ejpam-3415	383	15	l,∧,∨	l,∧,∨	X
ejpam-3415	383	16	)	)	PUNCT
ejpam-3415	383	17	is	be	AUX
ejpam-3415	383	18	modular	modular	ADJ
ejpam-3415	383	19	,	,	PUNCT
ejpam-3415	383	20	we	we	PRON
ejpam-3415	383	21	have	have	VERB
ejpam-3415	383	22	u	u	NOUN
ejpam-3415	383	23	∧	∧	NOUN
ejpam-3415	383	24	c	c	NOUN
ejpam-3415	383	25	=	=	PUNCT
ejpam-3415	383	26	(	(	PUNCT
ejpam-3415	383	27	a	a	DET
ejpam-3415	383	28	∨	∨	NUM
ejpam-3415	383	29	b	b	NOUN
ejpam-3415	383	30	)	)	PUNCT
ejpam-3415	383	31	∧	∧	NOUN
ejpam-3415	383	32	c	c	NOUN
ejpam-3415	383	33	=	=	PUNCT
ejpam-3415	383	34	(	(	PUNCT
ejpam-3415	383	35	a	a	DET
ejpam-3415	383	36	∨	∨	NUM
ejpam-3415	383	37	b	b	NOUN
ejpam-3415	383	38	)	)	PUNCT
ejpam-3415	383	39	∧	∧	PROPN
ejpam-3415	383	40	c	c	NOUN
ejpam-3415	383	41	,	,	PUNCT
ejpam-3415	383	42	then	then	ADV
ejpam-3415	383	43	u	u	PROPN
ejpam-3415	383	44	∧	∧	PROPN
ejpam-3415	383	45	c	c	PROPN
ejpam-3415	383	46	∈	∈	PROPN
ejpam-3415	383	47	a	a	PRON
ejpam-3415	383	48	.	.	PUNCT
ejpam-3415	384	1	∨(b	∨(b	ADJ
ejpam-3415	384	2	∧	∧	PROPN
ejpam-3415	384	3	c	c	NOUN
ejpam-3415	384	4	)	)	PUNCT
ejpam-3415	384	5	and	and	CCONJ
ejpam-3415	384	6	condition	condition	NOUN
ejpam-3415	384	7	(	(	PUNCT
ejpam-3415	384	8	2	2	NUM
ejpam-3415	384	9	)	)	PUNCT
ejpam-3415	384	10	of	of	ADP
ejpam-3415	384	11	definition	definition	NOUN
ejpam-3415	384	12	4.1	4.1	NUM
ejpam-3415	384	13	also	also	ADV
ejpam-3415	384	14	holds	hold	VERB
ejpam-3415	384	15	.	.	PUNCT
ejpam-3415	385	1	niovi	niovi	PROPN
ejpam-3415	385	2	kehayopulu	kehayopulu	PROPN
ejpam-3415	385	3	/	/	SYM
ejpam-3415	385	4	eur	eur	PROPN
ejpam-3415	385	5	.	.	PUNCT
ejpam-3415	386	1	j.	j.	PROPN
ejpam-3415	386	2	pure	pure	PROPN
ejpam-3415	386	3	appl	appl	PROPN
ejpam-3415	386	4	.	.	PROPN
ejpam-3415	386	5	math	math	PROPN
ejpam-3415	386	6	,	,	PUNCT
ejpam-3415	386	7	12	12	NUM
ejpam-3415	386	8	(	(	PUNCT
ejpam-3415	386	9	2	2	NUM
ejpam-3415	386	10	)	)	PUNCT
ejpam-3415	386	11	(	(	PUNCT
ejpam-3415	386	12	2019	2019	NUM
ejpam-3415	386	13	)	)	PUNCT
ejpam-3415	386	14	,	,	PUNCT
ejpam-3415	386	15	252	252	NUM
ejpam-3415	386	16	-	-	SYM
ejpam-3415	386	17	269	269	NUM
ejpam-3415	386	18	266	266	NUM
ejpam-3415	386	19	(	(	PUNCT
ejpam-3415	386	20	2	2	NUM
ejpam-3415	386	21	)	)	PUNCT
ejpam-3415	386	22	let	let	VERB
ejpam-3415	386	23	a	a	DET
ejpam-3415	386	24	∧	∧	NOUN
ejpam-3415	386	25	c	c	NOUN
ejpam-3415	386	26	=	=	SYM
ejpam-3415	386	27	a	a	PROPN
ejpam-3415	386	28	and	and	CCONJ
ejpam-3415	386	29	u	u	NOUN
ejpam-3415	386	30	∈	∈	PROPN
ejpam-3415	386	31	a	a	PRON
ejpam-3415	386	32	.	.	PUNCT
ejpam-3415	387	1	∨(b	∨(b	ADJ
ejpam-3415	387	2	∧	∧	PROPN
ejpam-3415	387	3	c	c	NOUN
ejpam-3415	387	4	)	)	PUNCT
ejpam-3415	387	5	.	.	PUNCT
ejpam-3415	388	1	if	if	SCONJ
ejpam-3415	388	2	u	u	PRON
ejpam-3415	388	3	=	=	NOUN
ejpam-3415	388	4	a	a	PRON
ejpam-3415	388	5	then	then	ADV
ejpam-3415	388	6	,	,	PUNCT
ejpam-3415	388	7	for	for	ADP
ejpam-3415	388	8	the	the	DET
ejpam-3415	388	9	element	element	NOUN
ejpam-3415	388	10	v	v	NOUN
ejpam-3415	388	11	:	:	PUNCT
ejpam-3415	388	12	=	=	PUNCT
ejpam-3415	388	13	a	a	DET
ejpam-3415	388	14	∈	∈	PROPN
ejpam-3415	388	15	a	a	PRON
ejpam-3415	388	16	.	.	PUNCT
ejpam-3415	389	1	∨	∨	NUM
ejpam-3415	389	2	b	b	PROPN
ejpam-3415	389	3	of	of	ADP
ejpam-3415	389	4	l	l	NOUN
ejpam-3415	389	5	,	,	PUNCT
ejpam-3415	389	6	we	we	PRON
ejpam-3415	389	7	have	have	VERB
ejpam-3415	389	8	u	u	NOUN
ejpam-3415	389	9	=	=	PROPN
ejpam-3415	389	10	v	v	ADP
ejpam-3415	389	11	∧	∧	PROPN
ejpam-3415	389	12	c	c	NOUN
ejpam-3415	389	13	;	;	PUNCT
ejpam-3415	389	14	if	if	SCONJ
ejpam-3415	389	15	u	u	PROPN
ejpam-3415	389	16	=	=	SYM
ejpam-3415	389	17	b	b	PROPN
ejpam-3415	389	18	∧	∧	PROPN
ejpam-3415	389	19	c	c	PROPN
ejpam-3415	389	20	then	then	ADV
ejpam-3415	389	21	,	,	PUNCT
ejpam-3415	389	22	for	for	ADP
ejpam-3415	389	23	the	the	DET
ejpam-3415	389	24	element	element	NOUN
ejpam-3415	389	25	v	v	NOUN
ejpam-3415	389	26	:	:	PUNCT
ejpam-3415	390	1	=	=	SYM
ejpam-3415	390	2	b	b	X
ejpam-3415	390	3	∈	∈	PROPN
ejpam-3415	390	4	a	a	PRON
ejpam-3415	390	5	.	.	PUNCT
ejpam-3415	391	1	∨	∨	NUM
ejpam-3415	391	2	b	b	PROPN
ejpam-3415	391	3	,	,	PUNCT
ejpam-3415	391	4	we	we	PRON
ejpam-3415	391	5	have	have	VERB
ejpam-3415	391	6	u	u	NOUN
ejpam-3415	391	7	=	=	PROPN
ejpam-3415	391	8	v	v	ADP
ejpam-3415	391	9	∧	∧	PROPN
ejpam-3415	391	10	c	c	NOUN
ejpam-3415	391	11	;	;	PUNCT
ejpam-3415	391	12	if	if	SCONJ
ejpam-3415	391	13	u	u	PROPN
ejpam-3415	391	14	=	=	SYM
ejpam-3415	391	15	a∨(b∧c	a∨(b∧c	NOUN
ejpam-3415	391	16	)	)	PUNCT
ejpam-3415	391	17	then	then	ADV
ejpam-3415	391	18	,	,	PUNCT
ejpam-3415	391	19	for	for	ADP
ejpam-3415	391	20	the	the	DET
ejpam-3415	391	21	element	element	NOUN
ejpam-3415	391	22	v	v	NOUN
ejpam-3415	391	23	:	:	PUNCT
ejpam-3415	391	24	=	=	PROPN
ejpam-3415	391	25	a∨b	a∨b	PROPN
ejpam-3415	391	26	∈	∈	PROPN
ejpam-3415	391	27	a	a	PRON
ejpam-3415	391	28	.	.	PUNCT
ejpam-3415	392	1	∨	∨	NUM
ejpam-3415	392	2	b	b	PROPN
ejpam-3415	392	3	,	,	PUNCT
ejpam-3415	392	4	we	we	PRON
ejpam-3415	392	5	have	have	VERB
ejpam-3415	392	6	u	u	NOUN
ejpam-3415	392	7	=	=	NOUN
ejpam-3415	392	8	a∨(b∧c	a∨(b∧c	NOUN
ejpam-3415	392	9	)	)	PUNCT
ejpam-3415	392	10	=	=	SYM
ejpam-3415	393	1	(	(	PUNCT
ejpam-3415	393	2	a∨b)∧c	a∨b)∧c	PROPN
ejpam-3415	393	3	=	=	PUNCT
ejpam-3415	393	4	v∧c	v∧c	PROPN
ejpam-3415	393	5	and	and	CCONJ
ejpam-3415	393	6	condition	condition	NOUN
ejpam-3415	393	7	(	(	PUNCT
ejpam-3415	393	8	1	1	NUM
ejpam-3415	393	9	)	)	PUNCT
ejpam-3415	393	10	of	of	ADP
ejpam-3415	393	11	definition	definition	NOUN
ejpam-3415	393	12	4.1	4.1	NUM
ejpam-3415	393	13	holds	hold	NOUN
ejpam-3415	393	14	.	.	PUNCT
ejpam-3415	394	1	let	let	VERB
ejpam-3415	394	2	now	now	ADV
ejpam-3415	394	3	a	a	DET
ejpam-3415	394	4	∧	∧	NOUN
ejpam-3415	394	5	c	c	NOUN
ejpam-3415	394	6	=	=	SYM
ejpam-3415	394	7	a	a	PROPN
ejpam-3415	394	8	and	and	CCONJ
ejpam-3415	394	9	u	u	NOUN
ejpam-3415	394	10	∈	∈	PROPN
ejpam-3415	394	11	a	a	PRON
ejpam-3415	394	12	.	.	PUNCT
ejpam-3415	395	1	∨	∨	PROPN
ejpam-3415	395	2	b.	b.	PROPN
ejpam-3415	396	1	if	if	SCONJ
ejpam-3415	396	2	u	u	PROPN
ejpam-3415	396	3	=	=	X
ejpam-3415	396	4	a	a	PROPN
ejpam-3415	396	5	,	,	PUNCT
ejpam-3415	396	6	then	then	ADV
ejpam-3415	396	7	u∧	u∧	PROPN
ejpam-3415	396	8	c	c	PROPN
ejpam-3415	396	9	=	=	PUNCT
ejpam-3415	396	10	a∧	a∧	NOUN
ejpam-3415	396	11	c	c	NOUN
ejpam-3415	396	12	=	=	PUNCT
ejpam-3415	396	13	a	a	DET
ejpam-3415	396	14	∈	∈	PROPN
ejpam-3415	396	15	a	a	PRON
ejpam-3415	396	16	.	.	PUNCT
ejpam-3415	397	1	∨(b∧	∨(b∧	NOUN
ejpam-3415	397	2	c	c	PROPN
ejpam-3415	397	3	)	)	PUNCT
ejpam-3415	398	1	;	;	PUNCT
ejpam-3415	398	2	if	if	SCONJ
ejpam-3415	398	3	u	u	PROPN
ejpam-3415	398	4	=	=	SYM
ejpam-3415	398	5	b	b	PROPN
ejpam-3415	398	6	,	,	PUNCT
ejpam-3415	398	7	then	then	ADV
ejpam-3415	398	8	u∧	u∧	PROPN
ejpam-3415	398	9	c	c	PROPN
ejpam-3415	398	10	=	=	PUNCT
ejpam-3415	399	1	b∧	b∧	PROPN
ejpam-3415	399	2	c	c	NOUN
ejpam-3415	399	3	∈	∈	PROPN
ejpam-3415	399	4	a	a	PRON
ejpam-3415	399	5	.	.	PUNCT
ejpam-3415	400	1	∨(b∧	∨(b∧	NOUN
ejpam-3415	400	2	c	c	NOUN
ejpam-3415	400	3	)	)	PUNCT
ejpam-3415	400	4	.	.	PUNCT
ejpam-3415	401	1	finally	finally	ADV
ejpam-3415	401	2	,	,	PUNCT
ejpam-3415	401	3	let	let	VERB
ejpam-3415	401	4	u	u	PRON
ejpam-3415	401	5	∈	∈	PROPN
ejpam-3415	401	6	a∨	a∨	PROPN
ejpam-3415	401	7	b.	b.	PROPN
ejpam-3415	402	1	then	then	ADV
ejpam-3415	402	2	we	we	PRON
ejpam-3415	402	3	have	have	VERB
ejpam-3415	402	4	u	u	NOUN
ejpam-3415	402	5	∧	∧	NOUN
ejpam-3415	402	6	c	c	NOUN
ejpam-3415	402	7	=	=	PUNCT
ejpam-3415	402	8	(	(	PUNCT
ejpam-3415	402	9	a	a	DET
ejpam-3415	402	10	∨	∨	NUM
ejpam-3415	402	11	b	b	NOUN
ejpam-3415	402	12	)	)	PUNCT
ejpam-3415	402	13	∧	∧	PROPN
ejpam-3415	402	14	c.	c.	NOUN
ejpam-3415	402	15	on	on	ADP
ejpam-3415	402	16	the	the	DET
ejpam-3415	402	17	other	other	ADJ
ejpam-3415	402	18	hand	hand	NOUN
ejpam-3415	402	19	,	,	PUNCT
ejpam-3415	402	20	since	since	SCONJ
ejpam-3415	402	21	a	a	DET
ejpam-3415	402	22	≤	≤	NUM
ejpam-3415	402	23	c	c	NOUN
ejpam-3415	402	24	and	and	CCONJ
ejpam-3415	402	25	l	l	NOUN
ejpam-3415	402	26	is	be	AUX
ejpam-3415	402	27	modular	modular	ADJ
ejpam-3415	402	28	,	,	PUNCT
ejpam-3415	402	29	we	we	PRON
ejpam-3415	402	30	have	have	VERB
ejpam-3415	402	31	(	(	PUNCT
ejpam-3415	402	32	a	a	DET
ejpam-3415	402	33	∨	∨	NUM
ejpam-3415	402	34	b	b	NOUN
ejpam-3415	402	35	)	)	PUNCT
ejpam-3415	402	36	∧	∧	NOUN
ejpam-3415	402	37	c	c	NOUN
ejpam-3415	402	38	=	=	PUNCT
ejpam-3415	402	39	a	a	DET
ejpam-3415	402	40	∨	∨	NOUN
ejpam-3415	402	41	(	(	PUNCT
ejpam-3415	402	42	b	b	PROPN
ejpam-3415	402	43	∧	∧	PROPN
ejpam-3415	402	44	c	c	NOUN
ejpam-3415	402	45	)	)	PUNCT
ejpam-3415	402	46	.	.	PUNCT
ejpam-3415	403	1	thus	thus	ADV
ejpam-3415	403	2	we	we	PRON
ejpam-3415	403	3	have	have	VERB
ejpam-3415	403	4	u	u	NOUN
ejpam-3415	403	5	∧	∧	NOUN
ejpam-3415	403	6	c	c	NOUN
ejpam-3415	403	7	=	=	PUNCT
ejpam-3415	403	8	a	a	DET
ejpam-3415	403	9	∨	∨	NOUN
ejpam-3415	403	10	(	(	PUNCT
ejpam-3415	403	11	b	b	PROPN
ejpam-3415	403	12	∧	∧	PROPN
ejpam-3415	403	13	c	c	NOUN
ejpam-3415	403	14	)	)	PUNCT
ejpam-3415	403	15	∈	∈	PROPN
ejpam-3415	403	16	a	a	PRON
ejpam-3415	403	17	.	.	PUNCT
ejpam-3415	403	18	∨(b	∨(b	ADJ
ejpam-3415	403	19	∧	∧	PROPN
ejpam-3415	403	20	c	c	NOUN
ejpam-3415	403	21	)	)	PUNCT
ejpam-3415	403	22	.	.	PUNCT
ejpam-3415	404	1	�	�	PROPN
ejpam-3415	404	2	we	we	PRON
ejpam-3415	404	3	apply	apply	VERB
ejpam-3415	404	4	proposition	proposition	NOUN
ejpam-3415	404	5	4.5	4.5	NUM
ejpam-3415	404	6	to	to	ADP
ejpam-3415	404	7	the	the	DET
ejpam-3415	404	8	following	follow	VERB
ejpam-3415	404	9	example	example	NOUN
ejpam-3415	404	10	example	example	NOUN
ejpam-3415	404	11	4.6	4.6	NUM
ejpam-3415	404	12	we	we	PRON
ejpam-3415	404	13	consider	consider	VERB
ejpam-3415	404	14	the	the	DET
ejpam-3415	404	15	modular	modular	ADJ
ejpam-3415	404	16	lattice	lattice	PROPN
ejpam-3415	404	17	l	l	NOUN
ejpam-3415	404	18	of	of	ADP
ejpam-3415	404	19	figure	figure	NOUN
ejpam-3415	404	20	5	5	NUM
ejpam-3415	404	21	.	.	PUNCT
ejpam-3415	405	1	the	the	DET
ejpam-3415	405	2	hyperlattice	hyperlattice	NOUN
ejpam-3415	405	3	that	that	PRON
ejpam-3415	405	4	corresponds	correspond	VERB
ejpam-3415	405	5	to	to	ADP
ejpam-3415	405	6	l	l	NOUN
ejpam-3415	405	7	via	via	ADP
ejpam-3415	405	8	the	the	DET
ejpam-3415	405	9	second	second	ADJ
ejpam-3415	405	10	proof	proof	NOUN
ejpam-3415	405	11	of	of	ADP
ejpam-3415	405	12	proposition	proposition	NOUN
ejpam-3415	405	13	2.5	2.5	NUM
ejpam-3415	405	14	is	be	AUX
ejpam-3415	405	15	given	give	VERB
ejpam-3415	405	16	by	by	ADP
ejpam-3415	405	17	table	table	NOUN
ejpam-3415	405	18	10	10	NUM
ejpam-3415	405	19	and	and	CCONJ
ejpam-3415	405	20	,	,	PUNCT
ejpam-3415	405	21	according	accord	VERB
ejpam-3415	405	22	to	to	ADP
ejpam-3415	405	23	proposition	proposition	NOUN
ejpam-3415	405	24	4.5	4.5	NUM
ejpam-3415	405	25	,	,	PUNCT
ejpam-3415	405	26	this	this	PRON
ejpam-3415	405	27	is	be	AUX
ejpam-3415	405	28	a	a	DET
ejpam-3415	405	29	modular	modular	ADJ
ejpam-3415	405	30	hyperlattice	hyperlattice	NOUN
ejpam-3415	405	31	.	.	PUNCT
ejpam-3415	406	1	a	a	DET
ejpam-3415	406	2	b	b	X
ejpam-3415	406	3	c	c	NOUN
ejpam-3415	406	4	d	d	X
ejpam-3415	406	5	e	e	X
ejpam-3415	406	6	f	f	PROPN
ejpam-3415	406	7	figure	figure	VERB
ejpam-3415	406	8	5	5	NUM
ejpam-3415	406	9	:	:	PUNCT
ejpam-3415	406	10	the	the	DET
ejpam-3415	406	11	modular	modular	ADJ
ejpam-3415	406	12	lattice	lattice	NOUN
ejpam-3415	406	13	of	of	ADP
ejpam-3415	406	14	the	the	DET
ejpam-3415	406	15	example	example	NOUN
ejpam-3415	406	16	4.6	4.6	NUM
ejpam-3415	406	17	.	.	PUNCT
ejpam-3415	406	18	table	table	NOUN
ejpam-3415	406	19	10	10	NUM
ejpam-3415	406	20	:	:	PUNCT
ejpam-3415	406	21	the	the	DET
ejpam-3415	406	22	modular	modular	ADJ
ejpam-3415	406	23	hyperlattice	hyperlattice	NOUN
ejpam-3415	406	24	of	of	ADP
ejpam-3415	406	25	the	the	DET
ejpam-3415	406	26	example	example	NOUN
ejpam-3415	406	27	4.6	4.6	NUM
ejpam-3415	406	28	.	.	PUNCT
ejpam-3415	407	1	∧	∧	NOUN
ejpam-3415	407	2	a	a	DET
ejpam-3415	407	3	b	b	NOUN
ejpam-3415	407	4	c	c	NOUN
ejpam-3415	407	5	d	d	PROPN
ejpam-3415	407	6	e	e	X
ejpam-3415	407	7	f	f	PROPN
ejpam-3415	407	8	a	a	PRON
ejpam-3415	407	9	a	a	DET
ejpam-3415	407	10	a	a	DET
ejpam-3415	407	11	a	a	DET
ejpam-3415	407	12	a	a	DET
ejpam-3415	407	13	a	a	DET
ejpam-3415	407	14	a	a	DET
ejpam-3415	407	15	b	b	NOUN
ejpam-3415	407	16	a	a	DET
ejpam-3415	407	17	b	b	PROPN
ejpam-3415	407	18	b	b	PROPN
ejpam-3415	407	19	a	a	DET
ejpam-3415	407	20	b	b	PROPN
ejpam-3415	407	21	b	b	PROPN
ejpam-3415	407	22	c	c	PROPN
ejpam-3415	407	23	a	a	DET
ejpam-3415	407	24	b	b	NOUN
ejpam-3415	407	25	c	c	NOUN
ejpam-3415	407	26	a	a	DET
ejpam-3415	407	27	b	b	NOUN
ejpam-3415	407	28	c	c	NOUN
ejpam-3415	407	29	d	d	NOUN
ejpam-3415	407	30	a	a	PRON
ejpam-3415	407	31	a	a	DET
ejpam-3415	407	32	a	a	PROPN
ejpam-3415	407	33	d	d	X
ejpam-3415	407	34	d	d	X
ejpam-3415	407	35	d	d	PROPN
ejpam-3415	407	36	e	e	X
ejpam-3415	407	37	a	a	DET
ejpam-3415	407	38	a	a	PRON
ejpam-3415	407	39	b	b	NOUN
ejpam-3415	407	40	d	d	X
ejpam-3415	407	41	e	e	X
ejpam-3415	407	42	e	e	X
ejpam-3415	407	43	f	f	PROPN
ejpam-3415	407	44	a	a	PRON
ejpam-3415	407	45	b	b	X
ejpam-3415	407	46	c	c	NOUN
ejpam-3415	407	47	d	d	X
ejpam-3415	407	48	e	e	X
ejpam-3415	407	49	f	f	X
ejpam-3415	407	50	(	(	PUNCT
ejpam-3415	407	51	a	a	PRON
ejpam-3415	407	52	)	)	PUNCT
ejpam-3415	407	53	niovi	niovi	NOUN
ejpam-3415	407	54	kehayopulu	kehayopulu	ADJ
ejpam-3415	407	55	/	/	SYM
ejpam-3415	407	56	eur	eur	PROPN
ejpam-3415	407	57	.	.	PUNCT
ejpam-3415	408	1	j.	j.	PROPN
ejpam-3415	408	2	pure	pure	PROPN
ejpam-3415	408	3	appl	appl	PROPN
ejpam-3415	408	4	.	.	PROPN
ejpam-3415	408	5	math	math	PROPN
ejpam-3415	408	6	,	,	PUNCT
ejpam-3415	408	7	12	12	NUM
ejpam-3415	408	8	(	(	PUNCT
ejpam-3415	408	9	2	2	NUM
ejpam-3415	408	10	)	)	PUNCT
ejpam-3415	408	11	(	(	PUNCT
ejpam-3415	408	12	2019	2019	NUM
ejpam-3415	408	13	)	)	PUNCT
ejpam-3415	408	14	,	,	PUNCT
ejpam-3415	408	15	252	252	NUM
ejpam-3415	408	16	-	-	SYM
ejpam-3415	408	17	269	269	NUM
ejpam-3415	408	18	267	267	NUM
ejpam-3415	408	19	.	.	PUNCT
ejpam-3415	409	1	∨	∨	NOUN
ejpam-3415	409	2	a	a	DET
ejpam-3415	409	3	b	b	NOUN
ejpam-3415	409	4	c	c	NOUN
ejpam-3415	409	5	d	d	PROPN
ejpam-3415	409	6	e	e	X
ejpam-3415	409	7	f	f	PROPN
ejpam-3415	409	8	a	a	DET
ejpam-3415	409	9	{	{	PUNCT
ejpam-3415	409	10	a	a	NOUN
ejpam-3415	409	11	}	}	PUNCT
ejpam-3415	409	12	{	{	PUNCT
ejpam-3415	409	13	a	a	DET
ejpam-3415	409	14	,	,	PUNCT
ejpam-3415	409	15	b	b	NOUN
ejpam-3415	409	16	}	}	PUNCT
ejpam-3415	409	17	{	{	PUNCT
ejpam-3415	409	18	a	a	PROPN
ejpam-3415	409	19	,	,	PUNCT
ejpam-3415	409	20	c	c	NOUN
ejpam-3415	409	21	}	}	PUNCT
ejpam-3415	409	22	{	{	PUNCT
ejpam-3415	409	23	a	a	DET
ejpam-3415	409	24	,	,	PUNCT
ejpam-3415	409	25	d	d	NOUN
ejpam-3415	409	26	}	}	PUNCT
ejpam-3415	409	27	{	{	PUNCT
ejpam-3415	409	28	a	a	NOUN
ejpam-3415	409	29	,	,	PUNCT
ejpam-3415	409	30	e	e	NOUN
ejpam-3415	409	31	}	}	PUNCT
ejpam-3415	409	32	{	{	PUNCT
ejpam-3415	409	33	a	a	NOUN
ejpam-3415	409	34	,	,	PUNCT
ejpam-3415	409	35	f	f	X
ejpam-3415	409	36	}	}	SYM
ejpam-3415	409	37	b	b	PROPN
ejpam-3415	409	38	{	{	PUNCT
ejpam-3415	409	39	a	a	PROPN
ejpam-3415	409	40	,	,	PUNCT
ejpam-3415	409	41	b	b	NOUN
ejpam-3415	409	42	}	}	PUNCT
ejpam-3415	409	43	{	{	PUNCT
ejpam-3415	409	44	b	b	NOUN
ejpam-3415	409	45	}	}	PUNCT
ejpam-3415	409	46	{	{	PUNCT
ejpam-3415	409	47	b	b	NOUN
ejpam-3415	409	48	,	,	PUNCT
ejpam-3415	409	49	c	c	NOUN
ejpam-3415	409	50	}	}	PUNCT
ejpam-3415	409	51	{	{	PUNCT
ejpam-3415	409	52	b	b	PROPN
ejpam-3415	409	53	,	,	PUNCT
ejpam-3415	409	54	d	d	NOUN
ejpam-3415	409	55	,	,	PUNCT
ejpam-3415	409	56	e	e	NOUN
ejpam-3415	409	57	}	}	PUNCT
ejpam-3415	409	58	{	{	PUNCT
ejpam-3415	409	59	b	b	NOUN
ejpam-3415	409	60	,	,	PUNCT
ejpam-3415	409	61	e	e	NOUN
ejpam-3415	409	62	}	}	PUNCT
ejpam-3415	409	63	{	{	PUNCT
ejpam-3415	409	64	b	b	NOUN
ejpam-3415	409	65	,	,	PUNCT
ejpam-3415	409	66	f	f	PROPN
ejpam-3415	409	67	}	}	PUNCT
ejpam-3415	409	68	c	c	NOUN
ejpam-3415	409	69	{	{	PUNCT
ejpam-3415	409	70	a	a	NOUN
ejpam-3415	409	71	,	,	PUNCT
ejpam-3415	409	72	c	c	NOUN
ejpam-3415	409	73	}	}	PUNCT
ejpam-3415	409	74	{	{	PUNCT
ejpam-3415	409	75	b	b	NOUN
ejpam-3415	409	76	,	,	PUNCT
ejpam-3415	409	77	c	c	NOUN
ejpam-3415	409	78	}	}	PUNCT
ejpam-3415	409	79	{	{	PUNCT
ejpam-3415	409	80	c	c	NOUN
ejpam-3415	409	81	}	}	PUNCT
ejpam-3415	409	82	{	{	PUNCT
ejpam-3415	409	83	c	c	NOUN
ejpam-3415	409	84	,	,	PUNCT
ejpam-3415	409	85	d	d	NOUN
ejpam-3415	409	86	,	,	PUNCT
ejpam-3415	409	87	f	f	NOUN
ejpam-3415	409	88	}	}	PUNCT
ejpam-3415	409	89	{	{	PUNCT
ejpam-3415	409	90	c	c	NOUN
ejpam-3415	409	91	,	,	PUNCT
ejpam-3415	409	92	e	e	NOUN
ejpam-3415	409	93	,	,	PUNCT
ejpam-3415	409	94	f	f	X
ejpam-3415	409	95	}	}	PUNCT
ejpam-3415	409	96	{	{	PUNCT
ejpam-3415	409	97	c	c	NOUN
ejpam-3415	409	98	,	,	PUNCT
ejpam-3415	409	99	f	f	X
ejpam-3415	409	100	}	}	PUNCT
ejpam-3415	409	101	d	d	X
ejpam-3415	409	102	{	{	PUNCT
ejpam-3415	409	103	a	a	PRON
ejpam-3415	409	104	,	,	PUNCT
ejpam-3415	409	105	d	d	NOUN
ejpam-3415	409	106	}	}	PUNCT
ejpam-3415	409	107	{	{	PUNCT
ejpam-3415	409	108	b	b	NOUN
ejpam-3415	409	109	,	,	PUNCT
ejpam-3415	409	110	d	d	NOUN
ejpam-3415	409	111	,	,	PUNCT
ejpam-3415	409	112	e	e	NOUN
ejpam-3415	409	113	}	}	PUNCT
ejpam-3415	409	114	{	{	PUNCT
ejpam-3415	409	115	c	c	NOUN
ejpam-3415	409	116	,	,	PUNCT
ejpam-3415	409	117	d	d	NOUN
ejpam-3415	409	118	,	,	PUNCT
ejpam-3415	409	119	f	f	NOUN
ejpam-3415	409	120	}	}	PUNCT
ejpam-3415	409	121	{	{	PUNCT
ejpam-3415	409	122	d	d	NOUN
ejpam-3415	409	123	}	}	PUNCT
ejpam-3415	409	124	{	{	PUNCT
ejpam-3415	409	125	d	d	NOUN
ejpam-3415	409	126	,	,	PUNCT
ejpam-3415	409	127	e	e	NOUN
ejpam-3415	409	128	}	}	PUNCT
ejpam-3415	409	129	{	{	PUNCT
ejpam-3415	409	130	d	d	NOUN
ejpam-3415	409	131	,	,	PUNCT
ejpam-3415	409	132	f	f	NOUN
ejpam-3415	409	133	}	}	PUNCT
ejpam-3415	409	134	e	e	X
ejpam-3415	409	135	{	{	PUNCT
ejpam-3415	409	136	a	a	PRON
ejpam-3415	409	137	,	,	PUNCT
ejpam-3415	409	138	e	e	NOUN
ejpam-3415	409	139	}	}	PUNCT
ejpam-3415	409	140	{	{	PUNCT
ejpam-3415	409	141	b	b	NOUN
ejpam-3415	409	142	,	,	PUNCT
ejpam-3415	409	143	e	e	NOUN
ejpam-3415	409	144	}	}	PUNCT
ejpam-3415	409	145	{	{	PUNCT
ejpam-3415	409	146	c	c	NOUN
ejpam-3415	409	147	,	,	PUNCT
ejpam-3415	409	148	e	e	NOUN
ejpam-3415	409	149	,	,	PUNCT
ejpam-3415	409	150	f	f	X
ejpam-3415	409	151	}	}	PUNCT
ejpam-3415	409	152	{	{	PUNCT
ejpam-3415	409	153	d	d	NOUN
ejpam-3415	409	154	,	,	PUNCT
ejpam-3415	409	155	e	e	NOUN
ejpam-3415	409	156	}	}	PUNCT
ejpam-3415	409	157	{	{	PUNCT
ejpam-3415	409	158	e	e	NOUN
ejpam-3415	409	159	}	}	PUNCT
ejpam-3415	409	160	{	{	PUNCT
ejpam-3415	409	161	e	e	NOUN
ejpam-3415	409	162	,	,	PUNCT
ejpam-3415	409	163	f	f	PROPN
ejpam-3415	409	164	}	}	PUNCT
ejpam-3415	409	165	f	f	PROPN
ejpam-3415	409	166	{	{	PUNCT
ejpam-3415	409	167	a	a	PROPN
ejpam-3415	409	168	,	,	PUNCT
ejpam-3415	409	169	f	f	NOUN
ejpam-3415	409	170	}	}	PUNCT
ejpam-3415	409	171	{	{	PUNCT
ejpam-3415	409	172	b	b	PROPN
ejpam-3415	409	173	,	,	PUNCT
ejpam-3415	409	174	f	f	NOUN
ejpam-3415	409	175	}	}	PUNCT
ejpam-3415	409	176	{	{	PUNCT
ejpam-3415	409	177	c	c	NOUN
ejpam-3415	409	178	,	,	PUNCT
ejpam-3415	409	179	f	f	NOUN
ejpam-3415	409	180	}	}	PUNCT
ejpam-3415	409	181	{	{	PUNCT
ejpam-3415	409	182	d	d	NOUN
ejpam-3415	409	183	,	,	PUNCT
ejpam-3415	409	184	f	f	NOUN
ejpam-3415	409	185	}	}	PUNCT
ejpam-3415	409	186	{	{	PUNCT
ejpam-3415	409	187	e	e	NOUN
ejpam-3415	409	188	,	,	PUNCT
ejpam-3415	409	189	f	f	NOUN
ejpam-3415	409	190	}	}	PUNCT
ejpam-3415	409	191	{	{	PUNCT
ejpam-3415	409	192	f	f	X
ejpam-3415	409	193	}	}	PUNCT
ejpam-3415	409	194	(	(	PUNCT
ejpam-3415	409	195	b	b	X
ejpam-3415	409	196	)	)	PUNCT
ejpam-3415	409	197	proposition	proposition	NOUN
ejpam-3415	409	198	4.7	4.7	NUM
ejpam-3415	409	199	if	if	SCONJ
ejpam-3415	409	200	(	(	PUNCT
ejpam-3415	409	201	l,∧,∨	l,∧,∨	X
ejpam-3415	409	202	)	)	PUNCT
ejpam-3415	409	203	is	be	AUX
ejpam-3415	409	204	a	a	DET
ejpam-3415	409	205	modular	modular	ADJ
ejpam-3415	409	206	lattice	lattice	NOUN
ejpam-3415	409	207	,	,	PUNCT
ejpam-3415	409	208	then	then	ADV
ejpam-3415	409	209	the	the	DET
ejpam-3415	409	210	hyperlattice	hyperlattice	NOUN
ejpam-3415	409	211	(	(	PUNCT
ejpam-3415	409	212	l,∧	l,∧	NOUN
ejpam-3415	409	213	,	,	PUNCT
ejpam-3415	409	214	.	.	PUNCT
ejpam-3415	410	1	∨	∨	NUM
ejpam-3415	410	2	)	)	PUNCT
ejpam-3415	410	3	,	,	PUNCT
ejpam-3415	410	4	with	with	ADP
ejpam-3415	410	5	the	the	DET
ejpam-3415	410	6	hyperoperation	hyperoperation	NOUN
ejpam-3415	410	7	a	a	PRON
ejpam-3415	410	8	.	.	PUNCT
ejpam-3415	411	1	∨	∨	NUM
ejpam-3415	411	2	b	b	X
ejpam-3415	411	3	:	:	PUNCT
ejpam-3415	411	4	=	=	X
ejpam-3415	411	5	{	{	PUNCT
ejpam-3415	411	6	t	t	NOUN
ejpam-3415	411	7	∈	∈	PROPN
ejpam-3415	411	8	l	l	NOUN
ejpam-3415	412	1	|	|	NOUN
ejpam-3415	412	2	t	t	X
ejpam-3415	412	3	≤	≤	NOUN
ejpam-3415	412	4	a	a	DET
ejpam-3415	412	5	∨	∨	NUM
ejpam-3415	412	6	b	b	NOUN
ejpam-3415	412	7	}	}	PUNCT
ejpam-3415	412	8	satisfies	satisfie	NOUN
ejpam-3415	412	9	condition	condition	NOUN
ejpam-3415	412	10	(	(	PUNCT
ejpam-3415	412	11	2	2	NUM
ejpam-3415	412	12	)	)	PUNCT
ejpam-3415	412	13	of	of	ADP
ejpam-3415	412	14	definition	definition	NOUN
ejpam-3415	412	15	4.1	4.1	NUM
ejpam-3415	412	16	.	.	PUNCT
ejpam-3415	413	1	proof	proof	NOUN
ejpam-3415	413	2	let	let	VERB
ejpam-3415	413	3	a	a	DET
ejpam-3415	413	4	∧	∧	NOUN
ejpam-3415	413	5	c	c	NOUN
ejpam-3415	413	6	=	=	SYM
ejpam-3415	413	7	a	a	PROPN
ejpam-3415	413	8	and	and	CCONJ
ejpam-3415	413	9	u	u	NOUN
ejpam-3415	413	10	∈	∈	PROPN
ejpam-3415	413	11	a	a	PRON
ejpam-3415	413	12	.	.	PUNCT
ejpam-3415	414	1	∨	∨	PROPN
ejpam-3415	414	2	b.	b.	PROPN
ejpam-3415	414	3	then	then	ADV
ejpam-3415	414	4	u	u	X
ejpam-3415	414	5	∧	∧	PROPN
ejpam-3415	414	6	c	c	PROPN
ejpam-3415	414	7	∈	∈	PROPN
ejpam-3415	414	8	a	a	PRON
ejpam-3415	414	9	.	.	PUNCT
ejpam-3415	415	1	∨(b	∨(b	ADJ
ejpam-3415	415	2	∧	∧	PROPN
ejpam-3415	415	3	c	c	NOUN
ejpam-3415	415	4	)	)	PUNCT
ejpam-3415	415	5	.	.	PUNCT
ejpam-3415	416	1	indeed	indeed	ADV
ejpam-3415	416	2	:	:	PUNCT
ejpam-3415	416	3	since	since	SCONJ
ejpam-3415	416	4	u	u	NOUN
ejpam-3415	416	5	≤	≤	VERB
ejpam-3415	416	6	a	a	DET
ejpam-3415	416	7	∨	∨	NUM
ejpam-3415	416	8	b	b	NOUN
ejpam-3415	416	9	,	,	PUNCT
ejpam-3415	416	10	we	we	PRON
ejpam-3415	416	11	have	have	VERB
ejpam-3415	416	12	u∧c	u∧c	NOUN
ejpam-3415	416	13	≤	≤	NOUN
ejpam-3415	416	14	(	(	PUNCT
ejpam-3415	416	15	a∨b)∧c	a∨b)∧c	PROPN
ejpam-3415	416	16	.	.	PROPN
ejpam-3415	417	1	since	since	SCONJ
ejpam-3415	417	2	a	a	DET
ejpam-3415	417	3	≤	≤	NUM
ejpam-3415	417	4	c	c	NOUN
ejpam-3415	417	5	and	and	CCONJ
ejpam-3415	417	6	(	(	PUNCT
ejpam-3415	417	7	l,∧,∨	l,∧,∨	X
ejpam-3415	417	8	)	)	PUNCT
ejpam-3415	417	9	is	be	AUX
ejpam-3415	417	10	modular	modular	ADJ
ejpam-3415	417	11	,	,	PUNCT
ejpam-3415	417	12	we	we	PRON
ejpam-3415	417	13	have	have	VERB
ejpam-3415	417	14	(	(	PUNCT
ejpam-3415	417	15	a∨b)∧c	a∨b)∧c	ADJ
ejpam-3415	417	16	=	=	NOUN
ejpam-3415	417	17	a∨(b∧c	a∨(b∧c	NOUN
ejpam-3415	417	18	)	)	PUNCT
ejpam-3415	417	19	.	.	PUNCT
ejpam-3415	418	1	thus	thus	ADV
ejpam-3415	418	2	we	we	PRON
ejpam-3415	418	3	get	get	VERB
ejpam-3415	418	4	u	u	PRON
ejpam-3415	418	5	∧	∧	PROPN
ejpam-3415	418	6	c	c	NOUN
ejpam-3415	418	7	≤	≤	NOUN
ejpam-3415	418	8	a	a	DET
ejpam-3415	418	9	∨	∨	NOUN
ejpam-3415	418	10	(	(	PUNCT
ejpam-3415	418	11	b	b	PROPN
ejpam-3415	418	12	∧	∧	PROPN
ejpam-3415	418	13	c	c	NOUN
ejpam-3415	418	14	)	)	PUNCT
ejpam-3415	418	15	and	and	CCONJ
ejpam-3415	418	16	so	so	ADV
ejpam-3415	418	17	u	u	X
ejpam-3415	418	18	∧	∧	PROPN
ejpam-3415	418	19	c	c	PROPN
ejpam-3415	418	20	∈	∈	PROPN
ejpam-3415	418	21	a	a	PRON
ejpam-3415	418	22	.	.	PUNCT
ejpam-3415	419	1	∨(b	∨(b	ADJ
ejpam-3415	419	2	∧	∧	PROPN
ejpam-3415	419	3	c	c	NOUN
ejpam-3415	419	4	)	)	PUNCT
ejpam-3415	419	5	.	.	PUNCT
ejpam-3415	420	1	�	�	PROPN
ejpam-3415	420	2	we	we	PRON
ejpam-3415	420	3	apply	apply	VERB
ejpam-3415	420	4	proposition	proposition	NOUN
ejpam-3415	420	5	4.7	4.7	NUM
ejpam-3415	420	6	to	to	ADP
ejpam-3415	420	7	the	the	DET
ejpam-3415	420	8	following	follow	VERB
ejpam-3415	420	9	example	example	NOUN
ejpam-3415	420	10	.	.	PUNCT
ejpam-3415	421	1	example	example	NOUN
ejpam-3415	421	2	4.8	4.8	NUM
ejpam-3415	422	1	we	we	PRON
ejpam-3415	422	2	consider	consider	VERB
ejpam-3415	422	3	the	the	DET
ejpam-3415	422	4	modular	modular	ADJ
ejpam-3415	422	5	lattice	lattice	NOUN
ejpam-3415	422	6	of	of	ADP
ejpam-3415	422	7	figure	figure	NOUN
ejpam-3415	422	8	5	5	NUM
ejpam-3415	422	9	(	(	PUNCT
ejpam-3415	422	10	example	example	NOUN
ejpam-3415	422	11	4.6	4.6	NUM
ejpam-3415	422	12	)	)	PUNCT
ejpam-3415	422	13	.	.	PUNCT
ejpam-3415	423	1	by	by	ADP
ejpam-3415	423	2	proposition	proposition	NOUN
ejpam-3415	423	3	4.7	4.7	NUM
ejpam-3415	423	4	,	,	PUNCT
ejpam-3415	423	5	the	the	DET
ejpam-3415	423	6	hyperlattice	hyperlattice	NOUN
ejpam-3415	423	7	defined	define	VERB
ejpam-3415	423	8	by	by	ADP
ejpam-3415	423	9	table	table	NOUN
ejpam-3415	423	10	11	11	NUM
ejpam-3415	423	11	satisfies	satisfie	NOUN
ejpam-3415	423	12	condition	condition	NOUN
ejpam-3415	423	13	(	(	PUNCT
ejpam-3415	423	14	2	2	NUM
ejpam-3415	423	15	)	)	PUNCT
ejpam-3415	423	16	of	of	ADP
ejpam-3415	423	17	definition	definition	NOUN
ejpam-3415	423	18	4.1	4.1	NUM
ejpam-3415	423	19	.	.	PUNCT
ejpam-3415	423	20	table	table	NOUN
ejpam-3415	423	21	11	11	NUM
ejpam-3415	423	22	:	:	PUNCT
ejpam-3415	423	23	the	the	DET
ejpam-3415	423	24	hyperlattice	hyperlattice	NOUN
ejpam-3415	423	25	of	of	ADP
ejpam-3415	423	26	the	the	DET
ejpam-3415	423	27	example	example	NOUN
ejpam-3415	423	28	4.8	4.8	NUM
ejpam-3415	423	29	.	.	PUNCT
ejpam-3415	424	1	∧	∧	NOUN
ejpam-3415	424	2	a	a	DET
ejpam-3415	424	3	b	b	NOUN
ejpam-3415	424	4	c	c	NOUN
ejpam-3415	424	5	d	d	PROPN
ejpam-3415	424	6	e	e	X
ejpam-3415	424	7	f	f	PROPN
ejpam-3415	424	8	a	a	PRON
ejpam-3415	424	9	a	a	DET
ejpam-3415	424	10	a	a	DET
ejpam-3415	424	11	a	a	DET
ejpam-3415	424	12	a	a	DET
ejpam-3415	424	13	a	a	DET
ejpam-3415	424	14	a	a	DET
ejpam-3415	424	15	b	b	NOUN
ejpam-3415	424	16	a	a	DET
ejpam-3415	424	17	b	b	PROPN
ejpam-3415	424	18	b	b	PROPN
ejpam-3415	424	19	a	a	DET
ejpam-3415	424	20	b	b	PROPN
ejpam-3415	424	21	b	b	PROPN
ejpam-3415	424	22	c	c	PROPN
ejpam-3415	424	23	a	a	DET
ejpam-3415	424	24	b	b	NOUN
ejpam-3415	424	25	c	c	NOUN
ejpam-3415	424	26	a	a	DET
ejpam-3415	424	27	b	b	NOUN
ejpam-3415	424	28	c	c	NOUN
ejpam-3415	424	29	d	d	NOUN
ejpam-3415	424	30	a	a	PRON
ejpam-3415	424	31	a	a	DET
ejpam-3415	424	32	a	a	PROPN
ejpam-3415	424	33	d	d	X
ejpam-3415	424	34	d	d	X
ejpam-3415	424	35	d	d	PROPN
ejpam-3415	424	36	e	e	X
ejpam-3415	424	37	a	a	PRON
ejpam-3415	424	38	a	a	DET
ejpam-3415	424	39	b	b	NOUN
ejpam-3415	424	40	d	d	X
ejpam-3415	424	41	e	e	X
ejpam-3415	424	42	e	e	X
ejpam-3415	424	43	f	f	PROPN
ejpam-3415	424	44	a	a	DET
ejpam-3415	424	45	b	b	X
ejpam-3415	424	46	c	c	NOUN
ejpam-3415	424	47	d	d	X
ejpam-3415	424	48	e	e	X
ejpam-3415	424	49	f	f	X
ejpam-3415	424	50	(	(	PUNCT
ejpam-3415	424	51	a	a	NOUN
ejpam-3415	424	52	)	)	PUNCT
ejpam-3415	424	53	.	.	PUNCT
ejpam-3415	425	1	∨	∨	NOUN
ejpam-3415	425	2	a	a	DET
ejpam-3415	425	3	b	b	NOUN
ejpam-3415	425	4	c	c	NOUN
ejpam-3415	425	5	d	d	PROPN
ejpam-3415	425	6	e	e	X
ejpam-3415	425	7	f	f	PROPN
ejpam-3415	425	8	a	a	DET
ejpam-3415	425	9	{	{	PUNCT
ejpam-3415	425	10	a	a	NOUN
ejpam-3415	425	11	}	}	PUNCT
ejpam-3415	425	12	{	{	PUNCT
ejpam-3415	425	13	a	a	DET
ejpam-3415	425	14	,	,	PUNCT
ejpam-3415	425	15	b	b	NOUN
ejpam-3415	425	16	}	}	PUNCT
ejpam-3415	425	17	{	{	PUNCT
ejpam-3415	425	18	a	a	DET
ejpam-3415	425	19	,	,	PUNCT
ejpam-3415	425	20	b	b	NOUN
ejpam-3415	425	21	,	,	PUNCT
ejpam-3415	425	22	c	c	NOUN
ejpam-3415	425	23	}	}	PUNCT
ejpam-3415	425	24	{	{	PUNCT
ejpam-3415	425	25	a	a	DET
ejpam-3415	425	26	,	,	PUNCT
ejpam-3415	425	27	d	d	NOUN
ejpam-3415	425	28	}	}	PUNCT
ejpam-3415	425	29	{	{	PUNCT
ejpam-3415	425	30	a	a	PRON
ejpam-3415	425	31	,	,	PUNCT
ejpam-3415	425	32	b	b	NOUN
ejpam-3415	425	33	,	,	PUNCT
ejpam-3415	425	34	d	d	NOUN
ejpam-3415	425	35	,	,	PUNCT
ejpam-3415	425	36	e	e	NOUN
ejpam-3415	425	37	}	}	PUNCT
ejpam-3415	425	38	s	s	PART
ejpam-3415	425	39	b	b	NOUN
ejpam-3415	425	40	{	{	PUNCT
ejpam-3415	425	41	a	a	PROPN
ejpam-3415	425	42	,	,	PUNCT
ejpam-3415	425	43	b	b	NOUN
ejpam-3415	425	44	}	}	PUNCT
ejpam-3415	425	45	{	{	PUNCT
ejpam-3415	425	46	a	a	DET
ejpam-3415	425	47	,	,	PUNCT
ejpam-3415	425	48	b	b	NOUN
ejpam-3415	425	49	}	}	PUNCT
ejpam-3415	425	50	{	{	PUNCT
ejpam-3415	425	51	a	a	DET
ejpam-3415	425	52	,	,	PUNCT
ejpam-3415	425	53	b	b	NOUN
ejpam-3415	425	54	,	,	PUNCT
ejpam-3415	425	55	c	c	NOUN
ejpam-3415	425	56	}	}	PUNCT
ejpam-3415	425	57	{	{	PUNCT
ejpam-3415	425	58	a	a	PRON
ejpam-3415	425	59	,	,	PUNCT
ejpam-3415	425	60	b	b	NOUN
ejpam-3415	425	61	,	,	PUNCT
ejpam-3415	425	62	d	d	NOUN
ejpam-3415	425	63	,	,	PUNCT
ejpam-3415	425	64	e	e	NOUN
ejpam-3415	425	65	}	}	PUNCT
ejpam-3415	425	66	{	{	PUNCT
ejpam-3415	425	67	a	a	PRON
ejpam-3415	425	68	,	,	PUNCT
ejpam-3415	425	69	b	b	NOUN
ejpam-3415	425	70	,	,	PUNCT
ejpam-3415	425	71	d	d	NOUN
ejpam-3415	425	72	,	,	PUNCT
ejpam-3415	425	73	e	e	NOUN
ejpam-3415	425	74	}	}	PUNCT
ejpam-3415	425	75	s	s	PART
ejpam-3415	425	76	c	c	NOUN
ejpam-3415	425	77	{	{	PUNCT
ejpam-3415	425	78	a	a	PRON
ejpam-3415	425	79	,	,	PUNCT
ejpam-3415	425	80	b	b	NOUN
ejpam-3415	425	81	,	,	PUNCT
ejpam-3415	425	82	c	c	NOUN
ejpam-3415	425	83	}	}	PUNCT
ejpam-3415	425	84	{	{	PUNCT
ejpam-3415	425	85	a	a	DET
ejpam-3415	425	86	,	,	PUNCT
ejpam-3415	425	87	b	b	NOUN
ejpam-3415	425	88	,	,	PUNCT
ejpam-3415	425	89	c	c	NOUN
ejpam-3415	425	90	}	}	PUNCT
ejpam-3415	425	91	{	{	PUNCT
ejpam-3415	425	92	a	a	PRON
ejpam-3415	425	93	,	,	PUNCT
ejpam-3415	425	94	b	b	NOUN
ejpam-3415	425	95	,	,	PUNCT
ejpam-3415	425	96	c	c	NOUN
ejpam-3415	425	97	}	}	PUNCT
ejpam-3415	425	98	s	s	PART
ejpam-3415	425	99	s	s	NOUN
ejpam-3415	425	100	s	s	X
ejpam-3415	425	101	d	d	X
ejpam-3415	425	102	{	{	PUNCT
ejpam-3415	425	103	a	a	PROPN
ejpam-3415	425	104	,	,	PUNCT
ejpam-3415	425	105	d	d	NOUN
ejpam-3415	425	106	}	}	PUNCT
ejpam-3415	425	107	{	{	PUNCT
ejpam-3415	425	108	a	a	PRON
ejpam-3415	425	109	,	,	PUNCT
ejpam-3415	425	110	b	b	NOUN
ejpam-3415	425	111	,	,	PUNCT
ejpam-3415	425	112	d	d	NOUN
ejpam-3415	425	113	,	,	PUNCT
ejpam-3415	425	114	e	e	NOUN
ejpam-3415	425	115	}	}	PUNCT
ejpam-3415	425	116	s	s	PART
ejpam-3415	425	117	{	{	PUNCT
ejpam-3415	425	118	a	a	DET
ejpam-3415	425	119	,	,	PUNCT
ejpam-3415	425	120	d	d	NOUN
ejpam-3415	425	121	}	}	PUNCT
ejpam-3415	425	122	{	{	PUNCT
ejpam-3415	425	123	a	a	PRON
ejpam-3415	425	124	,	,	PUNCT
ejpam-3415	425	125	b	b	NOUN
ejpam-3415	425	126	,	,	PUNCT
ejpam-3415	425	127	d	d	NOUN
ejpam-3415	425	128	,	,	PUNCT
ejpam-3415	425	129	e	e	NOUN
ejpam-3415	425	130	}	}	PUNCT
ejpam-3415	425	131	s	s	PART
ejpam-3415	425	132	e	e	NOUN
ejpam-3415	425	133	{	{	PUNCT
ejpam-3415	425	134	a	a	PRON
ejpam-3415	425	135	,	,	PUNCT
ejpam-3415	425	136	b	b	NOUN
ejpam-3415	425	137	,	,	PUNCT
ejpam-3415	425	138	d	d	NOUN
ejpam-3415	425	139	,	,	PUNCT
ejpam-3415	425	140	e	e	NOUN
ejpam-3415	425	141	}	}	PUNCT
ejpam-3415	425	142	{	{	PUNCT
ejpam-3415	425	143	a	a	PRON
ejpam-3415	425	144	,	,	PUNCT
ejpam-3415	425	145	b	b	NOUN
ejpam-3415	425	146	,	,	PUNCT
ejpam-3415	425	147	d	d	NOUN
ejpam-3415	425	148	,	,	PUNCT
ejpam-3415	425	149	e	e	NOUN
ejpam-3415	425	150	}	}	PUNCT
ejpam-3415	425	151	s	s	PART
ejpam-3415	425	152	{	{	PUNCT
ejpam-3415	425	153	a	a	PRON
ejpam-3415	425	154	,	,	PUNCT
ejpam-3415	425	155	b	b	NOUN
ejpam-3415	425	156	,	,	PUNCT
ejpam-3415	425	157	d	d	NOUN
ejpam-3415	425	158	,	,	PUNCT
ejpam-3415	425	159	e	e	NOUN
ejpam-3415	425	160	}	}	PUNCT
ejpam-3415	425	161	{	{	PUNCT
ejpam-3415	425	162	a	a	PRON
ejpam-3415	425	163	,	,	PUNCT
ejpam-3415	425	164	b	b	NOUN
ejpam-3415	425	165	,	,	PUNCT
ejpam-3415	425	166	d	d	NOUN
ejpam-3415	425	167	,	,	PUNCT
ejpam-3415	425	168	e	e	NOUN
ejpam-3415	425	169	}	}	PUNCT
ejpam-3415	425	170	s	s	PART
ejpam-3415	425	171	f	f	X
ejpam-3415	425	172	s	s	X
ejpam-3415	425	173	s	s	X
ejpam-3415	425	174	s	s	X
ejpam-3415	425	175	s	s	X
ejpam-3415	425	176	s	s	X
ejpam-3415	425	177	s	s	X
ejpam-3415	425	178	(	(	PUNCT
ejpam-3415	425	179	b	b	NOUN
ejpam-3415	425	180	)	)	PUNCT
ejpam-3415	425	181	references	reference	NOUN
ejpam-3415	425	182	268	268	NUM
ejpam-3415	425	183	the	the	DET
ejpam-3415	425	184	question	question	NOUN
ejpam-3415	425	185	is	be	AUX
ejpam-3415	425	186	:	:	PUNCT
ejpam-3415	425	187	are	be	AUX
ejpam-3415	425	188	there	there	PRON
ejpam-3415	425	189	modular	modular	ADJ
ejpam-3415	425	190	lattices	lattice	NOUN
ejpam-3415	425	191	for	for	ADP
ejpam-3415	425	192	which	which	PRON
ejpam-3415	425	193	the	the	DET
ejpam-3415	425	194	hypersemigroup	hypersemigroup	NOUN
ejpam-3415	425	195	defined	define	VERB
ejpam-3415	425	196	in	in	ADP
ejpam-3415	425	197	proposition	proposition	NOUN
ejpam-3415	425	198	4.7	4.7	NUM
ejpam-3415	425	199	satisfies	satisfie	NOUN
ejpam-3415	425	200	condition	condition	NOUN
ejpam-3415	425	201	(	(	PUNCT
ejpam-3415	425	202	1	1	NUM
ejpam-3415	425	203	)	)	PUNCT
ejpam-3415	425	204	of	of	ADP
ejpam-3415	425	205	definition	definition	NOUN
ejpam-3415	425	206	4.1	4.1	NUM
ejpam-3415	425	207	?	?	PUNCT
ejpam-3415	426	1	as	as	SCONJ
ejpam-3415	426	2	answer	answer	NOUN
ejpam-3415	426	3	is	be	AUX
ejpam-3415	426	4	given	give	VERB
ejpam-3415	426	5	by	by	ADP
ejpam-3415	426	6	the	the	DET
ejpam-3415	426	7	following	follow	VERB
ejpam-3415	426	8	proposition	proposition	NOUN
ejpam-3415	426	9	.	.	PUNCT
ejpam-3415	427	1	proposition	proposition	NOUN
ejpam-3415	427	2	4.9	4.9	NUM
ejpam-3415	427	3	let	let	VERB
ejpam-3415	427	4	(	(	PUNCT
ejpam-3415	427	5	l,∧,∨	l,∧,∨	ADV
ejpam-3415	427	6	)	)	PUNCT
ejpam-3415	427	7	be	be	AUX
ejpam-3415	427	8	a	a	DET
ejpam-3415	427	9	modular	modular	ADJ
ejpam-3415	427	10	lattice	lattice	NOUN
ejpam-3415	427	11	and	and	CCONJ
ejpam-3415	427	12	(	(	PUNCT
ejpam-3415	427	13	l,∧	l,∧	NOUN
ejpam-3415	427	14	,	,	PUNCT
ejpam-3415	427	15	.	.	PUNCT
ejpam-3415	428	1	∨	∨	NUM
ejpam-3415	428	2	)	)	PUNCT
ejpam-3415	428	3	the	the	DET
ejpam-3415	428	4	hyperlattice	hyperlattice	NOUN
ejpam-3415	428	5	with	with	ADP
ejpam-3415	428	6	the	the	DET
ejpam-3415	428	7	hypeoperation	hypeoperation	NOUN
ejpam-3415	428	8	a	a	PRON
ejpam-3415	428	9	.	.	PUNCT
ejpam-3415	429	1	∨	∨	NUM
ejpam-3415	429	2	b	b	X
ejpam-3415	429	3	:	:	PUNCT
ejpam-3415	429	4	=	=	X
ejpam-3415	429	5	{	{	PUNCT
ejpam-3415	429	6	t	t	NOUN
ejpam-3415	429	7	∈	∈	PROPN
ejpam-3415	429	8	l	l	NOUN
ejpam-3415	430	1	|	|	NOUN
ejpam-3415	430	2	t	t	X
ejpam-3415	430	3	≤	≤	NOUN
ejpam-3415	430	4	a	a	DET
ejpam-3415	430	5	∨	∨	NUM
ejpam-3415	430	6	b	b	NOUN
ejpam-3415	430	7	}	}	PUNCT
ejpam-3415	430	8	satisfying	satisfy	VERB
ejpam-3415	430	9	the	the	DET
ejpam-3415	430	10	property	property	NOUN
ejpam-3415	430	11	v	v	ADP
ejpam-3415	430	12	∈	∈	PROPN
ejpam-3415	430	13	a	a	PRON
ejpam-3415	430	14	.	.	PUNCT
ejpam-3415	431	1	∨	∨	NUM
ejpam-3415	431	2	b	b	NOUN
ejpam-3415	431	3	and	and	CCONJ
ejpam-3415	431	4	u	u	PROPN
ejpam-3415	431	5	∈	∈	PROPN
ejpam-3415	431	6	a	a	PRON
ejpam-3415	431	7	.	.	PUNCT
ejpam-3415	432	1	∨(b	∨(b	ADJ
ejpam-3415	432	2	∧	∧	PROPN
ejpam-3415	432	3	c	c	NOUN
ejpam-3415	432	4	)	)	PUNCT
ejpam-3415	432	5	imply	imply	VERB
ejpam-3415	432	6	v	v	ADP
ejpam-3415	432	7	∧	∧	PROPN
ejpam-3415	432	8	c	c	NOUN
ejpam-3415	432	9	≤	≤	NOUN
ejpam-3415	432	10	u	u	NOUN
ejpam-3415	432	11	(	(	PUNCT
ejpam-3415	432	12	4.1	4.1	NUM
ejpam-3415	432	13	)	)	PUNCT
ejpam-3415	432	14	then	then	ADV
ejpam-3415	432	15	(	(	PUNCT
ejpam-3415	432	16	l,∧	l,∧	NOUN
ejpam-3415	432	17	,	,	PUNCT
ejpam-3415	432	18	.	.	PUNCT
ejpam-3415	433	1	∨	∨	NUM
ejpam-3415	433	2	)	)	PUNCT
ejpam-3415	433	3	satisfies	satisfy	VERB
ejpam-3415	433	4	condition	condition	NOUN
ejpam-3415	433	5	(	(	PUNCT
ejpam-3415	433	6	1	1	NUM
ejpam-3415	433	7	)	)	PUNCT
ejpam-3415	433	8	of	of	ADP
ejpam-3415	433	9	definition	definition	NOUN
ejpam-3415	433	10	4.1	4.1	NUM
ejpam-3415	433	11	.	.	PUNCT
ejpam-3415	434	1	proof	proof	NOUN
ejpam-3415	434	2	let	let	VERB
ejpam-3415	434	3	a	a	DET
ejpam-3415	434	4	∧	∧	NOUN
ejpam-3415	434	5	c	c	NOUN
ejpam-3415	434	6	=	=	SYM
ejpam-3415	434	7	a	a	PROPN
ejpam-3415	434	8	and	and	CCONJ
ejpam-3415	434	9	u	u	NOUN
ejpam-3415	434	10	∈	∈	PROPN
ejpam-3415	434	11	a	a	PRON
ejpam-3415	434	12	.	.	PUNCT
ejpam-3415	435	1	∨(b	∨(b	ADJ
ejpam-3415	435	2	∧	∧	PROPN
ejpam-3415	435	3	c	c	NOUN
ejpam-3415	435	4	)	)	PUNCT
ejpam-3415	435	5	.	.	PUNCT
ejpam-3415	436	1	then	then	ADV
ejpam-3415	436	2	we	we	PRON
ejpam-3415	436	3	have	have	VERB
ejpam-3415	436	4	u	u	NOUN
ejpam-3415	436	5	≤	≤	NOUN
ejpam-3415	436	6	a	a	DET
ejpam-3415	436	7	∨	∨	NOUN
ejpam-3415	436	8	(	(	PUNCT
ejpam-3415	436	9	b	b	PROPN
ejpam-3415	436	10	∧	∧	PROPN
ejpam-3415	436	11	c	c	NOUN
ejpam-3415	436	12	)	)	PUNCT
ejpam-3415	436	13	=	=	NOUN
ejpam-3415	436	14	(	(	PUNCT
ejpam-3415	436	15	a	a	DET
ejpam-3415	436	16	∨	∨	NUM
ejpam-3415	436	17	b	b	NOUN
ejpam-3415	436	18	)	)	PUNCT
ejpam-3415	436	19	∧	∧	PROPN
ejpam-3415	436	20	c	c	PROPN
ejpam-3415	436	21	and	and	CCONJ
ejpam-3415	436	22	,	,	PUNCT
ejpam-3415	436	23	for	for	ADP
ejpam-3415	436	24	the	the	DET
ejpam-3415	436	25	element	element	NOUN
ejpam-3415	436	26	v	v	NOUN
ejpam-3415	436	27	:	:	PUNCT
ejpam-3415	436	28	=	=	PUNCT
ejpam-3415	436	29	a	a	DET
ejpam-3415	436	30	∨	∨	NUM
ejpam-3415	436	31	b	b	NOUN
ejpam-3415	436	32	,	,	PUNCT
ejpam-3415	436	33	we	we	PRON
ejpam-3415	436	34	have	have	VERB
ejpam-3415	436	35	u	u	NOUN
ejpam-3415	436	36	≤	≤	X
ejpam-3415	436	37	v	v	ADP
ejpam-3415	436	38	∧	∧	PROPN
ejpam-3415	436	39	c.	c.	NOUN
ejpam-3415	436	40	on	on	ADP
ejpam-3415	436	41	the	the	DET
ejpam-3415	436	42	other	other	ADJ
ejpam-3415	436	43	hand	hand	NOUN
ejpam-3415	436	44	,	,	PUNCT
ejpam-3415	436	45	since	since	SCONJ
ejpam-3415	436	46	v	v	NUM
ejpam-3415	436	47	∈	∈	PROPN
ejpam-3415	436	48	a	a	PRON
ejpam-3415	436	49	.	.	PUNCT
ejpam-3415	437	1	∨	∨	NUM
ejpam-3415	437	2	b	b	NOUN
ejpam-3415	437	3	and	and	CCONJ
ejpam-3415	437	4	u	u	PROPN
ejpam-3415	437	5	∈	∈	PROPN
ejpam-3415	437	6	a	a	PRON
ejpam-3415	437	7	.	.	PUNCT
ejpam-3415	438	1	∨(b∧	∨(b∧	NOUN
ejpam-3415	438	2	c	c	NOUN
ejpam-3415	438	3	)	)	PUNCT
ejpam-3415	438	4	,	,	PUNCT
ejpam-3415	438	5	by	by	ADP
ejpam-3415	438	6	(	(	PUNCT
ejpam-3415	438	7	4.1	4.1	NUM
ejpam-3415	438	8	)	)	PUNCT
ejpam-3415	438	9	,	,	PUNCT
ejpam-3415	438	10	we	we	PRON
ejpam-3415	438	11	have	have	VERB
ejpam-3415	438	12	v	v	NUM
ejpam-3415	438	13	∧	∧	PROPN
ejpam-3415	438	14	c	c	NOUN
ejpam-3415	438	15	≤	≤	X
ejpam-3415	439	1	u.	u.	VERB
ejpam-3415	440	1	hence	hence	ADV
ejpam-3415	440	2	we	we	PRON
ejpam-3415	440	3	obtain	obtain	VERB
ejpam-3415	440	4	u	u	NOUN
ejpam-3415	440	5	=	=	X
ejpam-3415	440	6	v	v	ADP
ejpam-3415	440	7	∧	∧	PROPN
ejpam-3415	440	8	c	c	NOUN
ejpam-3415	440	9	and	and	CCONJ
ejpam-3415	440	10	property	property	NOUN
ejpam-3415	440	11	(	(	PUNCT
ejpam-3415	440	12	1	1	NUM
ejpam-3415	440	13	)	)	PUNCT
ejpam-3415	440	14	of	of	ADP
ejpam-3415	440	15	definition	definition	NOUN
ejpam-3415	440	16	4.1	4.1	NUM
ejpam-3415	440	17	is	be	AUX
ejpam-3415	440	18	satisfied	satisfied	ADJ
ejpam-3415	440	19	.	.	PUNCT
ejpam-3415	441	1	�	�	NOUN
ejpam-3415	441	2	by	by	ADP
ejpam-3415	441	3	propositions	proposition	NOUN
ejpam-3415	441	4	4.7	4.7	NUM
ejpam-3415	441	5	and	and	CCONJ
ejpam-3415	441	6	4.9	4.9	NUM
ejpam-3415	441	7	we	we	PRON
ejpam-3415	441	8	have	have	VERB
ejpam-3415	441	9	the	the	DET
ejpam-3415	441	10	following	follow	VERB
ejpam-3415	441	11	corollary	corollary	NOUN
ejpam-3415	441	12	4.10	4.10	NUM
ejpam-3415	441	13	let	let	NOUN
ejpam-3415	441	14	(	(	PUNCT
ejpam-3415	441	15	l,∧,∨	l,∧,∨	ADV
ejpam-3415	441	16	)	)	PUNCT
ejpam-3415	441	17	be	be	AUX
ejpam-3415	441	18	a	a	DET
ejpam-3415	441	19	modular	modular	ADJ
ejpam-3415	441	20	lattice	lattice	NOUN
ejpam-3415	441	21	and	and	CCONJ
ejpam-3415	441	22	“	"	PUNCT
ejpam-3415	441	23	.	.	PUNCT
ejpam-3415	442	1	∨	∨	NOUN
ejpam-3415	442	2	”	"	PUNCT
ejpam-3415	442	3	the	the	DET
ejpam-3415	442	4	hyperoperation	hyperoperation	NOUN
ejpam-3415	442	5	on	on	ADP
ejpam-3415	442	6	l	l	NOUN
ejpam-3415	442	7	defined	define	VERB
ejpam-3415	442	8	by	by	ADP
ejpam-3415	442	9	a	a	PRON
ejpam-3415	442	10	.	.	PUNCT
ejpam-3415	443	1	∨	∨	NUM
ejpam-3415	443	2	b	b	X
ejpam-3415	443	3	:	:	PUNCT
ejpam-3415	443	4	=	=	X
ejpam-3415	443	5	{	{	PUNCT
ejpam-3415	443	6	t	t	NOUN
ejpam-3415	443	7	∈	∈	PROPN
ejpam-3415	443	8	l	l	NOUN
ejpam-3415	444	1	|	|	NOUN
ejpam-3415	444	2	t	t	X
ejpam-3415	444	3	≤	≤	NOUN
ejpam-3415	444	4	a	a	DET
ejpam-3415	444	5	∨	∨	NUM
ejpam-3415	444	6	b	b	NOUN
ejpam-3415	444	7	}	}	PUNCT
ejpam-3415	444	8	and	and	CCONJ
ejpam-3415	444	9	having	have	VERB
ejpam-3415	444	10	the	the	DET
ejpam-3415	444	11	property	property	NOUN
ejpam-3415	444	12	(	(	PUNCT
ejpam-3415	444	13	4.1	4.1	NUM
ejpam-3415	444	14	)	)	PUNCT
ejpam-3415	444	15	.	.	PUNCT
ejpam-3415	445	1	then	then	ADV
ejpam-3415	445	2	(	(	PUNCT
ejpam-3415	445	3	l,∧	l,∧	NOUN
ejpam-3415	445	4	,	,	PUNCT
ejpam-3415	445	5	.	.	PUNCT
ejpam-3415	445	6	∨	∨	NUM
ejpam-3415	445	7	)	)	PUNCT
ejpam-3415	445	8	is	be	AUX
ejpam-3415	445	9	a	a	DET
ejpam-3415	445	10	modular	modular	ADJ
ejpam-3415	445	11	hyperlattice	hyperlattice	NOUN
ejpam-3415	445	12	.	.	PUNCT
ejpam-3415	446	1	remark	remark	VERB
ejpam-3415	446	2	4.11	4.11	NUM
ejpam-3415	446	3	the	the	DET
ejpam-3415	446	4	hyperlattice	hyperlattice	NOUN
ejpam-3415	446	5	of	of	ADP
ejpam-3415	446	6	table	table	NOUN
ejpam-3415	446	7	11	11	NUM
ejpam-3415	446	8	does	do	AUX
ejpam-3415	446	9	not	not	PART
ejpam-3415	446	10	satisfy	satisfy	VERB
ejpam-3415	446	11	condition	condition	NOUN
ejpam-3415	446	12	(	(	PUNCT
ejpam-3415	446	13	4.1	4.1	NUM
ejpam-3415	446	14	)	)	PUNCT
ejpam-3415	446	15	;	;	PUNCT
ejpam-3415	446	16	indeed	indeed	ADV
ejpam-3415	446	17	,	,	PUNCT
ejpam-3415	446	18	we	we	PRON
ejpam-3415	446	19	have	have	VERB
ejpam-3415	446	20	b	b	NUM
ejpam-3415	446	21	∈	∈	PROPN
ejpam-3415	446	22	d	d	NOUN
ejpam-3415	446	23	.	.	PUNCT
ejpam-3415	447	1	∨	∨	NUM
ejpam-3415	447	2	b	b	PROPN
ejpam-3415	447	3	and	and	CCONJ
ejpam-3415	447	4	d	d	PROPN
ejpam-3415	447	5	∈	∈	PROPN
ejpam-3415	448	1	d	d	X
ejpam-3415	448	2	.	.	PUNCT
ejpam-3415	449	1	∨(b	∨(b	ADJ
ejpam-3415	449	2	∧	∧	PROPN
ejpam-3415	449	3	c	c	NOUN
ejpam-3415	449	4	)	)	PUNCT
ejpam-3415	450	1	but	but	CCONJ
ejpam-3415	450	2	b	b	X
ejpam-3415	450	3	∧	∧	PROPN
ejpam-3415	450	4	c	c	PROPN
ejpam-3415	450	5	6≤	6≤	NUM
ejpam-3415	450	6	d.	d.	NOUN
ejpam-3415	450	7	however	however	ADV
ejpam-3415	450	8	it	it	PRON
ejpam-3415	450	9	seems	seem	VERB
ejpam-3415	450	10	to	to	PART
ejpam-3415	450	11	be	be	AUX
ejpam-3415	450	12	modular	modular	ADJ
ejpam-3415	450	13	;	;	PUNCT
ejpam-3415	450	14	write	write	VERB
ejpam-3415	450	15	a	a	DET
ejpam-3415	450	16	program	program	NOUN
ejpam-3415	450	17	to	to	PART
ejpam-3415	450	18	check	check	VERB
ejpam-3415	450	19	it	it	PRON
ejpam-3415	450	20	.	.	PUNCT
ejpam-3415	451	1	problem	problem	NOUN
ejpam-3415	451	2	4.12	4.12	NUM
ejpam-3415	451	3	write	write	VERB
ejpam-3415	451	4	a	a	DET
ejpam-3415	451	5	program	program	NOUN
ejpam-3415	451	6	to	to	PART
ejpam-3415	451	7	show	show	VERB
ejpam-3415	451	8	that	that	SCONJ
ejpam-3415	451	9	the	the	DET
ejpam-3415	451	10	hyperlattice	hyperlattice	NOUN
ejpam-3415	451	11	considered	consider	VERB
ejpam-3415	451	12	in	in	ADP
ejpam-3415	451	13	proposition	proposition	NOUN
ejpam-3415	451	14	4.7	4.7	NUM
ejpam-3415	451	15	does	do	AUX
ejpam-3415	451	16	not	not	PART
ejpam-3415	451	17	satisfy	satisfy	VERB
ejpam-3415	451	18	condition	condition	NOUN
ejpam-3415	451	19	(	(	PUNCT
ejpam-3415	451	20	1	1	NUM
ejpam-3415	451	21	)	)	PUNCT
ejpam-3415	451	22	of	of	ADP
ejpam-3415	451	23	definition	definition	NOUN
ejpam-3415	451	24	4.1	4.1	NUM
ejpam-3415	451	25	in	in	ADP
ejpam-3415	451	26	general	general	ADJ
ejpam-3415	451	27	.	.	PUNCT
ejpam-3415	452	1	problem	problem	NOUN
ejpam-3415	452	2	4.13	4.13	NUM
ejpam-3415	452	3	write	write	VERB
ejpam-3415	452	4	a	a	DET
ejpam-3415	452	5	program	program	NOUN
ejpam-3415	452	6	to	to	PART
ejpam-3415	452	7	check	check	VERB
ejpam-3415	452	8	if	if	SCONJ
ejpam-3415	452	9	the	the	DET
ejpam-3415	452	10	hyperlattices	hyperlattice	NOUN
ejpam-3415	452	11	of	of	ADP
ejpam-3415	452	12	the	the	DET
ejpam-3415	452	13	examples	example	NOUN
ejpam-3415	452	14	of	of	ADP
ejpam-3415	452	15	the	the	DET
ejpam-3415	452	16	paper	paper	NOUN
ejpam-3415	452	17	satisfy	satisfy	VERB
ejpam-3415	452	18	the	the	DET
ejpam-3415	452	19	relation	relation	NOUN
ejpam-3415	452	20	a	a	DET
ejpam-3415	452	21	∈	∈	PROPN
ejpam-3415	452	22	a	a	DET
ejpam-3415	452	23	∨	∨	PROPN
ejpam-3415	452	24	b	b	PROPN
ejpam-3415	452	25	⇒	⇒	NOUN
ejpam-3415	452	26	a	a	DET
ejpam-3415	452	27	∧	∧	PROPN
ejpam-3415	452	28	b	b	PROPN
ejpam-3415	452	29	=	=	PROPN
ejpam-3415	452	30	b.	b.	PROPN
ejpam-3415	453	1	i	i	PRON
ejpam-3415	453	2	would	would	AUX
ejpam-3415	453	3	like	like	VERB
ejpam-3415	453	4	to	to	PART
ejpam-3415	453	5	thank	thank	VERB
ejpam-3415	453	6	the	the	DET
ejpam-3415	453	7	two	two	NUM
ejpam-3415	453	8	anonymous	anonymous	ADJ
ejpam-3415	453	9	referees	referee	NOUN
ejpam-3415	453	10	for	for	ADP
ejpam-3415	453	11	their	their	PRON
ejpam-3415	453	12	time	time	NOUN
ejpam-3415	453	13	to	to	PART
ejpam-3415	453	14	read	read	VERB
ejpam-3415	453	15	the	the	DET
ejpam-3415	453	16	paper	paper	NOUN
ejpam-3415	453	17	carefully	carefully	ADV
ejpam-3415	453	18	,	,	PUNCT
ejpam-3415	453	19	the	the	DET
ejpam-3415	453	20	useful	useful	ADJ
ejpam-3415	453	21	discussions	discussion	NOUN
ejpam-3415	453	22	through	through	ADP
ejpam-3415	453	23	the	the	DET
ejpam-3415	453	24	editor	editor	NOUN
ejpam-3415	453	25	we	we	PRON
ejpam-3415	453	26	had	have	VERB
ejpam-3415	453	27	,	,	PUNCT
ejpam-3415	453	28	and	and	CCONJ
ejpam-3415	453	29	their	their	PRON
ejpam-3415	453	30	prompt	prompt	ADJ
ejpam-3415	453	31	reply	reply	NOUN
ejpam-3415	453	32	.	.	PUNCT
ejpam-3415	454	1	references	reference	NOUN
ejpam-3415	454	2	[	[	X
ejpam-3415	454	3	1	1	NUM
ejpam-3415	454	4	]	]	X
ejpam-3415	454	5	ameri	ameri	PROPN
ejpam-3415	454	6	,	,	PUNCT
ejpam-3415	454	7	r.	r.	PROPN
ejpam-3415	454	8	,	,	PUNCT
ejpam-3415	454	9	amiri	amiri	PROPN
ejpam-3415	454	10	-	-	PUNCT
ejpam-3415	454	11	bideshki	bideshki	PROPN
ejpam-3415	454	12	,	,	PUNCT
ejpam-3415	454	13	m.	m.	NOUN
ejpam-3415	454	14	,	,	PUNCT
ejpam-3415	454	15	saeid	saeid	PROPN
ejpam-3415	454	16	,	,	PUNCT
ejpam-3415	454	17	a.b	a.b	PROPN
ejpam-3415	454	18	.	.	PROPN
ejpam-3415	454	19	,	,	PUNCT
ejpam-3415	454	20	hoskova	hoskova	PROPN
ejpam-3415	454	21	-	-	PUNCT
ejpam-3415	454	22	mayerova	mayerova	PROPN
ejpam-3415	454	23	,	,	PUNCT
ejpam-3415	454	24	s.	s.	PROPN
ejpam-3415	454	25	:	:	PUNCT
ejpam-3415	454	26	prime	prime	ADJ
ejpam-3415	454	27	filters	filter	NOUN
ejpam-3415	454	28	of	of	ADP
ejpam-3415	454	29	hyperlattices	hyperlattice	NOUN
ejpam-3415	454	30	.	.	PUNCT
ejpam-3415	455	1	an	an	DET
ejpam-3415	455	2	.	.	PUNCT
ejpam-3415	455	3	st	st	PROPN
ejpam-3415	455	4	.	.	PROPN
ejpam-3415	455	5	univ	univ	PROPN
ejpam-3415	455	6	.	.	PUNCT
ejpam-3415	456	1	ovidius	ovidius	PROPN
ejpam-3415	456	2	constanta	constanta	PROPN
ejpam-3415	456	3	24(2	24(2	PROPN
ejpam-3415	456	4	)	)	PUNCT
ejpam-3415	456	5	,	,	PUNCT
ejpam-3415	456	6	15–26	15–26	NUM
ejpam-3415	456	7	(	(	PUNCT
ejpam-3415	456	8	2016	2016	NUM
ejpam-3415	456	9	)	)	PUNCT
ejpam-3415	457	1	[	[	X
ejpam-3415	457	2	2	2	X
ejpam-3415	457	3	]	]	X
ejpam-3415	457	4	ameri	ameri	PROPN
ejpam-3415	457	5	r	r	NOUN
ejpam-3415	457	6	,	,	PUNCT
ejpam-3415	457	7	amiri	amiri	NOUN
ejpam-3415	457	8	-	-	PUNCT
ejpam-3415	457	9	bideshki	bideshki	PROPN
ejpam-3415	457	10	m.	m.	NOUN
ejpam-3415	457	11	,	,	PUNCT
ejpam-3415	457	12	s.	s.	PROPN
ejpam-3415	457	13	hoskova	hoskova	PROPN
ejpam-3415	457	14	-	-	PUNCT
ejpam-3415	457	15	mayerova	mayerova	PROPN
ejpam-3415	457	16	s.	s.	PROPN
ejpam-3415	457	17	,	,	PUNCT
ejpam-3415	457	18	saeid	saeid	PROPN
ejpam-3415	457	19	a.b	a.b	PROPN
ejpam-3415	457	20	.	.	PROPN
ejpam-3415	457	21	:	:	PUNCT
ejpam-3415	457	22	distributive	distributive	ADJ
ejpam-3415	457	23	and	and	CCONJ
ejpam-3415	457	24	dual	dual	ADJ
ejpam-3415	457	25	distributive	distributive	ADJ
ejpam-3415	457	26	elements	element	NOUN
ejpam-3415	457	27	in	in	ADP
ejpam-3415	457	28	hyperlattices	hyperlattice	NOUN
ejpam-3415	457	29	.	.	PUNCT
ejpam-3415	458	1	an	an	DET
ejpam-3415	458	2	.	.	PUNCT
ejpam-3415	458	3	st	st	PROPN
ejpam-3415	458	4	.	.	PROPN
ejpam-3415	458	5	univ	univ	PROPN
ejpam-3415	458	6	.	.	PUNCT
ejpam-3415	459	1	ovidius	ovidius	PROPN
ejpam-3415	459	2	constanta	constanta	PROPN
ejpam-3415	459	3	25(3	25(3	PROPN
ejpam-3415	459	4	)	)	PUNCT
ejpam-3415	459	5	,	,	PUNCT
ejpam-3415	459	6	25–36	25–36	NUM
ejpam-3415	459	7	(	(	PUNCT
ejpam-3415	459	8	2017	2017	NUM
ejpam-3415	459	9	)	)	PUNCT
ejpam-3415	460	1	[	[	X
ejpam-3415	460	2	3	3	NUM
ejpam-3415	460	3	]	]	X
ejpam-3415	460	4	koguep	koguep	NOUN
ejpam-3415	460	5	,	,	PUNCT
ejpam-3415	460	6	b.b.n	b.b.n	NOUN
ejpam-3415	460	7	.	.	PROPN
ejpam-3415	460	8	,	,	PUNCT
ejpam-3415	460	9	nkuimi	nkuimi	PROPN
ejpam-3415	460	10	,	,	PUNCT
ejpam-3415	460	11	c.	c.	PROPN
ejpam-3415	460	12	,	,	PUNCT
ejpam-3415	460	13	lele	lele	PROPN
ejpam-3415	460	14	,	,	PUNCT
ejpam-3415	460	15	c.	c.	PROPN
ejpam-3415	460	16	:	:	PUNCT
ejpam-3415	460	17	on	on	ADP
ejpam-3415	460	18	fuzzy	fuzzy	ADJ
ejpam-3415	460	19	ideals	ideal	NOUN
ejpam-3415	460	20	of	of	ADP
ejpam-3415	460	21	hyperlattice	hyperlattice	NOUN
ejpam-3415	460	22	.	.	PUNCT
ejpam-3415	461	1	int	int	NOUN
ejpam-3415	461	2	.	.	PUNCT
ejpam-3415	462	1	j.	j.	PROPN
ejpam-3415	462	2	algebra	algebra	PROPN
ejpam-3415	462	3	2(13–16	2(13–16	NUM
ejpam-3415	462	4	)	)	PUNCT
ejpam-3415	462	5	,	,	PUNCT
ejpam-3415	462	6	739–750	739–750	NUM
ejpam-3415	462	7	(	(	PUNCT
ejpam-3415	462	8	2008	2008	NUM
ejpam-3415	462	9	)	)	PUNCT
ejpam-3415	463	1	[	[	X
ejpam-3415	463	2	4	4	NUM
ejpam-3415	463	3	]	]	PUNCT
ejpam-3415	463	4	konstantinidou	konstantinidou	NOUN
ejpam-3415	463	5	,	,	PUNCT
ejpam-3415	463	6	m.	m.	NOUN
ejpam-3415	463	7	,	,	PUNCT
ejpam-3415	463	8	mittas	mitta	NOUN
ejpam-3415	463	9	,	,	PUNCT
ejpam-3415	463	10	j.	j.	PROPN
ejpam-3415	463	11	:	:	PUNCT
ejpam-3415	463	12	an	an	DET
ejpam-3415	463	13	introduction	introduction	NOUN
ejpam-3415	463	14	to	to	ADP
ejpam-3415	463	15	the	the	DET
ejpam-3415	463	16	theory	theory	NOUN
ejpam-3415	463	17	of	of	ADP
ejpam-3415	463	18	hyperlattices	hyperlattice	NOUN
ejpam-3415	463	19	.	.	PUNCT
ejpam-3415	464	1	math	math	NOUN
ejpam-3415	464	2	.	.	PUNCT
ejpam-3415	465	1	balkanica	balkanica	PROPN
ejpam-3415	465	2	7	7	NUM
ejpam-3415	465	3	,	,	PUNCT
ejpam-3415	465	4	187–193	187–193	NUM
ejpam-3415	465	5	(	(	PUNCT
ejpam-3415	465	6	1977	1977	NUM
ejpam-3415	465	7	)	)	PUNCT
ejpam-3415	465	8	references	reference	NOUN
ejpam-3415	465	9	269	269	NUM
ejpam-3415	465	10	[	[	SYM
ejpam-3415	465	11	5	5	NUM
ejpam-3415	465	12	]	]	PUNCT
ejpam-3415	465	13	konstantinidou	konstantinidou	NOUN
ejpam-3415	465	14	-	-	PUNCT
ejpam-3415	465	15	serafimidou	serafimidou	NOUN
ejpam-3415	465	16	,	,	PUNCT
ejpam-3415	465	17	m.	m.	NOUN
ejpam-3415	465	18	:	:	PUNCT
ejpam-3415	465	19	modular	modular	ADJ
ejpam-3415	465	20	hyperlattices	hyperlattice	NOUN
ejpam-3415	465	21	.	.	PUNCT
ejpam-3415	466	1	prakt	prakt	NOUN
ejpam-3415	466	2	.	.	PUNCT
ejpam-3415	467	1	akad	akad	PROPN
ejpam-3415	467	2	.	.	PUNCT
ejpam-3415	468	1	athenon	athenon	PROPN
ejpam-3415	468	2	53	53	NUM
ejpam-3415	468	3	(	(	PUNCT
ejpam-3415	468	4	1978	1978	NUM
ejpam-3415	468	5	)	)	PUNCT
ejpam-3415	468	6	,	,	PUNCT
ejpam-3415	468	7	202–218	202–218	NUM
ejpam-3415	468	8	(	(	PUNCT
ejpam-3415	468	9	1979	1979	NUM
ejpam-3415	468	10	)	)	PUNCT
ejpam-3415	469	1	[	[	X
ejpam-3415	469	2	6	6	NUM
ejpam-3415	469	3	]	]	PUNCT
ejpam-3415	469	4	konstantinidou	konstantinidou	NOUN
ejpam-3415	469	5	-	-	PUNCT
ejpam-3415	469	6	serafimidou	serafimidou	NOUN
ejpam-3415	469	7	,	,	PUNCT
ejpam-3415	469	8	m.	m.	NOUN
ejpam-3415	469	9	:	:	PUNCT
ejpam-3415	469	10	distributive	distributive	ADJ
ejpam-3415	469	11	and	and	CCONJ
ejpam-3415	469	12	complemented	complemented	ADJ
ejpam-3415	469	13	hyperlattices	hyperlattice	NOUN
ejpam-3415	469	14	.	.	PUNCT
ejpam-3415	470	1	prakt	prakt	NOUN
ejpam-3415	470	2	.	.	PUNCT
ejpam-3415	471	1	akad	akad	PROPN
ejpam-3415	471	2	.	.	PUNCT
ejpam-3415	472	1	athenon	athenon	PROPN
ejpam-3415	472	2	56	56	NUM
ejpam-3415	472	3	(	(	PUNCT
ejpam-3415	472	4	1981	1981	NUM
ejpam-3415	472	5	)	)	PUNCT
ejpam-3415	472	6	,	,	PUNCT
ejpam-3415	472	7	339–360	339–360	NUM
ejpam-3415	472	8	(	(	PUNCT
ejpam-3415	472	9	1982	1982	NUM
ejpam-3415	472	10	)	)	PUNCT
ejpam-3415	473	1	[	[	X
ejpam-3415	473	2	7	7	X
ejpam-3415	473	3	]	]	X
ejpam-3415	473	4	konstantinidou	konstantinidou	NOUN
ejpam-3415	473	5	,	,	PUNCT
ejpam-3415	473	6	m.	m.	NOUN
ejpam-3415	473	7	,	,	PUNCT
ejpam-3415	473	8	serafimidis	serafimidi	NOUN
ejpam-3415	473	9	,	,	PUNCT
ejpam-3415	473	10	m.	m.	NOUN
ejpam-3415	473	11	:	:	PUNCT
ejpam-3415	473	12	un	un	PROPN
ejpam-3415	473	13	théorèm	théorèm	ADJ
ejpam-3415	473	14	d’isomorphisme	d’isomorphisme	PROPN
ejpam-3415	473	15	concernant	concernant	X
ejpam-3415	473	16	des	des	PROPN
ejpam-3415	473	17	classes	classes	PROPN
ejpam-3415	473	18	particulières	particulière	NOUN
ejpam-3415	473	19	d’hypertreillis	d’hypertreillis	PROPN
ejpam-3415	473	20	.	.	PUNCT
ejpam-3415	474	1	honorary	honorary	ADJ
ejpam-3415	474	2	volume	volume	NOUN
ejpam-3415	474	3	dedicated	dedicate	VERB
ejpam-3415	474	4	to	to	ADP
ejpam-3415	474	5	j.d	j.d	PROPN
ejpam-3415	474	6	.	.	PROPN
ejpam-3415	474	7	mittas	mittas	PROPN
ejpam-3415	474	8	,	,	PUNCT
ejpam-3415	474	9	aristotle	aristotle	PROPN
ejpam-3415	474	10	univ	univ	PROPN
ejpam-3415	474	11	.	.	PROPN
ejpam-3415	474	12	of	of	ADP
ejpam-3415	474	13	thessaloniki	thessaloniki	PROPN
ejpam-3415	474	14	,	,	PUNCT
ejpam-3415	474	15	faculty	faculty	NOUN
ejpam-3415	474	16	of	of	ADP
ejpam-3415	474	17	engineering	engineering	NOUN
ejpam-3415	474	18	,	,	PUNCT
ejpam-3415	474	19	dept	dept	NOUN
ejpam-3415	474	20	.	.	PROPN
ejpam-3415	474	21	math	math	NOUN
ejpam-3415	474	22	.	.	PUNCT
ejpam-3415	475	1	263–271	263–271	NUM
ejpam-3415	475	2	(	(	PUNCT
ejpam-3415	475	3	1999–2000	1999–2000	NUM
ejpam-3415	475	4	)	)	PUNCT