id	sid	tid	token	lemma	pos
ap-1267	1	1	ap-5-10.dvi	ap-5-10.dvi	PROPN
ap-1267	1	2	acta	acta	PROPN
ap-1267	1	3	polytechnica	polytechnica	PROPN
ap-1267	1	4	vol	vol	NOUN
ap-1267	1	5	.	.	PROPN
ap-1267	2	1	50	50	NUM
ap-1267	2	2	no	no	NOUN
ap-1267	2	3	.	.	PUNCT
ap-1267	3	1	5/2010	5/2010	NUM
ap-1267	3	2	sharply	sharply	ADV
ap-1267	3	3	orthocomplete	orthocomplete	ADJ
ap-1267	3	4	effect	effect	NOUN
ap-1267	3	5	algebras	algebras	PROPN
ap-1267	3	6	m.	m.	PROPN
ap-1267	3	7	kalina	kalina	PROPN
ap-1267	3	8	,	,	PUNCT
ap-1267	3	9	j.	j.	PROPN
ap-1267	3	10	paseka	paseka	PROPN
ap-1267	3	11	,	,	PUNCT
ap-1267	3	12	z.	z.	PROPN
ap-1267	3	13	riečanová	riečanová	PROPN
ap-1267	3	14	abstract	abstract	ADJ
ap-1267	3	15	special	special	ADJ
ap-1267	3	16	types	type	NOUN
ap-1267	3	17	of	of	ADP
ap-1267	3	18	effect	effect	NOUN
ap-1267	3	19	algebras	algebras	PROPN
ap-1267	3	20	e	e	NOUN
ap-1267	3	21	called	call	VERB
ap-1267	3	22	sharply	sharply	ADV
ap-1267	3	23	dominating	dominating	NOUN
ap-1267	3	24	and	and	CCONJ
ap-1267	3	25	s	s	NOUN
ap-1267	3	26	-	-	PUNCT
ap-1267	3	27	dominating	dominating	NOUN
ap-1267	3	28	were	be	AUX
ap-1267	3	29	introduced	introduce	VERB
ap-1267	3	30	by	by	ADP
ap-1267	3	31	s.	s.	PROPN
ap-1267	3	32	gudder	gudder	PROPN
ap-1267	3	33	in	in	ADP
ap-1267	3	34	[	[	X
ap-1267	3	35	7	7	NUM
ap-1267	3	36	,	,	PUNCT
ap-1267	3	37	8	8	NUM
ap-1267	3	38	]	]	PUNCT
ap-1267	3	39	.	.	PUNCT
ap-1267	4	1	we	we	PRON
ap-1267	4	2	prove	prove	VERB
ap-1267	4	3	statements	statement	NOUN
ap-1267	4	4	about	about	ADP
ap-1267	4	5	connections	connection	NOUN
ap-1267	4	6	between	between	ADP
ap-1267	4	7	sharp	sharp	ADJ
ap-1267	4	8	orthocompleteness	orthocompleteness	NOUN
ap-1267	4	9	,	,	PUNCT
ap-1267	4	10	sharp	sharp	ADJ
ap-1267	4	11	dominancy	dominancy	NOUN
ap-1267	4	12	and	and	CCONJ
ap-1267	4	13	completeness	completeness	NOUN
ap-1267	4	14	of	of	ADP
ap-1267	4	15	e.	e.	PROPN
ap-1267	4	16	namely	namely	ADV
ap-1267	4	17	we	we	PRON
ap-1267	4	18	prove	prove	VERB
ap-1267	4	19	that	that	SCONJ
ap-1267	4	20	in	in	ADP
ap-1267	4	21	every	every	DET
ap-1267	4	22	sharply	sharply	ADV
ap-1267	4	23	orthocomplete	orthocomplete	ADJ
ap-1267	4	24	s	s	NOUN
ap-1267	4	25	-	-	PUNCT
ap-1267	4	26	dominating	dominating	ADJ
ap-1267	4	27	effect	effect	NOUN
ap-1267	4	28	algebra	algebra	NOUN
ap-1267	4	29	e	e	NOUN
ap-1267	4	30	the	the	DET
ap-1267	4	31	set	set	NOUN
ap-1267	4	32	of	of	ADP
ap-1267	4	33	sharp	sharp	ADJ
ap-1267	4	34	elements	element	NOUN
ap-1267	4	35	and	and	CCONJ
ap-1267	4	36	the	the	DET
ap-1267	4	37	center	center	NOUN
ap-1267	4	38	of	of	ADP
ap-1267	4	39	e	e	PROPN
ap-1267	4	40	are	be	AUX
ap-1267	4	41	complete	complete	ADJ
ap-1267	4	42	lattices	lattice	NOUN
ap-1267	4	43	bifull	bifull	PROPN
ap-1267	4	44	in	in	ADP
ap-1267	4	45	e.	e.	PROPN
ap-1267	4	46	if	if	SCONJ
ap-1267	4	47	an	an	DET
ap-1267	4	48	archimedean	archimedean	PROPN
ap-1267	4	49	atomic	atomic	ADJ
ap-1267	4	50	lattice	lattice	PROPN
ap-1267	4	51	effect	effect	NOUN
ap-1267	4	52	algebra	algebra	NOUN
ap-1267	4	53	e	e	NOUN
ap-1267	4	54	is	be	AUX
ap-1267	4	55	sharply	sharply	ADV
ap-1267	4	56	orthocomplete	orthocomplete	ADJ
ap-1267	4	57	then	then	ADV
ap-1267	4	58	it	it	PRON
ap-1267	4	59	is	be	AUX
ap-1267	4	60	complete	complete	ADJ
ap-1267	4	61	.	.	PUNCT
ap-1267	5	1	keywords	keyword	NOUN
ap-1267	5	2	:	:	PUNCT
ap-1267	5	3	effect	effect	NOUN
ap-1267	5	4	algebra	algebra	NOUN
ap-1267	5	5	,	,	PUNCT
ap-1267	5	6	sharp	sharp	ADJ
ap-1267	5	7	element	element	NOUN
ap-1267	5	8	,	,	PUNCT
ap-1267	5	9	central	central	ADJ
ap-1267	5	10	element	element	NOUN
ap-1267	5	11	,	,	PUNCT
ap-1267	5	12	block	block	NOUN
ap-1267	5	13	,	,	PUNCT
ap-1267	5	14	sharply	sharply	ADV
ap-1267	5	15	dominating	dominate	VERB
ap-1267	5	16	,	,	PUNCT
ap-1267	5	17	s	s	NOUN
ap-1267	5	18	-	-	PUNCT
ap-1267	5	19	dominating	dominating	ADJ
ap-1267	5	20	,	,	PUNCT
ap-1267	5	21	sharply	sharply	ADV
ap-1267	5	22	orthocomplete	orthocomplete	ADJ
ap-1267	5	23	.	.	PUNCT
ap-1267	6	1	1	1	NUM
ap-1267	6	2	introduction	introduction	NOUN
ap-1267	6	3	an	an	DET
ap-1267	6	4	algebraic	algebraic	ADJ
ap-1267	6	5	structure	structure	NOUN
ap-1267	6	6	called	call	VERB
ap-1267	6	7	an	an	DET
ap-1267	6	8	effect	effect	NOUN
ap-1267	6	9	algebra	algebra	NOUN
ap-1267	6	10	was	be	AUX
ap-1267	6	11	introduced	introduce	VERB
ap-1267	6	12	by	by	ADP
ap-1267	6	13	d.	d.	PROPN
ap-1267	6	14	j.	j.	PROPN
ap-1267	6	15	foulis	foulis	PROPN
ap-1267	6	16	and	and	CCONJ
ap-1267	6	17	m.	m.	PROPN
ap-1267	6	18	k.	k.	PROPN
ap-1267	6	19	bennett	bennett	PROPN
ap-1267	6	20	(	(	PUNCT
ap-1267	6	21	1994	1994	NUM
ap-1267	6	22	)	)	PUNCT
ap-1267	6	23	.	.	PUNCT
ap-1267	7	1	the	the	DET
ap-1267	7	2	advantage	advantage	NOUN
ap-1267	7	3	of	of	ADP
ap-1267	7	4	effect	effect	NOUN
ap-1267	7	5	algebras	algebra	NOUN
ap-1267	7	6	is	be	AUX
ap-1267	7	7	that	that	SCONJ
ap-1267	7	8	they	they	PRON
ap-1267	7	9	provide	provide	VERB
ap-1267	7	10	a	a	DET
ap-1267	7	11	mechanism	mechanism	NOUN
ap-1267	7	12	for	for	ADP
ap-1267	7	13	studying	study	VERB
ap-1267	7	14	quantum	quantum	ADJ
ap-1267	7	15	effects	effect	NOUN
ap-1267	7	16	,	,	PUNCT
ap-1267	7	17	or	or	CCONJ
ap-1267	7	18	more	more	ADV
ap-1267	7	19	generally	generally	ADV
ap-1267	7	20	,	,	PUNCT
ap-1267	7	21	in	in	ADP
ap-1267	7	22	non	non	ADJ
ap-1267	7	23	-	-	ADJ
ap-1267	7	24	classical	classical	ADJ
ap-1267	7	25	probability	probability	NOUN
ap-1267	7	26	theory	theory	NOUN
ap-1267	7	27	their	their	PRON
ap-1267	7	28	elements	element	NOUN
ap-1267	7	29	represent	represent	VERB
ap-1267	7	30	events	event	NOUN
ap-1267	7	31	that	that	PRON
ap-1267	7	32	may	may	AUX
ap-1267	7	33	be	be	AUX
ap-1267	7	34	unsharp	unsharp	ADJ
ap-1267	7	35	or	or	CCONJ
ap-1267	7	36	pairwise	pairwise	NOUN
ap-1267	7	37	non	non	ADJ
ap-1267	7	38	-	-	ADJ
ap-1267	7	39	compatible	compatible	ADJ
ap-1267	7	40	.	.	PUNCT
ap-1267	8	1	lattice	lattice	PROPN
ap-1267	8	2	effect	effect	PROPN
ap-1267	8	3	algebras	algebra	NOUN
ap-1267	8	4	are	be	AUX
ap-1267	8	5	in	in	ADP
ap-1267	8	6	some	some	DET
ap-1267	8	7	sense	sense	NOUN
ap-1267	8	8	a	a	DET
ap-1267	8	9	nearest	near	ADJ
ap-1267	8	10	common	common	ADJ
ap-1267	8	11	generalization	generalization	NOUN
ap-1267	8	12	of	of	ADP
ap-1267	8	13	orthomodular	orthomodular	ADJ
ap-1267	8	14	lattices	lattice	NOUN
ap-1267	8	15	[	[	X
ap-1267	8	16	13	13	NUM
ap-1267	8	17	]	]	PUNCT
ap-1267	8	18	that	that	PRON
ap-1267	8	19	may	may	AUX
ap-1267	8	20	include	include	VERB
ap-1267	8	21	noncompatible	noncompatible	ADJ
ap-1267	8	22	pairs	pair	NOUN
ap-1267	8	23	of	of	ADP
ap-1267	8	24	elements	element	NOUN
ap-1267	8	25	,	,	PUNCT
ap-1267	8	26	and	and	CCONJ
ap-1267	8	27	mv	mv	NOUN
ap-1267	8	28	-	-	PUNCT
ap-1267	8	29	algebras	algebras	X
ap-1267	8	30	[	[	X
ap-1267	8	31	3	3	NUM
ap-1267	8	32	]	]	PUNCT
ap-1267	8	33	that	that	PRON
ap-1267	8	34	may	may	AUX
ap-1267	8	35	include	include	VERB
ap-1267	8	36	unsharp	unsharp	ADJ
ap-1267	8	37	elements	element	NOUN
ap-1267	8	38	.	.	PUNCT
ap-1267	9	1	more	more	ADV
ap-1267	9	2	precisely	precisely	ADV
ap-1267	9	3	,	,	PUNCT
ap-1267	9	4	a	a	DET
ap-1267	9	5	lattice	lattice	ADJ
ap-1267	9	6	effect	effect	NOUN
ap-1267	9	7	algebra	algebra	NOUN
ap-1267	9	8	e	e	NOUN
ap-1267	9	9	is	be	AUX
ap-1267	9	10	an	an	DET
ap-1267	9	11	orthomodular	orthomodular	ADJ
ap-1267	9	12	lattice	lattice	NOUN
ap-1267	9	13	iff	iff	PROPN
ap-1267	9	14	every	every	DET
ap-1267	9	15	element	element	NOUN
ap-1267	9	16	of	of	ADP
ap-1267	9	17	e	e	PROPN
ap-1267	9	18	is	be	AUX
ap-1267	9	19	sharp	sharp	ADJ
ap-1267	9	20	(	(	PUNCT
ap-1267	9	21	i.e.	i.e.	X
ap-1267	9	22	,	,	PUNCT
ap-1267	9	23	x	x	PUNCT
ap-1267	9	24	and	and	CCONJ
ap-1267	9	25	“	"	PUNCT
ap-1267	9	26	non	non	X
ap-1267	9	27	x	x	NOUN
ap-1267	9	28	”	"	PUNCT
ap-1267	9	29	are	be	AUX
ap-1267	9	30	disjoint	disjoint	NOUN
ap-1267	9	31	)	)	PUNCT
ap-1267	9	32	and	and	CCONJ
ap-1267	9	33	it	it	PRON
ap-1267	9	34	is	be	AUX
ap-1267	9	35	an	an	DET
ap-1267	9	36	mv	mv	ADJ
ap-1267	9	37	-	-	PUNCT
ap-1267	9	38	effect	effect	NOUN
ap-1267	9	39	algebra	algebra	NOUN
ap-1267	9	40	iff	iff	VERB
ap-1267	9	41	every	every	DET
ap-1267	9	42	pair	pair	NOUN
ap-1267	9	43	of	of	ADP
ap-1267	9	44	elements	element	NOUN
ap-1267	9	45	of	of	ADP
ap-1267	9	46	e	e	NOUN
ap-1267	9	47	is	be	AUX
ap-1267	9	48	compatible	compatible	ADJ
ap-1267	9	49	.	.	PUNCT
ap-1267	10	1	moreover	moreover	ADV
ap-1267	10	2	,	,	PUNCT
ap-1267	10	3	in	in	ADP
ap-1267	10	4	every	every	DET
ap-1267	10	5	lattice	lattice	ADJ
ap-1267	10	6	effect	effect	NOUN
ap-1267	10	7	algebra	algebra	NOUN
ap-1267	10	8	e	e	NOUN
ap-1267	10	9	the	the	DET
ap-1267	10	10	set	set	NOUN
ap-1267	10	11	of	of	ADP
ap-1267	10	12	sharp	sharp	ADJ
ap-1267	10	13	elements	element	NOUN
ap-1267	10	14	is	be	AUX
ap-1267	10	15	an	an	DET
ap-1267	10	16	orthomodular	orthomodular	ADJ
ap-1267	10	17	lattice	lattice	NOUN
ap-1267	10	18	(	(	PUNCT
ap-1267	10	19	[	[	X
ap-1267	10	20	10	10	NUM
ap-1267	10	21	]	]	NUM
ap-1267	10	22	)	)	PUNCT
ap-1267	10	23	,	,	PUNCT
ap-1267	10	24	and	and	CCONJ
ap-1267	10	25	e	e	NOUN
ap-1267	10	26	is	be	AUX
ap-1267	10	27	a	a	DET
ap-1267	10	28	union	union	NOUN
ap-1267	10	29	of	of	ADP
ap-1267	10	30	its	its	PRON
ap-1267	10	31	blocks	block	NOUN
ap-1267	10	32	(	(	PUNCT
ap-1267	10	33	i.e.	i.e.	X
ap-1267	10	34	,	,	PUNCT
ap-1267	10	35	maximal	maximal	ADJ
ap-1267	10	36	subsets	subset	NOUN
ap-1267	10	37	of	of	ADP
ap-1267	10	38	pairwise	pairwise	NOUN
ap-1267	10	39	compatible	compatible	ADJ
ap-1267	10	40	elements	element	NOUN
ap-1267	10	41	that	that	PRON
ap-1267	10	42	are	be	AUX
ap-1267	10	43	mv	mv	ADJ
ap-1267	10	44	-	-	PUNCT
ap-1267	10	45	effect	effect	NOUN
ap-1267	10	46	algebras	algebra	NOUN
ap-1267	10	47	(	(	PUNCT
ap-1267	10	48	see	see	VERB
ap-1267	10	49	[	[	X
ap-1267	10	50	21	21	NUM
ap-1267	10	51	]	]	PUNCT
ap-1267	10	52	)	)	PUNCT
ap-1267	10	53	)	)	PUNCT
ap-1267	10	54	.	.	PUNCT
ap-1267	11	1	thus	thus	ADV
ap-1267	11	2	a	a	DET
ap-1267	11	3	lattice	lattice	ADJ
ap-1267	11	4	effect	effect	NOUN
ap-1267	11	5	algebra	algebra	NOUN
ap-1267	11	6	e	e	NOUN
ap-1267	11	7	is	be	AUX
ap-1267	11	8	a	a	DET
ap-1267	11	9	boolean	boolean	ADJ
ap-1267	11	10	algebra	algebra	NOUN
ap-1267	11	11	iff	iff	VERB
ap-1267	11	12	every	every	DET
ap-1267	11	13	pair	pair	NOUN
ap-1267	11	14	of	of	ADP
ap-1267	11	15	elements	element	NOUN
ap-1267	11	16	is	be	AUX
ap-1267	11	17	compatible	compatible	ADJ
ap-1267	11	18	and	and	CCONJ
ap-1267	11	19	every	every	DET
ap-1267	11	20	element	element	NOUN
ap-1267	11	21	of	of	ADP
ap-1267	11	22	e	e	PROPN
ap-1267	11	23	is	be	AUX
ap-1267	11	24	sharp	sharp	ADJ
ap-1267	11	25	.	.	PUNCT
ap-1267	12	1	however	however	ADV
ap-1267	12	2	,	,	PUNCT
ap-1267	12	3	non	non	ADJ
ap-1267	12	4	-	-	ADJ
ap-1267	12	5	lattice	lattice	ADJ
ap-1267	12	6	ordered	order	VERB
ap-1267	12	7	effect	effect	NOUN
ap-1267	12	8	algebra	algebra	NOUN
ap-1267	12	9	e	e	NOUN
ap-1267	12	10	is	be	AUX
ap-1267	12	11	so	so	ADV
ap-1267	12	12	general	general	ADJ
ap-1267	12	13	that	that	SCONJ
ap-1267	12	14	its	its	PRON
ap-1267	12	15	set	set	NOUN
ap-1267	12	16	s(e	s(e	PROPN
ap-1267	12	17	)	)	PUNCT
ap-1267	12	18	of	of	ADP
ap-1267	12	19	sharp	sharp	ADJ
ap-1267	12	20	elements	element	NOUN
ap-1267	12	21	may	may	AUX
ap-1267	12	22	form	form	VERB
ap-1267	12	23	neither	neither	CCONJ
ap-1267	12	24	an	an	DET
ap-1267	12	25	orthomodular	orthomodular	ADJ
ap-1267	12	26	lattice	lattice	NOUN
ap-1267	12	27	nor	nor	CCONJ
ap-1267	12	28	any	any	DET
ap-1267	12	29	regular	regular	ADJ
ap-1267	12	30	algebraic	algebraic	ADJ
ap-1267	12	31	structure	structure	NOUN
ap-1267	12	32	.	.	PUNCT
ap-1267	13	1	s.	s.	PROPN
ap-1267	13	2	gudder	gudder	PROPN
ap-1267	13	3	(	(	PUNCT
ap-1267	13	4	see	see	VERB
ap-1267	13	5	[	[	X
ap-1267	13	6	7	7	NUM
ap-1267	13	7	,	,	PUNCT
ap-1267	13	8	8	8	NUM
ap-1267	13	9	]	]	PUNCT
ap-1267	13	10	)	)	PUNCT
ap-1267	13	11	introduced	introduce	VERB
ap-1267	13	12	special	special	ADJ
ap-1267	13	13	types	type	NOUN
ap-1267	13	14	of	of	ADP
ap-1267	13	15	effect	effect	NOUN
ap-1267	13	16	algebras	algebras	PROPN
ap-1267	13	17	e	e	NOUN
ap-1267	13	18	called	call	VERB
ap-1267	13	19	sharply	sharply	ADV
ap-1267	13	20	dominating	dominate	VERB
ap-1267	13	21	effect	effect	NOUN
ap-1267	13	22	algebras	algebra	NOUN
ap-1267	13	23	,	,	PUNCT
ap-1267	13	24	whose	whose	DET
ap-1267	13	25	set	set	VERB
ap-1267	13	26	s(e	s(e	PROPN
ap-1267	13	27	)	)	PUNCT
ap-1267	13	28	of	of	ADP
ap-1267	13	29	sharp	sharp	ADJ
ap-1267	13	30	elements	element	NOUN
ap-1267	13	31	forms	form	VERB
ap-1267	13	32	an	an	DET
ap-1267	13	33	orthoalgebra	orthoalgebra	NOUN
ap-1267	13	34	and	and	CCONJ
ap-1267	13	35	also	also	ADV
ap-1267	13	36	socalled	socalle	VERB
ap-1267	13	37	s	s	PART
ap-1267	13	38	-	-	PUNCT
ap-1267	13	39	dominating	dominating	ADJ
ap-1267	13	40	effect	effect	NOUN
ap-1267	13	41	algebras	algebra	NOUN
ap-1267	13	42	,	,	PUNCT
ap-1267	13	43	whose	whose	DET
ap-1267	13	44	set	set	VERB
ap-1267	13	45	s(e	s(e	PROPN
ap-1267	13	46	)	)	PUNCT
ap-1267	13	47	of	of	ADP
ap-1267	13	48	sharp	sharp	ADJ
ap-1267	13	49	elements	element	NOUN
ap-1267	13	50	forms	form	VERB
ap-1267	13	51	an	an	DET
ap-1267	13	52	orthomodular	orthomodular	ADJ
ap-1267	13	53	lattice	lattice	NOUN
ap-1267	13	54	.	.	PUNCT
ap-1267	14	1	in	in	ADP
ap-1267	14	2	[	[	X
ap-1267	14	3	7	7	NUM
ap-1267	14	4	]	]	PUNCT
ap-1267	14	5	,	,	PUNCT
ap-1267	14	6	s.	s.	PROPN
ap-1267	14	7	gudder	gudder	PROPN
ap-1267	14	8	showed	show	VERB
ap-1267	14	9	that	that	SCONJ
ap-1267	14	10	a	a	DET
ap-1267	14	11	standard	standard	ADJ
ap-1267	14	12	hilbert	hilbert	NOUN
ap-1267	14	13	space	space	NOUN
ap-1267	14	14	effect	effect	NOUN
ap-1267	14	15	algebra	algebra	VERB
ap-1267	14	16	e(h	e(h	PROPN
ap-1267	14	17	)	)	PUNCT
ap-1267	14	18	of	of	ADP
ap-1267	14	19	bounded	bounded	ADJ
ap-1267	14	20	operators	operator	NOUN
ap-1267	14	21	on	on	ADP
ap-1267	14	22	a	a	DET
ap-1267	14	23	hilbert	hilbert	NOUN
ap-1267	14	24	space	space	NOUN
ap-1267	14	25	h	h	NOUN
ap-1267	14	26	between	between	ADP
ap-1267	14	27	zero	zero	NUM
ap-1267	14	28	and	and	CCONJ
ap-1267	14	29	identity	identity	NOUN
ap-1267	14	30	operators	operator	NOUN
ap-1267	14	31	(	(	PUNCT
ap-1267	14	32	with	with	ADP
ap-1267	14	33	partially	partially	ADV
ap-1267	14	34	defined	define	VERB
ap-1267	14	35	usual	usual	ADJ
ap-1267	14	36	operation+	operation+	NOUN
ap-1267	14	37	)	)	PUNCT
ap-1267	14	38	is	be	AUX
ap-1267	14	39	sdominating	sdominate	VERB
ap-1267	14	40	.	.	PUNCT
ap-1267	15	1	hence	hence	ADV
ap-1267	15	2	s	s	NOUN
ap-1267	15	3	-	-	PUNCT
ap-1267	15	4	dominating	dominating	ADJ
ap-1267	15	5	effect	effect	NOUN
ap-1267	15	6	algebras	algebra	NOUN
ap-1267	15	7	may	may	AUX
ap-1267	15	8	be	be	AUX
ap-1267	15	9	useful	useful	ADJ
ap-1267	15	10	abstract	abstract	ADJ
ap-1267	15	11	models	model	NOUN
ap-1267	15	12	for	for	ADP
ap-1267	15	13	sets	set	NOUN
ap-1267	15	14	of	of	ADP
ap-1267	15	15	quantum	quantum	ADJ
ap-1267	15	16	effects	effect	NOUN
ap-1267	15	17	in	in	ADP
ap-1267	15	18	physical	physical	ADJ
ap-1267	15	19	systems	system	NOUN
ap-1267	15	20	.	.	PUNCT
ap-1267	16	1	we	we	PRON
ap-1267	16	2	study	study	VERB
ap-1267	16	3	these	these	DET
ap-1267	16	4	two	two	NUM
ap-1267	16	5	special	special	ADJ
ap-1267	16	6	kinds	kind	NOUN
ap-1267	16	7	of	of	ADP
ap-1267	16	8	effect	effect	NOUN
ap-1267	16	9	algebras	algebra	VERB
ap-1267	16	10	.	.	PUNCT
ap-1267	17	1	we	we	PRON
ap-1267	17	2	show	show	VERB
ap-1267	17	3	properties	property	NOUN
ap-1267	17	4	of	of	ADP
ap-1267	17	5	some	some	DET
ap-1267	17	6	remarkable	remarkable	ADJ
ap-1267	17	7	subeffect	subeffect	NOUN
ap-1267	17	8	algebras	algebra	NOUN
ap-1267	17	9	of	of	ADP
ap-1267	17	10	such	such	ADJ
ap-1267	17	11	effect	effect	NOUN
ap-1267	17	12	algebras	algebra	NOUN
ap-1267	17	13	e	e	NOUN
ap-1267	17	14	satisfying	satisfy	VERB
ap-1267	17	15	the	the	DET
ap-1267	17	16	condition	condition	NOUN
ap-1267	17	17	that	that	SCONJ
ap-1267	17	18	e	e	NOUN
ap-1267	17	19	is	be	AUX
ap-1267	17	20	sharply	sharply	ADV
ap-1267	17	21	orthocomplete	orthocomplete	ADJ
ap-1267	17	22	.	.	PUNCT
ap-1267	18	1	namely	namely	ADV
ap-1267	18	2	properties	property	NOUN
ap-1267	18	3	of	of	ADP
ap-1267	18	4	their	their	PRON
ap-1267	18	5	blocks	block	NOUN
ap-1267	18	6	,	,	PUNCT
ap-1267	18	7	sets	set	NOUN
ap-1267	18	8	of	of	ADP
ap-1267	18	9	sharp	sharp	ADJ
ap-1267	18	10	elements	element	NOUN
ap-1267	18	11	and	and	CCONJ
ap-1267	18	12	their	their	PRON
ap-1267	18	13	centers	center	NOUN
ap-1267	18	14	.	.	PUNCT
ap-1267	19	1	it	it	PRON
ap-1267	19	2	is	be	AUX
ap-1267	19	3	worth	worth	ADJ
ap-1267	19	4	noting	note	VERB
ap-1267	19	5	that	that	SCONJ
ap-1267	19	6	it	it	PRON
ap-1267	19	7	was	be	AUX
ap-1267	19	8	proved	prove	VERB
ap-1267	19	9	in	in	ADP
ap-1267	19	10	[	[	X
ap-1267	19	11	11	11	NUM
ap-1267	19	12	]	]	PUNCT
ap-1267	19	13	that	that	SCONJ
ap-1267	19	14	there	there	PRON
ap-1267	19	15	are	be	VERB
ap-1267	19	16	even	even	ADV
ap-1267	19	17	archimedean	archimedean	ADJ
ap-1267	19	18	atomic	atomic	ADJ
ap-1267	19	19	mveffect	mveffect	NOUN
ap-1267	19	20	algebras	algebra	NOUN
ap-1267	19	21	which	which	PRON
ap-1267	19	22	are	be	AUX
ap-1267	19	23	not	not	PART
ap-1267	19	24	sharply	sharply	ADV
ap-1267	19	25	dominating	dominate	VERB
ap-1267	19	26	,	,	PUNCT
ap-1267	19	27	hence	hence	ADV
ap-1267	19	28	they	they	PRON
ap-1267	19	29	are	be	AUX
ap-1267	19	30	not	not	PART
ap-1267	19	31	s	s	NOUN
ap-1267	19	32	-	-	NOUN
ap-1267	19	33	dominating	dominating	NOUN
ap-1267	19	34	.	.	PUNCT
ap-1267	20	1	2	2	NUM
ap-1267	20	2	basic	basic	ADJ
ap-1267	20	3	definitions	definition	NOUN
ap-1267	20	4	and	and	CCONJ
ap-1267	20	5	some	some	DET
ap-1267	20	6	known	know	VERB
ap-1267	20	7	facts	fact	NOUN
ap-1267	20	8	definition	definition	NOUN
ap-1267	20	9	1	1	NUM
ap-1267	20	10	(	(	PUNCT
ap-1267	20	11	[	[	X
ap-1267	20	12	4	4	NUM
ap-1267	20	13	]	]	PUNCT
ap-1267	20	14	)	)	PUNCT
ap-1267	20	15	a	a	DET
ap-1267	20	16	partial	partial	ADJ
ap-1267	20	17	algebra	algebra	NOUN
ap-1267	20	18	(	(	PUNCT
ap-1267	20	19	e;⊕	e;⊕	ADJ
ap-1267	20	20	,	,	PUNCT
ap-1267	20	21	0	0	NUM
ap-1267	20	22	,	,	PUNCT
ap-1267	20	23	1	1	NUM
ap-1267	20	24	)	)	PUNCT
ap-1267	20	25	is	be	AUX
ap-1267	20	26	called	call	VERB
ap-1267	20	27	an	an	DET
ap-1267	20	28	effect	effect	NOUN
ap-1267	20	29	algebra	algebra	NOUN
ap-1267	20	30	if	if	SCONJ
ap-1267	20	31	0	0	NUM
ap-1267	20	32	,	,	PUNCT
ap-1267	20	33	1	1	NUM
ap-1267	20	34	are	be	AUX
ap-1267	20	35	two	two	NUM
ap-1267	20	36	distinct	distinct	ADJ
ap-1267	20	37	elements	element	NOUN
ap-1267	20	38	and	and	CCONJ
ap-1267	20	39	⊕	⊕	PROPN
ap-1267	20	40	is	be	AUX
ap-1267	20	41	a	a	DET
ap-1267	20	42	partially	partially	ADV
ap-1267	20	43	defined	define	VERB
ap-1267	20	44	binary	binary	ADJ
ap-1267	20	45	operation	operation	NOUN
ap-1267	20	46	on	on	ADP
ap-1267	20	47	e	e	PROPN
ap-1267	20	48	which	which	PRON
ap-1267	20	49	satisfy	satisfy	VERB
ap-1267	20	50	the	the	DET
ap-1267	20	51	following	follow	VERB
ap-1267	20	52	conditions	condition	NOUN
ap-1267	20	53	for	for	ADP
ap-1267	20	54	any	any	DET
ap-1267	20	55	x	x	NOUN
ap-1267	20	56	,	,	PUNCT
ap-1267	20	57	y	y	PROPN
ap-1267	20	58	,	,	PUNCT
ap-1267	20	59	z	z	NOUN
ap-1267	20	60	∈	∈	PROPN
ap-1267	21	1	e	e	NOUN
ap-1267	21	2	:	:	PUNCT
ap-1267	21	3	(	(	PUNCT
ap-1267	21	4	ei	ei	NOUN
ap-1267	21	5	)	)	PUNCT
ap-1267	21	6	x	x	PUNCT
ap-1267	21	7	⊕	⊕	NOUN
ap-1267	21	8	y	y	NOUN
ap-1267	21	9	=	=	SYM
ap-1267	21	10	y	y	PROPN
ap-1267	21	11	⊕	⊕	PROPN
ap-1267	21	12	x	x	PUNCT
ap-1267	22	1	if	if	SCONJ
ap-1267	22	2	x	x	PROPN
ap-1267	22	3	⊕	⊕	NOUN
ap-1267	22	4	y	y	PROPN
ap-1267	22	5	is	be	AUX
ap-1267	22	6	defined	define	VERB
ap-1267	22	7	,	,	PUNCT
ap-1267	22	8	(	(	PUNCT
ap-1267	22	9	eii	eii	PROPN
ap-1267	22	10	)	)	PUNCT
ap-1267	22	11	(	(	PUNCT
ap-1267	22	12	x⊕y)⊕z	x⊕y)⊕z	X
ap-1267	22	13	=	=	SYM
ap-1267	22	14	x⊕(y⊕z	x⊕(y⊕z	NOUN
ap-1267	22	15	)	)	PUNCT
ap-1267	22	16	if	if	SCONJ
ap-1267	22	17	one	one	NUM
ap-1267	22	18	side	side	NOUN
ap-1267	22	19	is	be	AUX
ap-1267	22	20	defined	define	VERB
ap-1267	22	21	,	,	PUNCT
ap-1267	22	22	(	(	PUNCT
ap-1267	22	23	eiii	eiii	PROPN
ap-1267	22	24	)	)	PUNCT
ap-1267	22	25	for	for	ADP
ap-1267	22	26	every	every	DET
ap-1267	22	27	x	x	SYM
ap-1267	22	28	∈	∈	PROPN
ap-1267	22	29	e	e	NOUN
ap-1267	22	30	there	there	PRON
ap-1267	22	31	exists	exist	VERB
ap-1267	22	32	a	a	DET
ap-1267	22	33	unique	unique	ADJ
ap-1267	22	34	y	y	PROPN
ap-1267	22	35	∈	∈	PROPN
ap-1267	22	36	e	e	NOUN
ap-1267	22	37	such	such	ADJ
ap-1267	22	38	that	that	SCONJ
ap-1267	22	39	x	x	PROPN
ap-1267	22	40	⊕	⊕	NOUN
ap-1267	22	41	y	y	NOUN
ap-1267	22	42	=	=	SYM
ap-1267	22	43	1	1	NUM
ap-1267	22	44	(	(	PUNCT
ap-1267	22	45	we	we	PRON
ap-1267	22	46	put	put	VERB
ap-1267	22	47	x′	x′	PROPN
ap-1267	22	48	=	=	SYM
ap-1267	22	49	y	y	PROPN
ap-1267	22	50	)	)	PUNCT
ap-1267	22	51	,	,	PUNCT
ap-1267	22	52	(	(	PUNCT
ap-1267	22	53	eiv	eiv	PROPN
ap-1267	22	54	)	)	PUNCT
ap-1267	22	55	if	if	SCONJ
ap-1267	22	56	1⊕	1⊕	NUM
ap-1267	22	57	x	x	SYM
ap-1267	22	58	is	be	AUX
ap-1267	22	59	defined	define	VERB
ap-1267	22	60	then	then	ADV
ap-1267	22	61	x	x	X
ap-1267	22	62	=	=	NOUN
ap-1267	23	1	0	0	X
ap-1267	23	2	.	.	PUNCT
ap-1267	24	1	we	we	PRON
ap-1267	24	2	often	often	ADV
ap-1267	24	3	denote	denote	VERB
ap-1267	24	4	the	the	DET
ap-1267	24	5	effect	effect	NOUN
ap-1267	24	6	algebra	algebra	NOUN
ap-1267	24	7	(	(	PUNCT
ap-1267	24	8	e;⊕	e;⊕	ADJ
ap-1267	24	9	,	,	PUNCT
ap-1267	24	10	0	0	NUM
ap-1267	24	11	,	,	PUNCT
ap-1267	24	12	1	1	NUM
ap-1267	24	13	)	)	PUNCT
ap-1267	24	14	briefly	briefly	ADV
ap-1267	24	15	by	by	ADP
ap-1267	24	16	e.	e.	PROPN
ap-1267	24	17	on	on	ADP
ap-1267	24	18	every	every	DET
ap-1267	24	19	effect	effect	NOUN
ap-1267	24	20	algebra	algebra	NOUN
ap-1267	24	21	e	e	NOUN
ap-1267	24	22	the	the	DET
ap-1267	24	23	partial	partial	ADJ
ap-1267	24	24	order	order	NOUN
ap-1267	24	25	≤	≤	NOUN
ap-1267	24	26	and	and	CCONJ
ap-1267	24	27	a	a	DET
ap-1267	24	28	partial	partial	ADJ
ap-1267	24	29	binary	binary	ADJ
ap-1267	24	30	operation	operation	NOUN
ap-1267	24	31	!	!	PUNCT
ap-1267	25	1	can	can	AUX
ap-1267	25	2	be	be	AUX
ap-1267	25	3	introduced	introduce	VERB
ap-1267	25	4	as	as	SCONJ
ap-1267	25	5	follows	follow	VERB
ap-1267	25	6	:	:	PUNCT
ap-1267	25	7	x	x	SYM
ap-1267	25	8	≤	≤	ADJ
ap-1267	25	9	y	y	NOUN
ap-1267	25	10	and	and	CCONJ
ap-1267	25	11	y!x	y!x	PROPN
ap-1267	25	12	=	=	SYM
ap-1267	25	13	z	z	PROPN
ap-1267	25	14	iff	iff	PROPN
ap-1267	25	15	x⊕z	x⊕z	PROPN
ap-1267	25	16	is	be	AUX
ap-1267	25	17	defined	define	VERB
ap-1267	25	18	and	and	CCONJ
ap-1267	25	19	x⊕z	x⊕z	PROPN
ap-1267	26	1	=	=	PUNCT
ap-1267	26	2	y.	y.	NOUN
ap-1267	26	3	if	if	SCONJ
ap-1267	26	4	e	e	NOUN
ap-1267	26	5	with	with	ADP
ap-1267	26	6	the	the	DET
ap-1267	26	7	defined	define	VERB
ap-1267	26	8	partial	partial	ADJ
ap-1267	26	9	order	order	NOUN
ap-1267	26	10	is	be	AUX
ap-1267	26	11	a	a	DET
ap-1267	26	12	lattice	lattice	NOUN
ap-1267	26	13	(	(	PUNCT
ap-1267	26	14	a	a	DET
ap-1267	26	15	complete	complete	ADJ
ap-1267	26	16	lattice	lattice	NOUN
ap-1267	26	17	)	)	PUNCT
ap-1267	26	18	then	then	ADV
ap-1267	26	19	(	(	PUNCT
ap-1267	26	20	e;⊕	e;⊕	ADJ
ap-1267	26	21	,	,	PUNCT
ap-1267	26	22	0	0	NUM
ap-1267	26	23	,	,	PUNCT
ap-1267	26	24	1	1	NUM
ap-1267	26	25	)	)	PUNCT
ap-1267	26	26	is	be	AUX
ap-1267	26	27	called	call	VERB
ap-1267	26	28	a	a	DET
ap-1267	26	29	lattice	lattice	ADJ
ap-1267	26	30	effect	effect	NOUN
ap-1267	26	31	algebra	algebra	NOUN
ap-1267	26	32	(	(	PUNCT
ap-1267	26	33	a	a	DET
ap-1267	26	34	complete	complete	ADJ
ap-1267	26	35	lattice	lattice	NOUN
ap-1267	26	36	effect	effect	NOUN
ap-1267	26	37	algebra	algebra	PROPN
ap-1267	26	38	)	)	PUNCT
ap-1267	26	39	.	.	PUNCT
ap-1267	27	1	this	this	DET
ap-1267	27	2	paper	paper	NOUN
ap-1267	27	3	is	be	AUX
ap-1267	27	4	a	a	DET
ap-1267	27	5	contribution	contribution	NOUN
ap-1267	27	6	to	to	ADP
ap-1267	27	7	the	the	DET
ap-1267	27	8	proceedings	proceeding	NOUN
ap-1267	27	9	of	of	ADP
ap-1267	27	10	the	the	DET
ap-1267	27	11	6	6	NUM
ap-1267	27	12	-	-	PUNCT
ap-1267	27	13	th	th	NUM
ap-1267	27	14	microconference	microconference	NOUN
ap-1267	27	15	“	"	PUNCT
ap-1267	27	16	analytic	analytic	ADJ
ap-1267	27	17	and	and	CCONJ
ap-1267	27	18	algebraic	algebraic	ADJ
ap-1267	27	19	methods	method	NOUN
ap-1267	27	20	vi	vi	PROPN
ap-1267	27	21	”	"	PUNCT
ap-1267	27	22	.	.	PUNCT
ap-1267	28	1	51	51	NUM
ap-1267	28	2	acta	acta	PROPN
ap-1267	28	3	polytechnica	polytechnica	PROPN
ap-1267	28	4	vol	vol	NOUN
ap-1267	28	5	.	.	PROPN
ap-1267	29	1	50	50	NUM
ap-1267	29	2	no	no	NOUN
ap-1267	29	3	.	.	PUNCT
ap-1267	30	1	5/2010	5/2010	NUM
ap-1267	30	2	definition	definition	NOUN
ap-1267	30	3	2	2	NUM
ap-1267	30	4	let	let	VERB
ap-1267	30	5	e	e	PRON
ap-1267	30	6	be	be	AUX
ap-1267	30	7	an	an	DET
ap-1267	30	8	effect	effect	NOUN
ap-1267	30	9	algebra	algebra	NOUN
ap-1267	30	10	.	.	PUNCT
ap-1267	31	1	then	then	ADV
ap-1267	31	2	q	q	X
ap-1267	31	3	⊆	⊆	NUM
ap-1267	31	4	e	e	NOUN
ap-1267	31	5	is	be	AUX
ap-1267	31	6	called	call	VERB
ap-1267	31	7	a	a	DET
ap-1267	31	8	sub	sub	ADJ
ap-1267	31	9	-	-	ADJ
ap-1267	31	10	effect	effect	ADJ
ap-1267	31	11	algebra	algebra	NOUN
ap-1267	31	12	of	of	ADP
ap-1267	31	13	e	e	PRON
ap-1267	31	14	if	if	SCONJ
ap-1267	31	15	(	(	PUNCT
ap-1267	31	16	i	i	NOUN
ap-1267	31	17	)	)	PUNCT
ap-1267	31	18	1	1	NUM
ap-1267	31	19	∈	∈	PROPN
ap-1267	31	20	q	q	NOUN
ap-1267	31	21	,	,	PUNCT
ap-1267	31	22	(	(	PUNCT
ap-1267	31	23	ii	ii	NOUN
ap-1267	31	24	)	)	PUNCT
ap-1267	31	25	if	if	SCONJ
ap-1267	31	26	out	out	ADP
ap-1267	31	27	of	of	ADP
ap-1267	31	28	elements	element	NOUN
ap-1267	31	29	x	x	X
ap-1267	31	30	,	,	PUNCT
ap-1267	31	31	y	y	PROPN
ap-1267	31	32	,	,	PUNCT
ap-1267	31	33	z	z	NOUN
ap-1267	31	34	∈	∈	PROPN
ap-1267	31	35	e	e	X
ap-1267	31	36	with	with	ADP
ap-1267	31	37	x	x	PROPN
ap-1267	31	38	⊕	⊕	PROPN
ap-1267	31	39	y	y	NOUN
ap-1267	32	1	=	=	SYM
ap-1267	32	2	z	z	PROPN
ap-1267	32	3	two	two	NUM
ap-1267	32	4	are	be	AUX
ap-1267	32	5	in	in	ADP
ap-1267	32	6	q	q	NOUN
ap-1267	32	7	,	,	PUNCT
ap-1267	32	8	then	then	ADV
ap-1267	32	9	x	x	X
ap-1267	32	10	,	,	PUNCT
ap-1267	32	11	y	y	PROPN
ap-1267	32	12	,	,	PUNCT
ap-1267	32	13	z	z	PROPN
ap-1267	32	14	∈	∈	PROPN
ap-1267	32	15	q.	q.	NOUN
ap-1267	32	16	if	if	SCONJ
ap-1267	32	17	e	e	NOUN
ap-1267	32	18	is	be	AUX
ap-1267	32	19	a	a	DET
ap-1267	32	20	lattice	lattice	ADJ
ap-1267	32	21	effect	effect	NOUN
ap-1267	32	22	algebra	algebra	NOUN
ap-1267	32	23	and	and	CCONJ
ap-1267	32	24	q	q	NOUN
ap-1267	32	25	is	be	AUX
ap-1267	32	26	a	a	DET
ap-1267	32	27	sub	sub	ADJ
ap-1267	32	28	-	-	ADJ
ap-1267	32	29	lattice	lattice	NOUN
ap-1267	32	30	and	and	CCONJ
ap-1267	32	31	a	a	DET
ap-1267	32	32	sub	sub	ADJ
ap-1267	32	33	-	-	ADJ
ap-1267	32	34	effect	effect	ADJ
ap-1267	32	35	algebra	algebra	NOUN
ap-1267	32	36	of	of	ADP
ap-1267	32	37	e	e	PROPN
ap-1267	32	38	then	then	ADV
ap-1267	32	39	q	q	X
ap-1267	32	40	is	be	AUX
ap-1267	32	41	called	call	VERB
ap-1267	32	42	a	a	DET
ap-1267	32	43	sublattice	sublattice	NOUN
ap-1267	32	44	effect	effect	NOUN
ap-1267	32	45	algebra	algebra	NOUN
ap-1267	32	46	of	of	ADP
ap-1267	32	47	e.	e.	PROPN
ap-1267	32	48	note	note	PROPN
ap-1267	32	49	that	that	SCONJ
ap-1267	32	50	a	a	DET
ap-1267	32	51	sub	sub	ADJ
ap-1267	32	52	-	-	ADJ
ap-1267	32	53	effect	effect	ADJ
ap-1267	32	54	algebra	algebra	NOUN
ap-1267	32	55	q	q	X
ap-1267	32	56	(	(	PUNCT
ap-1267	32	57	sub	sub	ADJ
ap-1267	32	58	-	-	ADJ
ap-1267	32	59	lattice	lattice	ADJ
ap-1267	32	60	effect	effect	NOUN
ap-1267	32	61	algebra	algebra	NOUN
ap-1267	32	62	q	q	NOUN
ap-1267	32	63	)	)	PUNCT
ap-1267	32	64	of	of	ADP
ap-1267	32	65	an	an	DET
ap-1267	32	66	effect	effect	NOUN
ap-1267	32	67	algebra	algebra	NOUN
ap-1267	32	68	e	e	NOUN
ap-1267	32	69	(	(	PUNCT
ap-1267	32	70	of	of	ADP
ap-1267	32	71	a	a	DET
ap-1267	32	72	lattice	lattice	ADJ
ap-1267	32	73	effect	effect	NOUN
ap-1267	32	74	algebra	algebra	NOUN
ap-1267	32	75	e	e	NOUN
ap-1267	32	76	)	)	PUNCT
ap-1267	32	77	with	with	ADP
ap-1267	32	78	inherited	inherit	VERB
ap-1267	32	79	operation	operation	NOUN
ap-1267	32	80	⊕	⊕	PROPN
ap-1267	32	81	is	be	AUX
ap-1267	32	82	an	an	DET
ap-1267	32	83	effect	effect	NOUN
ap-1267	32	84	algebra	algebra	NOUN
ap-1267	32	85	(	(	PUNCT
ap-1267	32	86	lattice	lattice	PROPN
ap-1267	32	87	effect	effect	NOUN
ap-1267	32	88	algebra	algebra	PROPN
ap-1267	32	89	)	)	PUNCT
ap-1267	32	90	in	in	ADP
ap-1267	32	91	its	its	PRON
ap-1267	32	92	own	own	ADJ
ap-1267	32	93	right	right	NOUN
ap-1267	32	94	.	.	PUNCT
ap-1267	33	1	for	for	ADP
ap-1267	33	2	an	an	DET
ap-1267	33	3	element	element	NOUN
ap-1267	33	4	x	x	PUNCT
ap-1267	33	5	of	of	ADP
ap-1267	33	6	an	an	DET
ap-1267	33	7	effect	effect	NOUN
ap-1267	33	8	algebra	algebra	NOUN
ap-1267	33	9	e	e	NOUN
ap-1267	33	10	we	we	PRON
ap-1267	33	11	write	write	VERB
ap-1267	33	12	ord	ord	PROPN
ap-1267	33	13	(	(	PUNCT
ap-1267	33	14	x	x	NOUN
ap-1267	33	15	)	)	PUNCT
ap-1267	34	1	=	=	NOUN
ap-1267	34	2	∞	∞	NOUN
ap-1267	34	3	if	if	SCONJ
ap-1267	34	4	nx	nx	PROPN
ap-1267	34	5	=	=	SYM
ap-1267	34	6	x	x	SYM
ap-1267	34	7	⊕	⊕	PROPN
ap-1267	34	8	x	x	PROPN
ap-1267	34	9	⊕	⊕	PROPN
ap-1267	34	10	.	.	PUNCT
ap-1267	34	11	.	.	PUNCT
ap-1267	34	12	.	.	PUNCT
ap-1267	35	1	⊕	⊕	PROPN
ap-1267	35	2	x	x	PUNCT
ap-1267	35	3	(	(	PUNCT
ap-1267	35	4	n	n	CCONJ
ap-1267	35	5	-	-	PUNCT
ap-1267	35	6	times	time	NOUN
ap-1267	35	7	)	)	PUNCT
ap-1267	35	8	exists	exist	VERB
ap-1267	35	9	for	for	ADP
ap-1267	35	10	every	every	DET
ap-1267	35	11	positive	positive	ADJ
ap-1267	35	12	integer	integer	NOUN
ap-1267	35	13	n	n	NOUN
ap-1267	35	14	and	and	CCONJ
ap-1267	35	15	we	we	PRON
ap-1267	35	16	write	write	VERB
ap-1267	35	17	ord	ord	PROPN
ap-1267	35	18	(	(	PUNCT
ap-1267	35	19	x	x	NOUN
ap-1267	35	20	)	)	PUNCT
ap-1267	35	21	=	=	SYM
ap-1267	35	22	nx	nx	X
ap-1267	35	23	if	if	SCONJ
ap-1267	35	24	nx	nx	PROPN
ap-1267	35	25	is	be	AUX
ap-1267	35	26	the	the	DET
ap-1267	35	27	greatest	great	ADJ
ap-1267	35	28	positive	positive	ADJ
ap-1267	35	29	integer	integer	NOUN
ap-1267	35	30	such	such	ADJ
ap-1267	35	31	that	that	SCONJ
ap-1267	35	32	nxx	nxx	PROPN
ap-1267	35	33	exists	exist	VERB
ap-1267	35	34	in	in	ADP
ap-1267	35	35	e.	e.	PROPN
ap-1267	35	36	an	an	DET
ap-1267	35	37	effect	effect	NOUN
ap-1267	35	38	algebra	algebra	NOUN
ap-1267	35	39	e	e	NOUN
ap-1267	35	40	is	be	AUX
ap-1267	35	41	archimedean	archimedean	ADJ
ap-1267	35	42	if	if	SCONJ
ap-1267	35	43	ord	ord	PROPN
ap-1267	35	44	(	(	PUNCT
ap-1267	35	45	x	x	X
ap-1267	35	46	)	)	PUNCT
ap-1267	35	47	<	<	X
ap-1267	35	48	∞	∞	PROPN
ap-1267	35	49	for	for	ADP
ap-1267	35	50	all	all	DET
ap-1267	35	51	x	x	SYM
ap-1267	35	52	∈	∈	PROPN
ap-1267	35	53	e.	e.	PROPN
ap-1267	35	54	a	a	DET
ap-1267	35	55	minimal	minimal	ADJ
ap-1267	35	56	nonzero	nonzero	NOUN
ap-1267	35	57	element	element	NOUN
ap-1267	35	58	of	of	ADP
ap-1267	35	59	an	an	DET
ap-1267	35	60	effect	effect	NOUN
ap-1267	35	61	algebra	algebra	NOUN
ap-1267	35	62	e	e	NOUN
ap-1267	35	63	is	be	AUX
ap-1267	35	64	called	call	VERB
ap-1267	35	65	an	an	DET
ap-1267	35	66	atom	atom	NOUN
ap-1267	35	67	and	and	CCONJ
ap-1267	35	68	e	e	NOUN
ap-1267	35	69	is	be	AUX
ap-1267	35	70	called	call	VERB
ap-1267	35	71	atomic	atomic	ADJ
ap-1267	35	72	if	if	SCONJ
ap-1267	35	73	under	under	ADP
ap-1267	35	74	every	every	DET
ap-1267	35	75	nonzero	nonzero	ADJ
ap-1267	35	76	element	element	NOUN
ap-1267	35	77	of	of	ADP
ap-1267	35	78	e	e	PROPN
ap-1267	35	79	there	there	PRON
ap-1267	35	80	is	be	VERB
ap-1267	35	81	an	an	DET
ap-1267	35	82	atom	atom	NOUN
ap-1267	35	83	.	.	PUNCT
ap-1267	36	1	for	for	ADP
ap-1267	36	2	a	a	DET
ap-1267	36	3	poset	poset	NOUN
ap-1267	36	4	p	p	NOUN
ap-1267	36	5	and	and	CCONJ
ap-1267	36	6	its	its	PRON
ap-1267	36	7	subposet	subposet	NOUN
ap-1267	36	8	q	q	NOUN
ap-1267	36	9	⊆	⊆	NUM
ap-1267	36	10	p	p	NOUN
ap-1267	36	11	we	we	PRON
ap-1267	36	12	denote	denote	VERB
ap-1267	36	13	,	,	PUNCT
ap-1267	36	14	for	for	ADP
ap-1267	36	15	all	all	PRON
ap-1267	36	16	x	x	SYM
ap-1267	36	17	⊆	⊆	NUM
ap-1267	36	18	q	q	NOUN
ap-1267	36	19	,	,	PUNCT
ap-1267	36	20	by	by	ADP
ap-1267	36	21	∨	∨	NUM
ap-1267	36	22	q	q	NOUN
ap-1267	36	23	x	x	NOUN
ap-1267	36	24	the	the	DET
ap-1267	36	25	join	join	NOUN
ap-1267	36	26	of	of	ADP
ap-1267	36	27	the	the	DET
ap-1267	36	28	subset	subset	NOUN
ap-1267	36	29	x	x	PUNCT
ap-1267	36	30	in	in	ADP
ap-1267	36	31	the	the	DET
ap-1267	36	32	poset	poset	NOUN
ap-1267	36	33	q	q	NOUN
ap-1267	36	34	whenever	whenever	SCONJ
ap-1267	36	35	it	it	PRON
ap-1267	36	36	exists	exist	VERB
ap-1267	36	37	.	.	PUNCT
ap-1267	37	1	we	we	PRON
ap-1267	37	2	say	say	VERB
ap-1267	37	3	that	that	SCONJ
ap-1267	37	4	a	a	DET
ap-1267	37	5	finite	finite	ADJ
ap-1267	37	6	system	system	NOUN
ap-1267	37	7	f	f	PROPN
ap-1267	37	8	=	=	SYM
ap-1267	37	9	(	(	PUNCT
ap-1267	37	10	xk)nk=1	xk)nk=1	NOUN
ap-1267	37	11	of	of	ADP
ap-1267	37	12	not	not	PART
ap-1267	37	13	necessarily	necessarily	ADV
ap-1267	37	14	different	different	ADJ
ap-1267	37	15	elements	element	NOUN
ap-1267	37	16	of	of	ADP
ap-1267	37	17	an	an	DET
ap-1267	37	18	effect	effect	NOUN
ap-1267	37	19	algebra	algebra	NOUN
ap-1267	37	20	(	(	PUNCT
ap-1267	37	21	e;⊕	e;⊕	ADJ
ap-1267	37	22	,	,	PUNCT
ap-1267	37	23	0	0	NUM
ap-1267	37	24	,	,	PUNCT
ap-1267	37	25	1	1	NUM
ap-1267	37	26	)	)	PUNCT
ap-1267	37	27	is	be	AUX
ap-1267	37	28	orthogonal	orthogonal	ADJ
ap-1267	38	1	if	if	SCONJ
ap-1267	38	2	x1	x1	PROPN
ap-1267	38	3	⊕	⊕	PROPN
ap-1267	38	4	x2	x2	PROPN
ap-1267	38	5	⊕	⊕	PROPN
ap-1267	38	6	.	.	PUNCT
ap-1267	38	7	.	.	PUNCT
ap-1267	39	1	.	.	PUNCT
ap-1267	40	1	⊕	⊕	PROPN
ap-1267	40	2	xn	xn	PROPN
ap-1267	41	1	(	(	PUNCT
ap-1267	41	2	written	write	VERB
ap-1267	41	3	n⊕	n⊕	PROPN
ap-1267	41	4	k=1	k=1	PUNCT
ap-1267	42	1	xk	xk	PROPN
ap-1267	42	2	or	or	CCONJ
ap-1267	42	3	⊕	⊕	PROPN
ap-1267	42	4	f	f	PROPN
ap-1267	42	5	)	)	PUNCT
ap-1267	42	6	exists	exist	VERB
ap-1267	42	7	in	in	ADP
ap-1267	42	8	e.	e.	PROPN
ap-1267	42	9	here	here	ADV
ap-1267	42	10	we	we	PRON
ap-1267	42	11	define	define	VERB
ap-1267	42	12	x1⊕x2⊕.	x1⊕x2⊕.	PROPN
ap-1267	42	13	.	.	PUNCT
ap-1267	43	1	.⊕xn	.⊕xn	X
ap-1267	44	1	=	=	PUNCT
ap-1267	44	2	(	(	PUNCT
ap-1267	44	3	x1⊕x2⊕.	x1⊕x2⊕.	PROPN
ap-1267	44	4	.	.	PUNCT
ap-1267	45	1	.⊕xn−1)⊕xn	.⊕xn−1)⊕xn	PROPN
ap-1267	46	1	supposing	suppose	VERB
ap-1267	46	2	that	that	SCONJ
ap-1267	46	3	n−1⊕	n−1⊕	ADJ
ap-1267	46	4	k=1	k=1	PROPN
ap-1267	46	5	xk	xk	PROPN
ap-1267	46	6	is	be	AUX
ap-1267	46	7	defined	define	VERB
ap-1267	46	8	and	and	CCONJ
ap-1267	46	9	n−1⊕	n−1⊕	ADJ
ap-1267	46	10	k=1	k=1	PUNCT
ap-1267	46	11	xk	xk	PROPN
ap-1267	46	12	≤	≤	PROPN
ap-1267	47	1	x′	x′	PROPN
ap-1267	47	2	n.	n.	NOUN
ap-1267	47	3	we	we	PRON
ap-1267	47	4	also	also	ADV
ap-1267	47	5	define	define	VERB
ap-1267	47	6	⊕	⊕	PROPN
ap-1267	47	7	"	"	PUNCT
ap-1267	48	1	=	=	SYM
ap-1267	48	2	0	0	X
ap-1267	48	3	.	.	PUNCT
ap-1267	49	1	an	an	DET
ap-1267	49	2	arbitrary	arbitrary	ADJ
ap-1267	49	3	system	system	NOUN
ap-1267	49	4	g	g	NOUN
ap-1267	49	5	=	=	SYM
ap-1267	49	6	(	(	PUNCT
ap-1267	49	7	xκ)κ∈h	xκ)κ∈h	NUM
ap-1267	49	8	of	of	ADP
ap-1267	49	9	not	not	PART
ap-1267	49	10	necessarily	necessarily	ADV
ap-1267	49	11	different	different	ADJ
ap-1267	49	12	elements	element	NOUN
ap-1267	49	13	of	of	ADP
ap-1267	49	14	e	e	PROPN
ap-1267	49	15	is	be	AUX
ap-1267	49	16	called	call	VERB
ap-1267	49	17	orthogonal	orthogonal	ADJ
ap-1267	49	18	if	if	SCONJ
ap-1267	49	19	⊕	⊕	PROPN
ap-1267	49	20	k	k	PROPN
ap-1267	49	21	exists	exist	VERB
ap-1267	49	22	for	for	ADP
ap-1267	49	23	every	every	DET
ap-1267	49	24	finite	finite	NOUN
ap-1267	49	25	k	k	PROPN
ap-1267	49	26	⊆	⊆	NUM
ap-1267	49	27	g.	g.	NOUN
ap-1267	49	28	we	we	PRON
ap-1267	49	29	say	say	VERB
ap-1267	49	30	that	that	SCONJ
ap-1267	49	31	for	for	ADP
ap-1267	49	32	an	an	DET
ap-1267	49	33	orthogonal	orthogonal	ADJ
ap-1267	49	34	system	system	NOUN
ap-1267	49	35	g	g	NOUN
ap-1267	49	36	=	=	SYM
ap-1267	49	37	(	(	PUNCT
ap-1267	49	38	xκ)κ∈h	xκ)κ∈h	NUM
ap-1267	49	39	the	the	DET
ap-1267	49	40	element	element	NOUN
ap-1267	49	41	⊕	⊕	PROPN
ap-1267	49	42	g	g	PROPN
ap-1267	49	43	(	(	PUNCT
ap-1267	49	44	more	more	ADV
ap-1267	49	45	precisely	precisely	ADV
ap-1267	49	46	⊕	⊕	NOUN
ap-1267	49	47	e	e	NOUN
ap-1267	49	48	g	g	NOUN
ap-1267	49	49	)	)	PUNCT
ap-1267	49	50	exists	exist	VERB
ap-1267	49	51	iff∨	iff∨	X
ap-1267	49	52	{	{	PUNCT
ap-1267	49	53	⊕	⊕	PROPN
ap-1267	49	54	k	k	PROPN
ap-1267	50	1	|	|	ADV
ap-1267	50	2	k	k	PROPN
ap-1267	50	3	⊆	⊆	NUM
ap-1267	50	4	g	g	NOUN
ap-1267	50	5	is	be	AUX
ap-1267	50	6	finite	finite	ADJ
ap-1267	50	7	}	}	PUNCT
ap-1267	50	8	exists	exist	VERB
ap-1267	50	9	in	in	ADP
ap-1267	50	10	e	e	NOUN
ap-1267	50	11	and	and	CCONJ
ap-1267	50	12	then	then	ADV
ap-1267	50	13	we	we	PRON
ap-1267	50	14	put	put	VERB
ap-1267	50	15	⊕	⊕	PROPN
ap-1267	50	16	g	g	NOUN
ap-1267	50	17	=	=	SYM
ap-1267	50	18	∨	∨	X
ap-1267	50	19	{	{	PUNCT
ap-1267	50	20	⊕	⊕	PROPN
ap-1267	50	21	k	k	PROPN
ap-1267	51	1	|	|	ADV
ap-1267	51	2	k	k	PROPN
ap-1267	51	3	⊆	⊆	NUM
ap-1267	51	4	g	g	NOUN
ap-1267	51	5	is	be	AUX
ap-1267	51	6	finite	finite	ADJ
ap-1267	51	7	}	}	PUNCT
ap-1267	51	8	.	.	PUNCT
ap-1267	52	1	(	(	PUNCT
ap-1267	52	2	here	here	ADV
ap-1267	52	3	we	we	PRON
ap-1267	52	4	write	write	VERB
ap-1267	52	5	g1	g1	PROPN
ap-1267	52	6	⊆	⊆	PRON
ap-1267	52	7	g	g	PROPN
ap-1267	52	8	iff	iff	NOUN
ap-1267	52	9	there	there	PRON
ap-1267	52	10	is	be	VERB
ap-1267	52	11	h1	h1	PROPN
ap-1267	52	12	⊆	⊆	X
ap-1267	52	13	h	h	NOUN
ap-1267	52	14	such	such	ADJ
ap-1267	52	15	that	that	SCONJ
ap-1267	52	16	g1	g1	PROPN
ap-1267	52	17	=	=	SYM
ap-1267	52	18	(	(	PUNCT
ap-1267	52	19	xκ)κ∈h1	xκ)κ∈h1	PROPN
ap-1267	52	20	)	)	PUNCT
ap-1267	52	21	.	.	PUNCT
ap-1267	53	1	we	we	PRON
ap-1267	53	2	call	call	VERB
ap-1267	53	3	an	an	DET
ap-1267	53	4	effect	effect	NOUN
ap-1267	53	5	algebra	algebra	NOUN
ap-1267	53	6	e	e	X
ap-1267	53	7	orthocomplete	orthocomplete	ADV
ap-1267	53	8	[	[	X
ap-1267	53	9	9	9	NUM
ap-1267	53	10	]	]	PUNCT
ap-1267	53	11	if	if	SCONJ
ap-1267	53	12	every	every	DET
ap-1267	53	13	orthogonal	orthogonal	ADJ
ap-1267	53	14	system	system	NOUN
ap-1267	53	15	g	g	NOUN
ap-1267	53	16	=	=	SYM
ap-1267	53	17	(	(	PUNCT
ap-1267	53	18	xκ)κ∈h	xκ)κ∈h	NUM
ap-1267	53	19	of	of	ADP
ap-1267	53	20	elements	element	NOUN
ap-1267	53	21	of	of	ADP
ap-1267	53	22	e	e	NOUN
ap-1267	53	23	has	have	VERB
ap-1267	53	24	the	the	DET
ap-1267	53	25	sum	sum	NOUN
ap-1267	53	26	⊕	⊕	PROPN
ap-1267	53	27	g.	g.	PROPN
ap-1267	54	1	it	it	PRON
ap-1267	54	2	is	be	AUX
ap-1267	54	3	known	know	VERB
ap-1267	54	4	that	that	SCONJ
ap-1267	54	5	every	every	DET
ap-1267	54	6	orthocomplete	orthocomplete	ADJ
ap-1267	54	7	archimedean	archimedean	PROPN
ap-1267	54	8	lattice	lattice	PROPN
ap-1267	54	9	effect	effect	NOUN
ap-1267	54	10	algebra	algebra	NOUN
ap-1267	54	11	e	e	NOUN
ap-1267	54	12	is	be	AUX
ap-1267	54	13	a	a	DET
ap-1267	54	14	complete	complete	ADJ
ap-1267	54	15	lattice	lattice	NOUN
ap-1267	54	16	(	(	PUNCT
ap-1267	54	17	see	see	VERB
ap-1267	54	18	[	[	X
ap-1267	54	19	22	22	NUM
ap-1267	54	20	,	,	PUNCT
ap-1267	54	21	theorem	theorem	VERB
ap-1267	54	22	2.6	2.6	NUM
ap-1267	54	23	]	]	PUNCT
ap-1267	54	24	)	)	PUNCT
ap-1267	54	25	.	.	PUNCT
ap-1267	55	1	recall	recall	VERB
ap-1267	55	2	that	that	SCONJ
ap-1267	55	3	elements	element	NOUN
ap-1267	55	4	x	x	X
ap-1267	55	5	,	,	PUNCT
ap-1267	55	6	y	y	PROPN
ap-1267	55	7	of	of	ADP
ap-1267	55	8	a	a	DET
ap-1267	55	9	lattice	lattice	ADJ
ap-1267	55	10	effect	effect	NOUN
ap-1267	55	11	algebra	algebra	NOUN
ap-1267	55	12	e	e	NOUN
ap-1267	55	13	are	be	AUX
ap-1267	55	14	called	call	VERB
ap-1267	55	15	compatible	compatible	ADJ
ap-1267	55	16	(	(	PUNCT
ap-1267	55	17	written	write	VERB
ap-1267	55	18	x	x	PUNCT
ap-1267	55	19	↔	↔	PROPN
ap-1267	55	20	y	y	PROPN
ap-1267	55	21	)	)	PUNCT
ap-1267	55	22	iff	iff	PROPN
ap-1267	55	23	x	x	PROPN
ap-1267	55	24	∨	∨	PROPN
ap-1267	55	25	y	y	PROPN
ap-1267	55	26	=	=	SYM
ap-1267	55	27	x	x	SYM
ap-1267	55	28	⊕	⊕	PROPN
ap-1267	55	29	(	(	PUNCT
ap-1267	55	30	y	y	PROPN
ap-1267	55	31	!	!	PUNCT
ap-1267	56	1	(	(	PUNCT
ap-1267	56	2	x	x	PUNCT
ap-1267	56	3	∧	∧	PROPN
ap-1267	56	4	y	y	PROPN
ap-1267	56	5	)	)	PUNCT
ap-1267	56	6	)	)	PUNCT
ap-1267	57	1	(	(	PUNCT
ap-1267	57	2	see	see	VERB
ap-1267	57	3	[	[	X
ap-1267	57	4	15	15	NUM
ap-1267	57	5	]	]	NUM
ap-1267	57	6	)	)	PUNCT
ap-1267	57	7	.	.	PUNCT
ap-1267	58	1	p	p	NOUN
ap-1267	59	1	⊆	⊆	NUM
ap-1267	59	2	e	e	NOUN
ap-1267	59	3	is	be	AUX
ap-1267	59	4	a	a	DET
ap-1267	59	5	set	set	NOUN
ap-1267	59	6	of	of	ADP
ap-1267	59	7	pairwise	pairwise	NOUN
ap-1267	59	8	compatible	compatible	ADJ
ap-1267	59	9	elements	element	NOUN
ap-1267	59	10	if	if	SCONJ
ap-1267	59	11	x	x	PROPN
ap-1267	59	12	↔	↔	PROPN
ap-1267	59	13	y	y	PROPN
ap-1267	59	14	for	for	ADP
ap-1267	59	15	all	all	DET
ap-1267	59	16	x	x	NOUN
ap-1267	59	17	,	,	PUNCT
ap-1267	59	18	y	y	PROPN
ap-1267	59	19	∈	∈	PROPN
ap-1267	59	20	p	p	PROPN
ap-1267	59	21	.	.	PUNCT
ap-1267	60	1	m	m	PROPN
ap-1267	60	2	⊆	⊆	NUM
ap-1267	60	3	e	e	NOUN
ap-1267	60	4	is	be	AUX
ap-1267	60	5	called	call	VERB
ap-1267	60	6	a	a	DET
ap-1267	60	7	block	block	NOUN
ap-1267	60	8	of	of	ADP
ap-1267	60	9	e	e	PROPN
ap-1267	60	10	iff	iff	PROPN
ap-1267	60	11	m	m	PROPN
ap-1267	60	12	is	be	AUX
ap-1267	60	13	a	a	DET
ap-1267	60	14	maximal	maximal	ADJ
ap-1267	60	15	subset	subset	NOUN
ap-1267	60	16	of	of	ADP
ap-1267	60	17	pairwise	pairwise	NOUN
ap-1267	60	18	compatible	compatible	ADJ
ap-1267	60	19	elements	element	NOUN
ap-1267	60	20	.	.	PUNCT
ap-1267	61	1	every	every	DET
ap-1267	61	2	block	block	NOUN
ap-1267	61	3	of	of	ADP
ap-1267	61	4	a	a	DET
ap-1267	61	5	lattice	lattice	ADJ
ap-1267	61	6	effect	effect	NOUN
ap-1267	61	7	algebra	algebra	NOUN
ap-1267	61	8	e	e	NOUN
ap-1267	61	9	is	be	AUX
ap-1267	61	10	a	a	DET
ap-1267	61	11	sub	sub	ADJ
ap-1267	61	12	-	-	ADJ
ap-1267	61	13	effect	effect	ADJ
ap-1267	61	14	algebra	algebra	NOUN
ap-1267	61	15	and	and	CCONJ
ap-1267	61	16	a	a	DET
ap-1267	61	17	sub	sub	NOUN
ap-1267	61	18	-	-	NOUN
ap-1267	61	19	lattice	lattice	NOUN
ap-1267	61	20	of	of	ADP
ap-1267	61	21	e	e	PROPN
ap-1267	61	22	and	and	CCONJ
ap-1267	61	23	e	e	PROPN
ap-1267	61	24	is	be	AUX
ap-1267	61	25	a	a	DET
ap-1267	61	26	union	union	NOUN
ap-1267	61	27	of	of	ADP
ap-1267	61	28	its	its	PRON
ap-1267	61	29	blocks	block	NOUN
ap-1267	61	30	(	(	PUNCT
ap-1267	61	31	see	see	VERB
ap-1267	61	32	[	[	X
ap-1267	61	33	21	21	NUM
ap-1267	61	34	]	]	PUNCT
ap-1267	61	35	)	)	PUNCT
ap-1267	61	36	.	.	PUNCT
ap-1267	62	1	a	a	DET
ap-1267	62	2	lattice	lattice	ADJ
ap-1267	62	3	effect	effect	NOUN
ap-1267	62	4	algebra	algebra	NOUN
ap-1267	62	5	with	with	ADP
ap-1267	62	6	a	a	DET
ap-1267	62	7	unique	unique	ADJ
ap-1267	62	8	block	block	NOUN
ap-1267	62	9	is	be	AUX
ap-1267	62	10	called	call	VERB
ap-1267	62	11	an	an	DET
ap-1267	62	12	mv	mv	ADJ
ap-1267	62	13	-	-	PUNCT
ap-1267	62	14	effect	effect	NOUN
ap-1267	62	15	algebra	algebra	NOUN
ap-1267	62	16	.	.	PUNCT
ap-1267	63	1	every	every	DET
ap-1267	63	2	block	block	NOUN
ap-1267	63	3	of	of	ADP
ap-1267	63	4	a	a	DET
ap-1267	63	5	lattice	lattice	ADJ
ap-1267	63	6	effect	effect	NOUN
ap-1267	63	7	algebra	algebra	NOUN
ap-1267	63	8	is	be	AUX
ap-1267	63	9	an	an	DET
ap-1267	63	10	mv	mv	ADJ
ap-1267	63	11	-	-	PUNCT
ap-1267	63	12	effect	effect	NOUN
ap-1267	63	13	algebra	algebra	NOUN
ap-1267	63	14	in	in	ADP
ap-1267	63	15	its	its	PRON
ap-1267	63	16	own	own	ADJ
ap-1267	63	17	right	right	NOUN
ap-1267	63	18	.	.	PUNCT
ap-1267	64	1	an	an	DET
ap-1267	64	2	element	element	NOUN
ap-1267	64	3	w	w	NOUN
ap-1267	64	4	of	of	ADP
ap-1267	64	5	an	an	DET
ap-1267	64	6	effect	effect	NOUN
ap-1267	64	7	algebrae	algebrae	NOUN
ap-1267	64	8	is	be	AUX
ap-1267	64	9	called	call	VERB
ap-1267	64	10	sharp	sharp	ADJ
ap-1267	64	11	(	(	PUNCT
ap-1267	64	12	see	see	VERB
ap-1267	64	13	[	[	X
ap-1267	64	14	7	7	NUM
ap-1267	64	15	,	,	PUNCT
ap-1267	64	16	8	8	NUM
ap-1267	64	17	]	]	PUNCT
ap-1267	64	18	)	)	PUNCT
ap-1267	64	19	if	if	SCONJ
ap-1267	64	20	w	w	PROPN
ap-1267	64	21	∧	∧	PROPN
ap-1267	64	22	w′	w′	VERB
ap-1267	64	23	=	=	SYM
ap-1267	65	1	0	0	X
ap-1267	65	2	.	.	PUNCT
ap-1267	65	3	definition	definition	NOUN
ap-1267	65	4	3	3	NUM
ap-1267	65	5	(	(	PUNCT
ap-1267	65	6	[	[	X
ap-1267	65	7	7	7	NUM
ap-1267	65	8	,	,	PUNCT
ap-1267	65	9	8	8	NUM
ap-1267	65	10	]	]	PUNCT
ap-1267	65	11	)	)	PUNCT
ap-1267	65	12	an	an	DET
ap-1267	65	13	effect	effect	NOUN
ap-1267	65	14	algebra	algebra	NOUN
ap-1267	65	15	e	e	NOUN
ap-1267	65	16	is	be	AUX
ap-1267	65	17	called	call	VERB
ap-1267	65	18	sharply	sharply	ADV
ap-1267	65	19	dominating	dominate	VERB
ap-1267	65	20	if	if	SCONJ
ap-1267	65	21	for	for	SCONJ
ap-1267	65	22	every	every	DET
ap-1267	65	23	x	x	SYM
ap-1267	65	24	∈	∈	PROPN
ap-1267	65	25	e	e	NOUN
ap-1267	65	26	there	there	PRON
ap-1267	65	27	exists	exist	VERB
ap-1267	65	28	x̂	x̂	PUNCT
ap-1267	65	29	∈	∈	PROPN
ap-1267	65	30	s(e	s(e	PROPN
ap-1267	65	31	)	)	PUNCT
ap-1267	65	32	such	such	ADJ
ap-1267	65	33	that	that	PRON
ap-1267	65	34	x̂	x̂	PUNCT
ap-1267	66	1	=	=	PUNCT
ap-1267	66	2	∧	∧	PROPN
ap-1267	66	3	e	e	X
ap-1267	66	4	{	{	PUNCT
ap-1267	66	5	w	w	PROPN
ap-1267	66	6	∈	∈	PROPN
ap-1267	66	7	s(e	s(e	NOUN
ap-1267	66	8	)	)	PUNCT
ap-1267	66	9	|	|	ADV
ap-1267	66	10	x	x	SYM
ap-1267	66	11	≤	≤	ADV
ap-1267	66	12	w	w	NOUN
ap-1267	66	13	}	}	PUNCT
ap-1267	66	14	=	=	NOUN
ap-1267	66	15	∧	∧	PROPN
ap-1267	66	16	s(e	s(e	PROPN
ap-1267	66	17	)	)	PUNCT
ap-1267	66	18	{	{	PUNCT
ap-1267	66	19	w	w	PROPN
ap-1267	66	20	∈	∈	PROPN
ap-1267	66	21	s(e	s(e	PROPN
ap-1267	66	22	)	)	PUNCT
ap-1267	66	23	|	|	ADV
ap-1267	66	24	x	x	SYM
ap-1267	66	25	≤	≤	PROPN
ap-1267	66	26	w	w	NOUN
ap-1267	66	27	}	}	PUNCT
ap-1267	66	28	.	.	PUNCT
ap-1267	67	1	note	note	VERB
ap-1267	67	2	that	that	SCONJ
ap-1267	67	3	clearly	clearly	ADV
ap-1267	67	4	e	e	X
ap-1267	67	5	is	be	AUX
ap-1267	67	6	sharply	sharply	ADV
ap-1267	67	7	dominating	dominate	VERB
ap-1267	67	8	iff	iff	PROPN
ap-1267	67	9	for	for	ADP
ap-1267	67	10	every	every	DET
ap-1267	67	11	x	x	SYM
ap-1267	67	12	∈	∈	PROPN
ap-1267	67	13	e	e	NOUN
ap-1267	67	14	there	there	PRON
ap-1267	67	15	exists	exist	VERB
ap-1267	67	16	x̃	x̃	PROPN
ap-1267	67	17	∈	∈	PROPN
ap-1267	67	18	s(e	s(e	PROPN
ap-1267	67	19	)	)	PUNCT
ap-1267	67	20	such	such	ADJ
ap-1267	67	21	that	that	SCONJ
ap-1267	67	22	x̃	x̃	PROPN
ap-1267	67	23	=	=	SYM
ap-1267	68	1	∨	∨	PROPN
ap-1267	68	2	e	e	X
ap-1267	68	3	{	{	PUNCT
ap-1267	68	4	w	w	PROPN
ap-1267	68	5	∈	∈	PROPN
ap-1267	68	6	s(e	s(e	NOUN
ap-1267	68	7	)	)	PUNCT
ap-1267	68	8	|	|	ADV
ap-1267	68	9	x	x	PUNCT
ap-1267	68	10	≥	≥	NUM
ap-1267	68	11	w	w	NOUN
ap-1267	68	12	}	}	PUNCT
ap-1267	68	13	=	=	NUM
ap-1267	68	14	∨	∨	NOUN
ap-1267	68	15	s(e	s(e	PROPN
ap-1267	68	16	)	)	PUNCT
ap-1267	68	17	{	{	PUNCT
ap-1267	68	18	w	w	PROPN
ap-1267	68	19	∈	∈	PROPN
ap-1267	68	20	s(e	s(e	PROPN
ap-1267	68	21	)	)	PUNCT
ap-1267	68	22	|	|	ADV
ap-1267	68	23	x	x	PUNCT
ap-1267	68	24	≥	≥	NOUN
ap-1267	68	25	w	w	NOUN
ap-1267	68	26	}	}	PUNCT
ap-1267	68	27	.	.	PUNCT
ap-1267	69	1	a	a	DET
ap-1267	69	2	sharply	sharply	ADV
ap-1267	69	3	dominating	dominating	NOUN
ap-1267	69	4	effect	effect	NOUN
ap-1267	69	5	algebra	algebra	NOUN
ap-1267	69	6	e	e	NOUN
ap-1267	69	7	is	be	AUX
ap-1267	69	8	called	call	VERB
ap-1267	69	9	s	s	NOUN
ap-1267	69	10	-	-	PUNCT
ap-1267	69	11	dominating	dominating	NOUN
ap-1267	69	12	[	[	X
ap-1267	69	13	8	8	NUM
ap-1267	69	14	]	]	X
ap-1267	69	15	if	if	SCONJ
ap-1267	69	16	x	x	SYM
ap-1267	69	17	∧	∧	NOUN
ap-1267	69	18	w	w	NOUN
ap-1267	69	19	exists	exist	VERB
ap-1267	69	20	for	for	ADP
ap-1267	69	21	every	every	DET
ap-1267	69	22	x	x	SYM
ap-1267	69	23	∈	∈	PROPN
ap-1267	69	24	e	e	NOUN
ap-1267	69	25	,	,	PUNCT
ap-1267	69	26	w	w	PROPN
ap-1267	69	27	∈	∈	PROPN
ap-1267	69	28	s(e	s(e	PROPN
ap-1267	69	29	)	)	PUNCT
ap-1267	69	30	.	.	PUNCT
ap-1267	70	1	it	it	PRON
ap-1267	70	2	is	be	AUX
ap-1267	70	3	a	a	DET
ap-1267	70	4	well	well	ADV
ap-1267	70	5	known	know	VERB
ap-1267	70	6	fact	fact	NOUN
ap-1267	70	7	that	that	SCONJ
ap-1267	70	8	in	in	ADP
ap-1267	70	9	every	every	DET
ap-1267	70	10	s	s	NOUN
ap-1267	70	11	-	-	PUNCT
ap-1267	70	12	dominating	dominating	ADJ
ap-1267	70	13	effect	effect	NOUN
ap-1267	70	14	algebra	algebra	NOUN
ap-1267	70	15	e	e	NOUN
ap-1267	70	16	the	the	DET
ap-1267	70	17	subset	subset	NOUN
ap-1267	70	18	s(e	s(e	PROPN
ap-1267	70	19	)	)	PUNCT
ap-1267	70	20	=	=	PRON
ap-1267	70	21	{	{	PUNCT
ap-1267	70	22	w	w	NOUN
ap-1267	70	23	∈	∈	NOUN
ap-1267	70	24	e	e	NOUN
ap-1267	70	25	|	|	ADV
ap-1267	70	26	w∧w′	w∧w′	ADJ
ap-1267	70	27	=	=	SYM
ap-1267	70	28	0	0	NUM
ap-1267	70	29	}	}	PUNCT
ap-1267	70	30	of	of	ADP
ap-1267	70	31	sharp	sharp	ADJ
ap-1267	70	32	elements	element	NOUN
ap-1267	70	33	of	of	ADP
ap-1267	70	34	e	e	PROPN
ap-1267	70	35	is	be	AUX
ap-1267	70	36	a	a	DET
ap-1267	70	37	sub	sub	ADJ
ap-1267	70	38	-	-	ADJ
ap-1267	70	39	effect	effect	ADJ
ap-1267	70	40	algebra	algebra	NOUN
ap-1267	70	41	of	of	ADP
ap-1267	70	42	e	e	PROPN
ap-1267	70	43	being	be	AUX
ap-1267	70	44	an	an	DET
ap-1267	70	45	orthomodular	orthomodular	ADJ
ap-1267	70	46	lattice	lattice	NOUN
ap-1267	70	47	(	(	PUNCT
ap-1267	70	48	see	see	VERB
ap-1267	70	49	[	[	X
ap-1267	70	50	8	8	NUM
ap-1267	70	51	,	,	PUNCT
ap-1267	70	52	theorem	theorem	VERB
ap-1267	70	53	2.6	2.6	NUM
ap-1267	70	54	]	]	PUNCT
ap-1267	70	55	)	)	PUNCT
ap-1267	70	56	.	.	PUNCT
ap-1267	71	1	moreover	moreover	ADV
ap-1267	71	2	if	if	SCONJ
ap-1267	71	3	for	for	ADP
ap-1267	71	4	d	d	PROPN
ap-1267	71	5	⊆	⊆	NUM
ap-1267	71	6	s(e	s(e	PROPN
ap-1267	71	7	)	)	PUNCT
ap-1267	71	8	the	the	DET
ap-1267	71	9	element	element	NOUN
ap-1267	71	10	∨	∨	NUM
ap-1267	71	11	e	e	PROPN
ap-1267	71	12	d	d	NOUN
ap-1267	71	13	exists	exist	VERB
ap-1267	71	14	then	then	ADV
ap-1267	71	15	∨	∨	NUM
ap-1267	71	16	e	e	PROPN
ap-1267	71	17	d	d	PROPN
ap-1267	71	18	∈	∈	PROPN
ap-1267	71	19	s(e	s(e	PROPN
ap-1267	71	20	)	)	PUNCT
ap-1267	71	21	hence	hence	ADV
ap-1267	71	22	∨	∨	NUM
ap-1267	71	23	s(e	s(e	PROPN
ap-1267	71	24	)	)	PUNCT
ap-1267	72	1	d	d	X
ap-1267	72	2	=	=	SYM
ap-1267	72	3	∨	∨	PROPN
ap-1267	72	4	e	e	X
ap-1267	72	5	d.	d.	NOUN
ap-1267	72	6	we	we	PRON
ap-1267	72	7	say	say	VERB
ap-1267	72	8	that	that	SCONJ
ap-1267	72	9	s(e	s(e	PROPN
ap-1267	72	10	)	)	PUNCT
ap-1267	72	11	is	be	AUX
ap-1267	72	12	a	a	DET
ap-1267	72	13	full	full	ADJ
ap-1267	72	14	sublattice	sublattice	NOUN
ap-1267	72	15	of	of	ADP
ap-1267	72	16	e	e	NOUN
ap-1267	72	17	(	(	PUNCT
ap-1267	72	18	see	see	VERB
ap-1267	72	19	[	[	X
ap-1267	72	20	10	10	NUM
ap-1267	72	21	]	]	NUM
ap-1267	72	22	)	)	PUNCT
ap-1267	72	23	.	.	PUNCT
ap-1267	73	1	let	let	VERB
ap-1267	73	2	g	g	PRON
ap-1267	73	3	be	be	AUX
ap-1267	73	4	a	a	DET
ap-1267	73	5	sub	sub	ADJ
ap-1267	73	6	-	-	ADJ
ap-1267	73	7	effect	effect	ADJ
ap-1267	73	8	algebra	algebra	NOUN
ap-1267	73	9	of	of	ADP
ap-1267	73	10	an	an	DET
ap-1267	73	11	effect	effect	NOUN
ap-1267	74	1	algebra	algebra	NOUN
ap-1267	74	2	e.	e.	PROPN
ap-1267	75	1	we	we	PRON
ap-1267	75	2	say	say	VERB
ap-1267	75	3	that	that	SCONJ
ap-1267	75	4	g	g	PROPN
ap-1267	75	5	is	be	AUX
ap-1267	75	6	bifull	bifull	PROPN
ap-1267	75	7	in	in	ADP
ap-1267	75	8	e	e	NOUN
ap-1267	75	9	,	,	PUNCT
ap-1267	75	10	if	if	SCONJ
ap-1267	75	11	,	,	PUNCT
ap-1267	75	12	for	for	ADP
ap-1267	75	13	any	any	DET
ap-1267	75	14	d	d	PROPN
ap-1267	75	15	⊆	⊆	NUM
ap-1267	75	16	g	g	ADP
ap-1267	75	17	the	the	DET
ap-1267	75	18	element	element	NOUN
ap-1267	75	19	∨	∨	PROPN
ap-1267	75	20	g	g	PROPN
ap-1267	75	21	d	d	PROPN
ap-1267	75	22	exists	exist	VERB
ap-1267	75	23	iff	iff	VERB
ap-1267	75	24	the	the	DET
ap-1267	75	25	element	element	NOUN
ap-1267	75	26	∨	∨	NOUN
ap-1267	75	27	e	e	PROPN
ap-1267	75	28	d	d	NOUN
ap-1267	75	29	exists	exist	VERB
ap-1267	75	30	and	and	CCONJ
ap-1267	75	31	they	they	PRON
ap-1267	75	32	are	be	AUX
ap-1267	75	33	equal	equal	ADJ
ap-1267	75	34	.	.	PUNCT
ap-1267	76	1	clearly	clearly	ADV
ap-1267	76	2	,	,	PUNCT
ap-1267	76	3	any	any	DET
ap-1267	76	4	bifull	bifull	DET
ap-1267	76	5	sub	sub	ADJ
ap-1267	76	6	-	-	ADJ
ap-1267	76	7	effect	effect	ADJ
ap-1267	76	8	algebra	algebra	NOUN
ap-1267	76	9	of	of	ADP
ap-1267	76	10	e	e	PROPN
ap-1267	76	11	is	be	AUX
ap-1267	76	12	full	full	ADJ
ap-1267	76	13	but	but	CCONJ
ap-1267	76	14	not	not	PART
ap-1267	76	15	conversely	conversely	ADV
ap-1267	76	16	(	(	PUNCT
ap-1267	76	17	see	see	VERB
ap-1267	76	18	[	[	X
ap-1267	76	19	12	12	NUM
ap-1267	76	20	]	]	NUM
ap-1267	76	21	)	)	PUNCT
ap-1267	76	22	.	.	PUNCT
ap-1267	77	1	the	the	DET
ap-1267	77	2	notion	notion	NOUN
ap-1267	77	3	of	of	ADP
ap-1267	77	4	a	a	DET
ap-1267	77	5	central	central	ADJ
ap-1267	77	6	element	element	NOUN
ap-1267	77	7	of	of	ADP
ap-1267	77	8	an	an	DET
ap-1267	77	9	effect	effect	NOUN
ap-1267	77	10	algebra	algebra	NOUN
ap-1267	77	11	e	e	NOUN
ap-1267	77	12	was	be	AUX
ap-1267	77	13	introduced	introduce	VERB
ap-1267	77	14	by	by	ADP
ap-1267	77	15	greechie	greechie	NOUN
ap-1267	77	16	-	-	PUNCT
ap-1267	77	17	foulispulmannová	foulispulmannová	NOUN
ap-1267	78	1	[	[	X
ap-1267	78	2	6	6	NUM
ap-1267	78	3	]	]	PUNCT
ap-1267	78	4	.	.	PUNCT
ap-1267	79	1	an	an	DET
ap-1267	79	2	element	element	NOUN
ap-1267	79	3	c	c	PROPN
ap-1267	79	4	∈	∈	PROPN
ap-1267	79	5	e	e	NOUN
ap-1267	79	6	is	be	AUX
ap-1267	79	7	called	call	VERB
ap-1267	79	8	central	central	ADJ
ap-1267	79	9	(	(	PUNCT
ap-1267	79	10	see	see	VERB
ap-1267	79	11	[	[	X
ap-1267	79	12	18	18	NUM
ap-1267	79	13	]	]	SYM
ap-1267	79	14	)	)	PUNCT
ap-1267	79	15	iff	iff	PROPN
ap-1267	79	16	for	for	SCONJ
ap-1267	79	17	every	every	DET
ap-1267	79	18	x	x	SYM
ap-1267	79	19	∈	∈	PROPN
ap-1267	79	20	e	e	NOUN
ap-1267	79	21	there	there	PRON
ap-1267	79	22	exist	exist	VERB
ap-1267	79	23	x	x	PUNCT
ap-1267	79	24	∧	∧	PROPN
ap-1267	79	25	c	c	PROPN
ap-1267	79	26	and	and	CCONJ
ap-1267	79	27	x	x	PART
ap-1267	79	28	∧	∧	PROPN
ap-1267	79	29	c′	c′	NOUN
ap-1267	79	30	and	and	CCONJ
ap-1267	79	31	x	x	SYM
ap-1267	79	32	=	=	SYM
ap-1267	79	33	(	(	PUNCT
ap-1267	79	34	x	x	PART
ap-1267	79	35	∧	∧	NOUN
ap-1267	79	36	c	c	NOUN
ap-1267	79	37	)	)	PUNCT
ap-1267	79	38	∨	∨	NOUN
ap-1267	79	39	(	(	PUNCT
ap-1267	79	40	x	x	X
ap-1267	79	41	∧	∧	PROPN
ap-1267	79	42	c′	c′	NUM
ap-1267	79	43	)	)	PUNCT
ap-1267	79	44	.	.	PUNCT
ap-1267	80	1	the	the	DET
ap-1267	80	2	center	center	PROPN
ap-1267	80	3	c(e	c(e	PROPN
ap-1267	80	4	)	)	PUNCT
ap-1267	80	5	of	of	ADP
ap-1267	80	6	e	e	PROPN
ap-1267	80	7	is	be	AUX
ap-1267	80	8	the	the	DET
ap-1267	80	9	set	set	NOUN
ap-1267	80	10	of	of	ADP
ap-1267	80	11	all	all	DET
ap-1267	80	12	central	central	ADJ
ap-1267	80	13	elements	element	NOUN
ap-1267	80	14	of	of	ADP
ap-1267	80	15	e.	e.	PROPN
ap-1267	80	16	moreover	moreover	ADV
ap-1267	80	17	,	,	PUNCT
ap-1267	80	18	c(e	c(e	NOUN
ap-1267	80	19	)	)	PUNCT
ap-1267	80	20	is	be	AUX
ap-1267	80	21	a	a	DET
ap-1267	80	22	boolean	boolean	ADJ
ap-1267	80	23	algebra	algebra	NOUN
ap-1267	80	24	,	,	PUNCT
ap-1267	80	25	see	see	VERB
ap-1267	80	26	[	[	X
ap-1267	80	27	6	6	NUM
ap-1267	80	28	]	]	PUNCT
ap-1267	80	29	.	.	PUNCT
ap-1267	81	1	if	if	SCONJ
ap-1267	81	2	e	e	PROPN
ap-1267	81	3	is	be	AUX
ap-1267	81	4	a	a	DET
ap-1267	81	5	lattice	lattice	ADJ
ap-1267	81	6	effect	effect	NOUN
ap-1267	81	7	algebra	algebra	NOUN
ap-1267	81	8	then	then	ADV
ap-1267	81	9	z	z	PROPN
ap-1267	81	10	∈	∈	PROPN
ap-1267	81	11	e	e	NOUN
ap-1267	81	12	is	be	AUX
ap-1267	81	13	central	central	ADJ
ap-1267	81	14	iff	iff	PROPN
ap-1267	81	15	z	z	PROPN
ap-1267	81	16	∧	∧	PROPN
ap-1267	81	17	z′	z′	NUM
ap-1267	81	18	=	=	SYM
ap-1267	81	19	0	0	NUM
ap-1267	82	1	and	and	CCONJ
ap-1267	82	2	z	z	NOUN
ap-1267	82	3	↔	↔	PROPN
ap-1267	82	4	x	x	PUNCT
ap-1267	82	5	for	for	ADP
ap-1267	82	6	all	all	DET
ap-1267	82	7	x	x	SYM
ap-1267	82	8	∈	∈	PROPN
ap-1267	82	9	e	e	NOUN
ap-1267	82	10	,	,	PUNCT
ap-1267	82	11	see	see	VERB
ap-1267	82	12	[	[	X
ap-1267	82	13	19	19	NUM
ap-1267	82	14	]	]	PUNCT
ap-1267	82	15	.	.	PUNCT
ap-1267	83	1	thus	thus	ADV
ap-1267	83	2	in	in	ADP
ap-1267	83	3	a	a	DET
ap-1267	83	4	lattice	lattice	ADJ
ap-1267	83	5	effect	effect	NOUN
ap-1267	83	6	algebra	algebra	NOUN
ap-1267	83	7	e	e	NOUN
ap-1267	83	8	,	,	PUNCT
ap-1267	83	9	c(e	c(e	NOUN
ap-1267	83	10	)	)	PUNCT
ap-1267	83	11	=	=	SYM
ap-1267	83	12	b(e	b(e	ADJ
ap-1267	83	13	)	)	PUNCT
ap-1267	83	14	∩	∩	PROPN
ap-1267	83	15	s(e	s(e	PROPN
ap-1267	83	16	)	)	PUNCT
ap-1267	83	17	,	,	PUNCT
ap-1267	83	18	where	where	SCONJ
ap-1267	83	19	b(e	b(e	ADJ
ap-1267	83	20	)	)	PUNCT
ap-1267	83	21	=	=	SYM
ap-1267	83	22	⋂	⋂	PROPN
ap-1267	83	23	{	{	PUNCT
ap-1267	83	24	m	m	PROPN
ap-1267	83	25	⊆	⊆	NUM
ap-1267	83	26	e	e	NOUN
ap-1267	84	1	|	|	ADV
ap-1267	84	2	m	m	VERB
ap-1267	84	3	is	be	AUX
ap-1267	84	4	a	a	DET
ap-1267	84	5	block	block	NOUN
ap-1267	84	6	of	of	ADP
ap-1267	84	7	e	e	NOUN
ap-1267	84	8	}	}	PUNCT
ap-1267	84	9	is	be	AUX
ap-1267	84	10	called	call	VERB
ap-1267	84	11	the	the	DET
ap-1267	84	12	compatibility	compatibility	NOUN
ap-1267	84	13	center	center	NOUN
ap-1267	84	14	of	of	ADP
ap-1267	84	15	e.	e.	PROPN
ap-1267	84	16	52	52	NUM
ap-1267	84	17	acta	acta	PROPN
ap-1267	84	18	polytechnica	polytechnica	PROPN
ap-1267	84	19	vol	vol	NOUN
ap-1267	84	20	.	.	PUNCT
ap-1267	85	1	50	50	NUM
ap-1267	85	2	no	no	NOUN
ap-1267	85	3	.	.	PUNCT
ap-1267	86	1	5/2010	5/2010	PRON
ap-1267	86	2	an	an	DET
ap-1267	86	3	effect	effect	NOUN
ap-1267	86	4	algebra	algebra	NOUN
ap-1267	86	5	e	e	NOUN
ap-1267	86	6	is	be	AUX
ap-1267	86	7	called	call	VERB
ap-1267	86	8	centrally	centrally	ADV
ap-1267	86	9	dominating	dominating	NOUN
ap-1267	86	10	(	(	PUNCT
ap-1267	86	11	see	see	VERB
ap-1267	86	12	also	also	ADV
ap-1267	86	13	[	[	X
ap-1267	86	14	5	5	NUM
ap-1267	86	15	]	]	PUNCT
ap-1267	86	16	for	for	ADP
ap-1267	86	17	the	the	DET
ap-1267	86	18	notion	notion	NOUN
ap-1267	86	19	central	central	ADJ
ap-1267	86	20	cover	cover	NOUN
ap-1267	86	21	)	)	PUNCT
ap-1267	86	22	if	if	SCONJ
ap-1267	86	23	for	for	ADP
ap-1267	86	24	every	every	DET
ap-1267	86	25	x	x	SYM
ap-1267	86	26	∈	∈	PROPN
ap-1267	86	27	e	e	NOUN
ap-1267	86	28	there	there	PRON
ap-1267	86	29	exists	exist	VERB
ap-1267	86	30	cx	cx	PROPN
ap-1267	86	31	∈	∈	PROPN
ap-1267	86	32	c(e	c(e	NOUN
ap-1267	86	33	)	)	PUNCT
ap-1267	86	34	such	such	ADJ
ap-1267	86	35	that	that	PRON
ap-1267	86	36	cx	cx	PROPN
ap-1267	86	37	=	=	PUNCT
ap-1267	86	38	∧	∧	PROPN
ap-1267	86	39	e	e	X
ap-1267	86	40	{	{	PUNCT
ap-1267	86	41	c	c	PROPN
ap-1267	86	42	∈	∈	PROPN
ap-1267	86	43	c(e	c(e	NOUN
ap-1267	86	44	)	)	PUNCT
ap-1267	87	1	|	|	ADV
ap-1267	87	2	x	x	SYM
ap-1267	87	3	≤	≤	NUM
ap-1267	87	4	c	c	X
ap-1267	87	5	}	}	PUNCT
ap-1267	87	6	=	=	NOUN
ap-1267	87	7	∧	∧	NOUN
ap-1267	87	8	c(e	c(e	NOUN
ap-1267	87	9	)	)	PUNCT
ap-1267	87	10	{	{	PUNCT
ap-1267	87	11	c	c	NOUN
ap-1267	87	12	∈	∈	PROPN
ap-1267	87	13	c(e	c(e	NOUN
ap-1267	87	14	)	)	PUNCT
ap-1267	88	1	|	|	ADV
ap-1267	88	2	x	x	SYM
ap-1267	88	3	≤	≤	PROPN
ap-1267	88	4	c	c	NOUN
ap-1267	88	5	}	}	PUNCT
ap-1267	88	6	.	.	PUNCT
ap-1267	89	1	an	an	DET
ap-1267	89	2	element	element	NOUN
ap-1267	89	3	a	a	PRON
ap-1267	89	4	of	of	ADP
ap-1267	89	5	a	a	DET
ap-1267	89	6	lattice	lattice	NOUN
ap-1267	89	7	l	l	NOUN
ap-1267	89	8	is	be	AUX
ap-1267	89	9	called	call	VERB
ap-1267	89	10	compact	compact	ADJ
ap-1267	89	11	iff	iff	NOUN
ap-1267	89	12	,	,	PUNCT
ap-1267	89	13	for	for	ADP
ap-1267	89	14	any	any	DET
ap-1267	89	15	d	d	PROPN
ap-1267	89	16	⊆	⊆	NUM
ap-1267	89	17	l	l	NOUN
ap-1267	89	18	,	,	PUNCT
ap-1267	89	19	a	a	DET
ap-1267	89	20	≤	≤	NUM
ap-1267	89	21	∨	∨	NUM
ap-1267	89	22	d	d	PROPN
ap-1267	89	23	implies	imply	VERB
ap-1267	89	24	a	a	DET
ap-1267	89	25	≤	≤	NUM
ap-1267	89	26	∨	∨	NUM
ap-1267	89	27	f	f	NOUN
ap-1267	89	28	for	for	ADP
ap-1267	89	29	some	some	DET
ap-1267	89	30	finite	finite	NOUN
ap-1267	89	31	f	f	PROPN
ap-1267	89	32	⊆	⊆	NUM
ap-1267	89	33	d.	d.	PROPN
ap-1267	89	34	a	a	DET
ap-1267	89	35	lattice	lattice	PROPN
ap-1267	89	36	l	l	NOUN
ap-1267	89	37	is	be	AUX
ap-1267	89	38	called	call	VERB
ap-1267	89	39	compactly	compactly	ADV
ap-1267	89	40	generated	generate	VERB
ap-1267	89	41	iff	iff	PROPN
ap-1267	89	42	every	every	DET
ap-1267	89	43	element	element	NOUN
ap-1267	89	44	of	of	ADP
ap-1267	89	45	l	l	NOUN
ap-1267	89	46	is	be	AUX
ap-1267	89	47	a	a	DET
ap-1267	89	48	join	join	NOUN
ap-1267	89	49	of	of	ADP
ap-1267	89	50	compact	compact	ADJ
ap-1267	89	51	elements	element	NOUN
ap-1267	89	52	.	.	PUNCT
ap-1267	90	1	3	3	NUM
ap-1267	90	2	sharply	sharply	ADV
ap-1267	90	3	orthocomplete	orthocomplete	ADJ
ap-1267	90	4	effect	effect	NOUN
ap-1267	90	5	algebras	algebra	NOUN
ap-1267	90	6	in	in	ADP
ap-1267	90	7	an	an	DET
ap-1267	90	8	effect	effect	NOUN
ap-1267	90	9	algebra	algebra	NOUN
ap-1267	90	10	e	e	NOUN
ap-1267	90	11	the	the	DET
ap-1267	90	12	set	set	NOUN
ap-1267	90	13	s(e	s(e	PROPN
ap-1267	90	14	)	)	PUNCT
ap-1267	90	15	=	=	PRON
ap-1267	91	1	{	{	PUNCT
ap-1267	91	2	x	x	PUNCT
ap-1267	91	3	∈	∈	NOUN
ap-1267	91	4	e	e	NOUN
ap-1267	91	5	|	|	ADV
ap-1267	91	6	x	x	PART
ap-1267	91	7	∧	∧	NOUN
ap-1267	91	8	x′	x′	X
ap-1267	91	9	=	=	SYM
ap-1267	91	10	0	0	NUM
ap-1267	91	11	}	}	PUNCT
ap-1267	91	12	of	of	ADP
ap-1267	91	13	sharp	sharp	ADJ
ap-1267	91	14	elements	element	NOUN
ap-1267	91	15	plays	play	VERB
ap-1267	91	16	an	an	DET
ap-1267	91	17	important	important	ADJ
ap-1267	91	18	role	role	NOUN
ap-1267	91	19	.	.	PUNCT
ap-1267	92	1	in	in	ADP
ap-1267	92	2	some	some	DET
ap-1267	92	3	sense	sense	NOUN
ap-1267	92	4	we	we	PRON
ap-1267	92	5	can	can	AUX
ap-1267	92	6	say	say	VERB
ap-1267	92	7	that	that	SCONJ
ap-1267	92	8	an	an	DET
ap-1267	92	9	effect	effect	NOUN
ap-1267	92	10	algebra	algebra	NOUN
ap-1267	92	11	e	e	NOUN
ap-1267	92	12	is	be	AUX
ap-1267	92	13	a	a	DET
ap-1267	92	14	“	"	PUNCT
ap-1267	92	15	smeared	smear	VERB
ap-1267	92	16	set	set	VERB
ap-1267	92	17	s(e	s(e	PROPN
ap-1267	92	18	)	)	PUNCT
ap-1267	92	19	”	"	PUNCT
ap-1267	92	20	of	of	ADP
ap-1267	92	21	its	its	PRON
ap-1267	92	22	sharp	sharp	ADJ
ap-1267	92	23	elements	element	NOUN
ap-1267	92	24	,	,	PUNCT
ap-1267	92	25	while	while	SCONJ
ap-1267	92	26	unsharp	unsharp	ADJ
ap-1267	92	27	effects	effect	NOUN
ap-1267	92	28	are	be	AUX
ap-1267	92	29	important	important	ADJ
ap-1267	92	30	in	in	ADP
ap-1267	92	31	studies	study	NOUN
ap-1267	92	32	of	of	ADP
ap-1267	92	33	unsharp	unsharp	ADJ
ap-1267	92	34	measurements	measurement	NOUN
ap-1267	92	35	[	[	X
ap-1267	92	36	4	4	NUM
ap-1267	92	37	,	,	PUNCT
ap-1267	92	38	2	2	NUM
ap-1267	92	39	]	]	PUNCT
ap-1267	92	40	.	.	PUNCT
ap-1267	93	1	s.	s.	PROPN
ap-1267	93	2	gudder	gudder	PROPN
ap-1267	93	3	proved	prove	VERB
ap-1267	93	4	(	(	PUNCT
ap-1267	93	5	see	see	VERB
ap-1267	93	6	[	[	X
ap-1267	93	7	8	8	NUM
ap-1267	93	8	]	]	SYM
ap-1267	93	9	)	)	PUNCT
ap-1267	93	10	that	that	SCONJ
ap-1267	93	11	,	,	PUNCT
ap-1267	93	12	in	in	ADP
ap-1267	93	13	standard	standard	ADJ
ap-1267	93	14	hilbert	hilbert	NOUN
ap-1267	93	15	space	space	NOUN
ap-1267	93	16	effect	effect	NOUN
ap-1267	93	17	algebra	algebra	VERB
ap-1267	93	18	e(h	e(h	PROPN
ap-1267	93	19	)	)	PUNCT
ap-1267	93	20	of	of	ADP
ap-1267	93	21	bounded	bounded	PROPN
ap-1267	93	22	operators	operator	NOUN
ap-1267	93	23	a	a	PRON
ap-1267	93	24	on	on	ADP
ap-1267	93	25	a	a	DET
ap-1267	93	26	hilbert	hilbert	NOUN
ap-1267	93	27	space	space	NOUN
ap-1267	93	28	h	h	NOUN
ap-1267	93	29	between	between	ADP
ap-1267	93	30	null	null	ADJ
ap-1267	93	31	operator	operator	NOUN
ap-1267	93	32	and	and	CCONJ
ap-1267	93	33	identity	identity	NOUN
ap-1267	93	34	operator	operator	NOUN
ap-1267	93	35	,	,	PUNCT
ap-1267	93	36	which	which	PRON
ap-1267	93	37	are	be	AUX
ap-1267	93	38	endowed	endow	VERB
ap-1267	93	39	with	with	ADP
ap-1267	93	40	usual	usual	ADJ
ap-1267	93	41	+	+	CCONJ
ap-1267	93	42	defined	define	VERB
ap-1267	93	43	iff	iff	PROPN
ap-1267	93	44	a	a	DET
ap-1267	93	45	+	+	NOUN
ap-1267	93	46	b	b	NOUN
ap-1267	93	47	is	be	AUX
ap-1267	93	48	in	in	ADP
ap-1267	93	49	e(h	e(h	PROPN
ap-1267	93	50	)	)	PUNCT
ap-1267	93	51	,	,	PUNCT
ap-1267	93	52	the	the	DET
ap-1267	93	53	set	set	NOUN
ap-1267	93	54	s(e(h	s(e(h	PROPN
ap-1267	93	55	)	)	PUNCT
ap-1267	93	56	)	)	PUNCT
ap-1267	93	57	of	of	ADP
ap-1267	93	58	sharp	sharp	ADJ
ap-1267	93	59	elements	element	NOUN
ap-1267	93	60	forms	form	VERB
ap-1267	93	61	an	an	DET
ap-1267	93	62	orthomodular	orthomodular	ADJ
ap-1267	93	63	lattice	lattice	NOUN
ap-1267	93	64	of	of	ADP
ap-1267	93	65	projection	projection	NOUN
ap-1267	93	66	operators	operator	NOUN
ap-1267	93	67	on	on	ADP
ap-1267	93	68	h	h	NOUN
ap-1267	93	69	.	.	PUNCT
ap-1267	94	1	further	far	ADV
ap-1267	94	2	in	in	ADP
ap-1267	94	3	[	[	X
ap-1267	94	4	8	8	NUM
ap-1267	94	5	,	,	PUNCT
ap-1267	94	6	theorem	theorem	VERB
ap-1267	94	7	2.2	2.2	NUM
ap-1267	94	8	]	]	PUNCT
ap-1267	94	9	it	it	PRON
ap-1267	94	10	was	be	AUX
ap-1267	94	11	shown	show	VERB
ap-1267	94	12	that	that	SCONJ
ap-1267	94	13	in	in	ADP
ap-1267	94	14	every	every	DET
ap-1267	94	15	sharply	sharply	ADV
ap-1267	94	16	dominating	dominating	NOUN
ap-1267	94	17	effect	effect	NOUN
ap-1267	94	18	algebra	algebra	VERB
ap-1267	94	19	the	the	DET
ap-1267	94	20	set	set	NOUN
ap-1267	94	21	s(e	s(e	PROPN
ap-1267	94	22	)	)	PUNCT
ap-1267	94	23	is	be	AUX
ap-1267	94	24	a	a	DET
ap-1267	94	25	sub	sub	ADJ
ap-1267	94	26	-	-	ADJ
ap-1267	94	27	effect	effect	ADJ
ap-1267	94	28	algebra	algebra	NOUN
ap-1267	94	29	of	of	ADP
ap-1267	94	30	e.	e.	PROPN
ap-1267	94	31	moreover	moreover	ADV
ap-1267	94	32	,	,	PUNCT
ap-1267	94	33	in	in	ADP
ap-1267	94	34	[	[	PUNCT
ap-1267	94	35	7	7	NUM
ap-1267	94	36	,	,	PUNCT
ap-1267	94	37	theorem	theorem	VERB
ap-1267	94	38	2.6	2.6	NUM
ap-1267	94	39	]	]	PUNCT
ap-1267	94	40	it	it	PRON
ap-1267	94	41	is	be	AUX
ap-1267	94	42	proved	prove	VERB
ap-1267	94	43	that	that	SCONJ
ap-1267	94	44	in	in	ADP
ap-1267	94	45	every	every	DET
ap-1267	94	46	s	s	NOUN
ap-1267	94	47	-	-	PUNCT
ap-1267	94	48	dominating	dominating	ADJ
ap-1267	94	49	effect	effect	NOUN
ap-1267	94	50	algebra	algebra	NOUN
ap-1267	94	51	e	e	NOUN
ap-1267	94	52	the	the	DET
ap-1267	94	53	set	set	NOUN
ap-1267	94	54	s(e	s(e	PROPN
ap-1267	94	55	)	)	PUNCT
ap-1267	94	56	is	be	AUX
ap-1267	94	57	an	an	DET
ap-1267	94	58	orthomodular	orthomodular	ADJ
ap-1267	94	59	lattice	lattice	NOUN
ap-1267	94	60	.	.	PUNCT
ap-1267	95	1	we	we	PRON
ap-1267	95	2	are	be	AUX
ap-1267	95	3	going	go	VERB
ap-1267	95	4	to	to	PART
ap-1267	95	5	show	show	VERB
ap-1267	95	6	that	that	SCONJ
ap-1267	95	7	in	in	ADP
ap-1267	95	8	this	this	DET
ap-1267	95	9	case	case	NOUN
ap-1267	95	10	s(e	s(e	PROPN
ap-1267	95	11	)	)	PUNCT
ap-1267	95	12	is	be	AUX
ap-1267	95	13	bifull	bifull	PROPN
ap-1267	95	14	in	in	ADP
ap-1267	95	15	e.	e.	PROPN
ap-1267	95	16	theorem	theorem	PROPN
ap-1267	95	17	1	1	NUM
ap-1267	95	18	let	let	VERB
ap-1267	95	19	e	e	PRON
ap-1267	95	20	be	be	AUX
ap-1267	95	21	an	an	DET
ap-1267	95	22	s	s	NOUN
ap-1267	95	23	-	-	PUNCT
ap-1267	95	24	dominating	dominating	ADJ
ap-1267	95	25	effect	effect	NOUN
ap-1267	95	26	algebra	algebra	NOUN
ap-1267	95	27	.	.	PUNCT
ap-1267	96	1	then	then	ADV
ap-1267	96	2	s(e	s(e	PROPN
ap-1267	96	3	)	)	PUNCT
ap-1267	96	4	is	be	AUX
ap-1267	96	5	bifull	bifull	PROPN
ap-1267	96	6	in	in	ADP
ap-1267	96	7	e.	e.	PROPN
ap-1267	96	8	proof	proof	PROPN
ap-1267	96	9	.	.	PUNCT
ap-1267	97	1	let	let	VERB
ap-1267	97	2	s	s	PRON
ap-1267	97	3	⊆	⊆	NUM
ap-1267	97	4	s(e	s(e	PROPN
ap-1267	97	5	)	)	PUNCT
ap-1267	97	6	.	.	PUNCT
ap-1267	98	1	(	(	PUNCT
ap-1267	98	2	1	1	X
ap-1267	98	3	)	)	PUNCT
ap-1267	98	4	assume	assume	VERB
ap-1267	98	5	that	that	SCONJ
ap-1267	98	6	z	z	NOUN
ap-1267	98	7	=	=	SYM
ap-1267	98	8	∨	∨	NUM
ap-1267	98	9	s(e	s(e	PROPN
ap-1267	98	10	)	)	PUNCT
ap-1267	98	11	s	s	PART
ap-1267	98	12	∈	∈	PROPN
ap-1267	98	13	s(e	s(e	PROPN
ap-1267	98	14	)	)	PUNCT
ap-1267	98	15	exists	exist	VERB
ap-1267	98	16	.	.	PUNCT
ap-1267	99	1	let	let	VERB
ap-1267	99	2	us	we	PRON
ap-1267	99	3	show	show	VERB
ap-1267	99	4	that	that	SCONJ
ap-1267	99	5	z	z	NOUN
ap-1267	99	6	is	be	AUX
ap-1267	99	7	the	the	DET
ap-1267	99	8	least	least	ADJ
ap-1267	99	9	upper	upper	ADJ
ap-1267	99	10	bound	bind	VERB
ap-1267	99	11	of	of	ADP
ap-1267	99	12	s	s	PROPN
ap-1267	99	13	in	in	ADP
ap-1267	99	14	e.	e.	PROPN
ap-1267	99	15	let	let	VERB
ap-1267	99	16	y	y	PROPN
ap-1267	99	17	∈	∈	PROPN
ap-1267	99	18	e	e	X
ap-1267	99	19	be	be	AUX
ap-1267	99	20	an	an	DET
ap-1267	99	21	upper	upper	ADJ
ap-1267	99	22	bound	bind	VERB
ap-1267	99	23	of	of	ADP
ap-1267	99	24	s.	s.	PROPN
ap-1267	99	25	then	then	ADV
ap-1267	99	26	y	y	PROPN
ap-1267	99	27	∧	∧	PROPN
ap-1267	99	28	z	z	PROPN
ap-1267	99	29	exists	exist	VERB
ap-1267	99	30	and	and	CCONJ
ap-1267	99	31	it	it	PRON
ap-1267	99	32	is	be	AUX
ap-1267	99	33	an	an	DET
ap-1267	99	34	upper	upper	ADJ
ap-1267	99	35	bound	bound	NOUN
ap-1267	99	36	of	of	ADP
ap-1267	99	37	s	s	PRON
ap-1267	99	38	as	as	ADV
ap-1267	99	39	well	well	ADV
ap-1267	99	40	.	.	PUNCT
ap-1267	100	1	hence	hence	ADV
ap-1267	100	2	,	,	PUNCT
ap-1267	100	3	for	for	ADP
ap-1267	100	4	any	any	DET
ap-1267	100	5	s	s	X
ap-1267	100	6	∈	∈	PROPN
ap-1267	100	7	s	s	NOUN
ap-1267	100	8	,	,	PUNCT
ap-1267	100	9	s	s	VERB
ap-1267	100	10	≤	≤	NUM
ap-1267	100	11	y	y	PROPN
ap-1267	100	12	∧	∧	PROPN
ap-1267	100	13	z.	z.	PROPN
ap-1267	100	14	as	as	SCONJ
ap-1267	100	15	e	e	PROPN
ap-1267	100	16	is	be	AUX
ap-1267	100	17	sharply	sharply	ADV
ap-1267	100	18	dominating	dominate	VERB
ap-1267	100	19	,	,	PUNCT
ap-1267	100	20	there	there	PRON
ap-1267	100	21	exists	exist	VERB
ap-1267	100	22	a	a	DET
ap-1267	100	23	greatest	great	ADJ
ap-1267	100	24	sharp	sharp	ADJ
ap-1267	100	25	element	element	NOUN
ap-1267	100	26	ỹ	ỹ	PROPN
ap-1267	100	27	∧	∧	PROPN
ap-1267	100	28	z	z	NOUN
ap-1267	100	29	≤	≤	NOUN
ap-1267	100	30	y	y	PROPN
ap-1267	100	31	∧	∧	PROPN
ap-1267	100	32	z	z	PROPN
ap-1267	100	33	this	this	DET
ap-1267	100	34	yields	yield	VERB
ap-1267	100	35	that	that	PRON
ap-1267	100	36	s	s	VERB
ap-1267	100	37	≤	≤	NOUN
ap-1267	101	1	ỹ	ỹ	PROPN
ap-1267	101	2	∧	∧	PROPN
ap-1267	101	3	z	z	NOUN
ap-1267	101	4	≤	≤	NOUN
ap-1267	101	5	y	y	PROPN
ap-1267	101	6	∧	∧	PROPN
ap-1267	101	7	z	z	PROPN
ap-1267	101	8	,	,	PUNCT
ap-1267	101	9	for	for	ADP
ap-1267	101	10	all	all	DET
ap-1267	101	11	s	s	PART
ap-1267	101	12	∈	∈	PROPN
ap-1267	101	13	s	s	NOUN
ap-1267	101	14	,	,	PUNCT
ap-1267	101	15	ỹ	ỹ	PROPN
ap-1267	101	16	∧	∧	PROPN
ap-1267	101	17	z	z	PROPN
ap-1267	101	18	∈	∈	PROPN
ap-1267	101	19	s(e	s(e	PROPN
ap-1267	101	20	)	)	PUNCT
ap-1267	101	21	.	.	PUNCT
ap-1267	102	1	hence	hence	ADV
ap-1267	102	2	z	z	NOUN
ap-1267	102	3	≤	≤	PUNCT
ap-1267	102	4	ỹ	ỹ	PROPN
ap-1267	102	5	∧	∧	PROPN
ap-1267	102	6	z	z	NOUN
ap-1267	102	7	≤	≤	NOUN
ap-1267	102	8	y	y	PROPN
ap-1267	102	9	∧	∧	PROPN
ap-1267	102	10	z	z	NOUN
ap-1267	102	11	≤	≤	PROPN
ap-1267	103	1	z.	z.	PROPN
ap-1267	103	2	then	then	ADV
ap-1267	103	3	z	z	PROPN
ap-1267	103	4	=	=	SYM
ap-1267	103	5	y	y	PROPN
ap-1267	103	6	∧	∧	PROPN
ap-1267	103	7	z	z	NOUN
ap-1267	103	8	≤	≤	NOUN
ap-1267	103	9	y	y	PROPN
ap-1267	103	10	i.e.	i.e.	X
ap-1267	103	11	,	,	PUNCT
ap-1267	103	12	z	z	NOUN
ap-1267	103	13	is	be	AUX
ap-1267	103	14	really	really	ADV
ap-1267	103	15	the	the	DET
ap-1267	103	16	least	least	ADV
ap-1267	103	17	upper	upper	ADJ
ap-1267	103	18	bound	bind	VERB
ap-1267	103	19	of	of	ADP
ap-1267	103	20	s	s	PROPN
ap-1267	103	21	in	in	ADP
ap-1267	103	22	e.	e.	PROPN
ap-1267	103	23	(	(	PUNCT
ap-1267	103	24	2	2	X
ap-1267	103	25	)	)	PUNCT
ap-1267	103	26	conversely	conversely	ADV
ap-1267	103	27	,	,	PUNCT
ap-1267	103	28	let	let	VERB
ap-1267	103	29	z	z	NOUN
ap-1267	103	30	=	=	PUNCT
ap-1267	104	1	∨	∨	NUM
ap-1267	104	2	e	e	NOUN
ap-1267	104	3	s	s	PROPN
ap-1267	104	4	∈	∈	NOUN
ap-1267	104	5	e	e	NOUN
ap-1267	104	6	exist	exist	VERB
ap-1267	104	7	.	.	PUNCT
ap-1267	105	1	let	let	VERB
ap-1267	105	2	y	y	PROPN
ap-1267	105	3	∈	∈	PROPN
ap-1267	105	4	s(e	s(e	PROPN
ap-1267	105	5	)	)	PUNCT
ap-1267	105	6	be	be	VERB
ap-1267	105	7	an	an	DET
ap-1267	105	8	upper	upper	ADJ
ap-1267	105	9	bound	bound	NOUN
ap-1267	105	10	of	of	ADP
ap-1267	105	11	s	s	PROPN
ap-1267	105	12	in	in	ADP
ap-1267	105	13	s(e	s(e	PROPN
ap-1267	105	14	)	)	PUNCT
ap-1267	105	15	.	.	PUNCT
ap-1267	106	1	then	then	ADV
ap-1267	106	2	y	y	PROPN
ap-1267	106	3	∧	∧	PROPN
ap-1267	106	4	z	z	PROPN
ap-1267	106	5	exists	exist	VERB
ap-1267	106	6	and	and	CCONJ
ap-1267	106	7	it	it	PRON
ap-1267	106	8	is	be	AUX
ap-1267	106	9	again	again	ADV
ap-1267	106	10	an	an	DET
ap-1267	106	11	upper	upper	ADJ
ap-1267	106	12	bound	bound	NOUN
ap-1267	106	13	of	of	ADP
ap-1267	106	14	s.	s.	PROPN
ap-1267	106	15	as	as	ADP
ap-1267	106	16	in	in	ADP
ap-1267	106	17	(	(	PUNCT
ap-1267	106	18	1	1	X
ap-1267	106	19	)	)	PUNCT
ap-1267	106	20	we	we	PRON
ap-1267	106	21	have	have	VERB
ap-1267	106	22	that	that	PRON
ap-1267	106	23	ỹ	ỹ	PROPN
ap-1267	106	24	∧	∧	PROPN
ap-1267	106	25	z	z	PROPN
ap-1267	106	26	is	be	AUX
ap-1267	106	27	the	the	DET
ap-1267	106	28	greatest	great	ADJ
ap-1267	106	29	sharp	sharp	ADJ
ap-1267	106	30	element	element	NOUN
ap-1267	106	31	under	under	ADP
ap-1267	106	32	y	y	PROPN
ap-1267	106	33	∧z	∧z	PROPN
ap-1267	106	34	and	and	CCONJ
ap-1267	106	35	hence	hence	ADV
ap-1267	106	36	s	s	VERB
ap-1267	106	37	≤	≤	NUM
ap-1267	106	38	ỹ	ỹ	PROPN
ap-1267	106	39	∧	∧	PROPN
ap-1267	106	40	z	z	NOUN
ap-1267	106	41	≤	≤	NOUN
ap-1267	106	42	y	y	PROPN
ap-1267	106	43	∧z	∧z	PROPN
ap-1267	106	44	≤	≤	PROPN
ap-1267	107	1	z	z	PROPN
ap-1267	107	2	,	,	PUNCT
ap-1267	107	3	for	for	ADP
ap-1267	107	4	all	all	DET
ap-1267	107	5	s	s	PROPN
ap-1267	107	6	∈	∈	PROPN
ap-1267	107	7	s.	s.	PROPN
ap-1267	107	8	this	this	PRON
ap-1267	107	9	gives	give	VERB
ap-1267	107	10	that	that	PRON
ap-1267	107	11	z	z	NOUN
ap-1267	107	12	=	=	SYM
ap-1267	107	13	ỹ	ỹ	PROPN
ap-1267	107	14	∧	∧	PROPN
ap-1267	107	15	z	z	PROPN
ap-1267	107	16	∈	∈	PROPN
ap-1267	107	17	s(e	s(e	PROPN
ap-1267	107	18	)	)	PUNCT
ap-1267	107	19	.	.	PUNCT
ap-1267	108	1	thus	thus	ADV
ap-1267	108	2	z	z	X
ap-1267	108	3	=	=	SYM
ap-1267	108	4	∨	∨	NUM
ap-1267	108	5	s(e	s(e	PROPN
ap-1267	108	6	)	)	PUNCT
ap-1267	108	7	s	s	PART
ap-1267	108	8	∈	∈	PROPN
ap-1267	108	9	s(e	s(e	PROPN
ap-1267	108	10	)	)	PUNCT
ap-1267	108	11	.	.	PUNCT
ap-1267	109	1	corollary	corollary	ADJ
ap-1267	109	2	1	1	NUM
ap-1267	109	3	if	if	SCONJ
ap-1267	109	4	e	e	NOUN
ap-1267	109	5	is	be	AUX
ap-1267	109	6	a	a	DET
ap-1267	109	7	sharply	sharply	ADV
ap-1267	109	8	dominating	dominate	VERB
ap-1267	109	9	lattice	lattice	NOUN
ap-1267	109	10	effect	effect	NOUN
ap-1267	109	11	algebra	algebra	NOUN
ap-1267	109	12	then	then	ADV
ap-1267	109	13	s(e	s(e	PROPN
ap-1267	109	14	)	)	PUNCT
ap-1267	109	15	is	be	AUX
ap-1267	109	16	bifull	bifull	PROPN
ap-1267	109	17	in	in	ADP
ap-1267	109	18	e.	e.	PROPN
ap-1267	109	19	definition	definition	NOUN
ap-1267	109	20	4	4	NUM
ap-1267	109	21	an	an	DET
ap-1267	109	22	effect	effect	NOUN
ap-1267	109	23	algebra	algebra	NOUN
ap-1267	109	24	e	e	NOUN
ap-1267	109	25	is	be	AUX
ap-1267	109	26	called	call	VERB
ap-1267	109	27	sharply	sharply	ADV
ap-1267	109	28	orthocomplete	orthocomplete	ADJ
ap-1267	109	29	(	(	PUNCT
ap-1267	109	30	centrally	centrally	ADV
ap-1267	109	31	orthocomplete	orthocomplete	ADJ
ap-1267	109	32	(	(	PUNCT
ap-1267	109	33	see	see	VERB
ap-1267	109	34	[	[	X
ap-1267	109	35	5	5	NUM
ap-1267	109	36	]	]	NUM
ap-1267	109	37	)	)	PUNCT
ap-1267	109	38	)	)	PUNCT
ap-1267	110	1	if	if	SCONJ
ap-1267	110	2	for	for	ADP
ap-1267	110	3	any	any	DET
ap-1267	110	4	system	system	NOUN
ap-1267	110	5	(	(	PUNCT
ap-1267	110	6	xκ)κ∈h	xκ)κ∈h	NUM
ap-1267	110	7	of	of	ADP
ap-1267	110	8	elements	element	NOUN
ap-1267	110	9	of	of	ADP
ap-1267	110	10	e	e	PRON
ap-1267	110	11	such	such	ADJ
ap-1267	110	12	that	that	SCONJ
ap-1267	110	13	there	there	PRON
ap-1267	110	14	exists	exist	VERB
ap-1267	110	15	an	an	DET
ap-1267	110	16	orthogonal	orthogonal	ADJ
ap-1267	110	17	system	system	NOUN
ap-1267	110	18	(	(	PUNCT
ap-1267	110	19	wκ)κ∈h	wκ)κ∈h	NUM
ap-1267	110	20	,	,	PUNCT
ap-1267	110	21	wκ	wκ	PROPN
ap-1267	110	22	∈	∈	PROPN
ap-1267	110	23	s(e	s(e	PROPN
ap-1267	110	24	)	)	PUNCT
ap-1267	110	25	with	with	ADP
ap-1267	110	26	xκ	xκ	PROPN
ap-1267	110	27	≤	≤	PROPN
ap-1267	110	28	wκ	wκ	PROPN
ap-1267	110	29	,	,	PUNCT
ap-1267	110	30	κ	κ	PROPN
ap-1267	110	31	∈	∈	PROPN
ap-1267	110	32	h	h	NOUN
ap-1267	110	33	(	(	PUNCT
ap-1267	110	34	an	an	DET
ap-1267	110	35	orthogonal	orthogonal	ADJ
ap-1267	110	36	system	system	NOUN
ap-1267	110	37	(	(	PUNCT
ap-1267	110	38	cκ)κ∈h	cκ)κ∈h	NUM
ap-1267	110	39	,	,	PUNCT
ap-1267	110	40	cκ	cκ	ADP
ap-1267	110	41	∈	∈	NOUN
ap-1267	110	42	c(e	c(e	NOUN
ap-1267	110	43	)	)	PUNCT
ap-1267	110	44	with	with	ADP
ap-1267	110	45	xκ	xκ	NOUN
ap-1267	110	46	≤	≤	NUM
ap-1267	110	47	cκ	cκ	VERB
ap-1267	110	48	,	,	PUNCT
ap-1267	110	49	κ	κ	PROPN
ap-1267	110	50	∈	∈	PROPN
ap-1267	110	51	h	h	NOUN
ap-1267	110	52	)	)	PUNCT
ap-1267	110	53	there	there	ADV
ap-1267	110	54	exists⊕	exists⊕	SYM
ap-1267	110	55	{	{	PUNCT
ap-1267	110	56	xκ	xκ	NOUN
ap-1267	111	1	|	|	ADV
ap-1267	111	2	κ	κ	PROPN
ap-1267	111	3	∈	∈	PROPN
ap-1267	111	4	h	h	NOUN
ap-1267	111	5	}	}	PUNCT
ap-1267	111	6	=	=	NOUN
ap-1267	111	7	∨	∨	NOUN
ap-1267	111	8	e	e	X
ap-1267	111	9	{	{	PUNCT
ap-1267	111	10	⊕	⊕	PROPN
ap-1267	111	11	e	e	PROPN
ap-1267	111	12	{	{	PUNCT
ap-1267	111	13	xκ	xκ	NOUN
ap-1267	111	14	|	|	ADV
ap-1267	111	15	κ	κ	PROPN
ap-1267	111	16	∈	∈	PROPN
ap-1267	112	1	f	f	NOUN
ap-1267	112	2	}	}	PUNCT
ap-1267	112	3	|	|	ADV
ap-1267	112	4	f	f	PROPN
ap-1267	112	5	⊆	⊆	NUM
ap-1267	112	6	h	h	NOUN
ap-1267	112	7	,	,	PUNCT
ap-1267	112	8	f	f	PROPN
ap-1267	112	9	finite	finite	PROPN
ap-1267	112	10	}	}	PUNCT
ap-1267	112	11	.	.	PUNCT
ap-1267	113	1	theorem	theorem	NOUN
ap-1267	113	2	2	2	NUM
ap-1267	113	3	let	let	VERB
ap-1267	113	4	e	e	PRON
ap-1267	113	5	be	be	AUX
ap-1267	113	6	a	a	DET
ap-1267	113	7	sharply	sharply	ADV
ap-1267	113	8	orthocomplete	orthocomplete	ADJ
ap-1267	113	9	sdominating	sdominate	VERB
ap-1267	113	10	effect	effect	NOUN
ap-1267	113	11	algebra	algebra	NOUN
ap-1267	113	12	.	.	PUNCT
ap-1267	114	1	then	then	ADV
ap-1267	114	2	(	(	PUNCT
ap-1267	114	3	i	i	NOUN
ap-1267	114	4	)	)	PUNCT
ap-1267	114	5	s(e	s(e	PROPN
ap-1267	114	6	)	)	PUNCT
ap-1267	114	7	is	be	AUX
ap-1267	114	8	a	a	DET
ap-1267	114	9	complete	complete	ADJ
ap-1267	114	10	orthomodular	orthomodular	ADJ
ap-1267	114	11	lattice	lattice	NOUN
ap-1267	114	12	bifull	bifull	PROPN
ap-1267	114	13	in	in	ADP
ap-1267	114	14	e.	e.	PROPN
ap-1267	114	15	(	(	PUNCT
ap-1267	114	16	ii	ii	PROPN
ap-1267	114	17	)	)	PUNCT
ap-1267	114	18	c(e	c(e	NOUN
ap-1267	114	19	)	)	PUNCT
ap-1267	115	1	is	be	AUX
ap-1267	115	2	a	a	DET
ap-1267	115	3	complete	complete	ADJ
ap-1267	115	4	boolean	boolean	ADJ
ap-1267	115	5	algebra	algebra	NOUN
ap-1267	115	6	bifull	bifull	PROPN
ap-1267	115	7	in	in	ADP
ap-1267	115	8	e.	e.	PROPN
ap-1267	115	9	(	(	PUNCT
ap-1267	115	10	iii	iii	PROPN
ap-1267	115	11	)	)	PUNCT
ap-1267	115	12	e	e	NOUN
ap-1267	115	13	is	be	AUX
ap-1267	115	14	centrally	centrally	ADV
ap-1267	115	15	dominating	dominate	VERB
ap-1267	115	16	and	and	CCONJ
ap-1267	115	17	centrally	centrally	ADV
ap-1267	115	18	orthocomplete	orthocomplete	ADJ
ap-1267	115	19	.	.	PUNCT
ap-1267	116	1	(	(	PUNCT
ap-1267	116	2	iv	iv	X
ap-1267	116	3	)	)	PUNCT
ap-1267	116	4	if	if	SCONJ
ap-1267	116	5	c(e	c(e	NOUN
ap-1267	116	6	)	)	PUNCT
ap-1267	116	7	is	be	AUX
ap-1267	116	8	atomic	atomic	ADJ
ap-1267	116	9	then	then	ADV
ap-1267	116	10	∨	∨	NUM
ap-1267	116	11	e	e	X
ap-1267	116	12	{	{	PUNCT
ap-1267	116	13	p	p	NOUN
ap-1267	116	14	∈	∈	PROPN
ap-1267	116	15	c(e	c(e	NOUN
ap-1267	116	16	)	)	PUNCT
ap-1267	116	17	|	|	ADV
ap-1267	116	18	p	p	X
ap-1267	116	19	atom	atom	NOUN
ap-1267	116	20	of	of	ADP
ap-1267	116	21	c(e	c(e	NOUN
ap-1267	116	22	)	)	PUNCT
ap-1267	116	23	}	}	PUNCT
ap-1267	116	24	=	=	SYM
ap-1267	116	25	1	1	X
ap-1267	116	26	.	.	PUNCT
ap-1267	116	27	proof	proof	NOUN
ap-1267	116	28	.	.	PUNCT
ap-1267	117	1	(	(	PUNCT
ap-1267	117	2	i	i	NOUN
ap-1267	117	3	):	):	PUNCT
ap-1267	117	4	from	from	ADP
ap-1267	117	5	[	[	X
ap-1267	117	6	8	8	NUM
ap-1267	117	7	,	,	PUNCT
ap-1267	117	8	theorem	theorem	VERB
ap-1267	117	9	2.6	2.6	NUM
ap-1267	117	10	]	]	PUNCT
ap-1267	117	11	we	we	PRON
ap-1267	117	12	know	know	VERB
ap-1267	117	13	that	that	SCONJ
ap-1267	117	14	s(e	s(e	PROPN
ap-1267	117	15	)	)	PUNCT
ap-1267	117	16	is	be	AUX
ap-1267	117	17	an	an	DET
ap-1267	117	18	orthomodular	orthomodular	ADJ
ap-1267	117	19	lattice	lattice	NOUN
ap-1267	117	20	and	and	CCONJ
ap-1267	117	21	a	a	DET
ap-1267	117	22	sub	sub	ADJ
ap-1267	117	23	-	-	ADJ
ap-1267	117	24	lattice	lattice	ADJ
ap-1267	117	25	effect	effect	NOUN
ap-1267	117	26	algebra	algebra	PROPN
ap-1267	117	27	of	of	ADP
ap-1267	117	28	e.	e.	PROPN
ap-1267	117	29	let	let	VERB
ap-1267	117	30	us	we	PRON
ap-1267	117	31	show	show	VERB
ap-1267	117	32	that	that	SCONJ
ap-1267	117	33	s(e	s(e	PROPN
ap-1267	117	34	)	)	PUNCT
ap-1267	117	35	is	be	AUX
ap-1267	117	36	orthocomplete	orthocomplete	ADJ
ap-1267	117	37	.	.	PUNCT
ap-1267	118	1	let	let	VERB
ap-1267	118	2	s	s	PRON
ap-1267	118	3	⊆	⊆	NUM
ap-1267	118	4	s(e	s(e	PROPN
ap-1267	118	5	)	)	PUNCT
ap-1267	118	6	,	,	PUNCT
ap-1267	118	7	s	s	VERB
ap-1267	118	8	orthogonal	orthogonal	NOUN
ap-1267	118	9	.	.	PUNCT
ap-1267	119	1	then	then	ADV
ap-1267	119	2	for	for	ADP
ap-1267	119	3	every	every	DET
ap-1267	119	4	finite	finite	NOUN
ap-1267	119	5	f	f	PROPN
ap-1267	119	6	⊆	⊆	NUM
ap-1267	119	7	s	s	PRON
ap-1267	119	8	we	we	PRON
ap-1267	119	9	have	have	VERB
ap-1267	119	10	that	that	PRON
ap-1267	119	11	⊕	⊕	PROPN
ap-1267	119	12	e	e	PROPN
ap-1267	119	13	f	f	PROPN
ap-1267	119	14	=	=	SYM
ap-1267	119	15	∨	∨	PROPN
ap-1267	119	16	e	e	NOUN
ap-1267	119	17	f	f	PROPN
ap-1267	119	18	=	=	SYM
ap-1267	119	19	∨	∨	PROPN
ap-1267	119	20	s(e	s(e	PROPN
ap-1267	119	21	)	)	PUNCT
ap-1267	119	22	f	f	PROPN
ap-1267	119	23	∈	∈	PROPN
ap-1267	119	24	s(e	s(e	PROPN
ap-1267	119	25	)	)	PUNCT
ap-1267	119	26	.	.	PUNCT
ap-1267	120	1	moreover	moreover	ADV
ap-1267	120	2	,	,	PUNCT
ap-1267	120	3	for	for	ADP
ap-1267	120	4	any	any	DET
ap-1267	120	5	s	s	X
ap-1267	120	6	∈	∈	PROPN
ap-1267	120	7	s	s	NOUN
ap-1267	120	8	,	,	PUNCT
ap-1267	120	9	s	s	PART
ap-1267	120	10	≤	≤	NUM
ap-1267	120	11	s.	s.	PROPN
ap-1267	120	12	since	since	SCONJ
ap-1267	120	13	s(e	s(e	PROPN
ap-1267	120	14	)	)	PUNCT
ap-1267	120	15	is	be	AUX
ap-1267	120	16	bifull	bifull	VERB
ap-1267	120	17	in	in	ADP
ap-1267	120	18	e	e	NOUN
ap-1267	120	19	by	by	ADP
ap-1267	120	20	theorem	theorem	NOUN
ap-1267	120	21	1	1	NUM
ap-1267	120	22	and	and	CCONJ
ap-1267	120	23	e	e	NOUN
ap-1267	120	24	is	be	AUX
ap-1267	120	25	sharply	sharply	ADV
ap-1267	120	26	orthocomplete	orthocomplete	ADJ
ap-1267	120	27	we	we	PRON
ap-1267	120	28	have	have	VERB
ap-1267	120	29	that	that	PRON
ap-1267	120	30	⊕	⊕	PROPN
ap-1267	120	31	e	e	PROPN
ap-1267	120	32	s	s	X
ap-1267	120	33	=	=	PUNCT
ap-1267	120	34	∨	∨	NUM
ap-1267	120	35	e	e	X
ap-1267	120	36	s	s	X
ap-1267	120	37	=	=	SYM
ap-1267	120	38	∨	∨	PROPN
ap-1267	120	39	s(e	s(e	PROPN
ap-1267	120	40	)	)	PUNCT
ap-1267	120	41	s	s	PART
ap-1267	120	42	∈	∈	PROPN
ap-1267	120	43	s(e	s(e	PROPN
ap-1267	120	44	)	)	PUNCT
ap-1267	120	45	exists	exist	VERB
ap-1267	120	46	.	.	PUNCT
ap-1267	121	1	since	since	SCONJ
ap-1267	121	2	s(e	s(e	PROPN
ap-1267	121	3	)	)	PUNCT
ap-1267	121	4	is	be	AUX
ap-1267	121	5	an	an	DET
ap-1267	121	6	archimedean	archimedean	ADJ
ap-1267	121	7	lattice	lattice	PROPN
ap-1267	121	8	effect	effect	NOUN
ap-1267	121	9	algebra	algebra	NOUN
ap-1267	121	10	we	we	PRON
ap-1267	121	11	have	have	VERB
ap-1267	121	12	from	from	ADP
ap-1267	121	13	[	[	X
ap-1267	121	14	22	22	NUM
ap-1267	121	15	,	,	PUNCT
ap-1267	121	16	theorem	theorem	VERB
ap-1267	121	17	2.6	2.6	NUM
ap-1267	121	18	]	]	PUNCT
ap-1267	121	19	that	that	SCONJ
ap-1267	121	20	s(e	s(e	PROPN
ap-1267	121	21	)	)	PUNCT
ap-1267	121	22	is	be	AUX
ap-1267	121	23	complete	complete	ADJ
ap-1267	121	24	.	.	PUNCT
ap-1267	122	1	(	(	PUNCT
ap-1267	122	2	ii	ii	NOUN
ap-1267	122	3	):	):	PUNCT
ap-1267	122	4	as	as	ADP
ap-1267	122	5	c(e	c(e	NOUN
ap-1267	122	6	)	)	PUNCT
ap-1267	122	7	=	=	PRON
ap-1267	123	1	{	{	PUNCT
ap-1267	123	2	x	x	PUNCT
ap-1267	123	3	∈	∈	PROPN
ap-1267	123	4	e	e	NOUN
ap-1267	123	5	|	|	NOUN
ap-1267	123	6	y	y	PROPN
ap-1267	123	7	=	=	PUNCT
ap-1267	123	8	(	(	PUNCT
ap-1267	123	9	y	y	PROPN
ap-1267	123	10	∧	∧	PROPN
ap-1267	123	11	x	x	PROPN
ap-1267	123	12	)	)	PUNCT
ap-1267	123	13	∨	∨	PROPN
ap-1267	123	14	(	(	PUNCT
ap-1267	123	15	y	y	PROPN
ap-1267	123	16	∧	∧	PROPN
ap-1267	123	17	x′	x′	PROPN
ap-1267	123	18	)	)	PUNCT
ap-1267	123	19	for	for	ADP
ap-1267	123	20	every	every	DET
ap-1267	123	21	y	y	PROPN
ap-1267	123	22	∈	∈	PROPN
ap-1267	123	23	e	e	X
ap-1267	123	24	}	}	PUNCT
ap-1267	123	25	,	,	PUNCT
ap-1267	123	26	we	we	PRON
ap-1267	123	27	obtain	obtain	VERB
ap-1267	123	28	that	that	PRON
ap-1267	123	29	1	1	NUM
ap-1267	123	30	=	=	SYM
ap-1267	123	31	x	x	SYM
ap-1267	124	1	∨	∨	NUM
ap-1267	124	2	x′	x′	NUM
ap-1267	124	3	for	for	ADP
ap-1267	124	4	every	every	DET
ap-1267	124	5	x	x	PROPN
ap-1267	124	6	∈	∈	PROPN
ap-1267	124	7	c(e	c(e	NOUN
ap-1267	124	8	)	)	PUNCT
ap-1267	124	9	and	and	CCONJ
ap-1267	124	10	by	by	ADP
ap-1267	124	11	the	the	DET
ap-1267	124	12	de	de	PROPN
ap-1267	124	13	morgan	morgan	PROPN
ap-1267	124	14	laws	law	NOUN
ap-1267	124	15	0	0	PUNCT
ap-1267	125	1	=	=	PUNCT
ap-1267	125	2	x	x	SYM
ap-1267	125	3	∧	∧	PROPN
ap-1267	125	4	x′	x′	PROPN
ap-1267	125	5	for	for	ADP
ap-1267	125	6	every	every	DET
ap-1267	125	7	x	x	PROPN
ap-1267	125	8	∈	∈	PROPN
ap-1267	125	9	c(e	c(e	NOUN
ap-1267	125	10	)	)	PUNCT
ap-1267	125	11	.	.	PUNCT
ap-1267	126	1	hence	hence	ADV
ap-1267	126	2	c(e	c(e	NOUN
ap-1267	126	3	)	)	PUNCT
ap-1267	126	4	⊆	⊆	NUM
ap-1267	126	5	s(e	s(e	PROPN
ap-1267	126	6	)	)	PUNCT
ap-1267	126	7	.	.	PUNCT
ap-1267	127	1	it	it	PRON
ap-1267	127	2	follows	follow	VERB
ap-1267	127	3	by	by	ADP
ap-1267	127	4	(	(	PUNCT
ap-1267	127	5	i	i	NOUN
ap-1267	127	6	)	)	PUNCT
ap-1267	127	7	that	that	SCONJ
ap-1267	127	8	,	,	PUNCT
ap-1267	127	9	for	for	ADP
ap-1267	127	10	any	any	DET
ap-1267	127	11	q	q	NOUN
ap-1267	127	12	⊆	⊆	NUM
ap-1267	127	13	c(e	c(e	NOUN
ap-1267	127	14	)	)	PUNCT
ap-1267	127	15	,	,	PUNCT
ap-1267	127	16	there	there	PRON
ap-1267	127	17	exists	exist	VERB
ap-1267	127	18	∨	∨	NUM
ap-1267	127	19	s(e	s(e	PROPN
ap-1267	127	20	)	)	PUNCT
ap-1267	127	21	q	q	NOUN
ap-1267	128	1	=	=	PUNCT
ap-1267	128	2	∨	∨	NUM
ap-1267	128	3	e	e	X
ap-1267	128	4	q	q	NOUN
ap-1267	128	5	∈	∈	PROPN
ap-1267	128	6	c(e	c(e	NOUN
ap-1267	128	7	)	)	PUNCT
ap-1267	128	8	because	because	SCONJ
ap-1267	128	9	c(e	c(e	NOUN
ap-1267	128	10	)	)	PUNCT
ap-1267	128	11	is	be	AUX
ap-1267	128	12	full	full	ADJ
ap-1267	128	13	in	in	ADP
ap-1267	128	14	e	e	NOUN
ap-1267	128	15	,	,	PUNCT
ap-1267	128	16	hence	hence	ADV
ap-1267	128	17	∨	∨	NUM
ap-1267	128	18	c(e	c(e	NOUN
ap-1267	128	19	)	)	PUNCT
ap-1267	128	20	q	q	NOUN
ap-1267	128	21	=	=	PUNCT
ap-1267	128	22	∨	∨	PROPN
ap-1267	128	23	e	e	NOUN
ap-1267	128	24	q.	q.	NOUN
ap-1267	128	25	by	by	ADP
ap-1267	128	26	the	the	DET
ap-1267	128	27	de	de	PROPN
ap-1267	128	28	morgan	morgan	PROPN
ap-1267	128	29	laws	law	NOUN
ap-1267	128	30	there	there	PRON
ap-1267	128	31	exists	exist	VERB
ap-1267	128	32	∧	∧	PROPN
ap-1267	128	33	e	e	NOUN
ap-1267	128	34	q	q	NOUN
ap-1267	128	35	=	=	PUNCT
ap-1267	128	36	(	(	PUNCT
ap-1267	128	37	∨	∨	X
ap-1267	128	38	e	e	X
ap-1267	128	39	q′)′	q′)′	PROPN
ap-1267	128	40	,	,	PUNCT
ap-1267	128	41	where	where	SCONJ
ap-1267	128	42	evidently	evidently	ADV
ap-1267	128	43	53	53	NUM
ap-1267	128	44	acta	acta	PROPN
ap-1267	128	45	polytechnica	polytechnica	PROPN
ap-1267	128	46	vol	vol	NOUN
ap-1267	128	47	.	.	PROPN
ap-1267	129	1	50	50	NUM
ap-1267	129	2	no	no	NOUN
ap-1267	129	3	.	.	PUNCT
ap-1267	130	1	5/2010	5/2010	NUM
ap-1267	130	2	q′	q′	NOUN
ap-1267	130	3	=	=	PUNCT
ap-1267	130	4	{	{	PUNCT
ap-1267	131	1	q′	q′	NOUN
ap-1267	131	2	∈	∈	NOUN
ap-1267	131	3	e	e	NOUN
ap-1267	131	4	|	|	ADV
ap-1267	131	5	q	q	PROPN
ap-1267	131	6	∈	∈	PROPN
ap-1267	131	7	q	q	X
ap-1267	131	8	}	}	PUNCT
ap-1267	131	9	⊆	⊆	NUM
ap-1267	131	10	c(e	c(e	NOUN
ap-1267	131	11	)	)	PUNCT
ap-1267	131	12	.	.	PUNCT
ap-1267	132	1	hence	hence	ADV
ap-1267	132	2	∧	∧	PROPN
ap-1267	132	3	e	e	PROPN
ap-1267	132	4	q	q	PROPN
ap-1267	132	5	∈	∈	PROPN
ap-1267	132	6	c(e	c(e	NOUN
ap-1267	132	7	)	)	PUNCT
ap-1267	132	8	which	which	PRON
ap-1267	132	9	gives	give	VERB
ap-1267	132	10	∧	∧	PROPN
ap-1267	132	11	c(e	c(e	NOUN
ap-1267	132	12	)	)	PUNCT
ap-1267	132	13	q	q	NOUN
ap-1267	133	1	=	=	PUNCT
ap-1267	133	2	∧	∧	PROPN
ap-1267	133	3	e	e	NOUN
ap-1267	133	4	q	q	PROPN
ap-1267	133	5	(	(	PUNCT
ap-1267	133	6	see	see	VERB
ap-1267	133	7	also	also	ADV
ap-1267	133	8	[	[	X
ap-1267	133	9	5	5	NUM
ap-1267	133	10	]	]	PUNCT
ap-1267	133	11	)	)	PUNCT
ap-1267	133	12	.	.	PUNCT
ap-1267	134	1	(	(	PUNCT
ap-1267	134	2	iii	iii	X
ap-1267	134	3	):	):	PUNCT
ap-1267	134	4	let	let	VERB
ap-1267	134	5	x	x	PROPN
ap-1267	134	6	∈	∈	PROPN
ap-1267	134	7	e.	e.	PROPN
ap-1267	134	8	using	use	VERB
ap-1267	134	9	(	(	PUNCT
ap-1267	134	10	ii	ii	NOUN
ap-1267	134	11	)	)	PUNCT
ap-1267	134	12	let	let	VERB
ap-1267	134	13	us	we	PRON
ap-1267	134	14	put	put	VERB
ap-1267	134	15	cx	cx	NOUN
ap-1267	134	16	=	=	PUNCT
ap-1267	135	1	∧	∧	PROPN
ap-1267	135	2	c(e	c(e	NOUN
ap-1267	135	3	)	)	PUNCT
ap-1267	135	4	{	{	PUNCT
ap-1267	135	5	c	c	NOUN
ap-1267	135	6	∈	∈	PROPN
ap-1267	135	7	c(e	c(e	NOUN
ap-1267	135	8	)	)	PUNCT
ap-1267	136	1	|	|	ADV
ap-1267	136	2	x	x	SYM
ap-1267	136	3	≤	≤	NUM
ap-1267	136	4	c	c	X
ap-1267	136	5	}	}	PUNCT
ap-1267	136	6	∈	∈	PROPN
ap-1267	136	7	c(e	c(e	NOUN
ap-1267	136	8	)	)	PUNCT
ap-1267	136	9	.	.	PUNCT
ap-1267	137	1	since	since	SCONJ
ap-1267	137	2	c(e	c(e	NOUN
ap-1267	137	3	)	)	PUNCT
ap-1267	137	4	is	be	AUX
ap-1267	137	5	bifull	bifull	VERB
ap-1267	137	6	in	in	ADP
ap-1267	137	7	e	e	NOUN
ap-1267	137	8	we	we	PRON
ap-1267	137	9	have	have	VERB
ap-1267	137	10	that	that	PRON
ap-1267	137	11	cx	cx	PROPN
ap-1267	138	1	=	=	PUNCT
ap-1267	138	2	∧	∧	PROPN
ap-1267	138	3	e	e	X
ap-1267	138	4	{	{	PUNCT
ap-1267	138	5	c	c	PROPN
ap-1267	138	6	∈	∈	PROPN
ap-1267	138	7	c(e	c(e	NOUN
ap-1267	138	8	)	)	PUNCT
ap-1267	139	1	|	|	ADV
ap-1267	139	2	x	x	SYM
ap-1267	139	3	≤	≤	NUM
ap-1267	139	4	c	c	X
ap-1267	139	5	}	}	PUNCT
ap-1267	139	6	(	(	PUNCT
ap-1267	139	7	see	see	VERB
ap-1267	139	8	again	again	ADV
ap-1267	139	9	[	[	X
ap-1267	139	10	5	5	NUM
ap-1267	139	11	]	]	PUNCT
ap-1267	139	12	)	)	PUNCT
ap-1267	139	13	.	.	PUNCT
ap-1267	140	1	since	since	SCONJ
ap-1267	140	2	c(e	c(e	NOUN
ap-1267	140	3	)	)	PUNCT
ap-1267	140	4	⊆	⊆	NUM
ap-1267	140	5	s(e	s(e	PROPN
ap-1267	140	6	)	)	PUNCT
ap-1267	140	7	we	we	PRON
ap-1267	140	8	immediately	immediately	ADV
ap-1267	140	9	obtain	obtain	VERB
ap-1267	140	10	that	that	SCONJ
ap-1267	140	11	e	e	NOUN
ap-1267	140	12	is	be	AUX
ap-1267	140	13	centrally	centrally	ADV
ap-1267	140	14	orthocomplete	orthocomplete	ADJ
ap-1267	140	15	.	.	PUNCT
ap-1267	141	1	(	(	PUNCT
ap-1267	141	2	iv	iv	NUM
ap-1267	141	3	):	):	PUNCT
ap-1267	141	4	since	since	SCONJ
ap-1267	141	5	c(e	c(e	NOUN
ap-1267	141	6	)	)	PUNCT
ap-1267	141	7	is	be	AUX
ap-1267	141	8	an	an	DET
ap-1267	141	9	atomic	atomic	ADJ
ap-1267	141	10	boolean	boolean	ADJ
ap-1267	141	11	algebra	algebra	NOUN
ap-1267	141	12	we	we	PRON
ap-1267	141	13	have	have	VERB
ap-1267	141	14	∨	∨	NOUN
ap-1267	141	15	c(e	c(e	NOUN
ap-1267	141	16	)	)	PUNCT
ap-1267	141	17	{	{	PUNCT
ap-1267	141	18	p	p	NOUN
ap-1267	141	19	∈	∈	PROPN
ap-1267	141	20	c(e	c(e	NOUN
ap-1267	141	21	)	)	PUNCT
ap-1267	142	1	|	|	ADV
ap-1267	142	2	p	p	X
ap-1267	142	3	atom	atom	NOUN
ap-1267	142	4	of	of	ADP
ap-1267	142	5	c(e	c(e	NOUN
ap-1267	142	6	)	)	PUNCT
ap-1267	142	7	}	}	PUNCT
ap-1267	143	1	=	=	SYM
ap-1267	143	2	1	1	X
ap-1267	143	3	.	.	NOUN
ap-1267	143	4	as	as	ADP
ap-1267	143	5	c(e	c(e	NOUN
ap-1267	143	6	)	)	PUNCT
ap-1267	143	7	is	be	AUX
ap-1267	143	8	bifull	bifull	VERB
ap-1267	143	9	in	in	ADP
ap-1267	143	10	e	e	NOUN
ap-1267	143	11	,	,	PUNCT
ap-1267	143	12	we	we	PRON
ap-1267	143	13	have	have	VERB
ap-1267	143	14	that	that	SCONJ
ap-1267	143	15	∨	∨	NUM
ap-1267	143	16	e	e	X
ap-1267	143	17	{	{	PUNCT
ap-1267	143	18	p	p	NOUN
ap-1267	143	19	∈	∈	PROPN
ap-1267	143	20	c(e	c(e	NOUN
ap-1267	143	21	)	)	PUNCT
ap-1267	143	22	|	|	ADV
ap-1267	143	23	p	p	X
ap-1267	143	24	atom	atom	NOUN
ap-1267	143	25	of	of	ADP
ap-1267	143	26	c(e	c(e	NOUN
ap-1267	143	27	)	)	PUNCT
ap-1267	143	28	}	}	PUNCT
ap-1267	143	29	=	=	SYM
ap-1267	143	30	∨	∨	NUM
ap-1267	143	31	c(e	c(e	NOUN
ap-1267	143	32	)	)	PUNCT
ap-1267	143	33	{	{	PUNCT
ap-1267	143	34	p	p	NOUN
ap-1267	143	35	∈	∈	PROPN
ap-1267	143	36	c(e	c(e	NOUN
ap-1267	143	37	)	)	PUNCT
ap-1267	143	38	|	|	ADV
ap-1267	143	39	p	p	X
ap-1267	143	40	atom	atom	NOUN
ap-1267	143	41	of	of	ADP
ap-1267	143	42	c(e	c(e	NOUN
ap-1267	143	43	)	)	PUNCT
ap-1267	143	44	}	}	PUNCT
ap-1267	143	45	=	=	SYM
ap-1267	144	1	1	1	X
ap-1267	144	2	.	.	NOUN
ap-1267	144	3	4	4	NUM
ap-1267	144	4	sharply	sharply	ADV
ap-1267	144	5	orthocomplete	orthocomplete	ADJ
ap-1267	144	6	lattice	lattice	PROPN
ap-1267	144	7	effect	effect	NOUN
ap-1267	144	8	algebras	algebras	PROPN
ap-1267	144	9	m.	m.	PROPN
ap-1267	144	10	kalina	kalina	PROPN
ap-1267	144	11	in	in	ADP
ap-1267	144	12	[	[	X
ap-1267	144	13	12	12	NUM
ap-1267	144	14	]	]	PUNCT
ap-1267	144	15	has	have	AUX
ap-1267	144	16	shown	show	VERB
ap-1267	144	17	that	that	SCONJ
ap-1267	144	18	even	even	ADV
ap-1267	144	19	in	in	ADP
ap-1267	144	20	an	an	DET
ap-1267	144	21	archimedean	archimedean	ADJ
ap-1267	144	22	atomic	atomic	ADJ
ap-1267	144	23	lattice	lattice	PROPN
ap-1267	144	24	effect	effect	NOUN
ap-1267	144	25	algebra	algebra	NOUN
ap-1267	144	26	e	e	NOUN
ap-1267	144	27	with	with	ADP
ap-1267	144	28	atomic	atomic	ADJ
ap-1267	144	29	center	center	NOUN
ap-1267	144	30	c(e	c(e	NOUN
ap-1267	144	31	)	)	PUNCT
ap-1267	144	32	the	the	DET
ap-1267	144	33	join	join	NOUN
ap-1267	144	34	of	of	ADP
ap-1267	144	35	atoms	atom	NOUN
ap-1267	144	36	of	of	ADP
ap-1267	144	37	c(e	c(e	NOUN
ap-1267	144	38	)	)	PUNCT
ap-1267	144	39	computed	compute	VERB
ap-1267	144	40	in	in	ADP
ap-1267	144	41	e	e	NOUN
ap-1267	144	42	need	need	AUX
ap-1267	144	43	not	not	PART
ap-1267	144	44	be	be	AUX
ap-1267	144	45	equal	equal	ADJ
ap-1267	144	46	to	to	ADP
ap-1267	144	47	1	1	NUM
ap-1267	144	48	.	.	PUNCT
ap-1267	145	1	next	next	ADJ
ap-1267	145	2	examples	example	NOUN
ap-1267	145	3	and	and	CCONJ
ap-1267	145	4	theorems	theorem	NOUN
ap-1267	145	5	show	show	VERB
ap-1267	145	6	connections	connection	NOUN
ap-1267	145	7	between	between	ADP
ap-1267	145	8	sharp	sharp	ADJ
ap-1267	145	9	orthocompleteness	orthocompleteness	NOUN
ap-1267	145	10	,	,	PUNCT
ap-1267	145	11	sharp	sharp	ADJ
ap-1267	145	12	dominancy	dominancy	NOUN
ap-1267	145	13	and	and	CCONJ
ap-1267	145	14	completeness	completeness	NOUN
ap-1267	145	15	of	of	ADP
ap-1267	145	16	an	an	DET
ap-1267	145	17	effect	effect	NOUN
ap-1267	145	18	algebra	algebra	NOUN
ap-1267	145	19	e	e	NOUN
ap-1267	145	20	as	as	ADV
ap-1267	145	21	well	well	ADV
ap-1267	145	22	as	as	ADP
ap-1267	145	23	bifullness	bifullness	NOUN
ap-1267	145	24	of	of	ADP
ap-1267	145	25	s(e	s(e	PROPN
ap-1267	145	26	)	)	PUNCT
ap-1267	145	27	,	,	PUNCT
ap-1267	145	28	c(e	c(e	NOUN
ap-1267	145	29	)	)	PUNCT
ap-1267	145	30	and	and	CCONJ
ap-1267	145	31	atomic	atomic	ADJ
ap-1267	145	32	blocks	block	NOUN
ap-1267	145	33	in	in	ADP
ap-1267	145	34	a	a	DET
ap-1267	145	35	lattice	lattice	ADJ
ap-1267	145	36	effect	effect	NOUN
ap-1267	145	37	algebra	algebra	PROPN
ap-1267	145	38	e.	e.	PROPN
ap-1267	146	1	it	it	PRON
ap-1267	146	2	is	be	AUX
ap-1267	146	3	worth	worth	ADJ
ap-1267	146	4	noting	note	VERB
ap-1267	146	5	that	that	SCONJ
ap-1267	146	6	if	if	SCONJ
ap-1267	146	7	s(e	s(e	PROPN
ap-1267	146	8	)	)	PUNCT
ap-1267	146	9	=	=	PUNCT
ap-1267	147	1	{	{	PUNCT
ap-1267	147	2	0	0	NUM
ap-1267	147	3	,	,	PUNCT
ap-1267	147	4	1	1	NUM
ap-1267	147	5	}	}	PUNCT
ap-1267	147	6	then	then	ADV
ap-1267	147	7	evidently	evidently	ADV
ap-1267	147	8	e	e	X
ap-1267	147	9	is	be	AUX
ap-1267	147	10	s	s	NOUN
ap-1267	147	11	-	-	PUNCT
ap-1267	147	12	dominating	dominating	NOUN
ap-1267	147	13	and	and	CCONJ
ap-1267	147	14	sharply	sharply	ADV
ap-1267	147	15	orthocomplete	orthocomplete	ADJ
ap-1267	147	16	.	.	PUNCT
ap-1267	148	1	example	example	NOUN
ap-1267	148	2	1	1	NUM
ap-1267	148	3	example	example	NOUN
ap-1267	148	4	of	of	ADP
ap-1267	148	5	a	a	DET
ap-1267	148	6	compactly	compactly	ADV
ap-1267	148	7	generated	generate	VERB
ap-1267	148	8	sharply	sharply	ADV
ap-1267	148	9	orthocomplete	orthocomplete	ADJ
ap-1267	148	10	mv	mv	NOUN
ap-1267	148	11	-	-	PUNCT
ap-1267	148	12	effect	effect	NOUN
ap-1267	148	13	algebra	algebra	NOUN
ap-1267	148	14	that	that	PRON
ap-1267	148	15	is	be	AUX
ap-1267	148	16	not	not	PART
ap-1267	148	17	complete	complete	ADJ
ap-1267	148	18	.	.	PUNCT
ap-1267	149	1	it	it	PRON
ap-1267	149	2	is	be	AUX
ap-1267	149	3	enough	enough	ADJ
ap-1267	149	4	to	to	PART
ap-1267	149	5	take	take	VERB
ap-1267	149	6	the	the	DET
ap-1267	149	7	chang	chang	PROPN
ap-1267	149	8	mv	mv	PROPN
ap-1267	149	9	-	-	PUNCT
ap-1267	149	10	effect	effect	NOUN
ap-1267	149	11	algebra	algebra	NOUN
ap-1267	149	12	e	e	NOUN
ap-1267	149	13	=	=	PUNCT
ap-1267	149	14	{	{	PUNCT
ap-1267	149	15	0	0	NUM
ap-1267	149	16	,	,	PUNCT
ap-1267	149	17	a	a	PRON
ap-1267	149	18	,	,	PUNCT
ap-1267	149	19	2a	2a	NUM
ap-1267	149	20	,	,	PUNCT
ap-1267	149	21	3a	3a	NUM
ap-1267	149	22	,	,	PUNCT
ap-1267	149	23	.	.	PUNCT
ap-1267	149	24	.	.	PUNCT
ap-1267	149	25	.	.	PUNCT
ap-1267	150	1	,	,	PUNCT
ap-1267	150	2	(	(	PUNCT
ap-1267	150	3	3a)′	3a)′	NUM
ap-1267	150	4	,	,	PUNCT
ap-1267	150	5	(	(	PUNCT
ap-1267	150	6	2a)′	2a)′	NUM
ap-1267	150	7	,	,	PUNCT
ap-1267	150	8	a′	a′	PROPN
ap-1267	150	9	,	,	PUNCT
ap-1267	150	10	1	1	X
ap-1267	150	11	}	}	PUNCT
ap-1267	150	12	that	that	PRON
ap-1267	150	13	is	be	AUX
ap-1267	150	14	not	not	PART
ap-1267	150	15	archimedean	archimedean	ADJ
ap-1267	150	16	(	(	PUNCT
ap-1267	150	17	hence	hence	ADV
ap-1267	150	18	it	it	PRON
ap-1267	150	19	is	be	AUX
ap-1267	150	20	not	not	PART
ap-1267	150	21	complete	complete	ADJ
ap-1267	150	22	)	)	PUNCT
ap-1267	150	23	.	.	PUNCT
ap-1267	151	1	it	it	PRON
ap-1267	151	2	is	be	AUX
ap-1267	151	3	compactly	compactly	ADV
ap-1267	151	4	generated	generate	VERB
ap-1267	151	5	(	(	PUNCT
ap-1267	151	6	every	every	DET
ap-1267	151	7	x	x	SYM
ap-1267	151	8	∈	∈	NOUN
ap-1267	151	9	e	e	NOUN
ap-1267	151	10	is	be	AUX
ap-1267	151	11	compact	compact	ADJ
ap-1267	151	12	)	)	PUNCT
ap-1267	151	13	and	and	CCONJ
ap-1267	151	14	obviously	obviously	ADV
ap-1267	151	15	sharply	sharply	ADV
ap-1267	151	16	orthocomplete	orthocomplete	ADV
ap-1267	151	17	(	(	PUNCT
ap-1267	151	18	the	the	DET
ap-1267	151	19	center	center	NOUN
ap-1267	151	20	c(e	c(e	NOUN
ap-1267	151	21	)	)	PUNCT
ap-1267	151	22	=	=	SYM
ap-1267	152	1	s(e	s(e	PROPN
ap-1267	152	2	)	)	PUNCT
ap-1267	152	3	is	be	AUX
ap-1267	152	4	trivial	trivial	ADJ
ap-1267	152	5	)	)	PUNCT
ap-1267	152	6	and	and	CCONJ
ap-1267	152	7	hence	hence	ADV
ap-1267	152	8	sharply	sharply	ADV
ap-1267	152	9	dominating	dominate	VERB
ap-1267	152	10	.	.	PUNCT
ap-1267	153	1	example	example	NOUN
ap-1267	153	2	2	2	NUM
ap-1267	153	3	example	example	NOUN
ap-1267	153	4	of	of	ADP
ap-1267	153	5	a	a	DET
ap-1267	153	6	sharply	sharply	ADV
ap-1267	153	7	dominating	dominate	VERB
ap-1267	153	8	archimedean	archimedean	ADJ
ap-1267	153	9	atomic	atomic	PROPN
ap-1267	153	10	lattice	lattice	PROPN
ap-1267	153	11	mv	mv	PROPN
ap-1267	153	12	-	-	PUNCT
ap-1267	153	13	effect	effect	NOUN
ap-1267	153	14	algebra	algebra	NOUN
ap-1267	153	15	e	e	NOUN
ap-1267	153	16	with	with	ADP
ap-1267	153	17	complete	complete	ADJ
ap-1267	153	18	and	and	CCONJ
ap-1267	153	19	bifull	bifull	PRON
ap-1267	153	20	s(e	s(e	PROPN
ap-1267	153	21	)	)	PUNCT
ap-1267	153	22	that	that	PRON
ap-1267	153	23	is	be	AUX
ap-1267	153	24	not	not	PART
ap-1267	153	25	sharply	sharply	ADV
ap-1267	153	26	orthocomplete	orthocomplete	ADJ
ap-1267	153	27	.	.	PUNCT
ap-1267	154	1	let	let	VERB
ap-1267	154	2	e	e	NOUN
ap-1267	154	3	=	=	SYM
ap-1267	154	4	∏	∏	X
ap-1267	154	5	{	{	PUNCT
ap-1267	154	6	{	{	PUNCT
ap-1267	154	7	0n	0n	NUM
ap-1267	154	8	,	,	PUNCT
ap-1267	154	9	an	an	PRON
ap-1267	154	10	,	,	PUNCT
ap-1267	154	11	1n	1n	NUM
ap-1267	154	12	}	}	PUNCT
ap-1267	154	13	|	|	CCONJ
ap-1267	154	14	n	n	NOUN
ap-1267	154	15	=	=	SYM
ap-1267	154	16	1	1	NUM
ap-1267	154	17	,	,	PUNCT
ap-1267	154	18	2	2	NUM
ap-1267	154	19	,	,	PUNCT
ap-1267	154	20	.	.	PUNCT
ap-1267	154	21	.	.	PUNCT
ap-1267	155	1	.	.	PUNCT
ap-1267	155	2	}	}	PUNCT
ap-1267	156	1	and	and	CCONJ
ap-1267	156	2	let	let	VERB
ap-1267	156	3	e0	e0	PROPN
ap-1267	156	4	=	=	PUNCT
ap-1267	156	5	{	{	PUNCT
ap-1267	156	6	(	(	PUNCT
ap-1267	156	7	xn)∞n=1	xn)∞n=1	SYM
ap-1267	156	8	∈	∈	PROPN
ap-1267	156	9	e	e	X
ap-1267	156	10	|	|	ADV
ap-1267	156	11	xk	xk	PROPN
ap-1267	156	12	=	=	PROPN
ap-1267	156	13	ak	ak	PROPN
ap-1267	156	14	for	for	ADP
ap-1267	156	15	at	at	ADV
ap-1267	156	16	most	most	ADV
ap-1267	156	17	finitely	finitely	ADV
ap-1267	156	18	many	many	ADJ
ap-1267	156	19	k	k	PROPN
ap-1267	156	20	∈	∈	PROPN
ap-1267	156	21	{	{	PUNCT
ap-1267	156	22	1	1	NUM
ap-1267	156	23	,	,	PUNCT
ap-1267	156	24	2	2	NUM
ap-1267	156	25	,	,	PUNCT
ap-1267	156	26	.	.	PUNCT
ap-1267	156	27	.	.	PUNCT
ap-1267	157	1	.	.	PUNCT
ap-1267	157	2	}	}	PUNCT
ap-1267	157	3	}	}	PUNCT
ap-1267	157	4	.	.	PUNCT
ap-1267	158	1	then	then	ADV
ap-1267	158	2	e0	e0	PROPN
ap-1267	158	3	is	be	AUX
ap-1267	158	4	a	a	DET
ap-1267	158	5	sub	sub	ADJ
ap-1267	158	6	-	-	ADJ
ap-1267	158	7	lattice	lattice	ADJ
ap-1267	158	8	effect	effect	NOUN
ap-1267	158	9	algebra	algebra	NOUN
ap-1267	158	10	of	of	ADP
ap-1267	158	11	e	e	PROPN
ap-1267	158	12	(	(	PUNCT
ap-1267	158	13	hence	hence	ADV
ap-1267	158	14	it	it	PRON
ap-1267	158	15	is	be	AUX
ap-1267	158	16	an	an	DET
ap-1267	158	17	mv	mv	ADJ
ap-1267	158	18	-	-	PUNCT
ap-1267	158	19	effect	effect	NOUN
ap-1267	158	20	algebra	algebra	NOUN
ap-1267	158	21	)	)	PUNCT
ap-1267	158	22	,	,	PUNCT
ap-1267	158	23	evidently	evidently	ADV
ap-1267	158	24	sharply	sharply	ADV
ap-1267	158	25	dominating	dominate	VERB
ap-1267	158	26	and	and	CCONJ
ap-1267	158	27	it	it	PRON
ap-1267	158	28	is	be	AUX
ap-1267	158	29	not	not	PART
ap-1267	158	30	sharply	sharply	ADV
ap-1267	158	31	orthocomplete	orthocomplete	ADJ
ap-1267	158	32	(	(	PUNCT
ap-1267	158	33	since	since	SCONJ
ap-1267	158	34	it	it	PRON
ap-1267	158	35	is	be	AUX
ap-1267	158	36	not	not	PART
ap-1267	158	37	complete	complete	ADJ
ap-1267	158	38	)	)	PUNCT
ap-1267	158	39	.	.	PUNCT
ap-1267	158	40	s(e0	s(e0	NOUN
ap-1267	158	41	)	)	PUNCT
ap-1267	158	42	=	=	SYM
ap-1267	158	43	∏	∏	PROPN
ap-1267	158	44	{	{	PUNCT
ap-1267	158	45	{	{	PUNCT
ap-1267	158	46	0n	0n	NUM
ap-1267	158	47	,	,	PUNCT
ap-1267	158	48	1n	1n	NUM
ap-1267	158	49	}	}	PUNCT
ap-1267	158	50	|	|	CCONJ
ap-1267	158	51	n	n	NOUN
ap-1267	158	52	=	=	SYM
ap-1267	158	53	1	1	NUM
ap-1267	158	54	,	,	PUNCT
ap-1267	158	55	2	2	NUM
ap-1267	158	56	,	,	PUNCT
ap-1267	158	57	.	.	PUNCT
ap-1267	158	58	.	.	PUNCT
ap-1267	159	1	.	.	PUNCT
ap-1267	159	2	}	}	PUNCT
ap-1267	159	3	is	be	AUX
ap-1267	159	4	a	a	DET
ap-1267	159	5	complete	complete	ADJ
ap-1267	159	6	boolean	boolean	ADJ
ap-1267	159	7	algebra	algebra	NOUN
ap-1267	159	8	and	and	CCONJ
ap-1267	159	9	s(e0	s(e0	NOUN
ap-1267	159	10	)	)	PUNCT
ap-1267	160	1	=	=	SYM
ap-1267	160	2	c(e0	c(e0	PROPN
ap-1267	160	3	)	)	PUNCT
ap-1267	160	4	is	be	AUX
ap-1267	160	5	a	a	DET
ap-1267	160	6	bifull	bifull	ADJ
ap-1267	160	7	sub	sub	NOUN
ap-1267	160	8	-	-	NOUN
ap-1267	160	9	lattice	lattice	NOUN
ap-1267	160	10	of	of	ADP
ap-1267	160	11	e0	e0	PROPN
ap-1267	160	12	.	.	PUNCT
ap-1267	161	1	lemma	lemma	PROPN
ap-1267	161	2	1	1	NUM
ap-1267	161	3	let	let	VERB
ap-1267	161	4	e	e	PRON
ap-1267	161	5	be	be	AUX
ap-1267	161	6	a	a	DET
ap-1267	161	7	sharply	sharply	ADV
ap-1267	161	8	orthocomplete	orthocomplete	ADJ
ap-1267	161	9	archimedean	archimedean	PROPN
ap-1267	161	10	atomic	atomic	ADJ
ap-1267	161	11	mv	mv	PROPN
ap-1267	161	12	-	-	PUNCT
ap-1267	161	13	effect	effect	NOUN
ap-1267	161	14	algebra	algebra	NOUN
ap-1267	161	15	.	.	PUNCT
ap-1267	162	1	then	then	ADV
ap-1267	162	2	e	e	PROPN
ap-1267	162	3	is	be	AUX
ap-1267	162	4	complete	complete	ADJ
ap-1267	162	5	.	.	PUNCT
ap-1267	163	1	proof	proof	NOUN
ap-1267	163	2	.	.	PUNCT
ap-1267	164	1	let	let	VERB
ap-1267	164	2	a	a	DET
ap-1267	164	3	⊆	⊆	NUM
ap-1267	164	4	e	e	NOUN
ap-1267	164	5	be	be	AUX
ap-1267	164	6	a	a	DET
ap-1267	164	7	set	set	NOUN
ap-1267	164	8	of	of	ADP
ap-1267	164	9	all	all	DET
ap-1267	164	10	atoms	atom	NOUN
ap-1267	164	11	of	of	ADP
ap-1267	164	12	e.	e.	PROPN
ap-1267	164	13	then	then	ADV
ap-1267	164	14	1	1	NUM
ap-1267	164	15	=	=	SYM
ap-1267	164	16	∨	∨	NUM
ap-1267	164	17	e	e	NOUN
ap-1267	164	18	{	{	PUNCT
ap-1267	164	19	naa|a	naa|a	NOUN
ap-1267	164	20	∈	∈	PROPN
ap-1267	164	21	a	a	DET
ap-1267	164	22	}	}	PUNCT
ap-1267	164	23	=	=	SYM
ap-1267	164	24	⊕	⊕	PROPN
ap-1267	164	25	e	e	NOUN
ap-1267	164	26	{	{	PUNCT
ap-1267	164	27	naa|a	naa|a	NOUN
ap-1267	164	28	∈	∈	PROPN
ap-1267	164	29	a	a	PRON
ap-1267	164	30	}	}	PUNCT
ap-1267	164	31	,	,	PUNCT
ap-1267	164	32	naa	naa	PROPN
ap-1267	164	33	∈	∈	PROPN
ap-1267	164	34	c(e	c(e	NOUN
ap-1267	164	35	)	)	PUNCT
ap-1267	164	36	=	=	SYM
ap-1267	165	1	s(e	s(e	PROPN
ap-1267	165	2	)	)	PUNCT
ap-1267	165	3	are	be	AUX
ap-1267	165	4	atoms	atom	NOUN
ap-1267	165	5	of	of	ADP
ap-1267	165	6	c(e	c(e	NOUN
ap-1267	165	7	)	)	PUNCT
ap-1267	165	8	for	for	ADP
ap-1267	165	9	all	all	DET
ap-1267	165	10	a	a	DET
ap-1267	165	11	∈	∈	NOUN
ap-1267	165	12	a.	a.	NOUN
ap-1267	165	13	by	by	ADP
ap-1267	165	14	[	[	X
ap-1267	165	15	23	23	NUM
ap-1267	165	16	,	,	PUNCT
ap-1267	165	17	theorem	theorem	VERB
ap-1267	165	18	3.1	3.1	NUM
ap-1267	165	19	]	]	PUNCT
ap-1267	165	20	we	we	PRON
ap-1267	165	21	have	have	VERB
ap-1267	165	22	that	that	PRON
ap-1267	165	23	e	e	NOUN
ap-1267	165	24	is	be	AUX
ap-1267	165	25	isomorphic	isomorphic	ADJ
ap-1267	165	26	to	to	ADP
ap-1267	165	27	a	a	DET
ap-1267	165	28	subdirect	subdirect	NOUN
ap-1267	165	29	product	product	NOUN
ap-1267	165	30	of	of	ADP
ap-1267	165	31	the	the	DET
ap-1267	165	32	family	family	NOUN
ap-1267	165	33	{	{	PUNCT
ap-1267	166	1	[	[	X
ap-1267	166	2	0	0	NUM
ap-1267	166	3	,	,	PUNCT
ap-1267	166	4	naa	naa	ADJ
ap-1267	166	5	]	]	X
ap-1267	166	6	|	|	ADV
ap-1267	166	7	a	a	DET
ap-1267	166	8	∈	∈	PROPN
ap-1267	166	9	a	a	PRON
ap-1267	166	10	}	}	PUNCT
ap-1267	166	11	.	.	PUNCT
ap-1267	167	1	the	the	DET
ap-1267	167	2	corresponding	correspond	VERB
ap-1267	167	3	lattice	lattice	PROPN
ap-1267	167	4	effect	effect	NOUN
ap-1267	167	5	algebra	algebra	NOUN
ap-1267	167	6	embedding	embed	VERB
ap-1267	167	7	ϕ:e	ϕ:e	X
ap-1267	167	8	→	→	SYM
ap-1267	167	9	∏	∏	X
ap-1267	167	10	{	{	PUNCT
ap-1267	167	11	[	[	X
ap-1267	167	12	0	0	NUM
ap-1267	167	13	,	,	PUNCT
ap-1267	167	14	naa	naa	ADJ
ap-1267	167	15	]	]	X
ap-1267	167	16	|	|	ADV
ap-1267	167	17	a	a	DET
ap-1267	167	18	∈	∈	PROPN
ap-1267	167	19	a	a	PRON
ap-1267	167	20	}	}	PUNCT
ap-1267	167	21	is	be	AUX
ap-1267	167	22	given	give	VERB
ap-1267	167	23	by	by	ADP
ap-1267	167	24	ϕ(x	ϕ(x	NOUN
ap-1267	167	25	)	)	PUNCT
ap-1267	167	26	=	=	SYM
ap-1267	168	1	(	(	PUNCT
ap-1267	168	2	x	x	PART
ap-1267	168	3	∧	∧	PROPN
ap-1267	168	4	naa)a∈a	naa)a∈a	PROPN
ap-1267	168	5	.	.	PUNCT
ap-1267	169	1	let	let	VERB
ap-1267	169	2	us	we	PRON
ap-1267	169	3	check	check	VERB
ap-1267	169	4	that	that	SCONJ
ap-1267	169	5	e	e	NOUN
ap-1267	169	6	is	be	AUX
ap-1267	169	7	isomorphic	isomorphic	ADJ
ap-1267	169	8	to	to	ADP
ap-1267	169	9	∏	∏	PROPN
ap-1267	169	10	{	{	PUNCT
ap-1267	170	1	[	[	X
ap-1267	170	2	0	0	NUM
ap-1267	170	3	,	,	PUNCT
ap-1267	170	4	naa	naa	ADJ
ap-1267	170	5	]	]	X
ap-1267	170	6	|	|	ADV
ap-1267	170	7	a	a	DET
ap-1267	170	8	∈	∈	PROPN
ap-1267	170	9	a	a	PRON
ap-1267	170	10	}	}	PUNCT
ap-1267	170	11	.	.	PUNCT
ap-1267	171	1	it	it	PRON
ap-1267	171	2	is	be	AUX
ap-1267	171	3	enough	enough	ADJ
ap-1267	171	4	to	to	PART
ap-1267	171	5	check	check	VERB
ap-1267	171	6	that	that	PRON
ap-1267	171	7	ϕ	ϕ	NOUN
ap-1267	171	8	is	be	AUX
ap-1267	171	9	onto	onto	ADP
ap-1267	171	10	.	.	PUNCT
ap-1267	172	1	let	let	VERB
ap-1267	172	2	(	(	PUNCT
ap-1267	172	3	xa)a∈a	xa)a∈a	PROPN
ap-1267	172	4	∈	∈	PROPN
ap-1267	172	5	∏	∏	X
ap-1267	172	6	{	{	PUNCT
ap-1267	172	7	[	[	X
ap-1267	172	8	0	0	NUM
ap-1267	172	9	,	,	PUNCT
ap-1267	172	10	naa	naa	ADJ
ap-1267	172	11	]	]	X
ap-1267	172	12	|	|	ADV
ap-1267	172	13	a	a	DET
ap-1267	172	14	∈	∈	PROPN
ap-1267	172	15	a	a	PRON
ap-1267	172	16	}	}	PUNCT
ap-1267	172	17	.	.	PUNCT
ap-1267	173	1	then	then	ADV
ap-1267	173	2	(	(	PUNCT
ap-1267	173	3	na)a∈a	na)a∈a	NUM
ap-1267	173	4	is	be	AUX
ap-1267	173	5	an	an	DET
ap-1267	173	6	orthogonal	orthogonal	ADJ
ap-1267	173	7	system	system	NOUN
ap-1267	173	8	and	and	CCONJ
ap-1267	173	9	xa	xa	NOUN
ap-1267	173	10	=	=	PROPN
ap-1267	173	11	kaa	kaa	PROPN
ap-1267	173	12	≤	≤	PROPN
ap-1267	173	13	naa	naa	PROPN
ap-1267	173	14	∈	∈	PROPN
ap-1267	173	15	s(e	s(e	PROPN
ap-1267	173	16	)	)	PUNCT
ap-1267	173	17	for	for	ADP
ap-1267	173	18	all	all	DET
ap-1267	173	19	a	a	DET
ap-1267	173	20	∈	∈	NOUN
ap-1267	173	21	a.	a.	NOUN
ap-1267	173	22	hence	hence	ADV
ap-1267	173	23	x	x	X
ap-1267	173	24	=	=	SYM
ap-1267	173	25	⊕	⊕	PROPN
ap-1267	173	26	e	e	PROPN
ap-1267	173	27	{	{	PUNCT
ap-1267	173	28	xa	xa	PROPN
ap-1267	173	29	|	|	ADV
ap-1267	173	30	a	a	DET
ap-1267	173	31	∈	∈	PROPN
ap-1267	173	32	a	a	DET
ap-1267	173	33	}	}	PUNCT
ap-1267	173	34	=	=	SYM
ap-1267	173	35	∨	∨	PROPN
ap-1267	173	36	e	e	X
ap-1267	173	37	{	{	PUNCT
ap-1267	173	38	kaa	kaa	PROPN
ap-1267	173	39	|	|	ADV
ap-1267	173	40	a	a	PRON
ap-1267	173	41	∈	∈	PROPN
ap-1267	173	42	a	a	DET
ap-1267	173	43	}	}	PUNCT
ap-1267	173	44	∈	∈	NOUN
ap-1267	173	45	e	e	NOUN
ap-1267	173	46	exists	exist	VERB
ap-1267	173	47	.	.	PUNCT
ap-1267	174	1	evidently	evidently	ADV
ap-1267	174	2	,	,	PUNCT
ap-1267	174	3	ϕ(x	ϕ(x	X
ap-1267	174	4	)	)	PUNCT
ap-1267	174	5	=	=	SYM
ap-1267	174	6	(	(	PUNCT
ap-1267	174	7	x∧naa)a∈a	x∧naa)a∈a	NOUN
ap-1267	174	8	=	=	SYM
ap-1267	174	9	(	(	PUNCT
ap-1267	174	10	kaa)a∈a	kaa)a∈a	NOUN
ap-1267	174	11	=	=	X
ap-1267	174	12	(	(	PUNCT
ap-1267	174	13	xa)a∈a	xa)a∈a	PROPN
ap-1267	174	14	.	.	PROPN
ap-1267	174	15	example	example	NOUN
ap-1267	174	16	3	3	NUM
ap-1267	174	17	example	example	NOUN
ap-1267	174	18	of	of	ADP
ap-1267	174	19	a	a	DET
ap-1267	174	20	sharply	sharply	ADV
ap-1267	174	21	orthocomplete	orthocomplete	ADJ
ap-1267	174	22	archimedean	archimedean	ADJ
ap-1267	174	23	mv	mv	PROPN
ap-1267	174	24	-	-	PUNCT
ap-1267	174	25	effect	effect	NOUN
ap-1267	174	26	algebra	algebra	NOUN
ap-1267	174	27	that	that	PRON
ap-1267	174	28	is	be	AUX
ap-1267	174	29	not	not	PART
ap-1267	174	30	complete	complete	ADJ
ap-1267	174	31	.	.	PUNCT
ap-1267	175	1	if	if	SCONJ
ap-1267	175	2	we	we	PRON
ap-1267	175	3	omit	omit	VERB
ap-1267	175	4	in	in	ADP
ap-1267	175	5	lemma	lemma	PROPN
ap-1267	175	6	1	1	NUM
ap-1267	175	7	the	the	DET
ap-1267	175	8	assumption	assumption	NOUN
ap-1267	175	9	of	of	ADP
ap-1267	175	10	atomicity	atomicity	NOUN
ap-1267	175	11	in	in	ADP
ap-1267	175	12	e	e	NOUN
ap-1267	175	13	it	it	PRON
ap-1267	175	14	is	be	AUX
ap-1267	175	15	enough	enough	ADJ
ap-1267	175	16	to	to	PART
ap-1267	175	17	take	take	VERB
ap-1267	175	18	the	the	DET
ap-1267	175	19	mv	mv	NOUN
ap-1267	175	20	-	-	PUNCT
ap-1267	175	21	effect	effect	NOUN
ap-1267	175	22	algebra	algebra	NOUN
ap-1267	175	23	e	e	NOUN
ap-1267	175	24	=	=	PRON
ap-1267	175	25	{	{	PUNCT
ap-1267	175	26	f	f	NOUN
ap-1267	175	27	:	:	PUNCT
ap-1267	176	1	[	[	X
ap-1267	176	2	0	0	NUM
ap-1267	176	3	,	,	PUNCT
ap-1267	176	4	1	1	NUM
ap-1267	176	5	]	]	PUNCT
ap-1267	176	6	→	→	PUNCT
ap-1267	176	7	[	[	X
ap-1267	176	8	0	0	NUM
ap-1267	176	9	,	,	PUNCT
ap-1267	176	10	1	1	NUM
ap-1267	176	11	]	]	PUNCT
ap-1267	176	12	|	|	ADV
ap-1267	176	13	f	f	PROPN
ap-1267	176	14	continuous	continuous	ADJ
ap-1267	176	15	function	function	NOUN
ap-1267	176	16	}	}	PUNCT
ap-1267	176	17	,	,	PUNCT
ap-1267	176	18	which	which	PRON
ap-1267	176	19	is	be	AUX
ap-1267	176	20	a	a	DET
ap-1267	176	21	sub	sub	ADJ
ap-1267	176	22	-	-	ADJ
ap-1267	176	23	lattice	lattice	ADJ
ap-1267	176	24	effect	effect	NOUN
ap-1267	176	25	algebra	algebra	NOUN
ap-1267	176	26	of	of	ADP
ap-1267	176	27	a	a	DET
ap-1267	176	28	direct	direct	ADJ
ap-1267	176	29	product	product	NOUN
ap-1267	176	30	of	of	ADP
ap-1267	176	31	copies	copy	NOUN
ap-1267	176	32	of	of	ADP
ap-1267	176	33	the	the	DET
ap-1267	176	34	standard	standard	ADJ
ap-1267	176	35	mv	mv	ADJ
ap-1267	176	36	-	-	PUNCT
ap-1267	176	37	effect	effect	NOUN
ap-1267	176	38	algebra	algebra	NOUN
ap-1267	176	39	of	of	ADP
ap-1267	176	40	real	real	ADJ
ap-1267	176	41	numbers	number	NOUN
ap-1267	176	42	[	[	X
ap-1267	176	43	0	0	NUM
ap-1267	176	44	,	,	PUNCT
ap-1267	176	45	1	1	NUM
ap-1267	176	46	]	]	PUNCT
ap-1267	176	47	that	that	PRON
ap-1267	176	48	is	be	AUX
ap-1267	176	49	archimedean	archimedean	ADJ
ap-1267	176	50	,	,	PUNCT
ap-1267	176	51	sharply	sharply	ADV
ap-1267	176	52	orthocomplete	orthocomplete	ADJ
ap-1267	176	53	(	(	PUNCT
ap-1267	176	54	the	the	DET
ap-1267	176	55	center	center	NOUN
ap-1267	176	56	c(e	c(e	NOUN
ap-1267	176	57	)	)	PUNCT
ap-1267	176	58	=	=	SYM
ap-1267	176	59	s(e	s(e	PROPN
ap-1267	176	60	)	)	PUNCT
ap-1267	176	61	=	=	PUNCT
ap-1267	176	62	{	{	PUNCT
ap-1267	176	63	0	0	NUM
ap-1267	176	64	,	,	PUNCT
ap-1267	176	65	1	1	NUM
ap-1267	176	66	}	}	PUNCT
ap-1267	176	67	is	be	AUX
ap-1267	176	68	trivial	trivial	ADJ
ap-1267	176	69	)	)	PUNCT
ap-1267	176	70	and	and	CCONJ
ap-1267	176	71	hence	hence	ADV
ap-1267	176	72	sharply	sharply	ADV
ap-1267	176	73	dominating	dominate	VERB
ap-1267	176	74	.	.	PUNCT
ap-1267	177	1	moreover	moreover	ADV
ap-1267	177	2	,	,	PUNCT
ap-1267	177	3	e	e	NOUN
ap-1267	177	4	is	be	AUX
ap-1267	177	5	not	not	PART
ap-1267	177	6	complete	complete	ADJ
ap-1267	177	7	.	.	PUNCT
ap-1267	178	1	it	it	PRON
ap-1267	178	2	is	be	AUX
ap-1267	178	3	well	well	ADV
ap-1267	178	4	known	know	VERB
ap-1267	178	5	that	that	SCONJ
ap-1267	178	6	an	an	DET
ap-1267	178	7	archimedean	archimedean	ADJ
ap-1267	178	8	lattice	lattice	PROPN
ap-1267	178	9	effect	effect	NOUN
ap-1267	178	10	algebra	algebra	NOUN
ap-1267	178	11	e	e	NOUN
ap-1267	178	12	is	be	AUX
ap-1267	178	13	complete	complete	ADJ
ap-1267	178	14	if	if	SCONJ
ap-1267	178	15	and	and	CCONJ
ap-1267	178	16	only	only	ADV
ap-1267	178	17	if	if	SCONJ
ap-1267	178	18	every	every	DET
ap-1267	178	19	block	block	NOUN
ap-1267	178	20	of	of	ADP
ap-1267	178	21	e	e	NOUN
ap-1267	178	22	is	be	AUX
ap-1267	178	23	complete	complete	ADJ
ap-1267	178	24	(	(	PUNCT
ap-1267	178	25	see	see	VERB
ap-1267	178	26	[	[	X
ap-1267	178	27	22	22	NUM
ap-1267	178	28	,	,	PUNCT
ap-1267	178	29	theorem	theorem	VERB
ap-1267	178	30	2.7	2.7	NUM
ap-1267	178	31	]	]	PUNCT
ap-1267	178	32	)	)	PUNCT
ap-1267	178	33	.	.	PUNCT
ap-1267	179	1	if	if	SCONJ
ap-1267	179	2	moreover	moreover	ADV
ap-1267	179	3	e	e	NOUN
ap-1267	179	4	is	be	AUX
ap-1267	179	5	atomic	atomic	ADJ
ap-1267	179	6	then	then	ADV
ap-1267	179	7	e	e	NOUN
ap-1267	179	8	may	may	AUX
ap-1267	179	9	have	have	VERB
ap-1267	179	10	atomic	atomic	ADJ
ap-1267	179	11	as	as	ADV
ap-1267	179	12	well	well	ADV
ap-1267	179	13	as	as	ADP
ap-1267	179	14	non	non	ADJ
ap-1267	179	15	-	-	ADJ
ap-1267	179	16	atomic	atomic	ADJ
ap-1267	179	17	blocks	block	NOUN
ap-1267	179	18	[	[	X
ap-1267	179	19	1	1	NUM
ap-1267	179	20	]	]	PUNCT
ap-1267	179	21	.	.	PUNCT
ap-1267	180	1	k.	k.	PROPN
ap-1267	180	2	mosná	mosná	PROPN
ap-1267	181	1	[	[	X
ap-1267	181	2	16	16	NUM
ap-1267	181	3	,	,	PUNCT
ap-1267	181	4	theorem	theorem	VERB
ap-1267	181	5	8	8	NUM
ap-1267	181	6	]	]	PUNCT
ap-1267	181	7	has	have	AUX
ap-1267	181	8	proved	prove	VERB
ap-1267	181	9	that	that	SCONJ
ap-1267	181	10	in	in	ADP
ap-1267	181	11	this	this	DET
ap-1267	181	12	case	case	NOUN
ap-1267	181	13	e	e	NOUN
ap-1267	181	14	=	=	X
ap-1267	181	15	⋃	⋃	X
ap-1267	181	16	{	{	PUNCT
ap-1267	181	17	m	m	NOUN
ap-1267	181	18	⊆	⊆	NUM
ap-1267	181	19	e	e	NOUN
ap-1267	181	20	|	|	ADV
ap-1267	181	21	m	m	VERB
ap-1267	181	22	atomic	atomic	ADJ
ap-1267	181	23	block	block	NOUN
ap-1267	181	24	of	of	ADP
ap-1267	181	25	e	e	NOUN
ap-1267	181	26	}	}	PUNCT
ap-1267	181	27	.	.	PUNCT
ap-1267	182	1	hence	hence	ADV
ap-1267	182	2	every	every	DET
ap-1267	182	3	non	non	ADJ
ap-1267	182	4	-	-	ADJ
ap-1267	182	5	atomic	atomic	ADJ
ap-1267	182	6	block	block	NOUN
ap-1267	182	7	of	of	ADP
ap-1267	182	8	e	e	PROPN
ap-1267	182	9	is	be	AUX
ap-1267	182	10	covered	cover	VERB
ap-1267	182	11	by	by	ADP
ap-1267	182	12	atomic	atomic	ADJ
ap-1267	182	13	blocks	block	NOUN
ap-1267	182	14	.	.	PUNCT
ap-1267	183	1	moreover	moreover	ADV
ap-1267	183	2	,	,	PUNCT
ap-1267	183	3	many	many	ADJ
ap-1267	183	4	properties	property	NOUN
ap-1267	183	5	of	of	ADP
ap-1267	183	6	archimedean	archimedean	ADJ
ap-1267	183	7	atomic	atomic	PROPN
ap-1267	183	8	lattice	lattice	PROPN
ap-1267	183	9	effect	effect	NOUN
ap-1267	183	10	algebras	algebra	VERB
ap-1267	183	11	as	as	ADV
ap-1267	183	12	well	well	ADV
ap-1267	183	13	as	as	ADP
ap-1267	183	14	their	their	PRON
ap-1267	183	15	non	non	ADJ
ap-1267	183	16	-	-	ADJ
ap-1267	183	17	atomic	atomic	ADJ
ap-1267	183	18	blocks	block	NOUN
ap-1267	183	19	depend	depend	VERB
ap-1267	183	20	on	on	ADP
ap-1267	183	21	properties	property	NOUN
ap-1267	183	22	of	of	ADP
ap-1267	183	23	their	their	PRON
ap-1267	183	24	atomic	atomic	ADJ
ap-1267	183	25	blocks	block	NOUN
ap-1267	183	26	.	.	PUNCT
ap-1267	184	1	namely	namely	ADV
ap-1267	184	2	,	,	PUNCT
ap-1267	184	3	the	the	DET
ap-1267	184	4	center	center	NOUN
ap-1267	184	5	c(e	c(e	PROPN
ap-1267	184	6	)	)	PUNCT
ap-1267	184	7	,	,	PUNCT
ap-1267	184	8	the	the	DET
ap-1267	184	9	compatibility	compatibility	NOUN
ap-1267	184	10	center	center	NOUN
ap-1267	184	11	b(e	b(e	PROPN
ap-1267	184	12	)	)	PUNCT
ap-1267	184	13	and	and	CCONJ
ap-1267	184	14	the	the	DET
ap-1267	184	15	set	set	NOUN
ap-1267	184	16	s(e	s(e	PROPN
ap-1267	184	17	)	)	PUNCT
ap-1267	184	18	of	of	ADP
ap-1267	184	19	sharp	sharp	ADJ
ap-1267	184	20	elements	element	NOUN
ap-1267	184	21	of	of	ADP
ap-1267	184	22	archimedean	archimedean	PROPN
ap-1267	184	23	atomic	atomic	PROPN
ap-1267	184	24	lattice	lattice	PROPN
ap-1267	184	25	effect	effect	NOUN
ap-1267	184	26	algebras	algebras	PROPN
ap-1267	184	27	e	e	PROPN
ap-1267	184	28	can	can	AUX
ap-1267	184	29	be	be	AUX
ap-1267	184	30	expressed	express	VERB
ap-1267	184	31	by	by	ADP
ap-1267	184	32	set	set	NOUN
ap-1267	184	33	-	-	PUNCT
ap-1267	184	34	theoretical	theoretical	ADJ
ap-1267	184	35	operations	operation	NOUN
ap-1267	184	36	on	on	ADP
ap-1267	184	37	their	their	PRON
ap-1267	184	38	atomic	atomic	ADJ
ap-1267	184	39	blocks	block	NOUN
ap-1267	184	40	.	.	PUNCT
ap-1267	185	1	as	as	SCONJ
ap-1267	185	2	follows	follow	VERB
ap-1267	185	3	,	,	PUNCT
ap-1267	185	4	b(e	b(e	ADJ
ap-1267	185	5	)	)	PUNCT
ap-1267	186	1	=	=	SYM
ap-1267	186	2	⋂	⋂	PROPN
ap-1267	186	3	{	{	PUNCT
ap-1267	186	4	m	m	PROPN
ap-1267	186	5	⊆	⊆	NUM
ap-1267	186	6	e	e	NOUN
ap-1267	186	7	|	|	ADV
ap-1267	186	8	m	m	VERB
ap-1267	186	9	atomic	atomic	ADJ
ap-1267	186	10	block	block	NOUN
ap-1267	186	11	of	of	ADP
ap-1267	186	12	e	e	NOUN
ap-1267	186	13	}	}	PUNCT
ap-1267	186	14	,	,	PUNCT
ap-1267	186	15	s(e	s(e	PROPN
ap-1267	186	16	)	)	PUNCT
ap-1267	186	17	=	=	SYM
ap-1267	186	18	⋃	⋃	NOUN
ap-1267	186	19	{	{	PUNCT
ap-1267	186	20	c(m	c(m	NOUN
ap-1267	186	21	)	)	PUNCT
ap-1267	187	1	|	|	ADV
ap-1267	187	2	m	m	VERB
ap-1267	187	3	⊆	⊆	NUM
ap-1267	187	4	e	e	NOUN
ap-1267	187	5	,	,	PUNCT
ap-1267	187	6	m	m	VERB
ap-1267	187	7	atomic	atomic	ADJ
ap-1267	187	8	block	block	NOUN
ap-1267	187	9	of	of	ADP
ap-1267	187	10	e	e	NOUN
ap-1267	187	11	}	}	PUNCT
ap-1267	187	12	and	and	CCONJ
ap-1267	187	13	c(e	c(e	NOUN
ap-1267	187	14	)	)	PUNCT
ap-1267	187	15	=	=	SYM
ap-1267	188	1	b(e	b(e	ADJ
ap-1267	188	2	)	)	PUNCT
ap-1267	188	3	∩	∩	PROPN
ap-1267	188	4	s(e	s(e	PROPN
ap-1267	188	5	)	)	PUNCT
ap-1267	189	1	(	(	PUNCT
ap-1267	189	2	see	see	VERB
ap-1267	189	3	[	[	X
ap-1267	189	4	16	16	NUM
ap-1267	189	5	]	]	SYM
ap-1267	189	6	)	)	PUNCT
ap-1267	189	7	.	.	PUNCT
ap-1267	190	1	54	54	NUM
ap-1267	190	2	acta	acta	PROPN
ap-1267	190	3	polytechnica	polytechnica	PROPN
ap-1267	190	4	vol	vol	NOUN
ap-1267	190	5	.	.	PROPN
ap-1267	191	1	50	50	NUM
ap-1267	191	2	no	no	NOUN
ap-1267	191	3	.	.	PUNCT
ap-1267	192	1	5/2010	5/2010	NUM
ap-1267	192	2	for	for	ADP
ap-1267	192	3	instance	instance	NOUN
ap-1267	192	4	,	,	PUNCT
ap-1267	192	5	an	an	DET
ap-1267	192	6	archimedean	archimedean	ADJ
ap-1267	192	7	atomic	atomic	ADJ
ap-1267	192	8	lattice	lattice	PROPN
ap-1267	192	9	effect	effect	NOUN
ap-1267	193	1	algebra	algebra	NOUN
ap-1267	193	2	e	e	NOUN
ap-1267	193	3	is	be	AUX
ap-1267	193	4	sharply	sharply	ADV
ap-1267	193	5	dominating	dominate	VERB
ap-1267	193	6	iff	iff	PROPN
ap-1267	193	7	every	every	DET
ap-1267	193	8	atomic	atomic	ADJ
ap-1267	193	9	block	block	NOUN
ap-1267	193	10	of	of	ADP
ap-1267	193	11	e	e	PROPN
ap-1267	193	12	is	be	AUX
ap-1267	193	13	sharply	sharply	ADV
ap-1267	193	14	dominating	dominate	VERB
ap-1267	193	15	(	(	PUNCT
ap-1267	193	16	see	see	VERB
ap-1267	193	17	[	[	X
ap-1267	193	18	11	11	NUM
ap-1267	193	19	]	]	NUM
ap-1267	193	20	)	)	PUNCT
ap-1267	193	21	.	.	PUNCT
ap-1267	194	1	moreover	moreover	ADV
ap-1267	194	2	,	,	PUNCT
ap-1267	194	3	we	we	PRON
ap-1267	194	4	can	can	AUX
ap-1267	194	5	prove	prove	VERB
ap-1267	194	6	the	the	DET
ap-1267	194	7	following	following	NOUN
ap-1267	194	8	:	:	PUNCT
ap-1267	194	9	theorem	theorem	VERB
ap-1267	194	10	3	3	NUM
ap-1267	194	11	let	let	VERB
ap-1267	194	12	e	e	PRON
ap-1267	194	13	be	be	AUX
ap-1267	194	14	an	an	DET
ap-1267	194	15	archimedean	archimedean	ADJ
ap-1267	194	16	atomic	atomic	ADJ
ap-1267	194	17	lattice	lattice	PROPN
ap-1267	194	18	effect	effect	PROPN
ap-1267	194	19	algebra	algebra	PROPN
ap-1267	194	20	.	.	PUNCT
ap-1267	195	1	then	then	ADV
ap-1267	195	2	the	the	DET
ap-1267	195	3	following	follow	VERB
ap-1267	195	4	conditions	condition	NOUN
ap-1267	195	5	are	be	AUX
ap-1267	195	6	equivalent	equivalent	ADJ
ap-1267	195	7	:	:	PUNCT
ap-1267	195	8	(	(	PUNCT
ap-1267	195	9	i	i	NOUN
ap-1267	195	10	)	)	PUNCT
ap-1267	195	11	e	e	NOUN
ap-1267	195	12	is	be	AUX
ap-1267	195	13	complete	complete	ADJ
ap-1267	195	14	.	.	PUNCT
ap-1267	196	1	(	(	PUNCT
ap-1267	196	2	ii	ii	NOUN
ap-1267	196	3	)	)	PUNCT
ap-1267	196	4	every	every	DET
ap-1267	196	5	atomic	atomic	ADJ
ap-1267	196	6	block	block	NOUN
ap-1267	196	7	of	of	ADP
ap-1267	196	8	e	e	NOUN
ap-1267	196	9	is	be	AUX
ap-1267	196	10	complete	complete	ADJ
ap-1267	196	11	.	.	PUNCT
ap-1267	197	1	in	in	ADP
ap-1267	197	2	this	this	DET
ap-1267	197	3	case	case	NOUN
ap-1267	197	4	every	every	DET
ap-1267	197	5	block	block	NOUN
ap-1267	197	6	of	of	ADP
ap-1267	197	7	e	e	NOUN
ap-1267	197	8	is	be	AUX
ap-1267	197	9	complete	complete	ADJ
ap-1267	197	10	.	.	PUNCT
ap-1267	198	1	proof	proof	NOUN
ap-1267	198	2	.	.	PUNCT
ap-1267	199	1	(	(	PUNCT
ap-1267	199	2	i	i	NOUN
ap-1267	199	3	)	)	PUNCT
ap-1267	200	1	=	=	NOUN
ap-1267	200	2	⇒	⇒	NOUN
ap-1267	200	3	(	(	PUNCT
ap-1267	200	4	ii	ii	NUM
ap-1267	200	5	):	):	PUNCT
ap-1267	200	6	this	this	PRON
ap-1267	200	7	is	be	AUX
ap-1267	200	8	trivial	trivial	ADJ
ap-1267	200	9	,	,	PUNCT
ap-1267	200	10	as	as	SCONJ
ap-1267	200	11	every	every	DET
ap-1267	200	12	blockm	blockm	NOUN
ap-1267	200	13	of	of	ADP
ap-1267	200	14	e	e	PROPN
ap-1267	200	15	is	be	AUX
ap-1267	200	16	a	a	DET
ap-1267	200	17	full	full	ADJ
ap-1267	200	18	sub	sub	ADJ
ap-1267	200	19	-	-	ADJ
ap-1267	200	20	lattice	lattice	ADJ
ap-1267	200	21	effect	effect	NOUN
ap-1267	200	22	algebra	algebra	PROPN
ap-1267	200	23	of	of	ADP
ap-1267	200	24	e.	e.	PROPN
ap-1267	200	25	(	(	PUNCT
ap-1267	200	26	ii	ii	PROPN
ap-1267	200	27	)	)	PUNCT
ap-1267	201	1	=	=	NOUN
ap-1267	201	2	⇒	⇒	NOUN
ap-1267	201	3	(	(	PUNCT
ap-1267	201	4	i	i	NOUN
ap-1267	201	5	):	):	PUNCT
ap-1267	201	6	it	it	PRON
ap-1267	201	7	is	be	AUX
ap-1267	201	8	enough	enough	ADJ
ap-1267	201	9	to	to	PART
ap-1267	201	10	show	show	VERB
ap-1267	201	11	that	that	SCONJ
ap-1267	201	12	e	e	NOUN
ap-1267	201	13	is	be	AUX
ap-1267	201	14	orthocomplete	orthocomplete	ADJ
ap-1267	201	15	.	.	PUNCT
ap-1267	202	1	from	from	ADP
ap-1267	202	2	[	[	X
ap-1267	202	3	22	22	NUM
ap-1267	202	4	,	,	PUNCT
ap-1267	202	5	theorem	theorem	VERB
ap-1267	202	6	2.6	2.6	NUM
ap-1267	202	7	]	]	PUNCT
ap-1267	202	8	we	we	PRON
ap-1267	202	9	then	then	ADV
ap-1267	202	10	get	get	VERB
ap-1267	202	11	that	that	SCONJ
ap-1267	202	12	e	e	NOUN
ap-1267	202	13	is	be	AUX
ap-1267	202	14	complete	complete	ADJ
ap-1267	202	15	.	.	PUNCT
ap-1267	203	1	let	let	VERB
ap-1267	203	2	g	g	PROPN
ap-1267	203	3	⊆	⊆	NUM
ap-1267	203	4	e	e	NOUN
ap-1267	203	5	be	be	AUX
ap-1267	203	6	a	a	DET
ap-1267	203	7	⊕	⊕	PROPN
ap-1267	203	8	-orthogonal	-orthogonal	ADJ
ap-1267	203	9	system	system	NOUN
ap-1267	203	10	.	.	PUNCT
ap-1267	204	1	then	then	ADV
ap-1267	204	2	,	,	PUNCT
ap-1267	204	3	for	for	ADP
ap-1267	204	4	every	every	DET
ap-1267	204	5	x	x	SYM
ap-1267	204	6	∈	∈	PROPN
ap-1267	204	7	g	g	NOUN
ap-1267	204	8	,	,	PUNCT
ap-1267	204	9	there	there	PRON
ap-1267	204	10	is	be	VERB
ap-1267	204	11	a	a	DET
ap-1267	204	12	set	set	ADJ
ap-1267	204	13	ax	ax	NOUN
ap-1267	204	14	of	of	ADP
ap-1267	204	15	atoms	atom	NOUN
ap-1267	204	16	of	of	ADP
ap-1267	204	17	e	e	NOUN
ap-1267	204	18	and	and	CCONJ
ap-1267	204	19	positive	positive	ADJ
ap-1267	204	20	integers	integer	NOUN
ap-1267	204	21	ka	ka	PROPN
ap-1267	204	22	,	,	PUNCT
ap-1267	204	23	a	a	DET
ap-1267	204	24	∈	∈	NOUN
ap-1267	204	25	ax	ax	NOUN
ap-1267	204	26	such	such	ADJ
ap-1267	204	27	that	that	SCONJ
ap-1267	204	28	x	x	X
ap-1267	204	29	=	=	SYM
ap-1267	204	30	⊕	⊕	PROPN
ap-1267	204	31	e	e	PROPN
ap-1267	204	32	{	{	PUNCT
ap-1267	204	33	kaa	kaa	PROPN
ap-1267	204	34	|	|	ADV
ap-1267	204	35	a	a	DET
ap-1267	204	36	∈	∈	NOUN
ap-1267	204	37	ax	ax	NOUN
ap-1267	204	38	}	}	PUNCT
ap-1267	204	39	.	.	PUNCT
ap-1267	205	1	moreover	moreover	ADV
ap-1267	205	2	,	,	PUNCT
ap-1267	205	3	for	for	ADP
ap-1267	205	4	any	any	DET
ap-1267	205	5	f	f	NOUN
ap-1267	205	6	⊆	⊆	NUM
ap-1267	205	7	g	g	NOUN
ap-1267	205	8	finite	finite	NOUN
ap-1267	205	9	we	we	PRON
ap-1267	205	10	have	have	VERB
ap-1267	205	11	that	that	PRON
ap-1267	205	12	⋃	⋃	NOUN
ap-1267	205	13	{	{	PUNCT
ap-1267	205	14	ax	ax	NOUN
ap-1267	205	15	|	|	ADV
ap-1267	205	16	x	x	SYM
ap-1267	205	17	∈	∈	PROPN
ap-1267	205	18	f	f	X
ap-1267	205	19	}	}	PUNCT
ap-1267	205	20	is	be	AUX
ap-1267	205	21	an	an	DET
ap-1267	205	22	orthogonal	orthogonal	ADJ
ap-1267	205	23	set	set	NOUN
ap-1267	205	24	of	of	ADP
ap-1267	205	25	atoms	atom	NOUN
ap-1267	205	26	.	.	PUNCT
ap-1267	206	1	hence	hence	ADV
ap-1267	206	2	ag	ag	PROPN
ap-1267	206	3	=	=	SYM
ap-1267	206	4	⋃	⋃	PROPN
ap-1267	206	5	{	{	PUNCT
ap-1267	206	6	ax	ax	NOUN
ap-1267	206	7	|	|	ADV
ap-1267	206	8	x	x	SYM
ap-1267	206	9	∈	∈	PROPN
ap-1267	206	10	g	g	NOUN
ap-1267	206	11	}	}	PUNCT
ap-1267	206	12	is	be	AUX
ap-1267	206	13	an	an	DET
ap-1267	206	14	orthogonal	orthogonal	ADJ
ap-1267	206	15	set	set	NOUN
ap-1267	206	16	of	of	ADP
ap-1267	206	17	atoms	atom	NOUN
ap-1267	206	18	of	of	ADP
ap-1267	206	19	e	e	NOUN
ap-1267	206	20	and	and	CCONJ
ap-1267	206	21	there	there	PRON
ap-1267	206	22	is	be	VERB
ap-1267	206	23	a	a	DET
ap-1267	206	24	maximal	maximal	ADJ
ap-1267	206	25	orthogonal	orthogonal	NOUN
ap-1267	206	26	set	set	NOUN
ap-1267	206	27	a	a	PRON
ap-1267	206	28	of	of	ADP
ap-1267	206	29	atoms	atom	NOUN
ap-1267	206	30	of	of	ADP
ap-1267	206	31	e	e	NOUN
ap-1267	206	32	such	such	ADJ
ap-1267	206	33	that	that	SCONJ
ap-1267	206	34	ag	ag	PROPN
ap-1267	206	35	⊆	⊆	NUM
ap-1267	206	36	a.	a.	NOUN
ap-1267	206	37	therefore	therefore	ADV
ap-1267	206	38	there	there	PRON
ap-1267	206	39	is	be	VERB
ap-1267	206	40	an	an	DET
ap-1267	206	41	atomic	atomic	ADJ
ap-1267	206	42	block	block	NOUN
ap-1267	206	43	m	m	VERB
ap-1267	206	44	of	of	ADP
ap-1267	206	45	e	e	PROPN
ap-1267	206	46	with	with	ADP
ap-1267	206	47	a	a	DET
ap-1267	206	48	⊆	⊆	NUM
ap-1267	206	49	m	m	NOUN
ap-1267	206	50	.	.	PUNCT
ap-1267	207	1	by	by	ADP
ap-1267	207	2	assumption	assumption	NOUN
ap-1267	207	3	⊕	⊕	PROPN
ap-1267	207	4	m	m	VERB
ap-1267	207	5	g	g	NOUN
ap-1267	207	6	exists	exist	NOUN
ap-1267	207	7	and	and	CCONJ
ap-1267	207	8	⊕	⊕	PROPN
ap-1267	207	9	m	m	VERB
ap-1267	207	10	g	g	PROPN
ap-1267	207	11	=	=	PROPN
ap-1267	207	12	⊕	⊕	PROPN
ap-1267	207	13	e	e	NOUN
ap-1267	207	14	g	g	PROPN
ap-1267	207	15	,	,	PUNCT
ap-1267	207	16	asm	asm	NOUN
ap-1267	207	17	is	be	AUX
ap-1267	207	18	bifull	bifull	ADJ
ap-1267	207	19	in	in	ADP
ap-1267	207	20	e	e	PROPN
ap-1267	207	21	because	because	SCONJ
ap-1267	207	22	e	e	NOUN
ap-1267	207	23	is	be	AUX
ap-1267	207	24	archimedean	archimedean	ADJ
ap-1267	207	25	and	and	CCONJ
ap-1267	207	26	atomic	atomic	ADJ
ap-1267	207	27	(	(	PUNCT
ap-1267	207	28	see	see	VERB
ap-1267	207	29	[	[	X
ap-1267	207	30	17	17	NUM
ap-1267	207	31	]	]	NUM
ap-1267	207	32	)	)	PUNCT
ap-1267	207	33	.	.	PUNCT
ap-1267	208	1	theorem	theorem	ADJ
ap-1267	208	2	4	4	NUM
ap-1267	208	3	let	let	VERB
ap-1267	208	4	e	e	PRON
ap-1267	208	5	be	be	AUX
ap-1267	208	6	a	a	DET
ap-1267	208	7	sharply	sharply	ADV
ap-1267	208	8	orthocomplete	orthocomplete	ADJ
ap-1267	208	9	lattice	lattice	PROPN
ap-1267	208	10	effect	effect	NOUN
ap-1267	208	11	algebra	algebra	NOUN
ap-1267	208	12	.	.	PUNCT
ap-1267	209	1	then	then	ADV
ap-1267	209	2	(	(	PUNCT
ap-1267	209	3	i	i	NOUN
ap-1267	209	4	)	)	PUNCT
ap-1267	209	5	s(e	s(e	PROPN
ap-1267	209	6	)	)	PUNCT
ap-1267	209	7	is	be	AUX
ap-1267	209	8	a	a	DET
ap-1267	209	9	complete	complete	ADJ
ap-1267	209	10	orthomodular	orthomodular	ADJ
ap-1267	209	11	lattice	lattice	NOUN
ap-1267	209	12	bifull	bifull	PROPN
ap-1267	209	13	in	in	ADP
ap-1267	209	14	e.	e.	PROPN
ap-1267	209	15	(	(	PUNCT
ap-1267	209	16	ii	ii	PROPN
ap-1267	209	17	)	)	PUNCT
ap-1267	209	18	c(e	c(e	NOUN
ap-1267	209	19	)	)	PUNCT
ap-1267	210	1	is	be	AUX
ap-1267	210	2	a	a	DET
ap-1267	210	3	complete	complete	ADJ
ap-1267	210	4	boolean	boolean	ADJ
ap-1267	210	5	algebra	algebra	NOUN
ap-1267	210	6	bifull	bifull	PROPN
ap-1267	210	7	in	in	ADP
ap-1267	210	8	e.	e.	PROPN
ap-1267	210	9	(	(	PUNCT
ap-1267	210	10	iii	iii	PROPN
ap-1267	210	11	)	)	PUNCT
ap-1267	210	12	e	e	NOUN
ap-1267	210	13	is	be	AUX
ap-1267	210	14	sharply	sharply	ADV
ap-1267	210	15	dominating	dominate	VERB
ap-1267	210	16	,	,	PUNCT
ap-1267	210	17	centrally	centrally	ADV
ap-1267	210	18	dominating	dominating	NOUN
ap-1267	210	19	and	and	CCONJ
ap-1267	210	20	s	s	NOUN
ap-1267	210	21	-	-	ADJ
ap-1267	210	22	dominating	dominating	NOUN
ap-1267	210	23	.	.	PUNCT
ap-1267	211	1	(	(	PUNCT
ap-1267	211	2	iv	iv	X
ap-1267	211	3	)	)	PUNCT
ap-1267	211	4	if	if	SCONJ
ap-1267	211	5	moreover	moreover	ADV
ap-1267	211	6	e	e	NOUN
ap-1267	211	7	is	be	AUX
ap-1267	211	8	archimedean	archimedean	ADJ
ap-1267	211	9	and	and	CCONJ
ap-1267	211	10	atomic	atomic	NOUN
ap-1267	211	11	then	then	ADV
ap-1267	211	12	e	e	PROPN
ap-1267	211	13	is	be	AUX
ap-1267	211	14	a	a	DET
ap-1267	211	15	complete	complete	ADJ
ap-1267	211	16	lattice	lattice	NOUN
ap-1267	211	17	effect	effect	NOUN
ap-1267	211	18	algebra	algebra	NOUN
ap-1267	211	19	.	.	PUNCT
ap-1267	212	1	proof	proof	NOUN
ap-1267	212	2	.	.	PUNCT
ap-1267	213	1	(	(	PUNCT
ap-1267	213	2	i	i	NOUN
ap-1267	213	3	)	)	PUNCT
ap-1267	213	4	,	,	PUNCT
ap-1267	213	5	(	(	PUNCT
ap-1267	213	6	iii	iii	NOUN
ap-1267	213	7	):	):	PUNCT
ap-1267	213	8	let	let	VERB
ap-1267	213	9	s	s	PRON
ap-1267	213	10	⊆	⊆	NUM
ap-1267	213	11	s(e	s(e	PROPN
ap-1267	213	12	)	)	PUNCT
ap-1267	213	13	,	,	PUNCT
ap-1267	213	14	s	s	AUX
ap-1267	213	15	be	be	AUX
ap-1267	213	16	orthogonal	orthogonal	ADJ
ap-1267	213	17	.	.	PUNCT
ap-1267	214	1	then	then	ADV
ap-1267	214	2	,	,	PUNCT
ap-1267	214	3	for	for	ADP
ap-1267	214	4	any	any	DET
ap-1267	214	5	s	s	X
ap-1267	214	6	∈	∈	PROPN
ap-1267	214	7	s	s	NOUN
ap-1267	214	8	,	,	PUNCT
ap-1267	214	9	s	s	PART
ap-1267	214	10	≤	≤	NUM
ap-1267	214	11	s.	s.	PROPN
ap-1267	214	12	hence	hence	ADV
ap-1267	214	13	(	(	PUNCT
ap-1267	214	14	since	since	SCONJ
ap-1267	214	15	s(e	s(e	PROPN
ap-1267	214	16	)	)	PUNCT
ap-1267	214	17	is	be	AUX
ap-1267	214	18	full	full	ADJ
ap-1267	214	19	in	in	ADP
ap-1267	214	20	e	e	NOUN
ap-1267	214	21	)	)	PUNCT
ap-1267	214	22	⊕	⊕	PROPN
ap-1267	215	1	e	e	NOUN
ap-1267	215	2	s	s	X
ap-1267	215	3	=	=	PUNCT
ap-1267	215	4	∨	∨	NUM
ap-1267	215	5	e	e	X
ap-1267	215	6	s	s	X
ap-1267	215	7	=	=	SYM
ap-1267	215	8	∨	∨	PROPN
ap-1267	215	9	s(e	s(e	PROPN
ap-1267	215	10	)	)	PUNCT
ap-1267	215	11	s	s	PART
ap-1267	215	12	∈	∈	PROPN
ap-1267	215	13	s(e	s(e	PROPN
ap-1267	215	14	)	)	PUNCT
ap-1267	215	15	exists	exist	VERB
ap-1267	215	16	.	.	PUNCT
ap-1267	216	1	since	since	SCONJ
ap-1267	216	2	s(e	s(e	PROPN
ap-1267	216	3	)	)	PUNCT
ap-1267	216	4	is	be	AUX
ap-1267	216	5	an	an	DET
ap-1267	216	6	archimedean	archimedean	ADJ
ap-1267	216	7	lattice	lattice	PROPN
ap-1267	216	8	effect	effect	NOUN
ap-1267	216	9	algebra	algebra	NOUN
ap-1267	216	10	we	we	PRON
ap-1267	216	11	have	have	VERB
ap-1267	216	12	from	from	ADP
ap-1267	216	13	[	[	X
ap-1267	216	14	22	22	NUM
ap-1267	216	15	,	,	PUNCT
ap-1267	216	16	theorem	theorem	VERB
ap-1267	216	17	2.6	2.6	NUM
ap-1267	216	18	]	]	PUNCT
ap-1267	216	19	that	that	SCONJ
ap-1267	216	20	s(e	s(e	PROPN
ap-1267	216	21	)	)	PUNCT
ap-1267	216	22	is	be	AUX
ap-1267	216	23	complete	complete	ADJ
ap-1267	216	24	.	.	PUNCT
ap-1267	217	1	moreover	moreover	ADV
ap-1267	217	2	,	,	PUNCT
ap-1267	217	3	let	let	VERB
ap-1267	217	4	x	x	SYM
ap-1267	217	5	∈	∈	NOUN
ap-1267	217	6	e	e	X
ap-1267	217	7	and	and	CCONJ
ap-1267	217	8	let	let	VERB
ap-1267	217	9	g	g	NOUN
ap-1267	217	10	=	=	PUNCT
ap-1267	217	11	(	(	PUNCT
ap-1267	217	12	wκ)κ∈h	wκ)κ∈h	NUM
ap-1267	217	13	,	,	PUNCT
ap-1267	217	14	wκ	wκ	PROPN
ap-1267	217	15	∈	∈	PROPN
ap-1267	217	16	s(e	s(e	PROPN
ap-1267	217	17	)	)	PUNCT
ap-1267	217	18	,	,	PUNCT
ap-1267	217	19	κ	κ	PROPN
ap-1267	217	20	∈	∈	PROPN
ap-1267	217	21	h	h	NOUN
ap-1267	217	22	be	be	AUX
ap-1267	217	23	a	a	DET
ap-1267	217	24	maximal	maximal	ADJ
ap-1267	217	25	orthogonal	orthogonal	ADJ
ap-1267	217	26	system	system	NOUN
ap-1267	217	27	of	of	ADP
ap-1267	217	28	mutually	mutually	ADV
ap-1267	217	29	different	different	ADJ
ap-1267	217	30	elements	element	NOUN
ap-1267	217	31	such	such	ADJ
ap-1267	217	32	that	that	SCONJ
ap-1267	217	33	wx	wx	PROPN
ap-1267	217	34	=	=	PROPN
ap-1267	217	35	⊕	⊕	PROPN
ap-1267	217	36	e	e	PROPN
ap-1267	217	37	{	{	PUNCT
ap-1267	217	38	wκ	wκ	INTJ
ap-1267	217	39	|	|	ADV
ap-1267	217	40	κ	κ	PROPN
ap-1267	217	41	∈	∈	PROPN
ap-1267	217	42	h	h	NOUN
ap-1267	217	43	}	}	PUNCT
ap-1267	217	44	≤	≤	NOUN
ap-1267	217	45	x.	x.	NOUN
ap-1267	217	46	let	let	VERB
ap-1267	217	47	us	we	PRON
ap-1267	217	48	show	show	VERB
ap-1267	217	49	that	that	SCONJ
ap-1267	217	50	y	y	PROPN
ap-1267	217	51	∈	∈	PROPN
ap-1267	217	52	s(e	s(e	PROPN
ap-1267	217	53	)	)	PUNCT
ap-1267	217	54	,	,	PUNCT
ap-1267	217	55	y	y	PROPN
ap-1267	217	56	≤	≤	NUM
ap-1267	217	57	x	x	PUNCT
ap-1267	218	1	=	=	X
ap-1267	218	2	⇒	⇒	X
ap-1267	218	3	y	y	PROPN
ap-1267	218	4	≤	≤	NUM
ap-1267	218	5	wx	wx	PROPN
ap-1267	218	6	∈	∈	PROPN
ap-1267	218	7	s(e	s(e	PROPN
ap-1267	218	8	)	)	PUNCT
ap-1267	218	9	.	.	PUNCT
ap-1267	219	1	clearly	clearly	ADV
ap-1267	219	2	,	,	PUNCT
ap-1267	219	3	wx	wx	PROPN
ap-1267	219	4	∈	∈	PROPN
ap-1267	219	5	s(e	s(e	PROPN
ap-1267	219	6	)	)	PUNCT
ap-1267	219	7	.	.	PUNCT
ap-1267	220	1	assume	assume	VERB
ap-1267	220	2	that	that	SCONJ
ap-1267	220	3	y	y	PROPN
ap-1267	220	4	≤	≤	NUM
ap-1267	220	5	wx	wx	PROPN
ap-1267	220	6	.	.	PUNCT
ap-1267	221	1	then	then	ADV
ap-1267	221	2	wx	wx	PROPN
ap-1267	221	3	<	<	X
ap-1267	221	4	y	y	PROPN
ap-1267	221	5	∨	∨	NUM
ap-1267	221	6	wx	wx	PROPN
ap-1267	221	7	≤	≤	NUM
ap-1267	221	8	x.	x.	NOUN
ap-1267	222	1	hence	hence	ADV
ap-1267	222	2	z	z	PROPN
ap-1267	223	1	=	=	PRON
ap-1267	223	2	(	(	PUNCT
ap-1267	223	3	y	y	PROPN
ap-1267	223	4	∨	∨	NUM
ap-1267	223	5	wx	wx	PROPN
ap-1267	223	6	)	)	PUNCT
ap-1267	223	7	!	!	PUNCT
ap-1267	224	1	wx	wx	X
ap-1267	224	2	=	=	SYM
ap-1267	224	3	0	0	PROPN
ap-1267	224	4	and	and	CCONJ
ap-1267	224	5	g	g	PROPN
ap-1267	224	6	∪	∪	VERB
ap-1267	224	7	{	{	PUNCT
ap-1267	224	8	z	z	NOUN
ap-1267	224	9	}	}	PUNCT
ap-1267	224	10	is	be	AUX
ap-1267	224	11	an	an	DET
ap-1267	224	12	orthogonal	orthogonal	ADJ
ap-1267	224	13	system	system	NOUN
ap-1267	224	14	of	of	ADP
ap-1267	224	15	mutually	mutually	ADV
ap-1267	224	16	different	different	ADJ
ap-1267	224	17	elements	element	NOUN
ap-1267	224	18	such	such	ADJ
ap-1267	224	19	that	that	SCONJ
ap-1267	224	20	y	y	PROPN
ap-1267	224	21	∨	∨	NUM
ap-1267	224	22	wx	wx	X
ap-1267	224	23	=	=	SYM
ap-1267	224	24	wx	wx	PROPN
ap-1267	224	25	⊕	⊕	PROPN
ap-1267	224	26	z	z	PROPN
ap-1267	224	27	=	=	SYM
ap-1267	224	28	⊕	⊕	PROPN
ap-1267	224	29	e	e	PROPN
ap-1267	224	30	{	{	PUNCT
ap-1267	224	31	wκ	wκ	INTJ
ap-1267	224	32	|	|	ADV
ap-1267	224	33	κ	κ	PROPN
ap-1267	224	34	∈	∈	PROPN
ap-1267	224	35	h	h	NOUN
ap-1267	224	36	}	}	PUNCT
ap-1267	224	37	⊕	⊕	PROPN
ap-1267	224	38	z	z	NOUN
ap-1267	224	39	≤	≤	NUM
ap-1267	224	40	x	x	X
ap-1267	224	41	,	,	PUNCT
ap-1267	224	42	a	a	DET
ap-1267	224	43	contradiction	contradiction	NOUN
ap-1267	224	44	with	with	ADP
ap-1267	224	45	the	the	DET
ap-1267	224	46	maximality	maximality	NOUN
ap-1267	224	47	of	of	ADP
ap-1267	224	48	g.	g.	PROPN
ap-1267	224	49	therefore	therefore	ADV
ap-1267	224	50	y	y	PROPN
ap-1267	224	51	≤	≤	PROPN
ap-1267	224	52	wx	wx	PROPN
ap-1267	224	53	and	and	CCONJ
ap-1267	224	54	e	e	PROPN
ap-1267	224	55	is	be	AUX
ap-1267	224	56	sharply	sharply	ADV
ap-1267	224	57	dominating	dominate	VERB
ap-1267	224	58	,	,	PUNCT
ap-1267	224	59	hence	hence	ADV
ap-1267	224	60	sdominating	sdominate	VERB
ap-1267	224	61	and	and	CCONJ
ap-1267	224	62	from	from	ADP
ap-1267	224	63	theorem	theorem	ADJ
ap-1267	224	64	2	2	NUM
ap-1267	224	65	we	we	PRON
ap-1267	224	66	get	get	VERB
ap-1267	224	67	that	that	SCONJ
ap-1267	224	68	e	e	NOUN
ap-1267	224	69	is	be	AUX
ap-1267	224	70	centrally	centrally	ADV
ap-1267	224	71	dominating	dominate	VERB
ap-1267	224	72	.	.	PUNCT
ap-1267	225	1	from	from	ADP
ap-1267	225	2	theorem	theorem	NOUN
ap-1267	225	3	1	1	NUM
ap-1267	225	4	,	,	PUNCT
ap-1267	225	5	we	we	PRON
ap-1267	225	6	get	get	VERB
ap-1267	225	7	that	that	DET
ap-1267	225	8	s(e	s(e	PROPN
ap-1267	225	9	)	)	PUNCT
ap-1267	225	10	is	be	AUX
ap-1267	225	11	bifull	bifull	PROPN
ap-1267	225	12	in	in	ADP
ap-1267	225	13	e.	e.	PROPN
ap-1267	225	14	(	(	PUNCT
ap-1267	225	15	ii	ii	PROPN
ap-1267	225	16	):	):	PUNCT
ap-1267	225	17	it	it	PRON
ap-1267	225	18	follows	follow	VERB
ap-1267	225	19	from	from	ADP
ap-1267	225	20	(	(	PUNCT
ap-1267	225	21	i	i	NOUN
ap-1267	225	22	)	)	PUNCT
ap-1267	225	23	,	,	PUNCT
ap-1267	225	24	(	(	PUNCT
ap-1267	225	25	iii	iii	NOUN
ap-1267	225	26	)	)	PUNCT
ap-1267	225	27	and	and	CCONJ
ap-1267	225	28	theorem	theorem	VERB
ap-1267	225	29	2	2	NUM
ap-1267	225	30	.	.	PUNCT
ap-1267	225	31	(	(	PUNCT
ap-1267	225	32	iv	iv	NUM
ap-1267	225	33	):	):	PUNCT
ap-1267	225	34	assume	assume	VERB
ap-1267	225	35	now	now	ADV
ap-1267	225	36	that	that	SCONJ
ap-1267	225	37	e	e	NOUN
ap-1267	225	38	is	be	AUX
ap-1267	225	39	a	a	DET
ap-1267	225	40	sharply	sharply	ADV
ap-1267	225	41	orthocomplete	orthocomplete	ADJ
ap-1267	225	42	archimedean	archimedean	PROPN
ap-1267	225	43	atomic	atomic	PROPN
ap-1267	225	44	lattice	lattice	PROPN
ap-1267	225	45	effect	effect	PROPN
ap-1267	225	46	algebra	algebra	PROPN
ap-1267	225	47	.	.	PUNCT
ap-1267	226	1	then	then	ADV
ap-1267	226	2	every	every	DET
ap-1267	226	3	atomic	atomic	ADJ
ap-1267	226	4	block	block	NOUN
ap-1267	226	5	m	m	VERB
ap-1267	226	6	of	of	ADP
ap-1267	226	7	e	e	PROPN
ap-1267	226	8	is	be	AUX
ap-1267	226	9	a	a	DET
ap-1267	226	10	sharply	sharply	ADV
ap-1267	226	11	orthocomplete	orthocomplete	ADJ
ap-1267	226	12	archimedean	archimedean	PROPN
ap-1267	226	13	atomic	atomic	ADJ
ap-1267	226	14	mv	mv	PROPN
ap-1267	226	15	-	-	PUNCT
ap-1267	226	16	effect	effect	NOUN
ap-1267	226	17	algebra	algebra	NOUN
ap-1267	226	18	and	and	CCONJ
ap-1267	226	19	hence	hence	ADV
ap-1267	226	20	it	it	PRON
ap-1267	226	21	is	be	AUX
ap-1267	226	22	a	a	DET
ap-1267	226	23	complete	complete	ADJ
ap-1267	226	24	mv	mv	NOUN
ap-1267	226	25	-	-	PUNCT
ap-1267	226	26	effect	effect	NOUN
ap-1267	226	27	algebra	algebra	NOUN
ap-1267	226	28	by	by	ADP
ap-1267	226	29	lemma	lemma	PROPN
ap-1267	226	30	1	1	NUM
ap-1267	226	31	.	.	PUNCT
ap-1267	226	32	by	by	ADP
ap-1267	226	33	theorem	theorem	NOUN
ap-1267	226	34	3	3	NUM
ap-1267	226	35	,	,	PUNCT
ap-1267	226	36	e	e	X
ap-1267	226	37	is	be	AUX
ap-1267	226	38	a	a	DET
ap-1267	226	39	complete	complete	ADJ
ap-1267	226	40	lattice	lattice	NOUN
ap-1267	226	41	effect	effect	NOUN
ap-1267	226	42	algebra	algebra	NOUN
ap-1267	226	43	.	.	PUNCT
ap-1267	227	1	theorem	theorem	NOUN
ap-1267	227	2	5	5	NUM
ap-1267	227	3	let	let	VERB
ap-1267	227	4	e	e	PRON
ap-1267	227	5	be	be	AUX
ap-1267	227	6	an	an	DET
ap-1267	227	7	atomic	atomic	ADJ
ap-1267	227	8	lattice	lattice	NOUN
ap-1267	227	9	effect	effect	NOUN
ap-1267	227	10	algebra	algebra	PROPN
ap-1267	227	11	.	.	PUNCT
ap-1267	228	1	then	then	ADV
ap-1267	228	2	the	the	DET
ap-1267	228	3	following	follow	VERB
ap-1267	228	4	conditions	condition	NOUN
ap-1267	228	5	are	be	AUX
ap-1267	228	6	equivalent	equivalent	ADJ
ap-1267	228	7	:	:	PUNCT
ap-1267	228	8	(	(	PUNCT
ap-1267	228	9	i	i	NOUN
ap-1267	228	10	)	)	PUNCT
ap-1267	228	11	e	e	NOUN
ap-1267	228	12	is	be	AUX
ap-1267	228	13	complete	complete	ADJ
ap-1267	228	14	.	.	PUNCT
ap-1267	229	1	(	(	PUNCT
ap-1267	229	2	ii	ii	NOUN
ap-1267	229	3	)	)	PUNCT
ap-1267	229	4	e	e	NOUN
ap-1267	229	5	is	be	AUX
ap-1267	229	6	archimedean	archimedean	ADJ
ap-1267	229	7	and	and	CCONJ
ap-1267	229	8	sharply	sharply	ADV
ap-1267	229	9	orthocomplete	orthocomplete	ADJ
ap-1267	229	10	.	.	PUNCT
ap-1267	230	1	proof	proof	NOUN
ap-1267	230	2	.	.	PUNCT
ap-1267	231	1	(	(	PUNCT
ap-1267	231	2	i	i	NOUN
ap-1267	231	3	)	)	PUNCT
ap-1267	232	1	=	=	NOUN
ap-1267	232	2	⇒	⇒	NOUN
ap-1267	232	3	(	(	PUNCT
ap-1267	232	4	ii	ii	NUM
ap-1267	232	5	):	):	PUNCT
ap-1267	232	6	by	by	ADP
ap-1267	232	7	[	[	X
ap-1267	232	8	20	20	NUM
ap-1267	232	9	,	,	PUNCT
ap-1267	232	10	theorem	theorem	VERB
ap-1267	232	11	3.3	3.3	NUM
ap-1267	232	12	]	]	PUNCT
ap-1267	232	13	we	we	PRON
ap-1267	232	14	have	have	VERB
ap-1267	232	15	that	that	SCONJ
ap-1267	232	16	any	any	DET
ap-1267	232	17	complete	complete	ADJ
ap-1267	232	18	lattice	lattice	NOUN
ap-1267	232	19	effect	effect	NOUN
ap-1267	232	20	algebra	algebra	NOUN
ap-1267	232	21	is	be	AUX
ap-1267	232	22	archimedean	archimedean	ADJ
ap-1267	232	23	.	.	PUNCT
ap-1267	233	1	evidently	evidently	ADV
ap-1267	233	2	,	,	PUNCT
ap-1267	233	3	any	any	DET
ap-1267	233	4	complete	complete	ADJ
ap-1267	233	5	lattice	lattice	NOUN
ap-1267	233	6	effect	effect	NOUN
ap-1267	233	7	algebra	algebra	NOUN
ap-1267	233	8	is	be	AUX
ap-1267	233	9	sharply	sharply	ADV
ap-1267	233	10	orthocomplete	orthocomplete	ADJ
ap-1267	233	11	.	.	PUNCT
ap-1267	234	1	(	(	PUNCT
ap-1267	234	2	ii	ii	NOUN
ap-1267	234	3	)	)	PUNCT
ap-1267	235	1	=	=	NOUN
ap-1267	235	2	⇒	⇒	NOUN
ap-1267	235	3	(	(	PUNCT
ap-1267	235	4	i	i	NOUN
ap-1267	235	5	):	):	PUNCT
ap-1267	235	6	it	it	PRON
ap-1267	235	7	follows	follow	VERB
ap-1267	235	8	from	from	ADP
ap-1267	235	9	theorem	theorem	ADJ
ap-1267	235	10	4	4	NUM
ap-1267	235	11	,	,	PUNCT
ap-1267	235	12	(	(	PUNCT
ap-1267	235	13	iv	iv	X
ap-1267	235	14	)	)	PUNCT
ap-1267	235	15	.	.	PUNCT
ap-1267	236	1	acknowledgement	acknowledgement	NOUN
ap-1267	236	2	the	the	DET
ap-1267	236	3	work	work	NOUN
ap-1267	236	4	of	of	ADP
ap-1267	236	5	the	the	DET
ap-1267	236	6	first	first	ADJ
ap-1267	236	7	author	author	NOUN
ap-1267	236	8	was	be	AUX
ap-1267	236	9	supported	support	VERB
ap-1267	236	10	by	by	ADP
ap-1267	236	11	the	the	DET
ap-1267	236	12	slovak	slovak	ADJ
ap-1267	236	13	research	research	NOUN
ap-1267	236	14	and	and	CCONJ
ap-1267	236	15	development	development	NOUN
ap-1267	236	16	agency	agency	NOUN
ap-1267	236	17	under	under	ADP
ap-1267	236	18	contract	contract	NOUN
ap-1267	236	19	no	no	INTJ
ap-1267	236	20	.	.	PUNCT
ap-1267	237	1	apvv–0375–06	apvv–0375–06	PUNCT
ap-1267	238	1	and	and	CCONJ
ap-1267	238	2	by	by	ADP
ap-1267	238	3	the	the	DET
ap-1267	238	4	vega	vega	PROPN
ap-1267	238	5	grant	grant	PROPN
ap-1267	238	6	agency	agency	PROPN
ap-1267	238	7	,	,	PUNCT
ap-1267	238	8	grant	grant	VERB
ap-1267	238	9	number	number	NOUN
ap-1267	238	10	1/0373/08	1/0373/08	NUM
ap-1267	238	11	.	.	PUNCT
ap-1267	239	1	the	the	DET
ap-1267	239	2	second	second	ADJ
ap-1267	239	3	author	author	NOUN
ap-1267	239	4	gratefully	gratefully	ADV
ap-1267	239	5	acknowledges	acknowledge	VERB
ap-1267	239	6	financial	financial	ADJ
ap-1267	239	7	support	support	NOUN
ap-1267	239	8	from	from	ADP
ap-1267	239	9	the	the	DET
ap-1267	239	10	ministry	ministry	PROPN
ap-1267	239	11	of	of	ADP
ap-1267	239	12	education	education	NOUN
ap-1267	239	13	of	of	ADP
ap-1267	239	14	the	the	DET
ap-1267	239	15	czech	czech	PROPN
ap-1267	239	16	republic	republic	NOUN
ap-1267	239	17	under	under	ADP
ap-1267	239	18	project	project	NOUN
ap-1267	239	19	msm0021622409	msm0021622409	NOUN
ap-1267	239	20	.	.	PUNCT
ap-1267	240	1	the	the	DET
ap-1267	240	2	third	third	ADJ
ap-1267	240	3	author	author	NOUN
ap-1267	240	4	was	be	AUX
ap-1267	240	5	supported	support	VERB
ap-1267	240	6	by	by	ADP
ap-1267	240	7	the	the	DET
ap-1267	240	8	slovak	slovak	ADJ
ap-1267	240	9	research	research	NOUN
ap-1267	240	10	and	and	CCONJ
ap-1267	240	11	development	development	NOUN
ap-1267	240	12	agency	agency	NOUN
ap-1267	240	13	under	under	ADP
ap-1267	240	14	contract	contract	NOUN
ap-1267	240	15	no	no	NOUN
ap-1267	240	16	.	.	PUNCT
ap-1267	241	1	apvv–0071–06	apvv–0071–06	NUM
ap-1267	241	2	.	.	PUNCT
ap-1267	242	1	the	the	DET
ap-1267	242	2	authors	author	NOUN
ap-1267	242	3	also	also	ADV
ap-1267	242	4	thank	thank	VERB
ap-1267	242	5	the	the	DET
ap-1267	242	6	referee	referee	NOUN
ap-1267	242	7	for	for	ADP
ap-1267	242	8	reading	read	VERB
ap-1267	242	9	very	very	ADV
ap-1267	242	10	thoroughly	thoroughly	ADV
ap-1267	242	11	and	and	CCONJ
ap-1267	242	12	for	for	ADP
ap-1267	242	13	improving	improve	VERB
ap-1267	242	14	the	the	DET
ap-1267	242	15	presentation	presentation	NOUN
ap-1267	242	16	of	of	ADP
ap-1267	242	17	the	the	DET
ap-1267	242	18	paper	paper	NOUN
ap-1267	242	19	.	.	PUNCT
ap-1267	243	1	references	reference	NOUN
ap-1267	243	2	[	[	X
ap-1267	243	3	1	1	NUM
ap-1267	243	4	]	]	PUNCT
ap-1267	243	5	beltrametti	beltrametti	PROPN
ap-1267	243	6	,	,	PUNCT
ap-1267	243	7	e.	e.	PROPN
ap-1267	243	8	g.	g.	PROPN
ap-1267	243	9	,	,	PUNCT
ap-1267	243	10	cassinelli	cassinelli	PROPN
ap-1267	243	11	,	,	PUNCT
ap-1267	243	12	g.	g.	PROPN
ap-1267	243	13	:	:	PUNCT
ap-1267	243	14	the	the	DET
ap-1267	243	15	logic	logic	NOUN
ap-1267	243	16	of	of	ADP
ap-1267	243	17	quantum	quantum	ADJ
ap-1267	243	18	mechanics	mechanic	NOUN
ap-1267	243	19	.	.	PUNCT
ap-1267	244	1	addison	addison	PROPN
ap-1267	244	2	-	-	PUNCT
ap-1267	244	3	wesley	wesley	PROPN
ap-1267	244	4	,	,	PUNCT
ap-1267	244	5	reading	reading	NOUN
ap-1267	244	6	,	,	PUNCT
ap-1267	244	7	ma	ma	PROPN
ap-1267	244	8	,	,	PUNCT
ap-1267	244	9	1981	1981	NUM
ap-1267	244	10	.	.	PUNCT
ap-1267	245	1	[	[	X
ap-1267	245	2	2	2	NUM
ap-1267	245	3	]	]	SYM
ap-1267	245	4	busch	busch	PROPN
ap-1267	245	5	,	,	PUNCT
ap-1267	245	6	p.	p.	NOUN
ap-1267	245	7	,	,	PUNCT
ap-1267	245	8	lahti	lahti	NOUN
ap-1267	245	9	,	,	PUNCT
ap-1267	245	10	p.	p.	PROPN
ap-1267	245	11	j.	j.	PROPN
ap-1267	245	12	,	,	PUNCT
ap-1267	245	13	mittelstaedt	mittelstaedt	NOUN
ap-1267	245	14	,	,	PUNCT
ap-1267	245	15	p.	p.	NOUN
ap-1267	245	16	:	:	PUNCT
ap-1267	245	17	the	the	DET
ap-1267	245	18	quantum	quantum	ADJ
ap-1267	245	19	theory	theory	NOUN
ap-1267	245	20	of	of	ADP
ap-1267	245	21	measurement	measurement	NOUN
ap-1267	245	22	,	,	PUNCT
ap-1267	245	23	lecture	lecture	NOUN
ap-1267	245	24	notes	note	NOUN
ap-1267	245	25	in	in	ADP
ap-1267	245	26	physics	physics	NOUN
ap-1267	245	27	,	,	PUNCT
ap-1267	245	28	new	new	ADJ
ap-1267	245	29	series	series	NOUN
ap-1267	245	30	m	m	PROPN
ap-1267	245	31	:	:	PUNCT
ap-1267	245	32	monographs	monograph	NOUN
ap-1267	245	33	,	,	PUNCT
ap-1267	245	34	vol	vol	NOUN
ap-1267	245	35	.	.	PROPN
ap-1267	245	36	2	2	NUM
ap-1267	245	37	,	,	PUNCT
ap-1267	245	38	springer	springer	NOUN
ap-1267	245	39	-	-	PUNCT
ap-1267	245	40	verlag	verlag	PROPN
ap-1267	245	41	,	,	PUNCT
ap-1267	245	42	berlin	berlin	PROPN
ap-1267	245	43	,	,	PUNCT
ap-1267	245	44	1991	1991	NUM
ap-1267	245	45	.	.	PUNCT
ap-1267	246	1	[	[	X
ap-1267	246	2	3	3	NUM
ap-1267	246	3	]	]	X
ap-1267	246	4	chang	chang	PROPN
ap-1267	246	5	,	,	PUNCT
ap-1267	246	6	c.	c.	PROPN
ap-1267	246	7	c.	c.	PROPN
ap-1267	246	8	:	:	PUNCT
ap-1267	246	9	algebraic	algebraic	ADJ
ap-1267	246	10	analysis	analysis	NOUN
ap-1267	246	11	of	of	ADP
ap-1267	246	12	many	many	ADJ
ap-1267	246	13	valued	value	VERB
ap-1267	246	14	logics	logic	NOUN
ap-1267	246	15	,	,	PUNCT
ap-1267	246	16	trans	trans	PROPN
ap-1267	246	17	.	.	PROPN
ap-1267	246	18	amer	amer	PROPN
ap-1267	246	19	.	.	PUNCT
ap-1267	246	20	math	math	PROPN
ap-1267	246	21	.	.	PUNCT
ap-1267	247	1	soc	soc	PROPN
ap-1267	247	2	.	.	PUNCT
ap-1267	248	1	88	88	NUM
ap-1267	248	2	(	(	PUNCT
ap-1267	248	3	1958	1958	NUM
ap-1267	248	4	)	)	PUNCT
ap-1267	248	5	,	,	PUNCT
ap-1267	248	6	467–490	467–490	NUM
ap-1267	248	7	.	.	PUNCT
ap-1267	249	1	[	[	X
ap-1267	249	2	4	4	NUM
ap-1267	249	3	]	]	X
ap-1267	249	4	foulis	foulis	PROPN
ap-1267	249	5	,	,	PUNCT
ap-1267	249	6	d.	d.	PROPN
ap-1267	249	7	j.	j.	PROPN
ap-1267	249	8	,	,	PUNCT
ap-1267	249	9	bennett	bennett	PROPN
ap-1267	249	10	,	,	PUNCT
ap-1267	249	11	m.	m.	PROPN
ap-1267	249	12	k.	k.	PROPN
ap-1267	249	13	:	:	PUNCT
ap-1267	249	14	effect	effect	NOUN
ap-1267	249	15	algebras	algebra	NOUN
ap-1267	249	16	and	and	CCONJ
ap-1267	249	17	unsharp	unsharp	ADJ
ap-1267	249	18	quantum	quantum	ADJ
ap-1267	249	19	logics	logic	NOUN
ap-1267	249	20	,	,	PUNCT
ap-1267	249	21	found	find	VERB
ap-1267	249	22	.	.	PUNCT
ap-1267	250	1	phys	phy	NOUN
ap-1267	250	2	.	.	PUNCT
ap-1267	251	1	24	24	NUM
ap-1267	251	2	(	(	PUNCT
ap-1267	251	3	1994	1994	NUM
ap-1267	251	4	)	)	PUNCT
ap-1267	251	5	,	,	PUNCT
ap-1267	251	6	1	1	NUM
ap-1267	251	7	331–1352	331–1352	NUM
ap-1267	251	8	.	.	PUNCT
ap-1267	252	1	55	55	NUM
ap-1267	252	2	acta	acta	PROPN
ap-1267	252	3	polytechnica	polytechnica	PROPN
ap-1267	252	4	vol	vol	NOUN
ap-1267	252	5	.	.	PROPN
ap-1267	253	1	50	50	NUM
ap-1267	253	2	no	no	NOUN
ap-1267	253	3	.	.	PUNCT
ap-1267	254	1	5/2010	5/2010	NUM
ap-1267	255	1	[	[	X
ap-1267	255	2	5	5	NUM
ap-1267	255	3	]	]	PUNCT
ap-1267	255	4	foulis	foulis	PROPN
ap-1267	255	5	,	,	PUNCT
ap-1267	255	6	d.	d.	PROPN
ap-1267	255	7	j.	j.	PROPN
ap-1267	255	8	,	,	PUNCT
ap-1267	255	9	pulmannová	pulmannová	PROPN
ap-1267	255	10	,	,	PUNCT
ap-1267	255	11	s.	s.	PROPN
ap-1267	255	12	:	:	PUNCT
ap-1267	255	13	type	type	NOUN
ap-1267	255	14	-	-	PUNCT
ap-1267	255	15	decomposition	decomposition	NOUN
ap-1267	255	16	of	of	ADP
ap-1267	255	17	an	an	DET
ap-1267	255	18	effect	effect	NOUN
ap-1267	255	19	algebra	algebra	NOUN
ap-1267	255	20	,	,	PUNCT
ap-1267	255	21	found	find	VERB
ap-1267	255	22	.	.	PUNCT
ap-1267	256	1	phys	phy	NOUN
ap-1267	256	2	.	.	PUNCT
ap-1267	257	1	[	[	X
ap-1267	257	2	6	6	NUM
ap-1267	257	3	]	]	X
ap-1267	257	4	greechie	greechie	NOUN
ap-1267	257	5	,	,	PUNCT
ap-1267	257	6	r.	r.	PROPN
ap-1267	257	7	j.	j.	PROPN
ap-1267	257	8	,	,	PUNCT
ap-1267	257	9	foulis	foulis	PROPN
ap-1267	257	10	,	,	PUNCT
ap-1267	257	11	d.	d.	PROPN
ap-1267	257	12	j.	j.	PROPN
ap-1267	257	13	,	,	PUNCT
ap-1267	257	14	pulmannová	pulmannová	PROPN
ap-1267	257	15	,	,	PUNCT
ap-1267	257	16	s.	s.	PROPN
ap-1267	257	17	:	:	PUNCT
ap-1267	257	18	the	the	DET
ap-1267	257	19	center	center	NOUN
ap-1267	257	20	of	of	ADP
ap-1267	257	21	an	an	DET
ap-1267	257	22	effect	effect	NOUN
ap-1267	257	23	algebra	algebra	NOUN
ap-1267	257	24	,	,	PUNCT
ap-1267	257	25	order	order	NOUN
ap-1267	257	26	12	12	NUM
ap-1267	257	27	(	(	PUNCT
ap-1267	257	28	1995	1995	NUM
ap-1267	257	29	)	)	PUNCT
ap-1267	257	30	,	,	PUNCT
ap-1267	257	31	91–106	91–106	NOUN
ap-1267	257	32	.	.	PUNCT
ap-1267	258	1	[	[	X
ap-1267	258	2	7	7	NUM
ap-1267	258	3	]	]	SYM
ap-1267	258	4	gudder	gudder	ADJ
ap-1267	258	5	,	,	PUNCT
ap-1267	258	6	s.	s.	PROPN
ap-1267	258	7	p.	p.	PROPN
ap-1267	258	8	:	:	PUNCT
ap-1267	258	9	sharply	sharply	ADV
ap-1267	258	10	dominating	dominate	VERB
ap-1267	258	11	effect	effect	NOUN
ap-1267	258	12	algebras	algebra	NOUN
ap-1267	258	13	,	,	PUNCT
ap-1267	258	14	tatra	tatra	PROPN
ap-1267	258	15	mt	mt	PROPN
ap-1267	258	16	.	.	PROPN
ap-1267	258	17	math	math	PROPN
ap-1267	258	18	.	.	PUNCT
ap-1267	259	1	publ	publ	PROPN
ap-1267	259	2	.	.	PUNCT
ap-1267	260	1	15	15	NUM
ap-1267	260	2	(	(	PUNCT
ap-1267	260	3	1998	1998	NUM
ap-1267	260	4	)	)	PUNCT
ap-1267	260	5	,	,	PUNCT
ap-1267	260	6	23–30	23–30	NUM
ap-1267	260	7	.	.	PUNCT
ap-1267	261	1	[	[	X
ap-1267	261	2	8	8	NUM
ap-1267	261	3	]	]	SYM
ap-1267	261	4	gudder	gudder	ADJ
ap-1267	261	5	,	,	PUNCT
ap-1267	261	6	s.	s.	PROPN
ap-1267	261	7	p.	p.	PROPN
ap-1267	261	8	:	:	PUNCT
ap-1267	262	1	s	s	X
ap-1267	262	2	-	-	PUNCT
ap-1267	262	3	dominating	dominating	ADJ
ap-1267	262	4	effect	effect	NOUN
ap-1267	262	5	algebras	algebra	NOUN
ap-1267	262	6	,	,	PUNCT
ap-1267	262	7	internat	internat	PROPN
ap-1267	262	8	.	.	PUNCT
ap-1267	263	1	j.	j.	PROPN
ap-1267	263	2	theoret	theoret	PROPN
ap-1267	263	3	.	.	PUNCT
ap-1267	264	1	phys	phy	NOUN
ap-1267	264	2	.	.	PUNCT
ap-1267	265	1	37	37	NUM
ap-1267	265	2	(	(	PUNCT
ap-1267	265	3	1998	1998	NUM
ap-1267	265	4	)	)	PUNCT
ap-1267	265	5	,	,	PUNCT
ap-1267	265	6	915–923	915–923	NUM
ap-1267	265	7	.	.	PUNCT
ap-1267	266	1	[	[	X
ap-1267	266	2	9	9	NUM
ap-1267	266	3	]	]	X
ap-1267	266	4	jenča	jenča	PROPN
ap-1267	266	5	,	,	PUNCT
ap-1267	266	6	g.	g.	PROPN
ap-1267	266	7	,	,	PUNCT
ap-1267	266	8	pulmannová	pulmannová	ADV
ap-1267	266	9	,	,	PUNCT
ap-1267	266	10	s.	s.	PROPN
ap-1267	266	11	:	:	PUNCT
ap-1267	266	12	orthocomplete	orthocomplete	ADJ
ap-1267	266	13	effect	effect	PROPN
ap-1267	266	14	algebras	algebra	NOUN
ap-1267	266	15	,	,	PUNCT
ap-1267	266	16	proc	proc	PROPN
ap-1267	266	17	.	.	PUNCT
ap-1267	267	1	amer	amer	PROPN
ap-1267	267	2	.	.	PUNCT
ap-1267	267	3	math	math	PROPN
ap-1267	267	4	.	.	PUNCT
ap-1267	268	1	soc	soc	PROPN
ap-1267	268	2	.	.	PUNCT
ap-1267	269	1	131	131	NUM
ap-1267	269	2	(	(	PUNCT
ap-1267	269	3	2003	2003	NUM
ap-1267	269	4	)	)	PUNCT
ap-1267	269	5	,	,	PUNCT
ap-1267	269	6	2	2	NUM
ap-1267	269	7	663–2671	663–2671	NUM
ap-1267	269	8	.	.	PUNCT
ap-1267	270	1	[	[	X
ap-1267	270	2	10	10	NUM
ap-1267	270	3	]	]	X
ap-1267	270	4	jenča	jenča	PROPN
ap-1267	270	5	,	,	PUNCT
ap-1267	270	6	g.	g.	PROPN
ap-1267	270	7	,	,	PUNCT
ap-1267	270	8	riečanová	riečanová	PROPN
ap-1267	270	9	,	,	PUNCT
ap-1267	270	10	z.	z.	PROPN
ap-1267	270	11	:	:	PUNCT
ap-1267	270	12	on	on	ADP
ap-1267	270	13	sharp	sharp	ADJ
ap-1267	270	14	elements	element	NOUN
ap-1267	270	15	in	in	ADP
ap-1267	270	16	lattice	lattice	NOUN
ap-1267	270	17	ordered	order	VERB
ap-1267	270	18	effect	effect	NOUN
ap-1267	270	19	algebras	algebra	NOUN
ap-1267	270	20	,	,	PUNCT
ap-1267	270	21	busefal	busefal	PROPN
ap-1267	270	22	80	80	NUM
ap-1267	270	23	(	(	PUNCT
ap-1267	270	24	1999	1999	NUM
ap-1267	270	25	)	)	PUNCT
ap-1267	270	26	,	,	PUNCT
ap-1267	270	27	24–29	24–29	NUM
ap-1267	270	28	.	.	PUNCT
ap-1267	271	1	[	[	X
ap-1267	271	2	11	11	NUM
ap-1267	271	3	]	]	PUNCT
ap-1267	271	4	kalina	kalina	PROPN
ap-1267	271	5	,	,	PUNCT
ap-1267	271	6	m.	m.	NOUN
ap-1267	271	7	,	,	PUNCT
ap-1267	271	8	olejček	olejček	PROPN
ap-1267	271	9	,	,	PUNCT
ap-1267	271	10	v.	v.	ADV
ap-1267	271	11	,	,	PUNCT
ap-1267	271	12	paseka	paseka	ADP
ap-1267	271	13	,	,	PUNCT
ap-1267	271	14	j.	j.	PROPN
ap-1267	271	15	,	,	PUNCT
ap-1267	271	16	riečanová	riečanová	PROPN
ap-1267	271	17	,	,	PUNCT
ap-1267	271	18	z.	z.	PROPN
ap-1267	271	19	:	:	PUNCT
ap-1267	271	20	sharply	sharply	ADV
ap-1267	271	21	dominating	dominate	VERB
ap-1267	271	22	mv	mv	ADJ
ap-1267	271	23	-	-	PUNCT
ap-1267	271	24	effect	effect	NOUN
ap-1267	271	25	algebras	algebra	NOUN
ap-1267	271	26	,	,	PUNCT
ap-1267	271	27	internat	internat	PROPN
ap-1267	271	28	.	.	PUNCT
ap-1267	272	1	j.	j.	PROPN
ap-1267	272	2	theoret	theoret	PROPN
ap-1267	272	3	.	.	PUNCT
ap-1267	273	1	phys	phy	NOUN
ap-1267	273	2	.	.	PUNCT
ap-1267	273	3	,	,	PUNCT
ap-1267	273	4	doi	doi	NOUN
ap-1267	273	5	:	:	PUNCT
ap-1267	273	6	10.1007	10.1007	NUM
ap-1267	273	7	/	/	SYM
ap-1267	273	8	s10773	s10773	NUM
ap-1267	273	9	-	-	PUNCT
ap-1267	273	10	010	010	NUM
ap-1267	273	11	-	-	PUNCT
ap-1267	273	12	0338	0338	NUM
ap-1267	273	13	-	-	PUNCT
ap-1267	273	14	x.	x.	NOUN
ap-1267	274	1	[	[	X
ap-1267	274	2	12	12	NUM
ap-1267	274	3	]	]	PUNCT
ap-1267	274	4	kalina	kalina	PROPN
ap-1267	274	5	,	,	PUNCT
ap-1267	274	6	m.	m.	NOUN
ap-1267	274	7	:	:	PUNCT
ap-1267	274	8	on	on	ADP
ap-1267	274	9	central	central	ADJ
ap-1267	274	10	atoms	atom	NOUN
ap-1267	274	11	of	of	ADP
ap-1267	274	12	archimedean	archimedean	ADJ
ap-1267	274	13	atomic	atomic	PROPN
ap-1267	274	14	lattice	lattice	PROPN
ap-1267	274	15	effect	effect	PROPN
ap-1267	274	16	algebras	algebra	NOUN
ap-1267	274	17	,	,	PUNCT
ap-1267	274	18	kybernetika	kybernetika	NOUN
ap-1267	274	19	,	,	PUNCT
ap-1267	274	20	accepted	accept	VERB
ap-1267	274	21	.	.	PUNCT
ap-1267	275	1	[	[	X
ap-1267	275	2	13	13	NUM
ap-1267	275	3	]	]	X
ap-1267	275	4	kalmbach	kalmbach	NOUN
ap-1267	275	5	,	,	PUNCT
ap-1267	275	6	g.	g.	NOUN
ap-1267	275	7	:	:	PUNCT
ap-1267	275	8	orthomodular	orthomodular	ADJ
ap-1267	275	9	lattices	lattice	NOUN
ap-1267	275	10	,	,	PUNCT
ap-1267	275	11	mathematics	mathematic	NOUN
ap-1267	275	12	and	and	CCONJ
ap-1267	275	13	its	its	PRON
ap-1267	275	14	applications	application	NOUN
ap-1267	275	15	,	,	PUNCT
ap-1267	275	16	vol	vol	NOUN
ap-1267	275	17	.	.	PROPN
ap-1267	275	18	453	453	NUM
ap-1267	275	19	,	,	PUNCT
ap-1267	275	20	kluwer	kluwer	NOUN
ap-1267	275	21	academic	academic	ADJ
ap-1267	275	22	publishers	publisher	NOUN
ap-1267	275	23	,	,	PUNCT
ap-1267	275	24	dordrecht	dordrecht	PROPN
ap-1267	275	25	,	,	PUNCT
ap-1267	275	26	1998	1998	NUM
ap-1267	275	27	,	,	PUNCT
ap-1267	275	28	1998	1998	NUM
ap-1267	275	29	.	.	PUNCT
ap-1267	276	1	[	[	X
ap-1267	276	2	14	14	NUM
ap-1267	276	3	]	]	X
ap-1267	276	4	kôpka	kôpka	NOUN
ap-1267	276	5	,	,	PUNCT
ap-1267	276	6	f.	f.	NOUN
ap-1267	276	7	:	:	PUNCT
ap-1267	276	8	compatibility	compatibility	NOUN
ap-1267	276	9	in	in	ADP
ap-1267	276	10	d	d	NOUN
ap-1267	276	11	-	-	NOUN
ap-1267	276	12	posets	poset	NOUN
ap-1267	276	13	,	,	PUNCT
ap-1267	276	14	internat	internat	NOUN
ap-1267	276	15	.	.	PUNCT
ap-1267	277	1	j.	j.	PROPN
ap-1267	277	2	theoret	theoret	PROPN
ap-1267	277	3	.	.	PUNCT
ap-1267	278	1	phys	phy	NOUN
ap-1267	278	2	.	.	PUNCT
ap-1267	279	1	34	34	NUM
ap-1267	279	2	(	(	PUNCT
ap-1267	279	3	1995	1995	NUM
ap-1267	279	4	)	)	PUNCT
ap-1267	279	5	,	,	PUNCT
ap-1267	279	6	1	1	NUM
ap-1267	279	7	525–1531	525–1531	NUM
ap-1267	279	8	.	.	PUNCT
ap-1267	280	1	[	[	X
ap-1267	280	2	15	15	NUM
ap-1267	280	3	]	]	X
ap-1267	280	4	kôpka	kôpka	NOUN
ap-1267	280	5	,	,	PUNCT
ap-1267	280	6	f.	f.	PROPN
ap-1267	280	7	,	,	PUNCT
ap-1267	280	8	chovanec	chovanec	PROPN
ap-1267	280	9	,	,	PUNCT
ap-1267	280	10	f.	f.	PROPN
ap-1267	280	11	:	:	PUNCT
ap-1267	280	12	boolean	boolean	ADJ
ap-1267	280	13	d	d	NOUN
ap-1267	280	14	-	-	PUNCT
ap-1267	280	15	posets	poset	NOUN
ap-1267	280	16	,	,	PUNCT
ap-1267	280	17	internat	internat	NOUN
ap-1267	280	18	.	.	PUNCT
ap-1267	281	1	j.	j.	PROPN
ap-1267	281	2	theoret	theoret	PROPN
ap-1267	281	3	.	.	PUNCT
ap-1267	282	1	phys	phy	NOUN
ap-1267	282	2	.	.	PUNCT
ap-1267	283	1	34	34	NUM
ap-1267	283	2	(	(	PUNCT
ap-1267	283	3	1995	1995	NUM
ap-1267	283	4	)	)	PUNCT
ap-1267	283	5	,	,	PUNCT
ap-1267	283	6	1	1	NUM
ap-1267	283	7	297–1302	297–1302	NUM
ap-1267	283	8	.	.	PUNCT
ap-1267	284	1	[	[	X
ap-1267	284	2	16	16	NUM
ap-1267	284	3	]	]	PUNCT
ap-1267	284	4	mosná	mosná	NOUN
ap-1267	284	5	,	,	PUNCT
ap-1267	284	6	k.	k.	PROPN
ap-1267	284	7	:	:	PUNCT
ap-1267	284	8	atomic	atomic	ADJ
ap-1267	284	9	lattice	lattice	PROPN
ap-1267	284	10	effect	effect	NOUN
ap-1267	284	11	algebras	algebra	NOUN
ap-1267	284	12	and	and	CCONJ
ap-1267	284	13	their	their	PRON
ap-1267	284	14	sub	sub	ADJ
ap-1267	284	15	-	-	ADJ
ap-1267	284	16	lattice	lattice	ADJ
ap-1267	284	17	effect	effect	NOUN
ap-1267	284	18	algebras	algebra	NOUN
ap-1267	284	19	,	,	PUNCT
ap-1267	284	20	j.	j.	PROPN
ap-1267	284	21	electrical	electrical	ADJ
ap-1267	284	22	engineering	engineering	NOUN
ap-1267	284	23	58	58	NUM
ap-1267	284	24	(	(	PUNCT
ap-1267	284	25	2007	2007	NUM
ap-1267	284	26	)	)	PUNCT
ap-1267	284	27	,	,	PUNCT
ap-1267	284	28	7	7	NUM
ap-1267	284	29	/	/	SYM
ap-1267	284	30	s	s	PROPN
ap-1267	284	31	,	,	PUNCT
ap-1267	284	32	3–6	3–6	NUM
ap-1267	284	33	.	.	PUNCT
ap-1267	285	1	[	[	X
ap-1267	285	2	17	17	NUM
ap-1267	285	3	]	]	PUNCT
ap-1267	285	4	paseka	paseka	NOUN
ap-1267	285	5	,	,	PUNCT
ap-1267	285	6	j.	j.	PROPN
ap-1267	285	7	,	,	PUNCT
ap-1267	285	8	riečanová	riečanová	PROPN
ap-1267	285	9	,	,	PUNCT
ap-1267	285	10	z.	z.	PROPN
ap-1267	285	11	:	:	PUNCT
ap-1267	285	12	the	the	DET
ap-1267	285	13	inheritance	inheritance	NOUN
ap-1267	285	14	of	of	ADP
ap-1267	285	15	bde	bde	NOUN
ap-1267	285	16	-	-	PUNCT
ap-1267	285	17	property	property	NOUN
ap-1267	285	18	in	in	ADP
ap-1267	285	19	sharply	sharply	ADV
ap-1267	285	20	dominating	dominate	VERB
ap-1267	285	21	lattice	lattice	NOUN
ap-1267	285	22	effect	effect	NOUN
ap-1267	285	23	algebras	algebra	NOUN
ap-1267	285	24	and	and	CCONJ
ap-1267	285	25	(	(	PUNCT
ap-1267	285	26	o)-continuous	o)-continuous	ADJ
ap-1267	285	27	states	state	NOUN
ap-1267	285	28	,	,	PUNCT
ap-1267	285	29	soft	soft	ADJ
ap-1267	285	30	comput	comput	NOUN
ap-1267	285	31	.	.	PUNCT
ap-1267	285	32	,	,	PUNCT
ap-1267	285	33	doi	doi	NOUN
ap-1267	285	34	:	:	PUNCT
ap-1267	285	35	10.1007	10.1007	NUM
ap-1267	285	36	/	/	SYM
ap-1267	285	37	s00500	s00500	PROPN
ap-1267	285	38	-	-	PUNCT
ap-1267	285	39	010	010	NUM
ap-1267	285	40	-	-	PUNCT
ap-1267	285	41	0561	0561	NUM
ap-1267	285	42	-	-	PUNCT
ap-1267	285	43	7	7	NUM
ap-1267	285	44	.	.	PUNCT
ap-1267	286	1	[	[	X
ap-1267	286	2	18	18	NUM
ap-1267	286	3	]	]	SYM
ap-1267	286	4	riečanová	riečanová	PROPN
ap-1267	286	5	,	,	PUNCT
ap-1267	286	6	z.	z.	PROPN
ap-1267	286	7	:	:	PUNCT
ap-1267	286	8	compatibility	compatibility	NOUN
ap-1267	286	9	and	and	CCONJ
ap-1267	286	10	central	central	ADJ
ap-1267	286	11	elements	element	NOUN
ap-1267	286	12	in	in	ADP
ap-1267	286	13	effect	effect	NOUN
ap-1267	286	14	algebras	algebra	NOUN
ap-1267	286	15	,	,	PUNCT
ap-1267	286	16	tatra	tatra	PROPN
ap-1267	286	17	mt	mt	PROPN
ap-1267	286	18	.	.	PROPN
ap-1267	286	19	math	math	PROPN
ap-1267	286	20	.	.	PUNCT
ap-1267	287	1	publ	publ	NOUN
ap-1267	287	2	.	.	PUNCT
ap-1267	288	1	16	16	NUM
ap-1267	288	2	(	(	PUNCT
ap-1267	288	3	1999	1999	NUM
ap-1267	288	4	)	)	PUNCT
ap-1267	288	5	,	,	PUNCT
ap-1267	288	6	151–158	151–158	NUM
ap-1267	288	7	.	.	PUNCT
ap-1267	289	1	[	[	X
ap-1267	289	2	19	19	NUM
ap-1267	289	3	]	]	SYM
ap-1267	289	4	riečanová	riečanová	PROPN
ap-1267	289	5	,	,	PUNCT
ap-1267	289	6	z.	z.	PROPN
ap-1267	289	7	:	:	PUNCT
ap-1267	289	8	subalgebras	subalgebras	PROPN
ap-1267	289	9	,	,	PUNCT
ap-1267	289	10	intervals	interval	NOUN
ap-1267	289	11	and	and	CCONJ
ap-1267	289	12	central	central	ADJ
ap-1267	289	13	elements	element	NOUN
ap-1267	289	14	of	of	ADP
ap-1267	289	15	generalized	generalized	ADJ
ap-1267	289	16	effect	effect	NOUN
ap-1267	289	17	algebras	algebra	NOUN
ap-1267	289	18	,	,	PUNCT
ap-1267	289	19	internat	internat	PROPN
ap-1267	289	20	.	.	PUNCT
ap-1267	290	1	j.	j.	PROPN
ap-1267	290	2	theoret	theoret	PROPN
ap-1267	290	3	.	.	PUNCT
ap-1267	291	1	phys	phy	NOUN
ap-1267	291	2	.	.	PUNCT
ap-1267	292	1	38	38	NUM
ap-1267	292	2	(	(	PUNCT
ap-1267	292	3	1999	1999	NUM
ap-1267	292	4	)	)	PUNCT
ap-1267	292	5	,	,	PUNCT
ap-1267	292	6	3	3	NUM
ap-1267	292	7	209–3220	209–3220	NUM
ap-1267	292	8	.	.	PUNCT
ap-1267	293	1	[	[	X
ap-1267	293	2	20	20	NUM
ap-1267	293	3	]	]	SYM
ap-1267	293	4	riečanová	riečanová	PROPN
ap-1267	293	5	,	,	PUNCT
ap-1267	293	6	z.	z.	PROPN
ap-1267	293	7	:	:	PUNCT
ap-1267	293	8	archimedean	archimedean	ADJ
ap-1267	293	9	and	and	CCONJ
ap-1267	293	10	block	block	NOUN
ap-1267	293	11	-	-	PUNCT
ap-1267	293	12	finite	finite	ADJ
ap-1267	293	13	lattice	lattice	PROPN
ap-1267	293	14	effect	effect	PROPN
ap-1267	293	15	algebras	algebras	PROPN
ap-1267	293	16	,	,	PUNCT
ap-1267	293	17	demonstratio	demonstratio	PROPN
ap-1267	293	18	mathematica	mathematica	PROPN
ap-1267	293	19	33	33	NUM
ap-1267	293	20	(	(	PUNCT
ap-1267	293	21	2000	2000	NUM
ap-1267	293	22	)	)	PUNCT
ap-1267	293	23	,	,	PUNCT
ap-1267	293	24	443–452	443–452	NUM
ap-1267	293	25	.	.	PUNCT
ap-1267	294	1	[	[	X
ap-1267	294	2	21	21	NUM
ap-1267	294	3	]	]	X
ap-1267	294	4	riečanová	riečanová	PROPN
ap-1267	294	5	,	,	PUNCT
ap-1267	294	6	z.	z.	PROPN
ap-1267	294	7	:	:	PUNCT
ap-1267	294	8	generalization	generalization	NOUN
ap-1267	294	9	of	of	ADP
ap-1267	294	10	blocks	block	NOUN
ap-1267	294	11	for	for	ADP
ap-1267	294	12	dlattices	dlattice	NOUN
ap-1267	294	13	and	and	CCONJ
ap-1267	294	14	lattice	lattice	NOUN
ap-1267	294	15	-	-	PUNCT
ap-1267	294	16	ordered	order	VERB
ap-1267	294	17	effect	effect	NOUN
ap-1267	294	18	algebras	algebra	NOUN
ap-1267	294	19	,	,	PUNCT
ap-1267	294	20	internat	internat	PROPN
ap-1267	294	21	.	.	PUNCT
ap-1267	295	1	j.	j.	PROPN
ap-1267	295	2	theoret	theoret	PROPN
ap-1267	295	3	.	.	PUNCT
ap-1267	296	1	phys	phy	NOUN
ap-1267	296	2	.	.	PUNCT
ap-1267	297	1	39	39	NUM
ap-1267	297	2	(	(	PUNCT
ap-1267	297	3	2000	2000	NUM
ap-1267	297	4	)	)	PUNCT
ap-1267	297	5	,	,	PUNCT
ap-1267	297	6	231–237	231–237	NUM
ap-1267	297	7	.	.	PUNCT
ap-1267	298	1	[	[	X
ap-1267	298	2	22	22	NUM
ap-1267	298	3	]	]	X
ap-1267	298	4	riečanová	riečanová	PROPN
ap-1267	298	5	,	,	PUNCT
ap-1267	298	6	z.	z.	PROPN
ap-1267	298	7	:	:	PUNCT
ap-1267	298	8	orthogonal	orthogonal	ADJ
ap-1267	298	9	sets	set	NOUN
ap-1267	298	10	in	in	ADP
ap-1267	298	11	effect	effect	NOUN
ap-1267	298	12	algebras	algebra	NOUN
ap-1267	298	13	,	,	PUNCT
ap-1267	298	14	demonstratio	demonstratio	PROPN
ap-1267	298	15	math	math	PROPN
ap-1267	298	16	.	.	PUNCT
ap-1267	299	1	34	34	NUM
ap-1267	299	2	(	(	PUNCT
ap-1267	299	3	2001	2001	NUM
ap-1267	299	4	)	)	PUNCT
ap-1267	299	5	,	,	PUNCT
ap-1267	299	6	525–532	525–532	NUM
ap-1267	299	7	.	.	PUNCT
ap-1267	300	1	[	[	X
ap-1267	300	2	23	23	NUM
ap-1267	300	3	]	]	X
ap-1267	300	4	riečanová	riečanová	PROPN
ap-1267	300	5	,	,	PUNCT
ap-1267	300	6	z.	z.	PROPN
ap-1267	300	7	:	:	PUNCT
ap-1267	300	8	subdirect	subdirect	VERB
ap-1267	300	9	decompositions	decomposition	NOUN
ap-1267	300	10	of	of	ADP
ap-1267	300	11	lattice	lattice	ADJ
ap-1267	300	12	effect	effect	NOUN
ap-1267	300	13	algebras	algebra	NOUN
ap-1267	300	14	,	,	PUNCT
ap-1267	300	15	internat	internat	PROPN
ap-1267	300	16	.	.	PUNCT
ap-1267	301	1	j.	j.	PROPN
ap-1267	301	2	theoret	theoret	PROPN
ap-1267	301	3	.	.	PUNCT
ap-1267	302	1	phys	phy	NOUN
ap-1267	302	2	.	.	PUNCT
ap-1267	303	1	42	42	NUM
ap-1267	303	2	(	(	PUNCT
ap-1267	303	3	2003	2003	NUM
ap-1267	303	4	)	)	PUNCT
ap-1267	303	5	,	,	PUNCT
ap-1267	303	6	1	1	NUM
ap-1267	303	7	415–1433	415–1433	NUM
ap-1267	303	8	.	.	PUNCT
ap-1267	304	1	doc	doc	PROPN
ap-1267	304	2	.	.	PROPN
ap-1267	304	3	rndr	rndr	PROPN
ap-1267	304	4	.	.	PUNCT
ap-1267	305	1	martin	martin	PROPN
ap-1267	305	2	kalina	kalina	PROPN
ap-1267	305	3	,	,	PUNCT
ap-1267	305	4	ph.d	ph.d	PROPN
ap-1267	305	5	.	.	PUNCT
ap-1267	306	1	e	e	X
ap-1267	306	2	-	-	NOUN
ap-1267	306	3	mail	mail	NOUN
ap-1267	306	4	:	:	PUNCT
ap-1267	306	5	kalina@math.sk	kalina@math.sk	PROPN
ap-1267	306	6	department	department	PROPN
ap-1267	306	7	of	of	ADP
ap-1267	306	8	mathematics	mathematics	PROPN
ap-1267	306	9	faculty	faculty	NOUN
ap-1267	306	10	of	of	ADP
ap-1267	306	11	civil	civil	ADJ
ap-1267	306	12	engineering	engineering	NOUN
ap-1267	306	13	slovak	slovak	ADJ
ap-1267	306	14	university	university	PROPN
ap-1267	306	15	of	of	ADP
ap-1267	306	16	technology	technology	PROPN
ap-1267	306	17	radlinského	radlinského	PROPN
ap-1267	306	18	11	11	NUM
ap-1267	306	19	,	,	PUNCT
ap-1267	306	20	sk-813	sk-813	NOUN
ap-1267	306	21	68	68	NUM
ap-1267	306	22	bratislava	bratislava	NOUN
ap-1267	306	23	,	,	PUNCT
ap-1267	306	24	slovakia	slovakia	PROPN
ap-1267	306	25	doc	doc	PROPN
ap-1267	306	26	.	.	PROPN
ap-1267	306	27	rndr	rndr	PROPN
ap-1267	306	28	.	.	PUNCT
ap-1267	307	1	jan	jan	PROPN
ap-1267	307	2	paseka	paseka	PROPN
ap-1267	307	3	,	,	PUNCT
ap-1267	307	4	csc	csc	PROPN
ap-1267	307	5	.	.	PUNCT
ap-1267	307	6	e	e	X
ap-1267	307	7	-	-	NOUN
ap-1267	307	8	mail	mail	NOUN
ap-1267	307	9	:	:	PUNCT
ap-1267	307	10	paseka@math.muni.cz	paseka@math.muni.cz	PROPN
ap-1267	307	11	department	department	NOUN
ap-1267	307	12	of	of	ADP
ap-1267	307	13	mathematics	mathematics	PROPN
ap-1267	307	14	and	and	CCONJ
ap-1267	307	15	statistics	statistic	NOUN
ap-1267	307	16	faculty	faculty	NOUN
ap-1267	307	17	of	of	ADP
ap-1267	307	18	science	science	PROPN
ap-1267	307	19	masaryk	masaryk	PROPN
ap-1267	307	20	university	university	PROPN
ap-1267	307	21	kotlářská	kotlářská	PROPN
ap-1267	307	22	2	2	NUM
ap-1267	307	23	,	,	PUNCT
ap-1267	307	24	cz-611	cz-611	VERB
ap-1267	307	25	37	37	NUM
ap-1267	307	26	brno	brno	NOUN
ap-1267	307	27	,	,	PUNCT
ap-1267	307	28	czech	czech	PROPN
ap-1267	307	29	republic	republic	PROPN
ap-1267	307	30	prof	prof	PROPN
ap-1267	307	31	.	.	PUNCT
ap-1267	308	1	rndr	rndr	PROPN
ap-1267	308	2	.	.	PUNCT
ap-1267	309	1	zdenka	zdenka	PROPN
ap-1267	309	2	riečanová	riečanová	PROPN
ap-1267	309	3	,	,	PUNCT
ap-1267	309	4	ph.d	ph.d	PROPN
ap-1267	309	5	.	.	PUNCT
ap-1267	310	1	e	e	X
ap-1267	310	2	-	-	NOUN
ap-1267	310	3	mail	mail	NOUN
ap-1267	310	4	:	:	PUNCT
ap-1267	310	5	zdena.riecanova@gmail.com	zdena.riecanova@gmail.com	NUM
ap-1267	310	6	department	department	NOUN
ap-1267	310	7	of	of	ADP
ap-1267	310	8	mathematics	mathematics	PROPN
ap-1267	310	9	faculty	faculty	NOUN
ap-1267	310	10	of	of	ADP
ap-1267	310	11	electrical	electrical	ADJ
ap-1267	310	12	engineering	engineering	NOUN
ap-1267	310	13	and	and	CCONJ
ap-1267	310	14	information	information	NOUN
ap-1267	310	15	technology	technology	NOUN
ap-1267	310	16	slovak	slovak	ADJ
ap-1267	310	17	university	university	PROPN
ap-1267	310	18	of	of	ADP
ap-1267	310	19	technology	technology	NOUN
ap-1267	310	20	ilkovičova	ilkovičova	X
ap-1267	310	21	3	3	NUM
ap-1267	310	22	,	,	PUNCT
ap-1267	310	23	sk-812	sk-812	PROPN
ap-1267	310	24	19	19	NUM
ap-1267	310	25	bratislava	bratislava	NOUN
ap-1267	310	26	,	,	PUNCT
ap-1267	310	27	slovak	slovak	ADJ
ap-1267	310	28	republic	republic	NOUN
ap-1267	310	29	56	56	NUM