id	sid	tid	token	lemma	pos
ejpam-6018	1	1	european	european	PROPN
ejpam-6018	1	2	journal	journal	PROPN
ejpam-6018	1	3	of	of	ADP
ejpam-6018	1	4	pure	pure	ADJ
ejpam-6018	1	5	and	and	CCONJ
ejpam-6018	1	6	applied	applied	ADJ
ejpam-6018	1	7	mathematics	mathematic	NOUN
ejpam-6018	1	8	2025	2025	NUM
ejpam-6018	1	9	,	,	PUNCT
ejpam-6018	1	10	vol	vol	NOUN
ejpam-6018	1	11	.	.	PROPN
ejpam-6018	1	12	18	18	NUM
ejpam-6018	1	13	,	,	PUNCT
ejpam-6018	1	14	issue	issue	NOUN
ejpam-6018	1	15	2	2	NUM
ejpam-6018	1	16	,	,	PUNCT
ejpam-6018	1	17	article	article	NOUN
ejpam-6018	1	18	number	number	NOUN
ejpam-6018	1	19	6018	6018	NUM
ejpam-6018	1	20	issn	issn	VERB
ejpam-6018	1	21	1307	1307	NUM
ejpam-6018	1	22	-	-	SYM
ejpam-6018	1	23	5543	5543	NUM
ejpam-6018	1	24	–	–	PUNCT
ejpam-6018	1	25	ejpam.com	ejpam.com	X
ejpam-6018	1	26	published	publish	VERB
ejpam-6018	1	27	by	by	ADP
ejpam-6018	1	28	new	new	PROPN
ejpam-6018	1	29	york	york	PROPN
ejpam-6018	1	30	business	business	PROPN
ejpam-6018	1	31	global	global	ADJ
ejpam-6018	1	32	soft	soft	ADJ
ejpam-6018	1	33	subalgebras	subalgebra	NOUN
ejpam-6018	1	34	and	and	CCONJ
ejpam-6018	1	35	ideals	ideal	NOUN
ejpam-6018	1	36	of	of	ADP
ejpam-6018	1	37	sheffer	sheffer	PROPN
ejpam-6018	1	38	stroke	stroke	PROPN
ejpam-6018	1	39	hilbert	hilbert	PROPN
ejpam-6018	1	40	algebras	algebras	PROPN
ejpam-6018	1	41	based	base	VERB
ejpam-6018	1	42	on	on	ADP
ejpam-6018	1	43	n	n	DET
ejpam-6018	1	44	-structures	-structure	NOUN
ejpam-6018	1	45	tahsin	tahsin	VERB
ejpam-6018	1	46	oner1	oner1	NOUN
ejpam-6018	1	47	,	,	PUNCT
ejpam-6018	1	48	neelamegarajan	neelamegarajan	NOUN
ejpam-6018	1	49	rajesh2	rajesh2	PROPN
ejpam-6018	1	50	,	,	PUNCT
ejpam-6018	1	51	aiyared	aiyare	VERB
ejpam-6018	1	52	iampan3,∗	iampan3,∗	ADJ
ejpam-6018	1	53	,	,	PUNCT
ejpam-6018	1	54	arsham	arsham	PROPN
ejpam-6018	2	1	borumand	borumand	INTJ
ejpam-6018	2	2	saeid4	saeid4	ADP
ejpam-6018	3	1	1	1	NUM
ejpam-6018	3	2	department	department	NOUN
ejpam-6018	3	3	of	of	ADP
ejpam-6018	3	4	mathematics	mathematic	NOUN
ejpam-6018	3	5	,	,	PUNCT
ejpam-6018	3	6	faculty	faculty	NOUN
ejpam-6018	3	7	of	of	ADP
ejpam-6018	3	8	science	science	NOUN
ejpam-6018	3	9	,	,	PUNCT
ejpam-6018	3	10	ege	ege	PROPN
ejpam-6018	3	11	university	university	NOUN
ejpam-6018	3	12	,	,	PUNCT
ejpam-6018	3	13	35100	35100	NUM
ejpam-6018	3	14	izmir	izmir	PROPN
ejpam-6018	3	15	,	,	PUNCT
ejpam-6018	3	16	turkey	turkey	PROPN
ejpam-6018	3	17	2	2	NUM
ejpam-6018	3	18	department	department	NOUN
ejpam-6018	3	19	of	of	ADP
ejpam-6018	3	20	mathematics	mathematic	NOUN
ejpam-6018	3	21	,	,	PUNCT
ejpam-6018	3	22	rajah	rajah	NOUN
ejpam-6018	3	23	serfoji	serfoji	ADJ
ejpam-6018	3	24	government	government	NOUN
ejpam-6018	3	25	college	college	NOUN
ejpam-6018	3	26	,	,	PUNCT
ejpam-6018	3	27	thanjavur-613005	thanjavur-613005	NOUN
ejpam-6018	3	28	,	,	PUNCT
ejpam-6018	3	29	tamil	tamil	PROPN
ejpam-6018	3	30	nadu	nadu	NOUN
ejpam-6018	3	31	,	,	PUNCT
ejpam-6018	3	32	india	india	PROPN
ejpam-6018	3	33	3	3	NUM
ejpam-6018	3	34	department	department	PROPN
ejpam-6018	3	35	of	of	ADP
ejpam-6018	3	36	mathematics	mathematic	NOUN
ejpam-6018	3	37	,	,	PUNCT
ejpam-6018	3	38	school	school	NOUN
ejpam-6018	3	39	of	of	ADP
ejpam-6018	3	40	science	science	NOUN
ejpam-6018	3	41	,	,	PUNCT
ejpam-6018	3	42	university	university	NOUN
ejpam-6018	3	43	of	of	ADP
ejpam-6018	3	44	phayao	phayao	NOUN
ejpam-6018	3	45	,	,	PUNCT
ejpam-6018	3	46	mae	mae	PROPN
ejpam-6018	3	47	ka	ka	PROPN
ejpam-6018	3	48	,	,	PUNCT
ejpam-6018	3	49	mueang	mueang	PROPN
ejpam-6018	3	50	,	,	PUNCT
ejpam-6018	3	51	phayao	phayao	NOUN
ejpam-6018	3	52	56000	56000	NUM
ejpam-6018	3	53	,	,	PUNCT
ejpam-6018	3	54	thailand	thailand	PROPN
ejpam-6018	3	55	4	4	NUM
ejpam-6018	3	56	department	department	NOUN
ejpam-6018	3	57	of	of	ADP
ejpam-6018	3	58	pure	pure	ADJ
ejpam-6018	3	59	mathematics	mathematic	NOUN
ejpam-6018	3	60	,	,	PUNCT
ejpam-6018	3	61	faculty	faculty	NOUN
ejpam-6018	3	62	of	of	ADP
ejpam-6018	3	63	mathematics	mathematic	NOUN
ejpam-6018	3	64	and	and	CCONJ
ejpam-6018	3	65	computer	computer	NOUN
ejpam-6018	3	66	,	,	PUNCT
ejpam-6018	3	67	shadid	shadid	AUX
ejpam-6018	3	68	bahonar	bahonar	PROPN
ejpam-6018	3	69	university	university	PROPN
ejpam-6018	3	70	of	of	ADP
ejpam-6018	3	71	kerman	kerman	PROPN
ejpam-6018	3	72	,	,	PUNCT
ejpam-6018	3	73	kerman	kerman	PROPN
ejpam-6018	3	74	,	,	PUNCT
ejpam-6018	3	75	iran	iran	PROPN
ejpam-6018	3	76	abstract	abstract	NOUN
ejpam-6018	3	77	.	.	PUNCT
ejpam-6018	4	1	in	in	ADP
ejpam-6018	4	2	this	this	DET
ejpam-6018	4	3	study	study	NOUN
ejpam-6018	4	4	,	,	PUNCT
ejpam-6018	4	5	we	we	PRON
ejpam-6018	4	6	introduce	introduce	VERB
ejpam-6018	4	7	the	the	DET
ejpam-6018	4	8	concepts	concept	NOUN
ejpam-6018	4	9	ofn	ofn	PROPN
ejpam-6018	4	10	-ideals	-ideal	NOUN
ejpam-6018	4	11	of	of	ADP
ejpam-6018	4	12	types	type	NOUN
ejpam-6018	4	13	(	(	PUNCT
ejpam-6018	4	14	∈,∈	∈,∈	X
ejpam-6018	4	15	)	)	PUNCT
ejpam-6018	4	16	and	and	CCONJ
ejpam-6018	4	17	(	(	PUNCT
ejpam-6018	4	18	∈,∈	∈,∈	X
ejpam-6018	4	19	∨q	∨q	NOUN
ejpam-6018	4	20	)	)	PUNCT
ejpam-6018	4	21	,	,	PUNCT
ejpam-6018	4	22	along	along	ADP
ejpam-6018	4	23	with	with	ADP
ejpam-6018	4	24	soft	soft	ADJ
ejpam-6018	4	25	n∈-sets	n∈-set	NOUN
ejpam-6018	4	26	,	,	PUNCT
ejpam-6018	4	27	soft	soft	ADJ
ejpam-6018	4	28	nq	nq	NOUN
ejpam-6018	4	29	-	-	PUNCT
ejpam-6018	4	30	sets	set	NOUN
ejpam-6018	4	31	,	,	PUNCT
ejpam-6018	4	32	and	and	CCONJ
ejpam-6018	4	33	soft	soft	ADJ
ejpam-6018	4	34	n∈∨q	n∈∨q	NOUN
ejpam-6018	4	35	-	-	PUNCT
ejpam-6018	4	36	sets	set	NOUN
ejpam-6018	4	37	.	.	PUNCT
ejpam-6018	5	1	additionally	additionally	ADV
ejpam-6018	5	2	,	,	PUNCT
ejpam-6018	5	3	we	we	PRON
ejpam-6018	5	4	define	define	VERB
ejpam-6018	5	5	soft	soft	ADJ
ejpam-6018	5	6	n	n	CCONJ
ejpam-6018	5	7	-subalgebras	-subalgebra	NOUN
ejpam-6018	5	8	and	and	CCONJ
ejpam-6018	5	9	n	n	NUM
ejpam-6018	5	10	-ideals	-ideal	NOUN
ejpam-6018	5	11	within	within	ADP
ejpam-6018	5	12	the	the	DET
ejpam-6018	5	13	context	context	NOUN
ejpam-6018	5	14	of	of	ADP
ejpam-6018	5	15	sheffer	sheffer	PROPN
ejpam-6018	5	16	stroke	stroke	PROPN
ejpam-6018	5	17	hilbert	hilbert	PROPN
ejpam-6018	5	18	algebras	algebras	PROPN
ejpam-6018	5	19	and	and	CCONJ
ejpam-6018	5	20	explore	explore	VERB
ejpam-6018	5	21	various	various	ADJ
ejpam-6018	5	22	properties	property	NOUN
ejpam-6018	5	23	of	of	ADP
ejpam-6018	5	24	these	these	DET
ejpam-6018	5	25	structures	structure	NOUN
ejpam-6018	5	26	.	.	PUNCT
ejpam-6018	6	1	the	the	DET
ejpam-6018	6	2	paper	paper	NOUN
ejpam-6018	6	3	also	also	ADV
ejpam-6018	6	4	provides	provide	VERB
ejpam-6018	6	5	characterizations	characterization	NOUN
ejpam-6018	6	6	of	of	ADP
ejpam-6018	6	7	n	n	NOUN
ejpam-6018	6	8	-subalgebras	-subalgebra	NOUN
ejpam-6018	6	9	of	of	ADP
ejpam-6018	6	10	types	type	NOUN
ejpam-6018	6	11	(	(	PUNCT
ejpam-6018	6	12	∈,∈	∈,∈	X
ejpam-6018	6	13	)	)	PUNCT
ejpam-6018	6	14	and	and	CCONJ
ejpam-6018	6	15	(	(	PUNCT
ejpam-6018	6	16	∈,∈	∈,∈	X
ejpam-6018	6	17	∨q	∨q	NOUN
ejpam-6018	6	18	)	)	PUNCT
ejpam-6018	6	19	,	,	PUNCT
ejpam-6018	6	20	as	as	ADV
ejpam-6018	6	21	well	well	ADV
ejpam-6018	6	22	as	as	ADP
ejpam-6018	6	23	n	n	PRON
ejpam-6018	6	24	-ideals	-ideal	NOUN
ejpam-6018	6	25	for	for	ADP
ejpam-6018	6	26	both	both	PRON
ejpam-6018	6	27	of	of	ADP
ejpam-6018	6	28	these	these	DET
ejpam-6018	6	29	types	type	NOUN
ejpam-6018	6	30	.	.	PUNCT
ejpam-6018	7	1	furthermore	furthermore	ADV
ejpam-6018	7	2	,	,	PUNCT
ejpam-6018	7	3	we	we	PRON
ejpam-6018	7	4	further	far	ADV
ejpam-6018	7	5	examine	examine	VERB
ejpam-6018	7	6	their	their	PRON
ejpam-6018	7	7	corresponding	corresponding	ADJ
ejpam-6018	7	8	soft	soft	ADJ
ejpam-6018	7	9	versions	version	NOUN
ejpam-6018	7	10	,	,	PUNCT
ejpam-6018	7	11	extending	extend	VERB
ejpam-6018	7	12	the	the	DET
ejpam-6018	7	13	algebraic	algebraic	ADJ
ejpam-6018	7	14	framework	framework	NOUN
ejpam-6018	7	15	in	in	ADP
ejpam-6018	7	16	the	the	DET
ejpam-6018	7	17	setting	setting	NOUN
ejpam-6018	7	18	of	of	ADP
ejpam-6018	7	19	sheffer	sheffer	PROPN
ejpam-6018	7	20	stroke	stroke	PROPN
ejpam-6018	7	21	hilbert	hilbert	PROPN
ejpam-6018	7	22	algebras	algebras	PROPN
ejpam-6018	7	23	.	.	PUNCT
ejpam-6018	8	1	2020	2020	NUM
ejpam-6018	8	2	mathematics	mathematics	PROPN
ejpam-6018	8	3	subject	subject	NOUN
ejpam-6018	8	4	classifications	classification	NOUN
ejpam-6018	8	5	:	:	PUNCT
ejpam-6018	8	6	06f35	06f35	NUM
ejpam-6018	8	7	,	,	PUNCT
ejpam-6018	8	8	03g25	03g25	NUM
ejpam-6018	8	9	,	,	PUNCT
ejpam-6018	8	10	03e72	03e72	NOUN
ejpam-6018	8	11	.	.	PUNCT
ejpam-6018	9	1	key	key	ADJ
ejpam-6018	9	2	words	word	NOUN
ejpam-6018	9	3	and	and	CCONJ
ejpam-6018	9	4	phrases	phrase	NOUN
ejpam-6018	9	5	:	:	PUNCT
ejpam-6018	9	6	sheffer	sheffer	NOUN
ejpam-6018	9	7	stroke	stroke	PROPN
ejpam-6018	9	8	hilbert	hilbert	PROPN
ejpam-6018	9	9	algebra	algebra	PROPN
ejpam-6018	9	10	,	,	PUNCT
ejpam-6018	9	11	n	n	PRON
ejpam-6018	9	12	-subalgebra	-subalgebra	NOUN
ejpam-6018	9	13	of	of	ADP
ejpam-6018	9	14	types	type	NOUN
ejpam-6018	9	15	(	(	PUNCT
ejpam-6018	9	16	∈,∈	∈,∈	X
ejpam-6018	9	17	)	)	PUNCT
ejpam-6018	9	18	and	and	CCONJ
ejpam-6018	9	19	(	(	PUNCT
ejpam-6018	9	20	∈,∈	∈,∈	X
ejpam-6018	9	21	∨q	∨q	NOUN
ejpam-6018	9	22	)	)	PUNCT
ejpam-6018	9	23	,	,	PUNCT
ejpam-6018	9	24	n	n	PRON
ejpam-6018	9	25	-ideal	-ideal	NOUN
ejpam-6018	9	26	of	of	ADP
ejpam-6018	9	27	types	type	NOUN
ejpam-6018	9	28	(	(	PUNCT
ejpam-6018	9	29	∈,∈	∈,∈	X
ejpam-6018	9	30	)	)	PUNCT
ejpam-6018	9	31	and	and	CCONJ
ejpam-6018	9	32	(	(	PUNCT
ejpam-6018	9	33	∈,∈	∈,∈	X
ejpam-6018	9	34	∨q	∨q	NOUN
ejpam-6018	9	35	)	)	PUNCT
ejpam-6018	9	36	.	.	PUNCT
ejpam-6018	10	1	1	1	X
ejpam-6018	10	2	.	.	X
ejpam-6018	10	3	introduction	introduction	NOUN
ejpam-6018	10	4	the	the	DET
ejpam-6018	10	5	sheffer	sheffer	NOUN
ejpam-6018	10	6	operation	operation	NOUN
ejpam-6018	10	7	,	,	PUNCT
ejpam-6018	10	8	also	also	ADV
ejpam-6018	10	9	known	know	VERB
ejpam-6018	10	10	as	as	ADP
ejpam-6018	10	11	the	the	DET
ejpam-6018	10	12	sheffer	sheffer	NOUN
ejpam-6018	10	13	stroke	stroke	NOUN
ejpam-6018	10	14	or	or	CCONJ
ejpam-6018	10	15	nand	nand	NOUN
ejpam-6018	10	16	operator	operator	NOUN
ejpam-6018	10	17	,	,	PUNCT
ejpam-6018	10	18	was	be	AUX
ejpam-6018	10	19	first	first	ADV
ejpam-6018	10	20	introduced	introduce	VERB
ejpam-6018	10	21	by	by	ADP
ejpam-6018	10	22	henry	henry	PROPN
ejpam-6018	10	23	maurice	maurice	PROPN
ejpam-6018	10	24	sheffer	sheffer	VERB
ejpam-6018	11	1	[	[	X
ejpam-6018	11	2	1	1	NUM
ejpam-6018	11	3	]	]	PUNCT
ejpam-6018	11	4	.	.	PUNCT
ejpam-6018	12	1	its	its	PRON
ejpam-6018	12	2	significance	significance	NOUN
ejpam-6018	12	3	arises	arise	VERB
ejpam-6018	12	4	from	from	ADP
ejpam-6018	12	5	its	its	PRON
ejpam-6018	12	6	ability	ability	NOUN
ejpam-6018	12	7	to	to	PART
ejpam-6018	12	8	function	function	VERB
ejpam-6018	12	9	as	as	ADP
ejpam-6018	12	10	a	a	DET
ejpam-6018	12	11	fundamental	fundamental	ADJ
ejpam-6018	12	12	logical	logical	ADJ
ejpam-6018	12	13	operator	operator	NOUN
ejpam-6018	12	14	capable	capable	ADJ
ejpam-6018	12	15	of	of	ADP
ejpam-6018	12	16	constructing	construct	VERB
ejpam-6018	12	17	an	an	DET
ejpam-6018	12	18	entire	entire	ADJ
ejpam-6018	12	19	logical	logical	ADJ
ejpam-6018	12	20	system	system	NOUN
ejpam-6018	12	21	on	on	ADP
ejpam-6018	12	22	its	its	PRON
ejpam-6018	12	23	own	own	ADJ
ejpam-6018	12	24	.	.	PUNCT
ejpam-6018	13	1	this	this	DET
ejpam-6018	13	2	feature	feature	NOUN
ejpam-6018	13	3	allows	allow	VERB
ejpam-6018	13	4	any	any	DET
ejpam-6018	13	5	axiom	axiom	NOUN
ejpam-6018	13	6	within	within	ADP
ejpam-6018	13	7	a	a	DET
ejpam-6018	13	8	logical	logical	ADJ
ejpam-6018	13	9	framework	framework	NOUN
ejpam-6018	13	10	to	to	PART
ejpam-6018	13	11	be	be	AUX
ejpam-6018	13	12	reformulated	reformulate	VERB
ejpam-6018	13	13	solely	solely	ADV
ejpam-6018	13	14	using	use	VERB
ejpam-6018	13	15	the	the	DET
ejpam-6018	13	16	sheffer	sheffer	NOUN
ejpam-6018	13	17	operation	operation	NOUN
ejpam-6018	13	18	,	,	PUNCT
ejpam-6018	13	19	simplifying	simplify	VERB
ejpam-6018	13	20	the	the	DET
ejpam-6018	13	21	manipulation	manipulation	NOUN
ejpam-6018	13	22	and	and	CCONJ
ejpam-6018	13	23	control	control	NOUN
ejpam-6018	13	24	of	of	ADP
ejpam-6018	13	25	the	the	DET
ejpam-6018	13	26	system	system	NOUN
ejpam-6018	13	27	’s	’s	PART
ejpam-6018	13	28	intrinsic	intrinsic	ADJ
ejpam-6018	13	29	properties	property	NOUN
ejpam-6018	13	30	.	.	PUNCT
ejpam-6018	14	1	moreover	moreover	ADV
ejpam-6018	14	2	,	,	PUNCT
ejpam-6018	14	3	the	the	DET
ejpam-6018	14	4	axioms	axiom	NOUN
ejpam-6018	14	5	of	of	ADP
ejpam-6018	14	6	boolean	boolean	ADJ
ejpam-6018	14	7	algebra	algebra	NOUN
ejpam-6018	14	8	,	,	PUNCT
ejpam-6018	14	9	which	which	PRON
ejpam-6018	14	10	serve	serve	VERB
ejpam-6018	14	11	as	as	ADP
ejpam-6018	14	12	the	the	DET
ejpam-6018	14	13	algebraic	algebraic	ADJ
ejpam-6018	14	14	foundation	foundation	NOUN
ejpam-6018	14	15	for	for	ADP
ejpam-6018	14	16	classical	classical	ADJ
ejpam-6018	14	17	propositional	propositional	ADJ
ejpam-6018	14	18	logic	logic	NOUN
ejpam-6018	14	19	,	,	PUNCT
ejpam-6018	14	20	can	can	AUX
ejpam-6018	14	21	also	also	ADV
ejpam-6018	14	22	be	be	AUX
ejpam-6018	14	23	completely	completely	ADV
ejpam-6018	14	24	expressed	express	VERB
ejpam-6018	14	25	through	through	ADP
ejpam-6018	14	26	the	the	DET
ejpam-6018	14	27	∗corresponding	∗corresponde	VERB
ejpam-6018	14	28	author	author	NOUN
ejpam-6018	14	29	.	.	PUNCT
ejpam-6018	15	1	doi	doi	PROPN
ejpam-6018	15	2	:	:	PUNCT
ejpam-6018	15	3	https://doi.org/10.29020/nybg.ejpam.v18i2.6018	https://doi.org/10.29020/nybg.ejpam.v18i2.6018	NUM
ejpam-6018	15	4	email	email	NOUN
ejpam-6018	15	5	addresses	address	NOUN
ejpam-6018	15	6	:	:	PUNCT
ejpam-6018	15	7	tahsin.oner@ege.edu.tr	tahsin.oner@ege.edu.tr	NOUN
ejpam-6018	15	8	(	(	PUNCT
ejpam-6018	15	9	t.	t.	NOUN
ejpam-6018	15	10	oner	oner	PROPN
ejpam-6018	15	11	)	)	PUNCT
ejpam-6018	15	12	,	,	PUNCT
ejpam-6018	15	13	nrajesh	nrajesh	PROPN
ejpam-6018	15	14	topology@yahoo.co.in	topology@yahoo.co.in	PROPN
ejpam-6018	15	15	(	(	PUNCT
ejpam-6018	15	16	n.	n.	PROPN
ejpam-6018	15	17	rajesh	rajesh	PROPN
ejpam-6018	15	18	)	)	PUNCT
ejpam-6018	15	19	,	,	PUNCT
ejpam-6018	15	20	aiyared.ia@up.ac.th	aiyared.ia@up.ac.th	NOUN
ejpam-6018	15	21	(	(	PUNCT
ejpam-6018	15	22	a.	a.	NOUN
ejpam-6018	15	23	iampan	iampan	PROPN
ejpam-6018	15	24	)	)	PUNCT
ejpam-6018	15	25	,	,	PUNCT
ejpam-6018	15	26	arsham@uk.ac.ir	arsham@uk.ac.ir	PROPN
ejpam-6018	15	27	(	(	PUNCT
ejpam-6018	15	28	a.	a.	PROPN
ejpam-6018	15	29	borumand	borumand	PROPN
ejpam-6018	15	30	saeid	saeid	PROPN
ejpam-6018	15	31	)	)	PUNCT
ejpam-6018	15	32	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6018	16	1	1	1	NUM
ejpam-6018	16	2	copyright	copyright	NOUN
ejpam-6018	16	3	:	:	PUNCT
ejpam-6018	16	4	©	©	PROPN
ejpam-6018	16	5	2025	2025	NUM
ejpam-6018	16	6	the	the	DET
ejpam-6018	16	7	author(s	author(s	NOUN
ejpam-6018	16	8	)	)	PUNCT
ejpam-6018	16	9	.	.	PUNCT
ejpam-6018	17	1	(	(	PUNCT
ejpam-6018	17	2	cc	cc	NOUN
ejpam-6018	17	3	by	by	ADP
ejpam-6018	17	4	-	-	PUNCT
ejpam-6018	17	5	nc	nc	PROPN
ejpam-6018	17	6	4.0	4.0	NUM
ejpam-6018	17	7	)	)	PUNCT
ejpam-6018	17	8	t.	t.	NOUN
ejpam-6018	17	9	oner	oner	NOUN
ejpam-6018	17	10	et	et	PROPN
ejpam-6018	17	11	al	al	PROPN
ejpam-6018	17	12	.	.	PUNCT
ejpam-6018	17	13	/	/	SYM
ejpam-6018	17	14	eur	eur	PROPN
ejpam-6018	17	15	.	.	PUNCT
ejpam-6018	18	1	j.	j.	PROPN
ejpam-6018	18	2	pure	pure	PROPN
ejpam-6018	18	3	appl	appl	PROPN
ejpam-6018	18	4	.	.	PROPN
ejpam-6018	18	5	math	math	PROPN
ejpam-6018	18	6	,	,	PUNCT
ejpam-6018	18	7	18	18	NUM
ejpam-6018	18	8	(	(	PUNCT
ejpam-6018	18	9	2	2	NUM
ejpam-6018	18	10	)	)	PUNCT
ejpam-6018	18	11	(	(	PUNCT
ejpam-6018	18	12	2025	2025	NUM
ejpam-6018	18	13	)	)	PUNCT
ejpam-6018	18	14	,	,	PUNCT
ejpam-6018	18	15	6018	6018	NUM
ejpam-6018	18	16	2	2	NUM
ejpam-6018	18	17	of	of	ADP
ejpam-6018	18	18	11	11	NUM
ejpam-6018	18	19	sheffer	sheffer	NOUN
ejpam-6018	18	20	operation	operation	NOUN
ejpam-6018	18	21	.	.	PUNCT
ejpam-6018	19	1	this	this	DET
ejpam-6018	19	2	highlights	highlight	VERB
ejpam-6018	19	3	the	the	DET
ejpam-6018	19	4	sheffer	sheffer	NOUN
ejpam-6018	19	5	operation	operation	NOUN
ejpam-6018	19	6	’s	’s	PART
ejpam-6018	19	7	pivotal	pivotal	ADJ
ejpam-6018	19	8	role	role	NOUN
ejpam-6018	19	9	and	and	CCONJ
ejpam-6018	19	10	versatility	versatility	NOUN
ejpam-6018	19	11	in	in	ADP
ejpam-6018	19	12	both	both	CCONJ
ejpam-6018	19	13	logical	logical	ADJ
ejpam-6018	19	14	and	and	CCONJ
ejpam-6018	19	15	algebraic	algebraic	ADJ
ejpam-6018	19	16	settings	setting	NOUN
ejpam-6018	19	17	.	.	PUNCT
ejpam-6018	20	1	the	the	DET
ejpam-6018	20	2	sheffer	sheffer	NOUN
ejpam-6018	20	3	stroke	stroke	NOUN
ejpam-6018	20	4	has	have	AUX
ejpam-6018	20	5	been	be	AUX
ejpam-6018	20	6	utilized	utilize	VERB
ejpam-6018	20	7	in	in	ADP
ejpam-6018	20	8	various	various	ADJ
ejpam-6018	20	9	algebraic	algebraic	ADJ
ejpam-6018	20	10	structures	structure	NOUN
ejpam-6018	20	11	,	,	PUNCT
ejpam-6018	20	12	including	include	VERB
ejpam-6018	20	13	boolean	boolean	ADJ
ejpam-6018	20	14	algebra	algebra	NOUN
ejpam-6018	20	15	,	,	PUNCT
ejpam-6018	20	16	mv	mv	PROPN
ejpam-6018	20	17	-	-	NOUN
ejpam-6018	20	18	algebra	algebra	NOUN
ejpam-6018	20	19	,	,	PUNCT
ejpam-6018	20	20	bl	bl	NOUN
ejpam-6018	20	21	-	-	PUNCT
ejpam-6018	20	22	algebra	algebra	NOUN
ejpam-6018	20	23	,	,	PUNCT
ejpam-6018	20	24	bck	bck	NOUN
ejpam-6018	20	25	-	-	PUNCT
ejpam-6018	20	26	algebra	algebra	NOUN
ejpam-6018	20	27	,	,	PUNCT
ejpam-6018	20	28	be	be	NOUN
ejpam-6018	20	29	-	-	PUNCT
ejpam-6018	20	30	algebra	algebra	NOUN
ejpam-6018	20	31	,	,	PUNCT
ejpam-6018	20	32	ortholattices	ortholattice	NOUN
ejpam-6018	20	33	,	,	PUNCT
ejpam-6018	20	34	and	and	CCONJ
ejpam-6018	20	35	hilbert	hilbert	PROPN
ejpam-6018	20	36	algebra	algebra	PROPN
ejpam-6018	20	37	,	,	PUNCT
ejpam-6018	20	38	among	among	ADP
ejpam-6018	20	39	others	other	NOUN
ejpam-6018	20	40	(	(	PUNCT
ejpam-6018	20	41	refer	refer	VERB
ejpam-6018	20	42	to	to	ADP
ejpam-6018	20	43	[	[	X
ejpam-6018	20	44	2–8	2–8	NUM
ejpam-6018	20	45	]	]	PUNCT
ejpam-6018	20	46	)	)	PUNCT
ejpam-6018	20	47	.	.	PUNCT
ejpam-6018	21	1	sheffer	sheffer	PROPN
ejpam-6018	21	2	stroke	stroke	PROPN
ejpam-6018	21	3	hilbert	hilbert	PROPN
ejpam-6018	21	4	algebras	algebras	PROPN
ejpam-6018	21	5	are	be	AUX
ejpam-6018	21	6	crucial	crucial	ADJ
ejpam-6018	21	7	structures	structure	NOUN
ejpam-6018	21	8	in	in	ADP
ejpam-6018	21	9	algebraic	algebraic	ADJ
ejpam-6018	21	10	logic	logic	NOUN
ejpam-6018	21	11	,	,	PUNCT
ejpam-6018	21	12	providing	provide	VERB
ejpam-6018	21	13	an	an	DET
ejpam-6018	21	14	essential	essential	ADJ
ejpam-6018	21	15	framework	framework	NOUN
ejpam-6018	21	16	for	for	ADP
ejpam-6018	21	17	modeling	model	VERB
ejpam-6018	21	18	logical	logical	ADJ
ejpam-6018	21	19	systems	system	NOUN
ejpam-6018	21	20	.	.	PUNCT
ejpam-6018	22	1	defined	define	VERB
ejpam-6018	22	2	through	through	ADP
ejpam-6018	22	3	the	the	DET
ejpam-6018	22	4	sheffer	sheffer	NOUN
ejpam-6018	22	5	stroke	stroke	NOUN
ejpam-6018	22	6	,	,	PUNCT
ejpam-6018	22	7	these	these	DET
ejpam-6018	22	8	algebras	algebra	NOUN
ejpam-6018	22	9	offer	offer	VERB
ejpam-6018	22	10	a	a	DET
ejpam-6018	22	11	means	mean	NOUN
ejpam-6018	22	12	to	to	PART
ejpam-6018	22	13	represent	represent	VERB
ejpam-6018	22	14	negation	negation	NOUN
ejpam-6018	22	15	and	and	CCONJ
ejpam-6018	22	16	other	other	ADJ
ejpam-6018	22	17	key	key	ADJ
ejpam-6018	22	18	logical	logical	ADJ
ejpam-6018	22	19	operations	operation	NOUN
ejpam-6018	22	20	.	.	PUNCT
ejpam-6018	23	1	as	as	ADP
ejpam-6018	23	2	such	such	ADJ
ejpam-6018	23	3	,	,	PUNCT
ejpam-6018	23	4	they	they	PRON
ejpam-6018	23	5	are	be	AUX
ejpam-6018	23	6	indispensable	indispensable	ADJ
ejpam-6018	23	7	in	in	ADP
ejpam-6018	23	8	the	the	DET
ejpam-6018	23	9	study	study	NOUN
ejpam-6018	23	10	of	of	ADP
ejpam-6018	23	11	algebraic	algebraic	ADJ
ejpam-6018	23	12	logic	logic	NOUN
ejpam-6018	23	13	,	,	PUNCT
ejpam-6018	23	14	particularly	particularly	ADV
ejpam-6018	23	15	in	in	ADP
ejpam-6018	23	16	areas	area	NOUN
ejpam-6018	23	17	like	like	ADP
ejpam-6018	23	18	boolean	boolean	ADJ
ejpam-6018	23	19	algebra	algebra	NOUN
ejpam-6018	23	20	and	and	CCONJ
ejpam-6018	23	21	lattice	lattice	PROPN
ejpam-6018	23	22	theory	theory	NOUN
ejpam-6018	23	23	.	.	PUNCT
ejpam-6018	24	1	recent	recent	ADJ
ejpam-6018	24	2	studies	study	NOUN
ejpam-6018	24	3	have	have	AUX
ejpam-6018	24	4	further	far	ADV
ejpam-6018	24	5	demonstrated	demonstrate	VERB
ejpam-6018	24	6	their	their	PRON
ejpam-6018	24	7	versatility	versatility	NOUN
ejpam-6018	24	8	—	—	PUNCT
ejpam-6018	24	9	for	for	ADP
ejpam-6018	24	10	instance	instance	NOUN
ejpam-6018	24	11	,	,	PUNCT
ejpam-6018	24	12	rajesh	rajesh	PROPN
ejpam-6018	24	13	et	et	PROPN
ejpam-6018	24	14	al	al	PROPN
ejpam-6018	24	15	.	.	PUNCT
ejpam-6018	25	1	[	[	X
ejpam-6018	25	2	9	9	NUM
ejpam-6018	25	3	]	]	PUNCT
ejpam-6018	25	4	investigated	investigate	VERB
ejpam-6018	25	5	the	the	DET
ejpam-6018	25	6	notions	notion	NOUN
ejpam-6018	25	7	of	of	ADP
ejpam-6018	25	8	length	length	NOUN
ejpam-6018	25	9	and	and	CCONJ
ejpam-6018	25	10	mean	mean	VERB
ejpam-6018	25	11	fuzzy	fuzzy	ADJ
ejpam-6018	25	12	ideals	ideal	NOUN
ejpam-6018	25	13	within	within	ADP
ejpam-6018	25	14	this	this	DET
ejpam-6018	25	15	algebraic	algebraic	ADJ
ejpam-6018	25	16	framework	framework	NOUN
ejpam-6018	25	17	,	,	PUNCT
ejpam-6018	25	18	revealing	reveal	VERB
ejpam-6018	25	19	new	new	ADJ
ejpam-6018	25	20	insights	insight	NOUN
ejpam-6018	25	21	into	into	ADP
ejpam-6018	25	22	their	their	PRON
ejpam-6018	25	23	structural	structural	ADJ
ejpam-6018	25	24	depth	depth	NOUN
ejpam-6018	25	25	and	and	CCONJ
ejpam-6018	25	26	fuzzy	fuzzy	ADJ
ejpam-6018	25	27	generalizations	generalization	NOUN
ejpam-6018	25	28	.	.	PUNCT
ejpam-6018	26	1	this	this	DET
ejpam-6018	26	2	line	line	NOUN
ejpam-6018	26	3	of	of	ADP
ejpam-6018	26	4	research	research	NOUN
ejpam-6018	26	5	continues	continue	VERB
ejpam-6018	26	6	to	to	PART
ejpam-6018	26	7	highlight	highlight	VERB
ejpam-6018	26	8	the	the	DET
ejpam-6018	26	9	richness	richness	NOUN
ejpam-6018	26	10	of	of	ADP
ejpam-6018	26	11	sheffer	sheffer	PROPN
ejpam-6018	26	12	stroke	stroke	PROPN
ejpam-6018	26	13	hilbert	hilbert	PROPN
ejpam-6018	26	14	algebras	algebras	PROPN
ejpam-6018	26	15	in	in	ADP
ejpam-6018	26	16	both	both	CCONJ
ejpam-6018	26	17	crisp	crisp	ADJ
ejpam-6018	26	18	and	and	CCONJ
ejpam-6018	26	19	fuzzy	fuzzy	ADJ
ejpam-6018	26	20	logical	logical	ADJ
ejpam-6018	26	21	environments	environment	NOUN
ejpam-6018	26	22	.	.	PUNCT
ejpam-6018	27	1	in	in	ADP
ejpam-6018	27	2	1999	1999	NUM
ejpam-6018	27	3	,	,	PUNCT
ejpam-6018	27	4	molodtsov	molodtsov	NOUN
ejpam-6018	27	5	[	[	X
ejpam-6018	27	6	10	10	NUM
ejpam-6018	27	7	]	]	PUNCT
ejpam-6018	27	8	introduced	introduce	VERB
ejpam-6018	27	9	the	the	DET
ejpam-6018	27	10	soft	soft	ADJ
ejpam-6018	27	11	set	set	NOUN
ejpam-6018	27	12	theory	theory	NOUN
ejpam-6018	27	13	,	,	PUNCT
ejpam-6018	27	14	offering	offer	VERB
ejpam-6018	27	15	a	a	DET
ejpam-6018	27	16	novel	novel	ADJ
ejpam-6018	27	17	mathematical	mathematical	ADJ
ejpam-6018	27	18	tool	tool	NOUN
ejpam-6018	27	19	designed	design	VERB
ejpam-6018	27	20	to	to	PART
ejpam-6018	27	21	address	address	VERB
ejpam-6018	27	22	uncertainties	uncertainty	NOUN
ejpam-6018	27	23	,	,	PUNCT
ejpam-6018	27	24	free	free	ADJ
ejpam-6018	27	25	from	from	ADP
ejpam-6018	27	26	the	the	DET
ejpam-6018	27	27	limitations	limitation	NOUN
ejpam-6018	27	28	of	of	ADP
ejpam-6018	27	29	traditional	traditional	ADJ
ejpam-6018	27	30	theoretical	theoretical	ADJ
ejpam-6018	27	31	models	model	NOUN
ejpam-6018	27	32	.	.	PUNCT
ejpam-6018	28	1	soft	soft	ADJ
ejpam-6018	28	2	sets	set	NOUN
ejpam-6018	28	3	have	have	AUX
ejpam-6018	28	4	recently	recently	ADV
ejpam-6018	28	5	emerged	emerge	VERB
ejpam-6018	28	6	as	as	ADP
ejpam-6018	28	7	a	a	DET
ejpam-6018	28	8	promising	promising	ADJ
ejpam-6018	28	9	approach	approach	NOUN
ejpam-6018	28	10	to	to	ADP
ejpam-6018	28	11	modeling	model	VERB
ejpam-6018	28	12	imprecision	imprecision	NOUN
ejpam-6018	28	13	and	and	CCONJ
ejpam-6018	28	14	flexibility	flexibility	NOUN
ejpam-6018	28	15	in	in	ADP
ejpam-6018	28	16	mathematical	mathematical	ADJ
ejpam-6018	28	17	frameworks	framework	NOUN
ejpam-6018	28	18	.	.	PUNCT
ejpam-6018	29	1	they	they	PRON
ejpam-6018	29	2	enable	enable	VERB
ejpam-6018	29	3	the	the	DET
ejpam-6018	29	4	handling	handling	NOUN
ejpam-6018	29	5	of	of	ADP
ejpam-6018	29	6	uncertainty	uncertainty	NOUN
ejpam-6018	29	7	within	within	ADP
ejpam-6018	29	8	algebraic	algebraic	ADJ
ejpam-6018	29	9	structures	structure	NOUN
ejpam-6018	29	10	,	,	PUNCT
ejpam-6018	29	11	allowing	allow	VERB
ejpam-6018	29	12	for	for	ADP
ejpam-6018	29	13	a	a	DET
ejpam-6018	29	14	more	more	ADV
ejpam-6018	29	15	adaptable	adaptable	ADJ
ejpam-6018	29	16	study	study	NOUN
ejpam-6018	29	17	of	of	ADP
ejpam-6018	29	18	these	these	DET
ejpam-6018	29	19	systems	system	NOUN
ejpam-6018	29	20	under	under	ADP
ejpam-6018	29	21	conditions	condition	NOUN
ejpam-6018	29	22	that	that	PRON
ejpam-6018	29	23	are	be	AUX
ejpam-6018	29	24	not	not	PART
ejpam-6018	29	25	precisely	precisely	ADV
ejpam-6018	29	26	defined	define	VERB
ejpam-6018	29	27	.	.	PUNCT
ejpam-6018	30	1	building	build	VERB
ejpam-6018	30	2	on	on	ADP
ejpam-6018	30	3	soft	soft	ADJ
ejpam-6018	30	4	set	set	NOUN
ejpam-6018	30	5	theory	theory	NOUN
ejpam-6018	30	6	,	,	PUNCT
ejpam-6018	30	7	soft	soft	ADJ
ejpam-6018	30	8	subalgebras	subalgebra	NOUN
ejpam-6018	30	9	extend	extend	VERB
ejpam-6018	30	10	these	these	DET
ejpam-6018	30	11	concepts	concept	NOUN
ejpam-6018	30	12	into	into	ADP
ejpam-6018	30	13	classical	classical	ADJ
ejpam-6018	30	14	algebraic	algebraic	ADJ
ejpam-6018	30	15	systems	system	NOUN
ejpam-6018	30	16	,	,	PUNCT
ejpam-6018	30	17	providing	provide	VERB
ejpam-6018	30	18	a	a	DET
ejpam-6018	30	19	broader	broad	ADJ
ejpam-6018	30	20	understanding	understanding	NOUN
ejpam-6018	30	21	of	of	ADP
ejpam-6018	30	22	their	their	PRON
ejpam-6018	30	23	properties	property	NOUN
ejpam-6018	30	24	and	and	CCONJ
ejpam-6018	30	25	behaviors	behavior	NOUN
ejpam-6018	30	26	.	.	PUNCT
ejpam-6018	31	1	this	this	DET
ejpam-6018	31	2	paper	paper	NOUN
ejpam-6018	31	3	explores	explore	VERB
ejpam-6018	31	4	new	new	ADJ
ejpam-6018	31	5	ideas	idea	NOUN
ejpam-6018	31	6	within	within	ADP
ejpam-6018	31	7	sheffer	sheffer	PROPN
ejpam-6018	31	8	stroke	stroke	PROPN
ejpam-6018	31	9	hilbert	hilbert	PROPN
ejpam-6018	31	10	algebras	algebras	PROPN
ejpam-6018	31	11	,	,	PUNCT
ejpam-6018	31	12	such	such	ADJ
ejpam-6018	31	13	as	as	ADP
ejpam-6018	31	14	soft	soft	ADJ
ejpam-6018	31	15	n	n	NOUN
ejpam-6018	31	16	sets	set	NOUN
ejpam-6018	31	17	,	,	PUNCT
ejpam-6018	31	18	soft	soft	ADJ
ejpam-6018	31	19	n	n	PRON
ejpam-6018	31	20	-subalgebras	-subalgebra	NOUN
ejpam-6018	31	21	,	,	PUNCT
ejpam-6018	31	22	and	and	CCONJ
ejpam-6018	31	23	soft	soft	ADJ
ejpam-6018	31	24	n	n	CCONJ
ejpam-6018	31	25	-ideals	-ideal	NOUN
ejpam-6018	31	26	,	,	PUNCT
ejpam-6018	31	27	with	with	ADP
ejpam-6018	31	28	a	a	DET
ejpam-6018	31	29	focus	focus	NOUN
ejpam-6018	31	30	on	on	ADP
ejpam-6018	31	31	types	type	NOUN
ejpam-6018	31	32	(	(	PUNCT
ejpam-6018	31	33	∈,∈	∈,∈	X
ejpam-6018	31	34	)	)	PUNCT
ejpam-6018	31	35	and	and	CCONJ
ejpam-6018	31	36	(	(	PUNCT
ejpam-6018	31	37	∈,∈	∈,∈	X
ejpam-6018	31	38	∨q	∨q	NOUN
ejpam-6018	31	39	)	)	PUNCT
ejpam-6018	31	40	.	.	PUNCT
ejpam-6018	32	1	these	these	DET
ejpam-6018	32	2	concepts	concept	NOUN
ejpam-6018	32	3	are	be	AUX
ejpam-6018	32	4	analyzed	analyze	VERB
ejpam-6018	32	5	through	through	ADP
ejpam-6018	32	6	the	the	DET
ejpam-6018	32	7	lens	lens	NOUN
ejpam-6018	32	8	of	of	ADP
ejpam-6018	32	9	n	n	DET
ejpam-6018	32	10	-structures	-structure	NOUN
ejpam-6018	32	11	,	,	PUNCT
ejpam-6018	32	12	a	a	DET
ejpam-6018	32	13	generalized	generalized	ADJ
ejpam-6018	32	14	framework	framework	NOUN
ejpam-6018	32	15	that	that	PRON
ejpam-6018	32	16	investigates	investigate	VERB
ejpam-6018	32	17	algebraic	algebraic	ADJ
ejpam-6018	32	18	systems	system	NOUN
ejpam-6018	32	19	in	in	ADP
ejpam-6018	32	20	more	more	ADV
ejpam-6018	32	21	flexible	flexible	ADJ
ejpam-6018	32	22	conditions	condition	NOUN
ejpam-6018	32	23	.	.	PUNCT
ejpam-6018	33	1	the	the	DET
ejpam-6018	33	2	study	study	NOUN
ejpam-6018	33	3	examines	examine	VERB
ejpam-6018	33	4	the	the	DET
ejpam-6018	33	5	features	feature	NOUN
ejpam-6018	33	6	of	of	ADP
ejpam-6018	33	7	n	n	NOUN
ejpam-6018	33	8	-subalgebras	-subalgebra	NOUN
ejpam-6018	33	9	and	and	CCONJ
ejpam-6018	33	10	n	n	PRON
ejpam-6018	33	11	-ideals	-ideal	NOUN
ejpam-6018	33	12	,	,	PUNCT
ejpam-6018	33	13	along	along	ADP
ejpam-6018	33	14	with	with	ADP
ejpam-6018	33	15	their	their	PRON
ejpam-6018	33	16	soft	soft	ADJ
ejpam-6018	33	17	variants	variant	NOUN
ejpam-6018	33	18	,	,	PUNCT
ejpam-6018	33	19	to	to	PART
ejpam-6018	33	20	provide	provide	VERB
ejpam-6018	33	21	a	a	DET
ejpam-6018	33	22	deeper	deep	ADJ
ejpam-6018	33	23	understanding	understanding	NOUN
ejpam-6018	33	24	of	of	ADP
ejpam-6018	33	25	their	their	PRON
ejpam-6018	33	26	behavior	behavior	NOUN
ejpam-6018	33	27	in	in	ADP
ejpam-6018	33	28	various	various	ADJ
ejpam-6018	33	29	contexts	contexts	NOUN
ejpam-6018	33	30	.	.	PUNCT
ejpam-6018	34	1	the	the	DET
ejpam-6018	34	2	main	main	ADJ
ejpam-6018	34	3	objective	objective	NOUN
ejpam-6018	34	4	of	of	ADP
ejpam-6018	34	5	this	this	DET
ejpam-6018	34	6	research	research	NOUN
ejpam-6018	34	7	is	be	AUX
ejpam-6018	34	8	to	to	PART
ejpam-6018	34	9	study	study	VERB
ejpam-6018	34	10	soft	soft	ADJ
ejpam-6018	34	11	n	n	CCONJ
ejpam-6018	34	12	-subalgebras	-subalgebra	NOUN
ejpam-6018	34	13	and	and	CCONJ
ejpam-6018	34	14	n	n	NUM
ejpam-6018	34	15	-ideals	-ideal	NOUN
ejpam-6018	34	16	within	within	ADP
ejpam-6018	34	17	sheffer	sheffer	PROPN
ejpam-6018	34	18	stroke	stroke	NOUN
ejpam-6018	34	19	hilbert	hilbert	PROPN
ejpam-6018	34	20	algebras	algebras	PROPN
ejpam-6018	34	21	.	.	PUNCT
ejpam-6018	35	1	additionally	additionally	ADV
ejpam-6018	35	2	,	,	PUNCT
ejpam-6018	35	3	the	the	DET
ejpam-6018	35	4	paper	paper	NOUN
ejpam-6018	35	5	aims	aim	VERB
ejpam-6018	35	6	to	to	PART
ejpam-6018	35	7	investigate	investigate	VERB
ejpam-6018	35	8	the	the	DET
ejpam-6018	35	9	interconnections	interconnection	NOUN
ejpam-6018	35	10	between	between	ADP
ejpam-6018	35	11	soft	soft	ADJ
ejpam-6018	35	12	n	n	CCONJ
ejpam-6018	35	13	-sets	-set	NOUN
ejpam-6018	35	14	and	and	CCONJ
ejpam-6018	35	15	n	n	PRON
ejpam-6018	35	16	-structures	-structure	NOUN
ejpam-6018	35	17	,	,	PUNCT
ejpam-6018	35	18	contributing	contribute	VERB
ejpam-6018	35	19	to	to	ADP
ejpam-6018	35	20	the	the	DET
ejpam-6018	35	21	broader	broad	ADJ
ejpam-6018	35	22	field	field	NOUN
ejpam-6018	35	23	of	of	ADP
ejpam-6018	35	24	algebraic	algebraic	ADJ
ejpam-6018	35	25	logic	logic	NOUN
ejpam-6018	35	26	.	.	PUNCT
ejpam-6018	36	1	through	through	ADP
ejpam-6018	36	2	this	this	DET
ejpam-6018	36	3	analysis	analysis	NOUN
ejpam-6018	36	4	,	,	PUNCT
ejpam-6018	36	5	we	we	PRON
ejpam-6018	36	6	seek	seek	VERB
ejpam-6018	36	7	to	to	PART
ejpam-6018	36	8	further	further	VERB
ejpam-6018	36	9	our	our	PRON
ejpam-6018	36	10	comprehension	comprehension	NOUN
ejpam-6018	36	11	of	of	ADP
ejpam-6018	36	12	the	the	DET
ejpam-6018	36	13	role	role	NOUN
ejpam-6018	36	14	that	that	PRON
ejpam-6018	36	15	sheffer	sheffer	VERB
ejpam-6018	36	16	stroke	stroke	NOUN
ejpam-6018	36	17	hilbert	hilbert	PROPN
ejpam-6018	36	18	algebras	algebras	PROPN
ejpam-6018	36	19	play	play	VERB
ejpam-6018	36	20	in	in	ADP
ejpam-6018	36	21	both	both	CCONJ
ejpam-6018	36	22	algebraic	algebraic	ADJ
ejpam-6018	36	23	and	and	CCONJ
ejpam-6018	36	24	logical	logical	ADJ
ejpam-6018	36	25	systems	system	NOUN
ejpam-6018	36	26	.	.	PUNCT
ejpam-6018	37	1	2	2	X
ejpam-6018	37	2	.	.	X
ejpam-6018	37	3	preliminaries	preliminary	NOUN
ejpam-6018	37	4	in	in	ADP
ejpam-6018	37	5	this	this	DET
ejpam-6018	37	6	section	section	NOUN
ejpam-6018	37	7	,	,	PUNCT
ejpam-6018	37	8	we	we	PRON
ejpam-6018	37	9	revisit	revisit	VERB
ejpam-6018	37	10	essential	essential	ADJ
ejpam-6018	37	11	concepts	concept	NOUN
ejpam-6018	37	12	and	and	CCONJ
ejpam-6018	37	13	results	result	NOUN
ejpam-6018	37	14	concerning	concern	VERB
ejpam-6018	37	15	sheffer	sheffer	NOUN
ejpam-6018	37	16	stroke	stroke	PROPN
ejpam-6018	37	17	hilbert	hilbert	PROPN
ejpam-6018	37	18	algebras	algebras	PROPN
ejpam-6018	37	19	,	,	PUNCT
ejpam-6018	37	20	which	which	PRON
ejpam-6018	37	21	will	will	AUX
ejpam-6018	37	22	be	be	AUX
ejpam-6018	37	23	referenced	reference	VERB
ejpam-6018	37	24	in	in	ADP
ejpam-6018	37	25	the	the	DET
ejpam-6018	37	26	subsequent	subsequent	ADJ
ejpam-6018	37	27	sections	section	NOUN
ejpam-6018	37	28	.	.	PUNCT
ejpam-6018	38	1	definition	definition	NOUN
ejpam-6018	38	2	1	1	NUM
ejpam-6018	38	3	.	.	PUNCT
ejpam-6018	39	1	[	[	X
ejpam-6018	39	2	1	1	X
ejpam-6018	39	3	]	]	PUNCT
ejpam-6018	39	4	let	let	VERB
ejpam-6018	39	5	a	a	PRON
ejpam-6018	39	6	:	:	PUNCT
ejpam-6018	39	7	=	=	SYM
ejpam-6018	39	8	(	(	PUNCT
ejpam-6018	39	9	a	a	PRON
ejpam-6018	39	10	,	,	PUNCT
ejpam-6018	39	11	|	|	NOUN
ejpam-6018	39	12	)	)	PUNCT
ejpam-6018	39	13	be	be	AUX
ejpam-6018	39	14	a	a	DET
ejpam-6018	39	15	groupoid	groupoid	NOUN
ejpam-6018	39	16	.	.	PUNCT
ejpam-6018	40	1	then	then	ADV
ejpam-6018	40	2	the	the	DET
ejpam-6018	40	3	operation	operation	NOUN
ejpam-6018	40	4	|	|	ADV
ejpam-6018	40	5	is	be	AUX
ejpam-6018	40	6	said	say	VERB
ejpam-6018	40	7	to	to	PART
ejpam-6018	40	8	be	be	AUX
ejpam-6018	40	9	a	a	DET
ejpam-6018	40	10	sheffer	sheffer	NOUN
ejpam-6018	40	11	stroke	stroke	NOUN
ejpam-6018	40	12	or	or	CCONJ
ejpam-6018	40	13	a	a	DET
ejpam-6018	40	14	sheffer	sheffer	NOUN
ejpam-6018	40	15	operation	operation	NOUN
ejpam-6018	40	16	if	if	SCONJ
ejpam-6018	40	17	it	it	PRON
ejpam-6018	40	18	satisfies	satisfy	VERB
ejpam-6018	40	19	:	:	PUNCT
ejpam-6018	40	20	(	(	PUNCT
ejpam-6018	40	21	s1	s1	NOUN
ejpam-6018	40	22	)	)	PUNCT
ejpam-6018	40	23	(	(	PUNCT
ejpam-6018	40	24	∀ξ	∀ξ	X
ejpam-6018	40	25	,	,	PUNCT
ejpam-6018	40	26	ζ	ζ	PROPN
ejpam-6018	40	27	∈	∈	PROPN
ejpam-6018	40	28	a	a	NOUN
ejpam-6018	40	29	)	)	PUNCT
ejpam-6018	40	30	(	(	PUNCT
ejpam-6018	40	31	ξ	ξ	X
ejpam-6018	40	32	|	|	ADV
ejpam-6018	40	33	ζ	ζ	NOUN
ejpam-6018	40	34	=	=	SYM
ejpam-6018	40	35	ζ	ζ	NOUN
ejpam-6018	40	36	|	|	NOUN
ejpam-6018	40	37	ξ	ξ	NOUN
ejpam-6018	40	38	)	)	PUNCT
ejpam-6018	40	39	,	,	PUNCT
ejpam-6018	41	1	t.	t.	PROPN
ejpam-6018	41	2	oner	oner	NOUN
ejpam-6018	41	3	et	et	PROPN
ejpam-6018	41	4	al	al	PROPN
ejpam-6018	41	5	.	.	PUNCT
ejpam-6018	41	6	/	/	SYM
ejpam-6018	41	7	eur	eur	PROPN
ejpam-6018	41	8	.	.	PUNCT
ejpam-6018	42	1	j.	j.	PROPN
ejpam-6018	42	2	pure	pure	PROPN
ejpam-6018	42	3	appl	appl	PROPN
ejpam-6018	42	4	.	.	PROPN
ejpam-6018	42	5	math	math	PROPN
ejpam-6018	42	6	,	,	PUNCT
ejpam-6018	42	7	18	18	NUM
ejpam-6018	42	8	(	(	PUNCT
ejpam-6018	42	9	2	2	NUM
ejpam-6018	42	10	)	)	PUNCT
ejpam-6018	42	11	(	(	PUNCT
ejpam-6018	42	12	2025	2025	NUM
ejpam-6018	42	13	)	)	PUNCT
ejpam-6018	42	14	,	,	PUNCT
ejpam-6018	42	15	6018	6018	NUM
ejpam-6018	42	16	3	3	NUM
ejpam-6018	42	17	of	of	ADP
ejpam-6018	42	18	11	11	NUM
ejpam-6018	42	19	(	(	PUNCT
ejpam-6018	42	20	s2	s2	PROPN
ejpam-6018	42	21	)	)	PUNCT
ejpam-6018	42	22	(	(	PUNCT
ejpam-6018	42	23	∀ξ	∀ξ	X
ejpam-6018	42	24	,	,	PUNCT
ejpam-6018	42	25	ζ	ζ	PROPN
ejpam-6018	42	26	∈	∈	PROPN
ejpam-6018	42	27	a	a	NOUN
ejpam-6018	42	28	)	)	PUNCT
ejpam-6018	42	29	(	(	PUNCT
ejpam-6018	42	30	(	(	PUNCT
ejpam-6018	42	31	ξ	ξ	PROPN
ejpam-6018	42	32	|	|	NOUN
ejpam-6018	42	33	ξ	ξ	NOUN
ejpam-6018	42	34	)	)	PUNCT
ejpam-6018	43	1	|	|	ADV
ejpam-6018	43	2	(	(	PUNCT
ejpam-6018	43	3	ξ	ξ	PROPN
ejpam-6018	43	4	|	|	NOUN
ejpam-6018	43	5	ζ	ζ	NOUN
ejpam-6018	43	6	)	)	PUNCT
ejpam-6018	43	7	=	=	SYM
ejpam-6018	43	8	ξ	ξ	NOUN
ejpam-6018	43	9	)	)	PUNCT
ejpam-6018	43	10	,	,	PUNCT
ejpam-6018	43	11	(	(	PUNCT
ejpam-6018	43	12	s3	s3	PROPN
ejpam-6018	43	13	)	)	PUNCT
ejpam-6018	43	14	(	(	PUNCT
ejpam-6018	43	15	∀ξ	∀ξ	X
ejpam-6018	43	16	,	,	PUNCT
ejpam-6018	43	17	ζ	ζ	NOUN
ejpam-6018	43	18	,	,	PUNCT
ejpam-6018	43	19	τ	τ	PROPN
ejpam-6018	43	20	∈	∈	PROPN
ejpam-6018	43	21	a	a	PRON
ejpam-6018	43	22	)	)	PUNCT
ejpam-6018	43	23	(	(	PUNCT
ejpam-6018	43	24	ξ	ξ	X
ejpam-6018	43	25	|	|	ADV
ejpam-6018	43	26	(	(	PUNCT
ejpam-6018	43	27	(	(	PUNCT
ejpam-6018	43	28	ζ	ζ	NOUN
ejpam-6018	43	29	|	|	NOUN
ejpam-6018	43	30	τ	τ	NOUN
ejpam-6018	43	31	)	)	PUNCT
ejpam-6018	44	1	|	|	ADV
ejpam-6018	44	2	(	(	PUNCT
ejpam-6018	44	3	ζ	ζ	NOUN
ejpam-6018	44	4	|	|	NOUN
ejpam-6018	44	5	τ	τ	NOUN
ejpam-6018	44	6	)	)	PUNCT
ejpam-6018	44	7	)	)	PUNCT
ejpam-6018	45	1	=	=	SYM
ejpam-6018	45	2	(	(	PUNCT
ejpam-6018	45	3	(	(	PUNCT
ejpam-6018	45	4	ξ	ξ	PROPN
ejpam-6018	45	5	|	|	NOUN
ejpam-6018	45	6	ζ	ζ	NOUN
ejpam-6018	45	7	)	)	PUNCT
ejpam-6018	45	8	|	|	ADV
ejpam-6018	45	9	(	(	PUNCT
ejpam-6018	45	10	ξ	ξ	PROPN
ejpam-6018	45	11	|	|	ADV
ejpam-6018	45	12	ζ	ζ	NOUN
ejpam-6018	45	13	)	)	PUNCT
ejpam-6018	45	14	)	)	PUNCT
ejpam-6018	46	1	|	|	ADV
ejpam-6018	46	2	τ	τ	PROPN
ejpam-6018	46	3	)	)	PUNCT
ejpam-6018	46	4	,	,	PUNCT
ejpam-6018	46	5	(	(	PUNCT
ejpam-6018	46	6	s4	s4	PROPN
ejpam-6018	46	7	)	)	PUNCT
ejpam-6018	46	8	(	(	PUNCT
ejpam-6018	46	9	∀ξ	∀ξ	X
ejpam-6018	46	10	,	,	PUNCT
ejpam-6018	46	11	ζ	ζ	NOUN
ejpam-6018	46	12	,	,	PUNCT
ejpam-6018	46	13	τ	τ	PROPN
ejpam-6018	46	14	∈	∈	PROPN
ejpam-6018	46	15	a	a	PRON
ejpam-6018	46	16	)	)	PUNCT
ejpam-6018	46	17	(	(	PUNCT
ejpam-6018	46	18	(	(	PUNCT
ejpam-6018	46	19	ξ	ξ	X
ejpam-6018	46	20	|	|	NOUN
ejpam-6018	46	21	(	(	PUNCT
ejpam-6018	46	22	(	(	PUNCT
ejpam-6018	46	23	ξ	ξ	PROPN
ejpam-6018	46	24	|	|	NOUN
ejpam-6018	46	25	ξ	ξ	NOUN
ejpam-6018	46	26	)	)	PUNCT
ejpam-6018	47	1	|	|	ADV
ejpam-6018	47	2	(	(	PUNCT
ejpam-6018	47	3	ζ	ζ	NOUN
ejpam-6018	47	4	|	|	ADV
ejpam-6018	47	5	ζ	ζ	NOUN
ejpam-6018	47	6	)	)	PUNCT
ejpam-6018	47	7	)	)	PUNCT
ejpam-6018	47	8	)	)	PUNCT
ejpam-6018	48	1	|	|	ADV
ejpam-6018	48	2	(	(	PUNCT
ejpam-6018	48	3	ξ	ξ	PROPN
ejpam-6018	48	4	|	|	ADV
ejpam-6018	48	5	(	(	PUNCT
ejpam-6018	48	6	(	(	PUNCT
ejpam-6018	48	7	ξ	ξ	PROPN
ejpam-6018	48	8	|	|	NOUN
ejpam-6018	48	9	ξ	ξ	NOUN
ejpam-6018	48	10	)	)	PUNCT
ejpam-6018	48	11	|	|	ADV
ejpam-6018	48	12	(	(	PUNCT
ejpam-6018	48	13	ζ	ζ	NOUN
ejpam-6018	48	14	|	|	ADV
ejpam-6018	48	15	ζ	ζ	NOUN
ejpam-6018	48	16	)	)	PUNCT
ejpam-6018	48	17	)	)	PUNCT
ejpam-6018	48	18	)	)	PUNCT
ejpam-6018	49	1	=	=	SYM
ejpam-6018	49	2	ξ	ξ	X
ejpam-6018	49	3	)	)	PUNCT
ejpam-6018	49	4	.	.	PUNCT
ejpam-6018	50	1	to	to	PART
ejpam-6018	50	2	improve	improve	VERB
ejpam-6018	50	3	the	the	DET
ejpam-6018	50	4	clarity	clarity	NOUN
ejpam-6018	50	5	of	of	ADP
ejpam-6018	50	6	this	this	DET
ejpam-6018	50	7	manuscript	manuscript	NOUN
ejpam-6018	50	8	,	,	PUNCT
ejpam-6018	50	9	we	we	PRON
ejpam-6018	50	10	introduce	introduce	VERB
ejpam-6018	50	11	the	the	DET
ejpam-6018	50	12	following	following	ADJ
ejpam-6018	50	13	notation	notation	NOUN
ejpam-6018	50	14	,	,	PUNCT
ejpam-6018	50	15	which	which	PRON
ejpam-6018	50	16	will	will	AUX
ejpam-6018	50	17	be	be	AUX
ejpam-6018	50	18	used	use	VERB
ejpam-6018	50	19	consistently	consistently	ADV
ejpam-6018	50	20	throughout	throughout	ADP
ejpam-6018	50	21	the	the	DET
ejpam-6018	50	22	text	text	NOUN
ejpam-6018	50	23	:	:	PUNCT
ejpam-6018	50	24	ξ	ξ	X
ejpam-6018	50	25	|	|	ADV
ejpam-6018	50	26	(	(	PUNCT
ejpam-6018	50	27	ζ	ζ	NOUN
ejpam-6018	50	28	|	|	ADV
ejpam-6018	50	29	ζ	ζ	NOUN
ejpam-6018	50	30	)	)	PUNCT
ejpam-6018	50	31	:	:	PUNCT
ejpam-6018	50	32	=	=	SYM
ejpam-6018	50	33	ξζ	ξζ	INTJ
ejpam-6018	50	34	.	.	PUNCT
ejpam-6018	51	1	for	for	ADP
ejpam-6018	51	2	all	all	DET
ejpam-6018	51	3	elements	element	NOUN
ejpam-6018	51	4	ξ	ξ	NOUN
ejpam-6018	51	5	,	,	PUNCT
ejpam-6018	51	6	ζ	ζ	PROPN
ejpam-6018	51	7	∈	∈	PROPN
ejpam-6018	51	8	a.	a.	NOUN
ejpam-6018	51	9	definition	definition	NOUN
ejpam-6018	51	10	2	2	NUM
ejpam-6018	51	11	.	.	PUNCT
ejpam-6018	52	1	[	[	X
ejpam-6018	52	2	11	11	NUM
ejpam-6018	52	3	]	]	PUNCT
ejpam-6018	52	4	a	a	DET
ejpam-6018	52	5	sheffer	sheffer	NOUN
ejpam-6018	52	6	stroke	stroke	NOUN
ejpam-6018	52	7	hilbert	hilbert	PROPN
ejpam-6018	52	8	algebra	algebra	PROPN
ejpam-6018	52	9	(	(	PUNCT
ejpam-6018	52	10	ssh	ssh	NOUN
ejpam-6018	52	11	-	-	PUNCT
ejpam-6018	52	12	algebra	algebra	NOUN
ejpam-6018	52	13	)	)	PUNCT
ejpam-6018	52	14	is	be	AUX
ejpam-6018	52	15	a	a	DET
ejpam-6018	52	16	structure	structure	NOUN
ejpam-6018	52	17	hs	hs	INTJ
ejpam-6018	52	18	:	:	PUNCT
ejpam-6018	52	19	=	=	SYM
ejpam-6018	52	20	(	(	PUNCT
ejpam-6018	52	21	h	h	NOUN
ejpam-6018	52	22	,	,	PUNCT
ejpam-6018	52	23	|	|	ADV
ejpam-6018	52	24	,	,	PUNCT
ejpam-6018	52	25	0	0	NUM
ejpam-6018	52	26	)	)	PUNCT
ejpam-6018	52	27	of	of	ADP
ejpam-6018	52	28	type	type	NOUN
ejpam-6018	52	29	(	(	PUNCT
ejpam-6018	52	30	2	2	NUM
ejpam-6018	52	31	,	,	PUNCT
ejpam-6018	52	32	0	0	NUM
ejpam-6018	52	33	)	)	PUNCT
ejpam-6018	52	34	,	,	PUNCT
ejpam-6018	52	35	in	in	ADP
ejpam-6018	52	36	which	which	PRON
ejpam-6018	52	37	h	h	NOUN
ejpam-6018	52	38	is	be	AUX
ejpam-6018	52	39	a	a	DET
ejpam-6018	52	40	nonempty	nonempty	ADJ
ejpam-6018	52	41	set	set	NOUN
ejpam-6018	52	42	,	,	PUNCT
ejpam-6018	52	43	|	|	ADV
ejpam-6018	52	44	is	be	AUX
ejpam-6018	52	45	a	a	DET
ejpam-6018	52	46	sheffer	sheffer	NOUN
ejpam-6018	52	47	stroke	stroke	NOUN
ejpam-6018	52	48	on	on	ADP
ejpam-6018	52	49	h	h	NOUN
ejpam-6018	52	50	,	,	PUNCT
ejpam-6018	52	51	and	and	CCONJ
ejpam-6018	52	52	0	0	NUM
ejpam-6018	52	53	is	be	AUX
ejpam-6018	52	54	the	the	DET
ejpam-6018	52	55	fixed	fix	VERB
ejpam-6018	52	56	element	element	NOUN
ejpam-6018	52	57	in	in	ADP
ejpam-6018	52	58	h	h	NOUN
ejpam-6018	52	59	satisfying	satisfy	VERB
ejpam-6018	52	60	specific	specific	ADJ
ejpam-6018	52	61	conditions	condition	NOUN
ejpam-6018	52	62	:	:	PUNCT
ejpam-6018	52	63	(	(	PUNCT
ejpam-6018	52	64	sh1	sh1	PROPN
ejpam-6018	52	65	)	)	PUNCT
ejpam-6018	52	66	(	(	PUNCT
ejpam-6018	52	67	∀ξ	∀ξ	X
ejpam-6018	52	68	,	,	PUNCT
ejpam-6018	52	69	ζ	ζ	NOUN
ejpam-6018	52	70	,	,	PUNCT
ejpam-6018	52	71	τ	τ	PROPN
ejpam-6018	52	72	∈	∈	PROPN
ejpam-6018	52	73	h	h	NOUN
ejpam-6018	52	74	)	)	PUNCT
ejpam-6018	52	75	(	(	PUNCT
ejpam-6018	52	76	(	(	PUNCT
ejpam-6018	52	77	ξ	ξ	X
ejpam-6018	52	78	|	|	ADV
ejpam-6018	52	79	(	(	PUNCT
ejpam-6018	52	80	ζτ	ζτ	NOUN
ejpam-6018	52	81	|	|	ADV
ejpam-6018	52	82	ζτ	ζτ	PROPN
ejpam-6018	52	83	)	)	PUNCT
ejpam-6018	52	84	)	)	PUNCT
ejpam-6018	53	1	|	|	ADV
ejpam-6018	53	2	(	(	PUNCT
ejpam-6018	53	3	(	(	PUNCT
ejpam-6018	53	4	ξζ	ξζ	INTJ
ejpam-6018	53	5	|	|	INTJ
ejpam-6018	53	6	(	(	PUNCT
ejpam-6018	53	7	ξτ	ξτ	ADV
ejpam-6018	53	8	|	|	ADV
ejpam-6018	53	9	ξτ	ξτ	NOUN
ejpam-6018	53	10	)	)	PUNCT
ejpam-6018	53	11	)	)	PUNCT
ejpam-6018	54	1	|	|	ADV
ejpam-6018	54	2	(	(	PUNCT
ejpam-6018	54	3	ξζ	ξζ	INTJ
ejpam-6018	54	4	|	|	INTJ
ejpam-6018	54	5	(	(	PUNCT
ejpam-6018	54	6	ξτ	ξτ	ADV
ejpam-6018	54	7	|	|	ADV
ejpam-6018	54	8	ξτ	ξτ	NOUN
ejpam-6018	54	9	)	)	PUNCT
ejpam-6018	54	10	)	)	PUNCT
ejpam-6018	54	11	)	)	PUNCT
ejpam-6018	55	1	=	=	PUNCT
ejpam-6018	55	2	ξξ	ξξ	X
ejpam-6018	55	3	)	)	PUNCT
ejpam-6018	55	4	,	,	PUNCT
ejpam-6018	55	5	(	(	PUNCT
ejpam-6018	55	6	sh2	sh2	NOUN
ejpam-6018	55	7	)	)	PUNCT
ejpam-6018	55	8	(	(	PUNCT
ejpam-6018	55	9	∀ξ	∀ξ	NOUN
ejpam-6018	55	10	,	,	PUNCT
ejpam-6018	55	11	ζ	ζ	PROPN
ejpam-6018	55	12	∈	∈	PROPN
ejpam-6018	55	13	h	h	NOUN
ejpam-6018	55	14	)	)	PUNCT
ejpam-6018	55	15	(	(	PUNCT
ejpam-6018	55	16	ξζ	ξζ	NOUN
ejpam-6018	55	17	=	=	NOUN
ejpam-6018	55	18	ζξ	ζξ	NOUN
ejpam-6018	55	19	=	=	PUNCT
ejpam-6018	55	20	ξξ	ξξ	NOUN
ejpam-6018	55	21	⇒	⇒	NOUN
ejpam-6018	55	22	ξ	ξ	X
ejpam-6018	55	23	=	=	SYM
ejpam-6018	55	24	ζ	ζ	NOUN
ejpam-6018	55	25	)	)	PUNCT
ejpam-6018	55	26	.	.	PUNCT
ejpam-6018	56	1	proposition	proposition	NOUN
ejpam-6018	56	2	1	1	NUM
ejpam-6018	56	3	.	.	PUNCT
ejpam-6018	57	1	[	[	X
ejpam-6018	57	2	11	11	NUM
ejpam-6018	57	3	]	]	PUNCT
ejpam-6018	57	4	let	let	VERB
ejpam-6018	57	5	hs	hs	PRON
ejpam-6018	57	6	:	:	PUNCT
ejpam-6018	57	7	=	=	SYM
ejpam-6018	57	8	(	(	PUNCT
ejpam-6018	57	9	h	h	NOUN
ejpam-6018	57	10	,	,	PUNCT
ejpam-6018	57	11	|	|	ADV
ejpam-6018	57	12	,	,	PUNCT
ejpam-6018	57	13	0	0	NUM
ejpam-6018	57	14	)	)	PUNCT
ejpam-6018	57	15	be	be	AUX
ejpam-6018	57	16	an	an	DET
ejpam-6018	57	17	ssh	ssh	NOUN
ejpam-6018	57	18	-	-	PUNCT
ejpam-6018	57	19	algebra	algebra	NOUN
ejpam-6018	57	20	.	.	PUNCT
ejpam-6018	58	1	then	then	ADV
ejpam-6018	58	2	the	the	DET
ejpam-6018	58	3	binary	binary	PROPN
ejpam-6018	58	4	relation	relation	NOUN
ejpam-6018	58	5	(	(	PUNCT
ejpam-6018	58	6	∀ξ	∀ξ	NOUN
ejpam-6018	58	7	,	,	PUNCT
ejpam-6018	58	8	ζ	ζ	PROPN
ejpam-6018	58	9	∈	∈	PROPN
ejpam-6018	58	10	h	h	NOUN
ejpam-6018	58	11	)	)	PUNCT
ejpam-6018	58	12	(	(	PUNCT
ejpam-6018	58	13	ξ	ξ	PROPN
ejpam-6018	58	14	≤	≤	PROPN
ejpam-6018	58	15	ζ	ζ	X
ejpam-6018	58	16	⇔	⇔	X
ejpam-6018	58	17	ξζ	ξζ	NOUN
ejpam-6018	58	18	=	=	NOUN
ejpam-6018	58	19	0	0	NUM
ejpam-6018	58	20	)	)	PUNCT
ejpam-6018	58	21	is	be	AUX
ejpam-6018	58	22	a	a	DET
ejpam-6018	58	23	partial	partial	ADJ
ejpam-6018	58	24	order	order	NOUN
ejpam-6018	58	25	on	on	ADP
ejpam-6018	58	26	h.	h.	PROPN
ejpam-6018	58	27	definition	definition	NOUN
ejpam-6018	58	28	3	3	NUM
ejpam-6018	58	29	.	.	PUNCT
ejpam-6018	59	1	[	[	X
ejpam-6018	59	2	11	11	NUM
ejpam-6018	59	3	]	]	PUNCT
ejpam-6018	59	4	let	let	VERB
ejpam-6018	59	5	hs	hs	PRON
ejpam-6018	59	6	:	:	PUNCT
ejpam-6018	59	7	=	=	SYM
ejpam-6018	59	8	(	(	PUNCT
ejpam-6018	59	9	h	h	NOUN
ejpam-6018	59	10	,	,	PUNCT
ejpam-6018	59	11	|	|	ADV
ejpam-6018	59	12	,	,	PUNCT
ejpam-6018	59	13	0	0	NUM
ejpam-6018	59	14	)	)	PUNCT
ejpam-6018	59	15	be	be	AUX
ejpam-6018	59	16	an	an	DET
ejpam-6018	59	17	ssh	ssh	NOUN
ejpam-6018	59	18	-	-	PUNCT
ejpam-6018	59	19	algebra	algebra	NOUN
ejpam-6018	59	20	.	.	PUNCT
ejpam-6018	60	1	a	a	DET
ejpam-6018	60	2	nonempty	nonempty	ADJ
ejpam-6018	60	3	subset	subset	VERB
ejpam-6018	60	4	s	s	NOUN
ejpam-6018	60	5	of	of	ADP
ejpam-6018	60	6	h	h	NOUN
ejpam-6018	60	7	is	be	AUX
ejpam-6018	60	8	said	say	VERB
ejpam-6018	60	9	to	to	PART
ejpam-6018	60	10	be	be	AUX
ejpam-6018	60	11	a	a	DET
ejpam-6018	60	12	subalgebra	subalgebra	NOUN
ejpam-6018	60	13	of	of	ADP
ejpam-6018	60	14	h	h	NOUN
ejpam-6018	61	1	if	if	SCONJ
ejpam-6018	61	2	ξζ	ξζ	INTJ
ejpam-6018	61	3	|	|	INTJ
ejpam-6018	61	4	ξζ	ξζ	INTJ
ejpam-6018	62	1	∈	∈	PROPN
ejpam-6018	63	1	s	s	VERB
ejpam-6018	63	2	for	for	ADP
ejpam-6018	63	3	all	all	DET
ejpam-6018	63	4	ξ	ξ	PROPN
ejpam-6018	63	5	,	,	PUNCT
ejpam-6018	63	6	ζ	ζ	PROPN
ejpam-6018	63	7	∈	∈	PROPN
ejpam-6018	63	8	s.	s.	PROPN
ejpam-6018	63	9	definition	definition	NOUN
ejpam-6018	63	10	4	4	NUM
ejpam-6018	63	11	.	.	PUNCT
ejpam-6018	64	1	[	[	X
ejpam-6018	64	2	11	11	NUM
ejpam-6018	64	3	]	]	PUNCT
ejpam-6018	64	4	let	let	VERB
ejpam-6018	64	5	hs	hs	PRON
ejpam-6018	64	6	:	:	PUNCT
ejpam-6018	64	7	=	=	SYM
ejpam-6018	64	8	(	(	PUNCT
ejpam-6018	64	9	h	h	NOUN
ejpam-6018	64	10	,	,	PUNCT
ejpam-6018	64	11	|	|	ADV
ejpam-6018	64	12	,	,	PUNCT
ejpam-6018	64	13	0	0	NUM
ejpam-6018	64	14	)	)	PUNCT
ejpam-6018	64	15	be	be	AUX
ejpam-6018	64	16	an	an	DET
ejpam-6018	64	17	ssh	ssh	NOUN
ejpam-6018	64	18	-	-	PUNCT
ejpam-6018	64	19	algebra	algebra	NOUN
ejpam-6018	64	20	.	.	PUNCT
ejpam-6018	65	1	a	a	DET
ejpam-6018	65	2	nonempty	nonempty	NOUN
ejpam-6018	65	3	subset	subset	VERB
ejpam-6018	65	4	i	i	PRON
ejpam-6018	65	5	of	of	ADP
ejpam-6018	65	6	h	h	NOUN
ejpam-6018	65	7	is	be	AUX
ejpam-6018	65	8	called	call	VERB
ejpam-6018	65	9	an	an	DET
ejpam-6018	65	10	ideal	ideal	NOUN
ejpam-6018	65	11	of	of	ADP
ejpam-6018	65	12	h	h	NOUN
ejpam-6018	66	1	if	if	SCONJ
ejpam-6018	66	2	(	(	PUNCT
ejpam-6018	66	3	1	1	NUM
ejpam-6018	66	4	)	)	PUNCT
ejpam-6018	66	5	0	0	NUM
ejpam-6018	67	1	∈	∈	PROPN
ejpam-6018	67	2	i	i	PRON
ejpam-6018	67	3	,	,	PUNCT
ejpam-6018	67	4	(	(	PUNCT
ejpam-6018	67	5	2	2	NUM
ejpam-6018	67	6	)	)	PUNCT
ejpam-6018	67	7	(	(	PUNCT
ejpam-6018	67	8	∀ξ	∀ξ	NOUN
ejpam-6018	67	9	,	,	PUNCT
ejpam-6018	67	10	ζ	ζ	PROPN
ejpam-6018	67	11	∈	∈	PROPN
ejpam-6018	67	12	h	h	NOUN
ejpam-6018	67	13	)	)	PUNCT
ejpam-6018	67	14	(	(	PUNCT
ejpam-6018	67	15	ξζ	ξζ	INTJ
ejpam-6018	68	1	|	|	INTJ
ejpam-6018	68	2	ξζ	ξζ	INTJ
ejpam-6018	68	3	∈	∈	PROPN
ejpam-6018	69	1	i	i	PRON
ejpam-6018	69	2	and	and	CCONJ
ejpam-6018	69	3	ζ	ζ	NOUN
ejpam-6018	69	4	∈	∈	NOUN
ejpam-6018	69	5	i	i	PRON
ejpam-6018	69	6	⇒	⇒	VERB
ejpam-6018	69	7	ξ	ξ	X
ejpam-6018	69	8	∈	∈	PROPN
ejpam-6018	69	9	i	i	PROPN
ejpam-6018	69	10	)	)	PUNCT
ejpam-6018	69	11	.	.	PUNCT
ejpam-6018	70	1	3	3	X
ejpam-6018	70	2	.	.	X
ejpam-6018	70	3	soft	soft	ADJ
ejpam-6018	70	4	subalgebras	subalgebra	NOUN
ejpam-6018	70	5	/	/	SYM
ejpam-6018	70	6	ideals	ideal	NOUN
ejpam-6018	70	7	of	of	ADP
ejpam-6018	70	8	sheffer	sheffer	PROPN
ejpam-6018	70	9	stroke	stroke	PROPN
ejpam-6018	70	10	hilbert	hilbert	PROPN
ejpam-6018	70	11	algebras	algebras	PROPN
ejpam-6018	70	12	let	let	VERB
ejpam-6018	70	13	hs	hs	PRON
ejpam-6018	70	14	:	:	PUNCT
ejpam-6018	70	15	=	=	SYM
ejpam-6018	70	16	(	(	PUNCT
ejpam-6018	70	17	h	h	NOUN
ejpam-6018	70	18	,	,	PUNCT
ejpam-6018	70	19	|	|	ADV
ejpam-6018	70	20	,	,	PUNCT
ejpam-6018	70	21	0	0	NUM
ejpam-6018	70	22	)	)	PUNCT
ejpam-6018	70	23	represent	represent	VERB
ejpam-6018	70	24	an	an	DET
ejpam-6018	70	25	ssh	ssh	NOUN
ejpam-6018	70	26	-	-	PUNCT
ejpam-6018	70	27	algebra	algebra	NOUN
ejpam-6018	70	28	.	.	PUNCT
ejpam-6018	71	1	for	for	ADP
ejpam-6018	71	2	a	a	DET
ejpam-6018	71	3	subset	subset	NOUN
ejpam-6018	71	4	υ	υ	NOUN
ejpam-6018	71	5	of	of	ADP
ejpam-6018	71	6	[	[	X
ejpam-6018	71	7	−1	−1	NOUN
ejpam-6018	71	8	,	,	PUNCT
ejpam-6018	71	9	0	0	NUM
ejpam-6018	71	10	]	]	PUNCT
ejpam-6018	71	11	,	,	PUNCT
ejpam-6018	71	12	the	the	DET
ejpam-6018	71	13	pair	pair	NOUN
ejpam-6018	71	14	(	(	PUNCT
ejpam-6018	71	15	s	s	X
ejpam-6018	71	16	,	,	PUNCT
ejpam-6018	71	17	υ	υ	NOUN
ejpam-6018	71	18	)	)	PUNCT
ejpam-6018	71	19	is	be	AUX
ejpam-6018	71	20	referred	refer	VERB
ejpam-6018	71	21	to	to	ADP
ejpam-6018	71	22	as	as	ADP
ejpam-6018	71	23	a	a	DET
ejpam-6018	71	24	soft	soft	ADJ
ejpam-6018	71	25	n	n	NOUN
ejpam-6018	71	26	-set	-set	PUNCT
ejpam-6018	71	27	over	over	ADP
ejpam-6018	71	28	h	h	NOUN
ejpam-6018	71	29	,	,	PUNCT
ejpam-6018	71	30	where	where	SCONJ
ejpam-6018	71	31	s	s	NOUN
ejpam-6018	71	32	is	be	AUX
ejpam-6018	71	33	a	a	DET
ejpam-6018	71	34	mapping	mapping	NOUN
ejpam-6018	71	35	from	from	ADP
ejpam-6018	71	36	υ	υ	NOUN
ejpam-6018	71	37	to	to	ADP
ejpam-6018	71	38	p	p	NOUN
ejpam-6018	71	39	(	(	PUNCT
ejpam-6018	71	40	h	h	NOUN
ejpam-6018	71	41	)	)	PUNCT
ejpam-6018	71	42	,	,	PUNCT
ejpam-6018	71	43	i.e.	i.e.	X
ejpam-6018	71	44	,	,	PUNCT
ejpam-6018	71	45	s	s	X
ejpam-6018	71	46	:	:	PUNCT
ejpam-6018	71	47	υ	υ	X
ejpam-6018	71	48	→	→	X
ejpam-6018	71	49	p	p	X
ejpam-6018	71	50	(	(	PUNCT
ejpam-6018	71	51	h	h	NOUN
ejpam-6018	71	52	)	)	PUNCT
ejpam-6018	71	53	.	.	PUNCT
ejpam-6018	72	1	given	give	VERB
ejpam-6018	72	2	an	an	DET
ejpam-6018	72	3	n	n	ADV
ejpam-6018	72	4	-structure	-structure	NOUN
ejpam-6018	72	5	(	(	PUNCT
ejpam-6018	72	6	h	h	NOUN
ejpam-6018	72	7	,	,	PUNCT
ejpam-6018	72	8	f	f	NOUN
ejpam-6018	72	9	)	)	PUNCT
ejpam-6018	72	10	and	and	CCONJ
ejpam-6018	72	11	υ	υ	NOUN
ejpam-6018	72	12	=	=	PUNCT
ejpam-6018	73	1	[	[	X
ejpam-6018	73	2	−1	−1	NOUN
ejpam-6018	73	3	,	,	PUNCT
ejpam-6018	73	4	0	0	NUM
ejpam-6018	73	5	]	]	PUNCT
ejpam-6018	73	6	,	,	PUNCT
ejpam-6018	73	7	we	we	PRON
ejpam-6018	73	8	introduce	introduce	VERB
ejpam-6018	73	9	two	two	NUM
ejpam-6018	73	10	mappings	mapping	NOUN
ejpam-6018	73	11	:	:	PUNCT
ejpam-6018	73	12	s∈	s∈	NOUN
ejpam-6018	73	13	:	:	PUNCT
ejpam-6018	73	14	υ	υ	X
ejpam-6018	73	15	→	→	SYM
ejpam-6018	73	16	p	p	X
ejpam-6018	73	17	(	(	PUNCT
ejpam-6018	73	18	h	h	NOUN
ejpam-6018	73	19	)	)	PUNCT
ejpam-6018	73	20	;	;	PUNCT
ejpam-6018	73	21	η	η	PROPN
ejpam-6018	73	22	7→	7→	PROPN
ejpam-6018	73	23	{	{	PUNCT
ejpam-6018	73	24	ξ	ξ	PROPN
ejpam-6018	73	25	∈	∈	PROPN
ejpam-6018	73	26	h	h	NOUN
ejpam-6018	73	27	:	:	PUNCT
ejpam-6018	73	28	(	(	PUNCT
ejpam-6018	73	29	h	h	NOUN
ejpam-6018	73	30	,	,	PUNCT
ejpam-6018	73	31	ξη	ξη	PRON
ejpam-6018	73	32	)	)	PUNCT
ejpam-6018	73	33	is	be	AUX
ejpam-6018	73	34	an	an	DET
ejpam-6018	73	35	n∈-subset	n∈-subset	NOUN
ejpam-6018	73	36	of	of	ADP
ejpam-6018	73	37	(	(	PUNCT
ejpam-6018	73	38	h	h	NOUN
ejpam-6018	73	39	,	,	PUNCT
ejpam-6018	73	40	f	f	NOUN
ejpam-6018	73	41	)	)	PUNCT
ejpam-6018	73	42	}	}	PUNCT
ejpam-6018	73	43	and	and	CCONJ
ejpam-6018	73	44	sq	sq	INTJ
ejpam-6018	73	45	:	:	PUNCT
ejpam-6018	73	46	∆	∆	PROPN
ejpam-6018	74	1	→	→	X
ejpam-6018	74	2	p	p	X
ejpam-6018	74	3	(	(	PUNCT
ejpam-6018	74	4	h	h	NOUN
ejpam-6018	74	5	)	)	PUNCT
ejpam-6018	74	6	;	;	PUNCT
ejpam-6018	74	7	η	η	PROPN
ejpam-6018	74	8	7→	7→	PROPN
ejpam-6018	74	9	{	{	PUNCT
ejpam-6018	74	10	ξ	ξ	PROPN
ejpam-6018	74	11	∈	∈	PROPN
ejpam-6018	74	12	h	h	NOUN
ejpam-6018	74	13	:	:	PUNCT
ejpam-6018	74	14	(	(	PUNCT
ejpam-6018	74	15	h	h	NOUN
ejpam-6018	74	16	,	,	PUNCT
ejpam-6018	74	17	ξη	ξη	PRON
ejpam-6018	74	18	)	)	PUNCT
ejpam-6018	74	19	is	be	AUX
ejpam-6018	74	20	an	an	DET
ejpam-6018	74	21	nq	nq	NOUN
ejpam-6018	74	22	-	-	PUNCT
ejpam-6018	74	23	subset	subset	NOUN
ejpam-6018	74	24	of	of	ADP
ejpam-6018	74	25	(	(	PUNCT
ejpam-6018	74	26	h	h	NOUN
ejpam-6018	74	27	,	,	PUNCT
ejpam-6018	74	28	f	f	NOUN
ejpam-6018	74	29	)	)	PUNCT
ejpam-6018	74	30	}	}	PUNCT
ejpam-6018	74	31	.	.	PUNCT
ejpam-6018	75	1	then	then	ADV
ejpam-6018	75	2	,	,	PUNCT
ejpam-6018	75	3	the	the	DET
ejpam-6018	75	4	pairs	pair	NOUN
ejpam-6018	75	5	(	(	PUNCT
ejpam-6018	75	6	s∈,υ	s∈,υ	NOUN
ejpam-6018	75	7	)	)	PUNCT
ejpam-6018	75	8	and	and	CCONJ
ejpam-6018	75	9	(	(	PUNCT
ejpam-6018	75	10	sq	sq	ADJ
ejpam-6018	75	11	,	,	PUNCT
ejpam-6018	75	12	υ	υ	NOUN
ejpam-6018	75	13	)	)	PUNCT
ejpam-6018	75	14	are	be	AUX
ejpam-6018	75	15	soft	soft	ADJ
ejpam-6018	75	16	n	n	DET
ejpam-6018	75	17	-sets	-set	NOUN
ejpam-6018	75	18	over	over	ADP
ejpam-6018	75	19	h.	h.	NOUN
ejpam-6018	75	20	if	if	SCONJ
ejpam-6018	75	21	s∈(η	s∈(η	ADJ
ejpam-6018	75	22	)	)	PUNCT
ejpam-6018	75	23	̸=	̸=	PROPN
ejpam-6018	75	24	∅	∅	NOUN
ejpam-6018	75	25	(	(	PUNCT
ejpam-6018	75	26	or	or	CCONJ
ejpam-6018	75	27	sq(η	sq(η	X
ejpam-6018	75	28	)	)	PUNCT
ejpam-6018	75	29	̸=	̸=	PROPN
ejpam-6018	75	30	∅	∅	NOUN
ejpam-6018	75	31	)	)	PUNCT
ejpam-6018	75	32	for	for	ADP
ejpam-6018	75	33	some	some	DET
ejpam-6018	75	34	η	η	PROPN
ejpam-6018	75	35	∈	∈	PROPN
ejpam-6018	75	36	υ	υ	NOUN
ejpam-6018	75	37	,	,	PUNCT
ejpam-6018	75	38	we	we	PRON
ejpam-6018	75	39	say	say	VERB
ejpam-6018	75	40	that	that	SCONJ
ejpam-6018	75	41	(	(	PUNCT
ejpam-6018	75	42	s∈,υ	s∈,υ	NOUN
ejpam-6018	75	43	)	)	PUNCT
ejpam-6018	75	44	(	(	PUNCT
ejpam-6018	75	45	or	or	CCONJ
ejpam-6018	75	46	(	(	PUNCT
ejpam-6018	75	47	sq	sq	ADJ
ejpam-6018	75	48	,	,	PUNCT
ejpam-6018	75	49	υ	υ	NOUN
ejpam-6018	75	50	)	)	PUNCT
ejpam-6018	75	51	)	)	PUNCT
ejpam-6018	75	52	forms	form	VERB
ejpam-6018	75	53	a	a	DET
ejpam-6018	75	54	soft	soft	ADJ
ejpam-6018	75	55	n∈-set	n∈-set	NOUN
ejpam-6018	75	56	(	(	PUNCT
ejpam-6018	75	57	or	or	CCONJ
ejpam-6018	75	58	soft	soft	ADJ
ejpam-6018	75	59	n	n	CCONJ
ejpam-6018	75	60	q	q	NOUN
ejpam-6018	75	61	-	-	PUNCT
ejpam-6018	75	62	set	set	NOUN
ejpam-6018	75	63	)	)	PUNCT
ejpam-6018	75	64	over	over	ADP
ejpam-6018	75	65	h.	h.	PROPN
ejpam-6018	75	66	a	a	DET
ejpam-6018	75	67	soft	soft	ADJ
ejpam-6018	75	68	n∈	n∈	NOUN
ejpam-6018	75	69	∨q	∨q	NOUN
ejpam-6018	75	70	-	-	PUNCT
ejpam-6018	75	71	set	set	VERB
ejpam-6018	75	72	over	over	ADP
ejpam-6018	75	73	h	h	NOUN
ejpam-6018	75	74	is	be	AUX
ejpam-6018	75	75	defined	define	VERB
ejpam-6018	75	76	as	as	ADP
ejpam-6018	75	77	the	the	DET
ejpam-6018	75	78	union	union	NOUN
ejpam-6018	75	79	of	of	ADP
ejpam-6018	75	80	a	a	DET
ejpam-6018	75	81	soft	soft	ADJ
ejpam-6018	75	82	n∈-set	n∈-set	NOUN
ejpam-6018	75	83	and	and	CCONJ
ejpam-6018	75	84	a	a	DET
ejpam-6018	75	85	soft	soft	ADJ
ejpam-6018	75	86	n	n	PRON
ejpam-6018	75	87	q	q	NOUN
ejpam-6018	75	88	-	-	PUNCT
ejpam-6018	75	89	set	set	VERB
ejpam-6018	75	90	over	over	ADP
ejpam-6018	75	91	h	h	NOUN
ejpam-6018	75	92	,	,	PUNCT
ejpam-6018	75	93	and	and	CCONJ
ejpam-6018	75	94	is	be	AUX
ejpam-6018	75	95	denoted	denote	VERB
ejpam-6018	75	96	by	by	ADP
ejpam-6018	75	97	(	(	PUNCT
ejpam-6018	75	98	s∈∨q	s∈∨q	PROPN
ejpam-6018	75	99	,	,	PUNCT
ejpam-6018	75	100	υ	υ	NOUN
ejpam-6018	75	101	)	)	PUNCT
ejpam-6018	75	102	,	,	PUNCT
ejpam-6018	75	103	where	where	SCONJ
ejpam-6018	75	104	s∈∨q(η	s∈∨q(η	NOUN
ejpam-6018	75	105	)	)	PUNCT
ejpam-6018	75	106	=	=	PUNCT
ejpam-6018	76	1	s∈(η	s∈(η	X
ejpam-6018	76	2	)	)	PUNCT
ejpam-6018	76	3	∨	∨	NUM
ejpam-6018	76	4	sq(η	sq(η	NUM
ejpam-6018	76	5	)	)	PUNCT
ejpam-6018	76	6	for	for	ADP
ejpam-6018	76	7	all	all	DET
ejpam-6018	76	8	η	η	PROPN
ejpam-6018	76	9	∈	∈	PROPN
ejpam-6018	76	10	υ	υ	PROPN
ejpam-6018	76	11	.	.	PUNCT
ejpam-6018	77	1	t.	t.	PROPN
ejpam-6018	77	2	oner	oner	PROPN
ejpam-6018	77	3	et	et	PROPN
ejpam-6018	77	4	al	al	PROPN
ejpam-6018	77	5	.	.	PUNCT
ejpam-6018	77	6	/	/	SYM
ejpam-6018	77	7	eur	eur	PROPN
ejpam-6018	77	8	.	.	PUNCT
ejpam-6018	78	1	j.	j.	PROPN
ejpam-6018	78	2	pure	pure	PROPN
ejpam-6018	78	3	appl	appl	PROPN
ejpam-6018	78	4	.	.	PROPN
ejpam-6018	78	5	math	math	PROPN
ejpam-6018	78	6	,	,	PUNCT
ejpam-6018	78	7	18	18	NUM
ejpam-6018	78	8	(	(	PUNCT
ejpam-6018	78	9	2	2	NUM
ejpam-6018	78	10	)	)	PUNCT
ejpam-6018	78	11	(	(	PUNCT
ejpam-6018	78	12	2025	2025	NUM
ejpam-6018	78	13	)	)	PUNCT
ejpam-6018	78	14	,	,	PUNCT
ejpam-6018	78	15	6018	6018	NUM
ejpam-6018	78	16	4	4	NUM
ejpam-6018	78	17	of	of	ADP
ejpam-6018	78	18	11	11	NUM
ejpam-6018	78	19	definition	definition	NOUN
ejpam-6018	78	20	5	5	NUM
ejpam-6018	78	21	.	.	PUNCT
ejpam-6018	79	1	let	let	VERB
ejpam-6018	79	2	hs	hs	PRON
ejpam-6018	79	3	:	:	PUNCT
ejpam-6018	79	4	=	=	SYM
ejpam-6018	79	5	(	(	PUNCT
ejpam-6018	79	6	h	h	NOUN
ejpam-6018	79	7	,	,	PUNCT
ejpam-6018	79	8	|	|	ADV
ejpam-6018	79	9	,	,	PUNCT
ejpam-6018	79	10	0	0	NUM
ejpam-6018	79	11	)	)	PUNCT
ejpam-6018	79	12	be	be	AUX
ejpam-6018	79	13	an	an	DET
ejpam-6018	79	14	ssh	ssh	NOUN
ejpam-6018	79	15	-	-	PUNCT
ejpam-6018	79	16	algebra	algebra	NOUN
ejpam-6018	79	17	.	.	PUNCT
ejpam-6018	80	1	a	a	DET
ejpam-6018	80	2	soft	soft	ADJ
ejpam-6018	80	3	n	n	X
ejpam-6018	80	4	-set	-set	X
ejpam-6018	80	5	(	(	PUNCT
ejpam-6018	80	6	s	s	X
ejpam-6018	80	7	,	,	PUNCT
ejpam-6018	80	8	υ	υ	NOUN
ejpam-6018	80	9	)	)	PUNCT
ejpam-6018	80	10	over	over	ADP
ejpam-6018	80	11	h	h	NOUN
ejpam-6018	80	12	is	be	AUX
ejpam-6018	80	13	called	call	VERB
ejpam-6018	80	14	a	a	DET
ejpam-6018	80	15	soft	soft	ADJ
ejpam-6018	80	16	n	n	CCONJ
ejpam-6018	80	17	-subalgebra	-subalgebra	NOUN
ejpam-6018	80	18	over	over	ADP
ejpam-6018	80	19	h	h	NOUN
ejpam-6018	80	20	if	if	SCONJ
ejpam-6018	80	21	(	(	PUNCT
ejpam-6018	80	22	∀η	∀η	NOUN
ejpam-6018	80	23	∈	∈	PROPN
ejpam-6018	80	24	υ	υ	PROPN
ejpam-6018	80	25	)	)	PUNCT
ejpam-6018	80	26	(	(	PUNCT
ejpam-6018	80	27	s(η	s(η	PROPN
ejpam-6018	80	28	)	)	PUNCT
ejpam-6018	80	29	̸=	̸=	PROPN
ejpam-6018	80	30	∅	∅	ADP
ejpam-6018	80	31	⇒	⇒	PROPN
ejpam-6018	80	32	s(η	s(η	PROPN
ejpam-6018	80	33	)	)	PUNCT
ejpam-6018	80	34	is	be	AUX
ejpam-6018	80	35	a	a	DET
ejpam-6018	80	36	subalgebra	subalgebra	NOUN
ejpam-6018	80	37	of	of	ADP
ejpam-6018	80	38	h	h	NOUN
ejpam-6018	80	39	)	)	PUNCT
ejpam-6018	80	40	.	.	PUNCT
ejpam-6018	81	1	(	(	PUNCT
ejpam-6018	81	2	1	1	X
ejpam-6018	81	3	)	)	PUNCT
ejpam-6018	81	4	theorem	theorem	NOUN
ejpam-6018	81	5	1	1	NUM
ejpam-6018	81	6	.	.	PUNCT
ejpam-6018	82	1	let	let	VERB
ejpam-6018	82	2	hs	hs	PRON
ejpam-6018	82	3	:	:	PUNCT
ejpam-6018	82	4	=	=	SYM
ejpam-6018	82	5	(	(	PUNCT
ejpam-6018	82	6	h	h	NOUN
ejpam-6018	82	7	,	,	PUNCT
ejpam-6018	82	8	|	|	ADV
ejpam-6018	82	9	,	,	PUNCT
ejpam-6018	82	10	0	0	NUM
ejpam-6018	82	11	)	)	PUNCT
ejpam-6018	82	12	be	be	AUX
ejpam-6018	82	13	an	an	DET
ejpam-6018	82	14	ssh	ssh	NOUN
ejpam-6018	82	15	-	-	PUNCT
ejpam-6018	82	16	algebra	algebra	NOUN
ejpam-6018	82	17	.	.	PUNCT
ejpam-6018	83	1	given	give	VERB
ejpam-6018	83	2	an	an	DET
ejpam-6018	83	3	n	n	ADV
ejpam-6018	83	4	-structure	-structure	NOUN
ejpam-6018	83	5	(	(	PUNCT
ejpam-6018	83	6	h	h	NOUN
ejpam-6018	83	7	,	,	PUNCT
ejpam-6018	83	8	f	f	NOUN
ejpam-6018	83	9	)	)	PUNCT
ejpam-6018	83	10	and	and	CCONJ
ejpam-6018	83	11	υ	υ	NOUN
ejpam-6018	83	12	=	=	PUNCT
ejpam-6018	84	1	[	[	X
ejpam-6018	84	2	−1	−1	NOUN
ejpam-6018	84	3	,	,	PUNCT
ejpam-6018	84	4	0	0	NUM
ejpam-6018	84	5	)	)	PUNCT
ejpam-6018	84	6	,	,	PUNCT
ejpam-6018	84	7	the	the	DET
ejpam-6018	84	8	soft	soft	ADJ
ejpam-6018	84	9	n∈-set	n∈-set	NOUN
ejpam-6018	84	10	(	(	PUNCT
ejpam-6018	84	11	s∈,υ	s∈,υ	NOUN
ejpam-6018	84	12	)	)	PUNCT
ejpam-6018	84	13	is	be	AUX
ejpam-6018	84	14	a	a	DET
ejpam-6018	84	15	soft	soft	ADJ
ejpam-6018	84	16	n	n	CCONJ
ejpam-6018	84	17	-subalgebra	-subalgebra	NOUN
ejpam-6018	84	18	over	over	ADP
ejpam-6018	84	19	h	h	NOUN
ejpam-6018	84	20	if	if	SCONJ
ejpam-6018	85	1	and	and	CCONJ
ejpam-6018	85	2	only	only	ADV
ejpam-6018	85	3	if	if	SCONJ
ejpam-6018	85	4	(	(	PUNCT
ejpam-6018	85	5	h	h	NOUN
ejpam-6018	85	6	,	,	PUNCT
ejpam-6018	85	7	f	f	X
ejpam-6018	85	8	)	)	PUNCT
ejpam-6018	85	9	is	be	AUX
ejpam-6018	85	10	an	an	DET
ejpam-6018	85	11	n	n	PRON
ejpam-6018	85	12	-subalgebra	-subalgebra	NOUN
ejpam-6018	85	13	of	of	ADP
ejpam-6018	85	14	type	type	NOUN
ejpam-6018	85	15	(	(	PUNCT
ejpam-6018	85	16	∈,∈	∈,∈	NOUN
ejpam-6018	85	17	)	)	PUNCT
ejpam-6018	85	18	.	.	PUNCT
ejpam-6018	86	1	proof	proof	NOUN
ejpam-6018	86	2	.	.	PUNCT
ejpam-6018	87	1	assume	assume	VERB
ejpam-6018	87	2	that	that	SCONJ
ejpam-6018	87	3	(	(	PUNCT
ejpam-6018	87	4	s∈,υ	s∈,υ	NOUN
ejpam-6018	87	5	)	)	PUNCT
ejpam-6018	87	6	is	be	AUX
ejpam-6018	87	7	a	a	DET
ejpam-6018	87	8	soft	soft	ADJ
ejpam-6018	87	9	n	n	CCONJ
ejpam-6018	87	10	-subalgebra	-subalgebra	NOUN
ejpam-6018	87	11	over	over	ADP
ejpam-6018	87	12	h.	h.	NOUN
ejpam-6018	87	13	if	if	SCONJ
ejpam-6018	87	14	(	(	PUNCT
ejpam-6018	87	15	h	h	NOUN
ejpam-6018	87	16	,	,	PUNCT
ejpam-6018	87	17	f	f	X
ejpam-6018	87	18	)	)	PUNCT
ejpam-6018	87	19	is	be	AUX
ejpam-6018	87	20	not	not	PART
ejpam-6018	87	21	an	an	DET
ejpam-6018	87	22	n	n	NOUN
ejpam-6018	87	23	subalgebra	subalgebra	NOUN
ejpam-6018	87	24	of	of	ADP
ejpam-6018	87	25	type	type	NOUN
ejpam-6018	87	26	(	(	PUNCT
ejpam-6018	87	27	∈,∈	∈,∈	X
ejpam-6018	87	28	)	)	PUNCT
ejpam-6018	87	29	,	,	PUNCT
ejpam-6018	87	30	then	then	ADV
ejpam-6018	87	31	there	there	PRON
ejpam-6018	87	32	exist	exist	VERB
ejpam-6018	87	33	ϱ,ϖ	ϱ,ϖ	NOUN
ejpam-6018	87	34	∈	∈	PROPN
ejpam-6018	87	35	h	h	NOUN
ejpam-6018	87	36	and	and	CCONJ
ejpam-6018	87	37	t	t	NOUN
ejpam-6018	87	38	∈	∈	PROPN
ejpam-6018	88	1	υ	υ	INTJ
ejpam-6018	88	2	such	such	ADJ
ejpam-6018	88	3	that	that	PRON
ejpam-6018	88	4	(	(	PUNCT
ejpam-6018	88	5	h	h	NOUN
ejpam-6018	88	6	,	,	PUNCT
ejpam-6018	88	7	ϱt	ϱt	NOUN
ejpam-6018	88	8	)	)	PUNCT
ejpam-6018	88	9	and	and	CCONJ
ejpam-6018	88	10	(	(	PUNCT
ejpam-6018	88	11	h,ϖt	h,ϖt	NOUN
ejpam-6018	88	12	)	)	PUNCT
ejpam-6018	88	13	are	be	AUX
ejpam-6018	88	14	n∈-subsets	n∈-subset	NOUN
ejpam-6018	88	15	of	of	ADP
ejpam-6018	88	16	(	(	PUNCT
ejpam-6018	88	17	h	h	NOUN
ejpam-6018	88	18	,	,	PUNCT
ejpam-6018	88	19	f	f	NOUN
ejpam-6018	88	20	)	)	PUNCT
ejpam-6018	88	21	,	,	PUNCT
ejpam-6018	88	22	but	but	CCONJ
ejpam-6018	88	23	(	(	PUNCT
ejpam-6018	88	24	h	h	NOUN
ejpam-6018	88	25	,	,	PUNCT
ejpam-6018	88	26	(	(	PUNCT
ejpam-6018	88	27	ϱϖ	ϱϖ	NOUN
ejpam-6018	88	28	|	|	ADV
ejpam-6018	88	29	ϱϖ)t	ϱϖ)t	NOUN
ejpam-6018	88	30	)	)	PUNCT
ejpam-6018	88	31	is	be	AUX
ejpam-6018	88	32	not	not	PART
ejpam-6018	88	33	an	an	DET
ejpam-6018	88	34	n∈-subset	n∈-subset	NOUN
ejpam-6018	88	35	of	of	ADP
ejpam-6018	88	36	(	(	PUNCT
ejpam-6018	88	37	h	h	NOUN
ejpam-6018	88	38	,	,	PUNCT
ejpam-6018	88	39	f	f	NOUN
ejpam-6018	88	40	)	)	PUNCT
ejpam-6018	88	41	.	.	PUNCT
ejpam-6018	89	1	therefore	therefore	ADV
ejpam-6018	89	2	,	,	PUNCT
ejpam-6018	89	3	ϱ,ϖ	ϱ,ϖ	PROPN
ejpam-6018	89	4	∈	∈	PROPN
ejpam-6018	89	5	s∈(t	s∈(t	VERB
ejpam-6018	89	6	)	)	PUNCT
ejpam-6018	89	7	and	and	CCONJ
ejpam-6018	89	8	ϱϖ	ϱϖ	VERB
ejpam-6018	89	9	|	|	ADV
ejpam-6018	89	10	ϱϖ	ϱϖ	NOUN
ejpam-6018	89	11	/∈	/∈	PUNCT
ejpam-6018	89	12	s∈(t	s∈(t	NOUN
ejpam-6018	89	13	)	)	PUNCT
ejpam-6018	89	14	,	,	PUNCT
ejpam-6018	89	15	implying	imply	VERB
ejpam-6018	89	16	that	that	SCONJ
ejpam-6018	89	17	s∈(t	s∈(t	VERB
ejpam-6018	89	18	)	)	PUNCT
ejpam-6018	89	19	is	be	AUX
ejpam-6018	89	20	not	not	PART
ejpam-6018	89	21	a	a	DET
ejpam-6018	89	22	subalgebra	subalgebra	NOUN
ejpam-6018	89	23	of	of	ADP
ejpam-6018	89	24	h.	h.	NOUN
ejpam-6018	89	25	this	this	PRON
ejpam-6018	89	26	leads	lead	VERB
ejpam-6018	89	27	to	to	ADP
ejpam-6018	89	28	a	a	DET
ejpam-6018	89	29	contradiction	contradiction	NOUN
ejpam-6018	89	30	,	,	PUNCT
ejpam-6018	89	31	which	which	PRON
ejpam-6018	89	32	means	mean	VERB
ejpam-6018	89	33	that	that	SCONJ
ejpam-6018	89	34	(	(	PUNCT
ejpam-6018	89	35	h	h	NOUN
ejpam-6018	89	36	,	,	PUNCT
ejpam-6018	89	37	f	f	X
ejpam-6018	89	38	)	)	PUNCT
ejpam-6018	89	39	must	must	AUX
ejpam-6018	89	40	be	be	AUX
ejpam-6018	89	41	an	an	DET
ejpam-6018	89	42	n	n	PRON
ejpam-6018	89	43	-subalgebra	-subalgebra	NOUN
ejpam-6018	89	44	of	of	ADP
ejpam-6018	89	45	type	type	NOUN
ejpam-6018	89	46	(	(	PUNCT
ejpam-6018	89	47	∈,∈	∈,∈	NOUN
ejpam-6018	89	48	)	)	PUNCT
ejpam-6018	89	49	.	.	PUNCT
ejpam-6018	90	1	conversely	conversely	ADV
ejpam-6018	90	2	,	,	PUNCT
ejpam-6018	90	3	suppose	suppose	VERB
ejpam-6018	90	4	(	(	PUNCT
ejpam-6018	90	5	h	h	NOUN
ejpam-6018	90	6	,	,	PUNCT
ejpam-6018	90	7	f	f	X
ejpam-6018	90	8	)	)	PUNCT
ejpam-6018	90	9	is	be	AUX
ejpam-6018	90	10	an	an	DET
ejpam-6018	90	11	n	n	PRON
ejpam-6018	90	12	-subalgebra	-subalgebra	NOUN
ejpam-6018	90	13	of	of	ADP
ejpam-6018	90	14	type	type	NOUN
ejpam-6018	90	15	(	(	PUNCT
ejpam-6018	90	16	∈,∈	∈,∈	NOUN
ejpam-6018	90	17	)	)	PUNCT
ejpam-6018	90	18	.	.	PUNCT
ejpam-6018	91	1	let	let	VERB
ejpam-6018	91	2	η	η	PROPN
ejpam-6018	91	3	∈	∈	PROPN
ejpam-6018	91	4	υ	υ	NOUN
ejpam-6018	91	5	be	be	AUX
ejpam-6018	91	6	such	such	ADJ
ejpam-6018	91	7	that	that	SCONJ
ejpam-6018	91	8	s∈(η	s∈(η	NOUN
ejpam-6018	91	9	)	)	PUNCT
ejpam-6018	91	10	̸=	̸=	PROPN
ejpam-6018	91	11	∅.	∅.	VERB
ejpam-6018	91	12	if	if	SCONJ
ejpam-6018	91	13	ξ	ξ	PROPN
ejpam-6018	91	14	,	,	PUNCT
ejpam-6018	91	15	ζ	ζ	PROPN
ejpam-6018	91	16	∈	∈	PROPN
ejpam-6018	91	17	s∈(η	s∈(η	ADV
ejpam-6018	91	18	)	)	PUNCT
ejpam-6018	91	19	,	,	PUNCT
ejpam-6018	91	20	then	then	ADV
ejpam-6018	91	21	both	both	DET
ejpam-6018	91	22	(	(	PUNCT
ejpam-6018	91	23	h	h	NOUN
ejpam-6018	91	24	,	,	PUNCT
ejpam-6018	91	25	ξη	ξη	PROPN
ejpam-6018	91	26	)	)	PUNCT
ejpam-6018	91	27	and	and	CCONJ
ejpam-6018	91	28	(	(	PUNCT
ejpam-6018	91	29	h	h	NOUN
ejpam-6018	91	30	,	,	PUNCT
ejpam-6018	91	31	ζη	ζη	ADJ
ejpam-6018	91	32	)	)	PUNCT
ejpam-6018	91	33	are	be	AUX
ejpam-6018	91	34	n∈-subsets	n∈-subset	NOUN
ejpam-6018	91	35	of	of	ADP
ejpam-6018	91	36	(	(	PUNCT
ejpam-6018	91	37	h	h	NOUN
ejpam-6018	91	38	,	,	PUNCT
ejpam-6018	91	39	f	f	NOUN
ejpam-6018	91	40	)	)	PUNCT
ejpam-6018	91	41	.	.	PUNCT
ejpam-6018	92	1	consequently	consequently	ADV
ejpam-6018	92	2	,	,	PUNCT
ejpam-6018	92	3	(	(	PUNCT
ejpam-6018	92	4	h	h	NOUN
ejpam-6018	92	5	,	,	PUNCT
ejpam-6018	92	6	(	(	PUNCT
ejpam-6018	92	7	ξζ	ξζ	NOUN
ejpam-6018	92	8	|	|	ADV
ejpam-6018	92	9	ξζ)η	ξζ)η	PROPN
ejpam-6018	92	10	)	)	PUNCT
ejpam-6018	92	11	=	=	PUNCT
ejpam-6018	92	12	(	(	PUNCT
ejpam-6018	92	13	h	h	NOUN
ejpam-6018	92	14	,	,	PUNCT
ejpam-6018	92	15	(	(	PUNCT
ejpam-6018	92	16	ξζ	ξζ	INTJ
ejpam-6018	92	17	|	|	ADV
ejpam-6018	92	18	ξζ))∨{η	ξζ))∨{η	PROPN
ejpam-6018	92	19	,	,	PUNCT
ejpam-6018	92	20	η	η	NOUN
ejpam-6018	92	21	}	}	PUNCT
ejpam-6018	92	22	)	)	PUNCT
ejpam-6018	92	23	is	be	AUX
ejpam-6018	92	24	an	an	DET
ejpam-6018	92	25	n∈-subset	n∈-subset	NOUN
ejpam-6018	92	26	of	of	ADP
ejpam-6018	92	27	(	(	PUNCT
ejpam-6018	92	28	h	h	NOUN
ejpam-6018	92	29	,	,	PUNCT
ejpam-6018	92	30	f	f	NOUN
ejpam-6018	92	31	)	)	PUNCT
ejpam-6018	92	32	.	.	PUNCT
ejpam-6018	93	1	this	this	PRON
ejpam-6018	93	2	implies	imply	VERB
ejpam-6018	93	3	that	that	SCONJ
ejpam-6018	93	4	(	(	PUNCT
ejpam-6018	93	5	ξζ	ξζ	INTJ
ejpam-6018	93	6	|	|	ADV
ejpam-6018	93	7	ξζ	ξζ	INTJ
ejpam-6018	93	8	)	)	PUNCT
ejpam-6018	93	9	∈	∈	PROPN
ejpam-6018	93	10	s∈(η	s∈(η	NOUN
ejpam-6018	93	11	)	)	PUNCT
ejpam-6018	93	12	,	,	PUNCT
ejpam-6018	93	13	showing	show	VERB
ejpam-6018	93	14	that	that	PRON
ejpam-6018	93	15	s∈(η	s∈(η	NOUN
ejpam-6018	93	16	)	)	PUNCT
ejpam-6018	93	17	is	be	AUX
ejpam-6018	93	18	a	a	DET
ejpam-6018	93	19	subalgebra	subalgebra	NOUN
ejpam-6018	93	20	of	of	ADP
ejpam-6018	93	21	h	h	NOUN
ejpam-6018	93	22	for	for	ADP
ejpam-6018	93	23	all	all	DET
ejpam-6018	93	24	η	η	PROPN
ejpam-6018	93	25	∈	∈	PROPN
ejpam-6018	93	26	υ	υ	PROPN
ejpam-6018	93	27	.	.	PUNCT
ejpam-6018	93	28	hence	hence	ADV
ejpam-6018	93	29	,	,	PUNCT
ejpam-6018	93	30	(	(	PUNCT
ejpam-6018	93	31	s∈,υ	s∈,υ	NOUN
ejpam-6018	93	32	)	)	PUNCT
ejpam-6018	93	33	is	be	AUX
ejpam-6018	93	34	a	a	DET
ejpam-6018	93	35	soft	soft	ADJ
ejpam-6018	93	36	n	n	CCONJ
ejpam-6018	93	37	-subalgebra	-subalgebra	NOUN
ejpam-6018	93	38	over	over	ADP
ejpam-6018	93	39	h.	h.	PROPN
ejpam-6018	93	40	lemma	lemma	PROPN
ejpam-6018	94	1	1	1	X
ejpam-6018	94	2	.	.	PUNCT
ejpam-6018	94	3	let	let	VERB
ejpam-6018	94	4	hs	hs	PRON
ejpam-6018	94	5	:	:	PUNCT
ejpam-6018	94	6	=	=	SYM
ejpam-6018	94	7	(	(	PUNCT
ejpam-6018	94	8	h	h	NOUN
ejpam-6018	94	9	,	,	PUNCT
ejpam-6018	94	10	|	|	ADV
ejpam-6018	94	11	,	,	PUNCT
ejpam-6018	94	12	0	0	NUM
ejpam-6018	94	13	)	)	PUNCT
ejpam-6018	94	14	be	be	AUX
ejpam-6018	94	15	an	an	DET
ejpam-6018	94	16	ssh	ssh	NOUN
ejpam-6018	94	17	-	-	PUNCT
ejpam-6018	94	18	algebra	algebra	NOUN
ejpam-6018	94	19	.	.	PUNCT
ejpam-6018	95	1	an	an	DET
ejpam-6018	95	2	n	n	ADV
ejpam-6018	95	3	-structure	-structure	NOUN
ejpam-6018	95	4	(	(	PUNCT
ejpam-6018	95	5	h	h	NOUN
ejpam-6018	95	6	,	,	PUNCT
ejpam-6018	95	7	f	f	X
ejpam-6018	95	8	)	)	PUNCT
ejpam-6018	95	9	is	be	AUX
ejpam-6018	95	10	an	an	DET
ejpam-6018	95	11	n	n	PRON
ejpam-6018	95	12	subalgebra	subalgebra	NOUN
ejpam-6018	95	13	of	of	ADP
ejpam-6018	95	14	type	type	NOUN
ejpam-6018	95	15	(	(	PUNCT
ejpam-6018	95	16	∈,∈	∈,∈	X
ejpam-6018	95	17	)	)	PUNCT
ejpam-6018	95	18	if	if	SCONJ
ejpam-6018	95	19	and	and	CCONJ
ejpam-6018	95	20	only	only	ADV
ejpam-6018	95	21	if	if	SCONJ
ejpam-6018	95	22	(	(	PUNCT
ejpam-6018	95	23	∀ξ	∀ξ	NOUN
ejpam-6018	95	24	,	,	PUNCT
ejpam-6018	95	25	ζ	ζ	PROPN
ejpam-6018	95	26	∈	∈	PROPN
ejpam-6018	95	27	h	h	NOUN
ejpam-6018	95	28	)	)	PUNCT
ejpam-6018	95	29	(	(	PUNCT
ejpam-6018	95	30	f(ξζ	f(ξζ	PROPN
ejpam-6018	95	31	|	|	ADV
ejpam-6018	95	32	ξζ	ξζ	NOUN
ejpam-6018	95	33	)	)	PUNCT
ejpam-6018	95	34	≤	≤	NOUN
ejpam-6018	95	35	∨	∨	NUM
ejpam-6018	95	36	{	{	PUNCT
ejpam-6018	95	37	f(ξ	f(ξ	NOUN
ejpam-6018	95	38	)	)	PUNCT
ejpam-6018	95	39	,	,	PUNCT
ejpam-6018	95	40	f(ζ	f(ζ	NOUN
ejpam-6018	95	41	)	)	PUNCT
ejpam-6018	95	42	}	}	PUNCT
ejpam-6018	95	43	)	)	PUNCT
ejpam-6018	95	44	.	.	PUNCT
ejpam-6018	96	1	(	(	PUNCT
ejpam-6018	96	2	2	2	X
ejpam-6018	96	3	)	)	PUNCT
ejpam-6018	96	4	proof	proof	NOUN
ejpam-6018	96	5	.	.	PUNCT
ejpam-6018	97	1	suppose	suppose	VERB
ejpam-6018	97	2	that	that	SCONJ
ejpam-6018	97	3	(	(	PUNCT
ejpam-6018	97	4	h	h	NOUN
ejpam-6018	97	5	,	,	PUNCT
ejpam-6018	97	6	f	f	X
ejpam-6018	97	7	)	)	PUNCT
ejpam-6018	97	8	is	be	AUX
ejpam-6018	97	9	an	an	DET
ejpam-6018	97	10	n	n	PRON
ejpam-6018	97	11	-subalgebra	-subalgebra	NOUN
ejpam-6018	97	12	of	of	ADP
ejpam-6018	97	13	type	type	NOUN
ejpam-6018	97	14	(	(	PUNCT
ejpam-6018	97	15	∈,∈	∈,∈	NOUN
ejpam-6018	97	16	)	)	PUNCT
ejpam-6018	97	17	.	.	PUNCT
ejpam-6018	98	1	then	then	ADV
ejpam-6018	98	2	for	for	ADP
ejpam-6018	98	3	all	all	DET
ejpam-6018	98	4	ξ	ξ	ADJ
ejpam-6018	98	5	,	,	PUNCT
ejpam-6018	98	6	ζ	ζ	PROPN
ejpam-6018	98	7	∈	∈	PROPN
ejpam-6018	98	8	h	h	NOUN
ejpam-6018	98	9	and	and	CCONJ
ejpam-6018	98	10	for	for	ADP
ejpam-6018	98	11	all	all	DET
ejpam-6018	98	12	η	η	PROPN
ejpam-6018	98	13	∈	∈	PROPN
ejpam-6018	98	14	υ	υ	NOUN
ejpam-6018	98	15	,	,	PUNCT
ejpam-6018	98	16	if	if	SCONJ
ejpam-6018	98	17	f(ξ	f(ξ	NOUN
ejpam-6018	98	18	)	)	PUNCT
ejpam-6018	98	19	≤	≤	NUM
ejpam-6018	98	20	η	η	PROPN
ejpam-6018	98	21	and	and	CCONJ
ejpam-6018	98	22	f(ζ	f(ζ	PROPN
ejpam-6018	98	23	)	)	PUNCT
ejpam-6018	98	24	≤	≤	PROPN
ejpam-6018	98	25	η	η	PROPN
ejpam-6018	98	26	,	,	PUNCT
ejpam-6018	98	27	then	then	ADV
ejpam-6018	98	28	f(ξζ	f(ξζ	PROPN
ejpam-6018	98	29	|	|	ADV
ejpam-6018	98	30	ξζ	ξζ	PROPN
ejpam-6018	98	31	)	)	PUNCT
ejpam-6018	98	32	≤	≤	PROPN
ejpam-6018	98	33	η	η	PROPN
ejpam-6018	98	34	.	.	PROPN
ejpam-6018	99	1	this	this	PRON
ejpam-6018	99	2	implies	imply	VERB
ejpam-6018	99	3	that	that	SCONJ
ejpam-6018	99	4	f(ξζ	f(ξζ	PROPN
ejpam-6018	99	5	|	|	ADV
ejpam-6018	99	6	ξζ	ξζ	NOUN
ejpam-6018	99	7	)	)	PUNCT
ejpam-6018	99	8	≤	≤	NOUN
ejpam-6018	99	9	∨	∨	NUM
ejpam-6018	99	10	{	{	PUNCT
ejpam-6018	99	11	f(ξ	f(ξ	NOUN
ejpam-6018	99	12	)	)	PUNCT
ejpam-6018	99	13	,	,	PUNCT
ejpam-6018	99	14	f(ζ	f(ζ	NOUN
ejpam-6018	99	15	)	)	PUNCT
ejpam-6018	99	16	}	}	PUNCT
ejpam-6018	99	17	.	.	PUNCT
ejpam-6018	100	1	conversely	conversely	ADV
ejpam-6018	100	2	,	,	PUNCT
ejpam-6018	100	3	suppose	suppose	VERB
ejpam-6018	100	4	that	that	SCONJ
ejpam-6018	100	5	the	the	DET
ejpam-6018	100	6	inequality	inequality	NOUN
ejpam-6018	100	7	holds	hold	VERB
ejpam-6018	100	8	for	for	ADP
ejpam-6018	100	9	all	all	DET
ejpam-6018	100	10	ξ	ξ	ADJ
ejpam-6018	100	11	,	,	PUNCT
ejpam-6018	100	12	ζ	ζ	PROPN
ejpam-6018	100	13	∈	∈	PROPN
ejpam-6018	100	14	h.	h.	NOUN
ejpam-6018	100	15	let	let	VERB
ejpam-6018	100	16	η	η	PROPN
ejpam-6018	100	17	∈	∈	PROPN
ejpam-6018	100	18	υ	υ	NOUN
ejpam-6018	100	19	,	,	PUNCT
ejpam-6018	100	20	and	and	CCONJ
ejpam-6018	100	21	suppose	suppose	VERB
ejpam-6018	100	22	that	that	SCONJ
ejpam-6018	100	23	f(ξ	f(ξ	NOUN
ejpam-6018	100	24	)	)	PUNCT
ejpam-6018	100	25	≤	≤	NUM
ejpam-6018	100	26	η	η	PROPN
ejpam-6018	100	27	and	and	CCONJ
ejpam-6018	100	28	f(ζ	f(ζ	PROPN
ejpam-6018	100	29	)	)	PUNCT
ejpam-6018	100	30	≤	≤	PROPN
ejpam-6018	100	31	η	η	PROPN
ejpam-6018	100	32	.	.	PUNCT
ejpam-6018	101	1	then,∨	then,∨	PROPN
ejpam-6018	101	2	{	{	PUNCT
ejpam-6018	101	3	f(ξ	f(ξ	PROPN
ejpam-6018	101	4	)	)	PUNCT
ejpam-6018	101	5	,	,	PUNCT
ejpam-6018	101	6	f(ζ	f(ζ	NOUN
ejpam-6018	101	7	)	)	PUNCT
ejpam-6018	101	8	}	}	PUNCT
ejpam-6018	101	9	≤	≤	NUM
ejpam-6018	101	10	η	η	PROPN
ejpam-6018	101	11	⇒	⇒	PROPN
ejpam-6018	101	12	f(ξζ	f(ξζ	PROPN
ejpam-6018	101	13	|	|	ADV
ejpam-6018	101	14	ξζ	ξζ	PROPN
ejpam-6018	101	15	)	)	PUNCT
ejpam-6018	101	16	≤	≤	PROPN
ejpam-6018	101	17	η	η	PROPN
ejpam-6018	101	18	.	.	PUNCT
ejpam-6018	101	19	thus	thus	ADV
ejpam-6018	101	20	,	,	PUNCT
ejpam-6018	101	21	(	(	PUNCT
ejpam-6018	101	22	h	h	NOUN
ejpam-6018	101	23	,	,	PUNCT
ejpam-6018	101	24	f	f	X
ejpam-6018	101	25	)	)	PUNCT
ejpam-6018	101	26	is	be	AUX
ejpam-6018	101	27	closed	close	VERB
ejpam-6018	101	28	under	under	ADP
ejpam-6018	101	29	the	the	DET
ejpam-6018	101	30	sheffer	sheffer	NOUN
ejpam-6018	101	31	operation	operation	NOUN
ejpam-6018	101	32	for	for	ADP
ejpam-6018	101	33	type	type	NOUN
ejpam-6018	101	34	(	(	PUNCT
ejpam-6018	101	35	∈,∈	∈,∈	NOUN
ejpam-6018	101	36	)	)	PUNCT
ejpam-6018	101	37	,	,	PUNCT
ejpam-6018	101	38	and	and	CCONJ
ejpam-6018	101	39	hence	hence	ADV
ejpam-6018	101	40	is	be	AUX
ejpam-6018	101	41	an	an	DET
ejpam-6018	101	42	n	n	PRON
ejpam-6018	101	43	subalgebra	subalgebra	NOUN
ejpam-6018	101	44	of	of	ADP
ejpam-6018	101	45	type	type	NOUN
ejpam-6018	101	46	(	(	PUNCT
ejpam-6018	101	47	∈,∈	∈,∈	NOUN
ejpam-6018	101	48	)	)	PUNCT
ejpam-6018	101	49	.	.	PUNCT
ejpam-6018	102	1	theorem	theorem	NOUN
ejpam-6018	102	2	2	2	NUM
ejpam-6018	102	3	.	.	PUNCT
ejpam-6018	103	1	let	let	VERB
ejpam-6018	103	2	hs	hs	PRON
ejpam-6018	103	3	:	:	PUNCT
ejpam-6018	103	4	=	=	SYM
ejpam-6018	103	5	(	(	PUNCT
ejpam-6018	103	6	h	h	NOUN
ejpam-6018	103	7	,	,	PUNCT
ejpam-6018	103	8	|	|	ADV
ejpam-6018	103	9	,	,	PUNCT
ejpam-6018	103	10	0	0	NUM
ejpam-6018	103	11	)	)	PUNCT
ejpam-6018	103	12	be	be	AUX
ejpam-6018	103	13	an	an	DET
ejpam-6018	103	14	ssh	ssh	NOUN
ejpam-6018	103	15	-	-	PUNCT
ejpam-6018	103	16	algebra	algebra	NOUN
ejpam-6018	103	17	.	.	PUNCT
ejpam-6018	104	1	given	give	VERB
ejpam-6018	104	2	an	an	DET
ejpam-6018	104	3	n	n	ADV
ejpam-6018	104	4	-structure	-structure	NOUN
ejpam-6018	104	5	(	(	PUNCT
ejpam-6018	104	6	h	h	NOUN
ejpam-6018	104	7	,	,	PUNCT
ejpam-6018	104	8	f	f	NOUN
ejpam-6018	104	9	)	)	PUNCT
ejpam-6018	104	10	and	and	CCONJ
ejpam-6018	104	11	υ	υ	NOUN
ejpam-6018	104	12	=	=	PUNCT
ejpam-6018	105	1	[	[	X
ejpam-6018	105	2	−1	−1	NOUN
ejpam-6018	105	3	,	,	PUNCT
ejpam-6018	105	4	0	0	NUM
ejpam-6018	105	5	)	)	PUNCT
ejpam-6018	105	6	,	,	PUNCT
ejpam-6018	105	7	the	the	DET
ejpam-6018	105	8	soft	soft	ADJ
ejpam-6018	105	9	nq	nq	NOUN
ejpam-6018	105	10	-	-	PUNCT
ejpam-6018	105	11	set	set	VERB
ejpam-6018	105	12	(	(	PUNCT
ejpam-6018	105	13	sq	sq	ADJ
ejpam-6018	105	14	,	,	PUNCT
ejpam-6018	105	15	υ	υ	NOUN
ejpam-6018	105	16	)	)	PUNCT
ejpam-6018	105	17	is	be	AUX
ejpam-6018	105	18	a	a	DET
ejpam-6018	105	19	soft	soft	ADJ
ejpam-6018	105	20	n	n	CCONJ
ejpam-6018	105	21	-subalgebra	-subalgebra	NOUN
ejpam-6018	105	22	over	over	ADP
ejpam-6018	105	23	h	h	NOUN
ejpam-6018	105	24	if	if	SCONJ
ejpam-6018	106	1	and	and	CCONJ
ejpam-6018	106	2	only	only	ADV
ejpam-6018	106	3	if	if	SCONJ
ejpam-6018	106	4	(	(	PUNCT
ejpam-6018	106	5	h	h	NOUN
ejpam-6018	106	6	,	,	PUNCT
ejpam-6018	106	7	f	f	X
ejpam-6018	106	8	)	)	PUNCT
ejpam-6018	106	9	is	be	AUX
ejpam-6018	106	10	an	an	DET
ejpam-6018	106	11	n	n	PRON
ejpam-6018	106	12	-subalgebra	-subalgebra	NOUN
ejpam-6018	106	13	of	of	ADP
ejpam-6018	106	14	type	type	NOUN
ejpam-6018	106	15	(	(	PUNCT
ejpam-6018	106	16	∈,∈	∈,∈	NOUN
ejpam-6018	106	17	)	)	PUNCT
ejpam-6018	106	18	.	.	PUNCT
ejpam-6018	107	1	proof	proof	NOUN
ejpam-6018	107	2	.	.	PUNCT
ejpam-6018	108	1	assume	assume	VERB
ejpam-6018	108	2	that	that	SCONJ
ejpam-6018	108	3	(	(	PUNCT
ejpam-6018	108	4	h	h	NOUN
ejpam-6018	108	5	,	,	PUNCT
ejpam-6018	108	6	f	f	X
ejpam-6018	108	7	)	)	PUNCT
ejpam-6018	108	8	is	be	AUX
ejpam-6018	108	9	an	an	DET
ejpam-6018	108	10	n	n	PRON
ejpam-6018	108	11	-subalgebra	-subalgebra	NOUN
ejpam-6018	108	12	of	of	ADP
ejpam-6018	108	13	type	type	NOUN
ejpam-6018	108	14	(	(	PUNCT
ejpam-6018	108	15	∈,∈	∈,∈	X
ejpam-6018	108	16	)	)	PUNCT
ejpam-6018	108	17	and	and	CCONJ
ejpam-6018	108	18	let	let	VERB
ejpam-6018	108	19	η	η	PROPN
ejpam-6018	108	20	∈	∈	PROPN
ejpam-6018	108	21	υ	υ	NOUN
ejpam-6018	108	22	be	be	AUX
ejpam-6018	108	23	such	such	ADJ
ejpam-6018	108	24	that	that	SCONJ
ejpam-6018	108	25	sq(η	sq(η	NOUN
ejpam-6018	108	26	)	)	PUNCT
ejpam-6018	108	27	̸=	̸=	PROPN
ejpam-6018	108	28	∅.	∅.	ADP
ejpam-6018	108	29	if	if	SCONJ
ejpam-6018	108	30	ξ	ξ	PROPN
ejpam-6018	108	31	,	,	PUNCT
ejpam-6018	108	32	ζ	ζ	PROPN
ejpam-6018	108	33	∈	∈	PROPN
ejpam-6018	108	34	sq(η	sq(η	NUM
ejpam-6018	108	35	)	)	PUNCT
ejpam-6018	108	36	,	,	PUNCT
ejpam-6018	108	37	then	then	ADV
ejpam-6018	108	38	(	(	PUNCT
ejpam-6018	108	39	h	h	NOUN
ejpam-6018	108	40	,	,	PUNCT
ejpam-6018	108	41	ξη	ξη	PROPN
ejpam-6018	108	42	)	)	PUNCT
ejpam-6018	108	43	and	and	CCONJ
ejpam-6018	108	44	(	(	PUNCT
ejpam-6018	108	45	h	h	NOUN
ejpam-6018	108	46	,	,	PUNCT
ejpam-6018	108	47	ζη	ζη	ADJ
ejpam-6018	108	48	)	)	PUNCT
ejpam-6018	108	49	are	be	AUX
ejpam-6018	108	50	nq	nq	NOUN
ejpam-6018	108	51	-	-	PUNCT
ejpam-6018	108	52	subsets	subset	NOUN
ejpam-6018	108	53	of	of	ADP
ejpam-6018	108	54	(	(	PUNCT
ejpam-6018	108	55	h	h	NOUN
ejpam-6018	108	56	,	,	PUNCT
ejpam-6018	108	57	f	f	NOUN
ejpam-6018	108	58	)	)	PUNCT
ejpam-6018	108	59	,	,	PUNCT
ejpam-6018	108	60	and	and	CCONJ
ejpam-6018	108	61	so	so	ADV
ejpam-6018	108	62	f(ξ	f(ξ	NOUN
ejpam-6018	108	63	)	)	PUNCT
ejpam-6018	109	1	+	+	NUM
ejpam-6018	109	2	η	η	X
ejpam-6018	109	3	+	+	ADP
ejpam-6018	109	4	1	1	NUM
ejpam-6018	109	5	<	<	X
ejpam-6018	109	6	0	0	NUM
ejpam-6018	109	7	and	and	CCONJ
ejpam-6018	109	8	f(ζ	f(ζ	PROPN
ejpam-6018	109	9	)	)	PUNCT
ejpam-6018	110	1	+	+	CCONJ
ejpam-6018	110	2	η	η	PROPN
ejpam-6018	110	3	+	+	ADP
ejpam-6018	110	4	1	1	NUM
ejpam-6018	110	5	<	<	X
ejpam-6018	110	6	0	0	NUM
ejpam-6018	110	7	.	.	PUNCT
ejpam-6018	111	1	it	it	PRON
ejpam-6018	111	2	follows	follow	VERB
ejpam-6018	111	3	from	from	ADP
ejpam-6018	111	4	(	(	PUNCT
ejpam-6018	111	5	2	2	NUM
ejpam-6018	111	6	)	)	PUNCT
ejpam-6018	111	7	that	that	PRON
ejpam-6018	111	8	f(ξζ	f(ξζ	PROPN
ejpam-6018	111	9	|	|	ADV
ejpam-6018	111	10	ξζ	ξζ	NOUN
ejpam-6018	111	11	)	)	PUNCT
ejpam-6018	112	1	+	+	CCONJ
ejpam-6018	112	2	η	η	PROPN
ejpam-6018	112	3	+	+	PROPN
ejpam-6018	112	4	1	1	NUM
ejpam-6018	112	5	≤	≤	NUM
ejpam-6018	112	6	∨	∨	NUM
ejpam-6018	112	7	{	{	PUNCT
ejpam-6018	112	8	f(ξ	f(ξ	NOUN
ejpam-6018	112	9	)	)	PUNCT
ejpam-6018	112	10	,	,	PUNCT
ejpam-6018	112	11	f(ζ)}+	f(ζ)}+	NUM
ejpam-6018	112	12	η	η	X
ejpam-6018	112	13	+	+	ADP
ejpam-6018	112	14	1	1	NUM
ejpam-6018	112	15	<	<	X
ejpam-6018	112	16	0	0	NUM
ejpam-6018	112	17	,	,	PUNCT
ejpam-6018	112	18	t.	t.	NOUN
ejpam-6018	112	19	oner	oner	NOUN
ejpam-6018	112	20	et	et	PROPN
ejpam-6018	112	21	al	al	PROPN
ejpam-6018	112	22	.	.	PUNCT
ejpam-6018	112	23	/	/	SYM
ejpam-6018	112	24	eur	eur	PROPN
ejpam-6018	112	25	.	.	PUNCT
ejpam-6018	113	1	j.	j.	PROPN
ejpam-6018	113	2	pure	pure	PROPN
ejpam-6018	113	3	appl	appl	PROPN
ejpam-6018	113	4	.	.	PROPN
ejpam-6018	113	5	math	math	PROPN
ejpam-6018	113	6	,	,	PUNCT
ejpam-6018	113	7	18	18	NUM
ejpam-6018	113	8	(	(	PUNCT
ejpam-6018	113	9	2	2	NUM
ejpam-6018	113	10	)	)	PUNCT
ejpam-6018	113	11	(	(	PUNCT
ejpam-6018	113	12	2025	2025	NUM
ejpam-6018	113	13	)	)	PUNCT
ejpam-6018	113	14	,	,	PUNCT
ejpam-6018	113	15	6018	6018	NUM
ejpam-6018	113	16	5	5	NUM
ejpam-6018	113	17	of	of	ADP
ejpam-6018	113	18	11	11	NUM
ejpam-6018	113	19	and	and	CCONJ
ejpam-6018	113	20	so	so	ADV
ejpam-6018	113	21	(	(	PUNCT
ejpam-6018	113	22	h	h	NOUN
ejpam-6018	113	23	,	,	PUNCT
ejpam-6018	113	24	(	(	PUNCT
ejpam-6018	113	25	ξζ	ξζ	NOUN
ejpam-6018	113	26	|	|	ADV
ejpam-6018	113	27	ξζ)η	ξζ)η	PROPN
ejpam-6018	113	28	)	)	PUNCT
ejpam-6018	113	29	=	=	PUNCT
ejpam-6018	113	30	(	(	PUNCT
ejpam-6018	113	31	h	h	NOUN
ejpam-6018	113	32	,	,	PUNCT
ejpam-6018	113	33	(	(	PUNCT
ejpam-6018	113	34	ξζ	ξζ	INTJ
ejpam-6018	113	35	|	|	ADV
ejpam-6018	113	36	ξζ)∨{η	ξζ)∨{η	NUM
ejpam-6018	113	37	,	,	PUNCT
ejpam-6018	113	38	η	η	NOUN
ejpam-6018	113	39	}	}	PUNCT
ejpam-6018	113	40	)	)	PUNCT
ejpam-6018	113	41	is	be	AUX
ejpam-6018	113	42	an	an	DET
ejpam-6018	113	43	nq	nq	NOUN
ejpam-6018	113	44	-	-	PUNCT
ejpam-6018	113	45	subset	subset	NOUN
ejpam-6018	113	46	of	of	ADP
ejpam-6018	113	47	(	(	PUNCT
ejpam-6018	113	48	h	h	NOUN
ejpam-6018	113	49	,	,	PUNCT
ejpam-6018	113	50	f	f	NOUN
ejpam-6018	113	51	)	)	PUNCT
ejpam-6018	113	52	.	.	PUNCT
ejpam-6018	114	1	hence	hence	ADV
ejpam-6018	114	2	,	,	PUNCT
ejpam-6018	114	3	ξζ	ξζ	INTJ
ejpam-6018	114	4	|	|	ADV
ejpam-6018	114	5	ξζ	ξζ	INTJ
ejpam-6018	114	6	∈	∈	PROPN
ejpam-6018	114	7	sq(η	sq(η	X
ejpam-6018	114	8	)	)	PUNCT
ejpam-6018	114	9	,	,	PUNCT
ejpam-6018	114	10	and	and	CCONJ
ejpam-6018	114	11	thus	thus	ADV
ejpam-6018	114	12	sq(η	sq(η	NUM
ejpam-6018	114	13	)	)	PUNCT
ejpam-6018	114	14	is	be	AUX
ejpam-6018	114	15	a	a	DET
ejpam-6018	114	16	subalgebra	subalgebra	NOUN
ejpam-6018	114	17	of	of	ADP
ejpam-6018	114	18	h	h	NOUN
ejpam-6018	114	19	for	for	ADP
ejpam-6018	114	20	all	all	DET
ejpam-6018	114	21	η	η	PROPN
ejpam-6018	114	22	∈	∈	PROPN
ejpam-6018	114	23	υ	υ	NOUN
ejpam-6018	114	24	with	with	ADP
ejpam-6018	114	25	sq(η	sq(η	NOUN
ejpam-6018	114	26	)	)	PUNCT
ejpam-6018	114	27	̸=	̸=	PROPN
ejpam-6018	114	28	∅.	∅.	PRON
ejpam-6018	114	29	therefore	therefore	ADV
ejpam-6018	114	30	,	,	PUNCT
ejpam-6018	114	31	(	(	PUNCT
ejpam-6018	114	32	sq	sq	ADJ
ejpam-6018	114	33	,	,	PUNCT
ejpam-6018	114	34	υ	υ	NOUN
ejpam-6018	114	35	)	)	PUNCT
ejpam-6018	114	36	is	be	AUX
ejpam-6018	114	37	a	a	DET
ejpam-6018	114	38	soft	soft	ADJ
ejpam-6018	114	39	n	n	CCONJ
ejpam-6018	114	40	-subalgebra	-subalgebra	NOUN
ejpam-6018	114	41	over	over	ADP
ejpam-6018	114	42	h.	h.	NOUN
ejpam-6018	114	43	conversely	conversely	ADV
ejpam-6018	114	44	,	,	PUNCT
ejpam-6018	114	45	suppose	suppose	VERB
ejpam-6018	114	46	that	that	SCONJ
ejpam-6018	114	47	the	the	DET
ejpam-6018	114	48	soft	soft	ADJ
ejpam-6018	114	49	nq	nq	NOUN
ejpam-6018	114	50	-	-	PUNCT
ejpam-6018	114	51	set	set	VERB
ejpam-6018	114	52	(	(	PUNCT
ejpam-6018	114	53	sq	sq	ADJ
ejpam-6018	114	54	,	,	PUNCT
ejpam-6018	114	55	υ	υ	NOUN
ejpam-6018	114	56	)	)	PUNCT
ejpam-6018	114	57	is	be	AUX
ejpam-6018	114	58	a	a	DET
ejpam-6018	114	59	soft	soft	ADJ
ejpam-6018	114	60	n	n	CCONJ
ejpam-6018	114	61	-subalgebra	-subalgebra	NOUN
ejpam-6018	114	62	over	over	ADP
ejpam-6018	114	63	h	h	NOUN
ejpam-6018	114	64	,	,	PUNCT
ejpam-6018	114	65	and	and	CCONJ
ejpam-6018	114	66	assume	assume	VERB
ejpam-6018	114	67	that	that	SCONJ
ejpam-6018	114	68	f(ϱϖ	f(ϱϖ	NOUN
ejpam-6018	114	69	|	|	ADV
ejpam-6018	114	70	ϱϖ	ϱϖ	PROPN
ejpam-6018	114	71	)	)	PUNCT
ejpam-6018	114	72	>	>	X
ejpam-6018	114	73	∨	∨	X
ejpam-6018	114	74	{	{	PUNCT
ejpam-6018	114	75	f(ϱ	f(ϱ	NOUN
ejpam-6018	114	76	)	)	PUNCT
ejpam-6018	114	77	,	,	PUNCT
ejpam-6018	114	78	f(ϖ	f(ϖ	PROPN
ejpam-6018	114	79	)	)	PUNCT
ejpam-6018	114	80	}	}	PUNCT
ejpam-6018	114	81	for	for	ADP
ejpam-6018	114	82	some	some	DET
ejpam-6018	114	83	ϱ,ϖ	ϱ,ϖ	NOUN
ejpam-6018	114	84	∈	∈	PROPN
ejpam-6018	114	85	h.	h.	NOUN
ejpam-6018	114	86	then	then	ADV
ejpam-6018	114	87	there	there	PRON
ejpam-6018	114	88	exists	exist	VERB
ejpam-6018	114	89	t	t	PROPN
ejpam-6018	114	90	∈	∈	PROPN
ejpam-6018	114	91	υ	υ	ADP
ejpam-6018	114	92	such	such	ADJ
ejpam-6018	114	93	that	that	DET
ejpam-6018	114	94	f(ϱϖ	f(ϱϖ	NOUN
ejpam-6018	114	95	|	|	NOUN
ejpam-6018	114	96	ϱϖ	ϱϖ	NOUN
ejpam-6018	114	97	)	)	PUNCT
ejpam-6018	114	98	+	+	CCONJ
ejpam-6018	114	99	t+	t+	NOUN
ejpam-6018	114	100	1	1	NUM
ejpam-6018	114	101	<	<	X
ejpam-6018	114	102	0	0	NUM
ejpam-6018	114	103	and	and	CCONJ
ejpam-6018	114	104	∨	∨	NUM
ejpam-6018	114	105	{	{	PUNCT
ejpam-6018	114	106	f(ϱ	f(ϱ	NOUN
ejpam-6018	114	107	)	)	PUNCT
ejpam-6018	114	108	,	,	PUNCT
ejpam-6018	114	109	f(ϖ)}+	f(ϖ)}+	NUM
ejpam-6018	114	110	t+	t+	NOUN
ejpam-6018	114	111	1	1	NUM
ejpam-6018	114	112	<	<	X
ejpam-6018	114	113	0	0	NUM
ejpam-6018	114	114	.	.	PUNCT
ejpam-6018	115	1	it	it	PRON
ejpam-6018	115	2	follows	follow	VERB
ejpam-6018	115	3	that	that	SCONJ
ejpam-6018	115	4	(	(	PUNCT
ejpam-6018	115	5	h	h	NOUN
ejpam-6018	115	6	,	,	PUNCT
ejpam-6018	115	7	ϱt	ϱt	NOUN
ejpam-6018	115	8	)	)	PUNCT
ejpam-6018	115	9	and	and	CCONJ
ejpam-6018	115	10	(	(	PUNCT
ejpam-6018	115	11	h,ϖt	h,ϖt	NOUN
ejpam-6018	115	12	)	)	PUNCT
ejpam-6018	115	13	are	be	AUX
ejpam-6018	115	14	nq	nq	NOUN
ejpam-6018	115	15	-	-	PUNCT
ejpam-6018	115	16	subsets	subset	NOUN
ejpam-6018	115	17	of	of	ADP
ejpam-6018	115	18	(	(	PUNCT
ejpam-6018	115	19	h	h	NOUN
ejpam-6018	115	20	,	,	PUNCT
ejpam-6018	115	21	f	f	PROPN
ejpam-6018	115	22	)	)	PUNCT
ejpam-6018	116	1	but	but	CCONJ
ejpam-6018	116	2	(	(	PUNCT
ejpam-6018	116	3	h	h	NOUN
ejpam-6018	116	4	,	,	PUNCT
ejpam-6018	116	5	(	(	PUNCT
ejpam-6018	116	6	ϱϖ	ϱϖ	NOUN
ejpam-6018	116	7	|	|	ADV
ejpam-6018	116	8	ϱϖ)t	ϱϖ)t	NOUN
ejpam-6018	116	9	)	)	PUNCT
ejpam-6018	116	10	is	be	AUX
ejpam-6018	116	11	not	not	PART
ejpam-6018	116	12	an	an	DET
ejpam-6018	116	13	nq	nq	NOUN
ejpam-6018	116	14	-	-	PUNCT
ejpam-6018	116	15	subset	subset	NOUN
ejpam-6018	116	16	of	of	ADP
ejpam-6018	116	17	(	(	PUNCT
ejpam-6018	116	18	h	h	NOUN
ejpam-6018	116	19	,	,	PUNCT
ejpam-6018	116	20	f	f	NOUN
ejpam-6018	116	21	)	)	PUNCT
ejpam-6018	116	22	.	.	PUNCT
ejpam-6018	117	1	this	this	PRON
ejpam-6018	117	2	is	be	AUX
ejpam-6018	117	3	a	a	DET
ejpam-6018	117	4	contradiction	contradiction	NOUN
ejpam-6018	117	5	,	,	PUNCT
ejpam-6018	117	6	and	and	CCONJ
ejpam-6018	117	7	hence	hence	ADV
ejpam-6018	117	8	(	(	PUNCT
ejpam-6018	117	9	∀ξ	∀ξ	NOUN
ejpam-6018	117	10	,	,	PUNCT
ejpam-6018	117	11	ζ	ζ	PROPN
ejpam-6018	117	12	∈	∈	PROPN
ejpam-6018	117	13	h	h	NOUN
ejpam-6018	117	14	)	)	PUNCT
ejpam-6018	117	15	(	(	PUNCT
ejpam-6018	117	16	f(ξζ	f(ξζ	PROPN
ejpam-6018	117	17	|	|	ADV
ejpam-6018	117	18	ξζ	ξζ	NOUN
ejpam-6018	117	19	)	)	PUNCT
ejpam-6018	117	20	≤	≤	NOUN
ejpam-6018	117	21	∨	∨	NUM
ejpam-6018	117	22	{	{	PUNCT
ejpam-6018	117	23	f(ξ	f(ξ	NOUN
ejpam-6018	117	24	)	)	PUNCT
ejpam-6018	117	25	,	,	PUNCT
ejpam-6018	117	26	f(ζ	f(ζ	NOUN
ejpam-6018	117	27	)	)	PUNCT
ejpam-6018	117	28	}	}	PUNCT
ejpam-6018	117	29	)	)	PUNCT
ejpam-6018	117	30	.	.	PUNCT
ejpam-6018	118	1	therefore	therefore	ADV
ejpam-6018	118	2	,	,	PUNCT
ejpam-6018	118	3	(	(	PUNCT
ejpam-6018	118	4	h	h	NOUN
ejpam-6018	118	5	,	,	PUNCT
ejpam-6018	118	6	f	f	X
ejpam-6018	118	7	)	)	PUNCT
ejpam-6018	118	8	is	be	AUX
ejpam-6018	118	9	an	an	DET
ejpam-6018	118	10	n	n	PRON
ejpam-6018	118	11	-subalgebra	-subalgebra	NOUN
ejpam-6018	118	12	of	of	ADP
ejpam-6018	118	13	type	type	NOUN
ejpam-6018	118	14	(	(	PUNCT
ejpam-6018	118	15	∈,∈	∈,∈	X
ejpam-6018	118	16	)	)	PUNCT
ejpam-6018	118	17	by	by	ADP
ejpam-6018	118	18	lemma	lemma	PROPN
ejpam-6018	118	19	1	1	NUM
ejpam-6018	118	20	.	.	PUNCT
ejpam-6018	118	21	theorem	theorem	NOUN
ejpam-6018	118	22	3	3	X
ejpam-6018	118	23	.	.	PUNCT
ejpam-6018	119	1	let	let	VERB
ejpam-6018	119	2	hs	hs	PRON
ejpam-6018	119	3	:	:	PUNCT
ejpam-6018	119	4	=	=	SYM
ejpam-6018	119	5	(	(	PUNCT
ejpam-6018	119	6	h	h	NOUN
ejpam-6018	119	7	,	,	PUNCT
ejpam-6018	119	8	|	|	ADV
ejpam-6018	119	9	,	,	PUNCT
ejpam-6018	119	10	0	0	NUM
ejpam-6018	119	11	)	)	PUNCT
ejpam-6018	119	12	be	be	AUX
ejpam-6018	119	13	an	an	DET
ejpam-6018	119	14	ssh	ssh	NOUN
ejpam-6018	119	15	-	-	PUNCT
ejpam-6018	119	16	algebra	algebra	NOUN
ejpam-6018	119	17	.	.	PUNCT
ejpam-6018	120	1	given	give	VERB
ejpam-6018	120	2	an	an	DET
ejpam-6018	120	3	n	n	ADV
ejpam-6018	120	4	-structure	-structure	NOUN
ejpam-6018	120	5	(	(	PUNCT
ejpam-6018	120	6	h	h	NOUN
ejpam-6018	120	7	,	,	PUNCT
ejpam-6018	120	8	f	f	NOUN
ejpam-6018	120	9	)	)	PUNCT
ejpam-6018	120	10	and	and	CCONJ
ejpam-6018	120	11	the	the	DET
ejpam-6018	120	12	soft	soft	ADJ
ejpam-6018	120	13	n∈-set	n∈-set	NOUN
ejpam-6018	120	14	(	(	PUNCT
ejpam-6018	120	15	s∈,υ	s∈,υ	NOUN
ejpam-6018	120	16	)	)	PUNCT
ejpam-6018	120	17	with	with	ADP
ejpam-6018	120	18	υ	υ	NOUN
ejpam-6018	120	19	=	=	PUNCT
ejpam-6018	120	20	[	[	X
ejpam-6018	120	21	−1,−0.5	−1,−0.5	PROPN
ejpam-6018	120	22	)	)	PUNCT
ejpam-6018	120	23	,	,	PUNCT
ejpam-6018	120	24	the	the	DET
ejpam-6018	120	25	following	follow	VERB
ejpam-6018	120	26	are	be	AUX
ejpam-6018	120	27	equivalent	equivalent	ADJ
ejpam-6018	120	28	:	:	PUNCT
ejpam-6018	120	29	(	(	PUNCT
ejpam-6018	120	30	1	1	X
ejpam-6018	120	31	)	)	PUNCT
ejpam-6018	120	32	(	(	PUNCT
ejpam-6018	120	33	s∈,υ	s∈,υ	NOUN
ejpam-6018	120	34	)	)	PUNCT
ejpam-6018	120	35	is	be	AUX
ejpam-6018	120	36	a	a	DET
ejpam-6018	120	37	soft	soft	ADJ
ejpam-6018	120	38	n	n	CCONJ
ejpam-6018	120	39	-subalgebra	-subalgebra	NOUN
ejpam-6018	120	40	over	over	ADP
ejpam-6018	120	41	h.	h.	PROPN
ejpam-6018	120	42	(	(	PUNCT
ejpam-6018	120	43	2	2	NUM
ejpam-6018	120	44	)	)	PUNCT
ejpam-6018	120	45	(	(	PUNCT
ejpam-6018	120	46	∀ξ	∀ξ	NOUN
ejpam-6018	120	47	,	,	PUNCT
ejpam-6018	120	48	ζ	ζ	PROPN
ejpam-6018	120	49	∈	∈	PROPN
ejpam-6018	120	50	h	h	NOUN
ejpam-6018	120	51	)	)	PUNCT
ejpam-6018	120	52	(	(	PUNCT
ejpam-6018	120	53	∧	∧	PROPN
ejpam-6018	120	54	{	{	PUNCT
ejpam-6018	120	55	f(ϱϖ	f(ϱϖ	NOUN
ejpam-6018	120	56	|	|	ADV
ejpam-6018	120	57	ϱϖ),−0.5	ϱϖ),−0.5	VERB
ejpam-6018	120	58	}	}	PUNCT
ejpam-6018	120	59	≤	≤	NUM
ejpam-6018	120	60	∨	∨	NUM
ejpam-6018	120	61	{	{	PUNCT
ejpam-6018	120	62	f(ξ	f(ξ	NOUN
ejpam-6018	120	63	)	)	PUNCT
ejpam-6018	120	64	,	,	PUNCT
ejpam-6018	120	65	f(ζ	f(ζ	NOUN
ejpam-6018	120	66	)	)	PUNCT
ejpam-6018	120	67	}	}	PUNCT
ejpam-6018	120	68	)	)	PUNCT
ejpam-6018	120	69	.	.	PUNCT
ejpam-6018	121	1	proof	proof	NOUN
ejpam-6018	121	2	.	.	PUNCT
ejpam-6018	122	1	assume	assume	VERB
ejpam-6018	122	2	that	that	SCONJ
ejpam-6018	122	3	the	the	DET
ejpam-6018	122	4	soft	soft	ADJ
ejpam-6018	122	5	n∈-set	n∈-set	NOUN
ejpam-6018	122	6	(	(	PUNCT
ejpam-6018	122	7	s∈,υ	s∈,υ	NOUN
ejpam-6018	122	8	)	)	PUNCT
ejpam-6018	122	9	is	be	AUX
ejpam-6018	122	10	a	a	DET
ejpam-6018	122	11	soft	soft	ADJ
ejpam-6018	122	12	n	n	CCONJ
ejpam-6018	122	13	-subalgebra	-subalgebra	NOUN
ejpam-6018	122	14	over	over	ADP
ejpam-6018	122	15	h.	h.	PROPN
ejpam-6018	122	16	then	then	ADV
ejpam-6018	122	17	s∈(η	s∈(η	X
ejpam-6018	122	18	)	)	PUNCT
ejpam-6018	122	19	is	be	AUX
ejpam-6018	122	20	a	a	DET
ejpam-6018	122	21	subalgebra	subalgebra	NOUN
ejpam-6018	122	22	of	of	ADP
ejpam-6018	122	23	h	h	NOUN
ejpam-6018	122	24	for	for	ADP
ejpam-6018	122	25	all	all	DET
ejpam-6018	122	26	η	η	PROPN
ejpam-6018	122	27	∈	∈	PROPN
ejpam-6018	122	28	υ	υ	NOUN
ejpam-6018	122	29	with	with	ADP
ejpam-6018	122	30	s∈(η	s∈(η	ADJ
ejpam-6018	122	31	)	)	PUNCT
ejpam-6018	123	1	̸=	̸=	PROPN
ejpam-6018	123	2	∅.	∅.	ADV
ejpam-6018	123	3	if	if	SCONJ
ejpam-6018	123	4	there	there	PRON
ejpam-6018	123	5	exist	exist	VERB
ejpam-6018	123	6	ϱ,ϖ	ϱ,ϖ	NOUN
ejpam-6018	123	7	∈	∈	PROPN
ejpam-6018	123	8	h	h	NOUN
ejpam-6018	123	9	such	such	ADJ
ejpam-6018	123	10	that∧	that∧	PROPN
ejpam-6018	123	11	{	{	PUNCT
ejpam-6018	123	12	f(ϱϖ	f(ϱϖ	NOUN
ejpam-6018	123	13	|	|	ADV
ejpam-6018	123	14	ϱϖ),−0.5	ϱϖ),−0.5	VERB
ejpam-6018	123	15	}	}	PUNCT
ejpam-6018	123	16	>	>	PUNCT
ejpam-6018	123	17	t	t	PROPN
ejpam-6018	123	18	=	=	PUNCT
ejpam-6018	123	19	∨	∨	X
ejpam-6018	123	20	{	{	PUNCT
ejpam-6018	123	21	f(ϱ	f(ϱ	NOUN
ejpam-6018	123	22	)	)	PUNCT
ejpam-6018	123	23	,	,	PUNCT
ejpam-6018	123	24	f(ϖ	f(ϖ	PROPN
ejpam-6018	123	25	)	)	PUNCT
ejpam-6018	123	26	}	}	PUNCT
ejpam-6018	123	27	,	,	PUNCT
ejpam-6018	123	28	then	then	ADV
ejpam-6018	123	29	t	t	PROPN
ejpam-6018	123	30	∈	∈	PROPN
ejpam-6018	123	31	υ	υ	PROPN
ejpam-6018	123	32	and	and	CCONJ
ejpam-6018	123	33	(	(	PUNCT
ejpam-6018	123	34	h	h	NOUN
ejpam-6018	123	35	,	,	PUNCT
ejpam-6018	123	36	ϱt	ϱt	NOUN
ejpam-6018	123	37	)	)	PUNCT
ejpam-6018	123	38	and	and	CCONJ
ejpam-6018	123	39	(	(	PUNCT
ejpam-6018	123	40	h,ϖt	h,ϖt	NOUN
ejpam-6018	123	41	)	)	PUNCT
ejpam-6018	123	42	are	be	AUX
ejpam-6018	123	43	n∈-subsets	n∈-subset	NOUN
ejpam-6018	123	44	of	of	ADP
ejpam-6018	123	45	(	(	PUNCT
ejpam-6018	123	46	h	h	NOUN
ejpam-6018	123	47	,	,	PUNCT
ejpam-6018	123	48	f	f	PROPN
ejpam-6018	123	49	)	)	PUNCT
ejpam-6018	123	50	,	,	PUNCT
ejpam-6018	123	51	that	that	ADV
ejpam-6018	123	52	is	is	ADV
ejpam-6018	123	53	,	,	PUNCT
ejpam-6018	123	54	ϱ,ϖ	ϱ,ϖ	PROPN
ejpam-6018	123	55	∈	∈	PROPN
ejpam-6018	123	56	s∈(t	s∈(t	VERB
ejpam-6018	123	57	)	)	PUNCT
ejpam-6018	123	58	,	,	PUNCT
ejpam-6018	123	59	but	but	CCONJ
ejpam-6018	123	60	(	(	PUNCT
ejpam-6018	123	61	h	h	NOUN
ejpam-6018	123	62	,	,	PUNCT
ejpam-6018	123	63	(	(	PUNCT
ejpam-6018	123	64	ϱϖ	ϱϖ	NOUN
ejpam-6018	123	65	|	|	ADV
ejpam-6018	123	66	ϱϖ)t	ϱϖ)t	NOUN
ejpam-6018	123	67	)	)	PUNCT
ejpam-6018	123	68	is	be	AUX
ejpam-6018	123	69	not	not	PART
ejpam-6018	123	70	an	an	DET
ejpam-6018	123	71	n∈-subset	n∈-subset	NOUN
ejpam-6018	123	72	of	of	ADP
ejpam-6018	123	73	(	(	PUNCT
ejpam-6018	123	74	h	h	NOUN
ejpam-6018	123	75	,	,	PUNCT
ejpam-6018	123	76	f	f	PROPN
ejpam-6018	123	77	)	)	PUNCT
ejpam-6018	123	78	,	,	PUNCT
ejpam-6018	123	79	that	that	ADV
ejpam-6018	123	80	is	is	ADV
ejpam-6018	123	81	,	,	PUNCT
ejpam-6018	123	82	ϱϖ	ϱϖ	VERB
ejpam-6018	123	83	|	|	ADV
ejpam-6018	123	84	ϱϖ	ϱϖ	PROPN
ejpam-6018	123	85	/∈	/∈	PUNCT
ejpam-6018	123	86	s∈(t	s∈(t	NOUN
ejpam-6018	123	87	)	)	PUNCT
ejpam-6018	123	88	,	,	PUNCT
ejpam-6018	123	89	a	a	DET
ejpam-6018	123	90	contradiction	contradiction	NOUN
ejpam-6018	123	91	.	.	PUNCT
ejpam-6018	124	1	thus	thus	ADV
ejpam-6018	124	2	,	,	PUNCT
ejpam-6018	124	3	∧	∧	PROPN
ejpam-6018	124	4	{	{	PUNCT
ejpam-6018	124	5	f(ξζ	f(ξζ	PROPN
ejpam-6018	124	6	|	|	CCONJ
ejpam-6018	124	7	ξζ),−0.5	ξζ),−0.5	VERB
ejpam-6018	124	8	}	}	PUNCT
ejpam-6018	124	9	≤	≤	NUM
ejpam-6018	124	10	∨	∨	NUM
ejpam-6018	124	11	{	{	PUNCT
ejpam-6018	124	12	f(ξ	f(ξ	NOUN
ejpam-6018	124	13	)	)	PUNCT
ejpam-6018	124	14	,	,	PUNCT
ejpam-6018	124	15	f(ζ	f(ζ	NOUN
ejpam-6018	124	16	)	)	PUNCT
ejpam-6018	124	17	}	}	PUNCT
ejpam-6018	124	18	for	for	ADP
ejpam-6018	124	19	all	all	DET
ejpam-6018	124	20	ξ	ξ	ADJ
ejpam-6018	124	21	,	,	PUNCT
ejpam-6018	124	22	ζ	ζ	PROPN
ejpam-6018	124	23	∈	∈	PROPN
ejpam-6018	124	24	h.	h.	NOUN
ejpam-6018	124	25	conversely	conversely	ADV
ejpam-6018	124	26	,	,	PUNCT
ejpam-6018	124	27	suppose	suppose	VERB
ejpam-6018	124	28	that	that	SCONJ
ejpam-6018	124	29	(	(	PUNCT
ejpam-6018	124	30	2	2	X
ejpam-6018	124	31	)	)	PUNCT
ejpam-6018	124	32	is	be	AUX
ejpam-6018	124	33	valid	valid	ADJ
ejpam-6018	124	34	.	.	PUNCT
ejpam-6018	125	1	let	let	VERB
ejpam-6018	125	2	ξ	ξ	X
ejpam-6018	125	3	,	,	PUNCT
ejpam-6018	125	4	ζ	ζ	PROPN
ejpam-6018	125	5	∈	∈	PROPN
ejpam-6018	125	6	s∈(η	s∈(η	ADV
ejpam-6018	125	7	)	)	PUNCT
ejpam-6018	125	8	for	for	ADP
ejpam-6018	125	9	every	every	DET
ejpam-6018	125	10	η	η	PROPN
ejpam-6018	125	11	∈	∈	PROPN
ejpam-6018	125	12	υ	υ	PROPN
ejpam-6018	125	13	.	.	PUNCT
ejpam-6018	126	1	then	then	ADV
ejpam-6018	126	2	(	(	PUNCT
ejpam-6018	126	3	h	h	NOUN
ejpam-6018	126	4	,	,	PUNCT
ejpam-6018	126	5	ξη	ξη	PROPN
ejpam-6018	126	6	)	)	PUNCT
ejpam-6018	126	7	and	and	CCONJ
ejpam-6018	126	8	(	(	PUNCT
ejpam-6018	126	9	h	h	NOUN
ejpam-6018	126	10	,	,	PUNCT
ejpam-6018	126	11	ζη	ζη	ADJ
ejpam-6018	126	12	)	)	PUNCT
ejpam-6018	126	13	are	be	AUX
ejpam-6018	126	14	n∈-subsets	n∈-subset	NOUN
ejpam-6018	126	15	of	of	ADP
ejpam-6018	126	16	(	(	PUNCT
ejpam-6018	126	17	h	h	NOUN
ejpam-6018	126	18	,	,	PUNCT
ejpam-6018	126	19	f	f	NOUN
ejpam-6018	126	20	)	)	PUNCT
ejpam-6018	126	21	,	,	PUNCT
ejpam-6018	126	22	and	and	CCONJ
ejpam-6018	126	23	so∧	so∧	PROPN
ejpam-6018	126	24	{	{	PUNCT
ejpam-6018	126	25	f(ξζ	f(ξζ	PROPN
ejpam-6018	126	26	|	|	CCONJ
ejpam-6018	126	27	ξζ),−0.5	ξζ),−0.5	VERB
ejpam-6018	126	28	}	}	PUNCT
ejpam-6018	126	29	≤	≤	NUM
ejpam-6018	126	30	∨	∨	NUM
ejpam-6018	126	31	{	{	PUNCT
ejpam-6018	126	32	f(ξ	f(ξ	NOUN
ejpam-6018	126	33	)	)	PUNCT
ejpam-6018	126	34	,	,	PUNCT
ejpam-6018	126	35	f(ζ	f(ζ	NOUN
ejpam-6018	126	36	)	)	PUNCT
ejpam-6018	126	37	}	}	PUNCT
ejpam-6018	126	38	≤	≤	NUM
ejpam-6018	126	39	η	η	X
ejpam-6018	126	40	<	<	X
ejpam-6018	126	41	−0.5	−0.5	PROPN
ejpam-6018	126	42	.	.	PUNCT
ejpam-6018	127	1	it	it	PRON
ejpam-6018	127	2	follows	follow	VERB
ejpam-6018	127	3	that	that	SCONJ
ejpam-6018	127	4	(	(	PUNCT
ejpam-6018	127	5	h	h	NOUN
ejpam-6018	127	6	,	,	PUNCT
ejpam-6018	127	7	(	(	PUNCT
ejpam-6018	127	8	ξζ	ξζ	NOUN
ejpam-6018	127	9	|	|	ADV
ejpam-6018	127	10	ξζ)η	ξζ)η	PROPN
ejpam-6018	127	11	)	)	PUNCT
ejpam-6018	127	12	is	be	AUX
ejpam-6018	127	13	an	an	DET
ejpam-6018	127	14	n∈-subset	n∈-subset	NOUN
ejpam-6018	127	15	of	of	ADP
ejpam-6018	127	16	(	(	PUNCT
ejpam-6018	127	17	h	h	NOUN
ejpam-6018	127	18	,	,	PUNCT
ejpam-6018	127	19	f	f	PROPN
ejpam-6018	127	20	)	)	PUNCT
ejpam-6018	127	21	,	,	PUNCT
ejpam-6018	127	22	that	that	ADV
ejpam-6018	127	23	is	is	ADV
ejpam-6018	127	24	,	,	PUNCT
ejpam-6018	127	25	ξζ	ξζ	INTJ
ejpam-6018	128	1	|	|	ADV
ejpam-6018	128	2	ξζ	ξζ	INTJ
ejpam-6018	128	3	∈	∈	PROPN
ejpam-6018	128	4	s∈(η	s∈(η	NOUN
ejpam-6018	128	5	)	)	PUNCT
ejpam-6018	128	6	.	.	PUNCT
ejpam-6018	129	1	thus	thus	ADV
ejpam-6018	129	2	,	,	PUNCT
ejpam-6018	129	3	s∈(η	s∈(η	ADV
ejpam-6018	129	4	)	)	PUNCT
ejpam-6018	129	5	is	be	AUX
ejpam-6018	129	6	a	a	DET
ejpam-6018	129	7	subalgebra	subalgebra	NOUN
ejpam-6018	129	8	of	of	ADP
ejpam-6018	129	9	h	h	NOUN
ejpam-6018	129	10	,	,	PUNCT
ejpam-6018	129	11	and	and	CCONJ
ejpam-6018	129	12	therefore	therefore	ADV
ejpam-6018	129	13	,	,	PUNCT
ejpam-6018	129	14	(	(	PUNCT
ejpam-6018	129	15	s∈,υ	s∈,υ	NOUN
ejpam-6018	129	16	)	)	PUNCT
ejpam-6018	129	17	is	be	AUX
ejpam-6018	129	18	a	a	DET
ejpam-6018	129	19	soft	soft	ADJ
ejpam-6018	129	20	n	n	CCONJ
ejpam-6018	129	21	-subalgebra	-subalgebra	NOUN
ejpam-6018	129	22	over	over	ADP
ejpam-6018	129	23	h.	h.	PROPN
ejpam-6018	129	24	lemma	lemma	PROPN
ejpam-6018	130	1	2	2	X
ejpam-6018	130	2	.	.	PUNCT
ejpam-6018	130	3	let	let	VERB
ejpam-6018	130	4	hs	hs	PRON
ejpam-6018	130	5	:	:	PUNCT
ejpam-6018	130	6	=	=	SYM
ejpam-6018	130	7	(	(	PUNCT
ejpam-6018	130	8	h	h	NOUN
ejpam-6018	130	9	,	,	PUNCT
ejpam-6018	130	10	|	|	ADV
ejpam-6018	130	11	,	,	PUNCT
ejpam-6018	130	12	0	0	NUM
ejpam-6018	130	13	)	)	PUNCT
ejpam-6018	130	14	be	be	AUX
ejpam-6018	130	15	an	an	DET
ejpam-6018	130	16	ssh	ssh	NOUN
ejpam-6018	130	17	-	-	PUNCT
ejpam-6018	130	18	algebra	algebra	NOUN
ejpam-6018	130	19	.	.	PUNCT
ejpam-6018	131	1	an	an	DET
ejpam-6018	131	2	n	n	ADV
ejpam-6018	131	3	-structure	-structure	NOUN
ejpam-6018	131	4	(	(	PUNCT
ejpam-6018	131	5	h	h	NOUN
ejpam-6018	131	6	,	,	PUNCT
ejpam-6018	131	7	f	f	X
ejpam-6018	131	8	)	)	PUNCT
ejpam-6018	131	9	is	be	AUX
ejpam-6018	131	10	an	an	DET
ejpam-6018	131	11	n	n	PRON
ejpam-6018	131	12	subalgebra	subalgebra	NOUN
ejpam-6018	131	13	of	of	ADP
ejpam-6018	131	14	type	type	NOUN
ejpam-6018	131	15	(	(	PUNCT
ejpam-6018	131	16	∈,∈	∈,∈	X
ejpam-6018	131	17	∨q	∨q	NOUN
ejpam-6018	131	18	)	)	PUNCT
ejpam-6018	131	19	if	if	SCONJ
ejpam-6018	131	20	and	and	CCONJ
ejpam-6018	131	21	only	only	ADV
ejpam-6018	131	22	if	if	SCONJ
ejpam-6018	131	23	(	(	PUNCT
ejpam-6018	131	24	∀ξ	∀ξ	NOUN
ejpam-6018	131	25	,	,	PUNCT
ejpam-6018	131	26	ζ	ζ	PROPN
ejpam-6018	131	27	∈	∈	PROPN
ejpam-6018	131	28	h	h	NOUN
ejpam-6018	131	29	)	)	PUNCT
ejpam-6018	131	30	(	(	PUNCT
ejpam-6018	131	31	f(ξζ	f(ξζ	PROPN
ejpam-6018	131	32	|	|	ADV
ejpam-6018	131	33	ξζ	ξζ	NOUN
ejpam-6018	131	34	)	)	PUNCT
ejpam-6018	131	35	≤	≤	NOUN
ejpam-6018	131	36	∨	∨	NUM
ejpam-6018	131	37	{	{	PUNCT
ejpam-6018	131	38	f(ξ	f(ξ	PROPN
ejpam-6018	131	39	)	)	PUNCT
ejpam-6018	131	40	,	,	PUNCT
ejpam-6018	131	41	f(ζ),−0.5	f(ζ),−0.5	PROPN
ejpam-6018	131	42	}	}	PUNCT
ejpam-6018	131	43	)	)	PUNCT
ejpam-6018	131	44	.	.	PUNCT
ejpam-6018	132	1	(	(	PUNCT
ejpam-6018	132	2	3	3	X
ejpam-6018	132	3	)	)	PUNCT
ejpam-6018	132	4	t.	t.	NOUN
ejpam-6018	132	5	oner	oner	NOUN
ejpam-6018	132	6	et	et	PROPN
ejpam-6018	132	7	al	al	PROPN
ejpam-6018	132	8	.	.	PUNCT
ejpam-6018	132	9	/	/	SYM
ejpam-6018	132	10	eur	eur	PROPN
ejpam-6018	132	11	.	.	PUNCT
ejpam-6018	133	1	j.	j.	PROPN
ejpam-6018	133	2	pure	pure	PROPN
ejpam-6018	133	3	appl	appl	PROPN
ejpam-6018	133	4	.	.	PROPN
ejpam-6018	133	5	math	math	PROPN
ejpam-6018	133	6	,	,	PUNCT
ejpam-6018	133	7	18	18	NUM
ejpam-6018	133	8	(	(	PUNCT
ejpam-6018	133	9	2	2	NUM
ejpam-6018	133	10	)	)	PUNCT
ejpam-6018	133	11	(	(	PUNCT
ejpam-6018	133	12	2025	2025	NUM
ejpam-6018	133	13	)	)	PUNCT
ejpam-6018	133	14	,	,	PUNCT
ejpam-6018	133	15	6018	6018	NUM
ejpam-6018	133	16	6	6	NUM
ejpam-6018	133	17	of	of	ADP
ejpam-6018	133	18	11	11	NUM
ejpam-6018	133	19	proof	proof	NOUN
ejpam-6018	133	20	.	.	PUNCT
ejpam-6018	133	21	suppose	suppose	VERB
ejpam-6018	133	22	that	that	SCONJ
ejpam-6018	133	23	(	(	PUNCT
ejpam-6018	133	24	h	h	NOUN
ejpam-6018	133	25	,	,	PUNCT
ejpam-6018	133	26	f	f	X
ejpam-6018	133	27	)	)	PUNCT
ejpam-6018	133	28	is	be	AUX
ejpam-6018	133	29	an	an	DET
ejpam-6018	133	30	n	n	PRON
ejpam-6018	133	31	-subalgebra	-subalgebra	NOUN
ejpam-6018	133	32	of	of	ADP
ejpam-6018	133	33	type	type	NOUN
ejpam-6018	133	34	(	(	PUNCT
ejpam-6018	133	35	∈,∈	∈,∈	X
ejpam-6018	133	36	∨q	∨q	NOUN
ejpam-6018	133	37	)	)	PUNCT
ejpam-6018	133	38	.	.	PUNCT
ejpam-6018	134	1	let	let	VERB
ejpam-6018	134	2	ξ	ξ	X
ejpam-6018	134	3	,	,	PUNCT
ejpam-6018	134	4	ζ	ζ	PROPN
ejpam-6018	134	5	∈	∈	PROPN
ejpam-6018	134	6	h.	h.	NOUN
ejpam-6018	134	7	then	then	ADV
ejpam-6018	134	8	,	,	PUNCT
ejpam-6018	134	9	if	if	SCONJ
ejpam-6018	134	10	both	both	DET
ejpam-6018	134	11	f(ξ	f(ξ	NOUN
ejpam-6018	134	12	)	)	PUNCT
ejpam-6018	134	13	≤	≤	NUM
ejpam-6018	134	14	η	η	PROPN
ejpam-6018	134	15	and	and	CCONJ
ejpam-6018	134	16	f(ζ	f(ζ	PROPN
ejpam-6018	134	17	)	)	PUNCT
ejpam-6018	134	18	≤	≤	NUM
ejpam-6018	134	19	η	η	PROPN
ejpam-6018	134	20	for	for	ADP
ejpam-6018	134	21	some	some	DET
ejpam-6018	134	22	η	η	PROPN
ejpam-6018	134	23	∈	∈	PROPN
ejpam-6018	134	24	υ	υ	PROPN
ejpam-6018	134	25	,	,	PUNCT
ejpam-6018	134	26	it	it	PRON
ejpam-6018	134	27	must	must	AUX
ejpam-6018	134	28	follow	follow	VERB
ejpam-6018	134	29	that	that	PRON
ejpam-6018	134	30	f(ξζ	f(ξζ	PROPN
ejpam-6018	134	31	|	|	ADV
ejpam-6018	134	32	ξζ	ξζ	NOUN
ejpam-6018	134	33	)	)	PUNCT
ejpam-6018	134	34	≤	≤	NOUN
ejpam-6018	134	35	∨	∨	NUM
ejpam-6018	134	36	{	{	PUNCT
ejpam-6018	134	37	f(ξ	f(ξ	PROPN
ejpam-6018	134	38	)	)	PUNCT
ejpam-6018	134	39	,	,	PUNCT
ejpam-6018	134	40	f(ζ),−0.5	f(ζ),−0.5	NOUN
ejpam-6018	134	41	}	}	PUNCT
ejpam-6018	134	42	.	.	PUNCT
ejpam-6018	135	1	conversely	conversely	ADV
ejpam-6018	135	2	,	,	PUNCT
ejpam-6018	135	3	suppose	suppose	VERB
ejpam-6018	135	4	the	the	DET
ejpam-6018	135	5	above	above	ADJ
ejpam-6018	135	6	inequality	inequality	NOUN
ejpam-6018	135	7	holds	hold	VERB
ejpam-6018	135	8	for	for	ADP
ejpam-6018	135	9	all	all	DET
ejpam-6018	135	10	ξ	ξ	ADJ
ejpam-6018	135	11	,	,	PUNCT
ejpam-6018	135	12	ζ	ζ	PROPN
ejpam-6018	135	13	∈	∈	PROPN
ejpam-6018	135	14	h.	h.	NOUN
ejpam-6018	135	15	let	let	VERB
ejpam-6018	135	16	η	η	PROPN
ejpam-6018	135	17	∈	∈	PROPN
ejpam-6018	135	18	υ	υ	NOUN
ejpam-6018	135	19	,	,	PUNCT
ejpam-6018	135	20	and	and	CCONJ
ejpam-6018	135	21	assume	assume	VERB
ejpam-6018	135	22	that	that	SCONJ
ejpam-6018	135	23	f(ξ	f(ξ	NOUN
ejpam-6018	135	24	)	)	PUNCT
ejpam-6018	135	25	≤	≤	NUM
ejpam-6018	135	26	η	η	PROPN
ejpam-6018	135	27	and	and	CCONJ
ejpam-6018	135	28	f(ζ	f(ζ	PROPN
ejpam-6018	135	29	)	)	PUNCT
ejpam-6018	135	30	≤	≤	PROPN
ejpam-6018	136	1	η	η	PROPN
ejpam-6018	136	2	.	.	PUNCT
ejpam-6018	137	1	then,∨	then,∨	PROPN
ejpam-6018	137	2	{	{	PUNCT
ejpam-6018	137	3	f(ξ	f(ξ	PROPN
ejpam-6018	137	4	)	)	PUNCT
ejpam-6018	137	5	,	,	PUNCT
ejpam-6018	137	6	f(ζ),−0.5	f(ζ),−0.5	PROPN
ejpam-6018	137	7	}	}	PUNCT
ejpam-6018	137	8	≤	≤	NUM
ejpam-6018	137	9	η	η	PROPN
ejpam-6018	137	10	⇒	⇒	PROPN
ejpam-6018	137	11	f(ξζ	f(ξζ	PROPN
ejpam-6018	137	12	|	|	ADV
ejpam-6018	137	13	ξζ	ξζ	PROPN
ejpam-6018	137	14	)	)	PUNCT
ejpam-6018	137	15	≤	≤	PROPN
ejpam-6018	137	16	η	η	PROPN
ejpam-6018	137	17	.	.	PROPN
ejpam-6018	138	1	this	this	PRON
ejpam-6018	138	2	confirms	confirm	VERB
ejpam-6018	138	3	that	that	SCONJ
ejpam-6018	138	4	(	(	PUNCT
ejpam-6018	138	5	h	h	NOUN
ejpam-6018	138	6	,	,	PUNCT
ejpam-6018	138	7	f	f	X
ejpam-6018	138	8	)	)	PUNCT
ejpam-6018	138	9	is	be	AUX
ejpam-6018	138	10	an	an	DET
ejpam-6018	138	11	n	n	PRON
ejpam-6018	138	12	-subalgebra	-subalgebra	NOUN
ejpam-6018	138	13	of	of	ADP
ejpam-6018	138	14	type	type	NOUN
ejpam-6018	138	15	(	(	PUNCT
ejpam-6018	138	16	∈,∈	∈,∈	X
ejpam-6018	138	17	∨q	∨q	NOUN
ejpam-6018	138	18	)	)	PUNCT
ejpam-6018	138	19	.	.	PUNCT
ejpam-6018	139	1	theorem	theorem	ADJ
ejpam-6018	139	2	4	4	NUM
ejpam-6018	139	3	.	.	PUNCT
ejpam-6018	140	1	let	let	VERB
ejpam-6018	140	2	hs	hs	PRON
ejpam-6018	140	3	:	:	PUNCT
ejpam-6018	140	4	=	=	SYM
ejpam-6018	140	5	(	(	PUNCT
ejpam-6018	140	6	h	h	NOUN
ejpam-6018	140	7	,	,	PUNCT
ejpam-6018	140	8	|	|	ADV
ejpam-6018	140	9	,	,	PUNCT
ejpam-6018	140	10	0	0	NUM
ejpam-6018	140	11	)	)	PUNCT
ejpam-6018	140	12	be	be	AUX
ejpam-6018	140	13	an	an	DET
ejpam-6018	140	14	ssh	ssh	NOUN
ejpam-6018	140	15	-	-	PUNCT
ejpam-6018	140	16	algebra	algebra	NOUN
ejpam-6018	140	17	.	.	PUNCT
ejpam-6018	141	1	given	give	VERB
ejpam-6018	141	2	an	an	DET
ejpam-6018	141	3	n	n	ADV
ejpam-6018	141	4	-structure	-structure	NOUN
ejpam-6018	141	5	(	(	PUNCT
ejpam-6018	141	6	h	h	NOUN
ejpam-6018	141	7	,	,	PUNCT
ejpam-6018	141	8	f	f	PROPN
ejpam-6018	141	9	)	)	PUNCT
ejpam-6018	141	10	and	and	CCONJ
ejpam-6018	141	11	a	a	DET
ejpam-6018	141	12	soft	soft	ADJ
ejpam-6018	141	13	n∈-set	n∈-set	NOUN
ejpam-6018	141	14	(	(	PUNCT
ejpam-6018	141	15	s∈,υ	s∈,υ	NOUN
ejpam-6018	141	16	)	)	PUNCT
ejpam-6018	141	17	,	,	PUNCT
ejpam-6018	141	18	the	the	DET
ejpam-6018	141	19	following	follow	VERB
ejpam-6018	141	20	assertions	assertion	NOUN
ejpam-6018	141	21	are	be	AUX
ejpam-6018	141	22	equivalent	equivalent	ADJ
ejpam-6018	141	23	:	:	PUNCT
ejpam-6018	141	24	(	(	PUNCT
ejpam-6018	141	25	1	1	X
ejpam-6018	141	26	)	)	PUNCT
ejpam-6018	141	27	(	(	PUNCT
ejpam-6018	141	28	h	h	NOUN
ejpam-6018	141	29	,	,	PUNCT
ejpam-6018	141	30	f	f	X
ejpam-6018	141	31	)	)	PUNCT
ejpam-6018	141	32	is	be	AUX
ejpam-6018	141	33	an	an	DET
ejpam-6018	141	34	n	n	PRON
ejpam-6018	141	35	-subalgebra	-subalgebra	NOUN
ejpam-6018	141	36	of	of	ADP
ejpam-6018	141	37	type	type	NOUN
ejpam-6018	141	38	(	(	PUNCT
ejpam-6018	141	39	∈,∈	∈,∈	X
ejpam-6018	141	40	∨q	∨q	NOUN
ejpam-6018	141	41	)	)	PUNCT
ejpam-6018	141	42	.	.	PUNCT
ejpam-6018	142	1	(	(	PUNCT
ejpam-6018	142	2	2	2	X
ejpam-6018	142	3	)	)	PUNCT
ejpam-6018	142	4	(	(	PUNCT
ejpam-6018	142	5	s∈,υ	s∈,υ	NOUN
ejpam-6018	142	6	)	)	PUNCT
ejpam-6018	142	7	is	be	AUX
ejpam-6018	142	8	a	a	DET
ejpam-6018	142	9	soft	soft	ADJ
ejpam-6018	142	10	n	n	CCONJ
ejpam-6018	142	11	-subalgebra	-subalgebra	NOUN
ejpam-6018	142	12	over	over	ADP
ejpam-6018	142	13	h	h	NOUN
ejpam-6018	142	14	for	for	ADP
ejpam-6018	142	15	υ	υ	NOUN
ejpam-6018	142	16	=	=	PUNCT
ejpam-6018	143	1	[	[	X
ejpam-6018	143	2	−0.5	−0.5	PROPN
ejpam-6018	143	3	,	,	PUNCT
ejpam-6018	143	4	0	0	NUM
ejpam-6018	143	5	)	)	PUNCT
ejpam-6018	143	6	.	.	PUNCT
ejpam-6018	144	1	proof	proof	NOUN
ejpam-6018	144	2	.	.	PUNCT
ejpam-6018	145	1	assume	assume	VERB
ejpam-6018	145	2	that	that	SCONJ
ejpam-6018	145	3	(	(	PUNCT
ejpam-6018	145	4	h	h	NOUN
ejpam-6018	145	5	,	,	PUNCT
ejpam-6018	145	6	f	f	X
ejpam-6018	145	7	)	)	PUNCT
ejpam-6018	145	8	is	be	AUX
ejpam-6018	145	9	an	an	DET
ejpam-6018	145	10	n	n	PRON
ejpam-6018	145	11	-subalgebra	-subalgebra	NOUN
ejpam-6018	145	12	of	of	ADP
ejpam-6018	145	13	type	type	NOUN
ejpam-6018	145	14	(	(	PUNCT
ejpam-6018	145	15	∈,∈	∈,∈	X
ejpam-6018	145	16	∨q	∨q	NOUN
ejpam-6018	145	17	)	)	PUNCT
ejpam-6018	145	18	.	.	PUNCT
ejpam-6018	146	1	let	let	VERB
ejpam-6018	146	2	ξ	ξ	X
ejpam-6018	146	3	,	,	PUNCT
ejpam-6018	146	4	ζ	ζ	PROPN
ejpam-6018	146	5	∈	∈	PROPN
ejpam-6018	146	6	h	h	NOUN
ejpam-6018	146	7	and	and	CCONJ
ejpam-6018	146	8	η	η	PROPN
ejpam-6018	146	9	∈	∈	PROPN
ejpam-6018	146	10	υ	υ	NOUN
ejpam-6018	146	11	be	be	AUX
ejpam-6018	146	12	such	such	ADJ
ejpam-6018	146	13	that	that	SCONJ
ejpam-6018	146	14	ξ	ξ	PROPN
ejpam-6018	146	15	,	,	PUNCT
ejpam-6018	146	16	ζ	ζ	PROPN
ejpam-6018	146	17	∈	∈	PROPN
ejpam-6018	146	18	s∈(η	s∈(η	NOUN
ejpam-6018	146	19	)	)	PUNCT
ejpam-6018	146	20	.	.	PUNCT
ejpam-6018	147	1	then	then	ADV
ejpam-6018	147	2	(	(	PUNCT
ejpam-6018	147	3	h	h	NOUN
ejpam-6018	147	4	,	,	PUNCT
ejpam-6018	147	5	ξη	ξη	PROPN
ejpam-6018	147	6	)	)	PUNCT
ejpam-6018	147	7	and	and	CCONJ
ejpam-6018	147	8	(	(	PUNCT
ejpam-6018	147	9	h	h	NOUN
ejpam-6018	147	10	,	,	PUNCT
ejpam-6018	147	11	ζη	ζη	ADJ
ejpam-6018	147	12	)	)	PUNCT
ejpam-6018	147	13	are	be	AUX
ejpam-6018	147	14	n∈-subsets	n∈-subset	NOUN
ejpam-6018	147	15	of	of	ADP
ejpam-6018	147	16	(	(	PUNCT
ejpam-6018	147	17	h	h	NOUN
ejpam-6018	147	18	,	,	PUNCT
ejpam-6018	147	19	f	f	NOUN
ejpam-6018	147	20	)	)	PUNCT
ejpam-6018	147	21	.	.	PUNCT
ejpam-6018	148	1	it	it	PRON
ejpam-6018	148	2	follows	follow	VERB
ejpam-6018	148	3	from	from	ADP
ejpam-6018	148	4	(	(	PUNCT
ejpam-6018	148	5	3	3	NUM
ejpam-6018	148	6	)	)	PUNCT
ejpam-6018	148	7	that	that	SCONJ
ejpam-6018	148	8	(	(	PUNCT
ejpam-6018	148	9	∀ξ	∀ξ	NOUN
ejpam-6018	148	10	,	,	PUNCT
ejpam-6018	148	11	ζ	ζ	PROPN
ejpam-6018	148	12	∈	∈	PROPN
ejpam-6018	148	13	h	h	NOUN
ejpam-6018	148	14	)	)	PUNCT
ejpam-6018	148	15	(	(	PUNCT
ejpam-6018	148	16	f(ξζ	f(ξζ	PROPN
ejpam-6018	148	17	|	|	ADV
ejpam-6018	148	18	ξζ	ξζ	NOUN
ejpam-6018	148	19	)	)	PUNCT
ejpam-6018	148	20	≤	≤	NOUN
ejpam-6018	148	21	∨	∨	NUM
ejpam-6018	148	22	{	{	PUNCT
ejpam-6018	148	23	f(ξ	f(ξ	PROPN
ejpam-6018	148	24	)	)	PUNCT
ejpam-6018	148	25	,	,	PUNCT
ejpam-6018	148	26	f(ζ),−0.5	f(ζ),−0.5	PROPN
ejpam-6018	148	27	}	}	PUNCT
ejpam-6018	148	28	≤	≤	ADJ
ejpam-6018	148	29	∨	∨	NUM
ejpam-6018	148	30	{	{	PUNCT
ejpam-6018	148	31	η,−0.5	η,−0.5	NOUN
ejpam-6018	148	32	}	}	PUNCT
ejpam-6018	148	33	=	=	SYM
ejpam-6018	148	34	η	η	PROPN
ejpam-6018	148	35	)	)	PUNCT
ejpam-6018	148	36	.	.	PUNCT
ejpam-6018	149	1	then	then	ADV
ejpam-6018	149	2	(	(	PUNCT
ejpam-6018	149	3	h	h	NOUN
ejpam-6018	149	4	,	,	PUNCT
ejpam-6018	149	5	(	(	PUNCT
ejpam-6018	149	6	ξζ	ξζ	NOUN
ejpam-6018	149	7	|	|	ADV
ejpam-6018	149	8	ξζ)η	ξζ)η	PROPN
ejpam-6018	149	9	)	)	PUNCT
ejpam-6018	149	10	is	be	AUX
ejpam-6018	149	11	an	an	DET
ejpam-6018	149	12	n∈-subset	n∈-subset	NOUN
ejpam-6018	149	13	of	of	ADP
ejpam-6018	149	14	(	(	PUNCT
ejpam-6018	149	15	h	h	NOUN
ejpam-6018	149	16	,	,	PUNCT
ejpam-6018	149	17	f	f	NOUN
ejpam-6018	149	18	)	)	PUNCT
ejpam-6018	149	19	.	.	PUNCT
ejpam-6018	150	1	thus	thus	ADV
ejpam-6018	150	2	ξζ	ξζ	INTJ
ejpam-6018	150	3	|	|	INTJ
ejpam-6018	150	4	ξζ	ξζ	INTJ
ejpam-6018	150	5	∈	∈	PROPN
ejpam-6018	150	6	s∈(η	s∈(η	ADV
ejpam-6018	150	7	)	)	PUNCT
ejpam-6018	150	8	,	,	PUNCT
ejpam-6018	150	9	and	and	CCONJ
ejpam-6018	150	10	so	so	ADV
ejpam-6018	150	11	(	(	PUNCT
ejpam-6018	150	12	s∈,υ	s∈,υ	NOUN
ejpam-6018	150	13	)	)	PUNCT
ejpam-6018	150	14	is	be	AUX
ejpam-6018	150	15	a	a	DET
ejpam-6018	150	16	soft	soft	ADJ
ejpam-6018	150	17	n	n	CCONJ
ejpam-6018	150	18	-subalgebra	-subalgebra	NOUN
ejpam-6018	150	19	over	over	ADP
ejpam-6018	150	20	h.	h.	NOUN
ejpam-6018	150	21	conversely	conversely	ADV
ejpam-6018	150	22	,	,	PUNCT
ejpam-6018	150	23	suppose	suppose	VERB
ejpam-6018	150	24	that	that	SCONJ
ejpam-6018	150	25	the	the	DET
ejpam-6018	150	26	soft	soft	ADJ
ejpam-6018	150	27	n∈-set	n∈-set	NOUN
ejpam-6018	150	28	(	(	PUNCT
ejpam-6018	150	29	s∈,υ	s∈,υ	NOUN
ejpam-6018	150	30	)	)	PUNCT
ejpam-6018	150	31	with	with	ADP
ejpam-6018	150	32	υ	υ	NOUN
ejpam-6018	150	33	=	=	PUNCT
ejpam-6018	151	1	[	[	X
ejpam-6018	151	2	−0.5	−0.5	PROPN
ejpam-6018	151	3	,	,	PUNCT
ejpam-6018	151	4	0	0	NUM
ejpam-6018	151	5	)	)	PUNCT
ejpam-6018	151	6	is	be	AUX
ejpam-6018	151	7	a	a	DET
ejpam-6018	151	8	soft	soft	ADJ
ejpam-6018	151	9	n	n	NOUN
ejpam-6018	151	10	subalgebra	subalgebra	NOUN
ejpam-6018	151	11	over	over	ADP
ejpam-6018	151	12	h.	h.	PROPN
ejpam-6018	151	13	assume	assume	VERB
ejpam-6018	151	14	that	that	SCONJ
ejpam-6018	151	15	(	(	PUNCT
ejpam-6018	151	16	3	3	X
ejpam-6018	151	17	)	)	PUNCT
ejpam-6018	151	18	is	be	AUX
ejpam-6018	151	19	not	not	PART
ejpam-6018	151	20	valid	valid	ADJ
ejpam-6018	151	21	.	.	PUNCT
ejpam-6018	152	1	then	then	ADV
ejpam-6018	152	2	f(ϱϖ	f(ϱϖ	PROPN
ejpam-6018	152	3	|	|	ADV
ejpam-6018	152	4	ϱϖ	ϱϖ	PROPN
ejpam-6018	152	5	)	)	PUNCT
ejpam-6018	152	6	>	>	X
ejpam-6018	152	7	t	t	PROPN
ejpam-6018	152	8	≥	≥	PROPN
ejpam-6018	152	9	∨	∨	NUM
ejpam-6018	152	10	{	{	PUNCT
ejpam-6018	152	11	f(ϱ	f(ϱ	NOUN
ejpam-6018	152	12	)	)	PUNCT
ejpam-6018	152	13	,	,	PUNCT
ejpam-6018	152	14	f(ϖ),−0.5	f(ϖ),−0.5	VERB
ejpam-6018	152	15	}	}	PUNCT
ejpam-6018	152	16	for	for	ADP
ejpam-6018	152	17	some	some	DET
ejpam-6018	152	18	t	t	NOUN
ejpam-6018	152	19	∈	∈	NOUN
ejpam-6018	152	20	υ	υ	NOUN
ejpam-6018	152	21	and	and	CCONJ
ejpam-6018	152	22	ϱ,ϖ	ϱ,ϖ	PROPN
ejpam-6018	152	23	∈	∈	PROPN
ejpam-6018	152	24	h.	h.	NOUN
ejpam-6018	153	1	it	it	PRON
ejpam-6018	153	2	follows	follow	VERB
ejpam-6018	153	3	that	that	SCONJ
ejpam-6018	153	4	(	(	PUNCT
ejpam-6018	153	5	h	h	NOUN
ejpam-6018	153	6	,	,	PUNCT
ejpam-6018	153	7	ϱt	ϱt	NOUN
ejpam-6018	153	8	)	)	PUNCT
ejpam-6018	153	9	and	and	CCONJ
ejpam-6018	153	10	(	(	PUNCT
ejpam-6018	153	11	h,ϖt	h,ϖt	NOUN
ejpam-6018	153	12	)	)	PUNCT
ejpam-6018	153	13	are	be	AUX
ejpam-6018	153	14	n∈-subsets	n∈-subset	NOUN
ejpam-6018	153	15	of	of	ADP
ejpam-6018	153	16	(	(	PUNCT
ejpam-6018	153	17	h	h	NOUN
ejpam-6018	153	18	,	,	PUNCT
ejpam-6018	153	19	f	f	NOUN
ejpam-6018	153	20	)	)	PUNCT
ejpam-6018	153	21	,	,	PUNCT
ejpam-6018	153	22	and	and	CCONJ
ejpam-6018	153	23	so	so	ADV
ejpam-6018	153	24	ϱ,ϖ	ϱ,ϖ	PROPN
ejpam-6018	153	25	∈	∈	PROPN
ejpam-6018	153	26	s∈(t	s∈(t	VERB
ejpam-6018	153	27	)	)	PUNCT
ejpam-6018	153	28	.	.	PUNCT
ejpam-6018	154	1	but	but	CCONJ
ejpam-6018	154	2	f(ϱ	f(ϱ	NOUN
ejpam-6018	154	3	ϖ	ϖ	PROPN
ejpam-6018	154	4	|	|	NOUN
ejpam-6018	154	5	ϱϖ	ϱϖ	NOUN
ejpam-6018	154	6	)	)	PUNCT
ejpam-6018	154	7	>	>	PUNCT
ejpam-6018	154	8	t	t	PROPN
ejpam-6018	154	9	induces	induce	VERB
ejpam-6018	154	10	that	that	SCONJ
ejpam-6018	154	11	(	(	PUNCT
ejpam-6018	154	12	h	h	NOUN
ejpam-6018	154	13	,	,	PUNCT
ejpam-6018	154	14	(	(	PUNCT
ejpam-6018	154	15	ϱϖ	ϱϖ	NOUN
ejpam-6018	154	16	|	|	ADV
ejpam-6018	154	17	ϱϖ)t	ϱϖ)t	NOUN
ejpam-6018	154	18	)	)	PUNCT
ejpam-6018	154	19	is	be	AUX
ejpam-6018	154	20	not	not	PART
ejpam-6018	154	21	an	an	DET
ejpam-6018	154	22	n∈-subset	n∈-subset	NOUN
ejpam-6018	154	23	of	of	ADP
ejpam-6018	154	24	(	(	PUNCT
ejpam-6018	154	25	h	h	NOUN
ejpam-6018	154	26	,	,	PUNCT
ejpam-6018	154	27	f	f	NOUN
ejpam-6018	154	28	)	)	PUNCT
ejpam-6018	154	29	.	.	PUNCT
ejpam-6018	155	1	this	this	PRON
ejpam-6018	155	2	is	be	AUX
ejpam-6018	155	3	a	a	DET
ejpam-6018	155	4	contradiction	contradiction	NOUN
ejpam-6018	155	5	,	,	PUNCT
ejpam-6018	155	6	and	and	CCONJ
ejpam-6018	155	7	thus	thus	ADV
ejpam-6018	155	8	(	(	PUNCT
ejpam-6018	155	9	∀ξ	∀ξ	NOUN
ejpam-6018	155	10	,	,	PUNCT
ejpam-6018	155	11	ζ	ζ	PROPN
ejpam-6018	155	12	∈	∈	PROPN
ejpam-6018	155	13	h	h	NOUN
ejpam-6018	155	14	)	)	PUNCT
ejpam-6018	155	15	(	(	PUNCT
ejpam-6018	155	16	f(ξζ	f(ξζ	PROPN
ejpam-6018	155	17	|	|	ADV
ejpam-6018	155	18	ξζ	ξζ	NOUN
ejpam-6018	155	19	)	)	PUNCT
ejpam-6018	155	20	≤	≤	NOUN
ejpam-6018	155	21	∨	∨	NUM
ejpam-6018	155	22	{	{	PUNCT
ejpam-6018	155	23	f(ξ	f(ξ	PROPN
ejpam-6018	155	24	)	)	PUNCT
ejpam-6018	155	25	,	,	PUNCT
ejpam-6018	155	26	f(ζ),−0.5	f(ζ),−0.5	PROPN
ejpam-6018	155	27	}	}	PUNCT
ejpam-6018	155	28	)	)	PUNCT
ejpam-6018	155	29	.	.	PUNCT
ejpam-6018	156	1	using	use	VERB
ejpam-6018	156	2	lemma	lemma	PROPN
ejpam-6018	156	3	2	2	NUM
ejpam-6018	156	4	,	,	PUNCT
ejpam-6018	156	5	we	we	PRON
ejpam-6018	156	6	know	know	VERB
ejpam-6018	156	7	that	that	SCONJ
ejpam-6018	156	8	(	(	PUNCT
ejpam-6018	156	9	h	h	NOUN
ejpam-6018	156	10	,	,	PUNCT
ejpam-6018	156	11	f	f	X
ejpam-6018	156	12	)	)	PUNCT
ejpam-6018	156	13	is	be	AUX
ejpam-6018	156	14	an	an	DET
ejpam-6018	156	15	n	n	PRON
ejpam-6018	156	16	-subalgebra	-subalgebra	NOUN
ejpam-6018	156	17	of	of	ADP
ejpam-6018	156	18	type	type	NOUN
ejpam-6018	156	19	(	(	PUNCT
ejpam-6018	156	20	∈,∈	∈,∈	X
ejpam-6018	156	21	∨q	∨q	NOUN
ejpam-6018	156	22	)	)	PUNCT
ejpam-6018	156	23	.	.	PUNCT
ejpam-6018	157	1	theorem	theorem	NOUN
ejpam-6018	157	2	5	5	NUM
ejpam-6018	157	3	.	.	PUNCT
ejpam-6018	158	1	let	let	VERB
ejpam-6018	158	2	hs	hs	PRON
ejpam-6018	158	3	:	:	PUNCT
ejpam-6018	158	4	=	=	SYM
ejpam-6018	158	5	(	(	PUNCT
ejpam-6018	158	6	h	h	NOUN
ejpam-6018	158	7	,	,	PUNCT
ejpam-6018	158	8	|	|	ADV
ejpam-6018	158	9	,	,	PUNCT
ejpam-6018	158	10	0	0	NUM
ejpam-6018	158	11	)	)	PUNCT
ejpam-6018	158	12	be	be	AUX
ejpam-6018	158	13	an	an	DET
ejpam-6018	158	14	ssh	ssh	NOUN
ejpam-6018	158	15	-	-	PUNCT
ejpam-6018	158	16	algebra	algebra	NOUN
ejpam-6018	158	17	.	.	PUNCT
ejpam-6018	159	1	let	let	AUX
ejpam-6018	159	2	(	(	PUNCT
ejpam-6018	159	3	s∈,υ	s∈,υ	VERB
ejpam-6018	159	4	)	)	PUNCT
ejpam-6018	159	5	be	be	AUX
ejpam-6018	159	6	a	a	DET
ejpam-6018	159	7	soft	soft	ADJ
ejpam-6018	159	8	n∈-set	n∈-set	NOUN
ejpam-6018	159	9	over	over	ADP
ejpam-6018	159	10	h.	h.	PROPN
ejpam-6018	159	11	if	if	SCONJ
ejpam-6018	159	12	υ	υ	PRON
ejpam-6018	159	13	=	=	PUNCT
ejpam-6018	160	1	[	[	X
ejpam-6018	160	2	−0.5	−0.5	PROPN
ejpam-6018	160	3	,	,	PUNCT
ejpam-6018	160	4	0	0	NUM
ejpam-6018	160	5	)	)	PUNCT
ejpam-6018	160	6	,	,	PUNCT
ejpam-6018	160	7	then	then	ADV
ejpam-6018	160	8	for	for	ADP
ejpam-6018	160	9	any	any	DET
ejpam-6018	160	10	subalgebra	subalgebra	NOUN
ejpam-6018	160	11	l	l	NOUN
ejpam-6018	160	12	of	of	ADP
ejpam-6018	160	13	h	h	NOUN
ejpam-6018	160	14	,	,	PUNCT
ejpam-6018	160	15	there	there	PRON
ejpam-6018	160	16	exists	exist	VERB
ejpam-6018	160	17	an	an	DET
ejpam-6018	160	18	n	n	ADV
ejpam-6018	160	19	-subalgebra	-subalgebra	NOUN
ejpam-6018	160	20	(	(	PUNCT
ejpam-6018	160	21	h	h	NOUN
ejpam-6018	160	22	,	,	PUNCT
ejpam-6018	160	23	f	f	NOUN
ejpam-6018	160	24	)	)	PUNCT
ejpam-6018	160	25	of	of	ADP
ejpam-6018	160	26	type	type	NOUN
ejpam-6018	160	27	(	(	PUNCT
ejpam-6018	160	28	∈,∈	∈,∈	NOUN
ejpam-6018	160	29	∨q	∨q	NOUN
ejpam-6018	160	30	)	)	PUNCT
ejpam-6018	160	31	such	such	ADJ
ejpam-6018	160	32	that	that	PRON
ejpam-6018	160	33	s∈(η	s∈(η	PUNCT
ejpam-6018	160	34	)	)	PUNCT
ejpam-6018	161	1	=	=	SYM
ejpam-6018	161	2	l	l	NOUN
ejpam-6018	161	3	for	for	ADP
ejpam-6018	161	4	all	all	DET
ejpam-6018	161	5	η	η	PROPN
ejpam-6018	161	6	∈	∈	PROPN
ejpam-6018	161	7	υ	υ	PROPN
ejpam-6018	161	8	.	.	PUNCT
ejpam-6018	162	1	t.	t.	PROPN
ejpam-6018	162	2	oner	oner	PROPN
ejpam-6018	162	3	et	et	PROPN
ejpam-6018	162	4	al	al	PROPN
ejpam-6018	162	5	.	.	PUNCT
ejpam-6018	162	6	/	/	SYM
ejpam-6018	162	7	eur	eur	PROPN
ejpam-6018	162	8	.	.	PUNCT
ejpam-6018	163	1	j.	j.	PROPN
ejpam-6018	163	2	pure	pure	PROPN
ejpam-6018	163	3	appl	appl	PROPN
ejpam-6018	163	4	.	.	PROPN
ejpam-6018	163	5	math	math	PROPN
ejpam-6018	163	6	,	,	PUNCT
ejpam-6018	163	7	18	18	NUM
ejpam-6018	163	8	(	(	PUNCT
ejpam-6018	163	9	2	2	NUM
ejpam-6018	163	10	)	)	PUNCT
ejpam-6018	163	11	(	(	PUNCT
ejpam-6018	163	12	2025	2025	NUM
ejpam-6018	163	13	)	)	PUNCT
ejpam-6018	163	14	,	,	PUNCT
ejpam-6018	163	15	6018	6018	NUM
ejpam-6018	163	16	7	7	NUM
ejpam-6018	163	17	of	of	ADP
ejpam-6018	163	18	11	11	NUM
ejpam-6018	163	19	proof	proof	NOUN
ejpam-6018	163	20	.	.	PUNCT
ejpam-6018	164	1	take	take	VERB
ejpam-6018	164	2	an	an	DET
ejpam-6018	164	3	n	n	ADV
ejpam-6018	164	4	-subalgebra	-subalgebra	NOUN
ejpam-6018	164	5	(	(	PUNCT
ejpam-6018	164	6	h	h	NOUN
ejpam-6018	164	7	,	,	PUNCT
ejpam-6018	164	8	f	f	NOUN
ejpam-6018	164	9	)	)	PUNCT
ejpam-6018	164	10	in	in	ADP
ejpam-6018	164	11	which	which	PRON
ejpam-6018	164	12	f	f	PROPN
ejpam-6018	164	13	is	be	AUX
ejpam-6018	164	14	given	give	VERB
ejpam-6018	164	15	as	as	SCONJ
ejpam-6018	164	16	follows	follow	VERB
ejpam-6018	164	17	:	:	PUNCT
ejpam-6018	164	18	f	f	X
ejpam-6018	165	1	:	:	PUNCT
ejpam-6018	165	2	h	h	NOUN
ejpam-6018	165	3	→	→	PUNCT
ejpam-6018	166	1	[	[	X
ejpam-6018	166	2	−1	−1	NOUN
ejpam-6018	166	3	,	,	PUNCT
ejpam-6018	166	4	0	0	NUM
ejpam-6018	166	5	]	]	PUNCT
ejpam-6018	166	6	;	;	PUNCT
ejpam-6018	166	7	x	x	SYM
ejpam-6018	166	8	7→	7→	NUM
ejpam-6018	166	9	{	{	PUNCT
ejpam-6018	166	10	η	η	PROPN
ejpam-6018	166	11	∈	∈	PROPN
ejpam-6018	166	12	υ	υ	NOUN
ejpam-6018	166	13	if	if	SCONJ
ejpam-6018	166	14	ξ	ξ	PROPN
ejpam-6018	166	15	∈	∈	PROPN
ejpam-6018	166	16	l	l	NOUN
ejpam-6018	166	17	0	0	PUNCT
ejpam-6018	166	18	otherwise	otherwise	ADV
ejpam-6018	166	19	obviously	obviously	ADV
ejpam-6018	166	20	,	,	PUNCT
ejpam-6018	166	21	s∈(η	s∈(η	ADV
ejpam-6018	166	22	)	)	PUNCT
ejpam-6018	166	23	=	=	SYM
ejpam-6018	166	24	l	l	NOUN
ejpam-6018	166	25	for	for	ADP
ejpam-6018	166	26	all	all	DET
ejpam-6018	166	27	η	η	PROPN
ejpam-6018	166	28	∈	∈	PROPN
ejpam-6018	166	29	υ	υ	PROPN
ejpam-6018	166	30	.	.	PROPN
ejpam-6018	166	31	assume	assume	VERB
ejpam-6018	166	32	that	that	SCONJ
ejpam-6018	166	33	f(ϱϖ	f(ϱϖ	NOUN
ejpam-6018	166	34	|	|	ADV
ejpam-6018	166	35	ϱϖ	ϱϖ	PROPN
ejpam-6018	166	36	)	)	PUNCT
ejpam-6018	166	37	>	>	X
ejpam-6018	166	38	∨	∨	X
ejpam-6018	166	39	{	{	PUNCT
ejpam-6018	166	40	f(ϱ	f(ϱ	NOUN
ejpam-6018	166	41	)	)	PUNCT
ejpam-6018	166	42	,	,	PUNCT
ejpam-6018	166	43	f(ϖ),−0.5	f(ϖ),−0.5	VERB
ejpam-6018	166	44	}	}	PUNCT
ejpam-6018	166	45	for	for	ADP
ejpam-6018	166	46	some	some	DET
ejpam-6018	166	47	ϱ,ϖ	ϱ,ϖ	NOUN
ejpam-6018	166	48	∈	∈	PROPN
ejpam-6018	166	49	h.	h.	PROPN
ejpam-6018	166	50	then	then	ADV
ejpam-6018	166	51	f(ϱϖ	f(ϱϖ	PROPN
ejpam-6018	166	52	|	|	ADV
ejpam-6018	166	53	ϱϖ	ϱϖ	NOUN
ejpam-6018	166	54	)	)	PUNCT
ejpam-6018	166	55	=	=	SYM
ejpam-6018	166	56	0	0	NUM
ejpam-6018	166	57	and	and	CCONJ
ejpam-6018	166	58	∨	∨	NUM
ejpam-6018	166	59	{	{	PUNCT
ejpam-6018	166	60	f(ϱ	f(ϱ	NOUN
ejpam-6018	166	61	)	)	PUNCT
ejpam-6018	166	62	,	,	PUNCT
ejpam-6018	166	63	f(ϖ),−0.5	f(ϖ),−0.5	X
ejpam-6018	166	64	}	}	PUNCT
ejpam-6018	166	65	=	=	SYM
ejpam-6018	166	66	η	η	PROPN
ejpam-6018	166	67	,	,	PUNCT
ejpam-6018	166	68	since	since	SCONJ
ejpam-6018	166	69	|im(f)|	|im(f)|	NOUN
ejpam-6018	166	70	=	=	SYM
ejpam-6018	166	71	2	2	X
ejpam-6018	166	72	.	.	PUNCT
ejpam-6018	167	1	it	it	PRON
ejpam-6018	167	2	follows	follow	VERB
ejpam-6018	167	3	that	that	SCONJ
ejpam-6018	167	4	f(ϱ	f(ϱ	NOUN
ejpam-6018	167	5	)	)	PUNCT
ejpam-6018	167	6	=	=	SYM
ejpam-6018	167	7	η	η	NOUN
ejpam-6018	167	8	=	=	SYM
ejpam-6018	167	9	f(ϖ	f(ϖ	PROPN
ejpam-6018	167	10	)	)	PUNCT
ejpam-6018	167	11	,	,	PUNCT
ejpam-6018	167	12	so	so	SCONJ
ejpam-6018	167	13	that	that	SCONJ
ejpam-6018	167	14	ϱ,ϖ	ϱ,ϖ	NOUN
ejpam-6018	167	15	∈	∈	PROPN
ejpam-6018	167	16	l.	l.	NOUN
ejpam-6018	167	17	but	but	CCONJ
ejpam-6018	167	18	ϱϖ	ϱϖ	NOUN
ejpam-6018	167	19	|	|	ADV
ejpam-6018	167	20	ϱϖ	ϱϖ	NOUN
ejpam-6018	167	21	/∈	/∈	PUNCT
ejpam-6018	168	1	l	l	NOUN
ejpam-6018	168	2	,	,	PUNCT
ejpam-6018	168	3	since	since	SCONJ
ejpam-6018	168	4	f(ϱϖ	f(ϱϖ	PROPN
ejpam-6018	168	5	|	|	ADV
ejpam-6018	168	6	ϱϖ	ϱϖ	NOUN
ejpam-6018	168	7	)	)	PUNCT
ejpam-6018	168	8	=	=	SYM
ejpam-6018	168	9	0	0	X
ejpam-6018	168	10	.	.	PUNCT
ejpam-6018	169	1	this	this	PRON
ejpam-6018	169	2	is	be	AUX
ejpam-6018	169	3	impossible	impossible	ADJ
ejpam-6018	169	4	,	,	PUNCT
ejpam-6018	169	5	and	and	CCONJ
ejpam-6018	169	6	so	so	ADV
ejpam-6018	169	7	(	(	PUNCT
ejpam-6018	169	8	∀ξ	∀ξ	NOUN
ejpam-6018	169	9	,	,	PUNCT
ejpam-6018	169	10	ζ	ζ	PROPN
ejpam-6018	169	11	∈	∈	PROPN
ejpam-6018	169	12	h	h	NOUN
ejpam-6018	169	13	)	)	PUNCT
ejpam-6018	169	14	(	(	PUNCT
ejpam-6018	169	15	f(ξζ	f(ξζ	PROPN
ejpam-6018	169	16	|	|	ADV
ejpam-6018	169	17	ξζ	ξζ	NOUN
ejpam-6018	169	18	)	)	PUNCT
ejpam-6018	169	19	≤	≤	NOUN
ejpam-6018	169	20	∨	∨	NUM
ejpam-6018	169	21	{	{	PUNCT
ejpam-6018	169	22	f(ξ	f(ξ	PROPN
ejpam-6018	169	23	)	)	PUNCT
ejpam-6018	169	24	,	,	PUNCT
ejpam-6018	169	25	f(ζ),−0.5	f(ζ),−0.5	PROPN
ejpam-6018	169	26	}	}	PUNCT
ejpam-6018	169	27	)	)	PUNCT
ejpam-6018	169	28	.	.	PUNCT
ejpam-6018	170	1	therefore	therefore	ADV
ejpam-6018	170	2	,	,	PUNCT
ejpam-6018	170	3	(	(	PUNCT
ejpam-6018	170	4	h	h	NOUN
ejpam-6018	170	5	,	,	PUNCT
ejpam-6018	170	6	f	f	X
ejpam-6018	170	7	)	)	PUNCT
ejpam-6018	170	8	is	be	AUX
ejpam-6018	170	9	an	an	DET
ejpam-6018	170	10	n	n	PRON
ejpam-6018	170	11	-subalgebra	-subalgebra	NOUN
ejpam-6018	170	12	of	of	ADP
ejpam-6018	170	13	type	type	NOUN
ejpam-6018	170	14	(	(	PUNCT
ejpam-6018	170	15	∈,∈	∈,∈	X
ejpam-6018	170	16	∨q	∨q	NOUN
ejpam-6018	170	17	)	)	PUNCT
ejpam-6018	170	18	by	by	ADP
ejpam-6018	170	19	lemma	lemma	PROPN
ejpam-6018	170	20	2	2	NUM
ejpam-6018	170	21	.	.	PUNCT
ejpam-6018	170	22	definition	definition	NOUN
ejpam-6018	170	23	6	6	NUM
ejpam-6018	170	24	.	.	PUNCT
ejpam-6018	171	1	let	let	VERB
ejpam-6018	171	2	hs	hs	PRON
ejpam-6018	171	3	:	:	PUNCT
ejpam-6018	171	4	=	=	SYM
ejpam-6018	171	5	(	(	PUNCT
ejpam-6018	171	6	h	h	NOUN
ejpam-6018	171	7	,	,	PUNCT
ejpam-6018	171	8	|	|	ADV
ejpam-6018	171	9	,	,	PUNCT
ejpam-6018	171	10	0	0	NUM
ejpam-6018	171	11	)	)	PUNCT
ejpam-6018	171	12	be	be	AUX
ejpam-6018	171	13	an	an	DET
ejpam-6018	171	14	ssh	ssh	NOUN
ejpam-6018	171	15	-	-	PUNCT
ejpam-6018	171	16	algebra	algebra	NOUN
ejpam-6018	171	17	.	.	PUNCT
ejpam-6018	172	1	an	an	DET
ejpam-6018	172	2	n	n	ADV
ejpam-6018	172	3	-structure	-structure	NOUN
ejpam-6018	172	4	(	(	PUNCT
ejpam-6018	172	5	h	h	NOUN
ejpam-6018	172	6	,	,	PUNCT
ejpam-6018	172	7	f	f	X
ejpam-6018	172	8	)	)	PUNCT
ejpam-6018	172	9	is	be	AUX
ejpam-6018	172	10	called	call	VERB
ejpam-6018	172	11	an	an	DET
ejpam-6018	172	12	n	n	NUM
ejpam-6018	172	13	-ideal	-ideal	NOUN
ejpam-6018	172	14	of	of	ADP
ejpam-6018	172	15	type	type	NOUN
ejpam-6018	172	16	(	(	PUNCT
ejpam-6018	172	17	∈,∈	∈,∈	X
ejpam-6018	172	18	)	)	PUNCT
ejpam-6018	172	19	(	(	PUNCT
ejpam-6018	172	20	resp	resp	NOUN
ejpam-6018	172	21	.	.	PUNCT
ejpam-6018	172	22	,	,	PUNCT
ejpam-6018	172	23	type	type	NOUN
ejpam-6018	172	24	(	(	PUNCT
ejpam-6018	172	25	∈,∈q	∈,∈q	NOUN
ejpam-6018	172	26	)	)	PUNCT
ejpam-6018	172	27	)	)	PUNCT
ejpam-6018	173	1	if	if	SCONJ
ejpam-6018	173	2	the	the	DET
ejpam-6018	173	3	following	follow	VERB
ejpam-6018	173	4	assertions	assertion	NOUN
ejpam-6018	173	5	are	be	AUX
ejpam-6018	173	6	valid	valid	ADJ
ejpam-6018	173	7	:	:	PUNCT
ejpam-6018	173	8	(	(	PUNCT
ejpam-6018	173	9	1	1	X
ejpam-6018	173	10	)	)	PUNCT
ejpam-6018	173	11	if	if	SCONJ
ejpam-6018	173	12	a	a	DET
ejpam-6018	173	13	point	point	NOUN
ejpam-6018	173	14	n	n	PRON
ejpam-6018	173	15	-structure	-structure	NOUN
ejpam-6018	173	16	(	(	PUNCT
ejpam-6018	173	17	h	h	NOUN
ejpam-6018	173	18	,	,	PUNCT
ejpam-6018	173	19	ξη	ξη	PRON
ejpam-6018	173	20	)	)	PUNCT
ejpam-6018	173	21	is	be	AUX
ejpam-6018	173	22	an	an	DET
ejpam-6018	173	23	n∈-subset	n∈-subset	NOUN
ejpam-6018	173	24	of	of	ADP
ejpam-6018	173	25	(	(	PUNCT
ejpam-6018	173	26	h	h	NOUN
ejpam-6018	173	27	,	,	PUNCT
ejpam-6018	173	28	f	f	PROPN
ejpam-6018	173	29	)	)	PUNCT
ejpam-6018	173	30	,	,	PUNCT
ejpam-6018	173	31	then	then	ADV
ejpam-6018	173	32	(	(	PUNCT
ejpam-6018	173	33	h	h	NOUN
ejpam-6018	173	34	,	,	PUNCT
ejpam-6018	173	35	0η	0η	NUM
ejpam-6018	173	36	)	)	PUNCT
ejpam-6018	173	37	is	be	AUX
ejpam-6018	173	38	an	an	DET
ejpam-6018	173	39	n∈-subset	n∈-subset	NOUN
ejpam-6018	173	40	(	(	PUNCT
ejpam-6018	173	41	resp	resp	NOUN
ejpam-6018	173	42	.	.	PUNCT
ejpam-6018	173	43	,	,	PUNCT
ejpam-6018	173	44	n∈∨q	n∈∨q	NOUN
ejpam-6018	173	45	-	-	PUNCT
ejpam-6018	173	46	subset	subset	NOUN
ejpam-6018	173	47	)	)	PUNCT
ejpam-6018	173	48	of	of	ADP
ejpam-6018	173	49	(	(	PUNCT
ejpam-6018	173	50	h	h	NOUN
ejpam-6018	173	51	,	,	PUNCT
ejpam-6018	173	52	f	f	NOUN
ejpam-6018	173	53	)	)	PUNCT
ejpam-6018	173	54	.	.	PUNCT
ejpam-6018	174	1	(	(	PUNCT
ejpam-6018	174	2	2	2	X
ejpam-6018	174	3	)	)	PUNCT
ejpam-6018	174	4	if	if	SCONJ
ejpam-6018	174	5	two	two	NUM
ejpam-6018	174	6	point	point	NOUN
ejpam-6018	174	7	n	n	PRON
ejpam-6018	174	8	-structures	-structure	NOUN
ejpam-6018	174	9	(	(	PUNCT
ejpam-6018	174	10	h	h	NOUN
ejpam-6018	174	11	,	,	PUNCT
ejpam-6018	174	12	(	(	PUNCT
ejpam-6018	174	13	ξζ	ξζ	NOUN
ejpam-6018	174	14	|	|	ADV
ejpam-6018	174	15	ξζ)η	ξζ)η	PROPN
ejpam-6018	174	16	)	)	PUNCT
ejpam-6018	174	17	and	and	CCONJ
ejpam-6018	174	18	(	(	PUNCT
ejpam-6018	174	19	h	h	NOUN
ejpam-6018	174	20	,	,	PUNCT
ejpam-6018	174	21	ζδ	ζδ	NOUN
ejpam-6018	174	22	)	)	PUNCT
ejpam-6018	174	23	are	be	AUX
ejpam-6018	174	24	n∈-subsets	n∈-subset	NOUN
ejpam-6018	174	25	of	of	ADP
ejpam-6018	174	26	(	(	PUNCT
ejpam-6018	174	27	h	h	NOUN
ejpam-6018	174	28	,	,	PUNCT
ejpam-6018	174	29	f	f	PROPN
ejpam-6018	174	30	)	)	PUNCT
ejpam-6018	174	31	,	,	PUNCT
ejpam-6018	174	32	then	then	ADV
ejpam-6018	174	33	the	the	DET
ejpam-6018	174	34	point	point	NOUN
ejpam-6018	174	35	n	n	PRON
ejpam-6018	174	36	-structure	-structure	NOUN
ejpam-6018	174	37	(	(	PUNCT
ejpam-6018	174	38	h	h	NOUN
ejpam-6018	174	39	,	,	PUNCT
ejpam-6018	174	40	ξη∨δ	ξη∨δ	NOUN
ejpam-6018	174	41	)	)	PUNCT
ejpam-6018	174	42	is	be	AUX
ejpam-6018	174	43	an	an	DET
ejpam-6018	174	44	n∈-subset	n∈-subset	NOUN
ejpam-6018	174	45	(	(	PUNCT
ejpam-6018	174	46	resp	resp	NOUN
ejpam-6018	174	47	.	.	PUNCT
ejpam-6018	174	48	,	,	PUNCT
ejpam-6018	174	49	n∈∨q	n∈∨q	NOUN
ejpam-6018	174	50	-	-	PUNCT
ejpam-6018	174	51	subset	subset	NOUN
ejpam-6018	174	52	)	)	PUNCT
ejpam-6018	174	53	of	of	ADP
ejpam-6018	174	54	(	(	PUNCT
ejpam-6018	174	55	h	h	NOUN
ejpam-6018	174	56	,	,	PUNCT
ejpam-6018	174	57	f	f	NOUN
ejpam-6018	174	58	)	)	PUNCT
ejpam-6018	174	59	.	.	PUNCT
ejpam-6018	175	1	lemma	lemma	PROPN
ejpam-6018	175	2	3	3	X
ejpam-6018	175	3	.	.	PUNCT
ejpam-6018	176	1	let	let	VERB
ejpam-6018	176	2	hs	hs	PRON
ejpam-6018	176	3	:	:	PUNCT
ejpam-6018	176	4	=	=	SYM
ejpam-6018	176	5	(	(	PUNCT
ejpam-6018	176	6	h	h	NOUN
ejpam-6018	176	7	,	,	PUNCT
ejpam-6018	176	8	|	|	ADV
ejpam-6018	176	9	,	,	PUNCT
ejpam-6018	176	10	0	0	NUM
ejpam-6018	176	11	)	)	PUNCT
ejpam-6018	176	12	be	be	AUX
ejpam-6018	176	13	an	an	DET
ejpam-6018	176	14	ssh	ssh	NOUN
ejpam-6018	176	15	-	-	PUNCT
ejpam-6018	176	16	algebra	algebra	NOUN
ejpam-6018	176	17	.	.	PUNCT
ejpam-6018	177	1	let	let	VERB
ejpam-6018	177	2	(	(	PUNCT
ejpam-6018	177	3	h	h	NOUN
ejpam-6018	177	4	,	,	PUNCT
ejpam-6018	177	5	f	f	X
ejpam-6018	177	6	)	)	PUNCT
ejpam-6018	177	7	be	be	AUX
ejpam-6018	177	8	an	an	DET
ejpam-6018	177	9	n	n	ADV
ejpam-6018	177	10	-structure	-structure	NOUN
ejpam-6018	177	11	.	.	PUNCT
ejpam-6018	178	1	then	then	ADV
ejpam-6018	178	2	f(0	f(0	NOUN
ejpam-6018	178	3	)	)	PUNCT
ejpam-6018	178	4	≤	≤	NOUN
ejpam-6018	178	5	f(ξ	f(ξ	NOUN
ejpam-6018	178	6	)	)	PUNCT
ejpam-6018	178	7	for	for	ADP
ejpam-6018	178	8	all	all	DET
ejpam-6018	178	9	ξ	ξ	PROPN
ejpam-6018	178	10	∈	∈	PROPN
ejpam-6018	178	11	h	h	NOUN
ejpam-6018	178	12	if	if	SCONJ
ejpam-6018	178	13	and	and	CCONJ
ejpam-6018	178	14	only	only	ADV
ejpam-6018	178	15	if	if	SCONJ
ejpam-6018	178	16	(	(	PUNCT
ejpam-6018	178	17	h	h	NOUN
ejpam-6018	178	18	,	,	PUNCT
ejpam-6018	178	19	0η	0η	NUM
ejpam-6018	178	20	)	)	PUNCT
ejpam-6018	178	21	is	be	AUX
ejpam-6018	178	22	an	an	DET
ejpam-6018	178	23	n∈-subset	n∈-subset	NOUN
ejpam-6018	178	24	of	of	ADP
ejpam-6018	178	25	(	(	PUNCT
ejpam-6018	178	26	h	h	NOUN
ejpam-6018	178	27	,	,	PUNCT
ejpam-6018	178	28	f	f	NOUN
ejpam-6018	178	29	)	)	PUNCT
ejpam-6018	178	30	whenever	whenever	SCONJ
ejpam-6018	178	31	(	(	PUNCT
ejpam-6018	178	32	h	h	NOUN
ejpam-6018	178	33	,	,	PUNCT
ejpam-6018	178	34	ξη	ξη	PRON
ejpam-6018	178	35	)	)	PUNCT
ejpam-6018	178	36	is	be	AUX
ejpam-6018	178	37	an	an	DET
ejpam-6018	178	38	n∈-subset	n∈-subset	NOUN
ejpam-6018	178	39	of	of	ADP
ejpam-6018	178	40	(	(	PUNCT
ejpam-6018	178	41	h	h	NOUN
ejpam-6018	178	42	,	,	PUNCT
ejpam-6018	178	43	f	f	NOUN
ejpam-6018	178	44	)	)	PUNCT
ejpam-6018	178	45	for	for	ADP
ejpam-6018	178	46	all	all	PRON
ejpam-6018	178	47	ξ	ξ	PROPN
ejpam-6018	178	48	∈	∈	PROPN
ejpam-6018	178	49	h	h	NOUN
ejpam-6018	178	50	and	and	CCONJ
ejpam-6018	178	51	η	η	PROPN
ejpam-6018	178	52	∈	∈	PROPN
ejpam-6018	179	1	υ	υ	NOUN
ejpam-6018	180	1	=	=	X
ejpam-6018	181	1	[	[	X
ejpam-6018	181	2	−1	−1	NOUN
ejpam-6018	181	3	,	,	PUNCT
ejpam-6018	181	4	0	0	NUM
ejpam-6018	181	5	)	)	PUNCT
ejpam-6018	181	6	.	.	PUNCT
ejpam-6018	182	1	proof	proof	NOUN
ejpam-6018	182	2	.	.	PUNCT
ejpam-6018	183	1	assume	assume	VERB
ejpam-6018	183	2	that	that	SCONJ
ejpam-6018	183	3	f(0	f(0	NOUN
ejpam-6018	183	4	)	)	PUNCT
ejpam-6018	183	5	≤	≤	NOUN
ejpam-6018	183	6	f(ξ	f(ξ	NOUN
ejpam-6018	183	7	)	)	PUNCT
ejpam-6018	183	8	for	for	ADP
ejpam-6018	183	9	all	all	DET
ejpam-6018	183	10	ξ	ξ	PROPN
ejpam-6018	183	11	∈	∈	PROPN
ejpam-6018	183	12	h	h	NOUN
ejpam-6018	183	13	and	and	CCONJ
ejpam-6018	183	14	let	let	VERB
ejpam-6018	183	15	η	η	PROPN
ejpam-6018	183	16	∈	∈	PROPN
ejpam-6018	183	17	υ	υ	NOUN
ejpam-6018	183	18	be	be	AUX
ejpam-6018	183	19	such	such	ADJ
ejpam-6018	183	20	that	that	SCONJ
ejpam-6018	183	21	(	(	PUNCT
ejpam-6018	183	22	h	h	NOUN
ejpam-6018	183	23	,	,	PUNCT
ejpam-6018	183	24	ξη	ξη	PRON
ejpam-6018	183	25	)	)	PUNCT
ejpam-6018	183	26	is	be	AUX
ejpam-6018	183	27	an	an	DET
ejpam-6018	183	28	n∈-subset	n∈-subset	NOUN
ejpam-6018	183	29	of	of	ADP
ejpam-6018	183	30	(	(	PUNCT
ejpam-6018	183	31	h	h	NOUN
ejpam-6018	183	32	,	,	PUNCT
ejpam-6018	183	33	f	f	NOUN
ejpam-6018	183	34	)	)	PUNCT
ejpam-6018	183	35	.	.	PUNCT
ejpam-6018	184	1	then	then	ADV
ejpam-6018	184	2	f(0	f(0	NOUN
ejpam-6018	184	3	)	)	PUNCT
ejpam-6018	184	4	≤	≤	NUM
ejpam-6018	184	5	f(ξ	f(ξ	NOUN
ejpam-6018	184	6	)	)	PUNCT
ejpam-6018	184	7	≤	≤	NUM
ejpam-6018	184	8	η	η	PROPN
ejpam-6018	184	9	,	,	PUNCT
ejpam-6018	184	10	and	and	CCONJ
ejpam-6018	184	11	so	so	ADV
ejpam-6018	184	12	(	(	PUNCT
ejpam-6018	184	13	h	h	NOUN
ejpam-6018	184	14	,	,	PUNCT
ejpam-6018	184	15	0η	0η	NUM
ejpam-6018	184	16	)	)	PUNCT
ejpam-6018	184	17	is	be	AUX
ejpam-6018	184	18	an	an	DET
ejpam-6018	184	19	n∈-subset	n∈-subset	NOUN
ejpam-6018	184	20	of	of	ADP
ejpam-6018	184	21	(	(	PUNCT
ejpam-6018	184	22	h	h	NOUN
ejpam-6018	184	23	,	,	PUNCT
ejpam-6018	184	24	f	f	NOUN
ejpam-6018	184	25	)	)	PUNCT
ejpam-6018	184	26	.	.	PUNCT
ejpam-6018	185	1	conversely	conversely	ADV
ejpam-6018	185	2	,	,	PUNCT
ejpam-6018	185	3	suppose	suppose	VERB
ejpam-6018	185	4	that	that	SCONJ
ejpam-6018	185	5	(	(	PUNCT
ejpam-6018	185	6	h	h	NOUN
ejpam-6018	185	7	,	,	PUNCT
ejpam-6018	185	8	0η	0η	NUM
ejpam-6018	185	9	)	)	PUNCT
ejpam-6018	185	10	is	be	AUX
ejpam-6018	185	11	an	an	DET
ejpam-6018	185	12	n∈-subset	n∈-subset	NOUN
ejpam-6018	185	13	of	of	ADP
ejpam-6018	185	14	(	(	PUNCT
ejpam-6018	185	15	h	h	NOUN
ejpam-6018	185	16	,	,	PUNCT
ejpam-6018	185	17	f	f	NOUN
ejpam-6018	185	18	)	)	PUNCT
ejpam-6018	185	19	whenever	whenever	SCONJ
ejpam-6018	185	20	(	(	PUNCT
ejpam-6018	185	21	h	h	NOUN
ejpam-6018	185	22	,	,	PUNCT
ejpam-6018	185	23	ξη	ξη	PRON
ejpam-6018	185	24	)	)	PUNCT
ejpam-6018	185	25	is	be	AUX
ejpam-6018	185	26	an	an	DET
ejpam-6018	185	27	n∈subset	n∈subset	PROPN
ejpam-6018	185	28	of	of	ADP
ejpam-6018	185	29	(	(	PUNCT
ejpam-6018	185	30	h	h	NOUN
ejpam-6018	185	31	,	,	PUNCT
ejpam-6018	185	32	f	f	NOUN
ejpam-6018	185	33	)	)	PUNCT
ejpam-6018	185	34	for	for	ADP
ejpam-6018	185	35	all	all	PRON
ejpam-6018	185	36	ξ	ξ	PROPN
ejpam-6018	185	37	∈	∈	PROPN
ejpam-6018	185	38	h	h	NOUN
ejpam-6018	185	39	and	and	CCONJ
ejpam-6018	185	40	η	η	PROPN
ejpam-6018	185	41	∈	∈	PROPN
ejpam-6018	185	42	υ	υ	NOUN
ejpam-6018	186	1	=	=	X
ejpam-6018	187	1	[	[	X
ejpam-6018	187	2	−1	−1	NOUN
ejpam-6018	187	3	,	,	PUNCT
ejpam-6018	187	4	0	0	NUM
ejpam-6018	187	5	)	)	PUNCT
ejpam-6018	187	6	.	.	PUNCT
ejpam-6018	188	1	if	if	SCONJ
ejpam-6018	188	2	we	we	PRON
ejpam-6018	188	3	take	take	VERB
ejpam-6018	188	4	η	η	NOUN
ejpam-6018	188	5	=	=	SYM
ejpam-6018	188	6	f(ξ	f(ξ	PROPN
ejpam-6018	188	7	)	)	PUNCT
ejpam-6018	188	8	for	for	ADP
ejpam-6018	188	9	any	any	DET
ejpam-6018	188	10	ξ	ξ	PROPN
ejpam-6018	188	11	∈	∈	PROPN
ejpam-6018	188	12	h	h	NOUN
ejpam-6018	188	13	,	,	PUNCT
ejpam-6018	188	14	then	then	ADV
ejpam-6018	188	15	(	(	PUNCT
ejpam-6018	188	16	h	h	NOUN
ejpam-6018	188	17	,	,	PUNCT
ejpam-6018	188	18	ξη	ξη	PRON
ejpam-6018	188	19	)	)	PUNCT
ejpam-6018	188	20	is	be	AUX
ejpam-6018	188	21	an	an	DET
ejpam-6018	188	22	n∈-subset	n∈-subset	NOUN
ejpam-6018	188	23	of	of	ADP
ejpam-6018	188	24	(	(	PUNCT
ejpam-6018	188	25	h	h	NOUN
ejpam-6018	188	26	,	,	PUNCT
ejpam-6018	188	27	f	f	NOUN
ejpam-6018	188	28	)	)	PUNCT
ejpam-6018	188	29	,	,	PUNCT
ejpam-6018	188	30	and	and	CCONJ
ejpam-6018	188	31	thus	thus	ADV
ejpam-6018	188	32	(	(	PUNCT
ejpam-6018	188	33	h	h	NOUN
ejpam-6018	188	34	,	,	PUNCT
ejpam-6018	188	35	0η	0η	NUM
ejpam-6018	188	36	)	)	PUNCT
ejpam-6018	188	37	is	be	AUX
ejpam-6018	188	38	an	an	DET
ejpam-6018	188	39	n∈-subset	n∈-subset	NOUN
ejpam-6018	188	40	of	of	ADP
ejpam-6018	188	41	(	(	PUNCT
ejpam-6018	188	42	h	h	NOUN
ejpam-6018	188	43	,	,	PUNCT
ejpam-6018	188	44	f	f	NOUN
ejpam-6018	188	45	)	)	PUNCT
ejpam-6018	188	46	.	.	PUNCT
ejpam-6018	189	1	hence	hence	ADV
ejpam-6018	189	2	,	,	PUNCT
ejpam-6018	189	3	f(0	f(0	NOUN
ejpam-6018	189	4	)	)	PUNCT
ejpam-6018	189	5	≤	≤	NUM
ejpam-6018	189	6	η	η	NOUN
ejpam-6018	189	7	=	=	SYM
ejpam-6018	189	8	f(ξ	f(ξ	PROPN
ejpam-6018	189	9	)	)	PUNCT
ejpam-6018	189	10	for	for	ADP
ejpam-6018	189	11	all	all	DET
ejpam-6018	189	12	ξ	ξ	PROPN
ejpam-6018	189	13	∈	∈	PROPN
ejpam-6018	189	14	h.	h.	PROPN
ejpam-6018	189	15	lemma	lemma	PROPN
ejpam-6018	189	16	4	4	X
ejpam-6018	189	17	.	.	PUNCT
ejpam-6018	190	1	let	let	VERB
ejpam-6018	190	2	hs	hs	PRON
ejpam-6018	190	3	:	:	PUNCT
ejpam-6018	190	4	=	=	SYM
ejpam-6018	190	5	(	(	PUNCT
ejpam-6018	190	6	h	h	NOUN
ejpam-6018	190	7	,	,	PUNCT
ejpam-6018	190	8	|	|	ADV
ejpam-6018	190	9	,	,	PUNCT
ejpam-6018	190	10	0	0	NUM
ejpam-6018	190	11	)	)	PUNCT
ejpam-6018	190	12	be	be	AUX
ejpam-6018	190	13	an	an	DET
ejpam-6018	190	14	ssh	ssh	NOUN
ejpam-6018	190	15	-	-	PUNCT
ejpam-6018	190	16	algebra	algebra	NOUN
ejpam-6018	190	17	.	.	PUNCT
ejpam-6018	191	1	given	give	VERB
ejpam-6018	191	2	an	an	DET
ejpam-6018	191	3	n	n	ADV
ejpam-6018	191	4	-structure	-structure	NOUN
ejpam-6018	191	5	(	(	PUNCT
ejpam-6018	191	6	h	h	NOUN
ejpam-6018	191	7	,	,	PUNCT
ejpam-6018	191	8	f	f	PROPN
ejpam-6018	191	9	)	)	PUNCT
ejpam-6018	191	10	,	,	PUNCT
ejpam-6018	191	11	the	the	DET
ejpam-6018	191	12	following	follow	VERB
ejpam-6018	191	13	are	be	AUX
ejpam-6018	191	14	equivalent	equivalent	ADJ
ejpam-6018	191	15	:	:	PUNCT
ejpam-6018	191	16	(	(	PUNCT
ejpam-6018	191	17	1	1	X
ejpam-6018	191	18	)	)	PUNCT
ejpam-6018	191	19	f(ξ	f(ξ	NOUN
ejpam-6018	191	20	)	)	PUNCT
ejpam-6018	191	21	≤	≤	NUM
ejpam-6018	191	22	∨	∨	NUM
ejpam-6018	191	23	{	{	PUNCT
ejpam-6018	191	24	f(ξζ	f(ξζ	PROPN
ejpam-6018	191	25	|	|	ADV
ejpam-6018	191	26	ξζ	ξζ	NOUN
ejpam-6018	191	27	)	)	PUNCT
ejpam-6018	191	28	,	,	PUNCT
ejpam-6018	191	29	f(ζ	f(ζ	NOUN
ejpam-6018	191	30	)	)	PUNCT
ejpam-6018	191	31	}	}	PUNCT
ejpam-6018	191	32	for	for	ADP
ejpam-6018	191	33	all	all	DET
ejpam-6018	191	34	ξ	ξ	ADJ
ejpam-6018	191	35	,	,	PUNCT
ejpam-6018	191	36	ζ	ζ	PROPN
ejpam-6018	191	37	∈	∈	PROPN
ejpam-6018	191	38	h.	h.	NOUN
ejpam-6018	191	39	(	(	PUNCT
ejpam-6018	191	40	2	2	NUM
ejpam-6018	191	41	)	)	PUNCT
ejpam-6018	191	42	for	for	ADP
ejpam-6018	191	43	any	any	DET
ejpam-6018	191	44	ξ	ξ	PROPN
ejpam-6018	191	45	,	,	PUNCT
ejpam-6018	191	46	ζ	ζ	PROPN
ejpam-6018	191	47	∈	∈	PROPN
ejpam-6018	191	48	h	h	NOUN
ejpam-6018	191	49	and	and	CCONJ
ejpam-6018	191	50	η	η	PROPN
ejpam-6018	191	51	,	,	PUNCT
ejpam-6018	191	52	δ	δ	PROPN
ejpam-6018	191	53	∈	∈	PROPN
ejpam-6018	191	54	υ	υ	NOUN
ejpam-6018	192	1	=	=	X
ejpam-6018	193	1	[	[	X
ejpam-6018	193	2	−1	−1	NOUN
ejpam-6018	193	3	,	,	PUNCT
ejpam-6018	193	4	0	0	NUM
ejpam-6018	193	5	)	)	PUNCT
ejpam-6018	193	6	,	,	PUNCT
ejpam-6018	193	7	if	if	SCONJ
ejpam-6018	193	8	(	(	PUNCT
ejpam-6018	193	9	h	h	NOUN
ejpam-6018	193	10	,	,	PUNCT
ejpam-6018	193	11	(	(	PUNCT
ejpam-6018	193	12	ξζ	ξζ	NOUN
ejpam-6018	193	13	|	|	ADV
ejpam-6018	193	14	ξζ)η	ξζ)η	PROPN
ejpam-6018	193	15	)	)	PUNCT
ejpam-6018	193	16	and	and	CCONJ
ejpam-6018	193	17	(	(	PUNCT
ejpam-6018	193	18	h	h	NOUN
ejpam-6018	193	19	,	,	PUNCT
ejpam-6018	193	20	ζδ	ζδ	NOUN
ejpam-6018	193	21	)	)	PUNCT
ejpam-6018	193	22	are	be	AUX
ejpam-6018	193	23	n∈-subsets	n∈-subset	NOUN
ejpam-6018	193	24	of	of	ADP
ejpam-6018	193	25	(	(	PUNCT
ejpam-6018	193	26	h	h	NOUN
ejpam-6018	193	27	,	,	PUNCT
ejpam-6018	193	28	f	f	PROPN
ejpam-6018	193	29	)	)	PUNCT
ejpam-6018	193	30	,	,	PUNCT
ejpam-6018	193	31	then	then	ADV
ejpam-6018	193	32	(	(	PUNCT
ejpam-6018	193	33	h	h	NOUN
ejpam-6018	193	34	,	,	PUNCT
ejpam-6018	193	35	ξη∨δ	ξη∨δ	NOUN
ejpam-6018	193	36	)	)	PUNCT
ejpam-6018	193	37	is	be	AUX
ejpam-6018	193	38	an	an	DET
ejpam-6018	193	39	n∈-subset	n∈-subset	NOUN
ejpam-6018	193	40	of	of	ADP
ejpam-6018	193	41	(	(	PUNCT
ejpam-6018	193	42	h	h	NOUN
ejpam-6018	193	43	,	,	PUNCT
ejpam-6018	193	44	f	f	NOUN
ejpam-6018	193	45	)	)	PUNCT
ejpam-6018	193	46	.	.	PUNCT
ejpam-6018	194	1	t.	t.	PROPN
ejpam-6018	194	2	oner	oner	PROPN
ejpam-6018	194	3	et	et	PROPN
ejpam-6018	194	4	al	al	PROPN
ejpam-6018	194	5	.	.	PUNCT
ejpam-6018	194	6	/	/	SYM
ejpam-6018	194	7	eur	eur	PROPN
ejpam-6018	194	8	.	.	PUNCT
ejpam-6018	195	1	j.	j.	PROPN
ejpam-6018	195	2	pure	pure	PROPN
ejpam-6018	195	3	appl	appl	PROPN
ejpam-6018	195	4	.	.	PROPN
ejpam-6018	195	5	math	math	PROPN
ejpam-6018	195	6	,	,	PUNCT
ejpam-6018	195	7	18	18	NUM
ejpam-6018	195	8	(	(	PUNCT
ejpam-6018	195	9	2	2	NUM
ejpam-6018	195	10	)	)	PUNCT
ejpam-6018	195	11	(	(	PUNCT
ejpam-6018	195	12	2025	2025	NUM
ejpam-6018	195	13	)	)	PUNCT
ejpam-6018	195	14	,	,	PUNCT
ejpam-6018	195	15	6018	6018	NUM
ejpam-6018	195	16	8	8	NUM
ejpam-6018	195	17	of	of	ADP
ejpam-6018	195	18	11	11	NUM
ejpam-6018	195	19	proof	proof	NOUN
ejpam-6018	195	20	.	.	PUNCT
ejpam-6018	196	1	assume	assume	VERB
ejpam-6018	196	2	that	that	SCONJ
ejpam-6018	196	3	f(ξ	f(ξ	NOUN
ejpam-6018	196	4	)	)	PUNCT
ejpam-6018	196	5	≤	≤	NUM
ejpam-6018	196	6	∨	∨	NUM
ejpam-6018	196	7	{	{	PUNCT
ejpam-6018	196	8	f(ξζ	f(ξζ	PROPN
ejpam-6018	196	9	|	|	ADV
ejpam-6018	196	10	ξζ	ξζ	NOUN
ejpam-6018	196	11	)	)	PUNCT
ejpam-6018	196	12	,	,	PUNCT
ejpam-6018	196	13	f(ζ	f(ζ	NOUN
ejpam-6018	196	14	)	)	PUNCT
ejpam-6018	196	15	}	}	PUNCT
ejpam-6018	196	16	for	for	ADP
ejpam-6018	196	17	all	all	DET
ejpam-6018	196	18	ξ	ξ	ADJ
ejpam-6018	196	19	,	,	PUNCT
ejpam-6018	196	20	ζ	ζ	PROPN
ejpam-6018	196	21	∈	∈	PROPN
ejpam-6018	196	22	h.	h.	NOUN
ejpam-6018	196	23	let	let	VERB
ejpam-6018	196	24	ξ	ξ	X
ejpam-6018	196	25	,	,	PUNCT
ejpam-6018	196	26	ζ	ζ	PROPN
ejpam-6018	196	27	∈	∈	PROPN
ejpam-6018	196	28	h	h	NOUN
ejpam-6018	196	29	and	and	CCONJ
ejpam-6018	196	30	η	η	PROPN
ejpam-6018	196	31	,	,	PUNCT
ejpam-6018	196	32	δ	δ	PROPN
ejpam-6018	196	33	∈	∈	PROPN
ejpam-6018	196	34	υ	υ	VERB
ejpam-6018	196	35	be	be	AUX
ejpam-6018	196	36	such	such	ADJ
ejpam-6018	196	37	that	that	SCONJ
ejpam-6018	196	38	(	(	PUNCT
ejpam-6018	196	39	h	h	NOUN
ejpam-6018	196	40	,	,	PUNCT
ejpam-6018	196	41	(	(	PUNCT
ejpam-6018	196	42	ξζ	ξζ	NOUN
ejpam-6018	196	43	|	|	ADV
ejpam-6018	196	44	ξζ)η	ξζ)η	PROPN
ejpam-6018	196	45	)	)	PUNCT
ejpam-6018	196	46	and	and	CCONJ
ejpam-6018	196	47	(	(	PUNCT
ejpam-6018	196	48	h	h	NOUN
ejpam-6018	196	49	,	,	PUNCT
ejpam-6018	196	50	ζδ	ζδ	NOUN
ejpam-6018	196	51	)	)	PUNCT
ejpam-6018	196	52	are	be	AUX
ejpam-6018	196	53	n∈-subsets	n∈-subset	NOUN
ejpam-6018	196	54	of	of	ADP
ejpam-6018	196	55	(	(	PUNCT
ejpam-6018	196	56	h	h	NOUN
ejpam-6018	196	57	,	,	PUNCT
ejpam-6018	196	58	f	f	NOUN
ejpam-6018	196	59	)	)	PUNCT
ejpam-6018	196	60	.	.	PUNCT
ejpam-6018	197	1	then	then	ADV
ejpam-6018	197	2	f(ξζ	f(ξζ	PROPN
ejpam-6018	197	3	|	|	ADV
ejpam-6018	197	4	ξζ	ξζ	PROPN
ejpam-6018	197	5	)	)	PUNCT
ejpam-6018	197	6	≤	≤	PROPN
ejpam-6018	197	7	η	η	PROPN
ejpam-6018	197	8	and	and	CCONJ
ejpam-6018	197	9	f(ζ	f(ζ	PROPN
ejpam-6018	197	10	)	)	PUNCT
ejpam-6018	197	11	≤	≤	NUM
ejpam-6018	197	12	δ	δ	PROPN
ejpam-6018	197	13	,	,	PUNCT
ejpam-6018	197	14	which	which	PRON
ejpam-6018	197	15	imply	imply	VERB
ejpam-6018	197	16	that	that	SCONJ
ejpam-6018	197	17	f(ξ	f(ξ	NOUN
ejpam-6018	197	18	)	)	PUNCT
ejpam-6018	197	19	≤	≤	NUM
ejpam-6018	197	20	∨	∨	NUM
ejpam-6018	197	21	{	{	PUNCT
ejpam-6018	197	22	f(ξζ	f(ξζ	PROPN
ejpam-6018	197	23	|	|	ADV
ejpam-6018	197	24	ξζ	ξζ	NOUN
ejpam-6018	197	25	)	)	PUNCT
ejpam-6018	197	26	,	,	PUNCT
ejpam-6018	197	27	f(ζ	f(ζ	PROPN
ejpam-6018	197	28	)	)	PUNCT
ejpam-6018	197	29	}	}	PUNCT
ejpam-6018	197	30	≤	≤	NUM
ejpam-6018	197	31	η	η	PROPN
ejpam-6018	197	32	∨	∨	PROPN
ejpam-6018	197	33	δ	δ	PROPN
ejpam-6018	197	34	.	.	PUNCT
ejpam-6018	198	1	hence	hence	ADV
ejpam-6018	198	2	,	,	PUNCT
ejpam-6018	198	3	(	(	PUNCT
ejpam-6018	198	4	h	h	NOUN
ejpam-6018	198	5	,	,	PUNCT
ejpam-6018	198	6	ξη∨δ	ξη∨δ	NOUN
ejpam-6018	198	7	)	)	PUNCT
ejpam-6018	198	8	is	be	AUX
ejpam-6018	198	9	an	an	DET
ejpam-6018	198	10	n∈-subset	n∈-subset	NOUN
ejpam-6018	198	11	of	of	ADP
ejpam-6018	198	12	(	(	PUNCT
ejpam-6018	198	13	h	h	NOUN
ejpam-6018	198	14	,	,	PUNCT
ejpam-6018	198	15	f	f	NOUN
ejpam-6018	198	16	)	)	PUNCT
ejpam-6018	198	17	.	.	PUNCT
ejpam-6018	199	1	conversely	conversely	ADV
ejpam-6018	199	2	,	,	PUNCT
ejpam-6018	199	3	suppose	suppose	VERB
ejpam-6018	199	4	(	(	PUNCT
ejpam-6018	199	5	2	2	X
ejpam-6018	199	6	)	)	PUNCT
ejpam-6018	199	7	is	be	AUX
ejpam-6018	199	8	valid	valid	ADJ
ejpam-6018	199	9	.	.	PUNCT
ejpam-6018	200	1	if	if	SCONJ
ejpam-6018	200	2	we	we	PRON
ejpam-6018	200	3	take	take	VERB
ejpam-6018	200	4	η	η	PROPN
ejpam-6018	200	5	=	=	PROPN
ejpam-6018	200	6	f(ξζ	f(ξζ	PROPN
ejpam-6018	200	7	|	|	ADV
ejpam-6018	200	8	ξζ	ξζ	NOUN
ejpam-6018	200	9	)	)	PUNCT
ejpam-6018	200	10	and	and	CCONJ
ejpam-6018	200	11	δ	δ	PROPN
ejpam-6018	200	12	=	=	PROPN
ejpam-6018	200	13	f(ζ	f(ζ	PROPN
ejpam-6018	200	14	)	)	PUNCT
ejpam-6018	200	15	,	,	PUNCT
ejpam-6018	200	16	then	then	ADV
ejpam-6018	200	17	(	(	PUNCT
ejpam-6018	200	18	h	h	NOUN
ejpam-6018	200	19	,	,	PUNCT
ejpam-6018	200	20	(	(	PUNCT
ejpam-6018	200	21	ξζ	ξζ	NOUN
ejpam-6018	200	22	|	|	ADV
ejpam-6018	200	23	ξζ)η	ξζ)η	PROPN
ejpam-6018	200	24	)	)	PUNCT
ejpam-6018	200	25	and	and	CCONJ
ejpam-6018	200	26	(	(	PUNCT
ejpam-6018	200	27	h	h	NOUN
ejpam-6018	200	28	,	,	PUNCT
ejpam-6018	200	29	ζδ	ζδ	NOUN
ejpam-6018	200	30	)	)	PUNCT
ejpam-6018	200	31	are	be	AUX
ejpam-6018	200	32	n∈-subsets	n∈-subset	NOUN
ejpam-6018	200	33	of	of	ADP
ejpam-6018	200	34	(	(	PUNCT
ejpam-6018	200	35	h	h	NOUN
ejpam-6018	200	36	,	,	PUNCT
ejpam-6018	200	37	f	f	NOUN
ejpam-6018	200	38	)	)	PUNCT
ejpam-6018	200	39	.	.	PUNCT
ejpam-6018	201	1	it	it	PRON
ejpam-6018	201	2	follows	follow	VERB
ejpam-6018	201	3	that	that	SCONJ
ejpam-6018	201	4	(	(	PUNCT
ejpam-6018	201	5	h	h	NOUN
ejpam-6018	201	6	,	,	PUNCT
ejpam-6018	201	7	ξη∨δ	ξη∨δ	NOUN
ejpam-6018	201	8	)	)	PUNCT
ejpam-6018	201	9	is	be	AUX
ejpam-6018	201	10	an	an	DET
ejpam-6018	201	11	n∈-subset	n∈-subset	NOUN
ejpam-6018	201	12	of	of	ADP
ejpam-6018	201	13	(	(	PUNCT
ejpam-6018	201	14	h	h	NOUN
ejpam-6018	201	15	,	,	PUNCT
ejpam-6018	201	16	f	f	NOUN
ejpam-6018	201	17	)	)	PUNCT
ejpam-6018	201	18	and	and	CCONJ
ejpam-6018	201	19	thus	thus	ADV
ejpam-6018	201	20	,	,	PUNCT
ejpam-6018	201	21	we	we	PRON
ejpam-6018	201	22	have	have	VERB
ejpam-6018	201	23	f(ξ	f(ξ	NOUN
ejpam-6018	201	24	)	)	PUNCT
ejpam-6018	201	25	≤	≤	NUM
ejpam-6018	201	26	η	η	PROPN
ejpam-6018	201	27	∨	∨	PROPN
ejpam-6018	201	28	δ	δ	PROPN
ejpam-6018	201	29	=	=	SYM
ejpam-6018	201	30	∨	∨	X
ejpam-6018	201	31	{	{	PUNCT
ejpam-6018	201	32	f(ξζ	f(ξζ	PROPN
ejpam-6018	201	33	|	|	ADV
ejpam-6018	201	34	ξζ	ξζ	NOUN
ejpam-6018	201	35	)	)	PUNCT
ejpam-6018	201	36	,	,	PUNCT
ejpam-6018	201	37	f(ζ	f(ζ	NOUN
ejpam-6018	201	38	)	)	PUNCT
ejpam-6018	201	39	}	}	PUNCT
ejpam-6018	201	40	.	.	PUNCT
ejpam-6018	202	1	combining	combine	VERB
ejpam-6018	202	2	lemmas	lemmas	PROPN
ejpam-6018	202	3	3	3	NUM
ejpam-6018	202	4	and	and	CCONJ
ejpam-6018	202	5	4	4	NUM
ejpam-6018	202	6	,	,	PUNCT
ejpam-6018	202	7	we	we	PRON
ejpam-6018	202	8	have	have	VERB
ejpam-6018	202	9	the	the	DET
ejpam-6018	202	10	following	follow	VERB
ejpam-6018	202	11	theorem	theorem	VERB
ejpam-6018	202	12	.	.	PUNCT
ejpam-6018	202	13	theorem	theorem	NOUN
ejpam-6018	202	14	6	6	NUM
ejpam-6018	202	15	.	.	PUNCT
ejpam-6018	203	1	let	let	VERB
ejpam-6018	203	2	hs	hs	PRON
ejpam-6018	203	3	:	:	PUNCT
ejpam-6018	203	4	=	=	SYM
ejpam-6018	203	5	(	(	PUNCT
ejpam-6018	203	6	h	h	NOUN
ejpam-6018	203	7	,	,	PUNCT
ejpam-6018	203	8	|	|	ADV
ejpam-6018	203	9	,	,	PUNCT
ejpam-6018	203	10	0	0	NUM
ejpam-6018	203	11	)	)	PUNCT
ejpam-6018	203	12	be	be	AUX
ejpam-6018	203	13	an	an	DET
ejpam-6018	203	14	ssh	ssh	NOUN
ejpam-6018	203	15	-	-	PUNCT
ejpam-6018	203	16	algebra	algebra	NOUN
ejpam-6018	203	17	.	.	PUNCT
ejpam-6018	204	1	an	an	DET
ejpam-6018	204	2	n	n	ADV
ejpam-6018	204	3	-structure	-structure	NOUN
ejpam-6018	204	4	(	(	PUNCT
ejpam-6018	204	5	h	h	NOUN
ejpam-6018	204	6	,	,	PUNCT
ejpam-6018	204	7	f	f	X
ejpam-6018	204	8	)	)	PUNCT
ejpam-6018	204	9	is	be	AUX
ejpam-6018	204	10	an	an	DET
ejpam-6018	204	11	n	n	ADV
ejpam-6018	204	12	-ideal	-ideal	NOUN
ejpam-6018	204	13	of	of	ADP
ejpam-6018	204	14	type	type	NOUN
ejpam-6018	204	15	(	(	PUNCT
ejpam-6018	204	16	∈,∈	∈,∈	X
ejpam-6018	204	17	)	)	PUNCT
ejpam-6018	205	1	if	if	SCONJ
ejpam-6018	205	2	and	and	CCONJ
ejpam-6018	205	3	only	only	ADV
ejpam-6018	205	4	if	if	SCONJ
ejpam-6018	205	5	(	(	PUNCT
ejpam-6018	205	6	∀ξ	∀ξ	NOUN
ejpam-6018	205	7	,	,	PUNCT
ejpam-6018	205	8	ζ	ζ	PROPN
ejpam-6018	205	9	∈	∈	PROPN
ejpam-6018	205	10	h	h	NOUN
ejpam-6018	205	11	)	)	PUNCT
ejpam-6018	205	12	(	(	PUNCT
ejpam-6018	205	13	f(0	f(0	NOUN
ejpam-6018	205	14	)	)	PUNCT
ejpam-6018	205	15	≤	≤	NOUN
ejpam-6018	205	16	f(ξ	f(ξ	NOUN
ejpam-6018	205	17	)	)	PUNCT
ejpam-6018	205	18	≤	≤	NUM
ejpam-6018	205	19	∨	∨	NUM
ejpam-6018	205	20	{	{	PUNCT
ejpam-6018	205	21	f(ξζ	f(ξζ	PROPN
ejpam-6018	205	22	|	|	ADV
ejpam-6018	205	23	ξζ	ξζ	NOUN
ejpam-6018	205	24	)	)	PUNCT
ejpam-6018	205	25	,	,	PUNCT
ejpam-6018	205	26	f(ζ	f(ζ	NOUN
ejpam-6018	205	27	)	)	PUNCT
ejpam-6018	205	28	}	}	PUNCT
ejpam-6018	205	29	)	)	PUNCT
ejpam-6018	205	30	.	.	PUNCT
ejpam-6018	206	1	(	(	PUNCT
ejpam-6018	206	2	4	4	X
ejpam-6018	206	3	)	)	PUNCT
ejpam-6018	206	4	definition	definition	NOUN
ejpam-6018	206	5	7	7	NUM
ejpam-6018	206	6	.	.	PUNCT
ejpam-6018	207	1	let	let	VERB
ejpam-6018	207	2	hs	hs	PRON
ejpam-6018	207	3	:	:	PUNCT
ejpam-6018	207	4	=	=	SYM
ejpam-6018	207	5	(	(	PUNCT
ejpam-6018	207	6	h	h	NOUN
ejpam-6018	207	7	,	,	PUNCT
ejpam-6018	207	8	|	|	ADV
ejpam-6018	207	9	,	,	PUNCT
ejpam-6018	207	10	0	0	NUM
ejpam-6018	207	11	)	)	PUNCT
ejpam-6018	207	12	be	be	AUX
ejpam-6018	207	13	an	an	DET
ejpam-6018	207	14	ssh	ssh	NOUN
ejpam-6018	207	15	-	-	PUNCT
ejpam-6018	207	16	algebra	algebra	NOUN
ejpam-6018	207	17	.	.	PUNCT
ejpam-6018	208	1	a	a	DET
ejpam-6018	208	2	soft	soft	ADJ
ejpam-6018	208	3	n	n	X
ejpam-6018	208	4	-set	-set	X
ejpam-6018	208	5	(	(	PUNCT
ejpam-6018	208	6	s	s	X
ejpam-6018	208	7	,	,	PUNCT
ejpam-6018	208	8	υ	υ	NOUN
ejpam-6018	208	9	)	)	PUNCT
ejpam-6018	208	10	over	over	ADP
ejpam-6018	208	11	h	h	NOUN
ejpam-6018	208	12	is	be	AUX
ejpam-6018	208	13	called	call	VERB
ejpam-6018	208	14	a	a	DET
ejpam-6018	208	15	soft	soft	ADJ
ejpam-6018	208	16	n	n	NOUN
ejpam-6018	208	17	-ideal	-ideal	NOUN
ejpam-6018	208	18	over	over	ADP
ejpam-6018	208	19	h	h	NOUN
ejpam-6018	208	20	if	if	SCONJ
ejpam-6018	208	21	(	(	PUNCT
ejpam-6018	208	22	∀η	∀η	NOUN
ejpam-6018	208	23	∈	∈	PROPN
ejpam-6018	208	24	υ	υ	PROPN
ejpam-6018	208	25	)	)	PUNCT
ejpam-6018	208	26	(	(	PUNCT
ejpam-6018	208	27	s(η	s(η	PROPN
ejpam-6018	208	28	)	)	PUNCT
ejpam-6018	208	29	̸=	̸=	PROPN
ejpam-6018	208	30	∅	∅	ADP
ejpam-6018	208	31	⇒	⇒	PROPN
ejpam-6018	208	32	s(η	s(η	PROPN
ejpam-6018	208	33	)	)	PUNCT
ejpam-6018	208	34	is	be	AUX
ejpam-6018	208	35	an	an	DET
ejpam-6018	208	36	ideal	ideal	NOUN
ejpam-6018	208	37	of	of	ADP
ejpam-6018	208	38	h	h	NOUN
ejpam-6018	208	39	)	)	PUNCT
ejpam-6018	208	40	.	.	PUNCT
ejpam-6018	209	1	(	(	PUNCT
ejpam-6018	209	2	5	5	X
ejpam-6018	209	3	)	)	PUNCT
ejpam-6018	209	4	theorem	theorem	NOUN
ejpam-6018	209	5	7	7	NUM
ejpam-6018	209	6	.	.	PUNCT
ejpam-6018	210	1	let	let	VERB
ejpam-6018	210	2	hs	hs	PRON
ejpam-6018	210	3	:	:	PUNCT
ejpam-6018	210	4	=	=	SYM
ejpam-6018	210	5	(	(	PUNCT
ejpam-6018	210	6	h	h	NOUN
ejpam-6018	210	7	,	,	PUNCT
ejpam-6018	210	8	|	|	ADV
ejpam-6018	210	9	,	,	PUNCT
ejpam-6018	210	10	0	0	NUM
ejpam-6018	210	11	)	)	PUNCT
ejpam-6018	210	12	be	be	AUX
ejpam-6018	210	13	an	an	DET
ejpam-6018	210	14	ssh	ssh	NOUN
ejpam-6018	210	15	-	-	PUNCT
ejpam-6018	210	16	algebra	algebra	NOUN
ejpam-6018	210	17	.	.	PUNCT
ejpam-6018	211	1	given	give	VERB
ejpam-6018	211	2	an	an	DET
ejpam-6018	211	3	n	n	ADV
ejpam-6018	211	4	-structure	-structure	NOUN
ejpam-6018	211	5	(	(	PUNCT
ejpam-6018	211	6	h	h	NOUN
ejpam-6018	211	7	,	,	PUNCT
ejpam-6018	211	8	f	f	NOUN
ejpam-6018	211	9	)	)	PUNCT
ejpam-6018	211	10	and	and	CCONJ
ejpam-6018	211	11	the	the	DET
ejpam-6018	211	12	soft	soft	ADJ
ejpam-6018	211	13	n∈-set	n∈-set	NOUN
ejpam-6018	211	14	(	(	PUNCT
ejpam-6018	211	15	s∈,υ	s∈,υ	NOUN
ejpam-6018	211	16	)	)	PUNCT
ejpam-6018	211	17	,	,	PUNCT
ejpam-6018	211	18	the	the	DET
ejpam-6018	211	19	following	follow	VERB
ejpam-6018	211	20	are	be	AUX
ejpam-6018	211	21	equivalent	equivalent	ADJ
ejpam-6018	211	22	:	:	PUNCT
ejpam-6018	211	23	(	(	PUNCT
ejpam-6018	211	24	1	1	X
ejpam-6018	211	25	)	)	PUNCT
ejpam-6018	211	26	(	(	PUNCT
ejpam-6018	211	27	s∈,υ	s∈,υ	NOUN
ejpam-6018	211	28	)	)	PUNCT
ejpam-6018	211	29	is	be	AUX
ejpam-6018	211	30	a	a	DET
ejpam-6018	211	31	soft	soft	ADJ
ejpam-6018	211	32	n	n	NOUN
ejpam-6018	211	33	-ideal	-ideal	ADJ
ejpam-6018	211	34	over	over	ADP
ejpam-6018	211	35	h	h	NOUN
ejpam-6018	211	36	for	for	ADP
ejpam-6018	211	37	υ	υ	NOUN
ejpam-6018	212	1	=	=	PUNCT
ejpam-6018	213	1	[	[	X
ejpam-6018	213	2	−1	−1	NOUN
ejpam-6018	213	3	,	,	PUNCT
ejpam-6018	213	4	0	0	NUM
ejpam-6018	213	5	)	)	PUNCT
ejpam-6018	213	6	.	.	PUNCT
ejpam-6018	214	1	(	(	PUNCT
ejpam-6018	214	2	2	2	X
ejpam-6018	214	3	)	)	PUNCT
ejpam-6018	214	4	(	(	PUNCT
ejpam-6018	214	5	h	h	NOUN
ejpam-6018	214	6	,	,	PUNCT
ejpam-6018	214	7	f	f	X
ejpam-6018	214	8	)	)	PUNCT
ejpam-6018	214	9	is	be	AUX
ejpam-6018	214	10	an	an	DET
ejpam-6018	214	11	n	n	ADV
ejpam-6018	214	12	-ideal	-ideal	NOUN
ejpam-6018	214	13	of	of	ADP
ejpam-6018	214	14	type	type	NOUN
ejpam-6018	214	15	(	(	PUNCT
ejpam-6018	214	16	∈,∈	∈,∈	NOUN
ejpam-6018	214	17	)	)	PUNCT
ejpam-6018	214	18	.	.	PUNCT
ejpam-6018	215	1	proof	proof	NOUN
ejpam-6018	215	2	.	.	PUNCT
ejpam-6018	216	1	assume	assume	VERB
ejpam-6018	216	2	that	that	SCONJ
ejpam-6018	216	3	(	(	PUNCT
ejpam-6018	216	4	s∈,υ	s∈,υ	NOUN
ejpam-6018	216	5	)	)	PUNCT
ejpam-6018	216	6	is	be	AUX
ejpam-6018	216	7	a	a	DET
ejpam-6018	216	8	soft	soft	ADJ
ejpam-6018	216	9	n	n	NOUN
ejpam-6018	216	10	-ideal	-ideal	ADJ
ejpam-6018	216	11	over	over	ADP
ejpam-6018	216	12	h	h	NOUN
ejpam-6018	216	13	for	for	ADP
ejpam-6018	216	14	υ	υ	NOUN
ejpam-6018	217	1	=	=	PUNCT
ejpam-6018	218	1	[	[	X
ejpam-6018	218	2	−1	−1	NOUN
ejpam-6018	218	3	,	,	PUNCT
ejpam-6018	218	4	0	0	NUM
ejpam-6018	218	5	)	)	PUNCT
ejpam-6018	218	6	.	.	PUNCT
ejpam-6018	219	1	if	if	SCONJ
ejpam-6018	219	2	there	there	PRON
ejpam-6018	219	3	exists	exist	VERB
ejpam-6018	219	4	ϱ	ϱ	ADP
ejpam-6018	219	5	∈	∈	PROPN
ejpam-6018	219	6	h	h	NOUN
ejpam-6018	219	7	such	such	ADJ
ejpam-6018	219	8	that	that	DET
ejpam-6018	219	9	f(0	f(0	NOUN
ejpam-6018	219	10	)	)	PUNCT
ejpam-6018	219	11	>	>	SYM
ejpam-6018	219	12	f(ϱ	f(ϱ	NOUN
ejpam-6018	219	13	)	)	PUNCT
ejpam-6018	219	14	,	,	PUNCT
ejpam-6018	219	15	then	then	ADV
ejpam-6018	219	16	we	we	PRON
ejpam-6018	219	17	can	can	AUX
ejpam-6018	219	18	take	take	VERB
ejpam-6018	219	19	η	η	PROPN
ejpam-6018	219	20	∈	∈	PROPN
ejpam-6018	219	21	υ	υ	ADP
ejpam-6018	219	22	such	such	ADJ
ejpam-6018	219	23	that	that	DET
ejpam-6018	219	24	f(0	f(0	NOUN
ejpam-6018	219	25	)	)	PUNCT
ejpam-6018	219	26	>	>	PUNCT
ejpam-6018	219	27	η	η	PROPN
ejpam-6018	219	28	≥	≥	PROPN
ejpam-6018	219	29	f(ϱ	f(ϱ	NOUN
ejpam-6018	219	30	)	)	PUNCT
ejpam-6018	219	31	.	.	PUNCT
ejpam-6018	220	1	thus	thus	ADV
ejpam-6018	220	2	,	,	PUNCT
ejpam-6018	220	3	(	(	PUNCT
ejpam-6018	220	4	h	h	NOUN
ejpam-6018	220	5	,	,	PUNCT
ejpam-6018	220	6	0η	0η	NUM
ejpam-6018	220	7	)	)	PUNCT
ejpam-6018	220	8	is	be	AUX
ejpam-6018	220	9	not	not	PART
ejpam-6018	220	10	an	an	DET
ejpam-6018	220	11	n∈-subset	n∈-subset	NOUN
ejpam-6018	220	12	of	of	ADP
ejpam-6018	220	13	(	(	PUNCT
ejpam-6018	220	14	h	h	NOUN
ejpam-6018	220	15	,	,	PUNCT
ejpam-6018	220	16	f	f	NOUN
ejpam-6018	220	17	)	)	PUNCT
ejpam-6018	220	18	,	,	PUNCT
ejpam-6018	220	19	and	and	CCONJ
ejpam-6018	220	20	so	so	ADV
ejpam-6018	220	21	0	0	NUM
ejpam-6018	220	22	/∈	/∈	PUNCT
ejpam-6018	220	23	s∈(η	s∈(η	ADJ
ejpam-6018	220	24	)	)	PUNCT
ejpam-6018	220	25	.	.	PUNCT
ejpam-6018	221	1	this	this	PRON
ejpam-6018	221	2	is	be	AUX
ejpam-6018	221	3	a	a	DET
ejpam-6018	221	4	contradiction	contradiction	NOUN
ejpam-6018	221	5	,	,	PUNCT
ejpam-6018	221	6	and	and	CCONJ
ejpam-6018	221	7	so	so	ADV
ejpam-6018	221	8	f(0	f(0	NOUN
ejpam-6018	221	9	)	)	PUNCT
ejpam-6018	221	10	≤	≤	NOUN
ejpam-6018	221	11	f(ξ	f(ξ	NOUN
ejpam-6018	221	12	)	)	PUNCT
ejpam-6018	221	13	for	for	ADP
ejpam-6018	221	14	all	all	DET
ejpam-6018	221	15	ξ	ξ	PROPN
ejpam-6018	221	16	∈	∈	PROPN
ejpam-6018	221	17	h.	h.	NOUN
ejpam-6018	221	18	suppose	suppose	VERB
ejpam-6018	221	19	that	that	SCONJ
ejpam-6018	221	20	there	there	PRON
ejpam-6018	221	21	exist	exist	VERB
ejpam-6018	221	22	ϱ,ϖ	ϱ,ϖ	NOUN
ejpam-6018	221	23	∈	∈	PROPN
ejpam-6018	221	24	h	h	NOUN
ejpam-6018	222	1	such	such	ADJ
ejpam-6018	222	2	that	that	SCONJ
ejpam-6018	222	3	f(ϱ	f(ϱ	NOUN
ejpam-6018	222	4	)	)	PUNCT
ejpam-6018	222	5	>	>	PUNCT
ejpam-6018	222	6	∨	∨	X
ejpam-6018	222	7	{	{	PUNCT
ejpam-6018	222	8	f(ϱϖ	f(ϱϖ	NOUN
ejpam-6018	222	9	|	|	NOUN
ejpam-6018	222	10	ϱϖ	ϱϖ	NOUN
ejpam-6018	222	11	)	)	PUNCT
ejpam-6018	222	12	,	,	PUNCT
ejpam-6018	222	13	f(ϖ	f(ϖ	PROPN
ejpam-6018	222	14	)	)	PUNCT
ejpam-6018	222	15	}	}	PUNCT
ejpam-6018	222	16	.	.	PUNCT
ejpam-6018	223	1	taking	take	VERB
ejpam-6018	223	2	η	η	PROPN
ejpam-6018	223	3	=	=	PROPN
ejpam-6018	223	4	∨	∨	X
ejpam-6018	223	5	{	{	PUNCT
ejpam-6018	223	6	f(ϱϖ	f(ϱϖ	NOUN
ejpam-6018	223	7	|	|	NOUN
ejpam-6018	223	8	ϱϖ	ϱϖ	NOUN
ejpam-6018	223	9	)	)	PUNCT
ejpam-6018	223	10	,	,	PUNCT
ejpam-6018	223	11	f(ϖ	f(ϖ	PROPN
ejpam-6018	223	12	)	)	PUNCT
ejpam-6018	223	13	}	}	PUNCT
ejpam-6018	223	14	implies	imply	VERB
ejpam-6018	223	15	that	that	SCONJ
ejpam-6018	223	16	(	(	PUNCT
ejpam-6018	223	17	h	h	NOUN
ejpam-6018	223	18	,	,	PUNCT
ejpam-6018	223	19	(	(	PUNCT
ejpam-6018	223	20	ϱϖ	ϱϖ	NOUN
ejpam-6018	223	21	|	|	ADV
ejpam-6018	223	22	ϱϖ)η	ϱϖ)η	NUM
ejpam-6018	223	23	)	)	PUNCT
ejpam-6018	223	24	and	and	CCONJ
ejpam-6018	223	25	(	(	PUNCT
ejpam-6018	223	26	h,ϖη	h,ϖη	PUNCT
ejpam-6018	223	27	)	)	PUNCT
ejpam-6018	223	28	are	be	AUX
ejpam-6018	223	29	n∈-subsets	n∈-subset	NOUN
ejpam-6018	223	30	of	of	ADP
ejpam-6018	223	31	(	(	PUNCT
ejpam-6018	223	32	h	h	NOUN
ejpam-6018	223	33	,	,	PUNCT
ejpam-6018	223	34	f	f	NOUN
ejpam-6018	223	35	)	)	PUNCT
ejpam-6018	223	36	.	.	PUNCT
ejpam-6018	224	1	that	that	PRON
ejpam-6018	224	2	is	be	AUX
ejpam-6018	224	3	,	,	PUNCT
ejpam-6018	224	4	ϱϖ	ϱϖ	VERB
ejpam-6018	224	5	|	|	ADV
ejpam-6018	224	6	ϱϖ	ϱϖ	VERB
ejpam-6018	224	7	∈	∈	PROPN
ejpam-6018	224	8	s∈(η	s∈(η	ADV
ejpam-6018	224	9	)	)	PUNCT
ejpam-6018	224	10	and	and	CCONJ
ejpam-6018	224	11	ϖ	ϖ	PRON
ejpam-6018	224	12	∈	∈	PROPN
ejpam-6018	224	13	s∈(η	s∈(η	NOUN
ejpam-6018	224	14	)	)	PUNCT
ejpam-6018	224	15	.	.	PUNCT
ejpam-6018	225	1	since	since	SCONJ
ejpam-6018	225	2	s∈(η	s∈(η	NOUN
ejpam-6018	225	3	)	)	PUNCT
ejpam-6018	225	4	is	be	AUX
ejpam-6018	225	5	an	an	DET
ejpam-6018	225	6	ideal	ideal	NOUN
ejpam-6018	225	7	of	of	ADP
ejpam-6018	225	8	h	h	NOUN
ejpam-6018	225	9	,	,	PUNCT
ejpam-6018	225	10	ϱ	ϱ	PROPN
ejpam-6018	225	11	∈	∈	PROPN
ejpam-6018	225	12	s∈(η	s∈(η	NOUN
ejpam-6018	225	13	)	)	PUNCT
ejpam-6018	225	14	.	.	PUNCT
ejpam-6018	226	1	hence	hence	ADV
ejpam-6018	226	2	,	,	PUNCT
ejpam-6018	226	3	(	(	PUNCT
ejpam-6018	226	4	h	h	NOUN
ejpam-6018	226	5	,	,	PUNCT
ejpam-6018	226	6	aη	aη	PROPN
ejpam-6018	226	7	)	)	PUNCT
ejpam-6018	226	8	is	be	AUX
ejpam-6018	226	9	an	an	DET
ejpam-6018	226	10	n∈-subset	n∈-subset	NOUN
ejpam-6018	226	11	of	of	ADP
ejpam-6018	226	12	(	(	PUNCT
ejpam-6018	226	13	h	h	NOUN
ejpam-6018	226	14	,	,	PUNCT
ejpam-6018	226	15	f	f	NOUN
ejpam-6018	226	16	)	)	PUNCT
ejpam-6018	226	17	,	,	PUNCT
ejpam-6018	226	18	and	and	CCONJ
ejpam-6018	226	19	so	so	ADV
ejpam-6018	226	20	f(ϱ	f(ϱ	NOUN
ejpam-6018	226	21	)	)	PUNCT
ejpam-6018	226	22	≤	≤	NUM
ejpam-6018	226	23	η	η	PROPN
ejpam-6018	226	24	.	.	PUNCT
ejpam-6018	227	1	this	this	PRON
ejpam-6018	227	2	is	be	AUX
ejpam-6018	227	3	a	a	DET
ejpam-6018	227	4	contradiction	contradiction	NOUN
ejpam-6018	227	5	,	,	PUNCT
ejpam-6018	227	6	and	and	CCONJ
ejpam-6018	227	7	therefore	therefore	ADV
ejpam-6018	227	8	f(ξ	f(ξ	NOUN
ejpam-6018	227	9	)	)	PUNCT
ejpam-6018	227	10	≤	≤	NUM
ejpam-6018	227	11	∨	∨	NUM
ejpam-6018	227	12	{	{	PUNCT
ejpam-6018	227	13	f(ξζ	f(ξζ	PROPN
ejpam-6018	227	14	|	|	ADV
ejpam-6018	227	15	ξζ	ξζ	NOUN
ejpam-6018	227	16	)	)	PUNCT
ejpam-6018	227	17	,	,	PUNCT
ejpam-6018	227	18	f(ζ	f(ζ	NOUN
ejpam-6018	227	19	)	)	PUNCT
ejpam-6018	227	20	}	}	PUNCT
ejpam-6018	227	21	for	for	ADP
ejpam-6018	227	22	all	all	DET
ejpam-6018	227	23	ξ	ξ	ADJ
ejpam-6018	227	24	,	,	PUNCT
ejpam-6018	227	25	ζ	ζ	PROPN
ejpam-6018	227	26	∈	∈	PROPN
ejpam-6018	227	27	h.	h.	NOUN
ejpam-6018	227	28	hence	hence	ADV
ejpam-6018	227	29	,	,	PUNCT
ejpam-6018	227	30	(	(	PUNCT
ejpam-6018	227	31	h	h	NOUN
ejpam-6018	227	32	,	,	PUNCT
ejpam-6018	227	33	f	f	X
ejpam-6018	227	34	)	)	PUNCT
ejpam-6018	227	35	is	be	AUX
ejpam-6018	227	36	an	an	DET
ejpam-6018	227	37	n	n	ADV
ejpam-6018	227	38	-ideal	-ideal	NOUN
ejpam-6018	227	39	of	of	ADP
ejpam-6018	227	40	type	type	NOUN
ejpam-6018	227	41	(	(	PUNCT
ejpam-6018	227	42	∈,∈	∈,∈	NOUN
ejpam-6018	227	43	)	)	PUNCT
ejpam-6018	227	44	.	.	PUNCT
ejpam-6018	228	1	conversely	conversely	ADV
ejpam-6018	228	2	,	,	PUNCT
ejpam-6018	228	3	assume	assume	VERB
ejpam-6018	228	4	that	that	SCONJ
ejpam-6018	228	5	(	(	PUNCT
ejpam-6018	228	6	h	h	NOUN
ejpam-6018	228	7	,	,	PUNCT
ejpam-6018	228	8	f	f	X
ejpam-6018	228	9	)	)	PUNCT
ejpam-6018	228	10	is	be	AUX
ejpam-6018	228	11	an	an	DET
ejpam-6018	228	12	n	n	ADV
ejpam-6018	228	13	-ideal	-ideal	NOUN
ejpam-6018	228	14	of	of	ADP
ejpam-6018	228	15	type	type	NOUN
ejpam-6018	228	16	(	(	PUNCT
ejpam-6018	228	17	∈,∈	∈,∈	X
ejpam-6018	228	18	)	)	PUNCT
ejpam-6018	228	19	and	and	CCONJ
ejpam-6018	228	20	let	let	VERB
ejpam-6018	228	21	η	η	PROPN
ejpam-6018	228	22	∈	∈	PROPN
ejpam-6018	228	23	υ	υ	NOUN
ejpam-6018	228	24	be	be	AUX
ejpam-6018	228	25	such	such	ADJ
ejpam-6018	228	26	that	that	SCONJ
ejpam-6018	228	27	s∈(η	s∈(η	NOUN
ejpam-6018	228	28	)	)	PUNCT
ejpam-6018	228	29	̸=	̸=	PROPN
ejpam-6018	228	30	∅.	∅.	ADV
ejpam-6018	228	31	then	then	ADV
ejpam-6018	228	32	there	there	PRON
ejpam-6018	228	33	exists	exist	VERB
ejpam-6018	228	34	ξ	ξ	PROPN
ejpam-6018	228	35	∈	∈	PROPN
ejpam-6018	228	36	s∈(η	s∈(η	X
ejpam-6018	228	37	)	)	PUNCT
ejpam-6018	228	38	,	,	PUNCT
ejpam-6018	228	39	and	and	CCONJ
ejpam-6018	228	40	so	so	ADV
ejpam-6018	228	41	(	(	PUNCT
ejpam-6018	228	42	h	h	NOUN
ejpam-6018	228	43	,	,	PUNCT
ejpam-6018	228	44	ξη	ξη	PRON
ejpam-6018	228	45	)	)	PUNCT
ejpam-6018	228	46	is	be	AUX
ejpam-6018	228	47	an	an	DET
ejpam-6018	228	48	n∈-subset	n∈-subset	NOUN
ejpam-6018	228	49	of	of	ADP
ejpam-6018	228	50	(	(	PUNCT
ejpam-6018	228	51	h	h	NOUN
ejpam-6018	228	52	,	,	PUNCT
ejpam-6018	228	53	f	f	NOUN
ejpam-6018	228	54	)	)	PUNCT
ejpam-6018	228	55	.	.	PUNCT
ejpam-6018	229	1	it	it	PRON
ejpam-6018	229	2	follows	follow	VERB
ejpam-6018	229	3	that	that	SCONJ
ejpam-6018	229	4	f(0	f(0	NOUN
ejpam-6018	229	5	)	)	PUNCT
ejpam-6018	229	6	≤	≤	NOUN
ejpam-6018	229	7	f(ξ	f(ξ	NOUN
ejpam-6018	229	8	)	)	PUNCT
ejpam-6018	229	9	≤	≤	NUM
ejpam-6018	229	10	η	η	PROPN
ejpam-6018	229	11	and	and	CCONJ
ejpam-6018	229	12	so	so	SCONJ
ejpam-6018	229	13	that	that	SCONJ
ejpam-6018	229	14	(	(	PUNCT
ejpam-6018	229	15	h	h	NOUN
ejpam-6018	229	16	,	,	PUNCT
ejpam-6018	229	17	0η	0η	NUM
ejpam-6018	229	18	)	)	PUNCT
ejpam-6018	229	19	is	be	AUX
ejpam-6018	229	20	an	an	DET
ejpam-6018	229	21	n∈-subset	n∈-subset	NOUN
ejpam-6018	229	22	of	of	ADP
ejpam-6018	229	23	(	(	PUNCT
ejpam-6018	229	24	h	h	NOUN
ejpam-6018	229	25	,	,	PUNCT
ejpam-6018	229	26	f	f	PROPN
ejpam-6018	229	27	)	)	PUNCT
ejpam-6018	229	28	,	,	PUNCT
ejpam-6018	229	29	that	that	ADV
ejpam-6018	229	30	is	is	ADV
ejpam-6018	229	31	,	,	PUNCT
ejpam-6018	229	32	0	0	NUM
ejpam-6018	229	33	∈	∈	PROPN
ejpam-6018	229	34	s∈(η	s∈(η	NOUN
ejpam-6018	229	35	)	)	PUNCT
ejpam-6018	229	36	.	.	PUNCT
ejpam-6018	230	1	let	let	VERB
ejpam-6018	231	1	ξζ	ξζ	INTJ
ejpam-6018	231	2	|	|	ADV
ejpam-6018	231	3	ξζ	ξζ	VERB
ejpam-6018	231	4	∈	∈	PROPN
ejpam-6018	231	5	s∈(η	s∈(η	ADV
ejpam-6018	231	6	)	)	PUNCT
ejpam-6018	231	7	and	and	CCONJ
ejpam-6018	231	8	ζ	ζ	NOUN
ejpam-6018	231	9	∈	∈	PROPN
ejpam-6018	231	10	s∈(η	s∈(η	NOUN
ejpam-6018	231	11	)	)	PUNCT
ejpam-6018	231	12	.	.	PUNCT
ejpam-6018	232	1	then	then	ADV
ejpam-6018	232	2	(	(	PUNCT
ejpam-6018	232	3	h	h	NOUN
ejpam-6018	232	4	,	,	PUNCT
ejpam-6018	232	5	(	(	PUNCT
ejpam-6018	232	6	ξζ	ξζ	NOUN
ejpam-6018	232	7	|	|	ADV
ejpam-6018	232	8	ξζ)η	ξζ)η	PROPN
ejpam-6018	232	9	)	)	PUNCT
ejpam-6018	232	10	and	and	CCONJ
ejpam-6018	232	11	(	(	PUNCT
ejpam-6018	232	12	h	h	NOUN
ejpam-6018	232	13	,	,	PUNCT
ejpam-6018	232	14	ζη	ζη	ADJ
ejpam-6018	232	15	)	)	PUNCT
ejpam-6018	232	16	are	be	AUX
ejpam-6018	232	17	n∈-subsets	n∈-subset	NOUN
ejpam-6018	232	18	of	of	ADP
ejpam-6018	232	19	(	(	PUNCT
ejpam-6018	232	20	h	h	NOUN
ejpam-6018	232	21	,	,	PUNCT
ejpam-6018	232	22	f	f	NOUN
ejpam-6018	232	23	)	)	PUNCT
ejpam-6018	232	24	.	.	PUNCT
ejpam-6018	233	1	thus	thus	ADV
ejpam-6018	233	2	,	,	PUNCT
ejpam-6018	233	3	f(ξζ	f(ξζ	PROPN
ejpam-6018	233	4	|	|	ADV
ejpam-6018	233	5	ξζ	ξζ	NOUN
ejpam-6018	233	6	)	)	PUNCT
ejpam-6018	233	7	≤	≤	PROPN
ejpam-6018	233	8	η	η	PROPN
ejpam-6018	233	9	and	and	CCONJ
ejpam-6018	233	10	f(ζ	f(ζ	PROPN
ejpam-6018	233	11	)	)	PUNCT
ejpam-6018	233	12	≤	≤	PROPN
ejpam-6018	233	13	η	η	PROPN
ejpam-6018	233	14	.	.	PUNCT
ejpam-6018	234	1	it	it	PRON
ejpam-6018	234	2	follows	follow	VERB
ejpam-6018	234	3	from	from	ADP
ejpam-6018	234	4	(	(	PUNCT
ejpam-6018	234	5	4	4	NUM
ejpam-6018	234	6	)	)	PUNCT
ejpam-6018	234	7	that	that	SCONJ
ejpam-6018	234	8	f(ξ	f(ξ	NOUN
ejpam-6018	234	9	)	)	PUNCT
ejpam-6018	234	10	≤	≤	NUM
ejpam-6018	234	11	∨	∨	NUM
ejpam-6018	234	12	{	{	PUNCT
ejpam-6018	234	13	f(ξζ	f(ξζ	PROPN
ejpam-6018	234	14	|	|	ADV
ejpam-6018	234	15	ξζ	ξζ	NOUN
ejpam-6018	234	16	)	)	PUNCT
ejpam-6018	234	17	,	,	PUNCT
ejpam-6018	234	18	f(y	f(y	NOUN
ejpam-6018	234	19	)	)	PUNCT
ejpam-6018	234	20	}	}	PUNCT
ejpam-6018	234	21	≤	≤	NUM
ejpam-6018	234	22	η	η	PROPN
ejpam-6018	234	23	.	.	PROPN
ejpam-6018	234	24	hence	hence	ADV
ejpam-6018	234	25	,	,	PUNCT
ejpam-6018	234	26	(	(	PUNCT
ejpam-6018	234	27	h	h	NOUN
ejpam-6018	234	28	,	,	PUNCT
ejpam-6018	234	29	ξη	ξη	NOUN
ejpam-6018	234	30	)	)	PUNCT
ejpam-6018	234	31	=	=	SYM
ejpam-6018	234	32	(	(	PUNCT
ejpam-6018	234	33	h	h	NOUN
ejpam-6018	234	34	,	,	PUNCT
ejpam-6018	234	35	ξη∨η	ξη∨η	NOUN
ejpam-6018	234	36	)	)	PUNCT
ejpam-6018	234	37	is	be	AUX
ejpam-6018	234	38	an	an	DET
ejpam-6018	234	39	n∈-subset	n∈-subset	NOUN
ejpam-6018	234	40	of	of	ADP
ejpam-6018	234	41	(	(	PUNCT
ejpam-6018	234	42	h	h	NOUN
ejpam-6018	234	43	,	,	PUNCT
ejpam-6018	234	44	f	f	NOUN
ejpam-6018	234	45	)	)	PUNCT
ejpam-6018	234	46	,	,	PUNCT
ejpam-6018	234	47	and	and	CCONJ
ejpam-6018	234	48	so	so	ADV
ejpam-6018	234	49	ξ	ξ	PROPN
ejpam-6018	234	50	∈	∈	PROPN
ejpam-6018	234	51	s∈(η	s∈(η	NOUN
ejpam-6018	234	52	)	)	PUNCT
ejpam-6018	234	53	.	.	PUNCT
ejpam-6018	235	1	thus	thus	ADV
ejpam-6018	235	2	,	,	PUNCT
ejpam-6018	235	3	s∈(η	s∈(η	ADV
ejpam-6018	235	4	)	)	PUNCT
ejpam-6018	235	5	is	be	AUX
ejpam-6018	235	6	an	an	DET
ejpam-6018	235	7	ideal	ideal	NOUN
ejpam-6018	235	8	of	of	ADP
ejpam-6018	235	9	h	h	NOUN
ejpam-6018	235	10	for	for	ADP
ejpam-6018	235	11	all	all	DET
ejpam-6018	235	12	η	η	PROPN
ejpam-6018	235	13	∈	∈	PROPN
ejpam-6018	235	14	υ	υ	NOUN
ejpam-6018	235	15	,	,	PUNCT
ejpam-6018	235	16	and	and	CCONJ
ejpam-6018	235	17	therefore	therefore	ADV
ejpam-6018	235	18	(	(	PUNCT
ejpam-6018	235	19	s∈,υ	s∈,υ	NOUN
ejpam-6018	235	20	)	)	PUNCT
ejpam-6018	235	21	is	be	AUX
ejpam-6018	235	22	a	a	DET
ejpam-6018	235	23	soft	soft	ADJ
ejpam-6018	235	24	n	n	NOUN
ejpam-6018	235	25	-ideal	-ideal	ADJ
ejpam-6018	235	26	over	over	ADP
ejpam-6018	235	27	h	h	NOUN
ejpam-6018	235	28	for	for	ADP
ejpam-6018	235	29	υ	υ	NOUN
ejpam-6018	235	30	=	=	PUNCT
ejpam-6018	236	1	[	[	X
ejpam-6018	236	2	−1	−1	NOUN
ejpam-6018	236	3	,	,	PUNCT
ejpam-6018	236	4	0	0	NUM
ejpam-6018	236	5	)	)	PUNCT
ejpam-6018	236	6	.	.	PUNCT
ejpam-6018	237	1	t.	t.	PROPN
ejpam-6018	237	2	oner	oner	PROPN
ejpam-6018	237	3	et	et	PROPN
ejpam-6018	237	4	al	al	PROPN
ejpam-6018	237	5	.	.	PUNCT
ejpam-6018	237	6	/	/	SYM
ejpam-6018	237	7	eur	eur	PROPN
ejpam-6018	237	8	.	.	PUNCT
ejpam-6018	238	1	j.	j.	PROPN
ejpam-6018	238	2	pure	pure	PROPN
ejpam-6018	238	3	appl	appl	PROPN
ejpam-6018	238	4	.	.	PROPN
ejpam-6018	238	5	math	math	PROPN
ejpam-6018	238	6	,	,	PUNCT
ejpam-6018	238	7	18	18	NUM
ejpam-6018	238	8	(	(	PUNCT
ejpam-6018	238	9	2	2	NUM
ejpam-6018	238	10	)	)	PUNCT
ejpam-6018	238	11	(	(	PUNCT
ejpam-6018	238	12	2025	2025	NUM
ejpam-6018	238	13	)	)	PUNCT
ejpam-6018	238	14	,	,	PUNCT
ejpam-6018	238	15	6018	6018	NUM
ejpam-6018	238	16	9	9	NUM
ejpam-6018	238	17	of	of	ADP
ejpam-6018	238	18	11	11	NUM
ejpam-6018	238	19	theorem	theorem	NOUN
ejpam-6018	238	20	8	8	NUM
ejpam-6018	238	21	.	.	PUNCT
ejpam-6018	239	1	let	let	VERB
ejpam-6018	239	2	hs	hs	PRON
ejpam-6018	239	3	:	:	PUNCT
ejpam-6018	239	4	=	=	SYM
ejpam-6018	239	5	(	(	PUNCT
ejpam-6018	239	6	h	h	NOUN
ejpam-6018	239	7	,	,	PUNCT
ejpam-6018	239	8	|	|	ADV
ejpam-6018	239	9	,	,	PUNCT
ejpam-6018	239	10	0	0	NUM
ejpam-6018	239	11	)	)	PUNCT
ejpam-6018	239	12	be	be	AUX
ejpam-6018	239	13	an	an	DET
ejpam-6018	239	14	ssh	ssh	NOUN
ejpam-6018	239	15	-	-	PUNCT
ejpam-6018	239	16	algebra	algebra	NOUN
ejpam-6018	239	17	.	.	PUNCT
ejpam-6018	240	1	the	the	DET
ejpam-6018	240	2	soft	soft	ADJ
ejpam-6018	240	3	nq	nq	NOUN
ejpam-6018	240	4	-	-	PUNCT
ejpam-6018	240	5	set	set	VERB
ejpam-6018	240	6	(	(	PUNCT
ejpam-6018	240	7	sq	sq	ADJ
ejpam-6018	240	8	,	,	PUNCT
ejpam-6018	240	9	υ	υ	NOUN
ejpam-6018	240	10	)	)	PUNCT
ejpam-6018	240	11	is	be	AUX
ejpam-6018	240	12	a	a	DET
ejpam-6018	240	13	soft	soft	ADJ
ejpam-6018	240	14	n	n	NOUN
ejpam-6018	240	15	-ideal	-ideal	ADJ
ejpam-6018	240	16	over	over	ADP
ejpam-6018	240	17	h	h	NOUN
ejpam-6018	240	18	for	for	ADP
ejpam-6018	240	19	υ	υ	NOUN
ejpam-6018	240	20	=	=	PUNCT
ejpam-6018	241	1	[	[	X
ejpam-6018	241	2	−1	−1	NOUN
ejpam-6018	241	3	,	,	PUNCT
ejpam-6018	241	4	0	0	NUM
ejpam-6018	241	5	)	)	PUNCT
ejpam-6018	241	6	if	if	SCONJ
ejpam-6018	241	7	and	and	CCONJ
ejpam-6018	241	8	only	only	ADV
ejpam-6018	241	9	if	if	SCONJ
ejpam-6018	241	10	the	the	DET
ejpam-6018	241	11	n	n	ADV
ejpam-6018	241	12	-structure	-structure	NOUN
ejpam-6018	241	13	(	(	PUNCT
ejpam-6018	241	14	h	h	NOUN
ejpam-6018	241	15	,	,	PUNCT
ejpam-6018	241	16	f	f	X
ejpam-6018	241	17	)	)	PUNCT
ejpam-6018	241	18	is	be	AUX
ejpam-6018	241	19	an	an	DET
ejpam-6018	241	20	n	n	ADV
ejpam-6018	241	21	-ideal	-ideal	NOUN
ejpam-6018	241	22	of	of	ADP
ejpam-6018	241	23	type	type	NOUN
ejpam-6018	241	24	(	(	PUNCT
ejpam-6018	241	25	∈,∈	∈,∈	NOUN
ejpam-6018	241	26	)	)	PUNCT
ejpam-6018	241	27	.	.	PUNCT
ejpam-6018	242	1	proof	proof	NOUN
ejpam-6018	242	2	.	.	PUNCT
ejpam-6018	243	1	assume	assume	VERB
ejpam-6018	243	2	that	that	SCONJ
ejpam-6018	243	3	(	(	PUNCT
ejpam-6018	243	4	h	h	NOUN
ejpam-6018	243	5	,	,	PUNCT
ejpam-6018	243	6	f	f	X
ejpam-6018	243	7	)	)	PUNCT
ejpam-6018	243	8	is	be	AUX
ejpam-6018	243	9	an	an	DET
ejpam-6018	243	10	n	n	ADV
ejpam-6018	243	11	-ideal	-ideal	NOUN
ejpam-6018	243	12	of	of	ADP
ejpam-6018	243	13	type	type	NOUN
ejpam-6018	243	14	(	(	PUNCT
ejpam-6018	243	15	∈,∈	∈,∈	NOUN
ejpam-6018	243	16	)	)	PUNCT
ejpam-6018	243	17	,	,	PUNCT
ejpam-6018	243	18	and	and	CCONJ
ejpam-6018	243	19	let	let	VERB
ejpam-6018	243	20	η	η	PROPN
ejpam-6018	243	21	∈	∈	PROPN
ejpam-6018	243	22	υ	υ	NOUN
ejpam-6018	243	23	be	be	AUX
ejpam-6018	243	24	such	such	ADJ
ejpam-6018	243	25	that	that	SCONJ
ejpam-6018	243	26	sq(η	sq(η	NOUN
ejpam-6018	243	27	)	)	PUNCT
ejpam-6018	243	28	̸=	̸=	PROPN
ejpam-6018	243	29	∅.	∅.	ADP
ejpam-6018	243	30	this	this	DET
ejpam-6018	243	31	implies	imply	VERB
ejpam-6018	243	32	there	there	PRON
ejpam-6018	243	33	exists	exist	VERB
ejpam-6018	243	34	ξ	ξ	PROPN
ejpam-6018	243	35	∈	∈	PROPN
ejpam-6018	243	36	sq(η	sq(η	NUM
ejpam-6018	243	37	)	)	PUNCT
ejpam-6018	243	38	,	,	PUNCT
ejpam-6018	243	39	so	so	CCONJ
ejpam-6018	243	40	(	(	PUNCT
ejpam-6018	243	41	h	h	NOUN
ejpam-6018	243	42	,	,	PUNCT
ejpam-6018	243	43	ξη	ξη	PRON
ejpam-6018	243	44	)	)	PUNCT
ejpam-6018	243	45	is	be	AUX
ejpam-6018	243	46	an	an	DET
ejpam-6018	243	47	nq	nq	NOUN
ejpam-6018	243	48	-	-	PUNCT
ejpam-6018	243	49	subset	subset	NOUN
ejpam-6018	243	50	of	of	ADP
ejpam-6018	243	51	(	(	PUNCT
ejpam-6018	243	52	h	h	NOUN
ejpam-6018	243	53	,	,	PUNCT
ejpam-6018	243	54	f	f	NOUN
ejpam-6018	243	55	)	)	PUNCT
ejpam-6018	243	56	.	.	PUNCT
ejpam-6018	244	1	if	if	SCONJ
ejpam-6018	244	2	0	0	NUM
ejpam-6018	244	3	/∈	/∈	NUM
ejpam-6018	244	4	sq(η	sq(η	NOUN
ejpam-6018	244	5	)	)	PUNCT
ejpam-6018	244	6	,	,	PUNCT
ejpam-6018	244	7	then	then	ADV
ejpam-6018	244	8	(	(	PUNCT
ejpam-6018	244	9	h	h	NOUN
ejpam-6018	244	10	,	,	PUNCT
ejpam-6018	244	11	0q	0q	NUM
ejpam-6018	244	12	)	)	PUNCT
ejpam-6018	244	13	is	be	AUX
ejpam-6018	244	14	not	not	PART
ejpam-6018	244	15	an	an	DET
ejpam-6018	244	16	nq	nq	NOUN
ejpam-6018	244	17	-	-	PUNCT
ejpam-6018	244	18	subset	subset	NOUN
ejpam-6018	244	19	of	of	ADP
ejpam-6018	244	20	(	(	PUNCT
ejpam-6018	244	21	h	h	NOUN
ejpam-6018	244	22	,	,	PUNCT
ejpam-6018	244	23	f	f	PROPN
ejpam-6018	244	24	)	)	PUNCT
ejpam-6018	244	25	,	,	PUNCT
ejpam-6018	244	26	which	which	PRON
ejpam-6018	244	27	implies	imply	VERB
ejpam-6018	244	28	f(0)+	f(0)+	NOUN
ejpam-6018	244	29	η+1	η+1	X
ejpam-6018	244	30	<	<	X
ejpam-6018	244	31	0	0	X
ejpam-6018	244	32	.	.	PUNCT
ejpam-6018	245	1	using	use	VERB
ejpam-6018	245	2	(	(	PUNCT
ejpam-6018	245	3	4	4	NUM
ejpam-6018	245	4	)	)	PUNCT
ejpam-6018	245	5	,	,	PUNCT
ejpam-6018	245	6	we	we	PRON
ejpam-6018	245	7	obtain	obtain	VERB
ejpam-6018	245	8	f(ξ	f(ξ	NOUN
ejpam-6018	245	9	)	)	PUNCT
ejpam-6018	246	1	+	+	NUM
ejpam-6018	246	2	η	η	PROPN
ejpam-6018	246	3	+	+	PROPN
ejpam-6018	246	4	1	1	NUM
ejpam-6018	246	5	≥	≥	NOUN
ejpam-6018	246	6	f(0	f(0	NOUN
ejpam-6018	246	7	)	)	PUNCT
ejpam-6018	247	1	+	+	NUM
ejpam-6018	247	2	η	η	PROPN
ejpam-6018	247	3	+	+	PROPN
ejpam-6018	247	4	1	1	NUM
ejpam-6018	247	5	≥	≥	NOUN
ejpam-6018	247	6	0	0	NUM
ejpam-6018	247	7	,	,	PUNCT
ejpam-6018	247	8	leading	lead	VERB
ejpam-6018	247	9	to	to	ADP
ejpam-6018	247	10	a	a	DET
ejpam-6018	247	11	contradiction	contradiction	NOUN
ejpam-6018	247	12	,	,	PUNCT
ejpam-6018	247	13	thus	thus	ADV
ejpam-6018	247	14	0	0	NUM
ejpam-6018	247	15	∈	∈	NOUN
ejpam-6018	247	16	sq(η	sq(η	NUM
ejpam-6018	247	17	)	)	PUNCT
ejpam-6018	247	18	.	.	PUNCT
ejpam-6018	248	1	next	next	ADV
ejpam-6018	248	2	,	,	PUNCT
ejpam-6018	248	3	consider	consider	VERB
ejpam-6018	248	4	ξζ	ξζ	NOUN
ejpam-6018	249	1	|	|	ADV
ejpam-6018	249	2	ξζ	ξζ	INTJ
ejpam-6018	249	3	∈	∈	PROPN
ejpam-6018	249	4	sq(η	sq(η	X
ejpam-6018	249	5	)	)	PUNCT
ejpam-6018	249	6	and	and	CCONJ
ejpam-6018	249	7	ζ	ζ	NOUN
ejpam-6018	249	8	∈	∈	NOUN
ejpam-6018	249	9	sq(η	sq(η	NUM
ejpam-6018	249	10	)	)	PUNCT
ejpam-6018	249	11	.	.	PUNCT
ejpam-6018	250	1	then	then	ADV
ejpam-6018	250	2	(	(	PUNCT
ejpam-6018	250	3	h	h	NOUN
ejpam-6018	250	4	,	,	PUNCT
ejpam-6018	250	5	(	(	PUNCT
ejpam-6018	250	6	ξζ	ξζ	NOUN
ejpam-6018	250	7	|	|	ADV
ejpam-6018	250	8	ξζ)η	ξζ)η	PROPN
ejpam-6018	250	9	)	)	PUNCT
ejpam-6018	250	10	and	and	CCONJ
ejpam-6018	250	11	(	(	PUNCT
ejpam-6018	250	12	h	h	NOUN
ejpam-6018	250	13	,	,	PUNCT
ejpam-6018	250	14	ζη	ζη	ADJ
ejpam-6018	250	15	)	)	PUNCT
ejpam-6018	250	16	are	be	AUX
ejpam-6018	250	17	nq	nq	NOUN
ejpam-6018	250	18	-	-	PUNCT
ejpam-6018	250	19	subsets	subset	NOUN
ejpam-6018	250	20	of	of	ADP
ejpam-6018	250	21	(	(	PUNCT
ejpam-6018	250	22	h	h	NOUN
ejpam-6018	250	23	,	,	PUNCT
ejpam-6018	250	24	f	f	NOUN
ejpam-6018	250	25	)	)	PUNCT
ejpam-6018	250	26	.	.	PUNCT
ejpam-6018	251	1	if	if	SCONJ
ejpam-6018	251	2	(	(	PUNCT
ejpam-6018	251	3	h	h	NOUN
ejpam-6018	251	4	,	,	PUNCT
ejpam-6018	251	5	ξη	ξη	PRON
ejpam-6018	251	6	)	)	PUNCT
ejpam-6018	251	7	is	be	AUX
ejpam-6018	251	8	not	not	PART
ejpam-6018	251	9	an	an	DET
ejpam-6018	251	10	nq	nq	NOUN
ejpam-6018	251	11	-	-	PUNCT
ejpam-6018	251	12	subset	subset	NOUN
ejpam-6018	251	13	of	of	ADP
ejpam-6018	251	14	(	(	PUNCT
ejpam-6018	251	15	h	h	NOUN
ejpam-6018	251	16	,	,	PUNCT
ejpam-6018	251	17	f	f	PROPN
ejpam-6018	251	18	)	)	PUNCT
ejpam-6018	251	19	,	,	PUNCT
ejpam-6018	251	20	then	then	ADV
ejpam-6018	251	21	f(ξ	f(ξ	NOUN
ejpam-6018	251	22	)	)	PUNCT
ejpam-6018	251	23	+	+	NUM
ejpam-6018	251	24	η	η	PROPN
ejpam-6018	251	25	+	+	PROPN
ejpam-6018	251	26	1	1	NUM
ejpam-6018	251	27	≥	≥	NOUN
ejpam-6018	251	28	0	0	NUM
ejpam-6018	251	29	.	.	PUNCT
ejpam-6018	252	1	from	from	ADP
ejpam-6018	252	2	(	(	PUNCT
ejpam-6018	252	3	4	4	NUM
ejpam-6018	252	4	)	)	PUNCT
ejpam-6018	252	5	,	,	PUNCT
ejpam-6018	252	6	we	we	PRON
ejpam-6018	252	7	have	have	VERB
ejpam-6018	252	8	∨	∨	NOUN
ejpam-6018	252	9	{	{	PUNCT
ejpam-6018	252	10	f(ξζ	f(ξζ	NOUN
ejpam-6018	252	11	|	|	ADV
ejpam-6018	252	12	ξζ	ξζ	NOUN
ejpam-6018	252	13	)	)	PUNCT
ejpam-6018	252	14	,	,	PUNCT
ejpam-6018	252	15	f(ζ)}+η+1	f(ζ)}+η+1	NOUN
ejpam-6018	252	16	≥	≥	X
ejpam-6018	252	17	f(ξ)+η+1	f(ξ)+η+1	VERB
ejpam-6018	252	18	≥	≥	NOUN
ejpam-6018	252	19	0	0	NUM
ejpam-6018	252	20	.	.	PUNCT
ejpam-6018	253	1	hence	hence	ADV
ejpam-6018	253	2	,	,	PUNCT
ejpam-6018	253	3	either	either	CCONJ
ejpam-6018	253	4	f(ξζ	f(ξζ	PROPN
ejpam-6018	253	5	|	|	ADV
ejpam-6018	253	6	ξζ)+η+1	ξζ)+η+1	X
ejpam-6018	253	7	≥	≥	PROPN
ejpam-6018	253	8	0	0	NUM
ejpam-6018	253	9	or	or	CCONJ
ejpam-6018	253	10	f(ζ	f(ζ	NOUN
ejpam-6018	253	11	)	)	PUNCT
ejpam-6018	254	1	+	+	CCONJ
ejpam-6018	254	2	η	η	PROPN
ejpam-6018	254	3	+	+	PROPN
ejpam-6018	254	4	1	1	NUM
ejpam-6018	254	5	≥	≥	NOUN
ejpam-6018	254	6	0	0	NUM
ejpam-6018	254	7	,	,	PUNCT
ejpam-6018	254	8	leading	lead	VERB
ejpam-6018	254	9	to	to	ADP
ejpam-6018	254	10	a	a	DET
ejpam-6018	254	11	contradiction	contradiction	NOUN
ejpam-6018	254	12	.	.	PUNCT
ejpam-6018	255	1	thus	thus	ADV
ejpam-6018	255	2	,	,	PUNCT
ejpam-6018	255	3	ξ	ξ	PROPN
ejpam-6018	255	4	∈	∈	PROPN
ejpam-6018	255	5	sq(η	sq(η	NUM
ejpam-6018	255	6	)	)	PUNCT
ejpam-6018	255	7	.	.	PUNCT
ejpam-6018	256	1	therefore	therefore	ADV
ejpam-6018	256	2	,	,	PUNCT
ejpam-6018	256	3	(	(	PUNCT
ejpam-6018	256	4	sq	sq	ADJ
ejpam-6018	256	5	,	,	PUNCT
ejpam-6018	256	6	υ	υ	NOUN
ejpam-6018	256	7	)	)	PUNCT
ejpam-6018	256	8	is	be	AUX
ejpam-6018	256	9	a	a	DET
ejpam-6018	256	10	soft	soft	ADJ
ejpam-6018	256	11	n	n	NOUN
ejpam-6018	256	12	-ideal	-ideal	ADJ
ejpam-6018	256	13	over	over	ADP
ejpam-6018	256	14	h	h	NOUN
ejpam-6018	256	15	for	for	ADP
ejpam-6018	256	16	υ	υ	NOUN
ejpam-6018	256	17	=	=	PUNCT
ejpam-6018	257	1	[	[	X
ejpam-6018	257	2	−1	−1	NOUN
ejpam-6018	257	3	,	,	PUNCT
ejpam-6018	257	4	0	0	NUM
ejpam-6018	257	5	)	)	PUNCT
ejpam-6018	257	6	.	.	PUNCT
ejpam-6018	258	1	conversely	conversely	ADV
ejpam-6018	258	2	,	,	PUNCT
ejpam-6018	258	3	suppose	suppose	VERB
ejpam-6018	258	4	that	that	SCONJ
ejpam-6018	258	5	the	the	DET
ejpam-6018	258	6	softnq	softnq	NOUN
ejpam-6018	258	7	-	-	PUNCT
ejpam-6018	258	8	set	set	VERB
ejpam-6018	258	9	(	(	PUNCT
ejpam-6018	258	10	sq	sq	ADJ
ejpam-6018	258	11	,	,	PUNCT
ejpam-6018	258	12	υ	υ	NOUN
ejpam-6018	258	13	)	)	PUNCT
ejpam-6018	258	14	is	be	AUX
ejpam-6018	258	15	a	a	DET
ejpam-6018	258	16	softn	softn	ADJ
ejpam-6018	258	17	-ideal	-ideal	ADJ
ejpam-6018	258	18	overh	overh	NOUN
ejpam-6018	258	19	for	for	ADP
ejpam-6018	258	20	υ	υ	NOUN
ejpam-6018	258	21	=	=	PUNCT
ejpam-6018	259	1	[	[	X
ejpam-6018	259	2	−1	−1	NOUN
ejpam-6018	259	3	,	,	PUNCT
ejpam-6018	259	4	0	0	NUM
ejpam-6018	259	5	)	)	PUNCT
ejpam-6018	259	6	.	.	PUNCT
ejpam-6018	260	1	if	if	SCONJ
ejpam-6018	260	2	f(0	f(0	NOUN
ejpam-6018	260	3	)	)	PUNCT
ejpam-6018	260	4	>	>	SYM
ejpam-6018	260	5	f(ϱ	f(ϱ	PROPN
ejpam-6018	260	6	)	)	PUNCT
ejpam-6018	260	7	for	for	ADP
ejpam-6018	260	8	some	some	DET
ejpam-6018	260	9	ϱ	ϱ	PROPN
ejpam-6018	260	10	∈	∈	PROPN
ejpam-6018	260	11	h	h	NOUN
ejpam-6018	260	12	,	,	PUNCT
ejpam-6018	260	13	then	then	ADV
ejpam-6018	260	14	there	there	PRON
ejpam-6018	260	15	exists	exist	VERB
ejpam-6018	260	16	δ	δ	PROPN
ejpam-6018	260	17	∈	∈	PROPN
ejpam-6018	260	18	υ	υ	ADP
ejpam-6018	260	19	such	such	ADJ
ejpam-6018	260	20	that	that	DET
ejpam-6018	260	21	f(0	f(0	NOUN
ejpam-6018	260	22	)	)	PUNCT
ejpam-6018	261	1	+	+	NUM
ejpam-6018	261	2	δ	δ	X
ejpam-6018	261	3	+	+	CCONJ
ejpam-6018	261	4	1	1	NUM
ejpam-6018	261	5	≥	≥	NOUN
ejpam-6018	261	6	0	0	NUM
ejpam-6018	261	7	and	and	CCONJ
ejpam-6018	261	8	f(ϱ	f(ϱ	NOUN
ejpam-6018	261	9	)	)	PUNCT
ejpam-6018	261	10	+	+	NUM
ejpam-6018	261	11	δ	δ	X
ejpam-6018	261	12	+	+	CCONJ
ejpam-6018	261	13	1	1	NUM
ejpam-6018	261	14	≥	≥	NOUN
ejpam-6018	261	15	0	0	NUM
ejpam-6018	261	16	.	.	PUNCT
ejpam-6018	262	1	this	this	PRON
ejpam-6018	262	2	implies	imply	VERB
ejpam-6018	262	3	that	that	SCONJ
ejpam-6018	262	4	(	(	PUNCT
ejpam-6018	262	5	h	h	NOUN
ejpam-6018	262	6	,	,	PUNCT
ejpam-6018	262	7	ϱδ	ϱδ	PROPN
ejpam-6018	262	8	)	)	PUNCT
ejpam-6018	262	9	is	be	AUX
ejpam-6018	262	10	an	an	DET
ejpam-6018	262	11	nq	nq	NOUN
ejpam-6018	262	12	-	-	PUNCT
ejpam-6018	262	13	subset	subset	NOUN
ejpam-6018	262	14	of	of	ADP
ejpam-6018	262	15	(	(	PUNCT
ejpam-6018	262	16	h	h	NOUN
ejpam-6018	262	17	,	,	PUNCT
ejpam-6018	262	18	f	f	NOUN
ejpam-6018	262	19	)	)	PUNCT
ejpam-6018	262	20	,	,	PUNCT
ejpam-6018	262	21	and	and	CCONJ
ejpam-6018	262	22	(	(	PUNCT
ejpam-6018	262	23	h	h	NOUN
ejpam-6018	262	24	,	,	PUNCT
ejpam-6018	262	25	0	0	NUM
ejpam-6018	262	26	)	)	PUNCT
ejpam-6018	262	27	is	be	AUX
ejpam-6018	262	28	an	an	DET
ejpam-6018	262	29	nq	nq	NOUN
ejpam-6018	262	30	-	-	PUNCT
ejpam-6018	262	31	subset	subset	NOUN
ejpam-6018	262	32	of	of	ADP
ejpam-6018	262	33	(	(	PUNCT
ejpam-6018	262	34	h	h	NOUN
ejpam-6018	262	35	,	,	PUNCT
ejpam-6018	262	36	f	f	PROPN
ejpam-6018	262	37	)	)	PUNCT
ejpam-6018	262	38	,	,	PUNCT
ejpam-6018	262	39	leading	lead	VERB
ejpam-6018	262	40	to	to	ADP
ejpam-6018	262	41	a	a	DET
ejpam-6018	262	42	contradiction	contradiction	NOUN
ejpam-6018	262	43	.	.	PUNCT
ejpam-6018	263	1	thus	thus	ADV
ejpam-6018	263	2	,	,	PUNCT
ejpam-6018	263	3	f(0	f(0	NOUN
ejpam-6018	263	4	)	)	PUNCT
ejpam-6018	263	5	≤	≤	NOUN
ejpam-6018	263	6	f(ξ	f(ξ	NOUN
ejpam-6018	263	7	)	)	PUNCT
ejpam-6018	263	8	for	for	ADP
ejpam-6018	263	9	all	all	DET
ejpam-6018	263	10	ξ	ξ	PROPN
ejpam-6018	263	11	∈	∈	PROPN
ejpam-6018	263	12	h.	h.	NOUN
ejpam-6018	263	13	suppose	suppose	VERB
ejpam-6018	263	14	there	there	PRON
ejpam-6018	263	15	exist	exist	VERB
ejpam-6018	263	16	ϱ,ϖ	ϱ,ϖ	NOUN
ejpam-6018	263	17	∈	∈	PROPN
ejpam-6018	263	18	h	h	NOUN
ejpam-6018	264	1	such	such	ADJ
ejpam-6018	264	2	that	that	SCONJ
ejpam-6018	264	3	f(ϱ	f(ϱ	NOUN
ejpam-6018	264	4	)	)	PUNCT
ejpam-6018	264	5	>	>	PUNCT
ejpam-6018	264	6	∨	∨	X
ejpam-6018	264	7	{	{	PUNCT
ejpam-6018	264	8	f(ϱϖ	f(ϱϖ	NOUN
ejpam-6018	264	9	|	|	NOUN
ejpam-6018	264	10	ϱϖ	ϱϖ	NOUN
ejpam-6018	264	11	)	)	PUNCT
ejpam-6018	264	12	,	,	PUNCT
ejpam-6018	264	13	f(ϖ	f(ϖ	PROPN
ejpam-6018	264	14	)	)	PUNCT
ejpam-6018	264	15	}	}	PUNCT
ejpam-6018	264	16	.	.	PUNCT
ejpam-6018	265	1	then	then	ADV
ejpam-6018	265	2	for	for	ADP
ejpam-6018	265	3	some	some	DET
ejpam-6018	265	4	δ	δ	NOUN
ejpam-6018	265	5	∈	∈	PROPN
ejpam-6018	265	6	υ	υ	NOUN
ejpam-6018	265	7	,	,	PUNCT
ejpam-6018	265	8	we	we	PRON
ejpam-6018	265	9	have	have	AUX
ejpam-6018	265	10	f(ϱ)+δ+1	f(ϱ)+δ+1	VERB
ejpam-6018	265	11	≥	≥	PRON
ejpam-6018	265	12	0	0	NUM
ejpam-6018	265	13	and	and	CCONJ
ejpam-6018	265	14	∨	∨	NUM
ejpam-6018	265	15	{	{	PUNCT
ejpam-6018	265	16	f(ϱϖ	f(ϱϖ	NOUN
ejpam-6018	265	17	|	|	NOUN
ejpam-6018	265	18	ϱϖ	ϱϖ	NOUN
ejpam-6018	265	19	)	)	PUNCT
ejpam-6018	265	20	,	,	PUNCT
ejpam-6018	265	21	f(ϖ)}+δ+1	f(ϖ)}+δ+1	ADP
ejpam-6018	265	22	≥	≥	NUM
ejpam-6018	265	23	0	0	NUM
ejpam-6018	265	24	.	.	PUNCT
ejpam-6018	266	1	this	this	PRON
ejpam-6018	266	2	implies	imply	VERB
ejpam-6018	266	3	that	that	SCONJ
ejpam-6018	266	4	f(ϱϖ	f(ϱϖ	NOUN
ejpam-6018	266	5	|	|	ADV
ejpam-6018	266	6	ϱϖ)+δ+1	ϱϖ)+δ+1	VERB
ejpam-6018	266	7	<	<	X
ejpam-6018	266	8	0	0	NUM
ejpam-6018	266	9	and	and	CCONJ
ejpam-6018	266	10	f(ϖ	f(ϖ	NOUN
ejpam-6018	266	11	)	)	PUNCT
ejpam-6018	266	12	+	+	NUM
ejpam-6018	266	13	δ	δ	X
ejpam-6018	266	14	+	+	CCONJ
ejpam-6018	266	15	1	1	NUM
ejpam-6018	266	16	<	<	X
ejpam-6018	266	17	0	0	NUM
ejpam-6018	266	18	,	,	PUNCT
ejpam-6018	266	19	meaning	mean	VERB
ejpam-6018	266	20	that	that	SCONJ
ejpam-6018	266	21	(	(	PUNCT
ejpam-6018	266	22	h	h	NOUN
ejpam-6018	266	23	,	,	PUNCT
ejpam-6018	266	24	(	(	PUNCT
ejpam-6018	266	25	ϱϖ	ϱϖ	NOUN
ejpam-6018	266	26	|	|	ADV
ejpam-6018	266	27	ϱϖ)δ	ϱϖ)δ	PROPN
ejpam-6018	266	28	)	)	PUNCT
ejpam-6018	266	29	and	and	CCONJ
ejpam-6018	266	30	(	(	PUNCT
ejpam-6018	266	31	h,ϖδ	h,ϖδ	NOUN
ejpam-6018	266	32	)	)	PUNCT
ejpam-6018	266	33	are	be	AUX
ejpam-6018	266	34	nq	nq	NOUN
ejpam-6018	266	35	-	-	PUNCT
ejpam-6018	266	36	subsets	subset	NOUN
ejpam-6018	266	37	of	of	ADP
ejpam-6018	266	38	(	(	PUNCT
ejpam-6018	266	39	h	h	NOUN
ejpam-6018	266	40	,	,	PUNCT
ejpam-6018	266	41	f	f	NOUN
ejpam-6018	266	42	)	)	PUNCT
ejpam-6018	266	43	.	.	PUNCT
ejpam-6018	267	1	therefore	therefore	ADV
ejpam-6018	267	2	,	,	PUNCT
ejpam-6018	267	3	ϱϖ	ϱϖ	VERB
ejpam-6018	267	4	|	|	ADV
ejpam-6018	267	5	ϱϖ	ϱϖ	NOUN
ejpam-6018	267	6	∈	∈	PROPN
ejpam-6018	267	7	sq(δ	sq(δ	NOUN
ejpam-6018	267	8	)	)	PUNCT
ejpam-6018	267	9	and	and	CCONJ
ejpam-6018	267	10	ϖ	ϖ	PRON
ejpam-6018	267	11	∈	∈	NOUN
ejpam-6018	267	12	sq(δ	sq(δ	ADJ
ejpam-6018	267	13	)	)	PUNCT
ejpam-6018	267	14	.	.	PUNCT
ejpam-6018	268	1	since	since	SCONJ
ejpam-6018	268	2	sq(δ	sq(δ	NOUN
ejpam-6018	268	3	)	)	PUNCT
ejpam-6018	268	4	is	be	AUX
ejpam-6018	268	5	an	an	DET
ejpam-6018	268	6	ideal	ideal	NOUN
ejpam-6018	268	7	of	of	ADP
ejpam-6018	268	8	h	h	NOUN
ejpam-6018	268	9	,	,	PUNCT
ejpam-6018	268	10	we	we	PRON
ejpam-6018	268	11	conclude	conclude	VERB
ejpam-6018	268	12	that	that	SCONJ
ejpam-6018	268	13	ϱ	ϱ	ADP
ejpam-6018	268	14	∈	∈	PROPN
ejpam-6018	268	15	sq(δ	sq(δ	ADJ
ejpam-6018	268	16	)	)	PUNCT
ejpam-6018	268	17	,	,	PUNCT
ejpam-6018	268	18	and	and	CCONJ
ejpam-6018	268	19	thus	thus	ADV
ejpam-6018	268	20	(	(	PUNCT
ejpam-6018	268	21	h	h	NOUN
ejpam-6018	268	22	,	,	PUNCT
ejpam-6018	268	23	ϱδ	ϱδ	PROPN
ejpam-6018	268	24	)	)	PUNCT
ejpam-6018	268	25	is	be	AUX
ejpam-6018	268	26	an	an	DET
ejpam-6018	268	27	nq	nq	NOUN
ejpam-6018	268	28	-	-	PUNCT
ejpam-6018	268	29	subset	subset	NOUN
ejpam-6018	268	30	of	of	ADP
ejpam-6018	268	31	(	(	PUNCT
ejpam-6018	268	32	h	h	NOUN
ejpam-6018	268	33	,	,	PUNCT
ejpam-6018	268	34	f	f	NOUN
ejpam-6018	268	35	)	)	PUNCT
ejpam-6018	268	36	.	.	PUNCT
ejpam-6018	269	1	this	this	PRON
ejpam-6018	269	2	is	be	AUX
ejpam-6018	269	3	a	a	DET
ejpam-6018	269	4	contradiction	contradiction	NOUN
ejpam-6018	269	5	,	,	PUNCT
ejpam-6018	269	6	so	so	ADV
ejpam-6018	269	7	f(ξ	f(ξ	NOUN
ejpam-6018	269	8	)	)	PUNCT
ejpam-6018	269	9	≤	≤	NUM
ejpam-6018	269	10	∨	∨	NUM
ejpam-6018	269	11	{	{	PUNCT
ejpam-6018	269	12	f(ξζ	f(ξζ	PROPN
ejpam-6018	269	13	|	|	ADV
ejpam-6018	269	14	ξζ	ξζ	NOUN
ejpam-6018	269	15	)	)	PUNCT
ejpam-6018	269	16	,	,	PUNCT
ejpam-6018	269	17	f(ζ	f(ζ	NOUN
ejpam-6018	269	18	)	)	PUNCT
ejpam-6018	269	19	}	}	PUNCT
ejpam-6018	269	20	for	for	ADP
ejpam-6018	269	21	all	all	DET
ejpam-6018	269	22	ξ	ξ	ADJ
ejpam-6018	269	23	,	,	PUNCT
ejpam-6018	269	24	ζ	ζ	PROPN
ejpam-6018	269	25	∈	∈	PROPN
ejpam-6018	269	26	h.	h.	NOUN
ejpam-6018	269	27	thus	thus	ADV
ejpam-6018	269	28	,	,	PUNCT
ejpam-6018	269	29	(	(	PUNCT
ejpam-6018	269	30	h	h	NOUN
ejpam-6018	269	31	,	,	PUNCT
ejpam-6018	269	32	f	f	X
ejpam-6018	269	33	)	)	PUNCT
ejpam-6018	269	34	is	be	AUX
ejpam-6018	269	35	an	an	DET
ejpam-6018	269	36	n	n	ADV
ejpam-6018	269	37	-ideal	-ideal	NOUN
ejpam-6018	269	38	of	of	ADP
ejpam-6018	269	39	type	type	NOUN
ejpam-6018	269	40	(	(	PUNCT
ejpam-6018	269	41	∈,∈	∈,∈	NOUN
ejpam-6018	269	42	)	)	PUNCT
ejpam-6018	269	43	.	.	PUNCT
ejpam-6018	270	1	theorem	theorem	NOUN
ejpam-6018	270	2	9	9	NUM
ejpam-6018	270	3	.	.	PUNCT
ejpam-6018	271	1	let	let	VERB
ejpam-6018	271	2	hs	hs	PRON
ejpam-6018	271	3	:	:	PUNCT
ejpam-6018	271	4	=	=	SYM
ejpam-6018	271	5	(	(	PUNCT
ejpam-6018	271	6	h	h	NOUN
ejpam-6018	271	7	,	,	PUNCT
ejpam-6018	271	8	|	|	ADV
ejpam-6018	271	9	,	,	PUNCT
ejpam-6018	271	10	0	0	NUM
ejpam-6018	271	11	)	)	PUNCT
ejpam-6018	271	12	be	be	AUX
ejpam-6018	271	13	an	an	DET
ejpam-6018	271	14	ssh	ssh	NOUN
ejpam-6018	271	15	-	-	PUNCT
ejpam-6018	271	16	algebra	algebra	NOUN
ejpam-6018	271	17	.	.	PUNCT
ejpam-6018	272	1	given	give	VERB
ejpam-6018	272	2	an	an	DET
ejpam-6018	272	3	n	n	ADV
ejpam-6018	272	4	-structure	-structure	NOUN
ejpam-6018	272	5	(	(	PUNCT
ejpam-6018	272	6	h	h	NOUN
ejpam-6018	272	7	,	,	PUNCT
ejpam-6018	272	8	f	f	NOUN
ejpam-6018	272	9	)	)	PUNCT
ejpam-6018	272	10	and	and	CCONJ
ejpam-6018	272	11	the	the	DET
ejpam-6018	272	12	soft	soft	ADJ
ejpam-6018	272	13	n∈-set	n∈-set	NOUN
ejpam-6018	272	14	(	(	PUNCT
ejpam-6018	272	15	s∈,υ	s∈,υ	NOUN
ejpam-6018	272	16	)	)	PUNCT
ejpam-6018	272	17	,	,	PUNCT
ejpam-6018	272	18	the	the	DET
ejpam-6018	272	19	following	follow	VERB
ejpam-6018	272	20	are	be	AUX
ejpam-6018	272	21	equivalent	equivalent	ADJ
ejpam-6018	272	22	:	:	PUNCT
ejpam-6018	272	23	(	(	PUNCT
ejpam-6018	272	24	1	1	X
ejpam-6018	272	25	)	)	PUNCT
ejpam-6018	272	26	(	(	PUNCT
ejpam-6018	272	27	h	h	NOUN
ejpam-6018	272	28	,	,	PUNCT
ejpam-6018	272	29	f	f	X
ejpam-6018	272	30	)	)	PUNCT
ejpam-6018	272	31	is	be	AUX
ejpam-6018	272	32	an	an	DET
ejpam-6018	272	33	n	n	ADV
ejpam-6018	272	34	-ideal	-ideal	NOUN
ejpam-6018	272	35	of	of	ADP
ejpam-6018	272	36	type	type	NOUN
ejpam-6018	272	37	(	(	PUNCT
ejpam-6018	272	38	∈,∈	∈,∈	X
ejpam-6018	272	39	∨q	∨q	NOUN
ejpam-6018	272	40	)	)	PUNCT
ejpam-6018	272	41	.	.	PUNCT
ejpam-6018	273	1	(	(	PUNCT
ejpam-6018	273	2	2	2	X
ejpam-6018	273	3	)	)	PUNCT
ejpam-6018	273	4	(	(	PUNCT
ejpam-6018	273	5	s∈,υ	s∈,υ	NOUN
ejpam-6018	273	6	)	)	PUNCT
ejpam-6018	273	7	is	be	AUX
ejpam-6018	273	8	a	a	DET
ejpam-6018	273	9	soft	soft	ADJ
ejpam-6018	273	10	n	n	NOUN
ejpam-6018	273	11	-ideal	-ideal	ADJ
ejpam-6018	273	12	over	over	ADP
ejpam-6018	273	13	h	h	NOUN
ejpam-6018	273	14	for	for	ADP
ejpam-6018	273	15	υ	υ	NOUN
ejpam-6018	273	16	=	=	PUNCT
ejpam-6018	274	1	[	[	X
ejpam-6018	274	2	−0.5	−0.5	PROPN
ejpam-6018	274	3	,	,	PUNCT
ejpam-6018	274	4	0	0	NUM
ejpam-6018	274	5	)	)	PUNCT
ejpam-6018	274	6	.	.	PUNCT
ejpam-6018	275	1	proof	proof	NOUN
ejpam-6018	275	2	.	.	PUNCT
ejpam-6018	276	1	assume	assume	VERB
ejpam-6018	276	2	that	that	SCONJ
ejpam-6018	276	3	(	(	PUNCT
ejpam-6018	276	4	h	h	NOUN
ejpam-6018	276	5	,	,	PUNCT
ejpam-6018	276	6	f	f	X
ejpam-6018	276	7	)	)	PUNCT
ejpam-6018	276	8	is	be	AUX
ejpam-6018	276	9	an	an	DET
ejpam-6018	276	10	n	n	ADV
ejpam-6018	276	11	-ideal	-ideal	NOUN
ejpam-6018	276	12	of	of	ADP
ejpam-6018	276	13	type	type	NOUN
ejpam-6018	276	14	(	(	PUNCT
ejpam-6018	276	15	∈,∈	∈,∈	X
ejpam-6018	276	16	∨q	∨q	NOUN
ejpam-6018	276	17	)	)	PUNCT
ejpam-6018	276	18	.	.	PUNCT
ejpam-6018	277	1	we	we	PRON
ejpam-6018	277	2	first	first	ADV
ejpam-6018	277	3	show	show	VERB
ejpam-6018	277	4	that	that	SCONJ
ejpam-6018	277	5	(	(	PUNCT
ejpam-6018	277	6	∀ξ	∀ξ	ADJ
ejpam-6018	277	7	∈	∈	NOUN
ejpam-6018	277	8	h	h	NOUN
ejpam-6018	277	9	)	)	PUNCT
ejpam-6018	277	10	(	(	PUNCT
ejpam-6018	277	11	f(0	f(0	NOUN
ejpam-6018	277	12	)	)	PUNCT
ejpam-6018	277	13	≤	≤	NOUN
ejpam-6018	277	14	∨	∨	NUM
ejpam-6018	277	15	{	{	PUNCT
ejpam-6018	277	16	f(ξ),−0.5	f(ξ),−0.5	NOUN
ejpam-6018	277	17	}	}	PUNCT
ejpam-6018	277	18	)	)	PUNCT
ejpam-6018	277	19	.	.	PUNCT
ejpam-6018	278	1	suppose	suppose	VERB
ejpam-6018	278	2	that	that	SCONJ
ejpam-6018	278	3	f(0	f(0	NOUN
ejpam-6018	278	4	)	)	PUNCT
ejpam-6018	278	5	>	>	X
ejpam-6018	279	1	f(ξ	f(ξ	X
ejpam-6018	279	2	)	)	PUNCT
ejpam-6018	279	3	>	>	X
ejpam-6018	280	1	−0.5	−0.5	PROPN
ejpam-6018	280	2	.	.	PUNCT
ejpam-6018	281	1	then	then	ADV
ejpam-6018	281	2	,	,	PUNCT
ejpam-6018	281	3	there	there	PRON
ejpam-6018	281	4	exists	exist	VERB
ejpam-6018	281	5	η	η	PROPN
ejpam-6018	281	6	∈	∈	PROPN
ejpam-6018	281	7	(	(	PUNCT
ejpam-6018	281	8	−0.5	−0.5	PROPN
ejpam-6018	281	9	,	,	PUNCT
ejpam-6018	281	10	0	0	NUM
ejpam-6018	281	11	)	)	PUNCT
ejpam-6018	281	12	such	such	ADJ
ejpam-6018	281	13	that	that	DET
ejpam-6018	281	14	f(0	f(0	NOUN
ejpam-6018	281	15	)	)	PUNCT
ejpam-6018	281	16	>	>	PUNCT
ejpam-6018	281	17	η	η	PROPN
ejpam-6018	281	18	≥	≥	PROPN
ejpam-6018	281	19	f(ξ	f(ξ	NOUN
ejpam-6018	281	20	)	)	PUNCT
ejpam-6018	281	21	,	,	PUNCT
ejpam-6018	281	22	which	which	PRON
ejpam-6018	281	23	implies	imply	VERB
ejpam-6018	281	24	that	that	SCONJ
ejpam-6018	281	25	(	(	PUNCT
ejpam-6018	281	26	h	h	NOUN
ejpam-6018	281	27	,	,	PUNCT
ejpam-6018	281	28	ξη	ξη	PRON
ejpam-6018	281	29	)	)	PUNCT
ejpam-6018	281	30	is	be	AUX
ejpam-6018	281	31	an	an	DET
ejpam-6018	281	32	n∈-subset	n∈-subset	NOUN
ejpam-6018	281	33	of	of	ADP
ejpam-6018	281	34	(	(	PUNCT
ejpam-6018	281	35	h	h	NOUN
ejpam-6018	281	36	,	,	PUNCT
ejpam-6018	281	37	f	f	NOUN
ejpam-6018	281	38	)	)	PUNCT
ejpam-6018	281	39	.	.	PUNCT
ejpam-6018	282	1	however	however	ADV
ejpam-6018	282	2	,	,	PUNCT
ejpam-6018	282	3	(	(	PUNCT
ejpam-6018	282	4	h	h	NOUN
ejpam-6018	282	5	,	,	PUNCT
ejpam-6018	282	6	0η	0η	NUM
ejpam-6018	282	7	)	)	PUNCT
ejpam-6018	282	8	is	be	AUX
ejpam-6018	282	9	not	not	PART
ejpam-6018	282	10	an	an	DET
ejpam-6018	282	11	n∈-subset	n∈-subset	NOUN
ejpam-6018	282	12	of	of	ADP
ejpam-6018	282	13	(	(	PUNCT
ejpam-6018	282	14	h	h	NOUN
ejpam-6018	282	15	,	,	PUNCT
ejpam-6018	282	16	f	f	NOUN
ejpam-6018	282	17	)	)	PUNCT
ejpam-6018	282	18	,	,	PUNCT
ejpam-6018	282	19	nor	nor	CCONJ
ejpam-6018	282	20	is	be	AUX
ejpam-6018	282	21	it	it	PRON
ejpam-6018	282	22	an	an	DET
ejpam-6018	282	23	nq	nq	NOUN
ejpam-6018	282	24	-	-	PUNCT
ejpam-6018	282	25	subset	subset	NOUN
ejpam-6018	282	26	of	of	ADP
ejpam-6018	282	27	(	(	PUNCT
ejpam-6018	282	28	h	h	NOUN
ejpam-6018	282	29	,	,	PUNCT
ejpam-6018	282	30	f	f	NOUN
ejpam-6018	282	31	)	)	PUNCT
ejpam-6018	282	32	because	because	SCONJ
ejpam-6018	282	33	f(0	f(0	NOUN
ejpam-6018	282	34	)	)	PUNCT
ejpam-6018	283	1	+	+	NUM
ejpam-6018	283	2	η	η	PROPN
ejpam-6018	283	3	+	+	PROPN
ejpam-6018	283	4	1	1	NUM
ejpam-6018	283	5	≥	≥	NOUN
ejpam-6018	283	6	0	0	NUM
ejpam-6018	283	7	.	.	PUNCT
ejpam-6018	284	1	this	this	PRON
ejpam-6018	284	2	is	be	AUX
ejpam-6018	284	3	a	a	DET
ejpam-6018	284	4	contradiction	contradiction	NOUN
ejpam-6018	284	5	.	.	PUNCT
ejpam-6018	285	1	hence	hence	ADV
ejpam-6018	285	2	,	,	PUNCT
ejpam-6018	285	3	f(0	f(0	NOUN
ejpam-6018	285	4	)	)	PUNCT
ejpam-6018	285	5	≤	≤	NOUN
ejpam-6018	285	6	f(ξ	f(ξ	NOUN
ejpam-6018	285	7	)	)	PUNCT
ejpam-6018	285	8	for	for	ADP
ejpam-6018	285	9	all	all	DET
ejpam-6018	285	10	ξ	ξ	PROPN
ejpam-6018	285	11	∈	∈	PROPN
ejpam-6018	285	12	h.	h.	NOUN
ejpam-6018	285	13	now	now	ADV
ejpam-6018	285	14	,	,	PUNCT
ejpam-6018	285	15	if	if	SCONJ
ejpam-6018	285	16	f(ξ	f(ξ	NOUN
ejpam-6018	285	17	)	)	PUNCT
ejpam-6018	285	18	≤	≤	NOUN
ejpam-6018	285	19	−0.5	−0.5	PROPN
ejpam-6018	285	20	,	,	PUNCT
ejpam-6018	285	21	then	then	ADV
ejpam-6018	285	22	(	(	PUNCT
ejpam-6018	285	23	h	h	NOUN
ejpam-6018	285	24	,	,	PUNCT
ejpam-6018	285	25	ξ−0.5	ξ−0.5	NOUN
ejpam-6018	285	26	)	)	PUNCT
ejpam-6018	285	27	is	be	AUX
ejpam-6018	285	28	an	an	DET
ejpam-6018	285	29	n∈-subset	n∈-subset	NOUN
ejpam-6018	285	30	of	of	ADP
ejpam-6018	285	31	(	(	PUNCT
ejpam-6018	285	32	h	h	NOUN
ejpam-6018	285	33	,	,	PUNCT
ejpam-6018	285	34	f	f	NOUN
ejpam-6018	285	35	)	)	PUNCT
ejpam-6018	285	36	,	,	PUNCT
ejpam-6018	285	37	and	and	CCONJ
ejpam-6018	285	38	thus	thus	ADV
ejpam-6018	285	39	(	(	PUNCT
ejpam-6018	285	40	h	h	NOUN
ejpam-6018	285	41	,	,	PUNCT
ejpam-6018	285	42	0−0.5	0−0.5	NUM
ejpam-6018	285	43	)	)	PUNCT
ejpam-6018	285	44	is	be	AUX
ejpam-6018	285	45	an	an	DET
ejpam-6018	285	46	n∈∨q	n∈∨q	NOUN
ejpam-6018	285	47	-	-	NOUN
ejpam-6018	285	48	subset	subset	NOUN
ejpam-6018	285	49	of	of	ADP
ejpam-6018	285	50	(	(	PUNCT
ejpam-6018	285	51	h	h	NOUN
ejpam-6018	285	52	,	,	PUNCT
ejpam-6018	285	53	f	f	NOUN
ejpam-6018	285	54	)	)	PUNCT
ejpam-6018	285	55	.	.	PUNCT
ejpam-6018	286	1	therefore	therefore	ADV
ejpam-6018	286	2	,	,	PUNCT
ejpam-6018	286	3	f(0	f(0	NOUN
ejpam-6018	286	4	)	)	PUNCT
ejpam-6018	286	5	≤	≤	NOUN
ejpam-6018	287	1	−0.5	−0.5	PROPN
ejpam-6018	287	2	,	,	PUNCT
ejpam-6018	287	3	as	as	ADP
ejpam-6018	287	4	if	if	SCONJ
ejpam-6018	287	5	f(0	f(0	NOUN
ejpam-6018	287	6	)	)	PUNCT
ejpam-6018	287	7	>	>	X
ejpam-6018	288	1	−0.5	−0.5	PROPN
ejpam-6018	288	2	,	,	PUNCT
ejpam-6018	288	3	we	we	PRON
ejpam-6018	288	4	would	would	AUX
ejpam-6018	288	5	have	have	VERB
ejpam-6018	288	6	f(0)−	f(0)−	NOUN
ejpam-6018	288	7	0.5	0.5	NUM
ejpam-6018	288	8	+	+	NOUN
ejpam-6018	288	9	1	1	NUM
ejpam-6018	288	10	>	>	SYM
ejpam-6018	288	11	0	0	NUM
ejpam-6018	288	12	,	,	PUNCT
ejpam-6018	288	13	which	which	PRON
ejpam-6018	288	14	is	be	AUX
ejpam-6018	288	15	a	a	DET
ejpam-6018	288	16	contradiction	contradiction	NOUN
ejpam-6018	288	17	.	.	PUNCT
ejpam-6018	289	1	let	let	VERB
ejpam-6018	289	2	η	η	PROPN
ejpam-6018	289	3	∈	∈	PROPN
ejpam-6018	289	4	υ	υ	NOUN
ejpam-6018	290	1	=	=	X
ejpam-6018	291	1	[	[	X
ejpam-6018	291	2	−0.5	−0.5	PROPN
ejpam-6018	291	3	,	,	PUNCT
ejpam-6018	291	4	0	0	NUM
ejpam-6018	291	5	)	)	PUNCT
ejpam-6018	291	6	.	.	PUNCT
ejpam-6018	292	1	then	then	ADV
ejpam-6018	292	2	for	for	ADP
ejpam-6018	292	3	all	all	DET
ejpam-6018	292	4	ξ	ξ	PROPN
ejpam-6018	292	5	∈	∈	PROPN
ejpam-6018	292	6	s∈(η	s∈(η	X
ejpam-6018	292	7	)	)	PUNCT
ejpam-6018	292	8	,	,	PUNCT
ejpam-6018	292	9	f(0	f(0	NOUN
ejpam-6018	292	10	)	)	PUNCT
ejpam-6018	292	11	≤	≤	NOUN
ejpam-6018	292	12	∨	∨	NUM
ejpam-6018	292	13	{	{	PUNCT
ejpam-6018	292	14	f(ξ),−0.5	f(ξ),−0.5	NOUN
ejpam-6018	292	15	}	}	PUNCT
ejpam-6018	292	16	,	,	PUNCT
ejpam-6018	292	17	and	and	CCONJ
ejpam-6018	292	18	so	so	ADV
ejpam-6018	292	19	f(0	f(0	NOUN
ejpam-6018	292	20	)	)	PUNCT
ejpam-6018	292	21	≤	≤	NUM
ejpam-6018	292	22	∨	∨	NUM
ejpam-6018	292	23	{	{	PUNCT
ejpam-6018	292	24	f(ξ),−0.5	f(ξ),−0.5	PROPN
ejpam-6018	292	25	}	}	PUNCT
ejpam-6018	292	26	≤	≤	NOUN
ejpam-6018	292	27	∨	∨	NUM
ejpam-6018	292	28	{	{	PUNCT
ejpam-6018	292	29	η,−0.5	η,−0.5	NOUN
ejpam-6018	292	30	}	}	PUNCT
ejpam-6018	292	31	=	=	SYM
ejpam-6018	292	32	η	η	PROPN
ejpam-6018	292	33	.	.	PROPN
ejpam-6018	292	34	thus	thus	ADV
ejpam-6018	292	35	,	,	PUNCT
ejpam-6018	292	36	(	(	PUNCT
ejpam-6018	292	37	h	h	NOUN
ejpam-6018	292	38	,	,	PUNCT
ejpam-6018	292	39	0η	0η	NUM
ejpam-6018	292	40	)	)	PUNCT
ejpam-6018	292	41	is	be	AUX
ejpam-6018	292	42	an	an	DET
ejpam-6018	292	43	n∈-subset	n∈-subset	NOUN
ejpam-6018	292	44	of	of	ADP
ejpam-6018	292	45	(	(	PUNCT
ejpam-6018	292	46	h	h	NOUN
ejpam-6018	292	47	,	,	PUNCT
ejpam-6018	292	48	f	f	PROPN
ejpam-6018	292	49	)	)	PUNCT
ejpam-6018	292	50	,	,	PUNCT
ejpam-6018	292	51	implying	imply	VERB
ejpam-6018	292	52	that	that	SCONJ
ejpam-6018	292	53	0	0	NUM
ejpam-6018	292	54	∈	∈	PROPN
ejpam-6018	292	55	s∈(η	s∈(η	NOUN
ejpam-6018	292	56	)	)	PUNCT
ejpam-6018	292	57	.	.	PUNCT
ejpam-6018	293	1	now	now	ADV
ejpam-6018	293	2	,	,	PUNCT
ejpam-6018	293	3	we	we	PRON
ejpam-6018	293	4	show	show	VERB
ejpam-6018	293	5	that	that	SCONJ
ejpam-6018	293	6	(	(	PUNCT
ejpam-6018	293	7	∀ξ	∀ξ	NOUN
ejpam-6018	293	8	,	,	PUNCT
ejpam-6018	293	9	ζ	ζ	PROPN
ejpam-6018	293	10	∈	∈	PROPN
ejpam-6018	293	11	h	h	NOUN
ejpam-6018	293	12	)	)	PUNCT
ejpam-6018	293	13	(	(	PUNCT
ejpam-6018	293	14	f(ξ	f(ξ	X
ejpam-6018	293	15	)	)	PUNCT
ejpam-6018	293	16	≤	≤	NUM
ejpam-6018	293	17	∨	∨	NUM
ejpam-6018	293	18	{	{	PUNCT
ejpam-6018	293	19	f(ξζ	f(ξζ	PROPN
ejpam-6018	293	20	|	|	ADV
ejpam-6018	293	21	ξζ	ξζ	NOUN
ejpam-6018	293	22	)	)	PUNCT
ejpam-6018	293	23	,	,	PUNCT
ejpam-6018	293	24	f(ζ),−0.5	f(ζ),−0.5	PROPN
ejpam-6018	293	25	}	}	PUNCT
ejpam-6018	293	26	)	)	PUNCT
ejpam-6018	293	27	.	.	PUNCT
ejpam-6018	294	1	t.	t.	PROPN
ejpam-6018	294	2	oner	oner	PROPN
ejpam-6018	294	3	et	et	PROPN
ejpam-6018	294	4	al	al	PROPN
ejpam-6018	294	5	.	.	PUNCT
ejpam-6018	294	6	/	/	SYM
ejpam-6018	294	7	eur	eur	PROPN
ejpam-6018	294	8	.	.	PUNCT
ejpam-6018	295	1	j.	j.	PROPN
ejpam-6018	295	2	pure	pure	PROPN
ejpam-6018	295	3	appl	appl	PROPN
ejpam-6018	295	4	.	.	PROPN
ejpam-6018	295	5	math	math	PROPN
ejpam-6018	295	6	,	,	PUNCT
ejpam-6018	295	7	18	18	NUM
ejpam-6018	295	8	(	(	PUNCT
ejpam-6018	295	9	2	2	NUM
ejpam-6018	295	10	)	)	PUNCT
ejpam-6018	295	11	(	(	PUNCT
ejpam-6018	295	12	2025	2025	NUM
ejpam-6018	295	13	)	)	PUNCT
ejpam-6018	295	14	,	,	PUNCT
ejpam-6018	295	15	6018	6018	NUM
ejpam-6018	295	16	10	10	NUM
ejpam-6018	295	17	of	of	ADP
ejpam-6018	295	18	11	11	NUM
ejpam-6018	295	19	if	if	SCONJ
ejpam-6018	295	20	∨	∨	X
ejpam-6018	295	21	{	{	PUNCT
ejpam-6018	295	22	f(ξζ	f(ξζ	PROPN
ejpam-6018	295	23	|	|	ADV
ejpam-6018	295	24	ξζ	ξζ	NOUN
ejpam-6018	295	25	)	)	PUNCT
ejpam-6018	295	26	,	,	PUNCT
ejpam-6018	295	27	f(ζ	f(ζ	PROPN
ejpam-6018	295	28	)	)	PUNCT
ejpam-6018	295	29	}	}	PUNCT
ejpam-6018	295	30	>	>	PUNCT
ejpam-6018	296	1	−0.5	−0.5	PROPN
ejpam-6018	296	2	,	,	PUNCT
ejpam-6018	296	3	then	then	ADV
ejpam-6018	296	4	f(ξ	f(ξ	NOUN
ejpam-6018	296	5	)	)	PUNCT
ejpam-6018	296	6	≤	≤	NUM
ejpam-6018	296	7	∨	∨	NUM
ejpam-6018	296	8	{	{	PUNCT
ejpam-6018	296	9	f(ξζ	f(ξζ	PROPN
ejpam-6018	296	10	|	|	ADV
ejpam-6018	296	11	ξζ	ξζ	NOUN
ejpam-6018	296	12	)	)	PUNCT
ejpam-6018	296	13	,	,	PUNCT
ejpam-6018	296	14	f(ζ	f(ζ	NOUN
ejpam-6018	296	15	)	)	PUNCT
ejpam-6018	296	16	}	}	PUNCT
ejpam-6018	296	17	.	.	PUNCT
ejpam-6018	297	1	otherwise	otherwise	ADV
ejpam-6018	297	2	,	,	PUNCT
ejpam-6018	297	3	there	there	PRON
ejpam-6018	297	4	exists	exist	VERB
ejpam-6018	297	5	δ	δ	PROPN
ejpam-6018	297	6	∈	∈	PROPN
ejpam-6018	297	7	(	(	PUNCT
ejpam-6018	297	8	−0.5	−0.5	PROPN
ejpam-6018	297	9	,	,	PUNCT
ejpam-6018	297	10	0	0	NUM
ejpam-6018	297	11	)	)	PUNCT
ejpam-6018	297	12	such	such	ADJ
ejpam-6018	297	13	that	that	SCONJ
ejpam-6018	297	14	f(ξ	f(ξ	NOUN
ejpam-6018	297	15	)	)	PUNCT
ejpam-6018	297	16	>	>	PUNCT
ejpam-6018	298	1	δ	δ	PROPN
ejpam-6018	298	2	≥	≥	PROPN
ejpam-6018	298	3	∨	∨	NUM
ejpam-6018	298	4	{	{	PUNCT
ejpam-6018	298	5	f(ξζ	f(ξζ	PROPN
ejpam-6018	298	6	|	|	ADV
ejpam-6018	298	7	ξζ	ξζ	NOUN
ejpam-6018	298	8	)	)	PUNCT
ejpam-6018	298	9	,	,	PUNCT
ejpam-6018	298	10	f(ζ	f(ζ	NOUN
ejpam-6018	298	11	)	)	PUNCT
ejpam-6018	298	12	}	}	PUNCT
ejpam-6018	298	13	.	.	PUNCT
ejpam-6018	299	1	then	then	ADV
ejpam-6018	299	2	(	(	PUNCT
ejpam-6018	299	3	h	h	NOUN
ejpam-6018	299	4	,	,	PUNCT
ejpam-6018	299	5	(	(	PUNCT
ejpam-6018	299	6	ξζ	ξζ	INTJ
ejpam-6018	299	7	|	|	ADV
ejpam-6018	299	8	ξζ)δ	ξζ)δ	NUM
ejpam-6018	299	9	)	)	PUNCT
ejpam-6018	299	10	and	and	CCONJ
ejpam-6018	299	11	(	(	PUNCT
ejpam-6018	299	12	h	h	NOUN
ejpam-6018	299	13	,	,	PUNCT
ejpam-6018	299	14	yδ	yδ	NOUN
ejpam-6018	299	15	)	)	PUNCT
ejpam-6018	299	16	are	be	AUX
ejpam-6018	299	17	n∈-subsets	n∈-subset	NOUN
ejpam-6018	299	18	of	of	ADP
ejpam-6018	299	19	(	(	PUNCT
ejpam-6018	299	20	h	h	NOUN
ejpam-6018	299	21	,	,	PUNCT
ejpam-6018	299	22	f	f	NOUN
ejpam-6018	299	23	)	)	PUNCT
ejpam-6018	299	24	,	,	PUNCT
ejpam-6018	299	25	but	but	CCONJ
ejpam-6018	299	26	(	(	PUNCT
ejpam-6018	299	27	h	h	NOUN
ejpam-6018	299	28	,	,	PUNCT
ejpam-6018	299	29	ξδ	ξδ	ADJ
ejpam-6018	299	30	)	)	PUNCT
ejpam-6018	299	31	is	be	AUX
ejpam-6018	299	32	not	not	PART
ejpam-6018	299	33	an	an	DET
ejpam-6018	299	34	n∈-subset	n∈-subset	NOUN
ejpam-6018	299	35	of	of	ADP
ejpam-6018	299	36	(	(	PUNCT
ejpam-6018	299	37	h	h	NOUN
ejpam-6018	299	38	,	,	PUNCT
ejpam-6018	299	39	f	f	NOUN
ejpam-6018	299	40	)	)	PUNCT
ejpam-6018	299	41	,	,	PUNCT
ejpam-6018	299	42	and	and	CCONJ
ejpam-6018	299	43	neither	neither	PRON
ejpam-6018	299	44	is	be	AUX
ejpam-6018	299	45	it	it	PRON
ejpam-6018	299	46	an	an	DET
ejpam-6018	299	47	nq	nq	NOUN
ejpam-6018	299	48	-	-	PUNCT
ejpam-6018	299	49	subset	subset	NOUN
ejpam-6018	299	50	of	of	ADP
ejpam-6018	299	51	(	(	PUNCT
ejpam-6018	299	52	h	h	NOUN
ejpam-6018	299	53	,	,	PUNCT
ejpam-6018	299	54	f	f	PROPN
ejpam-6018	299	55	)	)	PUNCT
ejpam-6018	299	56	,	,	PUNCT
ejpam-6018	299	57	as	as	ADP
ejpam-6018	299	58	f(ξ	f(ξ	NOUN
ejpam-6018	299	59	)	)	PUNCT
ejpam-6018	299	60	+	+	CCONJ
ejpam-6018	299	61	δ+1	δ+1	PROPN
ejpam-6018	299	62	>	>	X
ejpam-6018	299	63	2δ+1	2δ+1	PROPN
ejpam-6018	299	64	>	>	X
ejpam-6018	299	65	0	0	X
ejpam-6018	299	66	.	.	PUNCT
ejpam-6018	300	1	this	this	PRON
ejpam-6018	300	2	leads	lead	VERB
ejpam-6018	300	3	to	to	ADP
ejpam-6018	300	4	a	a	DET
ejpam-6018	300	5	contradiction	contradiction	NOUN
ejpam-6018	300	6	.	.	PUNCT
ejpam-6018	301	1	therefore	therefore	ADV
ejpam-6018	301	2	,	,	PUNCT
ejpam-6018	301	3	we	we	PRON
ejpam-6018	301	4	must	must	AUX
ejpam-6018	301	5	have	have	VERB
ejpam-6018	301	6	f(ξ	f(ξ	NOUN
ejpam-6018	301	7	)	)	PUNCT
ejpam-6018	301	8	≤	≤	NUM
ejpam-6018	301	9	∨	∨	NUM
ejpam-6018	301	10	{	{	PUNCT
ejpam-6018	301	11	f(ξζ	f(ξζ	PROPN
ejpam-6018	301	12	|	|	ADV
ejpam-6018	301	13	ξζ	ξζ	NOUN
ejpam-6018	301	14	)	)	PUNCT
ejpam-6018	301	15	,	,	PUNCT
ejpam-6018	301	16	f(ζ),−0.5	f(ζ),−0.5	PROPN
ejpam-6018	301	17	}	}	PUNCT
ejpam-6018	301	18	for	for	ADP
ejpam-6018	301	19	all	all	DET
ejpam-6018	301	20	ξ	ξ	ADJ
ejpam-6018	301	21	,	,	PUNCT
ejpam-6018	301	22	ζ	ζ	PROPN
ejpam-6018	301	23	∈	∈	PROPN
ejpam-6018	301	24	h.	h.	NOUN
ejpam-6018	301	25	let	let	VERB
ejpam-6018	301	26	ξ	ξ	X
ejpam-6018	301	27	,	,	PUNCT
ejpam-6018	301	28	ζ	ζ	PROPN
ejpam-6018	301	29	∈	∈	NOUN
ejpam-6018	301	30	h	h	NOUN
ejpam-6018	301	31	be	be	AUX
ejpam-6018	301	32	such	such	ADJ
ejpam-6018	301	33	that	that	SCONJ
ejpam-6018	301	34	ξζ	ξζ	NOUN
ejpam-6018	302	1	|	|	INTJ
ejpam-6018	302	2	ξζ	ξζ	INTJ
ejpam-6018	302	3	∈	∈	PROPN
ejpam-6018	302	4	s∈(η	s∈(η	ADV
ejpam-6018	302	5	)	)	PUNCT
ejpam-6018	303	1	and	and	CCONJ
ejpam-6018	303	2	ζ	ζ	NOUN
ejpam-6018	303	3	∈	∈	PROPN
ejpam-6018	303	4	s∈(η	s∈(η	NOUN
ejpam-6018	303	5	)	)	PUNCT
ejpam-6018	303	6	.	.	PUNCT
ejpam-6018	304	1	then	then	ADV
ejpam-6018	304	2	(	(	PUNCT
ejpam-6018	304	3	h	h	NOUN
ejpam-6018	304	4	,	,	PUNCT
ejpam-6018	304	5	(	(	PUNCT
ejpam-6018	304	6	ξζ	ξζ	NOUN
ejpam-6018	304	7	|	|	ADV
ejpam-6018	304	8	ξζ)η	ξζ)η	PROPN
ejpam-6018	304	9	)	)	PUNCT
ejpam-6018	304	10	and	and	CCONJ
ejpam-6018	304	11	(	(	PUNCT
ejpam-6018	304	12	h	h	NOUN
ejpam-6018	304	13	,	,	PUNCT
ejpam-6018	304	14	ζδ	ζδ	NOUN
ejpam-6018	304	15	)	)	PUNCT
ejpam-6018	304	16	are	be	AUX
ejpam-6018	304	17	n∈-subsets	n∈-subset	NOUN
ejpam-6018	304	18	of	of	ADP
ejpam-6018	304	19	(	(	PUNCT
ejpam-6018	304	20	h	h	NOUN
ejpam-6018	304	21	,	,	PUNCT
ejpam-6018	304	22	f	f	NOUN
ejpam-6018	304	23	)	)	PUNCT
ejpam-6018	304	24	,	,	PUNCT
ejpam-6018	304	25	and	and	CCONJ
ejpam-6018	304	26	so	so	SCONJ
ejpam-6018	304	27	f(ξζ	f(ξζ	PROPN
ejpam-6018	304	28	|	|	ADV
ejpam-6018	304	29	ξζ	ξζ	NOUN
ejpam-6018	304	30	)	)	PUNCT
ejpam-6018	304	31	≤	≤	PROPN
ejpam-6018	304	32	η	η	PROPN
ejpam-6018	304	33	and	and	CCONJ
ejpam-6018	304	34	f(ζ	f(ζ	PROPN
ejpam-6018	304	35	)	)	PUNCT
ejpam-6018	304	36	≤	≤	PROPN
ejpam-6018	304	37	η	η	PROPN
ejpam-6018	304	38	.	.	PROPN
ejpam-6018	304	39	hence	hence	ADV
ejpam-6018	304	40	,	,	PUNCT
ejpam-6018	304	41	f(ξ	f(ξ	X
ejpam-6018	304	42	)	)	PUNCT
ejpam-6018	304	43	≤	≤	NUM
ejpam-6018	304	44	∨	∨	NUM
ejpam-6018	304	45	{	{	PUNCT
ejpam-6018	304	46	f(ξζ	f(ξζ	PROPN
ejpam-6018	304	47	|	|	ADV
ejpam-6018	304	48	ξζ	ξζ	NOUN
ejpam-6018	304	49	)	)	PUNCT
ejpam-6018	304	50	,	,	PUNCT
ejpam-6018	304	51	f(ζ),−0.5	f(ζ),−0.5	PROPN
ejpam-6018	304	52	}	}	PUNCT
ejpam-6018	304	53	≤	≤	ADJ
ejpam-6018	304	54	∨	∨	NUM
ejpam-6018	304	55	{	{	PUNCT
ejpam-6018	304	56	η,−0.5	η,−0.5	NOUN
ejpam-6018	304	57	}	}	PUNCT
ejpam-6018	304	58	=	=	SYM
ejpam-6018	304	59	η	η	PROPN
ejpam-6018	304	60	,	,	PUNCT
ejpam-6018	304	61	which	which	PRON
ejpam-6018	304	62	implies	imply	VERB
ejpam-6018	304	63	that	that	SCONJ
ejpam-6018	304	64	(	(	PUNCT
ejpam-6018	304	65	h	h	NOUN
ejpam-6018	304	66	,	,	PUNCT
ejpam-6018	304	67	ξδ	ξδ	ADJ
ejpam-6018	304	68	)	)	PUNCT
ejpam-6018	304	69	is	be	AUX
ejpam-6018	304	70	ann∈-subset	ann∈-subset	PROPN
ejpam-6018	304	71	of	of	ADP
ejpam-6018	304	72	(	(	PUNCT
ejpam-6018	304	73	h	h	NOUN
ejpam-6018	304	74	,	,	PUNCT
ejpam-6018	304	75	f	f	NOUN
ejpam-6018	304	76	)	)	PUNCT
ejpam-6018	304	77	,	,	PUNCT
ejpam-6018	304	78	and	and	CCONJ
ejpam-6018	304	79	therefore	therefore	ADV
ejpam-6018	304	80	ξ	ξ	X
ejpam-6018	304	81	∈	∈	PROPN
ejpam-6018	304	82	s∈(η	s∈(η	NOUN
ejpam-6018	304	83	)	)	PUNCT
ejpam-6018	304	84	.	.	PUNCT
ejpam-6018	305	1	thus	thus	ADV
ejpam-6018	305	2	,	,	PUNCT
ejpam-6018	305	3	(	(	PUNCT
ejpam-6018	305	4	s∈,υ	s∈,υ	NOUN
ejpam-6018	305	5	)	)	PUNCT
ejpam-6018	305	6	is	be	AUX
ejpam-6018	305	7	a	a	DET
ejpam-6018	305	8	soft	soft	ADJ
ejpam-6018	305	9	n	n	NOUN
ejpam-6018	305	10	-ideal	-ideal	ADJ
ejpam-6018	305	11	over	over	ADP
ejpam-6018	305	12	h	h	NOUN
ejpam-6018	305	13	for	for	ADP
ejpam-6018	305	14	υ	υ	NOUN
ejpam-6018	305	15	=	=	PUNCT
ejpam-6018	306	1	[	[	X
ejpam-6018	306	2	−0.5	−0.5	PROPN
ejpam-6018	306	3	,	,	PUNCT
ejpam-6018	306	4	0	0	NUM
ejpam-6018	306	5	)	)	PUNCT
ejpam-6018	306	6	.	.	PUNCT
ejpam-6018	307	1	conversely	conversely	ADV
ejpam-6018	307	2	,	,	PUNCT
ejpam-6018	307	3	suppose	suppose	VERB
ejpam-6018	307	4	that	that	SCONJ
ejpam-6018	307	5	(	(	PUNCT
ejpam-6018	307	6	2	2	X
ejpam-6018	307	7	)	)	PUNCT
ejpam-6018	307	8	is	be	AUX
ejpam-6018	307	9	valid	valid	ADJ
ejpam-6018	307	10	.	.	PUNCT
ejpam-6018	308	1	if	if	SCONJ
ejpam-6018	308	2	f(0	f(0	NOUN
ejpam-6018	308	3	)	)	PUNCT
ejpam-6018	308	4	>	>	PUNCT
ejpam-6018	309	1	∨	∨	X
ejpam-6018	309	2	{	{	PUNCT
ejpam-6018	309	3	f(ϱ),−0.5	f(ϱ),−0.5	NOUN
ejpam-6018	309	4	}	}	PUNCT
ejpam-6018	309	5	for	for	ADP
ejpam-6018	309	6	some	some	DET
ejpam-6018	309	7	ϱ	ϱ	PROPN
ejpam-6018	309	8	∈	∈	PROPN
ejpam-6018	309	9	h	h	NOUN
ejpam-6018	309	10	,	,	PUNCT
ejpam-6018	309	11	then	then	ADV
ejpam-6018	309	12	there	there	PRON
ejpam-6018	309	13	exists	exist	VERB
ejpam-6018	309	14	η	η	PROPN
ejpam-6018	309	15	∈	∈	PROPN
ejpam-6018	309	16	υ	υ	ADP
ejpam-6018	309	17	such	such	ADJ
ejpam-6018	309	18	that	that	DET
ejpam-6018	309	19	f(0	f(0	NOUN
ejpam-6018	309	20	)	)	PUNCT
ejpam-6018	309	21	>	>	PUNCT
ejpam-6018	309	22	η	η	PROPN
ejpam-6018	309	23	≥	≥	PROPN
ejpam-6018	309	24	∨	∨	NUM
ejpam-6018	309	25	{	{	PUNCT
ejpam-6018	309	26	f(ϱ),−0.5	f(ϱ),−0.5	ADJ
ejpam-6018	309	27	}	}	PUNCT
ejpam-6018	309	28	.	.	PUNCT
ejpam-6018	310	1	then	then	ADV
ejpam-6018	310	2	η	η	PROPN
ejpam-6018	310	3	∈	∈	PROPN
ejpam-6018	310	4	υ	υ	PROPN
ejpam-6018	310	5	,	,	PUNCT
ejpam-6018	310	6	and	and	CCONJ
ejpam-6018	310	7	(	(	PUNCT
ejpam-6018	310	8	h	h	NOUN
ejpam-6018	310	9	,	,	PUNCT
ejpam-6018	310	10	ϱη	ϱη	NOUN
ejpam-6018	310	11	)	)	PUNCT
ejpam-6018	310	12	is	be	AUX
ejpam-6018	310	13	an	an	DET
ejpam-6018	310	14	n∈-subset	n∈-subset	NOUN
ejpam-6018	310	15	of	of	ADP
ejpam-6018	310	16	(	(	PUNCT
ejpam-6018	310	17	h	h	NOUN
ejpam-6018	310	18	,	,	PUNCT
ejpam-6018	310	19	f	f	NOUN
ejpam-6018	310	20	)	)	PUNCT
ejpam-6018	310	21	.	.	PUNCT
ejpam-6018	311	1	however	however	ADV
ejpam-6018	311	2	,	,	PUNCT
ejpam-6018	311	3	(	(	PUNCT
ejpam-6018	311	4	h	h	NOUN
ejpam-6018	311	5	,	,	PUNCT
ejpam-6018	311	6	0η	0η	NUM
ejpam-6018	311	7	)	)	PUNCT
ejpam-6018	311	8	is	be	AUX
ejpam-6018	311	9	not	not	PART
ejpam-6018	311	10	an	an	DET
ejpam-6018	311	11	n∈-subset	n∈-subset	NOUN
ejpam-6018	311	12	of	of	ADP
ejpam-6018	311	13	(	(	PUNCT
ejpam-6018	311	14	h	h	NOUN
ejpam-6018	311	15	,	,	PUNCT
ejpam-6018	311	16	f	f	PROPN
ejpam-6018	311	17	)	)	PUNCT
ejpam-6018	311	18	,	,	PUNCT
ejpam-6018	311	19	meaning	mean	VERB
ejpam-6018	311	20	0	0	NUM
ejpam-6018	311	21	/∈	/∈	PUNCT
ejpam-6018	311	22	s∈(η	s∈(η	ADJ
ejpam-6018	311	23	)	)	PUNCT
ejpam-6018	311	24	.	.	PUNCT
ejpam-6018	312	1	this	this	PRON
ejpam-6018	312	2	is	be	AUX
ejpam-6018	312	3	a	a	DET
ejpam-6018	312	4	contradiction	contradiction	NOUN
ejpam-6018	312	5	,	,	PUNCT
ejpam-6018	312	6	and	and	CCONJ
ejpam-6018	312	7	so	so	ADV
ejpam-6018	312	8	f(0	f(0	NOUN
ejpam-6018	312	9	)	)	PUNCT
ejpam-6018	312	10	≤	≤	NUM
ejpam-6018	312	11	∨	∨	NUM
ejpam-6018	312	12	{	{	PUNCT
ejpam-6018	312	13	f(ξ),−0.5	f(ξ),−0.5	NOUN
ejpam-6018	312	14	}	}	PUNCT
ejpam-6018	312	15	for	for	ADP
ejpam-6018	312	16	all	all	DET
ejpam-6018	312	17	ξ	ξ	PROPN
ejpam-6018	312	18	∈	∈	PROPN
ejpam-6018	312	19	h.	h.	NOUN
ejpam-6018	312	20	let	let	VERB
ejpam-6018	312	21	ξ	ξ	SYM
ejpam-6018	312	22	∈	∈	PROPN
ejpam-6018	312	23	h	h	NOUN
ejpam-6018	312	24	and	and	CCONJ
ejpam-6018	312	25	η	η	PROPN
ejpam-6018	312	26	∈	∈	PROPN
ejpam-6018	312	27	υ	υ	NOUN
ejpam-6018	312	28	be	be	AUX
ejpam-6018	312	29	such	such	ADJ
ejpam-6018	312	30	that	that	SCONJ
ejpam-6018	312	31	(	(	PUNCT
ejpam-6018	312	32	h	h	NOUN
ejpam-6018	312	33	,	,	PUNCT
ejpam-6018	312	34	ξδ	ξδ	ADJ
ejpam-6018	312	35	)	)	PUNCT
ejpam-6018	312	36	is	be	AUX
ejpam-6018	312	37	an	an	DET
ejpam-6018	312	38	n∈-subset	n∈-subset	NOUN
ejpam-6018	312	39	of	of	ADP
ejpam-6018	312	40	(	(	PUNCT
ejpam-6018	312	41	h	h	NOUN
ejpam-6018	312	42	,	,	PUNCT
ejpam-6018	312	43	f	f	NOUN
ejpam-6018	312	44	)	)	PUNCT
ejpam-6018	312	45	.	.	PUNCT
ejpam-6018	313	1	then	then	ADV
ejpam-6018	313	2	f(ξ	f(ξ	NOUN
ejpam-6018	313	3	)	)	PUNCT
ejpam-6018	313	4	≤	≤	NUM
ejpam-6018	313	5	η	η	PROPN
ejpam-6018	313	6	.	.	PROPN
ejpam-6018	313	7	suppose	suppose	VERB
ejpam-6018	313	8	that	that	SCONJ
ejpam-6018	313	9	(	(	PUNCT
ejpam-6018	313	10	h	h	NOUN
ejpam-6018	313	11	,	,	PUNCT
ejpam-6018	313	12	0η	0η	NUM
ejpam-6018	313	13	)	)	PUNCT
ejpam-6018	313	14	is	be	AUX
ejpam-6018	313	15	not	not	PART
ejpam-6018	313	16	an	an	DET
ejpam-6018	313	17	n∈-subset	n∈-subset	NOUN
ejpam-6018	313	18	of	of	ADP
ejpam-6018	313	19	(	(	PUNCT
ejpam-6018	313	20	h	h	NOUN
ejpam-6018	313	21	,	,	PUNCT
ejpam-6018	313	22	f	f	NOUN
ejpam-6018	313	23	)	)	PUNCT
ejpam-6018	313	24	.	.	PUNCT
ejpam-6018	314	1	then	then	ADV
ejpam-6018	314	2	f(0	f(0	NOUN
ejpam-6018	314	3	)	)	PUNCT
ejpam-6018	314	4	>	>	X
ejpam-6018	315	1	η	η	PROPN
ejpam-6018	315	2	.	.	PROPN
ejpam-6018	316	1	if	if	SCONJ
ejpam-6018	316	2	f(ξ	f(ξ	NOUN
ejpam-6018	316	3	)	)	PUNCT
ejpam-6018	316	4	>	>	X
ejpam-6018	317	1	−0.5	−0.5	PROPN
ejpam-6018	317	2	,	,	PUNCT
ejpam-6018	317	3	then	then	ADV
ejpam-6018	317	4	f(0	f(0	NOUN
ejpam-6018	317	5	)	)	PUNCT
ejpam-6018	317	6	≤	≤	NUM
ejpam-6018	317	7	∨	∨	NUM
ejpam-6018	317	8	{	{	PUNCT
ejpam-6018	317	9	f(ξ),−0.5	f(ξ),−0.5	X
ejpam-6018	317	10	}	}	PUNCT
ejpam-6018	317	11	=	=	SYM
ejpam-6018	317	12	f(ξ	f(ξ	X
ejpam-6018	317	13	)	)	PUNCT
ejpam-6018	317	14	≤	≤	NUM
ejpam-6018	317	15	η	η	PROPN
ejpam-6018	317	16	,	,	PUNCT
ejpam-6018	317	17	which	which	PRON
ejpam-6018	317	18	is	be	AUX
ejpam-6018	317	19	impossible	impossible	ADJ
ejpam-6018	317	20	.	.	PUNCT
ejpam-6018	318	1	thus	thus	ADV
ejpam-6018	318	2	,	,	PUNCT
ejpam-6018	318	3	f(ξ	f(ξ	NOUN
ejpam-6018	318	4	)	)	PUNCT
ejpam-6018	318	5	≤	≤	NOUN
ejpam-6018	318	6	−0.5	−0.5	PROPN
ejpam-6018	318	7	,	,	PUNCT
ejpam-6018	318	8	and	and	CCONJ
ejpam-6018	318	9	f(0	f(0	NOUN
ejpam-6018	318	10	)	)	PUNCT
ejpam-6018	318	11	+	+	NUM
ejpam-6018	318	12	η	η	PROPN
ejpam-6018	318	13	+	+	ADP
ejpam-6018	318	14	1	1	NUM
ejpam-6018	318	15	<	<	X
ejpam-6018	318	16	2f(0	2f(0	NUM
ejpam-6018	318	17	)	)	PUNCT
ejpam-6018	318	18	+	+	CCONJ
ejpam-6018	318	19	1	1	NUM
ejpam-6018	318	20	≤	≤	NUM
ejpam-6018	318	21	2	2	NUM
ejpam-6018	318	22	∨	∨	NOUN
ejpam-6018	318	23	{	{	PUNCT
ejpam-6018	318	24	f(ξ),−0.5}+	f(ξ),−0.5}+	NOUN
ejpam-6018	318	25	1	1	NUM
ejpam-6018	318	26	=	=	SYM
ejpam-6018	318	27	0	0	NUM
ejpam-6018	318	28	,	,	PUNCT
ejpam-6018	318	29	implying	imply	VERB
ejpam-6018	318	30	that	that	SCONJ
ejpam-6018	318	31	(	(	PUNCT
ejpam-6018	318	32	h	h	NOUN
ejpam-6018	318	33	,	,	PUNCT
ejpam-6018	318	34	0η	0η	NUM
ejpam-6018	318	35	)	)	PUNCT
ejpam-6018	318	36	is	be	AUX
ejpam-6018	318	37	an	an	DET
ejpam-6018	318	38	nq	nq	NOUN
ejpam-6018	318	39	-	-	PUNCT
ejpam-6018	318	40	subset	subset	NOUN
ejpam-6018	318	41	of	of	ADP
ejpam-6018	318	42	(	(	PUNCT
ejpam-6018	318	43	h	h	NOUN
ejpam-6018	318	44	,	,	PUNCT
ejpam-6018	318	45	f	f	NOUN
ejpam-6018	318	46	)	)	PUNCT
ejpam-6018	318	47	.	.	PUNCT
ejpam-6018	319	1	therefore	therefore	ADV
ejpam-6018	319	2	,	,	PUNCT
ejpam-6018	319	3	(	(	PUNCT
ejpam-6018	319	4	h	h	NOUN
ejpam-6018	319	5	,	,	PUNCT
ejpam-6018	319	6	0η	0η	NUM
ejpam-6018	319	7	)	)	PUNCT
ejpam-6018	319	8	is	be	AUX
ejpam-6018	319	9	an	an	DET
ejpam-6018	319	10	n∈∨q	n∈∨q	NOUN
ejpam-6018	319	11	-	-	NOUN
ejpam-6018	319	12	subset	subset	NOUN
ejpam-6018	319	13	of	of	ADP
ejpam-6018	319	14	(	(	PUNCT
ejpam-6018	319	15	h	h	NOUN
ejpam-6018	319	16	,	,	PUNCT
ejpam-6018	319	17	f	f	NOUN
ejpam-6018	319	18	)	)	PUNCT
ejpam-6018	319	19	.	.	PUNCT
ejpam-6018	320	1	assume	assume	VERB
ejpam-6018	320	2	that	that	SCONJ
ejpam-6018	320	3	there	there	PRON
ejpam-6018	320	4	exist	exist	VERB
ejpam-6018	320	5	ϱ,ϖ	ϱ,ϖ	NOUN
ejpam-6018	320	6	∈	∈	PROPN
ejpam-6018	320	7	h	h	NOUN
ejpam-6018	321	1	such	such	ADJ
ejpam-6018	321	2	that	that	SCONJ
ejpam-6018	321	3	f(ϱ	f(ϱ	NOUN
ejpam-6018	321	4	)	)	PUNCT
ejpam-6018	321	5	>	>	PUNCT
ejpam-6018	321	6	∨	∨	X
ejpam-6018	321	7	{	{	PUNCT
ejpam-6018	321	8	f(ϱϖ	f(ϱϖ	NOUN
ejpam-6018	321	9	|	|	NOUN
ejpam-6018	321	10	ϱϖ	ϱϖ	NOUN
ejpam-6018	321	11	)	)	PUNCT
ejpam-6018	321	12	,	,	PUNCT
ejpam-6018	321	13	f(ϖ),−0.5	f(ϖ),−0.5	VERB
ejpam-6018	321	14	}	}	PUNCT
ejpam-6018	321	15	.	.	PUNCT
ejpam-6018	322	1	let	let	VERB
ejpam-6018	322	2	η	η	PROPN
ejpam-6018	322	3	=	=	PROPN
ejpam-6018	322	4	∨	∨	X
ejpam-6018	322	5	{	{	PUNCT
ejpam-6018	322	6	f(ϱϖ	f(ϱϖ	NOUN
ejpam-6018	322	7	|	|	NOUN
ejpam-6018	322	8	ϱϖ	ϱϖ	NOUN
ejpam-6018	322	9	)	)	PUNCT
ejpam-6018	322	10	,	,	PUNCT
ejpam-6018	322	11	f(ϖ),−0.5	f(ϖ),−0.5	VERB
ejpam-6018	322	12	}	}	PUNCT
ejpam-6018	322	13	.	.	PUNCT
ejpam-6018	323	1	then	then	ADV
ejpam-6018	323	2	η	η	PROPN
ejpam-6018	323	3	∈	∈	PROPN
ejpam-6018	323	4	υ	υ	PROPN
ejpam-6018	323	5	,	,	PUNCT
ejpam-6018	323	6	and	and	CCONJ
ejpam-6018	323	7	(	(	PUNCT
ejpam-6018	323	8	h	h	NOUN
ejpam-6018	323	9	,	,	PUNCT
ejpam-6018	323	10	(	(	PUNCT
ejpam-6018	323	11	ϱϖ	ϱϖ	NOUN
ejpam-6018	323	12	|	|	ADV
ejpam-6018	323	13	ϱϖ)η	ϱϖ)η	NUM
ejpam-6018	323	14	)	)	PUNCT
ejpam-6018	323	15	and	and	CCONJ
ejpam-6018	323	16	(	(	PUNCT
ejpam-6018	323	17	h,ϖη	h,ϖη	PUNCT
ejpam-6018	323	18	)	)	PUNCT
ejpam-6018	323	19	are	be	AUX
ejpam-6018	323	20	n∈-subsets	n∈-subset	NOUN
ejpam-6018	323	21	of	of	ADP
ejpam-6018	323	22	(	(	PUNCT
ejpam-6018	323	23	h	h	NOUN
ejpam-6018	323	24	,	,	PUNCT
ejpam-6018	323	25	f	f	NOUN
ejpam-6018	323	26	)	)	PUNCT
ejpam-6018	323	27	.	.	PUNCT
ejpam-6018	324	1	but	but	CCONJ
ejpam-6018	324	2	(	(	PUNCT
ejpam-6018	324	3	h	h	NOUN
ejpam-6018	324	4	,	,	PUNCT
ejpam-6018	324	5	ϱη	ϱη	NOUN
ejpam-6018	324	6	)	)	PUNCT
ejpam-6018	324	7	is	be	AUX
ejpam-6018	324	8	not	not	PART
ejpam-6018	324	9	an	an	DET
ejpam-6018	324	10	n∈-subset	n∈-subset	NOUN
ejpam-6018	324	11	of	of	ADP
ejpam-6018	324	12	(	(	PUNCT
ejpam-6018	324	13	h	h	NOUN
ejpam-6018	324	14	,	,	PUNCT
ejpam-6018	324	15	f	f	PROPN
ejpam-6018	324	16	)	)	PUNCT
ejpam-6018	324	17	,	,	PUNCT
ejpam-6018	324	18	leading	lead	VERB
ejpam-6018	324	19	to	to	ADP
ejpam-6018	324	20	a	a	DET
ejpam-6018	324	21	contradiction	contradiction	NOUN
ejpam-6018	324	22	.	.	PUNCT
ejpam-6018	325	1	therefore	therefore	ADV
ejpam-6018	325	2	,	,	PUNCT
ejpam-6018	325	3	(	(	PUNCT
ejpam-6018	325	4	∀ξ	∀ξ	X
ejpam-6018	325	5	,	,	PUNCT
ejpam-6018	325	6	ζ	ζ	PROPN
ejpam-6018	325	7	∈	∈	PROPN
ejpam-6018	325	8	h	h	NOUN
ejpam-6018	325	9	)	)	PUNCT
ejpam-6018	325	10	(	(	PUNCT
ejpam-6018	325	11	f(ξ	f(ξ	X
ejpam-6018	325	12	)	)	PUNCT
ejpam-6018	325	13	≤	≤	NUM
ejpam-6018	325	14	∨	∨	NUM
ejpam-6018	325	15	{	{	PUNCT
ejpam-6018	325	16	f(ξζ	f(ξζ	PROPN
ejpam-6018	325	17	|	|	ADV
ejpam-6018	325	18	ξζ	ξζ	NOUN
ejpam-6018	325	19	)	)	PUNCT
ejpam-6018	325	20	,	,	PUNCT
ejpam-6018	325	21	f(ζ),−0.5	f(ζ),−0.5	PROPN
ejpam-6018	325	22	}	}	PUNCT
ejpam-6018	325	23	)	)	PUNCT
ejpam-6018	325	24	.	.	PUNCT
ejpam-6018	326	1	let	let	VERB
ejpam-6018	326	2	ξ	ξ	X
ejpam-6018	326	3	,	,	PUNCT
ejpam-6018	326	4	ζ	ζ	PROPN
ejpam-6018	326	5	∈	∈	PROPN
ejpam-6018	326	6	h	h	NOUN
ejpam-6018	326	7	and	and	CCONJ
ejpam-6018	326	8	η	η	PROPN
ejpam-6018	326	9	,	,	PUNCT
ejpam-6018	326	10	δ	δ	PROPN
ejpam-6018	326	11	∈	∈	PROPN
ejpam-6018	326	12	υ	υ	VERB
ejpam-6018	326	13	be	be	AUX
ejpam-6018	326	14	such	such	ADJ
ejpam-6018	326	15	that	that	SCONJ
ejpam-6018	326	16	(	(	PUNCT
ejpam-6018	326	17	h	h	NOUN
ejpam-6018	326	18	,	,	PUNCT
ejpam-6018	326	19	(	(	PUNCT
ejpam-6018	326	20	ξζ	ξζ	NOUN
ejpam-6018	326	21	|	|	ADV
ejpam-6018	326	22	ξζ)η	ξζ)η	PROPN
ejpam-6018	326	23	)	)	PUNCT
ejpam-6018	326	24	and	and	CCONJ
ejpam-6018	326	25	(	(	PUNCT
ejpam-6018	326	26	h	h	NOUN
ejpam-6018	326	27	,	,	PUNCT
ejpam-6018	326	28	ζδ	ζδ	NOUN
ejpam-6018	326	29	)	)	PUNCT
ejpam-6018	326	30	are	be	AUX
ejpam-6018	326	31	n∈-subsets	n∈-subset	NOUN
ejpam-6018	326	32	of	of	ADP
ejpam-6018	326	33	(	(	PUNCT
ejpam-6018	326	34	h	h	NOUN
ejpam-6018	326	35	,	,	PUNCT
ejpam-6018	326	36	f	f	NOUN
ejpam-6018	326	37	)	)	PUNCT
ejpam-6018	326	38	,	,	PUNCT
ejpam-6018	326	39	and	and	CCONJ
ejpam-6018	326	40	suppose	suppose	VERB
ejpam-6018	326	41	that	that	SCONJ
ejpam-6018	326	42	(	(	PUNCT
ejpam-6018	326	43	h	h	NOUN
ejpam-6018	326	44	,	,	PUNCT
ejpam-6018	326	45	ξη∨δ	ξη∨δ	NOUN
ejpam-6018	326	46	)	)	PUNCT
ejpam-6018	326	47	is	be	AUX
ejpam-6018	326	48	not	not	PART
ejpam-6018	326	49	an	an	DET
ejpam-6018	326	50	n∈-subset	n∈-subset	NOUN
ejpam-6018	326	51	of	of	ADP
ejpam-6018	326	52	(	(	PUNCT
ejpam-6018	326	53	h	h	NOUN
ejpam-6018	326	54	,	,	PUNCT
ejpam-6018	326	55	f	f	NOUN
ejpam-6018	326	56	)	)	PUNCT
ejpam-6018	326	57	.	.	PUNCT
ejpam-6018	327	1	then	then	ADV
ejpam-6018	327	2	,	,	PUNCT
ejpam-6018	327	3	f(ξζ	f(ξζ	PROPN
ejpam-6018	327	4	|	|	ADV
ejpam-6018	327	5	ξζ	ξζ	NOUN
ejpam-6018	327	6	)	)	PUNCT
ejpam-6018	327	7	≤	≤	PROPN
ejpam-6018	327	8	η	η	PROPN
ejpam-6018	327	9	,	,	PUNCT
ejpam-6018	327	10	f(ζ	f(ζ	PROPN
ejpam-6018	327	11	)	)	PUNCT
ejpam-6018	327	12	≤	≤	PROPN
ejpam-6018	327	13	η	η	PROPN
ejpam-6018	327	14	,	,	PUNCT
ejpam-6018	327	15	and	and	CCONJ
ejpam-6018	327	16	f(ξ	f(ξ	NOUN
ejpam-6018	327	17	)	)	PUNCT
ejpam-6018	327	18	>	>	X
ejpam-6018	327	19	η	η	PROPN
ejpam-6018	327	20	∨	∨	PROPN
ejpam-6018	327	21	δ	δ	PROPN
ejpam-6018	327	22	.	.	PUNCT
ejpam-6018	328	1	if	if	SCONJ
ejpam-6018	328	2	∨	∨	X
ejpam-6018	328	3	{	{	PUNCT
ejpam-6018	328	4	f(ξζ	f(ξζ	PROPN
ejpam-6018	328	5	|	|	ADV
ejpam-6018	328	6	ξζ	ξζ	NOUN
ejpam-6018	328	7	)	)	PUNCT
ejpam-6018	328	8	,	,	PUNCT
ejpam-6018	328	9	f(ζ	f(ζ	PROPN
ejpam-6018	328	10	)	)	PUNCT
ejpam-6018	328	11	}	}	PUNCT
ejpam-6018	328	12	>	>	PUNCT
ejpam-6018	329	1	−0.5	−0.5	PROPN
ejpam-6018	329	2	,	,	PUNCT
ejpam-6018	329	3	then	then	ADV
ejpam-6018	329	4	f(ξ	f(ξ	NOUN
ejpam-6018	329	5	)	)	PUNCT
ejpam-6018	329	6	≤	≤	NUM
ejpam-6018	329	7	∨	∨	NUM
ejpam-6018	329	8	{	{	PUNCT
ejpam-6018	329	9	f(ξζ	f(ξζ	PROPN
ejpam-6018	329	10	|	|	ADV
ejpam-6018	329	11	ξζ	ξζ	NOUN
ejpam-6018	329	12	)	)	PUNCT
ejpam-6018	329	13	,	,	PUNCT
ejpam-6018	329	14	f(ζ),−0.5	f(ζ),−0.5	PROPN
ejpam-6018	329	15	}	}	PUNCT
ejpam-6018	329	16	=	=	SYM
ejpam-6018	329	17	∨	∨	NUM
ejpam-6018	329	18	{	{	PUNCT
ejpam-6018	329	19	f(ξζ	f(ξζ	NOUN
ejpam-6018	329	20	|	|	ADV
ejpam-6018	329	21	ξζ	ξζ	NOUN
ejpam-6018	329	22	)	)	PUNCT
ejpam-6018	329	23	,	,	PUNCT
ejpam-6018	329	24	f(ζ	f(ζ	PROPN
ejpam-6018	329	25	)	)	PUNCT
ejpam-6018	329	26	}	}	PUNCT
ejpam-6018	329	27	≤	≤	NUM
ejpam-6018	329	28	η	η	PROPN
ejpam-6018	329	29	∨	∨	PROPN
ejpam-6018	329	30	δ	δ	PROPN
ejpam-6018	329	31	,	,	PUNCT
ejpam-6018	329	32	which	which	PRON
ejpam-6018	329	33	is	be	AUX
ejpam-6018	329	34	a	a	DET
ejpam-6018	329	35	contradiction	contradiction	NOUN
ejpam-6018	329	36	.	.	PUNCT
ejpam-6018	330	1	thus,∨	thus,∨	PROPN
ejpam-6018	330	2	{	{	PUNCT
ejpam-6018	330	3	f(ξζ	f(ξζ	PROPN
ejpam-6018	330	4	|	|	ADV
ejpam-6018	330	5	ξζ	ξζ	NOUN
ejpam-6018	330	6	)	)	PUNCT
ejpam-6018	330	7	,	,	PUNCT
ejpam-6018	330	8	f(ζ	f(ζ	PROPN
ejpam-6018	330	9	)	)	PUNCT
ejpam-6018	330	10	}	}	PUNCT
ejpam-6018	330	11	≤	≤	NOUN
ejpam-6018	331	1	−0.5	−0.5	PROPN
ejpam-6018	331	2	,	,	PUNCT
ejpam-6018	331	3	and	and	CCONJ
ejpam-6018	331	4	so	so	ADV
ejpam-6018	331	5	f(ξ	f(ξ	NOUN
ejpam-6018	331	6	)	)	PUNCT
ejpam-6018	332	1	+	+	CCONJ
ejpam-6018	332	2	(	(	PUNCT
ejpam-6018	332	3	η	η	PROPN
ejpam-6018	332	4	∨	∨	PROPN
ejpam-6018	332	5	δ	δ	PROPN
ejpam-6018	332	6	)	)	PUNCT
ejpam-6018	333	1	+	+	CCONJ
ejpam-6018	333	2	1	1	NUM
ejpam-6018	333	3	<	<	X
ejpam-6018	333	4	2f(ξ	2f(ξ	NUM
ejpam-6018	333	5	)	)	PUNCT
ejpam-6018	334	1	+	+	CCONJ
ejpam-6018	334	2	1	1	NUM
ejpam-6018	334	3	≤	≤	NUM
ejpam-6018	334	4	2	2	NUM
ejpam-6018	334	5	∨	∨	NUM
ejpam-6018	334	6	{	{	PUNCT
ejpam-6018	334	7	f(ξζ	f(ξζ	PROPN
ejpam-6018	334	8	|	|	ADV
ejpam-6018	334	9	ξζ	ξζ	NOUN
ejpam-6018	334	10	)	)	PUNCT
ejpam-6018	334	11	,	,	PUNCT
ejpam-6018	334	12	f(ζ),−0.5}+	f(ζ),−0.5}+	PROPN
ejpam-6018	334	13	1	1	NUM
ejpam-6018	334	14	=	=	SYM
ejpam-6018	334	15	0	0	NUM
ejpam-6018	334	16	,	,	PUNCT
ejpam-6018	334	17	which	which	PRON
ejpam-6018	334	18	shows	show	VERB
ejpam-6018	334	19	that	that	SCONJ
ejpam-6018	334	20	(	(	PUNCT
ejpam-6018	334	21	h	h	NOUN
ejpam-6018	334	22	,	,	PUNCT
ejpam-6018	334	23	ξη∨δ	ξη∨δ	NOUN
ejpam-6018	334	24	)	)	PUNCT
ejpam-6018	334	25	is	be	AUX
ejpam-6018	334	26	annq	annq	NOUN
ejpam-6018	334	27	-	-	PUNCT
ejpam-6018	334	28	subset	subset	NOUN
ejpam-6018	334	29	of	of	ADP
ejpam-6018	334	30	(	(	PUNCT
ejpam-6018	334	31	h	h	NOUN
ejpam-6018	334	32	,	,	PUNCT
ejpam-6018	334	33	f	f	NOUN
ejpam-6018	334	34	)	)	PUNCT
ejpam-6018	334	35	.	.	PUNCT
ejpam-6018	335	1	therefore	therefore	ADV
ejpam-6018	335	2	,	,	PUNCT
ejpam-6018	335	3	(	(	PUNCT
ejpam-6018	335	4	h	h	NOUN
ejpam-6018	335	5	,	,	PUNCT
ejpam-6018	335	6	ξη∨δ	ξη∨δ	NOUN
ejpam-6018	335	7	)	)	PUNCT
ejpam-6018	335	8	is	be	AUX
ejpam-6018	335	9	ann∈∨q	ann∈∨q	NOUN
ejpam-6018	335	10	-	-	PUNCT
ejpam-6018	335	11	subset	subset	NOUN
ejpam-6018	335	12	of	of	ADP
ejpam-6018	335	13	(	(	PUNCT
ejpam-6018	335	14	h	h	NOUN
ejpam-6018	335	15	,	,	PUNCT
ejpam-6018	335	16	f	f	NOUN
ejpam-6018	335	17	)	)	PUNCT
ejpam-6018	335	18	.	.	PUNCT
ejpam-6018	336	1	consequently	consequently	ADV
ejpam-6018	336	2	,	,	PUNCT
ejpam-6018	336	3	(	(	PUNCT
ejpam-6018	336	4	h	h	NOUN
ejpam-6018	336	5	,	,	PUNCT
ejpam-6018	336	6	f	f	X
ejpam-6018	336	7	)	)	PUNCT
ejpam-6018	336	8	is	be	AUX
ejpam-6018	336	9	an	an	DET
ejpam-6018	336	10	n	n	ADV
ejpam-6018	336	11	-ideal	-ideal	NOUN
ejpam-6018	336	12	of	of	ADP
ejpam-6018	336	13	type	type	NOUN
ejpam-6018	336	14	(	(	PUNCT
ejpam-6018	336	15	∈,∈	∈,∈	X
ejpam-6018	336	16	∨q	∨q	NOUN
ejpam-6018	336	17	)	)	PUNCT
ejpam-6018	336	18	.	.	PUNCT
ejpam-6018	337	1	t.	t.	PROPN
ejpam-6018	337	2	oner	oner	PROPN
ejpam-6018	337	3	et	et	PROPN
ejpam-6018	337	4	al	al	PROPN
ejpam-6018	337	5	.	.	PUNCT
ejpam-6018	337	6	/	/	SYM
ejpam-6018	337	7	eur	eur	PROPN
ejpam-6018	337	8	.	.	PUNCT
ejpam-6018	338	1	j.	j.	PROPN
ejpam-6018	338	2	pure	pure	PROPN
ejpam-6018	338	3	appl	appl	PROPN
ejpam-6018	338	4	.	.	PROPN
ejpam-6018	338	5	math	math	PROPN
ejpam-6018	338	6	,	,	PUNCT
ejpam-6018	338	7	18	18	NUM
ejpam-6018	338	8	(	(	PUNCT
ejpam-6018	338	9	2	2	NUM
ejpam-6018	338	10	)	)	PUNCT
ejpam-6018	338	11	(	(	PUNCT
ejpam-6018	338	12	2025	2025	NUM
ejpam-6018	338	13	)	)	PUNCT
ejpam-6018	338	14	,	,	PUNCT
ejpam-6018	338	15	6018	6018	NUM
ejpam-6018	338	16	11	11	NUM
ejpam-6018	338	17	of	of	ADP
ejpam-6018	338	18	11	11	NUM
ejpam-6018	338	19	4	4	NUM
ejpam-6018	338	20	.	.	PUNCT
ejpam-6018	339	1	conclusion	conclusion	NOUN
ejpam-6018	339	2	in	in	ADP
ejpam-6018	339	3	this	this	DET
ejpam-6018	339	4	study	study	NOUN
ejpam-6018	339	5	,	,	PUNCT
ejpam-6018	339	6	we	we	PRON
ejpam-6018	339	7	have	have	AUX
ejpam-6018	339	8	introduced	introduce	VERB
ejpam-6018	339	9	and	and	CCONJ
ejpam-6018	339	10	explored	explore	VERB
ejpam-6018	339	11	the	the	DET
ejpam-6018	339	12	notions	notion	NOUN
ejpam-6018	339	13	of	of	ADP
ejpam-6018	339	14	soft	soft	ADJ
ejpam-6018	339	15	n	n	CCONJ
ejpam-6018	339	16	-subalgebras	-subalgebra	NOUN
ejpam-6018	339	17	and	and	CCONJ
ejpam-6018	339	18	soft	soft	ADJ
ejpam-6018	339	19	n	n	CCONJ
ejpam-6018	339	20	-ideals	-ideal	NOUN
ejpam-6018	339	21	in	in	ADP
ejpam-6018	339	22	the	the	DET
ejpam-6018	339	23	context	context	NOUN
ejpam-6018	339	24	of	of	ADP
ejpam-6018	339	25	sheffer	sheffer	PROPN
ejpam-6018	339	26	stroke	stroke	PROPN
ejpam-6018	339	27	hilbert	hilbert	PROPN
ejpam-6018	339	28	algebras	algebras	PROPN
ejpam-6018	339	29	,	,	PUNCT
ejpam-6018	339	30	incorporating	incorporate	VERB
ejpam-6018	339	31	the	the	DET
ejpam-6018	339	32	framework	framework	NOUN
ejpam-6018	339	33	of	of	ADP
ejpam-6018	339	34	n	n	DET
ejpam-6018	339	35	-structures	-structure	NOUN
ejpam-6018	339	36	.	.	PUNCT
ejpam-6018	340	1	by	by	ADP
ejpam-6018	340	2	defining	define	VERB
ejpam-6018	340	3	and	and	CCONJ
ejpam-6018	340	4	characterizing	characterize	VERB
ejpam-6018	340	5	these	these	DET
ejpam-6018	340	6	algebraic	algebraic	ADJ
ejpam-6018	340	7	constructs	construct	NOUN
ejpam-6018	340	8	,	,	PUNCT
ejpam-6018	340	9	we	we	PRON
ejpam-6018	340	10	have	have	AUX
ejpam-6018	340	11	established	establish	VERB
ejpam-6018	340	12	fundamental	fundamental	ADJ
ejpam-6018	340	13	properties	property	NOUN
ejpam-6018	340	14	and	and	CCONJ
ejpam-6018	340	15	the	the	DET
ejpam-6018	340	16	interrelationships	interrelationship	NOUN
ejpam-6018	340	17	between	between	ADP
ejpam-6018	340	18	different	different	ADJ
ejpam-6018	340	19	types	type	NOUN
ejpam-6018	340	20	of	of	ADP
ejpam-6018	340	21	soft	soft	ADJ
ejpam-6018	340	22	n	n	CCONJ
ejpam-6018	340	23	-subalgebras	-subalgebras	NOUN
ejpam-6018	340	24	and	and	CCONJ
ejpam-6018	340	25	soft	soft	ADJ
ejpam-6018	340	26	n	n	CCONJ
ejpam-6018	340	27	-ideals	-ideal	NOUN
ejpam-6018	340	28	,	,	PUNCT
ejpam-6018	340	29	particularly	particularly	ADV
ejpam-6018	340	30	under	under	ADP
ejpam-6018	340	31	the	the	DET
ejpam-6018	340	32	types	type	NOUN
ejpam-6018	340	33	(	(	PUNCT
ejpam-6018	340	34	∈,∈	∈,∈	X
ejpam-6018	340	35	)	)	PUNCT
ejpam-6018	340	36	and	and	CCONJ
ejpam-6018	340	37	(	(	PUNCT
ejpam-6018	340	38	∈,∈	∈,∈	X
ejpam-6018	340	39	∨q	∨q	NOUN
ejpam-6018	340	40	)	)	PUNCT
ejpam-6018	340	41	.	.	PUNCT
ejpam-6018	341	1	our	our	PRON
ejpam-6018	341	2	results	result	NOUN
ejpam-6018	341	3	provide	provide	VERB
ejpam-6018	341	4	a	a	DET
ejpam-6018	341	5	deeper	deep	ADJ
ejpam-6018	341	6	understanding	understanding	NOUN
ejpam-6018	341	7	of	of	ADP
ejpam-6018	341	8	the	the	DET
ejpam-6018	341	9	algebraic	algebraic	ADJ
ejpam-6018	341	10	behavior	behavior	NOUN
ejpam-6018	341	11	of	of	ADP
ejpam-6018	341	12	sheffer	sheffer	PROPN
ejpam-6018	341	13	stroke	stroke	PROPN
ejpam-6018	341	14	hilbert	hilbert	PROPN
ejpam-6018	341	15	algebras	algebras	PROPN
ejpam-6018	341	16	under	under	ADP
ejpam-6018	341	17	soft	soft	ADJ
ejpam-6018	341	18	set	set	NOUN
ejpam-6018	341	19	theory	theory	NOUN
ejpam-6018	341	20	,	,	PUNCT
ejpam-6018	341	21	highlighting	highlight	VERB
ejpam-6018	341	22	their	their	PRON
ejpam-6018	341	23	flexibility	flexibility	NOUN
ejpam-6018	341	24	in	in	ADP
ejpam-6018	341	25	modeling	model	VERB
ejpam-6018	341	26	uncertainty	uncertainty	NOUN
ejpam-6018	341	27	within	within	ADP
ejpam-6018	341	28	logical	logical	ADJ
ejpam-6018	341	29	systems	system	NOUN
ejpam-6018	341	30	.	.	PUNCT
ejpam-6018	342	1	these	these	DET
ejpam-6018	342	2	findings	finding	NOUN
ejpam-6018	342	3	not	not	PART
ejpam-6018	342	4	only	only	ADV
ejpam-6018	342	5	contribute	contribute	VERB
ejpam-6018	342	6	to	to	ADP
ejpam-6018	342	7	the	the	DET
ejpam-6018	342	8	ongoing	ongoing	ADJ
ejpam-6018	342	9	development	development	NOUN
ejpam-6018	342	10	of	of	ADP
ejpam-6018	342	11	algebraic	algebraic	ADJ
ejpam-6018	342	12	logic	logic	NOUN
ejpam-6018	342	13	but	but	CCONJ
ejpam-6018	342	14	also	also	ADV
ejpam-6018	342	15	open	open	VERB
ejpam-6018	342	16	pathways	pathway	NOUN
ejpam-6018	342	17	for	for	ADP
ejpam-6018	342	18	further	further	ADJ
ejpam-6018	342	19	research	research	NOUN
ejpam-6018	342	20	in	in	ADP
ejpam-6018	342	21	generalizing	generalize	VERB
ejpam-6018	342	22	soft	soft	ADJ
ejpam-6018	342	23	algebraic	algebraic	ADJ
ejpam-6018	342	24	structures	structure	NOUN
ejpam-6018	342	25	in	in	ADP
ejpam-6018	342	26	broader	broad	ADJ
ejpam-6018	342	27	mathematical	mathematical	ADJ
ejpam-6018	342	28	settings	setting	NOUN
ejpam-6018	342	29	.	.	PUNCT
ejpam-6018	343	1	future	future	ADJ
ejpam-6018	343	2	work	work	NOUN
ejpam-6018	343	3	may	may	AUX
ejpam-6018	343	4	focus	focus	VERB
ejpam-6018	343	5	on	on	ADP
ejpam-6018	343	6	extending	extend	VERB
ejpam-6018	343	7	these	these	DET
ejpam-6018	343	8	concepts	concept	NOUN
ejpam-6018	343	9	to	to	ADP
ejpam-6018	343	10	other	other	ADJ
ejpam-6018	343	11	non	non	ADJ
ejpam-6018	343	12	-	-	ADJ
ejpam-6018	343	13	classical	classical	ADJ
ejpam-6018	343	14	algebraic	algebraic	ADJ
ejpam-6018	343	15	frameworks	framework	NOUN
ejpam-6018	343	16	and	and	CCONJ
ejpam-6018	343	17	exploring	explore	VERB
ejpam-6018	343	18	their	their	PRON
ejpam-6018	343	19	potential	potential	ADJ
ejpam-6018	343	20	applications	application	NOUN
ejpam-6018	343	21	in	in	ADP
ejpam-6018	343	22	computational	computational	ADJ
ejpam-6018	343	23	logic	logic	NOUN
ejpam-6018	343	24	and	and	CCONJ
ejpam-6018	343	25	fuzzy	fuzzy	ADJ
ejpam-6018	343	26	systems	system	NOUN
ejpam-6018	343	27	.	.	PUNCT
ejpam-6018	344	1	acknowledgements	acknowledgement	NOUN
ejpam-6018	344	2	this	this	DET
ejpam-6018	344	3	research	research	NOUN
ejpam-6018	344	4	was	be	AUX
ejpam-6018	344	5	supported	support	VERB
ejpam-6018	344	6	by	by	ADP
ejpam-6018	344	7	university	university	NOUN
ejpam-6018	344	8	of	of	ADP
ejpam-6018	344	9	phayao	phayao	NOUN
ejpam-6018	344	10	and	and	CCONJ
ejpam-6018	344	11	thailand	thailand	PROPN
ejpam-6018	344	12	science	science	PROPN
ejpam-6018	344	13	research	research	PROPN
ejpam-6018	344	14	and	and	CCONJ
ejpam-6018	344	15	innovation	innovation	NOUN
ejpam-6018	344	16	fund	fund	NOUN
ejpam-6018	344	17	(	(	PUNCT
ejpam-6018	344	18	fundamental	fundamental	ADJ
ejpam-6018	344	19	fund	fund	NOUN
ejpam-6018	344	20	2025	2025	NUM
ejpam-6018	344	21	,	,	PUNCT
ejpam-6018	344	22	grant	grant	VERB
ejpam-6018	344	23	no	no	NOUN
ejpam-6018	344	24	.	.	PROPN
ejpam-6018	345	1	5027/2567	5027/2567	NUM
ejpam-6018	345	2	)	)	PUNCT
ejpam-6018	345	3	.	.	PUNCT
ejpam-6018	346	1	references	reference	NOUN
ejpam-6018	346	2	[	[	X
ejpam-6018	346	3	1	1	NUM
ejpam-6018	346	4	]	]	PUNCT
ejpam-6018	346	5	h.	h.	PROPN
ejpam-6018	346	6	m.	m.	PROPN
ejpam-6018	346	7	sheffer	sheffer	PROPN
ejpam-6018	346	8	.	.	PUNCT
ejpam-6018	347	1	a	a	DET
ejpam-6018	347	2	set	set	NOUN
ejpam-6018	347	3	of	of	ADP
ejpam-6018	347	4	five	five	NUM
ejpam-6018	347	5	independent	independent	ADJ
ejpam-6018	347	6	postulates	postulate	NOUN
ejpam-6018	347	7	for	for	ADP
ejpam-6018	347	8	boolean	boolean	ADJ
ejpam-6018	347	9	algebras	algebra	NOUN
ejpam-6018	347	10	,	,	PUNCT
ejpam-6018	347	11	with	with	ADP
ejpam-6018	347	12	application	application	NOUN
ejpam-6018	347	13	to	to	ADP
ejpam-6018	347	14	logical	logical	ADJ
ejpam-6018	347	15	constants	constant	NOUN
ejpam-6018	347	16	.	.	PUNCT
ejpam-6018	348	1	trans	trans	AUX
ejpam-6018	348	2	.	.	PUNCT
ejpam-6018	348	3	am	be	AUX
ejpam-6018	348	4	.	.	PUNCT
ejpam-6018	349	1	math	math	NOUN
ejpam-6018	349	2	.	.	PUNCT
ejpam-6018	350	1	soc	soc	PROPN
ejpam-6018	350	2	.	.	PUNCT
ejpam-6018	350	3	,	,	PUNCT
ejpam-6018	350	4	14(4):481–488	14(4):481–488	NUM
ejpam-6018	350	5	,	,	PUNCT
ejpam-6018	350	6	1913	1913	NUM
ejpam-6018	350	7	.	.	PUNCT
ejpam-6018	351	1	[	[	X
ejpam-6018	351	2	2	2	NUM
ejpam-6018	351	3	]	]	PUNCT
ejpam-6018	351	4	i.	i.	NOUN
ejpam-6018	351	5	chajad	chajad	PROPN
ejpam-6018	351	6	.	.	PUNCT
ejpam-6018	352	1	sheffer	sheffer	PROPN
ejpam-6018	352	2	operation	operation	NOUN
ejpam-6018	352	3	in	in	ADP
ejpam-6018	352	4	ortholattices	ortholattice	NOUN
ejpam-6018	352	5	.	.	PUNCT
ejpam-6018	353	1	acta	acta	PROPN
ejpam-6018	353	2	univ	univ	PROPN
ejpam-6018	353	3	.	.	PUNCT
ejpam-6018	354	1	palacki	palacki	PROPN
ejpam-6018	354	2	.	.	PUNCT
ejpam-6018	355	1	olomuc	olomuc	PROPN
ejpam-6018	355	2	.	.	PUNCT
ejpam-6018	355	3	,	,	PUNCT
ejpam-6018	355	4	fac	fac	PROPN
ejpam-6018	355	5	.	.	PROPN
ejpam-6018	355	6	rerum	rerum	PROPN
ejpam-6018	355	7	nat	nat	PROPN
ejpam-6018	355	8	.	.	PROPN
ejpam-6018	355	9	,	,	PUNCT
ejpam-6018	355	10	math	math	NOUN
ejpam-6018	355	11	.	.	PUNCT
ejpam-6018	355	12	,	,	PUNCT
ejpam-6018	355	13	44(1):19–23	44(1):19–23	NUM
ejpam-6018	355	14	,	,	PUNCT
ejpam-6018	355	15	2005	2005	NUM
ejpam-6018	355	16	.	.	PUNCT
ejpam-6018	356	1	[	[	X
ejpam-6018	356	2	3	3	X
ejpam-6018	356	3	]	]	PUNCT
ejpam-6018	356	4	v.	v.	CCONJ
ejpam-6018	356	5	kozarkiewicz	kozarkiewicz	PROPN
ejpam-6018	356	6	and	and	CCONJ
ejpam-6018	356	7	a.	a.	PROPN
ejpam-6018	356	8	grabowski	grabowski	PROPN
ejpam-6018	356	9	.	.	PUNCT
ejpam-6018	357	1	axiomatization	axiomatization	NOUN
ejpam-6018	357	2	of	of	ADP
ejpam-6018	357	3	boolean	boolean	ADJ
ejpam-6018	357	4	algebras	algebra	NOUN
ejpam-6018	357	5	based	base	VERB
ejpam-6018	357	6	on	on	ADP
ejpam-6018	357	7	sheffer	sheffer	NOUN
ejpam-6018	357	8	stroke	stroke	NOUN
ejpam-6018	357	9	.	.	PUNCT
ejpam-6018	358	1	formaliz	formaliz	PROPN
ejpam-6018	358	2	.	.	PUNCT
ejpam-6018	359	1	math	math	NOUN
ejpam-6018	359	2	.	.	PUNCT
ejpam-6018	359	3	,	,	PUNCT
ejpam-6018	359	4	12(3):355–361	12(3):355–361	NUM
ejpam-6018	359	5	,	,	PUNCT
ejpam-6018	359	6	2004	2004	NUM
ejpam-6018	359	7	.	.	PUNCT
ejpam-6018	360	1	[	[	X
ejpam-6018	360	2	4	4	X
ejpam-6018	360	3	]	]	PUNCT
ejpam-6018	360	4	t.	t.	NOUN
ejpam-6018	360	5	oner	oner	NOUN
ejpam-6018	360	6	,	,	PUNCT
ejpam-6018	360	7	t.	t.	PROPN
ejpam-6018	360	8	katican	katican	PROPN
ejpam-6018	360	9	,	,	PUNCT
ejpam-6018	360	10	and	and	CCONJ
ejpam-6018	360	11	a.	a.	PROPN
ejpam-6018	360	12	borumand	borumand	PROPN
ejpam-6018	360	13	saeid	saeid	PROPN
ejpam-6018	360	14	.	.	PUNCT
ejpam-6018	360	15	bl	bl	VERB
ejpam-6018	360	16	-	-	PUNCT
ejpam-6018	360	17	algebras	algebras	PROPN
ejpam-6018	360	18	defined	define	VERB
ejpam-6018	360	19	by	by	ADP
ejpam-6018	360	20	an	an	DET
ejpam-6018	360	21	operator	operator	NOUN
ejpam-6018	360	22	.	.	PUNCT
ejpam-6018	361	1	honam	honam	PROPN
ejpam-6018	361	2	math	math	PROPN
ejpam-6018	361	3	.	.	PUNCT
ejpam-6018	362	1	j.	j.	PROPN
ejpam-6018	362	2	,	,	PUNCT
ejpam-6018	362	3	44(2):18–31	44(2):18–31	NUM
ejpam-6018	362	4	,	,	PUNCT
ejpam-6018	362	5	2022	2022	NUM
ejpam-6018	362	6	.	.	PUNCT
ejpam-6018	363	1	[	[	X
ejpam-6018	363	2	5	5	X
ejpam-6018	363	3	]	]	PUNCT
ejpam-6018	363	4	t.	t.	NOUN
ejpam-6018	363	5	oner	oner	NOUN
ejpam-6018	363	6	,	,	PUNCT
ejpam-6018	363	7	t.	t.	PROPN
ejpam-6018	363	8	katican	katican	PROPN
ejpam-6018	363	9	,	,	PUNCT
ejpam-6018	363	10	and	and	CCONJ
ejpam-6018	363	11	a.	a.	PROPN
ejpam-6018	363	12	borumand	borumand	PROPN
ejpam-6018	363	13	saeid	saeid	PROPN
ejpam-6018	363	14	.	.	PUNCT
ejpam-6018	364	1	class	class	NOUN
ejpam-6018	364	2	of	of	ADP
ejpam-6018	364	3	sheffer	sheffer	PROPN
ejpam-6018	364	4	stroke	stroke	NOUN
ejpam-6018	364	5	bck	bck	PROPN
ejpam-6018	364	6	-	-	PUNCT
ejpam-6018	364	7	algebras	algebras	PROPN
ejpam-6018	364	8	.	.	PUNCT
ejpam-6018	365	1	an	an	DET
ejpam-6018	365	2	.	.	PUNCT
ejpam-6018	365	3	ştiinţ.	ştiinţ.	PROPN
ejpam-6018	365	4	univ	univ	PROPN
ejpam-6018	365	5	.	.	PUNCT
ejpam-6018	366	1	“	"	PUNCT
ejpam-6018	366	2	ovidius	ovidius	ADJ
ejpam-6018	366	3	”	"	PUNCT
ejpam-6018	366	4	constanţa	constanţa	NOUN
ejpam-6018	366	5	,	,	PUNCT
ejpam-6018	366	6	ser	ser	NOUN
ejpam-6018	366	7	.	.	PROPN
ejpam-6018	366	8	mat	mat	PROPN
ejpam-6018	366	9	.	.	PROPN
ejpam-6018	366	10	,	,	PUNCT
ejpam-6018	366	11	30(1):247–269	30(1):247–269	PROPN
ejpam-6018	366	12	,	,	PUNCT
ejpam-6018	366	13	2022	2022	NUM
ejpam-6018	366	14	.	.	PUNCT
ejpam-6018	367	1	[	[	X
ejpam-6018	367	2	6	6	NUM
ejpam-6018	367	3	]	]	PUNCT
ejpam-6018	367	4	t.	t.	NOUN
ejpam-6018	367	5	oner	oner	NOUN
ejpam-6018	367	6	and	and	CCONJ
ejpam-6018	367	7	i.	i.	PROPN
ejpam-6018	367	8	senturk	senturk	PROPN
ejpam-6018	367	9	.	.	PUNCT
ejpam-6018	368	1	the	the	DET
ejpam-6018	368	2	sheffer	sheffer	PROPN
ejpam-6018	368	3	stroke	stroke	NOUN
ejpam-6018	368	4	operation	operation	NOUN
ejpam-6018	368	5	reducts	reduct	NOUN
ejpam-6018	368	6	of	of	ADP
ejpam-6018	368	7	basic	basic	ADJ
ejpam-6018	368	8	algebras	algebra	NOUN
ejpam-6018	368	9	.	.	PUNCT
ejpam-6018	369	1	open	open	ADJ
ejpam-6018	369	2	math	math	NOUN
ejpam-6018	369	3	.	.	PUNCT
ejpam-6018	369	4	,	,	PUNCT
ejpam-6018	369	5	15(1):926–935	15(1):926–935	PROPN
ejpam-6018	369	6	,	,	PUNCT
ejpam-6018	369	7	2017	2017	NUM
ejpam-6018	369	8	.	.	PUNCT
ejpam-6018	370	1	[	[	X
ejpam-6018	370	2	7	7	X
ejpam-6018	370	3	]	]	PUNCT
ejpam-6018	370	4	i.	i.	NOUN
ejpam-6018	370	5	senturk	senturk	PROPN
ejpam-6018	370	6	.	.	PUNCT
ejpam-6018	371	1	a	a	DET
ejpam-6018	371	2	new	new	ADJ
ejpam-6018	371	3	on	on	ADP
ejpam-6018	371	4	state	state	NOUN
ejpam-6018	371	5	operators	operator	NOUN
ejpam-6018	371	6	in	in	ADP
ejpam-6018	371	7	sheffer	sheffer	PROPN
ejpam-6018	371	8	stroke	stroke	NOUN
ejpam-6018	371	9	basic	basic	ADJ
ejpam-6018	371	10	algebras	algebra	NOUN
ejpam-6018	371	11	.	.	PUNCT
ejpam-6018	371	12	soft	soft	ADJ
ejpam-6018	371	13	comput	comput	NOUN
ejpam-6018	371	14	.	.	PUNCT
ejpam-6018	371	15	,	,	PUNCT
ejpam-6018	371	16	25(17):11471–11484	25(17):11471–11484	NUM
ejpam-6018	371	17	,	,	PUNCT
ejpam-6018	371	18	2021	2021	NUM
ejpam-6018	371	19	.	.	PUNCT
ejpam-6018	372	1	[	[	X
ejpam-6018	372	2	8	8	NUM
ejpam-6018	372	3	]	]	X
ejpam-6018	372	4	i.	i.	NOUN
ejpam-6018	372	5	senturk	senturk	PROPN
ejpam-6018	372	6	.	.	PUNCT
ejpam-6018	373	1	riečan	riečan	NOUN
ejpam-6018	373	2	and	and	CCONJ
ejpam-6018	373	3	bosbach	bosbach	ADJ
ejpam-6018	373	4	state	state	NOUN
ejpam-6018	373	5	operators	operator	NOUN
ejpam-6018	373	6	on	on	ADP
ejpam-6018	373	7	sheffer	sheffer	PROPN
ejpam-6018	373	8	stroke	stroke	NOUN
ejpam-6018	373	9	mtl	mtl	PROPN
ejpam-6018	373	10	-	-	PUNCT
ejpam-6018	373	11	algebras	algebras	PROPN
ejpam-6018	373	12	.	.	PUNCT
ejpam-6018	374	1	bull	bull	NOUN
ejpam-6018	374	2	.	.	PUNCT
ejpam-6018	375	1	int	int	NOUN
ejpam-6018	375	2	.	.	PUNCT
ejpam-6018	376	1	math	math	NOUN
ejpam-6018	376	2	.	.	PUNCT
ejpam-6018	377	1	virtual	virtual	ADJ
ejpam-6018	377	2	inst	inst	PROPN
ejpam-6018	377	3	.	.	PROPN
ejpam-6018	377	4	,	,	PUNCT
ejpam-6018	377	5	12(1):181–193	12(1):181–193	NUM
ejpam-6018	377	6	,	,	PUNCT
ejpam-6018	377	7	2022	2022	NUM
ejpam-6018	377	8	.	.	PUNCT
ejpam-6018	378	1	[	[	X
ejpam-6018	378	2	9	9	NUM
ejpam-6018	378	3	]	]	X
ejpam-6018	378	4	n.	n.	PROPN
ejpam-6018	378	5	rajesh	rajesh	PROPN
ejpam-6018	378	6	,	,	PUNCT
ejpam-6018	378	7	t.	t.	PROPN
ejpam-6018	378	8	oner	oner	NOUN
ejpam-6018	378	9	,	,	PUNCT
ejpam-6018	378	10	a.	a.	NOUN
ejpam-6018	378	11	iampan	iampan	PROPN
ejpam-6018	378	12	,	,	PUNCT
ejpam-6018	378	13	and	and	CCONJ
ejpam-6018	378	14	i.	i.	PROPN
ejpam-6018	378	15	senturk	senturk	PROPN
ejpam-6018	378	16	.	.	PUNCT
ejpam-6018	379	1	on	on	ADP
ejpam-6018	379	2	length	length	NOUN
ejpam-6018	379	3	and	and	CCONJ
ejpam-6018	379	4	mean	mean	VERB
ejpam-6018	379	5	fuzzy	fuzzy	ADJ
ejpam-6018	379	6	ideals	ideal	NOUN
ejpam-6018	379	7	of	of	ADP
ejpam-6018	379	8	sheffer	sheffer	PROPN
ejpam-6018	379	9	stroke	stroke	PROPN
ejpam-6018	379	10	hilbert	hilbert	PROPN
ejpam-6018	379	11	algebras	algebras	PROPN
ejpam-6018	379	12	.	.	PUNCT
ejpam-6018	380	1	eur	eur	PROPN
ejpam-6018	380	2	.	.	PUNCT
ejpam-6018	381	1	j.	j.	PROPN
ejpam-6018	381	2	pure	pure	PROPN
ejpam-6018	381	3	appl	appl	PROPN
ejpam-6018	381	4	.	.	PUNCT
ejpam-6018	381	5	math	math	PROPN
ejpam-6018	381	6	.	.	PUNCT
ejpam-6018	381	7	,	,	PUNCT
ejpam-6018	381	8	18(1):5779	18(1):5779	NUM
ejpam-6018	381	9	,	,	PUNCT
ejpam-6018	381	10	2025	2025	NUM
ejpam-6018	381	11	.	.	PUNCT
ejpam-6018	382	1	[	[	X
ejpam-6018	382	2	10	10	NUM
ejpam-6018	382	3	]	]	X
ejpam-6018	382	4	d.	d.	PROPN
ejpam-6018	382	5	molodstov	molodstov	PROPN
ejpam-6018	382	6	.	.	PUNCT
ejpam-6018	383	1	soft	soft	ADJ
ejpam-6018	383	2	set	set	NOUN
ejpam-6018	383	3	theory	theory	NOUN
ejpam-6018	383	4	-	-	PUNCT
ejpam-6018	383	5	first	first	ADJ
ejpam-6018	383	6	results	result	NOUN
ejpam-6018	383	7	.	.	PUNCT
ejpam-6018	384	1	comput	comput	NOUN
ejpam-6018	384	2	.	.	PUNCT
ejpam-6018	385	1	math	math	NOUN
ejpam-6018	385	2	.	.	PUNCT
ejpam-6018	386	1	appl	appl	PROPN
ejpam-6018	386	2	.	.	PROPN
ejpam-6018	387	1	,	,	PUNCT
ejpam-6018	388	1	37(4	37(4	PROPN
ejpam-6018	388	2	-	-	PUNCT
ejpam-6018	388	3	5):19–31	5):19–31	NUM
ejpam-6018	388	4	,	,	PUNCT
ejpam-6018	388	5	1999	1999	NUM
ejpam-6018	388	6	.	.	PUNCT
ejpam-6018	389	1	[	[	X
ejpam-6018	389	2	11	11	NUM
ejpam-6018	389	3	]	]	PUNCT
ejpam-6018	389	4	t.	t.	NOUN
ejpam-6018	389	5	oner	oner	NOUN
ejpam-6018	389	6	,	,	PUNCT
ejpam-6018	389	7	t.	t.	PROPN
ejpam-6018	389	8	katican	katican	PROPN
ejpam-6018	389	9	,	,	PUNCT
ejpam-6018	389	10	and	and	CCONJ
ejpam-6018	389	11	a.	a.	PROPN
ejpam-6018	389	12	borumand	borumand	PROPN
ejpam-6018	389	13	saeid	saeid	PROPN
ejpam-6018	389	14	.	.	PUNCT
ejpam-6018	390	1	relation	relation	NOUN
ejpam-6018	390	2	between	between	ADP
ejpam-6018	390	3	sheffer	sheffer	PROPN
ejpam-6018	390	4	stroke	stroke	PROPN
ejpam-6018	390	5	and	and	CCONJ
ejpam-6018	390	6	hilbert	hilbert	PROPN
ejpam-6018	390	7	algebras	algebras	PROPN
ejpam-6018	390	8	.	.	PUNCT
ejpam-6018	391	1	categ	categ	PROPN
ejpam-6018	391	2	.	.	PUNCT
ejpam-6018	392	1	gen	gen	PROPN
ejpam-6018	392	2	.	.	PROPN
ejpam-6018	392	3	algebr	algebr	PROPN
ejpam-6018	392	4	.	.	PUNCT
ejpam-6018	393	1	struct	struct	NOUN
ejpam-6018	393	2	.	.	PUNCT
ejpam-6018	394	1	appl	appl	PROPN
ejpam-6018	394	2	.	.	PROPN
ejpam-6018	394	3	,	,	PUNCT
ejpam-6018	395	1	14(1):245–268	14(1):245–268	NUM
ejpam-6018	395	2	,	,	PUNCT
ejpam-6018	395	3	2021	2021	NUM
ejpam-6018	395	4	.	.	PUNCT