id	sid	tid	token	lemma	pos
ejpam-5423	1	1	european	european	PROPN
ejpam-5423	1	2	journal	journal	PROPN
ejpam-5423	1	3	of	of	ADP
ejpam-5423	1	4	pure	pure	ADJ
ejpam-5423	1	5	and	and	CCONJ
ejpam-5423	1	6	applied	apply	VERB
ejpam-5423	1	7	mathematics	mathematic	NOUN
ejpam-5423	1	8	vol	vol	NOUN
ejpam-5423	1	9	.	.	PROPN
ejpam-5423	2	1	17	17	NUM
ejpam-5423	2	2	,	,	PUNCT
ejpam-5423	2	3	no	no	INTJ
ejpam-5423	2	4	.	.	NOUN
ejpam-5423	2	5	4	4	NUM
ejpam-5423	2	6	,	,	PUNCT
ejpam-5423	2	7	2024	2024	NUM
ejpam-5423	2	8	,	,	PUNCT
ejpam-5423	2	9	3223	3223	NUM
ejpam-5423	2	10	-	-	SYM
ejpam-5423	2	11	3241	3241	NUM
ejpam-5423	2	12	issn	issn	PROPN
ejpam-5423	2	13	1307	1307	NUM
ejpam-5423	2	14	-	-	SYM
ejpam-5423	2	15	5543	5543	NUM
ejpam-5423	2	16	–	–	PUNCT
ejpam-5423	2	17	ejpam.com	ejpam.com	X
ejpam-5423	2	18	published	publish	VERB
ejpam-5423	2	19	by	by	ADP
ejpam-5423	2	20	new	new	PROPN
ejpam-5423	2	21	york	york	PROPN
ejpam-5423	2	22	business	business	PROPN
ejpam-5423	2	23	global	global	ADJ
ejpam-5423	2	24	characterizations	characterization	NOUN
ejpam-5423	2	25	regular	regular	ADJ
ejpam-5423	2	26	and	and	CCONJ
ejpam-5423	2	27	intra	intra	ADJ
ejpam-5423	2	28	-	-	ADJ
ejpam-5423	2	29	regular	regular	ADJ
ejpam-5423	2	30	ordered	order	VERB
ejpam-5423	2	31	semigroups	semigroup	NOUN
ejpam-5423	2	32	by	by	ADP
ejpam-5423	2	33	using	use	VERB
ejpam-5423	2	34	generalized	generalized	ADJ
ejpam-5423	2	35	interval	interval	NOUN
ejpam-5423	2	36	valued	value	VERB
ejpam-5423	2	37	bipolar	bipolar	ADJ
ejpam-5423	2	38	fuzzy	fuzzy	ADJ
ejpam-5423	2	39	quasi	quasi	NOUN
ejpam-5423	2	40	-	-	NOUN
ejpam-5423	2	41	ideals	ideal	NOUN
ejpam-5423	2	42	thiti	thiti	PROPN
ejpam-5423	2	43	gaketem1	gaketem1	PROPN
ejpam-5423	2	44	,	,	PUNCT
ejpam-5423	2	45	tanaphong	tanaphong	ADP
ejpam-5423	2	46	prommai2,∗	prommai2,∗	PROPN
ejpam-5423	2	47	1,2	1,2	NUM
ejpam-5423	2	48	fuzzy	fuzzy	ADJ
ejpam-5423	2	49	algebras	algebra	NOUN
ejpam-5423	2	50	and	and	CCONJ
ejpam-5423	2	51	decision	decision	NOUN
ejpam-5423	2	52	-	-	PUNCT
ejpam-5423	2	53	making	make	VERB
ejpam-5423	2	54	problems	problem	NOUN
ejpam-5423	2	55	research	research	NOUN
ejpam-5423	2	56	unit	unit	NOUN
ejpam-5423	2	57	,	,	PUNCT
ejpam-5423	2	58	department	department	NOUN
ejpam-5423	2	59	of	of	ADP
ejpam-5423	2	60	mathematics	mathematic	NOUN
ejpam-5423	2	61	,	,	PUNCT
ejpam-5423	2	62	school	school	NOUN
ejpam-5423	2	63	of	of	ADP
ejpam-5423	2	64	science	science	NOUN
ejpam-5423	2	65	,	,	PUNCT
ejpam-5423	2	66	university	university	NOUN
ejpam-5423	2	67	of	of	ADP
ejpam-5423	2	68	phayao	phayao	NOUN
ejpam-5423	2	69	,	,	PUNCT
ejpam-5423	2	70	phayao	phayao	NOUN
ejpam-5423	2	71	56000	56000	NUM
ejpam-5423	2	72	,	,	PUNCT
ejpam-5423	2	73	thailand	thailand	PROPN
ejpam-5423	2	74	abstract	abstract	NOUN
ejpam-5423	2	75	.	.	PUNCT
ejpam-5423	3	1	in	in	ADP
ejpam-5423	3	2	this	this	DET
ejpam-5423	3	3	article	article	NOUN
ejpam-5423	3	4	,	,	PUNCT
ejpam-5423	3	5	we	we	PRON
ejpam-5423	3	6	introduce	introduce	VERB
ejpam-5423	3	7	the	the	DET
ejpam-5423	3	8	concept	concept	NOUN
ejpam-5423	3	9	of	of	ADP
ejpam-5423	3	10	a	a	DET
ejpam-5423	3	11	generalized	generalized	ADJ
ejpam-5423	3	12	interval	interval	NOUN
ejpam-5423	3	13	-	-	PUNCT
ejpam-5423	3	14	valued	value	VERB
ejpam-5423	3	15	bipolar	bipolar	ADJ
ejpam-5423	3	16	fuzzy	fuzzy	ADJ
ejpam-5423	3	17	quasi	quasi	NOUN
ejpam-5423	3	18	-	-	ADJ
ejpam-5423	3	19	ideal	ideal	ADJ
ejpam-5423	3	20	and	and	CCONJ
ejpam-5423	3	21	investigate	investigate	VERB
ejpam-5423	3	22	its	its	PRON
ejpam-5423	3	23	properties	property	NOUN
ejpam-5423	3	24	.	.	PUNCT
ejpam-5423	4	1	we	we	PRON
ejpam-5423	4	2	explore	explore	VERB
ejpam-5423	4	3	the	the	DET
ejpam-5423	4	4	relationship	relationship	NOUN
ejpam-5423	4	5	between	between	ADP
ejpam-5423	4	6	generalized	generalize	VERB
ejpam-5423	4	7	intervalvalued	intervalvalue	VERB
ejpam-5423	4	8	bipolar	bipolar	ADJ
ejpam-5423	4	9	fuzzy	fuzzy	ADJ
ejpam-5423	4	10	quasi	quasi	NOUN
ejpam-5423	4	11	-	-	NOUN
ejpam-5423	4	12	ideals	ideal	NOUN
ejpam-5423	4	13	and	and	CCONJ
ejpam-5423	4	14	generalized	generalized	ADJ
ejpam-5423	4	15	interval	interval	NOUN
ejpam-5423	4	16	-	-	PUNCT
ejpam-5423	4	17	valued	value	VERB
ejpam-5423	4	18	bipolar	bipolar	ADJ
ejpam-5423	4	19	fuzzy	fuzzy	ADJ
ejpam-5423	4	20	ideals	ideal	NOUN
ejpam-5423	4	21	.	.	PUNCT
ejpam-5423	5	1	furthermore	furthermore	ADV
ejpam-5423	5	2	,	,	PUNCT
ejpam-5423	5	3	we	we	PRON
ejpam-5423	5	4	characterize	characterize	VERB
ejpam-5423	5	5	regular	regular	ADJ
ejpam-5423	5	6	and	and	CCONJ
ejpam-5423	5	7	intra	intra	ADJ
ejpam-5423	5	8	-	-	ADJ
ejpam-5423	5	9	regular	regular	ADJ
ejpam-5423	5	10	ordered	order	VERB
ejpam-5423	5	11	semigroups	semigroup	NOUN
ejpam-5423	5	12	by	by	ADP
ejpam-5423	5	13	utilizing	utilize	VERB
ejpam-5423	5	14	generalized	generalized	ADJ
ejpam-5423	5	15	interval	interval	NOUN
ejpam-5423	5	16	valued	value	VERB
ejpam-5423	5	17	bipolar	bipolar	ADJ
ejpam-5423	5	18	fuzzy	fuzzy	ADJ
ejpam-5423	5	19	quasi	quasi	NOUN
ejpam-5423	5	20	-	-	NOUN
ejpam-5423	5	21	ideals	ideal	NOUN
ejpam-5423	5	22	.	.	PUNCT
ejpam-5423	6	1	2020	2020	NUM
ejpam-5423	6	2	mathematics	mathematic	NOUN
ejpam-5423	6	3	subject	subject	NOUN
ejpam-5423	6	4	classifications	classification	NOUN
ejpam-5423	6	5	:	:	PUNCT
ejpam-5423	6	6	06f05	06f05	NUM
ejpam-5423	6	7	,	,	PUNCT
ejpam-5423	6	8	06d72	06d72	NOUN
ejpam-5423	6	9	,	,	PUNCT
ejpam-5423	6	10	08a72	08a72	NOUN
ejpam-5423	6	11	key	key	ADJ
ejpam-5423	6	12	words	word	NOUN
ejpam-5423	6	13	and	and	CCONJ
ejpam-5423	6	14	phrases	phrase	NOUN
ejpam-5423	6	15	:	:	PUNCT
ejpam-5423	6	16	ordered	order	VERB
ejpam-5423	6	17	semigroup	semigroup	PROPN
ejpam-5423	6	18	,	,	PUNCT
ejpam-5423	6	19	interval	interval	NOUN
ejpam-5423	6	20	valued	value	VERB
ejpam-5423	6	21	bipolar	bipolar	ADJ
ejpam-5423	6	22	fuzzy	fuzzy	ADJ
ejpam-5423	6	23	quasi	quasi	NOUN
ejpam-5423	6	24	-	-	ADJ
ejpam-5423	6	25	ideal	ideal	ADJ
ejpam-5423	6	26	,	,	PUNCT
ejpam-5423	6	27	interval	interval	NOUN
ejpam-5423	6	28	valued	value	VERB
ejpam-5423	6	29	bipolar	bipolar	ADJ
ejpam-5423	6	30	fuzzy	fuzzy	ADJ
ejpam-5423	6	31	ideals	ideal	NOUN
ejpam-5423	6	32	1	1	NUM
ejpam-5423	6	33	.	.	PUNCT
ejpam-5423	6	34	introduction	introduction	NOUN
ejpam-5423	6	35	the	the	DET
ejpam-5423	6	36	tool	tool	NOUN
ejpam-5423	6	37	used	use	VERB
ejpam-5423	6	38	phenomena	phenomenon	NOUN
ejpam-5423	6	39	of	of	ADP
ejpam-5423	6	40	renowned	renowned	ADJ
ejpam-5423	6	41	vagueness	vagueness	NOUN
ejpam-5423	6	42	and	and	CCONJ
ejpam-5423	6	43	uncertainty	uncertainty	NOUN
ejpam-5423	6	44	of	of	ADP
ejpam-5423	6	45	data	datum	NOUN
ejpam-5423	6	46	scientists	scientist	NOUN
ejpam-5423	6	47	by	by	ADP
ejpam-5423	6	48	l.	l.	PROPN
ejpam-5423	6	49	a.	a.	PROPN
ejpam-5423	6	50	zadeh	zadeh	PROPN
ejpam-5423	6	51	in	in	ADP
ejpam-5423	6	52	1965	1965	NUM
ejpam-5423	6	53	[	[	X
ejpam-5423	6	54	15	15	NUM
ejpam-5423	6	55	]	]	PUNCT
ejpam-5423	6	56	.	.	PUNCT
ejpam-5423	7	1	the	the	DET
ejpam-5423	7	2	theory	theory	NOUN
ejpam-5423	7	3	of	of	ADP
ejpam-5423	7	4	fuzzy	fuzzy	ADJ
ejpam-5423	7	5	semigroups	semigroup	NOUN
ejpam-5423	7	6	was	be	AUX
ejpam-5423	7	7	contained	contain	VERB
ejpam-5423	7	8	by	by	ADP
ejpam-5423	7	9	kuroki	kuroki	NOUN
ejpam-5423	7	10	in	in	ADP
ejpam-5423	7	11	1979	1979	NUM
ejpam-5423	7	12	[	[	X
ejpam-5423	7	13	10	10	NUM
ejpam-5423	7	14	]	]	PUNCT
ejpam-5423	7	15	.	.	PUNCT
ejpam-5423	8	1	later	later	ADV
ejpam-5423	8	2	the	the	DET
ejpam-5423	8	3	theory	theory	NOUN
ejpam-5423	8	4	of	of	ADP
ejpam-5423	8	5	interval	interval	NOUN
ejpam-5423	8	6	valued	value	VERB
ejpam-5423	8	7	fuzzy	fuzzy	ADJ
ejpam-5423	8	8	sets	set	NOUN
ejpam-5423	8	9	was	be	AUX
ejpam-5423	8	10	introduced	introduce	VERB
ejpam-5423	8	11	by	by	ADP
ejpam-5423	8	12	l.	l.	PROPN
ejpam-5423	8	13	a.	a.	PROPN
ejpam-5423	8	14	zadeh	zadeh	PROPN
ejpam-5423	8	15	in	in	ADP
ejpam-5423	8	16	1975	1975	NUM
ejpam-5423	8	17	[	[	X
ejpam-5423	8	18	16	16	NUM
ejpam-5423	8	19	]	]	PUNCT
ejpam-5423	8	20	as	as	ADP
ejpam-5423	8	21	a	a	DET
ejpam-5423	8	22	generalization	generalization	NOUN
ejpam-5423	8	23	of	of	ADP
ejpam-5423	8	24	the	the	DET
ejpam-5423	8	25	notion	notion	NOUN
ejpam-5423	8	26	of	of	ADP
ejpam-5423	8	27	fuzzy	fuzzy	ADJ
ejpam-5423	8	28	sets	set	NOUN
ejpam-5423	8	29	.	.	PUNCT
ejpam-5423	9	1	interval	interval	NOUN
ejpam-5423	9	2	valued	value	VERB
ejpam-5423	9	3	fuzzy	fuzzy	ADJ
ejpam-5423	9	4	sets	set	NOUN
ejpam-5423	9	5	have	have	VERB
ejpam-5423	9	6	various	various	ADJ
ejpam-5423	9	7	applications	application	NOUN
ejpam-5423	9	8	in	in	ADP
ejpam-5423	9	9	several	several	ADJ
ejpam-5423	9	10	areas	area	NOUN
ejpam-5423	9	11	like	like	ADP
ejpam-5423	9	12	medical	medical	ADJ
ejpam-5423	9	13	science	science	NOUN
ejpam-5423	9	14	[	[	X
ejpam-5423	9	15	5	5	NUM
ejpam-5423	9	16	]	]	PUNCT
ejpam-5423	9	17	,	,	PUNCT
ejpam-5423	9	18	image	image	NOUN
ejpam-5423	9	19	processing	processing	NOUN
ejpam-5423	9	20	[	[	X
ejpam-5423	9	21	8	8	NUM
ejpam-5423	9	22	]	]	PUNCT
ejpam-5423	9	23	,	,	PUNCT
ejpam-5423	9	24	decision	decision	NOUN
ejpam-5423	9	25	making	make	VERB
ejpam-5423	9	26	[	[	X
ejpam-5423	9	27	18	18	NUM
ejpam-5423	9	28	]	]	PUNCT
ejpam-5423	9	29	,	,	PUNCT
ejpam-5423	9	30	etc	etc	X
ejpam-5423	9	31	.	.	X
ejpam-5423	9	32	in	in	ADP
ejpam-5423	9	33	2006	2006	NUM
ejpam-5423	9	34	,	,	PUNCT
ejpam-5423	9	35	narayanan	narayanan	PROPN
ejpam-5423	9	36	and	and	CCONJ
ejpam-5423	9	37	manikantan	manikantan	PROPN
ejpam-5423	10	1	[	[	X
ejpam-5423	10	2	13	13	NUM
ejpam-5423	10	3	]	]	PUNCT
ejpam-5423	10	4	developed	develop	VERB
ejpam-5423	10	5	the	the	DET
ejpam-5423	10	6	theory	theory	NOUN
ejpam-5423	10	7	of	of	ADP
ejpam-5423	10	8	interval	interval	NOUN
ejpam-5423	10	9	valued	value	VERB
ejpam-5423	10	10	fuzzy	fuzzy	ADJ
ejpam-5423	10	11	subsemigroup	subsemigroup	ADV
ejpam-5423	10	12	and	and	CCONJ
ejpam-5423	10	13	studied	study	VERB
ejpam-5423	10	14	types	type	NOUN
ejpam-5423	10	15	interval	interval	NOUN
ejpam-5423	10	16	valued	value	VERB
ejpam-5423	10	17	fuzzy	fuzzy	ADJ
ejpam-5423	10	18	ideals	ideal	NOUN
ejpam-5423	10	19	in	in	ADP
ejpam-5423	10	20	semigroups	semigroup	NOUN
ejpam-5423	10	21	.	.	PUNCT
ejpam-5423	11	1	in	in	ADP
ejpam-5423	11	2	1994	1994	NUM
ejpam-5423	11	3	zhang	zhang	X
ejpam-5423	12	1	[	[	X
ejpam-5423	12	2	17	17	NUM
ejpam-5423	12	3	]	]	PUNCT
ejpam-5423	12	4	introduced	introduce	VERB
ejpam-5423	12	5	the	the	DET
ejpam-5423	12	6	notion	notion	NOUN
ejpam-5423	12	7	of	of	ADP
ejpam-5423	12	8	bipolar	bipolar	ADJ
ejpam-5423	12	9	fuzzy	fuzzy	ADJ
ejpam-5423	12	10	sets	set	NOUN
ejpam-5423	12	11	with	with	ADP
ejpam-5423	12	12	the	the	DET
ejpam-5423	12	13	extension	extension	NOUN
ejpam-5423	12	14	of	of	ADP
ejpam-5423	12	15	fuzzy	fuzzy	ADJ
ejpam-5423	12	16	sets	set	NOUN
ejpam-5423	12	17	whose	whose	DET
ejpam-5423	12	18	membership	membership	NOUN
ejpam-5423	12	19	degree	degree	NOUN
ejpam-5423	12	20	range	range	NOUN
ejpam-5423	12	21	is	be	AUX
ejpam-5423	12	22	enlarged	enlarge	VERB
ejpam-5423	12	23	from	from	ADP
ejpam-5423	12	24	the	the	DET
ejpam-5423	12	25	interval	interval	NOUN
ejpam-5423	12	26	[	[	X
ejpam-5423	12	27	0	0	NUM
ejpam-5423	12	28	,	,	PUNCT
ejpam-5423	12	29	1	1	NUM
ejpam-5423	12	30	]	]	PUNCT
ejpam-5423	12	31	to	to	ADP
ejpam-5423	12	32	[	[	X
ejpam-5423	12	33	−1	−1	NOUN
ejpam-5423	12	34	,	,	PUNCT
ejpam-5423	12	35	1	1	NUM
ejpam-5423	12	36	]	]	PUNCT
ejpam-5423	12	37	,	,	PUNCT
ejpam-5423	12	38	and	and	CCONJ
ejpam-5423	12	39	used	use	VERB
ejpam-5423	12	40	them	they	PRON
ejpam-5423	12	41	for	for	ADP
ejpam-5423	12	42	modeling	modeling	NOUN
ejpam-5423	12	43	and	and	CCONJ
ejpam-5423	12	44	decision	decision	NOUN
ejpam-5423	12	45	analysis	analysis	NOUN
ejpam-5423	12	46	.	.	PUNCT
ejpam-5423	13	1	in	in	ADP
ejpam-5423	13	2	2000	2000	NUM
ejpam-5423	13	3	,	,	PUNCT
ejpam-5423	13	4	lee	lee	PROPN
ejpam-5423	14	1	[	[	X
ejpam-5423	14	2	11	11	NUM
ejpam-5423	14	3	]	]	PUNCT
ejpam-5423	14	4	used	use	VERB
ejpam-5423	14	5	the	the	DET
ejpam-5423	14	6	term	term	NOUN
ejpam-5423	14	7	bipolar	bipolar	ADJ
ejpam-5423	14	8	valued	value	VERB
ejpam-5423	14	9	fuzzy	fuzzy	ADJ
ejpam-5423	14	10	sets	set	NOUN
ejpam-5423	14	11	and	and	CCONJ
ejpam-5423	14	12	applied	apply	VERB
ejpam-5423	14	13	it	it	PRON
ejpam-5423	14	14	to	to	ADP
ejpam-5423	14	15	algebraic	algebraic	ADJ
ejpam-5423	14	16	structures	structure	NOUN
ejpam-5423	14	17	.	.	PUNCT
ejpam-5423	15	1	in	in	ADP
ejpam-5423	15	2	2016	2016	NUM
ejpam-5423	15	3	,	,	PUNCT
ejpam-5423	15	4	mumtaz	mumtaz	PROPN
ejpam-5423	15	5	ali	ali	PROPN
ejpam-5423	15	6	et	et	PROPN
ejpam-5423	15	7	al	al	PROPN
ejpam-5423	15	8	.	.	PROPN
ejpam-5423	15	9	extended	extend	VERB
ejpam-5423	15	10	the	the	DET
ejpam-5423	15	11	concept	concept	NOUN
ejpam-5423	15	12	of	of	ADP
ejpam-5423	15	13	interval	interval	NOUN
ejpam-5423	15	14	valued	value	VERB
ejpam-5423	15	15	fuzzy	fuzzy	ADJ
ejpam-5423	15	16	set	set	ADJ
ejpam-5423	15	17	and	and	CCONJ
ejpam-5423	15	18	bipolar	bipolar	ADJ
ejpam-5423	15	19	fuzzy	fuzzy	ADJ
ejpam-5423	15	20	set	set	VERB
ejpam-5423	15	21	to	to	ADP
ejpam-5423	15	22	interval	interval	NOUN
ejpam-5423	15	23	valued	value	VERB
ejpam-5423	15	24	bipolar	bipolar	ADJ
ejpam-5423	15	25	fuzzy	fuzzy	ADJ
ejpam-5423	15	26	set	set	NOUN
ejpam-5423	15	27	.	.	PUNCT
ejpam-5423	16	1	in	in	ADP
ejpam-5423	16	2	2019	2019	NUM
ejpam-5423	16	3	,	,	PUNCT
ejpam-5423	16	4	k.	k.	PROPN
ejpam-5423	16	5	arulmozhi	arulmozhi	PROPN
ejpam-5423	16	6	et	et	PROPN
ejpam-5423	16	7	al	al	PROPN
ejpam-5423	16	8	.	.	PROPN
ejpam-5423	17	1	studied	study	VERB
ejpam-5423	17	2	interval	interval	NOUN
ejpam-5423	17	3	valued	value	VERB
ejpam-5423	17	4	bipolar	bipolar	ADJ
ejpam-5423	17	5	fuzzy	fuzzy	ADJ
ejpam-5423	17	6	set	set	VERB
ejpam-5423	17	7	in	in	ADP
ejpam-5423	17	8	∗corresponding	∗corresponde	VERB
ejpam-5423	17	9	author	author	NOUN
ejpam-5423	17	10	.	.	PUNCT
ejpam-5423	18	1	doi	doi	NOUN
ejpam-5423	18	2	:	:	PUNCT
ejpam-5423	18	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5423	https://doi.org/10.29020/nybg.ejpam.v17i4.5423	NOUN
ejpam-5423	18	4	email	email	NOUN
ejpam-5423	18	5	addresses	address	VERB
ejpam-5423	18	6	:	:	PUNCT
ejpam-5423	19	1	thiti.ga@up.ac.th	thiti.ga@up.ac.th	PROPN
ejpam-5423	19	2	(	(	PUNCT
ejpam-5423	19	3	t.	t.	NOUN
ejpam-5423	19	4	gaketem	gaketem	PROPN
ejpam-5423	19	5	)	)	PUNCT
ejpam-5423	19	6	,	,	PUNCT
ejpam-5423	19	7	,	,	PUNCT
ejpam-5423	19	8	tanaphong.pr@up.ac.th	tanaphong.pr@up.ac.th	PRON
ejpam-5423	19	9	(	(	PUNCT
ejpam-5423	19	10	t.	t.	PROPN
ejpam-5423	19	11	prommai	prommai	PROPN
ejpam-5423	19	12	)	)	PUNCT
ejpam-5423	19	13	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5423	19	14	3223	3223	NUM
ejpam-5423	19	15	copyright	copyright	NOUN
ejpam-5423	19	16	:	:	PUNCT
ejpam-5423	19	17	©	©	PROPN
ejpam-5423	19	18	2024	2024	NUM
ejpam-5423	19	19	the	the	DET
ejpam-5423	19	20	author(s	author(s	NOUN
ejpam-5423	19	21	)	)	PUNCT
ejpam-5423	19	22	.	.	PUNCT
ejpam-5423	20	1	(	(	PUNCT
ejpam-5423	20	2	cc	cc	NOUN
ejpam-5423	20	3	by	by	ADP
ejpam-5423	20	4	-	-	PUNCT
ejpam-5423	20	5	nc	nc	PROPN
ejpam-5423	20	6	4.0	4.0	NUM
ejpam-5423	20	7	)	)	PUNCT
ejpam-5423	20	8	t.	t.	NOUN
ejpam-5423	20	9	gaketem	gaketem	NOUN
ejpam-5423	20	10	,	,	PUNCT
ejpam-5423	20	11	t.	t.	PROPN
ejpam-5423	20	12	prommai	prommai	PROPN
ejpam-5423	20	13	/	/	SYM
ejpam-5423	20	14	eur	eur	PROPN
ejpam-5423	20	15	.	.	PUNCT
ejpam-5423	21	1	j.	j.	PROPN
ejpam-5423	21	2	pure	pure	PROPN
ejpam-5423	21	3	appl	appl	PROPN
ejpam-5423	21	4	.	.	PROPN
ejpam-5423	21	5	math	math	PROPN
ejpam-5423	21	6	,	,	PUNCT
ejpam-5423	21	7	17	17	NUM
ejpam-5423	21	8	(	(	PUNCT
ejpam-5423	21	9	4	4	NUM
ejpam-5423	21	10	)	)	PUNCT
ejpam-5423	21	11	(	(	PUNCT
ejpam-5423	21	12	2024	2024	NUM
ejpam-5423	21	13	)	)	PUNCT
ejpam-5423	21	14	,	,	PUNCT
ejpam-5423	21	15	3223	3223	NUM
ejpam-5423	21	16	-	-	SYM
ejpam-5423	21	17	3241	3241	NUM
ejpam-5423	21	18	3224	3224	NUM
ejpam-5423	21	19	algebra	algebra	NOUN
ejpam-5423	21	20	structure	structure	NOUN
ejpam-5423	21	21	.	.	PUNCT
ejpam-5423	22	1	in	in	ADP
ejpam-5423	22	2	2019	2019	NUM
ejpam-5423	22	3	,	,	PUNCT
ejpam-5423	22	4	a.	a.	PROPN
ejpam-5423	22	5	salm	salm	PROPN
ejpam-5423	22	6	el	el	PROPN
ejpam-5423	23	1	at	at	ADP
ejpam-5423	23	2	[	[	X
ejpam-5423	23	3	4	4	X
ejpam-5423	23	4	]	]	PUNCT
ejpam-5423	23	5	characterize	characterize	NOUN
ejpam-5423	23	6	of	of	ADP
ejpam-5423	23	7	regular	regular	ADJ
ejpam-5423	23	8	ordered	order	VERB
ejpam-5423	23	9	semigroups	semigroup	NOUN
ejpam-5423	23	10	by	by	ADP
ejpam-5423	23	11	(	(	PUNCT
ejpam-5423	23	12	ε	ε	PROPN
ejpam-5423	23	13	,	,	PUNCT
ejpam-5423	23	14	ε,∨k	ε,∨k	PROPN
ejpam-5423	23	15	,	,	PUNCT
ejpam-5423	23	16	qk))-fuzzy	qk))-fuzzy	ADV
ejpam-5423	23	17	quasi	quasi	NOUN
ejpam-5423	23	18	-	-	NOUN
ejpam-5423	23	19	ideals	ideal	NOUN
ejpam-5423	23	20	.	.	PUNCT
ejpam-5423	24	1	in	in	ADP
ejpam-5423	24	2	2021	2021	NUM
ejpam-5423	24	3	,	,	PUNCT
ejpam-5423	24	4	s.	s.	PROPN
ejpam-5423	24	5	lekkoksung	lekkoksung	PROPN
ejpam-5423	25	1	[	[	X
ejpam-5423	25	2	7	7	NUM
ejpam-5423	25	3	]	]	PUNCT
ejpam-5423	25	4	developed	develop	VERB
ejpam-5423	25	5	interval	interval	NOUN
ejpam-5423	25	6	valued	value	VERB
ejpam-5423	25	7	bipolar	bipolar	ADJ
ejpam-5423	25	8	fuzzy	fuzzy	ADJ
ejpam-5423	25	9	ideal	ideal	NOUN
ejpam-5423	25	10	in	in	ADP
ejpam-5423	25	11	ordered	order	VERB
ejpam-5423	25	12	semigroup	semigroup	NOUN
ejpam-5423	25	13	and	and	CCONJ
ejpam-5423	25	14	characterized	characterize	VERB
ejpam-5423	25	15	regular	regular	ADJ
ejpam-5423	25	16	ordered	order	VERB
ejpam-5423	25	17	semigroup	semigroup	NOUN
ejpam-5423	25	18	in	in	ADP
ejpam-5423	25	19	terms	term	NOUN
ejpam-5423	25	20	of	of	ADP
ejpam-5423	25	21	generalized	generalized	ADJ
ejpam-5423	25	22	interval	interval	NOUN
ejpam-5423	25	23	valued	value	VERB
ejpam-5423	25	24	bipolar	bipolar	ADJ
ejpam-5423	25	25	fuzzy	fuzzy	ADJ
ejpam-5423	25	26	ideal	ideal	NOUN
ejpam-5423	25	27	and	and	CCONJ
ejpam-5423	25	28	bi	bi	NOUN
ejpam-5423	25	29	-	-	NOUN
ejpam-5423	25	30	ideal	ideal	ADJ
ejpam-5423	25	31	.	.	PUNCT
ejpam-5423	26	1	in	in	ADP
ejpam-5423	26	2	2024	2024	NUM
ejpam-5423	26	3	p.	p.	NOUN
ejpam-5423	26	4	khamrot	khamrot	PROPN
ejpam-5423	26	5	et	et	PROPN
ejpam-5423	26	6	.	.	PUNCT
ejpam-5423	27	1	al	al	PROPN
ejpam-5423	28	1	[	[	X
ejpam-5423	28	2	14	14	NUM
ejpam-5423	28	3	]	]	X
ejpam-5423	28	4	characterized	characterize	VERB
ejpam-5423	28	5	weakly	weakly	ADJ
ejpam-5423	28	6	ordered	order	VERB
ejpam-5423	28	7	semigroup	semigroup	NOUN
ejpam-5423	28	8	in	in	ADP
ejpam-5423	28	9	terms	term	NOUN
ejpam-5423	28	10	of	of	ADP
ejpam-5423	28	11	generalized	generalized	ADJ
ejpam-5423	28	12	interval	interval	NOUN
ejpam-5423	28	13	valued	value	VERB
ejpam-5423	28	14	bipolar	bipolar	ADJ
ejpam-5423	28	15	fuzzy	fuzzy	ADJ
ejpam-5423	28	16	ideal	ideal	NOUN
ejpam-5423	28	17	.	.	PUNCT
ejpam-5423	29	1	there	there	PRON
ejpam-5423	29	2	are	be	VERB
ejpam-5423	29	3	also	also	ADV
ejpam-5423	29	4	research	research	NOUN
ejpam-5423	29	5	studies	study	NOUN
ejpam-5423	29	6	related	relate	VERB
ejpam-5423	29	7	to	to	ADP
ejpam-5423	29	8	ordered	order	VERB
ejpam-5423	29	9	semigroup	semigroup	PROPN
ejpam-5423	29	10	like	like	ADP
ejpam-5423	29	11	fuzzy	fuzzy	ADJ
ejpam-5423	29	12	(	(	PUNCT
ejpam-5423	29	13	m	m	PROPN
ejpam-5423	29	14	,	,	PUNCT
ejpam-5423	29	15	n)-substructures	n)-substructure	VERB
ejpam-5423	29	16	[	[	X
ejpam-5423	29	17	3	3	NUM
ejpam-5423	29	18	]	]	PUNCT
ejpam-5423	29	19	,	,	PUNCT
ejpam-5423	29	20	fuzzy	fuzzy	ADJ
ejpam-5423	29	21	(	(	PUNCT
ejpam-5423	29	22	m	m	PROPN
ejpam-5423	29	23	,	,	PUNCT
ejpam-5423	29	24	n)-ideal	n)-ideal	NOUN
ejpam-5423	29	25	[	[	X
ejpam-5423	29	26	1	1	NUM
ejpam-5423	29	27	]	]	PUNCT
ejpam-5423	29	28	,	,	PUNCT
ejpam-5423	29	29	fuzzy	fuzzy	ADJ
ejpam-5423	29	30	(	(	PUNCT
ejpam-5423	29	31	m	m	PROPN
ejpam-5423	29	32	,	,	PUNCT
ejpam-5423	29	33	n)-filters	n)-filter	NOUN
ejpam-5423	29	34	[	[	X
ejpam-5423	29	35	2	2	NUM
ejpam-5423	29	36	]	]	PUNCT
ejpam-5423	29	37	,	,	PUNCT
ejpam-5423	29	38	fuzzy	fuzzy	ADJ
ejpam-5423	29	39	prime	prime	NOUN
ejpam-5423	29	40	subset	subset	NOUN
ejpam-5423	30	1	[	[	X
ejpam-5423	30	2	12	12	NUM
ejpam-5423	30	3	]	]	PUNCT
ejpam-5423	30	4	,	,	PUNCT
ejpam-5423	30	5	etc	etc	X
ejpam-5423	30	6	.	.	X
ejpam-5423	31	1	in	in	ADP
ejpam-5423	31	2	this	this	DET
ejpam-5423	31	3	paper	paper	NOUN
ejpam-5423	31	4	,	,	PUNCT
ejpam-5423	31	5	we	we	PRON
ejpam-5423	31	6	establish	establish	VERB
ejpam-5423	31	7	the	the	DET
ejpam-5423	31	8	concept	concept	NOUN
ejpam-5423	31	9	of	of	ADP
ejpam-5423	31	10	a	a	DET
ejpam-5423	31	11	generalized	generalized	ADJ
ejpam-5423	31	12	interval	interval	NOUN
ejpam-5423	31	13	valued	value	VERB
ejpam-5423	31	14	bipolar	bipolar	ADJ
ejpam-5423	31	15	fuzzy	fuzzy	ADJ
ejpam-5423	31	16	quasi	quasi	NOUN
ejpam-5423	31	17	ideal	ideal	NOUN
ejpam-5423	31	18	.	.	PUNCT
ejpam-5423	32	1	we	we	PRON
ejpam-5423	32	2	prove	prove	VERB
ejpam-5423	32	3	properties	property	NOUN
ejpam-5423	32	4	of	of	ADP
ejpam-5423	32	5	a	a	DET
ejpam-5423	32	6	generalized	generalized	ADJ
ejpam-5423	32	7	interval	interval	NOUN
ejpam-5423	32	8	valued	value	VERB
ejpam-5423	32	9	bipolar	bipolar	ADJ
ejpam-5423	32	10	fuzzy	fuzzy	ADJ
ejpam-5423	32	11	quasi	quasi	ADJ
ejpam-5423	32	12	ideal	ideal	NOUN
ejpam-5423	32	13	in	in	ADP
ejpam-5423	32	14	semigroups	semigroup	NOUN
ejpam-5423	32	15	.	.	PUNCT
ejpam-5423	33	1	main	main	ADJ
ejpam-5423	33	2	results	result	NOUN
ejpam-5423	33	3	,	,	PUNCT
ejpam-5423	33	4	we	we	PRON
ejpam-5423	33	5	will	will	AUX
ejpam-5423	33	6	characterize	characterize	VERB
ejpam-5423	33	7	regular	regular	ADJ
ejpam-5423	33	8	and	and	CCONJ
ejpam-5423	33	9	intra	intra	ADJ
ejpam-5423	33	10	-	-	ADJ
ejpam-5423	33	11	regular	regular	ADJ
ejpam-5423	33	12	ordered	order	VERB
ejpam-5423	33	13	semigroup	semigroup	NOUN
ejpam-5423	33	14	in	in	ADP
ejpam-5423	33	15	terms	term	NOUN
ejpam-5423	33	16	of	of	ADP
ejpam-5423	33	17	generalized	generalized	ADJ
ejpam-5423	33	18	interval	interval	NOUN
ejpam-5423	33	19	valued	value	VERB
ejpam-5423	33	20	bipolar	bipolar	ADJ
ejpam-5423	33	21	fuzzy	fuzzy	ADJ
ejpam-5423	33	22	quasi	quasi	NOUN
ejpam-5423	33	23	ideal	ideal	NOUN
ejpam-5423	33	24	.	.	PUNCT
ejpam-5423	34	1	2	2	X
ejpam-5423	34	2	.	.	X
ejpam-5423	34	3	preliminaries	preliminary	NOUN
ejpam-5423	34	4	in	in	ADP
ejpam-5423	34	5	this	this	DET
ejpam-5423	34	6	section	section	NOUN
ejpam-5423	34	7	,	,	PUNCT
ejpam-5423	34	8	we	we	PRON
ejpam-5423	34	9	give	give	VERB
ejpam-5423	34	10	some	some	DET
ejpam-5423	34	11	definitions	definition	NOUN
ejpam-5423	34	12	and	and	CCONJ
ejpam-5423	34	13	theory	theory	NOUN
ejpam-5423	34	14	helpful	helpful	ADJ
ejpam-5423	34	15	in	in	ADP
ejpam-5423	34	16	later	later	ADJ
ejpam-5423	34	17	sections	section	NOUN
ejpam-5423	34	18	.	.	PUNCT
ejpam-5423	35	1	an	an	DET
ejpam-5423	35	2	ordered	order	VERB
ejpam-5423	35	3	semigroup	semigroup	NOUN
ejpam-5423	35	4	is	be	AUX
ejpam-5423	35	5	a	a	DET
ejpam-5423	35	6	semigroup	semigroup	NOUN
ejpam-5423	35	7	together	together	ADV
ejpam-5423	35	8	with	with	ADP
ejpam-5423	35	9	a	a	DET
ejpam-5423	35	10	partial	partial	ADJ
ejpam-5423	35	11	order	order	NOUN
ejpam-5423	35	12	that	that	PRON
ejpam-5423	35	13	is	be	AUX
ejpam-5423	35	14	compatible	compatible	ADJ
ejpam-5423	35	15	with	with	ADP
ejpam-5423	35	16	the	the	DET
ejpam-5423	35	17	semigroup	semigroup	PROPN
ejpam-5423	35	18	operation	operation	NOUN
ejpam-5423	35	19	.	.	PUNCT
ejpam-5423	36	1	for	for	ADP
ejpam-5423	36	2	a	a	DET
ejpam-5423	36	3	nonempty	nonempty	NOUN
ejpam-5423	36	4	subset	subset	NOUN
ejpam-5423	36	5	x	x	PUNCT
ejpam-5423	36	6	and	and	CCONJ
ejpam-5423	36	7	y	y	PROPN
ejpam-5423	36	8	of	of	ADP
ejpam-5423	36	9	ordered	order	VERB
ejpam-5423	36	10	semigroup	semigroup	PROPN
ejpam-5423	36	11	s	s	PROPN
ejpam-5423	36	12	,	,	PUNCT
ejpam-5423	36	13	we	we	PRON
ejpam-5423	36	14	write	write	VERB
ejpam-5423	36	15	(	(	PUNCT
ejpam-5423	36	16	x	x	X
ejpam-5423	36	17	]	]	X
ejpam-5423	36	18	:	:	PUNCT
ejpam-5423	36	19	=	=	SYM
ejpam-5423	36	20	{	{	PUNCT
ejpam-5423	36	21	a	a	DET
ejpam-5423	36	22	∈	∈	NOUN
ejpam-5423	36	23	s	s	VERB
ejpam-5423	36	24	|	|	ADV
ejpam-5423	36	25	a	a	DET
ejpam-5423	36	26	≤	≤	NUM
ejpam-5423	36	27	b	b	NOUN
ejpam-5423	36	28	for	for	ADP
ejpam-5423	36	29	some	some	DET
ejpam-5423	36	30	b	b	NOUN
ejpam-5423	36	31	∈	∈	PROPN
ejpam-5423	36	32	x	x	NOUN
ejpam-5423	36	33	}	}	PUNCT
ejpam-5423	36	34	and	and	CCONJ
ejpam-5423	36	35	xy	xy	INTJ
ejpam-5423	36	36	:	:	PUNCT
ejpam-5423	36	37	=	=	X
ejpam-5423	36	38	{	{	PUNCT
ejpam-5423	37	1	xy	xy	INTJ
ejpam-5423	37	2	|	|	ADV
ejpam-5423	37	3	x	x	SYM
ejpam-5423	37	4	∈	∈	PROPN
ejpam-5423	37	5	x	x	X
ejpam-5423	37	6	and	and	CCONJ
ejpam-5423	37	7	y	y	PROPN
ejpam-5423	37	8	∈	∈	PROPN
ejpam-5423	37	9	y	y	PROPN
ejpam-5423	37	10	}	}	PUNCT
ejpam-5423	37	11	.	.	PUNCT
ejpam-5423	38	1	a	a	DET
ejpam-5423	38	2	non	non	ADJ
ejpam-5423	38	3	-	-	ADJ
ejpam-5423	38	4	empty	empty	ADJ
ejpam-5423	38	5	subset	subset	NOUN
ejpam-5423	38	6	l	l	NOUN
ejpam-5423	38	7	of	of	ADP
ejpam-5423	38	8	an	an	DET
ejpam-5423	38	9	ordered	order	VERB
ejpam-5423	38	10	semigroup	semigroup	NOUN
ejpam-5423	38	11	g	g	PROPN
ejpam-5423	38	12	is	be	AUX
ejpam-5423	38	13	called	call	VERB
ejpam-5423	38	14	(	(	PUNCT
ejpam-5423	38	15	1	1	NUM
ejpam-5423	38	16	)	)	PUNCT
ejpam-5423	38	17	a	a	DET
ejpam-5423	38	18	subsemigroup	subsemigroup	NOUN
ejpam-5423	38	19	of	of	ADP
ejpam-5423	38	20	g	g	NOUN
ejpam-5423	38	21	if	if	SCONJ
ejpam-5423	38	22	l2	l2	VERB
ejpam-5423	38	23	⊆	⊆	NUM
ejpam-5423	38	24	l	l	NOUN
ejpam-5423	38	25	,	,	PUNCT
ejpam-5423	38	26	(	(	PUNCT
ejpam-5423	38	27	2	2	X
ejpam-5423	38	28	)	)	PUNCT
ejpam-5423	38	29	a	a	DET
ejpam-5423	38	30	left	left	ADJ
ejpam-5423	38	31	(	(	PUNCT
ejpam-5423	38	32	right	right	ADJ
ejpam-5423	38	33	)	)	PUNCT
ejpam-5423	38	34	ideal	ideal	NOUN
ejpam-5423	38	35	of	of	ADP
ejpam-5423	38	36	g	g	PROPN
ejpam-5423	38	37	if	if	SCONJ
ejpam-5423	38	38	(	(	PUNCT
ejpam-5423	38	39	gl	gl	NOUN
ejpam-5423	38	40	]	]	X
ejpam-5423	38	41	⊆	⊆	NUM
ejpam-5423	38	42	l	l	NOUN
ejpam-5423	38	43	(	(	PUNCT
ejpam-5423	38	44	(	(	PUNCT
ejpam-5423	38	45	lg	lg	NOUN
ejpam-5423	38	46	]	]	X
ejpam-5423	38	47	⊆	⊆	NUM
ejpam-5423	38	48	l	l	NOUN
ejpam-5423	38	49	)	)	PUNCT
ejpam-5423	38	50	and	and	CCONJ
ejpam-5423	38	51	x	x	PUNCT
ejpam-5423	38	52	∈	∈	PROPN
ejpam-5423	38	53	l	l	NOUN
ejpam-5423	38	54	and	and	CCONJ
ejpam-5423	38	55	s	s	NOUN
ejpam-5423	38	56	∈	∈	NOUN
ejpam-5423	38	57	g	g	NOUN
ejpam-5423	38	58	such	such	DET
ejpam-5423	38	59	that	that	PRON
ejpam-5423	38	60	s	s	VERB
ejpam-5423	38	61	≤	≤	NUM
ejpam-5423	38	62	x	x	NOUN
ejpam-5423	38	63	,	,	PUNCT
ejpam-5423	38	64	then	then	ADV
ejpam-5423	38	65	s	s	VERB
ejpam-5423	38	66	∈	∈	PROPN
ejpam-5423	38	67	l	l	NOUN
ejpam-5423	38	68	,	,	PUNCT
ejpam-5423	38	69	that	that	ADV
ejpam-5423	38	70	is	is	ADV
ejpam-5423	38	71	(	(	PUNCT
ejpam-5423	38	72	l	l	NOUN
ejpam-5423	38	73	]	]	X
ejpam-5423	38	74	⊆	⊆	NUM
ejpam-5423	38	75	l	l	NOUN
ejpam-5423	38	76	,	,	PUNCT
ejpam-5423	38	77	(	(	PUNCT
ejpam-5423	38	78	3	3	X
ejpam-5423	38	79	)	)	PUNCT
ejpam-5423	38	80	a	a	DET
ejpam-5423	38	81	bi	bi	NOUN
ejpam-5423	38	82	-	-	NOUN
ejpam-5423	38	83	ideal	ideal	NOUN
ejpam-5423	38	84	of	of	ADP
ejpam-5423	38	85	g	g	PROPN
ejpam-5423	38	86	if	if	SCONJ
ejpam-5423	38	87	l	l	NOUN
ejpam-5423	38	88	is	be	AUX
ejpam-5423	38	89	a	a	DET
ejpam-5423	38	90	subsemigorup	subsemigorup	NOUN
ejpam-5423	38	91	and	and	CCONJ
ejpam-5423	38	92	lgl	lgl	VERB
ejpam-5423	38	93	⊆	⊆	NUM
ejpam-5423	38	94	l	l	NOUN
ejpam-5423	38	95	,	,	PUNCT
ejpam-5423	38	96	(	(	PUNCT
ejpam-5423	38	97	4	4	X
ejpam-5423	38	98	)	)	PUNCT
ejpam-5423	38	99	an	an	DET
ejpam-5423	38	100	quasi	quasi	NOUN
ejpam-5423	38	101	-	-	NOUN
ejpam-5423	38	102	ideal	ideal	NOUN
ejpam-5423	38	103	of	of	ADP
ejpam-5423	38	104	g	g	PROPN
ejpam-5423	38	105	if	if	SCONJ
ejpam-5423	38	106	(	(	PUNCT
ejpam-5423	38	107	lg	lg	NOUN
ejpam-5423	38	108	]	]	X
ejpam-5423	38	109	∩	∩	NOUN
ejpam-5423	38	110	(	(	PUNCT
ejpam-5423	38	111	gl	gl	X
ejpam-5423	38	112	]	]	X
ejpam-5423	38	113	⊆	⊆	NUM
ejpam-5423	38	114	l	l	NOUN
ejpam-5423	38	115	an	an	DET
ejpam-5423	38	116	ordered	order	VERB
ejpam-5423	38	117	semigroup	semigroup	NOUN
ejpam-5423	38	118	g	g	PROPN
ejpam-5423	38	119	is	be	AUX
ejpam-5423	38	120	called	call	VERB
ejpam-5423	38	121	a	a	DET
ejpam-5423	38	122	regular	regular	ADJ
ejpam-5423	38	123	if	if	SCONJ
ejpam-5423	38	124	,	,	PUNCT
ejpam-5423	38	125	for	for	ADP
ejpam-5423	38	126	each	each	DET
ejpam-5423	38	127	u	u	PROPN
ejpam-5423	38	128	∈	∈	PROPN
ejpam-5423	38	129	g	g	NOUN
ejpam-5423	38	130	,	,	PUNCT
ejpam-5423	38	131	there	there	PRON
ejpam-5423	38	132	exists	exist	VERB
ejpam-5423	38	133	x	x	X
ejpam-5423	38	134	∈	∈	PROPN
ejpam-5423	38	135	g	g	NOUN
ejpam-5423	38	136	such	such	ADJ
ejpam-5423	38	137	that	that	SCONJ
ejpam-5423	38	138	u	u	PROPN
ejpam-5423	38	139	≤	≤	X
ejpam-5423	38	140	uxu	uxu	NOUN
ejpam-5423	38	141	.	.	PUNCT
ejpam-5423	39	1	an	an	DET
ejpam-5423	39	2	ordered	order	VERB
ejpam-5423	39	3	semigroup	semigroup	NOUN
ejpam-5423	39	4	g	g	PROPN
ejpam-5423	39	5	called	call	VERB
ejpam-5423	39	6	an	an	DET
ejpam-5423	39	7	intra	intra	ADJ
ejpam-5423	39	8	-	-	ADJ
ejpam-5423	39	9	regular	regular	ADJ
ejpam-5423	39	10	if	if	SCONJ
ejpam-5423	39	11	,	,	PUNCT
ejpam-5423	39	12	for	for	ADP
ejpam-5423	39	13	each	each	DET
ejpam-5423	39	14	u	u	PROPN
ejpam-5423	39	15	∈	∈	PROPN
ejpam-5423	39	16	g	g	NOUN
ejpam-5423	39	17	,	,	PUNCT
ejpam-5423	39	18	there	there	PRON
ejpam-5423	39	19	exists	exist	VERB
ejpam-5423	39	20	a.b	a.b	PROPN
ejpam-5423	39	21	∈	∈	PROPN
ejpam-5423	39	22	g	g	NOUN
ejpam-5423	39	23	such	such	ADJ
ejpam-5423	40	1	that	that	SCONJ
ejpam-5423	40	2	u	u	PROPN
ejpam-5423	40	3	≤	≤	X
ejpam-5423	40	4	au2b	au2b	PROPN
ejpam-5423	40	5	.	.	PUNCT
ejpam-5423	41	1	for	for	ADP
ejpam-5423	41	2	any	any	DET
ejpam-5423	41	3	pi	pi	NOUN
ejpam-5423	41	4	∈	∈	PROPN
ejpam-5423	42	1	[	[	X
ejpam-5423	42	2	0	0	NUM
ejpam-5423	42	3	,	,	PUNCT
ejpam-5423	42	4	1	1	NUM
ejpam-5423	42	5	]	]	PUNCT
ejpam-5423	42	6	,	,	PUNCT
ejpam-5423	42	7	where	where	SCONJ
ejpam-5423	42	8	i	i	PRON
ejpam-5423	42	9	∈	∈	VERB
ejpam-5423	42	10	a	a	PRON
ejpam-5423	42	11	,	,	PUNCT
ejpam-5423	42	12	define	define	VERB
ejpam-5423	42	13	∨	∨	NUM
ejpam-5423	42	14	i∈a	i∈a	ADJ
ejpam-5423	42	15	pi	pi	NOUN
ejpam-5423	42	16	:	:	PUNCT
ejpam-5423	42	17	=	=	SYM
ejpam-5423	42	18	sup	sup	NOUN
ejpam-5423	42	19	i∈a	i∈a	ADJ
ejpam-5423	42	20	{	{	PUNCT
ejpam-5423	42	21	pi	pi	NOUN
ejpam-5423	42	22	}	}	PUNCT
ejpam-5423	42	23	and	and	CCONJ
ejpam-5423	42	24	∧	∧	PROPN
ejpam-5423	42	25	i∈a	i∈a	ADJ
ejpam-5423	42	26	pi	pi	NOUN
ejpam-5423	42	27	:	:	PUNCT
ejpam-5423	42	28	=	=	SYM
ejpam-5423	42	29	inf	inf	PROPN
ejpam-5423	42	30	i∈a	i∈a	ADJ
ejpam-5423	42	31	{	{	PUNCT
ejpam-5423	42	32	pi	pi	NOUN
ejpam-5423	42	33	}	}	PUNCT
ejpam-5423	42	34	.	.	PUNCT
ejpam-5423	43	1	we	we	PRON
ejpam-5423	43	2	see	see	VERB
ejpam-5423	43	3	that	that	PRON
ejpam-5423	43	4	for	for	ADP
ejpam-5423	43	5	any	any	DET
ejpam-5423	43	6	p	p	NOUN
ejpam-5423	43	7	,	,	PUNCT
ejpam-5423	43	8	q	q	NOUN
ejpam-5423	43	9	∈	∈	PROPN
ejpam-5423	44	1	[	[	X
ejpam-5423	44	2	0	0	NUM
ejpam-5423	44	3	,	,	PUNCT
ejpam-5423	44	4	1	1	NUM
ejpam-5423	44	5	]	]	PUNCT
ejpam-5423	44	6	,	,	PUNCT
ejpam-5423	44	7	we	we	PRON
ejpam-5423	44	8	have	have	VERB
ejpam-5423	44	9	p	p	PROPN
ejpam-5423	44	10	∨	∨	NUM
ejpam-5423	44	11	q	q	NOUN
ejpam-5423	44	12	=	=	SYM
ejpam-5423	44	13	max{p	max{p	NOUN
ejpam-5423	44	14	,	,	PUNCT
ejpam-5423	44	15	q	q	NOUN
ejpam-5423	44	16	}	}	PUNCT
ejpam-5423	44	17	and	and	CCONJ
ejpam-5423	44	18	p	p	X
ejpam-5423	44	19	∧	∧	PROPN
ejpam-5423	44	20	q	q	X
ejpam-5423	44	21	=	=	PUNCT
ejpam-5423	44	22	min{p	min{p	X
ejpam-5423	44	23	,	,	PUNCT
ejpam-5423	44	24	q	q	NOUN
ejpam-5423	44	25	}	}	PUNCT
ejpam-5423	44	26	.	.	PUNCT
ejpam-5423	45	1	a	a	DET
ejpam-5423	45	2	fuzzy	fuzzy	ADJ
ejpam-5423	45	3	set	set	NOUN
ejpam-5423	45	4	of	of	ADP
ejpam-5423	45	5	a	a	DET
ejpam-5423	45	6	non	non	ADJ
ejpam-5423	45	7	-	-	ADJ
ejpam-5423	45	8	empty	empty	ADJ
ejpam-5423	45	9	set	set	ADJ
ejpam-5423	45	10	t	t	PROPN
ejpam-5423	45	11	is	be	AUX
ejpam-5423	45	12	a	a	DET
ejpam-5423	45	13	function	function	NOUN
ejpam-5423	45	14	ω	ω	NOUN
ejpam-5423	45	15	:	:	PUNCT
ejpam-5423	46	1	l	l	X
ejpam-5423	46	2	→	→	PUNCT
ejpam-5423	47	1	[	[	X
ejpam-5423	47	2	0	0	NUM
ejpam-5423	47	3	,	,	PUNCT
ejpam-5423	47	4	1	1	NUM
ejpam-5423	47	5	]	]	PUNCT
ejpam-5423	47	6	.	.	PUNCT
ejpam-5423	48	1	let	let	VERB
ejpam-5423	48	2	ω[0	ω[0	PROPN
ejpam-5423	48	3	,	,	PUNCT
ejpam-5423	48	4	1	1	NUM
ejpam-5423	48	5	]	]	PUNCT
ejpam-5423	48	6	be	be	AUX
ejpam-5423	48	7	the	the	DET
ejpam-5423	48	8	set	set	NOUN
ejpam-5423	48	9	of	of	ADP
ejpam-5423	48	10	all	all	DET
ejpam-5423	48	11	closed	closed	ADJ
ejpam-5423	48	12	subintervals	subinterval	NOUN
ejpam-5423	48	13	of	of	ADP
ejpam-5423	48	14	[	[	X
ejpam-5423	48	15	0	0	NUM
ejpam-5423	48	16	,	,	PUNCT
ejpam-5423	48	17	1	1	NUM
ejpam-5423	48	18	]	]	PUNCT
ejpam-5423	48	19	,	,	PUNCT
ejpam-5423	48	20	i.e.	i.e.	X
ejpam-5423	48	21	,	,	PUNCT
ejpam-5423	48	22	ω[0	ω[0	PROPN
ejpam-5423	48	23	,	,	PUNCT
ejpam-5423	48	24	1	1	NUM
ejpam-5423	48	25	]	]	PUNCT
ejpam-5423	48	26	=	=	PUNCT
ejpam-5423	48	27	{	{	PUNCT
ejpam-5423	48	28	ω	ω	NOUN
ejpam-5423	48	29	=	=	PUNCT
ejpam-5423	49	1	[	[	X
ejpam-5423	49	2	ω−	ω−	PROPN
ejpam-5423	49	3	,	,	PUNCT
ejpam-5423	49	4	ω+	ω+	NOUN
ejpam-5423	49	5	]	]	X
ejpam-5423	49	6	|	|	NOUN
ejpam-5423	49	7	0	0	NUM
ejpam-5423	49	8	≤	≤	NOUN
ejpam-5423	49	9	ω−	ω−	ADP
ejpam-5423	49	10	≤	≤	NOUN
ejpam-5423	49	11	ω+	ω+	PUNCT
ejpam-5423	49	12	≤	≤	NUM
ejpam-5423	49	13	1	1	NUM
ejpam-5423	49	14	}	}	PUNCT
ejpam-5423	49	15	.	.	PUNCT
ejpam-5423	50	1	t.	t.	PROPN
ejpam-5423	50	2	gaketem	gaketem	PROPN
ejpam-5423	50	3	,	,	PUNCT
ejpam-5423	50	4	t.	t.	PROPN
ejpam-5423	50	5	prommai	prommai	PROPN
ejpam-5423	50	6	/	/	SYM
ejpam-5423	50	7	eur	eur	PROPN
ejpam-5423	50	8	.	.	PUNCT
ejpam-5423	51	1	j.	j.	PROPN
ejpam-5423	51	2	pure	pure	PROPN
ejpam-5423	51	3	appl	appl	PROPN
ejpam-5423	51	4	.	.	PROPN
ejpam-5423	51	5	math	math	PROPN
ejpam-5423	51	6	,	,	PUNCT
ejpam-5423	51	7	17	17	NUM
ejpam-5423	51	8	(	(	PUNCT
ejpam-5423	51	9	4	4	NUM
ejpam-5423	51	10	)	)	PUNCT
ejpam-5423	51	11	(	(	PUNCT
ejpam-5423	51	12	2024	2024	NUM
ejpam-5423	51	13	)	)	PUNCT
ejpam-5423	51	14	,	,	PUNCT
ejpam-5423	51	15	3223	3223	NUM
ejpam-5423	51	16	-	-	SYM
ejpam-5423	51	17	3241	3241	NUM
ejpam-5423	51	18	3225	3225	NUM
ejpam-5423	52	1	we	we	PRON
ejpam-5423	52	2	note	note	VERB
ejpam-5423	52	3	that	that	SCONJ
ejpam-5423	53	1	[	[	X
ejpam-5423	53	2	ω	ω	PROPN
ejpam-5423	53	3	,	,	PUNCT
ejpam-5423	53	4	ω	ω	NOUN
ejpam-5423	53	5	]	]	X
ejpam-5423	53	6	=	=	SYM
ejpam-5423	53	7	{	{	PUNCT
ejpam-5423	53	8	ω	ω	NOUN
ejpam-5423	53	9	}	}	PUNCT
ejpam-5423	53	10	for	for	ADP
ejpam-5423	53	11	all	all	DET
ejpam-5423	53	12	ω	ω	NUM
ejpam-5423	53	13	∈	∈	PROPN
ejpam-5423	54	1	[	[	X
ejpam-5423	54	2	0	0	NUM
ejpam-5423	54	3	,	,	PUNCT
ejpam-5423	54	4	1	1	NUM
ejpam-5423	54	5	]	]	PUNCT
ejpam-5423	54	6	.	.	PUNCT
ejpam-5423	55	1	for	for	ADP
ejpam-5423	55	2	ω	ω	NUM
ejpam-5423	55	3	=	=	SYM
ejpam-5423	55	4	0	0	NUM
ejpam-5423	55	5	or	or	CCONJ
ejpam-5423	55	6	1	1	NUM
ejpam-5423	55	7	we	we	PRON
ejpam-5423	55	8	shall	shall	AUX
ejpam-5423	55	9	denote	denote	VERB
ejpam-5423	55	10	[	[	X
ejpam-5423	55	11	0	0	NUM
ejpam-5423	55	12	,	,	PUNCT
ejpam-5423	55	13	0	0	NUM
ejpam-5423	55	14	]	]	PUNCT
ejpam-5423	55	15	by	by	ADP
ejpam-5423	55	16	0	0	NUM
ejpam-5423	55	17	and	and	CCONJ
ejpam-5423	55	18	[	[	X
ejpam-5423	55	19	1	1	NUM
ejpam-5423	55	20	,	,	PUNCT
ejpam-5423	55	21	1	1	NUM
ejpam-5423	55	22	]	]	PUNCT
ejpam-5423	55	23	by	by	ADP
ejpam-5423	55	24	1	1	NUM
ejpam-5423	55	25	.	.	PUNCT
ejpam-5423	56	1	let	let	VERB
ejpam-5423	56	2	ω	ω	NOUN
ejpam-5423	56	3	=	=	PUNCT
ejpam-5423	57	1	[	[	X
ejpam-5423	57	2	ω−	ω−	PROPN
ejpam-5423	57	3	,	,	PUNCT
ejpam-5423	57	4	ω+	ω+	NOUN
ejpam-5423	57	5	]	]	PUNCT
ejpam-5423	57	6	and	and	CCONJ
ejpam-5423	57	7	ϖ	ϖ	NOUN
ejpam-5423	57	8	=	=	SYM
ejpam-5423	58	1	[	[	X
ejpam-5423	58	2	ϖ−	ϖ−	X
ejpam-5423	58	3	,	,	PUNCT
ejpam-5423	58	4	ϖ+	ϖ+	X
ejpam-5423	58	5	]	]	X
ejpam-5423	58	6	∈	∈	PROPN
ejpam-5423	58	7	ω[0	ω[0	PROPN
ejpam-5423	58	8	,	,	PUNCT
ejpam-5423	58	9	1	1	NUM
ejpam-5423	58	10	]	]	PUNCT
ejpam-5423	58	11	.	.	PUNCT
ejpam-5423	59	1	define	define	VERB
ejpam-5423	59	2	the	the	DET
ejpam-5423	59	3	operations	operation	NOUN
ejpam-5423	59	4	⪯	⪯	NOUN
ejpam-5423	59	5	,	,	PUNCT
ejpam-5423	59	6	=	=	NOUN
ejpam-5423	59	7	,	,	PUNCT
ejpam-5423	59	8	⋏	⋏	PROPN
ejpam-5423	59	9	and	and	CCONJ
ejpam-5423	59	10	⋎	⋎	NOUN
ejpam-5423	59	11	as	as	SCONJ
ejpam-5423	59	12	follows	follow	VERB
ejpam-5423	59	13	:	:	PUNCT
ejpam-5423	59	14	(	(	PUNCT
ejpam-5423	59	15	1	1	X
ejpam-5423	59	16	)	)	PUNCT
ejpam-5423	59	17	ω	ω	NOUN
ejpam-5423	59	18	⪯	⪯	NOUN
ejpam-5423	59	19	ϖ	ϖ	INTJ
ejpam-5423	59	20	if	if	SCONJ
ejpam-5423	60	1	and	and	CCONJ
ejpam-5423	60	2	only	only	ADV
ejpam-5423	60	3	if	if	SCONJ
ejpam-5423	60	4	ω−	ω−	ADP
ejpam-5423	60	5	≤	≤	ADJ
ejpam-5423	60	6	ϖ−	ϖ−	PROPN
ejpam-5423	60	7	and	and	CCONJ
ejpam-5423	60	8	ω+	ω+	NOUN
ejpam-5423	60	9	≤	≤	X
ejpam-5423	60	10	ϖ+	ϖ+	PUNCT
ejpam-5423	60	11	(	(	PUNCT
ejpam-5423	60	12	2	2	X
ejpam-5423	60	13	)	)	PUNCT
ejpam-5423	60	14	ω	ω	NOUN
ejpam-5423	60	15	=	=	PUNCT
ejpam-5423	61	1	ϖ	ϖ	INTJ
ejpam-5423	61	2	if	if	SCONJ
ejpam-5423	61	3	and	and	CCONJ
ejpam-5423	61	4	only	only	ADV
ejpam-5423	61	5	if	if	SCONJ
ejpam-5423	61	6	ω−	ω−	ADP
ejpam-5423	61	7	=	=	SYM
ejpam-5423	61	8	ϖ−	ϖ−	PROPN
ejpam-5423	61	9	and	and	CCONJ
ejpam-5423	61	10	ω+	ω+	NUM
ejpam-5423	61	11	=	=	PUNCT
ejpam-5423	61	12	ϖ+	ϖ+	X
ejpam-5423	61	13	(	(	PUNCT
ejpam-5423	61	14	3	3	X
ejpam-5423	61	15	)	)	PUNCT
ejpam-5423	61	16	ω	ω	NOUN
ejpam-5423	62	1	⋏ϖ	⋏ϖ	NOUN
ejpam-5423	62	2	=	=	PUNCT
ejpam-5423	63	1	[	[	X
ejpam-5423	63	2	(	(	PUNCT
ejpam-5423	63	3	ω−	ω−	ADJ
ejpam-5423	63	4	∧ϖ−	∧ϖ−	NOUN
ejpam-5423	63	5	)	)	PUNCT
ejpam-5423	63	6	,	,	PUNCT
ejpam-5423	63	7	(	(	PUNCT
ejpam-5423	63	8	ω+	ω+	NOUN
ejpam-5423	63	9	∧ϖ+	∧ϖ+	NOUN
ejpam-5423	63	10	)	)	PUNCT
ejpam-5423	63	11	]	]	PUNCT
ejpam-5423	63	12	(	(	PUNCT
ejpam-5423	63	13	4	4	X
ejpam-5423	63	14	)	)	PUNCT
ejpam-5423	63	15	ω	ω	NOUN
ejpam-5423	63	16	⋎ϖ	⋎ϖ	NOUN
ejpam-5423	64	1	=	=	PUNCT
ejpam-5423	65	1	[	[	X
ejpam-5423	65	2	(	(	PUNCT
ejpam-5423	65	3	ω−	ω−	INTJ
ejpam-5423	65	4	∨ϖ−	∨ϖ−	NOUN
ejpam-5423	65	5	)	)	PUNCT
ejpam-5423	65	6	,	,	PUNCT
ejpam-5423	65	7	(	(	PUNCT
ejpam-5423	65	8	ω+	ω+	NOUN
ejpam-5423	65	9	∨ϖ+	∨ϖ+	NOUN
ejpam-5423	65	10	)	)	PUNCT
ejpam-5423	65	11	]	]	PUNCT
ejpam-5423	65	12	.	.	PUNCT
ejpam-5423	66	1	if	if	SCONJ
ejpam-5423	66	2	ω	ω	NUM
ejpam-5423	66	3	⪰	⪰	NOUN
ejpam-5423	66	4	ϖ	ϖ	NOUN
ejpam-5423	66	5	,	,	PUNCT
ejpam-5423	66	6	we	we	PRON
ejpam-5423	66	7	mean	mean	VERB
ejpam-5423	66	8	ϖ	ϖ	X
ejpam-5423	66	9	⪯	⪯	PROPN
ejpam-5423	66	10	ω	ω	PROPN
ejpam-5423	66	11	.	.	PUNCT
ejpam-5423	67	1	for	for	ADP
ejpam-5423	67	2	each	each	DET
ejpam-5423	67	3	interval	interval	NOUN
ejpam-5423	67	4	ωi	ωi	X
ejpam-5423	67	5	=	=	PUNCT
ejpam-5423	68	1	[	[	X
ejpam-5423	68	2	ω−	ω−	INTJ
ejpam-5423	68	3	i	i	PRON
ejpam-5423	68	4	,	,	PUNCT
ejpam-5423	68	5	ω	ω	PROPN
ejpam-5423	69	1	+	+	CCONJ
ejpam-5423	69	2	i	i	PRON
ejpam-5423	69	3	]	]	PUNCT
ejpam-5423	69	4	∈	∈	PROPN
ejpam-5423	69	5	ω[0	ω[0	PROPN
ejpam-5423	69	6	,	,	PUNCT
ejpam-5423	69	7	1	1	NUM
ejpam-5423	69	8	]	]	PUNCT
ejpam-5423	69	9	,	,	PUNCT
ejpam-5423	69	10	i	i	PRON
ejpam-5423	69	11	∈	∈	VERB
ejpam-5423	69	12	a	a	PRON
ejpam-5423	69	13	where	where	SCONJ
ejpam-5423	69	14	a	a	PRON
ejpam-5423	69	15	is	be	AUX
ejpam-5423	69	16	an	an	DET
ejpam-5423	69	17	index	index	NOUN
ejpam-5423	69	18	set	set	NOUN
ejpam-5423	69	19	,	,	PUNCT
ejpam-5423	69	20	we	we	PRON
ejpam-5423	69	21	define	define	VERB
ejpam-5423	69	22	⋏	⋏	PROPN
ejpam-5423	69	23	i∈a	i∈a	VERB
ejpam-5423	70	1	ωi	ωi	NOUN
ejpam-5423	70	2	=	=	PUNCT
ejpam-5423	70	3	[	[	PUNCT
ejpam-5423	70	4	∧	∧	NOUN
ejpam-5423	70	5	i∈a	i∈a	VERB
ejpam-5423	70	6	ω−	ω−	ADP
ejpam-5423	70	7	i	i	PRON
ejpam-5423	70	8	,	,	PUNCT
ejpam-5423	70	9	∧	∧	PROPN
ejpam-5423	70	10	i∈a	i∈a	ADJ
ejpam-5423	70	11	ω+	ω+	NUM
ejpam-5423	70	12	i	i	NOUN
ejpam-5423	70	13	]	]	PUNCT
ejpam-5423	70	14	and	and	CCONJ
ejpam-5423	70	15	⋎	⋎	NOUN
ejpam-5423	70	16	i∈a	i∈a	ADJ
ejpam-5423	70	17	ωi	ωi	PUNCT
ejpam-5423	70	18	=	=	SYM
ejpam-5423	70	19	[	[	PUNCT
ejpam-5423	70	20	∨	∨	NUM
ejpam-5423	70	21	i∈a	i∈a	ADJ
ejpam-5423	71	1	ω−	ω−	ADP
ejpam-5423	71	2	i	i	PRON
ejpam-5423	71	3	,	,	PUNCT
ejpam-5423	71	4	∨	∨	PROPN
ejpam-5423	71	5	i∈a	i∈a	PROPN
ejpam-5423	71	6	ω+	ω+	NUM
ejpam-5423	71	7	i	i	PRON
ejpam-5423	71	8	]	]	PUNCT
ejpam-5423	71	9	.	.	PUNCT
ejpam-5423	72	1	definition	definition	NOUN
ejpam-5423	72	2	1	1	NUM
ejpam-5423	72	3	.	.	PUNCT
ejpam-5423	73	1	[	[	X
ejpam-5423	73	2	13	13	NUM
ejpam-5423	73	3	]	]	PUNCT
ejpam-5423	73	4	let	let	VERB
ejpam-5423	73	5	t	t	NOUN
ejpam-5423	73	6	be	be	AUX
ejpam-5423	73	7	a	a	DET
ejpam-5423	73	8	non	non	ADJ
ejpam-5423	73	9	-	-	ADJ
ejpam-5423	73	10	empty	empty	ADJ
ejpam-5423	73	11	set	set	NOUN
ejpam-5423	73	12	.	.	PUNCT
ejpam-5423	74	1	then	then	ADV
ejpam-5423	74	2	the	the	DET
ejpam-5423	74	3	function	function	NOUN
ejpam-5423	74	4	f	f	PROPN
ejpam-5423	74	5	:	:	PUNCT
ejpam-5423	74	6	t	t	PROPN
ejpam-5423	74	7	→	→	SYM
ejpam-5423	74	8	ω[0	ω[0	PROPN
ejpam-5423	74	9	,	,	PUNCT
ejpam-5423	74	10	1	1	NUM
ejpam-5423	74	11	]	]	PUNCT
ejpam-5423	74	12	is	be	AUX
ejpam-5423	74	13	called	call	VERB
ejpam-5423	74	14	interval	interval	NOUN
ejpam-5423	74	15	valued	value	VERB
ejpam-5423	74	16	fuzzy	fuzzy	ADJ
ejpam-5423	74	17	set	set	NOUN
ejpam-5423	74	18	(	(	PUNCT
ejpam-5423	74	19	shortly	shortly	ADV
ejpam-5423	74	20	,	,	PUNCT
ejpam-5423	74	21	ivf	ivf	NOUN
ejpam-5423	74	22	set	set	NOUN
ejpam-5423	74	23	)	)	PUNCT
ejpam-5423	74	24	of	of	ADP
ejpam-5423	74	25	t	t	PROPN
ejpam-5423	74	26	.	.	PUNCT
ejpam-5423	75	1	definition	definition	NOUN
ejpam-5423	75	2	2	2	NUM
ejpam-5423	75	3	.	.	PUNCT
ejpam-5423	76	1	[	[	X
ejpam-5423	76	2	13	13	NUM
ejpam-5423	76	3	]	]	PUNCT
ejpam-5423	76	4	let	let	VERB
ejpam-5423	76	5	m	m	PRON
ejpam-5423	76	6	be	be	AUX
ejpam-5423	76	7	a	a	DET
ejpam-5423	76	8	subset	subset	NOUN
ejpam-5423	76	9	of	of	ADP
ejpam-5423	76	10	a	a	DET
ejpam-5423	76	11	non	non	ADJ
ejpam-5423	76	12	-	-	ADJ
ejpam-5423	76	13	empty	empty	ADJ
ejpam-5423	76	14	set	set	NOUN
ejpam-5423	76	15	g.	g.	NOUN
ejpam-5423	76	16	an	an	DET
ejpam-5423	76	17	interval	interval	NOUN
ejpam-5423	76	18	valued	value	VERB
ejpam-5423	76	19	characteristic	characteristic	ADJ
ejpam-5423	76	20	function	function	NOUN
ejpam-5423	76	21	of	of	ADP
ejpam-5423	76	22	m	m	PROPN
ejpam-5423	76	23	is	be	AUX
ejpam-5423	76	24	defined	define	VERB
ejpam-5423	76	25	to	to	PART
ejpam-5423	76	26	be	be	AUX
ejpam-5423	76	27	a	a	DET
ejpam-5423	76	28	function	function	NOUN
ejpam-5423	76	29	χm	χm	NOUN
ejpam-5423	76	30	:	:	PUNCT
ejpam-5423	76	31	g	g	PROPN
ejpam-5423	76	32	→	→	SYM
ejpam-5423	76	33	ω[0	ω[0	PROPN
ejpam-5423	76	34	,	,	PUNCT
ejpam-5423	76	35	1	1	NUM
ejpam-5423	76	36	]	]	PUNCT
ejpam-5423	76	37	by	by	ADP
ejpam-5423	76	38	χm	χm	PRON
ejpam-5423	76	39	(	(	PUNCT
ejpam-5423	76	40	e	e	NOUN
ejpam-5423	76	41	)	)	PUNCT
ejpam-5423	76	42	=	=	SYM
ejpam-5423	76	43	{	{	PUNCT
ejpam-5423	76	44	1	1	NUM
ejpam-5423	76	45	if	if	SCONJ
ejpam-5423	76	46	e	e	PROPN
ejpam-5423	76	47	∈	∈	PROPN
ejpam-5423	76	48	m	m	PROPN
ejpam-5423	76	49	,	,	PUNCT
ejpam-5423	76	50	0	0	PUNCT
ejpam-5423	77	1	if	if	SCONJ
ejpam-5423	77	2	e	e	PROPN
ejpam-5423	77	3	/∈	/∈	PUNCT
ejpam-5423	77	4	m	m	VERB
ejpam-5423	77	5	for	for	ADP
ejpam-5423	77	6	all	all	DET
ejpam-5423	77	7	e	e	PROPN
ejpam-5423	77	8	∈	∈	PROPN
ejpam-5423	77	9	g.	g.	NOUN
ejpam-5423	77	10	now	now	ADV
ejpam-5423	77	11	,	,	PUNCT
ejpam-5423	77	12	we	we	PRON
ejpam-5423	77	13	review	review	VERB
ejpam-5423	77	14	the	the	DET
ejpam-5423	77	15	definition	definition	NOUN
ejpam-5423	77	16	of	of	ADP
ejpam-5423	77	17	bipolar	bipolar	ADJ
ejpam-5423	77	18	valued	value	VERB
ejpam-5423	77	19	fuzzy	fuzzy	ADJ
ejpam-5423	77	20	set	set	NOUN
ejpam-5423	77	21	and	and	CCONJ
ejpam-5423	77	22	the	the	DET
ejpam-5423	77	23	basic	basic	ADJ
ejpam-5423	77	24	properties	property	NOUN
ejpam-5423	77	25	used	use	VERB
ejpam-5423	77	26	in	in	ADP
ejpam-5423	77	27	the	the	DET
ejpam-5423	77	28	next	next	ADJ
ejpam-5423	77	29	section	section	NOUN
ejpam-5423	77	30	.	.	PUNCT
ejpam-5423	78	1	definition	definition	NOUN
ejpam-5423	78	2	3	3	NUM
ejpam-5423	78	3	.	.	PUNCT
ejpam-5423	79	1	[	[	X
ejpam-5423	79	2	11	11	NUM
ejpam-5423	79	3	]	]	PUNCT
ejpam-5423	79	4	let	let	VERB
ejpam-5423	79	5	t	t	NOUN
ejpam-5423	79	6	be	be	AUX
ejpam-5423	79	7	a	a	DET
ejpam-5423	79	8	non	non	ADJ
ejpam-5423	79	9	-	-	ADJ
ejpam-5423	79	10	empty	empty	ADJ
ejpam-5423	79	11	set	set	NOUN
ejpam-5423	79	12	.	.	PUNCT
ejpam-5423	80	1	a	a	DET
ejpam-5423	80	2	bipolar	bipolar	ADJ
ejpam-5423	80	3	fuzzy	fuzzy	ADJ
ejpam-5423	80	4	set	set	NOUN
ejpam-5423	80	5	(	(	PUNCT
ejpam-5423	80	6	bf	bf	NOUN
ejpam-5423	80	7	set	set	NOUN
ejpam-5423	80	8	)	)	PUNCT
ejpam-5423	80	9	ω	ω	PROPN
ejpam-5423	80	10	on	on	ADP
ejpam-5423	80	11	t	t	PROPN
ejpam-5423	80	12	is	be	AUX
ejpam-5423	80	13	an	an	DET
ejpam-5423	80	14	object	object	NOUN
ejpam-5423	80	15	having	have	VERB
ejpam-5423	80	16	the	the	DET
ejpam-5423	80	17	form	form	NOUN
ejpam-5423	80	18	ω	ω	NOUN
ejpam-5423	80	19	:	:	PUNCT
ejpam-5423	80	20	=	=	SYM
ejpam-5423	80	21	{	{	PUNCT
ejpam-5423	80	22	(	(	PUNCT
ejpam-5423	80	23	k	k	NOUN
ejpam-5423	80	24	,	,	PUNCT
ejpam-5423	80	25	ωp(k	ωp(k	NOUN
ejpam-5423	80	26	)	)	PUNCT
ejpam-5423	80	27	,	,	PUNCT
ejpam-5423	80	28	ωn(k	ωn(k	NUM
ejpam-5423	80	29	)	)	PUNCT
ejpam-5423	80	30	)	)	PUNCT
ejpam-5423	81	1	|	|	ADV
ejpam-5423	81	2	k	k	PROPN
ejpam-5423	81	3	∈	∈	PROPN
ejpam-5423	81	4	t	t	PROPN
ejpam-5423	81	5	}	}	PUNCT
ejpam-5423	81	6	,	,	PUNCT
ejpam-5423	81	7	where	where	SCONJ
ejpam-5423	81	8	ωp	ωp	X
ejpam-5423	81	9	:	:	PUNCT
ejpam-5423	81	10	t	t	PROPN
ejpam-5423	81	11	→	→	PUNCT
ejpam-5423	82	1	[	[	X
ejpam-5423	82	2	0	0	NUM
ejpam-5423	82	3	,	,	PUNCT
ejpam-5423	82	4	1	1	NUM
ejpam-5423	82	5	]	]	PUNCT
ejpam-5423	82	6	and	and	CCONJ
ejpam-5423	82	7	ωn	ωn	ADP
ejpam-5423	82	8	:	:	PUNCT
ejpam-5423	82	9	t	t	PROPN
ejpam-5423	82	10	→	→	PUNCT
ejpam-5423	83	1	[	[	X
ejpam-5423	83	2	−1	−1	NOUN
ejpam-5423	83	3	,	,	PUNCT
ejpam-5423	83	4	0	0	NUM
ejpam-5423	83	5	]	]	PUNCT
ejpam-5423	83	6	.	.	PUNCT
ejpam-5423	84	1	remark	remark	PROPN
ejpam-5423	84	2	1	1	NUM
ejpam-5423	84	3	.	.	PUNCT
ejpam-5423	85	1	for	for	ADP
ejpam-5423	85	2	the	the	DET
ejpam-5423	85	3	sake	sake	NOUN
ejpam-5423	85	4	of	of	ADP
ejpam-5423	85	5	simplicity	simplicity	NOUN
ejpam-5423	85	6	we	we	PRON
ejpam-5423	85	7	shall	shall	AUX
ejpam-5423	85	8	use	use	VERB
ejpam-5423	85	9	the	the	DET
ejpam-5423	85	10	symbol	symbol	NOUN
ejpam-5423	85	11	ω	ω	NOUN
ejpam-5423	85	12	=	=	SYM
ejpam-5423	85	13	(	(	PUNCT
ejpam-5423	85	14	t	t	PROPN
ejpam-5423	85	15	;	;	PUNCT
ejpam-5423	85	16	ωp	ωp	INTJ
ejpam-5423	85	17	,	,	PUNCT
ejpam-5423	85	18	ωn	ωn	PROPN
ejpam-5423	85	19	)	)	PUNCT
ejpam-5423	85	20	for	for	SCONJ
ejpam-5423	85	21	the	the	DET
ejpam-5423	85	22	bf	bf	NOUN
ejpam-5423	85	23	set	set	VERB
ejpam-5423	85	24	ω	ω	PROPN
ejpam-5423	85	25	=	=	SYM
ejpam-5423	85	26	{	{	PUNCT
ejpam-5423	85	27	(	(	PUNCT
ejpam-5423	85	28	k	k	NOUN
ejpam-5423	85	29	,	,	PUNCT
ejpam-5423	85	30	ωp(k	ωp(k	NOUN
ejpam-5423	85	31	)	)	PUNCT
ejpam-5423	85	32	,	,	PUNCT
ejpam-5423	85	33	ωn(k	ωn(k	NUM
ejpam-5423	85	34	)	)	PUNCT
ejpam-5423	85	35	)	)	PUNCT
ejpam-5423	86	1	|	|	ADV
ejpam-5423	86	2	k	k	PROPN
ejpam-5423	86	3	∈	∈	PROPN
ejpam-5423	86	4	t	t	PROPN
ejpam-5423	86	5	}	}	PUNCT
ejpam-5423	86	6	.	.	PUNCT
ejpam-5423	87	1	the	the	DET
ejpam-5423	87	2	following	following	ADJ
ejpam-5423	87	3	example	example	NOUN
ejpam-5423	87	4	of	of	ADP
ejpam-5423	87	5	a	a	DET
ejpam-5423	87	6	bf	bf	NOUN
ejpam-5423	87	7	set	set	NOUN
ejpam-5423	87	8	.	.	PUNCT
ejpam-5423	88	1	t.	t.	PROPN
ejpam-5423	88	2	gaketem	gaketem	PROPN
ejpam-5423	88	3	,	,	PUNCT
ejpam-5423	88	4	t.	t.	PROPN
ejpam-5423	88	5	prommai	prommai	PROPN
ejpam-5423	88	6	/	/	SYM
ejpam-5423	88	7	eur	eur	PROPN
ejpam-5423	88	8	.	.	PUNCT
ejpam-5423	89	1	j.	j.	PROPN
ejpam-5423	89	2	pure	pure	PROPN
ejpam-5423	89	3	appl	appl	PROPN
ejpam-5423	89	4	.	.	PROPN
ejpam-5423	89	5	math	math	PROPN
ejpam-5423	89	6	,	,	PUNCT
ejpam-5423	89	7	17	17	NUM
ejpam-5423	89	8	(	(	PUNCT
ejpam-5423	89	9	4	4	NUM
ejpam-5423	89	10	)	)	PUNCT
ejpam-5423	89	11	(	(	PUNCT
ejpam-5423	89	12	2024	2024	NUM
ejpam-5423	89	13	)	)	PUNCT
ejpam-5423	89	14	,	,	PUNCT
ejpam-5423	89	15	3223	3223	NUM
ejpam-5423	89	16	-	-	SYM
ejpam-5423	89	17	3241	3241	NUM
ejpam-5423	89	18	3226	3226	NUM
ejpam-5423	89	19	example	example	NOUN
ejpam-5423	90	1	1	1	NUM
ejpam-5423	90	2	.	.	PUNCT
ejpam-5423	91	1	let	let	VERB
ejpam-5423	91	2	t	t	NOUN
ejpam-5423	91	3	=	=	PUNCT
ejpam-5423	91	4	{	{	PUNCT
ejpam-5423	91	5	21	21	NUM
ejpam-5423	91	6	,	,	PUNCT
ejpam-5423	91	7	22	22	NUM
ejpam-5423	91	8	,	,	PUNCT
ejpam-5423	91	9	23	23	NUM
ejpam-5423	91	10	...	...	PUNCT
ejpam-5423	91	11	}	}	PUNCT
ejpam-5423	91	12	.	.	PUNCT
ejpam-5423	92	1	define	define	VERB
ejpam-5423	92	2	ωp	ωp	PRON
ejpam-5423	92	3	:	:	PUNCT
ejpam-5423	92	4	t	t	PROPN
ejpam-5423	92	5	→	→	PUNCT
ejpam-5423	93	1	[	[	X
ejpam-5423	93	2	0	0	NUM
ejpam-5423	93	3	,	,	PUNCT
ejpam-5423	93	4	1	1	NUM
ejpam-5423	93	5	]	]	PUNCT
ejpam-5423	93	6	is	be	AUX
ejpam-5423	93	7	a	a	DET
ejpam-5423	93	8	function	function	NOUN
ejpam-5423	93	9	ωp(u	ωp(u	PUNCT
ejpam-5423	93	10	)	)	PUNCT
ejpam-5423	94	1	=	=	PRON
ejpam-5423	94	2	{	{	PUNCT
ejpam-5423	94	3	0	0	NUM
ejpam-5423	94	4	if	if	SCONJ
ejpam-5423	94	5	u	u	NOUN
ejpam-5423	94	6	is	be	AUX
ejpam-5423	94	7	old	old	ADJ
ejpam-5423	94	8	number	number	NOUN
ejpam-5423	94	9	1	1	NUM
ejpam-5423	94	10	if	if	SCONJ
ejpam-5423	94	11	u	u	NOUN
ejpam-5423	94	12	is	be	AUX
ejpam-5423	94	13	even	even	ADV
ejpam-5423	94	14	number	number	NOUN
ejpam-5423	94	15	and	and	CCONJ
ejpam-5423	94	16	ωn	ωn	ADP
ejpam-5423	94	17	:	:	PUNCT
ejpam-5423	94	18	t	t	PROPN
ejpam-5423	94	19	→	→	PUNCT
ejpam-5423	95	1	[	[	X
ejpam-5423	95	2	−1	−1	NOUN
ejpam-5423	95	3	,	,	PUNCT
ejpam-5423	95	4	0	0	NUM
ejpam-5423	95	5	]	]	PUNCT
ejpam-5423	95	6	is	be	AUX
ejpam-5423	95	7	a	a	DET
ejpam-5423	95	8	function	function	NOUN
ejpam-5423	95	9	ωn(u	ωn(u	NOUN
ejpam-5423	95	10	)	)	PUNCT
ejpam-5423	96	1	=	=	PRON
ejpam-5423	96	2	{	{	PUNCT
ejpam-5423	96	3	−1	−1	NOUN
ejpam-5423	96	4	if	if	SCONJ
ejpam-5423	96	5	u	u	NOUN
ejpam-5423	96	6	is	be	AUX
ejpam-5423	96	7	old	old	ADJ
ejpam-5423	96	8	number	number	NOUN
ejpam-5423	96	9	0	0	NUM
ejpam-5423	97	1	if	if	SCONJ
ejpam-5423	97	2	u	u	NOUN
ejpam-5423	97	3	is	be	AUX
ejpam-5423	97	4	even	even	ADV
ejpam-5423	97	5	number	number	NOUN
ejpam-5423	97	6	.	.	PUNCT
ejpam-5423	98	1	then	then	ADV
ejpam-5423	98	2	ω	ω	X
ejpam-5423	98	3	=	=	SYM
ejpam-5423	98	4	(	(	PUNCT
ejpam-5423	98	5	t	t	PROPN
ejpam-5423	98	6	;	;	PUNCT
ejpam-5423	98	7	ωp	ωp	INTJ
ejpam-5423	98	8	,	,	PUNCT
ejpam-5423	98	9	ωn	ωn	PRON
ejpam-5423	98	10	)	)	PUNCT
ejpam-5423	98	11	is	be	AUX
ejpam-5423	98	12	a	a	DET
ejpam-5423	98	13	bf	bf	NOUN
ejpam-5423	98	14	set	set	NOUN
ejpam-5423	98	15	.	.	PUNCT
ejpam-5423	99	1	for	for	ADP
ejpam-5423	99	2	k	k	PROPN
ejpam-5423	99	3	∈	∈	PROPN
ejpam-5423	99	4	t	t	PROPN
ejpam-5423	99	5	,	,	PUNCT
ejpam-5423	99	6	define	define	VERB
ejpam-5423	99	7	fk	fk	INTJ
ejpam-5423	99	8	=	=	SYM
ejpam-5423	99	9	{	{	PUNCT
ejpam-5423	99	10	(	(	PUNCT
ejpam-5423	99	11	y	y	PROPN
ejpam-5423	99	12	,	,	PUNCT
ejpam-5423	99	13	z	z	NOUN
ejpam-5423	99	14	)	)	PUNCT
ejpam-5423	99	15	∈	∈	PROPN
ejpam-5423	100	1	t	t	X
ejpam-5423	100	2	×	×	NOUN
ejpam-5423	100	3	t	t	NOUN
ejpam-5423	101	1	|	|	ADV
ejpam-5423	101	2	k	k	PROPN
ejpam-5423	101	3	=	=	SYM
ejpam-5423	101	4	yz	yz	PROPN
ejpam-5423	101	5	}	}	PUNCT
ejpam-5423	101	6	.	.	PUNCT
ejpam-5423	102	1	definition	definition	NOUN
ejpam-5423	102	2	4	4	NUM
ejpam-5423	102	3	.	.	PUNCT
ejpam-5423	103	1	[	[	X
ejpam-5423	103	2	6	6	NUM
ejpam-5423	103	3	]	]	PUNCT
ejpam-5423	103	4	let	let	AUX
ejpam-5423	103	5	m	m	PRON
ejpam-5423	103	6	be	be	AUX
ejpam-5423	103	7	a	a	DET
ejpam-5423	103	8	non	non	ADJ
ejpam-5423	103	9	-	-	ADJ
ejpam-5423	103	10	empty	empty	ADJ
ejpam-5423	103	11	set	set	NOUN
ejpam-5423	103	12	of	of	ADP
ejpam-5423	103	13	a	a	DET
ejpam-5423	103	14	semigroup	semigroup	PROPN
ejpam-5423	103	15	t	t	NOUN
ejpam-5423	103	16	.	.	PUNCT
ejpam-5423	104	1	a	a	DET
ejpam-5423	104	2	positive	positive	ADJ
ejpam-5423	104	3	characteristic	characteristic	ADJ
ejpam-5423	104	4	function	function	NOUN
ejpam-5423	104	5	and	and	CCONJ
ejpam-5423	104	6	a	a	DET
ejpam-5423	104	7	negative	negative	ADJ
ejpam-5423	104	8	characteristic	characteristic	ADJ
ejpam-5423	104	9	function	function	NOUN
ejpam-5423	104	10	are	be	AUX
ejpam-5423	104	11	respectively	respectively	ADV
ejpam-5423	104	12	defined	define	VERB
ejpam-5423	104	13	by	by	ADP
ejpam-5423	104	14	χp	χp	PROPN
ejpam-5423	104	15	m	m	PROPN
ejpam-5423	104	16	:	:	PUNCT
ejpam-5423	104	17	t	t	X
ejpam-5423	104	18	→	→	PUNCT
ejpam-5423	105	1	[	[	X
ejpam-5423	105	2	0	0	NUM
ejpam-5423	105	3	,	,	PUNCT
ejpam-5423	105	4	1	1	NUM
ejpam-5423	105	5	]	]	PUNCT
ejpam-5423	105	6	,	,	PUNCT
ejpam-5423	105	7	k	k	PROPN
ejpam-5423	106	1	7→	7→	NUM
ejpam-5423	106	2	λp	λp	ADP
ejpam-5423	106	3	m	m	PROPN
ejpam-5423	106	4	(	(	PUNCT
ejpam-5423	106	5	u	u	NOUN
ejpam-5423	106	6	)	)	PUNCT
ejpam-5423	106	7	:	:	PUNCT
ejpam-5423	106	8	=	=	SYM
ejpam-5423	106	9	{	{	PUNCT
ejpam-5423	106	10	1	1	NUM
ejpam-5423	106	11	k	k	X
ejpam-5423	106	12	∈	∈	PROPN
ejpam-5423	106	13	m	m	NOUN
ejpam-5423	106	14	,	,	PUNCT
ejpam-5423	106	15	0	0	PUNCT
ejpam-5423	107	1	k	k	NOUN
ejpam-5423	107	2	/∈	/∈	PUNCT
ejpam-5423	108	1	m	m	VERB
ejpam-5423	108	2	,	,	PUNCT
ejpam-5423	108	3	and	and	CCONJ
ejpam-5423	108	4	χn	χn	X
ejpam-5423	108	5	m	m	PROPN
ejpam-5423	108	6	:	:	PUNCT
ejpam-5423	108	7	t	t	X
ejpam-5423	108	8	→	→	PUNCT
ejpam-5423	109	1	[	[	X
ejpam-5423	109	2	−1	−1	NOUN
ejpam-5423	109	3	,	,	PUNCT
ejpam-5423	109	4	0	0	NUM
ejpam-5423	109	5	]	]	PUNCT
ejpam-5423	109	6	,	,	PUNCT
ejpam-5423	109	7	k	k	PROPN
ejpam-5423	110	1	7→	7→	NUM
ejpam-5423	110	2	λn	λn	NOUN
ejpam-5423	110	3	m	m	PROPN
ejpam-5423	110	4	(	(	PUNCT
ejpam-5423	110	5	k	k	NOUN
ejpam-5423	110	6	)	)	PUNCT
ejpam-5423	110	7	:	:	PUNCT
ejpam-5423	110	8	=	=	PRON
ejpam-5423	110	9	{	{	PUNCT
ejpam-5423	110	10	−1	−1	NOUN
ejpam-5423	110	11	k	k	PROPN
ejpam-5423	110	12	∈	∈	PROPN
ejpam-5423	110	13	m	m	PROPN
ejpam-5423	110	14	,	,	PUNCT
ejpam-5423	110	15	0	0	PUNCT
ejpam-5423	111	1	k	k	NOUN
ejpam-5423	111	2	/∈	/∈	PUNCT
ejpam-5423	112	1	m	m	VERB
ejpam-5423	112	2	.	.	PUNCT
ejpam-5423	113	1	remark	remark	PROPN
ejpam-5423	113	2	2	2	NUM
ejpam-5423	113	3	.	.	PUNCT
ejpam-5423	114	1	for	for	ADP
ejpam-5423	114	2	the	the	DET
ejpam-5423	114	3	sake	sake	NOUN
ejpam-5423	114	4	of	of	ADP
ejpam-5423	114	5	simplicity	simplicity	NOUN
ejpam-5423	114	6	we	we	PRON
ejpam-5423	114	7	shall	shall	AUX
ejpam-5423	114	8	use	use	VERB
ejpam-5423	114	9	the	the	DET
ejpam-5423	114	10	symbol	symbol	NOUN
ejpam-5423	114	11	χm	χm	NOUN
ejpam-5423	115	1	=	=	SYM
ejpam-5423	115	2	(	(	PUNCT
ejpam-5423	115	3	t	t	PROPN
ejpam-5423	115	4	;	;	PUNCT
ejpam-5423	115	5	χp	χp	PROPN
ejpam-5423	115	6	m	m	PROPN
ejpam-5423	115	7	,	,	PUNCT
ejpam-5423	115	8	χn	χn	X
ejpam-5423	115	9	m	m	PROPN
ejpam-5423	115	10	)	)	PUNCT
ejpam-5423	115	11	for	for	SCONJ
ejpam-5423	115	12	the	the	DET
ejpam-5423	115	13	bf	bf	NOUN
ejpam-5423	115	14	set	set	VERB
ejpam-5423	115	15	χi	χi	NOUN
ejpam-5423	115	16	:	:	PUNCT
ejpam-5423	115	17	=	=	SYM
ejpam-5423	115	18	{	{	PUNCT
ejpam-5423	115	19	(	(	PUNCT
ejpam-5423	115	20	k	k	NOUN
ejpam-5423	115	21	,	,	PUNCT
ejpam-5423	115	22	χp	χp	VERB
ejpam-5423	115	23	i(k	i(k	PROPN
ejpam-5423	115	24	)	)	PUNCT
ejpam-5423	115	25	,	,	PUNCT
ejpam-5423	115	26	χ	χ	NOUN
ejpam-5423	115	27	n	n	INTJ
ejpam-5423	115	28	i	i	PRON
ejpam-5423	115	29	(	(	PUNCT
ejpam-5423	115	30	k	k	NOUN
ejpam-5423	115	31	)	)	PUNCT
ejpam-5423	115	32	)	)	PUNCT
ejpam-5423	116	1	|	|	ADV
ejpam-5423	116	2	k	k	PROPN
ejpam-5423	116	3	∈	∈	PROPN
ejpam-5423	116	4	i	i	X
ejpam-5423	116	5	}	}	PUNCT
ejpam-5423	116	6	.	.	PUNCT
ejpam-5423	117	1	now	now	ADV
ejpam-5423	117	2	,	,	PUNCT
ejpam-5423	117	3	we	we	PRON
ejpam-5423	117	4	review	review	VERB
ejpam-5423	117	5	the	the	DET
ejpam-5423	117	6	definition	definition	NOUN
ejpam-5423	117	7	of	of	ADP
ejpam-5423	117	8	an	an	DET
ejpam-5423	117	9	interval	interval	NOUN
ejpam-5423	117	10	valued	value	VERB
ejpam-5423	117	11	bipolar	bipolar	ADJ
ejpam-5423	117	12	fuzzy	fuzzy	ADJ
ejpam-5423	117	13	set	set	NOUN
ejpam-5423	117	14	and	and	CCONJ
ejpam-5423	117	15	the	the	DET
ejpam-5423	117	16	basic	basic	ADJ
ejpam-5423	117	17	properties	property	NOUN
ejpam-5423	117	18	used	use	VERB
ejpam-5423	117	19	in	in	ADP
ejpam-5423	117	20	the	the	DET
ejpam-5423	117	21	next	next	ADJ
ejpam-5423	117	22	section	section	NOUN
ejpam-5423	117	23	.	.	PUNCT
ejpam-5423	118	1	definition	definition	NOUN
ejpam-5423	118	2	5	5	NUM
ejpam-5423	118	3	.	.	PUNCT
ejpam-5423	119	1	[	[	X
ejpam-5423	119	2	7	7	X
ejpam-5423	119	3	]	]	X
ejpam-5423	119	4	an	an	DET
ejpam-5423	119	5	interval	interval	NOUN
ejpam-5423	119	6	valued	value	VERB
ejpam-5423	119	7	bipolar	bipolar	ADJ
ejpam-5423	119	8	fuzzy	fuzzy	ADJ
ejpam-5423	119	9	set	set	NOUN
ejpam-5423	119	10	(	(	PUNCT
ejpam-5423	119	11	shortly	shortly	ADV
ejpam-5423	119	12	,	,	PUNCT
ejpam-5423	119	13	ivbf	ivbf	VERB
ejpam-5423	119	14	subset	subset	NOUN
ejpam-5423	119	15	)	)	PUNCT
ejpam-5423	119	16	t	t	PROPN
ejpam-5423	119	17	on	on	ADP
ejpam-5423	119	18	an	an	DET
ejpam-5423	119	19	ordered	order	VERB
ejpam-5423	119	20	semigroup	semigroup	NOUN
ejpam-5423	119	21	g	g	PROPN
ejpam-5423	119	22	is	be	AUX
ejpam-5423	119	23	form	form	NOUN
ejpam-5423	119	24	t	t	NOUN
ejpam-5423	119	25	:	:	PUNCT
ejpam-5423	119	26	=	=	SYM
ejpam-5423	119	27	{	{	PUNCT
ejpam-5423	119	28	e	e	PROPN
ejpam-5423	119	29	,	,	PUNCT
ejpam-5423	119	30	ω	ω	X
ejpam-5423	119	31	p(e	p(e	NOUN
ejpam-5423	119	32	)	)	PUNCT
ejpam-5423	119	33	,	,	PUNCT
ejpam-5423	119	34	ω	ω	NUM
ejpam-5423	119	35	n(e	n(e	PROPN
ejpam-5423	119	36	)	)	PUNCT
ejpam-5423	119	37	|	|	ADV
ejpam-5423	119	38	e	e	ADP
ejpam-5423	119	39	∈	∈	PROPN
ejpam-5423	119	40	g	g	PROPN
ejpam-5423	119	41	}	}	PUNCT
ejpam-5423	119	42	,	,	PUNCT
ejpam-5423	119	43	where	where	SCONJ
ejpam-5423	119	44	ω	ω	PROPN
ejpam-5423	119	45	p	p	X
ejpam-5423	119	46	:	:	PUNCT
ejpam-5423	119	47	g	g	PROPN
ejpam-5423	119	48	→	→	SYM
ejpam-5423	119	49	ω[0	ω[0	PROPN
ejpam-5423	119	50	,	,	PUNCT
ejpam-5423	119	51	1	1	NUM
ejpam-5423	119	52	]	]	PUNCT
ejpam-5423	119	53	and	and	CCONJ
ejpam-5423	119	54	ω	ω	NUM
ejpam-5423	119	55	n	n	X
ejpam-5423	119	56	:	:	PUNCT
ejpam-5423	119	57	g	g	PROPN
ejpam-5423	119	58	→	→	SYM
ejpam-5423	119	59	ω[−1	ω[−1	PROPN
ejpam-5423	119	60	,	,	PUNCT
ejpam-5423	119	61	0	0	NUM
ejpam-5423	119	62	]	]	PUNCT
ejpam-5423	119	63	.	.	PUNCT
ejpam-5423	120	1	in	in	ADP
ejpam-5423	120	2	this	this	DET
ejpam-5423	120	3	page	page	NOUN
ejpam-5423	120	4	we	we	PRON
ejpam-5423	120	5	shall	shall	AUX
ejpam-5423	120	6	use	use	VERB
ejpam-5423	120	7	the	the	DET
ejpam-5423	120	8	symbol	symbol	NOUN
ejpam-5423	120	9	t	t	NOUN
ejpam-5423	120	10	=	=	SYM
ejpam-5423	120	11	(	(	PUNCT
ejpam-5423	120	12	ω	ω	PROPN
ejpam-5423	120	13	p	p	PROPN
ejpam-5423	120	14	,	,	PUNCT
ejpam-5423	120	15	ω	ω	PROPN
ejpam-5423	120	16	n	n	CCONJ
ejpam-5423	120	17	)	)	PUNCT
ejpam-5423	120	18	instead	instead	ADV
ejpam-5423	120	19	of	of	ADP
ejpam-5423	120	20	the	the	DET
ejpam-5423	120	21	ivbf	ivbf	NOUN
ejpam-5423	120	22	set	set	VERB
ejpam-5423	120	23	t	t	PROPN
ejpam-5423	120	24	:	:	PUNCT
ejpam-5423	120	25	=	=	SYM
ejpam-5423	120	26	{	{	PUNCT
ejpam-5423	120	27	e	e	PROPN
ejpam-5423	120	28	,	,	PUNCT
ejpam-5423	120	29	ω	ω	X
ejpam-5423	120	30	p(e	p(e	NOUN
ejpam-5423	120	31	)	)	PUNCT
ejpam-5423	120	32	,	,	PUNCT
ejpam-5423	120	33	ω	ω	NUM
ejpam-5423	120	34	n(e	n(e	PROPN
ejpam-5423	120	35	)	)	PUNCT
ejpam-5423	121	1	|	|	ADV
ejpam-5423	121	2	e	e	ADP
ejpam-5423	121	3	∈	∈	PROPN
ejpam-5423	121	4	g	g	PROPN
ejpam-5423	121	5	}	}	PUNCT
ejpam-5423	121	6	.	.	PUNCT
ejpam-5423	122	1	for	for	ADP
ejpam-5423	122	2	two	two	NUM
ejpam-5423	122	3	ivbf	ivbf	NOUN
ejpam-5423	122	4	sets	set	NOUN
ejpam-5423	122	5	t	t	AUX
ejpam-5423	122	6	1	1	NUM
ejpam-5423	122	7	=	=	SYM
ejpam-5423	122	8	(	(	PUNCT
ejpam-5423	122	9	ω	ω	PROPN
ejpam-5423	122	10	p	p	PROPN
ejpam-5423	122	11	,	,	PUNCT
ejpam-5423	122	12	ω	ω	PROPN
ejpam-5423	122	13	n	n	CCONJ
ejpam-5423	122	14	)	)	PUNCT
ejpam-5423	122	15	and	and	CCONJ
ejpam-5423	122	16	t	t	X
ejpam-5423	122	17	2	2	NUM
ejpam-5423	122	18	=	=	SYM
ejpam-5423	122	19	(	(	PUNCT
ejpam-5423	122	20	ϖ	ϖ	X
ejpam-5423	122	21	p	p	X
ejpam-5423	122	22	,	,	PUNCT
ejpam-5423	122	23	ϖ	ϖ	NOUN
ejpam-5423	122	24	n	n	CCONJ
ejpam-5423	122	25	)	)	PUNCT
ejpam-5423	122	26	of	of	ADP
ejpam-5423	122	27	an	an	DET
ejpam-5423	122	28	ordered	order	VERB
ejpam-5423	122	29	semigroup	semigroup	NOUN
ejpam-5423	122	30	g	g	NOUN
ejpam-5423	122	31	,	,	PUNCT
ejpam-5423	122	32	define	define	VERB
ejpam-5423	122	33	(	(	PUNCT
ejpam-5423	122	34	1	1	NUM
ejpam-5423	122	35	)	)	PUNCT
ejpam-5423	122	36	t	t	NOUN
ejpam-5423	122	37	1	1	NUM
ejpam-5423	122	38	⊑	⊑	X
ejpam-5423	122	39	t	t	NOUN
ejpam-5423	122	40	2	2	NUM
ejpam-5423	122	41	if	if	SCONJ
ejpam-5423	122	42	and	and	CCONJ
ejpam-5423	122	43	only	only	ADV
ejpam-5423	122	44	if	if	SCONJ
ejpam-5423	122	45	ω	ω	X
ejpam-5423	122	46	p(e	p(e	NOUN
ejpam-5423	122	47	)	)	PUNCT
ejpam-5423	122	48	≤	≤	NOUN
ejpam-5423	122	49	ϖ	ϖ	SYM
ejpam-5423	122	50	p(e	p(e	NOUN
ejpam-5423	122	51	)	)	PUNCT
ejpam-5423	122	52	and	and	CCONJ
ejpam-5423	122	53	ω	ω	NUM
ejpam-5423	122	54	n(e	n(e	PROPN
ejpam-5423	122	55	)	)	PUNCT
ejpam-5423	122	56	≤	≤	NUM
ejpam-5423	122	57	ϖ	ϖ	DET
ejpam-5423	122	58	n(e	n(e	NOUN
ejpam-5423	122	59	)	)	PUNCT
ejpam-5423	122	60	for	for	ADP
ejpam-5423	122	61	all	all	DET
ejpam-5423	122	62	e	e	PROPN
ejpam-5423	122	63	∈	∈	PROPN
ejpam-5423	122	64	g	g	PROPN
ejpam-5423	122	65	,	,	PUNCT
ejpam-5423	122	66	(	(	PUNCT
ejpam-5423	122	67	2	2	X
ejpam-5423	122	68	)	)	PUNCT
ejpam-5423	122	69	t	t	NOUN
ejpam-5423	122	70	1	1	NUM
ejpam-5423	122	71	=	=	SYM
ejpam-5423	122	72	t	t	NOUN
ejpam-5423	122	73	1	1	NUM
ejpam-5423	122	74	if	if	SCONJ
ejpam-5423	122	75	and	and	CCONJ
ejpam-5423	122	76	only	only	ADV
ejpam-5423	122	77	if	if	SCONJ
ejpam-5423	122	78	t	t	PROPN
ejpam-5423	122	79	1	1	NUM
ejpam-5423	122	80	⊑	⊑	ADP
ejpam-5423	122	81	t	t	PROPN
ejpam-5423	122	82	2	2	NUM
ejpam-5423	122	83	and	and	CCONJ
ejpam-5423	122	84	t	t	PROPN
ejpam-5423	122	85	2	2	NUM
ejpam-5423	122	86	⊑	⊑	ADP
ejpam-5423	122	87	t	t	PROPN
ejpam-5423	122	88	1	1	NUM
ejpam-5423	122	89	,	,	PUNCT
ejpam-5423	122	90	(	(	PUNCT
ejpam-5423	122	91	3	3	X
ejpam-5423	122	92	)	)	PUNCT
ejpam-5423	122	93	t	t	NOUN
ejpam-5423	122	94	1⊔t	1⊔t	NUM
ejpam-5423	122	95	2	2	NUM
ejpam-5423	122	96	if	if	SCONJ
ejpam-5423	122	97	and	and	CCONJ
ejpam-5423	122	98	only	only	ADV
ejpam-5423	122	99	if	if	SCONJ
ejpam-5423	122	100	ω∪ϖ	ω∪ϖ	ADJ
ejpam-5423	122	101	where	where	SCONJ
ejpam-5423	122	102	(	(	PUNCT
ejpam-5423	122	103	ω	ω	NUM
ejpam-5423	122	104	p∪ϖ	p∪ϖ	X
ejpam-5423	122	105	p)(e	p)(e	PROPN
ejpam-5423	122	106	)	)	PUNCT
ejpam-5423	122	107	=	=	SYM
ejpam-5423	122	108	ω	ω	NUM
ejpam-5423	122	109	p(e)∨ϖ	p(e)∨ϖ	NOUN
ejpam-5423	122	110	p(e	p(e	NOUN
ejpam-5423	122	111	)	)	PUNCT
ejpam-5423	122	112	and	and	CCONJ
ejpam-5423	122	113	(	(	PUNCT
ejpam-5423	122	114	ω	ω	NUM
ejpam-5423	122	115	n∪ϖ	n∪ϖ	X
ejpam-5423	122	116	n)(e	n)(e	NOUN
ejpam-5423	122	117	)	)	PUNCT
ejpam-5423	122	118	=	=	SYM
ejpam-5423	122	119	ω	ω	NUM
ejpam-5423	122	120	n(e	n(e	PROPN
ejpam-5423	122	121	)	)	PUNCT
ejpam-5423	122	122	∧ϖ	∧ϖ	PROPN
ejpam-5423	122	123	n(e	n(e	PROPN
ejpam-5423	122	124	)	)	PUNCT
ejpam-5423	122	125	for	for	ADP
ejpam-5423	122	126	all	all	DET
ejpam-5423	122	127	e	e	PROPN
ejpam-5423	122	128	∈	∈	PROPN
ejpam-5423	122	129	g	g	PROPN
ejpam-5423	122	130	,	,	PUNCT
ejpam-5423	122	131	t.	t.	PROPN
ejpam-5423	122	132	gaketem	gaketem	PROPN
ejpam-5423	122	133	,	,	PUNCT
ejpam-5423	122	134	t.	t.	PROPN
ejpam-5423	122	135	prommai	prommai	PROPN
ejpam-5423	122	136	/	/	SYM
ejpam-5423	122	137	eur	eur	PROPN
ejpam-5423	122	138	.	.	PUNCT
ejpam-5423	123	1	j.	j.	PROPN
ejpam-5423	123	2	pure	pure	PROPN
ejpam-5423	123	3	appl	appl	PROPN
ejpam-5423	123	4	.	.	PROPN
ejpam-5423	123	5	math	math	PROPN
ejpam-5423	123	6	,	,	PUNCT
ejpam-5423	123	7	17	17	NUM
ejpam-5423	123	8	(	(	PUNCT
ejpam-5423	123	9	4	4	NUM
ejpam-5423	123	10	)	)	PUNCT
ejpam-5423	123	11	(	(	PUNCT
ejpam-5423	123	12	2024	2024	NUM
ejpam-5423	123	13	)	)	PUNCT
ejpam-5423	123	14	,	,	PUNCT
ejpam-5423	123	15	3223	3223	NUM
ejpam-5423	123	16	-	-	SYM
ejpam-5423	123	17	3241	3241	NUM
ejpam-5423	123	18	3227	3227	NUM
ejpam-5423	123	19	(	(	PUNCT
ejpam-5423	123	20	4	4	NUM
ejpam-5423	123	21	)	)	PUNCT
ejpam-5423	123	22	t	t	NOUN
ejpam-5423	123	23	1⊓t	1⊓t	NUM
ejpam-5423	123	24	2	2	NUM
ejpam-5423	123	25	if	if	SCONJ
ejpam-5423	123	26	and	and	CCONJ
ejpam-5423	123	27	only	only	ADV
ejpam-5423	123	28	if	if	SCONJ
ejpam-5423	123	29	ω∩ϖ	ω∩ϖ	NUM
ejpam-5423	123	30	where	where	SCONJ
ejpam-5423	123	31	(	(	PUNCT
ejpam-5423	123	32	ω	ω	NUM
ejpam-5423	123	33	p∩	p∩	PROPN
ejpam-5423	123	34	ϖ	ϖ	PROPN
ejpam-5423	123	35	p)(e	p)(e	PROPN
ejpam-5423	123	36	)	)	PUNCT
ejpam-5423	124	1	=	=	SYM
ejpam-5423	124	2	ω	ω	NUM
ejpam-5423	124	3	p(e)∧ϖ	p(e)∧ϖ	NOUN
ejpam-5423	124	4	p(e	p(e	NOUN
ejpam-5423	124	5	)	)	PUNCT
ejpam-5423	124	6	and	and	CCONJ
ejpam-5423	124	7	(	(	PUNCT
ejpam-5423	124	8	ω	ω	NUM
ejpam-5423	124	9	n∩ϖ	n∩ϖ	NOUN
ejpam-5423	124	10	n)(e	n)(e	ADV
ejpam-5423	124	11	)	)	PUNCT
ejpam-5423	124	12	=	=	SYM
ejpam-5423	124	13	ω	ω	NUM
ejpam-5423	124	14	n(e	n(e	PROPN
ejpam-5423	124	15	)	)	PUNCT
ejpam-5423	124	16	∨ϖ	∨ϖ	VERB
ejpam-5423	124	17	n(e)for	n(e)for	ADP
ejpam-5423	124	18	all	all	DET
ejpam-5423	124	19	e	e	PROPN
ejpam-5423	124	20	∈	∈	PROPN
ejpam-5423	124	21	g	g	PROPN
ejpam-5423	124	22	,	,	PUNCT
ejpam-5423	124	23	(	(	PUNCT
ejpam-5423	124	24	5	5	X
ejpam-5423	124	25	)	)	PUNCT
ejpam-5423	124	26	t	t	NOUN
ejpam-5423	124	27	1	1	NUM
ejpam-5423	124	28	◦	◦	NOUN
ejpam-5423	124	29	t	t	NOUN
ejpam-5423	124	30	2	2	NUM
ejpam-5423	124	31	if	if	SCONJ
ejpam-5423	124	32	and	and	CCONJ
ejpam-5423	124	33	on	on	ADP
ejpam-5423	124	34	if	if	SCONJ
ejpam-5423	124	35	ω	ω	PROPN
ejpam-5423	124	36	◦	◦	NOUN
ejpam-5423	124	37	ϖ	ϖ	X
ejpam-5423	124	38	where	where	SCONJ
ejpam-5423	124	39	(	(	PUNCT
ejpam-5423	124	40	ω	ω	NOUN
ejpam-5423	124	41	p	p	NOUN
ejpam-5423	124	42	◦	◦	NOUN
ejpam-5423	124	43	ϖ	ϖ	NOUN
ejpam-5423	124	44	p)(e	p)(e	NOUN
ejpam-5423	124	45	)	)	PUNCT
ejpam-5423	124	46	=	=	PUNCT
ejpam-5423	124	47			PUNCT
ejpam-5423	124	48	∨	∨	X
ejpam-5423	124	49	(	(	PUNCT
ejpam-5423	124	50	t	t	PROPN
ejpam-5423	124	51	,	,	PUNCT
ejpam-5423	124	52	h)∈fe	h)∈fe	PROPN
ejpam-5423	124	53	{	{	PUNCT
ejpam-5423	124	54	ω	ω	NUM
ejpam-5423	124	55	p(t	p(t	NOUN
ejpam-5423	124	56	)	)	PUNCT
ejpam-5423	124	57	∧ϖ	∧ϖ	PROPN
ejpam-5423	124	58	p(h	p(h	PROPN
ejpam-5423	124	59	)	)	PUNCT
ejpam-5423	124	60	}	}	PUNCT
ejpam-5423	124	61	if	if	SCONJ
ejpam-5423	124	62	fe	fe	X
ejpam-5423	124	63	̸=	̸=	PROPN
ejpam-5423	124	64	∅	∅	NOUN
ejpam-5423	124	65	,	,	PUNCT
ejpam-5423	124	66	0	0	PUNCT
ejpam-5423	125	1	if	if	SCONJ
ejpam-5423	125	2	fe	fe	X
ejpam-5423	125	3	=	=	NOUN
ejpam-5423	125	4	∅	∅	NOUN
ejpam-5423	125	5	,	,	PUNCT
ejpam-5423	125	6	and	and	CCONJ
ejpam-5423	125	7	(	(	PUNCT
ejpam-5423	125	8	ω	ω	NOUN
ejpam-5423	125	9	n	n	PRON
ejpam-5423	125	10	◦	◦	NOUN
ejpam-5423	125	11	ϖ	ϖ	NOUN
ejpam-5423	125	12	n)(e	n)(e	NOUN
ejpam-5423	125	13	)	)	PUNCT
ejpam-5423	125	14	=	=	PUNCT
ejpam-5423	125	15			PUNCT
ejpam-5423	125	16	∧	∧	PROPN
ejpam-5423	125	17	(	(	PUNCT
ejpam-5423	125	18	t	t	PROPN
ejpam-5423	125	19	,	,	PUNCT
ejpam-5423	125	20	h)∈fe	h)∈fe	PROPN
ejpam-5423	125	21	{	{	PUNCT
ejpam-5423	125	22	ω	ω	NUM
ejpam-5423	125	23	n(t	n(t	PROPN
ejpam-5423	125	24	)	)	PUNCT
ejpam-5423	125	25	∨ϖ	∨ϖ	VERB
ejpam-5423	125	26	n(h	n(h	PROPN
ejpam-5423	125	27	)	)	PUNCT
ejpam-5423	125	28	}	}	PUNCT
ejpam-5423	125	29	if	if	SCONJ
ejpam-5423	125	30	fe	fe	X
ejpam-5423	125	31	̸=	̸=	PROPN
ejpam-5423	125	32	∅	∅	NOUN
ejpam-5423	125	33	,	,	PUNCT
ejpam-5423	125	34	0	0	PUNCT
ejpam-5423	125	35	if	if	SCONJ
ejpam-5423	125	36	fe	fe	X
ejpam-5423	125	37	=	=	NOUN
ejpam-5423	125	38	∅	∅	NOUN
ejpam-5423	125	39	,	,	PUNCT
ejpam-5423	125	40	where	where	SCONJ
ejpam-5423	125	41	fe	fe	X
ejpam-5423	125	42	:	:	PUNCT
ejpam-5423	125	43	=	=	SYM
ejpam-5423	125	44	{	{	PUNCT
ejpam-5423	125	45	(	(	PUNCT
ejpam-5423	125	46	t	t	PROPN
ejpam-5423	125	47	,	,	PUNCT
ejpam-5423	125	48	h	h	NOUN
ejpam-5423	125	49	)	)	PUNCT
ejpam-5423	125	50	∈	∈	PROPN
ejpam-5423	125	51	g×g	g×g	PROPN
ejpam-5423	126	1	|	|	NOUN
ejpam-5423	126	2	e	e	X
ejpam-5423	126	3	≤	≤	X
ejpam-5423	126	4	th	th	NOUN
ejpam-5423	126	5	}	}	PUNCT
ejpam-5423	126	6	for	for	ADP
ejpam-5423	126	7	all	all	DET
ejpam-5423	126	8	e	e	PROPN
ejpam-5423	126	9	∈	∈	PROPN
ejpam-5423	126	10	g.	g.	NOUN
ejpam-5423	126	11	definition	definition	NOUN
ejpam-5423	126	12	6	6	NUM
ejpam-5423	126	13	.	.	PUNCT
ejpam-5423	127	1	[	[	X
ejpam-5423	127	2	7	7	X
ejpam-5423	127	3	]	]	X
ejpam-5423	127	4	let	let	AUX
ejpam-5423	127	5	m	m	PRON
ejpam-5423	127	6	be	be	AUX
ejpam-5423	127	7	a	a	DET
ejpam-5423	127	8	non	non	ADJ
ejpam-5423	127	9	-	-	ADJ
ejpam-5423	127	10	empty	empty	ADJ
ejpam-5423	127	11	set	set	NOUN
ejpam-5423	127	12	of	of	ADP
ejpam-5423	127	13	an	an	DET
ejpam-5423	127	14	ordered	order	VERB
ejpam-5423	127	15	semigroup	semigroup	NOUN
ejpam-5423	127	16	g.	g.	PROPN
ejpam-5423	127	17	an	an	DET
ejpam-5423	127	18	interval	interval	NOUN
ejpam-5423	127	19	valued	value	VERB
ejpam-5423	127	20	bipolar	bipolar	ADJ
ejpam-5423	127	21	characteristic	characteristic	ADJ
ejpam-5423	127	22	function	function	NOUN
ejpam-5423	127	23	are	be	AUX
ejpam-5423	127	24	respectively	respectively	ADV
ejpam-5423	127	25	defined	define	VERB
ejpam-5423	127	26	by	by	ADP
ejpam-5423	127	27	χ	χ	X
ejpam-5423	127	28	p	p	NOUN
ejpam-5423	127	29	m	m	NOUN
ejpam-5423	127	30	:	:	PUNCT
ejpam-5423	127	31	g	g	PROPN
ejpam-5423	127	32	→	→	SYM
ejpam-5423	127	33	ω[0	ω[0	PROPN
ejpam-5423	127	34	,	,	PUNCT
ejpam-5423	127	35	1	1	NUM
ejpam-5423	127	36	]	]	PUNCT
ejpam-5423	127	37	,	,	PUNCT
ejpam-5423	127	38	e	e	PROPN
ejpam-5423	127	39	7→	7→	NUM
ejpam-5423	127	40	χ	χ	PRON
ejpam-5423	127	41	p	p	PROPN
ejpam-5423	127	42	i(e	i(e	NOUN
ejpam-5423	127	43	)	)	PUNCT
ejpam-5423	128	1	:	:	PUNCT
ejpam-5423	128	2	=	=	SYM
ejpam-5423	128	3	{	{	PUNCT
ejpam-5423	128	4	1	1	NUM
ejpam-5423	128	5	e	e	NOUN
ejpam-5423	128	6	∈	∈	PROPN
ejpam-5423	128	7	m	m	NOUN
ejpam-5423	128	8	,	,	PUNCT
ejpam-5423	128	9	0	0	NUM
ejpam-5423	128	10	e	e	X
ejpam-5423	128	11	/∈	/∈	PUNCT
ejpam-5423	129	1	m	m	VERB
ejpam-5423	129	2	,	,	PUNCT
ejpam-5423	129	3	and	and	CCONJ
ejpam-5423	129	4	χ	χ	X
ejpam-5423	129	5	n	n	ADV
ejpam-5423	129	6	m	m	VERB
ejpam-5423	129	7	:	:	PUNCT
ejpam-5423	129	8	g	g	PROPN
ejpam-5423	129	9	→	→	SYM
ejpam-5423	129	10	ω[−1	ω[−1	PROPN
ejpam-5423	129	11	,	,	PUNCT
ejpam-5423	129	12	0	0	NUM
ejpam-5423	129	13	]	]	PUNCT
ejpam-5423	129	14	,	,	PUNCT
ejpam-5423	129	15	e	e	PROPN
ejpam-5423	129	16	7→	7→	NUM
ejpam-5423	129	17	χ	χ	NOUN
ejpam-5423	129	18	n	n	NOUN
ejpam-5423	129	19	i	i	PRON
ejpam-5423	129	20	(	(	PUNCT
ejpam-5423	129	21	e	e	NOUN
ejpam-5423	129	22	)	)	PUNCT
ejpam-5423	129	23	:	:	PUNCT
ejpam-5423	130	1	=	=	PRON
ejpam-5423	130	2	{	{	PUNCT
ejpam-5423	130	3	−1	−1	NOUN
ejpam-5423	130	4	e	e	X
ejpam-5423	130	5	∈	∈	PROPN
ejpam-5423	130	6	m	m	PROPN
ejpam-5423	130	7	,	,	PUNCT
ejpam-5423	130	8	0	0	NUM
ejpam-5423	131	1	e	e	X
ejpam-5423	131	2	/∈	/∈	PUNCT
ejpam-5423	132	1	m	m	VERB
ejpam-5423	132	2	.	.	PUNCT
ejpam-5423	133	1	remark	remark	PROPN
ejpam-5423	133	2	3	3	NUM
ejpam-5423	133	3	.	.	PUNCT
ejpam-5423	134	1	for	for	ADP
ejpam-5423	134	2	the	the	DET
ejpam-5423	134	3	sake	sake	NOUN
ejpam-5423	134	4	of	of	ADP
ejpam-5423	134	5	simplicity	simplicity	NOUN
ejpam-5423	134	6	we	we	PRON
ejpam-5423	134	7	shall	shall	AUX
ejpam-5423	134	8	use	use	VERB
ejpam-5423	134	9	the	the	DET
ejpam-5423	134	10	symbol	symbol	NOUN
ejpam-5423	134	11	χm	χm	NOUN
ejpam-5423	135	1	=	=	PUNCT
ejpam-5423	135	2	(	(	PUNCT
ejpam-5423	135	3	g;χ	g;χ	PROPN
ejpam-5423	135	4	p	p	NOUN
ejpam-5423	135	5	m	m	PROPN
ejpam-5423	135	6	,	,	PUNCT
ejpam-5423	135	7	χ	χ	PRON
ejpam-5423	135	8	n	n	INTJ
ejpam-5423	135	9	m	m	VERB
ejpam-5423	135	10	)	)	PUNCT
ejpam-5423	135	11	for	for	SCONJ
ejpam-5423	135	12	the	the	DET
ejpam-5423	135	13	ivbf	ivbf	NOUN
ejpam-5423	135	14	set	set	VERB
ejpam-5423	135	15	χm	χm	PRON
ejpam-5423	135	16	:	:	PUNCT
ejpam-5423	135	17	=	=	SYM
ejpam-5423	135	18	{	{	PUNCT
ejpam-5423	135	19	(	(	PUNCT
ejpam-5423	135	20	k	k	NOUN
ejpam-5423	135	21	,	,	PUNCT
ejpam-5423	135	22	χ	χ	X
ejpam-5423	135	23	p	p	X
ejpam-5423	135	24	m	m	PROPN
ejpam-5423	135	25	(	(	PUNCT
ejpam-5423	135	26	k	k	NOUN
ejpam-5423	135	27	)	)	PUNCT
ejpam-5423	135	28	,	,	PUNCT
ejpam-5423	135	29	χ	χ	PROPN
ejpam-5423	135	30	n	n	ADV
ejpam-5423	135	31	m	m	PROPN
ejpam-5423	135	32	(	(	PUNCT
ejpam-5423	135	33	k	k	NOUN
ejpam-5423	135	34	)	)	PUNCT
ejpam-5423	135	35	)	)	PUNCT
ejpam-5423	136	1	|	|	ADV
ejpam-5423	136	2	k	k	PROPN
ejpam-5423	136	3	∈	∈	PROPN
ejpam-5423	136	4	m	m	PRON
ejpam-5423	136	5	}	}	PUNCT
ejpam-5423	136	6	.	.	PUNCT
ejpam-5423	137	1	now	now	ADV
ejpam-5423	137	2	,	,	PUNCT
ejpam-5423	137	3	we	we	PRON
ejpam-5423	137	4	let	let	VERB
ejpam-5423	137	5	λ	λ	PROPN
ejpam-5423	137	6	p	p	NOUN
ejpam-5423	137	7	,	,	PUNCT
ejpam-5423	137	8	δ	δ	PROPN
ejpam-5423	137	9	p	p	NOUN
ejpam-5423	137	10	∈	∈	PROPN
ejpam-5423	137	11	ω[0	ω[0	PROPN
ejpam-5423	137	12	,	,	PUNCT
ejpam-5423	137	13	1	1	NUM
ejpam-5423	137	14	]	]	PUNCT
ejpam-5423	137	15	be	be	AUX
ejpam-5423	137	16	such	such	ADJ
ejpam-5423	137	17	that	that	SCONJ
ejpam-5423	137	18	0	0	NUM
ejpam-5423	137	19	≤	≤	NUM
ejpam-5423	137	20	λ	λ	X
ejpam-5423	137	21	p	p	X
ejpam-5423	137	22	<	<	X
ejpam-5423	137	23	δ	δ	X
ejpam-5423	137	24	p	p	NOUN
ejpam-5423	137	25	≤	≤	NUM
ejpam-5423	137	26	1	1	NUM
ejpam-5423	137	27	and	and	CCONJ
ejpam-5423	137	28	λ	λ	NOUN
ejpam-5423	137	29	n	n	CCONJ
ejpam-5423	137	30	,	,	PUNCT
ejpam-5423	137	31	δ	δ	PROPN
ejpam-5423	137	32	n	n	PRON
ejpam-5423	137	33	∈	∈	PROPN
ejpam-5423	137	34	ω[−1	ω[−1	NOUN
ejpam-5423	137	35	,	,	PUNCT
ejpam-5423	137	36	0	0	NUM
ejpam-5423	137	37	]	]	PUNCT
ejpam-5423	137	38	be	be	AUX
ejpam-5423	137	39	such	such	ADJ
ejpam-5423	137	40	that	that	DET
ejpam-5423	137	41	−1	−1	NOUN
ejpam-5423	137	42	≤	≤	NUM
ejpam-5423	137	43	δ	δ	PROPN
ejpam-5423	137	44	n	n	CCONJ
ejpam-5423	137	45	<	<	X
ejpam-5423	137	46	λ	λ	PROPN
ejpam-5423	137	47	n	n	CCONJ
ejpam-5423	137	48	≤	≤	NUM
ejpam-5423	137	49	1	1	NUM
ejpam-5423	137	50	.	.	PUNCT
ejpam-5423	138	1	both	both	DET
ejpam-5423	138	2	λ	λ	PROPN
ejpam-5423	138	3	,	,	PUNCT
ejpam-5423	138	4	δ	δ	PROPN
ejpam-5423	138	5	are	be	AUX
ejpam-5423	138	6	arbitrary	arbitrary	ADJ
ejpam-5423	138	7	but	but	CCONJ
ejpam-5423	138	8	fixed	fix	VERB
ejpam-5423	138	9	.	.	PUNCT
ejpam-5423	139	1	definition	definition	NOUN
ejpam-5423	139	2	7	7	NUM
ejpam-5423	139	3	.	.	PUNCT
ejpam-5423	140	1	[	[	X
ejpam-5423	140	2	7	7	X
ejpam-5423	140	3	]	]	PUNCT
ejpam-5423	140	4	let	let	VERB
ejpam-5423	140	5	g	g	PRON
ejpam-5423	140	6	be	be	AUX
ejpam-5423	140	7	an	an	DET
ejpam-5423	140	8	ordered	order	VERB
ejpam-5423	140	9	semigroup	semigroup	NOUN
ejpam-5423	140	10	and	and	CCONJ
ejpam-5423	140	11	t	t	NOUN
ejpam-5423	140	12	=	=	SYM
ejpam-5423	140	13	(	(	PUNCT
ejpam-5423	140	14	ω	ω	PROPN
ejpam-5423	140	15	p	p	PROPN
ejpam-5423	140	16	,	,	PUNCT
ejpam-5423	140	17	ω	ω	PROPN
ejpam-5423	140	18	n	n	CCONJ
ejpam-5423	140	19	)	)	PUNCT
ejpam-5423	140	20	be	be	AUX
ejpam-5423	140	21	an	an	DET
ejpam-5423	140	22	ivbf	ivbf	NOUN
ejpam-5423	140	23	set	set	NOUN
ejpam-5423	140	24	of	of	ADP
ejpam-5423	140	25	g	g	PROPN
ejpam-5423	140	26	is	be	AUX
ejpam-5423	140	27	called	call	VERB
ejpam-5423	140	28	an	an	DET
ejpam-5423	140	29	(	(	PUNCT
ejpam-5423	140	30	λ	λ	NOUN
ejpam-5423	140	31	,	,	PUNCT
ejpam-5423	140	32	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	140	33	subsemigroup	subsemigroup	NOUN
ejpam-5423	140	34	of	of	ADP
ejpam-5423	140	35	g	g	PROPN
ejpam-5423	141	1	if	if	SCONJ
ejpam-5423	141	2	(	(	PUNCT
ejpam-5423	141	3	1	1	X
ejpam-5423	141	4	)	)	PUNCT
ejpam-5423	141	5	ω	ω	NUM
ejpam-5423	141	6	p(e1e2	p(e1e2	NOUN
ejpam-5423	141	7	)	)	PUNCT
ejpam-5423	141	8	∨	∨	NUM
ejpam-5423	141	9	λ	λ	PROPN
ejpam-5423	141	10	p	p	X
ejpam-5423	141	11	≥	≥	PROPN
ejpam-5423	141	12	ω	ω	NUM
ejpam-5423	141	13	p(e1	p(e1	NOUN
ejpam-5423	141	14	)	)	PUNCT
ejpam-5423	141	15	∧	∧	PROPN
ejpam-5423	141	16	ω	ω	NUM
ejpam-5423	141	17	p(e2	p(e2	NOUN
ejpam-5423	141	18	)	)	PUNCT
ejpam-5423	141	19	∧	∧	PROPN
ejpam-5423	141	20	δ	δ	PROPN
ejpam-5423	141	21	p.	p.	NOUN
ejpam-5423	141	22	(	(	PUNCT
ejpam-5423	141	23	2	2	X
ejpam-5423	141	24	)	)	PUNCT
ejpam-5423	141	25	ω	ω	NUM
ejpam-5423	141	26	n(e1e2	n(e1e2	NOUN
ejpam-5423	141	27	)	)	PUNCT
ejpam-5423	141	28	∧	∧	PROPN
ejpam-5423	141	29	λ	λ	PROPN
ejpam-5423	141	30	n	n	CCONJ
ejpam-5423	141	31	≤	≤	PROPN
ejpam-5423	141	32	ω	ω	NUM
ejpam-5423	141	33	n(e1	n(e1	NOUN
ejpam-5423	141	34	)	)	PUNCT
ejpam-5423	141	35	∨	∨	NUM
ejpam-5423	141	36	ω	ω	PROPN
ejpam-5423	141	37	n(e2)⋏	n(e2)⋏	PROPN
ejpam-5423	141	38	δ	δ	PROPN
ejpam-5423	141	39	n.	n.	NOUN
ejpam-5423	141	40	for	for	ADP
ejpam-5423	141	41	all	all	DET
ejpam-5423	141	42	e1	e1	NOUN
ejpam-5423	141	43	,	,	PUNCT
ejpam-5423	141	44	e2	e2	PROPN
ejpam-5423	141	45	∈	∈	PROPN
ejpam-5423	141	46	g.	g.	NOUN
ejpam-5423	141	47	definition	definition	NOUN
ejpam-5423	141	48	8	8	NUM
ejpam-5423	141	49	.	.	PUNCT
ejpam-5423	142	1	[	[	X
ejpam-5423	142	2	7	7	X
ejpam-5423	142	3	]	]	PUNCT
ejpam-5423	142	4	let	let	VERB
ejpam-5423	142	5	g	g	PRON
ejpam-5423	142	6	be	be	AUX
ejpam-5423	142	7	an	an	DET
ejpam-5423	142	8	ordered	order	VERB
ejpam-5423	142	9	semigroup	semigroup	NOUN
ejpam-5423	142	10	and	and	CCONJ
ejpam-5423	142	11	t	t	NOUN
ejpam-5423	142	12	=	=	SYM
ejpam-5423	142	13	(	(	PUNCT
ejpam-5423	142	14	ω	ω	PROPN
ejpam-5423	142	15	p	p	PROPN
ejpam-5423	142	16	,	,	PUNCT
ejpam-5423	142	17	ω	ω	PROPN
ejpam-5423	142	18	n	n	CCONJ
ejpam-5423	142	19	)	)	PUNCT
ejpam-5423	142	20	be	be	AUX
ejpam-5423	142	21	an	an	DET
ejpam-5423	142	22	ivbf	ivbf	NOUN
ejpam-5423	142	23	set	set	NOUN
ejpam-5423	142	24	of	of	ADP
ejpam-5423	142	25	g	g	PROPN
ejpam-5423	142	26	is	be	AUX
ejpam-5423	142	27	called	call	VERB
ejpam-5423	142	28	an	an	DET
ejpam-5423	142	29	(	(	PUNCT
ejpam-5423	142	30	λ	λ	NOUN
ejpam-5423	142	31	,	,	PUNCT
ejpam-5423	142	32	δ)-ivbf	δ)-ivbf	NOUN
ejpam-5423	142	33	left	leave	VERB
ejpam-5423	142	34	ideal	ideal	NOUN
ejpam-5423	142	35	of	of	ADP
ejpam-5423	142	36	g	g	PROPN
ejpam-5423	143	1	if	if	SCONJ
ejpam-5423	143	2	(	(	PUNCT
ejpam-5423	143	3	1	1	X
ejpam-5423	143	4	)	)	PUNCT
ejpam-5423	143	5	ω	ω	NUM
ejpam-5423	143	6	p(e1e2	p(e1e2	NOUN
ejpam-5423	143	7	)	)	PUNCT
ejpam-5423	143	8	∨	∨	NUM
ejpam-5423	143	9	λ	λ	PROPN
ejpam-5423	143	10	p	p	X
ejpam-5423	143	11	≥	≥	PROPN
ejpam-5423	143	12	ω	ω	PROPN
ejpam-5423	143	13	p(e2)⋏	p(e2)⋏	PROPN
ejpam-5423	143	14	δ	δ	PROPN
ejpam-5423	143	15	p.	p.	NOUN
ejpam-5423	143	16	(	(	PUNCT
ejpam-5423	143	17	2	2	X
ejpam-5423	143	18	)	)	PUNCT
ejpam-5423	143	19	ω	ω	NUM
ejpam-5423	143	20	n(e1e2	n(e1e2	NOUN
ejpam-5423	143	21	)	)	PUNCT
ejpam-5423	143	22	∧	∧	PROPN
ejpam-5423	143	23	λ	λ	PROPN
ejpam-5423	143	24	n	n	CCONJ
ejpam-5423	143	25	≤	≤	PROPN
ejpam-5423	143	26	ω	ω	NUM
ejpam-5423	143	27	n(e2	n(e2	PROPN
ejpam-5423	143	28	)	)	PUNCT
ejpam-5423	143	29	∨	∨	NUM
ejpam-5423	143	30	δ	δ	PROPN
ejpam-5423	143	31	n.	n.	NOUN
ejpam-5423	143	32	(	(	PUNCT
ejpam-5423	143	33	3	3	NUM
ejpam-5423	143	34	)	)	PUNCT
ejpam-5423	143	35	if	if	SCONJ
ejpam-5423	143	36	e1	e1	NOUN
ejpam-5423	143	37	≤	≤	PROPN
ejpam-5423	143	38	e2	e2	PROPN
ejpam-5423	143	39	,	,	PUNCT
ejpam-5423	143	40	then	then	ADV
ejpam-5423	143	41	ω	ω	NUM
ejpam-5423	143	42	p(e1	p(e1	NOUN
ejpam-5423	143	43	)	)	PUNCT
ejpam-5423	143	44	∨	∨	PROPN
ejpam-5423	143	45	λ	λ	PROPN
ejpam-5423	143	46	p	p	X
ejpam-5423	143	47	≥	≥	PROPN
ejpam-5423	143	48	ω	ω	NUM
ejpam-5423	143	49	p(e2	p(e2	NOUN
ejpam-5423	143	50	)	)	PUNCT
ejpam-5423	143	51	∧	∧	PROPN
ejpam-5423	143	52	δ	δ	PROPN
ejpam-5423	143	53	p	p	NOUN
ejpam-5423	143	54	and	and	CCONJ
ejpam-5423	143	55	ω	ω	NUM
ejpam-5423	143	56	n(e1	n(e1	NOUN
ejpam-5423	143	57	)	)	PUNCT
ejpam-5423	143	58	∧	∧	PROPN
ejpam-5423	143	59	λ	λ	PROPN
ejpam-5423	143	60	n	n	CCONJ
ejpam-5423	143	61	≤	≤	PROPN
ejpam-5423	143	62	ω	ω	NUM
ejpam-5423	143	63	n(e2	n(e2	PROPN
ejpam-5423	143	64	)	)	PUNCT
ejpam-5423	143	65	∨	∨	NUM
ejpam-5423	143	66	δ	δ	PROPN
ejpam-5423	143	67	n.	n.	PROPN
ejpam-5423	143	68	t.	t.	PROPN
ejpam-5423	143	69	gaketem	gaketem	PROPN
ejpam-5423	143	70	,	,	PUNCT
ejpam-5423	143	71	t.	t.	PROPN
ejpam-5423	143	72	prommai	prommai	PROPN
ejpam-5423	143	73	/	/	SYM
ejpam-5423	143	74	eur	eur	PROPN
ejpam-5423	143	75	.	.	PUNCT
ejpam-5423	144	1	j.	j.	PROPN
ejpam-5423	144	2	pure	pure	PROPN
ejpam-5423	144	3	appl	appl	PROPN
ejpam-5423	144	4	.	.	PROPN
ejpam-5423	144	5	math	math	PROPN
ejpam-5423	144	6	,	,	PUNCT
ejpam-5423	144	7	17	17	NUM
ejpam-5423	144	8	(	(	PUNCT
ejpam-5423	144	9	4	4	NUM
ejpam-5423	144	10	)	)	PUNCT
ejpam-5423	144	11	(	(	PUNCT
ejpam-5423	144	12	2024	2024	NUM
ejpam-5423	144	13	)	)	PUNCT
ejpam-5423	144	14	,	,	PUNCT
ejpam-5423	144	15	3223	3223	NUM
ejpam-5423	144	16	-	-	SYM
ejpam-5423	144	17	3241	3241	NUM
ejpam-5423	144	18	3228	3228	NUM
ejpam-5423	144	19	for	for	ADP
ejpam-5423	144	20	all	all	DET
ejpam-5423	144	21	e1	e1	NOUN
ejpam-5423	144	22	,	,	PUNCT
ejpam-5423	144	23	e2	e2	PROPN
ejpam-5423	144	24	∈	∈	PROPN
ejpam-5423	144	25	g.	g.	NOUN
ejpam-5423	144	26	definition	definition	NOUN
ejpam-5423	144	27	9	9	NUM
ejpam-5423	144	28	.	.	PUNCT
ejpam-5423	145	1	[	[	X
ejpam-5423	145	2	7	7	X
ejpam-5423	145	3	]	]	PUNCT
ejpam-5423	145	4	let	let	VERB
ejpam-5423	145	5	g	g	PRON
ejpam-5423	145	6	be	be	AUX
ejpam-5423	145	7	an	an	DET
ejpam-5423	145	8	ordered	order	VERB
ejpam-5423	145	9	semigroup	semigroup	NOUN
ejpam-5423	145	10	and	and	CCONJ
ejpam-5423	145	11	t	t	NOUN
ejpam-5423	145	12	=	=	SYM
ejpam-5423	145	13	(	(	PUNCT
ejpam-5423	145	14	ω	ω	PROPN
ejpam-5423	145	15	p	p	PROPN
ejpam-5423	145	16	,	,	PUNCT
ejpam-5423	145	17	ω	ω	PROPN
ejpam-5423	145	18	n	n	CCONJ
ejpam-5423	145	19	)	)	PUNCT
ejpam-5423	145	20	be	be	AUX
ejpam-5423	145	21	an	an	DET
ejpam-5423	145	22	ivbf	ivbf	NOUN
ejpam-5423	145	23	set	set	NOUN
ejpam-5423	145	24	of	of	ADP
ejpam-5423	145	25	g	g	PROPN
ejpam-5423	145	26	is	be	AUX
ejpam-5423	145	27	called	call	VERB
ejpam-5423	145	28	an	an	DET
ejpam-5423	145	29	(	(	PUNCT
ejpam-5423	145	30	λ	λ	NOUN
ejpam-5423	145	31	,	,	PUNCT
ejpam-5423	145	32	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	145	33	right	right	ADJ
ejpam-5423	145	34	ideal	ideal	NOUN
ejpam-5423	145	35	of	of	ADP
ejpam-5423	145	36	g	g	PROPN
ejpam-5423	146	1	if	if	SCONJ
ejpam-5423	146	2	(	(	PUNCT
ejpam-5423	146	3	1	1	X
ejpam-5423	146	4	)	)	PUNCT
ejpam-5423	146	5	ω	ω	NUM
ejpam-5423	146	6	p(e1e2	p(e1e2	NOUN
ejpam-5423	146	7	)	)	PUNCT
ejpam-5423	146	8	∨	∨	NUM
ejpam-5423	146	9	λ	λ	PROPN
ejpam-5423	146	10	p	p	X
ejpam-5423	146	11	≥	≥	PROPN
ejpam-5423	146	12	ω	ω	NUM
ejpam-5423	146	13	p(e1	p(e1	NOUN
ejpam-5423	146	14	)	)	PUNCT
ejpam-5423	146	15	∧	∧	PROPN
ejpam-5423	146	16	δ	δ	PROPN
ejpam-5423	146	17	p	p	NOUN
ejpam-5423	146	18	,	,	PUNCT
ejpam-5423	146	19	(	(	PUNCT
ejpam-5423	146	20	2	2	X
ejpam-5423	146	21	)	)	PUNCT
ejpam-5423	146	22	ω	ω	NUM
ejpam-5423	146	23	n(e1e2	n(e1e2	NOUN
ejpam-5423	146	24	)	)	PUNCT
ejpam-5423	146	25	∧	∧	PROPN
ejpam-5423	146	26	λ	λ	PROPN
ejpam-5423	146	27	n	n	CCONJ
ejpam-5423	146	28	≥	≥	PROPN
ejpam-5423	146	29	ω	ω	NUM
ejpam-5423	146	30	n(e1	n(e1	NOUN
ejpam-5423	146	31	)	)	PUNCT
ejpam-5423	146	32	∨	∨	NUM
ejpam-5423	146	33	δ	δ	PROPN
ejpam-5423	146	34	n.	n.	PROPN
ejpam-5423	146	35	(	(	PUNCT
ejpam-5423	146	36	3	3	NUM
ejpam-5423	146	37	)	)	PUNCT
ejpam-5423	146	38	if	if	SCONJ
ejpam-5423	146	39	e1	e1	NOUN
ejpam-5423	146	40	≤	≤	PROPN
ejpam-5423	146	41	e2	e2	PROPN
ejpam-5423	146	42	,	,	PUNCT
ejpam-5423	146	43	then	then	ADV
ejpam-5423	146	44	ω	ω	NUM
ejpam-5423	146	45	p(e1	p(e1	NOUN
ejpam-5423	146	46	)	)	PUNCT
ejpam-5423	146	47	∨	∨	PROPN
ejpam-5423	146	48	λ	λ	PROPN
ejpam-5423	146	49	p	p	X
ejpam-5423	146	50	≥	≥	PROPN
ejpam-5423	146	51	ω	ω	NUM
ejpam-5423	146	52	p(e2	p(e2	NOUN
ejpam-5423	146	53	)	)	PUNCT
ejpam-5423	146	54	∧	∧	PROPN
ejpam-5423	146	55	δ	δ	PROPN
ejpam-5423	146	56	p	p	NOUN
ejpam-5423	146	57	and	and	CCONJ
ejpam-5423	146	58	ω	ω	NUM
ejpam-5423	146	59	n(e1	n(e1	NOUN
ejpam-5423	146	60	)	)	PUNCT
ejpam-5423	146	61	∧	∧	PROPN
ejpam-5423	146	62	λ	λ	PROPN
ejpam-5423	146	63	n	n	CCONJ
ejpam-5423	146	64	≤	≤	PROPN
ejpam-5423	146	65	ω	ω	NUM
ejpam-5423	146	66	n(e2	n(e2	PROPN
ejpam-5423	146	67	)	)	PUNCT
ejpam-5423	146	68	∨	∨	NUM
ejpam-5423	146	69	δ	δ	PROPN
ejpam-5423	146	70	n	n	CCONJ
ejpam-5423	146	71	,	,	PUNCT
ejpam-5423	146	72	for	for	ADP
ejpam-5423	146	73	all	all	DET
ejpam-5423	146	74	e1	e1	NOUN
ejpam-5423	146	75	,	,	PUNCT
ejpam-5423	146	76	e2	e2	PROPN
ejpam-5423	146	77	∈	∈	PROPN
ejpam-5423	146	78	g.	g.	NOUN
ejpam-5423	146	79	an	an	DET
ejpam-5423	146	80	ivbf	ivbf	NOUN
ejpam-5423	146	81	set	set	VERB
ejpam-5423	146	82	t	t	PROPN
ejpam-5423	146	83	=	=	SYM
ejpam-5423	146	84	(	(	PUNCT
ejpam-5423	146	85	ω	ω	PROPN
ejpam-5423	146	86	p	p	PROPN
ejpam-5423	146	87	,	,	PUNCT
ejpam-5423	146	88	ω	ω	PROPN
ejpam-5423	146	89	n	n	CCONJ
ejpam-5423	146	90	)	)	PUNCT
ejpam-5423	146	91	of	of	ADP
ejpam-5423	146	92	an	an	DET
ejpam-5423	146	93	ordered	order	VERB
ejpam-5423	146	94	semigroup	semigroup	NOUN
ejpam-5423	146	95	e	e	NOUN
ejpam-5423	146	96	is	be	AUX
ejpam-5423	146	97	called	call	VERB
ejpam-5423	146	98	(	(	PUNCT
ejpam-5423	146	99	λ	λ	PROPN
ejpam-5423	146	100	,	,	PUNCT
ejpam-5423	146	101	δ)-ivbf	δ)-ivbf	NOUN
ejpam-5423	146	102	ideal	ideal	NOUN
ejpam-5423	146	103	of	of	ADP
ejpam-5423	146	104	g	g	PROPN
ejpam-5423	146	105	if	if	SCONJ
ejpam-5423	146	106	it	it	PRON
ejpam-5423	146	107	is	be	AUX
ejpam-5423	146	108	both	both	DET
ejpam-5423	146	109	(	(	PUNCT
ejpam-5423	146	110	λ	λ	NOUN
ejpam-5423	146	111	,	,	PUNCT
ejpam-5423	146	112	δ)-ivbf	δ)-ivbf	NOUN
ejpam-5423	146	113	left	leave	VERB
ejpam-5423	146	114	ideal	ideal	ADJ
ejpam-5423	146	115	and	and	CCONJ
ejpam-5423	146	116	(	(	PUNCT
ejpam-5423	146	117	λ	λ	NOUN
ejpam-5423	146	118	,	,	PUNCT
ejpam-5423	146	119	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	146	120	right	right	ADJ
ejpam-5423	146	121	ideal	ideal	NOUN
ejpam-5423	146	122	of	of	ADP
ejpam-5423	146	123	g.	g.	PROPN
ejpam-5423	146	124	definition	definition	NOUN
ejpam-5423	146	125	10	10	NUM
ejpam-5423	146	126	.	.	PUNCT
ejpam-5423	147	1	[	[	X
ejpam-5423	147	2	7	7	X
ejpam-5423	147	3	]	]	PUNCT
ejpam-5423	147	4	let	let	VERB
ejpam-5423	147	5	g	g	PRON
ejpam-5423	147	6	be	be	AUX
ejpam-5423	147	7	an	an	DET
ejpam-5423	147	8	ordered	order	VERB
ejpam-5423	147	9	semigroup	semigroup	NOUN
ejpam-5423	147	10	and	and	CCONJ
ejpam-5423	147	11	t	t	NOUN
ejpam-5423	147	12	=	=	SYM
ejpam-5423	147	13	(	(	PUNCT
ejpam-5423	147	14	ω	ω	PROPN
ejpam-5423	147	15	p	p	PROPN
ejpam-5423	147	16	,	,	PUNCT
ejpam-5423	147	17	ω	ω	PROPN
ejpam-5423	147	18	n	n	CCONJ
ejpam-5423	147	19	)	)	PUNCT
ejpam-5423	147	20	be	be	AUX
ejpam-5423	147	21	an	an	DET
ejpam-5423	147	22	ivbf	ivbf	NOUN
ejpam-5423	147	23	set	set	NOUN
ejpam-5423	147	24	of	of	ADP
ejpam-5423	147	25	g	g	PROPN
ejpam-5423	147	26	is	be	AUX
ejpam-5423	147	27	called	call	VERB
ejpam-5423	147	28	an	an	DET
ejpam-5423	147	29	(	(	PUNCT
ejpam-5423	147	30	λ	λ	PROPN
ejpam-5423	147	31	,	,	PUNCT
ejpam-5423	147	32	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	147	33	bi	bi	NOUN
ejpam-5423	147	34	-	-	NOUN
ejpam-5423	147	35	ideal	ideal	NOUN
ejpam-5423	147	36	of	of	ADP
ejpam-5423	147	37	g	g	PROPN
ejpam-5423	147	38	if	if	SCONJ
ejpam-5423	147	39	(	(	PUNCT
ejpam-5423	147	40	1	1	X
ejpam-5423	147	41	)	)	PUNCT
ejpam-5423	147	42	t	t	NOUN
ejpam-5423	147	43	=	=	SYM
ejpam-5423	147	44	(	(	PUNCT
ejpam-5423	147	45	ω	ω	PROPN
ejpam-5423	147	46	p	p	PROPN
ejpam-5423	147	47	,	,	PUNCT
ejpam-5423	147	48	ω	ω	PROPN
ejpam-5423	147	49	n	n	CCONJ
ejpam-5423	147	50	)	)	PUNCT
ejpam-5423	147	51	is	be	AUX
ejpam-5423	147	52	an	an	DET
ejpam-5423	147	53	(	(	PUNCT
ejpam-5423	147	54	λ	λ	NOUN
ejpam-5423	147	55	,	,	PUNCT
ejpam-5423	147	56	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	147	57	subsemigroup	subsemigroup	NOUN
ejpam-5423	147	58	of	of	ADP
ejpam-5423	147	59	g	g	PROPN
ejpam-5423	147	60	(	(	PUNCT
ejpam-5423	147	61	2	2	NUM
ejpam-5423	147	62	)	)	PUNCT
ejpam-5423	147	63	ω	ω	NUM
ejpam-5423	147	64	p(e1e2e3	p(e1e2e3	PROPN
ejpam-5423	147	65	)	)	PUNCT
ejpam-5423	148	1	∨	∨	NUM
ejpam-5423	148	2	λ	λ	PROPN
ejpam-5423	148	3	p	p	X
ejpam-5423	148	4	≥	≥	PROPN
ejpam-5423	148	5	ω	ω	NUM
ejpam-5423	148	6	p(e1	p(e1	NOUN
ejpam-5423	148	7	)	)	PUNCT
ejpam-5423	148	8	∧	∧	PROPN
ejpam-5423	148	9	ω	ω	NUM
ejpam-5423	148	10	p(e3	p(e3	NOUN
ejpam-5423	148	11	)	)	PUNCT
ejpam-5423	148	12	∧	∧	PROPN
ejpam-5423	148	13	δ	δ	PROPN
ejpam-5423	148	14	p	p	NOUN
ejpam-5423	148	15	(	(	PUNCT
ejpam-5423	148	16	3	3	NUM
ejpam-5423	148	17	)	)	PUNCT
ejpam-5423	148	18	ω	ω	NUM
ejpam-5423	148	19	n(e1e2e3	n(e1e2e3	PROPN
ejpam-5423	148	20	)	)	PUNCT
ejpam-5423	148	21	∧	∧	PROPN
ejpam-5423	148	22	λ	λ	PROPN
ejpam-5423	148	23	n	n	CCONJ
ejpam-5423	148	24	≤	≤	PROPN
ejpam-5423	148	25	ω	ω	NUM
ejpam-5423	148	26	n(e1	n(e1	NOUN
ejpam-5423	148	27	)	)	PUNCT
ejpam-5423	148	28	∨	∨	PROPN
ejpam-5423	148	29	ω	ω	NUM
ejpam-5423	148	30	n(e3	n(e3	PROPN
ejpam-5423	148	31	)	)	PUNCT
ejpam-5423	148	32	∨	∨	PROPN
ejpam-5423	148	33	δ	δ	PROPN
ejpam-5423	148	34	n	n	CCONJ
ejpam-5423	148	35	,	,	PUNCT
ejpam-5423	148	36	for	for	ADP
ejpam-5423	148	37	all	all	DET
ejpam-5423	148	38	e1	e1	NOUN
ejpam-5423	148	39	,	,	PUNCT
ejpam-5423	148	40	e2	e2	PROPN
ejpam-5423	148	41	,	,	PUNCT
ejpam-5423	148	42	e3	e3	NOUN
ejpam-5423	148	43	∈	∈	PROPN
ejpam-5423	148	44	g.	g.	NOUN
ejpam-5423	148	45	for	for	ADP
ejpam-5423	148	46	two	two	NUM
ejpam-5423	148	47	ivbf	ivbf	NOUN
ejpam-5423	148	48	sets	set	NOUN
ejpam-5423	148	49	t	t	PROPN
ejpam-5423	148	50	1	1	NUM
ejpam-5423	148	51	=	=	SYM
ejpam-5423	148	52	(	(	PUNCT
ejpam-5423	148	53	ω	ω	PROPN
ejpam-5423	148	54	p	p	PROPN
ejpam-5423	148	55	,	,	PUNCT
ejpam-5423	148	56	ω	ω	PROPN
ejpam-5423	148	57	n	n	CCONJ
ejpam-5423	148	58	)	)	PUNCT
ejpam-5423	148	59	and	and	CCONJ
ejpam-5423	148	60	t	t	X
ejpam-5423	148	61	2	2	NUM
ejpam-5423	148	62	=	=	SYM
ejpam-5423	148	63	(	(	PUNCT
ejpam-5423	148	64	ϖ	ϖ	X
ejpam-5423	148	65	p	p	X
ejpam-5423	148	66	,	,	PUNCT
ejpam-5423	148	67	ϖ	ϖ	NOUN
ejpam-5423	148	68	n	n	CCONJ
ejpam-5423	148	69	)	)	PUNCT
ejpam-5423	148	70	of	of	ADP
ejpam-5423	148	71	an	an	DET
ejpam-5423	148	72	ordered	order	VERB
ejpam-5423	148	73	semigroup	semigroup	NOUN
ejpam-5423	148	74	g	g	NOUN
ejpam-5423	148	75	,	,	PUNCT
ejpam-5423	148	76	define	define	VERB
ejpam-5423	148	77	(	(	PUNCT
ejpam-5423	148	78	1	1	NUM
ejpam-5423	148	79	)	)	PUNCT
ejpam-5423	148	80	t	t	NOUN
ejpam-5423	148	81	λ	λ	PROPN
ejpam-5423	148	82	δ	δ	PROPN
ejpam-5423	148	83	(	(	PUNCT
ejpam-5423	148	84	x	x	NOUN
ejpam-5423	148	85	)	)	PUNCT
ejpam-5423	148	86	:	:	PUNCT
ejpam-5423	148	87	=	=	SYM
ejpam-5423	148	88	(	(	PUNCT
ejpam-5423	148	89	(	(	PUNCT
ejpam-5423	148	90	ω	ω	X
ejpam-5423	148	91	p)λ	p)λ	X
ejpam-5423	148	92	δ	δ	PROPN
ejpam-5423	148	93	(	(	PUNCT
ejpam-5423	148	94	x	x	NOUN
ejpam-5423	148	95	)	)	PUNCT
ejpam-5423	148	96	,	,	PUNCT
ejpam-5423	148	97	(	(	PUNCT
ejpam-5423	148	98	ω	ω	X
ejpam-5423	148	99	n)λ	n)λ	X
ejpam-5423	148	100	δ	δ	PROPN
ejpam-5423	148	101	(	(	PUNCT
ejpam-5423	148	102	x	x	NOUN
ejpam-5423	148	103	)	)	PUNCT
ejpam-5423	148	104	)	)	PUNCT
ejpam-5423	149	1	=	=	PUNCT
ejpam-5423	149	2	(	(	PUNCT
ejpam-5423	149	3	(	(	PUNCT
ejpam-5423	149	4	(	(	PUNCT
ejpam-5423	149	5	ω	ω	NUM
ejpam-5423	149	6	p)(x	p)(x	NOUN
ejpam-5423	149	7	)	)	PUNCT
ejpam-5423	149	8	∧	∧	PROPN
ejpam-5423	149	9	λ	λ	PROPN
ejpam-5423	149	10	p	p	NOUN
ejpam-5423	149	11	)	)	PUNCT
ejpam-5423	149	12	∨	∨	NUM
ejpam-5423	149	13	δ	δ	PROPN
ejpam-5423	149	14	p	p	X
ejpam-5423	149	15	,	,	PUNCT
ejpam-5423	149	16	(	(	PUNCT
ejpam-5423	149	17	(	(	PUNCT
ejpam-5423	149	18	ω	ω	X
ejpam-5423	149	19	n)(x	n)(x	PROPN
ejpam-5423	149	20	)	)	PUNCT
ejpam-5423	149	21	∨	∨	NUM
ejpam-5423	149	22	λ	λ	PROPN
ejpam-5423	149	23	n	n	CCONJ
ejpam-5423	149	24	)	)	PUNCT
ejpam-5423	149	25	∧	∧	PROPN
ejpam-5423	149	26	δ	δ	PROPN
ejpam-5423	149	27	p	p	NOUN
ejpam-5423	149	28	)	)	PUNCT
ejpam-5423	149	29	,	,	PUNCT
ejpam-5423	149	30	(	(	PUNCT
ejpam-5423	149	31	2	2	X
ejpam-5423	149	32	)	)	PUNCT
ejpam-5423	149	33	(	(	PUNCT
ejpam-5423	149	34	t	t	NOUN
ejpam-5423	149	35	1	1	NUM
ejpam-5423	149	36	⊓	⊓	PROPN
ejpam-5423	149	37	t	t	NOUN
ejpam-5423	149	38	2	2	NUM
ejpam-5423	149	39	)	)	PUNCT
ejpam-5423	149	40	λ	λ	PROPN
ejpam-5423	149	41	δ	δ	PROPN
ejpam-5423	149	42	(	(	PUNCT
ejpam-5423	149	43	x	x	NOUN
ejpam-5423	149	44	)	)	PUNCT
ejpam-5423	149	45	:	:	PUNCT
ejpam-5423	149	46	=	=	SYM
ejpam-5423	149	47	(	(	PUNCT
ejpam-5423	149	48	(	(	PUNCT
ejpam-5423	149	49	ω	ω	NOUN
ejpam-5423	149	50	p	p	X
ejpam-5423	149	51	∩ϖ	∩ϖ	PROPN
ejpam-5423	149	52	p)λ	p)λ	NOUN
ejpam-5423	149	53	δ	δ	NOUN
ejpam-5423	149	54	(	(	PUNCT
ejpam-5423	149	55	x	x	NOUN
ejpam-5423	149	56	)	)	PUNCT
ejpam-5423	149	57	,	,	PUNCT
ejpam-5423	149	58	(	(	PUNCT
ejpam-5423	149	59	ω	ω	NOUN
ejpam-5423	149	60	n	n	CCONJ
ejpam-5423	149	61	∩ϖ	∩ϖ	PROPN
ejpam-5423	149	62	n)λ	n)λ	X
ejpam-5423	149	63	δ	δ	PROPN
ejpam-5423	149	64	(	(	PUNCT
ejpam-5423	149	65	x	x	NOUN
ejpam-5423	149	66	)	)	PUNCT
ejpam-5423	149	67	)	)	PUNCT
ejpam-5423	150	1	=	=	PUNCT
ejpam-5423	150	2	(	(	PUNCT
ejpam-5423	150	3	(	(	PUNCT
ejpam-5423	150	4	(	(	PUNCT
ejpam-5423	150	5	ω	ω	X
ejpam-5423	150	6	p(x	p(x	PROPN
ejpam-5423	150	7	)	)	PUNCT
ejpam-5423	150	8	∧ϖ	∧ϖ	PROPN
ejpam-5423	150	9	p(x	p(x	PROPN
ejpam-5423	150	10	)	)	PUNCT
ejpam-5423	150	11	)	)	PUNCT
ejpam-5423	151	1	∧	∧	PROPN
ejpam-5423	151	2	λ	λ	PROPN
ejpam-5423	151	3	p	p	NOUN
ejpam-5423	151	4	)	)	PUNCT
ejpam-5423	151	5	∨	∨	NUM
ejpam-5423	151	6	δ	δ	PROPN
ejpam-5423	151	7	p	p	X
ejpam-5423	151	8	,	,	PUNCT
ejpam-5423	151	9	(	(	PUNCT
ejpam-5423	151	10	(	(	PUNCT
ejpam-5423	151	11	ω	ω	X
ejpam-5423	151	12	n(x	n(x	PROPN
ejpam-5423	151	13	)	)	PUNCT
ejpam-5423	151	14	∨ϖ	∨ϖ	ADJ
ejpam-5423	151	15	n(x	n(x	PROPN
ejpam-5423	151	16	)	)	PUNCT
ejpam-5423	151	17	)	)	PUNCT
ejpam-5423	151	18	∨	∨	NUM
ejpam-5423	151	19	λ	λ	PROPN
ejpam-5423	151	20	n	n	CCONJ
ejpam-5423	151	21	)	)	PUNCT
ejpam-5423	151	22	∧	∧	PROPN
ejpam-5423	151	23	δ	δ	PROPN
ejpam-5423	151	24	n	n	PROPN
ejpam-5423	151	25	)	)	PUNCT
ejpam-5423	151	26	,	,	PUNCT
ejpam-5423	151	27	(	(	PUNCT
ejpam-5423	151	28	3	3	X
ejpam-5423	151	29	)	)	PUNCT
ejpam-5423	151	30	(	(	PUNCT
ejpam-5423	151	31	t	t	PROPN
ejpam-5423	151	32	1	1	NUM
ejpam-5423	151	33	◦	◦	NOUN
ejpam-5423	151	34	t	t	NOUN
ejpam-5423	151	35	2	2	NUM
ejpam-5423	151	36	)	)	PUNCT
ejpam-5423	151	37	λ	λ	PROPN
ejpam-5423	151	38	δ	δ	PROPN
ejpam-5423	151	39	(	(	PUNCT
ejpam-5423	151	40	x	x	NOUN
ejpam-5423	151	41	)	)	PUNCT
ejpam-5423	151	42	:	:	PUNCT
ejpam-5423	152	1	=	=	SYM
ejpam-5423	152	2	(	(	PUNCT
ejpam-5423	152	3	(	(	PUNCT
ejpam-5423	152	4	ω	ω	NUM
ejpam-5423	152	5	p	p	NOUN
ejpam-5423	152	6	◦	◦	NOUN
ejpam-5423	152	7	ϖ	ϖ	NOUN
ejpam-5423	152	8	p)λ	p)λ	NOUN
ejpam-5423	152	9	δ	δ	X
ejpam-5423	152	10	(	(	PUNCT
ejpam-5423	152	11	x	x	NOUN
ejpam-5423	152	12	)	)	PUNCT
ejpam-5423	152	13	,	,	PUNCT
ejpam-5423	152	14	(	(	PUNCT
ejpam-5423	152	15	ω	ω	NOUN
ejpam-5423	152	16	n	n	PRON
ejpam-5423	152	17	◦	◦	NOUN
ejpam-5423	152	18	ϖ	ϖ	NOUN
ejpam-5423	152	19	n)λ	n)λ	X
ejpam-5423	152	20	δ	δ	PROPN
ejpam-5423	152	21	(	(	PUNCT
ejpam-5423	152	22	x	x	NOUN
ejpam-5423	152	23	)	)	PUNCT
ejpam-5423	152	24	)	)	PUNCT
ejpam-5423	153	1	=	=	PUNCT
ejpam-5423	153	2	(	(	PUNCT
ejpam-5423	153	3	(	(	PUNCT
ejpam-5423	153	4	(	(	PUNCT
ejpam-5423	153	5	ω	ω	X
ejpam-5423	153	6	p(x	p(x	PROPN
ejpam-5423	153	7	)	)	PUNCT
ejpam-5423	153	8	◦	◦	NOUN
ejpam-5423	153	9	ϖ	ϖ	NOUN
ejpam-5423	153	10	p(x	p(x	NOUN
ejpam-5423	153	11	)	)	PUNCT
ejpam-5423	153	12	)	)	PUNCT
ejpam-5423	154	1	∧	∧	PROPN
ejpam-5423	154	2	λ	λ	PROPN
ejpam-5423	154	3	p	p	NOUN
ejpam-5423	154	4	)	)	PUNCT
ejpam-5423	154	5	∨	∨	NUM
ejpam-5423	154	6	δ	δ	PROPN
ejpam-5423	154	7	p	p	X
ejpam-5423	154	8	,	,	PUNCT
ejpam-5423	154	9	(	(	PUNCT
ejpam-5423	154	10	(	(	PUNCT
ejpam-5423	154	11	ω	ω	X
ejpam-5423	154	12	n(x	n(x	NOUN
ejpam-5423	154	13	)	)	PUNCT
ejpam-5423	154	14	◦	◦	NOUN
ejpam-5423	154	15	ϖ	ϖ	NOUN
ejpam-5423	154	16	n(x	n(x	NOUN
ejpam-5423	154	17	)	)	PUNCT
ejpam-5423	154	18	)	)	PUNCT
ejpam-5423	154	19	∨	∨	NUM
ejpam-5423	154	20	λ	λ	PROPN
ejpam-5423	154	21	n	n	CCONJ
ejpam-5423	154	22	)	)	PUNCT
ejpam-5423	154	23	∧	∧	PROPN
ejpam-5423	154	24	δ	δ	PROPN
ejpam-5423	154	25	n	n	PROPN
ejpam-5423	154	26	)	)	PUNCT
ejpam-5423	154	27	where	where	SCONJ
ejpam-5423	154	28	(	(	PUNCT
ejpam-5423	154	29	ω	ω	NUM
ejpam-5423	154	30	p	p	NOUN
ejpam-5423	154	31	◦	◦	NOUN
ejpam-5423	154	32	ϖ	ϖ	NOUN
ejpam-5423	154	33	p)(e	p)(e	NOUN
ejpam-5423	154	34	)	)	PUNCT
ejpam-5423	154	35	=	=	PUNCT
ejpam-5423	154	36			PUNCT
ejpam-5423	154	37	∨	∨	X
ejpam-5423	154	38	(	(	PUNCT
ejpam-5423	154	39	t	t	PROPN
ejpam-5423	154	40	,	,	PUNCT
ejpam-5423	154	41	h)∈fe	h)∈fe	PROPN
ejpam-5423	154	42	{	{	PUNCT
ejpam-5423	154	43	ω	ω	NUM
ejpam-5423	154	44	p(t	p(t	NOUN
ejpam-5423	154	45	)	)	PUNCT
ejpam-5423	154	46	∧ϖ	∧ϖ	PROPN
ejpam-5423	154	47	p(h	p(h	PROPN
ejpam-5423	154	48	)	)	PUNCT
ejpam-5423	154	49	}	}	PUNCT
ejpam-5423	154	50	if	if	SCONJ
ejpam-5423	154	51	fe	fe	X
ejpam-5423	154	52	̸=	̸=	PROPN
ejpam-5423	154	53	∅	∅	NOUN
ejpam-5423	154	54	,	,	PUNCT
ejpam-5423	154	55	0	0	PUNCT
ejpam-5423	155	1	if	if	SCONJ
ejpam-5423	155	2	fe	fe	X
ejpam-5423	155	3	=	=	NOUN
ejpam-5423	155	4	∅	∅	NOUN
ejpam-5423	155	5	,	,	PUNCT
ejpam-5423	155	6	and	and	CCONJ
ejpam-5423	155	7	(	(	PUNCT
ejpam-5423	155	8	ω	ω	NOUN
ejpam-5423	155	9	n	n	PRON
ejpam-5423	155	10	◦	◦	NOUN
ejpam-5423	155	11	ϖ	ϖ	NOUN
ejpam-5423	155	12	n)(e	n)(e	NOUN
ejpam-5423	155	13	)	)	PUNCT
ejpam-5423	155	14	=	=	PUNCT
ejpam-5423	155	15			PUNCT
ejpam-5423	155	16	∧	∧	PROPN
ejpam-5423	155	17	(	(	PUNCT
ejpam-5423	155	18	t	t	PROPN
ejpam-5423	155	19	,	,	PUNCT
ejpam-5423	155	20	h)∈fe	h)∈fe	PROPN
ejpam-5423	155	21	{	{	PUNCT
ejpam-5423	155	22	ω	ω	NUM
ejpam-5423	155	23	n(t	n(t	PROPN
ejpam-5423	155	24	)	)	PUNCT
ejpam-5423	155	25	∨ϖ	∨ϖ	VERB
ejpam-5423	155	26	n(h	n(h	PROPN
ejpam-5423	155	27	)	)	PUNCT
ejpam-5423	155	28	}	}	PUNCT
ejpam-5423	155	29	if	if	SCONJ
ejpam-5423	155	30	fe	fe	X
ejpam-5423	155	31	̸=	̸=	PROPN
ejpam-5423	155	32	∅	∅	NOUN
ejpam-5423	155	33	,	,	PUNCT
ejpam-5423	155	34	0	0	PUNCT
ejpam-5423	156	1	if	if	SCONJ
ejpam-5423	156	2	fe	fe	X
ejpam-5423	156	3	=	=	NOUN
ejpam-5423	156	4	∅	∅	NOUN
ejpam-5423	156	5	,	,	PUNCT
ejpam-5423	156	6	in	in	ADP
ejpam-5423	156	7	the	the	DET
ejpam-5423	156	8	following	following	NOUN
ejpam-5423	156	9	theorem	theorem	NOUN
ejpam-5423	156	10	,	,	PUNCT
ejpam-5423	156	11	we	we	PRON
ejpam-5423	156	12	give	give	VERB
ejpam-5423	156	13	a	a	DET
ejpam-5423	156	14	relationship	relationship	NOUN
ejpam-5423	156	15	between	between	ADP
ejpam-5423	156	16	an	an	DET
ejpam-5423	156	17	ideal	ideal	NOUN
ejpam-5423	156	18	and	and	CCONJ
ejpam-5423	156	19	the	the	DET
ejpam-5423	156	20	interval	interval	NOUN
ejpam-5423	156	21	valued	value	VERB
ejpam-5423	156	22	bipolar	bipolar	ADJ
ejpam-5423	156	23	characteristic	characteristic	ADJ
ejpam-5423	156	24	function	function	NOUN
ejpam-5423	156	25	which	which	PRON
ejpam-5423	156	26	is	be	AUX
ejpam-5423	156	27	proved	prove	VERB
ejpam-5423	156	28	easily	easily	ADV
ejpam-5423	156	29	.	.	PUNCT
ejpam-5423	157	1	t.	t.	PROPN
ejpam-5423	157	2	gaketem	gaketem	PROPN
ejpam-5423	157	3	,	,	PUNCT
ejpam-5423	157	4	t.	t.	PROPN
ejpam-5423	157	5	prommai	prommai	PROPN
ejpam-5423	157	6	/	/	SYM
ejpam-5423	157	7	eur	eur	PROPN
ejpam-5423	157	8	.	.	PUNCT
ejpam-5423	158	1	j.	j.	PROPN
ejpam-5423	158	2	pure	pure	PROPN
ejpam-5423	158	3	appl	appl	PROPN
ejpam-5423	158	4	.	.	PROPN
ejpam-5423	158	5	math	math	PROPN
ejpam-5423	158	6	,	,	PUNCT
ejpam-5423	158	7	17	17	NUM
ejpam-5423	158	8	(	(	PUNCT
ejpam-5423	158	9	4	4	NUM
ejpam-5423	158	10	)	)	PUNCT
ejpam-5423	158	11	(	(	PUNCT
ejpam-5423	158	12	2024	2024	NUM
ejpam-5423	158	13	)	)	PUNCT
ejpam-5423	158	14	,	,	PUNCT
ejpam-5423	158	15	3223	3223	NUM
ejpam-5423	158	16	-	-	SYM
ejpam-5423	158	17	3241	3241	NUM
ejpam-5423	158	18	3229	3229	NUM
ejpam-5423	158	19	theorem	theorem	NOUN
ejpam-5423	158	20	1	1	NUM
ejpam-5423	158	21	.	.	PUNCT
ejpam-5423	159	1	let	let	VERB
ejpam-5423	159	2	m	m	PRON
ejpam-5423	159	3	be	be	AUX
ejpam-5423	159	4	a	a	DET
ejpam-5423	159	5	non	non	ADJ
ejpam-5423	159	6	-	-	ADJ
ejpam-5423	159	7	empty	empty	ADJ
ejpam-5423	159	8	subset	subset	NOUN
ejpam-5423	159	9	of	of	ADP
ejpam-5423	159	10	an	an	DET
ejpam-5423	159	11	ordered	order	VERB
ejpam-5423	159	12	semigroup	semigroup	PROPN
ejpam-5423	159	13	g.	g.	PROPN
ejpam-5423	160	1	then	then	ADV
ejpam-5423	160	2	m	m	PROPN
ejpam-5423	160	3	is	be	AUX
ejpam-5423	160	4	a	a	DET
ejpam-5423	160	5	left	left	ADJ
ejpam-5423	160	6	ideal	ideal	NOUN
ejpam-5423	160	7	(	(	PUNCT
ejpam-5423	160	8	right	right	ADV
ejpam-5423	160	9	ideal	ideal	ADJ
ejpam-5423	160	10	,	,	PUNCT
ejpam-5423	160	11	ideal	ideal	ADJ
ejpam-5423	160	12	)	)	PUNCT
ejpam-5423	160	13	of	of	ADP
ejpam-5423	160	14	g	g	NOUN
ejpam-5423	160	15	with	with	ADP
ejpam-5423	160	16	λ	λ	X
ejpam-5423	160	17	p	p	X
ejpam-5423	160	18	<	<	X
ejpam-5423	160	19	δ	δ	X
ejpam-5423	160	20	p	p	NOUN
ejpam-5423	160	21	and	and	CCONJ
ejpam-5423	160	22	λ	λ	PROPN
ejpam-5423	160	23	n	n	CCONJ
ejpam-5423	160	24	>	>	PUNCT
ejpam-5423	160	25	δ	δ	PROPN
ejpam-5423	160	26	n	n	CCONJ
ejpam-5423	160	27	if	if	SCONJ
ejpam-5423	161	1	and	and	CCONJ
ejpam-5423	161	2	only	only	ADV
ejpam-5423	161	3	if	if	SCONJ
ejpam-5423	161	4	χm	χm	ADJ
ejpam-5423	161	5	=	=	PUNCT
ejpam-5423	161	6	(	(	PUNCT
ejpam-5423	161	7	g;χ	g;χ	PROPN
ejpam-5423	161	8	p	p	NOUN
ejpam-5423	161	9	m	m	PROPN
ejpam-5423	161	10	,	,	PUNCT
ejpam-5423	161	11	χ	χ	PROPN
ejpam-5423	161	12	n	n	INTJ
ejpam-5423	161	13	m	m	VERB
ejpam-5423	161	14	)	)	PUNCT
ejpam-5423	161	15	is	be	AUX
ejpam-5423	161	16	an	an	DET
ejpam-5423	161	17	(	(	PUNCT
ejpam-5423	161	18	λ	λ	NOUN
ejpam-5423	161	19	,	,	PUNCT
ejpam-5423	161	20	δ)-ivbf	δ)-ivbf	NOUN
ejpam-5423	161	21	left	leave	VERB
ejpam-5423	161	22	ideal	ideal	NOUN
ejpam-5423	161	23	(	(	PUNCT
ejpam-5423	161	24	right	right	ADV
ejpam-5423	161	25	ideal	ideal	ADJ
ejpam-5423	161	26	,	,	PUNCT
ejpam-5423	161	27	ideal	ideal	ADJ
ejpam-5423	161	28	)	)	PUNCT
ejpam-5423	161	29	of	of	ADP
ejpam-5423	161	30	g.	g.	PROPN
ejpam-5423	161	31	3	3	NUM
ejpam-5423	161	32	.	.	PUNCT
ejpam-5423	162	1	generalized	generalize	VERB
ejpam-5423	162	2	interval	interval	NOUN
ejpam-5423	162	3	valued	value	VERB
ejpam-5423	162	4	bipolar	bipolar	ADJ
ejpam-5423	162	5	fuzzy	fuzzy	ADJ
ejpam-5423	162	6	quasi	quasi	NOUN
ejpam-5423	162	7	-	-	NOUN
ejpam-5423	162	8	ideals	ideal	NOUN
ejpam-5423	162	9	in	in	ADP
ejpam-5423	162	10	this	this	DET
ejpam-5423	162	11	section	section	NOUN
ejpam-5423	162	12	,	,	PUNCT
ejpam-5423	162	13	we	we	PRON
ejpam-5423	162	14	give	give	VERB
ejpam-5423	162	15	the	the	DET
ejpam-5423	162	16	concept	concept	NOUN
ejpam-5423	162	17	of	of	ADP
ejpam-5423	162	18	a	a	DET
ejpam-5423	162	19	generalized	generalized	ADJ
ejpam-5423	162	20	interval	interval	NOUN
ejpam-5423	162	21	valued	value	VERB
ejpam-5423	162	22	bipolar	bipolar	ADJ
ejpam-5423	162	23	fuzzy	fuzzy	ADJ
ejpam-5423	162	24	quasiideal	quasiideal	NOUN
ejpam-5423	162	25	and	and	CCONJ
ejpam-5423	162	26	investigate	investigate	VERB
ejpam-5423	162	27	properties	property	NOUN
ejpam-5423	162	28	of	of	ADP
ejpam-5423	162	29	generalized	generalized	ADJ
ejpam-5423	162	30	interval	interval	NOUN
ejpam-5423	162	31	valued	value	VERB
ejpam-5423	162	32	bipolar	bipolar	ADJ
ejpam-5423	162	33	fuzzy	fuzzy	ADJ
ejpam-5423	162	34	quasi	quasi	NOUN
ejpam-5423	162	35	-	-	NOUN
ejpam-5423	162	36	ideal	ideal	ADJ
ejpam-5423	162	37	in	in	ADP
ejpam-5423	162	38	ordered	order	VERB
ejpam-5423	162	39	semigroups	semigroup	NOUN
ejpam-5423	162	40	.	.	PUNCT
ejpam-5423	163	1	definition	definition	NOUN
ejpam-5423	163	2	11	11	NUM
ejpam-5423	163	3	.	.	PUNCT
ejpam-5423	164	1	let	let	VERB
ejpam-5423	164	2	g	g	PRON
ejpam-5423	164	3	be	be	AUX
ejpam-5423	164	4	an	an	DET
ejpam-5423	164	5	ordered	order	VERB
ejpam-5423	164	6	semigroup	semigroup	NOUN
ejpam-5423	164	7	and	and	CCONJ
ejpam-5423	164	8	t	t	NOUN
ejpam-5423	164	9	=	=	SYM
ejpam-5423	165	1	(	(	PUNCT
ejpam-5423	165	2	ω	ω	PROPN
ejpam-5423	165	3	p	p	PROPN
ejpam-5423	165	4	,	,	PUNCT
ejpam-5423	165	5	ω	ω	PROPN
ejpam-5423	165	6	n	n	CCONJ
ejpam-5423	165	7	)	)	PUNCT
ejpam-5423	165	8	be	be	AUX
ejpam-5423	165	9	an	an	DET
ejpam-5423	165	10	ivbf	ivbf	NOUN
ejpam-5423	165	11	set	set	NOUN
ejpam-5423	165	12	of	of	ADP
ejpam-5423	165	13	g	g	PROPN
ejpam-5423	165	14	is	be	AUX
ejpam-5423	165	15	called	call	VERB
ejpam-5423	165	16	an	an	DET
ejpam-5423	165	17	(	(	PUNCT
ejpam-5423	165	18	λ	λ	NOUN
ejpam-5423	165	19	,	,	PUNCT
ejpam-5423	165	20	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	165	21	quasi	quasi	NOUN
ejpam-5423	165	22	-	-	NOUN
ejpam-5423	165	23	ideal	ideal	ADJ
ejpam-5423	165	24	of	of	ADP
ejpam-5423	165	25	g	g	PROPN
ejpam-5423	165	26	if	if	SCONJ
ejpam-5423	165	27	(	(	PUNCT
ejpam-5423	165	28	1	1	NUM
ejpam-5423	165	29	)	)	PUNCT
ejpam-5423	165	30	(	(	PUNCT
ejpam-5423	165	31	g	g	PROPN
ejpam-5423	165	32	◦	◦	NOUN
ejpam-5423	165	33	t	t	PROPN
ejpam-5423	165	34	)	)	PUNCT
ejpam-5423	166	1	λ	λ	NOUN
ejpam-5423	166	2	δ	δ	X
ejpam-5423	166	3	⊓	⊓	PROPN
ejpam-5423	166	4	(	(	PUNCT
ejpam-5423	166	5	t	t	PROPN
ejpam-5423	166	6	◦	◦	NOUN
ejpam-5423	166	7	g)λ	g)λ	NOUN
ejpam-5423	166	8	δ	δ	X
ejpam-5423	166	9	⊑	⊑	X
ejpam-5423	166	10	t	t	PROPN
ejpam-5423	166	11	λ	λ	X
ejpam-5423	166	12	δ	δ	PROPN
ejpam-5423	166	13	.	.	PUNCT
ejpam-5423	167	1	(	(	PUNCT
ejpam-5423	167	2	2	2	X
ejpam-5423	167	3	)	)	PUNCT
ejpam-5423	167	4	if	if	SCONJ
ejpam-5423	167	5	e1	e1	NOUN
ejpam-5423	167	6	≤	≤	PROPN
ejpam-5423	167	7	e2	e2	PROPN
ejpam-5423	167	8	,	,	PUNCT
ejpam-5423	167	9	then	then	ADV
ejpam-5423	167	10	ω	ω	NUM
ejpam-5423	167	11	p(e1	p(e1	NOUN
ejpam-5423	167	12	)	)	PUNCT
ejpam-5423	167	13	∨	∨	PROPN
ejpam-5423	167	14	λ	λ	PROPN
ejpam-5423	167	15	p	p	X
ejpam-5423	167	16	≥	≥	PROPN
ejpam-5423	167	17	ω	ω	NUM
ejpam-5423	167	18	p(e2	p(e2	NOUN
ejpam-5423	167	19	)	)	PUNCT
ejpam-5423	167	20	∧	∧	PROPN
ejpam-5423	167	21	δ	δ	PROPN
ejpam-5423	167	22	p	p	NOUN
ejpam-5423	167	23	and	and	CCONJ
ejpam-5423	167	24	ω	ω	NUM
ejpam-5423	167	25	n(e1	n(e1	NOUN
ejpam-5423	167	26	)	)	PUNCT
ejpam-5423	167	27	∧	∧	PROPN
ejpam-5423	167	28	λ	λ	PROPN
ejpam-5423	167	29	n	n	CCONJ
ejpam-5423	167	30	≤	≤	PROPN
ejpam-5423	167	31	ω	ω	NUM
ejpam-5423	167	32	n(e2	n(e2	PROPN
ejpam-5423	167	33	)	)	PUNCT
ejpam-5423	167	34	∨	∨	NUM
ejpam-5423	167	35	δ	δ	PROPN
ejpam-5423	167	36	n	n	CCONJ
ejpam-5423	167	37	,	,	PUNCT
ejpam-5423	167	38	for	for	ADP
ejpam-5423	167	39	all	all	DET
ejpam-5423	167	40	e1	e1	NOUN
ejpam-5423	167	41	,	,	PUNCT
ejpam-5423	167	42	e2	e2	PROPN
ejpam-5423	167	43	∈	∈	PROPN
ejpam-5423	167	44	g.	g.	NOUN
ejpam-5423	168	1	the	the	DET
ejpam-5423	168	2	following	follow	VERB
ejpam-5423	168	3	example	example	NOUN
ejpam-5423	168	4	is	be	AUX
ejpam-5423	168	5	a	a	DET
ejpam-5423	168	6	(	(	PUNCT
ejpam-5423	168	7	λ	λ	NOUN
ejpam-5423	168	8	,	,	PUNCT
ejpam-5423	168	9	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	168	10	quasi	quasi	NOUN
ejpam-5423	168	11	-	-	NOUN
ejpam-5423	168	12	ideal	ideal	ADJ
ejpam-5423	168	13	of	of	ADP
ejpam-5423	168	14	a	a	DET
ejpam-5423	168	15	semigroup	semigroup	NOUN
ejpam-5423	168	16	.	.	PUNCT
ejpam-5423	168	17	example	example	NOUN
ejpam-5423	169	1	2	2	NUM
ejpam-5423	169	2	.	.	PUNCT
ejpam-5423	169	3	let	let	VERB
ejpam-5423	169	4	g	g	NOUN
ejpam-5423	169	5	be	be	AUX
ejpam-5423	169	6	an	an	DET
ejpam-5423	169	7	ordered	order	VERB
ejpam-5423	169	8	semigroup	semigroup	NOUN
ejpam-5423	169	9	given	give	VERB
ejpam-5423	169	10	by	by	ADP
ejpam-5423	169	11	the	the	DET
ejpam-5423	169	12	following	follow	VERB
ejpam-5423	169	13	table	table	NOUN
ejpam-5423	169	14	.	.	PUNCT
ejpam-5423	170	1	·	·	PUNCT
ejpam-5423	171	1	α	α	X
ejpam-5423	171	2	κ	κ	NOUN
ejpam-5423	171	3	ρ	ρ	NOUN
ejpam-5423	171	4	α	α	NOUN
ejpam-5423	171	5	α	α	NOUN
ejpam-5423	171	6	α	α	NOUN
ejpam-5423	171	7	α	α	NOUN
ejpam-5423	171	8	κ	κ	ADP
ejpam-5423	171	9	α	α	NOUN
ejpam-5423	171	10	κ	κ	NOUN
ejpam-5423	171	11	κ	κ	PROPN
ejpam-5423	171	12	ρ	ρ	PROPN
ejpam-5423	171	13	α	α	NOUN
ejpam-5423	171	14	α	α	NOUN
ejpam-5423	171	15	κ	κ	NOUN
ejpam-5423	171	16	define	define	NOUN
ejpam-5423	171	17	ivbf	ivbf	NOUN
ejpam-5423	171	18	set	set	VERB
ejpam-5423	171	19	t	t	PROPN
ejpam-5423	171	20	=	=	SYM
ejpam-5423	171	21	(	(	PUNCT
ejpam-5423	171	22	ω	ω	PROPN
ejpam-5423	171	23	p	p	PROPN
ejpam-5423	171	24	,	,	PUNCT
ejpam-5423	171	25	ω	ω	PROPN
ejpam-5423	171	26	n	n	CCONJ
ejpam-5423	171	27	)	)	PUNCT
ejpam-5423	171	28	in	in	ADP
ejpam-5423	171	29	g	g	PROPN
ejpam-5423	171	30	as	as	SCONJ
ejpam-5423	171	31	follows	follow	VERB
ejpam-5423	171	32	:	:	PUNCT
ejpam-5423	171	33	µp(α	µp(α	X
ejpam-5423	171	34	)	)	PUNCT
ejpam-5423	171	35	=	=	NOUN
ejpam-5423	172	1	[	[	X
ejpam-5423	172	2	0.1	0.1	NUM
ejpam-5423	172	3	,	,	PUNCT
ejpam-5423	172	4	0.8	0.8	NUM
ejpam-5423	172	5	]	]	PUNCT
ejpam-5423	172	6	,	,	PUNCT
ejpam-5423	172	7	µp(κ	µp(κ	NUM
ejpam-5423	172	8	)	)	PUNCT
ejpam-5423	172	9	=	=	PUNCT
ejpam-5423	173	1	[	[	X
ejpam-5423	173	2	0.1	0.1	NUM
ejpam-5423	173	3	,	,	PUNCT
ejpam-5423	173	4	0.8	0.8	NUM
ejpam-5423	173	5	]	]	PUNCT
ejpam-5423	173	6	,	,	PUNCT
ejpam-5423	173	7	µp(ρ	µp(ρ	NUM
ejpam-5423	173	8	)	)	PUNCT
ejpam-5423	173	9	=	=	PUNCT
ejpam-5423	174	1	[	[	X
ejpam-5423	174	2	0.3	0.3	NUM
ejpam-5423	174	3	,	,	PUNCT
ejpam-5423	174	4	0.6	0.6	NUM
ejpam-5423	174	5	]	]	PUNCT
ejpam-5423	174	6	and	and	CCONJ
ejpam-5423	174	7	µn(α	µn(α	PUNCT
ejpam-5423	174	8	)	)	PUNCT
ejpam-5423	174	9	=	=	PUNCT
ejpam-5423	175	1	[	[	X
ejpam-5423	175	2	−0.1,−0.7	−0.1,−0.7	ADP
ejpam-5423	175	3	]	]	PUNCT
ejpam-5423	175	4	,	,	PUNCT
ejpam-5423	175	5	µn(κ	µn(κ	NUM
ejpam-5423	175	6	)	)	PUNCT
ejpam-5423	175	7	=	=	PUNCT
ejpam-5423	176	1	[	[	X
ejpam-5423	176	2	−0.1,−0.7	−0.1,−0.7	ADP
ejpam-5423	176	3	]	]	X
ejpam-5423	176	4	,	,	PUNCT
ejpam-5423	176	5	µn(ρ	µn(ρ	PUNCT
ejpam-5423	176	6	)	)	PUNCT
ejpam-5423	176	7	=	=	PUNCT
ejpam-5423	177	1	[	[	X
ejpam-5423	177	2	−0.2,−0.5	−0.2,−0.5	X
ejpam-5423	177	3	]	]	X
ejpam-5423	177	4	.	.	PUNCT
ejpam-5423	178	1	and	and	CCONJ
ejpam-5423	178	2	define	define	VERB
ejpam-5423	178	3	a	a	DET
ejpam-5423	178	4	partial	partial	ADJ
ejpam-5423	178	5	order	order	NOUN
ejpam-5423	178	6	relation	relation	NOUN
ejpam-5423	178	7	≤	≤	NOUN
ejpam-5423	178	8	on	on	ADP
ejpam-5423	178	9	g	g	PROPN
ejpam-5423	178	10	as	as	SCONJ
ejpam-5423	178	11	follows	follow	VERB
ejpam-5423	178	12	:	:	PUNCT
ejpam-5423	178	13	≤	≤	NUM
ejpam-5423	178	14	:	:	PUNCT
ejpam-5423	178	15	{	{	PUNCT
ejpam-5423	178	16	(	(	PUNCT
ejpam-5423	178	17	α	α	NOUN
ejpam-5423	178	18	,	,	PUNCT
ejpam-5423	178	19	κ	κ	NOUN
ejpam-5423	178	20	)	)	PUNCT
ejpam-5423	178	21	,	,	PUNCT
ejpam-5423	178	22	(	(	PUNCT
ejpam-5423	178	23	α	α	X
ejpam-5423	178	24	,	,	PUNCT
ejpam-5423	178	25	ρ	ρ	PROPN
ejpam-5423	178	26	)	)	PUNCT
ejpam-5423	178	27	,	,	PUNCT
ejpam-5423	178	28	(	(	PUNCT
ejpam-5423	178	29	κ	κ	NOUN
ejpam-5423	178	30	,	,	PUNCT
ejpam-5423	178	31	ρ)}∪	ρ)}∪	NOUN
ejpam-5423	178	32	△	△	PROPN
ejpam-5423	178	33	g	g	NOUN
ejpam-5423	178	34	,	,	PUNCT
ejpam-5423	178	35	where	where	SCONJ
ejpam-5423	178	36	△	△	NOUN
ejpam-5423	178	37	g	g	PROPN
ejpam-5423	178	38	is	be	AUX
ejpam-5423	178	39	an	an	DET
ejpam-5423	178	40	equality	equality	NOUN
ejpam-5423	178	41	relation	relation	NOUN
ejpam-5423	178	42	on	on	ADP
ejpam-5423	178	43	g.	g.	PROPN
ejpam-5423	178	44	by	by	ADP
ejpam-5423	178	45	routine	routine	ADJ
ejpam-5423	178	46	calculation	calculation	NOUN
ejpam-5423	178	47	,	,	PUNCT
ejpam-5423	178	48	t	t	NOUN
ejpam-5423	178	49	=	=	SYM
ejpam-5423	178	50	(	(	PUNCT
ejpam-5423	178	51	ω	ω	PROPN
ejpam-5423	178	52	p	p	PROPN
ejpam-5423	178	53	,	,	PUNCT
ejpam-5423	178	54	ω	ω	PROPN
ejpam-5423	178	55	n	n	CCONJ
ejpam-5423	178	56	)	)	PUNCT
ejpam-5423	178	57	is	be	AUX
ejpam-5423	178	58	an	an	DET
ejpam-5423	178	59	(	(	PUNCT
ejpam-5423	178	60	[	[	X
ejpam-5423	178	61	0.3	0.3	NUM
ejpam-5423	178	62	,	,	PUNCT
ejpam-5423	178	63	0.3	0.3	NUM
ejpam-5423	178	64	]	]	PUNCT
ejpam-5423	178	65	,	,	PUNCT
ejpam-5423	178	66	[	[	X
ejpam-5423	178	67	0.5	0.5	NUM
ejpam-5423	178	68	,	,	PUNCT
ejpam-5423	178	69	0.5])ivbf	0.5])ivbf	ADJ
ejpam-5423	178	70	quasi	quasi	ADJ
ejpam-5423	178	71	-	-	NOUN
ejpam-5423	178	72	ideal	ideal	NOUN
ejpam-5423	178	73	of	of	ADP
ejpam-5423	178	74	g.	g.	PROPN
ejpam-5423	178	75	theorem	theorem	PROPN
ejpam-5423	178	76	2	2	NUM
ejpam-5423	178	77	.	.	PUNCT
ejpam-5423	179	1	every	every	DET
ejpam-5423	179	2	(	(	PUNCT
ejpam-5423	179	3	λ	λ	NOUN
ejpam-5423	179	4	,	,	PUNCT
ejpam-5423	179	5	δ)-ivbf	δ)-ivbf	NOUN
ejpam-5423	179	6	left	leave	VERB
ejpam-5423	179	7	(	(	PUNCT
ejpam-5423	179	8	right	right	ADJ
ejpam-5423	179	9	)	)	PUNCT
ejpam-5423	179	10	ideal	ideal	NOUN
ejpam-5423	179	11	of	of	ADP
ejpam-5423	179	12	an	an	DET
ejpam-5423	179	13	ordered	order	VERB
ejpam-5423	179	14	semigroup	semigroup	NOUN
ejpam-5423	179	15	g	g	PROPN
ejpam-5423	179	16	is	be	AUX
ejpam-5423	179	17	an	an	DET
ejpam-5423	179	18	(	(	PUNCT
ejpam-5423	179	19	λ	λ	PROPN
ejpam-5423	179	20	,	,	PUNCT
ejpam-5423	179	21	δ)ivbf	δ)ivbf	NOUN
ejpam-5423	179	22	quasi	quasi	ADJ
ejpam-5423	179	23	ideal	ideal	NOUN
ejpam-5423	179	24	of	of	ADP
ejpam-5423	179	25	g.	g.	PROPN
ejpam-5423	179	26	proof	proof	PROPN
ejpam-5423	179	27	.	.	PUNCT
ejpam-5423	180	1	suppose	suppose	VERB
ejpam-5423	180	2	that	that	SCONJ
ejpam-5423	180	3	t	t	NOUN
ejpam-5423	180	4	=	=	SYM
ejpam-5423	180	5	(	(	PUNCT
ejpam-5423	180	6	ω	ω	PROPN
ejpam-5423	180	7	p	p	PROPN
ejpam-5423	180	8	,	,	PUNCT
ejpam-5423	180	9	ω	ω	PROPN
ejpam-5423	180	10	n	n	CCONJ
ejpam-5423	180	11	)	)	PUNCT
ejpam-5423	180	12	is	be	AUX
ejpam-5423	180	13	an	an	DET
ejpam-5423	180	14	(	(	PUNCT
ejpam-5423	180	15	λ	λ	NOUN
ejpam-5423	180	16	,	,	PUNCT
ejpam-5423	180	17	δ)-ivbf	δ)-ivbf	NOUN
ejpam-5423	180	18	left	leave	VERB
ejpam-5423	180	19	ideal	ideal	NOUN
ejpam-5423	180	20	of	of	ADP
ejpam-5423	180	21	f	f	PROPN
ejpam-5423	180	22	and	and	CCONJ
ejpam-5423	180	23	let	let	VERB
ejpam-5423	180	24	e1	e1	NOUN
ejpam-5423	180	25	,	,	PUNCT
ejpam-5423	180	26	e2	e2	PROPN
ejpam-5423	180	27	∈	∈	PROPN
ejpam-5423	180	28	g	g	PROPN
ejpam-5423	180	29	with	with	ADP
ejpam-5423	180	30	e1	e1	PROPN
ejpam-5423	180	31	≥	≥	PROPN
ejpam-5423	180	32	e2	e2	PROPN
ejpam-5423	180	33	.	.	PUNCT
ejpam-5423	181	1	then	then	ADV
ejpam-5423	181	2	ω	ω	NUM
ejpam-5423	181	3	p(e1)∨λ	p(e1)∨λ	PROPN
ejpam-5423	181	4	p	p	PROPN
ejpam-5423	181	5	≥	≥	PROPN
ejpam-5423	181	6	ω	ω	NUM
ejpam-5423	181	7	p(e2)∧	p(e2)∧	X
ejpam-5423	181	8	δ	δ	PROPN
ejpam-5423	181	9	p	p	NOUN
ejpam-5423	181	10	and	and	CCONJ
ejpam-5423	181	11	ω	ω	NUM
ejpam-5423	181	12	n(e1)∧λ	n(e1)∧λ	PROPN
ejpam-5423	181	13	n	n	PRON
ejpam-5423	181	14	≤	≤	NOUN
ejpam-5423	181	15	ω	ω	NOUN
ejpam-5423	181	16	n(e2)∨	n(e2)∨	X
ejpam-5423	181	17	δ	δ	PROPN
ejpam-5423	181	18	n.	n.	PROPN
ejpam-5423	181	19	let	let	VERB
ejpam-5423	181	20	e	e	PROPN
ejpam-5423	181	21	∈	∈	PROPN
ejpam-5423	181	22	f.	f.	PROPN
ejpam-5423	181	23	if	if	SCONJ
ejpam-5423	181	24	ae	ae	PROPN
ejpam-5423	181	25	=	=	SYM
ejpam-5423	181	26	∅	∅	NOUN
ejpam-5423	181	27	,	,	PUNCT
ejpam-5423	181	28	then	then	ADV
ejpam-5423	181	29	it	it	PRON
ejpam-5423	181	30	is	be	AUX
ejpam-5423	181	31	easy	easy	ADJ
ejpam-5423	181	32	to	to	PART
ejpam-5423	181	33	verify	verify	VERB
ejpam-5423	181	34	that	that	SCONJ
ejpam-5423	181	35	(	(	PUNCT
ejpam-5423	181	36	g	g	PROPN
ejpam-5423	181	37	p	p	X
ejpam-5423	181	38	◦	◦	NOUN
ejpam-5423	181	39	ωp)δ	ωp)δ	PROPN
ejpam-5423	181	40	λ	λ	X
ejpam-5423	181	41	(	(	PUNCT
ejpam-5423	181	42	e	e	NOUN
ejpam-5423	181	43	)	)	PUNCT
ejpam-5423	181	44	∧	∧	NOUN
ejpam-5423	181	45	(	(	PUNCT
ejpam-5423	181	46	ωp	ωp	NOUN
ejpam-5423	181	47	◦	◦	NOUN
ejpam-5423	181	48	gp	gp	NOUN
ejpam-5423	181	49	)	)	PUNCT
ejpam-5423	182	1	δ	δ	PROPN
ejpam-5423	182	2	λ	λ	X
ejpam-5423	182	3	(	(	PUNCT
ejpam-5423	182	4	e	e	NOUN
ejpam-5423	182	5	)	)	PUNCT
ejpam-5423	182	6	≤	≤	NOUN
ejpam-5423	182	7	(	(	PUNCT
ejpam-5423	182	8	ω	ω	NOUN
ejpam-5423	182	9	p)δ	p)δ	X
ejpam-5423	182	10	λ	λ	X
ejpam-5423	182	11	(	(	PUNCT
ejpam-5423	182	12	e	e	NOUN
ejpam-5423	182	13	)	)	PUNCT
ejpam-5423	182	14	and	and	CCONJ
ejpam-5423	182	15	(	(	PUNCT
ejpam-5423	182	16	g	g	PROPN
ejpam-5423	182	17	n	n	CCONJ
ejpam-5423	182	18	◦	◦	VERB
ejpam-5423	182	19	ωn)λ	ωn)λ	PROPN
ejpam-5423	182	20	δ	δ	PROPN
ejpam-5423	182	21	(	(	PUNCT
ejpam-5423	182	22	e	e	NOUN
ejpam-5423	182	23	)	)	PUNCT
ejpam-5423	182	24	∨	∨	NOUN
ejpam-5423	182	25	(	(	PUNCT
ejpam-5423	182	26	ωn	ωn	ADP
ejpam-5423	182	27	◦	◦	NOUN
ejpam-5423	182	28	gn	gn	NOUN
ejpam-5423	182	29	)	)	PUNCT
ejpam-5423	182	30	λ	λ	PROPN
ejpam-5423	182	31	δ	δ	PROPN
ejpam-5423	182	32	(	(	PUNCT
ejpam-5423	182	33	e	e	NOUN
ejpam-5423	182	34	)	)	PUNCT
ejpam-5423	182	35	≥	≥	NOUN
ejpam-5423	182	36	(	(	PUNCT
ejpam-5423	182	37	ω	ω	PROPN
ejpam-5423	182	38	n)λ	n)λ	X
ejpam-5423	182	39	δ	δ	PROPN
ejpam-5423	182	40	(	(	PUNCT
ejpam-5423	182	41	e	e	NOUN
ejpam-5423	182	42	)	)	PUNCT
ejpam-5423	182	43	.	.	PUNCT
ejpam-5423	183	1	t.	t.	PROPN
ejpam-5423	183	2	gaketem	gaketem	PROPN
ejpam-5423	183	3	,	,	PUNCT
ejpam-5423	183	4	t.	t.	PROPN
ejpam-5423	183	5	prommai	prommai	PROPN
ejpam-5423	183	6	/	/	SYM
ejpam-5423	183	7	eur	eur	PROPN
ejpam-5423	183	8	.	.	PUNCT
ejpam-5423	184	1	j.	j.	PROPN
ejpam-5423	184	2	pure	pure	PROPN
ejpam-5423	184	3	appl	appl	PROPN
ejpam-5423	184	4	.	.	PROPN
ejpam-5423	184	5	math	math	PROPN
ejpam-5423	184	6	,	,	PUNCT
ejpam-5423	184	7	17	17	NUM
ejpam-5423	184	8	(	(	PUNCT
ejpam-5423	184	9	4	4	NUM
ejpam-5423	184	10	)	)	PUNCT
ejpam-5423	184	11	(	(	PUNCT
ejpam-5423	184	12	2024	2024	NUM
ejpam-5423	184	13	)	)	PUNCT
ejpam-5423	184	14	,	,	PUNCT
ejpam-5423	184	15	3223	3223	NUM
ejpam-5423	184	16	-	-	SYM
ejpam-5423	184	17	3241	3241	NUM
ejpam-5423	184	18	3230	3230	NUM
ejpam-5423	184	19	if	if	SCONJ
ejpam-5423	184	20	ae	ae	PROPN
ejpam-5423	184	21	̸=	̸=	PROPN
ejpam-5423	184	22	∅	∅	NOUN
ejpam-5423	184	23	,	,	PUNCT
ejpam-5423	184	24	then	then	ADV
ejpam-5423	184	25	(	(	PUNCT
ejpam-5423	184	26	g	g	PROPN
ejpam-5423	184	27	p	p	PROPN
ejpam-5423	184	28	◦	◦	NOUN
ejpam-5423	184	29	ωp)δ	ωp)δ	PROPN
ejpam-5423	184	30	λ	λ	X
ejpam-5423	184	31	(	(	PUNCT
ejpam-5423	184	32	e	e	NOUN
ejpam-5423	184	33	)	)	PUNCT
ejpam-5423	184	34	=	=	SYM
ejpam-5423	184	35	(	(	PUNCT
ejpam-5423	184	36	∨	∨	X
ejpam-5423	184	37	(	(	PUNCT
ejpam-5423	184	38	k	k	X
ejpam-5423	184	39	,	,	PUNCT
ejpam-5423	184	40	o)∈ae	o)∈ae	PROPN
ejpam-5423	184	41	{	{	PUNCT
ejpam-5423	184	42	gp	gp	NOUN
ejpam-5423	184	43	(	(	PUNCT
ejpam-5423	184	44	k	k	NOUN
ejpam-5423	184	45	)	)	PUNCT
ejpam-5423	184	46	∧	∧	NOUN
ejpam-5423	184	47	ωp(o	ωp(o	NOUN
ejpam-5423	184	48	)	)	PUNCT
ejpam-5423	184	49	}	}	PUNCT
ejpam-5423	184	50	∧	∧	PROPN
ejpam-5423	184	51	δ	δ	PROPN
ejpam-5423	184	52	p	p	NOUN
ejpam-5423	184	53	)	)	PUNCT
ejpam-5423	185	1	∨	∨	NUM
ejpam-5423	185	2	λ	λ	X
ejpam-5423	185	3	p	p	X
ejpam-5423	185	4	=	=	X
ejpam-5423	185	5	(	(	PUNCT
ejpam-5423	185	6	∨	∨	X
ejpam-5423	185	7	(	(	PUNCT
ejpam-5423	185	8	k	k	X
ejpam-5423	185	9	,	,	PUNCT
ejpam-5423	185	10	o)∈ae	o)∈ae	PROPN
ejpam-5423	185	11	{	{	PUNCT
ejpam-5423	185	12	1	1	NUM
ejpam-5423	185	13	∧	∧	PROPN
ejpam-5423	185	14	ωp(o	ωp(o	NUM
ejpam-5423	185	15	)	)	PUNCT
ejpam-5423	185	16	}	}	PUNCT
ejpam-5423	185	17	∧	∧	PROPN
ejpam-5423	185	18	δ	δ	PROPN
ejpam-5423	185	19	p	p	NOUN
ejpam-5423	185	20	)	)	PUNCT
ejpam-5423	185	21	∨	∨	NUM
ejpam-5423	185	22	λ	λ	X
ejpam-5423	185	23	p	p	X
ejpam-5423	185	24	=	=	X
ejpam-5423	185	25	(	(	PUNCT
ejpam-5423	185	26	∨	∨	X
ejpam-5423	185	27	(	(	PUNCT
ejpam-5423	185	28	k	k	X
ejpam-5423	185	29	,	,	PUNCT
ejpam-5423	185	30	o)∈ae	o)∈ae	PROPN
ejpam-5423	185	31	{	{	PUNCT
ejpam-5423	185	32	ωp(o	ωp(o	NOUN
ejpam-5423	185	33	)	)	PUNCT
ejpam-5423	185	34	}	}	PUNCT
ejpam-5423	185	35	∧	∧	PROPN
ejpam-5423	185	36	δ	δ	PROPN
ejpam-5423	185	37	p	p	NOUN
ejpam-5423	185	38	)	)	PUNCT
ejpam-5423	185	39	∨	∨	NUM
ejpam-5423	185	40	λ	λ	X
ejpam-5423	185	41	p	p	X
ejpam-5423	185	42	=	=	X
ejpam-5423	185	43	(	(	PUNCT
ejpam-5423	185	44	∨	∨	X
ejpam-5423	185	45	(	(	PUNCT
ejpam-5423	185	46	k	k	X
ejpam-5423	185	47	,	,	PUNCT
ejpam-5423	185	48	o)∈ae	o)∈ae	PROPN
ejpam-5423	185	49	{	{	PUNCT
ejpam-5423	185	50	ωp(o	ωp(o	NOUN
ejpam-5423	185	51	)	)	PUNCT
ejpam-5423	185	52	∧	∧	PROPN
ejpam-5423	185	53	δ	δ	NOUN
ejpam-5423	185	54	p	p	ADJ
ejpam-5423	185	55	}	}	PUNCT
ejpam-5423	185	56	∧	∧	PROPN
ejpam-5423	185	57	δ	δ	PROPN
ejpam-5423	185	58	p	p	NOUN
ejpam-5423	185	59	)	)	PUNCT
ejpam-5423	185	60	∨	∨	NUM
ejpam-5423	185	61	λ	λ	PROPN
ejpam-5423	185	62	p	p	NOUN
ejpam-5423	185	63	≤	≤	PROPN
ejpam-5423	185	64	(	(	PUNCT
ejpam-5423	185	65	∨	∨	X
ejpam-5423	185	66	(	(	PUNCT
ejpam-5423	185	67	k	k	X
ejpam-5423	185	68	,	,	PUNCT
ejpam-5423	185	69	o)∈ae	o)∈ae	PROPN
ejpam-5423	185	70	{	{	PUNCT
ejpam-5423	185	71	ωp(ko	ωp(ko	PROPN
ejpam-5423	185	72	)	)	PUNCT
ejpam-5423	185	73	∨	∨	NUM
ejpam-5423	185	74	λ	λ	X
ejpam-5423	185	75	p	p	X
ejpam-5423	185	76	}	}	PUNCT
ejpam-5423	185	77	∧	∧	PROPN
ejpam-5423	185	78	δ	δ	PROPN
ejpam-5423	185	79	p	p	NOUN
ejpam-5423	185	80	)	)	PUNCT
ejpam-5423	185	81	∨	∨	NUM
ejpam-5423	186	1	λ	λ	X
ejpam-5423	186	2	p	p	X
ejpam-5423	186	3	=	=	X
ejpam-5423	186	4	(	(	PUNCT
ejpam-5423	186	5	(	(	PUNCT
ejpam-5423	186	6	ωp(e	ωp(e	X
ejpam-5423	186	7	)	)	PUNCT
ejpam-5423	186	8	∨	∨	NUM
ejpam-5423	186	9	λ	λ	PROPN
ejpam-5423	186	10	p	p	NOUN
ejpam-5423	186	11	)	)	PUNCT
ejpam-5423	186	12	∧	∧	PROPN
ejpam-5423	186	13	δ	δ	PROPN
ejpam-5423	186	14	p	p	NOUN
ejpam-5423	186	15	)	)	PUNCT
ejpam-5423	186	16	∨	∨	NUM
ejpam-5423	186	17	λ	λ	X
ejpam-5423	186	18	p	p	X
ejpam-5423	186	19	=	=	X
ejpam-5423	186	20	(	(	PUNCT
ejpam-5423	186	21	(	(	PUNCT
ejpam-5423	186	22	ωp(e	ωp(e	X
ejpam-5423	186	23	)	)	PUNCT
ejpam-5423	186	24	∨	∨	NUM
ejpam-5423	186	25	λ	λ	PROPN
ejpam-5423	186	26	p	p	X
ejpam-5423	186	27	∨	∨	NUM
ejpam-5423	186	28	λ	λ	PROPN
ejpam-5423	186	29	p	p	NOUN
ejpam-5423	186	30	)	)	PUNCT
ejpam-5423	186	31	∧	∧	PROPN
ejpam-5423	186	32	δ	δ	PROPN
ejpam-5423	186	33	p	p	NOUN
ejpam-5423	186	34	∨	∨	NUM
ejpam-5423	186	35	λ	λ	PROPN
ejpam-5423	186	36	p	p	NOUN
ejpam-5423	186	37	)	)	PUNCT
ejpam-5423	186	38	=	=	SYM
ejpam-5423	186	39	(	(	PUNCT
ejpam-5423	186	40	(	(	PUNCT
ejpam-5423	186	41	ωp(e	ωp(e	X
ejpam-5423	186	42	)	)	PUNCT
ejpam-5423	186	43	∨	∨	NUM
ejpam-5423	186	44	λ	λ	PROPN
ejpam-5423	186	45	p	p	NOUN
ejpam-5423	186	46	)	)	PUNCT
ejpam-5423	186	47	∧	∧	PROPN
ejpam-5423	186	48	δ	δ	PROPN
ejpam-5423	186	49	p	p	NOUN
ejpam-5423	186	50	∨	∨	NUM
ejpam-5423	186	51	λ	λ	PROPN
ejpam-5423	186	52	p	p	NOUN
ejpam-5423	186	53	)	)	PUNCT
ejpam-5423	186	54	=	=	SYM
ejpam-5423	186	55	(	(	PUNCT
ejpam-5423	186	56	ωp(e	ωp(e	ADJ
ejpam-5423	186	57	)	)	PUNCT
ejpam-5423	186	58	∧	∧	PROPN
ejpam-5423	186	59	δ	δ	PROPN
ejpam-5423	186	60	p	p	NOUN
ejpam-5423	186	61	)	)	PUNCT
ejpam-5423	186	62	∨	∨	NUM
ejpam-5423	186	63	λ	λ	X
ejpam-5423	186	64	p	p	X
ejpam-5423	186	65	=	=	SYM
ejpam-5423	186	66	(	(	PUNCT
ejpam-5423	186	67	ω	ω	X
ejpam-5423	186	68	p)δ	p)δ	X
ejpam-5423	186	69	λ	λ	X
ejpam-5423	186	70	(	(	PUNCT
ejpam-5423	186	71	e	e	NOUN
ejpam-5423	186	72	)	)	PUNCT
ejpam-5423	186	73	and	and	CCONJ
ejpam-5423	186	74	(	(	PUNCT
ejpam-5423	186	75	g	g	PROPN
ejpam-5423	186	76	n	n	CCONJ
ejpam-5423	186	77	◦	◦	VERB
ejpam-5423	186	78	ωn)λ	ωn)λ	PROPN
ejpam-5423	186	79	δ	δ	PROPN
ejpam-5423	186	80	(	(	PUNCT
ejpam-5423	186	81	e	e	NOUN
ejpam-5423	186	82	)	)	PUNCT
ejpam-5423	186	83	=	=	SYM
ejpam-5423	186	84	(	(	PUNCT
ejpam-5423	186	85	∧	∧	PROPN
ejpam-5423	186	86	(	(	PUNCT
ejpam-5423	186	87	k	k	X
ejpam-5423	186	88	,	,	PUNCT
ejpam-5423	186	89	o)∈ae	o)∈ae	PROPN
ejpam-5423	186	90	{	{	PUNCT
ejpam-5423	186	91	gn	gn	PROPN
ejpam-5423	186	92	(	(	PUNCT
ejpam-5423	186	93	k	k	NOUN
ejpam-5423	186	94	)	)	PUNCT
ejpam-5423	186	95	∨	∨	NUM
ejpam-5423	186	96	ωn(o	ωn(o	NUM
ejpam-5423	186	97	)	)	PUNCT
ejpam-5423	186	98	}	}	PUNCT
ejpam-5423	186	99	∧	∧	PROPN
ejpam-5423	186	100	λ	λ	PROPN
ejpam-5423	186	101	n	n	CCONJ
ejpam-5423	186	102	)	)	PUNCT
ejpam-5423	186	103	∨	∨	NUM
ejpam-5423	186	104	δ	δ	PROPN
ejpam-5423	186	105	n	n	X
ejpam-5423	186	106	=	=	PUNCT
ejpam-5423	186	107	(	(	PUNCT
ejpam-5423	186	108	∧	∧	PROPN
ejpam-5423	186	109	(	(	PUNCT
ejpam-5423	186	110	k	k	X
ejpam-5423	186	111	,	,	PUNCT
ejpam-5423	186	112	o)∈ae	o)∈ae	PROPN
ejpam-5423	186	113	{	{	PUNCT
ejpam-5423	186	114	−1	−1	NOUN
ejpam-5423	186	115	∨	∨	NUM
ejpam-5423	186	116	ωn(o	ωn(o	NUM
ejpam-5423	186	117	)	)	PUNCT
ejpam-5423	186	118	}	}	PUNCT
ejpam-5423	186	119	∧	∧	PROPN
ejpam-5423	186	120	λ	λ	PROPN
ejpam-5423	186	121	n	n	CCONJ
ejpam-5423	186	122	)	)	PUNCT
ejpam-5423	186	123	∨	∨	NUM
ejpam-5423	186	124	δ	δ	PROPN
ejpam-5423	186	125	n	n	X
ejpam-5423	186	126	=	=	PUNCT
ejpam-5423	186	127	(	(	PUNCT
ejpam-5423	186	128	∧	∧	PROPN
ejpam-5423	186	129	(	(	PUNCT
ejpam-5423	186	130	k	k	X
ejpam-5423	186	131	,	,	PUNCT
ejpam-5423	186	132	o)∈ae	o)∈ae	PROPN
ejpam-5423	186	133	{	{	PUNCT
ejpam-5423	186	134	ωn(o	ωn(o	NUM
ejpam-5423	186	135	)	)	PUNCT
ejpam-5423	186	136	}	}	PUNCT
ejpam-5423	186	137	∧	∧	PROPN
ejpam-5423	186	138	λ	λ	PROPN
ejpam-5423	186	139	n	n	CCONJ
ejpam-5423	186	140	)	)	PUNCT
ejpam-5423	186	141	∨	∨	NUM
ejpam-5423	186	142	δ	δ	PROPN
ejpam-5423	186	143	n	n	X
ejpam-5423	186	144	=	=	PUNCT
ejpam-5423	186	145	(	(	PUNCT
ejpam-5423	186	146	∧	∧	PROPN
ejpam-5423	186	147	(	(	PUNCT
ejpam-5423	186	148	k	k	X
ejpam-5423	186	149	,	,	PUNCT
ejpam-5423	186	150	o)∈ae	o)∈ae	PROPN
ejpam-5423	186	151	{	{	PUNCT
ejpam-5423	186	152	ωn(o	ωn(o	NUM
ejpam-5423	186	153	)	)	PUNCT
ejpam-5423	186	154	∨	∨	NUM
ejpam-5423	186	155	δ	δ	PROPN
ejpam-5423	186	156	n	n	CCONJ
ejpam-5423	186	157	}	}	PUNCT
ejpam-5423	186	158	∧	∧	PROPN
ejpam-5423	186	159	λ	λ	PROPN
ejpam-5423	186	160	n	n	CCONJ
ejpam-5423	186	161	)	)	PUNCT
ejpam-5423	186	162	∨	∨	PROPN
ejpam-5423	186	163	δ	δ	PROPN
ejpam-5423	186	164	n	n	PRON
ejpam-5423	186	165	≥	≥	NUM
ejpam-5423	186	166	(	(	PUNCT
ejpam-5423	186	167	∧	∧	PROPN
ejpam-5423	186	168	(	(	PUNCT
ejpam-5423	186	169	k	k	X
ejpam-5423	186	170	,	,	PUNCT
ejpam-5423	186	171	o)∈ae	o)∈ae	PROPN
ejpam-5423	186	172	{	{	PUNCT
ejpam-5423	186	173	ωn(ko	ωn(ko	NOUN
ejpam-5423	186	174	)	)	PUNCT
ejpam-5423	186	175	∧	∧	PROPN
ejpam-5423	186	176	λ	λ	PROPN
ejpam-5423	186	177	n	n	CCONJ
ejpam-5423	186	178	}	}	PUNCT
ejpam-5423	186	179	∧	∧	PROPN
ejpam-5423	186	180	λ	λ	PROPN
ejpam-5423	186	181	n	n	CCONJ
ejpam-5423	186	182	)	)	PUNCT
ejpam-5423	186	183	∨	∨	NUM
ejpam-5423	186	184	δ	δ	PROPN
ejpam-5423	186	185	n	n	X
ejpam-5423	186	186	=	=	SYM
ejpam-5423	186	187	(	(	PUNCT
ejpam-5423	186	188	(	(	PUNCT
ejpam-5423	186	189	ωp(e	ωp(e	X
ejpam-5423	186	190	)	)	PUNCT
ejpam-5423	186	191	∧	∧	PROPN
ejpam-5423	186	192	λ	λ	PROPN
ejpam-5423	186	193	n	n	CCONJ
ejpam-5423	186	194	)	)	PUNCT
ejpam-5423	186	195	∧	∧	PROPN
ejpam-5423	186	196	λ	λ	PROPN
ejpam-5423	186	197	n	n	CCONJ
ejpam-5423	186	198	)	)	PUNCT
ejpam-5423	186	199	∨	∨	NUM
ejpam-5423	186	200	δ	δ	PROPN
ejpam-5423	186	201	n	n	X
ejpam-5423	186	202	=	=	SYM
ejpam-5423	186	203	(	(	PUNCT
ejpam-5423	186	204	ωp(r	ωp(r	NOUN
ejpam-5423	186	205	)	)	PUNCT
ejpam-5423	186	206	∧	∧	NOUN
ejpam-5423	186	207	λ	λ	PROPN
ejpam-5423	186	208	n	n	CCONJ
ejpam-5423	186	209	)	)	PUNCT
ejpam-5423	186	210	∨	∨	NUM
ejpam-5423	186	211	δ	δ	PROPN
ejpam-5423	186	212	n	n	X
ejpam-5423	186	213	=	=	SYM
ejpam-5423	186	214	(	(	PUNCT
ejpam-5423	186	215	ω	ω	PROPN
ejpam-5423	186	216	n)λ	n)λ	X
ejpam-5423	186	217	δ	δ	PROPN
ejpam-5423	186	218	(	(	PUNCT
ejpam-5423	186	219	e	e	NOUN
ejpam-5423	186	220	)	)	PUNCT
ejpam-5423	186	221	thus	thus	ADV
ejpam-5423	186	222	,	,	PUNCT
ejpam-5423	186	223	(	(	PUNCT
ejpam-5423	186	224	g	g	PROPN
ejpam-5423	186	225	p	p	PROPN
ejpam-5423	186	226	◦	◦	NOUN
ejpam-5423	186	227	ωp)δ	ωp)δ	PROPN
ejpam-5423	186	228	λ	λ	X
ejpam-5423	186	229	(	(	PUNCT
ejpam-5423	186	230	e	e	NOUN
ejpam-5423	186	231	)	)	PUNCT
ejpam-5423	186	232	≤	≤	NOUN
ejpam-5423	186	233	(	(	PUNCT
ejpam-5423	186	234	ω	ω	NOUN
ejpam-5423	186	235	p)δ	p)δ	X
ejpam-5423	186	236	λ	λ	X
ejpam-5423	186	237	(	(	PUNCT
ejpam-5423	186	238	e	e	NOUN
ejpam-5423	186	239	)	)	PUNCT
ejpam-5423	186	240	and	and	CCONJ
ejpam-5423	186	241	(	(	PUNCT
ejpam-5423	186	242	g	g	PROPN
ejpam-5423	186	243	n	n	CCONJ
ejpam-5423	186	244	◦	◦	VERB
ejpam-5423	186	245	ωn)λ	ωn)λ	PROPN
ejpam-5423	186	246	δ	δ	PROPN
ejpam-5423	186	247	(	(	PUNCT
ejpam-5423	186	248	e	e	NOUN
ejpam-5423	186	249	)	)	PUNCT
ejpam-5423	186	250	≥	≥	NOUN
ejpam-5423	186	251	(	(	PUNCT
ejpam-5423	186	252	ω	ω	PROPN
ejpam-5423	186	253	n)λ	n)λ	X
ejpam-5423	186	254	δ	δ	PROPN
ejpam-5423	186	255	(	(	PUNCT
ejpam-5423	186	256	e	e	NOUN
ejpam-5423	186	257	)	)	PUNCT
ejpam-5423	186	258	implies	imply	VERB
ejpam-5423	186	259	that	that	SCONJ
ejpam-5423	186	260	,	,	PUNCT
ejpam-5423	186	261	(	(	PUNCT
ejpam-5423	186	262	g	g	PROPN
ejpam-5423	186	263	p	p	PROPN
ejpam-5423	186	264	◦	◦	NOUN
ejpam-5423	186	265	ωp)δ	ωp)δ	PROPN
ejpam-5423	186	266	λ	λ	X
ejpam-5423	186	267	(	(	PUNCT
ejpam-5423	186	268	e	e	NOUN
ejpam-5423	186	269	)	)	PUNCT
ejpam-5423	186	270	∧	∧	NOUN
ejpam-5423	186	271	(	(	PUNCT
ejpam-5423	186	272	ωp	ωp	NOUN
ejpam-5423	186	273	◦	◦	NOUN
ejpam-5423	186	274	gp	gp	NOUN
ejpam-5423	186	275	)	)	PUNCT
ejpam-5423	187	1	δ	δ	PROPN
ejpam-5423	187	2	λ	λ	PROPN
ejpam-5423	187	3	(	(	PUNCT
ejpam-5423	187	4	r	r	NOUN
ejpam-5423	187	5	)	)	PUNCT
ejpam-5423	187	6	≤	≤	NOUN
ejpam-5423	187	7	(	(	PUNCT
ejpam-5423	187	8	ω	ω	NOUN
ejpam-5423	187	9	p)δ	p)δ	X
ejpam-5423	187	10	λ	λ	X
ejpam-5423	187	11	(	(	PUNCT
ejpam-5423	187	12	e	e	NOUN
ejpam-5423	187	13	)	)	PUNCT
ejpam-5423	187	14	and	and	CCONJ
ejpam-5423	187	15	(	(	PUNCT
ejpam-5423	187	16	g	g	PROPN
ejpam-5423	187	17	n	n	CCONJ
ejpam-5423	187	18	◦	◦	VERB
ejpam-5423	187	19	ωn)λ	ωn)λ	PROPN
ejpam-5423	187	20	δ	δ	PROPN
ejpam-5423	187	21	(	(	PUNCT
ejpam-5423	187	22	e	e	NOUN
ejpam-5423	187	23	)	)	PUNCT
ejpam-5423	187	24	∨	∨	NOUN
ejpam-5423	187	25	(	(	PUNCT
ejpam-5423	187	26	ωn	ωn	ADP
ejpam-5423	187	27	◦	◦	NOUN
ejpam-5423	187	28	gn	gn	PROPN
ejpam-5423	187	29	)	)	PUNCT
ejpam-5423	187	30	λ	λ	PROPN
ejpam-5423	187	31	δ	δ	PROPN
ejpam-5423	187	32	(	(	PUNCT
ejpam-5423	187	33	e	e	NOUN
ejpam-5423	187	34	)	)	PUNCT
ejpam-5423	187	35	≥	≥	NOUN
ejpam-5423	187	36	(	(	PUNCT
ejpam-5423	187	37	ω	ω	PROPN
ejpam-5423	187	38	n)λ	n)λ	X
ejpam-5423	187	39	δ	δ	PROPN
ejpam-5423	187	40	(	(	PUNCT
ejpam-5423	187	41	e	e	NOUN
ejpam-5423	187	42	)	)	PUNCT
ejpam-5423	187	43	.	.	PUNCT
ejpam-5423	188	1	hence	hence	ADV
ejpam-5423	188	2	t	t	PROPN
ejpam-5423	188	3	=	=	SYM
ejpam-5423	188	4	(	(	PUNCT
ejpam-5423	188	5	ω	ω	PROPN
ejpam-5423	188	6	p	p	PROPN
ejpam-5423	188	7	,	,	PUNCT
ejpam-5423	188	8	ω	ω	PROPN
ejpam-5423	188	9	n	n	CCONJ
ejpam-5423	188	10	)	)	PUNCT
ejpam-5423	188	11	is	be	AUX
ejpam-5423	188	12	an	an	DET
ejpam-5423	188	13	(	(	PUNCT
ejpam-5423	188	14	λ	λ	NOUN
ejpam-5423	188	15	,	,	PUNCT
ejpam-5423	188	16	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	188	17	quasi	quasi	NOUN
ejpam-5423	188	18	-	-	NOUN
ejpam-5423	188	19	ideal	ideal	NOUN
ejpam-5423	188	20	of	of	ADP
ejpam-5423	188	21	g.	g.	PROPN
ejpam-5423	188	22	the	the	DET
ejpam-5423	188	23	following	follow	VERB
ejpam-5423	188	24	theorem	theorem	NOUN
ejpam-5423	188	25	show	show	VERB
ejpam-5423	188	26	that	that	SCONJ
ejpam-5423	188	27	the	the	DET
ejpam-5423	188	28	(	(	PUNCT
ejpam-5423	188	29	λ	λ	NOUN
ejpam-5423	188	30	,	,	PUNCT
ejpam-5423	188	31	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	188	32	quasi	quasi	NOUN
ejpam-5423	188	33	-	-	ADJ
ejpam-5423	188	34	ideal	ideal	ADJ
ejpam-5423	188	35	and	and	CCONJ
ejpam-5423	188	36	(	(	PUNCT
ejpam-5423	188	37	λ	λ	PROPN
ejpam-5423	188	38	,	,	PUNCT
ejpam-5423	188	39	δ)-ivbf	δ)-ivbf	NOUN
ejpam-5423	188	40	subsemigroups	subsemigroup	NOUN
ejpam-5423	188	41	.	.	PUNCT
ejpam-5423	188	42	theorem	theorem	VERB
ejpam-5423	188	43	3	3	NUM
ejpam-5423	188	44	.	.	PUNCT
ejpam-5423	189	1	every	every	DET
ejpam-5423	189	2	(	(	PUNCT
ejpam-5423	189	3	λ	λ	NOUN
ejpam-5423	189	4	,	,	PUNCT
ejpam-5423	189	5	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	189	6	quasi	quasi	NOUN
ejpam-5423	189	7	-	-	NOUN
ejpam-5423	189	8	ideal	ideal	ADJ
ejpam-5423	189	9	of	of	ADP
ejpam-5423	189	10	an	an	DET
ejpam-5423	189	11	ordered	order	VERB
ejpam-5423	189	12	semigroup	semigroup	NOUN
ejpam-5423	189	13	g	g	PROPN
ejpam-5423	189	14	is	be	AUX
ejpam-5423	189	15	an	an	DET
ejpam-5423	189	16	(	(	PUNCT
ejpam-5423	189	17	λ	λ	NOUN
ejpam-5423	189	18	,	,	PUNCT
ejpam-5423	189	19	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	189	20	subsemigroup	subsemigroup	NOUN
ejpam-5423	189	21	of	of	ADP
ejpam-5423	189	22	g.	g.	PROPN
ejpam-5423	189	23	proof	proof	PROPN
ejpam-5423	189	24	.	.	PUNCT
ejpam-5423	190	1	assume	assume	VERB
ejpam-5423	190	2	that	that	SCONJ
ejpam-5423	190	3	t	t	NOUN
ejpam-5423	190	4	=	=	SYM
ejpam-5423	190	5	(	(	PUNCT
ejpam-5423	190	6	ω	ω	PROPN
ejpam-5423	190	7	p	p	PROPN
ejpam-5423	190	8	,	,	PUNCT
ejpam-5423	190	9	ω	ω	PROPN
ejpam-5423	190	10	n	n	CCONJ
ejpam-5423	190	11	)	)	PUNCT
ejpam-5423	190	12	is	be	AUX
ejpam-5423	190	13	an	an	DET
ejpam-5423	190	14	(	(	PUNCT
ejpam-5423	190	15	λ	λ	NOUN
ejpam-5423	190	16	,	,	PUNCT
ejpam-5423	190	17	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	190	18	quasi	quasi	NOUN
ejpam-5423	190	19	-	-	NOUN
ejpam-5423	190	20	ideal	ideal	ADJ
ejpam-5423	190	21	of	of	ADP
ejpam-5423	190	22	g	g	NOUN
ejpam-5423	190	23	and	and	CCONJ
ejpam-5423	190	24	let	let	VERB
ejpam-5423	190	25	e1	e1	NOUN
ejpam-5423	190	26	,	,	PUNCT
ejpam-5423	190	27	e2	e2	PROPN
ejpam-5423	190	28	∈	∈	PROPN
ejpam-5423	190	29	g	g	PROPN
ejpam-5423	190	30	with	with	ADP
ejpam-5423	190	31	e1	e1	PROPN
ejpam-5423	190	32	≥	≥	PROPN
ejpam-5423	190	33	e2	e2	PROPN
ejpam-5423	190	34	.	.	PUNCT
ejpam-5423	191	1	then	then	ADV
ejpam-5423	191	2	ω	ω	NUM
ejpam-5423	191	3	p(e1	p(e1	NOUN
ejpam-5423	191	4	)	)	PUNCT
ejpam-5423	191	5	∨	∨	PROPN
ejpam-5423	191	6	λ	λ	PROPN
ejpam-5423	191	7	p	p	X
ejpam-5423	191	8	≥	≥	PROPN
ejpam-5423	191	9	ω	ω	NUM
ejpam-5423	191	10	p(e2	p(e2	NOUN
ejpam-5423	191	11	)	)	PUNCT
ejpam-5423	191	12	∧	∧	PROPN
ejpam-5423	191	13	δ	δ	PROPN
ejpam-5423	191	14	p	p	NOUN
ejpam-5423	191	15	and	and	CCONJ
ejpam-5423	191	16	ω	ω	NUM
ejpam-5423	191	17	n(e1	n(e1	NOUN
ejpam-5423	191	18	)	)	PUNCT
ejpam-5423	191	19	∧	∧	PROPN
ejpam-5423	191	20	λ	λ	PROPN
ejpam-5423	191	21	n	n	CCONJ
ejpam-5423	191	22	≤	≤	PROPN
ejpam-5423	191	23	ω	ω	NUM
ejpam-5423	191	24	n(e2	n(e2	PROPN
ejpam-5423	191	25	)	)	PUNCT
ejpam-5423	191	26	∨	∨	NUM
ejpam-5423	191	27	δ	δ	PROPN
ejpam-5423	191	28	n.	n.	PROPN
ejpam-5423	191	29	t.	t.	PROPN
ejpam-5423	191	30	gaketem	gaketem	PROPN
ejpam-5423	191	31	,	,	PUNCT
ejpam-5423	191	32	t.	t.	PROPN
ejpam-5423	191	33	prommai	prommai	PROPN
ejpam-5423	191	34	/	/	SYM
ejpam-5423	191	35	eur	eur	PROPN
ejpam-5423	191	36	.	.	PUNCT
ejpam-5423	192	1	j.	j.	PROPN
ejpam-5423	192	2	pure	pure	PROPN
ejpam-5423	192	3	appl	appl	PROPN
ejpam-5423	192	4	.	.	PROPN
ejpam-5423	192	5	math	math	PROPN
ejpam-5423	192	6	,	,	PUNCT
ejpam-5423	192	7	17	17	NUM
ejpam-5423	192	8	(	(	PUNCT
ejpam-5423	192	9	4	4	NUM
ejpam-5423	192	10	)	)	PUNCT
ejpam-5423	192	11	(	(	PUNCT
ejpam-5423	192	12	2024	2024	NUM
ejpam-5423	192	13	)	)	PUNCT
ejpam-5423	192	14	,	,	PUNCT
ejpam-5423	192	15	3223	3223	NUM
ejpam-5423	192	16	-	-	SYM
ejpam-5423	192	17	3241	3241	NUM
ejpam-5423	192	18	3231	3231	NUM
ejpam-5423	192	19	consider	consider	VERB
ejpam-5423	192	20	ωp(e1e2	ωp(e1e2	NOUN
ejpam-5423	192	21	)	)	PUNCT
ejpam-5423	192	22	∨	∨	NUM
ejpam-5423	192	23	λ	λ	PROPN
ejpam-5423	192	24	p	p	NOUN
ejpam-5423	192	25	≥	≥	PROPN
ejpam-5423	192	26	ωp(e1e2	ωp(e1e2	SYM
ejpam-5423	192	27	)	)	PUNCT
ejpam-5423	192	28	∧	∧	PROPN
ejpam-5423	192	29	δ	δ	PROPN
ejpam-5423	192	30	p	p	PROPN
ejpam-5423	192	31	∨	∨	NUM
ejpam-5423	192	32	λ	λ	PROPN
ejpam-5423	192	33	p	p	X
ejpam-5423	192	34	≥	≥	X
ejpam-5423	192	35	(	(	PUNCT
ejpam-5423	192	36	ωp	ωp	ADP
ejpam-5423	192	37	◦	◦	NOUN
ejpam-5423	192	38	gp	gp	NOUN
ejpam-5423	192	39	)	)	PUNCT
ejpam-5423	193	1	δ	δ	PROPN
ejpam-5423	193	2	λ	λ	PROPN
ejpam-5423	193	3	(	(	PUNCT
ejpam-5423	193	4	e1e2	e1e2	NOUN
ejpam-5423	193	5	)	)	PUNCT
ejpam-5423	193	6	∧	∧	NOUN
ejpam-5423	193	7	(	(	PUNCT
ejpam-5423	193	8	g	g	PROPN
ejpam-5423	193	9	p	p	PROPN
ejpam-5423	193	10	◦	◦	NOUN
ejpam-5423	193	11	ωp)δ	ωp)δ	PROPN
ejpam-5423	193	12	λ	λ	NOUN
ejpam-5423	193	13	(	(	PUNCT
ejpam-5423	193	14	e1e2	e1e2	X
ejpam-5423	193	15	)	)	PUNCT
ejpam-5423	193	16	=	=	SYM
ejpam-5423	193	17	(	(	PUNCT
ejpam-5423	193	18	∨	∨	X
ejpam-5423	193	19	(	(	PUNCT
ejpam-5423	193	20	i	i	PROPN
ejpam-5423	193	21	,	,	PUNCT
ejpam-5423	193	22	j)∈ae1e2	j)∈ae1e2	PROPN
ejpam-5423	193	23	{	{	PUNCT
ejpam-5423	193	24	ωp(i	ωp(i	NOUN
ejpam-5423	193	25	)	)	PUNCT
ejpam-5423	193	26	∧g	∧g	PROPN
ejpam-5423	193	27	p	p	X
ejpam-5423	193	28	(	(	PUNCT
ejpam-5423	193	29	j	j	NOUN
ejpam-5423	193	30	)	)	PUNCT
ejpam-5423	193	31	}	}	PUNCT
ejpam-5423	193	32	∧	∧	PROPN
ejpam-5423	193	33	δ	δ	PROPN
ejpam-5423	193	34	p	p	NOUN
ejpam-5423	193	35	)	)	PUNCT
ejpam-5423	193	36	∨	∨	NUM
ejpam-5423	193	37	λ	λ	PROPN
ejpam-5423	193	38	p∧	p∧	NOUN
ejpam-5423	193	39	(	(	PUNCT
ejpam-5423	193	40	∨	∨	X
ejpam-5423	193	41	(	(	PUNCT
ejpam-5423	193	42	k	k	X
ejpam-5423	193	43	,	,	PUNCT
ejpam-5423	193	44	o)∈ae1e2	o)∈ae1e2	PROPN
ejpam-5423	193	45	{	{	PUNCT
ejpam-5423	193	46	gp	gp	NOUN
ejpam-5423	193	47	(	(	PUNCT
ejpam-5423	193	48	k	k	NOUN
ejpam-5423	193	49	)	)	PUNCT
ejpam-5423	193	50	∧	∧	NOUN
ejpam-5423	193	51	ωp(o	ωp(o	NOUN
ejpam-5423	193	52	)	)	PUNCT
ejpam-5423	193	53	}	}	PUNCT
ejpam-5423	193	54	∧	∧	PROPN
ejpam-5423	193	55	δ	δ	PROPN
ejpam-5423	193	56	p	p	NOUN
ejpam-5423	193	57	)	)	PUNCT
ejpam-5423	193	58	∨	∨	NUM
ejpam-5423	193	59	λ	λ	PROPN
ejpam-5423	193	60	p	p	X
ejpam-5423	193	61	≥	≥	X
ejpam-5423	193	62	(	(	PUNCT
ejpam-5423	193	63	ωp(e1	ωp(e1	NOUN
ejpam-5423	193	64	)	)	PUNCT
ejpam-5423	193	65	∧g	∧g	PROPN
ejpam-5423	193	66	p	p	X
ejpam-5423	193	67	(	(	PUNCT
ejpam-5423	193	68	e2	e2	PROPN
ejpam-5423	193	69	)	)	PUNCT
ejpam-5423	193	70	∧	∧	PROPN
ejpam-5423	193	71	δ	δ	PROPN
ejpam-5423	193	72	p	p	PROPN
ejpam-5423	193	73	∨	∨	NUM
ejpam-5423	193	74	λ	λ	PROPN
ejpam-5423	193	75	p	p	NOUN
ejpam-5423	193	76	)	)	PUNCT
ejpam-5423	193	77	∧	∧	PROPN
ejpam-5423	193	78	(	(	PUNCT
ejpam-5423	193	79	g	g	PROPN
ejpam-5423	193	80	p	p	X
ejpam-5423	193	81	(	(	PUNCT
ejpam-5423	193	82	e1	e1	PROPN
ejpam-5423	193	83	)	)	PUNCT
ejpam-5423	193	84	∧	∧	NOUN
ejpam-5423	193	85	ωp(e2	ωp(e2	NOUN
ejpam-5423	193	86	)	)	PUNCT
ejpam-5423	193	87	∧	∧	PROPN
ejpam-5423	193	88	δ	δ	PROPN
ejpam-5423	193	89	p	p	PROPN
ejpam-5423	193	90	∨	∨	NUM
ejpam-5423	193	91	λ	λ	PROPN
ejpam-5423	193	92	p	p	NOUN
ejpam-5423	193	93	)	)	PUNCT
ejpam-5423	193	94	=	=	SYM
ejpam-5423	193	95	(	(	PUNCT
ejpam-5423	193	96	ωp(e1	ωp(e1	NOUN
ejpam-5423	193	97	)	)	PUNCT
ejpam-5423	193	98	∧	∧	NOUN
ejpam-5423	193	99	1	1	NUM
ejpam-5423	193	100	∧	∧	PROPN
ejpam-5423	193	101	δ	δ	PROPN
ejpam-5423	193	102	p	p	NOUN
ejpam-5423	193	103	∨	∨	NUM
ejpam-5423	193	104	λ	λ	PROPN
ejpam-5423	193	105	p	p	NOUN
ejpam-5423	193	106	)	)	PUNCT
ejpam-5423	193	107	∧	∧	PROPN
ejpam-5423	193	108	(	(	PUNCT
ejpam-5423	193	109	1	1	NUM
ejpam-5423	193	110	∧	∧	PROPN
ejpam-5423	193	111	ωp(e2	ωp(e2	NOUN
ejpam-5423	193	112	)	)	PUNCT
ejpam-5423	193	113	∧	∧	PROPN
ejpam-5423	193	114	δ	δ	PROPN
ejpam-5423	193	115	p	p	PROPN
ejpam-5423	193	116	∨	∨	NUM
ejpam-5423	193	117	λ	λ	PROPN
ejpam-5423	193	118	p	p	NOUN
ejpam-5423	193	119	)	)	PUNCT
ejpam-5423	193	120	=	=	SYM
ejpam-5423	193	121	(	(	PUNCT
ejpam-5423	193	122	ωp(e1	ωp(e1	NOUN
ejpam-5423	193	123	)	)	PUNCT
ejpam-5423	193	124	∧	∧	PROPN
ejpam-5423	193	125	δ	δ	PROPN
ejpam-5423	193	126	p	p	PROPN
ejpam-5423	193	127	∨	∨	NUM
ejpam-5423	193	128	λ	λ	PROPN
ejpam-5423	193	129	p	p	NOUN
ejpam-5423	193	130	)	)	PUNCT
ejpam-5423	193	131	∧	∧	PROPN
ejpam-5423	193	132	(	(	PUNCT
ejpam-5423	193	133	µp(e2	µp(e2	NOUN
ejpam-5423	193	134	)	)	PUNCT
ejpam-5423	193	135	∧	∧	PROPN
ejpam-5423	193	136	δ	δ	PROPN
ejpam-5423	193	137	p	p	PROPN
ejpam-5423	193	138	∨	∨	NUM
ejpam-5423	193	139	λ	λ	PROPN
ejpam-5423	193	140	p	p	NOUN
ejpam-5423	193	141	)	)	PUNCT
ejpam-5423	193	142	=	=	SYM
ejpam-5423	193	143	(	(	PUNCT
ejpam-5423	193	144	ωp(e1	ωp(e1	NOUN
ejpam-5423	193	145	)	)	PUNCT
ejpam-5423	193	146	∧	∧	PROPN
ejpam-5423	193	147	ωp(e2	ωp(e2	NOUN
ejpam-5423	193	148	)	)	PUNCT
ejpam-5423	193	149	)	)	PUNCT
ejpam-5423	194	1	∧	∧	PROPN
ejpam-5423	194	2	δ	δ	PROPN
ejpam-5423	194	3	p	p	NOUN
ejpam-5423	194	4	∨	∨	NUM
ejpam-5423	194	5	λ	λ	PROPN
ejpam-5423	194	6	p	p	X
ejpam-5423	194	7	=	=	NOUN
ejpam-5423	194	8	ωp(e1	ωp(e1	NOUN
ejpam-5423	194	9	)	)	PUNCT
ejpam-5423	194	10	∧	∧	PROPN
ejpam-5423	194	11	ωp(e2	ωp(e2	NOUN
ejpam-5423	194	12	)	)	PUNCT
ejpam-5423	194	13	∧	∧	PROPN
ejpam-5423	194	14	δ	δ	PROPN
ejpam-5423	194	15	p	p	PROPN
ejpam-5423	194	16	∨	∨	NUM
ejpam-5423	194	17	λ	λ	PROPN
ejpam-5423	194	18	p	p	NOUN
ejpam-5423	194	19	≥	≥	PROPN
ejpam-5423	194	20	ωp(e1	ωp(e1	NOUN
ejpam-5423	194	21	)	)	PUNCT
ejpam-5423	194	22	∧	∧	PROPN
ejpam-5423	194	23	ωp(e2	ωp(e2	NOUN
ejpam-5423	194	24	)	)	PUNCT
ejpam-5423	194	25	∧	∧	PROPN
ejpam-5423	194	26	δ	δ	PROPN
ejpam-5423	194	27	p	p	NOUN
ejpam-5423	194	28	and	and	CCONJ
ejpam-5423	194	29	ωn(e1e2	ωn(e1e2	PROPN
ejpam-5423	194	30	)	)	PUNCT
ejpam-5423	194	31	∧	∧	PROPN
ejpam-5423	194	32	λ	λ	PROPN
ejpam-5423	194	33	n	n	CCONJ
ejpam-5423	194	34	≤	≤	NUM
ejpam-5423	194	35	ωp(e1e2	ωp(e1e2	NOUN
ejpam-5423	194	36	)	)	PUNCT
ejpam-5423	194	37	∧	∧	PROPN
ejpam-5423	194	38	λ	λ	PROPN
ejpam-5423	194	39	n	n	CCONJ
ejpam-5423	194	40	∨	∨	NUM
ejpam-5423	194	41	δ	δ	PROPN
ejpam-5423	194	42	n	n	CCONJ
ejpam-5423	194	43	≤	≤	NUM
ejpam-5423	194	44	(	(	PUNCT
ejpam-5423	194	45	ωn	ωn	ADP
ejpam-5423	194	46	◦	◦	NOUN
ejpam-5423	194	47	gn	gn	NOUN
ejpam-5423	194	48	)	)	PUNCT
ejpam-5423	194	49	λ	λ	PROPN
ejpam-5423	194	50	δ	δ	PROPN
ejpam-5423	194	51	(	(	PUNCT
ejpam-5423	194	52	e1e2	e1e2	NOUN
ejpam-5423	194	53	)	)	PUNCT
ejpam-5423	194	54	∨	∨	NOUN
ejpam-5423	194	55	(	(	PUNCT
ejpam-5423	194	56	g	g	NOUN
ejpam-5423	194	57	n	n	PRON
ejpam-5423	194	58	◦	◦	VERB
ejpam-5423	194	59	ωn)λ	ωn)λ	PROPN
ejpam-5423	194	60	δ	δ	PROPN
ejpam-5423	194	61	(	(	PUNCT
ejpam-5423	194	62	e1e2	e1e2	X
ejpam-5423	194	63	)	)	PUNCT
ejpam-5423	194	64	=	=	SYM
ejpam-5423	194	65	(	(	PUNCT
ejpam-5423	194	66	∧	∧	PROPN
ejpam-5423	194	67	(	(	PUNCT
ejpam-5423	194	68	i	i	PROPN
ejpam-5423	194	69	,	,	PUNCT
ejpam-5423	194	70	j)∈ae1e2	j)∈ae1e2	PROPN
ejpam-5423	194	71	{	{	PUNCT
ejpam-5423	194	72	ωn(i	ωn(i	NOUN
ejpam-5423	194	73	)	)	PUNCT
ejpam-5423	194	74	∨g	∨g	PROPN
ejpam-5423	194	75	n	n	CCONJ
ejpam-5423	194	76	(	(	PUNCT
ejpam-5423	194	77	j	j	NOUN
ejpam-5423	194	78	)	)	PUNCT
ejpam-5423	194	79	}	}	PUNCT
ejpam-5423	194	80	∧	∧	PROPN
ejpam-5423	194	81	λ	λ	PROPN
ejpam-5423	194	82	n	n	CCONJ
ejpam-5423	194	83	)	)	PUNCT
ejpam-5423	194	84	∨	∨	PROPN
ejpam-5423	194	85	δ	δ	PROPN
ejpam-5423	194	86	n∨	n∨	PROPN
ejpam-5423	194	87	(	(	PUNCT
ejpam-5423	194	88	∧	∧	PROPN
ejpam-5423	194	89	(	(	PUNCT
ejpam-5423	194	90	k	k	X
ejpam-5423	194	91	,	,	PUNCT
ejpam-5423	194	92	o)∈ae1e2	o)∈ae1e2	PROPN
ejpam-5423	194	93	{	{	PUNCT
ejpam-5423	194	94	gn	gn	PROPN
ejpam-5423	194	95	(	(	PUNCT
ejpam-5423	194	96	k	k	NOUN
ejpam-5423	194	97	)	)	PUNCT
ejpam-5423	194	98	∨	∨	NUM
ejpam-5423	194	99	ωn(o	ωn(o	NUM
ejpam-5423	194	100	)	)	PUNCT
ejpam-5423	194	101	}	}	PUNCT
ejpam-5423	194	102	∧	∧	PROPN
ejpam-5423	194	103	λ	λ	PROPN
ejpam-5423	194	104	n	n	CCONJ
ejpam-5423	194	105	)	)	PUNCT
ejpam-5423	194	106	∨	∨	NUM
ejpam-5423	194	107	δ	δ	PROPN
ejpam-5423	194	108	n	n	CCONJ
ejpam-5423	194	109	≤	≤	NUM
ejpam-5423	194	110	(	(	PUNCT
ejpam-5423	194	111	ωn(e1	ωn(e1	NOUN
ejpam-5423	194	112	)	)	PUNCT
ejpam-5423	194	113	∨g	∨g	NOUN
ejpam-5423	194	114	n	n	CCONJ
ejpam-5423	194	115	(	(	PUNCT
ejpam-5423	194	116	e2	e2	PROPN
ejpam-5423	194	117	)	)	PUNCT
ejpam-5423	194	118	∧	∧	PROPN
ejpam-5423	194	119	λ	λ	PROPN
ejpam-5423	194	120	n	n	CCONJ
ejpam-5423	194	121	∨	∨	NUM
ejpam-5423	194	122	δ	δ	PROPN
ejpam-5423	194	123	n	n	CCONJ
ejpam-5423	194	124	)	)	PUNCT
ejpam-5423	194	125	∨	∨	PROPN
ejpam-5423	194	126	(	(	PUNCT
ejpam-5423	194	127	g	g	PROPN
ejpam-5423	194	128	n	n	PROPN
ejpam-5423	194	129	(	(	PUNCT
ejpam-5423	194	130	e1	e1	PROPN
ejpam-5423	194	131	)	)	PUNCT
ejpam-5423	194	132	∨	∨	NUM
ejpam-5423	194	133	ωn(e2	ωn(e2	NOUN
ejpam-5423	194	134	)	)	PUNCT
ejpam-5423	194	135	∧	∧	PROPN
ejpam-5423	194	136	λ	λ	PROPN
ejpam-5423	194	137	n	n	CCONJ
ejpam-5423	194	138	∨	∨	NUM
ejpam-5423	194	139	δ	δ	PROPN
ejpam-5423	194	140	n	n	PART
ejpam-5423	194	141	)	)	PUNCT
ejpam-5423	194	142	=	=	SYM
ejpam-5423	194	143	(	(	PUNCT
ejpam-5423	194	144	ωn(e1	ωn(e1	NOUN
ejpam-5423	194	145	)	)	PUNCT
ejpam-5423	194	146	∨	∨	NUM
ejpam-5423	194	147	−1	−1	NOUN
ejpam-5423	194	148	∧	∧	PROPN
ejpam-5423	194	149	λ	λ	PROPN
ejpam-5423	194	150	n	n	CCONJ
ejpam-5423	194	151	∨	∨	NUM
ejpam-5423	194	152	δ	δ	PROPN
ejpam-5423	194	153	n	n	CCONJ
ejpam-5423	194	154	)	)	PUNCT
ejpam-5423	194	155	∨	∨	NOUN
ejpam-5423	194	156	(	(	PUNCT
ejpam-5423	194	157	−1	−1	NOUN
ejpam-5423	194	158	∨	∨	NUM
ejpam-5423	194	159	ωn(e2	ωn(e2	NOUN
ejpam-5423	194	160	)	)	PUNCT
ejpam-5423	194	161	∧	∧	PROPN
ejpam-5423	194	162	λ	λ	PROPN
ejpam-5423	194	163	n	n	CCONJ
ejpam-5423	194	164	∨	∨	NUM
ejpam-5423	194	165	δ	δ	PROPN
ejpam-5423	194	166	n	n	PART
ejpam-5423	194	167	)	)	PUNCT
ejpam-5423	194	168	=	=	SYM
ejpam-5423	194	169	(	(	PUNCT
ejpam-5423	194	170	ωn(e1	ωn(e1	NOUN
ejpam-5423	194	171	)	)	PUNCT
ejpam-5423	194	172	∧	∧	NOUN
ejpam-5423	194	173	λ	λ	PROPN
ejpam-5423	194	174	n	n	CCONJ
ejpam-5423	194	175	∨	∨	NUM
ejpam-5423	194	176	δ	δ	PROPN
ejpam-5423	194	177	n	n	CCONJ
ejpam-5423	194	178	)	)	PUNCT
ejpam-5423	194	179	∨	∨	PROPN
ejpam-5423	194	180	(	(	PUNCT
ejpam-5423	194	181	ωn(e2	ωn(e2	NOUN
ejpam-5423	194	182	)	)	PUNCT
ejpam-5423	194	183	∧	∧	PROPN
ejpam-5423	194	184	λ	λ	PROPN
ejpam-5423	194	185	n	n	CCONJ
ejpam-5423	194	186	∨	∨	NUM
ejpam-5423	194	187	δ	δ	PROPN
ejpam-5423	194	188	n	n	PART
ejpam-5423	194	189	)	)	PUNCT
ejpam-5423	194	190	=	=	SYM
ejpam-5423	194	191	(	(	PUNCT
ejpam-5423	194	192	ωn(e1	ωn(e1	NOUN
ejpam-5423	194	193	)	)	PUNCT
ejpam-5423	194	194	∨	∨	NUM
ejpam-5423	194	195	ωn(e2	ωn(e2	NUM
ejpam-5423	194	196	)	)	PUNCT
ejpam-5423	194	197	)	)	PUNCT
ejpam-5423	195	1	∧	∧	PROPN
ejpam-5423	195	2	λ	λ	PROPN
ejpam-5423	195	3	n	n	CCONJ
ejpam-5423	195	4	∨	∨	NUM
ejpam-5423	195	5	δ	δ	PROPN
ejpam-5423	195	6	n	n	CCONJ
ejpam-5423	195	7	=	=	SYM
ejpam-5423	195	8	ωn(e1	ωn(e1	NUM
ejpam-5423	195	9	)	)	PUNCT
ejpam-5423	195	10	∨	∨	NUM
ejpam-5423	195	11	ωnp(e2	ωnp(e2	PROPN
ejpam-5423	195	12	)	)	PUNCT
ejpam-5423	195	13	∧	∧	PROPN
ejpam-5423	195	14	λ	λ	PROPN
ejpam-5423	195	15	n	n	CCONJ
ejpam-5423	195	16	∨	∨	NUM
ejpam-5423	195	17	δ	δ	PROPN
ejpam-5423	195	18	n	n	CCONJ
ejpam-5423	195	19	≤	≤	NUM
ejpam-5423	195	20	ωn(e1	ωn(e1	NUM
ejpam-5423	195	21	)	)	PUNCT
ejpam-5423	195	22	∨	∨	NUM
ejpam-5423	195	23	ωn(e2	ωn(e2	NOUN
ejpam-5423	195	24	)	)	PUNCT
ejpam-5423	195	25	∨	∨	NUM
ejpam-5423	195	26	δ	δ	PROPN
ejpam-5423	195	27	n	n	X
ejpam-5423	195	28	.	.	PUNCT
ejpam-5423	196	1	thus	thus	ADV
ejpam-5423	196	2	,	,	PUNCT
ejpam-5423	196	3	ωp(e1e2	ωp(e1e2	X
ejpam-5423	196	4	)	)	PUNCT
ejpam-5423	196	5	∨	∨	NUM
ejpam-5423	196	6	λ	λ	PROPN
ejpam-5423	196	7	p	p	NOUN
ejpam-5423	196	8	≥	≥	PROPN
ejpam-5423	196	9	ωp(e1	ωp(e1	NOUN
ejpam-5423	196	10	)	)	PUNCT
ejpam-5423	196	11	∧	∧	PROPN
ejpam-5423	196	12	ωp(e2	ωp(e2	NOUN
ejpam-5423	196	13	)	)	PUNCT
ejpam-5423	196	14	∧	∧	PROPN
ejpam-5423	196	15	δ	δ	PROPN
ejpam-5423	196	16	p	p	NOUN
ejpam-5423	196	17	and	and	CCONJ
ejpam-5423	196	18	ωn(e1e2	ωn(e1e2	PROPN
ejpam-5423	196	19	)	)	PUNCT
ejpam-5423	196	20	∧	∧	PROPN
ejpam-5423	196	21	λ	λ	PROPN
ejpam-5423	196	22	n	n	CCONJ
ejpam-5423	196	23	≤	≤	NUM
ejpam-5423	196	24	ωn(e1	ωn(e1	NUM
ejpam-5423	196	25	)	)	PUNCT
ejpam-5423	196	26	∨	∨	NUM
ejpam-5423	196	27	ωn(e2	ωn(e2	NOUN
ejpam-5423	196	28	)	)	PUNCT
ejpam-5423	196	29	∨	∨	NUM
ejpam-5423	196	30	δ	δ	PROPN
ejpam-5423	196	31	n	n	X
ejpam-5423	196	32	.	.	PUNCT
ejpam-5423	197	1	hence	hence	ADV
ejpam-5423	197	2	t	t	PROPN
ejpam-5423	197	3	=	=	SYM
ejpam-5423	197	4	(	(	PUNCT
ejpam-5423	197	5	ω	ω	PROPN
ejpam-5423	197	6	p	p	PROPN
ejpam-5423	197	7	,	,	PUNCT
ejpam-5423	197	8	ω	ω	PROPN
ejpam-5423	197	9	n	n	CCONJ
ejpam-5423	197	10	)	)	PUNCT
ejpam-5423	197	11	is	be	AUX
ejpam-5423	197	12	an	an	DET
ejpam-5423	197	13	(	(	PUNCT
ejpam-5423	197	14	λ	λ	NOUN
ejpam-5423	197	15	,	,	PUNCT
ejpam-5423	197	16	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	197	17	subsemigroup	subsemigroup	NOUN
ejpam-5423	197	18	of	of	ADP
ejpam-5423	197	19	g.	g.	PROPN
ejpam-5423	197	20	the	the	DET
ejpam-5423	197	21	following	follow	VERB
ejpam-5423	197	22	theorem	theorem	NOUN
ejpam-5423	197	23	show	show	VERB
ejpam-5423	198	1	that	that	SCONJ
ejpam-5423	198	2	the	the	DET
ejpam-5423	198	3	(	(	PUNCT
ejpam-5423	198	4	λ	λ	NOUN
ejpam-5423	198	5	,	,	PUNCT
ejpam-5423	198	6	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	198	7	quasi	quasi	NOUN
ejpam-5423	198	8	-	-	ADJ
ejpam-5423	198	9	ideal	ideal	ADJ
ejpam-5423	198	10	and	and	CCONJ
ejpam-5423	198	11	(	(	PUNCT
ejpam-5423	198	12	λ	λ	PROPN
ejpam-5423	198	13	,	,	PUNCT
ejpam-5423	198	14	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	198	15	bi	bi	NOUN
ejpam-5423	198	16	-	-	NOUN
ejpam-5423	198	17	ideal	ideal	NOUN
ejpam-5423	198	18	in	in	ADP
ejpam-5423	198	19	semigroup	semigroup	PROPN
ejpam-5423	198	20	.	.	PUNCT
ejpam-5423	198	21	theorem	theorem	VERB
ejpam-5423	198	22	4	4	NUM
ejpam-5423	198	23	.	.	PUNCT
ejpam-5423	199	1	every	every	DET
ejpam-5423	199	2	(	(	PUNCT
ejpam-5423	199	3	λ	λ	NOUN
ejpam-5423	199	4	,	,	PUNCT
ejpam-5423	199	5	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	199	6	quasi	quasi	NOUN
ejpam-5423	199	7	-	-	NOUN
ejpam-5423	199	8	ideal	ideal	ADJ
ejpam-5423	199	9	of	of	ADP
ejpam-5423	199	10	an	an	DET
ejpam-5423	199	11	ordered	order	VERB
ejpam-5423	199	12	semigroup	semigroup	NOUN
ejpam-5423	199	13	g	g	PROPN
ejpam-5423	199	14	is	be	AUX
ejpam-5423	199	15	a	a	DET
ejpam-5423	199	16	(	(	PUNCT
ejpam-5423	199	17	λ	λ	NOUN
ejpam-5423	199	18	,	,	PUNCT
ejpam-5423	199	19	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	199	20	bi	bi	NOUN
ejpam-5423	199	21	-	-	NOUN
ejpam-5423	199	22	ideal	ideal	NOUN
ejpam-5423	199	23	of	of	ADP
ejpam-5423	199	24	g.	g.	PROPN
ejpam-5423	199	25	proof	proof	PROPN
ejpam-5423	199	26	.	.	PUNCT
ejpam-5423	200	1	assume	assume	VERB
ejpam-5423	200	2	that	that	SCONJ
ejpam-5423	200	3	t	t	NOUN
ejpam-5423	200	4	=	=	SYM
ejpam-5423	200	5	(	(	PUNCT
ejpam-5423	200	6	ω	ω	PROPN
ejpam-5423	200	7	p	p	PROPN
ejpam-5423	200	8	,	,	PUNCT
ejpam-5423	200	9	ω	ω	PROPN
ejpam-5423	200	10	n	n	CCONJ
ejpam-5423	200	11	)	)	PUNCT
ejpam-5423	200	12	is	be	AUX
ejpam-5423	200	13	an	an	DET
ejpam-5423	200	14	(	(	PUNCT
ejpam-5423	200	15	λ	λ	NOUN
ejpam-5423	200	16	,	,	PUNCT
ejpam-5423	200	17	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	200	18	quasi	quasi	NOUN
ejpam-5423	200	19	-	-	NOUN
ejpam-5423	200	20	ideal	ideal	ADJ
ejpam-5423	200	21	of	of	ADP
ejpam-5423	200	22	g	g	NOUN
ejpam-5423	200	23	and	and	CCONJ
ejpam-5423	200	24	let	let	VERB
ejpam-5423	200	25	e1	e1	NOUN
ejpam-5423	200	26	,	,	PUNCT
ejpam-5423	200	27	e2,∈	e2,∈	PROPN
ejpam-5423	200	28	g.	g.	NOUN
ejpam-5423	200	29	then	then	ADV
ejpam-5423	200	30	by	by	ADP
ejpam-5423	200	31	theorem	theorem	NOUN
ejpam-5423	200	32	3	3	NUM
ejpam-5423	200	33	,	,	PUNCT
ejpam-5423	200	34	t	t	NOUN
ejpam-5423	200	35	=	=	SYM
ejpam-5423	200	36	(	(	PUNCT
ejpam-5423	200	37	ω	ω	PROPN
ejpam-5423	200	38	p	p	PROPN
ejpam-5423	200	39	,	,	PUNCT
ejpam-5423	200	40	ω	ω	PROPN
ejpam-5423	200	41	n	n	CCONJ
ejpam-5423	200	42	)	)	PUNCT
ejpam-5423	200	43	is	be	AUX
ejpam-5423	200	44	an	an	DET
ejpam-5423	200	45	(	(	PUNCT
ejpam-5423	200	46	λ	λ	NOUN
ejpam-5423	200	47	,	,	PUNCT
ejpam-5423	200	48	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	200	49	subsemigroup	subsemigroup	NOUN
ejpam-5423	200	50	of	of	ADP
ejpam-5423	200	51	g.	g.	PROPN
ejpam-5423	200	52	t.	t.	PROPN
ejpam-5423	200	53	gaketem	gaketem	PROPN
ejpam-5423	200	54	,	,	PUNCT
ejpam-5423	200	55	t.	t.	PROPN
ejpam-5423	200	56	prommai	prommai	PROPN
ejpam-5423	200	57	/	/	SYM
ejpam-5423	200	58	eur	eur	PROPN
ejpam-5423	200	59	.	.	PUNCT
ejpam-5423	201	1	j.	j.	PROPN
ejpam-5423	201	2	pure	pure	PROPN
ejpam-5423	201	3	appl	appl	PROPN
ejpam-5423	201	4	.	.	PROPN
ejpam-5423	201	5	math	math	PROPN
ejpam-5423	201	6	,	,	PUNCT
ejpam-5423	201	7	17	17	NUM
ejpam-5423	201	8	(	(	PUNCT
ejpam-5423	201	9	4	4	NUM
ejpam-5423	201	10	)	)	PUNCT
ejpam-5423	201	11	(	(	PUNCT
ejpam-5423	201	12	2024	2024	NUM
ejpam-5423	201	13	)	)	PUNCT
ejpam-5423	201	14	,	,	PUNCT
ejpam-5423	201	15	3223	3223	NUM
ejpam-5423	201	16	-	-	SYM
ejpam-5423	201	17	3241	3241	NUM
ejpam-5423	201	18	3232	3232	NUM
ejpam-5423	201	19	let	let	VERB
ejpam-5423	201	20	e1	e1	PROPN
ejpam-5423	201	21	,	,	PUNCT
ejpam-5423	201	22	e2	e2	PROPN
ejpam-5423	201	23	,	,	PUNCT
ejpam-5423	201	24	e3	e3	PROPN
ejpam-5423	201	25	∈	∈	PROPN
ejpam-5423	201	26	g.	g.	NOUN
ejpam-5423	201	27	then	then	ADV
ejpam-5423	201	28	ωp(e1e2e3	ωp(e1e2e3	NUM
ejpam-5423	201	29	)	)	PUNCT
ejpam-5423	201	30	∨	∨	NUM
ejpam-5423	202	1	λ	λ	PROPN
ejpam-5423	202	2	p	p	NOUN
ejpam-5423	202	3	≥	≥	NUM
ejpam-5423	202	4	ωp(e1e2e3	ωp(e1e2e3	SYM
ejpam-5423	202	5	)	)	PUNCT
ejpam-5423	202	6	∧	∧	PROPN
ejpam-5423	202	7	δ	δ	PROPN
ejpam-5423	202	8	p	p	PROPN
ejpam-5423	202	9	∨	∨	NUM
ejpam-5423	202	10	λ	λ	PROPN
ejpam-5423	202	11	p	p	X
ejpam-5423	202	12	≥	≥	X
ejpam-5423	202	13	(	(	PUNCT
ejpam-5423	202	14	ωp	ωp	ADP
ejpam-5423	202	15	◦	◦	NOUN
ejpam-5423	202	16	gp	gp	NOUN
ejpam-5423	202	17	)	)	PUNCT
ejpam-5423	202	18	δ	δ	PROPN
ejpam-5423	202	19	λ	λ	PROPN
ejpam-5423	202	20	(	(	PUNCT
ejpam-5423	202	21	e1e2e3	e1e2e3	NOUN
ejpam-5423	202	22	)	)	PUNCT
ejpam-5423	202	23	∧	∧	PROPN
ejpam-5423	202	24	(	(	PUNCT
ejpam-5423	202	25	g	g	PROPN
ejpam-5423	202	26	p	p	PROPN
ejpam-5423	202	27	◦	◦	NOUN
ejpam-5423	202	28	ωp)δ	ωp)δ	PROPN
ejpam-5423	202	29	λ	λ	NOUN
ejpam-5423	202	30	(	(	PUNCT
ejpam-5423	202	31	e1e2e3	e1e2e3	NOUN
ejpam-5423	202	32	)	)	PUNCT
ejpam-5423	202	33	=	=	SYM
ejpam-5423	202	34	(	(	PUNCT
ejpam-5423	202	35	∨	∨	X
ejpam-5423	202	36	(	(	PUNCT
ejpam-5423	202	37	i	i	PRON
ejpam-5423	202	38	,	,	PUNCT
ejpam-5423	202	39	j)∈ae1e2e3	j)∈ae1e2e3	PROPN
ejpam-5423	202	40	{	{	PUNCT
ejpam-5423	202	41	ωp(i	ωp(i	NOUN
ejpam-5423	202	42	)	)	PUNCT
ejpam-5423	202	43	∧g	∧g	PROPN
ejpam-5423	202	44	p	p	X
ejpam-5423	202	45	(	(	PUNCT
ejpam-5423	202	46	j	j	NOUN
ejpam-5423	202	47	)	)	PUNCT
ejpam-5423	202	48	}	}	PUNCT
ejpam-5423	202	49	∧	∧	PROPN
ejpam-5423	202	50	δ	δ	PROPN
ejpam-5423	202	51	p	p	NOUN
ejpam-5423	202	52	)	)	PUNCT
ejpam-5423	202	53	∨	∨	NUM
ejpam-5423	202	54	λ	λ	PROPN
ejpam-5423	202	55	p∧	p∧	NOUN
ejpam-5423	202	56	(	(	PUNCT
ejpam-5423	202	57	∨	∨	X
ejpam-5423	202	58	(	(	PUNCT
ejpam-5423	202	59	k	k	NOUN
ejpam-5423	202	60	,	,	PUNCT
ejpam-5423	202	61	o)∈ae1e2e3	o)∈ae1e2e3	PRON
ejpam-5423	202	62	{	{	PUNCT
ejpam-5423	202	63	gp	gp	NOUN
ejpam-5423	202	64	(	(	PUNCT
ejpam-5423	202	65	k	k	NOUN
ejpam-5423	202	66	)	)	PUNCT
ejpam-5423	202	67	∧	∧	NOUN
ejpam-5423	202	68	ωp(o	ωp(o	NOUN
ejpam-5423	202	69	)	)	PUNCT
ejpam-5423	202	70	}	}	PUNCT
ejpam-5423	202	71	∧	∧	PROPN
ejpam-5423	202	72	δ	δ	PROPN
ejpam-5423	202	73	p	p	NOUN
ejpam-5423	202	74	)	)	PUNCT
ejpam-5423	202	75	∨	∨	NUM
ejpam-5423	202	76	λ	λ	PROPN
ejpam-5423	202	77	p	p	X
ejpam-5423	202	78	≥	≥	X
ejpam-5423	202	79	(	(	PUNCT
ejpam-5423	202	80	ωp(e1	ωp(e1	NOUN
ejpam-5423	202	81	)	)	PUNCT
ejpam-5423	202	82	∧g	∧g	PROPN
ejpam-5423	202	83	p	p	X
ejpam-5423	202	84	(	(	PUNCT
ejpam-5423	202	85	e2e3	e2e3	NOUN
ejpam-5423	202	86	)	)	PUNCT
ejpam-5423	202	87	∧	∧	PROPN
ejpam-5423	202	88	δ	δ	PROPN
ejpam-5423	202	89	p	p	PROPN
ejpam-5423	202	90	∨	∨	NUM
ejpam-5423	202	91	λ	λ	PROPN
ejpam-5423	202	92	p	p	NOUN
ejpam-5423	202	93	)	)	PUNCT
ejpam-5423	202	94	∧	∧	PROPN
ejpam-5423	202	95	(	(	PUNCT
ejpam-5423	202	96	g	g	PROPN
ejpam-5423	202	97	p	p	X
ejpam-5423	202	98	(	(	PUNCT
ejpam-5423	202	99	e1e2	e1e2	NOUN
ejpam-5423	202	100	)	)	PUNCT
ejpam-5423	202	101	∧	∧	NOUN
ejpam-5423	202	102	ωp(e3	ωp(e3	NUM
ejpam-5423	202	103	)	)	PUNCT
ejpam-5423	202	104	∧	∧	PROPN
ejpam-5423	202	105	δ	δ	PROPN
ejpam-5423	202	106	p	p	PROPN
ejpam-5423	202	107	∨	∨	NUM
ejpam-5423	202	108	λ	λ	PROPN
ejpam-5423	202	109	p	p	NOUN
ejpam-5423	202	110	)	)	PUNCT
ejpam-5423	202	111	=	=	SYM
ejpam-5423	202	112	(	(	PUNCT
ejpam-5423	202	113	ωp(e1	ωp(e1	NOUN
ejpam-5423	202	114	)	)	PUNCT
ejpam-5423	202	115	∧	∧	NOUN
ejpam-5423	202	116	1	1	NUM
ejpam-5423	202	117	∧	∧	PROPN
ejpam-5423	202	118	δ	δ	PROPN
ejpam-5423	202	119	p	p	NOUN
ejpam-5423	202	120	∨	∨	NUM
ejpam-5423	202	121	λ	λ	PROPN
ejpam-5423	202	122	p	p	NOUN
ejpam-5423	202	123	)	)	PUNCT
ejpam-5423	202	124	∧	∧	PROPN
ejpam-5423	202	125	(	(	PUNCT
ejpam-5423	202	126	1	1	NUM
ejpam-5423	202	127	∧	∧	PROPN
ejpam-5423	202	128	ωp(e3	ωp(e3	NUM
ejpam-5423	202	129	)	)	PUNCT
ejpam-5423	202	130	∧	∧	PROPN
ejpam-5423	202	131	δ	δ	PROPN
ejpam-5423	202	132	p	p	PROPN
ejpam-5423	202	133	∨	∨	NUM
ejpam-5423	202	134	λ	λ	PROPN
ejpam-5423	202	135	p	p	NOUN
ejpam-5423	202	136	)	)	PUNCT
ejpam-5423	202	137	=	=	SYM
ejpam-5423	202	138	(	(	PUNCT
ejpam-5423	202	139	ωp(e1	ωp(e1	NOUN
ejpam-5423	202	140	)	)	PUNCT
ejpam-5423	202	141	∧	∧	PROPN
ejpam-5423	202	142	δ	δ	PROPN
ejpam-5423	202	143	p	p	PROPN
ejpam-5423	202	144	∨	∨	NUM
ejpam-5423	202	145	λ	λ	PROPN
ejpam-5423	202	146	p	p	NOUN
ejpam-5423	202	147	)	)	PUNCT
ejpam-5423	202	148	∧	∧	PROPN
ejpam-5423	202	149	(	(	PUNCT
ejpam-5423	202	150	µp(e3	µp(e3	PROPN
ejpam-5423	202	151	)	)	PUNCT
ejpam-5423	202	152	∧	∧	PROPN
ejpam-5423	202	153	δ	δ	PROPN
ejpam-5423	202	154	p	p	PROPN
ejpam-5423	202	155	∨	∨	NUM
ejpam-5423	202	156	λ	λ	PROPN
ejpam-5423	202	157	p	p	NOUN
ejpam-5423	202	158	)	)	PUNCT
ejpam-5423	202	159	=	=	SYM
ejpam-5423	202	160	(	(	PUNCT
ejpam-5423	202	161	ωp(e1	ωp(e1	NOUN
ejpam-5423	202	162	)	)	PUNCT
ejpam-5423	202	163	∧	∧	NOUN
ejpam-5423	202	164	ωp(e3	ωp(e3	PROPN
ejpam-5423	202	165	)	)	PUNCT
ejpam-5423	202	166	)	)	PUNCT
ejpam-5423	203	1	∧	∧	PROPN
ejpam-5423	203	2	δ	δ	PROPN
ejpam-5423	203	3	p	p	NOUN
ejpam-5423	203	4	∨	∨	NUM
ejpam-5423	203	5	λ	λ	PROPN
ejpam-5423	203	6	p	p	X
ejpam-5423	203	7	=	=	NOUN
ejpam-5423	203	8	ωp(e1	ωp(e1	NOUN
ejpam-5423	203	9	)	)	PUNCT
ejpam-5423	203	10	∧	∧	PROPN
ejpam-5423	203	11	ωp(e3	ωp(e3	NUM
ejpam-5423	203	12	)	)	PUNCT
ejpam-5423	203	13	∧	∧	PROPN
ejpam-5423	203	14	δ	δ	PROPN
ejpam-5423	203	15	p	p	PROPN
ejpam-5423	203	16	∨	∨	NUM
ejpam-5423	203	17	λ	λ	PROPN
ejpam-5423	203	18	p	p	NOUN
ejpam-5423	203	19	≥	≥	NOUN
ejpam-5423	203	20	ωp(e1	ωp(e1	NOUN
ejpam-5423	203	21	)	)	PUNCT
ejpam-5423	203	22	∧	∧	PROPN
ejpam-5423	203	23	ωp(e3	ωp(e3	NUM
ejpam-5423	203	24	)	)	PUNCT
ejpam-5423	203	25	∧	∧	PROPN
ejpam-5423	203	26	δ	δ	PROPN
ejpam-5423	203	27	p	p	NOUN
ejpam-5423	203	28	and	and	CCONJ
ejpam-5423	203	29	ωn(e1e2e3	ωn(e1e2e3	NOUN
ejpam-5423	203	30	)	)	PUNCT
ejpam-5423	203	31	∧	∧	NOUN
ejpam-5423	203	32	λ	λ	PROPN
ejpam-5423	203	33	n	n	CCONJ
ejpam-5423	203	34	≤	≤	NUM
ejpam-5423	203	35	ωp(e1e2e3	ωp(e1e2e3	SYM
ejpam-5423	203	36	)	)	PUNCT
ejpam-5423	203	37	∧	∧	NOUN
ejpam-5423	203	38	λ	λ	PROPN
ejpam-5423	203	39	n	n	CCONJ
ejpam-5423	203	40	∨	∨	NUM
ejpam-5423	203	41	δ	δ	PROPN
ejpam-5423	203	42	n	n	CCONJ
ejpam-5423	203	43	≤	≤	NUM
ejpam-5423	203	44	(	(	PUNCT
ejpam-5423	203	45	ωn	ωn	ADP
ejpam-5423	203	46	◦	◦	NOUN
ejpam-5423	203	47	gn	gn	NOUN
ejpam-5423	203	48	)	)	PUNCT
ejpam-5423	203	49	λ	λ	PROPN
ejpam-5423	203	50	δ	δ	PROPN
ejpam-5423	203	51	(	(	PUNCT
ejpam-5423	203	52	e1e2e3	e1e2e3	NOUN
ejpam-5423	203	53	)	)	PUNCT
ejpam-5423	203	54	∨	∨	NOUN
ejpam-5423	203	55	(	(	PUNCT
ejpam-5423	203	56	g	g	NOUN
ejpam-5423	203	57	n	n	PRON
ejpam-5423	203	58	◦	◦	VERB
ejpam-5423	203	59	ωn)λ	ωn)λ	PROPN
ejpam-5423	203	60	δ	δ	PROPN
ejpam-5423	203	61	(	(	PUNCT
ejpam-5423	203	62	e1e2e3	e1e2e3	NOUN
ejpam-5423	203	63	)	)	PUNCT
ejpam-5423	203	64	=	=	PUNCT
ejpam-5423	204	1	(	(	PUNCT
ejpam-5423	204	2	∧	∧	PROPN
ejpam-5423	204	3	(	(	PUNCT
ejpam-5423	204	4	i	i	PROPN
ejpam-5423	204	5	,	,	PUNCT
ejpam-5423	204	6	j)∈ae1e2e3	j)∈ae1e2e3	PROPN
ejpam-5423	204	7	{	{	PUNCT
ejpam-5423	204	8	ωn(i	ωn(i	NOUN
ejpam-5423	204	9	)	)	PUNCT
ejpam-5423	204	10	∨g	∨g	NOUN
ejpam-5423	204	11	n	n	CCONJ
ejpam-5423	204	12	(	(	PUNCT
ejpam-5423	204	13	j	j	NOUN
ejpam-5423	204	14	)	)	PUNCT
ejpam-5423	204	15	}	}	PUNCT
ejpam-5423	204	16	∧	∧	PROPN
ejpam-5423	204	17	λ	λ	PROPN
ejpam-5423	204	18	n	n	CCONJ
ejpam-5423	204	19	)	)	PUNCT
ejpam-5423	204	20	∨	∨	PROPN
ejpam-5423	204	21	δ	δ	PROPN
ejpam-5423	204	22	n∨	n∨	PROPN
ejpam-5423	204	23	(	(	PUNCT
ejpam-5423	204	24	∧	∧	PROPN
ejpam-5423	204	25	(	(	PUNCT
ejpam-5423	204	26	k	k	NOUN
ejpam-5423	204	27	,	,	PUNCT
ejpam-5423	204	28	o)∈ae1e2e3	o)∈ae1e2e3	PRON
ejpam-5423	204	29	{	{	PUNCT
ejpam-5423	204	30	gn	gn	PROPN
ejpam-5423	204	31	(	(	PUNCT
ejpam-5423	204	32	k	k	NOUN
ejpam-5423	204	33	)	)	PUNCT
ejpam-5423	204	34	∨	∨	NUM
ejpam-5423	204	35	ωn(o	ωn(o	NUM
ejpam-5423	204	36	)	)	PUNCT
ejpam-5423	204	37	}	}	PUNCT
ejpam-5423	204	38	∧	∧	PROPN
ejpam-5423	204	39	λ	λ	PROPN
ejpam-5423	204	40	n	n	CCONJ
ejpam-5423	204	41	)	)	PUNCT
ejpam-5423	204	42	∨	∨	NUM
ejpam-5423	204	43	δ	δ	PROPN
ejpam-5423	204	44	n	n	CCONJ
ejpam-5423	204	45	≤	≤	NUM
ejpam-5423	204	46	(	(	PUNCT
ejpam-5423	204	47	ωn(e1	ωn(e1	NOUN
ejpam-5423	204	48	)	)	PUNCT
ejpam-5423	204	49	∨g	∨g	NOUN
ejpam-5423	204	50	n	n	CCONJ
ejpam-5423	204	51	(	(	PUNCT
ejpam-5423	204	52	e2e3	e2e3	NOUN
ejpam-5423	204	53	)	)	PUNCT
ejpam-5423	204	54	∧	∧	NOUN
ejpam-5423	204	55	λ	λ	PROPN
ejpam-5423	204	56	n	n	CCONJ
ejpam-5423	204	57	∨	∨	NUM
ejpam-5423	204	58	δ	δ	PROPN
ejpam-5423	204	59	n	n	CCONJ
ejpam-5423	204	60	)	)	PUNCT
ejpam-5423	204	61	∨	∨	PROPN
ejpam-5423	204	62	(	(	PUNCT
ejpam-5423	204	63	g	g	PROPN
ejpam-5423	204	64	n	n	PROPN
ejpam-5423	204	65	(	(	PUNCT
ejpam-5423	204	66	e1e2	e1e2	NOUN
ejpam-5423	204	67	)	)	PUNCT
ejpam-5423	204	68	∨	∨	NUM
ejpam-5423	204	69	ωn(e3	ωn(e3	PROPN
ejpam-5423	204	70	)	)	PUNCT
ejpam-5423	204	71	∧	∧	PROPN
ejpam-5423	204	72	λ	λ	PROPN
ejpam-5423	204	73	n	n	CCONJ
ejpam-5423	204	74	∨	∨	NUM
ejpam-5423	204	75	δ	δ	PROPN
ejpam-5423	204	76	n	n	PART
ejpam-5423	204	77	)	)	PUNCT
ejpam-5423	204	78	=	=	SYM
ejpam-5423	204	79	(	(	PUNCT
ejpam-5423	204	80	ωn(e1	ωn(e1	NOUN
ejpam-5423	204	81	)	)	PUNCT
ejpam-5423	204	82	∨	∨	NUM
ejpam-5423	204	83	−1	−1	NOUN
ejpam-5423	204	84	∧	∧	PROPN
ejpam-5423	204	85	λ	λ	PROPN
ejpam-5423	204	86	n	n	CCONJ
ejpam-5423	204	87	∨	∨	NUM
ejpam-5423	204	88	δ	δ	PROPN
ejpam-5423	204	89	n	n	CCONJ
ejpam-5423	204	90	)	)	PUNCT
ejpam-5423	204	91	∨	∨	NOUN
ejpam-5423	204	92	(	(	PUNCT
ejpam-5423	204	93	−1	−1	NOUN
ejpam-5423	204	94	∨	∨	NUM
ejpam-5423	204	95	ωn(e3	ωn(e3	PROPN
ejpam-5423	204	96	)	)	PUNCT
ejpam-5423	204	97	∧	∧	PROPN
ejpam-5423	204	98	λ	λ	PROPN
ejpam-5423	204	99	n	n	CCONJ
ejpam-5423	204	100	∨	∨	NUM
ejpam-5423	204	101	δ	δ	PROPN
ejpam-5423	204	102	n	n	PART
ejpam-5423	204	103	)	)	PUNCT
ejpam-5423	204	104	=	=	SYM
ejpam-5423	204	105	(	(	PUNCT
ejpam-5423	204	106	ωn(e1	ωn(e1	NOUN
ejpam-5423	204	107	)	)	PUNCT
ejpam-5423	204	108	∧	∧	NOUN
ejpam-5423	204	109	λ	λ	PROPN
ejpam-5423	204	110	n	n	CCONJ
ejpam-5423	204	111	∨	∨	NUM
ejpam-5423	204	112	δ	δ	PROPN
ejpam-5423	204	113	n	n	CCONJ
ejpam-5423	204	114	)	)	PUNCT
ejpam-5423	204	115	∨	∨	PROPN
ejpam-5423	204	116	(	(	PUNCT
ejpam-5423	204	117	ωn(e3	ωn(e3	PROPN
ejpam-5423	204	118	)	)	PUNCT
ejpam-5423	204	119	∧	∧	PROPN
ejpam-5423	204	120	λ	λ	PROPN
ejpam-5423	204	121	n	n	CCONJ
ejpam-5423	204	122	∨	∨	NUM
ejpam-5423	204	123	δ	δ	PROPN
ejpam-5423	204	124	n	n	PART
ejpam-5423	204	125	)	)	PUNCT
ejpam-5423	204	126	=	=	SYM
ejpam-5423	204	127	(	(	PUNCT
ejpam-5423	204	128	ωn(e1	ωn(e1	NOUN
ejpam-5423	204	129	)	)	PUNCT
ejpam-5423	204	130	∨	∨	NUM
ejpam-5423	204	131	ωn(e3	ωn(e3	PROPN
ejpam-5423	204	132	)	)	PUNCT
ejpam-5423	204	133	)	)	PUNCT
ejpam-5423	205	1	∧	∧	PROPN
ejpam-5423	205	2	λ	λ	PROPN
ejpam-5423	205	3	n	n	CCONJ
ejpam-5423	205	4	∨	∨	NUM
ejpam-5423	205	5	δ	δ	PROPN
ejpam-5423	205	6	n	n	CCONJ
ejpam-5423	205	7	=	=	SYM
ejpam-5423	205	8	ωn(e1	ωn(e1	NUM
ejpam-5423	205	9	)	)	PUNCT
ejpam-5423	205	10	∨	∨	NOUN
ejpam-5423	205	11	ωnp(e3	ωnp(e3	ADJ
ejpam-5423	205	12	)	)	PUNCT
ejpam-5423	205	13	∧	∧	PROPN
ejpam-5423	205	14	λ	λ	PROPN
ejpam-5423	205	15	n	n	CCONJ
ejpam-5423	205	16	∨	∨	NUM
ejpam-5423	205	17	δ	δ	PROPN
ejpam-5423	205	18	n	n	CCONJ
ejpam-5423	205	19	≤	≤	NUM
ejpam-5423	205	20	ωn(e1	ωn(e1	NUM
ejpam-5423	205	21	)	)	PUNCT
ejpam-5423	205	22	∨	∨	NUM
ejpam-5423	205	23	ωn(e3	ωn(e3	PROPN
ejpam-5423	205	24	)	)	PUNCT
ejpam-5423	205	25	∨	∨	NUM
ejpam-5423	205	26	δ	δ	PROPN
ejpam-5423	205	27	n	n	X
ejpam-5423	205	28	.	.	PUNCT
ejpam-5423	206	1	thus	thus	ADV
ejpam-5423	206	2	,	,	PUNCT
ejpam-5423	206	3	ωp(e1e2e3	ωp(e1e2e3	NUM
ejpam-5423	206	4	)	)	PUNCT
ejpam-5423	206	5	∨	∨	NUM
ejpam-5423	206	6	λ	λ	PROPN
ejpam-5423	206	7	p	p	NOUN
ejpam-5423	206	8	≥	≥	PROPN
ejpam-5423	206	9	ωp(e1	ωp(e1	NOUN
ejpam-5423	206	10	)	)	PUNCT
ejpam-5423	206	11	∧	∧	PROPN
ejpam-5423	206	12	ωp(e3	ωp(e3	NUM
ejpam-5423	206	13	)	)	PUNCT
ejpam-5423	206	14	∧	∧	PROPN
ejpam-5423	206	15	δ	δ	PROPN
ejpam-5423	206	16	p	p	NOUN
ejpam-5423	206	17	and	and	CCONJ
ejpam-5423	206	18	ωn(e1e2e3	ωn(e1e2e3	NOUN
ejpam-5423	206	19	)	)	PUNCT
ejpam-5423	206	20	∧	∧	NOUN
ejpam-5423	206	21	λ	λ	PROPN
ejpam-5423	206	22	n	n	CCONJ
ejpam-5423	206	23	≤	≤	NUM
ejpam-5423	206	24	ωn(e1	ωn(e1	NUM
ejpam-5423	206	25	)	)	PUNCT
ejpam-5423	206	26	∨	∨	NUM
ejpam-5423	206	27	ωn(e3	ωn(e3	PROPN
ejpam-5423	206	28	)	)	PUNCT
ejpam-5423	206	29	∨	∨	NUM
ejpam-5423	206	30	δ	δ	PROPN
ejpam-5423	206	31	n	n	X
ejpam-5423	206	32	.	.	PUNCT
ejpam-5423	207	1	hence	hence	ADV
ejpam-5423	207	2	t	t	PROPN
ejpam-5423	207	3	=	=	SYM
ejpam-5423	207	4	(	(	PUNCT
ejpam-5423	207	5	ω	ω	PROPN
ejpam-5423	207	6	p	p	PROPN
ejpam-5423	207	7	,	,	PUNCT
ejpam-5423	207	8	ω	ω	PROPN
ejpam-5423	207	9	n	n	CCONJ
ejpam-5423	207	10	)	)	PUNCT
ejpam-5423	207	11	is	be	AUX
ejpam-5423	207	12	an	an	DET
ejpam-5423	207	13	(	(	PUNCT
ejpam-5423	207	14	λ	λ	NOUN
ejpam-5423	207	15	,	,	PUNCT
ejpam-5423	207	16	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	207	17	bi	bi	NOUN
ejpam-5423	207	18	-	-	NOUN
ejpam-5423	207	19	ideal	ideal	NOUN
ejpam-5423	207	20	of	of	ADP
ejpam-5423	207	21	g.	g.	PROPN
ejpam-5423	207	22	the	the	DET
ejpam-5423	207	23	following	follow	VERB
ejpam-5423	207	24	theorems	theorem	NOUN
ejpam-5423	207	25	are	be	AUX
ejpam-5423	207	26	basic	basic	ADJ
ejpam-5423	207	27	properties	property	NOUN
ejpam-5423	207	28	.	.	PUNCT
ejpam-5423	208	1	theorem	theorem	NOUN
ejpam-5423	208	2	5	5	NUM
ejpam-5423	208	3	.	.	PUNCT
ejpam-5423	209	1	let	let	VERB
ejpam-5423	209	2	g	g	NOUN
ejpam-5423	209	3	be	be	AUX
ejpam-5423	209	4	an	an	DET
ejpam-5423	209	5	ordered	order	VERB
ejpam-5423	209	6	semigroup	semigroup	NOUN
ejpam-5423	209	7	.	.	PUNCT
ejpam-5423	210	1	then	then	ADV
ejpam-5423	210	2	the	the	DET
ejpam-5423	210	3	intersection	intersection	NOUN
ejpam-5423	210	4	of	of	ADP
ejpam-5423	210	5	two	two	NUM
ejpam-5423	210	6	(	(	PUNCT
ejpam-5423	210	7	λ	λ	NOUN
ejpam-5423	210	8	,	,	PUNCT
ejpam-5423	210	9	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	210	10	quasi	quasi	NOUN
ejpam-5423	210	11	-	-	NOUN
ejpam-5423	210	12	ideal	ideal	ADJ
ejpam-5423	210	13	of	of	ADP
ejpam-5423	210	14	g	g	PROPN
ejpam-5423	210	15	is	be	AUX
ejpam-5423	210	16	an	an	DET
ejpam-5423	210	17	(	(	PUNCT
ejpam-5423	210	18	λ	λ	NOUN
ejpam-5423	210	19	,	,	PUNCT
ejpam-5423	210	20	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	210	21	quasi	quasi	NOUN
ejpam-5423	210	22	-	-	NOUN
ejpam-5423	210	23	ideal	ideal	NOUN
ejpam-5423	210	24	of	of	ADP
ejpam-5423	210	25	g.	g.	PROPN
ejpam-5423	210	26	proof	proof	PROPN
ejpam-5423	210	27	.	.	PUNCT
ejpam-5423	211	1	assume	assume	VERB
ejpam-5423	211	2	that	that	SCONJ
ejpam-5423	211	3	t	t	PROPN
ejpam-5423	211	4	1	1	NUM
ejpam-5423	211	5	=	=	SYM
ejpam-5423	211	6	(	(	PUNCT
ejpam-5423	211	7	ω	ω	PROPN
ejpam-5423	211	8	p	p	PROPN
ejpam-5423	211	9	,	,	PUNCT
ejpam-5423	211	10	ω	ω	PROPN
ejpam-5423	211	11	n	n	CCONJ
ejpam-5423	211	12	)	)	PUNCT
ejpam-5423	211	13	and	and	CCONJ
ejpam-5423	211	14	t	t	X
ejpam-5423	211	15	2	2	NUM
ejpam-5423	211	16	=	=	SYM
ejpam-5423	211	17	(	(	PUNCT
ejpam-5423	211	18	ϖ	ϖ	X
ejpam-5423	211	19	p	p	X
ejpam-5423	211	20	,	,	PUNCT
ejpam-5423	211	21	ϖ	ϖ	PROPN
ejpam-5423	211	22	n	n	CCONJ
ejpam-5423	211	23	)	)	PUNCT
ejpam-5423	211	24	are	be	AUX
ejpam-5423	211	25	(	(	PUNCT
ejpam-5423	211	26	λ	λ	X
ejpam-5423	211	27	,	,	PUNCT
ejpam-5423	211	28	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	211	29	quasi	quasi	NOUN
ejpam-5423	211	30	-	-	NOUN
ejpam-5423	211	31	ideals	ideal	NOUN
ejpam-5423	211	32	t.	t.	NOUN
ejpam-5423	211	33	gaketem	gaketem	NOUN
ejpam-5423	211	34	,	,	PUNCT
ejpam-5423	211	35	t.	t.	PROPN
ejpam-5423	211	36	prommai	prommai	PROPN
ejpam-5423	211	37	/	/	SYM
ejpam-5423	211	38	eur	eur	PROPN
ejpam-5423	211	39	.	.	PUNCT
ejpam-5423	212	1	j.	j.	PROPN
ejpam-5423	212	2	pure	pure	PROPN
ejpam-5423	212	3	appl	appl	PROPN
ejpam-5423	212	4	.	.	PROPN
ejpam-5423	212	5	math	math	PROPN
ejpam-5423	212	6	,	,	PUNCT
ejpam-5423	212	7	17	17	NUM
ejpam-5423	212	8	(	(	PUNCT
ejpam-5423	212	9	4	4	NUM
ejpam-5423	212	10	)	)	PUNCT
ejpam-5423	212	11	(	(	PUNCT
ejpam-5423	212	12	2024	2024	NUM
ejpam-5423	212	13	)	)	PUNCT
ejpam-5423	212	14	,	,	PUNCT
ejpam-5423	212	15	3223	3223	NUM
ejpam-5423	212	16	-	-	SYM
ejpam-5423	212	17	3241	3241	NUM
ejpam-5423	212	18	3233	3233	NUM
ejpam-5423	212	19	of	of	ADP
ejpam-5423	212	20	g.	g.	PROPN
ejpam-5423	212	21	let	let	VERB
ejpam-5423	212	22	e	e	PROPN
ejpam-5423	212	23	∈	∈	PROPN
ejpam-5423	212	24	g.	g.	NOUN
ejpam-5423	213	1	then	then	ADV
ejpam-5423	213	2	(	(	PUNCT
ejpam-5423	213	3	ωp	ωp	NUM
ejpam-5423	213	4	⊓ϖp)(e	⊓ϖp)(e	NOUN
ejpam-5423	213	5	)	)	PUNCT
ejpam-5423	213	6	∨	∨	NUM
ejpam-5423	213	7	λ	λ	PROPN
ejpam-5423	213	8	p	p	X
ejpam-5423	213	9	≥	≥	X
ejpam-5423	213	10	(	(	PUNCT
ejpam-5423	213	11	ωp	ωp	NUM
ejpam-5423	213	12	⊓ϖp)(e	⊓ϖp)(e	NOUN
ejpam-5423	213	13	)	)	PUNCT
ejpam-5423	213	14	∨	∨	NUM
ejpam-5423	213	15	λ	λ	PROPN
ejpam-5423	213	16	p	p	PROPN
ejpam-5423	213	17	∧	∧	PROPN
ejpam-5423	213	18	δ	δ	PROPN
ejpam-5423	213	19	p	p	NOUN
ejpam-5423	213	20	=	=	X
ejpam-5423	213	21	(	(	PUNCT
ejpam-5423	213	22	ωp(e	ωp(e	ADJ
ejpam-5423	213	23	)	)	PUNCT
ejpam-5423	213	24	∧ϖp(e	∧ϖp(e	NOUN
ejpam-5423	213	25	)	)	PUNCT
ejpam-5423	213	26	)	)	PUNCT
ejpam-5423	214	1	∨	∨	NUM
ejpam-5423	214	2	λ	λ	PROPN
ejpam-5423	214	3	p	p	PROPN
ejpam-5423	214	4	∧	∧	PROPN
ejpam-5423	214	5	δ	δ	PROPN
ejpam-5423	214	6	p	p	NOUN
ejpam-5423	214	7	=	=	X
ejpam-5423	214	8	(	(	PUNCT
ejpam-5423	214	9	ωp(e	ωp(e	ADJ
ejpam-5423	214	10	)	)	PUNCT
ejpam-5423	214	11	∨	∨	NUM
ejpam-5423	215	1	λ	λ	PROPN
ejpam-5423	215	2	p	p	PROPN
ejpam-5423	215	3	∧	∧	PROPN
ejpam-5423	215	4	δ	δ	PROPN
ejpam-5423	215	5	p	p	NOUN
ejpam-5423	215	6	)	)	PUNCT
ejpam-5423	215	7	∧	∧	PROPN
ejpam-5423	215	8	(	(	PUNCT
ejpam-5423	215	9	ϖp(e	ϖp(e	PROPN
ejpam-5423	215	10	)	)	PUNCT
ejpam-5423	215	11	∨	∨	NUM
ejpam-5423	215	12	λ	λ	PROPN
ejpam-5423	215	13	p	p	PROPN
ejpam-5423	215	14	∧	∧	PROPN
ejpam-5423	215	15	δ	δ	PROPN
ejpam-5423	215	16	p	p	NOUN
ejpam-5423	215	17	)	)	PUNCT
ejpam-5423	215	18	≥	≥	X
ejpam-5423	215	19	(	(	PUNCT
ejpam-5423	215	20	ωp	ωp	ADP
ejpam-5423	215	21	◦	◦	NOUN
ejpam-5423	215	22	gp	gp	NOUN
ejpam-5423	215	23	)	)	PUNCT
ejpam-5423	215	24	δ	δ	PROPN
ejpam-5423	215	25	λ	λ	PROPN
ejpam-5423	215	26	(	(	PUNCT
ejpam-5423	215	27	e	e	NOUN
ejpam-5423	215	28	)	)	PUNCT
ejpam-5423	215	29	∧	∧	PROPN
ejpam-5423	215	30	(	(	PUNCT
ejpam-5423	215	31	g	g	PROPN
ejpam-5423	215	32	p	p	PROPN
ejpam-5423	215	33	◦	◦	NOUN
ejpam-5423	215	34	ωp)δ	ωp)δ	PROPN
ejpam-5423	215	35	λ	λ	NOUN
ejpam-5423	215	36	(	(	PUNCT
ejpam-5423	215	37	e)∧	e)∧	NOUN
ejpam-5423	215	38	(	(	PUNCT
ejpam-5423	215	39	ϖp	ϖp	ADP
ejpam-5423	215	40	◦	◦	NOUN
ejpam-5423	215	41	gp	gp	NOUN
ejpam-5423	215	42	)	)	PUNCT
ejpam-5423	216	1	δ	δ	PROPN
ejpam-5423	216	2	λ	λ	PROPN
ejpam-5423	216	3	(	(	PUNCT
ejpam-5423	216	4	e	e	NOUN
ejpam-5423	216	5	)	)	PUNCT
ejpam-5423	216	6	∧	∧	PROPN
ejpam-5423	216	7	(	(	PUNCT
ejpam-5423	216	8	g	g	PROPN
ejpam-5423	216	9	p	p	NOUN
ejpam-5423	216	10	◦	◦	NOUN
ejpam-5423	216	11	ϖp)δ	ϖp)δ	PROPN
ejpam-5423	216	12	p	p	X
ejpam-5423	216	13	λ	λ	X
ejpam-5423	216	14	(	(	PUNCT
ejpam-5423	216	15	e	e	NOUN
ejpam-5423	216	16	)	)	PUNCT
ejpam-5423	216	17	=	=	SYM
ejpam-5423	216	18	(	(	PUNCT
ejpam-5423	216	19	∨	∨	X
ejpam-5423	216	20	(	(	PUNCT
ejpam-5423	216	21	i	i	PROPN
ejpam-5423	216	22	,	,	PUNCT
ejpam-5423	216	23	j)∈ae	j)∈ae	PROPN
ejpam-5423	216	24	{	{	PUNCT
ejpam-5423	216	25	ωp(i	ωp(i	NOUN
ejpam-5423	216	26	)	)	PUNCT
ejpam-5423	216	27	∧g	∧g	PROPN
ejpam-5423	216	28	p	p	X
ejpam-5423	216	29	(	(	PUNCT
ejpam-5423	216	30	j	j	NOUN
ejpam-5423	216	31	)	)	PUNCT
ejpam-5423	216	32	}	}	PUNCT
ejpam-5423	216	33	∧	∧	PROPN
ejpam-5423	216	34	δ	δ	PROPN
ejpam-5423	216	35	p	p	NOUN
ejpam-5423	216	36	)	)	PUNCT
ejpam-5423	216	37	∨	∨	NUM
ejpam-5423	216	38	λ	λ	PROPN
ejpam-5423	216	39	p∧	p∧	NOUN
ejpam-5423	216	40	(	(	PUNCT
ejpam-5423	216	41	∨	∨	X
ejpam-5423	216	42	(	(	PUNCT
ejpam-5423	216	43	k	k	X
ejpam-5423	216	44	,	,	PUNCT
ejpam-5423	216	45	o)∈ae	o)∈ae	PROPN
ejpam-5423	216	46	{	{	PUNCT
ejpam-5423	216	47	gp	gp	NOUN
ejpam-5423	216	48	(	(	PUNCT
ejpam-5423	216	49	k	k	NOUN
ejpam-5423	216	50	)	)	PUNCT
ejpam-5423	216	51	∧	∧	NOUN
ejpam-5423	216	52	ωp(o	ωp(o	NOUN
ejpam-5423	216	53	)	)	PUNCT
ejpam-5423	216	54	}	}	PUNCT
ejpam-5423	216	55	∧	∧	PROPN
ejpam-5423	216	56	δ	δ	PROPN
ejpam-5423	216	57	p	p	NOUN
ejpam-5423	216	58	)	)	PUNCT
ejpam-5423	216	59	∨	∨	NUM
ejpam-5423	216	60	λ	λ	PROPN
ejpam-5423	216	61	p∧	p∧	NOUN
ejpam-5423	216	62	(	(	PUNCT
ejpam-5423	216	63	∨	∨	X
ejpam-5423	216	64	(	(	PUNCT
ejpam-5423	216	65	i	i	PROPN
ejpam-5423	216	66	,	,	PUNCT
ejpam-5423	216	67	j)∈ae	j)∈ae	PROPN
ejpam-5423	216	68	{	{	PUNCT
ejpam-5423	216	69	ϖp(i	ϖp(i	NOUN
ejpam-5423	216	70	)	)	PUNCT
ejpam-5423	216	71	∧g	∧g	NUM
ejpam-5423	216	72	p	p	X
ejpam-5423	216	73	(	(	PUNCT
ejpam-5423	216	74	j	j	NOUN
ejpam-5423	216	75	)	)	PUNCT
ejpam-5423	216	76	}	}	PUNCT
ejpam-5423	216	77	∧	∧	PROPN
ejpam-5423	216	78	δ	δ	PROPN
ejpam-5423	216	79	)	)	PUNCT
ejpam-5423	216	80	∨ϖp∧	∨ϖp∧	PROPN
ejpam-5423	216	81	(	(	PUNCT
ejpam-5423	216	82	∨	∨	X
ejpam-5423	216	83	(	(	PUNCT
ejpam-5423	216	84	k	k	X
ejpam-5423	216	85	,	,	PUNCT
ejpam-5423	216	86	o)∈ae	o)∈ae	PROPN
ejpam-5423	216	87	{	{	PUNCT
ejpam-5423	216	88	gp	gp	NOUN
ejpam-5423	216	89	(	(	PUNCT
ejpam-5423	216	90	k	k	NOUN
ejpam-5423	216	91	)	)	PUNCT
ejpam-5423	216	92	∧ϖp(o	∧ϖp(o	NOUN
ejpam-5423	216	93	)	)	PUNCT
ejpam-5423	216	94	}	}	PUNCT
ejpam-5423	216	95	∧	∧	PROPN
ejpam-5423	216	96	δ	δ	PROPN
ejpam-5423	216	97	p	p	NOUN
ejpam-5423	216	98	)	)	PUNCT
ejpam-5423	216	99	∨	∨	NUM
ejpam-5423	216	100	λ	λ	X
ejpam-5423	216	101	p	p	X
ejpam-5423	216	102	=	=	X
ejpam-5423	216	103	(	(	PUNCT
ejpam-5423	216	104	∨	∨	X
ejpam-5423	216	105	(	(	PUNCT
ejpam-5423	216	106	i	i	PROPN
ejpam-5423	216	107	,	,	PUNCT
ejpam-5423	216	108	j)∈ae	j)∈ae	PROPN
ejpam-5423	216	109	{	{	PUNCT
ejpam-5423	216	110	ωp(i	ωp(i	NOUN
ejpam-5423	216	111	)	)	PUNCT
ejpam-5423	216	112	∧ϖp(i	∧ϖp(i	NOUN
ejpam-5423	216	113	)	)	PUNCT
ejpam-5423	216	114	∧g	∧g	PROPN
ejpam-5423	216	115	p	p	X
ejpam-5423	216	116	(	(	PUNCT
ejpam-5423	216	117	j	j	NOUN
ejpam-5423	216	118	)	)	PUNCT
ejpam-5423	216	119	∧	∧	PROPN
ejpam-5423	216	120	δ	δ	PROPN
ejpam-5423	216	121	∨	∨	NUM
ejpam-5423	216	122	λ	λ	PROPN
ejpam-5423	216	123	p}∧	p}∧	NOUN
ejpam-5423	216	124	(	(	PUNCT
ejpam-5423	216	125	∨	∨	PROPN
ejpam-5423	216	126	(	(	PUNCT
ejpam-5423	216	127	k	k	X
ejpam-5423	216	128	,	,	PUNCT
ejpam-5423	216	129	o)∈ae	o)∈ae	PROPN
ejpam-5423	216	130	{	{	PUNCT
ejpam-5423	216	131	gp	gp	NOUN
ejpam-5423	216	132	(	(	PUNCT
ejpam-5423	216	133	k	k	NOUN
ejpam-5423	216	134	)	)	PUNCT
ejpam-5423	216	135	∧	∧	NOUN
ejpam-5423	216	136	µp(o	µp(o	NOUN
ejpam-5423	216	137	)	)	PUNCT
ejpam-5423	216	138	∧ϖp(o	∧ϖp(o	NOUN
ejpam-5423	216	139	)	)	PUNCT
ejpam-5423	216	140	}	}	PUNCT
ejpam-5423	216	141	∧	∧	PROPN
ejpam-5423	216	142	δ	δ	PROPN
ejpam-5423	216	143	)	)	PUNCT
ejpam-5423	216	144	∨	∨	NUM
ejpam-5423	216	145	λ	λ	X
ejpam-5423	216	146	p	p	X
ejpam-5423	216	147	=	=	X
ejpam-5423	216	148	(	(	PUNCT
ejpam-5423	216	149	∨	∨	X
ejpam-5423	216	150	(	(	PUNCT
ejpam-5423	216	151	i	i	PROPN
ejpam-5423	216	152	,	,	PUNCT
ejpam-5423	216	153	j)∈ae	j)∈ae	PROPN
ejpam-5423	216	154	{	{	PUNCT
ejpam-5423	216	155	(	(	PUNCT
ejpam-5423	216	156	ωp	ωp	NUM
ejpam-5423	216	157	⊓ϖp)(i	⊓ϖp)(i	NOUN
ejpam-5423	216	158	)	)	PUNCT
ejpam-5423	216	159	∧g	∧g	PROPN
ejpam-5423	216	160	p	p	X
ejpam-5423	216	161	(	(	PUNCT
ejpam-5423	216	162	j	j	NOUN
ejpam-5423	216	163	)	)	PUNCT
ejpam-5423	216	164	}	}	PUNCT
ejpam-5423	216	165	∧	∧	PROPN
ejpam-5423	216	166	δ	δ	PROPN
ejpam-5423	216	167	)	)	PUNCT
ejpam-5423	216	168	∨	∨	NUM
ejpam-5423	216	169	λ	λ	PROPN
ejpam-5423	216	170	p∧	p∧	NOUN
ejpam-5423	216	171	(	(	PUNCT
ejpam-5423	216	172	∨	∨	X
ejpam-5423	216	173	(	(	PUNCT
ejpam-5423	216	174	k	k	X
ejpam-5423	216	175	,	,	PUNCT
ejpam-5423	216	176	o)∈ae	o)∈ae	PROPN
ejpam-5423	216	177	{	{	PUNCT
ejpam-5423	216	178	gp	gp	NOUN
ejpam-5423	216	179	(	(	PUNCT
ejpam-5423	216	180	k	k	NOUN
ejpam-5423	216	181	)	)	PUNCT
ejpam-5423	216	182	∧	∧	NOUN
ejpam-5423	216	183	(	(	PUNCT
ejpam-5423	216	184	ωp	ωp	NOUN
ejpam-5423	216	185	⊓ϖp)(o	⊓ϖp)(o	ADJ
ejpam-5423	216	186	)	)	PUNCT
ejpam-5423	216	187	}	}	PUNCT
ejpam-5423	216	188	∧	∧	PROPN
ejpam-5423	216	189	δ	δ	PROPN
ejpam-5423	216	190	p	p	NOUN
ejpam-5423	216	191	)	)	PUNCT
ejpam-5423	216	192	∨	∨	NUM
ejpam-5423	216	193	λ	λ	X
ejpam-5423	216	194	p	p	X
ejpam-5423	216	195	=	=	X
ejpam-5423	216	196	(	(	PUNCT
ejpam-5423	216	197	ωp	ωp	NOUN
ejpam-5423	216	198	⊓ϖp	⊓ϖp	X
ejpam-5423	216	199	◦	◦	NOUN
ejpam-5423	216	200	gp	gp	NOUN
ejpam-5423	216	201	)	)	PUNCT
ejpam-5423	217	1	δ	δ	PROPN
ejpam-5423	217	2	λ	λ	PROPN
ejpam-5423	217	3	(	(	PUNCT
ejpam-5423	217	4	e	e	NOUN
ejpam-5423	217	5	)	)	PUNCT
ejpam-5423	217	6	∧	∧	PROPN
ejpam-5423	217	7	(	(	PUNCT
ejpam-5423	217	8	g	g	PROPN
ejpam-5423	217	9	p	p	PROPN
ejpam-5423	217	10	◦	◦	NOUN
ejpam-5423	217	11	ωp	ωp	PRON
ejpam-5423	217	12	⊓ϖp)δ	⊓ϖp)δ	PROPN
ejpam-5423	217	13	λ	λ	PROPN
ejpam-5423	217	14	(	(	PUNCT
ejpam-5423	217	15	e	e	NOUN
ejpam-5423	217	16	)	)	PUNCT
ejpam-5423	217	17	and	and	CCONJ
ejpam-5423	217	18	(	(	PUNCT
ejpam-5423	217	19	ωn	ωn	PROPN
ejpam-5423	217	20	⊔ϖn)(e	⊔ϖn)(e	PROPN
ejpam-5423	217	21	)	)	PUNCT
ejpam-5423	217	22	∧	∧	PROPN
ejpam-5423	217	23	λ	λ	PROPN
ejpam-5423	217	24	n	n	CCONJ
ejpam-5423	217	25	≤	≤	NUM
ejpam-5423	217	26	(	(	PUNCT
ejpam-5423	217	27	ωn	ωn	PROPN
ejpam-5423	217	28	⊔ϖn)(e	⊔ϖn)(e	PROPN
ejpam-5423	217	29	)	)	PUNCT
ejpam-5423	217	30	∧	∧	PROPN
ejpam-5423	217	31	λ	λ	PROPN
ejpam-5423	217	32	n	n	CCONJ
ejpam-5423	217	33	∨	∨	NUM
ejpam-5423	217	34	δ	δ	PROPN
ejpam-5423	217	35	n	n	X
ejpam-5423	217	36	=	=	SYM
ejpam-5423	217	37	(	(	PUNCT
ejpam-5423	217	38	ωn(e	ωn(e	NOUN
ejpam-5423	217	39	)	)	PUNCT
ejpam-5423	217	40	∨ϖn(e	∨ϖn(e	PROPN
ejpam-5423	217	41	)	)	PUNCT
ejpam-5423	217	42	)	)	PUNCT
ejpam-5423	217	43	∧	∧	PROPN
ejpam-5423	217	44	λ	λ	PROPN
ejpam-5423	217	45	n	n	CCONJ
ejpam-5423	217	46	∨	∨	NUM
ejpam-5423	217	47	δ	δ	PROPN
ejpam-5423	217	48	n	n	X
ejpam-5423	217	49	=	=	SYM
ejpam-5423	217	50	(	(	PUNCT
ejpam-5423	217	51	ωn(e	ωn(e	NUM
ejpam-5423	217	52	)	)	PUNCT
ejpam-5423	217	53	∨	∨	NUM
ejpam-5423	217	54	λ	λ	PROPN
ejpam-5423	217	55	n	n	CCONJ
ejpam-5423	217	56	∨	∨	NUM
ejpam-5423	217	57	δ	δ	PROPN
ejpam-5423	217	58	n	n	CCONJ
ejpam-5423	217	59	)	)	PUNCT
ejpam-5423	217	60	∨	∨	PROPN
ejpam-5423	217	61	(	(	PUNCT
ejpam-5423	217	62	ϖn(e	ϖn(e	NOUN
ejpam-5423	217	63	)	)	PUNCT
ejpam-5423	217	64	∨	∨	NUM
ejpam-5423	217	65	λ	λ	PROPN
ejpam-5423	217	66	n	n	CCONJ
ejpam-5423	217	67	)	)	PUNCT
ejpam-5423	217	68	∨	∨	NUM
ejpam-5423	217	69	δ	δ	PROPN
ejpam-5423	217	70	n	n	CCONJ
ejpam-5423	217	71	≤	≤	NUM
ejpam-5423	217	72	(	(	PUNCT
ejpam-5423	217	73	ωn	ωn	ADP
ejpam-5423	217	74	◦	◦	NOUN
ejpam-5423	217	75	gn	gn	NOUN
ejpam-5423	217	76	)	)	PUNCT
ejpam-5423	217	77	λ	λ	PROPN
ejpam-5423	217	78	δ	δ	PROPN
ejpam-5423	217	79	(	(	PUNCT
ejpam-5423	217	80	e	e	NOUN
ejpam-5423	217	81	)	)	PUNCT
ejpam-5423	217	82	∨	∨	NOUN
ejpam-5423	217	83	(	(	PUNCT
ejpam-5423	217	84	g	g	NOUN
ejpam-5423	217	85	n	n	PRON
ejpam-5423	217	86	◦	◦	VERB
ejpam-5423	217	87	ωn)λ	ωn)λ	PROPN
ejpam-5423	217	88	δ	δ	PROPN
ejpam-5423	217	89	(	(	PUNCT
ejpam-5423	217	90	e)∨	e)∨	PROPN
ejpam-5423	217	91	(	(	PUNCT
ejpam-5423	217	92	ϖn	ϖn	ADP
ejpam-5423	217	93	◦	◦	NOUN
ejpam-5423	217	94	gn	gn	NOUN
ejpam-5423	217	95	)	)	PUNCT
ejpam-5423	217	96	λ	λ	PROPN
ejpam-5423	217	97	δ	δ	PROPN
ejpam-5423	217	98	(	(	PUNCT
ejpam-5423	217	99	e	e	NOUN
ejpam-5423	217	100	)	)	PUNCT
ejpam-5423	217	101	∨	∨	NOUN
ejpam-5423	217	102	(	(	PUNCT
ejpam-5423	217	103	g	g	PROPN
ejpam-5423	217	104	n	n	PRON
ejpam-5423	217	105	◦	◦	NOUN
ejpam-5423	217	106	ϖn)λ	ϖn)λ	PROPN
ejpam-5423	217	107	δ	δ	PROPN
ejpam-5423	217	108	(	(	PUNCT
ejpam-5423	217	109	e	e	NOUN
ejpam-5423	217	110	)	)	PUNCT
ejpam-5423	217	111	=	=	SYM
ejpam-5423	217	112	(	(	PUNCT
ejpam-5423	217	113	∧	∧	PROPN
ejpam-5423	217	114	(	(	PUNCT
ejpam-5423	217	115	i	i	PROPN
ejpam-5423	217	116	,	,	PUNCT
ejpam-5423	217	117	j)∈ae	j)∈ae	PROPN
ejpam-5423	217	118	{	{	PUNCT
ejpam-5423	217	119	ωn(i	ωn(i	PROPN
ejpam-5423	217	120	)	)	PUNCT
ejpam-5423	217	121	∧g	∧g	NUM
ejpam-5423	217	122	n	n	CCONJ
ejpam-5423	217	123	(	(	PUNCT
ejpam-5423	217	124	j	j	NOUN
ejpam-5423	217	125	)	)	PUNCT
ejpam-5423	217	126	}	}	PUNCT
ejpam-5423	217	127	∧	∧	PROPN
ejpam-5423	217	128	λ	λ	PROPN
ejpam-5423	217	129	n	n	CCONJ
ejpam-5423	217	130	)	)	PUNCT
ejpam-5423	217	131	∨	∨	PROPN
ejpam-5423	217	132	δ	δ	PROPN
ejpam-5423	217	133	n∧	n∧	NUM
ejpam-5423	217	134	(	(	PUNCT
ejpam-5423	217	135	∧	∧	PROPN
ejpam-5423	217	136	(	(	PUNCT
ejpam-5423	217	137	k	k	X
ejpam-5423	217	138	,	,	PUNCT
ejpam-5423	217	139	o)∈ae	o)∈ae	PROPN
ejpam-5423	217	140	{	{	PUNCT
ejpam-5423	217	141	gn	gn	PROPN
ejpam-5423	217	142	(	(	PUNCT
ejpam-5423	217	143	k	k	NOUN
ejpam-5423	217	144	)	)	PUNCT
ejpam-5423	217	145	∧	∧	NOUN
ejpam-5423	217	146	ωn(o	ωn(o	NUM
ejpam-5423	217	147	)	)	PUNCT
ejpam-5423	217	148	}	}	PUNCT
ejpam-5423	217	149	∧	∧	PROPN
ejpam-5423	217	150	λ	λ	PROPN
ejpam-5423	217	151	n	n	CCONJ
ejpam-5423	217	152	)	)	PUNCT
ejpam-5423	217	153	∨	∨	PROPN
ejpam-5423	217	154	δ	δ	PROPN
ejpam-5423	217	155	n∨	n∨	PROPN
ejpam-5423	217	156	(	(	PUNCT
ejpam-5423	217	157	∧	∧	PROPN
ejpam-5423	217	158	(	(	PUNCT
ejpam-5423	217	159	i	i	PROPN
ejpam-5423	217	160	,	,	PUNCT
ejpam-5423	217	161	j)∈ae	j)∈ae	PROPN
ejpam-5423	217	162	{	{	PUNCT
ejpam-5423	217	163	ϖn(i	ϖn(i	PROPN
ejpam-5423	217	164	)	)	PUNCT
ejpam-5423	217	165	∧g	∧g	NUM
ejpam-5423	217	166	n	n	CCONJ
ejpam-5423	217	167	(	(	PUNCT
ejpam-5423	217	168	j	j	NOUN
ejpam-5423	217	169	)	)	PUNCT
ejpam-5423	217	170	}	}	PUNCT
ejpam-5423	217	171	∧	∧	PROPN
ejpam-5423	217	172	λ	λ	PROPN
ejpam-5423	217	173	n	n	CCONJ
ejpam-5423	217	174	)	)	PUNCT
ejpam-5423	217	175	∨	∨	PROPN
ejpam-5423	217	176	δ	δ	PROPN
ejpam-5423	217	177	n∨	n∨	PROPN
ejpam-5423	217	178	(	(	PUNCT
ejpam-5423	217	179	∧	∧	PROPN
ejpam-5423	217	180	(	(	PUNCT
ejpam-5423	217	181	k	k	X
ejpam-5423	217	182	,	,	PUNCT
ejpam-5423	217	183	o)∈ae	o)∈ae	PROPN
ejpam-5423	217	184	{	{	PUNCT
ejpam-5423	217	185	gn	gn	PROPN
ejpam-5423	217	186	(	(	PUNCT
ejpam-5423	217	187	k	k	NOUN
ejpam-5423	217	188	)	)	PUNCT
ejpam-5423	217	189	∧ϖn(o	∧ϖn(o	PROPN
ejpam-5423	217	190	)	)	PUNCT
ejpam-5423	217	191	}	}	PUNCT
ejpam-5423	217	192	∧	∧	PROPN
ejpam-5423	217	193	λ	λ	PROPN
ejpam-5423	217	194	n	n	CCONJ
ejpam-5423	217	195	)	)	PUNCT
ejpam-5423	217	196	∨	∨	NUM
ejpam-5423	217	197	δ	δ	PROPN
ejpam-5423	217	198	n	n	CCONJ
ejpam-5423	217	199	=	=	NOUN
ejpam-5423	217	200	{	{	PUNCT
ejpam-5423	217	201	∧	∧	PROPN
ejpam-5423	217	202	(	(	PUNCT
ejpam-5423	217	203	i	i	PROPN
ejpam-5423	217	204	,	,	PUNCT
ejpam-5423	217	205	j)∈ae	j)∈ae	PROPN
ejpam-5423	217	206	(	(	PUNCT
ejpam-5423	217	207	ωn(i	ωn(i	NOUN
ejpam-5423	217	208	)	)	PUNCT
ejpam-5423	217	209	∨ϖn(i	∨ϖn(i	PROPN
ejpam-5423	217	210	)	)	PUNCT
ejpam-5423	217	211	∧g	∧g	NUM
ejpam-5423	217	212	n	n	CCONJ
ejpam-5423	217	213	(	(	PUNCT
ejpam-5423	217	214	j	j	NOUN
ejpam-5423	217	215	)	)	PUNCT
ejpam-5423	217	216	∧	∧	PROPN
ejpam-5423	217	217	λ	λ	PROPN
ejpam-5423	217	218	n	n	CCONJ
ejpam-5423	217	219	)	)	PUNCT
ejpam-5423	217	220	∨	∨	PROPN
ejpam-5423	217	221	δ	δ	PROPN
ejpam-5423	217	222	n}∧	n}∧	PROPN
ejpam-5423	217	223	(	(	PUNCT
ejpam-5423	217	224	∧	∧	PROPN
ejpam-5423	217	225	(	(	PUNCT
ejpam-5423	217	226	k	k	X
ejpam-5423	217	227	,	,	PUNCT
ejpam-5423	217	228	o)∈ae	o)∈ae	PROPN
ejpam-5423	217	229	{	{	PUNCT
ejpam-5423	217	230	gp	gp	NOUN
ejpam-5423	217	231	(	(	PUNCT
ejpam-5423	217	232	k	k	NOUN
ejpam-5423	217	233	)	)	PUNCT
ejpam-5423	217	234	∧	∧	NOUN
ejpam-5423	217	235	µn(o	µn(o	PUNCT
ejpam-5423	217	236	)	)	PUNCT
ejpam-5423	217	237	∨ϖn(o	∨ϖn(o	PROPN
ejpam-5423	217	238	)	)	PUNCT
ejpam-5423	217	239	}	}	PUNCT
ejpam-5423	217	240	∧	∧	PROPN
ejpam-5423	217	241	λ	λ	PROPN
ejpam-5423	217	242	n	n	CCONJ
ejpam-5423	217	243	)	)	PUNCT
ejpam-5423	217	244	∨	∨	NUM
ejpam-5423	217	245	δ	δ	PROPN
ejpam-5423	217	246	n	n	X
ejpam-5423	217	247	=	=	PUNCT
ejpam-5423	217	248	(	(	PUNCT
ejpam-5423	217	249	∧	∧	PROPN
ejpam-5423	217	250	(	(	PUNCT
ejpam-5423	217	251	i	i	PROPN
ejpam-5423	217	252	,	,	PUNCT
ejpam-5423	217	253	j)∈ae	j)∈ae	PROPN
ejpam-5423	217	254	{	{	PUNCT
ejpam-5423	217	255	(	(	PUNCT
ejpam-5423	217	256	ωn	ωn	ADP
ejpam-5423	217	257	⊔ϖn)(i	⊔ϖn)(i	PROPN
ejpam-5423	217	258	)	)	PUNCT
ejpam-5423	217	259	∧g	∧g	NUM
ejpam-5423	217	260	n	n	CCONJ
ejpam-5423	217	261	(	(	PUNCT
ejpam-5423	217	262	j	j	NOUN
ejpam-5423	217	263	)	)	PUNCT
ejpam-5423	217	264	}	}	PUNCT
ejpam-5423	217	265	∧	∧	PROPN
ejpam-5423	217	266	λ	λ	PROPN
ejpam-5423	217	267	n	n	CCONJ
ejpam-5423	217	268	)	)	PUNCT
ejpam-5423	217	269	∨	∨	PROPN
ejpam-5423	217	270	δ	δ	PROPN
ejpam-5423	217	271	n∧	n∧	NUM
ejpam-5423	217	272	(	(	PUNCT
ejpam-5423	217	273	∧	∧	PROPN
ejpam-5423	217	274	(	(	PUNCT
ejpam-5423	217	275	k	k	X
ejpam-5423	217	276	,	,	PUNCT
ejpam-5423	217	277	o)∈ae	o)∈ae	PROPN
ejpam-5423	217	278	{	{	PUNCT
ejpam-5423	217	279	gn	gn	PROPN
ejpam-5423	217	280	(	(	PUNCT
ejpam-5423	217	281	k	k	NOUN
ejpam-5423	217	282	)	)	PUNCT
ejpam-5423	217	283	∧	∧	NOUN
ejpam-5423	217	284	(	(	PUNCT
ejpam-5423	217	285	ωn	ωn	NOUN
ejpam-5423	217	286	⊔ϖp)(o	⊔ϖp)(o	NOUN
ejpam-5423	217	287	)	)	PUNCT
ejpam-5423	217	288	}	}	PUNCT
ejpam-5423	217	289	∧	∧	PROPN
ejpam-5423	217	290	λ	λ	PROPN
ejpam-5423	217	291	n	n	CCONJ
ejpam-5423	217	292	)	)	PUNCT
ejpam-5423	217	293	∨	∨	NUM
ejpam-5423	217	294	δ	δ	PROPN
ejpam-5423	217	295	n	n	X
ejpam-5423	217	296	=	=	PUNCT
ejpam-5423	217	297	(	(	PUNCT
ejpam-5423	217	298	ωn	ωn	NOUN
ejpam-5423	217	299	⊔ϖn	⊔ϖn	PROPN
ejpam-5423	217	300	◦	◦	NOUN
ejpam-5423	217	301	gn	gn	NOUN
ejpam-5423	217	302	)	)	PUNCT
ejpam-5423	217	303	λ	λ	PROPN
ejpam-5423	217	304	δ	δ	PROPN
ejpam-5423	217	305	(	(	PUNCT
ejpam-5423	217	306	e	e	NOUN
ejpam-5423	217	307	)	)	PUNCT
ejpam-5423	217	308	∧	∧	PROPN
ejpam-5423	217	309	(	(	PUNCT
ejpam-5423	217	310	g	g	AUX
ejpam-5423	217	311	n	n	PRON
ejpam-5423	217	312	◦	◦	NOUN
ejpam-5423	217	313	ωn	ωn	VERB
ejpam-5423	217	314	⊔ϖn)λ	⊔ϖn)λ	ADJ
ejpam-5423	217	315	δ	δ	PROPN
ejpam-5423	217	316	(	(	PUNCT
ejpam-5423	217	317	e	e	NOUN
ejpam-5423	217	318	)	)	PUNCT
ejpam-5423	217	319	.	.	PUNCT
ejpam-5423	218	1	t.	t.	PROPN
ejpam-5423	218	2	gaketem	gaketem	PROPN
ejpam-5423	218	3	,	,	PUNCT
ejpam-5423	218	4	t.	t.	PROPN
ejpam-5423	218	5	prommai	prommai	PROPN
ejpam-5423	218	6	/	/	SYM
ejpam-5423	218	7	eur	eur	PROPN
ejpam-5423	218	8	.	.	PUNCT
ejpam-5423	219	1	j.	j.	PROPN
ejpam-5423	219	2	pure	pure	PROPN
ejpam-5423	219	3	appl	appl	PROPN
ejpam-5423	219	4	.	.	PROPN
ejpam-5423	219	5	math	math	PROPN
ejpam-5423	219	6	,	,	PUNCT
ejpam-5423	219	7	17	17	NUM
ejpam-5423	219	8	(	(	PUNCT
ejpam-5423	219	9	4	4	NUM
ejpam-5423	219	10	)	)	PUNCT
ejpam-5423	219	11	(	(	PUNCT
ejpam-5423	219	12	2024	2024	NUM
ejpam-5423	219	13	)	)	PUNCT
ejpam-5423	219	14	,	,	PUNCT
ejpam-5423	219	15	3223	3223	NUM
ejpam-5423	219	16	-	-	SYM
ejpam-5423	219	17	3241	3241	NUM
ejpam-5423	219	18	3234	3234	NUM
ejpam-5423	219	19	thus	thus	ADV
ejpam-5423	219	20	,	,	PUNCT
ejpam-5423	219	21	(	(	PUNCT
ejpam-5423	219	22	ωp	ωp	ADP
ejpam-5423	219	23	⊓ϖp)(e	⊓ϖp)(e	NOUN
ejpam-5423	219	24	)	)	PUNCT
ejpam-5423	219	25	∨	∨	NUM
ejpam-5423	219	26	λ	λ	PROPN
ejpam-5423	219	27	p	p	X
ejpam-5423	219	28	≥	≥	X
ejpam-5423	219	29	(	(	PUNCT
ejpam-5423	219	30	ωp	ωp	NOUN
ejpam-5423	219	31	⊓ϖp	⊓ϖp	X
ejpam-5423	219	32	◦	◦	NOUN
ejpam-5423	219	33	gp	gp	NOUN
ejpam-5423	219	34	)	)	PUNCT
ejpam-5423	220	1	δ	δ	PROPN
ejpam-5423	220	2	λ	λ	PROPN
ejpam-5423	220	3	(	(	PUNCT
ejpam-5423	220	4	e	e	NOUN
ejpam-5423	220	5	)	)	PUNCT
ejpam-5423	220	6	∧	∧	PROPN
ejpam-5423	220	7	(	(	PUNCT
ejpam-5423	220	8	g	g	PROPN
ejpam-5423	220	9	p	p	PROPN
ejpam-5423	220	10	◦	◦	NOUN
ejpam-5423	220	11	ωp	ωp	PRON
ejpam-5423	220	12	⊓ϖp)δ	⊓ϖp)δ	PROPN
ejpam-5423	220	13	λ	λ	PROPN
ejpam-5423	220	14	(	(	PUNCT
ejpam-5423	220	15	e	e	NOUN
ejpam-5423	220	16	)	)	PUNCT
ejpam-5423	220	17	and	and	CCONJ
ejpam-5423	220	18	(	(	PUNCT
ejpam-5423	220	19	ωn	ωn	PROPN
ejpam-5423	220	20	⊔ϖn)(e	⊔ϖn)(e	PROPN
ejpam-5423	220	21	)	)	PUNCT
ejpam-5423	220	22	∧	∧	PROPN
ejpam-5423	220	23	λ	λ	PROPN
ejpam-5423	220	24	n	n	CCONJ
ejpam-5423	220	25	≤	≤	NUM
ejpam-5423	220	26	(	(	PUNCT
ejpam-5423	220	27	ωn	ωn	NOUN
ejpam-5423	220	28	⊔ϖn	⊔ϖn	PROPN
ejpam-5423	220	29	◦	◦	NOUN
ejpam-5423	220	30	gn	gn	NOUN
ejpam-5423	220	31	)	)	PUNCT
ejpam-5423	220	32	λ	λ	PROPN
ejpam-5423	220	33	δ	δ	PROPN
ejpam-5423	220	34	(	(	PUNCT
ejpam-5423	220	35	e	e	NOUN
ejpam-5423	220	36	)	)	PUNCT
ejpam-5423	220	37	∧	∧	PROPN
ejpam-5423	220	38	(	(	PUNCT
ejpam-5423	220	39	g	g	AUX
ejpam-5423	220	40	n	n	PRON
ejpam-5423	220	41	◦	◦	NOUN
ejpam-5423	220	42	ωn	ωn	VERB
ejpam-5423	220	43	⊔ϖn)λ	⊔ϖn)λ	ADJ
ejpam-5423	220	44	δ	δ	PROPN
ejpam-5423	220	45	(	(	PUNCT
ejpam-5423	220	46	e	e	NOUN
ejpam-5423	220	47	)	)	PUNCT
ejpam-5423	220	48	hence	hence	ADV
ejpam-5423	220	49	t	t	NOUN
ejpam-5423	220	50	1	1	NUM
ejpam-5423	220	51	⊓	⊓	PROPN
ejpam-5423	220	52	t	t	PROPN
ejpam-5423	220	53	2	2	NUM
ejpam-5423	220	54	is	be	AUX
ejpam-5423	220	55	an	an	DET
ejpam-5423	220	56	(	(	PUNCT
ejpam-5423	220	57	λ	λ	NOUN
ejpam-5423	220	58	,	,	PUNCT
ejpam-5423	220	59	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	220	60	quasi	quasi	NOUN
ejpam-5423	220	61	-	-	NOUN
ejpam-5423	220	62	ideal	ideal	NOUN
ejpam-5423	220	63	of	of	ADP
ejpam-5423	220	64	g.	g.	PROPN
ejpam-5423	220	65	theorem	theorem	VERB
ejpam-5423	220	66	6	6	NUM
ejpam-5423	220	67	.	.	PUNCT
ejpam-5423	221	1	if	if	SCONJ
ejpam-5423	221	2	m	m	NOUN
ejpam-5423	221	3	is	be	AUX
ejpam-5423	221	4	a	a	DET
ejpam-5423	221	5	quasi	quasi	NOUN
ejpam-5423	221	6	-	-	NOUN
ejpam-5423	221	7	ideal	ideal	NOUN
ejpam-5423	221	8	of	of	ADP
ejpam-5423	221	9	an	an	DET
ejpam-5423	221	10	ordered	order	VERB
ejpam-5423	221	11	semigroup	semigroup	NOUN
ejpam-5423	221	12	g	g	PROPN
ejpam-5423	221	13	,	,	PUNCT
ejpam-5423	221	14	then	then	ADV
ejpam-5423	221	15	χm	χm	VERB
ejpam-5423	221	16	=	=	PUNCT
ejpam-5423	221	17	(	(	PUNCT
ejpam-5423	221	18	g;χ	g;χ	PROPN
ejpam-5423	221	19	p	p	NOUN
ejpam-5423	221	20	m	m	PROPN
ejpam-5423	221	21	,	,	PUNCT
ejpam-5423	221	22	χ	χ	PROPN
ejpam-5423	221	23	n	n	INTJ
ejpam-5423	221	24	m	m	VERB
ejpam-5423	221	25	)	)	PUNCT
ejpam-5423	221	26	is	be	AUX
ejpam-5423	221	27	an	an	DET
ejpam-5423	221	28	(	(	PUNCT
ejpam-5423	221	29	λ	λ	NOUN
ejpam-5423	221	30	,	,	PUNCT
ejpam-5423	221	31	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	221	32	quasi	quasi	NOUN
ejpam-5423	221	33	-	-	NOUN
ejpam-5423	221	34	ideal	ideal	NOUN
ejpam-5423	221	35	of	of	ADP
ejpam-5423	221	36	g.	g.	PROPN
ejpam-5423	221	37	proof	proof	PROPN
ejpam-5423	221	38	.	.	PUNCT
ejpam-5423	222	1	suppose	suppose	VERB
ejpam-5423	222	2	that	that	SCONJ
ejpam-5423	222	3	m	m	PROPN
ejpam-5423	222	4	is	be	AUX
ejpam-5423	222	5	a	a	DET
ejpam-5423	222	6	quasi	quasi	NOUN
ejpam-5423	222	7	-	-	NOUN
ejpam-5423	222	8	ideal	ideal	NOUN
ejpam-5423	222	9	of	of	ADP
ejpam-5423	222	10	g	g	PROPN
ejpam-5423	222	11	and	and	CCONJ
ejpam-5423	222	12	e1	e1	PROPN
ejpam-5423	222	13	,	,	PUNCT
ejpam-5423	222	14	e2	e2	PROPN
ejpam-5423	222	15	∈	∈	PROPN
ejpam-5423	222	16	g	g	PROPN
ejpam-5423	222	17	with	with	ADP
ejpam-5423	222	18	e1	e1	PROPN
ejpam-5423	222	19	≥	≥	PROPN
ejpam-5423	222	20	e2	e2	PROPN
ejpam-5423	222	21	.	.	PUNCT
ejpam-5423	223	1	then	then	ADV
ejpam-5423	223	2	ω	ω	NUM
ejpam-5423	223	3	p(e1	p(e1	NOUN
ejpam-5423	223	4	)	)	PUNCT
ejpam-5423	223	5	∨	∨	PROPN
ejpam-5423	223	6	λ	λ	PROPN
ejpam-5423	223	7	p	p	X
ejpam-5423	223	8	≥	≥	PROPN
ejpam-5423	223	9	ω	ω	NUM
ejpam-5423	223	10	p(e2	p(e2	NOUN
ejpam-5423	223	11	)	)	PUNCT
ejpam-5423	223	12	∧	∧	PROPN
ejpam-5423	223	13	δ	δ	PROPN
ejpam-5423	223	14	p	p	NOUN
ejpam-5423	223	15	and	and	CCONJ
ejpam-5423	223	16	ω	ω	NUM
ejpam-5423	223	17	n(e1	n(e1	NOUN
ejpam-5423	223	18	)	)	PUNCT
ejpam-5423	223	19	∧	∧	PROPN
ejpam-5423	223	20	λ	λ	PROPN
ejpam-5423	223	21	n	n	CCONJ
ejpam-5423	223	22	≤	≤	PROPN
ejpam-5423	223	23	ω	ω	NUM
ejpam-5423	223	24	n(e2	n(e2	PROPN
ejpam-5423	223	25	)	)	PUNCT
ejpam-5423	223	26	∨	∨	PROPN
ejpam-5423	223	27	δ	δ	PROPN
ejpam-5423	223	28	n.	n.	PROPN
ejpam-5423	223	29	let	let	VERB
ejpam-5423	223	30	e	e	X
ejpam-5423	223	31	∈	∈	PROPN
ejpam-5423	223	32	g.	g.	VERB
ejpam-5423	224	1	if	if	SCONJ
ejpam-5423	224	2	e	e	PROPN
ejpam-5423	224	3	∈	∈	PROPN
ejpam-5423	224	4	m	m	VERB
ejpam-5423	224	5	or	or	CCONJ
ejpam-5423	224	6	ae	ae	PROPN
ejpam-5423	224	7	=	=	NOUN
ejpam-5423	224	8	∅	∅	NOUN
ejpam-5423	224	9	,	,	PUNCT
ejpam-5423	224	10	then	then	ADV
ejpam-5423	224	11	(	(	PUNCT
ejpam-5423	224	12	χp	χp	PROPN
ejpam-5423	224	13	m	m	NOUN
ejpam-5423	224	14	)	)	PUNCT
ejpam-5423	224	15	δ	δ	PROPN
ejpam-5423	224	16	λ	λ	PROPN
ejpam-5423	224	17	(	(	PUNCT
ejpam-5423	224	18	e	e	NOUN
ejpam-5423	224	19	)	)	PUNCT
ejpam-5423	224	20	≥	≥	NOUN
ejpam-5423	224	21	(	(	PUNCT
ejpam-5423	224	22	χp	χp	PROPN
ejpam-5423	224	23	m	m	PROPN
ejpam-5423	224	24	◦	◦	NOUN
ejpam-5423	224	25	gp	gp	NOUN
ejpam-5423	224	26	)	)	PUNCT
ejpam-5423	225	1	δ	δ	PROPN
ejpam-5423	225	2	λ	λ	PROPN
ejpam-5423	225	3	(	(	PUNCT
ejpam-5423	225	4	e	e	NOUN
ejpam-5423	225	5	)	)	PUNCT
ejpam-5423	225	6	∧	∧	PROPN
ejpam-5423	225	7	(	(	PUNCT
ejpam-5423	225	8	g	g	PROPN
ejpam-5423	225	9	p	p	PROPN
ejpam-5423	225	10	◦	◦	NOUN
ejpam-5423	225	11	χp	χp	NOUN
ejpam-5423	225	12	m	m	NOUN
ejpam-5423	225	13	)	)	PUNCT
ejpam-5423	225	14	λ	λ	PROPN
ejpam-5423	225	15	δ	δ	PROPN
ejpam-5423	225	16	(	(	PUNCT
ejpam-5423	225	17	e	e	NOUN
ejpam-5423	225	18	)	)	PUNCT
ejpam-5423	225	19	,	,	PUNCT
ejpam-5423	225	20	(	(	PUNCT
ejpam-5423	225	21	χn	χn	X
ejpam-5423	225	22	m	m	NOUN
ejpam-5423	225	23	)	)	PUNCT
ejpam-5423	225	24	λ	λ	PROPN
ejpam-5423	225	25	δ	δ	PROPN
ejpam-5423	225	26	(	(	PUNCT
ejpam-5423	225	27	e	e	NOUN
ejpam-5423	225	28	)	)	PUNCT
ejpam-5423	225	29	≤	≤	NOUN
ejpam-5423	225	30	(	(	PUNCT
ejpam-5423	225	31	χn	χn	X
ejpam-5423	225	32	m	m	PROPN
ejpam-5423	225	33	◦	◦	NOUN
ejpam-5423	225	34	gn	gn	PROPN
ejpam-5423	225	35	)	)	PUNCT
ejpam-5423	225	36	(	(	PUNCT
ejpam-5423	225	37	e	e	NOUN
ejpam-5423	225	38	)	)	PUNCT
ejpam-5423	225	39	∨	∨	NOUN
ejpam-5423	225	40	(	(	PUNCT
ejpam-5423	225	41	g	g	NOUN
ejpam-5423	225	42	n	n	PRON
ejpam-5423	225	43	◦	◦	VERB
ejpam-5423	225	44	χn	χn	X
ejpam-5423	225	45	m	m	NOUN
ejpam-5423	225	46	)	)	PUNCT
ejpam-5423	225	47	λ	λ	PROPN
ejpam-5423	225	48	δ	δ	PROPN
ejpam-5423	225	49	(	(	PUNCT
ejpam-5423	225	50	e	e	NOUN
ejpam-5423	225	51	)	)	PUNCT
ejpam-5423	225	52	.	.	PUNCT
ejpam-5423	226	1	assume	assume	VERB
ejpam-5423	226	2	that	that	SCONJ
ejpam-5423	226	3	e	e	NOUN
ejpam-5423	226	4	/∈	/∈	PUNCT
ejpam-5423	227	1	m	m	AUX
ejpam-5423	227	2	and	and	CCONJ
ejpam-5423	227	3	ae	ae	PROPN
ejpam-5423	227	4	̸=	̸=	PROPN
ejpam-5423	227	5	∅.	∅.	ADV
ejpam-5423	227	6	let	let	VERB
ejpam-5423	227	7	k	k	PROPN
ejpam-5423	227	8	=	=	PRON
ejpam-5423	227	9	{	{	PUNCT
ejpam-5423	227	10	(	(	PUNCT
ejpam-5423	227	11	i	i	PROPN
ejpam-5423	227	12	,	,	PUNCT
ejpam-5423	227	13	j	j	PROPN
ejpam-5423	227	14	)	)	PUNCT
ejpam-5423	228	1	|	|	ADV
ejpam-5423	228	2	e	e	X
ejpam-5423	228	3	=	=	SYM
ejpam-5423	229	1	ij	ij	INTJ
ejpam-5423	229	2	and	and	CCONJ
ejpam-5423	229	3	(	(	PUNCT
ejpam-5423	229	4	i	i	PRON
ejpam-5423	229	5	/∈	/∈	VERB
ejpam-5423	230	1	m	m	VERB
ejpam-5423	230	2	and	and	CCONJ
ejpam-5423	230	3	j	j	PROPN
ejpam-5423	230	4	/∈	/∈	PUNCT
ejpam-5423	231	1	m	m	PROPN
ejpam-5423	231	2	)	)	PUNCT
ejpam-5423	231	3	}	}	PUNCT
ejpam-5423	231	4	.	.	PUNCT
ejpam-5423	232	1	thus	thus	ADV
ejpam-5423	232	2	k	k	PROPN
ejpam-5423	232	3	⊆	⊆	NUM
ejpam-5423	232	4	ae	ae	PROPN
ejpam-5423	232	5	on	on	ADP
ejpam-5423	232	6	the	the	DET
ejpam-5423	232	7	other	other	ADJ
ejpam-5423	232	8	hand	hand	NOUN
ejpam-5423	232	9	if	if	SCONJ
ejpam-5423	232	10	(	(	PUNCT
ejpam-5423	232	11	i	i	PROPN
ejpam-5423	232	12	,	,	PUNCT
ejpam-5423	232	13	j	j	PROPN
ejpam-5423	232	14	)	)	PUNCT
ejpam-5423	232	15	∈	∈	PROPN
ejpam-5423	232	16	ae	ae	PROPN
ejpam-5423	232	17	,	,	PUNCT
ejpam-5423	232	18	then	then	ADV
ejpam-5423	232	19	ae	ae	PROPN
ejpam-5423	232	20	=	=	PUNCT
ejpam-5423	233	1	ij	ij	INTJ
ejpam-5423	233	2	/∈	/∈	INTJ
ejpam-5423	233	3	m	m	VERB
ejpam-5423	233	4	which	which	PRON
ejpam-5423	233	5	it	it	PRON
ejpam-5423	233	6	implies	imply	VERB
ejpam-5423	233	7	that	that	PRON
ejpam-5423	234	1	ij	ij	INTJ
ejpam-5423	234	2	/∈	/∈	INTJ
ejpam-5423	234	3	mg	mg	PROPN
ejpam-5423	234	4	∩	∩	PROPN
ejpam-5423	234	5	gm	gm	PROPN
ejpam-5423	234	6	.	.	PUNCT
ejpam-5423	235	1	thus	thus	ADV
ejpam-5423	235	2	i	i	PRON
ejpam-5423	235	3	/∈	/∈	VERB
ejpam-5423	236	1	m	m	VERB
ejpam-5423	236	2	or	or	CCONJ
ejpam-5423	236	3	j	j	PROPN
ejpam-5423	236	4	/∈	/∈	PUNCT
ejpam-5423	237	1	m	m	VERB
ejpam-5423	237	2	e	e	NOUN
ejpam-5423	237	3	∈	∈	PROPN
ejpam-5423	237	4	gm	gm	PROPN
ejpam-5423	237	5	and	and	CCONJ
ejpam-5423	237	6	e	e	PROPN
ejpam-5423	237	7	∈	∈	PROPN
ejpam-5423	237	8	mg	mg	PROPN
ejpam-5423	238	1	and	and	CCONJ
ejpam-5423	238	2	so	so	ADV
ejpam-5423	238	3	(	(	PUNCT
ejpam-5423	238	4	i	i	PROPN
ejpam-5423	238	5	,	,	PUNCT
ejpam-5423	238	6	j	j	PROPN
ejpam-5423	238	7	)	)	PUNCT
ejpam-5423	238	8	∈	∈	PROPN
ejpam-5423	238	9	m	m	NOUN
ejpam-5423	238	10	.	.	PUNCT
ejpam-5423	239	1	hence	hence	ADV
ejpam-5423	239	2	ae	ae	PROPN
ejpam-5423	239	3	⊆	⊆	NUM
ejpam-5423	239	4	k.	k.	PROPN
ejpam-5423	240	1	therefore	therefore	ADV
ejpam-5423	240	2	,	,	PUNCT
ejpam-5423	240	3	ae	ae	PROPN
ejpam-5423	240	4	=	=	PROPN
ejpam-5423	240	5	k.	k.	PROPN
ejpam-5423	241	1	that	that	PRON
ejpam-5423	241	2	is	be	AUX
ejpam-5423	241	3	,	,	PUNCT
ejpam-5423	241	4	ae	ae	PROPN
ejpam-5423	241	5	=	=	PRON
ejpam-5423	241	6	{	{	PUNCT
ejpam-5423	241	7	(	(	PUNCT
ejpam-5423	241	8	i	i	PROPN
ejpam-5423	241	9	,	,	PUNCT
ejpam-5423	241	10	j	j	PROPN
ejpam-5423	241	11	)	)	PUNCT
ejpam-5423	242	1	|	|	ADV
ejpam-5423	242	2	i	i	PRON
ejpam-5423	242	3	/∈	/∈	VERB
ejpam-5423	243	1	m	m	VERB
ejpam-5423	243	2	or	or	CCONJ
ejpam-5423	243	3	j	j	PROPN
ejpam-5423	243	4	/∈	/∈	PUNCT
ejpam-5423	243	5	m	m	VERB
ejpam-5423	243	6	}	}	PUNCT
ejpam-5423	243	7	.	.	PUNCT
ejpam-5423	244	1	thus	thus	ADV
ejpam-5423	244	2	,	,	PUNCT
ejpam-5423	244	3	(	(	PUNCT
ejpam-5423	244	4	χp	χp	X
ejpam-5423	244	5	m	m	PROPN
ejpam-5423	244	6	◦	◦	NOUN
ejpam-5423	244	7	g)δ	g)δ	X
ejpam-5423	244	8	λ	λ	NOUN
ejpam-5423	244	9	∧	∧	PROPN
ejpam-5423	244	10	(	(	PUNCT
ejpam-5423	244	11	g	g	PROPN
ejpam-5423	244	12	◦	◦	PROPN
ejpam-5423	244	13	χp	χp	NOUN
ejpam-5423	244	14	m	m	NOUN
ejpam-5423	244	15	)	)	PUNCT
ejpam-5423	244	16	δ	δ	PROPN
ejpam-5423	244	17	λ	λ	NOUN
ejpam-5423	244	18	=	=	SYM
ejpam-5423	244	19	(	(	PUNCT
ejpam-5423	244	20	∨	∨	X
ejpam-5423	244	21	(	(	PUNCT
ejpam-5423	244	22	i	i	PROPN
ejpam-5423	244	23	,	,	PUNCT
ejpam-5423	244	24	j)∈ae	j)∈ae	PROPN
ejpam-5423	244	25	{	{	PUNCT
ejpam-5423	244	26	χp	χp	NOUN
ejpam-5423	244	27	m	m	PROPN
ejpam-5423	244	28	(	(	PUNCT
ejpam-5423	244	29	i	i	NOUN
ejpam-5423	244	30	)	)	PUNCT
ejpam-5423	244	31	∧g	∧g	PROPN
ejpam-5423	244	32	p	p	X
ejpam-5423	244	33	(	(	PUNCT
ejpam-5423	244	34	j	j	NOUN
ejpam-5423	244	35	)	)	PUNCT
ejpam-5423	244	36	}	}	PUNCT
ejpam-5423	244	37	∧	∧	PROPN
ejpam-5423	244	38	δ	δ	PROPN
ejpam-5423	244	39	p	p	NOUN
ejpam-5423	244	40	)	)	PUNCT
ejpam-5423	244	41	∨	∨	NUM
ejpam-5423	244	42	λ	λ	PROPN
ejpam-5423	244	43	p∧	p∧	NOUN
ejpam-5423	244	44	(	(	PUNCT
ejpam-5423	244	45	∨	∨	X
ejpam-5423	244	46	(	(	PUNCT
ejpam-5423	244	47	i	i	PROPN
ejpam-5423	244	48	,	,	PUNCT
ejpam-5423	244	49	j)∈ae	j)∈ae	PROPN
ejpam-5423	244	50	{	{	PUNCT
ejpam-5423	244	51	gp	gp	NOUN
ejpam-5423	244	52	(	(	PUNCT
ejpam-5423	244	53	i	i	NOUN
ejpam-5423	244	54	)	)	PUNCT
ejpam-5423	244	55	∧	∧	PROPN
ejpam-5423	244	56	χp	χp	VERB
ejpam-5423	244	57	m	m	PROPN
ejpam-5423	244	58	(	(	PUNCT
ejpam-5423	244	59	j	j	NOUN
ejpam-5423	244	60	)	)	PUNCT
ejpam-5423	244	61	}	}	PUNCT
ejpam-5423	244	62	∧	∧	PROPN
ejpam-5423	244	63	δ	δ	PROPN
ejpam-5423	244	64	p	p	NOUN
ejpam-5423	244	65	)	)	PUNCT
ejpam-5423	244	66	∨	∨	NUM
ejpam-5423	244	67	λ	λ	X
ejpam-5423	244	68	p	p	X
ejpam-5423	244	69	=	=	X
ejpam-5423	244	70	(	(	PUNCT
ejpam-5423	244	71	∨	∨	X
ejpam-5423	244	72	(	(	PUNCT
ejpam-5423	244	73	i	i	PROPN
ejpam-5423	244	74	,	,	PUNCT
ejpam-5423	244	75	j)∈ae	j)∈ae	PROPN
ejpam-5423	244	76	{	{	PUNCT
ejpam-5423	244	77	χp	χp	NOUN
ejpam-5423	244	78	m	m	PROPN
ejpam-5423	244	79	(	(	PUNCT
ejpam-5423	244	80	i	i	NOUN
ejpam-5423	244	81	)	)	PUNCT
ejpam-5423	244	82	∧	∧	PROPN
ejpam-5423	244	83	χp	χp	VERB
ejpam-5423	244	84	m	m	PROPN
ejpam-5423	244	85	(	(	PUNCT
ejpam-5423	244	86	j	j	NOUN
ejpam-5423	244	87	)	)	PUNCT
ejpam-5423	244	88	}	}	PUNCT
ejpam-5423	244	89	∧	∧	PROPN
ejpam-5423	244	90	δ	δ	PROPN
ejpam-5423	244	91	p	p	NOUN
ejpam-5423	244	92	)	)	PUNCT
ejpam-5423	244	93	∨	∨	NUM
ejpam-5423	244	94	λ	λ	NOUN
ejpam-5423	244	95	p	p	X
ejpam-5423	244	96	=	=	PUNCT
ejpam-5423	244	97	λ	λ	X
ejpam-5423	244	98	p	p	NOUN
ejpam-5423	244	99	and	and	CCONJ
ejpam-5423	244	100	(	(	PUNCT
ejpam-5423	244	101	χn	χn	X
ejpam-5423	244	102	m	m	PROPN
ejpam-5423	244	103	◦	◦	NOUN
ejpam-5423	244	104	g)λ	g)λ	NOUN
ejpam-5423	244	105	δ	δ	NOUN
ejpam-5423	244	106	∨	∨	X
ejpam-5423	244	107	(	(	PUNCT
ejpam-5423	244	108	g	g	PROPN
ejpam-5423	244	109	◦	◦	NOUN
ejpam-5423	244	110	χn	χn	X
ejpam-5423	244	111	m	m	NOUN
ejpam-5423	244	112	)	)	PUNCT
ejpam-5423	244	113	λ	λ	NOUN
ejpam-5423	244	114	δ	δ	NOUN
ejpam-5423	244	115	=	=	PUNCT
ejpam-5423	244	116	(	(	PUNCT
ejpam-5423	244	117	∧	∧	PROPN
ejpam-5423	244	118	(	(	PUNCT
ejpam-5423	244	119	i	i	PROPN
ejpam-5423	244	120	,	,	PUNCT
ejpam-5423	244	121	j)∈ae	j)∈ae	PROPN
ejpam-5423	244	122	{	{	PUNCT
ejpam-5423	244	123	χn	χn	PROPN
ejpam-5423	244	124	m	m	PROPN
ejpam-5423	244	125	(	(	PUNCT
ejpam-5423	244	126	i	i	NOUN
ejpam-5423	244	127	)	)	PUNCT
ejpam-5423	244	128	∨g	∨g	PROPN
ejpam-5423	244	129	n	n	CCONJ
ejpam-5423	244	130	(	(	PUNCT
ejpam-5423	244	131	j	j	NOUN
ejpam-5423	244	132	)	)	PUNCT
ejpam-5423	244	133	}	}	PUNCT
ejpam-5423	244	134	∧	∧	PROPN
ejpam-5423	244	135	λ	λ	PROPN
ejpam-5423	244	136	n	n	CCONJ
ejpam-5423	244	137	)	)	PUNCT
ejpam-5423	244	138	∨	∨	PROPN
ejpam-5423	244	139	δ	δ	PROPN
ejpam-5423	244	140	n∨	n∨	PROPN
ejpam-5423	244	141	(	(	PUNCT
ejpam-5423	244	142	∧	∧	PROPN
ejpam-5423	244	143	(	(	PUNCT
ejpam-5423	244	144	i	i	PROPN
ejpam-5423	244	145	,	,	PUNCT
ejpam-5423	244	146	j)∈ae	j)∈ae	PROPN
ejpam-5423	244	147	{	{	PUNCT
ejpam-5423	244	148	gn	gn	PROPN
ejpam-5423	244	149	(	(	PUNCT
ejpam-5423	244	150	i	i	NOUN
ejpam-5423	244	151	)	)	PUNCT
ejpam-5423	244	152	∨	∨	PROPN
ejpam-5423	244	153	χn	χn	X
ejpam-5423	244	154	m	m	PROPN
ejpam-5423	244	155	(	(	PUNCT
ejpam-5423	244	156	j	j	NOUN
ejpam-5423	244	157	)	)	PUNCT
ejpam-5423	244	158	}	}	PUNCT
ejpam-5423	244	159	∧	∧	PROPN
ejpam-5423	244	160	λ	λ	PROPN
ejpam-5423	244	161	n	n	CCONJ
ejpam-5423	244	162	)	)	PUNCT
ejpam-5423	244	163	∨	∨	NUM
ejpam-5423	244	164	δ	δ	PROPN
ejpam-5423	244	165	n	n	X
ejpam-5423	244	166	=	=	PUNCT
ejpam-5423	244	167	(	(	PUNCT
ejpam-5423	244	168	∧	∧	PROPN
ejpam-5423	244	169	(	(	PUNCT
ejpam-5423	244	170	i	i	PROPN
ejpam-5423	244	171	,	,	PUNCT
ejpam-5423	244	172	j)∈ae	j)∈ae	PROPN
ejpam-5423	244	173	{	{	PUNCT
ejpam-5423	244	174	χn	χn	PROPN
ejpam-5423	244	175	m	m	PROPN
ejpam-5423	244	176	(	(	PUNCT
ejpam-5423	244	177	i	i	NOUN
ejpam-5423	244	178	)	)	PUNCT
ejpam-5423	244	179	∨	∨	PROPN
ejpam-5423	244	180	χn	χn	X
ejpam-5423	244	181	m	m	PROPN
ejpam-5423	244	182	(	(	PUNCT
ejpam-5423	244	183	j	j	NOUN
ejpam-5423	244	184	)	)	PUNCT
ejpam-5423	244	185	}	}	PUNCT
ejpam-5423	244	186	∧	∧	PROPN
ejpam-5423	244	187	λ	λ	PROPN
ejpam-5423	244	188	n	n	CCONJ
ejpam-5423	244	189	)	)	PUNCT
ejpam-5423	244	190	∨	∨	NUM
ejpam-5423	244	191	δ	δ	PROPN
ejpam-5423	244	192	n	n	CCONJ
ejpam-5423	244	193	=	=	SYM
ejpam-5423	244	194	δ	δ	PROPN
ejpam-5423	244	195	n	n	NOUN
ejpam-5423	244	196	.	.	PUNCT
ejpam-5423	245	1	hence	hence	ADV
ejpam-5423	245	2	χm	χm	NOUN
ejpam-5423	246	1	=	=	PUNCT
ejpam-5423	246	2	(	(	PUNCT
ejpam-5423	246	3	g;χ	g;χ	PROPN
ejpam-5423	246	4	p	p	NOUN
ejpam-5423	246	5	m	m	PROPN
ejpam-5423	246	6	,	,	PUNCT
ejpam-5423	246	7	χ	χ	PROPN
ejpam-5423	246	8	n	n	INTJ
ejpam-5423	246	9	m	m	VERB
ejpam-5423	246	10	)	)	PUNCT
ejpam-5423	246	11	is	be	AUX
ejpam-5423	246	12	an	an	DET
ejpam-5423	246	13	(	(	PUNCT
ejpam-5423	246	14	λ	λ	NOUN
ejpam-5423	246	15	,	,	PUNCT
ejpam-5423	246	16	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	246	17	quasi	quasi	NOUN
ejpam-5423	246	18	-	-	NOUN
ejpam-5423	246	19	ideal	ideal	NOUN
ejpam-5423	246	20	of	of	ADP
ejpam-5423	246	21	g.	g.	PROPN
ejpam-5423	246	22	lemma	lemma	PROPN
ejpam-5423	247	1	1	1	X
ejpam-5423	247	2	.	.	PUNCT
ejpam-5423	248	1	if	if	SCONJ
ejpam-5423	248	2	χm	χm	ADJ
ejpam-5423	248	3	=	=	PUNCT
ejpam-5423	248	4	(	(	PUNCT
ejpam-5423	248	5	g;χ	g;χ	PROPN
ejpam-5423	248	6	p	p	NOUN
ejpam-5423	248	7	m	m	PROPN
ejpam-5423	248	8	,	,	PUNCT
ejpam-5423	248	9	χ	χ	PROPN
ejpam-5423	248	10	n	n	INTJ
ejpam-5423	248	11	m	m	VERB
ejpam-5423	248	12	)	)	PUNCT
ejpam-5423	248	13	is	be	AUX
ejpam-5423	248	14	an	an	DET
ejpam-5423	248	15	(	(	PUNCT
ejpam-5423	248	16	λ	λ	NOUN
ejpam-5423	248	17	,	,	PUNCT
ejpam-5423	248	18	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	248	19	quasi	quasi	NOUN
ejpam-5423	248	20	-	-	NOUN
ejpam-5423	248	21	ideal	ideal	ADJ
ejpam-5423	248	22	of	of	ADP
ejpam-5423	248	23	an	an	DET
ejpam-5423	248	24	ordered	order	VERB
ejpam-5423	248	25	semigroup	semigroup	NOUN
ejpam-5423	248	26	g	g	NOUN
ejpam-5423	248	27	with	with	ADP
ejpam-5423	248	28	λ	λ	PROPN
ejpam-5423	248	29	p	p	X
ejpam-5423	248	30	<	<	X
ejpam-5423	248	31	δ	δ	X
ejpam-5423	248	32	p	p	NOUN
ejpam-5423	248	33	and	and	CCONJ
ejpam-5423	248	34	λ	λ	PROPN
ejpam-5423	248	35	n	n	CCONJ
ejpam-5423	248	36	>	>	PUNCT
ejpam-5423	248	37	δ	δ	PROPN
ejpam-5423	248	38	n	n	CCONJ
ejpam-5423	248	39	,	,	PUNCT
ejpam-5423	248	40	then	then	ADV
ejpam-5423	248	41	m	m	VERB
ejpam-5423	248	42	is	be	AUX
ejpam-5423	248	43	a	a	DET
ejpam-5423	248	44	quasi	quasi	NOUN
ejpam-5423	248	45	-	-	NOUN
ejpam-5423	248	46	ideal	ideal	NOUN
ejpam-5423	248	47	of	of	ADP
ejpam-5423	248	48	g.	g.	PROPN
ejpam-5423	248	49	proof	proof	PROPN
ejpam-5423	248	50	.	.	PUNCT
ejpam-5423	249	1	suppose	suppose	VERB
ejpam-5423	249	2	that	that	SCONJ
ejpam-5423	249	3	χm	χm	PRON
ejpam-5423	249	4	=	=	PUNCT
ejpam-5423	249	5	(	(	PUNCT
ejpam-5423	249	6	s;χ	s;χ	PROPN
ejpam-5423	249	7	p	p	X
ejpam-5423	249	8	m	m	PROPN
ejpam-5423	249	9	,	,	PUNCT
ejpam-5423	249	10	χ	χ	PROPN
ejpam-5423	249	11	n	n	INTJ
ejpam-5423	249	12	m	m	VERB
ejpam-5423	249	13	)	)	PUNCT
ejpam-5423	249	14	is	be	AUX
ejpam-5423	249	15	an	an	DET
ejpam-5423	249	16	(	(	PUNCT
ejpam-5423	249	17	λ	λ	NOUN
ejpam-5423	249	18	,	,	PUNCT
ejpam-5423	249	19	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	249	20	quasi	quasi	NOUN
ejpam-5423	249	21	-	-	NOUN
ejpam-5423	249	22	ideal	ideal	ADJ
ejpam-5423	249	23	of	of	ADP
ejpam-5423	249	24	g	g	NOUN
ejpam-5423	249	25	with	with	ADP
ejpam-5423	249	26	λ	λ	X
ejpam-5423	249	27	p	p	X
ejpam-5423	249	28	<	<	X
ejpam-5423	249	29	δ	δ	X
ejpam-5423	249	30	p	p	NOUN
ejpam-5423	249	31	and	and	CCONJ
ejpam-5423	249	32	λ	λ	PROPN
ejpam-5423	249	33	n	n	CCONJ
ejpam-5423	249	34	>	>	PUNCT
ejpam-5423	249	35	δ	δ	PROPN
ejpam-5423	249	36	n.	n.	PROPN
ejpam-5423	249	37	let	let	VERB
ejpam-5423	249	38	e	e	SYM
ejpam-5423	249	39	∈	∈	PROPN
ejpam-5423	249	40	mg	mg	PROPN
ejpam-5423	249	41	∩	∩	PROPN
ejpam-5423	249	42	gm	gm	PROPN
ejpam-5423	249	43	.	.	PUNCT
ejpam-5423	250	1	then	then	ADV
ejpam-5423	250	2	there	there	PRON
ejpam-5423	250	3	exist	exist	VERB
ejpam-5423	250	4	i	i	PRON
ejpam-5423	250	5	,	,	PUNCT
ejpam-5423	250	6	j	j	PROPN
ejpam-5423	250	7	∈	∈	PROPN
ejpam-5423	250	8	g	g	PROPN
ejpam-5423	250	9	and	and	CCONJ
ejpam-5423	250	10	y	y	PROPN
ejpam-5423	250	11	,	,	PUNCT
ejpam-5423	250	12	z	z	PROPN
ejpam-5423	250	13	∈	∈	PROPN
ejpam-5423	250	14	g	g	ADP
ejpam-5423	250	15	such	such	ADJ
ejpam-5423	250	16	that	that	DET
ejpam-5423	250	17	e	e	PROPN
ejpam-5423	250	18	=	=	SYM
ejpam-5423	250	19	iy	iy	PROPN
ejpam-5423	250	20	and	and	CCONJ
ejpam-5423	250	21	e	e	X
ejpam-5423	250	22	=	=	PROPN
ejpam-5423	250	23	jz	jz	PROPN
ejpam-5423	250	24	.	.	PROPN
ejpam-5423	251	1	thus	thus	ADV
ejpam-5423	251	2	(	(	PUNCT
ejpam-5423	251	3	χp	χp	PROPN
ejpam-5423	251	4	m	m	VERB
ejpam-5423	251	5	◦	◦	NOUN
ejpam-5423	251	6	g)δ	g)δ	X
ejpam-5423	251	7	λ	λ	X
ejpam-5423	251	8	(	(	PUNCT
ejpam-5423	251	9	e	e	NOUN
ejpam-5423	251	10	)	)	PUNCT
ejpam-5423	251	11	=	=	SYM
ejpam-5423	251	12	(	(	PUNCT
ejpam-5423	251	13	∨	∨	X
ejpam-5423	251	14	(	(	PUNCT
ejpam-5423	251	15	i	i	PROPN
ejpam-5423	251	16	,	,	PUNCT
ejpam-5423	251	17	n)∈ae	n)∈ae	PROPN
ejpam-5423	251	18	{	{	PUNCT
ejpam-5423	251	19	χp	χp	NOUN
ejpam-5423	251	20	m	m	PROPN
ejpam-5423	251	21	(	(	PUNCT
ejpam-5423	251	22	i	i	NOUN
ejpam-5423	251	23	)	)	PUNCT
ejpam-5423	251	24	∧	∧	PROPN
ejpam-5423	251	25	g	g	PROPN
ejpam-5423	251	26	p	p	PROPN
ejpam-5423	251	27	(	(	PUNCT
ejpam-5423	251	28	n	n	CCONJ
ejpam-5423	251	29	)	)	PUNCT
ejpam-5423	251	30	}	}	PUNCT
ejpam-5423	251	31	∧	∧	PROPN
ejpam-5423	251	32	δ	δ	PROPN
ejpam-5423	251	33	p	p	NOUN
ejpam-5423	251	34	)	)	PUNCT
ejpam-5423	251	35	∨	∨	NUM
ejpam-5423	251	36	λ	λ	PROPN
ejpam-5423	251	37	p	p	X
ejpam-5423	251	38	≥	≥	X
ejpam-5423	251	39	(	(	PUNCT
ejpam-5423	251	40	∨	∨	X
ejpam-5423	251	41	(	(	PUNCT
ejpam-5423	251	42	j	j	PROPN
ejpam-5423	251	43	,	,	PUNCT
ejpam-5423	251	44	z)∈ae	z)∈ae	PROPN
ejpam-5423	251	45	{	{	PUNCT
ejpam-5423	251	46	χp	χp	PROPN
ejpam-5423	251	47	m	m	PROPN
ejpam-5423	251	48	(	(	PUNCT
ejpam-5423	251	49	j	j	PROPN
ejpam-5423	251	50	)	)	PUNCT
ejpam-5423	251	51	∧	∧	PROPN
ejpam-5423	251	52	g	g	PROPN
ejpam-5423	251	53	p	p	PROPN
ejpam-5423	251	54	(	(	PUNCT
ejpam-5423	251	55	z	z	NOUN
ejpam-5423	251	56	)	)	PUNCT
ejpam-5423	251	57	}	}	PUNCT
ejpam-5423	251	58	∧	∧	PROPN
ejpam-5423	251	59	δ	δ	PROPN
ejpam-5423	251	60	p	p	NOUN
ejpam-5423	251	61	)	)	PUNCT
ejpam-5423	251	62	∨	∨	NUM
ejpam-5423	251	63	λ	λ	X
ejpam-5423	251	64	p	p	X
ejpam-5423	251	65	=	=	PUNCT
ejpam-5423	251	66	δ	δ	PROPN
ejpam-5423	251	67	p	p	NOUN
ejpam-5423	251	68	.	.	PUNCT
ejpam-5423	252	1	similarly	similarly	ADV
ejpam-5423	252	2	(	(	PUNCT
ejpam-5423	252	3	g	g	PROPN
ejpam-5423	252	4	◦	◦	NOUN
ejpam-5423	252	5	χp	χp	NOUN
ejpam-5423	252	6	m	m	NOUN
ejpam-5423	252	7	)	)	PUNCT
ejpam-5423	252	8	δ	δ	PROPN
ejpam-5423	252	9	λ	λ	NOUN
ejpam-5423	252	10	=	=	PUNCT
ejpam-5423	252	11	δ	δ	PROPN
ejpam-5423	252	12	p	p	NOUN
ejpam-5423	252	13	.	.	PUNCT
ejpam-5423	253	1	and	and	CCONJ
ejpam-5423	253	2	(	(	PUNCT
ejpam-5423	253	3	χn	χn	X
ejpam-5423	253	4	m	m	PROPN
ejpam-5423	253	5	◦	◦	NOUN
ejpam-5423	253	6	g)λ	g)λ	NOUN
ejpam-5423	253	7	δ	δ	X
ejpam-5423	253	8	=	=	SYM
ejpam-5423	253	9	t.	t.	PROPN
ejpam-5423	253	10	gaketem	gaketem	NOUN
ejpam-5423	253	11	,	,	PUNCT
ejpam-5423	253	12	t.	t.	PROPN
ejpam-5423	253	13	prommai	prommai	PROPN
ejpam-5423	253	14	/	/	SYM
ejpam-5423	253	15	eur	eur	PROPN
ejpam-5423	253	16	.	.	PUNCT
ejpam-5423	254	1	j.	j.	PROPN
ejpam-5423	254	2	pure	pure	PROPN
ejpam-5423	254	3	appl	appl	PROPN
ejpam-5423	254	4	.	.	PROPN
ejpam-5423	254	5	math	math	PROPN
ejpam-5423	254	6	,	,	PUNCT
ejpam-5423	254	7	17	17	NUM
ejpam-5423	254	8	(	(	PUNCT
ejpam-5423	254	9	4	4	NUM
ejpam-5423	254	10	)	)	PUNCT
ejpam-5423	254	11	(	(	PUNCT
ejpam-5423	254	12	2024	2024	NUM
ejpam-5423	254	13	)	)	PUNCT
ejpam-5423	254	14	,	,	PUNCT
ejpam-5423	254	15	3223	3223	NUM
ejpam-5423	254	16	-	-	SYM
ejpam-5423	254	17	3241	3241	NUM
ejpam-5423	254	18	3235	3235	NUM
ejpam-5423	254	19	(	(	PUNCT
ejpam-5423	254	20	∧	∧	PROPN
ejpam-5423	254	21	(	(	PUNCT
ejpam-5423	254	22	i	i	PROPN
ejpam-5423	254	23	,	,	PUNCT
ejpam-5423	254	24	n)∈ae	n)∈ae	PROPN
ejpam-5423	254	25	{	{	PUNCT
ejpam-5423	254	26	χn	χn	NOUN
ejpam-5423	254	27	m	m	PROPN
ejpam-5423	254	28	(	(	PUNCT
ejpam-5423	254	29	i)∨gn	i)∨gn	X
ejpam-5423	254	30	(	(	PUNCT
ejpam-5423	254	31	n)}∧λn	n)}∧λn	NOUN
ejpam-5423	254	32	)	)	PUNCT
ejpam-5423	254	33	∨δn	∨δn	VERB
ejpam-5423	254	34	≤	≤	NUM
ejpam-5423	254	35	(	(	PUNCT
ejpam-5423	254	36	∨	∨	X
ejpam-5423	254	37	(	(	PUNCT
ejpam-5423	254	38	j	j	PROPN
ejpam-5423	254	39	,	,	PUNCT
ejpam-5423	254	40	z)∈ae	z)∈ae	PROPN
ejpam-5423	254	41	{	{	PUNCT
ejpam-5423	254	42	χn	χn	NOUN
ejpam-5423	254	43	m	m	PROPN
ejpam-5423	254	44	(	(	PUNCT
ejpam-5423	254	45	j)∨gn	j)∨gn	X
ejpam-5423	254	46	(	(	PUNCT
ejpam-5423	254	47	z)}∧λn	z)}∧λn	NOUN
ejpam-5423	254	48	)	)	PUNCT
ejpam-5423	254	49	∨δn	∨δn	VERB
ejpam-5423	254	50	=	=	PUNCT
ejpam-5423	254	51	δ	δ	PROPN
ejpam-5423	254	52	n	n	ADV
ejpam-5423	254	53	.	.	PUNCT
ejpam-5423	255	1	by	by	ADP
ejpam-5423	255	2	assumption	assumption	NOUN
ejpam-5423	255	3	,	,	PUNCT
ejpam-5423	255	4	(	(	PUNCT
ejpam-5423	255	5	χp	χp	NOUN
ejpam-5423	255	6	m	m	NOUN
ejpam-5423	255	7	)	)	PUNCT
ejpam-5423	255	8	δ	δ	PROPN
ejpam-5423	255	9	λ	λ	PROPN
ejpam-5423	255	10	(	(	PUNCT
ejpam-5423	255	11	e	e	NOUN
ejpam-5423	255	12	)	)	PUNCT
ejpam-5423	255	13	≥	≥	NOUN
ejpam-5423	255	14	(	(	PUNCT
ejpam-5423	255	15	χp	χp	PROPN
ejpam-5423	255	16	m	m	PROPN
ejpam-5423	255	17	◦	◦	NOUN
ejpam-5423	255	18	gp	gp	NOUN
ejpam-5423	255	19	)	)	PUNCT
ejpam-5423	255	20	δ	δ	PROPN
ejpam-5423	255	21	λ	λ	PROPN
ejpam-5423	255	22	(	(	PUNCT
ejpam-5423	255	23	e	e	NOUN
ejpam-5423	255	24	)	)	PUNCT
ejpam-5423	255	25	∧	∧	PROPN
ejpam-5423	255	26	(	(	PUNCT
ejpam-5423	255	27	g	g	PROPN
ejpam-5423	255	28	p	p	PROPN
ejpam-5423	255	29	◦	◦	NOUN
ejpam-5423	255	30	χp	χp	NOUN
ejpam-5423	255	31	m	m	NOUN
ejpam-5423	255	32	)	)	PUNCT
ejpam-5423	255	33	λ	λ	PROPN
ejpam-5423	255	34	δ	δ	PROPN
ejpam-5423	255	35	(	(	PUNCT
ejpam-5423	255	36	e	e	NOUN
ejpam-5423	255	37	)	)	PUNCT
ejpam-5423	255	38	and	and	CCONJ
ejpam-5423	255	39	(	(	PUNCT
ejpam-5423	255	40	χn	χn	INTJ
ejpam-5423	255	41	m	m	NOUN
ejpam-5423	255	42	)	)	PUNCT
ejpam-5423	255	43	λ	λ	PROPN
ejpam-5423	255	44	δ	δ	PROPN
ejpam-5423	255	45	(	(	PUNCT
ejpam-5423	255	46	e	e	NOUN
ejpam-5423	255	47	)	)	PUNCT
ejpam-5423	255	48	≤	≤	NOUN
ejpam-5423	255	49	(	(	PUNCT
ejpam-5423	255	50	χn	χn	X
ejpam-5423	255	51	m	m	PROPN
ejpam-5423	255	52	◦	◦	NOUN
ejpam-5423	255	53	gn	gn	PROPN
ejpam-5423	255	54	)	)	PUNCT
ejpam-5423	255	55	(	(	PUNCT
ejpam-5423	255	56	e)⋎	e)⋎	X
ejpam-5423	255	57	(	(	PUNCT
ejpam-5423	255	58	g	g	NOUN
ejpam-5423	255	59	n	n	PRON
ejpam-5423	255	60	◦	◦	VERB
ejpam-5423	255	61	χn	χn	X
ejpam-5423	255	62	m	m	NOUN
ejpam-5423	255	63	)	)	PUNCT
ejpam-5423	255	64	λ	λ	PROPN
ejpam-5423	255	65	δ	δ	PROPN
ejpam-5423	255	66	(	(	PUNCT
ejpam-5423	255	67	e	e	NOUN
ejpam-5423	255	68	)	)	PUNCT
ejpam-5423	255	69	.	.	PUNCT
ejpam-5423	256	1	(	(	PUNCT
ejpam-5423	256	2	1	1	X
ejpam-5423	256	3	)	)	PUNCT
ejpam-5423	256	4	if	if	SCONJ
ejpam-5423	256	5	e	e	PROPN
ejpam-5423	256	6	/∈	/∈	PUNCT
ejpam-5423	256	7	m	m	VERB
ejpam-5423	256	8	,	,	PUNCT
ejpam-5423	256	9	then	then	ADV
ejpam-5423	256	10	by	by	ADP
ejpam-5423	256	11	(	(	PUNCT
ejpam-5423	256	12	1	1	X
ejpam-5423	256	13	)	)	PUNCT
ejpam-5423	256	14	λ	λ	PROPN
ejpam-5423	256	15	p	p	NOUN
ejpam-5423	256	16	≥	≥	PROPN
ejpam-5423	256	17	δ	δ	PROPN
ejpam-5423	256	18	pand	pand	PROPN
ejpam-5423	256	19	λ	λ	PROPN
ejpam-5423	256	20	n	n	CCONJ
ejpam-5423	256	21	≤	≤	NUM
ejpam-5423	256	22	δ	δ	PROPN
ejpam-5423	256	23	n.	n.	NOUN
ejpam-5423	256	24	it	it	PRON
ejpam-5423	256	25	is	be	AUX
ejpam-5423	256	26	a	a	DET
ejpam-5423	256	27	contradiction	contradiction	NOUN
ejpam-5423	256	28	.	.	PUNCT
ejpam-5423	257	1	hence	hence	ADV
ejpam-5423	257	2	e	e	X
ejpam-5423	257	3	∈	∈	PROPN
ejpam-5423	257	4	m	m	VERB
ejpam-5423	257	5	.	.	PUNCT
ejpam-5423	258	1	therefore	therefore	ADV
ejpam-5423	258	2	m	m	PROPN
ejpam-5423	258	3	is	be	AUX
ejpam-5423	258	4	a	a	DET
ejpam-5423	258	5	quasi	quasi	NOUN
ejpam-5423	258	6	-	-	NOUN
ejpam-5423	258	7	ideal	ideal	NOUN
ejpam-5423	258	8	of	of	ADP
ejpam-5423	258	9	g.	g.	PROPN
ejpam-5423	258	10	4	4	NUM
ejpam-5423	258	11	.	.	PUNCT
ejpam-5423	259	1	characterizing	characterize	VERB
ejpam-5423	259	2	ordered	order	VERB
ejpam-5423	259	3	regular	regular	ADJ
ejpam-5423	259	4	and	and	CCONJ
ejpam-5423	259	5	intra	intra	ADJ
ejpam-5423	259	6	-	-	ADJ
ejpam-5423	259	7	regular	regular	ADJ
ejpam-5423	259	8	semigroups	semigroup	NOUN
ejpam-5423	259	9	by	by	ADP
ejpam-5423	259	10	using	use	VERB
ejpam-5423	259	11	generalized	generalized	ADJ
ejpam-5423	259	12	interval	interval	NOUN
ejpam-5423	259	13	valued	value	VERB
ejpam-5423	259	14	bipolar	bipolar	ADJ
ejpam-5423	259	15	fuzzy	fuzzy	ADJ
ejpam-5423	259	16	quasi	quasi	NOUN
ejpam-5423	259	17	-	-	NOUN
ejpam-5423	259	18	ideals	ideal	NOUN
ejpam-5423	259	19	.	.	PUNCT
ejpam-5423	260	1	in	in	ADP
ejpam-5423	260	2	this	this	DET
ejpam-5423	260	3	topic	topic	NOUN
ejpam-5423	260	4	,	,	PUNCT
ejpam-5423	260	5	we	we	PRON
ejpam-5423	260	6	will	will	AUX
ejpam-5423	260	7	use	use	VERB
ejpam-5423	260	8	knowledge	knowledge	NOUN
ejpam-5423	260	9	of	of	ADP
ejpam-5423	260	10	the	the	DET
ejpam-5423	260	11	characteristics	characteristic	NOUN
ejpam-5423	260	12	of	of	ADP
ejpam-5423	260	13	interval	interval	NOUN
ejpam-5423	260	14	valued	value	VERB
ejpam-5423	260	15	fuzzy	fuzzy	ADJ
ejpam-5423	260	16	set	set	ADJ
ejpam-5423	260	17	and	and	CCONJ
ejpam-5423	260	18	bipolar	bipolar	ADJ
ejpam-5423	260	19	fuzzy	fuzzy	ADJ
ejpam-5423	260	20	sets	set	NOUN
ejpam-5423	260	21	to	to	PART
ejpam-5423	260	22	characterize	characterize	VERB
ejpam-5423	260	23	regular	regular	ADJ
ejpam-5423	260	24	and	and	CCONJ
ejpam-5423	260	25	intra	intra	ADJ
ejpam-5423	260	26	-	-	ADJ
ejpam-5423	260	27	regular	regular	ADJ
ejpam-5423	260	28	semigroups	semigroup	NOUN
ejpam-5423	260	29	by	by	ADP
ejpam-5423	260	30	using	use	VERB
ejpam-5423	260	31	generalized	generalized	ADJ
ejpam-5423	260	32	interval	interval	NOUN
ejpam-5423	260	33	valued	value	VERB
ejpam-5423	260	34	bipolar	bipolar	ADJ
ejpam-5423	260	35	fuzzy	fuzzy	ADJ
ejpam-5423	260	36	quasi	quasi	NOUN
ejpam-5423	260	37	-	-	NOUN
ejpam-5423	260	38	ideals	ideal	NOUN
ejpam-5423	260	39	in	in	ADP
ejpam-5423	260	40	ordered	order	VERB
ejpam-5423	260	41	semigroups	semigroup	NOUN
ejpam-5423	260	42	.	.	PUNCT
ejpam-5423	261	1	theorem	theorem	VERB
ejpam-5423	261	2	7	7	NUM
ejpam-5423	261	3	.	.	PUNCT
ejpam-5423	262	1	[	[	X
ejpam-5423	262	2	14	14	NUM
ejpam-5423	262	3	]	]	PUNCT
ejpam-5423	262	4	let	let	VERB
ejpam-5423	262	5	i	i	PRON
ejpam-5423	262	6	and	and	CCONJ
ejpam-5423	262	7	k	k	PROPN
ejpam-5423	262	8	be	be	AUX
ejpam-5423	262	9	a	a	DET
ejpam-5423	262	10	non	non	ADJ
ejpam-5423	262	11	-	-	ADJ
ejpam-5423	262	12	empty	empty	ADJ
ejpam-5423	262	13	subsets	subset	NOUN
ejpam-5423	262	14	of	of	ADP
ejpam-5423	262	15	g.	g.	PROPN
ejpam-5423	262	16	then	then	ADV
ejpam-5423	263	1	(	(	PUNCT
ejpam-5423	263	2	1	1	X
ejpam-5423	263	3	)	)	PUNCT
ejpam-5423	263	4	(	(	PUNCT
ejpam-5423	263	5	χi	χi	NOUN
ejpam-5423	263	6	◦	◦	NOUN
ejpam-5423	263	7	χk)λ	χk)λ	PROPN
ejpam-5423	263	8	δ	δ	X
ejpam-5423	263	9	=	=	PUNCT
ejpam-5423	263	10	(	(	PUNCT
ejpam-5423	263	11	χik)λ	χik)λ	PROPN
ejpam-5423	263	12	δ	δ	X
ejpam-5423	263	13	i.e.	i.e.	X
ejpam-5423	263	14	⟨(χ	⟨(χ	PUNCT
ejpam-5423	264	1	p	p	X
ejpam-5423	264	2	i	i	PRON
ejpam-5423	264	3	◦	◦	VERB
ejpam-5423	264	4	χ	χ	DET
ejpam-5423	264	5	p	p	X
ejpam-5423	264	6	k)δ	k)δ	X
ejpam-5423	264	7	λ	λ	PROPN
ejpam-5423	264	8	,	,	PUNCT
ejpam-5423	264	9	(	(	PUNCT
ejpam-5423	264	10	χ	χ	X
ejpam-5423	264	11	n	n	VERB
ejpam-5423	264	12	i	i	PRON
ejpam-5423	264	13	◦	◦	VERB
ejpam-5423	264	14	χ	χ	PRON
ejpam-5423	264	15	n	n	NOUN
ejpam-5423	264	16	k)λ	k)λ	PUNCT
ejpam-5423	264	17	δ	δ	PROPN
ejpam-5423	264	18	⟩	⟩	NOUN
ejpam-5423	265	1	=	=	PUNCT
ejpam-5423	265	2	⟨(χ	⟨(χ	PROPN
ejpam-5423	265	3	p	p	NOUN
ejpam-5423	265	4	ik)δ	ik)δ	PROPN
ejpam-5423	265	5	λ	λ	PROPN
ejpam-5423	265	6	,	,	PUNCT
ejpam-5423	265	7	(	(	PUNCT
ejpam-5423	265	8	χ	χ	X
ejpam-5423	265	9	n	n	CCONJ
ejpam-5423	265	10	ik)λ	ik)λ	PROPN
ejpam-5423	265	11	δ	δ	PROPN
ejpam-5423	265	12	⟩	⟩	NOUN
ejpam-5423	265	13	(	(	PUNCT
ejpam-5423	265	14	2	2	NUM
ejpam-5423	265	15	)	)	PUNCT
ejpam-5423	265	16	(	(	PUNCT
ejpam-5423	265	17	χi	χi	NOUN
ejpam-5423	265	18	⊓χk)λ	⊓χk)λ	PUNCT
ejpam-5423	265	19	δ	δ	X
ejpam-5423	265	20	=	=	PUNCT
ejpam-5423	266	1	(	(	PUNCT
ejpam-5423	266	2	χ	χ	X
ejpam-5423	266	3	p	p	X
ejpam-5423	266	4	i	i	PRON
ejpam-5423	266	5	⊓χk)λ	⊓χk)λ	PUNCT
ejpam-5423	266	6	δ	δ	X
ejpam-5423	266	7	i.e.	i.e.	X
ejpam-5423	266	8	⟨(χ	⟨(χ	PUNCT
ejpam-5423	267	1	p	p	NOUN
ejpam-5423	267	2	i	i	PRON
ejpam-5423	267	3	∩χ	∩χ	VERB
ejpam-5423	267	4	p	p	X
ejpam-5423	267	5	k)δ	k)δ	X
ejpam-5423	267	6	λ	λ	PROPN
ejpam-5423	267	7	,	,	PUNCT
ejpam-5423	267	8	(	(	PUNCT
ejpam-5423	267	9	χ	χ	X
ejpam-5423	267	10	n	n	VERB
ejpam-5423	267	11	i	i	PRON
ejpam-5423	267	12	∪χ	∪χ	X
ejpam-5423	267	13	n	n	NOUN
ejpam-5423	267	14	i	i	PRON
ejpam-5423	267	15	)	)	PUNCT
ejpam-5423	268	1	λ	λ	PROPN
ejpam-5423	268	2	δ	δ	PROPN
ejpam-5423	268	3	⟩	⟩	NOUN
ejpam-5423	268	4	=	=	PUNCT
ejpam-5423	269	1	⟨(χ	⟨(χ	PROPN
ejpam-5423	269	2	p	p	PROPN
ejpam-5423	269	3	i∩k)δ	i∩k)δ	PROPN
ejpam-5423	269	4	λ	λ	PROPN
ejpam-5423	269	5	,	,	PUNCT
ejpam-5423	269	6	(	(	PUNCT
ejpam-5423	269	7	χ	χ	X
ejpam-5423	269	8	n	n	ADV
ejpam-5423	269	9	i∪k)λ	i∪k)λ	PROPN
ejpam-5423	269	10	δ	δ	PROPN
ejpam-5423	269	11	⟩	⟩	NOUN
ejpam-5423	269	12	,	,	PUNCT
ejpam-5423	269	13	where	where	SCONJ
ejpam-5423	269	14	χi	χi	NOUN
ejpam-5423	269	15	=	=	PUNCT
ejpam-5423	269	16	(	(	PUNCT
ejpam-5423	269	17	g;χ	g;χ	PROPN
ejpam-5423	269	18	p	p	X
ejpam-5423	270	1	i	i	PROPN
ejpam-5423	270	2	,	,	PUNCT
ejpam-5423	270	3	χ	χ	PRON
ejpam-5423	270	4	n	n	INTJ
ejpam-5423	270	5	i	i	PRON
ejpam-5423	270	6	)	)	PUNCT
ejpam-5423	270	7	and	and	CCONJ
ejpam-5423	270	8	χk	χk	X
ejpam-5423	270	9	=	=	SYM
ejpam-5423	270	10	(	(	PUNCT
ejpam-5423	270	11	g;χ	g;χ	PROPN
ejpam-5423	270	12	p	p	PROPN
ejpam-5423	270	13	k	k	PROPN
ejpam-5423	270	14	,	,	PUNCT
ejpam-5423	270	15	χ	χ	PROPN
ejpam-5423	270	16	n	n	X
ejpam-5423	270	17	k	k	NOUN
ejpam-5423	270	18	)	)	PUNCT
ejpam-5423	270	19	.	.	PUNCT
ejpam-5423	271	1	remark	remark	PROPN
ejpam-5423	271	2	4	4	NUM
ejpam-5423	271	3	.	.	PUNCT
ejpam-5423	272	1	since	since	SCONJ
ejpam-5423	272	2	χi	χi	PROPN
ejpam-5423	272	3	is	be	AUX
ejpam-5423	272	4	an	an	DET
ejpam-5423	272	5	interval	interval	NOUN
ejpam-5423	272	6	valued	value	VERB
ejpam-5423	272	7	characteristic	characteristic	ADJ
ejpam-5423	272	8	function	function	NOUN
ejpam-5423	272	9	we	we	PRON
ejpam-5423	272	10	have	have	VERB
ejpam-5423	272	11	(	(	PUNCT
ejpam-5423	272	12	χ	χ	X
ejpam-5423	272	13	p	p	X
ejpam-5423	272	14	i	i	PROPN
ejpam-5423	272	15	)	)	PUNCT
ejpam-5423	273	1	λ	λ	PROPN
ejpam-5423	273	2	δ	δ	PROPN
ejpam-5423	273	3	(	(	PUNCT
ejpam-5423	273	4	e	e	NOUN
ejpam-5423	273	5	)	)	PUNCT
ejpam-5423	273	6	=	=	SYM
ejpam-5423	273	7	{	{	PUNCT
ejpam-5423	273	8	λ	λ	X
ejpam-5423	273	9	p	p	NOUN
ejpam-5423	273	10	if	if	SCONJ
ejpam-5423	273	11	k	k	PROPN
ejpam-5423	273	12	∈	∈	PROPN
ejpam-5423	273	13	i	i	PRON
ejpam-5423	273	14	,	,	PUNCT
ejpam-5423	273	15	δ	δ	PROPN
ejpam-5423	273	16	p	p	NOUN
ejpam-5423	273	17	if	if	SCONJ
ejpam-5423	273	18	k	k	PROPN
ejpam-5423	273	19	/∈	/∈	PUNCT
ejpam-5423	274	1	i	i	PRON
ejpam-5423	274	2	and	and	CCONJ
ejpam-5423	274	3	(	(	PUNCT
ejpam-5423	274	4	χ	χ	X
ejpam-5423	274	5	n	n	X
ejpam-5423	274	6	i	i	PRON
ejpam-5423	274	7	)	)	PUNCT
ejpam-5423	275	1	λ	λ	PROPN
ejpam-5423	275	2	δ	δ	X
ejpam-5423	275	3	(	(	PUNCT
ejpam-5423	275	4	e	e	NOUN
ejpam-5423	275	5	)	)	PUNCT
ejpam-5423	275	6	=	=	SYM
ejpam-5423	275	7	{	{	PUNCT
ejpam-5423	275	8	δ	δ	NOUN
ejpam-5423	275	9	n	n	ADV
ejpam-5423	275	10	if	if	SCONJ
ejpam-5423	275	11	k	k	PROPN
ejpam-5423	275	12	∈	∈	PROPN
ejpam-5423	275	13	i	i	PRON
ejpam-5423	275	14	,	,	PUNCT
ejpam-5423	275	15	λ	λ	PROPN
ejpam-5423	275	16	n	n	NOUN
ejpam-5423	275	17	if	if	SCONJ
ejpam-5423	275	18	k	k	PROPN
ejpam-5423	275	19	/∈	/∈	PROPN
ejpam-5423	276	1	i	i	PRON
ejpam-5423	276	2	lemma	lemma	PROPN
ejpam-5423	276	3	2	2	X
ejpam-5423	276	4	.	.	PUNCT
ejpam-5423	277	1	[	[	X
ejpam-5423	277	2	4	4	X
ejpam-5423	277	3	]	]	PUNCT
ejpam-5423	277	4	for	for	ADP
ejpam-5423	277	5	an	an	DET
ejpam-5423	277	6	ordered	order	VERB
ejpam-5423	277	7	semigroup	semigroup	NOUN
ejpam-5423	277	8	g	g	PROPN
ejpam-5423	277	9	,	,	PUNCT
ejpam-5423	277	10	the	the	DET
ejpam-5423	277	11	following	following	ADJ
ejpam-5423	277	12	statements	statement	NOUN
ejpam-5423	277	13	are	be	AUX
ejpam-5423	277	14	equivalent	equivalent	ADJ
ejpam-5423	277	15	.	.	PUNCT
ejpam-5423	278	1	(	(	PUNCT
ejpam-5423	278	2	1	1	X
ejpam-5423	278	3	)	)	PUNCT
ejpam-5423	278	4	g	g	NOUN
ejpam-5423	278	5	is	be	AUX
ejpam-5423	278	6	a	a	DET
ejpam-5423	278	7	regular	regular	ADJ
ejpam-5423	278	8	(	(	PUNCT
ejpam-5423	278	9	2	2	NUM
ejpam-5423	278	10	)	)	PUNCT
ejpam-5423	278	11	q	q	NOUN
ejpam-5423	278	12	∩	∩	NOUN
ejpam-5423	278	13	l	l	NOUN
ejpam-5423	278	14	⊆	⊆	NUM
ejpam-5423	278	15	(	(	PUNCT
ejpam-5423	278	16	ql	ql	X
ejpam-5423	278	17	]	]	X
ejpam-5423	278	18	for	for	ADP
ejpam-5423	278	19	every	every	DET
ejpam-5423	278	20	quasi	quasi	ADJ
ejpam-5423	278	21	-	-	ADJ
ejpam-5423	278	22	ideal	ideal	ADJ
ejpam-5423	278	23	q	q	NOUN
ejpam-5423	278	24	and	and	CCONJ
ejpam-5423	278	25	every	every	DET
ejpam-5423	278	26	left	leave	VERB
ejpam-5423	278	27	ideal	ideal	ADJ
ejpam-5423	278	28	l	l	PROPN
ejpam-5423	278	29	of	of	ADP
ejpam-5423	278	30	g.	g.	PROPN
ejpam-5423	278	31	(	(	PUNCT
ejpam-5423	278	32	3	3	X
ejpam-5423	278	33	)	)	PUNCT
ejpam-5423	278	34	r	r	NOUN
ejpam-5423	278	35	∩q	∩q	PROPN
ejpam-5423	278	36	⊆	⊆	NUM
ejpam-5423	278	37	(	(	PUNCT
ejpam-5423	278	38	rq	rq	NOUN
ejpam-5423	278	39	]	]	PUNCT
ejpam-5423	278	40	for	for	ADP
ejpam-5423	278	41	every	every	DET
ejpam-5423	278	42	right	right	ADJ
ejpam-5423	278	43	ideal	ideal	NOUN
ejpam-5423	278	44	r	r	NOUN
ejpam-5423	278	45	every	every	DET
ejpam-5423	278	46	quasi	quasi	ADJ
ejpam-5423	278	47	-	-	ADJ
ejpam-5423	278	48	ideal	ideal	ADJ
ejpam-5423	278	49	q	q	NOUN
ejpam-5423	278	50	and	and	CCONJ
ejpam-5423	278	51	of	of	ADP
ejpam-5423	278	52	g.	g.	PROPN
ejpam-5423	278	53	theorem	theorem	VERB
ejpam-5423	278	54	8	8	NUM
ejpam-5423	278	55	.	.	PUNCT
ejpam-5423	279	1	for	for	ADP
ejpam-5423	279	2	an	an	DET
ejpam-5423	279	3	ordered	order	VERB
ejpam-5423	279	4	semigroup	semigroup	NOUN
ejpam-5423	279	5	g	g	PROPN
ejpam-5423	279	6	,	,	PUNCT
ejpam-5423	279	7	the	the	DET
ejpam-5423	279	8	following	follow	VERB
ejpam-5423	279	9	conditions	condition	NOUN
ejpam-5423	279	10	are	be	AUX
ejpam-5423	279	11	equivalent	equivalent	ADJ
ejpam-5423	279	12	.	.	PUNCT
ejpam-5423	280	1	(	(	PUNCT
ejpam-5423	280	2	1	1	X
ejpam-5423	280	3	)	)	PUNCT
ejpam-5423	280	4	g	g	NOUN
ejpam-5423	280	5	is	be	AUX
ejpam-5423	280	6	a	a	DET
ejpam-5423	280	7	regular	regular	ADJ
ejpam-5423	280	8	,	,	PUNCT
ejpam-5423	280	9	(	(	PUNCT
ejpam-5423	280	10	2	2	NUM
ejpam-5423	280	11	)	)	PUNCT
ejpam-5423	280	12	(	(	PUNCT
ejpam-5423	280	13	t	t	NOUN
ejpam-5423	280	14	⊓j	⊓j	NOUN
ejpam-5423	280	15	)	)	PUNCT
ejpam-5423	281	1	λ	λ	PROPN
ejpam-5423	281	2	δ	δ	NOUN
ejpam-5423	281	3	⊑	⊑	X
ejpam-5423	281	4	(	(	PUNCT
ejpam-5423	281	5	t	t	PROPN
ejpam-5423	281	6	◦	◦	NOUN
ejpam-5423	281	7	j	j	PROPN
ejpam-5423	281	8	)	)	PUNCT
ejpam-5423	281	9	λ	λ	PROPN
ejpam-5423	281	10	δ	δ	PROPN
ejpam-5423	281	11	,	,	PUNCT
ejpam-5423	281	12	for	for	ADP
ejpam-5423	281	13	every	every	DET
ejpam-5423	281	14	(	(	PUNCT
ejpam-5423	281	15	λ	λ	NOUN
ejpam-5423	281	16	,	,	PUNCT
ejpam-5423	281	17	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	281	18	quasi	quasi	ADJ
ejpam-5423	281	19	-	-	ADJ
ejpam-5423	281	20	ideal	ideal	ADJ
ejpam-5423	281	21	t	t	NOUN
ejpam-5423	281	22	=	=	SYM
ejpam-5423	281	23	(	(	PUNCT
ejpam-5423	281	24	ω	ω	PROPN
ejpam-5423	281	25	p	p	PROPN
ejpam-5423	281	26	,	,	PUNCT
ejpam-5423	281	27	ω	ω	PROPN
ejpam-5423	281	28	n	n	CCONJ
ejpam-5423	281	29	)	)	PUNCT
ejpam-5423	281	30	of	of	ADP
ejpam-5423	281	31	g	g	PROPN
ejpam-5423	281	32	and	and	CCONJ
ejpam-5423	281	33	every	every	DET
ejpam-5423	281	34	(	(	PUNCT
ejpam-5423	281	35	λ	λ	NOUN
ejpam-5423	281	36	,	,	PUNCT
ejpam-5423	281	37	δ)-ivbf	δ)-ivbf	NOUN
ejpam-5423	281	38	left	leave	VERB
ejpam-5423	281	39	ideal	ideal	ADJ
ejpam-5423	281	40	j	j	PROPN
ejpam-5423	282	1	=	=	PUNCT
ejpam-5423	282	2	(	(	PUNCT
ejpam-5423	282	3	ϖ	ϖ	X
ejpam-5423	282	4	p	p	X
ejpam-5423	282	5	,	,	PUNCT
ejpam-5423	282	6	ϖ	ϖ	NOUN
ejpam-5423	282	7	n	n	CCONJ
ejpam-5423	282	8	)	)	PUNCT
ejpam-5423	282	9	of	of	ADP
ejpam-5423	282	10	g	g	PROPN
ejpam-5423	282	11	,	,	PUNCT
ejpam-5423	282	12	t.	t.	PROPN
ejpam-5423	282	13	gaketem	gaketem	PROPN
ejpam-5423	282	14	,	,	PUNCT
ejpam-5423	282	15	t.	t.	PROPN
ejpam-5423	282	16	prommai	prommai	PROPN
ejpam-5423	282	17	/	/	SYM
ejpam-5423	282	18	eur	eur	PROPN
ejpam-5423	282	19	.	.	PUNCT
ejpam-5423	283	1	j.	j.	PROPN
ejpam-5423	283	2	pure	pure	PROPN
ejpam-5423	283	3	appl	appl	PROPN
ejpam-5423	283	4	.	.	PROPN
ejpam-5423	283	5	math	math	PROPN
ejpam-5423	283	6	,	,	PUNCT
ejpam-5423	283	7	17	17	NUM
ejpam-5423	283	8	(	(	PUNCT
ejpam-5423	283	9	4	4	NUM
ejpam-5423	283	10	)	)	PUNCT
ejpam-5423	283	11	(	(	PUNCT
ejpam-5423	283	12	2024	2024	NUM
ejpam-5423	283	13	)	)	PUNCT
ejpam-5423	283	14	,	,	PUNCT
ejpam-5423	283	15	3223	3223	NUM
ejpam-5423	283	16	-	-	SYM
ejpam-5423	283	17	3241	3241	NUM
ejpam-5423	283	18	3236	3236	NUM
ejpam-5423	283	19	(	(	PUNCT
ejpam-5423	283	20	3	3	NUM
ejpam-5423	283	21	)	)	PUNCT
ejpam-5423	283	22	(	(	PUNCT
ejpam-5423	283	23	t	t	PROPN
ejpam-5423	283	24	⊓	⊓	PROPN
ejpam-5423	283	25	j	j	PROPN
ejpam-5423	283	26	)	)	PUNCT
ejpam-5423	283	27	λ	λ	PROPN
ejpam-5423	283	28	δ	δ	PROPN
ejpam-5423	283	29	⊑	⊑	X
ejpam-5423	283	30	(	(	PUNCT
ejpam-5423	283	31	t	t	PROPN
ejpam-5423	283	32	◦	◦	NOUN
ejpam-5423	283	33	j	j	PROPN
ejpam-5423	283	34	)	)	PUNCT
ejpam-5423	283	35	λ	λ	PROPN
ejpam-5423	283	36	δ	δ	PROPN
ejpam-5423	283	37	,	,	PUNCT
ejpam-5423	283	38	for	for	ADP
ejpam-5423	283	39	every	every	DET
ejpam-5423	283	40	(	(	PUNCT
ejpam-5423	283	41	λ	λ	NOUN
ejpam-5423	283	42	,	,	PUNCT
ejpam-5423	283	43	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	283	44	right	right	ADJ
ejpam-5423	283	45	ideal	ideal	NOUN
ejpam-5423	283	46	t	t	PROPN
ejpam-5423	283	47	=	=	SYM
ejpam-5423	283	48	(	(	PUNCT
ejpam-5423	283	49	ω	ω	PROPN
ejpam-5423	283	50	p	p	PROPN
ejpam-5423	283	51	,	,	PUNCT
ejpam-5423	283	52	ω	ω	PROPN
ejpam-5423	283	53	n	n	CCONJ
ejpam-5423	283	54	)	)	PUNCT
ejpam-5423	283	55	of	of	ADP
ejpam-5423	283	56	g	g	PROPN
ejpam-5423	283	57	and	and	CCONJ
ejpam-5423	283	58	every	every	DET
ejpam-5423	283	59	(	(	PUNCT
ejpam-5423	283	60	λ	λ	NOUN
ejpam-5423	283	61	,	,	PUNCT
ejpam-5423	283	62	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	283	63	quasi	quasi	ADJ
ejpam-5423	283	64	-	-	ADJ
ejpam-5423	283	65	ideal	ideal	ADJ
ejpam-5423	283	66	j	j	PROPN
ejpam-5423	284	1	=	=	PUNCT
ejpam-5423	284	2	(	(	PUNCT
ejpam-5423	284	3	ϖ	ϖ	X
ejpam-5423	284	4	p	p	X
ejpam-5423	284	5	,	,	PUNCT
ejpam-5423	284	6	ϖ	ϖ	NOUN
ejpam-5423	284	7	n	n	CCONJ
ejpam-5423	284	8	)	)	PUNCT
ejpam-5423	284	9	of	of	ADP
ejpam-5423	284	10	g.	g.	PROPN
ejpam-5423	284	11	proof	proof	NOUN
ejpam-5423	284	12	.	.	PUNCT
ejpam-5423	285	1	(	(	PUNCT
ejpam-5423	285	2	1	1	X
ejpam-5423	285	3	)	)	PUNCT
ejpam-5423	285	4	⇒	⇒	NOUN
ejpam-5423	285	5	(	(	PUNCT
ejpam-5423	285	6	3	3	X
ejpam-5423	285	7	)	)	PUNCT
ejpam-5423	285	8	let	let	VERB
ejpam-5423	285	9	t	t	NOUN
ejpam-5423	285	10	=	=	SYM
ejpam-5423	285	11	(	(	PUNCT
ejpam-5423	285	12	ω	ω	PROPN
ejpam-5423	285	13	p	p	PROPN
ejpam-5423	285	14	,	,	PUNCT
ejpam-5423	285	15	ω	ω	PROPN
ejpam-5423	285	16	n	n	CCONJ
ejpam-5423	285	17	)	)	PUNCT
ejpam-5423	285	18	and	and	CCONJ
ejpam-5423	285	19	j	j	PROPN
ejpam-5423	285	20	=	=	PRON
ejpam-5423	285	21	(	(	PUNCT
ejpam-5423	285	22	ϖ	ϖ	X
ejpam-5423	285	23	p	p	X
ejpam-5423	285	24	,	,	PUNCT
ejpam-5423	285	25	ϖ	ϖ	PROPN
ejpam-5423	285	26	n	n	CCONJ
ejpam-5423	285	27	)	)	PUNCT
ejpam-5423	285	28	be	be	AUX
ejpam-5423	285	29	an	an	DET
ejpam-5423	285	30	(	(	PUNCT
ejpam-5423	285	31	λ	λ	NOUN
ejpam-5423	285	32	,	,	PUNCT
ejpam-5423	285	33	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	285	34	right	right	ADV
ejpam-5423	285	35	ideal	ideal	NOUN
ejpam-5423	285	36	and	and	CCONJ
ejpam-5423	285	37	an	an	DET
ejpam-5423	285	38	(	(	PUNCT
ejpam-5423	285	39	λ	λ	NOUN
ejpam-5423	285	40	,	,	PUNCT
ejpam-5423	285	41	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	285	42	quasi	quasi	NOUN
ejpam-5423	285	43	-	-	NOUN
ejpam-5423	285	44	ideal	ideal	ADJ
ejpam-5423	285	45	of	of	ADP
ejpam-5423	285	46	g	g	NOUN
ejpam-5423	285	47	respectively	respectively	ADV
ejpam-5423	285	48	and	and	CCONJ
ejpam-5423	285	49	let	let	VERB
ejpam-5423	285	50	e	e	X
ejpam-5423	285	51	∈	∈	PROPN
ejpam-5423	285	52	g.	g.	NOUN
ejpam-5423	285	53	since	since	SCONJ
ejpam-5423	285	54	g	g	PROPN
ejpam-5423	285	55	is	be	AUX
ejpam-5423	285	56	regular	regular	ADJ
ejpam-5423	285	57	,	,	PUNCT
ejpam-5423	285	58	there	there	PRON
ejpam-5423	285	59	exists	exist	VERB
ejpam-5423	285	60	g	g	PROPN
ejpam-5423	285	61	∈	∈	PROPN
ejpam-5423	285	62	g	g	PROPN
ejpam-5423	285	63	such	such	ADJ
ejpam-5423	285	64	that	that	SCONJ
ejpam-5423	285	65	e	e	PROPN
ejpam-5423	285	66	≤	≤	PROPN
ejpam-5423	285	67	ege	ege	PROPN
ejpam-5423	285	68	.	.	PUNCT
ejpam-5423	286	1	thus	thus	ADV
ejpam-5423	286	2	(	(	PUNCT
ejpam-5423	286	3	ωp	ωp	ADP
ejpam-5423	286	4	◦	◦	NOUN
ejpam-5423	286	5	ϖp)δ	ϖp)δ	PROPN
ejpam-5423	286	6	λ	λ	PROPN
ejpam-5423	286	7	(	(	PUNCT
ejpam-5423	286	8	e	e	NOUN
ejpam-5423	286	9	)	)	PUNCT
ejpam-5423	286	10	=	=	SYM
ejpam-5423	286	11	(	(	PUNCT
ejpam-5423	286	12	∨	∨	X
ejpam-5423	286	13	(	(	PUNCT
ejpam-5423	286	14	k	k	X
ejpam-5423	286	15	,	,	PUNCT
ejpam-5423	286	16	o)∈ae	o)∈ae	PROPN
ejpam-5423	286	17	{	{	PUNCT
ejpam-5423	286	18	ωp(k	ωp(k	NOUN
ejpam-5423	286	19	)	)	PUNCT
ejpam-5423	286	20	∧ϖp(o	∧ϖp(o	NOUN
ejpam-5423	286	21	)	)	PUNCT
ejpam-5423	286	22	}	}	PUNCT
ejpam-5423	286	23	∧	∧	PROPN
ejpam-5423	286	24	δ	δ	PROPN
ejpam-5423	286	25	p	p	NOUN
ejpam-5423	286	26	)	)	PUNCT
ejpam-5423	286	27	∨	∨	NUM
ejpam-5423	286	28	λ	λ	X
ejpam-5423	286	29	p	p	X
ejpam-5423	286	30	=	=	X
ejpam-5423	286	31	(	(	PUNCT
ejpam-5423	286	32	∨	∨	X
ejpam-5423	286	33	(	(	PUNCT
ejpam-5423	286	34	k	k	X
ejpam-5423	286	35	,	,	PUNCT
ejpam-5423	286	36	o)∈aege	o)∈aege	PROPN
ejpam-5423	286	37	{	{	PUNCT
ejpam-5423	286	38	ωp(k	ωp(k	NOUN
ejpam-5423	286	39	)	)	PUNCT
ejpam-5423	286	40	∧ϖp(o	∧ϖp(o	NOUN
ejpam-5423	286	41	)	)	PUNCT
ejpam-5423	286	42	}	}	PUNCT
ejpam-5423	286	43	∧	∧	PROPN
ejpam-5423	286	44	δ	δ	PROPN
ejpam-5423	286	45	p	p	NOUN
ejpam-5423	286	46	)	)	PUNCT
ejpam-5423	286	47	∨	∨	NUM
ejpam-5423	286	48	λ	λ	PROPN
ejpam-5423	286	49	p	p	X
ejpam-5423	286	50	≥	≥	X
ejpam-5423	286	51	(	(	PUNCT
ejpam-5423	286	52	(	(	PUNCT
ejpam-5423	286	53	ωp(e	ωp(e	X
ejpam-5423	286	54	)	)	PUNCT
ejpam-5423	286	55	∧ϖp(gr	∧ϖp(gr	NUM
ejpam-5423	286	56	)	)	PUNCT
ejpam-5423	286	57	)	)	PUNCT
ejpam-5423	287	1	∧	∧	PROPN
ejpam-5423	287	2	δ	δ	PROPN
ejpam-5423	287	3	p	p	NOUN
ejpam-5423	287	4	)	)	PUNCT
ejpam-5423	288	1	∨	∨	NUM
ejpam-5423	288	2	λ	λ	X
ejpam-5423	288	3	p	p	X
ejpam-5423	288	4	=	=	X
ejpam-5423	288	5	(	(	PUNCT
ejpam-5423	288	6	ωp(e	ωp(e	ADJ
ejpam-5423	288	7	)	)	PUNCT
ejpam-5423	288	8	∧ϖp(gr	∧ϖp(gr	NUM
ejpam-5423	288	9	)	)	PUNCT
ejpam-5423	288	10	∨	∨	NUM
ejpam-5423	288	11	λ	λ	PROPN
ejpam-5423	288	12	p	p	NOUN
ejpam-5423	288	13	)	)	PUNCT
ejpam-5423	288	14	∧	∧	PROPN
ejpam-5423	288	15	δ	δ	PROPN
ejpam-5423	288	16	p	p	PROPN
ejpam-5423	288	17	∨	∨	NUM
ejpam-5423	288	18	λ	λ	PROPN
ejpam-5423	288	19	p	p	X
ejpam-5423	288	20	≥	≥	X
ejpam-5423	288	21	(	(	PUNCT
ejpam-5423	288	22	ωp(e	ωp(e	ADJ
ejpam-5423	288	23	)	)	PUNCT
ejpam-5423	288	24	∧ϖp(e	∧ϖp(e	ADJ
ejpam-5423	288	25	)	)	PUNCT
ejpam-5423	288	26	∧	∧	PROPN
ejpam-5423	288	27	δ	δ	PROPN
ejpam-5423	288	28	p	p	NOUN
ejpam-5423	288	29	)	)	PUNCT
ejpam-5423	288	30	∧	∧	PROPN
ejpam-5423	288	31	δ	δ	PROPN
ejpam-5423	288	32	p	p	NOUN
ejpam-5423	288	33	∨	∨	NUM
ejpam-5423	288	34	λ	λ	PROPN
ejpam-5423	288	35	p	p	X
ejpam-5423	288	36	=	=	X
ejpam-5423	288	37	(	(	PUNCT
ejpam-5423	288	38	(	(	PUNCT
ejpam-5423	288	39	ωp(e	ωp(e	ADJ
ejpam-5423	288	40	)	)	PUNCT
ejpam-5423	288	41	∧ϖp(e	∧ϖp(e	NOUN
ejpam-5423	288	42	)	)	PUNCT
ejpam-5423	288	43	)	)	PUNCT
ejpam-5423	288	44	∧	∧	PROPN
ejpam-5423	288	45	δ	δ	PROPN
ejpam-5423	288	46	p	p	NOUN
ejpam-5423	288	47	)	)	PUNCT
ejpam-5423	288	48	∨	∨	NUM
ejpam-5423	289	1	λ	λ	X
ejpam-5423	289	2	p	p	X
ejpam-5423	289	3	=	=	X
ejpam-5423	289	4	(	(	PUNCT
ejpam-5423	289	5	ωp	ωp	ADP
ejpam-5423	289	6	∩ϖp)δ	∩ϖp)δ	PROPN
ejpam-5423	289	7	λ	λ	PROPN
ejpam-5423	289	8	(	(	PUNCT
ejpam-5423	289	9	e	e	NOUN
ejpam-5423	289	10	)	)	PUNCT
ejpam-5423	289	11	and	and	CCONJ
ejpam-5423	289	12	(	(	PUNCT
ejpam-5423	289	13	ωn	ωn	ADP
ejpam-5423	289	14	◦	◦	NOUN
ejpam-5423	289	15	ϖn)λ	ϖn)λ	PROPN
ejpam-5423	289	16	δ	δ	PROPN
ejpam-5423	289	17	(	(	PUNCT
ejpam-5423	289	18	e	e	NOUN
ejpam-5423	289	19	)	)	PUNCT
ejpam-5423	289	20	=	=	SYM
ejpam-5423	289	21	(	(	PUNCT
ejpam-5423	289	22	∧	∧	PROPN
ejpam-5423	289	23	(	(	PUNCT
ejpam-5423	289	24	k	k	X
ejpam-5423	289	25	,	,	PUNCT
ejpam-5423	289	26	o)∈ae	o)∈ae	PROPN
ejpam-5423	289	27	{	{	PUNCT
ejpam-5423	289	28	ωn(k	ωn(k	PROPN
ejpam-5423	289	29	)	)	PUNCT
ejpam-5423	289	30	∨ϖn(o	∨ϖn(o	PROPN
ejpam-5423	289	31	)	)	PUNCT
ejpam-5423	289	32	}	}	PUNCT
ejpam-5423	289	33	∧	∧	PROPN
ejpam-5423	289	34	λ	λ	PROPN
ejpam-5423	289	35	n	n	CCONJ
ejpam-5423	289	36	)	)	PUNCT
ejpam-5423	289	37	∨	∨	NUM
ejpam-5423	289	38	δ	δ	PROPN
ejpam-5423	289	39	n	n	X
ejpam-5423	289	40	=	=	PUNCT
ejpam-5423	289	41	(	(	PUNCT
ejpam-5423	289	42	∧	∧	PROPN
ejpam-5423	289	43	(	(	PUNCT
ejpam-5423	289	44	k	k	X
ejpam-5423	289	45	,	,	PUNCT
ejpam-5423	289	46	o)∈aege	o)∈aege	PROPN
ejpam-5423	289	47	{	{	PUNCT
ejpam-5423	289	48	ωn(k	ωn(k	PROPN
ejpam-5423	289	49	)	)	PUNCT
ejpam-5423	289	50	∨ϖn(o	∨ϖn(o	PROPN
ejpam-5423	289	51	)	)	PUNCT
ejpam-5423	289	52	}	}	PUNCT
ejpam-5423	289	53	∧	∧	PROPN
ejpam-5423	289	54	λ	λ	PROPN
ejpam-5423	289	55	n	n	CCONJ
ejpam-5423	289	56	)	)	PUNCT
ejpam-5423	289	57	∨	∨	NUM
ejpam-5423	289	58	δ	δ	PROPN
ejpam-5423	289	59	n	n	CCONJ
ejpam-5423	289	60	≤	≤	NUM
ejpam-5423	289	61	(	(	PUNCT
ejpam-5423	289	62	(	(	PUNCT
ejpam-5423	289	63	ωn(e	ωn(e	NUM
ejpam-5423	289	64	)	)	PUNCT
ejpam-5423	289	65	∨ϖn(ge	∨ϖn(ge	NOUN
ejpam-5423	289	66	)	)	PUNCT
ejpam-5423	289	67	)	)	PUNCT
ejpam-5423	290	1	∧	∧	NOUN
ejpam-5423	290	2	λ	λ	PROPN
ejpam-5423	290	3	n	n	CCONJ
ejpam-5423	290	4	)	)	PUNCT
ejpam-5423	290	5	∨	∨	NUM
ejpam-5423	290	6	δ	δ	PROPN
ejpam-5423	290	7	n	n	X
ejpam-5423	290	8	=	=	SYM
ejpam-5423	290	9	(	(	PUNCT
ejpam-5423	290	10	ωn(e	ωn(e	NOUN
ejpam-5423	290	11	)	)	PUNCT
ejpam-5423	290	12	∨ϖn(ge	∨ϖn(ge	NOUN
ejpam-5423	290	13	)	)	PUNCT
ejpam-5423	290	14	∧	∧	PROPN
ejpam-5423	290	15	λ	λ	PROPN
ejpam-5423	290	16	n	n	CCONJ
ejpam-5423	290	17	)	)	PUNCT
ejpam-5423	290	18	∧	∧	PROPN
ejpam-5423	290	19	λ	λ	PROPN
ejpam-5423	290	20	n	n	CCONJ
ejpam-5423	290	21	∨	∨	NUM
ejpam-5423	290	22	δ	δ	PROPN
ejpam-5423	290	23	n	n	CCONJ
ejpam-5423	290	24	≤	≤	NUM
ejpam-5423	290	25	(	(	PUNCT
ejpam-5423	290	26	ωn(e	ωn(e	NUM
ejpam-5423	290	27	)	)	PUNCT
ejpam-5423	290	28	∨ϖn(e	∨ϖn(e	PROPN
ejpam-5423	290	29	)	)	PUNCT
ejpam-5423	290	30	∨	∨	NUM
ejpam-5423	290	31	δ	δ	PROPN
ejpam-5423	290	32	n	n	CCONJ
ejpam-5423	290	33	)	)	PUNCT
ejpam-5423	290	34	∧	∧	PROPN
ejpam-5423	290	35	λ	λ	PROPN
ejpam-5423	290	36	n	n	CCONJ
ejpam-5423	290	37	∨	∨	NUM
ejpam-5423	290	38	δ	δ	PROPN
ejpam-5423	290	39	n	n	X
ejpam-5423	290	40	=	=	SYM
ejpam-5423	290	41	(	(	PUNCT
ejpam-5423	290	42	(	(	PUNCT
ejpam-5423	290	43	ωp(n	ωp(n	NOUN
ejpam-5423	290	44	)	)	PUNCT
ejpam-5423	290	45	∨ϖn(e	∨ϖn(e	PROPN
ejpam-5423	290	46	)	)	PUNCT
ejpam-5423	290	47	)	)	PUNCT
ejpam-5423	290	48	∧	∧	NOUN
ejpam-5423	290	49	λ	λ	PROPN
ejpam-5423	290	50	n	n	CCONJ
ejpam-5423	290	51	)	)	PUNCT
ejpam-5423	290	52	∨	∨	NUM
ejpam-5423	290	53	δ	δ	PROPN
ejpam-5423	290	54	n	n	X
ejpam-5423	290	55	=	=	PUNCT
ejpam-5423	290	56	(	(	PUNCT
ejpam-5423	290	57	ωn	ωn	PROPN
ejpam-5423	290	58	∪ϖn)λ	∪ϖn)λ	PROPN
ejpam-5423	290	59	δ	δ	PROPN
ejpam-5423	290	60	(	(	PUNCT
ejpam-5423	290	61	e	e	NOUN
ejpam-5423	290	62	)	)	PUNCT
ejpam-5423	290	63	,	,	PUNCT
ejpam-5423	290	64	thus	thus	ADV
ejpam-5423	290	65	,	,	PUNCT
ejpam-5423	290	66	(	(	PUNCT
ejpam-5423	290	67	ωp	ωp	ADP
ejpam-5423	290	68	◦	◦	NOUN
ejpam-5423	290	69	ϖp)δ	ϖp)δ	PROPN
ejpam-5423	290	70	λ	λ	PROPN
ejpam-5423	290	71	(	(	PUNCT
ejpam-5423	290	72	e	e	NOUN
ejpam-5423	290	73	)	)	PUNCT
ejpam-5423	290	74	≥	≥	NOUN
ejpam-5423	290	75	(	(	PUNCT
ejpam-5423	290	76	ωp	ωp	ADP
ejpam-5423	290	77	∩ϖp)δ	∩ϖp)δ	PROPN
ejpam-5423	290	78	λ	λ	PROPN
ejpam-5423	290	79	(	(	PUNCT
ejpam-5423	290	80	e	e	NOUN
ejpam-5423	290	81	)	)	PUNCT
ejpam-5423	290	82	and	and	CCONJ
ejpam-5423	290	83	(	(	PUNCT
ejpam-5423	290	84	ωn	ωn	ADP
ejpam-5423	290	85	◦	◦	NOUN
ejpam-5423	290	86	ϖn)λ	ϖn)λ	PROPN
ejpam-5423	290	87	δ	δ	PROPN
ejpam-5423	290	88	(	(	PUNCT
ejpam-5423	290	89	e	e	NOUN
ejpam-5423	290	90	)	)	PUNCT
ejpam-5423	290	91	≤	≤	NOUN
ejpam-5423	290	92	(	(	PUNCT
ejpam-5423	290	93	ωn	ωn	ADP
ejpam-5423	290	94	∪ϖn)λ	∪ϖn)λ	PROPN
ejpam-5423	290	95	δ	δ	PROPN
ejpam-5423	290	96	(	(	PUNCT
ejpam-5423	290	97	e	e	NOUN
ejpam-5423	290	98	)	)	PUNCT
ejpam-5423	290	99	hence	hence	ADV
ejpam-5423	290	100	,	,	PUNCT
ejpam-5423	290	101	(	(	PUNCT
ejpam-5423	290	102	t	t	PROPN
ejpam-5423	290	103	⊓	⊓	PROPN
ejpam-5423	290	104	j	j	PROPN
ejpam-5423	290	105	)	)	PUNCT
ejpam-5423	290	106	λ	λ	PROPN
ejpam-5423	290	107	δ	δ	PROPN
ejpam-5423	290	108	⊑	⊑	X
ejpam-5423	290	109	(	(	PUNCT
ejpam-5423	290	110	t	t	PROPN
ejpam-5423	290	111	◦	◦	NOUN
ejpam-5423	290	112	j	j	PROPN
ejpam-5423	290	113	)	)	PUNCT
ejpam-5423	290	114	λ	λ	PROPN
ejpam-5423	290	115	δ	δ	PROPN
ejpam-5423	290	116	.	.	PUNCT
ejpam-5423	291	1	(	(	PUNCT
ejpam-5423	291	2	3	3	X
ejpam-5423	291	3	)	)	PUNCT
ejpam-5423	291	4	⇒	⇒	NOUN
ejpam-5423	291	5	(	(	PUNCT
ejpam-5423	291	6	1	1	X
ejpam-5423	291	7	)	)	PUNCT
ejpam-5423	291	8	let	let	VERB
ejpam-5423	291	9	r	r	NOUN
ejpam-5423	291	10	and	and	CCONJ
ejpam-5423	291	11	q	q	AUX
ejpam-5423	291	12	be	be	AUX
ejpam-5423	291	13	a	a	DET
ejpam-5423	291	14	right	right	ADJ
ejpam-5423	291	15	ideal	ideal	NOUN
ejpam-5423	291	16	and	and	CCONJ
ejpam-5423	291	17	quasi	quasi	ADJ
ejpam-5423	291	18	-	-	NOUN
ejpam-5423	291	19	ideal	ideal	ADJ
ejpam-5423	291	20	of	of	ADP
ejpam-5423	291	21	f	f	PROPN
ejpam-5423	291	22	respectively	respectively	ADV
ejpam-5423	291	23	.	.	PUNCT
ejpam-5423	292	1	then	then	ADV
ejpam-5423	292	2	by	by	ADP
ejpam-5423	292	3	theorem	theorem	NOUN
ejpam-5423	292	4	1	1	NUM
ejpam-5423	292	5	and	and	CCONJ
ejpam-5423	292	6	6	6	NUM
ejpam-5423	292	7	,	,	PUNCT
ejpam-5423	292	8	χr	χr	VERB
ejpam-5423	292	9	=	=	PUNCT
ejpam-5423	292	10	(	(	PUNCT
ejpam-5423	292	11	g;χ	g;χ	PROPN
ejpam-5423	292	12	p	p	X
ejpam-5423	292	13	r	r	PROPN
ejpam-5423	292	14	,	,	PUNCT
ejpam-5423	292	15	χ	χ	NOUN
ejpam-5423	292	16	n	n	ADV
ejpam-5423	292	17	r	r	NOUN
ejpam-5423	292	18	)	)	PUNCT
ejpam-5423	292	19	and	and	CCONJ
ejpam-5423	292	20	χq	χq	PROPN
ejpam-5423	292	21	=	=	PUNCT
ejpam-5423	292	22	(	(	PUNCT
ejpam-5423	292	23	g;χ	g;χ	PROPN
ejpam-5423	292	24	p	p	PROPN
ejpam-5423	292	25	q	q	PROPN
ejpam-5423	292	26	,	,	PUNCT
ejpam-5423	292	27	χ	χ	PROPN
ejpam-5423	292	28	n	n	ADV
ejpam-5423	292	29	q	q	NOUN
ejpam-5423	292	30	)	)	PUNCT
ejpam-5423	292	31	is	be	AUX
ejpam-5423	292	32	an	an	DET
ejpam-5423	292	33	(	(	PUNCT
ejpam-5423	292	34	λ	λ	NOUN
ejpam-5423	292	35	,	,	PUNCT
ejpam-5423	292	36	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	292	37	right	right	ADV
ejpam-5423	292	38	ideal	ideal	NOUN
ejpam-5423	292	39	and	and	CCONJ
ejpam-5423	292	40	an	an	DET
ejpam-5423	292	41	(	(	PUNCT
ejpam-5423	292	42	λ	λ	NOUN
ejpam-5423	292	43	,	,	PUNCT
ejpam-5423	292	44	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	292	45	quasi	quasi	NOUN
ejpam-5423	292	46	-	-	NOUN
ejpam-5423	292	47	ideal	ideal	ADJ
ejpam-5423	292	48	of	of	ADP
ejpam-5423	292	49	g	g	NOUN
ejpam-5423	292	50	respectively	respectively	ADV
ejpam-5423	292	51	.	.	PUNCT
ejpam-5423	293	1	by	by	ADP
ejpam-5423	293	2	supposition	supposition	NOUN
ejpam-5423	293	3	and	and	CCONJ
ejpam-5423	293	4	thoerem7	thoerem7	PROPN
ejpam-5423	293	5	,	,	PUNCT
ejpam-5423	293	6	we	we	PRON
ejpam-5423	293	7	have	have	VERB
ejpam-5423	293	8	(	(	PUNCT
ejpam-5423	293	9	χ	χ	PRON
ejpam-5423	293	10	p	p	X
ejpam-5423	293	11	(	(	PUNCT
ejpam-5423	293	12	rq	rq	NOUN
ejpam-5423	293	13	]	]	PUNCT
ejpam-5423	293	14	)	)	PUNCT
ejpam-5423	293	15	δ	δ	PROPN
ejpam-5423	293	16	λ	λ	X
ejpam-5423	293	17	(	(	PUNCT
ejpam-5423	293	18	e	e	NOUN
ejpam-5423	293	19	)	)	PUNCT
ejpam-5423	293	20	=	=	SYM
ejpam-5423	294	1	(	(	PUNCT
ejpam-5423	294	2	χ	χ	NOUN
ejpam-5423	294	3	p	p	X
ejpam-5423	294	4	r	r	NOUN
ejpam-5423	294	5	◦	◦	NOUN
ejpam-5423	294	6	χ	χ	PRON
ejpam-5423	294	7	p	p	X
ejpam-5423	294	8	q	q	NOUN
ejpam-5423	294	9	)	)	PUNCT
ejpam-5423	294	10	δ	δ	PROPN
ejpam-5423	294	11	λ	λ	PROPN
ejpam-5423	294	12	(	(	PUNCT
ejpam-5423	294	13	e	e	NOUN
ejpam-5423	294	14	)	)	PUNCT
ejpam-5423	294	15	⊑	⊑	X
ejpam-5423	294	16	(	(	PUNCT
ejpam-5423	294	17	χ	χ	X
ejpam-5423	294	18	p	p	NOUN
ejpam-5423	294	19	r	r	NOUN
ejpam-5423	294	20	∩	∩	NOUN
ejpam-5423	294	21	χ	χ	X
ejpam-5423	294	22	p	p	PROPN
ejpam-5423	294	23	q	q	NOUN
ejpam-5423	294	24	)	)	PUNCT
ejpam-5423	294	25	δ	δ	PROPN
ejpam-5423	294	26	λ	λ	PROPN
ejpam-5423	294	27	(	(	PUNCT
ejpam-5423	294	28	e	e	NOUN
ejpam-5423	294	29	)	)	PUNCT
ejpam-5423	294	30	=	=	SYM
ejpam-5423	294	31	(	(	PUNCT
ejpam-5423	294	32	χ	χ	PRON
ejpam-5423	294	33	p	p	PROPN
ejpam-5423	294	34	r∩q	r∩q	PROPN
ejpam-5423	294	35	)	)	PUNCT
ejpam-5423	295	1	δ	δ	PROPN
ejpam-5423	295	2	λ	λ	PROPN
ejpam-5423	295	3	(	(	PUNCT
ejpam-5423	295	4	e	e	NOUN
ejpam-5423	295	5	)	)	PUNCT
ejpam-5423	295	6	=	=	SYM
ejpam-5423	295	7	δ	δ	X
ejpam-5423	295	8	p	p	NOUN
ejpam-5423	295	9	,	,	PUNCT
ejpam-5423	295	10	and	and	CCONJ
ejpam-5423	295	11	(	(	PUNCT
ejpam-5423	295	12	χ	χ	X
ejpam-5423	295	13	n	n	X
ejpam-5423	295	14	(	(	PUNCT
ejpam-5423	295	15	rq	rq	NOUN
ejpam-5423	295	16	]	]	PUNCT
ejpam-5423	295	17	)	)	PUNCT
ejpam-5423	296	1	λ	λ	PROPN
ejpam-5423	296	2	δ	δ	X
ejpam-5423	296	3	(	(	PUNCT
ejpam-5423	296	4	e	e	NOUN
ejpam-5423	296	5	)	)	PUNCT
ejpam-5423	296	6	=	=	SYM
ejpam-5423	296	7	(	(	PUNCT
ejpam-5423	296	8	χ	χ	NOUN
ejpam-5423	296	9	n	n	CCONJ
ejpam-5423	296	10	r	r	NOUN
ejpam-5423	296	11	◦	◦	NOUN
ejpam-5423	296	12	χ	χ	PRON
ejpam-5423	296	13	p	p	X
ejpam-5423	296	14	q	q	NOUN
ejpam-5423	296	15	)	)	PUNCT
ejpam-5423	296	16	λ	λ	PROPN
ejpam-5423	296	17	δ	δ	PROPN
ejpam-5423	296	18	(	(	PUNCT
ejpam-5423	296	19	e	e	NOUN
ejpam-5423	296	20	)	)	PUNCT
ejpam-5423	296	21	⊑	⊑	X
ejpam-5423	296	22	(	(	PUNCT
ejpam-5423	296	23	χ	χ	X
ejpam-5423	296	24	n	n	ADP
ejpam-5423	296	25	r	r	NOUN
ejpam-5423	296	26	∪	∪	NOUN
ejpam-5423	296	27	χ	χ	PRON
ejpam-5423	296	28	p	p	X
ejpam-5423	296	29	q	q	NOUN
ejpam-5423	296	30	)	)	PUNCT
ejpam-5423	296	31	λ	λ	PROPN
ejpam-5423	296	32	δ	δ	PROPN
ejpam-5423	296	33	(	(	PUNCT
ejpam-5423	296	34	e	e	NOUN
ejpam-5423	296	35	)	)	PUNCT
ejpam-5423	296	36	=	=	SYM
ejpam-5423	296	37	(	(	PUNCT
ejpam-5423	296	38	χ	χ	NOUN
ejpam-5423	296	39	n	n	DET
ejpam-5423	296	40	r∪q	r∪q	NOUN
ejpam-5423	296	41	)	)	PUNCT
ejpam-5423	297	1	λ	λ	PROPN
ejpam-5423	297	2	δ	δ	PROPN
ejpam-5423	297	3	(	(	PUNCT
ejpam-5423	297	4	e	e	NOUN
ejpam-5423	297	5	)	)	PUNCT
ejpam-5423	297	6	=	=	SYM
ejpam-5423	297	7	δ	δ	PROPN
ejpam-5423	297	8	n	n	NOUN
ejpam-5423	297	9	.	.	PUNCT
ejpam-5423	298	1	thus	thus	ADV
ejpam-5423	298	2	,	,	PUNCT
ejpam-5423	298	3	e	e	PROPN
ejpam-5423	298	4	∈	∈	PROPN
ejpam-5423	298	5	(	(	PUNCT
ejpam-5423	298	6	rq	rq	NOUN
ejpam-5423	298	7	]	]	PUNCT
ejpam-5423	298	8	.	.	PUNCT
ejpam-5423	299	1	hence	hence	ADV
ejpam-5423	299	2	,	,	PUNCT
ejpam-5423	299	3	r	r	NOUN
ejpam-5423	299	4	∩q	∩q	PROPN
ejpam-5423	299	5	⊆	⊆	NUM
ejpam-5423	299	6	(	(	PUNCT
ejpam-5423	299	7	rl	rl	X
ejpam-5423	299	8	]	]	PUNCT
ejpam-5423	299	9	.	.	PUNCT
ejpam-5423	300	1	therefore	therefore	ADV
ejpam-5423	300	2	by	by	ADP
ejpam-5423	300	3	lemma	lemma	PROPN
ejpam-5423	300	4	2	2	NUM
ejpam-5423	300	5	,	,	PUNCT
ejpam-5423	300	6	g	g	PROPN
ejpam-5423	300	7	is	be	AUX
ejpam-5423	300	8	regular	regular	ADJ
ejpam-5423	300	9	.	.	PUNCT
ejpam-5423	301	1	in	in	ADP
ejpam-5423	301	2	a	a	DET
ejpam-5423	301	3	similar	similar	ADJ
ejpam-5423	301	4	manner	manner	NOUN
ejpam-5423	301	5	,	,	PUNCT
ejpam-5423	301	6	it	it	PRON
ejpam-5423	301	7	may	may	AUX
ejpam-5423	301	8	be	be	AUX
ejpam-5423	301	9	shown	show	VERB
ejpam-5423	301	10	that	that	SCONJ
ejpam-5423	301	11	(	(	PUNCT
ejpam-5423	301	12	1	1	X
ejpam-5423	301	13	)	)	PUNCT
ejpam-5423	301	14	⇔	⇔	NOUN
ejpam-5423	301	15	(	(	PUNCT
ejpam-5423	301	16	2	2	NUM
ejpam-5423	301	17	)	)	PUNCT
ejpam-5423	301	18	.	.	PUNCT
ejpam-5423	302	1	corollary	corollary	ADJ
ejpam-5423	302	2	1	1	NUM
ejpam-5423	302	3	.	.	PUNCT
ejpam-5423	303	1	for	for	ADP
ejpam-5423	303	2	an	an	DET
ejpam-5423	303	3	ordered	order	VERB
ejpam-5423	303	4	semigroup	semigroup	NOUN
ejpam-5423	303	5	g	g	PROPN
ejpam-5423	303	6	and	and	CCONJ
ejpam-5423	303	7	let	let	VERB
ejpam-5423	303	8	t	t	NOUN
ejpam-5423	303	9	=	=	SYM
ejpam-5423	303	10	(	(	PUNCT
ejpam-5423	303	11	ω	ω	PROPN
ejpam-5423	303	12	p	p	PROPN
ejpam-5423	303	13	,	,	PUNCT
ejpam-5423	303	14	ω	ω	PROPN
ejpam-5423	303	15	n	n	CCONJ
ejpam-5423	303	16	)	)	PUNCT
ejpam-5423	303	17	and	and	CCONJ
ejpam-5423	303	18	j	j	PROPN
ejpam-5423	303	19	=	=	PRON
ejpam-5423	303	20	(	(	PUNCT
ejpam-5423	303	21	ϖ	ϖ	X
ejpam-5423	303	22	p	p	X
ejpam-5423	303	23	,	,	PUNCT
ejpam-5423	303	24	ϖ	ϖ	NOUN
ejpam-5423	303	25	n	n	CCONJ
ejpam-5423	303	26	)	)	PUNCT
ejpam-5423	303	27	,	,	PUNCT
ejpam-5423	303	28	the	the	DET
ejpam-5423	303	29	following	follow	VERB
ejpam-5423	303	30	conditions	condition	NOUN
ejpam-5423	303	31	are	be	AUX
ejpam-5423	303	32	equivalent	equivalent	ADJ
ejpam-5423	303	33	.	.	PUNCT
ejpam-5423	304	1	(	(	PUNCT
ejpam-5423	304	2	1	1	X
ejpam-5423	304	3	)	)	PUNCT
ejpam-5423	304	4	g	g	NOUN
ejpam-5423	304	5	is	be	AUX
ejpam-5423	304	6	a	a	DET
ejpam-5423	304	7	regular	regular	ADJ
ejpam-5423	304	8	,	,	PUNCT
ejpam-5423	304	9	t.	t.	PROPN
ejpam-5423	304	10	gaketem	gaketem	NOUN
ejpam-5423	304	11	,	,	PUNCT
ejpam-5423	304	12	t.	t.	PROPN
ejpam-5423	304	13	prommai	prommai	PROPN
ejpam-5423	304	14	/	/	SYM
ejpam-5423	304	15	eur	eur	PROPN
ejpam-5423	304	16	.	.	PUNCT
ejpam-5423	305	1	j.	j.	PROPN
ejpam-5423	305	2	pure	pure	PROPN
ejpam-5423	305	3	appl	appl	PROPN
ejpam-5423	305	4	.	.	PROPN
ejpam-5423	305	5	math	math	PROPN
ejpam-5423	305	6	,	,	PUNCT
ejpam-5423	305	7	17	17	NUM
ejpam-5423	305	8	(	(	PUNCT
ejpam-5423	305	9	4	4	NUM
ejpam-5423	305	10	)	)	PUNCT
ejpam-5423	305	11	(	(	PUNCT
ejpam-5423	305	12	2024	2024	NUM
ejpam-5423	305	13	)	)	PUNCT
ejpam-5423	305	14	,	,	PUNCT
ejpam-5423	305	15	3223	3223	NUM
ejpam-5423	305	16	-	-	SYM
ejpam-5423	305	17	3241	3241	NUM
ejpam-5423	305	18	3237	3237	NUM
ejpam-5423	305	19	(	(	PUNCT
ejpam-5423	305	20	2	2	NUM
ejpam-5423	305	21	)	)	PUNCT
ejpam-5423	305	22	(	(	PUNCT
ejpam-5423	305	23	t	t	PROPN
ejpam-5423	305	24	⊓	⊓	PROPN
ejpam-5423	305	25	j	j	PROPN
ejpam-5423	305	26	)	)	PUNCT
ejpam-5423	305	27	λ	λ	PROPN
ejpam-5423	305	28	δ	δ	PROPN
ejpam-5423	305	29	⊑	⊑	X
ejpam-5423	305	30	(	(	PUNCT
ejpam-5423	305	31	t	t	PROPN
ejpam-5423	305	32	◦	◦	NOUN
ejpam-5423	305	33	j	j	PROPN
ejpam-5423	305	34	)	)	PUNCT
ejpam-5423	305	35	λ	λ	PROPN
ejpam-5423	305	36	δ	δ	PROPN
ejpam-5423	305	37	,	,	PUNCT
ejpam-5423	305	38	for	for	ADP
ejpam-5423	305	39	every	every	DET
ejpam-5423	305	40	(	(	PUNCT
ejpam-5423	305	41	λ	λ	NOUN
ejpam-5423	305	42	,	,	PUNCT
ejpam-5423	305	43	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	305	44	quasi	quasi	ADJ
ejpam-5423	305	45	-	-	ADJ
ejpam-5423	305	46	ideal	ideal	ADJ
ejpam-5423	305	47	t	t	NOUN
ejpam-5423	305	48	and	and	CCONJ
ejpam-5423	305	49	every	every	DET
ejpam-5423	305	50	(	(	PUNCT
ejpam-5423	305	51	λ	λ	NOUN
ejpam-5423	305	52	,	,	PUNCT
ejpam-5423	305	53	δ)-ivbf	δ)-ivbf	NOUN
ejpam-5423	305	54	left	leave	VERB
ejpam-5423	305	55	ideal	ideal	ADJ
ejpam-5423	305	56	j	j	PROPN
ejpam-5423	305	57	of	of	ADP
ejpam-5423	305	58	f	f	PROPN
ejpam-5423	305	59	,	,	PUNCT
ejpam-5423	305	60	(	(	PUNCT
ejpam-5423	305	61	3	3	NUM
ejpam-5423	305	62	)	)	PUNCT
ejpam-5423	305	63	(	(	PUNCT
ejpam-5423	305	64	t	t	NOUN
ejpam-5423	305	65	⊓j	⊓j	NOUN
ejpam-5423	305	66	)	)	PUNCT
ejpam-5423	305	67	λ	λ	PROPN
ejpam-5423	305	68	δ	δ	NOUN
ejpam-5423	305	69	⊑	⊑	X
ejpam-5423	305	70	(	(	PUNCT
ejpam-5423	305	71	t	t	PROPN
ejpam-5423	305	72	◦	◦	PROPN
ejpam-5423	305	73	j	j	PROPN
ejpam-5423	305	74	)	)	PUNCT
ejpam-5423	305	75	λ	λ	PROPN
ejpam-5423	305	76	δ	δ	PROPN
ejpam-5423	305	77	,	,	PUNCT
ejpam-5423	305	78	for	for	ADP
ejpam-5423	305	79	every	every	DET
ejpam-5423	305	80	(	(	PUNCT
ejpam-5423	305	81	λ	λ	PROPN
ejpam-5423	305	82	,	,	PUNCT
ejpam-5423	305	83	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	305	84	bi	bi	ADJ
ejpam-5423	305	85	-	-	ADJ
ejpam-5423	305	86	ideal	ideal	ADJ
ejpam-5423	305	87	t	t	NOUN
ejpam-5423	305	88	and	and	CCONJ
ejpam-5423	305	89	every	every	DET
ejpam-5423	305	90	(	(	PUNCT
ejpam-5423	305	91	λ	λ	NOUN
ejpam-5423	305	92	,	,	PUNCT
ejpam-5423	305	93	δ)-ivbf	δ)-ivbf	NOUN
ejpam-5423	305	94	left	leave	VERB
ejpam-5423	305	95	ideal	ideal	ADJ
ejpam-5423	305	96	j	j	PROPN
ejpam-5423	305	97	of	of	ADP
ejpam-5423	305	98	f	f	PROPN
ejpam-5423	305	99	,	,	PUNCT
ejpam-5423	305	100	(	(	PUNCT
ejpam-5423	305	101	4	4	NUM
ejpam-5423	305	102	)	)	PUNCT
ejpam-5423	305	103	(	(	PUNCT
ejpam-5423	305	104	t	t	PROPN
ejpam-5423	305	105	⊓	⊓	PROPN
ejpam-5423	305	106	j	j	PROPN
ejpam-5423	305	107	)	)	PUNCT
ejpam-5423	305	108	λ	λ	PROPN
ejpam-5423	305	109	δ	δ	PROPN
ejpam-5423	305	110	⊑	⊑	X
ejpam-5423	305	111	(	(	PUNCT
ejpam-5423	305	112	t	t	PROPN
ejpam-5423	305	113	◦	◦	NOUN
ejpam-5423	305	114	j	j	PROPN
ejpam-5423	305	115	)	)	PUNCT
ejpam-5423	305	116	λ	λ	PROPN
ejpam-5423	305	117	δ	δ	PROPN
ejpam-5423	305	118	,	,	PUNCT
ejpam-5423	305	119	for	for	ADP
ejpam-5423	305	120	every	every	DET
ejpam-5423	305	121	(	(	PUNCT
ejpam-5423	305	122	λ	λ	NOUN
ejpam-5423	305	123	,	,	PUNCT
ejpam-5423	305	124	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	305	125	right	right	ADJ
ejpam-5423	305	126	ideal	ideal	NOUN
ejpam-5423	305	127	t	t	PROPN
ejpam-5423	305	128	and	and	CCONJ
ejpam-5423	305	129	every	every	DET
ejpam-5423	305	130	(	(	PUNCT
ejpam-5423	305	131	λ	λ	NOUN
ejpam-5423	305	132	,	,	PUNCT
ejpam-5423	305	133	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	305	134	quasi	quasi	ADJ
ejpam-5423	305	135	-	-	ADJ
ejpam-5423	305	136	ideal	ideal	ADJ
ejpam-5423	305	137	j	j	PROPN
ejpam-5423	305	138	of	of	ADP
ejpam-5423	305	139	f	f	PROPN
ejpam-5423	305	140	,	,	PUNCT
ejpam-5423	305	141	(	(	PUNCT
ejpam-5423	305	142	5	5	NUM
ejpam-5423	305	143	)	)	PUNCT
ejpam-5423	305	144	(	(	PUNCT
ejpam-5423	305	145	t	t	PROPN
ejpam-5423	305	146	⊓	⊓	PROPN
ejpam-5423	305	147	j	j	PROPN
ejpam-5423	305	148	)	)	PUNCT
ejpam-5423	306	1	λ	λ	PROPN
ejpam-5423	306	2	δ	δ	PROPN
ejpam-5423	306	3	⊑	⊑	X
ejpam-5423	306	4	(	(	PUNCT
ejpam-5423	306	5	t	t	PROPN
ejpam-5423	306	6	◦	◦	NOUN
ejpam-5423	306	7	j	j	PROPN
ejpam-5423	306	8	)	)	PUNCT
ejpam-5423	306	9	λ	λ	PROPN
ejpam-5423	306	10	δ	δ	PROPN
ejpam-5423	306	11	,	,	PUNCT
ejpam-5423	306	12	for	for	ADP
ejpam-5423	306	13	every	every	DET
ejpam-5423	306	14	(	(	PUNCT
ejpam-5423	306	15	λ	λ	NOUN
ejpam-5423	306	16	,	,	PUNCT
ejpam-5423	306	17	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	306	18	right	right	ADJ
ejpam-5423	306	19	ideal	ideal	NOUN
ejpam-5423	306	20	t	t	PROPN
ejpam-5423	306	21	and	and	CCONJ
ejpam-5423	306	22	every	every	DET
ejpam-5423	306	23	(	(	PUNCT
ejpam-5423	306	24	λ	λ	NOUN
ejpam-5423	306	25	,	,	PUNCT
ejpam-5423	306	26	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	306	27	bi	bi	ADJ
ejpam-5423	306	28	-	-	ADJ
ejpam-5423	306	29	ideal	ideal	ADJ
ejpam-5423	306	30	j	j	PROPN
ejpam-5423	306	31	of	of	ADP
ejpam-5423	306	32	f.	f.	PROPN
ejpam-5423	306	33	some	some	DET
ejpam-5423	306	34	equivalent	equivalent	ADJ
ejpam-5423	306	35	conditions	condition	NOUN
ejpam-5423	306	36	are	be	AUX
ejpam-5423	306	37	important	important	ADJ
ejpam-5423	306	38	properties	property	NOUN
ejpam-5423	306	39	for	for	ADP
ejpam-5423	306	40	(	(	PUNCT
ejpam-5423	306	41	λ	λ	PROPN
ejpam-5423	306	42	,	,	PUNCT
ejpam-5423	306	43	δ)-ivbf	δ)-ivbf	NOUN
ejpam-5423	306	44	-	-	SYM
ejpam-5423	306	45	subsemigroups	subsemigroup	NOUN
ejpam-5423	306	46	of	of	ADP
ejpam-5423	306	47	semigroups	semigroup	NOUN
ejpam-5423	306	48	.	.	PUNCT
ejpam-5423	307	1	theorem	theorem	VERB
ejpam-5423	307	2	9	9	NUM
ejpam-5423	307	3	.	.	PUNCT
ejpam-5423	308	1	an	an	DET
ejpam-5423	308	2	(	(	PUNCT
ejpam-5423	308	3	λ	λ	NOUN
ejpam-5423	308	4	,	,	PUNCT
ejpam-5423	308	5	δ)-ivbf	δ)-ivbf	NOUN
ejpam-5423	308	6	set	set	VERB
ejpam-5423	308	7	t	t	NOUN
ejpam-5423	308	8	=	=	SYM
ejpam-5423	308	9	(	(	PUNCT
ejpam-5423	308	10	ω	ω	PROPN
ejpam-5423	308	11	p	p	PROPN
ejpam-5423	308	12	,	,	PUNCT
ejpam-5423	308	13	ω	ω	PROPN
ejpam-5423	308	14	n	n	CCONJ
ejpam-5423	308	15	)	)	PUNCT
ejpam-5423	308	16	is	be	AUX
ejpam-5423	308	17	an	an	DET
ejpam-5423	308	18	(	(	PUNCT
ejpam-5423	308	19	λ	λ	NOUN
ejpam-5423	308	20	,	,	PUNCT
ejpam-5423	308	21	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	308	22	subsemigroup	subsemigroup	NOUN
ejpam-5423	308	23	of	of	ADP
ejpam-5423	308	24	an	an	DET
ejpam-5423	308	25	ordered	order	VERB
ejpam-5423	308	26	semigroup	semigroup	NOUN
ejpam-5423	308	27	g	g	PROPN
ejpam-5423	308	28	if	if	SCONJ
ejpam-5423	309	1	and	and	CCONJ
ejpam-5423	309	2	only	only	ADV
ejpam-5423	309	3	if	if	SCONJ
ejpam-5423	309	4	(	(	PUNCT
ejpam-5423	309	5	t	t	PROPN
ejpam-5423	309	6	◦	◦	NOUN
ejpam-5423	309	7	t	t	PROPN
ejpam-5423	309	8	)	)	PUNCT
ejpam-5423	309	9	λ	λ	PROPN
ejpam-5423	309	10	δ	δ	PROPN
ejpam-5423	309	11	⊑	⊑	X
ejpam-5423	309	12	t	t	PROPN
ejpam-5423	309	13	λ	λ	PROPN
ejpam-5423	309	14	δ	δ	PROPN
ejpam-5423	309	15	.	.	PUNCT
ejpam-5423	310	1	proof	proof	NOUN
ejpam-5423	310	2	.	.	PUNCT
ejpam-5423	311	1	(	(	PUNCT
ejpam-5423	311	2	⇒	⇒	NOUN
ejpam-5423	311	3	)	)	PUNCT
ejpam-5423	311	4	assume	assume	VERB
ejpam-5423	311	5	that	that	SCONJ
ejpam-5423	311	6	t	t	NOUN
ejpam-5423	311	7	=	=	SYM
ejpam-5423	311	8	(	(	PUNCT
ejpam-5423	311	9	ω	ω	PROPN
ejpam-5423	311	10	p	p	PROPN
ejpam-5423	311	11	,	,	PUNCT
ejpam-5423	311	12	ω	ω	PROPN
ejpam-5423	311	13	n	n	CCONJ
ejpam-5423	311	14	)	)	PUNCT
ejpam-5423	311	15	is	be	AUX
ejpam-5423	311	16	an	an	DET
ejpam-5423	311	17	(	(	PUNCT
ejpam-5423	311	18	λ	λ	NOUN
ejpam-5423	311	19	,	,	PUNCT
ejpam-5423	311	20	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	311	21	subsemigroup	subsemigroup	NOUN
ejpam-5423	311	22	of	of	ADP
ejpam-5423	311	23	an	an	DET
ejpam-5423	311	24	ordered	order	VERB
ejpam-5423	311	25	semigroup	semigroup	NOUN
ejpam-5423	311	26	g	g	PROPN
ejpam-5423	311	27	and	and	CCONJ
ejpam-5423	311	28	let	let	VERB
ejpam-5423	311	29	e	e	PROPN
ejpam-5423	311	30	∈	∈	PROPN
ejpam-5423	311	31	g.	g.	NOUN
ejpam-5423	312	1	if	if	SCONJ
ejpam-5423	312	2	ae	ae	PROPN
ejpam-5423	312	3	=	=	SYM
ejpam-5423	312	4	∅	∅	NOUN
ejpam-5423	312	5	,	,	PUNCT
ejpam-5423	312	6	then	then	ADV
ejpam-5423	312	7	it	it	PRON
ejpam-5423	312	8	is	be	AUX
ejpam-5423	312	9	easy	easy	ADJ
ejpam-5423	312	10	to	to	PART
ejpam-5423	312	11	verify	verify	VERB
ejpam-5423	312	12	that	that	SCONJ
ejpam-5423	312	13	,	,	PUNCT
ejpam-5423	312	14	(	(	PUNCT
ejpam-5423	312	15	ωp	ωp	PART
ejpam-5423	312	16	◦	◦	VERB
ejpam-5423	312	17	ωp)δ	ωp)δ	PROPN
ejpam-5423	312	18	λ	λ	X
ejpam-5423	312	19	(	(	PUNCT
ejpam-5423	312	20	e	e	NOUN
ejpam-5423	312	21	)	)	PUNCT
ejpam-5423	312	22	≤	≤	NOUN
ejpam-5423	312	23	(	(	PUNCT
ejpam-5423	312	24	ωp)δ	ωp)δ	PROPN
ejpam-5423	312	25	λ	λ	X
ejpam-5423	312	26	(	(	PUNCT
ejpam-5423	312	27	e	e	NOUN
ejpam-5423	312	28	)	)	PUNCT
ejpam-5423	312	29	and	and	CCONJ
ejpam-5423	312	30	(	(	PUNCT
ejpam-5423	312	31	µn	µn	NOUN
ejpam-5423	312	32	◦	◦	NOUN
ejpam-5423	312	33	ωn)λ	ωn)λ	PROPN
ejpam-5423	312	34	δ	δ	PROPN
ejpam-5423	312	35	(	(	PUNCT
ejpam-5423	312	36	e	e	NOUN
ejpam-5423	312	37	)	)	PUNCT
ejpam-5423	312	38	≥	≥	NOUN
ejpam-5423	312	39	(	(	PUNCT
ejpam-5423	312	40	µn)λ	µn)λ	PROPN
ejpam-5423	312	41	δ	δ	PROPN
ejpam-5423	312	42	(	(	PUNCT
ejpam-5423	312	43	e	e	NOUN
ejpam-5423	312	44	)	)	PUNCT
ejpam-5423	312	45	.	.	PUNCT
ejpam-5423	313	1	if	if	SCONJ
ejpam-5423	313	2	ae	ae	PROPN
ejpam-5423	313	3	̸=	̸=	PROPN
ejpam-5423	313	4	∅	∅	NOUN
ejpam-5423	313	5	,	,	PUNCT
ejpam-5423	313	6	then	then	ADV
ejpam-5423	313	7	(	(	PUNCT
ejpam-5423	313	8	ωp	ωp	PART
ejpam-5423	313	9	◦	◦	VERB
ejpam-5423	313	10	ωp)δ	ωp)δ	PROPN
ejpam-5423	313	11	λ	λ	X
ejpam-5423	313	12	(	(	PUNCT
ejpam-5423	313	13	e	e	NOUN
ejpam-5423	313	14	)	)	PUNCT
ejpam-5423	313	15	=	=	SYM
ejpam-5423	313	16	(	(	PUNCT
ejpam-5423	313	17	∨	∨	X
ejpam-5423	313	18	(	(	PUNCT
ejpam-5423	313	19	k	k	X
ejpam-5423	313	20	,	,	PUNCT
ejpam-5423	313	21	o)∈ae	o)∈ae	PROPN
ejpam-5423	313	22	{	{	PUNCT
ejpam-5423	313	23	ωp(k	ωp(k	NOUN
ejpam-5423	313	24	)	)	PUNCT
ejpam-5423	313	25	∧	∧	NOUN
ejpam-5423	313	26	ωp(o	ωp(o	NOUN
ejpam-5423	313	27	)	)	PUNCT
ejpam-5423	313	28	}	}	PUNCT
ejpam-5423	313	29	∧	∧	PROPN
ejpam-5423	313	30	δ	δ	PROPN
ejpam-5423	313	31	p	p	NOUN
ejpam-5423	313	32	)	)	PUNCT
ejpam-5423	313	33	∨	∨	NUM
ejpam-5423	314	1	λ	λ	X
ejpam-5423	314	2	p	p	X
ejpam-5423	314	3	=	=	X
ejpam-5423	314	4	(	(	PUNCT
ejpam-5423	314	5	∨	∨	X
ejpam-5423	314	6	(	(	PUNCT
ejpam-5423	314	7	k	k	X
ejpam-5423	314	8	,	,	PUNCT
ejpam-5423	314	9	o)∈ae	o)∈ae	PROPN
ejpam-5423	314	10	{	{	PUNCT
ejpam-5423	314	11	ωp(k	ωp(k	NOUN
ejpam-5423	314	12	)	)	PUNCT
ejpam-5423	314	13	∧	∧	NOUN
ejpam-5423	314	14	ωp(o	ωp(o	NOUN
ejpam-5423	314	15	)	)	PUNCT
ejpam-5423	314	16	∧	∧	PROPN
ejpam-5423	314	17	δ	δ	NOUN
ejpam-5423	314	18	p	p	ADJ
ejpam-5423	314	19	}	}	PUNCT
ejpam-5423	314	20	∧	∧	PROPN
ejpam-5423	314	21	δ	δ	PROPN
ejpam-5423	314	22	p	p	NOUN
ejpam-5423	314	23	)	)	PUNCT
ejpam-5423	314	24	∨	∨	NUM
ejpam-5423	314	25	λ	λ	PROPN
ejpam-5423	314	26	p	p	NOUN
ejpam-5423	314	27	≤	≤	PROPN
ejpam-5423	314	28	(	(	PUNCT
ejpam-5423	314	29	∨	∨	X
ejpam-5423	314	30	(	(	PUNCT
ejpam-5423	314	31	k	k	X
ejpam-5423	314	32	,	,	PUNCT
ejpam-5423	314	33	o)∈ae	o)∈ae	PROPN
ejpam-5423	314	34	{	{	PUNCT
ejpam-5423	314	35	ωp(ko	ωp(ko	PROPN
ejpam-5423	314	36	)	)	PUNCT
ejpam-5423	314	37	∨	∨	NUM
ejpam-5423	314	38	λ	λ	X
ejpam-5423	314	39	p	p	X
ejpam-5423	314	40	}	}	PUNCT
ejpam-5423	314	41	∧	∧	PROPN
ejpam-5423	314	42	δ	δ	PROPN
ejpam-5423	314	43	p	p	NOUN
ejpam-5423	314	44	)	)	PUNCT
ejpam-5423	314	45	∨	∨	NUM
ejpam-5423	315	1	λ	λ	X
ejpam-5423	315	2	p	p	X
ejpam-5423	315	3	=	=	X
ejpam-5423	315	4	(	(	PUNCT
ejpam-5423	315	5	ωp(e	ωp(e	ADJ
ejpam-5423	315	6	)	)	PUNCT
ejpam-5423	315	7	∨	∨	NUM
ejpam-5423	315	8	λ	λ	PROPN
ejpam-5423	315	9	p	p	PROPN
ejpam-5423	315	10	∧	∧	PROPN
ejpam-5423	315	11	δ	δ	PROPN
ejpam-5423	315	12	p	p	NOUN
ejpam-5423	315	13	)	)	PUNCT
ejpam-5423	315	14	∨	∨	NUM
ejpam-5423	316	1	λ	λ	X
ejpam-5423	316	2	p	p	X
ejpam-5423	316	3	=	=	X
ejpam-5423	316	4	(	(	PUNCT
ejpam-5423	316	5	ωp(e	ωp(e	ADJ
ejpam-5423	316	6	)	)	PUNCT
ejpam-5423	316	7	∧	∧	PROPN
ejpam-5423	316	8	δ	δ	PROPN
ejpam-5423	316	9	p	p	NOUN
ejpam-5423	316	10	)	)	PUNCT
ejpam-5423	316	11	∨	∨	NUM
ejpam-5423	316	12	λ	λ	X
ejpam-5423	316	13	p	p	X
ejpam-5423	316	14	=	=	X
ejpam-5423	316	15	(	(	PUNCT
ejpam-5423	316	16	ωp)δ	ωp)δ	PROPN
ejpam-5423	316	17	λ	λ	X
ejpam-5423	316	18	(	(	PUNCT
ejpam-5423	316	19	e	e	NOUN
ejpam-5423	316	20	)	)	PUNCT
ejpam-5423	316	21	and	and	CCONJ
ejpam-5423	316	22	(	(	PUNCT
ejpam-5423	316	23	ωn	ωn	ADP
ejpam-5423	316	24	◦	◦	PROPN
ejpam-5423	316	25	ωn)λ	ωn)λ	PROPN
ejpam-5423	316	26	δ	δ	PROPN
ejpam-5423	316	27	(	(	PUNCT
ejpam-5423	316	28	e	e	NOUN
ejpam-5423	316	29	)	)	PUNCT
ejpam-5423	316	30	=	=	SYM
ejpam-5423	316	31	(	(	PUNCT
ejpam-5423	316	32	∧	∧	PROPN
ejpam-5423	316	33	(	(	PUNCT
ejpam-5423	316	34	k	k	X
ejpam-5423	316	35	,	,	PUNCT
ejpam-5423	316	36	o)∈ae	o)∈ae	PROPN
ejpam-5423	316	37	{	{	PUNCT
ejpam-5423	316	38	ωn(k	ωn(k	NUM
ejpam-5423	316	39	)	)	PUNCT
ejpam-5423	316	40	∨	∨	NUM
ejpam-5423	316	41	µn(o	µn(o	PUNCT
ejpam-5423	316	42	)	)	PUNCT
ejpam-5423	316	43	}	}	PUNCT
ejpam-5423	316	44	∧	∧	PROPN
ejpam-5423	316	45	λ	λ	PROPN
ejpam-5423	316	46	n	n	CCONJ
ejpam-5423	316	47	)	)	PUNCT
ejpam-5423	316	48	∨	∨	NUM
ejpam-5423	316	49	δ	δ	PROPN
ejpam-5423	316	50	n	n	X
ejpam-5423	316	51	=	=	PUNCT
ejpam-5423	316	52	(	(	PUNCT
ejpam-5423	316	53	∧	∧	PROPN
ejpam-5423	316	54	(	(	PUNCT
ejpam-5423	316	55	k	k	X
ejpam-5423	316	56	,	,	PUNCT
ejpam-5423	316	57	o)∈ae	o)∈ae	PROPN
ejpam-5423	316	58	{	{	PUNCT
ejpam-5423	316	59	ωn(k	ωn(k	NUM
ejpam-5423	316	60	)	)	PUNCT
ejpam-5423	316	61	∨	∨	NUM
ejpam-5423	316	62	µn(o	µn(o	PUNCT
ejpam-5423	316	63	)	)	PUNCT
ejpam-5423	316	64	∨	∨	PROPN
ejpam-5423	316	65	δ	δ	PROPN
ejpam-5423	316	66	n	n	CCONJ
ejpam-5423	316	67	}	}	PUNCT
ejpam-5423	316	68	∧	∧	PROPN
ejpam-5423	316	69	λ	λ	PROPN
ejpam-5423	316	70	n	n	CCONJ
ejpam-5423	316	71	)	)	PUNCT
ejpam-5423	316	72	∨	∨	NUM
ejpam-5423	316	73	δ	δ	PROPN
ejpam-5423	316	74	n	n	CCONJ
ejpam-5423	316	75	≤	≤	NUM
ejpam-5423	316	76	(	(	PUNCT
ejpam-5423	316	77	∧	∧	PROPN
ejpam-5423	316	78	(	(	PUNCT
ejpam-5423	316	79	k	k	X
ejpam-5423	316	80	,	,	PUNCT
ejpam-5423	316	81	o)∈ae	o)∈ae	PROPN
ejpam-5423	316	82	{	{	PUNCT
ejpam-5423	316	83	ωn(ko	ωn(ko	NOUN
ejpam-5423	316	84	)	)	PUNCT
ejpam-5423	316	85	∧	∧	PROPN
ejpam-5423	316	86	λ	λ	PROPN
ejpam-5423	316	87	n	n	CCONJ
ejpam-5423	316	88	}	}	PUNCT
ejpam-5423	316	89	∧	∧	PROPN
ejpam-5423	316	90	λ	λ	PROPN
ejpam-5423	316	91	n	n	CCONJ
ejpam-5423	316	92	)	)	PUNCT
ejpam-5423	316	93	∨	∨	NUM
ejpam-5423	316	94	δ	δ	PROPN
ejpam-5423	316	95	n	n	X
ejpam-5423	316	96	=	=	SYM
ejpam-5423	316	97	(	(	PUNCT
ejpam-5423	316	98	ωn(e	ωn(e	NOUN
ejpam-5423	316	99	)	)	PUNCT
ejpam-5423	316	100	∧	∧	NOUN
ejpam-5423	316	101	λ	λ	PROPN
ejpam-5423	316	102	n	n	CCONJ
ejpam-5423	316	103	∧	∧	PROPN
ejpam-5423	316	104	λ	λ	PROPN
ejpam-5423	316	105	n	n	CCONJ
ejpam-5423	316	106	)	)	PUNCT
ejpam-5423	316	107	∨	∨	NUM
ejpam-5423	316	108	δ	δ	PROPN
ejpam-5423	316	109	n	n	X
ejpam-5423	316	110	=	=	SYM
ejpam-5423	316	111	(	(	PUNCT
ejpam-5423	316	112	ωp(e	ωp(e	ADJ
ejpam-5423	316	113	)	)	PUNCT
ejpam-5423	316	114	∧	∧	PROPN
ejpam-5423	316	115	λ	λ	PROPN
ejpam-5423	316	116	n	n	CCONJ
ejpam-5423	316	117	)	)	PUNCT
ejpam-5423	316	118	∨	∨	NUM
ejpam-5423	316	119	δ	δ	PROPN
ejpam-5423	316	120	n	n	X
ejpam-5423	316	121	=	=	SYM
ejpam-5423	316	122	(	(	PUNCT
ejpam-5423	316	123	ωn)λ	ωn)λ	PROPN
ejpam-5423	316	124	δ	δ	PROPN
ejpam-5423	316	125	(	(	PUNCT
ejpam-5423	316	126	e	e	NOUN
ejpam-5423	316	127	)	)	PUNCT
ejpam-5423	316	128	thus	thus	ADV
ejpam-5423	316	129	,	,	PUNCT
ejpam-5423	316	130	(	(	PUNCT
ejpam-5423	316	131	ωp	ωp	INTJ
ejpam-5423	316	132	◦	◦	VERB
ejpam-5423	316	133	ωp)δ	ωp)δ	PROPN
ejpam-5423	316	134	λ	λ	X
ejpam-5423	316	135	(	(	PUNCT
ejpam-5423	316	136	e	e	NOUN
ejpam-5423	316	137	)	)	PUNCT
ejpam-5423	316	138	≤	≤	NOUN
ejpam-5423	316	139	(	(	PUNCT
ejpam-5423	316	140	ωp)δ	ωp)δ	PROPN
ejpam-5423	316	141	λ	λ	X
ejpam-5423	316	142	(	(	PUNCT
ejpam-5423	316	143	e	e	NOUN
ejpam-5423	316	144	)	)	PUNCT
ejpam-5423	316	145	and	and	CCONJ
ejpam-5423	316	146	(	(	PUNCT
ejpam-5423	316	147	ωn	ωn	ADP
ejpam-5423	316	148	◦	◦	PROPN
ejpam-5423	316	149	ωn)λ	ωn)λ	PROPN
ejpam-5423	316	150	δ	δ	PROPN
ejpam-5423	316	151	(	(	PUNCT
ejpam-5423	316	152	e	e	NOUN
ejpam-5423	316	153	)	)	PUNCT
ejpam-5423	316	154	≥	≥	NOUN
ejpam-5423	316	155	(	(	PUNCT
ejpam-5423	316	156	µn)λ	µn)λ	PROPN
ejpam-5423	316	157	δ	δ	PROPN
ejpam-5423	316	158	(	(	PUNCT
ejpam-5423	316	159	e	e	NOUN
ejpam-5423	316	160	)	)	PUNCT
ejpam-5423	316	161	.	.	PUNCT
ejpam-5423	317	1	hence	hence	ADV
ejpam-5423	317	2	,	,	PUNCT
ejpam-5423	317	3	(	(	PUNCT
ejpam-5423	317	4	t	t	PROPN
ejpam-5423	317	5	◦	◦	NOUN
ejpam-5423	317	6	t	t	PROPN
ejpam-5423	317	7	)	)	PUNCT
ejpam-5423	318	1	λ	λ	PROPN
ejpam-5423	318	2	δ	δ	PROPN
ejpam-5423	318	3	⊑	⊑	X
ejpam-5423	318	4	t	t	PROPN
ejpam-5423	318	5	λ	λ	X
ejpam-5423	318	6	δ	δ	PROPN
ejpam-5423	318	7	.	.	PUNCT
ejpam-5423	319	1	t.	t.	PROPN
ejpam-5423	319	2	gaketem	gaketem	PROPN
ejpam-5423	319	3	,	,	PUNCT
ejpam-5423	319	4	t.	t.	PROPN
ejpam-5423	319	5	prommai	prommai	PROPN
ejpam-5423	319	6	/	/	SYM
ejpam-5423	319	7	eur	eur	PROPN
ejpam-5423	319	8	.	.	PUNCT
ejpam-5423	320	1	j.	j.	PROPN
ejpam-5423	320	2	pure	pure	PROPN
ejpam-5423	320	3	appl	appl	PROPN
ejpam-5423	320	4	.	.	PROPN
ejpam-5423	320	5	math	math	PROPN
ejpam-5423	320	6	,	,	PUNCT
ejpam-5423	320	7	17	17	NUM
ejpam-5423	320	8	(	(	PUNCT
ejpam-5423	320	9	4	4	NUM
ejpam-5423	320	10	)	)	PUNCT
ejpam-5423	320	11	(	(	PUNCT
ejpam-5423	320	12	2024	2024	NUM
ejpam-5423	320	13	)	)	PUNCT
ejpam-5423	320	14	,	,	PUNCT
ejpam-5423	320	15	3223	3223	NUM
ejpam-5423	320	16	-	-	SYM
ejpam-5423	320	17	3241	3241	NUM
ejpam-5423	320	18	3238	3238	NUM
ejpam-5423	320	19	(	(	PUNCT
ejpam-5423	320	20	⇐	⇐	NOUN
ejpam-5423	320	21	)	)	PUNCT
ejpam-5423	320	22	suppose	suppose	VERB
ejpam-5423	320	23	(	(	PUNCT
ejpam-5423	320	24	t	t	NOUN
ejpam-5423	320	25	◦	◦	NOUN
ejpam-5423	320	26	t	t	PROPN
ejpam-5423	320	27	)	)	PUNCT
ejpam-5423	321	1	λ	λ	PROPN
ejpam-5423	321	2	δ	δ	PROPN
ejpam-5423	321	3	⊑	⊑	X
ejpam-5423	321	4	t	t	PROPN
ejpam-5423	321	5	λ	λ	X
ejpam-5423	321	6	δ	δ	PROPN
ejpam-5423	321	7	and	and	CCONJ
ejpam-5423	321	8	let	let	VERB
ejpam-5423	321	9	e1	e1	NOUN
ejpam-5423	321	10	,	,	PUNCT
ejpam-5423	321	11	e2	e2	PROPN
ejpam-5423	321	12	∈	∈	PROPN
ejpam-5423	321	13	g.	g.	NOUN
ejpam-5423	321	14	then	then	ADV
ejpam-5423	321	15	(	(	PUNCT
ejpam-5423	321	16	ωp	ωp	INTJ
ejpam-5423	321	17	◦	◦	VERB
ejpam-5423	321	18	ωp)δ	ωp)δ	PROPN
ejpam-5423	321	19	λ	λ	NOUN
ejpam-5423	321	20	(	(	PUNCT
ejpam-5423	321	21	e1e2	e1e2	NOUN
ejpam-5423	321	22	)	)	PUNCT
ejpam-5423	321	23	≤	≤	NOUN
ejpam-5423	321	24	(	(	PUNCT
ejpam-5423	321	25	ωp)δ	ωp)δ	PROPN
ejpam-5423	321	26	λ	λ	PROPN
ejpam-5423	321	27	(	(	PUNCT
ejpam-5423	321	28	e1e2	e1e2	NOUN
ejpam-5423	321	29	)	)	PUNCT
ejpam-5423	321	30	and	and	CCONJ
ejpam-5423	321	31	(	(	PUNCT
ejpam-5423	321	32	ωn	ωn	ADP
ejpam-5423	321	33	◦	◦	NOUN
ejpam-5423	321	34	ωn)λ	ωn)λ	PROPN
ejpam-5423	321	35	δ	δ	PROPN
ejpam-5423	321	36	(	(	PUNCT
ejpam-5423	321	37	e1e2	e1e2	NOUN
ejpam-5423	321	38	)	)	PUNCT
ejpam-5423	321	39	≥	≥	NOUN
ejpam-5423	321	40	(	(	PUNCT
ejpam-5423	321	41	µn)λ	µn)λ	PROPN
ejpam-5423	321	42	δ	δ	PROPN
ejpam-5423	321	43	(	(	PUNCT
ejpam-5423	321	44	r1r2	r1r2	NOUN
ejpam-5423	321	45	)	)	PUNCT
ejpam-5423	321	46	.	.	PUNCT
ejpam-5423	322	1	thus	thus	ADV
ejpam-5423	322	2	ωp(e1e2	ωp(e1e2	NOUN
ejpam-5423	322	3	)	)	PUNCT
ejpam-5423	322	4	∨	∨	NUM
ejpam-5423	322	5	λ	λ	PROPN
ejpam-5423	322	6	p	p	X
ejpam-5423	322	7	≥	≥	X
ejpam-5423	322	8	(	(	PUNCT
ejpam-5423	322	9	ωp(e1e2	ωp(e1e2	NOUN
ejpam-5423	322	10	)	)	PUNCT
ejpam-5423	322	11	∧	∧	PROPN
ejpam-5423	322	12	δ	δ	PROPN
ejpam-5423	322	13	p	p	NOUN
ejpam-5423	322	14	)	)	PUNCT
ejpam-5423	323	1	∨	∨	NUM
ejpam-5423	323	2	λ	λ	X
ejpam-5423	323	3	p	p	X
ejpam-5423	323	4	=	=	X
ejpam-5423	323	5	(	(	PUNCT
ejpam-5423	323	6	ωp)δ	ωp)δ	PROPN
ejpam-5423	323	7	λ	λ	PROPN
ejpam-5423	323	8	(	(	PUNCT
ejpam-5423	323	9	e1e2	e1e2	NOUN
ejpam-5423	323	10	)	)	PUNCT
ejpam-5423	323	11	≥	≥	NOUN
ejpam-5423	323	12	(	(	PUNCT
ejpam-5423	323	13	ωp	ωp	PART
ejpam-5423	323	14	◦	◦	VERB
ejpam-5423	323	15	ωp)δ	ωp)δ	PROPN
ejpam-5423	323	16	λ	λ	NOUN
ejpam-5423	323	17	(	(	PUNCT
ejpam-5423	323	18	e1e2	e1e2	X
ejpam-5423	323	19	)	)	PUNCT
ejpam-5423	323	20	=	=	SYM
ejpam-5423	323	21	(	(	PUNCT
ejpam-5423	323	22	∨	∨	X
ejpam-5423	323	23	(	(	PUNCT
ejpam-5423	323	24	k	k	X
ejpam-5423	323	25	,	,	PUNCT
ejpam-5423	323	26	o)∈ae1e2	o)∈ae1e2	PROPN
ejpam-5423	323	27	{	{	PUNCT
ejpam-5423	323	28	µp(k	µp(k	NOUN
ejpam-5423	323	29	)	)	PUNCT
ejpam-5423	323	30	∧	∧	NOUN
ejpam-5423	323	31	µp(o	µp(o	NOUN
ejpam-5423	323	32	)	)	PUNCT
ejpam-5423	323	33	}	}	PUNCT
ejpam-5423	323	34	∧	∧	PROPN
ejpam-5423	323	35	δ	δ	PROPN
ejpam-5423	323	36	p	p	NOUN
ejpam-5423	323	37	)	)	PUNCT
ejpam-5423	323	38	∨	∨	NUM
ejpam-5423	323	39	λ	λ	PROPN
ejpam-5423	323	40	p	p	X
ejpam-5423	323	41	≥	≥	NOUN
ejpam-5423	323	42	(	(	PUNCT
ejpam-5423	323	43	µp(e1	µp(e1	NUM
ejpam-5423	323	44	)	)	PUNCT
ejpam-5423	323	45	∧	∧	NOUN
ejpam-5423	323	46	µp(e2	µp(e2	NOUN
ejpam-5423	323	47	)	)	PUNCT
ejpam-5423	323	48	∧	∧	PROPN
ejpam-5423	323	49	δ	δ	PROPN
ejpam-5423	323	50	p	p	NOUN
ejpam-5423	323	51	)	)	PUNCT
ejpam-5423	323	52	∨	∨	NUM
ejpam-5423	323	53	λ	λ	PROPN
ejpam-5423	323	54	p	p	NOUN
ejpam-5423	323	55	≥	≥	NOUN
ejpam-5423	323	56	µp(e1	µp(e1	NUM
ejpam-5423	323	57	)	)	PUNCT
ejpam-5423	323	58	∧	∧	PROPN
ejpam-5423	323	59	µp(e2	µp(e2	NOUN
ejpam-5423	323	60	)	)	PUNCT
ejpam-5423	323	61	∧	∧	PROPN
ejpam-5423	323	62	δ	δ	PROPN
ejpam-5423	323	63	p	p	NOUN
ejpam-5423	323	64	and	and	CCONJ
ejpam-5423	323	65	ωn(e1e2	ωn(e1e2	PROPN
ejpam-5423	323	66	)	)	PUNCT
ejpam-5423	323	67	∧	∧	PROPN
ejpam-5423	323	68	λ	λ	PROPN
ejpam-5423	323	69	n	n	CCONJ
ejpam-5423	323	70	≤	≤	NUM
ejpam-5423	323	71	(	(	PUNCT
ejpam-5423	323	72	ωn(e1e2	ωn(e1e2	PROPN
ejpam-5423	323	73	)	)	PUNCT
ejpam-5423	323	74	∧	∧	NOUN
ejpam-5423	323	75	λ	λ	PROPN
ejpam-5423	323	76	n	n	CCONJ
ejpam-5423	323	77	)	)	PUNCT
ejpam-5423	323	78	∨	∨	NUM
ejpam-5423	323	79	δ	δ	PROPN
ejpam-5423	323	80	n	n	X
ejpam-5423	323	81	=	=	SYM
ejpam-5423	323	82	(	(	PUNCT
ejpam-5423	323	83	ωn)λ	ωn)λ	PROPN
ejpam-5423	323	84	δ	δ	PROPN
ejpam-5423	323	85	(	(	PUNCT
ejpam-5423	323	86	e1e2	e1e2	NOUN
ejpam-5423	323	87	)	)	PUNCT
ejpam-5423	323	88	≥	≥	NOUN
ejpam-5423	323	89	(	(	PUNCT
ejpam-5423	323	90	ωn	ωn	ADP
ejpam-5423	323	91	◦	◦	VERB
ejpam-5423	323	92	ωn)λ	ωn)λ	PROPN
ejpam-5423	323	93	δ	δ	PROPN
ejpam-5423	323	94	(	(	PUNCT
ejpam-5423	323	95	e1e2	e1e2	X
ejpam-5423	323	96	)	)	PUNCT
ejpam-5423	323	97	=	=	SYM
ejpam-5423	323	98	(	(	PUNCT
ejpam-5423	323	99	∧	∧	PROPN
ejpam-5423	323	100	(	(	PUNCT
ejpam-5423	323	101	k	k	X
ejpam-5423	323	102	,	,	PUNCT
ejpam-5423	323	103	o)∈ae1e2	o)∈ae1e2	PROPN
ejpam-5423	323	104	{	{	PUNCT
ejpam-5423	323	105	µn(k	µn(k	NUM
ejpam-5423	323	106	)	)	PUNCT
ejpam-5423	323	107	∨	∨	NUM
ejpam-5423	323	108	µn(o	µn(o	PUNCT
ejpam-5423	323	109	)	)	PUNCT
ejpam-5423	323	110	}	}	PUNCT
ejpam-5423	323	111	∧	∧	PROPN
ejpam-5423	323	112	λ	λ	PROPN
ejpam-5423	323	113	n	n	CCONJ
ejpam-5423	323	114	)	)	PUNCT
ejpam-5423	323	115	∨	∨	NUM
ejpam-5423	323	116	δ	δ	PROPN
ejpam-5423	323	117	p	p	NOUN
ejpam-5423	323	118	≤	≤	PROPN
ejpam-5423	323	119	(	(	PUNCT
ejpam-5423	323	120	µn(e1	µn(e1	NUM
ejpam-5423	323	121	)	)	PUNCT
ejpam-5423	323	122	∨	∨	PROPN
ejpam-5423	323	123	µn(e2	µn(e2	PROPN
ejpam-5423	323	124	)	)	PUNCT
ejpam-5423	323	125	∧	∧	PROPN
ejpam-5423	323	126	λ	λ	PROPN
ejpam-5423	323	127	n	n	CCONJ
ejpam-5423	323	128	)	)	PUNCT
ejpam-5423	323	129	∨	∨	NUM
ejpam-5423	323	130	δ	δ	PROPN
ejpam-5423	323	131	n	n	PRON
ejpam-5423	323	132	≤	≤	PROPN
ejpam-5423	323	133	µn(e1	µn(e1	CCONJ
ejpam-5423	323	134	)	)	PUNCT
ejpam-5423	323	135	∨	∨	PROPN
ejpam-5423	323	136	µn(e2	µn(e2	PROPN
ejpam-5423	323	137	)	)	PUNCT
ejpam-5423	323	138	∨	∨	NUM
ejpam-5423	323	139	δ	δ	PROPN
ejpam-5423	323	140	n	n	PRON
ejpam-5423	323	141	hence	hence	ADV
ejpam-5423	323	142	,	,	PUNCT
ejpam-5423	323	143	ωp(e1e2	ωp(e1e2	X
ejpam-5423	323	144	)	)	PUNCT
ejpam-5423	323	145	∨	∨	NUM
ejpam-5423	323	146	λ	λ	PROPN
ejpam-5423	323	147	p	p	NOUN
ejpam-5423	323	148	≥	≥	NOUN
ejpam-5423	323	149	µp(e1	µp(e1	NUM
ejpam-5423	323	150	)	)	PUNCT
ejpam-5423	323	151	∧	∧	PROPN
ejpam-5423	323	152	µp(e2	µp(e2	NOUN
ejpam-5423	323	153	)	)	PUNCT
ejpam-5423	323	154	∧	∧	PROPN
ejpam-5423	323	155	δ	δ	PROPN
ejpam-5423	323	156	p	p	NOUN
ejpam-5423	323	157	and	and	CCONJ
ejpam-5423	323	158	ωn(e1e2	ωn(e1e2	PROPN
ejpam-5423	323	159	)	)	PUNCT
ejpam-5423	323	160	∧	∧	PROPN
ejpam-5423	323	161	λ	λ	PROPN
ejpam-5423	323	162	n	n	CCONJ
ejpam-5423	323	163	≤	≤	NUM
ejpam-5423	323	164	µn(e1	µn(e1	CCONJ
ejpam-5423	323	165	)	)	PUNCT
ejpam-5423	323	166	∨	∨	PROPN
ejpam-5423	323	167	µn(e2	µn(e2	PROPN
ejpam-5423	323	168	)	)	PUNCT
ejpam-5423	323	169	∨	∨	NUM
ejpam-5423	323	170	δ	δ	PROPN
ejpam-5423	323	171	n	n	X
ejpam-5423	323	172	.	.	PUNCT
ejpam-5423	324	1	therefore	therefore	ADV
ejpam-5423	324	2	t	t	PROPN
ejpam-5423	324	3	=	=	SYM
ejpam-5423	324	4	(	(	PUNCT
ejpam-5423	324	5	ω	ω	PROPN
ejpam-5423	324	6	p	p	PROPN
ejpam-5423	324	7	,	,	PUNCT
ejpam-5423	324	8	ω	ω	PROPN
ejpam-5423	324	9	n	n	CCONJ
ejpam-5423	324	10	)	)	PUNCT
ejpam-5423	324	11	is	be	AUX
ejpam-5423	324	12	an	an	DET
ejpam-5423	324	13	(	(	PUNCT
ejpam-5423	324	14	λ	λ	NOUN
ejpam-5423	324	15	,	,	PUNCT
ejpam-5423	324	16	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	324	17	subsemigroup	subsemigroup	NOUN
ejpam-5423	324	18	of	of	ADP
ejpam-5423	324	19	g.	g.	PROPN
ejpam-5423	324	20	lemma	lemma	PROPN
ejpam-5423	324	21	3	3	X
ejpam-5423	324	22	.	.	PUNCT
ejpam-5423	325	1	[	[	X
ejpam-5423	325	2	9	9	NUM
ejpam-5423	325	3	]	]	PUNCT
ejpam-5423	325	4	for	for	ADP
ejpam-5423	325	5	an	an	DET
ejpam-5423	325	6	ordered	order	VERB
ejpam-5423	325	7	semigroup	semigroup	NOUN
ejpam-5423	325	8	g	g	PROPN
ejpam-5423	325	9	,	,	PUNCT
ejpam-5423	325	10	the	the	DET
ejpam-5423	325	11	following	follow	VERB
ejpam-5423	325	12	conditions	condition	NOUN
ejpam-5423	325	13	are	be	AUX
ejpam-5423	325	14	equivalent	equivalent	ADJ
ejpam-5423	325	15	.	.	PUNCT
ejpam-5423	326	1	(	(	PUNCT
ejpam-5423	326	2	1	1	X
ejpam-5423	326	3	)	)	PUNCT
ejpam-5423	326	4	g	g	NOUN
ejpam-5423	326	5	is	be	AUX
ejpam-5423	326	6	regular	regular	ADJ
ejpam-5423	326	7	and	and	CCONJ
ejpam-5423	326	8	intra	intra	ADJ
ejpam-5423	326	9	-	-	ADJ
ejpam-5423	326	10	regular	regular	ADJ
ejpam-5423	326	11	.	.	PUNCT
ejpam-5423	327	1	(	(	PUNCT
ejpam-5423	327	2	2	2	X
ejpam-5423	327	3	)	)	PUNCT
ejpam-5423	327	4	every	every	DET
ejpam-5423	327	5	quasi	quasi	NOUN
ejpam-5423	327	6	-	-	NOUN
ejpam-5423	327	7	ideal	ideal	ADJ
ejpam-5423	327	8	of	of	ADP
ejpam-5423	327	9	f	f	PROPN
ejpam-5423	327	10	is	be	AUX
ejpam-5423	327	11	idempotent	idempotent	ADJ
ejpam-5423	327	12	.	.	PUNCT
ejpam-5423	328	1	(	(	PUNCT
ejpam-5423	328	2	3	3	X
ejpam-5423	328	3	)	)	PUNCT
ejpam-5423	328	4	every	every	DET
ejpam-5423	328	5	bi	bi	NOUN
ejpam-5423	328	6	-	-	NOUN
ejpam-5423	328	7	ideal	ideal	NOUN
ejpam-5423	328	8	of	of	ADP
ejpam-5423	328	9	f	f	PROPN
ejpam-5423	328	10	is	be	AUX
ejpam-5423	328	11	idempotent	idempotent	ADJ
ejpam-5423	328	12	.	.	PUNCT
ejpam-5423	329	1	theorem	theorem	ADJ
ejpam-5423	329	2	10	10	NUM
ejpam-5423	329	3	.	.	PUNCT
ejpam-5423	330	1	let	let	VERB
ejpam-5423	330	2	t	t	NOUN
ejpam-5423	330	3	=	=	SYM
ejpam-5423	330	4	(	(	PUNCT
ejpam-5423	330	5	ω	ω	PROPN
ejpam-5423	330	6	p	p	PROPN
ejpam-5423	330	7	,	,	PUNCT
ejpam-5423	330	8	ω	ω	PROPN
ejpam-5423	330	9	n	n	CCONJ
ejpam-5423	330	10	)	)	PUNCT
ejpam-5423	330	11	and	and	CCONJ
ejpam-5423	330	12	j	j	PROPN
ejpam-5423	330	13	=	=	PRON
ejpam-5423	331	1	(	(	PUNCT
ejpam-5423	331	2	ϖ	ϖ	X
ejpam-5423	331	3	p	p	X
ejpam-5423	331	4	,	,	PUNCT
ejpam-5423	331	5	ϖ	ϖ	PROPN
ejpam-5423	331	6	n	n	CCONJ
ejpam-5423	331	7	)	)	PUNCT
ejpam-5423	331	8	be	be	AUX
ejpam-5423	331	9	ivbf	ivbf	VERB
ejpam-5423	331	10	sets	set	NOUN
ejpam-5423	331	11	of	of	ADP
ejpam-5423	331	12	an	an	DET
ejpam-5423	331	13	ordered	order	VERB
ejpam-5423	331	14	semigroup	semigroup	PROPN
ejpam-5423	331	15	g.	g.	PROPN
ejpam-5423	332	1	then	then	ADV
ejpam-5423	332	2	the	the	DET
ejpam-5423	332	3	followings	following	NOUN
ejpam-5423	332	4	are	be	AUX
ejpam-5423	332	5	equivalent	equivalent	ADJ
ejpam-5423	332	6	.	.	PUNCT
ejpam-5423	333	1	(	(	PUNCT
ejpam-5423	333	2	1	1	X
ejpam-5423	333	3	)	)	PUNCT
ejpam-5423	333	4	g	g	NOUN
ejpam-5423	333	5	is	be	AUX
ejpam-5423	333	6	both	both	CCONJ
ejpam-5423	333	7	regular	regular	ADJ
ejpam-5423	333	8	and	and	CCONJ
ejpam-5423	333	9	intra	intra	ADJ
ejpam-5423	333	10	-	-	ADJ
ejpam-5423	333	11	regular	regular	ADJ
ejpam-5423	333	12	,	,	PUNCT
ejpam-5423	333	13	(	(	PUNCT
ejpam-5423	333	14	2	2	NUM
ejpam-5423	333	15	)	)	PUNCT
ejpam-5423	333	16	(	(	PUNCT
ejpam-5423	333	17	t	t	NOUN
ejpam-5423	333	18	◦	◦	NOUN
ejpam-5423	333	19	t	t	PROPN
ejpam-5423	333	20	)	)	PUNCT
ejpam-5423	334	1	λ	λ	NOUN
ejpam-5423	334	2	δ	δ	NOUN
ejpam-5423	334	3	=	=	PUNCT
ejpam-5423	334	4	t	t	PROPN
ejpam-5423	334	5	λ	λ	PROPN
ejpam-5423	334	6	δ	δ	PROPN
ejpam-5423	334	7	for	for	ADP
ejpam-5423	334	8	every	every	DET
ejpam-5423	334	9	(	(	PUNCT
ejpam-5423	334	10	λ	λ	PROPN
ejpam-5423	334	11	,	,	PUNCT
ejpam-5423	334	12	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	334	13	quasi	quasi	ADJ
ejpam-5423	334	14	-	-	ADJ
ejpam-5423	334	15	ideal	ideal	ADJ
ejpam-5423	334	16	t	t	PROPN
ejpam-5423	334	17	of	of	ADP
ejpam-5423	334	18	f	f	PROPN
ejpam-5423	334	19	,	,	PUNCT
ejpam-5423	334	20	(	(	PUNCT
ejpam-5423	334	21	3	3	NUM
ejpam-5423	334	22	)	)	PUNCT
ejpam-5423	334	23	(	(	PUNCT
ejpam-5423	334	24	t	t	NOUN
ejpam-5423	334	25	◦	◦	NOUN
ejpam-5423	334	26	t	t	PROPN
ejpam-5423	334	27	)	)	PUNCT
ejpam-5423	334	28	λ	λ	NOUN
ejpam-5423	334	29	δ	δ	NOUN
ejpam-5423	334	30	=	=	PUNCT
ejpam-5423	334	31	t	t	PROPN
ejpam-5423	334	32	λ	λ	PROPN
ejpam-5423	334	33	δ	δ	PROPN
ejpam-5423	334	34	for	for	ADP
ejpam-5423	334	35	every	every	DET
ejpam-5423	334	36	(	(	PUNCT
ejpam-5423	334	37	λ	λ	PROPN
ejpam-5423	334	38	,	,	PUNCT
ejpam-5423	334	39	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	334	40	bi	bi	ADJ
ejpam-5423	334	41	-	-	ADJ
ejpam-5423	334	42	ideal	ideal	ADJ
ejpam-5423	334	43	t	t	PROPN
ejpam-5423	334	44	of	of	ADP
ejpam-5423	334	45	f	f	PROPN
ejpam-5423	334	46	,	,	PUNCT
ejpam-5423	334	47	(	(	PUNCT
ejpam-5423	334	48	4	4	NUM
ejpam-5423	334	49	)	)	PUNCT
ejpam-5423	334	50	(	(	PUNCT
ejpam-5423	334	51	t	t	PROPN
ejpam-5423	334	52	⊓	⊓	PROPN
ejpam-5423	334	53	j	j	PROPN
ejpam-5423	334	54	)	)	PUNCT
ejpam-5423	334	55	λ	λ	PROPN
ejpam-5423	334	56	δ	δ	PROPN
ejpam-5423	334	57	⊑	⊑	X
ejpam-5423	334	58	(	(	PUNCT
ejpam-5423	334	59	t	t	PROPN
ejpam-5423	334	60	◦	◦	NOUN
ejpam-5423	334	61	j	j	PROPN
ejpam-5423	334	62	)	)	PUNCT
ejpam-5423	334	63	λ	λ	PROPN
ejpam-5423	334	64	δ	δ	PROPN
ejpam-5423	334	65	for	for	ADP
ejpam-5423	334	66	every	every	DET
ejpam-5423	334	67	(	(	PUNCT
ejpam-5423	334	68	λ	λ	PROPN
ejpam-5423	334	69	,	,	PUNCT
ejpam-5423	334	70	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	334	71	quasi	quasi	NOUN
ejpam-5423	334	72	-	-	NOUN
ejpam-5423	334	73	ideals	ideal	NOUN
ejpam-5423	334	74	t	t	NOUN
ejpam-5423	334	75	and	and	CCONJ
ejpam-5423	334	76	j	j	PROPN
ejpam-5423	334	77	of	of	ADP
ejpam-5423	334	78	f	f	PROPN
ejpam-5423	334	79	,	,	PUNCT
ejpam-5423	334	80	(	(	PUNCT
ejpam-5423	334	81	5	5	NUM
ejpam-5423	334	82	)	)	PUNCT
ejpam-5423	334	83	(	(	PUNCT
ejpam-5423	334	84	t	t	NOUN
ejpam-5423	334	85	⊓j	⊓j	NOUN
ejpam-5423	334	86	)	)	PUNCT
ejpam-5423	334	87	λ	λ	PROPN
ejpam-5423	334	88	δ	δ	NOUN
ejpam-5423	334	89	⊑	⊑	X
ejpam-5423	334	90	(	(	PUNCT
ejpam-5423	334	91	t	t	PROPN
ejpam-5423	334	92	◦	◦	PROPN
ejpam-5423	334	93	j	j	PROPN
ejpam-5423	334	94	)	)	PUNCT
ejpam-5423	334	95	λ	λ	PROPN
ejpam-5423	334	96	δ	δ	PROPN
ejpam-5423	334	97	for	for	ADP
ejpam-5423	334	98	every	every	DET
ejpam-5423	334	99	(	(	PUNCT
ejpam-5423	334	100	λ	λ	PROPN
ejpam-5423	334	101	,	,	PUNCT
ejpam-5423	334	102	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	334	103	quasi	quasi	ADJ
ejpam-5423	334	104	-	-	ADJ
ejpam-5423	334	105	ideal	ideal	ADJ
ejpam-5423	334	106	t	t	NOUN
ejpam-5423	334	107	and	and	CCONJ
ejpam-5423	334	108	every	every	DET
ejpam-5423	334	109	(	(	PUNCT
ejpam-5423	334	110	λ	λ	NOUN
ejpam-5423	334	111	,	,	PUNCT
ejpam-5423	334	112	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	334	113	bi	bi	ADJ
ejpam-5423	334	114	-	-	ADJ
ejpam-5423	334	115	ideal	ideal	ADJ
ejpam-5423	334	116	j	j	PROPN
ejpam-5423	334	117	of	of	ADP
ejpam-5423	334	118	f	f	PROPN
ejpam-5423	334	119	,	,	PUNCT
ejpam-5423	334	120	(	(	PUNCT
ejpam-5423	334	121	6	6	NUM
ejpam-5423	334	122	)	)	PUNCT
ejpam-5423	334	123	(	(	PUNCT
ejpam-5423	334	124	t	t	PROPN
ejpam-5423	334	125	⊓	⊓	PROPN
ejpam-5423	334	126	j	j	PROPN
ejpam-5423	334	127	)	)	PUNCT
ejpam-5423	334	128	λ	λ	PROPN
ejpam-5423	334	129	δ	δ	PROPN
ejpam-5423	334	130	⊑	⊑	X
ejpam-5423	334	131	(	(	PUNCT
ejpam-5423	334	132	t	t	PROPN
ejpam-5423	334	133	◦	◦	NOUN
ejpam-5423	334	134	j	j	PROPN
ejpam-5423	334	135	)	)	PUNCT
ejpam-5423	334	136	λ	λ	PROPN
ejpam-5423	334	137	δ	δ	PROPN
ejpam-5423	334	138	for	for	ADP
ejpam-5423	334	139	every	every	DET
ejpam-5423	334	140	(	(	PUNCT
ejpam-5423	334	141	λ	λ	PROPN
ejpam-5423	334	142	,	,	PUNCT
ejpam-5423	334	143	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	334	144	bi	bi	NOUN
ejpam-5423	334	145	-	-	NOUN
ejpam-5423	334	146	ideals	ideal	NOUN
ejpam-5423	334	147	t	t	NOUN
ejpam-5423	334	148	and	and	CCONJ
ejpam-5423	334	149	j	j	PROPN
ejpam-5423	334	150	of	of	ADP
ejpam-5423	334	151	f.	f.	PROPN
ejpam-5423	334	152	proof	proof	PROPN
ejpam-5423	334	153	.	.	PUNCT
ejpam-5423	335	1	(	(	PUNCT
ejpam-5423	335	2	1	1	X
ejpam-5423	335	3	)	)	PUNCT
ejpam-5423	335	4	⇒	⇒	NOUN
ejpam-5423	335	5	(	(	PUNCT
ejpam-5423	335	6	6	6	X
ejpam-5423	335	7	)	)	PUNCT
ejpam-5423	335	8	let	let	VERB
ejpam-5423	335	9	t	t	NOUN
ejpam-5423	335	10	=	=	SYM
ejpam-5423	335	11	(	(	PUNCT
ejpam-5423	335	12	ω	ω	PROPN
ejpam-5423	335	13	p	p	PROPN
ejpam-5423	335	14	,	,	PUNCT
ejpam-5423	335	15	ω	ω	PROPN
ejpam-5423	335	16	n	n	CCONJ
ejpam-5423	335	17	)	)	PUNCT
ejpam-5423	335	18	and	and	CCONJ
ejpam-5423	335	19	j	j	PROPN
ejpam-5423	335	20	=	=	PRON
ejpam-5423	335	21	(	(	PUNCT
ejpam-5423	335	22	ϖ	ϖ	X
ejpam-5423	335	23	p	p	X
ejpam-5423	335	24	,	,	PUNCT
ejpam-5423	335	25	ϖ	ϖ	PROPN
ejpam-5423	335	26	n	n	CCONJ
ejpam-5423	335	27	)	)	PUNCT
ejpam-5423	335	28	be	be	AUX
ejpam-5423	335	29	(	(	PUNCT
ejpam-5423	335	30	λ	λ	INTJ
ejpam-5423	335	31	,	,	PUNCT
ejpam-5423	335	32	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	335	33	bi	bi	NOUN
ejpam-5423	335	34	-	-	NOUN
ejpam-5423	335	35	ideals	ideal	NOUN
ejpam-5423	335	36	of	of	ADP
ejpam-5423	335	37	g	g	NOUN
ejpam-5423	335	38	and	and	CCONJ
ejpam-5423	335	39	let	let	VERB
ejpam-5423	335	40	e	e	PROPN
ejpam-5423	335	41	∈	∈	PROPN
ejpam-5423	335	42	g.	g.	NOUN
ejpam-5423	335	43	since	since	SCONJ
ejpam-5423	335	44	g	g	PROPN
ejpam-5423	335	45	is	be	AUX
ejpam-5423	335	46	both	both	CCONJ
ejpam-5423	335	47	regular	regular	ADJ
ejpam-5423	335	48	and	and	CCONJ
ejpam-5423	335	49	intra	intra	ADJ
ejpam-5423	335	50	-	-	ADJ
ejpam-5423	335	51	regular	regular	ADJ
ejpam-5423	335	52	,	,	PUNCT
ejpam-5423	335	53	there	there	PRON
ejpam-5423	335	54	exist	exist	VERB
ejpam-5423	335	55	k	k	PROPN
ejpam-5423	335	56	,	,	PUNCT
ejpam-5423	335	57	l	l	NOUN
ejpam-5423	335	58	,	,	PUNCT
ejpam-5423	335	59	e	e	PROPN
ejpam-5423	335	60	∈	∈	PROPN
ejpam-5423	335	61	g	g	PROPN
ejpam-5423	335	62	such	such	ADJ
ejpam-5423	335	63	that	that	SCONJ
ejpam-5423	335	64	t.	t.	PROPN
ejpam-5423	335	65	gaketem	gaketem	PROPN
ejpam-5423	335	66	,	,	PUNCT
ejpam-5423	335	67	t.	t.	PROPN
ejpam-5423	335	68	prommai	prommai	PROPN
ejpam-5423	335	69	/	/	SYM
ejpam-5423	335	70	eur	eur	PROPN
ejpam-5423	335	71	.	.	PUNCT
ejpam-5423	336	1	j.	j.	PROPN
ejpam-5423	336	2	pure	pure	PROPN
ejpam-5423	336	3	appl	appl	PROPN
ejpam-5423	336	4	.	.	PROPN
ejpam-5423	336	5	math	math	PROPN
ejpam-5423	336	6	,	,	PUNCT
ejpam-5423	336	7	17	17	NUM
ejpam-5423	336	8	(	(	PUNCT
ejpam-5423	336	9	4	4	NUM
ejpam-5423	336	10	)	)	PUNCT
ejpam-5423	336	11	(	(	PUNCT
ejpam-5423	336	12	2024	2024	NUM
ejpam-5423	336	13	)	)	PUNCT
ejpam-5423	336	14	,	,	PUNCT
ejpam-5423	336	15	3223	3223	NUM
ejpam-5423	336	16	-	-	SYM
ejpam-5423	336	17	3241	3241	NUM
ejpam-5423	336	18	3239	3239	NUM
ejpam-5423	336	19	e	e	X
ejpam-5423	336	20	=	=	PUNCT
ejpam-5423	337	1	rkr	rkr	PROPN
ejpam-5423	337	2	and	and	CCONJ
ejpam-5423	337	3	e	e	X
ejpam-5423	337	4	=	=	PROPN
ejpam-5423	337	5	km2e	km2e	PROPN
ejpam-5423	337	6	.	.	PUNCT
ejpam-5423	338	1	thus	thus	ADV
ejpam-5423	338	2	e	e	X
ejpam-5423	338	3	=	=	PUNCT
ejpam-5423	338	4	rkr	rkr	ADJ
ejpam-5423	338	5	=	=	PUNCT
ejpam-5423	338	6	rkrkm	rkrkm	NOUN
ejpam-5423	338	7	=	=	SYM
ejpam-5423	338	8	rk(lr2e)kr	rk(lr2e)kr	PROPN
ejpam-5423	338	9	=	=	SYM
ejpam-5423	338	10	(	(	PUNCT
ejpam-5423	338	11	rklr)(relr	rklr)(relr	NUM
ejpam-5423	338	12	)	)	PUNCT
ejpam-5423	338	13	.	.	PUNCT
ejpam-5423	339	1	it	it	PRON
ejpam-5423	339	2	follows	follow	VERB
ejpam-5423	339	3	that	that	SCONJ
ejpam-5423	339	4	(	(	PUNCT
ejpam-5423	339	5	ωp	ωp	ADP
ejpam-5423	339	6	◦	◦	NOUN
ejpam-5423	339	7	ϖp)δ	ϖp)δ	PROPN
ejpam-5423	339	8	λ	λ	PROPN
ejpam-5423	339	9	(	(	PUNCT
ejpam-5423	339	10	e	e	NOUN
ejpam-5423	339	11	)	)	PUNCT
ejpam-5423	340	1	=	=	SYM
ejpam-5423	340	2	∨	∨	X
ejpam-5423	340	3	(	(	PUNCT
ejpam-5423	340	4	i	i	PROPN
ejpam-5423	340	5	,	,	PUNCT
ejpam-5423	340	6	j)∈ae	j)∈ae	PROPN
ejpam-5423	340	7	{	{	PUNCT
ejpam-5423	340	8	ωp(i	ωp(i	NOUN
ejpam-5423	340	9	)	)	PUNCT
ejpam-5423	340	10	∧	∧	PROPN
ejpam-5423	340	11	λ	λ	NOUN
ejpam-5423	340	12	p	p	X
ejpam-5423	340	13	(	(	PUNCT
ejpam-5423	340	14	j	j	NOUN
ejpam-5423	340	15	)	)	PUNCT
ejpam-5423	340	16	}	}	PUNCT
ejpam-5423	340	17	=	=	SYM
ejpam-5423	340	18	(	(	PUNCT
ejpam-5423	340	19	∨	∨	X
ejpam-5423	340	20	(	(	PUNCT
ejpam-5423	340	21	i	i	PROPN
ejpam-5423	340	22	,	,	PUNCT
ejpam-5423	340	23	j)∈a(rklr)(relr	j)∈a(rklr)(relr	PROPN
ejpam-5423	340	24	)	)	PUNCT
ejpam-5423	340	25	{	{	PUNCT
ejpam-5423	340	26	ωp(i	ωp(i	NOUN
ejpam-5423	340	27	)	)	PUNCT
ejpam-5423	340	28	∧ϖp(j	∧ϖp(j	ADJ
ejpam-5423	340	29	)	)	PUNCT
ejpam-5423	340	30	}	}	PUNCT
ejpam-5423	340	31	∧	∧	PROPN
ejpam-5423	340	32	δ	δ	PROPN
ejpam-5423	340	33	p	p	NOUN
ejpam-5423	340	34	)	)	PUNCT
ejpam-5423	340	35	∨	∨	NUM
ejpam-5423	340	36	λ	λ	PROPN
ejpam-5423	340	37	p	p	X
ejpam-5423	340	38	≥	≥	X
ejpam-5423	340	39	(	(	PUNCT
ejpam-5423	340	40	ωp(rklr	ωp(rklr	PROPN
ejpam-5423	340	41	)	)	PUNCT
ejpam-5423	340	42	∧ϖp(relr	∧ϖp(relr	PROPN
ejpam-5423	340	43	)	)	PUNCT
ejpam-5423	340	44	∧	∧	PROPN
ejpam-5423	340	45	δ	δ	PROPN
ejpam-5423	340	46	p	p	NOUN
ejpam-5423	340	47	)	)	PUNCT
ejpam-5423	340	48	∨	∨	NUM
ejpam-5423	340	49	λ	λ	X
ejpam-5423	340	50	p	p	X
ejpam-5423	340	51	=	=	X
ejpam-5423	340	52	(	(	PUNCT
ejpam-5423	340	53	ωp(r(kl)r	ωp(r(kl)r	ADJ
ejpam-5423	340	54	)	)	PUNCT
ejpam-5423	340	55	∨	∨	NUM
ejpam-5423	340	56	λ	λ	PROPN
ejpam-5423	340	57	p	p	PROPN
ejpam-5423	340	58	∧ϖp(r(el)r	∧ϖp(r(el)r	PROPN
ejpam-5423	340	59	)	)	PUNCT
ejpam-5423	340	60	∨	∨	NUM
ejpam-5423	340	61	λ	λ	PROPN
ejpam-5423	340	62	p	p	PROPN
ejpam-5423	340	63	∧	∧	PROPN
ejpam-5423	340	64	δ	δ	PROPN
ejpam-5423	340	65	p	p	NOUN
ejpam-5423	340	66	)	)	PUNCT
ejpam-5423	340	67	∨	∨	NUM
ejpam-5423	340	68	λ	λ	PROPN
ejpam-5423	340	69	p	p	X
ejpam-5423	340	70	≥	≥	X
ejpam-5423	340	71	(	(	PUNCT
ejpam-5423	340	72	ωp(e	ωp(e	ADJ
ejpam-5423	340	73	)	)	PUNCT
ejpam-5423	340	74	∧	∧	NOUN
ejpam-5423	340	75	ωp(e	ωp(e	NOUN
ejpam-5423	340	76	)	)	PUNCT
ejpam-5423	340	77	∧	∧	PROPN
ejpam-5423	340	78	δ	δ	PROPN
ejpam-5423	340	79	p	p	PROPN
ejpam-5423	340	80	∧ϖp(e	∧ϖp(e	NOUN
ejpam-5423	340	81	)	)	PUNCT
ejpam-5423	340	82	∧ϖp(e	∧ϖp(e	NOUN
ejpam-5423	340	83	)	)	PUNCT
ejpam-5423	340	84	∧	∧	PROPN
ejpam-5423	340	85	δ	δ	PROPN
ejpam-5423	340	86	p	p	PROPN
ejpam-5423	340	87	∧	∧	PROPN
ejpam-5423	340	88	δ	δ	PROPN
ejpam-5423	340	89	p	p	NOUN
ejpam-5423	340	90	)	)	PUNCT
ejpam-5423	340	91	∨	∨	NUM
ejpam-5423	340	92	λ	λ	X
ejpam-5423	340	93	p	p	X
ejpam-5423	340	94	=	=	X
ejpam-5423	340	95	(	(	PUNCT
ejpam-5423	340	96	ωp(e	ωp(e	ADJ
ejpam-5423	340	97	)	)	PUNCT
ejpam-5423	340	98	∧	∧	PROPN
ejpam-5423	340	99	δ	δ	PROPN
ejpam-5423	340	100	p	p	PROPN
ejpam-5423	340	101	∧ϖp(e	∧ϖp(e	NOUN
ejpam-5423	340	102	)	)	PUNCT
ejpam-5423	340	103	∧	∧	PROPN
ejpam-5423	340	104	δ	δ	PROPN
ejpam-5423	340	105	p	p	PROPN
ejpam-5423	340	106	∧	∧	PROPN
ejpam-5423	340	107	δ	δ	PROPN
ejpam-5423	340	108	p	p	NOUN
ejpam-5423	340	109	)	)	PUNCT
ejpam-5423	340	110	∨	∨	NUM
ejpam-5423	340	111	λ	λ	X
ejpam-5423	340	112	p	p	X
ejpam-5423	340	113	=	=	X
ejpam-5423	340	114	(	(	PUNCT
ejpam-5423	340	115	(	(	PUNCT
ejpam-5423	340	116	ωp(e	ωp(e	ADJ
ejpam-5423	340	117	)	)	PUNCT
ejpam-5423	340	118	∧ϖp(e	∧ϖp(e	NOUN
ejpam-5423	340	119	)	)	PUNCT
ejpam-5423	340	120	)	)	PUNCT
ejpam-5423	341	1	∧	∧	PROPN
ejpam-5423	341	2	δ	δ	PROPN
ejpam-5423	341	3	p	p	PROPN
ejpam-5423	341	4	∧	∧	PROPN
ejpam-5423	341	5	δ	δ	PROPN
ejpam-5423	341	6	p	p	NOUN
ejpam-5423	341	7	)	)	PUNCT
ejpam-5423	341	8	∨	∨	NUM
ejpam-5423	341	9	λ	λ	X
ejpam-5423	341	10	p	p	X
ejpam-5423	341	11	=	=	X
ejpam-5423	341	12	(	(	PUNCT
ejpam-5423	341	13	(	(	PUNCT
ejpam-5423	341	14	ωp(e	ωp(e	ADJ
ejpam-5423	341	15	)	)	PUNCT
ejpam-5423	341	16	∧ϖp(e	∧ϖp(e	NOUN
ejpam-5423	341	17	)	)	PUNCT
ejpam-5423	341	18	)	)	PUNCT
ejpam-5423	342	1	∧	∧	PROPN
ejpam-5423	342	2	δ	δ	PROPN
ejpam-5423	342	3	p	p	NOUN
ejpam-5423	342	4	)	)	PUNCT
ejpam-5423	343	1	∨	∨	NUM
ejpam-5423	343	2	λ	λ	X
ejpam-5423	343	3	p	p	X
ejpam-5423	344	1	=	=	X
ejpam-5423	345	1	(	(	PUNCT
ejpam-5423	345	2	ωp	ωp	INTJ
ejpam-5423	345	3	⊓ϖp)δ	⊓ϖp)δ	PROPN
ejpam-5423	345	4	λ	λ	PROPN
ejpam-5423	345	5	(	(	PUNCT
ejpam-5423	345	6	e	e	NOUN
ejpam-5423	345	7	)	)	PUNCT
ejpam-5423	345	8	,	,	PUNCT
ejpam-5423	345	9	and	and	CCONJ
ejpam-5423	345	10	(	(	PUNCT
ejpam-5423	345	11	ωn	ωn	ADP
ejpam-5423	345	12	◦	◦	NOUN
ejpam-5423	345	13	ϖn)λ	ϖn)λ	PROPN
ejpam-5423	345	14	δ	δ	PROPN
ejpam-5423	345	15	(	(	PUNCT
ejpam-5423	345	16	e	e	NOUN
ejpam-5423	345	17	)	)	PUNCT
ejpam-5423	346	1	=	=	SYM
ejpam-5423	346	2	∧	∧	PROPN
ejpam-5423	346	3	(	(	PUNCT
ejpam-5423	346	4	i	i	PROPN
ejpam-5423	346	5	,	,	PUNCT
ejpam-5423	346	6	j)∈ae	j)∈ae	PROPN
ejpam-5423	346	7	{	{	PUNCT
ejpam-5423	346	8	ωn(i	ωn(i	PROPN
ejpam-5423	346	9	)	)	PUNCT
ejpam-5423	346	10	∨	∨	NUM
ejpam-5423	346	11	λ	λ	X
ejpam-5423	346	12	n	n	CCONJ
ejpam-5423	346	13	(	(	PUNCT
ejpam-5423	346	14	j	j	NOUN
ejpam-5423	346	15	)	)	PUNCT
ejpam-5423	346	16	}	}	PUNCT
ejpam-5423	346	17	=	=	SYM
ejpam-5423	346	18	(	(	PUNCT
ejpam-5423	346	19	∧	∧	PROPN
ejpam-5423	346	20	(	(	PUNCT
ejpam-5423	346	21	i	i	PROPN
ejpam-5423	346	22	,	,	PUNCT
ejpam-5423	346	23	j)∈a(rklr)(relr	j)∈a(rklr)(relr	PROPN
ejpam-5423	346	24	{	{	PUNCT
ejpam-5423	346	25	ωn(i	ωn(i	PROPN
ejpam-5423	346	26	)	)	PUNCT
ejpam-5423	346	27	∨ϖn(j	∨ϖn(j	PROPN
ejpam-5423	346	28	)	)	PUNCT
ejpam-5423	346	29	}	}	PUNCT
ejpam-5423	346	30	∧	∧	PROPN
ejpam-5423	346	31	λ	λ	PROPN
ejpam-5423	346	32	n	n	CCONJ
ejpam-5423	346	33	)	)	PUNCT
ejpam-5423	346	34	∨	∨	NUM
ejpam-5423	346	35	δ	δ	PROPN
ejpam-5423	346	36	n	n	CCONJ
ejpam-5423	346	37	≤	≤	NUM
ejpam-5423	346	38	(	(	PUNCT
ejpam-5423	346	39	ωn(rklr	ωn(rklr	PROPN
ejpam-5423	346	40	)	)	PUNCT
ejpam-5423	346	41	∨ϖn(relr	∨ϖn(relr	NOUN
ejpam-5423	346	42	)	)	PUNCT
ejpam-5423	346	43	∧	∧	PROPN
ejpam-5423	346	44	λ	λ	PROPN
ejpam-5423	346	45	n	n	CCONJ
ejpam-5423	346	46	)	)	PUNCT
ejpam-5423	346	47	∨	∨	NUM
ejpam-5423	346	48	δ	δ	PROPN
ejpam-5423	346	49	n	n	X
ejpam-5423	346	50	=	=	SYM
ejpam-5423	346	51	(	(	PUNCT
ejpam-5423	346	52	ωn(r(kl)r	ωn(r(kl)r	ADJ
ejpam-5423	346	53	)	)	PUNCT
ejpam-5423	346	54	∧	∧	PROPN
ejpam-5423	346	55	λ	λ	PROPN
ejpam-5423	346	56	n	n	X
ejpam-5423	346	57	∨ϖn(r(el)r	∨ϖn(r(el)r	NOUN
ejpam-5423	346	58	)	)	PUNCT
ejpam-5423	346	59	∧	∧	PROPN
ejpam-5423	346	60	λ	λ	PROPN
ejpam-5423	346	61	n	n	CCONJ
ejpam-5423	346	62	∧	∧	PROPN
ejpam-5423	346	63	λ	λ	PROPN
ejpam-5423	346	64	n	n	CCONJ
ejpam-5423	346	65	)	)	PUNCT
ejpam-5423	346	66	∨	∨	NUM
ejpam-5423	346	67	δ	δ	PROPN
ejpam-5423	346	68	n	n	CCONJ
ejpam-5423	346	69	≤	≤	NUM
ejpam-5423	346	70	(	(	PUNCT
ejpam-5423	346	71	ωn(e	ωn(e	NUM
ejpam-5423	346	72	)	)	PUNCT
ejpam-5423	346	73	∨	∨	NUM
ejpam-5423	346	74	ωn(e	ωn(e	NUM
ejpam-5423	346	75	)	)	PUNCT
ejpam-5423	346	76	∨	∨	NUM
ejpam-5423	346	77	δ	δ	PROPN
ejpam-5423	346	78	n	n	PRON
ejpam-5423	346	79	∨ϖn(e	∨ϖn(e	PROPN
ejpam-5423	346	80	)	)	PUNCT
ejpam-5423	346	81	∨ϖn(e	∨ϖn(e	PROPN
ejpam-5423	346	82	)	)	PUNCT
ejpam-5423	346	83	∨	∨	NUM
ejpam-5423	346	84	δ	δ	PROPN
ejpam-5423	346	85	n	n	CCONJ
ejpam-5423	346	86	∧	∧	PROPN
ejpam-5423	346	87	λ	λ	PROPN
ejpam-5423	346	88	n	n	CCONJ
ejpam-5423	346	89	)	)	PUNCT
ejpam-5423	346	90	∨	∨	NUM
ejpam-5423	346	91	δ	δ	PROPN
ejpam-5423	346	92	n	n	X
ejpam-5423	346	93	=	=	SYM
ejpam-5423	346	94	(	(	PUNCT
ejpam-5423	346	95	ωn(e	ωn(e	NUM
ejpam-5423	346	96	)	)	PUNCT
ejpam-5423	346	97	∨	∨	NUM
ejpam-5423	346	98	δ	δ	PROPN
ejpam-5423	346	99	n	n	PRON
ejpam-5423	346	100	∨ϖn(e	∨ϖn(e	PROPN
ejpam-5423	346	101	)	)	PUNCT
ejpam-5423	346	102	∨	∨	NUM
ejpam-5423	346	103	δ	δ	PROPN
ejpam-5423	346	104	n	n	CCONJ
ejpam-5423	346	105	∧	∧	PROPN
ejpam-5423	346	106	λ	λ	PROPN
ejpam-5423	346	107	n	n	CCONJ
ejpam-5423	346	108	)	)	PUNCT
ejpam-5423	346	109	∨	∨	NUM
ejpam-5423	346	110	δ	δ	PROPN
ejpam-5423	346	111	n	n	X
ejpam-5423	346	112	=	=	SYM
ejpam-5423	346	113	(	(	PUNCT
ejpam-5423	346	114	(	(	PUNCT
ejpam-5423	346	115	ωn(e	ωn(e	NOUN
ejpam-5423	346	116	)	)	PUNCT
ejpam-5423	346	117	∨ϖn(e	∨ϖn(e	PROPN
ejpam-5423	346	118	)	)	PUNCT
ejpam-5423	346	119	)	)	PUNCT
ejpam-5423	346	120	∨	∨	NUM
ejpam-5423	346	121	δ	δ	PROPN
ejpam-5423	346	122	n	n	CCONJ
ejpam-5423	346	123	∧	∧	PROPN
ejpam-5423	346	124	λ	λ	PROPN
ejpam-5423	346	125	n	n	CCONJ
ejpam-5423	346	126	)	)	PUNCT
ejpam-5423	346	127	∨	∨	NUM
ejpam-5423	346	128	δ	δ	PROPN
ejpam-5423	346	129	n	n	X
ejpam-5423	346	130	=	=	SYM
ejpam-5423	346	131	(	(	PUNCT
ejpam-5423	346	132	(	(	PUNCT
ejpam-5423	346	133	ωn(e	ωn(e	NOUN
ejpam-5423	346	134	)	)	PUNCT
ejpam-5423	346	135	∨ϖn(e	∨ϖn(e	PROPN
ejpam-5423	346	136	)	)	PUNCT
ejpam-5423	346	137	)	)	PUNCT
ejpam-5423	347	1	∧	∧	NOUN
ejpam-5423	347	2	λ	λ	PROPN
ejpam-5423	347	3	n	n	CCONJ
ejpam-5423	347	4	)	)	PUNCT
ejpam-5423	347	5	∨	∨	NUM
ejpam-5423	347	6	δ	δ	PROPN
ejpam-5423	347	7	n	n	X
ejpam-5423	347	8	=	=	PUNCT
ejpam-5423	347	9	(	(	PUNCT
ejpam-5423	347	10	ωn	ωn	PROPN
ejpam-5423	347	11	⊓ϖn)λ	⊓ϖn)λ	PUNCT
ejpam-5423	347	12	δ	δ	PROPN
ejpam-5423	347	13	(	(	PUNCT
ejpam-5423	347	14	e	e	NOUN
ejpam-5423	347	15	)	)	PUNCT
ejpam-5423	347	16	.	.	PUNCT
ejpam-5423	348	1	hence	hence	ADV
ejpam-5423	348	2	,	,	PUNCT
ejpam-5423	348	3	(	(	PUNCT
ejpam-5423	348	4	ωp	ωp	ADP
ejpam-5423	348	5	◦	◦	NOUN
ejpam-5423	348	6	ϖp)δ	ϖp)δ	PROPN
ejpam-5423	348	7	λ	λ	PROPN
ejpam-5423	348	8	(	(	PUNCT
ejpam-5423	348	9	e	e	NOUN
ejpam-5423	348	10	)	)	PUNCT
ejpam-5423	348	11	≥	≥	NOUN
ejpam-5423	348	12	(	(	PUNCT
ejpam-5423	348	13	ωp	ωp	NOUN
ejpam-5423	348	14	⊓ϖp)δ	⊓ϖp)δ	PROPN
ejpam-5423	348	15	λ	λ	PROPN
ejpam-5423	348	16	(	(	PUNCT
ejpam-5423	348	17	e	e	NOUN
ejpam-5423	348	18	)	)	PUNCT
ejpam-5423	348	19	and	and	CCONJ
ejpam-5423	348	20	(	(	PUNCT
ejpam-5423	348	21	ωn	ωn	ADP
ejpam-5423	348	22	◦	◦	NOUN
ejpam-5423	348	23	ϖn)λ	ϖn)λ	PROPN
ejpam-5423	348	24	δ	δ	PROPN
ejpam-5423	348	25	(	(	PUNCT
ejpam-5423	348	26	e	e	NOUN
ejpam-5423	348	27	)	)	PUNCT
ejpam-5423	348	28	≤	≤	NOUN
ejpam-5423	348	29	(	(	PUNCT
ejpam-5423	348	30	ωn	ωn	PROPN
ejpam-5423	348	31	⊓ϖn)λ	⊓ϖn)λ	PUNCT
ejpam-5423	348	32	δ	δ	PROPN
ejpam-5423	348	33	(	(	PUNCT
ejpam-5423	348	34	e	e	NOUN
ejpam-5423	348	35	)	)	PUNCT
ejpam-5423	348	36	.	.	PUNCT
ejpam-5423	349	1	therefore	therefore	ADV
ejpam-5423	349	2	,	,	PUNCT
ejpam-5423	349	3	(	(	PUNCT
ejpam-5423	349	4	t	t	PROPN
ejpam-5423	349	5	⊓	⊓	PROPN
ejpam-5423	349	6	j	j	PROPN
ejpam-5423	349	7	)	)	PUNCT
ejpam-5423	349	8	λ	λ	PROPN
ejpam-5423	349	9	δ	δ	PROPN
ejpam-5423	349	10	⊑	⊑	X
ejpam-5423	349	11	(	(	PUNCT
ejpam-5423	349	12	t	t	PROPN
ejpam-5423	349	13	◦	◦	NOUN
ejpam-5423	349	14	j	j	PROPN
ejpam-5423	349	15	)	)	PUNCT
ejpam-5423	349	16	λ	λ	PROPN
ejpam-5423	349	17	δ	δ	PROPN
ejpam-5423	349	18	.	.	PUNCT
ejpam-5423	350	1	(	(	PUNCT
ejpam-5423	350	2	6	6	NUM
ejpam-5423	350	3	)	)	PUNCT
ejpam-5423	350	4	⇒	⇒	NOUN
ejpam-5423	350	5	(	(	PUNCT
ejpam-5423	350	6	5	5	NUM
ejpam-5423	350	7	)	)	PUNCT
ejpam-5423	350	8	⇒	⇒	NOUN
ejpam-5423	350	9	(	(	PUNCT
ejpam-5423	350	10	4	4	NUM
ejpam-5423	350	11	)	)	PUNCT
ejpam-5423	350	12	and	and	CCONJ
ejpam-5423	350	13	(	(	PUNCT
ejpam-5423	350	14	3	3	X
ejpam-5423	350	15	)	)	PUNCT
ejpam-5423	350	16	⇒	⇒	NOUN
ejpam-5423	350	17	(	(	PUNCT
ejpam-5423	350	18	2	2	X
ejpam-5423	350	19	)	)	PUNCT
ejpam-5423	350	20	this	this	PRON
ejpam-5423	350	21	is	be	AUX
ejpam-5423	350	22	obvious	obvious	ADJ
ejpam-5423	350	23	because	because	SCONJ
ejpam-5423	350	24	every	every	DET
ejpam-5423	350	25	(	(	PUNCT
ejpam-5423	350	26	λ	λ	NOUN
ejpam-5423	350	27	,	,	PUNCT
ejpam-5423	350	28	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	350	29	quasi	quasi	NOUN
ejpam-5423	350	30	-	-	ADJ
ejpam-5423	350	31	ideal	ideal	ADJ
ejpam-5423	350	32	is	be	AUX
ejpam-5423	350	33	an	an	DET
ejpam-5423	350	34	(	(	PUNCT
ejpam-5423	350	35	λ	λ	NOUN
ejpam-5423	350	36	,	,	PUNCT
ejpam-5423	350	37	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	350	38	bi	bi	NOUN
ejpam-5423	350	39	-	-	NOUN
ejpam-5423	350	40	ideal	ideal	NOUN
ejpam-5423	350	41	of	of	ADP
ejpam-5423	350	42	g.	g.	PROPN
ejpam-5423	350	43	(	(	PUNCT
ejpam-5423	350	44	4	4	NUM
ejpam-5423	350	45	)	)	PUNCT
ejpam-5423	350	46	⇒	⇒	NOUN
ejpam-5423	350	47	(	(	PUNCT
ejpam-5423	350	48	2	2	X
ejpam-5423	350	49	)	)	PUNCT
ejpam-5423	350	50	take	take	VERB
ejpam-5423	350	51	t	t	NOUN
ejpam-5423	350	52	=	=	SYM
ejpam-5423	350	53	j	j	PROPN
ejpam-5423	350	54	in	in	ADP
ejpam-5423	350	55	(	(	PUNCT
ejpam-5423	350	56	4	4	NUM
ejpam-5423	350	57	)	)	PUNCT
ejpam-5423	350	58	,	,	PUNCT
ejpam-5423	350	59	we	we	PRON
ejpam-5423	350	60	get	get	VERB
ejpam-5423	350	61	t	t	PROPN
ejpam-5423	350	62	λ	λ	PROPN
ejpam-5423	350	63	δ	δ	X
ejpam-5423	350	64	=	=	PUNCT
ejpam-5423	350	65	(	(	PUNCT
ejpam-5423	350	66	t	t	PROPN
ejpam-5423	350	67	⊓	⊓	PROPN
ejpam-5423	350	68	t	t	NOUN
ejpam-5423	350	69	)	)	PUNCT
ejpam-5423	350	70	λ	λ	PROPN
ejpam-5423	350	71	δ	δ	PROPN
ejpam-5423	350	72	⊑	⊑	X
ejpam-5423	350	73	(	(	PUNCT
ejpam-5423	350	74	t	t	PROPN
ejpam-5423	350	75	◦	◦	NOUN
ejpam-5423	350	76	t	t	PROPN
ejpam-5423	350	77	)	)	PUNCT
ejpam-5423	350	78	λ	λ	PROPN
ejpam-5423	350	79	δ	δ	PROPN
ejpam-5423	350	80	.	.	PUNCT
ejpam-5423	351	1	since	since	SCONJ
ejpam-5423	351	2	every	every	DET
ejpam-5423	351	3	(	(	PUNCT
ejpam-5423	351	4	λ	λ	PROPN
ejpam-5423	351	5	,	,	PUNCT
ejpam-5423	351	6	δ)ivbf	δ)ivbf	NOUN
ejpam-5423	351	7	quasi	quasi	NOUN
ejpam-5423	351	8	-	-	NOUN
ejpam-5423	351	9	ideal	ideal	NOUN
ejpam-5423	351	10	of	of	ADP
ejpam-5423	351	11	g	g	PROPN
ejpam-5423	351	12	is	be	AUX
ejpam-5423	351	13	an	an	DET
ejpam-5423	351	14	(	(	PUNCT
ejpam-5423	351	15	λ	λ	NOUN
ejpam-5423	351	16	,	,	PUNCT
ejpam-5423	351	17	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	351	18	subsemigroup	subsemigroup	NOUN
ejpam-5423	351	19	of	of	ADP
ejpam-5423	351	20	g	g	NOUN
ejpam-5423	351	21	and	and	CCONJ
ejpam-5423	351	22	by	by	ADP
ejpam-5423	351	23	theorem	theorem	NOUN
ejpam-5423	351	24	9	9	NUM
ejpam-5423	351	25	,	,	PUNCT
ejpam-5423	351	26	we	we	PRON
ejpam-5423	351	27	have	have	VERB
ejpam-5423	351	28	(	(	PUNCT
ejpam-5423	351	29	t	t	X
ejpam-5423	351	30	◦	◦	NOUN
ejpam-5423	351	31	t	t	PROPN
ejpam-5423	351	32	)	)	PUNCT
ejpam-5423	352	1	λ	λ	PROPN
ejpam-5423	352	2	δ	δ	PROPN
ejpam-5423	352	3	⊑	⊑	X
ejpam-5423	352	4	t	t	PROPN
ejpam-5423	352	5	λ	λ	PROPN
ejpam-5423	352	6	δ	δ	PROPN
ejpam-5423	352	7	.	.	PUNCT
ejpam-5423	353	1	thus	thus	ADV
ejpam-5423	353	2	,	,	PUNCT
ejpam-5423	353	3	(	(	PUNCT
ejpam-5423	353	4	t	t	PROPN
ejpam-5423	353	5	◦	◦	NOUN
ejpam-5423	353	6	t	t	PROPN
ejpam-5423	353	7	)	)	PUNCT
ejpam-5423	353	8	λ	λ	NOUN
ejpam-5423	353	9	δ	δ	NOUN
ejpam-5423	353	10	=	=	PUNCT
ejpam-5423	353	11	t	t	PROPN
ejpam-5423	353	12	λ	λ	X
ejpam-5423	353	13	δ	δ	PROPN
ejpam-5423	353	14	.	.	PUNCT
ejpam-5423	354	1	(	(	PUNCT
ejpam-5423	354	2	2	2	X
ejpam-5423	354	3	)	)	PUNCT
ejpam-5423	354	4	⇒	⇒	NOUN
ejpam-5423	354	5	(	(	PUNCT
ejpam-5423	354	6	1	1	X
ejpam-5423	354	7	)	)	PUNCT
ejpam-5423	354	8	let	let	VERB
ejpam-5423	354	9	q	q	NOUN
ejpam-5423	354	10	be	be	AUX
ejpam-5423	354	11	a	a	DET
ejpam-5423	354	12	quasi	quasi	NOUN
ejpam-5423	354	13	-	-	NOUN
ejpam-5423	354	14	ideal	ideal	NOUN
ejpam-5423	354	15	of	of	ADP
ejpam-5423	354	16	g.	g.	PROPN
ejpam-5423	354	17	then	then	ADV
ejpam-5423	354	18	by	by	ADP
ejpam-5423	354	19	theorem	theorem	NOUN
ejpam-5423	354	20	6	6	NUM
ejpam-5423	354	21	,	,	PUNCT
ejpam-5423	354	22	χq	χq	NOUN
ejpam-5423	354	23	=	=	PUNCT
ejpam-5423	354	24	(	(	PUNCT
ejpam-5423	354	25	g;χ	g;χ	PROPN
ejpam-5423	354	26	p	p	PROPN
ejpam-5423	354	27	q	q	PROPN
ejpam-5423	354	28	,	,	PUNCT
ejpam-5423	354	29	χ	χ	PROPN
ejpam-5423	354	30	n	n	ADV
ejpam-5423	354	31	q	q	NOUN
ejpam-5423	354	32	)	)	PUNCT
ejpam-5423	354	33	is	be	AUX
ejpam-5423	354	34	an	an	DET
ejpam-5423	354	35	(	(	PUNCT
ejpam-5423	354	36	λ	λ	NOUN
ejpam-5423	354	37	,	,	PUNCT
ejpam-5423	354	38	δ)-ivbf	δ)-ivbf	PUNCT
ejpam-5423	354	39	quasi	quasi	NOUN
ejpam-5423	354	40	-	-	NOUN
ejpam-5423	354	41	ideal	ideal	NOUN
ejpam-5423	354	42	of	of	ADP
ejpam-5423	354	43	g.	g.	PROPN
ejpam-5423	354	44	by	by	ADP
ejpam-5423	354	45	supposition	supposition	NOUN
ejpam-5423	354	46	and	and	CCONJ
ejpam-5423	354	47	thoerem7	thoerem7	PROPN
ejpam-5423	354	48	,	,	PUNCT
ejpam-5423	354	49	we	we	PRON
ejpam-5423	354	50	have	have	VERB
ejpam-5423	354	51	(	(	PUNCT
ejpam-5423	354	52	χ	χ	PRON
ejpam-5423	354	53	p	p	X
ejpam-5423	354	54	(	(	PUNCT
ejpam-5423	354	55	q2	q2	NOUN
ejpam-5423	354	56	]	]	PUNCT
ejpam-5423	354	57	)	)	PUNCT
ejpam-5423	355	1	δ	δ	PROPN
ejpam-5423	355	2	λ	λ	X
ejpam-5423	355	3	(	(	PUNCT
ejpam-5423	355	4	e	e	NOUN
ejpam-5423	355	5	)	)	PUNCT
ejpam-5423	355	6	=	=	SYM
ejpam-5423	355	7	(	(	PUNCT
ejpam-5423	355	8	χ	χ	X
ejpam-5423	355	9	p	p	X
ejpam-5423	355	10	q	q	X
ejpam-5423	355	11	◦	◦	NOUN
ejpam-5423	355	12	χ	χ	PRON
ejpam-5423	355	13	p	p	X
ejpam-5423	355	14	q	q	NOUN
ejpam-5423	355	15	)	)	PUNCT
ejpam-5423	355	16	δ	δ	PROPN
ejpam-5423	355	17	λ	λ	PROPN
ejpam-5423	355	18	(	(	PUNCT
ejpam-5423	355	19	e	e	NOUN
ejpam-5423	355	20	)	)	PUNCT
ejpam-5423	355	21	=	=	SYM
ejpam-5423	355	22	(	(	PUNCT
ejpam-5423	355	23	χ	χ	PRON
ejpam-5423	355	24	p	p	X
ejpam-5423	355	25	q	q	NOUN
ejpam-5423	355	26	)	)	PUNCT
ejpam-5423	355	27	δ	δ	PROPN
ejpam-5423	355	28	λ	λ	PROPN
ejpam-5423	355	29	(	(	PUNCT
ejpam-5423	355	30	e	e	NOUN
ejpam-5423	355	31	)	)	PUNCT
ejpam-5423	355	32	=	=	SYM
ejpam-5423	355	33	δ	δ	X
ejpam-5423	355	34	p	p	NOUN
ejpam-5423	355	35	,	,	PUNCT
ejpam-5423	355	36	and	and	CCONJ
ejpam-5423	355	37	(	(	PUNCT
ejpam-5423	355	38	χ	χ	X
ejpam-5423	355	39	n	n	CCONJ
ejpam-5423	355	40	(	(	PUNCT
ejpam-5423	355	41	q2	q2	NOUN
ejpam-5423	355	42	]	]	PUNCT
ejpam-5423	355	43	)	)	PUNCT
ejpam-5423	356	1	λ	λ	PROPN
ejpam-5423	356	2	δ	δ	X
ejpam-5423	356	3	(	(	PUNCT
ejpam-5423	356	4	e	e	NOUN
ejpam-5423	356	5	)	)	PUNCT
ejpam-5423	356	6	=	=	SYM
ejpam-5423	356	7	(	(	PUNCT
ejpam-5423	356	8	χ	χ	NOUN
ejpam-5423	356	9	n	n	PRON
ejpam-5423	356	10	q	q	ADJ
ejpam-5423	356	11	◦	◦	NOUN
ejpam-5423	356	12	χ	χ	PRON
ejpam-5423	356	13	n	n	PRON
ejpam-5423	356	14	q	q	NOUN
ejpam-5423	356	15	)	)	PUNCT
ejpam-5423	356	16	λ	λ	PROPN
ejpam-5423	356	17	δ	δ	PROPN
ejpam-5423	356	18	(	(	PUNCT
ejpam-5423	356	19	e	e	NOUN
ejpam-5423	356	20	)	)	PUNCT
ejpam-5423	356	21	=	=	SYM
ejpam-5423	356	22	(	(	PUNCT
ejpam-5423	356	23	χ	χ	ADP
ejpam-5423	356	24	n	n	PRON
ejpam-5423	356	25	q	q	NOUN
ejpam-5423	356	26	)	)	PUNCT
ejpam-5423	356	27	λ	λ	PROPN
ejpam-5423	356	28	δ	δ	PROPN
ejpam-5423	356	29	(	(	PUNCT
ejpam-5423	356	30	e	e	NOUN
ejpam-5423	356	31	)	)	PUNCT
ejpam-5423	356	32	=	=	SYM
ejpam-5423	356	33	δ	δ	PROPN
ejpam-5423	356	34	n	n	NOUN
ejpam-5423	356	35	.	.	PUNCT
ejpam-5423	357	1	thus	thus	ADV
ejpam-5423	357	2	,	,	PUNCT
ejpam-5423	357	3	(	(	PUNCT
ejpam-5423	357	4	qq	qq	X
ejpam-5423	357	5	]	]	X
ejpam-5423	357	6	=	=	SYM
ejpam-5423	357	7	q.	q.	VERB
ejpam-5423	357	8	an	an	DET
ejpam-5423	357	9	application	application	NOUN
ejpam-5423	357	10	of	of	ADP
ejpam-5423	357	11	lemma	lemma	PROPN
ejpam-5423	357	12	3	3	NUM
ejpam-5423	357	13	shows	show	VERB
ejpam-5423	357	14	us	we	PRON
ejpam-5423	357	15	that	that	SCONJ
ejpam-5423	357	16	g	g	PROPN
ejpam-5423	357	17	is	be	AUX
ejpam-5423	357	18	both	both	CCONJ
ejpam-5423	357	19	regular	regular	ADJ
ejpam-5423	357	20	and	and	CCONJ
ejpam-5423	357	21	intra	intra	ADJ
ejpam-5423	357	22	-	-	ADJ
ejpam-5423	357	23	regular	regular	ADJ
ejpam-5423	357	24	.	.	PUNCT
ejpam-5423	358	1	references	reference	NOUN
ejpam-5423	358	2	3240	3240	NUM
ejpam-5423	358	3	5	5	NUM
ejpam-5423	358	4	.	.	PUNCT
ejpam-5423	358	5	conclusion	conclusion	VERB
ejpam-5423	358	6	the	the	DET
ejpam-5423	358	7	theory	theory	NOUN
ejpam-5423	358	8	of	of	ADP
ejpam-5423	358	9	fuzzy	fuzzy	ADJ
ejpam-5423	358	10	sets	set	NOUN
ejpam-5423	358	11	,	,	PUNCT
ejpam-5423	358	12	initially	initially	ADV
ejpam-5423	358	13	introduced	introduce	VERB
ejpam-5423	358	14	by	by	ADP
ejpam-5423	358	15	l.	l.	PROPN
ejpam-5423	358	16	a.	a.	PROPN
ejpam-5423	358	17	zadeh	zadeh	PROPN
ejpam-5423	358	18	,	,	PUNCT
ejpam-5423	358	19	was	be	AUX
ejpam-5423	358	20	later	later	ADV
ejpam-5423	358	21	extended	extend	VERB
ejpam-5423	358	22	to	to	ADP
ejpam-5423	358	23	interval	interval	NOUN
ejpam-5423	358	24	-	-	PUNCT
ejpam-5423	358	25	valued	value	VERB
ejpam-5423	358	26	fuzzy	fuzzy	ADJ
ejpam-5423	358	27	sets	set	NOUN
ejpam-5423	358	28	.	.	PUNCT
ejpam-5423	359	1	building	build	VERB
ejpam-5423	359	2	upon	upon	SCONJ
ejpam-5423	359	3	this	this	DET
ejpam-5423	359	4	foundation	foundation	NOUN
ejpam-5423	359	5	,	,	PUNCT
ejpam-5423	359	6	k.	k.	PROPN
ejpam-5423	359	7	arulmozhi	arulmozhi	PROPN
ejpam-5423	359	8	et	et	PROPN
ejpam-5423	359	9	al	al	PROPN
ejpam-5423	359	10	.	.	PROPN
ejpam-5423	360	1	explored	explore	VERB
ejpam-5423	360	2	interval	interval	NOUN
ejpam-5423	360	3	-	-	PUNCT
ejpam-5423	360	4	valued	value	VERB
ejpam-5423	360	5	bipolar	bipolar	ADJ
ejpam-5423	360	6	fuzzy	fuzzy	ADJ
ejpam-5423	360	7	sets	set	NOUN
ejpam-5423	360	8	in	in	ADP
ejpam-5423	360	9	algebraic	algebraic	ADJ
ejpam-5423	360	10	structures	structure	NOUN
ejpam-5423	360	11	.	.	PUNCT
ejpam-5423	361	1	in	in	ADP
ejpam-5423	361	2	2021	2021	NUM
ejpam-5423	361	3	,	,	PUNCT
ejpam-5423	361	4	s.	s.	PROPN
ejpam-5423	361	5	lekkoksung	lekkoksung	PROPN
ejpam-5423	361	6	advanced	advance	VERB
ejpam-5423	361	7	this	this	DET
ejpam-5423	361	8	area	area	NOUN
ejpam-5423	361	9	by	by	ADP
ejpam-5423	361	10	developing	develop	VERB
ejpam-5423	361	11	the	the	DET
ejpam-5423	361	12	concept	concept	NOUN
ejpam-5423	361	13	of	of	ADP
ejpam-5423	361	14	interval	interval	NOUN
ejpam-5423	361	15	-	-	PUNCT
ejpam-5423	361	16	valued	value	VERB
ejpam-5423	361	17	bipolar	bipolar	ADJ
ejpam-5423	361	18	fuzzy	fuzzy	ADJ
ejpam-5423	361	19	ideals	ideal	NOUN
ejpam-5423	361	20	in	in	ADP
ejpam-5423	361	21	ordered	order	VERB
ejpam-5423	361	22	semigroups	semigroup	NOUN
ejpam-5423	361	23	and	and	CCONJ
ejpam-5423	361	24	characterized	characterize	VERB
ejpam-5423	361	25	regular	regular	ADJ
ejpam-5423	361	26	ordered	order	VERB
ejpam-5423	361	27	semigroups	semigroup	NOUN
ejpam-5423	361	28	in	in	ADP
ejpam-5423	361	29	terms	term	NOUN
ejpam-5423	361	30	of	of	ADP
ejpam-5423	361	31	generalized	generalized	ADJ
ejpam-5423	361	32	intervalvalued	intervalvalue	VERB
ejpam-5423	361	33	bipolar	bipolar	ADJ
ejpam-5423	361	34	fuzzy	fuzzy	ADJ
ejpam-5423	361	35	ideals	ideal	NOUN
ejpam-5423	361	36	and	and	CCONJ
ejpam-5423	361	37	bi	bi	NOUN
ejpam-5423	361	38	-	-	NOUN
ejpam-5423	361	39	ideals	ideal	NOUN
ejpam-5423	361	40	.	.	PUNCT
ejpam-5423	362	1	in	in	ADP
ejpam-5423	362	2	this	this	DET
ejpam-5423	362	3	paper	paper	NOUN
ejpam-5423	362	4	,	,	PUNCT
ejpam-5423	362	5	we	we	PRON
ejpam-5423	362	6	introduce	introduce	VERB
ejpam-5423	362	7	new	new	ADJ
ejpam-5423	362	8	definitions	definition	NOUN
ejpam-5423	362	9	of	of	ADP
ejpam-5423	362	10	generalized	generalized	ADJ
ejpam-5423	362	11	interval	interval	NOUN
ejpam-5423	362	12	-	-	PUNCT
ejpam-5423	362	13	valued	value	VERB
ejpam-5423	362	14	bipolar	bipolar	ADJ
ejpam-5423	362	15	fuzzy	fuzzy	ADJ
ejpam-5423	362	16	quasi	quasi	NOUN
ejpam-5423	362	17	-	-	NOUN
ejpam-5423	362	18	ideals	ideal	NOUN
ejpam-5423	362	19	and	and	CCONJ
ejpam-5423	362	20	establish	establish	VERB
ejpam-5423	362	21	their	their	PRON
ejpam-5423	362	22	properties	property	NOUN
ejpam-5423	362	23	.	.	PUNCT
ejpam-5423	363	1	using	use	VERB
ejpam-5423	363	2	intra	intra	ADJ
ejpam-5423	363	3	-	-	ADJ
ejpam-5423	363	4	regular	regular	ADJ
ejpam-5423	363	5	ordered	order	VERB
ejpam-5423	363	6	semigroups	semigroup	NOUN
ejpam-5423	363	7	,	,	PUNCT
ejpam-5423	363	8	we	we	PRON
ejpam-5423	363	9	prove	prove	VERB
ejpam-5423	363	10	several	several	ADJ
ejpam-5423	363	11	properties	property	NOUN
ejpam-5423	363	12	of	of	ADP
ejpam-5423	363	13	these	these	DET
ejpam-5423	363	14	generalized	generalized	ADJ
ejpam-5423	363	15	quasiideals	quasiideal	NOUN
ejpam-5423	363	16	.	.	PUNCT
ejpam-5423	364	1	furthermore	furthermore	ADV
ejpam-5423	364	2	,	,	PUNCT
ejpam-5423	364	3	we	we	PRON
ejpam-5423	364	4	provide	provide	VERB
ejpam-5423	364	5	a	a	DET
ejpam-5423	364	6	characterization	characterization	NOUN
ejpam-5423	364	7	of	of	ADP
ejpam-5423	364	8	intra	intra	ADJ
ejpam-5423	364	9	-	-	ADJ
ejpam-5423	364	10	regular	regular	ADJ
ejpam-5423	364	11	ordered	order	VERB
ejpam-5423	364	12	semigroups	semigroup	NOUN
ejpam-5423	364	13	through	through	ADP
ejpam-5423	364	14	the	the	DET
ejpam-5423	364	15	framework	framework	NOUN
ejpam-5423	364	16	of	of	ADP
ejpam-5423	364	17	generalized	generalized	ADJ
ejpam-5423	364	18	interval	interval	NOUN
ejpam-5423	364	19	-	-	PUNCT
ejpam-5423	364	20	valued	value	VERB
ejpam-5423	364	21	bipolar	bipolar	ADJ
ejpam-5423	364	22	fuzzy	fuzzy	ADJ
ejpam-5423	364	23	quasi	quasi	NOUN
ejpam-5423	364	24	-	-	NOUN
ejpam-5423	364	25	ideals	ideal	NOUN
ejpam-5423	364	26	.	.	PUNCT
ejpam-5423	365	1	we	we	PRON
ejpam-5423	365	2	hope	hope	VERB
ejpam-5423	365	3	that	that	SCONJ
ejpam-5423	365	4	the	the	DET
ejpam-5423	365	5	study	study	NOUN
ejpam-5423	365	6	of	of	ADP
ejpam-5423	365	7	intra	intra	ADJ
ejpam-5423	365	8	-	-	ADJ
ejpam-5423	365	9	regular	regular	ADJ
ejpam-5423	365	10	ordered	order	VERB
ejpam-5423	365	11	semigroups	semigroup	NOUN
ejpam-5423	365	12	in	in	ADP
ejpam-5423	365	13	terms	term	NOUN
ejpam-5423	365	14	of	of	ADP
ejpam-5423	365	15	generalized	generalized	ADJ
ejpam-5423	365	16	interval	interval	NOUN
ejpam-5423	365	17	valued	value	VERB
ejpam-5423	365	18	bipolar	bipolar	ADJ
ejpam-5423	365	19	fuzzy	fuzzy	ADJ
ejpam-5423	365	20	quasi	quasi	NOUN
ejpam-5423	365	21	-	-	ADJ
ejpam-5423	365	22	ideal	ideal	ADJ
ejpam-5423	365	23	are	be	AUX
ejpam-5423	365	24	useful	useful	ADJ
ejpam-5423	365	25	mathematical	mathematical	ADJ
ejpam-5423	365	26	tools	tool	NOUN
ejpam-5423	365	27	.	.	PUNCT
ejpam-5423	366	1	in	in	ADP
ejpam-5423	366	2	the	the	DET
ejpam-5423	366	3	future	future	NOUN
ejpam-5423	366	4	,	,	PUNCT
ejpam-5423	366	5	we	we	PRON
ejpam-5423	366	6	study	study	VERB
ejpam-5423	366	7	characterized	characterize	VERB
ejpam-5423	366	8	semisimple	semisimple	NOUN
ejpam-5423	366	9	ordered	order	VERB
ejpam-5423	366	10	semigroups	semigroup	NOUN
ejpam-5423	366	11	in	in	ADP
ejpam-5423	366	12	terms	term	NOUN
ejpam-5423	366	13	of	of	ADP
ejpam-5423	366	14	generalized	generalized	ADJ
ejpam-5423	366	15	interval	interval	NOUN
ejpam-5423	366	16	valued	value	VERB
ejpam-5423	366	17	bipolar	bipolar	ADJ
ejpam-5423	366	18	fuzzy	fuzzy	ADJ
ejpam-5423	366	19	interior	interior	ADJ
ejpam-5423	366	20	ideals	ideal	NOUN
ejpam-5423	366	21	.	.	PUNCT
ejpam-5423	367	1	acknowledgements	acknowledgement	NOUN
ejpam-5423	367	2	the	the	DET
ejpam-5423	367	3	authors	author	NOUN
ejpam-5423	367	4	are	be	AUX
ejpam-5423	367	5	grateful	grateful	ADJ
ejpam-5423	367	6	to	to	ADP
ejpam-5423	367	7	the	the	DET
ejpam-5423	367	8	school	school	NOUN
ejpam-5423	367	9	of	of	ADP
ejpam-5423	367	10	science	science	NOUN
ejpam-5423	367	11	,	,	PUNCT
ejpam-5423	367	12	university	university	NOUN
ejpam-5423	367	13	of	of	ADP
ejpam-5423	367	14	phayao	phayao	NOUN
ejpam-5423	367	15	for	for	ADP
ejpam-5423	367	16	grant	grant	NOUN
ejpam-5423	367	17	support	support	NOUN
ejpam-5423	367	18	(	(	PUNCT
ejpam-5423	367	19	pbtsc67008	pbtsc67008	PROPN
ejpam-5423	367	20	)	)	PUNCT
ejpam-5423	367	21	.	.	PUNCT
ejpam-5423	368	1	references	reference	NOUN
ejpam-5423	368	2	[	[	X
ejpam-5423	368	3	1	1	NUM
ejpam-5423	368	4	]	]	PUNCT
ejpam-5423	368	5	b.	b.	PROPN
ejpam-5423	368	6	davvaz	davvaz	PROPN
ejpam-5423	368	7	a.	a.	PROPN
ejpam-5423	368	8	mahboob	mahboob	PROPN
ejpam-5423	368	9	and	and	CCONJ
ejpam-5423	368	10	n.m	n.m	PROPN
ejpam-5423	368	11	.	.	PROPN
ejpam-5423	368	12	khan	khan	PROPN
ejpam-5423	368	13	.	.	PUNCT
ejpam-5423	369	1	fuzzy	fuzzy	ADJ
ejpam-5423	369	2	(	(	PUNCT
ejpam-5423	369	3	m	m	PROPN
ejpam-5423	369	4	,	,	PUNCT
ejpam-5423	369	5	n)-ideals	n)-ideal	NOUN
ejpam-5423	369	6	in	in	ADP
ejpam-5423	369	7	semigroups	semigroup	NOUN
ejpam-5423	369	8	.	.	PUNCT
ejpam-5423	370	1	computational	computational	ADJ
ejpam-5423	370	2	and	and	CCONJ
ejpam-5423	370	3	applied	applied	ADJ
ejpam-5423	370	4	mathematics	mathematic	NOUN
ejpam-5423	370	5	,	,	PUNCT
ejpam-5423	370	6	38(189	38(189	NOUN
ejpam-5423	370	7	)	)	PUNCT
ejpam-5423	370	8	,	,	PUNCT
ejpam-5423	370	9	2019	2019	NUM
ejpam-5423	370	10	.	.	PUNCT
ejpam-5423	371	1	[	[	X
ejpam-5423	371	2	2	2	NUM
ejpam-5423	371	3	]	]	PUNCT
ejpam-5423	371	4	m.	m.	NOUN
ejpam-5423	371	5	al	al	PROPN
ejpam-5423	371	6	-	-	PUNCT
ejpam-5423	371	7	tahan	tahan	PROPN
ejpam-5423	371	8	a.	a.	NOUN
ejpam-5423	371	9	mahboob	mahboob	PROPN
ejpam-5423	371	10	and	and	CCONJ
ejpam-5423	371	11	g.	g.	PROPN
ejpam-5423	371	12	muhiuddin	muhiuddin	PROPN
ejpam-5423	371	13	.	.	PUNCT
ejpam-5423	372	1	fuzzy	fuzzy	ADJ
ejpam-5423	372	2	(	(	PUNCT
ejpam-5423	372	3	m	m	PROPN
ejpam-5423	372	4	,	,	PUNCT
ejpam-5423	372	5	n)-filters	n)-filter	NOUN
ejpam-5423	372	6	based	base	VERB
ejpam-5423	372	7	on	on	ADP
ejpam-5423	372	8	fuzzy	fuzzy	ADJ
ejpam-5423	372	9	points	point	NOUN
ejpam-5423	372	10	in	in	ADP
ejpam-5423	372	11	ordered	order	VERB
ejpam-5423	372	12	semigroups	semigroup	NOUN
ejpam-5423	372	13	.	.	PUNCT
ejpam-5423	373	1	computational	computational	ADJ
ejpam-5423	373	2	and	and	CCONJ
ejpam-5423	373	3	applied	applied	ADJ
ejpam-5423	373	4	mathematics	mathematic	NOUN
ejpam-5423	373	5	,	,	PUNCT
ejpam-5423	373	6	2023	2023	NUM
ejpam-5423	373	7	.	.	PUNCT
ejpam-5423	374	1	[	[	X
ejpam-5423	374	2	3	3	X
ejpam-5423	374	3	]	]	PUNCT
ejpam-5423	374	4	m.	m.	NOUN
ejpam-5423	374	5	al	al	PROPN
ejpam-5423	374	6	-	-	PUNCT
ejpam-5423	374	7	tahan	tahan	PROPN
ejpam-5423	374	8	a.	a.	NOUN
ejpam-5423	374	9	mahboob	mahboob	PROPN
ejpam-5423	374	10	and	and	CCONJ
ejpam-5423	374	11	g.	g.	PROPN
ejpam-5423	374	12	muhiuddin	muhiuddin	PROPN
ejpam-5423	374	13	.	.	PUNCT
ejpam-5423	375	1	characterizations	characterization	NOUN
ejpam-5423	375	2	of	of	ADP
ejpam-5423	375	3	ordered	order	VERB
ejpam-5423	375	4	semigroups	semigroup	NOUN
ejpam-5423	375	5	in	in	ADP
ejpam-5423	375	6	terms	term	NOUN
ejpam-5423	375	7	of	of	ADP
ejpam-5423	375	8	fuzzy	fuzzy	ADJ
ejpam-5423	375	9	(	(	PUNCT
ejpam-5423	375	10	m	m	PROPN
ejpam-5423	375	11	,	,	PUNCT
ejpam-5423	375	12	n)-substructures	n)-substructure	NOUN
ejpam-5423	375	13	.	.	NOUN
ejpam-5423	375	14	soft	soft	ADJ
ejpam-5423	375	15	computing	computing	NOUN
ejpam-5423	375	16	,	,	PUNCT
ejpam-5423	375	17	2024	2024	NUM
ejpam-5423	375	18	.	.	PUNCT
ejpam-5423	376	1	[	[	X
ejpam-5423	376	2	4	4	NUM
ejpam-5423	376	3	]	]	X
ejpam-5423	376	4	md	md	PROPN
ejpam-5423	376	5	.	.	PROPN
ejpam-5423	376	6	firoj	firoj	PROPN
ejpam-5423	376	7	ail	ail	PROPN
ejpam-5423	376	8	a.	a.	PROPN
ejpam-5423	376	9	salm	salm	PROPN
ejpam-5423	376	10	,	,	PUNCT
ejpam-5423	376	11	a.	a.	NOUN
ejpam-5423	376	12	mahboob	mahboob	PROPN
ejpam-5423	376	13	and	and	CCONJ
ejpam-5423	376	14	n.	n.	PROPN
ejpam-5423	376	15	m.	m.	PROPN
ejpam-5423	376	16	khan	khan	PROPN
ejpam-5423	376	17	.	.	PUNCT
ejpam-5423	377	1	characterizations	characterization	NOUN
ejpam-5423	377	2	of	of	ADP
ejpam-5423	377	3	regular	regular	ADJ
ejpam-5423	377	4	ordered	order	VERB
ejpam-5423	377	5	semigroups	semigroup	NOUN
ejpam-5423	377	6	by	by	ADP
ejpam-5423	377	7	(	(	PUNCT
ejpam-5423	377	8	ε	ε	PROPN
ejpam-5423	377	9	,	,	PUNCT
ejpam-5423	377	10	ε,∨k	ε,∨k	PROPN
ejpam-5423	377	11	,	,	PUNCT
ejpam-5423	377	12	qk))-fuzzy	qk))-fuzzy	ADV
ejpam-5423	377	13	qausi	qausi	NOUN
ejpam-5423	377	14	-	-	PUNCT
ejpam-5423	377	15	ideals	ideal	NOUN
ejpam-5423	377	16	.	.	PUNCT
ejpam-5423	378	1	fuzzy	fuzzy	ADJ
ejpam-5423	378	2	information	information	NOUN
ejpam-5423	378	3	and	and	CCONJ
ejpam-5423	378	4	engineering	engineering	NOUN
ejpam-5423	378	5	,	,	PUNCT
ejpam-5423	378	6	11(4):428–445	11(4):428–445	PROPN
ejpam-5423	378	7	,	,	PUNCT
ejpam-5423	378	8	2019	2019	NUM
ejpam-5423	378	9	.	.	PUNCT
ejpam-5423	379	1	[	[	X
ejpam-5423	379	2	5	5	X
ejpam-5423	379	3	]	]	PUNCT
ejpam-5423	379	4	h.	h.	NOUN
ejpam-5423	379	5	bustince	bustince	NOUN
ejpam-5423	379	6	.	.	PUNCT
ejpam-5423	380	1	indicator	indicator	NOUN
ejpam-5423	380	2	of	of	ADP
ejpam-5423	380	3	inclusion	inclusion	NOUN
ejpam-5423	380	4	grade	grade	NOUN
ejpam-5423	380	5	for	for	ADP
ejpam-5423	380	6	interval	interval	NOUN
ejpam-5423	380	7	valued	value	VERB
ejpam-5423	380	8	fuzzy	fuzzy	ADJ
ejpam-5423	380	9	sets	set	NOUN
ejpam-5423	380	10	.	.	PUNCT
ejpam-5423	381	1	application	application	NOUN
ejpam-5423	381	2	to	to	PART
ejpam-5423	381	3	approximate	approximate	ADJ
ejpam-5423	381	4	reasoning	reasoning	NOUN
ejpam-5423	381	5	based	base	VERB
ejpam-5423	381	6	on	on	ADP
ejpam-5423	381	7	interval	interval	NOUN
ejpam-5423	381	8	valued	value	VERB
ejpam-5423	381	9	fuzzy	fuzzy	ADJ
ejpam-5423	381	10	sets	set	NOUN
ejpam-5423	381	11	.	.	PUNCT
ejpam-5423	382	1	international	international	ADJ
ejpam-5423	382	2	journal	journal	PROPN
ejpam-5423	382	3	of	of	ADP
ejpam-5423	382	4	approximate	approximate	ADJ
ejpam-5423	382	5	reasoning	reasoning	NOUN
ejpam-5423	382	6	,	,	PUNCT
ejpam-5423	382	7	23:137–209	23:137–209	PROPN
ejpam-5423	382	8	,	,	PUNCT
ejpam-5423	382	9	1998	1998	NUM
ejpam-5423	382	10	.	.	PUNCT
ejpam-5423	383	1	[	[	X
ejpam-5423	383	2	6	6	NUM
ejpam-5423	383	3	]	]	PUNCT
ejpam-5423	383	4	j.	j.	PROPN
ejpam-5423	383	5	kang	kang	PROPN
ejpam-5423	383	6	c.	c.	PROPN
ejpam-5423	383	7	kim	kim	PROPN
ejpam-5423	383	8	and	and	CCONJ
ejpam-5423	383	9	j.	j.	PROPN
ejpam-5423	383	10	m.	m.	PROPN
ejpam-5423	383	11	kang	kang	PROPN
ejpam-5423	383	12	.	.	PUNCT
ejpam-5423	384	1	ideal	ideal	PROPN
ejpam-5423	384	2	theory	theory	NOUN
ejpam-5423	384	3	of	of	ADP
ejpam-5423	384	4	semigroups	semigroup	NOUN
ejpam-5423	384	5	based	base	VERB
ejpam-5423	384	6	on	on	ADP
ejpam-5423	384	7	the	the	DET
ejpam-5423	384	8	bipolar	bipolar	ADJ
ejpam-5423	384	9	valued	value	VERB
ejpam-5423	384	10	fuzzy	fuzzy	ADJ
ejpam-5423	384	11	set	set	NOUN
ejpam-5423	384	12	theory	theory	NOUN
ejpam-5423	384	13	.	.	PUNCT
ejpam-5423	385	1	annals	annal	NOUN
ejpam-5423	385	2	of	of	ADP
ejpam-5423	385	3	fuzzy	fuzzy	ADJ
ejpam-5423	385	4	mathematics	mathematic	NOUN
ejpam-5423	385	5	and	and	CCONJ
ejpam-5423	385	6	informatics	informatic	NOUN
ejpam-5423	385	7	,	,	PUNCT
ejpam-5423	385	8	2(2):193–206	2(2):193–206	NUM
ejpam-5423	385	9	,	,	PUNCT
ejpam-5423	385	10	2012	2012	NUM
ejpam-5423	385	11	.	.	PUNCT
ejpam-5423	386	1	references	reference	NOUN
ejpam-5423	386	2	3241	3241	NUM
ejpam-5423	386	3	[	[	X
ejpam-5423	386	4	7	7	NUM
ejpam-5423	386	5	]	]	PUNCT
ejpam-5423	386	6	l.	l.	PROPN
ejpam-5423	386	7	nareupanat	nareupanat	PROPN
ejpam-5423	386	8	h.	h.	PROPN
ejpam-5423	386	9	sanpan	sanpan	PROPN
ejpam-5423	386	10	and	and	CCONJ
ejpam-5423	386	11	l.	l.	PROPN
ejpam-5423	386	12	somsak	somsak	PROPN
ejpam-5423	386	13	.	.	PUNCT
ejpam-5423	387	1	on	on	ADP
ejpam-5423	387	2	generalized	generalized	ADJ
ejpam-5423	387	3	interval	interval	NOUN
ejpam-5423	387	4	valued	value	VERB
ejpam-5423	387	5	bipolar	bipolar	ADJ
ejpam-5423	387	6	fuzzy	fuzzy	ADJ
ejpam-5423	387	7	ideals	ideal	NOUN
ejpam-5423	387	8	in	in	ADP
ejpam-5423	387	9	ordered	order	VERB
ejpam-5423	387	10	semigroups	semigroup	NOUN
ejpam-5423	387	11	.	.	PUNCT
ejpam-5423	388	1	journal	journal	PROPN
ejpam-5423	388	2	mathematics	mathematics	PROPN
ejpam-5423	388	3	computre	computre	PROPN
ejpam-5423	388	4	science	science	NOUN
ejpam-5423	388	5	,	,	PUNCT
ejpam-5423	388	6	11(3):3613	11(3):3613	NUM
ejpam-5423	388	7	–	–	PUNCT
ejpam-5423	388	8	3636	3636	NUM
ejpam-5423	388	9	,	,	PUNCT
ejpam-5423	388	10	2021	2021	NUM
ejpam-5423	388	11	.	.	PUNCT
ejpam-5423	389	1	[	[	X
ejpam-5423	389	2	8	8	NUM
ejpam-5423	389	3	]	]	PUNCT
ejpam-5423	389	4	p.	p.	PROPN
ejpam-5423	389	5	daniel	daniel	PROPN
ejpam-5423	389	6	f.	f.	PROPN
ejpam-5423	389	7	javier	javier	PROPN
ejpam-5423	389	8	j.	j.	PROPN
ejpam-5423	389	9	aranzazu	aranzazu	PROPN
ejpam-5423	389	10	,	,	PUNCT
ejpam-5423	389	11	s.	s.	PROPN
ejpam-5423	389	12	antonio	antonio	PROPN
ejpam-5423	389	13	and	and	CCONJ
ejpam-5423	389	14	b.	b.	PROPN
ejpam-5423	389	15	humberto	humberto	PROPN
ejpam-5423	389	16	.	.	PUNCT
ejpam-5423	390	1	interval	interval	NOUN
ejpam-5423	390	2	valued	value	VERB
ejpam-5423	390	3	fuzzy	fuzzy	ADJ
ejpam-5423	390	4	sets	set	NOUN
ejpam-5423	390	5	for	for	ADP
ejpam-5423	390	6	color	color	NOUN
ejpam-5423	390	7	image	image	NOUN
ejpam-5423	390	8	super	super	NOUN
ejpam-5423	390	9	-	-	NOUN
ejpam-5423	390	10	resolution	resolution	NOUN
ejpam-5423	390	11	.	.	PUNCT
ejpam-5423	391	1	advances	advance	NOUN
ejpam-5423	391	2	in	in	ADP
ejpam-5423	391	3	artificial	artificial	ADJ
ejpam-5423	391	4	intelligence	intelligence	NOUN
ejpam-5423	391	5	,	,	PUNCT
ejpam-5423	391	6	pages	page	NOUN
ejpam-5423	391	7	373	373	NUM
ejpam-5423	391	8	–	–	PUNCT
ejpam-5423	391	9	382	382	NUM
ejpam-5423	391	10	,	,	PUNCT
ejpam-5423	391	11	2011	2011	NUM
ejpam-5423	391	12	.	.	PUNCT
ejpam-5423	392	1	[	[	X
ejpam-5423	392	2	9	9	NUM
ejpam-5423	392	3	]	]	PUNCT
ejpam-5423	392	4	x.	x.	NOUN
ejpam-5423	392	5	xie	xie	PROPN
ejpam-5423	392	6	j.	j.	PROPN
ejpam-5423	392	7	tang	tang	PROPN
ejpam-5423	392	8	and	and	CCONJ
ejpam-5423	392	9	y.	y.	PROPN
ejpam-5423	392	10	luo	luo	PROPN
ejpam-5423	392	11	.	.	PUNCT
ejpam-5423	393	1	characterizations	characterization	NOUN
ejpam-5423	393	2	of	of	ADP
ejpam-5423	393	3	ordered	order	VERB
ejpam-5423	393	4	semigroups	semigroup	NOUN
ejpam-5423	393	5	by	by	ADP
ejpam-5423	393	6	new	new	ADJ
ejpam-5423	393	7	type	type	NOUN
ejpam-5423	393	8	of	of	ADP
ejpam-5423	393	9	interval	interval	NOUN
ejpam-5423	393	10	valued	value	VERB
ejpam-5423	393	11	fuzzy	fuzzy	ADJ
ejpam-5423	393	12	quasi	quasi	NOUN
ejpam-5423	393	13	-	-	NOUN
ejpam-5423	393	14	ideals	ideal	NOUN
ejpam-5423	393	15	.	.	PUNCT
ejpam-5423	394	1	journal	journal	NOUN
ejpam-5423	394	2	of	of	ADP
ejpam-5423	394	3	applied	apply	VERB
ejpam-5423	394	4	mathematics	mathematic	NOUN
ejpam-5423	394	5	,	,	PUNCT
ejpam-5423	394	6	pages	page	NOUN
ejpam-5423	394	7	1–15	1–15	PROPN
ejpam-5423	394	8	,	,	PUNCT
ejpam-5423	394	9	2014	2014	NUM
ejpam-5423	394	10	.	.	PUNCT
ejpam-5423	395	1	[	[	X
ejpam-5423	395	2	10	10	NUM
ejpam-5423	395	3	]	]	X
ejpam-5423	395	4	n.	n.	PROPN
ejpam-5423	395	5	kuroki	kuroki	PROPN
ejpam-5423	395	6	.	.	PUNCT
ejpam-5423	396	1	fuzzy	fuzzy	ADJ
ejpam-5423	396	2	bi	bi	NOUN
ejpam-5423	396	3	-	-	NOUN
ejpam-5423	396	4	ideals	ideal	NOUN
ejpam-5423	396	5	in	in	ADP
ejpam-5423	396	6	semigroup	semigroup	PROPN
ejpam-5423	396	7	.	.	PUNCT
ejpam-5423	397	1	comment	comment	NOUN
ejpam-5423	397	2	.	.	PUNCT
ejpam-5423	398	1	math	math	NOUN
ejpam-5423	398	2	.	.	PUNCT
ejpam-5423	399	1	univ	univ	PROPN
ejpam-5423	399	2	.	.	PUNCT
ejpam-5423	400	1	st	st	PROPN
ejpam-5423	400	2	.	.	PROPN
ejpam-5423	400	3	paul	paul	PROPN
ejpam-5423	400	4	,	,	PUNCT
ejpam-5423	400	5	5:128–132	5:128–132	PROPN
ejpam-5423	400	6	,	,	PUNCT
ejpam-5423	400	7	1979	1979	NUM
ejpam-5423	400	8	.	.	PUNCT
ejpam-5423	401	1	[	[	X
ejpam-5423	401	2	11	11	NUM
ejpam-5423	401	3	]	]	PUNCT
ejpam-5423	401	4	k.	k.	PROPN
ejpam-5423	401	5	lee	lee	PROPN
ejpam-5423	401	6	.	.	PUNCT
ejpam-5423	402	1	bipolar	bipolar	ADJ
ejpam-5423	402	2	-	-	PUNCT
ejpam-5423	402	3	valued	value	VERB
ejpam-5423	402	4	fuzzy	fuzzy	ADJ
ejpam-5423	402	5	sets	set	NOUN
ejpam-5423	402	6	and	and	CCONJ
ejpam-5423	402	7	their	their	PRON
ejpam-5423	402	8	operations	operation	NOUN
ejpam-5423	402	9	.	.	PUNCT
ejpam-5423	403	1	in	in	ADP
ejpam-5423	403	2	proceeding	proceed	VERB
ejpam-5423	403	3	international	international	ADJ
ejpam-5423	403	4	conference	conference	NOUN
ejpam-5423	403	5	on	on	ADP
ejpam-5423	403	6	intelligent	intelligent	ADJ
ejpam-5423	403	7	technologies	technology	NOUN
ejpam-5423	403	8	bangkok	bangkok	PROPN
ejpam-5423	403	9	,	,	PUNCT
ejpam-5423	403	10	thailand	thailand	PROPN
ejpam-5423	403	11	,	,	PUNCT
ejpam-5423	403	12	pages	page	NOUN
ejpam-5423	403	13	307–312	307–312	NUM
ejpam-5423	403	14	,	,	PUNCT
ejpam-5423	403	15	2000	2000	NUM
ejpam-5423	403	16	.	.	PUNCT
ejpam-5423	404	1	[	[	X
ejpam-5423	404	2	12	12	NUM
ejpam-5423	404	3	]	]	PUNCT
ejpam-5423	404	4	a.	a.	NOUN
ejpam-5423	404	5	mahboob	mahboob	PROPN
ejpam-5423	404	6	and	and	CCONJ
ejpam-5423	404	7	g.	g.	PROPN
ejpam-5423	404	8	muhiuddin	muhiuddin	PROPN
ejpam-5423	404	9	.	.	PUNCT
ejpam-5423	405	1	a	a	DET
ejpam-5423	405	2	new	new	ADJ
ejpam-5423	405	3	type	type	NOUN
ejpam-5423	405	4	of	of	ADP
ejpam-5423	405	5	fuzzy	fuzzy	ADJ
ejpam-5423	405	6	prime	prime	NOUN
ejpam-5423	405	7	subset	subset	NOUN
ejpam-5423	405	8	in	in	ADP
ejpam-5423	405	9	ordered	order	VERB
ejpam-5423	405	10	semigroups	semigroup	NOUN
ejpam-5423	405	11	.	.	PUNCT
ejpam-5423	406	1	new	new	ADJ
ejpam-5423	406	2	mathematics	mathematic	NOUN
ejpam-5423	406	3	and	and	CCONJ
ejpam-5423	406	4	natural	natural	ADJ
ejpam-5423	406	5	computation	computation	NOUN
ejpam-5423	406	6	,	,	PUNCT
ejpam-5423	406	7	17(3):739–752	17(3):739–752	NUM
ejpam-5423	406	8	,	,	PUNCT
ejpam-5423	406	9	2021	2021	NUM
ejpam-5423	406	10	.	.	PUNCT
ejpam-5423	407	1	[	[	X
ejpam-5423	407	2	13	13	NUM
ejpam-5423	407	3	]	]	X
ejpam-5423	407	4	al	al	PROPN
ejpam-5423	407	5	.	.	PROPN
ejpam-5423	407	6	narayanan	narayanan	PROPN
ejpam-5423	407	7	and	and	CCONJ
ejpam-5423	407	8	t.	t.	PROPN
ejpam-5423	407	9	manikantan	manikantan	PROPN
ejpam-5423	407	10	.	.	PUNCT
ejpam-5423	408	1	interval	interval	NOUN
ejpam-5423	408	2	valued	value	VERB
ejpam-5423	408	3	fuzzy	fuzzy	ADJ
ejpam-5423	408	4	ideals	ideal	NOUN
ejpam-5423	408	5	generated	generate	VERB
ejpam-5423	408	6	by	by	ADP
ejpam-5423	408	7	an	an	DET
ejpam-5423	408	8	interval	interval	NOUN
ejpam-5423	408	9	valued	value	VERB
ejpam-5423	408	10	fuzzy	fuzzy	ADJ
ejpam-5423	408	11	subset	subset	NOUN
ejpam-5423	408	12	in	in	ADP
ejpam-5423	408	13	semigroups	semigroup	NOUN
ejpam-5423	408	14	.	.	PUNCT
ejpam-5423	409	1	journal	journal	NOUN
ejpam-5423	409	2	of	of	ADP
ejpam-5423	409	3	applied	apply	VERB
ejpam-5423	409	4	mathematics	mathematic	NOUN
ejpam-5423	409	5	and	and	CCONJ
ejpam-5423	409	6	computing	computing	NOUN
ejpam-5423	409	7	,	,	PUNCT
ejpam-5423	409	8	20(1	20(1	NUM
ejpam-5423	409	9	-	-	PUNCT
ejpam-5423	409	10	2):455–464	2):455–464	NUM
ejpam-5423	409	11	,	,	PUNCT
ejpam-5423	409	12	2006	2006	NUM
ejpam-5423	409	13	.	.	PUNCT
ejpam-5423	410	1	[	[	X
ejpam-5423	410	2	14	14	NUM
ejpam-5423	410	3	]	]	PUNCT
ejpam-5423	410	4	a.	a.	NOUN
ejpam-5423	410	5	iampan	iampan	PROPN
ejpam-5423	410	6	p.	p.	PROPN
ejpam-5423	410	7	khamrot	khamrot	PROPN
ejpam-5423	410	8	and	and	CCONJ
ejpam-5423	410	9	t.	t.	PROPN
ejpam-5423	410	10	gaketem	gaketem	PROPN
ejpam-5423	410	11	.	.	PUNCT
ejpam-5423	411	1	weakly	weakly	ADV
ejpam-5423	411	2	regular	regular	ADJ
ejpam-5423	411	3	ordered	order	VERB
ejpam-5423	411	4	semigroups	semigroup	NOUN
ejpam-5423	411	5	characterized	characterize	VERB
ejpam-5423	411	6	in	in	ADP
ejpam-5423	411	7	terms	term	NOUN
ejpam-5423	411	8	of	of	ADP
ejpam-5423	411	9	generalized	generalized	ADJ
ejpam-5423	411	10	interval	interval	NOUN
ejpam-5423	411	11	valued	value	VERB
ejpam-5423	411	12	bipolar	bipolar	ADJ
ejpam-5423	411	13	fuzzy	fuzzy	ADJ
ejpam-5423	411	14	ideals	ideal	NOUN
ejpam-5423	411	15	.	.	PUNCT
ejpam-5423	412	1	iaeng	iaeng	PROPN
ejpam-5423	412	2	international	international	PROPN
ejpam-5423	412	3	journal	journal	PROPN
ejpam-5423	412	4	of	of	ADP
ejpam-5423	412	5	applied	apply	VERB
ejpam-5423	412	6	mathematics	mathematic	NOUN
ejpam-5423	412	7	,	,	PUNCT
ejpam-5423	412	8	54(8):1553–1559	54(8):1553–1559	NUM
ejpam-5423	412	9	,	,	PUNCT
ejpam-5423	412	10	2024	2024	NUM
ejpam-5423	412	11	.	.	PUNCT
ejpam-5423	413	1	[	[	X
ejpam-5423	413	2	15	15	NUM
ejpam-5423	413	3	]	]	X
ejpam-5423	413	4	l.a	l.a	PROPN
ejpam-5423	413	5	.	.	PROPN
ejpam-5423	413	6	zadeh	zadeh	PROPN
ejpam-5423	413	7	.	.	PUNCT
ejpam-5423	413	8	fuzzy	fuzzy	ADJ
ejpam-5423	413	9	sets	set	NOUN
ejpam-5423	413	10	.	.	PUNCT
ejpam-5423	414	1	information	information	NOUN
ejpam-5423	414	2	and	and	CCONJ
ejpam-5423	414	3	control	control	NOUN
ejpam-5423	414	4	,	,	PUNCT
ejpam-5423	414	5	8:338–353	8:338–353	NUM
ejpam-5423	414	6	,	,	PUNCT
ejpam-5423	414	7	1965	1965	NUM
ejpam-5423	414	8	.	.	PUNCT
ejpam-5423	415	1	[	[	X
ejpam-5423	415	2	16	16	NUM
ejpam-5423	415	3	]	]	X
ejpam-5423	415	4	l.a	l.a	PROPN
ejpam-5423	415	5	.	.	PROPN
ejpam-5423	415	6	zadeh	zadeh	PROPN
ejpam-5423	415	7	.	.	PUNCT
ejpam-5423	416	1	the	the	DET
ejpam-5423	416	2	concept	concept	NOUN
ejpam-5423	416	3	of	of	ADP
ejpam-5423	416	4	a	a	DET
ejpam-5423	416	5	linguistic	linguistic	ADJ
ejpam-5423	416	6	variable	variable	NOUN
ejpam-5423	416	7	and	and	CCONJ
ejpam-5423	416	8	its	its	PRON
ejpam-5423	416	9	application	application	NOUN
ejpam-5423	416	10	to	to	PART
ejpam-5423	416	11	approximate	approximate	ADJ
ejpam-5423	416	12	reasoning	reasoning	NOUN
ejpam-5423	416	13	.	.	PUNCT
ejpam-5423	417	1	information	information	NOUN
ejpam-5423	417	2	sciences	sciences	PROPN
ejpam-5423	417	3	,	,	PUNCT
ejpam-5423	417	4	8:199–249	8:199–249	NUM
ejpam-5423	417	5	,	,	PUNCT
ejpam-5423	417	6	1975	1975	NUM
ejpam-5423	417	7	.	.	PUNCT
ejpam-5423	418	1	[	[	X
ejpam-5423	418	2	17	17	NUM
ejpam-5423	418	3	]	]	X
ejpam-5423	418	4	w.r	w.r	PROPN
ejpam-5423	418	5	.	.	PROPN
ejpam-5423	418	6	zhang	zhang	PROPN
ejpam-5423	418	7	.	.	PUNCT
ejpam-5423	418	8	bipolar	bipolar	ADJ
ejpam-5423	418	9	fuzzy	fuzzy	ADJ
ejpam-5423	418	10	sets	set	NOUN
ejpam-5423	418	11	and	and	CCONJ
ejpam-5423	418	12	relations	relation	NOUN
ejpam-5423	418	13	:	:	PUNCT
ejpam-5423	418	14	a	a	DET
ejpam-5423	418	15	computational	computational	ADJ
ejpam-5423	418	16	framework	framework	NOUN
ejpam-5423	418	17	forcognitive	forcognitive	ADJ
ejpam-5423	418	18	modeling	modeling	NOUN
ejpam-5423	418	19	and	and	CCONJ
ejpam-5423	418	20	multiagent	multiagent	ADJ
ejpam-5423	418	21	decision	decision	NOUN
ejpam-5423	418	22	analysis	analysis	NOUN
ejpam-5423	418	23	.	.	PUNCT
ejpam-5423	419	1	in	in	ADP
ejpam-5423	419	2	proceedings	proceeding	NOUN
ejpam-5423	419	3	of	of	ADP
ejpam-5423	419	4	ieee	ieee	NOUN
ejpam-5423	419	5	conference	conference	NOUN
ejpam-5423	419	6	,	,	PUNCT
ejpam-5423	419	7	pages	page	NOUN
ejpam-5423	419	8	305–309	305–309	NUM
ejpam-5423	419	9	,	,	PUNCT
ejpam-5423	419	10	1994	1994	NUM
ejpam-5423	419	11	.	.	PUNCT
ejpam-5423	420	1	[	[	X
ejpam-5423	420	2	18	18	NUM
ejpam-5423	420	3	]	]	PUNCT
ejpam-5423	420	4	m.	m.	NOUN
ejpam-5423	420	5	zulquanain	zulquanain	NOUN
ejpam-5423	420	6	and	and	CCONJ
ejpam-5423	420	7	m.	m.	PROPN
ejpam-5423	420	8	saeed	saeed	PROPN
ejpam-5423	420	9	.	.	PUNCT
ejpam-5423	421	1	a	a	DET
ejpam-5423	421	2	new	new	ADJ
ejpam-5423	421	3	decision	decision	NOUN
ejpam-5423	421	4	making	make	VERB
ejpam-5423	421	5	method	method	NOUN
ejpam-5423	421	6	on	on	ADP
ejpam-5423	421	7	interval	interval	NOUN
ejpam-5423	421	8	value	value	NOUN
ejpam-5423	421	9	fuzzy	fuzzy	ADJ
ejpam-5423	421	10	soft	soft	ADJ
ejpam-5423	421	11	matrix	matrix	NOUN
ejpam-5423	421	12	.	.	PUNCT
ejpam-5423	422	1	british	british	ADJ
ejpam-5423	422	2	journal	journal	PROPN
ejpam-5423	422	3	of	of	ADP
ejpam-5423	422	4	mathematics	mathematics	PROPN
ejpam-5423	422	5	and	and	CCONJ
ejpam-5423	422	6	computer	computer	NOUN
ejpam-5423	422	7	science	science	NOUN
ejpam-5423	422	8	,	,	PUNCT
ejpam-5423	422	9	20(5):1–17	20(5):1–17	NUM
ejpam-5423	422	10	,	,	PUNCT
ejpam-5423	422	11	2017	2017	NUM
ejpam-5423	422	12	.	.	PUNCT