id	sid	tid	token	lemma	pos
ejpam-5854	1	1	european	european	PROPN
ejpam-5854	1	2	journal	journal	PROPN
ejpam-5854	1	3	of	of	ADP
ejpam-5854	1	4	pure	pure	ADJ
ejpam-5854	1	5	and	and	CCONJ
ejpam-5854	1	6	applied	applied	ADJ
ejpam-5854	1	7	mathematics	mathematic	NOUN
ejpam-5854	1	8	2025	2025	NUM
ejpam-5854	1	9	,	,	PUNCT
ejpam-5854	1	10	vol	vol	NOUN
ejpam-5854	1	11	.	.	PROPN
ejpam-5854	1	12	18	18	NUM
ejpam-5854	1	13	,	,	PUNCT
ejpam-5854	1	14	issue	issue	NOUN
ejpam-5854	1	15	2	2	NUM
ejpam-5854	1	16	,	,	PUNCT
ejpam-5854	1	17	article	article	NOUN
ejpam-5854	1	18	number	number	NOUN
ejpam-5854	1	19	5854	5854	NUM
ejpam-5854	1	20	issn	issn	VERB
ejpam-5854	1	21	1307	1307	NUM
ejpam-5854	1	22	-	-	SYM
ejpam-5854	1	23	5543	5543	NUM
ejpam-5854	1	24	–	–	PUNCT
ejpam-5854	1	25	ejpam.com	ejpam.com	X
ejpam-5854	1	26	published	publish	VERB
ejpam-5854	1	27	by	by	ADP
ejpam-5854	1	28	new	new	PROPN
ejpam-5854	1	29	york	york	PROPN
ejpam-5854	1	30	business	business	PROPN
ejpam-5854	1	31	global	global	ADJ
ejpam-5854	1	32	on	on	ADP
ejpam-5854	1	33	weakly	weakly	ADJ
ejpam-5854	1	34	regular	regular	ADJ
ejpam-5854	1	35	semigroups	semigroup	NOUN
ejpam-5854	1	36	characterized	characterize	VERB
ejpam-5854	1	37	in	in	ADP
ejpam-5854	1	38	terms	term	NOUN
ejpam-5854	1	39	of	of	ADP
ejpam-5854	1	40	cubic	cubic	ADJ
ejpam-5854	1	41	bipolar	bipolar	ADJ
ejpam-5854	1	42	fuzzy	fuzzy	ADJ
ejpam-5854	1	43	ideals	ideal	NOUN
ejpam-5854	1	44	p.	p.	PROPN
ejpam-5854	1	45	khamrod1	khamrod1	PROPN
ejpam-5854	1	46	,	,	PUNCT
ejpam-5854	1	47	n.	n.	PROPN
ejpam-5854	1	48	deetae2	deetae2	PROPN
ejpam-5854	1	49	,	,	PUNCT
ejpam-5854	1	50	t.	t.	PROPN
ejpam-5854	1	51	gaketem3,∗	gaketem3,∗	PROPN
ejpam-5854	1	52	1	1	NUM
ejpam-5854	1	53	department	department	NOUN
ejpam-5854	1	54	of	of	ADP
ejpam-5854	1	55	mathematics	mathematic	NOUN
ejpam-5854	1	56	,	,	PUNCT
ejpam-5854	1	57	faculty	faculty	NOUN
ejpam-5854	1	58	of	of	ADP
ejpam-5854	1	59	science	science	NOUN
ejpam-5854	1	60	and	and	CCONJ
ejpam-5854	1	61	agricultural	agricultural	ADJ
ejpam-5854	1	62	technology	technology	NOUN
ejpam-5854	1	63	,	,	PUNCT
ejpam-5854	1	64	rajamangala	rajamangala	PROPN
ejpam-5854	1	65	university	university	PROPN
ejpam-5854	1	66	of	of	ADP
ejpam-5854	1	67	technology	technology	PROPN
ejpam-5854	1	68	lanna	lanna	PROPN
ejpam-5854	1	69	of	of	ADP
ejpam-5854	1	70	phitsanulok	phitsanulok	PROPN
ejpam-5854	1	71	,	,	PUNCT
ejpam-5854	1	72	thailand	thailand	PROPN
ejpam-5854	1	73	2	2	NUM
ejpam-5854	1	74	department	department	NOUN
ejpam-5854	1	75	of	of	ADP
ejpam-5854	1	76	statistics	statistic	NOUN
ejpam-5854	1	77	,	,	PUNCT
ejpam-5854	1	78	faculty	faculty	NOUN
ejpam-5854	1	79	of	of	ADP
ejpam-5854	1	80	science	science	NOUN
ejpam-5854	1	81	and	and	CCONJ
ejpam-5854	1	82	technology	technology	NOUN
ejpam-5854	1	83	,	,	PUNCT
ejpam-5854	1	84	pibulsongkram	pibulsongkram	PROPN
ejpam-5854	1	85	rajabhat	rajabhat	PROPN
ejpam-5854	1	86	university	university	NOUN
ejpam-5854	1	87	,	,	PUNCT
ejpam-5854	1	88	phitsanulok	phitsanulok	PROPN
ejpam-5854	1	89	,	,	PUNCT
ejpam-5854	1	90	thailand	thailand	PROPN
ejpam-5854	1	91	3	3	NUM
ejpam-5854	1	92	fuzzy	fuzzy	ADJ
ejpam-5854	1	93	algebras	algebra	NOUN
ejpam-5854	1	94	and	and	CCONJ
ejpam-5854	1	95	decision	decision	NOUN
ejpam-5854	1	96	-	-	PUNCT
ejpam-5854	1	97	making	make	VERB
ejpam-5854	1	98	problems	problem	NOUN
ejpam-5854	1	99	research	research	NOUN
ejpam-5854	1	100	unit	unit	NOUN
ejpam-5854	1	101	,	,	PUNCT
ejpam-5854	1	102	department	department	NOUN
ejpam-5854	1	103	of	of	ADP
ejpam-5854	1	104	mathematics	mathematic	NOUN
ejpam-5854	1	105	,	,	PUNCT
ejpam-5854	1	106	school	school	NOUN
ejpam-5854	1	107	of	of	ADP
ejpam-5854	1	108	science	science	NOUN
ejpam-5854	1	109	,	,	PUNCT
ejpam-5854	1	110	university	university	NOUN
ejpam-5854	1	111	of	of	ADP
ejpam-5854	1	112	phayao	phayao	NOUN
ejpam-5854	1	113	,	,	PUNCT
ejpam-5854	1	114	phayao	phayao	NOUN
ejpam-5854	1	115	56000	56000	NUM
ejpam-5854	1	116	,	,	PUNCT
ejpam-5854	1	117	thailand	thailand	PROPN
ejpam-5854	1	118	abstract	abstract	NOUN
ejpam-5854	1	119	.	.	PUNCT
ejpam-5854	2	1	in	in	ADP
ejpam-5854	2	2	this	this	DET
ejpam-5854	2	3	paper	paper	NOUN
ejpam-5854	2	4	,	,	PUNCT
ejpam-5854	2	5	we	we	PRON
ejpam-5854	2	6	introduce	introduce	VERB
ejpam-5854	2	7	the	the	DET
ejpam-5854	2	8	concept	concept	NOUN
ejpam-5854	2	9	of	of	ADP
ejpam-5854	2	10	cubic	cubic	ADJ
ejpam-5854	2	11	bipolar	bipolar	ADJ
ejpam-5854	2	12	fuzzy	fuzzy	ADJ
ejpam-5854	2	13	subsemigroups	subsemigroup	NOUN
ejpam-5854	2	14	and	and	CCONJ
ejpam-5854	2	15	cubic	cubic	ADJ
ejpam-5854	2	16	bipolar	bipolar	ADJ
ejpam-5854	2	17	fuzzy	fuzzy	ADJ
ejpam-5854	2	18	ideals	ideal	NOUN
ejpam-5854	2	19	in	in	ADP
ejpam-5854	2	20	the	the	DET
ejpam-5854	2	21	context	context	NOUN
ejpam-5854	2	22	of	of	ADP
ejpam-5854	2	23	semigroups	semigroup	NOUN
ejpam-5854	2	24	.	.	PUNCT
ejpam-5854	3	1	we	we	PRON
ejpam-5854	3	2	explore	explore	VERB
ejpam-5854	3	3	their	their	PRON
ejpam-5854	3	4	fundamental	fundamental	ADJ
ejpam-5854	3	5	properties	property	NOUN
ejpam-5854	3	6	and	and	CCONJ
ejpam-5854	3	7	examine	examine	VERB
ejpam-5854	3	8	how	how	SCONJ
ejpam-5854	3	9	these	these	DET
ejpam-5854	3	10	structures	structure	NOUN
ejpam-5854	3	11	interact	interact	VERB
ejpam-5854	3	12	within	within	ADP
ejpam-5854	3	13	semigroups	semigroup	NOUN
ejpam-5854	3	14	.	.	PUNCT
ejpam-5854	4	1	the	the	DET
ejpam-5854	4	2	main	main	ADJ
ejpam-5854	4	3	thing	thing	NOUN
ejpam-5854	4	4	this	this	DET
ejpam-5854	4	5	study	study	NOUN
ejpam-5854	4	6	adds	add	VERB
ejpam-5854	4	7	is	be	AUX
ejpam-5854	4	8	a	a	DET
ejpam-5854	4	9	way	way	NOUN
ejpam-5854	4	10	to	to	PART
ejpam-5854	4	11	describe	describe	VERB
ejpam-5854	4	12	weakly	weakly	ADJ
ejpam-5854	4	13	regular	regular	ADJ
ejpam-5854	4	14	semigroups	semigroup	NOUN
ejpam-5854	4	15	using	use	VERB
ejpam-5854	4	16	the	the	DET
ejpam-5854	4	17	features	feature	NOUN
ejpam-5854	4	18	of	of	ADP
ejpam-5854	4	19	cubic	cubic	ADJ
ejpam-5854	4	20	bipolar	bipolar	ADJ
ejpam-5854	4	21	fuzzy	fuzzy	ADJ
ejpam-5854	4	22	ideals	ideal	NOUN
ejpam-5854	4	23	.	.	PUNCT
ejpam-5854	5	1	through	through	ADP
ejpam-5854	5	2	a	a	DET
ejpam-5854	5	3	detailed	detailed	ADJ
ejpam-5854	5	4	analysis	analysis	NOUN
ejpam-5854	5	5	,	,	PUNCT
ejpam-5854	5	6	we	we	PRON
ejpam-5854	5	7	establish	establish	VERB
ejpam-5854	5	8	several	several	ADJ
ejpam-5854	5	9	key	key	ADJ
ejpam-5854	5	10	results	result	NOUN
ejpam-5854	5	11	that	that	PRON
ejpam-5854	5	12	highlight	highlight	VERB
ejpam-5854	5	13	the	the	DET
ejpam-5854	5	14	role	role	NOUN
ejpam-5854	5	15	of	of	ADP
ejpam-5854	5	16	these	these	DET
ejpam-5854	5	17	fuzzy	fuzzy	ADJ
ejpam-5854	5	18	ideals	ideal	NOUN
ejpam-5854	5	19	in	in	ADP
ejpam-5854	5	20	understanding	understand	VERB
ejpam-5854	5	21	the	the	DET
ejpam-5854	5	22	algebraic	algebraic	ADJ
ejpam-5854	5	23	structure	structure	NOUN
ejpam-5854	5	24	of	of	ADP
ejpam-5854	5	25	weakly	weakly	ADJ
ejpam-5854	5	26	regular	regular	ADJ
ejpam-5854	5	27	semigroups	semigroup	NOUN
ejpam-5854	5	28	.	.	PUNCT
ejpam-5854	6	1	2020	2020	NUM
ejpam-5854	6	2	mathematics	mathematic	NOUN
ejpam-5854	6	3	subject	subject	NOUN
ejpam-5854	6	4	classifications	classification	NOUN
ejpam-5854	6	5	:	:	PUNCT
ejpam-5854	6	6	03e72	03e72	NUM
ejpam-5854	6	7	,	,	PUNCT
ejpam-5854	6	8	18b40	18b40	NUM
ejpam-5854	6	9	key	key	ADJ
ejpam-5854	6	10	words	word	NOUN
ejpam-5854	6	11	and	and	CCONJ
ejpam-5854	6	12	phrases	phrase	NOUN
ejpam-5854	6	13	:	:	PUNCT
ejpam-5854	6	14	cubic	cubic	ADJ
ejpam-5854	6	15	bipolar	bipolar	ADJ
ejpam-5854	6	16	fuzzy	fuzzy	ADJ
ejpam-5854	6	17	ideal	ideal	NOUN
ejpam-5854	6	18	,	,	PUNCT
ejpam-5854	6	19	weakly	weakly	ADJ
ejpam-5854	6	20	regular	regular	ADJ
ejpam-5854	6	21	semigroup	semigroup	NOUN
ejpam-5854	6	22	1	1	NUM
ejpam-5854	6	23	.	.	PUNCT
ejpam-5854	6	24	introduction	introduction	NOUN
ejpam-5854	6	25	the	the	DET
ejpam-5854	6	26	theory	theory	NOUN
ejpam-5854	6	27	of	of	ADP
ejpam-5854	6	28	fuzzy	fuzzy	ADJ
ejpam-5854	6	29	sets	set	NOUN
ejpam-5854	6	30	was	be	AUX
ejpam-5854	6	31	conceptualized	conceptualize	VERB
ejpam-5854	6	32	by	by	ADP
ejpam-5854	6	33	zadeh	zadeh	PROPN
ejpam-5854	6	34	in	in	ADP
ejpam-5854	6	35	1965	1965	NUM
ejpam-5854	7	1	[	[	X
ejpam-5854	7	2	1	1	NUM
ejpam-5854	7	3	]	]	PUNCT
ejpam-5854	7	4	.	.	PUNCT
ejpam-5854	8	1	this	this	DET
ejpam-5854	8	2	researchers	researcher	NOUN
ejpam-5854	8	3	is	be	AUX
ejpam-5854	8	4	used	use	VERB
ejpam-5854	8	5	in	in	ADP
ejpam-5854	8	6	mathematics	mathematic	NOUN
ejpam-5854	8	7	and	and	CCONJ
ejpam-5854	8	8	logic	logic	NOUN
ejpam-5854	8	9	but	but	CCONJ
ejpam-5854	8	10	also	also	ADV
ejpam-5854	8	11	in	in	ADP
ejpam-5854	8	12	medical	medical	ADJ
ejpam-5854	8	13	science	science	NOUN
ejpam-5854	8	14	,	,	PUNCT
ejpam-5854	8	15	theoretical	theoretical	ADJ
ejpam-5854	8	16	physics	physics	NOUN
ejpam-5854	8	17	,	,	PUNCT
ejpam-5854	8	18	robotics	robotic	NOUN
ejpam-5854	8	19	,	,	PUNCT
ejpam-5854	8	20	computer	computer	NOUN
ejpam-5854	8	21	science	science	NOUN
ejpam-5854	8	22	,	,	PUNCT
ejpam-5854	8	23	control	control	NOUN
ejpam-5854	8	24	engineering	engineering	NOUN
ejpam-5854	8	25	,	,	PUNCT
ejpam-5854	8	26	information	information	NOUN
ejpam-5854	8	27	science	science	NOUN
ejpam-5854	8	28	,	,	PUNCT
ejpam-5854	8	29	etc	etc	X
ejpam-5854	8	30	.	.	X
ejpam-5854	9	1	after	after	ADP
ejpam-5854	9	2	that	that	DET
ejpam-5854	9	3	time	time	NOUN
ejpam-5854	9	4	,	,	PUNCT
ejpam-5854	9	5	in	in	ADP
ejpam-5854	9	6	1979	1979	NUM
ejpam-5854	9	7	,	,	PUNCT
ejpam-5854	9	8	kuroki	kuroki	X
ejpam-5854	9	9	[	[	X
ejpam-5854	9	10	2	2	NUM
ejpam-5854	9	11	]	]	PUNCT
ejpam-5854	9	12	defined	define	VERB
ejpam-5854	9	13	the	the	DET
ejpam-5854	9	14	fuzzy	fuzzy	ADJ
ejpam-5854	9	15	semigroup	semigroup	NOUN
ejpam-5854	9	16	and	and	CCONJ
ejpam-5854	9	17	various	various	ADJ
ejpam-5854	9	18	kinds	kind	NOUN
ejpam-5854	9	19	of	of	ADP
ejpam-5854	9	20	fuzzy	fuzzy	ADJ
ejpam-5854	9	21	ideals	ideal	NOUN
ejpam-5854	9	22	in	in	ADP
ejpam-5854	9	23	semigroups	semigroup	NOUN
ejpam-5854	9	24	and	and	CCONJ
ejpam-5854	9	25	characterized	characterize	VERB
ejpam-5854	9	26	them	they	PRON
ejpam-5854	9	27	.	.	PUNCT
ejpam-5854	10	1	later	later	ADV
ejpam-5854	10	2	in	in	ADP
ejpam-5854	10	3	1975	1975	NUM
ejpam-5854	10	4	,	,	PUNCT
ejpam-5854	10	5	zadeh	zadeh	PROPN
ejpam-5854	11	1	[	[	X
ejpam-5854	11	2	3	3	NUM
ejpam-5854	11	3	]	]	PUNCT
ejpam-5854	11	4	,	,	PUNCT
ejpam-5854	11	5	extended	extend	VERB
ejpam-5854	11	6	the	the	DET
ejpam-5854	11	7	concept	concept	NOUN
ejpam-5854	11	8	of	of	ADP
ejpam-5854	11	9	fuzzy	fuzzy	ADJ
ejpam-5854	11	10	sets	set	NOUN
ejpam-5854	11	11	by	by	ADP
ejpam-5854	11	12	interval	interval	NOUN
ejpam-5854	11	13	valued	value	VERB
ejpam-5854	11	14	fuzzy	fuzzy	ADJ
ejpam-5854	11	15	sets	set	NOUN
ejpam-5854	11	16	as	as	ADP
ejpam-5854	11	17	a	a	DET
ejpam-5854	11	18	generalization	generalization	NOUN
ejpam-5854	11	19	of	of	ADP
ejpam-5854	11	20	the	the	DET
ejpam-5854	11	21	notion	notion	NOUN
ejpam-5854	11	22	of	of	ADP
ejpam-5854	11	23	fuzzy	fuzzy	ADJ
ejpam-5854	11	24	sets	set	NOUN
ejpam-5854	11	25	.	.	PUNCT
ejpam-5854	12	1	in	in	ADP
ejpam-5854	12	2	1994	1994	NUM
ejpam-5854	12	3	zhang	zhang	X
ejpam-5854	13	1	[	[	X
ejpam-5854	13	2	4	4	X
ejpam-5854	13	3	]	]	PUNCT
ejpam-5854	13	4	introduced	introduce	VERB
ejpam-5854	13	5	the	the	DET
ejpam-5854	13	6	notion	notion	NOUN
ejpam-5854	13	7	of	of	ADP
ejpam-5854	13	8	bipolar	bipolar	ADJ
ejpam-5854	13	9	fuzzy	fuzzy	ADJ
ejpam-5854	13	10	sets	set	NOUN
ejpam-5854	13	11	with	with	ADP
ejpam-5854	13	12	the	the	DET
ejpam-5854	13	13	extension	extension	NOUN
ejpam-5854	13	14	of	of	ADP
ejpam-5854	13	15	fuzzy	fuzzy	ADJ
ejpam-5854	13	16	sets	set	NOUN
ejpam-5854	13	17	whose	whose	DET
ejpam-5854	13	18	membership	membership	NOUN
ejpam-5854	13	19	degree	degree	NOUN
ejpam-5854	13	20	range	range	NOUN
ejpam-5854	13	21	is	be	AUX
ejpam-5854	13	22	enlarged	enlarge	VERB
ejpam-5854	13	23	from	from	ADP
ejpam-5854	13	24	the	the	DET
ejpam-5854	13	25	interval	interval	NOUN
ejpam-5854	13	26	[	[	X
ejpam-5854	13	27	0	0	NUM
ejpam-5854	13	28	,	,	PUNCT
ejpam-5854	13	29	1	1	NUM
ejpam-5854	13	30	]	]	PUNCT
ejpam-5854	13	31	to	to	ADP
ejpam-5854	13	32	[	[	X
ejpam-5854	13	33	−1	−1	NOUN
ejpam-5854	13	34	,	,	PUNCT
ejpam-5854	13	35	1	1	NUM
ejpam-5854	13	36	]	]	PUNCT
ejpam-5854	13	37	,	,	PUNCT
ejpam-5854	13	38	and	and	CCONJ
ejpam-5854	13	39	used	use	VERB
ejpam-5854	13	40	them	they	PRON
ejpam-5854	13	41	for	for	ADP
ejpam-5854	13	42	modeling	modeling	NOUN
ejpam-5854	13	43	and	and	CCONJ
ejpam-5854	13	44	decision	decision	NOUN
ejpam-5854	13	45	analysis	analysis	NOUN
ejpam-5854	13	46	.	.	PUNCT
ejpam-5854	14	1	in	in	ADP
ejpam-5854	14	2	2000	2000	NUM
ejpam-5854	14	3	,	,	PUNCT
ejpam-5854	14	4	lee	lee	PROPN
ejpam-5854	15	1	[	[	X
ejpam-5854	15	2	5	5	NUM
ejpam-5854	15	3	]	]	PUNCT
ejpam-5854	15	4	used	use	VERB
ejpam-5854	15	5	the	the	DET
ejpam-5854	15	6	term	term	NOUN
ejpam-5854	15	7	bipolar	bipolar	ADJ
ejpam-5854	15	8	valued	value	VERB
ejpam-5854	15	9	fuzzy	fuzzy	ADJ
ejpam-5854	15	10	sets	set	NOUN
ejpam-5854	15	11	and	and	CCONJ
ejpam-5854	15	12	applied	apply	VERB
ejpam-5854	15	13	it	it	PRON
ejpam-5854	15	14	to	to	ADP
ejpam-5854	15	15	algebraic	algebraic	ADJ
ejpam-5854	15	16	structures	structure	NOUN
ejpam-5854	15	17	.	.	PUNCT
ejpam-5854	16	1	in	in	ADP
ejpam-5854	16	2	2012	2012	NUM
ejpam-5854	16	3	,	,	PUNCT
ejpam-5854	16	4	jun	jun	PROPN
ejpam-5854	16	5	et	et	PROPN
ejpam-5854	16	6	al	al	PROPN
ejpam-5854	16	7	.	.	PUNCT
ejpam-5854	17	1	[	[	X
ejpam-5854	17	2	6	6	NUM
ejpam-5854	17	3	]	]	PUNCT
ejpam-5854	17	4	introduced	introduce	VERB
ejpam-5854	17	5	a	a	DET
ejpam-5854	17	6	new	new	ADJ
ejpam-5854	17	7	notion	notion	NOUN
ejpam-5854	17	8	,	,	PUNCT
ejpam-5854	17	9	a	a	DET
ejpam-5854	17	10	cubic	cubic	ADJ
ejpam-5854	17	11	set	set	NOUN
ejpam-5854	17	12	,	,	PUNCT
ejpam-5854	17	13	and	and	CCONJ
ejpam-5854	17	14	investigated	investigate	VERB
ejpam-5854	17	15	several	several	ADJ
ejpam-5854	17	16	properties	property	NOUN
ejpam-5854	17	17	of	of	ADP
ejpam-5854	17	18	cubic	cubic	ADJ
ejpam-5854	17	19	setes	sete	NOUN
ejpam-5854	17	20	as	as	ADV
ejpam-5854	17	21	well	well	ADV
ejpam-5854	17	22	as	as	ADP
ejpam-5854	17	23	introducting	introducte	VERB
ejpam-5854	17	24	cubic	cubic	ADJ
ejpam-5854	17	25	∗corresponding	∗corresponde	VERB
ejpam-5854	17	26	author	author	NOUN
ejpam-5854	17	27	.	.	PUNCT
ejpam-5854	18	1	doi	doi	NOUN
ejpam-5854	18	2	:	:	PUNCT
ejpam-5854	18	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5854	https://doi.org/10.29020/nybg.ejpam.v18i2.5854	NUM
ejpam-5854	18	4	email	email	NOUN
ejpam-5854	18	5	addresses	address	VERB
ejpam-5854	18	6	:	:	PUNCT
ejpam-5854	18	7	pkg@rmutl.ac.th	pkg@rmutl.ac.th	PROPN
ejpam-5854	18	8	(	(	PUNCT
ejpam-5854	18	9	p.khamrot)natthinee@psru.ac.th	p.khamrot)natthinee@psru.ac.th	PROPN
ejpam-5854	18	10	(	(	PUNCT
ejpam-5854	18	11	n.deetae	n.deetae	NOUN
ejpam-5854	18	12	)	)	PUNCT
ejpam-5854	18	13	,	,	PUNCT
ejpam-5854	18	14	thiti.ga@up.ac.th	thiti.ga@up.ac.th	X
ejpam-5854	18	15	(	(	PUNCT
ejpam-5854	18	16	t.gaketem	t.gaketem	NOUN
ejpam-5854	18	17	)	)	PUNCT
ejpam-5854	18	18	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5854	19	1	1	1	NUM
ejpam-5854	19	2	copyright	copyright	NOUN
ejpam-5854	19	3	:	:	PUNCT
ejpam-5854	19	4	©	©	PROPN
ejpam-5854	19	5	2025	2025	NUM
ejpam-5854	19	6	the	the	DET
ejpam-5854	19	7	author(s	author(s	NOUN
ejpam-5854	19	8	)	)	PUNCT
ejpam-5854	19	9	.	.	PUNCT
ejpam-5854	20	1	(	(	PUNCT
ejpam-5854	20	2	cc	cc	NOUN
ejpam-5854	20	3	by	by	ADP
ejpam-5854	20	4	-	-	PUNCT
ejpam-5854	20	5	nc	nc	PROPN
ejpam-5854	20	6	4.0	4.0	NUM
ejpam-5854	20	7	)	)	PUNCT
ejpam-5854	20	8	p.	p.	NOUN
ejpam-5854	20	9	khamrot	khamrot	PROPN
ejpam-5854	20	10	,	,	PUNCT
ejpam-5854	20	11	n.	n.	PROPN
ejpam-5854	20	12	deetae	deetae	PROPN
ejpam-5854	20	13	,	,	PUNCT
ejpam-5854	20	14	t.	t.	PROPN
ejpam-5854	20	15	gaketem	gaketem	PROPN
ejpam-5854	20	16	/	/	SYM
ejpam-5854	20	17	eur	eur	PROPN
ejpam-5854	20	18	.	.	PUNCT
ejpam-5854	21	1	j.	j.	PROPN
ejpam-5854	21	2	pure	pure	PROPN
ejpam-5854	21	3	appl	appl	PROPN
ejpam-5854	21	4	.	.	PROPN
ejpam-5854	21	5	math	math	PROPN
ejpam-5854	21	6	,	,	PUNCT
ejpam-5854	21	7	18	18	NUM
ejpam-5854	21	8	(	(	PUNCT
ejpam-5854	21	9	2	2	NUM
ejpam-5854	21	10	)	)	PUNCT
ejpam-5854	21	11	(	(	PUNCT
ejpam-5854	21	12	2025	2025	NUM
ejpam-5854	21	13	)	)	PUNCT
ejpam-5854	21	14	,	,	PUNCT
ejpam-5854	21	15	5854	5854	NUM
ejpam-5854	21	16	2	2	NUM
ejpam-5854	21	17	of	of	ADP
ejpam-5854	21	18	14	14	NUM
ejpam-5854	21	19	subsemigroups	subsemigroup	NOUN
ejpam-5854	21	20	and	and	CCONJ
ejpam-5854	21	21	cubic	cubic	ADJ
ejpam-5854	21	22	left	left	ADJ
ejpam-5854	21	23	(	(	PUNCT
ejpam-5854	21	24	right	right	ADJ
ejpam-5854	21	25	)	)	PUNCT
ejpam-5854	21	26	ideals	ideal	NOUN
ejpam-5854	21	27	of	of	ADP
ejpam-5854	21	28	semigroups	semigroup	NOUN
ejpam-5854	21	29	.	.	PUNCT
ejpam-5854	22	1	in	in	ADP
ejpam-5854	22	2	2018	2018	NUM
ejpam-5854	22	3	,	,	PUNCT
ejpam-5854	22	4	wei	wei	PROPN
ejpam-5854	22	5	et	et	PROPN
ejpam-5854	22	6	al	al	PROPN
ejpam-5854	22	7	.	.	PUNCT
ejpam-5854	23	1	[	[	X
ejpam-5854	23	2	7	7	X
ejpam-5854	23	3	]	]	PUNCT
ejpam-5854	23	4	studied	study	VERB
ejpam-5854	23	5	the	the	DET
ejpam-5854	23	6	concept	concept	NOUN
ejpam-5854	23	7	of	of	ADP
ejpam-5854	23	8	interval	interval	NOUN
ejpam-5854	23	9	valued	value	VERB
ejpam-5854	23	10	bipolar	bipolar	ADJ
ejpam-5854	23	11	fuzzy	fuzzy	ADJ
ejpam-5854	23	12	set	set	VERB
ejpam-5854	23	13	with	with	ADP
ejpam-5854	23	14	the	the	DET
ejpam-5854	23	15	generalization	generalization	NOUN
ejpam-5854	23	16	ofa	ofa	PROPN
ejpam-5854	23	17	bipolarr	bipolarr	PROPN
ejpam-5854	23	18	fuzzy	fuzzy	ADJ
ejpam-5854	23	19	set	set	NOUN
ejpam-5854	23	20	.	.	PUNCT
ejpam-5854	24	1	it	it	PRON
ejpam-5854	24	2	is	be	AUX
ejpam-5854	24	3	a	a	DET
ejpam-5854	24	4	study	study	NOUN
ejpam-5854	24	5	of	of	ADP
ejpam-5854	24	6	the	the	DET
ejpam-5854	24	7	values	value	NOUN
ejpam-5854	24	8	of	of	ADP
ejpam-5854	24	9	positive	positive	ADJ
ejpam-5854	24	10	and	and	CCONJ
ejpam-5854	24	11	negative	negative	ADJ
ejpam-5854	24	12	function	function	NOUN
ejpam-5854	24	13	.	.	PUNCT
ejpam-5854	25	1	riaz	riaz	PROPN
ejpam-5854	26	1	and	and	CCONJ
ejpam-5854	26	2	tehrim	tehrim	VERB
ejpam-5854	26	3	[	[	X
ejpam-5854	26	4	8	8	NUM
ejpam-5854	26	5	]	]	PUNCT
ejpam-5854	26	6	discussed	discuss	VERB
ejpam-5854	26	7	the	the	DET
ejpam-5854	26	8	concept	concept	NOUN
ejpam-5854	26	9	of	of	ADP
ejpam-5854	26	10	cubic	cubic	ADJ
ejpam-5854	26	11	bipolar	bipolar	ADJ
ejpam-5854	26	12	fuzzy	fuzzy	ADJ
ejpam-5854	26	13	sets	set	NOUN
ejpam-5854	26	14	and	and	CCONJ
ejpam-5854	26	15	some	some	DET
ejpam-5854	26	16	properties	property	NOUN
ejpam-5854	26	17	.	.	PUNCT
ejpam-5854	27	1	in	in	ADP
ejpam-5854	27	2	this	this	DET
ejpam-5854	27	3	paper	paper	NOUN
ejpam-5854	27	4	,	,	PUNCT
ejpam-5854	27	5	we	we	PRON
ejpam-5854	27	6	consider	consider	VERB
ejpam-5854	27	7	the	the	DET
ejpam-5854	27	8	relationship	relationship	NOUN
ejpam-5854	27	9	between	between	ADP
ejpam-5854	27	10	of	of	ADP
ejpam-5854	27	11	cubic	cubic	ADJ
ejpam-5854	27	12	bipolar	bipolar	ADJ
ejpam-5854	27	13	fuzzy	fuzzy	ADJ
ejpam-5854	27	14	ideals	ideal	NOUN
ejpam-5854	27	15	and	and	CCONJ
ejpam-5854	27	16	interior	interior	ADJ
ejpam-5854	27	17	ideals	ideal	NOUN
ejpam-5854	27	18	on	on	ADP
ejpam-5854	27	19	semigroups	semigroup	NOUN
ejpam-5854	27	20	.	.	PUNCT
ejpam-5854	28	1	in	in	ADP
ejpam-5854	28	2	the	the	DET
ejpam-5854	28	3	goal	goal	NOUN
ejpam-5854	28	4	results	result	VERB
ejpam-5854	28	5	,	,	PUNCT
ejpam-5854	28	6	we	we	PRON
ejpam-5854	28	7	characterized	characterize	VERB
ejpam-5854	28	8	weak	weak	ADJ
ejpam-5854	28	9	regualr	regualr	NOUN
ejpam-5854	28	10	semigroup	semigroup	NOUN
ejpam-5854	28	11	by	by	ADP
ejpam-5854	28	12	using	use	VERB
ejpam-5854	28	13	of	of	ADP
ejpam-5854	28	14	cubic	cubic	ADJ
ejpam-5854	28	15	bipolar	bipolar	ADJ
ejpam-5854	28	16	fuzzy	fuzzy	ADJ
ejpam-5854	28	17	ideals	ideal	NOUN
ejpam-5854	28	18	on	on	ADP
ejpam-5854	28	19	semigroups	semigroup	NOUN
ejpam-5854	28	20	.	.	PUNCT
ejpam-5854	29	1	2	2	X
ejpam-5854	29	2	.	.	NUM
ejpam-5854	29	3	preliminaries	preliminary	NOUN
ejpam-5854	29	4	in	in	ADP
ejpam-5854	29	5	this	this	DET
ejpam-5854	29	6	section	section	NOUN
ejpam-5854	29	7	,	,	PUNCT
ejpam-5854	29	8	we	we	PRON
ejpam-5854	29	9	will	will	AUX
ejpam-5854	29	10	give	give	VERB
ejpam-5854	29	11	some	some	DET
ejpam-5854	29	12	basic	basic	ADJ
ejpam-5854	29	13	definitions	definition	NOUN
ejpam-5854	29	14	and	and	CCONJ
ejpam-5854	29	15	results	result	NOUN
ejpam-5854	29	16	needed	need	VERB
ejpam-5854	29	17	for	for	ADP
ejpam-5854	29	18	the	the	DET
ejpam-5854	29	19	next	next	ADJ
ejpam-5854	29	20	section	section	NOUN
ejpam-5854	29	21	.	.	PUNCT
ejpam-5854	30	1	a	a	DET
ejpam-5854	30	2	subsemigroup	subsemigroup	NOUN
ejpam-5854	30	3	of	of	ADP
ejpam-5854	30	4	a	a	DET
ejpam-5854	30	5	semigroup	semigroup	NOUN
ejpam-5854	30	6	s	s	VERB
ejpam-5854	30	7	is	be	AUX
ejpam-5854	30	8	a	a	DET
ejpam-5854	30	9	non	non	ADJ
ejpam-5854	30	10	-	-	ADJ
ejpam-5854	30	11	empty	empty	ADJ
ejpam-5854	30	12	subset	subset	NOUN
ejpam-5854	30	13	t	t	NOUN
ejpam-5854	30	14	of	of	ADP
ejpam-5854	30	15	s	s	PRON
ejpam-5854	30	16	such	such	ADJ
ejpam-5854	30	17	that	that	DET
ejpam-5854	30	18	t2	t2	NOUN
ejpam-5854	30	19	⊆	⊆	NUM
ejpam-5854	30	20	t.	t.	NOUN
ejpam-5854	30	21	a	a	DET
ejpam-5854	30	22	left	left	ADJ
ejpam-5854	30	23	(	(	PUNCT
ejpam-5854	30	24	right	right	ADJ
ejpam-5854	30	25	)	)	PUNCT
ejpam-5854	30	26	ideal	ideal	NOUN
ejpam-5854	30	27	of	of	ADP
ejpam-5854	30	28	a	a	DET
ejpam-5854	30	29	semigroup	semigroup	NOUN
ejpam-5854	30	30	s	s	VERB
ejpam-5854	30	31	is	be	AUX
ejpam-5854	30	32	a	a	DET
ejpam-5854	30	33	non	non	ADJ
ejpam-5854	30	34	-	-	ADJ
ejpam-5854	30	35	empty	empty	ADJ
ejpam-5854	30	36	subset	subset	NOUN
ejpam-5854	30	37	t	t	NOUN
ejpam-5854	30	38	of	of	ADP
ejpam-5854	30	39	s	s	PRON
ejpam-5854	31	1	such	such	ADJ
ejpam-5854	31	2	that	that	DET
ejpam-5854	31	3	st	st	PROPN
ejpam-5854	31	4	⊆	⊆	NUM
ejpam-5854	31	5	t	t	NOUN
ejpam-5854	31	6	(	(	PUNCT
ejpam-5854	31	7	ts	ts	ADP
ejpam-5854	31	8	⊆	⊆	NUM
ejpam-5854	31	9	t	t	NOUN
ejpam-5854	31	10	)	)	PUNCT
ejpam-5854	31	11	.	.	PUNCT
ejpam-5854	32	1	by	by	ADP
ejpam-5854	32	2	an	an	DET
ejpam-5854	32	3	ideal	ideal	NOUN
ejpam-5854	32	4	of	of	ADP
ejpam-5854	32	5	a	a	DET
ejpam-5854	32	6	semigroup	semigroup	NOUN
ejpam-5854	32	7	s	s	NOUN
ejpam-5854	32	8	,	,	PUNCT
ejpam-5854	32	9	we	we	PRON
ejpam-5854	32	10	mean	mean	VERB
ejpam-5854	32	11	a	a	DET
ejpam-5854	32	12	nonempty	nonempty	NOUN
ejpam-5854	32	13	subset	subset	NOUN
ejpam-5854	32	14	of	of	ADP
ejpam-5854	32	15	t	t	PROPN
ejpam-5854	32	16	which	which	PRON
ejpam-5854	32	17	is	be	AUX
ejpam-5854	32	18	both	both	CCONJ
ejpam-5854	32	19	a	a	DET
ejpam-5854	32	20	left	left	NOUN
ejpam-5854	32	21	and	and	CCONJ
ejpam-5854	32	22	a	a	DET
ejpam-5854	32	23	right	right	ADJ
ejpam-5854	32	24	ideal	ideal	NOUN
ejpam-5854	32	25	of	of	ADP
ejpam-5854	32	26	s.	s.	PROPN
ejpam-5854	32	27	a	a	DET
ejpam-5854	32	28	generalized	generalized	ADJ
ejpam-5854	32	29	bi	bi	NOUN
ejpam-5854	32	30	-	-	NOUN
ejpam-5854	32	31	ideal	ideal	NOUN
ejpam-5854	32	32	of	of	ADP
ejpam-5854	32	33	a	a	DET
ejpam-5854	32	34	semigroup	semigroup	NOUN
ejpam-5854	32	35	s	s	VERB
ejpam-5854	32	36	is	be	AUX
ejpam-5854	32	37	a	a	DET
ejpam-5854	32	38	non	non	ADJ
ejpam-5854	32	39	-	-	ADJ
ejpam-5854	32	40	empty	empty	ADJ
ejpam-5854	32	41	subset	subset	NOUN
ejpam-5854	32	42	t	t	NOUN
ejpam-5854	32	43	of	of	ADP
ejpam-5854	32	44	s	s	PRON
ejpam-5854	32	45	such	such	ADJ
ejpam-5854	32	46	that	that	DET
ejpam-5854	32	47	tst	tst	NOUN
ejpam-5854	32	48	⊆	⊆	NUM
ejpam-5854	32	49	t.	t.	NOUN
ejpam-5854	32	50	a	a	DET
ejpam-5854	32	51	subsemigroup	subsemigroup	PROPN
ejpam-5854	32	52	t	t	PROPN
ejpam-5854	32	53	of	of	ADP
ejpam-5854	32	54	a	a	DET
ejpam-5854	32	55	semigroup	semigroup	NOUN
ejpam-5854	32	56	s	s	PART
ejpam-5854	32	57	is	be	AUX
ejpam-5854	32	58	called	call	VERB
ejpam-5854	32	59	a	a	DET
ejpam-5854	32	60	bi	bi	NOUN
ejpam-5854	32	61	-	-	NOUN
ejpam-5854	32	62	ideal	ideal	ADJ
ejpam-5854	32	63	(	(	PUNCT
ejpam-5854	32	64	interior	interior	ADJ
ejpam-5854	32	65	ideal	ideal	NOUN
ejpam-5854	32	66	)	)	PUNCT
ejpam-5854	32	67	of	of	ADP
ejpam-5854	32	68	s	s	PRON
ejpam-5854	32	69	if	if	SCONJ
ejpam-5854	32	70	tst	tst	NOUN
ejpam-5854	32	71	⊆	⊆	NUM
ejpam-5854	32	72	t	t	NOUN
ejpam-5854	32	73	(	(	PUNCT
ejpam-5854	32	74	sts	st	VERB
ejpam-5854	32	75	⊆	⊆	NUM
ejpam-5854	32	76	t	t	NOUN
ejpam-5854	32	77	)	)	PUNCT
ejpam-5854	32	78	.	.	PUNCT
ejpam-5854	33	1	2.1	2.1	NUM
ejpam-5854	33	2	.	.	PUNCT
ejpam-5854	33	3	fuzzy	fuzzy	ADJ
ejpam-5854	33	4	sets	set	NOUN
ejpam-5854	33	5	and	and	CCONJ
ejpam-5854	33	6	interval	interval	NOUN
ejpam-5854	33	7	valued	value	VERB
ejpam-5854	33	8	fuzzy	fuzzy	ADJ
ejpam-5854	33	9	sets	set	NOUN
ejpam-5854	33	10	in	in	ADP
ejpam-5854	33	11	this	this	DET
ejpam-5854	33	12	subsection	subsection	NOUN
ejpam-5854	33	13	,	,	PUNCT
ejpam-5854	33	14	we	we	PRON
ejpam-5854	33	15	review	review	VERB
ejpam-5854	33	16	the	the	DET
ejpam-5854	33	17	concept	concept	NOUN
ejpam-5854	33	18	of	of	ADP
ejpam-5854	33	19	important	important	ADJ
ejpam-5854	33	20	fuzzy	fuzzy	ADJ
ejpam-5854	33	21	sets	set	NOUN
ejpam-5854	33	22	and	and	CCONJ
ejpam-5854	33	23	fuzzy	fuzzy	ADJ
ejpam-5854	33	24	sets	set	NOUN
ejpam-5854	33	25	valued	value	VERB
ejpam-5854	33	26	in	in	ADP
ejpam-5854	33	27	intervals	interval	NOUN
ejpam-5854	33	28	.	.	PUNCT
ejpam-5854	34	1	for	for	ADP
ejpam-5854	34	2	any	any	DET
ejpam-5854	34	3	hi	hi	NOUN
ejpam-5854	34	4	∈	∈	PROPN
ejpam-5854	35	1	[	[	X
ejpam-5854	35	2	0	0	NUM
ejpam-5854	35	3	,	,	PUNCT
ejpam-5854	35	4	1	1	NUM
ejpam-5854	35	5	]	]	PUNCT
ejpam-5854	35	6	,	,	PUNCT
ejpam-5854	35	7	i	i	PRON
ejpam-5854	35	8	∈	∈	PROPN
ejpam-5854	35	9	f	f	AUX
ejpam-5854	35	10	,	,	PUNCT
ejpam-5854	35	11	define	define	VERB
ejpam-5854	35	12	∨	∨	NUM
ejpam-5854	35	13	i∈f	i∈f	VERB
ejpam-5854	35	14	hi	hi	INTJ
ejpam-5854	35	15	:	:	PUNCT
ejpam-5854	35	16	=	=	NOUN
ejpam-5854	35	17	sup	sup	NOUN
ejpam-5854	35	18	i∈f	i∈f	VERB
ejpam-5854	35	19	{	{	PUNCT
ejpam-5854	35	20	hi	hi	INTJ
ejpam-5854	35	21	}	}	PUNCT
ejpam-5854	35	22	and	and	CCONJ
ejpam-5854	35	23	∧	∧	PROPN
ejpam-5854	35	24	i∈f	i∈f	VERB
ejpam-5854	35	25	hi	hi	INTJ
ejpam-5854	35	26	:	:	PUNCT
ejpam-5854	35	27	=	=	SYM
ejpam-5854	35	28	inf	inf	PROPN
ejpam-5854	35	29	i∈f	i∈f	VERB
ejpam-5854	35	30	{	{	PUNCT
ejpam-5854	35	31	hi	hi	INTJ
ejpam-5854	35	32	}	}	PUNCT
ejpam-5854	35	33	.	.	PUNCT
ejpam-5854	36	1	we	we	PRON
ejpam-5854	36	2	see	see	VERB
ejpam-5854	36	3	that	that	PRON
ejpam-5854	36	4	for	for	ADP
ejpam-5854	36	5	any	any	DET
ejpam-5854	36	6	h1	h1	NOUN
ejpam-5854	36	7	,	,	PUNCT
ejpam-5854	36	8	h2	h2	PROPN
ejpam-5854	36	9	∈	∈	PROPN
ejpam-5854	37	1	[	[	X
ejpam-5854	37	2	0	0	NUM
ejpam-5854	37	3	,	,	PUNCT
ejpam-5854	37	4	1	1	NUM
ejpam-5854	37	5	]	]	PUNCT
ejpam-5854	37	6	,	,	PUNCT
ejpam-5854	37	7	we	we	PRON
ejpam-5854	37	8	have	have	VERB
ejpam-5854	37	9	h1	h1	PROPN
ejpam-5854	37	10	∨	∨	NUM
ejpam-5854	37	11	h2	h2	NOUN
ejpam-5854	37	12	=	=	SYM
ejpam-5854	37	13	max{h1	max{h1	NUM
ejpam-5854	37	14	,	,	PUNCT
ejpam-5854	37	15	h2	h2	NOUN
ejpam-5854	37	16	}	}	PUNCT
ejpam-5854	37	17	and	and	CCONJ
ejpam-5854	37	18	h1	h1	VERB
ejpam-5854	37	19	∧	∧	PROPN
ejpam-5854	37	20	h2	h2	NOUN
ejpam-5854	37	21	=	=	SYM
ejpam-5854	37	22	min{h1	min{h1	ADV
ejpam-5854	37	23	,	,	PUNCT
ejpam-5854	37	24	h2	h2	NOUN
ejpam-5854	37	25	}	}	PUNCT
ejpam-5854	37	26	.	.	PUNCT
ejpam-5854	38	1	a	a	DET
ejpam-5854	38	2	fuzzy	fuzzy	ADJ
ejpam-5854	38	3	set	set	NOUN
ejpam-5854	38	4	ω	ω	PROPN
ejpam-5854	38	5	of	of	ADP
ejpam-5854	38	6	a	a	DET
ejpam-5854	38	7	non	non	ADJ
ejpam-5854	38	8	-	-	ADJ
ejpam-5854	38	9	empty	empty	ADJ
ejpam-5854	38	10	set	set	NOUN
ejpam-5854	38	11	s	s	VERB
ejpam-5854	38	12	is	be	AUX
ejpam-5854	38	13	a	a	DET
ejpam-5854	38	14	function	function	NOUN
ejpam-5854	38	15	such	such	ADJ
ejpam-5854	38	16	that	that	SCONJ
ejpam-5854	38	17	ω	ω	NOUN
ejpam-5854	38	18	:	:	PUNCT
ejpam-5854	38	19	s	s	X
ejpam-5854	38	20	→	→	SYM
ejpam-5854	38	21	[	[	X
ejpam-5854	38	22	0	0	NUM
ejpam-5854	38	23	,	,	PUNCT
ejpam-5854	38	24	1	1	NUM
ejpam-5854	38	25	]	]	PUNCT
ejpam-5854	38	26	.	.	PUNCT
ejpam-5854	39	1	now	now	ADV
ejpam-5854	39	2	,	,	PUNCT
ejpam-5854	39	3	we	we	PRON
ejpam-5854	39	4	review	review	VERB
ejpam-5854	39	5	the	the	DET
ejpam-5854	39	6	concept	concept	NOUN
ejpam-5854	39	7	of	of	ADP
ejpam-5854	39	8	interval	interval	NOUN
ejpam-5854	39	9	valued	value	VERB
ejpam-5854	39	10	fuzzy	fuzzy	ADJ
ejpam-5854	39	11	sets	set	NOUN
ejpam-5854	39	12	.	.	PUNCT
ejpam-5854	40	1	we	we	PRON
ejpam-5854	40	2	use	use	VERB
ejpam-5854	40	3	cs[0	cs[0	PROPN
ejpam-5854	40	4	,	,	PUNCT
ejpam-5854	40	5	1	1	NUM
ejpam-5854	40	6	]	]	PUNCT
ejpam-5854	40	7	to	to	PART
ejpam-5854	40	8	denote	denote	VERB
ejpam-5854	40	9	the	the	DET
ejpam-5854	40	10	set	set	NOUN
ejpam-5854	40	11	of	of	ADP
ejpam-5854	40	12	all	all	DET
ejpam-5854	40	13	closed	closed	ADJ
ejpam-5854	40	14	subintervals	subinterval	NOUN
ejpam-5854	40	15	in	in	ADP
ejpam-5854	40	16	[	[	X
ejpam-5854	40	17	0	0	NUM
ejpam-5854	40	18	,	,	PUNCT
ejpam-5854	40	19	1	1	NUM
ejpam-5854	40	20	]	]	PUNCT
ejpam-5854	40	21	,	,	PUNCT
ejpam-5854	40	22	i.e.	i.e.	X
ejpam-5854	40	23	,	,	PUNCT
ejpam-5854	40	24	cs[0	cs[0	PROPN
ejpam-5854	40	25	,	,	PUNCT
ejpam-5854	40	26	1	1	NUM
ejpam-5854	40	27	]	]	PUNCT
ejpam-5854	40	28	=	=	PRON
ejpam-5854	40	29	{	{	PUNCT
ejpam-5854	40	30	h	h	NOUN
ejpam-5854	40	31	:	:	PUNCT
ejpam-5854	40	32	=	=	SYM
ejpam-5854	41	1	[	[	X
ejpam-5854	41	2	hl	hl	X
ejpam-5854	41	3	,	,	PUNCT
ejpam-5854	41	4	hu	hu	PROPN
ejpam-5854	41	5	]	]	X
ejpam-5854	41	6	|	|	ADV
ejpam-5854	41	7	0	0	NUM
ejpam-5854	41	8	≤	≤	NUM
ejpam-5854	41	9	hl	hl	NOUN
ejpam-5854	41	10	≤	≤	NUM
ejpam-5854	41	11	hu	hu	PROPN
ejpam-5854	41	12	≤	≤	ADV
ejpam-5854	41	13	1	1	NUM
ejpam-5854	41	14	}	}	PUNCT
ejpam-5854	41	15	.	.	PUNCT
ejpam-5854	42	1	we	we	PRON
ejpam-5854	42	2	note	note	VERB
ejpam-5854	42	3	that	that	SCONJ
ejpam-5854	43	1	[	[	X
ejpam-5854	43	2	h	h	X
ejpam-5854	43	3	,	,	PUNCT
ejpam-5854	43	4	h	h	NOUN
ejpam-5854	43	5	]	]	X
ejpam-5854	43	6	=	=	SYM
ejpam-5854	43	7	{	{	PUNCT
ejpam-5854	43	8	h	h	NOUN
ejpam-5854	43	9	}	}	PUNCT
ejpam-5854	43	10	for	for	ADP
ejpam-5854	43	11	all	all	DET
ejpam-5854	43	12	h	h	NOUN
ejpam-5854	43	13	∈	∈	PROPN
ejpam-5854	44	1	[	[	X
ejpam-5854	44	2	0	0	NUM
ejpam-5854	44	3	,	,	PUNCT
ejpam-5854	44	4	1	1	NUM
ejpam-5854	44	5	]	]	PUNCT
ejpam-5854	44	6	.	.	PUNCT
ejpam-5854	45	1	for	for	ADP
ejpam-5854	45	2	h	h	NOUN
ejpam-5854	45	3	=	=	SYM
ejpam-5854	45	4	0	0	NUM
ejpam-5854	45	5	or	or	CCONJ
ejpam-5854	45	6	1	1	NUM
ejpam-5854	45	7	,	,	PUNCT
ejpam-5854	45	8	we	we	PRON
ejpam-5854	45	9	shall	shall	AUX
ejpam-5854	45	10	denote	denote	VERB
ejpam-5854	45	11	0	0	NUM
ejpam-5854	46	1	=	=	PUNCT
ejpam-5854	47	1	[	[	X
ejpam-5854	47	2	0	0	NUM
ejpam-5854	47	3	,	,	PUNCT
ejpam-5854	47	4	0	0	NUM
ejpam-5854	47	5	]	]	PUNCT
ejpam-5854	47	6	=	=	X
ejpam-5854	47	7	{	{	PUNCT
ejpam-5854	47	8	0	0	NUM
ejpam-5854	47	9	}	}	PUNCT
ejpam-5854	47	10	and	and	CCONJ
ejpam-5854	47	11	1	1	NUM
ejpam-5854	47	12	=	=	SYM
ejpam-5854	48	1	[	[	X
ejpam-5854	48	2	1	1	NUM
ejpam-5854	48	3	,	,	PUNCT
ejpam-5854	48	4	1	1	NUM
ejpam-5854	48	5	]	]	PUNCT
ejpam-5854	48	6	=	=	PUNCT
ejpam-5854	48	7	{	{	PUNCT
ejpam-5854	48	8	1	1	NUM
ejpam-5854	48	9	}	}	PUNCT
ejpam-5854	48	10	.	.	PUNCT
ejpam-5854	49	1	for	for	ADP
ejpam-5854	49	2	any	any	DET
ejpam-5854	49	3	two	two	NUM
ejpam-5854	49	4	interval	interval	NOUN
ejpam-5854	49	5	numbers	number	NOUN
ejpam-5854	49	6	h1	h1	ADJ
ejpam-5854	49	7	and	and	CCONJ
ejpam-5854	49	8	h2	h2	PROPN
ejpam-5854	49	9	in	in	ADP
ejpam-5854	49	10	cs[0	cs[0	PROPN
ejpam-5854	49	11	,	,	PUNCT
ejpam-5854	49	12	1	1	NUM
ejpam-5854	49	13	]	]	PUNCT
ejpam-5854	49	14	,	,	PUNCT
ejpam-5854	49	15	define	define	VERB
ejpam-5854	49	16	the	the	DET
ejpam-5854	49	17	operations	operation	NOUN
ejpam-5854	49	18	“	"	PUNCT
ejpam-5854	49	19	⪯	⪯	PROPN
ejpam-5854	49	20	”	"	PUNCT
ejpam-5854	49	21	,	,	PUNCT
ejpam-5854	49	22	“	"	PUNCT
ejpam-5854	49	23	=	=	NOUN
ejpam-5854	49	24	”	"	PUNCT
ejpam-5854	49	25	,	,	PUNCT
ejpam-5854	49	26	“	"	PUNCT
ejpam-5854	49	27	⋏	⋏	PROPN
ejpam-5854	49	28	”	"	PUNCT
ejpam-5854	49	29	“	"	PUNCT
ejpam-5854	49	30	⋎	⋎	NOUN
ejpam-5854	49	31	”	"	PUNCT
ejpam-5854	49	32	as	as	SCONJ
ejpam-5854	49	33	follows	follow	VERB
ejpam-5854	49	34	:	:	PUNCT
ejpam-5854	49	35	(	(	PUNCT
ejpam-5854	49	36	1	1	X
ejpam-5854	49	37	)	)	PUNCT
ejpam-5854	49	38	h1	h1	NOUN
ejpam-5854	49	39	⪯	⪯	VERB
ejpam-5854	49	40	h2	h2	PROPN
ejpam-5854	49	41	if	if	SCONJ
ejpam-5854	49	42	and	and	CCONJ
ejpam-5854	49	43	only	only	ADV
ejpam-5854	49	44	if	if	SCONJ
ejpam-5854	49	45	hl1	hl1	PROPN
ejpam-5854	49	46	≤	≤	NOUN
ejpam-5854	49	47	hl2	hl2	NOUN
ejpam-5854	49	48	and	and	CCONJ
ejpam-5854	49	49	hu1	hu1	ADP
ejpam-5854	49	50	≤	≤	NUM
ejpam-5854	49	51	hu2	hu2	NOUN
ejpam-5854	49	52	(	(	PUNCT
ejpam-5854	49	53	2	2	NUM
ejpam-5854	49	54	)	)	PUNCT
ejpam-5854	49	55	h1	h1	NOUN
ejpam-5854	49	56	=	=	SYM
ejpam-5854	49	57	h2	h2	NOUN
ejpam-5854	49	58	if	if	SCONJ
ejpam-5854	50	1	and	and	CCONJ
ejpam-5854	50	2	only	only	ADV
ejpam-5854	50	3	if	if	SCONJ
ejpam-5854	50	4	hl1	hl1	PROPN
ejpam-5854	50	5	=	=	PUNCT
ejpam-5854	50	6	hl2	hl2	NOUN
ejpam-5854	50	7	and	and	CCONJ
ejpam-5854	50	8	hu1	hu1	NOUN
ejpam-5854	50	9	=	=	PROPN
ejpam-5854	51	1	hu2	hu2	PROPN
ejpam-5854	51	2	p.	p.	NOUN
ejpam-5854	51	3	khamrot	khamrot	PROPN
ejpam-5854	51	4	,	,	PUNCT
ejpam-5854	51	5	n.	n.	PROPN
ejpam-5854	51	6	deetae	deetae	PROPN
ejpam-5854	51	7	,	,	PUNCT
ejpam-5854	51	8	t.	t.	PROPN
ejpam-5854	51	9	gaketem	gaketem	PROPN
ejpam-5854	51	10	/	/	SYM
ejpam-5854	51	11	eur	eur	PROPN
ejpam-5854	51	12	.	.	PUNCT
ejpam-5854	52	1	j.	j.	PROPN
ejpam-5854	52	2	pure	pure	PROPN
ejpam-5854	52	3	appl	appl	PROPN
ejpam-5854	52	4	.	.	PROPN
ejpam-5854	52	5	math	math	PROPN
ejpam-5854	52	6	,	,	PUNCT
ejpam-5854	52	7	18	18	NUM
ejpam-5854	52	8	(	(	PUNCT
ejpam-5854	52	9	2	2	NUM
ejpam-5854	52	10	)	)	PUNCT
ejpam-5854	52	11	(	(	PUNCT
ejpam-5854	52	12	2025	2025	NUM
ejpam-5854	52	13	)	)	PUNCT
ejpam-5854	52	14	,	,	PUNCT
ejpam-5854	52	15	5854	5854	NUM
ejpam-5854	52	16	3	3	NUM
ejpam-5854	52	17	of	of	ADP
ejpam-5854	52	18	14	14	NUM
ejpam-5854	52	19	(	(	PUNCT
ejpam-5854	52	20	3	3	X
ejpam-5854	52	21	)	)	PUNCT
ejpam-5854	52	22	h1	h1	PROPN
ejpam-5854	52	23	⋏	⋏	PROPN
ejpam-5854	52	24	h2	h2	NOUN
ejpam-5854	53	1	=	=	PUNCT
ejpam-5854	54	1	[	[	X
ejpam-5854	54	2	(	(	PUNCT
ejpam-5854	54	3	hl1	hl1	PROPN
ejpam-5854	54	4	∧	∧	PROPN
ejpam-5854	54	5	hl2	hl2	PROPN
ejpam-5854	54	6	)	)	PUNCT
ejpam-5854	54	7	,	,	PUNCT
ejpam-5854	54	8	(	(	PUNCT
ejpam-5854	54	9	h	h	NOUN
ejpam-5854	54	10	u	u	NOUN
ejpam-5854	54	11	1	1	NUM
ejpam-5854	54	12	∧	∧	PROPN
ejpam-5854	54	13	hu2	hu2	NOUN
ejpam-5854	54	14	)	)	PUNCT
ejpam-5854	54	15	]	]	PUNCT
ejpam-5854	54	16	(	(	PUNCT
ejpam-5854	54	17	4	4	X
ejpam-5854	54	18	)	)	PUNCT
ejpam-5854	54	19	h1	h1	PROPN
ejpam-5854	54	20	⋎	⋎	NOUN
ejpam-5854	54	21	h2	h2	NOUN
ejpam-5854	54	22	=	=	PUNCT
ejpam-5854	55	1	[	[	X
ejpam-5854	55	2	(	(	PUNCT
ejpam-5854	55	3	hl1	hl1	PROPN
ejpam-5854	55	4	∨	∨	NUM
ejpam-5854	55	5	hl2	hl2	PROPN
ejpam-5854	55	6	)	)	PUNCT
ejpam-5854	55	7	,	,	PUNCT
ejpam-5854	55	8	(	(	PUNCT
ejpam-5854	55	9	h	h	NOUN
ejpam-5854	55	10	u	u	NOUN
ejpam-5854	55	11	1	1	NUM
ejpam-5854	55	12	∨	∨	NUM
ejpam-5854	55	13	hu2	hu2	NOUN
ejpam-5854	55	14	)	)	PUNCT
ejpam-5854	55	15	]	]	PUNCT
ejpam-5854	55	16	.	.	PUNCT
ejpam-5854	56	1	if	if	SCONJ
ejpam-5854	56	2	h1	h1	PROPN
ejpam-5854	56	3	⪰	⪰	NOUN
ejpam-5854	56	4	h2	h2	NOUN
ejpam-5854	56	5	,	,	PUNCT
ejpam-5854	56	6	we	we	PRON
ejpam-5854	56	7	mean	mean	VERB
ejpam-5854	56	8	h2	h2	PROPN
ejpam-5854	56	9	⪯	⪯	NOUN
ejpam-5854	56	10	h1	h1	PROPN
ejpam-5854	56	11	.	.	PUNCT
ejpam-5854	57	1	proposition	proposition	NOUN
ejpam-5854	57	2	1	1	NUM
ejpam-5854	57	3	.	.	PUNCT
ejpam-5854	58	1	[	[	X
ejpam-5854	58	2	9	9	NUM
ejpam-5854	58	3	]	]	PUNCT
ejpam-5854	58	4	for	for	ADP
ejpam-5854	58	5	any	any	DET
ejpam-5854	58	6	elements	element	NOUN
ejpam-5854	58	7	h1	h1	PROPN
ejpam-5854	58	8	,	,	PUNCT
ejpam-5854	58	9	h2	h2	NOUN
ejpam-5854	58	10	and	and	CCONJ
ejpam-5854	58	11	h3	h3	NOUN
ejpam-5854	58	12	in	in	ADP
ejpam-5854	58	13	cs[0	cs[0	PROPN
ejpam-5854	58	14	,	,	PUNCT
ejpam-5854	58	15	1	1	NUM
ejpam-5854	58	16	]	]	PUNCT
ejpam-5854	58	17	,	,	PUNCT
ejpam-5854	58	18	the	the	DET
ejpam-5854	58	19	following	follow	VERB
ejpam-5854	58	20	properties	property	NOUN
ejpam-5854	58	21	are	be	AUX
ejpam-5854	58	22	satisfied	satisfied	ADJ
ejpam-5854	58	23	:	:	PUNCT
ejpam-5854	58	24	(	(	PUNCT
ejpam-5854	58	25	1	1	X
ejpam-5854	58	26	)	)	PUNCT
ejpam-5854	58	27	h1	h1	PROPN
ejpam-5854	58	28	⋏	⋏	PROPN
ejpam-5854	58	29	h1	h1	NOUN
ejpam-5854	58	30	=	=	PUNCT
ejpam-5854	58	31	h1	h1	ADJ
ejpam-5854	58	32	and	and	CCONJ
ejpam-5854	58	33	h1	h1	VERB
ejpam-5854	58	34	⋎	⋎	PROPN
ejpam-5854	58	35	h1	h1	PROPN
ejpam-5854	58	36	=	=	PUNCT
ejpam-5854	58	37	h1	h1	PROPN
ejpam-5854	58	38	,	,	PUNCT
ejpam-5854	58	39	(	(	PUNCT
ejpam-5854	58	40	2	2	X
ejpam-5854	58	41	)	)	PUNCT
ejpam-5854	58	42	h1	h1	PROPN
ejpam-5854	58	43	⋏	⋏	PROPN
ejpam-5854	58	44	h2	h2	NOUN
ejpam-5854	58	45	=	=	SYM
ejpam-5854	58	46	h2	h2	NOUN
ejpam-5854	58	47	⋏	⋏	PROPN
ejpam-5854	58	48	h1	h1	VERB
ejpam-5854	58	49	and	and	CCONJ
ejpam-5854	58	50	h1	h1	VERB
ejpam-5854	58	51	⋎	⋎	PROPN
ejpam-5854	58	52	h2	h2	NOUN
ejpam-5854	58	53	=	=	SYM
ejpam-5854	58	54	h2	h2	PROPN
ejpam-5854	58	55	⋎	⋎	PROPN
ejpam-5854	58	56	h1	h1	PROPN
ejpam-5854	58	57	,	,	PUNCT
ejpam-5854	58	58	(	(	PUNCT
ejpam-5854	58	59	3	3	X
ejpam-5854	58	60	)	)	PUNCT
ejpam-5854	58	61	(	(	PUNCT
ejpam-5854	58	62	h1	h1	PROPN
ejpam-5854	58	63	⋏	⋏	PROPN
ejpam-5854	58	64	h2)⋏	h2)⋏	VERB
ejpam-5854	58	65	h3	h3	NOUN
ejpam-5854	58	66	=	=	SYM
ejpam-5854	58	67	h1	h1	PROPN
ejpam-5854	58	68	⋏	⋏	PROPN
ejpam-5854	58	69	(	(	PUNCT
ejpam-5854	58	70	h2	h2	PROPN
ejpam-5854	58	71	⋏	⋏	PROPN
ejpam-5854	58	72	h3	h3	NOUN
ejpam-5854	58	73	)	)	PUNCT
ejpam-5854	58	74	and	and	CCONJ
ejpam-5854	58	75	(	(	PUNCT
ejpam-5854	58	76	h1	h1	PART
ejpam-5854	58	77	⋎	⋎	VERB
ejpam-5854	58	78	h2)⋎	h2)⋎	NOUN
ejpam-5854	58	79	h3	h3	NOUN
ejpam-5854	58	80	=	=	PUNCT
ejpam-5854	58	81	h1	h1	PROPN
ejpam-5854	58	82	⋎	⋎	NOUN
ejpam-5854	58	83	(	(	PUNCT
ejpam-5854	58	84	h2	h2	NOUN
ejpam-5854	58	85	⋎	⋎	NOUN
ejpam-5854	58	86	h3	h3	NOUN
ejpam-5854	58	87	)	)	PUNCT
ejpam-5854	58	88	,	,	PUNCT
ejpam-5854	58	89	(	(	PUNCT
ejpam-5854	58	90	4	4	X
ejpam-5854	58	91	)	)	PUNCT
ejpam-5854	58	92	(	(	PUNCT
ejpam-5854	58	93	h1	h1	PROPN
ejpam-5854	58	94	⋏	⋏	PROPN
ejpam-5854	58	95	h2)⋎	h2)⋎	VERB
ejpam-5854	58	96	h3	h3	NOUN
ejpam-5854	58	97	=	=	SYM
ejpam-5854	58	98	(	(	PUNCT
ejpam-5854	58	99	h1	h1	PROPN
ejpam-5854	58	100	⋎	⋎	PROPN
ejpam-5854	58	101	h3)⋏	h3)⋏	NOUN
ejpam-5854	58	102	(	(	PUNCT
ejpam-5854	58	103	h2	h2	PROPN
ejpam-5854	58	104	⋎	⋎	NOUN
ejpam-5854	58	105	h3	h3	NOUN
ejpam-5854	58	106	)	)	PUNCT
ejpam-5854	58	107	and	and	CCONJ
ejpam-5854	58	108	(	(	PUNCT
ejpam-5854	58	109	h1	h1	PROPN
ejpam-5854	58	110	⋎	⋎	NOUN
ejpam-5854	58	111	h2)⋏	h2)⋏	NOUN
ejpam-5854	58	112	h3	h3	NOUN
ejpam-5854	58	113	=	=	SYM
ejpam-5854	58	114	(	(	PUNCT
ejpam-5854	58	115	h1	h1	PROPN
ejpam-5854	58	116	⋏	⋏	PROPN
ejpam-5854	58	117	h3)⋎	h3)⋎	NOUN
ejpam-5854	58	118	(	(	PUNCT
ejpam-5854	58	119	h2	h2	PROPN
ejpam-5854	58	120	⋏	⋏	PROPN
ejpam-5854	58	121	h3	h3	NOUN
ejpam-5854	58	122	)	)	PUNCT
ejpam-5854	58	123	,	,	PUNCT
ejpam-5854	58	124	(	(	PUNCT
ejpam-5854	58	125	5	5	X
ejpam-5854	58	126	)	)	PUNCT
ejpam-5854	58	127	if	if	SCONJ
ejpam-5854	58	128	h1	h1	NOUN
ejpam-5854	58	129	⪯	⪯	NOUN
ejpam-5854	58	130	h3	h3	NOUN
ejpam-5854	58	131	,	,	PUNCT
ejpam-5854	58	132	then	then	ADV
ejpam-5854	58	133	,	,	PUNCT
ejpam-5854	58	134	h1	h1	PROPN
ejpam-5854	58	135	⋏	⋏	PROPN
ejpam-5854	58	136	h3	h3	NOUN
ejpam-5854	58	137	⪯	⪯	NOUN
ejpam-5854	58	138	h2	h2	NOUN
ejpam-5854	58	139	⋏	⋏	PROPN
ejpam-5854	58	140	h3	h3	NOUN
ejpam-5854	58	141	and	and	CCONJ
ejpam-5854	58	142	h1	h1	VERB
ejpam-5854	58	143	⋎	⋎	NOUN
ejpam-5854	58	144	h3	h3	NOUN
ejpam-5854	58	145	⪯	⪯	NOUN
ejpam-5854	58	146	h2	h2	PROPN
ejpam-5854	58	147	⋎	⋎	PROPN
ejpam-5854	58	148	h3	h3	NOUN
ejpam-5854	58	149	.	.	PUNCT
ejpam-5854	59	1	for	for	ADP
ejpam-5854	59	2	each	each	DET
ejpam-5854	59	3	interval	interval	NOUN
ejpam-5854	59	4	{	{	PUNCT
ejpam-5854	59	5	hi	hi	INTJ
ejpam-5854	59	6	:	:	PUNCT
ejpam-5854	59	7	=	=	SYM
ejpam-5854	60	1	[	[	X
ejpam-5854	60	2	hli	hli	PROPN
ejpam-5854	60	3	,	,	PUNCT
ejpam-5854	60	4	h	h	NOUN
ejpam-5854	60	5	u	u	NOUN
ejpam-5854	61	1	i	i	PRON
ejpam-5854	61	2	]	]	PUNCT
ejpam-5854	62	1	|	|	ADV
ejpam-5854	63	1	i	i	PRON
ejpam-5854	63	2	∈	∈	PROPN
ejpam-5854	64	1	f	f	AUX
ejpam-5854	64	2	}	}	PUNCT
ejpam-5854	64	3	be	be	AUX
ejpam-5854	64	4	a	a	DET
ejpam-5854	64	5	family	family	NOUN
ejpam-5854	64	6	of	of	ADP
ejpam-5854	64	7	closed	closed	ADJ
ejpam-5854	64	8	subintervals	subinterval	NOUN
ejpam-5854	64	9	of	of	ADP
ejpam-5854	64	10	[	[	X
ejpam-5854	64	11	0	0	NUM
ejpam-5854	64	12	,	,	PUNCT
ejpam-5854	64	13	1	1	NUM
ejpam-5854	64	14	]	]	PUNCT
ejpam-5854	64	15	.	.	PUNCT
ejpam-5854	65	1	define	define	VERB
ejpam-5854	65	2	⋏	⋏	PROPN
ejpam-5854	65	3	i∈f	i∈f	VERB
ejpam-5854	65	4	hi	hi	INTJ
ejpam-5854	65	5	=	=	PRON
ejpam-5854	65	6	[	[	PUNCT
ejpam-5854	65	7	∧	∧	PROPN
ejpam-5854	65	8	i∈f	i∈f	VERB
ejpam-5854	65	9	hli	hli	PROPN
ejpam-5854	65	10	,	,	PUNCT
ejpam-5854	65	11	∧	∧	PROPN
ejpam-5854	65	12	i∈f	i∈f	VERB
ejpam-5854	65	13	hui	hui	PROPN
ejpam-5854	65	14	]	]	PUNCT
ejpam-5854	65	15	and	and	CCONJ
ejpam-5854	65	16	⋎	⋎	NOUN
ejpam-5854	65	17	i∈f	i∈f	VERB
ejpam-5854	65	18	hi	hi	INTJ
ejpam-5854	65	19	=	=	PRON
ejpam-5854	65	20	[	[	PUNCT
ejpam-5854	65	21	∨	∨	X
ejpam-5854	65	22	i∈f	i∈f	VERB
ejpam-5854	65	23	hli	hli	PROPN
ejpam-5854	65	24	,	,	PUNCT
ejpam-5854	65	25	∨	∨	NOUN
ejpam-5854	65	26	i∈f	i∈f	VERB
ejpam-5854	65	27	hui	hui	PROPN
ejpam-5854	65	28	]	]	PUNCT
ejpam-5854	65	29	.	.	PUNCT
ejpam-5854	66	1	definition	definition	NOUN
ejpam-5854	66	2	1	1	NUM
ejpam-5854	66	3	.	.	PUNCT
ejpam-5854	67	1	[	[	X
ejpam-5854	67	2	10	10	NUM
ejpam-5854	67	3	]	]	X
ejpam-5854	67	4	an	an	DET
ejpam-5854	67	5	interval	interval	NOUN
ejpam-5854	67	6	valued	value	VERB
ejpam-5854	67	7	fuzzy	fuzzy	ADJ
ejpam-5854	67	8	subset	subset	NOUN
ejpam-5854	67	9	(	(	PUNCT
ejpam-5854	67	10	shortly	shortly	ADV
ejpam-5854	67	11	,	,	PUNCT
ejpam-5854	67	12	ivf	ivf	NOUN
ejpam-5854	67	13	subset	subset	NOUN
ejpam-5854	67	14	)	)	PUNCT
ejpam-5854	67	15	of	of	ADP
ejpam-5854	67	16	s	s	PROPN
ejpam-5854	67	17	is	be	AUX
ejpam-5854	67	18	a	a	DET
ejpam-5854	67	19	function	function	NOUN
ejpam-5854	67	20	such	such	ADJ
ejpam-5854	67	21	that	that	SCONJ
ejpam-5854	67	22	µ	µ	X
ejpam-5854	67	23	:	:	PUNCT
ejpam-5854	67	24	s	s	AUX
ejpam-5854	67	25	→	→	X
ejpam-5854	67	26	cs[0	cs[0	PROPN
ejpam-5854	67	27	,	,	PUNCT
ejpam-5854	67	28	1	1	NUM
ejpam-5854	67	29	]	]	PUNCT
ejpam-5854	67	30	.	.	PUNCT
ejpam-5854	68	1	definition	definition	NOUN
ejpam-5854	68	2	2	2	NUM
ejpam-5854	68	3	.	.	PUNCT
ejpam-5854	69	1	[	[	X
ejpam-5854	69	2	11	11	NUM
ejpam-5854	69	3	]	]	PUNCT
ejpam-5854	69	4	for	for	ADP
ejpam-5854	69	5	every	every	DET
ejpam-5854	69	6	subset	subset	NOUN
ejpam-5854	69	7	k	k	PROPN
ejpam-5854	69	8	of	of	ADP
ejpam-5854	69	9	set	set	PROPN
ejpam-5854	69	10	s	s	PROPN
ejpam-5854	69	11	,	,	PUNCT
ejpam-5854	69	12	an	an	DET
ejpam-5854	69	13	interval	interval	NOUN
ejpam-5854	69	14	valued	value	VERB
ejpam-5854	69	15	characteristic	characteristic	ADJ
ejpam-5854	69	16	function	function	NOUN
ejpam-5854	69	17	λk	λk	ADP
ejpam-5854	69	18	of	of	ADP
ejpam-5854	69	19	k	k	PROPN
ejpam-5854	69	20	is	be	AUX
ejpam-5854	69	21	defined	define	VERB
ejpam-5854	69	22	to	to	PART
ejpam-5854	69	23	be	be	AUX
ejpam-5854	69	24	a	a	DET
ejpam-5854	69	25	function	function	NOUN
ejpam-5854	69	26	λk	λk	X
ejpam-5854	69	27	:	:	PUNCT
ejpam-5854	69	28	s	s	X
ejpam-5854	69	29	→	→	X
ejpam-5854	69	30	cs[0	cs[0	PROPN
ejpam-5854	69	31	,	,	PUNCT
ejpam-5854	69	32	1	1	NUM
ejpam-5854	69	33	]	]	PUNCT
ejpam-5854	69	34	by	by	ADP
ejpam-5854	69	35	λk(h	λk(h	NOUN
ejpam-5854	69	36	)	)	PUNCT
ejpam-5854	69	37	=	=	PRON
ejpam-5854	69	38	{	{	PUNCT
ejpam-5854	69	39	1	1	NUM
ejpam-5854	70	1	if	if	SCONJ
ejpam-5854	70	2	h	h	NOUN
ejpam-5854	70	3	∈	∈	PROPN
ejpam-5854	70	4	k	k	NOUN
ejpam-5854	70	5	0	0	PUNCT
ejpam-5854	71	1	if	if	SCONJ
ejpam-5854	71	2	h	h	PROPN
ejpam-5854	71	3	/∈	/∈	PUNCT
ejpam-5854	72	1	k	k	PROPN
ejpam-5854	72	2	for	for	ADP
ejpam-5854	72	3	all	all	DET
ejpam-5854	72	4	h	h	NOUN
ejpam-5854	72	5	∈	∈	PROPN
ejpam-5854	72	6	s.	s.	PROPN
ejpam-5854	73	1	for	for	ADP
ejpam-5854	73	2	two	two	NUM
ejpam-5854	73	3	ivf	ivf	ADJ
ejpam-5854	73	4	subsets	subset	NOUN
ejpam-5854	73	5	µ	µ	X
ejpam-5854	73	6	and	and	CCONJ
ejpam-5854	73	7	λ	λ	PROPN
ejpam-5854	73	8	of	of	ADP
ejpam-5854	73	9	a	a	DET
ejpam-5854	73	10	non	non	ADJ
ejpam-5854	73	11	-	-	ADJ
ejpam-5854	73	12	empty	empty	ADJ
ejpam-5854	73	13	set	set	NOUN
ejpam-5854	73	14	s	s	PART
ejpam-5854	73	15	,	,	PUNCT
ejpam-5854	73	16	define	define	VERB
ejpam-5854	73	17	(	(	PUNCT
ejpam-5854	73	18	1	1	NUM
ejpam-5854	73	19	)	)	PUNCT
ejpam-5854	73	20	µ	µ	X
ejpam-5854	73	21	⊑	⊑	PRON
ejpam-5854	73	22	λ⇔	λ⇔	PROPN
ejpam-5854	73	23	µ(h	µ(h	PROPN
ejpam-5854	73	24	)	)	PUNCT
ejpam-5854	73	25	⪯	⪯	NOUN
ejpam-5854	73	26	λ(h	λ(h	NUM
ejpam-5854	73	27	)	)	PUNCT
ejpam-5854	73	28	for	for	ADP
ejpam-5854	73	29	all	all	DET
ejpam-5854	73	30	h	h	NOUN
ejpam-5854	73	31	∈	∈	PROPN
ejpam-5854	74	1	f	f	X
ejpam-5854	74	2	,	,	PUNCT
ejpam-5854	74	3	(	(	PUNCT
ejpam-5854	74	4	2	2	X
ejpam-5854	74	5	)	)	PUNCT
ejpam-5854	74	6	µ	µ	X
ejpam-5854	74	7	=	=	PUNCT
ejpam-5854	74	8	λ⇔	λ⇔	PROPN
ejpam-5854	74	9	µ	µ	X
ejpam-5854	74	10	⊑	⊑	X
ejpam-5854	74	11	λ	λ	PROPN
ejpam-5854	74	12	and	and	CCONJ
ejpam-5854	74	13	λ	λ	X
ejpam-5854	74	14	⊑	⊑	X
ejpam-5854	74	15	µ	µ	NUM
ejpam-5854	74	16	,	,	PUNCT
ejpam-5854	74	17	(	(	PUNCT
ejpam-5854	74	18	3	3	NUM
ejpam-5854	74	19	)	)	PUNCT
ejpam-5854	74	20	(	(	PUNCT
ejpam-5854	74	21	µ	µ	X
ejpam-5854	74	22	⊓	⊓	NOUN
ejpam-5854	74	23	λ)(h	λ)(h	PROPN
ejpam-5854	74	24	)	)	PUNCT
ejpam-5854	74	25	=	=	SYM
ejpam-5854	75	1	µ(h)⋏	µ(h)⋏	NOUN
ejpam-5854	75	2	λ(h	λ(h	X
ejpam-5854	75	3	)	)	PUNCT
ejpam-5854	75	4	for	for	ADP
ejpam-5854	75	5	all	all	DET
ejpam-5854	75	6	h	h	NOUN
ejpam-5854	75	7	∈	∈	PROPN
ejpam-5854	75	8	f.	f.	PROPN
ejpam-5854	75	9	for	for	ADP
ejpam-5854	75	10	h	h	PROPN
ejpam-5854	75	11	∈	∈	PROPN
ejpam-5854	75	12	s	s	PROPN
ejpam-5854	75	13	,	,	PUNCT
ejpam-5854	75	14	define	define	VERB
ejpam-5854	75	15	ah	ah	INTJ
ejpam-5854	75	16	:	:	PUNCT
ejpam-5854	75	17	=	=	SYM
ejpam-5854	75	18	{	{	PUNCT
ejpam-5854	75	19	(	(	PUNCT
ejpam-5854	75	20	k	k	X
ejpam-5854	75	21	,	,	PUNCT
ejpam-5854	75	22	o	o	NOUN
ejpam-5854	75	23	)	)	PUNCT
ejpam-5854	75	24	∈	∈	PROPN
ejpam-5854	75	25	f×	f×	VERB
ejpam-5854	75	26	f	f	X
ejpam-5854	76	1	|	|	ADV
ejpam-5854	76	2	h	h	NOUN
ejpam-5854	76	3	=	=	SYM
ejpam-5854	76	4	ko	ko	PROPN
ejpam-5854	76	5	}	}	PUNCT
ejpam-5854	76	6	.	.	PUNCT
ejpam-5854	77	1	for	for	ADP
ejpam-5854	77	2	two	two	NUM
ejpam-5854	77	3	ivf	ivf	NOUN
ejpam-5854	77	4	sets	set	NOUN
ejpam-5854	77	5	µ	µ	NOUN
ejpam-5854	77	6	and	and	CCONJ
ejpam-5854	77	7	λ	λ	PROPN
ejpam-5854	77	8	of	of	ADP
ejpam-5854	77	9	f	f	PROPN
ejpam-5854	77	10	,	,	PUNCT
ejpam-5854	77	11	define	define	VERB
ejpam-5854	77	12	the	the	DET
ejpam-5854	77	13	product	product	NOUN
ejpam-5854	77	14	µ⃝	µ⃝	NOUN
ejpam-5854	77	15	λ	λ	PROPN
ejpam-5854	77	16	as	as	SCONJ
ejpam-5854	77	17	follows	follow	VERB
ejpam-5854	77	18	:	:	PUNCT
ejpam-5854	77	19	for	for	ADP
ejpam-5854	77	20	all	all	DET
ejpam-5854	77	21	h	h	NOUN
ejpam-5854	77	22	∈	∈	NOUN
ejpam-5854	77	23	s	s	NOUN
ejpam-5854	77	24	,	,	PUNCT
ejpam-5854	77	25	(	(	PUNCT
ejpam-5854	77	26	µ⃝	µ⃝	ADV
ejpam-5854	77	27	λ)(h	λ)(h	NUM
ejpam-5854	77	28	)	)	PUNCT
ejpam-5854	78	1	=	=	PUNCT
ejpam-5854	78	2			PUNCT
ejpam-5854	78	3	⋎	⋎	NOUN
ejpam-5854	78	4	(	(	PUNCT
ejpam-5854	78	5	k	k	NOUN
ejpam-5854	78	6	,	,	PUNCT
ejpam-5854	78	7	o)∈ah	o)∈ah	PROPN
ejpam-5854	78	8	{	{	PUNCT
ejpam-5854	78	9	µ(k)⋏	µ(k)⋏	PROPN
ejpam-5854	78	10	λ(o	λ(o	PROPN
ejpam-5854	78	11	)	)	PUNCT
ejpam-5854	78	12	}	}	PUNCT
ejpam-5854	78	13	if	if	SCONJ
ejpam-5854	78	14	ah	ah	INTJ
ejpam-5854	78	15	̸=	̸=	PROPN
ejpam-5854	78	16	∅	∅	VERB
ejpam-5854	78	17	0	0	PUNCT
ejpam-5854	79	1	if	if	SCONJ
ejpam-5854	79	2	ah	ah	INTJ
ejpam-5854	79	3	=	=	PUNCT
ejpam-5854	79	4	∅.	∅.	NOUN
ejpam-5854	79	5	definition	definition	NOUN
ejpam-5854	79	6	3	3	NUM
ejpam-5854	80	1	.	.	PUNCT
ejpam-5854	81	1	[	[	X
ejpam-5854	81	2	11	11	NUM
ejpam-5854	81	3	]	]	X
ejpam-5854	81	4	an	an	DET
ejpam-5854	81	5	ivf	ivf	NOUN
ejpam-5854	81	6	set	set	VERB
ejpam-5854	81	7	µ	µ	PROPN
ejpam-5854	81	8	of	of	ADP
ejpam-5854	81	9	a	a	DET
ejpam-5854	81	10	semigroup	semigroup	NOUN
ejpam-5854	81	11	s	s	NOUN
ejpam-5854	81	12	is	be	AUX
ejpam-5854	81	13	said	say	VERB
ejpam-5854	81	14	to	to	PART
ejpam-5854	81	15	be	be	AUX
ejpam-5854	81	16	an	an	DET
ejpam-5854	81	17	(	(	PUNCT
ejpam-5854	81	18	1	1	NUM
ejpam-5854	81	19	)	)	PUNCT
ejpam-5854	81	20	ivf	ivf	ADJ
ejpam-5854	81	21	subsemigroup	subsemigroup	NOUN
ejpam-5854	81	22	of	of	ADP
ejpam-5854	81	23	s	s	PROPN
ejpam-5854	81	24	,	,	PUNCT
ejpam-5854	81	25	if	if	SCONJ
ejpam-5854	81	26	µ(h1h2	µ(h1h2	ADP
ejpam-5854	81	27	)	)	PUNCT
ejpam-5854	81	28	⪰	⪰	NOUN
ejpam-5854	81	29	µ(h1)⋏	µ(h1)⋏	NOUN
ejpam-5854	81	30	µ(h2	µ(h2	NOUN
ejpam-5854	81	31	)	)	PUNCT
ejpam-5854	81	32	for	for	ADP
ejpam-5854	81	33	all	all	DET
ejpam-5854	81	34	h1	h1	PROPN
ejpam-5854	81	35	,	,	PUNCT
ejpam-5854	81	36	h2	h2	PROPN
ejpam-5854	81	37	∈	∈	PROPN
ejpam-5854	81	38	s	s	PART
ejpam-5854	81	39	,	,	PUNCT
ejpam-5854	81	40	(	(	PUNCT
ejpam-5854	81	41	2	2	NUM
ejpam-5854	81	42	)	)	PUNCT
ejpam-5854	81	43	ivf	ivf	NOUN
ejpam-5854	81	44	left	left	NOUN
ejpam-5854	81	45	(	(	PUNCT
ejpam-5854	81	46	right	right	ADJ
ejpam-5854	81	47	)	)	PUNCT
ejpam-5854	81	48	ideal	ideal	NOUN
ejpam-5854	81	49	of	of	ADP
ejpam-5854	81	50	s	s	PROPN
ejpam-5854	81	51	,	,	PUNCT
ejpam-5854	81	52	if	if	SCONJ
ejpam-5854	81	53	µ(h1h2	µ(h1h2	ADP
ejpam-5854	81	54	)	)	PUNCT
ejpam-5854	81	55	⪰	⪰	NOUN
ejpam-5854	81	56	µ(h2	µ(h2	NOUN
ejpam-5854	81	57	)	)	PUNCT
ejpam-5854	81	58	(	(	PUNCT
ejpam-5854	81	59	µ(h1h2	µ(h1h2	ADP
ejpam-5854	81	60	)	)	PUNCT
ejpam-5854	81	61	⪰	⪰	NOUN
ejpam-5854	81	62	µ(h1))for	µ(h1))for	ADP
ejpam-5854	81	63	all	all	DET
ejpam-5854	81	64	h1	h1	PROPN
ejpam-5854	81	65	,	,	PUNCT
ejpam-5854	81	66	h2	h2	PROPN
ejpam-5854	81	67	∈	∈	PROPN
ejpam-5854	81	68	s.	s.	PROPN
ejpam-5854	81	69	an	an	DET
ejpam-5854	81	70	ivf	ivf	PROPN
ejpam-5854	81	71	ideal	ideal	NOUN
ejpam-5854	81	72	of	of	ADP
ejpam-5854	81	73	s	s	PRON
ejpam-5854	81	74	if	if	SCONJ
ejpam-5854	81	75	it	it	PRON
ejpam-5854	81	76	is	be	AUX
ejpam-5854	81	77	both	both	CCONJ
ejpam-5854	81	78	an	an	DET
ejpam-5854	81	79	ivf	ivf	NOUN
ejpam-5854	81	80	left	leave	VERB
ejpam-5854	81	81	ideal	ideal	NOUN
ejpam-5854	81	82	and	and	CCONJ
ejpam-5854	81	83	an	an	DET
ejpam-5854	81	84	ivf	ivf	ADJ
ejpam-5854	81	85	right	right	ADJ
ejpam-5854	81	86	ideal	ideal	NOUN
ejpam-5854	81	87	of	of	ADP
ejpam-5854	81	88	s	s	PROPN
ejpam-5854	81	89	,	,	PUNCT
ejpam-5854	81	90	p.	p.	NOUN
ejpam-5854	81	91	khamrot	khamrot	PROPN
ejpam-5854	81	92	,	,	PUNCT
ejpam-5854	81	93	n.	n.	PROPN
ejpam-5854	81	94	deetae	deetae	PROPN
ejpam-5854	81	95	,	,	PUNCT
ejpam-5854	81	96	t.	t.	PROPN
ejpam-5854	81	97	gaketem	gaketem	PROPN
ejpam-5854	81	98	/	/	SYM
ejpam-5854	81	99	eur	eur	PROPN
ejpam-5854	81	100	.	.	PUNCT
ejpam-5854	82	1	j.	j.	PROPN
ejpam-5854	82	2	pure	pure	PROPN
ejpam-5854	82	3	appl	appl	PROPN
ejpam-5854	82	4	.	.	PROPN
ejpam-5854	82	5	math	math	PROPN
ejpam-5854	82	6	,	,	PUNCT
ejpam-5854	82	7	18	18	NUM
ejpam-5854	82	8	(	(	PUNCT
ejpam-5854	82	9	2	2	NUM
ejpam-5854	82	10	)	)	PUNCT
ejpam-5854	82	11	(	(	PUNCT
ejpam-5854	82	12	2025	2025	NUM
ejpam-5854	82	13	)	)	PUNCT
ejpam-5854	82	14	,	,	PUNCT
ejpam-5854	82	15	5854	5854	NUM
ejpam-5854	82	16	4	4	NUM
ejpam-5854	82	17	of	of	ADP
ejpam-5854	82	18	14	14	NUM
ejpam-5854	82	19	(	(	PUNCT
ejpam-5854	82	20	3	3	NUM
ejpam-5854	82	21	)	)	PUNCT
ejpam-5854	82	22	ivf	ivf	NOUN
ejpam-5854	82	23	genralized	genralize	VERB
ejpam-5854	82	24	bi	bi	NOUN
ejpam-5854	82	25	-	-	NOUN
ejpam-5854	82	26	ideal	ideal	NOUN
ejpam-5854	82	27	of	of	ADP
ejpam-5854	82	28	s	s	PROPN
ejpam-5854	82	29	,	,	PUNCT
ejpam-5854	82	30	if	if	SCONJ
ejpam-5854	82	31	µ(h1h2h3	µ(h1h2h3	ADJ
ejpam-5854	82	32	)	)	PUNCT
ejpam-5854	82	33	⪰	⪰	NOUN
ejpam-5854	82	34	µ(h1)⋏	µ(h1)⋏	PROPN
ejpam-5854	82	35	µ(h3	µ(h3	NOUN
ejpam-5854	82	36	)	)	PUNCT
ejpam-5854	82	37	for	for	ADP
ejpam-5854	82	38	all	all	DET
ejpam-5854	82	39	h1	h1	PROPN
ejpam-5854	82	40	,	,	PUNCT
ejpam-5854	82	41	h2	h2	PROPN
ejpam-5854	82	42	,	,	PUNCT
ejpam-5854	82	43	h3	h3	VERB
ejpam-5854	82	44	∈	∈	PROPN
ejpam-5854	82	45	s	s	NOUN
ejpam-5854	82	46	,	,	PUNCT
ejpam-5854	82	47	(	(	PUNCT
ejpam-5854	82	48	4	4	X
ejpam-5854	82	49	)	)	PUNCT
ejpam-5854	82	50	ivf	ivf	ADJ
ejpam-5854	82	51	bi	bi	NOUN
ejpam-5854	82	52	-	-	NOUN
ejpam-5854	82	53	ideal	ideal	NOUN
ejpam-5854	82	54	of	of	ADP
ejpam-5854	82	55	s	s	PROPN
ejpam-5854	82	56	,	,	PUNCT
ejpam-5854	82	57	if	if	SCONJ
ejpam-5854	82	58	µ	µ	PRON
ejpam-5854	82	59	is	be	AUX
ejpam-5854	82	60	an	an	DET
ejpam-5854	82	61	ivf	ivf	ADJ
ejpam-5854	82	62	subsemigroup	subsemigroup	NOUN
ejpam-5854	82	63	of	of	ADP
ejpam-5854	82	64	s	s	PROPN
ejpam-5854	82	65	and	and	CCONJ
ejpam-5854	82	66	µ(h1h2h3	µ(h1h2h3	ADJ
ejpam-5854	82	67	)	)	PUNCT
ejpam-5854	82	68	⪰	⪰	NOUN
ejpam-5854	82	69	µ(h1	µ(h1	NOUN
ejpam-5854	82	70	)	)	PUNCT
ejpam-5854	82	71	⋏	⋏	PROPN
ejpam-5854	82	72	µ(h3	µ(h3	NUM
ejpam-5854	82	73	)	)	PUNCT
ejpam-5854	82	74	for	for	ADP
ejpam-5854	82	75	all	all	DET
ejpam-5854	82	76	h1	h1	PROPN
ejpam-5854	82	77	,	,	PUNCT
ejpam-5854	82	78	h2	h2	PROPN
ejpam-5854	82	79	,	,	PUNCT
ejpam-5854	82	80	h3	h3	VERB
ejpam-5854	82	81	∈	∈	PROPN
ejpam-5854	82	82	s	s	NOUN
ejpam-5854	82	83	,	,	PUNCT
ejpam-5854	82	84	(	(	PUNCT
ejpam-5854	82	85	5	5	NUM
ejpam-5854	82	86	)	)	PUNCT
ejpam-5854	82	87	ivf	ivf	ADJ
ejpam-5854	82	88	interior	interior	ADJ
ejpam-5854	82	89	ideal	ideal	NOUN
ejpam-5854	82	90	of	of	ADP
ejpam-5854	82	91	s	s	PROPN
ejpam-5854	82	92	,	,	PUNCT
ejpam-5854	82	93	if	if	SCONJ
ejpam-5854	82	94	µ	µ	PRON
ejpam-5854	82	95	is	be	AUX
ejpam-5854	82	96	an	an	DET
ejpam-5854	82	97	ivf	ivf	ADJ
ejpam-5854	82	98	subsemigroup	subsemigroup	NOUN
ejpam-5854	82	99	of	of	ADP
ejpam-5854	82	100	s	s	PROPN
ejpam-5854	82	101	and	and	CCONJ
ejpam-5854	82	102	µ(h1h2h3	µ(h1h2h3	ADJ
ejpam-5854	82	103	)	)	PUNCT
ejpam-5854	82	104	⪰	⪰	NOUN
ejpam-5854	82	105	µ(h2	µ(h2	NOUN
ejpam-5854	82	106	)	)	PUNCT
ejpam-5854	82	107	for	for	ADP
ejpam-5854	82	108	all	all	DET
ejpam-5854	82	109	h1	h1	PROPN
ejpam-5854	82	110	,	,	PUNCT
ejpam-5854	82	111	h2	h2	PROPN
ejpam-5854	82	112	,	,	PUNCT
ejpam-5854	82	113	h3	h3	VERB
ejpam-5854	82	114	∈	∈	PROPN
ejpam-5854	82	115	s	s	NOUN
ejpam-5854	82	116	,	,	PUNCT
ejpam-5854	82	117	(	(	PUNCT
ejpam-5854	82	118	6	6	NUM
ejpam-5854	82	119	)	)	PUNCT
ejpam-5854	82	120	ivf	ivf	NOUN
ejpam-5854	82	121	quasi	quasi	NOUN
ejpam-5854	82	122	ideal	ideal	NOUN
ejpam-5854	82	123	of	of	ADP
ejpam-5854	82	124	s	s	PROPN
ejpam-5854	82	125	,	,	PUNCT
ejpam-5854	82	126	if	if	SCONJ
ejpam-5854	82	127	(	(	PUNCT
ejpam-5854	82	128	s⃝	s⃝	PROPN
ejpam-5854	82	129	µ	µ	X
ejpam-5854	82	130	)	)	PUNCT
ejpam-5854	82	131	⊓	⊓	PROPN
ejpam-5854	82	132	(	(	PUNCT
ejpam-5854	82	133	µ⃝s	µ⃝s	PROPN
ejpam-5854	82	134	)	)	PUNCT
ejpam-5854	82	135	⊑	⊑	PROPN
ejpam-5854	82	136	µ	µ	NUM
ejpam-5854	82	137	,	,	PUNCT
ejpam-5854	82	138	where	where	SCONJ
ejpam-5854	82	139	s	s	NOUN
ejpam-5854	82	140	is	be	AUX
ejpam-5854	82	141	an	an	DET
ejpam-5854	82	142	ivf	ivf	ADJ
ejpam-5854	82	143	set	set	NOUN
ejpam-5854	82	144	of	of	ADP
ejpam-5854	82	145	s	s	PART
ejpam-5854	82	146	mapping	map	VERB
ejpam-5854	82	147	every	every	DET
ejpam-5854	82	148	element	element	NOUN
ejpam-5854	82	149	of	of	ADP
ejpam-5854	82	150	s	s	PRON
ejpam-5854	82	151	on	on	ADP
ejpam-5854	82	152	1	1	NUM
ejpam-5854	82	153	.	.	PUNCT
ejpam-5854	82	154	2.2	2.2	NUM
ejpam-5854	82	155	.	.	PUNCT
ejpam-5854	83	1	bipolar	bipolar	ADJ
ejpam-5854	83	2	fuzzy	fuzzy	ADJ
ejpam-5854	83	3	set	set	VERB
ejpam-5854	83	4	definition	definition	NOUN
ejpam-5854	83	5	4	4	NUM
ejpam-5854	83	6	.	.	PUNCT
ejpam-5854	84	1	[	[	X
ejpam-5854	84	2	4	4	X
ejpam-5854	84	3	]	]	X
ejpam-5854	84	4	a	a	DET
ejpam-5854	84	5	bipolar	bipolar	ADJ
ejpam-5854	84	6	fuzzy	fuzzy	ADJ
ejpam-5854	84	7	set	set	NOUN
ejpam-5854	84	8	(	(	PUNCT
ejpam-5854	84	9	shortly	shortly	ADV
ejpam-5854	84	10	,	,	PUNCT
ejpam-5854	84	11	bf	bf	NOUN
ejpam-5854	84	12	set	set	NOUN
ejpam-5854	84	13	)	)	PUNCT
ejpam-5854	84	14	ω	ω	PROPN
ejpam-5854	84	15	on	on	ADP
ejpam-5854	84	16	s	s	PROPN
ejpam-5854	84	17	is	be	AUX
ejpam-5854	84	18	an	an	DET
ejpam-5854	84	19	object	object	NOUN
ejpam-5854	84	20	having	have	VERB
ejpam-5854	84	21	the	the	DET
ejpam-5854	84	22	form	form	NOUN
ejpam-5854	84	23	ω	ω	NOUN
ejpam-5854	84	24	:	:	PUNCT
ejpam-5854	84	25	=	=	SYM
ejpam-5854	84	26	{	{	PUNCT
ejpam-5854	84	27	(	(	PUNCT
ejpam-5854	84	28	s	s	X
ejpam-5854	84	29	,	,	PUNCT
ejpam-5854	84	30	ωp(h	ωp(h	NOUN
ejpam-5854	84	31	)	)	PUNCT
ejpam-5854	84	32	,	,	PUNCT
ejpam-5854	84	33	ωn(h	ωn(h	NUM
ejpam-5854	84	34	)	)	PUNCT
ejpam-5854	84	35	)	)	PUNCT
ejpam-5854	85	1	|	|	ADV
ejpam-5854	85	2	h	h	NOUN
ejpam-5854	85	3	∈	∈	NOUN
ejpam-5854	85	4	s	s	PART
ejpam-5854	85	5	}	}	PUNCT
ejpam-5854	85	6	,	,	PUNCT
ejpam-5854	85	7	where	where	SCONJ
ejpam-5854	85	8	ωp	ωp	X
ejpam-5854	85	9	:	:	PUNCT
ejpam-5854	85	10	s	s	X
ejpam-5854	85	11	→	→	SYM
ejpam-5854	85	12	[	[	X
ejpam-5854	85	13	0	0	NUM
ejpam-5854	85	14	,	,	PUNCT
ejpam-5854	85	15	1	1	NUM
ejpam-5854	85	16	]	]	PUNCT
ejpam-5854	85	17	and	and	CCONJ
ejpam-5854	85	18	ωn	ωn	ADP
ejpam-5854	85	19	:	:	PUNCT
ejpam-5854	85	20	s	s	X
ejpam-5854	85	21	→	→	X
ejpam-5854	85	22	[	[	X
ejpam-5854	85	23	−1	−1	NOUN
ejpam-5854	85	24	,	,	PUNCT
ejpam-5854	85	25	0	0	NUM
ejpam-5854	85	26	]	]	PUNCT
ejpam-5854	85	27	.	.	PUNCT
ejpam-5854	86	1	remark	remark	PROPN
ejpam-5854	86	2	1	1	NUM
ejpam-5854	86	3	.	.	PUNCT
ejpam-5854	87	1	for	for	ADP
ejpam-5854	87	2	the	the	DET
ejpam-5854	87	3	sake	sake	NOUN
ejpam-5854	87	4	of	of	ADP
ejpam-5854	87	5	simplicity	simplicity	NOUN
ejpam-5854	87	6	,	,	PUNCT
ejpam-5854	87	7	we	we	PRON
ejpam-5854	87	8	shall	shall	AUX
ejpam-5854	87	9	use	use	VERB
ejpam-5854	87	10	the	the	DET
ejpam-5854	87	11	symbol	symbol	NOUN
ejpam-5854	87	12	ω	ω	NOUN
ejpam-5854	87	13	=	=	SYM
ejpam-5854	87	14	(	(	PUNCT
ejpam-5854	87	15	s;ωp	s;ωp	NOUN
ejpam-5854	87	16	,	,	PUNCT
ejpam-5854	87	17	ωn	ωn	PROPN
ejpam-5854	87	18	)	)	PUNCT
ejpam-5854	87	19	for	for	ADP
ejpam-5854	87	20	the	the	DET
ejpam-5854	87	21	bf	bf	NOUN
ejpam-5854	87	22	set	set	VERB
ejpam-5854	87	23	ω	ω	PROPN
ejpam-5854	87	24	=	=	SYM
ejpam-5854	87	25	{	{	PUNCT
ejpam-5854	87	26	(	(	PUNCT
ejpam-5854	87	27	s	s	X
ejpam-5854	87	28	,	,	PUNCT
ejpam-5854	87	29	ωp(h	ωp(h	NOUN
ejpam-5854	87	30	)	)	PUNCT
ejpam-5854	87	31	,	,	PUNCT
ejpam-5854	87	32	ωn(h	ωn(h	NUM
ejpam-5854	87	33	)	)	PUNCT
ejpam-5854	87	34	)	)	PUNCT
ejpam-5854	88	1	|	|	ADV
ejpam-5854	88	2	h	h	NOUN
ejpam-5854	88	3	∈	∈	NOUN
ejpam-5854	88	4	s	s	PART
ejpam-5854	88	5	}	}	PUNCT
ejpam-5854	88	6	.	.	PUNCT
ejpam-5854	89	1	define	define	VERB
ejpam-5854	89	2	products	product	NOUN
ejpam-5854	89	3	ωp	ωp	ADP
ejpam-5854	89	4	∗	∗	NOUN
ejpam-5854	89	5	ψp	ψp	NOUN
ejpam-5854	90	1	and	and	CCONJ
ejpam-5854	90	2	ωn	ωn	ADP
ejpam-5854	90	3	∗	∗	NOUN
ejpam-5854	90	4	ψn	ψn	INTJ
ejpam-5854	90	5	as	as	SCONJ
ejpam-5854	90	6	follows	follow	VERB
ejpam-5854	90	7	:	:	PUNCT
ejpam-5854	90	8	for	for	ADP
ejpam-5854	90	9	h	h	PRON
ejpam-5854	90	10	∈	∈	PROPN
ejpam-5854	90	11	s	s	PART
ejpam-5854	90	12	(	(	PUNCT
ejpam-5854	90	13	ωp	ωp	NOUN
ejpam-5854	90	14	∗	∗	NOUN
ejpam-5854	90	15	ψp)(h	ψp)(h	PROPN
ejpam-5854	90	16	)	)	PUNCT
ejpam-5854	90	17	=	=	PUNCT
ejpam-5854	91	1			PUNCT
ejpam-5854	91	2	∨	∨	X
ejpam-5854	91	3	(	(	PUNCT
ejpam-5854	91	4	k	k	NOUN
ejpam-5854	91	5	,	,	PUNCT
ejpam-5854	91	6	o)∈ah	o)∈ah	PROPN
ejpam-5854	91	7	{	{	PUNCT
ejpam-5854	91	8	ωp(k	ωp(k	NOUN
ejpam-5854	91	9	)	)	PUNCT
ejpam-5854	91	10	∧	∧	NOUN
ejpam-5854	91	11	ψp(o	ψp(o	NOUN
ejpam-5854	91	12	)	)	PUNCT
ejpam-5854	91	13	}	}	PUNCT
ejpam-5854	91	14	if	if	SCONJ
ejpam-5854	91	15	ah	ah	INTJ
ejpam-5854	91	16	̸=	̸=	PROPN
ejpam-5854	91	17	∅	∅	VERB
ejpam-5854	91	18	0	0	PUNCT
ejpam-5854	92	1	if	if	SCONJ
ejpam-5854	92	2	ah	ah	INTJ
ejpam-5854	92	3	=	=	NOUN
ejpam-5854	92	4	∅	∅	NOUN
ejpam-5854	92	5	and	and	CCONJ
ejpam-5854	92	6	(	(	PUNCT
ejpam-5854	92	7	ωn	ωn	NOUN
ejpam-5854	92	8	∗	∗	NOUN
ejpam-5854	92	9	ψn)(h	ψn)(h	PROPN
ejpam-5854	92	10	)	)	PUNCT
ejpam-5854	93	1	=	=	PUNCT
ejpam-5854	93	2			PUNCT
ejpam-5854	93	3	∧	∧	PROPN
ejpam-5854	93	4	(	(	PUNCT
ejpam-5854	93	5	k	k	NOUN
ejpam-5854	93	6	,	,	PUNCT
ejpam-5854	93	7	o)∈ah	o)∈ah	PROPN
ejpam-5854	93	8	{	{	PUNCT
ejpam-5854	93	9	ωn(k	ωn(k	NUM
ejpam-5854	93	10	)	)	PUNCT
ejpam-5854	93	11	∨	∨	NUM
ejpam-5854	93	12	ψn(o	ψn(o	NUM
ejpam-5854	93	13	)	)	PUNCT
ejpam-5854	93	14	}	}	PUNCT
ejpam-5854	93	15	if	if	SCONJ
ejpam-5854	93	16	ah	ah	INTJ
ejpam-5854	93	17	̸=	̸=	PROPN
ejpam-5854	93	18	∅	∅	VERB
ejpam-5854	93	19	0	0	PUNCT
ejpam-5854	94	1	if	if	SCONJ
ejpam-5854	94	2	ah	ah	INTJ
ejpam-5854	94	3	=	=	PUNCT
ejpam-5854	94	4	∅.	∅.	NOUN
ejpam-5854	94	5	definition	definition	NOUN
ejpam-5854	94	6	5	5	NUM
ejpam-5854	95	1	.	.	PUNCT
ejpam-5854	96	1	[	[	X
ejpam-5854	96	2	12	12	NUM
ejpam-5854	96	3	]	]	PUNCT
ejpam-5854	96	4	a	a	DET
ejpam-5854	96	5	positive	positive	ADJ
ejpam-5854	96	6	characteristic	characteristic	ADJ
ejpam-5854	96	7	function	function	NOUN
ejpam-5854	96	8	and	and	CCONJ
ejpam-5854	96	9	a	a	DET
ejpam-5854	96	10	negative	negative	ADJ
ejpam-5854	96	11	characteristic	characteristic	ADJ
ejpam-5854	96	12	function	function	NOUN
ejpam-5854	96	13	of	of	ADP
ejpam-5854	96	14	a	a	DET
ejpam-5854	96	15	non	non	ADJ
ejpam-5854	96	16	-	-	ADJ
ejpam-5854	96	17	empty	empty	ADJ
ejpam-5854	96	18	set	set	NOUN
ejpam-5854	96	19	k	k	PROPN
ejpam-5854	96	20	of	of	ADP
ejpam-5854	96	21	f	f	PROPN
ejpam-5854	96	22	defined	define	VERB
ejpam-5854	96	23	by	by	ADP
ejpam-5854	96	24	χp	χp	PROPN
ejpam-5854	96	25	k	k	X
ejpam-5854	96	26	:	:	PUNCT
ejpam-5854	96	27	s	s	X
ejpam-5854	96	28	→	→	SYM
ejpam-5854	96	29	[	[	X
ejpam-5854	96	30	0	0	NUM
ejpam-5854	96	31	,	,	PUNCT
ejpam-5854	96	32	1	1	NUM
ejpam-5854	96	33	]	]	PUNCT
ejpam-5854	96	34	,	,	PUNCT
ejpam-5854	96	35	h	h	PROPN
ejpam-5854	96	36	7→	7→	NUM
ejpam-5854	96	37	χp	χp	VERB
ejpam-5854	96	38	k(h	k(h	PROPN
ejpam-5854	96	39	)	)	PUNCT
ejpam-5854	96	40	:	:	PUNCT
ejpam-5854	97	1	=	=	SYM
ejpam-5854	97	2	{	{	PUNCT
ejpam-5854	97	3	1	1	NUM
ejpam-5854	97	4	h	h	NOUN
ejpam-5854	97	5	∈	∈	PROPN
ejpam-5854	97	6	k	k	NOUN
ejpam-5854	97	7	0	0	NUM
ejpam-5854	97	8	h	h	NOUN
ejpam-5854	97	9	/∈	/∈	PUNCT
ejpam-5854	98	1	k	k	NOUN
ejpam-5854	99	1	and	and	CCONJ
ejpam-5854	99	2	χn	χn	X
ejpam-5854	99	3	k	k	X
ejpam-5854	99	4	:	:	PUNCT
ejpam-5854	99	5	s	s	X
ejpam-5854	99	6	→	→	X
ejpam-5854	99	7	[	[	X
ejpam-5854	99	8	−1	−1	NOUN
ejpam-5854	99	9	,	,	PUNCT
ejpam-5854	99	10	0	0	NUM
ejpam-5854	99	11	]	]	PUNCT
ejpam-5854	99	12	,	,	PUNCT
ejpam-5854	99	13	h	h	PROPN
ejpam-5854	99	14	7→	7→	NUM
ejpam-5854	99	15	χn	χn	PRON
ejpam-5854	99	16	k(h	k(h	PROPN
ejpam-5854	99	17	)	)	PUNCT
ejpam-5854	99	18	:	:	PUNCT
ejpam-5854	100	1	=	=	PRON
ejpam-5854	100	2	{	{	PUNCT
ejpam-5854	100	3	−1	−1	NOUN
ejpam-5854	100	4	h	h	NOUN
ejpam-5854	100	5	∈	∈	PROPN
ejpam-5854	101	1	k	k	NOUN
ejpam-5854	101	2	0	0	NUM
ejpam-5854	101	3	h	h	NOUN
ejpam-5854	101	4	/∈	/∈	PUNCT
ejpam-5854	102	1	k.	k.	PROPN
ejpam-5854	102	2	respectively	respectively	ADV
ejpam-5854	102	3	.	.	PUNCT
ejpam-5854	103	1	definition	definition	NOUN
ejpam-5854	103	2	6	6	NUM
ejpam-5854	103	3	.	.	PUNCT
ejpam-5854	104	1	[	[	X
ejpam-5854	104	2	12	12	NUM
ejpam-5854	104	3	]	]	PUNCT
ejpam-5854	104	4	a	a	DET
ejpam-5854	104	5	bf	bf	NOUN
ejpam-5854	104	6	set	set	VERB
ejpam-5854	104	7	ω	ω	PROPN
ejpam-5854	104	8	=	=	SYM
ejpam-5854	104	9	(	(	PUNCT
ejpam-5854	104	10	s;ωp	s;ωp	NOUN
ejpam-5854	104	11	,	,	PUNCT
ejpam-5854	104	12	ωn	ωn	PROPN
ejpam-5854	104	13	)	)	PUNCT
ejpam-5854	104	14	on	on	ADP
ejpam-5854	104	15	a	a	DET
ejpam-5854	104	16	semigroup	semigroup	NOUN
ejpam-5854	104	17	s	s	PART
ejpam-5854	104	18	is	be	AUX
ejpam-5854	104	19	called	call	VERB
ejpam-5854	104	20	a	a	DET
ejpam-5854	104	21	(	(	PUNCT
ejpam-5854	104	22	1	1	NUM
ejpam-5854	104	23	)	)	PUNCT
ejpam-5854	104	24	bf	bf	NOUN
ejpam-5854	104	25	subsemigroup	subsemigroup	NOUN
ejpam-5854	104	26	on	on	ADP
ejpam-5854	104	27	s	s	SYM
ejpam-5854	104	28	,	,	PUNCT
ejpam-5854	104	29	if	if	SCONJ
ejpam-5854	104	30	ωp(h1h2	ωp(h1h2	NUM
ejpam-5854	104	31	)	)	PUNCT
ejpam-5854	104	32	≥	≥	NOUN
ejpam-5854	104	33	ωp(h1	ωp(h1	NUM
ejpam-5854	104	34	)	)	PUNCT
ejpam-5854	104	35	∧	∧	NOUN
ejpam-5854	104	36	ωp(h2	ωp(h2	NOUN
ejpam-5854	104	37	)	)	PUNCT
ejpam-5854	104	38	and	and	CCONJ
ejpam-5854	104	39	ωn(h1h2	ωn(h1h2	NUM
ejpam-5854	104	40	)	)	PUNCT
ejpam-5854	104	41	≤	≤	NUM
ejpam-5854	104	42	ωn(h1	ωn(h1	NOUN
ejpam-5854	104	43	)	)	PUNCT
ejpam-5854	104	44	∨	∨	NUM
ejpam-5854	104	45	ωn(h2	ωn(h2	NOUN
ejpam-5854	104	46	)	)	PUNCT
ejpam-5854	104	47	for	for	ADP
ejpam-5854	104	48	all	all	DET
ejpam-5854	104	49	h1	h1	PROPN
ejpam-5854	104	50	,	,	PUNCT
ejpam-5854	104	51	h2	h2	PROPN
ejpam-5854	104	52	∈	∈	PROPN
ejpam-5854	104	53	s	s	PART
ejpam-5854	104	54	,	,	PUNCT
ejpam-5854	104	55	(	(	PUNCT
ejpam-5854	104	56	2	2	X
ejpam-5854	104	57	)	)	PUNCT
ejpam-5854	104	58	bf	bf	NOUN
ejpam-5854	104	59	left	left	ADJ
ejpam-5854	104	60	(	(	PUNCT
ejpam-5854	104	61	right	right	ADJ
ejpam-5854	104	62	)	)	PUNCT
ejpam-5854	104	63	ideal	ideal	NOUN
ejpam-5854	104	64	on	on	ADP
ejpam-5854	104	65	s	s	SYM
ejpam-5854	104	66	,	,	PUNCT
ejpam-5854	104	67	if	if	SCONJ
ejpam-5854	104	68	ωp(h1h2	ωp(h1h2	NUM
ejpam-5854	104	69	)	)	PUNCT
ejpam-5854	104	70	≥	≥	NOUN
ejpam-5854	104	71	ωp(h2	ωp(h2	NOUN
ejpam-5854	104	72	)	)	PUNCT
ejpam-5854	104	73	(	(	PUNCT
ejpam-5854	104	74	ωp(h1h2	ωp(h1h2	NOUN
ejpam-5854	104	75	)	)	PUNCT
ejpam-5854	104	76	≥	≥	NOUN
ejpam-5854	104	77	ωp(h1	ωp(h1	NUM
ejpam-5854	104	78	)	)	PUNCT
ejpam-5854	104	79	)	)	PUNCT
ejpam-5854	104	80	and	and	CCONJ
ejpam-5854	104	81	ωn(h1h2	ωn(h1h2	NUM
ejpam-5854	104	82	)	)	PUNCT
ejpam-5854	104	83	≤	≤	NUM
ejpam-5854	104	84	ωn(h2	ωn(h2	NOUN
ejpam-5854	104	85	)	)	PUNCT
ejpam-5854	104	86	(	(	PUNCT
ejpam-5854	104	87	ωn(h1h2	ωn(h1h2	NOUN
ejpam-5854	104	88	)	)	PUNCT
ejpam-5854	104	89	≤	≤	NUM
ejpam-5854	104	90	ωn(h1	ωn(h1	NOUN
ejpam-5854	104	91	)	)	PUNCT
ejpam-5854	104	92	)	)	PUNCT
ejpam-5854	104	93	for	for	ADP
ejpam-5854	104	94	all	all	DET
ejpam-5854	104	95	h1	h1	PROPN
ejpam-5854	104	96	,	,	PUNCT
ejpam-5854	104	97	h2	h2	PROPN
ejpam-5854	104	98	∈	∈	PROPN
ejpam-5854	104	99	s	s	PART
ejpam-5854	104	100	,	,	PUNCT
ejpam-5854	104	101	(	(	PUNCT
ejpam-5854	104	102	3	3	X
ejpam-5854	104	103	)	)	PUNCT
ejpam-5854	104	104	bf	bf	NOUN
ejpam-5854	104	105	generalized	generalize	VERB
ejpam-5854	104	106	bi	bi	NOUN
ejpam-5854	104	107	-	-	NOUN
ejpam-5854	104	108	ideal	ideal	NOUN
ejpam-5854	104	109	on	on	ADP
ejpam-5854	104	110	s	s	SYM
ejpam-5854	104	111	,	,	PUNCT
ejpam-5854	104	112	if	if	SCONJ
ejpam-5854	104	113	ωp(h1h2h3	ωp(h1h2h3	ADJ
ejpam-5854	104	114	)	)	PUNCT
ejpam-5854	104	115	≥	≥	NOUN
ejpam-5854	104	116	ωp(h1	ωp(h1	NUM
ejpam-5854	104	117	)	)	PUNCT
ejpam-5854	104	118	∧	∧	NOUN
ejpam-5854	104	119	ωp(h3	ωp(h3	NOUN
ejpam-5854	104	120	)	)	PUNCT
ejpam-5854	104	121	and	and	CCONJ
ejpam-5854	104	122	ωn(h1h2h3	ωn(h1h2h3	NOUN
ejpam-5854	104	123	)	)	PUNCT
ejpam-5854	104	124	≤	≤	NUM
ejpam-5854	104	125	ωn(h1	ωn(h1	NOUN
ejpam-5854	104	126	)	)	PUNCT
ejpam-5854	104	127	∨	∨	NUM
ejpam-5854	104	128	ωn(h3	ωn(h3	NOUN
ejpam-5854	104	129	)	)	PUNCT
ejpam-5854	104	130	for	for	ADP
ejpam-5854	104	131	all	all	DET
ejpam-5854	104	132	h1	h1	PROPN
ejpam-5854	104	133	,	,	PUNCT
ejpam-5854	104	134	h2	h2	PROPN
ejpam-5854	104	135	,	,	PUNCT
ejpam-5854	104	136	h3	h3	VERB
ejpam-5854	104	137	∈	∈	PROPN
ejpam-5854	104	138	s	s	NOUN
ejpam-5854	104	139	,	,	PUNCT
ejpam-5854	104	140	p.	p.	NOUN
ejpam-5854	104	141	khamrot	khamrot	PROPN
ejpam-5854	104	142	,	,	PUNCT
ejpam-5854	104	143	n.	n.	PROPN
ejpam-5854	104	144	deetae	deetae	PROPN
ejpam-5854	104	145	,	,	PUNCT
ejpam-5854	104	146	t.	t.	PROPN
ejpam-5854	104	147	gaketem	gaketem	PROPN
ejpam-5854	104	148	/	/	SYM
ejpam-5854	104	149	eur	eur	PROPN
ejpam-5854	104	150	.	.	PUNCT
ejpam-5854	105	1	j.	j.	PROPN
ejpam-5854	105	2	pure	pure	PROPN
ejpam-5854	105	3	appl	appl	PROPN
ejpam-5854	105	4	.	.	PROPN
ejpam-5854	105	5	math	math	PROPN
ejpam-5854	105	6	,	,	PUNCT
ejpam-5854	105	7	18	18	NUM
ejpam-5854	105	8	(	(	PUNCT
ejpam-5854	105	9	2	2	NUM
ejpam-5854	105	10	)	)	PUNCT
ejpam-5854	105	11	(	(	PUNCT
ejpam-5854	105	12	2025	2025	NUM
ejpam-5854	105	13	)	)	PUNCT
ejpam-5854	105	14	,	,	PUNCT
ejpam-5854	105	15	5854	5854	NUM
ejpam-5854	105	16	5	5	NUM
ejpam-5854	105	17	of	of	ADP
ejpam-5854	105	18	14	14	NUM
ejpam-5854	105	19	(	(	PUNCT
ejpam-5854	105	20	4	4	NUM
ejpam-5854	105	21	)	)	PUNCT
ejpam-5854	105	22	bf	bf	NOUN
ejpam-5854	105	23	bi	bi	NOUN
ejpam-5854	105	24	-	-	NOUN
ejpam-5854	105	25	ideal	ideal	NOUN
ejpam-5854	105	26	on	on	ADP
ejpam-5854	105	27	s	s	SYM
ejpam-5854	105	28	,	,	PUNCT
ejpam-5854	105	29	if	if	SCONJ
ejpam-5854	105	30	ω	ω	NUM
ejpam-5854	105	31	=	=	SYM
ejpam-5854	105	32	(	(	PUNCT
ejpam-5854	105	33	s;ωp	s;ωp	NOUN
ejpam-5854	105	34	,	,	PUNCT
ejpam-5854	105	35	ωn	ωn	PRON
ejpam-5854	105	36	)	)	PUNCT
ejpam-5854	105	37	is	be	AUX
ejpam-5854	105	38	a	a	DET
ejpam-5854	105	39	bf	bf	NOUN
ejpam-5854	105	40	subsemigroup	subsemigroup	NOUN
ejpam-5854	105	41	of	of	ADP
ejpam-5854	105	42	s	s	PROPN
ejpam-5854	105	43	,	,	PUNCT
ejpam-5854	105	44	ωp(h1h2h3	ωp(h1h2h3	ADJ
ejpam-5854	105	45	)	)	PUNCT
ejpam-5854	105	46	≥	≥	NOUN
ejpam-5854	105	47	ωp(h1)∧ωp(h3	ωp(h1)∧ωp(h3	NOUN
ejpam-5854	105	48	)	)	PUNCT
ejpam-5854	105	49	and	and	CCONJ
ejpam-5854	105	50	ωn(h1h2h3	ωn(h1h2h3	NOUN
ejpam-5854	105	51	)	)	PUNCT
ejpam-5854	105	52	≤	≤	NUM
ejpam-5854	105	53	ωn(h1	ωn(h1	NOUN
ejpam-5854	105	54	)	)	PUNCT
ejpam-5854	105	55	∨	∨	NUM
ejpam-5854	105	56	ωn(h3	ωn(h3	NOUN
ejpam-5854	105	57	)	)	PUNCT
ejpam-5854	105	58	for	for	ADP
ejpam-5854	105	59	all	all	DET
ejpam-5854	105	60	h1	h1	PROPN
ejpam-5854	105	61	,	,	PUNCT
ejpam-5854	105	62	h2	h2	PROPN
ejpam-5854	105	63	,	,	PUNCT
ejpam-5854	105	64	h3	h3	VERB
ejpam-5854	105	65	∈	∈	PROPN
ejpam-5854	105	66	s	s	NOUN
ejpam-5854	105	67	,	,	PUNCT
ejpam-5854	105	68	(	(	PUNCT
ejpam-5854	105	69	5	5	X
ejpam-5854	105	70	)	)	PUNCT
ejpam-5854	105	71	bf	bf	NOUN
ejpam-5854	105	72	interior	interior	ADJ
ejpam-5854	105	73	ideal	ideal	NOUN
ejpam-5854	105	74	on	on	ADP
ejpam-5854	105	75	s	s	NOUN
ejpam-5854	105	76	,	,	PUNCT
ejpam-5854	105	77	if	if	SCONJ
ejpam-5854	105	78	ω	ω	NUM
ejpam-5854	105	79	=	=	SYM
ejpam-5854	105	80	(	(	PUNCT
ejpam-5854	105	81	s;ωp	s;ωp	NOUN
ejpam-5854	105	82	,	,	PUNCT
ejpam-5854	105	83	ωn	ωn	PRON
ejpam-5854	105	84	)	)	PUNCT
ejpam-5854	105	85	is	be	AUX
ejpam-5854	105	86	a	a	DET
ejpam-5854	105	87	bf	bf	NOUN
ejpam-5854	105	88	subsemigroup	subsemigroup	NOUN
ejpam-5854	105	89	of	of	ADP
ejpam-5854	105	90	s	s	PROPN
ejpam-5854	105	91	,	,	PUNCT
ejpam-5854	105	92	ωp(h1h2h3	ωp(h1h2h3	ADJ
ejpam-5854	105	93	)	)	PUNCT
ejpam-5854	105	94	≥	≥	NOUN
ejpam-5854	105	95	ωp(h2	ωp(h2	NOUN
ejpam-5854	105	96	)	)	PUNCT
ejpam-5854	105	97	and	and	CCONJ
ejpam-5854	105	98	ωn(h1h2h3	ωn(h1h2h3	NOUN
ejpam-5854	105	99	)	)	PUNCT
ejpam-5854	105	100	≤	≤	NOUN
ejpam-5854	105	101	ωn(h2	ωn(h2	NOUN
ejpam-5854	105	102	)	)	PUNCT
ejpam-5854	105	103	for	for	ADP
ejpam-5854	105	104	all	all	DET
ejpam-5854	105	105	h1	h1	PROPN
ejpam-5854	105	106	,	,	PUNCT
ejpam-5854	105	107	h2	h2	PROPN
ejpam-5854	105	108	,	,	PUNCT
ejpam-5854	105	109	h3	h3	VERB
ejpam-5854	105	110	∈	∈	PROPN
ejpam-5854	105	111	s	s	NOUN
ejpam-5854	105	112	,	,	PUNCT
ejpam-5854	105	113	(	(	PUNCT
ejpam-5854	105	114	6	6	NUM
ejpam-5854	105	115	)	)	PUNCT
ejpam-5854	105	116	bf	bf	NOUN
ejpam-5854	105	117	quasi	quasi	PROPN
ejpam-5854	105	118	ideal	ideal	NOUN
ejpam-5854	105	119	on	on	ADP
ejpam-5854	105	120	s	s	SYM
ejpam-5854	105	121	,	,	PUNCT
ejpam-5854	105	122	if	if	SCONJ
ejpam-5854	105	123	(	(	PUNCT
ejpam-5854	105	124	sp	sp	ADP
ejpam-5854	105	125	∗	∗	NOUN
ejpam-5854	105	126	ωp)∩	ωp)∩	PUNCT
ejpam-5854	105	127	(	(	PUNCT
ejpam-5854	105	128	ωp	ωp	NOUN
ejpam-5854	105	129	∗sp	∗sp	PROPN
ejpam-5854	105	130	)	)	PUNCT
ejpam-5854	105	131	⊆	⊆	NUM
ejpam-5854	105	132	ωp	ωp	NOUN
ejpam-5854	105	133	and	and	CCONJ
ejpam-5854	105	134	(	(	PUNCT
ejpam-5854	105	135	sn	sn	PROPN
ejpam-5854	105	136	∗	∗	NOUN
ejpam-5854	105	137	ωn)∩	ωn)∩	PUNCT
ejpam-5854	105	138	(	(	PUNCT
ejpam-5854	105	139	ωn	ωn	NOUN
ejpam-5854	105	140	∗sn	∗sn	NOUN
ejpam-5854	105	141	)	)	PUNCT
ejpam-5854	105	142	⊇	⊇	NOUN
ejpam-5854	105	143	ωn	ωn	ADP
ejpam-5854	105	144	,	,	PUNCT
ejpam-5854	105	145	where	where	SCONJ
ejpam-5854	105	146	s	s	NOUN
ejpam-5854	105	147	is	be	AUX
ejpam-5854	105	148	an	an	DET
ejpam-5854	105	149	bf	bf	NOUN
ejpam-5854	105	150	set	set	NOUN
ejpam-5854	105	151	of	of	ADP
ejpam-5854	105	152	s	s	VERB
ejpam-5854	105	153	mapping	map	VERB
ejpam-5854	105	154	every	every	DET
ejpam-5854	105	155	element	element	NOUN
ejpam-5854	105	156	of	of	ADP
ejpam-5854	105	157	s	s	PRON
ejpam-5854	105	158	on	on	ADP
ejpam-5854	105	159	[	[	X
ejpam-5854	105	160	−1	−1	NOUN
ejpam-5854	105	161	,	,	PUNCT
ejpam-5854	105	162	1	1	NUM
ejpam-5854	105	163	]	]	PUNCT
ejpam-5854	105	164	.	.	PUNCT
ejpam-5854	106	1	definition	definition	NOUN
ejpam-5854	106	2	7	7	NUM
ejpam-5854	106	3	.	.	PUNCT
ejpam-5854	107	1	[	[	X
ejpam-5854	107	2	7	7	X
ejpam-5854	107	3	]	]	X
ejpam-5854	107	4	an	an	DET
ejpam-5854	107	5	interval	interval	NOUN
ejpam-5854	107	6	valued	value	VERB
ejpam-5854	107	7	bipolar	bipolar	ADJ
ejpam-5854	107	8	fuzzy	fuzzy	ADJ
ejpam-5854	107	9	set	set	NOUN
ejpam-5854	107	10	(	(	PUNCT
ejpam-5854	107	11	shortly	shortly	ADV
ejpam-5854	107	12	,	,	PUNCT
ejpam-5854	107	13	ivbf	ivbf	VERB
ejpam-5854	107	14	set)c	set)c	PROPN
ejpam-5854	107	15	=	=	PUNCT
ejpam-5854	107	16	(	(	PUNCT
ejpam-5854	107	17	s;µp	s;µp	PROPN
ejpam-5854	107	18	,	,	PUNCT
ejpam-5854	107	19	µn	µn	PROPN
ejpam-5854	107	20	)	)	PUNCT
ejpam-5854	107	21	of	of	ADP
ejpam-5854	107	22	a	a	DET
ejpam-5854	107	23	non	non	ADJ
ejpam-5854	107	24	-	-	ADJ
ejpam-5854	107	25	empty	empty	ADJ
ejpam-5854	107	26	set	set	NOUN
ejpam-5854	107	27	f	f	NOUN
ejpam-5854	107	28	if	if	SCONJ
ejpam-5854	107	29	µp	µp	NOUN
ejpam-5854	107	30	:	:	PUNCT
ejpam-5854	107	31	s	s	X
ejpam-5854	107	32	→	→	X
ejpam-5854	107	33	cs[0	cs[0	PROPN
ejpam-5854	107	34	,	,	PUNCT
ejpam-5854	107	35	1	1	NUM
ejpam-5854	107	36	]	]	PUNCT
ejpam-5854	107	37	and	and	CCONJ
ejpam-5854	107	38	µn	µn	PROPN
ejpam-5854	107	39	:	:	PUNCT
ejpam-5854	107	40	s	s	X
ejpam-5854	107	41	→	→	SYM
ejpam-5854	107	42	cs[−1	cs[−1	ADJ
ejpam-5854	107	43	,	,	PUNCT
ejpam-5854	107	44	0	0	NUM
ejpam-5854	107	45	]	]	PUNCT
ejpam-5854	107	46	.	.	PUNCT
ejpam-5854	108	1	2.3	2.3	NUM
ejpam-5854	108	2	.	.	PUNCT
ejpam-5854	108	3	cubic	cubic	ADJ
ejpam-5854	108	4	sets	set	NOUN
ejpam-5854	108	5	definition	definition	NOUN
ejpam-5854	108	6	8	8	NUM
ejpam-5854	108	7	.	.	PUNCT
ejpam-5854	109	1	[	[	X
ejpam-5854	109	2	6	6	NUM
ejpam-5854	109	3	]	]	PUNCT
ejpam-5854	109	4	a	a	DET
ejpam-5854	109	5	cubic	cubic	ADJ
ejpam-5854	109	6	set	set	VERB
ejpam-5854	109	7	c	c	PROPN
ejpam-5854	109	8	of	of	ADP
ejpam-5854	109	9	a	a	DET
ejpam-5854	109	10	non	non	ADJ
ejpam-5854	109	11	-	-	ADJ
ejpam-5854	109	12	empty	empty	ADJ
ejpam-5854	109	13	set	set	NOUN
ejpam-5854	109	14	s	s	VERB
ejpam-5854	109	15	is	be	AUX
ejpam-5854	109	16	a	a	DET
ejpam-5854	109	17	structure	structure	NOUN
ejpam-5854	109	18	of	of	ADP
ejpam-5854	109	19	the	the	DET
ejpam-5854	109	20	form	form	NOUN
ejpam-5854	109	21	c	c	NOUN
ejpam-5854	109	22	=	=	SYM
ejpam-5854	109	23	{	{	PUNCT
ejpam-5854	109	24	⟨h	⟨h	PROPN
ejpam-5854	109	25	,	,	PUNCT
ejpam-5854	109	26	µ(h	µ(h	PROPN
ejpam-5854	109	27	)	)	PUNCT
ejpam-5854	109	28	,	,	PUNCT
ejpam-5854	109	29	ω(h)⟩	ω(h)⟩	NOUN
ejpam-5854	110	1	|	|	INTJ
ejpam-5854	110	2	h	h	NOUN
ejpam-5854	110	3	∈	∈	PROPN
ejpam-5854	111	1	s	s	AUX
ejpam-5854	111	2	}	}	PUNCT
ejpam-5854	111	3	and	and	CCONJ
ejpam-5854	111	4	denoted	denote	VERB
ejpam-5854	111	5	by	by	ADP
ejpam-5854	111	6	c	c	PROPN
ejpam-5854	111	7	=	=	SYM
ejpam-5854	111	8	⟨µ	⟨µ	PROPN
ejpam-5854	111	9	,	,	PUNCT
ejpam-5854	111	10	ω⟩	ω⟩	VERB
ejpam-5854	111	11	where	where	SCONJ
ejpam-5854	111	12	µ	µ	NOUN
ejpam-5854	111	13	is	be	AUX
ejpam-5854	111	14	an	an	DET
ejpam-5854	111	15	ivf	ivf	NOUN
ejpam-5854	111	16	set	set	NOUN
ejpam-5854	111	17	and	and	CCONJ
ejpam-5854	111	18	ω	ω	NOUN
ejpam-5854	111	19	is	be	AUX
ejpam-5854	111	20	a	a	DET
ejpam-5854	111	21	fuzzy	fuzzy	ADJ
ejpam-5854	111	22	set	set	NOUN
ejpam-5854	111	23	.	.	PUNCT
ejpam-5854	112	1	in	in	ADP
ejpam-5854	112	2	this	this	DET
ejpam-5854	112	3	case	case	NOUN
ejpam-5854	112	4	,	,	PUNCT
ejpam-5854	112	5	we	we	PRON
ejpam-5854	112	6	use	use	VERB
ejpam-5854	112	7	c(h	c(h	VERB
ejpam-5854	112	8	)	)	PUNCT
ejpam-5854	112	9	=	=	SYM
ejpam-5854	112	10	⟨µ(h	⟨µ(h	NOUN
ejpam-5854	112	11	)	)	PUNCT
ejpam-5854	112	12	,	,	PUNCT
ejpam-5854	112	13	ω(h)⟩	ω(h)⟩	NOUN
ejpam-5854	112	14	=	=	SYM
ejpam-5854	112	15	⟨[µn(h	⟨[µn(h	PROPN
ejpam-5854	112	16	)	)	PUNCT
ejpam-5854	112	17	,	,	PUNCT
ejpam-5854	112	18	µp(h	µp(h	NOUN
ejpam-5854	112	19	)	)	PUNCT
ejpam-5854	112	20	]	]	PUNCT
ejpam-5854	112	21	,	,	PUNCT
ejpam-5854	112	22	ω(h)⟩	ω(h)⟩	NOUN
ejpam-5854	112	23	for	for	ADP
ejpam-5854	112	24	all	all	DET
ejpam-5854	112	25	r	r	NOUN
ejpam-5854	112	26	∈	∈	PROPN
ejpam-5854	112	27	s.	s.	PROPN
ejpam-5854	112	28	definition	definition	NOUN
ejpam-5854	112	29	9	9	NUM
ejpam-5854	112	30	.	.	PUNCT
ejpam-5854	113	1	[	[	X
ejpam-5854	113	2	6	6	NUM
ejpam-5854	113	3	]	]	PUNCT
ejpam-5854	113	4	a	a	DET
ejpam-5854	113	5	cubic	cubic	ADJ
ejpam-5854	113	6	set	set	NOUN
ejpam-5854	113	7	c	c	NOUN
ejpam-5854	113	8	=	=	SYM
ejpam-5854	113	9	⟨µ	⟨µ	NOUN
ejpam-5854	113	10	,	,	PUNCT
ejpam-5854	113	11	ω⟩	ω⟩	NOUN
ejpam-5854	113	12	of	of	ADP
ejpam-5854	113	13	s	s	PROPN
ejpam-5854	113	14	is	be	AUX
ejpam-5854	113	15	called	call	VERB
ejpam-5854	113	16	(	(	PUNCT
ejpam-5854	113	17	1	1	NUM
ejpam-5854	113	18	)	)	PUNCT
ejpam-5854	113	19	a	a	DET
ejpam-5854	113	20	cubic	cubic	ADJ
ejpam-5854	113	21	subsemigroup	subsemigroup	NOUN
ejpam-5854	113	22	of	of	ADP
ejpam-5854	113	23	s	s	PROPN
ejpam-5854	113	24	,	,	PUNCT
ejpam-5854	113	25	if	if	SCONJ
ejpam-5854	113	26	µ(h1h2	µ(h1h2	ADP
ejpam-5854	113	27	)	)	PUNCT
ejpam-5854	113	28	⪰	⪰	NOUN
ejpam-5854	113	29	µ(h1	µ(h1	NOUN
ejpam-5854	113	30	)	)	PUNCT
ejpam-5854	113	31	⋏	⋏	PROPN
ejpam-5854	113	32	µ(h2	µ(h2	NOUN
ejpam-5854	113	33	)	)	PUNCT
ejpam-5854	113	34	and	and	CCONJ
ejpam-5854	113	35	ω(h1h2	ω(h1h2	X
ejpam-5854	113	36	)	)	PUNCT
ejpam-5854	113	37	≤	≤	NOUN
ejpam-5854	113	38	ω(h1	ω(h1	NOUN
ejpam-5854	113	39	)	)	PUNCT
ejpam-5854	113	40	∨	∨	PROPN
ejpam-5854	113	41	(	(	PUNCT
ejpam-5854	113	42	h2	h2	NOUN
ejpam-5854	113	43	)	)	PUNCT
ejpam-5854	113	44	for	for	ADP
ejpam-5854	113	45	all	all	DET
ejpam-5854	113	46	h1	h1	PROPN
ejpam-5854	113	47	,	,	PUNCT
ejpam-5854	113	48	h2	h2	PROPN
ejpam-5854	113	49	∈	∈	PROPN
ejpam-5854	113	50	s	s	PART
ejpam-5854	113	51	,	,	PUNCT
ejpam-5854	113	52	(	(	PUNCT
ejpam-5854	113	53	2	2	X
ejpam-5854	113	54	)	)	PUNCT
ejpam-5854	113	55	a	a	DET
ejpam-5854	113	56	cubic	cubic	ADJ
ejpam-5854	113	57	left(right)ideal	left(right)ideal	NOUN
ejpam-5854	113	58	of	of	ADP
ejpam-5854	113	59	s	s	NOUN
ejpam-5854	113	60	,	,	PUNCT
ejpam-5854	113	61	if	if	SCONJ
ejpam-5854	113	62	µ(h1h2	µ(h1h2	ADP
ejpam-5854	113	63	)	)	PUNCT
ejpam-5854	113	64	⪰	⪰	NOUN
ejpam-5854	113	65	µ(h2)(µ(h1h2	µ(h2)(µ(h1h2	NOUN
ejpam-5854	113	66	)	)	PUNCT
ejpam-5854	113	67	⪰	⪰	NOUN
ejpam-5854	113	68	µ(h1	µ(h1	NOUN
ejpam-5854	113	69	)	)	PUNCT
ejpam-5854	113	70	)	)	PUNCT
ejpam-5854	114	1	and	and	CCONJ
ejpam-5854	114	2	ω(h1h2	ω(h1h2	X
ejpam-5854	114	3	)	)	PUNCT
ejpam-5854	114	4	≤	≤	NUM
ejpam-5854	114	5	ω(h2)(ω(h1h2	ω(h2)(ω(h1h2	NOUN
ejpam-5854	114	6	)	)	PUNCT
ejpam-5854	114	7	≤	≤	NOUN
ejpam-5854	114	8	ω(h1	ω(h1	NOUN
ejpam-5854	114	9	)	)	PUNCT
ejpam-5854	114	10	)	)	PUNCT
ejpam-5854	114	11	for	for	ADP
ejpam-5854	114	12	all	all	DET
ejpam-5854	114	13	h1	h1	PROPN
ejpam-5854	114	14	,	,	PUNCT
ejpam-5854	114	15	h2	h2	PROPN
ejpam-5854	114	16	∈	∈	PROPN
ejpam-5854	114	17	s.	s.	PROPN
ejpam-5854	114	18	a	a	DET
ejpam-5854	114	19	cubic	cubic	ADJ
ejpam-5854	114	20	ideal	ideal	NOUN
ejpam-5854	114	21	of	of	ADP
ejpam-5854	114	22	s	s	PROPN
ejpam-5854	114	23	,	,	PUNCT
ejpam-5854	114	24	if	if	SCONJ
ejpam-5854	114	25	it	it	PRON
ejpam-5854	114	26	is	be	AUX
ejpam-5854	114	27	a	a	DET
ejpam-5854	114	28	cubic	cubic	ADJ
ejpam-5854	114	29	left	leave	VERB
ejpam-5854	114	30	ideal	ideal	NOUN
ejpam-5854	114	31	and	and	CCONJ
ejpam-5854	114	32	a	a	DET
ejpam-5854	114	33	cubic	cubic	ADJ
ejpam-5854	114	34	right	right	ADJ
ejpam-5854	114	35	ideal	ideal	NOUN
ejpam-5854	114	36	of	of	ADP
ejpam-5854	114	37	s	s	PROPN
ejpam-5854	114	38	,	,	PUNCT
ejpam-5854	114	39	(	(	PUNCT
ejpam-5854	114	40	3	3	X
ejpam-5854	114	41	)	)	PUNCT
ejpam-5854	114	42	a	a	DET
ejpam-5854	114	43	cubic	cubic	ADJ
ejpam-5854	114	44	genralized	genralize	VERB
ejpam-5854	114	45	bi	bi	ADJ
ejpam-5854	114	46	ideal	ideal	NOUN
ejpam-5854	114	47	of	of	ADP
ejpam-5854	114	48	s	s	PROPN
ejpam-5854	114	49	,	,	PUNCT
ejpam-5854	114	50	if	if	SCONJ
ejpam-5854	114	51	µ(h1h2h3	µ(h1h2h3	ADJ
ejpam-5854	114	52	)	)	PUNCT
ejpam-5854	114	53	⪰	⪰	NOUN
ejpam-5854	114	54	µ(h1)⋏	µ(h1)⋏	PROPN
ejpam-5854	114	55	µ(h3	µ(h3	NOUN
ejpam-5854	114	56	)	)	PUNCT
ejpam-5854	114	57	and	and	CCONJ
ejpam-5854	114	58	ω(h1h2h3	ω(h1h2h3	PROPN
ejpam-5854	114	59	)	)	PUNCT
ejpam-5854	114	60	≤	≤	NUM
ejpam-5854	114	61	ω(h1	ω(h1	NOUN
ejpam-5854	114	62	)	)	PUNCT
ejpam-5854	114	63	∨	∨	NUM
ejpam-5854	114	64	ω(h3	ω(h3	NOUN
ejpam-5854	114	65	)	)	PUNCT
ejpam-5854	114	66	for	for	ADP
ejpam-5854	114	67	all	all	DET
ejpam-5854	114	68	h1	h1	PROPN
ejpam-5854	114	69	,	,	PUNCT
ejpam-5854	114	70	h2	h2	PROPN
ejpam-5854	114	71	,	,	PUNCT
ejpam-5854	114	72	h3	h3	VERB
ejpam-5854	114	73	∈	∈	PROPN
ejpam-5854	114	74	s	s	NOUN
ejpam-5854	114	75	,	,	PUNCT
ejpam-5854	114	76	(	(	PUNCT
ejpam-5854	114	77	4	4	X
ejpam-5854	114	78	)	)	PUNCT
ejpam-5854	114	79	a	a	DET
ejpam-5854	114	80	cubic	cubic	ADJ
ejpam-5854	114	81	bi	bi	ADJ
ejpam-5854	114	82	ideal	ideal	NOUN
ejpam-5854	114	83	of	of	ADP
ejpam-5854	114	84	s	s	PROPN
ejpam-5854	114	85	,	,	PUNCT
ejpam-5854	114	86	if	if	SCONJ
ejpam-5854	114	87	µ	µ	PRON
ejpam-5854	114	88	is	be	AUX
ejpam-5854	114	89	a	a	DET
ejpam-5854	114	90	cubic	cubic	ADJ
ejpam-5854	114	91	subsemigorup	subsemigorup	NOUN
ejpam-5854	114	92	of	of	ADP
ejpam-5854	114	93	s	s	PROPN
ejpam-5854	114	94	and	and	CCONJ
ejpam-5854	114	95	µ(h1h2h3	µ(h1h2h3	ADJ
ejpam-5854	114	96	)	)	PUNCT
ejpam-5854	114	97	⪰	⪰	NOUN
ejpam-5854	114	98	µ(h1	µ(h1	NOUN
ejpam-5854	114	99	)	)	PUNCT
ejpam-5854	114	100	⋏	⋏	PROPN
ejpam-5854	114	101	µ(h3	µ(h3	NUM
ejpam-5854	114	102	)	)	PUNCT
ejpam-5854	114	103	and	and	CCONJ
ejpam-5854	114	104	ω(h1h2h3	ω(h1h2h3	PROPN
ejpam-5854	114	105	)	)	PUNCT
ejpam-5854	114	106	≤	≤	NUM
ejpam-5854	114	107	ω(h1	ω(h1	NOUN
ejpam-5854	114	108	)	)	PUNCT
ejpam-5854	114	109	∨	∨	NUM
ejpam-5854	114	110	ω(h3	ω(h3	NOUN
ejpam-5854	114	111	)	)	PUNCT
ejpam-5854	114	112	for	for	ADP
ejpam-5854	114	113	all	all	DET
ejpam-5854	114	114	h1	h1	PROPN
ejpam-5854	114	115	,	,	PUNCT
ejpam-5854	114	116	h2	h2	PROPN
ejpam-5854	114	117	,	,	PUNCT
ejpam-5854	114	118	h3	h3	VERB
ejpam-5854	114	119	∈	∈	PROPN
ejpam-5854	114	120	s	s	NOUN
ejpam-5854	114	121	,	,	PUNCT
ejpam-5854	114	122	(	(	PUNCT
ejpam-5854	114	123	5	5	X
ejpam-5854	114	124	)	)	PUNCT
ejpam-5854	114	125	a	a	DET
ejpam-5854	114	126	cubic	cubic	ADJ
ejpam-5854	114	127	interior	interior	ADJ
ejpam-5854	114	128	ideal	ideal	NOUN
ejpam-5854	114	129	of	of	ADP
ejpam-5854	114	130	s	s	PROPN
ejpam-5854	114	131	,	,	PUNCT
ejpam-5854	114	132	if	if	SCONJ
ejpam-5854	114	133	µ	µ	PRON
ejpam-5854	114	134	is	be	AUX
ejpam-5854	114	135	a	a	DET
ejpam-5854	114	136	cubic	cubic	ADJ
ejpam-5854	114	137	subsemigorup	subsemigorup	NOUN
ejpam-5854	114	138	of	of	ADP
ejpam-5854	114	139	s	s	PROPN
ejpam-5854	114	140	,	,	PUNCT
ejpam-5854	114	141	µ(h1h2h3	µ(h1h2h3	ADJ
ejpam-5854	114	142	)	)	PUNCT
ejpam-5854	114	143	⪰	⪰	NOUN
ejpam-5854	114	144	µ(h2	µ(h2	NOUN
ejpam-5854	114	145	)	)	PUNCT
ejpam-5854	114	146	and	and	CCONJ
ejpam-5854	114	147	ω(h1h2h3	ω(h1h2h3	PROPN
ejpam-5854	114	148	)	)	PUNCT
ejpam-5854	114	149	≤	≤	NUM
ejpam-5854	114	150	ω(h2	ω(h2	NOUN
ejpam-5854	114	151	)	)	PUNCT
ejpam-5854	114	152	for	for	ADP
ejpam-5854	114	153	all	all	DET
ejpam-5854	114	154	h1	h1	PROPN
ejpam-5854	114	155	,	,	PUNCT
ejpam-5854	114	156	h2	h2	PROPN
ejpam-5854	114	157	,	,	PUNCT
ejpam-5854	114	158	h3	h3	VERB
ejpam-5854	114	159	∈	∈	PROPN
ejpam-5854	114	160	s	s	NOUN
ejpam-5854	114	161	,	,	PUNCT
ejpam-5854	114	162	(	(	PUNCT
ejpam-5854	114	163	6	6	NUM
ejpam-5854	114	164	)	)	PUNCT
ejpam-5854	114	165	a	a	DET
ejpam-5854	114	166	cubic	cubic	ADJ
ejpam-5854	114	167	quasi	quasi	ADJ
ejpam-5854	114	168	ideal	ideal	NOUN
ejpam-5854	114	169	of	of	ADP
ejpam-5854	114	170	s	s	PROPN
ejpam-5854	114	171	,	,	PUNCT
ejpam-5854	114	172	if	if	SCONJ
ejpam-5854	114	173	(	(	PUNCT
ejpam-5854	114	174	s⃝	s⃝	PROPN
ejpam-5854	114	175	µ	µ	NUM
ejpam-5854	114	176	)	)	PUNCT
ejpam-5854	114	177	∩	∩	NOUN
ejpam-5854	114	178	(	(	PUNCT
ejpam-5854	114	179	µ⃝s	µ⃝s	PROPN
ejpam-5854	114	180	)	)	PUNCT
ejpam-5854	114	181	⊑	⊑	PRON
ejpam-5854	114	182	µ	µ	X
ejpam-5854	114	183	and	and	CCONJ
ejpam-5854	114	184	(	(	PUNCT
ejpam-5854	114	185	s	s	NOUN
ejpam-5854	114	186	∗	∗	NOUN
ejpam-5854	114	187	ω	ω	NOUN
ejpam-5854	114	188	)	)	PUNCT
ejpam-5854	114	189	∩	∩	NOUN
ejpam-5854	114	190	(	(	PUNCT
ejpam-5854	114	191	ω	ω	PROPN
ejpam-5854	114	192	∗s	∗s	NOUN
ejpam-5854	114	193	)	)	PUNCT
ejpam-5854	114	194	⊇	⊇	NOUN
ejpam-5854	114	195	ω	ω	PROPN
ejpam-5854	114	196	.	.	PUNCT
ejpam-5854	115	1	riaz	riaz	PROPN
ejpam-5854	116	1	and	and	CCONJ
ejpam-5854	116	2	tehrim	tehrim	VERB
ejpam-5854	116	3	[	[	X
ejpam-5854	116	4	8	8	NUM
ejpam-5854	116	5	]	]	PUNCT
ejpam-5854	116	6	discussed	discuss	VERB
ejpam-5854	116	7	the	the	DET
ejpam-5854	116	8	concept	concept	NOUN
ejpam-5854	116	9	of	of	ADP
ejpam-5854	116	10	cubic	cubic	ADJ
ejpam-5854	116	11	bipolar	bipolar	ADJ
ejpam-5854	116	12	fuzzy	fuzzy	ADJ
ejpam-5854	116	13	sets	set	NOUN
ejpam-5854	116	14	and	and	CCONJ
ejpam-5854	116	15	some	some	DET
ejpam-5854	116	16	properties	property	NOUN
ejpam-5854	116	17	.	.	PUNCT
ejpam-5854	117	1	in	in	ADP
ejpam-5854	117	2	this	this	DET
ejpam-5854	117	3	paper	paper	NOUN
ejpam-5854	117	4	,	,	PUNCT
ejpam-5854	117	5	we	we	PRON
ejpam-5854	117	6	consider	consider	VERB
ejpam-5854	117	7	the	the	DET
ejpam-5854	117	8	concepts	concept	NOUN
ejpam-5854	117	9	of	of	ADP
ejpam-5854	117	10	cubic	cubic	ADJ
ejpam-5854	117	11	bipolar	bipolar	ADJ
ejpam-5854	117	12	fuzzy	fuzzy	ADJ
ejpam-5854	117	13	subsemigroups	subsemigroup	NOUN
ejpam-5854	117	14	and	and	CCONJ
ejpam-5854	117	15	types	type	NOUN
ejpam-5854	117	16	of	of	ADP
ejpam-5854	117	17	cubic	cubic	ADJ
ejpam-5854	117	18	bipolar	bipolar	ADJ
ejpam-5854	117	19	fuzzy	fuzzy	ADJ
ejpam-5854	117	20	ideals	ideal	NOUN
ejpam-5854	117	21	.	.	PUNCT
ejpam-5854	118	1	we	we	PRON
ejpam-5854	118	2	provide	provide	VERB
ejpam-5854	118	3	properties	property	NOUN
ejpam-5854	118	4	of	of	ADP
ejpam-5854	118	5	cubic	cubic	ADJ
ejpam-5854	118	6	bipolar	bipolar	ADJ
ejpam-5854	118	7	fuzzy	fuzzy	ADJ
ejpam-5854	118	8	subsemigroups	subsemigroup	NOUN
ejpam-5854	118	9	and	and	CCONJ
ejpam-5854	118	10	quasi	quasi	NOUN
ejpam-5854	118	11	ideals	ideal	NOUN
ejpam-5854	118	12	.	.	PUNCT
ejpam-5854	119	1	in	in	ADP
ejpam-5854	119	2	the	the	DET
ejpam-5854	119	3	important	important	ADJ
ejpam-5854	119	4	results	result	NOUN
ejpam-5854	119	5	,	,	PUNCT
ejpam-5854	119	6	regular	regular	ADJ
ejpam-5854	119	7	and	and	CCONJ
ejpam-5854	119	8	intra	intra	ADJ
ejpam-5854	119	9	-	-	ADJ
ejpam-5854	119	10	regular	regular	ADJ
ejpam-5854	119	11	semigroups	semigroup	NOUN
ejpam-5854	119	12	are	be	AUX
ejpam-5854	119	13	characterized	characterize	VERB
ejpam-5854	119	14	in	in	ADP
ejpam-5854	119	15	terms	term	NOUN
ejpam-5854	119	16	of	of	ADP
ejpam-5854	119	17	cubic	cubic	ADJ
ejpam-5854	119	18	bipolar	bipolar	ADJ
ejpam-5854	119	19	fuzzy	fuzzy	ADJ
ejpam-5854	119	20	quasi	quasi	NOUN
ejpam-5854	119	21	ideals	ideal	NOUN
ejpam-5854	119	22	are	be	AUX
ejpam-5854	119	23	provided	provide	VERB
ejpam-5854	119	24	.	.	PUNCT
ejpam-5854	120	1	p.	p.	NOUN
ejpam-5854	120	2	khamrot	khamrot	PROPN
ejpam-5854	120	3	,	,	PUNCT
ejpam-5854	120	4	n.	n.	PROPN
ejpam-5854	120	5	deetae	deetae	PROPN
ejpam-5854	120	6	,	,	PUNCT
ejpam-5854	120	7	t.	t.	PROPN
ejpam-5854	120	8	gaketem	gaketem	PROPN
ejpam-5854	120	9	/	/	SYM
ejpam-5854	120	10	eur	eur	PROPN
ejpam-5854	120	11	.	.	PUNCT
ejpam-5854	121	1	j.	j.	PROPN
ejpam-5854	121	2	pure	pure	PROPN
ejpam-5854	121	3	appl	appl	PROPN
ejpam-5854	121	4	.	.	PROPN
ejpam-5854	121	5	math	math	PROPN
ejpam-5854	121	6	,	,	PUNCT
ejpam-5854	121	7	18	18	NUM
ejpam-5854	121	8	(	(	PUNCT
ejpam-5854	121	9	2	2	NUM
ejpam-5854	121	10	)	)	PUNCT
ejpam-5854	121	11	(	(	PUNCT
ejpam-5854	121	12	2025	2025	NUM
ejpam-5854	121	13	)	)	PUNCT
ejpam-5854	121	14	,	,	PUNCT
ejpam-5854	121	15	5854	5854	NUM
ejpam-5854	121	16	6	6	NUM
ejpam-5854	121	17	of	of	ADP
ejpam-5854	121	18	14	14	NUM
ejpam-5854	121	19	3	3	NUM
ejpam-5854	121	20	.	.	PUNCT
ejpam-5854	121	21	cubic	cubic	ADJ
ejpam-5854	121	22	bipolar	bipolar	ADJ
ejpam-5854	121	23	fuzzy	fuzzy	ADJ
ejpam-5854	121	24	subsemigroup	subsemigroup	NOUN
ejpam-5854	121	25	and	and	CCONJ
ejpam-5854	121	26	ideals	ideal	NOUN
ejpam-5854	121	27	in	in	ADP
ejpam-5854	121	28	semigroups	semigroup	NOUN
ejpam-5854	121	29	in	in	ADP
ejpam-5854	121	30	this	this	DET
ejpam-5854	121	31	part	part	NOUN
ejpam-5854	121	32	,	,	PUNCT
ejpam-5854	121	33	we	we	PRON
ejpam-5854	121	34	give	give	VERB
ejpam-5854	121	35	the	the	DET
ejpam-5854	121	36	concepts	concept	NOUN
ejpam-5854	121	37	of	of	ADP
ejpam-5854	121	38	cubic	cubic	ADJ
ejpam-5854	121	39	bipolar	bipolar	ADJ
ejpam-5854	121	40	fuzzy	fuzzy	ADJ
ejpam-5854	121	41	subsemigroups	subsemigroup	NOUN
ejpam-5854	121	42	and	and	CCONJ
ejpam-5854	121	43	ideals	ideal	NOUN
ejpam-5854	121	44	in	in	ADP
ejpam-5854	121	45	semigroup	semigroup	PROPN
ejpam-5854	121	46	.	.	PUNCT
ejpam-5854	122	1	and	and	CCONJ
ejpam-5854	122	2	we	we	PRON
ejpam-5854	122	3	study	study	VERB
ejpam-5854	122	4	important	important	ADJ
ejpam-5854	122	5	properties	property	NOUN
ejpam-5854	122	6	for	for	ADP
ejpam-5854	122	7	reference	reference	NOUN
ejpam-5854	122	8	in	in	ADP
ejpam-5854	122	9	the	the	DET
ejpam-5854	122	10	next	next	ADJ
ejpam-5854	122	11	part	part	NOUN
ejpam-5854	122	12	.	.	PUNCT
ejpam-5854	123	1	definition	definition	NOUN
ejpam-5854	123	2	10	10	NUM
ejpam-5854	123	3	.	.	PUNCT
ejpam-5854	124	1	a	a	DET
ejpam-5854	124	2	cubic	cubic	ADJ
ejpam-5854	124	3	bipolar	bipolar	ADJ
ejpam-5854	124	4	set	set	NOUN
ejpam-5854	124	5	(	(	PUNCT
ejpam-5854	124	6	shortly	shortly	ADV
ejpam-5854	124	7	,	,	PUNCT
ejpam-5854	124	8	cb	cb	PROPN
ejpam-5854	124	9	set	set	PROPN
ejpam-5854	124	10	)	)	PUNCT
ejpam-5854	124	11	c̈	c̈	NOUN
ejpam-5854	124	12	of	of	ADP
ejpam-5854	124	13	a	a	DET
ejpam-5854	124	14	set	set	NOUN
ejpam-5854	124	15	s	s	X
ejpam-5854	124	16	if	if	SCONJ
ejpam-5854	124	17	c̈	c̈	NOUN
ejpam-5854	124	18	=	=	SYM
ejpam-5854	124	19	{	{	PUNCT
ejpam-5854	124	20	⟨h	⟨h	PROPN
ejpam-5854	124	21	,	,	PUNCT
ejpam-5854	124	22	(	(	PUNCT
ejpam-5854	124	23	µp(h	µp(h	NOUN
ejpam-5854	124	24	)	)	PUNCT
ejpam-5854	124	25	,	,	PUNCT
ejpam-5854	124	26	µn(h	µn(h	NUM
ejpam-5854	124	27	)	)	PUNCT
ejpam-5854	124	28	)	)	PUNCT
ejpam-5854	124	29	,	,	PUNCT
ejpam-5854	124	30	ω(h)⟩	ω(h)⟩	NOUN
ejpam-5854	125	1	|	|	INTJ
ejpam-5854	125	2	h	h	NOUN
ejpam-5854	125	3	∈	∈	PROPN
ejpam-5854	126	1	s	s	AUX
ejpam-5854	126	2	}	}	PUNCT
ejpam-5854	126	3	and	and	CCONJ
ejpam-5854	126	4	denoted	denote	VERB
ejpam-5854	126	5	by	by	ADP
ejpam-5854	126	6	c̈	c̈	NOUN
ejpam-5854	126	7	=	=	SYM
ejpam-5854	126	8	⟨µ	⟨µ	NOUN
ejpam-5854	126	9	,	,	PUNCT
ejpam-5854	126	10	ω⟩	ω⟩	VERB
ejpam-5854	126	11	where	where	SCONJ
ejpam-5854	126	12	µ	µ	NOUN
ejpam-5854	126	13	is	be	AUX
ejpam-5854	126	14	an	an	DET
ejpam-5854	126	15	ivbf	ivbf	NOUN
ejpam-5854	126	16	set	set	NOUN
ejpam-5854	126	17	and	and	CCONJ
ejpam-5854	126	18	ω	ω	NOUN
ejpam-5854	126	19	is	be	AUX
ejpam-5854	126	20	a	a	DET
ejpam-5854	126	21	bf	bf	NOUN
ejpam-5854	126	22	set	set	NOUN
ejpam-5854	126	23	.	.	PUNCT
ejpam-5854	127	1	definition	definition	NOUN
ejpam-5854	127	2	11	11	NUM
ejpam-5854	127	3	.	.	PUNCT
ejpam-5854	128	1	a	a	DET
ejpam-5854	128	2	cb	cb	PROPN
ejpam-5854	128	3	set	set	VERB
ejpam-5854	128	4	c̈	c̈	NOUN
ejpam-5854	128	5	=	=	SYM
ejpam-5854	128	6	⟨µ	⟨µ	NOUN
ejpam-5854	128	7	,	,	PUNCT
ejpam-5854	128	8	ω⟩	ω⟩	NOUN
ejpam-5854	128	9	of	of	ADP
ejpam-5854	128	10	a	a	DET
ejpam-5854	128	11	semigroup	semigroup	NOUN
ejpam-5854	128	12	s	s	PART
ejpam-5854	128	13	is	be	AUX
ejpam-5854	128	14	called	call	VERB
ejpam-5854	128	15	a	a	DET
ejpam-5854	128	16	cubic	cubic	ADJ
ejpam-5854	128	17	bipolar	bipolar	ADJ
ejpam-5854	128	18	fuzzy	fuzzy	ADJ
ejpam-5854	128	19	subsemigroup	subsemigroup	NOUN
ejpam-5854	128	20	(	(	PUNCT
ejpam-5854	128	21	shortly	shortly	ADV
ejpam-5854	128	22	,	,	PUNCT
ejpam-5854	128	23	cbf	cbf	PROPN
ejpam-5854	128	24	subsemigroup	subsemigroup	PROPN
ejpam-5854	128	25	)	)	PUNCT
ejpam-5854	128	26	of	of	ADP
ejpam-5854	128	27	s	s	PRON
ejpam-5854	128	28	if	if	SCONJ
ejpam-5854	128	29	µp(h1h2	µp(h1h2	ADP
ejpam-5854	128	30	)	)	PUNCT
ejpam-5854	128	31	⪰	⪰	NOUN
ejpam-5854	128	32	µp(h1)⋏	µp(h1)⋏	ADP
ejpam-5854	128	33	µp(h2	µp(h2	NOUN
ejpam-5854	128	34	)	)	PUNCT
ejpam-5854	128	35	,	,	PUNCT
ejpam-5854	128	36	µ	µ	X
ejpam-5854	128	37	n(h1h2	n(h1h2	NOUN
ejpam-5854	128	38	)	)	PUNCT
ejpam-5854	128	39	⪯	⪯	NOUN
ejpam-5854	128	40	µn(h1)⋎	µn(h1)⋎	PROPN
ejpam-5854	128	41	µn(h2	µn(h2	NOUN
ejpam-5854	128	42	)	)	PUNCT
ejpam-5854	128	43	and	and	CCONJ
ejpam-5854	128	44	ωp(h1h2	ωp(h1h2	NUM
ejpam-5854	128	45	)	)	PUNCT
ejpam-5854	128	46	≥	≥	NOUN
ejpam-5854	128	47	ωp(h1	ωp(h1	NUM
ejpam-5854	128	48	)	)	PUNCT
ejpam-5854	128	49	∧	∧	PROPN
ejpam-5854	128	50	ωn(h2	ωn(h2	NOUN
ejpam-5854	128	51	)	)	PUNCT
ejpam-5854	128	52	,	,	PUNCT
ejpam-5854	128	53	ω	ω	PROPN
ejpam-5854	128	54	n(h1h2	n(h1h2	NOUN
ejpam-5854	128	55	)	)	PUNCT
ejpam-5854	128	56	≤	≤	NUM
ejpam-5854	128	57	ωn(h1	ωn(h1	NOUN
ejpam-5854	128	58	)	)	PUNCT
ejpam-5854	128	59	∨	∨	NUM
ejpam-5854	128	60	ωn(h2	ωn(h2	NOUN
ejpam-5854	128	61	)	)	PUNCT
ejpam-5854	128	62	for	for	ADP
ejpam-5854	128	63	all	all	DET
ejpam-5854	128	64	h1	h1	PROPN
ejpam-5854	128	65	,	,	PUNCT
ejpam-5854	128	66	h2	h2	PROPN
ejpam-5854	128	67	∈	∈	PROPN
ejpam-5854	128	68	s.	s.	PROPN
ejpam-5854	128	69	example	example	NOUN
ejpam-5854	129	1	1	1	X
ejpam-5854	129	2	.	.	PUNCT
ejpam-5854	130	1	let	let	VERB
ejpam-5854	130	2	s	s	PRON
ejpam-5854	130	3	be	be	AUX
ejpam-5854	130	4	a	a	DET
ejpam-5854	130	5	semigroup	semigroup	NOUN
ejpam-5854	130	6	defined	define	VERB
ejpam-5854	130	7	by	by	ADP
ejpam-5854	130	8	the	the	DET
ejpam-5854	130	9	following	follow	VERB
ejpam-5854	130	10	table	table	NOUN
ejpam-5854	130	11	:	:	PUNCT
ejpam-5854	130	12	·	·	PUNCT
ejpam-5854	130	13	a	a	DET
ejpam-5854	130	14	b	b	X
ejpam-5854	130	15	c	c	X
ejpam-5854	130	16	a	a	DET
ejpam-5854	130	17	a	a	DET
ejpam-5854	130	18	b	b	NOUN
ejpam-5854	130	19	c	c	PROPN
ejpam-5854	130	20	b	b	PROPN
ejpam-5854	130	21	b	b	PROPN
ejpam-5854	130	22	b	b	PROPN
ejpam-5854	130	23	c	c	NOUN
ejpam-5854	130	24	c	c	NOUN
ejpam-5854	130	25	c	c	NOUN
ejpam-5854	130	26	c	c	PROPN
ejpam-5854	130	27	b	b	PROPN
ejpam-5854	130	28	thus	thus	ADV
ejpam-5854	130	29	,	,	PUNCT
ejpam-5854	130	30	a	a	DET
ejpam-5854	130	31	cb	cb	NOUN
ejpam-5854	130	32	set	set	VERB
ejpam-5854	130	33	c̈	c̈	NOUN
ejpam-5854	130	34	=	=	SYM
ejpam-5854	130	35	⟨µ	⟨µ	NOUN
ejpam-5854	130	36	,	,	PUNCT
ejpam-5854	130	37	ω⟩	ω⟩	VERB
ejpam-5854	130	38	in	in	ADP
ejpam-5854	130	39	f	f	PROPN
ejpam-5854	130	40	as	as	SCONJ
ejpam-5854	130	41	follows	follow	VERB
ejpam-5854	130	42	:	:	PUNCT
ejpam-5854	130	43	µp(a	µp(a	NUM
ejpam-5854	130	44	)	)	PUNCT
ejpam-5854	130	45	=	=	PUNCT
ejpam-5854	131	1	[	[	X
ejpam-5854	131	2	0.6	0.6	NUM
ejpam-5854	131	3	,	,	PUNCT
ejpam-5854	131	4	0.7	0.7	NUM
ejpam-5854	131	5	]	]	PUNCT
ejpam-5854	131	6	,	,	PUNCT
ejpam-5854	131	7	µp(b	µp(b	ADJ
ejpam-5854	131	8	)	)	PUNCT
ejpam-5854	131	9	=	=	PUNCT
ejpam-5854	132	1	[	[	X
ejpam-5854	132	2	0.4	0.4	NUM
ejpam-5854	132	3	,	,	PUNCT
ejpam-5854	132	4	0.5	0.5	NUM
ejpam-5854	132	5	]	]	PUNCT
ejpam-5854	132	6	,	,	PUNCT
ejpam-5854	132	7	µp(c	µp(c	ADV
ejpam-5854	132	8	)	)	PUNCT
ejpam-5854	132	9	=	=	PUNCT
ejpam-5854	133	1	[	[	X
ejpam-5854	133	2	0.1	0.1	NUM
ejpam-5854	133	3	,	,	PUNCT
ejpam-5854	133	4	0.2	0.2	NUM
ejpam-5854	133	5	]	]	PUNCT
ejpam-5854	133	6	,	,	PUNCT
ejpam-5854	133	7	µn(a	µn(a	PUNCT
ejpam-5854	133	8	)	)	PUNCT
ejpam-5854	133	9	=	=	PUNCT
ejpam-5854	134	1	[	[	X
ejpam-5854	134	2	−0.9,−0.8	−0.9,−0.8	X
ejpam-5854	134	3	]	]	X
ejpam-5854	134	4	,	,	PUNCT
ejpam-5854	134	5	µn(b	µn(b	NUM
ejpam-5854	134	6	)	)	PUNCT
ejpam-5854	134	7	=	=	PUNCT
ejpam-5854	135	1	[	[	X
ejpam-5854	135	2	−0.7,−0.6	−0.7,−0.6	X
ejpam-5854	135	3	]	]	PUNCT
ejpam-5854	135	4	,	,	PUNCT
ejpam-5854	135	5	µp(c	µp(c	ADV
ejpam-5854	135	6	)	)	PUNCT
ejpam-5854	135	7	=	=	PUNCT
ejpam-5854	136	1	[	[	X
ejpam-5854	136	2	−0.3,−0.2	−0.3,−0.2	X
ejpam-5854	136	3	]	]	PUNCT
ejpam-5854	136	4	and	and	CCONJ
ejpam-5854	136	5	ωp(a	ωp(a	NUM
ejpam-5854	136	6	)	)	PUNCT
ejpam-5854	136	7	=	=	SYM
ejpam-5854	136	8	0.7	0.7	NUM
ejpam-5854	136	9	,	,	PUNCT
ejpam-5854	136	10	ωp(b	ωp(b	NUM
ejpam-5854	136	11	)	)	PUNCT
ejpam-5854	136	12	=	=	SYM
ejpam-5854	136	13	0.4	0.4	NUM
ejpam-5854	136	14	,	,	PUNCT
ejpam-5854	136	15	ωp(c	ωp(c	NUM
ejpam-5854	136	16	)	)	PUNCT
ejpam-5854	136	17	=	=	SYM
ejpam-5854	136	18	0.2	0.2	NUM
ejpam-5854	136	19	,	,	PUNCT
ejpam-5854	136	20	ωn(a	ωn(a	NUM
ejpam-5854	136	21	)	)	PUNCT
ejpam-5854	136	22	=	=	SYM
ejpam-5854	136	23	−0.7	−0.7	PROPN
ejpam-5854	136	24	,	,	PUNCT
ejpam-5854	136	25	ωn(b	ωn(b	NUM
ejpam-5854	136	26	)	)	PUNCT
ejpam-5854	136	27	=	=	SYM
ejpam-5854	136	28	−0.3	−0.3	NOUN
ejpam-5854	136	29	,	,	PUNCT
ejpam-5854	136	30	ωn(c	ωn(c	NOUN
ejpam-5854	136	31	)	)	PUNCT
ejpam-5854	136	32	=	=	SYM
ejpam-5854	136	33	−0.2	−0.2	PROPN
ejpam-5854	136	34	.	.	PUNCT
ejpam-5854	137	1	thus	thus	ADV
ejpam-5854	137	2	,	,	PUNCT
ejpam-5854	137	3	c̈	c̈	NOUN
ejpam-5854	137	4	=	=	SYM
ejpam-5854	137	5	⟨µ	⟨µ	NOUN
ejpam-5854	137	6	,	,	PUNCT
ejpam-5854	137	7	ω⟩	ω⟩	PRON
ejpam-5854	137	8	is	be	AUX
ejpam-5854	137	9	a	a	DET
ejpam-5854	137	10	cbf	cbf	PROPN
ejpam-5854	137	11	subsemigroup	subsemigroup	NOUN
ejpam-5854	137	12	of	of	ADP
ejpam-5854	137	13	s.	s.	PROPN
ejpam-5854	137	14	definition	definition	NOUN
ejpam-5854	137	15	12	12	NUM
ejpam-5854	137	16	.	.	PUNCT
ejpam-5854	138	1	a	a	DET
ejpam-5854	138	2	cb	cb	PROPN
ejpam-5854	138	3	set	set	VERB
ejpam-5854	138	4	c̈	c̈	NOUN
ejpam-5854	138	5	=	=	SYM
ejpam-5854	138	6	⟨µ	⟨µ	NOUN
ejpam-5854	138	7	,	,	PUNCT
ejpam-5854	138	8	ω⟩	ω⟩	NOUN
ejpam-5854	138	9	of	of	ADP
ejpam-5854	138	10	a	a	DET
ejpam-5854	138	11	semigroup	semigroup	NOUN
ejpam-5854	138	12	s	s	PART
ejpam-5854	138	13	is	be	AUX
ejpam-5854	138	14	called	call	VERB
ejpam-5854	138	15	(	(	PUNCT
ejpam-5854	138	16	1	1	NUM
ejpam-5854	138	17	)	)	PUNCT
ejpam-5854	138	18	a	a	DET
ejpam-5854	138	19	cubic	cubic	ADJ
ejpam-5854	138	20	bipolar	bipolar	ADJ
ejpam-5854	138	21	fuzzy	fuzzy	ADJ
ejpam-5854	138	22	left	leave	VERB
ejpam-5854	138	23	ideal	ideal	NOUN
ejpam-5854	138	24	(	(	PUNCT
ejpam-5854	138	25	shortly	shortly	ADV
ejpam-5854	138	26	,	,	PUNCT
ejpam-5854	138	27	cbf	cbf	PROPN
ejpam-5854	138	28	left	leave	VERB
ejpam-5854	138	29	ideal	ideal	NOUN
ejpam-5854	138	30	)	)	PUNCT
ejpam-5854	138	31	of	of	ADP
ejpam-5854	138	32	s	s	SYM
ejpam-5854	138	33	,	,	PUNCT
ejpam-5854	138	34	if	if	SCONJ
ejpam-5854	138	35	µp(h1h2	µp(h1h2	ADP
ejpam-5854	138	36	)	)	PUNCT
ejpam-5854	138	37	⪰	⪰	NOUN
ejpam-5854	138	38	µp(h2	µp(h2	NOUN
ejpam-5854	138	39	)	)	PUNCT
ejpam-5854	138	40	,	,	PUNCT
ejpam-5854	138	41	µ	µ	X
ejpam-5854	138	42	n(h1h2	n(h1h2	NOUN
ejpam-5854	138	43	)	)	PUNCT
ejpam-5854	138	44	⪯	⪯	NOUN
ejpam-5854	138	45	µn(h2	µn(h2	NOUN
ejpam-5854	138	46	)	)	PUNCT
ejpam-5854	138	47	and	and	CCONJ
ejpam-5854	138	48	ωp(h1h2	ωp(h1h2	NUM
ejpam-5854	138	49	)	)	PUNCT
ejpam-5854	138	50	≥	≥	NOUN
ejpam-5854	138	51	ωp(h2	ωp(h2	NOUN
ejpam-5854	138	52	)	)	PUNCT
ejpam-5854	138	53	,	,	PUNCT
ejpam-5854	138	54	ω	ω	PROPN
ejpam-5854	138	55	n(h1h2	n(h1h2	NOUN
ejpam-5854	138	56	)	)	PUNCT
ejpam-5854	138	57	≤	≤	NOUN
ejpam-5854	138	58	ωn(h2	ωn(h2	NOUN
ejpam-5854	138	59	)	)	PUNCT
ejpam-5854	138	60	for	for	ADP
ejpam-5854	138	61	all	all	DET
ejpam-5854	138	62	h1	h1	PROPN
ejpam-5854	138	63	,	,	PUNCT
ejpam-5854	138	64	h2	h2	PROPN
ejpam-5854	138	65	∈	∈	PROPN
ejpam-5854	138	66	s	s	PART
ejpam-5854	138	67	,	,	PUNCT
ejpam-5854	138	68	(	(	PUNCT
ejpam-5854	138	69	2	2	X
ejpam-5854	138	70	)	)	PUNCT
ejpam-5854	138	71	a	a	DET
ejpam-5854	138	72	cubic	cubic	ADJ
ejpam-5854	138	73	bipolar	bipolar	ADJ
ejpam-5854	138	74	fuzzy	fuzzy	ADJ
ejpam-5854	138	75	right	right	ADJ
ejpam-5854	138	76	ideal	ideal	NOUN
ejpam-5854	138	77	(	(	PUNCT
ejpam-5854	138	78	shortly	shortly	ADV
ejpam-5854	138	79	,	,	PUNCT
ejpam-5854	138	80	cbf	cbf	PROPN
ejpam-5854	138	81	rihgt	rihgt	AUX
ejpam-5854	138	82	ideal	ideal	VERB
ejpam-5854	138	83	)	)	PUNCT
ejpam-5854	138	84	of	of	ADP
ejpam-5854	138	85	s	s	SYM
ejpam-5854	138	86	,	,	PUNCT
ejpam-5854	138	87	if	if	SCONJ
ejpam-5854	138	88	µp(h1h2	µp(h1h2	ADP
ejpam-5854	138	89	)	)	PUNCT
ejpam-5854	138	90	⪰	⪰	NOUN
ejpam-5854	138	91	µp(h1	µp(h1	NOUN
ejpam-5854	138	92	)	)	PUNCT
ejpam-5854	138	93	,	,	PUNCT
ejpam-5854	138	94	µ	µ	X
ejpam-5854	138	95	n(h1h2	n(h1h2	NOUN
ejpam-5854	138	96	)	)	PUNCT
ejpam-5854	138	97	⪯	⪯	NOUN
ejpam-5854	138	98	µn(h1	µn(h1	NUM
ejpam-5854	138	99	)	)	PUNCT
ejpam-5854	138	100	and	and	CCONJ
ejpam-5854	138	101	ωp(h1h2	ωp(h1h2	NUM
ejpam-5854	138	102	)	)	PUNCT
ejpam-5854	138	103	≥	≥	NOUN
ejpam-5854	138	104	ωp(h1	ωp(h1	NUM
ejpam-5854	138	105	)	)	PUNCT
ejpam-5854	138	106	,	,	PUNCT
ejpam-5854	138	107	ω	ω	PROPN
ejpam-5854	138	108	n(h1h2	n(h1h2	NOUN
ejpam-5854	138	109	)	)	PUNCT
ejpam-5854	138	110	≤	≤	NOUN
ejpam-5854	138	111	ωn(h1	ωn(h1	NOUN
ejpam-5854	138	112	)	)	PUNCT
ejpam-5854	138	113	for	for	ADP
ejpam-5854	138	114	all	all	DET
ejpam-5854	138	115	h1	h1	PROPN
ejpam-5854	138	116	,	,	PUNCT
ejpam-5854	138	117	h2	h2	PROPN
ejpam-5854	138	118	∈	∈	PROPN
ejpam-5854	138	119	s	s	PART
ejpam-5854	138	120	,	,	PUNCT
ejpam-5854	138	121	(	(	PUNCT
ejpam-5854	138	122	3	3	X
ejpam-5854	138	123	)	)	PUNCT
ejpam-5854	138	124	a	a	DET
ejpam-5854	138	125	cubic	cubic	ADJ
ejpam-5854	138	126	bipolar	bipolar	ADJ
ejpam-5854	138	127	fuzzy	fuzzy	ADJ
ejpam-5854	138	128	ideal	ideal	NOUN
ejpam-5854	138	129	(	(	PUNCT
ejpam-5854	138	130	shortly	shortly	ADV
ejpam-5854	138	131	,	,	PUNCT
ejpam-5854	138	132	cbf	cbf	PROPN
ejpam-5854	138	133	ideal	ideal	NOUN
ejpam-5854	138	134	)	)	PUNCT
ejpam-5854	138	135	of	of	ADP
ejpam-5854	138	136	s	s	PROPN
ejpam-5854	138	137	,	,	PUNCT
ejpam-5854	138	138	if	if	SCONJ
ejpam-5854	138	139	it	it	PRON
ejpam-5854	138	140	is	be	AUX
ejpam-5854	138	141	a	a	DET
ejpam-5854	138	142	cbf	cbf	PROPN
ejpam-5854	138	143	left	leave	VERB
ejpam-5854	138	144	ideal	ideal	NOUN
ejpam-5854	138	145	and	and	CCONJ
ejpam-5854	138	146	a	a	DET
ejpam-5854	138	147	cbf	cbf	PROPN
ejpam-5854	138	148	right	right	PROPN
ejpam-5854	138	149	ideal	ideal	NOUN
ejpam-5854	138	150	of	of	ADP
ejpam-5854	138	151	s	s	PROPN
ejpam-5854	138	152	,	,	PUNCT
ejpam-5854	138	153	(	(	PUNCT
ejpam-5854	138	154	4	4	X
ejpam-5854	138	155	)	)	PUNCT
ejpam-5854	138	156	a	a	DET
ejpam-5854	138	157	cubic	cubic	ADJ
ejpam-5854	138	158	bipolar	bipolar	ADJ
ejpam-5854	138	159	fuzzy	fuzzy	ADJ
ejpam-5854	138	160	generalized	generalized	ADJ
ejpam-5854	138	161	bi	bi	NOUN
ejpam-5854	138	162	-	-	NOUN
ejpam-5854	138	163	ideal	ideal	ADJ
ejpam-5854	138	164	(	(	PUNCT
ejpam-5854	138	165	shortly	shortly	ADV
ejpam-5854	138	166	,	,	PUNCT
ejpam-5854	138	167	cbf	cbf	PROPN
ejpam-5854	138	168	generalized	generalize	VERB
ejpam-5854	138	169	bi	bi	NOUN
ejpam-5854	138	170	-	-	NOUN
ejpam-5854	138	171	ideal	ideal	ADJ
ejpam-5854	138	172	)	)	PUNCT
ejpam-5854	138	173	of	of	ADP
ejpam-5854	138	174	s	s	SYM
ejpam-5854	138	175	,	,	PUNCT
ejpam-5854	138	176	if	if	SCONJ
ejpam-5854	138	177	µp(h1h2h3	µp(h1h2h3	PROPN
ejpam-5854	138	178	)	)	PUNCT
ejpam-5854	138	179	⪰	⪰	NOUN
ejpam-5854	138	180	µp(h1)⋏µp(h3	µp(h1)⋏µp(h3	NOUN
ejpam-5854	138	181	)	)	PUNCT
ejpam-5854	138	182	,	,	PUNCT
ejpam-5854	138	183	µ	µ	PRON
ejpam-5854	138	184	n(h1h2h3	n(h1h2h3	NOUN
ejpam-5854	138	185	)	)	PUNCT
ejpam-5854	138	186	⪯	⪯	PROPN
ejpam-5854	138	187	µn(h1)⋎µn(h3	µn(h1)⋎µn(h3	PROPN
ejpam-5854	138	188	)	)	PUNCT
ejpam-5854	138	189	and	and	CCONJ
ejpam-5854	138	190	ω	ω	NUM
ejpam-5854	138	191	p(h1h2h3	p(h1h2h3	NOUN
ejpam-5854	138	192	)	)	PUNCT
ejpam-5854	138	193	≥	≥	NOUN
ejpam-5854	138	194	ωp(h1)∧ωn(h3	ωp(h1)∧ωn(h3	NOUN
ejpam-5854	138	195	)	)	PUNCT
ejpam-5854	138	196	,	,	PUNCT
ejpam-5854	139	1	ω	ω	NUM
ejpam-5854	139	2	n(h1h2h3	n(h1h2h3	NOUN
ejpam-5854	139	3	)	)	PUNCT
ejpam-5854	139	4	≤	≤	NOUN
ejpam-5854	139	5	ωn(h1	ωn(h1	NOUN
ejpam-5854	139	6	)	)	PUNCT
ejpam-5854	139	7	∨	∨	NUM
ejpam-5854	139	8	ωn(h3	ωn(h3	NOUN
ejpam-5854	139	9	)	)	PUNCT
ejpam-5854	139	10	for	for	ADP
ejpam-5854	139	11	all	all	DET
ejpam-5854	139	12	h1	h1	PROPN
ejpam-5854	139	13	,	,	PUNCT
ejpam-5854	139	14	h2	h2	PROPN
ejpam-5854	139	15	,	,	PUNCT
ejpam-5854	139	16	h3	h3	VERB
ejpam-5854	139	17	∈	∈	PROPN
ejpam-5854	139	18	s	s	NOUN
ejpam-5854	139	19	,	,	PUNCT
ejpam-5854	139	20	(	(	PUNCT
ejpam-5854	139	21	5	5	X
ejpam-5854	139	22	)	)	PUNCT
ejpam-5854	139	23	a	a	DET
ejpam-5854	139	24	cubic	cubic	ADJ
ejpam-5854	139	25	bipolar	bipolar	ADJ
ejpam-5854	139	26	fuzzy	fuzzy	ADJ
ejpam-5854	139	27	bi	bi	NOUN
ejpam-5854	139	28	-	-	NOUN
ejpam-5854	139	29	ideal	ideal	ADJ
ejpam-5854	139	30	(	(	PUNCT
ejpam-5854	139	31	shortly	shortly	ADV
ejpam-5854	139	32	,	,	PUNCT
ejpam-5854	139	33	cbf	cbf	PROPN
ejpam-5854	139	34	bi	bi	NOUN
ejpam-5854	139	35	-	-	NOUN
ejpam-5854	139	36	ideal	ideal	ADJ
ejpam-5854	139	37	)	)	PUNCT
ejpam-5854	139	38	of	of	ADP
ejpam-5854	139	39	s	s	PROPN
ejpam-5854	139	40	,	,	PUNCT
ejpam-5854	139	41	if	if	SCONJ
ejpam-5854	139	42	c̈	c̈	NOUN
ejpam-5854	139	43	=	=	SYM
ejpam-5854	139	44	⟨µ	⟨µ	NOUN
ejpam-5854	139	45	,	,	PUNCT
ejpam-5854	139	46	ω⟩	ω⟩	PRON
ejpam-5854	139	47	is	be	AUX
ejpam-5854	139	48	a	a	DET
ejpam-5854	139	49	cbf	cbf	PROPN
ejpam-5854	139	50	subsemigroup	subsemigroup	NOUN
ejpam-5854	139	51	of	of	ADP
ejpam-5854	139	52	s	s	PROPN
ejpam-5854	139	53	,	,	PUNCT
ejpam-5854	139	54	µp(h1h2h3	µp(h1h2h3	ADJ
ejpam-5854	139	55	)	)	PUNCT
ejpam-5854	139	56	⪰	⪰	NOUN
ejpam-5854	139	57	µp(h1)⋏µp(h3	µp(h1)⋏µp(h3	NOUN
ejpam-5854	139	58	)	)	PUNCT
ejpam-5854	139	59	µ	µ	PRON
ejpam-5854	139	60	n(h1h2h3	n(h1h2h3	NOUN
ejpam-5854	139	61	)	)	PUNCT
ejpam-5854	139	62	⪯	⪯	PROPN
ejpam-5854	139	63	µn(h1)⋎µn(h3	µn(h1)⋎µn(h3	PROPN
ejpam-5854	139	64	)	)	PUNCT
ejpam-5854	139	65	and	and	CCONJ
ejpam-5854	139	66	ω	ω	NUM
ejpam-5854	139	67	p(h1h2h3	p(h1h2h3	NOUN
ejpam-5854	139	68	)	)	PUNCT
ejpam-5854	139	69	≥	≥	NOUN
ejpam-5854	139	70	ωp(h1)∧	ωp(h1)∧	NUM
ejpam-5854	139	71	ωn(h3	ωn(h3	NOUN
ejpam-5854	139	72	)	)	PUNCT
ejpam-5854	139	73	,	,	PUNCT
ejpam-5854	140	1	ω	ω	NUM
ejpam-5854	140	2	n(h1h2h3	n(h1h2h3	NOUN
ejpam-5854	140	3	)	)	PUNCT
ejpam-5854	140	4	≤	≤	NOUN
ejpam-5854	140	5	ωn(h1	ωn(h1	NOUN
ejpam-5854	140	6	)	)	PUNCT
ejpam-5854	140	7	∨	∨	NUM
ejpam-5854	140	8	ωn(h3	ωn(h3	NOUN
ejpam-5854	140	9	)	)	PUNCT
ejpam-5854	140	10	for	for	ADP
ejpam-5854	140	11	all	all	DET
ejpam-5854	140	12	h1	h1	PROPN
ejpam-5854	140	13	,	,	PUNCT
ejpam-5854	140	14	h2	h2	PROPN
ejpam-5854	140	15	,	,	PUNCT
ejpam-5854	140	16	h3	h3	VERB
ejpam-5854	140	17	∈	∈	PROPN
ejpam-5854	140	18	s.	s.	PROPN
ejpam-5854	140	19	next	next	ADV
ejpam-5854	140	20	,	,	PUNCT
ejpam-5854	140	21	we	we	PRON
ejpam-5854	140	22	study	study	VERB
ejpam-5854	140	23	the	the	DET
ejpam-5854	140	24	subset	subset	NOUN
ejpam-5854	140	25	and	and	CCONJ
ejpam-5854	140	26	product	product	NOUN
ejpam-5854	140	27	of	of	ADP
ejpam-5854	140	28	the	the	DET
ejpam-5854	140	29	cbf	cbf	PROPN
ejpam-5854	140	30	set	set	VERB
ejpam-5854	140	31	as	as	SCONJ
ejpam-5854	140	32	defined	define	VERB
ejpam-5854	140	33	.	.	PUNCT
ejpam-5854	141	1	let	let	VERB
ejpam-5854	141	2	c̈1	c̈1	NOUN
ejpam-5854	141	3	=	=	SYM
ejpam-5854	141	4	⟨µ	⟨µ	NOUN
ejpam-5854	141	5	,	,	PUNCT
ejpam-5854	141	6	ω⟩	ω⟩	NOUN
ejpam-5854	141	7	and	and	CCONJ
ejpam-5854	141	8	c̈2	c̈2	NOUN
ejpam-5854	141	9	=	=	PUNCT
ejpam-5854	141	10	⟨λ	⟨λ	NUM
ejpam-5854	141	11	,	,	PUNCT
ejpam-5854	141	12	ψ⟩	ψ⟩	X
ejpam-5854	141	13	are	be	AUX
ejpam-5854	141	14	cbf	cbf	PROPN
ejpam-5854	141	15	sets	set	NOUN
ejpam-5854	141	16	of	of	ADP
ejpam-5854	141	17	a	a	DET
ejpam-5854	141	18	semigroup	semigroup	PROPN
ejpam-5854	141	19	s.	s.	PROPN
ejpam-5854	141	20	define	define	NOUN
ejpam-5854	141	21	(	(	PUNCT
ejpam-5854	141	22	i	i	NOUN
ejpam-5854	141	23	)	)	PUNCT
ejpam-5854	142	1	c̈1⊏c̈2	c̈1⊏c̈2	PROPN
ejpam-5854	142	2	if	if	SCONJ
ejpam-5854	142	3	and	and	CCONJ
ejpam-5854	142	4	only	only	ADV
ejpam-5854	142	5	if	if	SCONJ
ejpam-5854	142	6	µp(h	µp(h	NOUN
ejpam-5854	142	7	)	)	PUNCT
ejpam-5854	142	8	⪯	⪯	NOUN
ejpam-5854	142	9	λ	λ	X
ejpam-5854	142	10	p	p	X
ejpam-5854	142	11	(	(	PUNCT
ejpam-5854	142	12	h	h	NOUN
ejpam-5854	142	13	)	)	PUNCT
ejpam-5854	142	14	,	,	PUNCT
ejpam-5854	142	15	µn(h	µn(h	X
ejpam-5854	142	16	)	)	PUNCT
ejpam-5854	142	17	⪰	⪰	NOUN
ejpam-5854	142	18	λ	λ	X
ejpam-5854	142	19	n	n	CCONJ
ejpam-5854	142	20	(	(	PUNCT
ejpam-5854	142	21	h	h	NOUN
ejpam-5854	142	22	)	)	PUNCT
ejpam-5854	142	23	and	and	CCONJ
ejpam-5854	142	24	ωp(h	ωp(h	NOUN
ejpam-5854	142	25	)	)	PUNCT
ejpam-5854	142	26	≤	≤	NOUN
ejpam-5854	142	27	ψp(h	ψp(h	PUNCT
ejpam-5854	142	28	)	)	PUNCT
ejpam-5854	142	29	,	,	PUNCT
ejpam-5854	142	30	ωn(h	ωn(h	NUM
ejpam-5854	142	31	)	)	PUNCT
ejpam-5854	142	32	≥	≥	NOUN
ejpam-5854	142	33	ψn(h	ψn(h	NUM
ejpam-5854	142	34	)	)	PUNCT
ejpam-5854	142	35	,	,	PUNCT
ejpam-5854	142	36	for	for	ADP
ejpam-5854	142	37	all	all	DET
ejpam-5854	142	38	h	h	NOUN
ejpam-5854	142	39	∈	∈	PROPN
ejpam-5854	142	40	s.	s.	PROPN
ejpam-5854	142	41	p.	p.	PROPN
ejpam-5854	142	42	khamrot	khamrot	PROPN
ejpam-5854	142	43	,	,	PUNCT
ejpam-5854	142	44	n.	n.	PROPN
ejpam-5854	142	45	deetae	deetae	PROPN
ejpam-5854	142	46	,	,	PUNCT
ejpam-5854	142	47	t.	t.	PROPN
ejpam-5854	142	48	gaketem	gaketem	PROPN
ejpam-5854	142	49	/	/	SYM
ejpam-5854	142	50	eur	eur	PROPN
ejpam-5854	142	51	.	.	PUNCT
ejpam-5854	143	1	j.	j.	PROPN
ejpam-5854	143	2	pure	pure	PROPN
ejpam-5854	143	3	appl	appl	PROPN
ejpam-5854	143	4	.	.	PROPN
ejpam-5854	143	5	math	math	PROPN
ejpam-5854	143	6	,	,	PUNCT
ejpam-5854	143	7	18	18	NUM
ejpam-5854	143	8	(	(	PUNCT
ejpam-5854	143	9	2	2	NUM
ejpam-5854	143	10	)	)	PUNCT
ejpam-5854	143	11	(	(	PUNCT
ejpam-5854	143	12	2025	2025	NUM
ejpam-5854	143	13	)	)	PUNCT
ejpam-5854	143	14	,	,	PUNCT
ejpam-5854	143	15	5854	5854	NUM
ejpam-5854	143	16	7	7	NUM
ejpam-5854	143	17	of	of	ADP
ejpam-5854	143	18	14	14	NUM
ejpam-5854	143	19	(	(	PUNCT
ejpam-5854	143	20	ii	ii	NOUN
ejpam-5854	143	21	)	)	PUNCT
ejpam-5854	143	22	c̈1⊓c̈2	c̈1⊓c̈2	PROPN
ejpam-5854	143	23	=	=	SYM
ejpam-5854	143	24	⟨µ	⟨µ	NOUN
ejpam-5854	143	25	⊓	⊓	PROPN
ejpam-5854	143	26	λ	λ	PROPN
ejpam-5854	143	27	,	,	PUNCT
ejpam-5854	143	28	ω	ω	NOUN
ejpam-5854	143	29	∩	∩	NOUN
ejpam-5854	143	30	ψ⟩	ψ⟩	PUNCT
ejpam-5854	143	31	if	if	SCONJ
ejpam-5854	143	32	and	and	CCONJ
ejpam-5854	143	33	only	only	ADV
ejpam-5854	143	34	if	if	SCONJ
ejpam-5854	143	35	(	(	PUNCT
ejpam-5854	143	36	µp	µp	PROPN
ejpam-5854	143	37	⊓	⊓	PROPN
ejpam-5854	143	38	λp)(h	λp)(h	PROPN
ejpam-5854	143	39	)	)	PUNCT
ejpam-5854	144	1	=	=	PUNCT
ejpam-5854	145	1	(	(	PUNCT
ejpam-5854	145	2	µp(h)⋏	µp(h)⋏	X
ejpam-5854	145	3	λ	λ	X
ejpam-5854	145	4	p	p	X
ejpam-5854	145	5	(	(	PUNCT
ejpam-5854	145	6	h	h	NOUN
ejpam-5854	145	7	)	)	PUNCT
ejpam-5854	145	8	)	)	PUNCT
ejpam-5854	145	9	,	,	PUNCT
ejpam-5854	145	10	(	(	PUNCT
ejpam-5854	145	11	µn	µn	PROPN
ejpam-5854	145	12	⊓	⊓	PROPN
ejpam-5854	145	13	λn)(h	λn)(h	NUM
ejpam-5854	145	14	)	)	PUNCT
ejpam-5854	145	15	=	=	PUNCT
ejpam-5854	145	16	(	(	PUNCT
ejpam-5854	145	17	µn(h)⋎	µn(h)⋎	X
ejpam-5854	145	18	λ	λ	PROPN
ejpam-5854	145	19	n	n	X
ejpam-5854	145	20	(	(	PUNCT
ejpam-5854	145	21	h	h	NOUN
ejpam-5854	145	22	)	)	PUNCT
ejpam-5854	145	23	)	)	PUNCT
ejpam-5854	145	24	and	and	CCONJ
ejpam-5854	145	25	(	(	PUNCT
ejpam-5854	145	26	ωp	ωp	NOUN
ejpam-5854	145	27	∩	∩	NOUN
ejpam-5854	145	28	ψp)(h	ψp)(h	PROPN
ejpam-5854	145	29	)	)	PUNCT
ejpam-5854	145	30	=	=	PUNCT
ejpam-5854	145	31	(	(	PUNCT
ejpam-5854	145	32	ωp(h	ωp(h	NOUN
ejpam-5854	145	33	)	)	PUNCT
ejpam-5854	145	34	∧	∧	NOUN
ejpam-5854	145	35	ψp(h	ψp(h	NOUN
ejpam-5854	145	36	)	)	PUNCT
ejpam-5854	145	37	)	)	PUNCT
ejpam-5854	145	38	,	,	PUNCT
ejpam-5854	145	39	(	(	PUNCT
ejpam-5854	145	40	ωn	ωn	PROPN
ejpam-5854	145	41	∩	∩	NOUN
ejpam-5854	145	42	ψn)(h	ψn)(h	PROPN
ejpam-5854	145	43	)	)	PUNCT
ejpam-5854	145	44	=	=	PRON
ejpam-5854	145	45	(	(	PUNCT
ejpam-5854	145	46	ωn(h	ωn(h	NOUN
ejpam-5854	145	47	)	)	PUNCT
ejpam-5854	145	48	∨	∨	NUM
ejpam-5854	145	49	ψn(h	ψn(h	NUM
ejpam-5854	145	50	)	)	PUNCT
ejpam-5854	145	51	for	for	ADP
ejpam-5854	145	52	all	all	DET
ejpam-5854	145	53	h	h	NOUN
ejpam-5854	145	54	∈	∈	PROPN
ejpam-5854	145	55	s.	s.	PROPN
ejpam-5854	145	56	(	(	PUNCT
ejpam-5854	145	57	iii	iii	X
ejpam-5854	145	58	)	)	PUNCT
ejpam-5854	145	59	c̈1	c̈1	NOUN
ejpam-5854	145	60	⊛	⊛	NUM
ejpam-5854	145	61	c̈2	c̈2	NOUN
ejpam-5854	145	62	=	=	PUNCT
ejpam-5854	145	63	⟨µ⃝	⟨µ⃝	PROPN
ejpam-5854	145	64	λ	λ	PROPN
ejpam-5854	145	65	,	,	PUNCT
ejpam-5854	145	66	ω	ω	NUM
ejpam-5854	145	67	∗	∗	NOUN
ejpam-5854	145	68	ψ⟩	ψ⟩	PUNCT
ejpam-5854	145	69	and	and	CCONJ
ejpam-5854	145	70	define	define	VERB
ejpam-5854	145	71	µ⃝	µ⃝	NOUN
ejpam-5854	145	72	λ	λ	PROPN
ejpam-5854	145	73	as	as	SCONJ
ejpam-5854	145	74	follows	follow	VERB
ejpam-5854	145	75	.	.	PUNCT
ejpam-5854	146	1	for	for	ADP
ejpam-5854	146	2	h	h	PRON
ejpam-5854	146	3	∈	∈	PROPN
ejpam-5854	146	4	s	s	PART
ejpam-5854	146	5	(	(	PUNCT
ejpam-5854	146	6	µp	µp	NOUN
ejpam-5854	146	7	⃝	⃝	NOUN
ejpam-5854	146	8	λ	λ	PROPN
ejpam-5854	146	9	p	p	NOUN
ejpam-5854	146	10	)	)	PUNCT
ejpam-5854	146	11	(	(	PUNCT
ejpam-5854	146	12	h	h	NOUN
ejpam-5854	146	13	)	)	PUNCT
ejpam-5854	146	14	=	=	PUNCT
ejpam-5854	146	15			PUNCT
ejpam-5854	146	16	⋎	⋎	NOUN
ejpam-5854	146	17	(	(	PUNCT
ejpam-5854	146	18	k	k	NOUN
ejpam-5854	146	19	,	,	PUNCT
ejpam-5854	146	20	o)∈ah	o)∈ah	PROPN
ejpam-5854	146	21	{	{	PUNCT
ejpam-5854	146	22	µp(k)⋏	µp(k)⋏	NOUN
ejpam-5854	146	23	λ	λ	X
ejpam-5854	146	24	p	p	X
ejpam-5854	146	25	(	(	PUNCT
ejpam-5854	146	26	o	o	NOUN
ejpam-5854	146	27	)	)	PUNCT
ejpam-5854	146	28	}	}	PUNCT
ejpam-5854	146	29	if	if	SCONJ
ejpam-5854	146	30	ah	ah	INTJ
ejpam-5854	146	31	̸=	̸=	PROPN
ejpam-5854	146	32	∅	∅	VERB
ejpam-5854	146	33	0	0	PUNCT
ejpam-5854	146	34	if	if	SCONJ
ejpam-5854	146	35	ah	ah	INTJ
ejpam-5854	146	36	=	=	NOUN
ejpam-5854	146	37	∅	∅	NOUN
ejpam-5854	146	38	,	,	PUNCT
ejpam-5854	146	39	(	(	PUNCT
ejpam-5854	146	40	µn	µn	NOUN
ejpam-5854	146	41	⃝	⃝	NOUN
ejpam-5854	146	42	λ	λ	NOUN
ejpam-5854	146	43	n	n	PRON
ejpam-5854	146	44	)	)	PUNCT
ejpam-5854	146	45	(	(	PUNCT
ejpam-5854	146	46	h	h	NOUN
ejpam-5854	146	47	)	)	PUNCT
ejpam-5854	146	48	=	=	PUNCT
ejpam-5854	146	49			PUNCT
ejpam-5854	146	50	⋏	⋏	PROPN
ejpam-5854	146	51	(	(	PUNCT
ejpam-5854	146	52	k	k	X
ejpam-5854	146	53	,	,	PUNCT
ejpam-5854	146	54	o)∈ah	o)∈ah	PROPN
ejpam-5854	146	55	{	{	PUNCT
ejpam-5854	146	56	µn(k)⋎	µn(k)⋎	PROPN
ejpam-5854	146	57	λ	λ	PROPN
ejpam-5854	146	58	n	n	CCONJ
ejpam-5854	146	59	(	(	PUNCT
ejpam-5854	146	60	o	o	NOUN
ejpam-5854	146	61	)	)	PUNCT
ejpam-5854	146	62	}	}	PUNCT
ejpam-5854	146	63	if	if	SCONJ
ejpam-5854	146	64	ah	ah	INTJ
ejpam-5854	146	65	̸=	̸=	PROPN
ejpam-5854	146	66	∅	∅	VERB
ejpam-5854	146	67	0	0	PUNCT
ejpam-5854	147	1	if	if	SCONJ
ejpam-5854	147	2	ah	ah	INTJ
ejpam-5854	147	3	=	=	NOUN
ejpam-5854	147	4	∅	∅	NOUN
ejpam-5854	147	5	,	,	PUNCT
ejpam-5854	147	6	and	and	CCONJ
ejpam-5854	147	7	ω	ω	NUM
ejpam-5854	147	8	∗	∗	NOUN
ejpam-5854	147	9	ψ	ψ	NOUN
ejpam-5854	147	10	is	be	AUX
ejpam-5854	147	11	a	a	DET
ejpam-5854	147	12	product	product	NOUN
ejpam-5854	147	13	of	of	ADP
ejpam-5854	147	14	a	a	DET
ejpam-5854	147	15	bf	bf	NOUN
ejpam-5854	147	16	set	set	NOUN
ejpam-5854	147	17	.	.	PUNCT
ejpam-5854	148	1	definition	definition	NOUN
ejpam-5854	148	2	13	13	NUM
ejpam-5854	148	3	.	.	PUNCT
ejpam-5854	149	1	a	a	DET
ejpam-5854	149	2	cubic	cubic	ADJ
ejpam-5854	149	3	biopolar	biopolar	NOUN
ejpam-5854	149	4	set	set	NOUN
ejpam-5854	149	5	c̈	c̈	NOUN
ejpam-5854	149	6	=	=	SYM
ejpam-5854	149	7	⟨µ	⟨µ	NOUN
ejpam-5854	149	8	,	,	PUNCT
ejpam-5854	149	9	ω⟩	ω⟩	NOUN
ejpam-5854	149	10	of	of	ADP
ejpam-5854	149	11	s	s	PROPN
ejpam-5854	149	12	is	be	AUX
ejpam-5854	149	13	called	call	VERB
ejpam-5854	149	14	a	a	DET
ejpam-5854	149	15	cubic	cubic	ADJ
ejpam-5854	149	16	biopolar	biopolar	ADJ
ejpam-5854	149	17	fuzzy	fuzzy	ADJ
ejpam-5854	149	18	quasi	quasi	ADJ
ejpam-5854	149	19	ideal	ideal	NOUN
ejpam-5854	149	20	(	(	PUNCT
ejpam-5854	149	21	shortly	shortly	ADV
ejpam-5854	149	22	,	,	PUNCT
ejpam-5854	149	23	cbf	cbf	PROPN
ejpam-5854	149	24	quasi	quasi	PROPN
ejpam-5854	149	25	ideal	ideal	PROPN
ejpam-5854	149	26	)	)	PUNCT
ejpam-5854	149	27	of	of	ADP
ejpam-5854	149	28	s	s	PROPN
ejpam-5854	149	29	,	,	PUNCT
ejpam-5854	149	30	if	if	SCONJ
ejpam-5854	149	31	(	(	PUNCT
ejpam-5854	149	32	s⃝	s⃝	PROPN
ejpam-5854	149	33	µ	µ	X
ejpam-5854	149	34	)	)	PUNCT
ejpam-5854	149	35	⊓	⊓	PROPN
ejpam-5854	149	36	(	(	PUNCT
ejpam-5854	149	37	µ⃝s)⊏µ	µ⃝s)⊏µ	PROPN
ejpam-5854	149	38	and	and	CCONJ
ejpam-5854	149	39	(	(	PUNCT
ejpam-5854	149	40	s	s	NOUN
ejpam-5854	149	41	∗	∗	NOUN
ejpam-5854	149	42	ω	ω	NOUN
ejpam-5854	149	43	)	)	PUNCT
ejpam-5854	149	44	∩	∩	NOUN
ejpam-5854	149	45	(	(	PUNCT
ejpam-5854	149	46	ω	ω	NOUN
ejpam-5854	149	47	∗s	∗s	PROPN
ejpam-5854	149	48	)	)	PUNCT
ejpam-5854	149	49	⊆	⊆	NUM
ejpam-5854	149	50	ω	ω	NOUN
ejpam-5854	149	51	.	.	PUNCT
ejpam-5854	150	1	the	the	DET
ejpam-5854	150	2	follows	follow	NOUN
ejpam-5854	150	3	theorem	theorem	NOUN
ejpam-5854	150	4	are	be	AUX
ejpam-5854	150	5	basic	basic	ADJ
ejpam-5854	150	6	propeties	propetie	NOUN
ejpam-5854	150	7	of	of	ADP
ejpam-5854	150	8	cbf	cbf	PROPN
ejpam-5854	150	9	ideal	ideal	NOUN
ejpam-5854	150	10	of	of	ADP
ejpam-5854	150	11	a	a	DET
ejpam-5854	150	12	semigroup	semigroup	PROPN
ejpam-5854	150	13	s.	s.	PROPN
ejpam-5854	150	14	theorem	theorem	VERB
ejpam-5854	150	15	1	1	NUM
ejpam-5854	150	16	.	.	PUNCT
ejpam-5854	151	1	every	every	DET
ejpam-5854	151	2	cbf	cbf	PROPN
ejpam-5854	151	3	ideal	ideal	NOUN
ejpam-5854	151	4	of	of	ADP
ejpam-5854	151	5	a	a	DET
ejpam-5854	151	6	semigroup	semigroup	NOUN
ejpam-5854	151	7	s	s	PART
ejpam-5854	151	8	is	be	AUX
ejpam-5854	151	9	a	a	DET
ejpam-5854	151	10	cbf	cbf	PROPN
ejpam-5854	151	11	interior	interior	PROPN
ejpam-5854	151	12	ideal	ideal	NOUN
ejpam-5854	151	13	of	of	ADP
ejpam-5854	151	14	s.	s.	PROPN
ejpam-5854	151	15	proof	proof	PROPN
ejpam-5854	151	16	.	.	PUNCT
ejpam-5854	152	1	let	let	VERB
ejpam-5854	152	2	c̈	c̈	NOUN
ejpam-5854	152	3	=	=	SYM
ejpam-5854	152	4	⟨µ	⟨µ	NOUN
ejpam-5854	152	5	,	,	PUNCT
ejpam-5854	153	1	ω⟩	ω⟩	PRON
ejpam-5854	153	2	be	be	AUX
ejpam-5854	153	3	a	a	DET
ejpam-5854	153	4	cbf	cbf	PROPN
ejpam-5854	153	5	ideal	ideal	NOUN
ejpam-5854	153	6	of	of	ADP
ejpam-5854	153	7	s	s	PRON
ejpam-5854	153	8	and	and	CCONJ
ejpam-5854	153	9	let	let	VERB
ejpam-5854	153	10	h1	h1	PROPN
ejpam-5854	153	11	,	,	PUNCT
ejpam-5854	153	12	h2	h2	PROPN
ejpam-5854	153	13	∈	∈	PROPN
ejpam-5854	153	14	s.	s.	PROPN
ejpam-5854	153	15	then	then	ADV
ejpam-5854	153	16	,	,	PUNCT
ejpam-5854	153	17	c̈	c̈	PROPN
ejpam-5854	153	18	=	=	SYM
ejpam-5854	153	19	⟨µ	⟨µ	NOUN
ejpam-5854	153	20	,	,	PUNCT
ejpam-5854	153	21	ω⟩	ω⟩	PRON
ejpam-5854	153	22	is	be	AUX
ejpam-5854	153	23	a	a	DET
ejpam-5854	153	24	cbf	cbf	PROPN
ejpam-5854	153	25	left	leave	VERB
ejpam-5854	153	26	ideal	ideal	NOUN
ejpam-5854	153	27	and	and	CCONJ
ejpam-5854	153	28	cbf	cbf	PROPN
ejpam-5854	153	29	right	right	PROPN
ejpam-5854	153	30	ideal	ideal	NOUN
ejpam-5854	153	31	of	of	ADP
ejpam-5854	153	32	s.	s.	PROPN
ejpam-5854	153	33	thus	thus	ADV
ejpam-5854	153	34	,	,	PUNCT
ejpam-5854	153	35	µp(h1h2	µp(h1h2	ADP
ejpam-5854	153	36	)	)	PUNCT
ejpam-5854	153	37	⪰	⪰	NOUN
ejpam-5854	153	38	µp(h2	µp(h2	NOUN
ejpam-5854	153	39	)	)	PUNCT
ejpam-5854	153	40	,	,	PUNCT
ejpam-5854	153	41	µ	µ	X
ejpam-5854	153	42	n(h1h2	n(h1h2	NOUN
ejpam-5854	153	43	)	)	PUNCT
ejpam-5854	153	44	⪯	⪯	NOUN
ejpam-5854	153	45	µp(h2	µp(h2	NOUN
ejpam-5854	153	46	)	)	PUNCT
ejpam-5854	153	47	and	and	CCONJ
ejpam-5854	153	48	ωp(h1h2	ωp(h1h2	NUM
ejpam-5854	153	49	)	)	PUNCT
ejpam-5854	153	50	≥	≥	NOUN
ejpam-5854	153	51	ωn(h2	ωn(h2	NOUN
ejpam-5854	153	52	)	)	PUNCT
ejpam-5854	153	53	,	,	PUNCT
ejpam-5854	153	54	ω	ω	PROPN
ejpam-5854	153	55	n(h1h2	n(h1h2	NOUN
ejpam-5854	153	56	)	)	PUNCT
ejpam-5854	153	57	≤	≤	NOUN
ejpam-5854	153	58	ωn(h2	ωn(h2	NOUN
ejpam-5854	153	59	)	)	PUNCT
ejpam-5854	153	60	.	.	PUNCT
ejpam-5854	154	1	hence	hence	ADV
ejpam-5854	154	2	,	,	PUNCT
ejpam-5854	154	3	µp(h1h2	µp(h1h2	CCONJ
ejpam-5854	154	4	)	)	PUNCT
ejpam-5854	154	5	⪰	⪰	NOUN
ejpam-5854	154	6	µp(h1)⋏	µp(h1)⋏	ADP
ejpam-5854	154	7	µp(h2	µp(h2	NOUN
ejpam-5854	154	8	)	)	PUNCT
ejpam-5854	154	9	,	,	PUNCT
ejpam-5854	154	10	µ	µ	X
ejpam-5854	154	11	n(h1h2	n(h1h2	NOUN
ejpam-5854	154	12	)	)	PUNCT
ejpam-5854	154	13	⪯	⪯	NOUN
ejpam-5854	155	1	µp(h1)⋏	µp(h1)⋏	ADP
ejpam-5854	155	2	µp(h2	µp(h2	NOUN
ejpam-5854	155	3	)	)	PUNCT
ejpam-5854	155	4	and	and	CCONJ
ejpam-5854	155	5	ωp(h1h2	ωp(h1h2	NUM
ejpam-5854	155	6	)	)	PUNCT
ejpam-5854	155	7	≥	≥	NOUN
ejpam-5854	155	8	ωn(h2	ωn(h2	NOUN
ejpam-5854	155	9	)	)	PUNCT
ejpam-5854	155	10	∧	∧	PROPN
ejpam-5854	155	11	ωn(h2	ωn(h2	NOUN
ejpam-5854	155	12	)	)	PUNCT
ejpam-5854	155	13	,	,	PUNCT
ejpam-5854	155	14	ω	ω	PROPN
ejpam-5854	155	15	n(h1h2	n(h1h2	NOUN
ejpam-5854	155	16	)	)	PUNCT
ejpam-5854	155	17	≤	≤	NUM
ejpam-5854	155	18	ωn(h1	ωn(h1	NOUN
ejpam-5854	155	19	)	)	PUNCT
ejpam-5854	155	20	∨	∨	NUM
ejpam-5854	155	21	ωn(h2	ωn(h2	NOUN
ejpam-5854	155	22	)	)	PUNCT
ejpam-5854	155	23	.	.	PUNCT
ejpam-5854	156	1	this	this	PRON
ejpam-5854	156	2	shows	show	VERB
ejpam-5854	156	3	that	that	SCONJ
ejpam-5854	156	4	c̈	c̈	NOUN
ejpam-5854	156	5	=	=	SYM
ejpam-5854	156	6	⟨µ	⟨µ	NOUN
ejpam-5854	156	7	,	,	PUNCT
ejpam-5854	156	8	ω⟩	ω⟩	PRON
ejpam-5854	156	9	is	be	AUX
ejpam-5854	156	10	a	a	DET
ejpam-5854	156	11	cbf	cbf	PROPN
ejpam-5854	156	12	subsemigroup	subsemigroup	NOUN
ejpam-5854	156	13	of	of	ADP
ejpam-5854	156	14	s.	s.	PROPN
ejpam-5854	156	15	let	let	VERB
ejpam-5854	156	16	h1	h1	PROPN
ejpam-5854	156	17	,	,	PUNCT
ejpam-5854	156	18	h2	h2	PROPN
ejpam-5854	156	19	,	,	PUNCT
ejpam-5854	156	20	h3	h3	VERB
ejpam-5854	156	21	∈	∈	PROPN
ejpam-5854	156	22	s.	s.	PROPN
ejpam-5854	156	23	then	then	ADV
ejpam-5854	156	24	,	,	PUNCT
ejpam-5854	156	25	µp(h1h2h3	µp(h1h2h3	PROPN
ejpam-5854	156	26	)	)	PUNCT
ejpam-5854	156	27	=	=	SYM
ejpam-5854	156	28	µp(h1(h2h3	µp(h1(h2h3	ADJ
ejpam-5854	156	29	)	)	PUNCT
ejpam-5854	156	30	)	)	PUNCT
ejpam-5854	156	31	⪰	⪰	NOUN
ejpam-5854	156	32	µp(h2h3	µp(h2h3	ADV
ejpam-5854	156	33	)	)	PUNCT
ejpam-5854	156	34	⪰	⪰	NOUN
ejpam-5854	156	35	µp(h2	µp(h2	NOUN
ejpam-5854	156	36	)	)	PUNCT
ejpam-5854	156	37	,	,	PUNCT
ejpam-5854	156	38	µn(h1h2h3	µn(h1h2h3	ADV
ejpam-5854	156	39	)	)	PUNCT
ejpam-5854	156	40	=	=	SYM
ejpam-5854	156	41	µn(h1(h2h3	µn(h1(h2h3	PROPN
ejpam-5854	156	42	)	)	PUNCT
ejpam-5854	156	43	)	)	PUNCT
ejpam-5854	156	44	⪯	⪯	NOUN
ejpam-5854	156	45	µn(h2h3	µn(h2h3	PROPN
ejpam-5854	156	46	)	)	PUNCT
ejpam-5854	156	47	⪯	⪯	NOUN
ejpam-5854	156	48	µn(h2	µn(h2	NOUN
ejpam-5854	156	49	)	)	PUNCT
ejpam-5854	156	50	and	and	CCONJ
ejpam-5854	156	51	ωp(h1h2h3	ωp(h1h2h3	ADJ
ejpam-5854	156	52	)	)	PUNCT
ejpam-5854	156	53	=	=	SYM
ejpam-5854	156	54	ωp(h1(h2h3	ωp(h1(h2h3	PROPN
ejpam-5854	156	55	)	)	PUNCT
ejpam-5854	156	56	)	)	PUNCT
ejpam-5854	156	57	≥	≥	X
ejpam-5854	156	58	ωp(h2h3	ωp(h2h3	NUM
ejpam-5854	156	59	)	)	PUNCT
ejpam-5854	156	60	≥	≥	NOUN
ejpam-5854	156	61	ωp(h2	ωp(h2	NOUN
ejpam-5854	156	62	)	)	PUNCT
ejpam-5854	156	63	,	,	PUNCT
ejpam-5854	156	64	ωn(h1h2h3	ωn(h1h2h3	NOUN
ejpam-5854	156	65	)	)	PUNCT
ejpam-5854	156	66	=	=	SYM
ejpam-5854	156	67	ωn(h1(h2h3	ωn(h1(h2h3	PROPN
ejpam-5854	156	68	)	)	PUNCT
ejpam-5854	156	69	)	)	PUNCT
ejpam-5854	156	70	≤	≤	NUM
ejpam-5854	156	71	ωn(h2h3	ωn(h2h3	ADP
ejpam-5854	156	72	)	)	PUNCT
ejpam-5854	156	73	≥	≥	NUM
ejpam-5854	156	74	ωnωn(h2	ωnωn(h2	NOUN
ejpam-5854	156	75	)	)	PUNCT
ejpam-5854	156	76	.	.	PUNCT
ejpam-5854	157	1	thus	thus	ADV
ejpam-5854	157	2	,	,	PUNCT
ejpam-5854	157	3	c̈	c̈	NOUN
ejpam-5854	157	4	=	=	SYM
ejpam-5854	157	5	⟨µ	⟨µ	NOUN
ejpam-5854	157	6	,	,	PUNCT
ejpam-5854	157	7	ω⟩	ω⟩	PRON
ejpam-5854	157	8	is	be	AUX
ejpam-5854	157	9	a	a	DET
ejpam-5854	157	10	cbf	cbf	PROPN
ejpam-5854	157	11	interior	interior	PROPN
ejpam-5854	157	12	ideal	ideal	NOUN
ejpam-5854	157	13	of	of	ADP
ejpam-5854	157	14	s.	s.	PROPN
ejpam-5854	157	15	theorem	theorem	VERB
ejpam-5854	157	16	2	2	NUM
ejpam-5854	157	17	.	.	PUNCT
ejpam-5854	158	1	every	every	DET
ejpam-5854	158	2	cbf	cbf	PROPN
ejpam-5854	158	3	quasi	quasi	PROPN
ejpam-5854	158	4	ideal	ideal	NOUN
ejpam-5854	158	5	of	of	ADP
ejpam-5854	158	6	a	a	DET
ejpam-5854	158	7	semigroup	semigroup	NOUN
ejpam-5854	158	8	s	s	PART
ejpam-5854	158	9	is	be	AUX
ejpam-5854	158	10	a	a	DET
ejpam-5854	158	11	cbf	cbf	PROPN
ejpam-5854	158	12	bi	bi	NOUN
ejpam-5854	158	13	-	-	NOUN
ejpam-5854	158	14	ideal	ideal	NOUN
ejpam-5854	158	15	of	of	ADP
ejpam-5854	158	16	s.	s.	PROPN
ejpam-5854	158	17	proof	proof	PROPN
ejpam-5854	158	18	.	.	PUNCT
ejpam-5854	159	1	assume	assume	VERB
ejpam-5854	159	2	that	that	SCONJ
ejpam-5854	159	3	c̈	c̈	NOUN
ejpam-5854	159	4	=	=	SYM
ejpam-5854	159	5	⟨µ	⟨µ	NOUN
ejpam-5854	159	6	,	,	PUNCT
ejpam-5854	159	7	ω⟩	ω⟩	PRON
ejpam-5854	159	8	is	be	AUX
ejpam-5854	159	9	a	a	DET
ejpam-5854	159	10	cbf	cbf	PROPN
ejpam-5854	159	11	quasi	quasi	PROPN
ejpam-5854	159	12	ideal	ideal	NOUN
ejpam-5854	159	13	of	of	ADP
ejpam-5854	159	14	s	s	PRON
ejpam-5854	159	15	and	and	CCONJ
ejpam-5854	159	16	h1	h1	PROPN
ejpam-5854	159	17	,	,	PUNCT
ejpam-5854	159	18	h2	h2	PROPN
ejpam-5854	159	19	∈	∈	PROPN
ejpam-5854	159	20	s.	s.	PROPN
ejpam-5854	159	21	then	then	ADV
ejpam-5854	159	22	,	,	PUNCT
ejpam-5854	159	23	µp(h1h2	µp(h1h2	CCONJ
ejpam-5854	159	24	)	)	PUNCT
ejpam-5854	159	25	⪰	⪰	NOUN
ejpam-5854	159	26	(	(	PUNCT
ejpam-5854	159	27	µp	µp	NOUN
ejpam-5854	159	28	⃝s	⃝	VERB
ejpam-5854	159	29	p	p	NOUN
ejpam-5854	159	30	)	)	PUNCT
ejpam-5854	159	31	(	(	PUNCT
ejpam-5854	159	32	h1h2)⋏	h1h2)⋏	NOUN
ejpam-5854	159	33	(	(	PUNCT
ejpam-5854	159	34	s	s	VERB
ejpam-5854	159	35	p	p	NOUN
ejpam-5854	159	36	⃝	⃝	NOUN
ejpam-5854	159	37	µp)(h1h2	µp)(h1h2	NOUN
ejpam-5854	159	38	)	)	PUNCT
ejpam-5854	160	1	=	=	SYM
ejpam-5854	160	2	⋎	⋎	NOUN
ejpam-5854	160	3	(	(	PUNCT
ejpam-5854	160	4	i	i	PRON
ejpam-5854	160	5	,	,	PUNCT
ejpam-5854	160	6	j)∈ah1h2	j)∈ah1h2	PROPN
ejpam-5854	160	7	{	{	PUNCT
ejpam-5854	160	8	µp(i)⋏s	µp(i)⋏s	NOUN
ejpam-5854	160	9	p	p	X
ejpam-5854	160	10	(	(	PUNCT
ejpam-5854	160	11	j)}⋏	j)}⋏	NOUN
ejpam-5854	160	12	⋎	⋎	NOUN
ejpam-5854	160	13	(	(	PUNCT
ejpam-5854	160	14	k	k	NOUN
ejpam-5854	160	15	,	,	PUNCT
ejpam-5854	160	16	o)∈ah1h2	o)∈ah1h2	PROPN
ejpam-5854	160	17	{	{	PUNCT
ejpam-5854	160	18	sp	sp	NOUN
ejpam-5854	160	19	(	(	PUNCT
ejpam-5854	160	20	k)⋏	k)⋏	VERB
ejpam-5854	160	21	µp(o	µp(o	NOUN
ejpam-5854	160	22	)	)	PUNCT
ejpam-5854	160	23	}	}	PUNCT
ejpam-5854	160	24	⪰	⪰	VERB
ejpam-5854	160	25	µp(h1)⋏s	µp(h1)⋏s	NOUN
ejpam-5854	160	26	p	p	X
ejpam-5854	160	27	(	(	PUNCT
ejpam-5854	160	28	h2)⋏s	h2)⋏s	NOUN
ejpam-5854	160	29	p	p	X
ejpam-5854	160	30	(	(	PUNCT
ejpam-5854	160	31	h1)⋏	h1)⋏	NOUN
ejpam-5854	160	32	µp(h2	µp(h2	NOUN
ejpam-5854	160	33	)	)	PUNCT
ejpam-5854	160	34	=	=	PUNCT
ejpam-5854	160	35	µp(h1)⋏	µp(h1)⋏	VERB
ejpam-5854	160	36	1⋏	1⋏	NUM
ejpam-5854	160	37	1⋏	1⋏	NUM
ejpam-5854	160	38	µp(h2	µp(h2	NOUN
ejpam-5854	160	39	)	)	PUNCT
ejpam-5854	160	40	=	=	SYM
ejpam-5854	161	1	µp(h1)⋏	µp(h1)⋏	ADP
ejpam-5854	161	2	µp(h2	µp(h2	NOUN
ejpam-5854	161	3	)	)	PUNCT
ejpam-5854	161	4	,	,	PUNCT
ejpam-5854	161	5	µn(h1h2	µn(h1h2	PROPN
ejpam-5854	161	6	)	)	PUNCT
ejpam-5854	161	7	⪯	⪯	NOUN
ejpam-5854	161	8	(	(	PUNCT
ejpam-5854	161	9	µn	µn	PROPN
ejpam-5854	161	10	⃝s	⃝s	NUM
ejpam-5854	161	11	n	n	NOUN
ejpam-5854	161	12	)	)	PUNCT
ejpam-5854	161	13	(	(	PUNCT
ejpam-5854	161	14	h1h2)⋎	h1h2)⋎	PROPN
ejpam-5854	161	15	(	(	PUNCT
ejpam-5854	161	16	s	s	NOUN
ejpam-5854	161	17	n	n	PRON
ejpam-5854	161	18	⃝	⃝	DET
ejpam-5854	161	19	µn)(h1h2	µn)(h1h2	NOUN
ejpam-5854	161	20	)	)	PUNCT
ejpam-5854	162	1	=	=	SYM
ejpam-5854	162	2	⋏	⋏	PROPN
ejpam-5854	162	3	(	(	PUNCT
ejpam-5854	162	4	i	i	PRON
ejpam-5854	162	5	,	,	PUNCT
ejpam-5854	162	6	j)∈ah1h2	j)∈ah1h2	PROPN
ejpam-5854	162	7	{	{	PUNCT
ejpam-5854	162	8	µn(i)⋎s	µn(i)⋎s	PROPN
ejpam-5854	162	9	n	n	CCONJ
ejpam-5854	162	10	(	(	PUNCT
ejpam-5854	162	11	j)}⋎	j)}⋎	PROPN
ejpam-5854	162	12	⋏	⋏	PROPN
ejpam-5854	162	13	(	(	PUNCT
ejpam-5854	162	14	k	k	X
ejpam-5854	162	15	,	,	PUNCT
ejpam-5854	162	16	o)∈ah1h2	o)∈ah1h2	PROPN
ejpam-5854	162	17	{	{	PUNCT
ejpam-5854	162	18	sn	sn	PROPN
ejpam-5854	162	19	(	(	PUNCT
ejpam-5854	162	20	k)⋎	k)⋎	PROPN
ejpam-5854	162	21	µn(o	µn(o	PUNCT
ejpam-5854	162	22	)	)	PUNCT
ejpam-5854	162	23	}	}	PUNCT
ejpam-5854	162	24	⪯	⪯	VERB
ejpam-5854	162	25	µn(h1)⋎s	µn(h1)⋎s	X
ejpam-5854	162	26	n	n	CCONJ
ejpam-5854	162	27	(	(	PUNCT
ejpam-5854	162	28	h2)⋏s	h2)⋏s	NOUN
ejpam-5854	162	29	n	n	PRON
ejpam-5854	162	30	(	(	PUNCT
ejpam-5854	162	31	h1)⋏	h1)⋏	NOUN
ejpam-5854	162	32	µn(h2	µn(h2	NOUN
ejpam-5854	162	33	)	)	PUNCT
ejpam-5854	162	34	=	=	SYM
ejpam-5854	162	35	µn(h1)⋎−1⋏−1⋎	µn(h1)⋎−1⋏−1⋎	NOUN
ejpam-5854	162	36	µp(h2	µp(h2	NOUN
ejpam-5854	162	37	)	)	PUNCT
ejpam-5854	162	38	=	=	NOUN
ejpam-5854	162	39	µp(h1)⋎	µp(h1)⋎	ADJ
ejpam-5854	162	40	µp(h2	µp(h2	NOUN
ejpam-5854	162	41	)	)	PUNCT
ejpam-5854	162	42	.	.	PUNCT
ejpam-5854	163	1	p.	p.	NOUN
ejpam-5854	163	2	khamrot	khamrot	PROPN
ejpam-5854	163	3	,	,	PUNCT
ejpam-5854	163	4	n.	n.	PROPN
ejpam-5854	163	5	deetae	deetae	PROPN
ejpam-5854	163	6	,	,	PUNCT
ejpam-5854	163	7	t.	t.	PROPN
ejpam-5854	163	8	gaketem	gaketem	PROPN
ejpam-5854	163	9	/	/	SYM
ejpam-5854	163	10	eur	eur	PROPN
ejpam-5854	163	11	.	.	PUNCT
ejpam-5854	164	1	j.	j.	PROPN
ejpam-5854	164	2	pure	pure	PROPN
ejpam-5854	164	3	appl	appl	PROPN
ejpam-5854	164	4	.	.	PROPN
ejpam-5854	164	5	math	math	PROPN
ejpam-5854	164	6	,	,	PUNCT
ejpam-5854	164	7	18	18	NUM
ejpam-5854	164	8	(	(	PUNCT
ejpam-5854	164	9	2	2	NUM
ejpam-5854	164	10	)	)	PUNCT
ejpam-5854	164	11	(	(	PUNCT
ejpam-5854	164	12	2025	2025	NUM
ejpam-5854	164	13	)	)	PUNCT
ejpam-5854	164	14	,	,	PUNCT
ejpam-5854	164	15	5854	5854	NUM
ejpam-5854	164	16	8	8	NUM
ejpam-5854	164	17	of	of	ADP
ejpam-5854	164	18	14	14	NUM
ejpam-5854	164	19	and	and	CCONJ
ejpam-5854	164	20	ωp(h1h2	ωp(h1h2	NUM
ejpam-5854	164	21	)	)	PUNCT
ejpam-5854	164	22	≥	≥	NOUN
ejpam-5854	164	23	(	(	PUNCT
ejpam-5854	164	24	ωp	ωp	NOUN
ejpam-5854	164	25	∗sp)(h1h2	∗sp)(h1h2	NOUN
ejpam-5854	164	26	)	)	PUNCT
ejpam-5854	164	27	∧	∧	NOUN
ejpam-5854	164	28	(	(	PUNCT
ejpam-5854	164	29	sp	sp	ADP
ejpam-5854	164	30	∗	∗	NOUN
ejpam-5854	164	31	ωp)(h1h2	ωp)(h1h2	NOUN
ejpam-5854	164	32	)	)	PUNCT
ejpam-5854	165	1	=	=	SYM
ejpam-5854	165	2	∨	∨	X
ejpam-5854	165	3	(	(	PUNCT
ejpam-5854	165	4	i	i	PRON
ejpam-5854	165	5	,	,	PUNCT
ejpam-5854	165	6	j)∈ah1h2	j)∈ah1h2	PROPN
ejpam-5854	165	7	{	{	PUNCT
ejpam-5854	165	8	ωp(i	ωp(i	NOUN
ejpam-5854	165	9	)	)	PUNCT
ejpam-5854	165	10	∧	∧	NOUN
ejpam-5854	165	11	fp(j	fp(j	NOUN
ejpam-5854	165	12	)	)	PUNCT
ejpam-5854	165	13	}	}	PUNCT
ejpam-5854	165	14	∧	∧	PROPN
ejpam-5854	165	15	∨	∨	X
ejpam-5854	165	16	(	(	PUNCT
ejpam-5854	165	17	k	k	NOUN
ejpam-5854	165	18	,	,	PUNCT
ejpam-5854	165	19	o)∈ah1h2	o)∈ah1h2	NOUN
ejpam-5854	165	20	{	{	PUNCT
ejpam-5854	165	21	sp(k	sp(k	NOUN
ejpam-5854	165	22	)	)	PUNCT
ejpam-5854	165	23	∧	∧	NOUN
ejpam-5854	165	24	ωp(o	ωp(o	NOUN
ejpam-5854	165	25	)	)	PUNCT
ejpam-5854	165	26	}	}	PUNCT
ejpam-5854	165	27	≥	≥	NOUN
ejpam-5854	165	28	ωp(h1	ωp(h1	NUM
ejpam-5854	165	29	)	)	PUNCT
ejpam-5854	165	30	∧sp(h2	∧sp(h2	NOUN
ejpam-5854	165	31	)	)	PUNCT
ejpam-5854	165	32	∧sp(h1	∧sp(h1	PROPN
ejpam-5854	165	33	)	)	PUNCT
ejpam-5854	165	34	∧	∧	NOUN
ejpam-5854	165	35	ωp(h2	ωp(h2	NOUN
ejpam-5854	165	36	)	)	PUNCT
ejpam-5854	165	37	=	=	SYM
ejpam-5854	165	38	ωp(h1	ωp(h1	NUM
ejpam-5854	165	39	)	)	PUNCT
ejpam-5854	165	40	∧	∧	NOUN
ejpam-5854	165	41	1	1	NUM
ejpam-5854	165	42	∧	∧	PROPN
ejpam-5854	165	43	1	1	NUM
ejpam-5854	165	44	∧	∧	PROPN
ejpam-5854	165	45	ωp(h2	ωp(h2	NOUN
ejpam-5854	165	46	)	)	PUNCT
ejpam-5854	165	47	=	=	SYM
ejpam-5854	165	48	ωp(h1	ωp(h1	NUM
ejpam-5854	165	49	)	)	PUNCT
ejpam-5854	165	50	∧	∧	NOUN
ejpam-5854	165	51	ωp(h2	ωp(h2	NOUN
ejpam-5854	165	52	)	)	PUNCT
ejpam-5854	165	53	,	,	PUNCT
ejpam-5854	165	54	ωn(h1h2	ωn(h1h2	NOUN
ejpam-5854	165	55	)	)	PUNCT
ejpam-5854	165	56	≤	≤	NOUN
ejpam-5854	165	57	(	(	PUNCT
ejpam-5854	165	58	ωn	ωn	NOUN
ejpam-5854	165	59	∗sn)(h1h2	∗sn)(h1h2	PROPN
ejpam-5854	165	60	)	)	PUNCT
ejpam-5854	165	61	∨	∨	PROPN
ejpam-5854	165	62	(	(	PUNCT
ejpam-5854	165	63	sn	sn	PROPN
ejpam-5854	165	64	∗	∗	NOUN
ejpam-5854	165	65	ωn)(h1h2	ωn)(h1h2	NOUN
ejpam-5854	165	66	)	)	PUNCT
ejpam-5854	166	1	=	=	SYM
ejpam-5854	166	2	∧	∧	PROPN
ejpam-5854	166	3	(	(	PUNCT
ejpam-5854	166	4	i	i	PRON
ejpam-5854	166	5	,	,	PUNCT
ejpam-5854	166	6	j)∈ah1h2	j)∈ah1h2	PROPN
ejpam-5854	166	7	{	{	PUNCT
ejpam-5854	166	8	ωp(i	ωp(i	NOUN
ejpam-5854	166	9	)	)	PUNCT
ejpam-5854	166	10	∨sn(j	∨sn(j	NOUN
ejpam-5854	166	11	)	)	PUNCT
ejpam-5854	166	12	}	}	PUNCT
ejpam-5854	166	13	∨	∨	NUM
ejpam-5854	166	14	∧	∧	PROPN
ejpam-5854	166	15	(	(	PUNCT
ejpam-5854	166	16	k	k	X
ejpam-5854	166	17	,	,	PUNCT
ejpam-5854	166	18	o)∈ah1h2	o)∈ah1h2	PROPN
ejpam-5854	166	19	{	{	PUNCT
ejpam-5854	166	20	sn(k	sn(k	NOUN
ejpam-5854	166	21	)	)	PUNCT
ejpam-5854	166	22	∨	∨	NUM
ejpam-5854	166	23	ωn(o	ωn(o	NUM
ejpam-5854	166	24	)	)	PUNCT
ejpam-5854	166	25	}	}	PUNCT
ejpam-5854	166	26	≤	≤	NUM
ejpam-5854	166	27	ωn(h1	ωn(h1	NOUN
ejpam-5854	166	28	)	)	PUNCT
ejpam-5854	166	29	∨sn(h2	∨sn(h2	NOUN
ejpam-5854	166	30	)	)	PUNCT
ejpam-5854	166	31	∨sn(h1	∨sn(h1	PROPN
ejpam-5854	166	32	)	)	PUNCT
ejpam-5854	166	33	∨	∨	NUM
ejpam-5854	166	34	ωn(h2	ωn(h2	NOUN
ejpam-5854	166	35	)	)	PUNCT
ejpam-5854	166	36	=	=	SYM
ejpam-5854	166	37	ωn(h1	ωn(h1	NOUN
ejpam-5854	166	38	)	)	PUNCT
ejpam-5854	166	39	∨	∨	NUM
ejpam-5854	166	40	−1	−1	NOUN
ejpam-5854	166	41	∨	∨	NUM
ejpam-5854	166	42	−1	−1	NOUN
ejpam-5854	166	43	∨	∨	NUM
ejpam-5854	166	44	ωn(h2	ωn(h2	NOUN
ejpam-5854	166	45	)	)	PUNCT
ejpam-5854	166	46	=	=	SYM
ejpam-5854	166	47	ωn(h1	ωn(h1	NOUN
ejpam-5854	166	48	)	)	PUNCT
ejpam-5854	166	49	∧	∧	PROPN
ejpam-5854	166	50	ωn(h2	ωn(h2	NOUN
ejpam-5854	166	51	)	)	PUNCT
ejpam-5854	166	52	.	.	PUNCT
ejpam-5854	167	1	thus	thus	ADV
ejpam-5854	167	2	,	,	PUNCT
ejpam-5854	167	3	µp(h1h2	µp(h1h2	CCONJ
ejpam-5854	167	4	)	)	PUNCT
ejpam-5854	167	5	⪰	⪰	NOUN
ejpam-5854	167	6	µp(h1)⋏	µp(h1)⋏	ADP
ejpam-5854	167	7	µp(h2	µp(h2	NOUN
ejpam-5854	167	8	)	)	PUNCT
ejpam-5854	167	9	,	,	PUNCT
ejpam-5854	167	10	µ	µ	X
ejpam-5854	167	11	n(h1h2	n(h1h2	NOUN
ejpam-5854	167	12	)	)	PUNCT
ejpam-5854	167	13	⪯	⪯	NOUN
ejpam-5854	167	14	µn(h1)⋎	µn(h1)⋎	PROPN
ejpam-5854	167	15	µn(h2	µn(h2	NOUN
ejpam-5854	167	16	)	)	PUNCT
ejpam-5854	167	17	and	and	CCONJ
ejpam-5854	167	18	ωp(h1h2	ωp(h1h2	NUM
ejpam-5854	167	19	)	)	PUNCT
ejpam-5854	167	20	≥	≥	NOUN
ejpam-5854	167	21	ωp(h1	ωp(h1	NUM
ejpam-5854	167	22	)	)	PUNCT
ejpam-5854	167	23	∧	∧	NOUN
ejpam-5854	167	24	ωp(h2	ωp(h2	NOUN
ejpam-5854	167	25	)	)	PUNCT
ejpam-5854	167	26	,	,	PUNCT
ejpam-5854	167	27	ω	ω	PROPN
ejpam-5854	167	28	n(h1h2	n(h1h2	NOUN
ejpam-5854	167	29	)	)	PUNCT
ejpam-5854	167	30	≤	≤	NUM
ejpam-5854	167	31	ωn(h1	ωn(h1	NOUN
ejpam-5854	167	32	)	)	PUNCT
ejpam-5854	167	33	∨	∨	NUM
ejpam-5854	167	34	ωn(h2	ωn(h2	NOUN
ejpam-5854	167	35	)	)	PUNCT
ejpam-5854	167	36	.	.	PUNCT
ejpam-5854	168	1	hence	hence	ADV
ejpam-5854	168	2	,	,	PUNCT
ejpam-5854	168	3	c̈	c̈	NOUN
ejpam-5854	168	4	=	=	SYM
ejpam-5854	168	5	⟨µ	⟨µ	NOUN
ejpam-5854	168	6	,	,	PUNCT
ejpam-5854	168	7	ω⟩	ω⟩	PRON
ejpam-5854	168	8	is	be	AUX
ejpam-5854	168	9	a	a	DET
ejpam-5854	168	10	cbf	cbf	PROPN
ejpam-5854	168	11	subsemigroup	subsemigroup	NOUN
ejpam-5854	168	12	of	of	ADP
ejpam-5854	168	13	s.	s.	PROPN
ejpam-5854	168	14	in	in	ADP
ejpam-5854	168	15	a	a	DET
ejpam-5854	168	16	similar	similar	ADJ
ejpam-5854	168	17	way	way	NOUN
ejpam-5854	168	18	,	,	PUNCT
ejpam-5854	168	19	let	let	VERB
ejpam-5854	168	20	h1	h1	PROPN
ejpam-5854	168	21	,	,	PUNCT
ejpam-5854	168	22	h2	h2	PROPN
ejpam-5854	168	23	,	,	PUNCT
ejpam-5854	168	24	h3	h3	NOUN
ejpam-5854	168	25	∈	∈	PROPN
ejpam-5854	168	26	s	s	X
ejpam-5854	168	27	we	we	PRON
ejpam-5854	168	28	get	get	VERB
ejpam-5854	168	29	that	that	PRON
ejpam-5854	168	30	µp(h1h2h3	µp(h1h2h3	NOUN
ejpam-5854	168	31	)	)	PUNCT
ejpam-5854	168	32	⪰	⪰	NOUN
ejpam-5854	168	33	(	(	PUNCT
ejpam-5854	168	34	µp	µp	NOUN
ejpam-5854	168	35	⃝s	⃝	VERB
ejpam-5854	168	36	p	p	NOUN
ejpam-5854	168	37	)	)	PUNCT
ejpam-5854	168	38	(	(	PUNCT
ejpam-5854	168	39	h1h2h3)⋏	h1h2h3)⋏	PROPN
ejpam-5854	168	40	(	(	PUNCT
ejpam-5854	168	41	s	s	X
ejpam-5854	168	42	p	p	NOUN
ejpam-5854	168	43	⃝	⃝	NOUN
ejpam-5854	168	44	µp)(h1h2h3	µp)(h1h2h3	ADV
ejpam-5854	168	45	)	)	PUNCT
ejpam-5854	169	1	=	=	SYM
ejpam-5854	169	2	⋎	⋎	NOUN
ejpam-5854	169	3	(	(	PUNCT
ejpam-5854	169	4	i	i	PRON
ejpam-5854	169	5	,	,	PUNCT
ejpam-5854	169	6	j)∈ah1h2h3	j)∈ah1h2h3	X
ejpam-5854	169	7	{	{	PUNCT
ejpam-5854	169	8	µp(i)⋏s	µp(i)⋏s	NOUN
ejpam-5854	169	9	p	p	X
ejpam-5854	169	10	(	(	PUNCT
ejpam-5854	169	11	j)}⋏	j)}⋏	NOUN
ejpam-5854	169	12	⋎	⋎	NOUN
ejpam-5854	169	13	(	(	PUNCT
ejpam-5854	169	14	k	k	NOUN
ejpam-5854	169	15	,	,	PUNCT
ejpam-5854	169	16	o)∈ah1h2h3	o)∈ah1h2h3	X
ejpam-5854	169	17	{	{	PUNCT
ejpam-5854	169	18	sp	sp	PROPN
ejpam-5854	169	19	(	(	PUNCT
ejpam-5854	169	20	k)⋏	k)⋏	VERB
ejpam-5854	169	21	µp(o	µp(o	NOUN
ejpam-5854	169	22	)	)	PUNCT
ejpam-5854	169	23	}	}	PUNCT
ejpam-5854	169	24	⪰	⪰	VERB
ejpam-5854	169	25	µp(h1)⋏g	µp(h1)⋏g	ADP
ejpam-5854	169	26	p	p	X
ejpam-5854	169	27	(	(	PUNCT
ejpam-5854	169	28	h2h3)⋏g	h2h3)⋏g	PROPN
ejpam-5854	169	29	p	p	X
ejpam-5854	169	30	(	(	PUNCT
ejpam-5854	169	31	h1h2)⋏	h1h2)⋏	NOUN
ejpam-5854	169	32	µp(h3	µp(h3	NOUN
ejpam-5854	169	33	)	)	PUNCT
ejpam-5854	169	34	=	=	PUNCT
ejpam-5854	170	1	µp(h1)⋏	µp(h1)⋏	VERB
ejpam-5854	170	2	1⋏	1⋏	NUM
ejpam-5854	170	3	1⋏	1⋏	NUM
ejpam-5854	170	4	µp(h3	µp(h3	NOUN
ejpam-5854	170	5	)	)	PUNCT
ejpam-5854	170	6	=	=	PUNCT
ejpam-5854	170	7	µp(h1)⋏	µp(h1)⋏	NOUN
ejpam-5854	170	8	µp(h3	µp(h3	NOUN
ejpam-5854	170	9	)	)	PUNCT
ejpam-5854	170	10	,	,	PUNCT
ejpam-5854	170	11	µn(h1h2h3	µn(h1h2h3	PROPN
ejpam-5854	170	12	)	)	PUNCT
ejpam-5854	170	13	⪯	⪯	NOUN
ejpam-5854	170	14	(	(	PUNCT
ejpam-5854	170	15	µn	µn	PROPN
ejpam-5854	170	16	⃝s	⃝s	NUM
ejpam-5854	170	17	n	n	NOUN
ejpam-5854	170	18	)	)	PUNCT
ejpam-5854	170	19	(	(	PUNCT
ejpam-5854	170	20	h1h2h3)⋎	h1h2h3)⋎	NOUN
ejpam-5854	170	21	(	(	PUNCT
ejpam-5854	170	22	s	s	NOUN
ejpam-5854	170	23	n	n	PRON
ejpam-5854	170	24	⃝	⃝	NOUN
ejpam-5854	170	25	µn)(h1h2h3	µn)(h1h2h3	PUNCT
ejpam-5854	170	26	)	)	PUNCT
ejpam-5854	170	27	=	=	SYM
ejpam-5854	170	28	⋏	⋏	PROPN
ejpam-5854	170	29	(	(	PUNCT
ejpam-5854	170	30	i	i	PRON
ejpam-5854	170	31	,	,	PUNCT
ejpam-5854	170	32	j)∈ah1h2h3	j)∈ah1h2h3	PROPN
ejpam-5854	170	33	{	{	PUNCT
ejpam-5854	170	34	µn(i)⋎	µn(i)⋎	X
ejpam-5854	170	35	f	f	PROPN
ejpam-5854	170	36	n	n	PROPN
ejpam-5854	170	37	(	(	PUNCT
ejpam-5854	170	38	j)}⋎	j)}⋎	PROPN
ejpam-5854	170	39	⋏	⋏	PROPN
ejpam-5854	170	40	(	(	PUNCT
ejpam-5854	170	41	k	k	NOUN
ejpam-5854	170	42	,	,	PUNCT
ejpam-5854	170	43	o)∈ah1h2h3	o)∈ah1h2h3	X
ejpam-5854	170	44	{	{	PUNCT
ejpam-5854	170	45	fn	fn	X
ejpam-5854	170	46	(	(	PUNCT
ejpam-5854	170	47	k)⋎	k)⋎	PROPN
ejpam-5854	170	48	µn(o	µn(o	PUNCT
ejpam-5854	170	49	)	)	PUNCT
ejpam-5854	170	50	}	}	PUNCT
ejpam-5854	170	51	⪯	⪯	VERB
ejpam-5854	170	52	µn(h1)⋎s	µn(h1)⋎s	NUM
ejpam-5854	170	53	n	n	CCONJ
ejpam-5854	170	54	(	(	PUNCT
ejpam-5854	170	55	h2r3)⋏s	h2r3)⋏s	ADJ
ejpam-5854	170	56	n	n	CCONJ
ejpam-5854	170	57	(	(	PUNCT
ejpam-5854	170	58	h1h2)⋏	h1h2)⋏	NOUN
ejpam-5854	170	59	µn(h3	µn(h3	PART
ejpam-5854	170	60	)	)	PUNCT
ejpam-5854	170	61	=	=	SYM
ejpam-5854	170	62	µn(h1)⋎−1⋏−1⋎	µn(h1)⋎−1⋏−1⋎	NOUN
ejpam-5854	170	63	µp(h3	µp(h3	NOUN
ejpam-5854	170	64	)	)	PUNCT
ejpam-5854	171	1	=	=	SYM
ejpam-5854	171	2	µp(h1)⋎	µp(h1)⋎	ADJ
ejpam-5854	171	3	µp(h3	µp(h3	NOUN
ejpam-5854	171	4	)	)	PUNCT
ejpam-5854	171	5	.	.	PUNCT
ejpam-5854	172	1	and	and	CCONJ
ejpam-5854	172	2	ωp(h1h2h3	ωp(h1h2h3	ADJ
ejpam-5854	172	3	)	)	PUNCT
ejpam-5854	172	4	≥	≥	NUM
ejpam-5854	172	5	(	(	PUNCT
ejpam-5854	172	6	ωp	ωp	NOUN
ejpam-5854	172	7	∗	∗	PROPN
ejpam-5854	172	8	fp)(h1h2h3	fp)(h1h2h3	PROPN
ejpam-5854	172	9	)	)	PUNCT
ejpam-5854	173	1	∧	∧	NOUN
ejpam-5854	173	2	(	(	PUNCT
ejpam-5854	173	3	sp	sp	ADP
ejpam-5854	173	4	∗	∗	NOUN
ejpam-5854	173	5	ωp)(h1h2h3	ωp)(h1h2h3	NUM
ejpam-5854	173	6	)	)	PUNCT
ejpam-5854	173	7	=	=	SYM
ejpam-5854	174	1	∨	∨	X
ejpam-5854	174	2	(	(	PUNCT
ejpam-5854	174	3	i	i	PRON
ejpam-5854	174	4	,	,	PUNCT
ejpam-5854	174	5	j)∈ah1h2h3	j)∈ah1h2h3	PROPN
ejpam-5854	174	6	{	{	PUNCT
ejpam-5854	174	7	ωp(i	ωp(i	NOUN
ejpam-5854	174	8	)	)	PUNCT
ejpam-5854	174	9	∧sp(j	∧sp(j	NOUN
ejpam-5854	174	10	)	)	PUNCT
ejpam-5854	174	11	}	}	PUNCT
ejpam-5854	174	12	∧	∧	PROPN
ejpam-5854	174	13	∨	∨	X
ejpam-5854	174	14	(	(	PUNCT
ejpam-5854	174	15	k	k	NOUN
ejpam-5854	174	16	,	,	PUNCT
ejpam-5854	174	17	o)∈ah1h2h3	o)∈ah1h2h3	NUM
ejpam-5854	174	18	{	{	PUNCT
ejpam-5854	174	19	fp(k	fp(k	NOUN
ejpam-5854	174	20	)	)	PUNCT
ejpam-5854	174	21	∧	∧	NOUN
ejpam-5854	174	22	ωp(o	ωp(o	NOUN
ejpam-5854	174	23	)	)	PUNCT
ejpam-5854	174	24	}	}	PUNCT
ejpam-5854	174	25	≥	≥	NOUN
ejpam-5854	174	26	ωp(h1	ωp(h1	NUM
ejpam-5854	174	27	)	)	PUNCT
ejpam-5854	174	28	∧sp(h2h3	∧sp(h2h3	PROPN
ejpam-5854	174	29	)	)	PUNCT
ejpam-5854	174	30	∧sp(h1h2	∧sp(h1h2	PROPN
ejpam-5854	174	31	)	)	PUNCT
ejpam-5854	174	32	∧	∧	NOUN
ejpam-5854	174	33	ωp(h3	ωp(h3	NOUN
ejpam-5854	174	34	)	)	PUNCT
ejpam-5854	174	35	=	=	SYM
ejpam-5854	174	36	ωp(h1	ωp(h1	NUM
ejpam-5854	174	37	)	)	PUNCT
ejpam-5854	174	38	∧	∧	NOUN
ejpam-5854	174	39	1	1	NUM
ejpam-5854	174	40	∧	∧	PROPN
ejpam-5854	174	41	1	1	NUM
ejpam-5854	174	42	∧	∧	PROPN
ejpam-5854	174	43	ωp(h3	ωp(h3	NOUN
ejpam-5854	174	44	)	)	PUNCT
ejpam-5854	174	45	=	=	SYM
ejpam-5854	174	46	ωp(h1	ωp(h1	NUM
ejpam-5854	174	47	)	)	PUNCT
ejpam-5854	174	48	∧	∧	NOUN
ejpam-5854	174	49	ωp(h3	ωp(h3	NUM
ejpam-5854	174	50	)	)	PUNCT
ejpam-5854	174	51	,	,	PUNCT
ejpam-5854	174	52	ωn(h1h2h3	ωn(h1h2h3	NOUN
ejpam-5854	174	53	)	)	PUNCT
ejpam-5854	174	54	≤	≤	NOUN
ejpam-5854	174	55	(	(	PUNCT
ejpam-5854	174	56	ωn	ωn	NOUN
ejpam-5854	174	57	∗sn)(h1h2h3	∗sn)(h1h2h3	PROPN
ejpam-5854	174	58	)	)	PUNCT
ejpam-5854	174	59	∨	∨	PROPN
ejpam-5854	174	60	(	(	PUNCT
ejpam-5854	174	61	sn	sn	PROPN
ejpam-5854	174	62	∗	∗	NOUN
ejpam-5854	174	63	ωn)(h1h2h3	ωn)(h1h2h3	NUM
ejpam-5854	174	64	)	)	PUNCT
ejpam-5854	174	65	=	=	SYM
ejpam-5854	175	1	∧	∧	PROPN
ejpam-5854	175	2	(	(	PUNCT
ejpam-5854	175	3	i	i	PROPN
ejpam-5854	175	4	,	,	PUNCT
ejpam-5854	175	5	j)∈ah1h2h3	j)∈ah1h2h3	PROPN
ejpam-5854	175	6	{	{	PUNCT
ejpam-5854	175	7	ωp(i	ωp(i	NUM
ejpam-5854	175	8	)	)	PUNCT
ejpam-5854	175	9	∨	∨	NUM
ejpam-5854	175	10	fn(j	fn(j	NOUN
ejpam-5854	175	11	)	)	PUNCT
ejpam-5854	175	12	}	}	PUNCT
ejpam-5854	175	13	∨	∨	NUM
ejpam-5854	175	14	∧	∧	PROPN
ejpam-5854	175	15	(	(	PUNCT
ejpam-5854	175	16	k	k	NOUN
ejpam-5854	175	17	,	,	PUNCT
ejpam-5854	175	18	o)∈ah1h2h3	o)∈ah1h2h3	PROPN
ejpam-5854	175	19	{	{	PUNCT
ejpam-5854	175	20	sn(k	sn(k	NOUN
ejpam-5854	175	21	)	)	PUNCT
ejpam-5854	175	22	∨	∨	NUM
ejpam-5854	175	23	ωn(o	ωn(o	NUM
ejpam-5854	175	24	)	)	PUNCT
ejpam-5854	175	25	}	}	PUNCT
ejpam-5854	175	26	≤	≤	NUM
ejpam-5854	175	27	ωn(h1	ωn(h1	NOUN
ejpam-5854	175	28	)	)	PUNCT
ejpam-5854	175	29	∨	∨	NUM
ejpam-5854	175	30	fn(h2h3	fn(h2h3	PROPN
ejpam-5854	175	31	)	)	PUNCT
ejpam-5854	175	32	∨sn(h1h2	∨sn(h1h2	PROPN
ejpam-5854	175	33	)	)	PUNCT
ejpam-5854	175	34	∨	∨	NUM
ejpam-5854	175	35	ωn(h3	ωn(h3	NOUN
ejpam-5854	175	36	)	)	PUNCT
ejpam-5854	175	37	=	=	SYM
ejpam-5854	175	38	ωn(h1	ωn(h1	NOUN
ejpam-5854	175	39	)	)	PUNCT
ejpam-5854	175	40	∨	∨	NUM
ejpam-5854	175	41	−1	−1	NOUN
ejpam-5854	175	42	∨	∨	NUM
ejpam-5854	175	43	−1	−1	NOUN
ejpam-5854	175	44	∨	∨	NUM
ejpam-5854	175	45	ωn(h3	ωn(h3	NOUN
ejpam-5854	175	46	)	)	PUNCT
ejpam-5854	175	47	=	=	SYM
ejpam-5854	175	48	ωn(h1	ωn(h1	NOUN
ejpam-5854	175	49	)	)	PUNCT
ejpam-5854	175	50	∧	∧	NOUN
ejpam-5854	175	51	ωn(h3	ωn(h3	NOUN
ejpam-5854	175	52	)	)	PUNCT
ejpam-5854	175	53	.	.	PUNCT
ejpam-5854	176	1	thus	thus	ADV
ejpam-5854	176	2	,	,	PUNCT
ejpam-5854	176	3	µp(h1h2h3	µp(h1h2h3	ADP
ejpam-5854	176	4	)	)	PUNCT
ejpam-5854	176	5	⪰	⪰	NOUN
ejpam-5854	176	6	µp(h1)⋏	µp(h1)⋏	NOUN
ejpam-5854	176	7	µp(h3	µp(h3	NOUN
ejpam-5854	176	8	)	)	PUNCT
ejpam-5854	176	9	,	,	PUNCT
ejpam-5854	176	10	µ	µ	PROPN
ejpam-5854	176	11	n(h1r2h3	n(h1r2h3	PROPN
ejpam-5854	176	12	)	)	PUNCT
ejpam-5854	176	13	⪯	⪯	NOUN
ejpam-5854	176	14	µn(h1)⋎	µn(h1)⋎	PROPN
ejpam-5854	176	15	µn(h3	µn(h3	ADP
ejpam-5854	176	16	)	)	PUNCT
ejpam-5854	176	17	and	and	CCONJ
ejpam-5854	176	18	ωp(h1h2	ωp(h1h2	NUM
ejpam-5854	176	19	)	)	PUNCT
ejpam-5854	176	20	≥	≥	NOUN
ejpam-5854	176	21	ωp(h1	ωp(h1	NUM
ejpam-5854	176	22	)	)	PUNCT
ejpam-5854	176	23	∧	∧	NOUN
ejpam-5854	176	24	ωp(h3	ωp(h3	NUM
ejpam-5854	176	25	)	)	PUNCT
ejpam-5854	176	26	,	,	PUNCT
ejpam-5854	176	27	ω	ω	PROPN
ejpam-5854	176	28	n(h1h2	n(h1h2	NOUN
ejpam-5854	176	29	)	)	PUNCT
ejpam-5854	176	30	≤	≤	NUM
ejpam-5854	176	31	ωn(h1	ωn(h1	NOUN
ejpam-5854	176	32	)	)	PUNCT
ejpam-5854	176	33	∨	∨	NUM
ejpam-5854	176	34	ωn(h3	ωn(h3	NOUN
ejpam-5854	176	35	)	)	PUNCT
ejpam-5854	176	36	.	.	PUNCT
ejpam-5854	177	1	hence	hence	ADV
ejpam-5854	177	2	,	,	PUNCT
ejpam-5854	177	3	c̈	c̈	NOUN
ejpam-5854	177	4	=	=	SYM
ejpam-5854	177	5	⟨µ	⟨µ	NOUN
ejpam-5854	177	6	,	,	PUNCT
ejpam-5854	177	7	ω⟩	ω⟩	PRON
ejpam-5854	177	8	is	be	AUX
ejpam-5854	177	9	a	a	DET
ejpam-5854	177	10	cbf	cbf	PROPN
ejpam-5854	177	11	bi	bi	NOUN
ejpam-5854	177	12	-	-	NOUN
ejpam-5854	177	13	ideal	ideal	NOUN
ejpam-5854	177	14	of	of	ADP
ejpam-5854	177	15	s.	s.	PROPN
ejpam-5854	177	16	next	next	ADV
ejpam-5854	177	17	,	,	PUNCT
ejpam-5854	177	18	we	we	PRON
ejpam-5854	177	19	review	review	VERB
ejpam-5854	177	20	the	the	DET
ejpam-5854	177	21	definition	definition	NOUN
ejpam-5854	177	22	of	of	ADP
ejpam-5854	177	23	the	the	DET
ejpam-5854	177	24	characteristic	characteristic	ADJ
ejpam-5854	177	25	cubic	cubic	ADJ
ejpam-5854	177	26	bipolar	bipolar	ADJ
ejpam-5854	177	27	fuzzy	fuzzy	ADJ
ejpam-5854	177	28	function	function	NOUN
ejpam-5854	177	29	.	.	PUNCT
ejpam-5854	178	1	let	let	VERB
ejpam-5854	178	2	t	t	NOUN
ejpam-5854	178	3	be	be	AUX
ejpam-5854	178	4	a	a	DET
ejpam-5854	178	5	nonempty	nonempty	ADJ
ejpam-5854	178	6	subset	subset	NOUN
ejpam-5854	178	7	of	of	ADP
ejpam-5854	178	8	s.	s.	PROPN
ejpam-5854	178	9	the	the	DET
ejpam-5854	178	10	characteristic	characteristic	ADJ
ejpam-5854	178	11	cubic	cubic	ADJ
ejpam-5854	178	12	bipolar	bipolar	ADJ
ejpam-5854	178	13	fuzzy	fuzzy	ADJ
ejpam-5854	178	14	set	set	NOUN
ejpam-5854	178	15	(	(	PUNCT
ejpam-5854	178	16	shortly	shortly	ADV
ejpam-5854	178	17	,	,	PUNCT
ejpam-5854	178	18	ccbf	ccbf	NOUN
ejpam-5854	178	19	set	set	VERB
ejpam-5854	178	20	)	)	PUNCT
ejpam-5854	178	21	χt	χt	ADP
ejpam-5854	178	22	=	=	PUNCT
ejpam-5854	178	23	⟨µχt	⟨µχt	PROPN
ejpam-5854	178	24	,	,	PUNCT
ejpam-5854	178	25	ωχt	ωχt	ADJ
ejpam-5854	178	26	⟩	⟩	NOUN
ejpam-5854	178	27	is	be	AUX
ejpam-5854	178	28	defined	define	VERB
ejpam-5854	178	29	as	as	SCONJ
ejpam-5854	178	30	follows	follow	VERB
ejpam-5854	178	31	:	:	PUNCT
ejpam-5854	178	32	µp	µp	NOUN
ejpam-5854	178	33	χt	χt	ADP
ejpam-5854	178	34	(	(	PUNCT
ejpam-5854	178	35	h	h	NOUN
ejpam-5854	178	36	)	)	PUNCT
ejpam-5854	178	37	=	=	PRON
ejpam-5854	178	38	{	{	PUNCT
ejpam-5854	178	39	1	1	NUM
ejpam-5854	178	40	if	if	SCONJ
ejpam-5854	178	41	h	h	NOUN
ejpam-5854	178	42	∈	∈	PROPN
ejpam-5854	178	43	t	t	NOUN
ejpam-5854	178	44	0	0	PUNCT
ejpam-5854	179	1	if	if	SCONJ
ejpam-5854	179	2	h	h	PROPN
ejpam-5854	179	3	/∈	/∈	PROPN
ejpam-5854	180	1	t	t	PROPN
ejpam-5854	180	2	,	,	PUNCT
ejpam-5854	180	3	µn	µn	PROPN
ejpam-5854	180	4	χt	χt	ADP
ejpam-5854	180	5	(	(	PUNCT
ejpam-5854	180	6	h	h	NOUN
ejpam-5854	180	7	)	)	PUNCT
ejpam-5854	180	8	=	=	PRON
ejpam-5854	180	9	{	{	PUNCT
ejpam-5854	180	10	−1	−1	NOUN
ejpam-5854	180	11	if	if	SCONJ
ejpam-5854	180	12	h	h	NOUN
ejpam-5854	180	13	∈	∈	PROPN
ejpam-5854	180	14	t	t	NOUN
ejpam-5854	180	15	0	0	PUNCT
ejpam-5854	181	1	if	if	SCONJ
ejpam-5854	181	2	h	h	PROPN
ejpam-5854	181	3	/∈	/∈	PROPN
ejpam-5854	182	1	t	t	PROPN
ejpam-5854	182	2	p.	p.	NOUN
ejpam-5854	182	3	khamrot	khamrot	PROPN
ejpam-5854	182	4	,	,	PUNCT
ejpam-5854	182	5	n.	n.	PROPN
ejpam-5854	182	6	deetae	deetae	PROPN
ejpam-5854	182	7	,	,	PUNCT
ejpam-5854	182	8	t.	t.	PROPN
ejpam-5854	182	9	gaketem	gaketem	PROPN
ejpam-5854	182	10	/	/	SYM
ejpam-5854	182	11	eur	eur	PROPN
ejpam-5854	182	12	.	.	PUNCT
ejpam-5854	183	1	j.	j.	PROPN
ejpam-5854	183	2	pure	pure	PROPN
ejpam-5854	183	3	appl	appl	PROPN
ejpam-5854	183	4	.	.	PROPN
ejpam-5854	183	5	math	math	PROPN
ejpam-5854	183	6	,	,	PUNCT
ejpam-5854	183	7	18	18	NUM
ejpam-5854	183	8	(	(	PUNCT
ejpam-5854	183	9	2	2	NUM
ejpam-5854	183	10	)	)	PUNCT
ejpam-5854	183	11	(	(	PUNCT
ejpam-5854	183	12	2025	2025	NUM
ejpam-5854	183	13	)	)	PUNCT
ejpam-5854	183	14	,	,	PUNCT
ejpam-5854	183	15	5854	5854	NUM
ejpam-5854	183	16	9	9	NUM
ejpam-5854	183	17	of	of	ADP
ejpam-5854	183	18	14	14	NUM
ejpam-5854	183	19	for	for	ADP
ejpam-5854	183	20	all	all	DET
ejpam-5854	183	21	h	h	NOUN
ejpam-5854	183	22	∈	∈	PROPN
ejpam-5854	183	23	s	s	NOUN
ejpam-5854	183	24	and	and	CCONJ
ejpam-5854	183	25	ωχt	ωχt	NOUN
ejpam-5854	183	26	is	be	AUX
ejpam-5854	183	27	a	a	DET
ejpam-5854	183	28	characteristic	characteristic	ADJ
ejpam-5854	183	29	bipolar	bipolar	ADJ
ejpam-5854	183	30	fuzzy	fuzzy	ADJ
ejpam-5854	183	31	set	set	NOUN
ejpam-5854	183	32	.	.	PUNCT
ejpam-5854	184	1	in	in	ADP
ejpam-5854	184	2	the	the	DET
ejpam-5854	184	3	following	follow	VERB
ejpam-5854	184	4	theorems	theorem	NOUN
ejpam-5854	184	5	,	,	PUNCT
ejpam-5854	184	6	we	we	PRON
ejpam-5854	184	7	give	give	VERB
ejpam-5854	184	8	a	a	DET
ejpam-5854	184	9	relationship	relationship	NOUN
ejpam-5854	184	10	between	between	ADP
ejpam-5854	184	11	a	a	DET
ejpam-5854	184	12	left	left	ADJ
ejpam-5854	184	13	ideal	ideal	NOUN
ejpam-5854	184	14	(	(	PUNCT
ejpam-5854	184	15	right	right	ADV
ejpam-5854	184	16	ideal	ideal	NOUN
ejpam-5854	184	17	,	,	PUNCT
ejpam-5854	184	18	generalized	generalized	ADJ
ejpam-5854	184	19	bi	bi	NOUN
ejpam-5854	184	20	-	-	ADJ
ejpam-5854	184	21	ideal	ideal	ADJ
ejpam-5854	184	22	,	,	PUNCT
ejpam-5854	184	23	bi	bi	NOUN
ejpam-5854	184	24	-	-	ADJ
ejpam-5854	184	25	ideal	ideal	ADJ
ejpam-5854	184	26	,	,	PUNCT
ejpam-5854	184	27	interior	interior	ADJ
ejpam-5854	184	28	ideal	ideal	NOUN
ejpam-5854	184	29	,	,	PUNCT
ejpam-5854	184	30	quasi	quasi	ADJ
ejpam-5854	184	31	-	-	NOUN
ejpam-5854	184	32	ideal	ideal	ADJ
ejpam-5854	184	33	)	)	PUNCT
ejpam-5854	184	34	and	and	CCONJ
ejpam-5854	184	35	the	the	DET
ejpam-5854	184	36	ccbf	ccbf	NOUN
ejpam-5854	184	37	function	function	NOUN
ejpam-5854	184	38	.	.	PUNCT
ejpam-5854	185	1	theorem	theorem	NOUN
ejpam-5854	185	2	3	3	X
ejpam-5854	185	3	.	.	PUNCT
ejpam-5854	186	1	let	let	VERB
ejpam-5854	186	2	t	t	PROPN
ejpam-5854	186	3	be	be	AUX
ejpam-5854	186	4	a	a	DET
ejpam-5854	186	5	non	non	ADJ
ejpam-5854	186	6	-	-	ADJ
ejpam-5854	186	7	empty	empty	ADJ
ejpam-5854	186	8	subset	subset	NOUN
ejpam-5854	186	9	of	of	ADP
ejpam-5854	186	10	a	a	DET
ejpam-5854	186	11	semigroup	semigroup	PROPN
ejpam-5854	186	12	s.	s.	PROPN
ejpam-5854	186	13	then	then	ADV
ejpam-5854	186	14	,	,	PUNCT
ejpam-5854	186	15	t	t	PROPN
ejpam-5854	186	16	is	be	AUX
ejpam-5854	186	17	a	a	DET
ejpam-5854	186	18	left	left	ADJ
ejpam-5854	186	19	ideal	ideal	NOUN
ejpam-5854	186	20	(	(	PUNCT
ejpam-5854	186	21	right	right	ADV
ejpam-5854	186	22	ideal	ideal	NOUN
ejpam-5854	186	23	,	,	PUNCT
ejpam-5854	186	24	generalized	generalized	ADJ
ejpam-5854	186	25	bi	bi	NOUN
ejpam-5854	186	26	-	-	ADJ
ejpam-5854	186	27	ideal	ideal	ADJ
ejpam-5854	186	28	,	,	PUNCT
ejpam-5854	186	29	bi	bi	NOUN
ejpam-5854	186	30	-	-	ADJ
ejpam-5854	186	31	ideal	ideal	ADJ
ejpam-5854	186	32	,	,	PUNCT
ejpam-5854	186	33	interior	interior	ADJ
ejpam-5854	186	34	ideal	ideal	NOUN
ejpam-5854	186	35	,	,	PUNCT
ejpam-5854	186	36	quasi	quasi	ADJ
ejpam-5854	186	37	-	-	NOUN
ejpam-5854	186	38	ideal	ideal	ADJ
ejpam-5854	186	39	)	)	PUNCT
ejpam-5854	186	40	of	of	ADP
ejpam-5854	186	41	s	s	PRON
ejpam-5854	186	42	if	if	SCONJ
ejpam-5854	187	1	and	and	CCONJ
ejpam-5854	187	2	only	only	ADV
ejpam-5854	187	3	if	if	SCONJ
ejpam-5854	187	4	χt	χt	ADP
ejpam-5854	187	5	=	=	SYM
ejpam-5854	187	6	⟨µχt	⟨µχt	PROPN
ejpam-5854	187	7	,	,	PUNCT
ejpam-5854	187	8	ωχt	ωχt	ADJ
ejpam-5854	187	9	⟩	⟩	NOUN
ejpam-5854	187	10	is	be	AUX
ejpam-5854	187	11	a	a	DET
ejpam-5854	187	12	cbf	cbf	PROPN
ejpam-5854	187	13	left	leave	VERB
ejpam-5854	187	14	ideal	ideal	NOUN
ejpam-5854	187	15	(	(	PUNCT
ejpam-5854	187	16	right	right	ADV
ejpam-5854	187	17	ideal	ideal	NOUN
ejpam-5854	187	18	,	,	PUNCT
ejpam-5854	187	19	generalized	generalized	ADJ
ejpam-5854	187	20	bi	bi	NOUN
ejpam-5854	187	21	-	-	ADJ
ejpam-5854	187	22	ideal	ideal	ADJ
ejpam-5854	187	23	,	,	PUNCT
ejpam-5854	187	24	bi	bi	NOUN
ejpam-5854	187	25	-	-	ADJ
ejpam-5854	187	26	ideal	ideal	ADJ
ejpam-5854	187	27	,	,	PUNCT
ejpam-5854	187	28	interior	interior	ADJ
ejpam-5854	187	29	ideal	ideal	NOUN
ejpam-5854	187	30	,	,	PUNCT
ejpam-5854	187	31	quasi	quasi	ADJ
ejpam-5854	187	32	-	-	NOUN
ejpam-5854	187	33	ideal	ideal	ADJ
ejpam-5854	187	34	)	)	PUNCT
ejpam-5854	187	35	of	of	ADP
ejpam-5854	187	36	s.	s.	PROPN
ejpam-5854	187	37	proof	proof	PROPN
ejpam-5854	187	38	.	.	PUNCT
ejpam-5854	188	1	(	(	PUNCT
ejpam-5854	188	2	⇒	⇒	PROPN
ejpam-5854	188	3	)	)	PUNCT
ejpam-5854	188	4	suppose	suppose	VERB
ejpam-5854	188	5	that	that	SCONJ
ejpam-5854	188	6	t	t	PROPN
ejpam-5854	188	7	is	be	AUX
ejpam-5854	188	8	a	a	DET
ejpam-5854	188	9	left	left	ADJ
ejpam-5854	188	10	ideal	ideal	NOUN
ejpam-5854	188	11	of	of	ADP
ejpam-5854	188	12	s	s	PRON
ejpam-5854	188	13	and	and	CCONJ
ejpam-5854	188	14	let	let	VERB
ejpam-5854	188	15	h1	h1	PROPN
ejpam-5854	188	16	,	,	PUNCT
ejpam-5854	188	17	h2	h2	PROPN
ejpam-5854	188	18	∈	∈	PROPN
ejpam-5854	188	19	s.	s.	PROPN
ejpam-5854	188	20	if	if	SCONJ
ejpam-5854	188	21	h2	h2	PROPN
ejpam-5854	188	22	∈	∈	PROPN
ejpam-5854	188	23	t	t	PROPN
ejpam-5854	188	24	,	,	PUNCT
ejpam-5854	188	25	then	then	ADV
ejpam-5854	188	26	,	,	PUNCT
ejpam-5854	188	27	h1h2	h1h2	X
ejpam-5854	188	28	∈	∈	NOUN
ejpam-5854	188	29	t.	t.	NOUN
ejpam-5854	188	30	thus	thus	ADV
ejpam-5854	188	31	,	,	PUNCT
ejpam-5854	188	32	1	1	NUM
ejpam-5854	188	33	=	=	SYM
ejpam-5854	188	34	µp	µp	NOUN
ejpam-5854	188	35	χt	χt	ADP
ejpam-5854	188	36	(	(	PUNCT
ejpam-5854	188	37	h2	h2	NOUN
ejpam-5854	188	38	)	)	PUNCT
ejpam-5854	189	1	=	=	NOUN
ejpam-5854	189	2	µp	µp	NOUN
ejpam-5854	189	3	χt	χt	ADP
ejpam-5854	189	4	(	(	PUNCT
ejpam-5854	189	5	h1h2	h1h2	NOUN
ejpam-5854	189	6	)	)	PUNCT
ejpam-5854	189	7	,	,	PUNCT
ejpam-5854	189	8	−1	−1	NOUN
ejpam-5854	189	9	=	=	SYM
ejpam-5854	189	10	µn	µn	PROPN
ejpam-5854	189	11	χt	χt	ADP
ejpam-5854	189	12	(	(	PUNCT
ejpam-5854	189	13	h2	h2	NOUN
ejpam-5854	189	14	)	)	PUNCT
ejpam-5854	189	15	=	=	SYM
ejpam-5854	189	16	µn	µn	PROPN
ejpam-5854	189	17	χt	χt	ADP
ejpam-5854	189	18	(	(	PUNCT
ejpam-5854	189	19	h1h2	h1h2	NOUN
ejpam-5854	189	20	)	)	PUNCT
ejpam-5854	189	21	and	and	CCONJ
ejpam-5854	189	22	1	1	NUM
ejpam-5854	189	23	=	=	SYM
ejpam-5854	189	24	ωp	ωp	PRON
ejpam-5854	189	25	χt	χt	ADP
ejpam-5854	189	26	(	(	PUNCT
ejpam-5854	189	27	h2	h2	NOUN
ejpam-5854	189	28	)	)	PUNCT
ejpam-5854	189	29	=	=	SYM
ejpam-5854	190	1	ωp	ωp	NOUN
ejpam-5854	190	2	χt	χt	ADP
ejpam-5854	190	3	(	(	PUNCT
ejpam-5854	190	4	h1h2	h1h2	X
ejpam-5854	190	5	)	)	PUNCT
ejpam-5854	190	6	,	,	PUNCT
ejpam-5854	190	7	−1	−1	NOUN
ejpam-5854	190	8	=	=	SYM
ejpam-5854	190	9	ωn	ωn	PROPN
ejpam-5854	190	10	χt	χt	ADP
ejpam-5854	190	11	(	(	PUNCT
ejpam-5854	190	12	h2	h2	NOUN
ejpam-5854	190	13	)	)	PUNCT
ejpam-5854	190	14	=	=	SYM
ejpam-5854	190	15	ωn	ωn	PROPN
ejpam-5854	190	16	χt	χt	ADP
ejpam-5854	190	17	(	(	PUNCT
ejpam-5854	190	18	h1h2	h1h2	NOUN
ejpam-5854	190	19	)	)	PUNCT
ejpam-5854	190	20	.	.	PUNCT
ejpam-5854	191	1	hence	hence	ADV
ejpam-5854	191	2	,	,	PUNCT
ejpam-5854	191	3	µp	µp	NOUN
ejpam-5854	191	4	χt	χt	ADP
ejpam-5854	191	5	(	(	PUNCT
ejpam-5854	191	6	h1h2	h1h2	NOUN
ejpam-5854	191	7	)	)	PUNCT
ejpam-5854	191	8	⪰	⪰	NOUN
ejpam-5854	191	9	µp	µp	NOUN
ejpam-5854	191	10	χt	χt	ADP
ejpam-5854	191	11	(	(	PUNCT
ejpam-5854	191	12	h2	h2	NOUN
ejpam-5854	191	13	)	)	PUNCT
ejpam-5854	191	14	,	,	PUNCT
ejpam-5854	191	15	µ	µ	X
ejpam-5854	191	16	n	n	NOUN
ejpam-5854	191	17	χt	χt	ADP
ejpam-5854	191	18	(	(	PUNCT
ejpam-5854	191	19	h1h2	h1h2	X
ejpam-5854	191	20	)	)	PUNCT
ejpam-5854	191	21	⪯	⪯	NOUN
ejpam-5854	191	22	µn	µn	PROPN
ejpam-5854	191	23	χt	χt	ADP
ejpam-5854	191	24	(	(	PUNCT
ejpam-5854	191	25	h2	h2	NOUN
ejpam-5854	191	26	)	)	PUNCT
ejpam-5854	191	27	and	and	CCONJ
ejpam-5854	191	28	ωp	ωp	PRON
ejpam-5854	191	29	χt	χt	ADP
ejpam-5854	191	30	(	(	PUNCT
ejpam-5854	191	31	h1h2	h1h2	X
ejpam-5854	191	32	)	)	PUNCT
ejpam-5854	191	33	≥	≥	NOUN
ejpam-5854	191	34	ωp	ωp	ADV
ejpam-5854	191	35	χt	χt	ADP
ejpam-5854	191	36	(	(	PUNCT
ejpam-5854	191	37	h2	h2	NOUN
ejpam-5854	191	38	)	)	PUNCT
ejpam-5854	191	39	,	,	PUNCT
ejpam-5854	191	40	ω	ω	PROPN
ejpam-5854	191	41	n	n	ADV
ejpam-5854	191	42	χt	χt	ADP
ejpam-5854	191	43	(	(	PUNCT
ejpam-5854	191	44	h1h2	h1h2	NOUN
ejpam-5854	191	45	)	)	PUNCT
ejpam-5854	191	46	≤	≤	NOUN
ejpam-5854	191	47	∨ωn	∨ωn	PUNCT
ejpam-5854	191	48	χt	χt	ADP
ejpam-5854	191	49	(	(	PUNCT
ejpam-5854	191	50	h2	h2	NOUN
ejpam-5854	191	51	)	)	PUNCT
ejpam-5854	191	52	.	.	PUNCT
ejpam-5854	192	1	if	if	SCONJ
ejpam-5854	192	2	h2	h2	PROPN
ejpam-5854	192	3	/∈	/∈	PUNCT
ejpam-5854	192	4	t	t	PROPN
ejpam-5854	192	5	,	,	PUNCT
ejpam-5854	192	6	then	then	ADV
ejpam-5854	192	7	,	,	PUNCT
ejpam-5854	192	8	µp	µp	NOUN
ejpam-5854	192	9	χt	χt	ADP
ejpam-5854	192	10	(	(	PUNCT
ejpam-5854	192	11	h1h2	h1h2	NOUN
ejpam-5854	192	12	)	)	PUNCT
ejpam-5854	192	13	⪰	⪰	NOUN
ejpam-5854	192	14	µp	µp	NOUN
ejpam-5854	192	15	χt	χt	ADP
ejpam-5854	192	16	(	(	PUNCT
ejpam-5854	192	17	h2	h2	NOUN
ejpam-5854	192	18	)	)	PUNCT
ejpam-5854	192	19	,	,	PUNCT
ejpam-5854	192	20	µ	µ	X
ejpam-5854	192	21	n	n	NOUN
ejpam-5854	192	22	χt	χt	ADP
ejpam-5854	192	23	(	(	PUNCT
ejpam-5854	192	24	h1h2	h1h2	X
ejpam-5854	192	25	)	)	PUNCT
ejpam-5854	192	26	⪯	⪯	NOUN
ejpam-5854	192	27	µn	µn	PROPN
ejpam-5854	192	28	χt	χt	ADP
ejpam-5854	192	29	(	(	PUNCT
ejpam-5854	192	30	h2	h2	NOUN
ejpam-5854	192	31	)	)	PUNCT
ejpam-5854	192	32	and	and	CCONJ
ejpam-5854	192	33	ωp	ωp	PRON
ejpam-5854	192	34	χt	χt	ADP
ejpam-5854	192	35	(	(	PUNCT
ejpam-5854	192	36	h1h2	h1h2	X
ejpam-5854	192	37	)	)	PUNCT
ejpam-5854	192	38	≥	≥	NOUN
ejpam-5854	192	39	ωp	ωp	ADV
ejpam-5854	192	40	χt	χt	ADP
ejpam-5854	192	41	(	(	PUNCT
ejpam-5854	192	42	h2	h2	NOUN
ejpam-5854	192	43	)	)	PUNCT
ejpam-5854	192	44	,	,	PUNCT
ejpam-5854	192	45	ωn	ωn	PROPN
ejpam-5854	192	46	χt	χt	ADP
ejpam-5854	192	47	(	(	PUNCT
ejpam-5854	192	48	h1h2	h1h2	NOUN
ejpam-5854	192	49	)	)	PUNCT
ejpam-5854	192	50	≤	≤	NOUN
ejpam-5854	192	51	ωn	ωn	ADP
ejpam-5854	192	52	χt	χt	ADP
ejpam-5854	192	53	(	(	PUNCT
ejpam-5854	192	54	h2	h2	NOUN
ejpam-5854	192	55	)	)	PUNCT
ejpam-5854	192	56	.	.	PUNCT
ejpam-5854	193	1	thus	thus	ADV
ejpam-5854	193	2	,	,	PUNCT
ejpam-5854	193	3	χt	χt	ADP
ejpam-5854	193	4	=	=	SYM
ejpam-5854	193	5	⟨µχt	⟨µχt	PROPN
ejpam-5854	193	6	,	,	PUNCT
ejpam-5854	193	7	ωχt	ωχt	ADJ
ejpam-5854	193	8	⟩	⟩	NOUN
ejpam-5854	193	9	is	be	AUX
ejpam-5854	193	10	a	a	DET
ejpam-5854	193	11	cbf	cbf	PROPN
ejpam-5854	193	12	left	leave	VERB
ejpam-5854	193	13	ideal	ideal	NOUN
ejpam-5854	193	14	of	of	ADP
ejpam-5854	193	15	s.	s.	PROPN
ejpam-5854	193	16	⇐	⇐	PROPN
ejpam-5854	193	17	suppose	suppose	VERB
ejpam-5854	193	18	that	that	SCONJ
ejpam-5854	193	19	χt	χt	ADP
ejpam-5854	193	20	=	=	SYM
ejpam-5854	193	21	⟨µχt	⟨µχt	PROPN
ejpam-5854	193	22	,	,	PUNCT
ejpam-5854	193	23	ωχt	ωχt	ADJ
ejpam-5854	193	24	⟩	⟩	NOUN
ejpam-5854	193	25	is	be	AUX
ejpam-5854	193	26	a	a	DET
ejpam-5854	193	27	cbf	cbf	PROPN
ejpam-5854	193	28	left	leave	VERB
ejpam-5854	193	29	ideal	ideal	NOUN
ejpam-5854	193	30	of	of	ADP
ejpam-5854	193	31	s	s	PRON
ejpam-5854	193	32	and	and	CCONJ
ejpam-5854	193	33	let	let	VERB
ejpam-5854	193	34	h2	h2	PROPN
ejpam-5854	193	35	∈	∈	PROPN
ejpam-5854	193	36	t.	t.	NOUN
ejpam-5854	193	37	then	then	ADV
ejpam-5854	193	38	,	,	PUNCT
ejpam-5854	193	39	µp	µp	NOUN
ejpam-5854	193	40	χt	χt	ADP
ejpam-5854	193	41	(	(	PUNCT
ejpam-5854	193	42	h2	h2	NOUN
ejpam-5854	193	43	)	)	PUNCT
ejpam-5854	193	44	=	=	SYM
ejpam-5854	193	45	1	1	NUM
ejpam-5854	193	46	,	,	PUNCT
ejpam-5854	193	47	µn	µn	NOUN
ejpam-5854	193	48	χt	χt	ADP
ejpam-5854	193	49	(	(	PUNCT
ejpam-5854	193	50	h2	h2	NOUN
ejpam-5854	193	51	)	)	PUNCT
ejpam-5854	193	52	=	=	SYM
ejpam-5854	194	1	−1	−1	NOUN
ejpam-5854	194	2	and	and	CCONJ
ejpam-5854	194	3	ωp	ωp	PRON
ejpam-5854	194	4	χt	χt	ADP
ejpam-5854	194	5	(	(	PUNCT
ejpam-5854	194	6	h2	h2	NOUN
ejpam-5854	194	7	)	)	PUNCT
ejpam-5854	194	8	=	=	SYM
ejpam-5854	195	1	1	1	NUM
ejpam-5854	195	2	,	,	PUNCT
ejpam-5854	195	3	ωn	ωn	ADP
ejpam-5854	195	4	χt	χt	ADP
ejpam-5854	195	5	(	(	PUNCT
ejpam-5854	195	6	h2	h2	NOUN
ejpam-5854	195	7	)	)	PUNCT
ejpam-5854	195	8	=	=	PUNCT
ejpam-5854	196	1	−1	−1	NOUN
ejpam-5854	196	2	.	.	PUNCT
ejpam-5854	197	1	if	if	SCONJ
ejpam-5854	197	2	h1h2	h1h2	X
ejpam-5854	197	3	/∈	/∈	SYM
ejpam-5854	197	4	t	t	PROPN
ejpam-5854	197	5	,	,	PUNCT
ejpam-5854	197	6	then	then	ADV
ejpam-5854	197	7	,	,	PUNCT
ejpam-5854	197	8	µp	µp	NOUN
ejpam-5854	197	9	χt	χt	ADP
ejpam-5854	197	10	(	(	PUNCT
ejpam-5854	197	11	h1h2	h1h2	X
ejpam-5854	197	12	)	)	PUNCT
ejpam-5854	197	13	=	=	SYM
ejpam-5854	197	14	0	0	PUNCT
ejpam-5854	198	1	=	=	SYM
ejpam-5854	198	2	µn	µn	PROPN
ejpam-5854	198	3	χt	χt	ADP
ejpam-5854	198	4	(	(	PUNCT
ejpam-5854	198	5	h1h2	h1h2	NOUN
ejpam-5854	198	6	)	)	PUNCT
ejpam-5854	198	7	and	and	CCONJ
ejpam-5854	198	8	ωp	ωp	PRON
ejpam-5854	198	9	χt	χt	ADP
ejpam-5854	198	10	(	(	PUNCT
ejpam-5854	198	11	h1h2	h1h2	X
ejpam-5854	198	12	)	)	PUNCT
ejpam-5854	198	13	=	=	SYM
ejpam-5854	198	14	0	0	PUNCT
ejpam-5854	199	1	=	=	SYM
ejpam-5854	199	2	ωn	ωn	PROPN
ejpam-5854	199	3	χt	χt	ADP
ejpam-5854	199	4	(	(	PUNCT
ejpam-5854	199	5	h1h2	h1h2	NOUN
ejpam-5854	199	6	)	)	PUNCT
ejpam-5854	199	7	.	.	PUNCT
ejpam-5854	200	1	thus	thus	ADV
ejpam-5854	200	2	,	,	PUNCT
ejpam-5854	200	3	0	0	X
ejpam-5854	200	4	=	=	PUNCT
ejpam-5854	200	5	µp	µp	NOUN
ejpam-5854	200	6	χt	χt	ADP
ejpam-5854	200	7	(	(	PUNCT
ejpam-5854	200	8	h1h2	h1h2	NOUN
ejpam-5854	200	9	)	)	PUNCT
ejpam-5854	200	10	⪰	⪰	NOUN
ejpam-5854	200	11	µp	µp	NOUN
ejpam-5854	200	12	χt	χt	ADP
ejpam-5854	200	13	(	(	PUNCT
ejpam-5854	200	14	h2	h2	NOUN
ejpam-5854	200	15	)	)	PUNCT
ejpam-5854	200	16	=	=	SYM
ejpam-5854	200	17	1	1	NUM
ejpam-5854	200	18	,	,	PUNCT
ejpam-5854	200	19	0	0	NUM
ejpam-5854	200	20	=	=	SYM
ejpam-5854	200	21	µn	µn	PROPN
ejpam-5854	200	22	χt	χt	ADP
ejpam-5854	200	23	(	(	PUNCT
ejpam-5854	200	24	h1h2	h1h2	X
ejpam-5854	200	25	)	)	PUNCT
ejpam-5854	200	26	⪯	⪯	NOUN
ejpam-5854	200	27	µn	µn	PROPN
ejpam-5854	200	28	χt	χt	ADP
ejpam-5854	200	29	(	(	PUNCT
ejpam-5854	200	30	h2	h2	NOUN
ejpam-5854	200	31	)	)	PUNCT
ejpam-5854	200	32	=	=	SYM
ejpam-5854	200	33	−1	−1	NOUN
ejpam-5854	200	34	and	and	CCONJ
ejpam-5854	200	35	0	0	NUM
ejpam-5854	201	1	=	=	SYM
ejpam-5854	201	2	ωp	ωp	PROPN
ejpam-5854	201	3	χt	χt	ADP
ejpam-5854	201	4	(	(	PUNCT
ejpam-5854	201	5	h1h2	h1h2	X
ejpam-5854	201	6	)	)	PUNCT
ejpam-5854	201	7	≥	≥	NOUN
ejpam-5854	201	8	ωp	ωp	ADV
ejpam-5854	201	9	χt	χt	ADP
ejpam-5854	201	10	(	(	PUNCT
ejpam-5854	201	11	h2	h2	NOUN
ejpam-5854	201	12	)	)	PUNCT
ejpam-5854	201	13	=	=	SYM
ejpam-5854	201	14	1	1	NUM
ejpam-5854	201	15	,	,	PUNCT
ejpam-5854	201	16	0	0	NUM
ejpam-5854	202	1	=	=	SYM
ejpam-5854	202	2	ωn	ωn	PROPN
ejpam-5854	202	3	χt	χt	ADP
ejpam-5854	202	4	(	(	PUNCT
ejpam-5854	202	5	h1h2	h1h2	NOUN
ejpam-5854	202	6	)	)	PUNCT
ejpam-5854	202	7	≤	≤	NOUN
ejpam-5854	202	8	ωn	ωn	ADP
ejpam-5854	202	9	χt	χt	ADP
ejpam-5854	202	10	(	(	PUNCT
ejpam-5854	202	11	h2	h2	NOUN
ejpam-5854	202	12	)	)	PUNCT
ejpam-5854	202	13	=	=	PUNCT
ejpam-5854	202	14	−1	−1	NOUN
ejpam-5854	202	15	.	.	PUNCT
ejpam-5854	203	1	it	it	PRON
ejpam-5854	203	2	is	be	AUX
ejpam-5854	203	3	a	a	DET
ejpam-5854	203	4	contradiction	contradiction	NOUN
ejpam-5854	203	5	.	.	PUNCT
ejpam-5854	204	1	hence	hence	ADV
ejpam-5854	204	2	,	,	PUNCT
ejpam-5854	204	3	h1h2	h1h2	X
ejpam-5854	204	4	∈	∈	PROPN
ejpam-5854	204	5	t.	t.	NOUN
ejpam-5854	204	6	therefore	therefore	ADV
ejpam-5854	204	7	t	t	PROPN
ejpam-5854	204	8	is	be	AUX
ejpam-5854	204	9	a	a	DET
ejpam-5854	204	10	left	left	ADJ
ejpam-5854	204	11	ideal	ideal	NOUN
ejpam-5854	204	12	of	of	ADP
ejpam-5854	204	13	s.	s.	PROPN
ejpam-5854	204	14	4	4	NUM
ejpam-5854	204	15	.	.	PUNCT
ejpam-5854	205	1	characterizations	characterization	NOUN
ejpam-5854	205	2	of	of	ADP
ejpam-5854	205	3	weakly	weakly	ADJ
ejpam-5854	205	4	regular	regular	ADJ
ejpam-5854	205	5	semigroups	semigroup	NOUN
ejpam-5854	205	6	in	in	ADP
ejpam-5854	205	7	terms	term	NOUN
ejpam-5854	205	8	of	of	ADP
ejpam-5854	205	9	cubic	cubic	ADJ
ejpam-5854	205	10	bipolar	bipolar	ADJ
ejpam-5854	205	11	fuzzy	fuzzy	ADJ
ejpam-5854	205	12	ideals	ideal	NOUN
ejpam-5854	205	13	.	.	PUNCT
ejpam-5854	206	1	in	in	ADP
ejpam-5854	206	2	this	this	DET
ejpam-5854	206	3	section	section	NOUN
ejpam-5854	206	4	,	,	PUNCT
ejpam-5854	206	5	we	we	PRON
ejpam-5854	206	6	will	will	AUX
ejpam-5854	206	7	characterize	characterize	VERB
ejpam-5854	206	8	weakly	weakly	ADV
ejpam-5854	206	9	regular	regular	ADJ
ejpam-5854	206	10	semigroups	semigroup	NOUN
ejpam-5854	206	11	in	in	ADP
ejpam-5854	206	12	terms	term	NOUN
ejpam-5854	206	13	of	of	ADP
ejpam-5854	206	14	cbf	cbf	PROPN
ejpam-5854	206	15	subsemigroups	subsemigroup	NOUN
ejpam-5854	206	16	.	.	PUNCT
ejpam-5854	207	1	theorem	theorem	VERB
ejpam-5854	207	2	4	4	NUM
ejpam-5854	207	3	.	.	PUNCT
ejpam-5854	208	1	let	let	VERB
ejpam-5854	208	2	m	m	PRON
ejpam-5854	208	3	and	and	CCONJ
ejpam-5854	208	4	n	n	CCONJ
ejpam-5854	208	5	be	be	AUX
ejpam-5854	208	6	a	a	DET
ejpam-5854	208	7	non	non	ADJ
ejpam-5854	208	8	-	-	ADJ
ejpam-5854	208	9	empty	empty	ADJ
ejpam-5854	208	10	subsets	subset	NOUN
ejpam-5854	208	11	of	of	ADP
ejpam-5854	208	12	a	a	DET
ejpam-5854	208	13	semigroup	semigroup	PROPN
ejpam-5854	208	14	s.	s.	PROPN
ejpam-5854	208	15	then	then	ADV
ejpam-5854	208	16	,	,	PUNCT
ejpam-5854	208	17	(	(	PUNCT
ejpam-5854	208	18	1	1	X
ejpam-5854	208	19	)	)	PUNCT
ejpam-5854	208	20	χm	χm	ADP
ejpam-5854	208	21	⊛	⊛	NUM
ejpam-5854	208	22	χn	χn	VERB
ejpam-5854	209	1	=	=	NOUN
ejpam-5854	209	2	χmn	χmn	NOUN
ejpam-5854	209	3	i.e.	i.e.	X
ejpam-5854	209	4	⟨µχm	⟨µχm	VERB
ejpam-5854	209	5	⃝	⃝	NOUN
ejpam-5854	209	6	µχn	µχn	NOUN
ejpam-5854	209	7	,	,	PUNCT
ejpam-5854	209	8	ωχm	ωχm	NOUN
ejpam-5854	209	9	∗	∗	NOUN
ejpam-5854	209	10	ωχn	ωχn	NOUN
ejpam-5854	209	11	⟩	⟩	NOUN
ejpam-5854	209	12	=	=	SYM
ejpam-5854	209	13	⟨µχmn	⟨µχmn	NOUN
ejpam-5854	209	14	,	,	PUNCT
ejpam-5854	209	15	ωχmn	ωχmn	VERB
ejpam-5854	209	16	⟩	⟩	PROPN
ejpam-5854	209	17	(	(	PUNCT
ejpam-5854	209	18	2	2	NUM
ejpam-5854	209	19	)	)	PUNCT
ejpam-5854	209	20	χm⊓χn	χm⊓χn	NOUN
ejpam-5854	209	21	=	=	SYM
ejpam-5854	209	22	χm⊓n	χm⊓n	PROPN
ejpam-5854	209	23	i.e.	i.e.	X
ejpam-5854	209	24	⟨µχm	⟨µχm	PROPN
ejpam-5854	209	25	⊓	⊓	PROPN
ejpam-5854	209	26	µχn	µχn	NOUN
ejpam-5854	209	27	,	,	PUNCT
ejpam-5854	209	28	ωχm	ωχm	ADJ
ejpam-5854	209	29	∩	∩	X
ejpam-5854	209	30	ωχn	ωχn	VERB
ejpam-5854	209	31	⟩	⟩	NOUN
ejpam-5854	209	32	=	=	SYM
ejpam-5854	209	33	⟨µχm⊓n	⟨µχm⊓n	NOUN
ejpam-5854	209	34	,	,	PUNCT
ejpam-5854	209	35	ωχm∩n	ωχm∩n	X
ejpam-5854	209	36	⟩	⟩	NOUN
ejpam-5854	209	37	on	on	ADP
ejpam-5854	209	38	the	the	DET
ejpam-5854	209	39	basis	basis	NOUN
ejpam-5854	209	40	of	of	ADP
ejpam-5854	209	41	lemma	lemma	PROPN
ejpam-5854	209	42	1	1	NUM
ejpam-5854	209	43	,	,	PUNCT
ejpam-5854	209	44	we	we	PRON
ejpam-5854	209	45	can	can	AUX
ejpam-5854	209	46	prove	prove	VERB
ejpam-5854	209	47	theorem	theorem	ADJ
ejpam-5854	209	48	5	5	NUM
ejpam-5854	209	49	.	.	PUNCT
ejpam-5854	210	1	lemma	lemma	PROPN
ejpam-5854	210	2	1	1	NUM
ejpam-5854	210	3	.	.	PUNCT
ejpam-5854	211	1	if	if	SCONJ
ejpam-5854	211	2	c̈1	c̈1	NOUN
ejpam-5854	211	3	=	=	SYM
ejpam-5854	211	4	⟨µ	⟨µ	NOUN
ejpam-5854	211	5	,	,	PUNCT
ejpam-5854	211	6	ω⟩	ω⟩	PRON
ejpam-5854	211	7	is	be	AUX
ejpam-5854	211	8	a	a	DET
ejpam-5854	211	9	cbf	cbf	PROPN
ejpam-5854	211	10	right	right	ADV
ejpam-5854	211	11	ideal	ideal	NOUN
ejpam-5854	211	12	and	and	CCONJ
ejpam-5854	211	13	c̈2	c̈2	NOUN
ejpam-5854	211	14	=	=	SYM
ejpam-5854	211	15	⟨λ	⟨λ	NUM
ejpam-5854	211	16	,	,	PUNCT
ejpam-5854	211	17	ψ⟩	ψ⟩	X
ejpam-5854	211	18	is	be	AUX
ejpam-5854	211	19	a	a	DET
ejpam-5854	211	20	cbf	cbf	PROPN
ejpam-5854	211	21	left	leave	VERB
ejpam-5854	211	22	ideal	ideal	NOUN
ejpam-5854	211	23	of	of	ADP
ejpam-5854	211	24	s	s	PROPN
ejpam-5854	211	25	,	,	PUNCT
ejpam-5854	211	26	then	then	ADV
ejpam-5854	211	27	,	,	PUNCT
ejpam-5854	211	28	c̈1	c̈1	NOUN
ejpam-5854	211	29	⊛	⊛	ADJ
ejpam-5854	211	30	c̈2⊏c̈1⊓c̈2	c̈2⊏c̈1⊓c̈2	NOUN
ejpam-5854	211	31	.	.	PUNCT
ejpam-5854	212	1	proof	proof	NOUN
ejpam-5854	212	2	.	.	PUNCT
ejpam-5854	213	1	assume	assume	VERB
ejpam-5854	213	2	that	that	SCONJ
ejpam-5854	213	3	c̈1	c̈1	NOUN
ejpam-5854	213	4	=	=	SYM
ejpam-5854	213	5	⟨µ	⟨µ	NOUN
ejpam-5854	213	6	,	,	PUNCT
ejpam-5854	213	7	ω⟩	ω⟩	PRON
ejpam-5854	213	8	is	be	AUX
ejpam-5854	213	9	a	a	DET
ejpam-5854	213	10	cbf	cbf	PROPN
ejpam-5854	213	11	right	right	ADV
ejpam-5854	213	12	ideal	ideal	NOUN
ejpam-5854	213	13	and	and	CCONJ
ejpam-5854	213	14	c̈2	c̈2	NOUN
ejpam-5854	213	15	=	=	SYM
ejpam-5854	213	16	⟨λ	⟨λ	NUM
ejpam-5854	213	17	,	,	PUNCT
ejpam-5854	213	18	ψ⟩	ψ⟩	X
ejpam-5854	213	19	is	be	AUX
ejpam-5854	213	20	a	a	DET
ejpam-5854	213	21	cbf	cbf	PROPN
ejpam-5854	213	22	left	leave	VERB
ejpam-5854	213	23	ideal	ideal	NOUN
ejpam-5854	213	24	of	of	ADP
ejpam-5854	213	25	s	s	PRON
ejpam-5854	213	26	and	and	CCONJ
ejpam-5854	213	27	let	let	VERB
ejpam-5854	213	28	h	h	PRON
ejpam-5854	213	29	∈	∈	PROPN
ejpam-5854	213	30	s.	s.	PROPN
ejpam-5854	214	1	if	if	SCONJ
ejpam-5854	214	2	ah	ah	INTJ
ejpam-5854	214	3	=	=	NOUN
ejpam-5854	214	4	∅	∅	NOUN
ejpam-5854	214	5	,	,	PUNCT
ejpam-5854	214	6	then	then	ADV
ejpam-5854	214	7	,	,	PUNCT
ejpam-5854	214	8	it	it	PRON
ejpam-5854	214	9	is	be	AUX
ejpam-5854	214	10	easy	easy	ADJ
ejpam-5854	214	11	to	to	PART
ejpam-5854	214	12	verify	verify	VERB
ejpam-5854	214	13	that	that	SCONJ
ejpam-5854	214	14	,	,	PUNCT
ejpam-5854	214	15	(	(	PUNCT
ejpam-5854	214	16	µp	µp	NOUN
ejpam-5854	214	17	⃝	⃝	VERB
ejpam-5854	214	18	λ	λ	PROPN
ejpam-5854	214	19	p	p	NOUN
ejpam-5854	214	20	)	)	PUNCT
ejpam-5854	214	21	(	(	PUNCT
ejpam-5854	214	22	h	h	NOUN
ejpam-5854	214	23	)	)	PUNCT
ejpam-5854	214	24	⪯	⪯	NOUN
ejpam-5854	214	25	(	(	PUNCT
ejpam-5854	214	26	µp	µp	PROPN
ejpam-5854	214	27	⊓	⊓	PROPN
ejpam-5854	214	28	λp)(h	λp)(h	NUM
ejpam-5854	214	29	)	)	PUNCT
ejpam-5854	214	30	,	,	PUNCT
ejpam-5854	214	31	(	(	PUNCT
ejpam-5854	214	32	µn	µn	NOUN
ejpam-5854	214	33	⃝	⃝	NOUN
ejpam-5854	214	34	λ	λ	NOUN
ejpam-5854	214	35	n	n	PRON
ejpam-5854	214	36	)	)	PUNCT
ejpam-5854	214	37	(	(	PUNCT
ejpam-5854	214	38	h	h	NOUN
ejpam-5854	214	39	)	)	PUNCT
ejpam-5854	214	40	⪰	⪰	NOUN
ejpam-5854	214	41	(	(	PUNCT
ejpam-5854	214	42	µn	µn	PROPN
ejpam-5854	214	43	⊓	⊓	PROPN
ejpam-5854	214	44	λn)(h	λn)(h	PUNCT
ejpam-5854	214	45	)	)	PUNCT
ejpam-5854	214	46	and	and	CCONJ
ejpam-5854	214	47	(	(	PUNCT
ejpam-5854	214	48	ωp	ωp	NOUN
ejpam-5854	214	49	∗	∗	NOUN
ejpam-5854	214	50	ψp)(h	ψp)(h	PROPN
ejpam-5854	214	51	)	)	PUNCT
ejpam-5854	214	52	≤	≤	NOUN
ejpam-5854	214	53	(	(	PUNCT
ejpam-5854	214	54	ωp	ωp	X
ejpam-5854	214	55	∩	∩	NOUN
ejpam-5854	214	56	ψp)(h	ψp)(h	PROPN
ejpam-5854	214	57	)	)	PUNCT
ejpam-5854	214	58	,	,	PUNCT
ejpam-5854	214	59	(	(	PUNCT
ejpam-5854	214	60	ωn	ωn	ADP
ejpam-5854	214	61	∗	∗	NUM
ejpam-5854	214	62	ψn)(h	ψn)(h	PROPN
ejpam-5854	214	63	)	)	PUNCT
ejpam-5854	214	64	≥	≥	NOUN
ejpam-5854	214	65	(	(	PUNCT
ejpam-5854	214	66	ωn	ωn	PROPN
ejpam-5854	214	67	∩	∩	NOUN
ejpam-5854	214	68	ψn)(h	ψn)(h	PROPN
ejpam-5854	214	69	)	)	PUNCT
ejpam-5854	214	70	.	.	PUNCT
ejpam-5854	215	1	if	if	SCONJ
ejpam-5854	215	2	ah	ah	INTJ
ejpam-5854	215	3	̸=	̸=	PROPN
ejpam-5854	215	4	∅	∅	NOUN
ejpam-5854	215	5	,	,	PUNCT
ejpam-5854	215	6	then	then	ADV
ejpam-5854	215	7	,	,	PUNCT
ejpam-5854	215	8	(	(	PUNCT
ejpam-5854	215	9	µp	µp	NOUN
ejpam-5854	215	10	⃝	⃝	VERB
ejpam-5854	215	11	λ	λ	PROPN
ejpam-5854	215	12	p	p	NOUN
ejpam-5854	215	13	)	)	PUNCT
ejpam-5854	215	14	(	(	PUNCT
ejpam-5854	215	15	h	h	NOUN
ejpam-5854	215	16	)	)	PUNCT
ejpam-5854	215	17	=	=	SYM
ejpam-5854	215	18	⋎	⋎	NOUN
ejpam-5854	215	19	(	(	PUNCT
ejpam-5854	215	20	k	k	NOUN
ejpam-5854	215	21	,	,	PUNCT
ejpam-5854	215	22	o)∈ah	o)∈ah	PROPN
ejpam-5854	215	23	{	{	PUNCT
ejpam-5854	215	24	µp(k)⋏	µp(k)⋏	NOUN
ejpam-5854	215	25	λ	λ	X
ejpam-5854	215	26	p	p	X
ejpam-5854	215	27	(	(	PUNCT
ejpam-5854	215	28	o	o	NOUN
ejpam-5854	215	29	)	)	PUNCT
ejpam-5854	215	30	}	}	PUNCT
ejpam-5854	215	31	⪯	⪯	VERB
ejpam-5854	215	32	⋎	⋎	NOUN
ejpam-5854	215	33	(	(	PUNCT
ejpam-5854	215	34	k	k	NOUN
ejpam-5854	215	35	,	,	PUNCT
ejpam-5854	215	36	o)∈ah	o)∈ah	PROPN
ejpam-5854	215	37	{	{	PUNCT
ejpam-5854	215	38	µp(ko)⋏	µp(ko)⋏	NOUN
ejpam-5854	215	39	λ	λ	X
ejpam-5854	215	40	p	p	X
ejpam-5854	215	41	(	(	PUNCT
ejpam-5854	215	42	ko	ko	PROPN
ejpam-5854	215	43	)	)	PUNCT
ejpam-5854	215	44	}	}	PUNCT
ejpam-5854	216	1	=	=	PUNCT
ejpam-5854	216	2	µp(h)⋏	µp(h)⋏	ADP
ejpam-5854	216	3	λ	λ	X
ejpam-5854	216	4	p	p	X
ejpam-5854	216	5	(	(	PUNCT
ejpam-5854	216	6	h	h	NOUN
ejpam-5854	216	7	)	)	PUNCT
ejpam-5854	216	8	=	=	SYM
ejpam-5854	217	1	(	(	PUNCT
ejpam-5854	217	2	µp	µp	PROPN
ejpam-5854	217	3	⊓	⊓	PROPN
ejpam-5854	217	4	λp)(h	λp)(h	NUM
ejpam-5854	217	5	)	)	PUNCT
ejpam-5854	217	6	,	,	PUNCT
ejpam-5854	217	7	p.	p.	NOUN
ejpam-5854	217	8	khamrot	khamrot	PROPN
ejpam-5854	217	9	,	,	PUNCT
ejpam-5854	217	10	n.	n.	PROPN
ejpam-5854	217	11	deetae	deetae	PROPN
ejpam-5854	217	12	,	,	PUNCT
ejpam-5854	217	13	t.	t.	PROPN
ejpam-5854	217	14	gaketem	gaketem	PROPN
ejpam-5854	217	15	/	/	SYM
ejpam-5854	217	16	eur	eur	PROPN
ejpam-5854	217	17	.	.	PUNCT
ejpam-5854	218	1	j.	j.	PROPN
ejpam-5854	218	2	pure	pure	PROPN
ejpam-5854	218	3	appl	appl	PROPN
ejpam-5854	218	4	.	.	PROPN
ejpam-5854	218	5	math	math	PROPN
ejpam-5854	218	6	,	,	PUNCT
ejpam-5854	218	7	18	18	NUM
ejpam-5854	218	8	(	(	PUNCT
ejpam-5854	218	9	2	2	NUM
ejpam-5854	218	10	)	)	PUNCT
ejpam-5854	218	11	(	(	PUNCT
ejpam-5854	218	12	2025	2025	NUM
ejpam-5854	218	13	)	)	PUNCT
ejpam-5854	218	14	,	,	PUNCT
ejpam-5854	218	15	5854	5854	NUM
ejpam-5854	218	16	10	10	NUM
ejpam-5854	218	17	of	of	ADP
ejpam-5854	218	18	14	14	NUM
ejpam-5854	218	19	(	(	PUNCT
ejpam-5854	218	20	µn	µn	NOUN
ejpam-5854	218	21	⃝	⃝	NOUN
ejpam-5854	218	22	λ	λ	NOUN
ejpam-5854	218	23	n	n	PRON
ejpam-5854	218	24	)	)	PUNCT
ejpam-5854	218	25	(	(	PUNCT
ejpam-5854	218	26	h	h	NOUN
ejpam-5854	218	27	)	)	PUNCT
ejpam-5854	218	28	=	=	SYM
ejpam-5854	219	1	⋏	⋏	PROPN
ejpam-5854	219	2	(	(	PUNCT
ejpam-5854	219	3	k	k	X
ejpam-5854	219	4	,	,	PUNCT
ejpam-5854	219	5	o)∈ah	o)∈ah	PROPN
ejpam-5854	219	6	{	{	PUNCT
ejpam-5854	219	7	µn(k)⋎	µn(k)⋎	PROPN
ejpam-5854	219	8	λ	λ	PROPN
ejpam-5854	219	9	n	n	CCONJ
ejpam-5854	219	10	(	(	PUNCT
ejpam-5854	219	11	o	o	NOUN
ejpam-5854	219	12	)	)	PUNCT
ejpam-5854	219	13	}	}	PUNCT
ejpam-5854	219	14	⪰	⪰	VERB
ejpam-5854	219	15	⋏	⋏	PROPN
ejpam-5854	219	16	(	(	PUNCT
ejpam-5854	219	17	k	k	X
ejpam-5854	219	18	,	,	PUNCT
ejpam-5854	219	19	o)∈ah	o)∈ah	PROPN
ejpam-5854	219	20	{	{	PUNCT
ejpam-5854	219	21	µn(ko)⋎	µn(ko)⋎	NOUN
ejpam-5854	219	22	λ	λ	PROPN
ejpam-5854	219	23	n	n	PROPN
ejpam-5854	219	24	(	(	PUNCT
ejpam-5854	219	25	ko	ko	PROPN
ejpam-5854	219	26	)	)	PUNCT
ejpam-5854	219	27	}	}	PUNCT
ejpam-5854	219	28	=	=	PUNCT
ejpam-5854	219	29	µn(h)⋎	µn(h)⋎	PUNCT
ejpam-5854	219	30	λ	λ	X
ejpam-5854	219	31	n	n	X
ejpam-5854	219	32	(	(	PUNCT
ejpam-5854	219	33	h	h	NOUN
ejpam-5854	219	34	)	)	PUNCT
ejpam-5854	219	35	=	=	SYM
ejpam-5854	219	36	(	(	PUNCT
ejpam-5854	219	37	µn	µn	PROPN
ejpam-5854	219	38	⊓	⊓	PROPN
ejpam-5854	219	39	λn)(h	λn)(h	NUM
ejpam-5854	219	40	)	)	PUNCT
ejpam-5854	219	41	,	,	PUNCT
ejpam-5854	219	42	and	and	CCONJ
ejpam-5854	219	43	(	(	PUNCT
ejpam-5854	219	44	ωp	ωp	NOUN
ejpam-5854	219	45	∗	∗	NOUN
ejpam-5854	219	46	ψp)(h	ψp)(h	PROPN
ejpam-5854	219	47	)	)	PUNCT
ejpam-5854	219	48	=	=	PUNCT
ejpam-5854	220	1	∨	∨	X
ejpam-5854	220	2	(	(	PUNCT
ejpam-5854	220	3	k	k	NOUN
ejpam-5854	220	4	,	,	PUNCT
ejpam-5854	220	5	o)∈ah	o)∈ah	PROPN
ejpam-5854	220	6	{	{	PUNCT
ejpam-5854	220	7	ωp(k	ωp(k	NOUN
ejpam-5854	220	8	)	)	PUNCT
ejpam-5854	220	9	∧	∧	NOUN
ejpam-5854	220	10	ψp(o	ψp(o	NOUN
ejpam-5854	220	11	)	)	PUNCT
ejpam-5854	220	12	}	}	PUNCT
ejpam-5854	220	13	≤	≤	NUM
ejpam-5854	220	14	∨	∨	NUM
ejpam-5854	220	15	(	(	PUNCT
ejpam-5854	220	16	k	k	NOUN
ejpam-5854	220	17	,	,	PUNCT
ejpam-5854	220	18	o)∈ah	o)∈ah	PROPN
ejpam-5854	220	19	{	{	PUNCT
ejpam-5854	220	20	ωp(ko	ωp(ko	PROPN
ejpam-5854	220	21	)	)	PUNCT
ejpam-5854	220	22	∧	∧	NOUN
ejpam-5854	220	23	ψp(ko	ψp(ko	PROPN
ejpam-5854	220	24	)	)	PUNCT
ejpam-5854	220	25	}	}	PUNCT
ejpam-5854	220	26	=	=	SYM
ejpam-5854	220	27	ωp(h	ωp(h	NOUN
ejpam-5854	220	28	)	)	PUNCT
ejpam-5854	220	29	∧	∧	NOUN
ejpam-5854	220	30	ψp(h	ψp(h	X
ejpam-5854	220	31	)	)	PUNCT
ejpam-5854	220	32	=	=	SYM
ejpam-5854	220	33	(	(	PUNCT
ejpam-5854	220	34	ωp	ωp	X
ejpam-5854	220	35	∩	∩	NOUN
ejpam-5854	220	36	ψp)(h	ψp)(h	PROPN
ejpam-5854	220	37	)	)	PUNCT
ejpam-5854	220	38	,	,	PUNCT
ejpam-5854	220	39	(	(	PUNCT
ejpam-5854	220	40	ωn	ωn	ADP
ejpam-5854	220	41	∗	∗	NOUN
ejpam-5854	220	42	ψn)(h	ψn)(h	PROPN
ejpam-5854	220	43	)	)	PUNCT
ejpam-5854	221	1	=	=	PUNCT
ejpam-5854	221	2	∧	∧	PROPN
ejpam-5854	221	3	(	(	PUNCT
ejpam-5854	221	4	k	k	NOUN
ejpam-5854	221	5	,	,	PUNCT
ejpam-5854	221	6	o)∈ah	o)∈ah	PROPN
ejpam-5854	221	7	{	{	PUNCT
ejpam-5854	221	8	ωn(k	ωn(k	NUM
ejpam-5854	221	9	)	)	PUNCT
ejpam-5854	221	10	∨	∨	NUM
ejpam-5854	221	11	ψn(o	ψn(o	NUM
ejpam-5854	221	12	)	)	PUNCT
ejpam-5854	221	13	}	}	PUNCT
ejpam-5854	221	14	≥	≥	X
ejpam-5854	221	15	∧	∧	NOUN
ejpam-5854	221	16	(	(	PUNCT
ejpam-5854	221	17	k	k	X
ejpam-5854	221	18	,	,	PUNCT
ejpam-5854	221	19	o)∈ah	o)∈ah	PROPN
ejpam-5854	221	20	{	{	PUNCT
ejpam-5854	221	21	ωp(ko	ωp(ko	PROPN
ejpam-5854	221	22	)	)	PUNCT
ejpam-5854	221	23	∨	∨	NUM
ejpam-5854	221	24	ψn(ko	ψn(ko	PROPN
ejpam-5854	221	25	)	)	PUNCT
ejpam-5854	221	26	}	}	PUNCT
ejpam-5854	221	27	=	=	SYM
ejpam-5854	221	28	ωn(h	ωn(h	NUM
ejpam-5854	221	29	)	)	PUNCT
ejpam-5854	221	30	∨	∨	NUM
ejpam-5854	221	31	ψn(h	ψn(h	NUM
ejpam-5854	221	32	)	)	PUNCT
ejpam-5854	221	33	=	=	SYM
ejpam-5854	221	34	(	(	PUNCT
ejpam-5854	221	35	ωn	ωn	ADP
ejpam-5854	221	36	∩	∩	NOUN
ejpam-5854	221	37	ψn)(h	ψn)(h	PROPN
ejpam-5854	221	38	)	)	PUNCT
ejpam-5854	221	39	.	.	PUNCT
ejpam-5854	222	1	thus	thus	ADV
ejpam-5854	222	2	,	,	PUNCT
ejpam-5854	222	3	(	(	PUNCT
ejpam-5854	222	4	µp	µp	NOUN
ejpam-5854	222	5	⃝	⃝	VERB
ejpam-5854	222	6	λ	λ	PROPN
ejpam-5854	222	7	p	p	NOUN
ejpam-5854	222	8	)	)	PUNCT
ejpam-5854	222	9	(	(	PUNCT
ejpam-5854	222	10	h	h	NOUN
ejpam-5854	222	11	)	)	PUNCT
ejpam-5854	222	12	⪯	⪯	NOUN
ejpam-5854	222	13	(	(	PUNCT
ejpam-5854	222	14	µp	µp	PROPN
ejpam-5854	222	15	⊓	⊓	PROPN
ejpam-5854	222	16	λp)(h	λp)(h	NUM
ejpam-5854	222	17	)	)	PUNCT
ejpam-5854	222	18	,	,	PUNCT
ejpam-5854	222	19	(	(	PUNCT
ejpam-5854	222	20	µn	µn	NOUN
ejpam-5854	222	21	⃝	⃝	NOUN
ejpam-5854	222	22	λ	λ	NOUN
ejpam-5854	222	23	n	n	PRON
ejpam-5854	222	24	)	)	PUNCT
ejpam-5854	222	25	(	(	PUNCT
ejpam-5854	222	26	h	h	NOUN
ejpam-5854	222	27	)	)	PUNCT
ejpam-5854	222	28	⪰	⪰	NOUN
ejpam-5854	222	29	(	(	PUNCT
ejpam-5854	222	30	µn	µn	PROPN
ejpam-5854	222	31	⊓	⊓	PROPN
ejpam-5854	222	32	λn)(h	λn)(h	PUNCT
ejpam-5854	222	33	)	)	PUNCT
ejpam-5854	222	34	and	and	CCONJ
ejpam-5854	222	35	(	(	PUNCT
ejpam-5854	222	36	ωp	ωp	NOUN
ejpam-5854	222	37	∗	∗	NOUN
ejpam-5854	222	38	ψp)(h	ψp)(h	PROPN
ejpam-5854	222	39	)	)	PUNCT
ejpam-5854	222	40	≤	≤	NOUN
ejpam-5854	222	41	(	(	PUNCT
ejpam-5854	222	42	ωp	ωp	X
ejpam-5854	222	43	∩	∩	NOUN
ejpam-5854	222	44	ψp)(h	ψp)(h	PROPN
ejpam-5854	222	45	)	)	PUNCT
ejpam-5854	222	46	,	,	PUNCT
ejpam-5854	222	47	(	(	PUNCT
ejpam-5854	222	48	ωn	ωn	ADP
ejpam-5854	222	49	∗	∗	NUM
ejpam-5854	222	50	ψn)(h	ψn)(h	PROPN
ejpam-5854	222	51	)	)	PUNCT
ejpam-5854	222	52	≥	≥	NOUN
ejpam-5854	222	53	(	(	PUNCT
ejpam-5854	222	54	ωn	ωn	PROPN
ejpam-5854	222	55	∩	∩	NOUN
ejpam-5854	222	56	ψn)(h	ψn)(h	PROPN
ejpam-5854	222	57	)	)	PUNCT
ejpam-5854	222	58	.	.	PUNCT
ejpam-5854	223	1	hence	hence	ADV
ejpam-5854	223	2	,	,	PUNCT
ejpam-5854	223	3	c̈1	c̈1	NOUN
ejpam-5854	223	4	⊛	⊛	ADP
ejpam-5854	223	5	c̈2⊏c̈1⊓c̈2	c̈2⊏c̈1⊓c̈2	NOUN
ejpam-5854	223	6	.	.	PUNCT
ejpam-5854	224	1	any	any	DET
ejpam-5854	224	2	way	way	NOUN
ejpam-5854	224	3	,	,	PUNCT
ejpam-5854	224	4	in	in	ADP
ejpam-5854	224	5	the	the	DET
ejpam-5854	224	6	proof	proof	NOUN
ejpam-5854	224	7	of	of	ADP
ejpam-5854	224	8	theorem	theorem	NOUN
ejpam-5854	224	9	5	5	NUM
ejpam-5854	224	10	,	,	PUNCT
ejpam-5854	224	11	these	these	PRON
ejpam-5854	224	12	are	be	AUX
ejpam-5854	224	13	used	use	VERB
ejpam-5854	224	14	.	.	PUNCT
ejpam-5854	225	1	definition	definition	NOUN
ejpam-5854	225	2	14	14	NUM
ejpam-5854	225	3	.	.	PUNCT
ejpam-5854	226	1	[	[	X
ejpam-5854	226	2	13	13	NUM
ejpam-5854	226	3	]	]	X
ejpam-5854	226	4	a	a	DET
ejpam-5854	226	5	semigroup	semigroup	NOUN
ejpam-5854	226	6	s	s	VERB
ejpam-5854	226	7	is	be	AUX
ejpam-5854	226	8	called	call	VERB
ejpam-5854	226	9	weakly	weakly	ADV
ejpam-5854	226	10	regular	regular	ADJ
ejpam-5854	226	11	if	if	SCONJ
ejpam-5854	226	12	for	for	ADP
ejpam-5854	226	13	every	every	DET
ejpam-5854	226	14	h	h	NOUN
ejpam-5854	226	15	∈	∈	PROPN
ejpam-5854	226	16	s	s	PROPN
ejpam-5854	226	17	,	,	PUNCT
ejpam-5854	226	18	h	h	NOUN
ejpam-5854	226	19	∈	∈	PROPN
ejpam-5854	226	20	(	(	PUNCT
ejpam-5854	226	21	hs)2	hs)2	PROPN
ejpam-5854	226	22	.	.	PUNCT
ejpam-5854	227	1	lemma	lemma	PROPN
ejpam-5854	227	2	2	2	NUM
ejpam-5854	227	3	.	.	PUNCT
ejpam-5854	228	1	[	[	X
ejpam-5854	228	2	13	13	NUM
ejpam-5854	228	3	]	]	PUNCT
ejpam-5854	228	4	a	a	DET
ejpam-5854	228	5	monoid	monoid	NOUN
ejpam-5854	228	6	s	s	X
ejpam-5854	228	7	is	be	AUX
ejpam-5854	228	8	weakly	weakly	ADV
ejpam-5854	228	9	regular	regular	ADJ
ejpam-5854	228	10	if	if	SCONJ
ejpam-5854	228	11	and	and	CCONJ
ejpam-5854	228	12	only	only	ADV
ejpam-5854	228	13	if	if	SCONJ
ejpam-5854	228	14	r	r	NOUN
ejpam-5854	228	15	∩	∩	X
ejpam-5854	228	16	j	j	PROPN
ejpam-5854	228	17	=	=	SYM
ejpam-5854	228	18	rj	rj	PROPN
ejpam-5854	228	19	for	for	ADP
ejpam-5854	228	20	every	every	DET
ejpam-5854	228	21	right	right	ADJ
ejpam-5854	228	22	ideal	ideal	ADJ
ejpam-5854	228	23	r	r	NOUN
ejpam-5854	228	24	and	and	CCONJ
ejpam-5854	228	25	every	every	DET
ejpam-5854	228	26	ideal	ideal	ADJ
ejpam-5854	228	27	j	j	PROPN
ejpam-5854	228	28	of	of	ADP
ejpam-5854	228	29	s.	s.	PROPN
ejpam-5854	228	30	now	now	ADV
ejpam-5854	228	31	we	we	PRON
ejpam-5854	228	32	characterize	characterize	VERB
ejpam-5854	228	33	weakly	weakly	ADV
ejpam-5854	228	34	regular	regular	ADJ
ejpam-5854	228	35	semigroups	semigroup	NOUN
ejpam-5854	228	36	in	in	ADP
ejpam-5854	228	37	terms	term	NOUN
ejpam-5854	228	38	of	of	ADP
ejpam-5854	228	39	generalized	generalized	ADJ
ejpam-5854	228	40	ivf	ivf	ADJ
ejpam-5854	228	41	ideals	ideal	NOUN
ejpam-5854	228	42	.	.	PUNCT
ejpam-5854	229	1	theorem	theorem	VERB
ejpam-5854	229	2	5	5	NUM
ejpam-5854	229	3	.	.	PUNCT
ejpam-5854	230	1	a	a	DET
ejpam-5854	230	2	monoid	monoid	NOUN
ejpam-5854	230	3	s	s	X
ejpam-5854	230	4	is	be	AUX
ejpam-5854	230	5	weakly	weakly	ADV
ejpam-5854	230	6	regular	regular	ADJ
ejpam-5854	230	7	if	if	SCONJ
ejpam-5854	230	8	and	and	CCONJ
ejpam-5854	230	9	only	only	ADV
ejpam-5854	230	10	if	if	SCONJ
ejpam-5854	230	11	c̈1	c̈1	NOUN
ejpam-5854	230	12	⊛	⊛	NUM
ejpam-5854	230	13	c̈2	c̈2	NOUN
ejpam-5854	230	14	=	=	PUNCT
ejpam-5854	230	15	c̈1⊓c̈2	c̈1⊓c̈2	PROPN
ejpam-5854	230	16	for	for	ADP
ejpam-5854	230	17	every	every	DET
ejpam-5854	230	18	cbf	cbf	PROPN
ejpam-5854	230	19	right	right	ADV
ejpam-5854	230	20	ideal	ideal	ADJ
ejpam-5854	230	21	c̈1	c̈1	NOUN
ejpam-5854	230	22	=	=	SYM
ejpam-5854	230	23	⟨µ	⟨µ	NOUN
ejpam-5854	230	24	,	,	PUNCT
ejpam-5854	230	25	ω⟩	ω⟩	NOUN
ejpam-5854	230	26	and	and	CCONJ
ejpam-5854	230	27	every	every	DET
ejpam-5854	230	28	cbf	cbf	PROPN
ejpam-5854	230	29	ideal	ideal	ADJ
ejpam-5854	230	30	c̈2	c̈2	PROPN
ejpam-5854	230	31	=	=	PUNCT
ejpam-5854	230	32	⟨λ	⟨λ	NUM
ejpam-5854	230	33	,	,	PUNCT
ejpam-5854	230	34	ψ⟩	ψ⟩	NUM
ejpam-5854	230	35	of	of	ADP
ejpam-5854	230	36	s.	s.	PROPN
ejpam-5854	230	37	proof	proof	PROPN
ejpam-5854	230	38	.	.	PUNCT
ejpam-5854	231	1	assume	assume	VERB
ejpam-5854	231	2	that	that	SCONJ
ejpam-5854	231	3	c̈1	c̈1	NOUN
ejpam-5854	231	4	=	=	SYM
ejpam-5854	231	5	⟨µ	⟨µ	NOUN
ejpam-5854	231	6	,	,	PUNCT
ejpam-5854	231	7	ω⟩	ω⟩	PRON
ejpam-5854	231	8	is	be	AUX
ejpam-5854	231	9	a	a	DET
ejpam-5854	231	10	cbf	cbf	PROPN
ejpam-5854	231	11	right	right	ADV
ejpam-5854	231	12	ideal	ideal	NOUN
ejpam-5854	231	13	and	and	CCONJ
ejpam-5854	231	14	c̈2	c̈2	NOUN
ejpam-5854	231	15	=	=	SYM
ejpam-5854	231	16	⟨λ	⟨λ	NUM
ejpam-5854	231	17	,	,	PUNCT
ejpam-5854	231	18	ψ⟩	ψ⟩	X
ejpam-5854	231	19	is	be	AUX
ejpam-5854	231	20	a	a	DET
ejpam-5854	231	21	cbf	cbf	PROPN
ejpam-5854	231	22	ideal	ideal	NOUN
ejpam-5854	231	23	of	of	ADP
ejpam-5854	231	24	s.	s.	PROPN
ejpam-5854	231	25	let	let	VERB
ejpam-5854	231	26	h	h	PROPN
ejpam-5854	231	27	∈	∈	PROPN
ejpam-5854	231	28	s.	s.	PROPN
ejpam-5854	231	29	since	since	SCONJ
ejpam-5854	231	30	s	s	PROPN
ejpam-5854	231	31	is	be	AUX
ejpam-5854	231	32	weakly	weakly	ADV
ejpam-5854	231	33	regular	regular	ADJ
ejpam-5854	231	34	,	,	PUNCT
ejpam-5854	231	35	there	there	PRON
ejpam-5854	231	36	exist	exist	VERB
ejpam-5854	231	37	p	p	PRON
ejpam-5854	231	38	,	,	PUNCT
ejpam-5854	231	39	q	q	PROPN
ejpam-5854	231	40	∈	∈	PROPN
ejpam-5854	231	41	s	s	VERB
ejpam-5854	231	42	such	such	ADJ
ejpam-5854	231	43	that	that	DET
ejpam-5854	231	44	h	h	NOUN
ejpam-5854	231	45	=	=	NOUN
ejpam-5854	231	46	hphq	hphq	NOUN
ejpam-5854	231	47	.	.	PUNCT
ejpam-5854	232	1	thus	thus	ADV
ejpam-5854	232	2	,	,	PUNCT
ejpam-5854	232	3	(	(	PUNCT
ejpam-5854	232	4	µp	µp	NOUN
ejpam-5854	232	5	⃝	⃝	VERB
ejpam-5854	232	6	λ	λ	PROPN
ejpam-5854	232	7	p	p	NOUN
ejpam-5854	232	8	)	)	PUNCT
ejpam-5854	232	9	(	(	PUNCT
ejpam-5854	232	10	h	h	NOUN
ejpam-5854	232	11	)	)	PUNCT
ejpam-5854	232	12	=	=	SYM
ejpam-5854	232	13	⋎	⋎	NOUN
ejpam-5854	232	14	(	(	PUNCT
ejpam-5854	232	15	k	k	NOUN
ejpam-5854	232	16	,	,	PUNCT
ejpam-5854	232	17	o)∈ah	o)∈ah	PROPN
ejpam-5854	232	18	{	{	PUNCT
ejpam-5854	232	19	µp(k)⋏	µp(k)⋏	NOUN
ejpam-5854	232	20	λ	λ	X
ejpam-5854	232	21	p	p	X
ejpam-5854	232	22	(	(	PUNCT
ejpam-5854	232	23	o	o	NOUN
ejpam-5854	232	24	)	)	PUNCT
ejpam-5854	232	25	}	}	PUNCT
ejpam-5854	233	1	=	=	SYM
ejpam-5854	233	2	⋎	⋎	NOUN
ejpam-5854	233	3	(	(	PUNCT
ejpam-5854	233	4	k	k	NOUN
ejpam-5854	233	5	,	,	PUNCT
ejpam-5854	233	6	o)∈ahphq	o)∈ahphq	ADJ
ejpam-5854	233	7	{	{	PUNCT
ejpam-5854	233	8	µp(k)⋏	µp(k)⋏	NOUN
ejpam-5854	233	9	λ	λ	X
ejpam-5854	233	10	p	p	X
ejpam-5854	233	11	(	(	PUNCT
ejpam-5854	233	12	o	o	NOUN
ejpam-5854	233	13	)	)	PUNCT
ejpam-5854	233	14	}	}	PUNCT
ejpam-5854	233	15	⪰	⪰	VERB
ejpam-5854	233	16	µp(hp)⋏	µp(hp)⋏	PROPN
ejpam-5854	233	17	λ	λ	PROPN
ejpam-5854	233	18	p	p	X
ejpam-5854	233	19	(	(	PUNCT
ejpam-5854	233	20	hq	hq	NOUN
ejpam-5854	233	21	)	)	PUNCT
ejpam-5854	233	22	⪰	⪰	NOUN
ejpam-5854	233	23	µp(h)⋏	µp(h)⋏	X
ejpam-5854	233	24	λ	λ	X
ejpam-5854	233	25	p	p	X
ejpam-5854	233	26	(	(	PUNCT
ejpam-5854	233	27	h	h	NOUN
ejpam-5854	233	28	)	)	PUNCT
ejpam-5854	233	29	=	=	SYM
ejpam-5854	234	1	(	(	PUNCT
ejpam-5854	234	2	µp	µp	PROPN
ejpam-5854	234	3	⊓	⊓	PROPN
ejpam-5854	234	4	λp)(h	λp)(h	NUM
ejpam-5854	234	5	)	)	PUNCT
ejpam-5854	234	6	,	,	PUNCT
ejpam-5854	234	7	(	(	PUNCT
ejpam-5854	234	8	µn	µn	NOUN
ejpam-5854	234	9	⃝	⃝	NOUN
ejpam-5854	234	10	λ	λ	NOUN
ejpam-5854	234	11	n	n	PRON
ejpam-5854	234	12	)	)	PUNCT
ejpam-5854	234	13	(	(	PUNCT
ejpam-5854	234	14	h	h	NOUN
ejpam-5854	234	15	)	)	PUNCT
ejpam-5854	234	16	=	=	SYM
ejpam-5854	235	1	⋏	⋏	PROPN
ejpam-5854	235	2	(	(	PUNCT
ejpam-5854	235	3	k	k	X
ejpam-5854	235	4	,	,	PUNCT
ejpam-5854	235	5	o)∈ah	o)∈ah	PROPN
ejpam-5854	235	6	{	{	PUNCT
ejpam-5854	235	7	µn(k)⋎	µn(k)⋎	PROPN
ejpam-5854	235	8	λ	λ	PROPN
ejpam-5854	235	9	n	n	CCONJ
ejpam-5854	235	10	(	(	PUNCT
ejpam-5854	235	11	o	o	NOUN
ejpam-5854	235	12	)	)	PUNCT
ejpam-5854	235	13	}	}	PUNCT
ejpam-5854	235	14	=	=	SYM
ejpam-5854	236	1	⋏	⋏	PROPN
ejpam-5854	236	2	(	(	PUNCT
ejpam-5854	236	3	k	k	X
ejpam-5854	236	4	,	,	PUNCT
ejpam-5854	236	5	o)∈ahphq	o)∈ahphq	ADJ
ejpam-5854	236	6	{	{	PUNCT
ejpam-5854	236	7	µn(k)⋎	µn(k)⋎	NOUN
ejpam-5854	236	8	λ	λ	PROPN
ejpam-5854	236	9	n	n	CCONJ
ejpam-5854	236	10	(	(	PUNCT
ejpam-5854	236	11	o	o	NOUN
ejpam-5854	236	12	)	)	PUNCT
ejpam-5854	236	13	}	}	PUNCT
ejpam-5854	236	14	⪯	⪯	VERB
ejpam-5854	236	15	µn(hp)⋎	µn(hp)⋎	PROPN
ejpam-5854	236	16	λ	λ	PROPN
ejpam-5854	236	17	n	n	PRON
ejpam-5854	236	18	(	(	PUNCT
ejpam-5854	236	19	hq	hq	NOUN
ejpam-5854	236	20	)	)	PUNCT
ejpam-5854	236	21	⪯	⪯	NOUN
ejpam-5854	236	22	µn(h)⋎	µn(h)⋎	X
ejpam-5854	236	23	λ	λ	PROPN
ejpam-5854	236	24	n	n	X
ejpam-5854	236	25	(	(	PUNCT
ejpam-5854	236	26	h	h	NOUN
ejpam-5854	236	27	)	)	PUNCT
ejpam-5854	236	28	=	=	SYM
ejpam-5854	236	29	(	(	PUNCT
ejpam-5854	236	30	µn	µn	PROPN
ejpam-5854	236	31	⊓	⊓	PROPN
ejpam-5854	236	32	λn)(h	λn)(h	NUM
ejpam-5854	236	33	)	)	PUNCT
ejpam-5854	236	34	,	,	PUNCT
ejpam-5854	236	35	and	and	CCONJ
ejpam-5854	236	36	(	(	PUNCT
ejpam-5854	236	37	ωp	ωp	NOUN
ejpam-5854	236	38	∗	∗	NOUN
ejpam-5854	236	39	ψp)(h	ψp)(h	PROPN
ejpam-5854	236	40	)	)	PUNCT
ejpam-5854	237	1	=	=	PUNCT
ejpam-5854	237	2	∨	∨	X
ejpam-5854	237	3	(	(	PUNCT
ejpam-5854	237	4	k	k	NOUN
ejpam-5854	237	5	,	,	PUNCT
ejpam-5854	237	6	o)∈ah	o)∈ah	PROPN
ejpam-5854	237	7	{	{	PUNCT
ejpam-5854	237	8	ωp(k	ωp(k	NOUN
ejpam-5854	237	9	)	)	PUNCT
ejpam-5854	237	10	∧	∧	NOUN
ejpam-5854	237	11	ψp(o	ψp(o	NOUN
ejpam-5854	237	12	)	)	PUNCT
ejpam-5854	237	13	}	}	PUNCT
ejpam-5854	237	14	=	=	SYM
ejpam-5854	237	15	∨	∨	X
ejpam-5854	237	16	(	(	PUNCT
ejpam-5854	237	17	k	k	NOUN
ejpam-5854	237	18	,	,	PUNCT
ejpam-5854	237	19	o)∈ahphq	o)∈ahphq	ADJ
ejpam-5854	237	20	{	{	PUNCT
ejpam-5854	237	21	ωp(k	ωp(k	NOUN
ejpam-5854	237	22	)	)	PUNCT
ejpam-5854	237	23	∧	∧	NOUN
ejpam-5854	237	24	ψp(k	ψp(k	NOUN
ejpam-5854	237	25	)	)	PUNCT
ejpam-5854	237	26	}	}	PUNCT
ejpam-5854	237	27	≥	≥	NUM
ejpam-5854	237	28	ωp(hp	ωp(hp	ADJ
ejpam-5854	237	29	)	)	PUNCT
ejpam-5854	237	30	∧	∧	PROPN
ejpam-5854	237	31	ψp(hq	ψp(hq	PROPN
ejpam-5854	237	32	)	)	PUNCT
ejpam-5854	237	33	≥	≥	NOUN
ejpam-5854	237	34	ωp(h	ωp(h	NOUN
ejpam-5854	237	35	)	)	PUNCT
ejpam-5854	237	36	∧	∧	NOUN
ejpam-5854	237	37	ψp(h	ψp(h	X
ejpam-5854	237	38	)	)	PUNCT
ejpam-5854	237	39	=	=	SYM
ejpam-5854	237	40	(	(	PUNCT
ejpam-5854	237	41	ωp	ωp	X
ejpam-5854	237	42	∩	∩	NOUN
ejpam-5854	237	43	ψp)(h	ψp)(h	PROPN
ejpam-5854	237	44	)	)	PUNCT
ejpam-5854	237	45	,	,	PUNCT
ejpam-5854	237	46	(	(	PUNCT
ejpam-5854	237	47	ωn	ωn	ADP
ejpam-5854	237	48	∗	∗	NOUN
ejpam-5854	237	49	ψn)(h	ψn)(h	PROPN
ejpam-5854	237	50	)	)	PUNCT
ejpam-5854	238	1	=	=	PUNCT
ejpam-5854	238	2	∧	∧	PROPN
ejpam-5854	238	3	(	(	PUNCT
ejpam-5854	238	4	k	k	NOUN
ejpam-5854	238	5	,	,	PUNCT
ejpam-5854	238	6	o)∈ah	o)∈ah	PROPN
ejpam-5854	238	7	{	{	PUNCT
ejpam-5854	238	8	ωn(k	ωn(k	NUM
ejpam-5854	238	9	)	)	PUNCT
ejpam-5854	238	10	∨	∨	NUM
ejpam-5854	238	11	ψn(o	ψn(o	NUM
ejpam-5854	238	12	)	)	PUNCT
ejpam-5854	238	13	}	}	PUNCT
ejpam-5854	239	1	=	=	SYM
ejpam-5854	239	2	∧	∧	PROPN
ejpam-5854	239	3	(	(	PUNCT
ejpam-5854	239	4	k	k	NOUN
ejpam-5854	239	5	,	,	PUNCT
ejpam-5854	239	6	o)∈ahphq	o)∈ahphq	ADJ
ejpam-5854	239	7	{	{	PUNCT
ejpam-5854	239	8	ωn(ko	ωn(ko	NOUN
ejpam-5854	239	9	)	)	PUNCT
ejpam-5854	239	10	∨	∨	NOUN
ejpam-5854	239	11	ψn(ko	ψn(ko	PROPN
ejpam-5854	239	12	)	)	PUNCT
ejpam-5854	239	13	}	}	PUNCT
ejpam-5854	239	14	≤	≤	NUM
ejpam-5854	239	15	ωn(hp	ωn(hp	ADJ
ejpam-5854	239	16	)	)	PUNCT
ejpam-5854	239	17	∨	∨	NUM
ejpam-5854	239	18	ψn(hq	ψn(hq	NOUN
ejpam-5854	239	19	)	)	PUNCT
ejpam-5854	239	20	≤	≤	NOUN
ejpam-5854	239	21	ωn(h	ωn(h	NUM
ejpam-5854	239	22	)	)	PUNCT
ejpam-5854	239	23	∨	∨	NUM
ejpam-5854	239	24	ψn(h	ψn(h	NUM
ejpam-5854	239	25	)	)	PUNCT
ejpam-5854	239	26	=	=	SYM
ejpam-5854	239	27	(	(	PUNCT
ejpam-5854	239	28	ωn	ωn	ADP
ejpam-5854	239	29	∩	∩	NOUN
ejpam-5854	239	30	ψn)(h	ψn)(h	PROPN
ejpam-5854	239	31	)	)	PUNCT
ejpam-5854	239	32	.	.	PUNCT
ejpam-5854	240	1	hence	hence	ADV
ejpam-5854	240	2	,	,	PUNCT
ejpam-5854	240	3	(	(	PUNCT
ejpam-5854	240	4	µp	µp	PROPN
ejpam-5854	240	5	⊓λp)(h	⊓λp)(h	PROPN
ejpam-5854	240	6	)	)	PUNCT
ejpam-5854	240	7	⪯	⪯	NOUN
ejpam-5854	240	8	(	(	PUNCT
ejpam-5854	240	9	µp	µp	NOUN
ejpam-5854	240	10	⃝λ	⃝λ	PROPN
ejpam-5854	240	11	p	p	NOUN
ejpam-5854	240	12	)	)	PUNCT
ejpam-5854	240	13	(	(	PUNCT
ejpam-5854	240	14	h	h	NOUN
ejpam-5854	240	15	)	)	PUNCT
ejpam-5854	240	16	,	,	PUNCT
ejpam-5854	240	17	(	(	PUNCT
ejpam-5854	240	18	µn	µn	PROPN
ejpam-5854	240	19	⊓λn)(h	⊓λn)(h	NOUN
ejpam-5854	240	20	)	)	PUNCT
ejpam-5854	240	21	⪰	⪰	NOUN
ejpam-5854	240	22	(	(	PUNCT
ejpam-5854	240	23	µn	µn	PROPN
ejpam-5854	240	24	⃝λ	⃝λ	X
ejpam-5854	240	25	n	n	CCONJ
ejpam-5854	240	26	)	)	PUNCT
ejpam-5854	240	27	(	(	PUNCT
ejpam-5854	240	28	h	h	NOUN
ejpam-5854	240	29	)	)	PUNCT
ejpam-5854	240	30	and	and	CCONJ
ejpam-5854	240	31	(	(	PUNCT
ejpam-5854	240	32	ωp	ωp	NOUN
ejpam-5854	240	33	∩ψp)(h	∩ψp)(h	NOUN
ejpam-5854	240	34	)	)	PUNCT
ejpam-5854	240	35	≤	≤	NOUN
ejpam-5854	240	36	(	(	PUNCT
ejpam-5854	240	37	ωp	ωp	NUM
ejpam-5854	240	38	∗ψp)(h	∗ψp)(h	NUM
ejpam-5854	240	39	)	)	PUNCT
ejpam-5854	240	40	,	,	PUNCT
ejpam-5854	240	41	(	(	PUNCT
ejpam-5854	240	42	ωn	ωn	PROPN
ejpam-5854	240	43	∩	∩	NOUN
ejpam-5854	240	44	ψn)(h	ψn)(h	PROPN
ejpam-5854	240	45	)	)	PUNCT
ejpam-5854	240	46	≥	≥	NOUN
ejpam-5854	240	47	(	(	PUNCT
ejpam-5854	240	48	ωn	ωn	ADP
ejpam-5854	240	49	∗	∗	NOUN
ejpam-5854	240	50	ψn)(h	ψn)(h	PROPN
ejpam-5854	240	51	)	)	PUNCT
ejpam-5854	240	52	.	.	PUNCT
ejpam-5854	241	1	therefore	therefore	ADV
ejpam-5854	241	2	,	,	PUNCT
ejpam-5854	241	3	c̈1⊓c̈2⊏c̈1	c̈1⊓c̈2⊏c̈1	NOUN
ejpam-5854	241	4	⊛	⊛	NUM
ejpam-5854	241	5	c̈2	c̈2	NOUN
ejpam-5854	241	6	.	.	PUNCT
ejpam-5854	242	1	on	on	ADP
ejpam-5854	242	2	the	the	DET
ejpam-5854	242	3	other	other	ADJ
ejpam-5854	242	4	hand	hand	NOUN
ejpam-5854	242	5	,	,	PUNCT
ejpam-5854	242	6	since	since	SCONJ
ejpam-5854	242	7	c̈2	c̈2	NOUN
ejpam-5854	242	8	is	be	AUX
ejpam-5854	242	9	a	a	DET
ejpam-5854	242	10	cbf	cbf	PROPN
ejpam-5854	242	11	ideal	ideal	NOUN
ejpam-5854	242	12	of	of	ADP
ejpam-5854	242	13	s	s	PRON
ejpam-5854	242	14	we	we	PRON
ejpam-5854	242	15	see	see	VERB
ejpam-5854	242	16	that	that	DET
ejpam-5854	242	17	c̈2	c̈2	NOUN
ejpam-5854	242	18	is	be	AUX
ejpam-5854	242	19	a	a	DET
ejpam-5854	242	20	cbf	cbf	PROPN
ejpam-5854	242	21	left	leave	VERB
ejpam-5854	242	22	ideal	ideal	NOUN
ejpam-5854	242	23	of	of	ADP
ejpam-5854	242	24	s.	s.	PROPN
ejpam-5854	242	25	thus	thus	ADV
ejpam-5854	242	26	,	,	PUNCT
ejpam-5854	242	27	by	by	ADP
ejpam-5854	242	28	lemma	lemma	PROPN
ejpam-5854	242	29	1	1	NUM
ejpam-5854	242	30	,	,	PUNCT
ejpam-5854	242	31	c̈1	c̈1	NOUN
ejpam-5854	242	32	⊛	⊛	ADJ
ejpam-5854	242	33	c̈2⊏c̈1⊓c̈2	c̈2⊏c̈1⊓c̈2	NOUN
ejpam-5854	242	34	.	.	PUNCT
ejpam-5854	243	1	hence	hence	ADV
ejpam-5854	243	2	,	,	PUNCT
ejpam-5854	243	3	c̈1	c̈1	NOUN
ejpam-5854	243	4	⊛	⊛	NUM
ejpam-5854	243	5	c̈2	c̈2	NOUN
ejpam-5854	243	6	=	=	SYM
ejpam-5854	243	7	c̈1⊓c̈2	c̈1⊓c̈2	PROPN
ejpam-5854	243	8	.	.	PUNCT
ejpam-5854	244	1	conversely	conversely	ADV
ejpam-5854	244	2	,	,	PUNCT
ejpam-5854	244	3	let	let	VERB
ejpam-5854	244	4	r	r	PRON
ejpam-5854	244	5	and	and	CCONJ
ejpam-5854	244	6	j	j	PROPN
ejpam-5854	244	7	be	be	VERB
ejpam-5854	244	8	a	a	DET
ejpam-5854	244	9	right	right	ADJ
ejpam-5854	244	10	ideal	ideal	NOUN
ejpam-5854	244	11	and	and	CCONJ
ejpam-5854	244	12	ideal	ideal	NOUN
ejpam-5854	244	13	of	of	ADP
ejpam-5854	244	14	g.	g.	PROPN
ejpam-5854	244	15	then	then	ADV
ejpam-5854	244	16	,	,	PUNCT
ejpam-5854	244	17	by	by	ADP
ejpam-5854	244	18	theorem	theorem	NOUN
ejpam-5854	244	19	3	3	NUM
ejpam-5854	244	20	,	,	PUNCT
ejpam-5854	244	21	χr	χr	NOUN
ejpam-5854	244	22	and	and	CCONJ
ejpam-5854	244	23	χj	χj	PROPN
ejpam-5854	244	24	cbf	cbf	PROPN
ejpam-5854	244	25	right	right	PROPN
ejpam-5854	244	26	ideal	ideal	PROPN
ejpam-5854	244	27	and	and	CCONJ
ejpam-5854	244	28	cbf	cbf	PROPN
ejpam-5854	244	29	ideal	ideal	NOUN
ejpam-5854	244	30	of	of	ADP
ejpam-5854	244	31	s.	s.	PROPN
ejpam-5854	244	32	by	by	ADP
ejpam-5854	244	33	supposition	supposition	PROPN
ejpam-5854	244	34	and	and	CCONJ
ejpam-5854	244	35	lemma	lemma	PROPN
ejpam-5854	244	36	4	4	NUM
ejpam-5854	244	37	,	,	PUNCT
ejpam-5854	244	38	we	we	PRON
ejpam-5854	244	39	have	have	VERB
ejpam-5854	244	40	p.	p.	NOUN
ejpam-5854	244	41	khamrot	khamrot	PROPN
ejpam-5854	244	42	,	,	PUNCT
ejpam-5854	244	43	n.	n.	PROPN
ejpam-5854	244	44	deetae	deetae	PROPN
ejpam-5854	244	45	,	,	PUNCT
ejpam-5854	244	46	t.	t.	PROPN
ejpam-5854	244	47	gaketem	gaketem	PROPN
ejpam-5854	244	48	/	/	SYM
ejpam-5854	244	49	eur	eur	PROPN
ejpam-5854	244	50	.	.	PUNCT
ejpam-5854	245	1	j.	j.	PROPN
ejpam-5854	245	2	pure	pure	PROPN
ejpam-5854	245	3	appl	appl	PROPN
ejpam-5854	245	4	.	.	PROPN
ejpam-5854	245	5	math	math	PROPN
ejpam-5854	245	6	,	,	PUNCT
ejpam-5854	245	7	18	18	NUM
ejpam-5854	245	8	(	(	PUNCT
ejpam-5854	245	9	2	2	NUM
ejpam-5854	245	10	)	)	PUNCT
ejpam-5854	245	11	(	(	PUNCT
ejpam-5854	245	12	2025	2025	NUM
ejpam-5854	245	13	)	)	PUNCT
ejpam-5854	245	14	,	,	PUNCT
ejpam-5854	245	15	5854	5854	NUM
ejpam-5854	245	16	11	11	NUM
ejpam-5854	245	17	of	of	ADP
ejpam-5854	245	18	14	14	NUM
ejpam-5854	245	19	µp	µp	PROPN
ejpam-5854	245	20	χrj	χrj	NOUN
ejpam-5854	245	21	(	(	PUNCT
ejpam-5854	245	22	h	h	NOUN
ejpam-5854	245	23	)	)	PUNCT
ejpam-5854	245	24	=	=	SYM
ejpam-5854	246	1	(	(	PUNCT
ejpam-5854	246	2	µp	µp	NOUN
ejpam-5854	246	3	χr	χr	VERB
ejpam-5854	246	4	⃝	⃝	PROPN
ejpam-5854	246	5	µp	µp	NOUN
ejpam-5854	246	6	χj	χj	PROPN
ejpam-5854	246	7	)	)	PUNCT
ejpam-5854	246	8	(	(	PUNCT
ejpam-5854	246	9	h	h	NOUN
ejpam-5854	246	10	)	)	PUNCT
ejpam-5854	246	11	=	=	SYM
ejpam-5854	247	1	(	(	PUNCT
ejpam-5854	247	2	µp	µp	NOUN
ejpam-5854	247	3	χr	χr	VERB
ejpam-5854	247	4	⊓	⊓	PROPN
ejpam-5854	247	5	µp	µp	NOUN
ejpam-5854	247	6	χj	χj	PROPN
ejpam-5854	247	7	)	)	PUNCT
ejpam-5854	247	8	(	(	PUNCT
ejpam-5854	247	9	h	h	NOUN
ejpam-5854	247	10	)	)	PUNCT
ejpam-5854	247	11	=	=	NOUN
ejpam-5854	247	12	µp	µp	NOUN
ejpam-5854	247	13	χr⊓j	χr⊓j	NOUN
ejpam-5854	247	14	(	(	PUNCT
ejpam-5854	247	15	h	h	NOUN
ejpam-5854	247	16	)	)	PUNCT
ejpam-5854	247	17	=	=	SYM
ejpam-5854	247	18	1	1	NUM
ejpam-5854	247	19	,	,	PUNCT
ejpam-5854	247	20	µn	µn	NOUN
ejpam-5854	247	21	χrj	χrj	NOUN
ejpam-5854	247	22	(	(	PUNCT
ejpam-5854	247	23	h	h	NOUN
ejpam-5854	247	24	)	)	PUNCT
ejpam-5854	247	25	=	=	SYM
ejpam-5854	248	1	(	(	PUNCT
ejpam-5854	248	2	µp	µp	NOUN
ejpam-5854	248	3	χr	χr	VERB
ejpam-5854	248	4	⃝	⃝	PROPN
ejpam-5854	248	5	µp	µp	NOUN
ejpam-5854	248	6	χj	χj	PROPN
ejpam-5854	248	7	)	)	PUNCT
ejpam-5854	248	8	(	(	PUNCT
ejpam-5854	248	9	h	h	NOUN
ejpam-5854	248	10	)	)	PUNCT
ejpam-5854	248	11	=	=	SYM
ejpam-5854	249	1	(	(	PUNCT
ejpam-5854	249	2	µn	µn	INTJ
ejpam-5854	249	3	χr	χr	VERB
ejpam-5854	249	4	⊓	⊓	PROPN
ejpam-5854	249	5	µp	µp	PROPN
ejpam-5854	249	6	χj	χj	PROPN
ejpam-5854	249	7	)	)	PUNCT
ejpam-5854	249	8	(	(	PUNCT
ejpam-5854	249	9	h	h	NOUN
ejpam-5854	249	10	)	)	PUNCT
ejpam-5854	249	11	=	=	SYM
ejpam-5854	249	12	µn	µn	PROPN
ejpam-5854	249	13	χr⊓j	χr⊓j	NOUN
ejpam-5854	249	14	(	(	PUNCT
ejpam-5854	249	15	h	h	NOUN
ejpam-5854	249	16	)	)	PUNCT
ejpam-5854	249	17	=	=	SYM
ejpam-5854	249	18	−1	−1	NOUN
ejpam-5854	249	19	,	,	PUNCT
ejpam-5854	249	20	and	and	CCONJ
ejpam-5854	249	21	ωp	ωp	PRON
ejpam-5854	249	22	χrj	χrj	NOUN
ejpam-5854	249	23	(	(	PUNCT
ejpam-5854	249	24	h	h	NOUN
ejpam-5854	249	25	)	)	PUNCT
ejpam-5854	249	26	=	=	SYM
ejpam-5854	250	1	(	(	PUNCT
ejpam-5854	250	2	ωp	ωp	INTJ
ejpam-5854	250	3	χr	χr	VERB
ejpam-5854	250	4	∗	∗	NOUN
ejpam-5854	250	5	ωp	ωp	PRON
ejpam-5854	250	6	χj	χj	PROPN
ejpam-5854	250	7	)	)	PUNCT
ejpam-5854	250	8	(	(	PUNCT
ejpam-5854	250	9	h	h	NOUN
ejpam-5854	250	10	)	)	PUNCT
ejpam-5854	250	11	=	=	SYM
ejpam-5854	250	12	(	(	PUNCT
ejpam-5854	250	13	ωp	ωp	NOUN
ejpam-5854	250	14	χr	χr	VERB
ejpam-5854	250	15	∩	∩	PROPN
ejpam-5854	250	16	ωp	ωp	NOUN
ejpam-5854	250	17	χj	χj	PROPN
ejpam-5854	250	18	)	)	PUNCT
ejpam-5854	250	19	(	(	PUNCT
ejpam-5854	250	20	h	h	NOUN
ejpam-5854	250	21	)	)	PUNCT
ejpam-5854	250	22	=	=	NOUN
ejpam-5854	251	1	ωp	ωp	PRON
ejpam-5854	251	2	χr∩j	χr∩j	NOUN
ejpam-5854	251	3	(	(	PUNCT
ejpam-5854	251	4	h	h	NOUN
ejpam-5854	251	5	)	)	PUNCT
ejpam-5854	251	6	=	=	SYM
ejpam-5854	251	7	1	1	NUM
ejpam-5854	251	8	,	,	PUNCT
ejpam-5854	251	9	ωn	ωn	PRON
ejpam-5854	251	10	χrj	χrj	NOUN
ejpam-5854	251	11	(	(	PUNCT
ejpam-5854	251	12	h	h	NOUN
ejpam-5854	251	13	)	)	PUNCT
ejpam-5854	251	14	=	=	SYM
ejpam-5854	252	1	(	(	PUNCT
ejpam-5854	252	2	ωn	ωn	INTJ
ejpam-5854	252	3	χr	χr	PROPN
ejpam-5854	252	4	∗	∗	NOUN
ejpam-5854	252	5	ωn	ωn	ADP
ejpam-5854	252	6	χj	χj	PROPN
ejpam-5854	252	7	)	)	PUNCT
ejpam-5854	252	8	(	(	PUNCT
ejpam-5854	252	9	h	h	NOUN
ejpam-5854	252	10	)	)	PUNCT
ejpam-5854	252	11	=	=	SYM
ejpam-5854	253	1	(	(	PUNCT
ejpam-5854	253	2	ωn	ωn	NUM
ejpam-5854	253	3	χr	χr	PROPN
ejpam-5854	253	4	∩	∩	NOUN
ejpam-5854	253	5	ωn	ωn	PRON
ejpam-5854	253	6	χj	χj	PROPN
ejpam-5854	253	7	)	)	PUNCT
ejpam-5854	253	8	(	(	PUNCT
ejpam-5854	253	9	h	h	NOUN
ejpam-5854	253	10	)	)	PUNCT
ejpam-5854	253	11	=	=	SYM
ejpam-5854	253	12	ωn	ωn	PRON
ejpam-5854	253	13	χr∩j	χr∩j	X
ejpam-5854	253	14	(	(	PUNCT
ejpam-5854	253	15	h	h	NOUN
ejpam-5854	253	16	)	)	PUNCT
ejpam-5854	253	17	=	=	PUNCT
ejpam-5854	253	18	−1	−1	NOUN
ejpam-5854	253	19	.	.	PUNCT
ejpam-5854	254	1	thus	thus	ADV
ejpam-5854	254	2	,	,	PUNCT
ejpam-5854	254	3	h	h	PROPN
ejpam-5854	254	4	∈	∈	PROPN
ejpam-5854	254	5	rj	rj	PROPN
ejpam-5854	254	6	.	.	PUNCT
ejpam-5854	255	1	hence	hence	ADV
ejpam-5854	255	2	,	,	PUNCT
ejpam-5854	255	3	r	r	NOUN
ejpam-5854	255	4	∩	∩	ADJ
ejpam-5854	255	5	j	j	PROPN
ejpam-5854	255	6	=	=	SYM
ejpam-5854	255	7	rj	rj	PROPN
ejpam-5854	255	8	.	.	PUNCT
ejpam-5854	256	1	therefore	therefore	ADV
ejpam-5854	256	2	,	,	PUNCT
ejpam-5854	256	3	by	by	ADP
ejpam-5854	256	4	lemma	lemma	PROPN
ejpam-5854	256	5	2	2	NUM
ejpam-5854	256	6	,	,	PUNCT
ejpam-5854	256	7	s	s	VERB
ejpam-5854	256	8	is	be	AUX
ejpam-5854	256	9	weakly	weakly	ADV
ejpam-5854	256	10	regular	regular	ADJ
ejpam-5854	256	11	.	.	PUNCT
ejpam-5854	257	1	lemma	lemma	PROPN
ejpam-5854	257	2	3	3	X
ejpam-5854	257	3	.	.	PUNCT
ejpam-5854	258	1	[	[	X
ejpam-5854	258	2	13	13	NUM
ejpam-5854	258	3	]	]	PUNCT
ejpam-5854	258	4	let	let	VERB
ejpam-5854	258	5	s	s	PRON
ejpam-5854	258	6	be	be	AUX
ejpam-5854	258	7	a	a	DET
ejpam-5854	258	8	monoid	monoid	NOUN
ejpam-5854	258	9	.	.	PUNCT
ejpam-5854	259	1	then	then	ADV
ejpam-5854	259	2	,	,	PUNCT
ejpam-5854	259	3	the	the	DET
ejpam-5854	259	4	following	follow	VERB
ejpam-5854	259	5	statements	statement	NOUN
ejpam-5854	259	6	are	be	AUX
ejpam-5854	259	7	equivalent	equivalent	ADJ
ejpam-5854	259	8	:	:	PUNCT
ejpam-5854	259	9	(	(	PUNCT
ejpam-5854	259	10	1	1	X
ejpam-5854	259	11	)	)	PUNCT
ejpam-5854	259	12	s	s	VERB
ejpam-5854	259	13	is	be	AUX
ejpam-5854	259	14	weakly	weakly	ADV
ejpam-5854	259	15	regular	regular	ADJ
ejpam-5854	259	16	.	.	PUNCT
ejpam-5854	260	1	(	(	PUNCT
ejpam-5854	260	2	2	2	X
ejpam-5854	260	3	)	)	PUNCT
ejpam-5854	260	4	q	q	NOUN
ejpam-5854	260	5	∩	∩	ADJ
ejpam-5854	260	6	j	j	PROPN
ejpam-5854	260	7	⊆	⊆	NUM
ejpam-5854	260	8	qj	qj	PROPN
ejpam-5854	260	9	for	for	ADP
ejpam-5854	260	10	every	every	DET
ejpam-5854	260	11	quasi	quasi	ADJ
ejpam-5854	260	12	-	-	ADJ
ejpam-5854	260	13	ideal	ideal	ADJ
ejpam-5854	260	14	q	q	NOUN
ejpam-5854	260	15	and	and	CCONJ
ejpam-5854	260	16	every	every	DET
ejpam-5854	260	17	ideal	ideal	ADJ
ejpam-5854	260	18	j	j	PROPN
ejpam-5854	260	19	of	of	ADP
ejpam-5854	260	20	s.	s.	PROPN
ejpam-5854	260	21	on	on	ADP
ejpam-5854	260	22	the	the	DET
ejpam-5854	260	23	basis	basis	NOUN
ejpam-5854	260	24	of	of	ADP
ejpam-5854	260	25	lemma	lemma	PROPN
ejpam-5854	260	26	3	3	NUM
ejpam-5854	260	27	,	,	PUNCT
ejpam-5854	260	28	we	we	PRON
ejpam-5854	260	29	can	can	AUX
ejpam-5854	260	30	prove	prove	VERB
ejpam-5854	260	31	theorem	theorem	ADJ
ejpam-5854	260	32	6	6	NUM
ejpam-5854	260	33	.	.	PUNCT
ejpam-5854	260	34	theorem	theorem	VERB
ejpam-5854	260	35	6	6	NUM
ejpam-5854	260	36	.	.	PUNCT
ejpam-5854	260	37	for	for	ADP
ejpam-5854	260	38	a	a	DET
ejpam-5854	260	39	monoid	monoid	NOUN
ejpam-5854	260	40	s	s	PROPN
ejpam-5854	260	41	,	,	PUNCT
ejpam-5854	260	42	the	the	DET
ejpam-5854	260	43	following	following	ADJ
ejpam-5854	260	44	statements	statement	NOUN
ejpam-5854	260	45	are	be	AUX
ejpam-5854	260	46	equivalent	equivalent	ADJ
ejpam-5854	260	47	.	.	PUNCT
ejpam-5854	261	1	(	(	PUNCT
ejpam-5854	261	2	1	1	X
ejpam-5854	261	3	)	)	PUNCT
ejpam-5854	261	4	s	s	VERB
ejpam-5854	261	5	is	be	AUX
ejpam-5854	261	6	weakly	weakly	ADV
ejpam-5854	261	7	regular	regular	ADJ
ejpam-5854	261	8	.	.	PUNCT
ejpam-5854	262	1	(	(	PUNCT
ejpam-5854	262	2	2	2	X
ejpam-5854	262	3	)	)	PUNCT
ejpam-5854	262	4	c̈1⊓c̈2⊏c̈1	c̈1⊓c̈2⊏c̈1	NOUN
ejpam-5854	262	5	⊛	⊛	NUM
ejpam-5854	262	6	c̈2	c̈2	NOUN
ejpam-5854	262	7	for	for	ADP
ejpam-5854	262	8	every	every	DET
ejpam-5854	262	9	cbf	cbf	PROPN
ejpam-5854	262	10	quasi	quasi	ADJ
ejpam-5854	262	11	-	-	ADJ
ejpam-5854	262	12	ideal	ideal	ADJ
ejpam-5854	262	13	c̈1	c̈1	NOUN
ejpam-5854	262	14	=	=	SYM
ejpam-5854	262	15	⟨µ	⟨µ	NOUN
ejpam-5854	262	16	,	,	PUNCT
ejpam-5854	262	17	ω⟩	ω⟩	NOUN
ejpam-5854	262	18	and	and	CCONJ
ejpam-5854	262	19	every	every	DET
ejpam-5854	262	20	cbf	cbf	PROPN
ejpam-5854	262	21	ideal	ideal	ADJ
ejpam-5854	262	22	c̈2	c̈2	PROPN
ejpam-5854	262	23	=	=	PUNCT
ejpam-5854	262	24	⟨λ	⟨λ	NUM
ejpam-5854	262	25	,	,	PUNCT
ejpam-5854	262	26	ψ⟩	ψ⟩	NUM
ejpam-5854	262	27	of	of	ADP
ejpam-5854	262	28	s.	s.	PROPN
ejpam-5854	262	29	(	(	PUNCT
ejpam-5854	262	30	3	3	X
ejpam-5854	262	31	)	)	PUNCT
ejpam-5854	262	32	c̈1⊓c̈2⊏c̈1	c̈1⊓c̈2⊏c̈1	NOUN
ejpam-5854	262	33	⊛	⊛	NUM
ejpam-5854	262	34	c̈2	c̈2	NOUN
ejpam-5854	262	35	for	for	ADP
ejpam-5854	262	36	every	every	DET
ejpam-5854	262	37	cbf	cbf	PROPN
ejpam-5854	262	38	bi	bi	ADJ
ejpam-5854	262	39	-	-	ADJ
ejpam-5854	262	40	ideal	ideal	ADJ
ejpam-5854	262	41	c̈1	c̈1	NOUN
ejpam-5854	262	42	=	=	SYM
ejpam-5854	262	43	⟨µ	⟨µ	NOUN
ejpam-5854	262	44	,	,	PUNCT
ejpam-5854	262	45	ω⟩	ω⟩	NOUN
ejpam-5854	262	46	and	and	CCONJ
ejpam-5854	262	47	every	every	DET
ejpam-5854	262	48	cbvf	cbvf	NOUN
ejpam-5854	262	49	ideal	ideal	ADJ
ejpam-5854	262	50	c̈2	c̈2	NOUN
ejpam-5854	262	51	=	=	PUNCT
ejpam-5854	262	52	⟨λ	⟨λ	NUM
ejpam-5854	262	53	,	,	PUNCT
ejpam-5854	262	54	ψ⟩	ψ⟩	NUM
ejpam-5854	262	55	of	of	ADP
ejpam-5854	262	56	s.	s.	PROPN
ejpam-5854	262	57	(	(	PUNCT
ejpam-5854	262	58	4	4	X
ejpam-5854	262	59	)	)	PUNCT
ejpam-5854	262	60	c̈1⊓c̈2⊏c̈1	c̈1⊓c̈2⊏c̈1	NOUN
ejpam-5854	262	61	⊛	⊛	NUM
ejpam-5854	262	62	c̈2	c̈2	NOUN
ejpam-5854	262	63	for	for	SCONJ
ejpam-5854	262	64	every	every	DET
ejpam-5854	262	65	cbf	cbf	PROPN
ejpam-5854	262	66	generalized	generalize	VERB
ejpam-5854	262	67	bi	bi	ADJ
ejpam-5854	262	68	-	-	ADJ
ejpam-5854	262	69	ideal	ideal	ADJ
ejpam-5854	262	70	c̈1	c̈1	NOUN
ejpam-5854	262	71	=	=	SYM
ejpam-5854	262	72	⟨µ	⟨µ	NOUN
ejpam-5854	262	73	,	,	PUNCT
ejpam-5854	262	74	ω⟩	ω⟩	NOUN
ejpam-5854	262	75	and	and	CCONJ
ejpam-5854	262	76	every	every	DET
ejpam-5854	262	77	cbf	cbf	PROPN
ejpam-5854	262	78	interior	interior	ADJ
ejpam-5854	262	79	ideal	ideal	ADJ
ejpam-5854	262	80	c̈2	c̈2	NOUN
ejpam-5854	262	81	=	=	PUNCT
ejpam-5854	262	82	⟨λ	⟨λ	NUM
ejpam-5854	262	83	,	,	PUNCT
ejpam-5854	262	84	ψ⟩	ψ⟩	NUM
ejpam-5854	262	85	of	of	ADP
ejpam-5854	262	86	s.	s.	PROPN
ejpam-5854	262	87	proof	proof	PROPN
ejpam-5854	262	88	.	.	PUNCT
ejpam-5854	263	1	(	(	PUNCT
ejpam-5854	263	2	1	1	X
ejpam-5854	263	3	)	)	PUNCT
ejpam-5854	263	4	⇒	⇒	NOUN
ejpam-5854	263	5	(	(	PUNCT
ejpam-5854	263	6	4	4	X
ejpam-5854	263	7	)	)	PUNCT
ejpam-5854	263	8	assume	assume	VERB
ejpam-5854	263	9	that	that	SCONJ
ejpam-5854	263	10	c̈1	c̈1	NOUN
ejpam-5854	263	11	=	=	SYM
ejpam-5854	263	12	⟨µ	⟨µ	NOUN
ejpam-5854	263	13	,	,	PUNCT
ejpam-5854	263	14	ω⟩	ω⟩	PRON
ejpam-5854	263	15	is	be	AUX
ejpam-5854	263	16	a	a	DET
ejpam-5854	263	17	cbf	cbf	PROPN
ejpam-5854	263	18	generalized	generalize	VERB
ejpam-5854	263	19	bi	bi	NOUN
ejpam-5854	263	20	-	-	ADJ
ejpam-5854	263	21	ideal	ideal	ADJ
ejpam-5854	263	22	and	and	CCONJ
ejpam-5854	263	23	c̈2	c̈2	NOUN
ejpam-5854	263	24	=	=	PUNCT
ejpam-5854	263	25	⟨λ	⟨λ	NUM
ejpam-5854	263	26	,	,	PUNCT
ejpam-5854	263	27	ψ⟩	ψ⟩	X
ejpam-5854	263	28	is	be	AUX
ejpam-5854	263	29	a	a	DET
ejpam-5854	263	30	cbf	cbf	PROPN
ejpam-5854	263	31	interior	interior	PROPN
ejpam-5854	263	32	ideal	ideal	NOUN
ejpam-5854	263	33	of	of	ADP
ejpam-5854	263	34	s.	s.	PROPN
ejpam-5854	263	35	let	let	VERB
ejpam-5854	263	36	h	h	PROPN
ejpam-5854	263	37	∈	∈	PROPN
ejpam-5854	263	38	s.	s.	PROPN
ejpam-5854	264	1	then	then	ADV
ejpam-5854	264	2	,	,	PUNCT
ejpam-5854	264	3	there	there	PRON
ejpam-5854	264	4	exist	exist	VERB
ejpam-5854	264	5	p	p	PRON
ejpam-5854	264	6	,	,	PUNCT
ejpam-5854	264	7	q	q	PROPN
ejpam-5854	264	8	∈	∈	PROPN
ejpam-5854	264	9	s	s	VERB
ejpam-5854	264	10	such	such	ADJ
ejpam-5854	264	11	that	that	DET
ejpam-5854	264	12	h	h	NOUN
ejpam-5854	264	13	=	=	NOUN
ejpam-5854	264	14	hphq	hphq	NOUN
ejpam-5854	264	15	.	.	PUNCT
ejpam-5854	265	1	thus	thus	ADV
ejpam-5854	265	2	,	,	PUNCT
ejpam-5854	265	3	(	(	PUNCT
ejpam-5854	265	4	µp	µp	NOUN
ejpam-5854	265	5	⃝	⃝	VERB
ejpam-5854	265	6	λ	λ	PROPN
ejpam-5854	265	7	p	p	NOUN
ejpam-5854	265	8	)	)	PUNCT
ejpam-5854	265	9	(	(	PUNCT
ejpam-5854	265	10	h	h	NOUN
ejpam-5854	265	11	)	)	PUNCT
ejpam-5854	265	12	=	=	SYM
ejpam-5854	265	13	⋎	⋎	NOUN
ejpam-5854	265	14	(	(	PUNCT
ejpam-5854	265	15	k	k	NOUN
ejpam-5854	265	16	,	,	PUNCT
ejpam-5854	265	17	o)∈ah	o)∈ah	PROPN
ejpam-5854	265	18	{	{	PUNCT
ejpam-5854	265	19	µp(k)⋏	µp(k)⋏	NOUN
ejpam-5854	265	20	λ	λ	X
ejpam-5854	265	21	p	p	X
ejpam-5854	265	22	(	(	PUNCT
ejpam-5854	265	23	o	o	NOUN
ejpam-5854	265	24	)	)	PUNCT
ejpam-5854	265	25	}	}	PUNCT
ejpam-5854	266	1	=	=	SYM
ejpam-5854	266	2	⋎	⋎	NOUN
ejpam-5854	266	3	(	(	PUNCT
ejpam-5854	266	4	k	k	NOUN
ejpam-5854	266	5	,	,	PUNCT
ejpam-5854	266	6	o)∈ahphq	o)∈ahphq	ADJ
ejpam-5854	266	7	{	{	PUNCT
ejpam-5854	266	8	µp(k)⋏	µp(k)⋏	NOUN
ejpam-5854	266	9	λ	λ	X
ejpam-5854	266	10	p	p	X
ejpam-5854	266	11	(	(	PUNCT
ejpam-5854	266	12	o	o	NOUN
ejpam-5854	266	13	)	)	PUNCT
ejpam-5854	266	14	}	}	PUNCT
ejpam-5854	266	15	⪰	⪰	VERB
ejpam-5854	266	16	µp(h)⋏	µp(h)⋏	ADP
ejpam-5854	266	17	λ	λ	X
ejpam-5854	266	18	p	p	X
ejpam-5854	266	19	(	(	PUNCT
ejpam-5854	266	20	phq	phq	NOUN
ejpam-5854	266	21	)	)	PUNCT
ejpam-5854	266	22	⪰	⪰	NOUN
ejpam-5854	266	23	µp(h)⋏	µp(h)⋏	X
ejpam-5854	266	24	λ	λ	X
ejpam-5854	266	25	p	p	X
ejpam-5854	266	26	(	(	PUNCT
ejpam-5854	266	27	h	h	NOUN
ejpam-5854	266	28	)	)	PUNCT
ejpam-5854	266	29	=	=	SYM
ejpam-5854	266	30	(	(	PUNCT
ejpam-5854	266	31	µp	µp	PROPN
ejpam-5854	266	32	⊓	⊓	PROPN
ejpam-5854	266	33	λp)(h	λp)(h	NUM
ejpam-5854	266	34	)	)	PUNCT
ejpam-5854	266	35	,	,	PUNCT
ejpam-5854	266	36	(	(	PUNCT
ejpam-5854	266	37	µn	µn	NOUN
ejpam-5854	266	38	⃝	⃝	NOUN
ejpam-5854	266	39	λ	λ	NOUN
ejpam-5854	266	40	n	n	PRON
ejpam-5854	266	41	)	)	PUNCT
ejpam-5854	266	42	(	(	PUNCT
ejpam-5854	266	43	h	h	NOUN
ejpam-5854	266	44	)	)	PUNCT
ejpam-5854	266	45	=	=	SYM
ejpam-5854	267	1	⋏	⋏	PROPN
ejpam-5854	267	2	(	(	PUNCT
ejpam-5854	267	3	k	k	X
ejpam-5854	267	4	,	,	PUNCT
ejpam-5854	267	5	o)∈ah	o)∈ah	PROPN
ejpam-5854	267	6	{	{	PUNCT
ejpam-5854	267	7	µn(k)⋎	µn(k)⋎	PROPN
ejpam-5854	267	8	λ	λ	PROPN
ejpam-5854	267	9	n	n	CCONJ
ejpam-5854	267	10	(	(	PUNCT
ejpam-5854	267	11	o	o	NOUN
ejpam-5854	267	12	)	)	PUNCT
ejpam-5854	267	13	}	}	PUNCT
ejpam-5854	267	14	=	=	SYM
ejpam-5854	268	1	⋏	⋏	PROPN
ejpam-5854	268	2	(	(	PUNCT
ejpam-5854	268	3	k	k	X
ejpam-5854	268	4	,	,	PUNCT
ejpam-5854	268	5	o)∈ahphq	o)∈ahphq	ADJ
ejpam-5854	268	6	{	{	PUNCT
ejpam-5854	268	7	µn(k)⋎	µn(k)⋎	NOUN
ejpam-5854	268	8	λ	λ	PROPN
ejpam-5854	268	9	n	n	CCONJ
ejpam-5854	268	10	(	(	PUNCT
ejpam-5854	268	11	o	o	NOUN
ejpam-5854	268	12	)	)	PUNCT
ejpam-5854	268	13	}	}	PUNCT
ejpam-5854	268	14	⪯	⪯	VERB
ejpam-5854	268	15	µn(h)⋎	µn(h)⋎	X
ejpam-5854	268	16	λ	λ	PROPN
ejpam-5854	268	17	n	n	PRON
ejpam-5854	268	18	(	(	PUNCT
ejpam-5854	268	19	phq	phq	NOUN
ejpam-5854	268	20	)	)	PUNCT
ejpam-5854	268	21	⪯	⪯	NOUN
ejpam-5854	268	22	µn(h)⋎	µn(h)⋎	X
ejpam-5854	268	23	λ	λ	PROPN
ejpam-5854	268	24	n	n	X
ejpam-5854	268	25	(	(	PUNCT
ejpam-5854	268	26	h	h	NOUN
ejpam-5854	268	27	)	)	PUNCT
ejpam-5854	268	28	=	=	SYM
ejpam-5854	268	29	(	(	PUNCT
ejpam-5854	268	30	µn	µn	PROPN
ejpam-5854	268	31	⊓	⊓	PROPN
ejpam-5854	268	32	λn)(h	λn)(h	NUM
ejpam-5854	268	33	)	)	PUNCT
ejpam-5854	268	34	,	,	PUNCT
ejpam-5854	268	35	and	and	CCONJ
ejpam-5854	268	36	(	(	PUNCT
ejpam-5854	268	37	ωp	ωp	NOUN
ejpam-5854	268	38	∗	∗	NOUN
ejpam-5854	268	39	ψp)(h	ψp)(h	PROPN
ejpam-5854	268	40	)	)	PUNCT
ejpam-5854	269	1	=	=	PUNCT
ejpam-5854	269	2	∨	∨	X
ejpam-5854	269	3	(	(	PUNCT
ejpam-5854	269	4	k	k	NOUN
ejpam-5854	269	5	,	,	PUNCT
ejpam-5854	269	6	o)∈ah	o)∈ah	PROPN
ejpam-5854	269	7	{	{	PUNCT
ejpam-5854	269	8	ωp(k	ωp(k	NOUN
ejpam-5854	269	9	)	)	PUNCT
ejpam-5854	269	10	∧	∧	NOUN
ejpam-5854	269	11	ψp(o	ψp(o	NOUN
ejpam-5854	269	12	)	)	PUNCT
ejpam-5854	269	13	}	}	PUNCT
ejpam-5854	269	14	=	=	SYM
ejpam-5854	269	15	∨	∨	X
ejpam-5854	269	16	(	(	PUNCT
ejpam-5854	269	17	k	k	NOUN
ejpam-5854	269	18	,	,	PUNCT
ejpam-5854	269	19	o)∈ahphq	o)∈ahphq	ADJ
ejpam-5854	269	20	{	{	PUNCT
ejpam-5854	269	21	ωp(k	ωp(k	NOUN
ejpam-5854	269	22	)	)	PUNCT
ejpam-5854	269	23	∧	∧	NOUN
ejpam-5854	269	24	ψp(k	ψp(k	NOUN
ejpam-5854	269	25	)	)	PUNCT
ejpam-5854	269	26	}	}	PUNCT
ejpam-5854	269	27	≥	≥	NOUN
ejpam-5854	269	28	ωp(h	ωp(h	NOUN
ejpam-5854	269	29	)	)	PUNCT
ejpam-5854	269	30	∧	∧	PROPN
ejpam-5854	269	31	ψp(phq	ψp(phq	NOUN
ejpam-5854	269	32	)	)	PUNCT
ejpam-5854	269	33	≥	≥	NOUN
ejpam-5854	269	34	ωp(h	ωp(h	NOUN
ejpam-5854	269	35	)	)	PUNCT
ejpam-5854	269	36	∧	∧	NOUN
ejpam-5854	269	37	ψp(h	ψp(h	X
ejpam-5854	269	38	)	)	PUNCT
ejpam-5854	269	39	=	=	SYM
ejpam-5854	269	40	(	(	PUNCT
ejpam-5854	269	41	ωp	ωp	X
ejpam-5854	269	42	∩	∩	NOUN
ejpam-5854	269	43	ψp)(h	ψp)(h	PROPN
ejpam-5854	269	44	)	)	PUNCT
ejpam-5854	269	45	,	,	PUNCT
ejpam-5854	269	46	(	(	PUNCT
ejpam-5854	269	47	ωn	ωn	ADP
ejpam-5854	269	48	∗	∗	NOUN
ejpam-5854	269	49	ψn)(h	ψn)(h	PROPN
ejpam-5854	269	50	)	)	PUNCT
ejpam-5854	270	1	=	=	PUNCT
ejpam-5854	270	2	∧	∧	PROPN
ejpam-5854	270	3	(	(	PUNCT
ejpam-5854	270	4	k	k	NOUN
ejpam-5854	270	5	,	,	PUNCT
ejpam-5854	270	6	o)∈ah	o)∈ah	PROPN
ejpam-5854	270	7	{	{	PUNCT
ejpam-5854	270	8	ωn(k	ωn(k	NUM
ejpam-5854	270	9	)	)	PUNCT
ejpam-5854	270	10	∨	∨	NUM
ejpam-5854	270	11	ψn(o	ψn(o	NUM
ejpam-5854	270	12	)	)	PUNCT
ejpam-5854	270	13	}	}	PUNCT
ejpam-5854	271	1	=	=	SYM
ejpam-5854	271	2	∧	∧	PROPN
ejpam-5854	271	3	(	(	PUNCT
ejpam-5854	271	4	k	k	NOUN
ejpam-5854	271	5	,	,	PUNCT
ejpam-5854	271	6	o)∈ahphq	o)∈ahphq	ADJ
ejpam-5854	271	7	{	{	PUNCT
ejpam-5854	271	8	ωn(k	ωn(k	NUM
ejpam-5854	271	9	)	)	PUNCT
ejpam-5854	271	10	∨	∨	NUM
ejpam-5854	271	11	ψn(k	ψn(k	PUNCT
ejpam-5854	271	12	)	)	PUNCT
ejpam-5854	271	13	}	}	PUNCT
ejpam-5854	271	14	≤	≤	NUM
ejpam-5854	271	15	ωn(h	ωn(h	NOUN
ejpam-5854	271	16	)	)	PUNCT
ejpam-5854	271	17	∨	∨	NUM
ejpam-5854	271	18	ψn(phq	ψn(phq	NOUN
ejpam-5854	271	19	)	)	PUNCT
ejpam-5854	271	20	≤	≤	NOUN
ejpam-5854	271	21	ωn(h	ωn(h	NUM
ejpam-5854	271	22	)	)	PUNCT
ejpam-5854	271	23	∨	∨	NUM
ejpam-5854	271	24	ψn(h	ψn(h	NUM
ejpam-5854	271	25	)	)	PUNCT
ejpam-5854	271	26	=	=	SYM
ejpam-5854	271	27	(	(	PUNCT
ejpam-5854	271	28	ωn	ωn	ADP
ejpam-5854	271	29	∩	∩	NOUN
ejpam-5854	271	30	ψn)(h	ψn)(h	PROPN
ejpam-5854	271	31	)	)	PUNCT
ejpam-5854	271	32	.	.	PUNCT
ejpam-5854	272	1	hence	hence	ADV
ejpam-5854	272	2	,	,	PUNCT
ejpam-5854	272	3	(	(	PUNCT
ejpam-5854	272	4	µp	µp	PROPN
ejpam-5854	272	5	⊓λp)(h	⊓λp)(h	PROPN
ejpam-5854	272	6	)	)	PUNCT
ejpam-5854	272	7	⪯	⪯	NOUN
ejpam-5854	272	8	(	(	PUNCT
ejpam-5854	272	9	µp	µp	NOUN
ejpam-5854	272	10	⃝λ	⃝λ	PROPN
ejpam-5854	272	11	p	p	NOUN
ejpam-5854	272	12	)	)	PUNCT
ejpam-5854	272	13	(	(	PUNCT
ejpam-5854	272	14	h	h	NOUN
ejpam-5854	272	15	)	)	PUNCT
ejpam-5854	272	16	,	,	PUNCT
ejpam-5854	272	17	(	(	PUNCT
ejpam-5854	272	18	µn	µn	PROPN
ejpam-5854	272	19	⊓λn)(h	⊓λn)(h	NOUN
ejpam-5854	272	20	)	)	PUNCT
ejpam-5854	272	21	⪰	⪰	NOUN
ejpam-5854	272	22	(	(	PUNCT
ejpam-5854	272	23	µn	µn	PROPN
ejpam-5854	272	24	⃝λ	⃝λ	X
ejpam-5854	272	25	n	n	CCONJ
ejpam-5854	272	26	)	)	PUNCT
ejpam-5854	272	27	(	(	PUNCT
ejpam-5854	272	28	h	h	NOUN
ejpam-5854	272	29	)	)	PUNCT
ejpam-5854	272	30	and	and	CCONJ
ejpam-5854	272	31	(	(	PUNCT
ejpam-5854	272	32	ωp	ωp	NOUN
ejpam-5854	272	33	∩ψp)(h	∩ψp)(h	NOUN
ejpam-5854	272	34	)	)	PUNCT
ejpam-5854	272	35	≤	≤	NOUN
ejpam-5854	272	36	(	(	PUNCT
ejpam-5854	272	37	ωp	ωp	NUM
ejpam-5854	272	38	∗ψp)(h	∗ψp)(h	NUM
ejpam-5854	272	39	)	)	PUNCT
ejpam-5854	272	40	,	,	PUNCT
ejpam-5854	272	41	(	(	PUNCT
ejpam-5854	272	42	ωn	ωn	PROPN
ejpam-5854	272	43	∩	∩	NOUN
ejpam-5854	272	44	ψn)(h	ψn)(h	PROPN
ejpam-5854	272	45	)	)	PUNCT
ejpam-5854	272	46	≥	≥	NOUN
ejpam-5854	272	47	(	(	PUNCT
ejpam-5854	272	48	ωn	ωn	ADP
ejpam-5854	272	49	∗	∗	NOUN
ejpam-5854	272	50	ψn)(h	ψn)(h	PROPN
ejpam-5854	272	51	)	)	PUNCT
ejpam-5854	272	52	.	.	PUNCT
ejpam-5854	273	1	therefore	therefore	ADV
ejpam-5854	273	2	,	,	PUNCT
ejpam-5854	273	3	c̈1⊓c̈2⊏c̈1	c̈1⊓c̈2⊏c̈1	NOUN
ejpam-5854	273	4	⊛	⊛	NUM
ejpam-5854	273	5	c̈2	c̈2	NOUN
ejpam-5854	273	6	.	.	PUNCT
ejpam-5854	274	1	(	(	PUNCT
ejpam-5854	274	2	4	4	X
ejpam-5854	274	3	)	)	PUNCT
ejpam-5854	274	4	⇒	⇒	NOUN
ejpam-5854	274	5	(	(	PUNCT
ejpam-5854	274	6	3	3	NUM
ejpam-5854	274	7	)	)	PUNCT
ejpam-5854	274	8	⇒	⇒	NOUN
ejpam-5854	274	9	(	(	PUNCT
ejpam-5854	274	10	2	2	X
ejpam-5854	274	11	)	)	PUNCT
ejpam-5854	274	12	this	this	PRON
ejpam-5854	274	13	is	be	AUX
ejpam-5854	274	14	obvious	obvious	ADJ
ejpam-5854	274	15	because	because	SCONJ
ejpam-5854	274	16	every	every	DET
ejpam-5854	274	17	cbf	cbf	PROPN
ejpam-5854	274	18	bi	bi	NOUN
ejpam-5854	274	19	-	-	ADJ
ejpam-5854	274	20	ideal	ideal	NOUN
ejpam-5854	274	21	is	be	AUX
ejpam-5854	274	22	a	a	DET
ejpam-5854	274	23	cbf	cbf	PROPN
ejpam-5854	274	24	generalized	generalize	VERB
ejpam-5854	274	25	bi	bi	NOUN
ejpam-5854	274	26	-	-	NOUN
ejpam-5854	274	27	ideal	ideal	NOUN
ejpam-5854	274	28	of	of	ADP
ejpam-5854	274	29	s	s	PROPN
ejpam-5854	274	30	,	,	PUNCT
ejpam-5854	274	31	every	every	DET
ejpam-5854	274	32	cbf	cbf	PROPN
ejpam-5854	274	33	ideal	ideal	NOUN
ejpam-5854	274	34	is	be	AUX
ejpam-5854	274	35	a	a	DET
ejpam-5854	274	36	cbf	cbf	PROPN
ejpam-5854	274	37	interior	interior	PROPN
ejpam-5854	274	38	ideal	ideal	NOUN
ejpam-5854	274	39	of	of	ADP
ejpam-5854	274	40	s	s	PRON
ejpam-5854	274	41	and	and	CCONJ
ejpam-5854	274	42	every	every	DET
ejpam-5854	274	43	cbf	cbf	PROPN
ejpam-5854	274	44	quasi	quasi	PROPN
ejpam-5854	274	45	-	-	NOUN
ejpam-5854	274	46	ideal	ideal	ADJ
ejpam-5854	274	47	is	be	AUX
ejpam-5854	274	48	a	a	DET
ejpam-5854	274	49	cbf	cbf	PROPN
ejpam-5854	274	50	bi	bi	NOUN
ejpam-5854	274	51	-	-	NOUN
ejpam-5854	274	52	ideal	ideal	NOUN
ejpam-5854	274	53	of	of	ADP
ejpam-5854	274	54	s.	s.	PROPN
ejpam-5854	274	55	p.	p.	PROPN
ejpam-5854	274	56	khamrot	khamrot	PROPN
ejpam-5854	274	57	,	,	PUNCT
ejpam-5854	274	58	n.	n.	PROPN
ejpam-5854	274	59	deetae	deetae	PROPN
ejpam-5854	274	60	,	,	PUNCT
ejpam-5854	274	61	t.	t.	PROPN
ejpam-5854	274	62	gaketem	gaketem	PROPN
ejpam-5854	274	63	/	/	SYM
ejpam-5854	274	64	eur	eur	PROPN
ejpam-5854	274	65	.	.	PUNCT
ejpam-5854	275	1	j.	j.	PROPN
ejpam-5854	275	2	pure	pure	PROPN
ejpam-5854	275	3	appl	appl	PROPN
ejpam-5854	275	4	.	.	PROPN
ejpam-5854	275	5	math	math	PROPN
ejpam-5854	275	6	,	,	PUNCT
ejpam-5854	275	7	18	18	NUM
ejpam-5854	275	8	(	(	PUNCT
ejpam-5854	275	9	2	2	NUM
ejpam-5854	275	10	)	)	PUNCT
ejpam-5854	275	11	(	(	PUNCT
ejpam-5854	275	12	2025	2025	NUM
ejpam-5854	275	13	)	)	PUNCT
ejpam-5854	275	14	,	,	PUNCT
ejpam-5854	275	15	5854	5854	NUM
ejpam-5854	275	16	12	12	NUM
ejpam-5854	275	17	of	of	ADP
ejpam-5854	275	18	14	14	NUM
ejpam-5854	275	19	(	(	PUNCT
ejpam-5854	275	20	2	2	NUM
ejpam-5854	275	21	)	)	PUNCT
ejpam-5854	275	22	⇒	⇒	NOUN
ejpam-5854	275	23	(	(	PUNCT
ejpam-5854	275	24	1	1	X
ejpam-5854	275	25	)	)	PUNCT
ejpam-5854	275	26	let	let	VERB
ejpam-5854	275	27	q	q	NOUN
ejpam-5854	275	28	be	be	AUX
ejpam-5854	275	29	a	a	DET
ejpam-5854	275	30	quasi	quasi	NOUN
ejpam-5854	275	31	-	-	ADJ
ejpam-5854	275	32	ideal	ideal	ADJ
ejpam-5854	275	33	and	and	CCONJ
ejpam-5854	275	34	j	j	PROPN
ejpam-5854	275	35	be	be	AUX
ejpam-5854	275	36	an	an	DET
ejpam-5854	275	37	ideal	ideal	NOUN
ejpam-5854	275	38	of	of	ADP
ejpam-5854	275	39	s.	s.	PROPN
ejpam-5854	275	40	then	then	ADV
ejpam-5854	275	41	,	,	PUNCT
ejpam-5854	275	42	by	by	ADP
ejpam-5854	275	43	theorem	theorem	NOUN
ejpam-5854	275	44	3	3	NUM
ejpam-5854	275	45	,	,	PUNCT
ejpam-5854	275	46	χq	χq	PROPN
ejpam-5854	275	47	is	be	AUX
ejpam-5854	275	48	a	a	DET
ejpam-5854	275	49	cbf	cbf	PROPN
ejpam-5854	275	50	quasi	quasi	NOUN
ejpam-5854	275	51	-	-	NOUN
ejpam-5854	275	52	ideal	ideal	ADJ
ejpam-5854	275	53	and	and	CCONJ
ejpam-5854	275	54	χj	χj	PROPN
ejpam-5854	275	55	is	be	AUX
ejpam-5854	275	56	a	a	DET
ejpam-5854	275	57	cbf	cbf	PROPN
ejpam-5854	275	58	ideal	ideal	NOUN
ejpam-5854	275	59	of	of	ADP
ejpam-5854	275	60	s.	s.	PROPN
ejpam-5854	275	61	by	by	ADP
ejpam-5854	275	62	supposition	supposition	PROPN
ejpam-5854	275	63	and	and	CCONJ
ejpam-5854	275	64	lemma	lemma	PROPN
ejpam-5854	275	65	4	4	NUM
ejpam-5854	275	66	,	,	PUNCT
ejpam-5854	275	67	we	we	PRON
ejpam-5854	275	68	have	have	VERB
ejpam-5854	275	69	µp	µp	NOUN
ejpam-5854	275	70	χqj	χqj	ADJ
ejpam-5854	275	71	(	(	PUNCT
ejpam-5854	275	72	h	h	NOUN
ejpam-5854	275	73	)	)	PUNCT
ejpam-5854	275	74	=	=	SYM
ejpam-5854	276	1	(	(	PUNCT
ejpam-5854	276	2	µp	µp	NOUN
ejpam-5854	276	3	χq	χq	PROPN
ejpam-5854	276	4	⃝	⃝	NOUN
ejpam-5854	276	5	µp	µp	PROPN
ejpam-5854	276	6	χj	χj	PROPN
ejpam-5854	276	7	)	)	PUNCT
ejpam-5854	276	8	(	(	PUNCT
ejpam-5854	276	9	h	h	NOUN
ejpam-5854	276	10	)	)	PUNCT
ejpam-5854	276	11	⪰	⪰	NOUN
ejpam-5854	276	12	(	(	PUNCT
ejpam-5854	276	13	µp	µp	NOUN
ejpam-5854	276	14	χq	χq	NOUN
ejpam-5854	276	15	⊓	⊓	PROPN
ejpam-5854	276	16	µp	µp	PROPN
ejpam-5854	276	17	χj	χj	PROPN
ejpam-5854	276	18	)	)	PUNCT
ejpam-5854	276	19	(	(	PUNCT
ejpam-5854	276	20	h	h	NOUN
ejpam-5854	276	21	)	)	PUNCT
ejpam-5854	276	22	=	=	NOUN
ejpam-5854	277	1	µp	µp	PROPN
ejpam-5854	277	2	χq⊓j	χq⊓j	ADJ
ejpam-5854	277	3	(	(	PUNCT
ejpam-5854	277	4	h	h	NOUN
ejpam-5854	277	5	)	)	PUNCT
ejpam-5854	277	6	=	=	SYM
ejpam-5854	277	7	1	1	NUM
ejpam-5854	277	8	,	,	PUNCT
ejpam-5854	277	9	µn	µn	PROPN
ejpam-5854	277	10	χqj	χqj	ADJ
ejpam-5854	277	11	(	(	PUNCT
ejpam-5854	277	12	h	h	NOUN
ejpam-5854	277	13	)	)	PUNCT
ejpam-5854	277	14	=	=	SYM
ejpam-5854	278	1	(	(	PUNCT
ejpam-5854	278	2	µn	µn	PROPN
ejpam-5854	278	3	χq	χq	PROPN
ejpam-5854	278	4	⃝	⃝	PROPN
ejpam-5854	278	5	µn	µn	PROPN
ejpam-5854	278	6	χj	χj	PROPN
ejpam-5854	278	7	)	)	PUNCT
ejpam-5854	278	8	(	(	PUNCT
ejpam-5854	278	9	h	h	NOUN
ejpam-5854	278	10	)	)	PUNCT
ejpam-5854	278	11	⪯	⪯	NOUN
ejpam-5854	278	12	(	(	PUNCT
ejpam-5854	278	13	µn	µn	VERB
ejpam-5854	278	14	χq	χq	NOUN
ejpam-5854	278	15	⊓	⊓	PROPN
ejpam-5854	278	16	µn	µn	PROPN
ejpam-5854	278	17	χj	χj	PROPN
ejpam-5854	278	18	)	)	PUNCT
ejpam-5854	278	19	(	(	PUNCT
ejpam-5854	278	20	h	h	NOUN
ejpam-5854	278	21	)	)	PUNCT
ejpam-5854	278	22	=	=	SYM
ejpam-5854	278	23	µn	µn	PROPN
ejpam-5854	278	24	χq⊓j	χq⊓j	ADJ
ejpam-5854	278	25	(	(	PUNCT
ejpam-5854	278	26	h	h	NOUN
ejpam-5854	278	27	)	)	PUNCT
ejpam-5854	278	28	=	=	SYM
ejpam-5854	278	29	−1	−1	NOUN
ejpam-5854	278	30	,	,	PUNCT
ejpam-5854	278	31	and	and	CCONJ
ejpam-5854	278	32	ωp	ωp	PRON
ejpam-5854	278	33	χqj	χqj	ADV
ejpam-5854	278	34	(	(	PUNCT
ejpam-5854	278	35	h	h	NOUN
ejpam-5854	278	36	)	)	PUNCT
ejpam-5854	278	37	=	=	SYM
ejpam-5854	279	1	(	(	PUNCT
ejpam-5854	279	2	ωp	ωp	INTJ
ejpam-5854	279	3	χq	χq	PROPN
ejpam-5854	279	4	∗	∗	VERB
ejpam-5854	279	5	ωp	ωp	PRON
ejpam-5854	279	6	χj	χj	PROPN
ejpam-5854	279	7	)	)	PUNCT
ejpam-5854	279	8	(	(	PUNCT
ejpam-5854	279	9	h	h	NOUN
ejpam-5854	279	10	)	)	PUNCT
ejpam-5854	279	11	≥	≥	NOUN
ejpam-5854	279	12	(	(	PUNCT
ejpam-5854	279	13	ωp	ωp	NOUN
ejpam-5854	279	14	χq	χq	PROPN
ejpam-5854	279	15	∩	∩	PROPN
ejpam-5854	279	16	ωp	ωp	PRON
ejpam-5854	279	17	χj	χj	PROPN
ejpam-5854	279	18	)	)	PUNCT
ejpam-5854	279	19	(	(	PUNCT
ejpam-5854	279	20	h	h	NOUN
ejpam-5854	279	21	)	)	PUNCT
ejpam-5854	279	22	=	=	PUNCT
ejpam-5854	280	1	ωp	ωp	NOUN
ejpam-5854	280	2	χq∩j	χq∩j	X
ejpam-5854	280	3	(	(	PUNCT
ejpam-5854	280	4	h	h	NOUN
ejpam-5854	280	5	)	)	PUNCT
ejpam-5854	280	6	=	=	SYM
ejpam-5854	280	7	1	1	NUM
ejpam-5854	280	8	,	,	PUNCT
ejpam-5854	280	9	ωn	ωn	ADP
ejpam-5854	280	10	χq	χq	PROPN
ejpam-5854	280	11	(	(	PUNCT
ejpam-5854	280	12	h	h	NOUN
ejpam-5854	280	13	)	)	PUNCT
ejpam-5854	280	14	=	=	SYM
ejpam-5854	281	1	(	(	PUNCT
ejpam-5854	281	2	ωn	ωn	ADP
ejpam-5854	281	3	χq	χq	PROPN
ejpam-5854	281	4	∗	∗	NOUN
ejpam-5854	281	5	ωn	ωn	PROPN
ejpam-5854	281	6	χj	χj	PROPN
ejpam-5854	281	7	)	)	PUNCT
ejpam-5854	281	8	(	(	PUNCT
ejpam-5854	281	9	h	h	NOUN
ejpam-5854	281	10	)	)	PUNCT
ejpam-5854	281	11	≤	≤	NOUN
ejpam-5854	281	12	(	(	PUNCT
ejpam-5854	281	13	ωn	ωn	NOUN
ejpam-5854	281	14	χq	χq	PROPN
ejpam-5854	281	15	∩	∩	NOUN
ejpam-5854	281	16	ωn	ωn	PRON
ejpam-5854	281	17	χj	χj	PROPN
ejpam-5854	281	18	)	)	PUNCT
ejpam-5854	281	19	(	(	PUNCT
ejpam-5854	281	20	h	h	NOUN
ejpam-5854	281	21	)	)	PUNCT
ejpam-5854	281	22	=	=	SYM
ejpam-5854	281	23	ωn	ωn	ADP
ejpam-5854	281	24	χq∩j	χq∩j	X
ejpam-5854	281	25	(	(	PUNCT
ejpam-5854	281	26	h	h	NOUN
ejpam-5854	281	27	)	)	PUNCT
ejpam-5854	281	28	=	=	PUNCT
ejpam-5854	281	29	−1	−1	NOUN
ejpam-5854	281	30	.	.	PUNCT
ejpam-5854	282	1	thus	thus	ADV
ejpam-5854	282	2	,	,	PUNCT
ejpam-5854	282	3	h	h	PROPN
ejpam-5854	282	4	∈	∈	PROPN
ejpam-5854	282	5	qj	qj	PROPN
ejpam-5854	282	6	.	.	PUNCT
ejpam-5854	283	1	hence	hence	ADV
ejpam-5854	283	2	,	,	PUNCT
ejpam-5854	283	3	q	q	PROPN
ejpam-5854	283	4	∩	∩	ADJ
ejpam-5854	283	5	j	j	PROPN
ejpam-5854	283	6	⊑	⊑	PROPN
ejpam-5854	283	7	qj	qj	PROPN
ejpam-5854	283	8	.	.	PUNCT
ejpam-5854	284	1	therefore	therefore	ADV
ejpam-5854	284	2	,	,	PUNCT
ejpam-5854	284	3	by	by	ADP
ejpam-5854	284	4	lemma	lemma	PROPN
ejpam-5854	284	5	3	3	NUM
ejpam-5854	284	6	,	,	PUNCT
ejpam-5854	284	7	s	s	VERB
ejpam-5854	284	8	is	be	AUX
ejpam-5854	284	9	weakly	weakly	ADV
ejpam-5854	284	10	regular	regular	ADJ
ejpam-5854	284	11	.	.	PUNCT
ejpam-5854	285	1	lemma	lemma	PROPN
ejpam-5854	285	2	4	4	NUM
ejpam-5854	285	3	.	.	PUNCT
ejpam-5854	286	1	[	[	X
ejpam-5854	286	2	13	13	NUM
ejpam-5854	286	3	]	]	PUNCT
ejpam-5854	286	4	let	let	VERB
ejpam-5854	286	5	s	s	PRON
ejpam-5854	286	6	be	be	AUX
ejpam-5854	286	7	a	a	DET
ejpam-5854	286	8	monoid	monoid	NOUN
ejpam-5854	286	9	.	.	PUNCT
ejpam-5854	287	1	then	then	ADV
ejpam-5854	287	2	,	,	PUNCT
ejpam-5854	287	3	the	the	DET
ejpam-5854	287	4	following	follow	VERB
ejpam-5854	287	5	statements	statement	NOUN
ejpam-5854	287	6	are	be	AUX
ejpam-5854	287	7	equivalent	equivalent	ADJ
ejpam-5854	287	8	:	:	PUNCT
ejpam-5854	287	9	(	(	PUNCT
ejpam-5854	287	10	1	1	X
ejpam-5854	287	11	)	)	PUNCT
ejpam-5854	287	12	s	s	VERB
ejpam-5854	287	13	is	be	AUX
ejpam-5854	287	14	weakly	weakly	ADV
ejpam-5854	287	15	regular	regular	ADJ
ejpam-5854	287	16	.	.	PUNCT
ejpam-5854	288	1	(	(	PUNCT
ejpam-5854	288	2	2	2	X
ejpam-5854	288	3	)	)	PUNCT
ejpam-5854	288	4	q	q	NOUN
ejpam-5854	288	5	∩	∩	ADJ
ejpam-5854	288	6	j	j	PROPN
ejpam-5854	288	7	∩r	∩r	PROPN
ejpam-5854	288	8	⊆	⊆	NUM
ejpam-5854	288	9	qjr	qjr	NOUN
ejpam-5854	288	10	for	for	SCONJ
ejpam-5854	288	11	every	every	DET
ejpam-5854	288	12	quasi	quasi	ADJ
ejpam-5854	288	13	-	-	ADJ
ejpam-5854	288	14	ideal	ideal	ADJ
ejpam-5854	288	15	q	q	NOUN
ejpam-5854	288	16	,	,	PUNCT
ejpam-5854	288	17	every	every	DET
ejpam-5854	288	18	ideal	ideal	ADJ
ejpam-5854	288	19	j	j	PROPN
ejpam-5854	288	20	and	and	CCONJ
ejpam-5854	288	21	every	every	DET
ejpam-5854	288	22	right	right	ADJ
ejpam-5854	288	23	ideal	ideal	ADJ
ejpam-5854	288	24	r	r	NOUN
ejpam-5854	288	25	of	of	ADP
ejpam-5854	288	26	s.	s.	PROPN
ejpam-5854	288	27	on	on	ADP
ejpam-5854	288	28	the	the	DET
ejpam-5854	288	29	basis	basis	NOUN
ejpam-5854	288	30	of	of	ADP
ejpam-5854	288	31	lemma	lemma	PROPN
ejpam-5854	288	32	4	4	NUM
ejpam-5854	288	33	,	,	PUNCT
ejpam-5854	288	34	we	we	PRON
ejpam-5854	288	35	can	can	AUX
ejpam-5854	288	36	prove	prove	VERB
ejpam-5854	288	37	theorem	theorem	ADJ
ejpam-5854	288	38	7	7	NUM
ejpam-5854	288	39	.	.	PUNCT
ejpam-5854	288	40	theorem	theorem	NOUN
ejpam-5854	288	41	7	7	NUM
ejpam-5854	288	42	.	.	PUNCT
ejpam-5854	289	1	let	let	VERB
ejpam-5854	289	2	s	s	PRON
ejpam-5854	289	3	be	be	AUX
ejpam-5854	289	4	a	a	DET
ejpam-5854	289	5	monoid	monoid	NOUN
ejpam-5854	289	6	.	.	PUNCT
ejpam-5854	290	1	then	then	ADV
ejpam-5854	290	2	,	,	PUNCT
ejpam-5854	290	3	the	the	DET
ejpam-5854	290	4	following	follow	VERB
ejpam-5854	290	5	statements	statement	NOUN
ejpam-5854	290	6	are	be	AUX
ejpam-5854	290	7	equivalent	equivalent	ADJ
ejpam-5854	290	8	:	:	PUNCT
ejpam-5854	290	9	(	(	PUNCT
ejpam-5854	290	10	1	1	X
ejpam-5854	290	11	)	)	PUNCT
ejpam-5854	290	12	s	s	VERB
ejpam-5854	290	13	is	be	AUX
ejpam-5854	290	14	weakly	weakly	ADV
ejpam-5854	290	15	regular	regular	ADJ
ejpam-5854	290	16	.	.	PUNCT
ejpam-5854	291	1	(	(	PUNCT
ejpam-5854	291	2	2	2	X
ejpam-5854	291	3	)	)	PUNCT
ejpam-5854	291	4	c̈1⊓c̈2⊓c̈3⊏c̈1	c̈1⊓c̈2⊓c̈3⊏c̈1	NOUN
ejpam-5854	291	5	⊛	⊛	NUM
ejpam-5854	291	6	c̈2	c̈2	NOUN
ejpam-5854	291	7	⊛	⊛	NUM
ejpam-5854	291	8	c̈3	c̈3	PROPN
ejpam-5854	291	9	,	,	PUNCT
ejpam-5854	291	10	for	for	ADP
ejpam-5854	291	11	every	every	DET
ejpam-5854	291	12	cbf	cbf	PROPN
ejpam-5854	291	13	quasi	quasi	ADJ
ejpam-5854	291	14	-	-	ADJ
ejpam-5854	291	15	ideal	ideal	ADJ
ejpam-5854	291	16	c̈1	c̈1	NOUN
ejpam-5854	291	17	=	=	SYM
ejpam-5854	291	18	⟨µ	⟨µ	NOUN
ejpam-5854	291	19	,	,	PUNCT
ejpam-5854	291	20	ω⟩	ω⟩	NOUN
ejpam-5854	291	21	,	,	PUNCT
ejpam-5854	291	22	every	every	DET
ejpam-5854	291	23	cbf	cbf	PROPN
ejpam-5854	291	24	ideal	ideal	ADJ
ejpam-5854	291	25	c̈2	c̈2	PROPN
ejpam-5854	291	26	=	=	PUNCT
ejpam-5854	291	27	⟨λ	⟨λ	X
ejpam-5854	291	28	,	,	PUNCT
ejpam-5854	291	29	ψ⟩	ψ⟩	PUNCT
ejpam-5854	291	30	and	and	CCONJ
ejpam-5854	291	31	every	every	DET
ejpam-5854	291	32	cbf	cbf	PROPN
ejpam-5854	291	33	right	right	PROPN
ejpam-5854	291	34	ideal	ideal	PROPN
ejpam-5854	291	35	c̈3	c̈3	PROPN
ejpam-5854	291	36	=	=	SYM
ejpam-5854	291	37	⟨ν	⟨ν	X
ejpam-5854	291	38	,	,	PUNCT
ejpam-5854	291	39	κ⟩	κ⟩	NOUN
ejpam-5854	291	40	of	of	ADP
ejpam-5854	291	41	s.	s.	PROPN
ejpam-5854	291	42	(	(	PUNCT
ejpam-5854	291	43	3	3	X
ejpam-5854	291	44	)	)	PUNCT
ejpam-5854	291	45	c̈1⊓c̈2⊓c̈3⊏c̈1	c̈1⊓c̈2⊓c̈3⊏c̈1	NOUN
ejpam-5854	291	46	⊛	⊛	NUM
ejpam-5854	291	47	c̈2	c̈2	NOUN
ejpam-5854	291	48	⊛	⊛	NUM
ejpam-5854	291	49	c̈3	c̈3	PROPN
ejpam-5854	291	50	,	,	PUNCT
ejpam-5854	291	51	for	for	ADP
ejpam-5854	291	52	every	every	DET
ejpam-5854	291	53	cbf	cbf	PROPN
ejpam-5854	291	54	bi	bi	ADJ
ejpam-5854	291	55	-	-	ADJ
ejpam-5854	291	56	ideal	ideal	ADJ
ejpam-5854	291	57	c̈1	c̈1	NOUN
ejpam-5854	291	58	=	=	SYM
ejpam-5854	291	59	⟨µ	⟨µ	NOUN
ejpam-5854	291	60	,	,	PUNCT
ejpam-5854	291	61	ω⟩	ω⟩	NOUN
ejpam-5854	291	62	,	,	PUNCT
ejpam-5854	291	63	every	every	DET
ejpam-5854	291	64	cbf	cbf	PROPN
ejpam-5854	291	65	ideal	ideal	ADJ
ejpam-5854	291	66	c̈2	c̈2	PROPN
ejpam-5854	291	67	=	=	PUNCT
ejpam-5854	291	68	⟨λ	⟨λ	X
ejpam-5854	291	69	,	,	PUNCT
ejpam-5854	291	70	ψ⟩	ψ⟩	PUNCT
ejpam-5854	291	71	and	and	CCONJ
ejpam-5854	291	72	every	every	DET
ejpam-5854	291	73	cbf	cbf	PROPN
ejpam-5854	291	74	right	right	PROPN
ejpam-5854	291	75	ideal	ideal	PROPN
ejpam-5854	291	76	c̈3	c̈3	PROPN
ejpam-5854	291	77	=	=	SYM
ejpam-5854	291	78	⟨ν	⟨ν	X
ejpam-5854	291	79	,	,	PUNCT
ejpam-5854	291	80	κ⟩	κ⟩	NOUN
ejpam-5854	291	81	of	of	ADP
ejpam-5854	291	82	s.	s.	PROPN
ejpam-5854	291	83	(	(	PUNCT
ejpam-5854	291	84	4	4	X
ejpam-5854	291	85	)	)	PUNCT
ejpam-5854	291	86	c̈1⊓c̈2⊓c̈3⊏c̈1	c̈1⊓c̈2⊓c̈3⊏c̈1	NOUN
ejpam-5854	291	87	⊛	⊛	NUM
ejpam-5854	291	88	c̈2	c̈2	NOUN
ejpam-5854	291	89	⊛	⊛	NUM
ejpam-5854	291	90	c̈3	c̈3	PROPN
ejpam-5854	291	91	,	,	PUNCT
ejpam-5854	291	92	for	for	ADP
ejpam-5854	291	93	every	every	DET
ejpam-5854	291	94	cbf	cbf	PROPN
ejpam-5854	291	95	generalized	generalize	VERB
ejpam-5854	291	96	bi	bi	ADJ
ejpam-5854	291	97	-	-	ADJ
ejpam-5854	291	98	ideal	ideal	ADJ
ejpam-5854	291	99	c̈1	c̈1	NOUN
ejpam-5854	291	100	=	=	SYM
ejpam-5854	291	101	⟨µ	⟨µ	NOUN
ejpam-5854	291	102	,	,	PUNCT
ejpam-5854	291	103	ω⟩	ω⟩	NOUN
ejpam-5854	291	104	,	,	PUNCT
ejpam-5854	291	105	every	every	DET
ejpam-5854	291	106	cbf	cbf	PROPN
ejpam-5854	291	107	interior	interior	ADJ
ejpam-5854	291	108	ideal	ideal	ADJ
ejpam-5854	291	109	c̈2	c̈2	NOUN
ejpam-5854	291	110	=	=	PUNCT
ejpam-5854	291	111	⟨λ	⟨λ	X
ejpam-5854	291	112	,	,	PUNCT
ejpam-5854	291	113	ψ⟩	ψ⟩	PUNCT
ejpam-5854	291	114	and	and	CCONJ
ejpam-5854	291	115	every	every	DET
ejpam-5854	291	116	cbf	cbf	PROPN
ejpam-5854	291	117	right	right	PROPN
ejpam-5854	291	118	ideal	ideal	PROPN
ejpam-5854	291	119	c̈3	c̈3	PROPN
ejpam-5854	291	120	=	=	SYM
ejpam-5854	291	121	⟨ν	⟨ν	X
ejpam-5854	291	122	,	,	PUNCT
ejpam-5854	291	123	κ⟩	κ⟩	NOUN
ejpam-5854	291	124	of	of	ADP
ejpam-5854	291	125	s.	s.	PROPN
ejpam-5854	291	126	proof	proof	PROPN
ejpam-5854	291	127	.	.	PUNCT
ejpam-5854	292	1	(	(	PUNCT
ejpam-5854	292	2	1	1	X
ejpam-5854	292	3	)	)	PUNCT
ejpam-5854	292	4	⇒	⇒	NOUN
ejpam-5854	292	5	(	(	PUNCT
ejpam-5854	292	6	4	4	X
ejpam-5854	292	7	)	)	PUNCT
ejpam-5854	292	8	assume	assume	VERB
ejpam-5854	292	9	that	that	SCONJ
ejpam-5854	292	10	c̈1	c̈1	NOUN
ejpam-5854	292	11	=	=	SYM
ejpam-5854	292	12	⟨µ	⟨µ	NOUN
ejpam-5854	292	13	,	,	PUNCT
ejpam-5854	292	14	ω⟩	ω⟩	PRON
ejpam-5854	292	15	is	be	AUX
ejpam-5854	292	16	a	a	DET
ejpam-5854	292	17	cbf	cbf	PROPN
ejpam-5854	292	18	generalized	generalize	VERB
ejpam-5854	292	19	bi	bi	NOUN
ejpam-5854	292	20	-	-	ADJ
ejpam-5854	292	21	ideal	ideal	ADJ
ejpam-5854	292	22	,	,	PUNCT
ejpam-5854	292	23	c̈2	c̈2	NOUN
ejpam-5854	292	24	=	=	PUNCT
ejpam-5854	292	25	⟨λ	⟨λ	NUM
ejpam-5854	292	26	,	,	PUNCT
ejpam-5854	292	27	ψ⟩	ψ⟩	X
ejpam-5854	292	28	is	be	AUX
ejpam-5854	292	29	a	a	DET
ejpam-5854	292	30	cbf	cbf	PROPN
ejpam-5854	292	31	interior	interior	PROPN
ejpam-5854	292	32	ideal	ideal	NOUN
ejpam-5854	292	33	and	and	CCONJ
ejpam-5854	292	34	c̈3	c̈3	VERB
ejpam-5854	292	35	=	=	SYM
ejpam-5854	292	36	⟨ν	⟨ν	X
ejpam-5854	292	37	,	,	PUNCT
ejpam-5854	292	38	κ⟩	κ⟩	PROPN
ejpam-5854	292	39	is	be	AUX
ejpam-5854	292	40	a	a	DET
ejpam-5854	292	41	cbf	cbf	PROPN
ejpam-5854	292	42	right	right	ADV
ejpam-5854	292	43	ideal	ideal	NOUN
ejpam-5854	292	44	of	of	ADP
ejpam-5854	292	45	s.	s.	PROPN
ejpam-5854	292	46	let	let	VERB
ejpam-5854	292	47	h	h	PROPN
ejpam-5854	292	48	∈	∈	PROPN
ejpam-5854	292	49	s.	s.	PROPN
ejpam-5854	292	50	then	then	ADV
ejpam-5854	292	51	,	,	PUNCT
ejpam-5854	292	52	there	there	PRON
ejpam-5854	292	53	exist	exist	VERB
ejpam-5854	292	54	p	p	PRON
ejpam-5854	292	55	,	,	PUNCT
ejpam-5854	292	56	q	q	PROPN
ejpam-5854	292	57	∈	∈	PROPN
ejpam-5854	292	58	s	s	VERB
ejpam-5854	292	59	such	such	ADJ
ejpam-5854	292	60	that	that	DET
ejpam-5854	292	61	h	h	NOUN
ejpam-5854	292	62	=	=	NOUN
ejpam-5854	292	63	hphq	hphq	NOUN
ejpam-5854	292	64	.	.	PUNCT
ejpam-5854	293	1	thus	thus	ADV
ejpam-5854	293	2	,	,	PUNCT
ejpam-5854	293	3	(	(	PUNCT
ejpam-5854	293	4	µp	µp	NOUN
ejpam-5854	293	5	⃝	⃝	VERB
ejpam-5854	293	6	λ	λ	X
ejpam-5854	293	7	p	p	NOUN
ejpam-5854	293	8	⃝	⃝	NOUN
ejpam-5854	293	9	νp)(h	νp)(h	PUNCT
ejpam-5854	293	10	)	)	PUNCT
ejpam-5854	294	1	=	=	SYM
ejpam-5854	294	2	µp	µp	ADJ
ejpam-5854	294	3	⃝	⃝	NOUN
ejpam-5854	294	4	(	(	PUNCT
ejpam-5854	294	5	λ	λ	X
ejpam-5854	294	6	p	p	VERB
ejpam-5854	294	7	⃝	⃝	NOUN
ejpam-5854	294	8	νp)(h	νp)(h	PUNCT
ejpam-5854	294	9	)	)	PUNCT
ejpam-5854	294	10	=	=	SYM
ejpam-5854	294	11	⋎	⋎	NOUN
ejpam-5854	294	12	(	(	PUNCT
ejpam-5854	294	13	k	k	NOUN
ejpam-5854	294	14	,	,	PUNCT
ejpam-5854	294	15	o)∈ah	o)∈ah	PROPN
ejpam-5854	294	16	{	{	PUNCT
ejpam-5854	294	17	µp(k)⋏	µp(k)⋏	X
ejpam-5854	294	18	(	(	PUNCT
ejpam-5854	294	19	λ	λ	X
ejpam-5854	294	20	p	p	NOUN
ejpam-5854	294	21	⃝	⃝	NOUN
ejpam-5854	294	22	νp)(o	νp)(o	VERB
ejpam-5854	294	23	)	)	PUNCT
ejpam-5854	294	24	}	}	PUNCT
ejpam-5854	294	25	=	=	SYM
ejpam-5854	294	26	⋎	⋎	NOUN
ejpam-5854	294	27	(	(	PUNCT
ejpam-5854	294	28	k	k	NOUN
ejpam-5854	294	29	,	,	PUNCT
ejpam-5854	294	30	o)∈ahphq	o)∈ahphq	ADJ
ejpam-5854	294	31	{	{	PUNCT
ejpam-5854	294	32	µp(k)⋏	µp(k)⋏	X
ejpam-5854	294	33	(	(	PUNCT
ejpam-5854	294	34	λ	λ	X
ejpam-5854	294	35	p	p	NOUN
ejpam-5854	294	36	⃝	⃝	NOUN
ejpam-5854	294	37	νp)(o	νp)(o	ADJ
ejpam-5854	294	38	)	)	PUNCT
ejpam-5854	294	39	}	}	PUNCT
ejpam-5854	294	40	⪰	⪰	NOUN
ejpam-5854	294	41	µp(h)⋏	µp(h)⋏	NOUN
ejpam-5854	294	42	(	(	PUNCT
ejpam-5854	294	43	λ	λ	X
ejpam-5854	294	44	p	p	VERB
ejpam-5854	294	45	⃝	⃝	NOUN
ejpam-5854	294	46	νp)(phq	νp)(phq	NOUN
ejpam-5854	294	47	)	)	PUNCT
ejpam-5854	294	48	=	=	PUNCT
ejpam-5854	295	1	µp(h)⋏	µp(h)⋏	ADP
ejpam-5854	295	2	⋎	⋎	NOUN
ejpam-5854	295	3	(	(	PUNCT
ejpam-5854	295	4	y	y	NOUN
ejpam-5854	295	5	,	,	PUNCT
ejpam-5854	295	6	z)∈aphq	z)∈aphq	NOUN
ejpam-5854	295	7	(	(	PUNCT
ejpam-5854	295	8	λ	λ	X
ejpam-5854	295	9	p	p	X
ejpam-5854	295	10	(	(	PUNCT
ejpam-5854	295	11	y)⋏	y)⋏	NOUN
ejpam-5854	295	12	νp(z	νp(z	ADV
ejpam-5854	295	13	)	)	PUNCT
ejpam-5854	295	14	)	)	PUNCT
ejpam-5854	296	1	=	=	PUNCT
ejpam-5854	297	1	µp(h)⋏	µp(h)⋏	X
ejpam-5854	297	2	⋎	⋎	NOUN
ejpam-5854	297	3	(	(	PUNCT
ejpam-5854	297	4	y	y	NOUN
ejpam-5854	297	5	,	,	PUNCT
ejpam-5854	297	6	z)∈aphphqq	z)∈aphphqq	X
ejpam-5854	297	7	(	(	PUNCT
ejpam-5854	297	8	λ	λ	X
ejpam-5854	297	9	p	p	X
ejpam-5854	297	10	(	(	PUNCT
ejpam-5854	297	11	y)⋏	y)⋏	NOUN
ejpam-5854	297	12	νp(z	νp(z	ADV
ejpam-5854	297	13	)	)	PUNCT
ejpam-5854	297	14	)	)	PUNCT
ejpam-5854	298	1	=	=	PUNCT
ejpam-5854	298	2	µp(h)⋏	µp(h)⋏	NOUN
ejpam-5854	298	3	(	(	PUNCT
ejpam-5854	298	4	λ	λ	X
ejpam-5854	298	5	p	p	X
ejpam-5854	298	6	(	(	PUNCT
ejpam-5854	298	7	php)⋏	php)⋏	ADP
ejpam-5854	298	8	νp(hqq	νp(hqq	NUM
ejpam-5854	298	9	)	)	PUNCT
ejpam-5854	298	10	)	)	PUNCT
ejpam-5854	299	1	=	=	PUNCT
ejpam-5854	299	2	µp(h)⋏	µp(h)⋏	NOUN
ejpam-5854	299	3	(	(	PUNCT
ejpam-5854	299	4	λ	λ	X
ejpam-5854	299	5	p	p	X
ejpam-5854	299	6	(	(	PUNCT
ejpam-5854	299	7	php)⋏	php)⋏	PROPN
ejpam-5854	299	8	νp(hq2	νp(hq2	NUM
ejpam-5854	299	9	)	)	PUNCT
ejpam-5854	299	10	)	)	PUNCT
ejpam-5854	299	11	⪰	⪰	NOUN
ejpam-5854	299	12	µp(h)⋏	µp(h)⋏	X
ejpam-5854	299	13	(	(	PUNCT
ejpam-5854	299	14	λ	λ	X
ejpam-5854	299	15	p	p	X
ejpam-5854	299	16	(	(	PUNCT
ejpam-5854	299	17	h)⋏	h)⋏	NOUN
ejpam-5854	299	18	νp(h	νp(h	NOUN
ejpam-5854	299	19	)	)	PUNCT
ejpam-5854	299	20	)	)	PUNCT
ejpam-5854	300	1	=	=	PUNCT
ejpam-5854	300	2	µp(h)⋏	µp(h)⋏	NOUN
ejpam-5854	300	3	(	(	PUNCT
ejpam-5854	300	4	λ	λ	X
ejpam-5854	300	5	p	p	X
ejpam-5854	300	6	⊓	⊓	PROPN
ejpam-5854	300	7	νp)(h	νp)(h	ADJ
ejpam-5854	300	8	)	)	PUNCT
ejpam-5854	300	9	=	=	SYM
ejpam-5854	300	10	(	(	PUNCT
ejpam-5854	300	11	µp	µp	PROPN
ejpam-5854	300	12	⊓	⊓	PROPN
ejpam-5854	300	13	λp	λp	PRON
ejpam-5854	300	14	⊓	⊓	NOUN
ejpam-5854	300	15	νp)(h	νp)(h	ADJ
ejpam-5854	300	16	)	)	PUNCT
ejpam-5854	300	17	,	,	PUNCT
ejpam-5854	300	18	(	(	PUNCT
ejpam-5854	300	19	µn	µn	NOUN
ejpam-5854	300	20	⃝	⃝	PRON
ejpam-5854	300	21	λ	λ	NOUN
ejpam-5854	300	22	n	n	PRON
ejpam-5854	300	23	⃝	⃝	NOUN
ejpam-5854	300	24	νn)(h	νn)(h	PRON
ejpam-5854	300	25	)	)	PUNCT
ejpam-5854	301	1	=	=	SYM
ejpam-5854	302	1	µn	µn	NOUN
ejpam-5854	302	2	⃝	⃝	NOUN
ejpam-5854	302	3	(	(	PUNCT
ejpam-5854	302	4	λ	λ	X
ejpam-5854	302	5	n	n	CCONJ
ejpam-5854	302	6	⃝	⃝	NOUN
ejpam-5854	302	7	νn)(h	νn)(h	PRON
ejpam-5854	302	8	)	)	PUNCT
ejpam-5854	302	9	=	=	SYM
ejpam-5854	303	1	⋏	⋏	PROPN
ejpam-5854	303	2	(	(	PUNCT
ejpam-5854	303	3	k	k	X
ejpam-5854	303	4	,	,	PUNCT
ejpam-5854	303	5	o)∈ah	o)∈ah	PROPN
ejpam-5854	303	6	{	{	PUNCT
ejpam-5854	303	7	µn(k)⋎	µn(k)⋎	PROPN
ejpam-5854	303	8	(	(	PUNCT
ejpam-5854	303	9	λ	λ	X
ejpam-5854	303	10	n	n	CCONJ
ejpam-5854	303	11	⃝	⃝	NOUN
ejpam-5854	303	12	νn)(o	νn)(o	ADJ
ejpam-5854	303	13	)	)	PUNCT
ejpam-5854	303	14	}	}	PUNCT
ejpam-5854	304	1	=	=	SYM
ejpam-5854	304	2	⋏	⋏	PROPN
ejpam-5854	304	3	(	(	PUNCT
ejpam-5854	304	4	k	k	X
ejpam-5854	304	5	,	,	PUNCT
ejpam-5854	304	6	o)∈ahphq	o)∈ahphq	ADJ
ejpam-5854	304	7	{	{	PUNCT
ejpam-5854	304	8	µn(k)⋎	µn(k)⋎	PROPN
ejpam-5854	304	9	(	(	PUNCT
ejpam-5854	304	10	λ	λ	X
ejpam-5854	304	11	n	n	CCONJ
ejpam-5854	304	12	⃝	⃝	NOUN
ejpam-5854	304	13	νn)(o	νn)(o	ADJ
ejpam-5854	304	14	)	)	PUNCT
ejpam-5854	304	15	}	}	PUNCT
ejpam-5854	304	16	⪯	⪯	VERB
ejpam-5854	304	17	µn(h)⋎	µn(h)⋎	X
ejpam-5854	304	18	(	(	PUNCT
ejpam-5854	304	19	λ	λ	X
ejpam-5854	304	20	n	n	CCONJ
ejpam-5854	304	21	⃝	⃝	NOUN
ejpam-5854	304	22	νn)(phq	νn)(phq	NUM
ejpam-5854	304	23	)	)	PUNCT
ejpam-5854	304	24	=	=	SYM
ejpam-5854	305	1	µn(h)⋎	µn(h)⋎	PROPN
ejpam-5854	305	2	⋏	⋏	PROPN
ejpam-5854	305	3	(	(	PUNCT
ejpam-5854	305	4	y	y	NOUN
ejpam-5854	305	5	,	,	PUNCT
ejpam-5854	305	6	z)∈aphq	z)∈aphq	NOUN
ejpam-5854	305	7	(	(	PUNCT
ejpam-5854	305	8	λ	λ	SYM
ejpam-5854	305	9	n	n	CCONJ
ejpam-5854	305	10	(	(	PUNCT
ejpam-5854	305	11	y)⋎	y)⋎	PROPN
ejpam-5854	305	12	νn(z	νn(z	NUM
ejpam-5854	305	13	)	)	PUNCT
ejpam-5854	305	14	)	)	PUNCT
ejpam-5854	306	1	=	=	PUNCT
ejpam-5854	306	2	µn(h)⋎	µn(h)⋎	PRON
ejpam-5854	306	3	⋎	⋎	NOUN
ejpam-5854	306	4	(	(	PUNCT
ejpam-5854	306	5	y	y	NOUN
ejpam-5854	306	6	,	,	PUNCT
ejpam-5854	306	7	z)∈aphphqq	z)∈aphphqq	X
ejpam-5854	306	8	(	(	PUNCT
ejpam-5854	306	9	λ	λ	SYM
ejpam-5854	306	10	n	n	CCONJ
ejpam-5854	306	11	(	(	PUNCT
ejpam-5854	306	12	y)⋎	y)⋎	PROPN
ejpam-5854	306	13	νn(z	νn(z	NUM
ejpam-5854	306	14	)	)	PUNCT
ejpam-5854	306	15	)	)	PUNCT
ejpam-5854	307	1	=	=	SYM
ejpam-5854	307	2	µn(h)⋎	µn(h)⋎	PROPN
ejpam-5854	307	3	(	(	PUNCT
ejpam-5854	307	4	λ	λ	PROPN
ejpam-5854	307	5	n	n	CCONJ
ejpam-5854	307	6	(	(	PUNCT
ejpam-5854	307	7	php)⋎	php)⋎	PROPN
ejpam-5854	307	8	νn(hqq	νn(hqq	NOUN
ejpam-5854	307	9	)	)	PUNCT
ejpam-5854	307	10	)	)	PUNCT
ejpam-5854	308	1	=	=	SYM
ejpam-5854	308	2	µn(h)⋎	µn(h)⋎	PROPN
ejpam-5854	308	3	(	(	PUNCT
ejpam-5854	308	4	λ	λ	X
ejpam-5854	308	5	p	p	X
ejpam-5854	308	6	(	(	PUNCT
ejpam-5854	308	7	php)⋎	php)⋎	PROPN
ejpam-5854	308	8	νn(hq2	νn(hq2	NUM
ejpam-5854	308	9	)	)	PUNCT
ejpam-5854	308	10	)	)	PUNCT
ejpam-5854	308	11	⪯	⪯	NOUN
ejpam-5854	308	12	µn(h)⋎	µn(h)⋎	X
ejpam-5854	308	13	(	(	PUNCT
ejpam-5854	308	14	λ	λ	SYM
ejpam-5854	308	15	n	n	CCONJ
ejpam-5854	308	16	(	(	PUNCT
ejpam-5854	308	17	h)⋎	h)⋎	PROPN
ejpam-5854	308	18	νn(h	νn(h	VERB
ejpam-5854	308	19	)	)	PUNCT
ejpam-5854	308	20	)	)	PUNCT
ejpam-5854	309	1	=	=	SYM
ejpam-5854	309	2	µn(h)⋎	µn(h)⋎	PROPN
ejpam-5854	309	3	(	(	PUNCT
ejpam-5854	309	4	λ	λ	X
ejpam-5854	309	5	n	n	PRON
ejpam-5854	309	6	⊓	⊓	PROPN
ejpam-5854	309	7	νn)(h	νn)(h	PROPN
ejpam-5854	309	8	)	)	PUNCT
ejpam-5854	309	9	=	=	PUNCT
ejpam-5854	310	1	(	(	PUNCT
ejpam-5854	310	2	µn	µn	PROPN
ejpam-5854	310	3	⊓	⊓	PROPN
ejpam-5854	310	4	λn	λn	ADP
ejpam-5854	310	5	⊓	⊓	PROPN
ejpam-5854	310	6	νn)(h	νn)(h	PROPN
ejpam-5854	310	7	)	)	PUNCT
ejpam-5854	310	8	,	,	PUNCT
ejpam-5854	310	9	p.	p.	NOUN
ejpam-5854	310	10	khamrot	khamrot	PROPN
ejpam-5854	310	11	,	,	PUNCT
ejpam-5854	310	12	n.	n.	PROPN
ejpam-5854	310	13	deetae	deetae	PROPN
ejpam-5854	310	14	,	,	PUNCT
ejpam-5854	310	15	t.	t.	PROPN
ejpam-5854	310	16	gaketem	gaketem	PROPN
ejpam-5854	310	17	/	/	SYM
ejpam-5854	310	18	eur	eur	PROPN
ejpam-5854	310	19	.	.	PUNCT
ejpam-5854	311	1	j.	j.	PROPN
ejpam-5854	311	2	pure	pure	PROPN
ejpam-5854	311	3	appl	appl	PROPN
ejpam-5854	311	4	.	.	PROPN
ejpam-5854	311	5	math	math	PROPN
ejpam-5854	311	6	,	,	PUNCT
ejpam-5854	311	7	18	18	NUM
ejpam-5854	311	8	(	(	PUNCT
ejpam-5854	311	9	2	2	NUM
ejpam-5854	311	10	)	)	PUNCT
ejpam-5854	311	11	(	(	PUNCT
ejpam-5854	311	12	2025	2025	NUM
ejpam-5854	311	13	)	)	PUNCT
ejpam-5854	311	14	,	,	PUNCT
ejpam-5854	311	15	5854	5854	NUM
ejpam-5854	311	16	13	13	NUM
ejpam-5854	311	17	of	of	ADP
ejpam-5854	311	18	14	14	NUM
ejpam-5854	311	19	and	and	CCONJ
ejpam-5854	311	20	(	(	PUNCT
ejpam-5854	311	21	ωp	ωp	INTJ
ejpam-5854	311	22	∗	∗	NOUN
ejpam-5854	311	23	ψp	ψp	ADP
ejpam-5854	311	24	∗	∗	NOUN
ejpam-5854	311	25	κp)(h	κp)(h	ADV
ejpam-5854	311	26	)	)	PUNCT
ejpam-5854	312	1	=	=	PUNCT
ejpam-5854	312	2	ωp	ωp	SYM
ejpam-5854	312	3	∗	∗	NOUN
ejpam-5854	312	4	(	(	PUNCT
ejpam-5854	312	5	ψp	ψp	NOUN
ejpam-5854	312	6	∗	∗	NOUN
ejpam-5854	312	7	κp)(h	κp)(h	ADV
ejpam-5854	312	8	)	)	PUNCT
ejpam-5854	312	9	=	=	SYM
ejpam-5854	313	1	∨	∨	X
ejpam-5854	313	2	(	(	PUNCT
ejpam-5854	313	3	k	k	NOUN
ejpam-5854	313	4	,	,	PUNCT
ejpam-5854	313	5	o)∈ah	o)∈ah	PROPN
ejpam-5854	313	6	{	{	PUNCT
ejpam-5854	313	7	ωp(k	ωp(k	NOUN
ejpam-5854	313	8	)	)	PUNCT
ejpam-5854	313	9	∧	∧	NOUN
ejpam-5854	313	10	(	(	PUNCT
ejpam-5854	313	11	ψp	ψp	NOUN
ejpam-5854	313	12	∗	∗	NOUN
ejpam-5854	313	13	κp)(o	κp)(o	ADJ
ejpam-5854	313	14	)	)	PUNCT
ejpam-5854	313	15	}	}	PUNCT
ejpam-5854	313	16	=	=	SYM
ejpam-5854	313	17	∨	∨	X
ejpam-5854	313	18	(	(	PUNCT
ejpam-5854	313	19	k	k	NOUN
ejpam-5854	313	20	,	,	PUNCT
ejpam-5854	313	21	o)∈ahphq	o)∈ahphq	ADJ
ejpam-5854	313	22	{	{	PUNCT
ejpam-5854	313	23	ω(k	ω(k	PROPN
ejpam-5854	313	24	)	)	PUNCT
ejpam-5854	313	25	∧	∧	NOUN
ejpam-5854	313	26	(	(	PUNCT
ejpam-5854	313	27	ψp	ψp	NOUN
ejpam-5854	313	28	∗	∗	NOUN
ejpam-5854	313	29	κp)(o	κp)(o	ADJ
ejpam-5854	313	30	)	)	PUNCT
ejpam-5854	313	31	}	}	PUNCT
ejpam-5854	313	32	≥	≥	NOUN
ejpam-5854	313	33	ωp(h	ωp(h	NOUN
ejpam-5854	313	34	)	)	PUNCT
ejpam-5854	313	35	∧	∧	NOUN
ejpam-5854	313	36	(	(	PUNCT
ejpam-5854	313	37	ψp	ψp	NOUN
ejpam-5854	313	38	∗	∗	NOUN
ejpam-5854	313	39	κp)(phq	κp)(phq	NUM
ejpam-5854	313	40	)	)	PUNCT
ejpam-5854	313	41	=	=	SYM
ejpam-5854	313	42	ωp(h	ωp(h	X
ejpam-5854	313	43	)	)	PUNCT
ejpam-5854	313	44	∧	∧	NOUN
ejpam-5854	313	45	∨	∨	X
ejpam-5854	313	46	(	(	PUNCT
ejpam-5854	313	47	y	y	PROPN
ejpam-5854	313	48	,	,	PUNCT
ejpam-5854	313	49	z)∈aphq	z)∈aphq	NOUN
ejpam-5854	313	50	(	(	PUNCT
ejpam-5854	313	51	ψp(y	ψp(y	NOUN
ejpam-5854	313	52	)	)	PUNCT
ejpam-5854	313	53	∧	∧	NOUN
ejpam-5854	313	54	κp(z	κp(z	X
ejpam-5854	313	55	)	)	PUNCT
ejpam-5854	313	56	)	)	PUNCT
ejpam-5854	314	1	=	=	SYM
ejpam-5854	314	2	ωp(h	ωp(h	NOUN
ejpam-5854	314	3	)	)	PUNCT
ejpam-5854	314	4	∧	∧	NOUN
ejpam-5854	314	5	∨	∨	X
ejpam-5854	314	6	(	(	PUNCT
ejpam-5854	314	7	y	y	PROPN
ejpam-5854	314	8	,	,	PUNCT
ejpam-5854	314	9	z)∈aphphqq	z)∈aphphqq	X
ejpam-5854	314	10	(	(	PUNCT
ejpam-5854	314	11	ψp(y	ψp(y	NOUN
ejpam-5854	314	12	)	)	PUNCT
ejpam-5854	314	13	∧	∧	NOUN
ejpam-5854	314	14	κp(z	κp(z	X
ejpam-5854	314	15	)	)	PUNCT
ejpam-5854	314	16	)	)	PUNCT
ejpam-5854	314	17	=	=	SYM
ejpam-5854	314	18	ωp(h	ωp(h	NOUN
ejpam-5854	314	19	)	)	PUNCT
ejpam-5854	314	20	∧	∧	NOUN
ejpam-5854	314	21	(	(	PUNCT
ejpam-5854	314	22	ψp(php	ψp(php	ADJ
ejpam-5854	314	23	)	)	PUNCT
ejpam-5854	314	24	∧	∧	PROPN
ejpam-5854	314	25	κp(hqq	κp(hqq	NOUN
ejpam-5854	314	26	)	)	PUNCT
ejpam-5854	314	27	)	)	PUNCT
ejpam-5854	314	28	=	=	SYM
ejpam-5854	314	29	ωp(h	ωp(h	NOUN
ejpam-5854	314	30	)	)	PUNCT
ejpam-5854	314	31	∧	∧	NOUN
ejpam-5854	314	32	(	(	PUNCT
ejpam-5854	314	33	ψp(php	ψp(php	ADJ
ejpam-5854	314	34	)	)	PUNCT
ejpam-5854	314	35	∧	∧	PROPN
ejpam-5854	314	36	κp(hq2	κp(hq2	PROPN
ejpam-5854	314	37	)	)	PUNCT
ejpam-5854	314	38	)	)	PUNCT
ejpam-5854	314	39	≥	≥	NOUN
ejpam-5854	314	40	ωp(h	ωp(h	NOUN
ejpam-5854	314	41	)	)	PUNCT
ejpam-5854	314	42	∧	∧	NOUN
ejpam-5854	314	43	(	(	PUNCT
ejpam-5854	314	44	ψp(h	ψp(h	X
ejpam-5854	314	45	)	)	PUNCT
ejpam-5854	314	46	∧	∧	PROPN
ejpam-5854	314	47	κp(h	κp(h	NOUN
ejpam-5854	314	48	)	)	PUNCT
ejpam-5854	314	49	)	)	PUNCT
ejpam-5854	314	50	=	=	SYM
ejpam-5854	314	51	ωp(h	ωp(h	NOUN
ejpam-5854	314	52	)	)	PUNCT
ejpam-5854	314	53	∧	∧	NOUN
ejpam-5854	314	54	(	(	PUNCT
ejpam-5854	314	55	ψp	ψp	NOUN
ejpam-5854	314	56	∩	∩	NOUN
ejpam-5854	314	57	κp)(h	κp)(h	ADV
ejpam-5854	314	58	)	)	PUNCT
ejpam-5854	314	59	=	=	SYM
ejpam-5854	314	60	(	(	PUNCT
ejpam-5854	314	61	ωp	ωp	NOUN
ejpam-5854	314	62	∩	∩	NOUN
ejpam-5854	314	63	ψp	ψp	ADP
ejpam-5854	314	64	∩	∩	NOUN
ejpam-5854	314	65	κp)(h	κp)(h	ADV
ejpam-5854	314	66	)	)	PUNCT
ejpam-5854	314	67	,	,	PUNCT
ejpam-5854	314	68	(	(	PUNCT
ejpam-5854	314	69	ωn	ωn	NOUN
ejpam-5854	314	70	∗	∗	NOUN
ejpam-5854	314	71	ψn	ψn	INTJ
ejpam-5854	314	72	∗	∗	NOUN
ejpam-5854	314	73	κn)(h	κn)(h	PRON
ejpam-5854	314	74	)	)	PUNCT
ejpam-5854	315	1	=	=	SYM
ejpam-5854	315	2	ωn	ωn	ADP
ejpam-5854	315	3	∗	∗	NOUN
ejpam-5854	315	4	(	(	PUNCT
ejpam-5854	315	5	ψn	ψn	INTJ
ejpam-5854	315	6	∗	∗	NOUN
ejpam-5854	315	7	κn)(h	κn)(h	PRON
ejpam-5854	315	8	)	)	PUNCT
ejpam-5854	316	1	=	=	SYM
ejpam-5854	316	2	∧	∧	NOUN
ejpam-5854	316	3	(	(	PUNCT
ejpam-5854	316	4	k	k	NOUN
ejpam-5854	316	5	,	,	PUNCT
ejpam-5854	316	6	o)∈ah	o)∈ah	PROPN
ejpam-5854	316	7	{	{	PUNCT
ejpam-5854	316	8	ωn(k	ωn(k	NUM
ejpam-5854	316	9	)	)	PUNCT
ejpam-5854	316	10	∨	∨	NUM
ejpam-5854	316	11	(	(	PUNCT
ejpam-5854	316	12	ψn	ψn	INTJ
ejpam-5854	316	13	∗	∗	NOUN
ejpam-5854	316	14	κn)(o	κn)(o	PROPN
ejpam-5854	316	15	)	)	PUNCT
ejpam-5854	316	16	}	}	PUNCT
ejpam-5854	317	1	=	=	SYM
ejpam-5854	317	2	∧	∧	PROPN
ejpam-5854	317	3	(	(	PUNCT
ejpam-5854	317	4	k	k	NOUN
ejpam-5854	317	5	,	,	PUNCT
ejpam-5854	317	6	o)∈ahphq	o)∈ahphq	ADJ
ejpam-5854	317	7	{	{	PUNCT
ejpam-5854	317	8	ω(k	ω(k	PROPN
ejpam-5854	317	9	)	)	PUNCT
ejpam-5854	317	10	∧	∧	PROPN
ejpam-5854	317	11	(	(	PUNCT
ejpam-5854	317	12	ψn	ψn	INTJ
ejpam-5854	317	13	∗	∗	NOUN
ejpam-5854	317	14	κn)(o	κn)(o	PROPN
ejpam-5854	317	15	)	)	PUNCT
ejpam-5854	317	16	}	}	PUNCT
ejpam-5854	317	17	≤	≤	NUM
ejpam-5854	317	18	ωn(h	ωn(h	NUM
ejpam-5854	317	19	)	)	PUNCT
ejpam-5854	317	20	∨	∨	NOUN
ejpam-5854	317	21	(	(	PUNCT
ejpam-5854	317	22	ψn	ψn	PROPN
ejpam-5854	317	23	∗	∗	NOUN
ejpam-5854	317	24	κn)(phq	κn)(phq	NOUN
ejpam-5854	317	25	)	)	PUNCT
ejpam-5854	317	26	=	=	SYM
ejpam-5854	317	27	ωn(h	ωn(h	NUM
ejpam-5854	317	28	)	)	PUNCT
ejpam-5854	317	29	∨	∨	NUM
ejpam-5854	317	30	∧	∧	PROPN
ejpam-5854	317	31	(	(	PUNCT
ejpam-5854	317	32	y	y	PROPN
ejpam-5854	317	33	,	,	PUNCT
ejpam-5854	317	34	z)∈aphq	z)∈aphq	NOUN
ejpam-5854	317	35	(	(	PUNCT
ejpam-5854	317	36	ψn(y	ψn(y	NUM
ejpam-5854	317	37	)	)	PUNCT
ejpam-5854	317	38	∨	∨	NOUN
ejpam-5854	317	39	κn(z	κn(z	NUM
ejpam-5854	317	40	)	)	PUNCT
ejpam-5854	317	41	)	)	PUNCT
ejpam-5854	318	1	=	=	SYM
ejpam-5854	318	2	ωn(h	ωn(h	NUM
ejpam-5854	318	3	)	)	PUNCT
ejpam-5854	318	4	∨	∨	NUM
ejpam-5854	318	5	∧	∧	PROPN
ejpam-5854	318	6	(	(	PUNCT
ejpam-5854	318	7	y	y	PROPN
ejpam-5854	318	8	,	,	PUNCT
ejpam-5854	318	9	z)∈aphphqq	z)∈aphphqq	X
ejpam-5854	318	10	(	(	PUNCT
ejpam-5854	318	11	ψn(y	ψn(y	NUM
ejpam-5854	318	12	)	)	PUNCT
ejpam-5854	318	13	∨	∨	NOUN
ejpam-5854	318	14	κn(z	κn(z	NUM
ejpam-5854	318	15	)	)	PUNCT
ejpam-5854	318	16	)	)	PUNCT
ejpam-5854	319	1	=	=	SYM
ejpam-5854	319	2	ωn(h	ωn(h	NUM
ejpam-5854	319	3	)	)	PUNCT
ejpam-5854	319	4	∨	∨	NOUN
ejpam-5854	319	5	(	(	PUNCT
ejpam-5854	319	6	ψp(php	ψp(php	PROPN
ejpam-5854	319	7	)	)	PUNCT
ejpam-5854	319	8	∨	∨	NUM
ejpam-5854	319	9	κn(hqq	κn(hqq	NOUN
ejpam-5854	319	10	)	)	PUNCT
ejpam-5854	319	11	)	)	PUNCT
ejpam-5854	320	1	=	=	SYM
ejpam-5854	320	2	ωn(h	ωn(h	NUM
ejpam-5854	320	3	)	)	PUNCT
ejpam-5854	320	4	∨	∨	NOUN
ejpam-5854	320	5	(	(	PUNCT
ejpam-5854	320	6	ψn(php	ψn(php	PROPN
ejpam-5854	320	7	)	)	PUNCT
ejpam-5854	320	8	∨	∨	NUM
ejpam-5854	320	9	κn(hq2	κn(hq2	NUM
ejpam-5854	320	10	)	)	PUNCT
ejpam-5854	320	11	)	)	PUNCT
ejpam-5854	320	12	≤	≤	NOUN
ejpam-5854	320	13	ωn(h	ωn(h	NUM
ejpam-5854	320	14	)	)	PUNCT
ejpam-5854	320	15	∨	∨	NUM
ejpam-5854	320	16	(	(	PUNCT
ejpam-5854	320	17	ψn(h	ψn(h	NUM
ejpam-5854	320	18	)	)	PUNCT
ejpam-5854	320	19	∨	∨	NUM
ejpam-5854	320	20	κn(h	κn(h	NUM
ejpam-5854	320	21	)	)	PUNCT
ejpam-5854	320	22	)	)	PUNCT
ejpam-5854	321	1	=	=	SYM
ejpam-5854	321	2	ωn(h	ωn(h	NUM
ejpam-5854	321	3	)	)	PUNCT
ejpam-5854	321	4	∨	∨	NOUN
ejpam-5854	321	5	(	(	PUNCT
ejpam-5854	321	6	ψn	ψn	INTJ
ejpam-5854	321	7	∩	∩	NOUN
ejpam-5854	321	8	κn)(h	κn)(h	ADJ
ejpam-5854	321	9	)	)	PUNCT
ejpam-5854	321	10	=	=	SYM
ejpam-5854	322	1	(	(	PUNCT
ejpam-5854	322	2	ωn	ωn	PROPN
ejpam-5854	322	3	∩	∩	NOUN
ejpam-5854	322	4	ψn	ψn	VERB
ejpam-5854	322	5	∩	∩	NOUN
ejpam-5854	322	6	κn)(h	κn)(h	ADJ
ejpam-5854	322	7	)	)	PUNCT
ejpam-5854	322	8	.	.	PUNCT
ejpam-5854	323	1	hence	hence	ADV
ejpam-5854	323	2	,	,	PUNCT
ejpam-5854	323	3	(	(	PUNCT
ejpam-5854	323	4	µp⊓λp⊓νp)(h	µp⊓λp⊓νp)(h	X
ejpam-5854	323	5	)	)	PUNCT
ejpam-5854	323	6	⪯	⪯	NOUN
ejpam-5854	323	7	(	(	PUNCT
ejpam-5854	323	8	µp⃝λ	µp⃝λ	NOUN
ejpam-5854	323	9	p⃝νp)(h	p⃝νp)(h	VERB
ejpam-5854	323	10	)	)	PUNCT
ejpam-5854	323	11	,	,	PUNCT
ejpam-5854	323	12	(	(	PUNCT
ejpam-5854	323	13	µn⊓λn⊓νn)(h	µn⊓λn⊓νn)(h	NUM
ejpam-5854	323	14	)	)	PUNCT
ejpam-5854	323	15	⪰	⪰	NOUN
ejpam-5854	323	16	(	(	PUNCT
ejpam-5854	323	17	µn⃝λ	µn⃝λ	PROPN
ejpam-5854	323	18	n⃝νn)(h	n⃝νn)(h	PROPN
ejpam-5854	323	19	)	)	PUNCT
ejpam-5854	323	20	and	and	CCONJ
ejpam-5854	323	21	(	(	PUNCT
ejpam-5854	323	22	ωp∩ψp∩	ωp∩ψp∩	NUM
ejpam-5854	323	23	κp)(h	κp)(h	ADP
ejpam-5854	323	24	)	)	PUNCT
ejpam-5854	323	25	≤	≤	NOUN
ejpam-5854	323	26	(	(	PUNCT
ejpam-5854	323	27	ωp∗ψp∗κp)(h	ωp∗ψp∗κp)(h	PROPN
ejpam-5854	323	28	)	)	PUNCT
ejpam-5854	323	29	,	,	PUNCT
ejpam-5854	323	30	(	(	PUNCT
ejpam-5854	323	31	ωn∩ψn∩κn)(h	ωn∩ψn∩κn)(h	NOUN
ejpam-5854	323	32	)	)	PUNCT
ejpam-5854	323	33	≥	≥	NOUN
ejpam-5854	323	34	(	(	PUNCT
ejpam-5854	323	35	ωn∗ψn∗κn)(h	ωn∗ψn∗κn)(h	PROPN
ejpam-5854	323	36	)	)	PUNCT
ejpam-5854	323	37	therefore	therefore	ADV
ejpam-5854	323	38	,	,	PUNCT
ejpam-5854	323	39	c̈1⊓c̈2⊓c̈3⊏c̈1⊛c̈2⊛c̈3	c̈1⊓c̈2⊓c̈3⊏c̈1⊛c̈2⊛c̈3	PROPN
ejpam-5854	323	40	.	.	PUNCT
ejpam-5854	324	1	it	it	PRON
ejpam-5854	324	2	is	be	AUX
ejpam-5854	324	3	obvious	obvious	ADJ
ejpam-5854	324	4	that	that	SCONJ
ejpam-5854	324	5	(	(	PUNCT
ejpam-5854	324	6	4	4	X
ejpam-5854	324	7	)	)	PUNCT
ejpam-5854	324	8	⇒	⇒	NOUN
ejpam-5854	324	9	(	(	PUNCT
ejpam-5854	324	10	3	3	NUM
ejpam-5854	324	11	)	)	PUNCT
ejpam-5854	324	12	⇒	⇒	NOUN
ejpam-5854	324	13	(	(	PUNCT
ejpam-5854	324	14	2	2	NUM
ejpam-5854	324	15	)	)	PUNCT
ejpam-5854	324	16	.	.	PUNCT
ejpam-5854	325	1	(	(	PUNCT
ejpam-5854	325	2	2	2	X
ejpam-5854	325	3	)	)	PUNCT
ejpam-5854	325	4	⇒	⇒	NOUN
ejpam-5854	325	5	(	(	PUNCT
ejpam-5854	325	6	1	1	X
ejpam-5854	325	7	)	)	PUNCT
ejpam-5854	325	8	let	let	VERB
ejpam-5854	325	9	q	q	NOUN
ejpam-5854	325	10	be	be	AUX
ejpam-5854	325	11	a	a	DET
ejpam-5854	325	12	quasi	quasi	NOUN
ejpam-5854	325	13	-	-	NOUN
ejpam-5854	325	14	ideal	ideal	ADJ
ejpam-5854	325	15	,	,	PUNCT
ejpam-5854	325	16	h	h	NOUN
ejpam-5854	325	17	be	be	VERB
ejpam-5854	325	18	an	an	DET
ejpam-5854	325	19	ideal	ideal	NOUN
ejpam-5854	325	20	and	and	CCONJ
ejpam-5854	325	21	r	r	NOUN
ejpam-5854	325	22	be	be	AUX
ejpam-5854	325	23	a	a	DET
ejpam-5854	325	24	right	right	ADJ
ejpam-5854	325	25	ideal	ideal	NOUN
ejpam-5854	325	26	of	of	ADP
ejpam-5854	325	27	s.	s.	PROPN
ejpam-5854	325	28	then	then	ADV
ejpam-5854	325	29	,	,	PUNCT
ejpam-5854	325	30	by	by	ADP
ejpam-5854	325	31	theorem	theorem	NOUN
ejpam-5854	325	32	3	3	NUM
ejpam-5854	325	33	,	,	PUNCT
ejpam-5854	325	34	χq	χq	PROPN
ejpam-5854	325	35	is	be	AUX
ejpam-5854	325	36	a	a	DET
ejpam-5854	325	37	cbf	cbf	PROPN
ejpam-5854	325	38	quasi	quasi	NOUN
ejpam-5854	325	39	-	-	NOUN
ejpam-5854	325	40	ideal	ideal	ADJ
ejpam-5854	325	41	,	,	PUNCT
ejpam-5854	325	42	χj	χj	PROPN
ejpam-5854	325	43	is	be	AUX
ejpam-5854	325	44	a	a	DET
ejpam-5854	325	45	cbf	cbf	PROPN
ejpam-5854	325	46	ideal	ideal	NOUN
ejpam-5854	325	47	and	and	CCONJ
ejpam-5854	325	48	χr	χr	PROPN
ejpam-5854	325	49	is	be	AUX
ejpam-5854	325	50	a	a	DET
ejpam-5854	325	51	cbf	cbf	PROPN
ejpam-5854	325	52	right	right	ADV
ejpam-5854	325	53	ideal	ideal	NOUN
ejpam-5854	325	54	of	of	ADP
ejpam-5854	325	55	s.	s.	PROPN
ejpam-5854	325	56	by	by	ADP
ejpam-5854	325	57	supposition	supposition	PROPN
ejpam-5854	325	58	and	and	CCONJ
ejpam-5854	325	59	lemma	lemma	PROPN
ejpam-5854	325	60	4	4	NUM
ejpam-5854	325	61	,	,	PUNCT
ejpam-5854	325	62	we	we	PRON
ejpam-5854	325	63	have	have	VERB
ejpam-5854	325	64	µp	µp	NOUN
ejpam-5854	325	65	χqjr	χqjr	NOUN
ejpam-5854	325	66	(	(	PUNCT
ejpam-5854	325	67	h	h	NOUN
ejpam-5854	325	68	)	)	PUNCT
ejpam-5854	325	69	=	=	SYM
ejpam-5854	326	1	(	(	PUNCT
ejpam-5854	326	2	µp	µp	NOUN
ejpam-5854	326	3	χq	χq	PROPN
ejpam-5854	326	4	⃝	⃝	NOUN
ejpam-5854	326	5	µp	µp	ADP
ejpam-5854	326	6	χj	χj	PROPN
ejpam-5854	326	7	⃝	⃝	PROPN
ejpam-5854	326	8	µp	µp	PROPN
ejpam-5854	326	9	χr	χr	PROPN
ejpam-5854	326	10	)	)	PUNCT
ejpam-5854	326	11	(	(	PUNCT
ejpam-5854	326	12	h	h	NOUN
ejpam-5854	326	13	)	)	PUNCT
ejpam-5854	326	14	⪰	⪰	NOUN
ejpam-5854	326	15	(	(	PUNCT
ejpam-5854	326	16	µp	µp	NOUN
ejpam-5854	326	17	χq	χq	NOUN
ejpam-5854	326	18	⊓	⊓	PROPN
ejpam-5854	326	19	µp	µp	NOUN
ejpam-5854	326	20	χj	χj	ADJ
ejpam-5854	326	21	⊓	⊓	PROPN
ejpam-5854	326	22	µp	µp	PROPN
ejpam-5854	326	23	χr	χr	NOUN
ejpam-5854	326	24	)	)	PUNCT
ejpam-5854	326	25	(	(	PUNCT
ejpam-5854	326	26	h	h	NOUN
ejpam-5854	326	27	)	)	PUNCT
ejpam-5854	326	28	=	=	NOUN
ejpam-5854	327	1	µp	µp	PROPN
ejpam-5854	327	2	χq⊓j⊓r	χq⊓j⊓r	PROPN
ejpam-5854	327	3	(	(	PUNCT
ejpam-5854	327	4	h	h	NOUN
ejpam-5854	327	5	)	)	PUNCT
ejpam-5854	327	6	=	=	SYM
ejpam-5854	327	7	1	1	NUM
ejpam-5854	327	8	,	,	PUNCT
ejpam-5854	327	9	µn	µn	NOUN
ejpam-5854	327	10	χqjr	χqjr	NOUN
ejpam-5854	327	11	(	(	PUNCT
ejpam-5854	327	12	h	h	NOUN
ejpam-5854	327	13	)	)	PUNCT
ejpam-5854	327	14	=	=	SYM
ejpam-5854	328	1	(	(	PUNCT
ejpam-5854	328	2	µn	µn	PROPN
ejpam-5854	328	3	χq	χq	PROPN
ejpam-5854	328	4	⃝	⃝	PROPN
ejpam-5854	328	5	µn	µn	PROPN
ejpam-5854	328	6	χj	χj	PROPN
ejpam-5854	328	7	⃝	⃝	NOUN
ejpam-5854	328	8	µn	µn	PROPN
ejpam-5854	328	9	χr	χr	NOUN
ejpam-5854	328	10	)	)	PUNCT
ejpam-5854	328	11	(	(	PUNCT
ejpam-5854	328	12	h	h	NOUN
ejpam-5854	328	13	)	)	PUNCT
ejpam-5854	328	14	⪯	⪯	NOUN
ejpam-5854	328	15	(	(	PUNCT
ejpam-5854	328	16	µn	µn	VERB
ejpam-5854	328	17	χq	χq	NOUN
ejpam-5854	328	18	⊓	⊓	PROPN
ejpam-5854	328	19	µn	µn	PROPN
ejpam-5854	328	20	χj	χj	PRON
ejpam-5854	328	21	⊓	⊓	PROPN
ejpam-5854	328	22	µn	µn	NOUN
ejpam-5854	328	23	χr	χr	NOUN
ejpam-5854	328	24	)	)	PUNCT
ejpam-5854	328	25	(	(	PUNCT
ejpam-5854	328	26	h	h	NOUN
ejpam-5854	328	27	)	)	PUNCT
ejpam-5854	328	28	=	=	SYM
ejpam-5854	328	29	µn	µn	PROPN
ejpam-5854	328	30	χq⊓j⊓r	χq⊓j⊓r	PROPN
ejpam-5854	328	31	(	(	PUNCT
ejpam-5854	328	32	h	h	NOUN
ejpam-5854	328	33	)	)	PUNCT
ejpam-5854	328	34	=	=	SYM
ejpam-5854	328	35	−1	−1	NOUN
ejpam-5854	328	36	,	,	PUNCT
ejpam-5854	328	37	and	and	CCONJ
ejpam-5854	328	38	ωp	ωp	PRON
ejpam-5854	328	39	χqjr	χqjr	NOUN
ejpam-5854	328	40	(	(	PUNCT
ejpam-5854	328	41	h	h	NOUN
ejpam-5854	328	42	)	)	PUNCT
ejpam-5854	328	43	=	=	SYM
ejpam-5854	328	44	(	(	PUNCT
ejpam-5854	328	45	ωp	ωp	INTJ
ejpam-5854	328	46	χq	χq	PROPN
ejpam-5854	328	47	∗	∗	VERB
ejpam-5854	328	48	ωp	ωp	PRON
ejpam-5854	328	49	χj	χj	PROPN
ejpam-5854	328	50	∗	∗	X
ejpam-5854	328	51	ωp	ωp	NOUN
ejpam-5854	328	52	χr	χr	NOUN
ejpam-5854	328	53	)	)	PUNCT
ejpam-5854	328	54	(	(	PUNCT
ejpam-5854	328	55	h	h	NOUN
ejpam-5854	328	56	)	)	PUNCT
ejpam-5854	328	57	≥	≥	NOUN
ejpam-5854	328	58	(	(	PUNCT
ejpam-5854	328	59	ωp	ωp	NOUN
ejpam-5854	328	60	χq	χq	PROPN
ejpam-5854	328	61	∩	∩	PROPN
ejpam-5854	328	62	ωp	ωp	ADP
ejpam-5854	328	63	χj	χj	PROPN
ejpam-5854	328	64	∩	∩	X
ejpam-5854	328	65	ωn	ωn	PRON
ejpam-5854	328	66	χr	χr	PROPN
ejpam-5854	328	67	)	)	PUNCT
ejpam-5854	328	68	(	(	PUNCT
ejpam-5854	328	69	h	h	NOUN
ejpam-5854	328	70	)	)	PUNCT
ejpam-5854	328	71	=	=	SYM
ejpam-5854	328	72	ωp	ωp	PRON
ejpam-5854	328	73	χq∩j∩r	χq∩j∩r	PROPN
ejpam-5854	328	74	(	(	PUNCT
ejpam-5854	328	75	h	h	NOUN
ejpam-5854	328	76	)	)	PUNCT
ejpam-5854	328	77	=	=	SYM
ejpam-5854	328	78	1	1	NUM
ejpam-5854	328	79	,	,	PUNCT
ejpam-5854	328	80	ωn	ωn	ADP
ejpam-5854	328	81	χqjr	χqjr	NOUN
ejpam-5854	328	82	(	(	PUNCT
ejpam-5854	328	83	h	h	NOUN
ejpam-5854	328	84	)	)	PUNCT
ejpam-5854	328	85	=	=	SYM
ejpam-5854	328	86	(	(	PUNCT
ejpam-5854	328	87	ωn	ωn	ADP
ejpam-5854	328	88	χq	χq	PROPN
ejpam-5854	328	89	∗	∗	NOUN
ejpam-5854	328	90	ωn	ωn	ADP
ejpam-5854	328	91	χj	χj	PROPN
ejpam-5854	328	92	∗	∗	NOUN
ejpam-5854	328	93	ωn	ωn	ADP
ejpam-5854	328	94	χr	χr	PROPN
ejpam-5854	328	95	)	)	PUNCT
ejpam-5854	328	96	(	(	PUNCT
ejpam-5854	328	97	h	h	NOUN
ejpam-5854	328	98	)	)	PUNCT
ejpam-5854	328	99	≤	≤	NOUN
ejpam-5854	328	100	(	(	PUNCT
ejpam-5854	328	101	ωn	ωn	NOUN
ejpam-5854	328	102	χq	χq	PROPN
ejpam-5854	328	103	∩	∩	NOUN
ejpam-5854	328	104	ωn	ωn	ADP
ejpam-5854	328	105	χj	χj	PROPN
ejpam-5854	328	106	∩	∩	PROPN
ejpam-5854	328	107	ωp	ωp	PRON
ejpam-5854	328	108	χr	χr	NOUN
ejpam-5854	328	109	)	)	PUNCT
ejpam-5854	328	110	(	(	PUNCT
ejpam-5854	328	111	h	h	NOUN
ejpam-5854	328	112	)	)	PUNCT
ejpam-5854	328	113	=	=	SYM
ejpam-5854	328	114	ωn	ωn	PROPN
ejpam-5854	328	115	χq∩j∩r	χq∩j∩r	PROPN
ejpam-5854	328	116	(	(	PUNCT
ejpam-5854	328	117	h	h	NOUN
ejpam-5854	328	118	)	)	PUNCT
ejpam-5854	328	119	=	=	PUNCT
ejpam-5854	328	120	−1	−1	NOUN
ejpam-5854	328	121	.	.	PUNCT
ejpam-5854	329	1	thus	thus	ADV
ejpam-5854	329	2	,	,	PUNCT
ejpam-5854	329	3	h	h	PROPN
ejpam-5854	329	4	∈	∈	PROPN
ejpam-5854	329	5	qjr	qjr	NOUN
ejpam-5854	329	6	.	.	PUNCT
ejpam-5854	330	1	hence	hence	ADV
ejpam-5854	330	2	,	,	PUNCT
ejpam-5854	330	3	q	q	PROPN
ejpam-5854	330	4	∩	∩	ADJ
ejpam-5854	330	5	j	j	PROPN
ejpam-5854	330	6	∩r	∩r	PROPN
ejpam-5854	330	7	⊑	⊑	X
ejpam-5854	330	8	qjr	qjr	PROPN
ejpam-5854	330	9	.	.	PUNCT
ejpam-5854	331	1	therefore	therefore	ADV
ejpam-5854	331	2	,	,	PUNCT
ejpam-5854	331	3	by	by	ADP
ejpam-5854	331	4	lemma	lemma	PROPN
ejpam-5854	331	5	4	4	NUM
ejpam-5854	331	6	,	,	PUNCT
ejpam-5854	331	7	s	s	VERB
ejpam-5854	331	8	is	be	AUX
ejpam-5854	331	9	weakly	weakly	ADV
ejpam-5854	331	10	regular	regular	ADJ
ejpam-5854	331	11	.	.	PUNCT
ejpam-5854	332	1	5	5	X
ejpam-5854	332	2	.	.	X
ejpam-5854	332	3	conclusion	conclusion	NOUN
ejpam-5854	332	4	in	in	ADP
ejpam-5854	332	5	this	this	DET
ejpam-5854	332	6	article	article	NOUN
ejpam-5854	332	7	,	,	PUNCT
ejpam-5854	332	8	we	we	PRON
ejpam-5854	332	9	extend	extend	VERB
ejpam-5854	332	10	the	the	DET
ejpam-5854	332	11	concept	concept	NOUN
ejpam-5854	332	12	of	of	ADP
ejpam-5854	332	13	cubic	cubic	ADJ
ejpam-5854	332	14	fuzzy	fuzzy	ADJ
ejpam-5854	332	15	sets	set	NOUN
ejpam-5854	332	16	and	and	CCONJ
ejpam-5854	332	17	bipolar	bipolar	ADJ
ejpam-5854	332	18	fuzzy	fuzzy	ADJ
ejpam-5854	332	19	sets	set	NOUN
ejpam-5854	332	20	by	by	ADP
ejpam-5854	332	21	introducing	introduce	VERB
ejpam-5854	332	22	the	the	DET
ejpam-5854	332	23	notion	notion	NOUN
ejpam-5854	332	24	of	of	ADP
ejpam-5854	332	25	cubic	cubic	ADJ
ejpam-5854	332	26	bipolar	bipolar	ADJ
ejpam-5854	332	27	fuzzy	fuzzy	ADJ
ejpam-5854	332	28	sets	set	NOUN
ejpam-5854	332	29	,	,	PUNCT
ejpam-5854	332	30	which	which	PRON
ejpam-5854	332	31	serve	serve	VERB
ejpam-5854	332	32	as	as	ADP
ejpam-5854	332	33	a	a	DET
ejpam-5854	332	34	more	more	ADV
ejpam-5854	332	35	generalized	generalized	ADJ
ejpam-5854	332	36	framework	framework	NOUN
ejpam-5854	332	37	for	for	ADP
ejpam-5854	332	38	dealing	deal	VERB
ejpam-5854	332	39	with	with	ADP
ejpam-5854	332	40	uncertainty	uncertainty	NOUN
ejpam-5854	332	41	in	in	ADP
ejpam-5854	332	42	algebraic	algebraic	ADJ
ejpam-5854	332	43	structures	structure	NOUN
ejpam-5854	332	44	.	.	PUNCT
ejpam-5854	333	1	this	this	DET
ejpam-5854	333	2	extended	extend	VERB
ejpam-5854	333	3	concept	concept	NOUN
ejpam-5854	333	4	provides	provide	VERB
ejpam-5854	333	5	a	a	DET
ejpam-5854	333	6	powerful	powerful	ADJ
ejpam-5854	333	7	tool	tool	NOUN
ejpam-5854	333	8	for	for	ADP
ejpam-5854	333	9	analyzing	analyze	VERB
ejpam-5854	333	10	and	and	CCONJ
ejpam-5854	333	11	characterizing	characterize	VERB
ejpam-5854	333	12	various	various	ADJ
ejpam-5854	333	13	subsemigroups	subsemigroup	NOUN
ejpam-5854	333	14	,	,	PUNCT
ejpam-5854	333	15	offering	offer	VERB
ejpam-5854	333	16	a	a	DET
ejpam-5854	333	17	new	new	ADJ
ejpam-5854	333	18	perspective	perspective	NOUN
ejpam-5854	333	19	on	on	ADP
ejpam-5854	333	20	their	their	PRON
ejpam-5854	333	21	structural	structural	ADJ
ejpam-5854	333	22	properties	property	NOUN
ejpam-5854	333	23	.	.	PUNCT
ejpam-5854	334	1	one	one	NUM
ejpam-5854	334	2	of	of	ADP
ejpam-5854	334	3	the	the	DET
ejpam-5854	334	4	main	main	ADJ
ejpam-5854	334	5	contributions	contribution	NOUN
ejpam-5854	334	6	of	of	ADP
ejpam-5854	334	7	this	this	DET
ejpam-5854	334	8	paper	paper	NOUN
ejpam-5854	334	9	is	be	AUX
ejpam-5854	334	10	the	the	DET
ejpam-5854	334	11	characterization	characterization	NOUN
ejpam-5854	334	12	of	of	ADP
ejpam-5854	334	13	weakly	weakly	ADJ
ejpam-5854	334	14	regular	regular	ADJ
ejpam-5854	334	15	semigroups	semigroup	NOUN
ejpam-5854	334	16	in	in	ADP
ejpam-5854	334	17	terms	term	NOUN
ejpam-5854	334	18	of	of	ADP
ejpam-5854	334	19	cubic	cubic	ADJ
ejpam-5854	334	20	bipolar	bipolar	ADJ
ejpam-5854	334	21	fuzzy	fuzzy	ADJ
ejpam-5854	334	22	ideals	ideal	NOUN
ejpam-5854	334	23	.	.	PUNCT
ejpam-5854	335	1	by	by	ADP
ejpam-5854	335	2	exploring	explore	VERB
ejpam-5854	335	3	the	the	DET
ejpam-5854	335	4	fundamental	fundamental	ADJ
ejpam-5854	335	5	properties	property	NOUN
ejpam-5854	335	6	and	and	CCONJ
ejpam-5854	335	7	interactions	interaction	NOUN
ejpam-5854	335	8	of	of	ADP
ejpam-5854	335	9	these	these	DET
ejpam-5854	335	10	fuzzy	fuzzy	ADJ
ejpam-5854	335	11	ideals	ideal	NOUN
ejpam-5854	335	12	within	within	ADP
ejpam-5854	335	13	semigroups	semigroup	NOUN
ejpam-5854	335	14	,	,	PUNCT
ejpam-5854	335	15	we	we	PRON
ejpam-5854	335	16	establish	establish	VERB
ejpam-5854	335	17	key	key	ADJ
ejpam-5854	335	18	results	result	NOUN
ejpam-5854	335	19	that	that	PRON
ejpam-5854	335	20	enhance	enhance	VERB
ejpam-5854	335	21	our	our	PRON
ejpam-5854	335	22	understanding	understanding	NOUN
ejpam-5854	335	23	of	of	ADP
ejpam-5854	335	24	weakly	weakly	ADJ
ejpam-5854	335	25	regular	regular	ADJ
ejpam-5854	335	26	semigroups	semigroup	NOUN
ejpam-5854	335	27	and	and	CCONJ
ejpam-5854	335	28	their	their	PRON
ejpam-5854	335	29	algebraic	algebraic	ADJ
ejpam-5854	335	30	behavior	behavior	NOUN
ejpam-5854	335	31	.	.	PUNCT
ejpam-5854	336	1	for	for	ADP
ejpam-5854	336	2	future	future	ADJ
ejpam-5854	336	3	research	research	NOUN
ejpam-5854	336	4	,	,	PUNCT
ejpam-5854	336	5	we	we	PRON
ejpam-5854	336	6	aim	aim	VERB
ejpam-5854	336	7	to	to	PART
ejpam-5854	336	8	extend	extend	VERB
ejpam-5854	336	9	our	our	PRON
ejpam-5854	336	10	findings	finding	NOUN
ejpam-5854	336	11	by	by	ADP
ejpam-5854	336	12	characterizing	characterize	VERB
ejpam-5854	336	13	certain	certain	ADJ
ejpam-5854	336	14	classes	class	NOUN
ejpam-5854	336	15	of	of	ADP
ejpam-5854	336	16	subsemigroups	subsemigroup	NOUN
ejpam-5854	336	17	using	use	VERB
ejpam-5854	336	18	cubic	cubic	ADJ
ejpam-5854	336	19	bipolar	bipolar	ADJ
ejpam-5854	336	20	fuzzy	fuzzy	ADJ
ejpam-5854	336	21	ideals	ideal	NOUN
ejpam-5854	336	22	.	.	PUNCT
ejpam-5854	337	1	p.	p.	NOUN
ejpam-5854	337	2	khamrot	khamrot	PROPN
ejpam-5854	337	3	,	,	PUNCT
ejpam-5854	337	4	n.	n.	PROPN
ejpam-5854	337	5	deetae	deetae	PROPN
ejpam-5854	337	6	,	,	PUNCT
ejpam-5854	337	7	t.	t.	PROPN
ejpam-5854	337	8	gaketem	gaketem	PROPN
ejpam-5854	337	9	/	/	SYM
ejpam-5854	337	10	eur	eur	PROPN
ejpam-5854	337	11	.	.	PUNCT
ejpam-5854	338	1	j.	j.	PROPN
ejpam-5854	338	2	pure	pure	PROPN
ejpam-5854	338	3	appl	appl	PROPN
ejpam-5854	338	4	.	.	PROPN
ejpam-5854	338	5	math	math	PROPN
ejpam-5854	338	6	,	,	PUNCT
ejpam-5854	338	7	18	18	NUM
ejpam-5854	338	8	(	(	PUNCT
ejpam-5854	338	9	2	2	NUM
ejpam-5854	338	10	)	)	PUNCT
ejpam-5854	338	11	(	(	PUNCT
ejpam-5854	338	12	2025	2025	NUM
ejpam-5854	338	13	)	)	PUNCT
ejpam-5854	338	14	,	,	PUNCT
ejpam-5854	338	15	5854	5854	NUM
ejpam-5854	338	16	14	14	NUM
ejpam-5854	338	17	of	of	ADP
ejpam-5854	338	18	14	14	NUM
ejpam-5854	338	19	this	this	PRON
ejpam-5854	338	20	will	will	AUX
ejpam-5854	338	21	further	far	ADV
ejpam-5854	338	22	enrich	enrich	VERB
ejpam-5854	338	23	the	the	DET
ejpam-5854	338	24	theoretical	theoretical	ADJ
ejpam-5854	338	25	framework	framework	NOUN
ejpam-5854	338	26	and	and	CCONJ
ejpam-5854	338	27	provide	provide	VERB
ejpam-5854	338	28	deeper	deep	ADJ
ejpam-5854	338	29	insights	insight	NOUN
ejpam-5854	338	30	into	into	ADP
ejpam-5854	338	31	the	the	DET
ejpam-5854	338	32	role	role	NOUN
ejpam-5854	338	33	of	of	ADP
ejpam-5854	338	34	fuzzy	fuzzy	ADJ
ejpam-5854	338	35	structures	structure	NOUN
ejpam-5854	338	36	in	in	ADP
ejpam-5854	338	37	semigroup	semigroup	PROPN
ejpam-5854	338	38	theory	theory	NOUN
ejpam-5854	338	39	.	.	PUNCT
ejpam-5854	339	1	additionally	additionally	ADV
ejpam-5854	339	2	,	,	PUNCT
ejpam-5854	339	3	we	we	PRON
ejpam-5854	339	4	plan	plan	VERB
ejpam-5854	339	5	to	to	PART
ejpam-5854	339	6	investigate	investigate	VERB
ejpam-5854	339	7	potential	potential	ADJ
ejpam-5854	339	8	applications	application	NOUN
ejpam-5854	339	9	of	of	ADP
ejpam-5854	339	10	cubic	cubic	ADJ
ejpam-5854	339	11	bipolar	bipolar	ADJ
ejpam-5854	339	12	fuzzy	fuzzy	ADJ
ejpam-5854	339	13	sets	set	NOUN
ejpam-5854	339	14	in	in	ADP
ejpam-5854	339	15	other	other	ADJ
ejpam-5854	339	16	mathematical	mathematical	ADJ
ejpam-5854	339	17	and	and	CCONJ
ejpam-5854	339	18	computational	computational	ADJ
ejpam-5854	339	19	domains	domain	NOUN
ejpam-5854	339	20	,	,	PUNCT
ejpam-5854	339	21	particularly	particularly	ADV
ejpam-5854	339	22	in	in	ADP
ejpam-5854	339	23	decision	decision	NOUN
ejpam-5854	339	24	-	-	PUNCT
ejpam-5854	339	25	making	make	VERB
ejpam-5854	339	26	processes	process	NOUN
ejpam-5854	339	27	and	and	CCONJ
ejpam-5854	339	28	algebraic	algebraic	ADJ
ejpam-5854	339	29	systems	system	NOUN
ejpam-5854	339	30	with	with	ADP
ejpam-5854	339	31	uncertainty	uncertainty	NOUN
ejpam-5854	339	32	.	.	PUNCT
ejpam-5854	340	1	acknowledgements	acknowledgement	NOUN
ejpam-5854	340	2	this	this	DET
ejpam-5854	340	3	research	research	NOUN
ejpam-5854	340	4	was	be	AUX
ejpam-5854	340	5	supported	support	VERB
ejpam-5854	340	6	by	by	ADP
ejpam-5854	340	7	the	the	DET
ejpam-5854	340	8	rajamangala	rajamangala	PROPN
ejpam-5854	340	9	university	university	PROPN
ejpam-5854	340	10	technology	technology	NOUN
ejpam-5854	340	11	lanna	lanna	PROPN
ejpam-5854	340	12	,	,	PUNCT
ejpam-5854	340	13	phitsanulok	phitsanulok	PROPN
ejpam-5854	340	14	,	,	PUNCT
ejpam-5854	340	15	thailand	thailand	PROPN
ejpam-5854	340	16	(	(	PUNCT
ejpam-5854	340	17	fundamental	fundamental	ADJ
ejpam-5854	340	18	fund	fund	NOUN
ejpam-5854	340	19	2025	2025	NUM
ejpam-5854	340	20	,	,	PUNCT
ejpam-5854	340	21	grant	grant	VERB
ejpam-5854	340	22	no	no	INTJ
ejpam-5854	340	23	.	.	PUNCT
ejpam-5854	341	1	ff2568p089	ff2568p089	NOUN
ejpam-5854	341	2	)	)	PUNCT
ejpam-5854	341	3	.	.	PUNCT
ejpam-5854	342	1	references	reference	NOUN
ejpam-5854	342	2	[	[	X
ejpam-5854	342	3	1	1	NUM
ejpam-5854	342	4	]	]	X
ejpam-5854	342	5	l.a	l.a	PROPN
ejpam-5854	342	6	.	.	PROPN
ejpam-5854	342	7	zadeh	zadeh	PROPN
ejpam-5854	342	8	.	.	PUNCT
ejpam-5854	343	1	the	the	DET
ejpam-5854	343	2	concept	concept	NOUN
ejpam-5854	343	3	of	of	ADP
ejpam-5854	343	4	a	a	DET
ejpam-5854	343	5	linguistic	linguistic	ADJ
ejpam-5854	343	6	variable	variable	NOUN
ejpam-5854	343	7	and	and	CCONJ
ejpam-5854	343	8	its	its	PRON
ejpam-5854	343	9	application	application	NOUN
ejpam-5854	343	10	to	to	PART
ejpam-5854	343	11	approximate	approximate	ADJ
ejpam-5854	343	12	reasoning	reasoning	NOUN
ejpam-5854	343	13	.	.	PUNCT
ejpam-5854	344	1	information	information	NOUN
ejpam-5854	344	2	and	and	CCONJ
ejpam-5854	344	3	control	control	NOUN
ejpam-5854	344	4	,	,	PUNCT
ejpam-5854	344	5	8:338–353	8:338–353	NUM
ejpam-5854	344	6	,	,	PUNCT
ejpam-5854	344	7	1975	1975	NUM
ejpam-5854	344	8	.	.	PUNCT
ejpam-5854	345	1	[	[	X
ejpam-5854	345	2	2	2	NUM
ejpam-5854	345	3	]	]	X
ejpam-5854	345	4	n.	n.	PROPN
ejpam-5854	345	5	kuroki	kuroki	PROPN
ejpam-5854	345	6	.	.	PUNCT
ejpam-5854	346	1	fuzzy	fuzzy	ADJ
ejpam-5854	346	2	bi	bi	NOUN
ejpam-5854	346	3	-	-	NOUN
ejpam-5854	346	4	ideals	ideal	NOUN
ejpam-5854	346	5	in	in	ADP
ejpam-5854	346	6	semigroup	semigroup	PROPN
ejpam-5854	346	7	.	.	PUNCT
ejpam-5854	347	1	commentarii	commentarii	PROPN
ejpam-5854	347	2	mathematici	mathematici	PROPN
ejpam-5854	347	3	universitatis	universitatis	PROPN
ejpam-5854	347	4	sancti	sancti	PROPN
ejpam-5854	347	5	pauli	pauli	PROPN
ejpam-5854	347	6	,	,	PUNCT
ejpam-5854	347	7	5:128–132	5:128–132	NUM
ejpam-5854	347	8	,	,	PUNCT
ejpam-5854	347	9	1979	1979	NUM
ejpam-5854	347	10	.	.	PUNCT
ejpam-5854	348	1	[	[	X
ejpam-5854	348	2	3	3	NUM
ejpam-5854	348	3	]	]	X
ejpam-5854	348	4	l.a	l.a	PROPN
ejpam-5854	348	5	.	.	PROPN
ejpam-5854	348	6	zadeh	zadeh	PROPN
ejpam-5854	348	7	.	.	PUNCT
ejpam-5854	349	1	the	the	DET
ejpam-5854	349	2	concept	concept	NOUN
ejpam-5854	349	3	of	of	ADP
ejpam-5854	349	4	a	a	DET
ejpam-5854	349	5	linguistic	linguistic	ADJ
ejpam-5854	349	6	variable	variable	NOUN
ejpam-5854	349	7	and	and	CCONJ
ejpam-5854	349	8	its	its	PRON
ejpam-5854	349	9	application	application	NOUN
ejpam-5854	349	10	to	to	PART
ejpam-5854	349	11	approximate	approximate	ADJ
ejpam-5854	349	12	reasoning	reasoning	NOUN
ejpam-5854	349	13	.	.	PUNCT
ejpam-5854	350	1	information	information	NOUN
ejpam-5854	350	2	sciences	sciences	PROPN
ejpam-5854	350	3	,	,	PUNCT
ejpam-5854	350	4	8:199–249	8:199–249	NUM
ejpam-5854	350	5	,	,	PUNCT
ejpam-5854	350	6	1975	1975	NUM
ejpam-5854	350	7	.	.	PUNCT
ejpam-5854	351	1	[	[	X
ejpam-5854	351	2	4	4	X
ejpam-5854	351	3	]	]	PUNCT
ejpam-5854	351	4	w.	w.	PROPN
ejpam-5854	351	5	zhang	zhang	PROPN
ejpam-5854	351	6	.	.	PUNCT
ejpam-5854	351	7	bipolar	bipolar	ADJ
ejpam-5854	351	8	fuzzy	fuzzy	ADJ
ejpam-5854	351	9	sets	set	NOUN
ejpam-5854	351	10	and	and	CCONJ
ejpam-5854	351	11	relations	relation	NOUN
ejpam-5854	351	12	:	:	PUNCT
ejpam-5854	351	13	a	a	DET
ejpam-5854	351	14	computational	computational	ADJ
ejpam-5854	351	15	framework	framework	NOUN
ejpam-5854	351	16	for	for	ADP
ejpam-5854	351	17	cognitive	cognitive	ADJ
ejpam-5854	351	18	modeling	modeling	NOUN
ejpam-5854	351	19	and	and	CCONJ
ejpam-5854	351	20	multiagent	multiagent	ADJ
ejpam-5854	351	21	decision	decision	NOUN
ejpam-5854	351	22	analysis	analysis	NOUN
ejpam-5854	351	23	.	.	PUNCT
ejpam-5854	352	1	in	in	ADP
ejpam-5854	352	2	proceedings	proceeding	NOUN
ejpam-5854	352	3	of	of	ADP
ejpam-5854	352	4	ieee	ieee	NOUN
ejpam-5854	352	5	conference	conference	NOUN
ejpam-5854	352	6	,	,	PUNCT
ejpam-5854	352	7	pages	page	NOUN
ejpam-5854	352	8	305–309	305–309	NUM
ejpam-5854	352	9	,	,	PUNCT
ejpam-5854	352	10	1994	1994	NUM
ejpam-5854	352	11	.	.	PUNCT
ejpam-5854	353	1	[	[	X
ejpam-5854	353	2	5	5	X
ejpam-5854	353	3	]	]	PUNCT
ejpam-5854	353	4	k.	k.	PROPN
ejpam-5854	353	5	lee	lee	PROPN
ejpam-5854	353	6	.	.	PUNCT
ejpam-5854	354	1	bipolar	bipolar	ADJ
ejpam-5854	354	2	-	-	PUNCT
ejpam-5854	354	3	valued	value	VERB
ejpam-5854	354	4	fuzzy	fuzzy	ADJ
ejpam-5854	354	5	sets	set	NOUN
ejpam-5854	354	6	and	and	CCONJ
ejpam-5854	354	7	their	their	PRON
ejpam-5854	354	8	operations	operation	NOUN
ejpam-5854	354	9	.	.	PUNCT
ejpam-5854	355	1	in	in	ADP
ejpam-5854	355	2	proceeding	proceed	VERB
ejpam-5854	355	3	international	international	ADJ
ejpam-5854	355	4	conference	conference	NOUN
ejpam-5854	355	5	on	on	ADP
ejpam-5854	355	6	intelligent	intelligent	ADJ
ejpam-5854	355	7	technologies	technology	NOUN
ejpam-5854	355	8	bangkok	bangkok	PROPN
ejpam-5854	355	9	,	,	PUNCT
ejpam-5854	355	10	thailand	thailand	PROPN
ejpam-5854	355	11	,	,	PUNCT
ejpam-5854	355	12	pages	page	NOUN
ejpam-5854	355	13	307–312	307–312	NUM
ejpam-5854	355	14	,	,	PUNCT
ejpam-5854	355	15	2000	2000	NUM
ejpam-5854	355	16	.	.	PUNCT
ejpam-5854	356	1	[	[	X
ejpam-5854	356	2	6	6	NUM
ejpam-5854	356	3	]	]	X
ejpam-5854	356	4	c.s.kim	c.s.kim	PROPN
ejpam-5854	356	5	y.b.jun	y.b.jun	PROPN
ejpam-5854	356	6	and	and	CCONJ
ejpam-5854	356	7	k.o.yang	k.o.yang	PROPN
ejpam-5854	356	8	.	.	PUNCT
ejpam-5854	357	1	cubic	cubic	ADJ
ejpam-5854	357	2	sets	set	NOUN
ejpam-5854	357	3	.	.	PUNCT
ejpam-5854	358	1	annals	annal	NOUN
ejpam-5854	358	2	of	of	ADP
ejpam-5854	358	3	fuzzy	fuzzy	ADJ
ejpam-5854	358	4	mathematical	mathematical	ADJ
ejpam-5854	358	5	and	and	CCONJ
ejpam-5854	358	6	informatics	informatic	NOUN
ejpam-5854	358	7	,	,	PUNCT
ejpam-5854	358	8	4:83–98	4:83–98	NUM
ejpam-5854	358	9	,	,	PUNCT
ejpam-5854	358	10	2012	2012	NUM
ejpam-5854	358	11	.	.	PUNCT
ejpam-5854	359	1	[	[	X
ejpam-5854	359	2	7	7	X
ejpam-5854	359	3	]	]	X
ejpam-5854	359	4	c.	c.	PROPN
ejpam-5854	359	5	wei	wei	PROPN
ejpam-5854	359	6	g.	g.	PROPN
ejpam-5854	359	7	wei	wei	PROPN
ejpam-5854	359	8	and	and	CCONJ
ejpam-5854	359	9	h.	h.	PROPN
ejpam-5854	359	10	gao	gao	PROPN
ejpam-5854	359	11	.	.	PUNCT
ejpam-5854	360	1	multiple	multiple	ADJ
ejpam-5854	360	2	attribute	attribute	NOUN
ejpam-5854	360	3	decision	decision	NOUN
ejpam-5854	360	4	making	make	VERB
ejpam-5854	360	5	with	with	ADP
ejpam-5854	360	6	interval	interval	NOUN
ejpam-5854	360	7	-	-	PUNCT
ejpam-5854	360	8	valued	value	VERB
ejpam-5854	360	9	bipolar	bipolar	ADJ
ejpam-5854	360	10	fuzzy	fuzzy	ADJ
ejpam-5854	360	11	information	information	NOUN
ejpam-5854	360	12	and	and	CCONJ
ejpam-5854	360	13	their	their	PRON
ejpam-5854	360	14	application	application	NOUN
ejpam-5854	360	15	to	to	ADP
ejpam-5854	360	16	emerging	emerge	VERB
ejpam-5854	360	17	technology	technology	NOUN
ejpam-5854	360	18	commercialization	commercialization	NOUN
ejpam-5854	360	19	evaluation	evaluation	NOUN
ejpam-5854	360	20	.	.	PUNCT
ejpam-5854	361	1	ieee	ieee	NOUN
ejpam-5854	361	2	access	access	NOUN
ejpam-5854	361	3	,	,	PUNCT
ejpam-5854	361	4	6:60930–60955	6:60930–60955	ADV
ejpam-5854	361	5	,	,	PUNCT
ejpam-5854	361	6	2018	2018	NUM
ejpam-5854	361	7	.	.	PUNCT
ejpam-5854	362	1	[	[	X
ejpam-5854	362	2	8	8	NUM
ejpam-5854	362	3	]	]	PUNCT
ejpam-5854	362	4	m.	m.	NOUN
ejpam-5854	362	5	riaz	riaz	PROPN
ejpam-5854	362	6	and	and	CCONJ
ejpam-5854	362	7	st	st	PROPN
ejpam-5854	362	8	.	.	PROPN
ejpam-5854	362	9	tehrim	tehrim	PROPN
ejpam-5854	362	10	.	.	PUNCT
ejpam-5854	363	1	cubic	cubic	ADJ
ejpam-5854	363	2	bipolar	bipolar	ADJ
ejpam-5854	363	3	fuzzy	fuzzy	ADJ
ejpam-5854	363	4	set	set	VERB
ejpam-5854	363	5	with	with	ADP
ejpam-5854	363	6	application	application	NOUN
ejpam-5854	363	7	tomulti	tomulti	NOUN
ejpam-5854	363	8	-	-	PUNCT
ejpam-5854	363	9	criteria	criterion	NOUN
ejpam-5854	363	10	group	group	NOUN
ejpam-5854	363	11	decisionmaking	decisionmake	VERB
ejpam-5854	363	12	using	use	VERB
ejpam-5854	363	13	geometric	geometric	ADJ
ejpam-5854	363	14	aggregation	aggregation	NOUN
ejpam-5854	363	15	operators	operator	NOUN
ejpam-5854	363	16	.	.	PUNCT
ejpam-5854	364	1	soft	soft	ADJ
ejpam-5854	364	2	computing	computing	NOUN
ejpam-5854	364	3	,	,	PUNCT
ejpam-5854	364	4	24:1611–1633	24:1611–1633	NUM
ejpam-5854	364	5	,	,	PUNCT
ejpam-5854	364	6	2020	2020	NUM
ejpam-5854	364	7	.	.	PUNCT
ejpam-5854	365	1	[	[	X
ejpam-5854	365	2	9	9	NUM
ejpam-5854	365	3	]	]	X
ejpam-5854	365	4	d.tu	d.tu	PROPN
ejpam-5854	365	5	y.	y.	PROPN
ejpam-5854	365	6	feng	feng	PROPN
ejpam-5854	365	7	and	and	CCONJ
ejpam-5854	365	8	h.	h.	PROPN
ejpam-5854	365	9	li	li	PROPN
ejpam-5854	365	10	.	.	PROPN
ejpam-5854	365	11	interval	interval	NOUN
ejpam-5854	365	12	-	-	PUNCT
ejpam-5854	365	13	valued	value	VERB
ejpam-5854	365	14	fuzzy	fuzzy	ADJ
ejpam-5854	365	15	hypergraph	hypergraph	NOUN
ejpam-5854	365	16	and	and	CCONJ
ejpam-5854	365	17	interval	interval	NOUN
ejpam-5854	365	18	-	-	PUNCT
ejpam-5854	365	19	valued	value	VERB
ejpam-5854	365	20	fuzzy	fuzzy	ADJ
ejpam-5854	365	21	hyperopertions	hyperopertion	NOUN
ejpam-5854	365	22	.	.	PUNCT
ejpam-5854	366	1	italian	italian	ADJ
ejpam-5854	366	2	journal	journal	NOUN
ejpam-5854	366	3	of	of	ADP
ejpam-5854	366	4	pure	pure	ADJ
ejpam-5854	366	5	and	and	CCONJ
ejpam-5854	366	6	applied	applied	ADJ
ejpam-5854	366	7	mathematics	mathematic	NOUN
ejpam-5854	366	8	,	,	PUNCT
ejpam-5854	366	9	36:1–12	36:1–12	NUM
ejpam-5854	366	10	,	,	PUNCT
ejpam-5854	366	11	2016	2016	NUM
ejpam-5854	366	12	.	.	PUNCT
ejpam-5854	367	1	[	[	X
ejpam-5854	367	2	10	10	NUM
ejpam-5854	367	3	]	]	X
ejpam-5854	367	4	a.	a.	NOUN
ejpam-5854	367	5	ghareeb	ghareeb	PROPN
ejpam-5854	367	6	n.	n.	PROPN
ejpam-5854	367	7	yaqoob	yaqoob	PROPN
ejpam-5854	367	8	,	,	PUNCT
ejpam-5854	367	9	r.	r.	PROPN
ejpam-5854	367	10	chinram	chinram	PROPN
ejpam-5854	367	11	and	and	CCONJ
ejpam-5854	367	12	m.	m.	PROPN
ejpam-5854	367	13	aslam	aslam	PROPN
ejpam-5854	367	14	.	.	PUNCT
ejpam-5854	368	1	left	leave	VERB
ejpam-5854	368	2	almost	almost	ADV
ejpam-5854	368	3	semigroups	semigroup	NOUN
ejpam-5854	368	4	characterized	characterize	VERB
ejpam-5854	368	5	by	by	ADP
ejpam-5854	368	6	their	their	PRON
ejpam-5854	368	7	interval	interval	NOUN
ejpam-5854	368	8	valued	value	VERB
ejpam-5854	368	9	fuzzy	fuzzy	ADJ
ejpam-5854	368	10	ideals	ideal	NOUN
ejpam-5854	368	11	.	.	PUNCT
ejpam-5854	369	1	affika	affika	PROPN
ejpam-5854	369	2	mathematics	mathematics	PROPN
ejpam-5854	369	3	,	,	PUNCT
ejpam-5854	369	4	24:231–245	24:231–245	PROPN
ejpam-5854	369	5	,	,	PUNCT
ejpam-5854	369	6	2013	2013	NUM
ejpam-5854	369	7	.	.	PUNCT
ejpam-5854	370	1	[	[	X
ejpam-5854	370	2	11	11	NUM
ejpam-5854	370	3	]	]	X
ejpam-5854	370	4	d.	d.	PROPN
ejpam-5854	370	5	singaram	singaram	PROPN
ejpam-5854	370	6	and	and	CCONJ
ejpam-5854	370	7	pr	pr	NOUN
ejpam-5854	370	8	.	.	PUNCT
ejpam-5854	370	9	kandasamy	kandasamy	NOUN
ejpam-5854	370	10	.	.	PUNCT
ejpam-5854	371	1	interval	interval	NOUN
ejpam-5854	371	2	valued	value	VERB
ejpam-5854	371	3	fuzzy	fuzzy	ADJ
ejpam-5854	371	4	ideals	ideal	NOUN
ejpam-5854	371	5	of	of	ADP
ejpam-5854	371	6	regular	regular	ADJ
ejpam-5854	371	7	and	and	CCONJ
ejpam-5854	371	8	intra	intra	ADJ
ejpam-5854	371	9	-	-	ADJ
ejpam-5854	371	10	regular	regular	ADJ
ejpam-5854	371	11	semigroups	semigroup	NOUN
ejpam-5854	371	12	.	.	PUNCT
ejpam-5854	372	1	intern	intern	PROPN
ejpam-5854	372	2	.	.	PUNCT
ejpam-5854	373	1	j.	j.	PROPN
ejpam-5854	373	2	fuzzy	fuzzy	PROPN
ejpam-5854	373	3	mathematical	mathematical	PROPN
ejpam-5854	373	4	archive	archive	NOUN
ejpam-5854	373	5	,	,	PUNCT
ejpam-5854	373	6	3:50–57	3:50–57	NUM
ejpam-5854	373	7	,	,	PUNCT
ejpam-5854	373	8	2013	2013	NUM
ejpam-5854	373	9	.	.	PUNCT
ejpam-5854	374	1	[	[	X
ejpam-5854	374	2	12	12	NUM
ejpam-5854	374	3	]	]	X
ejpam-5854	374	4	chang	chang	PROPN
ejpam-5854	374	5	su	su	PROPN
ejpam-5854	374	6	kim	kim	PROPN
ejpam-5854	374	7	,	,	PUNCT
ejpam-5854	374	8	jeong	jeong	PROPN
ejpam-5854	374	9	gi	gi	PROPN
ejpam-5854	374	10	kang	kang	PROPN
ejpam-5854	374	11	,	,	PUNCT
ejpam-5854	374	12	and	and	CCONJ
ejpam-5854	374	13	jung	jung	PROPN
ejpam-5854	374	14	mi	mi	PROPN
ejpam-5854	374	15	kang	kang	PROPN
ejpam-5854	374	16	.	.	PUNCT
ejpam-5854	375	1	ideal	ideal	PROPN
ejpam-5854	375	2	theory	theory	NOUN
ejpam-5854	375	3	of	of	ADP
ejpam-5854	375	4	semigroups	semigroup	NOUN
ejpam-5854	375	5	based	base	VERB
ejpam-5854	375	6	on	on	ADP
ejpam-5854	375	7	the	the	DET
ejpam-5854	375	8	bipolar	bipolar	ADJ
ejpam-5854	375	9	valued	value	VERB
ejpam-5854	375	10	fuzzy	fuzzy	ADJ
ejpam-5854	375	11	set	set	NOUN
ejpam-5854	375	12	theory	theory	NOUN
ejpam-5854	375	13	.	.	PUNCT
ejpam-5854	376	1	annals	annal	NOUN
ejpam-5854	376	2	of	of	ADP
ejpam-5854	376	3	fuzzy	fuzzy	ADJ
ejpam-5854	376	4	mathematics	mathematic	NOUN
ejpam-5854	376	5	and	and	CCONJ
ejpam-5854	376	6	informatics	informatic	NOUN
ejpam-5854	376	7	,	,	PUNCT
ejpam-5854	376	8	2(2):193–206	2(2):193–206	NUM
ejpam-5854	376	9	,	,	PUNCT
ejpam-5854	376	10	2011	2011	NUM
ejpam-5854	376	11	.	.	PUNCT
ejpam-5854	377	1	[	[	X
ejpam-5854	377	2	13	13	NUM
ejpam-5854	377	3	]	]	X
ejpam-5854	377	4	n.	n.	NOUN
ejpam-5854	377	5	kuroki	kuroki	PROPN
ejpam-5854	377	6	j.n	j.n	PROPN
ejpam-5854	377	7	.	.	PROPN
ejpam-5854	377	8	mordeson	mordeson	PROPN
ejpam-5854	377	9	,	,	PUNCT
ejpam-5854	377	10	d.	d.	PROPN
ejpam-5854	377	11	s.	s.	PROPN
ejpam-5854	377	12	malik	malik	PROPN
ejpam-5854	377	13	.	.	PUNCT
ejpam-5854	378	1	fuzzy	fuzzy	PROPN
ejpam-5854	378	2	semigroup	semigroup	PROPN
ejpam-5854	378	3	.	.	PUNCT
ejpam-5854	379	1	springer	springer	NOUN
ejpam-5854	379	2	science	science	PROPN
ejpam-5854	379	3	and	and	CCONJ
ejpam-5854	379	4	business	business	NOUN
ejpam-5854	379	5	media	medium	NOUN
ejpam-5854	379	6	,	,	PUNCT
ejpam-5854	379	7	2003	2003	NUM
ejpam-5854	379	8	.	.	PUNCT