id	sid	tid	token	lemma	pos
ejpam-2779	1	1	european	european	PROPN
ejpam-2779	1	2	journal	journal	PROPN
ejpam-2779	1	3	of	of	ADP
ejpam-2779	1	4	pure	pure	ADJ
ejpam-2779	1	5	and	and	CCONJ
ejpam-2779	1	6	applied	apply	VERB
ejpam-2779	1	7	mathematics	mathematic	NOUN
ejpam-2779	1	8	vol	vol	NOUN
ejpam-2779	1	9	.	.	PROPN
ejpam-2779	2	1	10	10	NUM
ejpam-2779	2	2	,	,	PUNCT
ejpam-2779	2	3	no	no	INTJ
ejpam-2779	2	4	.	.	NOUN
ejpam-2779	2	5	3	3	NUM
ejpam-2779	2	6	,	,	PUNCT
ejpam-2779	2	7	2017	2017	NUM
ejpam-2779	2	8	,	,	PUNCT
ejpam-2779	2	9	455	455	NUM
ejpam-2779	2	10	-	-	SYM
ejpam-2779	2	11	472	472	NUM
ejpam-2779	2	12	issn	issn	VERB
ejpam-2779	2	13	1307	1307	NUM
ejpam-2779	2	14	-	-	SYM
ejpam-2779	2	15	5543	5543	NUM
ejpam-2779	2	16	–	–	PUNCT
ejpam-2779	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-2779	2	18	published	publish	VERB
ejpam-2779	2	19	by	by	ADP
ejpam-2779	2	20	new	new	PROPN
ejpam-2779	2	21	york	york	PROPN
ejpam-2779	2	22	business	business	PROPN
ejpam-2779	2	23	global	global	ADJ
ejpam-2779	2	24	states	state	NOUN
ejpam-2779	2	25	on	on	ADP
ejpam-2779	2	26	pseudo	pseudo	NOUN
ejpam-2779	2	27	-	-	ADJ
ejpam-2779	2	28	bci	bci	ADJ
ejpam-2779	2	29	algebras	algebras	PROPN
ejpam-2779	2	30	xiao	xiao	PROPN
ejpam-2779	2	31	long	long	PROPN
ejpam-2779	2	32	xin1,∗	xin1,∗	PROPN
ejpam-2779	2	33	,	,	PUNCT
ejpam-2779	2	34	yi	yi	PROPN
ejpam-2779	2	35	jun	jun	PROPN
ejpam-2779	2	36	li1	li1	PROPN
ejpam-2779	2	37	,	,	PUNCT
ejpam-2779	2	38	yu	yu	PROPN
ejpam-2779	2	39	long	long	ADJ
ejpam-2779	2	40	fu2	fu2	NOUN
ejpam-2779	2	41	1	1	NUM
ejpam-2779	2	42	school	school	NOUN
ejpam-2779	2	43	of	of	ADP
ejpam-2779	2	44	mathematics	mathematic	NOUN
ejpam-2779	2	45	,	,	PUNCT
ejpam-2779	2	46	northwest	northwest	PROPN
ejpam-2779	2	47	university	university	PROPN
ejpam-2779	2	48	,	,	PUNCT
ejpam-2779	2	49	xi’an	xi’an	PROPN
ejpam-2779	2	50	,	,	PUNCT
ejpam-2779	2	51	china	china	PROPN
ejpam-2779	2	52	2	2	NUM
ejpam-2779	2	53	school	school	NOUN
ejpam-2779	2	54	of	of	ADP
ejpam-2779	2	55	cyber	cyber	ADJ
ejpam-2779	2	56	engnieering	engnieering	NOUN
ejpam-2779	2	57	,	,	PUNCT
ejpam-2779	2	58	xidian	xidian	PROPN
ejpam-2779	2	59	university	university	NOUN
ejpam-2779	2	60	,	,	PUNCT
ejpam-2779	2	61	xi’an	xi’an	PROPN
ejpam-2779	2	62	,	,	PUNCT
ejpam-2779	2	63	china	china	PROPN
ejpam-2779	2	64	abstract	abstract	NOUN
ejpam-2779	2	65	.	.	PUNCT
ejpam-2779	3	1	in	in	ADP
ejpam-2779	3	2	this	this	DET
ejpam-2779	3	3	paper	paper	NOUN
ejpam-2779	3	4	,	,	PUNCT
ejpam-2779	3	5	we	we	PRON
ejpam-2779	3	6	discuss	discuss	VERB
ejpam-2779	3	7	the	the	DET
ejpam-2779	3	8	structure	structure	NOUN
ejpam-2779	3	9	of	of	ADP
ejpam-2779	3	10	pseudo	pseudo	NOUN
ejpam-2779	3	11	-	-	ADJ
ejpam-2779	3	12	bci	bci	ADJ
ejpam-2779	3	13	algebras	algebra	NOUN
ejpam-2779	3	14	and	and	CCONJ
ejpam-2779	3	15	get	get	VERB
ejpam-2779	3	16	that	that	SCONJ
ejpam-2779	3	17	any	any	DET
ejpam-2779	3	18	pseudobci	pseudobci	NOUN
ejpam-2779	3	19	algebra	algebra	NOUN
ejpam-2779	3	20	is	be	AUX
ejpam-2779	3	21	a	a	DET
ejpam-2779	3	22	union	union	NOUN
ejpam-2779	3	23	of	of	ADP
ejpam-2779	3	24	it	it	PRON
ejpam-2779	3	25	’s	’	VERB
ejpam-2779	3	26	branches	branch	NOUN
ejpam-2779	3	27	.	.	PUNCT
ejpam-2779	4	1	we	we	PRON
ejpam-2779	4	2	introduce	introduce	VERB
ejpam-2779	4	3	the	the	DET
ejpam-2779	4	4	notion	notion	NOUN
ejpam-2779	4	5	of	of	ADP
ejpam-2779	4	6	local	local	ADJ
ejpam-2779	4	7	bounded	bounded	ADJ
ejpam-2779	4	8	pseudo	pseudo	NOUN
ejpam-2779	4	9	-	-	ADJ
ejpam-2779	4	10	bci	bci	ADJ
ejpam-2779	4	11	algebras	algebra	NOUN
ejpam-2779	4	12	and	and	CCONJ
ejpam-2779	4	13	study	study	VERB
ejpam-2779	4	14	some	some	DET
ejpam-2779	4	15	related	relate	VERB
ejpam-2779	4	16	properties	property	NOUN
ejpam-2779	4	17	.	.	PUNCT
ejpam-2779	5	1	moreover	moreover	ADV
ejpam-2779	5	2	we	we	PRON
ejpam-2779	5	3	define	define	VERB
ejpam-2779	5	4	two	two	NUM
ejpam-2779	5	5	operations	operation	NOUN
ejpam-2779	5	6	∧1	∧1	ADV
ejpam-2779	5	7	,	,	PUNCT
ejpam-2779	5	8	∧2	∧2	NOUN
ejpam-2779	5	9	in	in	ADP
ejpam-2779	5	10	a	a	DET
ejpam-2779	5	11	local	local	ADJ
ejpam-2779	5	12	bounded	bounded	ADJ
ejpam-2779	5	13	pseudo	pseudo	NOUN
ejpam-2779	5	14	-	-	NOUN
ejpam-2779	5	15	bci	bci	ADJ
ejpam-2779	5	16	algebra	algebra	NOUN
ejpam-2779	5	17	a	a	DET
ejpam-2779	5	18	and	and	CCONJ
ejpam-2779	5	19	two	two	NUM
ejpam-2779	5	20	local	local	ADJ
ejpam-2779	5	21	operations	operation	NOUN
ejpam-2779	5	22	∨1	∨1	PROPN
ejpam-2779	5	23	and	and	CCONJ
ejpam-2779	5	24	∨2	∨2	VERB
ejpam-2779	5	25	in	in	ADP
ejpam-2779	5	26	v	v	NUM
ejpam-2779	5	27	(	(	PUNCT
ejpam-2779	5	28	a	a	NOUN
ejpam-2779	5	29	)	)	PUNCT
ejpam-2779	5	30	for	for	ADP
ejpam-2779	5	31	a	a	DET
ejpam-2779	5	32	∈m(a	∈m(a	NOUN
ejpam-2779	5	33	)	)	PUNCT
ejpam-2779	5	34	.	.	PUNCT
ejpam-2779	6	1	we	we	PRON
ejpam-2779	6	2	show	show	VERB
ejpam-2779	6	3	that	that	SCONJ
ejpam-2779	6	4	in	in	ADP
ejpam-2779	6	5	a	a	DET
ejpam-2779	6	6	∧1(∧2)-commutative	∧1(∧2)-commutative	PROPN
ejpam-2779	6	7	local	local	ADJ
ejpam-2779	6	8	bounded	bounded	ADJ
ejpam-2779	6	9	pseudo	pseudo	NOUN
ejpam-2779	6	10	-	-	NOUN
ejpam-2779	6	11	bci	bci	ADJ
ejpam-2779	6	12	algebra	algebra	NOUN
ejpam-2779	6	13	a	a	DET
ejpam-2779	6	14	,	,	PUNCT
ejpam-2779	6	15	(	(	PUNCT
ejpam-2779	6	16	v	v	NOUN
ejpam-2779	6	17	(	(	PUNCT
ejpam-2779	6	18	a),∧1,∨1)((v	a),∧1,∨1)((v	NOUN
ejpam-2779	6	19	(	(	PUNCT
ejpam-2779	6	20	a),∧2,∨2	a),∧2,∨2	NOUN
ejpam-2779	6	21	)	)	PUNCT
ejpam-2779	6	22	)	)	PUNCT
ejpam-2779	6	23	forms	form	VERB
ejpam-2779	6	24	a	a	DET
ejpam-2779	6	25	lattice	lattice	NOUN
ejpam-2779	6	26	for	for	ADP
ejpam-2779	6	27	all	all	DET
ejpam-2779	6	28	a	a	DET
ejpam-2779	6	29	∈	∈	PROPN
ejpam-2779	6	30	m(a	m(a	NOUN
ejpam-2779	6	31	)	)	PUNCT
ejpam-2779	6	32	.	.	PUNCT
ejpam-2779	7	1	we	we	PRON
ejpam-2779	7	2	define	define	VERB
ejpam-2779	7	3	a	a	DET
ejpam-2779	7	4	bosbach	bosbach	ADJ
ejpam-2779	7	5	state	state	NOUN
ejpam-2779	7	6	on	on	ADP
ejpam-2779	7	7	a	a	DET
ejpam-2779	7	8	local	local	ADJ
ejpam-2779	7	9	bounded	bounded	ADJ
ejpam-2779	7	10	pseudo	pseudo	NOUN
ejpam-2779	7	11	-	-	ADJ
ejpam-2779	7	12	bci	bci	ADJ
ejpam-2779	7	13	algebra	algebra	NOUN
ejpam-2779	7	14	.	.	PUNCT
ejpam-2779	8	1	then	then	ADV
ejpam-2779	8	2	we	we	PRON
ejpam-2779	8	3	give	give	VERB
ejpam-2779	8	4	two	two	NUM
ejpam-2779	8	5	examples	example	NOUN
ejpam-2779	8	6	of	of	ADP
ejpam-2779	8	7	local	local	ADJ
ejpam-2779	8	8	bounded	bounded	ADJ
ejpam-2779	8	9	pseudo	pseudo	NOUN
ejpam-2779	8	10	-	-	NOUN
ejpam-2779	8	11	bci	bci	NOUN
ejpam-2779	8	12	algebras	algebra	NOUN
ejpam-2779	8	13	to	to	PART
ejpam-2779	8	14	show	show	VERB
ejpam-2779	8	15	that	that	SCONJ
ejpam-2779	8	16	there	there	PRON
ejpam-2779	8	17	is	be	VERB
ejpam-2779	8	18	local	local	ADJ
ejpam-2779	8	19	bounded	bounded	ADJ
ejpam-2779	8	20	pseudo	pseudo	NOUN
ejpam-2779	8	21	-	-	ADJ
ejpam-2779	8	22	bci	bci	ADJ
ejpam-2779	8	23	algebras	algebra	NOUN
ejpam-2779	8	24	having	have	VERB
ejpam-2779	8	25	a	a	DET
ejpam-2779	8	26	bosbach	bosbach	ADJ
ejpam-2779	8	27	state	state	NOUN
ejpam-2779	8	28	but	but	CCONJ
ejpam-2779	8	29	there	there	PRON
ejpam-2779	8	30	is	be	VERB
ejpam-2779	8	31	some	some	DET
ejpam-2779	8	32	one	one	NOUN
ejpam-2779	8	33	having	have	VERB
ejpam-2779	8	34	no	no	DET
ejpam-2779	8	35	bosbach	bosbach	ADJ
ejpam-2779	8	36	states	state	NOUN
ejpam-2779	8	37	.	.	PUNCT
ejpam-2779	9	1	moreover	moreover	ADV
ejpam-2779	9	2	we	we	PRON
ejpam-2779	9	3	discuss	discuss	VERB
ejpam-2779	9	4	some	some	DET
ejpam-2779	9	5	basic	basic	ADJ
ejpam-2779	9	6	properties	property	NOUN
ejpam-2779	9	7	about	about	ADP
ejpam-2779	9	8	bosbach	bosbach	ADJ
ejpam-2779	9	9	states	state	NOUN
ejpam-2779	9	10	.	.	PUNCT
ejpam-2779	10	1	if	if	SCONJ
ejpam-2779	10	2	s	s	PROPN
ejpam-2779	10	3	is	be	AUX
ejpam-2779	10	4	a	a	DET
ejpam-2779	10	5	bosbach	bosbach	ADJ
ejpam-2779	10	6	state	state	NOUN
ejpam-2779	10	7	of	of	ADP
ejpam-2779	10	8	a	a	DET
ejpam-2779	10	9	local	local	ADJ
ejpam-2779	10	10	bounded	bounded	ADJ
ejpam-2779	10	11	pseudo	pseudo	NOUN
ejpam-2779	10	12	-	-	NOUN
ejpam-2779	10	13	bci	bci	ADJ
ejpam-2779	10	14	algebra	algebra	NOUN
ejpam-2779	10	15	a	a	PRON
ejpam-2779	10	16	,	,	PUNCT
ejpam-2779	10	17	we	we	PRON
ejpam-2779	10	18	prove	prove	VERB
ejpam-2779	10	19	that	that	SCONJ
ejpam-2779	10	20	a	a	X
ejpam-2779	10	21	/	/	SYM
ejpam-2779	10	22	ker(s	ker(s	NOUN
ejpam-2779	10	23	)	)	PUNCT
ejpam-2779	10	24	is	be	AUX
ejpam-2779	10	25	equivalent	equivalent	ADJ
ejpam-2779	10	26	to	to	ADP
ejpam-2779	10	27	an	an	DET
ejpam-2779	10	28	mv	mv	NOUN
ejpam-2779	10	29	-	-	NOUN
ejpam-2779	10	30	algebra	algebra	NOUN
ejpam-2779	10	31	.	.	PUNCT
ejpam-2779	11	1	we	we	PRON
ejpam-2779	11	2	also	also	ADV
ejpam-2779	11	3	introduce	introduce	VERB
ejpam-2779	11	4	the	the	DET
ejpam-2779	11	5	notion	notion	NOUN
ejpam-2779	11	6	of	of	ADP
ejpam-2779	11	7	state	state	NOUN
ejpam-2779	11	8	-	-	PUNCT
ejpam-2779	11	9	morphisms	morphism	NOUN
ejpam-2779	11	10	on	on	ADP
ejpam-2779	11	11	local	local	ADJ
ejpam-2779	11	12	bounded	bounded	ADJ
ejpam-2779	11	13	pseudo	pseudo	NOUN
ejpam-2779	11	14	-	-	ADJ
ejpam-2779	11	15	bci	bci	ADJ
ejpam-2779	11	16	algebras	algebra	NOUN
ejpam-2779	11	17	and	and	CCONJ
ejpam-2779	11	18	discuss	discuss	VERB
ejpam-2779	11	19	the	the	DET
ejpam-2779	11	20	relations	relation	NOUN
ejpam-2779	11	21	between	between	ADP
ejpam-2779	11	22	bosbach	bosbach	NOUN
ejpam-2779	11	23	states	state	NOUN
ejpam-2779	11	24	and	and	CCONJ
ejpam-2779	11	25	state	state	NOUN
ejpam-2779	11	26	-	-	PUNCT
ejpam-2779	11	27	morphisms	morphism	NOUN
ejpam-2779	11	28	.	.	PUNCT
ejpam-2779	12	1	finally	finally	ADV
ejpam-2779	12	2	we	we	PRON
ejpam-2779	12	3	give	give	VERB
ejpam-2779	12	4	some	some	DET
ejpam-2779	12	5	characterization	characterization	NOUN
ejpam-2779	12	6	of	of	ADP
ejpam-2779	12	7	bosbach	bosbach	ADJ
ejpam-2779	12	8	states	state	NOUN
ejpam-2779	12	9	.	.	PUNCT
ejpam-2779	13	1	2010	2010	NUM
ejpam-2779	13	2	mathematics	mathematic	NOUN
ejpam-2779	13	3	subject	subject	NOUN
ejpam-2779	13	4	classifications	classification	NOUN
ejpam-2779	13	5	:	:	PUNCT
ejpam-2779	13	6	03g25	03g25	NUM
ejpam-2779	13	7	key	key	ADJ
ejpam-2779	13	8	words	word	NOUN
ejpam-2779	13	9	and	and	CCONJ
ejpam-2779	13	10	phrases	phrase	NOUN
ejpam-2779	13	11	:	:	PUNCT
ejpam-2779	13	12	pseudo	pseudo	NOUN
ejpam-2779	13	13	-	-	ADJ
ejpam-2779	13	14	bci	bci	ADJ
ejpam-2779	13	15	algebra	algebra	NOUN
ejpam-2779	13	16	,	,	PUNCT
ejpam-2779	13	17	local	local	ADJ
ejpam-2779	13	18	bounded	bound	VERB
ejpam-2779	13	19	,	,	PUNCT
ejpam-2779	13	20	state	state	NOUN
ejpam-2779	13	21	,	,	PUNCT
ejpam-2779	13	22	state	state	NOUN
ejpam-2779	13	23	-	-	PUNCT
ejpam-2779	13	24	morphism	morphism	NOUN
ejpam-2779	13	25	,	,	PUNCT
ejpam-2779	13	26	mvalgebra	mvalgebra	NOUN
ejpam-2779	13	27	1	1	NUM
ejpam-2779	13	28	.	.	PUNCT
ejpam-2779	14	1	introduction	introduction	NOUN
ejpam-2779	14	2	bck	bck	PROPN
ejpam-2779	14	3	/	/	SYM
ejpam-2779	14	4	bci	bci	PROPN
ejpam-2779	14	5	algebras	algebra	NOUN
ejpam-2779	14	6	were	be	AUX
ejpam-2779	14	7	introduced	introduce	VERB
ejpam-2779	14	8	originally	originally	ADV
ejpam-2779	14	9	by	by	ADP
ejpam-2779	14	10	iséki	iséki	NUM
ejpam-2779	14	11	in	in	ADP
ejpam-2779	14	12	[	[	X
ejpam-2779	14	13	17	17	NUM
ejpam-2779	14	14	]	]	PUNCT
ejpam-2779	14	15	and	and	CCONJ
ejpam-2779	14	16	[	[	X
ejpam-2779	14	17	18	18	NUM
ejpam-2779	14	18	]	]	PUNCT
ejpam-2779	14	19	with	with	ADP
ejpam-2779	14	20	a	a	DET
ejpam-2779	14	21	binary	binary	ADJ
ejpam-2779	14	22	operation	operation	NOUN
ejpam-2779	14	23	∗	∗	NOUN
ejpam-2779	14	24	modeling	model	VERB
ejpam-2779	14	25	the	the	DET
ejpam-2779	14	26	set	set	NOUN
ejpam-2779	14	27	-	-	PUNCT
ejpam-2779	14	28	theoretical	theoretical	ADJ
ejpam-2779	14	29	difference	difference	NOUN
ejpam-2779	14	30	.	.	PUNCT
ejpam-2779	15	1	another	another	DET
ejpam-2779	15	2	motivation	motivation	NOUN
ejpam-2779	15	3	is	be	AUX
ejpam-2779	15	4	from	from	ADP
ejpam-2779	15	5	classical	classical	ADJ
ejpam-2779	15	6	and	and	CCONJ
ejpam-2779	15	7	non	non	ADJ
ejpam-2779	15	8	-	-	ADJ
ejpam-2779	15	9	classical	classical	ADJ
ejpam-2779	15	10	propositional	propositional	ADJ
ejpam-2779	15	11	calculi	calculi	NOUN
ejpam-2779	15	12	modeling	model	VERB
ejpam-2779	15	13	logical	logical	ADJ
ejpam-2779	15	14	implications	implication	NOUN
ejpam-2779	15	15	.	.	PUNCT
ejpam-2779	16	1	such	such	ADJ
ejpam-2779	16	2	algebras	algebra	NOUN
ejpam-2779	16	3	contain	contain	VERB
ejpam-2779	16	4	as	as	ADP
ejpam-2779	16	5	a	a	DET
ejpam-2779	16	6	special	special	ADJ
ejpam-2779	16	7	subfamily	subfamily	NOUN
ejpam-2779	16	8	of	of	ADP
ejpam-2779	16	9	a	a	DET
ejpam-2779	16	10	family	family	NOUN
ejpam-2779	16	11	of	of	ADP
ejpam-2779	16	12	mv	mv	PROPN
ejpam-2779	16	13	-	-	NOUN
ejpam-2779	16	14	algebras	algebra	NOUN
ejpam-2779	16	15	where	where	SCONJ
ejpam-2779	16	16	some	some	DET
ejpam-2779	16	17	important	important	ADJ
ejpam-2779	16	18	fuzzy	fuzzy	ADJ
ejpam-2779	16	19	structures	structure	NOUN
ejpam-2779	16	20	can	can	AUX
ejpam-2779	16	21	be	be	AUX
ejpam-2779	16	22	studied	study	VERB
ejpam-2779	16	23	.	.	PUNCT
ejpam-2779	17	1	for	for	ADP
ejpam-2779	17	2	more	more	ADJ
ejpam-2779	17	3	about	about	ADP
ejpam-2779	17	4	bck	bck	PROPN
ejpam-2779	17	5	algebras	algebra	NOUN
ejpam-2779	17	6	,	,	PUNCT
ejpam-2779	17	7	see	see	VERB
ejpam-2779	17	8	[	[	X
ejpam-2779	17	9	22	22	NUM
ejpam-2779	17	10	]	]	PUNCT
ejpam-2779	17	11	.	.	PUNCT
ejpam-2779	18	1	pseudo	pseudo	NOUN
ejpam-2779	18	2	-	-	ADJ
ejpam-2779	18	3	bck	bck	ADJ
ejpam-2779	18	4	algebras	algebra	NOUN
ejpam-2779	18	5	were	be	AUX
ejpam-2779	18	6	originally	originally	ADV
ejpam-2779	18	7	introduced	introduce	VERB
ejpam-2779	18	8	by	by	ADP
ejpam-2779	18	9	georgescu	georgescu	NOUN
ejpam-2779	18	10	and	and	CCONJ
ejpam-2779	18	11	iorgulescu	iorgulescu	VERB
ejpam-2779	18	12	in	in	ADP
ejpam-2779	18	13	[	[	X
ejpam-2779	18	14	13	13	NUM
ejpam-2779	18	15	]	]	PUNCT
ejpam-2779	18	16	as	as	ADP
ejpam-2779	18	17	algebras	algebra	NOUN
ejpam-2779	18	18	with	with	ADP
ejpam-2779	18	19	”	"	PUNCT
ejpam-2779	18	20	two	two	NUM
ejpam-2779	18	21	differences	difference	NOUN
ejpam-2779	18	22	”	"	PUNCT
ejpam-2779	18	23	,	,	PUNCT
ejpam-2779	18	24	a	a	DET
ejpam-2779	18	25	leftand	leftand	NOUN
ejpam-2779	18	26	right	right	NOUN
ejpam-2779	18	27	-	-	PUNCT
ejpam-2779	18	28	difference	difference	NOUN
ejpam-2779	18	29	,	,	PUNCT
ejpam-2779	18	30	instead	instead	ADV
ejpam-2779	18	31	of	of	ADP
ejpam-2779	18	32	one	one	NUM
ejpam-2779	18	33	∗	∗	NOUN
ejpam-2779	18	34	and	and	CCONJ
ejpam-2779	18	35	with	with	ADP
ejpam-2779	18	36	a	a	DET
ejpam-2779	18	37	constant	constant	ADJ
ejpam-2779	18	38	element	element	NOUN
ejpam-2779	18	39	0	0	NUM
ejpam-2779	18	40	as	as	ADP
ejpam-2779	18	41	the	the	DET
ejpam-2779	18	42	least	least	ADJ
ejpam-2779	18	43	element	element	NOUN
ejpam-2779	18	44	.	.	PUNCT
ejpam-2779	19	1	in	in	ADP
ejpam-2779	19	2	[	[	X
ejpam-2779	19	3	12	12	NUM
ejpam-2779	19	4	]	]	X
ejpam-2779	19	5	,	,	PUNCT
ejpam-2779	19	6	a	a	DET
ejpam-2779	19	7	special	special	ADJ
ejpam-2779	19	8	subclass	subclass	NOUN
ejpam-2779	19	9	of	of	ADP
ejpam-2779	19	10	pseudo	pseudo	NOUN
ejpam-2779	19	11	-	-	ADJ
ejpam-2779	19	12	bck	bck	ADJ
ejpam-2779	19	13	algebras	algebra	NOUN
ejpam-2779	19	14	,	,	PUNCT
ejpam-2779	19	15	called	call	VERB
ejpam-2779	19	16	lukasiewicz	lukasiewicz	ADJ
ejpam-2779	19	17	pseudo	pseudo	NOUN
ejpam-2779	19	18	-	-	ADJ
ejpam-2779	19	19	bck	bck	ADJ
ejpam-2779	19	20	algebras	algebra	NOUN
ejpam-2779	19	21	,	,	PUNCT
ejpam-2779	19	22	was	be	AUX
ejpam-2779	19	23	introduced	introduce	VERB
ejpam-2779	19	24	and	and	CCONJ
ejpam-2779	19	25	it	it	PRON
ejpam-2779	19	26	was	be	AUX
ejpam-2779	19	27	shown	show	VERB
ejpam-2779	19	28	that	that	SCONJ
ejpam-2779	19	29	∗corresponding	∗corresponde	VERB
ejpam-2779	19	30	author	author	NOUN
ejpam-2779	19	31	.	.	PUNCT
ejpam-2779	20	1	email	email	NOUN
ejpam-2779	20	2	addresses	address	NOUN
ejpam-2779	20	3	:	:	PUNCT
ejpam-2779	20	4	xlxin@nwu.edu.cn	xlxin@nwu.edu.cn	PROPN
ejpam-2779	20	5	(	(	PUNCT
ejpam-2779	20	6	x.l	x.l	PROPN
ejpam-2779	20	7	.	.	PUNCT
ejpam-2779	20	8	xin	xin	PROPN
ejpam-2779	20	9	)	)	PUNCT
ejpam-2779	20	10	,	,	PUNCT
ejpam-2779	20	11	liyijun2009@126.com	liyijun2009@126.com	X
ejpam-2779	20	12	(	(	PUNCT
ejpam-2779	20	13	y.j	y.j	PROPN
ejpam-2779	20	14	.	.	PUNCT
ejpam-2779	20	15	li	li	PROPN
ejpam-2779	20	16	)	)	PUNCT
ejpam-2779	20	17	,	,	PUNCT
ejpam-2779	20	18	ylfu@xidian.edu.cn	ylfu@xidian.edu.cn	PROPN
ejpam-2779	20	19	(	(	PUNCT
ejpam-2779	20	20	y.l	y.l	PROPN
ejpam-2779	20	21	.	.	PROPN
ejpam-2779	20	22	fu	fu	PROPN
ejpam-2779	20	23	)	)	PUNCT
ejpam-2779	20	24	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2779	21	1	455	455	NUM
ejpam-2779	22	1	c	c	X
ejpam-2779	22	2	©	©	PROPN
ejpam-2779	22	3	2017	2017	NUM
ejpam-2779	22	4	ejpam	ejpam	VERB
ejpam-2779	22	5	all	all	DET
ejpam-2779	22	6	rights	right	NOUN
ejpam-2779	22	7	reserved	reserve	VERB
ejpam-2779	22	8	.	.	PUNCT
ejpam-2779	23	1	x.l	x.l	PROPN
ejpam-2779	23	2	.	.	PUNCT
ejpam-2779	24	1	xin	xin	PROPN
ejpam-2779	24	2	,	,	PUNCT
ejpam-2779	24	3	y.j	y.j	PROPN
ejpam-2779	24	4	.	.	PUNCT
ejpam-2779	24	5	li	li	PROPN
ejpam-2779	24	6	,	,	PUNCT
ejpam-2779	24	7	y.l	y.l	PROPN
ejpam-2779	24	8	.	.	PROPN
ejpam-2779	24	9	fu	fu	PROPN
ejpam-2779	24	10	/	/	SYM
ejpam-2779	24	11	eur	eur	PROPN
ejpam-2779	24	12	.	.	PUNCT
ejpam-2779	25	1	j.	j.	PROPN
ejpam-2779	25	2	pure	pure	PROPN
ejpam-2779	25	3	appl	appl	PROPN
ejpam-2779	25	4	.	.	PROPN
ejpam-2779	25	5	math	math	PROPN
ejpam-2779	25	6	,	,	PUNCT
ejpam-2779	25	7	10	10	NUM
ejpam-2779	25	8	(	(	PUNCT
ejpam-2779	25	9	3	3	NUM
ejpam-2779	25	10	)	)	PUNCT
ejpam-2779	25	11	(	(	PUNCT
ejpam-2779	25	12	2017	2017	NUM
ejpam-2779	25	13	)	)	PUNCT
ejpam-2779	25	14	,	,	PUNCT
ejpam-2779	25	15	455	455	NUM
ejpam-2779	25	16	-	-	SYM
ejpam-2779	25	17	472	472	NUM
ejpam-2779	25	18	456	456	NUM
ejpam-2779	25	19	it	it	PRON
ejpam-2779	25	20	is	be	AUX
ejpam-2779	25	21	always	always	ADV
ejpam-2779	25	22	a	a	DET
ejpam-2779	25	23	subalgebra	subalgebra	NOUN
ejpam-2779	25	24	of	of	ADP
ejpam-2779	25	25	the	the	DET
ejpam-2779	25	26	positive	positive	ADJ
ejpam-2779	25	27	cone	cone	NOUN
ejpam-2779	25	28	of	of	ADP
ejpam-2779	25	29	some	some	DET
ejpam-2779	25	30	`	`	PUNCT
ejpam-2779	25	31	-group	-group	NOUN
ejpam-2779	25	32	(	(	PUNCT
ejpam-2779	25	33	not	not	PART
ejpam-2779	25	34	necessarily	necessarily	ADV
ejpam-2779	25	35	abelian	abelian	ADJ
ejpam-2779	25	36	)	)	PUNCT
ejpam-2779	25	37	.	.	PUNCT
ejpam-2779	26	1	the	the	DET
ejpam-2779	26	2	class	class	NOUN
ejpam-2779	26	3	of	of	ADP
ejpam-2779	26	4	lukasiewicz	lukasiewicz	ADJ
ejpam-2779	26	5	pseudo	pseudo	NOUN
ejpam-2779	26	6	-	-	VERB
ejpam-2779	26	7	bckalgebras	bckalgebras	X
ejpam-2779	26	8	is	be	AUX
ejpam-2779	26	9	a	a	DET
ejpam-2779	26	10	variety	variety	NOUN
ejpam-2779	26	11	whereas	whereas	SCONJ
ejpam-2779	26	12	the	the	DET
ejpam-2779	26	13	class	class	NOUN
ejpam-2779	26	14	of	of	ADP
ejpam-2779	26	15	pseudobckalgebras	pseudobckalgebras	NOUN
ejpam-2779	26	16	is	be	AUX
ejpam-2779	26	17	not	not	PART
ejpam-2779	26	18	;	;	PUNCT
ejpam-2779	26	19	it	it	PRON
ejpam-2779	26	20	is	be	AUX
ejpam-2779	26	21	only	only	ADV
ejpam-2779	26	22	a	a	DET
ejpam-2779	26	23	quasivariety	quasivariety	NOUN
ejpam-2779	26	24	because	because	SCONJ
ejpam-2779	26	25	it	it	PRON
ejpam-2779	26	26	is	be	AUX
ejpam-2779	26	27	not	not	PART
ejpam-2779	26	28	closed	close	VERB
ejpam-2779	26	29	under	under	ADP
ejpam-2779	26	30	homomorphic	homomorphic	ADJ
ejpam-2779	26	31	images	image	NOUN
ejpam-2779	26	32	.	.	PUNCT
ejpam-2779	27	1	for	for	ADP
ejpam-2779	27	2	a	a	DET
ejpam-2779	27	3	guide	guide	NOUN
ejpam-2779	27	4	through	through	ADP
ejpam-2779	27	5	the	the	DET
ejpam-2779	27	6	pseudo	pseudo	NOUN
ejpam-2779	27	7	-	-	ADJ
ejpam-2779	27	8	bck	bck	ADJ
ejpam-2779	27	9	algebras	algebras	PROPN
ejpam-2779	27	10	realm	realm	PROPN
ejpam-2779	27	11	,	,	PUNCT
ejpam-2779	27	12	see	see	VERB
ejpam-2779	27	13	the	the	DET
ejpam-2779	27	14	monograph	monograph	NOUN
ejpam-2779	28	1	[	[	X
ejpam-2779	28	2	16	16	NUM
ejpam-2779	28	3	]	]	PUNCT
ejpam-2779	28	4	.	.	PUNCT
ejpam-2779	29	1	in	in	ADP
ejpam-2779	29	2	[	[	X
ejpam-2779	29	3	8	8	NUM
ejpam-2779	29	4	]	]	PUNCT
ejpam-2779	29	5	,	,	PUNCT
ejpam-2779	29	6	w.	w.	PROPN
ejpam-2779	29	7	a.	a.	PROPN
ejpam-2779	29	8	dudek	dudek	PROPN
ejpam-2779	29	9	and	and	CCONJ
ejpam-2779	29	10	y.	y.	PROPN
ejpam-2779	29	11	b.	b.	PROPN
ejpam-2779	29	12	jun	jun	PROPN
ejpam-2779	29	13	introduced	introduce	VERB
ejpam-2779	29	14	the	the	DET
ejpam-2779	29	15	notion	notion	NOUN
ejpam-2779	29	16	of	of	ADP
ejpam-2779	29	17	pseudo	pseudo	NOUN
ejpam-2779	29	18	-	-	ADJ
ejpam-2779	29	19	bci	bci	ADJ
ejpam-2779	29	20	algebras	algebra	NOUN
ejpam-2779	29	21	as	as	ADP
ejpam-2779	29	22	an	an	DET
ejpam-2779	29	23	extension	extension	NOUN
ejpam-2779	29	24	of	of	ADP
ejpam-2779	29	25	bci	bci	NOUN
ejpam-2779	29	26	-	-	PUNCT
ejpam-2779	29	27	algebras	algebras	X
ejpam-2779	29	28	,	,	PUNCT
ejpam-2779	29	29	and	and	CCONJ
ejpam-2779	29	30	investigated	investigate	VERB
ejpam-2779	29	31	some	some	DET
ejpam-2779	29	32	properties	property	NOUN
ejpam-2779	29	33	.	.	PUNCT
ejpam-2779	30	1	mv	mv	PROPN
ejpam-2779	30	2	-	-	PUNCT
ejpam-2779	30	3	algebras	algebras	PROPN
ejpam-2779	30	4	entered	enter	VERB
ejpam-2779	30	5	into	into	ADP
ejpam-2779	30	6	mathematics	mathematic	NOUN
ejpam-2779	30	7	just	just	ADV
ejpam-2779	30	8	50	50	NUM
ejpam-2779	30	9	years	year	NOUN
ejpam-2779	30	10	ago	ago	ADV
ejpam-2779	30	11	due	due	ADP
ejpam-2779	30	12	to	to	ADP
ejpam-2779	30	13	chang	chang	PROPN
ejpam-2779	30	14	[	[	X
ejpam-2779	30	15	3	3	NUM
ejpam-2779	30	16	]	]	PUNCT
ejpam-2779	30	17	,	,	PUNCT
ejpam-2779	30	18	but	but	CCONJ
ejpam-2779	30	19	the	the	DET
ejpam-2779	30	20	notion	notion	NOUN
ejpam-2779	30	21	of	of	ADP
ejpam-2779	30	22	a	a	DET
ejpam-2779	30	23	state	state	NOUN
ejpam-2779	30	24	for	for	SCONJ
ejpam-2779	30	25	mv	mv	PROPN
ejpam-2779	30	26	-	-	PUNCT
ejpam-2779	30	27	algebras	algebras	PROPN
ejpam-2779	30	28	was	be	AUX
ejpam-2779	30	29	introduced	introduce	VERB
ejpam-2779	30	30	by	by	ADP
ejpam-2779	30	31	mundici	mundici	NOUN
ejpam-2779	31	1	[	[	X
ejpam-2779	31	2	23	23	NUM
ejpam-2779	31	3	]	]	PUNCT
ejpam-2779	31	4	in	in	ADP
ejpam-2779	31	5	1995	1995	NUM
ejpam-2779	31	6	as	as	ADP
ejpam-2779	31	7	averaging	average	VERB
ejpam-2779	31	8	of	of	ADP
ejpam-2779	31	9	the	the	DET
ejpam-2779	31	10	truth	truth	NOUN
ejpam-2779	31	11	-	-	PUNCT
ejpam-2779	31	12	value	value	NOUN
ejpam-2779	31	13	in	in	ADP
ejpam-2779	31	14	lukasiewicz	lukasiewicz	ADJ
ejpam-2779	31	15	logic	logic	NOUN
ejpam-2779	31	16	.	.	PUNCT
ejpam-2779	32	1	bl	bl	VERB
ejpam-2779	32	2	-	-	PUNCT
ejpam-2779	32	3	algebras	algebras	PROPN
ejpam-2779	32	4	were	be	AUX
ejpam-2779	32	5	introduced	introduce	VERB
ejpam-2779	32	6	in	in	ADP
ejpam-2779	32	7	the	the	DET
ejpam-2779	32	8	1990s	1990s	NUM
ejpam-2779	32	9	by	by	ADP
ejpam-2779	32	10	hájek	hájek	NOUN
ejpam-2779	32	11	[	[	X
ejpam-2779	32	12	14	14	NUM
ejpam-2779	32	13	]	]	PUNCT
ejpam-2779	32	14	as	as	ADP
ejpam-2779	32	15	the	the	DET
ejpam-2779	32	16	equivalent	equivalent	ADJ
ejpam-2779	32	17	algebraic	algebraic	ADJ
ejpam-2779	32	18	semantics	semantic	NOUN
ejpam-2779	32	19	for	for	ADP
ejpam-2779	32	20	its	its	PRON
ejpam-2779	32	21	basic	basic	ADJ
ejpam-2779	32	22	fuzzy	fuzzy	ADJ
ejpam-2779	32	23	logic	logic	NOUN
ejpam-2779	32	24	.	.	PUNCT
ejpam-2779	33	1	in	in	ADP
ejpam-2779	33	2	[	[	X
ejpam-2779	33	3	5	5	NUM
ejpam-2779	33	4	]	]	PUNCT
ejpam-2779	33	5	,	,	PUNCT
ejpam-2779	33	6	authors	author	NOUN
ejpam-2779	33	7	defined	define	VERB
ejpam-2779	33	8	a	a	DET
ejpam-2779	33	9	state	state	NOUN
ejpam-2779	33	10	-	-	PUNCT
ejpam-2779	33	11	operator	operator	NOUN
ejpam-2779	33	12	and	and	CCONJ
ejpam-2779	33	13	a	a	DET
ejpam-2779	33	14	strong	strong	ADJ
ejpam-2779	33	15	state	state	NOUN
ejpam-2779	33	16	-	-	PUNCT
ejpam-2779	33	17	operator	operator	NOUN
ejpam-2779	33	18	for	for	ADP
ejpam-2779	33	19	a	a	DET
ejpam-2779	33	20	bl	bl	NOUN
ejpam-2779	33	21	-	-	PUNCT
ejpam-2779	33	22	algebra	algebra	NOUN
ejpam-2779	33	23	and	and	CCONJ
ejpam-2779	33	24	prove	prove	VERB
ejpam-2779	33	25	some	some	PRON
ejpam-2779	33	26	of	of	ADP
ejpam-2779	33	27	their	their	PRON
ejpam-2779	33	28	basic	basic	ADJ
ejpam-2779	33	29	properties	property	NOUN
ejpam-2779	33	30	.	.	PUNCT
ejpam-2779	34	1	l.	l.	PROPN
ejpam-2779	34	2	z.	z.	PROPN
ejpam-2779	34	3	liu	liu	PROPN
ejpam-2779	34	4	studied	study	VERB
ejpam-2779	34	5	the	the	DET
ejpam-2779	34	6	existence	existence	NOUN
ejpam-2779	34	7	of	of	ADP
ejpam-2779	34	8	bosbach	bosbach	ADJ
ejpam-2779	34	9	states	state	NOUN
ejpam-2779	34	10	and	and	CCONJ
ejpam-2779	34	11	riečan	riečan	NOUN
ejpam-2779	34	12	states	state	NOUN
ejpam-2779	34	13	on	on	ADP
ejpam-2779	34	14	finite	finite	PROPN
ejpam-2779	34	15	monoidal	monoidal	PROPN
ejpam-2779	34	16	t	t	PROPN
ejpam-2779	34	17	-	-	PUNCT
ejpam-2779	34	18	norm	norm	NOUN
ejpam-2779	34	19	based	base	VERB
ejpam-2779	34	20	algebras	algebra	NOUN
ejpam-2779	34	21	in	in	ADP
ejpam-2779	34	22	[	[	X
ejpam-2779	34	23	21	21	NUM
ejpam-2779	34	24	]	]	PUNCT
ejpam-2779	34	25	.	.	PUNCT
ejpam-2779	35	1	some	some	DET
ejpam-2779	35	2	examples	example	NOUN
ejpam-2779	35	3	show	show	VERB
ejpam-2779	35	4	that	that	SCONJ
ejpam-2779	35	5	there	there	PRON
ejpam-2779	35	6	exist	exist	VERB
ejpam-2779	35	7	mtl	mtl	NOUN
ejpam-2779	35	8	-	-	PUNCT
ejpam-2779	35	9	algebras	algebra	NOUN
ejpam-2779	35	10	having	have	VERB
ejpam-2779	35	11	no	no	DET
ejpam-2779	35	12	bosbach	bosbach	ADJ
ejpam-2779	35	13	states	state	NOUN
ejpam-2779	35	14	and	and	CCONJ
ejpam-2779	35	15	riečan	riečan	NOUN
ejpam-2779	35	16	states	state	NOUN
ejpam-2779	35	17	.	.	PUNCT
ejpam-2779	36	1	in	in	ADP
ejpam-2779	36	2	[	[	X
ejpam-2779	36	3	10	10	NUM
ejpam-2779	36	4	]	]	PUNCT
ejpam-2779	36	5	,	,	PUNCT
ejpam-2779	36	6	dvurečenskij	dvurečenskij	PROPN
ejpam-2779	36	7	introduced	introduce	VERB
ejpam-2779	36	8	measures	measure	NOUN
ejpam-2779	36	9	and	and	CCONJ
ejpam-2779	36	10	states	state	NOUN
ejpam-2779	36	11	on	on	ADP
ejpam-2779	36	12	bck	bck	NOUN
ejpam-2779	36	13	-	-	PUNCT
ejpam-2779	36	14	algebras	algebras	X
ejpam-2779	36	15	,	,	PUNCT
ejpam-2779	36	16	and	and	CCONJ
ejpam-2779	36	17	showed	show	VERB
ejpam-2779	36	18	that	that	SCONJ
ejpam-2779	36	19	the	the	DET
ejpam-2779	36	20	set	set	NOUN
ejpam-2779	36	21	of	of	ADP
ejpam-2779	36	22	elements	element	NOUN
ejpam-2779	36	23	of	of	ADP
ejpam-2779	36	24	measure	measure	NOUN
ejpam-2779	36	25	0	0	NUM
ejpam-2779	36	26	is	be	AUX
ejpam-2779	36	27	an	an	DET
ejpam-2779	36	28	ideal	ideal	NOUN
ejpam-2779	36	29	,	,	PUNCT
ejpam-2779	36	30	and	and	CCONJ
ejpam-2779	36	31	the	the	DET
ejpam-2779	36	32	corresponding	corresponding	ADJ
ejpam-2779	36	33	quotient	quotient	NOUN
ejpam-2779	36	34	bckalgebra	bckalgebra	PROPN
ejpam-2779	36	35	is	be	AUX
ejpam-2779	36	36	commutative	commutative	ADJ
ejpam-2779	36	37	with	with	ADP
ejpam-2779	36	38	a	a	DET
ejpam-2779	36	39	lifted	lift	VERB
ejpam-2779	36	40	original	original	ADJ
ejpam-2779	36	41	measure	measure	NOUN
ejpam-2779	36	42	.	.	PUNCT
ejpam-2779	37	1	ciungu	ciungu	NOUN
ejpam-2779	37	2	and	and	CCONJ
ejpam-2779	37	3	dvurečenskij	dvurečenskij	NOUN
ejpam-2779	37	4	[	[	X
ejpam-2779	37	5	4	4	NUM
ejpam-2779	37	6	]	]	PUNCT
ejpam-2779	37	7	extended	extend	VERB
ejpam-2779	37	8	the	the	DET
ejpam-2779	37	9	notions	notion	NOUN
ejpam-2779	37	10	of	of	ADP
ejpam-2779	37	11	measures	measure	NOUN
ejpam-2779	37	12	and	and	CCONJ
ejpam-2779	37	13	states	state	NOUN
ejpam-2779	37	14	presented	present	VERB
ejpam-2779	37	15	in	in	ADP
ejpam-2779	37	16	dvurečen	dvurečen	NOUN
ejpam-2779	37	17	-	-	PUNCT
ejpam-2779	37	18	skij	skij	PROPN
ejpam-2779	37	19	and	and	CCONJ
ejpam-2779	37	20	pulmannová	pulmannová	ADJ
ejpam-2779	38	1	[	[	X
ejpam-2779	38	2	9	9	NUM
ejpam-2779	38	3	]	]	PUNCT
ejpam-2779	38	4	to	to	ADP
ejpam-2779	38	5	the	the	DET
ejpam-2779	38	6	case	case	NOUN
ejpam-2779	38	7	of	of	ADP
ejpam-2779	38	8	pseudo	pseudo	NOUN
ejpam-2779	38	9	-	-	ADJ
ejpam-2779	38	10	bck	bck	ADJ
ejpam-2779	38	11	algebras	algebra	NOUN
ejpam-2779	38	12	,	,	PUNCT
ejpam-2779	38	13	studied	study	VERB
ejpam-2779	38	14	similar	similar	ADJ
ejpam-2779	38	15	properties	property	NOUN
ejpam-2779	38	16	,	,	PUNCT
ejpam-2779	38	17	and	and	CCONJ
ejpam-2779	38	18	prove	prove	VERB
ejpam-2779	38	19	that	that	SCONJ
ejpam-2779	38	20	,	,	PUNCT
ejpam-2779	38	21	under	under	ADP
ejpam-2779	38	22	some	some	DET
ejpam-2779	38	23	conditions	condition	NOUN
ejpam-2779	38	24	,	,	PUNCT
ejpam-2779	38	25	the	the	DET
ejpam-2779	38	26	notion	notion	NOUN
ejpam-2779	38	27	of	of	ADP
ejpam-2779	38	28	a	a	DET
ejpam-2779	38	29	state	state	NOUN
ejpam-2779	38	30	in	in	ADP
ejpam-2779	38	31	the	the	DET
ejpam-2779	38	32	sense	sense	NOUN
ejpam-2779	38	33	of	of	ADP
ejpam-2779	38	34	dvurečenskij	dvurečenskij	PROPN
ejpam-2779	38	35	and	and	CCONJ
ejpam-2779	38	36	pulmannová	pulmannová	ADJ
ejpam-2779	38	37	[	[	X
ejpam-2779	38	38	9	9	NUM
ejpam-2779	38	39	]	]	PUNCT
ejpam-2779	38	40	coincides	coincide	VERB
ejpam-2779	38	41	with	with	ADP
ejpam-2779	38	42	the	the	DET
ejpam-2779	38	43	bosbach	bosbach	ADJ
ejpam-2779	38	44	state	state	NOUN
ejpam-2779	38	45	.	.	PUNCT
ejpam-2779	39	1	the	the	DET
ejpam-2779	39	2	aim	aim	NOUN
ejpam-2779	39	3	of	of	ADP
ejpam-2779	39	4	this	this	DET
ejpam-2779	39	5	paper	paper	NOUN
ejpam-2779	39	6	is	be	AUX
ejpam-2779	39	7	to	to	PART
ejpam-2779	39	8	introduce	introduce	VERB
ejpam-2779	39	9	and	and	CCONJ
ejpam-2779	39	10	study	study	VERB
ejpam-2779	39	11	the	the	DET
ejpam-2779	39	12	state	state	NOUN
ejpam-2779	39	13	theory	theory	NOUN
ejpam-2779	39	14	on	on	ADP
ejpam-2779	39	15	local	local	ADJ
ejpam-2779	39	16	bounded	bounded	ADJ
ejpam-2779	39	17	pseudo	pseudo	NOUN
ejpam-2779	39	18	-	-	ADJ
ejpam-2779	39	19	bci	bci	ADJ
ejpam-2779	39	20	algebras	algebra	NOUN
ejpam-2779	39	21	.	.	PUNCT
ejpam-2779	40	1	this	this	DET
ejpam-2779	40	2	paper	paper	NOUN
ejpam-2779	40	3	is	be	AUX
ejpam-2779	40	4	organized	organize	VERB
ejpam-2779	40	5	as	as	SCONJ
ejpam-2779	40	6	follows	follow	VERB
ejpam-2779	40	7	:	:	PUNCT
ejpam-2779	40	8	in	in	ADP
ejpam-2779	40	9	section	section	NOUN
ejpam-2779	40	10	2	2	NUM
ejpam-2779	40	11	,	,	PUNCT
ejpam-2779	40	12	we	we	PRON
ejpam-2779	40	13	recall	recall	VERB
ejpam-2779	40	14	notions	notion	NOUN
ejpam-2779	40	15	of	of	ADP
ejpam-2779	40	16	bci	bci	NOUN
ejpam-2779	40	17	-	-	PUNCT
ejpam-2779	40	18	algebras	algebra	NOUN
ejpam-2779	40	19	and	and	CCONJ
ejpam-2779	40	20	the	the	DET
ejpam-2779	40	21	notion	notion	NOUN
ejpam-2779	40	22	and	and	CCONJ
ejpam-2779	40	23	some	some	DET
ejpam-2779	40	24	properties	property	NOUN
ejpam-2779	40	25	of	of	ADP
ejpam-2779	40	26	pseudo	pseudo	NOUN
ejpam-2779	40	27	-	-	ADJ
ejpam-2779	40	28	bci	bci	ADJ
ejpam-2779	40	29	algebras	algebra	NOUN
ejpam-2779	40	30	.	.	PUNCT
ejpam-2779	41	1	in	in	ADP
ejpam-2779	41	2	the	the	DET
ejpam-2779	41	3	same	same	ADJ
ejpam-2779	41	4	time	time	NOUN
ejpam-2779	41	5	,	,	PUNCT
ejpam-2779	41	6	we	we	PRON
ejpam-2779	41	7	discuss	discuss	VERB
ejpam-2779	41	8	the	the	DET
ejpam-2779	41	9	structure	structure	NOUN
ejpam-2779	41	10	of	of	ADP
ejpam-2779	41	11	pseudo	pseudo	NOUN
ejpam-2779	41	12	-	-	ADJ
ejpam-2779	41	13	bci	bci	ADJ
ejpam-2779	41	14	algebras	algebra	NOUN
ejpam-2779	41	15	and	and	CCONJ
ejpam-2779	41	16	get	get	VERB
ejpam-2779	41	17	that	that	PRON
ejpam-2779	41	18	any	any	DET
ejpam-2779	41	19	pseudo	pseudo	NOUN
ejpam-2779	41	20	-	-	ADJ
ejpam-2779	41	21	bci	bci	ADJ
ejpam-2779	41	22	algebra	algebra	NOUN
ejpam-2779	41	23	is	be	AUX
ejpam-2779	41	24	a	a	DET
ejpam-2779	41	25	union	union	NOUN
ejpam-2779	41	26	of	of	ADP
ejpam-2779	41	27	it	it	PRON
ejpam-2779	41	28	’s	’	VERB
ejpam-2779	41	29	branches	branch	NOUN
ejpam-2779	41	30	.	.	PUNCT
ejpam-2779	42	1	in	in	ADP
ejpam-2779	42	2	section	section	NOUN
ejpam-2779	42	3	3	3	NUM
ejpam-2779	42	4	,	,	PUNCT
ejpam-2779	42	5	we	we	PRON
ejpam-2779	42	6	introduce	introduce	VERB
ejpam-2779	42	7	the	the	DET
ejpam-2779	42	8	notion	notion	NOUN
ejpam-2779	42	9	of	of	ADP
ejpam-2779	42	10	local	local	ADJ
ejpam-2779	42	11	bounded	bounded	ADJ
ejpam-2779	42	12	pseudobci	pseudobci	NOUN
ejpam-2779	42	13	algebras	algebra	NOUN
ejpam-2779	42	14	and	and	CCONJ
ejpam-2779	42	15	study	study	VERB
ejpam-2779	42	16	some	some	DET
ejpam-2779	42	17	related	relate	VERB
ejpam-2779	42	18	properties	property	NOUN
ejpam-2779	42	19	.	.	PUNCT
ejpam-2779	43	1	in	in	ADP
ejpam-2779	43	2	section	section	NOUN
ejpam-2779	43	3	4	4	NUM
ejpam-2779	43	4	,	,	PUNCT
ejpam-2779	43	5	we	we	PRON
ejpam-2779	43	6	define	define	VERB
ejpam-2779	43	7	a	a	DET
ejpam-2779	43	8	bosbach	bosbach	ADJ
ejpam-2779	43	9	state	state	NOUN
ejpam-2779	43	10	on	on	ADP
ejpam-2779	43	11	a	a	DET
ejpam-2779	43	12	local	local	ADJ
ejpam-2779	43	13	bounded	bounded	ADJ
ejpam-2779	43	14	pseudo	pseudo	NOUN
ejpam-2779	43	15	-	-	ADJ
ejpam-2779	43	16	bci	bci	ADJ
ejpam-2779	43	17	algebra	algebra	NOUN
ejpam-2779	43	18	.	.	PUNCT
ejpam-2779	44	1	then	then	ADV
ejpam-2779	44	2	we	we	PRON
ejpam-2779	44	3	give	give	VERB
ejpam-2779	44	4	two	two	NUM
ejpam-2779	44	5	examples	example	NOUN
ejpam-2779	44	6	of	of	ADP
ejpam-2779	44	7	local	local	ADJ
ejpam-2779	44	8	bounded	bounded	ADJ
ejpam-2779	44	9	pseudo	pseudo	NOUN
ejpam-2779	44	10	-	-	NOUN
ejpam-2779	44	11	bci	bci	NOUN
ejpam-2779	44	12	algebras	algebra	NOUN
ejpam-2779	44	13	to	to	PART
ejpam-2779	44	14	show	show	VERB
ejpam-2779	44	15	that	that	SCONJ
ejpam-2779	44	16	there	there	PRON
ejpam-2779	44	17	is	be	VERB
ejpam-2779	44	18	local	local	ADJ
ejpam-2779	44	19	bounded	bounded	ADJ
ejpam-2779	44	20	pseudo	pseudo	NOUN
ejpam-2779	44	21	-	-	ADJ
ejpam-2779	44	22	bci	bci	ADJ
ejpam-2779	44	23	algebras	algebra	NOUN
ejpam-2779	44	24	having	have	VERB
ejpam-2779	44	25	a	a	DET
ejpam-2779	44	26	bosbach	bosbach	ADJ
ejpam-2779	44	27	state	state	NOUN
ejpam-2779	44	28	but	but	CCONJ
ejpam-2779	44	29	there	there	PRON
ejpam-2779	44	30	is	be	VERB
ejpam-2779	44	31	some	some	DET
ejpam-2779	44	32	one	one	NOUN
ejpam-2779	44	33	having	have	VERB
ejpam-2779	44	34	no	no	DET
ejpam-2779	44	35	bosbach	bosbach	ADJ
ejpam-2779	44	36	states	state	NOUN
ejpam-2779	44	37	.	.	PUNCT
ejpam-2779	45	1	moreover	moreover	ADV
ejpam-2779	45	2	we	we	PRON
ejpam-2779	45	3	discuss	discuss	VERB
ejpam-2779	45	4	some	some	PRON
ejpam-2779	45	5	of	of	ADP
ejpam-2779	45	6	their	their	PRON
ejpam-2779	45	7	basic	basic	ADJ
ejpam-2779	45	8	properties	property	NOUN
ejpam-2779	45	9	.	.	PUNCT
ejpam-2779	46	1	we	we	PRON
ejpam-2779	46	2	discuss	discuss	VERB
ejpam-2779	46	3	the	the	DET
ejpam-2779	46	4	relation	relation	NOUN
ejpam-2779	46	5	between	between	ADP
ejpam-2779	46	6	local	local	ADJ
ejpam-2779	46	7	bounded	bounded	ADJ
ejpam-2779	46	8	pseudobci	pseudobci	PROPN
ejpam-2779	46	9	algebras	algebras	PROPN
ejpam-2779	46	10	and	and	CCONJ
ejpam-2779	46	11	mv	mv	PROPN
ejpam-2779	46	12	-algebras	-algebras	PROPN
ejpam-2779	46	13	.	.	PUNCT
ejpam-2779	47	1	we	we	PRON
ejpam-2779	47	2	also	also	ADV
ejpam-2779	47	3	introduce	introduce	VERB
ejpam-2779	47	4	the	the	DET
ejpam-2779	47	5	notion	notion	NOUN
ejpam-2779	47	6	of	of	ADP
ejpam-2779	47	7	state	state	NOUN
ejpam-2779	47	8	-	-	PUNCT
ejpam-2779	47	9	morphisms	morphism	NOUN
ejpam-2779	47	10	on	on	ADP
ejpam-2779	47	11	local	local	ADJ
ejpam-2779	47	12	bounded	bounded	ADJ
ejpam-2779	47	13	pseudo	pseudo	NOUN
ejpam-2779	47	14	-	-	ADJ
ejpam-2779	47	15	bci	bci	ADJ
ejpam-2779	47	16	algebras	algebra	NOUN
ejpam-2779	47	17	and	and	CCONJ
ejpam-2779	47	18	discuss	discuss	VERB
ejpam-2779	47	19	the	the	DET
ejpam-2779	47	20	relations	relation	NOUN
ejpam-2779	47	21	between	between	ADP
ejpam-2779	47	22	bosbach	bosbach	NOUN
ejpam-2779	47	23	states	state	NOUN
ejpam-2779	47	24	and	and	CCONJ
ejpam-2779	47	25	state	state	NOUN
ejpam-2779	47	26	-	-	PUNCT
ejpam-2779	47	27	morphisms	morphism	NOUN
ejpam-2779	47	28	.	.	PUNCT
ejpam-2779	48	1	finally	finally	ADV
ejpam-2779	48	2	we	we	PRON
ejpam-2779	48	3	give	give	VERB
ejpam-2779	48	4	some	some	DET
ejpam-2779	48	5	characterization	characterization	NOUN
ejpam-2779	48	6	on	on	ADP
ejpam-2779	48	7	bosbach	bosbach	ADJ
ejpam-2779	48	8	states	state	NOUN
ejpam-2779	48	9	.	.	PUNCT
ejpam-2779	49	1	2	2	X
ejpam-2779	49	2	.	.	X
ejpam-2779	49	3	pseudo	pseudo	NOUN
ejpam-2779	49	4	-	-	ADJ
ejpam-2779	49	5	bci	bci	ADJ
ejpam-2779	49	6	algebras	algebra	NOUN
ejpam-2779	49	7	recall	recall	VERB
ejpam-2779	49	8	that	that	SCONJ
ejpam-2779	49	9	a	a	DET
ejpam-2779	49	10	bci	bci	NOUN
ejpam-2779	49	11	-	-	NOUN
ejpam-2779	49	12	algebra	algebra	NOUN
ejpam-2779	49	13	is	be	AUX
ejpam-2779	49	14	an	an	DET
ejpam-2779	49	15	algebra	algebra	NOUN
ejpam-2779	49	16	(	(	PUNCT
ejpam-2779	49	17	x	x	X
ejpam-2779	49	18	,	,	PUNCT
ejpam-2779	49	19	∗	∗	NOUN
ejpam-2779	49	20	,	,	PUNCT
ejpam-2779	49	21	0	0	NUM
ejpam-2779	49	22	)	)	PUNCT
ejpam-2779	49	23	of	of	ADP
ejpam-2779	49	24	type	type	NOUN
ejpam-2779	49	25	(	(	PUNCT
ejpam-2779	49	26	2,0	2,0	NUM
ejpam-2779	49	27	)	)	PUNCT
ejpam-2779	49	28	satisfying	satisfy	VERB
ejpam-2779	49	29	the	the	DET
ejpam-2779	49	30	following	follow	VERB
ejpam-2779	49	31	axioms	axiom	NOUN
ejpam-2779	49	32	:	:	PUNCT
ejpam-2779	49	33	for	for	ADP
ejpam-2779	49	34	every	every	DET
ejpam-2779	49	35	x	x	PROPN
ejpam-2779	49	36	,	,	PUNCT
ejpam-2779	49	37	y	y	PROPN
ejpam-2779	49	38	,	,	PUNCT
ejpam-2779	49	39	z	z	PROPN
ejpam-2779	49	40	∈	∈	PROPN
ejpam-2779	49	41	x	x	X
ejpam-2779	49	42	,	,	PUNCT
ejpam-2779	49	43	(	(	PUNCT
ejpam-2779	49	44	1	1	NUM
ejpam-2779	49	45	)	)	PUNCT
ejpam-2779	49	46	(	(	PUNCT
ejpam-2779	49	47	(	(	PUNCT
ejpam-2779	49	48	x	x	SYM
ejpam-2779	49	49	∗	∗	PROPN
ejpam-2779	49	50	y	y	NOUN
ejpam-2779	49	51	)	)	PUNCT
ejpam-2779	49	52	∗	∗	NOUN
ejpam-2779	49	53	(	(	PUNCT
ejpam-2779	49	54	x	x	X
ejpam-2779	49	55	∗	∗	PROPN
ejpam-2779	49	56	z	z	NOUN
ejpam-2779	49	57	)	)	PUNCT
ejpam-2779	49	58	)	)	PUNCT
ejpam-2779	49	59	∗	∗	NOUN
ejpam-2779	49	60	(	(	PUNCT
ejpam-2779	49	61	z	z	NOUN
ejpam-2779	49	62	∗	∗	NOUN
ejpam-2779	49	63	y	y	NOUN
ejpam-2779	49	64	)	)	PUNCT
ejpam-2779	49	65	=	=	SYM
ejpam-2779	50	1	0	0	NUM
ejpam-2779	50	2	,	,	PUNCT
ejpam-2779	50	3	(	(	PUNCT
ejpam-2779	50	4	2	2	NUM
ejpam-2779	50	5	)	)	PUNCT
ejpam-2779	50	6	(	(	PUNCT
ejpam-2779	50	7	x	x	NOUN
ejpam-2779	50	8	∗	∗	NOUN
ejpam-2779	50	9	(	(	PUNCT
ejpam-2779	50	10	x	x	X
ejpam-2779	50	11	∗	∗	PROPN
ejpam-2779	50	12	y	y	NOUN
ejpam-2779	50	13	)	)	PUNCT
ejpam-2779	50	14	)	)	PUNCT
ejpam-2779	51	1	∗	∗	NOUN
ejpam-2779	51	2	y	y	NOUN
ejpam-2779	51	3	=	=	SYM
ejpam-2779	51	4	0	0	PROPN
ejpam-2779	51	5	,	,	PUNCT
ejpam-2779	51	6	(	(	PUNCT
ejpam-2779	51	7	3	3	X
ejpam-2779	51	8	)	)	PUNCT
ejpam-2779	52	1	x	x	NOUN
ejpam-2779	52	2	∗	∗	NOUN
ejpam-2779	52	3	x	x	SYM
ejpam-2779	52	4	=	=	SYM
ejpam-2779	52	5	0	0	NUM
ejpam-2779	52	6	,	,	PUNCT
ejpam-2779	52	7	(	(	PUNCT
ejpam-2779	52	8	4	4	NUM
ejpam-2779	52	9	)	)	PUNCT
ejpam-2779	52	10	x	x	NOUN
ejpam-2779	52	11	∗	∗	NOUN
ejpam-2779	52	12	y	y	NOUN
ejpam-2779	52	13	=	=	SYM
ejpam-2779	52	14	0	0	PROPN
ejpam-2779	53	1	and	and	CCONJ
ejpam-2779	53	2	y	y	PROPN
ejpam-2779	53	3	∗	∗	NOUN
ejpam-2779	53	4	x	x	PUNCT
ejpam-2779	54	1	=	=	SYM
ejpam-2779	54	2	0	0	NUM
ejpam-2779	54	3	imply	imply	VERB
ejpam-2779	54	4	x	x	X
ejpam-2779	54	5	=	=	PUNCT
ejpam-2779	54	6	y.	y.	NOUN
ejpam-2779	54	7	for	for	ADP
ejpam-2779	54	8	any	any	DET
ejpam-2779	54	9	bci	bci	NOUN
ejpam-2779	54	10	-	-	NOUN
ejpam-2779	54	11	algebra	algebra	NOUN
ejpam-2779	54	12	x	x	NOUN
ejpam-2779	54	13	,	,	PUNCT
ejpam-2779	54	14	the	the	DET
ejpam-2779	54	15	relation	relation	NOUN
ejpam-2779	54	16	≤	≤	NUM
ejpam-2779	54	17	defined	define	VERB
ejpam-2779	54	18	by	by	ADP
ejpam-2779	54	19	x	x	PROPN
ejpam-2779	54	20	≤	≤	NUM
ejpam-2779	54	21	y	y	NOUN
ejpam-2779	54	22	if	if	SCONJ
ejpam-2779	55	1	and	and	CCONJ
ejpam-2779	55	2	only	only	ADV
ejpam-2779	55	3	if	if	SCONJ
ejpam-2779	55	4	x	x	X
ejpam-2779	55	5	∗	∗	VERB
ejpam-2779	55	6	y	y	NOUN
ejpam-2779	55	7	=	=	SYM
ejpam-2779	55	8	0	0	NUM
ejpam-2779	55	9	is	be	AUX
ejpam-2779	55	10	a	a	DET
ejpam-2779	55	11	partial	partial	ADJ
ejpam-2779	55	12	order	order	NOUN
ejpam-2779	55	13	on	on	ADP
ejpam-2779	55	14	x.	x.	NOUN
ejpam-2779	55	15	a	a	DET
ejpam-2779	55	16	nonempty	nonempty	NOUN
ejpam-2779	55	17	subset	subset	VERB
ejpam-2779	55	18	i	i	PRON
ejpam-2779	55	19	of	of	ADP
ejpam-2779	55	20	a	a	DET
ejpam-2779	55	21	bci	bci	NOUN
ejpam-2779	55	22	-	-	NOUN
ejpam-2779	55	23	algebra	algebra	NOUN
ejpam-2779	55	24	x	x	PUNCT
ejpam-2779	55	25	is	be	AUX
ejpam-2779	55	26	called	call	VERB
ejpam-2779	55	27	a	a	DET
ejpam-2779	55	28	bciideal	bciideal	NOUN
ejpam-2779	55	29	of	of	ADP
ejpam-2779	55	30	x	x	PRON
ejpam-2779	55	31	if	if	SCONJ
ejpam-2779	55	32	it	it	PRON
ejpam-2779	55	33	satisfies	satisfy	VERB
ejpam-2779	55	34	(	(	PUNCT
ejpam-2779	55	35	1	1	NUM
ejpam-2779	55	36	)	)	PUNCT
ejpam-2779	55	37	0	0	NUM
ejpam-2779	56	1	∈	∈	PROPN
ejpam-2779	56	2	i	i	PRON
ejpam-2779	56	3	,	,	PUNCT
ejpam-2779	56	4	(	(	PUNCT
ejpam-2779	56	5	2	2	X
ejpam-2779	56	6	)	)	PUNCT
ejpam-2779	56	7	for	for	ADP
ejpam-2779	56	8	all	all	DET
ejpam-2779	56	9	x	x	NOUN
ejpam-2779	56	10	,	,	PUNCT
ejpam-2779	56	11	y	y	PROPN
ejpam-2779	56	12	∈	∈	PROPN
ejpam-2779	56	13	x	x	X
ejpam-2779	56	14	,	,	PUNCT
ejpam-2779	56	15	x	x	PROPN
ejpam-2779	56	16	∗	∗	NOUN
ejpam-2779	56	17	y	y	PROPN
ejpam-2779	56	18	∈	∈	PROPN
ejpam-2779	57	1	i	i	PRON
ejpam-2779	57	2	,	,	PUNCT
ejpam-2779	57	3	y	y	PROPN
ejpam-2779	57	4	∈	∈	PROPN
ejpam-2779	57	5	i	i	PRON
ejpam-2779	57	6	⇒	⇒	VERB
ejpam-2779	57	7	x	x	PUNCT
ejpam-2779	58	1	∈	∈	PROPN
ejpam-2779	58	2	i.	i.	NOUN
ejpam-2779	58	3	x.l	x.l	PROPN
ejpam-2779	58	4	.	.	PUNCT
ejpam-2779	59	1	xin	xin	PROPN
ejpam-2779	59	2	,	,	PUNCT
ejpam-2779	59	3	y.j	y.j	PROPN
ejpam-2779	59	4	.	.	PUNCT
ejpam-2779	59	5	li	li	PROPN
ejpam-2779	59	6	,	,	PUNCT
ejpam-2779	59	7	y.l	y.l	PROPN
ejpam-2779	59	8	.	.	PROPN
ejpam-2779	59	9	fu	fu	PROPN
ejpam-2779	59	10	/	/	SYM
ejpam-2779	59	11	eur	eur	PROPN
ejpam-2779	59	12	.	.	PUNCT
ejpam-2779	60	1	j.	j.	PROPN
ejpam-2779	60	2	pure	pure	PROPN
ejpam-2779	60	3	appl	appl	PROPN
ejpam-2779	60	4	.	.	PROPN
ejpam-2779	60	5	math	math	PROPN
ejpam-2779	60	6	,	,	PUNCT
ejpam-2779	60	7	10	10	NUM
ejpam-2779	60	8	(	(	PUNCT
ejpam-2779	60	9	3	3	NUM
ejpam-2779	60	10	)	)	PUNCT
ejpam-2779	60	11	(	(	PUNCT
ejpam-2779	60	12	2017	2017	NUM
ejpam-2779	60	13	)	)	PUNCT
ejpam-2779	60	14	,	,	PUNCT
ejpam-2779	60	15	455	455	NUM
ejpam-2779	60	16	-	-	SYM
ejpam-2779	60	17	472	472	NUM
ejpam-2779	60	18	457	457	NUM
ejpam-2779	60	19	we	we	PRON
ejpam-2779	60	20	recall	recall	VERB
ejpam-2779	60	21	the	the	DET
ejpam-2779	60	22	notion	notion	NOUN
ejpam-2779	60	23	and	and	CCONJ
ejpam-2779	60	24	some	some	DET
ejpam-2779	60	25	properties	property	NOUN
ejpam-2779	60	26	of	of	ADP
ejpam-2779	60	27	pseudo	pseudo	NOUN
ejpam-2779	60	28	-	-	ADJ
ejpam-2779	60	29	bci	bci	ADJ
ejpam-2779	60	30	algebras	algebra	NOUN
ejpam-2779	60	31	.	.	PUNCT
ejpam-2779	61	1	definition	definition	NOUN
ejpam-2779	61	2	1	1	NUM
ejpam-2779	61	3	.	.	PUNCT
ejpam-2779	62	1	[	[	X
ejpam-2779	62	2	19	19	NUM
ejpam-2779	62	3	]	]	PUNCT
ejpam-2779	62	4	a	a	DET
ejpam-2779	62	5	pseudo	pseudo	NOUN
ejpam-2779	62	6	-	-	ADJ
ejpam-2779	62	7	bci	bci	ADJ
ejpam-2779	62	8	algebras	algebra	NOUN
ejpam-2779	62	9	is	be	AUX
ejpam-2779	62	10	a	a	DET
ejpam-2779	62	11	structure	structure	NOUN
ejpam-2779	62	12	a	a	DET
ejpam-2779	62	13	=	=	X
ejpam-2779	62	14	(	(	PUNCT
ejpam-2779	62	15	a,≤	a,≤	NOUN
ejpam-2779	62	16	,	,	PUNCT
ejpam-2779	62	17	∗	∗	NOUN
ejpam-2779	62	18	,	,	PUNCT
ejpam-2779	62	19	◦	◦	NOUN
ejpam-2779	62	20	,	,	PUNCT
ejpam-2779	62	21	0	0	NUM
ejpam-2779	62	22	)	)	PUNCT
ejpam-2779	62	23	,	,	PUNCT
ejpam-2779	62	24	where	where	SCONJ
ejpam-2779	62	25	≤	≤	PROPN
ejpam-2779	62	26	is	be	AUX
ejpam-2779	62	27	a	a	DET
ejpam-2779	62	28	binary	binary	ADJ
ejpam-2779	62	29	relation	relation	NOUN
ejpam-2779	62	30	on	on	ADP
ejpam-2779	62	31	a	a	PRON
ejpam-2779	62	32	,	,	PUNCT
ejpam-2779	62	33	∗	∗	NOUN
ejpam-2779	62	34	and	and	CCONJ
ejpam-2779	62	35	◦	◦	NOUN
ejpam-2779	62	36	are	be	AUX
ejpam-2779	62	37	binary	binary	ADJ
ejpam-2779	62	38	operations	operation	NOUN
ejpam-2779	62	39	on	on	ADP
ejpam-2779	62	40	a	a	PRON
ejpam-2779	62	41	and	and	CCONJ
ejpam-2779	62	42	”	"	PUNCT
ejpam-2779	62	43	0	0	NUM
ejpam-2779	62	44	”	"	PUNCT
ejpam-2779	62	45	is	be	AUX
ejpam-2779	62	46	an	an	DET
ejpam-2779	62	47	element	element	NOUN
ejpam-2779	62	48	of	of	ADP
ejpam-2779	62	49	a	a	DET
ejpam-2779	62	50	,	,	PUNCT
ejpam-2779	62	51	satisfying	satisfying	ADJ
ejpam-2779	62	52	,	,	PUNCT
ejpam-2779	62	53	for	for	ADP
ejpam-2779	62	54	all	all	DET
ejpam-2779	62	55	x	x	NOUN
ejpam-2779	62	56	,	,	PUNCT
ejpam-2779	62	57	y	y	PROPN
ejpam-2779	62	58	,	,	PUNCT
ejpam-2779	62	59	z	z	PROPN
ejpam-2779	62	60	∈	∈	PROPN
ejpam-2779	62	61	a	a	DET
ejpam-2779	62	62	,	,	PUNCT
ejpam-2779	62	63	(	(	PUNCT
ejpam-2779	62	64	i1	i1	PROPN
ejpam-2779	62	65	)	)	PUNCT
ejpam-2779	62	66	(	(	PUNCT
ejpam-2779	62	67	x	x	SYM
ejpam-2779	62	68	∗	∗	PROPN
ejpam-2779	62	69	y	y	NOUN
ejpam-2779	62	70	)	)	PUNCT
ejpam-2779	62	71	◦	◦	NOUN
ejpam-2779	62	72	(	(	PUNCT
ejpam-2779	62	73	x	x	X
ejpam-2779	62	74	∗	∗	PROPN
ejpam-2779	62	75	z	z	NOUN
ejpam-2779	62	76	)	)	PUNCT
ejpam-2779	62	77	≤	≤	NUM
ejpam-2779	62	78	z	z	NOUN
ejpam-2779	62	79	∗	∗	NOUN
ejpam-2779	62	80	y	y	PROPN
ejpam-2779	62	81	,	,	PUNCT
ejpam-2779	62	82	(	(	PUNCT
ejpam-2779	62	83	x	x	SYM
ejpam-2779	62	84	◦	◦	VERB
ejpam-2779	62	85	y	y	NOUN
ejpam-2779	62	86	)	)	PUNCT
ejpam-2779	62	87	∗	∗	NOUN
ejpam-2779	62	88	(	(	PUNCT
ejpam-2779	62	89	x	x	SYM
ejpam-2779	62	90	◦	◦	NOUN
ejpam-2779	62	91	z	z	NOUN
ejpam-2779	62	92	)	)	PUNCT
ejpam-2779	62	93	≤	≤	NUM
ejpam-2779	62	94	z	z	NOUN
ejpam-2779	62	95	◦	◦	NOUN
ejpam-2779	62	96	y.	y.	PROPN
ejpam-2779	62	97	(	(	PUNCT
ejpam-2779	62	98	i2	i2	PROPN
ejpam-2779	62	99	)	)	PUNCT
ejpam-2779	63	1	x	x	SYM
ejpam-2779	63	2	∗	∗	NOUN
ejpam-2779	63	3	(	(	PUNCT
ejpam-2779	63	4	x	x	SYM
ejpam-2779	63	5	◦	◦	VERB
ejpam-2779	63	6	y	y	NOUN
ejpam-2779	63	7	)	)	PUNCT
ejpam-2779	63	8	≤	≤	NOUN
ejpam-2779	64	1	y	y	PROPN
ejpam-2779	64	2	,	,	PUNCT
ejpam-2779	64	3	x	x	X
ejpam-2779	64	4	◦	◦	NOUN
ejpam-2779	64	5	(	(	PUNCT
ejpam-2779	64	6	x	x	X
ejpam-2779	64	7	∗	∗	PROPN
ejpam-2779	64	8	y	y	NOUN
ejpam-2779	64	9	)	)	PUNCT
ejpam-2779	64	10	≤	≤	NOUN
ejpam-2779	65	1	y.	y.	NOUN
ejpam-2779	65	2	(	(	PUNCT
ejpam-2779	65	3	i3	i3	PROPN
ejpam-2779	65	4	)	)	PUNCT
ejpam-2779	65	5	x	x	SYM
ejpam-2779	65	6	≤	≤	NUM
ejpam-2779	65	7	x.	x.	NOUN
ejpam-2779	65	8	(	(	PUNCT
ejpam-2779	65	9	i4	i4	PROPN
ejpam-2779	65	10	)	)	PUNCT
ejpam-2779	65	11	x	x	SYM
ejpam-2779	65	12	≤	≤	NOUN
ejpam-2779	65	13	y	y	PROPN
ejpam-2779	65	14	and	and	CCONJ
ejpam-2779	65	15	y	y	PROPN
ejpam-2779	65	16	≤	≤	PROPN
ejpam-2779	65	17	x	x	PUNCT
ejpam-2779	65	18	imply	imply	VERB
ejpam-2779	65	19	x	x	X
ejpam-2779	65	20	=	=	SYM
ejpam-2779	65	21	y.	y.	NOUN
ejpam-2779	65	22	(	(	PUNCT
ejpam-2779	65	23	i5	i5	PROPN
ejpam-2779	65	24	)	)	PUNCT
ejpam-2779	65	25	x	x	SYM
ejpam-2779	65	26	≤	≤	NUM
ejpam-2779	65	27	y	y	PROPN
ejpam-2779	65	28	iff	iff	PROPN
ejpam-2779	65	29	x	x	PROPN
ejpam-2779	65	30	∗	∗	NOUN
ejpam-2779	65	31	y	y	NOUN
ejpam-2779	65	32	=	=	SYM
ejpam-2779	65	33	0	0	NUM
ejpam-2779	66	1	iff	iff	NOUN
ejpam-2779	66	2	x	x	VERB
ejpam-2779	66	3	◦	◦	NOUN
ejpam-2779	66	4	y	y	NOUN
ejpam-2779	66	5	=	=	SYM
ejpam-2779	66	6	0	0	PROPN
ejpam-2779	66	7	.	.	PUNCT
ejpam-2779	67	1	definition	definition	NOUN
ejpam-2779	67	2	2	2	NUM
ejpam-2779	67	3	.	.	PUNCT
ejpam-2779	68	1	[	[	X
ejpam-2779	68	2	13	13	NUM
ejpam-2779	68	3	]	]	PUNCT
ejpam-2779	68	4	a	a	DET
ejpam-2779	68	5	pseudo	pseudo	NOUN
ejpam-2779	68	6	-	-	ADJ
ejpam-2779	68	7	bck	bck	ADJ
ejpam-2779	68	8	algebra	algebra	NOUN
ejpam-2779	68	9	is	be	AUX
ejpam-2779	68	10	a	a	DET
ejpam-2779	68	11	structure	structure	NOUN
ejpam-2779	68	12	a	a	DET
ejpam-2779	68	13	=	=	SYM
ejpam-2779	68	14	(	(	PUNCT
ejpam-2779	68	15	a,	a,	PROPN
ejpam-2779	68	16	�	�	NOUN
ejpam-2779	68	17	,→	,→	PUNCT
ejpam-2779	68	18	,	,	PUNCT
ejpam-2779	68	19	,	,	PUNCT
ejpam-2779	68	20	1	1	X
ejpam-2779	68	21	)	)	PUNCT
ejpam-2779	68	22	where	where	SCONJ
ejpam-2779	68	23	�	�	PROPN
ejpam-2779	68	24	is	be	AUX
ejpam-2779	68	25	a	a	DET
ejpam-2779	68	26	binary	binary	ADJ
ejpam-2779	68	27	relation	relation	NOUN
ejpam-2779	68	28	on	on	ADP
ejpam-2779	68	29	a	a	PRON
ejpam-2779	68	30	,	,	PUNCT
ejpam-2779	68	31	and	and	CCONJ
ejpam-2779	68	32	→	→	PUNCT
ejpam-2779	68	33	and	and	CCONJ
ejpam-2779	68	34	are	be	AUX
ejpam-2779	68	35	binary	binary	ADJ
ejpam-2779	68	36	operations	operation	NOUN
ejpam-2779	68	37	on	on	ADP
ejpam-2779	68	38	a	a	PRON
ejpam-2779	68	39	and	and	CCONJ
ejpam-2779	68	40	1	1	NUM
ejpam-2779	68	41	is	be	AUX
ejpam-2779	68	42	an	an	DET
ejpam-2779	68	43	element	element	NOUN
ejpam-2779	68	44	of	of	ADP
ejpam-2779	68	45	a	a	DET
ejpam-2779	68	46	satisfying	satisfying	NOUN
ejpam-2779	68	47	,	,	PUNCT
ejpam-2779	68	48	for	for	ADP
ejpam-2779	68	49	all	all	DET
ejpam-2779	68	50	x	x	NOUN
ejpam-2779	68	51	,	,	PUNCT
ejpam-2779	68	52	y	y	PROPN
ejpam-2779	68	53	,	,	PUNCT
ejpam-2779	68	54	z	z	PROPN
ejpam-2779	68	55	∈	∈	PROPN
ejpam-2779	68	56	a	a	PRON
ejpam-2779	68	57	,	,	PUNCT
ejpam-2779	68	58	the	the	DET
ejpam-2779	68	59	axioms	axiom	NOUN
ejpam-2779	68	60	:	:	PUNCT
ejpam-2779	68	61	(	(	PUNCT
ejpam-2779	68	62	k1	k1	X
ejpam-2779	68	63	)	)	PUNCT
ejpam-2779	68	64	x→	x→	X
ejpam-2779	69	1	y	y	PROPN
ejpam-2779	69	2	�	�	PROPN
ejpam-2779	69	3	(	(	PUNCT
ejpam-2779	69	4	y	y	PROPN
ejpam-2779	69	5	→	→	SYM
ejpam-2779	69	6	z	z	NOUN
ejpam-2779	69	7	)	)	PUNCT
ejpam-2779	69	8	(	(	PUNCT
ejpam-2779	69	9	x→	x→	PROPN
ejpam-2779	69	10	z	z	X
ejpam-2779	69	11	)	)	PUNCT
ejpam-2779	69	12	,	,	PUNCT
ejpam-2779	69	13	x	x	PROPN
ejpam-2779	69	14	y	y	PROPN
ejpam-2779	69	15	�	�	PROPN
ejpam-2779	69	16	(	(	PUNCT
ejpam-2779	69	17	y	y	PROPN
ejpam-2779	69	18	z)→	z)→	PROPN
ejpam-2779	69	19	(	(	PUNCT
ejpam-2779	69	20	x	x	X
ejpam-2779	69	21	z	z	NOUN
ejpam-2779	69	22	)	)	PUNCT
ejpam-2779	69	23	.	.	PUNCT
ejpam-2779	70	1	(	(	PUNCT
ejpam-2779	70	2	k2	k2	PROPN
ejpam-2779	70	3	)	)	PUNCT
ejpam-2779	70	4	x	x	PROPN
ejpam-2779	70	5	�	�	PROPN
ejpam-2779	70	6	(	(	PUNCT
ejpam-2779	70	7	x→	x→	PROPN
ejpam-2779	70	8	y	y	X
ejpam-2779	70	9	)	)	PUNCT
ejpam-2779	70	10	y	y	PROPN
ejpam-2779	70	11	,	,	PUNCT
ejpam-2779	70	12	x	x	X
ejpam-2779	70	13	�	�	PROPN
ejpam-2779	70	14	(	(	PUNCT
ejpam-2779	70	15	x	x	SYM
ejpam-2779	70	16	y)→	y)→	PROPN
ejpam-2779	70	17	y.	y.	NOUN
ejpam-2779	70	18	(	(	PUNCT
ejpam-2779	70	19	k3	k3	PROPN
ejpam-2779	70	20	)	)	PUNCT
ejpam-2779	70	21	x	x	SYM
ejpam-2779	70	22	�	�	PROPN
ejpam-2779	70	23	x.	x.	NOUN
ejpam-2779	70	24	(	(	PUNCT
ejpam-2779	70	25	k4	k4	PROPN
ejpam-2779	70	26	)	)	PUNCT
ejpam-2779	70	27	x	x	SYM
ejpam-2779	70	28	�	�	PROPN
ejpam-2779	70	29	1	1	NUM
ejpam-2779	70	30	.	.	PUNCT
ejpam-2779	70	31	(	(	PUNCT
ejpam-2779	70	32	k5	k5	PROPN
ejpam-2779	70	33	)	)	PUNCT
ejpam-2779	70	34	if	if	SCONJ
ejpam-2779	70	35	x	x	PROPN
ejpam-2779	70	36	�	�	PROPN
ejpam-2779	70	37	y	y	PROPN
ejpam-2779	70	38	and	and	CCONJ
ejpam-2779	70	39	y	y	PROPN
ejpam-2779	70	40	�	�	PROPN
ejpam-2779	70	41	x	x	PROPN
ejpam-2779	70	42	,	,	PUNCT
ejpam-2779	70	43	then	then	ADV
ejpam-2779	70	44	x	x	X
ejpam-2779	70	45	=	=	PUNCT
ejpam-2779	70	46	y.	y.	PROPN
ejpam-2779	70	47	(	(	PUNCT
ejpam-2779	70	48	k6	k6	PROPN
ejpam-2779	70	49	)	)	PUNCT
ejpam-2779	70	50	x	x	SYM
ejpam-2779	70	51	�	�	PROPN
ejpam-2779	70	52	y	y	PROPN
ejpam-2779	70	53	iff	iff	PROPN
ejpam-2779	70	54	x→	x→	PROPN
ejpam-2779	71	1	y	y	NOUN
ejpam-2779	71	2	=	=	SYM
ejpam-2779	71	3	1	1	NUM
ejpam-2779	71	4	iff	iff	NOUN
ejpam-2779	71	5	x	x	SYM
ejpam-2779	71	6	y	y	PROPN
ejpam-2779	71	7	=	=	SYM
ejpam-2779	71	8	1	1	X
ejpam-2779	71	9	.	.	PUNCT
ejpam-2779	71	10	remark	remark	NOUN
ejpam-2779	71	11	1	1	NUM
ejpam-2779	71	12	.	.	PUNCT
ejpam-2779	72	1	(	(	PUNCT
ejpam-2779	72	2	1	1	X
ejpam-2779	72	3	)	)	PUNCT
ejpam-2779	72	4	a	a	DET
ejpam-2779	72	5	pseudo	pseudo	NOUN
ejpam-2779	72	6	-	-	ADJ
ejpam-2779	72	7	bck	bck	ADJ
ejpam-2779	72	8	algebra	algebra	NOUN
ejpam-2779	72	9	a	a	DET
ejpam-2779	72	10	=	=	SYM
ejpam-2779	72	11	(	(	PUNCT
ejpam-2779	72	12	a,	a,	PROPN
ejpam-2779	72	13	�	�	NOUN
ejpam-2779	72	14	,→	,→	PUNCT
ejpam-2779	72	15	,	,	PUNCT
ejpam-2779	72	16	1	1	X
ejpam-2779	72	17	)	)	PUNCT
ejpam-2779	72	18	can	can	AUX
ejpam-2779	72	19	be	be	AUX
ejpam-2779	72	20	seen	see	VERB
ejpam-2779	72	21	a	a	DET
ejpam-2779	72	22	pseudo	pseudo	NOUN
ejpam-2779	72	23	-	-	NOUN
ejpam-2779	72	24	bci	bci	ADJ
ejpam-2779	72	25	algebra	algebra	NOUN
ejpam-2779	72	26	a	a	DET
ejpam-2779	72	27	=	=	X
ejpam-2779	72	28	(	(	PUNCT
ejpam-2779	72	29	a,≤	a,≤	NOUN
ejpam-2779	72	30	,	,	PUNCT
ejpam-2779	72	31	∗	∗	NOUN
ejpam-2779	72	32	,	,	PUNCT
ejpam-2779	72	33	◦	◦	NOUN
ejpam-2779	72	34	,	,	PUNCT
ejpam-2779	72	35	0	0	NUM
ejpam-2779	72	36	)	)	PUNCT
ejpam-2779	72	37	if	if	SCONJ
ejpam-2779	72	38	x→	x→	PUNCT
ejpam-2779	73	1	y	y	NOUN
ejpam-2779	73	2	=	=	PUNCT
ejpam-2779	73	3	y	y	PROPN
ejpam-2779	73	4	∗	∗	NOUN
ejpam-2779	73	5	x	x	PROPN
ejpam-2779	73	6	,	,	PUNCT
ejpam-2779	73	7	x	x	PUNCT
ejpam-2779	73	8	y	y	NOUN
ejpam-2779	73	9	=	=	PUNCT
ejpam-2779	73	10	y	y	PROPN
ejpam-2779	73	11	◦	◦	NOUN
ejpam-2779	73	12	x	x	SYM
ejpam-2779	73	13	,	,	PUNCT
ejpam-2779	73	14	1	1	NUM
ejpam-2779	73	15	=	=	SYM
ejpam-2779	73	16	0	0	NUM
ejpam-2779	73	17	and	and	CCONJ
ejpam-2779	73	18	x	x	PROPN
ejpam-2779	73	19	�	�	PROPN
ejpam-2779	73	20	y	y	PROPN
ejpam-2779	73	21	iff	iff	PROPN
ejpam-2779	73	22	y	y	PROPN
ejpam-2779	73	23	≤	≤	PROPN
ejpam-2779	73	24	x	x	PUNCT
ejpam-2779	73	25	for	for	ADP
ejpam-2779	73	26	all	all	DET
ejpam-2779	73	27	x	x	NOUN
ejpam-2779	73	28	,	,	PUNCT
ejpam-2779	73	29	y	y	PROPN
ejpam-2779	73	30	∈	∈	PROPN
ejpam-2779	73	31	a.	a.	NOUN
ejpam-2779	73	32	(	(	PUNCT
ejpam-2779	73	33	2	2	NUM
ejpam-2779	73	34	)	)	PUNCT
ejpam-2779	73	35	a	a	DET
ejpam-2779	73	36	pseudo	pseudo	NOUN
ejpam-2779	73	37	-	-	ADJ
ejpam-2779	73	38	bci	bci	ADJ
ejpam-2779	73	39	algebra	algebra	NOUN
ejpam-2779	73	40	is	be	AUX
ejpam-2779	73	41	a	a	DET
ejpam-2779	73	42	bci	bci	NOUN
ejpam-2779	73	43	algebra	algebra	NOUN
ejpam-2779	73	44	if	if	SCONJ
ejpam-2779	73	45	∗	∗	NOUN
ejpam-2779	73	46	=	=	SYM
ejpam-2779	73	47	◦	◦	NOUN
ejpam-2779	73	48	.	.	PUNCT
ejpam-2779	74	1	(	(	PUNCT
ejpam-2779	74	2	3	3	X
ejpam-2779	74	3	)	)	PUNCT
ejpam-2779	74	4	the	the	DET
ejpam-2779	74	5	relation	relation	NOUN
ejpam-2779	74	6	≤	≤	PROPN
ejpam-2779	74	7	is	be	AUX
ejpam-2779	74	8	a	a	DET
ejpam-2779	74	9	partial	partial	ADJ
ejpam-2779	74	10	order	order	NOUN
ejpam-2779	74	11	on	on	ADP
ejpam-2779	74	12	a	a	DET
ejpam-2779	74	13	pseudo	pseudo	NOUN
ejpam-2779	74	14	-	-	ADJ
ejpam-2779	74	15	bci	bci	ADJ
ejpam-2779	74	16	algebra	algebra	NOUN
ejpam-2779	74	17	a.	a.	NOUN
ejpam-2779	74	18	now	now	ADV
ejpam-2779	74	19	we	we	PRON
ejpam-2779	74	20	give	give	VERB
ejpam-2779	74	21	two	two	NUM
ejpam-2779	74	22	pseudo	pseudo	NOUN
ejpam-2779	74	23	-	-	ADJ
ejpam-2779	74	24	bci	bci	ADJ
ejpam-2779	74	25	algebras	algebra	NOUN
ejpam-2779	74	26	which	which	PRON
ejpam-2779	74	27	are	be	AUX
ejpam-2779	74	28	not	not	PART
ejpam-2779	74	29	pseudo	pseudo	NOUN
ejpam-2779	74	30	-	-	ADJ
ejpam-2779	74	31	bck	bck	ADJ
ejpam-2779	74	32	algebras	algebra	NOUN
ejpam-2779	74	33	.	.	PUNCT
ejpam-2779	74	34	example	example	NOUN
ejpam-2779	75	1	1	1	NUM
ejpam-2779	75	2	.	.	PUNCT
ejpam-2779	75	3	let	let	VERB
ejpam-2779	75	4	a	a	DET
ejpam-2779	75	5	=	=	PUNCT
ejpam-2779	75	6	{	{	PUNCT
ejpam-2779	75	7	0	0	NUM
ejpam-2779	75	8	,	,	PUNCT
ejpam-2779	75	9	u	u	NOUN
ejpam-2779	75	10	,	,	PUNCT
ejpam-2779	75	11	v	v	NOUN
ejpam-2779	75	12	,	,	PUNCT
ejpam-2779	75	13	w	w	PROPN
ejpam-2779	75	14	,	,	PUNCT
ejpam-2779	75	15	t	t	PROPN
ejpam-2779	75	16	,	,	PUNCT
ejpam-2779	75	17	1	1	NUM
ejpam-2779	75	18	,	,	PUNCT
ejpam-2779	75	19	a	a	DET
ejpam-2779	75	20	,	,	PUNCT
ejpam-2779	75	21	b	b	NOUN
ejpam-2779	75	22	}	}	PUNCT
ejpam-2779	75	23	.	.	PUNCT
ejpam-2779	76	1	the	the	DET
ejpam-2779	76	2	order	order	NOUN
ejpam-2779	76	3	of	of	ADP
ejpam-2779	76	4	the	the	DET
ejpam-2779	76	5	elements	element	NOUN
ejpam-2779	76	6	in	in	ADP
ejpam-2779	76	7	a	a	PRON
ejpam-2779	76	8	is	be	AUX
ejpam-2779	76	9	as	as	ADP
ejpam-2779	76	10	the	the	DET
ejpam-2779	76	11	following	follow	VERB
ejpam-2779	76	12	hasse	hasse	PROPN
ejpam-2779	76	13	diagram	diagram	PROPN
ejpam-2779	76	14	:	:	PUNCT
ejpam-2779	76	15	c	c	NOUN
ejpam-2779	76	16	c	c	NOUN
ejpam-2779	76	17	c	c	NOUN
ejpam-2779	76	18	c	c	NOUN
ejpam-2779	76	19	c	c	NOUN
ejpam-2779	76	20	c	c	NOUN
ejpam-2779	76	21	c	c	PROPN
ejpam-2779	76	22	c	c	PROPN
ejpam-2779	76	23	�	�	PROPN
ejpam-2779	76	24	�	�	PROPN
ejpam-2779	76	25	�	�	PROPN
ejpam-2779	76	26	@	@	ADP
ejpam-2779	76	27	@@	@@	X
ejpam-2779	76	28	�	�	PROPN
ejpam-2779	76	29	�	�	PROPN
ejpam-2779	76	30	�	�	PROPN
ejpam-2779	76	31	@	@	ADP
ejpam-2779	76	32	@@	@@	X
ejpam-2779	76	33	0	0	PUNCT
ejpam-2779	77	1	u	u	PROPN
ejpam-2779	77	2	wv	wv	PROPN
ejpam-2779	77	3	t	t	PROPN
ejpam-2779	77	4	1	1	NUM
ejpam-2779	77	5	a	a	DET
ejpam-2779	77	6	b	b	NOUN
ejpam-2779	77	7	now	now	ADV
ejpam-2779	77	8	the	the	DET
ejpam-2779	77	9	operations	operation	NOUN
ejpam-2779	77	10	∗	∗	NOUN
ejpam-2779	77	11	and	and	CCONJ
ejpam-2779	77	12	◦	◦	NOUN
ejpam-2779	77	13	are	be	AUX
ejpam-2779	77	14	defined	define	VERB
ejpam-2779	77	15	by	by	ADP
ejpam-2779	77	16	tables	table	NOUN
ejpam-2779	77	17	2.1	2.1	NUM
ejpam-2779	77	18	and	and	CCONJ
ejpam-2779	77	19	2.2	2.2	NUM
ejpam-2779	77	20	,	,	PUNCT
ejpam-2779	77	21	respectively	respectively	ADV
ejpam-2779	77	22	.	.	PUNCT
ejpam-2779	78	1	simple	simple	ADJ
ejpam-2779	78	2	calculations	calculation	NOUN
ejpam-2779	78	3	show	show	VERB
ejpam-2779	78	4	that	that	SCONJ
ejpam-2779	78	5	(	(	PUNCT
ejpam-2779	78	6	a,6	a,6	PROPN
ejpam-2779	78	7	,	,	PUNCT
ejpam-2779	78	8	∗	∗	NOUN
ejpam-2779	78	9	,	,	PUNCT
ejpam-2779	78	10	◦	◦	NOUN
ejpam-2779	78	11	,	,	PUNCT
ejpam-2779	78	12	0	0	NUM
ejpam-2779	78	13	)	)	PUNCT
ejpam-2779	78	14	is	be	AUX
ejpam-2779	78	15	a	a	DET
ejpam-2779	78	16	pseudo	pseudo	NOUN
ejpam-2779	78	17	-	-	ADJ
ejpam-2779	78	18	bci	bci	ADJ
ejpam-2779	78	19	algebra	algebra	NOUN
ejpam-2779	78	20	.	.	PUNCT
ejpam-2779	79	1	example	example	NOUN
ejpam-2779	79	2	2	2	NUM
ejpam-2779	79	3	.	.	PUNCT
ejpam-2779	80	1	let	let	VERB
ejpam-2779	80	2	a	a	PRON
ejpam-2779	80	3	=	=	PUNCT
ejpam-2779	80	4	{	{	PUNCT
ejpam-2779	80	5	0	0	NUM
ejpam-2779	80	6	,	,	PUNCT
ejpam-2779	80	7	x	x	NOUN
ejpam-2779	80	8	,	,	PUNCT
ejpam-2779	80	9	y	y	PROPN
ejpam-2779	80	10	,	,	PUNCT
ejpam-2779	80	11	z	z	PROPN
ejpam-2779	80	12	,	,	PUNCT
ejpam-2779	80	13	1	1	NUM
ejpam-2779	80	14	,	,	PUNCT
ejpam-2779	80	15	a	a	DET
ejpam-2779	80	16	,	,	PUNCT
ejpam-2779	80	17	b	b	NOUN
ejpam-2779	80	18	}	}	PUNCT
ejpam-2779	80	19	in	in	ADP
ejpam-2779	80	20	which	which	PRON
ejpam-2779	80	21	the	the	DET
ejpam-2779	80	22	order	order	NOUN
ejpam-2779	80	23	of	of	ADP
ejpam-2779	80	24	elements	element	NOUN
ejpam-2779	80	25	in	in	ADP
ejpam-2779	80	26	a	a	PRON
ejpam-2779	80	27	is	be	AUX
ejpam-2779	80	28	as	as	ADP
ejpam-2779	80	29	the	the	DET
ejpam-2779	80	30	following	follow	VERB
ejpam-2779	80	31	hasse	hasse	PROPN
ejpam-2779	80	32	diagram	diagram	PROPN
ejpam-2779	80	33	:	:	PUNCT
ejpam-2779	81	1	x.l	x.l	PROPN
ejpam-2779	81	2	.	.	PUNCT
ejpam-2779	82	1	xin	xin	PROPN
ejpam-2779	82	2	,	,	PUNCT
ejpam-2779	82	3	y.j	y.j	PROPN
ejpam-2779	82	4	.	.	PUNCT
ejpam-2779	82	5	li	li	PROPN
ejpam-2779	82	6	,	,	PUNCT
ejpam-2779	82	7	y.l	y.l	PROPN
ejpam-2779	82	8	.	.	PROPN
ejpam-2779	82	9	fu	fu	PROPN
ejpam-2779	82	10	/	/	SYM
ejpam-2779	82	11	eur	eur	PROPN
ejpam-2779	82	12	.	.	PUNCT
ejpam-2779	83	1	j.	j.	PROPN
ejpam-2779	83	2	pure	pure	PROPN
ejpam-2779	83	3	appl	appl	PROPN
ejpam-2779	83	4	.	.	PROPN
ejpam-2779	83	5	math	math	PROPN
ejpam-2779	83	6	,	,	PUNCT
ejpam-2779	83	7	10	10	NUM
ejpam-2779	83	8	(	(	PUNCT
ejpam-2779	83	9	3	3	NUM
ejpam-2779	83	10	)	)	PUNCT
ejpam-2779	83	11	(	(	PUNCT
ejpam-2779	83	12	2017	2017	NUM
ejpam-2779	83	13	)	)	PUNCT
ejpam-2779	83	14	,	,	PUNCT
ejpam-2779	83	15	455	455	NUM
ejpam-2779	83	16	-	-	SYM
ejpam-2779	83	17	472	472	NUM
ejpam-2779	83	18	458	458	NUM
ejpam-2779	83	19	∗	∗	NOUN
ejpam-2779	83	20	0	0	NUM
ejpam-2779	83	21	u	u	PROPN
ejpam-2779	83	22	v	v	PROPN
ejpam-2779	83	23	w	w	PROPN
ejpam-2779	83	24	t	t	PROPN
ejpam-2779	83	25	1	1	NUM
ejpam-2779	83	26	a	a	DET
ejpam-2779	83	27	b	b	NOUN
ejpam-2779	83	28	0	0	NUM
ejpam-2779	83	29	0	0	NUM
ejpam-2779	83	30	0	0	NUM
ejpam-2779	83	31	0	0	NUM
ejpam-2779	83	32	0	0	NUM
ejpam-2779	83	33	0	0	NUM
ejpam-2779	83	34	0	0	NUM
ejpam-2779	84	1	a	a	DET
ejpam-2779	84	2	a	a	DET
ejpam-2779	84	3	u	u	NOUN
ejpam-2779	84	4	u	u	NOUN
ejpam-2779	84	5	0	0	NUM
ejpam-2779	84	6	0	0	NUM
ejpam-2779	84	7	0	0	NUM
ejpam-2779	84	8	0	0	NUM
ejpam-2779	84	9	0	0	NUM
ejpam-2779	85	1	a	a	DET
ejpam-2779	85	2	a	a	PRON
ejpam-2779	85	3	v	v	NOUN
ejpam-2779	85	4	v	v	NOUN
ejpam-2779	85	5	v	v	NOUN
ejpam-2779	85	6	0	0	NUM
ejpam-2779	85	7	v	v	NOUN
ejpam-2779	85	8	0	0	NUM
ejpam-2779	85	9	0	0	NUM
ejpam-2779	85	10	a	a	PRON
ejpam-2779	85	11	a	a	DET
ejpam-2779	85	12	w	w	NOUN
ejpam-2779	85	13	w	w	PROPN
ejpam-2779	85	14	w	w	PROPN
ejpam-2779	85	15	w	w	PROPN
ejpam-2779	85	16	0	0	NUM
ejpam-2779	85	17	0	0	NUM
ejpam-2779	85	18	0	0	NUM
ejpam-2779	86	1	a	a	DET
ejpam-2779	86	2	a	a	DET
ejpam-2779	86	3	t	t	NOUN
ejpam-2779	86	4	t	t	NOUN
ejpam-2779	86	5	t	t	PROPN
ejpam-2779	86	6	w	w	PROPN
ejpam-2779	86	7	t	t	PROPN
ejpam-2779	86	8	0	0	NUM
ejpam-2779	86	9	0	0	NUM
ejpam-2779	86	10	a	a	DET
ejpam-2779	86	11	a	a	DET
ejpam-2779	86	12	1	1	NUM
ejpam-2779	86	13	1	1	NUM
ejpam-2779	86	14	1	1	NUM
ejpam-2779	86	15	1	1	NUM
ejpam-2779	86	16	1	1	NUM
ejpam-2779	86	17	1	1	NUM
ejpam-2779	86	18	0	0	NUM
ejpam-2779	86	19	a	a	DET
ejpam-2779	86	20	a	a	DET
ejpam-2779	86	21	a	a	DET
ejpam-2779	86	22	a	a	DET
ejpam-2779	86	23	a	a	DET
ejpam-2779	86	24	a	a	DET
ejpam-2779	86	25	a	a	DET
ejpam-2779	86	26	a	a	DET
ejpam-2779	86	27	a	a	DET
ejpam-2779	86	28	0	0	NUM
ejpam-2779	86	29	0	0	NUM
ejpam-2779	86	30	b	b	PROPN
ejpam-2779	86	31	b	b	PROPN
ejpam-2779	86	32	b	b	PROPN
ejpam-2779	86	33	b	b	PROPN
ejpam-2779	86	34	b	b	PROPN
ejpam-2779	86	35	b	b	PROPN
ejpam-2779	86	36	a	a	DET
ejpam-2779	86	37	1	1	NUM
ejpam-2779	86	38	0	0	NUM
ejpam-2779	86	39	tables	table	NOUN
ejpam-2779	86	40	2.1	2.1	NUM
ejpam-2779	86	41	◦	◦	NOUN
ejpam-2779	86	42	0	0	NUM
ejpam-2779	86	43	u	u	NOUN
ejpam-2779	86	44	v	v	PROPN
ejpam-2779	86	45	w	w	PROPN
ejpam-2779	86	46	t	t	PROPN
ejpam-2779	86	47	1	1	NUM
ejpam-2779	86	48	a	a	DET
ejpam-2779	86	49	b	b	NOUN
ejpam-2779	86	50	0	0	NUM
ejpam-2779	86	51	0	0	NUM
ejpam-2779	86	52	0	0	NUM
ejpam-2779	86	53	0	0	NUM
ejpam-2779	86	54	0	0	NUM
ejpam-2779	86	55	0	0	NUM
ejpam-2779	86	56	0	0	NUM
ejpam-2779	87	1	a	a	DET
ejpam-2779	87	2	a	a	DET
ejpam-2779	87	3	u	u	NOUN
ejpam-2779	87	4	u	u	NOUN
ejpam-2779	87	5	0	0	NUM
ejpam-2779	87	6	0	0	NUM
ejpam-2779	87	7	0	0	NUM
ejpam-2779	87	8	0	0	NUM
ejpam-2779	87	9	0	0	NUM
ejpam-2779	88	1	a	a	DET
ejpam-2779	88	2	a	a	PRON
ejpam-2779	88	3	v	v	NOUN
ejpam-2779	88	4	v	v	NOUN
ejpam-2779	88	5	v	v	NOUN
ejpam-2779	88	6	0	0	NUM
ejpam-2779	88	7	v	v	NOUN
ejpam-2779	88	8	0	0	NUM
ejpam-2779	88	9	0	0	NUM
ejpam-2779	88	10	a	a	PRON
ejpam-2779	88	11	a	a	DET
ejpam-2779	88	12	w	w	NOUN
ejpam-2779	88	13	w	w	PROPN
ejpam-2779	88	14	w	w	PROPN
ejpam-2779	88	15	w	w	PROPN
ejpam-2779	88	16	0	0	NUM
ejpam-2779	88	17	0	0	NUM
ejpam-2779	88	18	0	0	NUM
ejpam-2779	89	1	a	a	DET
ejpam-2779	89	2	a	a	DET
ejpam-2779	89	3	t	t	NOUN
ejpam-2779	89	4	t	t	NOUN
ejpam-2779	89	5	t	t	PROPN
ejpam-2779	89	6	t	t	PROPN
ejpam-2779	89	7	v	v	ADP
ejpam-2779	89	8	0	0	NUM
ejpam-2779	89	9	0	0	NUM
ejpam-2779	90	1	a	a	DET
ejpam-2779	90	2	a	a	DET
ejpam-2779	90	3	1	1	NUM
ejpam-2779	90	4	1	1	NUM
ejpam-2779	90	5	1	1	NUM
ejpam-2779	90	6	1	1	NUM
ejpam-2779	90	7	1	1	NUM
ejpam-2779	90	8	1	1	NUM
ejpam-2779	90	9	0	0	NUM
ejpam-2779	90	10	a	a	DET
ejpam-2779	90	11	a	a	DET
ejpam-2779	90	12	a	a	DET
ejpam-2779	90	13	a	a	DET
ejpam-2779	90	14	a	a	DET
ejpam-2779	90	15	a	a	DET
ejpam-2779	90	16	a	a	DET
ejpam-2779	90	17	a	a	DET
ejpam-2779	90	18	a	a	DET
ejpam-2779	90	19	0	0	NUM
ejpam-2779	90	20	0	0	NUM
ejpam-2779	90	21	b	b	PROPN
ejpam-2779	90	22	b	b	PROPN
ejpam-2779	90	23	b	b	PROPN
ejpam-2779	90	24	b	b	PROPN
ejpam-2779	90	25	b	b	PROPN
ejpam-2779	90	26	b	b	PROPN
ejpam-2779	90	27	a	a	DET
ejpam-2779	90	28	1	1	NUM
ejpam-2779	90	29	0	0	NUM
ejpam-2779	90	30	tables	table	NOUN
ejpam-2779	90	31	2.2	2.2	NUM
ejpam-2779	90	32	c	c	NOUN
ejpam-2779	90	33	c	c	NOUN
ejpam-2779	90	34	c	c	NOUN
ejpam-2779	90	35	c	c	NOUN
ejpam-2779	90	36	c	c	NOUN
ejpam-2779	90	37	c	c	NOUN
ejpam-2779	90	38	c	c	NOUN
ejpam-2779	90	39	@	@	ADP
ejpam-2779	90	40	@	@	ADP
ejpam-2779	90	41	@	@	ADP
ejpam-2779	90	42	�	�	PROPN
ejpam-2779	90	43	�	�	PROPN
ejpam-2779	90	44	�	�	PROPN
ejpam-2779	90	45	@	@	ADP
ejpam-2779	90	46	@	@	ADP
ejpam-2779	90	47	@	@	ADP
ejpam-2779	90	48	�	�	PROPN
ejpam-2779	90	49	�	�	PROPN
ejpam-2779	90	50	�	�	PROPN
ejpam-2779	90	51	0	0	NUM
ejpam-2779	90	52	x	x	SYM
ejpam-2779	90	53	y	y	PROPN
ejpam-2779	90	54	z	z	PROPN
ejpam-2779	90	55	1	1	NUM
ejpam-2779	90	56	a	a	DET
ejpam-2779	90	57	b	b	NOUN
ejpam-2779	90	58	let	let	VERB
ejpam-2779	90	59	the	the	DET
ejpam-2779	90	60	operations	operation	NOUN
ejpam-2779	90	61	∗	∗	NOUN
ejpam-2779	90	62	,	,	PUNCT
ejpam-2779	90	63	◦	◦	NOUN
ejpam-2779	90	64	be	be	AUX
ejpam-2779	90	65	given	give	VERB
ejpam-2779	90	66	by	by	ADP
ejpam-2779	90	67	the	the	DET
ejpam-2779	90	68	following	follow	VERB
ejpam-2779	90	69	tables	table	NOUN
ejpam-2779	90	70	2.3	2.3	NUM
ejpam-2779	90	71	and	and	CCONJ
ejpam-2779	90	72	2.4	2.4	NUM
ejpam-2779	90	73	.	.	PUNCT
ejpam-2779	91	1	∗	∗	NOUN
ejpam-2779	91	2	0	0	NUM
ejpam-2779	92	1	x	x	SYM
ejpam-2779	92	2	y	y	PROPN
ejpam-2779	92	3	z	z	PROPN
ejpam-2779	92	4	1	1	NUM
ejpam-2779	92	5	a	a	DET
ejpam-2779	92	6	b	b	NOUN
ejpam-2779	92	7	0	0	NUM
ejpam-2779	92	8	0	0	NUM
ejpam-2779	92	9	0	0	NUM
ejpam-2779	92	10	0	0	NUM
ejpam-2779	92	11	0	0	NUM
ejpam-2779	92	12	0	0	NUM
ejpam-2779	92	13	a	a	DET
ejpam-2779	92	14	a	a	DET
ejpam-2779	92	15	x	x	SYM
ejpam-2779	92	16	x	x	SYM
ejpam-2779	92	17	0	0	NUM
ejpam-2779	92	18	0	0	NUM
ejpam-2779	92	19	0	0	NUM
ejpam-2779	92	20	0	0	NUM
ejpam-2779	93	1	a	a	DET
ejpam-2779	93	2	a	a	PRON
ejpam-2779	93	3	y	y	PROPN
ejpam-2779	93	4	y	y	PROPN
ejpam-2779	93	5	y	y	PROPN
ejpam-2779	93	6	0	0	PUNCT
ejpam-2779	93	7	y	y	PROPN
ejpam-2779	93	8	0	0	NUM
ejpam-2779	93	9	a	a	DET
ejpam-2779	93	10	a	a	DET
ejpam-2779	93	11	z	z	NOUN
ejpam-2779	93	12	z	z	NOUN
ejpam-2779	93	13	z	z	NOUN
ejpam-2779	93	14	z	z	NOUN
ejpam-2779	93	15	0	0	NUM
ejpam-2779	93	16	0	0	NUM
ejpam-2779	94	1	a	a	DET
ejpam-2779	94	2	a	a	DET
ejpam-2779	94	3	1	1	NUM
ejpam-2779	94	4	1	1	NUM
ejpam-2779	94	5	1	1	NUM
ejpam-2779	94	6	1	1	NUM
ejpam-2779	94	7	y	y	NOUN
ejpam-2779	94	8	0	0	NUM
ejpam-2779	94	9	a	a	PRON
ejpam-2779	94	10	a	a	DET
ejpam-2779	94	11	a	a	DET
ejpam-2779	94	12	a	a	DET
ejpam-2779	94	13	a	a	DET
ejpam-2779	94	14	a	a	DET
ejpam-2779	94	15	a	a	DET
ejpam-2779	94	16	a	a	DET
ejpam-2779	94	17	0	0	NUM
ejpam-2779	94	18	0	0	NUM
ejpam-2779	94	19	b	b	X
ejpam-2779	94	20	b	b	PROPN
ejpam-2779	94	21	a	a	PRON
ejpam-2779	94	22	a	a	DET
ejpam-2779	94	23	a	a	DET
ejpam-2779	94	24	a	a	DET
ejpam-2779	94	25	y	y	PROPN
ejpam-2779	94	26	0	0	NUM
ejpam-2779	94	27	tables	table	NOUN
ejpam-2779	94	28	2.3	2.3	NUM
ejpam-2779	94	29	◦	◦	NOUN
ejpam-2779	94	30	0	0	NUM
ejpam-2779	94	31	x	x	SYM
ejpam-2779	94	32	y	y	PROPN
ejpam-2779	94	33	z	z	PROPN
ejpam-2779	94	34	1	1	NUM
ejpam-2779	94	35	a	a	DET
ejpam-2779	94	36	b	b	NOUN
ejpam-2779	94	37	0	0	NUM
ejpam-2779	94	38	0	0	NUM
ejpam-2779	94	39	0	0	NUM
ejpam-2779	94	40	0	0	NUM
ejpam-2779	94	41	0	0	NUM
ejpam-2779	94	42	0	0	NUM
ejpam-2779	94	43	a	a	PRON
ejpam-2779	94	44	a	a	DET
ejpam-2779	94	45	x	x	SYM
ejpam-2779	94	46	x	x	SYM
ejpam-2779	94	47	0	0	NUM
ejpam-2779	94	48	0	0	NUM
ejpam-2779	94	49	0	0	NUM
ejpam-2779	94	50	0	0	NUM
ejpam-2779	94	51	a	a	PRON
ejpam-2779	94	52	a	a	PRON
ejpam-2779	94	53	y	y	PROPN
ejpam-2779	94	54	y	y	PROPN
ejpam-2779	94	55	y	y	PROPN
ejpam-2779	94	56	0	0	PUNCT
ejpam-2779	94	57	y	y	PROPN
ejpam-2779	94	58	0	0	NUM
ejpam-2779	94	59	a	a	DET
ejpam-2779	94	60	a	a	DET
ejpam-2779	94	61	z	z	NOUN
ejpam-2779	94	62	z	z	NOUN
ejpam-2779	94	63	z	z	NOUN
ejpam-2779	94	64	z	z	NOUN
ejpam-2779	94	65	0	0	NUM
ejpam-2779	94	66	0	0	NUM
ejpam-2779	94	67	a	a	DET
ejpam-2779	94	68	a	a	DET
ejpam-2779	94	69	1	1	NUM
ejpam-2779	94	70	1	1	NUM
ejpam-2779	94	71	1	1	NUM
ejpam-2779	94	72	z	z	NOUN
ejpam-2779	94	73	1	1	NUM
ejpam-2779	94	74	0	0	NUM
ejpam-2779	94	75	a	a	DET
ejpam-2779	94	76	a	a	DET
ejpam-2779	94	77	a	a	DET
ejpam-2779	94	78	a	a	DET
ejpam-2779	94	79	a	a	DET
ejpam-2779	94	80	a	a	DET
ejpam-2779	94	81	a	a	DET
ejpam-2779	94	82	a	a	DET
ejpam-2779	94	83	0	0	NUM
ejpam-2779	94	84	0	0	NUM
ejpam-2779	94	85	b	b	PROPN
ejpam-2779	94	86	b	b	X
ejpam-2779	94	87	b	b	PROPN
ejpam-2779	94	88	a	a	DET
ejpam-2779	94	89	b	b	NOUN
ejpam-2779	94	90	a	a	DET
ejpam-2779	94	91	x	x	SYM
ejpam-2779	94	92	0	0	NUM
ejpam-2779	94	93	tables	table	NOUN
ejpam-2779	94	94	2.4	2.4	NUM
ejpam-2779	94	95	then	then	ADV
ejpam-2779	94	96	(	(	PUNCT
ejpam-2779	94	97	a,6	a,6	PROPN
ejpam-2779	94	98	,	,	PUNCT
ejpam-2779	94	99	∗	∗	NOUN
ejpam-2779	94	100	,	,	PUNCT
ejpam-2779	94	101	◦	◦	NOUN
ejpam-2779	94	102	,	,	PUNCT
ejpam-2779	94	103	0	0	NUM
ejpam-2779	94	104	)	)	PUNCT
ejpam-2779	94	105	is	be	AUX
ejpam-2779	94	106	a	a	DET
ejpam-2779	94	107	pseudo	pseudo	NOUN
ejpam-2779	94	108	-	-	ADJ
ejpam-2779	94	109	bci	bci	ADJ
ejpam-2779	94	110	algebra	algebra	NOUN
ejpam-2779	94	111	.	.	PUNCT
ejpam-2779	95	1	proposition	proposition	NOUN
ejpam-2779	95	2	1	1	NUM
ejpam-2779	95	3	.	.	PUNCT
ejpam-2779	96	1	[	[	X
ejpam-2779	96	2	19	19	NUM
ejpam-2779	96	3	]	]	PUNCT
ejpam-2779	96	4	in	in	ADP
ejpam-2779	96	5	a	a	DET
ejpam-2779	96	6	pseudo	pseudo	NOUN
ejpam-2779	96	7	-	-	NOUN
ejpam-2779	96	8	bci	bci	NOUN
ejpam-2779	96	9	algebras	algebra	NOUN
ejpam-2779	96	10	a	a	DET
ejpam-2779	96	11	the	the	DET
ejpam-2779	96	12	following	following	ADJ
ejpam-2779	96	13	hold	hold	NOUN
ejpam-2779	96	14	:	:	PUNCT
ejpam-2779	96	15	(	(	PUNCT
ejpam-2779	96	16	p1	p1	NOUN
ejpam-2779	96	17	)	)	PUNCT
ejpam-2779	97	1	x	x	SYM
ejpam-2779	97	2	≤	≤	NUM
ejpam-2779	97	3	0⇒	0⇒	NOUN
ejpam-2779	97	4	x	x	X
ejpam-2779	98	1	=	=	NOUN
ejpam-2779	98	2	0	0	PROPN
ejpam-2779	98	3	.	.	PUNCT
ejpam-2779	99	1	(	(	PUNCT
ejpam-2779	99	2	p2	p2	PROPN
ejpam-2779	99	3	)	)	PUNCT
ejpam-2779	99	4	x	x	SYM
ejpam-2779	99	5	≤	≤	NUM
ejpam-2779	99	6	y	y	PROPN
ejpam-2779	99	7	⇒	⇒	PROPN
ejpam-2779	99	8	z	z	PROPN
ejpam-2779	99	9	∗	∗	PROPN
ejpam-2779	99	10	y	y	PROPN
ejpam-2779	99	11	≤	≤	PROPN
ejpam-2779	99	12	z	z	NOUN
ejpam-2779	99	13	∗	∗	NOUN
ejpam-2779	99	14	x	x	PUNCT
ejpam-2779	99	15	and	and	CCONJ
ejpam-2779	99	16	z	z	NOUN
ejpam-2779	99	17	◦	◦	NOUN
ejpam-2779	99	18	y	y	PROPN
ejpam-2779	99	19	≤	≤	PROPN
ejpam-2779	99	20	z	z	NOUN
ejpam-2779	99	21	◦	◦	NOUN
ejpam-2779	99	22	x.	x.	NOUN
ejpam-2779	99	23	(	(	PUNCT
ejpam-2779	99	24	p3	p3	PROPN
ejpam-2779	99	25	)	)	PUNCT
ejpam-2779	99	26	x	x	PUNCT
ejpam-2779	100	1	≤	≤	NOUN
ejpam-2779	100	2	y	y	PROPN
ejpam-2779	100	3	,	,	PUNCT
ejpam-2779	100	4	y	y	PROPN
ejpam-2779	100	5	≤	≤	PROPN
ejpam-2779	100	6	z	z	NOUN
ejpam-2779	100	7	⇒	⇒	NOUN
ejpam-2779	100	8	x	x	PUNCT
ejpam-2779	100	9	≤	≤	NUM
ejpam-2779	100	10	z.	z.	PROPN
ejpam-2779	100	11	(	(	PUNCT
ejpam-2779	100	12	p4	p4	ADJ
ejpam-2779	100	13	)	)	PUNCT
ejpam-2779	100	14	(	(	PUNCT
ejpam-2779	100	15	x	x	SYM
ejpam-2779	100	16	∗	∗	PROPN
ejpam-2779	100	17	y	y	NOUN
ejpam-2779	100	18	)	)	PUNCT
ejpam-2779	100	19	◦	◦	NOUN
ejpam-2779	100	20	z	z	NOUN
ejpam-2779	101	1	=	=	SYM
ejpam-2779	102	1	(	(	PUNCT
ejpam-2779	102	2	x	x	PART
ejpam-2779	102	3	◦	◦	NOUN
ejpam-2779	102	4	z	z	NOUN
ejpam-2779	102	5	)	)	PUNCT
ejpam-2779	102	6	∗	∗	NOUN
ejpam-2779	102	7	y.	y.	PROPN
ejpam-2779	102	8	(	(	PUNCT
ejpam-2779	102	9	p5	p5	PROPN
ejpam-2779	102	10	)	)	PUNCT
ejpam-2779	102	11	x	x	SYM
ejpam-2779	102	12	∗	∗	NOUN
ejpam-2779	102	13	y	y	PROPN
ejpam-2779	102	14	≤	≤	PROPN
ejpam-2779	102	15	z	z	PROPN
ejpam-2779	102	16	⇔	⇔	X
ejpam-2779	102	17	x	x	PUNCT
ejpam-2779	102	18	◦	◦	NOUN
ejpam-2779	102	19	z	z	NOUN
ejpam-2779	102	20	≤	≤	NOUN
ejpam-2779	103	1	y.	y.	NOUN
ejpam-2779	103	2	(	(	PUNCT
ejpam-2779	103	3	p6	p6	PROPN
ejpam-2779	103	4	)	)	PUNCT
ejpam-2779	103	5	(	(	PUNCT
ejpam-2779	103	6	x	x	SYM
ejpam-2779	103	7	∗	∗	PROPN
ejpam-2779	103	8	y	y	NOUN
ejpam-2779	103	9	)	)	PUNCT
ejpam-2779	103	10	∗	∗	NOUN
ejpam-2779	103	11	(	(	PUNCT
ejpam-2779	103	12	z	z	NOUN
ejpam-2779	103	13	∗	∗	PROPN
ejpam-2779	103	14	y	y	NOUN
ejpam-2779	103	15	)	)	PUNCT
ejpam-2779	103	16	≤	≤	NUM
ejpam-2779	103	17	x	x	PUNCT
ejpam-2779	103	18	∗	∗	NOUN
ejpam-2779	103	19	z	z	PROPN
ejpam-2779	103	20	,	,	PUNCT
ejpam-2779	103	21	(	(	PUNCT
ejpam-2779	103	22	x	x	SYM
ejpam-2779	103	23	◦	◦	VERB
ejpam-2779	103	24	y	y	NOUN
ejpam-2779	103	25	)	)	PUNCT
ejpam-2779	103	26	◦	◦	NOUN
ejpam-2779	103	27	(	(	PUNCT
ejpam-2779	103	28	z	z	AUX
ejpam-2779	103	29	◦	◦	NOUN
ejpam-2779	103	30	y	y	NOUN
ejpam-2779	103	31	)	)	PUNCT
ejpam-2779	103	32	≤	≤	NOUN
ejpam-2779	103	33	x	x	PUNCT
ejpam-2779	103	34	◦	◦	NOUN
ejpam-2779	103	35	z.	z.	PROPN
ejpam-2779	103	36	(	(	PUNCT
ejpam-2779	103	37	p7	p7	PROPN
ejpam-2779	103	38	)	)	PUNCT
ejpam-2779	103	39	x	x	SYM
ejpam-2779	103	40	≤	≤	NUM
ejpam-2779	103	41	y	y	PROPN
ejpam-2779	103	42	⇒	⇒	NOUN
ejpam-2779	103	43	x	x	PUNCT
ejpam-2779	103	44	∗	∗	NOUN
ejpam-2779	103	45	z	z	NOUN
ejpam-2779	103	46	≤	≤	NOUN
ejpam-2779	103	47	y	y	PROPN
ejpam-2779	103	48	∗	∗	NOUN
ejpam-2779	103	49	z	z	PROPN
ejpam-2779	103	50	,	,	PUNCT
ejpam-2779	103	51	x	x	PUNCT
ejpam-2779	103	52	◦	◦	NOUN
ejpam-2779	103	53	z	z	NOUN
ejpam-2779	103	54	≤	≤	NOUN
ejpam-2779	103	55	y	y	PROPN
ejpam-2779	103	56	◦	◦	NOUN
ejpam-2779	103	57	z.	z.	PROPN
ejpam-2779	104	1	x.l	x.l	PROPN
ejpam-2779	104	2	.	.	PUNCT
ejpam-2779	105	1	xin	xin	PROPN
ejpam-2779	105	2	,	,	PUNCT
ejpam-2779	105	3	y.j	y.j	PROPN
ejpam-2779	105	4	.	.	PUNCT
ejpam-2779	105	5	li	li	PROPN
ejpam-2779	105	6	,	,	PUNCT
ejpam-2779	105	7	y.l	y.l	PROPN
ejpam-2779	105	8	.	.	PROPN
ejpam-2779	105	9	fu	fu	PROPN
ejpam-2779	105	10	/	/	SYM
ejpam-2779	105	11	eur	eur	PROPN
ejpam-2779	105	12	.	.	PUNCT
ejpam-2779	106	1	j.	j.	PROPN
ejpam-2779	106	2	pure	pure	PROPN
ejpam-2779	106	3	appl	appl	PROPN
ejpam-2779	106	4	.	.	PROPN
ejpam-2779	106	5	math	math	PROPN
ejpam-2779	106	6	,	,	PUNCT
ejpam-2779	106	7	10	10	NUM
ejpam-2779	106	8	(	(	PUNCT
ejpam-2779	106	9	3	3	NUM
ejpam-2779	106	10	)	)	PUNCT
ejpam-2779	106	11	(	(	PUNCT
ejpam-2779	106	12	2017	2017	NUM
ejpam-2779	106	13	)	)	PUNCT
ejpam-2779	106	14	,	,	PUNCT
ejpam-2779	106	15	455	455	NUM
ejpam-2779	106	16	-	-	SYM
ejpam-2779	106	17	472	472	NUM
ejpam-2779	106	18	459	459	NUM
ejpam-2779	106	19	(	(	PUNCT
ejpam-2779	106	20	p8	p8	PROPN
ejpam-2779	106	21	)	)	PUNCT
ejpam-2779	106	22	x	x	SYM
ejpam-2779	106	23	∗	∗	NOUN
ejpam-2779	106	24	0	0	NUM
ejpam-2779	107	1	=	=	PUNCT
ejpam-2779	107	2	x	x	SYM
ejpam-2779	107	3	=	=	PUNCT
ejpam-2779	107	4	x	x	PUNCT
ejpam-2779	107	5	◦	◦	NOUN
ejpam-2779	107	6	0	0	NUM
ejpam-2779	107	7	.	.	PUNCT
ejpam-2779	108	1	(	(	PUNCT
ejpam-2779	108	2	p9	p9	PROPN
ejpam-2779	108	3	)	)	PUNCT
ejpam-2779	108	4	x	x	PROPN
ejpam-2779	108	5	∗	∗	NOUN
ejpam-2779	108	6	(	(	PUNCT
ejpam-2779	108	7	x	x	SYM
ejpam-2779	108	8	◦	◦	NOUN
ejpam-2779	108	9	(	(	PUNCT
ejpam-2779	108	10	x	x	X
ejpam-2779	108	11	∗	∗	PROPN
ejpam-2779	108	12	y	y	NOUN
ejpam-2779	108	13	)	)	PUNCT
ejpam-2779	108	14	)	)	PUNCT
ejpam-2779	109	1	=	=	PUNCT
ejpam-2779	110	1	x	x	X
ejpam-2779	110	2	∗	∗	NOUN
ejpam-2779	110	3	y	y	PROPN
ejpam-2779	110	4	,	,	PUNCT
ejpam-2779	110	5	x	x	SYM
ejpam-2779	110	6	◦	◦	NOUN
ejpam-2779	110	7	(	(	PUNCT
ejpam-2779	110	8	x	x	X
ejpam-2779	110	9	∗	∗	NOUN
ejpam-2779	110	10	(	(	PUNCT
ejpam-2779	110	11	x	x	SYM
ejpam-2779	110	12	◦	◦	VERB
ejpam-2779	110	13	y	y	PROPN
ejpam-2779	110	14	)	)	PUNCT
ejpam-2779	110	15	)	)	PUNCT
ejpam-2779	111	1	=	=	PUNCT
ejpam-2779	112	1	x	x	PUNCT
ejpam-2779	112	2	◦	◦	NOUN
ejpam-2779	112	3	y.	y.	NOUN
ejpam-2779	112	4	proposition	proposition	NOUN
ejpam-2779	112	5	2	2	NUM
ejpam-2779	112	6	.	.	PUNCT
ejpam-2779	113	1	[	[	X
ejpam-2779	113	2	19	19	NUM
ejpam-2779	113	3	]	]	PUNCT
ejpam-2779	113	4	in	in	ADP
ejpam-2779	113	5	a	a	DET
ejpam-2779	113	6	pseudo	pseudo	NOUN
ejpam-2779	113	7	-	-	NOUN
ejpam-2779	113	8	bci	bci	NOUN
ejpam-2779	113	9	algebra	algebra	NOUN
ejpam-2779	113	10	a	a	DET
ejpam-2779	113	11	the	the	DET
ejpam-2779	113	12	following	following	NOUN
ejpam-2779	113	13	holds	hold	VERB
ejpam-2779	113	14	for	for	ADP
ejpam-2779	113	15	all	all	DET
ejpam-2779	113	16	x	x	NOUN
ejpam-2779	113	17	,	,	PUNCT
ejpam-2779	113	18	y	y	PROPN
ejpam-2779	113	19	,	,	PUNCT
ejpam-2779	113	20	z	z	PROPN
ejpam-2779	113	21	∈	∈	PROPN
ejpam-2779	113	22	a	a	PRON
ejpam-2779	113	23	:	:	PUNCT
ejpam-2779	113	24	(	(	PUNCT
ejpam-2779	113	25	i	i	NOUN
ejpam-2779	113	26	)	)	PUNCT
ejpam-2779	113	27	0	0	NUM
ejpam-2779	114	1	∗	∗	NOUN
ejpam-2779	114	2	(	(	PUNCT
ejpam-2779	114	3	x	x	SYM
ejpam-2779	114	4	◦	◦	VERB
ejpam-2779	114	5	y	y	NOUN
ejpam-2779	114	6	)	)	PUNCT
ejpam-2779	114	7	≤	≤	NOUN
ejpam-2779	114	8	y	y	PROPN
ejpam-2779	114	9	◦	◦	NOUN
ejpam-2779	114	10	x.	x.	NOUN
ejpam-2779	114	11	(	(	PUNCT
ejpam-2779	114	12	ii	ii	PROPN
ejpam-2779	114	13	)	)	PUNCT
ejpam-2779	114	14	0	0	NUM
ejpam-2779	115	1	◦	◦	NOUN
ejpam-2779	115	2	(	(	PUNCT
ejpam-2779	115	3	x	x	X
ejpam-2779	115	4	∗	∗	PROPN
ejpam-2779	115	5	y	y	NOUN
ejpam-2779	115	6	)	)	PUNCT
ejpam-2779	115	7	≤	≤	PUNCT
ejpam-2779	115	8	y	y	PROPN
ejpam-2779	115	9	∗	∗	NOUN
ejpam-2779	115	10	x.	x.	NOUN
ejpam-2779	115	11	(	(	PUNCT
ejpam-2779	115	12	iii	iii	NOUN
ejpam-2779	115	13	)	)	PUNCT
ejpam-2779	115	14	0	0	NUM
ejpam-2779	115	15	∗	∗	NOUN
ejpam-2779	115	16	(	(	PUNCT
ejpam-2779	115	17	x	x	X
ejpam-2779	115	18	∗	∗	PROPN
ejpam-2779	115	19	y	y	NOUN
ejpam-2779	115	20	)	)	PUNCT
ejpam-2779	115	21	=	=	SYM
ejpam-2779	116	1	(	(	PUNCT
ejpam-2779	116	2	0	0	NUM
ejpam-2779	116	3	◦	◦	NOUN
ejpam-2779	116	4	x	x	NOUN
ejpam-2779	116	5	)	)	PUNCT
ejpam-2779	116	6	◦	◦	NOUN
ejpam-2779	116	7	(	(	PUNCT
ejpam-2779	116	8	0	0	NUM
ejpam-2779	116	9	∗	∗	PROPN
ejpam-2779	116	10	y	y	PROPN
ejpam-2779	116	11	)	)	PUNCT
ejpam-2779	116	12	.	.	PUNCT
ejpam-2779	117	1	(	(	PUNCT
ejpam-2779	117	2	iv	iv	X
ejpam-2779	117	3	)	)	PUNCT
ejpam-2779	117	4	0	0	NUM
ejpam-2779	118	1	◦	◦	NOUN
ejpam-2779	118	2	(	(	PUNCT
ejpam-2779	118	3	x	x	PART
ejpam-2779	118	4	◦	◦	VERB
ejpam-2779	118	5	y	y	NOUN
ejpam-2779	118	6	)	)	PUNCT
ejpam-2779	118	7	=	=	SYM
ejpam-2779	118	8	(	(	PUNCT
ejpam-2779	118	9	0	0	NUM
ejpam-2779	118	10	∗	∗	NOUN
ejpam-2779	118	11	x	x	NOUN
ejpam-2779	118	12	)	)	PUNCT
ejpam-2779	118	13	∗	∗	NOUN
ejpam-2779	118	14	(	(	PUNCT
ejpam-2779	118	15	0	0	NUM
ejpam-2779	118	16	◦	◦	NOUN
ejpam-2779	118	17	y	y	PROPN
ejpam-2779	118	18	)	)	PUNCT
ejpam-2779	118	19	.	.	PUNCT
ejpam-2779	119	1	definition	definition	NOUN
ejpam-2779	119	2	3	3	NUM
ejpam-2779	119	3	.	.	PUNCT
ejpam-2779	120	1	[	[	X
ejpam-2779	120	2	19	19	NUM
ejpam-2779	120	3	]	]	X
ejpam-2779	120	4	an	an	DET
ejpam-2779	120	5	element	element	NOUN
ejpam-2779	120	6	a	a	PRON
ejpam-2779	120	7	of	of	ADP
ejpam-2779	120	8	a	a	DET
ejpam-2779	120	9	pseudo	pseudo	NOUN
ejpam-2779	120	10	-	-	NOUN
ejpam-2779	120	11	bci	bci	ADJ
ejpam-2779	120	12	algebra	algebra	NOUN
ejpam-2779	120	13	a	a	PRON
ejpam-2779	120	14	is	be	AUX
ejpam-2779	120	15	called	call	VERB
ejpam-2779	120	16	a	a	DET
ejpam-2779	120	17	pseudo	pseudo	NOUN
ejpam-2779	120	18	-	-	NOUN
ejpam-2779	120	19	atom	atom	NOUN
ejpam-2779	120	20	if	if	SCONJ
ejpam-2779	120	21	for	for	ADP
ejpam-2779	120	22	every	every	DET
ejpam-2779	120	23	x	x	SYM
ejpam-2779	120	24	∈	∈	PROPN
ejpam-2779	120	25	a	a	PRON
ejpam-2779	120	26	,	,	PUNCT
ejpam-2779	120	27	x	x	SYM
ejpam-2779	120	28	≤	≤	NOUN
ejpam-2779	120	29	a	a	DET
ejpam-2779	120	30	implies	implie	NOUN
ejpam-2779	120	31	x	x	X
ejpam-2779	120	32	=	=	PUNCT
ejpam-2779	120	33	a.	a.	NOUN
ejpam-2779	120	34	the	the	DET
ejpam-2779	120	35	set	set	NOUN
ejpam-2779	120	36	of	of	ADP
ejpam-2779	120	37	all	all	DET
ejpam-2779	120	38	pseudo	pseudo	NOUN
ejpam-2779	120	39	-	-	NOUN
ejpam-2779	120	40	atoms	atom	NOUN
ejpam-2779	120	41	of	of	ADP
ejpam-2779	120	42	a	a	DET
ejpam-2779	120	43	pseudo	pseudo	NOUN
ejpam-2779	120	44	-	-	NOUN
ejpam-2779	120	45	bci	bci	ADJ
ejpam-2779	120	46	algebra	algebra	NOUN
ejpam-2779	120	47	a	a	PRON
ejpam-2779	120	48	is	be	AUX
ejpam-2779	120	49	denoted	denote	VERB
ejpam-2779	120	50	by	by	ADP
ejpam-2779	120	51	m(a	m(a	NOUN
ejpam-2779	120	52	)	)	PUNCT
ejpam-2779	120	53	.	.	PUNCT
ejpam-2779	121	1	obviously	obviously	ADV
ejpam-2779	121	2	,	,	PUNCT
ejpam-2779	121	3	0	0	NUM
ejpam-2779	121	4	∈m(a	∈m(a	NOUN
ejpam-2779	121	5	)	)	PUNCT
ejpam-2779	121	6	.	.	PUNCT
ejpam-2779	122	1	proposition	proposition	NOUN
ejpam-2779	122	2	3	3	X
ejpam-2779	122	3	.	.	PUNCT
ejpam-2779	123	1	let	let	VERB
ejpam-2779	123	2	a	a	PRON
ejpam-2779	123	3	be	be	AUX
ejpam-2779	123	4	a	a	DET
ejpam-2779	123	5	pseudo	pseudo	NOUN
ejpam-2779	123	6	-	-	ADJ
ejpam-2779	123	7	bci	bci	ADJ
ejpam-2779	123	8	algebra	algebra	NOUN
ejpam-2779	123	9	and	and	CCONJ
ejpam-2779	123	10	a	a	DET
ejpam-2779	123	11	∈	∈	NOUN
ejpam-2779	123	12	a.	a.	NOUN
ejpam-2779	123	13	the	the	DET
ejpam-2779	123	14	following	follow	VERB
ejpam-2779	123	15	conditions	condition	NOUN
ejpam-2779	123	16	are	be	AUX
ejpam-2779	123	17	equivalent	equivalent	ADJ
ejpam-2779	123	18	:	:	PUNCT
ejpam-2779	123	19	(	(	PUNCT
ejpam-2779	123	20	1	1	X
ejpam-2779	123	21	)	)	PUNCT
ejpam-2779	123	22	a	a	PRON
ejpam-2779	123	23	is	be	AUX
ejpam-2779	123	24	a	a	DET
ejpam-2779	123	25	pseudo	pseudo	NOUN
ejpam-2779	123	26	-	-	NOUN
ejpam-2779	123	27	atom	atom	NOUN
ejpam-2779	123	28	of	of	ADP
ejpam-2779	123	29	a	a	PRON
ejpam-2779	123	30	;	;	PUNCT
ejpam-2779	123	31	(	(	PUNCT
ejpam-2779	123	32	2	2	X
ejpam-2779	123	33	)	)	PUNCT
ejpam-2779	123	34	y	y	PROPN
ejpam-2779	123	35	∗	∗	NOUN
ejpam-2779	123	36	(	(	PUNCT
ejpam-2779	123	37	y	y	NOUN
ejpam-2779	123	38	◦	◦	VERB
ejpam-2779	123	39	a	a	X
ejpam-2779	123	40	)	)	PUNCT
ejpam-2779	123	41	=	=	SYM
ejpam-2779	123	42	a	a	DET
ejpam-2779	123	43	(	(	PUNCT
ejpam-2779	123	44	or	or	CCONJ
ejpam-2779	123	45	y	y	PROPN
ejpam-2779	123	46	◦	◦	NOUN
ejpam-2779	123	47	(	(	PUNCT
ejpam-2779	124	1	y	y	PROPN
ejpam-2779	124	2	∗	∗	NOUN
ejpam-2779	124	3	a	a	NOUN
ejpam-2779	124	4	)	)	PUNCT
ejpam-2779	124	5	=	=	SYM
ejpam-2779	124	6	a	a	X
ejpam-2779	124	7	)	)	PUNCT
ejpam-2779	124	8	for	for	ADP
ejpam-2779	124	9	all	all	DET
ejpam-2779	124	10	y	y	PROPN
ejpam-2779	124	11	∈	∈	PROPN
ejpam-2779	124	12	a	a	PRON
ejpam-2779	124	13	;	;	PUNCT
ejpam-2779	124	14	(	(	PUNCT
ejpam-2779	124	15	3	3	X
ejpam-2779	124	16	)	)	PUNCT
ejpam-2779	124	17	y	y	PROPN
ejpam-2779	124	18	∗	∗	NOUN
ejpam-2779	124	19	(	(	PUNCT
ejpam-2779	124	20	y	y	PROPN
ejpam-2779	124	21	◦	◦	NOUN
ejpam-2779	124	22	(	(	PUNCT
ejpam-2779	124	23	a	a	DET
ejpam-2779	124	24	∗	∗	NOUN
ejpam-2779	124	25	x	x	NOUN
ejpam-2779	124	26	)	)	PUNCT
ejpam-2779	124	27	)	)	PUNCT
ejpam-2779	125	1	=	=	PUNCT
ejpam-2779	125	2	a	a	DET
ejpam-2779	125	3	∗	∗	NOUN
ejpam-2779	125	4	x	x	PUNCT
ejpam-2779	125	5	(	(	PUNCT
ejpam-2779	125	6	or	or	CCONJ
ejpam-2779	125	7	y	y	PROPN
ejpam-2779	125	8	◦	◦	NOUN
ejpam-2779	125	9	(	(	PUNCT
ejpam-2779	125	10	y	y	PROPN
ejpam-2779	125	11	∗	∗	NOUN
ejpam-2779	125	12	(	(	PUNCT
ejpam-2779	125	13	a	a	DET
ejpam-2779	125	14	◦	◦	NOUN
ejpam-2779	125	15	x	x	NOUN
ejpam-2779	125	16	)	)	PUNCT
ejpam-2779	125	17	)	)	PUNCT
ejpam-2779	126	1	=	=	PUNCT
ejpam-2779	126	2	a	a	DET
ejpam-2779	126	3	◦	◦	NOUN
ejpam-2779	126	4	x	x	NOUN
ejpam-2779	126	5	)	)	PUNCT
ejpam-2779	126	6	for	for	ADP
ejpam-2779	126	7	all	all	DET
ejpam-2779	126	8	x	x	NOUN
ejpam-2779	126	9	,	,	PUNCT
ejpam-2779	126	10	y	y	PROPN
ejpam-2779	126	11	∈	∈	PROPN
ejpam-2779	126	12	a.	a.	NOUN
ejpam-2779	126	13	proof	proof	NOUN
ejpam-2779	126	14	.	.	PUNCT
ejpam-2779	127	1	(	(	PUNCT
ejpam-2779	127	2	1	1	X
ejpam-2779	127	3	)	)	PUNCT
ejpam-2779	127	4	⇒	⇒	NOUN
ejpam-2779	127	5	(	(	PUNCT
ejpam-2779	127	6	2	2	NUM
ejpam-2779	127	7	)	)	PUNCT
ejpam-2779	127	8	.	.	PUNCT
ejpam-2779	128	1	by	by	ADP
ejpam-2779	128	2	i2	i2	PROPN
ejpam-2779	128	3	,	,	PUNCT
ejpam-2779	128	4	y	y	PROPN
ejpam-2779	128	5	∗	∗	NOUN
ejpam-2779	128	6	(	(	PUNCT
ejpam-2779	128	7	y	y	NOUN
ejpam-2779	128	8	◦	◦	VERB
ejpam-2779	128	9	a	a	PRON
ejpam-2779	128	10	)	)	PUNCT
ejpam-2779	128	11	≤	≤	NUM
ejpam-2779	128	12	a.	a.	NOUN
ejpam-2779	128	13	since	since	SCONJ
ejpam-2779	128	14	a	a	PRON
ejpam-2779	128	15	is	be	AUX
ejpam-2779	128	16	a	a	DET
ejpam-2779	128	17	pseudo	pseudo	NOUN
ejpam-2779	128	18	-	-	NOUN
ejpam-2779	128	19	atom	atom	NOUN
ejpam-2779	128	20	of	of	ADP
ejpam-2779	128	21	a	a	PRON
ejpam-2779	128	22	,	,	PUNCT
ejpam-2779	128	23	we	we	PRON
ejpam-2779	128	24	have	have	VERB
ejpam-2779	128	25	y	y	PROPN
ejpam-2779	128	26	∗	∗	NOUN
ejpam-2779	128	27	(	(	PUNCT
ejpam-2779	128	28	y	y	NOUN
ejpam-2779	128	29	◦	◦	VERB
ejpam-2779	128	30	a	a	X
ejpam-2779	128	31	)	)	PUNCT
ejpam-2779	128	32	=	=	SYM
ejpam-2779	128	33	a.	a.	NOUN
ejpam-2779	128	34	(	(	PUNCT
ejpam-2779	128	35	2)⇒	2)⇒	NUM
ejpam-2779	128	36	(	(	PUNCT
ejpam-2779	128	37	3	3	NUM
ejpam-2779	128	38	)	)	PUNCT
ejpam-2779	128	39	obviously	obviously	ADV
ejpam-2779	128	40	.	.	PUNCT
ejpam-2779	129	1	(	(	PUNCT
ejpam-2779	129	2	3)⇒	3)⇒	NUM
ejpam-2779	129	3	(	(	PUNCT
ejpam-2779	129	4	1	1	NUM
ejpam-2779	129	5	)	)	PUNCT
ejpam-2779	129	6	it	it	PRON
ejpam-2779	129	7	follows	follow	VERB
ejpam-2779	129	8	from	from	ADP
ejpam-2779	129	9	proposition	proposition	NOUN
ejpam-2779	129	10	3.6	3.6	NUM
ejpam-2779	129	11	of	of	ADP
ejpam-2779	129	12	[	[	X
ejpam-2779	129	13	19	19	NUM
ejpam-2779	129	14	]	]	PUNCT
ejpam-2779	129	15	.	.	PUNCT
ejpam-2779	130	1	by	by	ADP
ejpam-2779	130	2	proposition	proposition	NOUN
ejpam-2779	130	3	3	3	NUM
ejpam-2779	130	4	,	,	PUNCT
ejpam-2779	130	5	we	we	PRON
ejpam-2779	130	6	have	have	VERB
ejpam-2779	130	7	x	x	NOUN
ejpam-2779	130	8	∗	∗	NOUN
ejpam-2779	130	9	(	(	PUNCT
ejpam-2779	130	10	x	x	SYM
ejpam-2779	130	11	◦	◦	VERB
ejpam-2779	130	12	a	a	X
ejpam-2779	130	13	)	)	PUNCT
ejpam-2779	130	14	=	=	SYM
ejpam-2779	130	15	x	x	PUNCT
ejpam-2779	130	16	◦	◦	NOUN
ejpam-2779	130	17	(	(	PUNCT
ejpam-2779	130	18	x	x	X
ejpam-2779	130	19	∗	∗	NOUN
ejpam-2779	130	20	a	a	NOUN
ejpam-2779	130	21	)	)	PUNCT
ejpam-2779	130	22	=	=	NOUN
ejpam-2779	130	23	a	a	PRON
ejpam-2779	130	24	for	for	ADP
ejpam-2779	130	25	all	all	DET
ejpam-2779	130	26	a	a	DET
ejpam-2779	130	27	∈m(a	∈m(a	NOUN
ejpam-2779	130	28	)	)	PUNCT
ejpam-2779	130	29	and	and	CCONJ
ejpam-2779	130	30	x	x	PUNCT
ejpam-2779	130	31	∈	∈	PROPN
ejpam-2779	130	32	a.	a.	NOUN
ejpam-2779	130	33	corollary	corollary	NOUN
ejpam-2779	130	34	1	1	PROPN
ejpam-2779	130	35	.	.	PUNCT
ejpam-2779	131	1	let	let	VERB
ejpam-2779	131	2	a	a	PRON
ejpam-2779	131	3	be	be	AUX
ejpam-2779	131	4	a	a	DET
ejpam-2779	131	5	pseudo	pseudo	NOUN
ejpam-2779	131	6	-	-	ADJ
ejpam-2779	131	7	bci	bci	ADJ
ejpam-2779	131	8	algebra	algebra	NOUN
ejpam-2779	131	9	.	.	PUNCT
ejpam-2779	132	1	then	then	ADV
ejpam-2779	132	2	for	for	ADP
ejpam-2779	132	3	all	all	DET
ejpam-2779	132	4	a	a	DET
ejpam-2779	132	5	∈m(a	∈m(a	NOUN
ejpam-2779	132	6	)	)	PUNCT
ejpam-2779	132	7	and	and	CCONJ
ejpam-2779	132	8	x	x	PUNCT
ejpam-2779	132	9	∈	∈	PROPN
ejpam-2779	132	10	a	a	X
ejpam-2779	132	11	,	,	PUNCT
ejpam-2779	132	12	we	we	PRON
ejpam-2779	132	13	have	have	VERB
ejpam-2779	132	14	a	a	DET
ejpam-2779	132	15	∗	∗	NOUN
ejpam-2779	132	16	x	x	PUNCT
ejpam-2779	132	17	∈m(a	∈m(a	NOUN
ejpam-2779	132	18	)	)	PUNCT
ejpam-2779	132	19	and	and	CCONJ
ejpam-2779	132	20	a	a	DET
ejpam-2779	132	21	◦	◦	NOUN
ejpam-2779	132	22	x	x	SYM
ejpam-2779	132	23	∈m(a	∈m(a	NOUN
ejpam-2779	132	24	)	)	PUNCT
ejpam-2779	132	25	.	.	PUNCT
ejpam-2779	133	1	proof	proof	NOUN
ejpam-2779	133	2	.	.	PUNCT
ejpam-2779	134	1	let	let	VERB
ejpam-2779	134	2	a	a	DET
ejpam-2779	134	3	∈m(a	∈m(a	NOUN
ejpam-2779	134	4	)	)	PUNCT
ejpam-2779	134	5	and	and	CCONJ
ejpam-2779	134	6	x	x	PUNCT
ejpam-2779	134	7	∈	∈	NOUN
ejpam-2779	134	8	a.	a.	NOUN
ejpam-2779	134	9	by	by	ADP
ejpam-2779	134	10	proposition	proposition	NOUN
ejpam-2779	134	11	3.8(3	3.8(3	NUM
ejpam-2779	134	12	)	)	PUNCT
ejpam-2779	134	13	,	,	PUNCT
ejpam-2779	134	14	we	we	PRON
ejpam-2779	134	15	have	have	VERB
ejpam-2779	134	16	y	y	PROPN
ejpam-2779	134	17	∗	∗	NOUN
ejpam-2779	134	18	(	(	PUNCT
ejpam-2779	134	19	y	y	PROPN
ejpam-2779	134	20	◦	◦	NOUN
ejpam-2779	134	21	(	(	PUNCT
ejpam-2779	134	22	a∗x	a∗x	NUM
ejpam-2779	134	23	)	)	PUNCT
ejpam-2779	134	24	)	)	PUNCT
ejpam-2779	135	1	=	=	PUNCT
ejpam-2779	135	2	a∗x	a∗x	PROPN
ejpam-2779	135	3	for	for	ADP
ejpam-2779	135	4	all	all	DET
ejpam-2779	135	5	y	y	PROPN
ejpam-2779	135	6	∈	∈	PROPN
ejpam-2779	135	7	a.	a.	NOUN
ejpam-2779	135	8	using	use	VERB
ejpam-2779	135	9	proposition	proposition	NOUN
ejpam-2779	135	10	3.8(2	3.8(2	NUM
ejpam-2779	135	11	)	)	PUNCT
ejpam-2779	135	12	,	,	PUNCT
ejpam-2779	135	13	we	we	PRON
ejpam-2779	135	14	get	get	VERB
ejpam-2779	135	15	that	that	PRON
ejpam-2779	135	16	a	a	DET
ejpam-2779	135	17	∗	∗	NOUN
ejpam-2779	135	18	x	x	PUNCT
ejpam-2779	135	19	is	be	AUX
ejpam-2779	135	20	a	a	DET
ejpam-2779	135	21	pseudo	pseudo	NOUN
ejpam-2779	135	22	-	-	NOUN
ejpam-2779	135	23	atom	atom	NOUN
ejpam-2779	135	24	of	of	ADP
ejpam-2779	135	25	a	a	PRON
ejpam-2779	135	26	,	,	PUNCT
ejpam-2779	135	27	that	that	PRON
ejpam-2779	135	28	is	be	AUX
ejpam-2779	135	29	a	a	DET
ejpam-2779	135	30	∗	∗	NOUN
ejpam-2779	135	31	x	x	PUNCT
ejpam-2779	135	32	∈m(a	∈m(a	NOUN
ejpam-2779	135	33	)	)	PUNCT
ejpam-2779	135	34	.	.	PUNCT
ejpam-2779	136	1	similarly	similarly	ADV
ejpam-2779	136	2	we	we	PRON
ejpam-2779	136	3	can	can	AUX
ejpam-2779	136	4	prove	prove	VERB
ejpam-2779	136	5	a	a	DET
ejpam-2779	136	6	◦	◦	NOUN
ejpam-2779	136	7	x	x	SYM
ejpam-2779	136	8	∈m(a	∈m(a	NOUN
ejpam-2779	136	9	)	)	PUNCT
ejpam-2779	136	10	.	.	PUNCT
ejpam-2779	137	1	let	let	VERB
ejpam-2779	137	2	a	a	PRON
ejpam-2779	137	3	be	be	AUX
ejpam-2779	137	4	a	a	DET
ejpam-2779	137	5	pseudo	pseudo	NOUN
ejpam-2779	137	6	-	-	ADJ
ejpam-2779	137	7	bci	bci	ADJ
ejpam-2779	137	8	algebra	algebra	NOUN
ejpam-2779	137	9	.	.	PUNCT
ejpam-2779	138	1	for	for	ADP
ejpam-2779	138	2	a	a	DET
ejpam-2779	138	3	∈	∈	PROPN
ejpam-2779	138	4	m(a	m(a	NOUN
ejpam-2779	138	5	)	)	PUNCT
ejpam-2779	138	6	,	,	PUNCT
ejpam-2779	138	7	define	define	VERB
ejpam-2779	138	8	v	v	ADP
ejpam-2779	138	9	(	(	PUNCT
ejpam-2779	138	10	a	a	NOUN
ejpam-2779	138	11	)	)	PUNCT
ejpam-2779	138	12	=	=	SYM
ejpam-2779	139	1	{	{	PUNCT
ejpam-2779	139	2	x	x	PUNCT
ejpam-2779	139	3	∈	∈	PROPN
ejpam-2779	139	4	a	a	DET
ejpam-2779	139	5	|	|	NOUN
ejpam-2779	139	6	a	a	DET
ejpam-2779	139	7	≤	≤	NOUN
ejpam-2779	139	8	x	x	X
ejpam-2779	139	9	}	}	PUNCT
ejpam-2779	139	10	.	.	PUNCT
ejpam-2779	140	1	v(a	v(a	NOUN
ejpam-2779	140	2	)	)	PUNCT
ejpam-2779	140	3	is	be	AUX
ejpam-2779	140	4	called	call	VERB
ejpam-2779	140	5	a	a	DET
ejpam-2779	140	6	branch	branch	NOUN
ejpam-2779	140	7	of	of	ADP
ejpam-2779	140	8	a.	a.	NOUN
ejpam-2779	140	9	obviously	obviously	ADV
ejpam-2779	140	10	a	a	DET
ejpam-2779	140	11	∈	∈	PROPN
ejpam-2779	140	12	v	v	NOUN
ejpam-2779	140	13	(	(	PUNCT
ejpam-2779	140	14	a	a	NOUN
ejpam-2779	140	15	)	)	PUNCT
ejpam-2779	140	16	.	.	PUNCT
ejpam-2779	141	1	proposition	proposition	NOUN
ejpam-2779	141	2	4	4	NUM
ejpam-2779	141	3	.	.	PUNCT
ejpam-2779	141	4	let	let	VERB
ejpam-2779	141	5	a	a	PRON
ejpam-2779	141	6	be	be	AUX
ejpam-2779	141	7	a	a	DET
ejpam-2779	141	8	pseudo	pseudo	NOUN
ejpam-2779	141	9	-	-	ADJ
ejpam-2779	141	10	bci	bci	ADJ
ejpam-2779	141	11	algebra	algebra	NOUN
ejpam-2779	141	12	,	,	PUNCT
ejpam-2779	141	13	a	a	DET
ejpam-2779	141	14	,	,	PUNCT
ejpam-2779	141	15	b	b	PROPN
ejpam-2779	141	16	∈	∈	PROPN
ejpam-2779	141	17	m(a	m(a	PROPN
ejpam-2779	141	18	)	)	PUNCT
ejpam-2779	141	19	and	and	CCONJ
ejpam-2779	141	20	a	a	DET
ejpam-2779	141	21	6=	6=	PROPN
ejpam-2779	141	22	b.	b.	PROPN
ejpam-2779	141	23	then	then	ADV
ejpam-2779	141	24	v	v	X
ejpam-2779	141	25	(	(	PUNCT
ejpam-2779	141	26	a	a	NOUN
ejpam-2779	141	27	)	)	PUNCT
ejpam-2779	141	28	∩	∩	ADJ
ejpam-2779	141	29	v	v	ADP
ejpam-2779	141	30	(	(	PUNCT
ejpam-2779	141	31	b	b	NOUN
ejpam-2779	141	32	)	)	PUNCT
ejpam-2779	141	33	=	=	PUNCT
ejpam-2779	141	34	∅.	∅.	NOUN
ejpam-2779	141	35	proof	proof	NOUN
ejpam-2779	141	36	.	.	PUNCT
ejpam-2779	142	1	assume	assume	VERB
ejpam-2779	142	2	v	v	X
ejpam-2779	142	3	(	(	PUNCT
ejpam-2779	142	4	a	a	NOUN
ejpam-2779	142	5	)	)	PUNCT
ejpam-2779	142	6	∩	∩	ADJ
ejpam-2779	142	7	v	v	ADP
ejpam-2779	142	8	(	(	PUNCT
ejpam-2779	142	9	b	b	NOUN
ejpam-2779	142	10	)	)	PUNCT
ejpam-2779	142	11	6=	6=	NOUN
ejpam-2779	142	12	∅	∅	NOUN
ejpam-2779	142	13	,	,	PUNCT
ejpam-2779	142	14	then	then	ADV
ejpam-2779	142	15	there	there	PRON
ejpam-2779	142	16	is	be	VERB
ejpam-2779	142	17	x	x	X
ejpam-2779	142	18	∈	∈	PROPN
ejpam-2779	142	19	v	v	ADP
ejpam-2779	142	20	(	(	PUNCT
ejpam-2779	142	21	a	a	NOUN
ejpam-2779	142	22	)	)	PUNCT
ejpam-2779	142	23	∩	∩	ADJ
ejpam-2779	142	24	v	v	ADP
ejpam-2779	142	25	(	(	PUNCT
ejpam-2779	142	26	b	b	NOUN
ejpam-2779	142	27	)	)	PUNCT
ejpam-2779	142	28	.	.	PUNCT
ejpam-2779	143	1	hence	hence	ADV
ejpam-2779	143	2	a	a	DET
ejpam-2779	143	3	≤	≤	NOUN
ejpam-2779	143	4	x	x	PUNCT
ejpam-2779	143	5	and	and	CCONJ
ejpam-2779	143	6	b	b	NOUN
ejpam-2779	143	7	≤	≤	NUM
ejpam-2779	143	8	x.	x.	NOUN
ejpam-2779	143	9	it	it	PRON
ejpam-2779	143	10	follows	follow	VERB
ejpam-2779	143	11	that	that	SCONJ
ejpam-2779	143	12	(	(	PUNCT
ejpam-2779	143	13	b	b	NOUN
ejpam-2779	143	14	∗	∗	NOUN
ejpam-2779	143	15	(	(	PUNCT
ejpam-2779	143	16	b	b	X
ejpam-2779	143	17	◦	◦	NOUN
ejpam-2779	143	18	a	a	X
ejpam-2779	143	19	)	)	PUNCT
ejpam-2779	143	20	)	)	PUNCT
ejpam-2779	143	21	◦	◦	NOUN
ejpam-2779	143	22	(	(	PUNCT
ejpam-2779	143	23	b	b	NOUN
ejpam-2779	143	24	∗	∗	NOUN
ejpam-2779	143	25	(	(	PUNCT
ejpam-2779	143	26	b	b	X
ejpam-2779	143	27	◦	◦	NOUN
ejpam-2779	143	28	x	x	NOUN
ejpam-2779	143	29	)	)	PUNCT
ejpam-2779	143	30	)	)	PUNCT
ejpam-2779	143	31	≤	≤	NOUN
ejpam-2779	143	32	(	(	PUNCT
ejpam-2779	143	33	b	b	X
ejpam-2779	143	34	◦	◦	NOUN
ejpam-2779	143	35	x	x	NOUN
ejpam-2779	143	36	)	)	PUNCT
ejpam-2779	143	37	∗	∗	NOUN
ejpam-2779	143	38	(	(	PUNCT
ejpam-2779	143	39	b	b	X
ejpam-2779	143	40	◦	◦	NOUN
ejpam-2779	143	41	a	a	X
ejpam-2779	143	42	)	)	PUNCT
ejpam-2779	143	43	≤	≤	NOUN
ejpam-2779	143	44	a	a	DET
ejpam-2779	143	45	◦	◦	NOUN
ejpam-2779	143	46	x	x	SYM
ejpam-2779	143	47	=	=	NOUN
ejpam-2779	143	48	0	0	NUM
ejpam-2779	143	49	.	.	PUNCT
ejpam-2779	144	1	so	so	ADV
ejpam-2779	144	2	(	(	PUNCT
ejpam-2779	144	3	b	b	NOUN
ejpam-2779	144	4	∗	∗	NOUN
ejpam-2779	144	5	(	(	PUNCT
ejpam-2779	144	6	b	b	X
ejpam-2779	144	7	◦	◦	NOUN
ejpam-2779	144	8	a	a	X
ejpam-2779	144	9	)	)	PUNCT
ejpam-2779	144	10	)	)	PUNCT
ejpam-2779	144	11	◦	◦	NOUN
ejpam-2779	144	12	(	(	PUNCT
ejpam-2779	144	13	b	b	NOUN
ejpam-2779	144	14	∗	∗	NOUN
ejpam-2779	144	15	(	(	PUNCT
ejpam-2779	144	16	b	b	X
ejpam-2779	144	17	◦	◦	NOUN
ejpam-2779	144	18	x	x	NOUN
ejpam-2779	144	19	)	)	PUNCT
ejpam-2779	144	20	)	)	PUNCT
ejpam-2779	145	1	=	=	PUNCT
ejpam-2779	145	2	0	0	X
ejpam-2779	145	3	.	.	PUNCT
ejpam-2779	146	1	hence	hence	ADV
ejpam-2779	146	2	b	b	X
ejpam-2779	146	3	∗	∗	NOUN
ejpam-2779	146	4	(	(	PUNCT
ejpam-2779	146	5	b	b	X
ejpam-2779	146	6	◦	◦	NOUN
ejpam-2779	146	7	a	a	PRON
ejpam-2779	146	8	)	)	PUNCT
ejpam-2779	146	9	≤	≤	NOUN
ejpam-2779	146	10	(	(	PUNCT
ejpam-2779	146	11	b	b	NOUN
ejpam-2779	146	12	∗	∗	NOUN
ejpam-2779	146	13	(	(	PUNCT
ejpam-2779	146	14	b	b	X
ejpam-2779	146	15	◦	◦	NOUN
ejpam-2779	146	16	x	x	NOUN
ejpam-2779	146	17	)	)	PUNCT
ejpam-2779	146	18	)	)	PUNCT
ejpam-2779	147	1	=	=	SYM
ejpam-2779	147	2	b.	b.	PROPN
ejpam-2779	147	3	since	since	SCONJ
ejpam-2779	147	4	b	b	PROPN
ejpam-2779	147	5	∈m(a	∈m(a	PROPN
ejpam-2779	147	6	)	)	PUNCT
ejpam-2779	147	7	,	,	PUNCT
ejpam-2779	147	8	we	we	PRON
ejpam-2779	147	9	have	have	VERB
ejpam-2779	148	1	b	b	NOUN
ejpam-2779	148	2	∗	∗	NOUN
ejpam-2779	148	3	(	(	PUNCT
ejpam-2779	148	4	b	b	X
ejpam-2779	148	5	◦	◦	NOUN
ejpam-2779	148	6	a	a	X
ejpam-2779	148	7	)	)	PUNCT
ejpam-2779	148	8	=	=	SYM
ejpam-2779	148	9	b.	b.	PROPN
ejpam-2779	148	10	note	note	VERB
ejpam-2779	148	11	that	that	PRON
ejpam-2779	148	12	b	b	X
ejpam-2779	148	13	=	=	SYM
ejpam-2779	148	14	(	(	PUNCT
ejpam-2779	148	15	b	b	NOUN
ejpam-2779	148	16	∗	∗	NOUN
ejpam-2779	148	17	(	(	PUNCT
ejpam-2779	148	18	b	b	X
ejpam-2779	148	19	◦	◦	NOUN
ejpam-2779	148	20	a	a	X
ejpam-2779	148	21	)	)	PUNCT
ejpam-2779	148	22	)	)	PUNCT
ejpam-2779	149	1	≤	≤	NUM
ejpam-2779	149	2	a.	a.	NOUN
ejpam-2779	149	3	similarly	similarly	ADV
ejpam-2779	149	4	a	a	DET
ejpam-2779	149	5	≤	≤	X
ejpam-2779	149	6	b.	b.	NOUN
ejpam-2779	149	7	by	by	ADP
ejpam-2779	149	8	definition	definition	NOUN
ejpam-2779	149	9	3.1	3.1	NUM
ejpam-2779	149	10	,	,	PUNCT
ejpam-2779	149	11	we	we	PRON
ejpam-2779	149	12	have	have	VERB
ejpam-2779	149	13	a	a	DET
ejpam-2779	149	14	=	=	SYM
ejpam-2779	149	15	b.	b.	NOUN
ejpam-2779	149	16	it	it	PRON
ejpam-2779	149	17	is	be	AUX
ejpam-2779	149	18	a	a	DET
ejpam-2779	149	19	contradiction	contradiction	NOUN
ejpam-2779	149	20	,	,	PUNCT
ejpam-2779	149	21	hence	hence	ADV
ejpam-2779	149	22	v	v	NOUN
ejpam-2779	149	23	(	(	PUNCT
ejpam-2779	149	24	a	a	NOUN
ejpam-2779	149	25	)	)	PUNCT
ejpam-2779	149	26	∩	∩	ADJ
ejpam-2779	149	27	v	v	ADP
ejpam-2779	149	28	(	(	PUNCT
ejpam-2779	149	29	b	b	NOUN
ejpam-2779	149	30	)	)	PUNCT
ejpam-2779	149	31	=	=	PUNCT
ejpam-2779	149	32	∅.	∅.	PROPN
ejpam-2779	149	33	x.l	x.l	PROPN
ejpam-2779	149	34	.	.	PUNCT
ejpam-2779	150	1	xin	xin	PROPN
ejpam-2779	150	2	,	,	PUNCT
ejpam-2779	150	3	y.j	y.j	PROPN
ejpam-2779	150	4	.	.	PUNCT
ejpam-2779	150	5	li	li	PROPN
ejpam-2779	150	6	,	,	PUNCT
ejpam-2779	150	7	y.l	y.l	PROPN
ejpam-2779	150	8	.	.	PROPN
ejpam-2779	150	9	fu	fu	PROPN
ejpam-2779	150	10	/	/	SYM
ejpam-2779	150	11	eur	eur	PROPN
ejpam-2779	150	12	.	.	PUNCT
ejpam-2779	151	1	j.	j.	PROPN
ejpam-2779	151	2	pure	pure	PROPN
ejpam-2779	151	3	appl	appl	PROPN
ejpam-2779	151	4	.	.	PROPN
ejpam-2779	151	5	math	math	PROPN
ejpam-2779	151	6	,	,	PUNCT
ejpam-2779	151	7	10	10	NUM
ejpam-2779	151	8	(	(	PUNCT
ejpam-2779	151	9	3	3	NUM
ejpam-2779	151	10	)	)	PUNCT
ejpam-2779	151	11	(	(	PUNCT
ejpam-2779	151	12	2017	2017	NUM
ejpam-2779	151	13	)	)	PUNCT
ejpam-2779	151	14	,	,	PUNCT
ejpam-2779	151	15	455	455	NUM
ejpam-2779	151	16	-	-	SYM
ejpam-2779	151	17	472	472	NUM
ejpam-2779	151	18	460	460	NUM
ejpam-2779	151	19	proposition	proposition	NOUN
ejpam-2779	151	20	5	5	NUM
ejpam-2779	151	21	.	.	PUNCT
ejpam-2779	152	1	let	let	VERB
ejpam-2779	152	2	a	a	PRON
ejpam-2779	152	3	be	be	AUX
ejpam-2779	152	4	a	a	DET
ejpam-2779	152	5	pseudo	pseudo	NOUN
ejpam-2779	152	6	-	-	ADJ
ejpam-2779	152	7	bci	bci	ADJ
ejpam-2779	152	8	algebra	algebra	NOUN
ejpam-2779	152	9	and	and	CCONJ
ejpam-2779	152	10	x	x	NOUN
ejpam-2779	152	11	,	,	PUNCT
ejpam-2779	152	12	y	y	PROPN
ejpam-2779	152	13	∈	∈	PROPN
ejpam-2779	152	14	a.	a.	NOUN
ejpam-2779	152	15	if	if	SCONJ
ejpam-2779	152	16	x	x	PROPN
ejpam-2779	152	17	≤	≤	PROPN
ejpam-2779	152	18	y	y	NOUN
ejpam-2779	152	19	,	,	PUNCT
ejpam-2779	152	20	then	then	ADV
ejpam-2779	152	21	x	x	X
ejpam-2779	152	22	,	,	PUNCT
ejpam-2779	152	23	y	y	PROPN
ejpam-2779	152	24	are	be	AUX
ejpam-2779	152	25	in	in	ADP
ejpam-2779	152	26	the	the	DET
ejpam-2779	152	27	same	same	ADJ
ejpam-2779	152	28	branch	branch	NOUN
ejpam-2779	152	29	of	of	ADP
ejpam-2779	152	30	a.	a.	NOUN
ejpam-2779	152	31	proof	proof	NOUN
ejpam-2779	152	32	.	.	PUNCT
ejpam-2779	153	1	assume	assume	VERB
ejpam-2779	153	2	that	that	SCONJ
ejpam-2779	153	3	x	x	SYM
ejpam-2779	153	4	∈	∈	NOUN
ejpam-2779	153	5	v	v	ADP
ejpam-2779	153	6	(	(	PUNCT
ejpam-2779	153	7	a	a	NOUN
ejpam-2779	153	8	)	)	PUNCT
ejpam-2779	153	9	and	and	CCONJ
ejpam-2779	153	10	y	y	PROPN
ejpam-2779	153	11	∈	∈	PROPN
ejpam-2779	153	12	v	v	ADP
ejpam-2779	153	13	(	(	PUNCT
ejpam-2779	153	14	b	b	NOUN
ejpam-2779	153	15	)	)	PUNCT
ejpam-2779	153	16	for	for	ADP
ejpam-2779	153	17	some	some	DET
ejpam-2779	153	18	a	a	PRON
ejpam-2779	153	19	,	,	PUNCT
ejpam-2779	153	20	b	b	PROPN
ejpam-2779	153	21	∈	∈	PROPN
ejpam-2779	153	22	m(a	m(a	PROPN
ejpam-2779	153	23	)	)	PUNCT
ejpam-2779	153	24	and	and	CCONJ
ejpam-2779	153	25	a	a	DET
ejpam-2779	153	26	6=	6=	PROPN
ejpam-2779	153	27	b.	b.	PROPN
ejpam-2779	153	28	then	then	ADV
ejpam-2779	153	29	a	a	DET
ejpam-2779	153	30	≤	≤	NOUN
ejpam-2779	153	31	x	x	PUNCT
ejpam-2779	153	32	≤	≤	NUM
ejpam-2779	153	33	y.	y.	NOUN
ejpam-2779	153	34	hence	hence	ADV
ejpam-2779	153	35	y	y	PROPN
ejpam-2779	153	36	∈	∈	PROPN
ejpam-2779	153	37	v	v	ADP
ejpam-2779	153	38	(	(	PUNCT
ejpam-2779	153	39	a	a	NOUN
ejpam-2779	153	40	)	)	PUNCT
ejpam-2779	153	41	and	and	CCONJ
ejpam-2779	153	42	so	so	ADV
ejpam-2779	153	43	y	y	PROPN
ejpam-2779	153	44	∈	∈	PROPN
ejpam-2779	153	45	v	v	ADP
ejpam-2779	153	46	(	(	PUNCT
ejpam-2779	153	47	a	a	NOUN
ejpam-2779	153	48	)	)	PUNCT
ejpam-2779	153	49	∩	∩	ADJ
ejpam-2779	153	50	v	v	ADP
ejpam-2779	153	51	(	(	PUNCT
ejpam-2779	153	52	b	b	NOUN
ejpam-2779	153	53	)	)	PUNCT
ejpam-2779	153	54	,	,	PUNCT
ejpam-2779	153	55	a	a	DET
ejpam-2779	153	56	contradiction	contradiction	NOUN
ejpam-2779	153	57	with	with	ADP
ejpam-2779	153	58	proposition	proposition	NOUN
ejpam-2779	153	59	4	4	NUM
ejpam-2779	153	60	.	.	X
ejpam-2779	153	61	proposition	proposition	NOUN
ejpam-2779	153	62	6	6	NUM
ejpam-2779	153	63	.	.	PUNCT
ejpam-2779	154	1	let	let	VERB
ejpam-2779	154	2	a	a	PRON
ejpam-2779	154	3	be	be	AUX
ejpam-2779	154	4	a	a	DET
ejpam-2779	154	5	pseudo	pseudo	NOUN
ejpam-2779	154	6	-	-	ADJ
ejpam-2779	154	7	bci	bci	ADJ
ejpam-2779	154	8	algebra	algebra	NOUN
ejpam-2779	154	9	and	and	CCONJ
ejpam-2779	154	10	x	x	PART
ejpam-2779	154	11	∈	∈	PROPN
ejpam-2779	154	12	v	v	ADP
ejpam-2779	154	13	(	(	PUNCT
ejpam-2779	154	14	a	a	NOUN
ejpam-2779	154	15	)	)	PUNCT
ejpam-2779	154	16	for	for	ADP
ejpam-2779	154	17	some	some	PRON
ejpam-2779	154	18	a	a	DET
ejpam-2779	154	19	∈m(a	∈m(a	NOUN
ejpam-2779	154	20	)	)	PUNCT
ejpam-2779	154	21	.	.	PUNCT
ejpam-2779	155	1	then	then	ADV
ejpam-2779	155	2	0	0	NUM
ejpam-2779	155	3	∗	∗	NOUN
ejpam-2779	155	4	(	(	PUNCT
ejpam-2779	155	5	0	0	NUM
ejpam-2779	155	6	◦	◦	NOUN
ejpam-2779	155	7	x	x	SYM
ejpam-2779	155	8	)	)	PUNCT
ejpam-2779	155	9	=	=	SYM
ejpam-2779	155	10	a	a	PRON
ejpam-2779	155	11	and	and	CCONJ
ejpam-2779	155	12	0	0	NUM
ejpam-2779	155	13	◦	◦	NOUN
ejpam-2779	155	14	(	(	PUNCT
ejpam-2779	155	15	0	0	NUM
ejpam-2779	155	16	∗	∗	NOUN
ejpam-2779	155	17	x	x	NOUN
ejpam-2779	155	18	)	)	PUNCT
ejpam-2779	155	19	=	=	SYM
ejpam-2779	155	20	a.	a.	NOUN
ejpam-2779	155	21	proof	proof	NOUN
ejpam-2779	155	22	.	.	PUNCT
ejpam-2779	156	1	since	since	SCONJ
ejpam-2779	156	2	0	0	NUM
ejpam-2779	156	3	∗	∗	NOUN
ejpam-2779	156	4	(	(	PUNCT
ejpam-2779	156	5	0	0	NUM
ejpam-2779	156	6	◦	◦	NOUN
ejpam-2779	156	7	x	x	SYM
ejpam-2779	156	8	)	)	PUNCT
ejpam-2779	156	9	≤	≤	NUM
ejpam-2779	156	10	x	x	X
ejpam-2779	156	11	,	,	PUNCT
ejpam-2779	156	12	we	we	PRON
ejpam-2779	156	13	have	have	VERB
ejpam-2779	156	14	0	0	NUM
ejpam-2779	156	15	∗	∗	NOUN
ejpam-2779	156	16	(	(	PUNCT
ejpam-2779	156	17	0	0	NUM
ejpam-2779	156	18	◦	◦	NOUN
ejpam-2779	156	19	x	x	SYM
ejpam-2779	156	20	)	)	PUNCT
ejpam-2779	156	21	∈	∈	NOUN
ejpam-2779	156	22	v	v	NOUN
ejpam-2779	156	23	(	(	PUNCT
ejpam-2779	156	24	a	a	NOUN
ejpam-2779	156	25	)	)	PUNCT
ejpam-2779	156	26	by	by	ADP
ejpam-2779	156	27	proposition	proposition	NOUN
ejpam-2779	156	28	5	5	NUM
ejpam-2779	156	29	.	.	PUNCT
ejpam-2779	156	30	hence	hence	ADV
ejpam-2779	156	31	a	a	DET
ejpam-2779	156	32	≤	≤	NUM
ejpam-2779	156	33	0	0	NUM
ejpam-2779	156	34	∗	∗	NOUN
ejpam-2779	156	35	(	(	PUNCT
ejpam-2779	156	36	0	0	NUM
ejpam-2779	156	37	◦	◦	NOUN
ejpam-2779	156	38	x	x	NOUN
ejpam-2779	156	39	)	)	PUNCT
ejpam-2779	156	40	.	.	PUNCT
ejpam-2779	157	1	on	on	ADP
ejpam-2779	157	2	the	the	DET
ejpam-2779	157	3	other	other	ADJ
ejpam-2779	157	4	hand	hand	NOUN
ejpam-2779	157	5	,	,	PUNCT
ejpam-2779	157	6	we	we	PRON
ejpam-2779	157	7	have	have	VERB
ejpam-2779	157	8	(	(	PUNCT
ejpam-2779	157	9	0	0	NUM
ejpam-2779	157	10	∗	∗	NOUN
ejpam-2779	157	11	(	(	PUNCT
ejpam-2779	157	12	0	0	NUM
ejpam-2779	157	13	◦	◦	NOUN
ejpam-2779	157	14	x	x	NOUN
ejpam-2779	157	15	)	)	PUNCT
ejpam-2779	157	16	)	)	PUNCT
ejpam-2779	158	1	◦	◦	VERB
ejpam-2779	158	2	a	a	DET
ejpam-2779	158	3	=	=	X
ejpam-2779	158	4	(	(	PUNCT
ejpam-2779	158	5	0	0	NUM
ejpam-2779	158	6	◦	◦	NOUN
ejpam-2779	158	7	a	a	X
ejpam-2779	158	8	)	)	PUNCT
ejpam-2779	158	9	∗	∗	NOUN
ejpam-2779	158	10	(	(	PUNCT
ejpam-2779	158	11	0	0	NUM
ejpam-2779	158	12	◦	◦	NOUN
ejpam-2779	158	13	x	x	NOUN
ejpam-2779	158	14	)	)	PUNCT
ejpam-2779	158	15	=	=	SYM
ejpam-2779	158	16	(	(	PUNCT
ejpam-2779	158	17	(	(	PUNCT
ejpam-2779	158	18	a	a	DET
ejpam-2779	158	19	∗	∗	NOUN
ejpam-2779	158	20	x	x	NOUN
ejpam-2779	158	21	)	)	PUNCT
ejpam-2779	158	22	◦	◦	NOUN
ejpam-2779	158	23	a	a	X
ejpam-2779	158	24	)	)	PUNCT
ejpam-2779	158	25	∗	∗	NOUN
ejpam-2779	158	26	(	(	PUNCT
ejpam-2779	158	27	0	0	NUM
ejpam-2779	158	28	◦	◦	NOUN
ejpam-2779	158	29	x	x	NOUN
ejpam-2779	158	30	)	)	PUNCT
ejpam-2779	159	1	=	=	SYM
ejpam-2779	159	2	(	(	PUNCT
ejpam-2779	159	3	(	(	PUNCT
ejpam-2779	159	4	a	a	DET
ejpam-2779	159	5	◦	◦	NOUN
ejpam-2779	159	6	a	a	X
ejpam-2779	159	7	)	)	PUNCT
ejpam-2779	159	8	∗	∗	NOUN
ejpam-2779	159	9	x	x	NOUN
ejpam-2779	159	10	)	)	PUNCT
ejpam-2779	159	11	∗	∗	NOUN
ejpam-2779	159	12	(	(	PUNCT
ejpam-2779	159	13	0	0	NUM
ejpam-2779	159	14	◦	◦	NOUN
ejpam-2779	159	15	x	x	NOUN
ejpam-2779	159	16	)	)	PUNCT
ejpam-2779	159	17	=	=	SYM
ejpam-2779	159	18	(	(	PUNCT
ejpam-2779	159	19	0	0	NUM
ejpam-2779	159	20	∗	∗	NOUN
ejpam-2779	159	21	x	x	NOUN
ejpam-2779	159	22	)	)	PUNCT
ejpam-2779	159	23	∗	∗	NOUN
ejpam-2779	159	24	(	(	PUNCT
ejpam-2779	159	25	0	0	NUM
ejpam-2779	159	26	∗	∗	NOUN
ejpam-2779	159	27	x	x	NOUN
ejpam-2779	159	28	)	)	PUNCT
ejpam-2779	159	29	=	=	SYM
ejpam-2779	159	30	0	0	X
ejpam-2779	159	31	.	.	PUNCT
ejpam-2779	159	32	therefore	therefore	ADV
ejpam-2779	159	33	0	0	NUM
ejpam-2779	159	34	∗	∗	NOUN
ejpam-2779	159	35	(	(	PUNCT
ejpam-2779	159	36	0	0	NUM
ejpam-2779	159	37	◦	◦	NOUN
ejpam-2779	159	38	x	x	NOUN
ejpam-2779	159	39	)	)	PUNCT
ejpam-2779	159	40	≤	≤	NUM
ejpam-2779	159	41	a.	a.	NOUN
ejpam-2779	159	42	this	this	PRON
ejpam-2779	159	43	shows	show	VERB
ejpam-2779	159	44	that	that	SCONJ
ejpam-2779	159	45	0	0	NUM
ejpam-2779	159	46	∗	∗	NOUN
ejpam-2779	159	47	(	(	PUNCT
ejpam-2779	159	48	0	0	NUM
ejpam-2779	159	49	◦	◦	NOUN
ejpam-2779	159	50	x	x	NOUN
ejpam-2779	159	51	)	)	PUNCT
ejpam-2779	159	52	=	=	SYM
ejpam-2779	159	53	a.	a.	NOUN
ejpam-2779	159	54	similarly	similarly	ADV
ejpam-2779	159	55	we	we	PRON
ejpam-2779	159	56	can	can	AUX
ejpam-2779	159	57	prove	prove	VERB
ejpam-2779	159	58	0	0	NUM
ejpam-2779	159	59	◦	◦	NOUN
ejpam-2779	159	60	(	(	PUNCT
ejpam-2779	159	61	0	0	NUM
ejpam-2779	159	62	∗	∗	NOUN
ejpam-2779	159	63	x	x	NOUN
ejpam-2779	159	64	)	)	PUNCT
ejpam-2779	159	65	=	=	SYM
ejpam-2779	159	66	a.	a.	NOUN
ejpam-2779	159	67	proposition	proposition	NOUN
ejpam-2779	159	68	7	7	NUM
ejpam-2779	159	69	.	.	PUNCT
ejpam-2779	159	70	let	let	VERB
ejpam-2779	159	71	a	a	PRON
ejpam-2779	159	72	be	be	AUX
ejpam-2779	159	73	a	a	DET
ejpam-2779	159	74	pseudo	pseudo	NOUN
ejpam-2779	159	75	-	-	ADJ
ejpam-2779	159	76	bci	bci	ADJ
ejpam-2779	159	77	algebra	algebra	NOUN
ejpam-2779	159	78	.	.	PUNCT
ejpam-2779	160	1	then	then	ADV
ejpam-2779	160	2	for	for	ADP
ejpam-2779	160	3	any	any	DET
ejpam-2779	160	4	x	x	SYM
ejpam-2779	160	5	∈	∈	PROPN
ejpam-2779	160	6	a	a	PRON
ejpam-2779	160	7	,	,	PUNCT
ejpam-2779	160	8	0	0	NUM
ejpam-2779	160	9	∗	∗	NOUN
ejpam-2779	160	10	(	(	PUNCT
ejpam-2779	160	11	0	0	NUM
ejpam-2779	160	12	◦	◦	NOUN
ejpam-2779	160	13	x	x	SYM
ejpam-2779	160	14	)	)	PUNCT
ejpam-2779	160	15	∈m(a	∈m(a	PROPN
ejpam-2779	160	16	)	)	PUNCT
ejpam-2779	160	17	and	and	CCONJ
ejpam-2779	160	18	0	0	NUM
ejpam-2779	160	19	◦	◦	NOUN
ejpam-2779	160	20	(	(	PUNCT
ejpam-2779	160	21	0	0	NUM
ejpam-2779	160	22	∗	∗	NOUN
ejpam-2779	160	23	x	x	NOUN
ejpam-2779	160	24	)	)	PUNCT
ejpam-2779	160	25	∈m(a	∈m(a	PROPN
ejpam-2779	160	26	)	)	PUNCT
ejpam-2779	160	27	.	.	PUNCT
ejpam-2779	161	1	proof	proof	NOUN
ejpam-2779	161	2	.	.	PUNCT
ejpam-2779	162	1	let	let	VERB
ejpam-2779	162	2	x	x	PUNCT
ejpam-2779	162	3	∈	∈	VERB
ejpam-2779	162	4	a.	a.	NOUN
ejpam-2779	162	5	in	in	ADP
ejpam-2779	162	6	order	order	NOUN
ejpam-2779	162	7	to	to	PART
ejpam-2779	162	8	prove	prove	VERB
ejpam-2779	162	9	0	0	NUM
ejpam-2779	162	10	◦	◦	NOUN
ejpam-2779	162	11	(	(	PUNCT
ejpam-2779	162	12	0	0	NUM
ejpam-2779	162	13	∗	∗	NOUN
ejpam-2779	162	14	x	x	NOUN
ejpam-2779	162	15	)	)	PUNCT
ejpam-2779	162	16	∈	∈	PROPN
ejpam-2779	162	17	m(a	m(a	PROPN
ejpam-2779	162	18	)	)	PUNCT
ejpam-2779	162	19	,	,	PUNCT
ejpam-2779	162	20	we	we	PRON
ejpam-2779	162	21	assume	assume	VERB
ejpam-2779	162	22	y	y	PROPN
ejpam-2779	162	23	≤	≤	NOUN
ejpam-2779	162	24	0	0	PUNCT
ejpam-2779	163	1	◦	◦	NOUN
ejpam-2779	163	2	(	(	PUNCT
ejpam-2779	163	3	0	0	NUM
ejpam-2779	163	4	∗	∗	NOUN
ejpam-2779	163	5	x	x	NOUN
ejpam-2779	163	6	)	)	PUNCT
ejpam-2779	163	7	.	.	PUNCT
ejpam-2779	164	1	then	then	ADV
ejpam-2779	164	2	y	y	PROPN
ejpam-2779	164	3	◦	◦	NOUN
ejpam-2779	164	4	(	(	PUNCT
ejpam-2779	164	5	0	0	NUM
ejpam-2779	164	6	◦	◦	NOUN
ejpam-2779	164	7	(	(	PUNCT
ejpam-2779	164	8	0	0	NUM
ejpam-2779	164	9	∗	∗	NOUN
ejpam-2779	164	10	x	x	NOUN
ejpam-2779	164	11	)	)	PUNCT
ejpam-2779	164	12	)	)	PUNCT
ejpam-2779	165	1	=	=	PUNCT
ejpam-2779	165	2	0	0	X
ejpam-2779	165	3	.	.	PUNCT
ejpam-2779	166	1	by	by	ADP
ejpam-2779	166	2	(	(	PUNCT
ejpam-2779	166	3	p4	p4	ADJ
ejpam-2779	166	4	)	)	PUNCT
ejpam-2779	166	5	and	and	CCONJ
ejpam-2779	166	6	(	(	PUNCT
ejpam-2779	166	7	p9	p9	PROPN
ejpam-2779	166	8	)	)	PUNCT
ejpam-2779	166	9	of	of	ADP
ejpam-2779	166	10	proposition	proposition	NOUN
ejpam-2779	166	11	3.3	3.3	NUM
ejpam-2779	166	12	,	,	PUNCT
ejpam-2779	166	13	we	we	PRON
ejpam-2779	166	14	have	have	VERB
ejpam-2779	166	15	(	(	PUNCT
ejpam-2779	166	16	0	0	NUM
ejpam-2779	166	17	◦	◦	NOUN
ejpam-2779	166	18	(	(	PUNCT
ejpam-2779	166	19	0	0	NUM
ejpam-2779	166	20	∗	∗	NOUN
ejpam-2779	166	21	x	x	NOUN
ejpam-2779	166	22	)	)	PUNCT
ejpam-2779	166	23	)	)	PUNCT
ejpam-2779	167	1	∗	∗	NOUN
ejpam-2779	167	2	y	y	NOUN
ejpam-2779	167	3	=	=	SYM
ejpam-2779	167	4	(	(	PUNCT
ejpam-2779	167	5	0	0	NUM
ejpam-2779	167	6	∗	∗	PROPN
ejpam-2779	167	7	y	y	NOUN
ejpam-2779	167	8	)	)	PUNCT
ejpam-2779	167	9	◦	◦	NOUN
ejpam-2779	167	10	(	(	PUNCT
ejpam-2779	167	11	0	0	NUM
ejpam-2779	167	12	∗	∗	NOUN
ejpam-2779	167	13	x	x	NOUN
ejpam-2779	167	14	)	)	PUNCT
ejpam-2779	168	1	=	=	SYM
ejpam-2779	168	2	(	(	PUNCT
ejpam-2779	168	3	(	(	PUNCT
ejpam-2779	168	4	y	y	PROPN
ejpam-2779	168	5	◦	◦	NOUN
ejpam-2779	168	6	(	(	PUNCT
ejpam-2779	168	7	0	0	NUM
ejpam-2779	168	8	◦	◦	NOUN
ejpam-2779	168	9	(	(	PUNCT
ejpam-2779	168	10	0	0	NUM
ejpam-2779	168	11	∗	∗	NOUN
ejpam-2779	168	12	x	x	NOUN
ejpam-2779	168	13	)	)	PUNCT
ejpam-2779	168	14	)	)	PUNCT
ejpam-2779	168	15	)	)	PUNCT
ejpam-2779	168	16	∗	∗	PROPN
ejpam-2779	168	17	y	y	NOUN
ejpam-2779	168	18	)	)	PUNCT
ejpam-2779	168	19	◦	◦	NOUN
ejpam-2779	168	20	(	(	PUNCT
ejpam-2779	168	21	0	0	NUM
ejpam-2779	168	22	∗	∗	NOUN
ejpam-2779	168	23	x	x	NOUN
ejpam-2779	168	24	)	)	PUNCT
ejpam-2779	168	25	=	=	SYM
ejpam-2779	168	26	(	(	PUNCT
ejpam-2779	168	27	(	(	PUNCT
ejpam-2779	168	28	y	y	PROPN
ejpam-2779	168	29	∗	∗	PROPN
ejpam-2779	168	30	y	y	PROPN
ejpam-2779	168	31	)	)	PUNCT
ejpam-2779	168	32	◦	◦	NOUN
ejpam-2779	168	33	(	(	PUNCT
ejpam-2779	168	34	(	(	PUNCT
ejpam-2779	168	35	0	0	NUM
ejpam-2779	168	36	◦	◦	NOUN
ejpam-2779	168	37	(	(	PUNCT
ejpam-2779	168	38	0	0	NUM
ejpam-2779	168	39	∗	∗	NOUN
ejpam-2779	168	40	x	x	NOUN
ejpam-2779	168	41	)	)	PUNCT
ejpam-2779	168	42	)	)	PUNCT
ejpam-2779	168	43	)	)	PUNCT
ejpam-2779	168	44	)	)	PUNCT
ejpam-2779	169	1	◦	◦	NOUN
ejpam-2779	169	2	(	(	PUNCT
ejpam-2779	169	3	0	0	NUM
ejpam-2779	169	4	∗	∗	NOUN
ejpam-2779	169	5	x	x	NOUN
ejpam-2779	169	6	)	)	PUNCT
ejpam-2779	169	7	=	=	SYM
ejpam-2779	169	8	(	(	PUNCT
ejpam-2779	169	9	0	0	NUM
ejpam-2779	169	10	◦	◦	NOUN
ejpam-2779	169	11	(	(	PUNCT
ejpam-2779	169	12	(	(	PUNCT
ejpam-2779	169	13	0	0	NUM
ejpam-2779	169	14	◦	◦	NOUN
ejpam-2779	169	15	(	(	PUNCT
ejpam-2779	169	16	0	0	NUM
ejpam-2779	169	17	∗	∗	NOUN
ejpam-2779	169	18	x	x	NOUN
ejpam-2779	169	19	)	)	PUNCT
ejpam-2779	169	20	)	)	PUNCT
ejpam-2779	169	21	)	)	PUNCT
ejpam-2779	169	22	)	)	PUNCT
ejpam-2779	170	1	◦	◦	NOUN
ejpam-2779	170	2	(	(	PUNCT
ejpam-2779	170	3	0	0	NUM
ejpam-2779	170	4	∗	∗	NOUN
ejpam-2779	170	5	x	x	NOUN
ejpam-2779	170	6	)	)	PUNCT
ejpam-2779	170	7	.	.	PUNCT
ejpam-2779	171	1	by	by	ADP
ejpam-2779	171	2	proposition	proposition	NOUN
ejpam-2779	171	3	2(iv	2(iv	NUM
ejpam-2779	171	4	)	)	PUNCT
ejpam-2779	171	5	,	,	PUNCT
ejpam-2779	171	6	0	0	NUM
ejpam-2779	171	7	◦	◦	NOUN
ejpam-2779	171	8	(	(	PUNCT
ejpam-2779	171	9	(	(	PUNCT
ejpam-2779	171	10	0	0	NUM
ejpam-2779	171	11	◦	◦	NOUN
ejpam-2779	171	12	(	(	PUNCT
ejpam-2779	171	13	0	0	NUM
ejpam-2779	171	14	∗	∗	NOUN
ejpam-2779	171	15	x	x	NOUN
ejpam-2779	171	16	)	)	PUNCT
ejpam-2779	171	17	)	)	PUNCT
ejpam-2779	171	18	)	)	PUNCT
ejpam-2779	172	1	=	=	PUNCT
ejpam-2779	172	2	(	(	PUNCT
ejpam-2779	172	3	0	0	NUM
ejpam-2779	172	4	∗	∗	NOUN
ejpam-2779	172	5	0	0	NUM
ejpam-2779	172	6	)	)	PUNCT
ejpam-2779	172	7	∗	∗	NOUN
ejpam-2779	172	8	(	(	PUNCT
ejpam-2779	172	9	0	0	NUM
ejpam-2779	172	10	◦	◦	NOUN
ejpam-2779	172	11	(	(	PUNCT
ejpam-2779	172	12	0	0	NUM
ejpam-2779	172	13	∗	∗	NOUN
ejpam-2779	172	14	x	x	NOUN
ejpam-2779	172	15	)	)	PUNCT
ejpam-2779	172	16	)	)	PUNCT
ejpam-2779	173	1	=	=	SYM
ejpam-2779	173	2	0	0	NUM
ejpam-2779	173	3	∗	∗	NOUN
ejpam-2779	173	4	(	(	PUNCT
ejpam-2779	173	5	0	0	NUM
ejpam-2779	173	6	◦	◦	NOUN
ejpam-2779	173	7	(	(	PUNCT
ejpam-2779	173	8	0	0	NUM
ejpam-2779	173	9	∗	∗	NOUN
ejpam-2779	173	10	x	x	NOUN
ejpam-2779	173	11	)	)	PUNCT
ejpam-2779	173	12	)	)	PUNCT
ejpam-2779	174	1	=	=	SYM
ejpam-2779	174	2	0	0	NUM
ejpam-2779	174	3	∗	∗	NOUN
ejpam-2779	174	4	x.	x.	NOUN
ejpam-2779	174	5	hence	hence	ADV
ejpam-2779	174	6	(	(	PUNCT
ejpam-2779	174	7	0	0	NUM
ejpam-2779	174	8	◦	◦	NOUN
ejpam-2779	174	9	(	(	PUNCT
ejpam-2779	174	10	0	0	NUM
ejpam-2779	174	11	∗	∗	NOUN
ejpam-2779	174	12	x	x	NOUN
ejpam-2779	174	13	)	)	PUNCT
ejpam-2779	174	14	)	)	PUNCT
ejpam-2779	174	15	∗	∗	NOUN
ejpam-2779	174	16	y	y	NOUN
ejpam-2779	174	17	=	=	SYM
ejpam-2779	174	18	(	(	PUNCT
ejpam-2779	174	19	0	0	NUM
ejpam-2779	174	20	◦	◦	NOUN
ejpam-2779	174	21	(	(	PUNCT
ejpam-2779	174	22	(	(	PUNCT
ejpam-2779	174	23	0	0	NUM
ejpam-2779	174	24	◦	◦	NOUN
ejpam-2779	174	25	(	(	PUNCT
ejpam-2779	174	26	0	0	NUM
ejpam-2779	174	27	∗	∗	NOUN
ejpam-2779	174	28	x	x	NOUN
ejpam-2779	174	29	)	)	PUNCT
ejpam-2779	174	30	)	)	PUNCT
ejpam-2779	174	31	)	)	PUNCT
ejpam-2779	174	32	)	)	PUNCT
ejpam-2779	175	1	◦	◦	NOUN
ejpam-2779	175	2	(	(	PUNCT
ejpam-2779	175	3	0	0	NUM
ejpam-2779	175	4	∗	∗	NOUN
ejpam-2779	175	5	x	x	NOUN
ejpam-2779	175	6	)	)	PUNCT
ejpam-2779	175	7	=	=	SYM
ejpam-2779	175	8	(	(	PUNCT
ejpam-2779	175	9	0	0	NUM
ejpam-2779	175	10	∗	∗	NOUN
ejpam-2779	175	11	x	x	NOUN
ejpam-2779	175	12	)	)	PUNCT
ejpam-2779	175	13	◦	◦	NOUN
ejpam-2779	175	14	(	(	PUNCT
ejpam-2779	175	15	0	0	NUM
ejpam-2779	175	16	∗	∗	NOUN
ejpam-2779	175	17	x	x	NOUN
ejpam-2779	175	18	)	)	PUNCT
ejpam-2779	175	19	=	=	SYM
ejpam-2779	175	20	0	0	X
ejpam-2779	175	21	.	.	PUNCT
ejpam-2779	176	1	this	this	PRON
ejpam-2779	176	2	shows	show	VERB
ejpam-2779	176	3	that	that	SCONJ
ejpam-2779	176	4	0	0	NUM
ejpam-2779	176	5	◦	◦	NOUN
ejpam-2779	176	6	(	(	PUNCT
ejpam-2779	176	7	0	0	NUM
ejpam-2779	176	8	∗	∗	NOUN
ejpam-2779	176	9	x	x	NOUN
ejpam-2779	176	10	)	)	PUNCT
ejpam-2779	176	11	≤	≤	NOUN
ejpam-2779	176	12	y	y	NOUN
ejpam-2779	176	13	and	and	CCONJ
ejpam-2779	176	14	hence	hence	ADV
ejpam-2779	176	15	y	y	PROPN
ejpam-2779	176	16	=	=	SYM
ejpam-2779	176	17	0	0	NUM
ejpam-2779	176	18	◦	◦	NOUN
ejpam-2779	176	19	(	(	PUNCT
ejpam-2779	176	20	0	0	NUM
ejpam-2779	176	21	∗	∗	NOUN
ejpam-2779	176	22	x	x	NOUN
ejpam-2779	176	23	)	)	PUNCT
ejpam-2779	176	24	.	.	PUNCT
ejpam-2779	177	1	similarly	similarly	ADV
ejpam-2779	177	2	we	we	PRON
ejpam-2779	177	3	can	can	AUX
ejpam-2779	177	4	prove	prove	VERB
ejpam-2779	177	5	0	0	NUM
ejpam-2779	177	6	∗	∗	NOUN
ejpam-2779	177	7	(	(	PUNCT
ejpam-2779	177	8	0	0	NUM
ejpam-2779	177	9	◦	◦	NOUN
ejpam-2779	177	10	x	x	SYM
ejpam-2779	177	11	)	)	PUNCT
ejpam-2779	177	12	∈m(a	∈m(a	PROPN
ejpam-2779	177	13	)	)	PUNCT
ejpam-2779	177	14	.	.	PUNCT
ejpam-2779	178	1	corollary	corollary	ADJ
ejpam-2779	178	2	2	2	NUM
ejpam-2779	178	3	.	.	PUNCT
ejpam-2779	179	1	let	let	VERB
ejpam-2779	179	2	a	a	PRON
ejpam-2779	179	3	be	be	AUX
ejpam-2779	179	4	a	a	DET
ejpam-2779	179	5	pseudo	pseudo	NOUN
ejpam-2779	179	6	-	-	ADJ
ejpam-2779	179	7	bci	bci	ADJ
ejpam-2779	179	8	algebra	algebra	NOUN
ejpam-2779	179	9	.	.	PUNCT
ejpam-2779	180	1	then	then	ADV
ejpam-2779	180	2	for	for	ADP
ejpam-2779	180	3	any	any	DET
ejpam-2779	180	4	x	x	SYM
ejpam-2779	180	5	∈	∈	PROPN
ejpam-2779	180	6	a	a	DET
ejpam-2779	180	7	,	,	PUNCT
ejpam-2779	180	8	(	(	PUNCT
ejpam-2779	180	9	0	0	NUM
ejpam-2779	180	10	◦	◦	NOUN
ejpam-2779	180	11	x	x	SYM
ejpam-2779	180	12	)	)	PUNCT
ejpam-2779	180	13	∈	∈	PROPN
ejpam-2779	180	14	m(a	m(a	PROPN
ejpam-2779	180	15	)	)	PUNCT
ejpam-2779	180	16	and	and	CCONJ
ejpam-2779	180	17	(	(	PUNCT
ejpam-2779	180	18	0	0	NUM
ejpam-2779	180	19	∗	∗	NOUN
ejpam-2779	180	20	x	x	NOUN
ejpam-2779	180	21	)	)	PUNCT
ejpam-2779	180	22	∈m(a	∈m(a	PROPN
ejpam-2779	180	23	)	)	PUNCT
ejpam-2779	180	24	.	.	PUNCT
ejpam-2779	181	1	proof	proof	NOUN
ejpam-2779	181	2	.	.	PUNCT
ejpam-2779	182	1	since	since	SCONJ
ejpam-2779	182	2	0	0	NUM
ejpam-2779	182	3	∗	∗	NOUN
ejpam-2779	182	4	x	x	X
ejpam-2779	182	5	=	=	SYM
ejpam-2779	182	6	0	0	NUM
ejpam-2779	182	7	∗	∗	NOUN
ejpam-2779	182	8	(	(	PUNCT
ejpam-2779	182	9	0	0	NUM
ejpam-2779	182	10	◦	◦	NOUN
ejpam-2779	182	11	(	(	PUNCT
ejpam-2779	182	12	0	0	NUM
ejpam-2779	182	13	∗	∗	NOUN
ejpam-2779	182	14	x	x	NOUN
ejpam-2779	182	15	)	)	PUNCT
ejpam-2779	182	16	)	)	PUNCT
ejpam-2779	182	17	and	and	CCONJ
ejpam-2779	182	18	0	0	NUM
ejpam-2779	182	19	◦	◦	NOUN
ejpam-2779	182	20	x	x	SYM
ejpam-2779	182	21	=	=	SYM
ejpam-2779	182	22	0	0	NUM
ejpam-2779	182	23	◦	◦	NOUN
ejpam-2779	182	24	(	(	PUNCT
ejpam-2779	182	25	0	0	NUM
ejpam-2779	182	26	∗	∗	NOUN
ejpam-2779	182	27	(	(	PUNCT
ejpam-2779	182	28	0	0	NUM
ejpam-2779	182	29	◦	◦	NOUN
ejpam-2779	182	30	x	x	NOUN
ejpam-2779	182	31	)	)	PUNCT
ejpam-2779	182	32	)	)	PUNCT
ejpam-2779	182	33	,	,	PUNCT
ejpam-2779	182	34	we	we	PRON
ejpam-2779	182	35	have	have	VERB
ejpam-2779	182	36	0	0	NUM
ejpam-2779	182	37	∗	∗	NOUN
ejpam-2779	182	38	x	x	PUNCT
ejpam-2779	182	39	∈m(a	∈m(a	NOUN
ejpam-2779	182	40	)	)	PUNCT
ejpam-2779	182	41	and	and	CCONJ
ejpam-2779	182	42	0	0	NUM
ejpam-2779	182	43	◦	◦	NOUN
ejpam-2779	182	44	x	x	SYM
ejpam-2779	182	45	∈m(a	∈m(a	NOUN
ejpam-2779	182	46	)	)	PUNCT
ejpam-2779	182	47	by	by	ADP
ejpam-2779	182	48	proposition	proposition	NOUN
ejpam-2779	182	49	7	7	NUM
ejpam-2779	182	50	.	.	PUNCT
ejpam-2779	182	51	by	by	ADP
ejpam-2779	182	52	propositions	proposition	NOUN
ejpam-2779	182	53	6	6	NUM
ejpam-2779	182	54	and	and	CCONJ
ejpam-2779	182	55	7	7	NUM
ejpam-2779	182	56	,	,	PUNCT
ejpam-2779	182	57	we	we	PRON
ejpam-2779	182	58	have	have	VERB
ejpam-2779	182	59	0	0	NUM
ejpam-2779	182	60	∗	∗	NOUN
ejpam-2779	182	61	(	(	PUNCT
ejpam-2779	182	62	0	0	NUM
ejpam-2779	182	63	◦	◦	NOUN
ejpam-2779	182	64	x	x	NOUN
ejpam-2779	182	65	)	)	PUNCT
ejpam-2779	182	66	=	=	SYM
ejpam-2779	182	67	0	0	NUM
ejpam-2779	183	1	◦	◦	NOUN
ejpam-2779	183	2	(	(	PUNCT
ejpam-2779	183	3	0	0	NUM
ejpam-2779	183	4	∗x	∗x	NOUN
ejpam-2779	183	5	)	)	PUNCT
ejpam-2779	183	6	∈m(a	∈m(a	NOUN
ejpam-2779	183	7	)	)	PUNCT
ejpam-2779	183	8	for	for	ADP
ejpam-2779	183	9	all	all	DET
ejpam-2779	183	10	x	x	SYM
ejpam-2779	183	11	∈	∈	PROPN
ejpam-2779	183	12	a.	a.	NOUN
ejpam-2779	183	13	denote	denote	NOUN
ejpam-2779	183	14	ax	ax	NOUN
ejpam-2779	183	15	=	=	SYM
ejpam-2779	183	16	0	0	NUM
ejpam-2779	183	17	∗	∗	NOUN
ejpam-2779	183	18	(	(	PUNCT
ejpam-2779	183	19	0	0	NUM
ejpam-2779	183	20	◦	◦	NOUN
ejpam-2779	183	21	x	x	NOUN
ejpam-2779	183	22	)	)	PUNCT
ejpam-2779	183	23	=	=	SYM
ejpam-2779	183	24	0	0	NUM
ejpam-2779	183	25	◦	◦	NOUN
ejpam-2779	183	26	(	(	PUNCT
ejpam-2779	183	27	0	0	NUM
ejpam-2779	183	28	∗	∗	NOUN
ejpam-2779	183	29	x	x	NOUN
ejpam-2779	183	30	)	)	PUNCT
ejpam-2779	183	31	,	,	PUNCT
ejpam-2779	183	32	for	for	ADP
ejpam-2779	183	33	x	x	PROPN
ejpam-2779	183	34	∈	∈	PROPN
ejpam-2779	183	35	a.	a.	NOUN
ejpam-2779	183	36	then	then	ADV
ejpam-2779	183	37	ax	ax	ADJ
ejpam-2779	183	38	∈m(a	∈m(a	PROPN
ejpam-2779	183	39	)	)	PUNCT
ejpam-2779	183	40	and	and	CCONJ
ejpam-2779	183	41	x	x	PUNCT
ejpam-2779	183	42	∈	∈	NOUN
ejpam-2779	183	43	v	v	NOUN
ejpam-2779	183	44	(	(	PUNCT
ejpam-2779	183	45	ax	ax	NOUN
ejpam-2779	183	46	)	)	PUNCT
ejpam-2779	183	47	.	.	PUNCT
ejpam-2779	184	1	using	use	VERB
ejpam-2779	184	2	above	above	ADP
ejpam-2779	184	3	arguments	argument	NOUN
ejpam-2779	184	4	we	we	PRON
ejpam-2779	184	5	can	can	AUX
ejpam-2779	184	6	get	get	VERB
ejpam-2779	184	7	the	the	DET
ejpam-2779	184	8	structure	structure	NOUN
ejpam-2779	184	9	of	of	ADP
ejpam-2779	184	10	a	a	DET
ejpam-2779	184	11	pseudo	pseudo	NOUN
ejpam-2779	184	12	-	-	ADJ
ejpam-2779	184	13	bci	bci	ADJ
ejpam-2779	184	14	algebra	algebra	NOUN
ejpam-2779	184	15	.	.	PUNCT
ejpam-2779	185	1	theorem	theorem	NOUN
ejpam-2779	185	2	1	1	NUM
ejpam-2779	185	3	.	.	PUNCT
ejpam-2779	186	1	let	let	VERB
ejpam-2779	186	2	a	a	PRON
ejpam-2779	186	3	be	be	AUX
ejpam-2779	186	4	a	a	DET
ejpam-2779	186	5	pseudo	pseudo	NOUN
ejpam-2779	186	6	-	-	ADJ
ejpam-2779	186	7	bci	bci	ADJ
ejpam-2779	186	8	algebra	algebra	NOUN
ejpam-2779	186	9	.	.	PUNCT
ejpam-2779	187	1	then	then	ADV
ejpam-2779	187	2	{	{	PUNCT
ejpam-2779	187	3	v	v	NOUN
ejpam-2779	187	4	(	(	PUNCT
ejpam-2779	187	5	a	a	NOUN
ejpam-2779	187	6	)	)	PUNCT
ejpam-2779	187	7	|	|	ADV
ejpam-2779	187	8	a	a	DET
ejpam-2779	187	9	∈m(a	∈m(a	NOUN
ejpam-2779	187	10	)	)	PUNCT
ejpam-2779	187	11	}	}	PUNCT
ejpam-2779	187	12	forms	form	VERB
ejpam-2779	187	13	a	a	DET
ejpam-2779	187	14	partition	partition	NOUN
ejpam-2779	187	15	of	of	ADP
ejpam-2779	187	16	a	a	PRON
ejpam-2779	187	17	,	,	PUNCT
ejpam-2779	187	18	that	that	ADV
ejpam-2779	187	19	is	is	ADV
ejpam-2779	187	20	,	,	PUNCT
ejpam-2779	187	21	a	a	DET
ejpam-2779	187	22	=	=	SYM
ejpam-2779	187	23	∪a∈m(a)v	∪a∈m(a)v	ADJ
ejpam-2779	187	24	(	(	PUNCT
ejpam-2779	187	25	a	a	NOUN
ejpam-2779	187	26	)	)	PUNCT
ejpam-2779	187	27	and	and	CCONJ
ejpam-2779	187	28	v	v	X
ejpam-2779	187	29	(	(	PUNCT
ejpam-2779	187	30	a	a	NOUN
ejpam-2779	187	31	)	)	PUNCT
ejpam-2779	187	32	∩	∩	ADJ
ejpam-2779	187	33	v	v	ADP
ejpam-2779	187	34	(	(	PUNCT
ejpam-2779	187	35	b	b	NOUN
ejpam-2779	187	36	)	)	PUNCT
ejpam-2779	187	37	=	=	NOUN
ejpam-2779	187	38	∅	∅	NOUN
ejpam-2779	187	39	for	for	ADP
ejpam-2779	187	40	all	all	DET
ejpam-2779	187	41	a	a	DET
ejpam-2779	187	42	,	,	PUNCT
ejpam-2779	187	43	b	b	NOUN
ejpam-2779	187	44	∈m(a	∈m(a	NOUN
ejpam-2779	187	45	)	)	PUNCT
ejpam-2779	187	46	and	and	CCONJ
ejpam-2779	187	47	a	a	DET
ejpam-2779	187	48	6=	6=	PROPN
ejpam-2779	187	49	b.	b.	PROPN
ejpam-2779	187	50	3	3	NUM
ejpam-2779	187	51	.	.	PUNCT
ejpam-2779	187	52	local	local	ADJ
ejpam-2779	187	53	bounded	bounded	ADJ
ejpam-2779	187	54	pseudo	pseudo	NOUN
ejpam-2779	187	55	-	-	ADJ
ejpam-2779	187	56	bci	bci	ADJ
ejpam-2779	187	57	algebras	algebra	NOUN
ejpam-2779	187	58	let	let	VERB
ejpam-2779	187	59	a	a	PRON
ejpam-2779	187	60	be	be	AUX
ejpam-2779	187	61	a	a	DET
ejpam-2779	187	62	pseudo	pseudo	NOUN
ejpam-2779	187	63	-	-	ADJ
ejpam-2779	187	64	bci	bci	ADJ
ejpam-2779	187	65	algebra	algebra	NOUN
ejpam-2779	187	66	.	.	PUNCT
ejpam-2779	188	1	for	for	ADP
ejpam-2779	188	2	a	a	DET
ejpam-2779	188	3	∈m(a	∈m(a	NOUN
ejpam-2779	188	4	)	)	PUNCT
ejpam-2779	188	5	,	,	PUNCT
ejpam-2779	188	6	if	if	SCONJ
ejpam-2779	188	7	there	there	PRON
ejpam-2779	188	8	is	be	VERB
ejpam-2779	188	9	an	an	DET
ejpam-2779	188	10	element	element	NOUN
ejpam-2779	188	11	1a	1a	PROPN
ejpam-2779	188	12	∈	∈	PROPN
ejpam-2779	188	13	v	v	ADP
ejpam-2779	188	14	(	(	PUNCT
ejpam-2779	188	15	a	a	NOUN
ejpam-2779	188	16	)	)	PUNCT
ejpam-2779	188	17	\	\	NOUN
ejpam-2779	188	18	{	{	PUNCT
ejpam-2779	188	19	a	a	NOUN
ejpam-2779	188	20	}	}	PUNCT
ejpam-2779	188	21	such	such	ADJ
ejpam-2779	188	22	that	that	PRON
ejpam-2779	188	23	for	for	ADP
ejpam-2779	188	24	all	all	PRON
ejpam-2779	188	25	x	x	SYM
ejpam-2779	188	26	∈	∈	PROPN
ejpam-2779	188	27	v	v	NOUN
ejpam-2779	188	28	(	(	PUNCT
ejpam-2779	188	29	a	a	NOUN
ejpam-2779	188	30	)	)	PUNCT
ejpam-2779	188	31	,	,	PUNCT
ejpam-2779	188	32	x	x	PUNCT
ejpam-2779	188	33	≤	≤	X
ejpam-2779	188	34	1a	1a	NOUN
ejpam-2779	188	35	,	,	PUNCT
ejpam-2779	188	36	then	then	ADV
ejpam-2779	188	37	1a	1a	PROPN
ejpam-2779	188	38	is	be	AUX
ejpam-2779	188	39	called	call	VERB
ejpam-2779	188	40	the	the	DET
ejpam-2779	188	41	local	local	ADJ
ejpam-2779	188	42	unit	unit	NOUN
ejpam-2779	188	43	of	of	ADP
ejpam-2779	188	44	v	v	NOUN
ejpam-2779	188	45	(	(	PUNCT
ejpam-2779	188	46	a	a	NOUN
ejpam-2779	188	47	)	)	PUNCT
ejpam-2779	188	48	.	.	PUNCT
ejpam-2779	189	1	note	note	VERB
ejpam-2779	189	2	that	that	SCONJ
ejpam-2779	189	3	1a	1a	NOUN
ejpam-2779	189	4	is	be	AUX
ejpam-2779	189	5	unique	unique	ADJ
ejpam-2779	189	6	.	.	PUNCT
ejpam-2779	190	1	x.l	x.l	PROPN
ejpam-2779	190	2	.	.	PUNCT
ejpam-2779	191	1	xin	xin	PROPN
ejpam-2779	191	2	,	,	PUNCT
ejpam-2779	191	3	y.j	y.j	PROPN
ejpam-2779	191	4	.	.	PUNCT
ejpam-2779	191	5	li	li	PROPN
ejpam-2779	191	6	,	,	PUNCT
ejpam-2779	191	7	y.l	y.l	PROPN
ejpam-2779	191	8	.	.	PROPN
ejpam-2779	191	9	fu	fu	PROPN
ejpam-2779	191	10	/	/	SYM
ejpam-2779	191	11	eur	eur	PROPN
ejpam-2779	191	12	.	.	PUNCT
ejpam-2779	192	1	j.	j.	PROPN
ejpam-2779	192	2	pure	pure	PROPN
ejpam-2779	192	3	appl	appl	PROPN
ejpam-2779	192	4	.	.	PROPN
ejpam-2779	192	5	math	math	PROPN
ejpam-2779	192	6	,	,	PUNCT
ejpam-2779	192	7	10	10	NUM
ejpam-2779	192	8	(	(	PUNCT
ejpam-2779	192	9	3	3	NUM
ejpam-2779	192	10	)	)	PUNCT
ejpam-2779	192	11	(	(	PUNCT
ejpam-2779	192	12	2017	2017	NUM
ejpam-2779	192	13	)	)	PUNCT
ejpam-2779	192	14	,	,	PUNCT
ejpam-2779	192	15	455	455	NUM
ejpam-2779	192	16	-	-	SYM
ejpam-2779	192	17	472	472	NUM
ejpam-2779	192	18	461	461	NUM
ejpam-2779	192	19	definition	definition	NOUN
ejpam-2779	192	20	4	4	NUM
ejpam-2779	192	21	.	.	PUNCT
ejpam-2779	193	1	let	let	VERB
ejpam-2779	193	2	a	a	PRON
ejpam-2779	193	3	be	be	AUX
ejpam-2779	193	4	a	a	DET
ejpam-2779	193	5	pseudo	pseudo	NOUN
ejpam-2779	193	6	-	-	ADJ
ejpam-2779	193	7	bci	bci	ADJ
ejpam-2779	193	8	algebra	algebra	NOUN
ejpam-2779	193	9	.	.	PUNCT
ejpam-2779	194	1	if	if	SCONJ
ejpam-2779	194	2	for	for	ADP
ejpam-2779	194	3	every	every	DET
ejpam-2779	194	4	a	a	DET
ejpam-2779	194	5	∈	∈	PROPN
ejpam-2779	194	6	m(a	m(a	PROPN
ejpam-2779	194	7	)	)	PUNCT
ejpam-2779	194	8	,	,	PUNCT
ejpam-2779	194	9	v	v	X
ejpam-2779	194	10	(	(	PUNCT
ejpam-2779	194	11	a	a	NOUN
ejpam-2779	194	12	)	)	PUNCT
ejpam-2779	194	13	has	have	VERB
ejpam-2779	194	14	a	a	DET
ejpam-2779	194	15	local	local	ADJ
ejpam-2779	194	16	unit	unit	NOUN
ejpam-2779	194	17	,	,	PUNCT
ejpam-2779	194	18	then	then	ADV
ejpam-2779	194	19	a	a	PRON
ejpam-2779	194	20	is	be	AUX
ejpam-2779	194	21	called	call	VERB
ejpam-2779	194	22	a	a	DET
ejpam-2779	194	23	local	local	ADJ
ejpam-2779	194	24	bounded	bounded	ADJ
ejpam-2779	194	25	pseudo	pseudo	NOUN
ejpam-2779	194	26	-	-	ADJ
ejpam-2779	194	27	bci	bci	ADJ
ejpam-2779	194	28	algebra	algebra	NOUN
ejpam-2779	194	29	.	.	PUNCT
ejpam-2779	195	1	for	for	ADP
ejpam-2779	195	2	convenience	convenience	NOUN
ejpam-2779	195	3	we	we	PRON
ejpam-2779	195	4	denote	denote	VERB
ejpam-2779	195	5	it	it	PRON
ejpam-2779	195	6	by	by	ADP
ejpam-2779	195	7	lbp	lbp	PROPN
ejpam-2779	195	8	-	-	PUNCT
ejpam-2779	195	9	bci	bci	PROPN
ejpam-2779	195	10	algebra	algebra	NOUN
ejpam-2779	195	11	.	.	PUNCT
ejpam-2779	196	1	note	note	VERB
ejpam-2779	196	2	that	that	SCONJ
ejpam-2779	196	3	the	the	DET
ejpam-2779	196	4	pseudo	pseudo	NOUN
ejpam-2779	196	5	-	-	ADJ
ejpam-2779	196	6	bci	bci	ADJ
ejpam-2779	196	7	algebras	algebra	NOUN
ejpam-2779	196	8	given	give	VERB
ejpam-2779	196	9	in	in	ADP
ejpam-2779	196	10	examples	example	NOUN
ejpam-2779	196	11	1	1	NUM
ejpam-2779	196	12	and	and	CCONJ
ejpam-2779	196	13	2	2	NUM
ejpam-2779	196	14	are	be	AUX
ejpam-2779	196	15	local	local	ADJ
ejpam-2779	196	16	bounded	bounded	ADJ
ejpam-2779	196	17	pseudo	pseudo	NOUN
ejpam-2779	196	18	-	-	ADJ
ejpam-2779	196	19	bci	bci	ADJ
ejpam-2779	196	20	algebras	algebra	NOUN
ejpam-2779	196	21	.	.	PUNCT
ejpam-2779	197	1	in	in	ADP
ejpam-2779	197	2	examples	example	NOUN
ejpam-2779	197	3	1	1	NUM
ejpam-2779	197	4	,	,	PUNCT
ejpam-2779	197	5	m(a	m(a	NOUN
ejpam-2779	197	6	)	)	PUNCT
ejpam-2779	197	7	=	=	SYM
ejpam-2779	197	8	{	{	PUNCT
ejpam-2779	197	9	0	0	NUM
ejpam-2779	197	10	,	,	PUNCT
ejpam-2779	197	11	a	a	PRON
ejpam-2779	197	12	}	}	PUNCT
ejpam-2779	197	13	,	,	PUNCT
ejpam-2779	197	14	v	v	X
ejpam-2779	197	15	(	(	PUNCT
ejpam-2779	197	16	0	0	NUM
ejpam-2779	197	17	)	)	PUNCT
ejpam-2779	197	18	=	=	PRON
ejpam-2779	197	19	{	{	PUNCT
ejpam-2779	197	20	0	0	NUM
ejpam-2779	197	21	,	,	PUNCT
ejpam-2779	197	22	u	u	NOUN
ejpam-2779	197	23	,	,	PUNCT
ejpam-2779	197	24	v	v	NOUN
ejpam-2779	197	25	,	,	PUNCT
ejpam-2779	197	26	w	w	PROPN
ejpam-2779	197	27	,	,	PUNCT
ejpam-2779	197	28	t	t	PROPN
ejpam-2779	197	29	,	,	PUNCT
ejpam-2779	197	30	1	1	NUM
ejpam-2779	197	31	}	}	PUNCT
ejpam-2779	197	32	,	,	PUNCT
ejpam-2779	197	33	10	10	NUM
ejpam-2779	197	34	=	=	SYM
ejpam-2779	197	35	0	0	NUM
ejpam-2779	197	36	,	,	PUNCT
ejpam-2779	197	37	v	v	NOUN
ejpam-2779	197	38	(	(	PUNCT
ejpam-2779	197	39	a	a	NOUN
ejpam-2779	197	40	)	)	PUNCT
ejpam-2779	197	41	=	=	PRON
ejpam-2779	197	42	{	{	PUNCT
ejpam-2779	197	43	a	a	DET
ejpam-2779	197	44	,	,	PUNCT
ejpam-2779	197	45	b	b	NOUN
ejpam-2779	197	46	}	}	PUNCT
ejpam-2779	197	47	,	,	PUNCT
ejpam-2779	197	48	1a	1a	X
ejpam-2779	197	49	=	=	SYM
ejpam-2779	197	50	b.	b.	PROPN
ejpam-2779	197	51	in	in	ADP
ejpam-2779	197	52	examples	example	NOUN
ejpam-2779	197	53	2	2	NUM
ejpam-2779	197	54	,	,	PUNCT
ejpam-2779	197	55	m(a	m(a	NOUN
ejpam-2779	197	56	)	)	PUNCT
ejpam-2779	197	57	=	=	SYM
ejpam-2779	197	58	{	{	PUNCT
ejpam-2779	197	59	0	0	NUM
ejpam-2779	197	60	,	,	PUNCT
ejpam-2779	197	61	a	a	PRON
ejpam-2779	197	62	}	}	PUNCT
ejpam-2779	197	63	,	,	PUNCT
ejpam-2779	197	64	v	v	X
ejpam-2779	197	65	(	(	PUNCT
ejpam-2779	197	66	0	0	NUM
ejpam-2779	197	67	)	)	PUNCT
ejpam-2779	197	68	=	=	PRON
ejpam-2779	197	69	{	{	PUNCT
ejpam-2779	197	70	0	0	NUM
ejpam-2779	197	71	,	,	PUNCT
ejpam-2779	197	72	x	x	NOUN
ejpam-2779	197	73	,	,	PUNCT
ejpam-2779	197	74	y	y	PROPN
ejpam-2779	197	75	,	,	PUNCT
ejpam-2779	197	76	z	z	PROPN
ejpam-2779	197	77	,	,	PUNCT
ejpam-2779	197	78	1	1	NUM
ejpam-2779	197	79	}	}	PUNCT
ejpam-2779	197	80	,	,	PUNCT
ejpam-2779	197	81	10	10	NUM
ejpam-2779	197	82	=	=	SYM
ejpam-2779	197	83	0	0	NUM
ejpam-2779	197	84	,	,	PUNCT
ejpam-2779	197	85	v	v	NOUN
ejpam-2779	197	86	(	(	PUNCT
ejpam-2779	197	87	a	a	NOUN
ejpam-2779	197	88	)	)	PUNCT
ejpam-2779	197	89	=	=	PRON
ejpam-2779	197	90	{	{	PUNCT
ejpam-2779	197	91	a	a	DET
ejpam-2779	197	92	,	,	PUNCT
ejpam-2779	197	93	b	b	NOUN
ejpam-2779	197	94	}	}	PUNCT
ejpam-2779	197	95	,	,	PUNCT
ejpam-2779	197	96	1a	1a	X
ejpam-2779	197	97	=	=	SYM
ejpam-2779	197	98	b.	b.	PROPN
ejpam-2779	197	99	in	in	ADP
ejpam-2779	197	100	the	the	DET
ejpam-2779	197	101	following	following	NOUN
ejpam-2779	197	102	,	,	PUNCT
ejpam-2779	197	103	a	a	PRON
ejpam-2779	197	104	shall	shall	AUX
ejpam-2779	197	105	mean	mean	VERB
ejpam-2779	197	106	a	a	DET
ejpam-2779	197	107	lbp	lbp	NOUN
ejpam-2779	197	108	-	-	PUNCT
ejpam-2779	197	109	bci	bci	NOUN
ejpam-2779	197	110	algebra	algebra	NOUN
ejpam-2779	197	111	unless	unless	SCONJ
ejpam-2779	197	112	otherwise	otherwise	ADV
ejpam-2779	197	113	specified	specify	VERB
ejpam-2779	197	114	.	.	PUNCT
ejpam-2779	198	1	we	we	PRON
ejpam-2779	198	2	define	define	VERB
ejpam-2779	198	3	two	two	NUM
ejpam-2779	198	4	negations	negation	NOUN
ejpam-2779	198	5	,	,	PUNCT
ejpam-2779	198	6	−	−	PROPN
ejpam-2779	198	7	and	and	CCONJ
ejpam-2779	198	8	∼	∼	NOUN
ejpam-2779	198	9	,	,	PUNCT
ejpam-2779	198	10	as	as	SCONJ
ejpam-2779	198	11	follows	follow	VERB
ejpam-2779	198	12	:	:	PUNCT
ejpam-2779	198	13	for	for	ADP
ejpam-2779	198	14	a	a	DET
ejpam-2779	198	15	∈m(a	∈m(a	NOUN
ejpam-2779	198	16	)	)	PUNCT
ejpam-2779	198	17	and	and	CCONJ
ejpam-2779	198	18	x	x	PUNCT
ejpam-2779	198	19	∈	∈	NOUN
ejpam-2779	198	20	v	v	ADP
ejpam-2779	198	21	(	(	PUNCT
ejpam-2779	198	22	a	a	NOUN
ejpam-2779	198	23	)	)	PUNCT
ejpam-2779	198	24	,	,	PUNCT
ejpam-2779	198	25	x−	x−	PROPN
ejpam-2779	198	26	.	.	PUNCT
ejpam-2779	199	1	=	=	PRON
ejpam-2779	199	2	1a	1a	PROPN
ejpam-2779	199	3	∗	∗	NOUN
ejpam-2779	199	4	x	x	PROPN
ejpam-2779	199	5	,	,	PUNCT
ejpam-2779	199	6	x∼	x∼	PROPN
ejpam-2779	199	7	.	.	PUNCT
ejpam-2779	200	1	=	=	PRON
ejpam-2779	200	2	1a	1a	NUM
ejpam-2779	200	3	◦	◦	NOUN
ejpam-2779	200	4	x.	x.	NOUN
ejpam-2779	200	5	proposition	proposition	NOUN
ejpam-2779	200	6	8	8	NUM
ejpam-2779	200	7	.	.	PUNCT
ejpam-2779	201	1	for	for	ADP
ejpam-2779	201	2	all	all	DET
ejpam-2779	201	3	x	x	NOUN
ejpam-2779	201	4	,	,	PUNCT
ejpam-2779	201	5	y	y	PROPN
ejpam-2779	201	6	∈	∈	PROPN
ejpam-2779	201	7	a	a	PRON
ejpam-2779	201	8	,	,	PUNCT
ejpam-2779	201	9	we	we	PRON
ejpam-2779	201	10	have	have	AUX
ejpam-2779	201	11	(	(	PUNCT
ejpam-2779	201	12	1	1	X
ejpam-2779	201	13	)	)	PUNCT
ejpam-2779	201	14	x−∼	x−∼	VERB
ejpam-2779	201	15	≤	≤	NUM
ejpam-2779	202	1	x	x	X
ejpam-2779	202	2	,	,	PUNCT
ejpam-2779	202	3	x∼−	x∼−	PROPN
ejpam-2779	202	4	≤	≤	NUM
ejpam-2779	202	5	x.	x.	NOUN
ejpam-2779	202	6	(	(	PUNCT
ejpam-2779	202	7	2	2	NUM
ejpam-2779	202	8	)	)	PUNCT
ejpam-2779	202	9	x	x	PUNCT
ejpam-2779	202	10	≤	≤	NUM
ejpam-2779	202	11	y	y	PROPN
ejpam-2779	202	12	⇒	⇒	VERB
ejpam-2779	202	13	y−	y−	PROPN
ejpam-2779	202	14	≤	≤	NOUN
ejpam-2779	202	15	x−	x−	PROPN
ejpam-2779	202	16	,	,	PUNCT
ejpam-2779	202	17	y∼	y∼	PROPN
ejpam-2779	202	18	≤	≤	PUNCT
ejpam-2779	202	19	x∼.	x∼.	NOUN
ejpam-2779	202	20	(	(	PUNCT
ejpam-2779	202	21	3	3	NUM
ejpam-2779	202	22	)	)	PUNCT
ejpam-2779	202	23	x−	x−	NOUN
ejpam-2779	203	1	=	=	SYM
ejpam-2779	203	2	x−∼−	x−∼−	PROPN
ejpam-2779	203	3	,	,	PUNCT
ejpam-2779	203	4	x∼	x∼	PROPN
ejpam-2779	203	5	=	=	PUNCT
ejpam-2779	204	1	x∼−∼.	x∼−∼.	PROPN
ejpam-2779	204	2	proof	proof	NOUN
ejpam-2779	204	3	.	.	PUNCT
ejpam-2779	205	1	(	(	PUNCT
ejpam-2779	205	2	1	1	X
ejpam-2779	205	3	)	)	PUNCT
ejpam-2779	205	4	by	by	ADP
ejpam-2779	205	5	(	(	PUNCT
ejpam-2779	205	6	i2	i2	PROPN
ejpam-2779	205	7	)	)	PUNCT
ejpam-2779	205	8	of	of	ADP
ejpam-2779	205	9	definition	definition	NOUN
ejpam-2779	205	10	1	1	NUM
ejpam-2779	205	11	,	,	PUNCT
ejpam-2779	205	12	we	we	PRON
ejpam-2779	205	13	have	have	VERB
ejpam-2779	205	14	x−∼	x−∼	ADJ
ejpam-2779	205	15	≤	≤	NUM
ejpam-2779	205	16	x	x	PUNCT
ejpam-2779	205	17	and	and	CCONJ
ejpam-2779	205	18	x∼−	x∼−	PROPN
ejpam-2779	205	19	≤	≤	NUM
ejpam-2779	205	20	x.	x.	NOUN
ejpam-2779	206	1	(	(	PUNCT
ejpam-2779	206	2	2	2	X
ejpam-2779	206	3	)	)	PUNCT
ejpam-2779	206	4	let	let	VERB
ejpam-2779	206	5	x	x	PUNCT
ejpam-2779	206	6	≤	≤	NOUN
ejpam-2779	206	7	y	y	NOUN
ejpam-2779	206	8	,	,	PUNCT
ejpam-2779	206	9	then	then	ADV
ejpam-2779	206	10	x	x	X
ejpam-2779	206	11	,	,	PUNCT
ejpam-2779	206	12	y	y	PROPN
ejpam-2779	206	13	∈	∈	PROPN
ejpam-2779	206	14	v	v	ADP
ejpam-2779	206	15	(	(	PUNCT
ejpam-2779	206	16	a	a	NOUN
ejpam-2779	206	17	)	)	PUNCT
ejpam-2779	206	18	for	for	ADP
ejpam-2779	206	19	some	some	PRON
ejpam-2779	206	20	a	a	DET
ejpam-2779	206	21	∈m(a	∈m(a	NOUN
ejpam-2779	206	22	)	)	PUNCT
ejpam-2779	206	23	.	.	PUNCT
ejpam-2779	207	1	hence	hence	ADV
ejpam-2779	207	2	(	(	PUNCT
ejpam-2779	207	3	1a	1a	X
ejpam-2779	207	4	◦	◦	NOUN
ejpam-2779	207	5	y)∗(1a	y)∗(1a	NOUN
ejpam-2779	207	6	◦	◦	NOUN
ejpam-2779	207	7	x	x	SYM
ejpam-2779	207	8	)	)	PUNCT
ejpam-2779	207	9	≤	≤	NUM
ejpam-2779	207	10	x	x	PUNCT
ejpam-2779	207	11	◦	◦	NOUN
ejpam-2779	207	12	y	y	NOUN
ejpam-2779	207	13	=	=	SYM
ejpam-2779	207	14	0	0	NUM
ejpam-2779	207	15	,	,	PUNCT
ejpam-2779	207	16	and	and	CCONJ
ejpam-2779	207	17	so	so	ADV
ejpam-2779	207	18	(	(	PUNCT
ejpam-2779	207	19	1a	1a	X
ejpam-2779	207	20	◦	◦	NOUN
ejpam-2779	207	21	y	y	NOUN
ejpam-2779	207	22	)	)	PUNCT
ejpam-2779	207	23	∗	∗	NOUN
ejpam-2779	207	24	(	(	PUNCT
ejpam-2779	207	25	1a	1a	X
ejpam-2779	207	26	◦	◦	NOUN
ejpam-2779	207	27	x	x	NOUN
ejpam-2779	207	28	)	)	PUNCT
ejpam-2779	207	29	=	=	SYM
ejpam-2779	208	1	0	0	X
ejpam-2779	208	2	.	.	PUNCT
ejpam-2779	209	1	it	it	PRON
ejpam-2779	209	2	follows	follow	VERB
ejpam-2779	209	3	that	that	SCONJ
ejpam-2779	209	4	1a	1a	NUM
ejpam-2779	209	5	◦	◦	VERB
ejpam-2779	209	6	y	y	PROPN
ejpam-2779	209	7	≤	≤	PROPN
ejpam-2779	209	8	1a	1a	PROPN
ejpam-2779	209	9	◦	◦	NOUN
ejpam-2779	209	10	x	x	NOUN
ejpam-2779	209	11	,	,	PUNCT
ejpam-2779	209	12	or	or	CCONJ
ejpam-2779	209	13	y∼	y∼	PROPN
ejpam-2779	209	14	≤	≤	NOUN
ejpam-2779	209	15	x∼.	x∼.	VERB
ejpam-2779	209	16	similarly	similarly	ADV
ejpam-2779	209	17	we	we	PRON
ejpam-2779	209	18	can	can	AUX
ejpam-2779	209	19	prove	prove	VERB
ejpam-2779	209	20	y−	y−	NOUN
ejpam-2779	209	21	≤	≤	ADJ
ejpam-2779	210	1	x−.	x−.	ADV
ejpam-2779	210	2	(	(	PUNCT
ejpam-2779	210	3	3	3	NUM
ejpam-2779	210	4	)	)	PUNCT
ejpam-2779	210	5	by	by	ADP
ejpam-2779	210	6	(	(	PUNCT
ejpam-2779	210	7	1	1	NUM
ejpam-2779	210	8	)	)	PUNCT
ejpam-2779	210	9	,	,	PUNCT
ejpam-2779	210	10	we	we	PRON
ejpam-2779	210	11	have	have	VERB
ejpam-2779	210	12	x∼−	x∼−	PROPN
ejpam-2779	210	13	≤	≤	NUM
ejpam-2779	210	14	x.	x.	NOUN
ejpam-2779	210	15	replace	replace	VERB
ejpam-2779	210	16	x	x	PUNCT
ejpam-2779	210	17	by	by	ADP
ejpam-2779	210	18	x−	x−	PROPN
ejpam-2779	210	19	,	,	PUNCT
ejpam-2779	210	20	we	we	PRON
ejpam-2779	210	21	get	get	VERB
ejpam-2779	210	22	x−∼−	x−∼−	PROPN
ejpam-2779	210	23	≤	≤	NOUN
ejpam-2779	210	24	x−.	x−.	ADV
ejpam-2779	210	25	on	on	ADP
ejpam-2779	210	26	the	the	DET
ejpam-2779	210	27	other	other	ADJ
ejpam-2779	210	28	hand	hand	NOUN
ejpam-2779	210	29	,	,	PUNCT
ejpam-2779	210	30	x−∼	x−∼	ADV
ejpam-2779	210	31	≤	≤	NUM
ejpam-2779	210	32	x	x	PUNCT
ejpam-2779	210	33	implies	imply	VERB
ejpam-2779	210	34	x−	x−	PROPN
ejpam-2779	210	35	≤	≤	PROPN
ejpam-2779	210	36	x−∼−	x−∼−	PROPN
ejpam-2779	210	37	by	by	ADP
ejpam-2779	210	38	(	(	PUNCT
ejpam-2779	210	39	2	2	NUM
ejpam-2779	210	40	)	)	PUNCT
ejpam-2779	210	41	.	.	PUNCT
ejpam-2779	211	1	so	so	ADV
ejpam-2779	211	2	x−	x−	PROPN
ejpam-2779	212	1	=	=	SYM
ejpam-2779	212	2	x−∼−.	x−∼−.	PROPN
ejpam-2779	213	1	similarly	similarly	ADV
ejpam-2779	213	2	we	we	PRON
ejpam-2779	213	3	can	can	AUX
ejpam-2779	213	4	prove	prove	VERB
ejpam-2779	213	5	x∼	x∼	PROPN
ejpam-2779	213	6	=	=	PRON
ejpam-2779	214	1	x∼−∼.	x∼−∼.	PROPN
ejpam-2779	214	2	let	let	VERB
ejpam-2779	214	3	a	a	PRON
ejpam-2779	214	4	be	be	AUX
ejpam-2779	214	5	a	a	DET
ejpam-2779	214	6	pseudo	pseudo	NOUN
ejpam-2779	214	7	-	-	ADJ
ejpam-2779	214	8	bci	bci	ADJ
ejpam-2779	214	9	algebra	algebra	NOUN
ejpam-2779	214	10	.	.	PUNCT
ejpam-2779	215	1	for	for	ADP
ejpam-2779	215	2	any	any	DET
ejpam-2779	215	3	x	x	NOUN
ejpam-2779	215	4	,	,	PUNCT
ejpam-2779	215	5	y	y	PROPN
ejpam-2779	215	6	∈	∈	PROPN
ejpam-2779	215	7	a	a	PRON
ejpam-2779	215	8	,	,	PUNCT
ejpam-2779	215	9	define	define	VERB
ejpam-2779	215	10	x	x	SYM
ejpam-2779	215	11	∧1	∧1	NOUN
ejpam-2779	215	12	y	y	NOUN
ejpam-2779	215	13	.	.	PUNCT
ejpam-2779	216	1	=	=	PUNCT
ejpam-2779	216	2	y	y	PROPN
ejpam-2779	216	3	◦	◦	NOUN
ejpam-2779	216	4	(	(	PUNCT
ejpam-2779	216	5	y	y	PROPN
ejpam-2779	216	6	∗	∗	NOUN
ejpam-2779	216	7	x	x	NOUN
ejpam-2779	216	8	)	)	PUNCT
ejpam-2779	216	9	,	,	PUNCT
ejpam-2779	216	10	x	x	PUNCT
ejpam-2779	216	11	∧2	∧2	PROPN
ejpam-2779	216	12	y	y	NOUN
ejpam-2779	216	13	.	.	PUNCT
ejpam-2779	217	1	=	=	SYM
ejpam-2779	217	2	y	y	PROPN
ejpam-2779	217	3	∗	∗	NOUN
ejpam-2779	217	4	(	(	PUNCT
ejpam-2779	217	5	y	y	PROPN
ejpam-2779	217	6	◦	◦	NOUN
ejpam-2779	217	7	x	x	NOUN
ejpam-2779	217	8	)	)	PUNCT
ejpam-2779	217	9	.	.	PUNCT
ejpam-2779	218	1	proposition	proposition	NOUN
ejpam-2779	218	2	9	9	NUM
ejpam-2779	218	3	.	.	PUNCT
ejpam-2779	219	1	in	in	ADP
ejpam-2779	219	2	a	a	DET
ejpam-2779	219	3	the	the	DET
ejpam-2779	219	4	following	follow	VERB
ejpam-2779	219	5	properties	property	NOUN
ejpam-2779	219	6	hold	hold	VERB
ejpam-2779	219	7	:	:	PUNCT
ejpam-2779	219	8	(	(	PUNCT
ejpam-2779	219	9	1	1	X
ejpam-2779	219	10	)	)	PUNCT
ejpam-2779	219	11	ax	ax	NOUN
ejpam-2779	219	12	∧1	∧1	NOUN
ejpam-2779	219	13	x	x	NOUN
ejpam-2779	219	14	=	=	SYM
ejpam-2779	219	15	x	x	SYM
ejpam-2779	219	16	∧1	∧1	NOUN
ejpam-2779	219	17	ax	ax	NOUN
ejpam-2779	219	18	=	=	NOUN
ejpam-2779	219	19	ax	ax	NOUN
ejpam-2779	219	20	and	and	CCONJ
ejpam-2779	219	21	ax	ax	NOUN
ejpam-2779	219	22	∧2	∧2	NOUN
ejpam-2779	219	23	x	x	SYM
ejpam-2779	219	24	=	=	SYM
ejpam-2779	219	25	x	x	SYM
ejpam-2779	219	26	∧2	∧2	NOUN
ejpam-2779	219	27	ax	ax	NOUN
ejpam-2779	219	28	=	=	NOUN
ejpam-2779	219	29	ax	ax	NOUN
ejpam-2779	219	30	for	for	ADP
ejpam-2779	219	31	all	all	DET
ejpam-2779	219	32	x	x	SYM
ejpam-2779	219	33	∈	∈	NOUN
ejpam-2779	219	34	a.	a.	NOUN
ejpam-2779	219	35	(	(	PUNCT
ejpam-2779	219	36	2	2	NUM
ejpam-2779	219	37	)	)	PUNCT
ejpam-2779	219	38	x	x	NOUN
ejpam-2779	219	39	≤	≤	NUM
ejpam-2779	219	40	y	y	NOUN
ejpam-2779	219	41	implies	imply	VERB
ejpam-2779	219	42	y	y	PROPN
ejpam-2779	219	43	∧1	∧1	PROPN
ejpam-2779	219	44	x	x	NOUN
ejpam-2779	219	45	=	=	PUNCT
ejpam-2779	219	46	x	x	X
ejpam-2779	219	47	and	and	CCONJ
ejpam-2779	219	48	y	y	PROPN
ejpam-2779	219	49	∧2	∧2	PROPN
ejpam-2779	219	50	x	x	PUNCT
ejpam-2779	219	51	=	=	PUNCT
ejpam-2779	219	52	x.	x.	NOUN
ejpam-2779	219	53	(	(	PUNCT
ejpam-2779	219	54	3	3	NUM
ejpam-2779	219	55	)	)	PUNCT
ejpam-2779	219	56	x	x	X
ejpam-2779	219	57	∧1	∧1	X
ejpam-2779	219	58	x	x	X
ejpam-2779	219	59	=	=	PUNCT
ejpam-2779	219	60	x	x	X
ejpam-2779	219	61	and	and	CCONJ
ejpam-2779	219	62	x	x	ADJ
ejpam-2779	219	63	∧2	∧2	NOUN
ejpam-2779	219	64	x	x	SYM
ejpam-2779	219	65	=	=	PUNCT
ejpam-2779	219	66	x.	x.	NOUN
ejpam-2779	219	67	(	(	PUNCT
ejpam-2779	219	68	4	4	NUM
ejpam-2779	219	69	)	)	PUNCT
ejpam-2779	219	70	if	if	SCONJ
ejpam-2779	219	71	x1	x1	ADJ
ejpam-2779	219	72	≤	≤	ADJ
ejpam-2779	219	73	x2	x2	PROPN
ejpam-2779	219	74	,	,	PUNCT
ejpam-2779	219	75	then	then	ADV
ejpam-2779	219	76	x1	x1	PROPN
ejpam-2779	219	77	∧1	∧1	PROPN
ejpam-2779	219	78	y	y	PROPN
ejpam-2779	219	79	≤	≤	NUM
ejpam-2779	219	80	x2	x2	PROPN
ejpam-2779	220	1	∧1	∧1	VERB
ejpam-2779	220	2	y	y	PROPN
ejpam-2779	220	3	and	and	CCONJ
ejpam-2779	220	4	x1	x1	PROPN
ejpam-2779	220	5	∧2	∧2	PROPN
ejpam-2779	220	6	y	y	PROPN
ejpam-2779	220	7	≤	≤	NUM
ejpam-2779	221	1	x2	x2	PROPN
ejpam-2779	222	1	∧2	∧2	PROPN
ejpam-2779	222	2	y.	y.	PROPN
ejpam-2779	222	3	proof	proof	NOUN
ejpam-2779	222	4	.	.	PUNCT
ejpam-2779	223	1	(	(	PUNCT
ejpam-2779	223	2	1	1	X
ejpam-2779	223	3	)	)	PUNCT
ejpam-2779	223	4	by	by	ADP
ejpam-2779	223	5	proposition	proposition	NOUN
ejpam-2779	223	6	3	3	NUM
ejpam-2779	223	7	,	,	PUNCT
ejpam-2779	223	8	we	we	PRON
ejpam-2779	223	9	have	have	VERB
ejpam-2779	223	10	ax	ax	NOUN
ejpam-2779	223	11	∧1	∧1	NOUN
ejpam-2779	223	12	x	x	NOUN
ejpam-2779	223	13	=	=	SYM
ejpam-2779	223	14	x	x	SYM
ejpam-2779	223	15	◦	◦	NOUN
ejpam-2779	223	16	(	(	PUNCT
ejpam-2779	223	17	x	x	NOUN
ejpam-2779	223	18	∗	∗	NOUN
ejpam-2779	223	19	ax	ax	NOUN
ejpam-2779	223	20	)	)	PUNCT
ejpam-2779	224	1	=	=	NOUN
ejpam-2779	224	2	ax	ax	NOUN
ejpam-2779	224	3	since	since	SCONJ
ejpam-2779	224	4	ax	ax	NOUN
ejpam-2779	224	5	∈	∈	PROPN
ejpam-2779	224	6	m(a	m(a	PROPN
ejpam-2779	224	7	)	)	PUNCT
ejpam-2779	224	8	.	.	PUNCT
ejpam-2779	225	1	note	note	VERB
ejpam-2779	225	2	that	that	SCONJ
ejpam-2779	225	3	for	for	ADP
ejpam-2779	225	4	x	x	PROPN
ejpam-2779	225	5	∈	∈	PROPN
ejpam-2779	225	6	v	v	NOUN
ejpam-2779	225	7	(	(	PUNCT
ejpam-2779	225	8	ax	ax	NOUN
ejpam-2779	225	9	)	)	PUNCT
ejpam-2779	225	10	,	,	PUNCT
ejpam-2779	225	11	we	we	PRON
ejpam-2779	225	12	get	get	VERB
ejpam-2779	225	13	x	x	X
ejpam-2779	225	14	∧1	∧1	NOUN
ejpam-2779	225	15	ax	ax	NOUN
ejpam-2779	225	16	=	=	NOUN
ejpam-2779	225	17	ax	ax	NOUN
ejpam-2779	225	18	◦	◦	NOUN
ejpam-2779	225	19	(	(	PUNCT
ejpam-2779	225	20	ax	ax	NOUN
ejpam-2779	225	21	∗	∗	X
ejpam-2779	225	22	x	x	NOUN
ejpam-2779	225	23	)	)	PUNCT
ejpam-2779	226	1	=	=	NOUN
ejpam-2779	226	2	ax	ax	NOUN
ejpam-2779	226	3	◦	◦	NOUN
ejpam-2779	226	4	0	0	NUM
ejpam-2779	227	1	=	=	NOUN
ejpam-2779	227	2	ax	ax	NOUN
ejpam-2779	227	3	.	.	PUNCT
ejpam-2779	228	1	so	so	ADV
ejpam-2779	228	2	we	we	PRON
ejpam-2779	228	3	shows	show	VERB
ejpam-2779	228	4	that	that	SCONJ
ejpam-2779	228	5	ax	ax	NOUN
ejpam-2779	228	6	∧1	∧1	NOUN
ejpam-2779	228	7	x	x	NOUN
ejpam-2779	228	8	=	=	SYM
ejpam-2779	228	9	x	x	SYM
ejpam-2779	228	10	∧1	∧1	NOUN
ejpam-2779	228	11	ax	ax	NOUN
ejpam-2779	228	12	=	=	NOUN
ejpam-2779	228	13	ax	ax	NOUN
ejpam-2779	228	14	.	.	PUNCT
ejpam-2779	229	1	similarly	similarly	ADV
ejpam-2779	229	2	we	we	PRON
ejpam-2779	229	3	can	can	AUX
ejpam-2779	229	4	prove	prove	VERB
ejpam-2779	229	5	ax	ax	ADJ
ejpam-2779	229	6	∧2	∧2	NOUN
ejpam-2779	229	7	x	x	SYM
ejpam-2779	229	8	=	=	SYM
ejpam-2779	229	9	x	x	SYM
ejpam-2779	229	10	∧2	∧2	NOUN
ejpam-2779	229	11	ax	ax	NOUN
ejpam-2779	229	12	=	=	NOUN
ejpam-2779	229	13	ax	ax	NOUN
ejpam-2779	229	14	for	for	ADP
ejpam-2779	229	15	all	all	DET
ejpam-2779	229	16	x	x	SYM
ejpam-2779	229	17	∈	∈	NOUN
ejpam-2779	229	18	a.	a.	NOUN
ejpam-2779	229	19	(	(	PUNCT
ejpam-2779	229	20	2	2	X
ejpam-2779	229	21	)	)	PUNCT
ejpam-2779	229	22	let	let	VERB
ejpam-2779	230	1	x	x	SYM
ejpam-2779	230	2	≤	≤	X
ejpam-2779	230	3	y.	y.	NOUN
ejpam-2779	230	4	then	then	ADV
ejpam-2779	230	5	y∧1	y∧1	VERB
ejpam-2779	230	6	x	x	X
ejpam-2779	230	7	=	=	PUNCT
ejpam-2779	231	1	x	x	X
ejpam-2779	231	2	◦	◦	NOUN
ejpam-2779	231	3	(	(	PUNCT
ejpam-2779	231	4	x∗y	x∗y	X
ejpam-2779	231	5	)	)	PUNCT
ejpam-2779	231	6	=	=	SYM
ejpam-2779	232	1	x	x	SYM
ejpam-2779	232	2	◦	◦	NOUN
ejpam-2779	232	3	0	0	NUM
ejpam-2779	232	4	=	=	SYM
ejpam-2779	232	5	x	x	X
ejpam-2779	232	6	and	and	CCONJ
ejpam-2779	232	7	y∧2	y∧2	NOUN
ejpam-2779	232	8	x	x	PUNCT
ejpam-2779	232	9	=	=	SYM
ejpam-2779	232	10	x∗	x∗	X
ejpam-2779	232	11	(	(	PUNCT
ejpam-2779	232	12	x	x	SYM
ejpam-2779	232	13	◦	◦	NOUN
ejpam-2779	232	14	y	y	NOUN
ejpam-2779	232	15	)	)	PUNCT
ejpam-2779	232	16	=	=	SYM
ejpam-2779	232	17	x∗0	x∗0	PROPN
ejpam-2779	232	18	=	=	PUNCT
ejpam-2779	232	19	x.	x.	NOUN
ejpam-2779	232	20	(	(	PUNCT
ejpam-2779	232	21	3	3	X
ejpam-2779	232	22	)	)	PUNCT
ejpam-2779	232	23	we	we	PRON
ejpam-2779	232	24	have	have	VERB
ejpam-2779	232	25	x	x	X
ejpam-2779	232	26	∧1	∧1	NOUN
ejpam-2779	232	27	x	x	NOUN
ejpam-2779	232	28	=	=	SYM
ejpam-2779	232	29	x	x	SYM
ejpam-2779	232	30	◦	◦	NOUN
ejpam-2779	232	31	(	(	PUNCT
ejpam-2779	232	32	x	x	X
ejpam-2779	232	33	∗	∗	NOUN
ejpam-2779	232	34	x	x	NOUN
ejpam-2779	232	35	)	)	PUNCT
ejpam-2779	233	1	=	=	SYM
ejpam-2779	233	2	x	x	PUNCT
ejpam-2779	234	1	and	and	CCONJ
ejpam-2779	234	2	x	x	ADJ
ejpam-2779	234	3	∧2	∧2	NOUN
ejpam-2779	234	4	x	x	SYM
ejpam-2779	234	5	=	=	SYM
ejpam-2779	234	6	x	x	SYM
ejpam-2779	234	7	∗	∗	NOUN
ejpam-2779	234	8	(	(	PUNCT
ejpam-2779	234	9	x	x	PART
ejpam-2779	234	10	◦	◦	NOUN
ejpam-2779	234	11	x	x	NOUN
ejpam-2779	234	12	)	)	PUNCT
ejpam-2779	234	13	=	=	SYM
ejpam-2779	234	14	x.	x.	NOUN
ejpam-2779	234	15	(	(	PUNCT
ejpam-2779	234	16	4	4	X
ejpam-2779	234	17	)	)	PUNCT
ejpam-2779	234	18	let	let	VERB
ejpam-2779	234	19	x1	x1	NOUN
ejpam-2779	234	20	≤	≤	ADJ
ejpam-2779	234	21	x2	x2	PROPN
ejpam-2779	234	22	.	.	PUNCT
ejpam-2779	235	1	note	note	VERB
ejpam-2779	235	2	that	that	SCONJ
ejpam-2779	235	3	(	(	PUNCT
ejpam-2779	235	4	x1	x1	PROPN
ejpam-2779	235	5	∧1	∧1	PROPN
ejpam-2779	235	6	y	y	NOUN
ejpam-2779	235	7	)	)	PUNCT
ejpam-2779	235	8	∗	∗	NOUN
ejpam-2779	235	9	(	(	PUNCT
ejpam-2779	235	10	x2	x2	PROPN
ejpam-2779	235	11	∧1	∧1	PROPN
ejpam-2779	235	12	y	y	NOUN
ejpam-2779	235	13	)	)	PUNCT
ejpam-2779	235	14	=	=	SYM
ejpam-2779	236	1	(	(	PUNCT
ejpam-2779	236	2	y	y	PROPN
ejpam-2779	236	3	◦	◦	NOUN
ejpam-2779	236	4	(	(	PUNCT
ejpam-2779	236	5	y	y	PROPN
ejpam-2779	236	6	∗	∗	PROPN
ejpam-2779	236	7	x1	x1	PROPN
ejpam-2779	236	8	)	)	PUNCT
ejpam-2779	236	9	)	)	PUNCT
ejpam-2779	236	10	∗	∗	NOUN
ejpam-2779	236	11	(	(	PUNCT
ejpam-2779	236	12	y	y	PROPN
ejpam-2779	236	13	◦	◦	NOUN
ejpam-2779	236	14	(	(	PUNCT
ejpam-2779	236	15	y	y	PROPN
ejpam-2779	236	16	∗	∗	NOUN
ejpam-2779	236	17	x2	x2	PROPN
ejpam-2779	236	18	)	)	PUNCT
ejpam-2779	236	19	)	)	PUNCT
ejpam-2779	236	20	≤	≤	NOUN
ejpam-2779	236	21	(	(	PUNCT
ejpam-2779	236	22	y	y	PROPN
ejpam-2779	236	23	∗	∗	PUNCT
ejpam-2779	236	24	x2	x2	PROPN
ejpam-2779	236	25	)	)	PUNCT
ejpam-2779	236	26	◦	◦	NOUN
ejpam-2779	236	27	(	(	PUNCT
ejpam-2779	236	28	y	y	PROPN
ejpam-2779	236	29	∗	∗	PROPN
ejpam-2779	236	30	x1	x1	PROPN
ejpam-2779	236	31	)	)	PUNCT
ejpam-2779	236	32	≤	≤	NOUN
ejpam-2779	237	1	x1	x1	NUM
ejpam-2779	237	2	∗	∗	NOUN
ejpam-2779	237	3	x2	x2	PROPN
ejpam-2779	238	1	=	=	NOUN
ejpam-2779	238	2	0	0	X
ejpam-2779	238	3	.	.	PUNCT
ejpam-2779	239	1	we	we	PRON
ejpam-2779	239	2	get	get	VERB
ejpam-2779	239	3	x1	x1	PROPN
ejpam-2779	239	4	∧1	∧1	NOUN
ejpam-2779	239	5	y	y	PROPN
ejpam-2779	239	6	≤	≤	NUM
ejpam-2779	239	7	x2	x2	PROPN
ejpam-2779	240	1	∧1	∧1	VERB
ejpam-2779	240	2	y.	y.	NOUN
ejpam-2779	240	3	similarly	similarly	ADV
ejpam-2779	240	4	we	we	PRON
ejpam-2779	240	5	can	can	AUX
ejpam-2779	240	6	prove	prove	VERB
ejpam-2779	240	7	x1	x1	PROPN
ejpam-2779	240	8	∧2	∧2	PROPN
ejpam-2779	240	9	y	y	PROPN
ejpam-2779	240	10	≤	≤	NUM
ejpam-2779	240	11	x2	x2	PROPN
ejpam-2779	241	1	∧2	∧2	PROPN
ejpam-2779	241	2	y.	y.	PROPN
ejpam-2779	241	3	proposition	proposition	NOUN
ejpam-2779	241	4	10	10	NUM
ejpam-2779	241	5	.	.	PUNCT
ejpam-2779	242	1	in	in	ADP
ejpam-2779	242	2	a	a	DET
ejpam-2779	242	3	the	the	DET
ejpam-2779	242	4	following	follow	VERB
ejpam-2779	242	5	properties	property	NOUN
ejpam-2779	242	6	hold	hold	VERB
ejpam-2779	242	7	for	for	ADP
ejpam-2779	242	8	all	all	DET
ejpam-2779	242	9	a	a	DET
ejpam-2779	242	10	∈m(a	∈m(a	NOUN
ejpam-2779	242	11	)	)	PUNCT
ejpam-2779	242	12	and	and	CCONJ
ejpam-2779	242	13	x	x	NOUN
ejpam-2779	242	14	,	,	PUNCT
ejpam-2779	242	15	y	y	PROPN
ejpam-2779	242	16	∈	∈	PROPN
ejpam-2779	242	17	v	v	ADP
ejpam-2779	242	18	(	(	PUNCT
ejpam-2779	242	19	a	a	NOUN
ejpam-2779	242	20	):	):	PUNCT
ejpam-2779	242	21	(	(	PUNCT
ejpam-2779	242	22	1	1	X
ejpam-2779	242	23	)	)	PUNCT
ejpam-2779	242	24	x	x	PUNCT
ejpam-2779	242	25	∧1	∧1	VERB
ejpam-2779	242	26	y−∼	y−∼	NOUN
ejpam-2779	242	27	=	=	SYM
ejpam-2779	243	1	x−∼	x−∼	PROPN
ejpam-2779	243	2	∧1	∧1	NUM
ejpam-2779	243	3	y−∼	y−∼	NOUN
ejpam-2779	243	4	and	and	CCONJ
ejpam-2779	243	5	x	x	ADJ
ejpam-2779	243	6	∧2	∧2	PROPN
ejpam-2779	243	7	y∼−	y∼−	NOUN
ejpam-2779	243	8	=	=	PROPN
ejpam-2779	243	9	x∼−	x∼−	PROPN
ejpam-2779	244	1	∧2	∧2	PROPN
ejpam-2779	244	2	y∼−.	y∼−.	NOUN
ejpam-2779	244	3	(	(	PUNCT
ejpam-2779	244	4	2	2	NUM
ejpam-2779	244	5	)	)	PUNCT
ejpam-2779	244	6	x	x	X
ejpam-2779	244	7	∧1	∧1	PROPN
ejpam-2779	244	8	y∼	y∼	PROPN
ejpam-2779	244	9	=	=	PUNCT
ejpam-2779	244	10	x−∼	x−∼	PROPN
ejpam-2779	244	11	∧1	∧1	VERB
ejpam-2779	244	12	y∼	y∼	PROPN
ejpam-2779	244	13	and	and	CCONJ
ejpam-2779	244	14	x	x	ADJ
ejpam-2779	244	15	∧2	∧2	PROPN
ejpam-2779	244	16	y−	y−	NOUN
ejpam-2779	244	17	=	=	SYM
ejpam-2779	244	18	x∼−	x∼−	PROPN
ejpam-2779	245	1	∧2	∧2	PROPN
ejpam-2779	245	2	y−.	y−.	PROPN
ejpam-2779	245	3	x.l	x.l	PROPN
ejpam-2779	245	4	.	.	PUNCT
ejpam-2779	246	1	xin	xin	PROPN
ejpam-2779	246	2	,	,	PUNCT
ejpam-2779	246	3	y.j	y.j	PROPN
ejpam-2779	246	4	.	.	PUNCT
ejpam-2779	246	5	li	li	PROPN
ejpam-2779	246	6	,	,	PUNCT
ejpam-2779	246	7	y.l	y.l	PROPN
ejpam-2779	246	8	.	.	PROPN
ejpam-2779	246	9	fu	fu	PROPN
ejpam-2779	246	10	/	/	SYM
ejpam-2779	246	11	eur	eur	PROPN
ejpam-2779	246	12	.	.	PUNCT
ejpam-2779	247	1	j.	j.	PROPN
ejpam-2779	247	2	pure	pure	PROPN
ejpam-2779	247	3	appl	appl	PROPN
ejpam-2779	247	4	.	.	PROPN
ejpam-2779	247	5	math	math	PROPN
ejpam-2779	247	6	,	,	PUNCT
ejpam-2779	247	7	10	10	NUM
ejpam-2779	247	8	(	(	PUNCT
ejpam-2779	247	9	3	3	NUM
ejpam-2779	247	10	)	)	PUNCT
ejpam-2779	247	11	(	(	PUNCT
ejpam-2779	247	12	2017	2017	NUM
ejpam-2779	247	13	)	)	PUNCT
ejpam-2779	247	14	,	,	PUNCT
ejpam-2779	247	15	455	455	NUM
ejpam-2779	247	16	-	-	SYM
ejpam-2779	247	17	472	472	NUM
ejpam-2779	247	18	462	462	NUM
ejpam-2779	247	19	proof	proof	NOUN
ejpam-2779	247	20	.	.	PUNCT
ejpam-2779	248	1	(	(	PUNCT
ejpam-2779	248	2	1	1	X
ejpam-2779	248	3	)	)	PUNCT
ejpam-2779	248	4	using	use	VERB
ejpam-2779	248	5	proposition	proposition	NOUN
ejpam-2779	248	6	1	1	NUM
ejpam-2779	248	7	,	,	PUNCT
ejpam-2779	248	8	we	we	PRON
ejpam-2779	248	9	have	have	VERB
ejpam-2779	248	10	y−v∗x	y−v∗x	NOUN
ejpam-2779	248	11	=	=	SYM
ejpam-2779	248	12	(	(	PUNCT
ejpam-2779	248	13	1a	1a	NUM
ejpam-2779	248	14	◦	◦	NOUN
ejpam-2779	248	15	(1a∗y))∗x	(1a∗y))∗x	X
ejpam-2779	248	16	=	=	SYM
ejpam-2779	248	17	(	(	PUNCT
ejpam-2779	248	18	1a∗x)	1a∗x)	NUM
ejpam-2779	248	19	◦	◦	NOUN
ejpam-2779	248	20	(1a∗y	(1a∗y	NOUN
ejpam-2779	248	21	)	)	PUNCT
ejpam-2779	248	22	=	=	SYM
ejpam-2779	248	23	(	(	PUNCT
ejpam-2779	248	24	1a	1a	X
ejpam-2779	248	25	∗	∗	X
ejpam-2779	248	26	(	(	PUNCT
ejpam-2779	248	27	1a	1a	X
ejpam-2779	248	28	◦	◦	NOUN
ejpam-2779	248	29	(	(	PUNCT
ejpam-2779	248	30	1a	1a	X
ejpam-2779	248	31	∗	∗	X
ejpam-2779	248	32	x	x	NOUN
ejpam-2779	248	33	)	)	PUNCT
ejpam-2779	248	34	)	)	PUNCT
ejpam-2779	248	35	)	)	PUNCT
ejpam-2779	249	1	◦	◦	NOUN
ejpam-2779	249	2	(	(	PUNCT
ejpam-2779	249	3	1a	1a	PROPN
ejpam-2779	249	4	∗	∗	X
ejpam-2779	249	5	y	y	NOUN
ejpam-2779	249	6	)	)	PUNCT
ejpam-2779	249	7	=	=	PUNCT
ejpam-2779	249	8	(	(	PUNCT
ejpam-2779	249	9	1a	1a	X
ejpam-2779	249	10	◦	◦	NOUN
ejpam-2779	249	11	(	(	PUNCT
ejpam-2779	249	12	1a	1a	PROPN
ejpam-2779	249	13	∗	∗	PROPN
ejpam-2779	249	14	y	y	PROPN
ejpam-2779	249	15	)	)	PUNCT
ejpam-2779	249	16	)	)	PUNCT
ejpam-2779	249	17	∗	∗	NOUN
ejpam-2779	249	18	(	(	PUNCT
ejpam-2779	249	19	1a	1a	X
ejpam-2779	249	20	◦	◦	NOUN
ejpam-2779	249	21	(	(	PUNCT
ejpam-2779	249	22	1a	1a	X
ejpam-2779	249	23	∗	∗	X
ejpam-2779	249	24	x	x	NOUN
ejpam-2779	249	25	)	)	PUNCT
ejpam-2779	249	26	)	)	PUNCT
ejpam-2779	250	1	=	=	PUNCT
ejpam-2779	250	2	y−v	y−v	NOUN
ejpam-2779	250	3	∗	∗	NOUN
ejpam-2779	250	4	x−∼.	x−∼.	X
ejpam-2779	250	5	thus	thus	ADV
ejpam-2779	250	6	x	x	SYM
ejpam-2779	250	7	∧1	∧1	NUM
ejpam-2779	250	8	y−∼	y−∼	NOUN
ejpam-2779	250	9	=	=	SYM
ejpam-2779	250	10	y−∼	y−∼	NOUN
ejpam-2779	251	1	◦	◦	NOUN
ejpam-2779	251	2	(	(	PUNCT
ejpam-2779	251	3	y−∼	y−∼	NOUN
ejpam-2779	251	4	∗	∗	NOUN
ejpam-2779	251	5	x	x	NOUN
ejpam-2779	251	6	)	)	PUNCT
ejpam-2779	251	7	=	=	SYM
ejpam-2779	252	1	y−∼	y−∼	PART
ejpam-2779	252	2	◦	◦	NOUN
ejpam-2779	252	3	(	(	PUNCT
ejpam-2779	252	4	y−v	y−v	NOUN
ejpam-2779	252	5	∗	∗	NOUN
ejpam-2779	252	6	x−∼	x−∼	ADV
ejpam-2779	252	7	)	)	PUNCT
ejpam-2779	252	8	=	=	PUNCT
ejpam-2779	253	1	x−∼	x−∼	PROPN
ejpam-2779	253	2	∧1	∧1	NUM
ejpam-2779	253	3	y−v	y−v	NOUN
ejpam-2779	253	4	.	.	PUNCT
ejpam-2779	254	1	(	(	PUNCT
ejpam-2779	254	2	2	2	X
ejpam-2779	254	3	)	)	PUNCT
ejpam-2779	254	4	by	by	ADP
ejpam-2779	254	5	proposition	proposition	NOUN
ejpam-2779	254	6	8	8	NUM
ejpam-2779	254	7	and	and	CCONJ
ejpam-2779	254	8	(	(	PUNCT
ejpam-2779	254	9	1	1	NUM
ejpam-2779	254	10	)	)	PUNCT
ejpam-2779	254	11	,	,	PUNCT
ejpam-2779	254	12	we	we	PRON
ejpam-2779	254	13	get	get	VERB
ejpam-2779	254	14	x	x	X
ejpam-2779	254	15	∧1	∧1	NOUN
ejpam-2779	254	16	y∼	y∼	NOUN
ejpam-2779	254	17	=	=	NOUN
ejpam-2779	254	18	x	x	SYM
ejpam-2779	254	19	∧1	∧1	X
ejpam-2779	254	20	(	(	PUNCT
ejpam-2779	254	21	y∼)−∼	y∼)−∼	NOUN
ejpam-2779	254	22	=	=	SYM
ejpam-2779	254	23	x−∼	x−∼	PROPN
ejpam-2779	254	24	∧1	∧1	PROPN
ejpam-2779	255	1	(	(	PUNCT
ejpam-2779	255	2	y∼)−∼	y∼)−∼	NOUN
ejpam-2779	255	3	=	=	PROPN
ejpam-2779	255	4	x−∼	x−∼	PROPN
ejpam-2779	255	5	∧1	∧1	NUM
ejpam-2779	255	6	y∼.	y∼.	NOUN
ejpam-2779	255	7	proposition	proposition	NOUN
ejpam-2779	255	8	11	11	NUM
ejpam-2779	255	9	.	.	PUNCT
ejpam-2779	256	1	in	in	ADP
ejpam-2779	256	2	a	a	DET
ejpam-2779	256	3	the	the	DET
ejpam-2779	256	4	following	follow	VERB
ejpam-2779	256	5	properties	property	NOUN
ejpam-2779	256	6	hold	hold	VERB
ejpam-2779	256	7	for	for	ADP
ejpam-2779	256	8	all	all	DET
ejpam-2779	256	9	x	x	NOUN
ejpam-2779	256	10	,	,	PUNCT
ejpam-2779	256	11	y	y	PROPN
ejpam-2779	256	12	∈	∈	PROPN
ejpam-2779	256	13	a	a	PRON
ejpam-2779	256	14	:	:	PUNCT
ejpam-2779	256	15	y	y	NOUN
ejpam-2779	256	16	∗	∗	NOUN
ejpam-2779	256	17	(	(	PUNCT
ejpam-2779	256	18	x	x	SYM
ejpam-2779	256	19	∧1	∧1	NUM
ejpam-2779	256	20	y	y	NOUN
ejpam-2779	256	21	)	)	PUNCT
ejpam-2779	256	22	=	=	SYM
ejpam-2779	256	23	y	y	PROPN
ejpam-2779	256	24	∗	∗	NOUN
ejpam-2779	256	25	x	x	PUNCT
ejpam-2779	256	26	and	and	CCONJ
ejpam-2779	256	27	y	y	PROPN
ejpam-2779	256	28	◦	◦	NOUN
ejpam-2779	256	29	(	(	PUNCT
ejpam-2779	256	30	x	x	INTJ
ejpam-2779	256	31	∧2	∧2	PROPN
ejpam-2779	256	32	y	y	NOUN
ejpam-2779	256	33	)	)	PUNCT
ejpam-2779	256	34	=	=	SYM
ejpam-2779	257	1	y	y	PROPN
ejpam-2779	257	2	◦	◦	NOUN
ejpam-2779	257	3	x.	x.	NOUN
ejpam-2779	257	4	proof	proof	NOUN
ejpam-2779	257	5	.	.	PUNCT
ejpam-2779	258	1	by	by	ADP
ejpam-2779	258	2	proposition	proposition	NOUN
ejpam-2779	258	3	1	1	NUM
ejpam-2779	258	4	,	,	PUNCT
ejpam-2779	258	5	we	we	PRON
ejpam-2779	258	6	have	have	VERB
ejpam-2779	258	7	y	y	PROPN
ejpam-2779	258	8	∗	∗	NOUN
ejpam-2779	258	9	(	(	PUNCT
ejpam-2779	258	10	x∧1	x∧1	PROPN
ejpam-2779	258	11	y	y	PROPN
ejpam-2779	258	12	)	)	PUNCT
ejpam-2779	259	1	=	=	SYM
ejpam-2779	259	2	y	y	PROPN
ejpam-2779	259	3	∗	∗	NOUN
ejpam-2779	259	4	(	(	PUNCT
ejpam-2779	259	5	y	y	PROPN
ejpam-2779	259	6	◦	◦	NOUN
ejpam-2779	259	7	(	(	PUNCT
ejpam-2779	259	8	y	y	NOUN
ejpam-2779	259	9	∗x	∗x	PROPN
ejpam-2779	259	10	)	)	PUNCT
ejpam-2779	259	11	=	=	SYM
ejpam-2779	259	12	y	y	PROPN
ejpam-2779	259	13	∗x	∗x	PROPN
ejpam-2779	259	14	and	and	CCONJ
ejpam-2779	259	15	y	y	PROPN
ejpam-2779	259	16	◦	◦	NOUN
ejpam-2779	259	17	(	(	PUNCT
ejpam-2779	259	18	x∧2	x∧2	NOUN
ejpam-2779	259	19	y	y	X
ejpam-2779	259	20	)	)	PUNCT
ejpam-2779	260	1	=	=	SYM
ejpam-2779	260	2	y	y	PROPN
ejpam-2779	260	3	◦	◦	NOUN
ejpam-2779	260	4	(	(	PUNCT
ejpam-2779	260	5	y	y	PROPN
ejpam-2779	260	6	∗	∗	NOUN
ejpam-2779	260	7	(	(	PUNCT
ejpam-2779	260	8	y	y	PROPN
ejpam-2779	260	9	◦	◦	NOUN
ejpam-2779	260	10	x	x	NOUN
ejpam-2779	260	11	)	)	PUNCT
ejpam-2779	260	12	)	)	PUNCT
ejpam-2779	261	1	=	=	SYM
ejpam-2779	261	2	y	y	PROPN
ejpam-2779	261	3	◦	◦	NOUN
ejpam-2779	261	4	x.	x.	NOUN
ejpam-2779	261	5	proposition	proposition	NOUN
ejpam-2779	261	6	12	12	NUM
ejpam-2779	261	7	.	.	PUNCT
ejpam-2779	262	1	let	let	VERB
ejpam-2779	262	2	a	a	DET
ejpam-2779	262	3	∈m(a	∈m(a	NOUN
ejpam-2779	262	4	)	)	PUNCT
ejpam-2779	262	5	.	.	PUNCT
ejpam-2779	263	1	if	if	SCONJ
ejpam-2779	263	2	x	x	X
ejpam-2779	263	3	,	,	PUNCT
ejpam-2779	263	4	y	y	PROPN
ejpam-2779	263	5	∈	∈	PROPN
ejpam-2779	263	6	v	v	ADP
ejpam-2779	263	7	(	(	PUNCT
ejpam-2779	263	8	a	a	NOUN
ejpam-2779	263	9	)	)	PUNCT
ejpam-2779	263	10	,	,	PUNCT
ejpam-2779	263	11	then	then	ADV
ejpam-2779	263	12	x	x	X
ejpam-2779	263	13	∗	∗	VERB
ejpam-2779	263	14	y	y	PROPN
ejpam-2779	263	15	∈	∈	PROPN
ejpam-2779	263	16	v	v	PROPN
ejpam-2779	263	17	(	(	PUNCT
ejpam-2779	263	18	0	0	NUM
ejpam-2779	263	19	)	)	PUNCT
ejpam-2779	263	20	and	and	CCONJ
ejpam-2779	263	21	x	x	PART
ejpam-2779	263	22	◦	◦	VERB
ejpam-2779	263	23	y	y	PROPN
ejpam-2779	263	24	∈	∈	PROPN
ejpam-2779	263	25	v	v	NOUN
ejpam-2779	263	26	(	(	PUNCT
ejpam-2779	263	27	0	0	NUM
ejpam-2779	263	28	)	)	PUNCT
ejpam-2779	263	29	.	.	PUNCT
ejpam-2779	264	1	proof	proof	NOUN
ejpam-2779	264	2	.	.	PUNCT
ejpam-2779	265	1	using	use	VERB
ejpam-2779	265	2	proposition	proposition	NOUN
ejpam-2779	265	3	2	2	NUM
ejpam-2779	265	4	and	and	CCONJ
ejpam-2779	265	5	6	6	NUM
ejpam-2779	265	6	,	,	PUNCT
ejpam-2779	265	7	we	we	PRON
ejpam-2779	265	8	get	get	VERB
ejpam-2779	265	9	0	0	NUM
ejpam-2779	265	10	◦	◦	NOUN
ejpam-2779	265	11	(	(	PUNCT
ejpam-2779	265	12	0	0	NUM
ejpam-2779	265	13	∗	∗	NOUN
ejpam-2779	265	14	(	(	PUNCT
ejpam-2779	265	15	x	x	X
ejpam-2779	265	16	∗	∗	PROPN
ejpam-2779	265	17	y	y	NOUN
ejpam-2779	265	18	)	)	PUNCT
ejpam-2779	265	19	)	)	PUNCT
ejpam-2779	266	1	=	=	SYM
ejpam-2779	266	2	0	0	NUM
ejpam-2779	267	1	◦	◦	NOUN
ejpam-2779	267	2	(	(	PUNCT
ejpam-2779	267	3	(	(	PUNCT
ejpam-2779	267	4	0	0	NUM
ejpam-2779	267	5	◦	◦	NOUN
ejpam-2779	267	6	x	x	NOUN
ejpam-2779	267	7	)	)	PUNCT
ejpam-2779	267	8	◦	◦	NOUN
ejpam-2779	267	9	(	(	PUNCT
ejpam-2779	267	10	0	0	NUM
ejpam-2779	267	11	∗	∗	PROPN
ejpam-2779	267	12	y	y	NOUN
ejpam-2779	267	13	)	)	PUNCT
ejpam-2779	267	14	)	)	PUNCT
ejpam-2779	268	1	=	=	PUNCT
ejpam-2779	268	2	(	(	PUNCT
ejpam-2779	268	3	0∗	0∗	NUM
ejpam-2779	268	4	(	(	PUNCT
ejpam-2779	268	5	0	0	NUM
ejpam-2779	268	6	◦	◦	NOUN
ejpam-2779	268	7	x))∗	x))∗	PROPN
ejpam-2779	268	8	(	(	PUNCT
ejpam-2779	268	9	0	0	NUM
ejpam-2779	268	10	◦	◦	NOUN
ejpam-2779	268	11	(	(	PUNCT
ejpam-2779	268	12	0∗y	0∗y	NOUN
ejpam-2779	268	13	)	)	PUNCT
ejpam-2779	268	14	)	)	PUNCT
ejpam-2779	269	1	=	=	SYM
ejpam-2779	269	2	a∗a	a∗a	PUNCT
ejpam-2779	269	3	=	=	SYM
ejpam-2779	269	4	0	0	PROPN
ejpam-2779	269	5	.	.	PUNCT
ejpam-2779	270	1	since	since	SCONJ
ejpam-2779	270	2	by	by	ADP
ejpam-2779	270	3	(	(	PUNCT
ejpam-2779	270	4	i2	i2	PROPN
ejpam-2779	270	5	)	)	PUNCT
ejpam-2779	270	6	0	0	NUM
ejpam-2779	270	7	◦	◦	NOUN
ejpam-2779	270	8	(	(	PUNCT
ejpam-2779	270	9	0∗	0∗	PUNCT
ejpam-2779	270	10	(	(	PUNCT
ejpam-2779	270	11	x∗y	x∗y	X
ejpam-2779	270	12	)	)	PUNCT
ejpam-2779	270	13	)	)	PUNCT
ejpam-2779	270	14	≤	≤	NOUN
ejpam-2779	270	15	x∗y	x∗y	NUM
ejpam-2779	270	16	,	,	PUNCT
ejpam-2779	270	17	we	we	PRON
ejpam-2779	270	18	have	have	VERB
ejpam-2779	270	19	0	0	NUM
ejpam-2779	270	20	≤	≤	NOUN
ejpam-2779	270	21	x∗y	x∗y	NUM
ejpam-2779	270	22	,	,	PUNCT
ejpam-2779	270	23	and	and	CCONJ
ejpam-2779	270	24	so	so	ADV
ejpam-2779	270	25	x	x	SYM
ejpam-2779	270	26	∗	∗	NOUN
ejpam-2779	270	27	y	y	PROPN
ejpam-2779	270	28	∈	∈	PROPN
ejpam-2779	270	29	v	v	PROPN
ejpam-2779	270	30	(	(	PUNCT
ejpam-2779	270	31	0	0	NUM
ejpam-2779	270	32	)	)	PUNCT
ejpam-2779	270	33	.	.	PUNCT
ejpam-2779	271	1	similarly	similarly	ADV
ejpam-2779	271	2	we	we	PRON
ejpam-2779	271	3	can	can	AUX
ejpam-2779	271	4	prove	prove	VERB
ejpam-2779	271	5	x	x	PUNCT
ejpam-2779	271	6	◦	◦	VERB
ejpam-2779	271	7	y	y	PROPN
ejpam-2779	271	8	∈	∈	PROPN
ejpam-2779	271	9	v	v	NOUN
ejpam-2779	271	10	(	(	PUNCT
ejpam-2779	271	11	0	0	NUM
ejpam-2779	271	12	)	)	PUNCT
ejpam-2779	271	13	.	.	PUNCT
ejpam-2779	272	1	proposition	proposition	NOUN
ejpam-2779	272	2	13	13	NUM
ejpam-2779	272	3	.	.	PUNCT
ejpam-2779	273	1	in	in	ADP
ejpam-2779	273	2	a	a	DET
ejpam-2779	273	3	the	the	DET
ejpam-2779	273	4	following	follow	VERB
ejpam-2779	273	5	properties	property	NOUN
ejpam-2779	273	6	hold	hold	VERB
ejpam-2779	273	7	for	for	ADP
ejpam-2779	273	8	all	all	DET
ejpam-2779	273	9	a	a	DET
ejpam-2779	273	10	∈m(a	∈m(a	NOUN
ejpam-2779	273	11	)	)	PUNCT
ejpam-2779	273	12	,	,	PUNCT
ejpam-2779	273	13	x	x	X
ejpam-2779	273	14	,	,	PUNCT
ejpam-2779	273	15	y	y	PROPN
ejpam-2779	273	16	∈	∈	PROPN
ejpam-2779	273	17	v	v	ADP
ejpam-2779	273	18	(	(	PUNCT
ejpam-2779	273	19	a	a	NOUN
ejpam-2779	273	20	):	):	PUNCT
ejpam-2779	273	21	(	(	PUNCT
ejpam-2779	273	22	1	1	X
ejpam-2779	273	23	)	)	PUNCT
ejpam-2779	273	24	x	x	PUNCT
ejpam-2779	273	25	∧1	∧1	AUX
ejpam-2779	273	26	y	y	PROPN
ejpam-2779	273	27	(	(	PUNCT
ejpam-2779	273	28	y	y	PROPN
ejpam-2779	273	29	∧1	∧1	PROPN
ejpam-2779	273	30	x	x	NOUN
ejpam-2779	273	31	)	)	PUNCT
ejpam-2779	273	32	is	be	AUX
ejpam-2779	273	33	a	a	DET
ejpam-2779	273	34	lower	low	ADJ
ejpam-2779	273	35	bound	bind	VERB
ejpam-2779	273	36	of	of	ADP
ejpam-2779	273	37	{	{	PUNCT
ejpam-2779	273	38	x	x	PROPN
ejpam-2779	273	39	,	,	PUNCT
ejpam-2779	273	40	y	y	PROPN
ejpam-2779	273	41	}	}	PUNCT
ejpam-2779	273	42	.	.	PUNCT
ejpam-2779	274	1	(	(	PUNCT
ejpam-2779	274	2	2	2	X
ejpam-2779	274	3	)	)	PUNCT
ejpam-2779	274	4	x	x	X
ejpam-2779	274	5	∧2	∧2	PROPN
ejpam-2779	274	6	y	y	PROPN
ejpam-2779	274	7	(	(	PUNCT
ejpam-2779	274	8	y	y	PROPN
ejpam-2779	274	9	∧2	∧2	PROPN
ejpam-2779	274	10	x	x	X
ejpam-2779	274	11	)	)	PUNCT
ejpam-2779	274	12	is	be	AUX
ejpam-2779	274	13	a	a	DET
ejpam-2779	274	14	lower	low	ADJ
ejpam-2779	274	15	bound	bind	VERB
ejpam-2779	274	16	of	of	ADP
ejpam-2779	274	17	{	{	PUNCT
ejpam-2779	274	18	x	x	PROPN
ejpam-2779	274	19	,	,	PUNCT
ejpam-2779	274	20	y	y	NOUN
ejpam-2779	274	21	}	}	PUNCT
ejpam-2779	274	22	.	.	PUNCT
ejpam-2779	275	1	proof	proof	NOUN
ejpam-2779	275	2	.	.	PUNCT
ejpam-2779	276	1	by	by	ADP
ejpam-2779	276	2	definition	definition	NOUN
ejpam-2779	276	3	3.1	3.1	NUM
ejpam-2779	276	4	,	,	PUNCT
ejpam-2779	276	5	we	we	PRON
ejpam-2779	276	6	have	have	VERB
ejpam-2779	276	7	x∧1	x∧1	NOUN
ejpam-2779	276	8	y	y	PROPN
ejpam-2779	276	9	=	=	SYM
ejpam-2779	276	10	y	y	PROPN
ejpam-2779	276	11	◦	◦	NOUN
ejpam-2779	276	12	(	(	PUNCT
ejpam-2779	276	13	y	y	NOUN
ejpam-2779	276	14	∗x	∗x	NOUN
ejpam-2779	276	15	)	)	PUNCT
ejpam-2779	276	16	≤	≤	NUM
ejpam-2779	276	17	x.	x.	VERB
ejpam-2779	277	1	moreover	moreover	ADV
ejpam-2779	277	2	by	by	ADP
ejpam-2779	277	3	proposition	proposition	NOUN
ejpam-2779	277	4	12	12	NUM
ejpam-2779	277	5	,	,	PUNCT
ejpam-2779	277	6	y	y	PROPN
ejpam-2779	277	7	∗	∗	NOUN
ejpam-2779	277	8	x	x	PUNCT
ejpam-2779	277	9	∈	∈	NOUN
ejpam-2779	277	10	v	v	NOUN
ejpam-2779	277	11	(	(	PUNCT
ejpam-2779	277	12	0	0	NUM
ejpam-2779	277	13	)	)	PUNCT
ejpam-2779	277	14	and	and	CCONJ
ejpam-2779	277	15	so	so	ADV
ejpam-2779	277	16	0	0	NUM
ejpam-2779	277	17	◦	◦	NOUN
ejpam-2779	277	18	(	(	PUNCT
ejpam-2779	277	19	y	y	PROPN
ejpam-2779	277	20	∗	∗	NOUN
ejpam-2779	277	21	x	x	NOUN
ejpam-2779	277	22	)	)	PUNCT
ejpam-2779	277	23	=	=	SYM
ejpam-2779	277	24	0	0	NUM
ejpam-2779	277	25	,	,	PUNCT
ejpam-2779	277	26	and	and	CCONJ
ejpam-2779	277	27	(	(	PUNCT
ejpam-2779	277	28	y	y	PROPN
ejpam-2779	277	29	◦	◦	NOUN
ejpam-2779	277	30	(	(	PUNCT
ejpam-2779	277	31	y	y	PROPN
ejpam-2779	277	32	∗	∗	NOUN
ejpam-2779	277	33	x	x	NOUN
ejpam-2779	277	34	)	)	PUNCT
ejpam-2779	277	35	)	)	PUNCT
ejpam-2779	277	36	∗	∗	NOUN
ejpam-2779	277	37	y	y	NOUN
ejpam-2779	278	1	=	=	PUNCT
ejpam-2779	279	1	(	(	PUNCT
ejpam-2779	279	2	y	y	PROPN
ejpam-2779	279	3	∗	∗	PROPN
ejpam-2779	279	4	y	y	PROPN
ejpam-2779	279	5	)	)	PUNCT
ejpam-2779	279	6	◦	◦	NOUN
ejpam-2779	279	7	(	(	PUNCT
ejpam-2779	279	8	y	y	PROPN
ejpam-2779	279	9	∗	∗	NOUN
ejpam-2779	279	10	x	x	NOUN
ejpam-2779	279	11	)	)	PUNCT
ejpam-2779	279	12	=	=	SYM
ejpam-2779	279	13	0	0	NUM
ejpam-2779	280	1	◦	◦	NOUN
ejpam-2779	280	2	(	(	PUNCT
ejpam-2779	280	3	y	y	PROPN
ejpam-2779	280	4	∗	∗	NOUN
ejpam-2779	280	5	x	x	NOUN
ejpam-2779	280	6	)	)	PUNCT
ejpam-2779	280	7	=	=	SYM
ejpam-2779	280	8	0	0	X
ejpam-2779	280	9	.	.	PUNCT
ejpam-2779	281	1	it	it	PRON
ejpam-2779	281	2	follows	follow	VERB
ejpam-2779	281	3	that	that	SCONJ
ejpam-2779	281	4	x	x	PROPN
ejpam-2779	281	5	∧1	∧1	VERB
ejpam-2779	282	1	y	y	NOUN
ejpam-2779	282	2	=	=	SYM
ejpam-2779	282	3	y	y	PROPN
ejpam-2779	282	4	◦	◦	NOUN
ejpam-2779	282	5	(	(	PUNCT
ejpam-2779	282	6	y	y	PROPN
ejpam-2779	282	7	∗	∗	X
ejpam-2779	282	8	x	x	NOUN
ejpam-2779	282	9	)	)	PUNCT
ejpam-2779	282	10	≤	≤	PUNCT
ejpam-2779	283	1	y.	y.	NOUN
ejpam-2779	283	2	similarly	similarly	ADV
ejpam-2779	283	3	we	we	PRON
ejpam-2779	283	4	can	can	AUX
ejpam-2779	283	5	get	get	VERB
ejpam-2779	283	6	that	that	PRON
ejpam-2779	283	7	(	(	PUNCT
ejpam-2779	283	8	y	y	PROPN
ejpam-2779	283	9	∧1	∧1	PROPN
ejpam-2779	283	10	x	x	VERB
ejpam-2779	283	11	)	)	PUNCT
ejpam-2779	283	12	is	be	AUX
ejpam-2779	283	13	also	also	ADV
ejpam-2779	283	14	a	a	DET
ejpam-2779	283	15	lower	low	ADJ
ejpam-2779	283	16	bound	bind	VERB
ejpam-2779	283	17	of	of	ADP
ejpam-2779	283	18	{	{	PUNCT
ejpam-2779	283	19	x	x	PROPN
ejpam-2779	283	20	,	,	PUNCT
ejpam-2779	283	21	y	y	PROPN
ejpam-2779	283	22	}	}	PUNCT
ejpam-2779	283	23	.	.	PUNCT
ejpam-2779	284	1	(	(	PUNCT
ejpam-2779	284	2	2	2	X
ejpam-2779	284	3	)	)	PUNCT
ejpam-2779	284	4	similar	similar	ADJ
ejpam-2779	284	5	to	to	ADP
ejpam-2779	284	6	the	the	DET
ejpam-2779	284	7	proof	proof	NOUN
ejpam-2779	284	8	of	of	ADP
ejpam-2779	284	9	(	(	PUNCT
ejpam-2779	284	10	1	1	NUM
ejpam-2779	284	11	)	)	PUNCT
ejpam-2779	284	12	.	.	PUNCT
ejpam-2779	285	1	definition	definition	NOUN
ejpam-2779	285	2	5	5	NUM
ejpam-2779	285	3	.	.	PUNCT
ejpam-2779	286	1	(	(	PUNCT
ejpam-2779	286	2	1	1	X
ejpam-2779	286	3	)	)	PUNCT
ejpam-2779	286	4	if	if	SCONJ
ejpam-2779	286	5	for	for	ADP
ejpam-2779	286	6	all	all	DET
ejpam-2779	286	7	a	a	DET
ejpam-2779	286	8	∈m(a	∈m(a	NOUN
ejpam-2779	286	9	)	)	PUNCT
ejpam-2779	286	10	and	and	CCONJ
ejpam-2779	286	11	x	x	NOUN
ejpam-2779	286	12	,	,	PUNCT
ejpam-2779	286	13	y	y	PROPN
ejpam-2779	286	14	∈	∈	PROPN
ejpam-2779	286	15	v	v	ADP
ejpam-2779	286	16	(	(	PUNCT
ejpam-2779	286	17	a	a	NOUN
ejpam-2779	286	18	)	)	PUNCT
ejpam-2779	286	19	,	,	PUNCT
ejpam-2779	286	20	x∧1	x∧1	PROPN
ejpam-2779	286	21	y	y	PROPN
ejpam-2779	286	22	=	=	PUNCT
ejpam-2779	286	23	y	y	PROPN
ejpam-2779	286	24	∧1	∧1	NUM
ejpam-2779	286	25	x	x	VERB
ejpam-2779	286	26	,	,	PUNCT
ejpam-2779	286	27	we	we	PRON
ejpam-2779	286	28	call	call	VERB
ejpam-2779	286	29	a	a	PRON
ejpam-2779	286	30	to	to	PART
ejpam-2779	286	31	be	be	AUX
ejpam-2779	286	32	a	a	DET
ejpam-2779	286	33	local	local	ADJ
ejpam-2779	286	34	∧1	∧1	NOUN
ejpam-2779	286	35	-	-	PUNCT
ejpam-2779	286	36	commutative	commutative	ADJ
ejpam-2779	286	37	pseudo	pseudo	NOUN
ejpam-2779	286	38	-	-	ADJ
ejpam-2779	286	39	bci	bci	ADJ
ejpam-2779	286	40	algebra	algebra	NOUN
ejpam-2779	286	41	.	.	PUNCT
ejpam-2779	287	1	(	(	PUNCT
ejpam-2779	287	2	2	2	X
ejpam-2779	287	3	)	)	PUNCT
ejpam-2779	287	4	if	if	SCONJ
ejpam-2779	287	5	for	for	ADP
ejpam-2779	287	6	all	all	DET
ejpam-2779	287	7	a	a	DET
ejpam-2779	287	8	∈	∈	PROPN
ejpam-2779	287	9	m(a	m(a	PROPN
ejpam-2779	287	10	)	)	PUNCT
ejpam-2779	287	11	and	and	CCONJ
ejpam-2779	287	12	x	x	X
ejpam-2779	287	13	,	,	PUNCT
ejpam-2779	287	14	y	y	PROPN
ejpam-2779	287	15	∈	∈	PROPN
ejpam-2779	287	16	v	v	ADP
ejpam-2779	287	17	(	(	PUNCT
ejpam-2779	287	18	a	a	NOUN
ejpam-2779	287	19	)	)	PUNCT
ejpam-2779	287	20	,	,	PUNCT
ejpam-2779	287	21	x	x	PUNCT
ejpam-2779	287	22	∧2	∧2	PROPN
ejpam-2779	287	23	y	y	PROPN
ejpam-2779	287	24	=	=	PUNCT
ejpam-2779	287	25	y	y	PROPN
ejpam-2779	287	26	∧2	∧2	PROPN
ejpam-2779	287	27	x	x	NOUN
ejpam-2779	287	28	,	,	PUNCT
ejpam-2779	287	29	we	we	PRON
ejpam-2779	287	30	call	call	VERB
ejpam-2779	287	31	a	a	PRON
ejpam-2779	287	32	to	to	PART
ejpam-2779	287	33	be	be	AUX
ejpam-2779	287	34	a	a	DET
ejpam-2779	287	35	local	local	ADJ
ejpam-2779	287	36	∧2commutative	∧2commutative	NOUN
ejpam-2779	287	37	pseudo	pseudo	NOUN
ejpam-2779	287	38	-	-	ADJ
ejpam-2779	287	39	bci	bci	ADJ
ejpam-2779	287	40	algebra	algebra	NOUN
ejpam-2779	287	41	.	.	PUNCT
ejpam-2779	288	1	(	(	PUNCT
ejpam-2779	288	2	3	3	X
ejpam-2779	288	3	)	)	PUNCT
ejpam-2779	288	4	if	if	SCONJ
ejpam-2779	288	5	a	a	PRON
ejpam-2779	288	6	is	be	AUX
ejpam-2779	288	7	local	local	ADJ
ejpam-2779	288	8	∧1	∧1	NOUN
ejpam-2779	288	9	-	-	PUNCT
ejpam-2779	288	10	commutative	commutative	ADJ
ejpam-2779	288	11	and	and	CCONJ
ejpam-2779	288	12	local	local	ADJ
ejpam-2779	288	13	∧2	∧2	PROPN
ejpam-2779	288	14	-	-	PUNCT
ejpam-2779	288	15	commutative	commutative	ADJ
ejpam-2779	288	16	,	,	PUNCT
ejpam-2779	288	17	we	we	PRON
ejpam-2779	288	18	call	call	VERB
ejpam-2779	288	19	a	a	PRON
ejpam-2779	288	20	to	to	PART
ejpam-2779	288	21	be	be	AUX
ejpam-2779	288	22	local	local	ADJ
ejpam-2779	288	23	commutative	commutative	ADJ
ejpam-2779	288	24	.	.	PUNCT
ejpam-2779	289	1	proposition	proposition	NOUN
ejpam-2779	289	2	14	14	NUM
ejpam-2779	289	3	.	.	PUNCT
ejpam-2779	290	1	(	(	PUNCT
ejpam-2779	290	2	1	1	X
ejpam-2779	290	3	)	)	PUNCT
ejpam-2779	290	4	if	if	SCONJ
ejpam-2779	290	5	a	a	PRON
ejpam-2779	290	6	is	be	AUX
ejpam-2779	290	7	local	local	ADJ
ejpam-2779	290	8	∧1	∧1	NOUN
ejpam-2779	290	9	-	-	PUNCT
ejpam-2779	290	10	commutative	commutative	ADJ
ejpam-2779	290	11	,	,	PUNCT
ejpam-2779	290	12	then	then	ADV
ejpam-2779	290	13	(	(	PUNCT
ejpam-2779	290	14	v	v	NOUN
ejpam-2779	290	15	(	(	PUNCT
ejpam-2779	290	16	a),∧1	a),∧1	NOUN
ejpam-2779	290	17	)	)	PUNCT
ejpam-2779	290	18	forms	form	VERB
ejpam-2779	290	19	a	a	DET
ejpam-2779	290	20	lower	low	ADJ
ejpam-2779	290	21	similattice	similattice	NOUN
ejpam-2779	290	22	for	for	ADP
ejpam-2779	290	23	all	all	DET
ejpam-2779	290	24	a	a	DET
ejpam-2779	290	25	∈m(a	∈m(a	NOUN
ejpam-2779	290	26	)	)	PUNCT
ejpam-2779	290	27	.	.	PUNCT
ejpam-2779	291	1	(	(	PUNCT
ejpam-2779	291	2	2	2	X
ejpam-2779	291	3	)	)	PUNCT
ejpam-2779	291	4	if	if	SCONJ
ejpam-2779	291	5	a	a	PRON
ejpam-2779	291	6	is	be	AUX
ejpam-2779	291	7	local	local	ADJ
ejpam-2779	291	8	∧2	∧2	NOUN
ejpam-2779	291	9	-	-	PUNCT
ejpam-2779	291	10	commutative	commutative	ADJ
ejpam-2779	291	11	,	,	PUNCT
ejpam-2779	291	12	then	then	ADV
ejpam-2779	291	13	(	(	PUNCT
ejpam-2779	291	14	v	v	NOUN
ejpam-2779	291	15	(	(	PUNCT
ejpam-2779	291	16	a),∧2	a),∧2	PROPN
ejpam-2779	291	17	)	)	PUNCT
ejpam-2779	291	18	forms	form	VERB
ejpam-2779	291	19	a	a	DET
ejpam-2779	291	20	lower	low	ADJ
ejpam-2779	291	21	similattice	similattice	NOUN
ejpam-2779	291	22	for	for	ADP
ejpam-2779	291	23	all	all	DET
ejpam-2779	291	24	a	a	DET
ejpam-2779	291	25	∈	∈	PROPN
ejpam-2779	291	26	m(a	m(a	NOUN
ejpam-2779	291	27	)	)	PUNCT
ejpam-2779	291	28	.	.	PUNCT
ejpam-2779	292	1	proof	proof	NOUN
ejpam-2779	292	2	.	.	PUNCT
ejpam-2779	293	1	(	(	PUNCT
ejpam-2779	293	2	1	1	X
ejpam-2779	293	3	)	)	PUNCT
ejpam-2779	293	4	it	it	PRON
ejpam-2779	293	5	needs	need	VERB
ejpam-2779	293	6	only	only	ADV
ejpam-2779	293	7	to	to	PART
ejpam-2779	293	8	prove	prove	VERB
ejpam-2779	293	9	that	that	SCONJ
ejpam-2779	293	10	x	x	PUNCT
ejpam-2779	293	11	∧1	∧1	PRON
ejpam-2779	293	12	y	y	PROPN
ejpam-2779	293	13	is	be	AUX
ejpam-2779	293	14	the	the	DET
ejpam-2779	293	15	greatest	greatest	ADV
ejpam-2779	293	16	lower	low	ADJ
ejpam-2779	293	17	bound	bind	VERB
ejpam-2779	293	18	of	of	ADP
ejpam-2779	293	19	{	{	PUNCT
ejpam-2779	293	20	x	x	PROPN
ejpam-2779	293	21	,	,	PUNCT
ejpam-2779	293	22	y	y	NOUN
ejpam-2779	293	23	}	}	PUNCT
ejpam-2779	293	24	for	for	ADP
ejpam-2779	293	25	all	all	DET
ejpam-2779	293	26	a	a	DET
ejpam-2779	293	27	∈m(a	∈m(a	NOUN
ejpam-2779	293	28	)	)	PUNCT
ejpam-2779	293	29	and	and	CCONJ
ejpam-2779	293	30	x	x	NOUN
ejpam-2779	293	31	,	,	PUNCT
ejpam-2779	293	32	y	y	PROPN
ejpam-2779	293	33	∈	∈	PROPN
ejpam-2779	293	34	v	v	ADP
ejpam-2779	293	35	(	(	PUNCT
ejpam-2779	293	36	a	a	NOUN
ejpam-2779	293	37	)	)	PUNCT
ejpam-2779	293	38	.	.	PUNCT
ejpam-2779	294	1	assume	assume	VERB
ejpam-2779	294	2	that	that	SCONJ
ejpam-2779	294	3	m	m	PROPN
ejpam-2779	294	4	is	be	AUX
ejpam-2779	294	5	a	a	DET
ejpam-2779	294	6	lower	low	ADJ
ejpam-2779	294	7	bound	bind	VERB
ejpam-2779	294	8	of	of	ADP
ejpam-2779	294	9	{	{	PUNCT
ejpam-2779	294	10	x	x	PROPN
ejpam-2779	294	11	,	,	PUNCT
ejpam-2779	294	12	y	y	PROPN
ejpam-2779	294	13	}	}	PUNCT
ejpam-2779	294	14	.	.	PUNCT
ejpam-2779	295	1	we	we	PRON
ejpam-2779	295	2	have	have	AUX
ejpam-2779	295	3	m∗(x∧1y	m∗(x∧1y	VERB
ejpam-2779	295	4	)	)	PUNCT
ejpam-2779	296	1	=	=	PRON
ejpam-2779	296	2	(	(	PUNCT
ejpam-2779	296	3	m	m	NOUN
ejpam-2779	296	4	◦	◦	NOUN
ejpam-2779	296	5	(m∗y))∗(y	(m∗y))∗(y	NOUN
ejpam-2779	296	6	◦	◦	NOUN
ejpam-2779	296	7	(y∗x	(y∗x	NOUN
ejpam-2779	296	8	)	)	PUNCT
ejpam-2779	296	9	)	)	PUNCT
ejpam-2779	297	1	=	=	SYM
ejpam-2779	297	2	(	(	PUNCT
ejpam-2779	297	3	y∧1m)∗(y	y∧1m)∗(y	PROPN
ejpam-2779	297	4	◦	◦	NOUN
ejpam-2779	297	5	(y∗x	(y∗x	NOUN
ejpam-2779	297	6	)	)	PUNCT
ejpam-2779	297	7	)	)	PUNCT
ejpam-2779	298	1	=	=	SYM
ejpam-2779	298	2	(	(	PUNCT
ejpam-2779	298	3	m∧1y)∗(y	m∧1y)∗(y	PROPN
ejpam-2779	298	4	◦	◦	NOUN
ejpam-2779	298	5	(y∗x	(y∗x	NOUN
ejpam-2779	298	6	)	)	PUNCT
ejpam-2779	298	7	)	)	PUNCT
ejpam-2779	299	1	=	=	PRON
ejpam-2779	299	2	(	(	PUNCT
ejpam-2779	299	3	y	y	PROPN
ejpam-2779	299	4	◦	◦	NOUN
ejpam-2779	299	5	(	(	PUNCT
ejpam-2779	299	6	y	y	PROPN
ejpam-2779	299	7	∗m	∗m	NOUN
ejpam-2779	299	8	)	)	PUNCT
ejpam-2779	299	9	)	)	PUNCT
ejpam-2779	300	1	∗	∗	NOUN
ejpam-2779	300	2	(	(	PUNCT
ejpam-2779	300	3	y	y	PROPN
ejpam-2779	300	4	◦	◦	NOUN
ejpam-2779	300	5	(	(	PUNCT
ejpam-2779	300	6	y	y	PROPN
ejpam-2779	300	7	∗	∗	NOUN
ejpam-2779	300	8	x	x	NOUN
ejpam-2779	300	9	)	)	PUNCT
ejpam-2779	300	10	)	)	PUNCT
ejpam-2779	300	11	≤	≤	NOUN
ejpam-2779	300	12	(	(	PUNCT
ejpam-2779	300	13	y	y	PROPN
ejpam-2779	300	14	∗	∗	X
ejpam-2779	300	15	x	x	NOUN
ejpam-2779	300	16	)	)	PUNCT
ejpam-2779	300	17	◦	◦	NOUN
ejpam-2779	300	18	(	(	PUNCT
ejpam-2779	300	19	y	y	PROPN
ejpam-2779	300	20	∗m	∗m	NOUN
ejpam-2779	300	21	)	)	PUNCT
ejpam-2779	300	22	≤	≤	NUM
ejpam-2779	300	23	m	m	VERB
ejpam-2779	300	24	∗	∗	NOUN
ejpam-2779	300	25	x	x	PUNCT
ejpam-2779	300	26	=	=	SYM
ejpam-2779	300	27	0	0	NUM
ejpam-2779	300	28	,	,	PUNCT
ejpam-2779	300	29	and	and	CCONJ
ejpam-2779	300	30	so	so	ADV
ejpam-2779	300	31	m	m	VERB
ejpam-2779	300	32	≤	≤	ADJ
ejpam-2779	300	33	(	(	PUNCT
ejpam-2779	300	34	x	x	SYM
ejpam-2779	300	35	∧1	∧1	NUM
ejpam-2779	300	36	y	y	NOUN
ejpam-2779	300	37	)	)	PUNCT
ejpam-2779	300	38	.	.	PUNCT
ejpam-2779	301	1	x.l	x.l	PROPN
ejpam-2779	301	2	.	.	PUNCT
ejpam-2779	302	1	xin	xin	PROPN
ejpam-2779	302	2	,	,	PUNCT
ejpam-2779	302	3	y.j	y.j	PROPN
ejpam-2779	302	4	.	.	PUNCT
ejpam-2779	302	5	li	li	PROPN
ejpam-2779	302	6	,	,	PUNCT
ejpam-2779	302	7	y.l	y.l	PROPN
ejpam-2779	302	8	.	.	PROPN
ejpam-2779	302	9	fu	fu	PROPN
ejpam-2779	302	10	/	/	SYM
ejpam-2779	302	11	eur	eur	PROPN
ejpam-2779	302	12	.	.	PUNCT
ejpam-2779	303	1	j.	j.	PROPN
ejpam-2779	303	2	pure	pure	PROPN
ejpam-2779	303	3	appl	appl	PROPN
ejpam-2779	303	4	.	.	PROPN
ejpam-2779	303	5	math	math	PROPN
ejpam-2779	303	6	,	,	PUNCT
ejpam-2779	303	7	10	10	NUM
ejpam-2779	303	8	(	(	PUNCT
ejpam-2779	303	9	3	3	NUM
ejpam-2779	303	10	)	)	PUNCT
ejpam-2779	303	11	(	(	PUNCT
ejpam-2779	303	12	2017	2017	NUM
ejpam-2779	303	13	)	)	PUNCT
ejpam-2779	303	14	,	,	PUNCT
ejpam-2779	303	15	455	455	NUM
ejpam-2779	303	16	-	-	SYM
ejpam-2779	303	17	472	472	NUM
ejpam-2779	303	18	463	463	NUM
ejpam-2779	303	19	(	(	PUNCT
ejpam-2779	303	20	2	2	NUM
ejpam-2779	303	21	)	)	PUNCT
ejpam-2779	303	22	similar	similar	ADJ
ejpam-2779	303	23	to	to	ADP
ejpam-2779	303	24	the	the	DET
ejpam-2779	303	25	proof	proof	NOUN
ejpam-2779	303	26	of	of	ADP
ejpam-2779	303	27	(	(	PUNCT
ejpam-2779	303	28	1	1	NUM
ejpam-2779	303	29	)	)	PUNCT
ejpam-2779	303	30	.	.	PUNCT
ejpam-2779	304	1	for	for	ADP
ejpam-2779	304	2	a	a	DET
ejpam-2779	304	3	lbp	lbp	NOUN
ejpam-2779	304	4	-	-	PUNCT
ejpam-2779	304	5	bci	bci	PROPN
ejpam-2779	304	6	algebra	algebra	PROPN
ejpam-2779	304	7	a	a	PRON
ejpam-2779	304	8	,	,	PUNCT
ejpam-2779	304	9	we	we	PRON
ejpam-2779	304	10	can	can	AUX
ejpam-2779	304	11	define	define	VERB
ejpam-2779	304	12	the	the	DET
ejpam-2779	304	13	following	follow	VERB
ejpam-2779	304	14	operations	operation	NOUN
ejpam-2779	304	15	in	in	ADP
ejpam-2779	304	16	v	v	NUM
ejpam-2779	304	17	(	(	PUNCT
ejpam-2779	304	18	a	a	NOUN
ejpam-2779	304	19	)	)	PUNCT
ejpam-2779	304	20	,	,	PUNCT
ejpam-2779	304	21	x	x	X
ejpam-2779	305	1	∨1	∨1	PROPN
ejpam-2779	305	2	y	y	PROPN
ejpam-2779	305	3	=	=	PUNCT
ejpam-2779	305	4	1a	1a	PROPN
ejpam-2779	305	5	◦	◦	NOUN
ejpam-2779	305	6	(	(	PUNCT
ejpam-2779	305	7	(	(	PUNCT
ejpam-2779	305	8	1a	1a	X
ejpam-2779	305	9	∗	∗	X
ejpam-2779	305	10	x	x	SYM
ejpam-2779	305	11	)	)	PUNCT
ejpam-2779	305	12	∧1	∧1	VERB
ejpam-2779	305	13	(	(	PUNCT
ejpam-2779	305	14	1a	1a	X
ejpam-2779	305	15	∗	∗	PROPN
ejpam-2779	305	16	y	y	PROPN
ejpam-2779	305	17	)	)	PUNCT
ejpam-2779	305	18	)	)	PUNCT
ejpam-2779	305	19	,	,	PUNCT
ejpam-2779	305	20	x	x	X
ejpam-2779	305	21	∨2	∨2	VERB
ejpam-2779	305	22	y	y	PROPN
ejpam-2779	305	23	=	=	SYM
ejpam-2779	305	24	1a	1a	PROPN
ejpam-2779	305	25	∗	∗	NOUN
ejpam-2779	305	26	(	(	PUNCT
ejpam-2779	305	27	(	(	PUNCT
ejpam-2779	305	28	1a	1a	X
ejpam-2779	305	29	◦	◦	NOUN
ejpam-2779	305	30	x	x	NOUN
ejpam-2779	305	31	)	)	PUNCT
ejpam-2779	305	32	∧2	∧2	PROPN
ejpam-2779	305	33	(	(	PUNCT
ejpam-2779	305	34	1a	1a	PROPN
ejpam-2779	305	35	◦	◦	NOUN
ejpam-2779	305	36	y	y	PROPN
ejpam-2779	305	37	)	)	PUNCT
ejpam-2779	305	38	)	)	PUNCT
ejpam-2779	305	39	,	,	PUNCT
ejpam-2779	305	40	for	for	ADP
ejpam-2779	305	41	all	all	DET
ejpam-2779	305	42	a	a	DET
ejpam-2779	305	43	∈m(a	∈m(a	NOUN
ejpam-2779	305	44	)	)	PUNCT
ejpam-2779	305	45	and	and	CCONJ
ejpam-2779	305	46	for	for	ADP
ejpam-2779	305	47	all	all	DET
ejpam-2779	305	48	x	x	NOUN
ejpam-2779	305	49	,	,	PUNCT
ejpam-2779	305	50	y	y	PROPN
ejpam-2779	305	51	∈	∈	PROPN
ejpam-2779	305	52	v	v	ADP
ejpam-2779	305	53	(	(	PUNCT
ejpam-2779	305	54	a	a	NOUN
ejpam-2779	305	55	)	)	PUNCT
ejpam-2779	305	56	.	.	PUNCT
ejpam-2779	306	1	proposition	proposition	NOUN
ejpam-2779	306	2	15	15	NUM
ejpam-2779	306	3	.	.	PUNCT
ejpam-2779	307	1	let	let	VERB
ejpam-2779	307	2	a	a	PRON
ejpam-2779	307	3	be	be	AUX
ejpam-2779	307	4	a	a	DET
ejpam-2779	307	5	lbp	lbp	NOUN
ejpam-2779	307	6	-	-	PUNCT
ejpam-2779	307	7	bci	bci	NOUN
ejpam-2779	307	8	algebra	algebra	NOUN
ejpam-2779	307	9	.	.	PUNCT
ejpam-2779	308	1	(	(	PUNCT
ejpam-2779	308	2	1	1	X
ejpam-2779	308	3	)	)	PUNCT
ejpam-2779	308	4	if	if	SCONJ
ejpam-2779	308	5	a	a	PRON
ejpam-2779	308	6	is	be	AUX
ejpam-2779	308	7	local	local	ADJ
ejpam-2779	308	8	∧1	∧1	NOUN
ejpam-2779	308	9	-	-	PUNCT
ejpam-2779	308	10	commutative	commutative	ADJ
ejpam-2779	308	11	,	,	PUNCT
ejpam-2779	308	12	then	then	ADV
ejpam-2779	308	13	(	(	PUNCT
ejpam-2779	308	14	v	v	NOUN
ejpam-2779	308	15	(	(	PUNCT
ejpam-2779	308	16	a),∧1,∨1	a),∧1,∨1	NOUN
ejpam-2779	308	17	)	)	PUNCT
ejpam-2779	308	18	forms	form	VERB
ejpam-2779	308	19	a	a	DET
ejpam-2779	308	20	lattice	lattice	NOUN
ejpam-2779	308	21	for	for	ADP
ejpam-2779	308	22	all	all	DET
ejpam-2779	308	23	a	a	DET
ejpam-2779	308	24	∈m(a	∈m(a	NOUN
ejpam-2779	308	25	)	)	PUNCT
ejpam-2779	308	26	.	.	PUNCT
ejpam-2779	309	1	(	(	PUNCT
ejpam-2779	309	2	2	2	X
ejpam-2779	309	3	)	)	PUNCT
ejpam-2779	309	4	if	if	SCONJ
ejpam-2779	309	5	a	a	PRON
ejpam-2779	309	6	is	be	AUX
ejpam-2779	309	7	local	local	ADJ
ejpam-2779	309	8	∧2	∧2	NOUN
ejpam-2779	309	9	-	-	PUNCT
ejpam-2779	309	10	commutative	commutative	ADJ
ejpam-2779	309	11	,	,	PUNCT
ejpam-2779	309	12	then	then	ADV
ejpam-2779	309	13	(	(	PUNCT
ejpam-2779	309	14	v	v	NOUN
ejpam-2779	309	15	(	(	PUNCT
ejpam-2779	309	16	a),∧2,∨2	a),∧2,∨2	NOUN
ejpam-2779	309	17	)	)	PUNCT
ejpam-2779	309	18	forms	form	VERB
ejpam-2779	309	19	a	a	DET
ejpam-2779	309	20	lattice	lattice	NOUN
ejpam-2779	309	21	for	for	ADP
ejpam-2779	309	22	all	all	DET
ejpam-2779	309	23	a	a	DET
ejpam-2779	309	24	∈m(a	∈m(a	NOUN
ejpam-2779	309	25	)	)	PUNCT
ejpam-2779	309	26	.	.	PUNCT
ejpam-2779	310	1	proof	proof	NOUN
ejpam-2779	310	2	.	.	PUNCT
ejpam-2779	311	1	(	(	PUNCT
ejpam-2779	311	2	1	1	X
ejpam-2779	311	3	)	)	PUNCT
ejpam-2779	311	4	let	let	VERB
ejpam-2779	311	5	a	a	DET
ejpam-2779	311	6	∈	∈	PROPN
ejpam-2779	311	7	m(a	m(a	PROPN
ejpam-2779	311	8	)	)	PUNCT
ejpam-2779	311	9	and	and	CCONJ
ejpam-2779	311	10	x	x	X
ejpam-2779	311	11	,	,	PUNCT
ejpam-2779	311	12	y	y	PROPN
ejpam-2779	311	13	∈	∈	PROPN
ejpam-2779	311	14	v	v	ADP
ejpam-2779	311	15	(	(	PUNCT
ejpam-2779	311	16	a	a	NOUN
ejpam-2779	311	17	)	)	PUNCT
ejpam-2779	311	18	.	.	PUNCT
ejpam-2779	312	1	since	since	SCONJ
ejpam-2779	312	2	a	a	PRON
ejpam-2779	312	3	is	be	AUX
ejpam-2779	312	4	local	local	ADJ
ejpam-2779	312	5	∧1	∧1	NOUN
ejpam-2779	312	6	-	-	PUNCT
ejpam-2779	312	7	commutative	commutative	ADJ
ejpam-2779	312	8	,	,	PUNCT
ejpam-2779	312	9	then	then	ADV
ejpam-2779	312	10	x	x	X
ejpam-2779	312	11	=	=	SYM
ejpam-2779	312	12	x	x	SYM
ejpam-2779	312	13	◦	◦	NOUN
ejpam-2779	312	14	(	(	PUNCT
ejpam-2779	313	1	x	x	X
ejpam-2779	313	2	∗	∗	NOUN
ejpam-2779	313	3	1a	1a	NOUN
ejpam-2779	313	4	)	)	PUNCT
ejpam-2779	314	1	=	=	SYM
ejpam-2779	314	2	1a	1a	X
ejpam-2779	314	3	◦	◦	NOUN
ejpam-2779	314	4	(	(	PUNCT
ejpam-2779	314	5	1a	1a	X
ejpam-2779	314	6	∗	∗	X
ejpam-2779	314	7	x	x	NOUN
ejpam-2779	314	8	)	)	PUNCT
ejpam-2779	314	9	≤	≤	NUM
ejpam-2779	314	10	1a	1a	X
ejpam-2779	314	11	◦	◦	NOUN
ejpam-2779	314	12	(	(	PUNCT
ejpam-2779	314	13	(	(	PUNCT
ejpam-2779	314	14	1a	1a	X
ejpam-2779	314	15	∗	∗	X
ejpam-2779	314	16	x)∧1	x)∧1	PROPN
ejpam-2779	314	17	(	(	PUNCT
ejpam-2779	314	18	1a	1a	PROPN
ejpam-2779	314	19	∗	∗	PROPN
ejpam-2779	314	20	y	y	PROPN
ejpam-2779	314	21	)	)	PUNCT
ejpam-2779	314	22	)	)	PUNCT
ejpam-2779	314	23	=	=	PUNCT
ejpam-2779	315	1	x∨1	x∨1	X
ejpam-2779	315	2	y.	y.	PROPN
ejpam-2779	315	3	similarly	similarly	ADV
ejpam-2779	315	4	we	we	PRON
ejpam-2779	315	5	can	can	AUX
ejpam-2779	315	6	prove	prove	VERB
ejpam-2779	315	7	y	y	NOUN
ejpam-2779	315	8	≤	≤	NUM
ejpam-2779	315	9	x	x	X
ejpam-2779	315	10	∨1	∨1	PROPN
ejpam-2779	315	11	y.	y.	PROPN
ejpam-2779	315	12	if	if	SCONJ
ejpam-2779	315	13	z	z	PROPN
ejpam-2779	315	14	≥	≥	NUM
ejpam-2779	315	15	x	x	X
ejpam-2779	315	16	and	and	CCONJ
ejpam-2779	315	17	z	z	PROPN
ejpam-2779	315	18	≥	≥	PROPN
ejpam-2779	315	19	y	y	NOUN
ejpam-2779	315	20	,	,	PUNCT
ejpam-2779	315	21	then	then	ADV
ejpam-2779	315	22	z	z	PROPN
ejpam-2779	315	23	∈	∈	PROPN
ejpam-2779	315	24	v	v	ADP
ejpam-2779	315	25	(	(	PUNCT
ejpam-2779	315	26	a	a	NOUN
ejpam-2779	315	27	)	)	PUNCT
ejpam-2779	315	28	,	,	PUNCT
ejpam-2779	315	29	1a	1a	PROPN
ejpam-2779	315	30	∗	∗	X
ejpam-2779	315	31	x	x	PUNCT
ejpam-2779	315	32	≥	≥	X
ejpam-2779	315	33	1a	1a	NOUN
ejpam-2779	315	34	∗	∗	X
ejpam-2779	315	35	z	z	PROPN
ejpam-2779	315	36	and	and	CCONJ
ejpam-2779	315	37	1a	1a	PROPN
ejpam-2779	315	38	∗	∗	X
ejpam-2779	315	39	y	y	PROPN
ejpam-2779	315	40	≥	≥	PROPN
ejpam-2779	315	41	1a	1a	PROPN
ejpam-2779	315	42	∗	∗	X
ejpam-2779	315	43	z.	z.	PROPN
ejpam-2779	315	44	by	by	ADP
ejpam-2779	315	45	proposition	proposition	NOUN
ejpam-2779	315	46	14	14	NUM
ejpam-2779	315	47	,	,	PUNCT
ejpam-2779	315	48	we	we	PRON
ejpam-2779	315	49	have	have	VERB
ejpam-2779	315	50	1a	1a	PROPN
ejpam-2779	315	51	∗	∗	NOUN
ejpam-2779	315	52	z	z	NOUN
ejpam-2779	315	53	≤	≤	NUM
ejpam-2779	315	54	(	(	PUNCT
ejpam-2779	315	55	1a	1a	X
ejpam-2779	315	56	∗	∗	X
ejpam-2779	315	57	x	x	SYM
ejpam-2779	315	58	)	)	PUNCT
ejpam-2779	315	59	∧1	∧1	VERB
ejpam-2779	315	60	(	(	PUNCT
ejpam-2779	315	61	1a	1a	X
ejpam-2779	315	62	∗	∗	PROPN
ejpam-2779	315	63	y	y	PROPN
ejpam-2779	315	64	)	)	PUNCT
ejpam-2779	315	65	.	.	PUNCT
ejpam-2779	316	1	therefore	therefore	ADV
ejpam-2779	316	2	x	x	X
ejpam-2779	316	3	∨1	∨1	PROPN
ejpam-2779	316	4	y	y	PROPN
ejpam-2779	316	5	=	=	PUNCT
ejpam-2779	316	6	1a	1a	PROPN
ejpam-2779	316	7	◦	◦	NOUN
ejpam-2779	316	8	(	(	PUNCT
ejpam-2779	316	9	(	(	PUNCT
ejpam-2779	316	10	1a	1a	X
ejpam-2779	316	11	∗	∗	X
ejpam-2779	316	12	x	x	SYM
ejpam-2779	316	13	)	)	PUNCT
ejpam-2779	316	14	∧1	∧1	VERB
ejpam-2779	316	15	(	(	PUNCT
ejpam-2779	316	16	1a	1a	X
ejpam-2779	316	17	∗	∗	PROPN
ejpam-2779	316	18	y	y	PROPN
ejpam-2779	316	19	)	)	PUNCT
ejpam-2779	316	20	)	)	PUNCT
ejpam-2779	316	21	≤	≤	NUM
ejpam-2779	317	1	1a	1a	X
ejpam-2779	317	2	◦	◦	NOUN
ejpam-2779	317	3	(	(	PUNCT
ejpam-2779	317	4	1a	1a	X
ejpam-2779	317	5	∗	∗	X
ejpam-2779	317	6	z	z	NOUN
ejpam-2779	317	7	)	)	PUNCT
ejpam-2779	317	8	=	=	SYM
ejpam-2779	317	9	z	z	X
ejpam-2779	317	10	◦	◦	NOUN
ejpam-2779	317	11	(	(	PUNCT
ejpam-2779	317	12	z	z	NOUN
ejpam-2779	317	13	∗	∗	NOUN
ejpam-2779	317	14	1a	1a	X
ejpam-2779	317	15	)	)	PUNCT
ejpam-2779	318	1	=	=	PUNCT
ejpam-2779	318	2	z.	z.	PROPN
ejpam-2779	319	1	it	it	PRON
ejpam-2779	319	2	follows	follow	VERB
ejpam-2779	319	3	that	that	SCONJ
ejpam-2779	319	4	x	x	PRON
ejpam-2779	319	5	∨1	∨1	PROPN
ejpam-2779	319	6	y	y	PROPN
ejpam-2779	319	7	is	be	AUX
ejpam-2779	319	8	the	the	DET
ejpam-2779	319	9	least	least	ADJ
ejpam-2779	319	10	upper	upper	ADJ
ejpam-2779	319	11	bound	bind	VERB
ejpam-2779	319	12	of	of	ADP
ejpam-2779	319	13	{	{	PUNCT
ejpam-2779	319	14	x	x	PROPN
ejpam-2779	319	15	,	,	PUNCT
ejpam-2779	319	16	y	y	NOUN
ejpam-2779	319	17	}	}	PUNCT
ejpam-2779	319	18	.	.	PUNCT
ejpam-2779	320	1	applying	apply	VERB
ejpam-2779	320	2	proposition	proposition	NOUN
ejpam-2779	320	3	14	14	NUM
ejpam-2779	320	4	,	,	PUNCT
ejpam-2779	320	5	we	we	PRON
ejpam-2779	320	6	get	get	VERB
ejpam-2779	320	7	(	(	PUNCT
ejpam-2779	320	8	v	v	NOUN
ejpam-2779	320	9	(	(	PUNCT
ejpam-2779	320	10	a),∧1,∨1	a),∧1,∨1	NOUN
ejpam-2779	320	11	)	)	PUNCT
ejpam-2779	320	12	forms	form	VERB
ejpam-2779	320	13	a	a	DET
ejpam-2779	320	14	lattice	lattice	NOUN
ejpam-2779	320	15	.	.	PUNCT
ejpam-2779	321	1	(	(	PUNCT
ejpam-2779	321	2	2	2	X
ejpam-2779	321	3	)	)	PUNCT
ejpam-2779	321	4	similar	similar	ADJ
ejpam-2779	321	5	to	to	ADP
ejpam-2779	321	6	the	the	DET
ejpam-2779	321	7	proof	proof	NOUN
ejpam-2779	321	8	of	of	ADP
ejpam-2779	321	9	(	(	PUNCT
ejpam-2779	321	10	1	1	NUM
ejpam-2779	321	11	)	)	PUNCT
ejpam-2779	321	12	.	.	PUNCT
ejpam-2779	322	1	definition	definition	NOUN
ejpam-2779	322	2	6	6	NUM
ejpam-2779	322	3	.	.	PUNCT
ejpam-2779	323	1	let	let	VERB
ejpam-2779	323	2	a	a	PRON
ejpam-2779	323	3	be	be	AUX
ejpam-2779	323	4	a	a	DET
ejpam-2779	323	5	pseudo	pseudo	NOUN
ejpam-2779	323	6	-	-	ADJ
ejpam-2779	323	7	bci	bci	ADJ
ejpam-2779	323	8	algebra	algebra	NOUN
ejpam-2779	323	9	.	.	PUNCT
ejpam-2779	324	1	(	(	PUNCT
ejpam-2779	324	2	1	1	X
ejpam-2779	324	3	)	)	PUNCT
ejpam-2779	324	4	if	if	SCONJ
ejpam-2779	324	5	for	for	ADP
ejpam-2779	324	6	all	all	DET
ejpam-2779	324	7	x	x	NOUN
ejpam-2779	324	8	,	,	PUNCT
ejpam-2779	324	9	y	y	PROPN
ejpam-2779	324	10	∈	∈	PROPN
ejpam-2779	324	11	a	a	PRON
ejpam-2779	324	12	,	,	PUNCT
ejpam-2779	324	13	x∧1	x∧1	PROPN
ejpam-2779	324	14	y	y	PROPN
ejpam-2779	324	15	=	=	PUNCT
ejpam-2779	324	16	y	y	PROPN
ejpam-2779	324	17	∧1	∧1	NUM
ejpam-2779	324	18	x	x	VERB
ejpam-2779	324	19	,	,	PUNCT
ejpam-2779	324	20	we	we	PRON
ejpam-2779	324	21	call	call	VERB
ejpam-2779	324	22	a	a	PRON
ejpam-2779	324	23	to	to	PART
ejpam-2779	324	24	be	be	AUX
ejpam-2779	324	25	∧1	∧1	VERB
ejpam-2779	324	26	-	-	PUNCT
ejpam-2779	324	27	commutative	commutative	ADJ
ejpam-2779	324	28	.	.	PUNCT
ejpam-2779	325	1	(	(	PUNCT
ejpam-2779	325	2	2	2	X
ejpam-2779	325	3	)	)	PUNCT
ejpam-2779	325	4	if	if	SCONJ
ejpam-2779	325	5	for	for	ADP
ejpam-2779	325	6	all	all	DET
ejpam-2779	325	7	x	x	NOUN
ejpam-2779	325	8	,	,	PUNCT
ejpam-2779	325	9	y	y	PROPN
ejpam-2779	325	10	∈	∈	PROPN
ejpam-2779	325	11	a	a	PRON
ejpam-2779	325	12	,	,	PUNCT
ejpam-2779	325	13	x	x	X
ejpam-2779	325	14	∧2	∧2	PROPN
ejpam-2779	325	15	y	y	PROPN
ejpam-2779	325	16	=	=	PUNCT
ejpam-2779	325	17	y	y	PROPN
ejpam-2779	325	18	∧2	∧2	PROPN
ejpam-2779	325	19	x	x	NOUN
ejpam-2779	325	20	,	,	PUNCT
ejpam-2779	325	21	we	we	PRON
ejpam-2779	325	22	call	call	VERB
ejpam-2779	325	23	a	a	PRON
ejpam-2779	325	24	to	to	PART
ejpam-2779	325	25	be	be	AUX
ejpam-2779	325	26	∧2	∧2	NOUN
ejpam-2779	325	27	-	-	PUNCT
ejpam-2779	325	28	commutative	commutative	ADJ
ejpam-2779	325	29	.	.	PUNCT
ejpam-2779	326	1	(	(	PUNCT
ejpam-2779	326	2	3	3	X
ejpam-2779	326	3	)	)	PUNCT
ejpam-2779	326	4	if	if	SCONJ
ejpam-2779	326	5	a	a	PRON
ejpam-2779	326	6	is	be	AUX
ejpam-2779	326	7	∧1	∧1	VERB
ejpam-2779	326	8	-	-	PUNCT
ejpam-2779	326	9	commutative	commutative	ADJ
ejpam-2779	326	10	and	and	CCONJ
ejpam-2779	326	11	∧2	∧2	NOUN
ejpam-2779	326	12	-	-	PUNCT
ejpam-2779	326	13	commutative	commutative	ADJ
ejpam-2779	326	14	,	,	PUNCT
ejpam-2779	326	15	we	we	PRON
ejpam-2779	326	16	call	call	VERB
ejpam-2779	326	17	a	a	PRON
ejpam-2779	326	18	to	to	PART
ejpam-2779	326	19	be	be	AUX
ejpam-2779	326	20	sup	sup	NOUN
ejpam-2779	326	21	-	-	PUNCT
ejpam-2779	326	22	commutative	commutative	ADJ
ejpam-2779	326	23	.	.	PUNCT
ejpam-2779	327	1	the	the	DET
ejpam-2779	327	2	following	follow	VERB
ejpam-2779	327	3	result	result	NOUN
ejpam-2779	327	4	shows	show	VERB
ejpam-2779	327	5	that	that	SCONJ
ejpam-2779	327	6	∧1	∧1	NOUN
ejpam-2779	327	7	-	-	PUNCT
ejpam-2779	327	8	commutative	commutative	ADJ
ejpam-2779	327	9	(	(	PUNCT
ejpam-2779	327	10	∧2	∧2	NOUN
ejpam-2779	327	11	-	-	PUNCT
ejpam-2779	327	12	commutative	commutative	ADJ
ejpam-2779	327	13	)	)	PUNCT
ejpam-2779	327	14	pseudo	pseudo	NOUN
ejpam-2779	327	15	-	-	PUNCT
ejpam-2779	327	16	bci	bci	ADJ
ejpam-2779	327	17	algebras	algebra	NOUN
ejpam-2779	327	18	must	must	AUX
ejpam-2779	327	19	be	be	AUX
ejpam-2779	327	20	pseudo	pseudo	NOUN
ejpam-2779	327	21	-	-	ADJ
ejpam-2779	327	22	bck	bck	ADJ
ejpam-2779	327	23	algebras	algebra	NOUN
ejpam-2779	327	24	.	.	PUNCT
ejpam-2779	328	1	proposition	proposition	NOUN
ejpam-2779	328	2	16	16	NUM
ejpam-2779	328	3	.	.	PUNCT
ejpam-2779	329	1	let	let	VERB
ejpam-2779	329	2	a	a	PRON
ejpam-2779	329	3	be	be	AUX
ejpam-2779	329	4	a	a	DET
ejpam-2779	329	5	pseudo	pseudo	NOUN
ejpam-2779	329	6	-	-	ADJ
ejpam-2779	329	7	bci	bci	ADJ
ejpam-2779	329	8	algebra	algebra	NOUN
ejpam-2779	329	9	.	.	PUNCT
ejpam-2779	330	1	then	then	ADV
ejpam-2779	330	2	the	the	DET
ejpam-2779	330	3	following	follow	VERB
ejpam-2779	330	4	are	be	AUX
ejpam-2779	330	5	equivalent	equivalent	ADJ
ejpam-2779	330	6	:	:	PUNCT
ejpam-2779	330	7	(	(	PUNCT
ejpam-2779	330	8	1	1	X
ejpam-2779	330	9	)	)	PUNCT
ejpam-2779	330	10	a	a	PRON
ejpam-2779	330	11	is	be	AUX
ejpam-2779	330	12	∧1	∧1	VERB
ejpam-2779	330	13	-	-	PUNCT
ejpam-2779	330	14	commutative	commutative	ADJ
ejpam-2779	330	15	(	(	PUNCT
ejpam-2779	330	16	∧2	∧2	NOUN
ejpam-2779	330	17	-	-	PUNCT
ejpam-2779	330	18	commutative	commutative	ADJ
ejpam-2779	330	19	)	)	PUNCT
ejpam-2779	330	20	.	.	PUNCT
ejpam-2779	331	1	(	(	PUNCT
ejpam-2779	331	2	2	2	X
ejpam-2779	331	3	)	)	PUNCT
ejpam-2779	331	4	a	a	PRON
ejpam-2779	331	5	is	be	AUX
ejpam-2779	331	6	a	a	DET
ejpam-2779	331	7	∧1	∧1	NOUN
ejpam-2779	331	8	-	-	PUNCT
ejpam-2779	331	9	commutative	commutative	ADJ
ejpam-2779	331	10	(	(	PUNCT
ejpam-2779	331	11	∧2	∧2	NOUN
ejpam-2779	331	12	-	-	PUNCT
ejpam-2779	331	13	commutative	commutative	ADJ
ejpam-2779	331	14	)	)	PUNCT
ejpam-2779	331	15	pseudo	pseudo	NOUN
ejpam-2779	331	16	-	-	ADJ
ejpam-2779	331	17	bck	bck	ADJ
ejpam-2779	331	18	algebra	algebra	NOUN
ejpam-2779	331	19	.	.	PUNCT
ejpam-2779	332	1	proof	proof	NOUN
ejpam-2779	332	2	.	.	PUNCT
ejpam-2779	333	1	(	(	PUNCT
ejpam-2779	333	2	1	1	X
ejpam-2779	333	3	)	)	PUNCT
ejpam-2779	333	4	⇒	⇒	NOUN
ejpam-2779	333	5	(	(	PUNCT
ejpam-2779	333	6	2	2	NUM
ejpam-2779	333	7	)	)	PUNCT
ejpam-2779	333	8	.	.	PUNCT
ejpam-2779	334	1	let	let	VERB
ejpam-2779	334	2	a	a	PRON
ejpam-2779	334	3	be	be	AUX
ejpam-2779	334	4	∧1	∧1	VERB
ejpam-2779	334	5	-	-	PUNCT
ejpam-2779	334	6	commutative	commutative	ADJ
ejpam-2779	334	7	.	.	PUNCT
ejpam-2779	335	1	then	then	ADV
ejpam-2779	335	2	for	for	ADP
ejpam-2779	335	3	any	any	DET
ejpam-2779	335	4	a	a	DET
ejpam-2779	335	5	∈	∈	PROPN
ejpam-2779	335	6	m(a	m(a	NOUN
ejpam-2779	335	7	)	)	PUNCT
ejpam-2779	335	8	,	,	PUNCT
ejpam-2779	335	9	we	we	PRON
ejpam-2779	335	10	have	have	VERB
ejpam-2779	335	11	a∧10	a∧10	PROPN
ejpam-2779	335	12	=	=	SYM
ejpam-2779	335	13	0∧1a	0∧1a	PROPN
ejpam-2779	335	14	.	.	PUNCT
ejpam-2779	336	1	note	note	VERB
ejpam-2779	336	2	that	that	SCONJ
ejpam-2779	336	3	a∧10	a∧10	PROPN
ejpam-2779	336	4	=	=	SYM
ejpam-2779	336	5	0	0	NUM
ejpam-2779	336	6	◦	◦	NOUN
ejpam-2779	336	7	(0∗a	(0∗a	NOUN
ejpam-2779	336	8	)	)	PUNCT
ejpam-2779	336	9	=	=	PUNCT
ejpam-2779	337	1	a	a	PRON
ejpam-2779	337	2	by	by	ADP
ejpam-2779	337	3	proposition	proposition	NOUN
ejpam-2779	337	4	6	6	NUM
ejpam-2779	337	5	and	and	CCONJ
ejpam-2779	337	6	0∧1a	0∧1a	NUM
ejpam-2779	337	7	=	=	PUNCT
ejpam-2779	337	8	a	a	DET
ejpam-2779	337	9	◦	◦	NOUN
ejpam-2779	337	10	(a∗0	(a∗0	NOUN
ejpam-2779	337	11	)	)	PUNCT
ejpam-2779	338	1	=	=	SYM
ejpam-2779	338	2	0	0	X
ejpam-2779	338	3	.	.	PUNCT
ejpam-2779	339	1	this	this	PRON
ejpam-2779	339	2	shows	show	VERB
ejpam-2779	339	3	that	that	SCONJ
ejpam-2779	339	4	a	a	DET
ejpam-2779	339	5	=	=	SYM
ejpam-2779	339	6	0	0	NUM
ejpam-2779	339	7	,	,	PUNCT
ejpam-2779	339	8	that	that	PRON
ejpam-2779	339	9	is	be	AUX
ejpam-2779	339	10	a	a	DET
ejpam-2779	339	11	=	=	ADJ
ejpam-2779	339	12	v	v	NOUN
ejpam-2779	339	13	(	(	PUNCT
ejpam-2779	339	14	0	0	NUM
ejpam-2779	339	15	)	)	PUNCT
ejpam-2779	339	16	.	.	PUNCT
ejpam-2779	340	1	thus	thus	ADV
ejpam-2779	340	2	a	a	PRON
ejpam-2779	340	3	is	be	AUX
ejpam-2779	340	4	a	a	DET
ejpam-2779	340	5	∧1	∧1	NOUN
ejpam-2779	340	6	-	-	PUNCT
ejpam-2779	340	7	commutative	commutative	ADJ
ejpam-2779	340	8	pseudo	pseudo	NOUN
ejpam-2779	340	9	-	-	ADJ
ejpam-2779	340	10	bck	bck	ADJ
ejpam-2779	340	11	algebra	algebra	NOUN
ejpam-2779	340	12	.	.	PUNCT
ejpam-2779	341	1	similarly	similarly	ADV
ejpam-2779	341	2	we	we	PRON
ejpam-2779	341	3	can	can	AUX
ejpam-2779	341	4	prove	prove	VERB
ejpam-2779	341	5	the	the	DET
ejpam-2779	341	6	result	result	NOUN
ejpam-2779	341	7	for	for	ADP
ejpam-2779	341	8	case	case	NOUN
ejpam-2779	341	9	of	of	ADP
ejpam-2779	341	10	∧2	∧2	NOUN
ejpam-2779	341	11	-	-	PUNCT
ejpam-2779	341	12	commutative	commutative	ADJ
ejpam-2779	341	13	.	.	PUNCT
ejpam-2779	342	1	(	(	PUNCT
ejpam-2779	342	2	2)⇒	2)⇒	NUM
ejpam-2779	342	3	(	(	PUNCT
ejpam-2779	342	4	1	1	NUM
ejpam-2779	342	5	)	)	PUNCT
ejpam-2779	342	6	.	.	PUNCT
ejpam-2779	343	1	it	it	PRON
ejpam-2779	343	2	is	be	AUX
ejpam-2779	343	3	straightforward	straightforward	ADJ
ejpam-2779	343	4	.	.	PUNCT
ejpam-2779	344	1	proposition	proposition	NOUN
ejpam-2779	344	2	17	17	NUM
ejpam-2779	344	3	.	.	PUNCT
ejpam-2779	345	1	[	[	X
ejpam-2779	345	2	15	15	NUM
ejpam-2779	345	3	]	]	X
ejpam-2779	345	4	if	if	SCONJ
ejpam-2779	345	5	a	a	PRON
ejpam-2779	345	6	is	be	AUX
ejpam-2779	345	7	a	a	DET
ejpam-2779	345	8	sup	sup	ADJ
ejpam-2779	345	9	-	-	PUNCT
ejpam-2779	345	10	commutative	commutative	ADJ
ejpam-2779	345	11	pseudo	pseudo	NOUN
ejpam-2779	345	12	-	-	ADJ
ejpam-2779	345	13	bck	bck	ADJ
ejpam-2779	345	14	algebra	algebra	NOUN
ejpam-2779	345	15	,	,	PUNCT
ejpam-2779	345	16	then	then	ADV
ejpam-2779	345	17	∧1	∧1	AUX
ejpam-2779	345	18	=	=	SYM
ejpam-2779	345	19	∧2	∧2	PROPN
ejpam-2779	345	20	.	.	PUNCT
ejpam-2779	345	21	by	by	ADP
ejpam-2779	345	22	proposition	proposition	NOUN
ejpam-2779	345	23	16	16	NUM
ejpam-2779	345	24	and	and	CCONJ
ejpam-2779	345	25	17	17	NUM
ejpam-2779	345	26	,	,	PUNCT
ejpam-2779	345	27	we	we	PRON
ejpam-2779	345	28	can	can	AUX
ejpam-2779	345	29	get	get	VERB
ejpam-2779	345	30	a	a	DET
ejpam-2779	345	31	characterization	characterization	NOUN
ejpam-2779	345	32	of	of	ADP
ejpam-2779	345	33	sup	sup	NOUN
ejpam-2779	345	34	-	-	PUNCT
ejpam-2779	345	35	commutative	commutative	ADJ
ejpam-2779	345	36	pseudobci	pseudobci	NOUN
ejpam-2779	345	37	algebras	algebra	NOUN
ejpam-2779	345	38	.	.	PUNCT
ejpam-2779	346	1	proposition	proposition	NOUN
ejpam-2779	346	2	18	18	NUM
ejpam-2779	346	3	.	.	PUNCT
ejpam-2779	347	1	let	let	VERB
ejpam-2779	347	2	a	a	PRON
ejpam-2779	347	3	be	be	AUX
ejpam-2779	347	4	a	a	DET
ejpam-2779	347	5	pseudo	pseudo	NOUN
ejpam-2779	347	6	-	-	ADJ
ejpam-2779	347	7	bci	bci	ADJ
ejpam-2779	347	8	algebra	algebra	NOUN
ejpam-2779	347	9	.	.	PUNCT
ejpam-2779	348	1	then	then	ADV
ejpam-2779	348	2	the	the	DET
ejpam-2779	348	3	following	follow	VERB
ejpam-2779	348	4	are	be	AUX
ejpam-2779	348	5	equivalent	equivalent	ADJ
ejpam-2779	348	6	:	:	PUNCT
ejpam-2779	348	7	(	(	PUNCT
ejpam-2779	348	8	1	1	X
ejpam-2779	348	9	)	)	PUNCT
ejpam-2779	348	10	a	a	PRON
ejpam-2779	348	11	is	be	AUX
ejpam-2779	348	12	a	a	DET
ejpam-2779	348	13	sup	sup	ADJ
ejpam-2779	348	14	-	-	PUNCT
ejpam-2779	348	15	commutative	commutative	ADJ
ejpam-2779	348	16	pseudo	pseudo	NOUN
ejpam-2779	348	17	-	-	ADJ
ejpam-2779	348	18	bci	bci	ADJ
ejpam-2779	348	19	algebra	algebra	NOUN
ejpam-2779	348	20	.	.	PUNCT
ejpam-2779	349	1	(	(	PUNCT
ejpam-2779	349	2	2	2	X
ejpam-2779	349	3	)	)	PUNCT
ejpam-2779	349	4	a	a	PRON
ejpam-2779	349	5	is	be	AUX
ejpam-2779	349	6	a	a	DET
ejpam-2779	349	7	sup	sup	ADJ
ejpam-2779	349	8	-	-	PUNCT
ejpam-2779	349	9	commutative	commutative	ADJ
ejpam-2779	349	10	pseudo	pseudo	NOUN
ejpam-2779	349	11	-	-	ADJ
ejpam-2779	349	12	bck	bck	ADJ
ejpam-2779	349	13	algebra	algebra	NOUN
ejpam-2779	349	14	.	.	PUNCT
ejpam-2779	350	1	x.l	x.l	PROPN
ejpam-2779	350	2	.	.	PUNCT
ejpam-2779	351	1	xin	xin	PROPN
ejpam-2779	351	2	,	,	PUNCT
ejpam-2779	351	3	y.j	y.j	PROPN
ejpam-2779	351	4	.	.	PUNCT
ejpam-2779	351	5	li	li	PROPN
ejpam-2779	351	6	,	,	PUNCT
ejpam-2779	351	7	y.l	y.l	PROPN
ejpam-2779	351	8	.	.	PROPN
ejpam-2779	351	9	fu	fu	PROPN
ejpam-2779	351	10	/	/	SYM
ejpam-2779	351	11	eur	eur	PROPN
ejpam-2779	351	12	.	.	PUNCT
ejpam-2779	352	1	j.	j.	PROPN
ejpam-2779	352	2	pure	pure	PROPN
ejpam-2779	352	3	appl	appl	PROPN
ejpam-2779	352	4	.	.	PROPN
ejpam-2779	352	5	math	math	PROPN
ejpam-2779	352	6	,	,	PUNCT
ejpam-2779	352	7	10	10	NUM
ejpam-2779	352	8	(	(	PUNCT
ejpam-2779	352	9	3	3	NUM
ejpam-2779	352	10	)	)	PUNCT
ejpam-2779	352	11	(	(	PUNCT
ejpam-2779	352	12	2017	2017	NUM
ejpam-2779	352	13	)	)	PUNCT
ejpam-2779	352	14	,	,	PUNCT
ejpam-2779	352	15	455	455	NUM
ejpam-2779	352	16	-	-	SYM
ejpam-2779	352	17	472	472	NUM
ejpam-2779	352	18	464	464	NUM
ejpam-2779	352	19	4	4	NUM
ejpam-2779	352	20	.	.	PUNCT
ejpam-2779	353	1	states	state	NOUN
ejpam-2779	353	2	on	on	ADP
ejpam-2779	353	3	local	local	ADJ
ejpam-2779	353	4	bounded	bounded	ADJ
ejpam-2779	353	5	pseudo	pseudo	NOUN
ejpam-2779	353	6	-	-	ADJ
ejpam-2779	353	7	bci	bci	ADJ
ejpam-2779	353	8	algebras	algebras	PROPN
ejpam-2779	353	9	definition	definition	NOUN
ejpam-2779	353	10	7	7	NUM
ejpam-2779	353	11	.	.	PUNCT
ejpam-2779	353	12	let	let	VERB
ejpam-2779	353	13	a	a	PRON
ejpam-2779	353	14	be	be	AUX
ejpam-2779	353	15	a	a	DET
ejpam-2779	353	16	lbp	lbp	NOUN
ejpam-2779	353	17	-	-	PUNCT
ejpam-2779	353	18	bci	bci	NOUN
ejpam-2779	353	19	algebra	algebra	NOUN
ejpam-2779	353	20	.	.	PUNCT
ejpam-2779	354	1	a	a	DET
ejpam-2779	354	2	bosbach	bosbach	ADJ
ejpam-2779	354	3	state	state	NOUN
ejpam-2779	354	4	on	on	ADP
ejpam-2779	354	5	a	a	PRON
ejpam-2779	354	6	is	be	AUX
ejpam-2779	354	7	a	a	DET
ejpam-2779	354	8	function	function	NOUN
ejpam-2779	354	9	s	s	PART
ejpam-2779	354	10	:	:	PUNCT
ejpam-2779	354	11	a	a	DET
ejpam-2779	354	12	→	→	SYM
ejpam-2779	354	13	[	[	X
ejpam-2779	354	14	0	0	NUM
ejpam-2779	354	15	,	,	PUNCT
ejpam-2779	354	16	1	1	NUM
ejpam-2779	354	17	]	]	PUNCT
ejpam-2779	354	18	such	such	ADJ
ejpam-2779	354	19	that	that	SCONJ
ejpam-2779	354	20	the	the	DET
ejpam-2779	354	21	following	follow	VERB
ejpam-2779	354	22	conditions	condition	NOUN
ejpam-2779	354	23	hold	hold	VERB
ejpam-2779	354	24	:	:	PUNCT
ejpam-2779	354	25	(	(	PUNCT
ejpam-2779	354	26	1	1	X
ejpam-2779	354	27	)	)	PUNCT
ejpam-2779	354	28	s(x	s(x	PROPN
ejpam-2779	354	29	)	)	PUNCT
ejpam-2779	355	1	+	+	CCONJ
ejpam-2779	355	2	s(y	s(y	PROPN
ejpam-2779	355	3	∗	∗	NOUN
ejpam-2779	355	4	x	x	NOUN
ejpam-2779	355	5	)	)	PUNCT
ejpam-2779	355	6	=	=	SYM
ejpam-2779	355	7	s(y	s(y	NOUN
ejpam-2779	355	8	)	)	PUNCT
ejpam-2779	356	1	+	+	NUM
ejpam-2779	356	2	s(x	s(x	PROPN
ejpam-2779	356	3	∗	∗	NOUN
ejpam-2779	356	4	y	y	PROPN
ejpam-2779	356	5	)	)	PUNCT
ejpam-2779	356	6	,	,	PUNCT
ejpam-2779	356	7	for	for	ADP
ejpam-2779	356	8	all	all	DET
ejpam-2779	356	9	x	x	NOUN
ejpam-2779	356	10	,	,	PUNCT
ejpam-2779	356	11	y	y	PROPN
ejpam-2779	356	12	∈	∈	PROPN
ejpam-2779	356	13	a	a	PRON
ejpam-2779	356	14	,	,	PUNCT
ejpam-2779	356	15	(	(	PUNCT
ejpam-2779	356	16	2	2	NUM
ejpam-2779	356	17	)	)	PUNCT
ejpam-2779	356	18	s(x	s(x	PROPN
ejpam-2779	356	19	)	)	PUNCT
ejpam-2779	357	1	+	+	CCONJ
ejpam-2779	357	2	s(y	s(y	PROPN
ejpam-2779	357	3	◦	◦	NOUN
ejpam-2779	357	4	x	x	X
ejpam-2779	357	5	)	)	PUNCT
ejpam-2779	357	6	=	=	SYM
ejpam-2779	357	7	s(y	s(y	NOUN
ejpam-2779	357	8	)	)	PUNCT
ejpam-2779	357	9	+	+	CCONJ
ejpam-2779	357	10	s(x	s(x	PROPN
ejpam-2779	357	11	◦	◦	NOUN
ejpam-2779	357	12	y	y	PROPN
ejpam-2779	357	13	)	)	PUNCT
ejpam-2779	357	14	,	,	PUNCT
ejpam-2779	357	15	for	for	ADP
ejpam-2779	357	16	all	all	DET
ejpam-2779	357	17	x	x	NOUN
ejpam-2779	357	18	,	,	PUNCT
ejpam-2779	357	19	y	y	PROPN
ejpam-2779	357	20	∈	∈	PROPN
ejpam-2779	357	21	a	a	PRON
ejpam-2779	357	22	,	,	PUNCT
ejpam-2779	357	23	(	(	PUNCT
ejpam-2779	357	24	3	3	X
ejpam-2779	357	25	)	)	PUNCT
ejpam-2779	357	26	s(a	s(a	PROPN
ejpam-2779	357	27	)	)	PUNCT
ejpam-2779	357	28	=	=	SYM
ejpam-2779	357	29	1	1	NUM
ejpam-2779	357	30	and	and	CCONJ
ejpam-2779	357	31	s(1a	s(1a	NUM
ejpam-2779	357	32	)	)	PUNCT
ejpam-2779	357	33	=	=	SYM
ejpam-2779	357	34	0	0	NUM
ejpam-2779	357	35	where	where	SCONJ
ejpam-2779	357	36	a	a	DET
ejpam-2779	357	37	∈m(a	∈m(a	NOUN
ejpam-2779	357	38	)	)	PUNCT
ejpam-2779	357	39	and	and	CCONJ
ejpam-2779	357	40	1a	1a	X
ejpam-2779	357	41	is	be	AUX
ejpam-2779	357	42	the	the	DET
ejpam-2779	357	43	local	local	ADJ
ejpam-2779	357	44	unit	unit	NOUN
ejpam-2779	357	45	of	of	ADP
ejpam-2779	357	46	v	v	NOUN
ejpam-2779	357	47	(	(	PUNCT
ejpam-2779	357	48	a	a	NOUN
ejpam-2779	357	49	)	)	PUNCT
ejpam-2779	357	50	.	.	PUNCT
ejpam-2779	358	1	example	example	NOUN
ejpam-2779	359	1	3	3	X
ejpam-2779	359	2	.	.	X
ejpam-2779	359	3	consider	consider	VERB
ejpam-2779	359	4	the	the	DET
ejpam-2779	359	5	local	local	ADJ
ejpam-2779	359	6	bounded	bounded	ADJ
ejpam-2779	359	7	pseudo	pseudo	NOUN
ejpam-2779	359	8	-	-	NOUN
ejpam-2779	359	9	bci	bci	NOUN
ejpam-2779	359	10	algebra	algebra	NOUN
ejpam-2779	359	11	a	a	PRON
ejpam-2779	359	12	given	give	VERB
ejpam-2779	359	13	in	in	ADP
ejpam-2779	359	14	example	example	NOUN
ejpam-2779	359	15	1	1	NUM
ejpam-2779	359	16	.	.	X
ejpam-2779	359	17	define	define	VERB
ejpam-2779	359	18	the	the	DET
ejpam-2779	359	19	function	function	NOUN
ejpam-2779	359	20	s	s	PART
ejpam-2779	359	21	:	:	PUNCT
ejpam-2779	359	22	a	a	DET
ejpam-2779	359	23	→	→	SYM
ejpam-2779	359	24	[	[	X
ejpam-2779	359	25	0	0	NUM
ejpam-2779	359	26	,	,	PUNCT
ejpam-2779	359	27	1	1	NUM
ejpam-2779	359	28	]	]	PUNCT
ejpam-2779	359	29	by	by	ADP
ejpam-2779	359	30	s(0	s(0	PROPN
ejpam-2779	359	31	)	)	PUNCT
ejpam-2779	359	32	=	=	SYM
ejpam-2779	359	33	1	1	NUM
ejpam-2779	359	34	,	,	PUNCT
ejpam-2779	359	35	s(u	s(u	PROPN
ejpam-2779	359	36	)	)	PUNCT
ejpam-2779	359	37	=	=	SYM
ejpam-2779	359	38	1	1	NUM
ejpam-2779	359	39	,	,	PUNCT
ejpam-2779	359	40	s(v	s(v	PROPN
ejpam-2779	359	41	)	)	PUNCT
ejpam-2779	359	42	=	=	SYM
ejpam-2779	359	43	1	1	NUM
ejpam-2779	359	44	,	,	PUNCT
ejpam-2779	359	45	s(w	s(w	NOUN
ejpam-2779	359	46	)	)	PUNCT
ejpam-2779	359	47	=	=	SYM
ejpam-2779	359	48	1	1	NUM
ejpam-2779	359	49	,	,	PUNCT
ejpam-2779	359	50	s(t	s(t	PROPN
ejpam-2779	359	51	)	)	PUNCT
ejpam-2779	359	52	=	=	SYM
ejpam-2779	360	1	1	1	NUM
ejpam-2779	360	2	,	,	PUNCT
ejpam-2779	360	3	s(1	s(1	PROPN
ejpam-2779	360	4	)	)	PUNCT
ejpam-2779	360	5	=	=	SYM
ejpam-2779	360	6	0	0	NUM
ejpam-2779	360	7	,	,	PUNCT
ejpam-2779	360	8	s(a	s(a	PROPN
ejpam-2779	360	9	)	)	PUNCT
ejpam-2779	360	10	=	=	SYM
ejpam-2779	360	11	1	1	NUM
ejpam-2779	360	12	,	,	PUNCT
ejpam-2779	360	13	s(b	s(b	NOUN
ejpam-2779	360	14	)	)	PUNCT
ejpam-2779	360	15	=	=	SYM
ejpam-2779	361	1	0	0	X
ejpam-2779	361	2	.	.	PUNCT
ejpam-2779	362	1	then	then	ADV
ejpam-2779	362	2	s	s	VERB
ejpam-2779	362	3	is	be	AUX
ejpam-2779	362	4	a	a	DET
ejpam-2779	362	5	unique	unique	ADJ
ejpam-2779	362	6	bosbach	bosbach	ADJ
ejpam-2779	362	7	state	state	NOUN
ejpam-2779	362	8	on	on	ADP
ejpam-2779	362	9	a.	a.	NOUN
ejpam-2779	362	10	example	example	NOUN
ejpam-2779	362	11	4	4	X
ejpam-2779	362	12	.	.	PUNCT
ejpam-2779	362	13	consider	consider	VERB
ejpam-2779	362	14	the	the	DET
ejpam-2779	362	15	local	local	ADJ
ejpam-2779	362	16	bounded	bounded	ADJ
ejpam-2779	362	17	pseudo	pseudo	NOUN
ejpam-2779	362	18	-	-	NOUN
ejpam-2779	362	19	bci	bci	NOUN
ejpam-2779	362	20	algebra	algebra	NOUN
ejpam-2779	362	21	a	a	DET
ejpam-2779	362	22	given	give	VERB
ejpam-2779	362	23	in	in	ADP
ejpam-2779	362	24	example	example	NOUN
ejpam-2779	362	25	2	2	NUM
ejpam-2779	362	26	.	.	PUNCT
ejpam-2779	362	27	define	define	VERB
ejpam-2779	362	28	a	a	DET
ejpam-2779	362	29	function	function	NOUN
ejpam-2779	362	30	s	s	PART
ejpam-2779	362	31	:	:	PUNCT
ejpam-2779	362	32	a→	a→	PUNCT
ejpam-2779	362	33	[	[	X
ejpam-2779	362	34	0	0	NUM
ejpam-2779	362	35	,	,	PUNCT
ejpam-2779	362	36	1	1	NUM
ejpam-2779	362	37	]	]	PUNCT
ejpam-2779	362	38	as	as	SCONJ
ejpam-2779	362	39	follows	follow	VERB
ejpam-2779	362	40	:	:	PUNCT
ejpam-2779	362	41	s(0	s(0	PROPN
ejpam-2779	362	42	)	)	PUNCT
ejpam-2779	362	43	=	=	SYM
ejpam-2779	362	44	1	1	NUM
ejpam-2779	362	45	,	,	PUNCT
ejpam-2779	362	46	s(x	s(x	NOUN
ejpam-2779	362	47	)	)	PUNCT
ejpam-2779	362	48	=	=	SYM
ejpam-2779	362	49	α	α	NOUN
ejpam-2779	362	50	,	,	PUNCT
ejpam-2779	362	51	s(y	s(y	PROPN
ejpam-2779	362	52	)	)	PUNCT
ejpam-2779	362	53	=	=	SYM
ejpam-2779	363	1	β	β	X
ejpam-2779	363	2	,	,	PUNCT
ejpam-2779	363	3	s(z	s(z	PROPN
ejpam-2779	363	4	)	)	PUNCT
ejpam-2779	363	5	=	=	SYM
ejpam-2779	364	1	γ	γ	X
ejpam-2779	364	2	,	,	PUNCT
ejpam-2779	364	3	s(1	s(1	PROPN
ejpam-2779	364	4	)	)	PUNCT
ejpam-2779	364	5	=	=	SYM
ejpam-2779	364	6	0	0	NUM
ejpam-2779	364	7	,	,	PUNCT
ejpam-2779	364	8	s(a	s(a	PROPN
ejpam-2779	364	9	)	)	PUNCT
ejpam-2779	364	10	=	=	SYM
ejpam-2779	364	11	1	1	NUM
ejpam-2779	364	12	,	,	PUNCT
ejpam-2779	364	13	s(b	s(b	NOUN
ejpam-2779	364	14	)	)	PUNCT
ejpam-2779	364	15	=	=	SYM
ejpam-2779	364	16	0	0	X
ejpam-2779	364	17	.	.	X
ejpam-2779	364	18	using	use	VERB
ejpam-2779	364	19	s(u	s(u	PROPN
ejpam-2779	364	20	)	)	PUNCT
ejpam-2779	364	21	+	+	NUM
ejpam-2779	364	22	s(v	s(v	PROPN
ejpam-2779	364	23	∗	∗	NOUN
ejpam-2779	364	24	u	u	NOUN
ejpam-2779	364	25	)	)	PUNCT
ejpam-2779	364	26	=	=	SYM
ejpam-2779	364	27	s(v	s(v	PROPN
ejpam-2779	364	28	)	)	PUNCT
ejpam-2779	365	1	+	+	NUM
ejpam-2779	365	2	s(u	s(u	PROPN
ejpam-2779	365	3	∗	∗	NOUN
ejpam-2779	365	4	v	v	NOUN
ejpam-2779	365	5	)	)	PUNCT
ejpam-2779	365	6	,	,	PUNCT
ejpam-2779	365	7	taking	take	VERB
ejpam-2779	365	8	u	u	NOUN
ejpam-2779	365	9	=	=	NOUN
ejpam-2779	365	10	x	x	PROPN
ejpam-2779	365	11	,	,	PUNCT
ejpam-2779	365	12	v	v	NOUN
ejpam-2779	365	13	=	=	SYM
ejpam-2779	365	14	1	1	NUM
ejpam-2779	365	15	,	,	PUNCT
ejpam-2779	365	16	u	u	NOUN
ejpam-2779	365	17	=	=	PROPN
ejpam-2779	365	18	y	y	PROPN
ejpam-2779	365	19	,	,	PUNCT
ejpam-2779	365	20	v	v	NOUN
ejpam-2779	365	21	=	=	SYM
ejpam-2779	365	22	1	1	NUM
ejpam-2779	365	23	and	and	CCONJ
ejpam-2779	365	24	u	u	NOUN
ejpam-2779	366	1	=	=	PROPN
ejpam-2779	366	2	z	z	PROPN
ejpam-2779	366	3	,	,	PUNCT
ejpam-2779	366	4	v	v	NOUN
ejpam-2779	366	5	=	=	SYM
ejpam-2779	366	6	1	1	NUM
ejpam-2779	366	7	,	,	PUNCT
ejpam-2779	366	8	respectively	respectively	ADV
ejpam-2779	366	9	,	,	PUNCT
ejpam-2779	366	10	we	we	PRON
ejpam-2779	366	11	get	get	VERB
ejpam-2779	366	12	α	α	NOUN
ejpam-2779	366	13	=	=	SYM
ejpam-2779	366	14	1	1	NUM
ejpam-2779	366	15	,	,	PUNCT
ejpam-2779	366	16	β	β	X
ejpam-2779	366	17	=	=	SYM
ejpam-2779	366	18	1	1	NUM
ejpam-2779	366	19	,	,	PUNCT
ejpam-2779	366	20	γ	γ	NOUN
ejpam-2779	366	21	=	=	SYM
ejpam-2779	366	22	0	0	NUM
ejpam-2779	366	23	.	.	PUNCT
ejpam-2779	367	1	on	on	ADP
ejpam-2779	367	2	the	the	DET
ejpam-2779	367	3	other	other	ADJ
ejpam-2779	367	4	hand	hand	NOUN
ejpam-2779	367	5	,	,	PUNCT
ejpam-2779	367	6	taking	take	VERB
ejpam-2779	367	7	u	u	NOUN
ejpam-2779	367	8	=	=	PROPN
ejpam-2779	367	9	z	z	PROPN
ejpam-2779	367	10	,	,	PUNCT
ejpam-2779	367	11	v	v	NOUN
ejpam-2779	367	12	=	=	SYM
ejpam-2779	367	13	1	1	NUM
ejpam-2779	367	14	in	in	ADP
ejpam-2779	367	15	s(u	s(u	PROPN
ejpam-2779	367	16	)	)	PUNCT
ejpam-2779	367	17	+	+	NUM
ejpam-2779	367	18	s(v	s(v	PROPN
ejpam-2779	367	19	◦	◦	NOUN
ejpam-2779	367	20	u	u	NOUN
ejpam-2779	367	21	)	)	PUNCT
ejpam-2779	367	22	=	=	SYM
ejpam-2779	367	23	s(v	s(v	PROPN
ejpam-2779	367	24	)	)	PUNCT
ejpam-2779	367	25	+	+	NUM
ejpam-2779	367	26	s(u	s(u	PROPN
ejpam-2779	367	27	◦	◦	NOUN
ejpam-2779	367	28	v	v	NOUN
ejpam-2779	367	29	)	)	PUNCT
ejpam-2779	367	30	,	,	PUNCT
ejpam-2779	367	31	we	we	PRON
ejpam-2779	367	32	get	get	VERB
ejpam-2779	367	33	γ	γ	X
ejpam-2779	367	34	+	+	NOUN
ejpam-2779	367	35	0	0	NUM
ejpam-2779	367	36	=	=	SYM
ejpam-2779	367	37	0	0	PUNCT
ejpam-2779	368	1	+	+	NUM
ejpam-2779	368	2	1	1	NUM
ejpam-2779	368	3	,	,	PUNCT
ejpam-2779	368	4	so	so	ADV
ejpam-2779	368	5	0	0	X
ejpam-2779	368	6	=	=	SYM
ejpam-2779	368	7	1	1	NUM
ejpam-2779	368	8	which	which	PRON
ejpam-2779	368	9	is	be	AUX
ejpam-2779	368	10	a	a	DET
ejpam-2779	368	11	contradiction	contradiction	NOUN
ejpam-2779	368	12	.	.	PUNCT
ejpam-2779	369	1	hence	hence	ADV
ejpam-2779	369	2	a	a	PRON
ejpam-2779	369	3	does	do	AUX
ejpam-2779	369	4	not	not	PART
ejpam-2779	369	5	admit	admit	VERB
ejpam-2779	369	6	a	a	DET
ejpam-2779	369	7	bosbach	bosbach	ADJ
ejpam-2779	369	8	state	state	NOUN
ejpam-2779	369	9	.	.	PUNCT
ejpam-2779	370	1	proposition	proposition	NOUN
ejpam-2779	370	2	19	19	NUM
ejpam-2779	370	3	.	.	PUNCT
ejpam-2779	371	1	let	let	VERB
ejpam-2779	371	2	a	a	PRON
ejpam-2779	371	3	be	be	AUX
ejpam-2779	371	4	a	a	DET
ejpam-2779	371	5	lbp	lbp	NOUN
ejpam-2779	371	6	-	-	PUNCT
ejpam-2779	371	7	bci	bci	NOUN
ejpam-2779	371	8	algebra	algebra	NOUN
ejpam-2779	371	9	and	and	CCONJ
ejpam-2779	371	10	s	s	VERB
ejpam-2779	371	11	a	a	DET
ejpam-2779	371	12	bosbach	bosbach	ADJ
ejpam-2779	371	13	state	state	NOUN
ejpam-2779	371	14	on	on	ADP
ejpam-2779	371	15	a.	a.	NOUN
ejpam-2779	371	16	then	then	ADV
ejpam-2779	371	17	the	the	DET
ejpam-2779	371	18	following	follow	VERB
ejpam-2779	371	19	properties	property	NOUN
ejpam-2779	371	20	hold	hold	VERB
ejpam-2779	371	21	for	for	ADP
ejpam-2779	371	22	all	all	DET
ejpam-2779	371	23	x	x	NOUN
ejpam-2779	371	24	,	,	PUNCT
ejpam-2779	371	25	y	y	PROPN
ejpam-2779	371	26	∈	∈	PROPN
ejpam-2779	371	27	a	a	DET
ejpam-2779	371	28	:	:	PUNCT
ejpam-2779	371	29	(	(	PUNCT
ejpam-2779	371	30	1	1	X
ejpam-2779	371	31	)	)	PUNCT
ejpam-2779	371	32	if	if	SCONJ
ejpam-2779	371	33	x	x	PROPN
ejpam-2779	371	34	≤	≤	NOUN
ejpam-2779	371	35	y	y	NOUN
ejpam-2779	371	36	,	,	PUNCT
ejpam-2779	371	37	then	then	ADV
ejpam-2779	371	38	s(y	s(y	PROPN
ejpam-2779	371	39	∗	∗	NOUN
ejpam-2779	371	40	x	x	NOUN
ejpam-2779	371	41	)	)	PUNCT
ejpam-2779	371	42	=	=	SYM
ejpam-2779	372	1	1	1	NUM
ejpam-2779	372	2	+	+	NUM
ejpam-2779	372	3	s(y)−	s(y)−	NUM
ejpam-2779	372	4	s(x	s(x	NOUN
ejpam-2779	372	5	)	)	PUNCT
ejpam-2779	372	6	=	=	SYM
ejpam-2779	373	1	s(y	s(y	PROPN
ejpam-2779	373	2	◦	◦	NOUN
ejpam-2779	373	3	x	x	X
ejpam-2779	373	4	)	)	PUNCT
ejpam-2779	373	5	and	and	CCONJ
ejpam-2779	373	6	s(y	s(y	NOUN
ejpam-2779	373	7	)	)	PUNCT
ejpam-2779	373	8	≤	≤	NUM
ejpam-2779	373	9	s(x	s(x	NOUN
ejpam-2779	373	10	)	)	PUNCT
ejpam-2779	373	11	.	.	PUNCT
ejpam-2779	374	1	(	(	PUNCT
ejpam-2779	374	2	2	2	X
ejpam-2779	374	3	)	)	PUNCT
ejpam-2779	374	4	if	if	SCONJ
ejpam-2779	374	5	x	x	X
ejpam-2779	374	6	,	,	PUNCT
ejpam-2779	374	7	y	y	PROPN
ejpam-2779	374	8	are	be	AUX
ejpam-2779	374	9	in	in	ADP
ejpam-2779	374	10	same	same	ADJ
ejpam-2779	374	11	branch	branch	NOUN
ejpam-2779	374	12	,	,	PUNCT
ejpam-2779	374	13	then	then	ADV
ejpam-2779	374	14	s(x	s(x	PROPN
ejpam-2779	374	15	∧1	∧1	NUM
ejpam-2779	374	16	y	y	NOUN
ejpam-2779	374	17	)	)	PUNCT
ejpam-2779	375	1	=	=	SYM
ejpam-2779	375	2	s(y	s(y	PROPN
ejpam-2779	375	3	∧1	∧1	PROPN
ejpam-2779	375	4	x	x	NOUN
ejpam-2779	375	5	)	)	PUNCT
ejpam-2779	375	6	,	,	PUNCT
ejpam-2779	375	7	s(x	s(x	PROPN
ejpam-2779	375	8	∧2	∧2	PROPN
ejpam-2779	375	9	y	y	PROPN
ejpam-2779	375	10	)	)	PUNCT
ejpam-2779	376	1	=	=	SYM
ejpam-2779	376	2	s(y	s(y	PROPN
ejpam-2779	376	3	∧2	∧2	PROPN
ejpam-2779	376	4	x	x	NOUN
ejpam-2779	376	5	)	)	PUNCT
ejpam-2779	376	6	.	.	PUNCT
ejpam-2779	377	1	(	(	PUNCT
ejpam-2779	377	2	3	3	X
ejpam-2779	377	3	)	)	PUNCT
ejpam-2779	377	4	if	if	SCONJ
ejpam-2779	377	5	x	x	X
ejpam-2779	377	6	,	,	PUNCT
ejpam-2779	377	7	y	y	PROPN
ejpam-2779	377	8	are	be	AUX
ejpam-2779	377	9	in	in	ADP
ejpam-2779	377	10	same	same	ADJ
ejpam-2779	377	11	branch	branch	NOUN
ejpam-2779	377	12	,	,	PUNCT
ejpam-2779	377	13	then	then	ADV
ejpam-2779	377	14	s(x∧1	s(x∧1	PROPN
ejpam-2779	377	15	y−∼	y−∼	NOUN
ejpam-2779	377	16	)	)	PUNCT
ejpam-2779	378	1	=	=	SYM
ejpam-2779	378	2	s(x−∼	s(x−∼	NOUN
ejpam-2779	378	3	∧1	∧1	NUM
ejpam-2779	378	4	y−∼	y−∼	NOUN
ejpam-2779	378	5	)	)	PUNCT
ejpam-2779	378	6	,	,	PUNCT
ejpam-2779	379	1	s(x∧2	s(x∧2	PROPN
ejpam-2779	379	2	y∼−	y∼−	PROPN
ejpam-2779	379	3	)	)	PUNCT
ejpam-2779	380	1	=	=	SYM
ejpam-2779	380	2	s(x∼−∧2	s(x∼−∧2	PROPN
ejpam-2779	380	3	y∼−	y∼−	PROPN
ejpam-2779	380	4	)	)	PUNCT
ejpam-2779	380	5	.	.	PUNCT
ejpam-2779	381	1	(	(	PUNCT
ejpam-2779	381	2	4	4	X
ejpam-2779	381	3	)	)	PUNCT
ejpam-2779	381	4	if	if	SCONJ
ejpam-2779	381	5	x	x	X
ejpam-2779	381	6	,	,	PUNCT
ejpam-2779	381	7	y	y	PROPN
ejpam-2779	381	8	are	be	AUX
ejpam-2779	381	9	in	in	ADP
ejpam-2779	381	10	same	same	ADJ
ejpam-2779	381	11	branch	branch	NOUN
ejpam-2779	381	12	,	,	PUNCT
ejpam-2779	381	13	then	then	ADV
ejpam-2779	381	14	s(x−∼∧1	s(x−∼∧1	ADJ
ejpam-2779	381	15	y	y	NOUN
ejpam-2779	381	16	)	)	PUNCT
ejpam-2779	381	17	=	=	PRON
ejpam-2779	381	18	s(x∧1	s(x∧1	PROPN
ejpam-2779	381	19	y−∼	y−∼	NOUN
ejpam-2779	381	20	)	)	PUNCT
ejpam-2779	381	21	,	,	PUNCT
ejpam-2779	381	22	s(x∼−∧2	s(x∼−∧2	PROPN
ejpam-2779	381	23	y	y	PROPN
ejpam-2779	381	24	)	)	PUNCT
ejpam-2779	382	1	=	=	PROPN
ejpam-2779	382	2	s(x∧2	s(x∧2	PROPN
ejpam-2779	382	3	y∼−	y∼−	PROPN
ejpam-2779	382	4	)	)	PUNCT
ejpam-2779	382	5	.	.	PUNCT
ejpam-2779	383	1	(	(	PUNCT
ejpam-2779	383	2	5	5	NUM
ejpam-2779	383	3	)	)	PUNCT
ejpam-2779	383	4	s(x−∼	s(x−∼	NOUN
ejpam-2779	383	5	)	)	PUNCT
ejpam-2779	384	1	=	=	SYM
ejpam-2779	384	2	s(x	s(x	PROPN
ejpam-2779	384	3	)	)	PUNCT
ejpam-2779	384	4	=	=	SYM
ejpam-2779	384	5	s(x∼−	s(x∼−	NOUN
ejpam-2779	384	6	)	)	PUNCT
ejpam-2779	384	7	.	.	PUNCT
ejpam-2779	385	1	(	(	PUNCT
ejpam-2779	385	2	6	6	NUM
ejpam-2779	385	3	)	)	PUNCT
ejpam-2779	385	4	s(x−	s(x−	NOUN
ejpam-2779	385	5	)	)	PUNCT
ejpam-2779	385	6	=	=	SYM
ejpam-2779	385	7	1−	1−	NUM
ejpam-2779	385	8	s(x	s(x	PROPN
ejpam-2779	385	9	)	)	PUNCT
ejpam-2779	385	10	=	=	SYM
ejpam-2779	385	11	s(x∼	s(x∼	X
ejpam-2779	385	12	)	)	PUNCT
ejpam-2779	385	13	.	.	PUNCT
ejpam-2779	386	1	proof	proof	NOUN
ejpam-2779	386	2	.	.	PUNCT
ejpam-2779	387	1	(	(	PUNCT
ejpam-2779	387	2	1	1	X
ejpam-2779	387	3	)	)	PUNCT
ejpam-2779	387	4	let	let	VERB
ejpam-2779	387	5	x	x	SYM
ejpam-2779	387	6	≤	≤	NUM
ejpam-2779	387	7	y.	y.	NOUN
ejpam-2779	387	8	it	it	PRON
ejpam-2779	387	9	follows	follow	VERB
ejpam-2779	387	10	from	from	ADP
ejpam-2779	387	11	definition	definition	NOUN
ejpam-2779	387	12	5.1	5.1	NUM
ejpam-2779	387	13	that	that	PRON
ejpam-2779	387	14	s(y	s(y	PROPN
ejpam-2779	387	15	∗	∗	NOUN
ejpam-2779	387	16	x	x	NOUN
ejpam-2779	387	17	)	)	PUNCT
ejpam-2779	387	18	=	=	SYM
ejpam-2779	388	1	1	1	NUM
ejpam-2779	388	2	+	+	NUM
ejpam-2779	388	3	s(y)−	s(y)−	NUM
ejpam-2779	388	4	s(x	s(x	NOUN
ejpam-2779	388	5	)	)	PUNCT
ejpam-2779	388	6	=	=	SYM
ejpam-2779	389	1	s(y	s(y	PROPN
ejpam-2779	389	2	◦	◦	NOUN
ejpam-2779	389	3	x	x	NOUN
ejpam-2779	389	4	)	)	PUNCT
ejpam-2779	389	5	.	.	PUNCT
ejpam-2779	390	1	moreover	moreover	ADV
ejpam-2779	390	2	s(x)−	s(x)−	PROPN
ejpam-2779	390	3	s(y	s(y	PROPN
ejpam-2779	390	4	)	)	PUNCT
ejpam-2779	391	1	=	=	SYM
ejpam-2779	392	1	1−	1−	NUM
ejpam-2779	392	2	s(y	s(y	PROPN
ejpam-2779	392	3	∗	∗	NOUN
ejpam-2779	392	4	x	x	NOUN
ejpam-2779	392	5	)	)	PUNCT
ejpam-2779	392	6	≥	≥	NOUN
ejpam-2779	392	7	0	0	NUM
ejpam-2779	392	8	and	and	CCONJ
ejpam-2779	392	9	hence	hence	ADV
ejpam-2779	392	10	s(y	s(y	NOUN
ejpam-2779	392	11	)	)	PUNCT
ejpam-2779	392	12	≤	≤	NUM
ejpam-2779	392	13	s(x	s(x	NOUN
ejpam-2779	392	14	)	)	PUNCT
ejpam-2779	392	15	.	.	PUNCT
ejpam-2779	393	1	(	(	PUNCT
ejpam-2779	393	2	2	2	X
ejpam-2779	393	3	)	)	PUNCT
ejpam-2779	393	4	by	by	ADP
ejpam-2779	393	5	proposition	proposition	NOUN
ejpam-2779	393	6	1	1	NUM
ejpam-2779	393	7	,	,	PUNCT
ejpam-2779	393	8	we	we	PRON
ejpam-2779	393	9	have	have	VERB
ejpam-2779	393	10	y	y	PROPN
ejpam-2779	393	11	∗	∗	NOUN
ejpam-2779	393	12	x	x	PUNCT
ejpam-2779	393	13	=	=	SYM
ejpam-2779	393	14	y	y	PROPN
ejpam-2779	393	15	∗	∗	NOUN
ejpam-2779	393	16	(	(	PUNCT
ejpam-2779	393	17	x∧1	x∧1	PROPN
ejpam-2779	393	18	y	y	PROPN
ejpam-2779	393	19	)	)	PUNCT
ejpam-2779	393	20	.	.	PUNCT
ejpam-2779	394	1	since	since	SCONJ
ejpam-2779	394	2	x	x	X
ejpam-2779	394	3	,	,	PUNCT
ejpam-2779	394	4	y	y	PROPN
ejpam-2779	394	5	are	be	AUX
ejpam-2779	394	6	in	in	ADP
ejpam-2779	394	7	same	same	ADJ
ejpam-2779	394	8	branch	branch	NOUN
ejpam-2779	394	9	,	,	PUNCT
ejpam-2779	394	10	then	then	ADV
ejpam-2779	394	11	x	x	PUNCT
ejpam-2779	394	12	∧1	∧1	VERB
ejpam-2779	394	13	y	y	PROPN
ejpam-2779	394	14	≤	≤	NUM
ejpam-2779	394	15	x	x	X
ejpam-2779	394	16	,	,	PUNCT
ejpam-2779	394	17	y	y	PROPN
ejpam-2779	394	18	by	by	ADP
ejpam-2779	394	19	proposition	proposition	NOUN
ejpam-2779	394	20	13	13	NUM
ejpam-2779	394	21	.	.	PUNCT
ejpam-2779	395	1	by	by	ADP
ejpam-2779	395	2	property	property	NOUN
ejpam-2779	395	3	(	(	PUNCT
ejpam-2779	395	4	1	1	NUM
ejpam-2779	395	5	)	)	PUNCT
ejpam-2779	395	6	,	,	PUNCT
ejpam-2779	395	7	we	we	PRON
ejpam-2779	395	8	have	have	VERB
ejpam-2779	395	9	s(y	s(y	PROPN
ejpam-2779	395	10	∗	∗	NOUN
ejpam-2779	395	11	x	x	NOUN
ejpam-2779	395	12	)	)	PUNCT
ejpam-2779	396	1	=	=	SYM
ejpam-2779	396	2	s(y	s(y	PROPN
ejpam-2779	396	3	∗	∗	NOUN
ejpam-2779	396	4	(	(	PUNCT
ejpam-2779	396	5	x	x	SYM
ejpam-2779	396	6	∧1	∧1	PROPN
ejpam-2779	396	7	y	y	NOUN
ejpam-2779	396	8	)	)	PUNCT
ejpam-2779	396	9	)	)	PUNCT
ejpam-2779	397	1	=	=	PUNCT
ejpam-2779	398	1	1+s(y)−s(x∧1	1+s(y)−s(x∧1	NUM
ejpam-2779	398	2	y	y	X
ejpam-2779	398	3	)	)	PUNCT
ejpam-2779	398	4	and	and	CCONJ
ejpam-2779	398	5	s(x∗y	s(x∗y	NUM
ejpam-2779	398	6	)	)	PUNCT
ejpam-2779	399	1	=	=	PUNCT
ejpam-2779	400	1	s(x∗	s(x∗	ADV
ejpam-2779	400	2	(	(	PUNCT
ejpam-2779	400	3	y∧1	y∧1	NOUN
ejpam-2779	400	4	x	x	NOUN
ejpam-2779	400	5	)	)	PUNCT
ejpam-2779	400	6	)	)	PUNCT
ejpam-2779	401	1	=	=	PUNCT
ejpam-2779	401	2	1+s(x)−s(y∧1	1+s(x)−s(y∧1	NUM
ejpam-2779	401	3	x	x	NOUN
ejpam-2779	401	4	)	)	PUNCT
ejpam-2779	401	5	.	.	PUNCT
ejpam-2779	402	1	using	use	VERB
ejpam-2779	402	2	condition	condition	NOUN
ejpam-2779	402	3	(	(	PUNCT
ejpam-2779	402	4	1	1	NUM
ejpam-2779	402	5	)	)	PUNCT
ejpam-2779	402	6	from	from	ADP
ejpam-2779	402	7	definition	definition	NOUN
ejpam-2779	402	8	7	7	NUM
ejpam-2779	402	9	we	we	PRON
ejpam-2779	402	10	get	get	VERB
ejpam-2779	402	11	s(x∧1	s(x∧1	VERB
ejpam-2779	402	12	y	y	X
ejpam-2779	402	13	)	)	PUNCT
ejpam-2779	402	14	=	=	SYM
ejpam-2779	402	15	s(y∧1x	s(y∧1x	PROPN
ejpam-2779	402	16	)	)	PUNCT
ejpam-2779	402	17	.	.	PUNCT
ejpam-2779	403	1	similarly	similarly	ADV
ejpam-2779	403	2	we	we	PRON
ejpam-2779	403	3	can	can	AUX
ejpam-2779	403	4	prove	prove	VERB
ejpam-2779	403	5	s(x∧2	s(x∧2	PROPN
ejpam-2779	403	6	y	y	PROPN
ejpam-2779	403	7	)	)	PUNCT
ejpam-2779	403	8	=	=	SYM
ejpam-2779	403	9	s(y∧2x	s(y∧2x	PROPN
ejpam-2779	403	10	)	)	PUNCT
ejpam-2779	403	11	.	.	PUNCT
ejpam-2779	404	1	(	(	PUNCT
ejpam-2779	404	2	3	3	X
ejpam-2779	404	3	)	)	PUNCT
ejpam-2779	404	4	it	it	PRON
ejpam-2779	404	5	follows	follow	VERB
ejpam-2779	404	6	from	from	ADP
ejpam-2779	404	7	proposition	proposition	NOUN
ejpam-2779	404	8	10	10	NUM
ejpam-2779	404	9	.	.	PUNCT
ejpam-2779	405	1	(	(	PUNCT
ejpam-2779	405	2	4	4	X
ejpam-2779	405	3	)	)	PUNCT
ejpam-2779	405	4	it	it	PRON
ejpam-2779	405	5	follows	follow	VERB
ejpam-2779	405	6	from	from	ADP
ejpam-2779	405	7	(	(	PUNCT
ejpam-2779	405	8	2	2	NUM
ejpam-2779	405	9	)	)	PUNCT
ejpam-2779	405	10	and	and	CCONJ
ejpam-2779	405	11	(	(	PUNCT
ejpam-2779	405	12	3	3	NUM
ejpam-2779	405	13	)	)	PUNCT
ejpam-2779	405	14	.	.	PUNCT
ejpam-2779	406	1	(	(	PUNCT
ejpam-2779	406	2	5	5	NUM
ejpam-2779	406	3	)	)	PUNCT
ejpam-2779	406	4	for	for	ADP
ejpam-2779	406	5	x	x	PROPN
ejpam-2779	406	6	∈	∈	PROPN
ejpam-2779	406	7	a	a	PRON
ejpam-2779	406	8	,	,	PUNCT
ejpam-2779	406	9	there	there	PRON
ejpam-2779	406	10	is	be	VERB
ejpam-2779	406	11	a	a	DET
ejpam-2779	406	12	∈	∈	PROPN
ejpam-2779	406	13	m(a	m(a	NOUN
ejpam-2779	406	14	)	)	PUNCT
ejpam-2779	406	15	such	such	ADJ
ejpam-2779	406	16	that	that	SCONJ
ejpam-2779	406	17	x	x	SYM
ejpam-2779	406	18	∈	∈	NOUN
ejpam-2779	406	19	v	v	ADP
ejpam-2779	406	20	(	(	PUNCT
ejpam-2779	406	21	a	a	NOUN
ejpam-2779	406	22	)	)	PUNCT
ejpam-2779	406	23	.	.	PUNCT
ejpam-2779	407	1	note	note	VERB
ejpam-2779	407	2	that	that	SCONJ
ejpam-2779	407	3	x−∼	x−∼	ADV
ejpam-2779	408	1	=	=	NOUN
ejpam-2779	408	2	x	x	X
ejpam-2779	408	3	∧1	∧1	NUM
ejpam-2779	408	4	1a	1a	X
ejpam-2779	408	5	.	.	PUNCT
ejpam-2779	409	1	by	by	ADP
ejpam-2779	409	2	(	(	PUNCT
ejpam-2779	409	3	2	2	NUM
ejpam-2779	409	4	)	)	PUNCT
ejpam-2779	409	5	,	,	PUNCT
ejpam-2779	409	6	we	we	PRON
ejpam-2779	409	7	have	have	VERB
ejpam-2779	409	8	s(x−∼	s(x−∼	NOUN
ejpam-2779	409	9	)	)	PUNCT
ejpam-2779	410	1	=	=	PUNCT
ejpam-2779	410	2	s(x	s(x	PROPN
ejpam-2779	410	3	∧1	∧1	NUM
ejpam-2779	410	4	1a	1a	NOUN
ejpam-2779	410	5	)	)	PUNCT
ejpam-2779	411	1	=	=	PUNCT
ejpam-2779	411	2	s(1a	s(1a	X
ejpam-2779	411	3	∧1	∧1	NOUN
ejpam-2779	411	4	x	x	NOUN
ejpam-2779	411	5	)	)	PUNCT
ejpam-2779	411	6	=	=	PUNCT
ejpam-2779	412	1	s(x	s(x	NOUN
ejpam-2779	412	2	◦	◦	NOUN
ejpam-2779	412	3	(	(	PUNCT
ejpam-2779	412	4	x	x	X
ejpam-2779	412	5	∗	∗	NOUN
ejpam-2779	412	6	1a	1a	NOUN
ejpam-2779	412	7	)	)	PUNCT
ejpam-2779	412	8	)	)	PUNCT
ejpam-2779	413	1	=	=	SYM
ejpam-2779	413	2	s(x	s(x	PROPN
ejpam-2779	413	3	)	)	PUNCT
ejpam-2779	413	4	.	.	PUNCT
ejpam-2779	414	1	in	in	ADP
ejpam-2779	414	2	a	a	DET
ejpam-2779	414	3	similar	similar	ADJ
ejpam-2779	414	4	way	way	NOUN
ejpam-2779	414	5	,	,	PUNCT
ejpam-2779	414	6	we	we	PRON
ejpam-2779	414	7	can	can	AUX
ejpam-2779	414	8	prove	prove	VERB
ejpam-2779	414	9	s(x	s(x	NOUN
ejpam-2779	414	10	)	)	PUNCT
ejpam-2779	414	11	=	=	SYM
ejpam-2779	414	12	s(x∼−	s(x∼−	NOUN
ejpam-2779	414	13	)	)	PUNCT
ejpam-2779	414	14	.	.	PUNCT
ejpam-2779	415	1	(	(	PUNCT
ejpam-2779	415	2	6	6	NUM
ejpam-2779	415	3	)	)	PUNCT
ejpam-2779	415	4	by	by	ADP
ejpam-2779	415	5	(	(	PUNCT
ejpam-2779	415	6	1	1	NUM
ejpam-2779	415	7	)	)	PUNCT
ejpam-2779	415	8	,	,	PUNCT
ejpam-2779	415	9	we	we	PRON
ejpam-2779	415	10	have	have	VERB
ejpam-2779	415	11	s(x−	s(x−	NOUN
ejpam-2779	415	12	)	)	PUNCT
ejpam-2779	415	13	=	=	PUNCT
ejpam-2779	416	1	s(1a	s(1a	PROPN
ejpam-2779	416	2	∗	∗	NOUN
ejpam-2779	416	3	x	x	NOUN
ejpam-2779	416	4	)	)	PUNCT
ejpam-2779	416	5	=	=	SYM
ejpam-2779	416	6	1	1	NUM
ejpam-2779	416	7	+	+	NUM
ejpam-2779	416	8	s(1a)−	s(1a)−	NOUN
ejpam-2779	416	9	s(x	s(x	PROPN
ejpam-2779	416	10	)	)	PUNCT
ejpam-2779	416	11	=	=	SYM
ejpam-2779	416	12	1−	1−	NUM
ejpam-2779	416	13	s(x	s(x	PROPN
ejpam-2779	416	14	)	)	PUNCT
ejpam-2779	416	15	.	.	PUNCT
ejpam-2779	417	1	in	in	ADP
ejpam-2779	417	2	a	a	DET
ejpam-2779	417	3	similar	similar	ADJ
ejpam-2779	417	4	way	way	NOUN
ejpam-2779	417	5	we	we	PRON
ejpam-2779	417	6	can	can	AUX
ejpam-2779	417	7	get	get	VERB
ejpam-2779	417	8	s(x∼	s(x∼	NUM
ejpam-2779	417	9	)	)	PUNCT
ejpam-2779	417	10	=	=	SYM
ejpam-2779	417	11	1−	1−	NUM
ejpam-2779	417	12	s(x	s(x	PROPN
ejpam-2779	417	13	)	)	PUNCT
ejpam-2779	417	14	.	.	PUNCT
ejpam-2779	418	1	x.l	x.l	PROPN
ejpam-2779	418	2	.	.	PUNCT
ejpam-2779	419	1	xin	xin	PROPN
ejpam-2779	419	2	,	,	PUNCT
ejpam-2779	419	3	y.j	y.j	PROPN
ejpam-2779	419	4	.	.	PUNCT
ejpam-2779	419	5	li	li	PROPN
ejpam-2779	419	6	,	,	PUNCT
ejpam-2779	419	7	y.l	y.l	PROPN
ejpam-2779	419	8	.	.	PROPN
ejpam-2779	419	9	fu	fu	PROPN
ejpam-2779	419	10	/	/	SYM
ejpam-2779	419	11	eur	eur	PROPN
ejpam-2779	419	12	.	.	PUNCT
ejpam-2779	420	1	j.	j.	PROPN
ejpam-2779	420	2	pure	pure	PROPN
ejpam-2779	420	3	appl	appl	PROPN
ejpam-2779	420	4	.	.	PROPN
ejpam-2779	420	5	math	math	PROPN
ejpam-2779	420	6	,	,	PUNCT
ejpam-2779	420	7	10	10	NUM
ejpam-2779	420	8	(	(	PUNCT
ejpam-2779	420	9	3	3	NUM
ejpam-2779	420	10	)	)	PUNCT
ejpam-2779	420	11	(	(	PUNCT
ejpam-2779	420	12	2017	2017	NUM
ejpam-2779	420	13	)	)	PUNCT
ejpam-2779	420	14	,	,	PUNCT
ejpam-2779	420	15	455	455	NUM
ejpam-2779	420	16	-	-	SYM
ejpam-2779	420	17	472	472	NUM
ejpam-2779	420	18	465	465	NUM
ejpam-2779	420	19	proposition	proposition	NOUN
ejpam-2779	420	20	20	20	NUM
ejpam-2779	420	21	.	.	PUNCT
ejpam-2779	421	1	let	let	VERB
ejpam-2779	421	2	a	a	PRON
ejpam-2779	421	3	be	be	AUX
ejpam-2779	421	4	a	a	DET
ejpam-2779	421	5	lbp	lbp	NOUN
ejpam-2779	421	6	-	-	PUNCT
ejpam-2779	421	7	bci	bci	NOUN
ejpam-2779	421	8	algebra	algebra	NOUN
ejpam-2779	421	9	and	and	CCONJ
ejpam-2779	421	10	s	s	AUX
ejpam-2779	421	11	be	be	AUX
ejpam-2779	421	12	a	a	DET
ejpam-2779	421	13	bosbach	bosbach	ADJ
ejpam-2779	421	14	state	state	NOUN
ejpam-2779	421	15	on	on	ADP
ejpam-2779	421	16	a.	a.	NOUN
ejpam-2779	421	17	then	then	ADV
ejpam-2779	421	18	the	the	DET
ejpam-2779	421	19	following	follow	VERB
ejpam-2779	421	20	properties	property	NOUN
ejpam-2779	421	21	hold	hold	VERB
ejpam-2779	421	22	for	for	ADP
ejpam-2779	421	23	all	all	DET
ejpam-2779	421	24	a	a	DET
ejpam-2779	421	25	∈m(a	∈m(a	NOUN
ejpam-2779	421	26	)	)	PUNCT
ejpam-2779	421	27	and	and	CCONJ
ejpam-2779	421	28	x	x	NOUN
ejpam-2779	421	29	,	,	PUNCT
ejpam-2779	421	30	y	y	PROPN
ejpam-2779	421	31	∈	∈	PROPN
ejpam-2779	421	32	v	v	ADP
ejpam-2779	421	33	(	(	PUNCT
ejpam-2779	421	34	a	a	NOUN
ejpam-2779	421	35	):	):	PUNCT
ejpam-2779	421	36	(	(	PUNCT
ejpam-2779	421	37	1	1	X
ejpam-2779	421	38	)	)	PUNCT
ejpam-2779	421	39	s(y	s(y	NOUN
ejpam-2779	421	40	∗	∗	NOUN
ejpam-2779	421	41	x−∼	x−∼	ADV
ejpam-2779	421	42	)	)	PUNCT
ejpam-2779	422	1	=	=	SYM
ejpam-2779	422	2	s(y−∼	s(y−∼	NOUN
ejpam-2779	422	3	∗	∗	NOUN
ejpam-2779	422	4	x	x	NOUN
ejpam-2779	422	5	)	)	PUNCT
ejpam-2779	422	6	,	,	PUNCT
ejpam-2779	422	7	s(y	s(y	PROPN
ejpam-2779	422	8	◦	◦	NOUN
ejpam-2779	422	9	x∼−	x∼−	PROPN
ejpam-2779	422	10	)	)	PUNCT
ejpam-2779	423	1	=	=	PRON
ejpam-2779	423	2	s(y∼−	s(y∼−	AUX
ejpam-2779	423	3	◦	◦	VERB
ejpam-2779	423	4	x	x	X
ejpam-2779	423	5	)	)	PUNCT
ejpam-2779	423	6	.	.	PUNCT
ejpam-2779	424	1	(	(	PUNCT
ejpam-2779	424	2	2	2	X
ejpam-2779	424	3	)	)	PUNCT
ejpam-2779	424	4	s(y−∼	s(y−∼	NOUN
ejpam-2779	424	5	∗	∗	NOUN
ejpam-2779	424	6	x	x	NOUN
ejpam-2779	424	7	)	)	PUNCT
ejpam-2779	424	8	=	=	SYM
ejpam-2779	424	9	s(x−	s(x−	PROPN
ejpam-2779	424	10	◦	◦	NOUN
ejpam-2779	424	11	y−	y−	NOUN
ejpam-2779	424	12	)	)	PUNCT
ejpam-2779	425	1	=	=	SYM
ejpam-2779	425	2	s(y−∼	s(y−∼	NOUN
ejpam-2779	425	3	∗	∗	NOUN
ejpam-2779	425	4	x−∼	x−∼	ADV
ejpam-2779	425	5	)	)	PUNCT
ejpam-2779	426	1	=	=	SYM
ejpam-2779	426	2	s(y	s(y	PROPN
ejpam-2779	426	3	∗	∗	NOUN
ejpam-2779	426	4	x−∼	x−∼	ADV
ejpam-2779	426	5	)	)	PUNCT
ejpam-2779	426	6	,	,	PUNCT
ejpam-2779	426	7	s(y∼−	s(y∼−	VERB
ejpam-2779	426	8	◦	◦	NOUN
ejpam-2779	426	9	x	x	X
ejpam-2779	426	10	)	)	PUNCT
ejpam-2779	426	11	=	=	SYM
ejpam-2779	426	12	s(x∼	s(x∼	X
ejpam-2779	426	13	∗	∗	NOUN
ejpam-2779	426	14	y∼	y∼	X
ejpam-2779	426	15	)	)	PUNCT
ejpam-2779	426	16	=	=	VERB
ejpam-2779	426	17	s(y∼−	s(y∼−	AUX
ejpam-2779	426	18	◦	◦	VERB
ejpam-2779	426	19	x∼−	x∼−	NUM
ejpam-2779	426	20	)	)	PUNCT
ejpam-2779	427	1	=	=	PUNCT
ejpam-2779	427	2	s(y	s(y	PROPN
ejpam-2779	427	3	◦	◦	NOUN
ejpam-2779	427	4	x∼−	x∼−	NUM
ejpam-2779	427	5	)	)	PUNCT
ejpam-2779	427	6	.	.	PUNCT
ejpam-2779	428	1	(	(	PUNCT
ejpam-2779	428	2	3	3	X
ejpam-2779	428	3	)	)	PUNCT
ejpam-2779	428	4	s(y−∼	s(y−∼	NOUN
ejpam-2779	428	5	∗	∗	NOUN
ejpam-2779	428	6	x∼	x∼	PROPN
ejpam-2779	428	7	)	)	PUNCT
ejpam-2779	429	1	=	=	SYM
ejpam-2779	429	2	s(y	s(y	PROPN
ejpam-2779	429	3	∗	∗	NOUN
ejpam-2779	429	4	x∼	x∼	PROPN
ejpam-2779	429	5	)	)	PUNCT
ejpam-2779	429	6	,	,	PUNCT
ejpam-2779	429	7	s(y∼−	s(y∼−	AUX
ejpam-2779	429	8	◦	◦	VERB
ejpam-2779	429	9	x−	x−	PROPN
ejpam-2779	429	10	)	)	PUNCT
ejpam-2779	430	1	=	=	SYM
ejpam-2779	430	2	s(y	s(y	PROPN
ejpam-2779	430	3	◦	◦	NOUN
ejpam-2779	430	4	x−	x−	PROPN
ejpam-2779	430	5	)	)	PUNCT
ejpam-2779	430	6	.	.	PUNCT
ejpam-2779	431	1	proof	proof	NOUN
ejpam-2779	431	2	.	.	PUNCT
ejpam-2779	432	1	(	(	PUNCT
ejpam-2779	432	2	1	1	X
ejpam-2779	432	3	)	)	PUNCT
ejpam-2779	432	4	note	note	NOUN
ejpam-2779	432	5	that	that	SCONJ
ejpam-2779	432	6	s(y	s(y	PROPN
ejpam-2779	432	7	∗	∗	NOUN
ejpam-2779	432	8	x−∼	x−∼	ADV
ejpam-2779	432	9	)	)	PUNCT
ejpam-2779	433	1	+	+	CCONJ
ejpam-2779	433	2	s(y	s(y	PROPN
ejpam-2779	433	3	◦	◦	NOUN
ejpam-2779	433	4	(	(	PUNCT
ejpam-2779	433	5	y	y	PROPN
ejpam-2779	433	6	∗	∗	NOUN
ejpam-2779	433	7	x−∼	x−∼	ADV
ejpam-2779	433	8	)	)	PUNCT
ejpam-2779	433	9	)	)	PUNCT
ejpam-2779	434	1	=	=	SYM
ejpam-2779	434	2	s(y	s(y	NOUN
ejpam-2779	434	3	)	)	PUNCT
ejpam-2779	435	1	+	+	CCONJ
ejpam-2779	435	2	s((y	s((y	NOUN
ejpam-2779	435	3	∗	∗	NOUN
ejpam-2779	435	4	x−∼	x−∼	ADV
ejpam-2779	435	5	)	)	PUNCT
ejpam-2779	435	6	◦	◦	NOUN
ejpam-2779	435	7	y	y	PROPN
ejpam-2779	435	8	)	)	PUNCT
ejpam-2779	435	9	,	,	PUNCT
ejpam-2779	435	10	or	or	CCONJ
ejpam-2779	435	11	s(y	s(y	PROPN
ejpam-2779	435	12	∗	∗	NOUN
ejpam-2779	435	13	x−∼	x−∼	ADV
ejpam-2779	435	14	)	)	PUNCT
ejpam-2779	436	1	+	+	NUM
ejpam-2779	436	2	s(x−∼	s(x−∼	NOUN
ejpam-2779	436	3	∧1	∧1	VERB
ejpam-2779	436	4	y	y	NOUN
ejpam-2779	436	5	)	)	PUNCT
ejpam-2779	436	6	=	=	PUNCT
ejpam-2779	436	7	s(y	s(y	NOUN
ejpam-2779	436	8	)	)	PUNCT
ejpam-2779	437	1	+	+	CCONJ
ejpam-2779	437	2	s((y	s((y	NOUN
ejpam-2779	437	3	∗	∗	NOUN
ejpam-2779	437	4	x−∼	x−∼	ADV
ejpam-2779	437	5	)	)	PUNCT
ejpam-2779	437	6	◦	◦	NOUN
ejpam-2779	437	7	y	y	NOUN
ejpam-2779	437	8	)	)	PUNCT
ejpam-2779	437	9	.	.	PUNCT
ejpam-2779	438	1	by	by	ADP
ejpam-2779	438	2	proposition	proposition	NOUN
ejpam-2779	438	3	19(4	19(4	NUM
ejpam-2779	438	4	)	)	PUNCT
ejpam-2779	438	5	,	,	PUNCT
ejpam-2779	438	6	we	we	PRON
ejpam-2779	438	7	have	have	VERB
ejpam-2779	438	8	s(y∗x−∼)+s(x∧1y−∼	s(y∗x−∼)+s(x∧1y−∼	NOUN
ejpam-2779	438	9	)	)	PUNCT
ejpam-2779	439	1	=	=	SYM
ejpam-2779	439	2	s(y)+s((y∗x−∼)	s(y)+s((y∗x−∼)	PROPN
ejpam-2779	439	3	◦	◦	NOUN
ejpam-2779	439	4	y	y	NOUN
ejpam-2779	439	5	)	)	PUNCT
ejpam-2779	439	6	=	=	PUNCT
ejpam-2779	440	1	s(y)+s((y	s(y)+s((y	PROPN
ejpam-2779	440	2	◦	◦	NOUN
ejpam-2779	440	3	y)∗x−∼	y)∗x−∼	PROPN
ejpam-2779	440	4	)	)	PUNCT
ejpam-2779	440	5	=	=	SYM
ejpam-2779	440	6	s(y)+s(0∗x−∼	s(y)+s(0∗x−∼	PROPN
ejpam-2779	440	7	)	)	PUNCT
ejpam-2779	440	8	.	.	PUNCT
ejpam-2779	441	1	using	use	VERB
ejpam-2779	441	2	corollary	corollary	ADJ
ejpam-2779	441	3	2	2	NUM
ejpam-2779	441	4	,	,	PUNCT
ejpam-2779	441	5	we	we	PRON
ejpam-2779	441	6	get	get	VERB
ejpam-2779	441	7	0	0	NUM
ejpam-2779	441	8	∗	∗	NOUN
ejpam-2779	441	9	x−∼	x−∼	PROPN
ejpam-2779	441	10	∈	∈	PROPN
ejpam-2779	441	11	m(a	m(a	PROPN
ejpam-2779	441	12	)	)	PUNCT
ejpam-2779	441	13	,	,	PUNCT
ejpam-2779	441	14	and	and	CCONJ
ejpam-2779	441	15	so	so	ADV
ejpam-2779	441	16	s(0	s(0	PROPN
ejpam-2779	441	17	∗	∗	NOUN
ejpam-2779	441	18	x−∼	x−∼	ADV
ejpam-2779	441	19	)	)	PUNCT
ejpam-2779	441	20	=	=	SYM
ejpam-2779	442	1	1	1	X
ejpam-2779	442	2	.	.	PUNCT
ejpam-2779	443	1	thus	thus	ADV
ejpam-2779	443	2	s(y	s(y	PROPN
ejpam-2779	443	3	∗	∗	NOUN
ejpam-2779	443	4	x−∼	x−∼	ADV
ejpam-2779	443	5	)	)	PUNCT
ejpam-2779	443	6	=	=	PUNCT
ejpam-2779	443	7	s(y)+1−s(x∧1y−∼	s(y)+1−s(x∧1y−∼	NOUN
ejpam-2779	443	8	)	)	PUNCT
ejpam-2779	443	9	=	=	SYM
ejpam-2779	444	1	1−s(x∧1y−∼)+s(y−∼	1−s(x∧1y−∼)+s(y−∼	NUM
ejpam-2779	444	2	)	)	PUNCT
ejpam-2779	444	3	=	=	PUNCT
ejpam-2779	444	4	s((y−∼∗x)	s((y−∼∗x)	VERB
ejpam-2779	444	5	◦	◦	NOUN
ejpam-2779	444	6	y−∼)−s(x∧1y−∼)+s(y−∼	y−∼)−s(x∧1y−∼)+s(y−∼	NOUN
ejpam-2779	444	7	)	)	PUNCT
ejpam-2779	445	1	=	=	SYM
ejpam-2779	445	2	s(y−∼	s(y−∼	NOUN
ejpam-2779	445	3	∗	∗	NOUN
ejpam-2779	445	4	x	x	NOUN
ejpam-2779	445	5	)	)	PUNCT
ejpam-2779	445	6	.	.	PUNCT
ejpam-2779	446	1	similarly	similarly	ADV
ejpam-2779	446	2	we	we	PRON
ejpam-2779	446	3	can	can	AUX
ejpam-2779	446	4	prove	prove	VERB
ejpam-2779	446	5	s(y	s(y	PROPN
ejpam-2779	446	6	◦	◦	NOUN
ejpam-2779	446	7	x∼−	x∼−	PROPN
ejpam-2779	446	8	)	)	PUNCT
ejpam-2779	447	1	=	=	PRON
ejpam-2779	447	2	s(y∼−	s(y∼−	AUX
ejpam-2779	447	3	◦	◦	VERB
ejpam-2779	447	4	x	x	X
ejpam-2779	447	5	)	)	PUNCT
ejpam-2779	447	6	.	.	PUNCT
ejpam-2779	448	1	(	(	PUNCT
ejpam-2779	448	2	2	2	X
ejpam-2779	448	3	)	)	PUNCT
ejpam-2779	448	4	by	by	ADP
ejpam-2779	448	5	(	(	PUNCT
ejpam-2779	448	6	p4	p4	ADJ
ejpam-2779	448	7	)	)	PUNCT
ejpam-2779	448	8	we	we	PRON
ejpam-2779	448	9	have	have	VERB
ejpam-2779	448	10	s(y−∼	s(y−∼	NOUN
ejpam-2779	448	11	∗	∗	NOUN
ejpam-2779	448	12	x	x	NOUN
ejpam-2779	448	13	)	)	PUNCT
ejpam-2779	448	14	=	=	SYM
ejpam-2779	448	15	s((1a	s((1a	AUX
ejpam-2779	448	16	◦	◦	NOUN
ejpam-2779	448	17	(	(	PUNCT
ejpam-2779	448	18	1a	1a	PROPN
ejpam-2779	448	19	∗	∗	PROPN
ejpam-2779	448	20	y	y	PROPN
ejpam-2779	448	21	)	)	PUNCT
ejpam-2779	448	22	)	)	PUNCT
ejpam-2779	448	23	∗	∗	NOUN
ejpam-2779	448	24	x	x	NOUN
ejpam-2779	448	25	)	)	PUNCT
ejpam-2779	448	26	=	=	SYM
ejpam-2779	448	27	s((1a	s((1a	VERB
ejpam-2779	448	28	∗	∗	NOUN
ejpam-2779	448	29	x	x	NOUN
ejpam-2779	448	30	)	)	PUNCT
ejpam-2779	448	31	◦	◦	NOUN
ejpam-2779	448	32	(	(	PUNCT
ejpam-2779	448	33	1a	1a	PROPN
ejpam-2779	448	34	∗	∗	PROPN
ejpam-2779	448	35	y	y	PROPN
ejpam-2779	448	36	)	)	PUNCT
ejpam-2779	448	37	)	)	PUNCT
ejpam-2779	449	1	=	=	SYM
ejpam-2779	449	2	s(x−	s(x−	X
ejpam-2779	449	3	◦	◦	NOUN
ejpam-2779	449	4	y−	y−	NOUN
ejpam-2779	449	5	)	)	PUNCT
ejpam-2779	449	6	.	.	PUNCT
ejpam-2779	450	1	moreover	moreover	ADV
ejpam-2779	450	2	we	we	PRON
ejpam-2779	450	3	have	have	VERB
ejpam-2779	450	4	s(y−∼	s(y−∼	NOUN
ejpam-2779	450	5	∗	∗	NOUN
ejpam-2779	450	6	x−∼	x−∼	ADV
ejpam-2779	450	7	)	)	PUNCT
ejpam-2779	451	1	=	=	VERB
ejpam-2779	451	2	s((1a	s((1a	VERB
ejpam-2779	451	3	◦	◦	NOUN
ejpam-2779	451	4	(	(	PUNCT
ejpam-2779	451	5	1a	1a	PROPN
ejpam-2779	451	6	∗	∗	PROPN
ejpam-2779	451	7	y	y	PROPN
ejpam-2779	451	8	)	)	PUNCT
ejpam-2779	451	9	)	)	PUNCT
ejpam-2779	451	10	∗	∗	NOUN
ejpam-2779	451	11	(	(	PUNCT
ejpam-2779	451	12	(	(	PUNCT
ejpam-2779	451	13	1a	1a	X
ejpam-2779	451	14	◦	◦	NOUN
ejpam-2779	451	15	(	(	PUNCT
ejpam-2779	451	16	1a	1a	X
ejpam-2779	451	17	∗	∗	X
ejpam-2779	451	18	x	x	NOUN
ejpam-2779	451	19	)	)	PUNCT
ejpam-2779	451	20	)	)	PUNCT
ejpam-2779	451	21	)	)	PUNCT
ejpam-2779	452	1	=	=	PRON
ejpam-2779	452	2	s((1a	s((1a	VERB
ejpam-2779	452	3	◦	◦	NOUN
ejpam-2779	452	4	(	(	PUNCT
ejpam-2779	452	5	(	(	PUNCT
ejpam-2779	452	6	1a	1a	X
ejpam-2779	452	7	◦	◦	NOUN
ejpam-2779	452	8	(	(	PUNCT
ejpam-2779	452	9	1a	1a	X
ejpam-2779	452	10	∗	∗	X
ejpam-2779	452	11	x	x	NOUN
ejpam-2779	452	12	)	)	PUNCT
ejpam-2779	452	13	)	)	PUNCT
ejpam-2779	452	14	)	)	PUNCT
ejpam-2779	452	15	◦	◦	NOUN
ejpam-2779	452	16	(	(	PUNCT
ejpam-2779	452	17	1a	1a	PROPN
ejpam-2779	452	18	∗	∗	PROPN
ejpam-2779	452	19	y	y	PROPN
ejpam-2779	452	20	)	)	PUNCT
ejpam-2779	452	21	)	)	PUNCT
ejpam-2779	453	1	=	=	PRON
ejpam-2779	453	2	s(x−∼−	s(x−∼−	X
ejpam-2779	453	3	◦	◦	NOUN
ejpam-2779	453	4	y−	y−	NOUN
ejpam-2779	453	5	)	)	PUNCT
ejpam-2779	454	1	=	=	SYM
ejpam-2779	454	2	s(x−	s(x−	PROPN
ejpam-2779	454	3	◦	◦	NOUN
ejpam-2779	454	4	y−	y−	NOUN
ejpam-2779	454	5	)	)	PUNCT
ejpam-2779	454	6	by	by	ADP
ejpam-2779	454	7	proposition	proposition	NOUN
ejpam-2779	454	8	8	8	NUM
ejpam-2779	454	9	.	.	PUNCT
ejpam-2779	455	1	using	use	VERB
ejpam-2779	455	2	(	(	PUNCT
ejpam-2779	455	3	1	1	X
ejpam-2779	455	4	)	)	PUNCT
ejpam-2779	455	5	we	we	PRON
ejpam-2779	455	6	can	can	AUX
ejpam-2779	455	7	get	get	VERB
ejpam-2779	455	8	s(y−∼	s(y−∼	NOUN
ejpam-2779	455	9	∗	∗	NOUN
ejpam-2779	455	10	x	x	NOUN
ejpam-2779	455	11	)	)	PUNCT
ejpam-2779	456	1	=	=	SYM
ejpam-2779	456	2	s(x−	s(x−	PROPN
ejpam-2779	456	3	◦	◦	NOUN
ejpam-2779	456	4	y−	y−	NOUN
ejpam-2779	456	5	)	)	PUNCT
ejpam-2779	457	1	=	=	SYM
ejpam-2779	457	2	s(y−∼	s(y−∼	NOUN
ejpam-2779	457	3	∗	∗	NOUN
ejpam-2779	457	4	x−∼	x−∼	ADV
ejpam-2779	457	5	)	)	PUNCT
ejpam-2779	458	1	=	=	SYM
ejpam-2779	458	2	s(y	s(y	PROPN
ejpam-2779	458	3	∗	∗	NOUN
ejpam-2779	458	4	x−∼	x−∼	ADV
ejpam-2779	458	5	)	)	PUNCT
ejpam-2779	458	6	.	.	PUNCT
ejpam-2779	459	1	similarly	similarly	ADV
ejpam-2779	459	2	we	we	PRON
ejpam-2779	459	3	have	have	AUX
ejpam-2779	459	4	s(y∼−	s(y∼−	VERB
ejpam-2779	459	5	◦	◦	NOUN
ejpam-2779	459	6	x	x	X
ejpam-2779	459	7	)	)	PUNCT
ejpam-2779	459	8	=	=	SYM
ejpam-2779	459	9	s(x∼	s(x∼	X
ejpam-2779	459	10	∗	∗	NOUN
ejpam-2779	459	11	y∼	y∼	X
ejpam-2779	459	12	)	)	PUNCT
ejpam-2779	459	13	=	=	VERB
ejpam-2779	459	14	s(y∼−	s(y∼−	AUX
ejpam-2779	459	15	◦	◦	VERB
ejpam-2779	459	16	x∼−	x∼−	NUM
ejpam-2779	459	17	)	)	PUNCT
ejpam-2779	460	1	=	=	PUNCT
ejpam-2779	460	2	s(y	s(y	PROPN
ejpam-2779	460	3	◦	◦	NOUN
ejpam-2779	460	4	x∼−	x∼−	NUM
ejpam-2779	460	5	)	)	PUNCT
ejpam-2779	460	6	.	.	PUNCT
ejpam-2779	461	1	(	(	PUNCT
ejpam-2779	461	2	3	3	X
ejpam-2779	461	3	)	)	PUNCT
ejpam-2779	461	4	by	by	ADP
ejpam-2779	461	5	proposition	proposition	NOUN
ejpam-2779	461	6	5.4(4	5.4(4	NOUN
ejpam-2779	461	7	)	)	PUNCT
ejpam-2779	461	8	we	we	PRON
ejpam-2779	461	9	get	get	VERB
ejpam-2779	461	10	s(y−∼	s(y−∼	NOUN
ejpam-2779	461	11	∗x∼	∗x∼	NOUN
ejpam-2779	461	12	)	)	PUNCT
ejpam-2779	461	13	=	=	SYM
ejpam-2779	461	14	s(y−∼	s(y−∼	NOUN
ejpam-2779	461	15	)	)	PUNCT
ejpam-2779	462	1	+	+	CCONJ
ejpam-2779	462	2	s((y−∼	s((y−∼	NOUN
ejpam-2779	462	3	∗x∼	∗x∼	X
ejpam-2779	462	4	)	)	PUNCT
ejpam-2779	462	5	◦	◦	NOUN
ejpam-2779	462	6	y−∼)−	y−∼)−	NUM
ejpam-2779	462	7	s(y−∼	s(y−∼	NOUN
ejpam-2779	462	8	◦	◦	NOUN
ejpam-2779	462	9	(	(	PUNCT
ejpam-2779	462	10	y−∼	y−∼	NOUN
ejpam-2779	462	11	∗x∼	∗x∼	NUM
ejpam-2779	462	12	)	)	PUNCT
ejpam-2779	462	13	)	)	PUNCT
ejpam-2779	463	1	=	=	SYM
ejpam-2779	463	2	s(y	s(y	NOUN
ejpam-2779	463	3	)	)	PUNCT
ejpam-2779	464	1	+	+	CCONJ
ejpam-2779	464	2	1−	1−	NUM
ejpam-2779	464	3	s(x∼	s(x∼	NUM
ejpam-2779	464	4	∧1	∧1	NUM
ejpam-2779	464	5	y−∼	y−∼	NOUN
ejpam-2779	464	6	)	)	PUNCT
ejpam-2779	464	7	=	=	SYM
ejpam-2779	464	8	s(y	s(y	NOUN
ejpam-2779	464	9	)	)	PUNCT
ejpam-2779	465	1	+	+	SYM
ejpam-2779	465	2	1−	1−	NUM
ejpam-2779	465	3	s(x∼−∼	s(x∼−∼	NOUN
ejpam-2779	465	4	∧1	∧1	VERB
ejpam-2779	465	5	y	y	NOUN
ejpam-2779	465	6	)	)	PUNCT
ejpam-2779	465	7	=	=	PUNCT
ejpam-2779	465	8	s(y	s(y	NOUN
ejpam-2779	465	9	)	)	PUNCT
ejpam-2779	466	1	+	+	CCONJ
ejpam-2779	466	2	1−	1−	NUM
ejpam-2779	466	3	s(x∼	s(x∼	NUM
ejpam-2779	466	4	∧1	∧1	PROPN
ejpam-2779	466	5	y	y	NOUN
ejpam-2779	466	6	)	)	PUNCT
ejpam-2779	466	7	=	=	SYM
ejpam-2779	466	8	s(y	s(y	PROPN
ejpam-2779	466	9	◦	◦	NOUN
ejpam-2779	466	10	x∼	x∼	PROPN
ejpam-2779	466	11	)	)	PUNCT
ejpam-2779	466	12	.	.	PUNCT
ejpam-2779	467	1	similarly	similarly	ADV
ejpam-2779	467	2	we	we	PRON
ejpam-2779	467	3	can	can	AUX
ejpam-2779	467	4	get	get	VERB
ejpam-2779	467	5	s(y∼−	s(y∼−	VERB
ejpam-2779	467	6	◦	◦	VERB
ejpam-2779	467	7	x−	x−	PROPN
ejpam-2779	467	8	)	)	PUNCT
ejpam-2779	468	1	=	=	SYM
ejpam-2779	468	2	s(y	s(y	PROPN
ejpam-2779	468	3	◦	◦	NOUN
ejpam-2779	468	4	x−	x−	PROPN
ejpam-2779	468	5	)	)	PUNCT
ejpam-2779	468	6	.	.	PUNCT
ejpam-2779	469	1	proposition	proposition	NOUN
ejpam-2779	469	2	21	21	NUM
ejpam-2779	469	3	.	.	PUNCT
ejpam-2779	470	1	let	let	VERB
ejpam-2779	470	2	a	a	PRON
ejpam-2779	470	3	be	be	AUX
ejpam-2779	470	4	a	a	DET
ejpam-2779	470	5	lbp	lbp	NOUN
ejpam-2779	470	6	-	-	PUNCT
ejpam-2779	470	7	bci	bci	NOUN
ejpam-2779	470	8	algebra	algebra	NOUN
ejpam-2779	470	9	and	and	CCONJ
ejpam-2779	470	10	s	s	AUX
ejpam-2779	470	11	be	be	AUX
ejpam-2779	470	12	a	a	DET
ejpam-2779	470	13	bosbach	bosbach	ADJ
ejpam-2779	470	14	state	state	NOUN
ejpam-2779	470	15	on	on	ADP
ejpam-2779	470	16	a.	a.	NOUN
ejpam-2779	470	17	then	then	ADV
ejpam-2779	470	18	for	for	ADP
ejpam-2779	470	19	all	all	DET
ejpam-2779	470	20	a	a	DET
ejpam-2779	470	21	∈m(a	∈m(a	NOUN
ejpam-2779	470	22	)	)	PUNCT
ejpam-2779	470	23	and	and	CCONJ
ejpam-2779	470	24	x	x	NOUN
ejpam-2779	470	25	,	,	PUNCT
ejpam-2779	470	26	y	y	PROPN
ejpam-2779	470	27	∈	∈	PROPN
ejpam-2779	470	28	v	v	ADP
ejpam-2779	470	29	(	(	PUNCT
ejpam-2779	470	30	a	a	NOUN
ejpam-2779	470	31	)	)	PUNCT
ejpam-2779	470	32	,	,	PUNCT
ejpam-2779	470	33	s(y∗x	s(y∗x	NOUN
ejpam-2779	470	34	)	)	PUNCT
ejpam-2779	470	35	=	=	PUNCT
ejpam-2779	470	36	1−s(x∧1y)+s(y	1−s(x∧1y)+s(y	NUM
ejpam-2779	470	37	)	)	PUNCT
ejpam-2779	470	38	and	and	CCONJ
ejpam-2779	470	39	s(y	s(y	PROPN
ejpam-2779	470	40	◦	◦	NOUN
ejpam-2779	470	41	x	x	NOUN
ejpam-2779	470	42	)	)	PUNCT
ejpam-2779	470	43	=	=	SYM
ejpam-2779	470	44	1−s(x∧2y)+s(y	1−s(x∧2y)+s(y	NUM
ejpam-2779	470	45	)	)	PUNCT
ejpam-2779	470	46	.	.	PUNCT
ejpam-2779	471	1	proof	proof	NOUN
ejpam-2779	471	2	.	.	PUNCT
ejpam-2779	472	1	let	let	VERB
ejpam-2779	472	2	a	a	DET
ejpam-2779	472	3	∈	∈	PROPN
ejpam-2779	472	4	m(a	m(a	PROPN
ejpam-2779	472	5	)	)	PUNCT
ejpam-2779	472	6	and	and	CCONJ
ejpam-2779	472	7	x	x	X
ejpam-2779	472	8	,	,	PUNCT
ejpam-2779	472	9	y	y	PROPN
ejpam-2779	472	10	∈	∈	PROPN
ejpam-2779	472	11	v	v	ADP
ejpam-2779	472	12	(	(	PUNCT
ejpam-2779	472	13	a	a	NOUN
ejpam-2779	472	14	)	)	PUNCT
ejpam-2779	472	15	.	.	PUNCT
ejpam-2779	473	1	note	note	VERB
ejpam-2779	473	2	that	that	SCONJ
ejpam-2779	473	3	x	x	PROPN
ejpam-2779	473	4	∧1	∧1	VERB
ejpam-2779	473	5	y	y	NOUN
ejpam-2779	473	6	≤	≤	NUM
ejpam-2779	473	7	x	x	X
ejpam-2779	473	8	,	,	PUNCT
ejpam-2779	473	9	y	y	PROPN
ejpam-2779	473	10	and	and	CCONJ
ejpam-2779	473	11	x	x	PROPN
ejpam-2779	473	12	∧2	∧2	PROPN
ejpam-2779	473	13	y	y	PROPN
ejpam-2779	473	14	≤	≤	NUM
ejpam-2779	473	15	x	x	PUNCT
ejpam-2779	473	16	,	,	PUNCT
ejpam-2779	473	17	y.	y.	NOUN
ejpam-2779	473	18	by	by	ADP
ejpam-2779	473	19	19(1	19(1	NUM
ejpam-2779	473	20	)	)	PUNCT
ejpam-2779	473	21	,	,	PUNCT
ejpam-2779	473	22	we	we	PRON
ejpam-2779	473	23	have	have	VERB
ejpam-2779	473	24	s(y∗x	s(y∗x	NOUN
ejpam-2779	473	25	)	)	PUNCT
ejpam-2779	474	1	=	=	SYM
ejpam-2779	474	2	s(y∗(x∧1y	s(y∗(x∧1y	NOUN
ejpam-2779	474	3	)	)	PUNCT
ejpam-2779	474	4	)	)	PUNCT
ejpam-2779	475	1	=	=	SYM
ejpam-2779	475	2	1−s(x∧1y)+s(y	1−s(x∧1y)+s(y	NUM
ejpam-2779	475	3	)	)	PUNCT
ejpam-2779	475	4	and	and	CCONJ
ejpam-2779	475	5	s(y	s(y	PROPN
ejpam-2779	475	6	◦	◦	NOUN
ejpam-2779	475	7	x	x	X
ejpam-2779	475	8	)	)	PUNCT
ejpam-2779	475	9	=	=	SYM
ejpam-2779	476	1	s(y	s(y	PROPN
ejpam-2779	476	2	◦	◦	NOUN
ejpam-2779	476	3	(x∧2y	(x∧2y	NOUN
ejpam-2779	476	4	)	)	PUNCT
ejpam-2779	476	5	)	)	PUNCT
ejpam-2779	477	1	=	=	SYM
ejpam-2779	478	1	1−	1−	NUM
ejpam-2779	478	2	s(x	s(x	PROPN
ejpam-2779	478	3	∧2	∧2	PROPN
ejpam-2779	478	4	y	y	PROPN
ejpam-2779	478	5	)	)	PUNCT
ejpam-2779	478	6	+	+	CCONJ
ejpam-2779	478	7	s(y	s(y	NOUN
ejpam-2779	478	8	)	)	PUNCT
ejpam-2779	478	9	.	.	PUNCT
ejpam-2779	479	1	the	the	DET
ejpam-2779	479	2	following	follow	VERB
ejpam-2779	479	3	results	result	NOUN
ejpam-2779	479	4	are	be	AUX
ejpam-2779	479	5	important	important	ADJ
ejpam-2779	479	6	for	for	ADP
ejpam-2779	479	7	our	our	PRON
ejpam-2779	479	8	study	study	NOUN
ejpam-2779	479	9	.	.	PUNCT
ejpam-2779	480	1	proposition	proposition	NOUN
ejpam-2779	480	2	22	22	NUM
ejpam-2779	480	3	.	.	PUNCT
ejpam-2779	481	1	let	let	VERB
ejpam-2779	481	2	a	a	PRON
ejpam-2779	481	3	be	be	AUX
ejpam-2779	481	4	a	a	DET
ejpam-2779	481	5	lbp	lbp	NOUN
ejpam-2779	481	6	-	-	PUNCT
ejpam-2779	481	7	bci	bci	NOUN
ejpam-2779	481	8	algebra	algebra	NOUN
ejpam-2779	481	9	and	and	CCONJ
ejpam-2779	481	10	s	s	AUX
ejpam-2779	481	11	be	be	AUX
ejpam-2779	481	12	a	a	DET
ejpam-2779	481	13	bosbach	bosbach	ADJ
ejpam-2779	481	14	state	state	NOUN
ejpam-2779	481	15	on	on	ADP
ejpam-2779	481	16	a.	a.	NOUN
ejpam-2779	481	17	then	then	ADV
ejpam-2779	481	18	for	for	ADP
ejpam-2779	481	19	all	all	DET
ejpam-2779	481	20	a	a	DET
ejpam-2779	481	21	∈m(a	∈m(a	NOUN
ejpam-2779	481	22	)	)	PUNCT
ejpam-2779	481	23	and	and	CCONJ
ejpam-2779	481	24	x	x	NOUN
ejpam-2779	481	25	,	,	PUNCT
ejpam-2779	481	26	y	y	PROPN
ejpam-2779	481	27	∈	∈	PROPN
ejpam-2779	481	28	v	v	ADP
ejpam-2779	481	29	(	(	PUNCT
ejpam-2779	481	30	a	a	NOUN
ejpam-2779	481	31	)	)	PUNCT
ejpam-2779	481	32	,	,	PUNCT
ejpam-2779	481	33	we	we	PRON
ejpam-2779	481	34	have	have	VERB
ejpam-2779	481	35	(	(	PUNCT
ejpam-2779	481	36	1	1	X
ejpam-2779	481	37	)	)	PUNCT
ejpam-2779	481	38	s(x	s(x	PROPN
ejpam-2779	481	39	∧1	∧1	NUM
ejpam-2779	481	40	y	y	NOUN
ejpam-2779	481	41	)	)	PUNCT
ejpam-2779	481	42	=	=	PUNCT
ejpam-2779	482	1	s(x	s(x	PROPN
ejpam-2779	482	2	∧2	∧2	PROPN
ejpam-2779	482	3	y	y	PROPN
ejpam-2779	482	4	)	)	PUNCT
ejpam-2779	482	5	.	.	PUNCT
ejpam-2779	483	1	(	(	PUNCT
ejpam-2779	483	2	2	2	X
ejpam-2779	483	3	)	)	PUNCT
ejpam-2779	483	4	s(x	s(x	PROPN
ejpam-2779	483	5	∗	∗	NOUN
ejpam-2779	483	6	y	y	NOUN
ejpam-2779	483	7	)	)	PUNCT
ejpam-2779	483	8	=	=	PUNCT
ejpam-2779	484	1	s(x	s(x	PROPN
ejpam-2779	484	2	◦	◦	NOUN
ejpam-2779	484	3	y	y	PROPN
ejpam-2779	484	4	)	)	PUNCT
ejpam-2779	484	5	.	.	PUNCT
ejpam-2779	485	1	proof	proof	NOUN
ejpam-2779	485	2	.	.	PUNCT
ejpam-2779	486	1	(	(	PUNCT
ejpam-2779	486	2	1	1	X
ejpam-2779	486	3	)	)	PUNCT
ejpam-2779	486	4	first	first	ADV
ejpam-2779	486	5	we	we	PRON
ejpam-2779	486	6	prove	prove	VERB
ejpam-2779	486	7	the	the	DET
ejpam-2779	486	8	equality	equality	NOUN
ejpam-2779	486	9	for	for	ADP
ejpam-2779	486	10	x	x	SYM
ejpam-2779	486	11	≤	≤	X
ejpam-2779	486	12	y.	y.	NOUN
ejpam-2779	486	13	by	by	ADP
ejpam-2779	486	14	propositions	proposition	NOUN
ejpam-2779	486	15	19(2	19(2	NUM
ejpam-2779	486	16	)	)	PUNCT
ejpam-2779	486	17	and	and	CCONJ
ejpam-2779	486	18	9(2	9(2	NUM
ejpam-2779	486	19	)	)	PUNCT
ejpam-2779	486	20	,	,	PUNCT
ejpam-2779	486	21	we	we	PRON
ejpam-2779	486	22	have	have	VERB
ejpam-2779	486	23	s(x	s(x	NOUN
ejpam-2779	486	24	∧1	∧1	NUM
ejpam-2779	486	25	y	y	NOUN
ejpam-2779	486	26	)	)	PUNCT
ejpam-2779	487	1	=	=	SYM
ejpam-2779	487	2	s(y	s(y	PROPN
ejpam-2779	487	3	∧1	∧1	NOUN
ejpam-2779	487	4	x	x	NOUN
ejpam-2779	487	5	)	)	PUNCT
ejpam-2779	487	6	=	=	SYM
ejpam-2779	487	7	s(x	s(x	PROPN
ejpam-2779	487	8	)	)	PUNCT
ejpam-2779	487	9	and	and	CCONJ
ejpam-2779	487	10	s(x	s(x	PROPN
ejpam-2779	487	11	∧2	∧2	PROPN
ejpam-2779	487	12	y	y	PROPN
ejpam-2779	487	13	)	)	PUNCT
ejpam-2779	488	1	=	=	SYM
ejpam-2779	489	1	s(y	s(y	PROPN
ejpam-2779	489	2	∧2	∧2	PROPN
ejpam-2779	489	3	x	x	SYM
ejpam-2779	489	4	)	)	PUNCT
ejpam-2779	489	5	=	=	SYM
ejpam-2779	489	6	s(x	s(x	PROPN
ejpam-2779	489	7	)	)	PUNCT
ejpam-2779	489	8	,	,	PUNCT
ejpam-2779	489	9	that	that	PRON
ejpam-2779	489	10	is	be	AUX
ejpam-2779	489	11	s(x	s(x	NOUN
ejpam-2779	489	12	∧1	∧1	NUM
ejpam-2779	489	13	y	y	NOUN
ejpam-2779	489	14	)	)	PUNCT
ejpam-2779	489	15	=	=	PUNCT
ejpam-2779	490	1	s(x	s(x	PROPN
ejpam-2779	490	2	∧2	∧2	PROPN
ejpam-2779	490	3	y	y	PROPN
ejpam-2779	490	4	)	)	PUNCT
ejpam-2779	490	5	.	.	PUNCT
ejpam-2779	491	1	now	now	ADV
ejpam-2779	491	2	assume	assume	VERB
ejpam-2779	491	3	that	that	SCONJ
ejpam-2779	491	4	x	x	PRON
ejpam-2779	491	5	and	and	CCONJ
ejpam-2779	491	6	y	y	PROPN
ejpam-2779	491	7	are	be	AUX
ejpam-2779	491	8	arbitrary	arbitrary	ADJ
ejpam-2779	491	9	elements	element	NOUN
ejpam-2779	491	10	of	of	ADP
ejpam-2779	491	11	v	v	NOUN
ejpam-2779	491	12	(	(	PUNCT
ejpam-2779	491	13	a	a	NOUN
ejpam-2779	491	14	)	)	PUNCT
ejpam-2779	491	15	,	,	PUNCT
ejpam-2779	491	16	where	where	SCONJ
ejpam-2779	491	17	a	a	DET
ejpam-2779	491	18	∈	∈	PROPN
ejpam-2779	491	19	m(a	m(a	PROPN
ejpam-2779	491	20	)	)	PUNCT
ejpam-2779	491	21	.	.	PUNCT
ejpam-2779	492	1	using	use	VERB
ejpam-2779	492	2	propositions	proposition	NOUN
ejpam-2779	492	3	19(2	19(2	NOUN
ejpam-2779	492	4	)	)	PUNCT
ejpam-2779	492	5	again	again	ADV
ejpam-2779	492	6	and	and	CCONJ
ejpam-2779	492	7	first	first	ADJ
ejpam-2779	492	8	part	part	NOUN
ejpam-2779	492	9	of	of	ADP
ejpam-2779	492	10	the	the	DET
ejpam-2779	492	11	proof	proof	NOUN
ejpam-2779	492	12	,	,	PUNCT
ejpam-2779	492	13	we	we	PRON
ejpam-2779	492	14	have	have	VERB
ejpam-2779	492	15	s(x∧1	s(x∧1	NOUN
ejpam-2779	492	16	y	y	X
ejpam-2779	492	17	)	)	PUNCT
ejpam-2779	492	18	=	=	PUNCT
ejpam-2779	493	1	s(x∧1	s(x∧1	PROPN
ejpam-2779	493	2	(	(	PUNCT
ejpam-2779	493	3	x∧1	x∧1	NOUN
ejpam-2779	493	4	y	y	PROPN
ejpam-2779	493	5	)	)	PUNCT
ejpam-2779	493	6	)	)	PUNCT
ejpam-2779	494	1	=	=	PUNCT
ejpam-2779	494	2	s((x	s((x	NOUN
ejpam-2779	494	3	∧1	∧1	NUM
ejpam-2779	494	4	y	y	NOUN
ejpam-2779	494	5	)	)	PUNCT
ejpam-2779	494	6	∧1	∧1	NOUN
ejpam-2779	494	7	x	x	NOUN
ejpam-2779	494	8	)	)	PUNCT
ejpam-2779	494	9	=	=	SYM
ejpam-2779	494	10	s((x	s((x	NOUN
ejpam-2779	494	11	∧1	∧1	NUM
ejpam-2779	494	12	y	y	NOUN
ejpam-2779	494	13	)	)	PUNCT
ejpam-2779	494	14	∧2	∧2	PROPN
ejpam-2779	494	15	x	x	NOUN
ejpam-2779	494	16	)	)	PUNCT
ejpam-2779	494	17	≤	≤	NOUN
ejpam-2779	495	1	s(y	s(y	PROPN
ejpam-2779	495	2	∧2	∧2	PROPN
ejpam-2779	495	3	x	x	SYM
ejpam-2779	495	4	)	)	PUNCT
ejpam-2779	495	5	=	=	SYM
ejpam-2779	495	6	s(x	s(x	PROPN
ejpam-2779	495	7	∧2	∧2	PROPN
ejpam-2779	495	8	y	y	PROPN
ejpam-2779	495	9	)	)	PUNCT
ejpam-2779	495	10	.	.	PUNCT
ejpam-2779	496	1	dually	dually	PROPN
ejpam-2779	496	2	,	,	PUNCT
ejpam-2779	496	3	we	we	PRON
ejpam-2779	496	4	can	can	AUX
ejpam-2779	496	5	prove	prove	VERB
ejpam-2779	496	6	s(x	s(x	PROPN
ejpam-2779	496	7	∧2	∧2	PROPN
ejpam-2779	496	8	y	y	PROPN
ejpam-2779	496	9	)	)	PUNCT
ejpam-2779	496	10	≤	≤	NUM
ejpam-2779	496	11	s(x	s(x	PROPN
ejpam-2779	496	12	∧1	∧1	NUM
ejpam-2779	496	13	y	y	NOUN
ejpam-2779	496	14	)	)	PUNCT
ejpam-2779	496	15	.	.	PUNCT
ejpam-2779	497	1	hence	hence	ADV
ejpam-2779	497	2	s(x	s(x	PROPN
ejpam-2779	497	3	∧1	∧1	NUM
ejpam-2779	497	4	y	y	NOUN
ejpam-2779	497	5	)	)	PUNCT
ejpam-2779	497	6	=	=	PUNCT
ejpam-2779	498	1	s(x	s(x	PROPN
ejpam-2779	498	2	∧2	∧2	PROPN
ejpam-2779	498	3	y	y	PROPN
ejpam-2779	498	4	)	)	PUNCT
ejpam-2779	498	5	.	.	PUNCT
ejpam-2779	499	1	x.l	x.l	PROPN
ejpam-2779	499	2	.	.	PUNCT
ejpam-2779	500	1	xin	xin	PROPN
ejpam-2779	500	2	,	,	PUNCT
ejpam-2779	500	3	y.j	y.j	PROPN
ejpam-2779	500	4	.	.	PUNCT
ejpam-2779	500	5	li	li	PROPN
ejpam-2779	500	6	,	,	PUNCT
ejpam-2779	500	7	y.l	y.l	PROPN
ejpam-2779	500	8	.	.	PROPN
ejpam-2779	500	9	fu	fu	PROPN
ejpam-2779	500	10	/	/	SYM
ejpam-2779	500	11	eur	eur	PROPN
ejpam-2779	500	12	.	.	PUNCT
ejpam-2779	501	1	j.	j.	PROPN
ejpam-2779	501	2	pure	pure	PROPN
ejpam-2779	501	3	appl	appl	PROPN
ejpam-2779	501	4	.	.	PROPN
ejpam-2779	501	5	math	math	PROPN
ejpam-2779	501	6	,	,	PUNCT
ejpam-2779	501	7	10	10	NUM
ejpam-2779	501	8	(	(	PUNCT
ejpam-2779	501	9	3	3	NUM
ejpam-2779	501	10	)	)	PUNCT
ejpam-2779	501	11	(	(	PUNCT
ejpam-2779	501	12	2017	2017	NUM
ejpam-2779	501	13	)	)	PUNCT
ejpam-2779	501	14	,	,	PUNCT
ejpam-2779	501	15	455	455	NUM
ejpam-2779	501	16	-	-	SYM
ejpam-2779	501	17	472	472	NUM
ejpam-2779	501	18	466	466	NUM
ejpam-2779	501	19	(	(	PUNCT
ejpam-2779	501	20	2	2	NUM
ejpam-2779	501	21	)	)	PUNCT
ejpam-2779	501	22	it	it	PRON
ejpam-2779	501	23	follows	follow	VERB
ejpam-2779	501	24	from	from	ADP
ejpam-2779	501	25	proposition	proposition	NOUN
ejpam-2779	501	26	21	21	NUM
ejpam-2779	501	27	and	and	CCONJ
ejpam-2779	501	28	the	the	DET
ejpam-2779	501	29	first	first	ADJ
ejpam-2779	501	30	equation	equation	NOUN
ejpam-2779	501	31	.	.	PUNCT
ejpam-2779	502	1	consider	consider	VERB
ejpam-2779	502	2	the	the	DET
ejpam-2779	502	3	real	real	ADJ
ejpam-2779	502	4	interval	interval	NOUN
ejpam-2779	503	1	[	[	X
ejpam-2779	503	2	0,1	0,1	NOUN
ejpam-2779	503	3	]	]	PUNCT
ejpam-2779	503	4	of	of	ADP
ejpam-2779	503	5	reals	real	NOUN
ejpam-2779	503	6	equipped	equip	VERB
ejpam-2779	503	7	with	with	ADP
ejpam-2779	503	8	the	the	DET
ejpam-2779	503	9	lukasiewicz	lukasiewicz	ADJ
ejpam-2779	503	10	implication	implication	NOUN
ejpam-2779	503	11	→	→	SYM
ejpam-2779	504	1	l	l	NOUN
ejpam-2779	504	2	defined	define	VERB
ejpam-2779	504	3	by	by	ADP
ejpam-2779	504	4	x→	x→	X
ejpam-2779	504	5	l	l	NOUN
ejpam-2779	504	6	y	y	PROPN
ejpam-2779	504	7	=	=	PUNCT
ejpam-2779	504	8	min{1−	min{1−	VERB
ejpam-2779	504	9	x+	x+	ADJ
ejpam-2779	504	10	y	y	PROPN
ejpam-2779	504	11	,	,	PUNCT
ejpam-2779	504	12	1	1	NUM
ejpam-2779	504	13	}	}	PUNCT
ejpam-2779	504	14	,	,	PUNCT
ejpam-2779	504	15	for	for	ADP
ejpam-2779	504	16	all	all	DET
ejpam-2779	504	17	x	x	NOUN
ejpam-2779	504	18	,	,	PUNCT
ejpam-2779	504	19	y	y	PROPN
ejpam-2779	504	20	∈	∈	PROPN
ejpam-2779	505	1	[	[	X
ejpam-2779	505	2	0	0	NUM
ejpam-2779	505	3	,	,	PUNCT
ejpam-2779	505	4	1	1	NUM
ejpam-2779	505	5	]	]	PUNCT
ejpam-2779	505	6	.	.	PUNCT
ejpam-2779	506	1	definition	definition	NOUN
ejpam-2779	506	2	8	8	NUM
ejpam-2779	506	3	.	.	PUNCT
ejpam-2779	507	1	let	let	VERB
ejpam-2779	507	2	a	a	PRON
ejpam-2779	507	3	be	be	AUX
ejpam-2779	507	4	a	a	DET
ejpam-2779	507	5	lbp	lbp	NOUN
ejpam-2779	507	6	-	-	PUNCT
ejpam-2779	507	7	bci	bci	NOUN
ejpam-2779	507	8	algebra	algebra	NOUN
ejpam-2779	507	9	.	.	PUNCT
ejpam-2779	508	1	a	a	DET
ejpam-2779	508	2	state	state	NOUN
ejpam-2779	508	3	-	-	PUNCT
ejpam-2779	508	4	morphism	morphism	NOUN
ejpam-2779	508	5	on	on	ADP
ejpam-2779	508	6	a	a	PRON
ejpam-2779	508	7	is	be	AUX
ejpam-2779	508	8	a	a	DET
ejpam-2779	508	9	function	function	NOUN
ejpam-2779	508	10	m	m	VERB
ejpam-2779	508	11	:	:	PUNCT
ejpam-2779	508	12	a→	a→	PUNCT
ejpam-2779	508	13	[	[	X
ejpam-2779	508	14	0	0	NUM
ejpam-2779	508	15	,	,	PUNCT
ejpam-2779	508	16	1	1	NUM
ejpam-2779	508	17	]	]	PUNCT
ejpam-2779	508	18	such	such	ADJ
ejpam-2779	508	19	that	that	SCONJ
ejpam-2779	508	20	:	:	PUNCT
ejpam-2779	508	21	(	(	PUNCT
ejpam-2779	508	22	sm1	sm1	NOUN
ejpam-2779	508	23	)	)	PUNCT
ejpam-2779	508	24	m(a	m(a	PROPN
ejpam-2779	508	25	)	)	PUNCT
ejpam-2779	508	26	=	=	SYM
ejpam-2779	508	27	0,m(1a	0,m(1a	NUM
ejpam-2779	508	28	)	)	PUNCT
ejpam-2779	508	29	=	=	SYM
ejpam-2779	508	30	1	1	NUM
ejpam-2779	508	31	for	for	ADP
ejpam-2779	508	32	all	all	DET
ejpam-2779	508	33	a	a	DET
ejpam-2779	508	34	∈m(a	∈m(a	NOUN
ejpam-2779	508	35	)	)	PUNCT
ejpam-2779	508	36	.	.	PUNCT
ejpam-2779	509	1	(	(	PUNCT
ejpam-2779	509	2	sm2	sm2	PROPN
ejpam-2779	509	3	)	)	PUNCT
ejpam-2779	509	4	m(y	m(y	NOUN
ejpam-2779	509	5	∗	∗	NOUN
ejpam-2779	509	6	x	x	NOUN
ejpam-2779	509	7	)	)	PUNCT
ejpam-2779	510	1	=	=	PUNCT
ejpam-2779	510	2	m(y	m(y	NOUN
ejpam-2779	510	3	◦	◦	NOUN
ejpam-2779	510	4	x	x	X
ejpam-2779	510	5	)	)	PUNCT
ejpam-2779	510	6	=	=	SYM
ejpam-2779	510	7	m(x)→	m(x)→	PROPN
ejpam-2779	510	8	l	l	PROPN
ejpam-2779	510	9	m(y	m(y	PROPN
ejpam-2779	510	10	)	)	PUNCT
ejpam-2779	510	11	,	,	PUNCT
ejpam-2779	510	12	for	for	ADP
ejpam-2779	510	13	all	all	DET
ejpam-2779	510	14	x	x	NOUN
ejpam-2779	510	15	,	,	PUNCT
ejpam-2779	510	16	y	y	PROPN
ejpam-2779	510	17	∈	∈	PROPN
ejpam-2779	510	18	a.	a.	NOUN
ejpam-2779	510	19	proposition	proposition	NOUN
ejpam-2779	510	20	23	23	NUM
ejpam-2779	510	21	.	.	PUNCT
ejpam-2779	511	1	let	let	VERB
ejpam-2779	511	2	a	a	PRON
ejpam-2779	511	3	be	be	AUX
ejpam-2779	511	4	a	a	DET
ejpam-2779	511	5	lbp	lbp	NOUN
ejpam-2779	511	6	-	-	PUNCT
ejpam-2779	511	7	bci	bci	NOUN
ejpam-2779	511	8	algebra	algebra	NOUN
ejpam-2779	511	9	.	.	PUNCT
ejpam-2779	512	1	then	then	ADV
ejpam-2779	512	2	every	every	DET
ejpam-2779	512	3	state	state	NOUN
ejpam-2779	512	4	-	-	PUNCT
ejpam-2779	512	5	morphism	morphism	NOUN
ejpam-2779	512	6	on	on	ADP
ejpam-2779	512	7	a	a	PRON
ejpam-2779	512	8	is	be	AUX
ejpam-2779	512	9	a	a	DET
ejpam-2779	512	10	bosbach	bosbach	ADJ
ejpam-2779	512	11	state	state	NOUN
ejpam-2779	512	12	on	on	ADP
ejpam-2779	512	13	a.	a.	NOUN
ejpam-2779	512	14	proof	proof	NOUN
ejpam-2779	512	15	.	.	PUNCT
ejpam-2779	513	1	it	it	PRON
ejpam-2779	513	2	is	be	AUX
ejpam-2779	513	3	similar	similar	ADJ
ejpam-2779	513	4	to	to	ADP
ejpam-2779	513	5	the	the	DET
ejpam-2779	513	6	proof	proof	NOUN
ejpam-2779	513	7	of	of	ADP
ejpam-2779	513	8	[	[	X
ejpam-2779	513	9	[	[	X
ejpam-2779	513	10	4	4	NUM
ejpam-2779	513	11	]	]	PUNCT
ejpam-2779	513	12	,	,	PUNCT
ejpam-2779	513	13	proposition	proposition	NOUN
ejpam-2779	513	14	3.9	3.9	NUM
ejpam-2779	513	15	]	]	PUNCT
ejpam-2779	513	16	.	.	PUNCT
ejpam-2779	514	1	proposition	proposition	NOUN
ejpam-2779	514	2	24	24	NUM
ejpam-2779	514	3	.	.	PUNCT
ejpam-2779	515	1	let	let	VERB
ejpam-2779	515	2	a	a	PRON
ejpam-2779	515	3	be	be	AUX
ejpam-2779	515	4	a	a	DET
ejpam-2779	515	5	lbp	lbp	NOUN
ejpam-2779	515	6	-	-	PUNCT
ejpam-2779	515	7	bci	bci	NOUN
ejpam-2779	515	8	algebra	algebra	NOUN
ejpam-2779	515	9	.	.	PUNCT
ejpam-2779	516	1	a	a	DET
ejpam-2779	516	2	bosbach	bosbach	ADJ
ejpam-2779	516	3	state	state	NOUN
ejpam-2779	516	4	m	m	PROPN
ejpam-2779	516	5	on	on	ADP
ejpam-2779	516	6	a	a	PRON
ejpam-2779	516	7	is	be	AUX
ejpam-2779	516	8	a	a	DET
ejpam-2779	516	9	state	state	NOUN
ejpam-2779	516	10	-	-	PUNCT
ejpam-2779	516	11	morphism	morphism	NOUN
ejpam-2779	516	12	if	if	SCONJ
ejpam-2779	516	13	and	and	CCONJ
ejpam-2779	516	14	only	only	ADV
ejpam-2779	516	15	if	if	SCONJ
ejpam-2779	516	16	m(x∧1	m(x∧1	PROPN
ejpam-2779	516	17	y	y	NOUN
ejpam-2779	516	18	)	)	PUNCT
ejpam-2779	516	19	=	=	SYM
ejpam-2779	516	20	min{m(x),m(y	min{m(x),m(y	NOUN
ejpam-2779	516	21	)	)	PUNCT
ejpam-2779	516	22	}	}	PUNCT
ejpam-2779	516	23	for	for	ADP
ejpam-2779	516	24	all	all	DET
ejpam-2779	516	25	x	x	NOUN
ejpam-2779	516	26	,	,	PUNCT
ejpam-2779	516	27	y	y	PROPN
ejpam-2779	516	28	∈	∈	PROPN
ejpam-2779	516	29	a	a	PRON
ejpam-2779	516	30	,	,	PUNCT
ejpam-2779	516	31	or	or	CCONJ
ejpam-2779	516	32	equivalently	equivalently	ADV
ejpam-2779	516	33	,	,	PUNCT
ejpam-2779	516	34	m(x∧2	m(x∧2	PROPN
ejpam-2779	516	35	y	y	PROPN
ejpam-2779	516	36	)	)	PUNCT
ejpam-2779	516	37	=	=	SYM
ejpam-2779	516	38	min{m(x),m(y	min{m(x),m(y	NOUN
ejpam-2779	516	39	)	)	PUNCT
ejpam-2779	516	40	}	}	PUNCT
ejpam-2779	516	41	for	for	ADP
ejpam-2779	516	42	all	all	DET
ejpam-2779	516	43	x	x	NOUN
ejpam-2779	516	44	,	,	PUNCT
ejpam-2779	516	45	y	y	PROPN
ejpam-2779	516	46	∈	∈	PROPN
ejpam-2779	516	47	a.	a.	NOUN
ejpam-2779	516	48	proof	proof	NOUN
ejpam-2779	516	49	.	.	PUNCT
ejpam-2779	517	1	it	it	PRON
ejpam-2779	517	2	is	be	AUX
ejpam-2779	517	3	similar	similar	ADJ
ejpam-2779	517	4	to	to	ADP
ejpam-2779	517	5	the	the	DET
ejpam-2779	517	6	proof	proof	NOUN
ejpam-2779	517	7	of	of	ADP
ejpam-2779	517	8	[	[	X
ejpam-2779	517	9	[	[	X
ejpam-2779	517	10	4	4	NUM
ejpam-2779	517	11	]	]	PUNCT
ejpam-2779	517	12	,	,	PUNCT
ejpam-2779	517	13	proposition	proposition	NOUN
ejpam-2779	517	14	3.10	3.10	NUM
ejpam-2779	517	15	]	]	PUNCT
ejpam-2779	517	16	.	.	PUNCT
ejpam-2779	518	1	let	let	VERB
ejpam-2779	518	2	a	a	PRON
ejpam-2779	518	3	be	be	AUX
ejpam-2779	518	4	a	a	DET
ejpam-2779	518	5	lbp	lbp	NOUN
ejpam-2779	518	6	-	-	PUNCT
ejpam-2779	518	7	bci	bci	NOUN
ejpam-2779	518	8	algebra	algebra	NOUN
ejpam-2779	518	9	and	and	CCONJ
ejpam-2779	518	10	s	s	AUX
ejpam-2779	518	11	be	be	AUX
ejpam-2779	518	12	a	a	DET
ejpam-2779	518	13	bosbach	bosbach	ADJ
ejpam-2779	518	14	state	state	NOUN
ejpam-2779	518	15	on	on	ADP
ejpam-2779	518	16	a.	a.	NOUN
ejpam-2779	518	17	define	define	VERB
ejpam-2779	518	18	a	a	DET
ejpam-2779	518	19	set	set	ADJ
ejpam-2779	518	20	ker(s	ker(s	NOUN
ejpam-2779	518	21	)	)	PUNCT
ejpam-2779	518	22	:	:	PUNCT
ejpam-2779	519	1	=	=	SYM
ejpam-2779	519	2	{	{	PUNCT
ejpam-2779	519	3	x	x	SYM
ejpam-2779	519	4	∈	∈	PROPN
ejpam-2779	519	5	a	a	DET
ejpam-2779	519	6	|	|	NOUN
ejpam-2779	519	7	s(x	s(x	NOUN
ejpam-2779	519	8	)	)	PUNCT
ejpam-2779	519	9	=	=	PUNCT
ejpam-2779	519	10	1	1	NUM
ejpam-2779	519	11	}	}	PUNCT
ejpam-2779	519	12	.	.	PUNCT
ejpam-2779	520	1	ker(s	ker(s	NOUN
ejpam-2779	520	2	)	)	PUNCT
ejpam-2779	520	3	is	be	AUX
ejpam-2779	520	4	called	call	VERB
ejpam-2779	520	5	the	the	DET
ejpam-2779	520	6	kernel	kernel	NOUN
ejpam-2779	520	7	of	of	ADP
ejpam-2779	520	8	s	s	PRON
ejpam-2779	520	9	on	on	ADP
ejpam-2779	520	10	a.	a.	NOUN
ejpam-2779	520	11	definition	definition	NOUN
ejpam-2779	520	12	9	9	NUM
ejpam-2779	520	13	.	.	PUNCT
ejpam-2779	521	1	let	let	VERB
ejpam-2779	521	2	a	a	DET
ejpam-2779	521	3	be	be	AUX
ejpam-2779	521	4	a	a	DET
ejpam-2779	521	5	pseudo	pseudo	NOUN
ejpam-2779	521	6	bci	bci	NOUN
ejpam-2779	521	7	algebra	algebra	NOUN
ejpam-2779	521	8	and	and	CCONJ
ejpam-2779	521	9	i	i	PRON
ejpam-2779	521	10	be	be	VERB
ejpam-2779	521	11	a	a	DET
ejpam-2779	521	12	nonempty	nonempty	ADJ
ejpam-2779	521	13	subset	subset	NOUN
ejpam-2779	521	14	of	of	ADP
ejpam-2779	521	15	a.	a.	NOUN
ejpam-2779	521	16	if	if	SCONJ
ejpam-2779	521	17	i	i	PRON
ejpam-2779	521	18	satisfies	satisfy	VERB
ejpam-2779	521	19	the	the	DET
ejpam-2779	521	20	following	follow	VERB
ejpam-2779	521	21	conditions	condition	NOUN
ejpam-2779	521	22	:	:	PUNCT
ejpam-2779	521	23	(	(	PUNCT
ejpam-2779	521	24	1	1	X
ejpam-2779	521	25	)	)	PUNCT
ejpam-2779	521	26	0	0	NUM
ejpam-2779	522	1	∈	∈	PROPN
ejpam-2779	523	1	i	i	PRON
ejpam-2779	523	2	,	,	PUNCT
ejpam-2779	523	3	(	(	PUNCT
ejpam-2779	523	4	2	2	X
ejpam-2779	523	5	)	)	PUNCT
ejpam-2779	523	6	x	x	SYM
ejpam-2779	523	7	∈	∈	PROPN
ejpam-2779	524	1	i	i	PRON
ejpam-2779	524	2	and	and	CCONJ
ejpam-2779	524	3	y	y	PROPN
ejpam-2779	524	4	∗	∗	NOUN
ejpam-2779	524	5	x	x	PUNCT
ejpam-2779	524	6	∈	∈	NOUN
ejpam-2779	524	7	i	i	PRON
ejpam-2779	524	8	(	(	PUNCT
ejpam-2779	524	9	or	or	CCONJ
ejpam-2779	524	10	y	y	PROPN
ejpam-2779	524	11	◦	◦	NOUN
ejpam-2779	524	12	x	x	PUNCT
ejpam-2779	524	13	∈	∈	PROPN
ejpam-2779	524	14	i	i	X
ejpam-2779	524	15	)	)	PUNCT
ejpam-2779	524	16	imply	imply	VERB
ejpam-2779	524	17	y	y	PROPN
ejpam-2779	524	18	∈	∈	PROPN
ejpam-2779	525	1	i	i	PRON
ejpam-2779	525	2	for	for	ADP
ejpam-2779	525	3	all	all	DET
ejpam-2779	525	4	x	x	NOUN
ejpam-2779	525	5	,	,	PUNCT
ejpam-2779	525	6	y	y	PROPN
ejpam-2779	525	7	∈	∈	PROPN
ejpam-2779	526	1	a	a	PRON
ejpam-2779	526	2	,	,	PUNCT
ejpam-2779	526	3	i	i	PRON
ejpam-2779	526	4	is	be	AUX
ejpam-2779	526	5	called	call	VERB
ejpam-2779	526	6	a	a	DET
ejpam-2779	526	7	pseudo	pseudo	NOUN
ejpam-2779	526	8	ideal	ideal	NOUN
ejpam-2779	526	9	of	of	ADP
ejpam-2779	526	10	a	a	PRON
ejpam-2779	526	11	,	,	PUNCT
ejpam-2779	526	12	simply	simply	ADV
ejpam-2779	526	13	called	call	VERB
ejpam-2779	526	14	an	an	DET
ejpam-2779	526	15	ideal	ideal	NOUN
ejpam-2779	526	16	of	of	ADP
ejpam-2779	526	17	a.	a.	NOUN
ejpam-2779	526	18	let	let	AUX
ejpam-2779	526	19	i	i	PRON
ejpam-2779	526	20	be	be	AUX
ejpam-2779	526	21	a	a	DET
ejpam-2779	526	22	pseudo	pseudo	NOUN
ejpam-2779	526	23	ideal	ideal	NOUN
ejpam-2779	526	24	of	of	ADP
ejpam-2779	526	25	a	a	DET
ejpam-2779	526	26	pseudo	pseudo	NOUN
ejpam-2779	526	27	bci	bci	NOUN
ejpam-2779	526	28	algebra	algebra	NOUN
ejpam-2779	526	29	a.	a.	NOUN
ejpam-2779	526	30	if	if	SCONJ
ejpam-2779	526	31	i	i	PRON
ejpam-2779	526	32	satisfies	satisfy	VERB
ejpam-2779	526	33	0∗x	0∗x	NOUN
ejpam-2779	526	34	∈	∈	NOUN
ejpam-2779	527	1	i	i	PRON
ejpam-2779	527	2	and	and	CCONJ
ejpam-2779	527	3	0	0	NUM
ejpam-2779	527	4	◦	◦	NOUN
ejpam-2779	527	5	x	x	SYM
ejpam-2779	527	6	∈	∈	PROPN
ejpam-2779	528	1	i	i	PRON
ejpam-2779	528	2	,	,	PUNCT
ejpam-2779	528	3	we	we	PRON
ejpam-2779	528	4	call	call	VERB
ejpam-2779	528	5	i	i	PRON
ejpam-2779	528	6	a	a	DET
ejpam-2779	528	7	closed	closed	ADJ
ejpam-2779	528	8	pseudo	pseudo	NOUN
ejpam-2779	528	9	ideal	ideal	NOUN
ejpam-2779	528	10	of	of	ADP
ejpam-2779	528	11	a.	a.	NOUN
ejpam-2779	528	12	if	if	SCONJ
ejpam-2779	528	13	i	i	PRON
ejpam-2779	528	14	satisfies	satisfy	VERB
ejpam-2779	528	15	x	x	X
ejpam-2779	528	16	∗	∗	NOUN
ejpam-2779	528	17	y	y	NOUN
ejpam-2779	528	18	∈	∈	PROPN
ejpam-2779	529	1	i	i	PRON
ejpam-2779	529	2	if	if	SCONJ
ejpam-2779	529	3	and	and	CCONJ
ejpam-2779	529	4	only	only	ADV
ejpam-2779	529	5	if	if	SCONJ
ejpam-2779	529	6	x	x	PRON
ejpam-2779	529	7	◦	◦	VERB
ejpam-2779	529	8	y	y	PROPN
ejpam-2779	529	9	∈	∈	PROPN
ejpam-2779	530	1	i	i	PRON
ejpam-2779	530	2	,	,	PUNCT
ejpam-2779	530	3	we	we	PRON
ejpam-2779	530	4	call	call	VERB
ejpam-2779	530	5	i	i	PRON
ejpam-2779	530	6	a	a	DET
ejpam-2779	530	7	normal	normal	ADJ
ejpam-2779	530	8	pseudo	pseudo	NOUN
ejpam-2779	530	9	ideal	ideal	NOUN
ejpam-2779	530	10	of	of	ADP
ejpam-2779	530	11	a.	a.	NOUN
ejpam-2779	530	12	if	if	SCONJ
ejpam-2779	530	13	i	i	PRON
ejpam-2779	530	14	satisfies	satisfy	VERB
ejpam-2779	530	15	x	x	X
ejpam-2779	530	16	∗	∗	NOUN
ejpam-2779	530	17	y	y	NOUN
ejpam-2779	530	18	∈	∈	PROPN
ejpam-2779	531	1	i	i	PRON
ejpam-2779	531	2	if	if	SCONJ
ejpam-2779	531	3	and	and	CCONJ
ejpam-2779	531	4	only	only	ADV
ejpam-2779	531	5	if	if	SCONJ
ejpam-2779	531	6	x	x	PRON
ejpam-2779	531	7	◦	◦	VERB
ejpam-2779	531	8	y	y	PROPN
ejpam-2779	531	9	∈	∈	PROPN
ejpam-2779	531	10	i	i	PRON
ejpam-2779	531	11	for	for	ADP
ejpam-2779	531	12	all	all	DET
ejpam-2779	531	13	a	a	DET
ejpam-2779	531	14	∈m(a	∈m(a	NOUN
ejpam-2779	531	15	)	)	PUNCT
ejpam-2779	531	16	,	,	PUNCT
ejpam-2779	531	17	x	x	X
ejpam-2779	531	18	,	,	PUNCT
ejpam-2779	531	19	y	y	PROPN
ejpam-2779	531	20	∈	∈	PROPN
ejpam-2779	531	21	v	v	ADP
ejpam-2779	531	22	(	(	PUNCT
ejpam-2779	531	23	a	a	NOUN
ejpam-2779	531	24	)	)	PUNCT
ejpam-2779	531	25	,	,	PUNCT
ejpam-2779	531	26	we	we	PRON
ejpam-2779	531	27	call	call	VERB
ejpam-2779	531	28	i	i	PRON
ejpam-2779	531	29	a	a	DET
ejpam-2779	531	30	local	local	ADJ
ejpam-2779	531	31	normal	normal	ADJ
ejpam-2779	531	32	pseudo	pseudo	NOUN
ejpam-2779	531	33	ideal	ideal	NOUN
ejpam-2779	531	34	of	of	ADP
ejpam-2779	531	35	a.	a.	NOUN
ejpam-2779	531	36	proposition	proposition	NOUN
ejpam-2779	531	37	25	25	NUM
ejpam-2779	531	38	.	.	PUNCT
ejpam-2779	532	1	let	let	VERB
ejpam-2779	532	2	a	a	PRON
ejpam-2779	532	3	be	be	AUX
ejpam-2779	532	4	a	a	DET
ejpam-2779	532	5	lbp	lbp	NOUN
ejpam-2779	532	6	-	-	PUNCT
ejpam-2779	532	7	bci	bci	NOUN
ejpam-2779	532	8	algebra	algebra	NOUN
ejpam-2779	532	9	and	and	CCONJ
ejpam-2779	532	10	s	s	AUX
ejpam-2779	532	11	be	be	AUX
ejpam-2779	532	12	a	a	DET
ejpam-2779	532	13	bosbach	bosbach	ADJ
ejpam-2779	532	14	state	state	NOUN
ejpam-2779	532	15	on	on	ADP
ejpam-2779	532	16	a.	a.	PROPN
ejpam-2779	532	17	then	then	ADV
ejpam-2779	532	18	ker(s	ker(s	PROPN
ejpam-2779	532	19	)	)	PUNCT
ejpam-2779	532	20	is	be	AUX
ejpam-2779	532	21	a	a	DET
ejpam-2779	532	22	closed	closed	ADJ
ejpam-2779	532	23	and	and	CCONJ
ejpam-2779	532	24	local	local	ADJ
ejpam-2779	532	25	normal	normal	ADJ
ejpam-2779	532	26	proper	proper	ADJ
ejpam-2779	532	27	ideal	ideal	NOUN
ejpam-2779	532	28	of	of	ADP
ejpam-2779	532	29	a.	a.	NOUN
ejpam-2779	532	30	proof	proof	NOUN
ejpam-2779	532	31	.	.	PUNCT
ejpam-2779	533	1	obviously	obviously	ADV
ejpam-2779	533	2	,	,	PUNCT
ejpam-2779	533	3	0	0	NUM
ejpam-2779	533	4	∈	∈	PROPN
ejpam-2779	533	5	ker(s	ker(s	PROPN
ejpam-2779	533	6	)	)	PUNCT
ejpam-2779	533	7	and	and	CCONJ
ejpam-2779	533	8	1	1	NUM
ejpam-2779	533	9	/∈	/∈	INTJ
ejpam-2779	533	10	ker(s	ker(s	NOUN
ejpam-2779	533	11	)	)	PUNCT
ejpam-2779	533	12	.	.	PUNCT
ejpam-2779	534	1	assume	assume	VERB
ejpam-2779	534	2	that	that	SCONJ
ejpam-2779	534	3	x	x	X
ejpam-2779	534	4	,	,	PUNCT
ejpam-2779	534	5	y	y	PROPN
ejpam-2779	534	6	∗	∗	NOUN
ejpam-2779	534	7	x	x	PUNCT
ejpam-2779	534	8	∈	∈	PROPN
ejpam-2779	534	9	ker(s	ker(s	PROPN
ejpam-2779	534	10	)	)	PUNCT
ejpam-2779	534	11	.	.	PUNCT
ejpam-2779	535	1	then	then	ADV
ejpam-2779	535	2	we	we	PRON
ejpam-2779	535	3	have	have	VERB
ejpam-2779	535	4	1	1	NUM
ejpam-2779	535	5	=	=	SYM
ejpam-2779	535	6	s(x	s(x	PROPN
ejpam-2779	535	7	)	)	PUNCT
ejpam-2779	535	8	and	and	CCONJ
ejpam-2779	535	9	s(y	s(y	PROPN
ejpam-2779	535	10	∗	∗	NOUN
ejpam-2779	535	11	x	x	NOUN
ejpam-2779	535	12	)	)	PUNCT
ejpam-2779	535	13	=	=	SYM
ejpam-2779	536	1	1	1	X
ejpam-2779	536	2	.	.	PUNCT
ejpam-2779	537	1	it	it	PRON
ejpam-2779	537	2	follows	follow	VERB
ejpam-2779	537	3	from	from	ADP
ejpam-2779	537	4	definition	definition	NOUN
ejpam-2779	537	5	5.1	5.1	NUM
ejpam-2779	537	6	that	that	PRON
ejpam-2779	537	7	s(y	s(y	NOUN
ejpam-2779	537	8	)	)	PUNCT
ejpam-2779	537	9	=	=	SYM
ejpam-2779	537	10	s(x	s(x	PROPN
ejpam-2779	537	11	)	)	PUNCT
ejpam-2779	538	1	+	+	CCONJ
ejpam-2779	538	2	s(y	s(y	PROPN
ejpam-2779	538	3	∗	∗	NOUN
ejpam-2779	538	4	x	x	NOUN
ejpam-2779	538	5	)	)	PUNCT
ejpam-2779	538	6	−	−	PROPN
ejpam-2779	539	1	s(x	s(x	PROPN
ejpam-2779	539	2	∗	∗	NOUN
ejpam-2779	539	3	y	y	NOUN
ejpam-2779	539	4	)	)	PUNCT
ejpam-2779	539	5	=	=	SYM
ejpam-2779	539	6	2	2	NUM
ejpam-2779	539	7	−	−	PROPN
ejpam-2779	539	8	s(x	s(x	PROPN
ejpam-2779	539	9	∗	∗	PROPN
ejpam-2779	539	10	y	y	PROPN
ejpam-2779	539	11	)	)	PUNCT
ejpam-2779	539	12	≥	≥	NOUN
ejpam-2779	539	13	1	1	NUM
ejpam-2779	539	14	and	and	CCONJ
ejpam-2779	539	15	thus	thus	ADV
ejpam-2779	539	16	s(y	s(y	NUM
ejpam-2779	539	17	)	)	PUNCT
ejpam-2779	539	18	=	=	SYM
ejpam-2779	540	1	1	1	X
ejpam-2779	540	2	.	.	X
ejpam-2779	540	3	hence	hence	ADV
ejpam-2779	540	4	y	y	PROPN
ejpam-2779	540	5	∈	∈	PROPN
ejpam-2779	540	6	ker(s	ker(s	PROPN
ejpam-2779	540	7	)	)	PUNCT
ejpam-2779	540	8	.	.	PUNCT
ejpam-2779	541	1	this	this	PRON
ejpam-2779	541	2	shows	show	VERB
ejpam-2779	541	3	that	that	SCONJ
ejpam-2779	541	4	ker(s	ker(s	PROPN
ejpam-2779	541	5	)	)	PUNCT
ejpam-2779	541	6	is	be	AUX
ejpam-2779	541	7	a	a	DET
ejpam-2779	541	8	proper	proper	ADJ
ejpam-2779	541	9	ideal	ideal	NOUN
ejpam-2779	541	10	of	of	ADP
ejpam-2779	541	11	a.	a.	NOUN
ejpam-2779	541	12	for	for	ADP
ejpam-2779	541	13	any	any	DET
ejpam-2779	541	14	x	x	SYM
ejpam-2779	541	15	∈	∈	PROPN
ejpam-2779	541	16	a	a	X
ejpam-2779	541	17	,	,	PUNCT
ejpam-2779	541	18	we	we	PRON
ejpam-2779	541	19	have	have	VERB
ejpam-2779	541	20	0	0	NUM
ejpam-2779	541	21	∗	∗	NOUN
ejpam-2779	541	22	x	x	SYM
ejpam-2779	541	23	∈	∈	PROPN
ejpam-2779	541	24	m(a	m(a	PROPN
ejpam-2779	541	25	)	)	PUNCT
ejpam-2779	541	26	and	and	CCONJ
ejpam-2779	541	27	0	0	NUM
ejpam-2779	541	28	∗	∗	NOUN
ejpam-2779	541	29	x	x	SYM
ejpam-2779	541	30	∈	∈	PROPN
ejpam-2779	541	31	m(a	m(a	PROPN
ejpam-2779	541	32	)	)	PUNCT
ejpam-2779	541	33	by	by	ADP
ejpam-2779	541	34	corollary	corollary	ADJ
ejpam-2779	541	35	2	2	NUM
ejpam-2779	541	36	.	.	PUNCT
ejpam-2779	541	37	hence	hence	ADV
ejpam-2779	541	38	s(0	s(0	PROPN
ejpam-2779	541	39	∗	∗	NOUN
ejpam-2779	541	40	x	x	NOUN
ejpam-2779	541	41	)	)	PUNCT
ejpam-2779	541	42	=	=	SYM
ejpam-2779	541	43	1	1	NUM
ejpam-2779	541	44	and	and	CCONJ
ejpam-2779	541	45	s(0	s(0	PROPN
ejpam-2779	541	46	◦	◦	NOUN
ejpam-2779	541	47	x	x	X
ejpam-2779	541	48	)	)	PUNCT
ejpam-2779	541	49	=	=	SYM
ejpam-2779	542	1	1	1	X
ejpam-2779	542	2	.	.	PUNCT
ejpam-2779	543	1	it	it	PRON
ejpam-2779	543	2	follows	follow	VERB
ejpam-2779	543	3	that	that	SCONJ
ejpam-2779	543	4	0	0	NUM
ejpam-2779	543	5	∗	∗	NOUN
ejpam-2779	543	6	x	x	SYM
ejpam-2779	543	7	∈	∈	PROPN
ejpam-2779	543	8	ker(s	ker(s	PROPN
ejpam-2779	543	9	)	)	PUNCT
ejpam-2779	543	10	and	and	CCONJ
ejpam-2779	543	11	0	0	NUM
ejpam-2779	543	12	◦	◦	NOUN
ejpam-2779	543	13	x	x	SYM
ejpam-2779	543	14	∈	∈	PROPN
ejpam-2779	543	15	ker(s	ker(s	PROPN
ejpam-2779	543	16	)	)	PUNCT
ejpam-2779	543	17	.	.	PUNCT
ejpam-2779	544	1	this	this	PRON
ejpam-2779	544	2	shows	show	VERB
ejpam-2779	544	3	that	that	SCONJ
ejpam-2779	544	4	i	i	PRON
ejpam-2779	544	5	is	be	AUX
ejpam-2779	544	6	a	a	DET
ejpam-2779	544	7	closed	closed	ADJ
ejpam-2779	544	8	pseudo	pseudo	NOUN
ejpam-2779	544	9	ideal	ideal	NOUN
ejpam-2779	544	10	of	of	ADP
ejpam-2779	544	11	a.	a.	NOUN
ejpam-2779	544	12	by	by	ADP
ejpam-2779	544	13	proposition	proposition	NOUN
ejpam-2779	544	14	22	22	NUM
ejpam-2779	544	15	,	,	PUNCT
ejpam-2779	544	16	we	we	PRON
ejpam-2779	544	17	can	can	AUX
ejpam-2779	544	18	get	get	VERB
ejpam-2779	544	19	that	that	PRON
ejpam-2779	544	20	a	a	PRON
ejpam-2779	544	21	is	be	AUX
ejpam-2779	544	22	local	local	ADJ
ejpam-2779	544	23	normal	normal	ADJ
ejpam-2779	544	24	.	.	PUNCT
ejpam-2779	545	1	x.l	x.l	PROPN
ejpam-2779	545	2	.	.	PUNCT
ejpam-2779	546	1	xin	xin	PROPN
ejpam-2779	546	2	,	,	PUNCT
ejpam-2779	546	3	y.j	y.j	PROPN
ejpam-2779	546	4	.	.	PUNCT
ejpam-2779	546	5	li	li	PROPN
ejpam-2779	546	6	,	,	PUNCT
ejpam-2779	546	7	y.l	y.l	PROPN
ejpam-2779	546	8	.	.	PROPN
ejpam-2779	546	9	fu	fu	PROPN
ejpam-2779	546	10	/	/	SYM
ejpam-2779	546	11	eur	eur	PROPN
ejpam-2779	546	12	.	.	PUNCT
ejpam-2779	547	1	j.	j.	PROPN
ejpam-2779	547	2	pure	pure	PROPN
ejpam-2779	547	3	appl	appl	PROPN
ejpam-2779	547	4	.	.	PROPN
ejpam-2779	547	5	math	math	PROPN
ejpam-2779	547	6	,	,	PUNCT
ejpam-2779	547	7	10	10	NUM
ejpam-2779	547	8	(	(	PUNCT
ejpam-2779	547	9	3	3	NUM
ejpam-2779	547	10	)	)	PUNCT
ejpam-2779	547	11	(	(	PUNCT
ejpam-2779	547	12	2017	2017	NUM
ejpam-2779	547	13	)	)	PUNCT
ejpam-2779	547	14	,	,	PUNCT
ejpam-2779	547	15	455	455	NUM
ejpam-2779	547	16	-	-	SYM
ejpam-2779	547	17	472	472	NUM
ejpam-2779	547	18	467	467	NUM
ejpam-2779	547	19	theorem	theorem	NOUN
ejpam-2779	547	20	2	2	NUM
ejpam-2779	547	21	.	.	PUNCT
ejpam-2779	547	22	let	let	VERB
ejpam-2779	547	23	a	a	DET
ejpam-2779	547	24	be	be	AUX
ejpam-2779	547	25	a	a	DET
ejpam-2779	547	26	pseudo	pseudo	NOUN
ejpam-2779	547	27	bci	bci	NOUN
ejpam-2779	547	28	algebra	algebra	NOUN
ejpam-2779	547	29	and	and	CCONJ
ejpam-2779	547	30	i	i	PRON
ejpam-2779	547	31	be	be	VERB
ejpam-2779	547	32	a	a	DET
ejpam-2779	547	33	pseudo	pseudo	NOUN
ejpam-2779	547	34	ideal	ideal	NOUN
ejpam-2779	547	35	of	of	ADP
ejpam-2779	547	36	a.	a.	NOUN
ejpam-2779	547	37	define	define	VERB
ejpam-2779	547	38	a	a	DET
ejpam-2779	547	39	binary	binary	ADJ
ejpam-2779	547	40	relation	relation	NOUN
ejpam-2779	547	41	”	"	PUNCT
ejpam-2779	547	42	∼	∼	NOUN
ejpam-2779	547	43	”	"	PUNCT
ejpam-2779	547	44	on	on	ADP
ejpam-2779	547	45	a	a	DET
ejpam-2779	547	46	by	by	NOUN
ejpam-2779	547	47	x	x	PUNCT
ejpam-2779	547	48	∼	∼	NOUN
ejpam-2779	547	49	y	y	NOUN
ejpam-2779	547	50	if	if	SCONJ
ejpam-2779	548	1	and	and	CCONJ
ejpam-2779	548	2	only	only	ADV
ejpam-2779	548	3	if	if	SCONJ
ejpam-2779	548	4	x∗y	x∗y	NOUN
ejpam-2779	548	5	,	,	PUNCT
ejpam-2779	548	6	y	y	PROPN
ejpam-2779	548	7	∗x	∗x	PROPN
ejpam-2779	548	8	∈	∈	PROPN
ejpam-2779	549	1	i	i	PRON
ejpam-2779	549	2	if	if	SCONJ
ejpam-2779	549	3	and	and	CCONJ
ejpam-2779	549	4	only	only	ADV
ejpam-2779	549	5	if	if	SCONJ
ejpam-2779	549	6	x	x	NOUN
ejpam-2779	549	7	◦	◦	VERB
ejpam-2779	549	8	y	y	PROPN
ejpam-2779	549	9	,	,	PUNCT
ejpam-2779	549	10	y	y	PROPN
ejpam-2779	549	11	◦	◦	NOUN
ejpam-2779	549	12	x	x	SYM
ejpam-2779	549	13	∈	∈	NOUN
ejpam-2779	549	14	i.	i.	NOUN
ejpam-2779	549	15	then	then	ADV
ejpam-2779	549	16	∼	∼	NOUN
ejpam-2779	549	17	is	be	AUX
ejpam-2779	549	18	a	a	DET
ejpam-2779	549	19	congruence	congruence	NOUN
ejpam-2779	549	20	relation	relation	NOUN
ejpam-2779	549	21	on	on	ADP
ejpam-2779	549	22	a.	a.	NOUN
ejpam-2779	549	23	denote	denote	NOUN
ejpam-2779	549	24	cx	cx	PROPN
ejpam-2779	550	1	=	=	PUNCT
ejpam-2779	550	2	{	{	PUNCT
ejpam-2779	550	3	y	y	PROPN
ejpam-2779	550	4	∈	∈	PROPN
ejpam-2779	550	5	a	a	DET
ejpam-2779	550	6	|	|	NOUN
ejpam-2779	550	7	x	x	SYM
ejpam-2779	550	8	∼	∼	NOUN
ejpam-2779	550	9	y	y	NOUN
ejpam-2779	550	10	}	}	PUNCT
ejpam-2779	550	11	.	.	PUNCT
ejpam-2779	551	1	define	define	VERB
ejpam-2779	551	2	cx	cx	PROPN
ejpam-2779	551	3	∗	∗	NOUN
ejpam-2779	551	4	cy	cy	PROPN
ejpam-2779	552	1	=	=	NOUN
ejpam-2779	552	2	cx∗y	cx∗y	PROPN
ejpam-2779	552	3	and	and	CCONJ
ejpam-2779	552	4	cx	cx	PROPN
ejpam-2779	552	5	◦	◦	NOUN
ejpam-2779	553	1	cy	cy	PROPN
ejpam-2779	553	2	=	=	SYM
ejpam-2779	553	3	cx	cx	PROPN
ejpam-2779	553	4	◦	◦	PROPN
ejpam-2779	553	5	y.	y.	PROPN
ejpam-2779	553	6	denote	denote	VERB
ejpam-2779	553	7	a	a	PRON
ejpam-2779	553	8	/	/	SYM
ejpam-2779	553	9	i	i	NOUN
ejpam-2779	553	10	=	=	PUNCT
ejpam-2779	553	11	{	{	PUNCT
ejpam-2779	554	1	cx	cx	NOUN
ejpam-2779	555	1	|	|	ADV
ejpam-2779	555	2	x	x	SYM
ejpam-2779	555	3	∈	∈	PROPN
ejpam-2779	555	4	a	a	PRON
ejpam-2779	555	5	}	}	PUNCT
ejpam-2779	555	6	.	.	PUNCT
ejpam-2779	556	1	then	then	ADV
ejpam-2779	556	2	(	(	PUNCT
ejpam-2779	556	3	a	a	X
ejpam-2779	556	4	/	/	SYM
ejpam-2779	556	5	i	i	PROPN
ejpam-2779	556	6	,	,	PUNCT
ejpam-2779	556	7	∗	∗	NOUN
ejpam-2779	556	8	,	,	PUNCT
ejpam-2779	556	9	◦	◦	NOUN
ejpam-2779	556	10	,	,	PUNCT
ejpam-2779	556	11	c0	c0	NOUN
ejpam-2779	556	12	)	)	PUNCT
ejpam-2779	556	13	is	be	AUX
ejpam-2779	556	14	a	a	DET
ejpam-2779	556	15	pseudo	pseudo	NOUN
ejpam-2779	556	16	bci	bci	NOUN
ejpam-2779	556	17	algebra	algebra	NOUN
ejpam-2779	556	18	.	.	PUNCT
ejpam-2779	557	1	if	if	SCONJ
ejpam-2779	557	2	i	i	PRON
ejpam-2779	557	3	is	be	AUX
ejpam-2779	557	4	a	a	DET
ejpam-2779	557	5	closed	closed	ADJ
ejpam-2779	557	6	pseudo	pseudo	NOUN
ejpam-2779	557	7	ideal	ideal	NOUN
ejpam-2779	557	8	of	of	ADP
ejpam-2779	557	9	a	a	PRON
ejpam-2779	557	10	,	,	PUNCT
ejpam-2779	557	11	then	then	ADV
ejpam-2779	557	12	c0	c0	PROPN
ejpam-2779	557	13	=	=	SYM
ejpam-2779	557	14	i.	i.	NOUN
ejpam-2779	557	15	proof	proof	NOUN
ejpam-2779	557	16	.	.	PUNCT
ejpam-2779	558	1	obviously	obviously	ADV
ejpam-2779	558	2	∼	∼	NOUN
ejpam-2779	558	3	is	be	AUX
ejpam-2779	558	4	reflexive	reflexive	ADJ
ejpam-2779	558	5	and	and	CCONJ
ejpam-2779	558	6	symmetric	symmetric	ADJ
ejpam-2779	558	7	.	.	PUNCT
ejpam-2779	559	1	now	now	ADV
ejpam-2779	559	2	we	we	PRON
ejpam-2779	559	3	prove	prove	VERB
ejpam-2779	559	4	that	that	SCONJ
ejpam-2779	559	5	it	it	PRON
ejpam-2779	559	6	is	be	AUX
ejpam-2779	559	7	transitive	transitive	ADJ
ejpam-2779	559	8	.	.	PUNCT
ejpam-2779	560	1	let	let	VERB
ejpam-2779	560	2	x	x	PUNCT
ejpam-2779	560	3	∼	∼	VERB
ejpam-2779	560	4	y	y	NOUN
ejpam-2779	560	5	and	and	CCONJ
ejpam-2779	560	6	y	y	PROPN
ejpam-2779	560	7	∼	∼	NOUN
ejpam-2779	560	8	z.	z.	PROPN
ejpam-2779	560	9	then	then	ADV
ejpam-2779	560	10	x	x	PROPN
ejpam-2779	560	11	∗	∗	PROPN
ejpam-2779	560	12	y	y	PROPN
ejpam-2779	560	13	,	,	PUNCT
ejpam-2779	560	14	y	y	PROPN
ejpam-2779	560	15	∗	∗	NOUN
ejpam-2779	560	16	z	z	PROPN
ejpam-2779	560	17	∈	∈	PROPN
ejpam-2779	560	18	i.	i.	NOUN
ejpam-2779	560	19	by	by	ADP
ejpam-2779	560	20	(	(	PUNCT
ejpam-2779	560	21	i1	i1	PROPN
ejpam-2779	560	22	)	)	PUNCT
ejpam-2779	560	23	,	,	PUNCT
ejpam-2779	560	24	(	(	PUNCT
ejpam-2779	560	25	x	x	X
ejpam-2779	560	26	∗	∗	PROPN
ejpam-2779	560	27	z	z	NOUN
ejpam-2779	560	28	)	)	PUNCT
ejpam-2779	560	29	◦	◦	NOUN
ejpam-2779	560	30	(	(	PUNCT
ejpam-2779	560	31	x	x	X
ejpam-2779	560	32	∗	∗	PROPN
ejpam-2779	560	33	y	y	NOUN
ejpam-2779	560	34	)	)	PUNCT
ejpam-2779	560	35	≤	≤	NOUN
ejpam-2779	561	1	y	y	PROPN
ejpam-2779	561	2	∗	∗	PROPN
ejpam-2779	561	3	z	z	PROPN
ejpam-2779	561	4	,	,	PUNCT
ejpam-2779	561	5	thus	thus	ADV
ejpam-2779	561	6	x	x	X
ejpam-2779	561	7	∗	∗	NOUN
ejpam-2779	561	8	z	z	PROPN
ejpam-2779	561	9	∈	∈	PROPN
ejpam-2779	561	10	i.	i.	NOUN
ejpam-2779	561	11	similarly	similarly	ADV
ejpam-2779	561	12	we	we	PRON
ejpam-2779	561	13	can	can	AUX
ejpam-2779	561	14	prove	prove	VERB
ejpam-2779	561	15	z	z	NOUN
ejpam-2779	561	16	∗	∗	NOUN
ejpam-2779	561	17	x	x	PUNCT
ejpam-2779	561	18	∈	∈	PROPN
ejpam-2779	561	19	i.	i.	NOUN
ejpam-2779	561	20	this	this	PRON
ejpam-2779	561	21	shows	show	VERB
ejpam-2779	561	22	that	that	SCONJ
ejpam-2779	561	23	x	x	PUNCT
ejpam-2779	561	24	∼	∼	NOUN
ejpam-2779	561	25	z	z	NOUN
ejpam-2779	561	26	and	and	CCONJ
ejpam-2779	561	27	hence	hence	ADV
ejpam-2779	561	28	∼	∼	NOUN
ejpam-2779	561	29	is	be	AUX
ejpam-2779	561	30	transitive	transitive	ADJ
ejpam-2779	561	31	.	.	PUNCT
ejpam-2779	562	1	thus	thus	ADV
ejpam-2779	562	2	it	it	PRON
ejpam-2779	562	3	is	be	AUX
ejpam-2779	562	4	an	an	DET
ejpam-2779	562	5	equivalent	equivalent	ADJ
ejpam-2779	562	6	relation	relation	NOUN
ejpam-2779	562	7	on	on	ADP
ejpam-2779	562	8	a.	a.	NOUN
ejpam-2779	562	9	we	we	PRON
ejpam-2779	562	10	also	also	ADV
ejpam-2779	562	11	can	can	AUX
ejpam-2779	562	12	show	show	VERB
ejpam-2779	562	13	that	that	SCONJ
ejpam-2779	562	14	∼	∼	NOUN
ejpam-2779	562	15	is	be	AUX
ejpam-2779	562	16	a	a	DET
ejpam-2779	562	17	congruence	congruence	NOUN
ejpam-2779	562	18	relation	relation	NOUN
ejpam-2779	562	19	on	on	ADP
ejpam-2779	562	20	a	a	PRON
ejpam-2779	562	21	and	and	CCONJ
ejpam-2779	562	22	omit	omit	VERB
ejpam-2779	562	23	it	it	PRON
ejpam-2779	562	24	.	.	PUNCT
ejpam-2779	563	1	denote	denote	VERB
ejpam-2779	563	2	a	a	PRON
ejpam-2779	563	3	/	/	SYM
ejpam-2779	563	4	i	i	NOUN
ejpam-2779	563	5	=	=	PUNCT
ejpam-2779	563	6	{	{	PUNCT
ejpam-2779	563	7	cx|x	cx|x	PROPN
ejpam-2779	563	8	∈	∈	PROPN
ejpam-2779	563	9	a	a	PRON
ejpam-2779	563	10	}	}	PUNCT
ejpam-2779	563	11	.	.	PUNCT
ejpam-2779	564	1	then	then	ADV
ejpam-2779	564	2	binary	binary	ADJ
ejpam-2779	564	3	operations	operation	NOUN
ejpam-2779	564	4	”	"	PUNCT
ejpam-2779	564	5	∗	∗	NOUN
ejpam-2779	564	6	”	"	PUNCT
ejpam-2779	564	7	and	and	CCONJ
ejpam-2779	564	8	”	"	PUNCT
ejpam-2779	564	9	◦	◦	NOUN
ejpam-2779	564	10	”	"	PUNCT
ejpam-2779	564	11	on	on	ADP
ejpam-2779	564	12	a	a	PRON
ejpam-2779	564	13	/	/	SYM
ejpam-2779	564	14	i	i	PRON
ejpam-2779	564	15	are	be	AUX
ejpam-2779	564	16	well	well	ADV
ejpam-2779	564	17	-	-	PUNCT
ejpam-2779	564	18	defined	define	VERB
ejpam-2779	564	19	.	.	PUNCT
ejpam-2779	565	1	moreover	moreover	ADV
ejpam-2779	565	2	we	we	PRON
ejpam-2779	565	3	can	can	AUX
ejpam-2779	565	4	show	show	VERB
ejpam-2779	565	5	that	that	SCONJ
ejpam-2779	565	6	(	(	PUNCT
ejpam-2779	565	7	a	a	X
ejpam-2779	565	8	/	/	SYM
ejpam-2779	565	9	i	i	PROPN
ejpam-2779	565	10	,	,	PUNCT
ejpam-2779	565	11	∗	∗	NOUN
ejpam-2779	565	12	,	,	PUNCT
ejpam-2779	565	13	◦	◦	NOUN
ejpam-2779	565	14	)	)	PUNCT
ejpam-2779	565	15	satisfies	satisfy	VERB
ejpam-2779	565	16	i1	i1	PROPN
ejpam-2779	565	17	−	−	PROPN
ejpam-2779	565	18	i5	i5	ADV
ejpam-2779	565	19	in	in	ADP
ejpam-2779	565	20	definition	definition	NOUN
ejpam-2779	565	21	3.1	3.1	NUM
ejpam-2779	565	22	.	.	PUNCT
ejpam-2779	566	1	it	it	PRON
ejpam-2779	566	2	follows	follow	VERB
ejpam-2779	566	3	that	that	SCONJ
ejpam-2779	566	4	(	(	PUNCT
ejpam-2779	566	5	a	a	X
ejpam-2779	566	6	/	/	SYM
ejpam-2779	566	7	i	i	PROPN
ejpam-2779	566	8	,	,	PUNCT
ejpam-2779	566	9	∗	∗	NOUN
ejpam-2779	566	10	,	,	PUNCT
ejpam-2779	566	11	◦	◦	NOUN
ejpam-2779	566	12	,	,	PUNCT
ejpam-2779	566	13	c0	c0	NOUN
ejpam-2779	566	14	)	)	PUNCT
ejpam-2779	566	15	is	be	AUX
ejpam-2779	566	16	a	a	DET
ejpam-2779	566	17	pseudo	pseudo	NOUN
ejpam-2779	566	18	bci	bci	NOUN
ejpam-2779	566	19	algebra	algebra	NOUN
ejpam-2779	566	20	.	.	PUNCT
ejpam-2779	567	1	finally	finally	ADV
ejpam-2779	567	2	we	we	PRON
ejpam-2779	567	3	assume	assume	VERB
ejpam-2779	567	4	that	that	SCONJ
ejpam-2779	567	5	i	i	PRON
ejpam-2779	567	6	is	be	AUX
ejpam-2779	567	7	a	a	DET
ejpam-2779	567	8	closed	closed	ADJ
ejpam-2779	567	9	pseudo	pseudo	NOUN
ejpam-2779	567	10	ideal	ideal	NOUN
ejpam-2779	567	11	of	of	ADP
ejpam-2779	567	12	a.	a.	NOUN
ejpam-2779	567	13	then	then	ADV
ejpam-2779	567	14	for	for	ADP
ejpam-2779	567	15	x	x	PROPN
ejpam-2779	567	16	∈	∈	PROPN
ejpam-2779	567	17	i	i	PRON
ejpam-2779	567	18	,	,	PUNCT
ejpam-2779	567	19	we	we	PRON
ejpam-2779	567	20	have	have	VERB
ejpam-2779	567	21	0	0	NUM
ejpam-2779	567	22	∗	∗	NOUN
ejpam-2779	567	23	x	x	PUNCT
ejpam-2779	567	24	∈	∈	NOUN
ejpam-2779	568	1	i	i	PRON
ejpam-2779	568	2	and	and	CCONJ
ejpam-2779	568	3	x	x	NOUN
ejpam-2779	568	4	∗	∗	NOUN
ejpam-2779	568	5	0	0	NUM
ejpam-2779	569	1	=	=	SYM
ejpam-2779	569	2	x	x	SYM
ejpam-2779	569	3	∈	∈	PROPN
ejpam-2779	569	4	i.	i.	NOUN
ejpam-2779	569	5	hence	hence	ADV
ejpam-2779	569	6	x	x	PUNCT
ejpam-2779	569	7	∼	∼	NOUN
ejpam-2779	569	8	0	0	NUM
ejpam-2779	569	9	,	,	PUNCT
ejpam-2779	569	10	that	that	ADV
ejpam-2779	569	11	is	is	ADV
ejpam-2779	569	12	,	,	PUNCT
ejpam-2779	569	13	x	x	PROPN
ejpam-2779	569	14	∈	∈	PROPN
ejpam-2779	569	15	c0	c0	NOUN
ejpam-2779	569	16	.	.	PUNCT
ejpam-2779	570	1	therefore	therefore	ADV
ejpam-2779	570	2	c0	c0	PROPN
ejpam-2779	570	3	=	=	SYM
ejpam-2779	570	4	i.	i.	PROPN
ejpam-2779	570	5	proposition	proposition	NOUN
ejpam-2779	570	6	26	26	NUM
ejpam-2779	570	7	.	.	PUNCT
ejpam-2779	571	1	let	let	VERB
ejpam-2779	571	2	s	s	PRON
ejpam-2779	571	3	be	be	AUX
ejpam-2779	571	4	a	a	DET
ejpam-2779	571	5	bosbach	bosbach	ADJ
ejpam-2779	571	6	state	state	NOUN
ejpam-2779	571	7	on	on	ADP
ejpam-2779	571	8	a	a	DET
ejpam-2779	571	9	lbp	lbp	NOUN
ejpam-2779	571	10	-	-	PUNCT
ejpam-2779	571	11	bci	bci	PROPN
ejpam-2779	571	12	algebra	algebra	NOUN
ejpam-2779	571	13	a	a	PRON
ejpam-2779	571	14	and	and	CCONJ
ejpam-2779	571	15	k	k	NOUN
ejpam-2779	571	16	=	=	SYM
ejpam-2779	571	17	ker(s	ker(s	PROPN
ejpam-2779	571	18	)	)	PUNCT
ejpam-2779	571	19	.	.	PUNCT
ejpam-2779	572	1	then	then	ADV
ejpam-2779	572	2	we	we	PRON
ejpam-2779	572	3	have	have	VERB
ejpam-2779	572	4	the	the	DET
ejpam-2779	572	5	following	following	NOUN
ejpam-2779	572	6	.	.	PUNCT
ejpam-2779	573	1	(	(	PUNCT
ejpam-2779	573	2	1	1	X
ejpam-2779	573	3	)	)	PUNCT
ejpam-2779	573	4	x	x	X
ejpam-2779	573	5	/	/	SYM
ejpam-2779	573	6	k	k	PROPN
ejpam-2779	573	7	≤	≤	PROPN
ejpam-2779	573	8	y	y	PROPN
ejpam-2779	573	9	/	/	SYM
ejpam-2779	573	10	k	k	PROPN
ejpam-2779	573	11	iff	iff	PROPN
ejpam-2779	573	12	s(x∗y	s(x∗y	PROPN
ejpam-2779	573	13	)	)	PUNCT
ejpam-2779	574	1	=	=	SYM
ejpam-2779	574	2	1	1	NUM
ejpam-2779	574	3	iff	iff	PROPN
ejpam-2779	574	4	s(x	s(x	PROPN
ejpam-2779	574	5	◦	◦	NOUN
ejpam-2779	574	6	y	y	NOUN
ejpam-2779	574	7	)	)	PUNCT
ejpam-2779	574	8	=	=	SYM
ejpam-2779	574	9	1	1	NUM
ejpam-2779	574	10	,	,	PUNCT
ejpam-2779	574	11	where	where	SCONJ
ejpam-2779	574	12	x	x	X
ejpam-2779	574	13	/	/	SYM
ejpam-2779	574	14	k	k	NOUN
ejpam-2779	574	15	=	=	PRON
ejpam-2779	574	16	{	{	PUNCT
ejpam-2779	574	17	y	y	NOUN
ejpam-2779	574	18	∈	∈	PROPN
ejpam-2779	574	19	a|y	a|y	NOUN
ejpam-2779	574	20	∼	∼	NOUN
ejpam-2779	574	21	x	x	NOUN
ejpam-2779	574	22	}	}	PUNCT
ejpam-2779	574	23	for	for	ADP
ejpam-2779	574	24	all	all	DET
ejpam-2779	574	25	x	x	SYM
ejpam-2779	574	26	∈	∈	PROPN
ejpam-2779	574	27	a.	a.	NOUN
ejpam-2779	574	28	(	(	PUNCT
ejpam-2779	574	29	2	2	NUM
ejpam-2779	574	30	)	)	PUNCT
ejpam-2779	574	31	for	for	ADP
ejpam-2779	574	32	all	all	DET
ejpam-2779	574	33	a	a	DET
ejpam-2779	574	34	∈	∈	PROPN
ejpam-2779	574	35	m(a	m(a	PROPN
ejpam-2779	574	36	)	)	PUNCT
ejpam-2779	574	37	and	and	CCONJ
ejpam-2779	574	38	all	all	DET
ejpam-2779	574	39	x	x	NOUN
ejpam-2779	574	40	,	,	PUNCT
ejpam-2779	574	41	y	y	PROPN
ejpam-2779	574	42	∈	∈	PROPN
ejpam-2779	574	43	v	v	ADP
ejpam-2779	574	44	(	(	PUNCT
ejpam-2779	574	45	a	a	NOUN
ejpam-2779	574	46	)	)	PUNCT
ejpam-2779	574	47	,	,	PUNCT
ejpam-2779	574	48	we	we	PRON
ejpam-2779	574	49	have	have	VERB
ejpam-2779	574	50	that	that	PRON
ejpam-2779	574	51	x	x	PROPN
ejpam-2779	574	52	/	/	SYM
ejpam-2779	574	53	k	k	PROPN
ejpam-2779	574	54	≤	≤	PROPN
ejpam-2779	574	55	y	y	PROPN
ejpam-2779	574	56	/	/	SYM
ejpam-2779	574	57	k	k	PROPN
ejpam-2779	574	58	iff	iff	PROPN
ejpam-2779	574	59	s(y	s(y	PROPN
ejpam-2779	574	60	∧1	∧1	PROPN
ejpam-2779	574	61	x	x	NOUN
ejpam-2779	574	62	)	)	PUNCT
ejpam-2779	574	63	=	=	SYM
ejpam-2779	574	64	s(x	s(x	PROPN
ejpam-2779	574	65	)	)	PUNCT
ejpam-2779	574	66	iff	iff	PROPN
ejpam-2779	574	67	s(y	s(y	PROPN
ejpam-2779	574	68	∧2	∧2	PROPN
ejpam-2779	574	69	x	x	SYM
ejpam-2779	574	70	)	)	PUNCT
ejpam-2779	574	71	=	=	SYM
ejpam-2779	574	72	s(x	s(x	PROPN
ejpam-2779	574	73	)	)	PUNCT
ejpam-2779	574	74	.	.	PUNCT
ejpam-2779	575	1	(	(	PUNCT
ejpam-2779	575	2	3	3	X
ejpam-2779	575	3	)	)	PUNCT
ejpam-2779	575	4	x	x	NOUN
ejpam-2779	575	5	/	/	SYM
ejpam-2779	575	6	k	k	NOUN
ejpam-2779	575	7	=	=	PUNCT
ejpam-2779	575	8	y	y	PROPN
ejpam-2779	575	9	/	/	SYM
ejpam-2779	575	10	k	k	PROPN
ejpam-2779	575	11	iff	iff	PROPN
ejpam-2779	575	12	s(x	s(x	PROPN
ejpam-2779	575	13	∗	∗	PROPN
ejpam-2779	575	14	y	y	NOUN
ejpam-2779	575	15	)	)	PUNCT
ejpam-2779	576	1	=	=	SYM
ejpam-2779	576	2	s(y	s(y	PROPN
ejpam-2779	576	3	∗	∗	NOUN
ejpam-2779	576	4	x	x	NOUN
ejpam-2779	576	5	)	)	PUNCT
ejpam-2779	576	6	=	=	SYM
ejpam-2779	576	7	1	1	NUM
ejpam-2779	576	8	iff	iff	PROPN
ejpam-2779	576	9	s(x	s(x	PROPN
ejpam-2779	576	10	◦	◦	PROPN
ejpam-2779	576	11	y	y	PROPN
ejpam-2779	576	12	)	)	PUNCT
ejpam-2779	577	1	=	=	SYM
ejpam-2779	577	2	s(y	s(y	PROPN
ejpam-2779	577	3	◦	◦	NOUN
ejpam-2779	577	4	x	x	X
ejpam-2779	577	5	)	)	PUNCT
ejpam-2779	577	6	=	=	SYM
ejpam-2779	577	7	1	1	X
ejpam-2779	577	8	.	.	PUNCT
ejpam-2779	577	9	(	(	PUNCT
ejpam-2779	577	10	4	4	NUM
ejpam-2779	577	11	)	)	PUNCT
ejpam-2779	577	12	for	for	ADP
ejpam-2779	577	13	all	all	DET
ejpam-2779	577	14	a	a	DET
ejpam-2779	577	15	∈	∈	PROPN
ejpam-2779	577	16	m(a	m(a	PROPN
ejpam-2779	577	17	)	)	PUNCT
ejpam-2779	577	18	and	and	CCONJ
ejpam-2779	577	19	all	all	DET
ejpam-2779	577	20	x	x	NOUN
ejpam-2779	577	21	,	,	PUNCT
ejpam-2779	577	22	y	y	PROPN
ejpam-2779	577	23	∈	∈	PROPN
ejpam-2779	577	24	v	v	ADP
ejpam-2779	577	25	(	(	PUNCT
ejpam-2779	577	26	a	a	NOUN
ejpam-2779	577	27	)	)	PUNCT
ejpam-2779	577	28	,	,	PUNCT
ejpam-2779	577	29	x	x	X
ejpam-2779	577	30	/	/	SYM
ejpam-2779	577	31	k	k	NOUN
ejpam-2779	577	32	=	=	PUNCT
ejpam-2779	577	33	y	y	PROPN
ejpam-2779	577	34	/	/	SYM
ejpam-2779	577	35	k	k	PROPN
ejpam-2779	577	36	iff	iff	PROPN
ejpam-2779	577	37	s(x	s(x	PROPN
ejpam-2779	577	38	)	)	PUNCT
ejpam-2779	577	39	=	=	SYM
ejpam-2779	577	40	s(y	s(y	NOUN
ejpam-2779	577	41	)	)	PUNCT
ejpam-2779	578	1	=	=	PUNCT
ejpam-2779	578	2	s(x	s(x	NOUN
ejpam-2779	578	3	∧1	∧1	NUM
ejpam-2779	578	4	y	y	NOUN
ejpam-2779	578	5	)	)	PUNCT
ejpam-2779	578	6	iff	iff	PROPN
ejpam-2779	578	7	s(x	s(x	PROPN
ejpam-2779	578	8	)	)	PUNCT
ejpam-2779	578	9	=	=	SYM
ejpam-2779	578	10	s(y	s(y	NOUN
ejpam-2779	578	11	)	)	PUNCT
ejpam-2779	579	1	=	=	SYM
ejpam-2779	579	2	s(x	s(x	PROPN
ejpam-2779	579	3	∧2	∧2	PROPN
ejpam-2779	579	4	y	y	PROPN
ejpam-2779	579	5	)	)	PUNCT
ejpam-2779	579	6	.	.	PUNCT
ejpam-2779	580	1	(	(	PUNCT
ejpam-2779	580	2	5	5	NUM
ejpam-2779	580	3	)	)	PUNCT
ejpam-2779	580	4	(	(	PUNCT
ejpam-2779	580	5	a	a	X
ejpam-2779	580	6	/	/	SYM
ejpam-2779	580	7	k,≤	k,≤	PROPN
ejpam-2779	580	8	,	,	PUNCT
ejpam-2779	580	9	∗	∗	NOUN
ejpam-2779	580	10	,	,	PUNCT
ejpam-2779	580	11	◦	◦	NOUN
ejpam-2779	580	12	,	,	PUNCT
ejpam-2779	580	13	0	0	NUM
ejpam-2779	580	14	/	/	SYM
ejpam-2779	580	15	k	k	NOUN
ejpam-2779	580	16	,	,	PUNCT
ejpam-2779	580	17	10	10	NUM
ejpam-2779	580	18	/	/	SYM
ejpam-2779	580	19	k	k	NOUN
ejpam-2779	580	20	)	)	PUNCT
ejpam-2779	580	21	is	be	AUX
ejpam-2779	580	22	a	a	DET
ejpam-2779	580	23	bounded	bounded	ADJ
ejpam-2779	580	24	pseudo	pseudo	NOUN
ejpam-2779	580	25	-	-	ADJ
ejpam-2779	580	26	bck	bck	ADJ
ejpam-2779	580	27	algebra	algebra	NOUN
ejpam-2779	580	28	where	where	SCONJ
ejpam-2779	580	29	10	10	NUM
ejpam-2779	580	30	is	be	AUX
ejpam-2779	580	31	the	the	DET
ejpam-2779	580	32	unit	unit	NOUN
ejpam-2779	580	33	of	of	ADP
ejpam-2779	580	34	v	v	PROPN
ejpam-2779	580	35	(	(	PUNCT
ejpam-2779	580	36	0	0	NUM
ejpam-2779	580	37	)	)	PUNCT
ejpam-2779	580	38	.	.	PUNCT
ejpam-2779	581	1	(	(	PUNCT
ejpam-2779	581	2	6	6	X
ejpam-2779	581	3	)	)	PUNCT
ejpam-2779	581	4	the	the	DET
ejpam-2779	581	5	mapping	mapping	NOUN
ejpam-2779	581	6	s̃	s̃	PROPN
ejpam-2779	581	7	:	:	PUNCT
ejpam-2779	581	8	a	a	X
ejpam-2779	581	9	/	/	SYM
ejpam-2779	581	10	k	k	X
ejpam-2779	581	11	→	→	PUNCT
ejpam-2779	582	1	[	[	X
ejpam-2779	582	2	0	0	NUM
ejpam-2779	582	3	,	,	PUNCT
ejpam-2779	582	4	1	1	NUM
ejpam-2779	582	5	]	]	PUNCT
ejpam-2779	582	6	defined	define	VERB
ejpam-2779	582	7	by	by	ADP
ejpam-2779	582	8	s̃(x	s̃(x	PROPN
ejpam-2779	582	9	/	/	SYM
ejpam-2779	582	10	k	k	NOUN
ejpam-2779	582	11	)	)	PUNCT
ejpam-2779	582	12	:	:	PUNCT
ejpam-2779	582	13	=	=	SYM
ejpam-2779	582	14	s(x)(x	s(x)(x	NUM
ejpam-2779	582	15	∈	∈	PROPN
ejpam-2779	582	16	a	a	PRON
ejpam-2779	582	17	)	)	PUNCT
ejpam-2779	582	18	is	be	AUX
ejpam-2779	582	19	a	a	DET
ejpam-2779	582	20	bosbach	bosbach	ADJ
ejpam-2779	582	21	state	state	NOUN
ejpam-2779	582	22	on	on	ADP
ejpam-2779	582	23	a	a	DET
ejpam-2779	582	24	/	/	SYM
ejpam-2779	582	25	k.	k.	NOUN
ejpam-2779	582	26	proof	proof	NOUN
ejpam-2779	582	27	.	.	PUNCT
ejpam-2779	583	1	(	(	PUNCT
ejpam-2779	583	2	1	1	X
ejpam-2779	583	3	)	)	PUNCT
ejpam-2779	583	4	by	by	ADP
ejpam-2779	583	5	theorem	theorem	NOUN
ejpam-2779	583	6	2	2	NUM
ejpam-2779	583	7	,	,	PUNCT
ejpam-2779	583	8	we	we	PRON
ejpam-2779	583	9	know	know	VERB
ejpam-2779	583	10	that	that	SCONJ
ejpam-2779	583	11	(	(	PUNCT
ejpam-2779	583	12	a	a	X
ejpam-2779	583	13	/	/	SYM
ejpam-2779	583	14	k,≤	k,≤	PROPN
ejpam-2779	583	15	,	,	PUNCT
ejpam-2779	583	16	∗	∗	NOUN
ejpam-2779	583	17	,	,	PUNCT
ejpam-2779	583	18	◦	◦	NOUN
ejpam-2779	583	19	,	,	PUNCT
ejpam-2779	583	20	0	0	NUM
ejpam-2779	583	21	/	/	SYM
ejpam-2779	583	22	k	k	NOUN
ejpam-2779	583	23	)	)	PUNCT
ejpam-2779	583	24	is	be	AUX
ejpam-2779	583	25	a	a	DET
ejpam-2779	583	26	pseudo	pseudo	NOUN
ejpam-2779	583	27	-	-	ADJ
ejpam-2779	583	28	bci	bci	ADJ
ejpam-2779	583	29	algebra	algebra	NOUN
ejpam-2779	583	30	.	.	PUNCT
ejpam-2779	584	1	note	note	VERB
ejpam-2779	584	2	that	that	SCONJ
ejpam-2779	584	3	x	x	X
ejpam-2779	584	4	/	/	SYM
ejpam-2779	584	5	k	k	PROPN
ejpam-2779	584	6	≤	≤	PROPN
ejpam-2779	584	7	y	y	PROPN
ejpam-2779	584	8	/	/	SYM
ejpam-2779	584	9	k	k	PROPN
ejpam-2779	584	10	iff	iff	PROPN
ejpam-2779	584	11	x	x	PROPN
ejpam-2779	584	12	/	/	SYM
ejpam-2779	584	13	k	k	PROPN
ejpam-2779	584	14	∗	∗	PROPN
ejpam-2779	584	15	y	y	PROPN
ejpam-2779	584	16	/	/	SYM
ejpam-2779	584	17	k	k	PROPN
ejpam-2779	584	18	=	=	PRON
ejpam-2779	584	19	(	(	PUNCT
ejpam-2779	584	20	x	x	NOUN
ejpam-2779	584	21	∗	∗	NOUN
ejpam-2779	584	22	y)/k	y)/k	NOUN
ejpam-2779	585	1	=	=	NOUN
ejpam-2779	585	2	0	0	NUM
ejpam-2779	585	3	/	/	SYM
ejpam-2779	585	4	k	k	PROPN
ejpam-2779	585	5	iff	iff	PROPN
ejpam-2779	585	6	x	x	PROPN
ejpam-2779	585	7	∗	∗	VERB
ejpam-2779	585	8	y	y	PROPN
ejpam-2779	585	9	∈	∈	PROPN
ejpam-2779	586	1	k	k	PROPN
ejpam-2779	586	2	iff	iff	PROPN
ejpam-2779	586	3	s(x	s(x	PROPN
ejpam-2779	586	4	∗	∗	PROPN
ejpam-2779	586	5	y	y	PROPN
ejpam-2779	586	6	)	)	PUNCT
ejpam-2779	586	7	=	=	SYM
ejpam-2779	587	1	1	1	X
ejpam-2779	587	2	.	.	X
ejpam-2779	587	3	similarly	similarly	ADV
ejpam-2779	587	4	,	,	PUNCT
ejpam-2779	587	5	x	x	X
ejpam-2779	587	6	/	/	SYM
ejpam-2779	587	7	k	k	PROPN
ejpam-2779	587	8	≤	≤	PROPN
ejpam-2779	587	9	y	y	PROPN
ejpam-2779	587	10	/	/	SYM
ejpam-2779	587	11	k	k	PROPN
ejpam-2779	587	12	iff	iff	PROPN
ejpam-2779	587	13	x	x	PROPN
ejpam-2779	587	14	/	/	SYM
ejpam-2779	587	15	k	k	PROPN
ejpam-2779	588	1	◦	◦	NOUN
ejpam-2779	588	2	y	y	PROPN
ejpam-2779	588	3	/	/	SYM
ejpam-2779	588	4	k	k	NOUN
ejpam-2779	588	5	=	=	PRON
ejpam-2779	588	6	(	(	PUNCT
ejpam-2779	588	7	x	x	SYM
ejpam-2779	588	8	◦	◦	VERB
ejpam-2779	588	9	y)/k	y)/k	NOUN
ejpam-2779	588	10	=	=	NOUN
ejpam-2779	588	11	0	0	NUM
ejpam-2779	588	12	/	/	SYM
ejpam-2779	588	13	k	k	PROPN
ejpam-2779	588	14	iff	iff	PROPN
ejpam-2779	588	15	x	x	INTJ
ejpam-2779	588	16	◦	◦	VERB
ejpam-2779	588	17	y	y	PROPN
ejpam-2779	588	18	∈	∈	PROPN
ejpam-2779	589	1	k	k	PROPN
ejpam-2779	589	2	iff	iff	PROPN
ejpam-2779	589	3	s(x	s(x	PROPN
ejpam-2779	589	4	◦	◦	PROPN
ejpam-2779	589	5	y	y	PROPN
ejpam-2779	589	6	)	)	PUNCT
ejpam-2779	589	7	=	=	SYM
ejpam-2779	590	1	1	1	X
ejpam-2779	590	2	.	.	PUNCT
ejpam-2779	590	3	(	(	PUNCT
ejpam-2779	590	4	2	2	X
ejpam-2779	590	5	)	)	PUNCT
ejpam-2779	590	6	let	let	VERB
ejpam-2779	590	7	a	a	DET
ejpam-2779	590	8	∈m(a	∈m(a	NOUN
ejpam-2779	590	9	)	)	PUNCT
ejpam-2779	590	10	and	and	CCONJ
ejpam-2779	590	11	x	x	NOUN
ejpam-2779	590	12	,	,	PUNCT
ejpam-2779	590	13	y	y	PROPN
ejpam-2779	590	14	∈	∈	PROPN
ejpam-2779	590	15	v	v	ADP
ejpam-2779	590	16	(	(	PUNCT
ejpam-2779	590	17	a	a	NOUN
ejpam-2779	590	18	)	)	PUNCT
ejpam-2779	590	19	.	.	PUNCT
ejpam-2779	591	1	as	as	ADP
ejpam-2779	591	2	s(x∗y	s(x∗y	PROPN
ejpam-2779	591	3	)	)	PUNCT
ejpam-2779	591	4	=	=	PUNCT
ejpam-2779	591	5	1−s(y∧1x)+s(x	1−s(y∧1x)+s(x	NUM
ejpam-2779	591	6	)	)	PUNCT
ejpam-2779	591	7	by	by	ADP
ejpam-2779	591	8	proposition	proposition	NOUN
ejpam-2779	591	9	21	21	NUM
ejpam-2779	591	10	,	,	PUNCT
ejpam-2779	591	11	we	we	PRON
ejpam-2779	591	12	get	get	VERB
ejpam-2779	591	13	x	x	X
ejpam-2779	591	14	/	/	SYM
ejpam-2779	591	15	k	k	PROPN
ejpam-2779	591	16	≤	≤	PROPN
ejpam-2779	591	17	y	y	PROPN
ejpam-2779	591	18	/	/	SYM
ejpam-2779	591	19	k	k	PROPN
ejpam-2779	591	20	iff	iff	PROPN
ejpam-2779	591	21	s(y∧1x	s(y∧1x	PROPN
ejpam-2779	591	22	)	)	PUNCT
ejpam-2779	591	23	=	=	SYM
ejpam-2779	591	24	s(x	s(x	PROPN
ejpam-2779	591	25	)	)	PUNCT
ejpam-2779	591	26	.	.	PUNCT
ejpam-2779	592	1	similarly	similarly	ADV
ejpam-2779	592	2	,	,	PUNCT
ejpam-2779	592	3	we	we	PRON
ejpam-2779	592	4	have	have	VERB
ejpam-2779	592	5	x	x	X
ejpam-2779	592	6	/	/	SYM
ejpam-2779	592	7	k	k	PROPN
ejpam-2779	592	8	≤	≤	PROPN
ejpam-2779	592	9	y	y	PROPN
ejpam-2779	592	10	/	/	SYM
ejpam-2779	592	11	k	k	PROPN
ejpam-2779	592	12	iff	iff	PROPN
ejpam-2779	592	13	s(y∧2x	s(y∧2x	PROPN
ejpam-2779	592	14	)	)	PUNCT
ejpam-2779	592	15	=	=	SYM
ejpam-2779	592	16	s(x	s(x	PROPN
ejpam-2779	592	17	)	)	PUNCT
ejpam-2779	592	18	.	.	PUNCT
ejpam-2779	593	1	(	(	PUNCT
ejpam-2779	593	2	3	3	X
ejpam-2779	593	3	)	)	PUNCT
ejpam-2779	593	4	it	it	PRON
ejpam-2779	593	5	follows	follow	VERB
ejpam-2779	593	6	easily	easily	ADV
ejpam-2779	593	7	from	from	ADP
ejpam-2779	593	8	(	(	PUNCT
ejpam-2779	593	9	1	1	NUM
ejpam-2779	593	10	)	)	PUNCT
ejpam-2779	593	11	.	.	PUNCT
ejpam-2779	594	1	(	(	PUNCT
ejpam-2779	594	2	4	4	X
ejpam-2779	594	3	)	)	PUNCT
ejpam-2779	594	4	it	it	PRON
ejpam-2779	594	5	follows	follow	VERB
ejpam-2779	594	6	easily	easily	ADV
ejpam-2779	594	7	from	from	ADP
ejpam-2779	594	8	(	(	PUNCT
ejpam-2779	594	9	2	2	NUM
ejpam-2779	594	10	)	)	PUNCT
ejpam-2779	594	11	.	.	PUNCT
ejpam-2779	595	1	(	(	PUNCT
ejpam-2779	595	2	5	5	X
ejpam-2779	595	3	)	)	PUNCT
ejpam-2779	595	4	first	first	ADV
ejpam-2779	595	5	we	we	PRON
ejpam-2779	595	6	prove	prove	VERB
ejpam-2779	595	7	m(a	m(a	PROPN
ejpam-2779	595	8	/	/	SYM
ejpam-2779	595	9	k	k	NOUN
ejpam-2779	595	10	)	)	PUNCT
ejpam-2779	595	11	=	=	PUNCT
ejpam-2779	596	1	{	{	PUNCT
ejpam-2779	596	2	0	0	NUM
ejpam-2779	596	3	/	/	SYM
ejpam-2779	596	4	k	k	NOUN
ejpam-2779	596	5	}	}	PUNCT
ejpam-2779	596	6	.	.	PUNCT
ejpam-2779	597	1	let	let	VERB
ejpam-2779	597	2	x	x	PRON
ejpam-2779	597	3	/	/	SYM
ejpam-2779	597	4	k	k	PROPN
ejpam-2779	597	5	≤	≤	NUM
ejpam-2779	597	6	0	0	NUM
ejpam-2779	597	7	/	/	SYM
ejpam-2779	597	8	k.	k.	NOUN
ejpam-2779	597	9	by	by	ADP
ejpam-2779	597	10	(	(	PUNCT
ejpam-2779	597	11	1	1	NUM
ejpam-2779	597	12	)	)	PUNCT
ejpam-2779	597	13	,	,	PUNCT
ejpam-2779	597	14	s(x	s(x	PROPN
ejpam-2779	597	15	∗	∗	NOUN
ejpam-2779	597	16	0	0	NUM
ejpam-2779	597	17	)	)	PUNCT
ejpam-2779	597	18	=	=	SYM
ejpam-2779	598	1	1	1	X
ejpam-2779	598	2	.	.	X
ejpam-2779	598	3	note	note	VERB
ejpam-2779	598	4	that	that	SCONJ
ejpam-2779	598	5	0∗x	0∗x	NUM
ejpam-2779	598	6	∈m(a	∈m(a	NOUN
ejpam-2779	598	7	)	)	PUNCT
ejpam-2779	598	8	,	,	PUNCT
ejpam-2779	598	9	then	then	ADV
ejpam-2779	598	10	we	we	PRON
ejpam-2779	598	11	have	have	VERB
ejpam-2779	598	12	s(0∗x	s(0∗x	NOUN
ejpam-2779	598	13	)	)	PUNCT
ejpam-2779	599	1	=	=	SYM
ejpam-2779	599	2	1	1	X
ejpam-2779	599	3	.	.	PUNCT
ejpam-2779	599	4	by	by	ADP
ejpam-2779	599	5	(	(	PUNCT
ejpam-2779	599	6	3	3	NUM
ejpam-2779	599	7	)	)	PUNCT
ejpam-2779	599	8	,	,	PUNCT
ejpam-2779	599	9	x	x	X
ejpam-2779	599	10	/	/	SYM
ejpam-2779	599	11	k	k	NOUN
ejpam-2779	599	12	=	=	PUNCT
ejpam-2779	599	13	0	0	NUM
ejpam-2779	599	14	/	/	SYM
ejpam-2779	599	15	k.	k.	NOUN
ejpam-2779	599	16	thus	thus	ADV
ejpam-2779	599	17	0	0	NUM
ejpam-2779	599	18	/	/	SYM
ejpam-2779	599	19	k	k	PROPN
ejpam-2779	599	20	∈m(a	∈m(a	PROPN
ejpam-2779	599	21	/	/	SYM
ejpam-2779	599	22	k	k	NOUN
ejpam-2779	599	23	)	)	PUNCT
ejpam-2779	599	24	.	.	PUNCT
ejpam-2779	600	1	conversely	conversely	ADV
ejpam-2779	600	2	let	let	VERB
ejpam-2779	600	3	x	x	X
ejpam-2779	600	4	/	/	SYM
ejpam-2779	600	5	k	k	PROPN
ejpam-2779	600	6	∈	∈	PROPN
ejpam-2779	600	7	m(a	m(a	PROPN
ejpam-2779	600	8	/	/	SYM
ejpam-2779	600	9	k	k	NOUN
ejpam-2779	600	10	)	)	PUNCT
ejpam-2779	600	11	.	.	PUNCT
ejpam-2779	601	1	obviously	obviously	ADV
ejpam-2779	601	2	(	(	PUNCT
ejpam-2779	601	3	0	0	NUM
ejpam-2779	601	4	∗	∗	NOUN
ejpam-2779	601	5	(	(	PUNCT
ejpam-2779	601	6	0	0	NUM
ejpam-2779	601	7	∗	∗	NOUN
ejpam-2779	601	8	x))/k	x))/k	PUNCT
ejpam-2779	602	1	≤	≤	NUM
ejpam-2779	602	2	x	x	X
ejpam-2779	602	3	/	/	SYM
ejpam-2779	602	4	k.	k.	PROPN
ejpam-2779	602	5	hence	hence	ADV
ejpam-2779	602	6	(	(	PUNCT
ejpam-2779	602	7	0	0	NUM
ejpam-2779	602	8	∗	∗	NOUN
ejpam-2779	602	9	(	(	PUNCT
ejpam-2779	602	10	0	0	NUM
ejpam-2779	602	11	∗	∗	NOUN
ejpam-2779	602	12	x))/k	x))/k	PUNCT
ejpam-2779	603	1	=	=	PUNCT
ejpam-2779	603	2	x	x	X
ejpam-2779	603	3	/	/	SYM
ejpam-2779	603	4	k.	k.	PROPN
ejpam-2779	603	5	since	since	SCONJ
ejpam-2779	603	6	for	for	ADP
ejpam-2779	603	7	any	any	DET
ejpam-2779	603	8	a	a	DET
ejpam-2779	603	9	∈	∈	PROPN
ejpam-2779	603	10	m(a	m(a	NOUN
ejpam-2779	603	11	)	)	PUNCT
ejpam-2779	603	12	,	,	PUNCT
ejpam-2779	603	13	s(a	s(a	PROPN
ejpam-2779	603	14	∗	∗	NOUN
ejpam-2779	603	15	0	0	NUM
ejpam-2779	603	16	)	)	PUNCT
ejpam-2779	604	1	=	=	SYM
ejpam-2779	604	2	s(0	s(0	PROPN
ejpam-2779	604	3	∗	∗	NOUN
ejpam-2779	604	4	a	a	X
ejpam-2779	604	5	)	)	PUNCT
ejpam-2779	604	6	=	=	SYM
ejpam-2779	604	7	1	1	NUM
ejpam-2779	604	8	,	,	PUNCT
ejpam-2779	604	9	we	we	PRON
ejpam-2779	604	10	have	have	VERB
ejpam-2779	604	11	0	0	NUM
ejpam-2779	604	12	/	/	SYM
ejpam-2779	604	13	k	k	NOUN
ejpam-2779	604	14	=	=	PUNCT
ejpam-2779	604	15	a	a	PROPN
ejpam-2779	604	16	/	/	SYM
ejpam-2779	604	17	k.	k.	NOUN
ejpam-2779	604	18	thus	thus	ADV
ejpam-2779	604	19	x	x	X
ejpam-2779	604	20	/	/	SYM
ejpam-2779	604	21	k	k	NOUN
ejpam-2779	605	1	=	=	SYM
ejpam-2779	605	2	(	(	PUNCT
ejpam-2779	605	3	0	0	NUM
ejpam-2779	605	4	∗	∗	NOUN
ejpam-2779	605	5	(	(	PUNCT
ejpam-2779	605	6	0	0	NUM
ejpam-2779	605	7	∗	∗	NOUN
ejpam-2779	605	8	x))/k	x))/k	PUNCT
ejpam-2779	606	1	=	=	PUNCT
ejpam-2779	606	2	0	0	NUM
ejpam-2779	606	3	/	/	SYM
ejpam-2779	606	4	k.	k.	NOUN
ejpam-2779	607	1	this	this	PRON
ejpam-2779	607	2	shows	show	VERB
ejpam-2779	607	3	that	that	SCONJ
ejpam-2779	607	4	m(a	m(a	PROPN
ejpam-2779	607	5	/	/	SYM
ejpam-2779	607	6	k	k	NOUN
ejpam-2779	607	7	)	)	PUNCT
ejpam-2779	607	8	=	=	PUNCT
ejpam-2779	607	9	{	{	PUNCT
ejpam-2779	607	10	0	0	NUM
ejpam-2779	607	11	/	/	SYM
ejpam-2779	607	12	k	k	NOUN
ejpam-2779	607	13	}	}	PUNCT
ejpam-2779	607	14	,	,	PUNCT
ejpam-2779	607	15	and	and	CCONJ
ejpam-2779	607	16	hence	hence	ADV
ejpam-2779	607	17	(	(	PUNCT
ejpam-2779	607	18	a	a	X
ejpam-2779	607	19	/	/	SYM
ejpam-2779	607	20	k,≤	k,≤	PROPN
ejpam-2779	607	21	,	,	PUNCT
ejpam-2779	607	22	∗	∗	NOUN
ejpam-2779	607	23	,	,	PUNCT
ejpam-2779	607	24	◦	◦	NOUN
ejpam-2779	607	25	,	,	PUNCT
ejpam-2779	607	26	0	0	NUM
ejpam-2779	607	27	/	/	SYM
ejpam-2779	607	28	k	k	NOUN
ejpam-2779	607	29	)	)	PUNCT
ejpam-2779	607	30	is	be	AUX
ejpam-2779	607	31	a	a	DET
ejpam-2779	607	32	pseudo	pseudo	NOUN
ejpam-2779	607	33	-	-	ADJ
ejpam-2779	607	34	bck	bck	ADJ
ejpam-2779	607	35	algebra	algebra	NOUN
ejpam-2779	607	36	.	.	PUNCT
ejpam-2779	608	1	now	now	ADV
ejpam-2779	608	2	we	we	PRON
ejpam-2779	608	3	prove	prove	VERB
ejpam-2779	608	4	that	that	SCONJ
ejpam-2779	608	5	10	10	NUM
ejpam-2779	608	6	/	/	SYM
ejpam-2779	608	7	k	k	PROPN
ejpam-2779	608	8	is	be	AUX
ejpam-2779	608	9	the	the	DET
ejpam-2779	608	10	greatest	great	ADJ
ejpam-2779	608	11	element	element	NOUN
ejpam-2779	608	12	of	of	ADP
ejpam-2779	608	13	a	a	PRON
ejpam-2779	608	14	/	/	SYM
ejpam-2779	608	15	k.	k.	PROPN
ejpam-2779	609	1	first	first	ADV
ejpam-2779	609	2	we	we	PRON
ejpam-2779	609	3	claim	claim	VERB
ejpam-2779	609	4	10	10	NUM
ejpam-2779	610	1	/	/	SYM
ejpam-2779	610	2	k	k	NOUN
ejpam-2779	610	3	=	=	PUNCT
ejpam-2779	610	4	1a	1a	X
ejpam-2779	610	5	/	/	SYM
ejpam-2779	610	6	k	k	PROPN
ejpam-2779	610	7	for	for	ADP
ejpam-2779	610	8	all	all	DET
ejpam-2779	610	9	a	a	DET
ejpam-2779	610	10	∈	∈	PROPN
ejpam-2779	610	11	m(a	m(a	NOUN
ejpam-2779	610	12	)	)	PUNCT
ejpam-2779	610	13	.	.	PUNCT
ejpam-2779	611	1	note	note	VERB
ejpam-2779	611	2	that	that	PRON
ejpam-2779	611	3	s(10	s(10	ADV
ejpam-2779	611	4	)	)	PUNCT
ejpam-2779	612	1	+	+	CCONJ
ejpam-2779	612	2	s(1a	s(1a	NOUN
ejpam-2779	612	3	∗	∗	PROPN
ejpam-2779	612	4	10	10	NUM
ejpam-2779	612	5	)	)	PUNCT
ejpam-2779	612	6	=	=	SYM
ejpam-2779	612	7	s(1a	s(1a	X
ejpam-2779	612	8	)	)	PUNCT
ejpam-2779	613	1	+	+	CCONJ
ejpam-2779	613	2	s(10	s(10	ADV
ejpam-2779	613	3	∗	∗	NOUN
ejpam-2779	613	4	1a	1a	NUM
ejpam-2779	613	5	)	)	PUNCT
ejpam-2779	613	6	and	and	CCONJ
ejpam-2779	613	7	s(10	s(10	ADJ
ejpam-2779	613	8	)	)	PUNCT
ejpam-2779	613	9	=	=	SYM
ejpam-2779	613	10	s(1a	s(1a	NOUN
ejpam-2779	613	11	)	)	PUNCT
ejpam-2779	613	12	=	=	PUNCT
ejpam-2779	613	13	0	0	PUNCT
ejpam-2779	614	1	x.l	x.l	PROPN
ejpam-2779	614	2	.	.	PUNCT
ejpam-2779	615	1	xin	xin	PROPN
ejpam-2779	615	2	,	,	PUNCT
ejpam-2779	615	3	y.j	y.j	PROPN
ejpam-2779	615	4	.	.	PUNCT
ejpam-2779	615	5	li	li	PROPN
ejpam-2779	615	6	,	,	PUNCT
ejpam-2779	615	7	y.l	y.l	PROPN
ejpam-2779	615	8	.	.	PROPN
ejpam-2779	615	9	fu	fu	PROPN
ejpam-2779	615	10	/	/	SYM
ejpam-2779	615	11	eur	eur	PROPN
ejpam-2779	615	12	.	.	PUNCT
ejpam-2779	616	1	j.	j.	PROPN
ejpam-2779	616	2	pure	pure	PROPN
ejpam-2779	616	3	appl	appl	PROPN
ejpam-2779	616	4	.	.	PROPN
ejpam-2779	616	5	math	math	PROPN
ejpam-2779	616	6	,	,	PUNCT
ejpam-2779	616	7	10	10	NUM
ejpam-2779	616	8	(	(	PUNCT
ejpam-2779	616	9	3	3	NUM
ejpam-2779	616	10	)	)	PUNCT
ejpam-2779	616	11	(	(	PUNCT
ejpam-2779	616	12	2017	2017	NUM
ejpam-2779	616	13	)	)	PUNCT
ejpam-2779	616	14	,	,	PUNCT
ejpam-2779	616	15	455	455	NUM
ejpam-2779	616	16	-	-	SYM
ejpam-2779	616	17	472	472	NUM
ejpam-2779	616	18	468	468	NUM
ejpam-2779	616	19	by	by	ADP
ejpam-2779	616	20	definition	definition	NOUN
ejpam-2779	616	21	7	7	NUM
ejpam-2779	616	22	,	,	PUNCT
ejpam-2779	616	23	we	we	PRON
ejpam-2779	616	24	have	have	AUX
ejpam-2779	616	25	s(1a	s(1a	NOUN
ejpam-2779	616	26	∗	∗	PROPN
ejpam-2779	616	27	10	10	NUM
ejpam-2779	616	28	)	)	PUNCT
ejpam-2779	616	29	=	=	VERB
ejpam-2779	616	30	s(10	s(10	ADV
ejpam-2779	616	31	∗	∗	NOUN
ejpam-2779	616	32	1a	1a	NUM
ejpam-2779	616	33	)	)	PUNCT
ejpam-2779	616	34	.	.	PUNCT
ejpam-2779	617	1	moreover	moreover	ADV
ejpam-2779	617	2	s(1a	s(1a	PROPN
ejpam-2779	617	3	∗	∗	PROPN
ejpam-2779	617	4	10	10	NUM
ejpam-2779	617	5	)	)	PUNCT
ejpam-2779	618	1	+	+	CCONJ
ejpam-2779	618	2	s(a	s(a	PROPN
ejpam-2779	618	3	◦	◦	NOUN
ejpam-2779	618	4	(	(	PUNCT
ejpam-2779	618	5	1a	1a	X
ejpam-2779	618	6	∗	∗	X
ejpam-2779	618	7	10	10	NUM
ejpam-2779	618	8	)	)	PUNCT
ejpam-2779	618	9	)	)	PUNCT
ejpam-2779	619	1	=	=	SYM
ejpam-2779	619	2	s(a	s(a	PROPN
ejpam-2779	619	3	)	)	PUNCT
ejpam-2779	620	1	+	+	CCONJ
ejpam-2779	620	2	s((1a	s((1a	VERB
ejpam-2779	620	3	∗	∗	NOUN
ejpam-2779	620	4	10	10	NUM
ejpam-2779	620	5	)	)	PUNCT
ejpam-2779	620	6	◦	◦	NOUN
ejpam-2779	620	7	a	a	X
ejpam-2779	620	8	)	)	PUNCT
ejpam-2779	620	9	by	by	ADP
ejpam-2779	620	10	definition	definition	NOUN
ejpam-2779	620	11	7	7	NUM
ejpam-2779	620	12	.	.	PUNCT
ejpam-2779	620	13	by	by	ADP
ejpam-2779	620	14	corollary	corollary	ADJ
ejpam-2779	620	15	1	1	NUM
ejpam-2779	620	16	,	,	PUNCT
ejpam-2779	620	17	a	a	DET
ejpam-2779	620	18	◦	◦	NOUN
ejpam-2779	620	19	(	(	PUNCT
ejpam-2779	620	20	1a	1a	X
ejpam-2779	620	21	∗	∗	X
ejpam-2779	620	22	10	10	NUM
ejpam-2779	620	23	)	)	PUNCT
ejpam-2779	620	24	∈	∈	PROPN
ejpam-2779	620	25	m(a	m(a	PROPN
ejpam-2779	620	26	)	)	PUNCT
ejpam-2779	620	27	,	,	PUNCT
ejpam-2779	620	28	and	and	CCONJ
ejpam-2779	620	29	so	so	ADV
ejpam-2779	620	30	s(a	s(a	PROPN
ejpam-2779	620	31	◦	◦	NOUN
ejpam-2779	620	32	(1a	(1a	SYM
ejpam-2779	620	33	∗10	∗10	NOUN
ejpam-2779	620	34	)	)	PUNCT
ejpam-2779	620	35	)	)	PUNCT
ejpam-2779	621	1	=	=	PUNCT
ejpam-2779	621	2	1	1	X
ejpam-2779	621	3	.	.	PUNCT
ejpam-2779	621	4	since	since	SCONJ
ejpam-2779	621	5	(	(	PUNCT
ejpam-2779	621	6	1a	1a	X
ejpam-2779	621	7	∗10)	∗10)	PROPN
ejpam-2779	621	8	◦	◦	NOUN
ejpam-2779	621	9	a	a	NOUN
ejpam-2779	621	10	=	=	X
ejpam-2779	621	11	(	(	PUNCT
ejpam-2779	621	12	1a	1a	X
ejpam-2779	621	13	◦	◦	NOUN
ejpam-2779	621	14	a)∗10	a)∗10	NOUN
ejpam-2779	621	15	and	and	CCONJ
ejpam-2779	621	16	1a	1a	PROPN
ejpam-2779	621	17	◦	◦	VERB
ejpam-2779	621	18	a	a	DET
ejpam-2779	621	19	∈	∈	NOUN
ejpam-2779	621	20	v	v	NOUN
ejpam-2779	621	21	(	(	PUNCT
ejpam-2779	621	22	0	0	NUM
ejpam-2779	621	23	)	)	PUNCT
ejpam-2779	621	24	by	by	ADP
ejpam-2779	621	25	proposition	proposition	NOUN
ejpam-2779	621	26	12	12	NUM
ejpam-2779	621	27	,	,	PUNCT
ejpam-2779	621	28	we	we	PRON
ejpam-2779	621	29	have	have	VERB
ejpam-2779	621	30	s((1a∗10)	s((1a∗10)	NOUN
ejpam-2779	621	31	◦	◦	NOUN
ejpam-2779	621	32	a	a	NOUN
ejpam-2779	621	33	)	)	PUNCT
ejpam-2779	621	34	=	=	SYM
ejpam-2779	621	35	s((1a	s((1a	NOUN
ejpam-2779	621	36	◦	◦	NOUN
ejpam-2779	621	37	a)∗10	a)∗10	NUM
ejpam-2779	621	38	)	)	PUNCT
ejpam-2779	622	1	=	=	SYM
ejpam-2779	622	2	s(0	s(0	PROPN
ejpam-2779	622	3	)	)	PUNCT
ejpam-2779	622	4	=	=	SYM
ejpam-2779	623	1	1	1	X
ejpam-2779	623	2	.	.	PUNCT
ejpam-2779	623	3	hence	hence	ADV
ejpam-2779	623	4	s(1a∗10	s(1a∗10	PUNCT
ejpam-2779	623	5	)	)	PUNCT
ejpam-2779	624	1	=	=	PUNCT
ejpam-2779	625	1	1	1	X
ejpam-2779	625	2	.	.	PUNCT
ejpam-2779	625	3	by	by	ADP
ejpam-2779	625	4	(	(	PUNCT
ejpam-2779	625	5	3	3	NUM
ejpam-2779	625	6	)	)	PUNCT
ejpam-2779	625	7	,	,	PUNCT
ejpam-2779	625	8	10	10	NUM
ejpam-2779	625	9	/	/	SYM
ejpam-2779	625	10	k	k	NOUN
ejpam-2779	625	11	=	=	PUNCT
ejpam-2779	625	12	1a	1a	X
ejpam-2779	625	13	/	/	SYM
ejpam-2779	625	14	k	k	PROPN
ejpam-2779	625	15	for	for	ADP
ejpam-2779	625	16	all	all	DET
ejpam-2779	625	17	a	a	DET
ejpam-2779	625	18	∈	∈	PROPN
ejpam-2779	625	19	m(a	m(a	NOUN
ejpam-2779	625	20	)	)	PUNCT
ejpam-2779	625	21	.	.	PUNCT
ejpam-2779	626	1	let	let	VERB
ejpam-2779	626	2	x	x	PRON
ejpam-2779	626	3	/	/	SYM
ejpam-2779	626	4	k	k	PROPN
ejpam-2779	626	5	∈	∈	PROPN
ejpam-2779	627	1	a	a	PRON
ejpam-2779	627	2	/	/	SYM
ejpam-2779	627	3	k.	k.	PROPN
ejpam-2779	627	4	then	then	ADV
ejpam-2779	627	5	x	x	X
ejpam-2779	627	6	/	/	SYM
ejpam-2779	627	7	k	k	PROPN
ejpam-2779	627	8	≤	≤	NUM
ejpam-2779	627	9	1(0∗(0	1(0∗(0	NUM
ejpam-2779	627	10	◦	◦	NOUN
ejpam-2779	627	11	x))/k	x))/k	NOUN
ejpam-2779	627	12	=	=	SYM
ejpam-2779	627	13	10	10	NUM
ejpam-2779	627	14	/	/	SYM
ejpam-2779	627	15	k.	k.	NOUN
ejpam-2779	628	1	this	this	PRON
ejpam-2779	628	2	shows	show	VERB
ejpam-2779	628	3	that	that	SCONJ
ejpam-2779	628	4	10	10	NUM
ejpam-2779	628	5	/	/	SYM
ejpam-2779	628	6	k	k	PROPN
ejpam-2779	628	7	is	be	AUX
ejpam-2779	628	8	the	the	DET
ejpam-2779	628	9	greatest	great	ADJ
ejpam-2779	628	10	element	element	NOUN
ejpam-2779	628	11	of	of	ADP
ejpam-2779	628	12	a	a	DET
ejpam-2779	628	13	/	/	SYM
ejpam-2779	628	14	k.	k.	PROPN
ejpam-2779	628	15	it	it	PRON
ejpam-2779	628	16	follows	follow	VERB
ejpam-2779	628	17	that	that	SCONJ
ejpam-2779	628	18	(	(	PUNCT
ejpam-2779	628	19	a	a	X
ejpam-2779	628	20	/	/	SYM
ejpam-2779	628	21	k,≤	k,≤	PROPN
ejpam-2779	628	22	,	,	PUNCT
ejpam-2779	628	23	∗	∗	NOUN
ejpam-2779	628	24	,	,	PUNCT
ejpam-2779	628	25	◦	◦	NOUN
ejpam-2779	628	26	,	,	PUNCT
ejpam-2779	628	27	0	0	NUM
ejpam-2779	628	28	/	/	SYM
ejpam-2779	628	29	k	k	NOUN
ejpam-2779	628	30	,	,	PUNCT
ejpam-2779	628	31	10	10	NUM
ejpam-2779	628	32	/	/	SYM
ejpam-2779	628	33	k	k	NOUN
ejpam-2779	628	34	)	)	PUNCT
ejpam-2779	628	35	is	be	AUX
ejpam-2779	628	36	a	a	DET
ejpam-2779	628	37	bounded	bounded	ADJ
ejpam-2779	628	38	pseudo	pseudo	NOUN
ejpam-2779	628	39	bck	bck	NOUN
ejpam-2779	628	40	algebra	algebra	PROPN
ejpam-2779	628	41	.	.	PUNCT
ejpam-2779	629	1	(	(	PUNCT
ejpam-2779	629	2	6	6	NUM
ejpam-2779	629	3	)	)	PUNCT
ejpam-2779	629	4	the	the	DET
ejpam-2779	629	5	fact	fact	NOUN
ejpam-2779	629	6	that	that	SCONJ
ejpam-2779	629	7	s̃	s̃	PROPN
ejpam-2779	629	8	is	be	AUX
ejpam-2779	629	9	a	a	DET
ejpam-2779	629	10	well	well	ADV
ejpam-2779	629	11	-	-	PUNCT
ejpam-2779	629	12	defined	define	VERB
ejpam-2779	629	13	bosbach	bosbach	ADJ
ejpam-2779	629	14	state	state	NOUN
ejpam-2779	629	15	on	on	ADP
ejpam-2779	629	16	a	a	PRON
ejpam-2779	629	17	/	/	SYM
ejpam-2779	629	18	k	k	PROPN
ejpam-2779	629	19	is	be	AUX
ejpam-2779	629	20	now	now	ADV
ejpam-2779	629	21	straightforward	straightforward	ADJ
ejpam-2779	629	22	.	.	PUNCT
ejpam-2779	630	1	definition	definition	NOUN
ejpam-2779	630	2	10	10	NUM
ejpam-2779	630	3	.	.	PUNCT
ejpam-2779	631	1	let	let	VERB
ejpam-2779	631	2	a	a	PRON
ejpam-2779	631	3	be	be	AUX
ejpam-2779	631	4	a	a	DET
ejpam-2779	631	5	lbp	lbp	NOUN
ejpam-2779	631	6	-	-	PUNCT
ejpam-2779	631	7	bci	bci	NOUN
ejpam-2779	631	8	algebra	algebra	NOUN
ejpam-2779	631	9	.	.	PUNCT
ejpam-2779	632	1	then	then	ADV
ejpam-2779	632	2	(	(	PUNCT
ejpam-2779	632	3	1	1	X
ejpam-2779	632	4	)	)	PUNCT
ejpam-2779	632	5	a	a	PRON
ejpam-2779	632	6	is	be	AUX
ejpam-2779	632	7	called	call	VERB
ejpam-2779	632	8	good	good	ADJ
ejpam-2779	632	9	if	if	SCONJ
ejpam-2779	632	10	x−∼	x−∼	ADV
ejpam-2779	632	11	=	=	SYM
ejpam-2779	632	12	x∼−	x∼−	PROPN
ejpam-2779	632	13	for	for	ADP
ejpam-2779	632	14	all	all	DET
ejpam-2779	632	15	x	x	SYM
ejpam-2779	632	16	∈	∈	NOUN
ejpam-2779	632	17	a.	a.	NOUN
ejpam-2779	632	18	(	(	PUNCT
ejpam-2779	632	19	2	2	NUM
ejpam-2779	632	20	)	)	PUNCT
ejpam-2779	632	21	a	a	PRON
ejpam-2779	632	22	is	be	AUX
ejpam-2779	632	23	with	with	ADP
ejpam-2779	632	24	the	the	DET
ejpam-2779	632	25	condition	condition	NOUN
ejpam-2779	632	26	(	(	PUNCT
ejpam-2779	632	27	pdn	pdn	NOUN
ejpam-2779	632	28	)	)	PUNCT
ejpam-2779	632	29	if	if	SCONJ
ejpam-2779	632	30	x−∼	x−∼	ADV
ejpam-2779	632	31	=	=	PUNCT
ejpam-2779	632	32	x∼−	x∼−	PROPN
ejpam-2779	633	1	=	=	PUNCT
ejpam-2779	633	2	x	x	PROPN
ejpam-2779	633	3	for	for	ADP
ejpam-2779	633	4	all	all	DET
ejpam-2779	633	5	x	x	SYM
ejpam-2779	633	6	∈	∈	NOUN
ejpam-2779	633	7	a.	a.	NOUN
ejpam-2779	633	8	proposition	proposition	NOUN
ejpam-2779	633	9	27	27	NUM
ejpam-2779	633	10	.	.	PUNCT
ejpam-2779	634	1	let	let	VERB
ejpam-2779	634	2	s	s	PRON
ejpam-2779	634	3	be	be	AUX
ejpam-2779	634	4	a	a	DET
ejpam-2779	634	5	bosbach	bosbach	ADJ
ejpam-2779	634	6	state	state	NOUN
ejpam-2779	634	7	on	on	ADP
ejpam-2779	634	8	a	a	DET
ejpam-2779	634	9	bounded	bounded	ADJ
ejpam-2779	634	10	pseudo	pseudo	NOUN
ejpam-2779	634	11	-	-	NOUN
ejpam-2779	634	12	bci	bci	ADJ
ejpam-2779	634	13	algebra	algebra	NOUN
ejpam-2779	634	14	a	a	PRON
ejpam-2779	634	15	and	and	CCONJ
ejpam-2779	634	16	let	let	VERB
ejpam-2779	634	17	k	k	PROPN
ejpam-2779	634	18	=	=	PUNCT
ejpam-2779	634	19	ker(s	ker(s	PROPN
ejpam-2779	634	20	)	)	PUNCT
ejpam-2779	634	21	.	.	PUNCT
ejpam-2779	635	1	for	for	ADP
ejpam-2779	635	2	every	every	DET
ejpam-2779	635	3	element	element	NOUN
ejpam-2779	635	4	x	x	PROPN
ejpam-2779	635	5	∈	∈	PROPN
ejpam-2779	635	6	a	a	X
ejpam-2779	635	7	,	,	PUNCT
ejpam-2779	635	8	we	we	PRON
ejpam-2779	635	9	have	have	VERB
ejpam-2779	635	10	x−∼/k	x−∼/k	PROPN
ejpam-2779	635	11	=	=	SYM
ejpam-2779	635	12	x	x	PROPN
ejpam-2779	635	13	/	/	SYM
ejpam-2779	635	14	k	k	NOUN
ejpam-2779	635	15	=	=	SYM
ejpam-2779	635	16	x∼−/k	x∼−/k	PROPN
ejpam-2779	635	17	,	,	PUNCT
ejpam-2779	635	18	that	that	ADV
ejpam-2779	635	19	is	is	ADV
ejpam-2779	635	20	,	,	PUNCT
ejpam-2779	635	21	a	a	PRON
ejpam-2779	635	22	/	/	SYM
ejpam-2779	635	23	k	k	NOUN
ejpam-2779	635	24	satisfies	satisfy	VERB
ejpam-2779	635	25	the	the	DET
ejpam-2779	635	26	(	(	PUNCT
ejpam-2779	635	27	pdn	pdn	NOUN
ejpam-2779	635	28	)	)	PUNCT
ejpam-2779	635	29	condition	condition	NOUN
ejpam-2779	635	30	.	.	PUNCT
ejpam-2779	636	1	proof	proof	NOUN
ejpam-2779	636	2	.	.	PUNCT
ejpam-2779	637	1	it	it	PRON
ejpam-2779	637	2	is	be	AUX
ejpam-2779	637	3	similar	similar	ADJ
ejpam-2779	637	4	to	to	ADP
ejpam-2779	637	5	the	the	DET
ejpam-2779	637	6	proof	proof	NOUN
ejpam-2779	637	7	of	of	ADP
ejpam-2779	637	8	[	[	X
ejpam-2779	637	9	[	[	X
ejpam-2779	637	10	4	4	NUM
ejpam-2779	637	11	]	]	PUNCT
ejpam-2779	637	12	,	,	PUNCT
ejpam-2779	637	13	proposition	proposition	NOUN
ejpam-2779	637	14	3.14	3.14	NUM
ejpam-2779	637	15	]	]	PUNCT
ejpam-2779	637	16	.	.	PUNCT
ejpam-2779	638	1	remark	remark	PROPN
ejpam-2779	638	2	2	2	NUM
ejpam-2779	638	3	.	.	PUNCT
ejpam-2779	639	1	let	let	VERB
ejpam-2779	639	2	s	s	PRON
ejpam-2779	639	3	be	be	AUX
ejpam-2779	639	4	a	a	DET
ejpam-2779	639	5	bosbach	bosbach	ADJ
ejpam-2779	639	6	state	state	NOUN
ejpam-2779	639	7	on	on	ADP
ejpam-2779	639	8	a	a	DET
ejpam-2779	639	9	pseudo	pseudo	NOUN
ejpam-2779	639	10	-	-	ADJ
ejpam-2779	639	11	bci	bci	ADJ
ejpam-2779	639	12	algebra	algebra	PROPN
ejpam-2779	639	13	a.	a.	NOUN
ejpam-2779	639	14	according	accord	VERB
ejpam-2779	639	15	to	to	ADP
ejpam-2779	639	16	the	the	DET
ejpam-2779	639	17	proof	proof	NOUN
ejpam-2779	639	18	of	of	ADP
ejpam-2779	639	19	proposition	proposition	NOUN
ejpam-2779	639	20	27	27	NUM
ejpam-2779	639	21	,	,	PUNCT
ejpam-2779	639	22	we	we	PRON
ejpam-2779	639	23	have	have	VERB
ejpam-2779	639	24	s(x	s(x	NOUN
ejpam-2779	639	25	∗	∗	NOUN
ejpam-2779	639	26	x−∼	x−∼	ADV
ejpam-2779	639	27	)	)	PUNCT
ejpam-2779	639	28	=	=	SYM
ejpam-2779	639	29	1	1	NUM
ejpam-2779	639	30	=	=	SYM
ejpam-2779	639	31	s(x	s(x	NOUN
ejpam-2779	639	32	∗	∗	NOUN
ejpam-2779	639	33	x∼−	x∼−	PROPN
ejpam-2779	639	34	)	)	PUNCT
ejpam-2779	639	35	and	and	CCONJ
ejpam-2779	639	36	s(x	s(x	PROPN
ejpam-2779	639	37	◦	◦	NOUN
ejpam-2779	639	38	x−∼	x−∼	X
ejpam-2779	639	39	)	)	PUNCT
ejpam-2779	639	40	=	=	SYM
ejpam-2779	639	41	1	1	NUM
ejpam-2779	639	42	=	=	SYM
ejpam-2779	639	43	s(x	s(x	PROPN
ejpam-2779	639	44	◦	◦	NOUN
ejpam-2779	639	45	x∼−	x∼−	PROPN
ejpam-2779	639	46	)	)	PUNCT
ejpam-2779	639	47	.	.	PUNCT
ejpam-2779	640	1	theorem	theorem	NOUN
ejpam-2779	640	2	3	3	X
ejpam-2779	640	3	.	.	PUNCT
ejpam-2779	641	1	let	let	VERB
ejpam-2779	641	2	a	a	PRON
ejpam-2779	641	3	be	be	AUX
ejpam-2779	641	4	a	a	DET
ejpam-2779	641	5	lbp	lbp	NOUN
ejpam-2779	641	6	-	-	PUNCT
ejpam-2779	641	7	bci	bci	PROPN
ejpam-2779	641	8	algebra	algebra	NOUN
ejpam-2779	641	9	,	,	PUNCT
ejpam-2779	641	10	s	s	AUX
ejpam-2779	641	11	be	be	AUX
ejpam-2779	641	12	a	a	DET
ejpam-2779	641	13	bosbach	bosbach	ADJ
ejpam-2779	641	14	state	state	NOUN
ejpam-2779	641	15	on	on	ADP
ejpam-2779	641	16	a	a	PRON
ejpam-2779	641	17	and	and	CCONJ
ejpam-2779	641	18	k	k	NOUN
ejpam-2779	641	19	=	=	SYM
ejpam-2779	641	20	ker(s	ker(s	PROPN
ejpam-2779	641	21	)	)	PUNCT
ejpam-2779	641	22	.	.	PUNCT
ejpam-2779	642	1	then	then	ADV
ejpam-2779	642	2	a	a	X
ejpam-2779	642	3	/	/	SYM
ejpam-2779	642	4	k	k	PROPN
ejpam-2779	642	5	is	be	AUX
ejpam-2779	642	6	∧1	∧1	VERB
ejpam-2779	642	7	-	-	PUNCT
ejpam-2779	642	8	commutative	commutative	ADJ
ejpam-2779	642	9	as	as	ADV
ejpam-2779	642	10	well	well	ADV
ejpam-2779	642	11	as	as	ADP
ejpam-2779	642	12	∧2	∧2	NOUN
ejpam-2779	642	13	-	-	PUNCT
ejpam-2779	642	14	commutative	commutative	ADJ
ejpam-2779	642	15	.	.	PUNCT
ejpam-2779	643	1	in	in	ADP
ejpam-2779	643	2	addition	addition	NOUN
ejpam-2779	643	3	,	,	PUNCT
ejpam-2779	643	4	a	a	PRON
ejpam-2779	643	5	/	/	SYM
ejpam-2779	643	6	k	k	PROPN
ejpam-2779	643	7	is	be	AUX
ejpam-2779	643	8	a	a	DET
ejpam-2779	643	9	∧-semilattice	∧-semilattice	NOUN
ejpam-2779	643	10	and	and	CCONJ
ejpam-2779	643	11	good	good	ADJ
ejpam-2779	643	12	.	.	PUNCT
ejpam-2779	644	1	proof	proof	NOUN
ejpam-2779	644	2	.	.	PUNCT
ejpam-2779	645	1	it	it	PRON
ejpam-2779	645	2	is	be	AUX
ejpam-2779	645	3	similar	similar	ADJ
ejpam-2779	645	4	to	to	ADP
ejpam-2779	645	5	the	the	DET
ejpam-2779	645	6	proof	proof	NOUN
ejpam-2779	645	7	of	of	ADP
ejpam-2779	645	8	[	[	X
ejpam-2779	645	9	[	[	X
ejpam-2779	645	10	4	4	NUM
ejpam-2779	645	11	]	]	PUNCT
ejpam-2779	645	12	,	,	PUNCT
ejpam-2779	645	13	proposition	proposition	NOUN
ejpam-2779	645	14	3.16	3.16	NUM
ejpam-2779	645	15	]	]	PUNCT
ejpam-2779	645	16	.	.	PUNCT
ejpam-2779	646	1	proposition	proposition	NOUN
ejpam-2779	646	2	28	28	NUM
ejpam-2779	646	3	.	.	PUNCT
ejpam-2779	647	1	(	(	PUNCT
ejpam-2779	647	2	[	[	X
ejpam-2779	647	3	4	4	NUM
ejpam-2779	647	4	]	]	PUNCT
ejpam-2779	647	5	)	)	PUNCT
ejpam-2779	647	6	let	let	VERB
ejpam-2779	647	7	a	a	PRON
ejpam-2779	647	8	be	be	AUX
ejpam-2779	647	9	a	a	DET
ejpam-2779	647	10	good	good	ADJ
ejpam-2779	647	11	pseudo	pseudo	NOUN
ejpam-2779	647	12	-	-	ADJ
ejpam-2779	647	13	bck	bck	ADJ
ejpam-2779	647	14	algebra	algebra	NOUN
ejpam-2779	647	15	.	.	PUNCT
ejpam-2779	648	1	we	we	PRON
ejpam-2779	648	2	define	define	VERB
ejpam-2779	648	3	a	a	DET
ejpam-2779	648	4	binary	binary	ADJ
ejpam-2779	648	5	operation	operation	NOUN
ejpam-2779	648	6	⊗	⊗	PROPN
ejpam-2779	648	7	on	on	ADP
ejpam-2779	648	8	a	a	PRON
ejpam-2779	648	9	by	by	ADP
ejpam-2779	648	10	x⊗	x⊗	PROPN
ejpam-2779	648	11	y	y	PROPN
ejpam-2779	649	1	:	:	PUNCT
ejpam-2779	649	2	=	=	SYM
ejpam-2779	649	3	y−∼	y−∼	NOUN
ejpam-2779	649	4	∗	∗	NOUN
ejpam-2779	649	5	x∼.	x∼.	NOUN
ejpam-2779	649	6	for	for	ADP
ejpam-2779	649	7	all	all	DET
ejpam-2779	649	8	x	x	NOUN
ejpam-2779	649	9	,	,	PUNCT
ejpam-2779	649	10	y	y	PROPN
ejpam-2779	649	11	∈	∈	PROPN
ejpam-2779	649	12	a	a	PRON
ejpam-2779	649	13	,	,	PUNCT
ejpam-2779	649	14	the	the	DET
ejpam-2779	649	15	following	follow	VERB
ejpam-2779	649	16	hold	hold	NOUN
ejpam-2779	649	17	:	:	PUNCT
ejpam-2779	649	18	(	(	PUNCT
ejpam-2779	649	19	1	1	X
ejpam-2779	649	20	)	)	PUNCT
ejpam-2779	649	21	x⊗	x⊗	PROPN
ejpam-2779	649	22	y	y	PROPN
ejpam-2779	649	23	=	=	PUNCT
ejpam-2779	649	24	x∼−	x∼−	PROPN
ejpam-2779	650	1	◦	◦	NOUN
ejpam-2779	650	2	y−.	y−.	NOUN
ejpam-2779	650	3	(	(	PUNCT
ejpam-2779	650	4	2	2	NUM
ejpam-2779	650	5	)	)	PUNCT
ejpam-2779	650	6	x⊗	x⊗	VERB
ejpam-2779	650	7	y	y	PROPN
ejpam-2779	650	8	≤	≤	PROPN
ejpam-2779	651	1	x	x	X
ejpam-2779	651	2	,	,	PUNCT
ejpam-2779	651	3	y.	y.	PROPN
ejpam-2779	651	4	(	(	PUNCT
ejpam-2779	651	5	3	3	X
ejpam-2779	651	6	)	)	PUNCT
ejpam-2779	651	7	x⊗	x⊗	NOUN
ejpam-2779	651	8	1	1	NUM
ejpam-2779	651	9	=	=	SYM
ejpam-2779	651	10	1⊗	1⊗	NUM
ejpam-2779	651	11	x	x	SYM
ejpam-2779	651	12	=	=	SYM
ejpam-2779	651	13	x∼−.	x∼−.	NOUN
ejpam-2779	651	14	(	(	PUNCT
ejpam-2779	651	15	4	4	NUM
ejpam-2779	651	16	)	)	PUNCT
ejpam-2779	651	17	x⊗	x⊗	NOUN
ejpam-2779	651	18	0	0	NUM
ejpam-2779	652	1	=	=	SYM
ejpam-2779	652	2	0⊗	0⊗	NOUN
ejpam-2779	652	3	x	x	SYM
ejpam-2779	652	4	=	=	NOUN
ejpam-2779	652	5	0	0	NUM
ejpam-2779	652	6	.	.	PUNCT
ejpam-2779	653	1	(	(	PUNCT
ejpam-2779	653	2	5	5	NUM
ejpam-2779	653	3	)	)	PUNCT
ejpam-2779	653	4	(	(	PUNCT
ejpam-2779	653	5	x⊗	x⊗	PROPN
ejpam-2779	653	6	y)−∼	y)−∼	PROPN
ejpam-2779	654	1	=	=	PRON
ejpam-2779	654	2	x⊗	x⊗	VERB
ejpam-2779	654	3	y	y	PROPN
ejpam-2779	654	4	=	=	PROPN
ejpam-2779	654	5	x−∼	x−∼	PROPN
ejpam-2779	655	1	⊗	⊗	PROPN
ejpam-2779	655	2	y−∼.	y−∼.	PROPN
ejpam-2779	655	3	(	(	PUNCT
ejpam-2779	655	4	6	6	NUM
ejpam-2779	655	5	)	)	PUNCT
ejpam-2779	655	6	⊗	⊗	PROPN
ejpam-2779	655	7	is	be	AUX
ejpam-2779	655	8	associative	associative	ADJ
ejpam-2779	655	9	.	.	PUNCT
ejpam-2779	656	1	an	an	DET
ejpam-2779	656	2	mv	mv	NOUN
ejpam-2779	656	3	-	-	NOUN
ejpam-2779	656	4	algebra	algebra	NOUN
ejpam-2779	656	5	is	be	AUX
ejpam-2779	656	6	an	an	DET
ejpam-2779	656	7	algebra	algebra	NOUN
ejpam-2779	656	8	(	(	PUNCT
ejpam-2779	656	9	a,⊕,−	a,⊕,−	PROPN
ejpam-2779	656	10	,	,	PUNCT
ejpam-2779	656	11	0	0	NUM
ejpam-2779	656	12	)	)	PUNCT
ejpam-2779	656	13	of	of	ADP
ejpam-2779	656	14	type	type	NOUN
ejpam-2779	656	15	(	(	PUNCT
ejpam-2779	656	16	2	2	NUM
ejpam-2779	656	17	,	,	PUNCT
ejpam-2779	656	18	1	1	NUM
ejpam-2779	656	19	,	,	PUNCT
ejpam-2779	656	20	0	0	NUM
ejpam-2779	656	21	)	)	PUNCT
ejpam-2779	656	22	such	such	ADJ
ejpam-2779	656	23	that	that	SCONJ
ejpam-2779	656	24	(	(	PUNCT
ejpam-2779	656	25	i	i	NOUN
ejpam-2779	656	26	)	)	PUNCT
ejpam-2779	656	27	⊕	⊕	PROPN
ejpam-2779	656	28	is	be	AUX
ejpam-2779	656	29	commutative	commutative	ADJ
ejpam-2779	656	30	and	and	CCONJ
ejpam-2779	656	31	associative	associative	ADJ
ejpam-2779	656	32	,	,	PUNCT
ejpam-2779	656	33	(	(	PUNCT
ejpam-2779	656	34	ii	ii	NOUN
ejpam-2779	656	35	)	)	PUNCT
ejpam-2779	656	36	x	x	PUNCT
ejpam-2779	656	37	⊕	⊕	NOUN
ejpam-2779	656	38	0	0	NUM
ejpam-2779	657	1	=	=	SYM
ejpam-2779	657	2	x	x	NOUN
ejpam-2779	657	3	,	,	PUNCT
ejpam-2779	657	4	(	(	PUNCT
ejpam-2779	657	5	iii	iii	NOUN
ejpam-2779	657	6	)	)	PUNCT
ejpam-2779	657	7	x	x	SYM
ejpam-2779	657	8	⊕	⊕	NOUN
ejpam-2779	657	9	0−	0−	NUM
ejpam-2779	657	10	=	=	SYM
ejpam-2779	657	11	0−,(iv	0−,(iv	PROPN
ejpam-2779	657	12	)	)	PUNCT
ejpam-2779	657	13	x−−	x−−	NOUN
ejpam-2779	658	1	=	=	SYM
ejpam-2779	658	2	x,(v	x,(v	PROPN
ejpam-2779	658	3	)	)	PUNCT
ejpam-2779	658	4	y	y	PROPN
ejpam-2779	658	5	⊕	⊕	PROPN
ejpam-2779	658	6	(	(	PUNCT
ejpam-2779	658	7	y	y	PROPN
ejpam-2779	658	8	⊕	⊕	PROPN
ejpam-2779	658	9	x−)−	x−)−	PUNCT
ejpam-2779	659	1	=	=	PUNCT
ejpam-2779	659	2	x	x	SYM
ejpam-2779	659	3	⊕	⊕	PROPN
ejpam-2779	659	4	(	(	PUNCT
ejpam-2779	659	5	x	x	PROPN
ejpam-2779	659	6	⊕	⊕	PROPN
ejpam-2779	659	7	y−)−.	y−)−.	NOUN
ejpam-2779	659	8	if	if	SCONJ
ejpam-2779	659	9	we	we	PRON
ejpam-2779	659	10	define	define	VERB
ejpam-2779	659	11	x	x	X
ejpam-2779	659	12	∗	∗	NOUN
ejpam-2779	659	13	y	y	NOUN
ejpam-2779	659	14	=	=	PUNCT
ejpam-2779	659	15	x	x	PUNCT
ejpam-2779	659	16	◦	◦	NOUN
ejpam-2779	659	17	y	y	NOUN
ejpam-2779	659	18	=	=	SYM
ejpam-2779	659	19	y−	y−	PROPN
ejpam-2779	659	20	⊕	⊕	PROPN
ejpam-2779	659	21	x	x	PROPN
ejpam-2779	659	22	,	,	PUNCT
ejpam-2779	659	23	then	then	ADV
ejpam-2779	659	24	(	(	PUNCT
ejpam-2779	659	25	a	a	PRON
ejpam-2779	659	26	,	,	PUNCT
ejpam-2779	659	27	∗	∗	NOUN
ejpam-2779	659	28	,	,	PUNCT
ejpam-2779	659	29	◦	◦	NOUN
ejpam-2779	659	30	,	,	PUNCT
ejpam-2779	659	31	1	1	NUM
ejpam-2779	659	32	,	,	PUNCT
ejpam-2779	659	33	0	0	NUM
ejpam-2779	659	34	)	)	PUNCT
ejpam-2779	659	35	is	be	AUX
ejpam-2779	659	36	a	a	DET
ejpam-2779	659	37	bounded	bounded	ADJ
ejpam-2779	659	38	pseudo	pseudo	NOUN
ejpam-2779	659	39	-	-	ADJ
ejpam-2779	659	40	bck	bck	ADJ
ejpam-2779	659	41	algebra	algebra	NOUN
ejpam-2779	659	42	.	.	PUNCT
ejpam-2779	660	1	an	an	DET
ejpam-2779	660	2	mv	mv	NOUN
ejpam-2779	660	3	-	-	NOUN
ejpam-2779	660	4	state	state	NOUN
ejpam-2779	660	5	on	on	ADP
ejpam-2779	660	6	an	an	DET
ejpam-2779	660	7	mv	mv	NOUN
ejpam-2779	660	8	-	-	NOUN
ejpam-2779	660	9	algebra	algebra	NOUN
ejpam-2779	660	10	a	a	PRON
ejpam-2779	660	11	is	be	AUX
ejpam-2779	660	12	a	a	DET
ejpam-2779	660	13	mapping	mapping	NOUN
ejpam-2779	660	14	s	s	PART
ejpam-2779	660	15	:	:	PUNCT
ejpam-2779	660	16	a→	a→	PUNCT
ejpam-2779	660	17	[	[	X
ejpam-2779	660	18	0	0	NUM
ejpam-2779	660	19	,	,	PUNCT
ejpam-2779	660	20	1	1	NUM
ejpam-2779	660	21	]	]	PUNCT
ejpam-2779	660	22	such	such	ADJ
ejpam-2779	660	23	that	that	SCONJ
ejpam-2779	660	24	s(1	s(1	PROPN
ejpam-2779	660	25	)	)	PUNCT
ejpam-2779	660	26	=	=	SYM
ejpam-2779	660	27	1	1	NUM
ejpam-2779	660	28	and	and	CCONJ
ejpam-2779	660	29	s(a⊕b	s(a⊕b	NOUN
ejpam-2779	660	30	)	)	PUNCT
ejpam-2779	660	31	=	=	SYM
ejpam-2779	660	32	s(a)+s(b	s(a)+s(b	PROPN
ejpam-2779	660	33	)	)	PUNCT
ejpam-2779	660	34	whenever	whenever	SCONJ
ejpam-2779	660	35	a	a	DET
ejpam-2779	660	36	�	�	PROPN
ejpam-2779	660	37	b	b	NOUN
ejpam-2779	660	38	=	=	SYM
ejpam-2779	660	39	0	0	PROPN
ejpam-2779	660	40	.	.	PUNCT
ejpam-2779	661	1	every	every	DET
ejpam-2779	661	2	mv	mv	PROPN
ejpam-2779	661	3	-	-	PUNCT
ejpam-2779	661	4	algebra	algebra	NOUN
ejpam-2779	661	5	admits	admit	VERB
ejpam-2779	661	6	at	at	ADP
ejpam-2779	661	7	least	least	ADV
ejpam-2779	661	8	one	one	NUM
ejpam-2779	661	9	mv	mv	NOUN
ejpam-2779	661	10	-	-	NOUN
ejpam-2779	661	11	state	state	NOUN
ejpam-2779	661	12	,	,	PUNCT
ejpam-2779	661	13	and	and	CCONJ
ejpam-2779	661	14	due	due	ADP
ejpam-2779	661	15	to	to	ADP
ejpam-2779	661	16	[	[	X
ejpam-2779	661	17	17	17	NUM
ejpam-2779	661	18	]	]	PUNCT
ejpam-2779	661	19	,	,	PUNCT
ejpam-2779	661	20	every	every	DET
ejpam-2779	661	21	mv	mv	PROPN
ejpam-2779	661	22	-	-	NOUN
ejpam-2779	661	23	state	state	NOUN
ejpam-2779	661	24	on	on	ADP
ejpam-2779	661	25	a	a	DET
ejpam-2779	661	26	coincides	coincide	NOUN
ejpam-2779	661	27	with	with	ADP
ejpam-2779	661	28	a	a	DET
ejpam-2779	661	29	bosbach	bosbach	ADJ
ejpam-2779	661	30	state	state	NOUN
ejpam-2779	661	31	on	on	ADP
ejpam-2779	661	32	the	the	DET
ejpam-2779	661	33	bck	bck	PROPN
ejpam-2779	661	34	algebra	algebra	PROPN
ejpam-2779	661	35	a	a	PRON
ejpam-2779	661	36	and	and	CCONJ
ejpam-2779	661	37	vice	vice	ADV
ejpam-2779	661	38	versa	versa	ADV
ejpam-2779	661	39	.	.	PUNCT
ejpam-2779	662	1	x.l	x.l	PROPN
ejpam-2779	662	2	.	.	PUNCT
ejpam-2779	663	1	xin	xin	PROPN
ejpam-2779	663	2	,	,	PUNCT
ejpam-2779	663	3	y.j	y.j	PROPN
ejpam-2779	663	4	.	.	PUNCT
ejpam-2779	663	5	li	li	PROPN
ejpam-2779	663	6	,	,	PUNCT
ejpam-2779	663	7	y.l	y.l	PROPN
ejpam-2779	663	8	.	.	PROPN
ejpam-2779	663	9	fu	fu	PROPN
ejpam-2779	663	10	/	/	SYM
ejpam-2779	663	11	eur	eur	PROPN
ejpam-2779	663	12	.	.	PUNCT
ejpam-2779	664	1	j.	j.	PROPN
ejpam-2779	664	2	pure	pure	PROPN
ejpam-2779	664	3	appl	appl	PROPN
ejpam-2779	664	4	.	.	PROPN
ejpam-2779	664	5	math	math	PROPN
ejpam-2779	664	6	,	,	PUNCT
ejpam-2779	664	7	10	10	NUM
ejpam-2779	664	8	(	(	PUNCT
ejpam-2779	664	9	3	3	NUM
ejpam-2779	664	10	)	)	PUNCT
ejpam-2779	664	11	(	(	PUNCT
ejpam-2779	664	12	2017	2017	NUM
ejpam-2779	664	13	)	)	PUNCT
ejpam-2779	664	14	,	,	PUNCT
ejpam-2779	664	15	455	455	NUM
ejpam-2779	664	16	-	-	SYM
ejpam-2779	664	17	472	472	NUM
ejpam-2779	664	18	469	469	NUM
ejpam-2779	664	19	we	we	PRON
ejpam-2779	664	20	note	note	VERB
ejpam-2779	664	21	that	that	SCONJ
ejpam-2779	664	22	the	the	DET
ejpam-2779	664	23	radical	radical	ADJ
ejpam-2779	664	24	,	,	PUNCT
ejpam-2779	664	25	rad(a	rad(a	PROPN
ejpam-2779	664	26	)	)	PUNCT
ejpam-2779	664	27	,	,	PUNCT
ejpam-2779	664	28	of	of	ADP
ejpam-2779	664	29	an	an	DET
ejpam-2779	664	30	mv	mv	NOUN
ejpam-2779	664	31	-	-	NOUN
ejpam-2779	664	32	algebra	algebra	NOUN
ejpam-2779	664	33	a	a	PRON
ejpam-2779	664	34	is	be	AUX
ejpam-2779	664	35	the	the	DET
ejpam-2779	664	36	intersection	intersection	NOUN
ejpam-2779	664	37	of	of	ADP
ejpam-2779	664	38	all	all	DET
ejpam-2779	664	39	maximal	maximal	ADJ
ejpam-2779	664	40	ideals	ideal	NOUN
ejpam-2779	664	41	of	of	ADP
ejpam-2779	664	42	a([7	a([7	PROPN
ejpam-2779	664	43	]	]	PUNCT
ejpam-2779	664	44	)	)	PUNCT
ejpam-2779	664	45	.	.	PUNCT
ejpam-2779	665	1	proposition	proposition	NOUN
ejpam-2779	665	2	29	29	NUM
ejpam-2779	665	3	.	.	PUNCT
ejpam-2779	666	1	(	(	PUNCT
ejpam-2779	666	2	[	[	X
ejpam-2779	666	3	9	9	NUM
ejpam-2779	666	4	]	]	NUM
ejpam-2779	666	5	)	)	PUNCT
ejpam-2779	666	6	.	.	PUNCT
ejpam-2779	667	1	in	in	ADP
ejpam-2779	667	2	any	any	DET
ejpam-2779	667	3	mv	mv	NOUN
ejpam-2779	667	4	-	-	NOUN
ejpam-2779	667	5	algebra	algebra	NOUN
ejpam-2779	667	6	a	a	DET
ejpam-2779	667	7	the	the	DET
ejpam-2779	667	8	following	following	ADJ
ejpam-2779	667	9	conditions	condition	NOUN
ejpam-2779	667	10	are	be	AUX
ejpam-2779	667	11	equivalent	equivalent	ADJ
ejpam-2779	667	12	:	:	PUNCT
ejpam-2779	667	13	(	(	PUNCT
ejpam-2779	667	14	a	a	X
ejpam-2779	667	15	)	)	PUNCT
ejpam-2779	667	16	rad(a	rad(a	PROPN
ejpam-2779	667	17	)	)	PUNCT
ejpam-2779	667	18	=	=	SYM
ejpam-2779	668	1	0	0	X
ejpam-2779	668	2	.	.	PUNCT
ejpam-2779	668	3	(	(	PUNCT
ejpam-2779	668	4	b	b	X
ejpam-2779	668	5	)	)	PUNCT
ejpam-2779	668	6	nx	nx	PROPN
ejpam-2779	668	7	≤	≤	NUM
ejpam-2779	668	8	x−	x−	PROPN
ejpam-2779	668	9	for	for	ADP
ejpam-2779	668	10	all	all	DET
ejpam-2779	668	11	n	n	PRON
ejpam-2779	668	12	∈	∈	NOUN
ejpam-2779	668	13	n	n	PRON
ejpam-2779	668	14	implies	imply	VERB
ejpam-2779	668	15	x	x	PUNCT
ejpam-2779	668	16	=	=	SYM
ejpam-2779	668	17	0	0	NUM
ejpam-2779	668	18	.	.	PUNCT
ejpam-2779	669	1	(	(	PUNCT
ejpam-2779	669	2	c	c	X
ejpam-2779	669	3	)	)	PUNCT
ejpam-2779	669	4	nx	nx	PROPN
ejpam-2779	669	5	≤	≤	ADJ
ejpam-2779	669	6	y−	y−	NOUN
ejpam-2779	669	7	for	for	ADP
ejpam-2779	669	8	all	all	DET
ejpam-2779	669	9	n	n	PRON
ejpam-2779	669	10	∈	∈	NOUN
ejpam-2779	669	11	n	n	NOUN
ejpam-2779	669	12	implies	imply	VERB
ejpam-2779	669	13	x	x	PUNCT
ejpam-2779	669	14	∧	∧	NOUN
ejpam-2779	669	15	y	y	PROPN
ejpam-2779	669	16	=	=	NOUN
ejpam-2779	669	17	0	0	PROPN
ejpam-2779	669	18	.	.	PUNCT
ejpam-2779	670	1	(	(	PUNCT
ejpam-2779	670	2	d	d	X
ejpam-2779	670	3	)	)	PUNCT
ejpam-2779	670	4	nx	nx	PROPN
ejpam-2779	670	5	≤	≤	PROPN
ejpam-2779	670	6	y	y	PROPN
ejpam-2779	670	7	for	for	ADP
ejpam-2779	670	8	all	all	DET
ejpam-2779	670	9	n	n	PRON
ejpam-2779	670	10	∈	∈	NOUN
ejpam-2779	670	11	n	n	NOUN
ejpam-2779	670	12	implies	imply	VERB
ejpam-2779	670	13	x	x	NOUN
ejpam-2779	670	14	�	�	PROPN
ejpam-2779	670	15	y	y	NOUN
ejpam-2779	670	16	=	=	SYM
ejpam-2779	670	17	x	x	PROPN
ejpam-2779	670	18	,	,	PUNCT
ejpam-2779	670	19	where	where	SCONJ
ejpam-2779	670	20	nx	nx	PROPN
ejpam-2779	670	21	=	=	SYM
ejpam-2779	670	22	x1⊕	x1⊕	PROPN
ejpam-2779	670	23	·	·	PUNCT
ejpam-2779	670	24	·	·	PUNCT
ejpam-2779	670	25	·	·	PUNCT
ejpam-2779	670	26	xn	xn	PROPN
ejpam-2779	670	27	with	with	ADP
ejpam-2779	670	28	x1	x1	PROPN
ejpam-2779	670	29	=	=	SYM
ejpam-2779	670	30	·	·	PUNCT
ejpam-2779	670	31	·	·	PUNCT
ejpam-2779	670	32	·	·	PUNCT
ejpam-2779	671	1	=	=	PUNCT
ejpam-2779	671	2	xn	xn	PUNCT
ejpam-2779	671	3	=	=	SYM
ejpam-2779	671	4	x.	x.	NOUN
ejpam-2779	671	5	remark	remark	VERB
ejpam-2779	671	6	3	3	NUM
ejpam-2779	671	7	.	.	PUNCT
ejpam-2779	672	1	an	an	DET
ejpam-2779	672	2	mv	mv	NOUN
ejpam-2779	672	3	-	-	NOUN
ejpam-2779	672	4	algebra	algebra	NOUN
ejpam-2779	672	5	a	a	PRON
ejpam-2779	672	6	is	be	AUX
ejpam-2779	672	7	archimedean	archimedean	ADJ
ejpam-2779	672	8	in	in	ADP
ejpam-2779	672	9	the	the	DET
ejpam-2779	672	10	sense	sense	NOUN
ejpam-2779	672	11	of	of	ADP
ejpam-2779	672	12	[	[	X
ejpam-2779	672	13	9	9	X
ejpam-2779	672	14	]	]	X
ejpam-2779	672	15	if	if	SCONJ
ejpam-2779	672	16	it	it	PRON
ejpam-2779	672	17	satisfies	satisfy	VERB
ejpam-2779	672	18	the	the	DET
ejpam-2779	672	19	condition	condition	NOUN
ejpam-2779	672	20	(	(	PUNCT
ejpam-2779	672	21	b	b	NOUN
ejpam-2779	672	22	)	)	PUNCT
ejpam-2779	672	23	of	of	ADP
ejpam-2779	672	24	proposition	proposition	NOUN
ejpam-2779	672	25	29	29	NUM
ejpam-2779	672	26	and	and	CCONJ
ejpam-2779	672	27	a	a	PRON
ejpam-2779	672	28	is	be	AUX
ejpam-2779	672	29	archimedean	archimedean	ADJ
ejpam-2779	672	30	in	in	SCONJ
ejpam-2779	672	31	belluces	belluce	NOUN
ejpam-2779	672	32	sense	sense	VERB
ejpam-2779	672	33	[	[	X
ejpam-2779	672	34	1	1	X
ejpam-2779	672	35	]	]	X
ejpam-2779	672	36	if	if	SCONJ
ejpam-2779	672	37	it	it	PRON
ejpam-2779	672	38	satisfies	satisfy	VERB
ejpam-2779	672	39	the	the	DET
ejpam-2779	672	40	condition	condition	NOUN
ejpam-2779	672	41	(	(	PUNCT
ejpam-2779	672	42	d	d	NOUN
ejpam-2779	672	43	)	)	PUNCT
ejpam-2779	672	44	of	of	ADP
ejpam-2779	672	45	proposition	proposition	NOUN
ejpam-2779	672	46	29	29	NUM
ejpam-2779	672	47	.	.	PUNCT
ejpam-2779	673	1	by	by	ADP
ejpam-2779	673	2	proposition	proposition	NOUN
ejpam-2779	673	3	29	29	NUM
ejpam-2779	673	4	the	the	DET
ejpam-2779	673	5	two	two	NUM
ejpam-2779	673	6	definitions	definition	NOUN
ejpam-2779	673	7	of	of	ADP
ejpam-2779	673	8	archimedean	archimedean	ADJ
ejpam-2779	673	9	mv	mv	PROPN
ejpam-2779	673	10	-	-	PUNCT
ejpam-2779	673	11	algebras	algebra	NOUN
ejpam-2779	673	12	are	be	AUX
ejpam-2779	673	13	equivalent	equivalent	ADJ
ejpam-2779	673	14	.	.	PUNCT
ejpam-2779	674	1	theorem	theorem	ADJ
ejpam-2779	674	2	4	4	NUM
ejpam-2779	674	3	.	.	PUNCT
ejpam-2779	675	1	let	let	VERB
ejpam-2779	675	2	s	s	PRON
ejpam-2779	675	3	be	be	AUX
ejpam-2779	675	4	a	a	DET
ejpam-2779	675	5	bosbach	bosbach	ADJ
ejpam-2779	675	6	state	state	NOUN
ejpam-2779	675	7	on	on	ADP
ejpam-2779	675	8	a	a	DET
ejpam-2779	675	9	lbp	lbp	NOUN
ejpam-2779	675	10	-	-	PUNCT
ejpam-2779	675	11	bci	bci	PROPN
ejpam-2779	675	12	algebra	algebra	NOUN
ejpam-2779	675	13	a	a	PRON
ejpam-2779	675	14	and	and	CCONJ
ejpam-2779	675	15	let	let	VERB
ejpam-2779	675	16	k	k	PROPN
ejpam-2779	675	17	=	=	PUNCT
ejpam-2779	675	18	ker(s	ker(s	PROPN
ejpam-2779	675	19	)	)	PUNCT
ejpam-2779	675	20	.	.	PUNCT
ejpam-2779	676	1	then	then	ADV
ejpam-2779	676	2	(	(	PUNCT
ejpam-2779	676	3	a	a	X
ejpam-2779	676	4	/	/	SYM
ejpam-2779	676	5	k,⊕,−	k,⊕,−	NOUN
ejpam-2779	676	6	,	,	PUNCT
ejpam-2779	676	7	0	0	X
ejpam-2779	676	8	/	/	SYM
ejpam-2779	676	9	k	k	NOUN
ejpam-2779	676	10	)	)	PUNCT
ejpam-2779	676	11	,	,	PUNCT
ejpam-2779	676	12	where	where	SCONJ
ejpam-2779	676	13	a	a	X
ejpam-2779	676	14	/	/	SYM
ejpam-2779	676	15	k	k	PROPN
ejpam-2779	676	16	⊕	⊕	PROPN
ejpam-2779	676	17	b	b	PROPN
ejpam-2779	676	18	/	/	SYM
ejpam-2779	676	19	k	k	NOUN
ejpam-2779	676	20	=	=	PUNCT
ejpam-2779	676	21	(	(	PUNCT
ejpam-2779	676	22	b	b	NOUN
ejpam-2779	676	23	∗	∗	NOUN
ejpam-2779	676	24	a−)/k	a−)/k	NOUN
ejpam-2779	676	25	and	and	CCONJ
ejpam-2779	676	26	(	(	PUNCT
ejpam-2779	676	27	a	a	PRON
ejpam-2779	676	28	/	/	SYM
ejpam-2779	676	29	k)−	k)−	PROPN
ejpam-2779	676	30	=	=	SYM
ejpam-2779	676	31	a−/k	a−/k	NOUN
ejpam-2779	676	32	,	,	PUNCT
ejpam-2779	676	33	is	be	AUX
ejpam-2779	676	34	an	an	DET
ejpam-2779	676	35	archimedean	archimedean	ADJ
ejpam-2779	676	36	mv	mv	NOUN
ejpam-2779	676	37	-	-	NOUN
ejpam-2779	676	38	algebra	algebra	NOUN
ejpam-2779	676	39	and	and	CCONJ
ejpam-2779	676	40	the	the	DET
ejpam-2779	676	41	map	map	NOUN
ejpam-2779	676	42	ŝ(a	ŝ(a	NOUN
ejpam-2779	676	43	/	/	SYM
ejpam-2779	676	44	k	k	NOUN
ejpam-2779	676	45	)	)	PUNCT
ejpam-2779	676	46	:	:	PUNCT
ejpam-2779	676	47	=	=	SYM
ejpam-2779	676	48	s(a	s(a	PROPN
ejpam-2779	676	49	)	)	PUNCT
ejpam-2779	676	50	is	be	AUX
ejpam-2779	676	51	an	an	DET
ejpam-2779	676	52	mv	mv	NOUN
ejpam-2779	676	53	-	-	NOUN
ejpam-2779	676	54	state	state	NOUN
ejpam-2779	676	55	on	on	ADP
ejpam-2779	676	56	this	this	DET
ejpam-2779	676	57	mv	mv	NOUN
ejpam-2779	676	58	-	-	NOUN
ejpam-2779	676	59	algebra	algebra	NOUN
ejpam-2779	676	60	.	.	PUNCT
ejpam-2779	677	1	proof	proof	NOUN
ejpam-2779	677	2	.	.	PUNCT
ejpam-2779	678	1	it	it	PRON
ejpam-2779	678	2	is	be	AUX
ejpam-2779	678	3	similar	similar	ADJ
ejpam-2779	678	4	to	to	ADP
ejpam-2779	678	5	the	the	DET
ejpam-2779	678	6	proof	proof	NOUN
ejpam-2779	678	7	of	of	ADP
ejpam-2779	678	8	[	[	X
ejpam-2779	678	9	[	[	X
ejpam-2779	678	10	4	4	NUM
ejpam-2779	678	11	]	]	PUNCT
ejpam-2779	678	12	,	,	PUNCT
ejpam-2779	678	13	theorem	theorem	VERB
ejpam-2779	678	14	3.20	3.20	NUM
ejpam-2779	678	15	]	]	PUNCT
ejpam-2779	678	16	.	.	PUNCT
ejpam-2779	679	1	by	by	ADP
ejpam-2779	679	2	theorem	theorem	NOUN
ejpam-2779	679	3	3	3	NUM
ejpam-2779	679	4	,	,	PUNCT
ejpam-2779	679	5	a	a	PRON
ejpam-2779	679	6	/	/	SYM
ejpam-2779	679	7	k	k	NOUN
ejpam-2779	679	8	is	be	AUX
ejpam-2779	679	9	a	a	DET
ejpam-2779	679	10	good	good	ADJ
ejpam-2779	679	11	pseudo	pseudo	NOUN
ejpam-2779	679	12	-	-	ADJ
ejpam-2779	679	13	bck	bck	ADJ
ejpam-2779	679	14	algebra	algebra	NOUN
ejpam-2779	679	15	that	that	PRON
ejpam-2779	679	16	is	be	AUX
ejpam-2779	679	17	a	a	DET
ejpam-2779	679	18	∧-semilattice	∧-semilattice	NOUN
ejpam-2779	679	19	and	and	CCONJ
ejpam-2779	679	20	s̃	s̃	PROPN
ejpam-2779	679	21	on	on	ADP
ejpam-2779	679	22	a	a	DET
ejpam-2779	679	23	/	/	SYM
ejpam-2779	679	24	k	k	PROPN
ejpam-2779	679	25	is	be	AUX
ejpam-2779	679	26	a	a	DET
ejpam-2779	679	27	bosbach	bosbach	ADJ
ejpam-2779	679	28	state	state	NOUN
ejpam-2779	679	29	such	such	ADJ
ejpam-2779	679	30	that	that	DET
ejpam-2779	679	31	ker(s̃	ker(s̃	NOUN
ejpam-2779	679	32	)	)	PUNCT
ejpam-2779	679	33	=	=	PUNCT
ejpam-2779	680	1	{	{	PUNCT
ejpam-2779	680	2	0	0	NUM
ejpam-2779	680	3	/	/	SYM
ejpam-2779	680	4	k	k	NOUN
ejpam-2779	680	5	}	}	PUNCT
ejpam-2779	680	6	.	.	PUNCT
ejpam-2779	681	1	due	due	ADP
ejpam-2779	681	2	to	to	ADP
ejpam-2779	681	3	[	[	X
ejpam-2779	681	4	[	[	X
ejpam-2779	681	5	20	20	NUM
ejpam-2779	681	6	]	]	PUNCT
ejpam-2779	681	7	,	,	PUNCT
ejpam-2779	681	8	proposition	proposition	NOUN
ejpam-2779	681	9	3.4.7	3.4.7	NOUN
ejpam-2779	681	10	]	]	PUNCT
ejpam-2779	681	11	,	,	PUNCT
ejpam-2779	681	12	(	(	PUNCT
ejpam-2779	681	13	a	a	DET
ejpam-2779	681	14	/	/	SYM
ejpam-2779	681	15	k)/ker(s̃	k)/ker(s̃	NOUN
ejpam-2779	681	16	)	)	PUNCT
ejpam-2779	681	17	is	be	AUX
ejpam-2779	681	18	term	term	NOUN
ejpam-2779	681	19	-	-	PUNCT
ejpam-2779	681	20	equivalent	equivalent	ADJ
ejpam-2779	681	21	to	to	ADP
ejpam-2779	681	22	an	an	DET
ejpam-2779	681	23	mv	mv	NOUN
ejpam-2779	681	24	-	-	NOUN
ejpam-2779	681	25	algebra	algebra	NOUN
ejpam-2779	681	26	that	that	PRON
ejpam-2779	681	27	is	be	AUX
ejpam-2779	681	28	archimedean	archimedean	ADJ
ejpam-2779	681	29	and	and	CCONJ
ejpam-2779	681	30	s̃	s̃	PROPN
ejpam-2779	681	31	is	be	AUX
ejpam-2779	681	32	an	an	DET
ejpam-2779	681	33	mvstate	mvstate	NOUN
ejpam-2779	681	34	on	on	ADP
ejpam-2779	681	35	it	it	PRON
ejpam-2779	681	36	.	.	PUNCT
ejpam-2779	682	1	since	since	SCONJ
ejpam-2779	682	2	a	a	DET
ejpam-2779	682	3	/	/	SYM
ejpam-2779	682	4	k	k	NOUN
ejpam-2779	682	5	=	=	X
ejpam-2779	682	6	(	(	PUNCT
ejpam-2779	682	7	a	a	DET
ejpam-2779	682	8	/	/	SYM
ejpam-2779	682	9	k)/ker(s̃	k)/ker(s̃	NOUN
ejpam-2779	682	10	)	)	PUNCT
ejpam-2779	682	11	,	,	PUNCT
ejpam-2779	682	12	the	the	DET
ejpam-2779	682	13	same	same	ADJ
ejpam-2779	682	14	is	be	AUX
ejpam-2779	682	15	true	true	ADJ
ejpam-2779	682	16	also	also	ADV
ejpam-2779	682	17	for	for	ADP
ejpam-2779	682	18	a	a	DET
ejpam-2779	682	19	/	/	SYM
ejpam-2779	682	20	k	k	NOUN
ejpam-2779	682	21	,	,	PUNCT
ejpam-2779	682	22	and	and	CCONJ
ejpam-2779	682	23	this	this	PRON
ejpam-2779	682	24	proves	prove	VERB
ejpam-2779	682	25	the	the	DET
ejpam-2779	682	26	theorem	theorem	NOUN
ejpam-2779	682	27	.	.	PROPN
ejpam-2779	683	1	in	in	ADP
ejpam-2779	683	2	the	the	DET
ejpam-2779	683	3	following	following	NOUN
ejpam-2779	683	4	,	,	PUNCT
ejpam-2779	683	5	we	we	PRON
ejpam-2779	683	6	give	give	VERB
ejpam-2779	683	7	properties	property	NOUN
ejpam-2779	683	8	of	of	ADP
ejpam-2779	683	9	state	state	NOUN
ejpam-2779	683	10	-	-	PUNCT
ejpam-2779	683	11	morphisms	morphism	NOUN
ejpam-2779	683	12	on	on	ADP
ejpam-2779	683	13	lbp	lbp	PROPN
ejpam-2779	683	14	-	-	PUNCT
ejpam-2779	683	15	bci	bci	PROPN
ejpam-2779	683	16	algebras	algebra	NOUN
ejpam-2779	683	17	.	.	PUNCT
ejpam-2779	684	1	lemma	lemma	PROPN
ejpam-2779	684	2	1	1	X
ejpam-2779	684	3	.	.	PUNCT
ejpam-2779	685	1	let	let	VERB
ejpam-2779	685	2	a	a	PRON
ejpam-2779	685	3	be	be	AUX
ejpam-2779	685	4	a	a	DET
ejpam-2779	685	5	lbp	lbp	NOUN
ejpam-2779	685	6	-	-	PUNCT
ejpam-2779	685	7	bci	bci	NOUN
ejpam-2779	685	8	algebra	algebra	NOUN
ejpam-2779	685	9	and	and	CCONJ
ejpam-2779	685	10	m	m	AUX
ejpam-2779	685	11	be	be	AUX
ejpam-2779	685	12	a	a	DET
ejpam-2779	685	13	state	state	NOUN
ejpam-2779	685	14	-	-	PUNCT
ejpam-2779	685	15	morphism	morphism	NOUN
ejpam-2779	685	16	on	on	ADP
ejpam-2779	685	17	a.	a.	NOUN
ejpam-2779	685	18	then	then	ADV
ejpam-2779	685	19	we	we	PRON
ejpam-2779	685	20	have	have	VERB
ejpam-2779	685	21	the	the	DET
ejpam-2779	685	22	following	following	NOUN
ejpam-2779	685	23	.	.	PUNCT
ejpam-2779	686	1	(	(	PUNCT
ejpam-2779	686	2	1	1	X
ejpam-2779	686	3	)	)	PUNCT
ejpam-2779	686	4	m(y−∼	m(y−∼	NOUN
ejpam-2779	686	5	∗	∗	NOUN
ejpam-2779	686	6	x∼	x∼	PROPN
ejpam-2779	686	7	)	)	PUNCT
ejpam-2779	686	8	=	=	SYM
ejpam-2779	686	9	min{m(x	min{m(x	PROPN
ejpam-2779	686	10	)	)	PUNCT
ejpam-2779	687	1	+	+	NOUN
ejpam-2779	687	2	m(y	m(y	NOUN
ejpam-2779	687	3	)	)	PUNCT
ejpam-2779	687	4	,	,	PUNCT
ejpam-2779	687	5	1	1	NUM
ejpam-2779	687	6	}	}	PUNCT
ejpam-2779	687	7	,	,	PUNCT
ejpam-2779	687	8	for	for	ADP
ejpam-2779	687	9	all	all	DET
ejpam-2779	687	10	a	a	DET
ejpam-2779	687	11	∈m(a	∈m(a	NOUN
ejpam-2779	687	12	)	)	PUNCT
ejpam-2779	687	13	and	and	CCONJ
ejpam-2779	687	14	x	x	NOUN
ejpam-2779	687	15	,	,	PUNCT
ejpam-2779	687	16	y	y	PROPN
ejpam-2779	687	17	∈	∈	PROPN
ejpam-2779	687	18	v	v	ADP
ejpam-2779	687	19	(	(	PUNCT
ejpam-2779	687	20	a	a	NOUN
ejpam-2779	687	21	)	)	PUNCT
ejpam-2779	687	22	.	.	PUNCT
ejpam-2779	688	1	(	(	PUNCT
ejpam-2779	688	2	2	2	X
ejpam-2779	688	3	)	)	PUNCT
ejpam-2779	688	4	m(x∼−	m(x∼−	NOUN
ejpam-2779	688	5	◦	◦	NOUN
ejpam-2779	688	6	y−	y−	NOUN
ejpam-2779	688	7	)	)	PUNCT
ejpam-2779	688	8	=	=	SYM
ejpam-2779	688	9	min{m(x	min{m(x	PROPN
ejpam-2779	688	10	)	)	PUNCT
ejpam-2779	689	1	+	+	NOUN
ejpam-2779	689	2	m(y	m(y	NOUN
ejpam-2779	689	3	)	)	PUNCT
ejpam-2779	689	4	,	,	PUNCT
ejpam-2779	689	5	1	1	NUM
ejpam-2779	689	6	}	}	PUNCT
ejpam-2779	689	7	,	,	PUNCT
ejpam-2779	689	8	for	for	ADP
ejpam-2779	689	9	all	all	DET
ejpam-2779	689	10	a	a	DET
ejpam-2779	689	11	∈m(a	∈m(a	NOUN
ejpam-2779	689	12	)	)	PUNCT
ejpam-2779	689	13	and	and	CCONJ
ejpam-2779	689	14	x	x	NOUN
ejpam-2779	689	15	,	,	PUNCT
ejpam-2779	689	16	y	y	PROPN
ejpam-2779	689	17	∈	∈	PROPN
ejpam-2779	689	18	v	v	ADP
ejpam-2779	689	19	(	(	PUNCT
ejpam-2779	689	20	a	a	NOUN
ejpam-2779	689	21	)	)	PUNCT
ejpam-2779	689	22	.	.	PUNCT
ejpam-2779	690	1	proof	proof	NOUN
ejpam-2779	690	2	.	.	PUNCT
ejpam-2779	691	1	assume	assume	VERB
ejpam-2779	691	2	that	that	SCONJ
ejpam-2779	691	3	m	m	PROPN
ejpam-2779	691	4	is	be	AUX
ejpam-2779	691	5	a	a	DET
ejpam-2779	691	6	state	state	NOUN
ejpam-2779	691	7	-	-	PUNCT
ejpam-2779	691	8	morphism	morphism	NOUN
ejpam-2779	691	9	on	on	ADP
ejpam-2779	691	10	a	a	PRON
ejpam-2779	691	11	,	,	PUNCT
ejpam-2779	691	12	so	so	SCONJ
ejpam-2779	691	13	it	it	PRON
ejpam-2779	691	14	is	be	AUX
ejpam-2779	691	15	a	a	DET
ejpam-2779	691	16	bosbach	bosbach	ADJ
ejpam-2779	691	17	state	state	NOUN
ejpam-2779	691	18	on	on	ADP
ejpam-2779	691	19	a.	a.	NOUN
ejpam-2779	691	20	by	by	ADP
ejpam-2779	691	21	propositions	proposition	NOUN
ejpam-2779	691	22	19	19	NUM
ejpam-2779	691	23	and	and	CCONJ
ejpam-2779	691	24	20	20	NUM
ejpam-2779	691	25	,	,	PUNCT
ejpam-2779	691	26	for	for	ADP
ejpam-2779	691	27	for	for	ADP
ejpam-2779	691	28	all	all	DET
ejpam-2779	691	29	a	a	DET
ejpam-2779	691	30	∈	∈	PROPN
ejpam-2779	691	31	m(a	m(a	PROPN
ejpam-2779	691	32	)	)	PUNCT
ejpam-2779	691	33	and	and	CCONJ
ejpam-2779	691	34	x	x	X
ejpam-2779	691	35	,	,	PUNCT
ejpam-2779	691	36	y	y	PROPN
ejpam-2779	691	37	∈	∈	PROPN
ejpam-2779	691	38	v	v	ADP
ejpam-2779	691	39	(	(	PUNCT
ejpam-2779	691	40	a	a	NOUN
ejpam-2779	691	41	)	)	PUNCT
ejpam-2779	691	42	,	,	PUNCT
ejpam-2779	691	43	we	we	PRON
ejpam-2779	691	44	have	have	VERB
ejpam-2779	691	45	m(y−∼	m(y−∼	NOUN
ejpam-2779	691	46	∗	∗	NOUN
ejpam-2779	691	47	x∼	x∼	PROPN
ejpam-2779	691	48	)	)	PUNCT
ejpam-2779	692	1	=	=	PUNCT
ejpam-2779	692	2	m(y	m(y	NOUN
ejpam-2779	692	3	∗	∗	NOUN
ejpam-2779	692	4	x∼	x∼	PROPN
ejpam-2779	692	5	)	)	PUNCT
ejpam-2779	692	6	=	=	PUNCT
ejpam-2779	692	7	m(x∼	m(x∼	X
ejpam-2779	692	8	)	)	PUNCT
ejpam-2779	692	9	→	→	SYM
ejpam-2779	692	10	l	l	NOUN
ejpam-2779	692	11	m(y	m(y	NOUN
ejpam-2779	692	12	)	)	PUNCT
ejpam-2779	693	1	=	=	PUNCT
ejpam-2779	693	2	m(x)∼	m(x)∼	PROPN
ejpam-2779	693	3	→	→	SYM
ejpam-2779	693	4	l	l	NOUN
ejpam-2779	693	5	m(y	m(y	NOUN
ejpam-2779	693	6	)	)	PUNCT
ejpam-2779	694	1	=	=	SYM
ejpam-2779	694	2	min{1	min{1	NOUN
ejpam-2779	695	1	−	−	PROPN
ejpam-2779	696	1	m(x)∼	m(x)∼	PROPN
ejpam-2779	696	2	+	+	PROPN
ejpam-2779	696	3	m(y	m(y	NOUN
ejpam-2779	696	4	)	)	PUNCT
ejpam-2779	696	5	,	,	PUNCT
ejpam-2779	696	6	1	1	X
ejpam-2779	696	7	}	}	PUNCT
ejpam-2779	696	8	=	=	SYM
ejpam-2779	696	9	min{m(x	min{m(x	PROPN
ejpam-2779	696	10	)	)	PUNCT
ejpam-2779	696	11	+	+	SYM
ejpam-2779	696	12	m(y	m(y	NOUN
ejpam-2779	696	13	)	)	PUNCT
ejpam-2779	696	14	,	,	PUNCT
ejpam-2779	696	15	1	1	NUM
ejpam-2779	696	16	}	}	PUNCT
ejpam-2779	696	17	.	.	PUNCT
ejpam-2779	697	1	similarly	similarly	ADV
ejpam-2779	697	2	we	we	PRON
ejpam-2779	697	3	can	can	AUX
ejpam-2779	697	4	prove	prove	VERB
ejpam-2779	697	5	m(x∼−	m(x∼−	NOUN
ejpam-2779	697	6	◦	◦	PROPN
ejpam-2779	697	7	y−	y−	NOUN
ejpam-2779	697	8	)	)	PUNCT
ejpam-2779	697	9	=	=	SYM
ejpam-2779	697	10	min{m(x	min{m(x	PROPN
ejpam-2779	697	11	)	)	PUNCT
ejpam-2779	697	12	+	+	SYM
ejpam-2779	697	13	m(y	m(y	NOUN
ejpam-2779	697	14	)	)	PUNCT
ejpam-2779	697	15	,	,	PUNCT
ejpam-2779	697	16	1	1	NUM
ejpam-2779	697	17	}	}	PUNCT
ejpam-2779	697	18	,	,	PUNCT
ejpam-2779	697	19	for	for	ADP
ejpam-2779	697	20	all	all	DET
ejpam-2779	697	21	a	a	DET
ejpam-2779	697	22	∈m(a	∈m(a	NOUN
ejpam-2779	697	23	)	)	PUNCT
ejpam-2779	697	24	and	and	CCONJ
ejpam-2779	697	25	x	x	NOUN
ejpam-2779	697	26	,	,	PUNCT
ejpam-2779	697	27	y	y	PROPN
ejpam-2779	697	28	∈	∈	PROPN
ejpam-2779	697	29	v	v	ADP
ejpam-2779	697	30	(	(	PUNCT
ejpam-2779	697	31	a	a	NOUN
ejpam-2779	697	32	)	)	PUNCT
ejpam-2779	697	33	.	.	PUNCT
ejpam-2779	698	1	proposition	proposition	NOUN
ejpam-2779	698	2	30	30	NUM
ejpam-2779	698	3	.	.	PUNCT
ejpam-2779	699	1	let	let	VERB
ejpam-2779	699	2	a	a	PRON
ejpam-2779	699	3	be	be	AUX
ejpam-2779	699	4	a	a	DET
ejpam-2779	699	5	lbp	lbp	NOUN
ejpam-2779	699	6	-	-	PUNCT
ejpam-2779	699	7	bci	bci	NOUN
ejpam-2779	699	8	algebra	algebra	NOUN
ejpam-2779	699	9	and	and	CCONJ
ejpam-2779	699	10	s	s	AUX
ejpam-2779	699	11	be	be	AUX
ejpam-2779	699	12	a	a	DET
ejpam-2779	699	13	bosbach	bosbach	ADJ
ejpam-2779	699	14	state	state	NOUN
ejpam-2779	699	15	on	on	ADP
ejpam-2779	699	16	a.	a.	NOUN
ejpam-2779	699	17	then	then	ADV
ejpam-2779	699	18	the	the	DET
ejpam-2779	699	19	following	following	NOUN
ejpam-2779	699	20	are	be	AUX
ejpam-2779	699	21	equivalent	equivalent	ADJ
ejpam-2779	699	22	:	:	PUNCT
ejpam-2779	699	23	(	(	PUNCT
ejpam-2779	699	24	1	1	X
ejpam-2779	699	25	)	)	PUNCT
ejpam-2779	699	26	s	s	VERB
ejpam-2779	699	27	is	be	AUX
ejpam-2779	699	28	a	a	DET
ejpam-2779	699	29	state	state	NOUN
ejpam-2779	699	30	-	-	PUNCT
ejpam-2779	699	31	morphism	morphism	NOUN
ejpam-2779	699	32	.	.	PUNCT
ejpam-2779	700	1	(	(	PUNCT
ejpam-2779	700	2	2	2	X
ejpam-2779	700	3	)	)	PUNCT
ejpam-2779	700	4	ker(s	ker(s	PROPN
ejpam-2779	700	5	)	)	PUNCT
ejpam-2779	700	6	is	be	AUX
ejpam-2779	700	7	a	a	DET
ejpam-2779	700	8	maximal	maximal	ADJ
ejpam-2779	700	9	ideal	ideal	NOUN
ejpam-2779	700	10	of	of	ADP
ejpam-2779	700	11	a.	a.	NOUN
ejpam-2779	700	12	proof	proof	NOUN
ejpam-2779	700	13	.	.	PUNCT
ejpam-2779	701	1	it	it	PRON
ejpam-2779	701	2	is	be	AUX
ejpam-2779	701	3	similar	similar	ADJ
ejpam-2779	701	4	to	to	ADP
ejpam-2779	701	5	the	the	DET
ejpam-2779	701	6	proof	proof	NOUN
ejpam-2779	701	7	of	of	ADP
ejpam-2779	701	8	[	[	X
ejpam-2779	701	9	[	[	X
ejpam-2779	701	10	4	4	NUM
ejpam-2779	701	11	]	]	PUNCT
ejpam-2779	701	12	,	,	PUNCT
ejpam-2779	701	13	proposition	proposition	NOUN
ejpam-2779	701	14	3.22	3.22	NUM
ejpam-2779	701	15	]	]	PUNCT
ejpam-2779	701	16	.	.	PUNCT
ejpam-2779	702	1	x.l	x.l	PROPN
ejpam-2779	702	2	.	.	PUNCT
ejpam-2779	703	1	xin	xin	PROPN
ejpam-2779	703	2	,	,	PUNCT
ejpam-2779	703	3	y.j	y.j	PROPN
ejpam-2779	703	4	.	.	PUNCT
ejpam-2779	703	5	li	li	PROPN
ejpam-2779	703	6	,	,	PUNCT
ejpam-2779	703	7	y.l	y.l	PROPN
ejpam-2779	703	8	.	.	PROPN
ejpam-2779	703	9	fu	fu	PROPN
ejpam-2779	703	10	/	/	SYM
ejpam-2779	703	11	eur	eur	PROPN
ejpam-2779	703	12	.	.	PUNCT
ejpam-2779	704	1	j.	j.	PROPN
ejpam-2779	704	2	pure	pure	PROPN
ejpam-2779	704	3	appl	appl	PROPN
ejpam-2779	704	4	.	.	PROPN
ejpam-2779	704	5	math	math	PROPN
ejpam-2779	704	6	,	,	PUNCT
ejpam-2779	704	7	10	10	NUM
ejpam-2779	704	8	(	(	PUNCT
ejpam-2779	704	9	3	3	NUM
ejpam-2779	704	10	)	)	PUNCT
ejpam-2779	704	11	(	(	PUNCT
ejpam-2779	704	12	2017	2017	NUM
ejpam-2779	704	13	)	)	PUNCT
ejpam-2779	704	14	,	,	PUNCT
ejpam-2779	704	15	455	455	NUM
ejpam-2779	704	16	-	-	SYM
ejpam-2779	704	17	472	472	NUM
ejpam-2779	704	18	470	470	NUM
ejpam-2779	704	19	lemma	lemma	PROPN
ejpam-2779	704	20	2	2	X
ejpam-2779	704	21	.	.	PUNCT
ejpam-2779	705	1	let	let	VERB
ejpam-2779	705	2	m	m	PRON
ejpam-2779	705	3	be	be	AUX
ejpam-2779	705	4	a	a	DET
ejpam-2779	705	5	state	state	NOUN
ejpam-2779	705	6	-	-	PUNCT
ejpam-2779	705	7	morphism	morphism	NOUN
ejpam-2779	705	8	on	on	ADP
ejpam-2779	705	9	a	a	DET
ejpam-2779	705	10	lbp	lbp	NOUN
ejpam-2779	705	11	-	-	PUNCT
ejpam-2779	705	12	bci	bci	PROPN
ejpam-2779	705	13	algebra	algebra	NOUN
ejpam-2779	705	14	a	a	PRON
ejpam-2779	705	15	and	and	CCONJ
ejpam-2779	705	16	k	k	PROPN
ejpam-2779	705	17	=	=	SYM
ejpam-2779	705	18	ker(m	ker(m	PROPN
ejpam-2779	705	19	)	)	PUNCT
ejpam-2779	705	20	.	.	PUNCT
ejpam-2779	706	1	then	then	ADV
ejpam-2779	706	2	(	(	PUNCT
ejpam-2779	706	3	1	1	X
ejpam-2779	706	4	)	)	PUNCT
ejpam-2779	706	5	a	a	PROPN
ejpam-2779	706	6	/	/	SYM
ejpam-2779	706	7	k	k	NOUN
ejpam-2779	706	8	≤	≤	PROPN
ejpam-2779	706	9	b	b	X
ejpam-2779	706	10	/	/	SYM
ejpam-2779	706	11	k	k	NOUN
ejpam-2779	706	12	if	if	SCONJ
ejpam-2779	706	13	and	and	CCONJ
ejpam-2779	706	14	only	only	ADV
ejpam-2779	706	15	if	if	SCONJ
ejpam-2779	706	16	m(a	m(a	NOUN
ejpam-2779	706	17	)	)	PUNCT
ejpam-2779	706	18	≤	≤	NUM
ejpam-2779	706	19	m(b	m(b	NOUN
ejpam-2779	706	20	)	)	PUNCT
ejpam-2779	706	21	,	,	PUNCT
ejpam-2779	706	22	(	(	PUNCT
ejpam-2779	706	23	2	2	X
ejpam-2779	706	24	)	)	PUNCT
ejpam-2779	706	25	a	a	PRON
ejpam-2779	706	26	/	/	SYM
ejpam-2779	706	27	k	k	NOUN
ejpam-2779	706	28	=	=	SYM
ejpam-2779	706	29	b	b	PROPN
ejpam-2779	706	30	/	/	SYM
ejpam-2779	706	31	k	k	NOUN
ejpam-2779	706	32	if	if	SCONJ
ejpam-2779	706	33	and	and	CCONJ
ejpam-2779	706	34	only	only	ADV
ejpam-2779	706	35	if	if	SCONJ
ejpam-2779	706	36	m(a	m(a	NOUN
ejpam-2779	706	37	)	)	PUNCT
ejpam-2779	706	38	=	=	SYM
ejpam-2779	706	39	m(b	m(b	NOUN
ejpam-2779	706	40	)	)	PUNCT
ejpam-2779	706	41	.	.	PUNCT
ejpam-2779	707	1	proof	proof	NOUN
ejpam-2779	707	2	.	.	PUNCT
ejpam-2779	708	1	it	it	PRON
ejpam-2779	708	2	is	be	AUX
ejpam-2779	708	3	similar	similar	ADJ
ejpam-2779	708	4	to	to	ADP
ejpam-2779	708	5	the	the	DET
ejpam-2779	708	6	proof	proof	NOUN
ejpam-2779	708	7	of	of	ADP
ejpam-2779	708	8	[	[	X
ejpam-2779	708	9	[	[	X
ejpam-2779	708	10	4	4	NUM
ejpam-2779	708	11	]	]	PUNCT
ejpam-2779	708	12	,	,	PUNCT
ejpam-2779	708	13	lemma	lemma	PROPN
ejpam-2779	708	14	3.23	3.23	NUM
ejpam-2779	708	15	]	]	PUNCT
ejpam-2779	708	16	.	.	PUNCT
ejpam-2779	709	1	proposition	proposition	NOUN
ejpam-2779	709	2	31	31	NUM
ejpam-2779	709	3	.	.	PUNCT
ejpam-2779	710	1	let	let	VERB
ejpam-2779	710	2	a	a	PRON
ejpam-2779	710	3	be	be	AUX
ejpam-2779	710	4	a	a	DET
ejpam-2779	710	5	lbp	lbp	NOUN
ejpam-2779	710	6	-	-	PUNCT
ejpam-2779	710	7	bci	bci	NOUN
ejpam-2779	710	8	algebra	algebra	NOUN
ejpam-2779	710	9	and	and	CCONJ
ejpam-2779	710	10	m1,m2	m1,m2	PROPN
ejpam-2779	710	11	be	be	AUX
ejpam-2779	710	12	two	two	NUM
ejpam-2779	710	13	state	state	NOUN
ejpam-2779	710	14	-	-	PUNCT
ejpam-2779	710	15	morphisms	morphism	NOUN
ejpam-2779	710	16	on	on	ADP
ejpam-2779	710	17	a	a	DET
ejpam-2779	710	18	such	such	ADJ
ejpam-2779	711	1	that	that	SCONJ
ejpam-2779	711	2	ker(m1	ker(m1	NOUN
ejpam-2779	711	3	)	)	PUNCT
ejpam-2779	711	4	=	=	SYM
ejpam-2779	711	5	ker(m2	ker(m2	NOUN
ejpam-2779	711	6	)	)	PUNCT
ejpam-2779	711	7	.	.	PUNCT
ejpam-2779	712	1	then	then	ADV
ejpam-2779	712	2	m1	m1	PROPN
ejpam-2779	712	3	=	=	SYM
ejpam-2779	712	4	m2	m2	PROPN
ejpam-2779	712	5	.	.	PUNCT
ejpam-2779	712	6	proof	proof	NOUN
ejpam-2779	712	7	.	.	PUNCT
ejpam-2779	713	1	by	by	ADP
ejpam-2779	713	2	proposition	proposition	NOUN
ejpam-2779	713	3	23	23	NUM
ejpam-2779	713	4	,	,	PUNCT
ejpam-2779	713	5	m1	m1	PROPN
ejpam-2779	713	6	and	and	CCONJ
ejpam-2779	713	7	m1	m1	PROPN
ejpam-2779	713	8	are	be	AUX
ejpam-2779	713	9	two	two	NUM
ejpam-2779	713	10	bosbach	bosbach	ADJ
ejpam-2779	713	11	states	state	NOUN
ejpam-2779	713	12	on	on	ADP
ejpam-2779	713	13	a.	a.	NOUN
ejpam-2779	713	14	since	since	SCONJ
ejpam-2779	713	15	ker(m1	ker(m1	NOUN
ejpam-2779	713	16	)	)	PUNCT
ejpam-2779	713	17	=	=	SYM
ejpam-2779	713	18	ker(m2	ker(m2	NOUN
ejpam-2779	713	19	)	)	PUNCT
ejpam-2779	713	20	,	,	PUNCT
ejpam-2779	713	21	we	we	PRON
ejpam-2779	713	22	have	have	VERB
ejpam-2779	713	23	a	a	DET
ejpam-2779	713	24	/	/	SYM
ejpam-2779	713	25	ker(m1	ker(m1	NOUN
ejpam-2779	713	26	)	)	PUNCT
ejpam-2779	713	27	=	=	SYM
ejpam-2779	713	28	a	a	X
ejpam-2779	713	29	/	/	SYM
ejpam-2779	713	30	ker(m2	ker(m2	NOUN
ejpam-2779	713	31	)	)	PUNCT
ejpam-2779	713	32	.	.	PUNCT
ejpam-2779	714	1	by	by	ADP
ejpam-2779	714	2	the	the	DET
ejpam-2779	714	3	proof	proof	NOUN
ejpam-2779	714	4	of	of	ADP
ejpam-2779	714	5	proposition	proposition	NOUN
ejpam-2779	714	6	30	30	NUM
ejpam-2779	714	7	,	,	PUNCT
ejpam-2779	714	8	we	we	PRON
ejpam-2779	714	9	have	have	VERB
ejpam-2779	714	10	that	that	PRON
ejpam-2779	714	11	a	a	X
ejpam-2779	714	12	/	/	SYM
ejpam-2779	714	13	ker(m1	ker(m1	NOUN
ejpam-2779	714	14	)	)	PUNCT
ejpam-2779	714	15	is	be	AUX
ejpam-2779	714	16	in	in	ADP
ejpam-2779	714	17	fact	fact	NOUN
ejpam-2779	714	18	an	an	DET
ejpam-2779	714	19	mv	mv	NOUN
ejpam-2779	714	20	-	-	NOUN
ejpam-2779	714	21	subalgebra	subalgebra	NOUN
ejpam-2779	714	22	of	of	ADP
ejpam-2779	714	23	the	the	DET
ejpam-2779	714	24	mv	mv	NOUN
ejpam-2779	714	25	-	-	NOUN
ejpam-2779	714	26	algebra	algebra	NOUN
ejpam-2779	714	27	of	of	ADP
ejpam-2779	714	28	the	the	DET
ejpam-2779	714	29	real	real	ADJ
ejpam-2779	714	30	interval	interval	NOUN
ejpam-2779	715	1	[	[	X
ejpam-2779	715	2	0	0	NUM
ejpam-2779	715	3	,	,	PUNCT
ejpam-2779	715	4	1	1	NUM
ejpam-2779	715	5	]	]	PUNCT
ejpam-2779	715	6	.	.	PUNCT
ejpam-2779	716	1	but	but	CCONJ
ejpam-2779	716	2	ker(m̂1	ker(m̂1	PROPN
ejpam-2779	716	3	)	)	PUNCT
ejpam-2779	717	1	=	=	PUNCT
ejpam-2779	717	2	0	0	NUM
ejpam-2779	717	3	/	/	SYM
ejpam-2779	717	4	k	k	NOUN
ejpam-2779	717	5	=	=	PUNCT
ejpam-2779	717	6	ker(m̂2	ker(m̂2	PROPN
ejpam-2779	717	7	)	)	PUNCT
ejpam-2779	717	8	.	.	PUNCT
ejpam-2779	718	1	hence	hence	ADV
ejpam-2779	718	2	,	,	PUNCT
ejpam-2779	718	3	by	by	ADP
ejpam-2779	718	4	[	[	X
ejpam-2779	718	5	[	[	X
ejpam-2779	718	6	11	11	NUM
ejpam-2779	718	7	]	]	PUNCT
ejpam-2779	718	8	,	,	PUNCT
ejpam-2779	718	9	proposition	proposition	NOUN
ejpam-2779	718	10	4.5	4.5	NUM
ejpam-2779	718	11	]	]	PUNCT
ejpam-2779	718	12	,	,	PUNCT
ejpam-2779	718	13	m̂1	m̂1	PROPN
ejpam-2779	718	14	=	=	SYM
ejpam-2779	718	15	m̂2	m̂2	PROPN
ejpam-2779	718	16	,	,	PUNCT
ejpam-2779	718	17	consequently	consequently	ADV
ejpam-2779	718	18	,	,	PUNCT
ejpam-2779	718	19	m1	m1	PROPN
ejpam-2779	718	20	=	=	SYM
ejpam-2779	718	21	m2	m2	PROPN
ejpam-2779	718	22	.	.	PUNCT
ejpam-2779	718	23	let	let	VERB
ejpam-2779	718	24	a	a	PRON
ejpam-2779	718	25	be	be	AUX
ejpam-2779	718	26	a	a	DET
ejpam-2779	718	27	lbp	lbp	NOUN
ejpam-2779	718	28	-	-	PUNCT
ejpam-2779	718	29	bci	bci	NOUN
ejpam-2779	718	30	algebra	algebra	NOUN
ejpam-2779	718	31	.	.	PUNCT
ejpam-2779	719	1	we	we	PRON
ejpam-2779	719	2	say	say	VERB
ejpam-2779	719	3	that	that	SCONJ
ejpam-2779	719	4	a	a	DET
ejpam-2779	719	5	bosbach	bosbach	ADJ
ejpam-2779	719	6	state	state	NOUN
ejpam-2779	719	7	s	s	NOUN
ejpam-2779	719	8	is	be	AUX
ejpam-2779	719	9	extremal	extremal	ADJ
ejpam-2779	719	10	if	if	SCONJ
ejpam-2779	719	11	for	for	ADP
ejpam-2779	719	12	any	any	DET
ejpam-2779	719	13	0	0	PUNCT
ejpam-2779	719	14	<	<	X
ejpam-2779	719	15	λ	λ	X
ejpam-2779	719	16	<	<	X
ejpam-2779	719	17	1	1	NUM
ejpam-2779	719	18	and	and	CCONJ
ejpam-2779	719	19	for	for	ADP
ejpam-2779	719	20	any	any	DET
ejpam-2779	719	21	two	two	NUM
ejpam-2779	719	22	bosbach	bosbach	ADJ
ejpam-2779	719	23	states	state	NOUN
ejpam-2779	719	24	s1	s1	NOUN
ejpam-2779	719	25	,	,	PUNCT
ejpam-2779	719	26	s2	s2	NOUN
ejpam-2779	719	27	on	on	ADP
ejpam-2779	719	28	a	a	DET
ejpam-2779	719	29	,	,	PUNCT
ejpam-2779	719	30	s	s	PART
ejpam-2779	719	31	=	=	X
ejpam-2779	719	32	λs1	λs1	X
ejpam-2779	719	33	+	+	CCONJ
ejpam-2779	719	34	(	(	PUNCT
ejpam-2779	719	35	1−λ)s2	1−λ)s2	NUM
ejpam-2779	719	36	implies	imply	VERB
ejpam-2779	719	37	s1	s1	PROPN
ejpam-2779	719	38	=	=	SYM
ejpam-2779	719	39	s2	s2	PROPN
ejpam-2779	719	40	.	.	PUNCT
ejpam-2779	720	1	summarizing	summarize	VERB
ejpam-2779	720	2	previous	previous	ADJ
ejpam-2779	720	3	characterizations	characterization	NOUN
ejpam-2779	720	4	of	of	ADP
ejpam-2779	720	5	state	state	NOUN
ejpam-2779	720	6	-	-	PUNCT
ejpam-2779	720	7	morphisms	morphism	NOUN
ejpam-2779	720	8	,	,	PUNCT
ejpam-2779	720	9	we	we	PRON
ejpam-2779	720	10	have	have	VERB
ejpam-2779	720	11	the	the	DET
ejpam-2779	720	12	following	follow	VERB
ejpam-2779	720	13	result	result	NOUN
ejpam-2779	720	14	.	.	PUNCT
ejpam-2779	721	1	theorem	theorem	NOUN
ejpam-2779	721	2	5	5	NUM
ejpam-2779	721	3	.	.	PUNCT
ejpam-2779	722	1	let	let	VERB
ejpam-2779	722	2	s	s	PRON
ejpam-2779	722	3	be	be	AUX
ejpam-2779	722	4	a	a	DET
ejpam-2779	722	5	bosbach	bosbach	ADJ
ejpam-2779	722	6	state	state	NOUN
ejpam-2779	722	7	on	on	ADP
ejpam-2779	722	8	a	a	DET
ejpam-2779	722	9	lbp	lbp	NOUN
ejpam-2779	722	10	-	-	PUNCT
ejpam-2779	722	11	bci	bci	PROPN
ejpam-2779	722	12	algebra	algebra	PROPN
ejpam-2779	722	13	a.	a.	NOUN
ejpam-2779	722	14	then	then	ADV
ejpam-2779	722	15	the	the	DET
ejpam-2779	722	16	following	follow	VERB
ejpam-2779	722	17	are	be	AUX
ejpam-2779	722	18	equivalent	equivalent	ADJ
ejpam-2779	722	19	:	:	PUNCT
ejpam-2779	722	20	(	(	PUNCT
ejpam-2779	722	21	1	1	X
ejpam-2779	722	22	)	)	PUNCT
ejpam-2779	722	23	s	s	VERB
ejpam-2779	722	24	is	be	AUX
ejpam-2779	722	25	an	an	DET
ejpam-2779	722	26	extremal	extremal	ADJ
ejpam-2779	722	27	bosbach	bosbach	NOUN
ejpam-2779	722	28	state	state	NOUN
ejpam-2779	722	29	.	.	PUNCT
ejpam-2779	723	1	(	(	PUNCT
ejpam-2779	723	2	2	2	X
ejpam-2779	723	3	)	)	PUNCT
ejpam-2779	723	4	s(x	s(x	PROPN
ejpam-2779	723	5	∧1	∧1	NUM
ejpam-2779	723	6	y	y	NOUN
ejpam-2779	723	7	)	)	PUNCT
ejpam-2779	723	8	=	=	SYM
ejpam-2779	723	9	max{s(x	max{s(x	PROPN
ejpam-2779	723	10	)	)	PUNCT
ejpam-2779	723	11	,	,	PUNCT
ejpam-2779	723	12	s(y	s(y	PROPN
ejpam-2779	723	13	)	)	PUNCT
ejpam-2779	723	14	}	}	PUNCT
ejpam-2779	723	15	for	for	ADP
ejpam-2779	723	16	all	all	DET
ejpam-2779	723	17	x	x	NOUN
ejpam-2779	723	18	,	,	PUNCT
ejpam-2779	723	19	y	y	PROPN
ejpam-2779	723	20	∈	∈	PROPN
ejpam-2779	723	21	a.	a.	NOUN
ejpam-2779	723	22	(	(	PUNCT
ejpam-2779	723	23	3	3	NUM
ejpam-2779	723	24	)	)	PUNCT
ejpam-2779	723	25	s(x	s(x	PROPN
ejpam-2779	723	26	∧2	∧2	PROPN
ejpam-2779	723	27	y	y	PROPN
ejpam-2779	723	28	)	)	PUNCT
ejpam-2779	723	29	=	=	SYM
ejpam-2779	723	30	max{s(x	max{s(x	PROPN
ejpam-2779	723	31	)	)	PUNCT
ejpam-2779	723	32	,	,	PUNCT
ejpam-2779	723	33	s(y	s(y	PROPN
ejpam-2779	723	34	)	)	PUNCT
ejpam-2779	723	35	}	}	PUNCT
ejpam-2779	723	36	for	for	ADP
ejpam-2779	723	37	all	all	DET
ejpam-2779	723	38	x	x	NOUN
ejpam-2779	723	39	,	,	PUNCT
ejpam-2779	723	40	y	y	PROPN
ejpam-2779	723	41	∈	∈	PROPN
ejpam-2779	723	42	a.	a.	NOUN
ejpam-2779	723	43	(	(	PUNCT
ejpam-2779	723	44	4	4	NUM
ejpam-2779	723	45	)	)	PUNCT
ejpam-2779	723	46	s	s	VERB
ejpam-2779	723	47	is	be	AUX
ejpam-2779	723	48	a	a	DET
ejpam-2779	723	49	state	state	NOUN
ejpam-2779	723	50	-	-	PUNCT
ejpam-2779	723	51	morphism	morphism	NOUN
ejpam-2779	723	52	.	.	PUNCT
ejpam-2779	724	1	(	(	PUNCT
ejpam-2779	724	2	5	5	X
ejpam-2779	724	3	)	)	PUNCT
ejpam-2779	724	4	ker(s	ker(s	PROPN
ejpam-2779	724	5	)	)	PUNCT
ejpam-2779	724	6	is	be	AUX
ejpam-2779	724	7	a	a	DET
ejpam-2779	724	8	maximal	maximal	ADJ
ejpam-2779	724	9	ideal	ideal	NOUN
ejpam-2779	724	10	.	.	PUNCT
ejpam-2779	725	1	proof	proof	NOUN
ejpam-2779	725	2	.	.	PUNCT
ejpam-2779	726	1	it	it	PRON
ejpam-2779	726	2	is	be	AUX
ejpam-2779	726	3	similar	similar	ADJ
ejpam-2779	726	4	to	to	ADP
ejpam-2779	726	5	the	the	DET
ejpam-2779	726	6	proof	proof	NOUN
ejpam-2779	726	7	of	of	ADP
ejpam-2779	726	8	[	[	X
ejpam-2779	726	9	[	[	X
ejpam-2779	726	10	4	4	NUM
ejpam-2779	726	11	]	]	PUNCT
ejpam-2779	726	12	,	,	PUNCT
ejpam-2779	726	13	theorem	theorem	VERB
ejpam-2779	726	14	3.26	3.26	NUM
ejpam-2779	726	15	]	]	PUNCT
ejpam-2779	726	16	.	.	PUNCT
ejpam-2779	727	1	5	5	X
ejpam-2779	727	2	.	.	X
ejpam-2779	727	3	conclusions	conclusion	NOUN
ejpam-2779	727	4	until	until	ADP
ejpam-2779	727	5	now	now	ADV
ejpam-2779	727	6	,	,	PUNCT
ejpam-2779	727	7	the	the	DET
ejpam-2779	727	8	states	state	NOUN
ejpam-2779	727	9	on	on	ADP
ejpam-2779	727	10	unbounded	unbounded	ADJ
ejpam-2779	727	11	algebraic	algebraic	ADJ
ejpam-2779	727	12	structures	structure	NOUN
ejpam-2779	727	13	have	have	AUX
ejpam-2779	727	14	been	be	AUX
ejpam-2779	727	15	studied	study	VERB
ejpam-2779	727	16	for	for	ADP
ejpam-2779	727	17	hilbert	hilbert	NOUN
ejpam-2779	727	18	algebras	algebra	NOUN
ejpam-2779	727	19	and	and	CCONJ
ejpam-2779	727	20	integral	integral	ADJ
ejpam-2779	727	21	residuated	residuate	VERB
ejpam-2779	727	22	lattices	lattice	NOUN
ejpam-2779	727	23	in	in	ADP
ejpam-2779	727	24	[	[	X
ejpam-2779	727	25	2	2	NUM
ejpam-2779	727	26	]	]	PUNCT
ejpam-2779	727	27	and	and	CCONJ
ejpam-2779	727	28	[	[	X
ejpam-2779	727	29	6	6	NUM
ejpam-2779	727	30	]	]	PUNCT
ejpam-2779	727	31	,	,	PUNCT
ejpam-2779	727	32	respectively	respectively	ADV
ejpam-2779	727	33	.	.	PUNCT
ejpam-2779	728	1	in	in	ADP
ejpam-2779	728	2	this	this	DET
ejpam-2779	728	3	paper	paper	NOUN
ejpam-2779	728	4	,	,	PUNCT
ejpam-2779	728	5	we	we	PRON
ejpam-2779	728	6	first	first	ADV
ejpam-2779	728	7	study	study	VERB
ejpam-2779	728	8	state	state	NOUN
ejpam-2779	728	9	theory	theory	NOUN
ejpam-2779	728	10	on	on	ADP
ejpam-2779	728	11	non	non	ADJ
ejpam-2779	728	12	-	-	ADJ
ejpam-2779	728	13	bounded	bounded	ADJ
ejpam-2779	728	14	algebraic	algebraic	ADJ
ejpam-2779	728	15	structures	structure	NOUN
ejpam-2779	728	16	,	,	PUNCT
ejpam-2779	728	17	and	and	CCONJ
ejpam-2779	728	18	introduce	introduce	VERB
ejpam-2779	728	19	a	a	DET
ejpam-2779	728	20	notion	notion	NOUN
ejpam-2779	728	21	of	of	ADP
ejpam-2779	728	22	state	state	NOUN
ejpam-2779	728	23	on	on	ADP
ejpam-2779	728	24	pseudo	pseudo	NOUN
ejpam-2779	728	25	-	-	ADJ
ejpam-2779	728	26	bci	bci	ADJ
ejpam-2779	728	27	algebras	algebra	NOUN
ejpam-2779	728	28	.	.	PUNCT
ejpam-2779	729	1	in	in	ADP
ejpam-2779	729	2	order	order	NOUN
ejpam-2779	729	3	to	to	PART
ejpam-2779	729	4	adapt	adapt	VERB
ejpam-2779	729	5	a	a	DET
ejpam-2779	729	6	state	state	NOUN
ejpam-2779	729	7	to	to	ADP
ejpam-2779	729	8	pseudo	pseudo	NOUN
ejpam-2779	729	9	-	-	PUNCT
ejpam-2779	729	10	bci	bci	ADJ
ejpam-2779	729	11	algebras	algebra	NOUN
ejpam-2779	729	12	,	,	PUNCT
ejpam-2779	729	13	we	we	PRON
ejpam-2779	729	14	first	first	ADV
ejpam-2779	729	15	discuss	discuss	VERB
ejpam-2779	729	16	the	the	DET
ejpam-2779	729	17	structure	structure	NOUN
ejpam-2779	729	18	of	of	ADP
ejpam-2779	729	19	pseudo	pseudo	NOUN
ejpam-2779	729	20	-	-	ADJ
ejpam-2779	729	21	bci	bci	ADJ
ejpam-2779	729	22	algebras	algebra	NOUN
ejpam-2779	729	23	,	,	PUNCT
ejpam-2779	729	24	which	which	PRON
ejpam-2779	729	25	can	can	AUX
ejpam-2779	729	26	be	be	AUX
ejpam-2779	729	27	decomposed	decompose	VERB
ejpam-2779	729	28	in	in	ADP
ejpam-2779	729	29	to	to	ADP
ejpam-2779	729	30	the	the	DET
ejpam-2779	729	31	union	union	NOUN
ejpam-2779	729	32	of	of	ADP
ejpam-2779	729	33	it	it	PRON
ejpam-2779	729	34	’s	’	VERB
ejpam-2779	729	35	branches	branch	NOUN
ejpam-2779	729	36	.	.	PUNCT
ejpam-2779	730	1	note	note	VERB
ejpam-2779	730	2	that	that	SCONJ
ejpam-2779	730	3	for	for	ADP
ejpam-2779	730	4	all	all	DET
ejpam-2779	730	5	a	a	DET
ejpam-2779	730	6	∈	∈	PROPN
ejpam-2779	730	7	m(a	m(a	PROPN
ejpam-2779	730	8	)	)	PUNCT
ejpam-2779	730	9	and	and	CCONJ
ejpam-2779	730	10	a	a	DET
ejpam-2779	730	11	6=	6=	NUM
ejpam-2779	730	12	0	0	NUM
ejpam-2779	730	13	,	,	PUNCT
ejpam-2779	730	14	v	v	NOUN
ejpam-2779	730	15	(	(	PUNCT
ejpam-2779	730	16	a	a	NOUN
ejpam-2779	730	17	)	)	PUNCT
ejpam-2779	730	18	is	be	AUX
ejpam-2779	730	19	not	not	PART
ejpam-2779	730	20	a	a	DET
ejpam-2779	730	21	bck	bck	NOUN
ejpam-2779	730	22	-	-	PUNCT
ejpam-2779	730	23	algebra	algebra	NOUN
ejpam-2779	730	24	,	,	PUNCT
ejpam-2779	730	25	hence	hence	ADV
ejpam-2779	730	26	the	the	DET
ejpam-2779	730	27	structure	structure	NOUN
ejpam-2779	730	28	of	of	ADP
ejpam-2779	730	29	pseudo	pseudo	NOUN
ejpam-2779	730	30	-	-	ADJ
ejpam-2779	730	31	bci	bci	ADJ
ejpam-2779	730	32	algebras	algebra	NOUN
ejpam-2779	730	33	is	be	AUX
ejpam-2779	730	34	different	different	ADJ
ejpam-2779	730	35	from	from	ADP
ejpam-2779	730	36	the	the	DET
ejpam-2779	730	37	structure	structure	NOUN
ejpam-2779	730	38	of	of	ADP
ejpam-2779	730	39	pseudo	pseudo	NOUN
ejpam-2779	730	40	-	-	ADJ
ejpam-2779	730	41	bck	bck	ADJ
ejpam-2779	730	42	algebras	algebra	NOUN
ejpam-2779	730	43	.	.	PUNCT
ejpam-2779	731	1	therefore	therefore	ADV
ejpam-2779	731	2	it	it	PRON
ejpam-2779	731	3	is	be	AUX
ejpam-2779	731	4	valuable	valuable	ADJ
ejpam-2779	731	5	to	to	PART
ejpam-2779	731	6	study	study	VERB
ejpam-2779	731	7	state	state	NOUN
ejpam-2779	731	8	theory	theory	NOUN
ejpam-2779	731	9	on	on	ADP
ejpam-2779	731	10	pseudo	pseudo	NOUN
ejpam-2779	731	11	-	-	ADJ
ejpam-2779	731	12	bci	bci	ADJ
ejpam-2779	731	13	algebras	algebra	NOUN
ejpam-2779	731	14	.	.	PUNCT
ejpam-2779	732	1	moreover	moreover	ADV
ejpam-2779	732	2	we	we	PRON
ejpam-2779	732	3	introduce	introduce	VERB
ejpam-2779	732	4	a	a	DET
ejpam-2779	732	5	notion	notion	NOUN
ejpam-2779	732	6	of	of	ADP
ejpam-2779	732	7	local	local	ADJ
ejpam-2779	732	8	bounded	bounded	ADJ
ejpam-2779	732	9	pseudo	pseudo	NOUN
ejpam-2779	732	10	-	-	ADJ
ejpam-2779	732	11	bci	bci	ADJ
ejpam-2779	732	12	algebras	algebra	NOUN
ejpam-2779	732	13	and	and	CCONJ
ejpam-2779	732	14	set	set	VERB
ejpam-2779	732	15	up	up	ADP
ejpam-2779	732	16	the	the	DET
ejpam-2779	732	17	theory	theory	NOUN
ejpam-2779	732	18	of	of	ADP
ejpam-2779	732	19	states	state	NOUN
ejpam-2779	732	20	on	on	ADP
ejpam-2779	732	21	such	such	ADJ
ejpam-2779	732	22	algebraic	algebraic	ADJ
ejpam-2779	732	23	structure	structure	NOUN
ejpam-2779	732	24	.	.	PUNCT
ejpam-2779	733	1	we	we	PRON
ejpam-2779	733	2	also	also	ADV
ejpam-2779	733	3	introduce	introduce	VERB
ejpam-2779	733	4	a	a	DET
ejpam-2779	733	5	notion	notion	NOUN
ejpam-2779	733	6	of	of	ADP
ejpam-2779	733	7	state	state	NOUN
ejpam-2779	733	8	-	-	PUNCT
ejpam-2779	733	9	morphisms	morphism	NOUN
ejpam-2779	733	10	on	on	ADP
ejpam-2779	733	11	local	local	ADJ
ejpam-2779	733	12	bounded	bounded	ADJ
ejpam-2779	733	13	pseudo	pseudo	NOUN
ejpam-2779	733	14	-	-	ADJ
ejpam-2779	733	15	bci	bci	ADJ
ejpam-2779	733	16	algebras	algebra	NOUN
ejpam-2779	733	17	and	and	CCONJ
ejpam-2779	733	18	discuss	discuss	VERB
ejpam-2779	733	19	the	the	DET
ejpam-2779	733	20	relations	relation	NOUN
ejpam-2779	733	21	between	between	ADP
ejpam-2779	733	22	bosbach	bosbach	NOUN
ejpam-2779	733	23	states	state	NOUN
ejpam-2779	733	24	and	and	CCONJ
ejpam-2779	733	25	state	state	NOUN
ejpam-2779	733	26	-	-	PUNCT
ejpam-2779	733	27	morphisms	morphism	NOUN
ejpam-2779	733	28	.	.	PUNCT
ejpam-2779	734	1	by	by	ADP
ejpam-2779	734	2	use	use	NOUN
ejpam-2779	734	3	of	of	ADP
ejpam-2779	734	4	state	state	NOUN
ejpam-2779	734	5	’s	’s	PART
ejpam-2779	734	6	theory	theory	NOUN
ejpam-2779	734	7	,	,	PUNCT
ejpam-2779	734	8	we	we	PRON
ejpam-2779	734	9	discuss	discuss	VERB
ejpam-2779	734	10	the	the	DET
ejpam-2779	734	11	relation	relation	NOUN
ejpam-2779	734	12	between	between	ADP
ejpam-2779	734	13	pseudobci	pseudobci	NOUN
ejpam-2779	734	14	algebras	algebra	NOUN
ejpam-2779	734	15	and	and	CCONJ
ejpam-2779	734	16	mv	mv	PROPN
ejpam-2779	734	17	-	-	PUNCT
ejpam-2779	734	18	algebras	algebras	PROPN
ejpam-2779	734	19	.	.	PUNCT
ejpam-2779	735	1	in	in	ADP
ejpam-2779	735	2	the	the	DET
ejpam-2779	735	3	next	next	ADJ
ejpam-2779	735	4	work	work	NOUN
ejpam-2779	735	5	,	,	PUNCT
ejpam-2779	735	6	we	we	PRON
ejpam-2779	735	7	will	will	AUX
ejpam-2779	735	8	consider	consider	VERB
ejpam-2779	735	9	the	the	DET
ejpam-2779	735	10	following	follow	VERB
ejpam-2779	735	11	problem	problem	NOUN
ejpam-2779	735	12	:	:	PUNCT
ejpam-2779	735	13	satisfying	satisfy	VERB
ejpam-2779	735	14	what	what	PRON
ejpam-2779	735	15	apposite	apposite	ADP
ejpam-2779	735	16	conditions	condition	VERB
ejpam-2779	735	17	a	a	DET
ejpam-2779	735	18	local	local	ADJ
ejpam-2779	735	19	bounded	bounded	ADJ
ejpam-2779	735	20	pseudo	pseudo	NOUN
ejpam-2779	735	21	-	-	ADJ
ejpam-2779	735	22	bci	bci	ADJ
ejpam-2779	735	23	algebra	algebra	NOUN
ejpam-2779	735	24	admits	admit	VERB
ejpam-2779	735	25	a	a	DET
ejpam-2779	735	26	bosbach	bosbach	ADJ
ejpam-2779	735	27	state	state	NOUN
ejpam-2779	735	28	?	?	PUNCT
ejpam-2779	736	1	references	reference	NOUN
ejpam-2779	736	2	471	471	NUM
ejpam-2779	736	3	acknowledgements	acknowledgement	NOUN
ejpam-2779	736	4	this	this	DET
ejpam-2779	736	5	research	research	NOUN
ejpam-2779	736	6	is	be	AUX
ejpam-2779	736	7	partially	partially	ADV
ejpam-2779	736	8	supported	support	VERB
ejpam-2779	736	9	by	by	ADP
ejpam-2779	736	10	a	a	DET
ejpam-2779	736	11	grant	grant	NOUN
ejpam-2779	736	12	of	of	ADP
ejpam-2779	736	13	national	national	ADJ
ejpam-2779	736	14	natural	natural	ADJ
ejpam-2779	736	15	science	science	PROPN
ejpam-2779	736	16	foundation	foundation	PROPN
ejpam-2779	736	17	of	of	ADP
ejpam-2779	736	18	china	china	PROPN
ejpam-2779	736	19	(	(	PUNCT
ejpam-2779	736	20	11571281,61602359	11571281,61602359	NOUN
ejpam-2779	736	21	)	)	PUNCT
ejpam-2779	736	22	,	,	PUNCT
ejpam-2779	736	23	china	china	PROPN
ejpam-2779	736	24	postdoctoral	postdoctoral	PROPN
ejpam-2779	736	25	science	science	PROPN
ejpam-2779	736	26	foundation	foundation	PROPN
ejpam-2779	736	27	(	(	PUNCT
ejpam-2779	736	28	2015m582618	2015m582618	NUM
ejpam-2779	736	29	)	)	PUNCT
ejpam-2779	736	30	,	,	PUNCT
ejpam-2779	736	31	china	china	PROPN
ejpam-2779	736	32	111	111	NUM
ejpam-2779	736	33	project	project	NOUN
ejpam-2779	736	34	(	(	PUNCT
ejpam-2779	736	35	b16037	b16037	PROPN
ejpam-2779	736	36	)	)	PUNCT
ejpam-2779	736	37	.	.	PUNCT
ejpam-2779	737	1	references	reference	NOUN
ejpam-2779	737	2	[	[	X
ejpam-2779	737	3	1	1	NUM
ejpam-2779	737	4	]	]	PUNCT
ejpam-2779	737	5	l	l	NOUN
ejpam-2779	737	6	p	p	NOUN
ejpam-2779	737	7	belluce	belluce	NOUN
ejpam-2779	737	8	.	.	PUNCT
ejpam-2779	738	1	semisimple	semisimple	NOUN
ejpam-2779	738	2	and	and	CCONJ
ejpam-2779	738	3	complete	complete	ADJ
ejpam-2779	738	4	mv	mv	PROPN
ejpam-2779	738	5	-	-	PUNCT
ejpam-2779	738	6	algebras	algebra	NOUN
ejpam-2779	738	7	.	.	PUNCT
ejpam-2779	739	1	algebra	algebra	PROPN
ejpam-2779	739	2	univ	univ	PROPN
ejpam-2779	739	3	.	.	PROPN
ejpam-2779	739	4	,	,	PUNCT
ejpam-2779	739	5	29:1	29:1	NUM
ejpam-2779	739	6	-	-	SYM
ejpam-2779	739	7	9	9	NUM
ejpam-2779	739	8	,	,	PUNCT
ejpam-2779	739	9	1992	1992	NUM
ejpam-2779	739	10	.	.	PUNCT
ejpam-2779	740	1	[	[	X
ejpam-2779	740	2	2	2	NUM
ejpam-2779	740	3	]	]	X
ejpam-2779	740	4	c	c	X
ejpam-2779	740	5	buşneag	buşneag	NOUN
ejpam-2779	740	6	.	.	PUNCT
ejpam-2779	741	1	states	state	NOUN
ejpam-2779	741	2	on	on	ADP
ejpam-2779	741	3	hilbert	hilbert	PROPN
ejpam-2779	741	4	algebras	algebras	PROPN
ejpam-2779	741	5	.	.	PUNCT
ejpam-2779	742	1	studia	studia	PROPN
ejpam-2779	742	2	logica	logica	PROPN
ejpam-2779	742	3	,	,	PUNCT
ejpam-2779	742	4	94:177	94:177	NUM
ejpam-2779	742	5	-	-	SYM
ejpam-2779	742	6	188	188	NUM
ejpam-2779	742	7	,	,	PUNCT
ejpam-2779	742	8	2010	2010	NUM
ejpam-2779	742	9	.	.	PUNCT
ejpam-2779	743	1	[	[	X
ejpam-2779	743	2	3	3	X
ejpam-2779	743	3	]	]	X
ejpam-2779	743	4	c	c	PROPN
ejpam-2779	743	5	c	c	PROPN
ejpam-2779	743	6	chang	chang	PROPN
ejpam-2779	743	7	.	.	PUNCT
ejpam-2779	744	1	algebraic	algebraic	ADJ
ejpam-2779	744	2	analysis	analysis	NOUN
ejpam-2779	744	3	of	of	ADP
ejpam-2779	744	4	many	many	ADJ
ejpam-2779	744	5	valued	value	VERB
ejpam-2779	744	6	logics	logic	NOUN
ejpam-2779	744	7	.	.	PUNCT
ejpam-2779	745	1	transactions	transaction	NOUN
ejpam-2779	745	2	of	of	ADP
ejpam-2779	745	3	the	the	DET
ejpam-2779	745	4	american	american	PROPN
ejpam-2779	745	5	mathematical	mathematical	PROPN
ejpam-2779	745	6	society	society	NOUN
ejpam-2779	745	7	,	,	PUNCT
ejpam-2779	745	8	88(2):467	88(2):467	NOUN
ejpam-2779	745	9	-	-	SYM
ejpam-2779	745	10	490	490	NUM
ejpam-2779	745	11	,	,	PUNCT
ejpam-2779	745	12	1958	1958	NUM
ejpam-2779	745	13	.	.	PUNCT
ejpam-2779	746	1	[	[	X
ejpam-2779	746	2	4	4	NUM
ejpam-2779	746	3	]	]	X
ejpam-2779	746	4	l	l	NOUN
ejpam-2779	746	5	c	c	NOUN
ejpam-2779	746	6	ciungu	ciungu	NOUN
ejpam-2779	746	7	and	and	CCONJ
ejpam-2779	746	8	a	a	DET
ejpam-2779	746	9	dvurečenskij	dvurečenskij	PROPN
ejpam-2779	746	10	.	.	PUNCT
ejpam-2779	747	1	measures	measure	NOUN
ejpam-2779	747	2	,	,	PUNCT
ejpam-2779	747	3	states	state	NOUN
ejpam-2779	747	4	and	and	CCONJ
ejpam-2779	747	5	de	de	X
ejpam-2779	747	6	finetti	finetti	PROPN
ejpam-2779	747	7	maps	map	NOUN
ejpam-2779	747	8	on	on	ADP
ejpam-2779	747	9	pseudo	pseudo	NOUN
ejpam-2779	747	10	-	-	ADJ
ejpam-2779	747	11	bck	bck	ADJ
ejpam-2779	747	12	algebras	algebra	NOUN
ejpam-2779	747	13	.	.	PUNCT
ejpam-2779	748	1	fuzzy	fuzzy	ADJ
ejpam-2779	748	2	sets	set	NOUN
ejpam-2779	748	3	and	and	CCONJ
ejpam-2779	748	4	systems	system	NOUN
ejpam-2779	748	5	,	,	PUNCT
ejpam-2779	748	6	161(22):2870	161(22):2870	PROPN
ejpam-2779	748	7	-	-	SYM
ejpam-2779	748	8	2896	2896	NUM
ejpam-2779	748	9	,	,	PUNCT
ejpam-2779	748	10	2010	2010	NUM
ejpam-2779	748	11	.	.	PUNCT
ejpam-2779	749	1	[	[	X
ejpam-2779	749	2	5	5	NUM
ejpam-2779	749	3	]	]	PUNCT
ejpam-2779	749	4	l	l	NOUN
ejpam-2779	749	5	c	c	NOUN
ejpam-2779	749	6	ciungu	ciungu	NOUN
ejpam-2779	749	7	,	,	PUNCT
ejpam-2779	749	8	a	a	DET
ejpam-2779	749	9	dvurečenskij	dvurečenskij	PROPN
ejpam-2779	749	10	and	and	CCONJ
ejpam-2779	749	11	m	m	NOUN
ejpam-2779	749	12	hycko	hycko	NOUN
ejpam-2779	749	13	.	.	PUNCT
ejpam-2779	750	1	state	state	PROPN
ejpam-2779	750	2	bl	bl	PROPN
ejpam-2779	750	3	-	-	PUNCT
ejpam-2779	750	4	algebras	algebras	PROPN
ejpam-2779	750	5	.	.	PUNCT
ejpam-2779	751	1	soft	soft	ADJ
ejpam-2779	751	2	computing	computing	NOUN
ejpam-2779	751	3	,	,	PUNCT
ejpam-2779	751	4	15(4):619	15(4):619	NUM
ejpam-2779	751	5	-	-	SYM
ejpam-2779	751	6	634	634	NUM
ejpam-2779	751	7	,	,	PUNCT
ejpam-2779	751	8	2011	2011	NUM
ejpam-2779	751	9	.	.	PUNCT
ejpam-2779	752	1	[	[	X
ejpam-2779	752	2	6	6	NUM
ejpam-2779	752	3	]	]	PUNCT
ejpam-2779	752	4	l	l	NOUN
ejpam-2779	752	5	c	c	NOUN
ejpam-2779	752	6	ciungu	ciungu	NOUN
ejpam-2779	752	7	.	.	PUNCT
ejpam-2779	753	1	relative	relative	ADJ
ejpam-2779	753	2	negations	negation	NOUN
ejpam-2779	753	3	in	in	ADP
ejpam-2779	753	4	non	non	ADJ
ejpam-2779	753	5	-	-	ADJ
ejpam-2779	753	6	commutative	commutative	ADJ
ejpam-2779	753	7	fuzzy	fuzzy	ADJ
ejpam-2779	753	8	structures	structure	NOUN
ejpam-2779	753	9	.	.	PUNCT
ejpam-2779	754	1	soft	soft	ADJ
ejpam-2779	754	2	computing	computing	NOUN
ejpam-2779	754	3	,	,	PUNCT
ejpam-2779	754	4	18:15	18:15	NUM
ejpam-2779	754	5	-	-	SYM
ejpam-2779	754	6	33	33	NUM
ejpam-2779	754	7	,	,	PUNCT
ejpam-2779	754	8	2014	2014	NUM
ejpam-2779	754	9	.	.	PUNCT
ejpam-2779	755	1	[	[	X
ejpam-2779	755	2	7	7	NUM
ejpam-2779	755	3	]	]	X
ejpam-2779	755	4	r	r	NOUN
ejpam-2779	755	5	cignoli	cignoli	NOUN
ejpam-2779	755	6	,	,	PUNCT
ejpam-2779	755	7	i	i	PRON
ejpam-2779	755	8	m	m	VERB
ejpam-2779	755	9	l	l	VERB
ejpam-2779	755	10	dottaviano	dottaviano	NOUN
ejpam-2779	755	11	and	and	CCONJ
ejpam-2779	755	12	d	d	ADP
ejpam-2779	755	13	mundici	mundici	NOUN
ejpam-2779	755	14	.	.	PUNCT
ejpam-2779	756	1	algebraic	algebraic	ADJ
ejpam-2779	756	2	foundations	foundation	NOUN
ejpam-2779	756	3	of	of	ADP
ejpam-2779	756	4	many	many	ADV
ejpam-2779	756	5	-	-	PUNCT
ejpam-2779	756	6	valued	value	VERB
ejpam-2779	756	7	reasoning	reasoning	NOUN
ejpam-2779	756	8	.	.	PUNCT
ejpam-2779	757	1	kluwer	kluwer	NOUN
ejpam-2779	757	2	academic	academic	ADJ
ejpam-2779	757	3	publishers	publisher	NOUN
ejpam-2779	757	4	,	,	PUNCT
ejpam-2779	757	5	dordrecht	dordrecht	PROPN
ejpam-2779	757	6	,	,	PUNCT
ejpam-2779	757	7	2000	2000	NUM
ejpam-2779	757	8	.	.	PUNCT
ejpam-2779	758	1	[	[	X
ejpam-2779	758	2	8	8	NUM
ejpam-2779	758	3	]	]	X
ejpam-2779	758	4	w	w	ADP
ejpam-2779	758	5	a	a	DET
ejpam-2779	758	6	dudek	dudek	PROPN
ejpam-2779	758	7	and	and	CCONJ
ejpam-2779	758	8	y	y	PROPN
ejpam-2779	758	9	b	b	PROPN
ejpam-2779	758	10	jun	jun	PROPN
ejpam-2779	758	11	.	.	PROPN
ejpam-2779	758	12	pseudo	pseudo	PROPN
ejpam-2779	758	13	-	-	PUNCT
ejpam-2779	758	14	bci	bci	ADJ
ejpam-2779	758	15	algebras	algebra	NOUN
ejpam-2779	758	16	.	.	PUNCT
ejpam-2779	759	1	east	east	PROPN
ejpam-2779	759	2	asian	asian	PROPN
ejpam-2779	759	3	math	math	PROPN
ejpam-2779	759	4	.	.	PUNCT
ejpam-2779	760	1	j.	j.	PROPN
ejpam-2779	760	2	,	,	PUNCT
ejpam-2779	760	3	24:187	24:187	NUM
ejpam-2779	760	4	-	-	SYM
ejpam-2779	760	5	190	190	NUM
ejpam-2779	760	6	,	,	PUNCT
ejpam-2779	760	7	2008	2008	NUM
ejpam-2779	760	8	.	.	PUNCT
ejpam-2779	761	1	[	[	X
ejpam-2779	761	2	9	9	NUM
ejpam-2779	761	3	]	]	X
ejpam-2779	761	4	a	a	DET
ejpam-2779	761	5	dvurečenskij	dvurečenskij	PROPN
ejpam-2779	761	6	and	and	CCONJ
ejpam-2779	761	7	s	s	NOUN
ejpam-2779	761	8	pulmannová.	pulmannová.	NOUN
ejpam-2779	761	9	new	new	ADJ
ejpam-2779	761	10	trends	trend	NOUN
ejpam-2779	761	11	in	in	ADP
ejpam-2779	761	12	quantum	quantum	ADJ
ejpam-2779	761	13	structures	structure	NOUN
ejpam-2779	761	14	.	.	PUNCT
ejpam-2779	762	1	kluwer	kluwer	NOUN
ejpam-2779	762	2	academic	academic	ADJ
ejpam-2779	762	3	publishers	publisher	NOUN
ejpam-2779	762	4	,	,	PUNCT
ejpam-2779	762	5	dordrecht	dordrecht	PROPN
ejpam-2779	762	6	,	,	PUNCT
ejpam-2779	762	7	boston	boston	PROPN
ejpam-2779	762	8	,	,	PUNCT
ejpam-2779	762	9	london	london	PROPN
ejpam-2779	762	10	,	,	PUNCT
ejpam-2779	762	11	2000	2000	NUM
ejpam-2779	762	12	.	.	PUNCT
ejpam-2779	763	1	[	[	X
ejpam-2779	763	2	10	10	NUM
ejpam-2779	763	3	]	]	X
ejpam-2779	763	4	a	a	DET
ejpam-2779	763	5	dvurečenskij	dvurečenskij	PROPN
ejpam-2779	763	6	.	.	PUNCT
ejpam-2779	763	7	measures	measure	NOUN
ejpam-2779	763	8	and	and	CCONJ
ejpam-2779	763	9	states	state	NOUN
ejpam-2779	763	10	on	on	ADP
ejpam-2779	763	11	bck	bck	NOUN
ejpam-2779	763	12	-	-	PUNCT
ejpam-2779	763	13	algebras	algebras	PROPN
ejpam-2779	763	14	.	.	PUNCT
ejpam-2779	764	1	atti	atti	PROPN
ejpam-2779	764	2	del	del	PROPN
ejpam-2779	764	3	seminario	seminario	PROPN
ejpam-2779	764	4	matematico	matematico	PROPN
ejpam-2779	764	5	e	e	PROPN
ejpam-2779	764	6	fisico	fisico	PROPN
ejpam-2779	764	7	universita	universita	PROPN
ejpam-2779	764	8	di	di	PROPN
ejpam-2779	764	9	modena	modena	PROPN
ejpam-2779	764	10	,	,	PUNCT
ejpam-2779	764	11	47:511	47:511	PROPN
ejpam-2779	764	12	-	-	SYM
ejpam-2779	764	13	528	528	NUM
ejpam-2779	764	14	,	,	PUNCT
ejpam-2779	764	15	1996	1996	NUM
ejpam-2779	764	16	.	.	PUNCT
ejpam-2779	765	1	[	[	X
ejpam-2779	765	2	11	11	NUM
ejpam-2779	765	3	]	]	PUNCT
ejpam-2779	765	4	a	a	DET
ejpam-2779	765	5	dvurečenskij	dvurečenskij	PROPN
ejpam-2779	765	6	.	.	PUNCT
ejpam-2779	766	1	states	state	NOUN
ejpam-2779	766	2	on	on	ADP
ejpam-2779	766	3	pseudo	pseudo	NOUN
ejpam-2779	766	4	mv	mv	PROPN
ejpam-2779	766	5	-	-	PUNCT
ejpam-2779	766	6	algebras	algebra	NOUN
ejpam-2779	766	7	.	.	PUNCT
ejpam-2779	767	1	studia	studia	PROPN
ejpam-2779	767	2	logica	logica	PROPN
ejpam-2779	767	3	,	,	PUNCT
ejpam-2779	767	4	68:301	68:301	PROPN
ejpam-2779	767	5	-	-	SYM
ejpam-2779	767	6	327	327	NUM
ejpam-2779	767	7	,	,	PUNCT
ejpam-2779	767	8	2001	2001	NUM
ejpam-2779	767	9	.	.	PUNCT
ejpam-2779	768	1	[	[	X
ejpam-2779	768	2	12	12	NUM
ejpam-2779	768	3	]	]	PUNCT
ejpam-2779	768	4	a	a	DET
ejpam-2779	768	5	dvurečenskij	dvurečenskij	PROPN
ejpam-2779	768	6	and	and	CCONJ
ejpam-2779	768	7	t	t	PROPN
ejpam-2779	768	8	vetterlein	vetterlein	NOUN
ejpam-2779	768	9	.	.	PUNCT
ejpam-2779	769	1	algebras	algebras	PROPN
ejpam-2779	769	2	in	in	ADP
ejpam-2779	769	3	the	the	DET
ejpam-2779	769	4	positive	positive	ADJ
ejpam-2779	769	5	cone	cone	NOUN
ejpam-2779	769	6	of	of	ADP
ejpam-2779	769	7	po	po	NOUN
ejpam-2779	769	8	-	-	PUNCT
ejpam-2779	769	9	groups	group	NOUN
ejpam-2779	769	10	order	order	NOUN
ejpam-2779	769	11	,	,	PUNCT
ejpam-2779	769	12	19:127	19:127	NUM
ejpam-2779	769	13	-	-	SYM
ejpam-2779	769	14	146	146	NUM
ejpam-2779	769	15	,	,	PUNCT
ejpam-2779	769	16	2002	2002	NUM
ejpam-2779	769	17	.	.	PUNCT
ejpam-2779	770	1	[	[	X
ejpam-2779	770	2	13	13	NUM
ejpam-2779	770	3	]	]	SYM
ejpam-2779	770	4	g	g	PROPN
ejpam-2779	770	5	georgescu	georgescu	NOUN
ejpam-2779	770	6	and	and	CCONJ
ejpam-2779	770	7	a	a	DET
ejpam-2779	770	8	iorgulescu	iorgulescu	NOUN
ejpam-2779	770	9	.	.	PUNCT
ejpam-2779	771	1	pseudo	pseudo	NOUN
ejpam-2779	771	2	-	-	PUNCT
ejpam-2779	771	3	bckalgebras	bckalgebras	PRON
ejpam-2779	771	4	:	:	PUNCT
ejpam-2779	771	5	an	an	DET
ejpam-2779	771	6	extension	extension	NOUN
ejpam-2779	771	7	of	of	ADP
ejpam-2779	771	8	bckalgebras	bckalgebras	PROPN
ejpam-2779	771	9	.	.	PUNCT
ejpam-2779	772	1	in	in	ADP
ejpam-2779	772	2	:	:	PUNCT
ejpam-2779	772	3	proc.dmtcs01	proc.dmtcs01	ADJ
ejpam-2779	772	4	:	:	PUNCT
ejpam-2779	772	5	combinatorics	combinatoric	NOUN
ejpam-2779	772	6	,	,	PUNCT
ejpam-2779	772	7	computability	computability	NOUN
ejpam-2779	772	8	and	and	CCONJ
ejpam-2779	772	9	logic	logic	NOUN
ejpam-2779	772	10	,	,	PUNCT
ejpam-2779	772	11	springer	springer	NOUN
ejpam-2779	772	12	,	,	PUNCT
ejpam-2779	772	13	london	london	PROPN
ejpam-2779	772	14	,	,	PUNCT
ejpam-2779	772	15	pp.97114	pp.97114	PROPN
ejpam-2779	772	16	,	,	PUNCT
ejpam-2779	772	17	2001	2001	NUM
ejpam-2779	772	18	.	.	PUNCT
ejpam-2779	773	1	[	[	X
ejpam-2779	773	2	14	14	NUM
ejpam-2779	773	3	]	]	X
ejpam-2779	773	4	p	p	NOUN
ejpam-2779	773	5	hájek	hájek	NOUN
ejpam-2779	773	6	.	.	PUNCT
ejpam-2779	774	1	metamathematics	metamathematic	NOUN
ejpam-2779	774	2	of	of	ADP
ejpam-2779	774	3	fuzzy	fuzzy	ADJ
ejpam-2779	774	4	logic	logic	NOUN
ejpam-2779	774	5	.	.	PUNCT
ejpam-2779	775	1	kluwer	kluwer	NOUN
ejpam-2779	775	2	academic	academic	ADJ
ejpam-2779	775	3	publishers	publisher	NOUN
ejpam-2779	775	4	,	,	PUNCT
ejpam-2779	775	5	dordrecht	dordrecht	PROPN
ejpam-2779	775	6	,	,	PUNCT
ejpam-2779	775	7	1998	1998	NUM
ejpam-2779	775	8	.	.	PUNCT
ejpam-2779	776	1	references	reference	NOUN
ejpam-2779	776	2	472	472	NUM
ejpam-2779	777	1	[	[	X
ejpam-2779	777	2	15	15	NUM
ejpam-2779	777	3	]	]	X
ejpam-2779	777	4	a	a	DET
ejpam-2779	777	5	iorgulescu	iorgulescu	NOUN
ejpam-2779	777	6	.	.	PUNCT
ejpam-2779	778	1	pseudo	pseudo	NOUN
ejpam-2779	778	2	-	-	NOUN
ejpam-2779	778	3	iséki	iséki	PUNCT
ejpam-2779	778	4	algebras	algebra	NOUN
ejpam-2779	778	5	.	.	PUNCT
ejpam-2779	778	6	connection	connection	NOUN
ejpam-2779	778	7	with	with	ADP
ejpam-2779	778	8	pseudo	pseudo	NOUN
ejpam-2779	778	9	-	-	PUNCT
ejpam-2779	778	10	bl	bl	PROPN
ejpam-2779	778	11	algebras	algebras	PROPN
ejpam-2779	778	12	.	.	PUNCT
ejpam-2779	779	1	j.	j.	PROPN
ejpam-2779	779	2	multiple	multiple	ADV
ejpam-2779	779	3	-	-	PUNCT
ejpam-2779	779	4	valued	value	VERB
ejpam-2779	779	5	logic	logic	NOUN
ejpam-2779	779	6	soft	soft	ADJ
ejpam-2779	779	7	comput	comput	NOUN
ejpam-2779	779	8	.	.	PUNCT
ejpam-2779	779	9	,	,	PUNCT
ejpam-2779	779	10	3	3	NUM
ejpam-2779	779	11	-	-	SYM
ejpam-2779	779	12	4:263	4:263	NUM
ejpam-2779	779	13	-	-	PUNCT
ejpam-2779	779	14	308	308	NUM
ejpam-2779	779	15	,	,	PUNCT
ejpam-2779	779	16	2005	2005	NUM
ejpam-2779	779	17	.	.	PUNCT
ejpam-2779	780	1	[	[	X
ejpam-2779	780	2	16	16	NUM
ejpam-2779	780	3	]	]	X
ejpam-2779	780	4	a	a	DET
ejpam-2779	780	5	iorgulescu	iorgulescu	NOUN
ejpam-2779	780	6	.	.	PUNCT
ejpam-2779	781	1	algebras	algebras	PROPN
ejpam-2779	781	2	of	of	ADP
ejpam-2779	781	3	logic	logic	NOUN
ejpam-2779	781	4	as	as	ADP
ejpam-2779	781	5	bck	bck	NOUN
ejpam-2779	781	6	-	-	PUNCT
ejpam-2779	781	7	algebras	algebras	PROPN
ejpam-2779	781	8	.	.	PUNCT
ejpam-2779	782	1	academy	academy	PROPN
ejpam-2779	782	2	of	of	ADP
ejpam-2779	782	3	economic	economic	PROPN
ejpam-2779	782	4	studies	study	NOUN
ejpam-2779	782	5	bucharest	buchar	ADJ
ejpam-2779	782	6	,	,	PUNCT
ejpam-2779	782	7	editura	editura	NOUN
ejpam-2779	782	8	,	,	PUNCT
ejpam-2779	782	9	2008	2008	NUM
ejpam-2779	782	10	.	.	PUNCT
ejpam-2779	783	1	[	[	X
ejpam-2779	783	2	17	17	NUM
ejpam-2779	783	3	]	]	X
ejpam-2779	783	4	k	k	PROPN
ejpam-2779	783	5	iséki	iséki	PROPN
ejpam-2779	783	6	.	.	PUNCT
ejpam-2779	784	1	an	an	DET
ejpam-2779	784	2	algebra	algebra	NOUN
ejpam-2779	784	3	related	relate	VERB
ejpam-2779	784	4	with	with	ADP
ejpam-2779	784	5	a	a	DET
ejpam-2779	784	6	propositional	propositional	ADJ
ejpam-2779	784	7	calculus	calculus	NOUN
ejpam-2779	784	8	.	.	PUNCT
ejpam-2779	785	1	proc	proc	PROPN
ejpam-2779	785	2	.	.	PUNCT
ejpam-2779	786	1	japan	japan	PROPN
ejpam-2779	786	2	acad	acad	PROPN
ejpam-2779	786	3	.	.	PROPN
ejpam-2779	786	4	,	,	PUNCT
ejpam-2779	786	5	42:26	42:26	NUM
ejpam-2779	786	6	-	-	SYM
ejpam-2779	786	7	29	29	NUM
ejpam-2779	786	8	,	,	PUNCT
ejpam-2779	786	9	1966	1966	NUM
ejpam-2779	786	10	.	.	PUNCT
ejpam-2779	787	1	[	[	X
ejpam-2779	787	2	18	18	NUM
ejpam-2779	787	3	]	]	X
ejpam-2779	787	4	k	k	PROPN
ejpam-2779	787	5	iséki	iséki	PROPN
ejpam-2779	787	6	.	.	PROPN
ejpam-2779	788	1	on	on	ADP
ejpam-2779	788	2	bci	bci	NOUN
ejpam-2779	788	3	-	-	PUNCT
ejpam-2779	788	4	algebras	algebra	NOUN
ejpam-2779	788	5	.	.	PUNCT
ejpam-2779	789	1	math	math	PROPN
ejpam-2779	789	2	.	.	PUNCT
ejpam-2779	790	1	sem	sem	PROPN
ejpam-2779	790	2	.	.	PUNCT
ejpam-2779	791	1	notes	notes	PROPN
ejpam-2779	791	2	kobe	kobe	PROPN
ejpam-2779	791	3	univ	univ	PROPN
ejpam-2779	791	4	.	.	PROPN
ejpam-2779	791	5	,	,	PUNCT
ejpam-2779	791	6	8(1):125	8(1):125	NUM
ejpam-2779	791	7	-	-	SYM
ejpam-2779	791	8	130	130	NUM
ejpam-2779	791	9	,	,	PUNCT
ejpam-2779	791	10	1980	1980	NUM
ejpam-2779	791	11	.	.	PUNCT
ejpam-2779	792	1	[	[	X
ejpam-2779	792	2	19	19	NUM
ejpam-2779	792	3	]	]	X
ejpam-2779	792	4	y	y	PROPN
ejpam-2779	792	5	b	b	PROPN
ejpam-2779	792	6	jun	jun	PROPN
ejpam-2779	792	7	,	,	PUNCT
ejpam-2779	792	8	h	h	PROPN
ejpam-2779	792	9	k	k	PROPN
ejpam-2779	792	10	kim	kim	PROPN
ejpam-2779	792	11	and	and	CCONJ
ejpam-2779	792	12	j	j	PROPN
ejpam-2779	792	13	neggers	negger	NOUN
ejpam-2779	792	14	.	.	PUNCT
ejpam-2779	793	1	on	on	ADP
ejpam-2779	793	2	pseudo	pseudo	NOUN
ejpam-2779	793	3	-	-	ADJ
ejpam-2779	793	4	bci	bci	ADJ
ejpam-2779	793	5	ideals	ideal	NOUN
ejpam-2779	793	6	of	of	ADP
ejpam-2779	793	7	pseudo	pseudo	NOUN
ejpam-2779	793	8	-	-	ADJ
ejpam-2779	793	9	bci	bci	ADJ
ejpam-2779	793	10	algebras	algebra	NOUN
ejpam-2779	793	11	.	.	PUNCT
ejpam-2779	793	12	matematiqki	matematiqki	PROPN
ejpam-2779	793	13	vesnik	vesnik	PROPN
ejpam-2779	793	14	,	,	PUNCT
ejpam-2779	793	15	58:39	58:39	NUM
ejpam-2779	793	16	-	-	SYM
ejpam-2779	793	17	46	46	NUM
ejpam-2779	793	18	,	,	PUNCT
ejpam-2779	793	19	2006	2006	NUM
ejpam-2779	793	20	.	.	PUNCT
ejpam-2779	794	1	[	[	X
ejpam-2779	794	2	20	20	NUM
ejpam-2779	794	3	]	]	SYM
ejpam-2779	794	4	j	j	PROPN
ejpam-2779	794	5	kuhr	kuhr	NOUN
ejpam-2779	794	6	.	.	PUNCT
ejpam-2779	795	1	pseudo	pseudo	NOUN
ejpam-2779	795	2	-	-	ADJ
ejpam-2779	795	3	bck	bck	ADJ
ejpam-2779	795	4	algebras	algebra	NOUN
ejpam-2779	795	5	and	and	CCONJ
ejpam-2779	795	6	related	related	ADJ
ejpam-2779	795	7	structures	structure	NOUN
ejpam-2779	795	8	.	.	PUNCT
ejpam-2779	796	1	univerzita	univerzita	PROPN
ejpam-2779	796	2	palackého	palackého	PROPN
ejpam-2779	796	3	v	v	NUM
ejpam-2779	796	4	olomouci	olomouci	ADJ
ejpam-2779	796	5	,	,	PUNCT
ejpam-2779	796	6	2007	2007	NUM
ejpam-2779	796	7	.	.	PUNCT
ejpam-2779	797	1	[	[	X
ejpam-2779	797	2	21	21	NUM
ejpam-2779	797	3	]	]	X
ejpam-2779	797	4	l	l	NOUN
ejpam-2779	797	5	lianzhen	lianzhen	ADV
ejpam-2779	797	6	.	.	PUNCT
ejpam-2779	798	1	states	state	NOUN
ejpam-2779	798	2	on	on	ADP
ejpam-2779	798	3	finite	finite	PROPN
ejpam-2779	798	4	monoidal	monoidal	PROPN
ejpam-2779	798	5	t	t	PROPN
ejpam-2779	798	6	-	-	PUNCT
ejpam-2779	798	7	norm	norm	NOUN
ejpam-2779	798	8	based	base	VERB
ejpam-2779	798	9	algebras	algebras	PROPN
ejpam-2779	798	10	.	.	PUNCT
ejpam-2779	799	1	information	information	NOUN
ejpam-2779	799	2	sciences	sciences	PROPN
ejpam-2779	799	3	,	,	PUNCT
ejpam-2779	799	4	181:1369	181:1369	NUM
ejpam-2779	799	5	-	-	SYM
ejpam-2779	799	6	1393	1393	NUM
ejpam-2779	799	7	,	,	PUNCT
ejpam-2779	799	8	2011	2011	NUM
ejpam-2779	799	9	.	.	PUNCT
ejpam-2779	800	1	[	[	X
ejpam-2779	800	2	22	22	NUM
ejpam-2779	800	3	]	]	X
ejpam-2779	800	4	j	j	PROPN
ejpam-2779	800	5	meng	meng	PROPN
ejpam-2779	800	6	and	and	CCONJ
ejpam-2779	800	7	y	y	PROPN
ejpam-2779	800	8	b	b	PROPN
ejpam-2779	800	9	jun	jun	PROPN
ejpam-2779	800	10	.	.	PUNCT
ejpam-2779	800	11	bck	bck	PROPN
ejpam-2779	800	12	-	-	PUNCT
ejpam-2779	800	13	algebras	algebras	PROPN
ejpam-2779	800	14	.	.	PUNCT
ejpam-2779	800	15	kyungmoon	kyungmoon	PROPN
ejpam-2779	800	16	sa	sa	PROPN
ejpam-2779	800	17	,	,	PUNCT
ejpam-2779	800	18	seoul	seoul	PROPN
ejpam-2779	800	19	,	,	PUNCT
ejpam-2779	800	20	1994	1994	NUM
ejpam-2779	800	21	.	.	PUNCT
ejpam-2779	801	1	[	[	X
ejpam-2779	801	2	23	23	NUM
ejpam-2779	801	3	]	]	X
ejpam-2779	801	4	d	d	X
ejpam-2779	801	5	mundici	mundici	NOUN
ejpam-2779	801	6	.	.	PUNCT
ejpam-2779	802	1	averaging	average	VERB
ejpam-2779	802	2	the	the	DET
ejpam-2779	802	3	truth	truth	NOUN
ejpam-2779	802	4	-	-	PUNCT
ejpam-2779	802	5	value	value	NOUN
ejpam-2779	802	6	in	in	ADP
ejpam-2779	802	7	lukasiewicz	lukasiewicz	ADJ
ejpam-2779	802	8	logic	logic	NOUN
ejpam-2779	802	9	.	.	PUNCT
ejpam-2779	803	1	studia	studia	PROPN
ejpam-2779	803	2	logica	logica	PROPN
ejpam-2779	803	3	,	,	PUNCT
ejpam-2779	803	4	55(1):113127	55(1):113127	NUM
ejpam-2779	803	5	,	,	PUNCT
ejpam-2779	803	6	1995	1995	NUM
ejpam-2779	803	7	.	.	PUNCT
ejpam-2779	804	1	[	[	X
ejpam-2779	804	2	24	24	NUM
ejpam-2779	804	3	]	]	X
ejpam-2779	804	4	d	d	NOUN
ejpam-2779	804	5	mundici	mundici	NOUN
ejpam-2779	804	6	.	.	PUNCT
ejpam-2779	805	1	interpretation	interpretation	NOUN
ejpam-2779	805	2	of	of	ADP
ejpam-2779	805	3	afc∗-algebras	afc∗-algebras	PROPN
ejpam-2779	805	4	in	in	ADP
ejpam-2779	805	5	lukasiewicz	lukasiewicz	ADJ
ejpam-2779	805	6	sentential	sentential	ADJ
ejpam-2779	805	7	calculus	calculus	NOUN
ejpam-2779	805	8	.	.	PUNCT
ejpam-2779	806	1	j.	j.	PROPN
ejpam-2779	806	2	funct	funct	PROPN
ejpam-2779	806	3	.	.	PUNCT
ejpam-2779	807	1	anal	anal	PROPN
ejpam-2779	807	2	,	,	PUNCT
ejpam-2779	807	3	65	65	NUM
ejpam-2779	807	4	:	:	SYM
ejpam-2779	807	5	15	15	NUM
ejpam-2779	807	6	-	-	SYM
ejpam-2779	807	7	53	53	NUM
ejpam-2779	807	8	,	,	PUNCT
ejpam-2779	807	9	1986	1986	NUM
ejpam-2779	807	10	.	.	PUNCT