id	sid	tid	token	lemma	pos
ap-1398	1	1	acta	acta	PROPN
ap-1398	1	2	polytechnica	polytechnica	PROPN
ap-1398	1	3	vol	vol	NOUN
ap-1398	1	4	.	.	PUNCT
ap-1398	2	1	51	51	NUM
ap-1398	2	2	no	no	INTJ
ap-1398	2	3	.	.	PUNCT
ap-1398	3	1	4/2011	4/2011	NUM
ap-1398	3	2	two	two	NUM
ap-1398	3	3	remarks	remark	NOUN
ap-1398	3	4	to	to	ADP
ap-1398	3	5	bifullness	bifullness	NOUN
ap-1398	3	6	of	of	ADP
ap-1398	3	7	centers	center	NOUN
ap-1398	3	8	of	of	ADP
ap-1398	3	9	archimedean	archimedean	PROPN
ap-1398	3	10	atomic	atomic	PROPN
ap-1398	3	11	lattice	lattice	PROPN
ap-1398	3	12	effect	effect	PROPN
ap-1398	3	13	algebras	algebras	PROPN
ap-1398	3	14	m.	m.	PROPN
ap-1398	3	15	kalina	kalina	PROPN
ap-1398	3	16	abstract	abstract	PROPN
ap-1398	3	17	lattice	lattice	PROPN
ap-1398	3	18	effect	effect	NOUN
ap-1398	3	19	algebras	algebra	NOUN
ap-1398	3	20	generalize	generalize	VERB
ap-1398	3	21	orthomodular	orthomodular	ADJ
ap-1398	3	22	lattices	lattice	NOUN
ap-1398	3	23	as	as	ADV
ap-1398	3	24	well	well	ADV
ap-1398	3	25	as	as	ADP
ap-1398	3	26	mv	mv	NOUN
ap-1398	3	27	-	-	PUNCT
ap-1398	3	28	algebras	algebras	X
ap-1398	3	29	.	.	PUNCT
ap-1398	4	1	this	this	PRON
ap-1398	4	2	means	mean	VERB
ap-1398	4	3	that	that	SCONJ
ap-1398	4	4	within	within	ADP
ap-1398	4	5	lattice	lattice	ADJ
ap-1398	4	6	effect	effect	NOUN
ap-1398	4	7	algebras	algebra	VERB
ap-1398	4	8	it	it	PRON
ap-1398	4	9	is	be	AUX
ap-1398	4	10	possible	possible	ADJ
ap-1398	4	11	to	to	PART
ap-1398	4	12	model	model	VERB
ap-1398	4	13	such	such	ADJ
ap-1398	4	14	effects	effect	NOUN
ap-1398	4	15	as	as	ADP
ap-1398	4	16	unsharpness	unsharpness	ADJ
ap-1398	4	17	(	(	PUNCT
ap-1398	4	18	fuzziness	fuzziness	NOUN
ap-1398	4	19	)	)	PUNCT
ap-1398	4	20	and/or	and/or	CCONJ
ap-1398	4	21	non	non	NOUN
ap-1398	4	22	-	-	NOUN
ap-1398	4	23	compatibility	compatibility	NOUN
ap-1398	4	24	.	.	PUNCT
ap-1398	5	1	the	the	DET
ap-1398	5	2	main	main	ADJ
ap-1398	5	3	problem	problem	NOUN
ap-1398	5	4	is	be	AUX
ap-1398	5	5	the	the	DET
ap-1398	5	6	existence	existence	NOUN
ap-1398	5	7	of	of	ADP
ap-1398	5	8	a	a	DET
ap-1398	5	9	state	state	NOUN
ap-1398	5	10	.	.	PUNCT
ap-1398	6	1	there	there	PRON
ap-1398	6	2	are	be	VERB
ap-1398	6	3	lattice	lattice	ADJ
ap-1398	6	4	effect	effect	NOUN
ap-1398	6	5	algebras	algebra	NOUN
ap-1398	6	6	with	with	ADP
ap-1398	6	7	no	no	DET
ap-1398	6	8	state	state	NOUN
ap-1398	6	9	.	.	PUNCT
ap-1398	7	1	for	for	ADP
ap-1398	7	2	this	this	DET
ap-1398	7	3	reason	reason	NOUN
ap-1398	7	4	we	we	PRON
ap-1398	7	5	need	need	VERB
ap-1398	7	6	some	some	DET
ap-1398	7	7	conditions	condition	NOUN
ap-1398	7	8	that	that	PRON
ap-1398	7	9	simplify	simplify	VERB
ap-1398	7	10	checking	check	VERB
ap-1398	7	11	the	the	DET
ap-1398	7	12	existence	existence	NOUN
ap-1398	7	13	of	of	ADP
ap-1398	7	14	a	a	DET
ap-1398	7	15	state	state	NOUN
ap-1398	7	16	.	.	PUNCT
ap-1398	8	1	if	if	SCONJ
ap-1398	8	2	we	we	PRON
ap-1398	8	3	know	know	VERB
ap-1398	8	4	that	that	SCONJ
ap-1398	8	5	the	the	DET
ap-1398	8	6	center	center	NOUN
ap-1398	8	7	c(e	c(e	NOUN
ap-1398	8	8	)	)	PUNCT
ap-1398	8	9	of	of	ADP
ap-1398	8	10	an	an	DET
ap-1398	8	11	atomic	atomic	ADJ
ap-1398	8	12	archimedean	archimedean	PROPN
ap-1398	8	13	lattice	lattice	PROPN
ap-1398	8	14	effect	effect	PROPN
ap-1398	8	15	algebra	algebra	NOUN
ap-1398	8	16	e	e	X
ap-1398	8	17	(	(	PUNCT
ap-1398	8	18	which	which	PRON
ap-1398	8	19	is	be	AUX
ap-1398	8	20	again	again	ADV
ap-1398	8	21	atomic	atomic	ADJ
ap-1398	8	22	)	)	PUNCT
ap-1398	8	23	is	be	AUX
ap-1398	8	24	a	a	DET
ap-1398	8	25	bifull	bifull	ADJ
ap-1398	8	26	sublattice	sublattice	NOUN
ap-1398	8	27	of	of	ADP
ap-1398	8	28	e	e	NOUN
ap-1398	8	29	,	,	PUNCT
ap-1398	8	30	then	then	ADV
ap-1398	8	31	we	we	PRON
ap-1398	8	32	are	be	AUX
ap-1398	8	33	able	able	ADJ
ap-1398	8	34	to	to	PART
ap-1398	8	35	represent	represent	VERB
ap-1398	8	36	e	e	PROPN
ap-1398	8	37	as	as	ADP
ap-1398	8	38	a	a	DET
ap-1398	8	39	subdirect	subdirect	NOUN
ap-1398	8	40	product	product	NOUN
ap-1398	8	41	of	of	ADP
ap-1398	8	42	lattice	lattice	ADJ
ap-1398	8	43	effect	effect	NOUN
ap-1398	8	44	algebras	algebras	X
ap-1398	8	45	ei	ei	ADP
ap-1398	8	46	where	where	SCONJ
ap-1398	8	47	the	the	DET
ap-1398	8	48	top	top	ADJ
ap-1398	8	49	element	element	NOUN
ap-1398	8	50	of	of	ADP
ap-1398	8	51	each	each	DET
ap-1398	8	52	one	one	NUM
ap-1398	8	53	of	of	ADP
ap-1398	8	54	ei	ei	NOUN
ap-1398	8	55	is	be	AUX
ap-1398	8	56	an	an	DET
ap-1398	8	57	atom	atom	NOUN
ap-1398	8	58	of	of	ADP
ap-1398	8	59	c(e	c(e	NOUN
ap-1398	8	60	)	)	PUNCT
ap-1398	8	61	.	.	PUNCT
ap-1398	9	1	in	in	ADP
ap-1398	9	2	this	this	DET
ap-1398	9	3	case	case	NOUN
ap-1398	9	4	it	it	PRON
ap-1398	9	5	is	be	AUX
ap-1398	9	6	enough	enough	ADJ
ap-1398	9	7	if	if	SCONJ
ap-1398	9	8	we	we	PRON
ap-1398	9	9	find	find	VERB
ap-1398	9	10	a	a	DET
ap-1398	9	11	state	state	NOUN
ap-1398	9	12	at	at	ADP
ap-1398	9	13	least	least	ADJ
ap-1398	9	14	in	in	ADP
ap-1398	9	15	one	one	NUM
ap-1398	9	16	of	of	ADP
ap-1398	9	17	ei	ei	NOUN
ap-1398	10	1	and	and	CCONJ
ap-1398	10	2	we	we	PRON
ap-1398	10	3	are	be	AUX
ap-1398	10	4	able	able	ADJ
ap-1398	10	5	to	to	PART
ap-1398	10	6	extend	extend	VERB
ap-1398	10	7	this	this	DET
ap-1398	10	8	state	state	NOUN
ap-1398	10	9	to	to	ADP
ap-1398	10	10	the	the	DET
ap-1398	10	11	whole	whole	ADJ
ap-1398	10	12	lattice	lattice	PROPN
ap-1398	10	13	effect	effect	NOUN
ap-1398	10	14	algebra	algebra	PROPN
ap-1398	10	15	e.	e.	PROPN
ap-1398	10	16	in	in	ADP
ap-1398	10	17	[	[	X
ap-1398	10	18	8	8	NUM
ap-1398	10	19	]	]	PUNCT
ap-1398	10	20	an	an	DET
ap-1398	10	21	atomic	atomic	ADJ
ap-1398	10	22	lattice	lattice	NOUN
ap-1398	10	23	effect	effect	NOUN
ap-1398	10	24	algebra	algebra	NOUN
ap-1398	10	25	e	e	X
ap-1398	10	26	(	(	PUNCT
ap-1398	10	27	in	in	ADP
ap-1398	10	28	fact	fact	NOUN
ap-1398	10	29	,	,	PUNCT
ap-1398	10	30	an	an	DET
ap-1398	10	31	atomic	atomic	ADJ
ap-1398	10	32	orthomodular	orthomodular	NOUN
ap-1398	10	33	lattice	lattice	NOUN
ap-1398	10	34	)	)	PUNCT
ap-1398	10	35	with	with	ADP
ap-1398	10	36	atomic	atomic	ADJ
ap-1398	10	37	center	center	NOUN
ap-1398	10	38	c(e	c(e	PROPN
ap-1398	10	39	)	)	PUNCT
ap-1398	10	40	was	be	AUX
ap-1398	10	41	constructed	construct	VERB
ap-1398	10	42	,	,	PUNCT
ap-1398	10	43	where	where	SCONJ
ap-1398	10	44	c(e	c(e	NOUN
ap-1398	10	45	)	)	PUNCT
ap-1398	10	46	is	be	AUX
ap-1398	10	47	not	not	PART
ap-1398	10	48	a	a	DET
ap-1398	10	49	bifull	bifull	ADJ
ap-1398	10	50	sublattice	sublattice	NOUN
ap-1398	10	51	of	of	ADP
ap-1398	10	52	e.	e.	PROPN
ap-1398	10	53	in	in	ADP
ap-1398	10	54	this	this	DET
ap-1398	10	55	paper	paper	NOUN
ap-1398	10	56	we	we	PRON
ap-1398	10	57	show	show	VERB
ap-1398	10	58	that	that	SCONJ
ap-1398	10	59	for	for	ADP
ap-1398	10	60	atomic	atomic	ADJ
ap-1398	10	61	lattice	lattice	PROPN
ap-1398	10	62	effect	effect	NOUN
ap-1398	10	63	algebras	algebras	PROPN
ap-1398	10	64	e	e	PROPN
ap-1398	10	65	(	(	PUNCT
ap-1398	10	66	atomic	atomic	ADJ
ap-1398	10	67	orthomodular	orthomodular	NOUN
ap-1398	10	68	lattices	lattice	NOUN
ap-1398	10	69	)	)	PUNCT
ap-1398	10	70	neither	neither	CCONJ
ap-1398	10	71	completeness	completeness	NOUN
ap-1398	10	72	(	(	PUNCT
ap-1398	10	73	and	and	CCONJ
ap-1398	10	74	atomicity	atomicity	NOUN
ap-1398	10	75	)	)	PUNCT
ap-1398	10	76	of	of	ADP
ap-1398	10	77	c(e	c(e	NOUN
ap-1398	10	78	)	)	PUNCT
ap-1398	10	79	nor	nor	CCONJ
ap-1398	10	80	σ	σ	NOUN
ap-1398	10	81	-	-	PUNCT
ap-1398	10	82	completeness	completeness	NOUN
ap-1398	10	83	of	of	ADP
ap-1398	10	84	e	e	NOUN
ap-1398	10	85	are	be	AUX
ap-1398	10	86	sufficient	sufficient	ADJ
ap-1398	10	87	conditions	condition	NOUN
ap-1398	10	88	for	for	ADP
ap-1398	10	89	c(e	c(e	NOUN
ap-1398	10	90	)	)	PUNCT
ap-1398	10	91	to	to	PART
ap-1398	10	92	be	be	AUX
ap-1398	10	93	a	a	DET
ap-1398	10	94	bifull	bifull	ADJ
ap-1398	10	95	sublattice	sublattice	NOUN
ap-1398	10	96	of	of	ADP
ap-1398	10	97	e.	e.	PROPN
ap-1398	10	98	keywords	keywords	PROPN
ap-1398	10	99	:	:	PUNCT
ap-1398	10	100	lattice	lattice	ADJ
ap-1398	10	101	effect	effect	NOUN
ap-1398	10	102	algebra	algebra	NOUN
ap-1398	10	103	,	,	PUNCT
ap-1398	10	104	orthomodular	orthomodular	ADJ
ap-1398	10	105	lattice	lattice	NOUN
ap-1398	10	106	,	,	PUNCT
ap-1398	10	107	center	center	NOUN
ap-1398	10	108	,	,	PUNCT
ap-1398	10	109	atom	atom	NOUN
ap-1398	10	110	,	,	PUNCT
ap-1398	10	111	bifullness	bifullness	NOUN
ap-1398	10	112	.	.	PUNCT
ap-1398	11	1	1	1	NUM
ap-1398	11	2	preliminaries	preliminary	NOUN
ap-1398	11	3	effect	effect	NOUN
ap-1398	11	4	algebras	algebra	NOUN
ap-1398	11	5	,	,	PUNCT
ap-1398	11	6	introduced	introduce	VERB
ap-1398	11	7	by	by	ADP
ap-1398	11	8	d.	d.	PROPN
ap-1398	11	9	j.	j.	PROPN
ap-1398	11	10	foulis	foulis	PROPN
ap-1398	11	11	and	and	CCONJ
ap-1398	11	12	m.	m.	PROPN
ap-1398	11	13	k.	k.	PROPN
ap-1398	11	14	bennett	bennett	PROPN
ap-1398	12	1	[	[	X
ap-1398	12	2	3	3	NUM
ap-1398	12	3	]	]	PUNCT
ap-1398	12	4	,	,	PUNCT
ap-1398	12	5	have	have	VERB
ap-1398	12	6	their	their	PRON
ap-1398	12	7	importance	importance	NOUN
ap-1398	12	8	in	in	ADP
ap-1398	12	9	the	the	DET
ap-1398	12	10	investigation	investigation	NOUN
ap-1398	12	11	of	of	ADP
ap-1398	12	12	uncertainty	uncertainty	NOUN
ap-1398	12	13	.	.	PUNCT
ap-1398	13	1	lattice	lattice	PROPN
ap-1398	13	2	ordered	order	VERB
ap-1398	13	3	effect	effect	NOUN
ap-1398	13	4	algebras	algebra	NOUN
ap-1398	13	5	generalize	generalize	VERB
ap-1398	13	6	orthomodular	orthomodular	ADJ
ap-1398	13	7	lattices	lattice	NOUN
ap-1398	13	8	and	and	CCONJ
ap-1398	13	9	mvalgebras	mvalgebra	NOUN
ap-1398	13	10	.	.	PUNCT
ap-1398	14	1	thus	thus	ADV
ap-1398	14	2	they	they	PRON
ap-1398	14	3	may	may	AUX
ap-1398	14	4	include	include	VERB
ap-1398	14	5	non	non	ADJ
ap-1398	14	6	-	-	ADJ
ap-1398	14	7	compatible	compatible	ADJ
ap-1398	14	8	pairs	pair	NOUN
ap-1398	14	9	of	of	ADP
ap-1398	14	10	elements	element	NOUN
ap-1398	14	11	as	as	ADV
ap-1398	14	12	well	well	ADV
ap-1398	14	13	as	as	ADP
ap-1398	14	14	unsharp	unsharp	ADJ
ap-1398	14	15	elements	element	NOUN
ap-1398	14	16	.	.	PUNCT
ap-1398	15	1	definition	definition	NOUN
ap-1398	15	2	1	1	NUM
ap-1398	15	3	(	(	PUNCT
ap-1398	15	4	foulis	foulis	PROPN
ap-1398	15	5	and	and	CCONJ
ap-1398	15	6	bennett	bennett	PROPN
ap-1398	16	1	[	[	X
ap-1398	16	2	3	3	NUM
ap-1398	16	3	]	]	PUNCT
ap-1398	16	4	)	)	PUNCT
ap-1398	16	5	an	an	DET
ap-1398	16	6	effect	effect	NOUN
ap-1398	16	7	algebra	algebra	NOUN
ap-1398	16	8	is	be	AUX
ap-1398	16	9	a	a	DET
ap-1398	16	10	system	system	NOUN
ap-1398	16	11	(	(	PUNCT
ap-1398	16	12	e;⊕,0,1	e;⊕,0,1	ADV
ap-1398	16	13	)	)	PUNCT
ap-1398	16	14	consisting	consist	VERB
ap-1398	16	15	of	of	ADP
ap-1398	16	16	a	a	DET
ap-1398	16	17	set	set	NOUN
ap-1398	16	18	e	e	NOUN
ap-1398	16	19	with	with	ADP
ap-1398	16	20	two	two	NUM
ap-1398	16	21	different	different	ADJ
ap-1398	16	22	elements	element	NOUN
ap-1398	16	23	0	0	NUM
ap-1398	16	24	and	and	CCONJ
ap-1398	16	25	1	1	NUM
ap-1398	16	26	,	,	PUNCT
ap-1398	16	27	called	call	VERB
ap-1398	16	28	zero	zero	NUM
ap-1398	16	29	and	and	CCONJ
ap-1398	16	30	unit	unit	NOUN
ap-1398	16	31	,	,	PUNCT
ap-1398	16	32	respectively	respectively	ADV
ap-1398	16	33	and	and	CCONJ
ap-1398	16	34	⊕	⊕	PROPN
ap-1398	16	35	is	be	AUX
ap-1398	16	36	a	a	DET
ap-1398	16	37	partially	partially	ADV
ap-1398	16	38	defined	define	VERB
ap-1398	16	39	binary	binary	ADJ
ap-1398	16	40	operation	operation	NOUN
ap-1398	16	41	satisfying	satisfy	VERB
ap-1398	16	42	the	the	DET
ap-1398	16	43	following	follow	VERB
ap-1398	16	44	conditions	condition	NOUN
ap-1398	16	45	for	for	ADP
ap-1398	16	46	all	all	DET
ap-1398	16	47	p	p	NOUN
ap-1398	16	48	,	,	PUNCT
ap-1398	16	49	q	q	ADJ
ap-1398	16	50	,	,	PUNCT
ap-1398	16	51	r	r	NOUN
ap-1398	16	52	∈	∈	PROPN
ap-1398	17	1	e	e	NOUN
ap-1398	17	2	:	:	PUNCT
ap-1398	17	3	(	(	PUNCT
ap-1398	17	4	e1	e1	NOUN
ap-1398	17	5	)	)	PUNCT
ap-1398	17	6	if	if	SCONJ
ap-1398	17	7	p	p	PROPN
ap-1398	17	8	⊕	⊕	PROPN
ap-1398	17	9	q	q	PROPN
ap-1398	17	10	is	be	AUX
ap-1398	17	11	defined	define	VERB
ap-1398	17	12	,	,	PUNCT
ap-1398	17	13	then	then	ADV
ap-1398	17	14	q	q	PROPN
ap-1398	17	15	⊕	⊕	PROPN
ap-1398	17	16	p	p	PROPN
ap-1398	17	17	is	be	AUX
ap-1398	17	18	defined	define	VERB
ap-1398	17	19	and	and	CCONJ
ap-1398	17	20	p	p	PRON
ap-1398	17	21	⊕	⊕	PROPN
ap-1398	17	22	q	q	PROPN
ap-1398	18	1	=	=	PUNCT
ap-1398	18	2	q	q	PROPN
ap-1398	18	3	⊕	⊕	PROPN
ap-1398	18	4	p.	p.	NOUN
ap-1398	18	5	(	(	PUNCT
ap-1398	18	6	e2	e2	PROPN
ap-1398	18	7	)	)	PUNCT
ap-1398	18	8	if	if	SCONJ
ap-1398	18	9	q	q	PROPN
ap-1398	18	10	⊕	⊕	PROPN
ap-1398	18	11	r	r	NOUN
ap-1398	18	12	is	be	AUX
ap-1398	18	13	defined	define	VERB
ap-1398	18	14	and	and	CCONJ
ap-1398	18	15	p	p	PROPN
ap-1398	18	16	⊕	⊕	PROPN
ap-1398	18	17	(	(	PUNCT
ap-1398	18	18	q	q	PROPN
ap-1398	18	19	⊕	⊕	PROPN
ap-1398	18	20	r	r	NOUN
ap-1398	18	21	)	)	PUNCT
ap-1398	18	22	is	be	AUX
ap-1398	18	23	defined	define	VERB
ap-1398	18	24	,	,	PUNCT
ap-1398	18	25	then	then	ADV
ap-1398	18	26	p	p	PROPN
ap-1398	18	27	⊕	⊕	PROPN
ap-1398	18	28	q	q	PROPN
ap-1398	19	1	and	and	CCONJ
ap-1398	19	2	(	(	PUNCT
ap-1398	19	3	p	p	PROPN
ap-1398	19	4	⊕	⊕	PROPN
ap-1398	19	5	q	q	NOUN
ap-1398	19	6	)	)	PUNCT
ap-1398	19	7	⊕	⊕	PROPN
ap-1398	19	8	r	r	NOUN
ap-1398	19	9	are	be	AUX
ap-1398	19	10	defined	define	VERB
ap-1398	19	11	and	and	CCONJ
ap-1398	19	12	p	p	PROPN
ap-1398	19	13	⊕	⊕	PROPN
ap-1398	19	14	(	(	PUNCT
ap-1398	19	15	q	q	PROPN
ap-1398	19	16	⊕	⊕	PROPN
ap-1398	19	17	r	r	NOUN
ap-1398	19	18	)	)	PUNCT
ap-1398	20	1	=	=	SYM
ap-1398	20	2	(	(	PUNCT
ap-1398	20	3	p	p	PROPN
ap-1398	20	4	⊕	⊕	PROPN
ap-1398	20	5	q	q	PROPN
ap-1398	20	6	)	)	PUNCT
ap-1398	20	7	⊕	⊕	PROPN
ap-1398	20	8	r.	r.	PROPN
ap-1398	20	9	(	(	PUNCT
ap-1398	20	10	e3	e3	PROPN
ap-1398	20	11	)	)	PUNCT
ap-1398	20	12	for	for	ADP
ap-1398	20	13	every	every	DET
ap-1398	20	14	p	p	NOUN
ap-1398	20	15	∈	∈	ADJ
ap-1398	20	16	e	e	NOUN
ap-1398	20	17	there	there	PRON
ap-1398	20	18	exists	exist	VERB
ap-1398	20	19	a	a	DET
ap-1398	20	20	unique	unique	ADJ
ap-1398	20	21	q	q	NOUN
ap-1398	20	22	∈	∈	NOUN
ap-1398	20	23	e	e	NOUN
ap-1398	20	24	such	such	ADJ
ap-1398	20	25	that	that	SCONJ
ap-1398	20	26	p	p	PROPN
ap-1398	20	27	⊕	⊕	PROPN
ap-1398	20	28	q	q	PROPN
ap-1398	20	29	is	be	AUX
ap-1398	20	30	defined	define	VERB
ap-1398	20	31	and	and	CCONJ
ap-1398	20	32	p	p	PRON
ap-1398	20	33	⊕	⊕	PROPN
ap-1398	20	34	q	q	PROPN
ap-1398	20	35	=	=	NOUN
ap-1398	20	36	1	1	X
ap-1398	20	37	.	.	PUNCT
ap-1398	20	38	(	(	PUNCT
ap-1398	20	39	e4	e4	PROPN
ap-1398	20	40	)	)	PUNCT
ap-1398	20	41	if	if	SCONJ
ap-1398	20	42	p	p	PROPN
ap-1398	20	43	⊕	⊕	PROPN
ap-1398	20	44	1	1	NUM
ap-1398	20	45	is	be	AUX
ap-1398	20	46	defined	define	VERB
ap-1398	20	47	then	then	ADV
ap-1398	20	48	p	p	X
ap-1398	20	49	=	=	NOUN
ap-1398	20	50	0	0	PROPN
ap-1398	20	51	.	.	PUNCT
ap-1398	21	1	the	the	DET
ap-1398	21	2	element	element	NOUN
ap-1398	21	3	q	q	NOUN
ap-1398	21	4	in	in	ADP
ap-1398	21	5	(	(	PUNCT
ap-1398	21	6	e3	e3	NOUN
ap-1398	21	7	)	)	PUNCT
ap-1398	21	8	will	will	AUX
ap-1398	21	9	be	be	AUX
ap-1398	21	10	called	call	VERB
ap-1398	21	11	the	the	DET
ap-1398	21	12	supplement	supplement	NOUN
ap-1398	21	13	of	of	ADP
ap-1398	21	14	p	p	NOUN
ap-1398	21	15	,	,	PUNCT
ap-1398	21	16	and	and	CCONJ
ap-1398	21	17	will	will	AUX
ap-1398	21	18	be	be	AUX
ap-1398	21	19	denoted	denote	VERB
ap-1398	21	20	as	as	ADP
ap-1398	21	21	p′.	p′.	NOUN
ap-1398	21	22	in	in	ADP
ap-1398	21	23	the	the	DET
ap-1398	21	24	whole	whole	ADJ
ap-1398	21	25	paper	paper	NOUN
ap-1398	21	26	,	,	PUNCT
ap-1398	21	27	for	for	ADP
ap-1398	21	28	an	an	DET
ap-1398	21	29	effect	effect	NOUN
ap-1398	21	30	algebra	algebra	NOUN
ap-1398	21	31	(	(	PUNCT
ap-1398	21	32	e,⊕,0,1	e,⊕,0,1	PROPN
ap-1398	21	33	)	)	PUNCT
ap-1398	21	34	,	,	PUNCT
ap-1398	21	35	writing	write	VERB
ap-1398	21	36	a	a	DET
ap-1398	21	37	⊕	⊕	PROPN
ap-1398	21	38	b	b	PROPN
ap-1398	21	39	for	for	ADP
ap-1398	21	40	arbitrary	arbitrary	ADJ
ap-1398	21	41	a	a	PRON
ap-1398	21	42	,	,	PUNCT
ap-1398	21	43	b	b	X
ap-1398	21	44	∈	∈	NOUN
ap-1398	21	45	e	e	NOUN
ap-1398	21	46	will	will	AUX
ap-1398	21	47	mean	mean	VERB
ap-1398	21	48	that	that	SCONJ
ap-1398	21	49	a	a	DET
ap-1398	21	50	⊕	⊕	PROPN
ap-1398	21	51	b	b	PROPN
ap-1398	21	52	exists	exist	VERB
ap-1398	21	53	.	.	PUNCT
ap-1398	22	1	on	on	ADP
ap-1398	22	2	an	an	DET
ap-1398	22	3	effect	effect	NOUN
ap-1398	22	4	algebra	algebra	NOUN
ap-1398	22	5	e	e	NOUN
ap-1398	22	6	we	we	PRON
ap-1398	22	7	may	may	AUX
ap-1398	22	8	define	define	VERB
ap-1398	22	9	another	another	DET
ap-1398	22	10	partial	partial	ADJ
ap-1398	22	11	binary	binary	NOUN
ap-1398	22	12	operation	operation	NOUN
ap-1398	22	13	�	�	PROPN
ap-1398	22	14	by	by	ADP
ap-1398	22	15	a	a	DET
ap-1398	22	16	�	�	PROPN
ap-1398	22	17	b	b	PROPN
ap-1398	22	18	=	=	SYM
ap-1398	22	19	c	c	PROPN
ap-1398	22	20	⇔	⇔	PROPN
ap-1398	22	21	b	b	PROPN
ap-1398	22	22	⊕	⊕	PROPN
ap-1398	22	23	c	c	AUX
ap-1398	23	1	=	=	PUNCT
ap-1398	23	2	a.	a.	NOUN
ap-1398	23	3	the	the	DET
ap-1398	23	4	operation	operation	NOUN
ap-1398	23	5	�	�	PROPN
ap-1398	23	6	induces	induce	VERB
ap-1398	23	7	a	a	DET
ap-1398	23	8	partial	partial	ADJ
ap-1398	23	9	order	order	NOUN
ap-1398	23	10	on	on	ADP
ap-1398	23	11	e.	e.	PROPN
ap-1398	23	12	namely	namely	ADV
ap-1398	23	13	,	,	PUNCT
ap-1398	23	14	for	for	ADP
ap-1398	23	15	a	a	DET
ap-1398	23	16	,	,	PUNCT
ap-1398	23	17	b	b	PROPN
ap-1398	23	18	∈	∈	PROPN
ap-1398	23	19	e	e	X
ap-1398	23	20	b	b	NOUN
ap-1398	23	21	≤	≤	NOUN
ap-1398	23	22	a	a	PRON
ap-1398	23	23	if	if	SCONJ
ap-1398	23	24	there	there	PRON
ap-1398	23	25	exists	exist	VERB
ap-1398	23	26	a	a	DET
ap-1398	23	27	c	c	NOUN
ap-1398	23	28	∈	∈	PROPN
ap-1398	23	29	e	e	NOUN
ap-1398	23	30	such	such	ADJ
ap-1398	23	31	that	that	SCONJ
ap-1398	23	32	a	a	DET
ap-1398	23	33	�	�	PROPN
ap-1398	23	34	b	b	PROPN
ap-1398	23	35	=	=	PROPN
ap-1398	23	36	c.	c.	NOUN
ap-1398	23	37	if	if	SCONJ
ap-1398	23	38	e	e	NOUN
ap-1398	23	39	with	with	ADP
ap-1398	23	40	respect	respect	NOUN
ap-1398	23	41	to	to	ADP
ap-1398	23	42	≤	≤	NUM
ap-1398	23	43	is	be	AUX
ap-1398	23	44	lattice	lattice	NOUN
ap-1398	23	45	ordered	order	VERB
ap-1398	23	46	,	,	PUNCT
ap-1398	23	47	we	we	PRON
ap-1398	23	48	say	say	VERB
ap-1398	23	49	that	that	SCONJ
ap-1398	23	50	e	e	NOUN
ap-1398	23	51	is	be	AUX
ap-1398	23	52	a	a	DET
ap-1398	23	53	lattice	lattice	ADJ
ap-1398	23	54	effect	effect	NOUN
ap-1398	23	55	algebra	algebra	NOUN
ap-1398	23	56	.	.	PUNCT
ap-1398	24	1	for	for	ADP
ap-1398	24	2	the	the	DET
ap-1398	24	3	sake	sake	NOUN
ap-1398	24	4	of	of	ADP
ap-1398	24	5	brevity	brevity	NOUN
ap-1398	24	6	we	we	PRON
ap-1398	24	7	will	will	AUX
ap-1398	24	8	write	write	VERB
ap-1398	24	9	just	just	ADV
ap-1398	24	10	lea	lea	PROPN
ap-1398	24	11	.	.	PUNCT
ap-1398	25	1	further	far	ADV
ap-1398	25	2	,	,	PUNCT
ap-1398	25	3	in	in	ADP
ap-1398	25	4	this	this	DET
ap-1398	25	5	article	article	NOUN
ap-1398	25	6	we	we	PRON
ap-1398	25	7	often	often	ADV
ap-1398	25	8	briefly	briefly	ADV
ap-1398	25	9	write	write	VERB
ap-1398	25	10	‘	'	PUNCT
ap-1398	25	11	an	an	DET
ap-1398	25	12	effect	effect	NOUN
ap-1398	25	13	algebra	algebra	NOUN
ap-1398	25	14	e	e	NOUN
ap-1398	25	15	’	'	PUNCT
ap-1398	25	16	skipping	skip	VERB
ap-1398	25	17	the	the	DET
ap-1398	25	18	operations	operation	NOUN
ap-1398	25	19	.	.	PUNCT
ap-1398	26	1	s.	s.	PROPN
ap-1398	26	2	p.	p.	PROPN
ap-1398	26	3	gudder	gudder	PROPN
ap-1398	26	4	(	(	PUNCT
ap-1398	26	5	[	[	X
ap-1398	26	6	5	5	NUM
ap-1398	26	7	,	,	PUNCT
ap-1398	26	8	6	6	NUM
ap-1398	26	9	]	]	PUNCT
ap-1398	26	10	)	)	PUNCT
ap-1398	26	11	introduced	introduce	VERB
ap-1398	26	12	the	the	DET
ap-1398	26	13	notion	notion	NOUN
ap-1398	26	14	of	of	ADP
ap-1398	26	15	sharp	sharp	ADJ
ap-1398	26	16	elements	element	NOUN
ap-1398	26	17	and	and	CCONJ
ap-1398	26	18	sharply	sharply	ADV
ap-1398	26	19	dominating	dominate	VERB
ap-1398	26	20	lattice	lattice	NOUN
ap-1398	26	21	effect	effect	NOUN
ap-1398	26	22	algebras	algebra	NOUN
ap-1398	26	23	.	.	PUNCT
ap-1398	27	1	recall	recall	VERB
ap-1398	27	2	that	that	SCONJ
ap-1398	27	3	an	an	DET
ap-1398	27	4	element	element	NOUN
ap-1398	27	5	x	x	PUNCT
ap-1398	27	6	of	of	ADP
ap-1398	27	7	the	the	DET
ap-1398	27	8	lea	lea	PROPN
ap-1398	27	9	e	e	PROPN
ap-1398	27	10	is	be	AUX
ap-1398	27	11	called	call	VERB
ap-1398	27	12	sharp	sharp	ADJ
ap-1398	27	13	if	if	SCONJ
ap-1398	27	14	x∧x′	x∧x′	PROPN
ap-1398	27	15	=	=	NOUN
ap-1398	27	16	0	0	PROPN
ap-1398	27	17	.	.	PUNCT
ap-1398	28	1	jenča	jenča	PROPN
ap-1398	28	2	and	and	CCONJ
ap-1398	28	3	riečanová	riečanová	PROPN
ap-1398	28	4	in	in	ADP
ap-1398	28	5	[	[	X
ap-1398	28	6	7	7	NUM
ap-1398	28	7	]	]	PUNCT
ap-1398	28	8	proved	prove	VERB
ap-1398	28	9	that	that	SCONJ
ap-1398	28	10	in	in	ADP
ap-1398	28	11	every	every	DET
ap-1398	28	12	lattice	lattice	ADJ
ap-1398	28	13	effect	effect	NOUN
ap-1398	28	14	algebra	algebra	NOUN
ap-1398	28	15	e	e	NOUN
ap-1398	28	16	the	the	DET
ap-1398	28	17	set	set	NOUN
ap-1398	28	18	s(e	s(e	PROPN
ap-1398	28	19	)	)	PUNCT
ap-1398	28	20	=	=	PRON
ap-1398	28	21	{	{	PUNCT
ap-1398	28	22	x	x	PUNCT
ap-1398	28	23	∈	∈	PROPN
ap-1398	28	24	e	e	NOUN
ap-1398	28	25	;	;	PUNCT
ap-1398	28	26	x	x	X
ap-1398	28	27	∧	∧	NOUN
ap-1398	28	28	x′	x′	X
ap-1398	28	29	=	=	SYM
ap-1398	28	30	0	0	NUM
ap-1398	28	31	}	}	PUNCT
ap-1398	28	32	of	of	ADP
ap-1398	28	33	sharp	sharp	ADJ
ap-1398	28	34	elements	element	NOUN
ap-1398	28	35	is	be	AUX
ap-1398	28	36	an	an	DET
ap-1398	28	37	orthomodular	orthomodular	ADJ
ap-1398	28	38	lattice	lattice	NOUN
ap-1398	28	39	which	which	PRON
ap-1398	28	40	is	be	AUX
ap-1398	28	41	a	a	DET
ap-1398	28	42	sub	sub	ADJ
ap-1398	28	43	-	-	ADJ
ap-1398	28	44	effect	effect	ADJ
ap-1398	28	45	algebra	algebra	NOUN
ap-1398	28	46	of	of	ADP
ap-1398	28	47	e	e	NOUN
ap-1398	28	48	,	,	PUNCT
ap-1398	28	49	meaning	mean	VERB
ap-1398	28	50	that	that	SCONJ
ap-1398	28	51	if	if	SCONJ
ap-1398	28	52	among	among	ADP
ap-1398	28	53	x	x	PROPN
ap-1398	28	54	,	,	PUNCT
ap-1398	28	55	y	y	PROPN
ap-1398	28	56	,	,	PUNCT
ap-1398	28	57	z	z	NOUN
ap-1398	28	58	∈	∈	PROPN
ap-1398	28	59	e	e	X
ap-1398	28	60	with	with	ADP
ap-1398	28	61	x	x	PROPN
ap-1398	28	62	⊕	⊕	PROPN
ap-1398	28	63	y	y	NOUN
ap-1398	28	64	=	=	PUNCT
ap-1398	28	65	z	z	NOUN
ap-1398	28	66	at	at	ADV
ap-1398	28	67	least	least	ADV
ap-1398	28	68	two	two	NUM
ap-1398	28	69	elements	element	NOUN
ap-1398	28	70	are	be	AUX
ap-1398	28	71	in	in	ADP
ap-1398	28	72	s(e	s(e	PROPN
ap-1398	28	73	)	)	PUNCT
ap-1398	28	74	then	then	ADV
ap-1398	28	75	x	x	X
ap-1398	28	76	,	,	PUNCT
ap-1398	28	77	y	y	PROPN
ap-1398	28	78	,	,	PUNCT
ap-1398	28	79	z	z	PROPN
ap-1398	28	80	∈	∈	PROPN
ap-1398	28	81	s(e	s(e	PROPN
ap-1398	28	82	)	)	PUNCT
ap-1398	28	83	.	.	PUNCT
ap-1398	29	1	moreover	moreover	ADV
ap-1398	29	2	s(e	s(e	PROPN
ap-1398	29	3	)	)	PUNCT
ap-1398	29	4	is	be	AUX
ap-1398	29	5	a	a	DET
ap-1398	29	6	full	full	ADJ
ap-1398	29	7	sublattice	sublattice	NOUN
ap-1398	29	8	of	of	ADP
ap-1398	29	9	e	e	NOUN
ap-1398	29	10	,	,	PUNCT
ap-1398	29	11	hence	hence	ADV
ap-1398	29	12	a	a	DET
ap-1398	29	13	supremum	supremum	NOUN
ap-1398	29	14	of	of	ADP
ap-1398	29	15	any	any	DET
ap-1398	29	16	set	set	NOUN
ap-1398	29	17	of	of	ADP
ap-1398	29	18	sharp	sharp	ADJ
ap-1398	29	19	elements	element	NOUN
ap-1398	29	20	,	,	PUNCT
ap-1398	29	21	which	which	PRON
ap-1398	29	22	exists	exist	VERB
ap-1398	29	23	in	in	ADP
ap-1398	29	24	e	e	NOUN
ap-1398	29	25	,	,	PUNCT
ap-1398	29	26	is	be	AUX
ap-1398	29	27	again	again	ADV
ap-1398	29	28	a	a	DET
ap-1398	29	29	sharp	sharp	ADJ
ap-1398	29	30	element	element	NOUN
ap-1398	29	31	.	.	PUNCT
ap-1398	30	1	further	far	ADV
ap-1398	30	2	,	,	PUNCT
ap-1398	30	3	each	each	DET
ap-1398	30	4	maximal	maximal	ADJ
ap-1398	30	5	subset	subset	NOUN
ap-1398	30	6	m	m	NOUN
ap-1398	30	7	of	of	ADP
ap-1398	30	8	pairwise	pairwise	NOUN
ap-1398	30	9	compatible	compatible	ADJ
ap-1398	30	10	elements	element	NOUN
ap-1398	30	11	of	of	ADP
ap-1398	30	12	e	e	NOUN
ap-1398	30	13	,	,	PUNCT
ap-1398	30	14	called	call	VERB
ap-1398	30	15	a	a	DET
ap-1398	30	16	block	block	NOUN
ap-1398	30	17	of	of	ADP
ap-1398	30	18	e	e	NOUN
ap-1398	30	19	,	,	PUNCT
ap-1398	30	20	is	be	AUX
ap-1398	30	21	a	a	DET
ap-1398	30	22	sub	sub	ADJ
ap-1398	30	23	-	-	ADJ
ap-1398	30	24	effect	effect	ADJ
ap-1398	30	25	algebra	algebra	NOUN
ap-1398	30	26	and	and	CCONJ
ap-1398	30	27	a	a	DET
ap-1398	30	28	full	full	ADJ
ap-1398	30	29	sublattice	sublattice	NOUN
ap-1398	30	30	of	of	ADP
ap-1398	30	31	e	e	NOUN
ap-1398	30	32	and	and	CCONJ
ap-1398	30	33	e	e	X
ap-1398	30	34	=	=	SYM
ap-1398	30	35	⋃	⋃	PROPN
ap-1398	30	36	{	{	PUNCT
ap-1398	30	37	m	m	PROPN
ap-1398	30	38	⊆	⊆	NUM
ap-1398	30	39	e	e	NOUN
ap-1398	30	40	;	;	PUNCT
ap-1398	30	41	m	m	VERB
ap-1398	30	42	is	be	AUX
ap-1398	30	43	a	a	DET
ap-1398	30	44	block	block	NOUN
ap-1398	30	45	of	of	ADP
ap-1398	30	46	e	e	NOUN
ap-1398	30	47	}	}	PUNCT
ap-1398	30	48	(	(	PUNCT
ap-1398	30	49	see	see	VERB
ap-1398	30	50	[	[	X
ap-1398	30	51	16	16	NUM
ap-1398	30	52	,	,	PUNCT
ap-1398	30	53	17	17	NUM
ap-1398	30	54	]	]	PUNCT
ap-1398	30	55	)	)	PUNCT
ap-1398	30	56	.	.	PUNCT
ap-1398	31	1	central	central	ADJ
ap-1398	31	2	elements	element	NOUN
ap-1398	31	3	and	and	CCONJ
ap-1398	31	4	centers	center	NOUN
ap-1398	31	5	of	of	ADP
ap-1398	31	6	effect	effect	NOUN
ap-1398	31	7	algebras	algebra	NOUN
ap-1398	31	8	were	be	AUX
ap-1398	31	9	defined	define	VERB
ap-1398	31	10	in	in	ADP
ap-1398	31	11	[	[	X
ap-1398	31	12	4	4	NUM
ap-1398	31	13	]	]	PUNCT
ap-1398	31	14	.	.	PUNCT
ap-1398	32	1	in	in	ADP
ap-1398	32	2	[	[	X
ap-1398	32	3	14,15	14,15	NUM
ap-1398	32	4	]	]	X
ap-1398	32	5	it	it	PRON
ap-1398	32	6	was	be	AUX
ap-1398	32	7	proved	prove	VERB
ap-1398	32	8	that	that	SCONJ
ap-1398	32	9	in	in	ADP
ap-1398	32	10	every	every	DET
ap-1398	32	11	lattice	lattice	ADJ
ap-1398	32	12	effect	effect	NOUN
ap-1398	32	13	algebra	algebra	NOUN
ap-1398	32	14	e	e	NOUN
ap-1398	32	15	the	the	DET
ap-1398	32	16	center	center	NOUN
ap-1398	32	17	c(e	c(e	NOUN
ap-1398	32	18	)	)	PUNCT
ap-1398	32	19	=	=	PRON
ap-1398	33	1	{	{	PUNCT
ap-1398	33	2	x	x	PUNCT
ap-1398	33	3	∈	∈	PROPN
ap-1398	33	4	e	e	NOUN
ap-1398	33	5	;	;	PUNCT
ap-1398	33	6	(	(	PUNCT
ap-1398	33	7	∀y	∀y	PROPN
ap-1398	33	8	∈	∈	PROPN
ap-1398	33	9	e)y	e)y	NOUN
ap-1398	33	10	=	=	SYM
ap-1398	33	11	(	(	PUNCT
ap-1398	33	12	y	y	PROPN
ap-1398	33	13	∧	∧	PROPN
ap-1398	33	14	x	x	PROPN
ap-1398	33	15	)	)	PUNCT
ap-1398	33	16	∨	∨	PROPN
ap-1398	33	17	(	(	PUNCT
ap-1398	33	18	y	y	PROPN
ap-1398	33	19	∧	∧	PROPN
ap-1398	33	20	x′	x′	PROPN
ap-1398	33	21	)	)	PUNCT
ap-1398	33	22	}	}	PUNCT
ap-1398	33	23	=	=	SYM
ap-1398	33	24	s(e	s(e	PROPN
ap-1398	33	25	)	)	PUNCT
ap-1398	33	26	∩	∩	NOUN
ap-1398	33	27	b(e	b(e	PROPN
ap-1398	33	28	)	)	PUNCT
ap-1398	33	29	,	,	PUNCT
ap-1398	33	30	(	(	PUNCT
ap-1398	33	31	1	1	X
ap-1398	33	32	)	)	PUNCT
ap-1398	33	33	where	where	SCONJ
ap-1398	33	34	b(e	b(e	ADJ
ap-1398	33	35	)	)	PUNCT
ap-1398	34	1	=	=	SYM
ap-1398	34	2	⋂	⋂	PROPN
ap-1398	34	3	{	{	PUNCT
ap-1398	34	4	m	m	PROPN
ap-1398	34	5	⊆	⊆	NUM
ap-1398	34	6	e	e	NOUN
ap-1398	34	7	;	;	PUNCT
ap-1398	34	8	m	m	VERB
ap-1398	34	9	is	be	AUX
ap-1398	34	10	a	a	DET
ap-1398	34	11	block	block	NOUN
ap-1398	34	12	of	of	ADP
ap-1398	34	13	e	e	NOUN
ap-1398	34	14	}	}	PUNCT
ap-1398	34	15	.	.	PUNCT
ap-1398	35	1	since	since	SCONJ
ap-1398	35	2	s(e	s(e	PROPN
ap-1398	35	3	)	)	PUNCT
ap-1398	35	4	is	be	AUX
ap-1398	35	5	an	an	DET
ap-1398	35	6	orthomodular	orthomodular	ADJ
ap-1398	35	7	lattice	lattice	NOUN
ap-1398	35	8	and	and	CCONJ
ap-1398	35	9	b(e	b(e	PROPN
ap-1398	35	10	)	)	PUNCT
ap-1398	35	11	is	be	AUX
ap-1398	35	12	an	an	DET
ap-1398	35	13	26	26	NUM
ap-1398	35	14	acta	acta	PROPN
ap-1398	35	15	polytechnica	polytechnica	PROPN
ap-1398	35	16	vol	vol	NOUN
ap-1398	35	17	.	.	PUNCT
ap-1398	36	1	51	51	NUM
ap-1398	36	2	no	no	NOUN
ap-1398	36	3	.	.	PUNCT
ap-1398	37	1	4/2011	4/2011	NUM
ap-1398	37	2	mv	mv	ADJ
ap-1398	37	3	-	-	PUNCT
ap-1398	37	4	effect	effect	NOUN
ap-1398	37	5	algebra	algebra	NOUN
ap-1398	37	6	,	,	PUNCT
ap-1398	37	7	we	we	PRON
ap-1398	37	8	obtain	obtain	VERB
ap-1398	37	9	that	that	PRON
ap-1398	37	10	c(e	c(e	NOUN
ap-1398	37	11	)	)	PUNCT
ap-1398	37	12	is	be	AUX
ap-1398	37	13	a	a	DET
ap-1398	37	14	boolean	boolean	ADJ
ap-1398	37	15	algebra	algebra	NOUN
ap-1398	37	16	.	.	PUNCT
ap-1398	38	1	note	note	VERB
ap-1398	38	2	that	that	SCONJ
ap-1398	38	3	e	e	NOUN
ap-1398	38	4	is	be	AUX
ap-1398	38	5	an	an	DET
ap-1398	38	6	orthomodular	orthomodular	ADJ
ap-1398	38	7	lattice	lattice	NOUN
ap-1398	38	8	if	if	SCONJ
ap-1398	38	9	and	and	CCONJ
ap-1398	38	10	only	only	ADV
ap-1398	38	11	if	if	SCONJ
ap-1398	38	12	e	e	PROPN
ap-1398	38	13	=	=	SYM
ap-1398	38	14	s(e	s(e	PROPN
ap-1398	38	15	)	)	PUNCT
ap-1398	38	16	and	and	CCONJ
ap-1398	38	17	e	e	NOUN
ap-1398	38	18	is	be	AUX
ap-1398	38	19	an	an	DET
ap-1398	38	20	mv	mv	ADJ
ap-1398	38	21	-	-	PUNCT
ap-1398	38	22	effect	effect	NOUN
ap-1398	38	23	algebra	algebra	NOUN
ap-1398	38	24	if	if	SCONJ
ap-1398	38	25	and	and	CCONJ
ap-1398	38	26	only	only	ADV
ap-1398	38	27	if	if	SCONJ
ap-1398	38	28	e	e	PROPN
ap-1398	38	29	=	=	PUNCT
ap-1398	38	30	b(e	b(e	PROPN
ap-1398	38	31	)	)	PUNCT
ap-1398	38	32	.	.	PUNCT
ap-1398	39	1	thus	thus	ADV
ap-1398	39	2	e	e	X
ap-1398	39	3	is	be	AUX
ap-1398	39	4	a	a	DET
ap-1398	39	5	boolean	boolean	ADJ
ap-1398	39	6	algebra	algebra	NOUN
ap-1398	39	7	if	if	SCONJ
ap-1398	39	8	and	and	CCONJ
ap-1398	39	9	only	only	ADV
ap-1398	39	10	if	if	SCONJ
ap-1398	39	11	e	e	PROPN
ap-1398	39	12	=	=	SYM
ap-1398	39	13	s(e	s(e	PROPN
ap-1398	39	14	)	)	PUNCT
ap-1398	39	15	=	=	SYM
ap-1398	39	16	b(e	b(e	ADJ
ap-1398	39	17	)	)	PUNCT
ap-1398	39	18	=	=	SYM
ap-1398	39	19	c(e	c(e	NOUN
ap-1398	39	20	)	)	PUNCT
ap-1398	39	21	.	.	PUNCT
ap-1398	40	1	recall	recall	VERB
ap-1398	40	2	that	that	SCONJ
ap-1398	40	3	an	an	DET
ap-1398	40	4	element	element	NOUN
ap-1398	40	5	p	p	NOUN
ap-1398	40	6	of	of	ADP
ap-1398	40	7	an	an	DET
ap-1398	40	8	effect	effect	NOUN
ap-1398	40	9	algebra	algebra	NOUN
ap-1398	40	10	e	e	NOUN
ap-1398	40	11	is	be	AUX
ap-1398	40	12	called	call	VERB
ap-1398	40	13	an	an	DET
ap-1398	40	14	atom	atom	NOUN
ap-1398	40	15	if	if	SCONJ
ap-1398	40	16	and	and	CCONJ
ap-1398	40	17	only	only	ADV
ap-1398	40	18	if	if	SCONJ
ap-1398	40	19	p	p	NOUN
ap-1398	40	20	is	be	AUX
ap-1398	40	21	a	a	DET
ap-1398	40	22	minimal	minimal	ADJ
ap-1398	40	23	nonzero	nonzero	NOUN
ap-1398	40	24	element	element	NOUN
ap-1398	40	25	of	of	ADP
ap-1398	40	26	e	e	PROPN
ap-1398	40	27	and	and	CCONJ
ap-1398	40	28	e	e	PROPN
ap-1398	40	29	is	be	AUX
ap-1398	40	30	atomic	atomic	ADJ
ap-1398	40	31	if	if	SCONJ
ap-1398	40	32	for	for	ADP
ap-1398	40	33	each	each	DET
ap-1398	40	34	x	x	SYM
ap-1398	40	35	∈	∈	PROPN
ap-1398	40	36	e	e	NOUN
ap-1398	40	37	,	,	PUNCT
ap-1398	40	38	x	x	SYM
ap-1398	40	39	�	�	PROPN
ap-1398	40	40	=	=	SYM
ap-1398	40	41	0	0	NUM
ap-1398	40	42	,	,	PUNCT
ap-1398	40	43	there	there	PRON
ap-1398	40	44	exists	exist	VERB
ap-1398	40	45	an	an	DET
ap-1398	40	46	atom	atom	NOUN
ap-1398	40	47	p	p	NOUN
ap-1398	40	48	≤	≤	NUM
ap-1398	40	49	x.	x.	NOUN
ap-1398	40	50	definition	definition	NOUN
ap-1398	40	51	2	2	NUM
ap-1398	40	52	let	let	VERB
ap-1398	40	53	(	(	PUNCT
ap-1398	40	54	e,⊕	e,⊕	ADJ
ap-1398	40	55	,	,	PUNCT
ap-1398	40	56	0	0	NUM
ap-1398	40	57	)	)	PUNCT
ap-1398	40	58	be	be	VERB
ap-1398	40	59	an	an	DET
ap-1398	40	60	effect	effect	NOUN
ap-1398	40	61	algebra	algebra	NOUN
ap-1398	40	62	.	.	PUNCT
ap-1398	41	1	to	to	ADP
ap-1398	41	2	each	each	PRON
ap-1398	41	3	a	a	DET
ap-1398	41	4	∈	∈	NOUN
ap-1398	41	5	e	e	NOUN
ap-1398	41	6	we	we	PRON
ap-1398	41	7	define	define	VERB
ap-1398	41	8	its	its	PRON
ap-1398	41	9	isotropic	isotropic	ADJ
ap-1398	41	10	index	index	NOUN
ap-1398	41	11	,	,	PUNCT
ap-1398	41	12	notation	notation	NOUN
ap-1398	41	13	ord(a	ord(a	PROPN
ap-1398	41	14	)	)	PUNCT
ap-1398	41	15	,	,	PUNCT
ap-1398	41	16	as	as	ADP
ap-1398	41	17	the	the	DET
ap-1398	41	18	maximal	maximal	ADJ
ap-1398	41	19	positive	positive	ADJ
ap-1398	41	20	integer	integer	NOUN
ap-1398	41	21	n	n	CCONJ
ap-1398	41	22	such	such	ADJ
ap-1398	41	23	that	that	SCONJ
ap-1398	41	24	na	na	ADP
ap-1398	41	25	:	:	PUNCT
ap-1398	41	26	=	=	PUNCT
ap-1398	41	27	a	a	DET
ap-1398	41	28	⊕	⊕	PROPN
ap-1398	41	29	.	.	PUNCT
ap-1398	41	30	.	.	PUNCT
ap-1398	42	1	.	.	PUNCT
ap-1398	43	1	⊕	⊕	PROPN
ap-1398	43	2	a︸	a︸	ADV
ap-1398	43	3	︷︷	︷︷	PROPN
ap-1398	43	4	︸	︸	SYM
ap-1398	43	5	n	n	CCONJ
ap-1398	43	6	-	-	PUNCT
ap-1398	43	7	times	time	NOUN
ap-1398	43	8	exists	exist	VERB
ap-1398	43	9	.	.	PUNCT
ap-1398	44	1	we	we	PRON
ap-1398	44	2	set	set	VERB
ap-1398	44	3	ord(a	ord(a	PROPN
ap-1398	44	4	)	)	PUNCT
ap-1398	44	5	=	=	SYM
ap-1398	44	6	∞	∞	NOUN
ap-1398	44	7	if	if	SCONJ
ap-1398	44	8	na	na	PROPN
ap-1398	44	9	exists	exist	VERB
ap-1398	44	10	for	for	ADP
ap-1398	44	11	each	each	DET
ap-1398	44	12	positive	positive	ADJ
ap-1398	44	13	integer	integer	NOUN
ap-1398	44	14	n.	n.	NOUN
ap-1398	44	15	we	we	PRON
ap-1398	44	16	say	say	VERB
ap-1398	44	17	that	that	SCONJ
ap-1398	44	18	e	e	NOUN
ap-1398	44	19	is	be	AUX
ap-1398	44	20	archimedean	archimedean	ADJ
ap-1398	44	21	,	,	PUNCT
ap-1398	44	22	if	if	SCONJ
ap-1398	44	23	for	for	ADP
ap-1398	44	24	each	each	DET
ap-1398	44	25	a	a	DET
ap-1398	44	26	∈	∈	PROPN
ap-1398	44	27	e	e	NOUN
ap-1398	44	28	,	,	PUNCT
ap-1398	44	29	a	a	DET
ap-1398	44	30	�	�	NOUN
ap-1398	44	31	=	=	SYM
ap-1398	44	32	0	0	NUM
ap-1398	44	33	,	,	PUNCT
ap-1398	44	34	ord(a	ord(a	PROPN
ap-1398	44	35	)	)	PUNCT
ap-1398	44	36	is	be	AUX
ap-1398	44	37	finite	finite	ADJ
ap-1398	44	38	.	.	PUNCT
ap-1398	45	1	an	an	DET
ap-1398	45	2	element	element	NOUN
ap-1398	45	3	u	u	NOUN
ap-1398	45	4	∈	∈	NOUN
ap-1398	45	5	e	e	NOUN
ap-1398	45	6	is	be	AUX
ap-1398	45	7	called	call	VERB
ap-1398	45	8	finite	finite	NOUN
ap-1398	45	9	,	,	PUNCT
ap-1398	45	10	if	if	SCONJ
ap-1398	45	11	there	there	PRON
ap-1398	45	12	exists	exist	VERB
ap-1398	45	13	a	a	DET
ap-1398	45	14	finite	finite	ADJ
ap-1398	45	15	system	system	NOUN
ap-1398	45	16	of	of	ADP
ap-1398	45	17	atoms	atom	NOUN
ap-1398	45	18	a1	a1	NOUN
ap-1398	45	19	,	,	PUNCT
ap-1398	45	20	.	.	PUNCT
ap-1398	45	21	.	.	PUNCT
ap-1398	46	1	.	.	PUNCT
ap-1398	47	1	,	,	PUNCT
ap-1398	47	2	an	an	PRON
ap-1398	47	3	(	(	PUNCT
ap-1398	47	4	which	which	PRON
ap-1398	47	5	are	be	AUX
ap-1398	47	6	not	not	PART
ap-1398	47	7	necessarily	necessarily	ADV
ap-1398	47	8	distinct	distinct	ADJ
ap-1398	47	9	)	)	PUNCT
ap-1398	47	10	such	such	ADJ
ap-1398	47	11	that	that	SCONJ
ap-1398	47	12	u	u	NOUN
ap-1398	47	13	=	=	NOUN
ap-1398	47	14	a1	a1	PROPN
ap-1398	47	15	⊕	⊕	PROPN
ap-1398	47	16	.	.	PUNCT
ap-1398	48	1	.	.	PUNCT
ap-1398	49	1	.⊕	.⊕	PROPN
ap-1398	50	1	an	an	PRON
ap-1398	50	2	.	.	PUNCT
ap-1398	51	1	an	an	DET
ap-1398	51	2	element	element	NOUN
ap-1398	51	3	v	v	ADP
ap-1398	51	4	∈	∈	NOUN
ap-1398	51	5	e	e	NOUN
ap-1398	51	6	is	be	AUX
ap-1398	51	7	called	call	VERB
ap-1398	51	8	cofinite	cofinite	NOUN
ap-1398	51	9	,	,	PUNCT
ap-1398	51	10	if	if	SCONJ
ap-1398	51	11	there	there	PRON
ap-1398	51	12	exists	exist	VERB
ap-1398	51	13	a	a	DET
ap-1398	51	14	finite	finite	ADJ
ap-1398	51	15	element	element	NOUN
ap-1398	51	16	u	u	NOUN
ap-1398	51	17	∈	∈	PROPN
ap-1398	51	18	e	e	NOUN
ap-1398	52	1	such	such	ADJ
ap-1398	52	2	that	that	DET
ap-1398	52	3	v	v	NOUN
ap-1398	52	4	=	=	PUNCT
ap-1398	53	1	u′.	u′.	NOUN
ap-1398	53	2	we	we	PRON
ap-1398	53	3	say	say	VERB
ap-1398	53	4	that	that	SCONJ
ap-1398	53	5	for	for	ADP
ap-1398	53	6	a	a	DET
ap-1398	53	7	finite	finite	ADJ
ap-1398	53	8	system	system	NOUN
ap-1398	53	9	f	f	NOUN
ap-1398	53	10	=	=	PRON
ap-1398	53	11	(	(	PUNCT
ap-1398	53	12	xj)k	xj)k	PROPN
ap-1398	53	13	j=1	j=1	PROPN
ap-1398	53	14	of	of	ADP
ap-1398	53	15	not	not	PART
ap-1398	53	16	necessarily	necessarily	ADV
ap-1398	53	17	different	different	ADJ
ap-1398	53	18	elements	element	NOUN
ap-1398	53	19	of	of	ADP
ap-1398	53	20	an	an	DET
ap-1398	53	21	effect	effect	NOUN
ap-1398	53	22	algebra	algebra	NOUN
ap-1398	53	23	(	(	PUNCT
ap-1398	53	24	e,⊕,0,1	e,⊕,0,1	ADJ
ap-1398	53	25	)	)	PUNCT
ap-1398	53	26	is	be	AUX
ap-1398	53	27	⊕-orthogonal	⊕-orthogonal	ADJ
ap-1398	53	28	if	if	SCONJ
ap-1398	53	29	for	for	ADP
ap-1398	53	30	all	all	DET
ap-1398	53	31	n	n	PRON
ap-1398	53	32	≤	≤	NOUN
ap-1398	54	1	k	k	PROPN
ap-1398	54	2	x1⊕x2⊕	x1⊕x2⊕	PROPN
ap-1398	54	3	·	·	PUNCT
ap-1398	54	4	·	·	PUNCT
ap-1398	54	5	·	·	PUNCT
ap-1398	54	6	⊕xn	⊕xn	PUNCT
ap-1398	54	7	=	=	SYM
ap-1398	54	8	(	(	PUNCT
ap-1398	54	9	x1⊕x2⊕	x1⊕x2⊕	PROPN
ap-1398	54	10	·	·	PUNCT
ap-1398	54	11	·	·	PUNCT
ap-1398	54	12	·	·	PUNCT
ap-1398	54	13	⊕xn−1)⊕xn	⊕xn−1)⊕xn	PRON
ap-1398	54	14	exists	exist	VERB
ap-1398	54	15	in	in	ADP
ap-1398	54	16	e	e	NOUN
ap-1398	54	17	(	(	PUNCT
ap-1398	54	18	briefly	briefly	ADV
ap-1398	54	19	we	we	PRON
ap-1398	54	20	will	will	AUX
ap-1398	54	21	write	write	VERB
ap-1398	54	22	n⊕	n⊕	PROPN
ap-1398	54	23	j=1	j=1	PROPN
ap-1398	54	24	xj	xj	PROPN
ap-1398	54	25	)	)	PUNCT
ap-1398	54	26	.	.	PUNCT
ap-1398	55	1	we	we	PRON
ap-1398	55	2	define	define	VERB
ap-1398	55	3	also	also	ADV
ap-1398	55	4	⊕∅	⊕∅	NUM
ap-1398	56	1	=	=	SYM
ap-1398	56	2	0	0	X
ap-1398	56	3	.	.	PUNCT
ap-1398	56	4	definition	definition	NOUN
ap-1398	56	5	3	3	NUM
ap-1398	56	6	for	for	ADP
ap-1398	56	7	a	a	DET
ap-1398	56	8	lattice	lattice	NOUN
ap-1398	56	9	(	(	PUNCT
ap-1398	56	10	l,∧,∨	l,∧,∨	X
ap-1398	56	11	)	)	PUNCT
ap-1398	56	12	and	and	CCONJ
ap-1398	56	13	a	a	DET
ap-1398	56	14	subset	subset	NOUN
ap-1398	56	15	d	d	NOUN
ap-1398	56	16	⊆	⊆	NUM
ap-1398	56	17	l	l	NOUN
ap-1398	56	18	we	we	PRON
ap-1398	56	19	say	say	VERB
ap-1398	56	20	that	that	SCONJ
ap-1398	56	21	d	d	PROPN
ap-1398	56	22	is	be	AUX
ap-1398	56	23	a	a	DET
ap-1398	56	24	bifull	bifull	ADJ
ap-1398	56	25	sublattice	sublattice	NOUN
ap-1398	56	26	of	of	ADP
ap-1398	56	27	l	l	NOUN
ap-1398	56	28	,	,	PUNCT
ap-1398	56	29	if	if	SCONJ
ap-1398	56	30	and	and	CCONJ
ap-1398	56	31	only	only	ADV
ap-1398	56	32	if	if	SCONJ
ap-1398	56	33	for	for	ADP
ap-1398	56	34	any	any	DET
ap-1398	56	35	x	x	SYM
ap-1398	56	36	⊆	⊆	NUM
ap-1398	56	37	d	d	PROPN
ap-1398	56	38	,	,	PUNCT
ap-1398	56	39	∨	∨	PROPN
ap-1398	56	40	l	l	NOUN
ap-1398	56	41	x	x	PRON
ap-1398	56	42	exists	exist	VERB
ap-1398	56	43	if	if	SCONJ
ap-1398	56	44	and	and	CCONJ
ap-1398	56	45	only	only	ADV
ap-1398	56	46	if∨	if∨	ADP
ap-1398	56	47	d	d	NOUN
ap-1398	56	48	x	x	NOUN
ap-1398	56	49	exists	exist	VERB
ap-1398	56	50	and	and	CCONJ
ap-1398	56	51	∧	∧	PROPN
ap-1398	56	52	l	l	NOUN
ap-1398	56	53	x	x	PRON
ap-1398	56	54	exists	exist	VERB
ap-1398	56	55	if	if	SCONJ
ap-1398	56	56	and	and	CCONJ
ap-1398	56	57	only	only	ADV
ap-1398	56	58	if	if	SCONJ
ap-1398	56	59	∧	∧	PROPN
ap-1398	56	60	d	d	NOUN
ap-1398	56	61	x	x	NOUN
ap-1398	56	62	exists	exist	VERB
ap-1398	56	63	,	,	PUNCT
ap-1398	56	64	in	in	ADP
ap-1398	56	65	which	which	DET
ap-1398	56	66	case	case	NOUN
ap-1398	56	67	∨	∨	NUM
ap-1398	56	68	l	l	NOUN
ap-1398	56	69	x	x	X
ap-1398	56	70	=	=	SYM
ap-1398	56	71	∨	∨	NUM
ap-1398	56	72	d	d	NOUN
ap-1398	56	73	x	x	X
ap-1398	56	74	and	and	CCONJ
ap-1398	56	75	∧	∧	PROPN
ap-1398	56	76	l	l	NOUN
ap-1398	56	77	x	x	PUNCT
ap-1398	57	1	=	=	SYM
ap-1398	57	2	∧	∧	PROPN
ap-1398	57	3	d	d	NOUN
ap-1398	57	4	x.	x.	NOUN
ap-1398	58	1	it	it	PRON
ap-1398	58	2	is	be	AUX
ap-1398	58	3	known	know	VERB
ap-1398	58	4	that	that	SCONJ
ap-1398	58	5	if	if	SCONJ
ap-1398	58	6	e	e	NOUN
ap-1398	58	7	is	be	AUX
ap-1398	58	8	a	a	DET
ap-1398	58	9	distributive	distributive	ADJ
ap-1398	58	10	effect	effect	NOUN
ap-1398	58	11	algebra	algebra	NOUN
ap-1398	58	12	(	(	PUNCT
ap-1398	58	13	i.	i.	PROPN
ap-1398	58	14	e.	e.	PROPN
ap-1398	58	15	,	,	PUNCT
ap-1398	58	16	the	the	DET
ap-1398	58	17	effect	effect	NOUN
ap-1398	58	18	algebra	algebra	NOUN
ap-1398	58	19	e	e	NOUN
ap-1398	58	20	is	be	AUX
ap-1398	58	21	a	a	DET
ap-1398	58	22	distributive	distributive	ADJ
ap-1398	58	23	lattice	lattice	NOUN
ap-1398	58	24	—	—	PUNCT
ap-1398	58	25	e.	e.	PROPN
ap-1398	58	26	g.	g.	PROPN
ap-1398	58	27	,	,	PUNCT
ap-1398	58	28	if	if	SCONJ
ap-1398	58	29	e	e	NOUN
ap-1398	58	30	is	be	AUX
ap-1398	58	31	an	an	DET
ap-1398	58	32	mv	mv	ADJ
ap-1398	58	33	-	-	PUNCT
ap-1398	58	34	effect	effect	NOUN
ap-1398	58	35	algebra	algebra	NOUN
ap-1398	58	36	)	)	PUNCT
ap-1398	58	37	then	then	ADV
ap-1398	58	38	c(e	c(e	NOUN
ap-1398	58	39	)	)	PUNCT
ap-1398	59	1	=	=	SYM
ap-1398	59	2	s(e	s(e	PROPN
ap-1398	59	3	)	)	PUNCT
ap-1398	59	4	.	.	PUNCT
ap-1398	60	1	if	if	SCONJ
ap-1398	60	2	moreover	moreover	ADV
ap-1398	60	3	e	e	NOUN
ap-1398	60	4	is	be	AUX
ap-1398	60	5	archimedean	archimedean	ADJ
ap-1398	60	6	and	and	CCONJ
ap-1398	60	7	atomic	atomic	NOUN
ap-1398	60	8	then	then	ADV
ap-1398	60	9	the	the	DET
ap-1398	60	10	set	set	NOUN
ap-1398	60	11	of	of	ADP
ap-1398	60	12	atoms	atom	NOUN
ap-1398	60	13	of	of	ADP
ap-1398	60	14	c(e	c(e	NOUN
ap-1398	60	15	)	)	PUNCT
ap-1398	61	1	=	=	SYM
ap-1398	61	2	s(e	s(e	PROPN
ap-1398	61	3	)	)	PUNCT
ap-1398	61	4	is	be	AUX
ap-1398	61	5	the	the	DET
ap-1398	61	6	set	set	NOUN
ap-1398	61	7	{	{	PUNCT
ap-1398	61	8	naa	naa	PROPN
ap-1398	61	9	;	;	PUNCT
ap-1398	61	10	a	a	DET
ap-1398	61	11	∈	∈	NOUN
ap-1398	61	12	e	e	NOUN
ap-1398	61	13	is	be	AUX
ap-1398	61	14	an	an	DET
ap-1398	61	15	atom	atom	NOUN
ap-1398	61	16	of	of	ADP
ap-1398	61	17	e	e	NOUN
ap-1398	61	18	}	}	PUNCT
ap-1398	61	19	,	,	PUNCT
ap-1398	61	20	where	where	SCONJ
ap-1398	61	21	na	na	ADP
ap-1398	61	22	=	=	SYM
ap-1398	61	23	ord(a	ord(a	PROPN
ap-1398	61	24	)	)	PUNCT
ap-1398	61	25	(	(	PUNCT
ap-1398	61	26	see	see	VERB
ap-1398	61	27	[	[	X
ap-1398	61	28	20	20	NUM
ap-1398	61	29	]	]	NUM
ap-1398	61	30	)	)	PUNCT
ap-1398	61	31	.	.	PUNCT
ap-1398	62	1	since	since	SCONJ
ap-1398	62	2	s(e	s(e	PROPN
ap-1398	62	3	)	)	PUNCT
ap-1398	62	4	is	be	AUX
ap-1398	62	5	a	a	DET
ap-1398	62	6	bifull	bifull	ADJ
ap-1398	62	7	sublattice	sublattice	NOUN
ap-1398	62	8	of	of	ADP
ap-1398	62	9	e	e	PRON
ap-1398	62	10	if	if	SCONJ
ap-1398	62	11	e	e	PROPN
ap-1398	62	12	is	be	AUX
ap-1398	62	13	an	an	DET
ap-1398	62	14	archimedean	archimedean	ADJ
ap-1398	62	15	atomic	atomic	ADJ
ap-1398	62	16	lea	lea	PROPN
ap-1398	62	17	(	(	PUNCT
ap-1398	62	18	see	see	VERB
ap-1398	62	19	[	[	X
ap-1398	62	20	13	13	NUM
ap-1398	62	21	]	]	NUM
ap-1398	62	22	)	)	PUNCT
ap-1398	62	23	,	,	PUNCT
ap-1398	62	24	we	we	PRON
ap-1398	62	25	obtain	obtain	VERB
ap-1398	62	26	that	that	PRON
ap-1398	62	27	1	1	NUM
ap-1398	62	28	=	=	SYM
ap-1398	62	29	∨	∨	NUM
ap-1398	62	30	c(e	c(e	NOUN
ap-1398	62	31	)	)	PUNCT
ap-1398	62	32	{	{	PUNCT
ap-1398	62	33	p	p	NOUN
ap-1398	62	34	∈	∈	PROPN
ap-1398	62	35	c(e	c(e	NOUN
ap-1398	62	36	)	)	PUNCT
ap-1398	62	37	;	;	PUNCT
ap-1398	62	38	p	p	PRON
ap-1398	62	39	is	be	AUX
ap-1398	62	40	an	an	DET
ap-1398	62	41	atom	atom	NOUN
ap-1398	62	42	of	of	ADP
ap-1398	62	43	c(e	c(e	NOUN
ap-1398	62	44	)	)	PUNCT
ap-1398	62	45	}	}	PUNCT
ap-1398	62	46	=	=	PUNCT
ap-1398	62	47	∨	∨	NUM
ap-1398	62	48	e	e	X
ap-1398	62	49	{	{	PUNCT
ap-1398	62	50	p	p	NOUN
ap-1398	62	51	∈	∈	PROPN
ap-1398	62	52	c(e	c(e	NOUN
ap-1398	62	53	)	)	PUNCT
ap-1398	62	54	;	;	PUNCT
ap-1398	62	55	p	p	PRON
ap-1398	62	56	is	be	AUX
ap-1398	62	57	an	an	DET
ap-1398	62	58	atom	atom	NOUN
ap-1398	62	59	of	of	ADP
ap-1398	62	60	c(e	c(e	NOUN
ap-1398	62	61	)	)	PUNCT
ap-1398	62	62	}	}	PUNCT
ap-1398	62	63	for	for	ADP
ap-1398	62	64	every	every	DET
ap-1398	62	65	archimedean	archimedean	ADJ
ap-1398	62	66	atomic	atomic	ADJ
ap-1398	62	67	distributive	distributive	ADJ
ap-1398	62	68	lattice	lattice	NOUN
ap-1398	62	69	effect	effect	NOUN
ap-1398	62	70	algebra	algebra	PROPN
ap-1398	62	71	e.	e.	PROPN
ap-1398	62	72	in	in	ADP
ap-1398	62	73	[	[	X
ap-1398	62	74	8	8	NUM
ap-1398	62	75	]	]	PUNCT
ap-1398	62	76	it	it	PRON
ap-1398	62	77	was	be	AUX
ap-1398	62	78	shown	show	VERB
ap-1398	62	79	that	that	SCONJ
ap-1398	62	80	there	there	PRON
ap-1398	62	81	exists	exist	VERB
ap-1398	62	82	an	an	DET
ap-1398	62	83	lea	lea	PROPN
ap-1398	62	84	e	e	NOUN
ap-1398	62	85	for	for	ADP
ap-1398	62	86	which	which	PRON
ap-1398	62	87	this	this	DET
ap-1398	62	88	property	property	NOUN
ap-1398	62	89	fails	fail	VERB
ap-1398	62	90	to	to	PART
ap-1398	62	91	be	be	AUX
ap-1398	62	92	true	true	ADJ
ap-1398	62	93	.	.	PUNCT
ap-1398	63	1	important	important	ADJ
ap-1398	63	2	properties	property	NOUN
ap-1398	63	3	of	of	ADP
ap-1398	63	4	archimedean	archimedean	ADJ
ap-1398	63	5	atomic	atomic	PROPN
ap-1398	63	6	lattice	lattice	PROPN
ap-1398	63	7	effect	effect	NOUN
ap-1398	63	8	algebras	algebra	VERB
ap-1398	63	9	with	with	ADP
ap-1398	63	10	an	an	DET
ap-1398	63	11	atomic	atomic	ADJ
ap-1398	63	12	center	center	NOUN
ap-1398	63	13	were	be	AUX
ap-1398	63	14	proven	prove	VERB
ap-1398	63	15	by	by	ADP
ap-1398	63	16	riečanová	riečanová	PROPN
ap-1398	63	17	in	in	ADP
ap-1398	63	18	[	[	X
ap-1398	63	19	21	21	NUM
ap-1398	63	20	]	]	PUNCT
ap-1398	63	21	.	.	PUNCT
ap-1398	64	1	theorem	theorem	ADJ
ap-1398	64	2	1	1	NUM
ap-1398	64	3	(	(	PUNCT
ap-1398	64	4	riečanová	riečanová	NOUN
ap-1398	65	1	[	[	X
ap-1398	65	2	21	21	NUM
ap-1398	65	3	]	]	PUNCT
ap-1398	65	4	)	)	PUNCT
ap-1398	65	5	let	let	VERB
ap-1398	65	6	e	e	PRON
ap-1398	65	7	be	be	AUX
ap-1398	65	8	an	an	DET
ap-1398	65	9	archimedean	archimedean	ADJ
ap-1398	65	10	atomic	atomic	ADJ
ap-1398	65	11	lattice	lattice	PROPN
ap-1398	65	12	effect	effect	NOUN
ap-1398	65	13	algebra	algebra	NOUN
ap-1398	65	14	with	with	ADP
ap-1398	65	15	an	an	DET
ap-1398	65	16	atomic	atomic	ADJ
ap-1398	65	17	center	center	NOUN
ap-1398	65	18	c(e	c(e	NOUN
ap-1398	65	19	)	)	PUNCT
ap-1398	65	20	.	.	PUNCT
ap-1398	66	1	let	let	VERB
ap-1398	66	2	ae	ae	PROPN
ap-1398	66	3	be	be	AUX
ap-1398	66	4	the	the	DET
ap-1398	66	5	set	set	NOUN
ap-1398	66	6	of	of	ADP
ap-1398	66	7	all	all	DET
ap-1398	66	8	atoms	atom	NOUN
ap-1398	66	9	of	of	ADP
ap-1398	66	10	e	e	NOUN
ap-1398	66	11	and	and	CCONJ
ap-1398	66	12	ac(e	ac(e	NOUN
ap-1398	66	13	)	)	PUNCT
ap-1398	66	14	the	the	DET
ap-1398	66	15	set	set	NOUN
ap-1398	66	16	of	of	ADP
ap-1398	66	17	all	all	DET
ap-1398	66	18	atoms	atom	NOUN
ap-1398	66	19	of	of	ADP
ap-1398	66	20	c(e	c(e	NOUN
ap-1398	66	21	)	)	PUNCT
ap-1398	66	22	.	.	PUNCT
ap-1398	67	1	the	the	DET
ap-1398	67	2	following	follow	VERB
ap-1398	67	3	conditions	condition	NOUN
ap-1398	67	4	are	be	AUX
ap-1398	67	5	equivalent	equivalent	ADJ
ap-1398	67	6	:	:	PUNCT
ap-1398	67	7	1	1	NUM
ap-1398	67	8	.	.	PUNCT
ap-1398	67	9	∨	∨	NUM
ap-1398	67	10	e	e	NOUN
ap-1398	67	11	ac(e	ac(e	X
ap-1398	67	12	)	)	PUNCT
ap-1398	67	13	=	=	SYM
ap-1398	68	1	1	1	NUM
ap-1398	68	2	.	.	NOUN
ap-1398	68	3	2	2	NUM
ap-1398	68	4	.	.	X
ap-1398	69	1	for	for	ADP
ap-1398	69	2	every	every	DET
ap-1398	69	3	atom	atom	NOUN
ap-1398	69	4	a	a	DET
ap-1398	69	5	∈	∈	NOUN
ap-1398	69	6	ae	ae	PROPN
ap-1398	69	7	there	there	PRON
ap-1398	69	8	exists	exist	VERB
ap-1398	69	9	an	an	DET
ap-1398	69	10	atom	atom	NOUN
ap-1398	69	11	pa	pa	PROPN
ap-1398	69	12	∈	∈	PROPN
ap-1398	69	13	ac(e	ac(e	NOUN
ap-1398	69	14	)	)	PUNCT
ap-1398	69	15	such	such	ADJ
ap-1398	69	16	that	that	SCONJ
ap-1398	69	17	a	a	DET
ap-1398	69	18	≤	≤	PROPN
ap-1398	69	19	pa	pa	PROPN
ap-1398	69	20	.	.	PROPN
ap-1398	70	1	3	3	X
ap-1398	70	2	.	.	X
ap-1398	70	3	for	for	ADP
ap-1398	70	4	every	every	DET
ap-1398	70	5	z	z	PROPN
ap-1398	70	6	∈	∈	PROPN
ap-1398	70	7	c(e	c(e	NOUN
ap-1398	70	8	)	)	PUNCT
ap-1398	70	9	it	it	PRON
ap-1398	70	10	holds	hold	VERB
ap-1398	70	11	z	z	NOUN
ap-1398	70	12	=	=	SYM
ap-1398	70	13	∨	∨	NUM
ap-1398	70	14	c(e	c(e	NOUN
ap-1398	70	15	)	)	PUNCT
ap-1398	70	16	{	{	PUNCT
ap-1398	70	17	p	p	NOUN
ap-1398	70	18	∈	∈	PROPN
ap-1398	70	19	ac(e	ac(e	NOUN
ap-1398	70	20	)	)	PUNCT
ap-1398	70	21	;	;	PUNCT
ap-1398	71	1	p	p	NOUN
ap-1398	71	2	≤	≤	PROPN
ap-1398	71	3	z	z	X
ap-1398	71	4	}	}	PUNCT
ap-1398	71	5	=	=	SYM
ap-1398	71	6	∨	∨	PROPN
ap-1398	71	7	e	e	X
ap-1398	71	8	{	{	PUNCT
ap-1398	71	9	p	p	PROPN
ap-1398	71	10	∈	∈	PROPN
ap-1398	71	11	ac(e	ac(e	NOUN
ap-1398	71	12	)	)	PUNCT
ap-1398	71	13	;	;	PUNCT
ap-1398	71	14	p	p	NOUN
ap-1398	71	15	≤	≤	PROPN
ap-1398	71	16	z	z	NOUN
ap-1398	71	17	}	}	PUNCT
ap-1398	71	18	.	.	PUNCT
ap-1398	72	1	4	4	X
ap-1398	72	2	.	.	X
ap-1398	72	3	c(e	c(e	NOUN
ap-1398	72	4	)	)	PUNCT
ap-1398	72	5	is	be	AUX
ap-1398	72	6	a	a	DET
ap-1398	72	7	bifull	bifull	ADJ
ap-1398	72	8	sub	sub	NOUN
ap-1398	72	9	-	-	NOUN
ap-1398	72	10	lattice	lattice	NOUN
ap-1398	72	11	of	of	ADP
ap-1398	72	12	e.	e.	PROPN
ap-1398	72	13	in	in	ADP
ap-1398	72	14	this	this	DET
ap-1398	72	15	case	case	NOUN
ap-1398	72	16	e	e	NOUN
ap-1398	72	17	is	be	AUX
ap-1398	72	18	isomorphic	isomorphic	ADJ
ap-1398	72	19	to	to	ADP
ap-1398	72	20	a	a	DET
ap-1398	72	21	subdirect	subdirect	NOUN
ap-1398	72	22	product	product	NOUN
ap-1398	72	23	of	of	ADP
ap-1398	72	24	archimedean	archimedean	ADJ
ap-1398	72	25	atomic	atomic	PROPN
ap-1398	72	26	irreducible	irreducible	ADJ
ap-1398	72	27	lattice	lattice	PROPN
ap-1398	72	28	effect	effect	NOUN
ap-1398	72	29	algebras	algebra	NOUN
ap-1398	72	30	.	.	PUNCT
ap-1398	73	1	theorem	theorem	ADJ
ap-1398	73	2	2	2	NUM
ap-1398	73	3	(	(	PUNCT
ap-1398	73	4	paseka	paseka	NOUN
ap-1398	73	5	,	,	PUNCT
ap-1398	73	6	riečanová	riečanová	PROPN
ap-1398	74	1	[	[	X
ap-1398	74	2	13	13	NUM
ap-1398	74	3	]	]	PUNCT
ap-1398	74	4	)	)	PUNCT
ap-1398	74	5	let	let	VERB
ap-1398	74	6	e	e	PRON
ap-1398	74	7	be	be	AUX
ap-1398	74	8	an	an	DET
ap-1398	74	9	atomic	atomic	ADJ
ap-1398	74	10	archimedean	archimedean	ADJ
ap-1398	74	11	lattice	lattice	PROPN
ap-1398	74	12	effect	effect	PROPN
ap-1398	74	13	algebra	algebra	PROPN
ap-1398	74	14	.	.	PUNCT
ap-1398	75	1	then	then	ADV
ap-1398	75	2	the	the	DET
ap-1398	75	3	set	set	NOUN
ap-1398	75	4	s(e	s(e	PROPN
ap-1398	75	5	)	)	PUNCT
ap-1398	75	6	of	of	ADP
ap-1398	75	7	all	all	DET
ap-1398	75	8	sharp	sharp	ADJ
ap-1398	75	9	elements	element	NOUN
ap-1398	75	10	of	of	ADP
ap-1398	75	11	e	e	PROPN
ap-1398	75	12	is	be	AUX
ap-1398	75	13	a	a	DET
ap-1398	75	14	bifull	bifull	ADJ
ap-1398	75	15	sublattice	sublattice	NOUN
ap-1398	75	16	of	of	ADP
ap-1398	75	17	e.	e.	PROPN
ap-1398	75	18	we	we	PRON
ap-1398	75	19	will	will	AUX
ap-1398	75	20	deal	deal	VERB
ap-1398	75	21	only	only	ADV
ap-1398	75	22	with	with	ADP
ap-1398	75	23	atomic	atomic	ADJ
ap-1398	75	24	archimedean	archimedean	PROPN
ap-1398	75	25	lattice	lattice	PROPN
ap-1398	75	26	effect	effect	NOUN
ap-1398	75	27	algebras	algebras	PROPN
ap-1398	75	28	e.	e.	PROPN
ap-1398	75	29	we	we	PRON
ap-1398	75	30	have	have	VERB
ap-1398	75	31	c(e	c(e	NOUN
ap-1398	75	32	)	)	PUNCT
ap-1398	75	33	⊂	⊂	PROPN
ap-1398	75	34	s(e	s(e	PROPN
ap-1398	75	35	)	)	PUNCT
ap-1398	76	1	⊂	⊂	PROPN
ap-1398	76	2	e.	e.	PROPN
ap-1398	77	1	because	because	SCONJ
ap-1398	77	2	of	of	ADP
ap-1398	77	3	this	this	DET
ap-1398	77	4	inclusion	inclusion	NOUN
ap-1398	77	5	and	and	CCONJ
ap-1398	77	6	theorem	theorem	NOUN
ap-1398	77	7	2	2	NUM
ap-1398	77	8	,	,	PUNCT
ap-1398	77	9	considering	consider	VERB
ap-1398	77	10	the	the	DET
ap-1398	77	11	bifullness	bifullness	NOUN
ap-1398	77	12	of	of	ADP
ap-1398	77	13	the	the	DET
ap-1398	77	14	center	center	NOUN
ap-1398	77	15	c(e	c(e	NOUN
ap-1398	77	16	)	)	PUNCT
ap-1398	77	17	in	in	ADP
ap-1398	77	18	e	e	NOUN
ap-1398	77	19	is	be	AUX
ap-1398	77	20	equivalent	equivalent	ADJ
ap-1398	77	21	to	to	ADP
ap-1398	77	22	considering	consider	VERB
ap-1398	77	23	the	the	DET
ap-1398	77	24	bifullness	bifullness	NOUN
ap-1398	77	25	of	of	ADP
ap-1398	77	26	c(e	c(e	NOUN
ap-1398	77	27	)	)	PUNCT
ap-1398	77	28	in	in	ADP
ap-1398	77	29	s(e	s(e	PROPN
ap-1398	77	30	)	)	PUNCT
ap-1398	77	31	.	.	PUNCT
ap-1398	78	1	and	and	CCONJ
ap-1398	78	2	s(e	s(e	PROPN
ap-1398	78	3	)	)	PUNCT
ap-1398	78	4	is	be	AUX
ap-1398	78	5	an	an	DET
ap-1398	78	6	orthomodular	orthomodular	ADJ
ap-1398	78	7	lattice	lattice	NOUN
ap-1398	78	8	.	.	PUNCT
ap-1398	79	1	for	for	ADP
ap-1398	79	2	this	this	DET
ap-1398	79	3	reason	reason	NOUN
ap-1398	79	4	,	,	PUNCT
ap-1398	79	5	in	in	ADP
ap-1398	79	6	the	the	DET
ap-1398	79	7	rest	rest	NOUN
ap-1398	79	8	of	of	ADP
ap-1398	79	9	the	the	DET
ap-1398	79	10	paper	paper	NOUN
ap-1398	79	11	we	we	PRON
ap-1398	79	12	will	will	AUX
ap-1398	79	13	restrict	restrict	VERB
ap-1398	79	14	our	our	PRON
ap-1398	79	15	attention	attention	NOUN
ap-1398	79	16	to	to	ADP
ap-1398	79	17	atomic	atomic	ADJ
ap-1398	79	18	orthomodular	orthomodular	NOUN
ap-1398	79	19	lattices	lattice	NOUN
ap-1398	79	20	l	l	NOUN
ap-1398	79	21	and	and	CCONJ
ap-1398	79	22	their	their	PRON
ap-1398	79	23	centers	center	NOUN
ap-1398	79	24	c(l	c(l	NOUN
ap-1398	79	25	)	)	PUNCT
ap-1398	79	26	.	.	PUNCT
ap-1398	80	1	for	for	ADP
ap-1398	80	2	the	the	DET
ap-1398	80	3	sake	sake	NOUN
ap-1398	80	4	of	of	ADP
ap-1398	80	5	completeness	completeness	NOUN
ap-1398	80	6	,	,	PUNCT
ap-1398	80	7	we	we	PRON
ap-1398	80	8	give	give	VERB
ap-1398	80	9	the	the	DET
ap-1398	80	10	definition	definition	NOUN
ap-1398	80	11	of	of	ADP
ap-1398	80	12	an	an	DET
ap-1398	80	13	orthomodular	orthomodular	ADJ
ap-1398	80	14	lattice	lattice	NOUN
ap-1398	80	15	.	.	PUNCT
ap-1398	81	1	definition	definition	NOUN
ap-1398	81	2	4	4	NUM
ap-1398	81	3	let	let	VERB
ap-1398	81	4	l	l	NOUN
ap-1398	81	5	be	be	AUX
ap-1398	81	6	a	a	DET
ap-1398	81	7	bounded	bounded	ADJ
ap-1398	81	8	lattice	lattice	NOUN
ap-1398	81	9	with	with	ADP
ap-1398	81	10	a	a	DET
ap-1398	81	11	unary	unary	ADJ
ap-1398	81	12	operation	operation	NOUN
ap-1398	81	13	′	′	NUM
ap-1398	81	14	(	(	PUNCT
ap-1398	81	15	called	call	VERB
ap-1398	81	16	complementation	complementation	NOUN
ap-1398	81	17	)	)	PUNCT
ap-1398	81	18	satisfying	satisfy	VERB
ap-1398	81	19	the	the	DET
ap-1398	81	20	following	follow	VERB
ap-1398	81	21	conditions	condition	NOUN
ap-1398	81	22	1	1	NUM
ap-1398	81	23	.	.	PUNCT
ap-1398	82	1	for	for	ADP
ap-1398	82	2	all	all	DET
ap-1398	82	3	a	a	DET
ap-1398	82	4	∈	∈	ADJ
ap-1398	82	5	l	l	NOUN
ap-1398	82	6	(	(	PUNCT
ap-1398	82	7	a′)′	a′)′	SYM
ap-1398	82	8	=	=	SYM
ap-1398	82	9	a	a	PRON
ap-1398	82	10	,	,	PUNCT
ap-1398	82	11	2	2	X
ap-1398	82	12	.	.	X
ap-1398	83	1	for	for	ADP
ap-1398	83	2	all	all	DET
ap-1398	83	3	a	a	PRON
ap-1398	83	4	,	,	PUNCT
ap-1398	83	5	b	b	X
ap-1398	83	6	∈	∈	ADJ
ap-1398	83	7	l	l	NOUN
ap-1398	83	8	if	if	SCONJ
ap-1398	83	9	a	a	DET
ap-1398	83	10	≤	≤	PROPN
ap-1398	83	11	b	b	NOUN
ap-1398	83	12	then	then	ADV
ap-1398	83	13	b′	b′	NUM
ap-1398	83	14	≤	≤	NOUN
ap-1398	83	15	a′	a′	PROPN
ap-1398	83	16	,	,	PUNCT
ap-1398	83	17	3	3	X
ap-1398	83	18	.	.	X
ap-1398	84	1	for	for	ADP
ap-1398	84	2	all	all	DET
ap-1398	84	3	a	a	PRON
ap-1398	84	4	,	,	PUNCT
ap-1398	84	5	b	b	X
ap-1398	84	6	∈	∈	ADJ
ap-1398	84	7	l	l	NOUN
ap-1398	85	1	if	if	SCONJ
ap-1398	85	2	a	a	DET
ap-1398	85	3	≤	≤	PROPN
ap-1398	85	4	b	b	NOUN
ap-1398	85	5	then	then	ADV
ap-1398	85	6	a	a	DET
ap-1398	85	7	∨	∨	NOUN
ap-1398	85	8	(	(	PUNCT
ap-1398	85	9	a′	a′	PROPN
ap-1398	85	10	∧	∧	PROPN
ap-1398	85	11	b	b	PROPN
ap-1398	85	12	)	)	PUNCT
ap-1398	86	1	=	=	SYM
ap-1398	86	2	b.	b.	PROPN
ap-1398	86	3	then	then	ADV
ap-1398	86	4	l	l	PROPN
ap-1398	86	5	is	be	AUX
ap-1398	86	6	said	say	VERB
ap-1398	86	7	to	to	PART
ap-1398	86	8	be	be	AUX
ap-1398	86	9	an	an	DET
ap-1398	86	10	orthomodular	orthomodular	ADJ
ap-1398	86	11	lattice	lattice	NOUN
ap-1398	86	12	(	(	PUNCT
ap-1398	86	13	oml	oml	PROPN
ap-1398	86	14	for	for	ADP
ap-1398	86	15	brevity	brevity	NOUN
ap-1398	86	16	)	)	PUNCT
ap-1398	86	17	.	.	PUNCT
ap-1398	87	1	remark	remark	VERB
ap-1398	87	2	1	1	NUM
ap-1398	87	3	though	though	ADV
ap-1398	87	4	in	in	ADP
ap-1398	87	5	oml	oml	PROPN
ap-1398	87	6	’s	’s	PART
ap-1398	87	7	we	we	PRON
ap-1398	87	8	have	have	VERB
ap-1398	87	9	just	just	ADV
ap-1398	87	10	latticetheoretical	latticetheoretical	ADJ
ap-1398	87	11	operations	operation	NOUN
ap-1398	87	12	∨	∨	NOUN
ap-1398	87	13	and	and	CCONJ
ap-1398	87	14	∧	∧	PROPN
ap-1398	87	15	,	,	PUNCT
ap-1398	87	16	we	we	PRON
ap-1398	87	17	will	will	AUX
ap-1398	87	18	use	use	AUX
ap-1398	87	19	also	also	ADV
ap-1398	87	20	effect	effect	VERB
ap-1398	87	21	algebraic	algebraic	ADJ
ap-1398	87	22	operations	operation	NOUN
ap-1398	87	23	⊕	⊕	PROPN
ap-1398	87	24	and	and	CCONJ
ap-1398	87	25	�	�	PROPN
ap-1398	87	26	with	with	ADP
ap-1398	87	27	the	the	DET
ap-1398	87	28	meaning	meaning	NOUN
ap-1398	87	29	a	a	DET
ap-1398	87	30	⊕	⊕	PROPN
ap-1398	87	31	b	b	X
ap-1398	87	32	=	=	PUNCT
ap-1398	87	33	a	a	DET
ap-1398	87	34	∨	∨	PROPN
ap-1398	87	35	b	b	X
ap-1398	87	36	iff	iff	PROPN
ap-1398	87	37	a	a	DET
ap-1398	87	38	≤	≤	NUM
ap-1398	87	39	b′	b′	NUM
ap-1398	87	40	and	and	CCONJ
ap-1398	87	41	a	a	DET
ap-1398	87	42	�	�	PROPN
ap-1398	87	43	b	b	PROPN
ap-1398	88	1	=	=	SYM
ap-1398	88	2	c	c	PROPN
ap-1398	88	3	iff	iff	PROPN
ap-1398	88	4	b	b	PROPN
ap-1398	88	5	⊕	⊕	PROPN
ap-1398	88	6	c	c	AUX
ap-1398	88	7	=	=	PUNCT
ap-1398	88	8	a.	a.	NOUN
ap-1398	88	9	27	27	NUM
ap-1398	88	10	acta	acta	PROPN
ap-1398	88	11	polytechnica	polytechnica	PROPN
ap-1398	88	12	vol	vol	NOUN
ap-1398	88	13	.	.	PUNCT
ap-1398	89	1	51	51	NUM
ap-1398	89	2	no	no	NOUN
ap-1398	89	3	.	.	PUNCT
ap-1398	90	1	4/2011	4/2011	NUM
ap-1398	90	2	2	2	NUM
ap-1398	90	3	orthomodular	orthomodular	NOUN
ap-1398	90	4	lattice	lattice	NOUN
ap-1398	90	5	l	l	NOUN
ap-1398	90	6	whose	whose	DET
ap-1398	90	7	center	center	NOUN
ap-1398	90	8	is	be	AUX
ap-1398	90	9	not	not	PART
ap-1398	90	10	a	a	DET
ap-1398	90	11	bifull	bifull	ADJ
ap-1398	90	12	sublattice	sublattice	NOUN
ap-1398	90	13	let	let	VERB
ap-1398	90	14	us	we	PRON
ap-1398	90	15	have	have	VERB
ap-1398	90	16	the	the	DET
ap-1398	90	17	following	follow	VERB
ap-1398	90	18	sequences	sequence	NOUN
ap-1398	90	19	of	of	ADP
ap-1398	90	20	atoms	atom	NOUN
ap-1398	90	21	(	(	PUNCT
ap-1398	90	22	sets	set	NOUN
ap-1398	90	23	):	):	PUNCT
ap-1398	90	24	a0	a0	PROPN
ap-1398	90	25	=	=	SYM
ap-1398	90	26	{	{	PUNCT
ap-1398	90	27	(	(	PUNCT
ap-1398	90	28	x	x	NOUN
ap-1398	90	29	,	,	PUNCT
ap-1398	90	30	y	y	NOUN
ap-1398	90	31	)	)	PUNCT
ap-1398	90	32	∈	∈	PROPN
ap-1398	90	33	r	r	NOUN
ap-1398	90	34	2	2	NUM
ap-1398	90	35	;	;	PUNCT
ap-1398	90	36	0	0	NUM
ap-1398	90	37	≤	≤	NUM
ap-1398	90	38	x	x	SYM
ap-1398	90	39	≤	≤	NUM
ap-1398	90	40	1	1	NUM
ap-1398	90	41	,	,	PUNCT
ap-1398	90	42	y	y	PROPN
ap-1398	90	43	∈	∈	PROPN
ap-1398	90	44	r	r	NOUN
ap-1398	90	45	}	}	PUNCT
ap-1398	90	46	,	,	PUNCT
ap-1398	90	47	al	al	PROPN
ap-1398	90	48	=	=	PRON
ap-1398	90	49	{	{	PUNCT
ap-1398	90	50	(	(	PUNCT
ap-1398	90	51	x	x	NOUN
ap-1398	90	52	,	,	PUNCT
ap-1398	90	53	y	y	NOUN
ap-1398	90	54	)	)	PUNCT
ap-1398	90	55	∈	∈	PROPN
ap-1398	90	56	r	r	NOUN
ap-1398	90	57	2	2	NUM
ap-1398	90	58	;	;	PUNCT
ap-1398	90	59	l	l	X
ap-1398	90	60	<	<	X
ap-1398	90	61	x	x	PUNCT
ap-1398	90	62	≤	≤	NUM
ap-1398	90	63	l	l	NOUN
ap-1398	91	1	+	+	CCONJ
ap-1398	91	2	1	1	NUM
ap-1398	91	3	,	,	PUNCT
ap-1398	91	4	y	y	PROPN
ap-1398	91	5	∈	∈	PROPN
ap-1398	91	6	r	r	NOUN
ap-1398	91	7	}	}	PUNCT
ap-1398	91	8	,	,	PUNCT
ap-1398	91	9	for	for	ADP
ap-1398	91	10	l	l	NOUN
ap-1398	91	11	=	=	SYM
ap-1398	91	12	1	1	NUM
ap-1398	91	13	,	,	PUNCT
ap-1398	91	14	2	2	NUM
ap-1398	91	15	,	,	PUNCT
ap-1398	91	16	.	.	PUNCT
ap-1398	91	17	.	.	PUNCT
ap-1398	92	1	.	.	PUNCT
ap-1398	92	2	,	,	PUNCT
ap-1398	92	3	b0	b0	NOUN
ap-1398	92	4	=	=	SYM
ap-1398	92	5	{	{	PUNCT
ap-1398	92	6	(	(	PUNCT
ap-1398	92	7	x	x	NOUN
ap-1398	92	8	,	,	PUNCT
ap-1398	92	9	y	y	NOUN
ap-1398	92	10	)	)	PUNCT
ap-1398	92	11	∈	∈	PROPN
ap-1398	92	12	r	r	NOUN
ap-1398	92	13	2;−1	2;−1	NUM
ap-1398	92	14	≤	≤	NUM
ap-1398	92	15	x	x	X
ap-1398	92	16	<	<	X
ap-1398	92	17	0	0	PROPN
ap-1398	92	18	,	,	PUNCT
ap-1398	92	19	y	y	PROPN
ap-1398	92	20	∈	∈	PROPN
ap-1398	92	21	r	r	NOUN
ap-1398	92	22	}	}	PUNCT
ap-1398	92	23	,	,	PUNCT
ap-1398	92	24	bl	bl	PROPN
ap-1398	92	25	=	=	SYM
ap-1398	92	26	{	{	PUNCT
ap-1398	92	27	(	(	PUNCT
ap-1398	92	28	x	x	NOUN
ap-1398	92	29	,	,	PUNCT
ap-1398	92	30	y	y	NOUN
ap-1398	92	31	)	)	PUNCT
ap-1398	92	32	∈	∈	NOUN
ap-1398	92	33	r2;−l	r2;−l	NOUN
ap-1398	92	34	−	−	PROPN
ap-1398	92	35	1	1	NUM
ap-1398	92	36	≤	≤	NUM
ap-1398	92	37	x	x	PUNCT
ap-1398	92	38	<	<	X
ap-1398	92	39	−l	−l	NOUN
ap-1398	92	40	,	,	PUNCT
ap-1398	92	41	y	y	PROPN
ap-1398	92	42	∈	∈	PROPN
ap-1398	92	43	r	r	NOUN
ap-1398	92	44	}	}	PUNCT
ap-1398	92	45	,	,	PUNCT
ap-1398	92	46	for	for	ADP
ap-1398	92	47	l	l	NOUN
ap-1398	92	48	=	=	SYM
ap-1398	92	49	1	1	NUM
ap-1398	92	50	,	,	PUNCT
ap-1398	92	51	2	2	NUM
ap-1398	92	52	,	,	PUNCT
ap-1398	92	53	.	.	PUNCT
ap-1398	92	54	.	.	PUNCT
ap-1398	93	1	.	.	PUNCT
ap-1398	94	1	,	,	PUNCT
ap-1398	94	2	(	(	PUNCT
ap-1398	94	3	2	2	X
ap-1398	94	4	)	)	PUNCT
ap-1398	94	5	cj	cj	NOUN
ap-1398	94	6	=	=	SYM
ap-1398	94	7	{	{	PUNCT
ap-1398	94	8	(	(	PUNCT
ap-1398	94	9	x	x	NOUN
ap-1398	94	10	,	,	PUNCT
ap-1398	94	11	y	y	NOUN
ap-1398	94	12	)	)	PUNCT
ap-1398	94	13	∈	∈	PROPN
ap-1398	94	14	r2;−j	r2;−j	NOUN
ap-1398	94	15	≤	≤	NUM
ap-1398	95	1	x	x	PUNCT
ap-1398	95	2	≤	≤	NUM
ap-1398	95	3	j	j	PROPN
ap-1398	95	4	,	,	PUNCT
ap-1398	95	5	y	y	PROPN
ap-1398	95	6	≤	≤	PROPN
ap-1398	95	7	j	j	PROPN
ap-1398	95	8	·	·	PUNCT
ap-1398	95	9	x	x	X
ap-1398	95	10	}	}	PUNCT
ap-1398	95	11	,	,	PUNCT
ap-1398	95	12	for	for	ADP
ap-1398	95	13	j	j	PROPN
ap-1398	95	14	=	=	SYM
ap-1398	95	15	1	1	NUM
ap-1398	95	16	,	,	PUNCT
ap-1398	95	17	2	2	NUM
ap-1398	95	18	,	,	PUNCT
ap-1398	95	19	.	.	PUNCT
ap-1398	95	20	.	.	PUNCT
ap-1398	96	1	.	.	PUNCT
ap-1398	96	2	,	,	PUNCT
ap-1398	96	3	dj	dj	NOUN
ap-1398	96	4	=	=	SYM
ap-1398	96	5	{	{	PUNCT
ap-1398	96	6	(	(	PUNCT
ap-1398	96	7	x	x	NOUN
ap-1398	96	8	,	,	PUNCT
ap-1398	96	9	y	y	NOUN
ap-1398	96	10	)	)	PUNCT
ap-1398	96	11	∈	∈	PROPN
ap-1398	96	12	r2;−j	r2;−j	NOUN
ap-1398	96	13	≤	≤	NUM
ap-1398	97	1	x	x	PUNCT
ap-1398	97	2	≤	≤	NUM
ap-1398	97	3	j	j	PROPN
ap-1398	97	4	,	,	PUNCT
ap-1398	97	5	y	y	PROPN
ap-1398	97	6	>	>	X
ap-1398	97	7	j	j	PROPN
ap-1398	97	8	·	·	PUNCT
ap-1398	97	9	x	x	X
ap-1398	97	10	}	}	PUNCT
ap-1398	97	11	,	,	PUNCT
ap-1398	97	12	for	for	ADP
ap-1398	97	13	j	j	PROPN
ap-1398	97	14	=	=	SYM
ap-1398	97	15	1	1	NUM
ap-1398	97	16	,	,	PUNCT
ap-1398	97	17	2	2	NUM
ap-1398	97	18	,	,	PUNCT
ap-1398	97	19	.	.	PUNCT
ap-1398	97	20	.	.	PUNCT
ap-1398	98	1	.	.	PUNCT
ap-1398	99	1	,	,	PUNCT
ap-1398	99	2	pj	pj	PROPN
ap-1398	99	3	=	=	PRON
ap-1398	99	4	{	{	PUNCT
ap-1398	99	5	j	j	NOUN
ap-1398	99	6	}	}	PUNCT
ap-1398	99	7	,	,	PUNCT
ap-1398	99	8	for	for	ADP
ap-1398	99	9	j	j	PROPN
ap-1398	99	10	=	=	SYM
ap-1398	99	11	1	1	NUM
ap-1398	99	12	,	,	PUNCT
ap-1398	99	13	2	2	NUM
ap-1398	99	14	,	,	PUNCT
ap-1398	99	15	.	.	PUNCT
ap-1398	99	16	.	.	PUNCT
ap-1398	100	1	..	..	PUNCT
ap-1398	100	2	for	for	ADP
ap-1398	100	3	such	such	DET
ap-1398	100	4	a	a	DET
ap-1398	100	5	choice	choice	NOUN
ap-1398	100	6	of	of	ADP
ap-1398	100	7	atoms	atom	NOUN
ap-1398	100	8	,	,	PUNCT
ap-1398	100	9	q1	q1	PROPN
ap-1398	100	10	�	�	PROPN
ap-1398	100	11	=	=	SYM
ap-1398	100	12	q2	q2	NOUN
ap-1398	100	13	are	be	AUX
ap-1398	100	14	compatible	compatible	ADJ
ap-1398	100	15	if	if	SCONJ
ap-1398	100	16	and	and	CCONJ
ap-1398	100	17	only	only	ADV
ap-1398	100	18	if	if	SCONJ
ap-1398	100	19	q1∩q2	q1∩q2	PROPN
ap-1398	100	20	=	=	PUNCT
ap-1398	100	21	∅.	∅.	VERB
ap-1398	100	22	fig	fig	NOUN
ap-1398	100	23	.	.	PUNCT
ap-1398	101	1	1	1	NUM
ap-1398	101	2	shows	show	VERB
ap-1398	101	3	the	the	DET
ap-1398	101	4	compatibility	compatibility	NOUN
ap-1398	101	5	among	among	ADP
ap-1398	101	6	atoms	atom	NOUN
ap-1398	101	7	.	.	PUNCT
ap-1398	102	1	for	for	ADP
ap-1398	102	2	their	their	PRON
ap-1398	102	3	non	non	ADJ
ap-1398	102	4	-	-	NOUN
ap-1398	102	5	compatibility	compatibility	NOUN
ap-1398	102	6	(	(	PUNCT
ap-1398	102	7	denoted	denote	VERB
ap-1398	102	8	by	by	ADP
ap-1398	102	9	�	�	PROPN
ap-1398	102	10	↔	↔	PROPN
ap-1398	102	11	)	)	PUNCT
ap-1398	102	12	the	the	DET
ap-1398	102	13	following	follow	VERB
ap-1398	102	14	rules	rule	NOUN
ap-1398	102	15	hold	hold	VERB
ap-1398	102	16	cj	cj	PRON
ap-1398	102	17	�	�	PROPN
ap-1398	102	18	↔	↔	PROPN
ap-1398	102	19	ai	ai	NOUN
ap-1398	102	20	,	,	PUNCT
ap-1398	102	21	cj	cj	PROPN
ap-1398	102	22	�	�	PROPN
ap-1398	102	23	↔	↔	PROPN
ap-1398	102	24	bi	bi	NOUN
ap-1398	102	25	for	for	ADP
ap-1398	102	26	all	all	PRON
ap-1398	102	27	j	j	NOUN
ap-1398	102	28	=	=	SYM
ap-1398	102	29	1	1	NUM
ap-1398	102	30	,	,	PUNCT
ap-1398	102	31	2	2	NUM
ap-1398	102	32	,	,	PUNCT
ap-1398	102	33	.	.	PUNCT
ap-1398	102	34	.	.	PUNCT
ap-1398	103	1	.	.	PUNCT
ap-1398	104	1	and	and	CCONJ
ap-1398	104	2	i	i	PRON
ap-1398	104	3	=	=	NOUN
ap-1398	104	4	0	0	NUM
ap-1398	104	5	,	,	PUNCT
ap-1398	104	6	.	.	PUNCT
ap-1398	104	7	.	.	PUNCT
ap-1398	105	1	.	.	PUNCT
ap-1398	106	1	,	,	PUNCT
ap-1398	106	2	j	j	PROPN
ap-1398	107	1	−	−	PROPN
ap-1398	107	2	1	1	NUM
ap-1398	107	3	,	,	PUNCT
ap-1398	107	4	dj	dj	X
ap-1398	107	5	�	�	PROPN
ap-1398	107	6	↔	↔	PROPN
ap-1398	107	7	ai	ai	NOUN
ap-1398	107	8	,	,	PUNCT
ap-1398	107	9	dj	dj	X
ap-1398	107	10	�	�	NOUN
ap-1398	107	11	↔	↔	PROPN
ap-1398	107	12	bi	bi	NOUN
ap-1398	107	13	for	for	ADP
ap-1398	107	14	all	all	PRON
ap-1398	107	15	j	j	NOUN
ap-1398	108	1	=	=	SYM
ap-1398	108	2	1	1	NUM
ap-1398	108	3	,	,	PUNCT
ap-1398	108	4	2	2	NUM
ap-1398	108	5	,	,	PUNCT
ap-1398	108	6	.	.	PUNCT
ap-1398	108	7	.	.	PUNCT
ap-1398	109	1	.	.	PUNCT
ap-1398	110	1	and	and	CCONJ
ap-1398	110	2	i	i	PRON
ap-1398	110	3	=	=	NOUN
ap-1398	110	4	0	0	NUM
ap-1398	110	5	,	,	PUNCT
ap-1398	110	6	.	.	PUNCT
ap-1398	110	7	.	.	PUNCT
ap-1398	111	1	.	.	PUNCT
ap-1398	112	1	,	,	PUNCT
ap-1398	112	2	j	j	PROPN
ap-1398	112	3	−	−	PROPN
ap-1398	112	4	1	1	NUM
ap-1398	112	5	,	,	PUNCT
ap-1398	112	6	cj	cj	PROPN
ap-1398	112	7	�	�	PROPN
ap-1398	112	8	↔	↔	PROPN
ap-1398	112	9	di	di	NOUN
ap-1398	112	10	for	for	ADP
ap-1398	112	11	all	all	DET
ap-1398	112	12	i	i	PROPN
ap-1398	112	13	,	,	PUNCT
ap-1398	112	14	j	j	PROPN
ap-1398	112	15	=	=	SYM
ap-1398	112	16	1	1	NUM
ap-1398	112	17	,	,	PUNCT
ap-1398	112	18	2	2	NUM
ap-1398	112	19	,	,	PUNCT
ap-1398	112	20	.	.	PUNCT
ap-1398	112	21	.	.	PUNCT
ap-1398	112	22	.	.	PUNCT
ap-1398	113	1	such	such	ADJ
ap-1398	113	2	that	that	SCONJ
ap-1398	113	3	i	i	PRON
ap-1398	113	4	�	�	PROPN
ap-1398	113	5	=	=	SYM
ap-1398	113	6	j	j	PROPN
ap-1398	113	7	,	,	PUNCT
ap-1398	113	8	cj	cj	PROPN
ap-1398	113	9	�	�	PROPN
ap-1398	113	10	↔	↔	PROPN
ap-1398	113	11	ci	ci	NOUN
ap-1398	113	12	,	,	PUNCT
ap-1398	113	13	dj	dj	X
ap-1398	113	14	�	�	PROPN
ap-1398	113	15	↔	↔	NOUN
ap-1398	113	16	di	di	NOUN
ap-1398	113	17	for	for	ADP
ap-1398	113	18	all	all	DET
ap-1398	113	19	i	i	PROPN
ap-1398	113	20	,	,	PUNCT
ap-1398	113	21	j	j	PROPN
ap-1398	113	22	=	=	SYM
ap-1398	113	23	1	1	NUM
ap-1398	113	24	,	,	PUNCT
ap-1398	113	25	2	2	NUM
ap-1398	113	26	,	,	PUNCT
ap-1398	113	27	.	.	PUNCT
ap-1398	113	28	.	.	PUNCT
ap-1398	114	1	.	.	PUNCT
ap-1398	115	1	such	such	ADJ
ap-1398	115	2	that	that	SCONJ
ap-1398	115	3	i	i	PRON
ap-1398	115	4	�	�	PROPN
ap-1398	115	5	=	=	SYM
ap-1398	115	6	j.	j.	PROPN
ap-1398	115	7	�	�	PROPN
ap-1398	115	8	�	�	PROPN
ap-1398	115	9	�	�	PROPN
ap-1398	115	10	�	�	PROPN
ap-1398	115	11	�	�	PROPN
ap-1398	115	12	�	�	PROPN
ap-1398	115	13	�	�	PROPN
ap-1398	115	14	�	�	PROPN
ap-1398	115	15	�	�	PROPN
ap-1398	115	16	�	�	PROPN
ap-1398	115	17	�	�	PROPN
ap-1398	115	18	�	�	PROPN
ap-1398	115	19	�	�	PROPN
ap-1398	115	20	�	�	PROPN
ap-1398	115	21	p1	p1	PROPN
ap-1398	115	22	p2	p2	PROPN
ap-1398	115	23	p3	p3	PROPN
ap-1398	115	24	p4	p4	ADJ
ap-1398	115	25	p5	p5	ADJ
ap-1398	115	26	p6	p6	PROPN
ap-1398	115	27	pn	pn	PROPN
ap-1398	115	28	pn+1	pn+1	PROPN
ap-1398	115	29	�	�	PROPN
ap-1398	115	30	�	�	PROPN
ap-1398	115	31	�	�	PROPN
ap-1398	115	32	�	�	PROPN
ap-1398	115	33	�	�	PROPN
ap-1398	115	34	�	�	PROPN
ap-1398	115	35	�	�	PROPN
ap-1398	115	36	�	�	PROPN
ap-1398	115	37	�	�	PROPN
ap-1398	115	38	�	�	PROPN
ap-1398	115	39	�	�	PROPN
ap-1398	115	40	�	�	PROPN
ap-1398	115	41	�	�	PROPN
ap-1398	115	42	�	�	PROPN
ap-1398	115	43	a0	a0	PROPN
ap-1398	115	44	b0	b0	PROPN
ap-1398	115	45	a1	a1	PROPN
ap-1398	115	46	b1	b1	PROPN
ap-1398	115	47	a2	a2	PROPN
ap-1398	115	48	b2	b2	PROPN
ap-1398	115	49	an	an	DET
ap-1398	115	50	bn	bn	PROPN
ap-1398	115	51	�	�	PROPN
ap-1398	115	52	�	�	PROPN
ap-1398	115	53	�	�	PROPN
ap-1398	115	54	�	�	PROPN
ap-1398	115	55	�	�	PROPN
ap-1398	115	56	�	�	PROPN
ap-1398	115	57	�	�	PROPN
ap-1398	115	58	�	�	PROPN
ap-1398	115	59	�	�	PROPN
ap-1398	115	60	�	�	PROPN
ap-1398	115	61	�	�	PROPN
ap-1398	115	62	�	�	PROPN
ap-1398	115	63	�	�	PROPN
ap-1398	115	64	�	�	PROPN
ap-1398	115	65	�	�	PROPN
ap-1398	115	66	�	�	PROPN
ap-1398	115	67	c1	c1	PROPN
ap-1398	115	68	c2	c2	PROPN
ap-1398	115	69	c3	c3	PROPN
ap-1398	115	70	cn−1	cn−1	PROPN
ap-1398	115	71	d1	d1	PROPN
ap-1398	115	72	d2	d2	PROPN
ap-1398	115	73	d3	d3	PROPN
ap-1398	115	74	dn−1	dn−1	PROPN
ap-1398	115	75	fig	fig	NOUN
ap-1398	115	76	.	.	PUNCT
ap-1398	116	1	1	1	NUM
ap-1398	116	2	:	:	PUNCT
ap-1398	116	3	greechie	greechie	NOUN
ap-1398	116	4	diagram	diagram	NOUN
ap-1398	116	5	of	of	ADP
ap-1398	116	6	sets	set	NOUN
ap-1398	116	7	of	of	ADP
ap-1398	116	8	atoms	atom	NOUN
ap-1398	116	9	for	for	ADP
ap-1398	116	10	non	non	ADJ
ap-1398	116	11	-	-	ADJ
ap-1398	116	12	compatible	compatible	ADJ
ap-1398	116	13	atoms	atom	NOUN
ap-1398	116	14	the	the	DET
ap-1398	116	15	following	follow	VERB
ap-1398	116	16	equalities	equality	NOUN
ap-1398	116	17	hold	hold	VERB
ap-1398	116	18	cj	cj	NOUN
ap-1398	116	19	⊕	⊕	PROPN
ap-1398	116	20	dj	dj	NOUN
ap-1398	117	1	=	=	PUNCT
ap-1398	117	2	j−1⊕	j−1⊕	PROPN
ap-1398	118	1	i=0	i=0	PROPN
ap-1398	118	2	(	(	PUNCT
ap-1398	118	3	ai	ai	PROPN
ap-1398	118	4	⊕	⊕	PROPN
ap-1398	118	5	bi	bi	PROPN
ap-1398	118	6	)	)	PUNCT
ap-1398	119	1	=	=	SYM
ap-1398	120	1	ck	ck	PROPN
ap-1398	120	2	∨	∨	NUM
ap-1398	120	3	cj	cj	NOUN
ap-1398	121	1	=	=	SYM
ap-1398	121	2	dk	dk	PROPN
ap-1398	121	3	∨	∨	NOUN
ap-1398	121	4	dj	dj	NOUN
ap-1398	121	5	=	=	PUNCT
ap-1398	121	6	ck	ck	PROPN
ap-1398	121	7	∨	∨	NUM
ap-1398	121	8	dj	dj	NOUN
ap-1398	122	1	=	=	SYM
ap-1398	123	1	dk	dk	PROPN
ap-1398	124	1	∨	∨	NUM
ap-1398	124	2	cj	cj	X
ap-1398	124	3	=	=	SYM
ap-1398	124	4	cj	cj	PROPN
ap-1398	124	5	∨	∨	NUM
ap-1398	124	6	al	al	PROPN
ap-1398	124	7	=	=	PROPN
ap-1398	124	8	cj	cj	PROPN
ap-1398	125	1	∨	∨	NUM
ap-1398	125	2	bl	bl	NOUN
ap-1398	125	3	=	=	NOUN
ap-1398	125	4	dj	dj	PROPN
ap-1398	125	5	∨	∨	PROPN
ap-1398	125	6	al	al	PROPN
ap-1398	125	7	=	=	PROPN
ap-1398	125	8	dj	dj	PROPN
ap-1398	125	9	∨	∨	PROPN
ap-1398	125	10	bl	bl	NOUN
ap-1398	125	11	for	for	ADP
ap-1398	125	12	1	1	NUM
ap-1398	125	13	≤	≤	NOUN
ap-1398	126	1	k	k	ADP
ap-1398	126	2	<	<	X
ap-1398	126	3	j	j	PROPN
ap-1398	126	4	and	and	CCONJ
ap-1398	126	5	0	0	NUM
ap-1398	126	6	≤	≤	NUM
ap-1398	126	7	l	l	NOUN
ap-1398	126	8	<	<	X
ap-1398	126	9	j.	j.	PROPN
ap-1398	126	10	denote	denote	PROPN
ap-1398	126	11	b̂0	b̂0	PROPN
ap-1398	126	12	,	,	PUNCT
ap-1398	126	13	b̂j	b̂j	NOUN
ap-1398	126	14	(	(	PUNCT
ap-1398	126	15	for	for	ADP
ap-1398	126	16	j	j	PROPN
ap-1398	126	17	=	=	SYM
ap-1398	126	18	1	1	NUM
ap-1398	126	19	,	,	PUNCT
ap-1398	126	20	2	2	NUM
ap-1398	126	21	,	,	PUNCT
ap-1398	126	22	.	.	PUNCT
ap-1398	126	23	.	.	PUNCT
ap-1398	126	24	.	.	PUNCT
ap-1398	126	25	)	)	PUNCT
ap-1398	127	1	complete	complete	ADJ
ap-1398	127	2	atomic	atomic	ADJ
ap-1398	127	3	boolean	boolean	ADJ
ap-1398	127	4	algebras	algebra	NOUN
ap-1398	127	5	with	with	ADP
ap-1398	127	6	the	the	DET
ap-1398	127	7	corresponding	corresponding	ADJ
ap-1398	127	8	sets	set	NOUN
ap-1398	127	9	of	of	ADP
ap-1398	127	10	atoms	atom	NOUN
ap-1398	127	11	a0	a0	PROPN
ap-1398	127	12	,	,	PUNCT
ap-1398	127	13	aj	aj	PROPN
ap-1398	127	14	(	(	PUNCT
ap-1398	127	15	j	j	PROPN
ap-1398	127	16	=	=	SYM
ap-1398	127	17	1	1	NUM
ap-1398	127	18	,	,	PUNCT
ap-1398	127	19	2	2	NUM
ap-1398	127	20	,	,	PUNCT
ap-1398	127	21	.	.	PUNCT
ap-1398	127	22	.	.	PUNCT
ap-1398	127	23	.	.	PUNCT
ap-1398	127	24	)	)	PUNCT
ap-1398	127	25	,	,	PUNCT
ap-1398	127	26	given	give	VERB
ap-1398	127	27	by	by	ADP
ap-1398	127	28	a0	a0	PROPN
ap-1398	127	29	=	=	SYM
ap-1398	127	30	∞⋃	∞⋃	PROPN
ap-1398	127	31	i=0	i=0	PROPN
ap-1398	127	32	{	{	PUNCT
ap-1398	127	33	ai	ai	VERB
ap-1398	127	34	}	}	PUNCT
ap-1398	127	35	∪	∪	ADJ
ap-1398	127	36	∞⋃	∞⋃	PROPN
ap-1398	127	37	i=0	i=0	PROPN
ap-1398	127	38	{	{	PUNCT
ap-1398	127	39	bi	bi	NOUN
ap-1398	127	40	}	}	PUNCT
ap-1398	127	41	∪	∪	ADP
ap-1398	127	42	∞⋃	∞⋃	NOUN
ap-1398	127	43	j=1	j=1	PROPN
ap-1398	127	44	{	{	PUNCT
ap-1398	127	45	pj	pj	PROPN
ap-1398	127	46	}	}	PUNCT
ap-1398	127	47	,	,	PUNCT
ap-1398	127	48	(	(	PUNCT
ap-1398	127	49	3	3	X
ap-1398	127	50	)	)	PUNCT
ap-1398	127	51	aj	aj	PROPN
ap-1398	127	52	=	=	PROPN
ap-1398	127	53	∞⋃	∞⋃	PROPN
ap-1398	128	1	i	i	PROPN
ap-1398	128	2	=	=	PROPN
ap-1398	128	3	j	j	X
ap-1398	128	4	{	{	PUNCT
ap-1398	128	5	ai	ai	VERB
ap-1398	128	6	}	}	PUNCT
ap-1398	128	7	∪	∪	ADJ
ap-1398	128	8	∞⋃	∞⋃	NOUN
ap-1398	128	9	i	i	PROPN
ap-1398	128	10	=	=	PROPN
ap-1398	128	11	j	j	X
ap-1398	128	12	{	{	PUNCT
ap-1398	128	13	bi	bi	NOUN
ap-1398	128	14	}	}	PUNCT
ap-1398	128	15	∪	∪	ADP
ap-1398	128	16	∞⋃	∞⋃	NOUN
ap-1398	128	17	j=1	j=1	PROPN
ap-1398	128	18	{	{	PUNCT
ap-1398	128	19	pj	pj	PROPN
ap-1398	128	20	}	}	PUNCT
ap-1398	128	21	∪{cj	∪{cj	PROPN
ap-1398	128	22	,	,	PUNCT
ap-1398	128	23	dj	dj	NOUN
ap-1398	128	24	}	}	PUNCT
ap-1398	128	25	.	.	PUNCT
ap-1398	129	1	(	(	PUNCT
ap-1398	129	2	4	4	X
ap-1398	129	3	)	)	PUNCT
ap-1398	129	4	disjointness	disjointness	NOUN
ap-1398	129	5	occurring	occur	VERB
ap-1398	129	6	among	among	ADP
ap-1398	129	7	some	some	DET
ap-1398	129	8	atoms	atom	NOUN
ap-1398	129	9	of	of	ADP
ap-1398	129	10	the	the	DET
ap-1398	129	11	system	system	NOUN
ap-1398	129	12	(	(	PUNCT
ap-1398	129	13	2	2	X
ap-1398	129	14	)	)	PUNCT
ap-1398	129	15	is	be	AUX
ap-1398	129	16	equivalent	equivalent	ADJ
ap-1398	129	17	to	to	ADP
ap-1398	129	18	the	the	DET
ap-1398	129	19	fact	fact	NOUN
ap-1398	129	20	that	that	SCONJ
ap-1398	129	21	a0	a0	PROPN
ap-1398	129	22	and	and	CCONJ
ap-1398	129	23	aj	aj	PROPN
ap-1398	129	24	(	(	PUNCT
ap-1398	129	25	j	j	PROPN
ap-1398	129	26	=	=	SYM
ap-1398	129	27	1	1	NUM
ap-1398	129	28	,	,	PUNCT
ap-1398	129	29	2	2	NUM
ap-1398	129	30	,	,	PUNCT
ap-1398	129	31	.	.	PUNCT
ap-1398	129	32	.	.	PUNCT
ap-1398	130	1	.	.	PUNCT
ap-1398	130	2	)	)	PUNCT
ap-1398	131	1	are	be	AUX
ap-1398	131	2	unique	unique	ADJ
ap-1398	131	3	maximal	maximal	ADJ
ap-1398	131	4	sets	set	NOUN
ap-1398	131	5	of	of	ADP
ap-1398	131	6	pairwise	pairwise	NOUN
ap-1398	131	7	compatible	compatible	ADJ
ap-1398	131	8	atoms	atom	NOUN
ap-1398	131	9	.	.	PUNCT
ap-1398	132	1	theorem	theorem	NOUN
ap-1398	132	2	3	3	NUM
ap-1398	132	3	(	(	PUNCT
ap-1398	132	4	kalina	kalina	X
ap-1398	133	1	[	[	X
ap-1398	133	2	9	9	NUM
ap-1398	133	3	]	]	PUNCT
ap-1398	133	4	)	)	PUNCT
ap-1398	133	5	let	let	VERB
ap-1398	133	6	l̂	l̂	PUNCT
ap-1398	133	7	=	=	SYM
ap-1398	133	8	∞⋃	∞⋃	PROPN
ap-1398	133	9	i=0	i=0	PROPN
ap-1398	133	10	b̂i	b̂i	PROPN
ap-1398	133	11	.	.	PUNCT
ap-1398	134	1	let	let	VERB
ap-1398	134	2	l1	l1	PROPN
ap-1398	134	3	be	be	AUX
ap-1398	134	4	the	the	DET
ap-1398	134	5	complete	complete	ADJ
ap-1398	134	6	oml	oml	PROPN
ap-1398	134	7	generated	generate	VERB
ap-1398	134	8	by	by	ADP
ap-1398	134	9	sets	set	NOUN
ap-1398	134	10	of	of	ADP
ap-1398	134	11	atoms	atom	NOUN
ap-1398	134	12	∞⋃	∞⋃	NOUN
ap-1398	134	13	i=0	i=0	PROPN
ap-1398	134	14	{	{	PUNCT
ap-1398	134	15	ai	ai	PROPN
ap-1398	134	16	,	,	PUNCT
ap-1398	134	17	bi	bi	ADJ
ap-1398	134	18	}	}	PUNCT
ap-1398	134	19	∪	∪	ADP
ap-1398	134	20	∞⋃	∞⋃	NOUN
ap-1398	134	21	j=1	j=1	PROPN
ap-1398	134	22	{	{	PUNCT
ap-1398	134	23	cj	cj	INTJ
ap-1398	134	24	,	,	PUNCT
ap-1398	134	25	dj	dj	NOUN
ap-1398	134	26	}	}	PUNCT
ap-1398	134	27	and	and	CCONJ
ap-1398	134	28	n	n	DET
ap-1398	134	29	the	the	DET
ap-1398	134	30	complete	complete	ADJ
ap-1398	134	31	boolean	boolean	ADJ
ap-1398	134	32	algebra	algebra	NOUN
ap-1398	134	33	generated	generate	VERB
ap-1398	134	34	by	by	ADP
ap-1398	134	35	the	the	DET
ap-1398	134	36	set	set	NOUN
ap-1398	134	37	of	of	ADP
ap-1398	134	38	atoms	atom	NOUN
ap-1398	134	39	∞⋃	∞⋃	NOUN
ap-1398	135	1	j=1	j=1	PROPN
ap-1398	135	2	{	{	PUNCT
ap-1398	135	3	pj	pj	PROPN
ap-1398	135	4	}	}	PUNCT
ap-1398	135	5	.	.	PUNCT
ap-1398	136	1	then	then	ADV
ap-1398	136	2	(	(	PUNCT
ap-1398	136	3	l̂,∨,∧,0,1	l̂,∨,∧,0,1	NOUN
ap-1398	136	4	)	)	PUNCT
ap-1398	136	5	is	be	AUX
ap-1398	136	6	a	a	DET
ap-1398	136	7	complete	complete	ADJ
ap-1398	136	8	oml	oml	PROPN
ap-1398	136	9	and	and	CCONJ
ap-1398	136	10	l̂	l̂	VERB
ap-1398	136	11	∼=	∼=	PROPN
ap-1398	136	12	l1	l1	PROPN
ap-1398	136	13	×n	×n	PROPN
ap-1398	136	14	.	.	PUNCT
ap-1398	137	1	an	an	DET
ap-1398	137	2	element	element	NOUN
ap-1398	137	3	u	u	NOUN
ap-1398	137	4	∈	∈	NOUN
ap-1398	137	5	b̂l	b̂l	X
ap-1398	137	6	is	be	AUX
ap-1398	137	7	finite	finite	ADJ
ap-1398	137	8	if	if	SCONJ
ap-1398	137	9	and	and	CCONJ
ap-1398	137	10	only	only	ADV
ap-1398	137	11	if	if	SCONJ
ap-1398	137	12	u	u	PRON
ap-1398	137	13	=	=	PUNCT
ap-1398	137	14	q1⊕	q1⊕	NOUN
ap-1398	137	15	q2⊕	q2⊕	X
ap-1398	137	16	.	.	PUNCT
ap-1398	137	17	.	.	PUNCT
ap-1398	138	1	.⊕	.⊕	PROPN
ap-1398	138	2	qn	qn	PROPN
ap-1398	138	3	for	for	ADP
ap-1398	138	4	an	an	DET
ap-1398	138	5	n	n	PRON
ap-1398	138	6	∈	∈	PROPN
ap-1398	138	7	n	n	NOUN
ap-1398	138	8	and	and	CCONJ
ap-1398	138	9	q1	q1	PROPN
ap-1398	138	10	,	,	PUNCT
ap-1398	138	11	q2	q2	NOUN
ap-1398	138	12	,	,	PUNCT
ap-1398	138	13	.	.	PUNCT
ap-1398	138	14	.	.	PUNCT
ap-1398	139	1	.	.	PUNCT
ap-1398	140	1	,	,	PUNCT
ap-1398	140	2	qn	qn	PROPN
ap-1398	140	3	∈	∈	PROPN
ap-1398	140	4	al	al	PROPN
ap-1398	140	5	.	.	PROPN
ap-1398	140	6	set	set	VERB
ap-1398	140	7	ql	ql	NOUN
ap-1398	141	1	=	=	PRON
ap-1398	141	2	{	{	PUNCT
ap-1398	141	3	u	u	X
ap-1398	141	4	∈	∈	PROPN
ap-1398	141	5	bl	bl	PROPN
ap-1398	141	6	;	;	PUNCT
ap-1398	141	7	u	u	NOUN
ap-1398	141	8	is	be	AUX
ap-1398	141	9	finite	finite	ADJ
ap-1398	141	10	}	}	PUNCT
ap-1398	141	11	,	,	PUNCT
ap-1398	141	12	l	l	NOUN
ap-1398	141	13	=	=	SYM
ap-1398	141	14	0	0	NUM
ap-1398	141	15	,	,	PUNCT
ap-1398	141	16	1	1	NUM
ap-1398	141	17	,	,	PUNCT
ap-1398	141	18	2	2	NUM
ap-1398	141	19	,	,	PUNCT
ap-1398	141	20	.	.	PUNCT
ap-1398	141	21	.	.	PUNCT
ap-1398	142	1	..	..	PUNCT
ap-1398	143	1	then	then	ADV
ap-1398	143	2	ql	ql	INTJ
ap-1398	143	3	is	be	AUX
ap-1398	143	4	a	a	DET
ap-1398	143	5	generalized	generalized	ADJ
ap-1398	143	6	boolean	boolean	ADJ
ap-1398	143	7	algebra	algebra	NOUN
ap-1398	143	8	,	,	PUNCT
ap-1398	143	9	since	since	SCONJ
ap-1398	143	10	bl	bl	PROPN
ap-1398	143	11	=	=	SYM
ap-1398	143	12	ql	ql	PROPN
ap-1398	143	13	∪̇q∗	∪̇q∗	PROPN
ap-1398	143	14	l	l	NOUN
ap-1398	143	15	is	be	AUX
ap-1398	143	16	a	a	DET
ap-1398	143	17	boolean	boolean	ADJ
ap-1398	143	18	algebra	algebra	NOUN
ap-1398	143	19	,	,	PUNCT
ap-1398	143	20	where	where	SCONJ
ap-1398	143	21	q∗	q∗	NOUN
ap-1398	143	22	l	l	NOUN
ap-1398	144	1	=	=	PUNCT
ap-1398	144	2	{	{	PUNCT
ap-1398	144	3	u∗	u∗	ADV
ap-1398	144	4	;	;	PUNCT
ap-1398	144	5	u∗	u∗	X
ap-1398	144	6	=	=	SYM
ap-1398	144	7	1l	1l	NUM
ap-1398	144	8	�	�	PROPN
ap-1398	144	9	u	u	NOUN
ap-1398	144	10	and	and	CCONJ
ap-1398	144	11	u	u	PROPN
ap-1398	144	12	∈	∈	PROPN
ap-1398	144	13	ql	ql	PROPN
ap-1398	144	14	}	}	PUNCT
ap-1398	144	15	(	(	PUNCT
ap-1398	144	16	see	see	VERB
ap-1398	144	17	[	[	X
ap-1398	144	18	22	22	NUM
ap-1398	144	19	]	]	PUNCT
ap-1398	144	20	,	,	PUNCT
ap-1398	144	21	or	or	CCONJ
ap-1398	144	22	[	[	X
ap-1398	144	23	2	2	NUM
ap-1398	144	24	,	,	PUNCT
ap-1398	144	25	pp	pp	ADJ
ap-1398	144	26	.	.	PUNCT
ap-1398	145	1	18	18	NUM
ap-1398	145	2	-	-	SYM
ap-1398	145	3	19	19	NUM
ap-1398	145	4	]	]	PUNCT
ap-1398	145	5	)	)	PUNCT
ap-1398	145	6	.	.	PUNCT
ap-1398	146	1	this	this	PRON
ap-1398	146	2	means	mean	VERB
ap-1398	146	3	that	that	SCONJ
ap-1398	146	4	bl	bl	PROPN
ap-1398	146	5	is	be	AUX
ap-1398	146	6	a	a	DET
ap-1398	146	7	boolean	boolean	ADJ
ap-1398	146	8	subalgebra	subalgebra	NOUN
ap-1398	146	9	of	of	ADP
ap-1398	146	10	finite	finite	NOUN
ap-1398	146	11	and	and	CCONJ
ap-1398	146	12	cofinite	cofinite	ADJ
ap-1398	146	13	elements	element	NOUN
ap-1398	146	14	of	of	ADP
ap-1398	146	15	b̂l	b̂l	PRON
ap-1398	146	16	(	(	PUNCT
ap-1398	146	17	l	l	NOUN
ap-1398	146	18	=	=	SYM
ap-1398	146	19	0	0	NUM
ap-1398	146	20	,	,	PUNCT
ap-1398	146	21	1	1	NUM
ap-1398	146	22	,	,	PUNCT
ap-1398	146	23	2	2	NUM
ap-1398	146	24	,	,	PUNCT
ap-1398	146	25	.	.	PUNCT
ap-1398	146	26	.	.	PUNCT
ap-1398	146	27	.	.	PUNCT
ap-1398	146	28	)	)	PUNCT
ap-1398	146	29	.	.	PUNCT
ap-1398	147	1	theorem	theorem	ADJ
ap-1398	147	2	4	4	NUM
ap-1398	147	3	(	(	PUNCT
ap-1398	147	4	kalina	kalina	X
ap-1398	148	1	[	[	X
ap-1398	148	2	8	8	NUM
ap-1398	148	3	]	]	PUNCT
ap-1398	148	4	)	)	PUNCT
ap-1398	148	5	denote	denote	NOUN
ap-1398	148	6	l	l	NOUN
ap-1398	148	7	=	=	SYM
ap-1398	148	8	∞⋃	∞⋃	PROPN
ap-1398	148	9	l=0	l=0	PROPN
ap-1398	148	10	bl	bl	PROPN
ap-1398	148	11	.	.	PUNCT
ap-1398	149	1	then	then	ADV
ap-1398	149	2	(	(	PUNCT
ap-1398	149	3	l,∨,∧,0,1	l,∨,∧,0,1	NOUN
ap-1398	149	4	)	)	PUNCT
ap-1398	149	5	is	be	AUX
ap-1398	149	6	a	a	DET
ap-1398	149	7	compactly	compactly	ADV
ap-1398	149	8	generated	generate	VERB
ap-1398	149	9	orthomodular	orthomodular	ADJ
ap-1398	149	10	lattice	lattice	NOUN
ap-1398	149	11	with	with	ADP
ap-1398	149	12	the	the	DET
ap-1398	149	13	family	family	NOUN
ap-1398	149	14	(	(	PUNCT
ap-1398	149	15	bl)∞l=0	bl)∞l=0	ADJ
ap-1398	149	16	of	of	ADP
ap-1398	149	17	atomic	atomic	ADJ
ap-1398	149	18	blocks	block	NOUN
ap-1398	149	19	of	of	ADP
ap-1398	149	20	l.	l.	PROPN
ap-1398	149	21	the	the	DET
ap-1398	149	22	center	center	NOUN
ap-1398	149	23	of	of	ADP
ap-1398	149	24	l	l	PROPN
ap-1398	149	25	,	,	PUNCT
ap-1398	149	26	c(l	c(l	PROPN
ap-1398	149	27	)	)	PUNCT
ap-1398	149	28	,	,	PUNCT
ap-1398	149	29	is	be	AUX
ap-1398	149	30	not	not	PART
ap-1398	149	31	a	a	DET
ap-1398	149	32	bifull	bifull	ADJ
ap-1398	149	33	sublattice	sublattice	NOUN
ap-1398	149	34	of	of	ADP
ap-1398	149	35	l.	l.	PROPN
ap-1398	149	36	3	3	NUM
ap-1398	149	37	completion	completion	NOUN
ap-1398	149	38	of	of	ADP
ap-1398	149	39	the	the	DET
ap-1398	149	40	center	center	NOUN
ap-1398	149	41	of	of	ADP
ap-1398	149	42	l	l	NOUN
ap-1398	149	43	we	we	PRON
ap-1398	149	44	are	be	AUX
ap-1398	149	45	going	go	VERB
ap-1398	149	46	to	to	PART
ap-1398	149	47	show	show	VERB
ap-1398	149	48	that	that	SCONJ
ap-1398	149	49	it	it	PRON
ap-1398	149	50	is	be	AUX
ap-1398	149	51	possible	possible	ADJ
ap-1398	149	52	to	to	PART
ap-1398	149	53	extend	extend	VERB
ap-1398	149	54	the	the	DET
ap-1398	149	55	orthomodular	orthomodular	ADJ
ap-1398	149	56	lattice	lattice	NOUN
ap-1398	149	57	l	l	NOUN
ap-1398	149	58	from	from	ADP
ap-1398	149	59	theorem	theorem	ADJ
ap-1398	149	60	4	4	NUM
ap-1398	149	61	to	to	PART
ap-1398	149	62	l̄	l̄	VERB
ap-1398	149	63	,	,	PUNCT
ap-1398	149	64	whose	whose	DET
ap-1398	149	65	center	center	NOUN
ap-1398	149	66	,	,	PUNCT
ap-1398	149	67	c(l̄	c(l̄	NOUN
ap-1398	149	68	)	)	PUNCT
ap-1398	149	69	,	,	PUNCT
ap-1398	149	70	is	be	AUX
ap-1398	149	71	a	a	DET
ap-1398	149	72	complete	complete	ADJ
ap-1398	149	73	boolean	boolean	ADJ
ap-1398	149	74	algebra	algebra	NOUN
ap-1398	149	75	which	which	PRON
ap-1398	149	76	is	be	AUX
ap-1398	149	77	not	not	PART
ap-1398	149	78	a	a	DET
ap-1398	149	79	bifull	bifull	ADJ
ap-1398	149	80	sublattice	sublattice	NOUN
ap-1398	149	81	of	of	ADP
ap-1398	149	82	l̄.	l̄.	PUNCT
ap-1398	149	83	denote	denote	VERB
ap-1398	149	84	f	f	PROPN
ap-1398	149	85	a	a	DET
ap-1398	149	86	fixed	fix	VERB
ap-1398	149	87	non	non	ADJ
ap-1398	149	88	-	-	ADJ
ap-1398	149	89	trivial	trivial	ADJ
ap-1398	149	90	ultrafilter	ultrafilter	NOUN
ap-1398	149	91	on	on	ADP
ap-1398	149	92	n	n	PROPN
ap-1398	149	93	(	(	PUNCT
ap-1398	149	94	the	the	DET
ap-1398	149	95	index	index	NOUN
ap-1398	149	96	set	set	NOUN
ap-1398	149	97	of	of	ADP
ap-1398	149	98	atoms	atom	NOUN
ap-1398	149	99	pj	pj	PROPN
ap-1398	149	100	)	)	PUNCT
ap-1398	149	101	.	.	PUNCT
ap-1398	150	1	then	then	ADV
ap-1398	150	2	f	f	PROPN
ap-1398	150	3	has	have	VERB
ap-1398	150	4	the	the	DET
ap-1398	150	5	following	follow	VERB
ap-1398	150	6	properties	property	NOUN
ap-1398	150	7	which	which	PRON
ap-1398	150	8	will	will	AUX
ap-1398	150	9	be	be	AUX
ap-1398	150	10	important	important	ADJ
ap-1398	150	11	for	for	ADP
ap-1398	150	12	our	our	PRON
ap-1398	150	13	construction	construction	NOUN
ap-1398	150	14	:	:	PUNCT
ap-1398	150	15	•	•	NUM
ap-1398	150	16	let	let	VERB
ap-1398	150	17	f	f	PROPN
ap-1398	150	18	⊂	⊂	PROPN
ap-1398	150	19	n.	n.	PROPN
ap-1398	150	20	then	then	ADV
ap-1398	150	21	either	either	CCONJ
ap-1398	150	22	f	f	PROPN
ap-1398	150	23	∈	∈	PROPN
ap-1398	150	24	f	f	PROPN
ap-1398	150	25	or	or	CCONJ
ap-1398	150	26	n	n	CCONJ
ap-1398	150	27	\	\	NOUN
ap-1398	150	28	f	f	PROPN
ap-1398	150	29	∈	∈	PROPN
ap-1398	150	30	f	f	PROPN
ap-1398	150	31	.	.	PUNCT
ap-1398	151	1	•	•	INTJ
ap-1398	151	2	let	let	VERB
ap-1398	151	3	f	f	PROPN
ap-1398	151	4	⊂	⊂	PROPN
ap-1398	151	5	n	n	AUX
ap-1398	151	6	be	be	AUX
ap-1398	151	7	a	a	DET
ap-1398	151	8	finite	finite	ADJ
ap-1398	151	9	set	set	NOUN
ap-1398	151	10	.	.	PUNCT
ap-1398	152	1	then	then	ADV
ap-1398	152	2	f	f	PROPN
ap-1398	152	3	/∈	/∈	PUNCT
ap-1398	153	1	f	f	PROPN
ap-1398	153	2	.	.	PUNCT
ap-1398	154	1	•	•	INTJ
ap-1398	154	2	if	if	SCONJ
ap-1398	154	3	f1	f1	PROPN
ap-1398	154	4	∈	∈	PROPN
ap-1398	154	5	f	f	PROPN
ap-1398	154	6	and	and	CCONJ
ap-1398	154	7	f2	f2	PROPN
ap-1398	154	8	∈	∈	PROPN
ap-1398	154	9	f	f	X
ap-1398	154	10	then	then	ADV
ap-1398	154	11	f1	f1	PROPN
ap-1398	154	12	∩	∩	NOUN
ap-1398	154	13	f2	f2	PROPN
ap-1398	154	14	∈	∈	PROPN
ap-1398	154	15	f	f	X
ap-1398	154	16	.	.	PUNCT
ap-1398	155	1	•	•	INTJ
ap-1398	155	2	if	if	SCONJ
ap-1398	155	3	f1	f1	PROPN
ap-1398	155	4	∈	∈	PROPN
ap-1398	155	5	f	f	PROPN
ap-1398	155	6	and	and	CCONJ
ap-1398	155	7	f2	f2	PROPN
ap-1398	155	8	⊃	⊃	PROPN
ap-1398	155	9	f1	f1	PROPN
ap-1398	155	10	then	then	ADV
ap-1398	155	11	f2	f2	PROPN
ap-1398	155	12	∈	∈	PROPN
ap-1398	156	1	f	f	X
ap-1398	156	2	.	.	PUNCT
ap-1398	157	1	28	28	NUM
ap-1398	157	2	acta	acta	PROPN
ap-1398	157	3	polytechnica	polytechnica	PROPN
ap-1398	157	4	vol	vol	NOUN
ap-1398	157	5	.	.	PUNCT
ap-1398	158	1	51	51	NUM
ap-1398	158	2	no	no	INTJ
ap-1398	158	3	.	.	PUNCT
ap-1398	159	1	4/2011	4/2011	PROPN
ap-1398	159	2	let	let	VERB
ap-1398	159	3	ql1	ql1	NOUN
ap-1398	159	4	denote	denote	VERB
ap-1398	159	5	the	the	DET
ap-1398	159	6	set	set	NOUN
ap-1398	159	7	of	of	ADP
ap-1398	159	8	all	all	DET
ap-1398	159	9	finite	finite	ADJ
ap-1398	159	10	elements	element	NOUN
ap-1398	159	11	of	of	ADP
ap-1398	159	12	l1	l1	PROPN
ap-1398	159	13	.	.	PUNCT
ap-1398	160	1	further	far	ADV
ap-1398	160	2	set	set	VERB
ap-1398	160	3	pf	pf	X
ap-1398	160	4	=	=	SYM
ap-1398	160	5	{	{	PUNCT
ap-1398	160	6	⊕	⊕	PROPN
ap-1398	160	7	i∈f	i∈f	VERB
ap-1398	160	8	pi	pi	NOUN
ap-1398	160	9	;	;	PUNCT
ap-1398	160	10	f	f	PROPN
ap-1398	160	11	/∈	/∈	PUNCT
ap-1398	161	1	f	f	PROPN
ap-1398	161	2	}	}	PUNCT
ap-1398	161	3	(	(	PUNCT
ap-1398	161	4	5	5	NUM
ap-1398	161	5	)	)	PUNCT
ap-1398	161	6	and	and	CCONJ
ap-1398	161	7	g	g	NOUN
ap-1398	161	8	=	=	SYM
ap-1398	161	9	{	{	PUNCT
ap-1398	161	10	f	f	PROPN
ap-1398	161	11	⊕	⊕	PROPN
ap-1398	161	12	g	g	PROPN
ap-1398	161	13	;	;	PUNCT
ap-1398	161	14	g	g	PROPN
ap-1398	161	15	∈	∈	PROPN
ap-1398	161	16	ql1	ql1	NOUN
ap-1398	161	17	,	,	PUNCT
ap-1398	161	18	f	f	PROPN
ap-1398	161	19	∈	∈	PROPN
ap-1398	161	20	pf	pf	PROPN
ap-1398	161	21	}	}	PUNCT
ap-1398	161	22	,	,	PUNCT
ap-1398	161	23	g⊥	g⊥	VERB
ap-1398	161	24	=	=	SYM
ap-1398	161	25	{	{	PUNCT
ap-1398	161	26	h′	h′	PROPN
ap-1398	161	27	∈	∈	PROPN
ap-1398	161	28	l̂	l̂	VERB
ap-1398	161	29	;	;	PUNCT
ap-1398	161	30	h	h	PROPN
ap-1398	161	31	∈	∈	PROPN
ap-1398	161	32	g	g	PROPN
ap-1398	161	33	}	}	PUNCT
ap-1398	161	34	.	.	PUNCT
ap-1398	162	1	theorem	theorem	NOUN
ap-1398	162	2	5	5	NUM
ap-1398	162	3	let	let	VERB
ap-1398	162	4	l̃	l̃	PROPN
ap-1398	162	5	=	=	PUNCT
ap-1398	163	1	g	g	PROPN
ap-1398	163	2	∪̇g⊥.	∪̇g⊥.	PROPN
ap-1398	163	3	then	then	ADV
ap-1398	163	4	the	the	DET
ap-1398	163	5	system	system	NOUN
ap-1398	163	6	(	(	PUNCT
ap-1398	163	7	l̃,∨,∧,0,1	l̃,∨,∧,0,1	NOUN
ap-1398	163	8	)	)	PUNCT
ap-1398	163	9	is	be	AUX
ap-1398	163	10	an	an	DET
ap-1398	163	11	orthomodular	orthomodular	ADJ
ap-1398	163	12	lattice	lattice	NOUN
ap-1398	163	13	.	.	PUNCT
ap-1398	164	1	the	the	DET
ap-1398	164	2	center	center	NOUN
ap-1398	164	3	c(l̃	c(l̃	PROPN
ap-1398	164	4	)	)	PUNCT
ap-1398	164	5	=	=	PRON
ap-1398	164	6	{	{	PUNCT
ap-1398	164	7	f	f	PROPN
ap-1398	164	8	∈	∈	PROPN
ap-1398	164	9	l̃	l̃	PROPN
ap-1398	164	10	;	;	PUNCT
ap-1398	164	11	f	f	PROPN
ap-1398	164	12	∈	∈	PROPN
ap-1398	164	13	pf	pf	PROPN
ap-1398	164	14	or	or	CCONJ
ap-1398	164	15	f	f	PROPN
ap-1398	164	16	′	′	NUM
ap-1398	164	17	∈	∈	PROPN
ap-1398	164	18	pf	pf	NOUN
ap-1398	164	19	}	}	PUNCT
ap-1398	164	20	,	,	PUNCT
ap-1398	164	21	and	and	CCONJ
ap-1398	164	22	c(l̃	c(l̃	NOUN
ap-1398	164	23	)	)	PUNCT
ap-1398	164	24	is	be	AUX
ap-1398	164	25	a	a	DET
ap-1398	164	26	complete	complete	ADJ
ap-1398	164	27	boolean	boolean	ADJ
ap-1398	164	28	algebra	algebra	NOUN
ap-1398	164	29	which	which	PRON
ap-1398	164	30	is	be	AUX
ap-1398	164	31	not	not	PART
ap-1398	164	32	bifull	bifull	ADJ
ap-1398	164	33	in	in	ADP
ap-1398	164	34	l̃.	l̃.	ADJ
ap-1398	164	35	proof	proof	NOUN
ap-1398	164	36	.	.	PUNCT
ap-1398	165	1	first	first	ADV
ap-1398	165	2	we	we	PRON
ap-1398	165	3	show	show	VERB
ap-1398	165	4	that	that	SCONJ
ap-1398	165	5	l̃	l̃	PROPN
ap-1398	165	6	is	be	AUX
ap-1398	165	7	a	a	DET
ap-1398	165	8	bounded	bounded	ADJ
ap-1398	165	9	lattice	lattice	NOUN
ap-1398	165	10	.	.	PUNCT
ap-1398	166	1	consider	consider	VERB
ap-1398	166	2	elements	element	NOUN
ap-1398	166	3	h1	h1	PROPN
ap-1398	166	4	,	,	PUNCT
ap-1398	166	5	h2	h2	PROPN
ap-1398	166	6	∈	∈	PROPN
ap-1398	166	7	g.	g.	NOUN
ap-1398	166	8	then	then	ADV
ap-1398	166	9	there	there	PRON
ap-1398	166	10	exist	exist	VERB
ap-1398	166	11	elements	element	NOUN
ap-1398	166	12	g1	g1	NOUN
ap-1398	166	13	,	,	PUNCT
ap-1398	166	14	g2	g2	PROPN
ap-1398	166	15	∈	∈	PROPN
ap-1398	166	16	ql1	ql1	NOUN
ap-1398	166	17	and	and	CCONJ
ap-1398	166	18	elements	element	NOUN
ap-1398	166	19	f1	f1	NOUN
ap-1398	166	20	,	,	PUNCT
ap-1398	166	21	f2	f2	PROPN
ap-1398	166	22	∈	∈	PROPN
ap-1398	166	23	pf	pf	ADP
ap-1398	166	24	such	such	ADJ
ap-1398	166	25	that	that	DET
ap-1398	166	26	h1	h1	PROPN
ap-1398	166	27	=	=	PUNCT
ap-1398	166	28	f1	f1	PROPN
ap-1398	166	29	⊕	⊕	PROPN
ap-1398	166	30	g1	g1	PROPN
ap-1398	166	31	,	,	PUNCT
ap-1398	166	32	h2	h2	NOUN
ap-1398	166	33	=	=	SYM
ap-1398	166	34	f2	f2	PROPN
ap-1398	166	35	⊕	⊕	PROPN
ap-1398	166	36	g2	g2	PROPN
ap-1398	166	37	.	.	PUNCT
ap-1398	167	1	(	(	PUNCT
ap-1398	167	2	6	6	NUM
ap-1398	167	3	)	)	PUNCT
ap-1398	167	4	by	by	ADP
ap-1398	167	5	the	the	DET
ap-1398	167	6	properties	property	NOUN
ap-1398	167	7	of	of	ADP
ap-1398	167	8	the	the	DET
ap-1398	167	9	non	non	ADJ
ap-1398	167	10	-	-	ADJ
ap-1398	167	11	trivial	trivial	ADJ
ap-1398	167	12	ultrafilter	ultrafilter	NOUN
ap-1398	167	13	f	f	NOUN
ap-1398	167	14	we	we	PRON
ap-1398	167	15	get	get	VERB
ap-1398	167	16	that	that	DET
ap-1398	167	17	f1	f1	PROPN
ap-1398	167	18	∨	∨	NUM
ap-1398	167	19	f2	f2	PROPN
ap-1398	167	20	∈	∈	PROPN
ap-1398	167	21	pf	pf	NOUN
ap-1398	167	22	and	and	CCONJ
ap-1398	167	23	f1	f1	PROPN
ap-1398	167	24	∧	∧	PROPN
ap-1398	167	25	f2	f2	PROPN
ap-1398	167	26	∈	∈	PROPN
ap-1398	167	27	pf	pf	X
ap-1398	167	28	.	.	PUNCT
ap-1398	168	1	since	since	SCONJ
ap-1398	168	2	g1	g1	PROPN
ap-1398	168	3	,	,	PUNCT
ap-1398	168	4	g2	g2	PROPN
ap-1398	168	5	are	be	AUX
ap-1398	168	6	finite	finite	ADJ
ap-1398	168	7	elements	element	NOUN
ap-1398	168	8	of	of	ADP
ap-1398	168	9	l1	l1	PROPN
ap-1398	168	10	,	,	PUNCT
ap-1398	168	11	we	we	PRON
ap-1398	168	12	get	get	VERB
ap-1398	168	13	that	that	SCONJ
ap-1398	168	14	g1	g1	PROPN
ap-1398	168	15	∨	∨	NUM
ap-1398	168	16	g2	g2	PROPN
ap-1398	168	17	∈	∈	PROPN
ap-1398	168	18	ql1	ql1	NOUN
ap-1398	168	19	and	and	CCONJ
ap-1398	168	20	also	also	ADV
ap-1398	168	21	g1	g1	VERB
ap-1398	168	22	∧	∧	PROPN
ap-1398	168	23	g2	g2	PROPN
ap-1398	168	24	∈	∈	PROPN
ap-1398	168	25	ql1	ql1	PROPN
ap-1398	168	26	.	.	PUNCT
ap-1398	169	1	since	since	SCONJ
ap-1398	169	2	l1	l1	PROPN
ap-1398	169	3	is	be	AUX
ap-1398	169	4	generated	generate	VERB
ap-1398	169	5	by	by	ADP
ap-1398	169	6	the	the	DET
ap-1398	169	7	sets	set	NOUN
ap-1398	169	8	of	of	ADP
ap-1398	169	9	atoms	atom	NOUN
ap-1398	169	10	∞⋃	∞⋃	NOUN
ap-1398	169	11	i=0	i=0	PROPN
ap-1398	169	12	{	{	PUNCT
ap-1398	169	13	ai	ai	PROPN
ap-1398	169	14	,	,	PUNCT
ap-1398	169	15	bi	bi	NOUN
ap-1398	169	16	}	}	PUNCT
ap-1398	169	17	and	and	CCONJ
ap-1398	169	18	∞⋃	∞⋃	PROPN
ap-1398	169	19	j=1	j=1	PROPN
ap-1398	169	20	{	{	PUNCT
ap-1398	169	21	cj	cj	X
ap-1398	169	22	,	,	PUNCT
ap-1398	169	23	dj	dj	PROPN
ap-1398	169	24	}	}	PUNCT
ap-1398	169	25	,	,	PUNCT
ap-1398	169	26	each	each	DET
ap-1398	169	27	g	g	PROPN
ap-1398	169	28	∈	∈	PROPN
ap-1398	169	29	ql1	ql1	NOUN
ap-1398	169	30	is	be	AUX
ap-1398	169	31	⊕-orthogonal	⊕-orthogonal	ADJ
ap-1398	169	32	to	to	ADP
ap-1398	169	33	each	each	DET
ap-1398	169	34	f	f	PROPN
ap-1398	169	35	∈	∈	PROPN
ap-1398	169	36	pf	pf	X
ap-1398	169	37	.	.	PUNCT
ap-1398	170	1	this	this	PRON
ap-1398	170	2	implies	imply	VERB
ap-1398	170	3	that	that	SCONJ
ap-1398	170	4	g	g	PROPN
ap-1398	170	5	is	be	AUX
ap-1398	170	6	closed	close	VERB
ap-1398	170	7	under	under	ADP
ap-1398	170	8	∨	∨	NOUN
ap-1398	170	9	and	and	CCONJ
ap-1398	170	10	∧.	∧.	PROPN
ap-1398	170	11	because	because	SCONJ
ap-1398	170	12	g⊥	g⊥	VERB
ap-1398	170	13	consists	consist	NOUN
ap-1398	170	14	of	of	ADP
ap-1398	170	15	complements	complement	NOUN
ap-1398	170	16	of	of	ADP
ap-1398	170	17	elements	element	NOUN
ap-1398	170	18	of	of	ADP
ap-1398	170	19	g	g	NOUN
ap-1398	170	20	,	,	PUNCT
ap-1398	170	21	we	we	PRON
ap-1398	170	22	have	have	AUX
ap-1398	170	23	that	that	PRON
ap-1398	170	24	also	also	ADV
ap-1398	170	25	g⊥	g⊥	VERB
ap-1398	170	26	is	be	AUX
ap-1398	170	27	closed	close	VERB
ap-1398	170	28	under	under	ADP
ap-1398	170	29	∨	∨	NOUN
ap-1398	170	30	and	and	CCONJ
ap-1398	170	31	∧.	∧.	PROPN
ap-1398	170	32	now	now	ADV
ap-1398	170	33	assume	assume	VERB
ap-1398	170	34	that	that	SCONJ
ap-1398	170	35	h1	h1	VERB
ap-1398	170	36	∈	∈	PROPN
ap-1398	170	37	g	g	PROPN
ap-1398	170	38	and	and	CCONJ
ap-1398	170	39	h2	h2	PROPN
ap-1398	170	40	∈	∈	PROPN
ap-1398	170	41	g⊥.	g⊥.	PROPN
ap-1398	170	42	then	then	ADV
ap-1398	170	43	h′	h′	PROPN
ap-1398	170	44	2	2	NUM
ap-1398	170	45	∈	∈	NOUN
ap-1398	170	46	g	g	NOUN
ap-1398	170	47	and	and	CCONJ
ap-1398	170	48	we	we	PRON
ap-1398	170	49	can	can	AUX
ap-1398	170	50	write	write	VERB
ap-1398	170	51	h1	h1	PROPN
ap-1398	170	52	=	=	PUNCT
ap-1398	170	53	f1	f1	PROPN
ap-1398	170	54	⊕	⊕	PROPN
ap-1398	170	55	g1	g1	PROPN
ap-1398	170	56	,	,	PUNCT
ap-1398	170	57	h′	h′	X
ap-1398	170	58	2	2	NUM
ap-1398	170	59	=	=	SYM
ap-1398	170	60	f2	f2	PROPN
ap-1398	170	61	⊕	⊕	PROPN
ap-1398	170	62	g2	g2	PROPN
ap-1398	170	63	with	with	ADP
ap-1398	170	64	the	the	DET
ap-1398	170	65	same	same	ADJ
ap-1398	170	66	meaning	meaning	NOUN
ap-1398	170	67	of	of	ADP
ap-1398	170	68	f1	f1	NOUN
ap-1398	170	69	,	,	PUNCT
ap-1398	170	70	f2	f2	PROPN
ap-1398	170	71	,	,	PUNCT
ap-1398	170	72	g1	g1	PROPN
ap-1398	170	73	,	,	PUNCT
ap-1398	170	74	g2	g2	PROPN
ap-1398	170	75	as	as	ADP
ap-1398	170	76	in	in	ADP
ap-1398	170	77	formula	formula	NOUN
ap-1398	170	78	(	(	PUNCT
ap-1398	170	79	6	6	NUM
ap-1398	170	80	)	)	PUNCT
ap-1398	170	81	.	.	PUNCT
ap-1398	171	1	this	this	PRON
ap-1398	171	2	means	mean	VERB
ap-1398	171	3	that	that	SCONJ
ap-1398	171	4	h2	h2	NOUN
ap-1398	171	5	=	=	PUNCT
ap-1398	171	6	f	f	PROPN
ap-1398	171	7	′	′	NUM
ap-1398	171	8	2	2	NUM
ap-1398	171	9	�	�	PROPN
ap-1398	171	10	g2	g2	PROPN
ap-1398	171	11	.	.	PUNCT
ap-1398	172	1	then	then	ADV
ap-1398	172	2	,	,	PUNCT
ap-1398	172	3	because	because	SCONJ
ap-1398	172	4	of	of	ADP
ap-1398	172	5	the	the	DET
ap-1398	172	6	monotonicity	monotonicity	NOUN
ap-1398	172	7	of	of	ADP
ap-1398	172	8	the	the	DET
ap-1398	172	9	ultrafilter	ultrafilter	NOUN
ap-1398	172	10	f	f	NOUN
ap-1398	172	11	,	,	PUNCT
ap-1398	172	12	we	we	PRON
ap-1398	172	13	have	have	VERB
ap-1398	172	14	(	(	PUNCT
ap-1398	172	15	f1	f1	PROPN
ap-1398	172	16	∨	∨	PROPN
ap-1398	172	17	f	f	PROPN
ap-1398	172	18	′	′	NUM
ap-1398	172	19	2	2	NUM
ap-1398	172	20	)	)	PUNCT
ap-1398	172	21	′	′	NUM
ap-1398	173	1	∈	∈	PROPN
ap-1398	173	2	pf	pf	NOUN
ap-1398	173	3	and	and	CCONJ
ap-1398	173	4	hence	hence	ADV
ap-1398	173	5	f1	f1	PROPN
ap-1398	173	6	∨	∨	NUM
ap-1398	173	7	f	f	PROPN
ap-1398	173	8	′	′	NUM
ap-1398	173	9	2	2	NUM
ap-1398	173	10	∈	∈	PROPN
ap-1398	173	11	g⊥.	g⊥.	NOUN
ap-1398	173	12	moreover	moreover	ADV
ap-1398	173	13	,	,	PUNCT
ap-1398	173	14	g2	g2	PROPN
ap-1398	173	15	∈	∈	PROPN
ap-1398	173	16	ql1	ql1	NOUN
ap-1398	173	17	is	be	AUX
ap-1398	173	18	orthogonal	orthogonal	ADJ
ap-1398	173	19	to	to	ADP
ap-1398	173	20	f1	f1	NOUN
ap-1398	173	21	which	which	PRON
ap-1398	173	22	implies	imply	VERB
ap-1398	173	23	(	(	PUNCT
ap-1398	173	24	f1	f1	PROPN
ap-1398	173	25	∨	∨	PROPN
ap-1398	173	26	f	f	PROPN
ap-1398	173	27	′	′	NUM
ap-1398	173	28	2	2	NUM
ap-1398	173	29	)	)	PUNCT
ap-1398	173	30	�	�	PROPN
ap-1398	173	31	g2	g2	PROPN
ap-1398	173	32	=	=	PROPN
ap-1398	173	33	f1	f1	PROPN
ap-1398	173	34	∨	∨	PROPN
ap-1398	173	35	(	(	PUNCT
ap-1398	173	36	f	f	NOUN
ap-1398	173	37	′	′	PROPN
ap-1398	173	38	2	2	NUM
ap-1398	173	39	�	�	PROPN
ap-1398	173	40	g2	g2	PROPN
ap-1398	173	41	)	)	PUNCT
ap-1398	173	42	∈	∈	PROPN
ap-1398	173	43	g⊥.	g⊥.	NOUN
ap-1398	173	44	since	since	SCONJ
ap-1398	173	45	g	g	PROPN
ap-1398	173	46	is	be	AUX
ap-1398	173	47	a	a	DET
ap-1398	173	48	monotone	monotone	ADJ
ap-1398	173	49	system	system	NOUN
ap-1398	173	50	(	(	PUNCT
ap-1398	173	51	meaning	mean	VERB
ap-1398	173	52	that	that	SCONJ
ap-1398	173	53	with	with	ADP
ap-1398	173	54	an	an	DET
ap-1398	173	55	arbitrary	arbitrary	ADJ
ap-1398	173	56	element	element	NOUN
ap-1398	173	57	δ1	δ1	NOUN
ap-1398	173	58	∈	∈	PROPN
ap-1398	173	59	g	g	PROPN
ap-1398	173	60	it	it	PRON
ap-1398	173	61	contains	contain	VERB
ap-1398	173	62	also	also	ADV
ap-1398	173	63	all	all	DET
ap-1398	173	64	elements	element	NOUN
ap-1398	173	65	δ2	δ2	VERB
ap-1398	173	66	∈	∈	NOUN
ap-1398	173	67	l̂	l̂	VERB
ap-1398	173	68	such	such	ADJ
ap-1398	173	69	that	that	SCONJ
ap-1398	173	70	δ2	δ2	VERB
ap-1398	173	71	≤	≤	NUM
ap-1398	173	72	δ1	δ1	NOUN
ap-1398	173	73	)	)	PUNCT
ap-1398	173	74	,	,	PUNCT
ap-1398	173	75	we	we	PRON
ap-1398	173	76	get	get	VERB
ap-1398	173	77	from	from	ADP
ap-1398	173	78	the	the	DET
ap-1398	173	79	duality	duality	NOUN
ap-1398	173	80	between	between	ADP
ap-1398	173	81	g	g	PROPN
ap-1398	173	82	and	and	CCONJ
ap-1398	173	83	g⊥	g⊥	VERB
ap-1398	173	84	that	that	SCONJ
ap-1398	173	85	(	(	PUNCT
ap-1398	173	86	f1	f1	PROPN
ap-1398	173	87	∨	∨	NUM
ap-1398	173	88	g1	g1	PROPN
ap-1398	173	89	)	)	PUNCT
ap-1398	173	90	∨	∨	NUM
ap-1398	173	91	(	(	PUNCT
ap-1398	173	92	f	f	NOUN
ap-1398	173	93	′	′	PROPN
ap-1398	173	94	2	2	NUM
ap-1398	173	95	�	�	PROPN
ap-1398	173	96	g2	g2	PROPN
ap-1398	173	97	)	)	PUNCT
ap-1398	174	1	=	=	PRON
ap-1398	174	2	h1	h1	PROPN
ap-1398	174	3	∨	∨	NUM
ap-1398	174	4	h2	h2	PROPN
ap-1398	174	5	∈	∈	PROPN
ap-1398	174	6	g⊥	g⊥	VERB
ap-1398	174	7	dually	dually	ADV
ap-1398	174	8	we	we	PRON
ap-1398	174	9	get	get	VERB
ap-1398	174	10	that	that	DET
ap-1398	174	11	h1	h1	PROPN
ap-1398	174	12	∧	∧	PROPN
ap-1398	174	13	h2	h2	PROPN
ap-1398	174	14	∈	∈	PROPN
ap-1398	174	15	g.	g.	NOUN
ap-1398	175	1	this	this	PRON
ap-1398	175	2	implies	imply	VERB
ap-1398	175	3	that	that	SCONJ
ap-1398	175	4	l̃	l̃	PROPN
ap-1398	175	5	=	=	SYM
ap-1398	175	6	g	g	PROPN
ap-1398	175	7	∪̇g⊥	∪̇g⊥	NOUN
ap-1398	175	8	is	be	AUX
ap-1398	175	9	a	a	DET
ap-1398	175	10	lattice	lattice	NOUN
ap-1398	175	11	.	.	PUNCT
ap-1398	176	1	obviously	obviously	ADV
ap-1398	176	2	it	it	PRON
ap-1398	176	3	is	be	AUX
ap-1398	176	4	a	a	DET
ap-1398	176	5	bounded	bounded	ADJ
ap-1398	176	6	and	and	CCONJ
ap-1398	176	7	orthocomplemented	orthocomplemented	ADJ
ap-1398	176	8	lattice	lattice	NOUN
ap-1398	176	9	.	.	PUNCT
ap-1398	177	1	showing	show	VERB
ap-1398	177	2	that	that	SCONJ
ap-1398	177	3	it	it	PRON
ap-1398	177	4	is	be	AUX
ap-1398	177	5	an	an	DET
ap-1398	177	6	oml	oml	PROPN
ap-1398	177	7	is	be	AUX
ap-1398	177	8	a	a	DET
ap-1398	177	9	matter	matter	NOUN
ap-1398	177	10	of	of	ADP
ap-1398	177	11	routine	routine	ADJ
ap-1398	177	12	.	.	PUNCT
ap-1398	178	1	we	we	PRON
ap-1398	178	2	will	will	AUX
ap-1398	178	3	omit	omit	VERB
ap-1398	178	4	the	the	DET
ap-1398	178	5	detailed	detailed	ADJ
ap-1398	178	6	proof	proof	NOUN
ap-1398	178	7	.	.	PUNCT
ap-1398	179	1	let	let	VERB
ap-1398	179	2	us	we	PRON
ap-1398	179	3	consider	consider	VERB
ap-1398	179	4	an	an	DET
ap-1398	179	5	element	element	NOUN
ap-1398	179	6	f	f	PROPN
ap-1398	179	7	∈	∈	PROPN
ap-1398	180	1	l̃	l̃	PROPN
ap-1398	180	2	such	such	ADJ
ap-1398	180	3	that	that	SCONJ
ap-1398	180	4	f	f	PROPN
ap-1398	180	5	∈	∈	PROPN
ap-1398	180	6	pf	pf	PROPN
ap-1398	180	7	or	or	CCONJ
ap-1398	180	8	f	f	PROPN
ap-1398	180	9	′	′	NUM
ap-1398	180	10	∈	∈	PROPN
ap-1398	181	1	pf	pf	INTJ
ap-1398	181	2	.	.	PUNCT
ap-1398	182	1	then	then	ADV
ap-1398	182	2	f	f	PROPN
ap-1398	182	3	is	be	AUX
ap-1398	182	4	a	a	DET
ap-1398	182	5	central	central	ADJ
ap-1398	182	6	element	element	NOUN
ap-1398	182	7	.	.	PUNCT
ap-1398	183	1	if	if	SCONJ
ap-1398	183	2	f	f	PROPN
ap-1398	183	3	is	be	AUX
ap-1398	183	4	such	such	ADJ
ap-1398	183	5	that	that	SCONJ
ap-1398	183	6	neither	neither	CCONJ
ap-1398	183	7	f	f	PROPN
ap-1398	183	8	∈	∈	PROPN
ap-1398	183	9	pf	pf	PROPN
ap-1398	183	10	nor	nor	CCONJ
ap-1398	183	11	f	f	PROPN
ap-1398	183	12	′	′	NUM
ap-1398	183	13	∈	∈	PROPN
ap-1398	183	14	pf	pf	INTJ
ap-1398	183	15	,	,	PUNCT
ap-1398	183	16	then	then	ADV
ap-1398	183	17	there	there	PRON
ap-1398	183	18	exist	exist	VERB
ap-1398	183	19	atoms	atom	NOUN
ap-1398	183	20	α1	α1	NOUN
ap-1398	183	21	,	,	PUNCT
ap-1398	183	22	α2	α2	PROPN
ap-1398	183	23	∈	∈	PROPN
ap-1398	183	24	∞⋃	∞⋃	NOUN
ap-1398	183	25	i=0	i=0	PROPN
ap-1398	183	26	{	{	PUNCT
ap-1398	183	27	ai	ai	PROPN
ap-1398	183	28	,	,	PUNCT
ap-1398	183	29	bi	bi	ADJ
ap-1398	183	30	}	}	PUNCT
ap-1398	183	31	∪	∪	ADP
ap-1398	183	32	∞⋃	∞⋃	NOUN
ap-1398	183	33	j=1	j=1	PROPN
ap-1398	183	34	{	{	PUNCT
ap-1398	183	35	cj	cj	INTJ
ap-1398	183	36	,	,	PUNCT
ap-1398	183	37	dj	dj	AUX
ap-1398	183	38	}	}	PUNCT
ap-1398	183	39	fulfilling	fulfil	VERB
ap-1398	183	40	α1	α1	PROPN
ap-1398	183	41	�	�	PROPN
ap-1398	183	42	↔	↔	PROPN
ap-1398	183	43	α2	α2	ADJ
ap-1398	183	44	and	and	CCONJ
ap-1398	183	45	α1	α1	PROPN
ap-1398	183	46	≤	≤	ADJ
ap-1398	183	47	f	f	PROPN
ap-1398	183	48	,	,	PUNCT
ap-1398	183	49	α2	α2	PROPN
ap-1398	183	50	�	�	PROPN
ap-1398	183	51	≤	≤	PROPN
ap-1398	183	52	f	f	NOUN
ap-1398	183	53	.	.	PUNCT
ap-1398	184	1	then	then	ADV
ap-1398	184	2	f	f	PROPN
ap-1398	184	3	is	be	AUX
ap-1398	184	4	not	not	PART
ap-1398	184	5	a	a	DET
ap-1398	184	6	central	central	ADJ
ap-1398	184	7	element	element	NOUN
ap-1398	184	8	.	.	PUNCT
ap-1398	185	1	this	this	PRON
ap-1398	185	2	proves	prove	VERB
ap-1398	185	3	that	that	SCONJ
ap-1398	185	4	c(l̃	c(l̃	NOUN
ap-1398	185	5	)	)	PUNCT
ap-1398	185	6	=	=	PRON
ap-1398	186	1	{	{	PUNCT
ap-1398	186	2	f	f	PROPN
ap-1398	186	3	∈	∈	PROPN
ap-1398	186	4	l̃	l̃	PROPN
ap-1398	186	5	;	;	PUNCT
ap-1398	186	6	f	f	PROPN
ap-1398	186	7	∈	∈	PROPN
ap-1398	186	8	pf	pf	PROPN
ap-1398	186	9	or	or	CCONJ
ap-1398	186	10	f	f	PROPN
ap-1398	186	11	′	′	NUM
ap-1398	186	12	∈	∈	PROPN
ap-1398	186	13	pf	pf	PROPN
ap-1398	186	14	}	}	PUNCT
ap-1398	186	15	.	.	PUNCT
ap-1398	187	1	due	due	ADP
ap-1398	187	2	to	to	ADP
ap-1398	187	3	the	the	DET
ap-1398	187	4	fact	fact	NOUN
ap-1398	187	5	that	that	SCONJ
ap-1398	187	6	f	f	PROPN
ap-1398	187	7	is	be	AUX
ap-1398	187	8	a	a	DET
ap-1398	187	9	non	non	ADJ
ap-1398	187	10	-	-	ADJ
ap-1398	187	11	trivial	trivial	ADJ
ap-1398	187	12	ultrafilter	ultrafilter	NOUN
ap-1398	187	13	,	,	PUNCT
ap-1398	187	14	c(l̃	c(l̃	PROPN
ap-1398	187	15	)	)	PUNCT
ap-1398	187	16	is	be	AUX
ap-1398	187	17	a	a	DET
ap-1398	187	18	complete	complete	ADJ
ap-1398	187	19	boolean	boolean	ADJ
ap-1398	187	20	algebra	algebra	NOUN
ap-1398	187	21	.	.	PUNCT
ap-1398	188	1	the	the	DET
ap-1398	188	2	only	only	ADJ
ap-1398	188	3	central	central	ADJ
ap-1398	188	4	element	element	NOUN
ap-1398	188	5	that	that	PRON
ap-1398	188	6	is	be	AUX
ap-1398	188	7	greater	great	ADJ
ap-1398	188	8	than	than	ADP
ap-1398	188	9	all	all	DET
ap-1398	188	10	atoms	atom	NOUN
ap-1398	188	11	pj	pj	PROPN
ap-1398	188	12	for	for	ADP
ap-1398	188	13	j	j	PROPN
ap-1398	188	14	=	=	SYM
ap-1398	188	15	1	1	NUM
ap-1398	188	16	,	,	PUNCT
ap-1398	188	17	2	2	NUM
ap-1398	188	18	,	,	PUNCT
ap-1398	188	19	.	.	PUNCT
ap-1398	188	20	.	.	PUNCT
ap-1398	189	1	.	.	PUNCT
ap-1398	189	2	,	,	PUNCT
ap-1398	189	3	is	be	AUX
ap-1398	189	4	1	1	NUM
ap-1398	189	5	,	,	PUNCT
ap-1398	189	6	hence	hence	ADV
ap-1398	189	7	we	we	PRON
ap-1398	189	8	have	have	VERB
ap-1398	189	9	that∨	that∨	PROPN
ap-1398	189	10	c(l̃	c(l̃	NOUN
ap-1398	189	11	)	)	PUNCT
ap-1398	189	12	{	{	PUNCT
ap-1398	189	13	pj	pj	PROPN
ap-1398	189	14	;	;	PUNCT
ap-1398	189	15	j	j	PROPN
ap-1398	189	16	=	=	SYM
ap-1398	189	17	1	1	NUM
ap-1398	189	18	,	,	PUNCT
ap-1398	189	19	2	2	NUM
ap-1398	189	20	,	,	PUNCT
ap-1398	189	21	.	.	PUNCT
ap-1398	189	22	.	.	PUNCT
ap-1398	190	1	.	.	PUNCT
ap-1398	190	2	}	}	PUNCT
ap-1398	191	1	=	=	PUNCT
ap-1398	191	2	1	1	X
ap-1398	191	3	.	.	PUNCT
ap-1398	192	1	on	on	ADP
ap-1398	192	2	the	the	DET
ap-1398	192	3	other	other	ADJ
ap-1398	192	4	hand	hand	NOUN
ap-1398	192	5	,	,	PUNCT
ap-1398	192	6	let	let	VERB
ap-1398	192	7	us	we	PRON
ap-1398	192	8	take	take	VERB
ap-1398	192	9	an	an	DET
ap-1398	192	10	arbitrary	arbitrary	ADJ
ap-1398	192	11	atom	atom	NOUN
ap-1398	192	12	α	α	PROPN
ap-1398	192	13	∈	∈	PROPN
ap-1398	192	14	∞⋃	∞⋃	NOUN
ap-1398	192	15	i=0	i=0	PROPN
ap-1398	192	16	{	{	PUNCT
ap-1398	192	17	ai	ai	PROPN
ap-1398	192	18	,	,	PUNCT
ap-1398	192	19	bi	bi	ADJ
ap-1398	192	20	}	}	PUNCT
ap-1398	192	21	∪	∪	ADP
ap-1398	192	22	∞⋃	∞⋃	NOUN
ap-1398	192	23	j=1	j=1	PROPN
ap-1398	192	24	{	{	PUNCT
ap-1398	192	25	cj	cj	INTJ
ap-1398	192	26	,	,	PUNCT
ap-1398	192	27	dj	dj	NOUN
ap-1398	192	28	}	}	PUNCT
ap-1398	192	29	and	and	CCONJ
ap-1398	192	30	assume	assume	VERB
ap-1398	192	31	that	that	SCONJ
ap-1398	192	32	∨	∨	PROPN
ap-1398	192	33	l̃	l̃	PROPN
ap-1398	192	34	{	{	PUNCT
ap-1398	192	35	pj	pj	PROPN
ap-1398	192	36	;	;	PUNCT
ap-1398	192	37	j	j	PROPN
ap-1398	192	38	=	=	SYM
ap-1398	192	39	1	1	NUM
ap-1398	192	40	,	,	PUNCT
ap-1398	192	41	2	2	NUM
ap-1398	192	42	,	,	PUNCT
ap-1398	192	43	.	.	PUNCT
ap-1398	192	44	.	.	PUNCT
ap-1398	193	1	.	.	PUNCT
ap-1398	193	2	}	}	PUNCT
ap-1398	193	3	does	do	AUX
ap-1398	193	4	exist	exist	VERB
ap-1398	193	5	.	.	PUNCT
ap-1398	194	1	since	since	SCONJ
ap-1398	194	2	α	α	NOUN
ap-1398	194	3	is	be	AUX
ap-1398	194	4	orthogonal	orthogonal	ADJ
ap-1398	194	5	to	to	ADP
ap-1398	194	6	all	all	DET
ap-1398	194	7	atoms	atom	NOUN
ap-1398	194	8	from	from	ADP
ap-1398	194	9	the	the	DET
ap-1398	194	10	set	set	ADJ
ap-1398	194	11	∞⋃	∞⋃	NOUN
ap-1398	194	12	j=1	j=1	PROPN
ap-1398	194	13	{	{	PUNCT
ap-1398	194	14	pj	pj	PROPN
ap-1398	194	15	}	}	PUNCT
ap-1398	194	16	,	,	PUNCT
ap-1398	194	17	we	we	PRON
ap-1398	194	18	have	have	VERB
ap-1398	194	19	that	that	SCONJ
ap-1398	194	20	α	α	NOUN
ap-1398	194	21	is	be	AUX
ap-1398	194	22	orthogonal	orthogonal	ADJ
ap-1398	194	23	to∨	to∨	X
ap-1398	195	1	l̃	l̃	PROPN
ap-1398	195	2	{	{	PUNCT
ap-1398	195	3	pj	pj	PROPN
ap-1398	195	4	;	;	PUNCT
ap-1398	195	5	j	j	PROPN
ap-1398	195	6	=	=	SYM
ap-1398	195	7	1	1	NUM
ap-1398	195	8	,	,	PUNCT
ap-1398	195	9	2	2	NUM
ap-1398	195	10	,	,	PUNCT
ap-1398	195	11	.	.	PUNCT
ap-1398	195	12	.	.	PUNCT
ap-1398	195	13	.	.	PUNCT
ap-1398	195	14	}	}	PUNCT
ap-1398	195	15	and	and	CCONJ
ap-1398	195	16	hence	hence	ADV
ap-1398	195	17	∨	∨	PROPN
ap-1398	195	18	l̃	l̃	PROPN
ap-1398	195	19	{	{	PUNCT
ap-1398	195	20	pj	pj	PROPN
ap-1398	195	21	;	;	PUNCT
ap-1398	195	22	j	j	PROPN
ap-1398	195	23	=	=	SYM
ap-1398	195	24	1	1	NUM
ap-1398	195	25	,	,	PUNCT
ap-1398	195	26	2	2	NUM
ap-1398	195	27	,	,	PUNCT
ap-1398	195	28	.	.	PUNCT
ap-1398	195	29	.	.	PUNCT
ap-1398	195	30	.	.	PUNCT
ap-1398	195	31	}	}	PUNCT
ap-1398	195	32	�	�	X
ap-1398	195	33	=	=	NOUN
ap-1398	195	34	1	1	NUM
ap-1398	195	35	.	.	PUNCT
ap-1398	196	1	it	it	PRON
ap-1398	196	2	can	can	AUX
ap-1398	196	3	be	be	AUX
ap-1398	196	4	shown	show	VERB
ap-1398	196	5	(	(	PUNCT
ap-1398	196	6	see	see	VERB
ap-1398	196	7	[	[	X
ap-1398	196	8	8	8	NUM
ap-1398	196	9	]	]	PUNCT
ap-1398	196	10	)	)	PUNCT
ap-1398	197	1	that	that	SCONJ
ap-1398	197	2	∨	∨	PROPN
ap-1398	197	3	l̃	l̃	PROPN
ap-1398	197	4	{	{	PUNCT
ap-1398	197	5	pj	pj	PROPN
ap-1398	197	6	;	;	PUNCT
ap-1398	197	7	j	j	PROPN
ap-1398	197	8	=	=	SYM
ap-1398	197	9	1	1	NUM
ap-1398	197	10	,	,	PUNCT
ap-1398	197	11	2	2	NUM
ap-1398	197	12	,	,	PUNCT
ap-1398	197	13	.	.	PUNCT
ap-1398	197	14	.	.	PUNCT
ap-1398	197	15	.	.	PUNCT
ap-1398	197	16	}	}	PUNCT
ap-1398	197	17	does	do	AUX
ap-1398	197	18	not	not	PART
ap-1398	197	19	exist	exist	VERB
ap-1398	197	20	.	.	PUNCT
ap-1398	198	1	this	this	PRON
ap-1398	198	2	implies	imply	VERB
ap-1398	198	3	that	that	SCONJ
ap-1398	198	4	c(l̃	c(l̃	NOUN
ap-1398	198	5	)	)	PUNCT
ap-1398	198	6	is	be	AUX
ap-1398	198	7	not	not	PART
ap-1398	198	8	a	a	DET
ap-1398	198	9	bifull	bifull	ADJ
ap-1398	198	10	sublattice	sublattice	NOUN
ap-1398	198	11	of	of	ADP
ap-1398	198	12	l̃.	l̃.	PROPN
ap-1398	198	13	�	�	PROPN
ap-1398	198	14	4	4	NUM
ap-1398	198	15	σ	σ	PROPN
ap-1398	198	16	-	-	PUNCT
ap-1398	198	17	complete	complete	ADJ
ap-1398	198	18	orthomodular	orthomodular	ADJ
ap-1398	198	19	lattice	lattice	NOUN
ap-1398	198	20	l̃σ	l̃σ	NOUN
ap-1398	198	21	whose	whose	DET
ap-1398	198	22	center	center	NOUN
ap-1398	198	23	is	be	AUX
ap-1398	198	24	not	not	PART
ap-1398	198	25	a	a	DET
ap-1398	198	26	bifull	bifull	ADJ
ap-1398	198	27	sublattice	sublattice	NOUN
ap-1398	198	28	let	let	VERB
ap-1398	198	29	i	i	PRON
ap-1398	198	30	denote	denote	VERB
ap-1398	198	31	the	the	DET
ap-1398	198	32	set	set	NOUN
ap-1398	198	33	of	of	ADP
ap-1398	198	34	all	all	DET
ap-1398	198	35	ordinal	ordinal	ADJ
ap-1398	198	36	numbers	number	NOUN
ap-1398	198	37	less	less	ADJ
ap-1398	198	38	than	than	ADP
ap-1398	198	39	ω	ω	PROPN
ap-1398	198	40	(	(	PUNCT
ap-1398	198	41	the	the	DET
ap-1398	198	42	first	first	ADJ
ap-1398	198	43	uncountable	uncountable	ADJ
ap-1398	198	44	ordinal	ordinal	ADJ
ap-1398	198	45	number	number	NOUN
ap-1398	198	46	)	)	PUNCT
ap-1398	198	47	.	.	PUNCT
ap-1398	199	1	further	far	ADV
ap-1398	199	2	,	,	PUNCT
ap-1398	199	3	denote	denote	VERB
ap-1398	199	4	e	e	PROPN
ap-1398	199	5	the	the	DET
ap-1398	199	6	set	set	NOUN
ap-1398	199	7	of	of	ADP
ap-1398	199	8	all	all	DET
ap-1398	199	9	limit	limit	NOUN
ap-1398	199	10	ordinal	ordinal	ADJ
ap-1398	199	11	numbers	number	NOUN
ap-1398	199	12	up	up	ADP
ap-1398	199	13	to	to	ADP
ap-1398	199	14	ω	ω	NUM
ap-1398	199	15	and	and	CCONJ
ap-1398	199	16	j	j	PROPN
ap-1398	200	1	=	=	SYM
ap-1398	200	2	i	i	NOUN
ap-1398	200	3	\	\	NOUN
ap-1398	200	4	e	e	X
ap-1398	200	5	.	.	PUNCT
ap-1398	201	1	assume	assume	VERB
ap-1398	201	2	sets	set	NOUN
ap-1398	201	3	of	of	ADP
ap-1398	201	4	elements	element	NOUN
ap-1398	201	5	{	{	PUNCT
ap-1398	201	6	pi	pi	NOUN
ap-1398	201	7	;	;	PUNCT
ap-1398	201	8	i	i	PRON
ap-1398	201	9	∈	∈	PROPN
ap-1398	201	10	i	i	X
ap-1398	201	11	}	}	PUNCT
ap-1398	201	12	,	,	PUNCT
ap-1398	201	13	{	{	PUNCT
ap-1398	201	14	ai	ai	VERB
ap-1398	201	15	;	;	PUNCT
ap-1398	201	16	i	i	PRON
ap-1398	201	17	∈	∈	PROPN
ap-1398	201	18	i	i	X
ap-1398	201	19	}	}	PUNCT
ap-1398	201	20	,	,	PUNCT
ap-1398	201	21	{	{	PUNCT
ap-1398	201	22	bi	bi	NOUN
ap-1398	201	23	;	;	PUNCT
ap-1398	201	24	i	i	PRON
ap-1398	201	25	∈	∈	PROPN
ap-1398	201	26	i	i	X
ap-1398	201	27	}	}	PUNCT
ap-1398	201	28	,	,	PUNCT
ap-1398	201	29	{	{	PUNCT
ap-1398	201	30	ci	ci	NOUN
ap-1398	201	31	;	;	PUNCT
ap-1398	201	32	i	i	PROPN
ap-1398	201	33	∈	∈	PROPN
ap-1398	201	34	i	i	X
ap-1398	201	35	}	}	PUNCT
ap-1398	201	36	,	,	PUNCT
ap-1398	201	37	{	{	PUNCT
ap-1398	201	38	di	di	NOUN
ap-1398	201	39	;	;	PUNCT
ap-1398	201	40	i	i	PROPN
ap-1398	201	41	∈	∈	PROPN
ap-1398	201	42	i	i	PRON
ap-1398	201	43	}	}	PUNCT
ap-1398	201	44	,	,	PUNCT
ap-1398	201	45	where	where	SCONJ
ap-1398	201	46	the	the	DET
ap-1398	201	47	corresponding	corresponding	ADJ
ap-1398	201	48	elements	element	NOUN
ap-1398	201	49	for	for	ADP
ap-1398	201	50	i	i	PRON
ap-1398	201	51	∈	∈	PROPN
ap-1398	201	52	j	j	PROPN
ap-1398	201	53	will	will	AUX
ap-1398	201	54	act	act	VERB
ap-1398	201	55	as	as	ADP
ap-1398	201	56	atoms	atom	NOUN
ap-1398	201	57	.	.	PUNCT
ap-1398	202	1	we	we	PRON
ap-1398	202	2	will	will	AUX
ap-1398	202	3	have	have	VERB
ap-1398	202	4	a	a	DET
ap-1398	202	5	partial	partial	ADJ
ap-1398	202	6	relation	relation	NOUN
ap-1398	202	7	�	�	NOUN
ap-1398	202	8	↔	↔	NOUN
ap-1398	202	9	modelling	model	VERB
ap-1398	202	10	noncompatibility	noncompatibility	NOUN
ap-1398	202	11	.	.	PUNCT
ap-1398	203	1	this	this	DET
ap-1398	203	2	partial	partial	ADJ
ap-1398	203	3	relation	relation	NOUN
ap-1398	203	4	will	will	AUX
ap-1398	203	5	have	have	VERB
ap-1398	203	6	the	the	DET
ap-1398	203	7	following	follow	VERB
ap-1398	203	8	form	form	NOUN
ap-1398	203	9	among	among	ADP
ap-1398	203	10	atoms	atom	NOUN
ap-1398	203	11	cj	cj	X
ap-1398	203	12	�	�	PROPN
ap-1398	203	13	↔	↔	PROPN
ap-1398	203	14	ai	ai	NOUN
ap-1398	203	15	,	,	PUNCT
ap-1398	203	16	cj	cj	PROPN
ap-1398	203	17	�	�	PROPN
ap-1398	203	18	↔	↔	PROPN
ap-1398	203	19	bi	bi	NOUN
ap-1398	203	20	for	for	ADP
ap-1398	203	21	all	all	DET
ap-1398	203	22	j	j	PROPN
ap-1398	203	23	∈	∈	PROPN
ap-1398	203	24	j	j	PROPN
ap-1398	203	25	and	and	CCONJ
ap-1398	203	26	i	i	PROPN
ap-1398	203	27	≤	≤	PROPN
ap-1398	203	28	j	j	PROPN
ap-1398	203	29	,	,	PUNCT
ap-1398	203	30	dj	dj	X
ap-1398	203	31	�	�	PROPN
ap-1398	203	32	↔	↔	PROPN
ap-1398	203	33	ai	ai	NOUN
ap-1398	203	34	,	,	PUNCT
ap-1398	203	35	dj	dj	X
ap-1398	203	36	�	�	NOUN
ap-1398	203	37	↔	↔	PROPN
ap-1398	203	38	bi	bi	NOUN
ap-1398	203	39	for	for	ADP
ap-1398	203	40	all	all	DET
ap-1398	203	41	j	j	PROPN
ap-1398	203	42	∈	∈	PROPN
ap-1398	203	43	j	j	PROPN
ap-1398	203	44	and	and	CCONJ
ap-1398	203	45	i	i	PROPN
ap-1398	203	46	≤	≤	PROPN
ap-1398	203	47	j	j	PROPN
ap-1398	203	48	,	,	PUNCT
ap-1398	203	49	29	29	NUM
ap-1398	203	50	acta	acta	PROPN
ap-1398	203	51	polytechnica	polytechnica	PROPN
ap-1398	203	52	vol	vol	NOUN
ap-1398	203	53	.	.	PUNCT
ap-1398	204	1	51	51	NUM
ap-1398	204	2	no	no	INTJ
ap-1398	204	3	.	.	PUNCT
ap-1398	205	1	4/2011	4/2011	NUM
ap-1398	205	2	cj	cj	NUM
ap-1398	205	3	�	�	PROPN
ap-1398	205	4	↔	↔	PROPN
ap-1398	205	5	di	di	NOUN
ap-1398	205	6	for	for	ADP
ap-1398	205	7	all	all	DET
ap-1398	205	8	i	i	PROPN
ap-1398	205	9	,	,	PUNCT
ap-1398	205	10	j	j	PROPN
ap-1398	205	11	∈	∈	PROPN
ap-1398	205	12	j	j	PROPN
ap-1398	205	13	such	such	ADJ
ap-1398	205	14	that	that	SCONJ
ap-1398	205	15	i	i	PRON
ap-1398	205	16	�	�	PROPN
ap-1398	205	17	=	=	SYM
ap-1398	205	18	j	j	PROPN
ap-1398	205	19	,	,	PUNCT
ap-1398	205	20	cj	cj	PROPN
ap-1398	205	21	�	�	PROPN
ap-1398	205	22	↔	↔	PROPN
ap-1398	205	23	ci	ci	NOUN
ap-1398	205	24	,	,	PUNCT
ap-1398	205	25	dj	dj	X
ap-1398	205	26	�	�	PROPN
ap-1398	205	27	↔	↔	NOUN
ap-1398	205	28	di	di	NOUN
ap-1398	205	29	for	for	ADP
ap-1398	205	30	all	all	DET
ap-1398	205	31	i	i	PROPN
ap-1398	205	32	,	,	PUNCT
ap-1398	205	33	j	j	PROPN
ap-1398	205	34	∈	∈	PROPN
ap-1398	205	35	j	j	PROPN
ap-1398	205	36	such	such	ADJ
ap-1398	205	37	that	that	SCONJ
ap-1398	205	38	i	i	PRON
ap-1398	205	39	�	�	PROPN
ap-1398	205	40	=	=	SYM
ap-1398	205	41	j.	j.	PROPN
ap-1398	205	42	sets	set	NOUN
ap-1398	205	43	of	of	ADP
ap-1398	205	44	elements	element	NOUN
ap-1398	205	45	{	{	PUNCT
ap-1398	205	46	pi	pi	NOUN
ap-1398	205	47	;	;	PUNCT
ap-1398	205	48	i	i	PRON
ap-1398	205	49	∈	∈	PROPN
ap-1398	205	50	i	i	X
ap-1398	205	51	}	}	PUNCT
ap-1398	205	52	,	,	PUNCT
ap-1398	205	53	{	{	PUNCT
ap-1398	205	54	ai	ai	VERB
ap-1398	205	55	;	;	PUNCT
ap-1398	205	56	i	i	PRON
ap-1398	205	57	∈	∈	PROPN
ap-1398	205	58	i	i	X
ap-1398	205	59	}	}	PUNCT
ap-1398	205	60	,	,	PUNCT
ap-1398	205	61	{	{	PUNCT
ap-1398	205	62	bi	bi	NOUN
ap-1398	205	63	;	;	PUNCT
ap-1398	205	64	i	i	PRON
ap-1398	205	65	∈	∈	PROPN
ap-1398	205	66	i	i	X
ap-1398	205	67	}	}	PUNCT
ap-1398	205	68	,	,	PUNCT
ap-1398	205	69	{	{	PUNCT
ap-1398	205	70	ci	ci	NOUN
ap-1398	205	71	;	;	PUNCT
ap-1398	205	72	i	i	PROPN
ap-1398	205	73	∈	∈	PROPN
ap-1398	205	74	i	i	X
ap-1398	205	75	}	}	PUNCT
ap-1398	205	76	,	,	PUNCT
ap-1398	205	77	{	{	PUNCT
ap-1398	205	78	di	di	NOUN
ap-1398	205	79	;	;	PUNCT
ap-1398	205	80	i	i	PROPN
ap-1398	205	81	∈	∈	PROPN
ap-1398	205	82	i	i	PRON
ap-1398	205	83	}	}	PUNCT
ap-1398	205	84	will	will	AUX
ap-1398	205	85	present	present	VERB
ap-1398	205	86	atoms	atom	NOUN
ap-1398	205	87	for	for	ADP
ap-1398	205	88	i	i	PROPN
ap-1398	205	89	∈	∈	PROPN
ap-1398	205	90	j	j	PROPN
ap-1398	205	91	and	and	CCONJ
ap-1398	205	92	for	for	ADP
ap-1398	205	93	κ	κ	PROPN
ap-1398	205	94	∈	∈	PROPN
ap-1398	205	95	e	e	NOUN
ap-1398	205	96	we	we	PRON
ap-1398	205	97	will	will	AUX
ap-1398	205	98	have	have	AUX
ap-1398	205	99	pκ	pκ	VERB
ap-1398	205	100	=	=	PUNCT
ap-1398	205	101	∨	∨	PROPN
ap-1398	206	1	i	i	PRON
ap-1398	206	2	<	<	X
ap-1398	206	3	κ	κ	NOUN
ap-1398	206	4	pi	pi	NOUN
ap-1398	206	5	,	,	PUNCT
ap-1398	206	6	(	(	PUNCT
ap-1398	206	7	7	7	X
ap-1398	206	8	)	)	PUNCT
ap-1398	206	9	aκ	aκ	NOUN
ap-1398	206	10	=	=	PUNCT
ap-1398	206	11	∨	∨	PROPN
ap-1398	206	12	i	i	PRON
ap-1398	206	13	<	<	X
ap-1398	206	14	κ	κ	X
ap-1398	206	15	ai	ai	VERB
ap-1398	206	16	,	,	PUNCT
ap-1398	206	17	(	(	PUNCT
ap-1398	206	18	8)	8)	NUM
ap-1398	206	19	bκ	bκ	NOUN
ap-1398	206	20	=	=	PUNCT
ap-1398	206	21	∨	∨	NUM
ap-1398	206	22	i	i	PROPN
ap-1398	206	23	<	<	X
ap-1398	206	24	κ	κ	PROPN
ap-1398	206	25	bi	bi	PROPN
ap-1398	206	26	,	,	PUNCT
ap-1398	206	27	(	(	PUNCT
ap-1398	206	28	9	9	X
ap-1398	206	29	)	)	PUNCT
ap-1398	206	30	cκ	cκ	NOUN
ap-1398	206	31	=	=	PUNCT
ap-1398	206	32	∨	∨	PROPN
ap-1398	206	33	i	i	PROPN
ap-1398	206	34	<	<	X
ap-1398	206	35	κ	κ	X
ap-1398	206	36	ci	ci	NOUN
ap-1398	206	37	=	=	PUNCT
ap-1398	206	38	∨	∨	PROPN
ap-1398	206	39	i	i	X
ap-1398	206	40	<	<	X
ap-1398	206	41	κ	κ	X
ap-1398	206	42	di	di	X
ap-1398	206	43	=	=	PUNCT
ap-1398	206	44	dκ	dκ	PROPN
ap-1398	206	45	=	=	PROPN
ap-1398	206	46	aκ	aκ	PROPN
ap-1398	206	47	⊕	⊕	PROPN
ap-1398	206	48	bκ	bκ	VERB
ap-1398	206	49	.	.	PUNCT
ap-1398	207	1	(	(	PUNCT
ap-1398	207	2	10	10	NUM
ap-1398	207	3	)	)	PUNCT
ap-1398	207	4	as	as	ADP
ap-1398	207	5	a	a	DET
ap-1398	207	6	possible	possible	ADJ
ap-1398	207	7	model	model	NOUN
ap-1398	207	8	for	for	ADP
ap-1398	207	9	the	the	DET
ap-1398	207	10	just	just	ADV
ap-1398	207	11	presented	present	VERB
ap-1398	207	12	sets	set	NOUN
ap-1398	207	13	of	of	ADP
ap-1398	207	14	elements	element	NOUN
ap-1398	207	15	fulfilling	fulfil	VERB
ap-1398	207	16	the	the	DET
ap-1398	207	17	non	non	ADJ
ap-1398	207	18	-	-	ADJ
ap-1398	207	19	compatibility	compatibility	NOUN
ap-1398	207	20	relation	relation	NOUN
ap-1398	207	21	we	we	PRON
ap-1398	207	22	may	may	AUX
ap-1398	207	23	have	have	VERB
ap-1398	207	24	the	the	DET
ap-1398	207	25	following	following	NOUN
ap-1398	207	26	:	:	PUNCT
ap-1398	207	27	let	let	VERB
ap-1398	207	28	us	we	PRON
ap-1398	207	29	choose	choose	VERB
ap-1398	207	30	a	a	DET
ap-1398	207	31	good	good	ADJ
ap-1398	207	32	order	order	NOUN
ap-1398	207	33	of	of	ADP
ap-1398	207	34	positive	positive	ADJ
ap-1398	207	35	real	real	ADJ
ap-1398	207	36	numbers	number	NOUN
ap-1398	207	37	of	of	ADP
ap-1398	207	38	type	type	NOUN
ap-1398	207	39	ω	ω	PROPN
ap-1398	207	40	,	,	PUNCT
ap-1398	207	41	i.e.	i.e.	X
ap-1398	207	42	,	,	PUNCT
ap-1398	207	43	positive	positive	ADJ
ap-1398	207	44	real	real	ADJ
ap-1398	207	45	numbers	number	NOUN
ap-1398	207	46	will	will	AUX
ap-1398	207	47	be	be	AUX
ap-1398	207	48	enumerated	enumerate	VERB
ap-1398	207	49	by	by	ADP
ap-1398	207	50	ordinal	ordinal	ADJ
ap-1398	207	51	numbers	number	NOUN
ap-1398	207	52	from	from	ADP
ap-1398	207	53	j	j	PROPN
ap-1398	207	54	.	.	PUNCT
ap-1398	208	1	for	for	ADP
ap-1398	208	2	i	i	PROPN
ap-1398	208	3	∈	∈	PROPN
ap-1398	208	4	j	j	PROPN
ap-1398	208	5	and	and	CCONJ
ap-1398	208	6	r	r	NOUN
ap-1398	208	7	>	>	X
ap-1398	208	8	0	0	NUM
ap-1398	208	9	,	,	PUNCT
ap-1398	208	10	r	r	NOUN
ap-1398	208	11	∈	∈	PROPN
ap-1398	208	12	r	r	NOUN
ap-1398	208	13	,	,	PUNCT
ap-1398	208	14	we	we	PRON
ap-1398	208	15	denote	denote	VERB
ap-1398	208	16	ri	ri	PROPN
ap-1398	208	17	the	the	DET
ap-1398	208	18	i	i	PROPN
ap-1398	208	19	-	-	PUNCT
ap-1398	208	20	th	th	VERB
ap-1398	208	21	number	number	NOUN
ap-1398	208	22	in	in	ADP
ap-1398	208	23	the	the	DET
ap-1398	208	24	chosen	choose	VERB
ap-1398	208	25	good	good	ADJ
ap-1398	208	26	order	order	NOUN
ap-1398	208	27	.	.	PUNCT
ap-1398	209	1	then	then	ADV
ap-1398	209	2	we	we	PRON
ap-1398	209	3	identify	identify	VERB
ap-1398	209	4	the	the	DET
ap-1398	209	5	set	set	NOUN
ap-1398	209	6	{	{	PUNCT
ap-1398	209	7	pi	pi	NOUN
ap-1398	209	8	;	;	PUNCT
ap-1398	209	9	i	i	PROPN
ap-1398	209	10	∈	∈	PROPN
ap-1398	209	11	j	j	PROPN
ap-1398	209	12	}	}	PUNCT
ap-1398	209	13	with	with	ADP
ap-1398	209	14	the	the	DET
ap-1398	209	15	set	set	NOUN
ap-1398	209	16	of	of	ADP
ap-1398	209	17	all	all	DET
ap-1398	209	18	positive	positive	ADJ
ap-1398	209	19	real	real	ADJ
ap-1398	209	20	numbers	number	NOUN
ap-1398	209	21	,	,	PUNCT
ap-1398	209	22	i.e.	i.e.	X
ap-1398	209	23	,	,	PUNCT
ap-1398	209	24	pi	pi	NOUN
ap-1398	209	25	=	=	SYM
ap-1398	209	26	ri	ri	PROPN
ap-1398	209	27	.	.	PUNCT
ap-1398	210	1	further	far	ADV
ap-1398	210	2	we	we	PRON
ap-1398	210	3	put	put	VERB
ap-1398	210	4	for	for	ADP
ap-1398	210	5	i	i	PRON
ap-1398	210	6	,	,	PUNCT
ap-1398	210	7	j	j	PROPN
ap-1398	210	8	∈	∈	PROPN
ap-1398	211	1	j	j	NOUN
ap-1398	211	2	ai	ai	VERB
ap-1398	211	3	=	=	PUNCT
ap-1398	211	4	{	{	PUNCT
ap-1398	211	5	(	(	PUNCT
ap-1398	211	6	ri	ri	PROPN
ap-1398	211	7	,	,	PUNCT
ap-1398	211	8	y	y	NOUN
ap-1398	211	9	)	)	PUNCT
ap-1398	211	10	∈	∈	PROPN
ap-1398	211	11	r	r	NOUN
ap-1398	211	12	2	2	NUM
ap-1398	211	13	;	;	PUNCT
ap-1398	211	14	y	y	PROPN
ap-1398	211	15	∈	∈	PROPN
ap-1398	211	16	r	r	X
ap-1398	211	17	}	}	PUNCT
ap-1398	211	18	,	,	PUNCT
ap-1398	211	19	bi	bi	NOUN
ap-1398	211	20	=	=	PRON
ap-1398	211	21	{	{	PUNCT
ap-1398	211	22	(	(	PUNCT
ap-1398	211	23	−ri	−ri	PROPN
ap-1398	211	24	,	,	PUNCT
ap-1398	211	25	y	y	NOUN
ap-1398	211	26	)	)	PUNCT
ap-1398	211	27	∈	∈	PROPN
ap-1398	211	28	r	r	NOUN
ap-1398	211	29	2	2	NUM
ap-1398	211	30	;	;	PUNCT
ap-1398	211	31	y	y	PROPN
ap-1398	211	32	∈	∈	PROPN
ap-1398	211	33	r	r	X
ap-1398	211	34	}	}	PUNCT
ap-1398	211	35	,	,	PUNCT
ap-1398	211	36	ci	ci	NOUN
ap-1398	211	37	=	=	SYM
ap-1398	211	38	{	{	PUNCT
ap-1398	211	39	(	(	PUNCT
ap-1398	211	40	rj	rj	PROPN
ap-1398	211	41	,	,	PUNCT
ap-1398	211	42	y	y	PROPN
ap-1398	211	43	)	)	PUNCT
ap-1398	211	44	∈	∈	PROPN
ap-1398	211	45	r2	r2	NOUN
ap-1398	211	46	;	;	PUNCT
ap-1398	211	47	j	j	PROPN
ap-1398	211	48	≤	≤	PROPN
ap-1398	212	1	i	i	PROPN
ap-1398	212	2	,	,	PUNCT
ap-1398	212	3	y	y	PROPN
ap-1398	212	4	≤	≤	PROPN
ap-1398	212	5	ri	ri	PROPN
ap-1398	212	6	·	·	PUNCT
ap-1398	212	7	rj	rj	PROPN
ap-1398	212	8	}	}	PUNCT
ap-1398	212	9	∪	∪	X
ap-1398	212	10	{	{	PUNCT
ap-1398	212	11	(	(	PUNCT
ap-1398	212	12	−rj	−rj	NOUN
ap-1398	212	13	,	,	PUNCT
ap-1398	212	14	y	y	PROPN
ap-1398	212	15	)	)	PUNCT
ap-1398	212	16	∈	∈	PROPN
ap-1398	212	17	r	r	NOUN
ap-1398	212	18	2	2	NUM
ap-1398	212	19	;	;	PUNCT
ap-1398	212	20	j	j	PROPN
ap-1398	212	21	≤	≤	PROPN
ap-1398	212	22	i	i	PROPN
ap-1398	212	23	,	,	PUNCT
ap-1398	212	24	y	y	PROPN
ap-1398	212	25	≤	≤	PROPN
ap-1398	212	26	−ri	−ri	PROPN
ap-1398	212	27	·	·	PUNCT
ap-1398	212	28	rj	rj	PROPN
ap-1398	212	29	}	}	PUNCT
ap-1398	212	30	,	,	PUNCT
ap-1398	212	31	di	di	NOUN
ap-1398	212	32	=	=	SYM
ap-1398	212	33	{	{	PUNCT
ap-1398	212	34	(	(	PUNCT
ap-1398	212	35	rj	rj	PROPN
ap-1398	212	36	,	,	PUNCT
ap-1398	212	37	y	y	PROPN
ap-1398	212	38	)	)	PUNCT
ap-1398	212	39	∈	∈	PROPN
ap-1398	212	40	r2	r2	NOUN
ap-1398	212	41	;	;	PUNCT
ap-1398	213	1	j	j	PROPN
ap-1398	213	2	≤	≤	PROPN
ap-1398	213	3	i	i	PROPN
ap-1398	213	4	,	,	PUNCT
ap-1398	213	5	y	y	PROPN
ap-1398	213	6	>	>	X
ap-1398	213	7	ri	ri	PROPN
ap-1398	213	8	·	·	PUNCT
ap-1398	213	9	rj	rj	PROPN
ap-1398	213	10	}	}	PUNCT
ap-1398	213	11	∪	∪	X
ap-1398	213	12	{	{	PUNCT
ap-1398	213	13	(	(	PUNCT
ap-1398	213	14	−rj	−rj	NOUN
ap-1398	213	15	,	,	PUNCT
ap-1398	213	16	y	y	PROPN
ap-1398	213	17	)	)	PUNCT
ap-1398	213	18	∈	∈	PROPN
ap-1398	213	19	r	r	NOUN
ap-1398	213	20	2	2	NUM
ap-1398	213	21	;	;	PUNCT
ap-1398	213	22	j	j	PROPN
ap-1398	213	23	≤	≤	PROPN
ap-1398	214	1	i	i	PROPN
ap-1398	214	2	,	,	PUNCT
ap-1398	214	3	y	y	PROPN
ap-1398	214	4	>	>	X
ap-1398	214	5	−ri	−ri	PROPN
ap-1398	214	6	·	·	PUNCT
ap-1398	214	7	rj	rj	PROPN
ap-1398	214	8	}	}	PUNCT
ap-1398	214	9	.	.	PUNCT
ap-1398	215	1	for	for	ADP
ap-1398	215	2	κ	κ	PROPN
ap-1398	215	3	∈	∈	PROPN
ap-1398	215	4	e	e	NOUN
ap-1398	215	5	we	we	PRON
ap-1398	215	6	define	define	VERB
ap-1398	215	7	the	the	DET
ap-1398	215	8	corresponding	correspond	VERB
ap-1398	215	9	elements	element	NOUN
ap-1398	215	10	pκ	pκ	VERB
ap-1398	215	11	,	,	PUNCT
ap-1398	215	12	aκ	aκ	ADV
ap-1398	215	13	,	,	PUNCT
ap-1398	215	14	bκ	bκ	VERB
ap-1398	215	15	,	,	PUNCT
ap-1398	215	16	cκ	cκ	VERB
ap-1398	215	17	,	,	PUNCT
ap-1398	215	18	dκ	dκ	PROPN
ap-1398	215	19	by	by	ADP
ap-1398	215	20	equalities	equality	NOUN
ap-1398	215	21	7	7	NUM
ap-1398	215	22	,	,	PUNCT
ap-1398	215	23	8	8	NUM
ap-1398	215	24	,	,	PUNCT
ap-1398	215	25	9	9	NUM
ap-1398	215	26	,	,	PUNCT
ap-1398	215	27	10	10	NUM
ap-1398	215	28	,	,	PUNCT
ap-1398	215	29	respectively	respectively	ADV
ap-1398	215	30	.	.	PUNCT
ap-1398	216	1	compatibility	compatibility	NOUN
ap-1398	216	2	among	among	ADP
ap-1398	216	3	different	different	ADJ
ap-1398	216	4	atoms	atom	NOUN
ap-1398	216	5	is	be	AUX
ap-1398	216	6	given	give	VERB
ap-1398	216	7	by	by	ADP
ap-1398	216	8	disjointness	disjointness	NOUN
ap-1398	216	9	of	of	ADP
ap-1398	216	10	the	the	DET
ap-1398	216	11	corresponding	corresponding	ADJ
ap-1398	216	12	sets	set	NOUN
ap-1398	216	13	.	.	PUNCT
ap-1398	217	1	this	this	PRON
ap-1398	217	2	implies	imply	VERB
ap-1398	217	3	that	that	SCONJ
ap-1398	217	4	the	the	DET
ap-1398	217	5	uniquely	uniquely	ADV
ap-1398	217	6	given	give	VERB
ap-1398	217	7	maximal	maximal	ADJ
ap-1398	217	8	sets	set	NOUN
ap-1398	217	9	of	of	ADP
ap-1398	217	10	pairwise	pairwise	NOUN
ap-1398	217	11	compatible	compatible	ADJ
ap-1398	217	12	atoms	atom	NOUN
ap-1398	217	13	are	be	AUX
ap-1398	217	14	ã0	ã0	PROPN
ap-1398	217	15	=	=	PUNCT
ap-1398	218	1	⋃	⋃	ADP
ap-1398	218	2	i∈j	i∈j	NOUN
ap-1398	218	3	{	{	PUNCT
ap-1398	218	4	ai	ai	NOUN
ap-1398	218	5	,	,	PUNCT
ap-1398	218	6	bi	bi	NOUN
ap-1398	218	7	,	,	PUNCT
ap-1398	218	8	pi	pi	NOUN
ap-1398	218	9	}	}	PUNCT
ap-1398	218	10	,	,	PUNCT
ap-1398	218	11	ãj	ãj	NOUN
ap-1398	218	12	=	=	SYM
ap-1398	219	1	⋃	⋃	PROPN
ap-1398	219	2	i	i	PRON
ap-1398	219	3	∈	∈	AUX
ap-1398	219	4	j	j	NOUN
ap-1398	220	1	i	i	PRON
ap-1398	220	2	>	>	X
ap-1398	220	3	j	j	PROPN
ap-1398	220	4	{	{	PUNCT
ap-1398	220	5	ai	ai	PROPN
ap-1398	220	6	,	,	PUNCT
ap-1398	220	7	bi	bi	ADJ
ap-1398	220	8	}	}	PUNCT
ap-1398	220	9	∪	∪	ADP
ap-1398	220	10	⋃	⋃	NOUN
ap-1398	220	11	i∈j	i∈j	NOUN
ap-1398	220	12	{	{	PUNCT
ap-1398	220	13	pi	pi	NOUN
ap-1398	220	14	}	}	PUNCT
ap-1398	220	15	∪	∪	X
ap-1398	220	16	{	{	PUNCT
ap-1398	220	17	cj	cj	NOUN
ap-1398	220	18	,	,	PUNCT
ap-1398	220	19	dj	dj	NOUN
ap-1398	220	20	}	}	PUNCT
ap-1398	220	21	for	for	ADP
ap-1398	220	22	j	j	PROPN
ap-1398	220	23	∈	∈	PROPN
ap-1398	220	24	j	j	PROPN
ap-1398	220	25	.	.	PUNCT
ap-1398	221	1	sets	set	NOUN
ap-1398	221	2	of	of	ADP
ap-1398	221	3	atoms	atom	NOUN
ap-1398	221	4	ã0	ã0	PROPN
ap-1398	221	5	and	and	CCONJ
ap-1398	221	6	ãj	ãj	NOUN
ap-1398	221	7	for	for	ADP
ap-1398	221	8	j	j	PROPN
ap-1398	221	9	∈	∈	PROPN
ap-1398	221	10	j	j	PROPN
ap-1398	221	11	,	,	PUNCT
ap-1398	221	12	generate	generate	VERB
ap-1398	221	13	complete	complete	ADJ
ap-1398	221	14	boolean	boolean	ADJ
ap-1398	221	15	algebras	algebra	NOUN
ap-1398	221	16	b̃0	b̃0	NOUN
ap-1398	221	17	and	and	CCONJ
ap-1398	221	18	b̃j	b̃j	NOUN
ap-1398	221	19	for	for	ADP
ap-1398	221	20	j	j	PROPN
ap-1398	221	21	∈	∈	PROPN
ap-1398	221	22	j	j	PROPN
ap-1398	221	23	,	,	PUNCT
ap-1398	221	24	respectively	respectively	ADV
ap-1398	221	25	.	.	PUNCT
ap-1398	222	1	for	for	ADP
ap-1398	222	2	κ	κ	PROPN
ap-1398	222	3	∈	∈	PROPN
ap-1398	222	4	e	e	NOUN
ap-1398	222	5	we	we	PRON
ap-1398	222	6	get	get	VERB
ap-1398	222	7	complete	complete	ADJ
ap-1398	222	8	atomic	atomic	ADJ
ap-1398	222	9	boolean	boolean	ADJ
ap-1398	222	10	algebras	algebras	PROPN
ap-1398	222	11	b̃κ	b̃κ	PROPN
ap-1398	222	12	generated	generate	VERB
ap-1398	222	13	by	by	ADP
ap-1398	222	14	sets	set	NOUN
ap-1398	222	15	of	of	ADP
ap-1398	222	16	atoms	atom	NOUN
ap-1398	222	17	ãκ	ãκ	VERB
ap-1398	223	1	=	=	SYM
ap-1398	223	2	⋃	⋃	NOUN
ap-1398	223	3	i∈j	i∈j	NOUN
ap-1398	223	4	{	{	PUNCT
ap-1398	223	5	pi	pi	NOUN
ap-1398	223	6	}	}	PUNCT
ap-1398	223	7	∪	∪	X
ap-1398	223	8	{	{	PUNCT
ap-1398	223	9	aκ	aκ	ADJ
ap-1398	223	10	,	,	PUNCT
ap-1398	223	11	bκ	bκ	VERB
ap-1398	223	12	}	}	PUNCT
ap-1398	223	13	∪	∪	NOUN
ap-1398	223	14	⋃	⋃	PUNCT
ap-1398	223	15	i	i	PROPN
ap-1398	223	16	∈	∈	PROPN
ap-1398	224	1	j	j	NOUN
ap-1398	225	1	i	i	X
ap-1398	225	2	>	>	X
ap-1398	225	3	κ	κ	X
ap-1398	225	4	{	{	PUNCT
ap-1398	225	5	ai	ai	NOUN
ap-1398	225	6	,	,	PUNCT
ap-1398	225	7	bi	bi	NOUN
ap-1398	225	8	}	}	PUNCT
ap-1398	225	9	.	.	PUNCT
ap-1398	226	1	this	this	PRON
ap-1398	226	2	means	mean	VERB
ap-1398	226	3	that	that	SCONJ
ap-1398	226	4	for	for	ADP
ap-1398	226	5	κ	κ	PROPN
ap-1398	226	6	∈	∈	PROPN
ap-1398	226	7	e	e	X
ap-1398	226	8	b̃κ	b̃κ	NOUN
ap-1398	226	9	⊂	⊂	X
ap-1398	226	10	b̃0	b̃0	PROPN
ap-1398	226	11	.	.	PUNCT
ap-1398	227	1	the	the	DET
ap-1398	227	2	union	union	NOUN
ap-1398	227	3	of	of	ADP
ap-1398	227	4	all	all	DET
ap-1398	227	5	complete	complete	ADJ
ap-1398	227	6	atomic	atomic	ADJ
ap-1398	227	7	boolean	boolean	ADJ
ap-1398	227	8	algebras	algebra	NOUN
ap-1398	227	9	,	,	PUNCT
ap-1398	227	10	l̃	l̃	PROPN
ap-1398	227	11	=	=	PUNCT
ap-1398	227	12	b̃0	b̃0	NOUN
ap-1398	227	13	∪	∪	ADP
ap-1398	227	14	⋃	⋃	PUNCT
ap-1398	227	15	i∈i	i∈i	ADJ
ap-1398	227	16	b̃i	b̃i	NOUN
ap-1398	227	17	,	,	PUNCT
ap-1398	227	18	is	be	AUX
ap-1398	227	19	a	a	DET
ap-1398	227	20	complete	complete	ADJ
ap-1398	227	21	oml	oml	PROPN
ap-1398	227	22	.	.	PUNCT
ap-1398	228	1	an	an	DET
ap-1398	228	2	element	element	NOUN
ap-1398	228	3	f	f	PROPN
ap-1398	228	4	∈	∈	PROPN
ap-1398	229	1	l̃	l̃	PROPN
ap-1398	229	2	will	will	AUX
ap-1398	229	3	be	be	AUX
ap-1398	229	4	called	call	VERB
ap-1398	229	5	countable	countable	ADJ
ap-1398	229	6	if	if	SCONJ
ap-1398	229	7	there	there	PRON
ap-1398	229	8	exists	exist	VERB
ap-1398	229	9	an	an	DET
ap-1398	229	10	at	at	ADP
ap-1398	229	11	most	most	ADV
ap-1398	229	12	countable	countable	ADJ
ap-1398	229	13	set	set	NOUN
ap-1398	229	14	of	of	ADP
ap-1398	229	15	atoms	atom	NOUN
ap-1398	229	16	(	(	PUNCT
ap-1398	229	17	an	an	DET
ap-1398	229	18	at	at	ADP
ap-1398	229	19	most	most	ADV
ap-1398	229	20	countable	countable	ADJ
ap-1398	229	21	set	set	NOUN
ap-1398	229	22	of	of	ADP
ap-1398	229	23	indices	index	NOUN
ap-1398	229	24	k	k	X
ap-1398	229	25	)	)	PUNCT
ap-1398	229	26	{	{	PUNCT
ap-1398	229	27	qk}k∈k	qk}k∈k	NUM
ap-1398	229	28	⊂	⊂	PROPN
ap-1398	229	29	ã0	ã0	PROPN
ap-1398	229	30	or	or	CCONJ
ap-1398	229	31	{	{	PUNCT
ap-1398	229	32	qk}k∈k	qk}k∈k	X
ap-1398	229	33	⊂	⊂	PROPN
ap-1398	229	34	ãi	ãi	VERB
ap-1398	229	35	for	for	ADP
ap-1398	229	36	i	i	PROPN
ap-1398	229	37	∈	∈	PROPN
ap-1398	229	38	j	j	PROPN
ap-1398	229	39	,	,	PUNCT
ap-1398	230	1	such	such	ADJ
ap-1398	230	2	that	that	SCONJ
ap-1398	230	3	f	f	PROPN
ap-1398	230	4	=	=	SYM
ap-1398	230	5	⊕	⊕	PROPN
ap-1398	230	6	k∈k	k∈k	NOUN
ap-1398	230	7	qk	qk	PROPN
ap-1398	230	8	.	.	PUNCT
ap-1398	231	1	by	by	ADP
ap-1398	231	2	definition	definition	NOUN
ap-1398	231	3	of	of	ADP
ap-1398	231	4	elements	element	NOUN
ap-1398	231	5	pi	pi	ADV
ap-1398	231	6	,	,	PUNCT
ap-1398	231	7	ai	ai	VERB
ap-1398	231	8	,	,	PUNCT
ap-1398	231	9	bi	bi	NOUN
ap-1398	231	10	,	,	PUNCT
ap-1398	231	11	ci	ci	PROPN
ap-1398	231	12	,	,	PUNCT
ap-1398	231	13	di	di	NOUN
ap-1398	231	14	for	for	ADP
ap-1398	231	15	i	i	PRON
ap-1398	231	16	∈	∈	PROPN
ap-1398	232	1	i	i	PRON
ap-1398	232	2	we	we	PRON
ap-1398	232	3	get	get	VERB
ap-1398	232	4	that	that	SCONJ
ap-1398	232	5	each	each	PRON
ap-1398	232	6	of	of	ADP
ap-1398	232	7	these	these	DET
ap-1398	232	8	elements	element	NOUN
ap-1398	232	9	is	be	AUX
ap-1398	232	10	countable	countable	ADJ
ap-1398	232	11	.	.	PUNCT
ap-1398	233	1	let	let	VERB
ap-1398	233	2	k	k	PROPN
ap-1398	233	3	denote	denote	VERB
ap-1398	233	4	the	the	DET
ap-1398	233	5	set	set	NOUN
ap-1398	233	6	of	of	ADP
ap-1398	233	7	all	all	DET
ap-1398	233	8	countable	countable	ADJ
ap-1398	233	9	elements	element	NOUN
ap-1398	233	10	of	of	ADP
ap-1398	233	11	l̃	l̃	PROPN
ap-1398	233	12	and	and	CCONJ
ap-1398	233	13	k⊥	k⊥	PROPN
ap-1398	234	1	=	=	SYM
ap-1398	234	2	{	{	PUNCT
ap-1398	234	3	f	f	PROPN
ap-1398	234	4	∈	∈	PROPN
ap-1398	234	5	l̃	l̃	PROPN
ap-1398	234	6	;	;	PUNCT
ap-1398	234	7	f	f	NUM
ap-1398	234	8	′	′	NOUN
ap-1398	234	9	∈	∈	PROPN
ap-1398	234	10	k	k	NOUN
ap-1398	234	11	}	}	PUNCT
ap-1398	234	12	.	.	PUNCT
ap-1398	235	1	further	far	ADV
ap-1398	235	2	,	,	PUNCT
ap-1398	235	3	let	let	VERB
ap-1398	235	4	p	p	PRON
ap-1398	235	5	denote	denote	VERB
ap-1398	235	6	the	the	DET
ap-1398	235	7	set	set	NOUN
ap-1398	235	8	of	of	ADP
ap-1398	235	9	all	all	DET
ap-1398	235	10	countable	countable	ADJ
ap-1398	235	11	elements	element	NOUN
ap-1398	235	12	generated	generate	VERB
ap-1398	235	13	by	by	ADP
ap-1398	235	14	{	{	PUNCT
ap-1398	235	15	pi	pi	NOUN
ap-1398	235	16	,	,	PUNCT
ap-1398	235	17	i	i	PROPN
ap-1398	235	18	∈	∈	PROPN
ap-1398	235	19	j	j	PROPN
ap-1398	235	20	}	}	PUNCT
ap-1398	235	21	,	,	PUNCT
ap-1398	235	22	and	and	CCONJ
ap-1398	235	23	p⊥	p⊥	NOUN
ap-1398	235	24	=	=	PUNCT
ap-1398	235	25	{	{	PUNCT
ap-1398	235	26	f	f	PROPN
ap-1398	235	27	∈	∈	PROPN
ap-1398	235	28	l̃	l̃	PROPN
ap-1398	235	29	;	;	PUNCT
ap-1398	235	30	f	f	NUM
ap-1398	235	31	′	′	NOUN
ap-1398	235	32	∈	∈	PROPN
ap-1398	236	1	p	p	X
ap-1398	236	2	}	}	PUNCT
ap-1398	236	3	.	.	PUNCT
ap-1398	237	1	theorem	theorem	NOUN
ap-1398	237	2	6	6	NUM
ap-1398	237	3	let	let	VERB
ap-1398	237	4	l̃σ	l̃σ	NOUN
ap-1398	237	5	=	=	PUNCT
ap-1398	238	1	k∪̇k⊥.	k∪̇k⊥.	PROPN
ap-1398	238	2	then	then	ADV
ap-1398	238	3	(	(	PUNCT
ap-1398	238	4	l̃σ,∨,∧,0,1	l̃σ,∨,∧,0,1	NOUN
ap-1398	238	5	)	)	PUNCT
ap-1398	238	6	is	be	AUX
ap-1398	238	7	a	a	DET
ap-1398	238	8	σ	σ	PROPN
ap-1398	238	9	-	-	PUNCT
ap-1398	238	10	complete	complete	PROPN
ap-1398	238	11	oml	oml	PROPN
ap-1398	238	12	.	.	PUNCT
ap-1398	239	1	the	the	DET
ap-1398	239	2	center	center	PROPN
ap-1398	239	3	c(l̃σ	c(l̃σ	PROPN
ap-1398	239	4	)	)	PUNCT
ap-1398	239	5	=	=	SYM
ap-1398	239	6	p∪̇p⊥	p∪̇p⊥	NOUN
ap-1398	239	7	and	and	CCONJ
ap-1398	239	8	it	it	PRON
ap-1398	239	9	is	be	AUX
ap-1398	239	10	not	not	PART
ap-1398	239	11	a	a	DET
ap-1398	239	12	bifull	bifull	ADJ
ap-1398	239	13	sublattice	sublattice	NOUN
ap-1398	239	14	of	of	ADP
ap-1398	239	15	l̃σ	l̃σ	PROPN
ap-1398	239	16	.	.	PUNCT
ap-1398	240	1	proof	proof	NOUN
ap-1398	240	2	.	.	PUNCT
ap-1398	241	1	each	each	PRON
ap-1398	241	2	of	of	ADP
ap-1398	241	3	the	the	DET
ap-1398	241	4	atoms	atom	NOUN
ap-1398	241	5	pi	pi	NOUN
ap-1398	241	6	,	,	PUNCT
ap-1398	241	7	ai	ai	VERB
ap-1398	241	8	,	,	PUNCT
ap-1398	241	9	bi	bi	NOUN
ap-1398	241	10	,	,	PUNCT
ap-1398	241	11	ci	ci	PROPN
ap-1398	241	12	,	,	PUNCT
ap-1398	241	13	di	di	NOUN
ap-1398	241	14	for	for	ADP
ap-1398	241	15	i	i	PROPN
ap-1398	241	16	∈	∈	PROPN
ap-1398	241	17	j	j	PROPN
ap-1398	241	18	(	(	PUNCT
ap-1398	241	19	and	and	CCONJ
ap-1398	241	20	hence	hence	ADV
ap-1398	241	21	also	also	ADV
ap-1398	241	22	each	each	PRON
ap-1398	241	23	of	of	ADP
ap-1398	241	24	the	the	DET
ap-1398	241	25	elements	element	NOUN
ap-1398	241	26	pi	pi	ADV
ap-1398	241	27	,	,	PUNCT
ap-1398	241	28	ai	ai	VERB
ap-1398	241	29	,	,	PUNCT
ap-1398	241	30	bi	bi	NOUN
ap-1398	241	31	,	,	PUNCT
ap-1398	241	32	ci	ci	PROPN
ap-1398	241	33	,	,	PUNCT
ap-1398	241	34	di	di	NOUN
ap-1398	241	35	for	for	ADP
ap-1398	241	36	i	i	PROPN
ap-1398	241	37	∈	∈	PROPN
ap-1398	242	1	i	i	X
ap-1398	242	2	)	)	PUNCT
ap-1398	242	3	is	be	AUX
ap-1398	242	4	countable	countable	ADJ
ap-1398	242	5	.	.	PUNCT
ap-1398	243	1	this	this	PRON
ap-1398	243	2	implies	imply	VERB
ap-1398	243	3	that	that	SCONJ
ap-1398	243	4	l̃σ	l̃σ	NOUN
ap-1398	243	5	is	be	AUX
ap-1398	243	6	an	an	DET
ap-1398	243	7	oml	oml	PROPN
ap-1398	243	8	.	.	PUNCT
ap-1398	244	1	since	since	SCONJ
ap-1398	244	2	it	it	PRON
ap-1398	244	3	is	be	AUX
ap-1398	244	4	by	by	ADP
ap-1398	244	5	definition	definition	NOUN
ap-1398	244	6	closed	close	VERB
ap-1398	244	7	under	under	ADP
ap-1398	244	8	countable	countable	ADJ
ap-1398	244	9	meets	meet	NOUN
ap-1398	244	10	and	and	CCONJ
ap-1398	244	11	joins	join	VERB
ap-1398	244	12	,	,	PUNCT
ap-1398	244	13	it	it	PRON
ap-1398	244	14	is	be	AUX
ap-1398	244	15	σ	σ	NOUN
ap-1398	244	16	-	-	PUNCT
ap-1398	244	17	complete	complete	ADJ
ap-1398	244	18	.	.	PUNCT
ap-1398	245	1	elements	element	NOUN
ap-1398	245	2	pi	pi	VERB
ap-1398	245	3	for	for	ADP
ap-1398	245	4	i	i	PRON
ap-1398	245	5	∈	∈	PROPN
ap-1398	246	1	i	i	PRON
ap-1398	246	2	are	be	AUX
ap-1398	246	3	central	central	ADJ
ap-1398	246	4	because	because	SCONJ
ap-1398	246	5	each	each	PRON
ap-1398	246	6	of	of	ADP
ap-1398	246	7	the	the	DET
ap-1398	246	8	elements	element	NOUN
ap-1398	246	9	pi	pi	NOUN
ap-1398	246	10	is	be	AUX
ap-1398	246	11	compatible	compatible	ADJ
ap-1398	246	12	with	with	ADP
ap-1398	246	13	all	all	DET
ap-1398	246	14	atoms	atom	NOUN
ap-1398	246	15	of	of	ADP
ap-1398	246	16	l̃σ	l̃σ	NOUN
ap-1398	246	17	.	.	PUNCT
ap-1398	247	1	this	this	PRON
ap-1398	247	2	implies	imply	VERB
ap-1398	247	3	that	that	SCONJ
ap-1398	247	4	p∪̇p⊥	p∪̇p⊥	PROPN
ap-1398	247	5	⊂	⊂	PROPN
ap-1398	247	6	c(l̃σ	c(l̃σ	PROPN
ap-1398	247	7	)	)	PUNCT
ap-1398	247	8	.	.	PUNCT
ap-1398	248	1	on	on	ADP
ap-1398	248	2	the	the	DET
ap-1398	248	3	other	other	ADJ
ap-1398	248	4	hand	hand	NOUN
ap-1398	248	5	,	,	PUNCT
ap-1398	248	6	let	let	VERB
ap-1398	248	7	f	f	PRON
ap-1398	248	8	be	be	AUX
ap-1398	248	9	a	a	DET
ap-1398	248	10	countable	countable	ADJ
ap-1398	248	11	element	element	NOUN
ap-1398	248	12	,	,	PUNCT
ap-1398	248	13	f	f	PROPN
ap-1398	248	14	/∈	/∈	PUNCT
ap-1398	249	1	p	p	X
ap-1398	249	2	.	.	PUNCT
ap-1398	250	1	then	then	ADV
ap-1398	250	2	there	there	PRON
ap-1398	250	3	exists	exist	VERB
ap-1398	250	4	ci	ci	NOUN
ap-1398	250	5	such	such	ADJ
ap-1398	250	6	that	that	DET
ap-1398	250	7	ci	ci	PROPN
ap-1398	250	8	�	�	PROPN
ap-1398	250	9	≤	≤	PROPN
ap-1398	250	10	f	f	NOUN
ap-1398	250	11	for	for	ADP
ap-1398	250	12	i	i	PROPN
ap-1398	250	13	∈	∈	PROPN
ap-1398	250	14	j	j	PROPN
ap-1398	250	15	and	and	CCONJ
ap-1398	250	16	an	an	DET
ap-1398	250	17	atom	atom	NOUN
ap-1398	250	18	out	out	ADP
ap-1398	250	19	of	of	ADP
ap-1398	250	20	e	e	PROPN
ap-1398	250	21	∈	∈	PROPN
ap-1398	250	22	{	{	PUNCT
ap-1398	250	23	aj	aj	PROPN
ap-1398	250	24	,	,	PUNCT
ap-1398	250	25	bj	bj	VERB
ap-1398	250	26	,	,	PUNCT
ap-1398	250	27	cj	cj	X
ap-1398	250	28	,	,	PUNCT
ap-1398	250	29	dj	dj	NOUN
ap-1398	250	30	}	}	PUNCT
ap-1398	250	31	for	for	ADP
ap-1398	250	32	j	j	PROPN
ap-1398	250	33	<	<	X
ap-1398	250	34	i	i	PROPN
ap-1398	250	35	,	,	PUNCT
ap-1398	250	36	e	e	PROPN
ap-1398	250	37	≤	≤	NUM
ap-1398	250	38	f	f	X
ap-1398	250	39	.	.	PUNCT
ap-1398	251	1	then	then	ADV
ap-1398	251	2	ci	ci	PROPN
ap-1398	251	3	�	�	PROPN
ap-1398	251	4	↔	↔	PROPN
ap-1398	251	5	e	e	NOUN
ap-1398	251	6	and	and	CCONJ
ap-1398	251	7	hence	hence	ADV
ap-1398	251	8	cj	cj	PROPN
ap-1398	251	9	�	�	PROPN
ap-1398	251	10	↔	↔	PROPN
ap-1398	251	11	f	f	PROPN
ap-1398	251	12	.	.	PUNCT
ap-1398	252	1	similarly	similarly	ADV
ap-1398	252	2	,	,	PUNCT
ap-1398	252	3	if	if	SCONJ
ap-1398	252	4	f	f	PROPN
ap-1398	252	5	∈	∈	PROPN
ap-1398	252	6	k⊥	k⊥	PROPN
ap-1398	252	7	,	,	PUNCT
ap-1398	252	8	there	there	PRON
ap-1398	252	9	exists	exist	VERB
ap-1398	252	10	ci	ci	PROPN
ap-1398	252	11	≤	≤	ADJ
ap-1398	252	12	f	f	PROPN
ap-1398	252	13	and	and	CCONJ
ap-1398	252	14	an	an	DET
ap-1398	252	15	atom	atom	NOUN
ap-1398	252	16	out	out	ADP
ap-1398	252	17	of	of	ADP
ap-1398	252	18	e	e	PROPN
ap-1398	252	19	∈	∈	PROPN
ap-1398	252	20	{	{	PUNCT
ap-1398	252	21	aj	aj	PROPN
ap-1398	252	22	,	,	PUNCT
ap-1398	252	23	bj	bj	VERB
ap-1398	252	24	,	,	PUNCT
ap-1398	252	25	cj	cj	X
ap-1398	252	26	,	,	PUNCT
ap-1398	252	27	dj	dj	NOUN
ap-1398	252	28	}	}	PUNCT
ap-1398	252	29	for	for	ADP
ap-1398	252	30	j	j	PROPN
ap-1398	252	31	<	<	X
ap-1398	252	32	i	i	PRON
ap-1398	252	33	such	such	ADJ
ap-1398	252	34	that	that	SCONJ
ap-1398	252	35	e	e	PROPN
ap-1398	252	36	�	�	PROPN
ap-1398	252	37	≤	≤	PROPN
ap-1398	252	38	f	f	NOUN
ap-1398	252	39	.	.	PUNCT
ap-1398	253	1	in	in	ADP
ap-1398	253	2	this	this	DET
ap-1398	253	3	case	case	NOUN
ap-1398	253	4	e	e	NOUN
ap-1398	253	5	�	�	PROPN
ap-1398	253	6	↔	↔	PROPN
ap-1398	253	7	ci	ci	NOUN
ap-1398	253	8	and	and	CCONJ
ap-1398	253	9	hence	hence	ADV
ap-1398	253	10	also	also	ADV
ap-1398	253	11	e	e	NOUN
ap-1398	253	12	�	�	ADP
ap-1398	253	13	↔	↔	PROPN
ap-1398	253	14	f	f	NOUN
ap-1398	253	15	.	.	PUNCT
ap-1398	254	1	we	we	PRON
ap-1398	254	2	conclude	conclude	VERB
ap-1398	254	3	that	that	SCONJ
ap-1398	254	4	c(l̃σ	c(l̃σ	NOUN
ap-1398	254	5	)	)	PUNCT
ap-1398	254	6	=	=	PUNCT
ap-1398	255	1	p∪̇p⊥.	p∪̇p⊥.	PROPN
ap-1398	255	2	we	we	PRON
ap-1398	255	3	show	show	VERB
ap-1398	255	4	that	that	SCONJ
ap-1398	255	5	c(l̃σ	c(l̃σ	NOUN
ap-1398	255	6	)	)	PUNCT
ap-1398	255	7	is	be	AUX
ap-1398	255	8	not	not	PART
ap-1398	255	9	a	a	DET
ap-1398	255	10	bifull	bifull	ADJ
ap-1398	255	11	sublattice	sublattice	NOUN
ap-1398	255	12	of	of	ADP
ap-1398	255	13	l̃σ	l̃σ	PROPN
ap-1398	255	14	.	.	PUNCT
ap-1398	256	1	obviously	obviously	ADV
ap-1398	256	2	∨	∨	NUM
ap-1398	256	3	c(l̃σ	c(l̃σ	PROPN
ap-1398	256	4	)	)	PUNCT
ap-1398	256	5	{	{	PUNCT
ap-1398	256	6	pi	pi	NOUN
ap-1398	256	7	,	,	PUNCT
ap-1398	256	8	i	i	PRON
ap-1398	256	9	∈	∈	VERB
ap-1398	256	10	i	i	X
ap-1398	256	11	}	}	PUNCT
ap-1398	256	12	=	=	SYM
ap-1398	256	13	1	1	X
ap-1398	256	14	.	.	X
ap-1398	256	15	assume	assume	VERB
ap-1398	256	16	that	that	SCONJ
ap-1398	256	17	∨	∨	PROPN
ap-1398	256	18	l̃σ	l̃σ	NOUN
ap-1398	256	19	{	{	PUNCT
ap-1398	256	20	pi	pi	NOUN
ap-1398	256	21	,	,	PUNCT
ap-1398	256	22	i	i	PRON
ap-1398	256	23	∈	∈	VERB
ap-1398	256	24	i	i	PRON
ap-1398	256	25	}	}	PUNCT
ap-1398	256	26	does	do	AUX
ap-1398	256	27	exist	exist	VERB
ap-1398	256	28	.	.	PUNCT
ap-1398	257	1	then	then	ADV
ap-1398	257	2	all	all	DET
ap-1398	257	3	elements	element	NOUN
ap-1398	257	4	e	e	X
ap-1398	257	5	∈	∈	PROPN
ap-1398	257	6	⋃	⋃	PROPN
ap-1398	257	7	i∈i	i∈i	NOUN
ap-1398	257	8	{	{	PUNCT
ap-1398	257	9	ai	ai	NOUN
ap-1398	257	10	,	,	PUNCT
ap-1398	257	11	bi	bi	NOUN
ap-1398	257	12	,	,	PUNCT
ap-1398	257	13	ci	ci	PROPN
ap-1398	257	14	,	,	PUNCT
ap-1398	257	15	di	di	NOUN
ap-1398	257	16	}	}	PUNCT
ap-1398	257	17	are	be	AUX
ap-1398	257	18	orthogonal	orthogonal	ADJ
ap-1398	257	19	with	with	ADP
ap-1398	257	20	all	all	DET
ap-1398	257	21	elements	element	NOUN
ap-1398	257	22	from	from	ADP
ap-1398	257	23	the	the	DET
ap-1398	257	24	set	set	NOUN
ap-1398	257	25	⋃	⋃	PROPN
ap-1398	257	26	i	i	PRON
ap-1398	257	27	{	{	PUNCT
ap-1398	257	28	pj	pj	PROPN
ap-1398	257	29	}	}	PUNCT
ap-1398	257	30	and	and	CCONJ
ap-1398	257	31	consequently	consequently	ADV
ap-1398	257	32	also	also	ADV
ap-1398	257	33	with	with	ADP
ap-1398	257	34	∨	∨	NUM
ap-1398	257	35	l̃σ	l̃σ	NOUN
ap-1398	257	36	{	{	PUNCT
ap-1398	257	37	pi	pi	NOUN
ap-1398	257	38	,	,	PUNCT
ap-1398	257	39	i	i	PRON
ap-1398	257	40	∈	∈	VERB
ap-1398	257	41	i	i	PRON
ap-1398	257	42	}	}	PUNCT
ap-1398	257	43	.	.	PUNCT
ap-1398	258	1	this	this	PRON
ap-1398	258	2	implies	imply	VERB
ap-1398	258	3	∨	∨	PROPN
ap-1398	258	4	l̃σ	l̃σ	NOUN
ap-1398	258	5	{	{	PUNCT
ap-1398	258	6	pi	pi	NOUN
ap-1398	258	7	,	,	PUNCT
ap-1398	258	8	i	i	PRON
ap-1398	258	9	∈	∈	VERB
ap-1398	258	10	i	i	PRON
ap-1398	258	11	}	}	PUNCT
ap-1398	258	12	�	�	PROPN
ap-1398	258	13	=	=	SYM
ap-1398	258	14	1	1	NUM
ap-1398	258	15	.	.	PUNCT
ap-1398	259	1	this	this	PRON
ap-1398	259	2	means	mean	VERB
ap-1398	259	3	that	that	SCONJ
ap-1398	259	4	c(l̃σ	c(l̃σ	NOUN
ap-1398	259	5	)	)	PUNCT
ap-1398	259	6	is	be	AUX
ap-1398	259	7	not	not	PART
ap-1398	259	8	a	a	DET
ap-1398	259	9	bifull	bifull	ADJ
ap-1398	259	10	sublattice	sublattice	NOUN
ap-1398	259	11	of	of	ADP
ap-1398	259	12	l̃σ	l̃σ	PROPN
ap-1398	259	13	.	.	PUNCT
ap-1398	260	1	�	�	PROPN
ap-1398	260	2	30	30	NUM
ap-1398	260	3	acta	acta	PROPN
ap-1398	260	4	polytechnica	polytechnica	PROPN
ap-1398	260	5	vol	vol	NOUN
ap-1398	260	6	.	.	PUNCT
ap-1398	261	1	51	51	NUM
ap-1398	261	2	no	no	INTJ
ap-1398	261	3	.	.	PUNCT
ap-1398	262	1	4/2011	4/2011	NUM
ap-1398	262	2	acknowledgement	acknowledgement	NOUN
ap-1398	262	3	support	support	NOUN
ap-1398	262	4	from	from	ADP
ap-1398	262	5	the	the	DET
ap-1398	262	6	science	science	NOUN
ap-1398	262	7	and	and	CCONJ
ap-1398	262	8	technology	technology	NOUN
ap-1398	262	9	assistance	assistance	NOUN
ap-1398	262	10	agency	agency	NOUN
ap-1398	262	11	under	under	ADP
ap-1398	262	12	contract	contract	NOUN
ap-1398	262	13	no	no	INTJ
ap-1398	262	14	.	.	PUNCT
ap-1398	263	1	apvv-0073	apvv-0073	NOUN
ap-1398	263	2	-	-	PUNCT
ap-1398	263	3	10	10	NUM
ap-1398	263	4	,	,	PUNCT
ap-1398	263	5	and	and	CCONJ
ap-1398	263	6	from	from	ADP
ap-1398	263	7	the	the	DET
ap-1398	263	8	vega	vega	PROPN
ap-1398	263	9	grant	grant	PROPN
ap-1398	263	10	agency	agency	PROPN
ap-1398	263	11	,	,	PUNCT
ap-1398	263	12	grant	grant	VERB
ap-1398	263	13	number	number	NOUN
ap-1398	263	14	1/0297/11	1/0297/11	NUM
ap-1398	263	15	,	,	PUNCT
ap-1398	263	16	is	be	AUX
ap-1398	263	17	gratefully	gratefully	ADV
ap-1398	263	18	acknowledged	acknowledge	VERB
ap-1398	263	19	.	.	PUNCT
ap-1398	264	1	references	reference	NOUN
ap-1398	264	2	[	[	X
ap-1398	264	3	1	1	NUM
ap-1398	264	4	]	]	X
ap-1398	264	5	chang	chang	PROPN
ap-1398	264	6	,	,	PUNCT
ap-1398	264	7	c.	c.	PROPN
ap-1398	264	8	c.	c.	PROPN
ap-1398	264	9	:	:	PUNCT
ap-1398	265	1	algebraic	algebraic	ADJ
ap-1398	265	2	analysis	analysis	NOUN
ap-1398	265	3	of	of	ADP
ap-1398	265	4	many	many	ADV
ap-1398	265	5	-	-	PUNCT
ap-1398	265	6	valued	value	VERB
ap-1398	265	7	logics	logic	NOUN
ap-1398	265	8	.	.	PUNCT
ap-1398	266	1	trans	trans	PROPN
ap-1398	266	2	.	.	PUNCT
ap-1398	267	1	amer	amer	PROPN
ap-1398	267	2	.	.	PUNCT
ap-1398	267	3	math	math	PROPN
ap-1398	267	4	.	.	PUNCT
ap-1398	268	1	soc	soc	PROPN
ap-1398	268	2	.	.	PUNCT
ap-1398	269	1	88	88	NUM
ap-1398	269	2	(	(	PUNCT
ap-1398	269	3	1958	1958	NUM
ap-1398	269	4	)	)	PUNCT
ap-1398	269	5	,	,	PUNCT
ap-1398	269	6	467–490	467–490	NUM
ap-1398	269	7	.	.	PUNCT
ap-1398	270	1	[	[	X
ap-1398	270	2	2	2	NUM
ap-1398	270	3	]	]	X
ap-1398	270	4	dvurečenskij	dvurečenskij	PROPN
ap-1398	270	5	,	,	PUNCT
ap-1398	270	6	a.	a.	NOUN
ap-1398	270	7	,	,	PUNCT
ap-1398	270	8	pulmannová	pulmannová	ADJ
ap-1398	270	9	,	,	PUNCT
ap-1398	270	10	s.	s.	PROPN
ap-1398	270	11	:	:	PUNCT
ap-1398	270	12	new	new	ADJ
ap-1398	270	13	trends	trend	NOUN
ap-1398	270	14	in	in	ADP
ap-1398	270	15	quantum	quantum	ADJ
ap-1398	270	16	structures	structure	NOUN
ap-1398	270	17	.	.	PUNCT
ap-1398	271	1	dordrecht	dordrecht	PROPN
ap-1398	271	2	,	,	PUNCT
ap-1398	271	3	boston	boston	PROPN
ap-1398	271	4	,	,	PUNCT
ap-1398	271	5	london	london	PROPN
ap-1398	271	6	,	,	PUNCT
ap-1398	271	7	and	and	CCONJ
ap-1398	271	8	isterscience	isterscience	NOUN
ap-1398	271	9	,	,	PUNCT
ap-1398	271	10	bratislava	bratislava	NOUN
ap-1398	271	11	:	:	PUNCT
ap-1398	271	12	kluwer	kluwer	PROPN
ap-1398	271	13	acad	acad	PROPN
ap-1398	271	14	.	.	PUNCT
ap-1398	271	15	publisher	publisher	NOUN
ap-1398	271	16	,	,	PUNCT
ap-1398	271	17	2000	2000	NUM
ap-1398	271	18	.	.	PUNCT
ap-1398	272	1	[	[	X
ap-1398	272	2	3	3	NUM
ap-1398	272	3	]	]	X
ap-1398	272	4	foulis	foulis	PROPN
ap-1398	272	5	,	,	PUNCT
ap-1398	272	6	d.	d.	PROPN
ap-1398	272	7	j.	j.	PROPN
ap-1398	272	8	,	,	PUNCT
ap-1398	272	9	bennett	bennett	PROPN
ap-1398	272	10	,	,	PUNCT
ap-1398	272	11	m.	m.	PROPN
ap-1398	272	12	k.	k.	PROPN
ap-1398	272	13	:	:	PUNCT
ap-1398	272	14	effect	effect	NOUN
ap-1398	272	15	algebras	algebra	NOUN
ap-1398	272	16	and	and	CCONJ
ap-1398	272	17	unsharp	unsharp	ADJ
ap-1398	272	18	quantum	quantum	ADJ
ap-1398	272	19	logics	logic	NOUN
ap-1398	272	20	.	.	PUNCT
ap-1398	273	1	found	find	VERB
ap-1398	273	2	.	.	PUNCT
ap-1398	274	1	phys	phy	NOUN
ap-1398	274	2	.	.	PUNCT
ap-1398	275	1	24	24	NUM
ap-1398	275	2	(	(	PUNCT
ap-1398	275	3	1994	1994	NUM
ap-1398	275	4	)	)	PUNCT
ap-1398	275	5	,	,	PUNCT
ap-1398	275	6	1	1	NUM
ap-1398	275	7	325–1346	325–1346	NUM
ap-1398	275	8	.	.	PUNCT
ap-1398	276	1	[	[	X
ap-1398	276	2	4	4	NUM
ap-1398	276	3	]	]	X
ap-1398	276	4	greechie	greechie	NOUN
ap-1398	276	5	,	,	PUNCT
ap-1398	276	6	r.	r.	PROPN
ap-1398	276	7	j.	j.	PROPN
ap-1398	276	8	,	,	PUNCT
ap-1398	276	9	foulis	foulis	PROPN
ap-1398	276	10	,	,	PUNCT
ap-1398	276	11	d.	d.	PROPN
ap-1398	276	12	j.	j.	PROPN
ap-1398	276	13	,	,	PUNCT
ap-1398	276	14	pulmannová	pulmannová	PROPN
ap-1398	276	15	,	,	PUNCT
ap-1398	276	16	s.	s.	PROPN
ap-1398	276	17	:	:	PUNCT
ap-1398	276	18	the	the	DET
ap-1398	276	19	center	center	NOUN
ap-1398	276	20	of	of	ADP
ap-1398	276	21	an	an	DET
ap-1398	276	22	effect	effect	NOUN
ap-1398	276	23	algebra	algebra	NOUN
ap-1398	276	24	.	.	PUNCT
ap-1398	277	1	order	order	NOUN
ap-1398	277	2	12	12	NUM
ap-1398	277	3	(	(	PUNCT
ap-1398	277	4	1995	1995	NUM
ap-1398	277	5	)	)	PUNCT
ap-1398	277	6	,	,	PUNCT
ap-1398	277	7	91–106	91–106	NOUN
ap-1398	277	8	.	.	PUNCT
ap-1398	278	1	[	[	X
ap-1398	278	2	5	5	NUM
ap-1398	278	3	]	]	SYM
ap-1398	278	4	gudder	gudder	NOUN
ap-1398	278	5	,	,	PUNCT
ap-1398	278	6	s.	s.	PROPN
ap-1398	278	7	p.	p.	PROPN
ap-1398	278	8	:	:	PUNCT
ap-1398	278	9	sharply	sharply	ADV
ap-1398	278	10	dominating	dominate	VERB
ap-1398	278	11	effect	effect	NOUN
ap-1398	278	12	algebras	algebra	NOUN
ap-1398	278	13	.	.	PUNCT
ap-1398	279	1	tatra	tatra	PROPN
ap-1398	279	2	mountains	mountains	PROPN
ap-1398	279	3	math	math	NOUN
ap-1398	279	4	.	.	PUNCT
ap-1398	280	1	publ	publ	NOUN
ap-1398	280	2	.	.	PUNCT
ap-1398	281	1	15	15	NUM
ap-1398	281	2	(	(	PUNCT
ap-1398	281	3	1998	1998	NUM
ap-1398	281	4	)	)	PUNCT
ap-1398	281	5	,	,	PUNCT
ap-1398	281	6	23–30	23–30	NUM
ap-1398	281	7	.	.	PUNCT
ap-1398	282	1	[	[	X
ap-1398	282	2	6	6	NUM
ap-1398	282	3	]	]	SYM
ap-1398	282	4	gudder	gudder	ADJ
ap-1398	282	5	,	,	PUNCT
ap-1398	282	6	s.	s.	PROPN
ap-1398	282	7	p.	p.	PROPN
ap-1398	282	8	:	:	PUNCT
ap-1398	283	1	s	s	X
ap-1398	283	2	-	-	PUNCT
ap-1398	283	3	dominating	dominating	ADJ
ap-1398	283	4	effect	effect	NOUN
ap-1398	283	5	algebras	algebra	NOUN
ap-1398	283	6	.	.	PUNCT
ap-1398	284	1	internat	internat	PROPN
ap-1398	284	2	.	.	PUNCT
ap-1398	285	1	j.	j.	PROPN
ap-1398	285	2	theor	theor	PROPN
ap-1398	285	3	.	.	PUNCT
ap-1398	286	1	phys	phy	NOUN
ap-1398	286	2	.	.	PUNCT
ap-1398	287	1	37	37	NUM
ap-1398	287	2	(	(	PUNCT
ap-1398	287	3	1998	1998	NUM
ap-1398	287	4	)	)	PUNCT
ap-1398	287	5	,	,	PUNCT
ap-1398	287	6	915–923	915–923	NUM
ap-1398	287	7	.	.	PUNCT
ap-1398	288	1	[	[	X
ap-1398	288	2	7	7	NUM
ap-1398	288	3	]	]	X
ap-1398	288	4	jenča	jenča	PROPN
ap-1398	288	5	,	,	PUNCT
ap-1398	288	6	g.	g.	PROPN
ap-1398	288	7	,	,	PUNCT
ap-1398	288	8	riečanová	riečanová	PROPN
ap-1398	288	9	,	,	PUNCT
ap-1398	288	10	z.	z.	PROPN
ap-1398	288	11	:	:	PUNCT
ap-1398	288	12	on	on	ADP
ap-1398	288	13	sharp	sharp	ADJ
ap-1398	288	14	elements	element	NOUN
ap-1398	288	15	in	in	ADP
ap-1398	288	16	lattice	lattice	NOUN
ap-1398	288	17	ordered	order	VERB
ap-1398	288	18	effect	effect	NOUN
ap-1398	288	19	algebras	algebra	NOUN
ap-1398	288	20	.	.	PUNCT
ap-1398	289	1	busefal	busefal	PROPN
ap-1398	289	2	80	80	NUM
ap-1398	289	3	(	(	PUNCT
ap-1398	289	4	1999	1999	NUM
ap-1398	289	5	)	)	PUNCT
ap-1398	289	6	,	,	PUNCT
ap-1398	289	7	24–29	24–29	NUM
ap-1398	289	8	.	.	PUNCT
ap-1398	290	1	[	[	X
ap-1398	290	2	8	8	NUM
ap-1398	290	3	]	]	X
ap-1398	290	4	kalina	kalina	PROPN
ap-1398	290	5	,	,	PUNCT
ap-1398	290	6	m.	m.	NOUN
ap-1398	290	7	:	:	PUNCT
ap-1398	290	8	on	on	ADP
ap-1398	290	9	central	central	ADJ
ap-1398	290	10	atoms	atom	NOUN
ap-1398	290	11	of	of	ADP
ap-1398	290	12	archimedean	archimedean	ADJ
ap-1398	290	13	atomic	atomic	PROPN
ap-1398	290	14	lattice	lattice	PROPN
ap-1398	290	15	effect	effect	PROPN
ap-1398	290	16	algebras	algebras	PROPN
ap-1398	290	17	.	.	PUNCT
ap-1398	290	18	kybernetika	kybernetika	PROPN
ap-1398	290	19	46	46	NUM
ap-1398	290	20	(	(	PUNCT
ap-1398	290	21	2010	2010	NUM
ap-1398	290	22	)	)	PUNCT
ap-1398	290	23	,	,	PUNCT
ap-1398	290	24	4	4	NUM
ap-1398	290	25	,	,	PUNCT
ap-1398	290	26	609–620	609–620	NUM
ap-1398	290	27	.	.	PUNCT
ap-1398	291	1	[	[	X
ap-1398	291	2	9	9	NUM
ap-1398	291	3	]	]	PUNCT
ap-1398	291	4	kalina	kalina	PROPN
ap-1398	291	5	,	,	PUNCT
ap-1398	291	6	m.	m.	NOUN
ap-1398	291	7	:	:	PUNCT
ap-1398	291	8	mac	mac	PROPN
ap-1398	291	9	neille	neille	PROPN
ap-1398	291	10	completion	completion	NOUN
ap-1398	291	11	of	of	ADP
ap-1398	291	12	centers	center	NOUN
ap-1398	291	13	and	and	CCONJ
ap-1398	291	14	centers	center	NOUN
ap-1398	291	15	of	of	ADP
ap-1398	291	16	mac	mac	PROPN
ap-1398	291	17	neille	neille	NOUN
ap-1398	291	18	completions	completion	NOUN
ap-1398	291	19	of	of	ADP
ap-1398	291	20	lattice	lattice	ADJ
ap-1398	291	21	effect	effect	NOUN
ap-1398	291	22	algebras	algebras	PROPN
ap-1398	291	23	.	.	PUNCT
ap-1398	291	24	kybernetika	kybernetika	PROPN
ap-1398	291	25	46	46	NUM
ap-1398	291	26	(	(	PUNCT
ap-1398	291	27	2010	2010	NUM
ap-1398	291	28	)	)	PUNCT
ap-1398	291	29	,	,	PUNCT
ap-1398	291	30	6	6	NUM
ap-1398	291	31	,	,	PUNCT
ap-1398	291	32	635–647	635–647	NUM
ap-1398	291	33	.	.	PUNCT
ap-1398	292	1	[	[	X
ap-1398	292	2	10	10	NUM
ap-1398	292	3	]	]	X
ap-1398	292	4	kôpka	kôpka	NOUN
ap-1398	292	5	,	,	PUNCT
ap-1398	292	6	f.	f.	NOUN
ap-1398	292	7	:	:	PUNCT
ap-1398	292	8	compatibility	compatibility	NOUN
ap-1398	292	9	in	in	ADP
ap-1398	292	10	d	d	NOUN
ap-1398	292	11	-	-	NOUN
ap-1398	292	12	posets	poset	NOUN
ap-1398	292	13	.	.	PUNCT
ap-1398	293	1	internat	internat	PROPN
ap-1398	293	2	.	.	PUNCT
ap-1398	294	1	j.	j.	PROPN
ap-1398	294	2	theor	theor	PROPN
ap-1398	294	3	.	.	PUNCT
ap-1398	295	1	phys	phy	NOUN
ap-1398	295	2	.	.	PUNCT
ap-1398	296	1	34	34	NUM
ap-1398	296	2	(	(	PUNCT
ap-1398	296	3	1995	1995	NUM
ap-1398	296	4	)	)	PUNCT
ap-1398	296	5	,	,	PUNCT
ap-1398	296	6	1	1	NUM
ap-1398	296	7	525–1	525–1	NUM
ap-1398	296	8	531	531	NUM
ap-1398	296	9	.	.	PUNCT
ap-1398	297	1	[	[	X
ap-1398	297	2	11	11	NUM
ap-1398	297	3	]	]	PUNCT
ap-1398	297	4	mosná	mosná	NOUN
ap-1398	297	5	,	,	PUNCT
ap-1398	297	6	k.	k.	PROPN
ap-1398	297	7	:	:	PUNCT
ap-1398	297	8	about	about	ADP
ap-1398	297	9	atoms	atom	NOUN
ap-1398	297	10	in	in	ADP
ap-1398	297	11	generalized	generalized	ADJ
ap-1398	297	12	efect	efect	NOUN
ap-1398	297	13	algebras	algebra	NOUN
ap-1398	297	14	and	and	CCONJ
ap-1398	297	15	their	their	PRON
ap-1398	297	16	effect	effect	NOUN
ap-1398	297	17	algebraic	algebraic	ADJ
ap-1398	297	18	extensions	extension	NOUN
ap-1398	297	19	.	.	PUNCT
ap-1398	298	1	j.	j.	PROPN
ap-1398	298	2	electr	electr	PROPN
ap-1398	298	3	.	.	PUNCT
ap-1398	299	1	engrg	engrg	PROPN
ap-1398	299	2	.	.	PROPN
ap-1398	300	1	57	57	NUM
ap-1398	300	2	(	(	PUNCT
ap-1398	300	3	2006	2006	NUM
ap-1398	300	4	)	)	PUNCT
ap-1398	300	5	,	,	PUNCT
ap-1398	300	6	7	7	NUM
ap-1398	300	7	/	/	SYM
ap-1398	300	8	s	s	PROPN
ap-1398	300	9	,	,	PUNCT
ap-1398	300	10	110–113	110–113	NUM
ap-1398	300	11	.	.	PUNCT
ap-1398	301	1	[	[	X
ap-1398	301	2	12	12	NUM
ap-1398	301	3	]	]	PUNCT
ap-1398	301	4	mosná	mosná	NOUN
ap-1398	301	5	,	,	PUNCT
ap-1398	301	6	k.	k.	PROPN
ap-1398	301	7	,	,	PUNCT
ap-1398	301	8	paseka	paseka	PROPN
ap-1398	301	9	,	,	PUNCT
ap-1398	301	10	j.	j.	PROPN
ap-1398	301	11	,	,	PUNCT
ap-1398	301	12	riečanová	riečanová	PROPN
ap-1398	301	13	,	,	PUNCT
ap-1398	301	14	z.	z.	PROPN
ap-1398	301	15	:	:	PUNCT
ap-1398	301	16	order	order	NOUN
ap-1398	301	17	convergence	convergence	NOUN
ap-1398	301	18	and	and	CCONJ
ap-1398	301	19	order	order	NOUN
ap-1398	301	20	and	and	CCONJ
ap-1398	301	21	interval	interval	NOUN
ap-1398	301	22	topologies	topology	NOUN
ap-1398	301	23	on	on	ADP
ap-1398	301	24	posets	poset	NOUN
ap-1398	301	25	and	and	CCONJ
ap-1398	301	26	lattice	lattice	ADJ
ap-1398	301	27	effect	effect	NOUN
ap-1398	301	28	algebras	algebra	NOUN
ap-1398	301	29	.	.	PUNCT
ap-1398	302	1	in	in	ADP
ap-1398	302	2	proc	proc	NOUN
ap-1398	302	3	.	.	PUNCT
ap-1398	303	1	internat	internat	NOUN
ap-1398	303	2	.	.	PUNCT
ap-1398	304	1	seminar	seminar	NOUN
ap-1398	304	2	uncertainty	uncertainty	NOUN
ap-1398	304	3	2008	2008	NUM
ap-1398	304	4	,	,	PUNCT
ap-1398	304	5	publishing	publish	VERB
ap-1398	304	6	house	house	NOUN
ap-1398	304	7	of	of	ADP
ap-1398	304	8	stu	stu	PROPN
ap-1398	304	9	2008	2008	NUM
ap-1398	304	10	,	,	PUNCT
ap-1398	304	11	45–62	45–62	NUM
ap-1398	304	12	.	.	PUNCT
ap-1398	305	1	[	[	X
ap-1398	305	2	13	13	NUM
ap-1398	305	3	]	]	PUNCT
ap-1398	305	4	paseka	paseka	NOUN
ap-1398	305	5	,	,	PUNCT
ap-1398	305	6	j.	j.	PROPN
ap-1398	305	7	,	,	PUNCT
ap-1398	305	8	riečanová	riečanová	PROPN
ap-1398	305	9	,	,	PUNCT
ap-1398	305	10	z.	z.	PROPN
ap-1398	305	11	:	:	PUNCT
ap-1398	305	12	the	the	DET
ap-1398	305	13	inheritance	inheritance	NOUN
ap-1398	305	14	of	of	ADP
ap-1398	305	15	bde	bde	NOUN
ap-1398	305	16	-	-	PUNCT
ap-1398	305	17	property	property	NOUN
ap-1398	305	18	in	in	ADP
ap-1398	305	19	sharply	sharply	ADV
ap-1398	305	20	dominating	dominate	VERB
ap-1398	305	21	lattice	lattice	NOUN
ap-1398	305	22	effect	effect	NOUN
ap-1398	305	23	algebras	algebra	NOUN
ap-1398	305	24	and	and	CCONJ
ap-1398	305	25	(	(	PUNCT
ap-1398	305	26	o)-continuous	o)-continuous	ADJ
ap-1398	305	27	states	state	NOUN
ap-1398	305	28	.	.	PUNCT
ap-1398	306	1	soft	soft	ADJ
ap-1398	306	2	computing	computing	NOUN
ap-1398	306	3	,	,	PUNCT
ap-1398	306	4	15	15	NUM
ap-1398	306	5	(	(	PUNCT
ap-1398	306	6	2011	2011	NUM
ap-1398	306	7	)	)	PUNCT
ap-1398	306	8	,	,	PUNCT
ap-1398	306	9	543–555	543–555	NUM
ap-1398	306	10	.	.	PUNCT
ap-1398	307	1	[	[	X
ap-1398	307	2	14	14	NUM
ap-1398	307	3	]	]	X
ap-1398	307	4	riečanová	riečanová	PROPN
ap-1398	307	5	,	,	PUNCT
ap-1398	307	6	z.	z.	PROPN
ap-1398	307	7	:	:	PUNCT
ap-1398	307	8	compatibility	compatibility	NOUN
ap-1398	307	9	and	and	CCONJ
ap-1398	307	10	central	central	ADJ
ap-1398	307	11	elements	element	NOUN
ap-1398	307	12	in	in	ADP
ap-1398	307	13	effect	effect	NOUN
ap-1398	307	14	algebras	algebras	PROPN
ap-1398	307	15	.	.	PUNCT
ap-1398	308	1	tatra	tatra	PROPN
ap-1398	308	2	mountains	mountains	PROPN
ap-1398	308	3	math	math	NOUN
ap-1398	308	4	.	.	PUNCT
ap-1398	309	1	publ	publ	NOUN
ap-1398	309	2	.	.	PUNCT
ap-1398	310	1	16	16	NUM
ap-1398	310	2	(	(	PUNCT
ap-1398	310	3	1999	1999	NUM
ap-1398	310	4	)	)	PUNCT
ap-1398	310	5	,	,	PUNCT
ap-1398	310	6	151–158	151–158	NUM
ap-1398	310	7	.	.	PUNCT
ap-1398	311	1	[	[	X
ap-1398	311	2	15	15	NUM
ap-1398	311	3	]	]	X
ap-1398	311	4	riečanová	riečanová	PROPN
ap-1398	311	5	,	,	PUNCT
ap-1398	311	6	z.	z.	PROPN
ap-1398	311	7	:	:	PUNCT
ap-1398	311	8	subalgebras	subalgebras	PROPN
ap-1398	311	9	,	,	PUNCT
ap-1398	311	10	intervals	interval	NOUN
ap-1398	311	11	and	and	CCONJ
ap-1398	311	12	central	central	ADJ
ap-1398	311	13	elements	element	NOUN
ap-1398	311	14	of	of	ADP
ap-1398	311	15	generalized	generalized	ADJ
ap-1398	311	16	effect	effect	NOUN
ap-1398	311	17	algebras	algebra	NOUN
ap-1398	311	18	.	.	PUNCT
ap-1398	311	19	internat	internat	PROPN
ap-1398	311	20	.	.	PUNCT
ap-1398	312	1	j.	j.	PROPN
ap-1398	312	2	theor	theor	PROPN
ap-1398	312	3	.	.	PUNCT
ap-1398	313	1	phys	phy	NOUN
ap-1398	313	2	.	.	PUNCT
ap-1398	313	3	,	,	PUNCT
ap-1398	313	4	38	38	NUM
ap-1398	313	5	(	(	PUNCT
ap-1398	313	6	1999	1999	NUM
ap-1398	313	7	)	)	PUNCT
ap-1398	313	8	,	,	PUNCT
ap-1398	313	9	3	3	NUM
ap-1398	313	10	209–3220	209–3220	NUM
ap-1398	313	11	.	.	PUNCT
ap-1398	314	1	[	[	X
ap-1398	314	2	16	16	NUM
ap-1398	314	3	]	]	X
ap-1398	314	4	riečanová	riečanová	PROPN
ap-1398	314	5	,	,	PUNCT
ap-1398	314	6	z.	z.	PROPN
ap-1398	314	7	:	:	PUNCT
ap-1398	314	8	generalization	generalization	NOUN
ap-1398	314	9	of	of	ADP
ap-1398	314	10	blocks	block	NOUN
ap-1398	314	11	for	for	ADP
ap-1398	314	12	dlattices	dlattice	NOUN
ap-1398	314	13	and	and	CCONJ
ap-1398	314	14	lattice	lattice	PROPN
ap-1398	314	15	ordered	order	VERB
ap-1398	314	16	effect	effect	NOUN
ap-1398	314	17	algebras	algebra	NOUN
ap-1398	314	18	.	.	PUNCT
ap-1398	315	1	internat	internat	PROPN
ap-1398	315	2	.	.	PUNCT
ap-1398	316	1	j.	j.	PROPN
ap-1398	316	2	theor	theor	PROPN
ap-1398	316	3	.	.	PUNCT
ap-1398	317	1	phys	phy	NOUN
ap-1398	317	2	.	.	PUNCT
ap-1398	318	1	39	39	NUM
ap-1398	318	2	(	(	PUNCT
ap-1398	318	3	2000	2000	NUM
ap-1398	318	4	)	)	PUNCT
ap-1398	318	5	,	,	PUNCT
ap-1398	318	6	231–237	231–237	NUM
ap-1398	318	7	.	.	PUNCT
ap-1398	319	1	[	[	X
ap-1398	319	2	17	17	NUM
ap-1398	319	3	]	]	X
ap-1398	319	4	riečanová	riečanová	PROPN
ap-1398	319	5	,	,	PUNCT
ap-1398	319	6	z.	z.	PROPN
ap-1398	319	7	:	:	PUNCT
ap-1398	319	8	orthogonal	orthogonal	ADJ
ap-1398	319	9	sets	set	NOUN
ap-1398	319	10	in	in	ADP
ap-1398	319	11	effect	effect	NOUN
ap-1398	319	12	algebras	algebra	NOUN
ap-1398	319	13	.	.	PUNCT
ap-1398	320	1	demontratio	demontratio	PROPN
ap-1398	320	2	mathematica	mathematica	PROPN
ap-1398	320	3	34	34	NUM
ap-1398	320	4	(	(	PUNCT
ap-1398	320	5	2001	2001	NUM
ap-1398	320	6	)	)	PUNCT
ap-1398	320	7	,	,	PUNCT
ap-1398	320	8	525–532	525–532	NUM
ap-1398	320	9	.	.	PUNCT
ap-1398	321	1	[	[	X
ap-1398	321	2	18	18	NUM
ap-1398	321	3	]	]	SYM
ap-1398	321	4	riečanová	riečanová	PROPN
ap-1398	321	5	,	,	PUNCT
ap-1398	321	6	z.	z.	PROPN
ap-1398	321	7	:	:	PUNCT
ap-1398	321	8	smearing	smearing	NOUN
ap-1398	321	9	of	of	ADP
ap-1398	321	10	states	state	NOUN
ap-1398	321	11	defined	define	VERB
ap-1398	321	12	on	on	ADP
ap-1398	321	13	sharp	sharp	ADJ
ap-1398	321	14	elements	element	NOUN
ap-1398	321	15	onto	onto	ADP
ap-1398	321	16	effect	effect	NOUN
ap-1398	321	17	algebras	algebra	NOUN
ap-1398	321	18	.	.	PUNCT
ap-1398	321	19	internat	internat	PROPN
ap-1398	321	20	.	.	PUNCT
ap-1398	322	1	j.	j.	PROPN
ap-1398	322	2	theor	theor	PROPN
ap-1398	322	3	.	.	PUNCT
ap-1398	323	1	phys	phy	NOUN
ap-1398	323	2	.	.	PUNCT
ap-1398	324	1	41	41	NUM
ap-1398	324	2	(	(	PUNCT
ap-1398	324	3	2002	2002	NUM
ap-1398	324	4	)	)	PUNCT
ap-1398	324	5	,	,	PUNCT
ap-1398	324	6	1	1	NUM
ap-1398	324	7	511–1524	511–1524	NUM
ap-1398	324	8	.	.	PUNCT
ap-1398	325	1	[	[	X
ap-1398	325	2	19	19	NUM
ap-1398	325	3	]	]	SYM
ap-1398	325	4	riečanová	riečanová	PROPN
ap-1398	325	5	,	,	PUNCT
ap-1398	325	6	z.	z.	PROPN
ap-1398	325	7	:	:	PUNCT
ap-1398	325	8	subdirect	subdirect	VERB
ap-1398	325	9	decompositions	decomposition	NOUN
ap-1398	325	10	of	of	ADP
ap-1398	325	11	lattice	lattice	ADJ
ap-1398	325	12	effect	effect	NOUN
ap-1398	325	13	algebras	algebra	NOUN
ap-1398	325	14	.	.	PUNCT
ap-1398	325	15	internat	internat	PROPN
ap-1398	325	16	.	.	PUNCT
ap-1398	326	1	j.	j.	PROPN
ap-1398	326	2	theor	theor	PROPN
ap-1398	326	3	.	.	PUNCT
ap-1398	327	1	phys	phy	NOUN
ap-1398	327	2	.	.	PUNCT
ap-1398	328	1	42	42	NUM
ap-1398	328	2	(	(	PUNCT
ap-1398	328	3	2003	2003	NUM
ap-1398	328	4	)	)	PUNCT
ap-1398	328	5	,	,	PUNCT
ap-1398	328	6	1	1	NUM
ap-1398	328	7	425–1433	425–1433	NUM
ap-1398	328	8	.	.	PUNCT
ap-1398	329	1	[	[	X
ap-1398	329	2	20	20	NUM
ap-1398	329	3	]	]	SYM
ap-1398	329	4	riečanová	riečanová	PROPN
ap-1398	329	5	,	,	PUNCT
ap-1398	329	6	z.	z.	PROPN
ap-1398	329	7	:	:	PUNCT
ap-1398	329	8	distributive	distributive	ADJ
ap-1398	329	9	atomic	atomic	ADJ
ap-1398	329	10	effect	effect	NOUN
ap-1398	329	11	akgebras	akgebras	PROPN
ap-1398	329	12	.	.	PUNCT
ap-1398	330	1	demontratio	demontratio	PROPN
ap-1398	330	2	mathematica	mathematica	PROPN
ap-1398	330	3	36	36	NUM
ap-1398	330	4	(	(	PUNCT
ap-1398	330	5	2003	2003	NUM
ap-1398	330	6	)	)	PUNCT
ap-1398	330	7	,	,	PUNCT
ap-1398	330	8	247–259	247–259	NUM
ap-1398	330	9	.	.	PUNCT
ap-1398	331	1	[	[	X
ap-1398	331	2	21	21	NUM
ap-1398	331	3	]	]	X
ap-1398	331	4	riečanová	riečanová	PROPN
ap-1398	331	5	,	,	PUNCT
ap-1398	331	6	z.	z.	PROPN
ap-1398	331	7	:	:	PUNCT
ap-1398	331	8	lattice	lattice	PROPN
ap-1398	331	9	effect	effect	NOUN
ap-1398	331	10	algebras	algebra	VERB
ap-1398	331	11	densely	densely	ADV
ap-1398	331	12	embeddable	embeddable	ADJ
ap-1398	331	13	into	into	ADP
ap-1398	331	14	complete	complete	ADJ
ap-1398	331	15	ones	one	NOUN
ap-1398	331	16	.	.	PUNCT
ap-1398	332	1	kybernetika	kybernetika	NOUN
ap-1398	332	2	,	,	PUNCT
ap-1398	332	3	47	47	NUM
ap-1398	332	4	(	(	PUNCT
ap-1398	332	5	2011	2011	NUM
ap-1398	332	6	)	)	PUNCT
ap-1398	332	7	,	,	PUNCT
ap-1398	332	8	1	1	NUM
ap-1398	332	9	,	,	PUNCT
ap-1398	332	10	100–109	100–109	NUM
ap-1398	332	11	.	.	PUNCT
ap-1398	333	1	[	[	X
ap-1398	333	2	22	22	NUM
ap-1398	333	3	]	]	X
ap-1398	333	4	riečanová	riečanová	PROPN
ap-1398	333	5	,	,	PUNCT
ap-1398	333	6	z.	z.	PROPN
ap-1398	333	7	,	,	PUNCT
ap-1398	333	8	marinová	marinová	PROPN
ap-1398	333	9	,	,	PUNCT
ap-1398	333	10	i.	i.	NOUN
ap-1398	333	11	:	:	PUNCT
ap-1398	333	12	generalized	generalize	VERB
ap-1398	333	13	homogenous	homogenous	ADJ
ap-1398	333	14	,	,	PUNCT
ap-1398	333	15	prelattice	prelattice	NOUN
ap-1398	333	16	and	and	CCONJ
ap-1398	333	17	mv	mv	ADJ
ap-1398	333	18	-	-	PUNCT
ap-1398	333	19	effect	effect	NOUN
ap-1398	333	20	algebras	algebras	PROPN
ap-1398	333	21	.	.	PUNCT
ap-1398	333	22	kybernetika	kybernetika	PROPN
ap-1398	333	23	41	41	NUM
ap-1398	333	24	(	(	PUNCT
ap-1398	333	25	2005	2005	NUM
ap-1398	333	26	)	)	PUNCT
ap-1398	333	27	,	,	PUNCT
ap-1398	333	28	129–142	129–142	NUM
ap-1398	333	29	.	.	PUNCT
ap-1398	334	1	martin	martin	PROPN
ap-1398	334	2	kalina	kalina	PROPN
ap-1398	334	3	e	e	PROPN
ap-1398	334	4	-	-	NOUN
ap-1398	334	5	mail	mail	NOUN
ap-1398	334	6	:	:	PUNCT
ap-1398	334	7	kalina@math.sk	kalina@math.sk	PROPN
ap-1398	334	8	dept	dept	PROPN
ap-1398	334	9	.	.	PROPN
ap-1398	335	1	of	of	ADP
ap-1398	335	2	mathematics	mathematics	PROPN
ap-1398	335	3	faculty	faculty	NOUN
ap-1398	335	4	of	of	ADP
ap-1398	335	5	civil	civil	ADJ
ap-1398	335	6	engineering	engineering	NOUN
ap-1398	335	7	slovak	slovak	PROPN
ap-1398	335	8	univ	univ	PROPN
ap-1398	335	9	.	.	PUNCT
ap-1398	336	1	of	of	ADP
ap-1398	336	2	technology	technology	PROPN
ap-1398	336	3	radlinského	radlinského	PROPN
ap-1398	336	4	11	11	NUM
ap-1398	336	5	,	,	PUNCT
ap-1398	336	6	sk-813	sk-813	NOUN
ap-1398	336	7	68	68	NUM
ap-1398	336	8	bratislava	bratislava	NOUN
ap-1398	336	9	,	,	PUNCT
ap-1398	336	10	slovakia	slovakia	PROPN
ap-1398	336	11	31	31	NUM